diff --git a/-J_xL4IGhJA.txt b/-J_xL4IGhJA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1f839b9a9ceb37d02bb4b1ec0a7f51c0cc6444b
--- /dev/null
+++ b/-J_xL4IGhJA.txt
@@ -0,0 +1,10995 @@
+align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'd like to welcome you to this course
+
+ align:start position:0%
+I'd like to welcome you to this course
+ 
+
+ align:start position:0%
+I'd like to welcome you to this course
+on computer science actually that's a
+
+ align:start position:0%
+on computer science actually that's a
+ 
+
+ align:start position:0%
+on computer science actually that's a
+terrible way to start computer science
+
+ align:start position:0%
+terrible way to start computer science
+ 
+
+ align:start position:0%
+terrible way to start computer science
+is a terrible name for this business
+
+ align:start position:0%
+is a terrible name for this business
+ 
+
+ align:start position:0%
+is a terrible name for this business
+first of all it's not a science it uh
+
+ align:start position:0%
+first of all it's not a science it uh
+ 
+
+ align:start position:0%
+first of all it's not a science it uh
+might be engineering or it might be art
+
+ align:start position:0%
+might be engineering or it might be art
+ 
+
+ align:start position:0%
+might be engineering or it might be art
+well we'll actually see that computer
+
+ align:start position:0%
+well we'll actually see that computer
+ 
+
+ align:start position:0%
+well we'll actually see that computer
+so-called science actually has a lot in
+
+ align:start position:0%
+so-called science actually has a lot in
+ 
+
+ align:start position:0%
+so-called science actually has a lot in
+common with magic you'll see that in
+
+ align:start position:0%
+common with magic you'll see that in
+ 
+
+ align:start position:0%
+common with magic you'll see that in
+this course so it's not a science it's
+
+ align:start position:0%
+this course so it's not a science it's
+ 
+
+ align:start position:0%
+this course so it's not a science it's
+also not really very much about
+
+ align:start position:0%
+also not really very much about
+ 
+
+ align:start position:0%
+also not really very much about
+computers and it's not about computers
+
+ align:start position:0%
+computers and it's not about computers
+ 
+
+ align:start position:0%
+computers and it's not about computers
+in the same sense that that physics is
+
+ align:start position:0%
+in the same sense that that physics is
+ 
+
+ align:start position:0%
+in the same sense that that physics is
+not really about particle accelerators
+
+ align:start position:0%
+not really about particle accelerators
+ 
+
+ align:start position:0%
+not really about particle accelerators
+and biology is not really about
+
+ align:start position:0%
+and biology is not really about
+ 
+
+ align:start position:0%
+and biology is not really about
+microscopes and petri dishes and it's
+
+ align:start position:0%
+microscopes and petri dishes and it's
+ 
+
+ align:start position:0%
+microscopes and petri dishes and it's
+not about computers in the same set
+
+ align:start position:0%
+not about computers in the same set
+ 
+
+ align:start position:0%
+not about computers in the same set
+sense that geometry is not really about
+
+ align:start position:0%
+sense that geometry is not really about
+ 
+
+ align:start position:0%
+sense that geometry is not really about
+using surveying instruments in fact
+
+ align:start position:0%
+using surveying instruments in fact
+ 
+
+ align:start position:0%
+using surveying instruments in fact
+there's a lot of commonality between
+
+ align:start position:0%
+there's a lot of commonality between
+ 
+
+ align:start position:0%
+there's a lot of commonality between
+computer science and geometry geometry
+
+ align:start position:0%
+computer science and geometry geometry
+ 
+
+ align:start position:0%
+computer science and geometry geometry
+first of all is another subject with a
+
+ align:start position:0%
+first of all is another subject with a
+ 
+
+ align:start position:0%
+first of all is another subject with a
+lousy name the name comes from Gaia
+
+ align:start position:0%
+lousy name the name comes from Gaia
+ 
+
+ align:start position:0%
+lousy name the name comes from Gaia
+meaning the earth and Metron meaning to
+
+ align:start position:0%
+meaning the earth and Metron meaning to
+ 
+
+ align:start position:0%
+meaning the earth and Metron meaning to
+measure geometry originally meant
+
+ align:start position:0%
+measure geometry originally meant
+ 
+
+ align:start position:0%
+measure geometry originally meant
+measuring the earth were or surveying
+
+ align:start position:0%
+measuring the earth were or surveying
+ 
+
+ align:start position:0%
+measuring the earth were or surveying
+and the reason for that was that
+
+ align:start position:0%
+and the reason for that was that
+ 
+
+ align:start position:0%
+and the reason for that was that
+thousands of years ago the Egyptian
+
+ align:start position:0%
+thousands of years ago the Egyptian
+ 
+
+ align:start position:0%
+thousands of years ago the Egyptian
+priesthood
+
+ align:start position:0%
+priesthood
+ 
+
+ align:start position:0%
+priesthood
+developed the rudiments of geometry in
+
+ align:start position:0%
+developed the rudiments of geometry in
+ 
+
+ align:start position:0%
+developed the rudiments of geometry in
+order to figure out how to restore the
+
+ align:start position:0%
+order to figure out how to restore the
+ 
+
+ align:start position:0%
+order to figure out how to restore the
+boundaries of fields that were destroyed
+
+ align:start position:0%
+boundaries of fields that were destroyed
+ 
+
+ align:start position:0%
+boundaries of fields that were destroyed
+in the annual flooding of the Nile to
+
+ align:start position:0%
+in the annual flooding of the Nile to
+ 
+
+ align:start position:0%
+in the annual flooding of the Nile to
+the Egyptians who did that geometry
+
+ align:start position:0%
+the Egyptians who did that geometry
+ 
+
+ align:start position:0%
+the Egyptians who did that geometry
+really was the use of surveying
+
+ align:start position:0%
+really was the use of surveying
+ 
+
+ align:start position:0%
+really was the use of surveying
+instruments now the reason that we think
+
+ align:start position:0%
+instruments now the reason that we think
+ 
+
+ align:start position:0%
+instruments now the reason that we think
+computer science is about computers is
+
+ align:start position:0%
+computer science is about computers is
+ 
+
+ align:start position:0%
+computer science is about computers is
+pretty much the same reason that the
+
+ align:start position:0%
+pretty much the same reason that the
+ 
+
+ align:start position:0%
+pretty much the same reason that the
+Egyptians thought geometry was about
+
+ align:start position:0%
+Egyptians thought geometry was about
+ 
+
+ align:start position:0%
+Egyptians thought geometry was about
+surveying instruments and that is when
+
+ align:start position:0%
+surveying instruments and that is when
+ 
+
+ align:start position:0%
+surveying instruments and that is when
+some field is just getting started and
+
+ align:start position:0%
+some field is just getting started and
+ 
+
+ align:start position:0%
+some field is just getting started and
+you don't really understand it very well
+
+ align:start position:0%
+you don't really understand it very well
+ 
+
+ align:start position:0%
+you don't really understand it very well
+it's very easy to confuse the essence of
+
+ align:start position:0%
+it's very easy to confuse the essence of
+ 
+
+ align:start position:0%
+it's very easy to confuse the essence of
+what you're doing with the tools that
+
+ align:start position:0%
+what you're doing with the tools that
+ 
+
+ align:start position:0%
+what you're doing with the tools that
+you use and indeed on some absolute
+
+ align:start position:0%
+you use and indeed on some absolute
+ 
+
+ align:start position:0%
+you use and indeed on some absolute
+scale of things we probably know less
+
+ align:start position:0%
+scale of things we probably know less
+ 
+
+ align:start position:0%
+scale of things we probably know less
+about the essence of computer science
+
+ align:start position:0%
+about the essence of computer science
+ 
+
+ align:start position:0%
+about the essence of computer science
+than the ancient Egyptians really knew
+
+ align:start position:0%
+than the ancient Egyptians really knew
+ 
+
+ align:start position:0%
+than the ancient Egyptians really knew
+about genomics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what's what I mean by the essence
+
+ align:start position:0%
+well what's what I mean by the essence
+ 
+
+ align:start position:0%
+well what's what I mean by the essence
+of computer science what I mean by the
+
+ align:start position:0%
+of computer science what I mean by the
+ 
+
+ align:start position:0%
+of computer science what I mean by the
+essence of geometry see it's certainly
+
+ align:start position:0%
+essence of geometry see it's certainly
+ 
+
+ align:start position:0%
+essence of geometry see it's certainly
+true that these Egyptians went off and
+
+ align:start position:0%
+true that these Egyptians went off and
+ 
+
+ align:start position:0%
+true that these Egyptians went off and
+used surveying instruments but when we
+
+ align:start position:0%
+used surveying instruments but when we
+ 
+
+ align:start position:0%
+used surveying instruments but when we
+look back on them after a couple of
+
+ align:start position:0%
+look back on them after a couple of
+ 
+
+ align:start position:0%
+look back on them after a couple of
+thousand years we say gee what they were
+
+ align:start position:0%
+thousand years we say gee what they were
+ 
+
+ align:start position:0%
+thousand years we say gee what they were
+doing the important stuff they were
+
+ align:start position:0%
+doing the important stuff they were
+ 
+
+ align:start position:0%
+doing the important stuff they were
+doing was to begin to formalize notions
+
+ align:start position:0%
+doing was to begin to formalize notions
+ 
+
+ align:start position:0%
+doing was to begin to formalize notions
+about space and time to start a way of
+
+ align:start position:0%
+about space and time to start a way of
+ 
+
+ align:start position:0%
+about space and time to start a way of
+talking about mathematical truths
+
+ align:start position:0%
+talking about mathematical truths
+ 
+
+ align:start position:0%
+talking about mathematical truths
+formally that led to the axiomatic
+
+ align:start position:0%
+formally that led to the axiomatic
+ 
+
+ align:start position:0%
+formally that led to the axiomatic
+method that led to serve all of modern
+
+ align:start position:0%
+method that led to serve all of modern
+ 
+
+ align:start position:0%
+method that led to serve all of modern
+mathematics figuring out a way to talk
+
+ align:start position:0%
+mathematics figuring out a way to talk
+ 
+
+ align:start position:0%
+mathematics figuring out a way to talk
+precisely about so-called declarative
+
+ align:start position:0%
+precisely about so-called declarative
+ 
+
+ align:start position:0%
+precisely about so-called declarative
+knowledge what is true well similarly
+
+ align:start position:0%
+knowledge what is true well similarly
+ 
+
+ align:start position:0%
+knowledge what is true well similarly
+think in the future people will look
+
+ align:start position:0%
+think in the future people will look
+ 
+
+ align:start position:0%
+think in the future people will look
+back and say yes those those primitives
+
+ align:start position:0%
+back and say yes those those primitives
+ 
+
+ align:start position:0%
+back and say yes those those primitives
+in the 20th century we're fiddling
+
+ align:start position:0%
+in the 20th century we're fiddling
+ 
+
+ align:start position:0%
+in the 20th century we're fiddling
+around with these gadgets called
+
+ align:start position:0%
+around with these gadgets called
+ 
+
+ align:start position:0%
+around with these gadgets called
+computers but really what they were
+
+ align:start position:0%
+computers but really what they were
+ 
+
+ align:start position:0%
+computers but really what they were
+doing is starting to learn how to
+
+ align:start position:0%
+doing is starting to learn how to
+ 
+
+ align:start position:0%
+doing is starting to learn how to
+formalize formalize intuitions about
+
+ align:start position:0%
+formalize formalize intuitions about
+ 
+
+ align:start position:0%
+formalize formalize intuitions about
+process how to do things starting to to
+
+ align:start position:0%
+process how to do things starting to to
+ 
+
+ align:start position:0%
+process how to do things starting to to
+develop a way to talk precisely about
+
+ align:start position:0%
+develop a way to talk precisely about
+ 
+
+ align:start position:0%
+develop a way to talk precisely about
+about how to knowledge as opposed to
+
+ align:start position:0%
+about how to knowledge as opposed to
+ 
+
+ align:start position:0%
+about how to knowledge as opposed to
+geometry that talks about what is true
+
+ align:start position:0%
+geometry that talks about what is true
+ 
+
+ align:start position:0%
+geometry that talks about what is true
+we give you an example of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take a look here is a piece of a piece
+
+ align:start position:0%
+take a look here is a piece of a piece
+ 
+
+ align:start position:0%
+take a look here is a piece of a piece
+of mathematics right that says what a
+
+ align:start position:0%
+of mathematics right that says what a
+ 
+
+ align:start position:0%
+of mathematics right that says what a
+square root is and if the square root of
+
+ align:start position:0%
+square root is and if the square root of
+ 
+
+ align:start position:0%
+square root is and if the square root of
+the x is the number Y such that Y
+
+ align:start position:0%
+the x is the number Y such that Y
+ 
+
+ align:start position:0%
+the x is the number Y such that Y
+squared is equal to x and Y is greater
+
+ align:start position:0%
+squared is equal to x and Y is greater
+ 
+
+ align:start position:0%
+squared is equal to x and Y is greater
+than zero now that's a fine piece of
+
+ align:start position:0%
+than zero now that's a fine piece of
+ 
+
+ align:start position:0%
+than zero now that's a fine piece of
+mathematics but just telling you what a
+
+ align:start position:0%
+mathematics but just telling you what a
+ 
+
+ align:start position:0%
+mathematics but just telling you what a
+square root is doesn't really say
+
+ align:start position:0%
+square root is doesn't really say
+ 
+
+ align:start position:0%
+square root is doesn't really say
+anything about about how you might go
+
+ align:start position:0%
+anything about about how you might go
+ 
+
+ align:start position:0%
+anything about about how you might go
+out and find one right so let's contrast
+
+ align:start position:0%
+out and find one right so let's contrast
+ 
+
+ align:start position:0%
+out and find one right so let's contrast
+that with a piece of imperative
+
+ align:start position:0%
+that with a piece of imperative
+ 
+
+ align:start position:0%
+that with a piece of imperative
+knowledge right how you might go out and
+
+ align:start position:0%
+knowledge right how you might go out and
+ 
+
+ align:start position:0%
+knowledge right how you might go out and
+find a square root this in fact also
+
+ align:start position:0%
+find a square root this in fact also
+ 
+
+ align:start position:0%
+find a square root this in fact also
+comes from Egypt not not a not ancient
+
+ align:start position:0%
+comes from Egypt not not a not ancient
+ 
+
+ align:start position:0%
+comes from Egypt not not a not ancient
+ancient Egypt this isn't an algorithm
+
+ align:start position:0%
+ancient Egypt this isn't an algorithm
+ 
+
+ align:start position:0%
+ancient Egypt this isn't an algorithm
+due to here on earth alexandria called
+
+ align:start position:0%
+due to here on earth alexandria called
+ 
+
+ align:start position:0%
+due to here on earth alexandria called
+how to find a square root by successive
+
+ align:start position:0%
+how to find a square root by successive
+ 
+
+ align:start position:0%
+how to find a square root by successive
+averaging and what it says is that in
+
+ align:start position:0%
+averaging and what it says is that in
+ 
+
+ align:start position:0%
+averaging and what it says is that in
+order to find a square root in order to
+
+ align:start position:0%
+order to find a square root in order to
+ 
+
+ align:start position:0%
+order to find a square root in order to
+find a square root you make a guess
+
+ align:start position:0%
+find a square root you make a guess
+ 
+
+ align:start position:0%
+find a square root you make a guess
+you improve that guess and the way you
+
+ align:start position:0%
+you improve that guess and the way you
+ 
+
+ align:start position:0%
+you improve that guess and the way you
+improve the guess is to average the
+
+ align:start position:0%
+improve the guess is to average the
+ 
+
+ align:start position:0%
+improve the guess is to average the
+guess and x over the gas and we'll talk
+
+ align:start position:0%
+guess and x over the gas and we'll talk
+ 
+
+ align:start position:0%
+guess and x over the gas and we'll talk
+a little bit later about what why that's
+
+ align:start position:0%
+a little bit later about what why that's
+ 
+
+ align:start position:0%
+a little bit later about what why that's
+a reasonable thing and you keep
+
+ align:start position:0%
+a reasonable thing and you keep
+ 
+
+ align:start position:0%
+a reasonable thing and you keep
+improving to guess until it's good
+
+ align:start position:0%
+improving to guess until it's good
+ 
+
+ align:start position:0%
+improving to guess until it's good
+enough but that's a method that's how to
+
+ align:start position:0%
+enough but that's a method that's how to
+ 
+
+ align:start position:0%
+enough but that's a method that's how to
+do something as opposed to declarative
+
+ align:start position:0%
+do something as opposed to declarative
+ 
+
+ align:start position:0%
+do something as opposed to declarative
+knowledge that says what you're looking
+
+ align:start position:0%
+knowledge that says what you're looking
+ 
+
+ align:start position:0%
+knowledge that says what you're looking
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+right that's a process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what's the process in general it's
+
+ align:start position:0%
+well what's the process in general it's
+ 
+
+ align:start position:0%
+well what's the process in general it's
+kind of hard to say you can think of it
+
+ align:start position:0%
+kind of hard to say you can think of it
+ 
+
+ align:start position:0%
+kind of hard to say you can think of it
+as like a magical spirit that sort of
+
+ align:start position:0%
+as like a magical spirit that sort of
+ 
+
+ align:start position:0%
+as like a magical spirit that sort of
+listen the computer and does something
+
+ align:start position:0%
+listen the computer and does something
+ 
+
+ align:start position:0%
+listen the computer and does something
+and the thing that directs the process
+
+ align:start position:0%
+and the thing that directs the process
+ 
+
+ align:start position:0%
+and the thing that directs the process
+is a pattern of rules called a procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so procedures are the are the spells if
+
+ align:start position:0%
+so procedures are the are the spells if
+ 
+
+ align:start position:0%
+so procedures are the are the spells if
+you like that control these magical
+
+ align:start position:0%
+you like that control these magical
+ 
+
+ align:start position:0%
+you like that control these magical
+spirits that are the processes and well
+
+ align:start position:0%
+spirits that are the processes and well
+ 
+
+ align:start position:0%
+spirits that are the processes and well
+I guess you know everyone needs a
+
+ align:start position:0%
+I guess you know everyone needs a
+ 
+
+ align:start position:0%
+I guess you know everyone needs a
+magical language and sorcerers but real
+
+ align:start position:0%
+magical language and sorcerers but real
+ 
+
+ align:start position:0%
+magical language and sorcerers but real
+sorcerer is used ancient Akkadian or or
+
+ align:start position:0%
+sorcerer is used ancient Akkadian or or
+ 
+
+ align:start position:0%
+sorcerer is used ancient Akkadian or or
+Sumerian or Babylonian or whatever we're
+
+ align:start position:0%
+Sumerian or Babylonian or whatever we're
+ 
+
+ align:start position:0%
+Sumerian or Babylonian or whatever we're
+gonna conjure up spirits in a magical
+
+ align:start position:0%
+gonna conjure up spirits in a magical
+ 
+
+ align:start position:0%
+gonna conjure up spirits in a magical
+language called Lisp
+
+ align:start position:0%
+language called Lisp
+ 
+
+ align:start position:0%
+language called Lisp
+which is a language designed for talking
+
+ align:start position:0%
+which is a language designed for talking
+ 
+
+ align:start position:0%
+which is a language designed for talking
+about for casting the spells that are
+
+ align:start position:0%
+about for casting the spells that are
+ 
+
+ align:start position:0%
+about for casting the spells that are
+procedures to direct the prophesies now
+
+ align:start position:0%
+procedures to direct the prophesies now
+ 
+
+ align:start position:0%
+procedures to direct the prophesies now
+it's very easy to learn Lisp in fact in
+
+ align:start position:0%
+it's very easy to learn Lisp in fact in
+ 
+
+ align:start position:0%
+it's very easy to learn Lisp in fact in
+a few minutes I'm going to teach you
+
+ align:start position:0%
+a few minutes I'm going to teach you
+ 
+
+ align:start position:0%
+a few minutes I'm going to teach you
+essentially all of Lisp and teach you
+
+ align:start position:0%
+essentially all of Lisp and teach you
+ 
+
+ align:start position:0%
+essentially all of Lisp and teach you
+essentially all of the rules and you
+
+ align:start position:0%
+essentially all of the rules and you
+ 
+
+ align:start position:0%
+essentially all of the rules and you
+shouldn't find that uh that particularly
+
+ align:start position:0%
+shouldn't find that uh that particularly
+ 
+
+ align:start position:0%
+shouldn't find that uh that particularly
+surprising that's sort of like saying
+
+ align:start position:0%
+surprising that's sort of like saying
+ 
+
+ align:start position:0%
+surprising that's sort of like saying
+it's very easy to learn the rules of
+
+ align:start position:0%
+it's very easy to learn the rules of
+ 
+
+ align:start position:0%
+it's very easy to learn the rules of
+chess and indeed in a few minutes you
+
+ align:start position:0%
+chess and indeed in a few minutes you
+ 
+
+ align:start position:0%
+chess and indeed in a few minutes you
+can tell somebody the rules of chess but
+
+ align:start position:0%
+can tell somebody the rules of chess but
+ 
+
+ align:start position:0%
+can tell somebody the rules of chess but
+of course that's very different from
+
+ align:start position:0%
+of course that's very different from
+ 
+
+ align:start position:0%
+of course that's very different from
+saying you understand the implications
+
+ align:start position:0%
+saying you understand the implications
+ 
+
+ align:start position:0%
+saying you understand the implications
+of those rules and how to use those
+
+ align:start position:0%
+of those rules and how to use those
+ 
+
+ align:start position:0%
+of those rules and how to use those
+rules to become a masterful chess player
+
+ align:start position:0%
+rules to become a masterful chess player
+ 
+
+ align:start position:0%
+rules to become a masterful chess player
+well listen it's the same way we're
+
+ align:start position:0%
+well listen it's the same way we're
+ 
+
+ align:start position:0%
+well listen it's the same way we're
+going to state the rules in a few
+
+ align:start position:0%
+going to state the rules in a few
+ 
+
+ align:start position:0%
+going to state the rules in a few
+minutes and we'll be very easy to see
+
+ align:start position:0%
+minutes and we'll be very easy to see
+ 
+
+ align:start position:0%
+minutes and we'll be very easy to see
+but what's really hard is going to be
+
+ align:start position:0%
+but what's really hard is going to be
+ 
+
+ align:start position:0%
+but what's really hard is going to be
+the implications of those rules right
+
+ align:start position:0%
+the implications of those rules right
+ 
+
+ align:start position:0%
+the implications of those rules right
+how you exploit those rules to be a
+
+ align:start position:0%
+how you exploit those rules to be a
+ 
+
+ align:start position:0%
+how you exploit those rules to be a
+master programmer and the implications
+
+ align:start position:0%
+master programmer and the implications
+ 
+
+ align:start position:0%
+master programmer and the implications
+of those rules are going to take us the
+
+ align:start position:0%
+of those rules are going to take us the
+ 
+
+ align:start position:0%
+of those rules are going to take us the
+well the whole rest of the subject and
+
+ align:start position:0%
+well the whole rest of the subject and
+ 
+
+ align:start position:0%
+well the whole rest of the subject and
+of course way beyond okay so in computer
+
+ align:start position:0%
+of course way beyond okay so in computer
+ 
+
+ align:start position:0%
+of course way beyond okay so in computer
+science we're in the business of
+
+ align:start position:0%
+science we're in the business of
+ 
+
+ align:start position:0%
+science we're in the business of
+formalizing is sort of have to
+
+ align:start position:0%
+formalizing is sort of have to
+ 
+
+ align:start position:0%
+formalizing is sort of have to
+imperative knowledge like how to do
+
+ align:start position:0%
+imperative knowledge like how to do
+ 
+
+ align:start position:0%
+imperative knowledge like how to do
+stuff and the real issues of computer
+
+ align:start position:0%
+stuff and the real issues of computer
+ 
+
+ align:start position:0%
+stuff and the real issues of computer
+science are of course not
+
+ align:start position:0%
+science are of course not
+ 
+
+ align:start position:0%
+science are of course not
+you know it's telling people how to do
+
+ align:start position:0%
+you know it's telling people how to do
+ 
+
+ align:start position:0%
+you know it's telling people how to do
+square is so that that was all it was
+
+ align:start position:0%
+square is so that that was all it was
+ 
+
+ align:start position:0%
+square is so that that was all it was
+there wouldn't be no big deal the real
+
+ align:start position:0%
+there wouldn't be no big deal the real
+ 
+
+ align:start position:0%
+there wouldn't be no big deal the real
+problems come when we try to build very
+
+ align:start position:0%
+problems come when we try to build very
+ 
+
+ align:start position:0%
+problems come when we try to build very
+very large system
+
+ align:start position:0%
+very large system
+ 
+
+ align:start position:0%
+very large system
+the computer programs that are that are
+
+ align:start position:0%
+the computer programs that are that are
+ 
+
+ align:start position:0%
+the computer programs that are that are
+thousands of pages long so wrong that
+
+ align:start position:0%
+thousands of pages long so wrong that
+ 
+
+ align:start position:0%
+thousands of pages long so wrong that
+nobody can really hold them in their
+
+ align:start position:0%
+nobody can really hold them in their
+ 
+
+ align:start position:0%
+nobody can really hold them in their
+heads all at once and the only reason
+
+ align:start position:0%
+heads all at once and the only reason
+ 
+
+ align:start position:0%
+heads all at once and the only reason
+that that's possible is because there
+
+ align:start position:0%
+that that's possible is because there
+ 
+
+ align:start position:0%
+that that's possible is because there
+are techniques there techniques for
+
+ align:start position:0%
+are techniques there techniques for
+ 
+
+ align:start position:0%
+are techniques there techniques for
+controlling the complexity of these
+
+ align:start position:0%
+controlling the complexity of these
+ 
+
+ align:start position:0%
+controlling the complexity of these
+large systems and these techniques for
+
+ align:start position:0%
+large systems and these techniques for
+ 
+
+ align:start position:0%
+large systems and these techniques for
+component controlling complexity or what
+
+ align:start position:0%
+component controlling complexity or what
+ 
+
+ align:start position:0%
+component controlling complexity or what
+this course is really that and in some
+
+ align:start position:0%
+this course is really that and in some
+ 
+
+ align:start position:0%
+this course is really that and in some
+sense that's really what computer
+
+ align:start position:0%
+sense that's really what computer
+ 
+
+ align:start position:0%
+sense that's really what computer
+science is about now that may seem like
+
+ align:start position:0%
+science is about now that may seem like
+ 
+
+ align:start position:0%
+science is about now that may seem like
+a very strange thing to say because they
+
+ align:start position:0%
+a very strange thing to say because they
+ 
+
+ align:start position:0%
+a very strange thing to say because they
+after all a lot of people besides
+
+ align:start position:0%
+after all a lot of people besides
+ 
+
+ align:start position:0%
+after all a lot of people besides
+computer scientists deal with
+
+ align:start position:0%
+computer scientists deal with
+ 
+
+ align:start position:0%
+computer scientists deal with
+controlling complexity are they a large
+
+ align:start position:0%
+controlling complexity are they a large
+ 
+
+ align:start position:0%
+controlling complexity are they a large
+airliner is an extremely complex system
+
+ align:start position:0%
+airliner is an extremely complex system
+ 
+
+ align:start position:0%
+airliner is an extremely complex system
+and the aeronautical engineers who
+
+ align:start position:0%
+and the aeronautical engineers who
+ 
+
+ align:start position:0%
+and the aeronautical engineers who
+design that or you know are dealing with
+
+ align:start position:0%
+design that or you know are dealing with
+ 
+
+ align:start position:0%
+design that or you know are dealing with
+immense complexity but there's a
+
+ align:start position:0%
+immense complexity but there's a
+ 
+
+ align:start position:0%
+immense complexity but there's a
+difference between that kind of
+
+ align:start position:0%
+difference between that kind of
+ 
+
+ align:start position:0%
+difference between that kind of
+complexity and what we deal with in
+
+ align:start position:0%
+complexity and what we deal with in
+ 
+
+ align:start position:0%
+complexity and what we deal with in
+computer science and that is that that
+
+ align:start position:0%
+computer science and that is that that
+ 
+
+ align:start position:0%
+computer science and that is that that
+computer science and sometimes isn't
+
+ align:start position:0%
+computer science and sometimes isn't
+ 
+
+ align:start position:0%
+computer science and sometimes isn't
+real you see when an engineer is
+
+ align:start position:0%
+real you see when an engineer is
+ 
+
+ align:start position:0%
+real you see when an engineer is
+designing a physical system that's made
+
+ align:start position:0%
+designing a physical system that's made
+ 
+
+ align:start position:0%
+designing a physical system that's made
+out of real parts like the engineer to
+
+ align:start position:0%
+out of real parts like the engineer to
+ 
+
+ align:start position:0%
+out of real parts like the engineer to
+worry about that has to address problems
+
+ align:start position:0%
+worry about that has to address problems
+ 
+
+ align:start position:0%
+worry about that has to address problems
+of tolerance and approximation and noise
+
+ align:start position:0%
+of tolerance and approximation and noise
+ 
+
+ align:start position:0%
+of tolerance and approximation and noise
+in the system so for example as an
+
+ align:start position:0%
+in the system so for example as an
+ 
+
+ align:start position:0%
+in the system so for example as an
+electrical engineer I can go off and
+
+ align:start position:0%
+electrical engineer I can go off and
+ 
+
+ align:start position:0%
+electrical engineer I can go off and
+easily build a one stage amplifier or a
+
+ align:start position:0%
+easily build a one stage amplifier or a
+ 
+
+ align:start position:0%
+easily build a one stage amplifier or a
+two stage amplifier and I can imagine
+
+ align:start position:0%
+two stage amplifier and I can imagine
+ 
+
+ align:start position:0%
+two stage amplifier and I can imagine
+cascading a lot of them to build a
+
+ align:start position:0%
+cascading a lot of them to build a
+ 
+
+ align:start position:0%
+cascading a lot of them to build a
+million stage amplifier but it's
+
+ align:start position:0%
+million stage amplifier but it's
+ 
+
+ align:start position:0%
+million stage amplifier but it's
+ridiculous to build such a thing because
+
+ align:start position:0%
+ridiculous to build such a thing because
+ 
+
+ align:start position:0%
+ridiculous to build such a thing because
+by the long before the million stage the
+
+ align:start position:0%
+by the long before the million stage the
+ 
+
+ align:start position:0%
+by the long before the million stage the
+thermal noise in those components way at
+
+ align:start position:0%
+thermal noise in those components way at
+ 
+
+ align:start position:0%
+thermal noise in those components way at
+the beginning is going to get amplified
+
+ align:start position:0%
+the beginning is going to get amplified
+ 
+
+ align:start position:0%
+the beginning is going to get amplified
+and make the whole thing meaningless
+
+ align:start position:0%
+and make the whole thing meaningless
+ 
+
+ align:start position:0%
+and make the whole thing meaningless
+computer science deals with idealized
+
+ align:start position:0%
+computer science deals with idealized
+ 
+
+ align:start position:0%
+computer science deals with idealized
+components we know as much as we want
+
+ align:start position:0%
+components we know as much as we want
+ 
+
+ align:start position:0%
+components we know as much as we want
+about these little program and data
+
+ align:start position:0%
+about these little program and data
+ 
+
+ align:start position:0%
+about these little program and data
+pieces that we're fitting things
+
+ align:start position:0%
+pieces that we're fitting things
+ 
+
+ align:start position:0%
+pieces that we're fitting things
+together right so there's we don't have
+
+ align:start position:0%
+together right so there's we don't have
+ 
+
+ align:start position:0%
+together right so there's we don't have
+to worry about tolerance and that means
+
+ align:start position:0%
+to worry about tolerance and that means
+ 
+
+ align:start position:0%
+to worry about tolerance and that means
+that in building a large program
+
+ align:start position:0%
+that in building a large program
+ 
+
+ align:start position:0%
+that in building a large program
+there's not all that much difference
+
+ align:start position:0%
+there's not all that much difference
+ 
+
+ align:start position:0%
+there's not all that much difference
+between what I can build and what I can
+
+ align:start position:0%
+between what I can build and what I can
+ 
+
+ align:start position:0%
+between what I can build and what I can
+imagine because the parts are these
+
+ align:start position:0%
+imagine because the parts are these
+ 
+
+ align:start position:0%
+imagine because the parts are these
+abstract entities that I know as much as
+
+ align:start position:0%
+abstract entities that I know as much as
+ 
+
+ align:start position:0%
+abstract entities that I know as much as
+as much as I want I know about them as
+
+ align:start position:0%
+as much as I want I know about them as
+ 
+
+ align:start position:0%
+as much as I want I know about them as
+precisely as I like so as opposed to
+
+ align:start position:0%
+precisely as I like so as opposed to
+ 
+
+ align:start position:0%
+precisely as I like so as opposed to
+other kinds of engineering where the
+
+ align:start position:0%
+other kinds of engineering where the
+ 
+
+ align:start position:0%
+other kinds of engineering where the
+constraints on which you can build are
+
+ align:start position:0%
+constraints on which you can build are
+ 
+
+ align:start position:0%
+constraints on which you can build are
+the constraints of physical systems the
+
+ align:start position:0%
+the constraints of physical systems the
+ 
+
+ align:start position:0%
+the constraints of physical systems the
+constraints of physics and noise and
+
+ align:start position:0%
+constraints of physics and noise and
+ 
+
+ align:start position:0%
+constraints of physics and noise and
+approximation the constraints imposed in
+
+ align:start position:0%
+approximation the constraints imposed in
+ 
+
+ align:start position:0%
+approximation the constraints imposed in
+building large software systems are the
+
+ align:start position:0%
+building large software systems are the
+ 
+
+ align:start position:0%
+building large software systems are the
+limitations of our own minds so in that
+
+ align:start position:0%
+limitations of our own minds so in that
+ 
+
+ align:start position:0%
+limitations of our own minds so in that
+sense computer science is like an
+
+ align:start position:0%
+sense computer science is like an
+ 
+
+ align:start position:0%
+sense computer science is like an
+abstract form of engineering it's the
+
+ align:start position:0%
+abstract form of engineering it's the
+ 
+
+ align:start position:0%
+abstract form of engineering it's the
+kind of engineering where you ignore the
+
+ align:start position:0%
+kind of engineering where you ignore the
+ 
+
+ align:start position:0%
+kind of engineering where you ignore the
+constraints that are imposed by reality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok well what are what are some of these
+
+ align:start position:0%
+ok well what are what are some of these
+ 
+
+ align:start position:0%
+ok well what are what are some of these
+techniques they're not special to
+
+ align:start position:0%
+techniques they're not special to
+ 
+
+ align:start position:0%
+techniques they're not special to
+computer science first technique which
+
+ align:start position:0%
+computer science first technique which
+ 
+
+ align:start position:0%
+computer science first technique which
+is used in all of engineering is kind of
+
+ align:start position:0%
+is used in all of engineering is kind of
+ 
+
+ align:start position:0%
+is used in all of engineering is kind of
+abstraction called blackbox abstraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it takes something and uh they'll build
+
+ align:start position:0%
+it takes something and uh they'll build
+ 
+
+ align:start position:0%
+it takes something and uh they'll build
+a box of doubt yet let's see for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look at that square root method I might
+
+ align:start position:0%
+look at that square root method I might
+ 
+
+ align:start position:0%
+look at that square root method I might
+want to take that and build a box that
+
+ align:start position:0%
+want to take that and build a box that
+ 
+
+ align:start position:0%
+want to take that and build a box that
+says to find the square root of x and
+
+ align:start position:0%
+says to find the square root of x and
+ 
+
+ align:start position:0%
+says to find the square root of x and
+that might be a whole complicated set of
+
+ align:start position:0%
+that might be a whole complicated set of
+ 
+
+ align:start position:0%
+that might be a whole complicated set of
+rules and that might end up being a kind
+
+ align:start position:0%
+rules and that might end up being a kind
+ 
+
+ align:start position:0%
+rules and that might end up being a kind
+of thing where I can put in say 36 and
+
+ align:start position:0%
+of thing where I can put in say 36 and
+ 
+
+ align:start position:0%
+of thing where I can put in say 36 and
+say what's the square root of 36 and out
+
+ align:start position:0%
+say what's the square root of 36 and out
+ 
+
+ align:start position:0%
+say what's the square root of 36 and out
+comes 6 and the important thing is that
+
+ align:start position:0%
+comes 6 and the important thing is that
+ 
+
+ align:start position:0%
+comes 6 and the important thing is that
+I'd like to design that so that if
+
+ align:start position:0%
+I'd like to design that so that if
+ 
+
+ align:start position:0%
+I'd like to design that so that if
+George comes along and we'd like to
+
+ align:start position:0%
+George comes along and we'd like to
+ 
+
+ align:start position:0%
+George comes along and we'd like to
+compute the square root of a plus the
+
+ align:start position:0%
+compute the square root of a plus the
+ 
+
+ align:start position:0%
+compute the square root of a plus the
+square root of B you can take this thing
+
+ align:start position:0%
+square root of B you can take this thing
+ 
+
+ align:start position:0%
+square root of B you can take this thing
+and use it as a as a module without
+
+ align:start position:0%
+and use it as a as a module without
+ 
+
+ align:start position:0%
+and use it as a as a module without
+having to look inside and build
+
+ align:start position:0%
+having to look inside and build
+ 
+
+ align:start position:0%
+having to look inside and build
+something that looks like this I mean a
+
+ align:start position:0%
+something that looks like this I mean a
+ 
+
+ align:start position:0%
+something that looks like this I mean a
+and B square root box and another square
+
+ align:start position:0%
+and B square root box and another square
+ 
+
+ align:start position:0%
+and B square root box and another square
+root box and then something that adds
+
+ align:start position:0%
+root box and then something that adds
+ 
+
+ align:start position:0%
+root box and then something that adds
+that would put out the answer and you
+
+ align:start position:0%
+that would put out the answer and you
+ 
+
+ align:start position:0%
+that would put out the answer and you
+can see just from the fact that I want
+
+ align:start position:0%
+can see just from the fact that I want
+ 
+
+ align:start position:0%
+can see just from the fact that I want
+to do that is from George's point of
+
+ align:start position:0%
+to do that is from George's point of
+ 
+
+ align:start position:0%
+to do that is from George's point of
+view the internals of what's in here
+
+ align:start position:0%
+view the internals of what's in here
+ 
+
+ align:start position:0%
+view the internals of what's in here
+should not be important so for instance
+
+ align:start position:0%
+should not be important so for instance
+ 
+
+ align:start position:0%
+should not be important so for instance
+shouldn't matter that when I wrote this
+
+ align:start position:0%
+shouldn't matter that when I wrote this
+ 
+
+ align:start position:0%
+shouldn't matter that when I wrote this
+I said I want to find the square root of
+
+ align:start position:0%
+I said I want to find the square root of
+ 
+
+ align:start position:0%
+I said I want to find the square root of
+x I could have said the square root of Y
+
+ align:start position:0%
+x I could have said the square root of Y
+ 
+
+ align:start position:0%
+x I could have said the square root of Y
+or the square root of ay or or anything
+
+ align:start position:0%
+or the square root of ay or or anything
+ 
+
+ align:start position:0%
+or the square root of ay or or anything
+at all but that's the fundamental notion
+
+ align:start position:0%
+at all but that's the fundamental notion
+ 
+
+ align:start position:0%
+at all but that's the fundamental notion
+of putting something in a box using
+
+ align:start position:0%
+of putting something in a box using
+ 
+
+ align:start position:0%
+of putting something in a box using
+blackbox abstraction to suppress detail
+
+ align:start position:0%
+blackbox abstraction to suppress detail
+ 
+
+ align:start position:0%
+blackbox abstraction to suppress detail
+and the reason for that is you want to
+
+ align:start position:0%
+and the reason for that is you want to
+ 
+
+ align:start position:0%
+and the reason for that is you want to
+go off and build your bigger boxes now
+
+ align:start position:0%
+go off and build your bigger boxes now
+ 
+
+ align:start position:0%
+go off and build your bigger boxes now
+there's another reason for doing
+
+ align:start position:0%
+there's another reason for doing
+ 
+
+ align:start position:0%
+there's another reason for doing
+blackbox abstraction other than you want
+
+ align:start position:0%
+blackbox abstraction other than you want
+ 
+
+ align:start position:0%
+blackbox abstraction other than you want
+to suppress detail for building bigger
+
+ align:start position:0%
+to suppress detail for building bigger
+ 
+
+ align:start position:0%
+to suppress detail for building bigger
+boxes sometimes
+
+ align:start position:0%
+boxes sometimes
+ 
+
+ align:start position:0%
+boxes sometimes
+you want to say that your way of doing
+
+ align:start position:0%
+you want to say that your way of doing
+ 
+
+ align:start position:0%
+you want to say that your way of doing
+something your how to method is an
+
+ align:start position:0%
+something your how to method is an
+ 
+
+ align:start position:0%
+something your how to method is an
+instance of a more general thing and
+
+ align:start position:0%
+instance of a more general thing and
+ 
+
+ align:start position:0%
+instance of a more general thing and
+you'd like your language to be able to
+
+ align:start position:0%
+you'd like your language to be able to
+ 
+
+ align:start position:0%
+you'd like your language to be able to
+express their generality let me show you
+
+ align:start position:0%
+express their generality let me show you
+ 
+
+ align:start position:0%
+express their generality let me show you
+another example sticking with square
+
+ align:start position:0%
+another example sticking with square
+ 
+
+ align:start position:0%
+another example sticking with square
+roots let's go back and take another
+
+ align:start position:0%
+roots let's go back and take another
+ 
+
+ align:start position:0%
+roots let's go back and take another
+look at that slide with the square root
+
+ align:start position:0%
+look at that slide with the square root
+ 
+
+ align:start position:0%
+look at that slide with the square root
+algorithm on it remember what that says
+
+ align:start position:0%
+algorithm on it remember what that says
+ 
+
+ align:start position:0%
+algorithm on it remember what that says
+that says in order to to do something I
+
+ align:start position:0%
+that says in order to to do something I
+ 
+
+ align:start position:0%
+that says in order to to do something I
+make a guess and I improve that guess
+
+ align:start position:0%
+make a guess and I improve that guess
+ 
+
+ align:start position:0%
+make a guess and I improve that guess
+and I sort of keep improving that yes
+
+ align:start position:0%
+and I sort of keep improving that yes
+ 
+
+ align:start position:0%
+and I sort of keep improving that yes
+very nice reduce so there's a general
+
+ align:start position:0%
+very nice reduce so there's a general
+ 
+
+ align:start position:0%
+very nice reduce so there's a general
+strategy of are looking for something
+
+ align:start position:0%
+strategy of are looking for something
+ 
+
+ align:start position:0%
+strategy of are looking for something
+and the way I find it is that I keep
+
+ align:start position:0%
+and the way I find it is that I keep
+ 
+
+ align:start position:0%
+and the way I find it is that I keep
+improving it
+
+ align:start position:0%
+improving it
+ 
+
+ align:start position:0%
+improving it
+now that's a particular case of another
+
+ align:start position:0%
+now that's a particular case of another
+ 
+
+ align:start position:0%
+now that's a particular case of another
+kind of strategy for finding a fixed
+
+ align:start position:0%
+kind of strategy for finding a fixed
+ 
+
+ align:start position:0%
+kind of strategy for finding a fixed
+point of something see a fixed point of
+
+ align:start position:0%
+point of something see a fixed point of
+ 
+
+ align:start position:0%
+point of something see a fixed point of
+the function a fixed point of the
+
+ align:start position:0%
+the function a fixed point of the
+ 
+
+ align:start position:0%
+the function a fixed point of the
+function is something this is the ru6
+
+ align:start position:0%
+function is something this is the ru6
+ 
+
+ align:start position:0%
+function is something this is the ru6
+point of the function f is a value Y
+
+ align:start position:0%
+point of the function f is a value Y
+ 
+
+ align:start position:0%
+point of the function f is a value Y
+such that that f of y equals y and the
+
+ align:start position:0%
+such that that f of y equals y and the
+ 
+
+ align:start position:0%
+such that that f of y equals y and the
+way I might do that you
+
+ align:start position:0%
+way I might do that you
+ 
+
+ align:start position:0%
+way I might do that you
+start with a guess and if I want
+
+ align:start position:0%
+start with a guess and if I want
+ 
+
+ align:start position:0%
+start with a guess and if I want
+something that doesn't change when I
+
+ align:start position:0%
+something that doesn't change when I
+ 
+
+ align:start position:0%
+something that doesn't change when I
+keep applying FSI I'll keep applying up
+
+ align:start position:0%
+keep applying FSI I'll keep applying up
+ 
+
+ align:start position:0%
+keep applying FSI I'll keep applying up
+over and over until that result doesn't
+
+ align:start position:0%
+over and over until that result doesn't
+ 
+
+ align:start position:0%
+over and over until that result doesn't
+change very much that's so there's a
+
+ align:start position:0%
+change very much that's so there's a
+ 
+
+ align:start position:0%
+change very much that's so there's a
+general strategy and then for example to
+
+ align:start position:0%
+general strategy and then for example to
+ 
+
+ align:start position:0%
+general strategy and then for example to
+compute the square root of x I can try
+
+ align:start position:0%
+compute the square root of x I can try
+ 
+
+ align:start position:0%
+compute the square root of x I can try
+and find a fixed point of the function
+
+ align:start position:0%
+and find a fixed point of the function
+ 
+
+ align:start position:0%
+and find a fixed point of the function
+which takes Y to the average of x over Y
+
+ align:start position:0%
+which takes Y to the average of x over Y
+ 
+
+ align:start position:0%
+which takes Y to the average of x over Y
+and the idea of that is that if I really
+
+ align:start position:0%
+and the idea of that is that if I really
+ 
+
+ align:start position:0%
+and the idea of that is that if I really
+had y equal to the square root of x then
+
+ align:start position:0%
+had y equal to the square root of x then
+ 
+
+ align:start position:0%
+had y equal to the square root of x then
+y and x over Y would be the same value
+
+ align:start position:0%
+y and x over Y would be the same value
+ 
+
+ align:start position:0%
+y and x over Y would be the same value
+they'd both be the square root of x
+
+ align:start position:0%
+they'd both be the square root of x
+ 
+
+ align:start position:0%
+they'd both be the square root of x
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+x over the square root of x is the
+
+ align:start position:0%
+x over the square root of x is the
+ 
+
+ align:start position:0%
+x over the square root of x is the
+square root of x and so the average if Y
+
+ align:start position:0%
+square root of x and so the average if Y
+ 
+
+ align:start position:0%
+square root of x and so the average if Y
+were equal to the square root of x then
+
+ align:start position:0%
+were equal to the square root of x then
+ 
+
+ align:start position:0%
+were equal to the square root of x then
+the average wouldn't change right so the
+
+ align:start position:0%
+the average wouldn't change right so the
+ 
+
+ align:start position:0%
+the average wouldn't change right so the
+square root of x is a fixed point of
+
+ align:start position:0%
+square root of x is a fixed point of
+ 
+
+ align:start position:0%
+square root of x is a fixed point of
+that particular function now what I'd
+
+ align:start position:0%
+that particular function now what I'd
+ 
+
+ align:start position:0%
+that particular function now what I'd
+like to have I'd like to express the
+
+ align:start position:0%
+like to have I'd like to express the
+ 
+
+ align:start position:0%
+like to have I'd like to express the
+general strategy for finding six points
+
+ align:start position:0%
+general strategy for finding six points
+ 
+
+ align:start position:0%
+general strategy for finding six points
+so what I might imagine doing is to find
+
+ align:start position:0%
+so what I might imagine doing is to find
+ 
+
+ align:start position:0%
+so what I might imagine doing is to find
+is to be able to use my language to
+
+ align:start position:0%
+is to be able to use my language to
+ 
+
+ align:start position:0%
+is to be able to use my language to
+define a box that says fixed point just
+
+ align:start position:0%
+define a box that says fixed point just
+ 
+
+ align:start position:0%
+define a box that says fixed point just
+like I could make a box that says square
+
+ align:start position:0%
+like I could make a box that says square
+ 
+
+ align:start position:0%
+like I could make a box that says square
+root and I'd like to be able to express
+
+ align:start position:0%
+root and I'd like to be able to express
+ 
+
+ align:start position:0%
+root and I'd like to be able to express
+this in my language all right so I'd
+
+ align:start position:0%
+this in my language all right so I'd
+ 
+
+ align:start position:0%
+this in my language all right so I'd
+like to express not only the imperative
+
+ align:start position:0%
+like to express not only the imperative
+ 
+
+ align:start position:0%
+like to express not only the imperative
+how-to knowledge of a particular thing
+
+ align:start position:0%
+how-to knowledge of a particular thing
+ 
+
+ align:start position:0%
+how-to knowledge of a particular thing
+like square root but I'd like to be able
+
+ align:start position:0%
+like square root but I'd like to be able
+ 
+
+ align:start position:0%
+like square root but I'd like to be able
+to express the imperative knowledge of
+
+ align:start position:0%
+to express the imperative knowledge of
+ 
+
+ align:start position:0%
+to express the imperative knowledge of
+how to do a general thing like how to
+
+ align:start position:0%
+how to do a general thing like how to
+ 
+
+ align:start position:0%
+how to do a general thing like how to
+find six points and in fact let's go
+
+ align:start position:0%
+find six points and in fact let's go
+ 
+
+ align:start position:0%
+find six points and in fact let's go
+back and look at that slide again she
+
+ align:start position:0%
+back and look at that slide again she
+ 
+
+ align:start position:0%
+back and look at that slide again she
+not only is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this a piece of imperative knowledge
+
+ align:start position:0%
+is this a piece of imperative knowledge
+ 
+
+ align:start position:0%
+is this a piece of imperative knowledge
+how to find a fixed point but over here
+
+ align:start position:0%
+how to find a fixed point but over here
+ 
+
+ align:start position:0%
+how to find a fixed point but over here
+on the bottom there's another piece of
+
+ align:start position:0%
+on the bottom there's another piece of
+ 
+
+ align:start position:0%
+on the bottom there's another piece of
+imperative knowledge which is one way to
+
+ align:start position:0%
+imperative knowledge which is one way to
+ 
+
+ align:start position:0%
+imperative knowledge which is one way to
+compute square is is to apply this
+
+ align:start position:0%
+compute square is is to apply this
+ 
+
+ align:start position:0%
+compute square is is to apply this
+general fixed point method so I'd like
+
+ align:start position:0%
+general fixed point method so I'd like
+ 
+
+ align:start position:0%
+general fixed point method so I'd like
+to also be able to express that in
+
+ align:start position:0%
+to also be able to express that in
+ 
+
+ align:start position:0%
+to also be able to express that in
+period of knowledge what would that look
+
+ align:start position:0%
+period of knowledge what would that look
+ 
+
+ align:start position:0%
+period of knowledge what would that look
+like that would say this fixed point box
+
+ align:start position:0%
+like that would say this fixed point box
+ 
+
+ align:start position:0%
+like that would say this fixed point box
+is such that if I input to it the
+
+ align:start position:0%
+is such that if I input to it the
+ 
+
+ align:start position:0%
+is such that if I input to it the
+function that takes Y to the average of
+
+ align:start position:0%
+function that takes Y to the average of
+ 
+
+ align:start position:0%
+function that takes Y to the average of
+Y and X over Y then what should come out
+
+ align:start position:0%
+Y and X over Y then what should come out
+ 
+
+ align:start position:0%
+Y and X over Y then what should come out
+of that fixed point box is a method for
+
+ align:start position:0%
+of that fixed point box is a method for
+ 
+
+ align:start position:0%
+of that fixed point box is a method for
+finding square is so in these boxes
+
+ align:start position:0%
+finding square is so in these boxes
+ 
+
+ align:start position:0%
+finding square is so in these boxes
+we're building we're not only building
+
+ align:start position:0%
+we're building we're not only building
+ 
+
+ align:start position:0%
+we're building we're not only building
+boxes that you input numbers and output
+
+ align:start position:0%
+boxes that you input numbers and output
+ 
+
+ align:start position:0%
+boxes that you input numbers and output
+numbers we can be building in boxes that
+
+ align:start position:0%
+numbers we can be building in boxes that
+ 
+
+ align:start position:0%
+numbers we can be building in boxes that
+in effect compute methods like finding
+
+ align:start position:0%
+in effect compute methods like finding
+ 
+
+ align:start position:0%
+in effect compute methods like finding
+square roots and my take is they're in
+
+ align:start position:0%
+square roots and my take is they're in
+ 
+
+ align:start position:0%
+square roots and my take is they're in
+point inputs functions like Y goes to
+
+ align:start position:0%
+point inputs functions like Y goes to
+ 
+
+ align:start position:0%
+point inputs functions like Y goes to
+the average of y and x over y like we
+
+ align:start position:0%
+the average of y and x over y like we
+ 
+
+ align:start position:0%
+the average of y and x over y like we
+can you want to do that see the reason
+
+ align:start position:0%
+can you want to do that see the reason
+ 
+
+ align:start position:0%
+can you want to do that see the reason
+this is a procedure will end up being a
+
+ align:start position:0%
+this is a procedure will end up being a
+ 
+
+ align:start position:0%
+this is a procedure will end up being a
+procedure as we'll see whose value is
+
+ align:start position:0%
+procedure as we'll see whose value is
+ 
+
+ align:start position:0%
+procedure as we'll see whose value is
+another procedure the reason we want to
+
+ align:start position:0%
+another procedure the reason we want to
+ 
+
+ align:start position:0%
+another procedure the reason we want to
+do that is because procedures are going
+
+ align:start position:0%
+do that is because procedures are going
+ 
+
+ align:start position:0%
+do that is because procedures are going
+to be our ways of talking about
+
+ align:start position:0%
+to be our ways of talking about
+ 
+
+ align:start position:0%
+to be our ways of talking about
+imperative knowledge and the way to make
+
+ align:start position:0%
+imperative knowledge and the way to make
+ 
+
+ align:start position:0%
+imperative knowledge and the way to make
+that very powerful is to be able to talk
+
+ align:start position:0%
+that very powerful is to be able to talk
+ 
+
+ align:start position:0%
+that very powerful is to be able to talk
+about other kinds of knowledge so here
+
+ align:start position:0%
+about other kinds of knowledge so here
+ 
+
+ align:start position:0%
+about other kinds of knowledge so here
+is a procedure that mystech talks about
+
+ align:start position:0%
+is a procedure that mystech talks about
+ 
+
+ align:start position:0%
+is a procedure that mystech talks about
+another procedure by the general
+
+ align:start position:0%
+another procedure by the general
+ 
+
+ align:start position:0%
+another procedure by the general
+strategy that itself talks about general
+
+ align:start position:0%
+strategy that itself talks about general
+ 
+
+ align:start position:0%
+strategy that itself talks about general
+strategy okay well our first topic in
+
+ align:start position:0%
+strategy okay well our first topic in
+ 
+
+ align:start position:0%
+strategy okay well our first topic in
+this course there'll be three major
+
+ align:start position:0%
+this course there'll be three major
+ 
+
+ align:start position:0%
+this course there'll be three major
+major topics will be blackbox
+
+ align:start position:0%
+major topics will be blackbox
+ 
+
+ align:start position:0%
+major topics will be blackbox
+abstraction let's look at that in a
+
+ align:start position:0%
+abstraction let's look at that in a
+ 
+
+ align:start position:0%
+abstraction let's look at that in a
+little bit more detail what we're going
+
+ align:start position:0%
+little bit more detail what we're going
+ 
+
+ align:start position:0%
+little bit more detail what we're going
+to do is we will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll start out talking about how list
+
+ align:start position:0%
+we'll start out talking about how list
+ 
+
+ align:start position:0%
+we'll start out talking about how list
+is built up at a primitive object like
+
+ align:start position:0%
+is built up at a primitive object like
+ 
+
+ align:start position:0%
+is built up at a primitive object like
+what is the language supply with us and
+
+ align:start position:0%
+what is the language supply with us and
+ 
+
+ align:start position:0%
+what is the language supply with us and
+we'll see that there are primitive
+
+ align:start position:0%
+we'll see that there are primitive
+ 
+
+ align:start position:0%
+we'll see that there are primitive
+procedures and primitive data then we're
+
+ align:start position:0%
+procedures and primitive data then we're
+ 
+
+ align:start position:0%
+procedures and primitive data then we're
+going to see how do you take those
+
+ align:start position:0%
+going to see how do you take those
+ 
+
+ align:start position:0%
+going to see how do you take those
+primitives and combine them to make more
+
+ align:start position:0%
+primitives and combine them to make more
+ 
+
+ align:start position:0%
+primitives and combine them to make more
+complicated things that means of
+
+ align:start position:0%
+complicated things that means of
+ 
+
+ align:start position:0%
+complicated things that means of
+combinations and what we'll see is that
+
+ align:start position:0%
+combinations and what we'll see is that
+ 
+
+ align:start position:0%
+combinations and what we'll see is that
+there ways of putting things together
+
+ align:start position:0%
+there ways of putting things together
+ 
+
+ align:start position:0%
+there ways of putting things together
+putting primitive procedures together to
+
+ align:start position:0%
+putting primitive procedures together to
+ 
+
+ align:start position:0%
+putting primitive procedures together to
+make more complicated procedures and
+
+ align:start position:0%
+make more complicated procedures and
+ 
+
+ align:start position:0%
+make more complicated procedures and
+we'll see how to put primitive data
+
+ align:start position:0%
+we'll see how to put primitive data
+ 
+
+ align:start position:0%
+we'll see how to put primitive data
+together to make compound data then
+
+ align:start position:0%
+together to make compound data then
+ 
+
+ align:start position:0%
+together to make compound data then
+we'll say well having made those
+
+ align:start position:0%
+we'll say well having made those
+ 
+
+ align:start position:0%
+we'll say well having made those
+compound things how do you abstract them
+
+ align:start position:0%
+compound things how do you abstract them
+ 
+
+ align:start position:0%
+compound things how do you abstract them
+how do you put those black boxes around
+
+ align:start position:0%
+how do you put those black boxes around
+ 
+
+ align:start position:0%
+how do you put those black boxes around
+them so you can use them as components
+
+ align:start position:0%
+them so you can use them as components
+ 
+
+ align:start position:0%
+them so you can use them as components
+in more complex things and we'll see
+
+ align:start position:0%
+in more complex things and we'll see
+ 
+
+ align:start position:0%
+in more complex things and we'll see
+that's done by defining procedures and a
+
+ align:start position:0%
+that's done by defining procedures and a
+ 
+
+ align:start position:0%
+that's done by defining procedures and a
+technique for dealing with compound data
+
+ align:start position:0%
+technique for dealing with compound data
+ 
+
+ align:start position:0%
+technique for dealing with compound data
+called data abstraction and then what's
+
+ align:start position:0%
+called data abstraction and then what's
+ 
+
+ align:start position:0%
+called data abstraction and then what's
+maybe the most important thing is going
+
+ align:start position:0%
+maybe the most important thing is going
+ 
+
+ align:start position:0%
+maybe the most important thing is going
+from just the rule to add as an expert
+
+ align:start position:0%
+from just the rule to add as an expert
+ 
+
+ align:start position:0%
+from just the rule to add as an expert
+work how do you express common patterns
+
+ align:start position:0%
+work how do you express common patterns
+ 
+
+ align:start position:0%
+work how do you express common patterns
+of doing things like saying well there's
+
+ align:start position:0%
+of doing things like saying well there's
+ 
+
+ align:start position:0%
+of doing things like saying well there's
+a general method of fixed point and
+
+ align:start position:0%
+a general method of fixed point and
+ 
+
+ align:start position:0%
+a general method of fixed point and
+square root is a particular case of that
+
+ align:start position:0%
+square root is a particular case of that
+ 
+
+ align:start position:0%
+square root is a particular case of that
+and we're going to use I've already
+
+ align:start position:0%
+and we're going to use I've already
+ 
+
+ align:start position:0%
+and we're going to use I've already
+hinted at it something called
+
+ align:start position:0%
+hinted at it something called
+ 
+
+ align:start position:0%
+hinted at it something called
+higher-order procedures namely
+
+ align:start position:0%
+higher-order procedures namely
+ 
+
+ align:start position:0%
+higher-order procedures namely
+procedures whose inputs and outputs are
+
+ align:start position:0%
+procedures whose inputs and outputs are
+ 
+
+ align:start position:0%
+procedures whose inputs and outputs are
+themselves procedures and then we'll
+
+ align:start position:0%
+themselves procedures and then we'll
+ 
+
+ align:start position:0%
+themselves procedures and then we'll
+also see something very interesting
+
+ align:start position:0%
+also see something very interesting
+ 
+
+ align:start position:0%
+also see something very interesting
+we'll see as we go further and further
+
+ align:start position:0%
+we'll see as we go further and further
+ 
+
+ align:start position:0%
+we'll see as we go further and further
+on and become more abstract they'll be
+
+ align:start position:0%
+on and become more abstract they'll be
+ 
+
+ align:start position:0%
+on and become more abstract they'll be
+very well the line between what we
+
+ align:start position:0%
+very well the line between what we
+ 
+
+ align:start position:0%
+very well the line between what we
+consider to be data and what we consider
+
+ align:start position:0%
+consider to be data and what we consider
+ 
+
+ align:start position:0%
+consider to be data and what we consider
+to be procedures is going to blur at an
+
+ align:start position:0%
+to be procedures is going to blur at an
+ 
+
+ align:start position:0%
+to be procedures is going to blur at an
+incredible rate well that's a that's our
+
+ align:start position:0%
+incredible rate well that's a that's our
+ 
+
+ align:start position:0%
+incredible rate well that's a that's our
+first subject blackbox abstraction let's
+
+ align:start position:0%
+first subject blackbox abstraction let's
+ 
+
+ align:start position:0%
+first subject blackbox abstraction let's
+look at the second topic he introduced
+
+ align:start position:0%
+look at the second topic he introduced
+ 
+
+ align:start position:0%
+look at the second topic he introduced
+it like this he suppose I I want to
+
+ align:start position:0%
+it like this he suppose I I want to
+ 
+
+ align:start position:0%
+it like this he suppose I I want to
+express the idea and remember we're
+
+ align:start position:0%
+express the idea and remember we're
+ 
+
+ align:start position:0%
+express the idea and remember we're
+we're talking about ideas I don't want
+
+ align:start position:0%
+we're talking about ideas I don't want
+ 
+
+ align:start position:0%
+we're talking about ideas I don't want
+to express the idea that I can take
+
+ align:start position:0%
+to express the idea that I can take
+ 
+
+ align:start position:0%
+to express the idea that I can take
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+and multiply it by the sum of two other
+
+ align:start position:0%
+and multiply it by the sum of two other
+ 
+
+ align:start position:0%
+and multiply it by the sum of two other
+things so for example I might say if I
+
+ align:start position:0%
+things so for example I might say if I
+ 
+
+ align:start position:0%
+things so for example I might say if I
+add one entry and multiply that by 2 I
+
+ align:start position:0%
+add one entry and multiply that by 2 I
+ 
+
+ align:start position:0%
+add one entry and multiply that by 2 I
+get a but I'm talking about the general
+
+ align:start position:0%
+get a but I'm talking about the general
+ 
+
+ align:start position:0%
+get a but I'm talking about the general
+idea of what's called linear combination
+
+ align:start position:0%
+idea of what's called linear combination
+ 
+
+ align:start position:0%
+idea of what's called linear combination
+that you can add two things and multiply
+
+ align:start position:0%
+that you can add two things and multiply
+ 
+
+ align:start position:0%
+that you can add two things and multiply
+them by something else very easy when I
+
+ align:start position:0%
+them by something else very easy when I
+ 
+
+ align:start position:0%
+them by something else very easy when I
+think about it for numbers but suppose I
+
+ align:start position:0%
+think about it for numbers but suppose I
+ 
+
+ align:start position:0%
+think about it for numbers but suppose I
+I also want to use that same idea to
+
+ align:start position:0%
+I also want to use that same idea to
+ 
+
+ align:start position:0%
+I also want to use that same idea to
+think about I could add two vectors a 1
+
+ align:start position:0%
+think about I could add two vectors a 1
+ 
+
+ align:start position:0%
+think about I could add two vectors a 1
+and a 2 and then scale them by some say
+
+ align:start position:0%
+and a 2 and then scale them by some say
+ 
+
+ align:start position:0%
+and a 2 and then scale them by some say
+after X and get another vector or I
+
+ align:start position:0%
+after X and get another vector or I
+ 
+
+ align:start position:0%
+after X and get another vector or I
+might say I want to think about a 1 and
+
+ align:start position:0%
+might say I want to think about a 1 and
+ 
+
+ align:start position:0%
+might say I want to think about a 1 and
+a 2 as being polynomials and I might
+
+ align:start position:0%
+a 2 as being polynomials and I might
+ 
+
+ align:start position:0%
+a 2 as being polynomials and I might
+want to add those two polynomials and
+
+ align:start position:0%
+want to add those two polynomials and
+ 
+
+ align:start position:0%
+want to add those two polynomials and
+then multiply them by 2 to get a more
+
+ align:start position:0%
+then multiply them by 2 to get a more
+ 
+
+ align:start position:0%
+then multiply them by 2 to get a more
+complicated one or a 1 and H you might
+
+ align:start position:0%
+complicated one or a 1 and H you might
+ 
+
+ align:start position:0%
+complicated one or a 1 and H you might
+be electrical signals and I might want
+
+ align:start position:0%
+be electrical signals and I might want
+ 
+
+ align:start position:0%
+be electrical signals and I might want
+to think of that summing those two
+
+ align:start position:0%
+to think of that summing those two
+ 
+
+ align:start position:0%
+to think of that summing those two
+electrical signals and then amp putting
+
+ align:start position:0%
+electrical signals and then amp putting
+ 
+
+ align:start position:0%
+electrical signals and then amp putting
+the whole thing to an amplifier
+
+ align:start position:0%
+the whole thing to an amplifier
+ 
+
+ align:start position:0%
+the whole thing to an amplifier
+multiplying it by by some factor of 2 or
+
+ align:start position:0%
+multiplying it by by some factor of 2 or
+ 
+
+ align:start position:0%
+multiplying it by by some factor of 2 or
+something the idea is I want to think
+
+ align:start position:0%
+something the idea is I want to think
+ 
+
+ align:start position:0%
+something the idea is I want to think
+about the general notion of that now if
+
+ align:start position:0%
+about the general notion of that now if
+ 
+
+ align:start position:0%
+about the general notion of that now if
+our language is going to be a good
+
+ align:start position:0%
+our language is going to be a good
+ 
+
+ align:start position:0%
+our language is going to be a good
+language for expressing those kind of
+
+ align:start position:0%
+language for expressing those kind of
+ 
+
+ align:start position:0%
+language for expressing those kind of
+general ideas I really really can do
+
+ align:start position:0%
+general ideas I really really can do
+ 
+
+ align:start position:0%
+general ideas I really really can do
+that so I'd like to be able to say I'm
+
+ align:start position:0%
+that so I'd like to be able to say I'm
+ 
+
+ align:start position:0%
+that so I'd like to be able to say I'm
+going to multiply by X the sum of a 1
+
+ align:start position:0%
+going to multiply by X the sum of a 1
+ 
+
+ align:start position:0%
+going to multiply by X the sum of a 1
+and a 2 and I'd like that to express the
+
+ align:start position:0%
+and a 2 and I'd like that to express the
+ 
+
+ align:start position:0%
+and a 2 and I'd like that to express the
+general idea of all different kinds of
+
+ align:start position:0%
+general idea of all different kinds of
+ 
+
+ align:start position:0%
+general idea of all different kinds of
+things that a 1 and a 2 could be now if
+
+ align:start position:0%
+things that a 1 and a 2 could be now if
+ 
+
+ align:start position:0%
+things that a 1 and a 2 could be now if
+you think about that there's a problem
+
+ align:start position:0%
+you think about that there's a problem
+ 
+
+ align:start position:0%
+you think about that there's a problem
+because after all the actual primitive
+
+ align:start position:0%
+because after all the actual primitive
+ 
+
+ align:start position:0%
+because after all the actual primitive
+operations that go on in the machine are
+
+ align:start position:0%
+operations that go on in the machine are
+ 
+
+ align:start position:0%
+operations that go on in the machine are
+obviously going to be different if I'm
+
+ align:start position:0%
+obviously going to be different if I'm
+ 
+
+ align:start position:0%
+obviously going to be different if I'm
+adding two numbers than finally adding
+
+ align:start position:0%
+adding two numbers than finally adding
+ 
+
+ align:start position:0%
+adding two numbers than finally adding
+two polynomials or if I'm adding the
+
+ align:start position:0%
+two polynomials or if I'm adding the
+ 
+
+ align:start position:0%
+two polynomials or if I'm adding the
+representation of two electrical signals
+
+ align:start position:0%
+representation of two electrical signals
+ 
+
+ align:start position:0%
+representation of two electrical signals
+or waveforms somewhere there has to be
+
+ align:start position:0%
+or waveforms somewhere there has to be
+ 
+
+ align:start position:0%
+or waveforms somewhere there has to be
+the knowledge of the kinds of various
+
+ align:start position:0%
+the knowledge of the kinds of various
+ 
+
+ align:start position:0%
+the knowledge of the kinds of various
+things that you can add and the ways of
+
+ align:start position:0%
+things that you can add and the ways of
+ 
+
+ align:start position:0%
+things that you can add and the ways of
+adding them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+construct such a system the question is
+
+ align:start position:0%
+construct such a system the question is
+ 
+
+ align:start position:0%
+construct such a system the question is
+where do I put that knowledge how do I
+
+ align:start position:0%
+where do I put that knowledge how do I
+ 
+
+ align:start position:0%
+where do I put that knowledge how do I
+think about the different kinds of
+
+ align:start position:0%
+think about the different kinds of
+ 
+
+ align:start position:0%
+think about the different kinds of
+choices I have and if tomorrow George
+
+ align:start position:0%
+choices I have and if tomorrow George
+ 
+
+ align:start position:0%
+choices I have and if tomorrow George
+comes up with a new kind of object that
+
+ align:start position:0%
+comes up with a new kind of object that
+ 
+
+ align:start position:0%
+comes up with a new kind of object that
+might be added and multiplied how do I
+
+ align:start position:0%
+might be added and multiplied how do I
+ 
+
+ align:start position:0%
+might be added and multiplied how do I
+add George's new object to the system
+
+ align:start position:0%
+add George's new object to the system
+ 
+
+ align:start position:0%
+add George's new object to the system
+without screwing up everything that was
+
+ align:start position:0%
+without screwing up everything that was
+ 
+
+ align:start position:0%
+without screwing up everything that was
+already here but well that's going to be
+
+ align:start position:0%
+already here but well that's going to be
+ 
+
+ align:start position:0%
+already here but well that's going to be
+the the second big topic the way of
+
+ align:start position:0%
+the the second big topic the way of
+ 
+
+ align:start position:0%
+the the second big topic the way of
+controlling that kind of complexity and
+
+ align:start position:0%
+controlling that kind of complexity and
+ 
+
+ align:start position:0%
+controlling that kind of complexity and
+the way you do that is by establishing
+
+ align:start position:0%
+the way you do that is by establishing
+ 
+
+ align:start position:0%
+the way you do that is by establishing
+conventional interfaces agreed-upon ways
+
+ align:start position:0%
+conventional interfaces agreed-upon ways
+ 
+
+ align:start position:0%
+conventional interfaces agreed-upon ways
+of plugging things together just like in
+
+ align:start position:0%
+of plugging things together just like in
+ 
+
+ align:start position:0%
+of plugging things together just like in
+electrical engineering people have
+
+ align:start position:0%
+electrical engineering people have
+ 
+
+ align:start position:0%
+electrical engineering people have
+standard impedances for connectors and
+
+ align:start position:0%
+standard impedances for connectors and
+ 
+
+ align:start position:0%
+standard impedances for connectors and
+then you know if you build something
+
+ align:start position:0%
+then you know if you build something
+ 
+
+ align:start position:0%
+then you know if you build something
+with one of those standard impedances
+
+ align:start position:0%
+with one of those standard impedances
+ 
+
+ align:start position:0%
+with one of those standard impedances
+you can plug it together with something
+
+ align:start position:0%
+you can plug it together with something
+ 
+
+ align:start position:0%
+you can plug it together with something
+else like that's going to be our second
+
+ align:start position:0%
+else like that's going to be our second
+ 
+
+ align:start position:0%
+else like that's going to be our second
+large topic conventional interfaces what
+
+ align:start position:0%
+large topic conventional interfaces what
+ 
+
+ align:start position:0%
+large topic conventional interfaces what
+we're going to see is when first we're
+
+ align:start position:0%
+we're going to see is when first we're
+ 
+
+ align:start position:0%
+we're going to see is when first we're
+going to talk about the problem of
+
+ align:start position:0%
+going to talk about the problem of
+ 
+
+ align:start position:0%
+going to talk about the problem of
+generic operations which is the one I
+
+ align:start position:0%
+generic operations which is the one I
+ 
+
+ align:start position:0%
+generic operations which is the one I
+alluded to things like plus that that
+
+ align:start position:0%
+alluded to things like plus that that
+ 
+
+ align:start position:0%
+alluded to things like plus that that
+have to work with all different kinds of
+
+ align:start position:0%
+have to work with all different kinds of
+ 
+
+ align:start position:0%
+have to work with all different kinds of
+data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we talked about generic operations then
+
+ align:start position:0%
+we talked about generic operations then
+ 
+
+ align:start position:0%
+we talked about generic operations then
+we're going to talk about really
+
+ align:start position:0%
+we're going to talk about really
+ 
+
+ align:start position:0%
+we're going to talk about really
+large-scale structures how do you put
+
+ align:start position:0%
+large-scale structures how do you put
+ 
+
+ align:start position:0%
+large-scale structures how do you put
+together very large programs that model
+
+ align:start position:0%
+together very large programs that model
+ 
+
+ align:start position:0%
+together very large programs that model
+the kinds of complex systems in the real
+
+ align:start position:0%
+the kinds of complex systems in the real
+ 
+
+ align:start position:0%
+the kinds of complex systems in the real
+world that you'd like to model and what
+
+ align:start position:0%
+world that you'd like to model and what
+ 
+
+ align:start position:0%
+world that you'd like to model and what
+we're going to see is that there are two
+
+ align:start position:0%
+we're going to see is that there are two
+ 
+
+ align:start position:0%
+we're going to see is that there are two
+very important metaphors for putting
+
+ align:start position:0%
+very important metaphors for putting
+ 
+
+ align:start position:0%
+very important metaphors for putting
+together such systems one is called
+
+ align:start position:0%
+together such systems one is called
+ 
+
+ align:start position:0%
+together such systems one is called
+object-oriented programming where you
+
+ align:start position:0%
+object-oriented programming where you
+ 
+
+ align:start position:0%
+object-oriented programming where you
+sort of think of your system as a kind
+
+ align:start position:0%
+sort of think of your system as a kind
+ 
+
+ align:start position:0%
+sort of think of your system as a kind
+of society full of little things that
+
+ align:start position:0%
+of society full of little things that
+ 
+
+ align:start position:0%
+of society full of little things that
+interact by sending information between
+
+ align:start position:0%
+interact by sending information between
+ 
+
+ align:start position:0%
+interact by sending information between
+them and then the second one is
+
+ align:start position:0%
+them and then the second one is
+ 
+
+ align:start position:0%
+them and then the second one is
+operations on aggregates called streams
+
+ align:start position:0%
+operations on aggregates called streams
+ 
+
+ align:start position:0%
+operations on aggregates called streams
+where you think of a large system put
+
+ align:start position:0%
+where you think of a large system put
+ 
+
+ align:start position:0%
+where you think of a large system put
+together kind of like a signal
+
+ align:start position:0%
+together kind of like a signal
+ 
+
+ align:start position:0%
+together kind of like a signal
+processing engineer puts together a
+
+ align:start position:0%
+processing engineer puts together a
+ 
+
+ align:start position:0%
+processing engineer puts together a
+large electrical system that's going to
+
+ align:start position:0%
+large electrical system that's going to
+ 
+
+ align:start position:0%
+large electrical system that's going to
+be our second topic now the third thing
+
+ align:start position:0%
+be our second topic now the third thing
+ 
+
+ align:start position:0%
+be our second topic now the third thing
+we're going to come to the third basic
+
+ align:start position:0%
+we're going to come to the third basic
+ 
+
+ align:start position:0%
+we're going to come to the third basic
+technique for controlling complexity is
+
+ align:start position:0%
+technique for controlling complexity is
+ 
+
+ align:start position:0%
+technique for controlling complexity is
+making new languages sometimes when
+
+ align:start position:0%
+making new languages sometimes when
+ 
+
+ align:start position:0%
+making new languages sometimes when
+you're sort of overwhelmed by the
+
+ align:start position:0%
+you're sort of overwhelmed by the
+ 
+
+ align:start position:0%
+you're sort of overwhelmed by the
+complexity of a design the way that you
+
+ align:start position:0%
+complexity of a design the way that you
+ 
+
+ align:start position:0%
+complexity of a design the way that you
+control that complexity is to pick a new
+
+ align:start position:0%
+control that complexity is to pick a new
+ 
+
+ align:start position:0%
+control that complexity is to pick a new
+design language and the purpose of the
+
+ align:start position:0%
+design language and the purpose of the
+ 
+
+ align:start position:0%
+design language and the purpose of the
+new design language will be to highlight
+
+ align:start position:0%
+new design language will be to highlight
+ 
+
+ align:start position:0%
+new design language will be to highlight
+different aspects of the system it'll
+
+ align:start position:0%
+different aspects of the system it'll
+ 
+
+ align:start position:0%
+different aspects of the system it'll
+suppress some kinds of details and
+
+ align:start position:0%
+suppress some kinds of details and
+ 
+
+ align:start position:0%
+suppress some kinds of details and
+emphasize other kinds of detail this is
+
+ align:start position:0%
+emphasize other kinds of detail this is
+ 
+
+ align:start position:0%
+emphasize other kinds of detail this is
+going to be the sort of the most magical
+
+ align:start position:0%
+going to be the sort of the most magical
+ 
+
+ align:start position:0%
+going to be the sort of the most magical
+part of the course we're going to start
+
+ align:start position:0%
+part of the course we're going to start
+ 
+
+ align:start position:0%
+part of the course we're going to start
+out by actually looking at the
+
+ align:start position:0%
+out by actually looking at the
+ 
+
+ align:start position:0%
+out by actually looking at the
+technology for building new computer
+
+ align:start position:0%
+technology for building new computer
+ 
+
+ align:start position:0%
+technology for building new computer
+languages and will be the first thing
+
+ align:start position:0%
+languages and will be the first thing
+ 
+
+ align:start position:0%
+languages and will be the first thing
+we're going to do is actually build in
+
+ align:start position:0%
+we're going to do is actually build in
+ 
+
+ align:start position:0%
+we're going to do is actually build in
+Lisp a problem we're going to express in
+
+ align:start position:0%
+Lisp a problem we're going to express in
+ 
+
+ align:start position:0%
+Lisp a problem we're going to express in
+list the process of interpreting list
+
+ align:start position:0%
+list the process of interpreting list
+ 
+
+ align:start position:0%
+list the process of interpreting list
+itself and that's going to be a very
+
+ align:start position:0%
+itself and that's going to be a very
+ 
+
+ align:start position:0%
+itself and that's going to be a very
+sort of self circular thing there's a
+
+ align:start position:0%
+sort of self circular thing there's a
+ 
+
+ align:start position:0%
+sort of self circular thing there's a
+little mystical symbol that have to do
+
+ align:start position:0%
+little mystical symbol that have to do
+ 
+
+ align:start position:0%
+little mystical symbol that have to do
+with that will see itself the process of
+
+ align:start position:0%
+with that will see itself the process of
+ 
+
+ align:start position:0%
+with that will see itself the process of
+interpreting lists is sort of a a giant
+
+ align:start position:0%
+interpreting lists is sort of a a giant
+ 
+
+ align:start position:0%
+interpreting lists is sort of a a giant
+wheel of two processes apply an eval
+
+ align:start position:0%
+wheel of two processes apply an eval
+ 
+
+ align:start position:0%
+wheel of two processes apply an eval
+which sort of constantly reduce
+
+ align:start position:0%
+which sort of constantly reduce
+ 
+
+ align:start position:0%
+which sort of constantly reduce
+expressions to each other then we're
+
+ align:start position:0%
+expressions to each other then we're
+ 
+
+ align:start position:0%
+expressions to each other then we're
+gonna see all sorts of other magical
+
+ align:start position:0%
+gonna see all sorts of other magical
+ 
+
+ align:start position:0%
+gonna see all sorts of other magical
+things here's another another magical
+
+ align:start position:0%
+things here's another another magical
+ 
+
+ align:start position:0%
+things here's another another magical
+system symbol this is kind of the sort
+
+ align:start position:0%
+system symbol this is kind of the sort
+ 
+
+ align:start position:0%
+system symbol this is kind of the sort
+of the why operator which is in some
+
+ align:start position:0%
+of the why operator which is in some
+ 
+
+ align:start position:0%
+of the why operator which is in some
+sense the expression of infinity inside
+
+ align:start position:0%
+sense the expression of infinity inside
+ 
+
+ align:start position:0%
+sense the expression of infinity inside
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+Sidra language we'll take a look at that
+
+ align:start position:0%
+Sidra language we'll take a look at that
+ 
+
+ align:start position:0%
+Sidra language we'll take a look at that
+in any case this section of the course
+
+ align:start position:0%
+in any case this section of the course
+ 
+
+ align:start position:0%
+in any case this section of the course
+is called metalinguistic abstraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking abstract
+
+ align:start position:0%
+talking abstract
+ 
+
+ align:start position:0%
+talking abstract
+by talking about how you construct new
+
+ align:start position:0%
+by talking about how you construct new
+ 
+
+ align:start position:0%
+by talking about how you construct new
+languages as I said we're going to start
+
+ align:start position:0%
+languages as I said we're going to start
+ 
+
+ align:start position:0%
+languages as I said we're going to start
+out by looking at the process of
+
+ align:start position:0%
+out by looking at the process of
+ 
+
+ align:start position:0%
+out by looking at the process of
+interpretation we're going to look at
+
+ align:start position:0%
+interpretation we're going to look at
+ 
+
+ align:start position:0%
+interpretation we're going to look at
+this apply eval loop and build lists
+
+ align:start position:0%
+this apply eval loop and build lists
+ 
+
+ align:start position:0%
+this apply eval loop and build lists
+then just to show you that this is very
+
+ align:start position:0%
+then just to show you that this is very
+ 
+
+ align:start position:0%
+then just to show you that this is very
+general we're going to use exactly the
+
+ align:start position:0%
+general we're going to use exactly the
+ 
+
+ align:start position:0%
+general we're going to use exactly the
+same technology to build a very
+
+ align:start position:0%
+same technology to build a very
+ 
+
+ align:start position:0%
+same technology to build a very
+different kind of language so called
+
+ align:start position:0%
+different kind of language so called
+ 
+
+ align:start position:0%
+different kind of language so called
+logic programming language where you
+
+ align:start position:0%
+logic programming language where you
+ 
+
+ align:start position:0%
+logic programming language where you
+don't really talk about procedures at
+
+ align:start position:0%
+don't really talk about procedures at
+ 
+
+ align:start position:0%
+don't really talk about procedures at
+all that have inputs and outputs what
+
+ align:start position:0%
+all that have inputs and outputs what
+ 
+
+ align:start position:0%
+all that have inputs and outputs what
+you do is talk about relations between
+
+ align:start position:0%
+you do is talk about relations between
+ 
+
+ align:start position:0%
+you do is talk about relations between
+things and then finally we're going to
+
+ align:start position:0%
+things and then finally we're going to
+ 
+
+ align:start position:0%
+things and then finally we're going to
+talk about how you implement these
+
+ align:start position:0%
+talk about how you implement these
+ 
+
+ align:start position:0%
+talk about how you implement these
+things very concretely on the very
+
+ align:start position:0%
+things very concretely on the very
+ 
+
+ align:start position:0%
+things very concretely on the very
+simplest kind of machines even though
+
+ align:start position:0%
+simplest kind of machines even though
+ 
+
+ align:start position:0%
+simplest kind of machines even though
+we'll see something like this which is
+
+ align:start position:0%
+we'll see something like this which is
+ 
+
+ align:start position:0%
+we'll see something like this which is
+this is a picture of the of the chip
+
+ align:start position:0%
+this is a picture of the of the chip
+ 
+
+ align:start position:0%
+this is a picture of the of the chip
+which is the Lisp interpreter that we
+
+ align:start position:0%
+which is the Lisp interpreter that we
+ 
+
+ align:start position:0%
+which is the Lisp interpreter that we
+will be talking about then in hardware
+
+ align:start position:0%
+will be talking about then in hardware
+ 
+
+ align:start position:0%
+will be talking about then in hardware
+okay well there's there's an outline of
+
+ align:start position:0%
+okay well there's there's an outline of
+ 
+
+ align:start position:0%
+okay well there's there's an outline of
+the course three big topics black out
+
+ align:start position:0%
+the course three big topics black out
+ 
+
+ align:start position:0%
+the course three big topics black out
+box abstraction conventional interfaces
+
+ align:start position:0%
+box abstraction conventional interfaces
+ 
+
+ align:start position:0%
+box abstraction conventional interfaces
+middle linguistic abstraction
+
+ align:start position:0%
+middle linguistic abstraction
+ 
+
+ align:start position:0%
+middle linguistic abstraction
+now let's take a break now and then
+
+ align:start position:0%
+now let's take a break now and then
+ 
+
+ align:start position:0%
+now let's take a break now and then
+we'll get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's let's actually start in
+
+ align:start position:0%
+well let's let's actually start in
+ 
+
+ align:start position:0%
+well let's let's actually start in
+learning list now actually we'll start
+
+ align:start position:0%
+learning list now actually we'll start
+ 
+
+ align:start position:0%
+learning list now actually we'll start
+out by learning something much more
+
+ align:start position:0%
+out by learning something much more
+ 
+
+ align:start position:0%
+out by learning something much more
+important maybe the very most important
+
+ align:start position:0%
+important maybe the very most important
+ 
+
+ align:start position:0%
+important maybe the very most important
+thing in this course which is not list
+
+ align:start position:0%
+thing in this course which is not list
+ 
+
+ align:start position:0%
+thing in this course which is not list
+in particular of course but rather a
+
+ align:start position:0%
+in particular of course but rather a
+ 
+
+ align:start position:0%
+in particular of course but rather a
+general framework for thinking about
+
+ align:start position:0%
+general framework for thinking about
+ 
+
+ align:start position:0%
+general framework for thinking about
+languages they already alluded to when
+
+ align:start position:0%
+languages they already alluded to when
+ 
+
+ align:start position:0%
+languages they already alluded to when
+somebody tells you they're going to show
+
+ align:start position:0%
+somebody tells you they're going to show
+ 
+
+ align:start position:0%
+somebody tells you they're going to show
+you a language what you should say is
+
+ align:start position:0%
+you a language what you should say is
+ 
+
+ align:start position:0%
+you a language what you should say is
+all right what I'd like you to tell me
+
+ align:start position:0%
+all right what I'd like you to tell me
+ 
+
+ align:start position:0%
+all right what I'd like you to tell me
+is what are the what are the primitive
+
+ align:start position:0%
+is what are the what are the primitive
+ 
+
+ align:start position:0%
+is what are the what are the primitive
+elements what is the language come with
+
+ align:start position:0%
+elements what is the language come with
+ 
+
+ align:start position:0%
+elements what is the language come with
+then what are the ways you put those
+
+ align:start position:0%
+then what are the ways you put those
+ 
+
+ align:start position:0%
+then what are the ways you put those
+together what are the means of
+
+ align:start position:0%
+together what are the means of
+ 
+
+ align:start position:0%
+together what are the means of
+combination what are the things that
+
+ align:start position:0%
+combination what are the things that
+ 
+
+ align:start position:0%
+combination what are the things that
+allow you to take these primitive
+
+ align:start position:0%
+allow you to take these primitive
+ 
+
+ align:start position:0%
+allow you to take these primitive
+elements and build bigger things out of
+
+ align:start position:0%
+elements and build bigger things out of
+ 
+
+ align:start position:0%
+elements and build bigger things out of
+them what are the ways of putting things
+
+ align:start position:0%
+them what are the ways of putting things
+ 
+
+ align:start position:0%
+them what are the ways of putting things
+together and then what are the means of
+
+ align:start position:0%
+together and then what are the means of
+ 
+
+ align:start position:0%
+together and then what are the means of
+abstraction how do we take those
+
+ align:start position:0%
+abstraction how do we take those
+ 
+
+ align:start position:0%
+abstraction how do we take those
+complicated things and draw those boxes
+
+ align:start position:0%
+complicated things and draw those boxes
+ 
+
+ align:start position:0%
+complicated things and draw those boxes
+around them how do we name them so that
+
+ align:start position:0%
+around them how do we name them so that
+ 
+
+ align:start position:0%
+around them how do we name them so that
+we can now use them as if they were
+
+ align:start position:0%
+we can now use them as if they were
+ 
+
+ align:start position:0%
+we can now use them as if they were
+primitive elements in making still more
+
+ align:start position:0%
+primitive elements in making still more
+ 
+
+ align:start position:0%
+primitive elements in making still more
+complex things and so on and so on and
+
+ align:start position:0%
+complex things and so on and so on and
+ 
+
+ align:start position:0%
+complex things and so on and so on and
+so on so when someone says to you gee I
+
+ align:start position:0%
+so on so when someone says to you gee I
+ 
+
+ align:start position:0%
+so on so when someone says to you gee I
+have a great new computer language you
+
+ align:start position:0%
+have a great new computer language you
+ 
+
+ align:start position:0%
+have a great new computer language you
+don't say how many characters does it
+
+ align:start position:0%
+don't say how many characters does it
+ 
+
+ align:start position:0%
+don't say how many characters does it
+take to invert a matrix that it's
+
+ align:start position:0%
+take to invert a matrix that it's
+ 
+
+ align:start position:0%
+take to invert a matrix that it's
+irrelevant right what you say is how if
+
+ align:start position:0%
+irrelevant right what you say is how if
+ 
+
+ align:start position:0%
+irrelevant right what you say is how if
+the language did not come with matrices
+
+ align:start position:0%
+the language did not come with matrices
+ 
+
+ align:start position:0%
+the language did not come with matrices
+built-in or with something else then how
+
+ align:start position:0%
+built-in or with something else then how
+ 
+
+ align:start position:0%
+built-in or with something else then how
+could I then build that thing what are
+
+ align:start position:0%
+could I then build that thing what are
+ 
+
+ align:start position:0%
+could I then build that thing what are
+the means of combination which would
+
+ align:start position:0%
+the means of combination which would
+ 
+
+ align:start position:0%
+the means of combination which would
+allow me to do that and then what are
+
+ align:start position:0%
+allow me to do that and then what are
+ 
+
+ align:start position:0%
+allow me to do that and then what are
+the needs of the abstraction which allow
+
+ align:start position:0%
+the needs of the abstraction which allow
+ 
+
+ align:start position:0%
+the needs of the abstraction which allow
+me then to use those are the elements in
+
+ align:start position:0%
+me then to use those are the elements in
+ 
+
+ align:start position:0%
+me then to use those are the elements in
+making more complicated things yet well
+
+ align:start position:0%
+making more complicated things yet well
+ 
+
+ align:start position:0%
+making more complicated things yet well
+we're going to see that list has some
+
+ align:start position:0%
+we're going to see that list has some
+ 
+
+ align:start position:0%
+we're going to see that list has some
+primitive data and some primitive
+
+ align:start position:0%
+primitive data and some primitive
+ 
+
+ align:start position:0%
+primitive data and some primitive
+procedures in fact let's let's really
+
+ align:start position:0%
+procedures in fact let's let's really
+ 
+
+ align:start position:0%
+procedures in fact let's let's really
+start and here's a piece of primitive
+
+ align:start position:0%
+start and here's a piece of primitive
+ 
+
+ align:start position:0%
+start and here's a piece of primitive
+data and Lisp let's say
+
+ align:start position:0%
+data and Lisp let's say
+ 
+
+ align:start position:0%
+data and Lisp let's say
+right number three actually from being
+
+ align:start position:0%
+right number three actually from being
+ 
+
+ align:start position:0%
+right number three actually from being
+very pedantic that's not the number
+
+ align:start position:0%
+very pedantic that's not the number
+ 
+
+ align:start position:0%
+very pedantic that's not the number
+three that's some symbol that represents
+
+ align:start position:0%
+three that's some symbol that represents
+ 
+
+ align:start position:0%
+three that's some symbol that represents
+no Plato's concept of the number three
+
+ align:start position:0%
+no Plato's concept of the number three
+ 
+
+ align:start position:0%
+no Plato's concept of the number three
+right and here's another here's some
+
+ align:start position:0%
+right and here's another here's some
+ 
+
+ align:start position:0%
+right and here's another here's some
+more primitive data in Lisp right it's
+
+ align:start position:0%
+more primitive data in Lisp right it's
+ 
+
+ align:start position:0%
+more primitive data in Lisp right it's
+seventeen point four actually some
+
+ align:start position:0%
+seventeen point four actually some
+ 
+
+ align:start position:0%
+seventeen point four actually some
+representation of seventeen point four
+
+ align:start position:0%
+representation of seventeen point four
+ 
+
+ align:start position:0%
+representation of seventeen point four
+and here's another one five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's another primitive object that's
+
+ align:start position:0%
+here's another primitive object that's
+ 
+
+ align:start position:0%
+here's another primitive object that's
+built in Lisp addition actually use the
+
+ align:start position:0%
+built in Lisp addition actually use the
+ 
+
+ align:start position:0%
+built in Lisp addition actually use the
+same kind of pedantic this is a name for
+
+ align:start position:0%
+same kind of pedantic this is a name for
+ 
+
+ align:start position:0%
+same kind of pedantic this is a name for
+the primitive method of adding things
+
+ align:start position:0%
+the primitive method of adding things
+ 
+
+ align:start position:0%
+the primitive method of adding things
+just like this is a name for Plato's
+
+ align:start position:0%
+just like this is a name for Plato's
+ 
+
+ align:start position:0%
+just like this is a name for Plato's
+number three
+
+ align:start position:0%
+number three
+ 
+
+ align:start position:0%
+number three
+this is a name for Plato's concept of
+
+ align:start position:0%
+this is a name for Plato's concept of
+ 
+
+ align:start position:0%
+this is a name for Plato's concept of
+how you how you add things but sure
+
+ align:start position:0%
+how you how you add things but sure
+ 
+
+ align:start position:0%
+how you how you add things but sure
+those are some primitive the elements I
+
+ align:start position:0%
+those are some primitive the elements I
+ 
+
+ align:start position:0%
+those are some primitive the elements I
+can put them together I can say gee
+
+ align:start position:0%
+can put them together I can say gee
+ 
+
+ align:start position:0%
+can put them together I can say gee
+watch the sum of three and seventeen
+
+ align:start position:0%
+watch the sum of three and seventeen
+ 
+
+ align:start position:0%
+watch the sum of three and seventeen
+point four and five the way I do that is
+
+ align:start position:0%
+point four and five the way I do that is
+ 
+
+ align:start position:0%
+point four and five the way I do that is
+to say let's apply the Sun operator to
+
+ align:start position:0%
+to say let's apply the Sun operator to
+ 
+
+ align:start position:0%
+to say let's apply the Sun operator to
+these three numbers and I should get
+
+ align:start position:0%
+these three numbers and I should get
+ 
+
+ align:start position:0%
+these three numbers and I should get
+what eight seventeen twenty five point
+
+ align:start position:0%
+what eight seventeen twenty five point
+ 
+
+ align:start position:0%
+what eight seventeen twenty five point
+four I should be able to ask Lisp what
+
+ align:start position:0%
+four I should be able to ask Lisp what
+ 
+
+ align:start position:0%
+four I should be able to ask Lisp what
+the value of this is and we'll return
+
+ align:start position:0%
+the value of this is and we'll return
+ 
+
+ align:start position:0%
+the value of this is and we'll return
+twenty five point four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's introduce some names this thing
+
+ align:start position:0%
+let's introduce some names this thing
+ 
+
+ align:start position:0%
+let's introduce some names this thing
+that I typed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's called a combination and a
+
+ align:start position:0%
+it's called a combination and a
+ 
+
+ align:start position:0%
+it's called a combination and a
+combination consistent general of
+
+ align:start position:0%
+combination consistent general of
+ 
+
+ align:start position:0%
+combination consistent general of
+applying an operator so this is an
+
+ align:start position:0%
+applying an operator so this is an
+ 
+
+ align:start position:0%
+applying an operator so this is an
+operator to some operands these are the
+
+ align:start position:0%
+operator to some operands these are the
+ 
+
+ align:start position:0%
+operator to some operands these are the
+operands
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course I can make more complex
+
+ align:start position:0%
+and of course I can make more complex
+ 
+
+ align:start position:0%
+and of course I can make more complex
+things the reason I can get complexity
+
+ align:start position:0%
+things the reason I can get complexity
+ 
+
+ align:start position:0%
+things the reason I can get complexity
+out of this is because the operands
+
+ align:start position:0%
+out of this is because the operands
+ 
+
+ align:start position:0%
+out of this is because the operands
+themselves in general can be
+
+ align:start position:0%
+themselves in general can be
+ 
+
+ align:start position:0%
+themselves in general can be
+combinations so for instance I could say
+
+ align:start position:0%
+combinations so for instance I could say
+ 
+
+ align:start position:0%
+combinations so for instance I could say
+what is the sum of 3 and the product of
+
+ align:start position:0%
+what is the sum of 3 and the product of
+ 
+
+ align:start position:0%
+what is the sum of 3 and the product of
+five and six and eight and two and I
+
+ align:start position:0%
+five and six and eight and two and I
+ 
+
+ align:start position:0%
+five and six and eight and two and I
+should get let's say 30 40 43 so this
+
+ align:start position:0%
+should get let's say 30 40 43 so this
+ 
+
+ align:start position:0%
+should get let's say 30 40 43 so this
+should tell me that that's 43 forming
+
+ align:start position:0%
+should tell me that that's 43 forming
+ 
+
+ align:start position:0%
+should tell me that that's 43 forming
+combinations well is that basic means
+
+ align:start position:0%
+combinations well is that basic means
+ 
+
+ align:start position:0%
+combinations well is that basic means
+the combination that we'll be looking at
+
+ align:start position:0%
+the combination that we'll be looking at
+ 
+
+ align:start position:0%
+the combination that we'll be looking at
+and then well you see some some syntax
+
+ align:start position:0%
+and then well you see some some syntax
+ 
+
+ align:start position:0%
+and then well you see some some syntax
+here Lisp uses what's called prefix
+
+ align:start position:0%
+here Lisp uses what's called prefix
+ 
+
+ align:start position:0%
+here Lisp uses what's called prefix
+notation which means that the operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the operator is written to the left
+
+ align:start position:0%
+that the operator is written to the left
+ 
+
+ align:start position:0%
+that the operator is written to the left
+of the operands it's just a convention
+
+ align:start position:0%
+of the operands it's just a convention
+ 
+
+ align:start position:0%
+of the operands it's just a convention
+and notice it's fully parenthesized and
+
+ align:start position:0%
+and notice it's fully parenthesized and
+ 
+
+ align:start position:0%
+and notice it's fully parenthesized and
+the parenthesis make it completely
+
+ align:start position:0%
+the parenthesis make it completely
+ 
+
+ align:start position:0%
+the parenthesis make it completely
+unambiguous so by looking at this I can
+
+ align:start position:0%
+unambiguous so by looking at this I can
+ 
+
+ align:start position:0%
+unambiguous so by looking at this I can
+see that there's the operator and there
+
+ align:start position:0%
+see that there's the operator and there
+ 
+
+ align:start position:0%
+see that there's the operator and there
+1 2 3 4 operands right and I can see
+
+ align:start position:0%
+1 2 3 4 operands right and I can see
+ 
+
+ align:start position:0%
+1 2 3 4 operands right and I can see
+that the second operand here is itself
+
+ align:start position:0%
+that the second operand here is itself
+ 
+
+ align:start position:0%
+that the second operand here is itself
+some combination that has one Operator
+
+ align:start position:0%
+some combination that has one Operator
+ 
+
+ align:start position:0%
+some combination that has one Operator
+and two operands parentheses in list
+
+ align:start position:0%
+and two operands parentheses in list
+ 
+
+ align:start position:0%
+and two operands parentheses in list
+they're a little bit or are very unlike
+
+ align:start position:0%
+they're a little bit or are very unlike
+ 
+
+ align:start position:0%
+they're a little bit or are very unlike
+parentheses and conventional mathematics
+
+ align:start position:0%
+parentheses and conventional mathematics
+ 
+
+ align:start position:0%
+parentheses and conventional mathematics
+mathematics we sort of use them to mean
+
+ align:start position:0%
+mathematics we sort of use them to mean
+ 
+
+ align:start position:0%
+mathematics we sort of use them to mean
+grouping and it sort of doesn't hurt if
+
+ align:start position:0%
+grouping and it sort of doesn't hurt if
+ 
+
+ align:start position:0%
+grouping and it sort of doesn't hurt if
+sometimes you leave out parentheses if
+
+ align:start position:0%
+sometimes you leave out parentheses if
+ 
+
+ align:start position:0%
+sometimes you leave out parentheses if
+people understand that that's a group
+
+ align:start position:0%
+people understand that that's a group
+ 
+
+ align:start position:0%
+people understand that that's a group
+and in general it doesn't hurt if you
+
+ align:start position:0%
+and in general it doesn't hurt if you
+ 
+
+ align:start position:0%
+and in general it doesn't hurt if you
+put in extra parentheses that because
+
+ align:start position:0%
+put in extra parentheses that because
+ 
+
+ align:start position:0%
+put in extra parentheses that because
+that maybe makes the grouping more
+
+ align:start position:0%
+that maybe makes the grouping more
+ 
+
+ align:start position:0%
+that maybe makes the grouping more
+distinct list is not like that enlist
+
+ align:start position:0%
+distinct list is not like that enlist
+ 
+
+ align:start position:0%
+distinct list is not like that enlist
+you cannot leave out parentheses and you
+
+ align:start position:0%
+you cannot leave out parentheses and you
+ 
+
+ align:start position:0%
+you cannot leave out parentheses and you
+cannot put in extra parentheses right
+
+ align:start position:0%
+cannot put in extra parentheses right
+ 
+
+ align:start position:0%
+cannot put in extra parentheses right
+because putting in parentheses always
+
+ align:start position:0%
+because putting in parentheses always
+ 
+
+ align:start position:0%
+because putting in parentheses always
+mean exactly and precisely this is a
+
+ align:start position:0%
+mean exactly and precisely this is a
+ 
+
+ align:start position:0%
+mean exactly and precisely this is a
+combination which has meaning apply an
+
+ align:start position:0%
+combination which has meaning apply an
+ 
+
+ align:start position:0%
+combination which has meaning apply an
+operator to operands and if I lift this
+
+ align:start position:0%
+operator to operands and if I lift this
+ 
+
+ align:start position:0%
+operator to operands and if I lift this
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+let those parentheses out it would mean
+
+ align:start position:0%
+let those parentheses out it would mean
+ 
+
+ align:start position:0%
+let those parentheses out it would mean
+something else in fact the way to think
+
+ align:start position:0%
+something else in fact the way to think
+ 
+
+ align:start position:0%
+something else in fact the way to think
+about this is really what I'm doing when
+
+ align:start position:0%
+about this is really what I'm doing when
+ 
+
+ align:start position:0%
+about this is really what I'm doing when
+I write something like this is writing a
+
+ align:start position:0%
+I write something like this is writing a
+ 
+
+ align:start position:0%
+I write something like this is writing a
+tree so this combination is a tree that
+
+ align:start position:0%
+tree so this combination is a tree that
+ 
+
+ align:start position:0%
+tree so this combination is a tree that
+has a plus and then a 3 and then there's
+
+ align:start position:0%
+has a plus and then a 3 and then there's
+ 
+
+ align:start position:0%
+has a plus and then a 3 and then there's
+something else and an 8 and a 2 and then
+
+ align:start position:0%
+something else and an 8 and a 2 and then
+ 
+
+ align:start position:0%
+something else and an 8 and a 2 and then
+there's something else here is itself
+
+ align:start position:0%
+there's something else here is itself
+ 
+
+ align:start position:0%
+there's something else here is itself
+little subtree that has a star and a
+
+ align:start position:0%
+little subtree that has a star and a
+ 
+
+ align:start position:0%
+little subtree that has a star and a
+five and a six and the way to think of
+
+ align:start position:0%
+five and a six and the way to think of
+ 
+
+ align:start position:0%
+five and a six and the way to think of
+that is really what's going on or we're
+
+ align:start position:0%
+that is really what's going on or we're
+ 
+
+ align:start position:0%
+that is really what's going on or we're
+writing these trees and parentheses are
+
+ align:start position:0%
+writing these trees and parentheses are
+ 
+
+ align:start position:0%
+writing these trees and parentheses are
+just a way to write this two-dimensional
+
+ align:start position:0%
+just a way to write this two-dimensional
+ 
+
+ align:start position:0%
+just a way to write this two-dimensional
+structure as a linear character string
+
+ align:start position:0%
+structure as a linear character string
+ 
+
+ align:start position:0%
+structure as a linear character string
+because at least one whisper started and
+
+ align:start position:0%
+because at least one whisper started and
+ 
+
+ align:start position:0%
+because at least one whisper started and
+people had teletypes or punch cards or
+
+ align:start position:0%
+people had teletypes or punch cards or
+ 
+
+ align:start position:0%
+people had teletypes or punch cards or
+whatever this was more convenient they
+
+ align:start position:0%
+whatever this was more convenient they
+ 
+
+ align:start position:0%
+whatever this was more convenient they
+couldn't maybe if lists started today we
+
+ align:start position:0%
+couldn't maybe if lists started today we
+ 
+
+ align:start position:0%
+couldn't maybe if lists started today we
+would the syntax of Lisp would look like
+
+ align:start position:0%
+would the syntax of Lisp would look like
+ 
+
+ align:start position:0%
+would the syntax of Lisp would look like
+that well let's let's look at what that
+
+ align:start position:0%
+that well let's let's look at what that
+ 
+
+ align:start position:0%
+that well let's let's look at what that
+actually looks like on the computer
+
+ align:start position:0%
+actually looks like on the computer
+ 
+
+ align:start position:0%
+actually looks like on the computer
+right here I have a lisp interaction
+
+ align:start position:0%
+right here I have a lisp interaction
+ 
+
+ align:start position:0%
+right here I have a lisp interaction
+setup there's an editor and on the top
+
+ align:start position:0%
+setup there's an editor and on the top
+ 
+
+ align:start position:0%
+setup there's an editor and on the top
+I'm going to type some values and ask
+
+ align:start position:0%
+I'm going to type some values and ask
+ 
+
+ align:start position:0%
+I'm going to type some values and ask
+Lisp what they are so for instance I can
+
+ align:start position:0%
+Lisp what they are so for instance I can
+ 
+
+ align:start position:0%
+Lisp what they are so for instance I can
+say to Lisp what's the value of that
+
+ align:start position:0%
+say to Lisp what's the value of that
+ 
+
+ align:start position:0%
+say to Lisp what's the value of that
+symbol that's 3 and I asked to evaluate
+
+ align:start position:0%
+symbol that's 3 and I asked to evaluate
+ 
+
+ align:start position:0%
+symbol that's 3 and I asked to evaluate
+it and there you see list is returned on
+
+ align:start position:0%
+it and there you see list is returned on
+ 
+
+ align:start position:0%
+it and there you see list is returned on
+the bottom and said oh yeah that's 3 or
+
+ align:start position:0%
+the bottom and said oh yeah that's 3 or
+ 
+
+ align:start position:0%
+the bottom and said oh yeah that's 3 or
+I can say what's the sum of 3 & 4 & 8
+
+ align:start position:0%
+I can say what's the sum of 3 & 4 & 8
+ 
+
+ align:start position:0%
+I can say what's the sum of 3 & 4 & 8
+what's that combination and ask list to
+
+ align:start position:0%
+what's that combination and ask list to
+ 
+
+ align:start position:0%
+what's that combination and ask list to
+evaluate it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's 15 well I can type in
+
+ align:start position:0%
+and that's 15 well I can type in
+ 
+
+ align:start position:0%
+and that's 15 well I can type in
+something more complicated I can say
+
+ align:start position:0%
+something more complicated I can say
+ 
+
+ align:start position:0%
+something more complicated I can say
+what's the sum of the product of three
+
+ align:start position:0%
+what's the sum of the product of three
+ 
+
+ align:start position:0%
+what's the sum of the product of three
+and the sum of seven and nineteen and a
+
+ align:start position:0%
+and the sum of seven and nineteen and a
+ 
+
+ align:start position:0%
+and the sum of seven and nineteen and a
+half and you'll notice here that list
+
+ align:start position:0%
+half and you'll notice here that list
+ 
+
+ align:start position:0%
+half and you'll notice here that list
+has something built in that helped me
+
+ align:start position:0%
+has something built in that helped me
+ 
+
+ align:start position:0%
+has something built in that helped me
+keep track of all these parentheses
+
+ align:start position:0%
+keep track of all these parentheses
+ 
+
+ align:start position:0%
+keep track of all these parentheses
+watch as I type the next closed
+
+ align:start position:0%
+watch as I type the next closed
+ 
+
+ align:start position:0%
+watch as I type the next closed
+parenthesis which is going to close the
+
+ align:start position:0%
+parenthesis which is going to close the
+ 
+
+ align:start position:0%
+parenthesis which is going to close the
+combination starting with the star the
+
+ align:start position:0%
+combination starting with the star the
+ 
+
+ align:start position:0%
+combination starting with the star the
+opening one will flash there I'll rub
+
+ align:start position:0%
+opening one will flash there I'll rub
+ 
+
+ align:start position:0%
+opening one will flash there I'll rub
+this out and do it again type closed and
+
+ align:start position:0%
+this out and do it again type closed and
+ 
+
+ align:start position:0%
+this out and do it again type closed and
+you see that closed as the plus closed
+
+ align:start position:0%
+you see that closed as the plus closed
+ 
+
+ align:start position:0%
+you see that closed as the plus closed
+again that quizzes the star right now
+
+ align:start position:0%
+again that quizzes the star right now
+ 
+
+ align:start position:0%
+again that quizzes the star right now
+I'm back to the sum and maybe I'm going
+
+ align:start position:0%
+I'm back to the sum and maybe I'm going
+ 
+
+ align:start position:0%
+I'm back to the sum and maybe I'm going
+to add that all to for that closes the
+
+ align:start position:0%
+to add that all to for that closes the
+ 
+
+ align:start position:0%
+to add that all to for that closes the
+plus now I have a complete combination
+
+ align:start position:0%
+plus now I have a complete combination
+ 
+
+ align:start position:0%
+plus now I have a complete combination
+and I can ask this for the value of that
+
+ align:start position:0%
+and I can ask this for the value of that
+ 
+
+ align:start position:0%
+and I can ask this for the value of that
+that kind of paren balancing is
+
+ align:start position:0%
+that kind of paren balancing is
+ 
+
+ align:start position:0%
+that kind of paren balancing is
+something that's that's built into a lot
+
+ align:start position:0%
+something that's that's built into a lot
+ 
+
+ align:start position:0%
+something that's that's built into a lot
+of Lisp systems to help you keep track
+
+ align:start position:0%
+of Lisp systems to help you keep track
+ 
+
+ align:start position:0%
+of Lisp systems to help you keep track
+because it is kind of hard just by hand
+
+ align:start position:0%
+because it is kind of hard just by hand
+ 
+
+ align:start position:0%
+because it is kind of hard just by hand
+doing all these parentheses there's
+
+ align:start position:0%
+doing all these parentheses there's
+ 
+
+ align:start position:0%
+doing all these parentheses there's
+another there's another kind of
+
+ align:start position:0%
+another there's another kind of
+ 
+
+ align:start position:0%
+another there's another kind of
+convention for keeping track of
+
+ align:start position:0%
+convention for keeping track of
+ 
+
+ align:start position:0%
+convention for keeping track of
+parentheses let me write another
+
+ align:start position:0%
+parentheses let me write another
+ 
+
+ align:start position:0%
+parentheses let me write another
+complicated combination let's take the
+
+ align:start position:0%
+complicated combination let's take the
+ 
+
+ align:start position:0%
+complicated combination let's take the
+sum of the product of 3 & 5 and add that
+
+ align:start position:0%
+sum of the product of 3 & 5 and add that
+ 
+
+ align:start position:0%
+sum of the product of 3 & 5 and add that
+to something and now what I'm going to
+
+ align:start position:0%
+to something and now what I'm going to
+ 
+
+ align:start position:0%
+to something and now what I'm going to
+do is I'm going to indent so that the
+
+ align:start position:0%
+do is I'm going to indent so that the
+ 
+
+ align:start position:0%
+do is I'm going to indent so that the
+operands are written vertically what's
+
+ align:start position:0%
+operands are written vertically what's
+ 
+
+ align:start position:0%
+operands are written vertically what's
+the sum of that and the product of 47
+
+ align:start position:0%
+the sum of that and the product of 47
+ 
+
+ align:start position:0%
+the sum of that and the product of 47
+and let's say the product of 47 with the
+
+ align:start position:0%
+and let's say the product of 47 with the
+ 
+
+ align:start position:0%
+and let's say the product of 47 with the
+difference of 20 and 6.8 that means
+
+ align:start position:0%
+difference of 20 and 6.8 that means
+ 
+
+ align:start position:0%
+difference of 20 and 6.8 that means
+subtract 6.8 from 20 you see the
+
+ align:start position:0%
+subtract 6.8 from 20 you see the
+ 
+
+ align:start position:0%
+subtract 6.8 from 20 you see the
+parentheses close close the - close the
+
+ align:start position:0%
+parentheses close close the - close the
+ 
+
+ align:start position:0%
+parentheses close close the - close the
+store and now let's get another operator
+
+ align:start position:0%
+store and now let's get another operator
+ 
+
+ align:start position:0%
+store and now let's get another operator
+you see the list editor here it's
+
+ align:start position:0%
+you see the list editor here it's
+ 
+
+ align:start position:0%
+you see the list editor here it's
+indenting to the right position
+
+ align:start position:0%
+indenting to the right position
+ 
+
+ align:start position:0%
+indenting to the right position
+automatically help me keep track hey do
+
+ align:start position:0%
+automatically help me keep track hey do
+ 
+
+ align:start position:0%
+automatically help me keep track hey do
+that again I'll close that last
+
+ align:start position:0%
+that again I'll close that last
+ 
+
+ align:start position:0%
+that again I'll close that last
+parenthesis again is he it balances the
+
+ align:start position:0%
+parenthesis again is he it balances the
+ 
+
+ align:start position:0%
+parenthesis again is he it balances the
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now I can say what's the value of
+
+ align:start position:0%
+right now I can say what's the value of
+ 
+
+ align:start position:0%
+right now I can say what's the value of
+that all right so uh those two things
+
+ align:start position:0%
+that all right so uh those two things
+ 
+
+ align:start position:0%
+that all right so uh those two things
+indenting to the right level which is
+
+ align:start position:0%
+indenting to the right level which is
+ 
+
+ align:start position:0%
+indenting to the right level which is
+called pretty printing and flashing
+
+ align:start position:0%
+called pretty printing and flashing
+ 
+
+ align:start position:0%
+called pretty printing and flashing
+parentheses are two things that a lot of
+
+ align:start position:0%
+parentheses are two things that a lot of
+ 
+
+ align:start position:0%
+parentheses are two things that a lot of
+systems have have built in to help you
+
+ align:start position:0%
+systems have have built in to help you
+ 
+
+ align:start position:0%
+systems have have built in to help you
+keep track and you should learn how to
+
+ align:start position:0%
+keep track and you should learn how to
+ 
+
+ align:start position:0%
+keep track and you should learn how to
+use them okay well those are the
+
+ align:start position:0%
+use them okay well those are the
+ 
+
+ align:start position:0%
+use them okay well those are the
+primitives there's a means of
+
+ align:start position:0%
+primitives there's a means of
+ 
+
+ align:start position:0%
+primitives there's a means of
+combination now let's go up to the means
+
+ align:start position:0%
+combination now let's go up to the means
+ 
+
+ align:start position:0%
+combination now let's go up to the means
+of abstraction right I'd like to be able
+
+ align:start position:0%
+of abstraction right I'd like to be able
+ 
+
+ align:start position:0%
+of abstraction right I'd like to be able
+to take the idea that I do some
+
+ align:start position:0%
+to take the idea that I do some
+ 
+
+ align:start position:0%
+to take the idea that I do some
+combination like this and abstract it
+
+ align:start position:0%
+combination like this and abstract it
+ 
+
+ align:start position:0%
+combination like this and abstract it
+and give it a simple name so I can use
+
+ align:start position:0%
+and give it a simple name so I can use
+ 
+
+ align:start position:0%
+and give it a simple name so I can use
+that as an element and I do that in Lisp
+
+ align:start position:0%
+that as an element and I do that in Lisp
+ 
+
+ align:start position:0%
+that as an element and I do that in Lisp
+with define so I could say for example
+
+ align:start position:0%
+with define so I could say for example
+ 
+
+ align:start position:0%
+with define so I could say for example
+define a to be the product of five and
+
+ align:start position:0%
+define a to be the product of five and
+ 
+
+ align:start position:0%
+define a to be the product of five and
+five and now I could say so say for
+
+ align:start position:0%
+five and now I could say so say for
+ 
+
+ align:start position:0%
+five and now I could say so say for
+example two lists what is the product of
+
+ align:start position:0%
+example two lists what is the product of
+ 
+
+ align:start position:0%
+example two lists what is the product of
+a and a this should be 25 and there
+
+ align:start position:0%
+a and a this should be 25 and there
+ 
+
+ align:start position:0%
+a and a this should be 25 and there
+should be six twenty five and then
+
+ align:start position:0%
+should be six twenty five and then
+ 
+
+ align:start position:0%
+should be six twenty five and then
+crucial thing I can now use a here I've
+
+ align:start position:0%
+crucial thing I can now use a here I've
+ 
+
+ align:start position:0%
+crucial thing I can now use a here I've
+used it in the combination but I could
+
+ align:start position:0%
+used it in the combination but I could
+ 
+
+ align:start position:0%
+used it in the combination but I could
+use that in other more complicated
+
+ align:start position:0%
+use that in other more complicated
+ 
+
+ align:start position:0%
+use that in other more complicated
+things that I need in turn so I could
+
+ align:start position:0%
+things that I need in turn so I could
+ 
+
+ align:start position:0%
+things that I need in turn so I could
+say define B to be the sum of will say a
+
+ align:start position:0%
+say define B to be the sum of will say a
+ 
+
+ align:start position:0%
+say define B to be the sum of will say a
+and the product of five and a you close
+
+ align:start position:0%
+and the product of five and a you close
+ 
+
+ align:start position:0%
+and the product of five and a you close
+the plus let's take a look at that on
+
+ align:start position:0%
+the plus let's take a look at that on
+ 
+
+ align:start position:0%
+the plus let's take a look at that on
+the computer see how that looks
+
+ align:start position:0%
+the computer see how that looks
+ 
+
+ align:start position:0%
+the computer see how that looks
+it's all I'll just type what I wrote on
+
+ align:start position:0%
+it's all I'll just type what I wrote on
+ 
+
+ align:start position:0%
+it's all I'll just type what I wrote on
+the board I can say define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a to be the product of five and five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll tell that to lift and notice what
+
+ align:start position:0%
+I'll tell that to lift and notice what
+ 
+
+ align:start position:0%
+I'll tell that to lift and notice what
+Lisp responded there with with an A in
+
+ align:start position:0%
+Lisp responded there with with an A in
+ 
+
+ align:start position:0%
+Lisp responded there with with an A in
+the bottom in general when you type in a
+
+ align:start position:0%
+the bottom in general when you type in a
+ 
+
+ align:start position:0%
+the bottom in general when you type in a
+definition that lifts it responds with
+
+ align:start position:0%
+definition that lifts it responds with
+ 
+
+ align:start position:0%
+definition that lifts it responds with
+the knee the symbol being defined and I
+
+ align:start position:0%
+the knee the symbol being defined and I
+ 
+
+ align:start position:0%
+the knee the symbol being defined and I
+could say the list what is the product
+
+ align:start position:0%
+could say the list what is the product
+ 
+
+ align:start position:0%
+could say the list what is the product
+of a and a it says that's 625 I can
+
+ align:start position:0%
+of a and a it says that's 625 I can
+ 
+
+ align:start position:0%
+of a and a it says that's 625 I can
+define B to be the sum of a and the
+
+ align:start position:0%
+define B to be the sum of a and the
+ 
+
+ align:start position:0%
+define B to be the sum of a and the
+product of five and a close a friend
+
+ align:start position:0%
+product of five and a close a friend
+ 
+
+ align:start position:0%
+product of five and a close a friend
+closes the store close the press close
+
+ align:start position:0%
+closes the store close the press close
+ 
+
+ align:start position:0%
+closes the store close the press close
+the define this says okay be there on
+
+ align:start position:0%
+the define this says okay be there on
+ 
+
+ align:start position:0%
+the define this says okay be there on
+the bottom and now I can tell you list
+
+ align:start position:0%
+the bottom and now I can tell you list
+ 
+
+ align:start position:0%
+the bottom and now I can tell you list
+what's the value of B and I can say
+
+ align:start position:0%
+what's the value of B and I can say
+ 
+
+ align:start position:0%
+what's the value of B and I can say
+something more complicated like what's
+
+ align:start position:0%
+something more complicated like what's
+ 
+
+ align:start position:0%
+something more complicated like what's
+the sum of a and the quotient of B and
+
+ align:start position:0%
+the sum of a and the quotient of B and
+ 
+
+ align:start position:0%
+the sum of a and the quotient of B and
+five that slash is divided another
+
+ align:start position:0%
+five that slash is divided another
+ 
+
+ align:start position:0%
+five that slash is divided another
+primitive operator I've divided you by
+
+ align:start position:0%
+primitive operator I've divided you by
+ 
+
+ align:start position:0%
+primitive operator I've divided you by
+far the entity to a this is okay that's
+
+ align:start position:0%
+far the entity to a this is okay that's
+ 
+
+ align:start position:0%
+far the entity to a this is okay that's
+55 all right so there's what it looks
+
+ align:start position:0%
+55 all right so there's what it looks
+ 
+
+ align:start position:0%
+55 all right so there's what it looks
+like there's the basic means of defining
+
+ align:start position:0%
+like there's the basic means of defining
+ 
+
+ align:start position:0%
+like there's the basic means of defining
+some something it's the simplest kind of
+
+ align:start position:0%
+some something it's the simplest kind of
+ 
+
+ align:start position:0%
+some something it's the simplest kind of
+naming but it's not really very powerful
+
+ align:start position:0%
+naming but it's not really very powerful
+ 
+
+ align:start position:0%
+naming but it's not really very powerful
+see what I'd really like to name we're
+
+ align:start position:0%
+see what I'd really like to name we're
+ 
+
+ align:start position:0%
+see what I'd really like to name we're
+talking about general methods I'd like
+
+ align:start position:0%
+talking about general methods I'd like
+ 
+
+ align:start position:0%
+talking about general methods I'd like
+to name or the general idea that for
+
+ align:start position:0%
+to name or the general idea that for
+ 
+
+ align:start position:0%
+to name or the general idea that for
+example I could multiply five by five or
+
+ align:start position:0%
+example I could multiply five by five or
+ 
+
+ align:start position:0%
+example I could multiply five by five or
+six by six Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thousand and one by a thousand and one a
+
+ align:start position:0%
+thousand and one by a thousand and one a
+ 
+
+ align:start position:0%
+thousand and one by a thousand and one a
+thousand 1.7 by a thousand and 1.7 right
+
+ align:start position:0%
+thousand 1.7 by a thousand and 1.7 right
+ 
+
+ align:start position:0%
+thousand 1.7 by a thousand and 1.7 right
+I'd like to be able to name the general
+
+ align:start position:0%
+I'd like to be able to name the general
+ 
+
+ align:start position:0%
+I'd like to be able to name the general
+idea of multiplying something by itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know what that is that's called
+
+ align:start position:0%
+we know what that is that's called
+ 
+
+ align:start position:0%
+we know what that is that's called
+squaring the way I can do that and Lisp
+
+ align:start position:0%
+squaring the way I can do that and Lisp
+ 
+
+ align:start position:0%
+squaring the way I can do that and Lisp
+is I can say you're fine just square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something X multiply X by itself and
+
+ align:start position:0%
+something X multiply X by itself and
+ 
+
+ align:start position:0%
+something X multiply X by itself and
+then having having done that I could say
+
+ align:start position:0%
+then having having done that I could say
+ 
+
+ align:start position:0%
+then having having done that I could say
+so list for example what's the square of
+
+ align:start position:0%
+so list for example what's the square of
+ 
+
+ align:start position:0%
+so list for example what's the square of
+10 and this will say a hundred yeah
+
+ align:start position:0%
+10 and this will say a hundred yeah
+ 
+
+ align:start position:0%
+10 and this will say a hundred yeah
+let's actually look at that a little
+
+ align:start position:0%
+let's actually look at that a little
+ 
+
+ align:start position:0%
+let's actually look at that a little
+more closely Yeah right there's the
+
+ align:start position:0%
+more closely Yeah right there's the
+ 
+
+ align:start position:0%
+more closely Yeah right there's the
+definition of square to square something
+
+ align:start position:0%
+definition of square to square something
+ 
+
+ align:start position:0%
+definition of square to square something
+right multiply it by itself all right
+
+ align:start position:0%
+right multiply it by itself all right
+ 
+
+ align:start position:0%
+right multiply it by itself all right
+you see this X here right that X is kind
+
+ align:start position:0%
+you see this X here right that X is kind
+ 
+
+ align:start position:0%
+you see this X here right that X is kind
+of a pronoun which is the something that
+
+ align:start position:0%
+of a pronoun which is the something that
+ 
+
+ align:start position:0%
+of a pronoun which is the something that
+I'm going to square and then what I do
+
+ align:start position:0%
+I'm going to square and then what I do
+ 
+
+ align:start position:0%
+I'm going to square and then what I do
+with it is I multiply X by multiply it
+
+ align:start position:0%
+with it is I multiply X by multiply it
+ 
+
+ align:start position:0%
+with it is I multiply X by multiply it
+by itself okay right so there's a
+
+ align:start position:0%
+by itself okay right so there's a
+ 
+
+ align:start position:0%
+by itself okay right so there's a
+notation for a for defining a procedure
+
+ align:start position:0%
+notation for a for defining a procedure
+ 
+
+ align:start position:0%
+notation for a for defining a procedure
+actually this is a little bit confusing
+
+ align:start position:0%
+actually this is a little bit confusing
+ 
+
+ align:start position:0%
+actually this is a little bit confusing
+because sort of how I might use square
+
+ align:start position:0%
+because sort of how I might use square
+ 
+
+ align:start position:0%
+because sort of how I might use square
+and I say square of X or square of 10
+
+ align:start position:0%
+and I say square of X or square of 10
+ 
+
+ align:start position:0%
+and I say square of X or square of 10
+but it's not making it very clear that
+
+ align:start position:0%
+but it's not making it very clear that
+ 
+
+ align:start position:0%
+but it's not making it very clear that
+I'm actually naming something so let me
+
+ align:start position:0%
+I'm actually naming something so let me
+ 
+
+ align:start position:0%
+I'm actually naming something so let me
+write this definition in another way
+
+ align:start position:0%
+write this definition in another way
+ 
+
+ align:start position:0%
+write this definition in another way
+that makes a little bit more clear that
+
+ align:start position:0%
+that makes a little bit more clear that
+ 
+
+ align:start position:0%
+that makes a little bit more clear that
+I'm naming something I'll say define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square to be lambda of X times X X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I'm meaning something square but
+
+ align:start position:0%
+here I'm meaning something square but
+ 
+
+ align:start position:0%
+here I'm meaning something square but
+just like over here I'm naming something
+
+ align:start position:0%
+just like over here I'm naming something
+ 
+
+ align:start position:0%
+just like over here I'm naming something
+a the thing that I'm naming square here
+
+ align:start position:0%
+a the thing that I'm naming square here
+ 
+
+ align:start position:0%
+a the thing that I'm naming square here
+I named the thing I named a was the
+
+ align:start position:0%
+I named the thing I named a was the
+ 
+
+ align:start position:0%
+I named the thing I named a was the
+value of this combination here the thing
+
+ align:start position:0%
+value of this combination here the thing
+ 
+
+ align:start position:0%
+value of this combination here the thing
+that I'm naming square is this thing
+
+ align:start position:0%
+that I'm naming square is this thing
+ 
+
+ align:start position:0%
+that I'm naming square is this thing
+that begins with lambda and lambda is
+
+ align:start position:0%
+that begins with lambda and lambda is
+ 
+
+ align:start position:0%
+that begins with lambda and lambda is
+lisps way of saying make up procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look at that more closely on the
+
+ align:start position:0%
+let's look at that more closely on the
+ 
+
+ align:start position:0%
+let's look at that more closely on the
+slide the way I read that definition is
+
+ align:start position:0%
+slide the way I read that definition is
+ 
+
+ align:start position:0%
+slide the way I read that definition is
+to say I define Square to be make a
+
+ align:start position:0%
+to say I define Square to be make a
+ 
+
+ align:start position:0%
+to say I define Square to be make a
+procedure that's what the lambda is make
+
+ align:start position:0%
+procedure that's what the lambda is make
+ 
+
+ align:start position:0%
+procedure that's what the lambda is make
+a procedure with an argument named X and
+
+ align:start position:0%
+a procedure with an argument named X and
+ 
+
+ align:start position:0%
+a procedure with an argument named X and
+what it does is return the result of
+
+ align:start position:0%
+what it does is return the result of
+ 
+
+ align:start position:0%
+what it does is return the result of
+multiplying X by itself now in general
+
+ align:start position:0%
+multiplying X by itself now in general
+ 
+
+ align:start position:0%
+multiplying X by itself now in general
+we're going to be using we're going to
+
+ align:start position:0%
+we're going to be using we're going to
+ 
+
+ align:start position:0%
+we're going to be using we're going to
+be using this top form of defining this
+
+ align:start position:0%
+be using this top form of defining this
+ 
+
+ align:start position:0%
+be using this top form of defining this
+because it's a little bit more
+
+ align:start position:0%
+because it's a little bit more
+ 
+
+ align:start position:0%
+because it's a little bit more
+convenient but don't lose sight of the
+
+ align:start position:0%
+convenient but don't lose sight of the
+ 
+
+ align:start position:0%
+convenient but don't lose sight of the
+fact that it's really this in fact as
+
+ align:start position:0%
+fact that it's really this in fact as
+ 
+
+ align:start position:0%
+fact that it's really this in fact as
+far as the Lisp interpreter is concerned
+
+ align:start position:0%
+far as the Lisp interpreter is concerned
+ 
+
+ align:start position:0%
+far as the Lisp interpreter is concerned
+there's no difference between typing
+
+ align:start position:0%
+there's no difference between typing
+ 
+
+ align:start position:0%
+there's no difference between typing
+this to it and typing this to it and
+
+ align:start position:0%
+this to it and typing this to it and
+ 
+
+ align:start position:0%
+this to it and typing this to it and
+there's a word for that we're sort of
+
+ align:start position:0%
+there's a word for that we're sort of
+ 
+
+ align:start position:0%
+there's a word for that we're sort of
+syntactic sugar
+
+ align:start position:0%
+syntactic sugar
+ 
+
+ align:start position:0%
+syntactic sugar
+what syntactic sugar means it's having
+
+ align:start position:0%
+what syntactic sugar means it's having
+ 
+
+ align:start position:0%
+what syntactic sugar means it's having
+somewhat more convenient surface forms
+
+ align:start position:0%
+somewhat more convenient surface forms
+ 
+
+ align:start position:0%
+somewhat more convenient surface forms
+for typing something so this is just
+
+ align:start position:0%
+for typing something so this is just
+ 
+
+ align:start position:0%
+for typing something so this is just
+really syntactic sugar for this
+
+ align:start position:0%
+really syntactic sugar for this
+ 
+
+ align:start position:0%
+really syntactic sugar for this
+underlying weak thing with the lambda
+
+ align:start position:0%
+underlying weak thing with the lambda
+ 
+
+ align:start position:0%
+underlying weak thing with the lambda
+and the reason you should remember that
+
+ align:start position:0%
+and the reason you should remember that
+ 
+
+ align:start position:0%
+and the reason you should remember that
+is don't forget that when I write
+
+ align:start position:0%
+is don't forget that when I write
+ 
+
+ align:start position:0%
+is don't forget that when I write
+something like this I'm really naming
+
+ align:start position:0%
+something like this I'm really naming
+ 
+
+ align:start position:0%
+something like this I'm really naming
+something I'm naming something square
+
+ align:start position:0%
+something I'm naming something square
+ 
+
+ align:start position:0%
+something I'm naming something square
+and the something that I'm naming square
+
+ align:start position:0%
+and the something that I'm naming square
+ 
+
+ align:start position:0%
+and the something that I'm naming square
+is a procedure that's getting
+
+ align:start position:0%
+is a procedure that's getting
+ 
+
+ align:start position:0%
+is a procedure that's getting
+constructed ok well let's let's look at
+
+ align:start position:0%
+constructed ok well let's let's look at
+ 
+
+ align:start position:0%
+constructed ok well let's let's look at
+that on the computer too so I'll come in
+
+ align:start position:0%
+that on the computer too so I'll come in
+ 
+
+ align:start position:0%
+that on the computer too so I'll come in
+I'll say define square of X give you
+
+ align:start position:0%
+I'll say define square of X give you
+ 
+
+ align:start position:0%
+I'll say define square of X give you
+times X X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know I'll tell this fat to square
+
+ align:start position:0%
+you know I'll tell this fat to square
+ 
+
+ align:start position:0%
+you know I'll tell this fat to square
+you have named something square and now
+
+ align:start position:0%
+you have named something square and now
+ 
+
+ align:start position:0%
+you have named something square and now
+having done that I can ask list for
+
+ align:start position:0%
+having done that I can ask list for
+ 
+
+ align:start position:0%
+having done that I can ask list for
+what's the square of a thousand and one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or in general I could say what's the
+
+ align:start position:0%
+or in general I could say what's the
+ 
+
+ align:start position:0%
+or in general I could say what's the
+square of the sum of five and seven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right square twelves 144 or I can
+
+ align:start position:0%
+all right square twelves 144 or I can
+ 
+
+ align:start position:0%
+all right square twelves 144 or I can
+use square itself as an element in some
+
+ align:start position:0%
+use square itself as an element in some
+ 
+
+ align:start position:0%
+use square itself as an element in some
+combination I can say what's the sum of
+
+ align:start position:0%
+combination I can say what's the sum of
+ 
+
+ align:start position:0%
+combination I can say what's the sum of
+the square of 3 and the square of 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hey 1916 is 25 or I can use square as an
+
+ align:start position:0%
+hey 1916 is 25 or I can use square as an
+ 
+
+ align:start position:0%
+hey 1916 is 25 or I can use square as an
+element in some much more complicated
+
+ align:start position:0%
+element in some much more complicated
+ 
+
+ align:start position:0%
+element in some much more complicated
+thing I can say what's the what's the
+
+ align:start position:0%
+thing I can say what's the what's the
+ 
+
+ align:start position:0%
+thing I can say what's the what's the
+square of the square of the square of
+
+ align:start position:0%
+square of the square of the square of
+ 
+
+ align:start position:0%
+square of the square of the square of
+1,001
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's the square of the square of the
+
+ align:start position:0%
+there's the square of the square of the
+ 
+
+ align:start position:0%
+there's the square of the square of the
+square of 1,001 or I can say the list
+
+ align:start position:0%
+square of 1,001 or I can say the list
+ 
+
+ align:start position:0%
+square of 1,001 or I can say the list
+what is square itself what's the value
+
+ align:start position:0%
+what is square itself what's the value
+ 
+
+ align:start position:0%
+what is square itself what's the value
+of that and Lisp returns some
+
+ align:start position:0%
+of that and Lisp returns some
+ 
+
+ align:start position:0%
+of that and Lisp returns some
+conventional way of telling me that
+
+ align:start position:0%
+conventional way of telling me that
+ 
+
+ align:start position:0%
+conventional way of telling me that
+that's a procedure does compound
+
+ align:start position:0%
+that's a procedure does compound
+ 
+
+ align:start position:0%
+that's a procedure does compound
+procedure Square and what the value of
+
+ align:start position:0%
+procedure Square and what the value of
+ 
+
+ align:start position:0%
+procedure Square and what the value of
+square is this procedure and the thing
+
+ align:start position:0%
+square is this procedure and the thing
+ 
+
+ align:start position:0%
+square is this procedure and the thing
+with the Stars and the brackets are just
+
+ align:start position:0%
+with the Stars and the brackets are just
+ 
+
+ align:start position:0%
+with the Stars and the brackets are just
+lisps conventional way of describing
+
+ align:start position:0%
+lisps conventional way of describing
+ 
+
+ align:start position:0%
+lisps conventional way of describing
+that let's look at two more examples of
+
+ align:start position:0%
+that let's look at two more examples of
+ 
+
+ align:start position:0%
+that let's look at two more examples of
+defining this right here there are two
+
+ align:start position:0%
+defining this right here there are two
+ 
+
+ align:start position:0%
+defining this right here there are two
+more procedures I can define the average
+
+ align:start position:0%
+more procedures I can define the average
+ 
+
+ align:start position:0%
+more procedures I can define the average
+of x and y to be the sum of x and y / -
+
+ align:start position:0%
+of x and y to be the sum of x and y / -
+ 
+
+ align:start position:0%
+of x and y to be the sum of x and y / -
+we're having had average and mean square
+
+ align:start position:0%
+we're having had average and mean square
+ 
+
+ align:start position:0%
+we're having had average and mean square
+having had average in square I can use
+
+ align:start position:0%
+having had average in square I can use
+ 
+
+ align:start position:0%
+having had average in square I can use
+that to talk about the mean square of
+
+ align:start position:0%
+that to talk about the mean square of
+ 
+
+ align:start position:0%
+that to talk about the mean square of
+something which is the average of the
+
+ align:start position:0%
+something which is the average of the
+ 
+
+ align:start position:0%
+something which is the average of the
+square of X and the square of Y so for
+
+ align:start position:0%
+square of X and the square of Y so for
+ 
+
+ align:start position:0%
+square of X and the square of Y so for
+example having done that I could say
+
+ align:start position:0%
+example having done that I could say
+ 
+
+ align:start position:0%
+example having done that I could say
+what's the mean square of 2 + 3 and I
+
+ align:start position:0%
+what's the mean square of 2 + 3 and I
+ 
+
+ align:start position:0%
+what's the mean square of 2 + 3 and I
+should get the average of 4 + 9 which is
+
+ align:start position:0%
+should get the average of 4 + 9 which is
+ 
+
+ align:start position:0%
+should get the average of 4 + 9 which is
+6 and 1/2 the key thing here is that
+
+ align:start position:0%
+6 and 1/2 the key thing here is that
+ 
+
+ align:start position:0%
+6 and 1/2 the key thing here is that
+having defined square I can use it as if
+
+ align:start position:0%
+having defined square I can use it as if
+ 
+
+ align:start position:0%
+having defined square I can use it as if
+it were primitive right so if we look
+
+ align:start position:0%
+it were primitive right so if we look
+ 
+
+ align:start position:0%
+it were primitive right so if we look
+here on the slide I look at mean square
+
+ align:start position:0%
+here on the slide I look at mean square
+ 
+
+ align:start position:0%
+here on the slide I look at mean square
+write the person defining mean square
+
+ align:start position:0%
+write the person defining mean square
+ 
+
+ align:start position:0%
+write the person defining mean square
+doesn't have to know at this point
+
+ align:start position:0%
+doesn't have to know at this point
+ 
+
+ align:start position:0%
+doesn't have to know at this point
+whether Square was something built into
+
+ align:start position:0%
+whether Square was something built into
+ 
+
+ align:start position:0%
+whether Square was something built into
+the language or whether it was a
+
+ align:start position:0%
+the language or whether it was a
+ 
+
+ align:start position:0%
+the language or whether it was a
+procedure that was defined and that's
+
+ align:start position:0%
+procedure that was defined and that's
+ 
+
+ align:start position:0%
+procedure that was defined and that's
+key thing in Lisp that you not make
+
+ align:start position:0%
+key thing in Lisp that you not make
+ 
+
+ align:start position:0%
+key thing in Lisp that you not make
+arbitrary distinctions between things
+
+ align:start position:0%
+arbitrary distinctions between things
+ 
+
+ align:start position:0%
+arbitrary distinctions between things
+that happen to be primitive in the
+
+ align:start position:0%
+that happen to be primitive in the
+ 
+
+ align:start position:0%
+that happen to be primitive in the
+language and things that happen to be
+
+ align:start position:0%
+language and things that happen to be
+ 
+
+ align:start position:0%
+language and things that happen to be
+built in person you think that shouldn't
+
+ align:start position:0%
+built in person you think that shouldn't
+ 
+
+ align:start position:0%
+built in person you think that shouldn't
+even have to know so the things you
+
+ align:start position:0%
+even have to know so the things you
+ 
+
+ align:start position:0%
+even have to know so the things you
+construct get used with all the power
+
+ align:start position:0%
+construct get used with all the power
+ 
+
+ align:start position:0%
+construct get used with all the power
+and flexibility as if they were
+
+ align:start position:0%
+and flexibility as if they were
+ 
+
+ align:start position:0%
+and flexibility as if they were
+primitives in fact can drive that home
+
+ align:start position:0%
+primitives in fact can drive that home
+ 
+
+ align:start position:0%
+primitives in fact can drive that home
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+looking on the computer one more time we
+
+ align:start position:0%
+looking on the computer one more time we
+ 
+
+ align:start position:0%
+looking on the computer one more time we
+talked about plus and in fact if I come
+
+ align:start position:0%
+talked about plus and in fact if I come
+ 
+
+ align:start position:0%
+talked about plus and in fact if I come
+here on the computer screen and say what
+
+ align:start position:0%
+here on the computer screen and say what
+ 
+
+ align:start position:0%
+here on the computer screen and say what
+is the value of plus notice what Lisp
+
+ align:start position:0%
+is the value of plus notice what Lisp
+ 
+
+ align:start position:0%
+is the value of plus notice what Lisp
+types out on the bottom there typed that
+
+ align:start position:0%
+types out on the bottom there typed that
+ 
+
+ align:start position:0%
+types out on the bottom there typed that
+compound procedure plus because in this
+
+ align:start position:0%
+compound procedure plus because in this
+ 
+
+ align:start position:0%
+compound procedure plus because in this
+system it turns out that the addition
+
+ align:start position:0%
+system it turns out that the addition
+ 
+
+ align:start position:0%
+system it turns out that the addition
+operator is itself a compound procedure
+
+ align:start position:0%
+operator is itself a compound procedure
+ 
+
+ align:start position:0%
+operator is itself a compound procedure
+and if I didn't just type that in you'd
+
+ align:start position:0%
+and if I didn't just type that in you'd
+ 
+
+ align:start position:0%
+and if I didn't just type that in you'd
+never know that and it wouldn't make any
+
+ align:start position:0%
+never know that and it wouldn't make any
+ 
+
+ align:start position:0%
+never know that and it wouldn't make any
+difference anyway we don't care it's
+
+ align:start position:0%
+difference anyway we don't care it's
+ 
+
+ align:start position:0%
+difference anyway we don't care it's
+below the level of the abstraction that
+
+ align:start position:0%
+below the level of the abstraction that
+ 
+
+ align:start position:0%
+below the level of the abstraction that
+we're dealing with so the key thing is
+
+ align:start position:0%
+we're dealing with so the key thing is
+ 
+
+ align:start position:0%
+we're dealing with so the key thing is
+you cannot tell should not be able to
+
+ align:start position:0%
+you cannot tell should not be able to
+ 
+
+ align:start position:0%
+you cannot tell should not be able to
+tell in general the difference between
+
+ align:start position:0%
+tell in general the difference between
+ 
+
+ align:start position:0%
+tell in general the difference between
+things that are built-in and things that
+
+ align:start position:0%
+things that are built-in and things that
+ 
+
+ align:start position:0%
+things that are built-in and things that
+are compound why is that because the
+
+ align:start position:0%
+are compound why is that because the
+ 
+
+ align:start position:0%
+are compound why is that because the
+things that are compound have an
+
+ align:start position:0%
+things that are compound have an
+ 
+
+ align:start position:0%
+things that are compound have an
+abstraction wrapper wrapped around them
+
+ align:start position:0%
+abstraction wrapper wrapped around them
+ 
+
+ align:start position:0%
+abstraction wrapper wrapped around them
+okay we've seen almost all the elements
+
+ align:start position:0%
+okay we've seen almost all the elements
+ 
+
+ align:start position:0%
+okay we've seen almost all the elements
+of Lisp now there's only one more we
+
+ align:start position:0%
+of Lisp now there's only one more we
+ 
+
+ align:start position:0%
+of Lisp now there's only one more we
+have to look at and that is how to make
+
+ align:start position:0%
+have to look at and that is how to make
+ 
+
+ align:start position:0%
+have to look at and that is how to make
+a case analysis let me show you what I
+
+ align:start position:0%
+a case analysis let me show you what I
+ 
+
+ align:start position:0%
+a case analysis let me show you what I
+mean we might want to think about the
+
+ align:start position:0%
+mean we might want to think about the
+ 
+
+ align:start position:0%
+mean we might want to think about the
+the mathematical definition of the
+
+ align:start position:0%
+the mathematical definition of the
+ 
+
+ align:start position:0%
+the mathematical definition of the
+absolute value functions I might say the
+
+ align:start position:0%
+absolute value functions I might say the
+ 
+
+ align:start position:0%
+absolute value functions I might say the
+absolute value of X is the function
+
+ align:start position:0%
+absolute value of X is the function
+ 
+
+ align:start position:0%
+absolute value of X is the function
+which has the property that it's
+
+ align:start position:0%
+which has the property that it's
+ 
+
+ align:start position:0%
+which has the property that it's
+negative of the X for X less than 0 it's
+
+ align:start position:0%
+negative of the X for X less than 0 it's
+ 
+
+ align:start position:0%
+negative of the X for X less than 0 it's
+0 for X equal to 0 and it's X for X
+
+ align:start position:0%
+0 for X equal to 0 and it's X for X
+ 
+
+ align:start position:0%
+0 for X equal to 0 and it's X for X
+greater than 0 and let's pass a way of
+
+ align:start position:0%
+greater than 0 and let's pass a way of
+ 
+
+ align:start position:0%
+greater than 0 and let's pass a way of
+making case analyses let me define for
+
+ align:start position:0%
+making case analyses let me define for
+ 
+
+ align:start position:0%
+making case analyses let me define for
+you absolute value they define the
+
+ align:start position:0%
+you absolute value they define the
+ 
+
+ align:start position:0%
+you absolute value they define the
+absolute value of X is conditional right
+
+ align:start position:0%
+absolute value of X is conditional right
+ 
+
+ align:start position:0%
+absolute value of X is conditional right
+this means case analysis cond okay if X
+
+ align:start position:0%
+this means case analysis cond okay if X
+ 
+
+ align:start position:0%
+this means case analysis cond okay if X
+is less than 0 the answer is negate X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what I've written here is a clause
+
+ align:start position:0%
+right what I've written here is a clause
+ 
+
+ align:start position:0%
+right what I've written here is a clause
+this is a this whole thing is a
+
+ align:start position:0%
+this is a this whole thing is a
+ 
+
+ align:start position:0%
+this is a this whole thing is a
+conditional clause and it has two parts
+
+ align:start position:0%
+conditional clause and it has two parts
+ 
+
+ align:start position:0%
+conditional clause and it has two parts
+this part here is a is a predicate or a
+
+ align:start position:0%
+this part here is a is a predicate or a
+ 
+
+ align:start position:0%
+this part here is a is a predicate or a
+condition that's a condition and the
+
+ align:start position:0%
+condition that's a condition and the
+ 
+
+ align:start position:0%
+condition that's a condition and the
+condition is expressed by something
+
+ align:start position:0%
+condition is expressed by something
+ 
+
+ align:start position:0%
+condition is expressed by something
+called a predicate and a predicate and
+
+ align:start position:0%
+called a predicate and a predicate and
+ 
+
+ align:start position:0%
+called a predicate and a predicate and
+Lisp is some sort of thing that returns
+
+ align:start position:0%
+Lisp is some sort of thing that returns
+ 
+
+ align:start position:0%
+Lisp is some sort of thing that returns
+either true or false and you see Lisp
+
+ align:start position:0%
+either true or false and you see Lisp
+ 
+
+ align:start position:0%
+either true or false and you see Lisp
+has a primitive procedure less then that
+
+ align:start position:0%
+has a primitive procedure less then that
+ 
+
+ align:start position:0%
+has a primitive procedure less then that
+tests whether something is true or false
+
+ align:start position:0%
+tests whether something is true or false
+ 
+
+ align:start position:0%
+tests whether something is true or false
+and the other part of a clause is an
+
+ align:start position:0%
+and the other part of a clause is an
+ 
+
+ align:start position:0%
+and the other part of a clause is an
+action or a thing to do in the case
+
+ align:start position:0%
+action or a thing to do in the case
+ 
+
+ align:start position:0%
+action or a thing to do in the case
+where that's true and here what I'm
+
+ align:start position:0%
+where that's true and here what I'm
+ 
+
+ align:start position:0%
+where that's true and here what I'm
+doing is negating X the negation
+
+ align:start position:0%
+doing is negating X the negation
+ 
+
+ align:start position:0%
+doing is negating X the negation
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+well the minus sign and Lisp is a little
+
+ align:start position:0%
+well the minus sign and Lisp is a little
+ 
+
+ align:start position:0%
+well the minus sign and Lisp is a little
+bit funny if there are more than if
+
+ align:start position:0%
+bit funny if there are more than if
+ 
+
+ align:start position:0%
+bit funny if there are more than if
+there are two or more arguments if
+
+ align:start position:0%
+there are two or more arguments if
+ 
+
+ align:start position:0%
+there are two or more arguments if
+there's two arguments and subtract the
+
+ align:start position:0%
+there's two arguments and subtract the
+ 
+
+ align:start position:0%
+there's two arguments and subtract the
+second one from the first we saw that if
+
+ align:start position:0%
+second one from the first we saw that if
+ 
+
+ align:start position:0%
+second one from the first we saw that if
+there's one argument it negates it all
+
+ align:start position:0%
+there's one argument it negates it all
+ 
+
+ align:start position:0%
+there's one argument it negates it all
+right so this corresponds to that and
+
+ align:start position:0%
+right so this corresponds to that and
+ 
+
+ align:start position:0%
+right so this corresponds to that and
+then there's another Cronk laws it says
+
+ align:start position:0%
+then there's another Cronk laws it says
+ 
+
+ align:start position:0%
+then there's another Cronk laws it says
+in the case where X is equal to 0 the
+
+ align:start position:0%
+in the case where X is equal to 0 the
+ 
+
+ align:start position:0%
+in the case where X is equal to 0 the
+answer is 0 and the case where X is
+
+ align:start position:0%
+answer is 0 and the case where X is
+ 
+
+ align:start position:0%
+answer is 0 and the case where X is
+greater than 0 the answer is X close
+
+ align:start position:0%
+greater than 0 the answer is X close
+ 
+
+ align:start position:0%
+greater than 0 the answer is X close
+that Clause close the cond
+
+ align:start position:0%
+that Clause close the cond
+ 
+
+ align:start position:0%
+that Clause close the cond
+close the definition there's a
+
+ align:start position:0%
+close the definition there's a
+ 
+
+ align:start position:0%
+close the definition there's a
+definition of absolute value and you see
+
+ align:start position:0%
+definition of absolute value and you see
+ 
+
+ align:start position:0%
+definition of absolute value and you see
+it's a case analysis that looks very
+
+ align:start position:0%
+it's a case analysis that looks very
+ 
+
+ align:start position:0%
+it's a case analysis that looks very
+much like the case analysis you use in
+
+ align:start position:0%
+much like the case analysis you use in
+ 
+
+ align:start position:0%
+much like the case analysis you use in
+mathematics ok there's a somewhat
+
+ align:start position:0%
+mathematics ok there's a somewhat
+ 
+
+ align:start position:0%
+mathematics ok there's a somewhat
+different way of writing a restricted
+
+ align:start position:0%
+different way of writing a restricted
+ 
+
+ align:start position:0%
+different way of writing a restricted
+case analysis often you have a case
+
+ align:start position:0%
+case analysis often you have a case
+ 
+
+ align:start position:0%
+case analysis often you have a case
+analysis where you only have one case
+
+ align:start position:0%
+analysis where you only have one case
+ 
+
+ align:start position:0%
+analysis where you only have one case
+where you test something and then
+
+ align:start position:0%
+where you test something and then
+ 
+
+ align:start position:0%
+where you test something and then
+depending on whether it's true or false
+
+ align:start position:0%
+depending on whether it's true or false
+ 
+
+ align:start position:0%
+depending on whether it's true or false
+you do something and here's another
+
+ align:start position:0%
+you do something and here's another
+ 
+
+ align:start position:0%
+you do something and here's another
+definition of the absolute value which
+
+ align:start position:0%
+definition of the absolute value which
+ 
+
+ align:start position:0%
+definition of the absolute value which
+looks almost the same which says if X is
+
+ align:start position:0%
+looks almost the same which says if X is
+ 
+
+ align:start position:0%
+looks almost the same which says if X is
+less than 0 the result is negate X
+
+ align:start position:0%
+less than 0 the result is negate X
+ 
+
+ align:start position:0%
+less than 0 the result is negate X
+otherwise the answer is X and we'll be
+
+ align:start position:0%
+otherwise the answer is X and we'll be
+ 
+
+ align:start position:0%
+otherwise the answer is X and we'll be
+using if a lot but again the thing to
+
+ align:start position:0%
+using if a lot but again the thing to
+ 
+
+ align:start position:0%
+using if a lot but again the thing to
+remember is that this form of absolute
+
+ align:start position:0%
+remember is that this form of absolute
+ 
+
+ align:start position:0%
+remember is that this form of absolute
+value that you're looking at here
+
+ align:start position:0%
+value that you're looking at here
+ 
+
+ align:start position:0%
+value that you're looking at here
+and then this one over here that I wrote
+
+ align:start position:0%
+and then this one over here that I wrote
+ 
+
+ align:start position:0%
+and then this one over here that I wrote
+on the board are essentially the same
+
+ align:start position:0%
+on the board are essentially the same
+ 
+
+ align:start position:0%
+on the board are essentially the same
+and if and Condor or whichever way you
+
+ align:start position:0%
+and if and Condor or whichever way you
+ 
+
+ align:start position:0%
+and if and Condor or whichever way you
+like it you can think of con distinct
+
+ align:start position:0%
+like it you can think of con distinct
+ 
+
+ align:start position:0%
+like it you can think of con distinct
+tactic sugar for if or you can think of
+
+ align:start position:0%
+tactic sugar for if or you can think of
+ 
+
+ align:start position:0%
+tactic sugar for if or you can think of
+if as syntactic sugar for con and it
+
+ align:start position:0%
+if as syntactic sugar for con and it
+ 
+
+ align:start position:0%
+if as syntactic sugar for con and it
+doesn't make any difference person
+
+ align:start position:0%
+doesn't make any difference person
+ 
+
+ align:start position:0%
+doesn't make any difference person
+implementing a list system will pick one
+
+ align:start position:0%
+implementing a list system will pick one
+ 
+
+ align:start position:0%
+implementing a list system will pick one
+and implement the other in terms of that
+
+ align:start position:0%
+and implement the other in terms of that
+ 
+
+ align:start position:0%
+and implement the other in terms of that
+and it doesn't matter which one you pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay why don't we break now and then
+
+ align:start position:0%
+okay why don't we break now and then
+ 
+
+ align:start position:0%
+okay why don't we break now and then
+take some questions how come sometimes
+
+ align:start position:0%
+take some questions how come sometimes
+ 
+
+ align:start position:0%
+take some questions how come sometimes
+when I write to fine
+
+ align:start position:0%
+when I write to fine
+ 
+
+ align:start position:0%
+when I write to fine
+I put an open paren here and say define
+
+ align:start position:0%
+I put an open paren here and say define
+ 
+
+ align:start position:0%
+I put an open paren here and say define
+open paren something or other and
+
+ align:start position:0%
+open paren something or other and
+ 
+
+ align:start position:0%
+open paren something or other and
+sometimes when I write this I don't put
+
+ align:start position:0%
+sometimes when I write this I don't put
+ 
+
+ align:start position:0%
+sometimes when I write this I don't put
+an open paren okay the answer is this
+
+ align:start position:0%
+an open paren okay the answer is this
+ 
+
+ align:start position:0%
+an open paren okay the answer is this
+particular form of define where you say
+
+ align:start position:0%
+particular form of define where you say
+ 
+
+ align:start position:0%
+particular form of define where you say
+define some expression is this very
+
+ align:start position:0%
+define some expression is this very
+ 
+
+ align:start position:0%
+define some expression is this very
+special thing for defining procedures
+
+ align:start position:0%
+special thing for defining procedures
+ 
+
+ align:start position:0%
+special thing for defining procedures
+but again what it really means is I'm
+
+ align:start position:0%
+but again what it really means is I'm
+ 
+
+ align:start position:0%
+but again what it really means is I'm
+defining the symbol square to be there
+
+ align:start position:0%
+defining the symbol square to be there
+ 
+
+ align:start position:0%
+defining the symbol square to be there
+so way you should think about it is what
+
+ align:start position:0%
+so way you should think about it is what
+ 
+
+ align:start position:0%
+so way you should think about it is what
+to find us is you right to find and the
+
+ align:start position:0%
+to find us is you right to find and the
+ 
+
+ align:start position:0%
+to find us is you right to find and the
+second thing you write is the symbol
+
+ align:start position:0%
+second thing you write is the symbol
+ 
+
+ align:start position:0%
+second thing you write is the symbol
+here no open paren the symbol you're
+
+ align:start position:0%
+here no open paren the symbol you're
+ 
+
+ align:start position:0%
+here no open paren the symbol you're
+defining and what you're defining it to
+
+ align:start position:0%
+defining and what you're defining it to
+ 
+
+ align:start position:0%
+defining and what you're defining it to
+be that's like here and like here that's
+
+ align:start position:0%
+be that's like here and like here that's
+ 
+
+ align:start position:0%
+be that's like here and like here that's
+the sort of the basic way you use define
+
+ align:start position:0%
+the sort of the basic way you use define
+ 
+
+ align:start position:0%
+the sort of the basic way you use define
+and then there's this special syntactic
+
+ align:start position:0%
+and then there's this special syntactic
+ 
+
+ align:start position:0%
+and then there's this special syntactic
+trick which allows you to define
+
+ align:start position:0%
+trick which allows you to define
+ 
+
+ align:start position:0%
+trick which allows you to define
+procedures that look like this so the
+
+ align:start position:0%
+procedures that look like this so the
+ 
+
+ align:start position:0%
+procedures that look like this so the
+difference is it's whether or not you're
+
+ align:start position:0%
+difference is it's whether or not you're
+ 
+
+ align:start position:0%
+difference is it's whether or not you're
+defining a procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right well believe it or not you
+
+ align:start position:0%
+all right well believe it or not you
+ 
+
+ align:start position:0%
+all right well believe it or not you
+actually now know enough Lisp to write
+
+ align:start position:0%
+actually now know enough Lisp to write
+ 
+
+ align:start position:0%
+actually now know enough Lisp to write
+essentially any numerical procedure that
+
+ align:start position:0%
+essentially any numerical procedure that
+ 
+
+ align:start position:0%
+essentially any numerical procedure that
+you'd write in a language like Fortran
+
+ align:start position:0%
+you'd write in a language like Fortran
+ 
+
+ align:start position:0%
+you'd write in a language like Fortran
+or basic or whatever essentially any
+
+ align:start position:0%
+or basic or whatever essentially any
+ 
+
+ align:start position:0%
+or basic or whatever essentially any
+other language you probably think that's
+
+ align:start position:0%
+other language you probably think that's
+ 
+
+ align:start position:0%
+other language you probably think that's
+a that's not believable right because
+
+ align:start position:0%
+a that's not believable right because
+ 
+
+ align:start position:0%
+a that's not believable right because
+you know that these languages have
+
+ align:start position:0%
+you know that these languages have
+ 
+
+ align:start position:0%
+you know that these languages have
+things like four statements and and do
+
+ align:start position:0%
+things like four statements and and do
+ 
+
+ align:start position:0%
+things like four statements and and do
+until a while or something but uh we
+
+ align:start position:0%
+until a while or something but uh we
+ 
+
+ align:start position:0%
+until a while or something but uh we
+don't really need any of that fact we're
+
+ align:start position:0%
+don't really need any of that fact we're
+ 
+
+ align:start position:0%
+don't really need any of that fact we're
+not gonna use any of that in this course
+
+ align:start position:0%
+not gonna use any of that in this course
+ 
+
+ align:start position:0%
+not gonna use any of that in this course
+let me let me show you why again looking
+
+ align:start position:0%
+let me let me show you why again looking
+ 
+
+ align:start position:0%
+let me let me show you why again looking
+back at that square root let's go back
+
+ align:start position:0%
+back at that square root let's go back
+ 
+
+ align:start position:0%
+back at that square root let's go back
+to this square root algorithm of Heron
+
+ align:start position:0%
+to this square root algorithm of Heron
+ 
+
+ align:start position:0%
+to this square root algorithm of Heron
+of Alexandria remember what that said it
+
+ align:start position:0%
+of Alexandria remember what that said it
+ 
+
+ align:start position:0%
+of Alexandria remember what that said it
+said to find an approximation to the
+
+ align:start position:0%
+said to find an approximation to the
+ 
+
+ align:start position:0%
+said to find an approximation to the
+square root of x you make a guess you
+
+ align:start position:0%
+square root of x you make a guess you
+ 
+
+ align:start position:0%
+square root of x you make a guess you
+improve that guess by averaging the
+
+ align:start position:0%
+improve that guess by averaging the
+ 
+
+ align:start position:0%
+improve that guess by averaging the
+guess and x over the guess you keep
+
+ align:start position:0%
+guess and x over the guess you keep
+ 
+
+ align:start position:0%
+guess and x over the guess you keep
+improving that until the guess is good
+
+ align:start position:0%
+improving that until the guess is good
+ 
+
+ align:start position:0%
+improving that until the guess is good
+enough and already alluded to the idea
+
+ align:start position:0%
+enough and already alluded to the idea
+ 
+
+ align:start position:0%
+enough and already alluded to the idea
+the idea is that if the initial guess
+
+ align:start position:0%
+the idea is that if the initial guess
+ 
+
+ align:start position:0%
+the idea is that if the initial guess
+that she took if that initial guess was
+
+ align:start position:0%
+that she took if that initial guess was
+ 
+
+ align:start position:0%
+that she took if that initial guess was
+actually equal to the square root of x
+
+ align:start position:0%
+actually equal to the square root of x
+ 
+
+ align:start position:0%
+actually equal to the square root of x
+then G here would be equal to x over G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you hit the square root averaging
+
+ align:start position:0%
+so if you hit the square root averaging
+ 
+
+ align:start position:0%
+so if you hit the square root averaging
+them wouldn't change it if the G that
+
+ align:start position:0%
+them wouldn't change it if the G that
+ 
+
+ align:start position:0%
+them wouldn't change it if the G that
+you picked was larger than the square
+
+ align:start position:0%
+you picked was larger than the square
+ 
+
+ align:start position:0%
+you picked was larger than the square
+root of x then x over G will be smaller
+
+ align:start position:0%
+root of x then x over G will be smaller
+ 
+
+ align:start position:0%
+root of x then x over G will be smaller
+than the square root of x so that when
+
+ align:start position:0%
+than the square root of x so that when
+ 
+
+ align:start position:0%
+than the square root of x so that when
+you average G and x over G you get
+
+ align:start position:0%
+you average G and x over G you get
+ 
+
+ align:start position:0%
+you average G and x over G you get
+something in between all right so if you
+
+ align:start position:0%
+something in between all right so if you
+ 
+
+ align:start position:0%
+something in between all right so if you
+pick a G that's that's too small your
+
+ align:start position:0%
+pick a G that's that's too small your
+ 
+
+ align:start position:0%
+pick a G that's that's too small your
+answer will be too large if you pick a G
+
+ align:start position:0%
+answer will be too large if you pick a G
+ 
+
+ align:start position:0%
+answer will be too large if you pick a G
+that's too large if your G is larger
+
+ align:start position:0%
+that's too large if your G is larger
+ 
+
+ align:start position:0%
+that's too large if your G is larger
+than the square root of x and x over G
+
+ align:start position:0%
+than the square root of x and x over G
+ 
+
+ align:start position:0%
+than the square root of x and x over G
+will be smaller than the square root of
+
+ align:start position:0%
+will be smaller than the square root of
+ 
+
+ align:start position:0%
+will be smaller than the square root of
+x so averaging always gives you
+
+ align:start position:0%
+x so averaging always gives you
+ 
+
+ align:start position:0%
+x so averaging always gives you
+something in between and then it's not
+
+ align:start position:0%
+something in between and then it's not
+ 
+
+ align:start position:0%
+something in between and then it's not
+quite trivial but it's it's possible to
+
+ align:start position:0%
+quite trivial but it's it's possible to
+ 
+
+ align:start position:0%
+quite trivial but it's it's possible to
+show that in fact if G misses the square
+
+ align:start position:0%
+show that in fact if G misses the square
+ 
+
+ align:start position:0%
+show that in fact if G misses the square
+root of x by a little bit the average of
+
+ align:start position:0%
+root of x by a little bit the average of
+ 
+
+ align:start position:0%
+root of x by a little bit the average of
+G and x over G will actually keep
+
+ align:start position:0%
+G and x over G will actually keep
+ 
+
+ align:start position:0%
+G and x over G will actually keep
+getting closer to the square root of x
+
+ align:start position:0%
+getting closer to the square root of x
+ 
+
+ align:start position:0%
+getting closer to the square root of x
+so if you keep doing this enough you'll
+
+ align:start position:0%
+so if you keep doing this enough you'll
+ 
+
+ align:start position:0%
+so if you keep doing this enough you'll
+eventually get as close as you want and
+
+ align:start position:0%
+eventually get as close as you want and
+ 
+
+ align:start position:0%
+eventually get as close as you want and
+then there's another fact that you can
+
+ align:start position:0%
+then there's another fact that you can
+ 
+
+ align:start position:0%
+then there's another fact that you can
+always start out this process by using 1
+
+ align:start position:0%
+always start out this process by using 1
+ 
+
+ align:start position:0%
+always start out this process by using 1
+as an initial guess
+
+ align:start position:0%
+as an initial guess
+ 
+
+ align:start position:0%
+as an initial guess
+and always converge to the square root
+
+ align:start position:0%
+and always converge to the square root
+ 
+
+ align:start position:0%
+and always converge to the square root
+of the axe and so that's this method of
+
+ align:start position:0%
+of the axe and so that's this method of
+ 
+
+ align:start position:0%
+of the axe and so that's this method of
+success of the averaging due to Heron of
+
+ align:start position:0%
+success of the averaging due to Heron of
+ 
+
+ align:start position:0%
+success of the averaging due to Heron of
+Alexandria let's uh let's write it and
+
+ align:start position:0%
+Alexandria let's uh let's write it and
+ 
+
+ align:start position:0%
+Alexandria let's uh let's write it and
+Lisp well the central idea is what does
+
+ align:start position:0%
+Lisp well the central idea is what does
+ 
+
+ align:start position:0%
+Lisp well the central idea is what does
+it mean to try a guess for the square
+
+ align:start position:0%
+it mean to try a guess for the square
+ 
+
+ align:start position:0%
+it mean to try a guess for the square
+root of x let's write that
+
+ align:start position:0%
+root of x let's write that
+ 
+
+ align:start position:0%
+root of x let's write that
+so we'll say fine to try a guess for the
+
+ align:start position:0%
+so we'll say fine to try a guess for the
+ 
+
+ align:start position:0%
+so we'll say fine to try a guess for the
+square root of x what do we do we'll say
+
+ align:start position:0%
+square root of x what do we do we'll say
+ 
+
+ align:start position:0%
+square root of x what do we do we'll say
+if the guess is good enough the guess is
+
+ align:start position:0%
+if the guess is good enough the guess is
+ 
+
+ align:start position:0%
+if the guess is good enough the guess is
+good enough to be a guess for the square
+
+ align:start position:0%
+good enough to be a guess for the square
+ 
+
+ align:start position:0%
+good enough to be a guess for the square
+root of x then as an answer we'll take
+
+ align:start position:0%
+root of x then as an answer we'll take
+ 
+
+ align:start position:0%
+root of x then as an answer we'll take
+the guess otherwise we will try the
+
+ align:start position:0%
+the guess otherwise we will try the
+ 
+
+ align:start position:0%
+the guess otherwise we will try the
+improved guess we'll improve that guess
+
+ align:start position:0%
+improved guess we'll improve that guess
+ 
+
+ align:start position:0%
+improved guess we'll improve that guess
+for the square root of x and we'll try
+
+ align:start position:0%
+for the square root of x and we'll try
+ 
+
+ align:start position:0%
+for the square root of x and we'll try
+that as a guess for the square root of x
+
+ align:start position:0%
+that as a guess for the square root of x
+ 
+
+ align:start position:0%
+that as a guess for the square root of x
+close the try close the if close the
+
+ align:start position:0%
+close the try close the if close the
+ 
+
+ align:start position:0%
+close the try close the if close the
+define so that's how we try a guess and
+
+ align:start position:0%
+define so that's how we try a guess and
+ 
+
+ align:start position:0%
+define so that's how we try a guess and
+then the next part of the process said
+
+ align:start position:0%
+then the next part of the process said
+ 
+
+ align:start position:0%
+then the next part of the process said
+in order to compute square roots
+
+ align:start position:0%
+in order to compute square roots
+ 
+
+ align:start position:0%
+in order to compute square roots
+we'll say define to compute the square
+
+ align:start position:0%
+we'll say define to compute the square
+ 
+
+ align:start position:0%
+we'll say define to compute the square
+root of the X we will try one as a guess
+
+ align:start position:0%
+root of the X we will try one as a guess
+ 
+
+ align:start position:0%
+root of the X we will try one as a guess
+for the square root of x well we have to
+
+ align:start position:0%
+for the square root of x well we have to
+ 
+
+ align:start position:0%
+for the square root of x well we have to
+define a couple more things we have to
+
+ align:start position:0%
+define a couple more things we have to
+ 
+
+ align:start position:0%
+define a couple more things we have to
+say how is it guess good enough and how
+
+ align:start position:0%
+say how is it guess good enough and how
+ 
+
+ align:start position:0%
+say how is it guess good enough and how
+do we improve a guess so let's look at
+
+ align:start position:0%
+do we improve a guess so let's look at
+ 
+
+ align:start position:0%
+do we improve a guess so let's look at
+that the algorithm to improve the guess
+
+ align:start position:0%
+that the algorithm to improve the guess
+ 
+
+ align:start position:0%
+that the algorithm to improve the guess
+right to improve a guess for the square
+
+ align:start position:0%
+right to improve a guess for the square
+ 
+
+ align:start position:0%
+right to improve a guess for the square
+root of x we average that was the
+
+ align:start position:0%
+root of x we average that was the
+ 
+
+ align:start position:0%
+root of x we average that was the
+algorithm we average to guess with the
+
+ align:start position:0%
+algorithm we average to guess with the
+ 
+
+ align:start position:0%
+algorithm we average to guess with the
+quotient of dividing X by the guess
+
+ align:start position:0%
+quotient of dividing X by the guess
+ 
+
+ align:start position:0%
+quotient of dividing X by the guess
+all right that's how we improve a guess
+
+ align:start position:0%
+all right that's how we improve a guess
+ 
+
+ align:start position:0%
+all right that's how we improve a guess
+and to tell whether he guess is good
+
+ align:start position:0%
+and to tell whether he guess is good
+ 
+
+ align:start position:0%
+and to tell whether he guess is good
+enough well we have to decide something
+
+ align:start position:0%
+enough well we have to decide something
+ 
+
+ align:start position:0%
+enough well we have to decide something
+let's this is supposed to be a guess for
+
+ align:start position:0%
+let's this is supposed to be a guess for
+ 
+
+ align:start position:0%
+let's this is supposed to be a guess for
+the square root of x so one possible
+
+ align:start position:0%
+the square root of x so one possible
+ 
+
+ align:start position:0%
+the square root of x so one possible
+thing you can do is say when you take
+
+ align:start position:0%
+thing you can do is say when you take
+ 
+
+ align:start position:0%
+thing you can do is say when you take
+that guess and square it do you get
+
+ align:start position:0%
+that guess and square it do you get
+ 
+
+ align:start position:0%
+that guess and square it do you get
+something very close to X for example so
+
+ align:start position:0%
+something very close to X for example so
+ 
+
+ align:start position:0%
+something very close to X for example so
+what that one way to say that is to say
+
+ align:start position:0%
+what that one way to say that is to say
+ 
+
+ align:start position:0%
+what that one way to say that is to say
+I square the guess subtract X from that
+
+ align:start position:0%
+I square the guess subtract X from that
+ 
+
+ align:start position:0%
+I square the guess subtract X from that
+and see if the absolute value of that
+
+ align:start position:0%
+and see if the absolute value of that
+ 
+
+ align:start position:0%
+and see if the absolute value of that
+whole thing is less than some small
+
+ align:start position:0%
+whole thing is less than some small
+ 
+
+ align:start position:0%
+whole thing is less than some small
+number which depends on my purposes
+
+ align:start position:0%
+number which depends on my purposes
+ 
+
+ align:start position:0%
+number which depends on my purposes
+right okay so there's a there's a
+
+ align:start position:0%
+right okay so there's a there's a
+ 
+
+ align:start position:0%
+right okay so there's a there's a
+complete procedure for how to compute
+
+ align:start position:0%
+complete procedure for how to compute
+ 
+
+ align:start position:0%
+complete procedure for how to compute
+the square root of x let's look at the
+
+ align:start position:0%
+the square root of x let's look at the
+ 
+
+ align:start position:0%
+the square root of x let's look at the
+structure of that a little bit all right
+
+ align:start position:0%
+structure of that a little bit all right
+ 
+
+ align:start position:0%
+structure of that a little bit all right
+have the whole thing I have the notion
+
+ align:start position:0%
+have the whole thing I have the notion
+ 
+
+ align:start position:0%
+have the whole thing I have the notion
+of how to how to compute a square root
+
+ align:start position:0%
+of how to how to compute a square root
+ 
+
+ align:start position:0%
+of how to how to compute a square root
+that's some kind of module right that's
+
+ align:start position:0%
+that's some kind of module right that's
+ 
+
+ align:start position:0%
+that's some kind of module right that's
+some kind of black box it's defined in
+
+ align:start position:0%
+some kind of black box it's defined in
+ 
+
+ align:start position:0%
+some kind of black box it's defined in
+terms of right it's defined in terms of
+
+ align:start position:0%
+terms of right it's defined in terms of
+ 
+
+ align:start position:0%
+terms of right it's defined in terms of
+how to try a guess for the square root
+
+ align:start position:0%
+how to try a guess for the square root
+ 
+
+ align:start position:0%
+how to try a guess for the square root
+of x try is to find in terms of well
+
+ align:start position:0%
+of x try is to find in terms of well
+ 
+
+ align:start position:0%
+of x try is to find in terms of well
+telling whether something is good enough
+
+ align:start position:0%
+telling whether something is good enough
+ 
+
+ align:start position:0%
+telling whether something is good enough
+and telling how to improve something so
+
+ align:start position:0%
+and telling how to improve something so
+ 
+
+ align:start position:0%
+and telling how to improve something so
+good enough try us to find in terms of
+
+ align:start position:0%
+good enough try us to find in terms of
+ 
+
+ align:start position:0%
+good enough try us to find in terms of
+good enough and improve and let's see
+
+ align:start position:0%
+good enough and improve and let's see
+ 
+
+ align:start position:0%
+good enough and improve and let's see
+what else I still in Wolfe you'll go
+
+ align:start position:0%
+what else I still in Wolfe you'll go
+ 
+
+ align:start position:0%
+what else I still in Wolfe you'll go
+down this tree good enough was defined
+
+ align:start position:0%
+down this tree good enough was defined
+ 
+
+ align:start position:0%
+down this tree good enough was defined
+in terms of absolute value and square
+
+ align:start position:0%
+in terms of absolute value and square
+ 
+
+ align:start position:0%
+in terms of absolute value and square
+and improve was defined in terms of
+
+ align:start position:0%
+and improve was defined in terms of
+ 
+
+ align:start position:0%
+and improve was defined in terms of
+something called averaging and then some
+
+ align:start position:0%
+something called averaging and then some
+ 
+
+ align:start position:0%
+something called averaging and then some
+other primitive operators so try square
+
+ align:start position:0%
+other primitive operators so try square
+ 
+
+ align:start position:0%
+other primitive operators so try square
+roots defined in terms of try tries to
+
+ align:start position:0%
+roots defined in terms of try tries to
+ 
+
+ align:start position:0%
+roots defined in terms of try tries to
+find in terms of good enough and improve
+
+ align:start position:0%
+find in terms of good enough and improve
+ 
+
+ align:start position:0%
+find in terms of good enough and improve
+but also try itself so try is also
+
+ align:start position:0%
+but also try itself so try is also
+ 
+
+ align:start position:0%
+but also try itself so try is also
+defined in terms of how to try itself
+
+ align:start position:0%
+defined in terms of how to try itself
+ 
+
+ align:start position:0%
+defined in terms of how to try itself
+well that may give you give you some
+
+ align:start position:0%
+well that may give you give you some
+ 
+
+ align:start position:0%
+well that may give you give you some
+problem right here your high school
+
+ align:start position:0%
+problem right here your high school
+ 
+
+ align:start position:0%
+problem right here your high school
+geometry teacher probably told you that
+
+ align:start position:0%
+geometry teacher probably told you that
+ 
+
+ align:start position:0%
+geometry teacher probably told you that
+it's it's naughty to try and define
+
+ align:start position:0%
+it's it's naughty to try and define
+ 
+
+ align:start position:0%
+it's it's naughty to try and define
+things in terms of themselves because it
+
+ align:start position:0%
+things in terms of themselves because it
+ 
+
+ align:start position:0%
+things in terms of themselves because it
+doesn't make sense but that's false
+
+ align:start position:0%
+doesn't make sense but that's false
+ 
+
+ align:start position:0%
+doesn't make sense but that's false
+all right sometimes it makes perfect
+
+ align:start position:0%
+all right sometimes it makes perfect
+ 
+
+ align:start position:0%
+all right sometimes it makes perfect
+sense to defy the things in terms of
+
+ align:start position:0%
+sense to defy the things in terms of
+ 
+
+ align:start position:0%
+sense to defy the things in terms of
+themselves and this is a case and we can
+
+ align:start position:0%
+themselves and this is a case and we can
+ 
+
+ align:start position:0%
+themselves and this is a case and we can
+look at that we can write down what this
+
+ align:start position:0%
+look at that we can write down what this
+ 
+
+ align:start position:0%
+look at that we can write down what this
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+you'd say suppose I ask Lisp what the
+
+ align:start position:0%
+you'd say suppose I ask Lisp what the
+ 
+
+ align:start position:0%
+you'd say suppose I ask Lisp what the
+square root of two is what's the square
+
+ align:start position:0%
+square root of two is what's the square
+ 
+
+ align:start position:0%
+square root of two is what's the square
+root of two mean well that means I try
+
+ align:start position:0%
+root of two mean well that means I try
+ 
+
+ align:start position:0%
+root of two mean well that means I try
+one as a guess for this square root of
+
+ align:start position:0%
+one as a guess for this square root of
+ 
+
+ align:start position:0%
+one as a guess for this square root of
+two right now I look I say gee is is one
+
+ align:start position:0%
+two right now I look I say gee is is one
+ 
+
+ align:start position:0%
+two right now I look I say gee is is one
+a good enough guess for the square root
+
+ align:start position:0%
+a good enough guess for the square root
+ 
+
+ align:start position:0%
+a good enough guess for the square root
+of two and that depends on the test that
+
+ align:start position:0%
+of two and that depends on the test that
+ 
+
+ align:start position:0%
+of two and that depends on the test that
+good enough does and in this case we'll
+
+ align:start position:0%
+good enough does and in this case we'll
+ 
+
+ align:start position:0%
+good enough does and in this case we'll
+do good enough we'll say no one is not a
+
+ align:start position:0%
+do good enough we'll say no one is not a
+ 
+
+ align:start position:0%
+do good enough we'll say no one is not a
+good enough guess for the square root of
+
+ align:start position:0%
+good enough guess for the square root of
+ 
+
+ align:start position:0%
+good enough guess for the square root of
+two so that will reduce to saying I have
+
+ align:start position:0%
+two so that will reduce to saying I have
+ 
+
+ align:start position:0%
+two so that will reduce to saying I have
+to try the improved and improved improve
+
+ align:start position:0%
+to try the improved and improved improve
+ 
+
+ align:start position:0%
+to try the improved and improved improve
+one as a guess for the square root of
+
+ align:start position:0%
+one as a guess for the square root of
+ 
+
+ align:start position:0%
+one as a guess for the square root of
+two and try that as a guess for the
+
+ align:start position:0%
+two and try that as a guess for the
+ 
+
+ align:start position:0%
+two and try that as a guess for the
+square root of two improving one for
+
+ align:start position:0%
+square root of two improving one for
+ 
+
+ align:start position:0%
+square root of two improving one for
+this as a guess for the square root of
+
+ align:start position:0%
+this as a guess for the square root of
+ 
+
+ align:start position:0%
+this as a guess for the square root of
+two means I averaged one and two divided
+
+ align:start position:0%
+two means I averaged one and two divided
+ 
+
+ align:start position:0%
+two means I averaged one and two divided
+by one all right so this is going to be
+
+ align:start position:0%
+by one all right so this is going to be
+ 
+
+ align:start position:0%
+by one all right so this is going to be
+the average this piece here will be the
+
+ align:start position:0%
+the average this piece here will be the
+ 
+
+ align:start position:0%
+the average this piece here will be the
+average of one and the quotient of two
+
+ align:start position:0%
+average of one and the quotient of two
+ 
+
+ align:start position:0%
+average of one and the quotient of two
+by one and so that's that's this piece
+
+ align:start position:0%
+by one and so that's that's this piece
+ 
+
+ align:start position:0%
+by one and so that's that's this piece
+here and I'm going to try right and this
+
+ align:start position:0%
+here and I'm going to try right and this
+ 
+
+ align:start position:0%
+here and I'm going to try right and this
+is 1.5 so this square root of two
+
+ align:start position:0%
+is 1.5 so this square root of two
+ 
+
+ align:start position:0%
+is 1.5 so this square root of two
+reduces to trying one for the square
+
+ align:start position:0%
+reduces to trying one for the square
+ 
+
+ align:start position:0%
+reduces to trying one for the square
+root of two which reduces to trying 1.5
+
+ align:start position:0%
+root of two which reduces to trying 1.5
+ 
+
+ align:start position:0%
+root of two which reduces to trying 1.5
+as a guess for the square root of two
+
+ align:start position:0%
+as a guess for the square root of two
+ 
+
+ align:start position:0%
+as a guess for the square root of two
+all right so that makes that makes sense
+
+ align:start position:0%
+all right so that makes that makes sense
+ 
+
+ align:start position:0%
+all right so that makes that makes sense
+let's look at the rest of the process
+
+ align:start position:0%
+let's look at the rest of the process
+ 
+
+ align:start position:0%
+let's look at the rest of the process
+here if I try 1.5 all right that reduces
+
+ align:start position:0%
+here if I try 1.5 all right that reduces
+ 
+
+ align:start position:0%
+here if I try 1.5 all right that reduces
+1.5 turns out to be not good enough as a
+
+ align:start position:0%
+1.5 turns out to be not good enough as a
+ 
+
+ align:start position:0%
+1.5 turns out to be not good enough as a
+guess for the square root of 2 so that
+
+ align:start position:0%
+guess for the square root of 2 so that
+ 
+
+ align:start position:0%
+guess for the square root of 2 so that
+reduces to trying the average of 1.5 and
+
+ align:start position:0%
+reduces to trying the average of 1.5 and
+ 
+
+ align:start position:0%
+reduces to trying the average of 1.5 and
+2 divided by 1.5 as a guess for the
+
+ align:start position:0%
+2 divided by 1.5 as a guess for the
+ 
+
+ align:start position:0%
+2 divided by 1.5 as a guess for the
+square root of 2
+
+ align:start position:0%
+square root of 2
+ 
+
+ align:start position:0%
+square root of 2
+that average turns out to be one point
+
+ align:start position:0%
+that average turns out to be one point
+ 
+
+ align:start position:0%
+that average turns out to be one point
+three three three so this whole thing
+
+ align:start position:0%
+three three three so this whole thing
+ 
+
+ align:start position:0%
+three three three so this whole thing
+reduces to trying one point three three
+
+ align:start position:0%
+reduces to trying one point three three
+ 
+
+ align:start position:0%
+reduces to trying one point three three
+three is a guess for the square root of
+
+ align:start position:0%
+three is a guess for the square root of
+ 
+
+ align:start position:0%
+three is a guess for the square root of
+two and then so on right that reduces to
+
+ align:start position:0%
+two and then so on right that reduces to
+ 
+
+ align:start position:0%
+two and then so on right that reduces to
+another called a good enough one point
+
+ align:start position:0%
+another called a good enough one point
+ 
+
+ align:start position:0%
+another called a good enough one point
+for something or other and then it keeps
+
+ align:start position:0%
+for something or other and then it keeps
+ 
+
+ align:start position:0%
+for something or other and then it keeps
+going until the process finally stops
+
+ align:start position:0%
+going until the process finally stops
+ 
+
+ align:start position:0%
+going until the process finally stops
+with something that that good enough
+
+ align:start position:0%
+with something that that good enough
+ 
+
+ align:start position:0%
+with something that that good enough
+thinks is good enough which in this case
+
+ align:start position:0%
+thinks is good enough which in this case
+ 
+
+ align:start position:0%
+thinks is good enough which in this case
+is is 1.4142 something or other all
+
+ align:start position:0%
+is is 1.4142 something or other all
+ 
+
+ align:start position:0%
+is is 1.4142 something or other all
+right so the process makes makes perfect
+
+ align:start position:0%
+right so the process makes makes perfect
+ 
+
+ align:start position:0%
+right so the process makes makes perfect
+sense by the way is called a recursive
+
+ align:start position:0%
+sense by the way is called a recursive
+ 
+
+ align:start position:0%
+sense by the way is called a recursive
+definition and the ability to make
+
+ align:start position:0%
+definition and the ability to make
+ 
+
+ align:start position:0%
+definition and the ability to make
+recursive definitions is a source of
+
+ align:start position:0%
+recursive definitions is a source of
+ 
+
+ align:start position:0%
+recursive definitions is a source of
+incredible power and is can already see
+
+ align:start position:0%
+incredible power and is can already see
+ 
+
+ align:start position:0%
+incredible power and is can already see
+I've hinted at it's the thing that
+
+ align:start position:0%
+I've hinted at it's the thing that
+ 
+
+ align:start position:0%
+I've hinted at it's the thing that
+effectively allows you to do these
+
+ align:start position:0%
+effectively allows you to do these
+ 
+
+ align:start position:0%
+effectively allows you to do these
+infinite computations that go on until
+
+ align:start position:0%
+infinite computations that go on until
+ 
+
+ align:start position:0%
+infinite computations that go on until
+something is true right without having
+
+ align:start position:0%
+something is true right without having
+ 
+
+ align:start position:0%
+something is true right without having
+any other constructs other than the
+
+ align:start position:0%
+any other constructs other than the
+ 
+
+ align:start position:0%
+any other constructs other than the
+ability to call a procedure let's see
+
+ align:start position:0%
+ability to call a procedure let's see
+ 
+
+ align:start position:0%
+ability to call a procedure let's see
+there's one more thing that I say let me
+
+ align:start position:0%
+there's one more thing that I say let me
+ 
+
+ align:start position:0%
+there's one more thing that I say let me
+show you a variant of this definition of
+
+ align:start position:0%
+show you a variant of this definition of
+ 
+
+ align:start position:0%
+show you a variant of this definition of
+square root come on the slide here's a
+
+ align:start position:0%
+square root come on the slide here's a
+ 
+
+ align:start position:0%
+square root come on the slide here's a
+here's a sort of the same thing what
+
+ align:start position:0%
+here's a sort of the same thing what
+ 
+
+ align:start position:0%
+here's a sort of the same thing what
+I've done here is packaged the
+
+ align:start position:0%
+I've done here is packaged the
+ 
+
+ align:start position:0%
+I've done here is packaged the
+definitions of improve and good enough
+
+ align:start position:0%
+definitions of improve and good enough
+ 
+
+ align:start position:0%
+definitions of improve and good enough
+and try inside square root so in effect
+
+ align:start position:0%
+and try inside square root so in effect
+ 
+
+ align:start position:0%
+and try inside square root so in effect
+what I've done is I've built a square
+
+ align:start position:0%
+what I've done is I've built a square
+ 
+
+ align:start position:0%
+what I've done is I've built a square
+root box so I built a box that's this
+
+ align:start position:0%
+root box so I built a box that's this
+ 
+
+ align:start position:0%
+root box so I built a box that's this
+square root procedure that someone can
+
+ align:start position:0%
+square root procedure that someone can
+ 
+
+ align:start position:0%
+square root procedure that someone can
+use they might put in 36 and get out six
+
+ align:start position:0%
+use they might put in 36 and get out six
+ 
+
+ align:start position:0%
+use they might put in 36 and get out six
+and then packaged inside this box are
+
+ align:start position:0%
+and then packaged inside this box are
+ 
+
+ align:start position:0%
+and then packaged inside this box are
+the definitions of try and good enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and improve right so they're hidden
+
+ align:start position:0%
+and improve right so they're hidden
+ 
+
+ align:start position:0%
+and improve right so they're hidden
+inside this box and the reason for doing
+
+ align:start position:0%
+inside this box and the reason for doing
+ 
+
+ align:start position:0%
+inside this box and the reason for doing
+that is that if someone's using the
+
+ align:start position:0%
+that is that if someone's using the
+ 
+
+ align:start position:0%
+that is that if someone's using the
+square root if George is using the
+
+ align:start position:0%
+square root if George is using the
+ 
+
+ align:start position:0%
+square root if George is using the
+square of George probably doesn't care
+
+ align:start position:0%
+square of George probably doesn't care
+ 
+
+ align:start position:0%
+square of George probably doesn't care
+very much that when I implemented square
+
+ align:start position:0%
+very much that when I implemented square
+ 
+
+ align:start position:0%
+very much that when I implemented square
+root I had things inside they're called
+
+ align:start position:0%
+root I had things inside they're called
+ 
+
+ align:start position:0%
+root I had things inside they're called
+try and good enough and improve and in
+
+ align:start position:0%
+try and good enough and improve and in
+ 
+
+ align:start position:0%
+try and good enough and improve and in
+fact Harry might have a cube root
+
+ align:start position:0%
+fact Harry might have a cube root
+ 
+
+ align:start position:0%
+fact Harry might have a cube root
+procedure that has try and good enough
+
+ align:start position:0%
+procedure that has try and good enough
+ 
+
+ align:start position:0%
+procedure that has try and good enough
+and improve and in order to not get the
+
+ align:start position:0%
+and improve and in order to not get the
+ 
+
+ align:start position:0%
+and improve and in order to not get the
+whole system confused would be good for
+
+ align:start position:0%
+whole system confused would be good for
+ 
+
+ align:start position:0%
+whole system confused would be good for
+Harry to package his internal procedures
+
+ align:start position:0%
+Harry to package his internal procedures
+ 
+
+ align:start position:0%
+Harry to package his internal procedures
+inside his cube root procedure way this
+
+ align:start position:0%
+inside his cube root procedure way this
+ 
+
+ align:start position:0%
+inside his cube root procedure way this
+is called block structure this
+
+ align:start position:0%
+is called block structure this
+ 
+
+ align:start position:0%
+is called block structure this
+particular way of packaging internals
+
+ align:start position:0%
+particular way of packaging internals
+ 
+
+ align:start position:0%
+particular way of packaging internals
+inside of a definition and let's go back
+
+ align:start position:0%
+inside of a definition and let's go back
+ 
+
+ align:start position:0%
+inside of a definition and let's go back
+and look at the slide again the way to
+
+ align:start position:0%
+and look at the slide again the way to
+ 
+
+ align:start position:0%
+and look at the slide again the way to
+read this this kind of procedure is to
+
+ align:start position:0%
+read this this kind of procedure is to
+ 
+
+ align:start position:0%
+read this this kind of procedure is to
+say to define square root well inside
+
+ align:start position:0%
+say to define square root well inside
+ 
+
+ align:start position:0%
+say to define square root well inside
+that definition
+
+ align:start position:0%
+that definition
+ 
+
+ align:start position:0%
+that definition
+I'll have the definition of an improve
+
+ align:start position:0%
+I'll have the definition of an improve
+ 
+
+ align:start position:0%
+I'll have the definition of an improve
+and the definition of good enough and
+
+ align:start position:0%
+and the definition of good enough and
+ 
+
+ align:start position:0%
+and the definition of good enough and
+the definition of try and then subject
+
+ align:start position:0%
+the definition of try and then subject
+ 
+
+ align:start position:0%
+the definition of try and then subject
+to those definitions the way I do square
+
+ align:start position:0%
+to those definitions the way I do square
+ 
+
+ align:start position:0%
+to those definitions the way I do square
+root is to try 1 and notice here I don't
+
+ align:start position:0%
+root is to try 1 and notice here I don't
+ 
+
+ align:start position:0%
+root is to try 1 and notice here I don't
+have to say 1 as a guest for the square
+
+ align:start position:0%
+have to say 1 as a guest for the square
+ 
+
+ align:start position:0%
+have to say 1 as a guest for the square
+root of the X because since it's all
+
+ align:start position:0%
+root of the X because since it's all
+ 
+
+ align:start position:0%
+root of the X because since it's all
+inside this square root it sort of has
+
+ align:start position:0%
+inside this square root it sort of has
+ 
+
+ align:start position:0%
+inside this square root it sort of has
+this X known
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well let me let me summarize we
+
+ align:start position:0%
+okay well let me let me summarize we
+ 
+
+ align:start position:0%
+okay well let me let me summarize we
+started out with the idea that what
+
+ align:start position:0%
+started out with the idea that what
+ 
+
+ align:start position:0%
+started out with the idea that what
+we're going to be doing is expressing
+
+ align:start position:0%
+we're going to be doing is expressing
+ 
+
+ align:start position:0%
+we're going to be doing is expressing
+imperative knowledge and in fact here's
+
+ align:start position:0%
+imperative knowledge and in fact here's
+ 
+
+ align:start position:0%
+imperative knowledge and in fact here's
+a here's a slide that summarizes the way
+
+ align:start position:0%
+a here's a slide that summarizes the way
+ 
+
+ align:start position:0%
+a here's a slide that summarizes the way
+we we looked at lists we started out by
+
+ align:start position:0%
+we we looked at lists we started out by
+ 
+
+ align:start position:0%
+we we looked at lists we started out by
+looking at some primitive elements and
+
+ align:start position:0%
+looking at some primitive elements and
+ 
+
+ align:start position:0%
+looking at some primitive elements and
+addition and multiplication some
+
+ align:start position:0%
+addition and multiplication some
+ 
+
+ align:start position:0%
+addition and multiplication some
+predicates for testing whether
+
+ align:start position:0%
+predicates for testing whether
+ 
+
+ align:start position:0%
+predicates for testing whether
+something's less than or something's
+
+ align:start position:0%
+something's less than or something's
+ 
+
+ align:start position:0%
+something's less than or something's
+equal and in fact we saw a really
+
+ align:start position:0%
+equal and in fact we saw a really
+ 
+
+ align:start position:0%
+equal and in fact we saw a really
+sneakily in the system we're actually
+
+ align:start position:0%
+sneakily in the system we're actually
+ 
+
+ align:start position:0%
+sneakily in the system we're actually
+using these aren't actually primitives
+
+ align:start position:0%
+using these aren't actually primitives
+ 
+
+ align:start position:0%
+using these aren't actually primitives
+but it doesn't matter what matters is
+
+ align:start position:0%
+but it doesn't matter what matters is
+ 
+
+ align:start position:0%
+but it doesn't matter what matters is
+we're going to use them as if they're
+
+ align:start position:0%
+we're going to use them as if they're
+ 
+
+ align:start position:0%
+we're going to use them as if they're
+primitives we're not going to look
+
+ align:start position:0%
+primitives we're not going to look
+ 
+
+ align:start position:0%
+primitives we're not going to look
+inside we also have some primitive data
+
+ align:start position:0%
+inside we also have some primitive data
+ 
+
+ align:start position:0%
+inside we also have some primitive data
+and some numbers we saw some means of
+
+ align:start position:0%
+and some numbers we saw some means of
+ 
+
+ align:start position:0%
+and some numbers we saw some means of
+composition means of combination the
+
+ align:start position:0%
+composition means of combination the
+ 
+
+ align:start position:0%
+composition means of combination the
+basic one being composing functions and
+
+ align:start position:0%
+basic one being composing functions and
+ 
+
+ align:start position:0%
+basic one being composing functions and
+building combinations with operators and
+
+ align:start position:0%
+building combinations with operators and
+ 
+
+ align:start position:0%
+building combinations with operators and
+operands and there were some other
+
+ align:start position:0%
+operands and there were some other
+ 
+
+ align:start position:0%
+operands and there were some other
+things like cond and if and define but
+
+ align:start position:0%
+things like cond and if and define but
+ 
+
+ align:start position:0%
+things like cond and if and define but
+the main thing about define in
+
+ align:start position:0%
+the main thing about define in
+ 
+
+ align:start position:0%
+the main thing about define in
+particular was that it was the means of
+
+ align:start position:0%
+particular was that it was the means of
+ 
+
+ align:start position:0%
+particular was that it was the means of
+abstraction it was the way that we named
+
+ align:start position:0%
+abstraction it was the way that we named
+ 
+
+ align:start position:0%
+abstraction it was the way that we named
+things you can also see from this slide
+
+ align:start position:0%
+things you can also see from this slide
+ 
+
+ align:start position:0%
+things you can also see from this slide
+not only where we've been but holes we
+
+ align:start position:0%
+not only where we've been but holes we
+ 
+
+ align:start position:0%
+not only where we've been but holes we
+have to fill in at some point we'll have
+
+ align:start position:0%
+have to fill in at some point we'll have
+ 
+
+ align:start position:0%
+have to fill in at some point we'll have
+to talk about how you combine primitive
+
+ align:start position:0%
+to talk about how you combine primitive
+ 
+
+ align:start position:0%
+to talk about how you combine primitive
+data to get compound data and how you
+
+ align:start position:0%
+data to get compound data and how you
+ 
+
+ align:start position:0%
+data to get compound data and how you
+abstract data so you can use large globs
+
+ align:start position:0%
+abstract data so you can use large globs
+ 
+
+ align:start position:0%
+abstract data so you can use large globs
+of data as if they were primitive so
+
+ align:start position:0%
+of data as if they were primitive so
+ 
+
+ align:start position:0%
+of data as if they were primitive so
+that's where that's where we're going
+
+ align:start position:0%
+that's where that's where we're going
+ 
+
+ align:start position:0%
+that's where that's where we're going
+but before we do that for the next
+
+ align:start position:0%
+but before we do that for the next
+ 
+
+ align:start position:0%
+but before we do that for the next
+couple of lectures we're going to be
+
+ align:start position:0%
+couple of lectures we're going to be
+ 
+
+ align:start position:0%
+couple of lectures we're going to be
+talking about first of all how it is
+
+ align:start position:0%
+talking about first of all how it is
+ 
+
+ align:start position:0%
+talking about first of all how it is
+that you make a link between these
+
+ align:start position:0%
+that you make a link between these
+ 
+
+ align:start position:0%
+that you make a link between these
+procedures we write and the processes
+
+ align:start position:0%
+procedures we write and the processes
+ 
+
+ align:start position:0%
+procedures we write and the processes
+that happen in the machine and then how
+
+ align:start position:0%
+that happen in the machine and then how
+ 
+
+ align:start position:0%
+that happen in the machine and then how
+it is that you start using the power of
+
+ align:start position:0%
+it is that you start using the power of
+ 
+
+ align:start position:0%
+it is that you start using the power of
+Lisp to talk not only about these
+
+ align:start position:0%
+Lisp to talk not only about these
+ 
+
+ align:start position:0%
+Lisp to talk not only about these
+individual little computations but about
+
+ align:start position:0%
+individual little computations but about
+ 
+
+ align:start position:0%
+individual little computations but about
+general conventional methods of doing
+
+ align:start position:0%
+general conventional methods of doing
+ 
+
+ align:start position:0%
+general conventional methods of doing
+things okay are there any questions yes
+
+ align:start position:0%
+things okay are there any questions yes
+ 
+
+ align:start position:0%
+things okay are there any questions yes
+if we define a using parentheses instead
+
+ align:start position:0%
+if we define a using parentheses instead
+ 
+
+ align:start position:0%
+if we define a using parentheses instead
+of as we did what would be the
+
+ align:start position:0%
+of as we did what would be the
+ 
+
+ align:start position:0%
+of as we did what would be the
+difference if I wrote this if I really
+
+ align:start position:0%
+difference if I wrote this if I really
+ 
+
+ align:start position:0%
+difference if I wrote this if I really
+that what I would be doing is defining a
+
+ align:start position:0%
+that what I would be doing is defining a
+ 
+
+ align:start position:0%
+that what I would be doing is defining a
+procedure named a in this case a
+
+ align:start position:0%
+procedure named a in this case a
+ 
+
+ align:start position:0%
+procedure named a in this case a
+procedure of no arguments
+
+ align:start position:0%
+procedure of no arguments
+ 
+
+ align:start position:0%
+procedure of no arguments
+which one Iran it would give me back
+
+ align:start position:0%
+which one Iran it would give me back
+ 
+
+ align:start position:0%
+which one Iran it would give me back
+five times five I mean you come over the
+
+ align:start position:0%
+five times five I mean you come over the
+ 
+
+ align:start position:0%
+five times five I mean you come over the
+same thing except for you really got a
+
+ align:start position:0%
+same thing except for you really got a
+ 
+
+ align:start position:0%
+same thing except for you really got a
+different right and the difference the
+
+ align:start position:0%
+different right and the difference the
+ 
+
+ align:start position:0%
+different right and the difference the
+difference would be in the old one let
+
+ align:start position:0%
+difference would be in the old one let
+ 
+
+ align:start position:0%
+difference would be in the old one let
+me be a little bit clearer here let's
+
+ align:start position:0%
+me be a little bit clearer here let's
+ 
+
+ align:start position:0%
+me be a little bit clearer here let's
+let's call this a like here and that
+
+ align:start position:0%
+let's call this a like here and that
+ 
+
+ align:start position:0%
+let's call this a like here and that
+pretend here just for contrast
+
+ align:start position:0%
+pretend here just for contrast
+ 
+
+ align:start position:0%
+pretend here just for contrast
+I wrote define D to be the product of
+
+ align:start position:0%
+I wrote define D to be the product of
+ 
+
+ align:start position:0%
+I wrote define D to be the product of
+five and five and the difference between
+
+ align:start position:0%
+five and five and the difference between
+ 
+
+ align:start position:0%
+five and five and the difference between
+those let's think about interactions
+
+ align:start position:0%
+those let's think about interactions
+ 
+
+ align:start position:0%
+those let's think about interactions
+with the Lisp interpreter I would take a
+
+ align:start position:0%
+with the Lisp interpreter I would take a
+ 
+
+ align:start position:0%
+with the Lisp interpreter I would take a
+type in a and list would return twenty
+
+ align:start position:0%
+type in a and list would return twenty
+ 
+
+ align:start position:0%
+type in a and list would return twenty
+five I could type in D if I just type in
+
+ align:start position:0%
+five I could type in D if I just type in
+ 
+
+ align:start position:0%
+five I could type in D if I just type in
+D Lisp would return compound procedure D
+
+ align:start position:0%
+D Lisp would return compound procedure D
+ 
+
+ align:start position:0%
+D Lisp would return compound procedure D
+because that's what it is it's a
+
+ align:start position:0%
+because that's what it is it's a
+ 
+
+ align:start position:0%
+because that's what it is it's a
+procedure I could run D I could say
+
+ align:start position:0%
+procedure I could run D I could say
+ 
+
+ align:start position:0%
+procedure I could run D I could say
+what's the value of running D here is a
+
+ align:start position:0%
+what's the value of running D here is a
+ 
+
+ align:start position:0%
+what's the value of running D here is a
+combination with no operands and I see
+
+ align:start position:0%
+combination with no operands and I see
+ 
+
+ align:start position:0%
+combination with no operands and I see
+there no operands I didn't put any after
+
+ align:start position:0%
+there no operands I didn't put any after
+ 
+
+ align:start position:0%
+there no operands I didn't put any after
+D and it would say oh that's 25 or I
+
+ align:start position:0%
+D and it would say oh that's 25 or I
+ 
+
+ align:start position:0%
+D and it would say oh that's 25 or I
+could say district just for completeness
+
+ align:start position:0%
+could say district just for completeness
+ 
+
+ align:start position:0%
+could say district just for completeness
+if I typed in what's the value of
+
+ align:start position:0%
+if I typed in what's the value of
+ 
+
+ align:start position:0%
+if I typed in what's the value of
+running a I get an error the error would
+
+ align:start position:0%
+running a I get an error the error would
+ 
+
+ align:start position:0%
+running a I get an error the error would
+be the same one as as over there I'd be
+
+ align:start position:0%
+be the same one as as over there I'd be
+ 
+
+ align:start position:0%
+be the same one as as over there I'd be
+the error would say sorry 25 which is
+
+ align:start position:0%
+the error would say sorry 25 which is
+ 
+
+ align:start position:0%
+the error would say sorry 25 which is
+the value of a is not an operator that I
+
+ align:start position:0%
+the value of a is not an operator that I
+ 
+
+ align:start position:0%
+the value of a is not an operator that I
+can apply to something
+
+ align:start position:0%
+can apply to something
+ 
+
+ align:start position:0%
+can apply to something
+[Music]
\ No newline at end of file
diff --git a/-Zg3fxOmjVs.txt b/-Zg3fxOmjVs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a2e716f15223e43e2772d771152f2185b2cc47fb
--- /dev/null
+++ b/-Zg3fxOmjVs.txt
@@ -0,0 +1,174 @@
+Okay, here's our final contract for how procedure
+calls will work:
+
+The calling procedure ("caller") will
+PUSH the argument values onto the stack in
+
+reverse order
+Branch to the entry point of the callee, putting
+
+the return address into the linkage pointer.
+
+When the callee returns, remove the argument
+values from the stack.
+
+The called procedure ("callee") will
+Perform the promised computation, leaving
+
+the result in R0.
+
+Jump to the return address when the computation
+has finished
+
+Remove any items it has placed on the stack,
+leaving the stack as it was when the procedure
+
+was entered.
+
+Note that the arguments were PUSHed on the
+stack by the caller, so it will be up to the
+
+caller to remove them.
+
+Preserve the values in all registers except
+R0, which holds the return value.
+
+So the caller can assume any values placed
+in registers before a nested call will be
+
+there when the nested call returns.
+
+We saw the code template for procedure calls
+on an earlier slide.
+
+Here's the template for the entry point to
+a procedure F.
+
+The code saves the caller's LP and BP values,
+initializes BP for the current stack frame
+
+and allocates words on the stack to hold any
+local variable values.
+
+The final step is to PUSH the value of any
+registers (besides R0) that will be used by
+
+the remainder of the procedure's code.
+
+The template for the exit sequence mirrors
+the actions of the entry sequence, restoring
+
+all the values saved by the entry sequence,
+performing the POP operations in the reverse
+
+of the order of the PUSH operations in the
+entry sequence.
+
+Note that in moving the BP value into SP we've
+reset the stack to its state at the point
+
+of the MOVE(SP,BP) in the entry sequence.
+
+This implicitly undoes the effect of the ALLOCATE
+statement in the entry sequence, so we don't
+
+need a matching DEALLOCATE in the exit sequence.
+
+The last instruction in the exit sequence
+transfers control back to the calling procedure.
+
+With practice you'll become familiar with
+these code templates.
+
+Meanwhile, you can refer back to this slide
+whenever you need to generate code for a procedure
+
+call.
+
+Here's the code our compiler would generate
+for the C implementation of factorial shown
+
+on the left.
+
+The entry sequence saves the caller's LP and
+BP, then initializes BP for the current stack
+
+frame.
+
+The value of R1 is saved so we can use R1
+in code that follows.
+
+The exit sequence restores all the saved values,
+including that for R1.
+
+The code for the body of the procedure has
+arranged for R0 to contain the return value
+
+by the time execution reaches the exit sequence.
+
+The nested procedure call passes the argument
+value on the stack and removes it after the
+
+nested call returns.
+
+The remainder of the code is generated using
+the templates we saw in the previous lecture.
+
+Aside from computing and pushing the values
+of the arguments, there are approximately
+
+10 instructions needed to implement the linking
+approach to a procedure call.
+
+That's not much for a procedure of any size,
+but might be significant for a trivial procedure.
+
+As mentioned earlier, some optimizing compilers
+can make the tradeoff of inlining small non-recursive
+
+procedures saving this small amount of overhead.
+
+So have we solved the activation record storage
+issue for recursive procedures?
+
+Yes!
+
+A new stack from is allocated for each procedure
+call.
+
+In each frame we see the storage for the argument
+and return address.
+
+And as the nested calls return the stack frames
+will be deallocated in inverse order.
+
+Interestingly we can learn a lot about the
+current state of execution by looking at the
+
+active stack frames.
+
+The current value of BP, along the older values
+saved in the activation records, allow us
+
+to identify the active procedure calls and
+determine their arguments, the values of any
+
+local variables for active calls, and so on.
+
+If we print out all this information at any
+given time we would have a "stack trace" showing
+
+the progress of the computation.
+
+In fact, when an problem occurs, many language
+runtimes will print out that stack trace to
+
+help the programmer determine what happened.
+
+And, of course, if you can interpret the information
+in the stack frames, you can show you understand
+
+our conventions for procedure call and return.
+
+Don't be surprised to find such a question
+on a quiz :)
\ No newline at end of file
diff --git a/-mrxN8XcQOQ.txt b/-mrxN8XcQOQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b98612427e77e3760d197ca93d564ababa57fa26
--- /dev/null
+++ b/-mrxN8XcQOQ.txt
@@ -0,0 +1,12735 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay let's start uh so let
+
+ align:start position:0%
+ocw.mit.edu okay let's start uh so let
+ 
+
+ align:start position:0%
+ocw.mit.edu okay let's start uh so let
+me just mention uh brief uh first let me
+
+ align:start position:0%
+me just mention uh brief uh first let me
+ 
+
+ align:start position:0%
+me just mention uh brief uh first let me
+just mention briefly uh this uh story
+
+ align:start position:0%
+just mention briefly uh this uh story
+ 
+
+ align:start position:0%
+just mention briefly uh this uh story
+regarding the de brain
+
+ align:start position:0%
+regarding the de brain
+ 
+
+ align:start position:0%
+regarding the de brain
+and the he
+
+ align:start position:0%
+and the he
+ 
+
+ align:start position:0%
+and the he
+mechanism uh which we uh discussed at
+
+ align:start position:0%
+mechanism uh which we uh discussed at
+ 
+
+ align:start position:0%
+mechanism uh which we uh discussed at
+the end of last lecture so there was a
+
+ align:start position:0%
+the end of last lecture so there was a
+ 
+
+ align:start position:0%
+the end of last lecture so there was a
+pide problem uh which was related to
+
+ align:start position:0%
+pide problem uh which was related to
+ 
+
+ align:start position:0%
+pide problem uh which was related to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um yes I expected maybe the P problem
+
+ align:start position:0%
+um yes I expected maybe the P problem
+ 
+
+ align:start position:0%
+um yes I expected maybe the P problem
+was a little bit tough because we did
+
+ align:start position:0%
+was a little bit tough because we did
+ 
+
+ align:start position:0%
+was a little bit tough because we did
+not go to many details uh we did not go
+
+ align:start position:0%
+not go to many details uh we did not go
+ 
+
+ align:start position:0%
+not go to many details uh we did not go
+to many details
+
+ align:start position:0%
+to many details
+ 
+
+ align:start position:0%
+to many details
+um um yeah so in grading we will be very
+
+ align:start position:0%
+um um yeah so in grading we will be very
+ 
+
+ align:start position:0%
+um um yeah so in grading we will be very
+um flexible because we
+
+ align:start position:0%
+um flexible because we
+ 
+
+ align:start position:0%
+um flexible because we
+um um yeah but so let me just say a few
+
+ align:start position:0%
+um um yeah but so let me just say a few
+ 
+
+ align:start position:0%
+um um yeah but so let me just say a few
+more things about that just to make sure
+
+ align:start position:0%
+more things about that just to make sure
+ 
+
+ align:start position:0%
+more things about that just to make sure
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um yeah so here is the say the the
+
+ align:start position:0%
+um yeah so here is the say the the
+ 
+
+ align:start position:0%
+um yeah so here is the say the the
+action if you have n say if you suppose
+
+ align:start position:0%
+action if you have n say if you suppose
+ 
+
+ align:start position:0%
+action if you have n say if you suppose
+you have n de brains
+
+ align:start position:0%
+you have n de brains
+ 
+
+ align:start position:0%
+you have n de brains
+together and then in such case so this
+
+ align:start position:0%
+together and then in such case so this
+ 
+
+ align:start position:0%
+together and then in such case so this
+is a l effective action for the Mist de
+
+ align:start position:0%
+is a l effective action for the Mist de
+ 
+
+ align:start position:0%
+is a l effective action for the Mist de
+freedom on the D brain so which you have
+
+ align:start position:0%
+freedom on the D brain so which you have
+ 
+
+ align:start position:0%
+freedom on the D brain so which you have
+a gauge field which is a matrix and then
+
+ align:start position:0%
+a gauge field which is a matrix and then
+ 
+
+ align:start position:0%
+a gauge field which is a matrix and then
+you also have a a uh a scalar field a l
+
+ align:start position:0%
+you also have a a uh a scalar field a l
+ 
+
+ align:start position:0%
+you also have a a uh a scalar field a l
+of scalar fields which are also inbi
+
+ align:start position:0%
+of scalar fields which are also inbi
+ 
+
+ align:start position:0%
+of scalar fields which are also inbi
+matrices and the L of scalar field is
+
+ align:start position:0%
+matrices and the L of scalar field is
+ 
+
+ align:start position:0%
+matrices and the L of scalar field is
+the same as number of transverse
+
+ align:start position:0%
+the same as number of transverse
+ 
+
+ align:start position:0%
+the same as number of transverse
+Dimensions okay and we also
+
+ align:start position:0%
+Dimensions okay and we also
+ 
+
+ align:start position:0%
+Dimensions okay and we also
+discussed that the uh the the scalar
+
+ align:start position:0%
+discussed that the uh the the scalar
+ 
+
+ align:start position:0%
+discussed that the uh the the scalar
+Fields can be considered as be as
+
+ align:start position:0%
+Fields can be considered as be as
+ 
+
+ align:start position:0%
+Fields can be considered as be as
+describing the transverse dynamics of
+
+ align:start position:0%
+describing the transverse dynamics of
+ 
+
+ align:start position:0%
+describing the transverse dynamics of
+the brain say say let's consider you
+
+ align:start position:0%
+the brain say say let's consider you
+ 
+
+ align:start position:0%
+the brain say say let's consider you
+have a case of a yeah let's consider you
+
+ align:start position:0%
+have a case of a yeah let's consider you
+ 
+
+ align:start position:0%
+have a case of a yeah let's consider you
+have a single single
+
+ align:start position:0%
+have a single single
+ 
+
+ align:start position:0%
+have a single single
+brain and there's only one trans
+
+ align:start position:0%
+brain and there's only one trans
+ 
+
+ align:start position:0%
+brain and there's only one trans
+Direction say let's call it uh um say
+
+ align:start position:0%
+Direction say let's call it uh um say
+ 
+
+ align:start position:0%
+Direction say let's call it uh um say
+the the five direction there's only one
+
+ align:start position:0%
+the the five direction there's only one
+ 
+
+ align:start position:0%
+the the five direction there's only one
+direction say Five One
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction then the the essentially
+
+ align:start position:0%
+Direction then the the essentially
+ 
+
+ align:start position:0%
+Direction then the the essentially
+location of the brain then essentially
+
+ align:start position:0%
+location of the brain then essentially
+ 
+
+ align:start position:0%
+location of the brain then essentially
+the expectation value of 51 can be
+
+ align:start position:0%
+the expectation value of 51 can be
+ 
+
+ align:start position:0%
+the expectation value of 51 can be
+considered say yeah suppose this is the
+
+ align:start position:0%
+considered say yeah suppose this is the
+ 
+
+ align:start position:0%
+considered say yeah suppose this is the
+direction of X1 and the corresponding
+
+ align:start position:0%
+direction of X1 and the corresponding
+ 
+
+ align:start position:0%
+direction of X1 and the corresponding
+scal of field is 51 and then then
+
+ align:start position:0%
+scal of field is 51 and then then
+ 
+
+ align:start position:0%
+scal of field is 51 and then then
+expectation value of 51 can be
+
+ align:start position:0%
+expectation value of 51 can be
+ 
+
+ align:start position:0%
+expectation value of 51 can be
+considered as a location of the brain
+
+ align:start position:0%
+considered as a location of the brain
+ 
+
+ align:start position:0%
+considered as a location of the brain
+and and this F is the string which U
+
+ align:start position:0%
+and and this F is the string which U
+ 
+
+ align:start position:0%
+and and this F is the string which U
+ending on this brain and come back to
+
+ align:start position:0%
+ending on this brain and come back to
+ 
+
+ align:start position:0%
+ending on this brain and come back to
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+okay so now let's consider if you have
+
+ align:start position:0%
+okay so now let's consider if you have
+ 
+
+ align:start position:0%
+okay so now let's consider if you have
+two brains uh now consider you have M
+
+ align:start position:0%
+two brains uh now consider you have M
+ 
+
+ align:start position:0%
+two brains uh now consider you have M
+brains again there only one transverse
+
+ align:start position:0%
+brains again there only one transverse
+ 
+
+ align:start position:0%
+brains again there only one transverse
+Direction and I have EMB
+
+ align:start position:0%
+Direction and I have EMB
+ 
+
+ align:start position:0%
+Direction and I have EMB
+braines this one transverse Direction
+
+ align:start position:0%
+braines this one transverse Direction
+ 
+
+ align:start position:0%
+braines this one transverse Direction
+which again this X1 and now you can just
+
+ align:start position:0%
+which again this X1 and now you can just
+ 
+
+ align:start position:0%
+which again this X1 and now you can just
+separate them so now let's consider the
+
+ align:start position:0%
+separate them so now let's consider the
+ 
+
+ align:start position:0%
+separate them so now let's consider the
+process which you separate this embrane
+
+ align:start position:0%
+process which you separate this embrane
+ 
+
+ align:start position:0%
+process which you separate this embrane
+into say completely separate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in different locations say so this is X1
+
+ align:start position:0%
+in different locations say so this is X1
+ 
+
+ align:start position:0%
+in different locations say so this is X1
+X2 to xn okay to
+
+ align:start position:0%
+X2 to xn okay to
+ 
+
+ align:start position:0%
+X2 to xn okay to
+XM so so this situation can be
+
+ align:start position:0%
+XM so so this situation can be
+ 
+
+ align:start position:0%
+XM so so this situation can be
+considered as a situation so in this
+
+ align:start position:0%
+considered as a situation so in this
+ 
+
+ align:start position:0%
+considered as a situation so in this
+case the f is a a f is M byn matrices
+
+ align:start position:0%
+case the f is a a f is M byn matrices
+ 
+
+ align:start position:0%
+case the f is a a f is M byn matrices
+and then this can be considered as five
+
+ align:start position:0%
+and then this can be considered as five
+ 
+
+ align:start position:0%
+and then this can be considered as five
+having a expectation
+
+ align:start position:0%
+having a expectation
+ 
+
+ align:start position:0%
+having a expectation
+value which is only in the diagonal
+
+ align:start position:0%
+value which is only in the diagonal
+ 
+
+ align:start position:0%
+value which is only in the diagonal
+entry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay which is only in the diagonal
+
+ align:start position:0%
+okay which is only in the diagonal
+ 
+
+ align:start position:0%
+okay which is only in the diagonal
+entry uh uh and each diagonal
+
+ align:start position:0%
+entry uh uh and each diagonal
+ 
+
+ align:start position:0%
+entry uh uh and each diagonal
+entry describes the location of the uh
+
+ align:start position:0%
+entry describes the location of the uh
+ 
+
+ align:start position:0%
+entry describes the location of the uh
+HD brain and it's natural to think that
+
+ align:start position:0%
+HD brain and it's natural to think that
+ 
+
+ align:start position:0%
+HD brain and it's natural to think that
+why this is diagonal entry because the
+
+ align:start position:0%
+why this is diagonal entry because the
+ 
+
+ align:start position:0%
+why this is diagonal entry because the
+diagonal entry describe the string which
+
+ align:start position:0%
+diagonal entry describe the string which
+ 
+
+ align:start position:0%
+diagonal entry describe the string which
+ending on the brain itself okay so this
+
+ align:start position:0%
+ending on the brain itself okay so this
+ 
+
+ align:start position:0%
+ending on the brain itself okay so this
+is one one one one string and this is
+
+ align:start position:0%
+is one one one one string and this is
+ 
+
+ align:start position:0%
+is one one one one string and this is
+two two string and n n string and so the
+
+ align:start position:0%
+two two string and n n string and so the
+ 
+
+ align:start position:0%
+two two string and n n string and so the
+diagonal string uh uh is the excitation
+
+ align:start position:0%
+diagonal string uh uh is the excitation
+ 
+
+ align:start position:0%
+diagonal string uh uh is the excitation
+on the brain itself and the off diagonal
+
+ align:start position:0%
+on the brain itself and the off diagonal
+ 
+
+ align:start position:0%
+on the brain itself and the off diagonal
+corresponding to essentially
+
+ align:start position:0%
+corresponding to essentially
+ 
+
+ align:start position:0%
+corresponding to essentially
+corresponding to excitation between the
+
+ align:start position:0%
+corresponding to excitation between the
+ 
+
+ align:start position:0%
+corresponding to excitation between the
+stream between the brains and so it's
+
+ align:start position:0%
+stream between the brains and so it's
+ 
+
+ align:start position:0%
+stream between the brains and so it's
+natural that the location of the brain
+
+ align:start position:0%
+natural that the location of the brain
+ 
+
+ align:start position:0%
+natural that the location of the brain
+and then just corresponding to the
+
+ align:start position:0%
+and then just corresponding to the
+ 
+
+ align:start position:0%
+and then just corresponding to the
+diagonal INRI okay and so so now we can
+
+ align:start position:0%
+diagonal INRI okay and so so now we can
+ 
+
+ align:start position:0%
+diagonal INRI okay and so so now we can
+generalize to to the general Dimensions
+
+ align:start position:0%
+generalize to to the general Dimensions
+ 
+
+ align:start position:0%
+generalize to to the general Dimensions
+now they more now Suppose there are two
+
+ align:start position:0%
+now they more now Suppose there are two
+ 
+
+ align:start position:0%
+now they more now Suppose there are two
+transverse
+
+ align:start position:0%
+transverse
+ 
+
+ align:start position:0%
+transverse
+Dimensions okay suppose now there are
+
+ align:start position:0%
+Dimensions okay suppose now there are
+ 
+
+ align:start position:0%
+Dimensions okay suppose now there are
+two transverse dimensions me call X1 and
+
+ align:start position:0%
+two transverse dimensions me call X1 and
+ 
+
+ align:start position:0%
+two transverse dimensions me call X1 and
+X2 and then now you have two scal
+
+ align:start position:0%
+X2 and then now you have two scal
+ 
+
+ align:start position:0%
+X2 and then now you have two scal
+Fields so now the story is a little bit
+
+ align:start position:0%
+Fields so now the story is a little bit
+ 
+
+ align:start position:0%
+Fields so now the story is a little bit
+more complicated because when you have
+
+ align:start position:0%
+more complicated because when you have
+ 
+
+ align:start position:0%
+more complicated because when you have
+two transverse directions say if you
+
+ align:start position:0%
+two transverse directions say if you
+ 
+
+ align:start position:0%
+two transverse directions say if you
+have more than two transverse Direction
+
+ align:start position:0%
+have more than two transverse Direction
+ 
+
+ align:start position:0%
+have more than two transverse Direction
+now you have long Tri potential
+
+ align:start position:0%
+now you have long Tri potential
+ 
+
+ align:start position:0%
+now you have long Tri potential
+term and uh and the lot
+
+ align:start position:0%
+term and uh and the lot
+ 
+
+ align:start position:0%
+term and uh and the lot
+configuration say supposed to F have low
+
+ align:start position:0%
+configuration say supposed to F have low
+ 
+
+ align:start position:0%
+configuration say supposed to F have low
+space time dependent than lot of
+
+ align:start position:0%
+space time dependent than lot of
+ 
+
+ align:start position:0%
+space time dependent than lot of
+configuration say the uh so the uh say
+
+ align:start position:0%
+configuration say the uh so the uh say
+ 
+
+ align:start position:0%
+configuration say the uh so the uh say
+the minimum of the potential the must
+
+ align:start position:0%
+the minimum of the potential the must
+ 
+
+ align:start position:0%
+the minimum of the potential the must
+for correspond into the configuration
+
+ align:start position:0%
+for correspond into the configuration
+ 
+
+ align:start position:0%
+for correspond into the configuration
+which the commutator of 5 and 5 b to be
+
+ align:start position:0%
+which the commutator of 5 and 5 b to be
+ 
+
+ align:start position:0%
+which the commutator of 5 and 5 b to be
+zero for for all all say say right now
+
+ align:start position:0%
+zero for for all all say say right now
+ 
+
+ align:start position:0%
+zero for for all all say say right now
+we just two have trans say so we have
+
+ align:start position:0%
+we just two have trans say so we have
+ 
+
+ align:start position:0%
+we just two have trans say so we have
+two transverse directions so we only
+
+ align:start position:0%
+two transverse directions so we only
+ 
+
+ align:start position:0%
+two transverse directions so we only
+have two okay but you can generalize to
+
+ align:start position:0%
+have two okay but you can generalize to
+ 
+
+ align:start position:0%
+have two okay but you can generalize to
+any number of transverse directions okay
+
+ align:start position:0%
+any number of transverse directions okay
+ 
+
+ align:start position:0%
+any number of transverse directions okay
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+means that the five all the five
+
+ align:start position:0%
+means that the five all the five
+ 
+
+ align:start position:0%
+means that the five all the five
+correspond all the scal of field they
+
+ align:start position:0%
+correspond all the scal of field they
+ 
+
+ align:start position:0%
+correspond all the scal of field they
+have to commute with each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other that means they can be
+
+ align:start position:0%
+other that means they can be
+ 
+
+ align:start position:0%
+other that means they can be
+simultaneous
+
+ align:start position:0%
+simultaneous
+ 
+
+ align:start position:0%
+simultaneous
+diagonalized okay that means it be
+
+ align:start position:0%
+diagonalized okay that means it be
+ 
+
+ align:start position:0%
+diagonalized okay that means it be
+simultaneously diagonalized then that
+
+ align:start position:0%
+simultaneously diagonalized then that
+ 
+
+ align:start position:0%
+simultaneously diagonalized then that
+means we can choose a
+
+ align:start position:0%
+means we can choose a
+ 
+
+ align:start position:0%
+means we can choose a
+basis then we can choose a basis say if
+
+ align:start position:0%
+basis then we can choose a basis say if
+ 
+
+ align:start position:0%
+basis then we can choose a basis say if
+I write five the The Collection all the
+
+ align:start position:0%
+I write five the The Collection all the
+ 
+
+ align:start position:0%
+I write five the The Collection all the
+all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+de then I can simultaneous diagonalize
+
+ align:start position:0%
+de then I can simultaneous diagonalize
+ 
+
+ align:start position:0%
+de then I can simultaneous diagonalize
+them and uh and then they have the
+
+ align:start position:0%
+them and uh and then they have the
+ 
+
+ align:start position:0%
+them and uh and then they have the
+following form okay so so each X
+
+ align:start position:0%
+following form okay so so each X
+ 
+
+ align:start position:0%
+following form okay so so each X
+so each X1 corresponding to so each
+
+ align:start position:0%
+so each X1 corresponding to so each
+ 
+
+ align:start position:0%
+so each X1 corresponding to so each
+Vector corresponding to yes say for
+
+ align:start position:0%
+Vector corresponding to yes say for
+ 
+
+ align:start position:0%
+Vector corresponding to yes say for
+example here is X1 yeah I should I use a
+
+ align:start position:0%
+example here is X1 yeah I should I use a
+ 
+
+ align:start position:0%
+example here is X1 yeah I should I use a
+different notation so let me call the
+
+ align:start position:0%
+different notation so let me call the
+ 
+
+ align:start position:0%
+different notation so let me call the
+space time y1 Y 2 and uh and say this is
+
+ align:start position:0%
+space time y1 Y 2 and uh and say this is
+ 
+
+ align:start position:0%
+space time y1 Y 2 and uh and say this is
+X2 Etc so so this defines the
+
+ align:start position:0%
+X2 Etc so so this defines the
+ 
+
+ align:start position:0%
+X2 Etc so so this defines the
+configuration which you have one D brain
+
+ align:start position:0%
+configuration which you have one D brain
+ 
+
+ align:start position:0%
+configuration which you have one D brain
+here and One D brain at this point and
+
+ align:start position:0%
+here and One D brain at this point and
+ 
+
+ align:start position:0%
+here and One D brain at this point and
+at X3 and Etc okay and again it's only
+
+ align:start position:0%
+at X3 and Etc okay and again it's only
+ 
+
+ align:start position:0%
+at X3 and Etc okay and again it's only
+the diagonal inch
+
+ align:start position:0%
+the diagonal inch
+ 
+
+ align:start position:0%
+the diagonal inch
+uh describe the location of the de Brin
+
+ align:start position:0%
+uh describe the location of the de Brin
+ 
+
+ align:start position:0%
+uh describe the location of the de Brin
+the diagonal in describe location of
+
+ align:start position:0%
+the diagonal in describe location of
+ 
+
+ align:start position:0%
+the diagonal in describe location of
+debrin and this because the because they
+
+ align:start position:0%
+debrin and this because the because they
+ 
+
+ align:start position:0%
+debrin and this because the because they
+all diagonal and the commutator is zero
+
+ align:start position:0%
+all diagonal and the commutator is zero
+ 
+
+ align:start position:0%
+all diagonal and the commutator is zero
+and these are the low configurations
+
+ align:start position:0%
+and these are the low configurations
+ 
+
+ align:start position:0%
+and these are the low configurations
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this is a very important lesson it
+
+ align:start position:0%
+so so this is a very important lesson it
+ 
+
+ align:start position:0%
+so so this is a very important lesson it
+tells you that even you have a potential
+
+ align:start position:0%
+tells you that even you have a potential
+ 
+
+ align:start position:0%
+tells you that even you have a potential
+still the deeper end you can put it
+
+ align:start position:0%
+still the deeper end you can put it
+ 
+
+ align:start position:0%
+still the deeper end you can put it
+anywhere you want and you have the
+
+ align:start position:0%
+anywhere you want and you have the
+ 
+
+ align:start position:0%
+anywhere you want and you have the
+freedom to put the Deep you don't break
+
+ align:start position:0%
+freedom to put the Deep you don't break
+ 
+
+ align:start position:0%
+freedom to put the Deep you don't break
+translation symmetry
+
+ align:start position:0%
+translation symmetry
+ 
+
+ align:start position:0%
+translation symmetry
+okay uh any more uh any questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this of course when you say when the
+
+ align:start position:0%
+this of course when you say when the
+ 
+
+ align:start position:0%
+this of course when you say when the
+scal of field develop expectation such
+
+ align:start position:0%
+scal of field develop expectation such
+ 
+
+ align:start position:0%
+scal of field develop expectation such
+such expectation value and then your
+
+ align:start position:0%
+such expectation value and then your
+ 
+
+ align:start position:0%
+such expectation value and then your
+original you engage symmetry is broken
+
+ align:start position:0%
+original you engage symmetry is broken
+ 
+
+ align:start position:0%
+original you engage symmetry is broken
+and then broken the uh uh broken into
+
+ align:start position:0%
+and then broken the uh uh broken into
+ 
+
+ align:start position:0%
+and then broken the uh uh broken into
+the uh just in the St the
+
+ align:start position:0%
+the uh just in the St the
+ 
+
+ align:start position:0%
+the uh just in the St the
+story um yeah to whatever subgroup
+
+ align:start position:0%
+story um yeah to whatever subgroup
+ 
+
+ align:start position:0%
+story um yeah to whatever subgroup
+Allowed by this um so if all the X1 are
+
+ align:start position:0%
+Allowed by this um so if all the X1 are
+ 
+
+ align:start position:0%
+Allowed by this um so if all the X1 are
+if all of them are are different then
+
+ align:start position:0%
+if all of them are are different then
+ 
+
+ align:start position:0%
+if all of them are are different then
+you only then the remaining just youu
+
+ align:start position:0%
+you only then the remaining just youu
+ 
+
+ align:start position:0%
+you only then the remaining just youu
+one to the power n because now you just
+
+ align:start position:0%
+one to the power n because now you just
+ 
+
+ align:start position:0%
+one to the power n because now you just
+have each brand separated then you just
+
+ align:start position:0%
+have each brand separated then you just
+ 
+
+ align:start position:0%
+have each brand separated then you just
+have to you one to the power n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good okay so so now let Let's uh um move
+
+ align:start position:0%
+good okay so so now let Let's uh um move
+ 
+
+ align:start position:0%
+good okay so so now let Let's uh um move
+to new
+
+ align:start position:0%
+to new
+ 
+
+ align:start position:0%
+to new
+stuff so now let's say a little bit
+
+ align:start position:0%
+stuff so now let's say a little bit
+ 
+
+ align:start position:0%
+stuff so now let's say a little bit
+about the difference in Super Screen
+
+ align:start position:0%
+about the difference in Super Screen
+ 
+
+ align:start position:0%
+about the difference in Super Screen
+Theory so what we said so far actually
+
+ align:start position:0%
+Theory so what we said so far actually
+ 
+
+ align:start position:0%
+Theory so what we said so far actually
+applies to De brains in both a bosonic
+
+ align:start position:0%
+applies to De brains in both a bosonic
+ 
+
+ align:start position:0%
+applies to De brains in both a bosonic
+string and in super
+
+ align:start position:0%
+string and in super
+ 
+
+ align:start position:0%
+string and in super
+string so now let's say a little bit
+
+ align:start position:0%
+string so now let's say a little bit
+ 
+
+ align:start position:0%
+string so now let's say a little bit
+more about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differ
+
+ align:start position:0%
+differ
+ 
+
+ align:start position:0%
+differ
+okay so as we discussed before when we
+
+ align:start position:0%
+okay so as we discussed before when we
+ 
+
+ align:start position:0%
+okay so as we discussed before when we
+quantize the open string that the Deep
+
+ align:start position:0%
+quantize the open string that the Deep
+ 
+
+ align:start position:0%
+quantize the open string that the Deep
+brains in bonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stream always have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tum always have a open screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no matter what deep you have because the
+
+ align:start position:0%
+no matter what deep you have because the
+ 
+
+ align:start position:0%
+no matter what deep you have because the
+as we discussed before the quantization
+
+ align:start position:0%
+as we discussed before the quantization
+ 
+
+ align:start position:0%
+as we discussed before the quantization
+the Zero Point Energy on the stren is
+
+ align:start position:0%
+the Zero Point Energy on the stren is
+ 
+
+ align:start position:0%
+the Zero Point Energy on the stren is
+the same and no matter which dimension
+
+ align:start position:0%
+the same and no matter which dimension
+ 
+
+ align:start position:0%
+the same and no matter which dimension
+of the brain is ETC and you always have
+
+ align:start position:0%
+of the brain is ETC and you always have
+ 
+
+ align:start position:0%
+of the brain is ETC and you always have
+a open string T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here uh attack
+
+ align:start position:0%
+here uh attack
+ 
+
+ align:start position:0%
+here uh attack
+here so that
+
+ align:start position:0%
+here so that
+ 
+
+ align:start position:0%
+here so that
+means as we said before t means that you
+
+ align:start position:0%
+means as we said before t means that you
+ 
+
+ align:start position:0%
+means as we said before t means that you
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+sitting if you have a if you have a
+
+ align:start position:0%
+sitting if you have a if you have a
+ 
+
+ align:start position:0%
+sitting if you have a if you have a
+scale
+
+ align:start position:0%
+scale
+ 
+
+ align:start position:0%
+scale
+fields which have a negative mass square
+
+ align:start position:0%
+fields which have a negative mass square
+ 
+
+ align:start position:0%
+fields which have a negative mass square
+that means you essentially sitting at
+
+ align:start position:0%
+that means you essentially sitting at
+ 
+
+ align:start position:0%
+that means you essentially sitting at
+the top of the potential in the top of
+
+ align:start position:0%
+the top of the potential in the top of
+ 
+
+ align:start position:0%
+the top of the potential in the top of
+some potential and so that's why you get
+
+ align:start position:0%
+some potential and so that's why you get
+ 
+
+ align:start position:0%
+some potential and so that's why you get
+the netive mass square and so that means
+
+ align:start position:0%
+the netive mass square and so that means
+ 
+
+ align:start position:0%
+the netive mass square and so that means
+we have this is unstable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configuration because if you say give
+
+ align:start position:0%
+configuration because if you say give
+ 
+
+ align:start position:0%
+configuration because if you say give
+the tan a little bit of valve then the T
+
+ align:start position:0%
+the tan a little bit of valve then the T
+ 
+
+ align:start position:0%
+the tan a little bit of valve then the T
+want to roll down and then then you move
+
+ align:start position:0%
+want to roll down and then then you move
+ 
+
+ align:start position:0%
+want to roll down and then then you move
+away from this configuration okay
+
+ align:start position:0%
+away from this configuration okay
+ 
+
+ align:start position:0%
+away from this configuration okay
+okay uh you move away from this
+
+ align:start position:0%
+okay uh you move away from this
+ 
+
+ align:start position:0%
+okay uh you move away from this
+configuration
+
+ align:start position:0%
+configuration
+ 
+
+ align:start position:0%
+configuration
+so when you go to super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stream so we also discussed before that
+
+ align:start position:0%
+stream so we also discussed before that
+ 
+
+ align:start position:0%
+stream so we also discussed before that
+for the for the bosonic stram the close
+
+ align:start position:0%
+for the for the bosonic stram the close
+ 
+
+ align:start position:0%
+for the for the bosonic stram the close
+stram sector also has a attack here and
+
+ align:start position:0%
+stram sector also has a attack here and
+ 
+
+ align:start position:0%
+stram sector also has a attack here and
+then you can get rid of those tens by by
+
+ align:start position:0%
+then you can get rid of those tens by by
+ 
+
+ align:start position:0%
+then you can get rid of those tens by by
+going to the Super stream okay so
+
+ align:start position:0%
+going to the Super stream okay so
+ 
+
+ align:start position:0%
+going to the Super stream okay so
+similarly uh uh go going to the Super
+
+ align:start position:0%
+similarly uh uh go going to the Super
+ 
+
+ align:start position:0%
+similarly uh uh go going to the Super
+string the
+
+ align:start position:0%
+string the
+ 
+
+ align:start position:0%
+string the
+difference of certain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dimensions not for all Dimensions but
+
+ align:start position:0%
+Dimensions not for all Dimensions but
+ 
+
+ align:start position:0%
+Dimensions not for all Dimensions but
+only only for some
+
+ align:start position:0%
+only only for some
+ 
+
+ align:start position:0%
+only only for some
+Dimensions do not have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tums so they are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+so the lowest modes are just a massless
+
+ align:start position:0%
+so the lowest modes are just a massless
+ 
+
+ align:start position:0%
+so the lowest modes are just a massless
+mode they don't have lactive mass square
+
+ align:start position:0%
+mode they don't have lactive mass square
+ 
+
+ align:start position:0%
+mode they don't have lactive mass square
+modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh and uh um in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular in
+
+ align:start position:0%
+particular in
+ 
+
+ align:start position:0%
+particular in
+particular so this I will this is a long
+
+ align:start position:0%
+particular so this I will this is a long
+ 
+
+ align:start position:0%
+particular so this I will this is a long
+story uh this is somewhat long story
+
+ align:start position:0%
+story uh this is somewhat long story
+ 
+
+ align:start position:0%
+story uh this is somewhat long story
+which I will not explain here uh but I
+
+ align:start position:0%
+which I will not explain here uh but I
+ 
+
+ align:start position:0%
+which I will not explain here uh but I
+will just uh make the statement in
+
+ align:start position:0%
+will just uh make the statement in
+ 
+
+ align:start position:0%
+will just uh make the statement in
+particular you you can show that for
+
+ align:start position:0%
+particular you you can show that for
+ 
+
+ align:start position:0%
+particular you you can show that for
+those stable de brains in super string
+
+ align:start position:0%
+those stable de brains in super string
+ 
+
+ align:start position:0%
+those stable de brains in super string
+they always carry a conserved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge so I will explain where does this
+
+ align:start position:0%
+charge so I will explain where does this
+ 
+
+ align:start position:0%
+charge so I will explain where does this
+conserved charge come from and they
+
+ align:start position:0%
+conserved charge come from and they
+ 
+
+ align:start position:0%
+conserved charge come from and they
+always carry some conserved charge and
+
+ align:start position:0%
+always carry some conserved charge and
+ 
+
+ align:start position:0%
+always carry some conserved charge and
+which which is also a reason why they're
+
+ align:start position:0%
+which which is also a reason why they're
+ 
+
+ align:start position:0%
+which which is also a reason why they're
+stable and the second feature is that
+
+ align:start position:0%
+stable and the second feature is that
+ 
+
+ align:start position:0%
+stable and the second feature is that
+the the world volume Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric okay super symmetric so in
+
+ align:start position:0%
+symmetric okay super symmetric so in
+ 
+
+ align:start position:0%
+symmetric okay super symmetric so in
+addition to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A5 so in addition to this a this a alpha
+
+ align:start position:0%
+A5 so in addition to this a this a alpha
+ 
+
+ align:start position:0%
+A5 so in addition to this a this a alpha
+five we looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so in addition to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha and F A which we already see in
+
+ align:start position:0%
+Alpha and F A which we already see in
+ 
+
+ align:start position:0%
+Alpha and F A which we already see in
+the bosonic Stream there are also M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fans so so the open string excitations
+
+ align:start position:0%
+fans so so the open string excitations
+ 
+
+ align:start position:0%
+fans so so the open string excitations
+also include M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fans uh they also include Mass fans and
+
+ align:start position:0%
+fans uh they also include Mass fans and
+ 
+
+ align:start position:0%
+fans uh they also include Mass fans and
+in particular the the L
+
+ align:start position:0%
+in particular the the L
+ 
+
+ align:start position:0%
+in particular the the L
+Series well of all of them together is a
+
+ align:start position:0%
+Series well of all of them together is a
+ 
+
+ align:start position:0%
+Series well of all of them together is a
+super symmetric version of this it's a
+
+ align:start position:0%
+super symmetric version of this it's a
+ 
+
+ align:start position:0%
+super symmetric version of this it's a
+Super Y series a super symmetric version
+
+ align:start position:0%
+Super Y series a super symmetric version
+ 
+
+ align:start position:0%
+Super Y series a super symmetric version
+of this and it's some kind of Super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y
+
+ align:start position:0%
+Y
+ 
+
+ align:start position:0%
+Y
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we uh so now let me
+
+ align:start position:0%
+we uh so now let me
+ 
+
+ align:start position:0%
+we uh so now let me
+um let me elaborate a little bit on the
+
+ align:start position:0%
+um let me elaborate a little bit on the
+ 
+
+ align:start position:0%
+um let me elaborate a little bit on the
+first point that they carry a conserve
+
+ align:start position:0%
+first point that they carry a conserve
+ 
+
+ align:start position:0%
+first point that they carry a conserve
+chart
+
+ align:start position:0%
+chart
+ 
+
+ align:start position:0%
+chart
+okay now let me mate a little bit on the
+
+ align:start position:0%
+okay now let me mate a little bit on the
+ 
+
+ align:start position:0%
+okay now let me mate a little bit on the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+point so
+
+ align:start position:0%
+point so
+ 
+
+ align:start position:0%
+point so
+um so let me go to the one elaborate
+
+ align:start position:0%
+um so let me go to the one elaborate
+ 
+
+ align:start position:0%
+um so let me go to the one elaborate
+more on one so let me just remind you
+
+ align:start position:0%
+more on one so let me just remind you
+ 
+
+ align:start position:0%
+more on one so let me just remind you
+again the bosonic part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the bonic
+
+ align:start position:0%
+the bonic
+ 
+
+ align:start position:0%
+the bonic
+part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mat closed supering
+
+ align:start position:0%
+mat closed supering
+ 
+
+ align:start position:0%
+mat closed supering
+Spectrum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we briefly mentioned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before so this is soal the type two
+
+ align:start position:0%
+before so this is soal the type two
+ 
+
+ align:start position:0%
+before so this is soal the type two
+string soal type two string yeah when I
+
+ align:start position:0%
+string soal type two string yeah when I
+ 
+
+ align:start position:0%
+string soal type two string yeah when I
+say the super string I always mean type
+
+ align:start position:0%
+say the super string I always mean type
+ 
+
+ align:start position:0%
+say the super string I always mean type
+two stren
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so if you qu the super string then
+
+ align:start position:0%
+so so if you qu the super string then
+ 
+
+ align:start position:0%
+so so if you qu the super string then
+you find there again you find the
+
+ align:start position:0%
+you find there again you find the
+ 
+
+ align:start position:0%
+you find there again you find the
+metric you find a graviton then you find
+
+ align:start position:0%
+metric you find a graviton then you find
+ 
+
+ align:start position:0%
+metric you find a graviton then you find
+this an symmetric tensor and you find
+
+ align:start position:0%
+this an symmetric tensor and you find
+ 
+
+ align:start position:0%
+this an symmetric tensor and you find
+this scal Fields just as what we did in
+
+ align:start position:0%
+this scal Fields just as what we did in
+ 
+
+ align:start position:0%
+this scal Fields just as what we did in
+the uh in the bonic stream but but there
+
+ align:start position:0%
+the uh in the bonic stream but but there
+ 
+
+ align:start position:0%
+the uh in the bonic stream but but there
+are some additional uh M this
+
+ align:start position:0%
+are some additional uh M this
+ 
+
+ align:start position:0%
+are some additional uh M this
+mode depending on your conation or how
+
+ align:start position:0%
+mode depending on your conation or how
+ 
+
+ align:start position:0%
+mode depending on your conation or how
+you treat the fance in the super string
+
+ align:start position:0%
+you treat the fance in the super string
+ 
+
+ align:start position:0%
+you treat the fance in the super string
+then there can be say 2 a or 2
+
+ align:start position:0%
+then there can be say 2 a or 2
+ 
+
+ align:start position:0%
+then there can be say 2 a or 2
+B there two type of super string and one
+
+ align:start position:0%
+B there two type of super string and one
+ 
+
+ align:start position:0%
+B there two type of super string and one
+and and for 2 a you have one additional
+
+ align:start position:0%
+and and for 2 a you have one additional
+ 
+
+ align:start position:0%
+and and for 2 a you have one additional
+one form field and additional three form
+
+ align:start position:0%
+one form field and additional three form
+ 
+
+ align:start position:0%
+one form field and additional three form
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh and for 2B you have additional Scala
+
+ align:start position:0%
+uh and for 2B you have additional Scala
+ 
+
+ align:start position:0%
+uh and for 2B you have additional Scala
+field and additional two form
+
+ align:start position:0%
+field and additional two form
+ 
+
+ align:start position:0%
+field and additional two form
+field and additional four form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+okay in
+
+ align:start position:0%
+okay in
+ 
+
+ align:start position:0%
+okay in
+particular this is so- called
+
+ align:start position:0%
+particular this is so- called
+ 
+
+ align:start position:0%
+particular this is so- called
+selfdual I will explain that a little
+
+ align:start position:0%
+selfdual I will explain that a little
+ 
+
+ align:start position:0%
+selfdual I will explain that a little
+bit in the 2B container sa du for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form and
+
+ align:start position:0%
+form and
+ 
+
+ align:start position:0%
+form and
+this this additional field are called
+
+ align:start position:0%
+this this additional field are called
+ 
+
+ align:start position:0%
+this this additional field are called
+the raon remon field typically just a l
+
+ align:start position:0%
+the raon remon field typically just a l
+ 
+
+ align:start position:0%
+the raon remon field typically just a l
+called raon remon
+
+ align:start position:0%
+called raon remon
+ 
+
+ align:start position:0%
+called raon remon
+field and so this are called field
+
+ align:start position:0%
+field and so this are called field
+ 
+
+ align:start position:0%
+field and so this are called field
+okay uh C1 C3 uh C1 and C3 that's right
+
+ align:start position:0%
+okay uh C1 C3 uh C1 and C3 that's right
+ 
+
+ align:start position:0%
+okay uh C1 C3 uh C1 and C3 that's right
+they all called one field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so the story is essentially the
+
+ align:start position:0%
+yeah so the story is essentially the
+ 
+
+ align:start position:0%
+yeah so the story is essentially the
+same very similar as what we did for the
+
+ align:start position:0%
+same very similar as what we did for the
+ 
+
+ align:start position:0%
+same very similar as what we did for the
+bosonic string for the bosonic string
+
+ align:start position:0%
+bosonic string for the bosonic string
+ 
+
+ align:start position:0%
+bosonic string for the bosonic string
+you only have
+
+ align:start position:0%
+you only have
+ 
+
+ align:start position:0%
+you only have
+X on worksheet when you quantize X then
+
+ align:start position:0%
+X on worksheet when you quantize X then
+ 
+
+ align:start position:0%
+X on worksheet when you quantize X then
+you find the graviton you find the dot b
+
+ align:start position:0%
+you find the graviton you find the dot b
+ 
+
+ align:start position:0%
+you find the graviton you find the dot b
+you find the five and in the super
+
+ align:start position:0%
+you find the five and in the super
+ 
+
+ align:start position:0%
+you find the five and in the super
+string you put some additional fans on
+
+ align:start position:0%
+string you put some additional fans on
+ 
+
+ align:start position:0%
+string you put some additional fans on
+the worksheet and those fans give you
+
+ align:start position:0%
+the worksheet and those fans give you
+ 
+
+ align:start position:0%
+the worksheet and those fans give you
+additional modes and then you will uh
+
+ align:start position:0%
+additional modes and then you will uh
+ 
+
+ align:start position:0%
+additional modes and then you will uh
+have those additional uh that will also
+
+ align:start position:0%
+have those additional uh that will also
+ 
+
+ align:start position:0%
+have those additional uh that will also
+give rise to additional Mist modes in
+
+ align:start position:0%
+give rise to additional Mist modes in
+ 
+
+ align:start position:0%
+give rise to additional Mist modes in
+the SpaceTime and uh and those are this
+
+ align:start position:0%
+the SpaceTime and uh and those are this
+ 
+
+ align:start position:0%
+the SpaceTime and uh and those are this
+remon Fields okay um also there are they
+
+ align:start position:0%
+remon Fields okay um also there are they
+ 
+
+ align:start position:0%
+remon Fields okay um also there are they
+also Mass this fans which I we not right
+
+ align:start position:0%
+also Mass this fans which I we not right
+ 
+
+ align:start position:0%
+also Mass this fans which I we not right
+here yes so why is it the type 2 a and
+
+ align:start position:0%
+here yes so why is it the type 2 a and
+ 
+
+ align:start position:0%
+here yes so why is it the type 2 a and
+type 2 b string theory they appear to be
+
+ align:start position:0%
+type 2 b string theory they appear to be
+ 
+
+ align:start position:0%
+type 2 b string theory they appear to be
+very very different which seems bad it
+
+ align:start position:0%
+very very different which seems bad it
+ 
+
+ align:start position:0%
+very very different which seems bad it
+just seems like there's this arbitrary
+
+ align:start position:0%
+just seems like there's this arbitrary
+ 
+
+ align:start position:0%
+just seems like there's this arbitrary
+choice about how you go about doing the
+
+ align:start position:0%
+choice about how you go about doing the
+ 
+
+ align:start position:0%
+choice about how you go about doing the
+mathematics and you get this spectrum of
+
+ align:start position:0%
+mathematics and you get this spectrum of
+ 
+
+ align:start position:0%
+mathematics and you get this spectrum of
+particles or the Spectrum so how do you
+
+ align:start position:0%
+particles or the Spectrum so how do you
+ 
+
+ align:start position:0%
+particles or the Spectrum so how do you
+get around this problem
+
+ align:start position:0%
+get around this problem
+ 
+
+ align:start position:0%
+get around this problem
+um this is not the problem this is a
+
+ align:start position:0%
+um this is not the problem this is a
+ 
+
+ align:start position:0%
+um this is not the problem this is a
+fact of
+
+ align:start position:0%
+fact of
+ 
+
+ align:start position:0%
+fact of
+life um okay this is just what you
+
+ align:start position:0%
+life um okay this is just what you
+ 
+
+ align:start position:0%
+life um okay this is just what you
+find this is just what you find so which
+
+ align:start position:0%
+find this is just what you find so which
+ 
+
+ align:start position:0%
+find this is just what you find so which
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+right uh uh
+
+ align:start position:0%
+right uh uh
+ 
+
+ align:start position:0%
+right uh uh
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um they both can be right and they both
+
+ align:start position:0%
+um they both can be right and they both
+ 
+
+ align:start position:0%
+um they both can be right and they both
+can be wrong and uh and our our goal
+
+ align:start position:0%
+can be wrong and uh and our our goal
+ 
+
+ align:start position:0%
+can be wrong and uh and our our goal
+just to find all possible theories are
+
+ align:start position:0%
+just to find all possible theories are
+ 
+
+ align:start position:0%
+just to find all possible theories are
+there and uh and and these are just a
+
+ align:start position:0%
+there and uh and and these are just a
+ 
+
+ align:start position:0%
+there and uh and and these are just a
+loud
+
+ align:start position:0%
+loud
+ 
+
+ align:start position:0%
+loud
+quantizations a lot consistent
+
+ align:start position:0%
+quantizations a lot consistent
+ 
+
+ align:start position:0%
+quantizations a lot consistent
+quantizations okay yeah and and both
+
+ align:start position:0%
+quantizations okay yeah and and both
+ 
+
+ align:start position:0%
+quantizations okay yeah and and both
+both of them give you consistent quantum
+
+ align:start position:0%
+both of them give you consistent quantum
+ 
+
+ align:start position:0%
+both of them give you consistent quantum
+gravity and uh if I have time if this is
+
+ align:start position:0%
+gravity and uh if I have time if this is
+ 
+
+ align:start position:0%
+gravity and uh if I have time if this is
+a stren three class If This Were a stren
+
+ align:start position:0%
+a stren three class If This Were a stren
+ 
+
+ align:start position:0%
+a stren three class If This Were a stren
+class then I would explain that actually
+
+ align:start position:0%
+class then I would explain that actually
+ 
+
+ align:start position:0%
+class then I would explain that actually
+uh secretly they are equivalent
+
+ align:start position:0%
+uh secretly they are equivalent
+ 
+
+ align:start position:0%
+uh secretly they are equivalent
+SEC they equivalent okay and uh um yeah
+
+ align:start position:0%
+SEC they equivalent okay and uh um yeah
+ 
+
+ align:start position:0%
+SEC they equivalent okay and uh um yeah
+so so in some sense uh they're not that
+
+ align:start position:0%
+so so in some sense uh they're not that
+ 
+
+ align:start position:0%
+so so in some sense uh they're not that
+different I see yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay anyway for our purpose at the
+
+ align:start position:0%
+yeah okay anyway for our purpose at the
+ 
+
+ align:start position:0%
+yeah okay anyway for our purpose at the
+perative level uh uh when we consider
+
+ align:start position:0%
+perative level uh uh when we consider
+ 
+
+ align:start position:0%
+perative level uh uh when we consider
+the coupling string coupling to be small
+
+ align:start position:0%
+the coupling string coupling to be small
+ 
+
+ align:start position:0%
+the coupling string coupling to be small
+then then they appear to be different
+
+ align:start position:0%
+then then they appear to be different
+ 
+
+ align:start position:0%
+then then they appear to be different
+uh and yeah we have two type of stren
+
+ align:start position:0%
+uh and yeah we have two type of stren
+ 
+
+ align:start position:0%
+uh and yeah we have two type of stren
+here okay and let me mention a little
+
+ align:start position:0%
+here okay and let me mention a little
+ 
+
+ align:start position:0%
+here okay and let me mention a little
+bit those forms so this all these are
+
+ align:start position:0%
+bit those forms so this all these are
+ 
+
+ align:start position:0%
+bit those forms so this all these are
+anti- symmetric
+
+ align:start position:0%
+anti- symmetric
+ 
+
+ align:start position:0%
+anti- symmetric
+potentials so this anti symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentials are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generations of the uh of the ma Max real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field the max real field a
+
+ align:start position:0%
+field the max real field a
+ 
+
+ align:start position:0%
+field the max real field a
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+okay so so mathematically you can write
+
+ align:start position:0%
+okay so so mathematically you can write
+ 
+
+ align:start position:0%
+okay so so mathematically you can write
+the uh uh uh say for example
+
+ align:start position:0%
+the uh uh uh say for example
+ 
+
+ align:start position:0%
+the uh uh uh say for example
+mathematically you can write the gauge
+
+ align:start position:0%
+mathematically you can write the gauge
+ 
+
+ align:start position:0%
+mathematically you can write the gauge
+field a
+
+ align:start position:0%
+field a
+ 
+
+ align:start position:0%
+field a
+mu as a so-called one
+
+ align:start position:0%
+mu as a so-called one
+ 
+
+ align:start position:0%
+mu as a so-called one
+form so-called one form and a mu is just
+
+ align:start position:0%
+form so-called one form and a mu is just
+ 
+
+ align:start position:0%
+form so-called one form and a mu is just
+coecient of this one form and then and
+
+ align:start position:0%
+coecient of this one form and then and
+ 
+
+ align:start position:0%
+coecient of this one form and then and
+then the field strings is just the
+
+ align:start position:0%
+then the field strings is just the
+ 
+
+ align:start position:0%
+then the field strings is just the
+derivative is just exterior derivative
+
+ align:start position:0%
+derivative is just exterior derivative
+ 
+
+ align:start position:0%
+derivative is just exterior derivative
+of this one
+
+ align:start position:0%
+of this one
+ 
+
+ align:start position:0%
+of this one
+form and then the uh
+
+ align:start position:0%
+form and then the uh
+ 
+
+ align:start position:0%
+form and then the uh
+Lin will be just minus one quarter F mu
+
+ align:start position:0%
+Lin will be just minus one quarter F mu
+ 
+
+ align:start position:0%
+Lin will be just minus one quarter F mu
+mu F mu mu okay construct from this uh
+
+ align:start position:0%
+mu F mu mu okay construct from this uh
+ 
+
+ align:start position:0%
+mu F mu mu okay construct from this uh
+procedure
+
+ align:start position:0%
+procedure
+ 
+
+ align:start position:0%
+procedure
+okay so you can just gener
+
+ align:start position:0%
+okay so you can just gener
+ 
+
+ align:start position:0%
+okay so you can just gener
+mathematically straightforward to
+
+ align:start position:0%
+mathematically straightforward to
+ 
+
+ align:start position:0%
+mathematically straightforward to
+generalize this to higher dimensional
+
+ align:start position:0%
+generalize this to higher dimensional
+ 
+
+ align:start position:0%
+generalize this to higher dimensional
+forms so for example we can consider n
+
+ align:start position:0%
+forms so for example we can consider n
+ 
+
+ align:start position:0%
+forms so for example we can consider n
+form which is the uh n component
+
+ align:start position:0%
+form which is the uh n component
+ 
+
+ align:start position:0%
+form which is the uh n component
+tensor
+
+ align:start position:0%
+tensor
+ 
+
+ align:start position:0%
+tensor
+but all indices are fully antisymmetric
+
+ align:start position:0%
+but all indices are fully antisymmetric
+ 
+
+ align:start position:0%
+but all indices are fully antisymmetric
+with each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other okay so all the indices are fully
+
+ align:start position:0%
+other okay so all the indices are fully
+ 
+
+ align:start position:0%
+other okay so all the indices are fully
+an symmetric with each other so this are
+
+ align:start position:0%
+an symmetric with each other so this are
+ 
+
+ align:start position:0%
+an symmetric with each other so this are
+fully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+antisymmetric okay depend on the
+
+ align:start position:0%
+antisymmetric okay depend on the
+ 
+
+ align:start position:0%
+antisymmetric okay depend on the
+convention sometimes we also put the one
+
+ align:start position:0%
+convention sometimes we also put the one
+ 
+
+ align:start position:0%
+convention sometimes we also put the one
+over factorial here okay
+
+ align:start position:0%
+over factorial here okay
+ 
+
+ align:start position:0%
+over factorial here okay
+anyway um so so you can Define such
+
+ align:start position:0%
+anyway um so so you can Define such
+ 
+
+ align:start position:0%
+anyway um so so you can Define such
+object such the generation of a and the
+
+ align:start position:0%
+object such the generation of a and the
+ 
+
+ align:start position:0%
+object such the generation of a and the
+corresponding fi strings for this
+
+ align:start position:0%
+corresponding fi strings for this
+ 
+
+ align:start position:0%
+corresponding fi strings for this
+C we also call
+
+ align:start position:0%
+C we also call
+ 
+
+ align:start position:0%
+C we also call
+F so we
+
+ align:start position:0%
+F so we
+ 
+
+ align:start position:0%
+F so we
+call so the F strength for C is just a m
+
+ align:start position:0%
+call so the F strength for C is just a m
+ 
+
+ align:start position:0%
+call so the F strength for C is just a m
+plus one form which is exterior
+
+ align:start position:0%
+plus one form which is exterior
+ 
+
+ align:start position:0%
+plus one form which is exterior
+derivative of
+
+ align:start position:0%
+derivative of
+ 
+
+ align:start position:0%
+derivative of
+DC okay and then this is n plus one form
+
+ align:start position:0%
+DC okay and then this is n plus one form
+ 
+
+ align:start position:0%
+DC okay and then this is n plus one form
+again this is a fully antisymmetric
+
+ align:start position:0%
+again this is a fully antisymmetric
+ 
+
+ align:start position:0%
+again this is a fully antisymmetric
+tensor now with n plus y indices okay
+
+ align:start position:0%
+tensor now with n plus y indices okay
+ 
+
+ align:start position:0%
+tensor now with n plus y indices okay
+and then you can write down your
+
+ align:start position:0%
+and then you can write down your
+ 
+
+ align:start position:0%
+and then you can write down your
+L similarly by by generalizing this you
+
+ align:start position:0%
+L similarly by by generalizing this you
+ 
+
+ align:start position:0%
+L similarly by by generalizing this you
+can write as one
+
+ align:start position:0%
+can write as one
+ 
+
+ align:start position:0%
+can write as one
+over maybe let me write it here can
+
+ align:start position:0%
+over maybe let me write it here can
+ 
+
+ align:start position:0%
+over maybe let me write it here can
+write it the grin as - 1/ half time M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factorial 2 * m factorial not 2 m
+
+ align:start position:0%
+factorial 2 * m factorial not 2 m
+ 
+
+ align:start position:0%
+factorial 2 * m factorial not 2 m
+factorial 2 * m factorial f 1 mu +
+
+ align:start position:0%
+factorial 2 * m factorial f 1 mu +
+ 
+
+ align:start position:0%
+factorial 2 * m factorial f 1 mu +
+1 F mu1 mu + 1 okay so f is a two form f
+
+ align:start position:0%
+1 F mu1 mu + 1 okay so f is a two form f
+ 
+
+ align:start position:0%
+1 F mu1 mu + 1 okay so f is a two form f
+is M plus one form so so it's a tensor
+
+ align:start position:0%
+is M plus one form so so it's a tensor
+ 
+
+ align:start position:0%
+is M plus one form so so it's a tensor
+with M plus one indices a fully anti
+
+ align:start position:0%
+with M plus one indices a fully anti
+ 
+
+ align:start position:0%
+with M plus one indices a fully anti
+symmetric symmetric under those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields so so those field essentially
+
+ align:start position:0%
+fields so so those field essentially
+ 
+
+ align:start position:0%
+fields so so those field essentially
+have this kind of structure okay
+
+ align:start position:0%
+have this kind of structure okay
+ 
+
+ align:start position:0%
+have this kind of structure okay
+essentially have this kind of structure
+
+ align:start position:0%
+essentially have this kind of structure
+ 
+
+ align:start position:0%
+essentially have this kind of structure
+and uh say the one form is is very
+
+ align:start position:0%
+and uh say the one form is is very
+ 
+
+ align:start position:0%
+and uh say the one form is is very
+similar to our Max well so this is a
+
+ align:start position:0%
+similar to our Max well so this is a
+ 
+
+ align:start position:0%
+similar to our Max well so this is a
+three form and this is a
+
+ align:start position:0%
+three form and this is a
+ 
+
+ align:start position:0%
+three form and this is a
+scaler then just a massive scaler then
+
+ align:start position:0%
+scaler then just a massive scaler then
+ 
+
+ align:start position:0%
+scaler then just a massive scaler then
+this is a two form whose failed strength
+
+ align:start position:0%
+this is a two form whose failed strength
+ 
+
+ align:start position:0%
+this is a two form whose failed strength
+will be a three form and then this is a
+
+ align:start position:0%
+will be a three form and then this is a
+ 
+
+ align:start position:0%
+will be a three form and then this is a
+four form such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and just by
+
+ align:start position:0%
+okay and just by
+ 
+
+ align:start position:0%
+okay and just by
+definition just
+
+ align:start position:0%
+definition just
+ 
+
+ align:start position:0%
+definition just
+like here there's a gauge symmetry
+
+ align:start position:0%
+like here there's a gauge symmetry
+ 
+
+ align:start position:0%
+like here there's a gauge symmetry
+because F equal to
+
+ align:start position:0%
+because F equal to
+ 
+
+ align:start position:0%
+because F equal to
+Da here because this is f equal to DC so
+
+ align:start position:0%
+Da here because this is f equal to DC so
+ 
+
+ align:start position:0%
+Da here because this is f equal to DC so
+there's a gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry because I can add
+
+ align:start position:0%
+symmetry because I can add
+ 
+
+ align:start position:0%
+symmetry because I can add
+CN the total
+
+ align:start position:0%
+CN the total
+ 
+
+ align:start position:0%
+CN the total
+derivative of n n +1 n minus one
+
+ align:start position:0%
+derivative of n n +1 n minus one
+ 
+
+ align:start position:0%
+derivative of n n +1 n minus one
+form okay so I can make a gug symmetry
+
+ align:start position:0%
+form okay so I can make a gug symmetry
+ 
+
+ align:start position:0%
+form okay so I can make a gug symmetry
+so so so Lambda n minus one can be n m
+
+ align:start position:0%
+so so so Lambda n minus one can be n m
+ 
+
+ align:start position:0%
+so so so Lambda n minus one can be n m
+minus y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+and because of this Square equal to
+
+ align:start position:0%
+and because of this Square equal to
+ 
+
+ align:start position:0%
+and because of this Square equal to
+zero then f is in wariant okay so FN
+
+ align:start position:0%
+zero then f is in wariant okay so FN
+ 
+
+ align:start position:0%
+zero then f is in wariant okay so FN
+plus one is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wariant so if you put this into here and
+
+ align:start position:0%
+wariant so if you put this into here and
+ 
+
+ align:start position:0%
+wariant so if you put this into here and
+because this is the because this is
+
+ align:start position:0%
+because this is the because this is
+ 
+
+ align:start position:0%
+because this is the because this is
+already a total derivative and so so f
+
+ align:start position:0%
+already a total derivative and so so f
+ 
+
+ align:start position:0%
+already a total derivative and so so f
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invariant
+
+ align:start position:0%
+invariant
+ 
+
+ align:start position:0%
+invariant
+um so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a gauge symmetry then there
+
+ align:start position:0%
+so there's a gauge symmetry then there
+ 
+
+ align:start position:0%
+so there's a gauge symmetry then there
+will be a conserved charge say
+
+ align:start position:0%
+will be a conserved charge say
+ 
+
+ align:start position:0%
+will be a conserved charge say
+associated with those M forms okay uh uh
+
+ align:start position:0%
+associated with those M forms okay uh uh
+ 
+
+ align:start position:0%
+associated with those M forms okay uh uh
+you can Define conserve charge associate
+
+ align:start position:0%
+you can Define conserve charge associate
+ 
+
+ align:start position:0%
+you can Define conserve charge associate
+with those M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forms so so far any
+
+ align:start position:0%
+forms so so far any
+ 
+
+ align:start position:0%
+forms so so far any
+questions so yes maybe so this C field
+
+ align:start position:0%
+questions so yes maybe so this C field
+ 
+
+ align:start position:0%
+questions so yes maybe so this C field
+does it denote Firs or B B it's all
+
+ align:start position:0%
+does it denote Firs or B B it's all
+ 
+
+ align:start position:0%
+does it denote Firs or B B it's all
+bosons that uh it
+
+ align:start position:0%
+bosons that uh it
+ 
+
+ align:start position:0%
+bosons that uh it
+looks so this anti symmetric has nothing
+
+ align:start position:0%
+looks so this anti symmetric has nothing
+ 
+
+ align:start position:0%
+looks so this anti symmetric has nothing
+to do with form no uh this just the
+
+ align:start position:0%
+to do with form no uh this just the
+ 
+
+ align:start position:0%
+to do with form no uh this just the
+indices this just indices which is
+
+ align:start position:0%
+indices this just indices which is
+ 
+
+ align:start position:0%
+indices this just indices which is
+symmetric this is not the uh this is not
+
+ align:start position:0%
+symmetric this is not the uh this is not
+ 
+
+ align:start position:0%
+symmetric this is not the uh this is not
+the uh location SpaceTime location yeah
+
+ align:start position:0%
+the uh location SpaceTime location yeah
+ 
+
+ align:start position:0%
+the uh location SpaceTime location yeah
+this just
+
+ align:start position:0%
+this just
+ 
+
+ align:start position:0%
+this just
+indices it's the same thing as in F mu
+
+ align:start position:0%
+indices it's the same thing as in F mu
+ 
+
+ align:start position:0%
+indices it's the same thing as in F mu
+in F mu the IND this anti symmetric yeah
+
+ align:start position:0%
+in F mu the IND this anti symmetric yeah
+ 
+
+ align:start position:0%
+in F mu the IND this anti symmetric yeah
+it's the same thing
+
+ align:start position:0%
+it's the same thing
+ 
+
+ align:start position:0%
+it's the same thing
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and are people comfortable with this
+
+ align:start position:0%
+and are people comfortable with this
+ 
+
+ align:start position:0%
+and are people comfortable with this
+differential form
+
+ align:start position:0%
+differential form
+ 
+
+ align:start position:0%
+differential form
+rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes B sounds they're all B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sounds sorry h and f are where are their
+
+ align:start position:0%
+sounds sorry h and f are where are their
+ 
+
+ align:start position:0%
+sounds sorry h and f are where are their
+supern oh the super part I did not write
+
+ align:start position:0%
+supern oh the super part I did not write
+ 
+
+ align:start position:0%
+supern oh the super part I did not write
+them down so they are also fonics they
+
+ align:start position:0%
+them down so they are also fonics they
+ 
+
+ align:start position:0%
+them down so they are also fonics they
+also M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fons yeah we will not worry we will not
+
+ align:start position:0%
+Fons yeah we will not worry we will not
+ 
+
+ align:start position:0%
+Fons yeah we will not worry we will not
+need to worry about them so there are M
+
+ align:start position:0%
+need to worry about them so there are M
+ 
+
+ align:start position:0%
+need to worry about them so there are M
+fans in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+right yeah just come from uh because uh
+
+ align:start position:0%
+right yeah just come from uh because uh
+ 
+
+ align:start position:0%
+right yeah just come from uh because uh
+um when you go to super string you have
+
+ align:start position:0%
+um when you go to super string you have
+ 
+
+ align:start position:0%
+um when you go to super string you have
+additional Fons on the worksheet and
+
+ align:start position:0%
+additional Fons on the worksheet and
+ 
+
+ align:start position:0%
+additional Fons on the worksheet and
+then they can give you additional uh
+
+ align:start position:0%
+then they can give you additional uh
+ 
+
+ align:start position:0%
+then they can give you additional uh
+masses modes essentially come from
+
+ align:start position:0%
+masses modes essentially come from
+ 
+
+ align:start position:0%
+masses modes essentially come from
+them yeah the
+
+ align:start position:0%
+them yeah the
+ 
+
+ align:start position:0%
+them yeah the
+story the real story is a littleit more
+
+ align:start position:0%
+story the real story is a littleit more
+ 
+
+ align:start position:0%
+story the real story is a littleit more
+complicated because actually in the
+
+ align:start position:0%
+complicated because actually in the
+ 
+
+ align:start position:0%
+complicated because actually in the
+super string even those come from those
+
+ align:start position:0%
+super string even those come from those
+ 
+
+ align:start position:0%
+super string even those come from those
+Fons War sheet Fons yeah but anyway uh
+
+ align:start position:0%
+Fons War sheet Fons yeah but anyway uh
+ 
+
+ align:start position:0%
+Fons War sheet Fons yeah but anyway uh
+because you have add fance to the W
+
+ align:start position:0%
+because you have add fance to the W
+ 
+
+ align:start position:0%
+because you have add fance to the W
+sheet then you have more more
+
+ align:start position:0%
+sheet then you have more more
+ 
+
+ align:start position:0%
+sheet then you have more more
+possibilities than that give rise to
+
+ align:start position:0%
+possibilities than that give rise to
+ 
+
+ align:start position:0%
+possibilities than that give rise to
+those modes yeah that's the r story that
+
+ align:start position:0%
+those modes yeah that's the r story that
+ 
+
+ align:start position:0%
+those modes yeah that's the r story that
+modes are also for bz not for FS no
+
+ align:start position:0%
+modes are also for bz not for FS no
+ 
+
+ align:start position:0%
+modes are also for bz not for FS no
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+are these are all the SpaceTime bonic
+
+ align:start position:0%
+are these are all the SpaceTime bonic
+ 
+
+ align:start position:0%
+are these are all the SpaceTime bonic
+fields which are low excitations of the
+
+ align:start position:0%
+fields which are low excitations of the
+ 
+
+ align:start position:0%
+fields which are low excitations of the
+strings and they how they arise on the W
+
+ align:start position:0%
+strings and they how they arise on the W
+ 
+
+ align:start position:0%
+strings and they how they arise on the W
+sheet whether they come from fans or
+
+ align:start position:0%
+sheet whether they come from fans or
+ 
+
+ align:start position:0%
+sheet whether they come from fans or
+from bosons on the W sheet it's a
+
+ align:start position:0%
+from bosons on the W sheet it's a
+ 
+
+ align:start position:0%
+from bosons on the W sheet it's a
+separate issue yeah and uh in fact all
+
+ align:start position:0%
+separate issue yeah and uh in fact all
+ 
+
+ align:start position:0%
+separate issue yeah and uh in fact all
+of them actually arise from war she
+
+ align:start position:0%
+of them actually arise from war she
+ 
+
+ align:start position:0%
+of them actually arise from war she
+fans but their space time
+
+ align:start position:0%
+fans but their space time
+ 
+
+ align:start position:0%
+fans but their space time
+bons yes that's for the spin ority of
+
+ align:start position:0%
+bons yes that's for the spin ority of
+ 
+
+ align:start position:0%
+bons yes that's for the spin ority of
+these yeah you you just work out their
+
+ align:start position:0%
+these yeah you you just work out their
+ 
+
+ align:start position:0%
+these yeah you you just work out their
+uh their representations under the um
+
+ align:start position:0%
+uh their representations under the um
+ 
+
+ align:start position:0%
+uh their representations under the um
+under the St laen symetry okay it's
+
+ align:start position:0%
+under the St laen symetry okay it's
+ 
+
+ align:start position:0%
+under the St laen symetry okay it's
+not they're all integer spin they're all
+
+ align:start position:0%
+not they're all integer spin they're all
+ 
+
+ align:start position:0%
+not they're all integer spin they're all
+integer spin they're all integer spin
+
+ align:start position:0%
+integer spin they're all integer spin
+ 
+
+ align:start position:0%
+integer spin they're all integer spin
+reputations say of the Len group and not
+
+ align:start position:0%
+reputations say of the Len group and not
+ 
+
+ align:start position:0%
+reputations say of the Len group and not
+like fans then will be half integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah they they're generating
+
+ align:start position:0%
+yeah yeah they they're generating
+ 
+
+ align:start position:0%
+yeah yeah they they're generating
+representations of the rotational group
+
+ align:start position:0%
+representations of the rotational group
+ 
+
+ align:start position:0%
+representations of the rotational group
+yeah so so so they are like a spin two
+
+ align:start position:0%
+yeah so so so they are like a spin two
+ 
+
+ align:start position:0%
+yeah so so so they are like a spin two
+SP no normally we don't call them spin
+
+ align:start position:0%
+SP no normally we don't call them spin
+ 
+
+ align:start position:0%
+SP no normally we don't call them spin
+two or spin three when when we call spin
+
+ align:start position:0%
+two or spin three when when we call spin
+ 
+
+ align:start position:0%
+two or spin three when when we call spin
+two we mean the fully symmetric indices
+
+ align:start position:0%
+two we mean the fully symmetric indices
+ 
+
+ align:start position:0%
+two we mean the fully symmetric indices
+symmetric and
+
+ align:start position:0%
+symmetric and
+ 
+
+ align:start position:0%
+symmetric and
+we never call uh uh yeah we don't call
+
+ align:start position:0%
+we never call uh uh yeah we don't call
+ 
+
+ align:start position:0%
+we never call uh uh yeah we don't call
+them spin uh yeah but yeah just the
+
+ align:start position:0%
+them spin uh yeah but yeah just the
+ 
+
+ align:start position:0%
+them spin uh yeah but yeah just the
+representation of L group it's yeah just
+
+ align:start position:0%
+representation of L group it's yeah just
+ 
+
+ align:start position:0%
+representation of L group it's yeah just
+some representations uh this integer um
+
+ align:start position:0%
+some representations uh this integer um
+ 
+
+ align:start position:0%
+some representations uh this integer um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+good and in the case of the
+
+ align:start position:0%
+good and in the case of the
+ 
+
+ align:start position:0%
+good and in the case of the
+Maxwell we
+
+ align:start position:0%
+Maxwell we
+ 
+
+ align:start position:0%
+Maxwell we
+know that for the one
+
+ align:start position:0%
+know that for the one
+ 
+
+ align:start position:0%
+know that for the one
+form for the for the case of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Maxwell it source we are familiar with
+
+ align:start position:0%
+Maxwell it source we are familiar with
+ 
+
+ align:start position:0%
+Maxwell it source we are familiar with
+this it's a source is a point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle okay
+
+ align:start position:0%
+particle okay
+ 
+
+ align:start position:0%
+particle okay
+so we can we can CLE
+
+ align:start position:0%
+so we can we can CLE
+ 
+
+ align:start position:0%
+so we can we can CLE
+the so the point particle interact say
+
+ align:start position:0%
+the so the point particle interact say
+ 
+
+ align:start position:0%
+the so the point particle interact say
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+external EV potential in the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so suppose a particle following some
+
+ align:start position:0%
+way so suppose a particle following some
+ 
+
+ align:start position:0%
+way so suppose a particle following some
+trajectory described by uh by X
+
+ align:start position:0%
+trajectory described by uh by X
+ 
+
+ align:start position:0%
+trajectory described by uh by X
+mutal and then and then this particle
+
+ align:start position:0%
+mutal and then and then this particle
+ 
+
+ align:start position:0%
+mutal and then and then this particle
+will interact with this gate uh this
+
+ align:start position:0%
+will interact with this gate uh this
+ 
+
+ align:start position:0%
+will interact with this gate uh this
+Vector potential in the following way
+
+ align:start position:0%
+Vector potential in the following way
+ 
+
+ align:start position:0%
+Vector potential in the following way
+this is familiar from E and
+
+ align:start position:0%
+this is familiar from E and
+ 
+
+ align:start position:0%
+this is familiar from E and
+M uh so you just integrate essentially
+
+ align:start position:0%
+M uh so you just integrate essentially
+ 
+
+ align:start position:0%
+M uh so you just integrate essentially
+this a along the trajectory
+
+ align:start position:0%
+this a along the trajectory
+ 
+
+ align:start position:0%
+this a along the trajectory
+uh of the particle and you can write it
+
+ align:start position:0%
+uh of the particle and you can write it
+ 
+
+ align:start position:0%
+uh of the particle and you can write it
+this in the more compact mathematical
+
+ align:start position:0%
+this in the more compact mathematical
+ 
+
+ align:start position:0%
+this in the more compact mathematical
+form you just say you integrate along
+
+ align:start position:0%
+form you just say you integrate along
+ 
+
+ align:start position:0%
+form you just say you integrate along
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+trajectory and they and a is a one form
+
+ align:start position:0%
+trajectory and they and a is a one form
+ 
+
+ align:start position:0%
+trajectory and they and a is a one form
+and you just integrate this one form
+
+ align:start position:0%
+and you just integrate this one form
+ 
+
+ align:start position:0%
+and you just integrate this one form
+along the trajectory okay and uh so this
+
+ align:start position:0%
+along the trajectory okay and uh so this
+ 
+
+ align:start position:0%
+along the trajectory okay and uh so this
+is um say it's so-call
+
+ align:start position:0%
+is um say it's so-call
+ 
+
+ align:start position:0%
+is um say it's so-call
+pullback of this one form a to c okay to
+
+ align:start position:0%
+pullback of this one form a to c okay to
+ 
+
+ align:start position:0%
+pullback of this one form a to c okay to
+see okay yeah so this is the
+
+ align:start position:0%
+see okay yeah so this is the
+ 
+
+ align:start position:0%
+see okay yeah so this is the
+mathematical language um um um yeah
+
+ align:start position:0%
+mathematical language um um um yeah
+ 
+
+ align:start position:0%
+mathematical language um um um yeah
+similarly you can generalize to this
+
+ align:start position:0%
+similarly you can generalize to this
+ 
+
+ align:start position:0%
+similarly you can generalize to this
+higher dimensional
+
+ align:start position:0%
+higher dimensional
+ 
+
+ align:start position:0%
+higher dimensional
+forms
+
+ align:start position:0%
+forms
+ 
+
+ align:start position:0%
+forms
+so so one form naturally coup to a point
+
+ align:start position:0%
+so so one form naturally coup to a point
+ 
+
+ align:start position:0%
+so so one form naturally coup to a point
+particle which can be considered as a
+
+ align:start position:0%
+particle which can be considered as a
+ 
+
+ align:start position:0%
+particle which can be considered as a
+zero dimensional
+
+ align:start position:0%
+zero dimensional
+ 
+
+ align:start position:0%
+zero dimensional
+object so a p+ one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form p+ one form then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+naturally
+
+ align:start position:0%
+naturally
+ 
+
+ align:start position:0%
+naturally
+then yeah I should say is for then a p
+
+ align:start position:0%
+then yeah I should say is for then a p
+ 
+
+ align:start position:0%
+then yeah I should say is for then a p
+dimensional object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the naturally compost just as a
+
+ align:start position:0%
+the naturally compost just as a
+ 
+
+ align:start position:0%
+the naturally compost just as a
+generation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+compose to a p+ one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form okay as follows you can just you so
+
+ align:start position:0%
+form okay as follows you can just you so
+ 
+
+ align:start position:0%
+form okay as follows you can just you so
+the W volume of a p dimensional
+
+ align:start position:0%
+the W volume of a p dimensional
+ 
+
+ align:start position:0%
+the W volume of a p dimensional
+object is a surface of p plus one
+
+ align:start position:0%
+object is a surface of p plus one
+ 
+
+ align:start position:0%
+object is a surface of p plus one
+dimension okay so the world volume of P
+
+ align:start position:0%
+dimension okay so the world volume of P
+ 
+
+ align:start position:0%
+dimension okay so the world volume of P
+Dimension object P plus one dimension
+
+ align:start position:0%
+Dimension object P plus one dimension
+ 
+
+ align:start position:0%
+Dimension object P plus one dimension
+because there's also time you also moov
+
+ align:start position:0%
+because there's also time you also moov
+ 
+
+ align:start position:0%
+because there's also time you also moov
+in the it's a p dimensional object
+
+ align:start position:0%
+in the it's a p dimensional object
+ 
+
+ align:start position:0%
+in the it's a p dimensional object
+moving in the time then a p plus y
+
+ align:start position:0%
+moving in the time then a p plus y
+ 
+
+ align:start position:0%
+moving in the time then a p plus y
+Dimension so let me call that one volume
+
+ align:start position:0%
+Dimension so let me call that one volume
+ 
+
+ align:start position:0%
+Dimension so let me call that one volume
+Sigma and then the L generation of this
+
+ align:start position:0%
+Sigma and then the L generation of this
+ 
+
+ align:start position:0%
+Sigma and then the L generation of this
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+the cing between a two diens a p
+
+ align:start position:0%
+the cing between a two diens a p
+ 
+
+ align:start position:0%
+the cing between a two diens a p
+dimensional object to a p plus one form
+
+ align:start position:0%
+dimensional object to a p plus one form
+ 
+
+ align:start position:0%
+dimensional object to a p plus one form
+will be like this just you integrate
+
+ align:start position:0%
+will be like this just you integrate
+ 
+
+ align:start position:0%
+will be like this just you integrate
+this p+ one form on the word
+
+ align:start position:0%
+this p+ one form on the word
+ 
+
+ align:start position:0%
+this p+ one form on the word
+volume of this P dimensional object
+
+ align:start position:0%
+volume of this P dimensional object
+ 
+
+ align:start position:0%
+volume of this P dimensional object
+okay and again this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pullback of C to
+
+ align:start position:0%
+pullback of C to
+ 
+
+ align:start position:0%
+pullback of C to
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+okay C+ one to
+
+ align:start position:0%
+okay C+ one to
+ 
+
+ align:start position:0%
+okay C+ one to
+Sigma and uh and let me just write it in
+
+ align:start position:0%
+Sigma and uh and let me just write it in
+ 
+
+ align:start position:0%
+Sigma and uh and let me just write it in
+a more explicit
+
+ align:start position:0%
+a more explicit
+ 
+
+ align:start position:0%
+a more explicit
+form so here I use a tow to parameterize
+
+ align:start position:0%
+form so here I use a tow to parameterize
+ 
+
+ align:start position:0%
+form so here I use a tow to parameterize
+a trajectory along the W line so here
+
+ align:start position:0%
+a trajectory along the W line so here
+ 
+
+ align:start position:0%
+a trajectory along the W line so here
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+use to parameterize the world volume
+
+ align:start position:0%
+use to parameterize the world volume
+ 
+
+ align:start position:0%
+use to parameterize the world volume
+coordinate of this brain then then this
+
+ align:start position:0%
+coordinate of this brain then then this
+ 
+
+ align:start position:0%
+coordinate of this brain then then this
+pullback
+
+ align:start position:0%
+pullback
+ 
+
+ align:start position:0%
+pullback
+means mu1 mu p + 1
+
+ align:start position:0%
+means mu1 mu p + 1
+ 
+
+ align:start position:0%
+means mu1 mu p + 1
+partial X
+
+ align:start position:0%
+partial X
+ 
+
+ align:start position:0%
+partial X
+mu1 partial s
+
+ align:start position:0%
+mu1 partial s
+ 
+
+ align:start position:0%
+mu1 partial s
+One X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu+ and X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu i
+
+ align:start position:0%
+mu i
+ 
+
+ align:start position:0%
+mu i
+1ai z to
+
+ align:start position:0%
+1ai z to
+ 
+
+ align:start position:0%
+1ai z to
+p uh
+
+ align:start position:0%
+p uh
+ 
+
+ align:start position:0%
+p uh
+um describe the iding of Sigma in space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so it tells you that yeah so this
+
+ align:start position:0%
+this so it tells you that yeah so this
+ 
+
+ align:start position:0%
+this so it tells you that yeah so this
+just tells you that the uh um well there
+
+ align:start position:0%
+just tells you that the uh um well there
+ 
+
+ align:start position:0%
+just tells you that the uh um well there
+is one to P plus one but there is z to
+
+ align:start position:0%
+is one to P plus one but there is z to
+ 
+
+ align:start position:0%
+is one to P plus one but there is z to
+P good notation may we just do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+yes so here the the the P dimensional
+
+ align:start position:0%
+yes so here the the the P dimensional
+ 
+
+ align:start position:0%
+yes so here the the the P dimensional
+object in the simple case is just like
+
+ align:start position:0%
+object in the simple case is just like
+ 
+
+ align:start position:0%
+object in the simple case is just like
+the the point particle is a zero
+
+ align:start position:0%
+the the point particle is a zero
+ 
+
+ align:start position:0%
+the the point particle is a zero
+dimensional object so that's what the
+
+ align:start position:0%
+dimensional object so that's what the
+ 
+
+ align:start position:0%
+dimensional object so that's what the
+object is that's right that's right yeah
+
+ align:start position:0%
+object is that's right that's right yeah
+ 
+
+ align:start position:0%
+object is that's right that's right yeah
+so so yeah uh the zero dimensional
+
+ align:start position:0%
+so so yeah uh the zero dimensional
+ 
+
+ align:start position:0%
+so so yeah uh the zero dimensional
+object naturally C to one form in this
+
+ align:start position:0%
+object naturally C to one form in this
+ 
+
+ align:start position:0%
+object naturally C to one form in this
+way and then a p dimensional object
+
+ align:start position:0%
+way and then a p dimensional object
+ 
+
+ align:start position:0%
+way and then a p dimensional object
+naturally C of p plus one dimensional
+
+ align:start position:0%
+naturally C of p plus one dimensional
+ 
+
+ align:start position:0%
+naturally C of p plus one dimensional
+this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just just like in the in the MK Square
+
+ align:start position:0%
+just just like in the in the MK Square
+ 
+
+ align:start position:0%
+just just like in the in the MK Square
+case the gug Symmetry
+
+ align:start position:0%
+case the gug Symmetry
+ 
+
+ align:start position:0%
+case the gug Symmetry
+here the gug Symmetry here implies that
+
+ align:start position:0%
+here the gug Symmetry here implies that
+ 
+
+ align:start position:0%
+here the gug Symmetry here implies that
+electric charge is conserved okay the
+
+ align:start position:0%
+electric charge is conserved okay the
+ 
+
+ align:start position:0%
+electric charge is conserved okay the
+electric charge is conserved so for for
+
+ align:start position:0%
+electric charge is conserved so for for
+ 
+
+ align:start position:0%
+electric charge is conserved so for for
+p dimensional
+
+ align:start position:0%
+p dimensional
+ 
+
+ align:start position:0%
+p dimensional
+object C to a p plus one dimensional
+
+ align:start position:0%
+object C to a p plus one dimensional
+ 
+
+ align:start position:0%
+object C to a p plus one dimensional
+form and because of this gaug
+
+ align:start position:0%
+form and because of this gaug
+ 
+
+ align:start position:0%
+form and because of this gaug
+Symmetry and uh and this charge is also
+
+ align:start position:0%
+Symmetry and uh and this charge is also
+ 
+
+ align:start position:0%
+Symmetry and uh and this charge is also
+conserved okay uh uh this charge is also
+
+ align:start position:0%
+conserved okay uh uh this charge is also
+ 
+
+ align:start position:0%
+conserved okay uh uh this charge is also
+conserved in particular the object with
+
+ align:start position:0%
+conserved in particular the object with
+ 
+
+ align:start position:0%
+conserved in particular the object with
+a minimal charge must be a stable object
+
+ align:start position:0%
+a minimal charge must be a stable object
+ 
+
+ align:start position:0%
+a minimal charge must be a stable object
+okay because there's nothing to Decay
+
+ align:start position:0%
+okay because there's nothing to Decay
+ 
+
+ align:start position:0%
+okay because there's nothing to Decay
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+so again as a
+
+ align:start position:0%
+so again as a
+ 
+
+ align:start position:0%
+so again as a
+generation of this
+
+ align:start position:0%
+generation of this
+ 
+
+ align:start position:0%
+generation of this
+case so in the standard
+
+ align:start position:0%
+case so in the standard
+ 
+
+ align:start position:0%
+case so in the standard
+story in the standard electromagnetism
+
+ align:start position:0%
+story in the standard electromagnetism
+ 
+
+ align:start position:0%
+story in the standard electromagnetism
+we can have electric charged
+
+ align:start position:0%
+we can have electric charged
+ 
+
+ align:start position:0%
+we can have electric charged
+particle we can also have a magnetic
+
+ align:start position:0%
+particle we can also have a magnetic
+ 
+
+ align:start position:0%
+particle we can also have a magnetic
+charged particle okay we can have a um
+
+ align:start position:0%
+charged particle okay we can have a um
+ 
+
+ align:start position:0%
+charged particle okay we can have a um
+magnetic charged particle um in
+
+ align:start position:0%
+magnetic charged particle um in
+ 
+
+ align:start position:0%
+magnetic charged particle um in
+particular you can
+
+ align:start position:0%
+particular you can
+ 
+
+ align:start position:0%
+particular you can
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+um talk about the magnetic monopo in
+
+ align:start position:0%
+um talk about the magnetic monopo in
+ 
+
+ align:start position:0%
+um talk about the magnetic monopo in
+quantum mechanics and Etc even though we
+
+ align:start position:0%
+quantum mechanics and Etc even though we
+ 
+
+ align:start position:0%
+quantum mechanics and Etc even though we
+have not observed them even though we
+
+ align:start position:0%
+have not observed them even though we
+ 
+
+ align:start position:0%
+have not observed them even though we
+have not observed them so similarly one
+
+ align:start position:0%
+have not observed them so similarly one
+ 
+
+ align:start position:0%
+have not observed them so similarly one
+can generalize that concept to to higher
+
+ align:start position:0%
+can generalize that concept to to higher
+ 
+
+ align:start position:0%
+can generalize that concept to to higher
+Dimensions so let me uh first just
+
+ align:start position:0%
+Dimensions so let me uh first just
+ 
+
+ align:start position:0%
+Dimensions so let me uh first just
+remind you uh how we Define the magnetic
+
+ align:start position:0%
+remind you uh how we Define the magnetic
+ 
+
+ align:start position:0%
+remind you uh how we Define the magnetic
+so mathematical way how we Define the
+
+ align:start position:0%
+so mathematical way how we Define the
+ 
+
+ align:start position:0%
+so mathematical way how we Define the
+mathematically charged object in m so
+
+ align:start position:0%
+mathematically charged object in m so
+ 
+
+ align:start position:0%
+mathematically charged object in m so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+M so because f is a twofold
+
+ align:start position:0%
+M so because f is a twofold
+ 
+
+ align:start position:0%
+M so because f is a twofold
+okay we can dualize f so this is H
+
+ align:start position:0%
+okay we can dualize f so this is H
+ 
+
+ align:start position:0%
+okay we can dualize f so this is H
+dual we can Define another form which I
+
+ align:start position:0%
+dual we can Define another form which I
+ 
+
+ align:start position:0%
+dual we can Define another form which I
+call F
+
+ align:start position:0%
+call F
+ 
+
+ align:start position:0%
+call F
+Thea which is related to original F by
+
+ align:start position:0%
+Thea which is related to original F by
+ 
+
+ align:start position:0%
+Thea which is related to original F by
+by H du so this is a two form the HUD of
+
+ align:start position:0%
+by H du so this is a two form the HUD of
+ 
+
+ align:start position:0%
+by H du so this is a two form the HUD of
+a two form in the four dimension is
+
+ align:start position:0%
+a two form in the four dimension is
+ 
+
+ align:start position:0%
+a two form in the four dimension is
+another two
+
+ align:start position:0%
+another two
+ 
+
+ align:start position:0%
+another two
+form and then then I can write it
+
+ align:start position:0%
+form and then then I can write it
+ 
+
+ align:start position:0%
+form and then then I can write it
+as the total derivative of the of L one
+
+ align:start position:0%
+as the total derivative of the of L one
+ 
+
+ align:start position:0%
+as the total derivative of the of L one
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+potential and then the then the
+
+ align:start position:0%
+potential and then the then the
+ 
+
+ align:start position:0%
+potential and then the then the
+object so you know that under this dual
+
+ align:start position:0%
+object so you know that under this dual
+ 
+
+ align:start position:0%
+object so you know that under this dual
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+f01 is mapped to F TAA 23 so electric
+
+ align:start position:0%
+f01 is mapped to F TAA 23 so electric
+ 
+
+ align:start position:0%
+f01 is mapped to F TAA 23 so electric
+field is mapped to magnetic field and
+
+ align:start position:0%
+field is mapped to magnetic field and
+ 
+
+ align:start position:0%
+field is mapped to magnetic field and
+similarly the magnetic field here is
+
+ align:start position:0%
+similarly the magnetic field here is
+ 
+
+ align:start position:0%
+similarly the magnetic field here is
+mapped to the electric field here okay
+
+ align:start position:0%
+mapped to the electric field here okay
+ 
+
+ align:start position:0%
+mapped to the electric field here okay
+so under this hu okay under this H yeah
+
+ align:start position:0%
+so under this hu okay under this H yeah
+ 
+
+ align:start position:0%
+so under this hu okay under this H yeah
+I should not just write just write this
+
+ align:start position:0%
+I should not just write just write this
+ 
+
+ align:start position:0%
+I should not just write just write this
+so after some Min sign we not
+
+ align:start position:0%
+so after some Min sign we not
+ 
+
+ align:start position:0%
+so after some Min sign we not
+keep track of and uh on this H
+
+ align:start position:0%
+keep track of and uh on this H
+ 
+
+ align:start position:0%
+keep track of and uh on this H
+essentially say the electric field now I
+
+ align:start position:0%
+essentially say the electric field now I
+ 
+
+ align:start position:0%
+essentially say the electric field now I
+call magnetic field okay so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object cou to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thea then is magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charged
+
+ align:start position:0%
+charged
+ 
+
+ align:start position:0%
+charged
+okay mag that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charged because the because of the in
+
+ align:start position:0%
+charged because the because of the in
+ 
+
+ align:start position:0%
+charged because the because of the in
+terms of a
+
+ align:start position:0%
+terms of a
+ 
+
+ align:start position:0%
+terms of a
+Thea such objects that will generate
+
+ align:start position:0%
+Thea such objects that will generate
+ 
+
+ align:start position:0%
+Thea such objects that will generate
+electric field and from the our original
+
+ align:start position:0%
+electric field and from the our original
+ 
+
+ align:start position:0%
+electric field and from the our original
+F point is a magnetic field okay so that
+
+ align:start position:0%
+F point is a magnetic field okay so that
+ 
+
+ align:start position:0%
+F point is a magnetic field okay so that
+will be a magnetically charged
+
+ align:start position:0%
+will be a magnetically charged
+ 
+
+ align:start position:0%
+will be a magnetically charged
+object so uh essentially that's how we
+
+ align:start position:0%
+object so uh essentially that's how we
+ 
+
+ align:start position:0%
+object so uh essentially that's how we
+think about the magnetic miple in and
+
+ align:start position:0%
+think about the magnetic miple in and
+ 
+
+ align:start position:0%
+think about the magnetic miple in and
+M so this can also be generalized to
+
+ align:start position:0%
+M so this can also be generalized to
+ 
+
+ align:start position:0%
+M so this can also be generalized to
+this uh uh M form case so one can also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dualize duze
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+okay is that we introduce a lot of C
+
+ align:start position:0%
+okay is that we introduce a lot of C
+ 
+
+ align:start position:0%
+okay is that we introduce a lot of C
+Thea which is the Dual of DC so DC is
+
+ align:start position:0%
+Thea which is the Dual of DC so DC is
+ 
+
+ align:start position:0%
+Thea which is the Dual of DC so DC is
+the field strings for C so supp this is
+
+ align:start position:0%
+the field strings for C so supp this is
+ 
+
+ align:start position:0%
+the field strings for C so supp this is
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+form and uh and the D d c is a du is a
+
+ align:start position:0%
+form and uh and the D d c is a du is a
+ 
+
+ align:start position:0%
+form and uh and the D d c is a du is a
+fi strength of uh uh C and then I do a h
+
+ align:start position:0%
+fi strength of uh uh C and then I do a h
+ 
+
+ align:start position:0%
+fi strength of uh uh C and then I do a h
+dual and then uh I Define to be DCA
+
+ align:start position:0%
+dual and then uh I Define to be DCA
+ 
+
+ align:start position:0%
+dual and then uh I Define to be DCA
+okay I Define to be DCA and uh and
+
+ align:start position:0%
+okay I Define to be DCA and uh and
+ 
+
+ align:start position:0%
+okay I Define to be DCA and uh and
+DCA uh so this have M so this is M form
+
+ align:start position:0%
+DCA uh so this have M so this is M form
+ 
+
+ align:start position:0%
+DCA uh so this have M so this is M form
+when you do a field strange become M
+
+ align:start position:0%
+when you do a field strange become M
+ 
+
+ align:start position:0%
+when you do a field strange become M
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+form and when you do the H
+
+ align:start position:0%
+form and when you do the H
+ 
+
+ align:start position:0%
+form and when you do the H
+duel take uh when you take a h duel take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a the hot dual of M form is D minus n
+
+ align:start position:0%
+a the hot dual of M form is D minus n
+ 
+
+ align:start position:0%
+a the hot dual of M form is D minus n
+okay so so this is D minus
+
+ align:start position:0%
+okay so so this is D minus
+ 
+
+ align:start position:0%
+okay so so this is D minus
+nus
+
+ align:start position:0%
+nus
+ 
+
+ align:start position:0%
+nus
+2 okay so so this should be di should be
+
+ align:start position:0%
+2 okay so so this should be di should be
+ 
+
+ align:start position:0%
+2 okay so so this should be di should be
+a D minus nus 2 form because when you
+
+ align:start position:0%
+a D minus nus 2 form because when you
+ 
+
+ align:start position:0%
+a D minus nus 2 form because when you
+take the d then that makes into D minus
+
+ align:start position:0%
+take the d then that makes into D minus
+ 
+
+ align:start position:0%
+take the d then that makes into D minus
+nus one form and this H du take this m
+
+ align:start position:0%
+nus one form and this H du take this m
+ 
+
+ align:start position:0%
+nus one form and this H du take this m
+plus1 form into D minus n - one form
+
+ align:start position:0%
+plus1 form into D minus n - one form
+ 
+
+ align:start position:0%
+plus1 form into D minus n - one form
+okay so so you map M form to a D minus
+
+ align:start position:0%
+okay so so you map M form to a D minus
+ 
+
+ align:start position:0%
+okay so so you map M form to a D minus
+nus 2 form uh this du this so
+
+ align:start position:0%
+nus 2 form uh this du this so
+ 
+
+ align:start position:0%
+nus 2 form uh this du this so
+essentially it's the generation of the
+
+ align:start position:0%
+essentially it's the generation of the
+ 
+
+ align:start position:0%
+essentially it's the generation of the
+Electric magnetic
+
+ align:start position:0%
+Electric magnetic
+ 
+
+ align:start position:0%
+Electric magnetic
+dual of
+
+ align:start position:0%
+dual of
+ 
+
+ align:start position:0%
+dual of
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now now it's now you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coule a D minus M minus three
+
+ align:start position:0%
+coule a D minus M minus three
+ 
+
+ align:start position:0%
+coule a D minus M minus three
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CA okay to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ca and in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C in terms of original C so this is a
+
+ align:start position:0%
+C in terms of original C so this is a
+ 
+
+ align:start position:0%
+C in terms of original C so this is a
+magnetic object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a magnetic object just the same
+
+ align:start position:0%
+this is a magnetic object just the same
+ 
+
+ align:start position:0%
+this is a magnetic object just the same
+as we Define magnetic mon magnetic
+
+ align:start position:0%
+as we Define magnetic mon magnetic
+ 
+
+ align:start position:0%
+as we Define magnetic mon magnetic
+object or magnetic monopole for um for
+
+ align:start position:0%
+object or magnetic monopole for um for
+ 
+
+ align:start position:0%
+object or magnetic monopole for um for
+ym so is this clear yes um in order to
+
+ align:start position:0%
+ym so is this clear yes um in order to
+ 
+
+ align:start position:0%
+ym so is this clear yes um in order to
+write F A do we have to assume that
+
+ align:start position:0%
+write F A do we have to assume that
+ 
+
+ align:start position:0%
+write F A do we have to assume that
+there are no electric charges present oh
+
+ align:start position:0%
+there are no electric charges present oh
+ 
+
+ align:start position:0%
+there are no electric charges present oh
+yeah yeah that's a good point uh um no
+
+ align:start position:0%
+yeah yeah that's a good point uh um no
+ 
+
+ align:start position:0%
+yeah yeah that's a good point uh um no
+no you don't have to um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so so you do this you have to assume
+
+ align:start position:0%
+um so so you do this you have to assume
+ 
+
+ align:start position:0%
+um so so you do this you have to assume
+that the equation motion is satisfied
+
+ align:start position:0%
+that the equation motion is satisfied
+ 
+
+ align:start position:0%
+that the equation motion is satisfied
+you have to assume equation motion is
+
+ align:start position:0%
+you have to assume equation motion is
+ 
+
+ align:start position:0%
+you have to assume equation motion is
+satisfied then you can write this
+
+ align:start position:0%
+satisfied then you can write this
+ 
+
+ align:start position:0%
+satisfied then you can write this
+procedure
+
+ align:start position:0%
+procedure
+ 
+
+ align:start position:0%
+procedure
+yeah so but if if DF is equal to J and
+
+ align:start position:0%
+yeah so but if if DF is equal to J and
+ 
+
+ align:start position:0%
+yeah so but if if DF is equal to J and
+that is non zero so there are yeah uh so
+
+ align:start position:0%
+that is non zero so there are yeah uh so
+ 
+
+ align:start position:0%
+that is non zero so there are yeah uh so
+you have exactly the similar situation
+
+ align:start position:0%
+you have exactly the similar situation
+ 
+
+ align:start position:0%
+you have exactly the similar situation
+with and M just identical situation with
+
+ align:start position:0%
+with and M just identical situation with
+ 
+
+ align:start position:0%
+with and M just identical situation with
+and M just whatever you do in the e m
+
+ align:start position:0%
+and M just whatever you do in the e m
+ 
+
+ align:start position:0%
+and M just whatever you do in the e m
+you do it here
+
+ align:start position:0%
+you do it here
+ 
+
+ align:start position:0%
+you do it here
+so I I thought that we could only write
+
+ align:start position:0%
+so I I thought that we could only write
+ 
+
+ align:start position:0%
+so I I thought that we could only write
+FAL to
+
+ align:start position:0%
+FAL to
+ 
+
+ align:start position:0%
+FAL to
+Da because there were no
+
+ align:start position:0%
+Da because there were no
+ 
+
+ align:start position:0%
+Da because there were no
+magnetic uh no so so you can do that now
+
+ align:start position:0%
+magnetic uh no so so you can do that now
+ 
+
+ align:start position:0%
+magnetic uh no so so you can do that now
+you have to introduce some
+
+ align:start position:0%
+you have to introduce some
+ 
+
+ align:start position:0%
+you have to introduce some
+similarity so that's why the magnetic
+
+ align:start position:0%
+similarity so that's why the magnetic
+ 
+
+ align:start position:0%
+similarity so that's why the magnetic
+mon have a direct string uh that's why
+
+ align:start position:0%
+mon have a direct string uh that's why
+ 
+
+ align:start position:0%
+mon have a direct string uh that's why
+the magnetic mon have direct string then
+
+ align:start position:0%
+the magnetic mon have direct string then
+ 
+
+ align:start position:0%
+the magnetic mon have direct string then
+you have this direct quation condition
+
+ align:start position:0%
+you have this direct quation condition
+ 
+
+ align:start position:0%
+you have this direct quation condition
+ET say you would then say either in and
+
+ align:start position:0%
+ET say you would then say either in and
+ 
+
+ align:start position:0%
+ET say you would then say either in and
+M or in the in the uh in the quantum
+
+ align:start position:0%
+M or in the in the uh in the quantum
+ 
+
+ align:start position:0%
+M or in the in the uh in the quantum
+mechanics say in the gra quantum
+
+ align:start position:0%
+mechanics say in the gra quantum
+ 
+
+ align:start position:0%
+mechanics say in the gra quantum
+mechanics or or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orm um so are people familiar with the
+
+ align:start position:0%
+orm um so are people familiar with the
+ 
+
+ align:start position:0%
+orm um so are people familiar with the
+concept of magnetic monopo and d soal d
+
+ align:start position:0%
+concept of magnetic monopo and d soal d
+ 
+
+ align:start position:0%
+concept of magnetic monopo and d soal d
+string and D quantization
+
+ align:start position:0%
+string and D quantization
+ 
+
+ align:start position:0%
+string and D quantization
+condition yeah I saw some loading head
+
+ align:start position:0%
+condition yeah I saw some loading head
+ 
+
+ align:start position:0%
+condition yeah I saw some loading head
+yeah yeah so uh so you're not familiar
+
+ align:start position:0%
+yeah yeah so uh so you're not familiar
+ 
+
+ align:start position:0%
+yeah yeah so uh so you're not familiar
+with it and look at for for example uh
+
+ align:start position:0%
+with it and look at for for example uh
+ 
+
+ align:start position:0%
+with it and look at for for example uh
+uh in in one chapter of Jackson uh have
+
+ align:start position:0%
+uh in in one chapter of Jackson uh have
+ 
+
+ align:start position:0%
+uh in in one chapter of Jackson uh have
+a very uh detailed discussion of
+
+ align:start position:0%
+a very uh detailed discussion of
+ 
+
+ align:start position:0%
+a very uh detailed discussion of
+magnetic monopoles and uh um but the
+
+ align:start position:0%
+magnetic monopoles and uh um but the
+ 
+
+ align:start position:0%
+magnetic monopoles and uh um but the
+best actually was the original paper uh
+
+ align:start position:0%
+best actually was the original paper uh
+ 
+
+ align:start position:0%
+best actually was the original paper uh
+it was really beautiful very very
+
+ align:start position:0%
+it was really beautiful very very
+ 
+
+ align:start position:0%
+it was really beautiful very very
+beautiful uh yeah but Jackson has a
+
+ align:start position:0%
+beautiful uh yeah but Jackson has a
+ 
+
+ align:start position:0%
+beautiful uh yeah but Jackson has a
+rather pedagogic discussion yeah
+
+ align:start position:0%
+rather pedagogic discussion yeah
+ 
+
+ align:start position:0%
+rather pedagogic discussion yeah
+Jackson's in actual in actual Dynamics
+
+ align:start position:0%
+Jackson's in actual in actual Dynamics
+ 
+
+ align:start position:0%
+Jackson's in actual in actual Dynamics
+has rather yeah we do see discussion
+
+ align:start position:0%
+has rather yeah we do see discussion
+ 
+
+ align:start position:0%
+has rather yeah we do see discussion
+differential form though or I don't
+
+ align:start position:0%
+differential form though or I don't
+ 
+
+ align:start position:0%
+differential form though or I don't
+remember you mean Jackson yeah I don't
+
+ align:start position:0%
+remember you mean Jackson yeah I don't
+ 
+
+ align:start position:0%
+remember you mean Jackson yeah I don't
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+yeah yeah it's the fact that you you can
+
+ align:start position:0%
+yeah yeah it's the fact that you you can
+ 
+
+ align:start position:0%
+yeah yeah it's the fact that you you can
+allow the magnetic monopo uh uh then if
+
+ align:start position:0%
+allow the magnetic monopo uh uh then if
+ 
+
+ align:start position:0%
+allow the magnetic monopo uh uh then if
+you allow the certain singularities in
+
+ align:start position:0%
+you allow the certain singularities in
+ 
+
+ align:start position:0%
+you allow the certain singularities in
+the vector potential and so that's soal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derx yeah so you don't have to introduce
+
+ align:start position:0%
+derx yeah so you don't have to introduce
+ 
+
+ align:start position:0%
+derx yeah so you don't have to introduce
+yeah so the idea is that
+
+ align:start position:0%
+yeah so the idea is that
+ 
+
+ align:start position:0%
+yeah so the idea is that
+you what you were saying is right the
+
+ align:start position:0%
+you what you were saying is right the
+ 
+
+ align:start position:0%
+you what you were saying is right the
+fact that you can write f as a da means
+
+ align:start position:0%
+fact that you can write f as a da means
+ 
+
+ align:start position:0%
+fact that you can write f as a da means
+there's no magnetic Source but you can
+
+ align:start position:0%
+there's no magnetic Source but you can
+ 
+
+ align:start position:0%
+there's no magnetic Source but you can
+introduce a magnetic Source if you allow
+
+ align:start position:0%
+introduce a magnetic Source if you allow
+ 
+
+ align:start position:0%
+introduce a magnetic Source if you allow
+certain similarities and uh and that's
+
+ align:start position:0%
+certain similarities and uh and that's
+ 
+
+ align:start position:0%
+certain similarities and uh and that's
+what the uh uh uh what rock
+
+ align:start position:0%
+what the uh uh uh what rock
+ 
+
+ align:start position:0%
+what the uh uh uh what rock
+realized
+
+ align:start position:0%
+realized
+ 
+
+ align:start position:0%
+realized
+yeah good
+
+ align:start position:0%
+yeah good
+ 
+
+ align:start position:0%
+yeah good
+so now these are St this are the gauge
+
+ align:start position:0%
+so now these are St this are the gauge
+ 
+
+ align:start position:0%
+so now these are St this are the gauge
+fields in type 2 a and type 2 b string
+
+ align:start position:0%
+fields in type 2 a and type 2 b string
+ 
+
+ align:start position:0%
+fields in type 2 a and type 2 b string
+and then then they can give rise to um
+
+ align:start position:0%
+and then then they can give rise to um
+ 
+
+ align:start position:0%
+and then then they can give rise to um
+to Extended object which CER to them and
+
+ align:start position:0%
+to Extended object which CER to them and
+ 
+
+ align:start position:0%
+to Extended object which CER to them and
+turn out the the extended object cover
+
+ align:start position:0%
+turn out the the extended object cover
+ 
+
+ align:start position:0%
+turn out the the extended object cover
+to those remone remon fields are
+
+ align:start position:0%
+to those remone remon fields are
+ 
+
+ align:start position:0%
+to those remone remon fields are
+precisely
+
+ align:start position:0%
+precisely
+ 
+
+ align:start position:0%
+precisely
+deep a precisely de brains and uh and
+
+ align:start position:0%
+deep a precisely de brains and uh and
+ 
+
+ align:start position:0%
+deep a precisely de brains and uh and
+the precisely de brains and because the
+
+ align:start position:0%
+the precisely de brains and because the
+ 
+
+ align:start position:0%
+the precisely de brains and because the
+couple to those gauge fields and they
+
+ align:start position:0%
+couple to those gauge fields and they
+ 
+
+ align:start position:0%
+couple to those gauge fields and they
+they are a stable object at least the
+
+ align:start position:0%
+they are a stable object at least the
+ 
+
+ align:start position:0%
+they are a stable object at least the
+minimal charge ones are stable object
+
+ align:start position:0%
+minimal charge ones are stable object
+ 
+
+ align:start position:0%
+minimal charge ones are stable object
+okay and so this is related to the
+
+ align:start position:0%
+okay and so this is related to the
+ 
+
+ align:start position:0%
+okay and so this is related to the
+statement that actually in super string
+
+ align:start position:0%
+statement that actually in super string
+ 
+
+ align:start position:0%
+statement that actually in super string
+you actually find some stable brains and
+
+ align:start position:0%
+you actually find some stable brains and
+ 
+
+ align:start position:0%
+you actually find some stable brains and
+for other di yeah so let me just list
+
+ align:start position:0%
+for other di yeah so let me just list
+ 
+
+ align:start position:0%
+for other di yeah so let me just list
+them just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to so so with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preparation the then in 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so we can have the
+
+ align:start position:0%
+a so we can have the
+ 
+
+ align:start position:0%
+a so we can have the
+following electric and F magnetic
+
+ align:start position:0%
+following electric and F magnetic
+ 
+
+ align:start position:0%
+following electric and F magnetic
+object so in the 2A we have a c mu1 we
+
+ align:start position:0%
+object so in the 2A we have a c mu1 we
+ 
+
+ align:start position:0%
+object so in the 2A we have a c mu1 we
+have a one
+
+ align:start position:0%
+have a one
+ 
+
+ align:start position:0%
+have a one
+form so that means this
+
+ align:start position:0%
+form so that means this
+ 
+
+ align:start position:0%
+form so that means this
+natural object C to
+
+ align:start position:0%
+natural object C to
+ 
+
+ align:start position:0%
+natural object C to
+it electric object C out this is a dzero
+
+ align:start position:0%
+it electric object C out this is a dzero
+ 
+
+ align:start position:0%
+it electric object C out this is a dzero
+brain okay a zero Di object C to one
+
+ align:start position:0%
+brain okay a zero Di object C to one
+ 
+
+ align:start position:0%
+brain okay a zero Di object C to one
+form this is the zero
+
+ align:start position:0%
+form this is the zero
+ 
+
+ align:start position:0%
+form this is the zero
+brain and a one form in 10
+
+ align:start position:0%
+brain and a one form in 10
+ 
+
+ align:start position:0%
+brain and a one form in 10
+Dimension so in super Str we have 10
+
+ align:start position:0%
+Dimension so in super Str we have 10
+ 
+
+ align:start position:0%
+Dimension so in super Str we have 10
+Dimension is dual to uh so D is 10 minus
+
+ align:start position:0%
+Dimension is dual to uh so D is 10 minus
+ 
+
+ align:start position:0%
+Dimension is dual to uh so D is 10 minus
+1 is 9 - 3 is
+
+ align:start position:0%
+1 is 9 - 3 is
+ 
+
+ align:start position:0%
+1 is 9 - 3 is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+no uh yeah yeah yeah yeah it's six and
+
+ align:start position:0%
+no uh yeah yeah yeah yeah it's six and
+ 
+
+ align:start position:0%
+no uh yeah yeah yeah yeah it's six and
+then the magnetic object will be a D6
+
+ align:start position:0%
+then the magnetic object will be a D6
+ 
+
+ align:start position:0%
+then the magnetic object will be a D6
+spring
+
+ align:start position:0%
+spring
+ 
+
+ align:start position:0%
+spring
+okay so similarly we have a three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form and then this give electric D2
+
+ align:start position:0%
+form and then this give electric D2
+ 
+
+ align:start position:0%
+form and then this give electric D2
+brain and the Magnetic def4
+
+ align:start position:0%
+brain and the Magnetic def4
+ 
+
+ align:start position:0%
+brain and the Magnetic def4
+brain okay magnetic def4 brain so if you
+
+ align:start position:0%
+brain okay magnetic def4 brain so if you
+ 
+
+ align:start position:0%
+brain okay magnetic def4 brain so if you
+just follow this
+
+ align:start position:0%
+just follow this
+ 
+
+ align:start position:0%
+just follow this
+rule so for the type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+QB for the type to B so so let me not uh
+
+ align:start position:0%
+QB for the type to B so so let me not uh
+ 
+
+ align:start position:0%
+QB for the type to B so so let me not uh
+uh first start with this
+
+ align:start position:0%
+uh first start with this
+ 
+
+ align:start position:0%
+uh first start with this
+C2 so this give you a this string one
+
+ align:start position:0%
+C2 so this give you a this string one
+ 
+
+ align:start position:0%
+C2 so this give you a this string one
+dimensional object coupl to it for the
+
+ align:start position:0%
+dimensional object coupl to it for the
+ 
+
+ align:start position:0%
+dimensional object coupl to it for the
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+string and then then the then the
+
+ align:start position:0%
+string and then then the then the
+ 
+
+ align:start position:0%
+string and then then the then the
+magnetic object will be a five
+
+ align:start position:0%
+magnetic object will be a five
+ 
+
+ align:start position:0%
+magnetic object will be a five
+dimensional object it's called the D5
+
+ align:start position:0%
+dimensional object it's called the D5
+ 
+
+ align:start position:0%
+dimensional object it's called the D5
+brain so this string is a D1
+
+ align:start position:0%
+brain so this string is a D1
+ 
+
+ align:start position:0%
+brain so this string is a D1
+brain so now let's look at this four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form this four form so so called self
+
+ align:start position:0%
+form this four form so so called self
+ 
+
+ align:start position:0%
+form this four form so so called self
+duel so sometimes we put a plus here to
+
+ align:start position:0%
+duel so sometimes we put a plus here to
+ 
+
+ align:start position:0%
+duel so sometimes we put a plus here to
+indicate this is a self duel so let me
+
+ align:start position:0%
+indicate this is a self duel so let me
+ 
+
+ align:start position:0%
+indicate this is a self duel so let me
+now explain what what this say self dual
+
+ align:start position:0%
+now explain what what this say self dual
+ 
+
+ align:start position:0%
+now explain what what this say self dual
+means so self
+
+ align:start position:0%
+means so self
+ 
+
+ align:start position:0%
+means so self
+dual means that from C4 I can construct
+
+ align:start position:0%
+dual means that from C4 I can construct
+ 
+
+ align:start position:0%
+dual means that from C4 I can construct
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F5 and construct F5 from this D
+
+ align:start position:0%
+F5 and construct F5 from this D
+ 
+
+ align:start position:0%
+F5 and construct F5 from this D
+C4 okay to be a self dual form means
+
+ align:start position:0%
+C4 okay to be a self dual form means
+ 
+
+ align:start position:0%
+C4 okay to be a self dual form means
+that this form satisfy the condition
+
+ align:start position:0%
+that this form satisfy the condition
+ 
+
+ align:start position:0%
+that this form satisfy the condition
+that F5 equal to F5
+
+ align:start position:0%
+that F5 equal to F5
+ 
+
+ align:start position:0%
+that F5 equal to F5
+duel this is a self duel just means just
+
+ align:start position:0%
+duel this is a self duel just means just
+ 
+
+ align:start position:0%
+duel this is a self duel just means just
+this is a constraint that this C has to
+
+ align:start position:0%
+this is a constraint that this C has to
+ 
+
+ align:start position:0%
+this is a constraint that this C has to
+satisfy so this is called the selfdual
+
+ align:start position:0%
+satisfy so this is called the selfdual
+ 
+
+ align:start position:0%
+satisfy so this is called the selfdual
+for form
+
+ align:start position:0%
+for form
+ 
+
+ align:start position:0%
+for form
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh that just form
+
+ align:start position:0%
+uh that just form
+ 
+
+ align:start position:0%
+uh that just form
+the yeah if you look at the
+
+ align:start position:0%
+the yeah if you look at the
+ 
+
+ align:start position:0%
+the yeah if you look at the
+representations of the r IM you find
+
+ align:start position:0%
+representations of the r IM you find
+ 
+
+ align:start position:0%
+representations of the r IM you find
+this is actually a representation and so
+
+ align:start position:0%
+this is actually a representation and so
+ 
+
+ align:start position:0%
+this is actually a representation and so
+so for for this C you have to satisfy
+
+ align:start position:0%
+so for for this C you have to satisfy
+ 
+
+ align:start position:0%
+so for for this C you have to satisfy
+the S of Duality
+
+ align:start position:0%
+the S of Duality
+ 
+
+ align:start position:0%
+the S of Duality
+condition then now for object which C to
+
+ align:start position:0%
+condition then now for object which C to
+ 
+
+ align:start position:0%
+condition then now for object which C to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+C will be a a l D3 brain because the
+
+ align:start position:0%
+C will be a a l D3 brain because the
+ 
+
+ align:start position:0%
+C will be a a l D3 brain because the
+three form uh three dimension object C
+
+ align:start position:0%
+three form uh three dimension object C
+ 
+
+ align:start position:0%
+three form uh three dimension object C
+to four form so will be a D3
+
+ align:start position:0%
+to four form so will be a D3
+ 
+
+ align:start position:0%
+to four form so will be a D3
+brain and this this re brain because of
+
+ align:start position:0%
+brain and this this re brain because of
+ 
+
+ align:start position:0%
+brain and this this re brain because of
+this self Duality
+
+ align:start position:0%
+this self Duality
+ 
+
+ align:start position:0%
+this self Duality
+condition we have to be both electric
+
+ align:start position:0%
+condition we have to be both electric
+ 
+
+ align:start position:0%
+condition we have to be both electric
+and magnetically charged
+
+ align:start position:0%
+and magnetically charged
+ 
+
+ align:start position:0%
+and magnetically charged
+okay okay because the uh um yeah because
+
+ align:start position:0%
+okay okay because the uh um yeah because
+ 
+
+ align:start position:0%
+okay okay because the uh um yeah because
+this is the self dual form
+
+ align:start position:0%
+this is the self dual form
+ 
+
+ align:start position:0%
+this is the self dual form
+okay uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the so this must Source both
+
+ align:start position:0%
+so so the so this must Source both
+ 
+
+ align:start position:0%
+so so the so this must Source both
+electric flux and magnetic flux to be
+
+ align:start position:0%
+electric flux and magnetic flux to be
+ 
+
+ align:start position:0%
+electric flux and magnetic flux to be
+consistent with s of
+
+ align:start position:0%
+consistent with s of
+ 
+
+ align:start position:0%
+consistent with s of
+Duality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and and
+
+ align:start position:0%
+okay and and
+ 
+
+ align:start position:0%
+okay and and
+finally you can also have a scaler
+
+ align:start position:0%
+finally you can also have a scaler
+ 
+
+ align:start position:0%
+finally you can also have a scaler
+field in the type Tob and the Scala
+
+ align:start position:0%
+field in the type Tob and the Scala
+ 
+
+ align:start position:0%
+field in the type Tob and the Scala
+field naively you will couple to soall D
+
+ align:start position:0%
+field naively you will couple to soall D
+ 
+
+ align:start position:0%
+field naively you will couple to soall D
+minus one dimensional brain because
+
+ align:start position:0%
+minus one dimensional brain because
+ 
+
+ align:start position:0%
+minus one dimensional brain because
+Scala field by itself is zero dimension
+
+ align:start position:0%
+Scala field by itself is zero dimension
+ 
+
+ align:start position:0%
+Scala field by itself is zero dimension
+okay it's already Zero Dimensional form
+
+ align:start position:0%
+okay it's already Zero Dimensional form
+ 
+
+ align:start position:0%
+okay it's already Zero Dimensional form
+so so so so follow this convention Will
+
+ align:start position:0%
+so so so so follow this convention Will
+ 
+
+ align:start position:0%
+so so so so follow this convention Will
+C to D minus one dimensional brain and
+
+ align:start position:0%
+C to D minus one dimensional brain and
+ 
+
+ align:start position:0%
+C to D minus one dimensional brain and
+uh and that obviously does not make much
+
+ align:start position:0%
+uh and that obviously does not make much
+ 
+
+ align:start position:0%
+uh and that obviously does not make much
+sense and but but actually can be made
+
+ align:start position:0%
+sense and but but actually can be made
+ 
+
+ align:start position:0%
+sense and but but actually can be made
+sense when you go to cing signature and
+
+ align:start position:0%
+sense when you go to cing signature and
+ 
+
+ align:start position:0%
+sense when you go to cing signature and
+then uh this um this scalar field cou to
+
+ align:start position:0%
+then uh this um this scalar field cou to
+ 
+
+ align:start position:0%
+then uh this um this scalar field cou to
+something called instanton which I we
+
+ align:start position:0%
+something called instanton which I we
+ 
+
+ align:start position:0%
+something called instanton which I we
+not going to there something called D Sy
+
+ align:start position:0%
+not going to there something called D Sy
+ 
+
+ align:start position:0%
+not going to there something called D Sy
+okay so so the bottom
+
+ align:start position:0%
+okay so so the bottom
+ 
+
+ align:start position:0%
+okay so so the bottom
+line is said
+
+ align:start position:0%
+line is said
+ 
+
+ align:start position:0%
+line is said
+the the object we are charged on those R
+
+ align:start position:0%
+the the object we are charged on those R
+ 
+
+ align:start position:0%
+the the object we are charged on those R
+Roman field they all deep brains they
+
+ align:start position:0%
+Roman field they all deep brains they
+ 
+
+ align:start position:0%
+Roman field they all deep brains they
+all deep brains and then they come into
+
+ align:start position:0%
+all deep brains and then they come into
+ 
+
+ align:start position:0%
+all deep brains and then they come into
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+dimensions and any deep bra of course
+
+ align:start position:0%
+dimensions and any deep bra of course
+ 
+
+ align:start position:0%
+dimensions and any deep bra of course
+you can define deep brain with other
+
+ align:start position:0%
+you can define deep brain with other
+ 
+
+ align:start position:0%
+you can define deep brain with other
+dimensions so you can consider in a a
+
+ align:start position:0%
+dimensions so you can consider in a a
+ 
+
+ align:start position:0%
+dimensions so you can consider in a a
+this three brain but the in a a this3
+
+ align:start position:0%
+this three brain but the in a a this3
+ 
+
+ align:start position:0%
+this three brain but the in a a this3
+brain will not be a stable object
+
+ align:start position:0%
+brain will not be a stable object
+ 
+
+ align:start position:0%
+brain will not be a stable object
+because there's no conserved charge for
+
+ align:start position:0%
+because there's no conserved charge for
+ 
+
+ align:start position:0%
+because there's no conserved charge for
+carer two so so even though uh Ina you
+
+ align:start position:0%
+carer two so so even though uh Ina you
+ 
+
+ align:start position:0%
+carer two so so even though uh Ina you
+can can see the this rein but it's not a
+
+ align:start position:0%
+can can see the this rein but it's not a
+ 
+
+ align:start position:0%
+can can see the this rein but it's not a
+stable object and actually uh when you
+
+ align:start position:0%
+stable object and actually uh when you
+ 
+
+ align:start position:0%
+stable object and actually uh when you
+Contex the Spectrum on the this rebrin
+
+ align:start position:0%
+Contex the Spectrum on the this rebrin
+ 
+
+ align:start position:0%
+Contex the Spectrum on the this rebrin
+into a then you find there a tan again
+
+ align:start position:0%
+into a then you find there a tan again
+ 
+
+ align:start position:0%
+into a then you find there a tan again
+there's a tang in the world volume
+
+ align:start position:0%
+there's a tang in the world volume
+ 
+
+ align:start position:0%
+there's a tang in the world volume
+indicate that's not stable object and
+
+ align:start position:0%
+indicate that's not stable object and
+ 
+
+ align:start position:0%
+indicate that's not stable object and
+but those brains uh don't have TS
+
+ align:start position:0%
+but those brains uh don't have TS
+ 
+
+ align:start position:0%
+but those brains uh don't have TS
+okay and in particular on those brains
+
+ align:start position:0%
+okay and in particular on those brains
+ 
+
+ align:start position:0%
+okay and in particular on those brains
+this all super symmetric field
+
+ align:start position:0%
+this all super symmetric field
+ 
+
+ align:start position:0%
+this all super symmetric field
+series for example uh the the most
+
+ align:start position:0%
+series for example uh the the most
+ 
+
+ align:start position:0%
+series for example uh the the most
+important one is this this rebrin
+
+ align:start position:0%
+important one is this this rebrin
+ 
+
+ align:start position:0%
+important one is this this rebrin
+because then then you have four
+
+ align:start position:0%
+because then then you have four
+ 
+
+ align:start position:0%
+because then then you have four
+dimensional W volume then you actually
+
+ align:start position:0%
+dimensional W volume then you actually
+ 
+
+ align:start position:0%
+dimensional W volume then you actually
+have a four dimensional Ser on this this
+
+ align:start position:0%
+have a four dimensional Ser on this this
+ 
+
+ align:start position:0%
+have a four dimensional Ser on this this
+rebrin and uh and that's what I give you
+
+ align:start position:0%
+rebrin and uh and that's what I give you
+ 
+
+ align:start position:0%
+rebrin and uh and that's what I give you
+So-Cal inqu for Super Y Ser okay so on
+
+ align:start position:0%
+So-Cal inqu for Super Y Ser okay so on
+ 
+
+ align:start position:0%
+So-Cal inqu for Super Y Ser okay so on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+brains on these stable
+
+ align:start position:0%
+brains on these stable
+ 
+
+ align:start position:0%
+brains on these stable
+brains the energy
+
+ align:start position:0%
+brains the energy
+ 
+
+ align:start position:0%
+brains the energy
+theories are super smat super yam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ser
+
+ align:start position:0%
+ser
+ 
+
+ align:start position:0%
+ser
+in particular for for
+
+ align:start position:0%
+in particular for for
+ 
+
+ align:start position:0%
+in particular for for
+D3 it given by soal in4 Super Y
+
+ align:start position:0%
+D3 it given by soal in4 Super Y
+ 
+
+ align:start position:0%
+D3 it given by soal in4 Super Y
+Ser in in four dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensions yeah it can Decay it can
+
+ align:start position:0%
+dimensions yeah it can Decay it can
+ 
+
+ align:start position:0%
+dimensions yeah it can Decay it can
+Decay into lower dimensional brand it
+
+ align:start position:0%
+Decay into lower dimensional brand it
+ 
+
+ align:start position:0%
+Decay into lower dimensional brand it
+can it actually um it's possible for you
+
+ align:start position:0%
+can it actually um it's possible for you
+ 
+
+ align:start position:0%
+can it actually um it's possible for you
+to Decay into lower dimensional brain it
+
+ align:start position:0%
+to Decay into lower dimensional brain it
+ 
+
+ align:start position:0%
+to Decay into lower dimensional brain it
+can also for it just to Decay into close
+
+ align:start position:0%
+can also for it just to Decay into close
+ 
+
+ align:start position:0%
+can also for it just to Decay into close
+stream modes radiate Clos stre mod yeah
+
+ align:start position:0%
+stream modes radiate Clos stre mod yeah
+ 
+
+ align:start position:0%
+stream modes radiate Clos stre mod yeah
+okay I mean the dimension of these two
+
+ align:start position:0%
+okay I mean the dimension of these two
+ 
+
+ align:start position:0%
+okay I mean the dimension of these two
+object are different it sounds like you
+
+ align:start position:0%
+object are different it sounds like you
+ 
+
+ align:start position:0%
+object are different it sounds like you
+have if your brains to decate Str you
+
+ align:start position:0%
+have if your brains to decate Str you
+ 
+
+ align:start position:0%
+have if your brains to decate Str you
+will become INF yeah that's right you
+
+ align:start position:0%
+will become INF yeah that's right you
+ 
+
+ align:start position:0%
+will become INF yeah that's right you
+did have a density of
+
+ align:start position:0%
+did have a density of
+ 
+
+ align:start position:0%
+did have a density of
+strings
+
+ align:start position:0%
+strings
+ 
+
+ align:start position:0%
+strings
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um yeah it's actually a beautiful
+
+ align:start position:0%
+um yeah it's actually a beautiful
+ 
+
+ align:start position:0%
+um yeah it's actually a beautiful
+subject to to discuss those brains how
+
+ align:start position:0%
+subject to to discuss those brains how
+ 
+
+ align:start position:0%
+subject to to discuss those brains how
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+Decay um yeah yeah one can actually
+
+ align:start position:0%
+Decay um yeah yeah one can actually
+ 
+
+ align:start position:0%
+Decay um yeah yeah one can actually
+do um yeah it's a it's a it's a it's a
+
+ align:start position:0%
+do um yeah it's a it's a it's a it's a
+ 
+
+ align:start position:0%
+do um yeah it's a it's a it's a it's a
+nice subject yeah but it's way out of
+
+ align:start position:0%
+nice subject yeah but it's way out of
+ 
+
+ align:start position:0%
+nice subject yeah but it's way out of
+our discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here any questions yes as before if we
+
+ align:start position:0%
+here any questions yes as before if we
+ 
+
+ align:start position:0%
+here any questions yes as before if we
+consider stacks of such brains do we get
+
+ align:start position:0%
+consider stacks of such brains do we get
+ 
+
+ align:start position:0%
+consider stacks of such brains do we get
+higher rank AG groups yeah that's right
+
+ align:start position:0%
+higher rank AG groups yeah that's right
+ 
+
+ align:start position:0%
+higher rank AG groups yeah that's right
+exactly it's always give you un
+
+ align:start position:0%
+exactly it's always give you un
+ 
+
+ align:start position:0%
+exactly it's always give you un
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so that conclude our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussion of the deep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brains in from the point of view as
+
+ align:start position:0%
+brains in from the point of view as
+ 
+
+ align:start position:0%
+brains in from the point of view as
+dally boundary conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay as a the rich boundary
+
+ align:start position:0%
+okay as a the rich boundary
+ 
+
+ align:start position:0%
+okay as a the rich boundary
+conditions so now I want to take a
+
+ align:start position:0%
+conditions so now I want to take a
+ 
+
+ align:start position:0%
+conditions so now I want to take a
+slightly different perspective on the
+
+ align:start position:0%
+slightly different perspective on the
+ 
+
+ align:start position:0%
+slightly different perspective on the
+Deep
+
+ align:start position:0%
+Deep
+ 
+
+ align:start position:0%
+Deep
+brains
+
+ align:start position:0%
+brains
+ 
+
+ align:start position:0%
+brains
+from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perspective from there from the
+
+ align:start position:0%
+perspective from there from the
+ 
+
+ align:start position:0%
+perspective from there from the
+perspective there object which are
+
+ align:start position:0%
+perspective there object which are
+ 
+
+ align:start position:0%
+perspective there object which are
+charged under those generalized Gate
+
+ align:start position:0%
+charged under those generalized Gate
+ 
+
+ align:start position:0%
+charged under those generalized Gate
+Fields okay uh and now I want to view
+
+ align:start position:0%
+Fields okay uh and now I want to view
+ 
+
+ align:start position:0%
+Fields okay uh and now I want to view
+those difference as some object some sol
+
+ align:start position:0%
+those difference as some object some sol
+ 
+
+ align:start position:0%
+those difference as some object some sol
+T if you if you want some sol T which
+
+ align:start position:0%
+T if you if you want some sol T which
+ 
+
+ align:start position:0%
+T if you if you want some sol T which
+are charged under those generalized gaug
+
+ align:start position:0%
+are charged under those generalized gaug
+ 
+
+ align:start position:0%
+are charged under those generalized gaug
+Fields okay I want to take I want to
+
+ align:start position:0%
+Fields okay I want to take I want to
+ 
+
+ align:start position:0%
+Fields okay I want to take I want to
+elaborate from this perspective okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I talk about the
+
+ align:start position:0%
+now I talk about the
+ 
+
+ align:start position:0%
+now I talk about the
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perspective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so deep brain has a
+
+ align:start position:0%
+okay so deep brain has a
+ 
+
+ align:start position:0%
+okay so deep brain has a
+mass has a tension also deep BR carry so
+
+ align:start position:0%
+mass has a tension also deep BR carry so
+ 
+
+ align:start position:0%
+mass has a tension also deep BR carry so
+now we only consider the stable deep
+
+ align:start position:0%
+now we only consider the stable deep
+ 
+
+ align:start position:0%
+now we only consider the stable deep
+Brands so they have a mass they also
+
+ align:start position:0%
+Brands so they have a mass they also
+ 
+
+ align:start position:0%
+Brands so they have a mass they also
+carry those charges conserved charges so
+
+ align:start position:0%
+carry those charges conserved charges so
+ 
+
+ align:start position:0%
+carry those charges conserved charges so
+that means there will be flux coming out
+
+ align:start position:0%
+that means there will be flux coming out
+ 
+
+ align:start position:0%
+that means there will be flux coming out
+electric or magnetic flux coming out of
+
+ align:start position:0%
+electric or magnetic flux coming out of
+ 
+
+ align:start position:0%
+electric or magnetic flux coming out of
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brains so that will deform the space
+
+ align:start position:0%
+brains so that will deform the space
+ 
+
+ align:start position:0%
+brains so that will deform the space
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay uh um yeah because the the
+
+ align:start position:0%
+okay uh um yeah because the the
+ 
+
+ align:start position:0%
+okay uh um yeah because the the
+gravitate will deform space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and so now we would like to find
+
+ align:start position:0%
+time and so now we would like to find
+ 
+
+ align:start position:0%
+time and so now we would like to find
+out what are the space time around those
+
+ align:start position:0%
+out what are the space time around those
+ 
+
+ align:start position:0%
+out what are the space time around those
+uh de brains okay how do they deform
+
+ align:start position:0%
+uh de brains okay how do they deform
+ 
+
+ align:start position:0%
+uh de brains okay how do they deform
+space time so to
+
+ align:start position:0%
+space time so to
+ 
+
+ align:start position:0%
+space time so to
+example say it's consider say consider
+
+ align:start position:0%
+example say it's consider say consider
+ 
+
+ align:start position:0%
+example say it's consider say consider
+charge as a to example of this say let's
+
+ align:start position:0%
+charge as a to example of this say let's
+ 
+
+ align:start position:0%
+charge as a to example of this say let's
+consider just again in the Maxwell
+
+ align:start position:0%
+consider just again in the Maxwell
+ 
+
+ align:start position:0%
+consider just again in the Maxwell
+theory in Einstein Max wheell Theory
+
+ align:start position:0%
+theory in Einstein Max wheell Theory
+ 
+
+ align:start position:0%
+theory in Einstein Max wheell Theory
+consider for example a Charged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+sitting say at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+origin say of four dimensional space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time say cute space time for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example so if you include both gr and M
+
+ align:start position:0%
+example so if you include both gr and M
+ 
+
+ align:start position:0%
+example so if you include both gr and M
+then the Dynamics of this series
+
+ align:start position:0%
+then the Dynamics of this series
+ 
+
+ align:start position:0%
+then the Dynamics of this series
+controlled by soall Einstein Max well so
+
+ align:start position:0%
+controlled by soall Einstein Max well so
+ 
+
+ align:start position:0%
+controlled by soall Einstein Max well so
+so you will have a Einstein
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory and the max will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so dynamics of such particles
+
+ align:start position:0%
+okay so dynamics of such particles
+ 
+
+ align:start position:0%
+okay so dynamics of such particles
+should cap should be captured by them
+
+ align:start position:0%
+should cap should be captured by them
+ 
+
+ align:start position:0%
+should cap should be captured by them
+and so this C so this capture the
+
+ align:start position:0%
+and so this C so this capture the
+ 
+
+ align:start position:0%
+and so this C so this capture the
+gravity due to the particle this
+
+ align:start position:0%
+gravity due to the particle this
+ 
+
+ align:start position:0%
+gravity due to the particle this
+captures the y m due to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle so from here you can work out
+
+ align:start position:0%
+particle so from here you can work out
+ 
+
+ align:start position:0%
+particle so from here you can work out
+how does this particle say a deform
+
+ align:start position:0%
+how does this particle say a deform
+ 
+
+ align:start position:0%
+how does this particle say a deform
+space time okay from the Einstein
+
+ align:start position:0%
+space time okay from the Einstein
+ 
+
+ align:start position:0%
+space time okay from the Einstein
+equation so so the equation motion of
+
+ align:start position:0%
+equation so so the equation motion of
+ 
+
+ align:start position:0%
+equation so so the equation motion of
+this system would be
+
+ align:start position:0%
+this system would be
+ 
+
+ align:start position:0%
+this system would be
+you have a a standard max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so I not be careful about the minus
+
+ align:start position:0%
+well so I not be careful about the minus
+ 
+
+ align:start position:0%
+well so I not be careful about the minus
+sign uh and the also the Einstein
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation the stress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sensor okay so so the J so J is just the
+
+ align:start position:0%
+sensor okay so so the J so J is just the
+ 
+
+ align:start position:0%
+sensor okay so so the J so J is just the
+J is just the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um say if I have a charge particle
+
+ align:start position:0%
+um say if I have a charge particle
+ 
+
+ align:start position:0%
+um say if I have a charge particle
+sitting there there's no current there's
+
+ align:start position:0%
+sitting there there's no current there's
+ 
+
+ align:start position:0%
+sitting there there's no current there's
+only a charge
+
+ align:start position:0%
+only a charge
+ 
+
+ align:start position:0%
+only a charge
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+okay and the stress
+
+ align:start position:0%
+okay and the stress
+ 
+
+ align:start position:0%
+okay and the stress
+tensor containing two
+
+ align:start position:0%
+tensor containing two
+ 
+
+ align:start position:0%
+tensor containing two
+parts is the stress tens due to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle and also the stress due to the
+
+ align:start position:0%
+particle and also the stress due to the
+ 
+
+ align:start position:0%
+particle and also the stress due to the
+electromagnetic
+
+ align:start position:0%
+electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic
+field okay okay because this exciting
+
+ align:start position:0%
+field okay okay because this exciting
+ 
+
+ align:start position:0%
+field okay okay because this exciting
+that to magnetic
+
+ align:start position:0%
+that to magnetic
+ 
+
+ align:start position:0%
+that to magnetic
+field and uh and the and the particle
+
+ align:start position:0%
+field and uh and the and the particle
+ 
+
+ align:start position:0%
+field and uh and the and the particle
+part only have a zero zero component so
+
+ align:start position:0%
+part only have a zero zero component so
+ 
+
+ align:start position:0%
+part only have a zero zero component so
+you only have a mass there's no momentum
+
+ align:start position:0%
+you only have a mass there's no momentum
+ 
+
+ align:start position:0%
+you only have a mass there's no momentum
+so this is just a say maybe I should
+
+ align:start position:0%
+so this is just a say maybe I should
+ 
+
+ align:start position:0%
+so this is just a say maybe I should
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+R yeah I think I'm using notation of R
+
+ align:start position:0%
+R yeah I think I'm using notation of R
+ 
+
+ align:start position:0%
+R yeah I think I'm using notation of R
+okay so the so the uh um the particle
+
+ align:start position:0%
+okay so the so the uh um the particle
+ 
+
+ align:start position:0%
+okay so the so the uh um the particle
+part of the Str tensor would be just the
+
+ align:start position:0%
+part of the Str tensor would be just the
+ 
+
+ align:start position:0%
+part of the Str tensor would be just the
+data function uh uh uh the only non zero
+
+ align:start position:0%
+data function uh uh uh the only non zero
+ 
+
+ align:start position:0%
+data function uh uh uh the only non zero
+component are Z zero component you only
+
+ align:start position:0%
+component are Z zero component you only
+ 
+
+ align:start position:0%
+component are Z zero component you only
+have energy density and it's just given
+
+ align:start position:0%
+have energy density and it's just given
+ 
+
+ align:start position:0%
+have energy density and it's just given
+by the by the data function of the
+
+ align:start position:0%
+by the by the data function of the
+ 
+
+ align:start position:0%
+by the by the data function of the
+mass so so so from
+
+ align:start position:0%
+mass so so so from
+ 
+
+ align:start position:0%
+mass so so so from
+here by solving those equations with
+
+ align:start position:0%
+here by solving those equations with
+ 
+
+ align:start position:0%
+here by solving those equations with
+those sources then you can work out how
+
+ align:start position:0%
+those sources then you can work out how
+ 
+
+ align:start position:0%
+those sources then you can work out how
+a Charged particle deform your space
+
+ align:start position:0%
+a Charged particle deform your space
+ 
+
+ align:start position:0%
+a Charged particle deform your space
+time okay how charge particle deform
+
+ align:start position:0%
+time okay how charge particle deform
+ 
+
+ align:start position:0%
+time okay how charge particle deform
+your space
+
+ align:start position:0%
+your space
+ 
+
+ align:start position:0%
+your space
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so let me just say a little bit
+
+ align:start position:0%
+so so let me just say a little bit
+ 
+
+ align:start position:0%
+so so let me just say a little bit
+further for example you can easily solve
+
+ align:start position:0%
+further for example you can easily solve
+ 
+
+ align:start position:0%
+further for example you can easily solve
+the an equation we allow the
+
+ align:start position:0%
+the an equation we allow the
+ 
+
+ align:start position:0%
+the an equation we allow the
+Solutions so you just have a coolum
+
+ align:start position:0%
+Solutions so you just have a coolum
+ 
+
+ align:start position:0%
+Solutions so you just have a coolum
+potential you just have a
+
+ align:start position:0%
+potential you just have a
+ 
+
+ align:start position:0%
+potential you just have a
+potential and uh and and the other words
+
+ align:start position:0%
+potential and uh and and the other words
+ 
+
+ align:start position:0%
+potential and uh and and the other words
+you have in other words you have
+
+ align:start position:0%
+you have in other words you have
+ 
+
+ align:start position:0%
+you have in other words you have
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+flux surrounding the S2 around the point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle equal to Q
+
+ align:start position:0%
+particle equal to Q
+ 
+
+ align:start position:0%
+particle equal to Q
+okay again this is the Dual of f uh you
+
+ align:start position:0%
+okay again this is the Dual of f uh you
+ 
+
+ align:start position:0%
+okay again this is the Dual of f uh you
+have electric field when you dual
+
+ align:start position:0%
+have electric field when you dual
+ 
+
+ align:start position:0%
+have electric field when you dual
+dualize then then have special component
+
+ align:start position:0%
+dualize then then have special component
+ 
+
+ align:start position:0%
+dualize then then have special component
+then that give you this yeah so this is
+
+ align:start position:0%
+then that give you this yeah so this is
+ 
+
+ align:start position:0%
+then that give you this yeah so this is
+a g La
+
+ align:start position:0%
+a g La
+ 
+
+ align:start position:0%
+a g La
+okay this is G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LA and you can also work
+
+ align:start position:0%
+LA and you can also work
+ 
+
+ align:start position:0%
+LA and you can also work
+out uh the matric surrounding this
+
+ align:start position:0%
+out uh the matric surrounding this
+ 
+
+ align:start position:0%
+out uh the matric surrounding this
+charge particles so because the space
+
+ align:start position:0%
+charge particles so because the space
+ 
+
+ align:start position:0%
+charge particles so because the space
+time is symmetric spical symmetric then
+
+ align:start position:0%
+time is symmetric spical symmetric then
+ 
+
+ align:start position:0%
+time is symmetric spical symmetric then
+you can actually write down a spical
+
+ align:start position:0%
+you can actually write down a spical
+ 
+
+ align:start position:0%
+you can actually write down a spical
+symmetric an for the metric around the
+
+ align:start position:0%
+symmetric an for the metric around the
+ 
+
+ align:start position:0%
+symmetric an for the metric around the
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation you can find out what you can
+
+ align:start position:0%
+equation you can find out what you can
+ 
+
+ align:start position:0%
+equation you can find out what you can
+work out what is fr and HR okay so some
+
+ align:start position:0%
+work out what is fr and HR okay so some
+ 
+
+ align:start position:0%
+work out what is fr and HR okay so some
+of you may have already done this
+
+ align:start position:0%
+of you may have already done this
+ 
+
+ align:start position:0%
+of you may have already done this
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+before so if your Q is zero what answer
+
+ align:start position:0%
+before so if your Q is zero what answer
+ 
+
+ align:start position:0%
+before so if your Q is zero what answer
+would you
+
+ align:start position:0%
+would you
+ 
+
+ align:start position:0%
+would you
+get that's right
+
+ align:start position:0%
+get that's right
+ 
+
+ align:start position:0%
+get that's right
+so if the um Q is zero then you just get
+
+ align:start position:0%
+so if the um Q is zero then you just get
+ 
+
+ align:start position:0%
+so if the um Q is zero then you just get
+a swash matric and it's exactly the
+
+ align:start position:0%
+a swash matric and it's exactly the
+ 
+
+ align:start position:0%
+a swash matric and it's exactly the
+metric as say produced by a s Etc far
+
+ align:start position:0%
+metric as say produced by a s Etc far
+ 
+
+ align:start position:0%
+metric as say produced by a s Etc far
+away okay and uh um so so here we have a
+
+ align:start position:0%
+away okay and uh um so so here we have a
+ 
+
+ align:start position:0%
+away okay and uh um so so here we have a
+charge then what you get is something
+
+ align:start position:0%
+charge then what you get is something
+ 
+
+ align:start position:0%
+charge then what you get is something
+called the Ral nostrom matric and uh uh
+
+ align:start position:0%
+called the Ral nostrom matric and uh uh
+ 
+
+ align:start position:0%
+called the Ral nostrom matric and uh uh
+uh when you have a charge have
+
+ align:start position:0%
+uh when you have a charge have
+ 
+
+ align:start position:0%
+uh when you have a charge have
+electromagnetic
+
+ align:start position:0%
+electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic
+field okay so so you will
+
+ align:start position:0%
+field okay so so you will
+ 
+
+ align:start position:0%
+field okay so so you will
+get so called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay that's Q z h if Q equal Z no no
+
+ align:start position:0%
+no okay that's Q z h if Q equal Z no no
+ 
+
+ align:start position:0%
+no okay that's Q z h if Q equal Z no no
+no that's the Q to Z is nostrum and when
+
+ align:start position:0%
+no that's the Q to Z is nostrum and when
+ 
+
+ align:start position:0%
+no that's the Q to Z is nostrum and when
+Q equal to zero then you just get the
+
+ align:start position:0%
+Q equal to zero then you just get the
+ 
+
+ align:start position:0%
+Q equal to zero then you just get the
+swashi um yeah that's that's how you
+
+ align:start position:0%
+swashi um yeah that's that's how you
+ 
+
+ align:start position:0%
+swashi um yeah that's that's how you
+calculate the uh precession yeah that's
+
+ align:start position:0%
+calculate the uh precession yeah that's
+ 
+
+ align:start position:0%
+calculate the uh precession yeah that's
+what you use to calculate the precession
+
+ align:start position:0%
+what you use to calculate the precession
+ 
+
+ align:start position:0%
+what you use to calculate the precession
+of say of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mercury similarly you can also do this
+
+ align:start position:0%
+Mercury similarly you can also do this
+ 
+
+ align:start position:0%
+Mercury similarly you can also do this
+for for magnetic charge particle so the
+
+ align:start position:0%
+for for magnetic charge particle so the
+ 
+
+ align:start position:0%
+for for magnetic charge particle so the
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+difference for magnetic charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the difference is that this
+
+ align:start position:0%
+the difference is that this
+ 
+
+ align:start position:0%
+the difference is that this
+equation now
+
+ align:start position:0%
+equation now
+ 
+
+ align:start position:0%
+equation now
+become just directly magnetic flux equal
+
+ align:start position:0%
+become just directly magnetic flux equal
+ 
+
+ align:start position:0%
+become just directly magnetic flux equal
+to G say for example if it's a uh say if
+
+ align:start position:0%
+to G say for example if it's a uh say if
+ 
+
+ align:start position:0%
+to G say for example if it's a uh say if
+the magnetic charge is
+
+ align:start position:0%
+the magnetic charge is
+ 
+
+ align:start position:0%
+the magnetic charge is
+G of charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G and then you will get this then then
+
+ align:start position:0%
+G and then you will get this then then
+ 
+
+ align:start position:0%
+G and then you will get this then then
+you that you have this and then and then
+
+ align:start position:0%
+you that you have this and then and then
+ 
+
+ align:start position:0%
+you that you have this and then and then
+you have um yeah you have magnetic flux
+
+ align:start position:0%
+you have um yeah you have magnetic flux
+ 
+
+ align:start position:0%
+you have um yeah you have magnetic flux
+and again you can plug into Einstein
+
+ align:start position:0%
+and again you can plug into Einstein
+ 
+
+ align:start position:0%
+and again you can plug into Einstein
+equation you solve you get the same rum
+
+ align:start position:0%
+equation you solve you get the same rum
+ 
+
+ align:start position:0%
+equation you solve you get the same rum
+matric so also a direct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantization tell you that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qg should be quantized in integers of 2
+
+ align:start position:0%
+qg should be quantized in integers of 2
+ 
+
+ align:start position:0%
+qg should be quantized in integers of 2
+pi n Nal to 1 2 Etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the familiar story in
+
+ align:start position:0%
+okay so this is the familiar story in
+ 
+
+ align:start position:0%
+okay so this is the familiar story in
+the gr so if you want to look at how uh
+
+ align:start position:0%
+the gr so if you want to look at how uh
+ 
+
+ align:start position:0%
+the gr so if you want to look at how uh
+how the gravity and uh and the and them
+
+ align:start position:0%
+how the gravity and uh and the and them
+ 
+
+ align:start position:0%
+how the gravity and uh and the and them
+surrounding a charged
+
+ align:start position:0%
+surrounding a charged
+ 
+
+ align:start position:0%
+surrounding a charged
+object and so you can generalize this
+
+ align:start position:0%
+object and so you can generalize this
+ 
+
+ align:start position:0%
+object and so you can generalize this
+story immediately to those
+
+ align:start position:0%
+story immediately to those
+ 
+
+ align:start position:0%
+story immediately to those
+brains which are charg which they have
+
+ align:start position:0%
+brains which are charg which they have
+ 
+
+ align:start position:0%
+brains which are charg which they have
+their own mass and charged under some
+
+ align:start position:0%
+their own mass and charged under some
+ 
+
+ align:start position:0%
+their own mass and charged under some
+some generalized gaug Fields okay so you
+
+ align:start position:0%
+some generalized gaug Fields okay so you
+ 
+
+ align:start position:0%
+some generalized gaug Fields okay so you
+can generalize that
+
+ align:start position:0%
+can generalize that
+ 
+
+ align:start position:0%
+can generalize that
+immediately so you can generalize
+
+ align:start position:0%
+immediately so you can generalize
+ 
+
+ align:start position:0%
+immediately so you can generalize
+procedure immediately to higher
+
+ align:start position:0%
+procedure immediately to higher
+ 
+
+ align:start position:0%
+procedure immediately to higher
+Dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object so uh so you can
+
+ align:start position:0%
+object so uh so you can
+ 
+
+ align:start position:0%
+object so uh so you can
+just as a simple exercise in
+
+ align:start position:0%
+just as a simple exercise in
+ 
+
+ align:start position:0%
+just as a simple exercise in
+gr you can just carry out this
+
+ align:start position:0%
+gr you can just carry out this
+ 
+
+ align:start position:0%
+gr you can just carry out this
+procedure just replace this to some
+
+ align:start position:0%
+procedure just replace this to some
+ 
+
+ align:start position:0%
+procedure just replace this to some
+higher dimensional
+
+ align:start position:0%
+higher dimensional
+ 
+
+ align:start position:0%
+higher dimensional
+form and the and the source is some
+
+ align:start position:0%
+form and the and the source is some
+ 
+
+ align:start position:0%
+form and the and the source is some
+higher dimensional object then you can
+
+ align:start position:0%
+higher dimensional object then you can
+ 
+
+ align:start position:0%
+higher dimensional object then you can
+work out the solutions
+
+ align:start position:0%
+work out the solutions
+ 
+
+ align:start position:0%
+work out the solutions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um and that was a simple
+
+ align:start position:0%
+um and that was a simple
+ 
+
+ align:start position:0%
+um and that was a simple
+exercise which actually hor and storing
+
+ align:start position:0%
+exercise which actually hor and storing
+ 
+
+ align:start position:0%
+exercise which actually hor and storing
+did in early 90s in
+
+ align:start position:0%
+did in early 90s in
+ 
+
+ align:start position:0%
+did in early 90s in
+1991 yeah it's a triv generalization you
+
+ align:start position:0%
+1991 yeah it's a triv generalization you
+ 
+
+ align:start position:0%
+1991 yeah it's a triv generalization you
+can do while not do it but turns out to
+
+ align:start position:0%
+can do while not do it but turns out to
+ 
+
+ align:start position:0%
+can do while not do it but turns out to
+be a tend out that's a very very
+
+ align:start position:0%
+be a tend out that's a very very
+ 
+
+ align:start position:0%
+be a tend out that's a very very
+important step to do uh for the reason U
+
+ align:start position:0%
+important step to do uh for the reason U
+ 
+
+ align:start position:0%
+important step to do uh for the reason U
+uh which I will
+
+ align:start position:0%
+uh which I will
+ 
+
+ align:start position:0%
+uh which I will
+explain so for Simplicity let me just
+
+ align:start position:0%
+explain so for Simplicity let me just
+ 
+
+ align:start position:0%
+explain so for Simplicity let me just
+talk a little bit about doing this for
+
+ align:start position:0%
+talk a little bit about doing this for
+ 
+
+ align:start position:0%
+talk a little bit about doing this for
+this rebrin also for definitely you can
+
+ align:start position:0%
+this rebrin also for definitely you can
+ 
+
+ align:start position:0%
+this rebrin also for definitely you can
+do it for any of these and the name me
+
+ align:start position:0%
+do it for any of these and the name me
+ 
+
+ align:start position:0%
+do it for any of these and the name me
+just say for to to this re
+
+ align:start position:0%
+just say for to to this re
+ 
+
+ align:start position:0%
+just say for to to this re
+brain so now
+
+ align:start position:0%
+brain so now
+ 
+
+ align:start position:0%
+brain so now
+consider say this three
+
+ align:start position:0%
+consider say this three
+ 
+
+ align:start position:0%
+consider say this three
+brain so this re brain is part of the
+
+ align:start position:0%
+brain so this re brain is part of the
+ 
+
+ align:start position:0%
+brain so this re brain is part of the
+type 2B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory so of course we don't know how
+
+ align:start position:0%
+Theory so of course we don't know how
+ 
+
+ align:start position:0%
+Theory so of course we don't know how
+really do this in the full type Tob
+
+ align:start position:0%
+really do this in the full type Tob
+ 
+
+ align:start position:0%
+really do this in the full type Tob
+string so we will do the Lowery limit
+
+ align:start position:0%
+string so we will do the Lowery limit
+ 
+
+ align:start position:0%
+string so we will do the Lowery limit
+type Tob string so we do this for the
+
+ align:start position:0%
+type Tob string so we do this for the
+ 
+
+ align:start position:0%
+type Tob string so we do this for the
+this R brain in the lower limit of type
+
+ align:start position:0%
+this R brain in the lower limit of type
+ 
+
+ align:start position:0%
+this R brain in the lower limit of type
+Tob
+
+ align:start position:0%
+Tob
+ 
+
+ align:start position:0%
+Tob
+string which is soal type Tob super
+
+ align:start position:0%
+string which is soal type Tob super
+ 
+
+ align:start position:0%
+string which is soal type Tob super
+gravity okay so so it doesn't matter you
+
+ align:start position:0%
+gravity okay so so it doesn't matter you
+ 
+
+ align:start position:0%
+gravity okay so so it doesn't matter you
+don't know anything about type to be
+
+ align:start position:0%
+don't know anything about type to be
+ 
+
+ align:start position:0%
+don't know anything about type to be
+super gravity and essentially
+
+ align:start position:0%
+super gravity and essentially
+ 
+
+ align:start position:0%
+super gravity and essentially
+that's just some generation of this
+
+ align:start position:0%
+that's just some generation of this
+ 
+
+ align:start position:0%
+that's just some generation of this
+equation okay type to B graphity just
+
+ align:start position:0%
+equation okay type to B graphity just
+ 
+
+ align:start position:0%
+equation okay type to B graphity just
+some generation of this
+
+ align:start position:0%
+some generation of this
+ 
+
+ align:start position:0%
+some generation of this
+equation but the 11 is let me just
+
+ align:start position:0%
+equation but the 11 is let me just
+ 
+
+ align:start position:0%
+equation but the 11 is let me just
+introduce some notations just to be uh
+
+ align:start position:0%
+introduce some notations just to be uh
+ 
+
+ align:start position:0%
+introduce some notations just to be uh
+uh to be
+
+ align:start position:0%
+uh to be
+ 
+
+ align:start position:0%
+uh to be
+um so type to be super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity we will do this in the in the in
+
+ align:start position:0%
+gravity we will do this in the in the in
+ 
+
+ align:start position:0%
+gravity we will do this in the in the in
+the low energy limit of the two to be
+
+ align:start position:0%
+the low energy limit of the two to be
+ 
+
+ align:start position:0%
+the low energy limit of the two to be
+string so this is the low energy
+
+ align:start position:0%
+string so this is the low energy
+ 
+
+ align:start position:0%
+string so this is the low energy
+effctive Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for M this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modes of to be string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it has the form as the what we
+
+ align:start position:0%
+okay so it has the form as the what we
+ 
+
+ align:start position:0%
+okay so it has the form as the what we
+have before
+
+ align:start position:0%
+have before
+ 
+
+ align:start position:0%
+have before
+we have 1 / 6 Pi T Pi GN but now this is
+
+ align:start position:0%
+we have 1 / 6 Pi T Pi GN but now this is
+ 
+
+ align:start position:0%
+we have 1 / 6 Pi T Pi GN but now this is
+a 10 dimensional Newton constant so this
+
+ align:start position:0%
+a 10 dimensional Newton constant so this
+ 
+
+ align:start position:0%
+a 10 dimensional Newton constant so this
+is a 10 dimensional
+
+ align:start position:0%
+is a 10 dimensional
+ 
+
+ align:start position:0%
+is a 10 dimensional
+Ser equal to
+
+ align:start position:0%
+Ser equal to
+ 
+
+ align:start position:0%
+Ser equal to
+10 and uh and you have a yeah you have
+
+ align:start position:0%
+10 and uh and you have a yeah you have
+ 
+
+ align:start position:0%
+10 and uh and you have a yeah you have
+the Einstein term and then you have
+
+ align:start position:0%
+the Einstein term and then you have
+ 
+
+ align:start position:0%
+the Einstein term and then you have
+forms associated with all this flock uh
+
+ align:start position:0%
+forms associated with all this flock uh
+ 
+
+ align:start position:0%
+forms associated with all this flock uh
+uh uh generalized gaug field etc for
+
+ align:start position:0%
+uh uh generalized gaug field etc for
+ 
+
+ align:start position:0%
+uh uh generalized gaug field etc for
+ETC okay and as we said
+
+ align:start position:0%
+ETC okay and as we said
+ 
+
+ align:start position:0%
+ETC okay and as we said
+before the relation with String Theory
+
+ align:start position:0%
+before the relation with String Theory
+ 
+
+ align:start position:0%
+before the relation with String Theory
+the Newton
+
+ align:start position:0%
+the Newton
+ 
+
+ align:start position:0%
+the Newton
+constant should be proportional to GS
+
+ align:start position:0%
+constant should be proportional to GS
+ 
+
+ align:start position:0%
+constant should be proportional to GS
+squ okay so you can actually work the
+
+ align:start position:0%
+squ okay so you can actually work the
+ 
+
+ align:start position:0%
+squ okay so you can actually work the
+work out the prefactor precisely so let
+
+ align:start position:0%
+work out the prefactor precisely so let
+ 
+
+ align:start position:0%
+work out the prefactor precisely so let
+me just write down the preactor so the
+
+ align:start position:0%
+me just write down the preactor so the
+ 
+
+ align:start position:0%
+me just write down the preactor so the
+relation with the string is yeah just on
+
+ align:start position:0%
+relation with the string is yeah just on
+ 
+
+ align:start position:0%
+relation with the string is yeah just on
+dimensional ground so this is the Newton
+
+ align:start position:0%
+dimensional ground so this is the Newton
+ 
+
+ align:start position:0%
+dimensional ground so this is the Newton
+constant in 10 Dimension so this would
+
+ align:start position:0%
+constant in 10 Dimension so this would
+ 
+
+ align:start position:0%
+constant in 10 Dimension so this would
+have Dimension
+
+ align:start position:0%
+have Dimension
+ 
+
+ align:start position:0%
+have Dimension
+eight in terms of the length have a
+
+ align:start position:0%
+eight in terms of the length have a
+ 
+
+ align:start position:0%
+eight in terms of the length have a
+dimension eight so the right hand side
+
+ align:start position:0%
+dimension eight so the right hand side
+ 
+
+ align:start position:0%
+dimension eight so the right hand side
+must be Alpha Prime to the power four
+
+ align:start position:0%
+must be Alpha Prime to the power four
+ 
+
+ align:start position:0%
+must be Alpha Prime to the power four
+because this is only L scale in Str
+
+ align:start position:0%
+because this is only L scale in Str
+ 
+
+ align:start position:0%
+because this is only L scale in Str
+the and then the prefactor turn out to
+
+ align:start position:0%
+the and then the prefactor turn out to
+ 
+
+ align:start position:0%
+the and then the prefactor turn out to
+be so you can work out the prefactor so
+
+ align:start position:0%
+be so you can work out the prefactor so
+ 
+
+ align:start position:0%
+be so you can work out the prefactor so
+turn out 16 Pi GN is equal to 2 pi 2
+
+ align:start position:0%
+turn out 16 Pi GN is equal to 2 pi 2
+ 
+
+ align:start position:0%
+turn out 16 Pi GN is equal to 2 pi 2
+the^
+
+ align:start position:0%
+the^
+ 
+
+ align:start position:0%
+the^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh uh uh say when you work out the
+
+ align:start position:0%
+okay uh uh uh say when you work out the
+ 
+
+ align:start position:0%
+okay uh uh uh say when you work out the
+Lo Factor Ser you can work out this pre
+
+ align:start position:0%
+Lo Factor Ser you can work out this pre
+ 
+
+ align:start position:0%
+Lo Factor Ser you can work out this pre
+precise
+
+ align:start position:0%
+precise
+ 
+
+ align:start position:0%
+precise
+factor and the regime of the validity of
+
+ align:start position:0%
+factor and the regime of the validity of
+ 
+
+ align:start position:0%
+factor and the regime of the validity of
+this type to be super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity is that the GS is much much
+
+ align:start position:0%
+gravity is that the GS is much much
+ 
+
+ align:start position:0%
+gravity is that the GS is much much
+smaller than one string com should be
+
+ align:start position:0%
+smaller than one string com should be
+ 
+
+ align:start position:0%
+smaller than one string com should be
+much much smaller than
+
+ align:start position:0%
+much much smaller than
+ 
+
+ align:start position:0%
+much much smaller than
+one so that just tell this is a
+
+ align:start position:0%
+one so that just tell this is a
+ 
+
+ align:start position:0%
+one so that just tell this is a
+statement that the string Loop
+
+ align:start position:0%
+statement that the string Loop
+ 
+
+ align:start position:0%
+statement that the string Loop
+correction should be small because when
+
+ align:start position:0%
+correction should be small because when
+ 
+
+ align:start position:0%
+correction should be small because when
+the G stram become big the loop
+
+ align:start position:0%
+the G stram become big the loop
+ 
+
+ align:start position:0%
+the G stram become big the loop
+correction become more more and more
+
+ align:start position:0%
+correction become more more and more
+ 
+
+ align:start position:0%
+correction become more more and more
+important uh uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the loop correction will be more
+
+ align:start position:0%
+the loop correction will be more
+ 
+
+ align:start position:0%
+the loop correction will be more
+important from the point of view of
+
+ align:start position:0%
+important from the point of view of
+ 
+
+ align:start position:0%
+important from the point of view of
+gravity uh these are quantum
+
+ align:start position:0%
+gravity uh these are quantum
+ 
+
+ align:start position:0%
+gravity uh these are quantum
+gravitational Corrections and so so when
+
+ align:start position:0%
+gravitational Corrections and so so when
+ 
+
+ align:start position:0%
+gravitational Corrections and so so when
+G stram become bigger the quantum
+
+ align:start position:0%
+G stram become bigger the quantum
+ 
+
+ align:start position:0%
+G stram become bigger the quantum
+gravitational Corrections so the space
+
+ align:start position:0%
+gravitational Corrections so the space
+ 
+
+ align:start position:0%
+gravitational Corrections so the space
+time we fluctuate more and then of
+
+ align:start position:0%
+time we fluctuate more and then of
+ 
+
+ align:start position:0%
+time we fluctuate more and then of
+course you cannot trust the classical
+
+ align:start position:0%
+course you cannot trust the classical
+ 
+
+ align:start position:0%
+course you cannot trust the classical
+gravity in that regime so if you want to
+
+ align:start position:0%
+gravity in that regime so if you want to
+ 
+
+ align:start position:0%
+gravity in that regime so if you want to
+trust the classical gravity you want to
+
+ align:start position:0%
+trust the classical gravity you want to
+ 
+
+ align:start position:0%
+trust the classical gravity you want to
+have small cing or translate into this
+
+ align:start position:0%
+have small cing or translate into this
+ 
+
+ align:start position:0%
+have small cing or translate into this
+language as a newon con have to be small
+
+ align:start position:0%
+language as a newon con have to be small
+ 
+
+ align:start position:0%
+language as a newon con have to be small
+okay the Newton constant have to be
+
+ align:start position:0%
+okay the Newton constant have to be
+ 
+
+ align:start position:0%
+okay the Newton constant have to be
+small that means the gravity is weak
+
+ align:start position:0%
+small that means the gravity is weak
+ 
+
+ align:start position:0%
+small that means the gravity is weak
+okay that means gravity is weak but in
+
+ align:start position:0%
+okay that means gravity is weak but in
+ 
+
+ align:start position:0%
+okay that means gravity is weak but in
+real life gravity is weak so it's
+
+ align:start position:0%
+real life gravity is weak so it's
+ 
+
+ align:start position:0%
+real life gravity is weak so it's
+okay and uh so this means the quantum
+
+ align:start position:0%
+okay and uh so this means the quantum
+ 
+
+ align:start position:0%
+okay and uh so this means the quantum
+correction is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small so you can trust classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity okay so you can TR a classical
+
+ align:start position:0%
+gravity okay so you can TR a classical
+ 
+
+ align:start position:0%
+gravity okay so you can TR a classical
+gravity and we also want the uh the
+
+ align:start position:0%
+gravity and we also want the uh the
+ 
+
+ align:start position:0%
+gravity and we also want the uh the
+energy no energy so we want the energy
+
+ align:start position:0%
+energy no energy so we want the energy
+ 
+
+ align:start position:0%
+energy no energy so we want the energy
+Square to be smaller than one over Alpha
+
+ align:start position:0%
+Square to be smaller than one over Alpha
+ 
+
+ align:start position:0%
+Square to be smaller than one over Alpha
+Prime because when when the energy
+
+ align:start position:0%
+Prime because when when the energy
+ 
+
+ align:start position:0%
+Prime because when when the energy
+Square become with all the One alha
+
+ align:start position:0%
+Square become with all the One alha
+ 
+
+ align:start position:0%
+Square become with all the One alha
+Prime then the massive stream modes
+
+ align:start position:0%
+Prime then the massive stream modes
+ 
+
+ align:start position:0%
+Prime then the massive stream modes
+become important because all the massive
+
+ align:start position:0%
+become important because all the massive
+ 
+
+ align:start position:0%
+become important because all the massive
+stream mode have mass square of one of
+
+ align:start position:0%
+stream mode have mass square of one of
+ 
+
+ align:start position:0%
+stream mode have mass square of one of
+AL Prime and if we only want to
+
+ align:start position:0%
+AL Prime and if we only want to
+ 
+
+ align:start position:0%
+AL Prime and if we only want to
+concentrate on the massless modes and
+
+ align:start position:0%
+concentrate on the massless modes and
+ 
+
+ align:start position:0%
+concentrate on the massless modes and
+you don't want to excite them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and also you want the curvature of
+
+ align:start position:0%
+okay and also you want the curvature of
+ 
+
+ align:start position:0%
+okay and also you want the curvature of
+the space time here we consider in curve
+
+ align:start position:0%
+the space time here we consider in curve
+ 
+
+ align:start position:0%
+the space time here we consider in curve
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+time so you want want the curvature to
+
+ align:start position:0%
+time so you want want the curvature to
+ 
+
+ align:start position:0%
+time so you want want the curvature to
+be much smaller than one of alpha
+
+ align:start position:0%
+be much smaller than one of alpha
+ 
+
+ align:start position:0%
+be much smaller than one of alpha
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+okay so um so this gravity essentially
+
+ align:start position:0%
+okay so um so this gravity essentially
+ 
+
+ align:start position:0%
+okay so um so this gravity essentially
+when you consider the mass this particle
+
+ align:start position:0%
+when you consider the mass this particle
+ 
+
+ align:start position:0%
+when you consider the mass this particle
+you consider the particle limit of the
+
+ align:start position:0%
+you consider the particle limit of the
+ 
+
+ align:start position:0%
+you consider the particle limit of the
+space time so so this can be considered
+
+ align:start position:0%
+space time so so this can be considered
+ 
+
+ align:start position:0%
+space time so so this can be considered
+say as that you consider the space time
+
+ align:start position:0%
+say as that you consider the space time
+ 
+
+ align:start position:0%
+say as that you consider the space time
+curv the space time curvature radius is
+
+ align:start position:0%
+curv the space time curvature radius is
+ 
+
+ align:start position:0%
+curv the space time curvature radius is
+much much so so Alpha primeti this gives
+
+ align:start position:0%
+much much so so Alpha primeti this gives
+ 
+
+ align:start position:0%
+much much so so Alpha primeti this gives
+the rough lens scale of a
+
+ align:start position:0%
+the rough lens scale of a
+ 
+
+ align:start position:0%
+the rough lens scale of a
+string and when the curvature is much
+
+ align:start position:0%
+string and when the curvature is much
+ 
+
+ align:start position:0%
+string and when the curvature is much
+much smaller one prime that means that
+
+ align:start position:0%
+much smaller one prime that means that
+ 
+
+ align:start position:0%
+much smaller one prime that means that
+the side of the string is
+
+ align:start position:0%
+the side of the string is
+ 
+
+ align:start position:0%
+the side of the string is
+Tiny compare to the curvature radius
+
+ align:start position:0%
+Tiny compare to the curvature radius
+ 
+
+ align:start position:0%
+Tiny compare to the curvature radius
+okay the typical Sid of your system and
+
+ align:start position:0%
+okay the typical Sid of your system and
+ 
+
+ align:start position:0%
+okay the typical Sid of your system and
+that's you can roughly treat them as a
+
+ align:start position:0%
+that's you can roughly treat them as a
+ 
+
+ align:start position:0%
+that's you can roughly treat them as a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+particles and that's what the gravity
+
+ align:start position:0%
+particles and that's what the gravity
+ 
+
+ align:start position:0%
+particles and that's what the gravity
+Theory does yeah in the super gravity
+
+ align:start position:0%
+Theory does yeah in the super gravity
+ 
+
+ align:start position:0%
+Theory does yeah in the super gravity
+Theory it's all Point particles
+
+ align:start position:0%
+Theory it's all Point particles
+ 
+
+ align:start position:0%
+Theory it's all Point particles
+okay and uh and so this means we
+
+ align:start position:0%
+okay and uh and so this means we
+ 
+
+ align:start position:0%
+okay and uh and so this means we
+toule massive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modes okay massive
+
+ align:start position:0%
+modes okay massive
+ 
+
+ align:start position:0%
+modes okay massive
+modes so you can concentrate on mass
+
+ align:start position:0%
+modes so you can concentrate on mass
+ 
+
+ align:start position:0%
+modes so you can concentrate on mass
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modes
+
+ align:start position:0%
+modes
+ 
+
+ align:start position:0%
+modes
+so whenever you take a limit you always
+
+ align:start position:0%
+so whenever you take a limit you always
+ 
+
+ align:start position:0%
+so whenever you take a limit you always
+have to take the dimension is numers
+
+ align:start position:0%
+have to take the dimension is numers
+ 
+
+ align:start position:0%
+have to take the dimension is numers
+more so the dimension is number is Alpha
+
+ align:start position:0%
+more so the dimension is number is Alpha
+ 
+
+ align:start position:0%
+more so the dimension is number is Alpha
+Prime Times curvature Al time times
+
+ align:start position:0%
+Prime Times curvature Al time times
+ 
+
+ align:start position:0%
+Prime Times curvature Al time times
+energy square but in reality we often
+
+ align:start position:0%
+energy square but in reality we often
+ 
+
+ align:start position:0%
+energy square but in reality we often
+when we work with the series we often
+
+ align:start position:0%
+when we work with the series we often
+ 
+
+ align:start position:0%
+when we work with the series we often
+just keep our curvature or our energy
+
+ align:start position:0%
+just keep our curvature or our energy
+ 
+
+ align:start position:0%
+just keep our curvature or our energy
+scale as what we want and then in
+
+ align:start position:0%
+scale as what we want and then in
+ 
+
+ align:start position:0%
+scale as what we want and then in
+talking about this limit we just say we
+
+ align:start position:0%
+talking about this limit we just say we
+ 
+
+ align:start position:0%
+talking about this limit we just say we
+take Alpa Prime goes to zero limit okay
+
+ align:start position:0%
+take Alpa Prime goes to zero limit okay
+ 
+
+ align:start position:0%
+take Alpa Prime goes to zero limit okay
+we say we take Alpa Prime goes to zero
+
+ align:start position:0%
+we say we take Alpa Prime goes to zero
+ 
+
+ align:start position:0%
+we say we take Alpa Prime goes to zero
+limit so that means a low energy limit
+
+ align:start position:0%
+limit so that means a low energy limit
+ 
+
+ align:start position:0%
+limit so that means a low energy limit
+okay even though uh uh legitimately this
+
+ align:start position:0%
+okay even though uh uh legitimately this
+ 
+
+ align:start position:0%
+okay even though uh uh legitimately this
+is not the right thing to say because
+
+ align:start position:0%
+is not the right thing to say because
+ 
+
+ align:start position:0%
+is not the right thing to say because
+this is dimensional
+
+ align:start position:0%
+this is dimensional
+ 
+
+ align:start position:0%
+this is dimensional
+parameter and so so the regime which
+
+ align:start position:0%
+parameter and so so the regime which
+ 
+
+ align:start position:0%
+parameter and so so the regime which
+super gravity Works can be form at say
+
+ align:start position:0%
+super gravity Works can be form at say
+ 
+
+ align:start position:0%
+super gravity Works can be form at say
+as Alpha Prime go to zero and the g
+
+ align:start position:0%
+as Alpha Prime go to zero and the g
+ 
+
+ align:start position:0%
+as Alpha Prime go to zero and the g
+string go to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so in this regime now you can
+
+ align:start position:0%
+okay so so in this regime now you can
+ 
+
+ align:start position:0%
+okay so so in this regime now you can
+work with super gravity and now you can
+
+ align:start position:0%
+work with super gravity and now you can
+ 
+
+ align:start position:0%
+work with super gravity and now you can
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+generalize this story to the brains okay
+
+ align:start position:0%
+generalize this story to the brains okay
+ 
+
+ align:start position:0%
+generalize this story to the brains okay
+now gener this story for brains so now
+
+ align:start position:0%
+now gener this story for brains so now
+ 
+
+ align:start position:0%
+now gener this story for brains so now
+let me say a few things about the D
+
+ align:start position:0%
+let me say a few things about the D
+ 
+
+ align:start position:0%
+let me say a few things about the D
+brain d three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so de bra this rebr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charged
+
+ align:start position:0%
+charged
+ 
+
+ align:start position:0%
+charged
+under C4 Plus
+
+ align:start position:0%
+under C4 Plus
+ 
+
+ align:start position:0%
+under C4 Plus
+this C4
+
+ align:start position:0%
+this C4
+ 
+
+ align:start position:0%
+this C4
+plus and we said this C4 plus is
+
+ align:start position:0%
+plus and we said this C4 plus is
+ 
+
+ align:start position:0%
+plus and we said this C4 plus is
+required to be
+
+ align:start position:0%
+required to be
+ 
+
+ align:start position:0%
+required to be
+selfdual that means any source of C4
+
+ align:start position:0%
+selfdual that means any source of C4
+ 
+
+ align:start position:0%
+selfdual that means any source of C4
+plus must carry both electric and
+
+ align:start position:0%
+plus must carry both electric and
+ 
+
+ align:start position:0%
+plus must carry both electric and
+magnetic charge so that
+
+ align:start position:0%
+magnetic charge so that
+ 
+
+ align:start position:0%
+magnetic charge so that
+means that for the this re
+
+ align:start position:0%
+means that for the this re
+ 
+
+ align:start position:0%
+means that for the this re
+brain say if you define an electric
+
+ align:start position:0%
+brain say if you define an electric
+ 
+
+ align:start position:0%
+brain say if you define an electric
+charge to
+
+ align:start position:0%
+charge to
+ 
+
+ align:start position:0%
+charge to
+be so now so the this three brain is a
+
+ align:start position:0%
+be so now so the this three brain is a
+ 
+
+ align:start position:0%
+be so now so the this three brain is a
+threedimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object and the transverse direction is a
+
+ align:start position:0%
+object and the transverse direction is a
+ 
+
+ align:start position:0%
+object and the transverse direction is a
+six dimensional okay because this is
+
+ align:start position:0%
+six dimensional okay because this is
+ 
+
+ align:start position:0%
+six dimensional okay because this is
+three plus one including time so the
+
+ align:start position:0%
+three plus one including time so the
+ 
+
+ align:start position:0%
+three plus one including time so the
+transverse direction is is six
+
+ align:start position:0%
+transverse direction is is six
+ 
+
+ align:start position:0%
+transverse direction is is six
+dimensional so we can simply just think
+
+ align:start position:0%
+dimensional so we can simply just think
+ 
+
+ align:start position:0%
+dimensional so we can simply just think
+about the this Rin so if we if we ignore
+
+ align:start position:0%
+about the this Rin so if we if we ignore
+ 
+
+ align:start position:0%
+about the this Rin so if we if we ignore
+the spal direction along the
+
+ align:start position:0%
+the spal direction along the
+ 
+
+ align:start position:0%
+the spal direction along the
+brain then then this re brain the
+
+ align:start position:0%
+brain then then this re brain the
+ 
+
+ align:start position:0%
+brain then then this re brain the
+transverse Direction then can be just
+
+ align:start position:0%
+transverse Direction then can be just
+ 
+
+ align:start position:0%
+transverse Direction then can be just
+consider a point in R six okay okay so
+
+ align:start position:0%
+consider a point in R six okay okay so
+ 
+
+ align:start position:0%
+consider a point in R six okay okay so
+so way to think about the this rant the
+
+ align:start position:0%
+so way to think about the this rant the
+ 
+
+ align:start position:0%
+so way to think about the this rant the
+surrounding the dis rant just it's
+
+ align:start position:0%
+surrounding the dis rant just it's
+ 
+
+ align:start position:0%
+surrounding the dis rant just it's
+analog of a point in R6 in the six
+
+ align:start position:0%
+analog of a point in R6 in the six
+ 
+
+ align:start position:0%
+analog of a point in R6 in the six
+dimensional space this this
+
+ align:start position:0%
+dimensional space this this
+ 
+
+ align:start position:0%
+dimensional space this this
+clear this is going to be very important
+
+ align:start position:0%
+clear this is going to be very important
+ 
+
+ align:start position:0%
+clear this is going to be very important
+and then the surrounding this
+
+ align:start position:0%
+and then the surrounding this
+ 
+
+ align:start position:0%
+and then the surrounding this
+point the sphere will be
+
+ align:start position:0%
+point the sphere will be
+ 
+
+ align:start position:0%
+point the sphere will be
+S5 okay just like in the electric case
+
+ align:start position:0%
+S5 okay just like in the electric case
+ 
+
+ align:start position:0%
+S5 okay just like in the electric case
+just in the like and M case this is the
+
+ align:start position:0%
+just in the like and M case this is the
+ 
+
+ align:start position:0%
+just in the like and M case this is the
+S2 surrounding the point particle and
+
+ align:start position:0%
+S2 surrounding the point particle and
+ 
+
+ align:start position:0%
+S2 surrounding the point particle and
+this S5 is the sphere which surrounding
+
+ align:start position:0%
+this S5 is the sphere which surrounding
+ 
+
+ align:start position:0%
+this S5 is the sphere which surrounding
+the whole this rein and and then this D
+
+ align:start position:0%
+the whole this rein and and then this D
+ 
+
+ align:start position:0%
+the whole this rein and and then this D
+can have electric and magnetic flux
+
+ align:start position:0%
+can have electric and magnetic flux
+ 
+
+ align:start position:0%
+can have electric and magnetic flux
+through this S5 okay and so electric
+
+ align:start position:0%
+through this S5 okay and so electric
+ 
+
+ align:start position:0%
+through this S5 okay and so electric
+charge would
+
+ align:start position:0%
+charge would
+ 
+
+ align:start position:0%
+charge would
+be just the five
+
+ align:start position:0%
+be just the five
+ 
+
+ align:start position:0%
+be just the five
+form surrounding through
+
+ align:start position:0%
+form surrounding through
+ 
+
+ align:start position:0%
+form surrounding through
+it and uh and uh uh uh um magnetic
+
+ align:start position:0%
+it and uh and uh uh uh um magnetic
+ 
+
+ align:start position:0%
+it and uh and uh uh uh um magnetic
+charge would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be just uh uh um right why is the Dual
+
+ align:start position:0%
+be just uh uh um right why is the Dual
+ 
+
+ align:start position:0%
+be just uh uh um right why is the Dual
+of a five form is one form just just
+
+ align:start position:0%
+of a five form is one form just just
+ 
+
+ align:start position:0%
+of a five form is one form just just
+like the relation between these
+
+ align:start position:0%
+like the relation between these
+ 
+
+ align:start position:0%
+like the relation between these
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+okay and now because of self Duality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition then it must be the same so
+
+ align:start position:0%
+condition then it must be the same so
+ 
+
+ align:start position:0%
+condition then it must be the same so
+that means for this re brain the
+
+ align:start position:0%
+that means for this re brain the
+ 
+
+ align:start position:0%
+that means for this re brain the
+electric and magnetic charge must be the
+
+ align:start position:0%
+electric and magnetic charge must be the
+ 
+
+ align:start position:0%
+electric and magnetic charge must be the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+okay and also for higher dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object same why not it's because F5 you
+
+ align:start position:0%
+object same why not it's because F5 you
+ 
+
+ align:start position:0%
+object same why not it's because F5 you
+F5 star
+
+ align:start position:0%
+F5 star
+ 
+
+ align:start position:0%
+F5 star
+it's because of that because of that
+
+ align:start position:0%
+it's because of that because of that
+ 
+
+ align:start position:0%
+it's because of that because of that
+self du condition
+
+ align:start position:0%
+self du condition
+ 
+
+ align:start position:0%
+self du condition
+yeah so Electric magnetic charge of the
+
+ align:start position:0%
+yeah so Electric magnetic charge of the
+ 
+
+ align:start position:0%
+yeah so Electric magnetic charge of the
+this R must be the same they must carry
+
+ align:start position:0%
+this R must be the same they must carry
+ 
+
+ align:start position:0%
+this R must be the same they must carry
+both electric and magnetic
+
+ align:start position:0%
+both electric and magnetic
+ 
+
+ align:start position:0%
+both electric and magnetic
+charge and now this direct quation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition also
+
+ align:start position:0%
+condition also
+ 
+
+ align:start position:0%
+condition also
+works for higher dimensional
+
+ align:start position:0%
+works for higher dimensional
+ 
+
+ align:start position:0%
+works for higher dimensional
+objects and again it's a very simple
+
+ align:start position:0%
+objects and again it's a very simple
+ 
+
+ align:start position:0%
+objects and again it's a very simple
+exercise to do it
+
+ align:start position:0%
+exercise to do it
+ 
+
+ align:start position:0%
+exercise to do it
+very simple exercise to General
+
+ align:start position:0%
+very simple exercise to General
+ 
+
+ align:start position:0%
+very simple exercise to General
+generalize The Rock's argument to higher
+
+ align:start position:0%
+generalize The Rock's argument to higher
+ 
+
+ align:start position:0%
+generalize The Rock's argument to higher
+Dimension again it just related how you
+
+ align:start position:0%
+Dimension again it just related how you
+ 
+
+ align:start position:0%
+Dimension again it just related how you
+treat those higher dimensional forms
+
+ align:start position:0%
+treat those higher dimensional forms
+ 
+
+ align:start position:0%
+treat those higher dimensional forms
+ex again it's a very simple step but
+
+ align:start position:0%
+ex again it's a very simple step but
+ 
+
+ align:start position:0%
+ex again it's a very simple step but
+it's a very important
+
+ align:start position:0%
+it's a very important
+ 
+
+ align:start position:0%
+it's a very important
+step so that tells
+
+ align:start position:0%
+step so that tells
+ 
+
+ align:start position:0%
+step so that tells
+me that for this re brain which is
+
+ align:start position:0%
+me that for this re brain which is
+ 
+
+ align:start position:0%
+me that for this re brain which is
+selfdual which is carry both INRI and
+
+ align:start position:0%
+selfdual which is carry both INRI and
+ 
+
+ align:start position:0%
+selfdual which is carry both INRI and
+magnetic
+
+ align:start position:0%
+magnetic
+ 
+
+ align:start position:0%
+magnetic
+charge then you have to satisfy this
+
+ align:start position:0%
+charge then you have to satisfy this
+ 
+
+ align:start position:0%
+charge then you have to satisfy this
+quation condition then that means the
+
+ align:start position:0%
+quation condition then that means the
+ 
+
+ align:start position:0%
+quation condition then that means the
+minimum
+
+ align:start position:0%
+minimum
+ 
+
+ align:start position:0%
+minimum
+single this
+
+ align:start position:0%
+single this
+ 
+
+ align:start position:0%
+single this
+rebrin the minimal charged object must
+
+ align:start position:0%
+rebrin the minimal charged object must
+ 
+
+ align:start position:0%
+rebrin the minimal charged object must
+be the charge must be square otk 2
+
+ align:start position:0%
+be the charge must be square otk 2
+ 
+
+ align:start position:0%
+be the charge must be square otk 2
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+okay and for n of
+
+ align:start position:0%
+okay and for n of
+ 
+
+ align:start position:0%
+okay and for n of
+them so must be G3 = to Q3 = to 2
+
+ align:start position:0%
+them so must be G3 = to Q3 = to 2
+ 
+
+ align:start position:0%
+them so must be G3 = to Q3 = to 2
+pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now we have specified the analog
+
+ align:start position:0%
+so so now we have specified the analog
+ 
+
+ align:start position:0%
+so so now we have specified the analog
+for the for and M those conditions okay
+
+ align:start position:0%
+for the for and M those conditions okay
+ 
+
+ align:start position:0%
+for the for and M those conditions okay
+for uh now we also have to specify the
+
+ align:start position:0%
+for uh now we also have to specify the
+ 
+
+ align:start position:0%
+for uh now we also have to specify the
+mass of the this rebrin so as we
+
+ align:start position:0%
+mass of the this rebrin so as we
+ 
+
+ align:start position:0%
+mass of the this rebrin so as we
+discussed before tension of the dist re
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain tension of a de
+
+ align:start position:0%
+brain tension of a de
+ 
+
+ align:start position:0%
+brain tension of a de
+brain should be proportional to one over
+
+ align:start position:0%
+brain should be proportional to one over
+ 
+
+ align:start position:0%
+brain should be proportional to one over
+G string okay that's you also did in
+
+ align:start position:0%
+G string okay that's you also did in
+ 
+
+ align:start position:0%
+G string okay that's you also did in
+your P set and again you
+
+ align:start position:0%
+your P set and again you
+ 
+
+ align:start position:0%
+your P set and again you
+can by doing a precise calculation you
+
+ align:start position:0%
+can by doing a precise calculation you
+ 
+
+ align:start position:0%
+can by doing a precise calculation you
+can work out the precise prefactors it
+
+ align:start position:0%
+can work out the precise prefactors it
+ 
+
+ align:start position:0%
+can work out the precise prefactors it
+turns out it turns out actually to be
+
+ align:start position:0%
+turns out it turns out actually to be
+ 
+
+ align:start position:0%
+turns out it turns out actually to be
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+form uh to be the following form is the
+
+ align:start position:0%
+form uh to be the following form is the
+ 
+
+ align:start position:0%
+form uh to be the following form is the
+Q3 divided by 16 Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+GN okay and and the GN is g g string
+
+ align:start position:0%
+GN okay and and the GN is g g string
+ 
+
+ align:start position:0%
+GN okay and and the GN is g g string
+Square so if it translate into
+
+ align:start position:0%
+Square so if it translate into
+ 
+
+ align:start position:0%
+Square so if it translate into
+so for n this rein then would be n ided
+
+ align:start position:0%
+so for n this rein then would be n ided
+ 
+
+ align:start position:0%
+so for n this rein then would be n ided
+by 2 pi Cub GS Alpha Prime Square okay
+
+ align:start position:0%
+by 2 pi Cub GS Alpha Prime Square okay
+ 
+
+ align:start position:0%
+by 2 pi Cub GS Alpha Prime Square okay
+so so this GS Alpha Prime Square we know
+
+ align:start position:0%
+so so this GS Alpha Prime Square we know
+ 
+
+ align:start position:0%
+so so this GS Alpha Prime Square we know
+on General ground so GS with one over GS
+
+ align:start position:0%
+on General ground so GS with one over GS
+ 
+
+ align:start position:0%
+on General ground so GS with one over GS
+Bel on General ground and Alpha Prime
+
+ align:start position:0%
+Bel on General ground and Alpha Prime
+ 
+
+ align:start position:0%
+Bel on General ground and Alpha Prime
+Square just from dimensional analysis
+
+ align:start position:0%
+Square just from dimensional analysis
+ 
+
+ align:start position:0%
+Square just from dimensional analysis
+because this is a threedimensional
+
+ align:start position:0%
+because this is a threedimensional
+ 
+
+ align:start position:0%
+because this is a threedimensional
+object the tension is ATT tension we
+
+ align:start position:0%
+object the tension is ATT tension we
+ 
+
+ align:start position:0%
+object the tension is ATT tension we
+have mass Dimension four so that's why
+
+ align:start position:0%
+have mass Dimension four so that's why
+ 
+
+ align:start position:0%
+have mass Dimension four so that's why
+you have one over Alpha Prime Square
+
+ align:start position:0%
+you have one over Alpha Prime Square
+ 
+
+ align:start position:0%
+you have one over Alpha Prime Square
+here and then than the other 2 pi Cube
+
+ align:start position:0%
+here and then than the other 2 pi Cube
+ 
+
+ align:start position:0%
+here and then than the other 2 pi Cube
+from precise calculations and you can
+
+ align:start position:0%
+from precise calculations and you can
+ 
+
+ align:start position:0%
+from precise calculations and you can
+also write it in this form so in terms
+
+ align:start position:0%
+also write it in this form so in terms
+ 
+
+ align:start position:0%
+also write it in this form so in terms
+of newon constant
+
+ align:start position:0%
+of newon constant
+ 
+
+ align:start position:0%
+of newon constant
+okay and the reason I write this form
+
+ align:start position:0%
+okay and the reason I write this form
+ 
+
+ align:start position:0%
+okay and the reason I write this form
+because this is a very special case and
+
+ align:start position:0%
+because this is a very special case and
+ 
+
+ align:start position:0%
+because this is a very special case and
+you see that the tension is actually
+
+ align:start position:0%
+you see that the tension is actually
+ 
+
+ align:start position:0%
+you see that the tension is actually
+precisely related to the charge and
+
+ align:start position:0%
+precisely related to the charge and
+ 
+
+ align:start position:0%
+precisely related to the charge and
+divided by the square root of lutant
+
+ align:start position:0%
+divided by the square root of lutant
+ 
+
+ align:start position:0%
+divided by the square root of lutant
+constant and turns out only special
+
+ align:start position:0%
+constant and turns out only special
+ 
+
+ align:start position:0%
+constant and turns out only special
+object only special object have this
+
+ align:start position:0%
+object only special object have this
+ 
+
+ align:start position:0%
+object only special object have this
+kind of property and this so- called BPS
+
+ align:start position:0%
+kind of property and this so- called BPS
+ 
+
+ align:start position:0%
+kind of property and this so- called BPS
+objects will not go to there it's ready
+
+ align:start position:0%
+objects will not go to there it's ready
+ 
+
+ align:start position:0%
+objects will not go to there it's ready
+to those brain a super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric anyway so so these are the
+
+ align:start position:0%
+symmetric anyway so so these are the
+ 
+
+ align:start position:0%
+symmetric anyway so so these are the
+mass of the essentially this is the mass
+
+ align:start position:0%
+mass of the essentially this is the mass
+ 
+
+ align:start position:0%
+mass of the essentially this is the mass
+of the brain and this are the charge of
+
+ align:start position:0%
+of the brain and this are the charge of
+ 
+
+ align:start position:0%
+of the brain and this are the charge of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+brain when you specify the charge then
+
+ align:start position:0%
+brain when you specify the charge then
+ 
+
+ align:start position:0%
+brain when you specify the charge then
+those fields then those flux areally
+
+ align:start position:0%
+those fields then those flux areally
+ 
+
+ align:start position:0%
+those fields then those flux areally
+determined and then then the then the C4
+
+ align:start position:0%
+determined and then then the then the C4
+ 
+
+ align:start position:0%
+determined and then then the then the C4
+potential are uniquely
+
+ align:start position:0%
+potential are uniquely
+ 
+
+ align:start position:0%
+potential are uniquely
+determined up to gaug symmetry are
+
+ align:start position:0%
+determined up to gaug symmetry are
+ 
+
+ align:start position:0%
+determined up to gaug symmetry are
+determined and then now you can plug
+
+ align:start position:0%
+determined and then now you can plug
+ 
+
+ align:start position:0%
+determined and then now you can plug
+into the generation of the einin you
+
+ align:start position:0%
+into the generation of the einin you
+ 
+
+ align:start position:0%
+into the generation of the einin you
+equation to work out the geometry okay
+
+ align:start position:0%
+equation to work out the geometry okay
+ 
+
+ align:start position:0%
+equation to work out the geometry okay
+so so again the Symmetry
+
+ align:start position:0%
+so so again the Symmetry
+ 
+
+ align:start position:0%
+so so again the Symmetry
+here yeah so I won't have time for the
+
+ align:start position:0%
+here yeah so I won't have time for the
+ 
+
+ align:start position:0%
+here yeah so I won't have time for the
+bottom line so that's okay um so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Symmetry preserved by the de brain by
+
+ align:start position:0%
+Symmetry preserved by the de brain by
+ 
+
+ align:start position:0%
+Symmetry preserved by the de brain by
+this re brain as we said before similar
+
+ align:start position:0%
+this re brain as we said before similar
+ 
+
+ align:start position:0%
+this re brain as we said before similar
+to all de brains is you have a pite
+
+ align:start position:0%
+to all de brains is you have a pite
+ 
+
+ align:start position:0%
+to all de brains is you have a pite
+symmetry along the brain
+
+ align:start position:0%
+symmetry along the brain
+ 
+
+ align:start position:0%
+symmetry along the brain
+Direction and then you have rotation
+
+ align:start position:0%
+Direction and then you have rotation
+ 
+
+ align:start position:0%
+Direction and then you have rotation
+symmetry in the transverse Direction
+
+ align:start position:0%
+symmetry in the transverse Direction
+ 
+
+ align:start position:0%
+symmetry in the transverse Direction
+along the brain so the transverse we
+
+ align:start position:0%
+along the brain so the transverse we
+ 
+
+ align:start position:0%
+along the brain so the transverse we
+have six Dimension so there's s so6 uh
+
+ align:start position:0%
+have six Dimension so there's s so6 uh
+ 
+
+ align:start position:0%
+have six Dimension so there's s so6 uh
+directions you can rotate in the and
+
+ align:start position:0%
+directions you can rotate in the and
+ 
+
+ align:start position:0%
+directions you can rotate in the and
+then then you have P symmetry in the one
+
+ align:start position:0%
+then then you have P symmetry in the one
+ 
+
+ align:start position:0%
+then then you have P symmetry in the one
+three Direction So based on these
+
+ align:start position:0%
+three Direction So based on these
+ 
+
+ align:start position:0%
+three Direction So based on these
+symmetries you can write
+
+ align:start position:0%
+symmetries you can write
+ 
+
+ align:start position:0%
+symmetries you can write
+down what the matric looks like you can
+
+ align:start position:0%
+down what the matric looks like you can
+ 
+
+ align:start position:0%
+down what the matric looks like you can
+write down answers for the matric okay
+
+ align:start position:0%
+write down answers for the matric okay
+ 
+
+ align:start position:0%
+write down answers for the matric okay
+just like what here you can write down
+
+ align:start position:0%
+just like what here you can write down
+ 
+
+ align:start position:0%
+just like what here you can write down
+the answers for the uh for the matric of
+
+ align:start position:0%
+the answers for the uh for the matric of
+ 
+
+ align:start position:0%
+the answers for the uh for the matric of
+a point particle B based on symmetry so
+
+ align:start position:0%
+a point particle B based on symmetry so
+ 
+
+ align:start position:0%
+a point particle B based on symmetry so
+here you can uh write down ansers uh
+
+ align:start position:0%
+here you can uh write down ansers uh
+ 
+
+ align:start position:0%
+here you can uh write down ansers uh
+for the matric based on symmetry so
+
+ align:start position:0%
+for the matric based on symmetry so
+ 
+
+ align:start position:0%
+for the matric based on symmetry so
+first you should have a
+
+ align:start position:0%
+first you should have a
+ 
+
+ align:start position:0%
+first you should have a
+part which is
+
+ align:start position:0%
+part which is
+ 
+
+ align:start position:0%
+part which is
+preserve PCR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry means this part can only be
+
+ align:start position:0%
+symmetry means this part can only be
+ 
+
+ align:start position:0%
+symmetry means this part can only be
+this form say along the brain Direction
+
+ align:start position:0%
+this form say along the brain Direction
+ 
+
+ align:start position:0%
+this form say along the brain Direction
+can only be this form times some overall
+
+ align:start position:0%
+can only be this form times some overall
+ 
+
+ align:start position:0%
+can only be this form times some overall
+factor which depend on R so R is the
+
+ align:start position:0%
+factor which depend on R so R is the
+ 
+
+ align:start position:0%
+factor which depend on R so R is the
+transverse radius from the brain and
+
+ align:start position:0%
+transverse radius from the brain and
+ 
+
+ align:start position:0%
+transverse radius from the brain and
+then the other Dimension must
+
+ align:start position:0%
+then the other Dimension must
+ 
+
+ align:start position:0%
+then the other Dimension must
+be then the other dimension must be
+
+ align:start position:0%
+be then the other dimension must be
+ 
+
+ align:start position:0%
+be then the other dimension must be
+spical symmetric so you can have a lot
+
+ align:start position:0%
+spical symmetric so you can have a lot
+ 
+
+ align:start position:0%
+spical symmetric so you can have a lot
+of factors and then d r squ and r Square
+
+ align:start position:0%
+of factors and then d r squ and r Square
+ 
+
+ align:start position:0%
+of factors and then d r squ and r Square
+D Omega 5 Square so this is S5
+
+ align:start position:0%
+D Omega 5 Square so this is S5
+ 
+
+ align:start position:0%
+D Omega 5 Square so this is S5
+surrounding the brain and then this is a
+
+ align:start position:0%
+surrounding the brain and then this is a
+ 
+
+ align:start position:0%
+surrounding the brain and then this is a
+radial Direction so this is the only uh
+
+ align:start position:0%
+radial Direction so this is the only uh
+ 
+
+ align:start position:0%
+radial Direction so this is the only uh
+form of the
+
+ align:start position:0%
+form of the
+ 
+
+ align:start position:0%
+form of the
+metric and essentially again as in the
+
+ align:start position:0%
+metric and essentially again as in the
+ 
+
+ align:start position:0%
+metric and essentially again as in the
+charge particle case you need to
+
+ align:start position:0%
+charge particle case you need to
+ 
+
+ align:start position:0%
+charge particle case you need to
+determine these two functions okay which
+
+ align:start position:0%
+determine these two functions okay which
+ 
+
+ align:start position:0%
+determine these two functions okay which
+you can plug in Einstein equation just
+
+ align:start position:0%
+you can plug in Einstein equation just
+ 
+
+ align:start position:0%
+you can plug in Einstein equation just
+determine these two
+
+ align:start position:0%
+determine these two
+ 
+
+ align:start position:0%
+determine these two
+functions so let me just write down the
+
+ align:start position:0%
+functions so let me just write down the
+ 
+
+ align:start position:0%
+functions so let me just write down the
+form of those functions then we discuss
+
+ align:start position:0%
+form of those functions then we discuss
+ 
+
+ align:start position:0%
+form of those functions then we discuss
+what they mean uh next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time somehow this year I'm consistently
+
+ align:start position:0%
+time somehow this year I'm consistently
+ 
+
+ align:start position:0%
+time somehow this year I'm consistently
+much much slower than what I did before
+
+ align:start position:0%
+much much slower than what I did before
+ 
+
+ align:start position:0%
+much much slower than what I did before
+maybe I'm explaining physics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better yeah um anyway so so now it's
+
+ align:start position:0%
+better yeah um anyway so so now it's
+ 
+
+ align:start position:0%
+better yeah um anyway so so now it's
+just a mechanical exercise sides you
+
+ align:start position:0%
+just a mechanical exercise sides you
+ 
+
+ align:start position:0%
+just a mechanical exercise sides you
+plug in these answers into the Einstein
+
+ align:start position:0%
+plug in these answers into the Einstein
+ 
+
+ align:start position:0%
+plug in these answers into the Einstein
+equation then you can find the two
+
+ align:start position:0%
+equation then you can find the two
+ 
+
+ align:start position:0%
+equation then you can find the two
+equations for for f and H then you can
+
+ align:start position:0%
+equations for for f and H then you can
+ 
+
+ align:start position:0%
+equations for for f and H then you can
+solve it in the old days when hor and
+
+ align:start position:0%
+solve it in the old days when hor and
+ 
+
+ align:start position:0%
+solve it in the old days when hor and
+singer did it uh uh maybe they don't
+
+ align:start position:0%
+singer did it uh uh maybe they don't
+ 
+
+ align:start position:0%
+singer did it uh uh maybe they don't
+maybe they did not have Mathematica yet
+
+ align:start position:0%
+maybe they did not have Mathematica yet
+ 
+
+ align:start position:0%
+maybe they did not have Mathematica yet
+but nowadays you can do it using
+
+ align:start position:0%
+but nowadays you can do it using
+ 
+
+ align:start position:0%
+but nowadays you can do it using
+Mathematica if you have the right
+
+ align:start position:0%
+Mathematica if you have the right
+ 
+
+ align:start position:0%
+Mathematica if you have the right
+program you can do it in five
+
+ align:start position:0%
+program you can do it in five
+ 
+
+ align:start position:0%
+program you can do it in five
+minutes but in the old days they were
+
+ align:start position:0%
+minutes but in the old days they were
+ 
+
+ align:start position:0%
+minutes but in the old days they were
+friend with wfr maybe they already have
+
+ align:start position:0%
+friend with wfr maybe they already have
+ 
+
+ align:start position:0%
+friend with wfr maybe they already have
+the program at that time anyway so so it
+
+ align:start position:0%
+the program at that time anyway so so it
+ 
+
+ align:start position:0%
+the program at that time anyway so so it
+was a more unch exercise to do at the
+
+ align:start position:0%
+was a more unch exercise to do at the
+ 
+
+ align:start position:0%
+was a more unch exercise to do at the
+time so you find actually the answer is
+
+ align:start position:0%
+time so you find actually the answer is
+ 
+
+ align:start position:0%
+time so you find actually the answer is
+very simple turns out both F and H they
+
+ align:start position:0%
+very simple turns out both F and H they
+ 
+
+ align:start position:0%
+very simple turns out both F and H they
+just yeah can be WR in the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form so
+
+ align:start position:0%
+form so
+ 
+
+ align:start position:0%
+form so
+H so H is lot function H is just a
+
+ align:start position:0%
+H so H is lot function H is just a
+ 
+
+ align:start position:0%
+H so H is lot function H is just a
+harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and R to the power 4 is given by some
+
+ align:start position:0%
+and R to the power 4 is given by some
+ 
+
+ align:start position:0%
+and R to the power 4 is given by some
+constant some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+GN new Newton constant times the this
+
+ align:start position:0%
+GN new Newton constant times the this
+ 
+
+ align:start position:0%
+GN new Newton constant times the this
+reent tension times n and can also be
+
+ align:start position:0%
+reent tension times n and can also be
+ 
+
+ align:start position:0%
+reent tension times n and can also be
+written as 4 Pi GSN Alp Prime
+
+ align:start position:0%
+written as 4 Pi GSN Alp Prime
+ 
+
+ align:start position:0%
+written as 4 Pi GSN Alp Prime
+squar
+
+ align:start position:0%
+squar
+ 
+
+ align:start position:0%
+squar
+okay so turn out those function are very
+
+ align:start position:0%
+okay so turn out those function are very
+ 
+
+ align:start position:0%
+okay so turn out those function are very
+simple they're just square root of a
+
+ align:start position:0%
+simple they're just square root of a
+ 
+
+ align:start position:0%
+simple they're just square root of a
+harmonic function so this is a harmonic
+
+ align:start position:0%
+harmonic function so this is a harmonic
+ 
+
+ align:start position:0%
+harmonic function so this is a harmonic
+function for the transverse R six so if
+
+ align:start position:0%
+function for the transverse R six so if
+ 
+
+ align:start position:0%
+function for the transverse R six so if
+you solve say a coolant problem and and
+
+ align:start position:0%
+you solve say a coolant problem and and
+ 
+
+ align:start position:0%
+you solve say a coolant problem and and
+that would be the solution this is the
+
+ align:start position:0%
+that would be the solution this is the
+ 
+
+ align:start position:0%
+that would be the solution this is the
+harmonic yeah so this is generation of
+
+ align:start position:0%
+harmonic yeah so this is generation of
+ 
+
+ align:start position:0%
+harmonic yeah so this is generation of
+one / R potential so this is just
+
+ align:start position:0%
+one / R potential so this is just
+ 
+
+ align:start position:0%
+one / R potential so this is just
+generation of one over R potential and
+
+ align:start position:0%
+generation of one over R potential and
+ 
+
+ align:start position:0%
+generation of one over R potential and
+then f and g is very simply related to
+
+ align:start position:0%
+then f and g is very simply related to
+ 
+
+ align:start position:0%
+then f and g is very simply related to
+this by square root and this uh this
+
+ align:start position:0%
+this by square root and this uh this
+ 
+
+ align:start position:0%
+this by square root and this uh this
+constant R to the^ 4 so this is not
+
+ align:start position:0%
+constant R to the^ 4 so this is not
+ 
+
+ align:start position:0%
+constant R to the^ 4 so this is not
+curvature this is just some constant uh
+
+ align:start position:0%
+curvature this is just some constant uh
+ 
+
+ align:start position:0%
+curvature this is just some constant uh
+stand
+
+ align:start position:0%
+stand
+ 
+
+ align:start position:0%
+stand
+I'm using the standard rotation and then
+
+ align:start position:0%
+I'm using the standard rotation and then
+ 
+
+ align:start position:0%
+I'm using the standard rotation and then
+this can be this is just related to the
+
+ align:start position:0%
+this can be this is just related to the
+ 
+
+ align:start position:0%
+this can be this is just related to the
+mass of the
+
+ align:start position:0%
+mass of the
+ 
+
+ align:start position:0%
+mass of the
+brain uh a mass of the brain of course
+
+ align:start position:0%
+brain uh a mass of the brain of course
+ 
+
+ align:start position:0%
+brain uh a mass of the brain of course
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+n um yeah in this Cas is mass the charge
+
+ align:start position:0%
+n um yeah in this Cas is mass the charge
+ 
+
+ align:start position:0%
+n um yeah in this Cas is mass the charge
+is Mass sorry the charge is mass yeah
+
+ align:start position:0%
+is Mass sorry the charge is mass yeah
+ 
+
+ align:start position:0%
+is Mass sorry the charge is mass yeah
+sorry the okay is the charge considered
+
+ align:start position:0%
+sorry the okay is the charge considered
+ 
+
+ align:start position:0%
+sorry the okay is the charge considered
+on the D brain mass or massive
+
+ align:start position:0%
+on the D brain mass or massive
+ 
+
+ align:start position:0%
+on the D brain mass or massive
+no no no charge charger just charge what
+
+ align:start position:0%
+no no no charge charger just charge what
+ 
+
+ align:start position:0%
+no no no charge charger just charge what
+do you mean by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge okay yeah this is just a charge
+
+ align:start position:0%
+charge okay yeah this is just a charge
+ 
+
+ align:start position:0%
+charge okay yeah this is just a charge
+carried by this rebr oh yeah anyway so
+
+ align:start position:0%
+carried by this rebr oh yeah anyway so
+ 
+
+ align:start position:0%
+carried by this rebr oh yeah anyway so
+so so this
+
+ align:start position:0%
+so so this
+ 
+
+ align:start position:0%
+so so this
+R4 is just like GN times the tension uh
+
+ align:start position:0%
+R4 is just like GN times the tension uh
+ 
+
+ align:start position:0%
+R4 is just like GN times the tension uh
+n times the tension if we have n n
+
+ align:start position:0%
+n times the tension if we have n n
+ 
+
+ align:start position:0%
+n times the tension if we have n n
+object just yeah so this is what you
+
+ align:start position:0%
+object just yeah so this is what you
+ 
+
+ align:start position:0%
+object just yeah so this is what you
+familiar with with the SW black ho SW
+
+ align:start position:0%
+familiar with with the SW black ho SW
+ 
+
+ align:start position:0%
+familiar with with the SW black ho SW
+matric just doent constant times mass so
+
+ align:start position:0%
+matric just doent constant times mass so
+ 
+
+ align:start position:0%
+matric just doent constant times mass so
+this is just generalization of that
+
+ align:start position:0%
+this is just generalization of that
+ 
+
+ align:start position:0%
+this is just generalization of that
+Newton constant times the tension and
+
+ align:start position:0%
+Newton constant times the tension and
+ 
+
+ align:start position:0%
+Newton constant times the tension and
+you have Ence you just multiply n and
+
+ align:start position:0%
+you have Ence you just multiply n and
+ 
+
+ align:start position:0%
+you have Ence you just multiply n and
+you can write it if you write everything
+
+ align:start position:0%
+you can write it if you write everything
+ 
+
+ align:start position:0%
+you can write it if you write everything
+ter GS this is proportional to GS squ
+
+ align:start position:0%
+ter GS this is proportional to GS squ
+ 
+
+ align:start position:0%
+ter GS this is proportional to GS squ
+this is propor to one over GS so then
+
+ align:start position:0%
+this is propor to one over GS so then
+ 
+
+ align:start position:0%
+this is propor to one over GS so then
+end up this thing is proportional to GS
+
+ align:start position:0%
+end up this thing is proportional to GS
+ 
+
+ align:start position:0%
+end up this thing is proportional to GS
+okay okay I will stop here
\ No newline at end of file
diff --git a/0DCrIAxEv_Y.txt b/0DCrIAxEv_Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f8dad96784f4e043df8f63f30b0445e97dd0acf7
--- /dev/null
+++ b/0DCrIAxEv_Y.txt
@@ -0,0 +1,10219 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu well welcome back for the
+
+ align:start position:0%
+ocw.mit.edu well welcome back for the
+ 
+
+ align:start position:0%
+ocw.mit.edu well welcome back for the
+for the last hour in this uh in this
+
+ align:start position:0%
+for the last hour in this uh in this
+ 
+
+ align:start position:0%
+for the last hour in this uh in this
+course uh and we've discussed all kinds
+
+ align:start position:0%
+course uh and we've discussed all kinds
+ 
+
+ align:start position:0%
+course uh and we've discussed all kinds
+of things about lasers certainly not
+
+ align:start position:0%
+of things about lasers certainly not
+ 
+
+ align:start position:0%
+of things about lasers certainly not
+everything I haven't touched on Q
+
+ align:start position:0%
+everything I haven't touched on Q
+ 
+
+ align:start position:0%
+everything I haven't touched on Q
+switching uh cavity dumping and uh
+
+ align:start position:0%
+switching uh cavity dumping and uh
+ 
+
+ align:start position:0%
+switching uh cavity dumping and uh
+techniques for mode locking and so on
+
+ align:start position:0%
+techniques for mode locking and so on
+ 
+
+ align:start position:0%
+techniques for mode locking and so on
+but I think uh I hope if if you didn't
+
+ align:start position:0%
+but I think uh I hope if if you didn't
+ 
+
+ align:start position:0%
+but I think uh I hope if if you didn't
+have too much of a background now at
+
+ align:start position:0%
+have too much of a background now at
+ 
+
+ align:start position:0%
+have too much of a background now at
+least you can see that there's nothing
+
+ align:start position:0%
+least you can see that there's nothing
+ 
+
+ align:start position:0%
+least you can see that there's nothing
+that magical about lasers they all makes
+
+ align:start position:0%
+that magical about lasers they all makes
+ 
+
+ align:start position:0%
+that magical about lasers they all makes
+sense and uh and if you were on some
+
+ align:start position:0%
+sense and uh and if you were on some
+ 
+
+ align:start position:0%
+sense and uh and if you were on some
+desert island with a bag of tricks you
+
+ align:start position:0%
+desert island with a bag of tricks you
+ 
+
+ align:start position:0%
+desert island with a bag of tricks you
+could probably create a laser for
+
+ align:start position:0%
+could probably create a laser for
+ 
+
+ align:start position:0%
+could probably create a laser for
+yourself now as I mentioned earlier I
+
+ align:start position:0%
+yourself now as I mentioned earlier I
+ 
+
+ align:start position:0%
+yourself now as I mentioned earlier I
+want to change topics now I want to
+
+ align:start position:0%
+want to change topics now I want to
+ 
+
+ align:start position:0%
+want to change topics now I want to
+switch to fiber optics because fiber
+
+ align:start position:0%
+switch to fiber optics because fiber
+ 
+
+ align:start position:0%
+switch to fiber optics because fiber
+optics is playing a key role in our
+
+ align:start position:0%
+optics is playing a key role in our
+ 
+
+ align:start position:0%
+optics is playing a key role in our
+lives today and I think it's it's good
+
+ align:start position:0%
+lives today and I think it's it's good
+ 
+
+ align:start position:0%
+lives today and I think it's it's good
+for for all sorts of people to know uh
+
+ align:start position:0%
+for for all sorts of people to know uh
+ 
+
+ align:start position:0%
+for for all sorts of people to know uh
+how uh how fiber optics uh how it works
+
+ align:start position:0%
+how uh how fiber optics uh how it works
+ 
+
+ align:start position:0%
+how uh how fiber optics uh how it works
+you know how it works and and some of
+
+ align:start position:0%
+you know how it works and and some of
+ 
+
+ align:start position:0%
+you know how it works and and some of
+the uh developments have been going on
+
+ align:start position:0%
+the uh developments have been going on
+ 
+
+ align:start position:0%
+the uh developments have been going on
+in in fiber optics and maybe a few words
+
+ align:start position:0%
+in in fiber optics and maybe a few words
+ 
+
+ align:start position:0%
+in in fiber optics and maybe a few words
+about some applications of uh fiber
+
+ align:start position:0%
+about some applications of uh fiber
+ 
+
+ align:start position:0%
+about some applications of uh fiber
+optics so so here is the the uh very
+
+ align:start position:0%
+optics so so here is the the uh very
+ 
+
+ align:start position:0%
+optics so so here is the the uh very
+short course on on basics of fiber
+
+ align:start position:0%
+short course on on basics of fiber
+ 
+
+ align:start position:0%
+short course on on basics of fiber
+optics so the first question one asked
+
+ align:start position:0%
+optics so the first question one asked
+ 
+
+ align:start position:0%
+optics so the first question one asked
+well what's a fiber all right now
+
+ align:start position:0%
+well what's a fiber all right now
+ 
+
+ align:start position:0%
+well what's a fiber all right now
+fibers uh have been developed for for
+
+ align:start position:0%
+fibers uh have been developed for for
+ 
+
+ align:start position:0%
+fibers uh have been developed for for
+many years way before uh lasers and they
+
+ align:start position:0%
+many years way before uh lasers and they
+ 
+
+ align:start position:0%
+many years way before uh lasers and they
+basically look look like this if you
+
+ align:start position:0%
+basically look look like this if you
+ 
+
+ align:start position:0%
+basically look look like this if you
+look from from the end they look like
+
+ align:start position:0%
+look from from the end they look like
+ 
+
+ align:start position:0%
+look from from the end they look like
+have a core you see which is one type of
+
+ align:start position:0%
+have a core you see which is one type of
+ 
+
+ align:start position:0%
+have a core you see which is one type of
+glass and of certain index let's say
+
+ align:start position:0%
+glass and of certain index let's say
+ 
+
+ align:start position:0%
+glass and of certain index let's say
+index N1 and surrounded by another glass
+
+ align:start position:0%
+index N1 and surrounded by another glass
+ 
+
+ align:start position:0%
+index N1 and surrounded by another glass
+uh of index N2 called the CL cladding
+
+ align:start position:0%
+uh of index N2 called the CL cladding
+ 
+
+ align:start position:0%
+uh of index N2 called the CL cladding
+and then the cladding is surrounded by a
+
+ align:start position:0%
+and then the cladding is surrounded by a
+ 
+
+ align:start position:0%
+and then the cladding is surrounded by a
+jacket and depends on the type of
+
+ align:start position:0%
+jacket and depends on the type of
+ 
+
+ align:start position:0%
+jacket and depends on the type of
+material that you use but whatever the
+
+ align:start position:0%
+material that you use but whatever the
+ 
+
+ align:start position:0%
+material that you use but whatever the
+jacket then protects the uh protects the
+
+ align:start position:0%
+jacket then protects the uh protects the
+ 
+
+ align:start position:0%
+jacket then protects the uh protects the
+clading the index the refractive index
+
+ align:start position:0%
+clading the index the refractive index
+ 
+
+ align:start position:0%
+clading the index the refractive index
+N1 of the core is bigger than N2 uh
+
+ align:start position:0%
+N1 of the core is bigger than N2 uh
+ 
+
+ align:start position:0%
+N1 of the core is bigger than N2 uh
+sometimes N2 the the the clading
+
+ align:start position:0%
+sometimes N2 the the the clading
+ 
+
+ align:start position:0%
+sometimes N2 the the the clading
+material is just plain silicon
+
+ align:start position:0%
+material is just plain silicon
+ 
+
+ align:start position:0%
+material is just plain silicon
+dioxide uh and the index uh uh the
+
+ align:start position:0%
+dioxide uh and the index uh uh the
+ 
+
+ align:start position:0%
+dioxide uh and the index uh uh the
+material in in the core is silicon
+
+ align:start position:0%
+material in in the core is silicon
+ 
+
+ align:start position:0%
+material in in the core is silicon
+dioxide plus some impurity with geranium
+
+ align:start position:0%
+dioxide plus some impurity with geranium
+ 
+
+ align:start position:0%
+dioxide plus some impurity with geranium
+dioxide to raise to raise the index the
+
+ align:start position:0%
+dioxide to raise to raise the index the
+ 
+
+ align:start position:0%
+dioxide to raise to raise the index the
+question is what's going on in here why
+
+ align:start position:0%
+question is what's going on in here why
+ 
+
+ align:start position:0%
+question is what's going on in here why
+play with with all the these indices so
+
+ align:start position:0%
+play with with all the these indices so
+ 
+
+ align:start position:0%
+play with with all the these indices so
+the the key thing here is a uh total
+
+ align:start position:0%
+the the key thing here is a uh total
+ 
+
+ align:start position:0%
+the the key thing here is a uh total
+internal reflection all right total the
+
+ align:start position:0%
+internal reflection all right total the
+ 
+
+ align:start position:0%
+internal reflection all right total the
+propagation of light in fibers based on
+
+ align:start position:0%
+propagation of light in fibers based on
+ 
+
+ align:start position:0%
+propagation of light in fibers based on
+total internal reflection so let's let's
+
+ align:start position:0%
+total internal reflection so let's let's
+ 
+
+ align:start position:0%
+total internal reflection so let's let's
+then uh review it uh here's a ray of
+
+ align:start position:0%
+then uh review it uh here's a ray of
+ 
+
+ align:start position:0%
+then uh review it uh here's a ray of
+light uh hitting the uh surface the
+
+ align:start position:0%
+light uh hitting the uh surface the
+ 
+
+ align:start position:0%
+light uh hitting the uh surface the
+interface here between N1 and N2 between
+
+ align:start position:0%
+interface here between N1 and N2 between
+ 
+
+ align:start position:0%
+interface here between N1 and N2 between
+the core and the and the cladding if
+
+ align:start position:0%
+the core and the and the cladding if
+ 
+
+ align:start position:0%
+the core and the and the cladding if
+this angle if this incident angle is
+
+ align:start position:0%
+this angle if this incident angle is
+ 
+
+ align:start position:0%
+this angle if this incident angle is
+bigger than the critical angle then the
+
+ align:start position:0%
+bigger than the critical angle then the
+ 
+
+ align:start position:0%
+bigger than the critical angle then the
+light will be reflected and bounce
+
+ align:start position:0%
+light will be reflected and bounce
+ 
+
+ align:start position:0%
+light will be reflected and bounce
+around until it comes out the other
+
+ align:start position:0%
+around until it comes out the other
+ 
+
+ align:start position:0%
+around until it comes out the other
+end and uh because just like going from
+
+ align:start position:0%
+end and uh because just like going from
+ 
+
+ align:start position:0%
+end and uh because just like going from
+glass uh to Air and the the critical
+
+ align:start position:0%
+glass uh to Air and the the critical
+ 
+
+ align:start position:0%
+glass uh to Air and the the critical
+angle is given as we remember from high
+
+ align:start position:0%
+angle is given as we remember from high
+ 
+
+ align:start position:0%
+angle is given as we remember from high
+school as s to minus1 of N2 over N1
+
+ align:start position:0%
+school as s to minus1 of N2 over N1
+ 
+
+ align:start position:0%
+school as s to minus1 of N2 over N1
+where N2 is the in the smaller index and
+
+ align:start position:0%
+where N2 is the in the smaller index and
+ 
+
+ align:start position:0%
+where N2 is the in the smaller index and
+N1 is the is the bigger one if this
+
+ align:start position:0%
+N1 is the is the bigger one if this
+ 
+
+ align:start position:0%
+N1 is the is the bigger one if this
+angle of incidence is smaller than Theta
+
+ align:start position:0%
+angle of incidence is smaller than Theta
+ 
+
+ align:start position:0%
+angle of incidence is smaller than Theta
+critical then there will be some
+
+ align:start position:0%
+critical then there will be some
+ 
+
+ align:start position:0%
+critical then there will be some
+transmission of light and not all the
+
+ align:start position:0%
+transmission of light and not all the
+ 
+
+ align:start position:0%
+transmission of light and not all the
+light will be will be
+
+ align:start position:0%
+light will be will be
+ 
+
+ align:start position:0%
+light will be will be
+reflected the uh just to remind you some
+
+ align:start position:0%
+reflected the uh just to remind you some
+ 
+
+ align:start position:0%
+reflected the uh just to remind you some
+more uh of uh what's going on let me
+
+ align:start position:0%
+more uh of uh what's going on let me
+ 
+
+ align:start position:0%
+more uh of uh what's going on let me
+remind you of the of the perfect mirror
+
+ align:start position:0%
+remind you of the of the perfect mirror
+ 
+
+ align:start position:0%
+remind you of the of the perfect mirror
+when I have a perfect mirror the light
+
+ align:start position:0%
+when I have a perfect mirror the light
+ 
+
+ align:start position:0%
+when I have a perfect mirror the light
+comes in then essentially close to 100%
+
+ align:start position:0%
+comes in then essentially close to 100%
+ 
+
+ align:start position:0%
+comes in then essentially close to 100%
+the light gets reflected and the
+
+ align:start position:0%
+the light gets reflected and the
+ 
+
+ align:start position:0%
+the light gets reflected and the
+reflectivity is close to 100% as I say
+
+ align:start position:0%
+reflectivity is close to 100% as I say
+ 
+
+ align:start position:0%
+reflectivity is close to 100% as I say
+is one as a function of angle of of of
+
+ align:start position:0%
+is one as a function of angle of of of
+ 
+
+ align:start position:0%
+is one as a function of angle of of of
+incidents but if you have again the the
+
+ align:start position:0%
+incidents but if you have again the the
+ 
+
+ align:start position:0%
+incidents but if you have again the the
+glass air interface now we're coming
+
+ align:start position:0%
+glass air interface now we're coming
+ 
+
+ align:start position:0%
+glass air interface now we're coming
+from the glass side then as we vary this
+
+ align:start position:0%
+from the glass side then as we vary this
+ 
+
+ align:start position:0%
+from the glass side then as we vary this
+this angle the angle of incidence then
+
+ align:start position:0%
+this angle the angle of incidence then
+ 
+
+ align:start position:0%
+this angle the angle of incidence then
+the the reflectivity uh uh of this
+
+ align:start position:0%
+the the reflectivity uh uh of this
+ 
+
+ align:start position:0%
+the the reflectivity uh uh of this
+interface then depends on the
+
+ align:start position:0%
+interface then depends on the
+ 
+
+ align:start position:0%
+interface then depends on the
+polarization but right now we're not
+
+ align:start position:0%
+polarization but right now we're not
+ 
+
+ align:start position:0%
+polarization but right now we're not
+going to get involved with polarization
+
+ align:start position:0%
+going to get involved with polarization
+ 
+
+ align:start position:0%
+going to get involved with polarization
+but basically starts let's say between
+
+ align:start position:0%
+but basically starts let's say between
+ 
+
+ align:start position:0%
+but basically starts let's say between
+glass air starts like 4% and for one
+
+ align:start position:0%
+glass air starts like 4% and for one
+ 
+
+ align:start position:0%
+glass air starts like 4% and for one
+polarization goes through zero which is
+
+ align:start position:0%
+polarization goes through zero which is
+ 
+
+ align:start position:0%
+polarization goes through zero which is
+the Brewster angle here and then Rises
+
+ align:start position:0%
+the Brewster angle here and then Rises
+ 
+
+ align:start position:0%
+the Brewster angle here and then Rises
+uh at the Theta critical to 100% and for
+
+ align:start position:0%
+uh at the Theta critical to 100% and for
+ 
+
+ align:start position:0%
+uh at the Theta critical to 100% and for
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+polarization uh then it doesn't quite go
+
+ align:start position:0%
+polarization uh then it doesn't quite go
+ 
+
+ align:start position:0%
+polarization uh then it doesn't quite go
+to zero but again still rises and goes
+
+ align:start position:0%
+to zero but again still rises and goes
+ 
+
+ align:start position:0%
+to zero but again still rises and goes
+to 100% at the Theta critical so it
+
+ align:start position:0%
+to 100% at the Theta critical so it
+ 
+
+ align:start position:0%
+to 100% at the Theta critical so it
+doesn't matter which polarization the
+
+ align:start position:0%
+doesn't matter which polarization the
+ 
+
+ align:start position:0%
+doesn't matter which polarization the
+both polarization will go to 100% for
+
+ align:start position:0%
+both polarization will go to 100% for
+ 
+
+ align:start position:0%
+both polarization will go to 100% for
+Theta critical and and Beyond and that's
+
+ align:start position:0%
+Theta critical and and Beyond and that's
+ 
+
+ align:start position:0%
+Theta critical and and Beyond and that's
+what we take advantage of in fibers let
+
+ align:start position:0%
+what we take advantage of in fibers let
+ 
+
+ align:start position:0%
+what we take advantage of in fibers let
+me tell you this is really 100% because
+
+ align:start position:0%
+me tell you this is really 100% because
+ 
+
+ align:start position:0%
+me tell you this is really 100% because
+you wouldn't get such low loss fibers if
+
+ align:start position:0%
+you wouldn't get such low loss fibers if
+ 
+
+ align:start position:0%
+you wouldn't get such low loss fibers if
+this weren now the other interesting
+
+ align:start position:0%
+this weren now the other interesting
+ 
+
+ align:start position:0%
+this weren now the other interesting
+thing that I want to point out again
+
+ align:start position:0%
+thing that I want to point out again
+ 
+
+ align:start position:0%
+thing that I want to point out again
+from high school staff is that that
+
+ align:start position:0%
+from high school staff is that that
+ 
+
+ align:start position:0%
+from high school staff is that that
+there is what we call evanescent wave
+
+ align:start position:0%
+there is what we call evanescent wave
+ 
+
+ align:start position:0%
+there is what we call evanescent wave
+here there's a field that is propagates
+
+ align:start position:0%
+here there's a field that is propagates
+ 
+
+ align:start position:0%
+here there's a field that is propagates
+in the in the vacuum or in the air here
+
+ align:start position:0%
+in the in the vacuum or in the air here
+ 
+
+ align:start position:0%
+in the in the vacuum or in the air here
+uh but essentially just goes in and
+
+ align:start position:0%
+uh but essentially just goes in and
+ 
+
+ align:start position:0%
+uh but essentially just goes in and
+comes back again it's not a loss it's
+
+ align:start position:0%
+comes back again it's not a loss it's
+ 
+
+ align:start position:0%
+comes back again it's not a loss it's
+just that the uh the in when you have a
+
+ align:start position:0%
+just that the uh the in when you have a
+ 
+
+ align:start position:0%
+just that the uh the in when you have a
+glass air interface there is a field
+
+ align:start position:0%
+glass air interface there is a field
+ 
+
+ align:start position:0%
+glass air interface there is a field
+that does penetrate but is still not
+
+ align:start position:0%
+that does penetrate but is still not
+ 
+
+ align:start position:0%
+that does penetrate but is still not
+considered as a loss but and then and
+
+ align:start position:0%
+considered as a loss but and then and
+ 
+
+ align:start position:0%
+considered as a loss but and then and
+then uh but then comes back here and
+
+ align:start position:0%
+then uh but then comes back here and
+ 
+
+ align:start position:0%
+then uh but then comes back here and
+gives us 100% while in a perfect
+
+ align:start position:0%
+gives us 100% while in a perfect
+ 
+
+ align:start position:0%
+gives us 100% while in a perfect
+reflector there is no field present on
+
+ align:start position:0%
+reflector there is no field present on
+ 
+
+ align:start position:0%
+reflector there is no field present on
+the other side because the the light
+
+ align:start position:0%
+the other side because the the light
+ 
+
+ align:start position:0%
+the other side because the the light
+100% the light gets reflected at the
+
+ align:start position:0%
+100% the light gets reflected at the
+ 
+
+ align:start position:0%
+100% the light gets reflected at the
+interface okay so if you keep that in
+
+ align:start position:0%
+interface okay so if you keep that in
+ 
+
+ align:start position:0%
+interface okay so if you keep that in
+mind that there is an evanescent fi
+
+ align:start position:0%
+mind that there is an evanescent fi
+ 
+
+ align:start position:0%
+mind that there is an evanescent fi
+there's a field penetration into the
+
+ align:start position:0%
+there's a field penetration into the
+ 
+
+ align:start position:0%
+there's a field penetration into the
+lower index medium the smaller index
+
+ align:start position:0%
+lower index medium the smaller index
+ 
+
+ align:start position:0%
+lower index medium the smaller index
+medium in this case it's air all right
+
+ align:start position:0%
+medium in this case it's air all right
+ 
+
+ align:start position:0%
+medium in this case it's air all right
+so with this as uh as background now
+
+ align:start position:0%
+so with this as uh as background now
+ 
+
+ align:start position:0%
+so with this as uh as background now
+let's look at the the propagation in a
+
+ align:start position:0%
+let's look at the the propagation in a
+ 
+
+ align:start position:0%
+let's look at the the propagation in a
+in a fiber now uh uh it's not the like I
+
+ align:start position:0%
+in a fiber now uh uh it's not the like I
+ 
+
+ align:start position:0%
+in a fiber now uh uh it's not the like I
+showed you here exactly like I showed
+
+ align:start position:0%
+showed you here exactly like I showed
+ 
+
+ align:start position:0%
+showed you here exactly like I showed
+you is the ray the ray approximation but
+
+ align:start position:0%
+you is the ray the ray approximation but
+ 
+
+ align:start position:0%
+you is the ray the ray approximation but
+basically uh when you do the
+
+ align:start position:0%
+basically uh when you do the
+ 
+
+ align:start position:0%
+basically uh when you do the
+calculations what you get is a uh is a a
+
+ align:start position:0%
+calculations what you get is a uh is a a
+ 
+
+ align:start position:0%
+calculations what you get is a uh is a a
+uh a mode essentially like just like the
+
+ align:start position:0%
+uh a mode essentially like just like the
+ 
+
+ align:start position:0%
+uh a mode essentially like just like the
+one in lasers is a a field distribution
+
+ align:start position:0%
+one in lasers is a a field distribution
+ 
+
+ align:start position:0%
+one in lasers is a a field distribution
+here where that Peaks at the center of
+
+ align:start position:0%
+here where that Peaks at the center of
+ 
+
+ align:start position:0%
+here where that Peaks at the center of
+the core and also uh uh extends a little
+
+ align:start position:0%
+the core and also uh uh extends a little
+ 
+
+ align:start position:0%
+the core and also uh uh extends a little
+bit into the uh the evanescent Fe this
+
+ align:start position:0%
+bit into the uh the evanescent Fe this
+ 
+
+ align:start position:0%
+bit into the uh the evanescent Fe this
+is the evanescent Fe extends into the
+
+ align:start position:0%
+is the evanescent Fe extends into the
+ 
+
+ align:start position:0%
+is the evanescent Fe extends into the
+cladic so so uh so you can see this is
+
+ align:start position:0%
+cladic so so uh so you can see this is
+ 
+
+ align:start position:0%
+cladic so so uh so you can see this is
+the side of size of the core but you see
+
+ align:start position:0%
+the side of size of the core but you see
+ 
+
+ align:start position:0%
+the side of size of the core but you see
+the orange this orange if you can uh see
+
+ align:start position:0%
+the orange this orange if you can uh see
+ 
+
+ align:start position:0%
+the orange this orange if you can uh see
+it as orange it basically extends beyond
+
+ align:start position:0%
+it as orange it basically extends beyond
+ 
+
+ align:start position:0%
+it as orange it basically extends beyond
+the size of the core and that's what we
+
+ align:start position:0%
+the size of the core and that's what we
+ 
+
+ align:start position:0%
+the size of the core and that's what we
+call single mode uh propagation okay
+
+ align:start position:0%
+call single mode uh propagation okay
+ 
+
+ align:start position:0%
+call single mode uh propagation okay
+here's the field distribution here's the
+
+ align:start position:0%
+here's the field distribution here's the
+ 
+
+ align:start position:0%
+here's the field distribution here's the
+side of mode so it extends a little bit
+
+ align:start position:0%
+side of mode so it extends a little bit
+ 
+
+ align:start position:0%
+side of mode so it extends a little bit
+into into the cladding most of it let's
+
+ align:start position:0%
+into into the cladding most of it let's
+ 
+
+ align:start position:0%
+into into the cladding most of it let's
+say goes into the core part of it goes
+
+ align:start position:0%
+say goes into the core part of it goes
+ 
+
+ align:start position:0%
+say goes into the core part of it goes
+in the CL and propagates right down the
+
+ align:start position:0%
+in the CL and propagates right down the
+ 
+
+ align:start position:0%
+in the CL and propagates right down the
+fiber I mean this Ray idea is fine for
+
+ align:start position:0%
+fiber I mean this Ray idea is fine for
+ 
+
+ align:start position:0%
+fiber I mean this Ray idea is fine for
+explanation but basically when you when
+
+ align:start position:0%
+explanation but basically when you when
+ 
+
+ align:start position:0%
+explanation but basically when you when
+you do the calculation proper
+
+ align:start position:0%
+you do the calculation proper
+ 
+
+ align:start position:0%
+you do the calculation proper
+calculation that's what you get you get
+
+ align:start position:0%
+calculation that's what you get you get
+ 
+
+ align:start position:0%
+calculation that's what you get you get
+this for the uh lowest order uh mod now
+
+ align:start position:0%
+this for the uh lowest order uh mod now
+ 
+
+ align:start position:0%
+this for the uh lowest order uh mod now
+the uh the how how does the light look
+
+ align:start position:0%
+the uh the how how does the light look
+ 
+
+ align:start position:0%
+the uh the how how does the light look
+like when it comes out then then
+
+ align:start position:0%
+like when it comes out then then
+ 
+
+ align:start position:0%
+like when it comes out then then
+basically let's go back to the ray
+
+ align:start position:0%
+basically let's go back to the ray
+ 
+
+ align:start position:0%
+basically let's go back to the ray
+picture well the ray picture remember we
+
+ align:start position:0%
+picture well the ray picture remember we
+ 
+
+ align:start position:0%
+picture well the ray picture remember we
+said that the angle has to here be uh
+
+ align:start position:0%
+said that the angle has to here be uh
+ 
+
+ align:start position:0%
+said that the angle has to here be uh
+either equal to the critical or or
+
+ align:start position:0%
+either equal to the critical or or
+ 
+
+ align:start position:0%
+either equal to the critical or or
+bigger and then that then determines the
+
+ align:start position:0%
+bigger and then that then determines the
+ 
+
+ align:start position:0%
+bigger and then that then determines the
+the acceptance angle going in because uh
+
+ align:start position:0%
+the acceptance angle going in because uh
+ 
+
+ align:start position:0%
+the acceptance angle going in because uh
+because rays of light coming in outside
+
+ align:start position:0%
+because rays of light coming in outside
+ 
+
+ align:start position:0%
+because rays of light coming in outside
+this this cone here will be then will
+
+ align:start position:0%
+this this cone here will be then will
+ 
+
+ align:start position:0%
+this this cone here will be then will
+will not undergo total internal
+
+ align:start position:0%
+will not undergo total internal
+ 
+
+ align:start position:0%
+will not undergo total internal
+reflection complete total internal
+
+ align:start position:0%
+reflection complete total internal
+ 
+
+ align:start position:0%
+reflection complete total internal
+reflection and will will be in trouble
+
+ align:start position:0%
+reflection and will will be in trouble
+ 
+
+ align:start position:0%
+reflection and will will be in trouble
+because they won't propagate for too far
+
+ align:start position:0%
+because they won't propagate for too far
+ 
+
+ align:start position:0%
+because they won't propagate for too far
+and they will be attenuated now uh for
+
+ align:start position:0%
+and they will be attenuated now uh for
+ 
+
+ align:start position:0%
+and they will be attenuated now uh for
+the for the light that is within this
+
+ align:start position:0%
+the for the light that is within this
+ 
+
+ align:start position:0%
+the for the light that is within this
+cone here and by the way this cone is
+
+ align:start position:0%
+cone here and by the way this cone is
+ 
+
+ align:start position:0%
+cone here and by the way this cone is
+referred to as a numerical aperture na
+
+ align:start position:0%
+referred to as a numerical aperture na
+ 
+
+ align:start position:0%
+referred to as a numerical aperture na
+for the fiber and na is basically the N
+
+ align:start position:0%
+for the fiber and na is basically the N
+ 
+
+ align:start position:0%
+for the fiber and na is basically the N
+zero the the refractive index of air or
+
+ align:start position:0%
+zero the the refractive index of air or
+ 
+
+ align:start position:0%
+zero the the refractive index of air or
+vacuum outside s uh s uh Theta 0 and and
+
+ align:start position:0%
+vacuum outside s uh s uh Theta 0 and and
+ 
+
+ align:start position:0%
+vacuum outside s uh s uh Theta 0 and and
+and Theta 0 is half this angle here
+
+ align:start position:0%
+and Theta 0 is half this angle here
+ 
+
+ align:start position:0%
+and Theta 0 is half this angle here
+which is determined by then the index
+
+ align:start position:0%
+which is determined by then the index
+ 
+
+ align:start position:0%
+which is determined by then the index
+difference and so on to uh so get us to
+
+ align:start position:0%
+difference and so on to uh so get us to
+ 
+
+ align:start position:0%
+difference and so on to uh so get us to
+the angle here to be bigger than the
+
+ align:start position:0%
+the angle here to be bigger than the
+ 
+
+ align:start position:0%
+the angle here to be bigger than the
+critical angle all right so uh so then
+
+ align:start position:0%
+critical angle all right so uh so then
+ 
+
+ align:start position:0%
+critical angle all right so uh so then
+that then this acceptance angle here The
+
+ align:start position:0%
+that then this acceptance angle here The
+ 
+
+ align:start position:0%
+that then this acceptance angle here The
+Light Within this cone will will
+
+ align:start position:0%
+Light Within this cone will will
+ 
+
+ align:start position:0%
+Light Within this cone will will
+propagate uh and uh in the fiber and
+
+ align:start position:0%
+propagate uh and uh in the fiber and
+ 
+
+ align:start position:0%
+propagate uh and uh in the fiber and
+when it comes out essentially it comes
+
+ align:start position:0%
+when it comes out essentially it comes
+ 
+
+ align:start position:0%
+when it comes out essentially it comes
+out just like this cone here again with
+
+ align:start position:0%
+out just like this cone here again with
+ 
+
+ align:start position:0%
+out just like this cone here again with
+an angle 2 Theta 0 so the light coming
+
+ align:start position:0%
+an angle 2 Theta 0 so the light coming
+ 
+
+ align:start position:0%
+an angle 2 Theta 0 so the light coming
+out from a fiber is uh expands uh pretty
+
+ align:start position:0%
+out from a fiber is uh expands uh pretty
+ 
+
+ align:start position:0%
+out from a fiber is uh expands uh pretty
+fast that's using the ray picture if you
+
+ align:start position:0%
+fast that's using the ray picture if you
+ 
+
+ align:start position:0%
+fast that's using the ray picture if you
+look at the the uh the the true picture
+
+ align:start position:0%
+look at the the uh the the true picture
+ 
+
+ align:start position:0%
+look at the the uh the the true picture
+what happens actually you bring in light
+
+ align:start position:0%
+what happens actually you bring in light
+ 
+
+ align:start position:0%
+what happens actually you bring in light
+that you focus into into the core even
+
+ align:start position:0%
+that you focus into into the core even
+ 
+
+ align:start position:0%
+that you focus into into the core even
+though it spills over the core a little
+
+ align:start position:0%
+though it spills over the core a little
+ 
+
+ align:start position:0%
+though it spills over the core a little
+bit because of the essent wave then will
+
+ align:start position:0%
+bit because of the essent wave then will
+ 
+
+ align:start position:0%
+bit because of the essent wave then will
+propagate down the fiber and then will
+
+ align:start position:0%
+propagate down the fiber and then will
+ 
+
+ align:start position:0%
+propagate down the fiber and then will
+come out on the other side almost like
+
+ align:start position:0%
+come out on the other side almost like
+ 
+
+ align:start position:0%
+come out on the other side almost like
+like it came in so uh and this is very
+
+ align:start position:0%
+like it came in so uh and this is very
+ 
+
+ align:start position:0%
+like it came in so uh and this is very
+close close to the defraction angle
+
+ align:start position:0%
+close close to the defraction angle
+ 
+
+ align:start position:0%
+close close to the defraction angle
+which is of the order of Lambda over D
+
+ align:start position:0%
+which is of the order of Lambda over D
+ 
+
+ align:start position:0%
+which is of the order of Lambda over D
+where D is the size as we discussed way
+
+ align:start position:0%
+where D is the size as we discussed way
+ 
+
+ align:start position:0%
+where D is the size as we discussed way
+early in this uh in this course so even
+
+ align:start position:0%
+early in this uh in this course so even
+ 
+
+ align:start position:0%
+early in this uh in this course so even
+though it propagates as a as a
+
+ align:start position:0%
+though it propagates as a as a
+ 
+
+ align:start position:0%
+though it propagates as a as a
+columnated beam in the fiber but as soon
+
+ align:start position:0%
+columnated beam in the fiber but as soon
+ 
+
+ align:start position:0%
+columnated beam in the fiber but as soon
+as it leaves the fiber it expands uh it
+
+ align:start position:0%
+as it leaves the fiber it expands uh it
+ 
+
+ align:start position:0%
+as it leaves the fiber it expands uh it
+expands very very rapidly all right so
+
+ align:start position:0%
+expands very very rapidly all right so
+ 
+
+ align:start position:0%
+expands very very rapidly all right so
+that's basically then how uh in a simple
+
+ align:start position:0%
+that's basically then how uh in a simple
+ 
+
+ align:start position:0%
+that's basically then how uh in a simple
+way how how light propagates now the
+
+ align:start position:0%
+way how how light propagates now the
+ 
+
+ align:start position:0%
+way how how light propagates now the
+fact that we have low loss where does
+
+ align:start position:0%
+fact that we have low loss where does
+ 
+
+ align:start position:0%
+fact that we have low loss where does
+that come from and and let me show you
+
+ align:start position:0%
+that come from and and let me show you
+ 
+
+ align:start position:0%
+that come from and and let me show you
+some data on on low loss uh uh
+
+ align:start position:0%
+some data on on low loss uh uh
+ 
+
+ align:start position:0%
+some data on on low loss uh uh
+propagation if you if you plot the loss
+
+ align:start position:0%
+propagation if you if you plot the loss
+ 
+
+ align:start position:0%
+propagation if you if you plot the loss
+uh in in propagation as DBS per
+
+ align:start position:0%
+uh in in propagation as DBS per
+ 
+
+ align:start position:0%
+uh in in propagation as DBS per
+kilometer and as a function of
+
+ align:start position:0%
+kilometer and as a function of
+ 
+
+ align:start position:0%
+kilometer and as a function of
+wavelength you find that there is a
+
+ align:start position:0%
+wavelength you find that there is a
+ 
+
+ align:start position:0%
+wavelength you find that there is a
+certain wavelength like 1.55 or 1.3 the
+
+ align:start position:0%
+certain wavelength like 1.55 or 1.3 the
+ 
+
+ align:start position:0%
+certain wavelength like 1.55 or 1.3 the
+loss is is very low it's about let's say
+
+ align:start position:0%
+loss is is very low it's about let's say
+ 
+
+ align:start position:0%
+loss is is very low it's about let's say
+2% or .1% or so per kilometer at at
+
+ align:start position:0%
+2% or .1% or so per kilometer at at
+ 
+
+ align:start position:0%
+2% or .1% or so per kilometer at at
+these uh wavelengths now
+
+ align:start position:0%
+these uh wavelengths now
+ 
+
+ align:start position:0%
+these uh wavelengths now
+0.1% uh 0.1 DB I'm sorry 0.1 DB per
+
+ align:start position:0%
+0.1% uh 0.1 DB I'm sorry 0.1 DB per
+ 
+
+ align:start position:0%
+0.1% uh 0.1 DB I'm sorry 0.1 DB per
+kilometer is like 2% per kilometer loss
+
+ align:start position:0%
+kilometer is like 2% per kilometer loss
+ 
+
+ align:start position:0%
+kilometer is like 2% per kilometer loss
+and that's that's very small that's much
+
+ align:start position:0%
+and that's that's very small that's much
+ 
+
+ align:start position:0%
+and that's that's very small that's much
+smaller than propagating in in wires and
+
+ align:start position:0%
+smaller than propagating in in wires and
+ 
+
+ align:start position:0%
+smaller than propagating in in wires and
+the reason why it's small is first of
+
+ align:start position:0%
+the reason why it's small is first of
+ 
+
+ align:start position:0%
+the reason why it's small is first of
+all is because the the total internal
+
+ align:start position:0%
+all is because the the total internal
+ 
+
+ align:start position:0%
+all is because the the total internal
+reflection is really 100% all right
+
+ align:start position:0%
+reflection is really 100% all right
+ 
+
+ align:start position:0%
+reflection is really 100% all right
+there is there is no loss because of
+
+ align:start position:0%
+there is there is no loss because of
+ 
+
+ align:start position:0%
+there is there is no loss because of
+that and the reason there's any loss at
+
+ align:start position:0%
+that and the reason there's any loss at
+ 
+
+ align:start position:0%
+that and the reason there's any loss at
+all is because you're you're squeezing
+
+ align:start position:0%
+all is because you're you're squeezing
+ 
+
+ align:start position:0%
+all is because you're you're squeezing
+in from one side on this side you have
+
+ align:start position:0%
+in from one side on this side you have
+ 
+
+ align:start position:0%
+in from one side on this side you have
+what we call RA scattering uh the fact
+
+ align:start position:0%
+what we call RA scattering uh the fact
+ 
+
+ align:start position:0%
+what we call RA scattering uh the fact
+that uh I don't want to get into it
+
+ align:start position:0%
+that uh I don't want to get into it
+ 
+
+ align:start position:0%
+that uh I don't want to get into it
+right now but the fact that that you get
+
+ align:start position:0%
+right now but the fact that that you get
+ 
+
+ align:start position:0%
+right now but the fact that that you get
+scaning essentially from uh from the uh
+
+ align:start position:0%
+scaning essentially from uh from the uh
+ 
+
+ align:start position:0%
+scaning essentially from uh from the uh
+fluctuations of density fluctuations
+
+ align:start position:0%
+fluctuations of density fluctuations
+ 
+
+ align:start position:0%
+fluctuations of density fluctuations
+within the glass that's on one side so
+
+ align:start position:0%
+within the glass that's on one side so
+ 
+
+ align:start position:0%
+within the glass that's on one side so
+as the wavelength gets shorter the
+
+ align:start position:0%
+as the wavelength gets shorter the
+ 
+
+ align:start position:0%
+as the wavelength gets shorter the
+scattering gets larger and larger and
+
+ align:start position:0%
+scattering gets larger and larger and
+ 
+
+ align:start position:0%
+scattering gets larger and larger and
+then you're in trouble that's the same
+
+ align:start position:0%
+then you're in trouble that's the same
+ 
+
+ align:start position:0%
+then you're in trouble that's the same
+reason why the sky is blue and so on now
+
+ align:start position:0%
+reason why the sky is blue and so on now
+ 
+
+ align:start position:0%
+reason why the sky is blue and so on now
+on the other side on this side here not
+
+ align:start position:0%
+on the other side on this side here not
+ 
+
+ align:start position:0%
+on the other side on this side here not
+shown is the uh is essentially the
+
+ align:start position:0%
+shown is the uh is essentially the
+ 
+
+ align:start position:0%
+shown is the uh is essentially the
+material uh absorption uh or the
+
+ align:start position:0%
+material uh absorption uh or the
+ 
+
+ align:start position:0%
+material uh absorption uh or the
+infrared absorption and so on for the
+
+ align:start position:0%
+infrared absorption and so on for the
+ 
+
+ align:start position:0%
+infrared absorption and so on for the
+for the let's say for the quartz for the
+
+ align:start position:0%
+for the let's say for the quartz for the
+ 
+
+ align:start position:0%
+for the let's say for the quartz for the
+glass so you're you're boxed in on one
+
+ align:start position:0%
+glass so you're you're boxed in on one
+ 
+
+ align:start position:0%
+glass so you're you're boxed in on one
+side you have R scaning the other side
+
+ align:start position:0%
+side you have R scaning the other side
+ 
+
+ align:start position:0%
+side you have R scaning the other side
+going up is the material absorption and
+
+ align:start position:0%
+going up is the material absorption and
+ 
+
+ align:start position:0%
+going up is the material absorption and
+that's why you have the lowest loss
+
+ align:start position:0%
+that's why you have the lowest loss
+ 
+
+ align:start position:0%
+that's why you have the lowest loss
+around here and that's about the best
+
+ align:start position:0%
+around here and that's about the best
+ 
+
+ align:start position:0%
+around here and that's about the best
+you can do if you want to reduce this
+
+ align:start position:0%
+you can do if you want to reduce this
+ 
+
+ align:start position:0%
+you can do if you want to reduce this
+loss from let's say 0.1 or02 DPS per
+
+ align:start position:0%
+loss from let's say 0.1 or02 DPS per
+ 
+
+ align:start position:0%
+loss from let's say 0.1 or02 DPS per
+kilometer then you have to use other
+
+ align:start position:0%
+kilometer then you have to use other
+ 
+
+ align:start position:0%
+kilometer then you have to use other
+materials and materials whose material
+
+ align:start position:0%
+materials and materials whose material
+ 
+
+ align:start position:0%
+materials and materials whose material
+absorption is further into the infrared
+
+ align:start position:0%
+absorption is further into the infrared
+ 
+
+ align:start position:0%
+absorption is further into the infrared
+so I'm afraid uh uh we're not going to
+
+ align:start position:0%
+so I'm afraid uh uh we're not going to
+ 
+
+ align:start position:0%
+so I'm afraid uh uh we're not going to
+get uh into the visible uh and have low
+
+ align:start position:0%
+get uh into the visible uh and have low
+ 
+
+ align:start position:0%
+get uh into the visible uh and have low
+loss because the uh because of the ra
+
+ align:start position:0%
+loss because the uh because of the ra
+ 
+
+ align:start position:0%
+loss because the uh because of the ra
+scaning so it's going to be if we're
+
+ align:start position:0%
+scaning so it's going to be if we're
+ 
+
+ align:start position:0%
+scaning so it's going to be if we're
+going to go any we're going to do better
+
+ align:start position:0%
+going to go any we're going to do better
+ 
+
+ align:start position:0%
+going to go any we're going to do better
+than this we're going to go further into
+
+ align:start position:0%
+than this we're going to go further into
+ 
+
+ align:start position:0%
+than this we're going to go further into
+into the uh into the infrared which
+
+ align:start position:0%
+into the uh into the infrared which
+ 
+
+ align:start position:0%
+into the uh into the infrared which
+means we have to have the right sources
+
+ align:start position:0%
+means we have to have the right sources
+ 
+
+ align:start position:0%
+means we have to have the right sources
+and and the components and so on to work
+
+ align:start position:0%
+and and the components and so on to work
+ 
+
+ align:start position:0%
+and and the components and so on to work
+in the in the infrared and and the uh
+
+ align:start position:0%
+in the in the infrared and and the uh
+ 
+
+ align:start position:0%
+in the in the infrared and and the uh
+and then deeper in
+
+ align:start position:0%
+and then deeper in
+ 
+
+ align:start position:0%
+and then deeper in
+infrared okay so uh so now we know a
+
+ align:start position:0%
+infrared okay so uh so now we know a
+ 
+
+ align:start position:0%
+infrared okay so uh so now we know a
+little bit about the loss in in the
+
+ align:start position:0%
+little bit about the loss in in the
+ 
+
+ align:start position:0%
+little bit about the loss in in the
+fiber uh and uh basically it's very very
+
+ align:start position:0%
+fiber uh and uh basically it's very very
+ 
+
+ align:start position:0%
+fiber uh and uh basically it's very very
+low loss if if the fiber is is
+
+ align:start position:0%
+low loss if if the fiber is is
+ 
+
+ align:start position:0%
+low loss if if the fiber is is
+constructed very carefully in the sense
+
+ align:start position:0%
+constructed very carefully in the sense
+ 
+
+ align:start position:0%
+constructed very carefully in the sense
+that it's uh it's uh uh synthesized from
+
+ align:start position:0%
+that it's uh it's uh uh synthesized from
+ 
+
+ align:start position:0%
+that it's uh it's uh uh synthesized from
+from Pure materials and not just uh any
+
+ align:start position:0%
+from Pure materials and not just uh any
+ 
+
+ align:start position:0%
+from Pure materials and not just uh any
+old piece of glass that you find
+
+ align:start position:0%
+old piece of glass that you find
+ 
+
+ align:start position:0%
+old piece of glass that you find
+somewhere okay synthesize it from
+
+ align:start position:0%
+somewhere okay synthesize it from
+ 
+
+ align:start position:0%
+somewhere okay synthesize it from
+scratch all right and it's drawn
+
+ align:start position:0%
+scratch all right and it's drawn
+ 
+
+ align:start position:0%
+scratch all right and it's drawn
+together and then you you have this core
+
+ align:start position:0%
+together and then you you have this core
+ 
+
+ align:start position:0%
+together and then you you have this core
+that has slightly higher index than the
+
+ align:start position:0%
+that has slightly higher index than the
+ 
+
+ align:start position:0%
+that has slightly higher index than the
+the clading so you think everything is
+
+ align:start position:0%
+the clading so you think everything is
+ 
+
+ align:start position:0%
+the clading so you think everything is
+fine but there's there's a problem and
+
+ align:start position:0%
+fine but there's there's a problem and
+ 
+
+ align:start position:0%
+fine but there's there's a problem and
+that we want to discuss just like with
+
+ align:start position:0%
+that we want to discuss just like with
+ 
+
+ align:start position:0%
+that we want to discuss just like with
+lasers everybody here wants the the
+
+ align:start position:0%
+lasers everybody here wants the the
+ 
+
+ align:start position:0%
+lasers everybody here wants the the
+lowest order mode which is the single
+
+ align:start position:0%
+lowest order mode which is the single
+ 
+
+ align:start position:0%
+lowest order mode which is the single
+spot that comes out but uh what we find
+
+ align:start position:0%
+spot that comes out but uh what we find
+ 
+
+ align:start position:0%
+spot that comes out but uh what we find
+that there are other uh intensity
+
+ align:start position:0%
+that there are other uh intensity
+ 
+
+ align:start position:0%
+that there are other uh intensity
+distributions that come out and again
+
+ align:start position:0%
+distributions that come out and again
+ 
+
+ align:start position:0%
+distributions that come out and again
+these are called the transverse modes
+
+ align:start position:0%
+these are called the transverse modes
+ 
+
+ align:start position:0%
+these are called the transverse modes
+that can propagate in a fiber satisfying
+
+ align:start position:0%
+that can propagate in a fiber satisfying
+ 
+
+ align:start position:0%
+that can propagate in a fiber satisfying
+Maxell uh equations and so on and the
+
+ align:start position:0%
+Maxell uh equations and so on and the
+ 
+
+ align:start position:0%
+Maxell uh equations and so on and the
+boundary conditions in a in a fiber and
+
+ align:start position:0%
+boundary conditions in a in a fiber and
+ 
+
+ align:start position:0%
+boundary conditions in a in a fiber and
+for and and this is called if a fiber is
+
+ align:start position:0%
+for and and this is called if a fiber is
+ 
+
+ align:start position:0%
+for and and this is called if a fiber is
+then then allows these modes to
+
+ align:start position:0%
+then then allows these modes to
+ 
+
+ align:start position:0%
+then then allows these modes to
+propagate then it's called a multimode
+
+ align:start position:0%
+propagate then it's called a multimode
+ 
+
+ align:start position:0%
+propagate then it's called a multimode
+uh fiber single mode fiber is the fiber
+
+ align:start position:0%
+uh fiber single mode fiber is the fiber
+ 
+
+ align:start position:0%
+uh fiber single mode fiber is the fiber
+that only allows this to go all the
+
+ align:start position:0%
+that only allows this to go all the
+ 
+
+ align:start position:0%
+that only allows this to go all the
+others have high loss and they and they
+
+ align:start position:0%
+others have high loss and they and they
+ 
+
+ align:start position:0%
+others have high loss and they and they
+don't go so now let's let's uh spend a
+
+ align:start position:0%
+don't go so now let's let's uh spend a
+ 
+
+ align:start position:0%
+don't go so now let's let's uh spend a
+couple of minutes on uh on single mode
+
+ align:start position:0%
+couple of minutes on uh on single mode
+ 
+
+ align:start position:0%
+couple of minutes on uh on single mode
+and multi mode fibers before I show you
+
+ align:start position:0%
+and multi mode fibers before I show you
+ 
+
+ align:start position:0%
+and multi mode fibers before I show you
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+demonstrations the uh the in in this
+
+ align:start position:0%
+demonstrations the uh the in in this
+ 
+
+ align:start position:0%
+demonstrations the uh the in in this
+case here I have this is the core and
+
+ align:start position:0%
+case here I have this is the core and
+ 
+
+ align:start position:0%
+case here I have this is the core and
+that's the cladding and the index of the
+
+ align:start position:0%
+that's the cladding and the index of the
+ 
+
+ align:start position:0%
+that's the cladding and the index of the
+core is is N1 Which is higher than the
+
+ align:start position:0%
+core is is N1 Which is higher than the
+ 
+
+ align:start position:0%
+core is is N1 Which is higher than the
+index of the clading which is N2 down
+
+ align:start position:0%
+index of the clading which is N2 down
+ 
+
+ align:start position:0%
+index of the clading which is N2 down
+here now uh the on the x- axis here I'm
+
+ align:start position:0%
+here now uh the on the x- axis here I'm
+ 
+
+ align:start position:0%
+here now uh the on the x- axis here I'm
+plotting what we call the V number
+
+ align:start position:0%
+plotting what we call the V number
+ 
+
+ align:start position:0%
+plotting what we call the V number
+what's the V number right now we're not
+
+ align:start position:0%
+what's the V number right now we're not
+ 
+
+ align:start position:0%
+what's the V number right now we're not
+we don't have time to get into any
+
+ align:start position:0%
+we don't have time to get into any
+ 
+
+ align:start position:0%
+we don't have time to get into any
+detail but the V number is essentially a
+
+ align:start position:0%
+detail but the V number is essentially a
+ 
+
+ align:start position:0%
+detail but the V number is essentially a
+a parameter that depends on on one over
+
+ align:start position:0%
+a parameter that depends on on one over
+ 
+
+ align:start position:0%
+a parameter that depends on on one over
+the wavelength of the light on the D
+
+ align:start position:0%
+the wavelength of the light on the D
+ 
+
+ align:start position:0%
+the wavelength of the light on the D
+subc which is the diameter of the core
+
+ align:start position:0%
+subc which is the diameter of the core
+ 
+
+ align:start position:0%
+subc which is the diameter of the core
+and the square root of N1 squar that's
+
+ align:start position:0%
+and the square root of N1 squar that's
+ 
+
+ align:start position:0%
+and the square root of N1 squar that's
+N1 being the core index and N2 is the
+
+ align:start position:0%
+N1 being the core index and N2 is the
+ 
+
+ align:start position:0%
+N1 being the core index and N2 is the
+cladding index the square root of N1 squ
+
+ align:start position:0%
+cladding index the square root of N1 squ
+ 
+
+ align:start position:0%
+cladding index the square root of N1 squ
+minus N2 squ now turns out when this V
+
+ align:start position:0%
+minus N2 squ now turns out when this V
+ 
+
+ align:start position:0%
+minus N2 squ now turns out when this V
+number has a certain value let's say 2.4
+
+ align:start position:0%
+number has a certain value let's say 2.4
+ 
+
+ align:start position:0%
+number has a certain value let's say 2.4
+or or so on then you only get uh if it's
+
+ align:start position:0%
+or or so on then you only get uh if it's
+ 
+
+ align:start position:0%
+or or so on then you only get uh if it's
+if it's if it's that value or less then
+
+ align:start position:0%
+if it's if it's that value or less then
+ 
+
+ align:start position:0%
+if it's if it's that value or less then
+you only get single mode propagation all
+
+ align:start position:0%
+you only get single mode propagation all
+ 
+
+ align:start position:0%
+you only get single mode propagation all
+the other modes have too much loss and
+
+ align:start position:0%
+the other modes have too much loss and
+ 
+
+ align:start position:0%
+the other modes have too much loss and
+they uh they don't they don't propagate
+
+ align:start position:0%
+they uh they don't they don't propagate
+ 
+
+ align:start position:0%
+they uh they don't they don't propagate
+so single mode fiber then is one where
+
+ align:start position:0%
+so single mode fiber then is one where
+ 
+
+ align:start position:0%
+so single mode fiber then is one where
+the V parameter which means the the size
+
+ align:start position:0%
+the V parameter which means the the size
+ 
+
+ align:start position:0%
+the V parameter which means the the size
+of the core the wavelength and the
+
+ align:start position:0%
+of the core the wavelength and the
+ 
+
+ align:start position:0%
+of the core the wavelength and the
+difference of in the indices are such
+
+ align:start position:0%
+difference of in the indices are such
+ 
+
+ align:start position:0%
+difference of in the indices are such
+that gives you v v parameter smaller
+
+ align:start position:0%
+that gives you v v parameter smaller
+ 
+
+ align:start position:0%
+that gives you v v parameter smaller
+than 2.4 and that's single M if you if
+
+ align:start position:0%
+than 2.4 and that's single M if you if
+ 
+
+ align:start position:0%
+than 2.4 and that's single M if you if
+the let's say you change the wavelength
+
+ align:start position:0%
+the let's say you change the wavelength
+ 
+
+ align:start position:0%
+the let's say you change the wavelength
+you make it shorter or so on V will go
+
+ align:start position:0%
+you make it shorter or so on V will go
+ 
+
+ align:start position:0%
+you make it shorter or so on V will go
+up and then you'll start getting all
+
+ align:start position:0%
+up and then you'll start getting all
+ 
+
+ align:start position:0%
+up and then you'll start getting all
+these uh uh uh multim modes or the just
+
+ align:start position:0%
+these uh uh uh multim modes or the just
+ 
+
+ align:start position:0%
+these uh uh uh multim modes or the just
+like I showed you I showed you before
+
+ align:start position:0%
+like I showed you I showed you before
+ 
+
+ align:start position:0%
+like I showed you I showed you before
+and uh and uh and then you'll be in
+
+ align:start position:0%
+and uh and uh and then you'll be in
+ 
+
+ align:start position:0%
+and uh and uh and then you'll be in
+trouble so for some application not all
+
+ align:start position:0%
+trouble so for some application not all
+ 
+
+ align:start position:0%
+trouble so for some application not all
+applications the uh in this particular
+
+ align:start position:0%
+applications the uh in this particular
+ 
+
+ align:start position:0%
+applications the uh in this particular
+case what I show you is the field
+
+ align:start position:0%
+case what I show you is the field
+ 
+
+ align:start position:0%
+case what I show you is the field
+distribution and the intensity
+
+ align:start position:0%
+distribution and the intensity
+ 
+
+ align:start position:0%
+distribution and the intensity
+distribution uh uh in the in the fiber
+
+ align:start position:0%
+distribution uh uh in the in the fiber
+ 
+
+ align:start position:0%
+distribution uh uh in the in the fiber
+here's the core is the size of the core
+
+ align:start position:0%
+here's the core is the size of the core
+ 
+
+ align:start position:0%
+here's the core is the size of the core
+and that's the clading and you can see
+
+ align:start position:0%
+and that's the clading and you can see
+ 
+
+ align:start position:0%
+and that's the clading and you can see
+here depending on on the parameters that
+
+ align:start position:0%
+here depending on on the parameters that
+ 
+
+ align:start position:0%
+here depending on on the parameters that
+I choose
+
+ align:start position:0%
+I choose
+ 
+
+ align:start position:0%
+I choose
+some light uh in in this lowest auto
+
+ align:start position:0%
+some light uh in in this lowest auto
+ 
+
+ align:start position:0%
+some light uh in in this lowest auto
+mode in the field will will propagate in
+
+ align:start position:0%
+mode in the field will will propagate in
+ 
+
+ align:start position:0%
+mode in the field will will propagate in
+the in the cladding and so with the
+
+ align:start position:0%
+the in the cladding and so with the
+ 
+
+ align:start position:0%
+the in the cladding and so with the
+essentially intensity for the next high
+
+ align:start position:0%
+essentially intensity for the next high
+ 
+
+ align:start position:0%
+essentially intensity for the next high
+order mode okay which is similar to the
+
+ align:start position:0%
+order mode okay which is similar to the
+ 
+
+ align:start position:0%
+order mode okay which is similar to the
+laser cavity modes the field
+
+ align:start position:0%
+laser cavity modes the field
+ 
+
+ align:start position:0%
+laser cavity modes the field
+distribution is something like this and
+
+ align:start position:0%
+distribution is something like this and
+ 
+
+ align:start position:0%
+distribution is something like this and
+again part of it will will propagate
+
+ align:start position:0%
+again part of it will will propagate
+ 
+
+ align:start position:0%
+again part of it will will propagate
+into into uh in the cladding and when
+
+ align:start position:0%
+into into uh in the cladding and when
+ 
+
+ align:start position:0%
+into into uh in the cladding and when
+you square it up if you look at the
+
+ align:start position:0%
+you square it up if you look at the
+ 
+
+ align:start position:0%
+you square it up if you look at the
+intensity it looks like this that's what
+
+ align:start position:0%
+intensity it looks like this that's what
+ 
+
+ align:start position:0%
+intensity it looks like this that's what
+the two spots look like that but the
+
+ align:start position:0%
+the two spots look like that but the
+ 
+
+ align:start position:0%
+the two spots look like that but the
+field is really one is let's say
+
+ align:start position:0%
+field is really one is let's say
+ 
+
+ align:start position:0%
+field is really one is let's say
+positive the other one is is negative
+
+ align:start position:0%
+positive the other one is is negative
+ 
+
+ align:start position:0%
+positive the other one is is negative
+and what you see here is that the the uh
+
+ align:start position:0%
+and what you see here is that the the uh
+ 
+
+ align:start position:0%
+and what you see here is that the the uh
+size of the uh of this uh higher aut
+
+ align:start position:0%
+size of the uh of this uh higher aut
+ 
+
+ align:start position:0%
+size of the uh of this uh higher aut
+mode is bigger than the lowest aut mode
+
+ align:start position:0%
+mode is bigger than the lowest aut mode
+ 
+
+ align:start position:0%
+mode is bigger than the lowest aut mode
+and more of it will propagate in the
+
+ align:start position:0%
+and more of it will propagate in the
+ 
+
+ align:start position:0%
+and more of it will propagate in the
+cladding than in the core so in terms of
+
+ align:start position:0%
+cladding than in the core so in terms of
+ 
+
+ align:start position:0%
+cladding than in the core so in terms of
+propagation constant or how fast they
+
+ align:start position:0%
+propagation constant or how fast they
+ 
+
+ align:start position:0%
+propagation constant or how fast they
+propagate uh this one propagates more in
+
+ align:start position:0%
+propagate uh this one propagates more in
+ 
+
+ align:start position:0%
+propagate uh this one propagates more in
+the in the in the cladding than this one
+
+ align:start position:0%
+the in the in the cladding than this one
+ 
+
+ align:start position:0%
+the in the in the cladding than this one
+and since the index is smaller in the
+
+ align:start position:0%
+and since the index is smaller in the
+ 
+
+ align:start position:0%
+and since the index is smaller in the
+cladding than in the core then this one
+
+ align:start position:0%
+cladding than in the core then this one
+ 
+
+ align:start position:0%
+cladding than in the core then this one
+will go faster than this one and that's
+
+ align:start position:0%
+will go faster than this one and that's
+ 
+
+ align:start position:0%
+will go faster than this one and that's
+a problem in in Communications in using
+
+ align:start position:0%
+a problem in in Communications in using
+ 
+
+ align:start position:0%
+a problem in in Communications in using
+uh transverse modes in this in this next
+
+ align:start position:0%
+uh transverse modes in this in this next
+ 
+
+ align:start position:0%
+uh transverse modes in this in this next
+uh uh uh graphic I show how much again
+
+ align:start position:0%
+uh uh uh graphic I show how much again
+ 
+
+ align:start position:0%
+uh uh uh graphic I show how much again
+as a function of v number but how much
+
+ align:start position:0%
+as a function of v number but how much
+ 
+
+ align:start position:0%
+as a function of v number but how much
+of the light propagates in the core and
+
+ align:start position:0%
+of the light propagates in the core and
+ 
+
+ align:start position:0%
+of the light propagates in the core and
+how much propagates in the cladding so
+
+ align:start position:0%
+how much propagates in the cladding so
+ 
+
+ align:start position:0%
+how much propagates in the cladding so
+again for V number below this 2.4 or so
+
+ align:start position:0%
+again for V number below this 2.4 or so
+ 
+
+ align:start position:0%
+again for V number below this 2.4 or so
+the for single mode operation it turns
+
+ align:start position:0%
+the for single mode operation it turns
+ 
+
+ align:start position:0%
+the for single mode operation it turns
+out that when the V number is very very
+
+ align:start position:0%
+out that when the V number is very very
+ 
+
+ align:start position:0%
+out that when the V number is very very
+small most of the light I'm plotting
+
+ align:start position:0%
+small most of the light I'm plotting
+ 
+
+ align:start position:0%
+small most of the light I'm plotting
+here uh Power in the core transmitting
+
+ align:start position:0%
+here uh Power in the core transmitting
+ 
+
+ align:start position:0%
+here uh Power in the core transmitting
+the core over the total power
+
+ align:start position:0%
+the core over the total power
+ 
+
+ align:start position:0%
+the core over the total power
+propagated through the fiber then it
+
+ align:start position:0%
+propagated through the fiber then it
+ 
+
+ align:start position:0%
+propagated through the fiber then it
+turns out when the V number is very
+
+ align:start position:0%
+turns out when the V number is very
+ 
+
+ align:start position:0%
+turns out when the V number is very
+small even the single mode propagates
+
+ align:start position:0%
+small even the single mode propagates
+ 
+
+ align:start position:0%
+small even the single mode propagates
+more in the in the cladding than the
+
+ align:start position:0%
+more in the in the cladding than the
+ 
+
+ align:start position:0%
+more in the in the cladding than the
+core okay because uh the ratio of P core
+
+ align:start position:0%
+core okay because uh the ratio of P core
+ 
+
+ align:start position:0%
+core okay because uh the ratio of P core
+to P is very small and as I approach uh
+
+ align:start position:0%
+to P is very small and as I approach uh
+ 
+
+ align:start position:0%
+to P is very small and as I approach uh
+the uh multi mode operation the the
+
+ align:start position:0%
+the uh multi mode operation the the
+ 
+
+ align:start position:0%
+the uh multi mode operation the the
+single mode travels let's say about uh
+
+ align:start position:0%
+single mode travels let's say about uh
+ 
+
+ align:start position:0%
+single mode travels let's say about uh
+80% or so in the core but not in the
+
+ align:start position:0%
+80% or so in the core but not in the
+ 
+
+ align:start position:0%
+80% or so in the core but not in the
+clading now when the multi when the
+
+ align:start position:0%
+clading now when the multi when the
+ 
+
+ align:start position:0%
+clading now when the multi when the
+onset of multim modes comes about then
+
+ align:start position:0%
+onset of multim modes comes about then
+ 
+
+ align:start position:0%
+onset of multim modes comes about then
+the multim mode will at mostly in the in
+
+ align:start position:0%
+the multim mode will at mostly in the in
+ 
+
+ align:start position:0%
+the multim mode will at mostly in the in
+the clading first more in the clading
+
+ align:start position:0%
+the clading first more in the clading
+ 
+
+ align:start position:0%
+the clading first more in the clading
+than in the core and then as I increase
+
+ align:start position:0%
+than in the core and then as I increase
+ 
+
+ align:start position:0%
+than in the core and then as I increase
+the V number they again will start
+
+ align:start position:0%
+the V number they again will start
+ 
+
+ align:start position:0%
+the V number they again will start
+coming in to the propagating in the core
+
+ align:start position:0%
+coming in to the propagating in the core
+ 
+
+ align:start position:0%
+coming in to the propagating in the core
+and and their index th to approach the
+
+ align:start position:0%
+and and their index th to approach the
+ 
+
+ align:start position:0%
+and and their index th to approach the
+index of the single mode but in always
+
+ align:start position:0%
+index of the single mode but in always
+ 
+
+ align:start position:0%
+index of the single mode but in always
+it's lower than that of the of the
+
+ align:start position:0%
+it's lower than that of the of the
+ 
+
+ align:start position:0%
+it's lower than that of the of the
+single mode okay so they all travel
+
+ align:start position:0%
+single mode okay so they all travel
+ 
+
+ align:start position:0%
+single mode okay so they all travel
+essentially at at different speeds and
+
+ align:start position:0%
+essentially at at different speeds and
+ 
+
+ align:start position:0%
+essentially at at different speeds and
+also the transverse modes occupy they
+
+ align:start position:0%
+also the transverse modes occupy they
+ 
+
+ align:start position:0%
+also the transverse modes occupy they
+travel more in the in the uh in the uh
+
+ align:start position:0%
+travel more in the in the uh in the uh
+ 
+
+ align:start position:0%
+travel more in the in the uh in the uh
+uh cladding than in the than in the than
+
+ align:start position:0%
+uh cladding than in the than in the than
+ 
+
+ align:start position:0%
+uh cladding than in the than in the than
+the core as compared with the with a
+
+ align:start position:0%
+the core as compared with the with a
+ 
+
+ align:start position:0%
+the core as compared with the with a
+single mode now to give you to give you
+
+ align:start position:0%
+single mode now to give you to give you
+ 
+
+ align:start position:0%
+single mode now to give you to give you
+an an
+
+ align:start position:0%
+an an
+ 
+
+ align:start position:0%
+an an
+example uh for single mode fiber uh
+
+ align:start position:0%
+example uh for single mode fiber uh
+ 
+
+ align:start position:0%
+example uh for single mode fiber uh
+let's say for a diameter core diameter
+
+ align:start position:0%
+let's say for a diameter core diameter
+ 
+
+ align:start position:0%
+let's say for a diameter core diameter
+of 5 microns and a wavelength of 08
+
+ align:start position:0%
+of 5 microns and a wavelength of 08
+ 
+
+ align:start position:0%
+of 5 microns and a wavelength of 08
+microns uh you need the you need N1
+
+ align:start position:0%
+microns uh you need the you need N1
+ 
+
+ align:start position:0%
+microns uh you need the you need N1
+minus N2 the difference in the index to
+
+ align:start position:0%
+minus N2 the difference in the index to
+ 
+
+ align:start position:0%
+minus N2 the difference in the index to
+be 10 Theus 3 now if you want to make uh
+
+ align:start position:0%
+be 10 Theus 3 now if you want to make uh
+ 
+
+ align:start position:0%
+be 10 Theus 3 now if you want to make uh
+the core diameter uh larger then you're
+
+ align:start position:0%
+the core diameter uh larger then you're
+ 
+
+ align:start position:0%
+the core diameter uh larger then you're
+going to end up with N1 minus N2 even
+
+ align:start position:0%
+going to end up with N1 minus N2 even
+ 
+
+ align:start position:0%
+going to end up with N1 minus N2 even
+smaller so it's very tricky to make uh
+
+ align:start position:0%
+smaller so it's very tricky to make uh
+ 
+
+ align:start position:0%
+smaller so it's very tricky to make uh
+uh single mode fibers otherwise you have
+
+ align:start position:0%
+uh single mode fibers otherwise you have
+ 
+
+ align:start position:0%
+uh single mode fibers otherwise you have
+multi mode operation all right so now
+
+ align:start position:0%
+multi mode operation all right so now
+ 
+
+ align:start position:0%
+multi mode operation all right so now
+that I have talked about about single
+
+ align:start position:0%
+that I have talked about about single
+ 
+
+ align:start position:0%
+that I have talked about about single
+mode and and uh and uh multimode fibers
+
+ align:start position:0%
+mode and and uh and uh multimode fibers
+ 
+
+ align:start position:0%
+mode and and uh and uh multimode fibers
+I have uh two demonstrations for you one
+
+ align:start position:0%
+I have uh two demonstrations for you one
+ 
+
+ align:start position:0%
+I have uh two demonstrations for you one
+basically shows single mode fiber and
+
+ align:start position:0%
+basically shows single mode fiber and
+ 
+
+ align:start position:0%
+basically shows single mode fiber and
+coupling into it and what the output
+
+ align:start position:0%
+coupling into it and what the output
+ 
+
+ align:start position:0%
+coupling into it and what the output
+looks like and also is bend the fiber
+
+ align:start position:0%
+looks like and also is bend the fiber
+ 
+
+ align:start position:0%
+looks like and also is bend the fiber
+and show that whatever you do is still
+
+ align:start position:0%
+and show that whatever you do is still
+ 
+
+ align:start position:0%
+and show that whatever you do is still
+single mode it doesn't change on you all
+
+ align:start position:0%
+single mode it doesn't change on you all
+ 
+
+ align:start position:0%
+single mode it doesn't change on you all
+happens is that you kick light out and
+
+ align:start position:0%
+happens is that you kick light out and
+ 
+
+ align:start position:0%
+happens is that you kick light out and
+and you reduce the intensity but when we
+
+ align:start position:0%
+and you reduce the intensity but when we
+ 
+
+ align:start position:0%
+and you reduce the intensity but when we
+came to multimode something else happens
+
+ align:start position:0%
+came to multimode something else happens
+ 
+
+ align:start position:0%
+came to multimode something else happens
+so now first let's go to the single mode
+
+ align:start position:0%
+so now first let's go to the single mode
+ 
+
+ align:start position:0%
+so now first let's go to the single mode
+uh fiber
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demonstration in this demonstration
+
+ align:start position:0%
+demonstration in this demonstration
+ 
+
+ align:start position:0%
+demonstration in this demonstration
+we're going to illustrate the
+
+ align:start position:0%
+we're going to illustrate the
+ 
+
+ align:start position:0%
+we're going to illustrate the
+propagation of light in a fiber a glass
+
+ align:start position:0%
+propagation of light in a fiber a glass
+ 
+
+ align:start position:0%
+propagation of light in a fiber a glass
+fiber as we know today Optical fibers
+
+ align:start position:0%
+fiber as we know today Optical fibers
+ 
+
+ align:start position:0%
+fiber as we know today Optical fibers
+have a lot of low loss very low loss of
+
+ align:start position:0%
+have a lot of low loss very low loss of
+ 
+
+ align:start position:0%
+have a lot of low loss very low loss of
+the order of uh one or two DBS per
+
+ align:start position:0%
+the order of uh one or two DBS per
+ 
+
+ align:start position:0%
+the order of uh one or two DBS per
+kilometer and of course they're being
+
+ align:start position:0%
+kilometer and of course they're being
+ 
+
+ align:start position:0%
+kilometer and of course they're being
+used for communication as well as other
+
+ align:start position:0%
+used for communication as well as other
+ 
+
+ align:start position:0%
+used for communication as well as other
+applications like
+
+ align:start position:0%
+applications like
+ 
+
+ align:start position:0%
+applications like
+sensors so the setup we have is a uh is
+
+ align:start position:0%
+sensors so the setup we have is a uh is
+ 
+
+ align:start position:0%
+sensors so the setup we have is a uh is
+a laser a helium neon laser over here
+
+ align:start position:0%
+a laser a helium neon laser over here
+ 
+
+ align:start position:0%
+a laser a helium neon laser over here
+here's the output from from the laser
+
+ align:start position:0%
+here's the output from from the laser
+ 
+
+ align:start position:0%
+here's the output from from the laser
+we're going to reflect it by this mirror
+
+ align:start position:0%
+we're going to reflect it by this mirror
+ 
+
+ align:start position:0%
+we're going to reflect it by this mirror
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+mirror and then pass it through a lens
+
+ align:start position:0%
+mirror and then pass it through a lens
+ 
+
+ align:start position:0%
+mirror and then pass it through a lens
+this lens over here here focuses the
+
+ align:start position:0%
+this lens over here here focuses the
+ 
+
+ align:start position:0%
+this lens over here here focuses the
+light into the fiber end and if we can
+
+ align:start position:0%
+light into the fiber end and if we can
+ 
+
+ align:start position:0%
+light into the fiber end and if we can
+take a
+
+ align:start position:0%
+take a
+ 
+
+ align:start position:0%
+take a
+closeup of what's going on over here
+
+ align:start position:0%
+closeup of what's going on over here
+ 
+
+ align:start position:0%
+closeup of what's going on over here
+what you would see is then a lens this
+
+ align:start position:0%
+what you would see is then a lens this
+ 
+
+ align:start position:0%
+what you would see is then a lens this
+lens then focusing the light and fiber
+
+ align:start position:0%
+lens then focusing the light and fiber
+ 
+
+ align:start position:0%
+lens then focusing the light and fiber
+and the fiber is very close to the
+
+ align:start position:0%
+and the fiber is very close to the
+ 
+
+ align:start position:0%
+and the fiber is very close to the
+lens and then the rest of the fiber is
+
+ align:start position:0%
+lens and then the rest of the fiber is
+ 
+
+ align:start position:0%
+lens and then the rest of the fiber is
+here all right so here is the the rest
+
+ align:start position:0%
+here all right so here is the the rest
+ 
+
+ align:start position:0%
+here all right so here is the the rest
+of the fiber now this fiber uh in fact
+
+ align:start position:0%
+of the fiber now this fiber uh in fact
+ 
+
+ align:start position:0%
+of the fiber now this fiber uh in fact
+what you're seeing over here is the uh
+
+ align:start position:0%
+what you're seeing over here is the uh
+ 
+
+ align:start position:0%
+what you're seeing over here is the uh
+essentially the plastic jacket the fiber
+
+ align:start position:0%
+essentially the plastic jacket the fiber
+ 
+
+ align:start position:0%
+essentially the plastic jacket the fiber
+core is about four microns in in
+
+ align:start position:0%
+core is about four microns in in
+ 
+
+ align:start position:0%
+core is about four microns in in
+diameter and the cladding is 125 microns
+
+ align:start position:0%
+diameter and the cladding is 125 microns
+ 
+
+ align:start position:0%
+diameter and the cladding is 125 microns
+and the rest that you see here is the is
+
+ align:start position:0%
+and the rest that you see here is the is
+ 
+
+ align:start position:0%
+and the rest that you see here is the is
+the plastic jacket that's why it looks
+
+ align:start position:0%
+the plastic jacket that's why it looks
+ 
+
+ align:start position:0%
+the plastic jacket that's why it looks
+so so visible uh because it's so thick
+
+ align:start position:0%
+so so visible uh because it's so thick
+ 
+
+ align:start position:0%
+so so visible uh because it's so thick
+the other end of the fiber then uh goes
+
+ align:start position:0%
+the other end of the fiber then uh goes
+ 
+
+ align:start position:0%
+the other end of the fiber then uh goes
+into this
+
+ align:start position:0%
+into this
+ 
+
+ align:start position:0%
+into this
+holder and the the Chuck here it's in AO
+
+ align:start position:0%
+holder and the the Chuck here it's in AO
+ 
+
+ align:start position:0%
+holder and the the Chuck here it's in AO
+fiber hold in a Chuck and the output of
+
+ align:start position:0%
+fiber hold in a Chuck and the output of
+ 
+
+ align:start position:0%
+fiber hold in a Chuck and the output of
+the of the fiber then is is over here
+
+ align:start position:0%
+the of the fiber then is is over here
+ 
+
+ align:start position:0%
+the of the fiber then is is over here
+onto this uh onto this little
+
+ align:start position:0%
+onto this uh onto this little
+ 
+
+ align:start position:0%
+onto this uh onto this little
+screen now if if we can maybe we can
+
+ align:start position:0%
+screen now if if we can maybe we can
+ 
+
+ align:start position:0%
+screen now if if we can maybe we can
+take a close look at the at the fiber
+
+ align:start position:0%
+take a close look at the at the fiber
+ 
+
+ align:start position:0%
+take a close look at the at the fiber
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+here what which
+
+ align:start position:0%
+here what which
+ 
+
+ align:start position:0%
+here what which
+shows that uh what you see over here uh
+
+ align:start position:0%
+shows that uh what you see over here uh
+ 
+
+ align:start position:0%
+shows that uh what you see over here uh
+in fact let me point to it what you see
+
+ align:start position:0%
+in fact let me point to it what you see
+ 
+
+ align:start position:0%
+in fact let me point to it what you see
+over here is the the cladding
+
+ align:start position:0%
+over here is the the cladding
+ 
+
+ align:start position:0%
+over here is the the cladding
+essentially we've stripped the jacket
+
+ align:start position:0%
+essentially we've stripped the jacket
+ 
+
+ align:start position:0%
+essentially we've stripped the jacket
+and what you see here is just the
+
+ align:start position:0%
+and what you see here is just the
+ 
+
+ align:start position:0%
+and what you see here is just the
+cladding and this is the 125 micron
+
+ align:start position:0%
+cladding and this is the 125 micron
+ 
+
+ align:start position:0%
+cladding and this is the 125 micron
+while over here over
+
+ align:start position:0%
+while over here over
+ 
+
+ align:start position:0%
+while over here over
+here is the is the the fiber with the
+
+ align:start position:0%
+here is the is the the fiber with the
+ 
+
+ align:start position:0%
+here is the is the the fiber with the
+plastic with the plastic jacket so when
+
+ align:start position:0%
+plastic with the plastic jacket so when
+ 
+
+ align:start position:0%
+plastic with the plastic jacket so when
+you remove the plastic jacket then you
+
+ align:start position:0%
+you remove the plastic jacket then you
+ 
+
+ align:start position:0%
+you remove the plastic jacket then you
+have essentially what you're seeing is
+
+ align:start position:0%
+have essentially what you're seeing is
+ 
+
+ align:start position:0%
+have essentially what you're seeing is
+the is just the 125 Micron cladding all
+
+ align:start position:0%
+the is just the 125 Micron cladding all
+ 
+
+ align:start position:0%
+the is just the 125 Micron cladding all
+right so this is then uh the fiber and
+
+ align:start position:0%
+right so this is then uh the fiber and
+ 
+
+ align:start position:0%
+right so this is then uh the fiber and
+there's the output of the of the fiber
+
+ align:start position:0%
+there's the output of the of the fiber
+ 
+
+ align:start position:0%
+there's the output of the of the fiber
+now what we see if we can then enhance
+
+ align:start position:0%
+now what we see if we can then enhance
+ 
+
+ align:start position:0%
+now what we see if we can then enhance
+this and bring it bring it in what we
+
+ align:start position:0%
+this and bring it bring it in what we
+ 
+
+ align:start position:0%
+this and bring it bring it in what we
+see is the uh is the single mode uh
+
+ align:start position:0%
+see is the uh is the single mode uh
+ 
+
+ align:start position:0%
+see is the uh is the single mode uh
+behavior of of a
+
+ align:start position:0%
+behavior of of a
+ 
+
+ align:start position:0%
+behavior of of a
+fiber it looks like almost like a
+
+ align:start position:0%
+fiber it looks like almost like a
+ 
+
+ align:start position:0%
+fiber it looks like almost like a
+gaussian kind of
+
+ align:start position:0%
+gaussian kind of
+ 
+
+ align:start position:0%
+gaussian kind of
+spot not quite gaussian but it looks
+
+ align:start position:0%
+spot not quite gaussian but it looks
+ 
+
+ align:start position:0%
+spot not quite gaussian but it looks
+like a gaussian kind of spot now what
+
+ align:start position:0%
+like a gaussian kind of spot now what
+ 
+
+ align:start position:0%
+like a gaussian kind of spot now what
+I'm doing
+
+ align:start position:0%
+I'm doing
+ 
+
+ align:start position:0%
+I'm doing
+now uh is just it just adjusting the the
+
+ align:start position:0%
+now uh is just it just adjusting the the
+ 
+
+ align:start position:0%
+now uh is just it just adjusting the the
+uh coupling into into the fiber and it's
+
+ align:start position:0%
+uh coupling into into the fiber and it's
+ 
+
+ align:start position:0%
+uh coupling into into the fiber and it's
+very touchy because as said the core is
+
+ align:start position:0%
+very touchy because as said the core is
+ 
+
+ align:start position:0%
+very touchy because as said the core is
+only about four four
+
+ align:start position:0%
+only about four four
+ 
+
+ align:start position:0%
+only about four four
+microns all right so this is what then a
+
+ align:start position:0%
+microns all right so this is what then a
+ 
+
+ align:start position:0%
+microns all right so this is what then a
+single mode uh uh fiber the output from
+
+ align:start position:0%
+single mode uh uh fiber the output from
+ 
+
+ align:start position:0%
+single mode uh uh fiber the output from
+a single mode fiber looks like and if as
+
+ align:start position:0%
+a single mode fiber looks like and if as
+ 
+
+ align:start position:0%
+a single mode fiber looks like and if as
+I miss a line here doesn't make any
+
+ align:start position:0%
+I miss a line here doesn't make any
+ 
+
+ align:start position:0%
+I miss a line here doesn't make any
+difference all you get is just a loss in
+
+ align:start position:0%
+difference all you get is just a loss in
+ 
+
+ align:start position:0%
+difference all you get is just a loss in
+intensity the shape of the mode stays
+
+ align:start position:0%
+intensity the shape of the mode stays
+ 
+
+ align:start position:0%
+intensity the shape of the mode stays
+stays the same so remember the core is
+
+ align:start position:0%
+stays the same so remember the core is
+ 
+
+ align:start position:0%
+stays the same so remember the core is
+four microns cladding is 125 the
+
+ align:start position:0%
+four microns cladding is 125 the
+ 
+
+ align:start position:0%
+four microns cladding is 125 the
+wavelength of the light is 6328 anrom
+
+ align:start position:0%
+wavelength of the light is 6328 anrom
+ 
+
+ align:start position:0%
+wavelength of the light is 6328 anrom
+and the core to index uh difference is
+
+ align:start position:0%
+and the core to index uh difference is
+ 
+
+ align:start position:0%
+and the core to index uh difference is
+about one part in in 10 to the three so
+
+ align:start position:0%
+about one part in in 10 to the three so
+ 
+
+ align:start position:0%
+about one part in in 10 to the three so
+this way you can show that indeed you
+
+ align:start position:0%
+this way you can show that indeed you
+ 
+
+ align:start position:0%
+this way you can show that indeed you
+get uh single mode
+
+ align:start position:0%
+get uh single mode
+ 
+
+ align:start position:0%
+get uh single mode
+propagation now I would like to
+
+ align:start position:0%
+propagation now I would like to
+ 
+
+ align:start position:0%
+propagation now I would like to
+illustrate some interesting phenomena
+
+ align:start position:0%
+illustrate some interesting phenomena
+ 
+
+ align:start position:0%
+illustrate some interesting phenomena
+about fibers so if we get the camera to
+
+ align:start position:0%
+about fibers so if we get the camera to
+ 
+
+ align:start position:0%
+about fibers so if we get the camera to
+look over
+
+ align:start position:0%
+look over
+ 
+
+ align:start position:0%
+look over
+here I want to illustrate how touchy uh
+
+ align:start position:0%
+here I want to illustrate how touchy uh
+ 
+
+ align:start position:0%
+here I want to illustrate how touchy uh
+uh is the propagation of light in a in a
+
+ align:start position:0%
+uh is the propagation of light in a in a
+ 
+
+ align:start position:0%
+uh is the propagation of light in a in a
+single mode fiber now here is here's a
+
+ align:start position:0%
+single mode fiber now here is here's a
+ 
+
+ align:start position:0%
+single mode fiber now here is here's a
+piece of fiber and you can see that
+
+ align:start position:0%
+piece of fiber and you can see that
+ 
+
+ align:start position:0%
+piece of fiber and you can see that
+there's no light uh scattered from the
+
+ align:start position:0%
+there's no light uh scattered from the
+ 
+
+ align:start position:0%
+there's no light uh scattered from the
+fiber
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now all I have to do is bend the fiber
+
+ align:start position:0%
+now all I have to do is bend the fiber
+ 
+
+ align:start position:0%
+now all I have to do is bend the fiber
+bend the F and you're beginning to see
+
+ align:start position:0%
+bend the F and you're beginning to see
+ 
+
+ align:start position:0%
+bend the F and you're beginning to see
+light that gets gets transmitted out of
+
+ align:start position:0%
+light that gets gets transmitted out of
+ 
+
+ align:start position:0%
+light that gets gets transmitted out of
+the fiber gets essentially kicked out
+
+ align:start position:0%
+the fiber gets essentially kicked out
+ 
+
+ align:start position:0%
+the fiber gets essentially kicked out
+the fiber and uh because because of the
+
+ align:start position:0%
+the fiber and uh because because of the
+ 
+
+ align:start position:0%
+the fiber and uh because because of the
+bend now and and and the reason for that
+
+ align:start position:0%
+bend now and and and the reason for that
+ 
+
+ align:start position:0%
+bend now and and and the reason for that
+because it's you start uh going against
+
+ align:start position:0%
+because it's you start uh going against
+ 
+
+ align:start position:0%
+because it's you start uh going against
+the rules of uh propagation of light in
+
+ align:start position:0%
+the rules of uh propagation of light in
+ 
+
+ align:start position:0%
+the rules of uh propagation of light in
+a fiber
+
+ align:start position:0%
+a fiber
+ 
+
+ align:start position:0%
+a fiber
+for example if you take the ray uh
+
+ align:start position:0%
+for example if you take the ray uh
+ 
+
+ align:start position:0%
+for example if you take the ray uh
+explanation is that what you're doing
+
+ align:start position:0%
+explanation is that what you're doing
+ 
+
+ align:start position:0%
+explanation is that what you're doing
+you are exceeding or or you're changing
+
+ align:start position:0%
+you are exceeding or or you're changing
+ 
+
+ align:start position:0%
+you are exceeding or or you're changing
+the angle of
+
+ align:start position:0%
+the angle of
+ 
+
+ align:start position:0%
+the angle of
+light uh with respect to the to the to
+
+ align:start position:0%
+light uh with respect to the to the to
+ 
+
+ align:start position:0%
+light uh with respect to the to the to
+the uh to the fiber which means that if
+
+ align:start position:0%
+the uh to the fiber which means that if
+ 
+
+ align:start position:0%
+the uh to the fiber which means that if
+you're if you're below the critical
+
+ align:start position:0%
+you're if you're below the critical
+ 
+
+ align:start position:0%
+you're if you're below the critical
+angle then you uh the light is no longer
+
+ align:start position:0%
+angle then you uh the light is no longer
+ 
+
+ align:start position:0%
+angle then you uh the light is no longer
+totally internally reflected and
+
+ align:start position:0%
+totally internally reflected and
+ 
+
+ align:start position:0%
+totally internally reflected and
+therefore gets kicked out all right so
+
+ align:start position:0%
+therefore gets kicked out all right so
+ 
+
+ align:start position:0%
+therefore gets kicked out all right so
+here it is it's very dramatic as soon as
+
+ align:start position:0%
+here it is it's very dramatic as soon as
+ 
+
+ align:start position:0%
+here it is it's very dramatic as soon as
+you put Little Bend in this fiber you
+
+ align:start position:0%
+you put Little Bend in this fiber you
+ 
+
+ align:start position:0%
+you put Little Bend in this fiber you
+can you can kick out a lot of light in
+
+ align:start position:0%
+can you can kick out a lot of light in
+ 
+
+ align:start position:0%
+can you can kick out a lot of light in
+fact there is the glow uh right here now
+
+ align:start position:0%
+fact there is the glow uh right here now
+ 
+
+ align:start position:0%
+fact there is the glow uh right here now
+if we can bring in the the output of the
+
+ align:start position:0%
+if we can bring in the the output of the
+ 
+
+ align:start position:0%
+if we can bring in the the output of the
+fiber into the inset over here now you
+
+ align:start position:0%
+fiber into the inset over here now you
+ 
+
+ align:start position:0%
+fiber into the inset over here now you
+can see that as I increase the the band
+
+ align:start position:0%
+can see that as I increase the the band
+ 
+
+ align:start position:0%
+can see that as I increase the the band
+all right you can see that the intensity
+
+ align:start position:0%
+all right you can see that the intensity
+ 
+
+ align:start position:0%
+all right you can see that the intensity
+here I'll do it even more the intensity
+
+ align:start position:0%
+here I'll do it even more the intensity
+ 
+
+ align:start position:0%
+here I'll do it even more the intensity
+then drops quite a bit which means I've
+
+ align:start position:0%
+then drops quite a bit which means I've
+ 
+
+ align:start position:0%
+then drops quite a bit which means I've
+kicked out almost all all the light by
+
+ align:start position:0%
+kicked out almost all all the light by
+ 
+
+ align:start position:0%
+kicked out almost all all the light by
+simply putting a Bend into into the
+
+ align:start position:0%
+simply putting a Bend into into the
+ 
+
+ align:start position:0%
+simply putting a Bend into into the
+fiber so the the illustration here then
+
+ align:start position:0%
+fiber so the the illustration here then
+ 
+
+ align:start position:0%
+fiber so the the illustration here then
+shows that if you leave the fiber alone
+
+ align:start position:0%
+shows that if you leave the fiber alone
+ 
+
+ align:start position:0%
+shows that if you leave the fiber alone
+without sharp bends everything is fine
+
+ align:start position:0%
+without sharp bends everything is fine
+ 
+
+ align:start position:0%
+without sharp bends everything is fine
+if you put in a band then you can kick
+
+ align:start position:0%
+if you put in a band then you can kick
+ 
+
+ align:start position:0%
+if you put in a band then you can kick
+out a lot of light and then not much
+
+ align:start position:0%
+out a lot of light and then not much
+ 
+
+ align:start position:0%
+out a lot of light and then not much
+will be will be will be
+
+ align:start position:0%
+will be will be will be
+ 
+
+ align:start position:0%
+will be will be will be
+transmitted so you have to be careful
+
+ align:start position:0%
+transmitted so you have to be careful
+ 
+
+ align:start position:0%
+transmitted so you have to be careful
+you don't put it too tight a Bend
+
+ align:start position:0%
+you don't put it too tight a Bend
+ 
+
+ align:start position:0%
+you don't put it too tight a Bend
+otherwise you fiber is brittle and you
+
+ align:start position:0%
+otherwise you fiber is brittle and you
+ 
+
+ align:start position:0%
+otherwise you fiber is brittle and you
+break the fiber so you have to be be
+
+ align:start position:0%
+break the fiber so you have to be be
+ 
+
+ align:start position:0%
+break the fiber so you have to be be
+careful how you how you do
+
+ align:start position:0%
+careful how you how you do
+ 
+
+ align:start position:0%
+careful how you how you do
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+this in this previous demonstration then
+
+ align:start position:0%
+this in this previous demonstration then
+ 
+
+ align:start position:0%
+this in this previous demonstration then
+what we had was a single mode single
+
+ align:start position:0%
+what we had was a single mode single
+ 
+
+ align:start position:0%
+what we had was a single mode single
+mode fiber which means that it's a fiber
+
+ align:start position:0%
+mode fiber which means that it's a fiber
+ 
+
+ align:start position:0%
+mode fiber which means that it's a fiber
+that satisfied this V number being uh
+
+ align:start position:0%
+that satisfied this V number being uh
+ 
+
+ align:start position:0%
+that satisfied this V number being uh
+less than 2.4 or
+
+ align:start position:0%
+less than 2.4 or
+ 
+
+ align:start position:0%
+less than 2.4 or
+so and uh and uh because of again the
+
+ align:start position:0%
+so and uh and uh because of again the
+ 
+
+ align:start position:0%
+so and uh and uh because of again the
+choice of the cord diameter the
+
+ align:start position:0%
+choice of the cord diameter the
+ 
+
+ align:start position:0%
+choice of the cord diameter the
+wavelength and the difference in the in
+
+ align:start position:0%
+wavelength and the difference in the in
+ 
+
+ align:start position:0%
+wavelength and the difference in the in
+the in the indices now in this next
+
+ align:start position:0%
+the in the indices now in this next
+ 
+
+ align:start position:0%
+the in the indices now in this next
+demonstration we're going to uh violate
+
+ align:start position:0%
+demonstration we're going to uh violate
+ 
+
+ align:start position:0%
+demonstration we're going to uh violate
+this we're going to uh create a v that
+
+ align:start position:0%
+this we're going to uh create a v that
+ 
+
+ align:start position:0%
+this we're going to uh create a v that
+is bigger than uh than this value here
+
+ align:start position:0%
+is bigger than uh than this value here
+ 
+
+ align:start position:0%
+is bigger than uh than this value here
+by uh in our case we did it by have
+
+ align:start position:0%
+by uh in our case we did it by have
+ 
+
+ align:start position:0%
+by uh in our case we did it by have
+choosing a fiber that has a that's a
+
+ align:start position:0%
+choosing a fiber that has a that's a
+ 
+
+ align:start position:0%
+choosing a fiber that has a that's a
+bigger cord diameter but we could have
+
+ align:start position:0%
+bigger cord diameter but we could have
+ 
+
+ align:start position:0%
+bigger cord diameter but we could have
+also done it with by changing the
+
+ align:start position:0%
+also done it with by changing the
+ 
+
+ align:start position:0%
+also done it with by changing the
+wavelength and if you just shorten the
+
+ align:start position:0%
+wavelength and if you just shorten the
+ 
+
+ align:start position:0%
+wavelength and if you just shorten the
+wavelength go more into into the uh into
+
+ align:start position:0%
+wavelength go more into into the uh into
+ 
+
+ align:start position:0%
+wavelength go more into into the uh into
+the blue side of the spectrum then you
+
+ align:start position:0%
+the blue side of the spectrum then you
+ 
+
+ align:start position:0%
+the blue side of the spectrum then you
+can uh you start to see uh transverse
+
+ align:start position:0%
+can uh you start to see uh transverse
+ 
+
+ align:start position:0%
+can uh you start to see uh transverse
+modes like I uh I showed you uh I showed
+
+ align:start position:0%
+modes like I uh I showed you uh I showed
+ 
+
+ align:start position:0%
+modes like I uh I showed you uh I showed
+you before okay and I think now
+
+ align:start position:0%
+you before okay and I think now
+ 
+
+ align:start position:0%
+you before okay and I think now
+uh we're ready to uh have fun with a
+
+ align:start position:0%
+uh we're ready to uh have fun with a
+ 
+
+ align:start position:0%
+uh we're ready to uh have fun with a
+multimode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fiber now we've replaced the previous
+
+ align:start position:0%
+fiber now we've replaced the previous
+ 
+
+ align:start position:0%
+fiber now we've replaced the previous
+fiber with another one the only
+
+ align:start position:0%
+fiber with another one the only
+ 
+
+ align:start position:0%
+fiber with another one the only
+difference between this fiber and the
+
+ align:start position:0%
+difference between this fiber and the
+ 
+
+ align:start position:0%
+difference between this fiber and the
+previous one is that the core diameter
+
+ align:start position:0%
+previous one is that the core diameter
+ 
+
+ align:start position:0%
+previous one is that the core diameter
+is now a little bit bigger it's about
+
+ align:start position:0%
+is now a little bit bigger it's about
+ 
+
+ align:start position:0%
+is now a little bit bigger it's about
+six microns instead of four microns in
+
+ align:start position:0%
+six microns instead of four microns in
+ 
+
+ align:start position:0%
+six microns instead of four microns in
+the previous finer setup is exactly the
+
+ align:start position:0%
+the previous finer setup is exactly the
+ 
+
+ align:start position:0%
+the previous finer setup is exactly the
+same again we have the laser here
+
+ align:start position:0%
+same again we have the laser here
+ 
+
+ align:start position:0%
+same again we have the laser here
+getting reflected by this mirror and
+
+ align:start position:0%
+getting reflected by this mirror and
+ 
+
+ align:start position:0%
+getting reflected by this mirror and
+this mirror into the lens into this
+
+ align:start position:0%
+this mirror into the lens into this
+ 
+
+ align:start position:0%
+this mirror into the lens into this
+fiber this new fiber and then the the
+
+ align:start position:0%
+fiber this new fiber and then the the
+ 
+
+ align:start position:0%
+fiber this new fiber and then the the
+output of the Fiber goes onto the screen
+
+ align:start position:0%
+output of the Fiber goes onto the screen
+ 
+
+ align:start position:0%
+output of the Fiber goes onto the screen
+so let's now take a look at the output
+
+ align:start position:0%
+so let's now take a look at the output
+ 
+
+ align:start position:0%
+so let's now take a look at the output
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+fi uhhuh so what first thing we see that
+
+ align:start position:0%
+fi uhhuh so what first thing we see that
+ 
+
+ align:start position:0%
+fi uhhuh so what first thing we see that
+doesn't look like a single mode at all
+
+ align:start position:0%
+doesn't look like a single mode at all
+ 
+
+ align:start position:0%
+doesn't look like a single mode at all
+that single low and if I change the the
+
+ align:start position:0%
+that single low and if I change the the
+ 
+
+ align:start position:0%
+that single low and if I change the the
+adjustment if we can have the camera
+
+ align:start position:0%
+adjustment if we can have the camera
+ 
+
+ align:start position:0%
+adjustment if we can have the camera
+looking at my adjustment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ments then you see that I can get a
+
+ align:start position:0%
+ments then you see that I can get a
+ 
+
+ align:start position:0%
+ments then you see that I can get a
+variety of
+
+ align:start position:0%
+variety of
+ 
+
+ align:start position:0%
+variety of
+uh uh of shapes all I'm doing is
+
+ align:start position:0%
+uh uh of shapes all I'm doing is
+ 
+
+ align:start position:0%
+uh uh of shapes all I'm doing is
+changing the adjustment I can get a
+
+ align:start position:0%
+changing the adjustment I can get a
+ 
+
+ align:start position:0%
+changing the adjustment I can get a
+variety of shapes and clearly it's not
+
+ align:start position:0%
+variety of shapes and clearly it's not
+ 
+
+ align:start position:0%
+variety of shapes and clearly it's not
+like what we had before the single mode
+
+ align:start position:0%
+like what we had before the single mode
+ 
+
+ align:start position:0%
+like what we had before the single mode
+be behavior that we had
+
+ align:start position:0%
+be behavior that we had
+ 
+
+ align:start position:0%
+be behavior that we had
+before and this is then the so-called
+
+ align:start position:0%
+before and this is then the so-called
+ 
+
+ align:start position:0%
+before and this is then the so-called
+multi mode what you're seeing are are
+
+ align:start position:0%
+multi mode what you're seeing are are
+ 
+
+ align:start position:0%
+multi mode what you're seeing are are
+different transverse modes that are that
+
+ align:start position:0%
+different transverse modes that are that
+ 
+
+ align:start position:0%
+different transverse modes that are that
+can propagate in in this fiber because
+
+ align:start position:0%
+can propagate in in this fiber because
+ 
+
+ align:start position:0%
+can propagate in in this fiber because
+the core diameter is bigger but I'm
+
+ align:start position:0%
+the core diameter is bigger but I'm
+ 
+
+ align:start position:0%
+the core diameter is bigger but I'm
+going to leave it to you then to explain
+
+ align:start position:0%
+going to leave it to you then to explain
+ 
+
+ align:start position:0%
+going to leave it to you then to explain
+uh why exactly why you get higher o
+
+ align:start position:0%
+uh why exactly why you get higher o
+ 
+
+ align:start position:0%
+uh why exactly why you get higher o
+higher mode higher transverse modes
+
+ align:start position:0%
+higher mode higher transverse modes
+ 
+
+ align:start position:0%
+higher mode higher transverse modes
+propagated in this in this fiber again
+
+ align:start position:0%
+propagated in this in this fiber again
+ 
+
+ align:start position:0%
+propagated in this in this fiber again
+the wavelength is the same the only
+
+ align:start position:0%
+the wavelength is the same the only
+ 
+
+ align:start position:0%
+the wavelength is the same the only
+thing the only difference is that the
+
+ align:start position:0%
+thing the only difference is that the
+ 
+
+ align:start position:0%
+thing the only difference is that the
+core diameter is is
+
+ align:start position:0%
+core diameter is is
+ 
+
+ align:start position:0%
+core diameter is is
+bigger you can see this one here you get
+
+ align:start position:0%
+bigger you can see this one here you get
+ 
+
+ align:start position:0%
+bigger you can see this one here you get
+nice dark line in the middle
+
+ align:start position:0%
+nice dark line in the middle
+ 
+
+ align:start position:0%
+nice dark line in the middle
+and then then if I align it over here
+
+ align:start position:0%
+and then then if I align it over here
+ 
+
+ align:start position:0%
+and then then if I align it over here
+you can see it's Blobby it's a mixture
+
+ align:start position:0%
+you can see it's Blobby it's a mixture
+ 
+
+ align:start position:0%
+you can see it's Blobby it's a mixture
+of modes that's why you don't see uh
+
+ align:start position:0%
+of modes that's why you don't see uh
+ 
+
+ align:start position:0%
+of modes that's why you don't see uh
+sharp dark line in the middle but you
+
+ align:start position:0%
+sharp dark line in the middle but you
+ 
+
+ align:start position:0%
+sharp dark line in the middle but you
+get a mixture of modes while remember in
+
+ align:start position:0%
+get a mixture of modes while remember in
+ 
+
+ align:start position:0%
+get a mixture of modes while remember in
+the other one no matter what I did in
+
+ align:start position:0%
+the other one no matter what I did in
+ 
+
+ align:start position:0%
+the other one no matter what I did in
+the alignment uh it was still single
+
+ align:start position:0%
+the alignment uh it was still single
+ 
+
+ align:start position:0%
+the alignment uh it was still single
+mode uh coming out just one lob coming
+
+ align:start position:0%
+mode uh coming out just one lob coming
+ 
+
+ align:start position:0%
+mode uh coming out just one lob coming
+out all right now multimode fibers have
+
+ align:start position:0%
+out all right now multimode fibers have
+ 
+
+ align:start position:0%
+out all right now multimode fibers have
+many applications also but for today for
+
+ align:start position:0%
+many applications also but for today for
+ 
+
+ align:start position:0%
+many applications also but for today for
+a lot of sophisticated sensor
+
+ align:start position:0%
+a lot of sophisticated sensor
+ 
+
+ align:start position:0%
+a lot of sophisticated sensor
+applications and Communications
+
+ align:start position:0%
+applications and Communications
+ 
+
+ align:start position:0%
+applications and Communications
+uh one uses one generally uses single
+
+ align:start position:0%
+uh one uses one generally uses single
+ 
+
+ align:start position:0%
+uh one uses one generally uses single
+mode fibers so here here's a here's a
+
+ align:start position:0%
+mode fibers so here here's a here's a
+ 
+
+ align:start position:0%
+mode fibers so here here's a here's a
+pretty pretty mode with had a dark line
+
+ align:start position:0%
+pretty pretty mode with had a dark line
+ 
+
+ align:start position:0%
+pretty pretty mode with had a dark line
+down the uh down the middle now what I
+
+ align:start position:0%
+down the uh down the middle now what I
+ 
+
+ align:start position:0%
+down the uh down the middle now what I
+would like to do is show how how touchy
+
+ align:start position:0%
+would like to do is show how how touchy
+ 
+
+ align:start position:0%
+would like to do is show how how touchy
+uh this fiber is to to uh bending in
+
+ align:start position:0%
+uh this fiber is to to uh bending in
+ 
+
+ align:start position:0%
+uh this fiber is to to uh bending in
+fact if we take a look at the fiber here
+
+ align:start position:0%
+fact if we take a look at the fiber here
+ 
+
+ align:start position:0%
+fact if we take a look at the fiber here
+as soon as I just press on it if we get
+
+ align:start position:0%
+as soon as I just press on it if we get
+ 
+
+ align:start position:0%
+as soon as I just press on it if we get
+take a close look at if I just press on
+
+ align:start position:0%
+take a close look at if I just press on
+ 
+
+ align:start position:0%
+take a close look at if I just press on
+it uh I can kick light kick light out if
+
+ align:start position:0%
+it uh I can kick light kick light out if
+ 
+
+ align:start position:0%
+it uh I can kick light kick light out if
+I just simp press on it I can kick the
+
+ align:start position:0%
+I just simp press on it I can kick the
+ 
+
+ align:start position:0%
+I just simp press on it I can kick the
+some light out so it's very touchy to to
+
+ align:start position:0%
+some light out so it's very touchy to to
+ 
+
+ align:start position:0%
+some light out so it's very touchy to to
+to stress and to bend but I would like
+
+ align:start position:0%
+to stress and to bend but I would like
+ 
+
+ align:start position:0%
+to stress and to bend but I would like
+to do then is show
+
+ align:start position:0%
+to do then is show
+ 
+
+ align:start position:0%
+to do then is show
+that I can kick out some of the
+
+ align:start position:0%
+that I can kick out some of the
+ 
+
+ align:start position:0%
+that I can kick out some of the
+transverse modes by by simply bending or
+
+ align:start position:0%
+transverse modes by by simply bending or
+ 
+
+ align:start position:0%
+transverse modes by by simply bending or
+stressing the fiber what I'm going to do
+
+ align:start position:0%
+stressing the fiber what I'm going to do
+ 
+
+ align:start position:0%
+stressing the fiber what I'm going to do
+is then bend this fiber and if you watch
+
+ align:start position:0%
+is then bend this fiber and if you watch
+ 
+
+ align:start position:0%
+is then bend this fiber and if you watch
+in the in the inset and see that the
+
+ align:start position:0%
+in the in the inset and see that the
+ 
+
+ align:start position:0%
+in the in the inset and see that the
+intensity will go down but but if I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keep increasing the bend I end up with
+
+ align:start position:0%
+keep increasing the bend I end up with
+ 
+
+ align:start position:0%
+keep increasing the bend I end up with
+single mod with a single mod propagation
+
+ align:start position:0%
+single mod with a single mod propagation
+ 
+
+ align:start position:0%
+single mod with a single mod propagation
+but but weat and this illustrates that
+
+ align:start position:0%
+but but weat and this illustrates that
+ 
+
+ align:start position:0%
+but but weat and this illustrates that
+you can strip
+
+ align:start position:0%
+you can strip
+ 
+
+ align:start position:0%
+you can strip
+off the high order modes uh by simply uh
+
+ align:start position:0%
+off the high order modes uh by simply uh
+ 
+
+ align:start position:0%
+off the high order modes uh by simply uh
+bending bending the fiber but the
+
+ align:start position:0%
+bending bending the fiber but the
+ 
+
+ align:start position:0%
+bending bending the fiber but the
+penalty is you get uh much less light uh
+
+ align:start position:0%
+penalty is you get uh much less light uh
+ 
+
+ align:start position:0%
+penalty is you get uh much less light uh
+getting propagate so here we have single
+
+ align:start position:0%
+getting propagate so here we have single
+ 
+
+ align:start position:0%
+getting propagate so here we have single
+mode propagation and here we have multi
+
+ align:start position:0%
+mode propagation and here we have multi
+ 
+
+ align:start position:0%
+mode propagation and here we have multi
+mode or mixture multi mode propagating
+
+ align:start position:0%
+mode or mixture multi mode propagating
+ 
+
+ align:start position:0%
+mode or mixture multi mode propagating
+in the in the fiber again you can see
+
+ align:start position:0%
+in the in the fiber again you can see
+ 
+
+ align:start position:0%
+in the in the fiber again you can see
+that the there's a lot of light that
+
+ align:start position:0%
+that the there's a lot of light that
+ 
+
+ align:start position:0%
+that the there's a lot of light that
+gets kicked out has to be kicked out of
+
+ align:start position:0%
+gets kicked out has to be kicked out of
+ 
+
+ align:start position:0%
+gets kicked out has to be kicked out of
+the fiber you can see the the bend
+
+ align:start position:0%
+the fiber you can see the the bend
+ 
+
+ align:start position:0%
+the fiber you can see the the bend
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+glows in fact this this
+
+ align:start position:0%
+glows in fact this this
+ 
+
+ align:start position:0%
+glows in fact this this
+bending effect on on the transmission of
+
+ align:start position:0%
+bending effect on on the transmission of
+ 
+
+ align:start position:0%
+bending effect on on the transmission of
+light in a fiber can be used as a as a
+
+ align:start position:0%
+light in a fiber can be used as a as a
+ 
+
+ align:start position:0%
+light in a fiber can be used as a as a
+sensor a sensor of uh pressure sensor of
+
+ align:start position:0%
+sensor a sensor of uh pressure sensor of
+ 
+
+ align:start position:0%
+sensor a sensor of uh pressure sensor of
+stress bends and and what have you
+
+ align:start position:0%
+stress bends and and what have you
+ 
+
+ align:start position:0%
+stress bends and and what have you
+all right so then in in
+
+ align:start position:0%
+all right so then in in
+ 
+
+ align:start position:0%
+all right so then in in
+summary
+
+ align:start position:0%
+summary
+ 
+
+ align:start position:0%
+summary
+we've well that's uh that was all about
+
+ align:start position:0%
+we've well that's uh that was all about
+ 
+
+ align:start position:0%
+we've well that's uh that was all about
+transverse modes in fibers it's not uh
+
+ align:start position:0%
+transverse modes in fibers it's not uh
+ 
+
+ align:start position:0%
+transverse modes in fibers it's not uh
+easy to see these modes in normal fibers
+
+ align:start position:0%
+easy to see these modes in normal fibers
+ 
+
+ align:start position:0%
+easy to see these modes in normal fibers
+but uh I think this was a nice
+
+ align:start position:0%
+but uh I think this was a nice
+ 
+
+ align:start position:0%
+but uh I think this was a nice
+opportunity uh for you to see them and
+
+ align:start position:0%
+opportunity uh for you to see them and
+ 
+
+ align:start position:0%
+opportunity uh for you to see them and
+how how they get uh
+
+ align:start position:0%
+how how they get uh
+ 
+
+ align:start position:0%
+how how they get uh
+manipulate so what we know now about
+
+ align:start position:0%
+manipulate so what we know now about
+ 
+
+ align:start position:0%
+manipulate so what we know now about
+fibers then is that there's low loss
+
+ align:start position:0%
+fibers then is that there's low loss
+ 
+
+ align:start position:0%
+fibers then is that there's low loss
+because uh the material is correct we go
+
+ align:start position:0%
+because uh the material is correct we go
+ 
+
+ align:start position:0%
+because uh the material is correct we go
+the let's say the right wavelength and
+
+ align:start position:0%
+the let's say the right wavelength and
+ 
+
+ align:start position:0%
+the let's say the right wavelength and
+we have the let's say lowest loss if you
+
+ align:start position:0%
+we have the let's say lowest loss if you
+ 
+
+ align:start position:0%
+we have the let's say lowest loss if you
+need the lowest loss for a lot of other
+
+ align:start position:0%
+need the lowest loss for a lot of other
+ 
+
+ align:start position:0%
+need the lowest loss for a lot of other
+application like sensors and so on you
+
+ align:start position:0%
+application like sensors and so on you
+ 
+
+ align:start position:0%
+application like sensors and so on you
+know the the fact that the low loss is
+
+ align:start position:0%
+know the the fact that the low loss is
+ 
+
+ align:start position:0%
+know the the fact that the low loss is
+not the most critical
+
+ align:start position:0%
+not the most critical
+ 
+
+ align:start position:0%
+not the most critical
+fact but for certainly for
+
+ align:start position:0%
+fact but for certainly for
+ 
+
+ align:start position:0%
+fact but for certainly for
+communications and longdistance
+
+ align:start position:0%
+communications and longdistance
+ 
+
+ align:start position:0%
+communications and longdistance
+propagation that is that is very
+
+ align:start position:0%
+propagation that is that is very
+ 
+
+ align:start position:0%
+propagation that is that is very
+critical and then we also learned that
+
+ align:start position:0%
+critical and then we also learned that
+ 
+
+ align:start position:0%
+critical and then we also learned that
+we have to be careful with this V number
+
+ align:start position:0%
+we have to be careful with this V number
+ 
+
+ align:start position:0%
+we have to be careful with this V number
+so that we make sure that we have let's
+
+ align:start position:0%
+so that we make sure that we have let's
+ 
+
+ align:start position:0%
+so that we make sure that we have let's
+say when we need it we have single mode
+
+ align:start position:0%
+say when we need it we have single mode
+ 
+
+ align:start position:0%
+say when we need it we have single mode
+uh propagation see the problem problem
+
+ align:start position:0%
+uh propagation see the problem problem
+ 
+
+ align:start position:0%
+uh propagation see the problem problem
+with these multim modes they travel at
+
+ align:start position:0%
+with these multim modes they travel at
+ 
+
+ align:start position:0%
+with these multim modes they travel at
+different speeds and then as as we
+
+ align:start position:0%
+different speeds and then as as we
+ 
+
+ align:start position:0%
+different speeds and then as as we
+showed and then uh and then it prevents
+
+ align:start position:0%
+showed and then uh and then it prevents
+ 
+
+ align:start position:0%
+showed and then uh and then it prevents
+you from from using these fibers for
+
+ align:start position:0%
+you from from using these fibers for
+ 
+
+ align:start position:0%
+you from from using these fibers for
+whiteband communication so for wi band
+
+ align:start position:0%
+whiteband communication so for wi band
+ 
+
+ align:start position:0%
+whiteband communication so for wi band
+communication you really need uh the
+
+ align:start position:0%
+communication you really need uh the
+ 
+
+ align:start position:0%
+communication you really need uh the
+single mode and also what's nice about
+
+ align:start position:0%
+single mode and also what's nice about
+ 
+
+ align:start position:0%
+single mode and also what's nice about
+uh propagating it around 1.5 microns or
+
+ align:start position:0%
+uh propagating it around 1.5 microns or
+ 
+
+ align:start position:0%
+uh propagating it around 1.5 microns or
+so is that the even the refractive index
+
+ align:start position:0%
+so is that the even the refractive index
+ 
+
+ align:start position:0%
+so is that the even the refractive index
+uh uh the the variations uh in there is
+
+ align:start position:0%
+uh uh the the variations uh in there is
+ 
+
+ align:start position:0%
+uh uh the the variations uh in there is
+uh is is also small so it's it's a it's
+
+ align:start position:0%
+uh is is also small so it's it's a it's
+ 
+
+ align:start position:0%
+uh is is also small so it's it's a it's
+a nice region to propagate for for
+
+ align:start position:0%
+a nice region to propagate for for
+ 
+
+ align:start position:0%
+a nice region to propagate for for
+communication
+
+ align:start position:0%
+communication
+ 
+
+ align:start position:0%
+communication
+applications but just fibers alone is
+
+ align:start position:0%
+applications but just fibers alone is
+ 
+
+ align:start position:0%
+applications but just fibers alone is
+not everything you still have to make
+
+ align:start position:0%
+not everything you still have to make
+ 
+
+ align:start position:0%
+not everything you still have to make
+connections you know like couplers you
+
+ align:start position:0%
+connections you know like couplers you
+ 
+
+ align:start position:0%
+connections you know like couplers you
+have to have other components and so on
+
+ align:start position:0%
+have to have other components and so on
+ 
+
+ align:start position:0%
+have to have other components and so on
+so let's now spend spend a few minutes
+
+ align:start position:0%
+so let's now spend spend a few minutes
+ 
+
+ align:start position:0%
+so let's now spend spend a few minutes
+on on uh fiber optic components like
+
+ align:start position:0%
+on on uh fiber optic components like
+ 
+
+ align:start position:0%
+on on uh fiber optic components like
+couplers because if you want to split
+
+ align:start position:0%
+couplers because if you want to split
+ 
+
+ align:start position:0%
+couplers because if you want to split
+the light by 50 50 or 80 20 or so on you
+
+ align:start position:0%
+the light by 50 50 or 80 20 or so on you
+ 
+
+ align:start position:0%
+the light by 50 50 or 80 20 or so on you
+need these directional couplets all done
+
+ align:start position:0%
+need these directional couplets all done
+ 
+
+ align:start position:0%
+need these directional couplets all done
+with fibers you need the polarizers
+
+ align:start position:0%
+with fibers you need the polarizers
+ 
+
+ align:start position:0%
+with fibers you need the polarizers
+because you don't want to come out of
+
+ align:start position:0%
+because you don't want to come out of
+ 
+
+ align:start position:0%
+because you don't want to come out of
+the fiber go through a bulk optic
+
+ align:start position:0%
+the fiber go through a bulk optic
+ 
+
+ align:start position:0%
+the fiber go through a bulk optic
+polarizer and go back into the fiber
+
+ align:start position:0%
+polarizer and go back into the fiber
+ 
+
+ align:start position:0%
+polarizer and go back into the fiber
+again you'd like to create polarizers
+
+ align:start position:0%
+again you'd like to create polarizers
+ 
+
+ align:start position:0%
+again you'd like to create polarizers
+right on the fibers you like to also
+
+ align:start position:0%
+right on the fibers you like to also
+ 
+
+ align:start position:0%
+right on the fibers you like to also
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+polarization uh You' like to maybe
+
+ align:start position:0%
+polarization uh You' like to maybe
+ 
+
+ align:start position:0%
+polarization uh You' like to maybe
+create phase modulators frequency
+
+ align:start position:0%
+create phase modulators frequency
+ 
+
+ align:start position:0%
+create phase modulators frequency
+shifter and so on all in fibers now I'm
+
+ align:start position:0%
+shifter and so on all in fibers now I'm
+ 
+
+ align:start position:0%
+shifter and so on all in fibers now I'm
+not going to have time to talk about all
+
+ align:start position:0%
+not going to have time to talk about all
+ 
+
+ align:start position:0%
+not going to have time to talk about all
+these things but I'm just going to talk
+
+ align:start position:0%
+these things but I'm just going to talk
+ 
+
+ align:start position:0%
+these things but I'm just going to talk
+a little bit about couplers maybe a
+
+ align:start position:0%
+a little bit about couplers maybe a
+ 
+
+ align:start position:0%
+a little bit about couplers maybe a
+little bit about phase uh phas
+
+ align:start position:0%
+little bit about phase uh phas
+ 
+
+ align:start position:0%
+little bit about phase uh phas
+modulators so how do you make now how do
+
+ align:start position:0%
+modulators so how do you make now how do
+ 
+
+ align:start position:0%
+modulators so how do you make now how do
+we make a a uh a coupler how do we
+
+ align:start position:0%
+we make a a uh a coupler how do we
+ 
+
+ align:start position:0%
+we make a a uh a coupler how do we
+transfer light let's say we have a fiber
+
+ align:start position:0%
+transfer light let's say we have a fiber
+ 
+
+ align:start position:0%
+transfer light let's say we have a fiber
+in here and we have a core in it and
+
+ align:start position:0%
+in here and we have a core in it and
+ 
+
+ align:start position:0%
+in here and we have a core in it and
+we're propagating down the core and
+
+ align:start position:0%
+we're propagating down the core and
+ 
+
+ align:start position:0%
+we're propagating down the core and
+normally the light would come out here
+
+ align:start position:0%
+normally the light would come out here
+ 
+
+ align:start position:0%
+normally the light would come out here
+but now I'd like to transfer the light
+
+ align:start position:0%
+but now I'd like to transfer the light
+ 
+
+ align:start position:0%
+but now I'd like to transfer the light
+to to another fiber so what one one does
+
+ align:start position:0%
+to to another fiber so what one one does
+ 
+
+ align:start position:0%
+to to another fiber so what one one does
+here you bring another fiber uh close to
+
+ align:start position:0%
+here you bring another fiber uh close to
+ 
+
+ align:start position:0%
+here you bring another fiber uh close to
+to this one now if with with fibers uh
+
+ align:start position:0%
+to this one now if with with fibers uh
+ 
+
+ align:start position:0%
+to this one now if with with fibers uh
+as we said before they have a core and
+
+ align:start position:0%
+as we said before they have a core and
+ 
+
+ align:start position:0%
+as we said before they have a core and
+they have a cladding and the cladding is
+
+ align:start position:0%
+they have a cladding and the cladding is
+ 
+
+ align:start position:0%
+they have a cladding and the cladding is
+usually much bigger than the core the
+
+ align:start position:0%
+usually much bigger than the core the
+ 
+
+ align:start position:0%
+usually much bigger than the core the
+core is usually few microns the cladding
+
+ align:start position:0%
+core is usually few microns the cladding
+ 
+
+ align:start position:0%
+core is usually few microns the cladding
+is uh as I mentioned in the Dem in the
+
+ align:start position:0%
+is uh as I mentioned in the Dem in the
+ 
+
+ align:start position:0%
+is uh as I mentioned in the Dem in the
+demo it's about 125 microns so if you
+
+ align:start position:0%
+demo it's about 125 microns so if you
+ 
+
+ align:start position:0%
+demo it's about 125 microns so if you
+bring that close to this one then the
+
+ align:start position:0%
+bring that close to this one then the
+ 
+
+ align:start position:0%
+bring that close to this one then the
+the uh the two uh cladding spacing will
+
+ align:start position:0%
+the uh the two uh cladding spacing will
+ 
+
+ align:start position:0%
+the uh the two uh cladding spacing will
+not let you uh transfer any light from
+
+ align:start position:0%
+not let you uh transfer any light from
+ 
+
+ align:start position:0%
+not let you uh transfer any light from
+one fiber to the other so in order to
+
+ align:start position:0%
+one fiber to the other so in order to
+ 
+
+ align:start position:0%
+one fiber to the other so in order to
+transfer light what you have to do take
+
+ align:start position:0%
+transfer light what you have to do take
+ 
+
+ align:start position:0%
+transfer light what you have to do take
+advantage of this evanescent wave the
+
+ align:start position:0%
+advantage of this evanescent wave the
+ 
+
+ align:start position:0%
+advantage of this evanescent wave the
+part of the evanescent wave that's
+
+ align:start position:0%
+part of the evanescent wave that's
+ 
+
+ align:start position:0%
+part of the evanescent wave that's
+traveling in the clading so what you
+
+ align:start position:0%
+traveling in the clading so what you
+ 
+
+ align:start position:0%
+traveling in the clading so what you
+have to do then you have to shave off
+
+ align:start position:0%
+have to do then you have to shave off
+ 
+
+ align:start position:0%
+have to do then you have to shave off
+the cladding so that the EV that
+
+ align:start position:0%
+the cladding so that the EV that
+ 
+
+ align:start position:0%
+the cladding so that the EV that
+evanescent wave in in this fiber here
+
+ align:start position:0%
+evanescent wave in in this fiber here
+ 
+
+ align:start position:0%
+evanescent wave in in this fiber here
+Fiber One okay if if the if you shave
+
+ align:start position:0%
+Fiber One okay if if the if you shave
+ 
+
+ align:start position:0%
+Fiber One okay if if the if you shave
+enough of the cladding this evanescent
+
+ align:start position:0%
+enough of the cladding this evanescent
+ 
+
+ align:start position:0%
+enough of the cladding this evanescent
+wave can start propagating in the uh in
+
+ align:start position:0%
+wave can start propagating in the uh in
+ 
+
+ align:start position:0%
+wave can start propagating in the uh in
+the uh second fiber in fiber 2 so when
+
+ align:start position:0%
+the uh second fiber in fiber 2 so when
+ 
+
+ align:start position:0%
+the uh second fiber in fiber 2 so when
+it does that then you can transfer
+
+ align:start position:0%
+it does that then you can transfer
+ 
+
+ align:start position:0%
+it does that then you can transfer
+energy to to fiber 2 and depending on
+
+ align:start position:0%
+energy to to fiber 2 and depending on
+ 
+
+ align:start position:0%
+energy to to fiber 2 and depending on
+this interaction length length of the
+
+ align:start position:0%
+this interaction length length of the
+ 
+
+ align:start position:0%
+this interaction length length of the
+interaction the closeness of the two
+
+ align:start position:0%
+interaction the closeness of the two
+ 
+
+ align:start position:0%
+interaction the closeness of the two
+cores uh then you can transfer and uh
+
+ align:start position:0%
+cores uh then you can transfer and uh
+ 
+
+ align:start position:0%
+cores uh then you can transfer and uh
+100% and back to zero so in this plot
+
+ align:start position:0%
+100% and back to zero so in this plot
+ 
+
+ align:start position:0%
+100% and back to zero so in this plot
+here we show show that as a function of
+
+ align:start position:0%
+here we show show that as a function of
+ 
+
+ align:start position:0%
+here we show show that as a function of
+either the separation between the cores
+
+ align:start position:0%
+either the separation between the cores
+ 
+
+ align:start position:0%
+either the separation between the cores
+d sub cores the core separation or as a
+
+ align:start position:0%
+d sub cores the core separation or as a
+ 
+
+ align:start position:0%
+d sub cores the core separation or as a
+function of the interaction length for a
+
+ align:start position:0%
+function of the interaction length for a
+ 
+
+ align:start position:0%
+function of the interaction length for a
+given core separation you can transfer
+
+ align:start position:0%
+given core separation you can transfer
+ 
+
+ align:start position:0%
+given core separation you can transfer
+as much as 100% of the light you can
+
+ align:start position:0%
+as much as 100% of the light you can
+ 
+
+ align:start position:0%
+as much as 100% of the light you can
+make 100% the light come out at Port two
+
+ align:start position:0%
+make 100% the light come out at Port two
+ 
+
+ align:start position:0%
+make 100% the light come out at Port two
+instead of Port one and if you keep
+
+ align:start position:0%
+instead of Port one and if you keep
+ 
+
+ align:start position:0%
+instead of Port one and if you keep
+changing this uh coupling then you can
+
+ align:start position:0%
+changing this uh coupling then you can
+ 
+
+ align:start position:0%
+changing this uh coupling then you can
+bring it back to zero again and up again
+
+ align:start position:0%
+bring it back to zero again and up again
+ 
+
+ align:start position:0%
+bring it back to zero again and up again
+and so on so that uh so that by uh by
+
+ align:start position:0%
+and so on so that uh so that by uh by
+ 
+
+ align:start position:0%
+and so on so that uh so that by uh by
+selecting the the right uh separation
+
+ align:start position:0%
+selecting the the right uh separation
+ 
+
+ align:start position:0%
+selecting the the right uh separation
+between the cores and the right
+
+ align:start position:0%
+between the cores and the right
+ 
+
+ align:start position:0%
+between the cores and the right
+interaction length then you can have uh
+
+ align:start position:0%
+interaction length then you can have uh
+ 
+
+ align:start position:0%
+interaction length then you can have uh
+you can transfer any amount of light
+
+ align:start position:0%
+you can transfer any amount of light
+ 
+
+ align:start position:0%
+you can transfer any amount of light
+that you want and uh and this is great
+
+ align:start position:0%
+that you want and uh and this is great
+ 
+
+ align:start position:0%
+that you want and uh and this is great
+because it's it's pretty low loss and is
+
+ align:start position:0%
+because it's it's pretty low loss and is
+ 
+
+ align:start position:0%
+because it's it's pretty low loss and is
+used of course all the time today uh
+
+ align:start position:0%
+used of course all the time today uh
+ 
+
+ align:start position:0%
+used of course all the time today uh
+these couplet can be what we call the
+
+ align:start position:0%
+these couplet can be what we call the
+ 
+
+ align:start position:0%
+these couplet can be what we call the
+Polish type or the fuse type and so on
+
+ align:start position:0%
+Polish type or the fuse type and so on
+ 
+
+ align:start position:0%
+Polish type or the fuse type and so on
+they're different types of couplers but
+
+ align:start position:0%
+they're different types of couplers but
+ 
+
+ align:start position:0%
+they're different types of couplers but
+basically they work on that principle of
+
+ align:start position:0%
+basically they work on that principle of
+ 
+
+ align:start position:0%
+basically they work on that principle of
+bringing the two cores uh close enough
+
+ align:start position:0%
+bringing the two cores uh close enough
+ 
+
+ align:start position:0%
+bringing the two cores uh close enough
+together so that the evanescent wave
+
+ align:start position:0%
+together so that the evanescent wave
+ 
+
+ align:start position:0%
+together so that the evanescent wave
+that little tail of of that field
+
+ align:start position:0%
+that little tail of of that field
+ 
+
+ align:start position:0%
+that little tail of of that field
+distribution then will propagate in the
+
+ align:start position:0%
+distribution then will propagate in the
+ 
+
+ align:start position:0%
+distribution then will propagate in the
+in the other core and will drive the
+
+ align:start position:0%
+in the other core and will drive the
+ 
+
+ align:start position:0%
+in the other core and will drive the
+dipoles over there all right so that's
+
+ align:start position:0%
+dipoles over there all right so that's
+ 
+
+ align:start position:0%
+dipoles over there all right so that's
+basically the principle of a U of A of a
+
+ align:start position:0%
+basically the principle of a U of A of a
+ 
+
+ align:start position:0%
+basically the principle of a U of A of a
+coupla all right and uh now I wanted toh
+
+ align:start position:0%
+coupla all right and uh now I wanted toh
+ 
+
+ align:start position:0%
+coupla all right and uh now I wanted toh
+just say again a few words about phase
+
+ align:start position:0%
+just say again a few words about phase
+ 
+
+ align:start position:0%
+just say again a few words about phase
+modulators now uh phase modulators well
+
+ align:start position:0%
+modulators now uh phase modulators well
+ 
+
+ align:start position:0%
+modulators now uh phase modulators well
+how do you do that how do you modulate
+
+ align:start position:0%
+how do you do that how do you modulate
+ 
+
+ align:start position:0%
+how do you do that how do you modulate
+the phase of the light propagating in
+
+ align:start position:0%
+the phase of the light propagating in
+ 
+
+ align:start position:0%
+the phase of the light propagating in
+the fiber well again in many ways
+
+ align:start position:0%
+the fiber well again in many ways
+ 
+
+ align:start position:0%
+the fiber well again in many ways
+because if we stretch the fiber if we do
+
+ align:start position:0%
+because if we stretch the fiber if we do
+ 
+
+ align:start position:0%
+because if we stretch the fiber if we do
+something to the fiber uh we can uh
+
+ align:start position:0%
+something to the fiber uh we can uh
+ 
+
+ align:start position:0%
+something to the fiber uh we can uh
+change the essentially the index let's
+
+ align:start position:0%
+change the essentially the index let's
+ 
+
+ align:start position:0%
+change the essentially the index let's
+say in the in the fiber or change the
+
+ align:start position:0%
+say in the in the fiber or change the
+ 
+
+ align:start position:0%
+say in the in the fiber or change the
+physical length of the fiber and then we
+
+ align:start position:0%
+physical length of the fiber and then we
+ 
+
+ align:start position:0%
+physical length of the fiber and then we
+get a change in Phase Delta fi that's
+
+ align:start position:0%
+get a change in Phase Delta fi that's
+ 
+
+ align:start position:0%
+get a change in Phase Delta fi that's
+proportional to either change in the the
+
+ align:start position:0%
+proportional to either change in the the
+ 
+
+ align:start position:0%
+proportional to either change in the the
+length of the fiber or change in the
+
+ align:start position:0%
+length of the fiber or change in the
+ 
+
+ align:start position:0%
+length of the fiber or change in the
+index of the Fiber One way of doing this
+
+ align:start position:0%
+index of the Fiber One way of doing this
+ 
+
+ align:start position:0%
+index of the Fiber One way of doing this
+is to take the fiber and wrap it around
+
+ align:start position:0%
+is to take the fiber and wrap it around
+ 
+
+ align:start position:0%
+is to take the fiber and wrap it around
+a p Electric Crystal if we put a voltage
+
+ align:start position:0%
+a p Electric Crystal if we put a voltage
+ 
+
+ align:start position:0%
+a p Electric Crystal if we put a voltage
+between the inside the outer uh surfaces
+
+ align:start position:0%
+between the inside the outer uh surfaces
+ 
+
+ align:start position:0%
+between the inside the outer uh surfaces
+of this Crystal then we can uh change
+
+ align:start position:0%
+of this Crystal then we can uh change
+ 
+
+ align:start position:0%
+of this Crystal then we can uh change
+the diameter of this uh of this uh
+
+ align:start position:0%
+the diameter of this uh of this uh
+ 
+
+ align:start position:0%
+the diameter of this uh of this uh
+cylinder and then in this way we can
+
+ align:start position:0%
+cylinder and then in this way we can
+ 
+
+ align:start position:0%
+cylinder and then in this way we can
+change the uh the physical length of the
+
+ align:start position:0%
+change the uh the physical length of the
+ 
+
+ align:start position:0%
+change the uh the physical length of the
+fiber or by stressing it you know
+
+ align:start position:0%
+fiber or by stressing it you know
+ 
+
+ align:start position:0%
+fiber or by stressing it you know
+essentially CH could change also the
+
+ align:start position:0%
+essentially CH could change also the
+ 
+
+ align:start position:0%
+essentially CH could change also the
+index but whatever uh uh yet you get a
+
+ align:start position:0%
+index but whatever uh uh yet you get a
+ 
+
+ align:start position:0%
+index but whatever uh uh yet you get a
+change in the phase of the light
+
+ align:start position:0%
+change in the phase of the light
+ 
+
+ align:start position:0%
+change in the phase of the light
+propagating by by uh applying a voltage
+
+ align:start position:0%
+propagating by by uh applying a voltage
+ 
+
+ align:start position:0%
+propagating by by uh applying a voltage
+either DC voltage or sinusal voltage to
+
+ align:start position:0%
+either DC voltage or sinusal voltage to
+ 
+
+ align:start position:0%
+either DC voltage or sinusal voltage to
+this uh cylinder p Electric cylinder the
+
+ align:start position:0%
+this uh cylinder p Electric cylinder the
+ 
+
+ align:start position:0%
+this uh cylinder p Electric cylinder the
+another type of uh of p Electric device
+
+ align:start position:0%
+another type of uh of p Electric device
+ 
+
+ align:start position:0%
+another type of uh of p Electric device
+is is a sheet is a is a p Electric strip
+
+ align:start position:0%
+is is a sheet is a is a p Electric strip
+ 
+
+ align:start position:0%
+is is a sheet is a is a p Electric strip
+or sheet where the fiber is just uh
+
+ align:start position:0%
+or sheet where the fiber is just uh
+ 
+
+ align:start position:0%
+or sheet where the fiber is just uh
+attached to Bonded to this it doesn't
+
+ align:start position:0%
+attached to Bonded to this it doesn't
+ 
+
+ align:start position:0%
+attached to Bonded to this it doesn't
+have to Bonded that rigidly to this to
+
+ align:start position:0%
+have to Bonded that rigidly to this to
+ 
+
+ align:start position:0%
+have to Bonded that rigidly to this to
+this sheet and then by applying a
+
+ align:start position:0%
+this sheet and then by applying a
+ 
+
+ align:start position:0%
+this sheet and then by applying a
+voltage between the upper and the lower
+
+ align:start position:0%
+voltage between the upper and the lower
+ 
+
+ align:start position:0%
+voltage between the upper and the lower
+uh surface you can again stretch the uh
+
+ align:start position:0%
+uh surface you can again stretch the uh
+ 
+
+ align:start position:0%
+uh surface you can again stretch the uh
+stretch the fiber and then you can
+
+ align:start position:0%
+stretch the fiber and then you can
+ 
+
+ align:start position:0%
+stretch the fiber and then you can
+essentially modulate the the light
+
+ align:start position:0%
+essentially modulate the the light
+ 
+
+ align:start position:0%
+essentially modulate the the light
+that's propagating so uh so that's a
+
+ align:start position:0%
+that's propagating so uh so that's a
+ 
+
+ align:start position:0%
+that's propagating so uh so that's a
+very neat way you don't have to break
+
+ align:start position:0%
+very neat way you don't have to break
+ 
+
+ align:start position:0%
+very neat way you don't have to break
+the fiber it's is still still intact and
+
+ align:start position:0%
+the fiber it's is still still intact and
+ 
+
+ align:start position:0%
+the fiber it's is still still intact and
+you can get uh phase uh phase
+
+ align:start position:0%
+you can get uh phase uh phase
+ 
+
+ align:start position:0%
+you can get uh phase uh phase
+modulation now uh and then say I said
+
+ align:start position:0%
+modulation now uh and then say I said
+ 
+
+ align:start position:0%
+modulation now uh and then say I said
+before there are all kinds of uh neat uh
+
+ align:start position:0%
+before there are all kinds of uh neat uh
+ 
+
+ align:start position:0%
+before there are all kinds of uh neat uh
+devices that that uh use fibers you can
+
+ align:start position:0%
+devices that that uh use fibers you can
+ 
+
+ align:start position:0%
+devices that that uh use fibers you can
+make polarizers frequency shifters and
+
+ align:start position:0%
+make polarizers frequency shifters and
+ 
+
+ align:start position:0%
+make polarizers frequency shifters and
+uh and so on but now there is another
+
+ align:start position:0%
+uh and so on but now there is another
+ 
+
+ align:start position:0%
+uh and so on but now there is another
+field that uh is gaining momentum a lot
+
+ align:start position:0%
+field that uh is gaining momentum a lot
+ 
+
+ align:start position:0%
+field that uh is gaining momentum a lot
+and that's called integrated Optics
+
+ align:start position:0%
+and that's called integrated Optics
+ 
+
+ align:start position:0%
+and that's called integrated Optics
+because sometimes to to make these all
+
+ align:start position:0%
+because sometimes to to make these all
+ 
+
+ align:start position:0%
+because sometimes to to make these all
+fiber couplers all fiber devices becomes
+
+ align:start position:0%
+fiber couplers all fiber devices becomes
+ 
+
+ align:start position:0%
+fiber couplers all fiber devices becomes
+a little tricky and very delicate so it
+
+ align:start position:0%
+a little tricky and very delicate so it
+ 
+
+ align:start position:0%
+a little tricky and very delicate so it
+would be nice to to replace them with
+
+ align:start position:0%
+would be nice to to replace them with
+ 
+
+ align:start position:0%
+would be nice to to replace them with
+something that's more more robust so I'd
+
+ align:start position:0%
+something that's more more robust so I'd
+ 
+
+ align:start position:0%
+something that's more more robust so I'd
+like to talk a little bit about uh
+
+ align:start position:0%
+like to talk a little bit about uh
+ 
+
+ align:start position:0%
+like to talk a little bit about uh
+integrated optic
+
+ align:start position:0%
+integrated optic
+ 
+
+ align:start position:0%
+integrated optic
+components and uh and what what are uh
+
+ align:start position:0%
+components and uh and what what are uh
+ 
+
+ align:start position:0%
+components and uh and what what are uh
+integrated uh Optics first of all uh let
+
+ align:start position:0%
+integrated uh Optics first of all uh let
+ 
+
+ align:start position:0%
+integrated uh Optics first of all uh let
+me let me then uh explain to you a
+
+ align:start position:0%
+me let me then uh explain to you a
+ 
+
+ align:start position:0%
+me let me then uh explain to you a
+little bit about what's an integrated
+
+ align:start position:0%
+little bit about what's an integrated
+ 
+
+ align:start position:0%
+little bit about what's an integrated
+optic wave guide is so in this case the
+
+ align:start position:0%
+optic wave guide is so in this case the
+ 
+
+ align:start position:0%
+optic wave guide is so in this case the
+instead of it's not it's not a fiber but
+
+ align:start position:0%
+instead of it's not it's not a fiber but
+ 
+
+ align:start position:0%
+instead of it's not it's not a fiber but
+basically uh let's say you start with
+
+ align:start position:0%
+basically uh let's say you start with
+ 
+
+ align:start position:0%
+basically uh let's say you start with
+with with with some material like glass
+
+ align:start position:0%
+with with with some material like glass
+ 
+
+ align:start position:0%
+with with with some material like glass
+and then you IND defuse uh some impurity
+
+ align:start position:0%
+and then you IND defuse uh some impurity
+ 
+
+ align:start position:0%
+and then you IND defuse uh some impurity
+that raises the index and if this is
+
+ align:start position:0%
+that raises the index and if this is
+ 
+
+ align:start position:0%
+that raises the index and if this is
+controlled uh then using photo
+
+ align:start position:0%
+controlled uh then using photo
+ 
+
+ align:start position:0%
+controlled uh then using photo
+lithographic techniques and so on uh
+
+ align:start position:0%
+lithographic techniques and so on uh
+ 
+
+ align:start position:0%
+lithographic techniques and so on uh
+that you can raise the index over here
+
+ align:start position:0%
+that you can raise the index over here
+ 
+
+ align:start position:0%
+that you can raise the index over here
+so if you look from the side you have a
+
+ align:start position:0%
+so if you look from the side you have a
+ 
+
+ align:start position:0%
+so if you look from the side you have a
+material that has a little higher index
+
+ align:start position:0%
+material that has a little higher index
+ 
+
+ align:start position:0%
+material that has a little higher index
+than than uh the cladding over here and
+
+ align:start position:0%
+than than uh the cladding over here and
+ 
+
+ align:start position:0%
+than than uh the cladding over here and
+then you can propagate light down this
+
+ align:start position:0%
+then you can propagate light down this
+ 
+
+ align:start position:0%
+then you can propagate light down this
+uh this uh wave guide becomes a wave
+
+ align:start position:0%
+uh this uh wave guide becomes a wave
+ 
+
+ align:start position:0%
+uh this uh wave guide becomes a wave
+guide and you can uh and then the light
+
+ align:start position:0%
+guide and you can uh and then the light
+ 
+
+ align:start position:0%
+guide and you can uh and then the light
+is guided through the wave guide just
+
+ align:start position:0%
+is guided through the wave guide just
+ 
+
+ align:start position:0%
+is guided through the wave guide just
+like in a fiber because the index here
+
+ align:start position:0%
+like in a fiber because the index here
+ 
+
+ align:start position:0%
+like in a fiber because the index here
+is higher than one's on the side and
+
+ align:start position:0%
+is higher than one's on the side and
+ 
+
+ align:start position:0%
+is higher than one's on the side and
+then you can coat this and protect it
+
+ align:start position:0%
+then you can coat this and protect it
+ 
+
+ align:start position:0%
+then you can coat this and protect it
+and so on but the principle is that you
+
+ align:start position:0%
+and so on but the principle is that you
+ 
+
+ align:start position:0%
+and so on but the principle is that you
+can get single mode or multi mode uh uh
+
+ align:start position:0%
+can get single mode or multi mode uh uh
+ 
+
+ align:start position:0%
+can get single mode or multi mode uh uh
+wave guides in a in a substrate and it's
+
+ align:start position:0%
+wave guides in a in a substrate and it's
+ 
+
+ align:start position:0%
+wave guides in a in a substrate and it's
+rigid doesn't go anywhere and you can do
+
+ align:start position:0%
+rigid doesn't go anywhere and you can do
+ 
+
+ align:start position:0%
+rigid doesn't go anywhere and you can do
+all kinds of things with it so now with
+
+ align:start position:0%
+all kinds of things with it so now with
+ 
+
+ align:start position:0%
+all kinds of things with it so now with
+this with this idea here uh you can uh
+
+ align:start position:0%
+this with this idea here uh you can uh
+ 
+
+ align:start position:0%
+this with this idea here uh you can uh
+you can create a uh a directional
+
+ align:start position:0%
+you can create a uh a directional
+ 
+
+ align:start position:0%
+you can create a uh a directional
+coupler uh either fixed or variable
+
+ align:start position:0%
+coupler uh either fixed or variable
+ 
+
+ align:start position:0%
+coupler uh either fixed or variable
+again you can create polar ier by
+
+ align:start position:0%
+again you can create polar ier by
+ 
+
+ align:start position:0%
+again you can create polar ier by
+preventing certain polarizations the or
+
+ align:start position:0%
+preventing certain polarizations the or
+ 
+
+ align:start position:0%
+preventing certain polarizations the or
+one polarization from from going by
+
+ align:start position:0%
+one polarization from from going by
+ 
+
+ align:start position:0%
+one polarization from from going by
+attenuating it uh you can create the
+
+ align:start position:0%
+attenuating it uh you can create the
+ 
+
+ align:start position:0%
+attenuating it uh you can create the
+phase modulators frequency shifters
+
+ align:start position:0%
+phase modulators frequency shifters
+ 
+
+ align:start position:0%
+phase modulators frequency shifters
+intensity modul and so on all using
+
+ align:start position:0%
+intensity modul and so on all using
+ 
+
+ align:start position:0%
+intensity modul and so on all using
+integrated Optics so let's look at uh at
+
+ align:start position:0%
+integrated Optics so let's look at uh at
+ 
+
+ align:start position:0%
+integrated Optics so let's look at uh at
+a an
+
+ align:start position:0%
+a an
+ 
+
+ align:start position:0%
+a an
+example here again is is the substrate
+
+ align:start position:0%
+example here again is is the substrate
+ 
+
+ align:start position:0%
+example here again is is the substrate
+and here's the wave guide now if this
+
+ align:start position:0%
+and here's the wave guide now if this
+ 
+
+ align:start position:0%
+and here's the wave guide now if this
+material here is is uh before even I get
+
+ align:start position:0%
+material here is is uh before even I get
+ 
+
+ align:start position:0%
+material here is is uh before even I get
+to what I want to talk about is that you
+
+ align:start position:0%
+to what I want to talk about is that you
+ 
+
+ align:start position:0%
+to what I want to talk about is that you
+have to first couple couple to this wave
+
+ align:start position:0%
+have to first couple couple to this wave
+ 
+
+ align:start position:0%
+have to first couple couple to this wave
+guide remember the core can be very
+
+ align:start position:0%
+guide remember the core can be very
+ 
+
+ align:start position:0%
+guide remember the core can be very
+small just a few microns so you have to
+
+ align:start position:0%
+small just a few microns so you have to
+ 
+
+ align:start position:0%
+small just a few microns so you have to
+take the output from the fiber and
+
+ align:start position:0%
+take the output from the fiber and
+ 
+
+ align:start position:0%
+take the output from the fiber and
+couple it into into this core so that's
+
+ align:start position:0%
+couple it into into this core so that's
+ 
+
+ align:start position:0%
+couple it into into this core so that's
+a tricky uh device but again people have
+
+ align:start position:0%
+a tricky uh device but again people have
+ 
+
+ align:start position:0%
+a tricky uh device but again people have
+found nice techniques to to do that so
+
+ align:start position:0%
+found nice techniques to to do that so
+ 
+
+ align:start position:0%
+found nice techniques to to do that so
+basically you want a fiber to couple
+
+ align:start position:0%
+basically you want a fiber to couple
+ 
+
+ align:start position:0%
+basically you want a fiber to couple
+into this and and this to couple into
+
+ align:start position:0%
+into this and and this to couple into
+ 
+
+ align:start position:0%
+into this and and this to couple into
+the fiber going out if you can do that
+
+ align:start position:0%
+the fiber going out if you can do that
+ 
+
+ align:start position:0%
+the fiber going out if you can do that
+and and and these couplers stay uh stay
+
+ align:start position:0%
+and and and these couplers stay uh stay
+ 
+
+ align:start position:0%
+and and and these couplers stay uh stay
+together then you you've got something
+
+ align:start position:0%
+together then you you've got something
+ 
+
+ align:start position:0%
+together then you you've got something
+all right so now how do you create a
+
+ align:start position:0%
+all right so now how do you create a
+ 
+
+ align:start position:0%
+all right so now how do you create a
+phase modulator here now if this
+
+ align:start position:0%
+phase modulator here now if this
+ 
+
+ align:start position:0%
+phase modulator here now if this
+material is for example is slightly
+
+ align:start position:0%
+material is for example is slightly
+ 
+
+ align:start position:0%
+material is for example is slightly
+Electro optic or electrooptic then by
+
+ align:start position:0%
+Electro optic or electrooptic then by
+ 
+
+ align:start position:0%
+Electro optic or electrooptic then by
+putting electrodes here and applying a a
+
+ align:start position:0%
+putting electrodes here and applying a a
+ 
+
+ align:start position:0%
+putting electrodes here and applying a a
+voltage difference between them then you
+
+ align:start position:0%
+voltage difference between them then you
+ 
+
+ align:start position:0%
+voltage difference between them then you
+can change the index either in the
+
+ align:start position:0%
+can change the index either in the
+ 
+
+ align:start position:0%
+can change the index either in the
+cladding or in the core and then and
+
+ align:start position:0%
+cladding or in the core and then and
+ 
+
+ align:start position:0%
+cladding or in the core and then and
+then uh just by simply applying a
+
+ align:start position:0%
+then uh just by simply applying a
+ 
+
+ align:start position:0%
+then uh just by simply applying a
+voltage and this way you can then phase
+
+ align:start position:0%
+voltage and this way you can then phase
+ 
+
+ align:start position:0%
+voltage and this way you can then phase
+modulate the light propagating in this
+
+ align:start position:0%
+modulate the light propagating in this
+ 
+
+ align:start position:0%
+modulate the light propagating in this
+section you can do it pretty fast and
+
+ align:start position:0%
+section you can do it pretty fast and
+ 
+
+ align:start position:0%
+section you can do it pretty fast and
+then you can get very fast uh phase
+
+ align:start position:0%
+then you can get very fast uh phase
+ 
+
+ align:start position:0%
+then you can get very fast uh phase
+modulators and if you ramp the phase and
+
+ align:start position:0%
+modulators and if you ramp the phase and
+ 
+
+ align:start position:0%
+modulators and if you ramp the phase and
+so on using Codine techniques that we
+
+ align:start position:0%
+so on using Codine techniques that we
+ 
+
+ align:start position:0%
+so on using Codine techniques that we
+hear about today you can also do
+
+ align:start position:0%
+hear about today you can also do
+ 
+
+ align:start position:0%
+hear about today you can also do
+frequency shifting uh quite easily using
+
+ align:start position:0%
+frequency shifting uh quite easily using
+ 
+
+ align:start position:0%
+frequency shifting uh quite easily using
+this device now if you want to use it as
+
+ align:start position:0%
+this device now if you want to use it as
+ 
+
+ align:start position:0%
+this device now if you want to use it as
+a coupler or or as an intensity
+
+ align:start position:0%
+a coupler or or as an intensity
+ 
+
+ align:start position:0%
+a coupler or or as an intensity
+modulator and so on you have to uh
+
+ align:start position:0%
+modulator and so on you have to uh
+ 
+
+ align:start position:0%
+modulator and so on you have to uh
+combine uh several wave guides two wave
+
+ align:start position:0%
+combine uh several wave guides two wave
+ 
+
+ align:start position:0%
+combine uh several wave guides two wave
+guides together and then you can create
+
+ align:start position:0%
+guides together and then you can create
+ 
+
+ align:start position:0%
+guides together and then you can create
+a coupl and so on but here I've chosen
+
+ align:start position:0%
+a coupl and so on but here I've chosen
+ 
+
+ align:start position:0%
+a coupl and so on but here I've chosen
+uh this example here where I have one
+
+ align:start position:0%
+uh this example here where I have one
+ 
+
+ align:start position:0%
+uh this example here where I have one
+guy that looks like this and then the
+
+ align:start position:0%
+guy that looks like this and then the
+ 
+
+ align:start position:0%
+guy that looks like this and then the
+other guy that looks like that now if I
+
+ align:start position:0%
+other guy that looks like that now if I
+ 
+
+ align:start position:0%
+other guy that looks like that now if I
+put light in in in one arm then then
+
+ align:start position:0%
+put light in in in one arm then then
+ 
+
+ align:start position:0%
+put light in in in one arm then then
+again normally it would come out on uh
+
+ align:start position:0%
+again normally it would come out on uh
+ 
+
+ align:start position:0%
+again normally it would come out on uh
+over here uh but depending on the
+
+ align:start position:0%
+over here uh but depending on the
+ 
+
+ align:start position:0%
+over here uh but depending on the
+closeness of these two cores then I can
+
+ align:start position:0%
+closeness of these two cores then I can
+ 
+
+ align:start position:0%
+closeness of these two cores then I can
+get some light that will be coupled into
+
+ align:start position:0%
+get some light that will be coupled into
+ 
+
+ align:start position:0%
+get some light that will be coupled into
+this other side will come out over here
+
+ align:start position:0%
+this other side will come out over here
+ 
+
+ align:start position:0%
+this other side will come out over here
+so this is a uh let say a fixed
+
+ align:start position:0%
+so this is a uh let say a fixed
+ 
+
+ align:start position:0%
+so this is a uh let say a fixed
+coupler uh if you uh if you want to have
+
+ align:start position:0%
+coupler uh if you uh if you want to have
+ 
+
+ align:start position:0%
+coupler uh if you uh if you want to have
+a variable coupler again if this
+
+ align:start position:0%
+a variable coupler again if this
+ 
+
+ align:start position:0%
+a variable coupler again if this
+material of the substrate is is
+
+ align:start position:0%
+material of the substrate is is
+ 
+
+ align:start position:0%
+material of the substrate is is
+electrooptic then again putting
+
+ align:start position:0%
+electrooptic then again putting
+ 
+
+ align:start position:0%
+electrooptic then again putting
+electrodes on the material then you can
+
+ align:start position:0%
+electrodes on the material then you can
+ 
+
+ align:start position:0%
+electrodes on the material then you can
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+the the essentially the index here
+
+ align:start position:0%
+the the essentially the index here
+ 
+
+ align:start position:0%
+the the essentially the index here
+between the between the cores and uh and
+
+ align:start position:0%
+between the between the cores and uh and
+ 
+
+ align:start position:0%
+between the between the cores and uh and
+this way we'll change the uh the
+
+ align:start position:0%
+this way we'll change the uh the
+ 
+
+ align:start position:0%
+this way we'll change the uh the
+coupling the coupling ratio then will
+
+ align:start position:0%
+coupling the coupling ratio then will
+ 
+
+ align:start position:0%
+coupling the coupling ratio then will
+change depending on the index so I can
+
+ align:start position:0%
+change depending on the index so I can
+ 
+
+ align:start position:0%
+change depending on the index so I can
+couple more light or less light by
+
+ align:start position:0%
+couple more light or less light by
+ 
+
+ align:start position:0%
+couple more light or less light by
+applying a voltage so this is a neat
+
+ align:start position:0%
+applying a voltage so this is a neat
+ 
+
+ align:start position:0%
+applying a voltage so this is a neat
+little device and uh and then there's
+
+ align:start position:0%
+little device and uh and then there's
+ 
+
+ align:start position:0%
+little device and uh and then there's
+also other applications uh you can also
+
+ align:start position:0%
+also other applications uh you can also
+ 
+
+ align:start position:0%
+also other applications uh you can also
+use it as a as a for example as a
+
+ align:start position:0%
+use it as a as a for example as a
+ 
+
+ align:start position:0%
+use it as a as a for example as a
+intensity uh modulator by uh by again uh
+
+ align:start position:0%
+intensity uh modulator by uh by again uh
+ 
+
+ align:start position:0%
+intensity uh modulator by uh by again uh
+applying a variable voltage here and
+
+ align:start position:0%
+applying a variable voltage here and
+ 
+
+ align:start position:0%
+applying a variable voltage here and
+then you can transfer you can vary the
+
+ align:start position:0%
+then you can transfer you can vary the
+ 
+
+ align:start position:0%
+then you can transfer you can vary the
+transfer of light from here to uh from
+
+ align:start position:0%
+transfer of light from here to uh from
+ 
+
+ align:start position:0%
+transfer of light from here to uh from
+this port uh to this port and and so on
+
+ align:start position:0%
+this port uh to this port and and so on
+ 
+
+ align:start position:0%
+this port uh to this port and and so on
+so it has many many applications sensors
+
+ align:start position:0%
+so it has many many applications sensors
+ 
+
+ align:start position:0%
+so it has many many applications sensors
+and so on so this is a a very important
+
+ align:start position:0%
+and so on so this is a a very important
+ 
+
+ align:start position:0%
+and so on so this is a a very important
+uh field in in fiber optics as long as
+
+ align:start position:0%
+uh field in in fiber optics as long as
+ 
+
+ align:start position:0%
+uh field in in fiber optics as long as
+you can as long as you know how to
+
+ align:start position:0%
+you can as long as you know how to
+ 
+
+ align:start position:0%
+you can as long as you know how to
+couple uh back into fibers and in in a
+
+ align:start position:0%
+couple uh back into fibers and in in a
+ 
+
+ align:start position:0%
+couple uh back into fibers and in in a
+in a rigid way without any reflection or
+
+ align:start position:0%
+in a rigid way without any reflection or
+ 
+
+ align:start position:0%
+in a rigid way without any reflection or
+big Reflections and and so on so it's a
+
+ align:start position:0%
+big Reflections and and so on so it's a
+ 
+
+ align:start position:0%
+big Reflections and and so on so it's a
+very very very exciting uh uh
+
+ align:start position:0%
+very very very exciting uh uh
+ 
+
+ align:start position:0%
+very very very exciting uh uh
+development now what I'd like to do is
+
+ align:start position:0%
+development now what I'd like to do is
+ 
+
+ align:start position:0%
+development now what I'd like to do is
+talk a little bit about uh uh fibers for
+
+ align:start position:0%
+talk a little bit about uh uh fibers for
+ 
+
+ align:start position:0%
+talk a little bit about uh uh fibers for
+for sensors special fibers for sensors
+
+ align:start position:0%
+for sensors special fibers for sensors
+ 
+
+ align:start position:0%
+for sensors special fibers for sensors
+so far the fibers I've talked about are
+
+ align:start position:0%
+so far the fibers I've talked about are
+ 
+
+ align:start position:0%
+so far the fibers I've talked about are
+good for for
+
+ align:start position:0%
+good for for
+ 
+
+ align:start position:0%
+good for for
+communication okay single mode fibers
+
+ align:start position:0%
+communication okay single mode fibers
+ 
+
+ align:start position:0%
+communication okay single mode fibers
+low loss and and so on but for sensors
+
+ align:start position:0%
+low loss and and so on but for sensors
+ 
+
+ align:start position:0%
+low loss and and so on but for sensors
+there are all kinds of uh fibers that
+
+ align:start position:0%
+there are all kinds of uh fibers that
+ 
+
+ align:start position:0%
+there are all kinds of uh fibers that
+have been uh uh developed
+
+ align:start position:0%
+have been uh uh developed
+ 
+
+ align:start position:0%
+have been uh uh developed
+uh and it's a field that is growing a
+
+ align:start position:0%
+uh and it's a field that is growing a
+ 
+
+ align:start position:0%
+uh and it's a field that is growing a
+little difficult get started but it is
+
+ align:start position:0%
+little difficult get started but it is
+ 
+
+ align:start position:0%
+little difficult get started but it is
+it is growing now the uh the this today
+
+ align:start position:0%
+it is growing now the uh the this today
+ 
+
+ align:start position:0%
+it is growing now the uh the this today
+we have what we call polarization
+
+ align:start position:0%
+we have what we call polarization
+ 
+
+ align:start position:0%
+we have what we call polarization
+maintaining fibers these are fibers that
+
+ align:start position:0%
+maintaining fibers these are fibers that
+ 
+
+ align:start position:0%
+maintaining fibers these are fibers that
+will will if you launch the field at one
+
+ align:start position:0%
+will will if you launch the field at one
+ 
+
+ align:start position:0%
+will will if you launch the field at one
+polarization will stay in that
+
+ align:start position:0%
+polarization will stay in that
+ 
+
+ align:start position:0%
+polarization will stay in that
+polarization uh there are fibers that uh
+
+ align:start position:0%
+polarization uh there are fibers that uh
+ 
+
+ align:start position:0%
+polarization uh there are fibers that uh
+that will only propagate one one
+
+ align:start position:0%
+that will only propagate one one
+ 
+
+ align:start position:0%
+that will only propagate one one
+polarization the other polarization will
+
+ align:start position:0%
+polarization the other polarization will
+ 
+
+ align:start position:0%
+polarization the other polarization will
+not propagate is too much loss and so
+
+ align:start position:0%
+not propagate is too much loss and so
+ 
+
+ align:start position:0%
+not propagate is too much loss and so
+you have essentially like very long uh
+
+ align:start position:0%
+you have essentially like very long uh
+ 
+
+ align:start position:0%
+you have essentially like very long uh
+polarizer linear polarizer then we get
+
+ align:start position:0%
+polarizer linear polarizer then we get
+ 
+
+ align:start position:0%
+polarizer linear polarizer then we get
+to what we call coated fibers these are
+
+ align:start position:0%
+to what we call coated fibers these are
+ 
+
+ align:start position:0%
+to what we call coated fibers these are
+fibers that are coated with special
+
+ align:start position:0%
+fibers that are coated with special
+ 
+
+ align:start position:0%
+fibers that are coated with special
+materials that if they are placed in a
+
+ align:start position:0%
+materials that if they are placed in a
+ 
+
+ align:start position:0%
+materials that if they are placed in a
+certain environment then that material
+
+ align:start position:0%
+certain environment then that material
+ 
+
+ align:start position:0%
+certain environment then that material
+will will start stretching and will
+
+ align:start position:0%
+will will start stretching and will
+ 
+
+ align:start position:0%
+will will start stretching and will
+stretch the fiber with it and then you
+
+ align:start position:0%
+stretch the fiber with it and then you
+ 
+
+ align:start position:0%
+stretch the fiber with it and then you
+can make a sensor for that particular
+
+ align:start position:0%
+can make a sensor for that particular
+ 
+
+ align:start position:0%
+can make a sensor for that particular
+species that the fiber is dipped into
+
+ align:start position:0%
+species that the fiber is dipped into
+ 
+
+ align:start position:0%
+species that the fiber is dipped into
+you can also get
+
+ align:start position:0%
+you can also get
+ 
+
+ align:start position:0%
+you can also get
+uh uh other types of Coatings you can
+
+ align:start position:0%
+uh uh other types of Coatings you can
+ 
+
+ align:start position:0%
+uh uh other types of Coatings you can
+coat the material with with with a
+
+ align:start position:0%
+coat the material with with with a
+ 
+
+ align:start position:0%
+coat the material with with with a
+conducting uh material like copper or so
+
+ align:start position:0%
+conducting uh material like copper or so
+ 
+
+ align:start position:0%
+conducting uh material like copper or so
+on you can make it more sensitive to
+
+ align:start position:0%
+on you can make it more sensitive to
+ 
+
+ align:start position:0%
+on you can make it more sensitive to
+temperature you can coat the fiber with
+
+ align:start position:0%
+temperature you can coat the fiber with
+ 
+
+ align:start position:0%
+temperature you can coat the fiber with
+p Electric material and you can make it
+
+ align:start position:0%
+p Electric material and you can make it
+ 
+
+ align:start position:0%
+p Electric material and you can make it
+into phase modulator or magnetostrictive
+
+ align:start position:0%
+into phase modulator or magnetostrictive
+ 
+
+ align:start position:0%
+into phase modulator or magnetostrictive
+material and so on you can do all put
+
+ align:start position:0%
+material and so on you can do all put
+ 
+
+ align:start position:0%
+material and so on you can do all put
+all kinds of coatings on fibers and and
+
+ align:start position:0%
+all kinds of coatings on fibers and and
+ 
+
+ align:start position:0%
+all kinds of coatings on fibers and and
+use them for sensors and the jacketed
+
+ align:start position:0%
+use them for sensors and the jacketed
+ 
+
+ align:start position:0%
+use them for sensors and the jacketed
+fibers is almost like the the fiber you
+
+ align:start position:0%
+fibers is almost like the the fiber you
+ 
+
+ align:start position:0%
+fibers is almost like the the fiber you
+you put it with a jacket and then you
+
+ align:start position:0%
+you put it with a jacket and then you
+ 
+
+ align:start position:0%
+you put it with a jacket and then you
+make the jacket sensitive to just like I
+
+ align:start position:0%
+make the jacket sensitive to just like I
+ 
+
+ align:start position:0%
+make the jacket sensitive to just like I
+mentioned before to the to the species
+
+ align:start position:0%
+mentioned before to the to the species
+ 
+
+ align:start position:0%
+mentioned before to the to the species
+that the fiber is dipped into then there
+
+ align:start position:0%
+that the fiber is dipped into then there
+ 
+
+ align:start position:0%
+that the fiber is dipped into then there
+are today is a big field now the doping
+
+ align:start position:0%
+are today is a big field now the doping
+ 
+
+ align:start position:0%
+are today is a big field now the doping
+of uh of fibers and for example if you
+
+ align:start position:0%
+of uh of fibers and for example if you
+ 
+
+ align:start position:0%
+of uh of fibers and for example if you
+dope glass fiber with the admium you
+
+ align:start position:0%
+dope glass fiber with the admium you
+ 
+
+ align:start position:0%
+dope glass fiber with the admium you
+have uh and you can uh pump it with h
+
+ align:start position:0%
+have uh and you can uh pump it with h
+ 
+
+ align:start position:0%
+have uh and you can uh pump it with h
+with a laser with a semiconductor laser
+
+ align:start position:0%
+with a laser with a semiconductor laser
+ 
+
+ align:start position:0%
+with a laser with a semiconductor laser
+then you can have you can have a
+
+ align:start position:0%
+then you can have you can have a
+ 
+
+ align:start position:0%
+then you can have you can have a
+essentially an emium laser a fiber laser
+
+ align:start position:0%
+essentially an emium laser a fiber laser
+ 
+
+ align:start position:0%
+essentially an emium laser a fiber laser
+and you can make them into a uh linear
+
+ align:start position:0%
+and you can make them into a uh linear
+ 
+
+ align:start position:0%
+and you can make them into a uh linear
+lasers or ring lasers and so on uh today
+
+ align:start position:0%
+lasers or ring lasers and so on uh today
+ 
+
+ align:start position:0%
+lasers or ring lasers and so on uh today
+by doping uh doping the fiber and and
+
+ align:start position:0%
+by doping uh doping the fiber and and
+ 
+
+ align:start position:0%
+by doping uh doping the fiber and and
+this is the the background for or the
+
+ align:start position:0%
+this is the the background for or the
+ 
+
+ align:start position:0%
+this is the the background for or the
+fiber optic lasers because you dope the
+
+ align:start position:0%
+fiber optic lasers because you dope the
+ 
+
+ align:start position:0%
+fiber optic lasers because you dope the
+fiber with all kinds of uh uh uh
+
+ align:start position:0%
+fiber with all kinds of uh uh uh
+ 
+
+ align:start position:0%
+fiber with all kinds of uh uh uh
+impurities and then you you get then you
+
+ align:start position:0%
+impurities and then you you get then you
+ 
+
+ align:start position:0%
+impurities and then you you get then you
+pump you have to pump them and then
+
+ align:start position:0%
+pump you have to pump them and then
+ 
+
+ align:start position:0%
+pump you have to pump them and then
+usually these are pumped uh with a
+
+ align:start position:0%
+usually these are pumped uh with a
+ 
+
+ align:start position:0%
+usually these are pumped uh with a
+semiconductor laser or some other laser
+
+ align:start position:0%
+semiconductor laser or some other laser
+ 
+
+ align:start position:0%
+semiconductor laser or some other laser
+and then you can create all sorts of
+
+ align:start position:0%
+and then you can create all sorts of
+ 
+
+ align:start position:0%
+and then you can create all sorts of
+lasers so you got to watch this this
+
+ align:start position:0%
+lasers so you got to watch this this
+ 
+
+ align:start position:0%
+lasers so you got to watch this this
+field now it's going to be it's going to
+
+ align:start position:0%
+field now it's going to be it's going to
+ 
+
+ align:start position:0%
+field now it's going to be it's going to
+be very big then uh there's another type
+
+ align:start position:0%
+be very big then uh there's another type
+ 
+
+ align:start position:0%
+be very big then uh there's another type
+of uh of fiber where you expose the
+
+ align:start position:0%
+of uh of fiber where you expose the
+ 
+
+ align:start position:0%
+of uh of fiber where you expose the
+cladding you shave off the cladding
+
+ align:start position:0%
+cladding you shave off the cladding
+ 
+
+ align:start position:0%
+cladding you shave off the cladding
+expose the core all right so so by
+
+ align:start position:0%
+expose the core all right so so by
+ 
+
+ align:start position:0%
+expose the core all right so so by
+exposing core means that you're exposing
+
+ align:start position:0%
+exposing core means that you're exposing
+ 
+
+ align:start position:0%
+exposing core means that you're exposing
+the evanescent wave that I've talked
+
+ align:start position:0%
+the evanescent wave that I've talked
+ 
+
+ align:start position:0%
+the evanescent wave that I've talked
+about before and that can be used that
+
+ align:start position:0%
+about before and that can be used that
+ 
+
+ align:start position:0%
+about before and that can be used that
+tail of the evanescent wave can be used
+
+ align:start position:0%
+tail of the evanescent wave can be used
+ 
+
+ align:start position:0%
+tail of the evanescent wave can be used
+to uh to uh interact with Vapor or gas
+
+ align:start position:0%
+to uh to uh interact with Vapor or gas
+ 
+
+ align:start position:0%
+to uh to uh interact with Vapor or gas
+or liquid or whatever that is placed in
+
+ align:start position:0%
+or liquid or whatever that is placed in
+ 
+
+ align:start position:0%
+or liquid or whatever that is placed in
+and you can use that as a as a chemical
+
+ align:start position:0%
+and you can use that as a as a chemical
+ 
+
+ align:start position:0%
+and you can use that as a as a chemical
+sensor and then we have twin core fibers
+
+ align:start position:0%
+sensor and then we have twin core fibers
+ 
+
+ align:start position:0%
+sensor and then we have twin core fibers
+where the two cores are closed and then
+
+ align:start position:0%
+where the two cores are closed and then
+ 
+
+ align:start position:0%
+where the two cores are closed and then
+you can transfer light from one core to
+
+ align:start position:0%
+you can transfer light from one core to
+ 
+
+ align:start position:0%
+you can transfer light from one core to
+the other all the way down the fiber and
+
+ align:start position:0%
+the other all the way down the fiber and
+ 
+
+ align:start position:0%
+the other all the way down the fiber and
+this can be used for uh for temperature
+
+ align:start position:0%
+this can be used for uh for temperature
+ 
+
+ align:start position:0%
+this can be used for uh for temperature
+stress and and so on let's say there's
+
+ align:start position:0%
+stress and and so on let's say there's
+ 
+
+ align:start position:0%
+stress and and so on let's say there's
+is a this is a huge field and I think we
+
+ align:start position:0%
+is a this is a huge field and I think we
+ 
+
+ align:start position:0%
+is a this is a huge field and I think we
+need a whole uh one day uh on uh uh
+
+ align:start position:0%
+need a whole uh one day uh on uh uh
+ 
+
+ align:start position:0%
+need a whole uh one day uh on uh uh
+course on uh on fibers so so now I'm
+
+ align:start position:0%
+course on uh on fibers so so now I'm
+ 
+
+ align:start position:0%
+course on uh on fibers so so now I'm
+getting close to to the end uh and I
+
+ align:start position:0%
+getting close to to the end uh and I
+ 
+
+ align:start position:0%
+getting close to to the end uh and I
+hope I've got some ideas across about
+
+ align:start position:0%
+hope I've got some ideas across about
+ 
+
+ align:start position:0%
+hope I've got some ideas across about
+basics of fibers without again without
+
+ align:start position:0%
+basics of fibers without again without
+ 
+
+ align:start position:0%
+basics of fibers without again without
+using math without scaring you off but
+
+ align:start position:0%
+using math without scaring you off but
+ 
+
+ align:start position:0%
+using math without scaring you off but
+obviously if if uh if you have interest
+
+ align:start position:0%
+obviously if if uh if you have interest
+ 
+
+ align:start position:0%
+obviously if if uh if you have interest
+in these things you have to consult the
+
+ align:start position:0%
+in these things you have to consult the
+ 
+
+ align:start position:0%
+in these things you have to consult the
+literature or take uh take other courses
+
+ align:start position:0%
+literature or take uh take other courses
+ 
+
+ align:start position:0%
+literature or take uh take other courses
+uh in the few minutes remaining I would
+
+ align:start position:0%
+uh in the few minutes remaining I would
+ 
+
+ align:start position:0%
+uh in the few minutes remaining I would
+like to talk about just a few words
+
+ align:start position:0%
+like to talk about just a few words
+ 
+
+ align:start position:0%
+like to talk about just a few words
+about some future uh developments both
+
+ align:start position:0%
+about some future uh developments both
+ 
+
+ align:start position:0%
+about some future uh developments both
+in lasers and and fiber optics uh the uh
+
+ align:start position:0%
+in lasers and and fiber optics uh the uh
+ 
+
+ align:start position:0%
+in lasers and and fiber optics uh the uh
+in terms of lasers uh suddenly we're
+
+ align:start position:0%
+in terms of lasers uh suddenly we're
+ 
+
+ align:start position:0%
+in terms of lasers uh suddenly we're
+going to see the rise and we're already
+
+ align:start position:0%
+going to see the rise and we're already
+ 
+
+ align:start position:0%
+going to see the rise and we're already
+seeing the rise of semiconductor lasers
+
+ align:start position:0%
+seeing the rise of semiconductor lasers
+ 
+
+ align:start position:0%
+seeing the rise of semiconductor lasers
+you know for all sorts of applications
+
+ align:start position:0%
+you know for all sorts of applications
+ 
+
+ align:start position:0%
+you know for all sorts of applications
+CDs and so on but we're also we're going
+
+ align:start position:0%
+CDs and so on but we're also we're going
+ 
+
+ align:start position:0%
+CDs and so on but we're also we're going
+to see them
+
+ align:start position:0%
+to see them
+ 
+
+ align:start position:0%
+to see them
+replacing the red helium neon laser
+
+ align:start position:0%
+replacing the red helium neon laser
+ 
+
+ align:start position:0%
+replacing the red helium neon laser
+today they're already available and in
+
+ align:start position:0%
+today they're already available and in
+ 
+
+ align:start position:0%
+today they're already available and in
+fact you see them as pointers and so on
+
+ align:start position:0%
+fact you see them as pointers and so on
+ 
+
+ align:start position:0%
+fact you see them as pointers and so on
+uh and uh and and so they have very neat
+
+ align:start position:0%
+uh and uh and and so they have very neat
+ 
+
+ align:start position:0%
+uh and uh and and so they have very neat
+little devices and for applications that
+
+ align:start position:0%
+little devices and for applications that
+ 
+
+ align:start position:0%
+little devices and for applications that
+don't require strict uh wavelength
+
+ align:start position:0%
+don't require strict uh wavelength
+ 
+
+ align:start position:0%
+don't require strict uh wavelength
+stability and what have you I mean the
+
+ align:start position:0%
+stability and what have you I mean the
+ 
+
+ align:start position:0%
+stability and what have you I mean the
+these These are great uh lasers we're
+
+ align:start position:0%
+these These are great uh lasers we're
+ 
+
+ align:start position:0%
+these These are great uh lasers we're
+also seeing and we'll see much more
+
+ align:start position:0%
+also seeing and we'll see much more
+ 
+
+ align:start position:0%
+also seeing and we'll see much more
+semiconductor lasers that are used to
+
+ align:start position:0%
+semiconductor lasers that are used to
+ 
+
+ align:start position:0%
+semiconductor lasers that are used to
+pump solid state lasers and fiber lasers
+
+ align:start position:0%
+pump solid state lasers and fiber lasers
+ 
+
+ align:start position:0%
+pump solid state lasers and fiber lasers
+waveguide lasers and and so on and this
+
+ align:start position:0%
+waveguide lasers and and so on and this
+ 
+
+ align:start position:0%
+waveguide lasers and and so on and this
+is a very nice application for
+
+ align:start position:0%
+is a very nice application for
+ 
+
+ align:start position:0%
+is a very nice application for
+Semiconductor lasers because again you
+
+ align:start position:0%
+Semiconductor lasers because again you
+ 
+
+ align:start position:0%
+Semiconductor lasers because again you
+don't have to worry about the the
+
+ align:start position:0%
+don't have to worry about the the
+ 
+
+ align:start position:0%
+don't have to worry about the the
+stability of wavelength and so on and
+
+ align:start position:0%
+stability of wavelength and so on and
+ 
+
+ align:start position:0%
+stability of wavelength and so on and
+then they can they can uh pump very well
+
+ align:start position:0%
+then they can they can uh pump very well
+ 
+
+ align:start position:0%
+then they can they can uh pump very well
+behaved uh Solid State uh lasers and
+
+ align:start position:0%
+behaved uh Solid State uh lasers and
+ 
+
+ align:start position:0%
+behaved uh Solid State uh lasers and
+today these can be also very big they
+
+ align:start position:0%
+today these can be also very big they
+ 
+
+ align:start position:0%
+today these can be also very big they
+don't have to be very small they can be
+
+ align:start position:0%
+don't have to be very small they can be
+ 
+
+ align:start position:0%
+don't have to be very small they can be
+very big and you have the array of
+
+ align:start position:0%
+very big and you have the array of
+ 
+
+ align:start position:0%
+very big and you have the array of
+semiconductor lasers that will will pump
+
+ align:start position:0%
+semiconductor lasers that will will pump
+ 
+
+ align:start position:0%
+semiconductor lasers that will will pump
+them and then we go from the big to the
+
+ align:start position:0%
+them and then we go from the big to the
+ 
+
+ align:start position:0%
+them and then we go from the big to the
+small we have even microchip lasers they
+
+ align:start position:0%
+small we have even microchip lasers they
+ 
+
+ align:start position:0%
+small we have even microchip lasers they
+very tiny crystals and then they are
+
+ align:start position:0%
+very tiny crystals and then they are
+ 
+
+ align:start position:0%
+very tiny crystals and then they are
+pumped again with let's say
+
+ align:start position:0%
+pumped again with let's say
+ 
+
+ align:start position:0%
+pumped again with let's say
+semiconductor lasers or other lasers but
+
+ align:start position:0%
+semiconductor lasers or other lasers but
+ 
+
+ align:start position:0%
+semiconductor lasers or other lasers but
+they're very tiny and they can be single
+
+ align:start position:0%
+they're very tiny and they can be single
+ 
+
+ align:start position:0%
+they're very tiny and they can be single
+frequency and tunable and so on and the
+
+ align:start position:0%
+frequency and tunable and so on and the
+ 
+
+ align:start position:0%
+frequency and tunable and so on and the
+fiber optic lasers well we already we
+
+ align:start position:0%
+fiber optic lasers well we already we
+ 
+
+ align:start position:0%
+fiber optic lasers well we already we
+already mentioned there all sorts of
+
+ align:start position:0%
+already mentioned there all sorts of
+ 
+
+ align:start position:0%
+already mentioned there all sorts of
+materials being looked at and uh and
+
+ align:start position:0%
+materials being looked at and uh and
+ 
+
+ align:start position:0%
+materials being looked at and uh and
+pumping uh sources and then the thin
+
+ align:start position:0%
+pumping uh sources and then the thin
+ 
+
+ align:start position:0%
+pumping uh sources and then the thin
+film wave guides well we talked about
+
+ align:start position:0%
+film wave guides well we talked about
+ 
+
+ align:start position:0%
+film wave guides well we talked about
+wave guides all you have to do is you
+
+ align:start position:0%
+wave guides all you have to do is you
+ 
+
+ align:start position:0%
+wave guides all you have to do is you
+dope that wave guide pump it with a with
+
+ align:start position:0%
+dope that wave guide pump it with a with
+ 
+
+ align:start position:0%
+dope that wave guide pump it with a with
+a with a optical pump and then you've
+
+ align:start position:0%
+a with a optical pump and then you've
+ 
+
+ align:start position:0%
+a with a optical pump and then you've
+got yourself a a laser in that in that
+
+ align:start position:0%
+got yourself a a laser in that in that
+ 
+
+ align:start position:0%
+got yourself a a laser in that in that
+substrate and then we vacuum ultraviolet
+
+ align:start position:0%
+substrate and then we vacuum ultraviolet
+ 
+
+ align:start position:0%
+substrate and then we vacuum ultraviolet
+lasers are very important in medical
+
+ align:start position:0%
+lasers are very important in medical
+ 
+
+ align:start position:0%
+lasers are very important in medical
+applications and other applications and
+
+ align:start position:0%
+applications and other applications and
+ 
+
+ align:start position:0%
+applications and other applications and
+we're seeing lots of uh new developments
+
+ align:start position:0%
+we're seeing lots of uh new developments
+ 
+
+ align:start position:0%
+we're seeing lots of uh new developments
+uh in here and also x-ray lasers you
+
+ align:start position:0%
+uh in here and also x-ray lasers you
+ 
+
+ align:start position:0%
+uh in here and also x-ray lasers you
+know the early uh early stages they
+
+ align:start position:0%
+know the early uh early stages they
+ 
+
+ align:start position:0%
+know the early uh early stages they
+classified the development but now I
+
+ align:start position:0%
+classified the development but now I
+ 
+
+ align:start position:0%
+classified the development but now I
+think uh the literature now we we see
+
+ align:start position:0%
+think uh the literature now we we see
+ 
+
+ align:start position:0%
+think uh the literature now we we see
+all kinds of work going on in x-ray
+
+ align:start position:0%
+all kinds of work going on in x-ray
+ 
+
+ align:start position:0%
+all kinds of work going on in x-ray
+lasers with again completely exciting
+
+ align:start position:0%
+lasers with again completely exciting
+ 
+
+ align:start position:0%
+lasers with again completely exciting
+area of of applications for x-ray lasers
+
+ align:start position:0%
+area of of applications for x-ray lasers
+ 
+
+ align:start position:0%
+area of of applications for x-ray lasers
+now this is the lasers now in terms of
+
+ align:start position:0%
+now this is the lasers now in terms of
+ 
+
+ align:start position:0%
+now this is the lasers now in terms of
+applications the uh you know I mentioned
+
+ align:start position:0%
+applications the uh you know I mentioned
+ 
+
+ align:start position:0%
+applications the uh you know I mentioned
+before fiber optic communication that's
+
+ align:start position:0%
+before fiber optic communication that's
+ 
+
+ align:start position:0%
+before fiber optic communication that's
+a huge application and we're going to
+
+ align:start position:0%
+a huge application and we're going to
+ 
+
+ align:start position:0%
+a huge application and we're going to
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+uh I think uh not that far uh uh we're
+
+ align:start position:0%
+uh I think uh not that far uh uh we're
+ 
+
+ align:start position:0%
+uh I think uh not that far uh uh we're
+going to see that our homes and all that
+
+ align:start position:0%
+going to see that our homes and all that
+ 
+
+ align:start position:0%
+going to see that our homes and all that
+will be linked with with fiber optic uh
+
+ align:start position:0%
+will be linked with with fiber optic uh
+ 
+
+ align:start position:0%
+will be linked with with fiber optic uh
+uh cables and this way we can have huge
+
+ align:start position:0%
+uh cables and this way we can have huge
+ 
+
+ align:start position:0%
+uh cables and this way we can have huge
+bandwidth it's going to be uh
+
+ align:start position:0%
+bandwidth it's going to be uh
+ 
+
+ align:start position:0%
+bandwidth it's going to be uh
+transmitted in uh in these fibers and
+
+ align:start position:0%
+transmitted in uh in these fibers and
+ 
+
+ align:start position:0%
+transmitted in uh in these fibers and
+then uh we can send all kinds of
+
+ align:start position:0%
+then uh we can send all kinds of
+ 
+
+ align:start position:0%
+then uh we can send all kinds of
+information all over the place uh this
+
+ align:start position:0%
+information all over the place uh this
+ 
+
+ align:start position:0%
+information all over the place uh this
+area is of materials processing again
+
+ align:start position:0%
+area is of materials processing again
+ 
+
+ align:start position:0%
+area is of materials processing again
+because of the availability of variety
+
+ align:start position:0%
+because of the availability of variety
+ 
+
+ align:start position:0%
+because of the availability of variety
+of lasers that is uh that certainly uh
+
+ align:start position:0%
+of lasers that is uh that certainly uh
+ 
+
+ align:start position:0%
+of lasers that is uh that certainly uh
+is increasing and uh and the variety is
+
+ align:start position:0%
+is increasing and uh and the variety is
+ 
+
+ align:start position:0%
+is increasing and uh and the variety is
+also increasing and medical procedures
+
+ align:start position:0%
+also increasing and medical procedures
+ 
+
+ align:start position:0%
+also increasing and medical procedures
+is uh if you keep up with what's going
+
+ align:start position:0%
+is uh if you keep up with what's going
+ 
+
+ align:start position:0%
+is uh if you keep up with what's going
+on it's it's it's incredible what the uh
+
+ align:start position:0%
+on it's it's it's incredible what the uh
+ 
+
+ align:start position:0%
+on it's it's it's incredible what the uh
+lasers are being used for procedures and
+
+ align:start position:0%
+lasers are being used for procedures and
+ 
+
+ align:start position:0%
+lasers are being used for procedures and
+for Diagnostics and and so on now here's
+
+ align:start position:0%
+for Diagnostics and and so on now here's
+ 
+
+ align:start position:0%
+for Diagnostics and and so on now here's
+a here's a tough area data processing uh
+
+ align:start position:0%
+a here's a tough area data processing uh
+ 
+
+ align:start position:0%
+a here's a tough area data processing uh
+lasers are being used but uh but
+
+ align:start position:0%
+lasers are being used but uh but
+ 
+
+ align:start position:0%
+lasers are being used but uh but
+hopefully uh the uh the uh will increase
+
+ align:start position:0%
+hopefully uh the uh the uh will increase
+ 
+
+ align:start position:0%
+hopefully uh the uh the uh will increase
+more you can take very fast for your
+
+ align:start position:0%
+more you can take very fast for your
+ 
+
+ align:start position:0%
+more you can take very fast for your
+transforms Optical Techni techniques but
+
+ align:start position:0%
+transforms Optical Techni techniques but
+ 
+
+ align:start position:0%
+transforms Optical Techni techniques but
+again you have the implementation of
+
+ align:start position:0%
+again you have the implementation of
+ 
+
+ align:start position:0%
+again you have the implementation of
+them is not is not that easy uh now
+
+ align:start position:0%
+them is not is not that easy uh now
+ 
+
+ align:start position:0%
+them is not is not that easy uh now
+sensors I've already mentioned some
+
+ align:start position:0%
+sensors I've already mentioned some
+ 
+
+ align:start position:0%
+sensors I've already mentioned some
+words about sensors but not just fiber
+
+ align:start position:0%
+words about sensors but not just fiber
+ 
+
+ align:start position:0%
+words about sensors but not just fiber
+optic sensors but all kinds of optical
+
+ align:start position:0%
+optic sensors but all kinds of optical
+ 
+
+ align:start position:0%
+optic sensors but all kinds of optical
+sensors they are they are incredible
+
+ align:start position:0%
+sensors they are they are incredible
+ 
+
+ align:start position:0%
+sensors they are they are incredible
+devices in the sense that that they're
+
+ align:start position:0%
+devices in the sense that that they're
+ 
+
+ align:start position:0%
+devices in the sense that that they're
+not affected by especially the fiber
+
+ align:start position:0%
+not affected by especially the fiber
+ 
+
+ align:start position:0%
+not affected by especially the fiber
+optic sensors they're not affected by
+
+ align:start position:0%
+optic sensors they're not affected by
+ 
+
+ align:start position:0%
+optic sensors they're not affected by
+electromagnetic interference and uh and
+
+ align:start position:0%
+electromagnetic interference and uh and
+ 
+
+ align:start position:0%
+electromagnetic interference and uh and
+they can be used in all sorts of uh
+
+ align:start position:0%
+they can be used in all sorts of uh
+ 
+
+ align:start position:0%
+they can be used in all sorts of uh
+hostile kind of uh environments that
+
+ align:start position:0%
+hostile kind of uh environments that
+ 
+
+ align:start position:0%
+hostile kind of uh environments that
+normal electrical s would not would not
+
+ align:start position:0%
+normal electrical s would not would not
+ 
+
+ align:start position:0%
+normal electrical s would not would not
+work at all because they will be uh
+
+ align:start position:0%
+work at all because they will be uh
+ 
+
+ align:start position:0%
+work at all because they will be uh
+affected by uh the electromagnetic
+
+ align:start position:0%
+affected by uh the electromagnetic
+ 
+
+ align:start position:0%
+affected by uh the electromagnetic
+interference um the uh also because uh
+
+ align:start position:0%
+interference um the uh also because uh
+ 
+
+ align:start position:0%
+interference um the uh also because uh
+fiber optics uh fibers have low loss you
+
+ align:start position:0%
+fiber optics uh fibers have low loss you
+ 
+
+ align:start position:0%
+fiber optics uh fibers have low loss you
+can have all kinds of distributed uh
+
+ align:start position:0%
+can have all kinds of distributed uh
+ 
+
+ align:start position:0%
+can have all kinds of distributed uh
+sensors and uh and uh and so on because
+
+ align:start position:0%
+sensors and uh and uh and so on because
+ 
+
+ align:start position:0%
+sensors and uh and uh and so on because
+the uh the the the fiber as I say
+
+ align:start position:0%
+the uh the the the fiber as I say
+ 
+
+ align:start position:0%
+the uh the the the fiber as I say
+doesn't have any law so you can place
+
+ align:start position:0%
+doesn't have any law so you can place
+ 
+
+ align:start position:0%
+doesn't have any law so you can place
+sort of sensors all over the place place
+
+ align:start position:0%
+sort of sensors all over the place place
+ 
+
+ align:start position:0%
+sort of sensors all over the place place
+and collect data from a large area now I
+
+ align:start position:0%
+and collect data from a large area now I
+ 
+
+ align:start position:0%
+and collect data from a large area now I
+mentioned earlier Precision positioning
+
+ align:start position:0%
+mentioned earlier Precision positioning
+ 
+
+ align:start position:0%
+mentioned earlier Precision positioning
+this is based on interferometry laser
+
+ align:start position:0%
+this is based on interferometry laser
+ 
+
+ align:start position:0%
+this is based on interferometry laser
+interferometry using laser
+
+ align:start position:0%
+interferometry using laser
+ 
+
+ align:start position:0%
+interferometry using laser
+interferometry you can uh uh monitor the
+
+ align:start position:0%
+interferometry you can uh uh monitor the
+ 
+
+ align:start position:0%
+interferometry you can uh uh monitor the
+positions of work pieces and uh and so
+
+ align:start position:0%
+positions of work pieces and uh and so
+ 
+
+ align:start position:0%
+positions of work pieces and uh and so
+on uh and dimensions and sizes and
+
+ align:start position:0%
+on uh and dimensions and sizes and
+ 
+
+ align:start position:0%
+on uh and dimensions and sizes and
+movements of all kinds of things and you
+
+ align:start position:0%
+movements of all kinds of things and you
+ 
+
+ align:start position:0%
+movements of all kinds of things and you
+can put them in feedback loops and they
+
+ align:start position:0%
+can put them in feedback loops and they
+ 
+
+ align:start position:0%
+can put them in feedback loops and they
+uh they improve things for you then
+
+ align:start position:0%
+uh they improve things for you then
+ 
+
+ align:start position:0%
+uh they improve things for you then
+laser shows I don't know I don't keep up
+
+ align:start position:0%
+laser shows I don't know I don't keep up
+ 
+
+ align:start position:0%
+laser shows I don't know I don't keep up
+with laser shows but every time I see
+
+ align:start position:0%
+with laser shows but every time I see
+ 
+
+ align:start position:0%
+with laser shows but every time I see
+them they always fascinate me because
+
+ align:start position:0%
+them they always fascinate me because
+ 
+
+ align:start position:0%
+them they always fascinate me because
+I'm always curious about what kind of
+
+ align:start position:0%
+I'm always curious about what kind of
+ 
+
+ align:start position:0%
+I'm always curious about what kind of
+lasers they using and today they can use
+
+ align:start position:0%
+lasers they using and today they can use
+ 
+
+ align:start position:0%
+lasers they using and today they can use
+them to write all kinds of patterns and
+
+ align:start position:0%
+them to write all kinds of patterns and
+ 
+
+ align:start position:0%
+them to write all kinds of patterns and
+uh and messages and so on uh for people
+
+ align:start position:0%
+uh and messages and so on uh for people
+ 
+
+ align:start position:0%
+uh and messages and so on uh for people
+then there's the computer interconnects
+
+ align:start position:0%
+then there's the computer interconnects
+ 
+
+ align:start position:0%
+then there's the computer interconnects
+these are the fiber optics or integrated
+
+ align:start position:0%
+these are the fiber optics or integrated
+ 
+
+ align:start position:0%
+these are the fiber optics or integrated
+Optics that are being used for for
+
+ align:start position:0%
+Optics that are being used for for
+ 
+
+ align:start position:0%
+Optics that are being used for for
+connecting uh computers or even
+
+ align:start position:0%
+connecting uh computers or even
+ 
+
+ align:start position:0%
+connecting uh computers or even
+connecting uh boards and uh and
+
+ align:start position:0%
+connecting uh boards and uh and
+ 
+
+ align:start position:0%
+connecting uh boards and uh and
+hopefully U sometime in the near future
+
+ align:start position:0%
+hopefully U sometime in the near future
+ 
+
+ align:start position:0%
+hopefully U sometime in the near future
+we will see all Optical computers now
+
+ align:start position:0%
+we will see all Optical computers now
+ 
+
+ align:start position:0%
+we will see all Optical computers now
+these will be very fast based on these
+
+ align:start position:0%
+these will be very fast based on these
+ 
+
+ align:start position:0%
+these will be very fast based on these
+mod loock very short pulses and but
+
+ align:start position:0%
+mod loock very short pulses and but
+ 
+
+ align:start position:0%
+mod loock very short pulses and but
+there are a lot of challenges and uh
+
+ align:start position:0%
+there are a lot of challenges and uh
+ 
+
+ align:start position:0%
+there are a lot of challenges and uh
+hopefully some of these challenges will
+
+ align:start position:0%
+hopefully some of these challenges will
+ 
+
+ align:start position:0%
+hopefully some of these challenges will
+be overcome then in terms of high
+
+ align:start position:0%
+be overcome then in terms of high
+ 
+
+ align:start position:0%
+be overcome then in terms of high
+density memories well we already seeing
+
+ align:start position:0%
+density memories well we already seeing
+ 
+
+ align:start position:0%
+density memories well we already seeing
+that now and uh and then but hopefully
+
+ align:start position:0%
+that now and uh and then but hopefully
+ 
+
+ align:start position:0%
+that now and uh and then but hopefully
+they will even be uh even more dense you
+
+ align:start position:0%
+they will even be uh even more dense you
+ 
+
+ align:start position:0%
+they will even be uh even more dense you
+taking advantage of uh of
+
+ align:start position:0%
+taking advantage of uh of
+ 
+
+ align:start position:0%
+taking advantage of uh of
+three-dimensional uh uh structures and
+
+ align:start position:0%
+three-dimensional uh uh structures and
+ 
+
+ align:start position:0%
+three-dimensional uh uh structures and
+so on and finally I'd love to see some
+
+ align:start position:0%
+so on and finally I'd love to see some
+ 
+
+ align:start position:0%
+so on and finally I'd love to see some
+color holography becoming uh becoming
+
+ align:start position:0%
+color holography becoming uh becoming
+ 
+
+ align:start position:0%
+color holography becoming uh becoming
+popular so that we can have all sorts of
+
+ align:start position:0%
+popular so that we can have all sorts of
+ 
+
+ align:start position:0%
+popular so that we can have all sorts of
+color Holograms around around our
+
+ align:start position:0%
+color Holograms around around our
+ 
+
+ align:start position:0%
+color Holograms around around our
+workplaces around our homes and so on
+
+ align:start position:0%
+workplaces around our homes and so on
+ 
+
+ align:start position:0%
+workplaces around our homes and so on
+it's a uh so far there's all kinds of
+
+ align:start position:0%
+it's a uh so far there's all kinds of
+ 
+
+ align:start position:0%
+it's a uh so far there's all kinds of
+kind of holography available but the
+
+ align:start position:0%
+kind of holography available but the
+ 
+
+ align:start position:0%
+kind of holography available but the
+true color holography even though it is
+
+ align:start position:0%
+true color holography even though it is
+ 
+
+ align:start position:0%
+true color holography even though it is
+feasible we haven't we haven't seen them
+
+ align:start position:0%
+feasible we haven't we haven't seen them
+ 
+
+ align:start position:0%
+feasible we haven't we haven't seen them
+at least uh that available so that one
+
+ align:start position:0%
+at least uh that available so that one
+ 
+
+ align:start position:0%
+at least uh that available so that one
+can uh purchase them and uh put them up
+
+ align:start position:0%
+can uh purchase them and uh put them up
+ 
+
+ align:start position:0%
+can uh purchase them and uh put them up
+on the wall I I see that uh that my time
+
+ align:start position:0%
+on the wall I I see that uh that my time
+ 
+
+ align:start position:0%
+on the wall I I see that uh that my time
+is uh is close to coming up uh to an end
+
+ align:start position:0%
+is uh is close to coming up uh to an end
+ 
+
+ align:start position:0%
+is uh is close to coming up uh to an end
+and I hope that I've been able to to get
+
+ align:start position:0%
+and I hope that I've been able to to get
+ 
+
+ align:start position:0%
+and I hope that I've been able to to get
+some ideas across to you again without
+
+ align:start position:0%
+some ideas across to you again without
+ 
+
+ align:start position:0%
+some ideas across to you again without
+without scaring you off certainly I hope
+
+ align:start position:0%
+without scaring you off certainly I hope
+ 
+
+ align:start position:0%
+without scaring you off certainly I hope
+that for those of you who didn't have
+
+ align:start position:0%
+that for those of you who didn't have
+ 
+
+ align:start position:0%
+that for those of you who didn't have
+too much background I hope you have
+
+ align:start position:0%
+too much background I hope you have
+ 
+
+ align:start position:0%
+too much background I hope you have
+motivate motivated you take some
+
+ align:start position:0%
+motivate motivated you take some
+ 
+
+ align:start position:0%
+motivate motivated you take some
+interest in lasers in fiber optics and
+
+ align:start position:0%
+interest in lasers in fiber optics and
+ 
+
+ align:start position:0%
+interest in lasers in fiber optics and
+maybe you can find some new applications
+
+ align:start position:0%
+maybe you can find some new applications
+ 
+
+ align:start position:0%
+maybe you can find some new applications
+uh for them because the field is is very
+
+ align:start position:0%
+uh for them because the field is is very
+ 
+
+ align:start position:0%
+uh for them because the field is is very
+young and it needs it needs some
+
+ align:start position:0%
+young and it needs it needs some
+ 
+
+ align:start position:0%
+young and it needs it needs some
+energetic people that will come in and
+
+ align:start position:0%
+energetic people that will come in and
+ 
+
+ align:start position:0%
+energetic people that will come in and
+especially from from different fields
+
+ align:start position:0%
+especially from from different fields
+ 
+
+ align:start position:0%
+especially from from different fields
+it's not always you want should always
+
+ align:start position:0%
+it's not always you want should always
+ 
+
+ align:start position:0%
+it's not always you want should always
+uh talk to people in in in the Optics
+
+ align:start position:0%
+uh talk to people in in in the Optics
+ 
+
+ align:start position:0%
+uh talk to people in in in the Optics
+and Laser field one should be talking to
+
+ align:start position:0%
+and Laser field one should be talking to
+ 
+
+ align:start position:0%
+and Laser field one should be talking to
+to others in other fields maybe they'll
+
+ align:start position:0%
+to others in other fields maybe they'll
+ 
+
+ align:start position:0%
+to others in other fields maybe they'll
+recognize they'll recognize uh some new
+
+ align:start position:0%
+recognize they'll recognize uh some new
+ 
+
+ align:start position:0%
+recognize they'll recognize uh some new
+applications as we can see there really
+
+ align:start position:0%
+applications as we can see there really
+ 
+
+ align:start position:0%
+applications as we can see there really
+so many applications of of lasers and
+
+ align:start position:0%
+so many applications of of lasers and
+ 
+
+ align:start position:0%
+so many applications of of lasers and
+fiber optics now be before I close I I'd
+
+ align:start position:0%
+fiber optics now be before I close I I'd
+ 
+
+ align:start position:0%
+fiber optics now be before I close I I'd
+like to thank uh two of my graduate
+
+ align:start position:0%
+like to thank uh two of my graduate
+ 
+
+ align:start position:0%
+like to thank uh two of my graduate
+students um Steve Smith and farads
+
+ align:start position:0%
+students um Steve Smith and farads
+ 
+
+ align:start position:0%
+students um Steve Smith and farads
+arichi uh now I have put them in a
+
+ align:start position:0%
+arichi uh now I have put them in a
+ 
+
+ align:start position:0%
+arichi uh now I have put them in a
+circle here because it's uh difficult to
+
+ align:start position:0%
+circle here because it's uh difficult to
+ 
+
+ align:start position:0%
+circle here because it's uh difficult to
+uh choose between them uh although farad
+
+ align:start position:0%
+uh choose between them uh although farad
+ 
+
+ align:start position:0%
+uh choose between them uh although farad
+zarich has now uh graduated uh Steve
+
+ align:start position:0%
+zarich has now uh graduated uh Steve
+ 
+
+ align:start position:0%
+zarich has now uh graduated uh Steve
+Smith is uh is uh going to be graduating
+
+ align:start position:0%
+Smith is uh is uh going to be graduating
+ 
+
+ align:start position:0%
+Smith is uh is uh going to be graduating
+soon and uh they've helped uh
+
+ align:start position:0%
+soon and uh they've helped uh
+ 
+
+ align:start position:0%
+soon and uh they've helped uh
+considerably in the in the creation of
+
+ align:start position:0%
+considerably in the in the creation of
+ 
+
+ align:start position:0%
+considerably in the in the creation of
+the of the demonstrations and also in
+
+ align:start position:0%
+the of the demonstrations and also in
+ 
+
+ align:start position:0%
+the of the demonstrations and also in
+the Creations creation of the of these
+
+ align:start position:0%
+the Creations creation of the of these
+ 
+
+ align:start position:0%
+the Creations creation of the of these
+visuals uh I hope that you found them uh
+
+ align:start position:0%
+visuals uh I hope that you found them uh
+ 
+
+ align:start position:0%
+visuals uh I hope that you found them uh
+readable and and without without a
+
+ align:start position:0%
+readable and and without without a
+ 
+
+ align:start position:0%
+readable and and without without a
+strain so I think I'm I'm almost dead on
+
+ align:start position:0%
+strain so I think I'm I'm almost dead on
+ 
+
+ align:start position:0%
+strain so I think I'm I'm almost dead on
+time and I'd like to thank you for uh
+
+ align:start position:0%
+time and I'd like to thank you for uh
+ 
+
+ align:start position:0%
+time and I'd like to thank you for uh
+for listening and and if you have any
+
+ align:start position:0%
+for listening and and if you have any
+ 
+
+ align:start position:0%
+for listening and and if you have any
+questions or so on I think you have our
+
+ align:start position:0%
+questions or so on I think you have our
+ 
+
+ align:start position:0%
+questions or so on I think you have our
+phone numbers here at MIT and you can
+
+ align:start position:0%
+phone numbers here at MIT and you can
+ 
+
+ align:start position:0%
+phone numbers here at MIT and you can
+call and we can continue with this uh
+
+ align:start position:0%
+call and we can continue with this uh
+ 
+
+ align:start position:0%
+call and we can continue with this uh
+conversation goodbye for now
\ No newline at end of file
diff --git a/0XjWRilFPQY.txt b/0XjWRilFPQY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4a2be198fec7d2d3510282fdf6e01631c8c5e50a
--- /dev/null
+++ b/0XjWRilFPQY.txt
@@ -0,0 +1,13384 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so welcome tonight
+
+ align:start position:0%
+so welcome tonight
+ 
+
+ align:start position:0%
+so welcome tonight
+a very special lecture for me tonight
+
+ align:start position:0%
+a very special lecture for me tonight
+ 
+
+ align:start position:0%
+a very special lecture for me tonight
+in more ways i can express
+
+ align:start position:0%
+in more ways i can express
+ 
+
+ align:start position:0%
+in more ways i can express
+this is the last of my lectures but i
+
+ align:start position:0%
+this is the last of my lectures but i
+ 
+
+ align:start position:0%
+this is the last of my lectures but i
+look forward to uh
+
+ align:start position:0%
+look forward to uh
+ 
+
+ align:start position:0%
+look forward to uh
+your lectures coming up i really do i've
+
+ align:start position:0%
+your lectures coming up i really do i've
+ 
+
+ align:start position:0%
+your lectures coming up i really do i've
+heard from the ts and from what i've
+
+ align:start position:0%
+heard from the ts and from what i've
+ 
+
+ align:start position:0%
+heard from the ts and from what i've
+seen from talking to many of you this is
+
+ align:start position:0%
+seen from talking to many of you this is
+ 
+
+ align:start position:0%
+seen from talking to many of you this is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+a really amazing set of projects this
+
+ align:start position:0%
+a really amazing set of projects this
+ 
+
+ align:start position:0%
+a really amazing set of projects this
+year more than any other year
+
+ align:start position:0%
+year more than any other year
+ 
+
+ align:start position:0%
+year more than any other year
+anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last week we asked what can biology do
+
+ align:start position:0%
+last week we asked what can biology do
+ 
+
+ align:start position:0%
+last week we asked what can biology do
+for computing
+
+ align:start position:0%
+for computing
+ 
+
+ align:start position:0%
+for computing
+and this week
+
+ align:start position:0%
+and this week
+ 
+
+ align:start position:0%
+and this week
+is going to be a little less nuts and
+
+ align:start position:0%
+is going to be a little less nuts and
+ 
+
+ align:start position:0%
+is going to be a little less nuts and
+bolts than usual the entire course as
+
+ align:start position:0%
+bolts than usual the entire course as
+ 
+
+ align:start position:0%
+bolts than usual the entire course as
+you all understand you're all
+
+ align:start position:0%
+you all understand you're all
+ 
+
+ align:start position:0%
+you all understand you're all
+self-selected to like survey courses or
+
+ align:start position:0%
+self-selected to like survey courses or
+ 
+
+ align:start position:0%
+self-selected to like survey courses or
+at least this one
+
+ align:start position:0%
+at least this one
+ 
+
+ align:start position:0%
+at least this one
+because you're still here and tonight's
+
+ align:start position:0%
+because you're still here and tonight's
+ 
+
+ align:start position:0%
+because you're still here and tonight's
+going to be more of a survey
+
+ align:start position:0%
+going to be more of a survey
+ 
+
+ align:start position:0%
+going to be more of a survey
+than ever before and to be talking about
+
+ align:start position:0%
+than ever before and to be talking about
+ 
+
+ align:start position:0%
+than ever before and to be talking about
+topics for which we don't have answers
+
+ align:start position:0%
+topics for which we don't have answers
+ 
+
+ align:start position:0%
+topics for which we don't have answers
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+for the most part there'll be some
+
+ align:start position:0%
+for the most part there'll be some
+ 
+
+ align:start position:0%
+for the most part there'll be some
+interesting details along the way
+
+ align:start position:0%
+interesting details along the way
+ 
+
+ align:start position:0%
+interesting details along the way
+but anyway instead of what computing can
+
+ align:start position:0%
+but anyway instead of what computing can
+ 
+
+ align:start position:0%
+but anyway instead of what computing can
+biology can do for computing this is
+
+ align:start position:0%
+biology can do for computing this is
+ 
+
+ align:start position:0%
+biology can do for computing this is
+more about what biology and computing
+
+ align:start position:0%
+more about what biology and computing
+ 
+
+ align:start position:0%
+more about what biology and computing
+can do for the world that's really what
+
+ align:start position:0%
+can do for the world that's really what
+ 
+
+ align:start position:0%
+can do for the world that's really what
+we want to do
+
+ align:start position:0%
+we want to do
+ 
+
+ align:start position:0%
+we want to do
+and also sort of the higher level
+
+ align:start position:0%
+and also sort of the higher level
+ 
+
+ align:start position:0%
+and also sort of the higher level
+network models that we can build since
+
+ align:start position:0%
+network models that we can build since
+ 
+
+ align:start position:0%
+network models that we can build since
+this is network number three
+
+ align:start position:0%
+this is network number three
+ 
+
+ align:start position:0%
+this is network number three
+so we'll start out
+
+ align:start position:0%
+so we'll start out
+ 
+
+ align:start position:0%
+so we'll start out
+we've been talking mainly about cellular
+
+ align:start position:0%
+we've been talking mainly about cellular
+ 
+
+ align:start position:0%
+we've been talking mainly about cellular
+models as our highest level of
+
+ align:start position:0%
+models as our highest level of
+ 
+
+ align:start position:0%
+models as our highest level of
+networking and so we'll talk about
+
+ align:start position:0%
+networking and so we'll talk about
+ 
+
+ align:start position:0%
+networking and so we'll talk about
+multi-cellular models
+
+ align:start position:0%
+multi-cellular models
+ 
+
+ align:start position:0%
+multi-cellular models
+in particular the sun multicellular
+
+ align:start position:0%
+in particular the sun multicellular
+ 
+
+ align:start position:0%
+in particular the sun multicellular
+models that you get that involve
+
+ align:start position:0%
+models that you get that involve
+ 
+
+ align:start position:0%
+models that you get that involve
+sensory integration integration of
+
+ align:start position:0%
+sensory integration integration of
+ 
+
+ align:start position:0%
+sensory integration integration of
+higher levels
+
+ align:start position:0%
+higher levels
+ 
+
+ align:start position:0%
+higher levels
+and then uh
+
+ align:start position:0%
+and then uh
+ 
+
+ align:start position:0%
+and then uh
+and then mult then uh multi-organ all
+
+ align:start position:0%
+and then mult then uh multi-organ all
+ 
+
+ align:start position:0%
+and then mult then uh multi-organ all
+the way up to multi-organ systems where
+
+ align:start position:0%
+the way up to multi-organ systems where
+ 
+
+ align:start position:0%
+the way up to multi-organ systems where
+we'll take an example sort of from the
+
+ align:start position:0%
+we'll take an example sort of from the
+ 
+
+ align:start position:0%
+we'll take an example sort of from the
+atomic scale all the way up to organ
+
+ align:start position:0%
+atomic scale all the way up to organ
+ 
+
+ align:start position:0%
+atomic scale all the way up to organ
+system failure
+
+ align:start position:0%
+system failure
+ 
+
+ align:start position:0%
+system failure
+and then uh and then we'll go from there
+
+ align:start position:0%
+and then uh and then we'll go from there
+ 
+
+ align:start position:0%
+and then uh and then we'll go from there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's start with multicellular models
+
+ align:start position:0%
+so let's start with multicellular models
+ 
+
+ align:start position:0%
+so let's start with multicellular models
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+this is something that i
+
+ align:start position:0%
+this is something that i
+ 
+
+ align:start position:0%
+this is something that i
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+i'll show you a few slides that will
+
+ align:start position:0%
+i'll show you a few slides that will
+ 
+
+ align:start position:0%
+i'll show you a few slides that will
+remind you of the first lecture they
+
+ align:start position:0%
+remind you of the first lecture they
+ 
+
+ align:start position:0%
+remind you of the first lecture they
+either were taken from the first lecture
+
+ align:start position:0%
+either were taken from the first lecture
+ 
+
+ align:start position:0%
+either were taken from the first lecture
+in this case this is a wildly different
+
+ align:start position:0%
+in this case this is a wildly different
+ 
+
+ align:start position:0%
+in this case this is a wildly different
+author and approach and so forth but
+
+ align:start position:0%
+author and approach and so forth but
+ 
+
+ align:start position:0%
+author and approach and so forth but
+it's the same lesson as from the first
+
+ align:start position:0%
+it's the same lesson as from the first
+ 
+
+ align:start position:0%
+it's the same lesson as from the first
+lecture which is we not only have these
+
+ align:start position:0%
+lecture which is we not only have these
+ 
+
+ align:start position:0%
+lecture which is we not only have these
+exponential curves going from the 1900s
+
+ align:start position:0%
+exponential curves going from the 1900s
+ 
+
+ align:start position:0%
+exponential curves going from the 1900s
+but they're super exponential they go up
+
+ align:start position:0%
+but they're super exponential they go up
+ 
+
+ align:start position:0%
+but they're super exponential they go up
+from the trend lines you get depend on
+
+ align:start position:0%
+from the trend lines you get depend on
+ 
+
+ align:start position:0%
+from the trend lines you get depend on
+which set of points you use the steepest
+
+ align:start position:0%
+which set of points you use the steepest
+ 
+
+ align:start position:0%
+which set of points you use the steepest
+one being the most recent one 1995
+
+ align:start position:0%
+one being the most recent one 1995
+ 
+
+ align:start position:0%
+one being the most recent one 1995
+and this basically is part of when it is
+
+ align:start position:0%
+and this basically is part of when it is
+ 
+
+ align:start position:0%
+and this basically is part of when it is
+that we will have computing power that
+
+ align:start position:0%
+that we will have computing power that
+ 
+
+ align:start position:0%
+that we will have computing power that
+might be on the order of
+
+ align:start position:0%
+might be on the order of
+ 
+
+ align:start position:0%
+might be on the order of
+an integrated
+
+ align:start position:0%
+an integrated
+ 
+
+ align:start position:0%
+an integrated
+human neural net we talked about neural
+
+ align:start position:0%
+human neural net we talked about neural
+ 
+
+ align:start position:0%
+human neural net we talked about neural
+nets last time kind of as a metaphor or
+
+ align:start position:0%
+nets last time kind of as a metaphor or
+ 
+
+ align:start position:0%
+nets last time kind of as a metaphor or
+as a an algorithm
+
+ align:start position:0%
+as a an algorithm
+ 
+
+ align:start position:0%
+as a an algorithm
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+when will we actually have a computer
+
+ align:start position:0%
+when will we actually have a computer
+ 
+
+ align:start position:0%
+when will we actually have a computer
+that has the capability of the human um
+
+ align:start position:0%
+that has the capability of the human um
+ 
+
+ align:start position:0%
+that has the capability of the human um
+cerebral cortex
+
+ align:start position:0%
+cerebral cortex
+ 
+
+ align:start position:0%
+cerebral cortex
+or entire integrated nervous system
+
+ align:start position:0%
+or entire integrated nervous system
+ 
+
+ align:start position:0%
+or entire integrated nervous system
+and the basis of those calculations that
+
+ align:start position:0%
+and the basis of those calculations that
+ 
+
+ align:start position:0%
+and the basis of those calculations that
+morovec made
+
+ align:start position:0%
+morovec made
+ 
+
+ align:start position:0%
+morovec made
+and and in lecture
+
+ align:start position:0%
+and and in lecture
+ 
+
+ align:start position:0%
+and and in lecture
+one kurzweil was the ex super
+
+ align:start position:0%
+one kurzweil was the ex super
+ 
+
+ align:start position:0%
+one kurzweil was the ex super
+exponential curve that i showed
+
+ align:start position:0%
+exponential curve that i showed
+ 
+
+ align:start position:0%
+exponential curve that i showed
+fourvec made them
+
+ align:start position:0%
+fourvec made them
+ 
+
+ align:start position:0%
+fourvec made them
+based on his studies on how the retina
+
+ align:start position:0%
+based on his studies on how the retina
+ 
+
+ align:start position:0%
+based on his studies on how the retina
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+those of you who have done a lot of
+
+ align:start position:0%
+those of you who have done a lot of
+ 
+
+ align:start position:0%
+those of you who have done a lot of
+computer programming
+
+ align:start position:0%
+computer programming
+ 
+
+ align:start position:0%
+computer programming
+uh that understanding how
+
+ align:start position:0%
+uh that understanding how
+ 
+
+ align:start position:0%
+uh that understanding how
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the retina works is probably one of the
+
+ align:start position:0%
+the retina works is probably one of the
+ 
+
+ align:start position:0%
+the retina works is probably one of the
+more intuitive of our various human
+
+ align:start position:0%
+more intuitive of our various human
+ 
+
+ align:start position:0%
+more intuitive of our various human
+senses
+
+ align:start position:0%
+senses
+ 
+
+ align:start position:0%
+senses
+uh in the sense that you can kind of
+
+ align:start position:0%
+uh in the sense that you can kind of
+ 
+
+ align:start position:0%
+uh in the sense that you can kind of
+program an algorithm that might do in
+
+ align:start position:0%
+program an algorithm that might do in
+ 
+
+ align:start position:0%
+program an algorithm that might do in
+the lower
+
+ align:start position:0%
+the lower
+ 
+
+ align:start position:0%
+the lower
+right of slide four edge or motion
+
+ align:start position:0%
+right of slide four edge or motion
+ 
+
+ align:start position:0%
+right of slide four edge or motion
+detection you know when a a frog sees a
+
+ align:start position:0%
+detection you know when a a frog sees a
+ 
+
+ align:start position:0%
+detection you know when a a frog sees a
+fly black and white go high contrast
+
+ align:start position:0%
+fly black and white go high contrast
+ 
+
+ align:start position:0%
+fly black and white go high contrast
+zoom across his visual field
+
+ align:start position:0%
+zoom across his visual field
+ 
+
+ align:start position:0%
+zoom across his visual field
+something goes off
+
+ align:start position:0%
+something goes off
+ 
+
+ align:start position:0%
+something goes off
+and you could write an algorithm that
+
+ align:start position:0%
+and you could write an algorithm that
+ 
+
+ align:start position:0%
+and you could write an algorithm that
+could do that given a few frames of uh
+
+ align:start position:0%
+could do that given a few frames of uh
+ 
+
+ align:start position:0%
+could do that given a few frames of uh
+of any kind of format
+
+ align:start position:0%
+of any kind of format
+ 
+
+ align:start position:0%
+of any kind of format
+so anyway but but there's there's been
+
+ align:start position:0%
+so anyway but but there's there's been
+ 
+
+ align:start position:0%
+so anyway but but there's there's been
+quite a literature on this subject and
+
+ align:start position:0%
+quite a literature on this subject and
+ 
+
+ align:start position:0%
+quite a literature on this subject and
+when you go through even the best
+
+ align:start position:0%
+when you go through even the best
+ 
+
+ align:start position:0%
+when you go through even the best
+algorithms right now for doing these
+
+ align:start position:0%
+algorithms right now for doing these
+ 
+
+ align:start position:0%
+algorithms right now for doing these
+kind of calculations and you figure out
+
+ align:start position:0%
+kind of calculations and you figure out
+ 
+
+ align:start position:0%
+kind of calculations and you figure out
+how long it takes uh
+
+ align:start position:0%
+how long it takes uh
+ 
+
+ align:start position:0%
+how long it takes uh
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+the retina is doing about 10 million
+
+ align:start position:0%
+the retina is doing about 10 million
+ 
+
+ align:start position:0%
+the retina is doing about 10 million
+detections per second and uh and then
+
+ align:start position:0%
+detections per second and uh and then
+ 
+
+ align:start position:0%
+detections per second and uh and then
+you scale up from that
+
+ align:start position:0%
+you scale up from that
+ 
+
+ align:start position:0%
+you scale up from that
+0.02 gram
+
+ align:start position:0%
+0.02 gram
+ 
+
+ align:start position:0%
+0.02 gram
+chunk of retina
+
+ align:start position:0%
+chunk of retina
+ 
+
+ align:start position:0%
+chunk of retina
+up to of the 1500 gram human brain and
+
+ align:start position:0%
+up to of the 1500 gram human brain and
+ 
+
+ align:start position:0%
+up to of the 1500 gram human brain and
+then you kind of get the extrapolation
+
+ align:start position:0%
+then you kind of get the extrapolation
+ 
+
+ align:start position:0%
+then you kind of get the extrapolation
+that was in the previous slide
+
+ align:start position:0%
+that was in the previous slide
+ 
+
+ align:start position:0%
+that was in the previous slide
+i think this is interesting both as an
+
+ align:start position:0%
+i think this is interesting both as an
+ 
+
+ align:start position:0%
+i think this is interesting both as an
+introduction to the kind of algorithms
+
+ align:start position:0%
+introduction to the kind of algorithms
+ 
+
+ align:start position:0%
+introduction to the kind of algorithms
+we'd like to think about when we think
+
+ align:start position:0%
+we'd like to think about when we think
+ 
+
+ align:start position:0%
+we'd like to think about when we think
+about integrating a multicellular system
+
+ align:start position:0%
+about integrating a multicellular system
+ 
+
+ align:start position:0%
+about integrating a multicellular system
+but also in terms of where the compute
+
+ align:start position:0%
+but also in terms of where the compute
+ 
+
+ align:start position:0%
+but also in terms of where the compute
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+and both biological and computational is
+
+ align:start position:0%
+and both biological and computational is
+ 
+
+ align:start position:0%
+and both biological and computational is
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+do we want to
+
+ align:start position:0%
+do we want to
+ 
+
+ align:start position:0%
+do we want to
+engineer biological systems to keep up
+
+ align:start position:0%
+engineer biological systems to keep up
+ 
+
+ align:start position:0%
+engineer biological systems to keep up
+with the copy the
+
+ align:start position:0%
+with the copy the
+ 
+
+ align:start position:0%
+with the copy the
+silicon or whatever other computational
+
+ align:start position:0%
+silicon or whatever other computational
+ 
+
+ align:start position:0%
+silicon or whatever other computational
+system we're using
+
+ align:start position:0%
+system we're using
+ 
+
+ align:start position:0%
+system we're using
+uh a decade or so from now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so i said that the the
+
+ align:start position:0%
+now so i said that the the
+ 
+
+ align:start position:0%
+now so i said that the the
+visual system is a relatively intuitive
+
+ align:start position:0%
+visual system is a relatively intuitive
+ 
+
+ align:start position:0%
+visual system is a relatively intuitive
+computational system to program
+
+ align:start position:0%
+computational system to program
+ 
+
+ align:start position:0%
+computational system to program
+in contrast i would say the old factory
+
+ align:start position:0%
+in contrast i would say the old factory
+ 
+
+ align:start position:0%
+in contrast i would say the old factory
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+is less intuitive at least for me
+
+ align:start position:0%
+is less intuitive at least for me
+ 
+
+ align:start position:0%
+is less intuitive at least for me
+we know now quite a bit about the
+
+ align:start position:0%
+we know now quite a bit about the
+ 
+
+ align:start position:0%
+we know now quite a bit about the
+molecular biology of the system there
+
+ align:start position:0%
+molecular biology of the system there
+ 
+
+ align:start position:0%
+molecular biology of the system there
+are a thousand receptors it's probably
+
+ align:start position:0%
+are a thousand receptors it's probably
+ 
+
+ align:start position:0%
+are a thousand receptors it's probably
+one of the largest classes
+
+ align:start position:0%
+one of the largest classes
+ 
+
+ align:start position:0%
+one of the largest classes
+of genomic repeated proteins
+
+ align:start position:0%
+of genomic repeated proteins
+ 
+
+ align:start position:0%
+of genomic repeated proteins
+and these receptors are in the same
+
+ align:start position:0%
+and these receptors are in the same
+ 
+
+ align:start position:0%
+and these receptors are in the same
+family as the receptors that are the
+
+ align:start position:0%
+family as the receptors that are the
+ 
+
+ align:start position:0%
+family as the receptors that are the
+major class of drug receptors
+
+ align:start position:0%
+major class of drug receptors
+ 
+
+ align:start position:0%
+major class of drug receptors
+protein coupled receptors
+
+ align:start position:0%
+protein coupled receptors
+ 
+
+ align:start position:0%
+protein coupled receptors
+and there is
+
+ align:start position:0%
+and there is
+ 
+
+ align:start position:0%
+and there is
+basically one receptor per cell which is
+
+ align:start position:0%
+basically one receptor per cell which is
+ 
+
+ align:start position:0%
+basically one receptor per cell which is
+quite a trick right because you got one
+
+ align:start position:0%
+quite a trick right because you got one
+ 
+
+ align:start position:0%
+quite a trick right because you got one
+receptor from mom and one for dad and
+
+ align:start position:0%
+receptor from mom and one for dad and
+ 
+
+ align:start position:0%
+receptor from mom and one for dad and
+you've got uh thousands of receptors but
+
+ align:start position:0%
+you've got uh thousands of receptors but
+ 
+
+ align:start position:0%
+you've got uh thousands of receptors but
+there's basically one per cell and they
+
+ align:start position:0%
+there's basically one per cell and they
+ 
+
+ align:start position:0%
+there's basically one per cell and they
+and they detect uh
+
+ align:start position:0%
+and they detect uh
+ 
+
+ align:start position:0%
+and they detect uh
+olfactory uh molecule concentrations
+
+ align:start position:0%
+olfactory uh molecule concentrations
+ 
+
+ align:start position:0%
+olfactory uh molecule concentrations
+uh over about seven logs
+
+ align:start position:0%
+uh over about seven logs
+ 
+
+ align:start position:0%
+uh over about seven logs
+um where the concentration thresh where
+
+ align:start position:0%
+um where the concentration thresh where
+ 
+
+ align:start position:0%
+um where the concentration thresh where
+where they can detect
+
+ align:start position:0%
+where they can detect
+ 
+
+ align:start position:0%
+where they can detect
+uh uh a concentration threshold with a
+
+ align:start position:0%
+uh uh a concentration threshold with a
+ 
+
+ align:start position:0%
+uh uh a concentration threshold with a
+particular standard deviation
+
+ align:start position:0%
+particular standard deviation
+ 
+
+ align:start position:0%
+particular standard deviation
+now this this is the beginnings of the
+
+ align:start position:0%
+now this this is the beginnings of the
+ 
+
+ align:start position:0%
+now this this is the beginnings of the
+model just stating the facts that you
+
+ align:start position:0%
+model just stating the facts that you
+ 
+
+ align:start position:0%
+model just stating the facts that you
+know about it you've got when you look
+
+ align:start position:0%
+know about it you've got when you look
+ 
+
+ align:start position:0%
+know about it you've got when you look
+at the neuroanatomy you've got
+
+ align:start position:0%
+at the neuroanatomy you've got
+ 
+
+ align:start position:0%
+at the neuroanatomy you've got
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+deodorant molecules down at the very
+
+ align:start position:0%
+deodorant molecules down at the very
+ 
+
+ align:start position:0%
+deodorant molecules down at the very
+bottom of this figure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cilia olfactory neurons which is a
+
+ align:start position:0%
+cilia olfactory neurons which is a
+ 
+
+ align:start position:0%
+cilia olfactory neurons which is a
+primary uh signal transduction this then
+
+ align:start position:0%
+primary uh signal transduction this then
+ 
+
+ align:start position:0%
+primary uh signal transduction this then
+goes up where it's integrated
+
+ align:start position:0%
+goes up where it's integrated
+ 
+
+ align:start position:0%
+goes up where it's integrated
+in the glomeruli and you can think of
+
+ align:start position:0%
+in the glomeruli and you can think of
+ 
+
+ align:start position:0%
+in the glomeruli and you can think of
+this sort of like the neural nets we
+
+ align:start position:0%
+this sort of like the neural nets we
+ 
+
+ align:start position:0%
+this sort of like the neural nets we
+were talking about last time where you
+
+ align:start position:0%
+were talking about last time where you
+ 
+
+ align:start position:0%
+were talking about last time where you
+had these
+
+ align:start position:0%
+had these
+ 
+
+ align:start position:0%
+had these
+interneurons you had the the
+
+ align:start position:0%
+interneurons you had the the
+ 
+
+ align:start position:0%
+interneurons you had the the
+extra layer that we showed was so
+
+ align:start position:0%
+extra layer that we showed was so
+ 
+
+ align:start position:0%
+extra layer that we showed was so
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the thing that's amazing about this
+
+ align:start position:0%
+and the thing that's amazing about this
+ 
+
+ align:start position:0%
+and the thing that's amazing about this
+system are are
+
+ align:start position:0%
+system are are
+ 
+
+ align:start position:0%
+system are are
+lodged in these
+
+ align:start position:0%
+lodged in these
+ 
+
+ align:start position:0%
+lodged in these
+four basic olfactory facts which i take
+
+ align:start position:0%
+four basic olfactory facts which i take
+ 
+
+ align:start position:0%
+four basic olfactory facts which i take
+from hotfield's uh
+
+ align:start position:0%
+from hotfield's uh
+ 
+
+ align:start position:0%
+from hotfield's uh
+work which is really just like this is
+
+ align:start position:0%
+work which is really just like this is
+ 
+
+ align:start position:0%
+work which is really just like this is
+the same hot field that introduced us to
+
+ align:start position:0%
+the same hot field that introduced us to
+ 
+
+ align:start position:0%
+the same hot field that introduced us to
+neuro or really
+
+ align:start position:0%
+neuro or really
+ 
+
+ align:start position:0%
+neuro or really
+champion the concept of neural nets as a
+
+ align:start position:0%
+champion the concept of neural nets as a
+ 
+
+ align:start position:0%
+champion the concept of neural nets as a
+computational algorithmic metaphor
+
+ align:start position:0%
+computational algorithmic metaphor
+ 
+
+ align:start position:0%
+computational algorithmic metaphor
+and here
+
+ align:start position:0%
+and here
+ 
+
+ align:start position:0%
+and here
+the idea is
+
+ align:start position:0%
+the idea is
+ 
+
+ align:start position:0%
+the idea is
+you have odor and memory recognition
+
+ align:start position:0%
+you have odor and memory recognition
+ 
+
+ align:start position:0%
+you have odor and memory recognition
+you have background elimination
+
+ align:start position:0%
+you have background elimination
+ 
+
+ align:start position:0%
+you have background elimination
+as just like
+
+ align:start position:0%
+as just like
+ 
+
+ align:start position:0%
+as just like
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know how your eyes adapt to a mostly
+
+ align:start position:0%
+you know how your eyes adapt to a mostly
+ 
+
+ align:start position:0%
+you know how your eyes adapt to a mostly
+red room your your nose is great your
+
+ align:start position:0%
+red room your your nose is great your
+ 
+
+ align:start position:0%
+red room your your nose is great your
+your whole factory system is great at
+
+ align:start position:0%
+your whole factory system is great at
+ 
+
+ align:start position:0%
+your whole factory system is great at
+adapting to uh background
+
+ align:start position:0%
+adapting to uh background
+ 
+
+ align:start position:0%
+adapting to uh background
+odorants so you have one
+
+ align:start position:0%
+odorants so you have one
+ 
+
+ align:start position:0%
+odorants so you have one
+known and one unknown thoroughly mixed
+
+ align:start position:0%
+known and one unknown thoroughly mixed
+ 
+
+ align:start position:0%
+known and one unknown thoroughly mixed
+number three you can have component
+
+ align:start position:0%
+number three you can have component
+ 
+
+ align:start position:0%
+number three you can have component
+separation you can have a few different
+
+ align:start position:0%
+separation you can have a few different
+ 
+
+ align:start position:0%
+separation you can have a few different
+odors at once
+
+ align:start position:0%
+odors at once
+ 
+
+ align:start position:0%
+odors at once
+you have odor
+
+ align:start position:0%
+you have odor
+ 
+
+ align:start position:0%
+you have odor
+separation where you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unknowns
+
+ align:start position:0%
+unknowns
+ 
+
+ align:start position:0%
+unknowns
+and each of these tasks
+
+ align:start position:0%
+and each of these tasks
+ 
+
+ align:start position:0%
+and each of these tasks
+i mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the combination of these is quite
+
+ align:start position:0%
+the combination of these is quite
+ 
+
+ align:start position:0%
+the combination of these is quite
+remarkable so the basis of the model
+
+ align:start position:0%
+remarkable so the basis of the model
+ 
+
+ align:start position:0%
+remarkable so the basis of the model
+that hotfield has proposed
+
+ align:start position:0%
+that hotfield has proposed
+ 
+
+ align:start position:0%
+that hotfield has proposed
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+is this you have a coverage
+
+ align:start position:0%
+is this you have a coverage
+ 
+
+ align:start position:0%
+is this you have a coverage
+for each of the i receptors where i goes
+
+ align:start position:0%
+for each of the i receptors where i goes
+ 
+
+ align:start position:0%
+for each of the i receptors where i goes
+from one to a thousand this will vary
+
+ align:start position:0%
+from one to a thousand this will vary
+ 
+
+ align:start position:0%
+from one to a thousand this will vary
+depending on the organism mice have
+
+ align:start position:0%
+depending on the organism mice have
+ 
+
+ align:start position:0%
+depending on the organism mice have
+twice as many as we do probably so on
+
+ align:start position:0%
+twice as many as we do probably so on
+ 
+
+ align:start position:0%
+twice as many as we do probably so on
+but the coverage of each the of each of
+
+ align:start position:0%
+but the coverage of each the of each of
+ 
+
+ align:start position:0%
+but the coverage of each the of each of
+those receptors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to the minimum coverage
+
+ align:start position:0%
+is equal to the minimum coverage
+ 
+
+ align:start position:0%
+is equal to the minimum coverage
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+for the concentration of the target
+
+ align:start position:0%
+for the concentration of the target
+ 
+
+ align:start position:0%
+for the concentration of the target
+where the say the target is the target
+
+ align:start position:0%
+where the say the target is the target
+ 
+
+ align:start position:0%
+where the say the target is the target
+odorant that you're looking for
+
+ align:start position:0%
+odorant that you're looking for
+ 
+
+ align:start position:0%
+odorant that you're looking for
+over the
+
+ align:start position:0%
+over the
+ 
+
+ align:start position:0%
+over the
+concentration that's the threshold for
+
+ align:start position:0%
+concentration that's the threshold for
+ 
+
+ align:start position:0%
+concentration that's the threshold for
+firing that neuron for that target
+
+ align:start position:0%
+firing that neuron for that target
+ 
+
+ align:start position:0%
+firing that neuron for that target
+threshold of t
+
+ align:start position:0%
+threshold of t
+ 
+
+ align:start position:0%
+threshold of t
+then you multiply that times either one
+
+ align:start position:0%
+then you multiply that times either one
+ 
+
+ align:start position:0%
+then you multiply that times either one
+or some fraction it's one if you really
+
+ align:start position:0%
+or some fraction it's one if you really
+ 
+
+ align:start position:0%
+or some fraction it's one if you really
+hit the target
+
+ align:start position:0%
+hit the target
+ 
+
+ align:start position:0%
+hit the target
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+this fraction of for that particular
+
+ align:start position:0%
+this fraction of for that particular
+ 
+
+ align:start position:0%
+this fraction of for that particular
+receptor and that particular target
+
+ align:start position:0%
+receptor and that particular target
+ 
+
+ align:start position:0%
+receptor and that particular target
+you've got some crosstalk and the amount
+
+ align:start position:0%
+you've got some crosstalk and the amount
+ 
+
+ align:start position:0%
+you've got some crosstalk and the amount
+of crosstalk
+
+ align:start position:0%
+of crosstalk
+ 
+
+ align:start position:0%
+of crosstalk
+uh you can think of this as a field of
+
+ align:start position:0%
+uh you can think of this as a field of
+ 
+
+ align:start position:0%
+uh you can think of this as a field of
+receptors which are all uh
+
+ align:start position:0%
+receptors which are all uh
+ 
+
+ align:start position:0%
+receptors which are all uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+have variable binding and that binding
+
+ align:start position:0%
+have variable binding and that binding
+ 
+
+ align:start position:0%
+have variable binding and that binding
+is over these seven six or seven logs
+
+ align:start position:0%
+is over these seven six or seven logs
+ 
+
+ align:start position:0%
+is over these seven six or seven logs
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um and that's this just reflects that
+
+ align:start position:0%
+um and that's this just reflects that
+ 
+
+ align:start position:0%
+um and that's this just reflects that
+same thing that we were talking about
+
+ align:start position:0%
+same thing that we were talking about
+ 
+
+ align:start position:0%
+same thing that we were talking about
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+so that so the the total
+
+ align:start position:0%
+so that so the the total
+ 
+
+ align:start position:0%
+so that so the the total
+uh number of inputs going to the next
+
+ align:start position:0%
+uh number of inputs going to the next
+ 
+
+ align:start position:0%
+uh number of inputs going to the next
+layer in the neural net the coverage
+
+ align:start position:0%
+layer in the neural net the coverage
+ 
+
+ align:start position:0%
+layer in the neural net the coverage
+here is me the sum of this
+
+ align:start position:0%
+here is me the sum of this
+ 
+
+ align:start position:0%
+here is me the sum of this
+of this target
+
+ align:start position:0%
+of this target
+ 
+
+ align:start position:0%
+of this target
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+the background signal so the first term
+
+ align:start position:0%
+the background signal so the first term
+ 
+
+ align:start position:0%
+the background signal so the first term
+is target and the right hand term is the
+
+ align:start position:0%
+is target and the right hand term is the
+ 
+
+ align:start position:0%
+is target and the right hand term is the
+background as you can see they have the
+
+ align:start position:0%
+background as you can see they have the
+ 
+
+ align:start position:0%
+background as you can see they have the
+same form the same threshold and
+
+ align:start position:0%
+same form the same threshold and
+ 
+
+ align:start position:0%
+same form the same threshold and
+concentration c sub b is concentration
+
+ align:start position:0%
+concentration c sub b is concentration
+ 
+
+ align:start position:0%
+concentration c sub b is concentration
+background
+
+ align:start position:0%
+background
+ 
+
+ align:start position:0%
+background
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+so let's see how this plays out when you
+
+ align:start position:0%
+so let's see how this plays out when you
+ 
+
+ align:start position:0%
+so let's see how this plays out when you
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+try this out
+
+ align:start position:0%
+try this out
+ 
+
+ align:start position:0%
+try this out
+in a olfactory processing problem here
+
+ align:start position:0%
+in a olfactory processing problem here
+ 
+
+ align:start position:0%
+in a olfactory processing problem here
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+outer space
+
+ align:start position:0%
+outer space
+ 
+
+ align:start position:0%
+outer space
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+what what you have here is
+
+ align:start position:0%
+what what you have here is
+ 
+
+ align:start position:0%
+what what you have here is
+80 different neurons is the y-axis at
+
+ align:start position:0%
+80 different neurons is the y-axis at
+ 
+
+ align:start position:0%
+80 different neurons is the y-axis at
+the top of slide seven
+
+ align:start position:0%
+the top of slide seven
+ 
+
+ align:start position:0%
+the top of slide seven
+and then across the bottom uh sorry
+
+ align:start position:0%
+and then across the bottom uh sorry
+ 
+
+ align:start position:0%
+and then across the bottom uh sorry
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+the x-axis is time in milliseconds going
+
+ align:start position:0%
+the x-axis is time in milliseconds going
+ 
+
+ align:start position:0%
+the x-axis is time in milliseconds going
+from zero to 800 milliseconds and this
+
+ align:start position:0%
+from zero to 800 milliseconds and this
+ 
+
+ align:start position:0%
+from zero to 800 milliseconds and this
+is all uh modeled on
+
+ align:start position:0%
+is all uh modeled on
+ 
+
+ align:start position:0%
+is all uh modeled on
+on fairly realistic parameters
+
+ align:start position:0%
+on fairly realistic parameters
+ 
+
+ align:start position:0%
+on fairly realistic parameters
+based on experiments
+
+ align:start position:0%
+based on experiments
+ 
+
+ align:start position:0%
+based on experiments
+and so what you have here is 80 adapting
+
+ align:start position:0%
+and so what you have here is 80 adapting
+ 
+
+ align:start position:0%
+and so what you have here is 80 adapting
+neurons
+
+ align:start position:0%
+neurons
+ 
+
+ align:start position:0%
+neurons
+and what you're doing is two sniffs of a
+
+ align:start position:0%
+and what you're doing is two sniffs of a
+ 
+
+ align:start position:0%
+and what you're doing is two sniffs of a
+mixed odor that's what this is modeling
+
+ align:start position:0%
+mixed odor that's what this is modeling
+ 
+
+ align:start position:0%
+mixed odor that's what this is modeling
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+first you have a 100 to 500 milliseconds
+
+ align:start position:0%
+first you have a 100 to 500 milliseconds
+ 
+
+ align:start position:0%
+first you have a 100 to 500 milliseconds
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the the range from so so you have
+
+ align:start position:0%
+the the range from so so you have
+ 
+
+ align:start position:0%
+the the range from so so you have
+you can see that something's happening
+
+ align:start position:0%
+you can see that something's happening
+ 
+
+ align:start position:0%
+you can see that something's happening
+at 100 milliseconds and up to 500 you
+
+ align:start position:0%
+at 100 milliseconds and up to 500 you
+ 
+
+ align:start position:0%
+at 100 milliseconds and up to 500 you
+have a mixed odor which is 50 parts of x
+
+ align:start position:0%
+have a mixed odor which is 50 parts of x
+ 
+
+ align:start position:0%
+have a mixed odor which is 50 parts of x
+plus a thousand parts of y
+
+ align:start position:0%
+plus a thousand parts of y
+ 
+
+ align:start position:0%
+plus a thousand parts of y
+per thousand times uh y
+
+ align:start position:0%
+per thousand times uh y
+ 
+
+ align:start position:0%
+per thousand times uh y
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and then at 500 milliseconds you change
+
+ align:start position:0%
+and then at 500 milliseconds you change
+ 
+
+ align:start position:0%
+and then at 500 milliseconds you change
+this this ratio very slightly you see
+
+ align:start position:0%
+this this ratio very slightly you see
+ 
+
+ align:start position:0%
+this this ratio very slightly you see
+just uh up x by 75 and y up to from a
+
+ align:start position:0%
+just uh up x by 75 and y up to from a
+ 
+
+ align:start position:0%
+just uh up x by 75 and y up to from a
+thousand to eleven hundred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the paradigm
+
+ align:start position:0%
+so that's the paradigm
+ 
+
+ align:start position:0%
+so that's the paradigm
+fifty a thousand to seventy five and
+
+ align:start position:0%
+fifty a thousand to seventy five and
+ 
+
+ align:start position:0%
+fifty a thousand to seventy five and
+eleven hundred and then sniff at a
+
+ align:start position:0%
+eleven hundred and then sniff at a
+ 
+
+ align:start position:0%
+eleven hundred and then sniff at a
+hundred milliseconds that that
+
+ align:start position:0%
+hundred milliseconds that that
+ 
+
+ align:start position:0%
+hundred milliseconds that that
+that first one that mixed odor
+
+ align:start position:0%
+that first one that mixed odor
+ 
+
+ align:start position:0%
+that first one that mixed odor
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it activates more than half the neurons
+
+ align:start position:0%
+it activates more than half the neurons
+ 
+
+ align:start position:0%
+it activates more than half the neurons
+so this is not like your retina where if
+
+ align:start position:0%
+so this is not like your retina where if
+ 
+
+ align:start position:0%
+so this is not like your retina where if
+you have a single point source it'll
+
+ align:start position:0%
+you have a single point source it'll
+ 
+
+ align:start position:0%
+you have a single point source it'll
+activate that one
+
+ align:start position:0%
+activate that one
+ 
+
+ align:start position:0%
+activate that one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+rod cell or maybe a cinder surround uh
+
+ align:start position:0%
+rod cell or maybe a cinder surround uh
+ 
+
+ align:start position:0%
+rod cell or maybe a cinder surround uh
+sort of effect
+
+ align:start position:0%
+sort of effect
+ 
+
+ align:start position:0%
+sort of effect
+but it's really activating half of the
+
+ align:start position:0%
+but it's really activating half of the
+ 
+
+ align:start position:0%
+but it's really activating half of the
+neurons okay
+
+ align:start position:0%
+neurons okay
+ 
+
+ align:start position:0%
+neurons okay
+and then the change smith at 500
+
+ align:start position:0%
+and then the change smith at 500
+ 
+
+ align:start position:0%
+and then the change smith at 500
+milliseconds remember just these two
+
+ align:start position:0%
+milliseconds remember just these two
+ 
+
+ align:start position:0%
+milliseconds remember just these two
+small changes
+
+ align:start position:0%
+small changes
+ 
+
+ align:start position:0%
+small changes
+is almost invisible
+
+ align:start position:0%
+is almost invisible
+ 
+
+ align:start position:0%
+is almost invisible
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's what you're seeing uh
+
+ align:start position:0%
+that's what you're seeing uh
+ 
+
+ align:start position:0%
+that's what you're seeing uh
+right here okay
+
+ align:start position:0%
+right here okay
+ 
+
+ align:start position:0%
+right here okay
+is this this huge this huge swamping
+
+ align:start position:0%
+is this this huge this huge swamping
+ 
+
+ align:start position:0%
+is this this huge this huge swamping
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+in in b so that that's what happened in
+
+ align:start position:0%
+in in b so that that's what happened in
+ 
+
+ align:start position:0%
+in in b so that that's what happened in
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+you've now uh
+
+ align:start position:0%
+you've now uh
+ 
+
+ align:start position:0%
+you've now uh
+plotting instead of
+
+ align:start position:0%
+plotting instead of
+ 
+
+ align:start position:0%
+plotting instead of
+individual neurons you're doing the
+
+ align:start position:0%
+individual neurons you're doing the
+ 
+
+ align:start position:0%
+individual neurons you're doing the
+instantaneous rate in hertz
+
+ align:start position:0%
+instantaneous rate in hertz
+ 
+
+ align:start position:0%
+instantaneous rate in hertz
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh when you could you can see the sixth
+
+ align:start position:0%
+uh when you could you can see the sixth
+ 
+
+ align:start position:0%
+uh when you could you can see the sixth
+second smith here as the as at the 500
+
+ align:start position:0%
+second smith here as the as at the 500
+ 
+
+ align:start position:0%
+second smith here as the as at the 500
+milliseconds which even though you
+
+ align:start position:0%
+milliseconds which even though you
+ 
+
+ align:start position:0%
+milliseconds which even though you
+really can't see it in the corresponding
+
+ align:start position:0%
+really can't see it in the corresponding
+ 
+
+ align:start position:0%
+really can't see it in the corresponding
+point where you're looking at all these
+
+ align:start position:0%
+point where you're looking at all these
+ 
+
+ align:start position:0%
+point where you're looking at all these
+individual neurons
+
+ align:start position:0%
+individual neurons
+ 
+
+ align:start position:0%
+individual neurons
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+so you can see that even a 20
+
+ align:start position:0%
+so you can see that even a 20
+ 
+
+ align:start position:0%
+so you can see that even a 20
+spread
+
+ align:start position:0%
+spread
+ 
+
+ align:start position:0%
+spread
+in the in one of these parameters is
+
+ align:start position:0%
+in the in one of these parameters is
+ 
+
+ align:start position:0%
+in the in one of these parameters is
+enough to uh to get this kind of uh
+
+ align:start position:0%
+enough to uh to get this kind of uh
+ 
+
+ align:start position:0%
+enough to uh to get this kind of uh
+easily detectable signal
+
+ align:start position:0%
+easily detectable signal
+ 
+
+ align:start position:0%
+easily detectable signal
+now that's the example of a simulation
+
+ align:start position:0%
+now that's the example of a simulation
+ 
+
+ align:start position:0%
+now that's the example of a simulation
+that's not a simulation a particular
+
+ align:start position:0%
+that's not a simulation a particular
+ 
+
+ align:start position:0%
+that's not a simulation a particular
+experimental data set but it's based on
+
+ align:start position:0%
+experimental data set but it's based on
+ 
+
+ align:start position:0%
+experimental data set but it's based on
+experimental data sets and the code this
+
+ align:start position:0%
+experimental data sets and the code this
+ 
+
+ align:start position:0%
+experimental data sets and the code this
+is not mathematica this is map lab which
+
+ align:start position:0%
+is not mathematica this is map lab which
+ 
+
+ align:start position:0%
+is not mathematica this is map lab which
+we almost we could have interchangeably
+
+ align:start position:0%
+we almost we could have interchangeably
+ 
+
+ align:start position:0%
+we almost we could have interchangeably
+taught in this course and you can see
+
+ align:start position:0%
+taught in this course and you can see
+ 
+
+ align:start position:0%
+taught in this course and you can see
+here in green are the comments and you
+
+ align:start position:0%
+here in green are the comments and you
+ 
+
+ align:start position:0%
+here in green are the comments and you
+can see some of the things that we've
+
+ align:start position:0%
+can see some of the things that we've
+ 
+
+ align:start position:0%
+can see some of the things that we've
+been talking about here
+
+ align:start position:0%
+been talking about here
+ 
+
+ align:start position:0%
+been talking about here
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+the number of receptor types is actually
+
+ align:start position:0%
+the number of receptor types is actually
+ 
+
+ align:start position:0%
+the number of receptor types is actually
+here two thousand one thousand you see
+
+ align:start position:0%
+here two thousand one thousand you see
+ 
+
+ align:start position:0%
+here two thousand one thousand you see
+the the target remember i said could be
+
+ align:start position:0%
+the the target remember i said could be
+ 
+
+ align:start position:0%
+the the target remember i said could be
+some random number that that goes over
+
+ align:start position:0%
+some random number that that goes over
+ 
+
+ align:start position:0%
+some random number that that goes over
+six logarithms well the way that's done
+
+ align:start position:0%
+six logarithms well the way that's done
+ 
+
+ align:start position:0%
+six logarithms well the way that's done
+here is here's a random number generated
+
+ align:start position:0%
+here is here's a random number generated
+ 
+
+ align:start position:0%
+here is here's a random number generated
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and and you you generate as the log of
+
+ align:start position:0%
+and and you you generate as the log of
+ 
+
+ align:start position:0%
+and and you you generate as the log of
+the target and then you get the target
+
+ align:start position:0%
+the target and then you get the target
+ 
+
+ align:start position:0%
+the target and then you get the target
+by taking the exponential it's very
+
+ align:start position:0%
+by taking the exponential it's very
+ 
+
+ align:start position:0%
+by taking the exponential it's very
+straightforward
+
+ align:start position:0%
+straightforward
+ 
+
+ align:start position:0%
+straightforward
+and the code goes on from there
+
+ align:start position:0%
+and the code goes on from there
+ 
+
+ align:start position:0%
+and the code goes on from there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this brings us to a very interesting
+
+ align:start position:0%
+now this brings us to a very interesting
+ 
+
+ align:start position:0%
+now this brings us to a very interesting
+point um
+
+ align:start position:0%
+point um
+ 
+
+ align:start position:0%
+point um
+since these three lectures on networks
+
+ align:start position:0%
+since these three lectures on networks
+ 
+
+ align:start position:0%
+since these three lectures on networks
+and in a certain sense the whole course
+
+ align:start position:0%
+and in a certain sense the whole course
+ 
+
+ align:start position:0%
+and in a certain sense the whole course
+is building for
+
+ align:start position:0%
+is building for
+ 
+
+ align:start position:0%
+is building for
+systems biology network models
+
+ align:start position:0%
+systems biology network models
+ 
+
+ align:start position:0%
+systems biology network models
+and for these models be useful in the
+
+ align:start position:0%
+and for these models be useful in the
+ 
+
+ align:start position:0%
+and for these models be useful in the
+same sense that the models we had for
+
+ align:start position:0%
+same sense that the models we had for
+ 
+
+ align:start position:0%
+same sense that the models we had for
+x-ray crystallography and the models
+
+ align:start position:0%
+x-ray crystallography and the models
+ 
+
+ align:start position:0%
+x-ray crystallography and the models
+we've had for
+
+ align:start position:0%
+we've had for
+ 
+
+ align:start position:0%
+we've had for
+genome interpretation in terms of
+
+ align:start position:0%
+genome interpretation in terms of
+ 
+
+ align:start position:0%
+genome interpretation in terms of
+homology and sequence
+
+ align:start position:0%
+homology and sequence
+ 
+
+ align:start position:0%
+homology and sequence
+folding and so forth
+
+ align:start position:0%
+folding and so forth
+ 
+
+ align:start position:0%
+folding and so forth
+needed to be shared it's the mock the
+
+ align:start position:0%
+needed to be shared it's the mock the
+ 
+
+ align:start position:0%
+needed to be shared it's the mock the
+models even more than the data need to
+
+ align:start position:0%
+models even more than the data need to
+ 
+
+ align:start position:0%
+models even more than the data need to
+be shareable because in a certain sense
+
+ align:start position:0%
+be shareable because in a certain sense
+ 
+
+ align:start position:0%
+be shareable because in a certain sense
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+even modest manipulation of the data
+
+ align:start position:0%
+even modest manipulation of the data
+ 
+
+ align:start position:0%
+even modest manipulation of the data
+involves some usually involves some good
+
+ align:start position:0%
+involves some usually involves some good
+ 
+
+ align:start position:0%
+involves some usually involves some good
+model behind it and so these are some of
+
+ align:start position:0%
+model behind it and so these are some of
+ 
+
+ align:start position:0%
+model behind it and so these are some of
+the work groups that are working on
+
+ align:start position:0%
+the work groups that are working on
+ 
+
+ align:start position:0%
+the work groups that are working on
+uh different modeling schemes in
+
+ align:start position:0%
+uh different modeling schemes in
+ 
+
+ align:start position:0%
+uh different modeling schemes in
+particular i should point out the the
+
+ align:start position:0%
+particular i should point out the the
+ 
+
+ align:start position:0%
+particular i should point out the the
+biospice is now darpa biospice and svml
+
+ align:start position:0%
+biospice is now darpa biospice and svml
+ 
+
+ align:start position:0%
+biospice is now darpa biospice and svml
+is kind of a growing part of that system
+
+ align:start position:0%
+is kind of a growing part of that system
+ 
+
+ align:start position:0%
+is kind of a growing part of that system
+biology markup language is a way of
+
+ align:start position:0%
+biology markup language is a way of
+ 
+
+ align:start position:0%
+biology markup language is a way of
+sharing this data
+
+ align:start position:0%
+sharing this data
+ 
+
+ align:start position:0%
+sharing this data
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+as yet there's not the kind of
+
+ align:start position:0%
+as yet there's not the kind of
+ 
+
+ align:start position:0%
+as yet there's not the kind of
+convention that we have in
+
+ align:start position:0%
+convention that we have in
+ 
+
+ align:start position:0%
+convention that we have in
+crystallography and dna sequencing where
+
+ align:start position:0%
+crystallography and dna sequencing where
+ 
+
+ align:start position:0%
+crystallography and dna sequencing where
+you submit at the time that you publish
+
+ align:start position:0%
+you submit at the time that you publish
+ 
+
+ align:start position:0%
+you submit at the time that you publish
+a paper you submit
+
+ align:start position:0%
+a paper you submit
+ 
+
+ align:start position:0%
+a paper you submit
+your data and model data slash model
+
+ align:start position:0%
+your data and model data slash model
+ 
+
+ align:start position:0%
+your data and model data slash model
+with an accession number to the database
+
+ align:start position:0%
+with an accession number to the database
+ 
+
+ align:start position:0%
+with an accession number to the database
+or else you don't get it published we're
+
+ align:start position:0%
+or else you don't get it published we're
+ 
+
+ align:start position:0%
+or else you don't get it published we're
+nowhere near that now for the rest of
+
+ align:start position:0%
+nowhere near that now for the rest of
+ 
+
+ align:start position:0%
+nowhere near that now for the rest of
+biology but these kind of efforts
+
+ align:start position:0%
+biology but these kind of efforts
+ 
+
+ align:start position:0%
+biology but these kind of efforts
+probably are moving in that direction
+
+ align:start position:0%
+probably are moving in that direction
+ 
+
+ align:start position:0%
+probably are moving in that direction
+and you can see that that the features
+
+ align:start position:0%
+and you can see that that the features
+ 
+
+ align:start position:0%
+and you can see that that the features
+of each of these
+
+ align:start position:0%
+of each of these
+ 
+
+ align:start position:0%
+of each of these
+are some of the things that we've been
+
+ align:start position:0%
+are some of the things that we've been
+ 
+
+ align:start position:0%
+are some of the things that we've been
+talking about before you've got
+
+ align:start position:0%
+talking about before you've got
+ 
+
+ align:start position:0%
+talking about before you've got
+stochastic modeling
+
+ align:start position:0%
+stochastic modeling
+ 
+
+ align:start position:0%
+stochastic modeling
+kinetic modeling enzyme receptor
+
+ align:start position:0%
+kinetic modeling enzyme receptor
+ 
+
+ align:start position:0%
+kinetic modeling enzyme receptor
+sort of cell geometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neural nets
+
+ align:start position:0%
+neural nets
+ 
+
+ align:start position:0%
+neural nets
+and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is by no means comprehensive and
+
+ align:start position:0%
+this is by no means comprehensive and
+ 
+
+ align:start position:0%
+this is by no means comprehensive and
+their hypertext links here if you really
+
+ align:start position:0%
+their hypertext links here if you really
+ 
+
+ align:start position:0%
+their hypertext links here if you really
+want to dig into them and some of the
+
+ align:start position:0%
+want to dig into them and some of the
+ 
+
+ align:start position:0%
+want to dig into them and some of the
+platforms that they've been thinking
+
+ align:start position:0%
+platforms that they've been thinking
+ 
+
+ align:start position:0%
+platforms that they've been thinking
+about different
+
+ align:start position:0%
+about different
+ 
+
+ align:start position:0%
+about different
+different ways of making it slightly
+
+ align:start position:0%
+different ways of making it slightly
+ 
+
+ align:start position:0%
+different ways of making it slightly
+less system dependent everyone has you
+
+ align:start position:0%
+less system dependent everyone has you
+ 
+
+ align:start position:0%
+less system dependent everyone has you
+know their attempts obviously windows is
+
+ align:start position:0%
+know their attempts obviously windows is
+ 
+
+ align:start position:0%
+know their attempts obviously windows is
+not system independent
+
+ align:start position:0%
+not system independent
+ 
+
+ align:start position:0%
+not system independent
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+two very brief examples of multicellular
+
+ align:start position:0%
+two very brief examples of multicellular
+ 
+
+ align:start position:0%
+two very brief examples of multicellular
+models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both of them being neural models kind of
+
+ align:start position:0%
+both of them being neural models kind of
+ 
+
+ align:start position:0%
+both of them being neural models kind of
+building from what we were thinking
+
+ align:start position:0%
+building from what we were thinking
+ 
+
+ align:start position:0%
+building from what we were thinking
+about last time but now we're going to a
+
+ align:start position:0%
+about last time but now we're going to a
+ 
+
+ align:start position:0%
+about last time but now we're going to a
+completely different kind of
+
+ align:start position:0%
+completely different kind of
+ 
+
+ align:start position:0%
+completely different kind of
+multicellular model all the way up from
+
+ align:start position:0%
+multicellular model all the way up from
+ 
+
+ align:start position:0%
+multicellular model all the way up from
+sort of individual
+
+ align:start position:0%
+sort of individual
+ 
+
+ align:start position:0%
+sort of individual
+effects that a single nucleotide how
+
+ align:start position:0%
+effects that a single nucleotide how
+ 
+
+ align:start position:0%
+effects that a single nucleotide how
+much effect the single nucleotide can
+
+ align:start position:0%
+much effect the single nucleotide can
+ 
+
+ align:start position:0%
+much effect the single nucleotide can
+have on a whole organ system
+
+ align:start position:0%
+have on a whole organ system
+ 
+
+ align:start position:0%
+have on a whole organ system
+which in this case will be
+
+ align:start position:0%
+which in this case will be
+ 
+
+ align:start position:0%
+which in this case will be
+cardiovascular
+
+ align:start position:0%
+cardiovascular
+ 
+
+ align:start position:0%
+cardiovascular
+so we go from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+there are a number of physiom and
+
+ align:start position:0%
+there are a number of physiom and
+ 
+
+ align:start position:0%
+there are a number of physiom and
+cardiom projects uh that are
+
+ align:start position:0%
+cardiom projects uh that are
+ 
+
+ align:start position:0%
+cardiom projects uh that are
+of active interest
+
+ align:start position:0%
+of active interest
+ 
+
+ align:start position:0%
+of active interest
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+just like the previous slides that i
+
+ align:start position:0%
+just like the previous slides that i
+ 
+
+ align:start position:0%
+just like the previous slides that i
+showed showing all the ways of sharing
+
+ align:start position:0%
+showed showing all the ways of sharing
+ 
+
+ align:start position:0%
+showed showing all the ways of sharing
+system models many of these efforts
+
+ align:start position:0%
+system models many of these efforts
+ 
+
+ align:start position:0%
+system models many of these efforts
+are kind of loose consortium alliances
+
+ align:start position:0%
+are kind of loose consortium alliances
+ 
+
+ align:start position:0%
+are kind of loose consortium alliances
+where people have
+
+ align:start position:0%
+where people have
+ 
+
+ align:start position:0%
+where people have
+put together different models either
+
+ align:start position:0%
+put together different models either
+ 
+
+ align:start position:0%
+put together different models either
+deal with the
+
+ align:start position:0%
+deal with the
+ 
+
+ align:start position:0%
+deal with the
+anatomy
+
+ align:start position:0%
+anatomy
+ 
+
+ align:start position:0%
+anatomy
+physiology or sometimes
+
+ align:start position:0%
+physiology or sometimes
+ 
+
+ align:start position:0%
+physiology or sometimes
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+integration of
+
+ align:start position:0%
+integration of
+ 
+
+ align:start position:0%
+integration of
+molecular to cellular cellular to
+
+ align:start position:0%
+molecular to cellular cellular to
+ 
+
+ align:start position:0%
+molecular to cellular cellular to
+say neural or muscular and all the way
+
+ align:start position:0%
+say neural or muscular and all the way
+ 
+
+ align:start position:0%
+say neural or muscular and all the way
+up to
+
+ align:start position:0%
+up to
+ 
+
+ align:start position:0%
+up to
+fluid dynamics and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's start with a single base pair
+
+ align:start position:0%
+so let's start with a single base pair
+ 
+
+ align:start position:0%
+so let's start with a single base pair
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+i start with this one because you should
+
+ align:start position:0%
+i start with this one because you should
+ 
+
+ align:start position:0%
+i start with this one because you should
+feel comfortable with it at this point
+
+ align:start position:0%
+feel comfortable with it at this point
+ 
+
+ align:start position:0%
+feel comfortable with it at this point
+we mentioned it briefly before
+
+ align:start position:0%
+we mentioned it briefly before
+ 
+
+ align:start position:0%
+we mentioned it briefly before
+we'll talk about it in more detail now
+
+ align:start position:0%
+we'll talk about it in more detail now
+ 
+
+ align:start position:0%
+we'll talk about it in more detail now
+this is the single nucleotide
+
+ align:start position:0%
+this is the single nucleotide
+ 
+
+ align:start position:0%
+this is the single nucleotide
+polymorphism which causes the change
+
+ align:start position:0%
+polymorphism which causes the change
+ 
+
+ align:start position:0%
+polymorphism which causes the change
+of the beta subunit of hemoglobin which
+
+ align:start position:0%
+of the beta subunit of hemoglobin which
+ 
+
+ align:start position:0%
+of the beta subunit of hemoglobin which
+is a tetramer to go
+
+ align:start position:0%
+is a tetramer to go
+ 
+
+ align:start position:0%
+is a tetramer to go
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+glutamate
+
+ align:start position:0%
+glutamate
+ 
+
+ align:start position:0%
+glutamate
+normally in most people at position six
+
+ align:start position:0%
+normally in most people at position six
+ 
+
+ align:start position:0%
+normally in most people at position six
+of the beta chain to availing
+
+ align:start position:0%
+of the beta chain to availing
+ 
+
+ align:start position:0%
+of the beta chain to availing
+or so that's the the purple
+
+ align:start position:0%
+or so that's the the purple
+ 
+
+ align:start position:0%
+or so that's the the purple
+set of tetramers or to tryptophan that's
+
+ align:start position:0%
+set of tetramers or to tryptophan that's
+ 
+
+ align:start position:0%
+set of tetramers or to tryptophan that's
+the cyan set on the far right
+
+ align:start position:0%
+the cyan set on the far right
+ 
+
+ align:start position:0%
+the cyan set on the far right
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+from combinations of x-ray
+
+ align:start position:0%
+from combinations of x-ray
+ 
+
+ align:start position:0%
+from combinations of x-ray
+crystallography and three-dimensional
+
+ align:start position:0%
+crystallography and three-dimensional
+ 
+
+ align:start position:0%
+crystallography and three-dimensional
+modeling and this is not speculation
+
+ align:start position:0%
+modeling and this is not speculation
+ 
+
+ align:start position:0%
+modeling and this is not speculation
+just based on primary sequence data even
+
+ align:start position:0%
+just based on primary sequence data even
+ 
+
+ align:start position:0%
+just based on primary sequence data even
+though the primary sequence here is very
+
+ align:start position:0%
+though the primary sequence here is very
+ 
+
+ align:start position:0%
+though the primary sequence here is very
+very close just a single nucleotide a
+
+ align:start position:0%
+very close just a single nucleotide a
+ 
+
+ align:start position:0%
+very close just a single nucleotide a
+single amino acid change nevertheless
+
+ align:start position:0%
+single amino acid change nevertheless
+ 
+
+ align:start position:0%
+single amino acid change nevertheless
+these authors have been building this
+
+ align:start position:0%
+these authors have been building this
+ 
+
+ align:start position:0%
+these authors have been building this
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+uh the crystallographic data where not
+
+ align:start position:0%
+uh the crystallographic data where not
+ 
+
+ align:start position:0%
+uh the crystallographic data where not
+only do you care about the tetramer
+
+ align:start position:0%
+only do you care about the tetramer
+ 
+
+ align:start position:0%
+only do you care about the tetramer
+itself but how the tetramers interact
+
+ align:start position:0%
+itself but how the tetramers interact
+ 
+
+ align:start position:0%
+itself but how the tetramers interact
+with one another to make these long
+
+ align:start position:0%
+with one another to make these long
+ 
+
+ align:start position:0%
+with one another to make these long
+fibrous chains which are
+
+ align:start position:0%
+fibrous chains which are
+ 
+
+ align:start position:0%
+fibrous chains which are
+considerably more stable
+
+ align:start position:0%
+considerably more stable
+ 
+
+ align:start position:0%
+considerably more stable
+in the sickle cell and what you see here
+
+ align:start position:0%
+in the sickle cell and what you see here
+ 
+
+ align:start position:0%
+in the sickle cell and what you see here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the valine substitution is locked in one
+
+ align:start position:0%
+the valine substitution is locked in one
+ 
+
+ align:start position:0%
+the valine substitution is locked in one
+kind of conformation and the
+
+ align:start position:0%
+kind of conformation and the
+ 
+
+ align:start position:0%
+kind of conformation and the
+tryptophan and another and you can see
+
+ align:start position:0%
+tryptophan and another and you can see
+ 
+
+ align:start position:0%
+tryptophan and another and you can see
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+these authors have have
+
+ align:start position:0%
+these authors have have
+ 
+
+ align:start position:0%
+these authors have have
+decided how a potential fiber can form
+
+ align:start position:0%
+decided how a potential fiber can form
+ 
+
+ align:start position:0%
+decided how a potential fiber can form
+in the different cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now those fibers
+
+ align:start position:0%
+now those fibers
+ 
+
+ align:start position:0%
+now those fibers
+in one way or another which is not
+
+ align:start position:0%
+in one way or another which is not
+ 
+
+ align:start position:0%
+in one way or another which is not
+totally mapped out
+
+ align:start position:0%
+totally mapped out
+ 
+
+ align:start position:0%
+totally mapped out
+but you uh
+
+ align:start position:0%
+but you uh
+ 
+
+ align:start position:0%
+but you uh
+affect the efficiency of uh
+
+ align:start position:0%
+affect the efficiency of uh
+ 
+
+ align:start position:0%
+affect the efficiency of uh
+of the hemoglobin slightly and this in
+
+ align:start position:0%
+of the hemoglobin slightly and this in
+ 
+
+ align:start position:0%
+of the hemoglobin slightly and this in
+the shape of the cell much more
+
+ align:start position:0%
+the shape of the cell much more
+ 
+
+ align:start position:0%
+the shape of the cell much more
+radically
+
+ align:start position:0%
+radically
+ 
+
+ align:start position:0%
+radically
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this combination uh results in the in
+
+ align:start position:0%
+this combination uh results in the in
+ 
+
+ align:start position:0%
+this combination uh results in the in
+this in the cell especially under any
+
+ align:start position:0%
+this in the cell especially under any
+ 
+
+ align:start position:0%
+this in the cell especially under any
+kind of stress either oxidative or other
+
+ align:start position:0%
+kind of stress either oxidative or other
+ 
+
+ align:start position:0%
+kind of stress either oxidative or other
+metabolic stress becoming sickled so you
+
+ align:start position:0%
+metabolic stress becoming sickled so you
+ 
+
+ align:start position:0%
+metabolic stress becoming sickled so you
+can have a
+
+ align:start position:0%
+can have a
+ 
+
+ align:start position:0%
+can have a
+a combination of cells which have
+
+ align:start position:0%
+a combination of cells which have
+ 
+
+ align:start position:0%
+a combination of cells which have
+varying degrees of sickling here in uh
+
+ align:start position:0%
+varying degrees of sickling here in uh
+ 
+
+ align:start position:0%
+varying degrees of sickling here in uh
+in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this microscopic slide on the left you
+
+ align:start position:0%
+this microscopic slide on the left you
+ 
+
+ align:start position:0%
+this microscopic slide on the left you
+have both the sickle cell and the normal
+
+ align:start position:0%
+have both the sickle cell and the normal
+ 
+
+ align:start position:0%
+have both the sickle cell and the normal
+cell side by side
+
+ align:start position:0%
+cell side by side
+ 
+
+ align:start position:0%
+cell side by side
+i think when we built up the red blood
+
+ align:start position:0%
+i think when we built up the red blood
+ 
+
+ align:start position:0%
+i think when we built up the red blood
+cell metabolic model we talked about
+
+ align:start position:0%
+cell metabolic model we talked about
+ 
+
+ align:start position:0%
+cell metabolic model we talked about
+some of the non-metabolic considerations
+
+ align:start position:0%
+some of the non-metabolic considerations
+ 
+
+ align:start position:0%
+some of the non-metabolic considerations
+of that which were that
+
+ align:start position:0%
+of that which were that
+ 
+
+ align:start position:0%
+of that which were that
+you know this function is a transport
+
+ align:start position:0%
+you know this function is a transport
+ 
+
+ align:start position:0%
+you know this function is a transport
+oxygen and so forth
+
+ align:start position:0%
+oxygen and so forth
+ 
+
+ align:start position:0%
+oxygen and so forth
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+what we're talking about now is more
+
+ align:start position:0%
+what we're talking about now is more
+ 
+
+ align:start position:0%
+what we're talking about now is more
+cell brim brain issue that's on slide 13
+
+ align:start position:0%
+cell brim brain issue that's on slide 13
+ 
+
+ align:start position:0%
+cell brim brain issue that's on slide 13
+where the internal environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the hemoglobin is greatly
+
+ align:start position:0%
+which is the hemoglobin is greatly
+ 
+
+ align:start position:0%
+which is the hemoglobin is greatly
+affecting now the external environment
+
+ align:start position:0%
+affecting now the external environment
+ 
+
+ align:start position:0%
+affecting now the external environment
+which is the hemodynamic flow in the in
+
+ align:start position:0%
+which is the hemodynamic flow in the in
+ 
+
+ align:start position:0%
+which is the hemodynamic flow in the in
+this in the uh
+
+ align:start position:0%
+this in the uh
+ 
+
+ align:start position:0%
+this in the uh
+capillaries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this falls under the heading it now
+
+ align:start position:0%
+so this falls under the heading it now
+ 
+
+ align:start position:0%
+so this falls under the heading it now
+of how is it that we can go from that
+
+ align:start position:0%
+of how is it that we can go from that
+ 
+
+ align:start position:0%
+of how is it that we can go from that
+single nucleotide change to a very
+
+ align:start position:0%
+single nucleotide change to a very
+ 
+
+ align:start position:0%
+single nucleotide change to a very
+dramatic morphological change in this
+
+ align:start position:0%
+dramatic morphological change in this
+ 
+
+ align:start position:0%
+dramatic morphological change in this
+case is pathological but you could
+
+ align:start position:0%
+case is pathological but you could
+ 
+
+ align:start position:0%
+case is pathological but you could
+imagine that in the hands of
+
+ align:start position:0%
+imagine that in the hands of
+ 
+
+ align:start position:0%
+imagine that in the hands of
+evolutionary adaptation
+
+ align:start position:0%
+evolutionary adaptation
+ 
+
+ align:start position:0%
+evolutionary adaptation
+an organism could take this and run with
+
+ align:start position:0%
+an organism could take this and run with
+ 
+
+ align:start position:0%
+an organism could take this and run with
+it maybe not sickle cell mutation but
+
+ align:start position:0%
+it maybe not sickle cell mutation but
+ 
+
+ align:start position:0%
+it maybe not sickle cell mutation but
+some other one that causes some other
+
+ align:start position:0%
+some other one that causes some other
+ 
+
+ align:start position:0%
+some other one that causes some other
+morphological change in some other cell
+
+ align:start position:0%
+morphological change in some other cell
+ 
+
+ align:start position:0%
+morphological change in some other cell
+or complex
+
+ align:start position:0%
+or complex
+ 
+
+ align:start position:0%
+or complex
+aggregate of cells
+
+ align:start position:0%
+aggregate of cells
+ 
+
+ align:start position:0%
+aggregate of cells
+because here you can see a whole variety
+
+ align:start position:0%
+because here you can see a whole variety
+ 
+
+ align:start position:0%
+because here you can see a whole variety
+of different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shapes of of red blood cells and
+
+ align:start position:0%
+shapes of of red blood cells and
+ 
+
+ align:start position:0%
+shapes of of red blood cells and
+remember these red blood cells are very
+
+ align:start position:0%
+remember these red blood cells are very
+ 
+
+ align:start position:0%
+remember these red blood cells are very
+simple they have no
+
+ align:start position:0%
+simple they have no
+ 
+
+ align:start position:0%
+simple they have no
+macromolecular system no dna no rna so
+
+ align:start position:0%
+macromolecular system no dna no rna so
+ 
+
+ align:start position:0%
+macromolecular system no dna no rna so
+we're really just talking about a bag of
+
+ align:start position:0%
+we're really just talking about a bag of
+ 
+
+ align:start position:0%
+we're really just talking about a bag of
+proteins which are greatly affected by
+
+ align:start position:0%
+proteins which are greatly affected by
+ 
+
+ align:start position:0%
+proteins which are greatly affected by
+these different
+
+ align:start position:0%
+these different
+ 
+
+ align:start position:0%
+these different
+conditions or enzyme deficiencies so the
+
+ align:start position:0%
+conditions or enzyme deficiencies so the
+ 
+
+ align:start position:0%
+conditions or enzyme deficiencies so the
+system models that were built up where
+
+ align:start position:0%
+system models that were built up where
+ 
+
+ align:start position:0%
+system models that were built up where
+we had the kinetic parameters for it for
+
+ align:start position:0%
+we had the kinetic parameters for it for
+ 
+
+ align:start position:0%
+we had the kinetic parameters for it for
+the enzymes here can can in principle be
+
+ align:start position:0%
+the enzymes here can can in principle be
+ 
+
+ align:start position:0%
+the enzymes here can can in principle be
+modeled under the impact it would have
+
+ align:start position:0%
+modeled under the impact it would have
+ 
+
+ align:start position:0%
+modeled under the impact it would have
+on the on the osmolarity
+
+ align:start position:0%
+on the on the osmolarity
+ 
+
+ align:start position:0%
+on the on the osmolarity
+or the other membrane properties were
+
+ align:start position:0%
+or the other membrane properties were
+ 
+
+ align:start position:0%
+or the other membrane properties were
+listed in the previous slide or the
+
+ align:start position:0%
+listed in the previous slide or the
+ 
+
+ align:start position:0%
+listed in the previous slide or the
+sickling was in two slides back
+
+ align:start position:0%
+sickling was in two slides back
+ 
+
+ align:start position:0%
+sickling was in two slides back
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from a single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleotide polymorphism we've gone to
+
+ align:start position:0%
+nucleotide polymorphism we've gone to
+ 
+
+ align:start position:0%
+nucleotide polymorphism we've gone to
+this three-dimensional fiber of
+
+ align:start position:0%
+this three-dimensional fiber of
+ 
+
+ align:start position:0%
+this three-dimensional fiber of
+hemoglobin
+
+ align:start position:0%
+hemoglobin
+ 
+
+ align:start position:0%
+hemoglobin
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+change in the three-dimensional
+
+ align:start position:0%
+change in the three-dimensional
+ 
+
+ align:start position:0%
+change in the three-dimensional
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+of this bicon
+
+ align:start position:0%
+of this bicon
+ 
+
+ align:start position:0%
+of this bicon
+cave
+
+ align:start position:0%
+cave
+ 
+
+ align:start position:0%
+cave
+disc
+
+ align:start position:0%
+disc
+ 
+
+ align:start position:0%
+disc
+to a sickle disc
+
+ align:start position:0%
+to a sickle disc
+ 
+
+ align:start position:0%
+to a sickle disc
+but you can also go sort of in parallel
+
+ align:start position:0%
+but you can also go sort of in parallel
+ 
+
+ align:start position:0%
+but you can also go sort of in parallel
+the same single nucleotide polymorphism
+
+ align:start position:0%
+the same single nucleotide polymorphism
+ 
+
+ align:start position:0%
+the same single nucleotide polymorphism
+or some like it can can take you up to
+
+ align:start position:0%
+or some like it can can take you up to
+ 
+
+ align:start position:0%
+or some like it can can take you up to
+pathogen resistance we've already
+
+ align:start position:0%
+pathogen resistance we've already
+ 
+
+ align:start position:0%
+pathogen resistance we've already
+mentioned that the sickle cell
+
+ align:start position:0%
+mentioned that the sickle cell
+ 
+
+ align:start position:0%
+mentioned that the sickle cell
+hemoglobin can take you to malarial
+
+ align:start position:0%
+hemoglobin can take you to malarial
+ 
+
+ align:start position:0%
+hemoglobin can take you to malarial
+resistance but in addition
+
+ align:start position:0%
+resistance but in addition
+ 
+
+ align:start position:0%
+resistance but in addition
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you can get
+
+ align:start position:0%
+you can get
+ 
+
+ align:start position:0%
+you can get
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+components of the
+
+ align:start position:0%
+components of the
+ 
+
+ align:start position:0%
+components of the
+enzymatic metabolic pathway such as
+
+ align:start position:0%
+enzymatic metabolic pathway such as
+ 
+
+ align:start position:0%
+enzymatic metabolic pathway such as
+the one that we modeled the
+
+ align:start position:0%
+the one that we modeled the
+ 
+
+ align:start position:0%
+the one that we modeled the
+two lectures back
+
+ align:start position:0%
+two lectures back
+ 
+
+ align:start position:0%
+two lectures back
+such as glutathione prostates this is
+
+ align:start position:0%
+such as glutathione prostates this is
+ 
+
+ align:start position:0%
+such as glutathione prostates this is
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+redox components
+
+ align:start position:0%
+redox components
+ 
+
+ align:start position:0%
+redox components
+and here uh erythrocytes that have that
+
+ align:start position:0%
+and here uh erythrocytes that have that
+ 
+
+ align:start position:0%
+and here uh erythrocytes that have that
+are heterozygous for this this
+
+ align:start position:0%
+are heterozygous for this this
+ 
+
+ align:start position:0%
+are heterozygous for this this
+particular allele
+
+ align:start position:0%
+particular allele
+ 
+
+ align:start position:0%
+particular allele
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should be more efficient in sheltering
+
+ align:start position:0%
+should be more efficient in sheltering
+ 
+
+ align:start position:0%
+should be more efficient in sheltering
+the cell membrane from irreversible
+
+ align:start position:0%
+the cell membrane from irreversible
+ 
+
+ align:start position:0%
+the cell membrane from irreversible
+oxidation and binding hemoglobin caused
+
+ align:start position:0%
+oxidation and binding hemoglobin caused
+ 
+
+ align:start position:0%
+oxidation and binding hemoglobin caused
+by the oxygen stress this exerted by
+
+ align:start position:0%
+by the oxygen stress this exerted by
+ 
+
+ align:start position:0%
+by the oxygen stress this exerted by
+the malarial parasite
+
+ align:start position:0%
+the malarial parasite
+ 
+
+ align:start position:0%
+the malarial parasite
+and what they observe here is actually
+
+ align:start position:0%
+and what they observe here is actually
+ 
+
+ align:start position:0%
+and what they observe here is actually
+an interaction between
+
+ align:start position:0%
+an interaction between
+ 
+
+ align:start position:0%
+an interaction between
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+these two possible
+
+ align:start position:0%
+these two possible
+ 
+
+ align:start position:0%
+these two possible
+haplotypes
+
+ align:start position:0%
+haplotypes
+ 
+
+ align:start position:0%
+haplotypes
+so it's not so it's actually you can
+
+ align:start position:0%
+so it's not so it's actually you can
+ 
+
+ align:start position:0%
+so it's not so it's actually you can
+think of it as a pair of haplotypes it's
+
+ align:start position:0%
+think of it as a pair of haplotypes it's
+ 
+
+ align:start position:0%
+think of it as a pair of haplotypes it's
+the one is
+
+ align:start position:0%
+the one is
+ 
+
+ align:start position:0%
+the one is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the hemoglobin as the one we've been
+
+ align:start position:0%
+the hemoglobin as the one we've been
+ 
+
+ align:start position:0%
+the hemoglobin as the one we've been
+talking about the sickling
+
+ align:start position:0%
+talking about the sickling
+ 
+
+ align:start position:0%
+talking about the sickling
+and then this glutathione peroxidase
+
+ align:start position:0%
+and then this glutathione peroxidase
+ 
+
+ align:start position:0%
+and then this glutathione peroxidase
+and so you can imagine is that since
+
+ align:start position:0%
+and so you can imagine is that since
+ 
+
+ align:start position:0%
+and so you can imagine is that since
+both of these things interact with
+
+ align:start position:0%
+both of these things interact with
+ 
+
+ align:start position:0%
+both of these things interact with
+malaria parasite that that your genotype
+
+ align:start position:0%
+malaria parasite that that your genotype
+ 
+
+ align:start position:0%
+malaria parasite that that your genotype
+will depend i'm sorry your phenotype of
+
+ align:start position:0%
+will depend i'm sorry your phenotype of
+ 
+
+ align:start position:0%
+will depend i'm sorry your phenotype of
+respective malaria will depend on
+
+ align:start position:0%
+respective malaria will depend on
+ 
+
+ align:start position:0%
+respective malaria will depend on
+the alleles that you have at both cases
+
+ align:start position:0%
+the alleles that you have at both cases
+ 
+
+ align:start position:0%
+the alleles that you have at both cases
+and so you can hear you have an a over s
+
+ align:start position:0%
+and so you can hear you have an a over s
+ 
+
+ align:start position:0%
+and so you can hear you have an a over s
+heterozygote and a two over one
+
+ align:start position:0%
+heterozygote and a two over one
+ 
+
+ align:start position:0%
+heterozygote and a two over one
+heterozygote
+
+ align:start position:0%
+heterozygote
+ 
+
+ align:start position:0%
+heterozygote
+and so that's something to take into
+
+ align:start position:0%
+and so that's something to take into
+ 
+
+ align:start position:0%
+and so that's something to take into
+account when you're trying to do any
+
+ align:start position:0%
+account when you're trying to do any
+ 
+
+ align:start position:0%
+account when you're trying to do any
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+predictive modeling or x modeling it to
+
+ align:start position:0%
+predictive modeling or x modeling it to
+ 
+
+ align:start position:0%
+predictive modeling or x modeling it to
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+the functional genomics that you have in
+
+ align:start position:0%
+the functional genomics that you have in
+ 
+
+ align:start position:0%
+the functional genomics that you have in
+a patient who's a compound heterozygote
+
+ align:start position:0%
+a patient who's a compound heterozygote
+ 
+
+ align:start position:0%
+a patient who's a compound heterozygote
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so now with the third pathway from now
+
+ align:start position:0%
+so now with the third pathway from now
+ 
+
+ align:start position:0%
+so now with the third pathway from now
+from single nu same set of single
+
+ align:start position:0%
+from single nu same set of single
+ 
+
+ align:start position:0%
+from single nu same set of single
+nucleotide polymorphisms that affect
+
+ align:start position:0%
+nucleotide polymorphisms that affect
+ 
+
+ align:start position:0%
+nucleotide polymorphisms that affect
+either hemoglobin or one of the major
+
+ align:start position:0%
+either hemoglobin or one of the major
+ 
+
+ align:start position:0%
+either hemoglobin or one of the major
+enzymes in red blood cell now
+
+ align:start position:0%
+enzymes in red blood cell now
+ 
+
+ align:start position:0%
+enzymes in red blood cell now
+you know one to cell morphology one to
+
+ align:start position:0%
+you know one to cell morphology one to
+ 
+
+ align:start position:0%
+you know one to cell morphology one to
+pathogen interaction and finally to
+
+ align:start position:0%
+pathogen interaction and finally to
+ 
+
+ align:start position:0%
+pathogen interaction and finally to
+interact with drugs we talked about
+
+ align:start position:0%
+interact with drugs we talked about
+ 
+
+ align:start position:0%
+interact with drugs we talked about
+pharmacogenomics here's another example
+
+ align:start position:0%
+pharmacogenomics here's another example
+ 
+
+ align:start position:0%
+pharmacogenomics here's another example
+where you have
+
+ align:start position:0%
+where you have
+ 
+
+ align:start position:0%
+where you have
+the drug induced oxidative hemolysis
+
+ align:start position:0%
+the drug induced oxidative hemolysis
+ 
+
+ align:start position:0%
+the drug induced oxidative hemolysis
+that you occur with certain
+
+ align:start position:0%
+that you occur with certain
+ 
+
+ align:start position:0%
+that you occur with certain
+enzyme opathies like glucose-6-phosphate
+
+ align:start position:0%
+enzyme opathies like glucose-6-phosphate
+ 
+
+ align:start position:0%
+enzyme opathies like glucose-6-phosphate
+dehydrogenase
+
+ align:start position:0%
+dehydrogenase
+ 
+
+ align:start position:0%
+dehydrogenase
+this these this enzyme
+
+ align:start position:0%
+this these this enzyme
+ 
+
+ align:start position:0%
+this these this enzyme
+glucose-6 phosphate dehydrogenase
+
+ align:start position:0%
+glucose-6 phosphate dehydrogenase
+ 
+
+ align:start position:0%
+glucose-6 phosphate dehydrogenase
+interacts with drugs such as
+
+ align:start position:0%
+interacts with drugs such as
+ 
+
+ align:start position:0%
+interacts with drugs such as
+primocline
+
+ align:start position:0%
+primocline
+ 
+
+ align:start position:0%
+primocline
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+it disrupts
+
+ align:start position:0%
+it disrupts
+ 
+
+ align:start position:0%
+it disrupts
+mitochondrial function heme biosynthesis
+
+ align:start position:0%
+mitochondrial function heme biosynthesis
+ 
+
+ align:start position:0%
+mitochondrial function heme biosynthesis
+and so forth and so on
+
+ align:start position:0%
+and so forth and so on
+ 
+
+ align:start position:0%
+and so forth and so on
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+a very significant uh
+
+ align:start position:0%
+a very significant uh
+ 
+
+ align:start position:0%
+a very significant uh
+consideration whether with a long list
+
+ align:start position:0%
+consideration whether with a long list
+ 
+
+ align:start position:0%
+consideration whether with a long list
+of 20-some drugs that has to be taken
+
+ align:start position:0%
+of 20-some drugs that has to be taken
+ 
+
+ align:start position:0%
+of 20-some drugs that has to be taken
+into account when you have any of a
+
+ align:start position:0%
+into account when you have any of a
+ 
+
+ align:start position:0%
+into account when you have any of a
+variety of red blood cell enzyme changes
+
+ align:start position:0%
+variety of red blood cell enzyme changes
+ 
+
+ align:start position:0%
+variety of red blood cell enzyme changes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we've got these three effects
+
+ align:start position:0%
+we've got these three effects
+ 
+
+ align:start position:0%
+we've got these three effects
+of a limited number of single nucleotide
+
+ align:start position:0%
+of a limited number of single nucleotide
+ 
+
+ align:start position:0%
+of a limited number of single nucleotide
+polymorphisms
+
+ align:start position:0%
+polymorphisms
+ 
+
+ align:start position:0%
+polymorphisms
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+do you make this transition from
+
+ align:start position:0%
+do you make this transition from
+ 
+
+ align:start position:0%
+do you make this transition from
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and they're all somewhat interconnected
+
+ align:start position:0%
+and they're all somewhat interconnected
+ 
+
+ align:start position:0%
+and they're all somewhat interconnected
+part of the reason is resistant to
+
+ align:start position:0%
+part of the reason is resistant to
+ 
+
+ align:start position:0%
+part of the reason is resistant to
+malaria is because it's less effective
+
+ align:start position:0%
+malaria is because it's less effective
+ 
+
+ align:start position:0%
+malaria is because it's less effective
+in its cell shape and its ability to
+
+ align:start position:0%
+in its cell shape and its ability to
+ 
+
+ align:start position:0%
+in its cell shape and its ability to
+transport
+
+ align:start position:0%
+transport
+ 
+
+ align:start position:0%
+transport
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+do its metabolism
+
+ align:start position:0%
+do its metabolism
+ 
+
+ align:start position:0%
+do its metabolism
+the same thing with drug uh sensitivity
+
+ align:start position:0%
+the same thing with drug uh sensitivity
+ 
+
+ align:start position:0%
+the same thing with drug uh sensitivity
+how how are these uh changes in the in
+
+ align:start position:0%
+how how are these uh changes in the in
+ 
+
+ align:start position:0%
+how how are these uh changes in the in
+the hemoglobin
+
+ align:start position:0%
+the hemoglobin
+ 
+
+ align:start position:0%
+the hemoglobin
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+might they be reflected in the
+
+ align:start position:0%
+might they be reflected in the
+ 
+
+ align:start position:0%
+might they be reflected in the
+three-dimensional shape of the
+
+ align:start position:0%
+three-dimensional shape of the
+ 
+
+ align:start position:0%
+three-dimensional shape of the
+erythrocyte which is a kind of a
+
+ align:start position:0%
+erythrocyte which is a kind of a
+ 
+
+ align:start position:0%
+erythrocyte which is a kind of a
+membrane-bound compartment and here's a
+
+ align:start position:0%
+membrane-bound compartment and here's a
+ 
+
+ align:start position:0%
+membrane-bound compartment and here's a
+model that described me as interesting
+
+ align:start position:0%
+model that described me as interesting
+ 
+
+ align:start position:0%
+model that described me as interesting
+it's not it's
+
+ align:start position:0%
+it's not it's
+ 
+
+ align:start position:0%
+it's not it's
+not been that extensively tested since
+
+ align:start position:0%
+not been that extensively tested since
+ 
+
+ align:start position:0%
+not been that extensively tested since
+1998 but the idea is that band three
+
+ align:start position:0%
+1998 but the idea is that band three
+ 
+
+ align:start position:0%
+1998 but the idea is that band three
+this is uh one of those names that just
+
+ align:start position:0%
+this is uh one of those names that just
+ 
+
+ align:start position:0%
+this is uh one of those names that just
+comes out of the
+
+ align:start position:0%
+comes out of the
+ 
+
+ align:start position:0%
+comes out of the
+the molecular biologists literature that
+
+ align:start position:0%
+the molecular biologists literature that
+ 
+
+ align:start position:0%
+the molecular biologists literature that
+they ran a gel and they count the bands
+
+ align:start position:0%
+they ran a gel and they count the bands
+ 
+
+ align:start position:0%
+they ran a gel and they count the bands
+and number three and it turns out it's
+
+ align:start position:0%
+and number three and it turns out it's
+ 
+
+ align:start position:0%
+and number three and it turns out it's
+uh it's that it's about 10 of the of red
+
+ align:start position:0%
+uh it's that it's about 10 of the of red
+ 
+
+ align:start position:0%
+uh it's that it's about 10 of the of red
+blood cell membrane it's a very abundant
+
+ align:start position:0%
+blood cell membrane it's a very abundant
+ 
+
+ align:start position:0%
+blood cell membrane it's a very abundant
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and it's responsible for
+
+ align:start position:0%
+and it's responsible for
+ 
+
+ align:start position:0%
+and it's responsible for
+the uh equilibration of anions such as
+
+ align:start position:0%
+the uh equilibration of anions such as
+ 
+
+ align:start position:0%
+the uh equilibration of anions such as
+carbonate and chloride across the
+
+ align:start position:0%
+carbonate and chloride across the
+ 
+
+ align:start position:0%
+carbonate and chloride across the
+regular cell membrane
+
+ align:start position:0%
+regular cell membrane
+ 
+
+ align:start position:0%
+regular cell membrane
+it's not a pump it just kind of
+
+ align:start position:0%
+it's not a pump it just kind of
+ 
+
+ align:start position:0%
+it's not a pump it just kind of
+allows these anions to go across because
+
+ align:start position:0%
+allows these anions to go across because
+ 
+
+ align:start position:0%
+allows these anions to go across because
+the pump here is the pumps that are
+
+ align:start position:0%
+the pump here is the pumps that are
+ 
+
+ align:start position:0%
+the pump here is the pumps that are
+involved in proton
+
+ align:start position:0%
+involved in proton
+ 
+
+ align:start position:0%
+involved in proton
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's also sodium potassium and that's
+
+ align:start position:0%
+there's also sodium potassium and that's
+ 
+
+ align:start position:0%
+there's also sodium potassium and that's
+what your atp in the blood blood cell is
+
+ align:start position:0%
+what your atp in the blood blood cell is
+ 
+
+ align:start position:0%
+what your atp in the blood blood cell is
+going for and this these are just kind
+
+ align:start position:0%
+going for and this these are just kind
+ 
+
+ align:start position:0%
+going for and this these are just kind
+of following along
+
+ align:start position:0%
+of following along
+ 
+
+ align:start position:0%
+of following along
+now you can the idea here is that uh
+
+ align:start position:0%
+now you can the idea here is that uh
+ 
+
+ align:start position:0%
+now you can the idea here is that uh
+if you can if you change
+
+ align:start position:0%
+if you can if you change
+ 
+
+ align:start position:0%
+if you can if you change
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+degree let's see i think this is covered
+
+ align:start position:0%
+degree let's see i think this is covered
+ 
+
+ align:start position:0%
+degree let's see i think this is covered
+in more detail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this the uh
+
+ align:start position:0%
+this the uh
+ 
+
+ align:start position:0%
+this the uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mechanism of action here is a greatly
+
+ align:start position:0%
+mechanism of action here is a greatly
+ 
+
+ align:start position:0%
+mechanism of action here is a greatly
+affected by its disulfide effects if you
+
+ align:start position:0%
+affected by its disulfide effects if you
+ 
+
+ align:start position:0%
+affected by its disulfide effects if you
+change the the redox uh
+
+ align:start position:0%
+change the the redox uh
+ 
+
+ align:start position:0%
+change the the redox uh
+components in the red blood cell you get
+
+ align:start position:0%
+components in the red blood cell you get
+ 
+
+ align:start position:0%
+components in the red blood cell you get
+a slight just a slight change in
+
+ align:start position:0%
+a slight just a slight change in
+ 
+
+ align:start position:0%
+a slight just a slight change in
+confirmation of this molecule and then
+
+ align:start position:0%
+confirmation of this molecule and then
+ 
+
+ align:start position:0%
+confirmation of this molecule and then
+that can result in a net difference
+
+ align:start position:0%
+that can result in a net difference
+ 
+
+ align:start position:0%
+that can result in a net difference
+between this the cross-sectional area of
+
+ align:start position:0%
+between this the cross-sectional area of
+ 
+
+ align:start position:0%
+between this the cross-sectional area of
+this protein on the outside and the
+
+ align:start position:0%
+this protein on the outside and the
+ 
+
+ align:start position:0%
+this protein on the outside and the
+inside
+
+ align:start position:0%
+inside
+ 
+
+ align:start position:0%
+inside
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+translates into a net change since since
+
+ align:start position:0%
+translates into a net change since since
+ 
+
+ align:start position:0%
+translates into a net change since since
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+fossil lipids don't exchange uh the or
+
+ align:start position:0%
+fossil lipids don't exchange uh the or
+ 
+
+ align:start position:0%
+fossil lipids don't exchange uh the or
+the rate constant for the fossil lipid
+
+ align:start position:0%
+the rate constant for the fossil lipid
+ 
+
+ align:start position:0%
+the rate constant for the fossil lipid
+exchange is slow and known
+
+ align:start position:0%
+exchange is slow and known
+ 
+
+ align:start position:0%
+exchange is slow and known
+then this results in a uh
+
+ align:start position:0%
+then this results in a uh
+ 
+
+ align:start position:0%
+then this results in a uh
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+conformational change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway that's the model
+
+ align:start position:0%
+anyway that's the model
+ 
+
+ align:start position:0%
+anyway that's the model
+that connects the single nucleotide to
+
+ align:start position:0%
+that connects the single nucleotide to
+ 
+
+ align:start position:0%
+that connects the single nucleotide to
+could connect it to the the three muscle
+
+ align:start position:0%
+could connect it to the the three muscle
+ 
+
+ align:start position:0%
+could connect it to the the three muscle
+structure of the cell then you want to
+
+ align:start position:0%
+structure of the cell then you want to
+ 
+
+ align:start position:0%
+structure of the cell then you want to
+connect the three-dimensional structure
+
+ align:start position:0%
+connect the three-dimensional structure
+ 
+
+ align:start position:0%
+connect the three-dimensional structure
+of cell
+
+ align:start position:0%
+of cell
+ 
+
+ align:start position:0%
+of cell
+to uh its ability to carry out its
+
+ align:start position:0%
+to uh its ability to carry out its
+ 
+
+ align:start position:0%
+to uh its ability to carry out its
+function in the capillaries and function
+
+ align:start position:0%
+function in the capillaries and function
+ 
+
+ align:start position:0%
+function in the capillaries and function
+there is to
+
+ align:start position:0%
+there is to
+ 
+
+ align:start position:0%
+there is to
+allow the fusion of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+oxygen and carbon dioxide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here the each of these cells is
+
+ align:start position:0%
+so here the each of these cells is
+ 
+
+ align:start position:0%
+so here the each of these cells is
+shaped by a mechanical process and
+
+ align:start position:0%
+shaped by a mechanical process and
+ 
+
+ align:start position:0%
+shaped by a mechanical process and
+mechanical process here you can take the
+
+ align:start position:0%
+mechanical process here you can take the
+ 
+
+ align:start position:0%
+mechanical process here you can take the
+known uh
+
+ align:start position:0%
+known uh
+ 
+
+ align:start position:0%
+known uh
+or the measurable mechanical properties
+
+ align:start position:0%
+or the measurable mechanical properties
+ 
+
+ align:start position:0%
+or the measurable mechanical properties
+of red blood cell
+
+ align:start position:0%
+of red blood cell
+ 
+
+ align:start position:0%
+of red blood cell
+and subject them
+
+ align:start position:0%
+and subject them
+ 
+
+ align:start position:0%
+and subject them
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+method called finite elements
+
+ align:start position:0%
+method called finite elements
+ 
+
+ align:start position:0%
+method called finite elements
+analysis where you're where you you're
+
+ align:start position:0%
+analysis where you're where you you're
+ 
+
+ align:start position:0%
+analysis where you're where you you're
+solving these uh partial differential
+
+ align:start position:0%
+solving these uh partial differential
+ 
+
+ align:start position:0%
+solving these uh partial differential
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+and look and you can calculate the
+
+ align:start position:0%
+and look and you can calculate the
+ 
+
+ align:start position:0%
+and look and you can calculate the
+exchange of the
+
+ align:start position:0%
+exchange of the
+ 
+
+ align:start position:0%
+exchange of the
+oxygen of the
+
+ align:start position:0%
+oxygen of the
+ 
+
+ align:start position:0%
+oxygen of the
+alveolar just refers to this would be in
+
+ align:start position:0%
+alveolar just refers to this would be in
+ 
+
+ align:start position:0%
+alveolar just refers to this would be in
+in the lungs this would be a small
+
+ align:start position:0%
+in the lungs this would be a small
+ 
+
+ align:start position:0%
+in the lungs this would be a small
+catholic lungs and you see the capillary
+
+ align:start position:0%
+catholic lungs and you see the capillary
+ 
+
+ align:start position:0%
+catholic lungs and you see the capillary
+now endothelial walls are close enough
+
+ align:start position:0%
+now endothelial walls are close enough
+ 
+
+ align:start position:0%
+now endothelial walls are close enough
+so the red blood cells are basically uh
+
+ align:start position:0%
+so the red blood cells are basically uh
+ 
+
+ align:start position:0%
+so the red blood cells are basically uh
+deformed in their shape as they go
+
+ align:start position:0%
+deformed in their shape as they go
+ 
+
+ align:start position:0%
+deformed in their shape as they go
+through there and the exact shapes that
+
+ align:start position:0%
+through there and the exact shapes that
+ 
+
+ align:start position:0%
+through there and the exact shapes that
+are compatible with this will determine
+
+ align:start position:0%
+are compatible with this will determine
+ 
+
+ align:start position:0%
+are compatible with this will determine
+the rate these little arrows that go
+
+ align:start position:0%
+the rate these little arrows that go
+ 
+
+ align:start position:0%
+the rate these little arrows that go
+from the oxygen on the outside
+
+ align:start position:0%
+from the oxygen on the outside
+ 
+
+ align:start position:0%
+from the oxygen on the outside
+the longest uh epithelium get through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's uh you know a reference uh
+
+ align:start position:0%
+so that's uh you know a reference uh
+ 
+
+ align:start position:0%
+so that's uh you know a reference uh
+that deals with that kind of problem
+
+ align:start position:0%
+that deals with that kind of problem
+ 
+
+ align:start position:0%
+that deals with that kind of problem
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as we start thinking about building up a
+
+ align:start position:0%
+as we start thinking about building up a
+ 
+
+ align:start position:0%
+as we start thinking about building up a
+larger system model the other parts of
+
+ align:start position:0%
+larger system model the other parts of
+ 
+
+ align:start position:0%
+larger system model the other parts of
+the system each of them so we've got a
+
+ align:start position:0%
+the system each of them so we've got a
+ 
+
+ align:start position:0%
+the system each of them so we've got a
+red blood cell model it's a metabolic
+
+ align:start position:0%
+red blood cell model it's a metabolic
+ 
+
+ align:start position:0%
+red blood cell model it's a metabolic
+model in principle it could also be
+
+ align:start position:0%
+model in principle it could also be
+ 
+
+ align:start position:0%
+model in principle it could also be
+a shape model and a diffusion model
+
+ align:start position:0%
+a shape model and a diffusion model
+ 
+
+ align:start position:0%
+a shape model and a diffusion model
+but the other parts of the of the system
+
+ align:start position:0%
+but the other parts of the of the system
+ 
+
+ align:start position:0%
+but the other parts of the of the system
+typically involve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+muscle cells they have the the smooth
+
+ align:start position:0%
+muscle cells they have the the smooth
+ 
+
+ align:start position:0%
+muscle cells they have the the smooth
+muscles
+
+ align:start position:0%
+muscles
+ 
+
+ align:start position:0%
+muscles
+throughout the entire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arterial and venous system and and most
+
+ align:start position:0%
+arterial and venous system and and most
+ 
+
+ align:start position:0%
+arterial and venous system and and most
+significantly
+
+ align:start position:0%
+significantly
+ 
+
+ align:start position:0%
+significantly
+the the heart muscles and so
+
+ align:start position:0%
+the the heart muscles and so
+ 
+
+ align:start position:0%
+the the heart muscles and so
+here you have an example of an action
+
+ align:start position:0%
+here you have an example of an action
+ 
+
+ align:start position:0%
+here you have an example of an action
+potential in
+
+ align:start position:0%
+potential in
+ 
+
+ align:start position:0%
+potential in
+in one of the ventricular cells of the
+
+ align:start position:0%
+in one of the ventricular cells of the
+ 
+
+ align:start position:0%
+in one of the ventricular cells of the
+of the dog heart
+
+ align:start position:0%
+of the dog heart
+ 
+
+ align:start position:0%
+of the dog heart
+and it includes all the components that
+
+ align:start position:0%
+and it includes all the components that
+ 
+
+ align:start position:0%
+and it includes all the components that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+at least least this is not an entire
+
+ align:start position:0%
+at least least this is not an entire
+ 
+
+ align:start position:0%
+at least least this is not an entire
+course on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ventricular
+
+ align:start position:0%
+ventricular
+ 
+
+ align:start position:0%
+ventricular
+part modeling
+
+ align:start position:0%
+part modeling
+ 
+
+ align:start position:0%
+part modeling
+this this is for sort of parameters in
+
+ align:start position:0%
+this this is for sort of parameters in
+ 
+
+ align:start position:0%
+this this is for sort of parameters in
+terms of all the eyes the currents for
+
+ align:start position:0%
+terms of all the eyes the currents for
+ 
+
+ align:start position:0%
+terms of all the eyes the currents for
+each of the different potassium channels
+
+ align:start position:0%
+each of the different potassium channels
+ 
+
+ align:start position:0%
+each of the different potassium channels
+the k
+
+ align:start position:0%
+the k
+ 
+
+ align:start position:0%
+the k
+all the features of the ones the i sub k
+
+ align:start position:0%
+all the features of the ones the i sub k
+ 
+
+ align:start position:0%
+all the features of the ones the i sub k
+is all potassium and then there's some
+
+ align:start position:0%
+is all potassium and then there's some
+ 
+
+ align:start position:0%
+is all potassium and then there's some
+of sodium and sodium and calcium calcium
+
+ align:start position:0%
+of sodium and sodium and calcium calcium
+ 
+
+ align:start position:0%
+of sodium and sodium and calcium calcium
+calcium sodium alone it's the east of
+
+ align:start position:0%
+calcium sodium alone it's the east of
+ 
+
+ align:start position:0%
+calcium sodium alone it's the east of
+these things that internal source of
+
+ align:start position:0%
+these things that internal source of
+ 
+
+ align:start position:0%
+these things that internal source of
+calcium that go from one
+
+ align:start position:0%
+calcium that go from one
+ 
+
+ align:start position:0%
+calcium that go from one
+subcellular compartment to another
+
+ align:start position:0%
+subcellular compartment to another
+ 
+
+ align:start position:0%
+subcellular compartment to another
+and and and so on you get the idea each
+
+ align:start position:0%
+and and and so on you get the idea each
+ 
+
+ align:start position:0%
+and and and so on you get the idea each
+of these things has to have the
+
+ align:start position:0%
+of these things has to have the
+ 
+
+ align:start position:0%
+of these things has to have the
+parameters measured
+
+ align:start position:0%
+parameters measured
+ 
+
+ align:start position:0%
+parameters measured
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+any other absent you have to uh have
+
+ align:start position:0%
+any other absent you have to uh have
+ 
+
+ align:start position:0%
+any other absent you have to uh have
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+ways of getting
+
+ align:start position:0%
+ways of getting
+ 
+
+ align:start position:0%
+ways of getting
+surrogates
+
+ align:start position:0%
+surrogates
+ 
+
+ align:start position:0%
+surrogates
+and so this is the sort this is just
+
+ align:start position:0%
+and so this is the sort this is just
+ 
+
+ align:start position:0%
+and so this is the sort this is just
+the sort of data that would go into the
+
+ align:start position:0%
+the sort of data that would go into the
+ 
+
+ align:start position:0%
+the sort of data that would go into the
+other major type of cell that is that
+
+ align:start position:0%
+other major type of cell that is that
+ 
+
+ align:start position:0%
+other major type of cell that is that
+comes into this cardiovascular
+
+ align:start position:0%
+comes into this cardiovascular
+ 
+
+ align:start position:0%
+comes into this cardiovascular
+modeling
+
+ align:start position:0%
+modeling
+ 
+
+ align:start position:0%
+modeling
+and finally you can integrate this uh up
+
+ align:start position:0%
+and finally you can integrate this uh up
+ 
+
+ align:start position:0%
+and finally you can integrate this uh up
+to a fairly complete system it's
+
+ align:start position:0%
+to a fairly complete system it's
+ 
+
+ align:start position:0%
+to a fairly complete system it's
+obviously not complete if you get to the
+
+ align:start position:0%
+obviously not complete if you get to the
+ 
+
+ align:start position:0%
+obviously not complete if you get to the
+whole organism but
+
+ align:start position:0%
+whole organism but
+ 
+
+ align:start position:0%
+whole organism but
+higher level and we're how we're talking
+
+ align:start position:0%
+higher level and we're how we're talking
+ 
+
+ align:start position:0%
+higher level and we're how we're talking
+about whole body recirculation
+
+ align:start position:0%
+about whole body recirculation
+ 
+
+ align:start position:0%
+about whole body recirculation
+uh this nsr group uh this is the
+
+ align:start position:0%
+uh this nsr group uh this is the
+ 
+
+ align:start position:0%
+uh this nsr group uh this is the
+hypertext link for this particular model
+
+ align:start position:0%
+hypertext link for this particular model
+ 
+
+ align:start position:0%
+hypertext link for this particular model
+that you can download and it has a four
+
+ align:start position:0%
+that you can download and it has a four
+ 
+
+ align:start position:0%
+that you can download and it has a four
+chambered heart we were just talking
+
+ align:start position:0%
+chambered heart we were just talking
+ 
+
+ align:start position:0%
+chambered heart we were just talking
+about one ventricular cell in the
+
+ align:start position:0%
+about one ventricular cell in the
+ 
+
+ align:start position:0%
+about one ventricular cell in the
+previous slide but that would be
+
+ align:start position:0%
+previous slide but that would be
+ 
+
+ align:start position:0%
+previous slide but that would be
+we looked at the second box from the top
+
+ align:start position:0%
+we looked at the second box from the top
+ 
+
+ align:start position:0%
+we looked at the second box from the top
+here this is the where the heart from
+
+ align:start position:0%
+here this is the where the heart from
+ 
+
+ align:start position:0%
+here this is the where the heart from
+lung
+
+ align:start position:0%
+lung
+ 
+
+ align:start position:0%
+lung
+models which fit in there it's got seven
+
+ align:start position:0%
+models which fit in there it's got seven
+ 
+
+ align:start position:0%
+models which fit in there it's got seven
+different organs which include kidney
+
+ align:start position:0%
+different organs which include kidney
+ 
+
+ align:start position:0%
+different organs which include kidney
+liver gut flower limbs and so forth down
+
+ align:start position:0%
+liver gut flower limbs and so forth down
+ 
+
+ align:start position:0%
+liver gut flower limbs and so forth down
+the bottom part of the bag
+
+ align:start position:0%
+the bottom part of the bag
+ 
+
+ align:start position:0%
+the bottom part of the bag
+get the picture each of these things you
+
+ align:start position:0%
+get the picture each of these things you
+ 
+
+ align:start position:0%
+get the picture each of these things you
+your mod you're modeling the the volumes
+
+ align:start position:0%
+your mod you're modeling the the volumes
+ 
+
+ align:start position:0%
+your mod you're modeling the the volumes
+and flows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this is systems biology this is
+
+ align:start position:0%
+now this is systems biology this is
+ 
+
+ align:start position:0%
+now this is systems biology this is
+really uh
+
+ align:start position:0%
+really uh
+ 
+
+ align:start position:0%
+really uh
+kind of a renaissance of interest in
+
+ align:start position:0%
+kind of a renaissance of interest in
+ 
+
+ align:start position:0%
+kind of a renaissance of interest in
+physiology is what it would have been
+
+ align:start position:0%
+physiology is what it would have been
+ 
+
+ align:start position:0%
+physiology is what it would have been
+called before and there are some really
+
+ align:start position:0%
+called before and there are some really
+ 
+
+ align:start position:0%
+called before and there are some really
+interesting um
+
+ align:start position:0%
+interesting um
+ 
+
+ align:start position:0%
+interesting um
+mysteries out there to be solved
+
+ align:start position:0%
+mysteries out there to be solved
+ 
+
+ align:start position:0%
+mysteries out there to be solved
+that are really only solvable or
+
+ align:start position:0%
+that are really only solvable or
+ 
+
+ align:start position:0%
+that are really only solvable or
+possibly only solve with the system
+
+ align:start position:0%
+possibly only solve with the system
+ 
+
+ align:start position:0%
+possibly only solve with the system
+level you know you never know you
+
+ align:start position:0%
+level you know you never know you
+ 
+
+ align:start position:0%
+level you know you never know you
+somebody could come up and say oh yeah
+
+ align:start position:0%
+somebody could come up and say oh yeah
+ 
+
+ align:start position:0%
+somebody could come up and say oh yeah
+this is this is really well understood
+
+ align:start position:0%
+this is this is really well understood
+ 
+
+ align:start position:0%
+this is this is really well understood
+uh immunology and that answers
+
+ align:start position:0%
+uh immunology and that answers
+ 
+
+ align:start position:0%
+uh immunology and that answers
+everything but even if it's some kind of
+
+ align:start position:0%
+everything but even if it's some kind of
+ 
+
+ align:start position:0%
+everything but even if it's some kind of
+immunology
+
+ align:start position:0%
+immunology
+ 
+
+ align:start position:0%
+immunology
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you still have to say how does it play
+
+ align:start position:0%
+you still have to say how does it play
+ 
+
+ align:start position:0%
+you still have to say how does it play
+out and what happens is we've been
+
+ align:start position:0%
+out and what happens is we've been
+ 
+
+ align:start position:0%
+out and what happens is we've been
+talking about sickle cell disease
+
+ align:start position:0%
+talking about sickle cell disease
+ 
+
+ align:start position:0%
+talking about sickle cell disease
+and you can have fairly mild pain as one
+
+ align:start position:0%
+and you can have fairly mild pain as one
+ 
+
+ align:start position:0%
+and you can have fairly mild pain as one
+of the major symptoms um but then all of
+
+ align:start position:0%
+of the major symptoms um but then all of
+ 
+
+ align:start position:0%
+of the major symptoms um but then all of
+a sudden out of nowhere you'll get this
+
+ align:start position:0%
+a sudden out of nowhere you'll get this
+ 
+
+ align:start position:0%
+a sudden out of nowhere you'll get this
+multi-organ system failure where uh
+
+ align:start position:0%
+multi-organ system failure where uh
+ 
+
+ align:start position:0%
+multi-organ system failure where uh
+you know almost every major organ in
+
+ align:start position:0%
+you know almost every major organ in
+ 
+
+ align:start position:0%
+you know almost every major organ in
+that previous slide long as the
+
+ align:start position:0%
+that previous slide long as the
+ 
+
+ align:start position:0%
+that previous slide long as the
+so-called fill up with fluid and
+
+ align:start position:0%
+so-called fill up with fluid and
+ 
+
+ align:start position:0%
+so-called fill up with fluid and
+and you have a very high chance of dying
+
+ align:start position:0%
+and you have a very high chance of dying
+ 
+
+ align:start position:0%
+and you have a very high chance of dying
+and this could happen to every one of us
+
+ align:start position:0%
+and this could happen to every one of us
+ 
+
+ align:start position:0%
+and this could happen to every one of us
+in this room because it's not restricted
+
+ align:start position:0%
+in this room because it's not restricted
+ 
+
+ align:start position:0%
+in this room because it's not restricted
+to sickle cell
+
+ align:start position:0%
+to sickle cell
+ 
+
+ align:start position:0%
+to sickle cell
+if any of you have severe uh
+
+ align:start position:0%
+if any of you have severe uh
+ 
+
+ align:start position:0%
+if any of you have severe uh
+burn or or car crash
+
+ align:start position:0%
+burn or or car crash
+ 
+
+ align:start position:0%
+burn or or car crash
+major bone injuries
+
+ align:start position:0%
+major bone injuries
+ 
+
+ align:start position:0%
+major bone injuries
+you have a very good chance of dealing
+
+ align:start position:0%
+you have a very good chance of dealing
+ 
+
+ align:start position:0%
+you have a very good chance of dealing
+with multi-organ system failure it
+
+ align:start position:0%
+with multi-organ system failure it
+ 
+
+ align:start position:0%
+with multi-organ system failure it
+really isn't known how
+
+ align:start position:0%
+really isn't known how
+ 
+
+ align:start position:0%
+really isn't known how
+that plays out i mean not even that not
+
+ align:start position:0%
+that plays out i mean not even that not
+ 
+
+ align:start position:0%
+that plays out i mean not even that not
+just a quantitative model but uh even
+
+ align:start position:0%
+just a quantitative model but uh even
+ 
+
+ align:start position:0%
+just a quantitative model but uh even
+qualitatively
+
+ align:start position:0%
+qualitatively
+ 
+
+ align:start position:0%
+qualitatively
+so i think this is something there are
+
+ align:start position:0%
+so i think this is something there are
+ 
+
+ align:start position:0%
+so i think this is something there are
+projects now to do to get genomic data
+
+ align:start position:0%
+projects now to do to get genomic data
+ 
+
+ align:start position:0%
+projects now to do to get genomic data
+collection both genetic and um
+
+ align:start position:0%
+collection both genetic and um
+ 
+
+ align:start position:0%
+collection both genetic and um
+expression data and time will tell
+
+ align:start position:0%
+expression data and time will tell
+ 
+
+ align:start position:0%
+expression data and time will tell
+whether that is
+
+ align:start position:0%
+whether that is
+ 
+
+ align:start position:0%
+whether that is
+actually a
+
+ align:start position:0%
+actually a
+ 
+
+ align:start position:0%
+actually a
+the best route to solving that mystery
+
+ align:start position:0%
+the best route to solving that mystery
+ 
+
+ align:start position:0%
+the best route to solving that mystery
+so that was multi-organ now we're
+
+ align:start position:0%
+so that was multi-organ now we're
+ 
+
+ align:start position:0%
+so that was multi-organ now we're
+talking about multi-organism okay
+
+ align:start position:0%
+talking about multi-organism okay
+ 
+
+ align:start position:0%
+talking about multi-organism okay
+after you've built up
+
+ align:start position:0%
+after you've built up
+ 
+
+ align:start position:0%
+after you've built up
+an entire organism uh
+
+ align:start position:0%
+an entire organism uh
+ 
+
+ align:start position:0%
+an entire organism uh
+then you want to know how it acts at the
+
+ align:start position:0%
+then you want to know how it acts at the
+ 
+
+ align:start position:0%
+then you want to know how it acts at the
+next level of network analysis which is
+
+ align:start position:0%
+next level of network analysis which is
+ 
+
+ align:start position:0%
+next level of network analysis which is
+how does it fit in with other organisms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+none of us
+
+ align:start position:0%
+none of us
+ 
+
+ align:start position:0%
+none of us
+almost no organism really belongs in
+
+ align:start position:0%
+almost no organism really belongs in
+ 
+
+ align:start position:0%
+almost no organism really belongs in
+ecological niche all by itself
+
+ align:start position:0%
+ecological niche all by itself
+ 
+
+ align:start position:0%
+ecological niche all by itself
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+some of the modeling we've talked in
+
+ align:start position:0%
+some of the modeling we've talked in
+ 
+
+ align:start position:0%
+some of the modeling we've talked in
+this course could be called simulation
+
+ align:start position:0%
+this course could be called simulation
+ 
+
+ align:start position:0%
+this course could be called simulation
+and uh probably one of the longest
+
+ align:start position:0%
+and uh probably one of the longest
+ 
+
+ align:start position:0%
+and uh probably one of the longest
+lasting uh
+
+ align:start position:0%
+lasting uh
+ 
+
+ align:start position:0%
+lasting uh
+computer games
+
+ align:start position:0%
+computer games
+ 
+
+ align:start position:0%
+computer games
+in the world and one of the most
+
+ align:start position:0%
+in the world and one of the most
+ 
+
+ align:start position:0%
+in the world and one of the most
+successful i've i've heard
+
+ align:start position:0%
+successful i've i've heard
+ 
+
+ align:start position:0%
+successful i've i've heard
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+the sims
+
+ align:start position:0%
+the sims
+ 
+
+ align:start position:0%
+the sims
+starting with sim city in uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simcity in 87
+
+ align:start position:0%
+simcity in 87
+ 
+
+ align:start position:0%
+simcity in 87
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and then this particular one illustrated
+
+ align:start position:0%
+and then this particular one illustrated
+ 
+
+ align:start position:0%
+and then this particular one illustrated
+here is sim life which is all about
+
+ align:start position:0%
+here is sim life which is all about
+ 
+
+ align:start position:0%
+here is sim life which is all about
+ecological modeling and it's not
+
+ align:start position:0%
+ecological modeling and it's not
+ 
+
+ align:start position:0%
+ecological modeling and it's not
+entirely different from what you know a
+
+ align:start position:0%
+entirely different from what you know a
+ 
+
+ align:start position:0%
+entirely different from what you know a
+serious
+
+ align:start position:0%
+serious
+ 
+
+ align:start position:0%
+serious
+uh ecological modeling program would do
+
+ align:start position:0%
+uh ecological modeling program would do
+ 
+
+ align:start position:0%
+uh ecological modeling program would do
+it certainly has a lot of the
+
+ align:start position:0%
+it certainly has a lot of the
+ 
+
+ align:start position:0%
+it certainly has a lot of the
+interesting parameters such as the
+
+ align:start position:0%
+interesting parameters such as the
+ 
+
+ align:start position:0%
+interesting parameters such as the
+lifespan
+
+ align:start position:0%
+lifespan
+ 
+
+ align:start position:0%
+lifespan
+here you know you're doing demographics
+
+ align:start position:0%
+here you know you're doing demographics
+ 
+
+ align:start position:0%
+here you know you're doing demographics
+here so you have the lifespan
+
+ align:start position:0%
+here so you have the lifespan
+ 
+
+ align:start position:0%
+here so you have the lifespan
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know food needed uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the size
+
+ align:start position:0%
+the size
+ 
+
+ align:start position:0%
+the size
+kind of vision roaming so forth of all
+
+ align:start position:0%
+kind of vision roaming so forth of all
+ 
+
+ align:start position:0%
+kind of vision roaming so forth of all
+these different different kinds of
+
+ align:start position:0%
+these different different kinds of
+ 
+
+ align:start position:0%
+these different different kinds of
+animals you can have uh
+
+ align:start position:0%
+animals you can have uh
+ 
+
+ align:start position:0%
+animals you can have uh
+herbert
+
+ align:start position:0%
+herbert
+ 
+
+ align:start position:0%
+herbert
+you can have plants you have herbivores
+
+ align:start position:0%
+you can have plants you have herbivores
+ 
+
+ align:start position:0%
+you can have plants you have herbivores
+carnivores
+
+ align:start position:0%
+carnivores
+ 
+
+ align:start position:0%
+carnivores
+and so on and then you can set up the
+
+ align:start position:0%
+and so on and then you can set up the
+ 
+
+ align:start position:0%
+and so on and then you can set up the
+population sizes and then it will do
+
+ align:start position:0%
+population sizes and then it will do
+ 
+
+ align:start position:0%
+population sizes and then it will do
+simulations
+
+ align:start position:0%
+simulations
+ 
+
+ align:start position:0%
+simulations
+uh based on that where each each
+
+ align:start position:0%
+uh based on that where each each
+ 
+
+ align:start position:0%
+uh based on that where each each
+individual animal
+
+ align:start position:0%
+individual animal
+ 
+
+ align:start position:0%
+individual animal
+is uh tracked in terms of uh positioning
+
+ align:start position:0%
+is uh tracked in terms of uh positioning
+ 
+
+ align:start position:0%
+is uh tracked in terms of uh positioning
+and quantity and
+
+ align:start position:0%
+and quantity and
+ 
+
+ align:start position:0%
+and quantity and
+uh and as you would expect as the you
+
+ align:start position:0%
+uh and as you would expect as the you
+ 
+
+ align:start position:0%
+uh and as you would expect as the you
+know carnivores build up and they knock
+
+ align:start position:0%
+know carnivores build up and they knock
+ 
+
+ align:start position:0%
+know carnivores build up and they knock
+down the herbivores and the plants go up
+
+ align:start position:0%
+down the herbivores and the plants go up
+ 
+
+ align:start position:0%
+down the herbivores and the plants go up
+and and so forth and it goes through
+
+ align:start position:0%
+and and so forth and it goes through
+ 
+
+ align:start position:0%
+and and so forth and it goes through
+these cycles
+
+ align:start position:0%
+these cycles
+ 
+
+ align:start position:0%
+these cycles
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so this is basically a stochastic
+
+ align:start position:0%
+and so this is basically a stochastic
+ 
+
+ align:start position:0%
+and so this is basically a stochastic
+model just like the stochastic models
+
+ align:start position:0%
+model just like the stochastic models
+ 
+
+ align:start position:0%
+model just like the stochastic models
+that we had for um
+
+ align:start position:0%
+that we had for um
+ 
+
+ align:start position:0%
+that we had for um
+for molecules but here at the organism
+
+ align:start position:0%
+for molecules but here at the organism
+ 
+
+ align:start position:0%
+for molecules but here at the organism
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+and what's happening here in the slower
+
+ align:start position:0%
+and what's happening here in the slower
+ 
+
+ align:start position:0%
+and what's happening here in the slower
+right-hand section is you've got little
+
+ align:start position:0%
+right-hand section is you've got little
+ 
+
+ align:start position:0%
+right-hand section is you've got little
+green plants uh
+
+ align:start position:0%
+green plants uh
+ 
+
+ align:start position:0%
+green plants uh
+getting eaten by herbivores and the
+
+ align:start position:0%
+getting eaten by herbivores and the
+ 
+
+ align:start position:0%
+getting eaten by herbivores and the
+orbitals getting in by carnivores
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully this course
+
+ align:start position:0%
+hopefully this course
+ 
+
+ align:start position:0%
+hopefully this course
+has already or will inspire you to to
+
+ align:start position:0%
+has already or will inspire you to to
+ 
+
+ align:start position:0%
+has already or will inspire you to to
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+think globally to think not only
+
+ align:start position:0%
+think globally to think not only
+ 
+
+ align:start position:0%
+think globally to think not only
+globally in terms of
+
+ align:start position:0%
+globally in terms of
+ 
+
+ align:start position:0%
+globally in terms of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+little pieces of molecular tools fit
+
+ align:start position:0%
+little pieces of molecular tools fit
+ 
+
+ align:start position:0%
+little pieces of molecular tools fit
+together into systems and networks but
+
+ align:start position:0%
+together into systems and networks but
+ 
+
+ align:start position:0%
+together into systems and networks but
+how our systems and networks we model
+
+ align:start position:0%
+how our systems and networks we model
+ 
+
+ align:start position:0%
+how our systems and networks we model
+fit into the big picture of what's what
+
+ align:start position:0%
+fit into the big picture of what's what
+ 
+
+ align:start position:0%
+fit into the big picture of what's what
+are really important problems
+
+ align:start position:0%
+are really important problems
+ 
+
+ align:start position:0%
+are really important problems
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+maybe a slightly improved
+
+ align:start position:0%
+maybe a slightly improved
+ 
+
+ align:start position:0%
+maybe a slightly improved
+viagra is not
+
+ align:start position:0%
+viagra is not
+ 
+
+ align:start position:0%
+viagra is not
+in the same category as a new
+
+ align:start position:0%
+in the same category as a new
+ 
+
+ align:start position:0%
+in the same category as a new
+tuberculosis drug or maybe it is i mean
+
+ align:start position:0%
+tuberculosis drug or maybe it is i mean
+ 
+
+ align:start position:0%
+tuberculosis drug or maybe it is i mean
+you decide for yourself
+
+ align:start position:0%
+you decide for yourself
+ 
+
+ align:start position:0%
+you decide for yourself
+what is thinking globally but you have
+
+ align:start position:0%
+what is thinking globally but you have
+ 
+
+ align:start position:0%
+what is thinking globally but you have
+to act locally and that's what we're
+
+ align:start position:0%
+to act locally and that's what we're
+ 
+
+ align:start position:0%
+to act locally and that's what we're
+doing in this class
+
+ align:start position:0%
+doing in this class
+ 
+
+ align:start position:0%
+doing in this class
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+when we're thinking globally and we're
+
+ align:start position:0%
+when we're thinking globally and we're
+ 
+
+ align:start position:0%
+when we're thinking globally and we're
+thinking about ecological systems
+
+ align:start position:0%
+thinking about ecological systems
+ 
+
+ align:start position:0%
+thinking about ecological systems
+we're thinking about
+
+ align:start position:0%
+we're thinking about
+ 
+
+ align:start position:0%
+we're thinking about
+the lithosphere
+
+ align:start position:0%
+the lithosphere
+ 
+
+ align:start position:0%
+the lithosphere
+for the most part
+
+ align:start position:0%
+for the most part
+ 
+
+ align:start position:0%
+for the most part
+and its interaction with
+
+ align:start position:0%
+and its interaction with
+ 
+
+ align:start position:0%
+and its interaction with
+the hydrosphere
+
+ align:start position:0%
+the hydrosphere
+ 
+
+ align:start position:0%
+the hydrosphere
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+lithosphere is mostly silicon dioxide a
+
+ align:start position:0%
+lithosphere is mostly silicon dioxide a
+ 
+
+ align:start position:0%
+lithosphere is mostly silicon dioxide a
+tiny bit of carbon
+
+ align:start position:0%
+tiny bit of carbon
+ 
+
+ align:start position:0%
+tiny bit of carbon
+and it gets very hot very quickly so
+
+ align:start position:0%
+and it gets very hot very quickly so
+ 
+
+ align:start position:0%
+and it gets very hot very quickly so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only the top
+
+ align:start position:0%
+only the top
+ 
+
+ align:start position:0%
+only the top
+point one percent the top four
+
+ align:start position:0%
+point one percent the top four
+ 
+
+ align:start position:0%
+point one percent the top four
+kilometers of it is uh survivable in any
+
+ align:start position:0%
+kilometers of it is uh survivable in any
+ 
+
+ align:start position:0%
+kilometers of it is uh survivable in any
+type of organism we know of about 110
+
+ align:start position:0%
+type of organism we know of about 110
+ 
+
+ align:start position:0%
+type of organism we know of about 110
+degrees centigrade is where organisms
+
+ align:start position:0%
+degrees centigrade is where organisms
+ 
+
+ align:start position:0%
+degrees centigrade is where organisms
+start having uh gay field trouble you
+
+ align:start position:0%
+start having uh gay field trouble you
+ 
+
+ align:start position:0%
+start having uh gay field trouble you
+and i would have trouble before that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the biosphere
+
+ align:start position:0%
+the biosphere
+ 
+
+ align:start position:0%
+the biosphere
+here is about 315 grams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+my estimate
+
+ align:start position:0%
+my estimate
+ 
+
+ align:start position:0%
+my estimate
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+marine
+
+ align:start position:0%
+marine
+ 
+
+ align:start position:0%
+marine
+organisms
+
+ align:start position:0%
+organisms
+ 
+
+ align:start position:0%
+organisms
+and maybe 10 to the
+
+ align:start position:0%
+and maybe 10 to the
+ 
+
+ align:start position:0%
+and maybe 10 to the
+18th gram for
+
+ align:start position:0%
+18th gram for
+ 
+
+ align:start position:0%
+18th gram for
+all land plants and animals and
+
+ align:start position:0%
+all land plants and animals and
+ 
+
+ align:start position:0%
+all land plants and animals and
+microorganisms
+
+ align:start position:0%
+microorganisms
+ 
+
+ align:start position:0%
+microorganisms
+the microbial hydrosphere uh
+
+ align:start position:0%
+the microbial hydrosphere uh
+ 
+
+ align:start position:0%
+the microbial hydrosphere uh
+here is about uh
+
+ align:start position:0%
+here is about uh
+ 
+
+ align:start position:0%
+here is about uh
+10 to the 24 20
+
+ align:start position:0%
+10 to the 24 20
+ 
+
+ align:start position:0%
+10 to the 24 20
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+milliliters which works at about 10 to
+
+ align:start position:0%
+milliliters which works at about 10 to
+ 
+
+ align:start position:0%
+milliliters which works at about 10 to
+27 cells a phenomenal number of these
+
+ align:start position:0%
+27 cells a phenomenal number of these
+ 
+
+ align:start position:0%
+27 cells a phenomenal number of these
+cells about 10 to the 26 of those cells
+
+ align:start position:0%
+cells about 10 to the 26 of those cells
+ 
+
+ align:start position:0%
+cells about 10 to the 26 of those cells
+is a single species which is
+
+ align:start position:0%
+is a single species which is
+ 
+
+ align:start position:0%
+is a single species which is
+prochlorococcus which is responsible for
+
+ align:start position:0%
+prochlorococcus which is responsible for
+ 
+
+ align:start position:0%
+prochlorococcus which is responsible for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+maybe about 50
+
+ align:start position:0%
+maybe about 50
+ 
+
+ align:start position:0%
+maybe about 50
+of your photosynthesis
+
+ align:start position:0%
+of your photosynthesis
+ 
+
+ align:start position:0%
+of your photosynthesis
+a lot of that photosynthesis does not
+
+ align:start position:0%
+a lot of that photosynthesis does not
+ 
+
+ align:start position:0%
+a lot of that photosynthesis does not
+end up in fixed carbon because it
+
+ align:start position:0%
+end up in fixed carbon because it
+ 
+
+ align:start position:0%
+end up in fixed carbon because it
+is immediately consumed by one of its
+
+ align:start position:0%
+is immediately consumed by one of its
+ 
+
+ align:start position:0%
+is immediately consumed by one of its
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+predators basically um
+
+ align:start position:0%
+predators basically um
+ 
+
+ align:start position:0%
+predators basically um
+but there's a you know there's really
+
+ align:start position:0%
+but there's a you know there's really
+ 
+
+ align:start position:0%
+but there's a you know there's really
+quite a lot of uh
+
+ align:start position:0%
+quite a lot of uh
+ 
+
+ align:start position:0%
+quite a lot of uh
+cells out there
+
+ align:start position:0%
+cells out there
+ 
+
+ align:start position:0%
+cells out there
+which to the extent that they're well
+
+ align:start position:0%
+which to the extent that they're well
+ 
+
+ align:start position:0%
+which to the extent that they're well
+mixed and they're not of course it's not
+
+ align:start position:0%
+mixed and they're not of course it's not
+ 
+
+ align:start position:0%
+mixed and they're not of course it's not
+perfectly mixed all the pacific and
+
+ align:start position:0%
+perfectly mixed all the pacific and
+ 
+
+ align:start position:0%
+perfectly mixed all the pacific and
+atlantic and so forth but it's it's a
+
+ align:start position:0%
+atlantic and so forth but it's it's a
+ 
+
+ align:start position:0%
+atlantic and so forth but it's it's a
+considerably more well mixed say than
+
+ align:start position:0%
+considerably more well mixed say than
+ 
+
+ align:start position:0%
+considerably more well mixed say than
+the lithosphere organisms where you have
+
+ align:start position:0%
+the lithosphere organisms where you have
+ 
+
+ align:start position:0%
+the lithosphere organisms where you have
+organisms down
+
+ align:start position:0%
+organisms down
+ 
+
+ align:start position:0%
+organisms down
+a kilometer into the ground they don't
+
+ align:start position:0%
+a kilometer into the ground they don't
+ 
+
+ align:start position:0%
+a kilometer into the ground they don't
+move around
+
+ align:start position:0%
+move around
+ 
+
+ align:start position:0%
+move around
+very rapidly
+
+ align:start position:0%
+very rapidly
+ 
+
+ align:start position:0%
+very rapidly
+so when you have a population of that
+
+ align:start position:0%
+so when you have a population of that
+ 
+
+ align:start position:0%
+so when you have a population of that
+size you'll remember from our one of our
+
+ align:start position:0%
+size you'll remember from our one of our
+ 
+
+ align:start position:0%
+size you'll remember from our one of our
+first lectures on population science the
+
+ align:start position:0%
+first lectures on population science the
+ 
+
+ align:start position:0%
+first lectures on population science the
+effect of population size determines the
+
+ align:start position:0%
+effect of population size determines the
+ 
+
+ align:start position:0%
+effect of population size determines the
+rate of drift and the sort of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optimality of the organism
+
+ align:start position:0%
+optimality of the organism
+ 
+
+ align:start position:0%
+optimality of the organism
+so one of the things that we do when we
+
+ align:start position:0%
+so one of the things that we do when we
+ 
+
+ align:start position:0%
+so one of the things that we do when we
+we've been talking about mining the
+
+ align:start position:0%
+we've been talking about mining the
+ 
+
+ align:start position:0%
+we've been talking about mining the
+biosphere one of the things we're
+
+ align:start position:0%
+biosphere one of the things we're
+ 
+
+ align:start position:0%
+biosphere one of the things we're
+looking for are new
+
+ align:start position:0%
+looking for are new
+ 
+
+ align:start position:0%
+looking for are new
+tools that we can use for um
+
+ align:start position:0%
+tools that we can use for um
+ 
+
+ align:start position:0%
+tools that we can use for um
+for nano engineering
+
+ align:start position:0%
+for nano engineering
+ 
+
+ align:start position:0%
+for nano engineering
+and one of the one kind of one of my pet
+
+ align:start position:0%
+and one of the one kind of one of my pet
+ 
+
+ align:start position:0%
+and one of the one kind of one of my pet
+ones that i'm becoming interested in we
+
+ align:start position:0%
+ones that i'm becoming interested in we
+ 
+
+ align:start position:0%
+ones that i'm becoming interested in we
+don't work on this i think they're just
+
+ align:start position:0%
+don't work on this i think they're just
+ 
+
+ align:start position:0%
+don't work on this i think they're just
+kind of interesting is uh there's a set
+
+ align:start position:0%
+kind of interesting is uh there's a set
+ 
+
+ align:start position:0%
+kind of interesting is uh there's a set
+of we mentioned this briefly in the drug
+
+ align:start position:0%
+of we mentioned this briefly in the drug
+ 
+
+ align:start position:0%
+of we mentioned this briefly in the drug
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+protein interaction lecture
+
+ align:start position:0%
+protein interaction lecture
+ 
+
+ align:start position:0%
+protein interaction lecture
+where uh but i don't think i've
+
+ align:start position:0%
+where uh but i don't think i've
+ 
+
+ align:start position:0%
+where uh but i don't think i've
+mentioned this particular one where you
+
+ align:start position:0%
+mentioned this particular one where you
+ 
+
+ align:start position:0%
+mentioned this particular one where you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+they polypeptides together it's kind of
+
+ align:start position:0%
+they polypeptides together it's kind of
+ 
+
+ align:start position:0%
+they polypeptides together it's kind of
+a pau it's another polymer that has
+
+ align:start position:0%
+a pau it's another polymer that has
+ 
+
+ align:start position:0%
+a pau it's another polymer that has
+certain similarities to the basic
+
+ align:start position:0%
+certain similarities to the basic
+ 
+
+ align:start position:0%
+certain similarities to the basic
+polymer to talk about but each step in
+
+ align:start position:0%
+polymer to talk about but each step in
+ 
+
+ align:start position:0%
+polymer to talk about but each step in
+it had to have a protein enzyme um
+
+ align:start position:0%
+it had to have a protein enzyme um
+ 
+
+ align:start position:0%
+it had to have a protein enzyme um
+an enzymatic domain to accomplish now
+
+ align:start position:0%
+an enzymatic domain to accomplish now
+ 
+
+ align:start position:0%
+an enzymatic domain to accomplish now
+and so one of these is tetracycline and
+
+ align:start position:0%
+and so one of these is tetracycline and
+ 
+
+ align:start position:0%
+and so one of these is tetracycline and
+this is one of the more aromatic you
+
+ align:start position:0%
+this is one of the more aromatic you
+ 
+
+ align:start position:0%
+this is one of the more aromatic you
+know kind of coupled aromatic compounds
+
+ align:start position:0%
+know kind of coupled aromatic compounds
+ 
+
+ align:start position:0%
+know kind of coupled aromatic compounds
+that's made because you have these
+
+ align:start position:0%
+that's made because you have these
+ 
+
+ align:start position:0%
+that's made because you have these
+cyclases and aromatases in addition to
+
+ align:start position:0%
+cyclases and aromatases in addition to
+ 
+
+ align:start position:0%
+cyclases and aromatases in addition to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sort of polymerization steps
+
+ align:start position:0%
+sort of polymerization steps
+ 
+
+ align:start position:0%
+sort of polymerization steps
+as you make this thing that's a it looks
+
+ align:start position:0%
+as you make this thing that's a it looks
+ 
+
+ align:start position:0%
+as you make this thing that's a it looks
+kind of like a poly uh
+
+ align:start position:0%
+kind of like a poly uh
+ 
+
+ align:start position:0%
+kind of like a poly uh
+aromatic hydrocarbon
+
+ align:start position:0%
+aromatic hydrocarbon
+ 
+
+ align:start position:0%
+aromatic hydrocarbon
+and and also in nature you will find
+
+ align:start position:0%
+and and also in nature you will find
+ 
+
+ align:start position:0%
+and and also in nature you will find
+in soot in forest fires and all kinds of
+
+ align:start position:0%
+in soot in forest fires and all kinds of
+ 
+
+ align:start position:0%
+in soot in forest fires and all kinds of
+natural phenomena you'll find prostate
+
+ align:start position:0%
+natural phenomena you'll find prostate
+ 
+
+ align:start position:0%
+natural phenomena you'll find prostate
+hydro
+
+ align:start position:0%
+hydro
+ 
+
+ align:start position:0%
+hydro
+aromatic hydrocarbons for some of you
+
+ align:start position:0%
+aromatic hydrocarbons for some of you
+ 
+
+ align:start position:0%
+aromatic hydrocarbons for some of you
+may know about as being a potent
+
+ align:start position:0%
+may know about as being a potent
+ 
+
+ align:start position:0%
+may know about as being a potent
+carcinogen but they're also just you
+
+ align:start position:0%
+carcinogen but they're also just you
+ 
+
+ align:start position:0%
+carcinogen but they're also just you
+know natural
+
+ align:start position:0%
+know natural
+ 
+
+ align:start position:0%
+know natural
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+but they're also
+
+ align:start position:0%
+but they're also
+ 
+
+ align:start position:0%
+but they're also
+you can start to see this looks a little
+
+ align:start position:0%
+you can start to see this looks a little
+ 
+
+ align:start position:0%
+you can start to see this looks a little
+bit like the bucky balls and bucky tubes
+
+ align:start position:0%
+bit like the bucky balls and bucky tubes
+ 
+
+ align:start position:0%
+bit like the bucky balls and bucky tubes
+that we talked about when we were
+
+ align:start position:0%
+that we talked about when we were
+ 
+
+ align:start position:0%
+that we talked about when we were
+talking about molecular
+
+ align:start position:0%
+talking about molecular
+ 
+
+ align:start position:0%
+talking about molecular
+uh type transistors
+
+ align:start position:0%
+uh type transistors
+ 
+
+ align:start position:0%
+uh type transistors
+so the possibility of mining the
+
+ align:start position:0%
+so the possibility of mining the
+ 
+
+ align:start position:0%
+so the possibility of mining the
+biosphere for these for enzymes that act
+
+ align:start position:0%
+biosphere for these for enzymes that act
+ 
+
+ align:start position:0%
+biosphere for these for enzymes that act
+to synthesize or degrade this class of
+
+ align:start position:0%
+to synthesize or degrade this class of
+ 
+
+ align:start position:0%
+to synthesize or degrade this class of
+just an example we could list many
+
+ align:start position:0%
+just an example we could list many
+ 
+
+ align:start position:0%
+just an example we could list many
+others but the the part of it is just to
+
+ align:start position:0%
+others but the the part of it is just to
+ 
+
+ align:start position:0%
+others but the the part of it is just to
+dream to imagine what it is you would
+
+ align:start position:0%
+dream to imagine what it is you would
+ 
+
+ align:start position:0%
+dream to imagine what it is you would
+like to find out there
+
+ align:start position:0%
+like to find out there
+ 
+
+ align:start position:0%
+like to find out there
+and if there's an abundant
+
+ align:start position:0%
+and if there's an abundant
+ 
+
+ align:start position:0%
+and if there's an abundant
+source of it
+
+ align:start position:0%
+source of it
+ 
+
+ align:start position:0%
+source of it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then then uh you should be able to
+
+ align:start position:0%
+then then uh you should be able to
+ 
+
+ align:start position:0%
+then then uh you should be able to
+abundant sources of say the compound in
+
+ align:start position:0%
+abundant sources of say the compound in
+ 
+
+ align:start position:0%
+abundant sources of say the compound in
+this case you should be able to find a
+
+ align:start position:0%
+this case you should be able to find a
+ 
+
+ align:start position:0%
+this case you should be able to find a
+a microorganism an enzyme that goes with
+
+ align:start position:0%
+a microorganism an enzyme that goes with
+ 
+
+ align:start position:0%
+a microorganism an enzyme that goes with
+that because there's a truly phenomenal
+
+ align:start position:0%
+that because there's a truly phenomenal
+ 
+
+ align:start position:0%
+that because there's a truly phenomenal
+amount of diversity
+
+ align:start position:0%
+amount of diversity
+ 
+
+ align:start position:0%
+amount of diversity
+the other asp the other another very
+
+ align:start position:0%
+the other asp the other another very
+ 
+
+ align:start position:0%
+the other asp the other another very
+important global consideration rather
+
+ align:start position:0%
+important global consideration rather
+ 
+
+ align:start position:0%
+important global consideration rather
+than just mining it for new tools
+
+ align:start position:0%
+than just mining it for new tools
+ 
+
+ align:start position:0%
+than just mining it for new tools
+is thinking about ways that either we
+
+ align:start position:0%
+is thinking about ways that either we
+ 
+
+ align:start position:0%
+is thinking about ways that either we
+could engineer or accidentally mess up
+
+ align:start position:0%
+could engineer or accidentally mess up
+ 
+
+ align:start position:0%
+could engineer or accidentally mess up
+our entire planet um
+
+ align:start position:0%
+our entire planet um
+ 
+
+ align:start position:0%
+our entire planet um
+as we are could be doing with global
+
+ align:start position:0%
+as we are could be doing with global
+ 
+
+ align:start position:0%
+as we are could be doing with global
+warming or could do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and perhaps it's naive to think that we
+
+ align:start position:0%
+and perhaps it's naive to think that we
+ 
+
+ align:start position:0%
+and perhaps it's naive to think that we
+actually are having such a big effect
+
+ align:start position:0%
+actually are having such a big effect
+ 
+
+ align:start position:0%
+actually are having such a big effect
+because we know that global warming
+
+ align:start position:0%
+because we know that global warming
+ 
+
+ align:start position:0%
+because we know that global warming
+changes periodically over
+
+ align:start position:0%
+changes periodically over
+ 
+
+ align:start position:0%
+changes periodically over
+millennia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it is it is very clear from the
+
+ align:start position:0%
+but it is it is very clear from the
+ 
+
+ align:start position:0%
+but it is it is very clear from the
+record that
+
+ align:start position:0%
+record that
+ 
+
+ align:start position:0%
+record that
+just exactly how much carbon dioxide we
+
+ align:start position:0%
+just exactly how much carbon dioxide we
+ 
+
+ align:start position:0%
+just exactly how much carbon dioxide we
+are releasing and it makes sense
+
+ align:start position:0%
+are releasing and it makes sense
+ 
+
+ align:start position:0%
+are releasing and it makes sense
+that it's consistent with the kind of
+
+ align:start position:0%
+that it's consistent with the kind of
+ 
+
+ align:start position:0%
+that it's consistent with the kind of
+temperature changes that have been
+
+ align:start position:0%
+temperature changes that have been
+ 
+
+ align:start position:0%
+temperature changes that have been
+observed since the industrial revolution
+
+ align:start position:0%
+observed since the industrial revolution
+ 
+
+ align:start position:0%
+observed since the industrial revolution
+in any case when you look at uh
+
+ align:start position:0%
+in any case when you look at uh
+ 
+
+ align:start position:0%
+in any case when you look at uh
+in particular
+
+ align:start position:0%
+in particular
+ 
+
+ align:start position:0%
+in particular
+the southern ocean
+
+ align:start position:0%
+the southern ocean
+ 
+
+ align:start position:0%
+the southern ocean
+up at the top of slide 27 you can see
+
+ align:start position:0%
+up at the top of slide 27 you can see
+ 
+
+ align:start position:0%
+up at the top of slide 27 you can see
+there's a few places in particular
+
+ align:start position:0%
+there's a few places in particular
+ 
+
+ align:start position:0%
+there's a few places in particular
+southern ocean seems like it's a prime
+
+ align:start position:0%
+southern ocean seems like it's a prime
+ 
+
+ align:start position:0%
+southern ocean seems like it's a prime
+candidate where you have high nutrients
+
+ align:start position:0%
+candidate where you have high nutrients
+ 
+
+ align:start position:0%
+candidate where you have high nutrients
+but low chlorophyll you say well why
+
+ align:start position:0%
+but low chlorophyll you say well why
+ 
+
+ align:start position:0%
+but low chlorophyll you say well why
+would you have high nutrients but very
+
+ align:start position:0%
+would you have high nutrients but very
+ 
+
+ align:start position:0%
+would you have high nutrients but very
+little uh you know of the
+
+ align:start position:0%
+little uh you know of the
+ 
+
+ align:start position:0%
+little uh you know of the
+chlorophyll around
+
+ align:start position:0%
+chlorophyll around
+ 
+
+ align:start position:0%
+chlorophyll around
+uh that you would which which is a tip
+
+ align:start position:0%
+uh that you would which which is a tip
+ 
+
+ align:start position:0%
+uh that you would which which is a tip
+off that you have of the photosynthetic
+
+ align:start position:0%
+off that you have of the photosynthetic
+ 
+
+ align:start position:0%
+off that you have of the photosynthetic
+bacteria
+
+ align:start position:0%
+bacteria
+ 
+
+ align:start position:0%
+bacteria
+and the reason is that you have a
+
+ align:start position:0%
+and the reason is that you have a
+ 
+
+ align:start position:0%
+and the reason is that you have a
+limitation of some micronutrient
+
+ align:start position:0%
+limitation of some micronutrient
+ 
+
+ align:start position:0%
+limitation of some micronutrient
+micronutrient means it's not needed in
+
+ align:start position:0%
+micronutrient means it's not needed in
+ 
+
+ align:start position:0%
+micronutrient means it's not needed in
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know the vast quantities you need
+
+ align:start position:0%
+you know the vast quantities you need
+ 
+
+ align:start position:0%
+you know the vast quantities you need
+nitrogen phosphorus carbon oxygen and so
+
+ align:start position:0%
+nitrogen phosphorus carbon oxygen and so
+ 
+
+ align:start position:0%
+nitrogen phosphorus carbon oxygen and so
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+so iron typically is the limiting
+
+ align:start position:0%
+so iron typically is the limiting
+ 
+
+ align:start position:0%
+so iron typically is the limiting
+micronutrient in the southern ocean and
+
+ align:start position:0%
+micronutrient in the southern ocean and
+ 
+
+ align:start position:0%
+micronutrient in the southern ocean and
+so there are actually have been little
+
+ align:start position:0%
+so there are actually have been little
+ 
+
+ align:start position:0%
+so there are actually have been little
+pilot experiments to drop iron off the
+
+ align:start position:0%
+pilot experiments to drop iron off the
+ 
+
+ align:start position:0%
+pilot experiments to drop iron off the
+backs of huge tankers
+
+ align:start position:0%
+backs of huge tankers
+ 
+
+ align:start position:0%
+backs of huge tankers
+and there are now at least seven patents
+
+ align:start position:0%
+and there are now at least seven patents
+ 
+
+ align:start position:0%
+and there are now at least seven patents
+that have been filed on doing this in
+
+ align:start position:0%
+that have been filed on doing this in
+ 
+
+ align:start position:0%
+that have been filed on doing this in
+order to balance out
+
+ align:start position:0%
+order to balance out
+ 
+
+ align:start position:0%
+order to balance out
+carbon credits for different nations
+
+ align:start position:0%
+carbon credits for different nations
+ 
+
+ align:start position:0%
+carbon credits for different nations
+this is potentially a very big
+
+ align:start position:0%
+this is potentially a very big
+ 
+
+ align:start position:0%
+this is potentially a very big
+bit of terrestrial engineering that
+
+ align:start position:0%
+bit of terrestrial engineering that
+ 
+
+ align:start position:0%
+bit of terrestrial engineering that
+might happen that involves trying to
+
+ align:start position:0%
+might happen that involves trying to
+ 
+
+ align:start position:0%
+might happen that involves trying to
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+phytoplankton
+
+ align:start position:0%
+phytoplankton
+ 
+
+ align:start position:0%
+phytoplankton
+and as this line here begins to point
+
+ align:start position:0%
+and as this line here begins to point
+ 
+
+ align:start position:0%
+and as this line here begins to point
+out even though phytoplankton are only
+
+ align:start position:0%
+out even though phytoplankton are only
+ 
+
+ align:start position:0%
+out even though phytoplankton are only
+one percent of the total global biomass
+
+ align:start position:0%
+one percent of the total global biomass
+ 
+
+ align:start position:0%
+one percent of the total global biomass
+it's about 50 of the carbon fixation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the source of this 50-fold
+
+ align:start position:0%
+what is the source of this 50-fold
+ 
+
+ align:start position:0%
+what is the source of this 50-fold
+anomaly why is it that even though it's
+
+ align:start position:0%
+anomaly why is it that even though it's
+ 
+
+ align:start position:0%
+anomaly why is it that even though it's
+doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know how is it doing 50 of carbon
+
+ align:start position:0%
+you know how is it doing 50 of carbon
+ 
+
+ align:start position:0%
+you know how is it doing 50 of carbon
+fixation and what's happening is a lot
+
+ align:start position:0%
+fixation and what's happening is a lot
+ 
+
+ align:start position:0%
+fixation and what's happening is a lot
+of the carbon is going right back out uh
+
+ align:start position:0%
+of the carbon is going right back out uh
+ 
+
+ align:start position:0%
+of the carbon is going right back out uh
+after being fixed instead of settling to
+
+ align:start position:0%
+after being fixed instead of settling to
+ 
+
+ align:start position:0%
+after being fixed instead of settling to
+the bottom of the ocean and never
+
+ align:start position:0%
+the bottom of the ocean and never
+ 
+
+ align:start position:0%
+the bottom of the ocean and never
+bothering us again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it gets
+
+ align:start position:0%
+it gets
+ 
+
+ align:start position:0%
+it gets
+returned and the exact modeling of that
+
+ align:start position:0%
+returned and the exact modeling of that
+ 
+
+ align:start position:0%
+returned and the exact modeling of that
+requires a much deeper knowledge
+
+ align:start position:0%
+requires a much deeper knowledge
+ 
+
+ align:start position:0%
+requires a much deeper knowledge
+of exactly what organisms are present in
+
+ align:start position:0%
+of exactly what organisms are present in
+ 
+
+ align:start position:0%
+of exactly what organisms are present in
+the ocean
+
+ align:start position:0%
+the ocean
+ 
+
+ align:start position:0%
+the ocean
+one of the problems of this however is a
+
+ align:start position:0%
+one of the problems of this however is a
+ 
+
+ align:start position:0%
+one of the problems of this however is a
+genomic
+
+ align:start position:0%
+genomic
+ 
+
+ align:start position:0%
+genomic
+problem in a certain sense uh
+
+ align:start position:0%
+problem in a certain sense uh
+ 
+
+ align:start position:0%
+problem in a certain sense uh
+which is that very few of these
+
+ align:start position:0%
+which is that very few of these
+ 
+
+ align:start position:0%
+which is that very few of these
+organisms
+
+ align:start position:0%
+organisms
+ 
+
+ align:start position:0%
+organisms
+can be cultivated in a laboratory
+
+ align:start position:0%
+can be cultivated in a laboratory
+ 
+
+ align:start position:0%
+can be cultivated in a laboratory
+on the order of 99.9
+
+ align:start position:0%
+on the order of 99.9
+ 
+
+ align:start position:0%
+on the order of 99.9
+of the organisms you sample from the
+
+ align:start position:0%
+of the organisms you sample from the
+ 
+
+ align:start position:0%
+of the organisms you sample from the
+ocean or from the soil a number of
+
+ align:start position:0%
+ocean or from the soil a number of
+ 
+
+ align:start position:0%
+ocean or from the soil a number of
+different environments
+
+ align:start position:0%
+different environments
+ 
+
+ align:start position:0%
+different environments
+do not grow well in the laboratory
+
+ align:start position:0%
+do not grow well in the laboratory
+ 
+
+ align:start position:0%
+do not grow well in the laboratory
+so if you were to study them
+
+ align:start position:0%
+so if you were to study them
+ 
+
+ align:start position:0%
+so if you were to study them
+some people are feeling that the best
+
+ align:start position:0%
+some people are feeling that the best
+ 
+
+ align:start position:0%
+some people are feeling that the best
+route to studying them is going directly
+
+ align:start position:0%
+route to studying them is going directly
+ 
+
+ align:start position:0%
+route to studying them is going directly
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+looking at their genomes without
+
+ align:start position:0%
+looking at their genomes without
+ 
+
+ align:start position:0%
+looking at their genomes without
+necessarily being able to grow them in
+
+ align:start position:0%
+necessarily being able to grow them in
+ 
+
+ align:start position:0%
+necessarily being able to grow them in
+the laboratory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when we talk about this this problem
+
+ align:start position:0%
+now when we talk about this this problem
+ 
+
+ align:start position:0%
+now when we talk about this this problem
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+even if we fertilize the oceans and uh
+
+ align:start position:0%
+even if we fertilize the oceans and uh
+ 
+
+ align:start position:0%
+even if we fertilize the oceans and uh
+and you know we can model this whole
+
+ align:start position:0%
+and you know we can model this whole
+ 
+
+ align:start position:0%
+and you know we can model this whole
+procedure we'll go into details but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if there are predators there that that
+
+ align:start position:0%
+if there are predators there that that
+ 
+
+ align:start position:0%
+if there are predators there that that
+take the fixed carbon
+
+ align:start position:0%
+take the fixed carbon
+ 
+
+ align:start position:0%
+take the fixed carbon
+and turn it back into carbon dioxide you
+
+ align:start position:0%
+and turn it back into carbon dioxide you
+ 
+
+ align:start position:0%
+and turn it back into carbon dioxide you
+want to be able to monitor that now of
+
+ align:start position:0%
+want to be able to monitor that now of
+ 
+
+ align:start position:0%
+want to be able to monitor that now of
+course the ocean is a large complex
+
+ align:start position:0%
+course the ocean is a large complex
+ 
+
+ align:start position:0%
+course the ocean is a large complex
+set of prokaryotic
+
+ align:start position:0%
+set of prokaryotic
+ 
+
+ align:start position:0%
+set of prokaryotic
+autotrophs that is say photosynthetic
+
+ align:start position:0%
+autotrophs that is say photosynthetic
+ 
+
+ align:start position:0%
+autotrophs that is say photosynthetic
+bacteria and eukaryotic potential
+
+ align:start position:0%
+bacteria and eukaryotic potential
+ 
+
+ align:start position:0%
+bacteria and eukaryotic potential
+bacteria and prokaryotic and eukaryotic
+
+ align:start position:0%
+bacteria and prokaryotic and eukaryotic
+ 
+
+ align:start position:0%
+bacteria and prokaryotic and eukaryotic
+uh predators
+
+ align:start position:0%
+uh predators
+ 
+
+ align:start position:0%
+uh predators
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+of various sorts
+
+ align:start position:0%
+of various sorts
+ 
+
+ align:start position:0%
+of various sorts
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is what i think one of the more
+
+ align:start position:0%
+this is what i think one of the more
+ 
+
+ align:start position:0%
+this is what i think one of the more
+interesting predator prey um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differential equation models it's very
+
+ align:start position:0%
+differential equation models it's very
+ 
+
+ align:start position:0%
+differential equation models it's very
+it's almost the same as many of the
+
+ align:start position:0%
+it's almost the same as many of the
+ 
+
+ align:start position:0%
+it's almost the same as many of the
+other different equations that we did
+
+ align:start position:0%
+other different equations that we did
+ 
+
+ align:start position:0%
+other different equations that we did
+from from the first lecture on on
+
+ align:start position:0%
+from from the first lecture on on
+ 
+
+ align:start position:0%
+from from the first lecture on on
+growth we did the logistic equation some
+
+ align:start position:0%
+growth we did the logistic equation some
+ 
+
+ align:start position:0%
+growth we did the logistic equation some
+of the ones we did on repressor function
+
+ align:start position:0%
+of the ones we did on repressor function
+ 
+
+ align:start position:0%
+of the ones we did on repressor function
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+but things kind of interesting about
+
+ align:start position:0%
+but things kind of interesting about
+ 
+
+ align:start position:0%
+but things kind of interesting about
+this one is it's not
+
+ align:start position:0%
+this one is it's not
+ 
+
+ align:start position:0%
+this one is it's not
+simply a
+
+ align:start position:0%
+simply a
+ 
+
+ align:start position:0%
+simply a
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+single cell bacteria
+
+ align:start position:0%
+single cell bacteria
+ 
+
+ align:start position:0%
+single cell bacteria
+being eaten by a single cell heterotroph
+
+ align:start position:0%
+being eaten by a single cell heterotroph
+ 
+
+ align:start position:0%
+being eaten by a single cell heterotroph
+single you know let's say a blue green
+
+ align:start position:0%
+single you know let's say a blue green
+ 
+
+ align:start position:0%
+single you know let's say a blue green
+algae being in by a single cell
+
+ align:start position:0%
+algae being in by a single cell
+ 
+
+ align:start position:0%
+algae being in by a single cell
+heterotroph here you they're both
+
+ align:start position:0%
+heterotroph here you they're both
+ 
+
+ align:start position:0%
+heterotroph here you they're both
+multicellular uh they're sort of the
+
+ align:start position:0%
+multicellular uh they're sort of the
+ 
+
+ align:start position:0%
+multicellular uh they're sort of the
+minimal multicellular but because
+
+ align:start position:0%
+minimal multicellular but because
+ 
+
+ align:start position:0%
+minimal multicellular but because
+they're multi so chlorella is one of the
+
+ align:start position:0%
+they're multi so chlorella is one of the
+ 
+
+ align:start position:0%
+they're multi so chlorella is one of the
+smallest plants the multicellular plants
+
+ align:start position:0%
+smallest plants the multicellular plants
+ 
+
+ align:start position:0%
+smallest plants the multicellular plants
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+brachionas is a
+
+ align:start position:0%
+brachionas is a
+ 
+
+ align:start position:0%
+brachionas is a
+small rotifer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multicellular animal
+
+ align:start position:0%
+multicellular animal
+ 
+
+ align:start position:0%
+multicellular animal
+because they're all cellular though now
+
+ align:start position:0%
+because they're all cellular though now
+ 
+
+ align:start position:0%
+because they're all cellular though now
+you have the demographic mortality
+
+ align:start position:0%
+you have the demographic mortality
+ 
+
+ align:start position:0%
+you have the demographic mortality
+and fecundity of each of these things
+
+ align:start position:0%
+and fecundity of each of these things
+ 
+
+ align:start position:0%
+and fecundity of each of these things
+that has to be modeled in that's the
+
+ align:start position:0%
+that has to be modeled in that's the
+ 
+
+ align:start position:0%
+that has to be modeled in that's the
+m and the lambda for brachionas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this plays into these equations where
+
+ align:start position:0%
+this plays into these equations where
+ 
+
+ align:start position:0%
+this plays into these equations where
+you have here the in the upper uh right
+
+ align:start position:0%
+you have here the in the upper uh right
+ 
+
+ align:start position:0%
+you have here the in the upper uh right
+slide 28 the
+
+ align:start position:0%
+slide 28 the
+ 
+
+ align:start position:0%
+slide 28 the
+rate of change of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nitrogen with respect to time
+
+ align:start position:0%
+nitrogen with respect to time
+ 
+
+ align:start position:0%
+nitrogen with respect to time
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+concentration of corella so nitrogen is
+
+ align:start position:0%
+concentration of corella so nitrogen is
+ 
+
+ align:start position:0%
+concentration of corella so nitrogen is
+in corella is c
+
+ align:start position:0%
+in corella is c
+ 
+
+ align:start position:0%
+in corella is c
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+r is the brachionas
+
+ align:start position:0%
+r is the brachionas
+ 
+
+ align:start position:0%
+r is the brachionas
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that are reproducing and b are the
+
+ align:start position:0%
+that are reproducing and b are the
+ 
+
+ align:start position:0%
+that are reproducing and b are the
+brachionas which are the total
+
+ align:start position:0%
+brachionas which are the total
+ 
+
+ align:start position:0%
+brachionas which are the total
+and you can see each of these equations
+
+ align:start position:0%
+and you can see each of these equations
+ 
+
+ align:start position:0%
+and you can see each of these equations
+and how it plays out now this is how
+
+ align:start position:0%
+and how it plays out now this is how
+ 
+
+ align:start position:0%
+and how it plays out now this is how
+uh and the way they play it out here is
+
+ align:start position:0%
+uh and the way they play it out here is
+ 
+
+ align:start position:0%
+uh and the way they play it out here is
+you do it by dilution rate delta here
+
+ align:start position:0%
+you do it by dilution rate delta here
+ 
+
+ align:start position:0%
+you do it by dilution rate delta here
+and the dilution rate
+
+ align:start position:0%
+and the dilution rate
+ 
+
+ align:start position:0%
+and the dilution rate
+is shown
+
+ align:start position:0%
+is shown
+ 
+
+ align:start position:0%
+is shown
+along the
+
+ align:start position:0%
+along the
+ 
+
+ align:start position:0%
+along the
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the horizontal x-axis for each of these
+
+ align:start position:0%
+the horizontal x-axis for each of these
+ 
+
+ align:start position:0%
+the horizontal x-axis for each of these
+three plots here
+
+ align:start position:0%
+three plots here
+ 
+
+ align:start position:0%
+three plots here
+and what they're modeling
+
+ align:start position:0%
+and what they're modeling
+ 
+
+ align:start position:0%
+and what they're modeling
+uh is uh on the far left the nitrogen
+
+ align:start position:0%
+uh is uh on the far left the nitrogen
+ 
+
+ align:start position:0%
+uh is uh on the far left the nitrogen
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a function of dilution rate and you
+
+ align:start position:0%
+as a function of dilution rate and you
+ 
+
+ align:start position:0%
+as a function of dilution rate and you
+can see you get these different uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different sectors of behavior
+
+ align:start position:0%
+different sectors of behavior
+ 
+
+ align:start position:0%
+different sectors of behavior
+when you look at the corella this is the
+
+ align:start position:0%
+when you look at the corella this is the
+ 
+
+ align:start position:0%
+when you look at the corella this is the
+green
+
+ align:start position:0%
+green
+ 
+
+ align:start position:0%
+green
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the photosynthetic multicellular
+
+ align:start position:0%
+the photosynthetic multicellular
+ 
+
+ align:start position:0%
+the photosynthetic multicellular
+organism in units of millions of cells
+
+ align:start position:0%
+organism in units of millions of cells
+ 
+
+ align:start position:0%
+organism in units of millions of cells
+per milliliter that can take different
+
+ align:start position:0%
+per milliliter that can take different
+ 
+
+ align:start position:0%
+per milliliter that can take different
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there's a you can take different
+
+ align:start position:0%
+there's a you can take different
+ 
+
+ align:start position:0%
+there's a you can take different
+pathways here um
+
+ align:start position:0%
+pathways here um
+ 
+
+ align:start position:0%
+pathways here um
+where as a function of dilution rate you
+
+ align:start position:0%
+where as a function of dilution rate you
+ 
+
+ align:start position:0%
+where as a function of dilution rate you
+get this bifurcation where you get a
+
+ align:start position:0%
+get this bifurcation where you get a
+ 
+
+ align:start position:0%
+get this bifurcation where you get a
+huge uh split in the
+
+ align:start position:0%
+huge uh split in the
+ 
+
+ align:start position:0%
+huge uh split in the
+possible uh
+
+ align:start position:0%
+possible uh
+ 
+
+ align:start position:0%
+possible uh
+concentrations of corella
+
+ align:start position:0%
+concentrations of corella
+ 
+
+ align:start position:0%
+concentrations of corella
+is the one curve and the brachionas
+
+ align:start position:0%
+is the one curve and the brachionas
+ 
+
+ align:start position:0%
+is the one curve and the brachionas
+the predator is the other curve this
+
+ align:start position:0%
+the predator is the other curve this
+ 
+
+ align:start position:0%
+the predator is the other curve this
+kind of bifurcation is the sort of thing
+
+ align:start position:0%
+kind of bifurcation is the sort of thing
+ 
+
+ align:start position:0%
+kind of bifurcation is the sort of thing
+we talked about
+
+ align:start position:0%
+we talked about
+ 
+
+ align:start position:0%
+we talked about
+earlier in both from the logistic
+
+ align:start position:0%
+earlier in both from the logistic
+ 
+
+ align:start position:0%
+earlier in both from the logistic
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what in the upper right hand your here's
+
+ align:start position:0%
+what in the upper right hand your here's
+ 
+
+ align:start position:0%
+what in the upper right hand your here's
+our friend the coefficient of variation
+
+ align:start position:0%
+our friend the coefficient of variation
+ 
+
+ align:start position:0%
+our friend the coefficient of variation
+in percent ranging from 0 to 8 80 or so
+
+ align:start position:0%
+in percent ranging from 0 to 8 80 or so
+ 
+
+ align:start position:0%
+in percent ranging from 0 to 8 80 or so
+on the vertical axis and the dilution
+
+ align:start position:0%
+on the vertical axis and the dilution
+ 
+
+ align:start position:0%
+on the vertical axis and the dilution
+rate and again you can see
+
+ align:start position:0%
+rate and again you can see
+ 
+
+ align:start position:0%
+rate and again you can see
+that you get a peak in the dilution rate
+
+ align:start position:0%
+that you get a peak in the dilution rate
+ 
+
+ align:start position:0%
+that you get a peak in the dilution rate
+at around seven five so these are these
+
+ align:start position:0%
+at around seven five so these are these
+ 
+
+ align:start position:0%
+at around seven five so these are these
+are the bottom two models in the upper
+
+ align:start position:0%
+are the bottom two models in the upper
+ 
+
+ align:start position:0%
+are the bottom two models in the upper
+right is a data
+
+ align:start position:0%
+right is a data
+ 
+
+ align:start position:0%
+right is a data
+um but you can actually see when you run
+
+ align:start position:0%
+um but you can actually see when you run
+ 
+
+ align:start position:0%
+um but you can actually see when you run
+real chlorella and brachionas in here
+
+ align:start position:0%
+real chlorella and brachionas in here
+ 
+
+ align:start position:0%
+real chlorella and brachionas in here
+but you do get a peak just as you would
+
+ align:start position:0%
+but you do get a peak just as you would
+ 
+
+ align:start position:0%
+but you do get a peak just as you would
+predict this kind of bifurcation now
+
+ align:start position:0%
+predict this kind of bifurcation now
+ 
+
+ align:start position:0%
+predict this kind of bifurcation now
+with kinetic modeling
+
+ align:start position:0%
+with kinetic modeling
+ 
+
+ align:start position:0%
+with kinetic modeling
+that's due to
+
+ align:start position:0%
+that's due to
+ 
+
+ align:start position:0%
+that's due to
+where you get
+
+ align:start position:0%
+where you get
+ 
+
+ align:start position:0%
+where you get
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+behavior in this
+
+ align:start position:0%
+behavior in this
+ 
+
+ align:start position:0%
+behavior in this
+complicated there's a fairly simple
+
+ align:start position:0%
+complicated there's a fairly simple
+ 
+
+ align:start position:0%
+complicated there's a fairly simple
+model ecosystem where you just have two
+
+ align:start position:0%
+model ecosystem where you just have two
+ 
+
+ align:start position:0%
+model ecosystem where you just have two
+species
+
+ align:start position:0%
+species
+ 
+
+ align:start position:0%
+species
+in the ocean of course you have a lot
+
+ align:start position:0%
+in the ocean of course you have a lot
+ 
+
+ align:start position:0%
+in the ocean of course you have a lot
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+that's out in the wide world where you
+
+ align:start position:0%
+that's out in the wide world where you
+ 
+
+ align:start position:0%
+that's out in the wide world where you
+have 10 to the 26 cells
+
+ align:start position:0%
+have 10 to the 26 cells
+ 
+
+ align:start position:0%
+have 10 to the 26 cells
+but inside every one of us in this room
+
+ align:start position:0%
+but inside every one of us in this room
+ 
+
+ align:start position:0%
+but inside every one of us in this room
+no offense but there are about uh
+
+ align:start position:0%
+no offense but there are about uh
+ 
+
+ align:start position:0%
+no offense but there are about uh
+ten times as many non-human cells in
+
+ align:start position:0%
+ten times as many non-human cells in
+ 
+
+ align:start position:0%
+ten times as many non-human cells in
+each of us as there are human cells
+
+ align:start position:0%
+each of us as there are human cells
+ 
+
+ align:start position:0%
+each of us as there are human cells
+and we have our own ecology
+
+ align:start position:0%
+and we have our own ecology
+ 
+
+ align:start position:0%
+and we have our own ecology
+and there is a literature where
+
+ align:start position:0%
+and there is a literature where
+ 
+
+ align:start position:0%
+and there is a literature where
+you know certain organisms we know cause
+
+ align:start position:0%
+you know certain organisms we know cause
+ 
+
+ align:start position:0%
+you know certain organisms we know cause
+diseases and they're put into one
+
+ align:start position:0%
+diseases and they're put into one
+ 
+
+ align:start position:0%
+diseases and they're put into one
+category infectious diseases but then
+
+ align:start position:0%
+category infectious diseases but then
+ 
+
+ align:start position:0%
+category infectious diseases but then
+there's another set that takes some time
+
+ align:start position:0%
+there's another set that takes some time
+ 
+
+ align:start position:0%
+there's another set that takes some time
+to sort out and you can see here are
+
+ align:start position:0%
+to sort out and you can see here are
+ 
+
+ align:start position:0%
+to sort out and you can see here are
+candidate diseases and candidate
+
+ align:start position:0%
+candidate diseases and candidate
+ 
+
+ align:start position:0%
+candidate diseases and candidate
+organisms and all these little bars that
+
+ align:start position:0%
+organisms and all these little bars that
+ 
+
+ align:start position:0%
+organisms and all these little bars that
+are going in here are uh
+
+ align:start position:0%
+are going in here are uh
+ 
+
+ align:start position:0%
+are going in here are uh
+you know references that you can look up
+
+ align:start position:0%
+you know references that you can look up
+ 
+
+ align:start position:0%
+you know references that you can look up
+where uh maybe it's not an airtight case
+
+ align:start position:0%
+where uh maybe it's not an airtight case
+ 
+
+ align:start position:0%
+where uh maybe it's not an airtight case
+yet or maybe it's not even maybe this
+
+ align:start position:0%
+yet or maybe it's not even maybe this
+ 
+
+ align:start position:0%
+yet or maybe it's not even maybe this
+controversial or discredited at this
+
+ align:start position:0%
+controversial or discredited at this
+ 
+
+ align:start position:0%
+controversial or discredited at this
+point but these are links where
+
+ align:start position:0%
+point but these are links where
+ 
+
+ align:start position:0%
+point but these are links where
+eventually this will be called an
+
+ align:start position:0%
+eventually this will be called an
+ 
+
+ align:start position:0%
+eventually this will be called an
+infectious disease helicobacter hydride
+
+ align:start position:0%
+infectious disease helicobacter hydride
+ 
+
+ align:start position:0%
+infectious disease helicobacter hydride
+causes chemicals which i think that's
+
+ align:start position:0%
+causes chemicals which i think that's
+ 
+
+ align:start position:0%
+causes chemicals which i think that's
+basically already accepted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some australian doctor named marshall
+
+ align:start position:0%
+some australian doctor named marshall
+ 
+
+ align:start position:0%
+some australian doctor named marshall
+decided to drink a bunch of helicobacter
+
+ align:start position:0%
+decided to drink a bunch of helicobacter
+ 
+
+ align:start position:0%
+decided to drink a bunch of helicobacter
+to prove to his colleagues he didn't
+
+ align:start position:0%
+to prove to his colleagues he didn't
+ 
+
+ align:start position:0%
+to prove to his colleagues he didn't
+believe any stomach ulcers were caused
+
+ align:start position:0%
+believe any stomach ulcers were caused
+ 
+
+ align:start position:0%
+believe any stomach ulcers were caused
+by the back but much less all of them
+
+ align:start position:0%
+by the back but much less all of them
+ 
+
+ align:start position:0%
+by the back but much less all of them
+and uh he drank it through himself again
+
+ align:start position:0%
+and uh he drank it through himself again
+ 
+
+ align:start position:0%
+and uh he drank it through himself again
+and he caused stomach ulcers
+
+ align:start position:0%
+and he caused stomach ulcers
+ 
+
+ align:start position:0%
+and he caused stomach ulcers
+in himself
+
+ align:start position:0%
+in himself
+ 
+
+ align:start position:0%
+in himself
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and hopefully um none of you will
+
+ align:start position:0%
+and hopefully um none of you will
+ 
+
+ align:start position:0%
+and hopefully um none of you will
+volunteer to do similar things with some
+
+ align:start position:0%
+volunteer to do similar things with some
+ 
+
+ align:start position:0%
+volunteer to do similar things with some
+of these other uh
+
+ align:start position:0%
+of these other uh
+ 
+
+ align:start position:0%
+of these other uh
+nasty guys here because i think
+
+ align:start position:0%
+nasty guys here because i think
+ 
+
+ align:start position:0%
+nasty guys here because i think
+some of the lists of things that they
+
+ align:start position:0%
+some of the lists of things that they
+ 
+
+ align:start position:0%
+some of the lists of things that they
+cause are a little more serious and
+
+ align:start position:0%
+cause are a little more serious and
+ 
+
+ align:start position:0%
+cause are a little more serious and
+stomach ulcers and the cures are a
+
+ align:start position:0%
+stomach ulcers and the cures are a
+ 
+
+ align:start position:0%
+stomach ulcers and the cures are a
+little less obvious than the cures for a
+
+ align:start position:0%
+little less obvious than the cures for a
+ 
+
+ align:start position:0%
+little less obvious than the cures for a
+gram-negative bacterium like
+
+ align:start position:0%
+gram-negative bacterium like
+ 
+
+ align:start position:0%
+gram-negative bacterium like
+helicobacter
+
+ align:start position:0%
+helicobacter
+ 
+
+ align:start position:0%
+helicobacter
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there have been various efforts
+
+ align:start position:0%
+there have been various efforts
+ 
+
+ align:start position:0%
+there have been various efforts
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+to actually mine you know what's the
+
+ align:start position:0%
+to actually mine you know what's the
+ 
+
+ align:start position:0%
+to actually mine you know what's the
+connection with uh genomics and
+
+ align:start position:0%
+connection with uh genomics and
+ 
+
+ align:start position:0%
+connection with uh genomics and
+computational biology to mine the
+
+ align:start position:0%
+computational biology to mine the
+ 
+
+ align:start position:0%
+computational biology to mine the
+transcriptome
+
+ align:start position:0%
+transcriptome
+ 
+
+ align:start position:0%
+transcriptome
+uh for evidence of these
+
+ align:start position:0%
+uh for evidence of these
+ 
+
+ align:start position:0%
+uh for evidence of these
+you can look for bacteria very easily
+
+ align:start position:0%
+you can look for bacteria very easily
+ 
+
+ align:start position:0%
+you can look for bacteria very easily
+because they have ribosomal rna
+
+ align:start position:0%
+because they have ribosomal rna
+ 
+
+ align:start position:0%
+because they have ribosomal rna
+components which you can pcr viruses are
+
+ align:start position:0%
+components which you can pcr viruses are
+ 
+
+ align:start position:0%
+components which you can pcr viruses are
+more complicated because they're not
+
+ align:start position:0%
+more complicated because they're not
+ 
+
+ align:start position:0%
+more complicated because they're not
+conserved
+
+ align:start position:0%
+conserved
+ 
+
+ align:start position:0%
+conserved
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or they don't have any universally
+
+ align:start position:0%
+or they don't have any universally
+ 
+
+ align:start position:0%
+or they don't have any universally
+conserved element like rival rna
+
+ align:start position:0%
+conserved element like rival rna
+ 
+
+ align:start position:0%
+conserved element like rival rna
+but they've been efforts to take uh
+
+ align:start position:0%
+but they've been efforts to take uh
+ 
+
+ align:start position:0%
+but they've been efforts to take uh
+look for what's present in the human
+
+ align:start position:0%
+look for what's present in the human
+ 
+
+ align:start position:0%
+look for what's present in the human
+transcriptome that's not present in the
+
+ align:start position:0%
+transcriptome that's not present in the
+ 
+
+ align:start position:0%
+transcriptome that's not present in the
+human genome human genome is something
+
+ align:start position:0%
+human genome human genome is something
+ 
+
+ align:start position:0%
+human genome human genome is something
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+highly purified and cloned and so forth
+
+ align:start position:0%
+highly purified and cloned and so forth
+ 
+
+ align:start position:0%
+highly purified and cloned and so forth
+while the transcriptome
+
+ align:start position:0%
+while the transcriptome
+ 
+
+ align:start position:0%
+while the transcriptome
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+you know it's whatever cells they grind
+
+ align:start position:0%
+you know it's whatever cells they grind
+ 
+
+ align:start position:0%
+you know it's whatever cells they grind
+ground up that day and they and indeed
+
+ align:start position:0%
+ground up that day and they and indeed
+ 
+
+ align:start position:0%
+ground up that day and they and indeed
+lurking in there are many of these uh
+
+ align:start position:0%
+lurking in there are many of these uh
+ 
+
+ align:start position:0%
+lurking in there are many of these uh
+hepatitis papilloma antibar virus um
+
+ align:start position:0%
+hepatitis papilloma antibar virus um
+ 
+
+ align:start position:0%
+hepatitis papilloma antibar virus um
+retroviral like elements which are not
+
+ align:start position:0%
+retroviral like elements which are not
+ 
+
+ align:start position:0%
+retroviral like elements which are not
+present in the human genome as yet human
+
+ align:start position:0%
+present in the human genome as yet human
+ 
+
+ align:start position:0%
+present in the human genome as yet human
+genome is not completely finished so
+
+ align:start position:0%
+genome is not completely finished so
+ 
+
+ align:start position:0%
+genome is not completely finished so
+that's still a escape clause but
+
+ align:start position:0%
+that's still a escape clause but
+ 
+
+ align:start position:0%
+that's still a escape clause but
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+these are smoking guns for at least
+
+ align:start position:0%
+these are smoking guns for at least
+ 
+
+ align:start position:0%
+these are smoking guns for at least
+commensals
+
+ align:start position:0%
+commensals
+ 
+
+ align:start position:0%
+commensals
+micro organisms and viruses that are
+
+ align:start position:0%
+micro organisms and viruses that are
+ 
+
+ align:start position:0%
+micro organisms and viruses that are
+living in
+
+ align:start position:0%
+living in
+ 
+
+ align:start position:0%
+living in
+tissues then some of them may be tissue
+
+ align:start position:0%
+tissues then some of them may be tissue
+ 
+
+ align:start position:0%
+tissues then some of them may be tissue
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+some of them subset may actually cause
+
+ align:start position:0%
+some of them subset may actually cause
+ 
+
+ align:start position:0%
+some of them subset may actually cause
+disease and that's the whole problem
+
+ align:start position:0%
+disease and that's the whole problem
+ 
+
+ align:start position:0%
+disease and that's the whole problem
+then is sorting out cause and effect we
+
+ align:start position:0%
+then is sorting out cause and effect we
+ 
+
+ align:start position:0%
+then is sorting out cause and effect we
+know how
+
+ align:start position:0%
+know how
+ 
+
+ align:start position:0%
+know how
+how it's been done
+
+ align:start position:0%
+how it's been done
+ 
+
+ align:start position:0%
+how it's been done
+heroically with helicobacter pylori but
+
+ align:start position:0%
+heroically with helicobacter pylori but
+ 
+
+ align:start position:0%
+heroically with helicobacter pylori but
+how do we do it with the other ones some
+
+ align:start position:0%
+how do we do it with the other ones some
+ 
+
+ align:start position:0%
+how do we do it with the other ones some
+of them will have tissue culture models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+at the time this slide was done
+
+ align:start position:0%
+at the time this slide was done
+ 
+
+ align:start position:0%
+at the time this slide was done
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is just uh
+
+ align:start position:0%
+this is just uh
+ 
+
+ align:start position:0%
+this is just uh
+illustrating kind of the flow of uh
+
+ align:start position:0%
+illustrating kind of the flow of uh
+ 
+
+ align:start position:0%
+illustrating kind of the flow of uh
+nucleic acid information that comes in
+
+ align:start position:0%
+nucleic acid information that comes in
+ 
+
+ align:start position:0%
+nucleic acid information that comes in
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh you know it was capable of being
+
+ align:start position:0%
+uh you know it was capable of being
+ 
+
+ align:start position:0%
+uh you know it was capable of being
+mined for new microorganisms new viruses
+
+ align:start position:0%
+mined for new microorganisms new viruses
+ 
+
+ align:start position:0%
+mined for new microorganisms new viruses
+that might be present in a
+
+ align:start position:0%
+that might be present in a
+ 
+
+ align:start position:0%
+that might be present in a
+tissue-specific fashion might be
+
+ align:start position:0%
+tissue-specific fashion might be
+ 
+
+ align:start position:0%
+tissue-specific fashion might be
+pathogens
+
+ align:start position:0%
+pathogens
+ 
+
+ align:start position:0%
+pathogens
+this is some of the most popular
+
+ align:start position:0%
+this is some of the most popular
+ 
+
+ align:start position:0%
+this is some of the most popular
+sequences from which we're mining
+
+ align:start position:0%
+sequences from which we're mining
+ 
+
+ align:start position:0%
+sequences from which we're mining
+obviously
+
+ align:start position:0%
+obviously
+ 
+
+ align:start position:0%
+obviously
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+was popular at the time this was done
+
+ align:start position:0%
+was popular at the time this was done
+ 
+
+ align:start position:0%
+was popular at the time this was done
+because human genome was in place here's
+
+ align:start position:0%
+because human genome was in place here's
+ 
+
+ align:start position:0%
+because human genome was in place here's
+brachionas our friend which was pretty
+
+ align:start position:0%
+brachionas our friend which was pretty
+ 
+
+ align:start position:0%
+brachionas our friend which was pretty
+high up on this list considering most of
+
+ align:start position:0%
+high up on this list considering most of
+ 
+
+ align:start position:0%
+high up on this list considering most of
+you probably didn't hear about greek
+
+ align:start position:0%
+you probably didn't hear about greek
+ 
+
+ align:start position:0%
+you probably didn't hear about greek
+units before this lecture now you've
+
+ align:start position:0%
+units before this lecture now you've
+ 
+
+ align:start position:0%
+units before this lecture now you've
+heard of it twice
+
+ align:start position:0%
+heard of it twice
+ 
+
+ align:start position:0%
+heard of it twice
+it just was a spurt in uh sequencing
+
+ align:start position:0%
+it just was a spurt in uh sequencing
+ 
+
+ align:start position:0%
+it just was a spurt in uh sequencing
+interest and of course hiv is the winner
+
+ align:start position:0%
+interest and of course hiv is the winner
+ 
+
+ align:start position:0%
+interest and of course hiv is the winner
+year after year because of the
+
+ align:start position:0%
+year after year because of the
+ 
+
+ align:start position:0%
+year after year because of the
+importance of resequencing it for
+
+ align:start position:0%
+importance of resequencing it for
+ 
+
+ align:start position:0%
+importance of resequencing it for
+for new mutations and it really has a
+
+ align:start position:0%
+for new mutations and it really has a
+ 
+
+ align:start position:0%
+for new mutations and it really has a
+record number of new mutations
+
+ align:start position:0%
+record number of new mutations
+ 
+
+ align:start position:0%
+record number of new mutations
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we've talked about hiv uh
+
+ align:start position:0%
+we've talked about hiv uh
+ 
+
+ align:start position:0%
+we've talked about hiv uh
+from different from a variety of
+
+ align:start position:0%
+from different from a variety of
+ 
+
+ align:start position:0%
+from different from a variety of
+different standpoints
+
+ align:start position:0%
+different standpoints
+ 
+
+ align:start position:0%
+different standpoints
+uh one of them you know it's polymerase
+
+ align:start position:0%
+uh one of them you know it's polymerase
+ 
+
+ align:start position:0%
+uh one of them you know it's polymerase
+is proteases drug targets
+
+ align:start position:0%
+is proteases drug targets
+ 
+
+ align:start position:0%
+is proteases drug targets
+and is uh sources of drug resistance
+
+ align:start position:0%
+and is uh sources of drug resistance
+ 
+
+ align:start position:0%
+and is uh sources of drug resistance
+and that you can follow up that that
+
+ align:start position:0%
+and that you can follow up that that
+ 
+
+ align:start position:0%
+and that you can follow up that that
+model you know that sort of atomic scale
+
+ align:start position:0%
+model you know that sort of atomic scale
+ 
+
+ align:start position:0%
+model you know that sort of atomic scale
+protein modeling where you're looking
+
+ align:start position:0%
+protein modeling where you're looking
+ 
+
+ align:start position:0%
+protein modeling where you're looking
+for new drugs well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the polymerase of the mutant
+
+ align:start position:0%
+where the polymerase of the mutant
+ 
+
+ align:start position:0%
+where the polymerase of the mutant
+polymerase will not be resistant to
+
+ align:start position:0%
+polymerase will not be resistant to
+ 
+
+ align:start position:0%
+polymerase will not be resistant to
+neutron
+
+ align:start position:0%
+neutron
+ 
+
+ align:start position:0%
+neutron
+but you can also monitor the population
+
+ align:start position:0%
+but you can also monitor the population
+ 
+
+ align:start position:0%
+but you can also monitor the population
+scale as
+
+ align:start position:0%
+scale as
+ 
+
+ align:start position:0%
+scale as
+hiv goes through a particular patient or
+
+ align:start position:0%
+hiv goes through a particular patient or
+ 
+
+ align:start position:0%
+hiv goes through a particular patient or
+through a population of patients how
+
+ align:start position:0%
+through a population of patients how
+ 
+
+ align:start position:0%
+through a population of patients how
+does the
+
+ align:start position:0%
+does the
+ 
+
+ align:start position:0%
+does the
+drug resistance change as a function of
+
+ align:start position:0%
+drug resistance change as a function of
+ 
+
+ align:start position:0%
+drug resistance change as a function of
+time here the horizontal axis is in days
+
+ align:start position:0%
+time here the horizontal axis is in days
+ 
+
+ align:start position:0%
+time here the horizontal axis is in days
+up to 30 days
+
+ align:start position:0%
+up to 30 days
+ 
+
+ align:start position:0%
+up to 30 days
+and then the vertical axis
+
+ align:start position:0%
+and then the vertical axis
+ 
+
+ align:start position:0%
+and then the vertical axis
+is the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the titers of the viruses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you have here is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rates of exponential increase these are
+
+ align:start position:0%
+rates of exponential increase these are
+ 
+
+ align:start position:0%
+rates of exponential increase these are
+all these are on logarithmic scales and
+
+ align:start position:0%
+all these are on logarithmic scales and
+ 
+
+ align:start position:0%
+all these are on logarithmic scales and
+you can't where you're modeling such
+
+ align:start position:0%
+you can't where you're modeling such
+ 
+
+ align:start position:0%
+you can't where you're modeling such
+thing as the
+
+ align:start position:0%
+thing as the
+ 
+
+ align:start position:0%
+thing as the
+clearance to the immune system and so
+
+ align:start position:0%
+clearance to the immune system and so
+ 
+
+ align:start position:0%
+clearance to the immune system and so
+forth originally this virus was thought
+
+ align:start position:0%
+forth originally this virus was thought
+ 
+
+ align:start position:0%
+forth originally this virus was thought
+to be a very slow virus very slowly
+
+ align:start position:0%
+to be a very slow virus very slowly
+ 
+
+ align:start position:0%
+to be a very slow virus very slowly
+replicating virus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost cryptic and then later was found
+
+ align:start position:0%
+almost cryptic and then later was found
+ 
+
+ align:start position:0%
+almost cryptic and then later was found
+that this is actually a very rapidly
+
+ align:start position:0%
+that this is actually a very rapidly
+ 
+
+ align:start position:0%
+that this is actually a very rapidly
+replicating but an immune system that's
+
+ align:start position:0%
+replicating but an immune system that's
+ 
+
+ align:start position:0%
+replicating but an immune system that's
+very rapidly responding
+
+ align:start position:0%
+very rapidly responding
+ 
+
+ align:start position:0%
+very rapidly responding
+the sort of model print just each of
+
+ align:start position:0%
+the sort of model print just each of
+ 
+
+ align:start position:0%
+the sort of model print just each of
+these models we've gone through has a
+
+ align:start position:0%
+these models we've gone through has a
+ 
+
+ align:start position:0%
+these models we've gone through has a
+set of parameters that it goes along
+
+ align:start position:0%
+set of parameters that it goes along
+ 
+
+ align:start position:0%
+set of parameters that it goes along
+with in certain sense there's quite a
+
+ align:start position:0%
+with in certain sense there's quite a
+ 
+
+ align:start position:0%
+with in certain sense there's quite a
+bit you can learn about a model just by
+
+ align:start position:0%
+bit you can learn about a model just by
+ 
+
+ align:start position:0%
+bit you can learn about a model just by
+seeing what parameters are present or
+
+ align:start position:0%
+seeing what parameters are present or
+ 
+
+ align:start position:0%
+seeing what parameters are present or
+absent before they're experimentally
+
+ align:start position:0%
+absent before they're experimentally
+ 
+
+ align:start position:0%
+absent before they're experimentally
+determined how accurately and so on and
+
+ align:start position:0%
+determined how accurately and so on and
+ 
+
+ align:start position:0%
+determined how accurately and so on and
+sort of model parameters here are
+
+ align:start position:0%
+sort of model parameters here are
+ 
+
+ align:start position:0%
+sort of model parameters here are
+mortality rate of uninfected cd4 plus t
+
+ align:start position:0%
+mortality rate of uninfected cd4 plus t
+ 
+
+ align:start position:0%
+mortality rate of uninfected cd4 plus t
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+same thing for infected cells
+
+ align:start position:0%
+same thing for infected cells
+ 
+
+ align:start position:0%
+same thing for infected cells
+and they're going to have differences
+
+ align:start position:0%
+and they're going to have differences
+ 
+
+ align:start position:0%
+and they're going to have differences
+you can see on the far right if there's
+
+ align:start position:0%
+you can see on the far right if there's
+ 
+
+ align:start position:0%
+you can see on the far right if there's
+a huge difference
+
+ align:start position:0%
+a huge difference
+ 
+
+ align:start position:0%
+a huge difference
+they die at a point a quarter per day
+
+ align:start position:0%
+they die at a point a quarter per day
+ 
+
+ align:start position:0%
+they die at a point a quarter per day
+versus
+
+ align:start position:0%
+versus
+ 
+
+ align:start position:0%
+versus
+5 000
+
+ align:start position:0%
+5 000
+ 
+
+ align:start position:0%
+5 000
+and so on there's rates for
+
+ align:start position:0%
+and so on there's rates for
+ 
+
+ align:start position:0%
+and so on there's rates for
+getting infected rates of virus loss
+
+ align:start position:0%
+getting infected rates of virus loss
+ 
+
+ align:start position:0%
+getting infected rates of virus loss
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+threshold value for remission
+
+ align:start position:0%
+threshold value for remission
+ 
+
+ align:start position:0%
+threshold value for remission
+so on and so forth
+
+ align:start position:0%
+so on and so forth
+ 
+
+ align:start position:0%
+so on and so forth
+and these are important
+
+ align:start position:0%
+and these are important
+ 
+
+ align:start position:0%
+and these are important
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+the virus population changes within a
+
+ align:start position:0%
+the virus population changes within a
+ 
+
+ align:start position:0%
+the virus population changes within a
+person within population how it spreads
+
+ align:start position:0%
+person within population how it spreads
+ 
+
+ align:start position:0%
+person within population how it spreads
+through the population depends
+
+ align:start position:0%
+through the population depends
+ 
+
+ align:start position:0%
+through the population depends
+on um
+
+ align:start position:0%
+on um
+ 
+
+ align:start position:0%
+on um
+in many cases on the
+
+ align:start position:0%
+in many cases on the
+ 
+
+ align:start position:0%
+in many cases on the
+herd immunity and so forth and we get
+
+ align:start position:0%
+herd immunity and so forth and we get
+ 
+
+ align:start position:0%
+herd immunity and so forth and we get
+into issues of
+
+ align:start position:0%
+into issues of
+ 
+
+ align:start position:0%
+into issues of
+public health
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+almost a truism that that most of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+additional quality years of life
+
+ align:start position:0%
+additional quality years of life
+ 
+
+ align:start position:0%
+additional quality years of life
+uh quality adjusted life years here
+
+ align:start position:0%
+uh quality adjusted life years here
+ 
+
+ align:start position:0%
+uh quality adjusted life years here
+qali that we have in the world the fact
+
+ align:start position:0%
+qali that we have in the world the fact
+ 
+
+ align:start position:0%
+qali that we have in the world the fact
+that you know our life expectancy is so
+
+ align:start position:0%
+that you know our life expectancy is so
+ 
+
+ align:start position:0%
+that you know our life expectancy is so
+much longer so forth are mainly public
+
+ align:start position:0%
+much longer so forth are mainly public
+ 
+
+ align:start position:0%
+much longer so forth are mainly public
+health
+
+ align:start position:0%
+health
+ 
+
+ align:start position:0%
+health
+decisions that have been made
+
+ align:start position:0%
+decisions that have been made
+ 
+
+ align:start position:0%
+decisions that have been made
+not so much pharmaceutical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such things as
+
+ align:start position:0%
+such things as
+ 
+
+ align:start position:0%
+such things as
+clean water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has made a huge impact and so we need to
+
+ align:start position:0%
+has made a huge impact and so we need to
+ 
+
+ align:start position:0%
+has made a huge impact and so we need to
+think but
+
+ align:start position:0%
+think but
+ 
+
+ align:start position:0%
+think but
+even when you think about the
+
+ align:start position:0%
+even when you think about the
+ 
+
+ align:start position:0%
+even when you think about the
+pharmaceutical aspects it needs to be
+
+ align:start position:0%
+pharmaceutical aspects it needs to be
+ 
+
+ align:start position:0%
+pharmaceutical aspects it needs to be
+thought in a public health sense and a
+
+ align:start position:0%
+thought in a public health sense and a
+ 
+
+ align:start position:0%
+thought in a public health sense and a
+surprising amount of public health
+
+ align:start position:0%
+surprising amount of public health
+ 
+
+ align:start position:0%
+surprising amount of public health
+officials in even the most developed
+
+ align:start position:0%
+officials in even the most developed
+ 
+
+ align:start position:0%
+officials in even the most developed
+nations maybe
+
+ align:start position:0%
+nations maybe
+ 
+
+ align:start position:0%
+nations maybe
+most of them are do not have formal
+
+ align:start position:0%
+most of them are do not have formal
+ 
+
+ align:start position:0%
+most of them are do not have formal
+education public health and so i urge
+
+ align:start position:0%
+education public health and so i urge
+ 
+
+ align:start position:0%
+education public health and so i urge
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+all to get at least some education in
+
+ align:start position:0%
+all to get at least some education in
+ 
+
+ align:start position:0%
+all to get at least some education in
+this because in this we have you know
+
+ align:start position:0%
+this because in this we have you know
+ 
+
+ align:start position:0%
+this because in this we have you know
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+quan they're trying to build and have
+
+ align:start position:0%
+quan they're trying to build and have
+ 
+
+ align:start position:0%
+quan they're trying to build and have
+built quantitative models not only for
+
+ align:start position:0%
+built quantitative models not only for
+ 
+
+ align:start position:0%
+built quantitative models not only for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the kinetics which the disease will go
+
+ align:start position:0%
+the kinetics which the disease will go
+ 
+
+ align:start position:0%
+the kinetics which the disease will go
+through a population or through even
+
+ align:start position:0%
+through a population or through even
+ 
+
+ align:start position:0%
+through a population or through even
+through an individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but the way that you make decisions
+
+ align:start position:0%
+but but the way that you make decisions
+ 
+
+ align:start position:0%
+but but the way that you make decisions
+and this is having an impact on the way
+
+ align:start position:0%
+and this is having an impact on the way
+ 
+
+ align:start position:0%
+and this is having an impact on the way
+decisions are
+
+ align:start position:0%
+decisions are
+ 
+
+ align:start position:0%
+decisions are
+how these different uh projects are
+
+ align:start position:0%
+how these different uh projects are
+ 
+
+ align:start position:0%
+how these different uh projects are
+prioritized at any given time you might
+
+ align:start position:0%
+prioritized at any given time you might
+ 
+
+ align:start position:0%
+prioritized at any given time you might
+have hundreds of different candidate
+
+ align:start position:0%
+have hundreds of different candidate
+ 
+
+ align:start position:0%
+have hundreds of different candidate
+vaccines
+
+ align:start position:0%
+vaccines
+ 
+
+ align:start position:0%
+vaccines
+which is one of a major very effective
+
+ align:start position:0%
+which is one of a major very effective
+ 
+
+ align:start position:0%
+which is one of a major very effective
+public health strategy
+
+ align:start position:0%
+public health strategy
+ 
+
+ align:start position:0%
+public health strategy
+and this is the way they prioritize it
+
+ align:start position:0%
+and this is the way they prioritize it
+ 
+
+ align:start position:0%
+and this is the way they prioritize it
+so that level one saves money and it
+
+ align:start position:0%
+so that level one saves money and it
+ 
+
+ align:start position:0%
+so that level one saves money and it
+improves life so that's
+
+ align:start position:0%
+improves life so that's
+ 
+
+ align:start position:0%
+improves life so that's
+almost a no-brainer
+
+ align:start position:0%
+almost a no-brainer
+ 
+
+ align:start position:0%
+almost a no-brainer
+you have different levels we have
+
+ align:start position:0%
+you have different levels we have
+ 
+
+ align:start position:0%
+you have different levels we have
+might cost ten thousand dollars
+
+ align:start position:0%
+might cost ten thousand dollars
+ 
+
+ align:start position:0%
+might cost ten thousand dollars
+or a hundred thousand dollars per
+
+ align:start position:0%
+or a hundred thousand dollars per
+ 
+
+ align:start position:0%
+or a hundred thousand dollars per
+quality adjusted life here to save
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the level one candidates are
+
+ align:start position:0%
+and so the level one candidates are
+ 
+
+ align:start position:0%
+and so the level one candidates are
+cytomegalovirus and uh therapeutic
+
+ align:start position:0%
+cytomegalovirus and uh therapeutic
+ 
+
+ align:start position:0%
+cytomegalovirus and uh therapeutic
+vaccines which these are not aimed at
+
+ align:start position:0%
+vaccines which these are not aimed at
+ 
+
+ align:start position:0%
+vaccines which these are not aimed at
+infectious
+
+ align:start position:0%
+infectious
+ 
+
+ align:start position:0%
+infectious
+disease for diabetes rheumatoid
+
+ align:start position:0%
+disease for diabetes rheumatoid
+ 
+
+ align:start position:0%
+disease for diabetes rheumatoid
+arthritis multiple sclerosis
+
+ align:start position:0%
+arthritis multiple sclerosis
+ 
+
+ align:start position:0%
+arthritis multiple sclerosis
+various bacterial ones of course hiv was
+
+ align:start position:0%
+various bacterial ones of course hiv was
+ 
+
+ align:start position:0%
+various bacterial ones of course hiv was
+not even a study because it was such a
+
+ align:start position:0%
+not even a study because it was such a
+ 
+
+ align:start position:0%
+not even a study because it was such a
+high prio priority already
+
+ align:start position:0%
+high prio priority already
+ 
+
+ align:start position:0%
+high prio priority already
+within the nih
+
+ align:start position:0%
+within the nih
+ 
+
+ align:start position:0%
+within the nih
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is there a role for genomics and
+
+ align:start position:0%
+so is there a role for genomics and
+ 
+
+ align:start position:0%
+so is there a role for genomics and
+computational biology the title of this
+
+ align:start position:0%
+computational biology the title of this
+ 
+
+ align:start position:0%
+computational biology the title of this
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+in this vaccine research and development
+
+ align:start position:0%
+in this vaccine research and development
+ 
+
+ align:start position:0%
+in this vaccine research and development
+i think the answer is
+
+ align:start position:0%
+i think the answer is
+ 
+
+ align:start position:0%
+i think the answer is
+yes but it requires a great deal of
+
+ align:start position:0%
+yes but it requires a great deal of
+ 
+
+ align:start position:0%
+yes but it requires a great deal of
+creativity and resourcefulness on on all
+
+ align:start position:0%
+creativity and resourcefulness on on all
+ 
+
+ align:start position:0%
+creativity and resourcefulness on on all
+of your parts
+
+ align:start position:0%
+of your parts
+ 
+
+ align:start position:0%
+of your parts
+there are new opportunities with dna
+
+ align:start position:0%
+there are new opportunities with dna
+ 
+
+ align:start position:0%
+there are new opportunities with dna
+vaccines that where you can have one or
+
+ align:start position:0%
+vaccines that where you can have one or
+ 
+
+ align:start position:0%
+vaccines that where you can have one or
+more dnas
+
+ align:start position:0%
+more dnas
+ 
+
+ align:start position:0%
+more dnas
+shot
+
+ align:start position:0%
+shot
+ 
+
+ align:start position:0%
+shot
+intramuscular or a variety of other
+
+ align:start position:0%
+intramuscular or a variety of other
+ 
+
+ align:start position:0%
+intramuscular or a variety of other
+ways what is delivered by the dna
+
+ align:start position:0%
+ways what is delivered by the dna
+ 
+
+ align:start position:0%
+ways what is delivered by the dna
+vaccine can be
+
+ align:start position:0%
+vaccine can be
+ 
+
+ align:start position:0%
+vaccine can be
+various so-called intracellular vaccines
+
+ align:start position:0%
+various so-called intracellular vaccines
+ 
+
+ align:start position:0%
+various so-called intracellular vaccines
+which can either act through
+
+ align:start position:0%
+which can either act through
+ 
+
+ align:start position:0%
+which can either act through
+cell-mediated immunity or in some other
+
+ align:start position:0%
+cell-mediated immunity or in some other
+ 
+
+ align:start position:0%
+cell-mediated immunity or in some other
+way intracellularly
+
+ align:start position:0%
+way intracellularly
+ 
+
+ align:start position:0%
+way intracellularly
+rnai is a is a rapidly
+
+ align:start position:0%
+rnai is a is a rapidly
+ 
+
+ align:start position:0%
+rnai is a is a rapidly
+emerging
+
+ align:start position:0%
+emerging
+ 
+
+ align:start position:0%
+emerging
+way of
+
+ align:start position:0%
+way of
+ 
+
+ align:start position:0%
+way of
+delivering
+
+ align:start position:0%
+delivering
+ 
+
+ align:start position:0%
+delivering
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+that wouldn't may not be classically
+
+ align:start position:0%
+that wouldn't may not be classically
+ 
+
+ align:start position:0%
+that wouldn't may not be classically
+considered uh therapeutics or vaccines
+
+ align:start position:0%
+considered uh therapeutics or vaccines
+ 
+
+ align:start position:0%
+considered uh therapeutics or vaccines
+the concept of multiplexing you me
+
+ align:start position:0%
+the concept of multiplexing you me
+ 
+
+ align:start position:0%
+the concept of multiplexing you me
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+of us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have received multiple vaccines at a
+
+ align:start position:0%
+have received multiple vaccines at a
+ 
+
+ align:start position:0%
+have received multiple vaccines at a
+time typically every year your flu
+
+ align:start position:0%
+time typically every year your flu
+ 
+
+ align:start position:0%
+time typically every year your flu
+vaccine will have two or three strains
+
+ align:start position:0%
+vaccine will have two or three strains
+ 
+
+ align:start position:0%
+vaccine will have two or three strains
+in it but um as you can see from this
+
+ align:start position:0%
+in it but um as you can see from this
+ 
+
+ align:start position:0%
+in it but um as you can see from this
+middle article the diversity of certain
+
+ align:start position:0%
+middle article the diversity of certain
+ 
+
+ align:start position:0%
+middle article the diversity of certain
+diseases like hiv and influenza almost
+
+ align:start position:0%
+diseases like hiv and influenza almost
+ 
+
+ align:start position:0%
+diseases like hiv and influenza almost
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+attention to the genomics the diversity
+
+ align:start position:0%
+attention to the genomics the diversity
+ 
+
+ align:start position:0%
+attention to the genomics the diversity
+that can occur either from year to year
+
+ align:start position:0%
+that can occur either from year to year
+ 
+
+ align:start position:0%
+that can occur either from year to year
+or throughout the entire
+
+ align:start position:0%
+or throughout the entire
+ 
+
+ align:start position:0%
+or throughout the entire
+global
+
+ align:start position:0%
+global
+ 
+
+ align:start position:0%
+global
+set of viruses
+
+ align:start position:0%
+set of viruses
+ 
+
+ align:start position:0%
+set of viruses
+another opportunity is when we have um
+
+ align:start position:0%
+another opportunity is when we have um
+ 
+
+ align:start position:0%
+another opportunity is when we have um
+vectors for say uh
+
+ align:start position:0%
+vectors for say uh
+ 
+
+ align:start position:0%
+vectors for say uh
+arthropod vectors insect vectors like
+
+ align:start position:0%
+arthropod vectors insect vectors like
+ 
+
+ align:start position:0%
+arthropod vectors insect vectors like
+mosquito and we have uh
+
+ align:start position:0%
+mosquito and we have uh
+ 
+
+ align:start position:0%
+mosquito and we have uh
+opportunities to and to hit malaria at
+
+ align:start position:0%
+opportunities to and to hit malaria at
+ 
+
+ align:start position:0%
+opportunities to and to hit malaria at
+all the different life stages not just
+
+ align:start position:0%
+all the different life stages not just
+ 
+
+ align:start position:0%
+all the different life stages not just
+there are multiple life stages within
+
+ align:start position:0%
+there are multiple life stages within
+ 
+
+ align:start position:0%
+there are multiple life stages within
+humans and multiple stages within um
+
+ align:start position:0%
+humans and multiple stages within um
+ 
+
+ align:start position:0%
+humans and multiple stages within um
+within the insect vector
+
+ align:start position:0%
+within the insect vector
+ 
+
+ align:start position:0%
+within the insect vector
+and now the genomics of these two just
+
+ align:start position:0%
+and now the genomics of these two just
+ 
+
+ align:start position:0%
+and now the genomics of these two just
+came out recently
+
+ align:start position:0%
+came out recently
+ 
+
+ align:start position:0%
+came out recently
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the same week in nature and science this
+
+ align:start position:0%
+the same week in nature and science this
+ 
+
+ align:start position:0%
+the same week in nature and science this
+provides a whole new set of
+
+ align:start position:0%
+provides a whole new set of
+ 
+
+ align:start position:0%
+provides a whole new set of
+inspirations for work that can be done
+
+ align:start position:0%
+inspirations for work that can be done
+ 
+
+ align:start position:0%
+inspirations for work that can be done
+on these i think we should take a little
+
+ align:start position:0%
+on these i think we should take a little
+ 
+
+ align:start position:0%
+on these i think we should take a little
+break now
+
+ align:start position:0%
+break now
+ 
+
+ align:start position:0%
+break now
+and we'll wrap up the talk after that
+
+ align:start position:0%
+and we'll wrap up the talk after that
+ 
+
+ align:start position:0%
+and we'll wrap up the talk after that
+break
\ No newline at end of file
diff --git a/2B7e19xi4Sw.txt b/2B7e19xi4Sw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f22a522298957ca2af77563bd5d36285213c4d35
--- /dev/null
+++ b/2B7e19xi4Sw.txt
@@ -0,0 +1,2027 @@
+align:start position:0%
+ 
+hi welcome back to recitation I've got a
+
+ align:start position:0%
+hi welcome back to recitation I've got a
+ 
+
+ align:start position:0%
+hi welcome back to recitation I've got a
+nice exercise here on Stokes theorem for
+
+ align:start position:0%
+nice exercise here on Stokes theorem for
+ 
+
+ align:start position:0%
+nice exercise here on Stokes theorem for
+you now this problem is a little bit
+
+ align:start position:0%
+you now this problem is a little bit
+ 
+
+ align:start position:0%
+you now this problem is a little bit
+more sophisticated than a lot of
+
+ align:start position:0%
+more sophisticated than a lot of
+ 
+
+ align:start position:0%
+more sophisticated than a lot of
+problems we've been doing in recitation
+
+ align:start position:0%
+problems we've been doing in recitation
+ 
+
+ align:start position:0%
+problems we've been doing in recitation
+so it requires a little bit more thought
+
+ align:start position:0%
+so it requires a little bit more thought
+ 
+
+ align:start position:0%
+so it requires a little bit more thought
+and it also involves more mathematical
+
+ align:start position:0%
+and it also involves more mathematical
+ 
+
+ align:start position:0%
+and it also involves more mathematical
+sophistication so so we're really we're
+
+ align:start position:0%
+sophistication so so we're really we're
+ 
+
+ align:start position:0%
+sophistication so so we're really we're
+we're doing a a sort of clever kind of
+
+ align:start position:0%
+we're doing a a sort of clever kind of
+ 
+
+ align:start position:0%
+we're doing a a sort of clever kind of
+proof here that that I like so hopefully
+
+ align:start position:0%
+proof here that that I like so hopefully
+ 
+
+ align:start position:0%
+proof here that that I like so hopefully
+hopefully you'll you like this one it's
+
+ align:start position:0%
+hopefully you'll you like this one it's
+ 
+
+ align:start position:0%
+hopefully you'll you like this one it's
+not it's a little bit in a different
+
+ align:start position:0%
+not it's a little bit in a different
+ 
+
+ align:start position:0%
+not it's a little bit in a different
+style than some of the ones we've done
+
+ align:start position:0%
+style than some of the ones we've done
+ 
+
+ align:start position:0%
+style than some of the ones we've done
+so so let me so I I think I need to talk
+
+ align:start position:0%
+so so let me so I I think I need to talk
+ 
+
+ align:start position:0%
+so so let me so I I think I need to talk
+about it a little bit before we get
+
+ align:start position:0%
+about it a little bit before we get
+ 
+
+ align:start position:0%
+about it a little bit before we get
+started so let's let F be the field XYZ
+
+ align:start position:0%
+started so let's let F be the field XYZ
+ 
+
+ align:start position:0%
+started so let's let F be the field XYZ
+so this is our our radial field that
+
+ align:start position:0%
+so this is our our radial field that
+ 
+
+ align:start position:0%
+so this is our our radial field that
+we've seen a lot in recitation so what
+
+ align:start position:0%
+we've seen a lot in recitation so what
+ 
+
+ align:start position:0%
+we've seen a lot in recitation so what
+I'd like you to do is prove that this
+
+ align:start position:0%
+I'd like you to do is prove that this
+ 
+
+ align:start position:0%
+I'd like you to do is prove that this
+field is not the curl of any field G all
+
+ align:start position:0%
+field is not the curl of any field G all
+ 
+
+ align:start position:0%
+field is not the curl of any field G all
+right so I'd like you to show that
+
+ align:start position:0%
+right so I'd like you to show that
+ 
+
+ align:start position:0%
+right so I'd like you to show that
+there's no field G such that f is equal
+
+ align:start position:0%
+there's no field G such that f is equal
+ 
+
+ align:start position:0%
+there's no field G such that f is equal
+to the curl of G now
+
+ align:start position:0%
+to the curl of G now
+ 
+
+ align:start position:0%
+to the curl of G now
+rather than just saying that to you and
+
+ align:start position:0%
+rather than just saying that to you and
+ 
+
+ align:start position:0%
+rather than just saying that to you and
+let you run off I have I have a
+
+ align:start position:0%
+let you run off I have I have a
+ 
+
+ align:start position:0%
+let you run off I have I have a
+suggestion for an interesting way you
+
+ align:start position:0%
+suggestion for an interesting way you
+ 
+
+ align:start position:0%
+suggestion for an interesting way you
+could go about this um and this this
+
+ align:start position:0%
+could go about this um and this this
+ 
+
+ align:start position:0%
+could go about this um and this this
+interesting way is going to use Stokes
+
+ align:start position:0%
+interesting way is going to use Stokes
+ 
+
+ align:start position:0%
+interesting way is going to use Stokes
+theorem so what I'd like you to do is is
+
+ align:start position:0%
+theorem so what I'd like you to do is is
+ 
+
+ align:start position:0%
+theorem so what I'd like you to do is is
+a proof by
+
+ align:start position:0%
+a proof by
+ 
+
+ align:start position:0%
+a proof by
+contradiction okay so what you're going
+
+ align:start position:0%
+contradiction okay so what you're going
+ 
+
+ align:start position:0%
+contradiction okay so what you're going
+to do is you're going to assume that f
+
+ align:start position:0%
+to do is you're going to assume that f
+ 
+
+ align:start position:0%
+to do is you're going to assume that f
+is a curl okay you're so you're going to
+
+ align:start position:0%
+is a curl okay you're so you're going to
+ 
+
+ align:start position:0%
+is a curl okay you're so you're going to
+assume that there is some G such that f
+
+ align:start position:0%
+assume that there is some G such that f
+ 
+
+ align:start position:0%
+assume that there is some G such that f
+is curl G and then you're going to use
+
+ align:start position:0%
+is curl G and then you're going to use
+ 
+
+ align:start position:0%
+is curl G and then you're going to use
+that to to to get a ridiculous
+
+ align:start position:0%
+that to to to get a ridiculous
+ 
+
+ align:start position:0%
+that to to to get a ridiculous
+conclusion so you're going to start with
+
+ align:start position:0%
+conclusion so you're going to start with
+ 
+
+ align:start position:0%
+conclusion so you're going to start with
+that premise and you're going to Res end
+
+ align:start position:0%
+that premise and you're going to Res end
+ 
+
+ align:start position:0%
+that premise and you're going to Res end
+up with a with a contradiction so this
+
+ align:start position:0%
+up with a with a contradiction so this
+ 
+
+ align:start position:0%
+up with a with a contradiction so this
+is the these two sort of arrows
+
+ align:start position:0%
+is the these two sort of arrows
+ 
+
+ align:start position:0%
+is the these two sort of arrows
+colliding into each other is a is a
+
+ align:start position:0%
+colliding into each other is a is a
+ 
+
+ align:start position:0%
+colliding into each other is a is a
+symbol that that mathematicians use for
+
+ align:start position:0%
+symbol that that mathematicians use for
+ 
+
+ align:start position:0%
+symbol that that mathematicians use for
+a contradiction so you're going to start
+
+ align:start position:0%
+a contradiction so you're going to start
+ 
+
+ align:start position:0%
+a contradiction so you're going to start
+from this premise and you're going to
+
+ align:start position:0%
+from this premise and you're going to
+ 
+
+ align:start position:0%
+from this premise and you're going to
+reach a contradiction and what that's
+
+ align:start position:0%
+reach a contradiction and what that's
+ 
+
+ align:start position:0%
+reach a contradiction and what that's
+going to show is that your premise
+
+ align:start position:0%
+going to show is that your premise
+ 
+
+ align:start position:0%
+going to show is that your premise
+couldn't be right yeah because if you if
+
+ align:start position:0%
+couldn't be right yeah because if you if
+ 
+
+ align:start position:0%
+couldn't be right yeah because if you if
+you start from a true premise well then
+
+ align:start position:0%
+you start from a true premise well then
+ 
+
+ align:start position:0%
+you start from a true premise well then
+all your conclusions should be true as
+
+ align:start position:0%
+all your conclusions should be true as
+ 
+
+ align:start position:0%
+all your conclusions should be true as
+well so so if you reach a false
+
+ align:start position:0%
+well so so if you reach a false
+ 
+
+ align:start position:0%
+well so so if you reach a false
+conclusion then then you must have had a
+
+ align:start position:0%
+conclusion then then you must have had a
+ 
+
+ align:start position:0%
+conclusion then then you must have had a
+false
+
+ align:start position:0%
+false
+ 
+
+ align:start position:0%
+false
+premise so what what what you're going
+
+ align:start position:0%
+premise so what what what you're going
+ 
+
+ align:start position:0%
+premise so what what what you're going
+to do is you're going to take a sphere
+
+ align:start position:0%
+to do is you're going to take a sphere
+ 
+
+ align:start position:0%
+to do is you're going to take a sphere
+of radius B centered at the origin and a
+
+ align:start position:0%
+of radius B centered at the origin and a
+ 
+
+ align:start position:0%
+of radius B centered at the origin and a
+curve C on the sphere you know a simple
+
+ align:start position:0%
+curve C on the sphere you know a simple
+ 
+
+ align:start position:0%
+curve C on the sphere you know a simple
+closed curve um so assuming that f is
+
+ align:start position:0%
+closed curve um so assuming that f is
+ 
+
+ align:start position:0%
+closed curve um so assuming that f is
+this curl of G what I'd like you to do
+
+ align:start position:0%
+this curl of G what I'd like you to do
+ 
+
+ align:start position:0%
+this curl of G what I'd like you to do
+is use Stokes theorem to interpret the
+
+ align:start position:0%
+is use Stokes theorem to interpret the
+ 
+
+ align:start position:0%
+is use Stokes theorem to interpret the
+the line integral of G dodr over C in
+
+ align:start position:0%
+the line integral of G dodr over C in
+ 
+
+ align:start position:0%
+the line integral of G dodr over C in
+two different ways okay and and
+
+ align:start position:0%
+two different ways okay and and
+ 
+
+ align:start position:0%
+two different ways okay and and
+interpreting this line integral in two
+
+ align:start position:0%
+interpreting this line integral in two
+ 
+
+ align:start position:0%
+interpreting this line integral in two
+different ways you're going to reach a
+
+ align:start position:0%
+different ways you're going to reach a
+ 
+
+ align:start position:0%
+different ways you're going to reach a
+contradiction and that will show that F
+
+ align:start position:0%
+contradiction and that will show that F
+ 
+
+ align:start position:0%
+contradiction and that will show that F
+really isn't a curl so that's what I'd
+
+ align:start position:0%
+really isn't a curl so that's what I'd
+ 
+
+ align:start position:0%
+really isn't a curl so that's what I'd
+like you to do so why don't you pause
+
+ align:start position:0%
+like you to do so why don't you pause
+ 
+
+ align:start position:0%
+like you to do so why don't you pause
+the video go ahead see if you can work
+
+ align:start position:0%
+the video go ahead see if you can work
+ 
+
+ align:start position:0%
+the video go ahead see if you can work
+that out come back and we'll talk about
+
+ align:start position:0%
+that out come back and we'll talk about
+ 
+
+ align:start position:0%
+that out come back and we'll talk about
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together I hope you enjoyed working on
+
+ align:start position:0%
+together I hope you enjoyed working on
+ 
+
+ align:start position:0%
+together I hope you enjoyed working on
+this problem let's let's get started on
+
+ align:start position:0%
+this problem let's let's get started on
+ 
+
+ align:start position:0%
+this problem let's let's get started on
+it so
+
+ align:start position:0%
+it so
+ 
+
+ align:start position:0%
+it so
+the the as I was saying before we
+
+ align:start position:0%
+the the as I was saying before we
+ 
+
+ align:start position:0%
+the the as I was saying before we
+started what we're going to do is we're
+
+ align:start position:0%
+started what we're going to do is we're
+ 
+
+ align:start position:0%
+started what we're going to do is we're
+we're looking for a proof by
+
+ align:start position:0%
+we're looking for a proof by
+ 
+
+ align:start position:0%
+we're looking for a proof by
+contradiction so as the problem says
+
+ align:start position:0%
+contradiction so as the problem says
+ 
+
+ align:start position:0%
+contradiction so as the problem says
+we're going to start with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sphere and I'm going to take this curve
+
+ align:start position:0%
+sphere and I'm going to take this curve
+ 
+
+ align:start position:0%
+sphere and I'm going to take this curve
+C and it's a some Simply Connected
+
+ align:start position:0%
+C and it's a some Simply Connected
+ 
+
+ align:start position:0%
+C and it's a some Simply Connected
+closed curve there it's going to go
+
+ align:start position:0%
+closed curve there it's going to go
+ 
+
+ align:start position:0%
+closed curve there it's going to go
+around the back of the sphere and it's
+
+ align:start position:0%
+around the back of the sphere and it's
+ 
+
+ align:start position:0%
+around the back of the sphere and it's
+going to be oriented one way or the
+
+ align:start position:0%
+going to be oriented one way or the
+ 
+
+ align:start position:0%
+going to be oriented one way or the
+other and it's going to divide the
+
+ align:start position:0%
+other and it's going to divide the
+ 
+
+ align:start position:0%
+other and it's going to divide the
+sphere into two pieces so there's the
+
+ align:start position:0%
+sphere into two pieces so there's the
+ 
+
+ align:start position:0%
+sphere into two pieces so there's the
+the sort of one cap on one side of it S1
+
+ align:start position:0%
+the sort of one cap on one side of it S1
+ 
+
+ align:start position:0%
+the sort of one cap on one side of it S1
+and then there's the whatever the other
+
+ align:start position:0%
+and then there's the whatever the other
+ 
+
+ align:start position:0%
+and then there's the whatever the other
+piece on the other side of it is
+
+ align:start position:0%
+piece on the other side of it is
+ 
+
+ align:start position:0%
+piece on the other side of it is
+S2 okay and so what we're going to do is
+
+ align:start position:0%
+S2 okay and so what we're going to do is
+ 
+
+ align:start position:0%
+S2 okay and so what we're going to do is
+we're going to talk about we're going to
+
+ align:start position:0%
+we're going to talk about we're going to
+ 
+
+ align:start position:0%
+we're going to talk about we're going to
+think about what what is this line
+
+ align:start position:0%
+think about what what is this line
+ 
+
+ align:start position:0%
+think about what what is this line
+integral okay so this this is our curve
+
+ align:start position:0%
+integral okay so this this is our curve
+ 
+
+ align:start position:0%
+integral okay so this this is our curve
+C here on the sphere so the integral
+
+ align:start position:0%
+C here on the sphere so the integral
+ 
+
+ align:start position:0%
+C here on the sphere so the integral
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+C of
+
+ align:start position:0%
+C of
+ 
+
+ align:start position:0%
+C of
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+dodr so this is what the problem
+
+ align:start position:0%
+dodr so this is what the problem
+ 
+
+ align:start position:0%
+dodr so this is what the problem
+suggests we think about so this is a
+
+ align:start position:0%
+suggests we think about so this is a
+ 
+
+ align:start position:0%
+suggests we think about so this is a
+line integral of a field. drr over the
+
+ align:start position:0%
+line integral of a field. drr over the
+ 
+
+ align:start position:0%
+line integral of a field. drr over the
+boundary of a surface well actually it's
+
+ align:start position:0%
+boundary of a surface well actually it's
+ 
+
+ align:start position:0%
+boundary of a surface well actually it's
+the boundary of two surfaces right it's
+
+ align:start position:0%
+the boundary of two surfaces right it's
+ 
+
+ align:start position:0%
+the boundary of two surfaces right it's
+it's C1 is the boundary of S1 sorry C is
+
+ align:start position:0%
+it's C1 is the boundary of S1 sorry C is
+ 
+
+ align:start position:0%
+it's C1 is the boundary of S1 sorry C is
+the boundary of S1 and C if we Orient it
+
+ align:start position:0%
+the boundary of S1 and C if we Orient it
+ 
+
+ align:start position:0%
+the boundary of S1 and C if we Orient it
+the other way is the boundary of S2 when
+
+ align:start position:0%
+the other way is the boundary of S2 when
+ 
+
+ align:start position:0%
+the other way is the boundary of S2 when
+we when we Orient them both
+
+ align:start position:0%
+we when we Orient them both
+ 
+
+ align:start position:0%
+we when we Orient them both
+outwards well um okay so so what is this
+
+ align:start position:0%
+outwards well um okay so so what is this
+ 
+
+ align:start position:0%
+outwards well um okay so so what is this
+um so this line integral so Stokes
+
+ align:start position:0%
+um so this line integral so Stokes
+ 
+
+ align:start position:0%
+um so this line integral so Stokes
+theorem tells us something about this
+
+ align:start position:0%
+theorem tells us something about this
+ 
+
+ align:start position:0%
+theorem tells us something about this
+line integral so let's let's first think
+
+ align:start position:0%
+line integral so let's let's first think
+ 
+
+ align:start position:0%
+line integral so let's let's first think
+about this as as the top cap that cap S1
+
+ align:start position:0%
+about this as as the top cap that cap S1
+ 
+
+ align:start position:0%
+about this as as the top cap that cap S1
+with boundary C oriented so that they
+
+ align:start position:0%
+with boundary C oriented so that they
+ 
+
+ align:start position:0%
+with boundary C oriented so that they
+agree with each other so the normal is
+
+ align:start position:0%
+agree with each other so the normal is
+ 
+
+ align:start position:0%
+agree with each other so the normal is
+outwards on the sphere and C is
+
+ align:start position:0%
+outwards on the sphere and C is
+ 
+
+ align:start position:0%
+outwards on the sphere and C is
+proceeding in the direction that I've
+
+ align:start position:0%
+proceeding in the direction that I've
+ 
+
+ align:start position:0%
+proceeding in the direction that I've
+drawn the arrow here well in that
+
+ align:start position:0%
+drawn the arrow here well in that
+ 
+
+ align:start position:0%
+drawn the arrow here well in that
+circumstance we have that the that the
+
+ align:start position:0%
+circumstance we have that the that the
+ 
+
+ align:start position:0%
+circumstance we have that the that the
+integral around C of G dodr is equal to
+
+ align:start position:0%
+integral around C of G dodr is equal to
+ 
+
+ align:start position:0%
+integral around C of G dodr is equal to
+by Stokes theorem this is equal to the
+
+ align:start position:0%
+by Stokes theorem this is equal to the
+ 
+
+ align:start position:0%
+by Stokes theorem this is equal to the
+double integral or the surface integral
+
+ align:start position:0%
+double integral or the surface integral
+ 
+
+ align:start position:0%
+double integral or the surface integral
+over S1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of curl of G
+
+ align:start position:0%
+of curl of G
+ 
+
+ align:start position:0%
+of curl of G
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+n with respect to surface
+
+ align:start position:0%
+n with respect to surface
+ 
+
+ align:start position:0%
+n with respect to surface
+area right so this is just Stokes
+
+ align:start position:0%
+area right so this is just Stokes
+ 
+
+ align:start position:0%
+area right so this is just Stokes
+theorem Stokes theorem says the line
+
+ align:start position:0%
+theorem Stokes theorem says the line
+ 
+
+ align:start position:0%
+theorem Stokes theorem says the line
+integral of G around the boundary curve
+
+ align:start position:0%
+integral of G around the boundary curve
+ 
+
+ align:start position:0%
+integral of G around the boundary curve
+is equal to the surface integral of of
+
+ align:start position:0%
+is equal to the surface integral of of
+ 
+
+ align:start position:0%
+is equal to the surface integral of of
+the curl of G over over the region
+
+ align:start position:0%
+the curl of G over over the region
+ 
+
+ align:start position:0%
+the curl of G over over the region
+provided all our orientations are
+
+ align:start position:0%
+provided all our orientations are
+ 
+
+ align:start position:0%
+provided all our orientations are
+correct okay well we know though what
+
+ align:start position:0%
+correct okay well we know though what
+ 
+
+ align:start position:0%
+correct okay well we know though what
+what curl of G is because by assumption
+
+ align:start position:0%
+what curl of G is because by assumption
+ 
+
+ align:start position:0%
+what curl of G is because by assumption
+f is equal to curl of G okay so this is
+
+ align:start position:0%
+f is equal to curl of G okay so this is
+ 
+
+ align:start position:0%
+f is equal to curl of G okay so this is
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to the surface integral over
+
+ align:start position:0%
+to the surface integral over
+ 
+
+ align:start position:0%
+to the surface integral over
+1 of f do n DS so this is here so in the
+
+ align:start position:0%
+1 of f do n DS so this is here so in the
+ 
+
+ align:start position:0%
+1 of f do n DS so this is here so in the
+first step we use Stokes theorem in the
+
+ align:start position:0%
+first step we use Stokes theorem in the
+ 
+
+ align:start position:0%
+first step we use Stokes theorem in the
+second step we use our assumption that
+
+ align:start position:0%
+second step we use our assumption that
+ 
+
+ align:start position:0%
+second step we use our assumption that
+that curl G is equal to
+
+ align:start position:0%
+that curl G is equal to
+ 
+
+ align:start position:0%
+that curl G is equal to
+F Well now what well okay but we know
+
+ align:start position:0%
+F Well now what well okay but we know
+ 
+
+ align:start position:0%
+F Well now what well okay but we know
+what f is Right f is this radial field
+
+ align:start position:0%
+what f is Right f is this radial field
+ 
+
+ align:start position:0%
+what f is Right f is this radial field
+XYZ so F and N are are pointing in the
+
+ align:start position:0%
+XYZ so F and N are are pointing in the
+ 
+
+ align:start position:0%
+XYZ so F and N are are pointing in the
+same direction they're they're parallel
+
+ align:start position:0%
+same direction they're they're parallel
+ 
+
+ align:start position:0%
+same direction they're they're parallel
+to each other N is a unit Vector so this
+
+ align:start position:0%
+to each other N is a unit Vector so this
+ 
+
+ align:start position:0%
+to each other N is a unit Vector so this
+is just the length of F this f.n is just
+
+ align:start position:0%
+is just the length of F this f.n is just
+ 
+
+ align:start position:0%
+is just the length of F this f.n is just
+the length of f and since we're on a
+
+ align:start position:0%
+the length of f and since we're on a
+ 
+
+ align:start position:0%
+the length of f and since we're on a
+sphere of radius B this is just B okay
+
+ align:start position:0%
+sphere of radius B this is just B okay
+ 
+
+ align:start position:0%
+sphere of radius B this is just B okay
+so the the integrand is just B so this
+
+ align:start position:0%
+so the the integrand is just B so this
+ 
+
+ align:start position:0%
+so the the integrand is just B so this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the integral over
+
+ align:start position:0%
+the integral over
+ 
+
+ align:start position:0%
+the integral over
+S1 of
+
+ align:start position:0%
+S1 of
+ 
+
+ align:start position:0%
+S1 of
+B DS which is B * the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area of
+
+ align:start position:0%
+area of
+ 
+
+ align:start position:0%
+area of
+S1 okay one thing I'd like you to notice
+
+ align:start position:0%
+S1 okay one thing I'd like you to notice
+ 
+
+ align:start position:0%
+S1 okay one thing I'd like you to notice
+is that in particular this is a positive
+
+ align:start position:0%
+is that in particular this is a positive
+ 
+
+ align:start position:0%
+is that in particular this is a positive
+number B is positive and the area is
+
+ align:start position:0%
+number B is positive and the area is
+ 
+
+ align:start position:0%
+number B is positive and the area is
+positive okay so that's our our first
+
+ align:start position:0%
+positive okay so that's our our first
+ 
+
+ align:start position:0%
+positive okay so that's our our first
+interpretation so we took our we took
+
+ align:start position:0%
+interpretation so we took our we took
+ 
+
+ align:start position:0%
+interpretation so we took our we took
+our field G that we suppose exists and
+
+ align:start position:0%
+our field G that we suppose exists and
+ 
+
+ align:start position:0%
+our field G that we suppose exists and
+we integrate it around this curve C and
+
+ align:start position:0%
+we integrate it around this curve C and
+ 
+
+ align:start position:0%
+we integrate it around this curve C and
+we apply Stokes theorem and then the
+
+ align:start position:0%
+we apply Stokes theorem and then the
+ 
+
+ align:start position:0%
+we apply Stokes theorem and then the
+fact that we know what f is means that
+
+ align:start position:0%
+fact that we know what f is means that
+ 
+
+ align:start position:0%
+fact that we know what f is means that
+we know what F do n is and so that makes
+
+ align:start position:0%
+we know what F do n is and so that makes
+ 
+
+ align:start position:0%
+we know what F do n is and so that makes
+our our surface integral very easy to
+
+ align:start position:0%
+our our surface integral very easy to
+ 
+
+ align:start position:0%
+our our surface integral very easy to
+compute and it turns out to be B time
+
+ align:start position:0%
+compute and it turns out to be B time
+ 
+
+ align:start position:0%
+compute and it turns out to be B time
+the area of s which I just happened to
+
+ align:start position:0%
+the area of s which I just happened to
+ 
+
+ align:start position:0%
+the area of s which I just happened to
+notice is a positive number okay well
+
+ align:start position:0%
+notice is a positive number okay well
+ 
+
+ align:start position:0%
+notice is a positive number okay well
+now we can do the same trick on the
+
+ align:start position:0%
+now we can do the same trick on the
+ 
+
+ align:start position:0%
+now we can do the same trick on the
+other half of the sphere right so we
+
+ align:start position:0%
+other half of the sphere right so we
+ 
+
+ align:start position:0%
+other half of the sphere right so we
+just did the top cap here we did S1 so
+
+ align:start position:0%
+just did the top cap here we did S1 so
+ 
+
+ align:start position:0%
+just did the top cap here we did S1 so
+now we have the bottom cap or you know
+
+ align:start position:0%
+now we have the bottom cap or you know
+ 
+
+ align:start position:0%
+now we have the bottom cap or you know
+whatever the all the rest of the sphere
+
+ align:start position:0%
+whatever the all the rest of the sphere
+ 
+
+ align:start position:0%
+whatever the all the rest of the sphere
+S2 okay so we can also get that the
+
+ align:start position:0%
+S2 okay so we can also get that the
+ 
+
+ align:start position:0%
+S2 okay so we can also get that the
+integral over C of g. drr we can
+
+ align:start position:0%
+integral over C of g. drr we can
+ 
+
+ align:start position:0%
+integral over C of g. drr we can
+interpret it in terms of Stokes theorem
+
+ align:start position:0%
+interpret it in terms of Stokes theorem
+ 
+
+ align:start position:0%
+interpret it in terms of Stokes theorem
+but notice then that c we we want we
+
+ align:start position:0%
+but notice then that c we we want we
+ 
+
+ align:start position:0%
+but notice then that c we we want we
+still want to use the same normal we
+
+ align:start position:0%
+still want to use the same normal we
+ 
+
+ align:start position:0%
+still want to use the same normal we
+like outwards pointing normals so we so
+
+ align:start position:0%
+like outwards pointing normals so we so
+ 
+
+ align:start position:0%
+like outwards pointing normals so we so
+we're going to have to orient C the
+
+ align:start position:0%
+we're going to have to orient C the
+ 
+
+ align:start position:0%
+we're going to have to orient C the
+other way in order to make Stokes
+
+ align:start position:0%
+other way in order to make Stokes
+ 
+
+ align:start position:0%
+other way in order to make Stokes
+theorem make sense so let's let's walk
+
+ align:start position:0%
+theorem make sense so let's let's walk
+ 
+
+ align:start position:0%
+theorem make sense so let's let's walk
+over here where we have some empty board
+
+ align:start position:0%
+over here where we have some empty board
+ 
+
+ align:start position:0%
+over here where we have some empty board
+space so we want to orient C the other
+
+ align:start position:0%
+space so we want to orient C the other
+ 
+
+ align:start position:0%
+space so we want to orient C the other
+way so in other words we want to take
+
+ align:start position:0%
+way so in other words we want to take
+ 
+
+ align:start position:0%
+way so in other words we want to take
+the negative of this line integral so
+
+ align:start position:0%
+the negative of this line integral so
+ 
+
+ align:start position:0%
+the negative of this line integral so
+it's minus G do Dr and if we apply
+
+ align:start position:0%
+it's minus G do Dr and if we apply
+ 
+
+ align:start position:0%
+it's minus G do Dr and if we apply
+Stokes theorem to this line integral so
+
+ align:start position:0%
+Stokes theorem to this line integral so
+ 
+
+ align:start position:0%
+Stokes theorem to this line integral so
+this is the same line integral but with
+
+ align:start position:0%
+this is the same line integral but with
+ 
+
+ align:start position:0%
+this is the same line integral but with
+the opposite orientation on C so with
+
+ align:start position:0%
+the opposite orientation on C so with
+ 
+
+ align:start position:0%
+the opposite orientation on C so with
+the opposite sign um well by Stokes
+
+ align:start position:0%
+the opposite sign um well by Stokes
+ 
+
+ align:start position:0%
+the opposite sign um well by Stokes
+theorem this is equal to the integral
+
+ align:start position:0%
+theorem this is equal to the integral
+ 
+
+ align:start position:0%
+theorem this is equal to the integral
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+S2 of the
+
+ align:start position:0%
+S2 of the
+ 
+
+ align:start position:0%
+S2 of the
+curl of
+
+ align:start position:0%
+curl of
+ 
+
+ align:start position:0%
+curl of
+G do
+
+ align:start position:0%
+G do
+ 
+
+ align:start position:0%
+G do
+n DS and so the way I've set this up
+
+ align:start position:0%
+n DS and so the way I've set this up
+ 
+
+ align:start position:0%
+n DS and so the way I've set this up
+this is still my outward pointing normal
+
+ align:start position:0%
+this is still my outward pointing normal
+ 
+
+ align:start position:0%
+this is still my outward pointing normal
+okay but again we can use our assumption
+
+ align:start position:0%
+okay but again we can use our assumption
+ 
+
+ align:start position:0%
+okay but again we can use our assumption
+and and we can get Curl
+
+ align:start position:0%
+and and we can get Curl
+ 
+
+ align:start position:0%
+and and we can get Curl
+of G is equal to F because that because
+
+ align:start position:0%
+of G is equal to F because that because
+ 
+
+ align:start position:0%
+of G is equal to F because that because
+we're assuming that g has this property
+
+ align:start position:0%
+we're assuming that g has this property
+ 
+
+ align:start position:0%
+we're assuming that g has this property
+so this is equal to again now it's the
+
+ align:start position:0%
+so this is equal to again now it's the
+ 
+
+ align:start position:0%
+so this is equal to again now it's the
+integral over
+
+ align:start position:0%
+integral over
+ 
+
+ align:start position:0%
+integral over
+S2 of
+
+ align:start position:0%
+S2 of
+ 
+
+ align:start position:0%
+S2 of
+f do
+
+ align:start position:0%
+f do
+ 
+
+ align:start position:0%
+f do
+n with respect to surface area and again
+
+ align:start position:0%
+n with respect to surface area and again
+ 
+
+ align:start position:0%
+n with respect to surface area and again
+n is the outward pointing normal and F
+
+ align:start position:0%
+n is the outward pointing normal and F
+ 
+
+ align:start position:0%
+n is the outward pointing normal and F
+is parallel to it so these two um so
+
+ align:start position:0%
+is parallel to it so these two um so
+ 
+
+ align:start position:0%
+is parallel to it so these two um so
+this do product is just the length of of
+
+ align:start position:0%
+this do product is just the length of of
+ 
+
+ align:start position:0%
+this do product is just the length of of
+f the outward pointing unit normal so
+
+ align:start position:0%
+f the outward pointing unit normal so
+ 
+
+ align:start position:0%
+f the outward pointing unit normal so
+this is just the length of f which is B
+
+ align:start position:0%
+this is just the length of f which is B
+ 
+
+ align:start position:0%
+this is just the length of f which is B
+so this is equal to B *
+
+ align:start position:0%
+so this is equal to B *
+ 
+
+ align:start position:0%
+so this is equal to B *
+the area of S2 which is also
+
+ align:start position:0%
+the area of S2 which is also
+ 
+
+ align:start position:0%
+the area of S2 which is also
+positive so what if we just shown well
+
+ align:start position:0%
+positive so what if we just shown well
+ 
+
+ align:start position:0%
+positive so what if we just shown well
+we started from the assumption that that
+
+ align:start position:0%
+we started from the assumption that that
+ 
+
+ align:start position:0%
+we started from the assumption that that
+there exists a g such that f is the curl
+
+ align:start position:0%
+there exists a g such that f is the curl
+ 
+
+ align:start position:0%
+there exists a g such that f is the curl
+of G and starting from that assumption
+
+ align:start position:0%
+of G and starting from that assumption
+ 
+
+ align:start position:0%
+of G and starting from that assumption
+we showed let's look we showed that the
+
+ align:start position:0%
+we showed let's look we showed that the
+ 
+
+ align:start position:0%
+we showed let's look we showed that the
+line integral around C of g.
+
+ align:start position:0%
+line integral around C of g.
+ 
+
+ align:start position:0%
+line integral around C of g.
+drr is equal to some positive
+
+ align:start position:0%
+drr is equal to some positive
+ 
+
+ align:start position:0%
+drr is equal to some positive
+number and we also
+
+ align:start position:0%
+number and we also
+ 
+
+ align:start position:0%
+number and we also
+showed over here that the negative of
+
+ align:start position:0%
+showed over here that the negative of
+ 
+
+ align:start position:0%
+showed over here that the negative of
+the line integral of G around C is equal
+
+ align:start position:0%
+the line integral of G around C is equal
+ 
+
+ align:start position:0%
+the line integral of G around C is equal
+to some positive number well this is
+
+ align:start position:0%
+to some positive number well this is
+ 
+
+ align:start position:0%
+to some positive number well this is
+clearly absurd that can't be true so
+
+ align:start position:0%
+clearly absurd that can't be true so
+ 
+
+ align:start position:0%
+clearly absurd that can't be true so
+starting from our assumption that F was
+
+ align:start position:0%
+starting from our assumption that F was
+ 
+
+ align:start position:0%
+starting from our assumption that F was
+the curl of G that there is a g such
+
+ align:start position:0%
+the curl of G that there is a g such
+ 
+
+ align:start position:0%
+the curl of G that there is a g such
+that f is the curl of G we reached an
+
+ align:start position:0%
+that f is the curl of G we reached an
+ 
+
+ align:start position:0%
+that f is the curl of G we reached an
+absurd conclusion we reached a
+
+ align:start position:0%
+absurd conclusion we reached a
+ 
+
+ align:start position:0%
+absurd conclusion we reached a
+conclusion that the same number is both
+
+ align:start position:0%
+conclusion that the same number is both
+ 
+
+ align:start position:0%
+conclusion that the same number is both
+positive and negative all right but that
+
+ align:start position:0%
+positive and negative all right but that
+ 
+
+ align:start position:0%
+positive and negative all right but that
+can't happen so that means our premise
+
+ align:start position:0%
+can't happen so that means our premise
+ 
+
+ align:start position:0%
+can't happen so that means our premise
+had to be false okay so this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contradiction so our assumption is false
+
+ align:start position:0%
+contradiction so our assumption is false
+ 
+
+ align:start position:0%
+contradiction so our assumption is false
+and our assumption was that we used to
+
+ align:start position:0%
+and our assumption was that we used to
+ 
+
+ align:start position:0%
+and our assumption was that we used to
+get this whole thing started that F was
+
+ align:start position:0%
+get this whole thing started that F was
+ 
+
+ align:start position:0%
+get this whole thing started that F was
+the curl of some
+
+ align:start position:0%
+the curl of some
+ 
+
+ align:start position:0%
+the curl of some
+G all right so what have we shown so we
+
+ align:start position:0%
+G all right so what have we shown so we
+ 
+
+ align:start position:0%
+G all right so what have we shown so we
+used a nice argument here with Stokes
+
+ align:start position:0%
+used a nice argument here with Stokes
+ 
+
+ align:start position:0%
+used a nice argument here with Stokes
+theorem in order to show that certain
+
+ align:start position:0%
+theorem in order to show that certain
+ 
+
+ align:start position:0%
+theorem in order to show that certain
+Fields aren't the curl of other fields
+
+ align:start position:0%
+Fields aren't the curl of other fields
+ 
+
+ align:start position:0%
+Fields aren't the curl of other fields
+so Stokes theorem limits the kind of
+
+ align:start position:0%
+so Stokes theorem limits the kind of
+ 
+
+ align:start position:0%
+so Stokes theorem limits the kind of
+fields that can be curls of other fields
+
+ align:start position:0%
+fields that can be curls of other fields
+ 
+
+ align:start position:0%
+fields that can be curls of other fields
+now perhaps you may have thought of
+
+ align:start position:0%
+now perhaps you may have thought of
+ 
+
+ align:start position:0%
+now perhaps you may have thought of
+other theorems that you can use that
+
+ align:start position:0%
+other theorems that you can use that
+ 
+
+ align:start position:0%
+other theorems that you can use that
+also limit what sorts of fields can be
+
+ align:start position:0%
+also limit what sorts of fields can be
+ 
+
+ align:start position:0%
+also limit what sorts of fields can be
+curls and there so there are other ways
+
+ align:start position:0%
+curls and there so there are other ways
+ 
+
+ align:start position:0%
+curls and there so there are other ways
+to reach this true conclusion that our
+
+ align:start position:0%
+to reach this true conclusion that our
+ 
+
+ align:start position:0%
+to reach this true conclusion that our
+field F whose components are X Y and Z
+
+ align:start position:0%
+field F whose components are X Y and Z
+ 
+
+ align:start position:0%
+field F whose components are X Y and Z
+is not the curl of any field this isn't
+
+ align:start position:0%
+is not the curl of any field this isn't
+ 
+
+ align:start position:0%
+is not the curl of any field this isn't
+the only way to reach that conclusion
+
+ align:start position:0%
+the only way to reach that conclusion
+ 
+
+ align:start position:0%
+the only way to reach that conclusion
+but this is a nice way that shows that
+
+ align:start position:0%
+but this is a nice way that shows that
+ 
+
+ align:start position:0%
+but this is a nice way that shows that
+Stokes theorem puts some limitations on
+
+ align:start position:0%
+Stokes theorem puts some limitations on
+ 
+
+ align:start position:0%
+Stokes theorem puts some limitations on
+what Fields can behave like if they're
+
+ align:start position:0%
+what Fields can behave like if they're
+ 
+
+ align:start position:0%
+what Fields can behave like if they're
+going to be curls I'll stop there
\ No newline at end of file
diff --git a/2JxUXSG9rKo.txt b/2JxUXSG9rKo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3be0ebdffc43c16cd286931856ab6aba3ce1d62a
--- /dev/null
+++ b/2JxUXSG9rKo.txt
@@ -0,0 +1,191 @@
+Now that we have some sense about how MOSFETs
+function, let's use them to build circuits
+
+to process our digitally encoded information.
+
+We have two simple rules we'll use when building
+the circuits, which, if they're followed,
+
+will allow us to abstract the behavior of
+the MOSFET as a simple voltage-controlled
+
+switch.
+
+The first rule is that we'll only use n-channel
+MOSFETs, which we'll call NFETs for short,
+
+when building pulldown circuits that connect
+a signaling node to the GROUND rail of the
+
+power supply.
+
+When the pulldown circuit is conducting, the
+signaling node will be at 0V and qualify as
+
+the digital value "0".
+
+If we obey this rule, NFETs will act switches
+controlled by V_GS, the difference between
+
+the voltage of the gate terminal and the voltage
+of the source terminal.
+
+When V_GS is lower than the MOSFET's threshold
+voltage, the switch is "open" or not conducting
+
+and there is no connection between the MOSFET's
+source and drain terminals.
+
+If V_GS is greater than the threshold voltage,
+the switch is "on" or conducting and there
+
+is a connection between the source and drain
+terminals.
+
+That path has a resistance determined by the
+magnitude of V_GS.
+
+The larger V_GS, the lower the effective resistance
+of the switch and the more current that will
+
+flow from drain to source.
+
+When designing pulldown circuits of NFET switches,
+we can use the following simple mental model
+
+for each NFET switch:
+if the gate voltage is a digital 0, the switch
+
+will be off; if the gate voltage is a digital
+1, the switch will be on.
+
+The situation with PFET switches is analogous,
+except that the potentials are reversed.
+
+Our rule is that PFETs can only be used in
+pullup circuits, used to connect a signaling
+
+node to the power supply voltage, which we'll
+call V_DD.
+
+When the pullup circuit is conducting, the
+signaling node will be at V_DD volts and qualify
+
+as the digital value "1".
+
+PFETs have a negative threshold voltage and
+V_GS has to be less than the threshold voltage
+
+in order for the PFET switch to be conducting.
+
+All these negatives can be a bit confusing,
+but, happily there's a simple mental model
+
+we can use for each PFET switch in the pullup
+circuit:
+
+if the gate voltage is a digital 0, the switch
+will be on; if the gate voltage is a digital
+
+1, the switch will be off - basically the
+opposite behavior of the NFET switch.
+
+You may be wondering why we can't use NFETs
+in pullup circuits or PFETs in pulldown circuits.
+
+You'll get to explore the answer to this question
+in the first lab of Assignment 2.
+
+Meanwhile, the short answer is that the signaling
+node will experience degraded signaling levels
+
+and we'll loose the noise margins we've worked
+so hard to create!
+
+Now consider the CMOS implementation of a
+combinational inverter.
+
+If the inverter's input is a digital 0, its
+output is a digital 1, and vice versa.
+
+The inverter circuit consists of a single
+NFET switch for the pulldown circuit, connecting
+
+the output node to GROUND and a single PFET
+switch for the pullup circuit, connecting
+
+the output to V_DD.
+
+The gate terminals of both switches are connected
+to the inverter's input node.
+
+The inverter's voltage transfer characteristic
+is shown in the figure.
+
+When V_IN is a digital 0 input, we see that
+V_OUT is greater than or equal to V_OH, representing
+
+a digital 1 output.
+
+Let's look at the state of the pullup and
+pulldown switches when the input is a digital
+
+0.
+
+Recalling the simple mental model for the
+NFET and PFET switches, a 0-input means the
+
+NFET switch is off, so there's no connection
+between the output node and ground, and the
+
+PFET switch is on, making a connection between
+the output node and V_DD.
+
+Current will flow through the pullup switch,
+charging the output node until its voltage
+
+reaches V_DD.
+
+Once both the source and drain terminals are
+at V_DD, there's no voltage difference across
+
+the switch and hence no more current will
+flow through the switch.
+
+Similarly, when V_IN is a digital 1, the NFET
+switch is on and PFET switch is off, so the
+
+output is connected to ground and eventually
+reaches a voltage of 0V.
+
+Again, current flow through pulldown switch
+will cease once the output node reaches 0V.
+
+When the input voltage is in the middle of
+its range, it's possible, depending on the
+
+particular power supply voltage used and the
+threshold voltage of the MOSFETs, that both
+
+the pullup and pulldown circuits will be conducting
+for a short period of time.
+
+That's okay.
+
+In fact, with both MOSFET switches on, small
+changes in the input voltage will produce
+
+large changes in the output voltage, leading
+to the very high gain exhibited by CMOS devices.
+
+This in turn will mean we can pick signaling
+thresholds that incorporate generous noise
+
+margins, allowing CMOS devices to work reliably
+in many different operating environments.
+
+This is our first CMOS combinational logic
+gate.
+
+In the next video, we'll explore how to build
+other, more interesting logic functions.
\ No newline at end of file
diff --git a/2q7gqUuG_EA.txt b/2q7gqUuG_EA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b88d4f2a3bb3b00f819179c22f10780de1c28a83
--- /dev/null
+++ b/2q7gqUuG_EA.txt
@@ -0,0 +1,435 @@
+align:start position:0%
+ 
+co- teing with seren uh professors s of
+
+ align:start position:0%
+co- teing with seren uh professors s of
+ 
+
+ align:start position:0%
+co- teing with seren uh professors s of
+us David S um is really a lot of fun uh
+
+ align:start position:0%
+us David S um is really a lot of fun uh
+ 
+
+ align:start position:0%
+us David S um is really a lot of fun uh
+We've taught before we taught the 66
+
+ align:start position:0%
+We've taught before we taught the 66
+ 
+
+ align:start position:0%
+We've taught before we taught the 66
+that's on ocw together um and serini is
+
+ align:start position:0%
+that's on ocw together um and serini is
+ 
+
+ align:start position:0%
+that's on ocw together um and serini is
+uh I would say one of the uh most
+
+ align:start position:0%
+uh I would say one of the uh most
+ 
+
+ align:start position:0%
+uh I would say one of the uh most
+humorous professors that I know at MIT
+
+ align:start position:0%
+humorous professors that I know at MIT
+ 
+
+ align:start position:0%
+humorous professors that I know at MIT
+so it's really a lot of fun to teach
+
+ align:start position:0%
+so it's really a lot of fun to teach
+ 
+
+ align:start position:0%
+so it's really a lot of fun to teach
+with him and uh I mean sometimes it's
+
+ align:start position:0%
+with him and uh I mean sometimes it's
+ 
+
+ align:start position:0%
+with him and uh I mean sometimes it's
+like a comedy R in his lectures and I
+
+ align:start position:0%
+like a comedy R in his lectures and I
+ 
+
+ align:start position:0%
+like a comedy R in his lectures and I
+like to do that too and lectures tell
+
+ align:start position:0%
+like to do that too and lectures tell
+ 
+
+ align:start position:0%
+like to do that too and lectures tell
+lots of jokes and and uh play together
+
+ align:start position:0%
+lots of jokes and and uh play together
+ 
+
+ align:start position:0%
+lots of jokes and and uh play together
+so it's really nice working together we
+
+ align:start position:0%
+so it's really nice working together we
+ 
+
+ align:start position:0%
+so it's really nice working together we
+have a good Dynamic for uh we're both
+
+ align:start position:0%
+have a good Dynamic for uh we're both
+ 
+
+ align:start position:0%
+have a good Dynamic for uh we're both
+super flexible like oh I need you to
+
+ align:start position:0%
+super flexible like oh I need you to
+ 
+
+ align:start position:0%
+super flexible like oh I need you to
+cover this lecture oh no problem I love
+
+ align:start position:0%
+cover this lecture oh no problem I love
+ 
+
+ align:start position:0%
+cover this lecture oh no problem I love
+that stuff in fact we were both kind of
+
+ align:start position:0%
+that stuff in fact we were both kind of
+ 
+
+ align:start position:0%
+that stuff in fact we were both kind of
+fighting over which lectures we wanted
+
+ align:start position:0%
+fighting over which lectures we wanted
+ 
+
+ align:start position:0%
+fighting over which lectures we wanted
+to teach because like I really want to
+
+ align:start position:0%
+to teach because like I really want to
+ 
+
+ align:start position:0%
+to teach because like I really want to
+teach this no no I taught it I really
+
+ align:start position:0%
+teach this no no I taught it I really
+ 
+
+ align:start position:0%
+teach this no no I taught it I really
+want to teach it this time and uh so
+
+ align:start position:0%
+want to teach it this time and uh so
+ 
+
+ align:start position:0%
+want to teach it this time and uh so
+that's a nice Dynamic to have it's not
+
+ align:start position:0%
+that's a nice Dynamic to have it's not
+ 
+
+ align:start position:0%
+that's a nice Dynamic to have it's not
+like oh you taught one too few lectures
+
+ align:start position:0%
+like oh you taught one too few lectures
+ 
+
+ align:start position:0%
+like oh you taught one too few lectures
+it's not balanced totally totally not
+
+ align:start position:0%
+it's not balanced totally totally not
+ 
+
+ align:start position:0%
+it's not balanced totally totally not
+like that um and both in 66 and 6046 in
+
+ align:start position:0%
+like that um and both in 66 and 6046 in
+ 
+
+ align:start position:0%
+like that um and both in 66 and 6046 in
+the last lecture we do a kind of actual
+
+ align:start position:0%
+the last lecture we do a kind of actual
+ 
+
+ align:start position:0%
+the last lecture we do a kind of actual
+comedy routine where we're somehow like
+
+ align:start position:0%
+comedy routine where we're somehow like
+ 
+
+ align:start position:0%
+comedy routine where we're somehow like
+fighting each other it's all all uh in
+
+ align:start position:0%
+fighting each other it's all all uh in
+ 
+
+ align:start position:0%
+fighting each other it's all all uh in
+good humor and it's pretty fun students
+
+ align:start position:0%
+good humor and it's pretty fun students
+ 
+
+ align:start position:0%
+good humor and it's pretty fun students
+really like it uh he's also uh in in
+
+ align:start position:0%
+really like it uh he's also uh in in
+ 
+
+ align:start position:0%
+really like it uh he's also uh in in
+both classes he has creative ideas and
+
+ align:start position:0%
+both classes he has creative ideas and
+ 
+
+ align:start position:0%
+both classes he has creative ideas and
+how to reward students for uh answering
+
+ align:start position:0%
+how to reward students for uh answering
+ 
+
+ align:start position:0%
+how to reward students for uh answering
+questions um so in 66 uh we were in a
+
+ align:start position:0%
+questions um so in 66 uh we were in a
+ 
+
+ align:start position:0%
+questions um so in 66 uh we were in a
+relatively uncomfortable lecture hall
+
+ align:start position:0%
+relatively uncomfortable lecture hall
+ 
+
+ align:start position:0%
+relatively uncomfortable lecture hall
+and so we had these uh pillows uh that
+
+ align:start position:0%
+and so we had these uh pillows uh that
+ 
+
+ align:start position:0%
+and so we had these uh pillows uh that
+we had custom printed and it had the
+
+ align:start position:0%
+we had custom printed and it had the
+ 
+
+ align:start position:0%
+we had custom printed and it had the
+name of the class and a little Rubik's
+
+ align:start position:0%
+name of the class and a little Rubik's
+ 
+
+ align:start position:0%
+name of the class and a little Rubik's
+Cube on it um and so if anyone ever
+
+ align:start position:0%
+Cube on it um and so if anyone ever
+ 
+
+ align:start position:0%
+Cube on it um and so if anyone ever
+answered a question in class or asked a
+
+ align:start position:0%
+answered a question in class or asked a
+ 
+
+ align:start position:0%
+answered a question in class or asked a
+good question then we would throw them a
+
+ align:start position:0%
+good question then we would throw them a
+ 
+
+ align:start position:0%
+good question then we would throw them a
+pillow kind of like a Frisbee and so for
+
+ align:start position:0%
+pillow kind of like a Frisbee and so for
+ 
+
+ align:start position:0%
+pillow kind of like a Frisbee and so for
+6046 Ser is like you know what we have
+
+ align:start position:0%
+6046 Ser is like you know what we have
+ 
+
+ align:start position:0%
+6046 Ser is like you know what we have
+to do this time is get actual Frisbees
+
+ align:start position:0%
+to do this time is get actual Frisbees
+ 
+
+ align:start position:0%
+to do this time is get actual Frisbees
+and so we got these blue and purple
+
+ align:start position:0%
+and so we got these blue and purple
+ 
+
+ align:start position:0%
+and so we got these blue and purple
+frisbees also custom printed with the
+
+ align:start position:0%
+frisbees also custom printed with the
+ 
+
+ align:start position:0%
+frisbees also custom printed with the
+class number and and a little diagram
+
+ align:start position:0%
+class number and and a little diagram
+ 
+
+ align:start position:0%
+class number and and a little diagram
+that is in lecture 20 or something
+
+ align:start position:0%
+that is in lecture 20 or something
+ 
+
+ align:start position:0%
+that is in lecture 20 or something
+um and so whenever anyone asked or
+
+ align:start position:0%
+um and so whenever anyone asked or
+ 
+
+ align:start position:0%
+um and so whenever anyone asked or
+answered a question we would throw them
+
+ align:start position:0%
+answered a question we would throw them
+ 
+
+ align:start position:0%
+answered a question we would throw them
+a Frisbee and we make jokes about
+
+ align:start position:0%
+a Frisbee and we make jokes about
+ 
+
+ align:start position:0%
+a Frisbee and we make jokes about
+whether blue was better or purple was
+
+ align:start position:0%
+whether blue was better or purple was
+ 
+
+ align:start position:0%
+whether blue was better or purple was
+better there was no better it was just
+
+ align:start position:0%
+better there was no better it was just
+ 
+
+ align:start position:0%
+better there was no better it was just
+uh so this is this is tough for me
+
+ align:start position:0%
+uh so this is this is tough for me
+ 
+
+ align:start position:0%
+uh so this is this is tough for me
+because I had to really learn how to
+
+ align:start position:0%
+because I had to really learn how to
+ 
+
+ align:start position:0%
+because I had to really learn how to
+throw frisbees but I think by the end of
+
+ align:start position:0%
+throw frisbees but I think by the end of
+ 
+
+ align:start position:0%
+throw frisbees but I think by the end of
+the semester I got pretty good
\ No newline at end of file
diff --git a/2x3F08_8B80.txt b/2x3F08_8B80.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4eaef392f1f0f6feddc1f5466af7607d36b25fb3
--- /dev/null
+++ b/2x3F08_8B80.txt
@@ -0,0 +1,6651 @@
+align:start position:0%
+ 
+all right um so what we're going to do
+
+ align:start position:0%
+all right um so what we're going to do
+ 
+
+ align:start position:0%
+all right um so what we're going to do
+today is that I'm going to start talking
+
+ align:start position:0%
+today is that I'm going to start talking
+ 
+
+ align:start position:0%
+today is that I'm going to start talking
+about the development of atomic theory
+
+ align:start position:0%
+about the development of atomic theory
+ 
+
+ align:start position:0%
+about the development of atomic theory
+so in the next few minutes I'm going to
+
+ align:start position:0%
+so in the next few minutes I'm going to
+ 
+
+ align:start position:0%
+so in the next few minutes I'm going to
+whiz through the observations that led
+
+ align:start position:0%
+whiz through the observations that led
+ 
+
+ align:start position:0%
+whiz through the observations that led
+to the belief that
+
+ align:start position:0%
+to the belief that
+ 
+
+ align:start position:0%
+to the belief that
+Adams were the most basic constituent of
+
+ align:start position:0%
+Adams were the most basic constituent of
+ 
+
+ align:start position:0%
+Adams were the most basic constituent of
+manner and then what we're going to see
+
+ align:start position:0%
+manner and then what we're going to see
+ 
+
+ align:start position:0%
+manner and then what we're going to see
+is that the atom can actually be split
+
+ align:start position:0%
+is that the atom can actually be split
+ 
+
+ align:start position:0%
+is that the atom can actually be split
+up that the atom is not the most basic
+
+ align:start position:0%
+up that the atom is not the most basic
+ 
+
+ align:start position:0%
+up that the atom is not the most basic
+constituent of matter that there's an at
+
+ align:start position:0%
+constituent of matter that there's an at
+ 
+
+ align:start position:0%
+constituent of matter that there's an at
+least an electron in a nucleus and we're
+
+ align:start position:0%
+least an electron in a nucleus and we're
+ 
+
+ align:start position:0%
+least an electron in a nucleus and we're
+going to start talking about what are
+
+ align:start position:0%
+going to start talking about what are
+ 
+
+ align:start position:0%
+going to start talking about what are
+the fundamental principles that um have
+
+ align:start position:0%
+the fundamental principles that um have
+ 
+
+ align:start position:0%
+the fundamental principles that um have
+to obtain in order for that electron and
+
+ align:start position:0%
+to obtain in order for that electron and
+ 
+
+ align:start position:0%
+to obtain in order for that electron and
+nucleus to hang together to remain an
+
+ align:start position:0%
+nucleus to hang together to remain an
+ 
+
+ align:start position:0%
+nucleus to hang together to remain an
+entity and what we're going to see is
+
+ align:start position:0%
+entity and what we're going to see is
+ 
+
+ align:start position:0%
+entity and what we're going to see is
+that we're going to have to
+
+ align:start position:0%
+that we're going to have to
+ 
+
+ align:start position:0%
+that we're going to have to
+to understand a new kind of mechanics to
+
+ align:start position:0%
+to understand a new kind of mechanics to
+ 
+
+ align:start position:0%
+to understand a new kind of mechanics to
+understand how that electron and nucleus
+
+ align:start position:0%
+understand how that electron and nucleus
+ 
+
+ align:start position:0%
+understand how that electron and nucleus
+hang
+
+ align:start position:0%
+hang
+ 
+
+ align:start position:0%
+hang
+together and then further on in the
+
+ align:start position:0%
+together and then further on in the
+ 
+
+ align:start position:0%
+together and then further on in the
+course we're going to see we're going to
+
+ align:start position:0%
+course we're going to see we're going to
+ 
+
+ align:start position:0%
+course we're going to see we're going to
+need that new kind of mechanics to also
+
+ align:start position:0%
+need that new kind of mechanics to also
+ 
+
+ align:start position:0%
+need that new kind of mechanics to also
+understand how two atoms hang together
+
+ align:start position:0%
+understand how two atoms hang together
+ 
+
+ align:start position:0%
+understand how two atoms hang together
+how two atoms bind uh to form a
+
+ align:start position:0%
+how two atoms bind uh to form a
+ 
+
+ align:start position:0%
+how two atoms bind uh to form a
+molecule all right but today I'll
+
+ align:start position:0%
+molecule all right but today I'll
+ 
+
+ align:start position:0%
+molecule all right but today I'll
+lecture for the first twoth thirds or
+
+ align:start position:0%
+lecture for the first twoth thirds or
+ 
+
+ align:start position:0%
+lecture for the first twoth thirds or
+three uh 3/4s of the course and then
+
+ align:start position:0%
+three uh 3/4s of the course and then
+ 
+
+ align:start position:0%
+three uh 3/4s of the course and then
+I'll stop and then I'll uh introduce the
+
+ align:start position:0%
+I'll stop and then I'll uh introduce the
+ 
+
+ align:start position:0%
+I'll stop and then I'll uh introduce the
+rest of our teaching team and we'll talk
+
+ align:start position:0%
+rest of our teaching team and we'll talk
+ 
+
+ align:start position:0%
+rest of our teaching team and we'll talk
+about the mechanics of the course we'll
+
+ align:start position:0%
+about the mechanics of the course we'll
+ 
+
+ align:start position:0%
+about the mechanics of the course we'll
+talk about the expectations of the
+
+ align:start position:0%
+talk about the expectations of the
+ 
+
+ align:start position:0%
+talk about the expectations of the
+course and uh some details like that
+
+ align:start position:0%
+course and uh some details like that
+ 
+
+ align:start position:0%
+course and uh some details like that
+okay okay so uh let's get going here and
+
+ align:start position:0%
+okay okay so uh let's get going here and
+ 
+
+ align:start position:0%
+okay okay so uh let's get going here and
+now we could turn the lights down
+
+ align:start position:0%
+now we could turn the lights down
+ 
+
+ align:start position:0%
+now we could turn the lights down
+because I am going to use the slide here
+
+ align:start position:0%
+because I am going to use the slide here
+ 
+
+ align:start position:0%
+because I am going to use the slide here
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+front all right so the ancient Greek
+
+ align:start position:0%
+front all right so the ancient Greek
+ 
+
+ align:start position:0%
+front all right so the ancient Greek
+philosophers they certainly were known
+
+ align:start position:0%
+philosophers they certainly were known
+ 
+
+ align:start position:0%
+philosophers they certainly were known
+who have uh pondered whether matter can
+
+ align:start position:0%
+who have uh pondered whether matter can
+ 
+
+ align:start position:0%
+who have uh pondered whether matter can
+be divided endlessly into smaller and
+
+ align:start position:0%
+be divided endlessly into smaller and
+ 
+
+ align:start position:0%
+be divided endlessly into smaller and
+smaller pieces or whether there was a
+
+ align:start position:0%
+smaller pieces or whether there was a
+ 
+
+ align:start position:0%
+smaller pieces or whether there was a
+point at which you couldn't divide
+
+ align:start position:0%
+point at which you couldn't divide
+ 
+
+ align:start position:0%
+point at which you couldn't divide
+matter any
+
+ align:start position:0%
+matter any
+ 
+
+ align:start position:0%
+matter any
+further and Aristotle here well he was
+
+ align:start position:0%
+further and Aristotle here well he was
+ 
+
+ align:start position:0%
+further and Aristotle here well he was
+one of the philosophers who argued that
+
+ align:start position:0%
+one of the philosophers who argued that
+ 
+
+ align:start position:0%
+one of the philosophers who argued that
+matter could be divided into smaller and
+
+ align:start position:0%
+matter could be divided into smaller and
+ 
+
+ align:start position:0%
+matter could be divided into smaller and
+smaller particles chopped up into
+
+ align:start position:0%
+smaller particles chopped up into
+ 
+
+ align:start position:0%
+smaller particles chopped up into
+smaller and smaller pieces add infinitum
+
+ align:start position:0%
+smaller and smaller pieces add infinitum
+ 
+
+ align:start position:0%
+smaller and smaller pieces add infinitum
+matter was visible this is called the
+
+ align:start position:0%
+matter was visible this is called the
+ 
+
+ align:start position:0%
+matter was visible this is called the
+Continuum theory of matter Continuum
+
+ align:start position:0%
+Continuum theory of matter Continuum
+ 
+
+ align:start position:0%
+Continuum theory of matter Continuum
+because you don't have any discrete
+
+ align:start position:0%
+because you don't have any discrete
+ 
+
+ align:start position:0%
+because you don't have any discrete
+points it's a Continuum No Boundaries
+
+ align:start position:0%
+points it's a Continuum No Boundaries
+ 
+
+ align:start position:0%
+points it's a Continuum No Boundaries
+right but there was a contrary
+
+ align:start position:0%
+right but there was a contrary
+ 
+
+ align:start position:0%
+right but there was a contrary
+philosophy a contrary Philosophy
+
+ align:start position:0%
+philosophy a contrary Philosophy
+ 
+
+ align:start position:0%
+philosophy a contrary Philosophy
+heralded by democratus who actually was
+
+ align:start position:0%
+heralded by democratus who actually was
+ 
+
+ align:start position:0%
+heralded by democratus who actually was
+about a hundred years older than
+
+ align:start position:0%
+about a hundred years older than
+ 
+
+ align:start position:0%
+about a hundred years older than
+Aristotle and he held that matter indeed
+
+ align:start position:0%
+Aristotle and he held that matter indeed
+ 
+
+ align:start position:0%
+Aristotle and he held that matter indeed
+was composed of individual discreet part
+
+ align:start position:0%
+was composed of individual discreet part
+ 
+
+ align:start position:0%
+was composed of individual discreet part
+particles these discrete particles he
+
+ align:start position:0%
+particles these discrete particles he
+ 
+
+ align:start position:0%
+particles these discrete particles he
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+atomos a for not thos for divisible
+
+ align:start position:0%
+atomos a for not thos for divisible
+ 
+
+ align:start position:0%
+atomos a for not thos for divisible
+that's the origin of our word of course
+
+ align:start position:0%
+that's the origin of our word of course
+ 
+
+ align:start position:0%
+that's the origin of our word of course
+atams now in the fourth fifth century BC
+
+ align:start position:0%
+atams now in the fourth fifth century BC
+ 
+
+ align:start position:0%
+atams now in the fourth fifth century BC
+there wasn't uh much evidence one way or
+
+ align:start position:0%
+there wasn't uh much evidence one way or
+ 
+
+ align:start position:0%
+there wasn't uh much evidence one way or
+the other for these kinds of uh either
+
+ align:start position:0%
+the other for these kinds of uh either
+ 
+
+ align:start position:0%
+the other for these kinds of uh either
+one of these philosophies and I call it
+
+ align:start position:0%
+one of these philosophies and I call it
+ 
+
+ align:start position:0%
+one of these philosophies and I call it
+a philosophy because it was a search for
+
+ align:start position:0%
+a philosophy because it was a search for
+ 
+
+ align:start position:0%
+a philosophy because it was a search for
+understanding Reality by a speculative
+
+ align:start position:0%
+understanding Reality by a speculative
+ 
+
+ align:start position:0%
+understanding Reality by a speculative
+as opposed to a
+
+ align:start position:0%
+as opposed to a
+ 
+
+ align:start position:0%
+as opposed to a
+uh investigational or observational
+
+ align:start position:0%
+uh investigational or observational
+ 
+
+ align:start position:0%
+uh investigational or observational
+means but for whatever reason it was
+
+ align:start position:0%
+means but for whatever reason it was
+ 
+
+ align:start position:0%
+means but for whatever reason it was
+Aristotle here his Continuum theory of
+
+ align:start position:0%
+Aristotle here his Continuum theory of
+ 
+
+ align:start position:0%
+Aristotle here his Continuum theory of
+matter prevailed all the way to the 17th
+
+ align:start position:0%
+matter prevailed all the way to the 17th
+ 
+
+ align:start position:0%
+matter prevailed all the way to the 17th
+century and here in fact he is depicted
+
+ align:start position:0%
+century and here in fact he is depicted
+ 
+
+ align:start position:0%
+century and here in fact he is depicted
+by Raphael on a fresco in um on the
+
+ align:start position:0%
+by Raphael on a fresco in um on the
+ 
+
+ align:start position:0%
+by Raphael on a fresco in um on the
+walls of the Vatican holding Court the
+
+ align:start position:0%
+walls of the Vatican holding Court the
+ 
+
+ align:start position:0%
+walls of the Vatican holding Court the
+Continuum theory of
+
+ align:start position:0%
+Continuum theory of
+ 
+
+ align:start position:0%
+Continuum theory of
+matter but just about at the same time
+
+ align:start position:0%
+matter but just about at the same time
+ 
+
+ align:start position:0%
+matter but just about at the same time
+at which r
+
+ align:start position:0%
+at which r
+ 
+
+ align:start position:0%
+at which r
+painted this uh picture there were
+
+ align:start position:0%
+painted this uh picture there were
+ 
+
+ align:start position:0%
+painted this uh picture there were
+observations a set of observations that
+
+ align:start position:0%
+observations a set of observations that
+ 
+
+ align:start position:0%
+observations a set of observations that
+were being made that began to uh point
+
+ align:start position:0%
+were being made that began to uh point
+ 
+
+ align:start position:0%
+were being made that began to uh point
+out that matter wasn't really behaving
+
+ align:start position:0%
+out that matter wasn't really behaving
+ 
+
+ align:start position:0%
+out that matter wasn't really behaving
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+reacting like a Continuum that matter
+
+ align:start position:0%
+reacting like a Continuum that matter
+ 
+
+ align:start position:0%
+reacting like a Continuum that matter
+was uh behaving more like uh at some
+
+ align:start position:0%
+was uh behaving more like uh at some
+ 
+
+ align:start position:0%
+was uh behaving more like uh at some
+discreet nature uh to it so what were
+
+ align:start position:0%
+discreet nature uh to it so what were
+ 
+
+ align:start position:0%
+discreet nature uh to it so what were
+those observations well one of them was
+
+ align:start position:0%
+those observations well one of them was
+ 
+
+ align:start position:0%
+those observations well one of them was
+by this gentleman here Robert Boyle and
+
+ align:start position:0%
+by this gentleman here Robert Boyle and
+ 
+
+ align:start position:0%
+by this gentleman here Robert Boyle and
+uh guess what his formal occupation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was chemistry yeah that's a good guess
+
+ align:start position:0%
+was chemistry yeah that's a good guess
+ 
+
+ align:start position:0%
+was chemistry yeah that's a good guess
+but his formal occupation was a
+
+ align:start position:0%
+but his formal occupation was a
+ 
+
+ align:start position:0%
+but his formal occupation was a
+theologian as most scientists were at at
+
+ align:start position:0%
+theologian as most scientists were at at
+ 
+
+ align:start position:0%
+theologian as most scientists were at at
+that time and you of course know him for
+
+ align:start position:0%
+that time and you of course know him for
+ 
+
+ align:start position:0%
+that time and you of course know him for
+um the empirical observation that the
+
+ align:start position:0%
+um the empirical observation that the
+ 
+
+ align:start position:0%
+um the empirical observation that the
+pressure times the volume is all
+
+ align:start position:0%
+pressure times the volume is all
+ 
+
+ align:start position:0%
+pressure times the volume is all
+constant as long as the temperature is
+
+ align:start position:0%
+constant as long as the temperature is
+ 
+
+ align:start position:0%
+constant as long as the temperature is
+constant but he actually Advanced the
+
+ align:start position:0%
+constant but he actually Advanced the
+ 
+
+ align:start position:0%
+constant but he actually Advanced the
+one of the first ideas of an element and
+
+ align:start position:0%
+one of the first ideas of an element and
+ 
+
+ align:start position:0%
+one of the first ideas of an element and
+that is he called an element a certain
+
+ align:start position:0%
+that is he called an element a certain
+ 
+
+ align:start position:0%
+that is he called an element a certain
+primitive unmingled
+
+ align:start position:0%
+primitive unmingled
+ 
+
+ align:start position:0%
+primitive unmingled
+body and that somehow you can take these
+
+ align:start position:0%
+body and that somehow you can take these
+ 
+
+ align:start position:0%
+body and that somehow you can take these
+primitive unmingled bodies and put them
+
+ align:start position:0%
+primitive unmingled bodies and put them
+ 
+
+ align:start position:0%
+primitive unmingled bodies and put them
+together to form a perfectly mixed body
+
+ align:start position:0%
+together to form a perfectly mixed body
+ 
+
+ align:start position:0%
+together to form a perfectly mixed body
+a compound a molecule so this was one of
+
+ align:start position:0%
+a compound a molecule so this was one of
+ 
+
+ align:start position:0%
+a compound a molecule so this was one of
+the first ideas of an element that comes
+
+ align:start position:0%
+the first ideas of an element that comes
+ 
+
+ align:start position:0%
+the first ideas of an element that comes
+together to form elements that come
+
+ align:start position:0%
+together to form elements that come
+ 
+
+ align:start position:0%
+together to form elements that come
+together to form
+
+ align:start position:0%
+together to form
+ 
+
+ align:start position:0%
+together to form
+molecules and then there was this
+
+ align:start position:0%
+molecules and then there was this
+ 
+
+ align:start position:0%
+molecules and then there was this
+gentleman Joseph priestle guess what his
+
+ align:start position:0%
+gentleman Joseph priestle guess what his
+ 
+
+ align:start position:0%
+gentleman Joseph priestle guess what his
+occupation
+
+ align:start position:0%
+occupation
+ 
+
+ align:start position:0%
+occupation
+was he was a priest of course and what
+
+ align:start position:0%
+was he was a priest of course and what
+ 
+
+ align:start position:0%
+was he was a priest of course and what
+did he do well he uh looked at reactions
+
+ align:start position:0%
+did he do well he uh looked at reactions
+ 
+
+ align:start position:0%
+did he do well he uh looked at reactions
+with def fisticated air def fisticated
+
+ align:start position:0%
+with def fisticated air def fisticated
+ 
+
+ align:start position:0%
+with def fisticated air def fisticated
+air reacting with materials and what he
+
+ align:start position:0%
+air reacting with materials and what he
+ 
+
+ align:start position:0%
+air reacting with materials and what he
+observed was that these materials
+
+ align:start position:0%
+observed was that these materials
+ 
+
+ align:start position:0%
+observed was that these materials
+reacted more vigorously in deep
+
+ align:start position:0%
+reacted more vigorously in deep
+ 
+
+ align:start position:0%
+reacted more vigorously in deep
+fisticated air well what's deep
+
+ align:start position:0%
+fisticated air well what's deep
+ 
+
+ align:start position:0%
+fisticated air well what's deep
+fisticated air well of course now we
+
+ align:start position:0%
+fisticated air well of course now we
+ 
+
+ align:start position:0%
+fisticated air well of course now we
+know de fisticated air is oxygen it's
+
+ align:start position:0%
+know de fisticated air is oxygen it's
+ 
+
+ align:start position:0%
+know de fisticated air is oxygen it's
+air with the nitrogen predominantly
+
+ align:start position:0%
+air with the nitrogen predominantly
+ 
+
+ align:start position:0%
+air with the nitrogen predominantly
+removed but it really took this
+
+ align:start position:0%
+removed but it really took this
+ 
+
+ align:start position:0%
+removed but it really took this
+gentleman
+
+ align:start position:0%
+gentleman
+ 
+
+ align:start position:0%
+gentleman
+laier it took this gentleman to really
+
+ align:start position:0%
+laier it took this gentleman to really
+ 
+
+ align:start position:0%
+laier it took this gentleman to really
+understand what Priestley was doing in
+
+ align:start position:0%
+understand what Priestley was doing in
+ 
+
+ align:start position:0%
+understand what Priestley was doing in
+his experiments and what leazier
+
+ align:start position:0%
+his experiments and what leazier
+ 
+
+ align:start position:0%
+his experiments and what leazier
+realized is that this deistic air was
+
+ align:start position:0%
+realized is that this deistic air was
+ 
+
+ align:start position:0%
+realized is that this deistic air was
+adding to the
+
+ align:start position:0%
+adding to the
+ 
+
+ align:start position:0%
+adding to the
+material when it did this
+
+ align:start position:0%
+material when it did this
+ 
+
+ align:start position:0%
+material when it did this
+reaction and he made those observations
+
+ align:start position:0%
+reaction and he made those observations
+ 
+
+ align:start position:0%
+reaction and he made those observations
+or he came to those conclusions by doing
+
+ align:start position:0%
+or he came to those conclusions by doing
+ 
+
+ align:start position:0%
+or he came to those conclusions by doing
+some very careful measurements of the
+
+ align:start position:0%
+some very careful measurements of the
+ 
+
+ align:start position:0%
+some very careful measurements of the
+mass before the reaction so the mass of
+
+ align:start position:0%
+mass before the reaction so the mass of
+ 
+
+ align:start position:0%
+mass before the reaction so the mass of
+the deistic air plus the mass of the
+
+ align:start position:0%
+the deistic air plus the mass of the
+ 
+
+ align:start position:0%
+the deistic air plus the mass of the
+material and he found that indeed the
+
+ align:start position:0%
+material and he found that indeed the
+ 
+
+ align:start position:0%
+material and he found that indeed the
+mass after the reaction was equivalent
+
+ align:start position:0%
+mass after the reaction was equivalent
+ 
+
+ align:start position:0%
+mass after the reaction was equivalent
+to that before the
+
+ align:start position:0%
+to that before the
+ 
+
+ align:start position:0%
+to that before the
+reaction and so he was one of the first
+
+ align:start position:0%
+reaction and so he was one of the first
+ 
+
+ align:start position:0%
+reaction and so he was one of the first
+IND indviduals to realize that a
+
+ align:start position:0%
+IND indviduals to realize that a
+ 
+
+ align:start position:0%
+IND indviduals to realize that a
+chemical reaction can be written down
+
+ align:start position:0%
+chemical reaction can be written down
+ 
+
+ align:start position:0%
+chemical reaction can be written down
+analogous to writing a algebraic
+
+ align:start position:0%
+analogous to writing a algebraic
+ 
+
+ align:start position:0%
+analogous to writing a algebraic
+equation well Lavoisier also did a lot
+
+ align:start position:0%
+equation well Lavoisier also did a lot
+ 
+
+ align:start position:0%
+equation well Lavoisier also did a lot
+of work with isolating uh elements he
+
+ align:start position:0%
+of work with isolating uh elements he
+ 
+
+ align:start position:0%
+of work with isolating uh elements he
+identified 17 metals and nine non-metals
+
+ align:start position:0%
+identified 17 metals and nine non-metals
+ 
+
+ align:start position:0%
+identified 17 metals and nine non-metals
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+elements well for all of his efforts we
+
+ align:start position:0%
+elements well for all of his efforts we
+ 
+
+ align:start position:0%
+elements well for all of his efforts we
+all know what happened to
+
+ align:start position:0%
+all know what happened to
+ 
+
+ align:start position:0%
+all know what happened to
+Lavoisier um because of his connection
+
+ align:start position:0%
+Lavoisier um because of his connection
+ 
+
+ align:start position:0%
+Lavoisier um because of his connection
+to the French monarchy you know the
+
+ align:start position:0%
+to the French monarchy you know the
+ 
+
+ align:start position:0%
+to the French monarchy you know the
+judge at his trial uh claimed that the
+
+ align:start position:0%
+judge at his trial uh claimed that the
+ 
+
+ align:start position:0%
+judge at his trial uh claimed that the
+Republic has no use for Sant lrange at
+
+ align:start position:0%
+Republic has no use for Sant lrange at
+ 
+
+ align:start position:0%
+Republic has no use for Sant lrange at
+that time a French mathematician said it
+
+ align:start position:0%
+that time a French mathematician said it
+ 
+
+ align:start position:0%
+that time a French mathematician said it
+took but a moment to uh cut through that
+
+ align:start position:0%
+took but a moment to uh cut through that
+ 
+
+ align:start position:0%
+took but a moment to uh cut through that
+head but it will require a hundred years
+
+ align:start position:0%
+head but it will require a hundred years
+ 
+
+ align:start position:0%
+head but it will require a hundred years
+to produce another like
+
+ align:start position:0%
+to produce another like
+ 
+
+ align:start position:0%
+to produce another like
+it well what there was another Frenchman
+
+ align:start position:0%
+it well what there was another Frenchman
+ 
+
+ align:start position:0%
+it well what there was another Frenchman
+at that time JL PR he was a little more
+
+ align:start position:0%
+at that time JL PR he was a little more
+ 
+
+ align:start position:0%
+at that time JL PR he was a little more
+politically savvy so he High tailed it
+
+ align:start position:0%
+politically savvy so he High tailed it
+ 
+
+ align:start position:0%
+politically savvy so he High tailed it
+over to Spain and led a long and
+
+ align:start position:0%
+over to Spain and led a long and
+ 
+
+ align:start position:0%
+over to Spain and led a long and
+healthful life as a professor in
+
+ align:start position:0%
+healthful life as a professor in
+ 
+
+ align:start position:0%
+healthful life as a professor in
+Madrid but what he did is he did some
+
+ align:start position:0%
+Madrid but what he did is he did some
+ 
+
+ align:start position:0%
+Madrid but what he did is he did some
+experiments and he observed that when
+
+ align:start position:0%
+experiments and he observed that when
+ 
+
+ align:start position:0%
+experiments and he observed that when
+two or more elements combined well they
+
+ align:start position:0%
+two or more elements combined well they
+ 
+
+ align:start position:0%
+two or more elements combined well they
+combine to form a compound they always
+
+ align:start position:0%
+combine to form a compound they always
+ 
+
+ align:start position:0%
+combine to form a compound they always
+combine in definite proportions by
+
+ align:start position:0%
+combine in definite proportions by
+ 
+
+ align:start position:0%
+combine in definite proportions by
+weight and it didn't matter what the
+
+ align:start position:0%
+weight and it didn't matter what the
+ 
+
+ align:start position:0%
+weight and it didn't matter what the
+method of preparation was and so because
+
+ align:start position:0%
+method of preparation was and so because
+ 
+
+ align:start position:0%
+method of preparation was and so because
+he made this observation over and over
+
+ align:start position:0%
+he made this observation over and over
+ 
+
+ align:start position:0%
+he made this observation over and over
+and over again with many different
+
+ align:start position:0%
+and over again with many different
+ 
+
+ align:start position:0%
+and over again with many different
+elements this became known as the law
+
+ align:start position:0%
+elements this became known as the law
+ 
+
+ align:start position:0%
+elements this became known as the law
+here of definite proportions again some
+
+ align:start position:0%
+here of definite proportions again some
+ 
+
+ align:start position:0%
+here of definite proportions again some
+indication that matter was had a discret
+
+ align:start position:0%
+indication that matter was had a discret
+ 
+
+ align:start position:0%
+indication that matter was had a discret
+nature to it right it wasn't just the
+
+ align:start position:0%
+nature to it right it wasn't just the
+ 
+
+ align:start position:0%
+nature to it right it wasn't just the
+Continuum some numbers were involved
+
+ align:start position:0%
+Continuum some numbers were involved
+ 
+
+ align:start position:0%
+Continuum some numbers were involved
+here all right but it really took this
+
+ align:start position:0%
+here all right but it really took this
+ 
+
+ align:start position:0%
+here all right but it really took this
+guy John Dalton English school teacher
+
+ align:start position:0%
+guy John Dalton English school teacher
+ 
+
+ align:start position:0%
+guy John Dalton English school teacher
+with a lot of
+
+ align:start position:0%
+with a lot of
+ 
+
+ align:start position:0%
+with a lot of
+interest he uh was aware of the
+
+ align:start position:0%
+interest he uh was aware of the
+ 
+
+ align:start position:0%
+interest he uh was aware of the
+observations of Bole and Priestley and
+
+ align:start position:0%
+observations of Bole and Priestley and
+ 
+
+ align:start position:0%
+observations of Bole and Priestley and
+Lavoisier and
+
+ align:start position:0%
+Lavoisier and
+ 
+
+ align:start position:0%
+Lavoisier and
+PR and what he realized is that he could
+
+ align:start position:0%
+PR and what he realized is that he could
+ 
+
+ align:start position:0%
+PR and what he realized is that he could
+begin to understand all of those
+
+ align:start position:0%
+begin to understand all of those
+ 
+
+ align:start position:0%
+begin to understand all of those
+observations if he went back all the way
+
+ align:start position:0%
+observations if he went back all the way
+ 
+
+ align:start position:0%
+observations if he went back all the way
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+democratus and democratus is idea of
+
+ align:start position:0%
+democratus and democratus is idea of
+ 
+
+ align:start position:0%
+democratus and democratus is idea of
+Atmos or atams these individual discreet
+
+ align:start position:0%
+Atmos or atams these individual discreet
+ 
+
+ align:start position:0%
+Atmos or atams these individual discreet
+particles of matter and so he set forth
+
+ align:start position:0%
+particles of matter and so he set forth
+ 
+
+ align:start position:0%
+particles of matter and so he set forth
+some postulates some postulates which of
+
+ align:start position:0%
+some postulates some postulates which of
+ 
+
+ align:start position:0%
+some postulates some postulates which of
+course now know are known as Dalton's
+
+ align:start position:0%
+course now know are known as Dalton's
+ 
+
+ align:start position:0%
+course now know are known as Dalton's
+atomic theory but what he said is that
+
+ align:start position:0%
+atomic theory but what he said is that
+ 
+
+ align:start position:0%
+atomic theory but what he said is that
+each element is composed of atoms he
+
+ align:start position:0%
+each element is composed of atoms he
+ 
+
+ align:start position:0%
+each element is composed of atoms he
+said that atoms of Any Given element are
+
+ align:start position:0%
+said that atoms of Any Given element are
+ 
+
+ align:start position:0%
+said that atoms of Any Given element are
+identical he said that compounds form
+
+ align:start position:0%
+identical he said that compounds form
+ 
+
+ align:start position:0%
+identical he said that compounds form
+when atoms of more than one element
+
+ align:start position:0%
+when atoms of more than one element
+ 
+
+ align:start position:0%
+when atoms of more than one element
+combined and he realized of course from
+
+ align:start position:0%
+combined and he realized of course from
+ 
+
+ align:start position:0%
+combined and he realized of course from
+Leer's OB observations that atoms are
+
+ align:start position:0%
+Leer's OB observations that atoms are
+ 
+
+ align:start position:0%
+Leer's OB observations that atoms are
+neither created nor are they
+
+ align:start position:0%
+neither created nor are they
+ 
+
+ align:start position:0%
+neither created nor are they
+destroyed now just in aside Dalton John
+
+ align:start position:0%
+destroyed now just in aside Dalton John
+ 
+
+ align:start position:0%
+destroyed now just in aside Dalton John
+Dalton with his breaths of breath of
+
+ align:start position:0%
+Dalton with his breaths of breath of
+ 
+
+ align:start position:0%
+Dalton with his breaths of breath of
+Interest he also was the first
+
+ align:start position:0%
+Interest he also was the first
+ 
+
+ align:start position:0%
+Interest he also was the first
+individual to document color blindness
+
+ align:start position:0%
+individual to document color blindness
+ 
+
+ align:start position:0%
+individual to document color blindness
+in human beings and in fact we do call
+
+ align:start position:0%
+in human beings and in fact we do call
+ 
+
+ align:start position:0%
+in human beings and in fact we do call
+color blindness
+
+ align:start position:0%
+color blindness
+ 
+
+ align:start position:0%
+color blindness
+daltonism so see we're getting you ready
+
+ align:start position:0%
+daltonism so see we're getting you ready
+ 
+
+ align:start position:0%
+daltonism so see we're getting you ready
+for medical school already all
+
+ align:start position:0%
+for medical school already all
+ 
+
+ align:start position:0%
+for medical school already all
+right okay but um what I want you to
+
+ align:start position:0%
+right okay but um what I want you to
+ 
+
+ align:start position:0%
+right okay but um what I want you to
+recognize here is that Mr Dalton didn't
+
+ align:start position:0%
+recognize here is that Mr Dalton didn't
+ 
+
+ align:start position:0%
+recognize here is that Mr Dalton didn't
+actually do any of the experiments
+
+ align:start position:0%
+actually do any of the experiments
+ 
+
+ align:start position:0%
+actually do any of the experiments
+himself although from what I know of him
+
+ align:start position:0%
+himself although from what I know of him
+ 
+
+ align:start position:0%
+himself although from what I know of him
+I think he could have done the
+
+ align:start position:0%
+I think he could have done the
+ 
+
+ align:start position:0%
+I think he could have done the
+experiments himself but rather he was
+
+ align:start position:0%
+experiments himself but rather he was
+ 
+
+ align:start position:0%
+experiments himself but rather he was
+aware of the seemingly disperate
+
+ align:start position:0%
+aware of the seemingly disperate
+ 
+
+ align:start position:0%
+aware of the seemingly disperate
+observations made by leier and Bo and PR
+
+ align:start position:0%
+observations made by leier and Bo and PR
+ 
+
+ align:start position:0%
+observations made by leier and Bo and PR
+and he just said well you
+
+ align:start position:0%
+and he just said well you
+ 
+
+ align:start position:0%
+and he just said well you
+know if I take those
+
+ align:start position:0%
+know if I take those
+ 
+
+ align:start position:0%
+know if I take those
+observations and I use this framework
+
+ align:start position:0%
+observations and I use this framework
+ 
+
+ align:start position:0%
+observations and I use this framework
+well then I can understand them they
+
+ align:start position:0%
+well then I can understand them they
+ 
+
+ align:start position:0%
+well then I can understand them they
+make sense within this
+
+ align:start position:0%
+make sense within this
+ 
+
+ align:start position:0%
+make sense within this
+framework and this is a powerful
+
+ align:start position:0%
+framework and this is a powerful
+ 
+
+ align:start position:0%
+framework and this is a powerful
+approach in science a lot of science
+
+ align:start position:0%
+approach in science a lot of science
+ 
+
+ align:start position:0%
+approach in science a lot of science
+progresses this way that is that there's
+
+ align:start position:0%
+progresses this way that is that there's
+ 
+
+ align:start position:0%
+progresses this way that is that there's
+this collection of seemingly disperate
+
+ align:start position:0%
+this collection of seemingly disperate
+ 
+
+ align:start position:0%
+this collection of seemingly disperate
+observations and then all of a sudden
+
+ align:start position:0%
+observations and then all of a sudden
+ 
+
+ align:start position:0%
+observations and then all of a sudden
+somebody comes along and sees an
+
+ align:start position:0%
+somebody comes along and sees an
+ 
+
+ align:start position:0%
+somebody comes along and sees an
+organizing principle in all of those
+
+ align:start position:0%
+organizing principle in all of those
+ 
+
+ align:start position:0%
+organizing principle in all of those
+observations and puts forth then these
+
+ align:start position:0%
+observations and puts forth then these
+ 
+
+ align:start position:0%
+observations and puts forth then these
+postulates that's what Dalton did here
+
+ align:start position:0%
+postulates that's what Dalton did here
+ 
+
+ align:start position:0%
+postulates that's what Dalton did here
+now of course course these postulates uh
+
+ align:start position:0%
+now of course course these postulates uh
+ 
+
+ align:start position:0%
+now of course course these postulates uh
+weren't accepted IM immediately and
+
+ align:start position:0%
+weren't accepted IM immediately and
+ 
+
+ align:start position:0%
+weren't accepted IM immediately and
+rightfully so because they were just
+
+ align:start position:0%
+rightfully so because they were just
+ 
+
+ align:start position:0%
+rightfully so because they were just
+postulates they needed further
+
+ align:start position:0%
+postulates they needed further
+ 
+
+ align:start position:0%
+postulates they needed further
+substantiation and that further
+
+ align:start position:0%
+substantiation and that further
+ 
+
+ align:start position:0%
+substantiation and that further
+substantiation came in terms of the work
+
+ align:start position:0%
+substantiation came in terms of the work
+ 
+
+ align:start position:0%
+substantiation came in terms of the work
+by this this gentleman Joseph gusak the
+
+ align:start position:0%
+by this this gentleman Joseph gusak the
+ 
+
+ align:start position:0%
+by this this gentleman Joseph gusak the
+law of combining
+
+ align:start position:0%
+law of combining
+ 
+
+ align:start position:0%
+law of combining
+volumes it came by the work of this
+
+ align:start position:0%
+volumes it came by the work of this
+ 
+
+ align:start position:0%
+volumes it came by the work of this
+gentleman this gentleman is Lorenzo
+
+ align:start position:0%
+gentleman this gentleman is Lorenzo
+ 
+
+ align:start position:0%
+gentleman this gentleman is Lorenzo
+Romano Amadeo Carl avagadro
+
+ align:start position:0%
+Romano Amadeo Carl avagadro
+ 
+
+ align:start position:0%
+Romano Amadeo Carl avagadro
+hypothesis and of course um you can all
+
+ align:start position:0%
+hypothesis and of course um you can all
+ 
+
+ align:start position:0%
+hypothesis and of course um you can all
+read Italian so you can read what's on
+
+ align:start position:0%
+read Italian so you can read what's on
+ 
+
+ align:start position:0%
+read Italian so you can read what's on
+the stamp here right it just says equal
+
+ align:start position:0%
+the stamp here right it just says equal
+ 
+
+ align:start position:0%
+the stamp here right it just says equal
+volumes of gas under the same uh
+
+ align:start position:0%
+volumes of gas under the same uh
+ 
+
+ align:start position:0%
+volumes of gas under the same uh
+conditions of temperature uh lead to the
+
+ align:start position:0%
+conditions of temperature uh lead to the
+ 
+
+ align:start position:0%
+conditions of temperature uh lead to the
+same number of molecules see you didn't
+
+ align:start position:0%
+same number of molecules see you didn't
+ 
+
+ align:start position:0%
+same number of molecules see you didn't
+know you could read Italian but there it
+
+ align:start position:0%
+know you could read Italian but there it
+ 
+
+ align:start position:0%
+know you could read Italian but there it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+okay and further substantiation for this
+
+ align:start position:0%
+okay and further substantiation for this
+ 
+
+ align:start position:0%
+okay and further substantiation for this
+idea of an atom and the discreetness of
+
+ align:start position:0%
+idea of an atom and the discreetness of
+ 
+
+ align:start position:0%
+idea of an atom and the discreetness of
+matter came from this gentleman lewick
+
+ align:start position:0%
+matter came from this gentleman lewick
+ 
+
+ align:start position:0%
+matter came from this gentleman lewick
+boltzman gas kinetic theory who proposed
+
+ align:start position:0%
+boltzman gas kinetic theory who proposed
+ 
+
+ align:start position:0%
+boltzman gas kinetic theory who proposed
+that well you know pressure that must be
+
+ align:start position:0%
+that well you know pressure that must be
+ 
+
+ align:start position:0%
+that well you know pressure that must be
+due to these atoms that are moving
+
+ align:start position:0%
+due to these atoms that are moving
+ 
+
+ align:start position:0%
+due to these atoms that are moving
+around and hitting the walls of a vessel
+
+ align:start position:0%
+around and hitting the walls of a vessel
+ 
+
+ align:start position:0%
+around and hitting the walls of a vessel
+those impacts give rise to the pressure
+
+ align:start position:0%
+those impacts give rise to the pressure
+ 
+
+ align:start position:0%
+those impacts give rise to the pressure
+that is exerted on the walls of that
+
+ align:start position:0%
+that is exerted on the walls of that
+ 
+
+ align:start position:0%
+that is exerted on the walls of that
+vessel and then finally it took this
+
+ align:start position:0%
+vessel and then finally it took this
+ 
+
+ align:start position:0%
+vessel and then finally it took this
+gentleman canazaro and it took his
+
+ align:start position:0%
+gentleman canazaro and it took his
+ 
+
+ align:start position:0%
+gentleman canazaro and it took his
+statesmanship because what canazaro did
+
+ align:start position:0%
+statesmanship because what canazaro did
+ 
+
+ align:start position:0%
+statesmanship because what canazaro did
+and now this is the later 1800s or so
+
+ align:start position:0%
+and now this is the later 1800s or so
+ 
+
+ align:start position:0%
+and now this is the later 1800s or so
+what canazaro did is that he got the
+
+ align:start position:0%
+what canazaro did is that he got the
+ 
+
+ align:start position:0%
+what canazaro did is that he got the
+scientific establishment at that time
+
+ align:start position:0%
+scientific establishment at that time
+ 
+
+ align:start position:0%
+scientific establishment at that time
+and the scientific establishment at that
+
+ align:start position:0%
+and the scientific establishment at that
+ 
+
+ align:start position:0%
+and the scientific establishment at that
+time of course is this small group of
+
+ align:start position:0%
+time of course is this small group of
+ 
+
+ align:start position:0%
+time of course is this small group of
+pale males but he got them to listen to
+
+ align:start position:0%
+pale males but he got them to listen to
+ 
+
+ align:start position:0%
+pale males but he got them to listen to
+Dalton's atomic theory and then the
+
+ align:start position:0%
+Dalton's atomic theory and then the
+ 
+
+ align:start position:0%
+Dalton's atomic theory and then the
+ensuing experiments of avagadro
+
+ align:start position:0%
+ensuing experiments of avagadro
+ 
+
+ align:start position:0%
+ensuing experiments of avagadro
+and um and uh gayus saac etc etc and
+
+ align:start position:0%
+and um and uh gayus saac etc etc and
+ 
+
+ align:start position:0%
+and um and uh gayus saac etc etc and
+finally he he got them to say yes
+
+ align:start position:0%
+finally he he got them to say yes
+ 
+
+ align:start position:0%
+finally he he got them to say yes
+there's something right about uh this
+
+ align:start position:0%
+there's something right about uh this
+ 
+
+ align:start position:0%
+there's something right about uh this
+atomic theory of matter the idea that
+
+ align:start position:0%
+atomic theory of matter the idea that
+ 
+
+ align:start position:0%
+atomic theory of matter the idea that
+mass was made up of discrete particles
+
+ align:start position:0%
+mass was made up of discrete particles
+ 
+
+ align:start position:0%
+mass was made up of discrete particles
+called atomos or
+
+ align:start position:0%
+called atomos or
+ 
+
+ align:start position:0%
+called atomos or
+atoms well
+
+ align:start position:0%
+atoms well
+ 
+
+ align:start position:0%
+atoms well
+nowadays we of course can uh actually
+
+ align:start position:0%
+nowadays we of course can uh actually
+ 
+
+ align:start position:0%
+nowadays we of course can uh actually
+image individual atoms or
+
+ align:start position:0%
+image individual atoms or
+ 
+
+ align:start position:0%
+image individual atoms or
+molecules and uh what you see
+
+ align:start position:0%
+molecules and uh what you see
+ 
+
+ align:start position:0%
+molecules and uh what you see
+here is uh is a an array of 28 Co
+
+ align:start position:0%
+here is uh is a an array of 28 Co
+ 
+
+ align:start position:0%
+here is uh is a an array of 28 Co
+molecules and these 28 Co molecules are
+
+ align:start position:0%
+molecules and these 28 Co molecules are
+ 
+
+ align:start position:0%
+molecules and these 28 Co molecules are
+arranged in the form of a little
+
+ align:start position:0%
+arranged in the form of a little
+ 
+
+ align:start position:0%
+arranged in the form of a little
+man or a little
+
+ align:start position:0%
+man or a little
+ 
+
+ align:start position:0%
+man or a little
+woman um I'll let you figure it out but
+
+ align:start position:0%
+woman um I'll let you figure it out but
+ 
+
+ align:start position:0%
+woman um I'll let you figure it out but
+what these are molecule sitting on a
+
+ align:start position:0%
+what these are molecule sitting on a
+ 
+
+ align:start position:0%
+what these are molecule sitting on a
+platinum
+
+ align:start position:0%
+platinum
+ 
+
+ align:start position:0%
+platinum
+surface and so uh each one of these
+
+ align:start position:0%
+surface and so uh each one of these
+ 
+
+ align:start position:0%
+surface and so uh each one of these
+orange balls here is a CL molecule but
+
+ align:start position:0%
+orange balls here is a CL molecule but
+ 
+
+ align:start position:0%
+orange balls here is a CL molecule but
+when CL binds to a platinum surface it
+
+ align:start position:0%
+when CL binds to a platinum surface it
+ 
+
+ align:start position:0%
+when CL binds to a platinum surface it
+does so with the carbon end down and the
+
+ align:start position:0%
+does so with the carbon end down and the
+ 
+
+ align:start position:0%
+does so with the carbon end down and the
+oxygen end up and there's a really good
+
+ align:start position:0%
+oxygen end up and there's a really good
+ 
+
+ align:start position:0%
+oxygen end up and there's a really good
+reason for why that is the case and
+
+ align:start position:0%
+reason for why that is the case and
+ 
+
+ align:start position:0%
+reason for why that is the case and
+we'll talk about that when we talk about
+
+ align:start position:0%
+we'll talk about that when we talk about
+ 
+
+ align:start position:0%
+we'll talk about that when we talk about
+molecular orbitals so what you're seeing
+
+ align:start position:0%
+molecular orbitals so what you're seeing
+ 
+
+ align:start position:0%
+molecular orbitals so what you're seeing
+here is really just the the tops of the
+
+ align:start position:0%
+here is really just the the tops of the
+ 
+
+ align:start position:0%
+here is really just the the tops of the
+the co molecules you're seeing the
+
+ align:start position:0%
+the co molecules you're seeing the
+ 
+
+ align:start position:0%
+the co molecules you're seeing the
+oxygen ends of the co
+
+ align:start position:0%
+oxygen ends of the co
+ 
+
+ align:start position:0%
+oxygen ends of the co
+molecule all right well this image here
+
+ align:start position:0%
+molecule all right well this image here
+ 
+
+ align:start position:0%
+molecule all right well this image here
+was taken by something called a scanning
+
+ align:start position:0%
+was taken by something called a scanning
+ 
+
+ align:start position:0%
+was taken by something called a scanning
+tunneling
+
+ align:start position:0%
+tunneling
+ 
+
+ align:start position:0%
+tunneling
+microscope and um I'm sorry to say but
+
+ align:start position:0%
+microscope and um I'm sorry to say but
+ 
+
+ align:start position:0%
+microscope and um I'm sorry to say but
+this was actually invented just before
+
+ align:start position:0%
+this was actually invented just before
+ 
+
+ align:start position:0%
+this was actually invented just before
+you were
+
+ align:start position:0%
+you were
+ 
+
+ align:start position:0%
+you were
+born and uh it was invented was actually
+
+ align:start position:0%
+born and uh it was invented was actually
+ 
+
+ align:start position:0%
+born and uh it was invented was actually
+worked on by rusa and then perfected by
+
+ align:start position:0%
+worked on by rusa and then perfected by
+ 
+
+ align:start position:0%
+worked on by rusa and then perfected by
+benig and Roar and they earned a Nobel
+
+ align:start position:0%
+benig and Roar and they earned a Nobel
+ 
+
+ align:start position:0%
+benig and Roar and they earned a Nobel
+Prize for their work and um the way the
+
+ align:start position:0%
+Prize for their work and um the way the
+ 
+
+ align:start position:0%
+Prize for their work and um the way the
+technique works is uh the following let
+
+ align:start position:0%
+technique works is uh the following let
+ 
+
+ align:start position:0%
+technique works is uh the following let
+me uh maybe have the the board lights
+
+ align:start position:0%
+me uh maybe have the the board lights
+ 
+
+ align:start position:0%
+me uh maybe have the the board lights
+here so that we can uh I'm going to do
+
+ align:start position:0%
+here so that we can uh I'm going to do
+ 
+
+ align:start position:0%
+here so that we can uh I'm going to do
+some board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+so what you do to to do this is that you
+
+ align:start position:0%
+so what you do to to do this is that you
+ 
+
+ align:start position:0%
+so what you do to to do this is that you
+take a Tungsten
+
+ align:start position:0%
+take a Tungsten
+ 
+
+ align:start position:0%
+take a Tungsten
+wire and you do a little chemistry you
+
+ align:start position:0%
+wire and you do a little chemistry you
+ 
+
+ align:start position:0%
+wire and you do a little chemistry you
+et the tungsten wire down to as fine a
+
+ align:start position:0%
+et the tungsten wire down to as fine a
+ 
+
+ align:start position:0%
+et the tungsten wire down to as fine a
+tip as you can so you um put it in some
+
+ align:start position:0%
+tip as you can so you um put it in some
+ 
+
+ align:start position:0%
+tip as you can so you um put it in some
+potassium hydroxide and some some
+
+ align:start position:0%
+potassium hydroxide and some some
+ 
+
+ align:start position:0%
+potassium hydroxide and some some
+current through it do a little cheem uh
+
+ align:start position:0%
+current through it do a little cheem uh
+ 
+
+ align:start position:0%
+current through it do a little cheem uh
+electrochemistry and what you'll get
+
+ align:start position:0%
+electrochemistry and what you'll get
+ 
+
+ align:start position:0%
+electrochemistry and what you'll get
+then is a a pretty fine tip at the end
+
+ align:start position:0%
+then is a a pretty fine tip at the end
+ 
+
+ align:start position:0%
+then is a a pretty fine tip at the end
+of this tungsten
+
+ align:start position:0%
+of this tungsten
+ 
+
+ align:start position:0%
+of this tungsten
+wire but then what you do is you take
+
+ align:start position:0%
+wire but then what you do is you take
+ 
+
+ align:start position:0%
+wire but then what you do is you take
+that tungsten wire and you attach it to
+
+ align:start position:0%
+that tungsten wire and you attach it to
+ 
+
+ align:start position:0%
+that tungsten wire and you attach it to
+a Paso Electric Crystal all right so a
+
+ align:start position:0%
+a Paso Electric Crystal all right so a
+ 
+
+ align:start position:0%
+a Paso Electric Crystal all right so a
+pazo electric Crystal and uh let me put
+
+ align:start position:0%
+pazo electric Crystal and uh let me put
+ 
+
+ align:start position:0%
+pazo electric Crystal and uh let me put
+it this way here a pzo
+
+ align:start position:0%
+it this way here a pzo
+ 
+
+ align:start position:0%
+it this way here a pzo
+electric material is some
+
+ align:start position:0%
+electric material is some
+ 
+
+ align:start position:0%
+electric material is some
+material that if you put a voltage
+
+ align:start position:0%
+material that if you put a voltage
+ 
+
+ align:start position:0%
+material that if you put a voltage
+across it it expands a little bit little
+
+ align:start position:0%
+across it it expands a little bit little
+ 
+
+ align:start position:0%
+across it it expands a little bit little
+bit meaning 10 20 angstroms okay and so
+
+ align:start position:0%
+bit meaning 10 20 angstroms okay and so
+ 
+
+ align:start position:0%
+bit meaning 10 20 angstroms okay and so
+um now if you attach the tungsten wire
+
+ align:start position:0%
+um now if you attach the tungsten wire
+ 
+
+ align:start position:0%
+um now if you attach the tungsten wire
+to that material you have some control
+
+ align:start position:0%
+to that material you have some control
+ 
+
+ align:start position:0%
+to that material you have some control
+on the angstrom scale right so that's
+
+ align:start position:0%
+on the angstrom scale right so that's
+ 
+
+ align:start position:0%
+on the angstrom scale right so that's
+what happens in order to move that tip
+
+ align:start position:0%
+what happens in order to move that tip
+ 
+
+ align:start position:0%
+what happens in order to move that tip
+around but then what you do is you take
+
+ align:start position:0%
+around but then what you do is you take
+ 
+
+ align:start position:0%
+around but then what you do is you take
+this tip and you bring it say within
+
+ align:start position:0%
+this tip and you bring it say within
+ 
+
+ align:start position:0%
+this tip and you bring it say within
+five angstroms of the top of this CL
+
+ align:start position:0%
+five angstroms of the top of this CL
+ 
+
+ align:start position:0%
+five angstroms of the top of this CL
+molecule so if I have my Platinum
+
+ align:start position:0%
+molecule so if I have my Platinum
+ 
+
+ align:start position:0%
+molecule so if I have my Platinum
+surface here and my carbon here and
+
+ align:start position:0%
+surface here and my carbon here and
+ 
+
+ align:start position:0%
+surface here and my carbon here and
+here's my oxygen all right what I'm
+
+ align:start position:0%
+here's my oxygen all right what I'm
+ 
+
+ align:start position:0%
+here's my oxygen all right what I'm
+going to do is I'm going to bring this
+
+ align:start position:0%
+going to do is I'm going to bring this
+ 
+
+ align:start position:0%
+going to do is I'm going to bring this
+this tip say within five angstroms here
+
+ align:start position:0%
+this tip say within five angstroms here
+ 
+
+ align:start position:0%
+this tip say within five angstroms here
+of this uh oxygen end of the co
+
+ align:start position:0%
+of this uh oxygen end of the co
+ 
+
+ align:start position:0%
+of this uh oxygen end of the co
+molecule okay and
+
+ align:start position:0%
+molecule okay and
+ 
+
+ align:start position:0%
+molecule okay and
+then I'm going to put a negative voltage
+
+ align:start position:0%
+then I'm going to put a negative voltage
+ 
+
+ align:start position:0%
+then I'm going to put a negative voltage
+on this tungsten tip here and I'm going
+
+ align:start position:0%
+on this tungsten tip here and I'm going
+ 
+
+ align:start position:0%
+on this tungsten tip here and I'm going
+to take the co molecule the I'm going to
+
+ align:start position:0%
+to take the co molecule the I'm going to
+ 
+
+ align:start position:0%
+to take the co molecule the I'm going to
+take the Platinum surface and I'm going
+
+ align:start position:0%
+take the Platinum surface and I'm going
+ 
+
+ align:start position:0%
+take the Platinum surface and I'm going
+to ground it now in this tungsten tip
+
+ align:start position:0%
+to ground it now in this tungsten tip
+ 
+
+ align:start position:0%
+to ground it now in this tungsten tip
+there are of course electrons and since
+
+ align:start position:0%
+there are of course electrons and since
+ 
+
+ align:start position:0%
+there are of course electrons and since
+this is a metal metal has a
+
+ align:start position:0%
+this is a metal metal has a
+ 
+
+ align:start position:0%
+this is a metal metal has a
+characteristic where some of those
+
+ align:start position:0%
+characteristic where some of those
+ 
+
+ align:start position:0%
+characteristic where some of those
+electrons aren't strongly bound to the
+
+ align:start position:0%
+electrons aren't strongly bound to the
+ 
+
+ align:start position:0%
+electrons aren't strongly bound to the
+nucleus they are actually um uh they
+
+ align:start position:0%
+nucleus they are actually um uh they
+ 
+
+ align:start position:0%
+nucleus they are actually um uh they
+actually roam around the solid
+
+ align:start position:0%
+actually roam around the solid
+ 
+
+ align:start position:0%
+actually roam around the solid
+okay and um this is a high energy State
+
+ align:start position:0%
+okay and um this is a high energy State
+ 
+
+ align:start position:0%
+okay and um this is a high energy State
+given that electrons are negatively
+
+ align:start position:0%
+given that electrons are negatively
+ 
+
+ align:start position:0%
+given that electrons are negatively
+charged and they're in an environment of
+
+ align:start position:0%
+charged and they're in an environment of
+ 
+
+ align:start position:0%
+charged and they're in an environment of
+this negative potential hey that's a
+
+ align:start position:0%
+this negative potential hey that's a
+ 
+
+ align:start position:0%
+this negative potential hey that's a
+rather high energy state for those
+
+ align:start position:0%
+rather high energy state for those
+ 
+
+ align:start position:0%
+rather high energy state for those
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+so if I were to draw an energy level
+
+ align:start position:0%
+so if I were to draw an energy level
+ 
+
+ align:start position:0%
+so if I were to draw an energy level
+diagram here so this is energy and I'm
+
+ align:start position:0%
+diagram here so this is energy and I'm
+ 
+
+ align:start position:0%
+diagram here so this is energy and I'm
+going to represent those electrons on
+
+ align:start position:0%
+going to represent those electrons on
+ 
+
+ align:start position:0%
+going to represent those electrons on
+the tungsten tip it's going to be at a
+
+ align:start position:0%
+the tungsten tip it's going to be at a
+ 
+
+ align:start position:0%
+the tungsten tip it's going to be at a
+some high energy level so this is
+
+ align:start position:0%
+some high energy level so this is
+ 
+
+ align:start position:0%
+some high energy level so this is
+electrons on the tungsten right however
+
+ align:start position:0%
+electrons on the tungsten right however
+ 
+
+ align:start position:0%
+electrons on the tungsten right however
+there are also some electrons down here
+
+ align:start position:0%
+there are also some electrons down here
+ 
+
+ align:start position:0%
+there are also some electrons down here
+and they're at Ground potential so these
+
+ align:start position:0%
+and they're at Ground potential so these
+ 
+
+ align:start position:0%
+and they're at Ground potential so these
+electrons at are at a lower energy so
+
+ align:start position:0%
+electrons at are at a lower energy so
+ 
+
+ align:start position:0%
+electrons at are at a lower energy so
+I'm going to draw energy level
+
+ align:start position:0%
+I'm going to draw energy level
+ 
+
+ align:start position:0%
+I'm going to draw energy level
+representing them this is the electrons
+
+ align:start position:0%
+representing them this is the electrons
+ 
+
+ align:start position:0%
+representing them this is the electrons
+on the Platinum all right and so this
+
+ align:start position:0%
+on the Platinum all right and so this
+ 
+
+ align:start position:0%
+on the Platinum all right and so this
+coordinate here is kind of like a
+
+ align:start position:0%
+coordinate here is kind of like a
+ 
+
+ align:start position:0%
+coordinate here is kind of like a
+distance right this is the distance this
+
+ align:start position:0%
+distance right this is the distance this
+ 
+
+ align:start position:0%
+distance right this is the distance this
+is the electrons on the tungsten over
+
+ align:start position:0%
+is the electrons on the tungsten over
+ 
+
+ align:start position:0%
+is the electrons on the tungsten over
+here the electrons on the
+
+ align:start position:0%
+here the electrons on the
+ 
+
+ align:start position:0%
+here the electrons on the
+platinum and um what these electrons on
+
+ align:start position:0%
+platinum and um what these electrons on
+ 
+
+ align:start position:0%
+platinum and um what these electrons on
+the tungsten tip would like to do is to
+
+ align:start position:0%
+the tungsten tip would like to do is to
+ 
+
+ align:start position:0%
+the tungsten tip would like to do is to
+be here on the Platinum because that's a
+
+ align:start position:0%
+be here on the Platinum because that's a
+ 
+
+ align:start position:0%
+be here on the Platinum because that's a
+lower energy
+
+ align:start position:0%
+lower energy
+ 
+
+ align:start position:0%
+lower energy
+state but the problem is that there's a
+
+ align:start position:0%
+state but the problem is that there's a
+ 
+
+ align:start position:0%
+state but the problem is that there's a
+a gap right here there's no material
+
+ align:start position:0%
+a gap right here there's no material
+ 
+
+ align:start position:0%
+a gap right here there's no material
+between the tip and the oxygen end of
+
+ align:start position:0%
+between the tip and the oxygen end of
+ 
+
+ align:start position:0%
+between the tip and the oxygen end of
+this Co
+
+ align:start position:0%
+this Co
+ 
+
+ align:start position:0%
+this Co
+molecule there's if you do it in a
+
+ align:start position:0%
+molecule there's if you do it in a
+ 
+
+ align:start position:0%
+molecule there's if you do it in a
+vacuum there's a vacuum here there's a
+
+ align:start position:0%
+vacuum there's a vacuum here there's a
+ 
+
+ align:start position:0%
+vacuum there's a vacuum here there's a
+vacuum
+
+ align:start position:0%
+vacuum
+ 
+
+ align:start position:0%
+vacuum
+Gap and so for the electrons to go from
+
+ align:start position:0%
+Gap and so for the electrons to go from
+ 
+
+ align:start position:0%
+Gap and so for the electrons to go from
+here to here well there's a very large
+
+ align:start position:0%
+here to here well there's a very large
+ 
+
+ align:start position:0%
+here to here well there's a very large
+barrier this is a very high energy state
+
+ align:start position:0%
+barrier this is a very high energy state
+ 
+
+ align:start position:0%
+barrier this is a very high energy state
+if an electron were in between this Gap
+
+ align:start position:0%
+if an electron were in between this Gap
+ 
+
+ align:start position:0%
+if an electron were in between this Gap
+here so I'm going to represent that
+
+ align:start position:0%
+here so I'm going to represent that
+ 
+
+ align:start position:0%
+here so I'm going to represent that
+energy change as the electrons go from
+
+ align:start position:0%
+energy change as the electrons go from
+ 
+
+ align:start position:0%
+energy change as the electrons go from
+the tungsten tip to the Tung to the uh
+
+ align:start position:0%
+the tungsten tip to the Tung to the uh
+ 
+
+ align:start position:0%
+the tungsten tip to the Tung to the uh
+Platinum surface as is a barrier like
+
+ align:start position:0%
+Platinum surface as is a barrier like
+ 
+
+ align:start position:0%
+Platinum surface as is a barrier like
+this all right very large
+
+ align:start position:0%
+this all right very large
+ 
+
+ align:start position:0%
+this all right very large
+barrier now you've seen these kinds of
+
+ align:start position:0%
+barrier now you've seen these kinds of
+ 
+
+ align:start position:0%
+barrier now you've seen these kinds of
+uh we call them reaction coordinates in
+
+ align:start position:0%
+uh we call them reaction coordinates in
+ 
+
+ align:start position:0%
+uh we call them reaction coordinates in
+chemistry in in high school that as
+
+ align:start position:0%
+chemistry in in high school that as
+ 
+
+ align:start position:0%
+chemistry in in high school that as
+you've
+
+ align:start position:0%
+you've
+ 
+
+ align:start position:0%
+you've
+seen situations where we might have if
+
+ align:start position:0%
+seen situations where we might have if
+ 
+
+ align:start position:0%
+seen situations where we might have if
+we're doing an energy level diagram this
+
+ align:start position:0%
+we're doing an energy level diagram this
+ 
+
+ align:start position:0%
+we're doing an energy level diagram this
+is the energy of the reactant
+
+ align:start position:0%
+is the energy of the reactant
+ 
+
+ align:start position:0%
+is the energy of the reactant
+out here this is the energy of the
+
+ align:start position:0%
+out here this is the energy of the
+ 
+
+ align:start position:0%
+out here this is the energy of the
+products right and in between is this
+
+ align:start position:0%
+products right and in between is this
+ 
+
+ align:start position:0%
+products right and in between is this
+activation energy barrier that we call
+
+ align:start position:0%
+activation energy barrier that we call
+ 
+
+ align:start position:0%
+activation energy barrier that we call
+EAC in other words you have to put
+
+ align:start position:0%
+EAC in other words you have to put
+ 
+
+ align:start position:0%
+EAC in other words you have to put
+energy into the system in order to get
+
+ align:start position:0%
+energy into the system in order to get
+ 
+
+ align:start position:0%
+energy into the system in order to get
+their reaction to go you have to put
+
+ align:start position:0%
+their reaction to go you have to put
+ 
+
+ align:start position:0%
+their reaction to go you have to put
+energy into the system before you get
+
+ align:start position:0%
+energy into the system before you get
+ 
+
+ align:start position:0%
+energy into the system before you get
+any energy back out right and that's
+
+ align:start position:0%
+any energy back out right and that's
+ 
+
+ align:start position:0%
+any energy back out right and that's
+what happens in a chemical reaction we
+
+ align:start position:0%
+what happens in a chemical reaction we
+ 
+
+ align:start position:0%
+what happens in a chemical reaction we
+put energy into the system before we
+
+ align:start position:0%
+put energy into the system before we
+ 
+
+ align:start position:0%
+put energy into the system before we
+make it go or can make it
+
+ align:start position:0%
+make it go or can make it
+ 
+
+ align:start position:0%
+make it go or can make it
+go but in this particular case the
+
+ align:start position:0%
+go but in this particular case the
+ 
+
+ align:start position:0%
+go but in this particular case the
+electrons they don't behave like most
+
+ align:start position:0%
+electrons they don't behave like most
+ 
+
+ align:start position:0%
+electrons they don't behave like most
+reactants the electrons right here you
+
+ align:start position:0%
+reactants the electrons right here you
+ 
+
+ align:start position:0%
+reactants the electrons right here you
+know what they do these electrons hey
+
+ align:start position:0%
+know what they do these electrons hey
+ 
+
+ align:start position:0%
+know what they do these electrons hey
+they go right through that barrier they
+
+ align:start position:0%
+they go right through that barrier they
+ 
+
+ align:start position:0%
+they go right through that barrier they
+don't care that there's a brick wall
+
+ align:start position:0%
+don't care that there's a brick wall
+ 
+
+ align:start position:0%
+don't care that there's a brick wall
+there right they just go right through
+
+ align:start position:0%
+there right they just go right through
+ 
+
+ align:start position:0%
+there right they just go right through
+the barrier we call that
+
+ align:start position:0%
+the barrier we call that
+ 
+
+ align:start position:0%
+the barrier we call that
+tunneling and how in the world can that
+
+ align:start position:0%
+tunneling and how in the world can that
+ 
+
+ align:start position:0%
+tunneling and how in the world can that
+happen well that can happen because
+
+ align:start position:0%
+happen well that can happen because
+ 
+
+ align:start position:0%
+happen well that can happen because
+electrons unlike most atoms and
+
+ align:start position:0%
+electrons unlike most atoms and
+ 
+
+ align:start position:0%
+electrons unlike most atoms and
+molecules over here electrons are
+
+ align:start position:0%
+molecules over here electrons are
+ 
+
+ align:start position:0%
+molecules over here electrons are
+quantum mechanical particles and they do
+
+ align:start position:0%
+quantum mechanical particles and they do
+ 
+
+ align:start position:0%
+quantum mechanical particles and they do
+not obey classical mechanical rules and
+
+ align:start position:0%
+not obey classical mechanical rules and
+ 
+
+ align:start position:0%
+not obey classical mechanical rules and
+that's a subject that we're going to
+
+ align:start position:0%
+that's a subject that we're going to
+ 
+
+ align:start position:0%
+that's a subject that we're going to
+start talking about today and tomorrow
+
+ align:start position:0%
+start talking about today and tomorrow
+ 
+
+ align:start position:0%
+start talking about today and tomorrow
+and for the next few days so these
+
+ align:start position:0%
+and for the next few days so these
+ 
+
+ align:start position:0%
+and for the next few days so these
+electrons they just Tunnel right through
+
+ align:start position:0%
+electrons they just Tunnel right through
+ 
+
+ align:start position:0%
+electrons they just Tunnel right through
+that barrier and get over here to the
+
+ align:start position:0%
+that barrier and get over here to the
+ 
+
+ align:start position:0%
+that barrier and get over here to the
+other side all right so that means in
+
+ align:start position:0%
+other side all right so that means in
+ 
+
+ align:start position:0%
+other side all right so that means in
+this experimental setup if I were to
+
+ align:start position:0%
+this experimental setup if I were to
+ 
+
+ align:start position:0%
+this experimental setup if I were to
+connect a wire from this tungsten tip
+
+ align:start position:0%
+connect a wire from this tungsten tip
+ 
+
+ align:start position:0%
+connect a wire from this tungsten tip
+here to the platinum and I put in an
+
+ align:start position:0%
+here to the platinum and I put in an
+ 
+
+ align:start position:0%
+here to the platinum and I put in an
+ameter right there so I measure the
+
+ align:start position:0%
+ameter right there so I measure the
+ 
+
+ align:start position:0%
+ameter right there so I measure the
+current hey I'd be seeing some current
+
+ align:start position:0%
+current hey I'd be seeing some current
+ 
+
+ align:start position:0%
+current hey I'd be seeing some current
+flowed some measure of this flow of
+
+ align:start position:0%
+flowed some measure of this flow of
+ 
+
+ align:start position:0%
+flowed some measure of this flow of
+electrons from the tip to the tungsten
+
+ align:start position:0%
+electrons from the tip to the tungsten
+ 
+
+ align:start position:0%
+electrons from the tip to the tungsten
+and so that's what's done in the
+
+ align:start position:0%
+and so that's what's done in the
+ 
+
+ align:start position:0%
+and so that's what's done in the
+technique all right but now how do you
+
+ align:start position:0%
+technique all right but now how do you
+ 
+
+ align:start position:0%
+technique all right but now how do you
+get this image that I showed you earlier
+
+ align:start position:0%
+get this image that I showed you earlier
+ 
+
+ align:start position:0%
+get this image that I showed you earlier
+all right from this kind of
+
+ align:start position:0%
+all right from this kind of
+ 
+
+ align:start position:0%
+all right from this kind of
+arrangement well what you do is you now
+
+ align:start position:0%
+arrangement well what you do is you now
+ 
+
+ align:start position:0%
+arrangement well what you do is you now
+take this tungsten tip and you mount it
+
+ align:start position:0%
+take this tungsten tip and you mount it
+ 
+
+ align:start position:0%
+take this tungsten tip and you mount it
+on a um pazo electric Crystal which I
+
+ align:start position:0%
+on a um pazo electric Crystal which I
+ 
+
+ align:start position:0%
+on a um pazo electric Crystal which I
+forgot to tell you sometimes pazo
+
+ align:start position:0%
+forgot to tell you sometimes pazo
+ 
+
+ align:start position:0%
+forgot to tell you sometimes pazo
+electric crystal quartz is a Paso
+
+ align:start position:0%
+electric crystal quartz is a Paso
+ 
+
+ align:start position:0%
+electric crystal quartz is a Paso
+Electric barium titanate is a Paso
+
+ align:start position:0%
+Electric barium titanate is a Paso
+ 
+
+ align:start position:0%
+Electric barium titanate is a Paso
+Electric but you mount it on a pazal
+
+ align:start position:0%
+Electric but you mount it on a pazal
+ 
+
+ align:start position:0%
+Electric but you mount it on a pazal
+electric Crystal that will allow you to
+
+ align:start position:0%
+electric Crystal that will allow you to
+ 
+
+ align:start position:0%
+electric Crystal that will allow you to
+move from side to side all right so I
+
+ align:start position:0%
+move from side to side all right so I
+ 
+
+ align:start position:0%
+move from side to side all right so I
+move now my tungsten tip over a little
+
+ align:start position:0%
+move now my tungsten tip over a little
+ 
+
+ align:start position:0%
+move now my tungsten tip over a little
+bit all right and I know exactly how
+
+ align:start position:0%
+bit all right and I know exactly how
+ 
+
+ align:start position:0%
+bit all right and I know exactly how
+much over I moved it because I've
+
+ align:start position:0%
+much over I moved it because I've
+ 
+
+ align:start position:0%
+much over I moved it because I've
+calibrated my pazo electric Crystal but
+
+ align:start position:0%
+calibrated my pazo electric Crystal but
+ 
+
+ align:start position:0%
+calibrated my pazo electric Crystal but
+now what do you
+
+ align:start position:0%
+now what do you
+ 
+
+ align:start position:0%
+now what do you
+see well if you just moved it over you
+
+ align:start position:0%
+see well if you just moved it over you
+ 
+
+ align:start position:0%
+see well if you just moved it over you
+didn't change the vertical distance if
+
+ align:start position:0%
+didn't change the vertical distance if
+ 
+
+ align:start position:0%
+didn't change the vertical distance if
+you just moved it over what do you think
+
+ align:start position:0%
+you just moved it over what do you think
+ 
+
+ align:start position:0%
+you just moved it over what do you think
+would happen to the current
+
+ align:start position:0%
+would happen to the current
+ 
+
+ align:start position:0%
+would happen to the current
+here decrease would absolutely decrease
+
+ align:start position:0%
+here decrease would absolutely decrease
+ 
+
+ align:start position:0%
+here decrease would absolutely decrease
+why because you've now right changed the
+
+ align:start position:0%
+why because you've now right changed the
+ 
+
+ align:start position:0%
+why because you've now right changed the
+distance between the oxygen and and and
+
+ align:start position:0%
+distance between the oxygen and and and
+ 
+
+ align:start position:0%
+distance between the oxygen and and and
+that tungsten tip over here on this
+
+ align:start position:0%
+that tungsten tip over here on this
+ 
+
+ align:start position:0%
+that tungsten tip over here on this
+diagram you made this barrier
+
+ align:start position:0%
+diagram you made this barrier
+ 
+
+ align:start position:0%
+diagram you made this barrier
+thicker right and the thicker you make
+
+ align:start position:0%
+thicker right and the thicker you make
+ 
+
+ align:start position:0%
+thicker right and the thicker you make
+it the more difficult it is for those
+
+ align:start position:0%
+it the more difficult it is for those
+ 
+
+ align:start position:0%
+it the more difficult it is for those
+electrons to get through so the
+
+ align:start position:0%
+electrons to get through so the
+ 
+
+ align:start position:0%
+electrons to get through so the
+current's going to go down so in order
+
+ align:start position:0%
+current's going to go down so in order
+ 
+
+ align:start position:0%
+current's going to go down so in order
+to bring the current back up what you're
+
+ align:start position:0%
+to bring the current back up what you're
+ 
+
+ align:start position:0%
+to bring the current back up what you're
+going to do is you're going to take that
+
+ align:start position:0%
+going to do is you're going to take that
+ 
+
+ align:start position:0%
+going to do is you're going to take that
+tungsten tip and you're going to move it
+
+ align:start position:0%
+tungsten tip and you're going to move it
+ 
+
+ align:start position:0%
+tungsten tip and you're going to move it
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+slightly so that the distance now
+
+ align:start position:0%
+slightly so that the distance now
+ 
+
+ align:start position:0%
+slightly so that the distance now
+between the tip and the oxygen is going
+
+ align:start position:0%
+between the tip and the oxygen is going
+ 
+
+ align:start position:0%
+between the tip and the oxygen is going
+to be the same as it was in this
+
+ align:start position:0%
+to be the same as it was in this
+ 
+
+ align:start position:0%
+to be the same as it was in this
+particular position from here to here so
+
+ align:start position:0%
+particular position from here to here so
+ 
+
+ align:start position:0%
+particular position from here to here so
+then you bring the current back up but
+
+ align:start position:0%
+then you bring the current back up but
+ 
+
+ align:start position:0%
+then you bring the current back up but
+again you know exactly how far down you
+
+ align:start position:0%
+again you know exactly how far down you
+ 
+
+ align:start position:0%
+again you know exactly how far down you
+moveed that tip and how far over you
+
+ align:start position:0%
+moveed that tip and how far over you
+ 
+
+ align:start position:0%
+moveed that tip and how far over you
+move that tip
+
+ align:start position:0%
+move that tip
+ 
+
+ align:start position:0%
+move that tip
+right okay so you got now two
+
+ align:start position:0%
+right okay so you got now two
+ 
+
+ align:start position:0%
+right okay so you got now two
+points now we got to keep going so what
+
+ align:start position:0%
+points now we got to keep going so what
+ 
+
+ align:start position:0%
+points now we got to keep going so what
+are we going to do to scan well we're
+
+ align:start position:0%
+are we going to do to scan well we're
+ 
+
+ align:start position:0%
+are we going to do to scan well we're
+going to move this tungsten tip over
+
+ align:start position:0%
+going to move this tungsten tip over
+ 
+
+ align:start position:0%
+going to move this tungsten tip over
+again and again you know the current in
+
+ align:start position:0%
+again and again you know the current in
+ 
+
+ align:start position:0%
+again and again you know the current in
+this particular case is going to go down
+
+ align:start position:0%
+this particular case is going to go down
+ 
+
+ align:start position:0%
+this particular case is going to go down
+in order to bring it back up you're
+
+ align:start position:0%
+in order to bring it back up you're
+ 
+
+ align:start position:0%
+in order to bring it back up you're
+going to move this tip further down so
+
+ align:start position:0%
+going to move this tip further down so
+ 
+
+ align:start position:0%
+going to move this tip further down so
+that the distance between here and here
+
+ align:start position:0%
+that the distance between here and here
+ 
+
+ align:start position:0%
+that the distance between here and here
+is the same as it was originally so you
+
+ align:start position:0%
+is the same as it was originally so you
+ 
+
+ align:start position:0%
+is the same as it was originally so you
+reestablish the current but again then
+
+ align:start position:0%
+reestablish the current but again then
+ 
+
+ align:start position:0%
+reestablish the current but again then
+you know exactly how far down and how
+
+ align:start position:0%
+you know exactly how far down and how
+ 
+
+ align:start position:0%
+you know exactly how far down and how
+far over you move the
+
+ align:start position:0%
+far over you move the
+ 
+
+ align:start position:0%
+far over you move the
+tip and then what you do you assign a
+
+ align:start position:0%
+tip and then what you do you assign a
+ 
+
+ align:start position:0%
+tip and then what you do you assign a
+different color to the different
+
+ align:start position:0%
+different color to the different
+ 
+
+ align:start position:0%
+different color to the different
+distances above the co molecule and if
+
+ align:start position:0%
+distances above the co molecule and if
+ 
+
+ align:start position:0%
+distances above the co molecule and if
+you assign different colors you can get
+
+ align:start position:0%
+you assign different colors you can get
+ 
+
+ align:start position:0%
+you assign different colors you can get
+this image so for example if we can uh
+
+ align:start position:0%
+this image so for example if we can uh
+ 
+
+ align:start position:0%
+this image so for example if we can uh
+dim the lights on the Blackboard again
+
+ align:start position:0%
+dim the lights on the Blackboard again
+ 
+
+ align:start position:0%
+dim the lights on the Blackboard again
+and uh we'll look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+so if the tip is very far from the
+
+ align:start position:0%
+so if the tip is very far from the
+ 
+
+ align:start position:0%
+so if the tip is very far from the
+surface we give it kind of a whitish
+
+ align:start position:0%
+surface we give it kind of a whitish
+ 
+
+ align:start position:0%
+surface we give it kind of a whitish
+color and as it gets closer and closer
+
+ align:start position:0%
+color and as it gets closer and closer
+ 
+
+ align:start position:0%
+color and as it gets closer and closer
+to the surface we give it a darker and
+
+ align:start position:0%
+to the surface we give it a darker and
+ 
+
+ align:start position:0%
+to the surface we give it a darker and
+darker orangey color and then finally
+
+ align:start position:0%
+darker orangey color and then finally
+ 
+
+ align:start position:0%
+darker orangey color and then finally
+when it's so far down that it's actually
+
+ align:start position:0%
+when it's so far down that it's actually
+ 
+
+ align:start position:0%
+when it's so far down that it's actually
+in contact or tunneling to the Platinum
+
+ align:start position:0%
+in contact or tunneling to the Platinum
+ 
+
+ align:start position:0%
+in contact or tunneling to the Platinum
+we give it a blue color all right so
+
+ align:start position:0%
+we give it a blue color all right so
+ 
+
+ align:start position:0%
+we give it a blue color all right so
+that's how you get this image that's the
+
+ align:start position:0%
+that's how you get this image that's the
+ 
+
+ align:start position:0%
+that's how you get this image that's the
+basis of this uh
+
+ align:start position:0%
+basis of this uh
+ 
+
+ align:start position:0%
+basis of this uh
+technique
+
+ align:start position:0%
+technique
+ 
+
+ align:start position:0%
+technique
+okay so now you also notice that these
+
+ align:start position:0%
+okay so now you also notice that these
+ 
+
+ align:start position:0%
+okay so now you also notice that these
+Co molecules have a A peculiar
+
+ align:start position:0%
+Co molecules have a A peculiar
+ 
+
+ align:start position:0%
+Co molecules have a A peculiar
+Arrangement and uh this is not due to in
+
+ align:start position:0%
+Arrangement and uh this is not due to in
+ 
+
+ align:start position:0%
+Arrangement and uh this is not due to in
+the most urant language intelligent
+
+ align:start position:0%
+the most urant language intelligent
+ 
+
+ align:start position:0%
+the most urant language intelligent
+design rather this is due to a very
+
+ align:start position:0%
+design rather this is due to a very
+ 
+
+ align:start position:0%
+design rather this is due to a very
+patient experimentalist I.E graduate
+
+ align:start position:0%
+patient experimentalist I.E graduate
+ 
+
+ align:start position:0%
+patient experimentalist I.E graduate
+student
+
+ align:start position:0%
+student
+ 
+
+ align:start position:0%
+student
+who spent 24 hours putting these Co
+
+ align:start position:0%
+who spent 24 hours putting these Co
+ 
+
+ align:start position:0%
+who spent 24 hours putting these Co
+molecules into this particular position
+
+ align:start position:0%
+molecules into this particular position
+ 
+
+ align:start position:0%
+molecules into this particular position
+so how did he do that well he did it in
+
+ align:start position:0%
+so how did he do that well he did it in
+ 
+
+ align:start position:0%
+so how did he do that well he did it in
+the following way he first uh took a few
+
+ align:start position:0%
+the following way he first uh took a few
+ 
+
+ align:start position:0%
+the following way he first uh took a few
+Co molecules and put them anywhere on
+
+ align:start position:0%
+Co molecules and put them anywhere on
+ 
+
+ align:start position:0%
+Co molecules and put them anywhere on
+the surface just exposed the surface to
+
+ align:start position:0%
+the surface just exposed the surface to
+ 
+
+ align:start position:0%
+the surface just exposed the surface to
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+gas and then he imaged the surface to
+
+ align:start position:0%
+gas and then he imaged the surface to
+ 
+
+ align:start position:0%
+gas and then he imaged the surface to
+figure out where they were and so if the
+
+ align:start position:0%
+figure out where they were and so if the
+ 
+
+ align:start position:0%
+figure out where they were and so if the
+the co molecules or my balls my soccer
+
+ align:start position:0%
+the co molecules or my balls my soccer
+ 
+
+ align:start position:0%
+the co molecules or my balls my soccer
+balls are the co molecules and if my
+
+ align:start position:0%
+balls are the co molecules and if my
+ 
+
+ align:start position:0%
+balls are the co molecules and if my
+foot here is the tungston tip right he
+
+ align:start position:0%
+foot here is the tungston tip right he
+ 
+
+ align:start position:0%
+foot here is the tungston tip right he
+just imaged the surface right to figure
+
+ align:start position:0%
+just imaged the surface right to figure
+ 
+
+ align:start position:0%
+just imaged the surface right to figure
+out where they were so you knew where
+
+ align:start position:0%
+out where they were so you knew where
+ 
+
+ align:start position:0%
+out where they were so you knew where
+they were so then he's got to move these
+
+ align:start position:0%
+they were so then he's got to move these
+ 
+
+ align:start position:0%
+they were so then he's got to move these
+Co molecules so he brings the tip you
+
+ align:start position:0%
+Co molecules so he brings the tip you
+ 
+
+ align:start position:0%
+Co molecules so he brings the tip you
+know close to uh one of the co
+
+ align:start position:0%
+know close to uh one of the co
+ 
+
+ align:start position:0%
+know close to uh one of the co
+molecules and then if you put a voltage
+
+ align:start position:0%
+molecules and then if you put a voltage
+ 
+
+ align:start position:0%
+molecules and then if you put a voltage
+pulse on that Paso Electric and actually
+
+ align:start position:0%
+pulse on that Paso Electric and actually
+ 
+
+ align:start position:0%
+pulse on that Paso Electric and actually
+jerk the tip well you can jerk it such
+
+ align:start position:0%
+jerk the tip well you can jerk it such
+ 
+
+ align:start position:0%
+jerk the tip well you can jerk it such
+that you hit the co molecule and it goes
+
+ align:start position:0%
+that you hit the co molecule and it goes
+ 
+
+ align:start position:0%
+that you hit the co molecule and it goes
+flying away that's nice but now where
+
+ align:start position:0%
+flying away that's nice but now where
+ 
+
+ align:start position:0%
+flying away that's nice but now where
+did it go well in order to find out you
+
+ align:start position:0%
+did it go well in order to find out you
+ 
+
+ align:start position:0%
+did it go well in order to find out you
+got to do image the whole surface again
+
+ align:start position:0%
+got to do image the whole surface again
+ 
+
+ align:start position:0%
+got to do image the whole surface again
+right and you find that it is somewhere
+
+ align:start position:0%
+right and you find that it is somewhere
+ 
+
+ align:start position:0%
+right and you find that it is somewhere
+all the way over here all right now you
+
+ align:start position:0%
+all the way over here all right now you
+ 
+
+ align:start position:0%
+all the way over here all right now you
+really want it over there so you repeat
+
+ align:start position:0%
+really want it over there so you repeat
+ 
+
+ align:start position:0%
+really want it over there so you repeat
+the operation and uh well 24 hours later
+
+ align:start position:0%
+the operation and uh well 24 hours later
+ 
+
+ align:start position:0%
+the operation and uh well 24 hours later
+you get this little
+
+ align:start position:0%
+you get this little
+ 
+
+ align:start position:0%
+you get this little
+man and I know it was 24 hours later all
+
+ align:start position:0%
+man and I know it was 24 hours later all
+ 
+
+ align:start position:0%
+man and I know it was 24 hours later all
+right so um it's going to be a while
+
+ align:start position:0%
+right so um it's going to be a while
+ 
+
+ align:start position:0%
+right so um it's going to be a while
+before this kind of uh nanot technology
+
+ align:start position:0%
+before this kind of uh nanot technology
+ 
+
+ align:start position:0%
+before this kind of uh nanot technology
+assembling a molecule by molecule uh
+
+ align:start position:0%
+assembling a molecule by molecule uh
+ 
+
+ align:start position:0%
+assembling a molecule by molecule uh
+beats the synthesis in a beaker to put
+
+ align:start position:0%
+beats the synthesis in a beaker to put
+ 
+
+ align:start position:0%
+beats the synthesis in a beaker to put
+the molecules where you want them all
+
+ align:start position:0%
+the molecules where you want them all
+ 
+
+ align:start position:0%
+the molecules where you want them all
+right but
+
+ align:start position:0%
+right but
+ 
+
+ align:start position:0%
+right but
+um even though this uh kind of visual
+
+ align:start position:0%
+um even though this uh kind of visual
+ 
+
+ align:start position:0%
+um even though this uh kind of visual
+observation of atoms and molecules uh
+
+ align:start position:0%
+observation of atoms and molecules uh
+ 
+
+ align:start position:0%
+observation of atoms and molecules uh
+really wasn't possible
+
+ align:start position:0%
+really wasn't possible
+ 
+
+ align:start position:0%
+really wasn't possible
+100 years ago the evidence that I
+
+ align:start position:0%
+100 years ago the evidence that I
+ 
+
+ align:start position:0%
+100 years ago the evidence that I
+alluded to or quickly went through
+
+ align:start position:0%
+alluded to or quickly went through
+ 
+
+ align:start position:0%
+alluded to or quickly went through
+earlier was really quite uh compelling
+
+ align:start position:0%
+earlier was really quite uh compelling
+ 
+
+ align:start position:0%
+earlier was really quite uh compelling
+for the existence of atoms and the
+
+ align:start position:0%
+for the existence of atoms and the
+ 
+
+ align:start position:0%
+for the existence of atoms and the
+observation or the belief that the atom
+
+ align:start position:0%
+observation or the belief that the atom
+ 
+
+ align:start position:0%
+observation or the belief that the atom
+was the most basic constituent of matter
+
+ align:start position:0%
+was the most basic constituent of matter
+ 
+
+ align:start position:0%
+was the most basic constituent of matter
+the elementary particle you couldn't
+
+ align:start position:0%
+the elementary particle you couldn't
+ 
+
+ align:start position:0%
+the elementary particle you couldn't
+have anything smaller uh than an atam
+
+ align:start position:0%
+have anything smaller uh than an atam
+ 
+
+ align:start position:0%
+have anything smaller uh than an atam
+and in fact at the end of the last
+
+ align:start position:0%
+and in fact at the end of the last
+ 
+
+ align:start position:0%
+and in fact at the end of the last
+century it was generally believed that
+
+ align:start position:0%
+century it was generally believed that
+ 
+
+ align:start position:0%
+century it was generally believed that
+the theoretical structure of the
+
+ align:start position:0%
+the theoretical structure of the
+ 
+
+ align:start position:0%
+the theoretical structure of the
+universe was complete nature was
+
+ align:start position:0%
+universe was complete nature was
+ 
+
+ align:start position:0%
+universe was complete nature was
+understood there were no more
+
+ align:start position:0%
+understood there were no more
+ 
+
+ align:start position:0%
+understood there were no more
+discoveries to be made and after all you
+
+ align:start position:0%
+discoveries to be made and after all you
+ 
+
+ align:start position:0%
+discoveries to be made and after all you
+know there were by this time in the late
+
+ align:start position:0%
+know there were by this time in the late
+ 
+
+ align:start position:0%
+know there were by this time in the late
+1800s a lot of advances well Newtonian
+
+ align:start position:0%
+1800s a lot of advances well Newtonian
+ 
+
+ align:start position:0%
+1800s a lot of advances well Newtonian
+mechanics that had already been known
+
+ align:start position:0%
+mechanics that had already been known
+ 
+
+ align:start position:0%
+mechanics that had already been known
+for 250 years the mechanics that guides
+
+ align:start position:0%
+for 250 years the mechanics that guides
+ 
+
+ align:start position:0%
+for 250 years the mechanics that guides
+the motion of all bodies around us even
+
+ align:start position:0%
+the motion of all bodies around us even
+ 
+
+ align:start position:0%
+the motion of all bodies around us even
+astronomical bodies thermodynamics was
+
+ align:start position:0%
+astronomical bodies thermodynamics was
+ 
+
+ align:start position:0%
+astronomical bodies thermodynamics was
+completely developed statistical
+
+ align:start position:0%
+completely developed statistical
+ 
+
+ align:start position:0%
+completely developed statistical
+mechanics was developed statistical
+
+ align:start position:0%
+mechanics was developed statistical
+ 
+
+ align:start position:0%
+mechanics was developed statistical
+mechanics which relates the microscopic
+
+ align:start position:0%
+mechanics which relates the microscopic
+ 
+
+ align:start position:0%
+mechanics which relates the microscopic
+description of the behavior of matter to
+
+ align:start position:0%
+description of the behavior of matter to
+ 
+
+ align:start position:0%
+description of the behavior of matter to
+the macroscopic description of the
+
+ align:start position:0%
+the macroscopic description of the
+ 
+
+ align:start position:0%
+the macroscopic description of the
+behavior of matter and also there were
+
+ align:start position:0%
+behavior of matter and also there were
+ 
+
+ align:start position:0%
+behavior of matter and also there were
+these Optics experiments of young
+
+ align:start position:0%
+these Optics experiments of young
+ 
+
+ align:start position:0%
+these Optics experiments of young
+fresnell and Herz that seemed to put to
+
+ align:start position:0%
+fresnell and Herz that seemed to put to
+ 
+
+ align:start position:0%
+fresnell and Herz that seemed to put to
+rest the question of whether or not
+
+ align:start position:0%
+rest the question of whether or not
+ 
+
+ align:start position:0%
+rest the question of whether or not
+light was a particle or a wave boy those
+
+ align:start position:0%
+light was a particle or a wave boy those
+ 
+
+ align:start position:0%
+light was a particle or a wave boy those
+experiments seemed to be absolutely
+
+ align:start position:0%
+experiments seemed to be absolutely
+ 
+
+ align:start position:0%
+experiments seemed to be absolutely
+conclusive that light was a wave those
+
+ align:start position:0%
+conclusive that light was a wave those
+ 
+
+ align:start position:0%
+conclusive that light was a wave those
+experiments demonstrated Maxwell's
+
+ align:start position:0%
+experiments demonstrated Maxwell's
+ 
+
+ align:start position:0%
+experiments demonstrated Maxwell's
+equations Maxwell's equations that
+
+ align:start position:0%
+equations Maxwell's equations that
+ 
+
+ align:start position:0%
+equations Maxwell's equations that
+unified the field of uh Optics and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electromagnetism so um you know by this
+
+ align:start position:0%
+electromagnetism so um you know by this
+ 
+
+ align:start position:0%
+electromagnetism so um you know by this
+time uh there was all of these
+
+ align:start position:0%
+time uh there was all of these
+ 
+
+ align:start position:0%
+time uh there was all of these
+accomplishments the idea was that uh
+
+ align:start position:0%
+accomplishments the idea was that uh
+ 
+
+ align:start position:0%
+accomplishments the idea was that uh
+everything was done and the idea was
+
+ align:start position:0%
+everything was done and the idea was
+ 
+
+ align:start position:0%
+everything was done and the idea was
+remaining that the work that remained
+
+ align:start position:0%
+remaining that the work that remained
+ 
+
+ align:start position:0%
+remaining that the work that remained
+was largely to investigate the next
+
+ align:start position:0%
+was largely to investigate the next
+ 
+
+ align:start position:0%
+was largely to investigate the next
+decimal place everything else was
+
+ align:start position:0%
+decimal place everything else was
+ 
+
+ align:start position:0%
+decimal place everything else was
+done however at the same time by the
+
+ align:start position:0%
+done however at the same time by the
+ 
+
+ align:start position:0%
+done however at the same time by the
+late
+
+ align:start position:0%
+late
+ 
+
+ align:start position:0%
+late
+1800s there began to be a two sets of
+
+ align:start position:0%
+1800s there began to be a two sets of
+ 
+
+ align:start position:0%
+1800s there began to be a two sets of
+observations two tracks of
+
+ align:start position:0%
+observations two tracks of
+ 
+
+ align:start position:0%
+observations two tracks of
+observations that if you look closely
+
+ align:start position:0%
+observations that if you look closely
+ 
+
+ align:start position:0%
+observations that if you look closely
+began to illustrate that maybe things
+
+ align:start position:0%
+began to illustrate that maybe things
+ 
+
+ align:start position:0%
+began to illustrate that maybe things
+weren't quite so uh clear maybe things
+
+ align:start position:0%
+weren't quite so uh clear maybe things
+ 
+
+ align:start position:0%
+weren't quite so uh clear maybe things
+weren't quite as well understood and
+
+ align:start position:0%
+weren't quite as well understood and
+ 
+
+ align:start position:0%
+weren't quite as well understood and
+what were those
+
+ align:start position:0%
+what were those
+ 
+
+ align:start position:0%
+what were those
+observations well one of those
+
+ align:start position:0%
+observations well one of those
+ 
+
+ align:start position:0%
+observations well one of those
+observations is the discovery that we're
+
+ align:start position:0%
+observations is the discovery that we're
+ 
+
+ align:start position:0%
+observations is the discovery that we're
+going to start looking at today that the
+
+ align:start position:0%
+going to start looking at today that the
+ 
+
+ align:start position:0%
+going to start looking at today that the
+atom is not the most basic constituent
+
+ align:start position:0%
+atom is not the most basic constituent
+ 
+
+ align:start position:0%
+atom is not the most basic constituent
+of matter that you can take an atom
+
+ align:start position:0%
+of matter that you can take an atom
+ 
+
+ align:start position:0%
+of matter that you can take an atom
+apart into an electron and a nucleus at
+
+ align:start position:0%
+apart into an electron and a nucleus at
+ 
+
+ align:start position:0%
+apart into an electron and a nucleus at
+least an electron and a nucleus so
+
+ align:start position:0%
+least an electron and a nucleus so
+ 
+
+ align:start position:0%
+least an electron and a nucleus so
+that's one track track the other track
+
+ align:start position:0%
+that's one track track the other track
+ 
+
+ align:start position:0%
+that's one track track the other track
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+light appeared to behave in some cases
+
+ align:start position:0%
+light appeared to behave in some cases
+ 
+
+ align:start position:0%
+light appeared to behave in some cases
+like a particle and not a wave and one
+
+ align:start position:0%
+like a particle and not a wave and one
+ 
+
+ align:start position:0%
+like a particle and not a wave and one
+of those cases is this observation here
+
+ align:start position:0%
+of those cases is this observation here
+ 
+
+ align:start position:0%
+of those cases is this observation here
+of the photoelectric effect so what
+
+ align:start position:0%
+of the photoelectric effect so what
+ 
+
+ align:start position:0%
+of the photoelectric effect so what
+we're going to do is we're going to look
+
+ align:start position:0%
+we're going to do is we're going to look
+ 
+
+ align:start position:0%
+we're going to do is we're going to look
+at both tracks of observations here and
+
+ align:start position:0%
+at both tracks of observations here and
+ 
+
+ align:start position:0%
+at both tracks of observations here and
+we're going to see how these
+
+ align:start position:0%
+we're going to see how these
+ 
+
+ align:start position:0%
+we're going to see how these
+observations made it such that it was
+
+ align:start position:0%
+observations made it such that it was
+ 
+
+ align:start position:0%
+observations made it such that it was
+impossible to explain how an atom held
+
+ align:start position:0%
+impossible to explain how an atom held
+ 
+
+ align:start position:0%
+impossible to explain how an atom held
+together how an electron and a nucleus
+
+ align:start position:0%
+together how an electron and a nucleus
+ 
+
+ align:start position:0%
+together how an electron and a nucleus
+held together within the classical way
+
+ align:start position:0%
+held together within the classical way
+ 
+
+ align:start position:0%
+held together within the classical way
+of thinking within the newtonium
+
+ align:start position:0%
+of thinking within the newtonium
+ 
+
+ align:start position:0%
+of thinking within the newtonium
+mechanics the mechanics that you're
+
+ align:start position:0%
+mechanics the mechanics that you're
+ 
+
+ align:start position:0%
+mechanics the mechanics that you're
+going to be looking at this semester in
+
+ align:start position:0%
+going to be looking at this semester in
+ 
+
+ align:start position:0%
+going to be looking at this semester in
+801 you can't use that mechanics to
+
+ align:start position:0%
+801 you can't use that mechanics to
+ 
+
+ align:start position:0%
+801 you can't use that mechanics to
+understand how this electron in the
+
+ align:start position:0%
+understand how this electron in the
+ 
+
+ align:start position:0%
+understand how this electron in the
+nucleus stay together you can't use that
+
+ align:start position:0%
+nucleus stay together you can't use that
+ 
+
+ align:start position:0%
+nucleus stay together you can't use that
+mechanics to understand how two atoms
+
+ align:start position:0%
+mechanics to understand how two atoms
+ 
+
+ align:start position:0%
+mechanics to understand how two atoms
+are bound together we need a new way of
+
+ align:start position:0%
+are bound together we need a new way of
+ 
+
+ align:start position:0%
+are bound together we need a new way of
+thinking and it's these two tracks of
+
+ align:start position:0%
+thinking and it's these two tracks of
+ 
+
+ align:start position:0%
+thinking and it's these two tracks of
+observations that led to the Discovery
+
+ align:start position:0%
+observations that led to the Discovery
+ 
+
+ align:start position:0%
+observations that led to the Discovery
+in a sense of this new kind of mechanics
+
+ align:start position:0%
+in a sense of this new kind of mechanics
+ 
+
+ align:start position:0%
+in a sense of this new kind of mechanics
+that we're going to be talking
+
+ align:start position:0%
+that we're going to be talking
+ 
+
+ align:start position:0%
+that we're going to be talking
+about okay so let's start on one of
+
+ align:start position:0%
+about okay so let's start on one of
+ 
+
+ align:start position:0%
+about okay so let's start on one of
+these tracks and that track is
+
+ align:start position:0%
+these tracks and that track is
+ 
+
+ align:start position:0%
+these tracks and that track is
+the a track of seeing that the atom is
+
+ align:start position:0%
+the a track of seeing that the atom is
+ 
+
+ align:start position:0%
+the a track of seeing that the atom is
+not the most basic constituent of
+
+ align:start position:0%
+not the most basic constituent of
+ 
+
+ align:start position:0%
+not the most basic constituent of
+matter and uh the first observation is
+
+ align:start position:0%
+matter and uh the first observation is
+ 
+
+ align:start position:0%
+matter and uh the first observation is
+done done by this gentleman JJ Thomas
+
+ align:start position:0%
+done done by this gentleman JJ Thomas
+ 
+
+ align:start position:0%
+done done by this gentleman JJ Thomas
+it's the discovery of the
+
+ align:start position:0%
+it's the discovery of the
+ 
+
+ align:start position:0%
+it's the discovery of the
+electron okay so uh I'm going to need
+
+ align:start position:0%
+electron okay so uh I'm going to need
+ 
+
+ align:start position:0%
+electron okay so uh I'm going to need
+the lights on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again all right so what JJ Thomas was
+
+ align:start position:0%
+again all right so what JJ Thomas was
+ 
+
+ align:start position:0%
+again all right so what JJ Thomas was
+interested in doing was understanding
+
+ align:start position:0%
+interested in doing was understanding
+ 
+
+ align:start position:0%
+interested in doing was understanding
+what discharges were made up right so he
+
+ align:start position:0%
+what discharges were made up right so he
+ 
+
+ align:start position:0%
+what discharges were made up right so he
+had a a glass tube that was evacuated
+
+ align:start position:0%
+had a a glass tube that was evacuated
+ 
+
+ align:start position:0%
+had a a glass tube that was evacuated
+and in it he had what we're going to
+
+ align:start position:0%
+and in it he had what we're going to
+ 
+
+ align:start position:0%
+and in it he had what we're going to
+call here a
+
+ align:start position:0%
+call here a
+ 
+
+ align:start position:0%
+call here a
+cathode and he had an
+
+ align:start position:0%
+cathode and he had an
+ 
+
+ align:start position:0%
+cathode and he had an
+anode and uh as I said a glass tube he
+
+ align:start position:0%
+anode and uh as I said a glass tube he
+ 
+
+ align:start position:0%
+anode and uh as I said a glass tube he
+pumps out the air and then he fills it
+
+ align:start position:0%
+pumps out the air and then he fills it
+ 
+
+ align:start position:0%
+pumps out the air and then he fills it
+up with uh hydrogen
+
+ align:start position:0%
+up with uh hydrogen
+ 
+
+ align:start position:0%
+up with uh hydrogen
+H2 and what he does is he puts a large
+
+ align:start position:0%
+H2 and what he does is he puts a large
+ 
+
+ align:start position:0%
+H2 and what he does is he puts a large
+negative potential on this cathod and on
+
+ align:start position:0%
+negative potential on this cathod and on
+ 
+
+ align:start position:0%
+negative potential on this cathod and on
+the anode he puts a large positive
+
+ align:start position:0%
+the anode he puts a large positive
+ 
+
+ align:start position:0%
+the anode he puts a large positive
+potential and he cranks up the potential
+
+ align:start position:0%
+potential and he cranks up the potential
+ 
+
+ align:start position:0%
+potential and he cranks up the potential
+difference here and he keeps cranking it
+
+ align:start position:0%
+difference here and he keeps cranking it
+ 
+
+ align:start position:0%
+difference here and he keeps cranking it
+up until at some point the gas begins to
+
+ align:start position:0%
+up until at some point the gas begins to
+ 
+
+ align:start position:0%
+up until at some point the gas begins to
+glow and it's at that point that this
+
+ align:start position:0%
+glow and it's at that point that this
+ 
+
+ align:start position:0%
+glow and it's at that point that this
+discharge here is
+
+ align:start position:0%
+discharge here is
+ 
+
+ align:start position:0%
+discharge here is
+ignited and uh this kind of a plasma and
+
+ align:start position:0%
+ignited and uh this kind of a plasma and
+ 
+
+ align:start position:0%
+ignited and uh this kind of a plasma and
+he wanted to understand what's in this
+
+ align:start position:0%
+he wanted to understand what's in this
+ 
+
+ align:start position:0%
+he wanted to understand what's in this
+plasma he's just curious he wants to
+
+ align:start position:0%
+plasma he's just curious he wants to
+ 
+
+ align:start position:0%
+plasma he's just curious he wants to
+know and so what he does is that he
+
+ align:start position:0%
+know and so what he does is that he
+ 
+
+ align:start position:0%
+know and so what he does is that he
+pokes a hole here in this anode right
+
+ align:start position:0%
+pokes a hole here in this anode right
+ 
+
+ align:start position:0%
+pokes a hole here in this anode right
+there's a hole and he lets out a little
+
+ align:start position:0%
+there's a hole and he lets out a little
+ 
+
+ align:start position:0%
+there's a hole and he lets out a little
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+discharge and uh he lets it out and my
+
+ align:start position:0%
+discharge and uh he lets it out and my
+ 
+
+ align:start position:0%
+discharge and uh he lets it out and my
+chalk is breaking and he lets it out and
+
+ align:start position:0%
+chalk is breaking and he lets it out and
+ 
+
+ align:start position:0%
+chalk is breaking and he lets it out and
+way back here he has some kind of a uh a
+
+ align:start position:0%
+way back here he has some kind of a uh a
+ 
+
+ align:start position:0%
+way back here he has some kind of a uh a
+screen a phosphor screen so that not
+
+ align:start position:0%
+screen a phosphor screen so that not
+ 
+
+ align:start position:0%
+screen a phosphor screen so that not
+only does this uh discharge here uh kind
+
+ align:start position:0%
+only does this uh discharge here uh kind
+ 
+
+ align:start position:0%
+only does this uh discharge here uh kind
+of glow as it's moving along but when it
+
+ align:start position:0%
+of glow as it's moving along but when it
+ 
+
+ align:start position:0%
+of glow as it's moving along but when it
+hits the phosphor screen it lights up
+
+ align:start position:0%
+hits the phosphor screen it lights up
+ 
+
+ align:start position:0%
+hits the phosphor screen it lights up
+okay and so that that's nice but then
+
+ align:start position:0%
+okay and so that that's nice but then
+ 
+
+ align:start position:0%
+okay and so that that's nice but then
+what he does is he takes two parallel
+
+ align:start position:0%
+what he does is he takes two parallel
+ 
+
+ align:start position:0%
+what he does is he takes two parallel
+plates and he puts it above and below
+
+ align:start position:0%
+plates and he puts it above and below
+ 
+
+ align:start position:0%
+plates and he puts it above and below
+this luminous beam and there's a
+
+ align:start position:0%
+this luminous beam and there's a
+ 
+
+ align:start position:0%
+this luminous beam and there's a
+positive charge on one of these and a
+
+ align:start position:0%
+positive charge on one of these and a
+ 
+
+ align:start position:0%
+positive charge on one of these and a
+negative charge on the other and Lan
+
+ align:start position:0%
+negative charge on the other and Lan
+ 
+
+ align:start position:0%
+negative charge on the other and Lan
+behold when he increases this potential
+
+ align:start position:0%
+behold when he increases this potential
+ 
+
+ align:start position:0%
+behold when he increases this potential
+difference this Delta V what happens is
+
+ align:start position:0%
+difference this Delta V what happens is
+ 
+
+ align:start position:0%
+difference this Delta V what happens is
+that this luminous beam some of that
+
+ align:start position:0%
+that this luminous beam some of that
+ 
+
+ align:start position:0%
+that this luminous beam some of that
+luminous beam is actually deflected a
+
+ align:start position:0%
+luminous beam is actually deflected a
+ 
+
+ align:start position:0%
+luminous beam is actually deflected a
+little bit and so now there's another
+
+ align:start position:0%
+little bit and so now there's another
+ 
+
+ align:start position:0%
+little bit and so now there's another
+very bright
+
+ align:start position:0%
+very bright
+ 
+
+ align:start position:0%
+very bright
+spot and he can measure this uh
+
+ align:start position:0%
+spot and he can measure this uh
+ 
+
+ align:start position:0%
+spot and he can measure this uh
+deflection and we're going to call it
+
+ align:start position:0%
+deflection and we're going to call it
+ 
+
+ align:start position:0%
+deflection and we're going to call it
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X now since some of this luminous beam
+
+ align:start position:0%
+X now since some of this luminous beam
+ 
+
+ align:start position:0%
+X now since some of this luminous beam
+was deflected toward positively charged
+
+ align:start position:0%
+was deflected toward positively charged
+ 
+
+ align:start position:0%
+was deflected toward positively charged
+plate what kind of particles did he
+
+ align:start position:0%
+plate what kind of particles did he
+ 
+
+ align:start position:0%
+plate what kind of particles did he
+decide were in this luminous
+
+ align:start position:0%
+decide were in this luminous
+ 
+
+ align:start position:0%
+decide were in this luminous
+beam negatives particles because they're
+
+ align:start position:0%
+beam negatives particles because they're
+ 
+
+ align:start position:0%
+beam negatives particles because they're
+attracted to the positively charged
+
+ align:start position:0%
+attracted to the positively charged
+ 
+
+ align:start position:0%
+attracted to the positively charged
+plate so we called this deflection Delta
+
+ align:start position:0%
+plate so we called this deflection Delta
+ 
+
+ align:start position:0%
+plate so we called this deflection Delta
+X we'll call it Delta x sub
+
+ align:start position:0%
+X we'll call it Delta x sub
+ 
+
+ align:start position:0%
+X we'll call it Delta x sub
+minus now he knew enough
+
+ align:start position:0%
+minus now he knew enough
+ 
+
+ align:start position:0%
+minus now he knew enough
+electromagnetism at that
+
+ align:start position:0%
+electromagnetism at that
+ 
+
+ align:start position:0%
+electromagnetism at that
+time to realize that the amount of that
+
+ align:start position:0%
+time to realize that the amount of that
+ 
+
+ align:start position:0%
+time to realize that the amount of that
+deflection has to be directly
+
+ align:start position:0%
+deflection has to be directly
+ 
+
+ align:start position:0%
+deflection has to be directly
+proportional to how much charge was on
+
+ align:start position:0%
+proportional to how much charge was on
+ 
+
+ align:start position:0%
+proportional to how much charge was on
+the negatively charged particle and I'm
+
+ align:start position:0%
+the negatively charged particle and I'm
+ 
+
+ align:start position:0%
+the negatively charged particle and I'm
+going to call that e sub minus because
+
+ align:start position:0%
+going to call that e sub minus because
+ 
+
+ align:start position:0%
+going to call that e sub minus because
+the more charge the easier it would be
+
+ align:start position:0%
+the more charge the easier it would be
+ 
+
+ align:start position:0%
+the more charge the easier it would be
+to deflect
+
+ align:start position:0%
+to deflect
+ 
+
+ align:start position:0%
+to deflect
+it and he recognized that the amount of
+
+ align:start position:0%
+it and he recognized that the amount of
+ 
+
+ align:start position:0%
+it and he recognized that the amount of
+deflection has to be inversely
+
+ align:start position:0%
+deflection has to be inversely
+ 
+
+ align:start position:0%
+deflection has to be inversely
+proportional to the mass of that
+
+ align:start position:0%
+proportional to the mass of that
+ 
+
+ align:start position:0%
+proportional to the mass of that
+negatively charged particle because
+
+ align:start position:0%
+negatively charged particle because
+ 
+
+ align:start position:0%
+negatively charged particle because
+after all the more massive that was the
+
+ align:start position:0%
+after all the more massive that was the
+ 
+
+ align:start position:0%
+after all the more massive that was the
+more difficult it was going to be to
+
+ align:start position:0%
+more difficult it was going to be to
+ 
+
+ align:start position:0%
+more difficult it was going to be to
+deflect it
+
+ align:start position:0%
+deflect it
+ 
+
+ align:start position:0%
+deflect it
+right and then what he did is he cranked
+
+ align:start position:0%
+right and then what he did is he cranked
+ 
+
+ align:start position:0%
+right and then what he did is he cranked
+up Delta v as much as he could and here
+
+ align:start position:0%
+up Delta v as much as he could and here
+ 
+
+ align:start position:0%
+up Delta v as much as he could and here
+I'm taking a little liberty with the
+
+ align:start position:0%
+I'm taking a little liberty with the
+ 
+
+ align:start position:0%
+I'm taking a little liberty with the
+story but I'm telling you essentially
+
+ align:start position:0%
+story but I'm telling you essentially
+ 
+
+ align:start position:0%
+story but I'm telling you essentially
+the essence of the experiment but it's a
+
+ align:start position:0%
+the essence of the experiment but it's a
+ 
+
+ align:start position:0%
+the essence of the experiment but it's a
+little more complicated than what it is
+
+ align:start position:0%
+little more complicated than what it is
+ 
+
+ align:start position:0%
+little more complicated than what it is
+I'm going to tell you right here but he
+
+ align:start position:0%
+I'm going to tell you right here but he
+ 
+
+ align:start position:0%
+I'm going to tell you right here but he
+cranked that
+
+ align:start position:0%
+cranked that
+ 
+
+ align:start position:0%
+cranked that
+up and when he did he realized that
+
+ align:start position:0%
+up and when he did he realized that
+ 
+
+ align:start position:0%
+up and when he did he realized that
+there actually was some other particles
+
+ align:start position:0%
+there actually was some other particles
+ 
+
+ align:start position:0%
+there actually was some other particles
+that were being deflected toward the
+
+ align:start position:0%
+that were being deflected toward the
+ 
+
+ align:start position:0%
+that were being deflected toward the
+negatively charged plate just a little
+
+ align:start position:0%
+negatively charged plate just a little
+ 
+
+ align:start position:0%
+negatively charged plate just a little
+bit all right not a lot just a little
+
+ align:start position:0%
+bit all right not a lot just a little
+ 
+
+ align:start position:0%
+bit all right not a lot just a little
+bit and again he could measure that
+
+ align:start position:0%
+bit and again he could measure that
+ 
+
+ align:start position:0%
+bit and again he could measure that
+deflection and he called that or we're
+
+ align:start position:0%
+deflection and he called that or we're
+ 
+
+ align:start position:0%
+deflection and he called that or we're
+going to call that Delta x sub plus all
+
+ align:start position:0%
+going to call that Delta x sub plus all
+ 
+
+ align:start position:0%
+going to call that Delta x sub plus all
+right these got to be positively charged
+
+ align:start position:0%
+right these got to be positively charged
+ 
+
+ align:start position:0%
+right these got to be positively charged
+particles because they're attracted to
+
+ align:start position:0%
+particles because they're attracted to
+ 
+
+ align:start position:0%
+particles because they're attracted to
+the negatively charged plate and again
+
+ align:start position:0%
+the negatively charged plate and again
+ 
+
+ align:start position:0%
+the negatively charged plate and again
+he realized that Delta x sub plus is
+
+ align:start position:0%
+he realized that Delta x sub plus is
+ 
+
+ align:start position:0%
+he realized that Delta x sub plus is
+proportional to the charge on that
+
+ align:start position:0%
+proportional to the charge on that
+ 
+
+ align:start position:0%
+proportional to the charge on that
+positively charged particle and
+
+ align:start position:0%
+positively charged particle and
+ 
+
+ align:start position:0%
+positively charged particle and
+inversely proportional to the mass of
+
+ align:start position:0%
+inversely proportional to the mass of
+ 
+
+ align:start position:0%
+inversely proportional to the mass of
+that positively charged
+
+ align:start position:0%
+that positively charged
+ 
+
+ align:start position:0%
+that positively charged
+particle all right but now here comes
+
+ align:start position:0%
+particle all right but now here comes
+ 
+
+ align:start position:0%
+particle all right but now here comes
+his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thinking what he
+
+ align:start position:0%
+thinking what he
+ 
+
+ align:start position:0%
+thinking what he
+guessed is that these positively charged
+
+ align:start position:0%
+guessed is that these positively charged
+ 
+
+ align:start position:0%
+guessed is that these positively charged
+particles he guessed that they were
+
+ align:start position:0%
+particles he guessed that they were
+ 
+
+ align:start position:0%
+particles he guessed that they were
+H+ a hydrogen ion how did he know that
+
+ align:start position:0%
+H+ a hydrogen ion how did he know that
+ 
+
+ align:start position:0%
+H+ a hydrogen ion how did he know that
+well this is a guess
+
+ align:start position:0%
+well this is a guess
+ 
+
+ align:start position:0%
+well this is a guess
+however he did know that in this plasma
+
+ align:start position:0%
+however he did know that in this plasma
+ 
+
+ align:start position:0%
+however he did know that in this plasma
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+discharge that there were hydrogen atoms
+
+ align:start position:0%
+discharge that there were hydrogen atoms
+ 
+
+ align:start position:0%
+discharge that there were hydrogen atoms
+and how he knew that is something we're
+
+ align:start position:0%
+and how he knew that is something we're
+ 
+
+ align:start position:0%
+and how he knew that is something we're
+going to talk about in a few days but he
+
+ align:start position:0%
+going to talk about in a few days but he
+ 
+
+ align:start position:0%
+going to talk about in a few days but he
+knew that he also knew h plus h here
+
+ align:start position:0%
+knew that he also knew h plus h here
+ 
+
+ align:start position:0%
+knew that he also knew h plus h here
+these hydrogen atoms that are produced
+
+ align:start position:0%
+these hydrogen atoms that are produced
+ 
+
+ align:start position:0%
+these hydrogen atoms that are produced
+in the plasma somehow the plasma breaks
+
+ align:start position:0%
+in the plasma somehow the plasma breaks
+ 
+
+ align:start position:0%
+in the plasma somehow the plasma breaks
+the H2 Bond these hydrogen atoms were
+
+ align:start position:0%
+the H2 Bond these hydrogen atoms were
+ 
+
+ align:start position:0%
+the H2 Bond these hydrogen atoms were
+neutral okay and so he said well if it's
+
+ align:start position:0%
+neutral okay and so he said well if it's
+ 
+
+ align:start position:0%
+neutral okay and so he said well if it's
+a positively charged Char particle well
+
+ align:start position:0%
+a positively charged Char particle well
+ 
+
+ align:start position:0%
+a positively charged Char particle well
+gee you know it must be that something
+
+ align:start position:0%
+gee you know it must be that something
+ 
+
+ align:start position:0%
+gee you know it must be that something
+was removed from the hydrogen atom to
+
+ align:start position:0%
+was removed from the hydrogen atom to
+ 
+
+ align:start position:0%
+was removed from the hydrogen atom to
+make it positively charged and that
+
+ align:start position:0%
+make it positively charged and that
+ 
+
+ align:start position:0%
+make it positively charged and that
+something must be this negatively
+
+ align:start position:0%
+something must be this negatively
+ 
+
+ align:start position:0%
+something must be this negatively
+charged particle that I'm
+
+ align:start position:0%
+charged particle that I'm
+ 
+
+ align:start position:0%
+charged particle that I'm
+observing okay because I know that
+
+ align:start position:0%
+observing okay because I know that
+ 
+
+ align:start position:0%
+observing okay because I know that
+originally right the hydrogen atom has
+
+ align:start position:0%
+originally right the hydrogen atom has
+ 
+
+ align:start position:0%
+originally right the hydrogen atom has
+to be neutral so therefore I'm going to
+
+ align:start position:0%
+to be neutral so therefore I'm going to
+ 
+
+ align:start position:0%
+to be neutral so therefore I'm going to
+guess that the
+
+ align:start position:0%
+guess that the
+ 
+
+ align:start position:0%
+guess that the
+magnitude of the charge on the
+
+ align:start position:0%
+magnitude of the charge on the
+ 
+
+ align:start position:0%
+magnitude of the charge on the
+negatively charged particle is equal to
+
+ align:start position:0%
+negatively charged particle is equal to
+ 
+
+ align:start position:0%
+negatively charged particle is equal to
+the magnitude of the charge on that
+
+ align:start position:0%
+the magnitude of the charge on that
+ 
+
+ align:start position:0%
+the magnitude of the charge on that
+positively charged
+
+ align:start position:0%
+positively charged
+ 
+
+ align:start position:0%
+positively charged
+particle and if it's that's the case
+
+ align:start position:0%
+particle and if it's that's the case
+ 
+
+ align:start position:0%
+particle and if it's that's the case
+then I can take a ratio here of the
+
+ align:start position:0%
+then I can take a ratio here of the
+ 
+
+ align:start position:0%
+then I can take a ratio here of the
+deflection of the negatively charged
+
+ align:start position:0%
+deflection of the negatively charged
+ 
+
+ align:start position:0%
+deflection of the negatively charged
+particle to the deflection on the
+
+ align:start position:0%
+particle to the deflection on the
+ 
+
+ align:start position:0%
+particle to the deflection on the
+positively charged particle and since
+
+ align:start position:0%
+positively charged particle and since
+ 
+
+ align:start position:0%
+positively charged particle and since
+these two are equal I'm guessing that
+
+ align:start position:0%
+these two are equal I'm guessing that
+ 
+
+ align:start position:0%
+these two are equal I'm guessing that
+since these two are equal well then this
+
+ align:start position:0%
+since these two are equal well then this
+ 
+
+ align:start position:0%
+since these two are equal well then this
+ratio has to just be equal to the mass
+
+ align:start position:0%
+ratio has to just be equal to the mass
+ 
+
+ align:start position:0%
+ratio has to just be equal to the mass
+of that positively charged hydrogen atom
+
+ align:start position:0%
+of that positively charged hydrogen atom
+ 
+
+ align:start position:0%
+of that positively charged hydrogen atom
+to the mass of that negatively charged
+
+ align:start position:0%
+to the mass of that negatively charged
+ 
+
+ align:start position:0%
+to the mass of that negatively charged
+uh particle all
+
+ align:start position:0%
+uh particle all
+ 
+
+ align:start position:0%
+uh particle all
+right and now here's the important point
+
+ align:start position:0%
+right and now here's the important point
+ 
+
+ align:start position:0%
+right and now here's the important point
+the important point is that no matter
+
+ align:start position:0%
+the important point is that no matter
+ 
+
+ align:start position:0%
+the important point is that no matter
+how he made these
+
+ align:start position:0%
+how he made these
+ 
+
+ align:start position:0%
+how he made these
+measurements no matter how he did that
+
+ align:start position:0%
+measurements no matter how he did that
+ 
+
+ align:start position:0%
+measurements no matter how he did that
+the deflection for that negatively
+
+ align:start position:0%
+the deflection for that negatively
+ 
+
+ align:start position:0%
+the deflection for that negatively
+charged particle was much much much
+
+ align:start position:0%
+charged particle was much much much
+ 
+
+ align:start position:0%
+charged particle was much much much
+larger than the def flection for that
+
+ align:start position:0%
+larger than the def flection for that
+ 
+
+ align:start position:0%
+larger than the def flection for that
+positively charged
+
+ align:start position:0%
+positively charged
+ 
+
+ align:start position:0%
+positively charged
+particle that then meant that the mass
+
+ align:start position:0%
+particle that then meant that the mass
+ 
+
+ align:start position:0%
+particle that then meant that the mass
+of this positively charged particle
+
+ align:start position:0%
+of this positively charged particle
+ 
+
+ align:start position:0%
+of this positively charged particle
+which he guessed to be hydrogen atom
+
+ align:start position:0%
+which he guessed to be hydrogen atom
+ 
+
+ align:start position:0%
+which he guessed to be hydrogen atom
+right that must be much much larger than
+
+ align:start position:0%
+right that must be much much larger than
+ 
+
+ align:start position:0%
+right that must be much much larger than
+the mass of the negatively charged
+
+ align:start position:0%
+the mass of the negatively charged
+ 
+
+ align:start position:0%
+the mass of the negatively charged
+particle but he also knew that at that
+
+ align:start position:0%
+particle but he also knew that at that
+ 
+
+ align:start position:0%
+particle but he also knew that at that
+time that a hydrogen atom was the least
+
+ align:start position:0%
+time that a hydrogen atom was the least
+ 
+
+ align:start position:0%
+time that a hydrogen atom was the least
+massive atom but here's an
+
+ align:start position:0%
+massive atom but here's an
+ 
+
+ align:start position:0%
+massive atom but here's an
+experiment that showed that there was a
+
+ align:start position:0%
+experiment that showed that there was a
+ 
+
+ align:start position:0%
+experiment that showed that there was a
+particle that was less massive than a
+
+ align:start position:0%
+particle that was less massive than a
+ 
+
+ align:start position:0%
+particle that was less massive than a
+hydrogen atom hey but you know up to
+
+ align:start position:0%
+hydrogen atom hey but you know up to
+ 
+
+ align:start position:0%
+hydrogen atom hey but you know up to
+then it was the atom is the most basic
+
+ align:start position:0%
+then it was the atom is the most basic
+ 
+
+ align:start position:0%
+then it was the atom is the most basic
+constituent of matter you can't chop it
+
+ align:start position:0%
+constituent of matter you can't chop it
+ 
+
+ align:start position:0%
+constituent of matter you can't chop it
+up anymore but here was the evidence
+
+ align:start position:0%
+up anymore but here was the evidence
+ 
+
+ align:start position:0%
+up anymore but here was the evidence
+that there was a particle less massive
+
+ align:start position:0%
+that there was a particle less massive
+ 
+
+ align:start position:0%
+that there was a particle less massive
+than the hydrogen atom eventually it's
+
+ align:start position:0%
+than the hydrogen atom eventually it's
+ 
+
+ align:start position:0%
+than the hydrogen atom eventually it's
+called an electron but this is the first
+
+ align:start position:0%
+called an electron but this is the first
+ 
+
+ align:start position:0%
+called an electron but this is the first
+evidence here that the atom wasn't the
+
+ align:start position:0%
+evidence here that the atom wasn't the
+ 
+
+ align:start position:0%
+evidence here that the atom wasn't the
+most basic constituent of
+
+ align:start position:0%
+most basic constituent of
+ 
+
+ align:start position:0%
+most basic constituent of
+matter now it actually took another 10
+
+ align:start position:0%
+matter now it actually took another 10
+ 
+
+ align:start position:0%
+matter now it actually took another 10
+years with the Milan oil drop experiment
+
+ align:start position:0%
+years with the Milan oil drop experiment
+ 
+
+ align:start position:0%
+years with the Milan oil drop experiment
+to actually measure this ratio correctly
+
+ align:start position:0%
+to actually measure this ratio correctly
+ 
+
+ align:start position:0%
+to actually measure this ratio correctly
+and to determine the mass of the
+
+ align:start position:0%
+and to determine the mass of the
+ 
+
+ align:start position:0%
+and to determine the mass of the
+electron we won't go in that into this
+
+ align:start position:0%
+electron we won't go in that into this
+ 
+
+ align:start position:0%
+electron we won't go in that into this
+but this ratio here you probably all
+
+ align:start position:0%
+but this ratio here you probably all
+ 
+
+ align:start position:0%
+but this ratio here you probably all
+know the mass of the electron is about
+
+ align:start position:0%
+know the mass of the electron is about
+ 
+
+ align:start position:0%
+know the mass of the electron is about
+836 times that of the mass of the
+
+ align:start position:0%
+836 times that of the mass of the
+ 
+
+ align:start position:0%
+836 times that of the mass of the
+hydrogen atom or hydrogen atom ion
+
+ align:start position:0%
+hydrogen atom or hydrogen atom ion
+ 
+
+ align:start position:0%
+hydrogen atom or hydrogen atom ion
+okay
\ No newline at end of file
diff --git a/4BwB43Smu7o.txt b/4BwB43Smu7o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..756e512aea0db37f22ed085295c04a75aaab6c43
--- /dev/null
+++ b/4BwB43Smu7o.txt
@@ -0,0 +1,3544 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer high quality educational
+
+ align:start position:0%
+to offer high quality educational
+ 
+
+ align:start position:0%
+to offer high quality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu greetings and welcome to 507
+
+ align:start position:0%
+ocw.mit.edu greetings and welcome to 507
+ 
+
+ align:start position:0%
+ocw.mit.edu greetings and welcome to 507
+biochemistry online I'm Dr bdan felish
+
+ align:start position:0%
+biochemistry online I'm Dr bdan felish
+ 
+
+ align:start position:0%
+biochemistry online I'm Dr bdan felish
+let's metabolize some problems today
+
+ align:start position:0%
+let's metabolize some problems today
+ 
+
+ align:start position:0%
+let's metabolize some problems today
+we're going to be talking about problem
+
+ align:start position:0%
+we're going to be talking about problem
+ 
+
+ align:start position:0%
+we're going to be talking about problem
+one of problem set 7 now this is a
+
+ align:start position:0%
+one of problem set 7 now this is a
+ 
+
+ align:start position:0%
+one of problem set 7 now this is a
+problem we are chasing labels through
+
+ align:start position:0%
+problem we are chasing labels through
+ 
+
+ align:start position:0%
+problem we are chasing labels through
+biochemical Pathways although it sounds
+
+ align:start position:0%
+biochemical Pathways although it sounds
+ 
+
+ align:start position:0%
+biochemical Pathways although it sounds
+funny it's actually one of the
+
+ align:start position:0%
+funny it's actually one of the
+ 
+
+ align:start position:0%
+funny it's actually one of the
+established ways through which we can
+
+ align:start position:0%
+established ways through which we can
+ 
+
+ align:start position:0%
+established ways through which we can
+test whether the mechanism we propose
+
+ align:start position:0%
+test whether the mechanism we propose
+ 
+
+ align:start position:0%
+test whether the mechanism we propose
+for these Pathways is in fact consistent
+
+ align:start position:0%
+for these Pathways is in fact consistent
+ 
+
+ align:start position:0%
+for these Pathways is in fact consistent
+with what we observe inside the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+in part A of this problem we're going to
+
+ align:start position:0%
+in part A of this problem we're going to
+ 
+
+ align:start position:0%
+in part A of this problem we're going to
+be looking at glycogen and try to figure
+
+ align:start position:0%
+be looking at glycogen and try to figure
+ 
+
+ align:start position:0%
+be looking at glycogen and try to figure
+out which carbons in glycogen end up
+
+ align:start position:0%
+out which carbons in glycogen end up
+ 
+
+ align:start position:0%
+out which carbons in glycogen end up
+being lost as CO2 in the pyrovate
+
+ align:start position:0%
+being lost as CO2 in the pyrovate
+ 
+
+ align:start position:0%
+being lost as CO2 in the pyrovate
+dehydrogenase step of the metabolism
+
+ align:start position:0%
+dehydrogenase step of the metabolism
+ 
+
+ align:start position:0%
+dehydrogenase step of the metabolism
+here is a Shand representation of
+
+ align:start position:0%
+here is a Shand representation of
+ 
+
+ align:start position:0%
+here is a Shand representation of
+glycogen as you know glycogen is a
+
+ align:start position:0%
+glycogen as you know glycogen is a
+ 
+
+ align:start position:0%
+glycogen as you know glycogen is a
+polymer formed of glucose monomers here
+
+ align:start position:0%
+polymer formed of glucose monomers here
+ 
+
+ align:start position:0%
+polymer formed of glucose monomers here
+is a cyclic form of glucose and in
+
+ align:start position:0%
+is a cyclic form of glucose and in
+ 
+
+ align:start position:0%
+is a cyclic form of glucose and in
+glycogen we have these one4 linkages as
+
+ align:start position:0%
+glycogen we have these one4 linkages as
+ 
+
+ align:start position:0%
+glycogen we have these one4 linkages as
+shown here occasionally we'll have one
+
+ align:start position:0%
+shown here occasionally we'll have one
+ 
+
+ align:start position:0%
+shown here occasionally we'll have one
+six linkages
+
+ align:start position:0%
+six linkages
+ 
+
+ align:start position:0%
+six linkages
+as in the case for branches but for
+
+ align:start position:0%
+as in the case for branches but for
+ 
+
+ align:start position:0%
+as in the case for branches but for
+Simplicity we're not going to represent
+
+ align:start position:0%
+Simplicity we're not going to represent
+ 
+
+ align:start position:0%
+Simplicity we're not going to represent
+them here now we want to figure out
+
+ align:start position:0%
+them here now we want to figure out
+ 
+
+ align:start position:0%
+them here now we want to figure out
+which one of these carbons in glycogen
+
+ align:start position:0%
+which one of these carbons in glycogen
+ 
+
+ align:start position:0%
+which one of these carbons in glycogen
+we can label them starting from here 1 2
+
+ align:start position:0%
+we can label them starting from here 1 2
+ 
+
+ align:start position:0%
+we can label them starting from here 1 2
+3 4 five and six which one of these
+
+ align:start position:0%
+3 4 five and six which one of these
+ 
+
+ align:start position:0%
+3 4 five and six which one of these
+carbons is going to be lost as CO2 in
+
+ align:start position:0%
+carbons is going to be lost as CO2 in
+ 
+
+ align:start position:0%
+carbons is going to be lost as CO2 in
+the pyate dehydrogenase step now let's
+
+ align:start position:0%
+the pyate dehydrogenase step now let's
+ 
+
+ align:start position:0%
+the pyate dehydrogenase step now let's
+take a look at the pyoid dehydrogenase
+
+ align:start position:0%
+take a look at the pyoid dehydrogenase
+ 
+
+ align:start position:0%
+take a look at the pyoid dehydrogenase
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+as you remember one of the endings of
+
+ align:start position:0%
+as you remember one of the endings of
+ 
+
+ align:start position:0%
+as you remember one of the endings of
+glycolysis is the pyate de hydrogenous
+
+ align:start position:0%
+glycolysis is the pyate de hydrogenous
+ 
+
+ align:start position:0%
+glycolysis is the pyate de hydrogenous
+reaction in which pyate loses a CO2
+
+ align:start position:0%
+reaction in which pyate loses a CO2
+ 
+
+ align:start position:0%
+reaction in which pyate loses a CO2
+molecules and forms atil COA which later
+
+ align:start position:0%
+molecules and forms atil COA which later
+ 
+
+ align:start position:0%
+molecules and forms atil COA which later
+can enter the TCA cycle now this carbon
+
+ align:start position:0%
+can enter the TCA cycle now this carbon
+ 
+
+ align:start position:0%
+can enter the TCA cycle now this carbon
+in the carboxy group of
+
+ align:start position:0%
+in the carboxy group of
+ 
+
+ align:start position:0%
+in the carboxy group of
+pyate going to label with a red dot this
+
+ align:start position:0%
+pyate going to label with a red dot this
+ 
+
+ align:start position:0%
+pyate going to label with a red dot this
+is the carbon that be is being lost as
+
+ align:start position:0%
+is the carbon that be is being lost as
+ 
+
+ align:start position:0%
+is the carbon that be is being lost as
+CO2 so we want to find out which of the
+
+ align:start position:0%
+CO2 so we want to find out which of the
+ 
+
+ align:start position:0%
+CO2 so we want to find out which of the
+carbons in our G ien molecule ends up
+
+ align:start position:0%
+carbons in our G ien molecule ends up
+ 
+
+ align:start position:0%
+carbons in our G ien molecule ends up
+being this red dotted carbon that's
+
+ align:start position:0%
+being this red dotted carbon that's
+ 
+
+ align:start position:0%
+being this red dotted carbon that's
+being lost at
+
+ align:start position:0%
+being lost at
+ 
+
+ align:start position:0%
+being lost at
+CO2 to figure this out we have to
+
+ align:start position:0%
+CO2 to figure this out we have to
+ 
+
+ align:start position:0%
+CO2 to figure this out we have to
+backtrack from pyrovate all the way to
+
+ align:start position:0%
+backtrack from pyrovate all the way to
+ 
+
+ align:start position:0%
+backtrack from pyrovate all the way to
+the beginning of glycolysis to figure
+
+ align:start position:0%
+the beginning of glycolysis to figure
+ 
+
+ align:start position:0%
+the beginning of glycolysis to figure
+out where this carbon is coming
+
+ align:start position:0%
+out where this carbon is coming
+ 
+
+ align:start position:0%
+out where this carbon is coming
+from shown here is a layout of the
+
+ align:start position:0%
+from shown here is a layout of the
+ 
+
+ align:start position:0%
+from shown here is a layout of the
+entire glycolysis Pathways starting from
+
+ align:start position:0%
+entire glycolysis Pathways starting from
+ 
+
+ align:start position:0%
+entire glycolysis Pathways starting from
+glycogen let me walk you through it very
+
+ align:start position:0%
+glycogen let me walk you through it very
+ 
+
+ align:start position:0%
+glycogen let me walk you through it very
+quickly glycogen shown here we shown
+
+ align:start position:0%
+quickly glycogen shown here we shown
+ 
+
+ align:start position:0%
+quickly glycogen shown here we shown
+only a couple of monomers attached to
+
+ align:start position:0%
+only a couple of monomers attached to
+ 
+
+ align:start position:0%
+only a couple of monomers attached to
+the glycogenin
+
+ align:start position:0%
+the glycogenin
+ 
+
+ align:start position:0%
+the glycogenin
+protein it's going to get hydrolized by
+
+ align:start position:0%
+protein it's going to get hydrolized by
+ 
+
+ align:start position:0%
+protein it's going to get hydrolized by
+glycogen phosphor to form glucose one
+
+ align:start position:0%
+glycogen phosphor to form glucose one
+ 
+
+ align:start position:0%
+glycogen phosphor to form glucose one
+phosphate which then mutates to glucose
+
+ align:start position:0%
+phosphate which then mutates to glucose
+ 
+
+ align:start position:0%
+phosphate which then mutates to glucose
+six phosphat shown here and then becomes
+
+ align:start position:0%
+six phosphat shown here and then becomes
+ 
+
+ align:start position:0%
+six phosphat shown here and then becomes
+fructose 6
+
+ align:start position:0%
+fructose 6
+ 
+
+ align:start position:0%
+fructose 6
+phosphate fructose one 6 Bas phosphate
+
+ align:start position:0%
+phosphate fructose one 6 Bas phosphate
+ 
+
+ align:start position:0%
+phosphate fructose one 6 Bas phosphate
+then the alalas reaction splits it into
+
+ align:start position:0%
+then the alalas reaction splits it into
+ 
+
+ align:start position:0%
+then the alalas reaction splits it into
+dihydro acetone phosphate and glycer
+
+ align:start position:0%
+dihydro acetone phosphate and glycer
+ 
+
+ align:start position:0%
+dihydro acetone phosphate and glycer
+alide three phosphate or Gap then the
+
+ align:start position:0%
+alide three phosphate or Gap then the
+ 
+
+ align:start position:0%
+alide three phosphate or Gap then the
+Gap dehydrogenase converts it to 1 to
+
+ align:start position:0%
+Gap dehydrogenase converts it to 1 to
+ 
+
+ align:start position:0%
+Gap dehydrogenase converts it to 1 to
+three bis phosphoglycerate and then we
+
+ align:start position:0%
+three bis phosphoglycerate and then we
+ 
+
+ align:start position:0%
+three bis phosphoglycerate and then we
+go down three phosphoglycerate two
+
+ align:start position:0%
+go down three phosphoglycerate two
+ 
+
+ align:start position:0%
+go down three phosphoglycerate two
+phosphoglycerate phosphino pyate and
+
+ align:start position:0%
+phosphoglycerate phosphino pyate and
+ 
+
+ align:start position:0%
+phosphoglycerate phosphino pyate and
+finally pyate and here I've also written
+
+ align:start position:0%
+finally pyate and here I've also written
+ 
+
+ align:start position:0%
+finally pyate and here I've also written
+the pyate dehydrogenase reaction pyate
+
+ align:start position:0%
+the pyate dehydrogenase reaction pyate
+ 
+
+ align:start position:0%
+the pyate dehydrogenase reaction pyate
+becomes acety COA by losing the CO2 once
+
+ align:start position:0%
+becomes acety COA by losing the CO2 once
+ 
+
+ align:start position:0%
+becomes acety COA by losing the CO2 once
+again this carbon that's lost the CO2 is
+
+ align:start position:0%
+again this carbon that's lost the CO2 is
+ 
+
+ align:start position:0%
+again this carbon that's lost the CO2 is
+the carbon that we want to track so I'm
+
+ align:start position:0%
+the carbon that we want to track so I'm
+ 
+
+ align:start position:0%
+the carbon that we want to track so I'm
+going to put a red dot on it and as we
+
+ align:start position:0%
+going to put a red dot on it and as we
+ 
+
+ align:start position:0%
+going to put a red dot on it and as we
+just said this carbon is the carboxy
+
+ align:start position:0%
+just said this carbon is the carboxy
+ 
+
+ align:start position:0%
+just said this carbon is the carboxy
+group in the
+
+ align:start position:0%
+group in the
+ 
+
+ align:start position:0%
+group in the
+pyrovate so the way to solve this
+
+ align:start position:0%
+pyrovate so the way to solve this
+ 
+
+ align:start position:0%
+pyrovate so the way to solve this
+problem is basically go backwards
+
+ align:start position:0%
+problem is basically go backwards
+ 
+
+ align:start position:0%
+problem is basically go backwards
+through the pathway and figure out where
+
+ align:start position:0%
+through the pathway and figure out where
+ 
+
+ align:start position:0%
+through the pathway and figure out where
+this carbon is coming from in the
+
+ align:start position:0%
+this carbon is coming from in the
+ 
+
+ align:start position:0%
+this carbon is coming from in the
+original glycogen
+
+ align:start position:0%
+original glycogen
+ 
+
+ align:start position:0%
+original glycogen
+molecule for the for these couple of
+
+ align:start position:0%
+molecule for the for these couple of
+ 
+
+ align:start position:0%
+molecule for the for these couple of
+steps it's pretty clear it's going to be
+
+ align:start position:0%
+steps it's pretty clear it's going to be
+ 
+
+ align:start position:0%
+steps it's pretty clear it's going to be
+the carboxy in each one of these
+
+ align:start position:0%
+the carboxy in each one of these
+ 
+
+ align:start position:0%
+the carboxy in each one of these
+molecules all the way to 13 B
+
+ align:start position:0%
+molecules all the way to 13 B
+ 
+
+ align:start position:0%
+molecules all the way to 13 B
+phosphoglycerate right there all right
+
+ align:start position:0%
+phosphoglycerate right there all right
+ 
+
+ align:start position:0%
+phosphoglycerate right there all right
+now this 13B phosphoglyceride is coming
+
+ align:start position:0%
+now this 13B phosphoglyceride is coming
+ 
+
+ align:start position:0%
+now this 13B phosphoglyceride is coming
+from Gap so this carbon is in fact the
+
+ align:start position:0%
+from Gap so this carbon is in fact the
+ 
+
+ align:start position:0%
+from Gap so this carbon is in fact the
+alahh carbon in gap
+
+ align:start position:0%
+alahh carbon in gap
+ 
+
+ align:start position:0%
+alahh carbon in gap
+now as you guys know trios isomerase
+
+ align:start position:0%
+now as you guys know trios isomerase
+ 
+
+ align:start position:0%
+now as you guys know trios isomerase
+interconverts between dihydro acetone
+
+ align:start position:0%
+interconverts between dihydro acetone
+ 
+
+ align:start position:0%
+interconverts between dihydro acetone
+phosphate and GAP so this carbon in
+
+ align:start position:0%
+phosphate and GAP so this carbon in
+ 
+
+ align:start position:0%
+phosphate and GAP so this carbon in
+dihydro acetone phosphate is actually
+
+ align:start position:0%
+dihydro acetone phosphate is actually
+ 
+
+ align:start position:0%
+dihydro acetone phosphate is actually
+this carbon right because the phosphate
+
+ align:start position:0%
+this carbon right because the phosphate
+ 
+
+ align:start position:0%
+this carbon right because the phosphate
+group is going to stay unchanged and
+
+ align:start position:0%
+group is going to stay unchanged and
+ 
+
+ align:start position:0%
+group is going to stay unchanged and
+then the car carbonal group at C2 can
+
+ align:start position:0%
+then the car carbonal group at C2 can
+ 
+
+ align:start position:0%
+then the car carbonal group at C2 can
+interconvert with C1 to form an alahh
+
+ align:start position:0%
+interconvert with C1 to form an alahh
+ 
+
+ align:start position:0%
+interconvert with C1 to form an alahh
+here so any of these two carbons if they
+
+ align:start position:0%
+here so any of these two carbons if they
+ 
+
+ align:start position:0%
+here so any of these two carbons if they
+were labeled they would end up being
+
+ align:start position:0%
+were labeled they would end up being
+ 
+
+ align:start position:0%
+were labeled they would end up being
+lost as CO2 in the P dehydrogenate
+
+ align:start position:0%
+lost as CO2 in the P dehydrogenate
+ 
+
+ align:start position:0%
+lost as CO2 in the P dehydrogenate
+step now if we go backwards in the aler
+
+ align:start position:0%
+step now if we go backwards in the aler
+ 
+
+ align:start position:0%
+step now if we go backwards in the aler
+reaction Gap and
+
+ align:start position:0%
+reaction Gap and
+ 
+
+ align:start position:0%
+reaction Gap and
+dhap when put together these carbons are
+
+ align:start position:0%
+dhap when put together these carbons are
+ 
+
+ align:start position:0%
+dhap when put together these carbons are
+going to be carbons three and
+
+ align:start position:0%
+going to be carbons three and
+ 
+
+ align:start position:0%
+going to be carbons three and
+four so we're calling here 1 2 3 this is
+
+ align:start position:0%
+four so we're calling here 1 2 3 this is
+ 
+
+ align:start position:0%
+four so we're calling here 1 2 3 this is
+the carbon that comes from dihydro acone
+
+ align:start position:0%
+the carbon that comes from dihydro acone
+ 
+
+ align:start position:0%
+the carbon that comes from dihydro acone
+phosphate and this is the carbon that
+
+ align:start position:0%
+phosphate and this is the carbon that
+ 
+
+ align:start position:0%
+phosphate and this is the carbon that
+comes from Gap so carbon 3 and four and
+
+ align:start position:0%
+comes from Gap so carbon 3 and four and
+ 
+
+ align:start position:0%
+comes from Gap so carbon 3 and four and
+obviously they're going to be staying
+
+ align:start position:0%
+obviously they're going to be staying
+ 
+
+ align:start position:0%
+obviously they're going to be staying
+carbons 3 and four all the way back to
+
+ align:start position:0%
+carbons 3 and four all the way back to
+ 
+
+ align:start position:0%
+carbons 3 and four all the way back to
+glucose 1 2 3 and four right there
+
+ align:start position:0%
+glucose 1 2 3 and four right there
+ 
+
+ align:start position:0%
+glucose 1 2 3 and four right there
+and also in glucose one phosphate and
+
+ align:start position:0%
+and also in glucose one phosphate and
+ 
+
+ align:start position:0%
+and also in glucose one phosphate and
+consequently in glycogen as
+
+ align:start position:0%
+consequently in glycogen as
+ 
+
+ align:start position:0%
+consequently in glycogen as
+well so to answer part
+
+ align:start position:0%
+well so to answer part
+ 
+
+ align:start position:0%
+well so to answer part
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh we can now write here that carbon's
+
+ align:start position:0%
+uh we can now write here that carbon's
+ 
+
+ align:start position:0%
+uh we can now write here that carbon's
+three and four
+
+ align:start position:0%
+three and four
+ 
+
+ align:start position:0%
+three and four
+of glycogen are going to be lost at the
+
+ align:start position:0%
+of glycogen are going to be lost at the
+ 
+
+ align:start position:0%
+of glycogen are going to be lost at the
+pyate dehydrogenate step as carbon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dioxide Part B of the problem deals with
+
+ align:start position:0%
+dioxide Part B of the problem deals with
+ 
+
+ align:start position:0%
+dioxide Part B of the problem deals with
+the metabolism of glycerol as you know
+
+ align:start position:0%
+the metabolism of glycerol as you know
+ 
+
+ align:start position:0%
+the metabolism of glycerol as you know
+glycerol is formed by the hydrolysis of
+
+ align:start position:0%
+glycerol is formed by the hydrolysis of
+ 
+
+ align:start position:0%
+glycerol is formed by the hydrolysis of
+trial glycerides now we are asked to
+
+ align:start position:0%
+trial glycerides now we are asked to
+ 
+
+ align:start position:0%
+trial glycerides now we are asked to
+trace a label from the C2 carbon of
+
+ align:start position:0%
+trace a label from the C2 carbon of
+ 
+
+ align:start position:0%
+trace a label from the C2 carbon of
+glycerol all the way to the first step
+
+ align:start position:0%
+glycerol all the way to the first step
+ 
+
+ align:start position:0%
+glycerol all the way to the first step
+in which this carbon is lost as carbon
+
+ align:start position:0%
+in which this carbon is lost as carbon
+ 
+
+ align:start position:0%
+in which this carbon is lost as carbon
+dioxide let's first take a look at the
+
+ align:start position:0%
+dioxide let's first take a look at the
+ 
+
+ align:start position:0%
+dioxide let's first take a look at the
+metabolism of
+
+ align:start position:0%
+metabolism of
+ 
+
+ align:start position:0%
+metabolism of
+glycerol as I've shown here trial
+
+ align:start position:0%
+glycerol as I've shown here trial
+ 
+
+ align:start position:0%
+glycerol as I've shown here trial
+glycerides can be hydrolized to form
+
+ align:start position:0%
+glycerides can be hydrolized to form
+ 
+
+ align:start position:0%
+glycerides can be hydrolized to form
+glycerol which is 1 2 3 propane triol
+
+ align:start position:0%
+glycerol which is 1 2 3 propane triol
+ 
+
+ align:start position:0%
+glycerol which is 1 2 3 propane triol
+now as you know glycerol is metabolized
+
+ align:start position:0%
+now as you know glycerol is metabolized
+ 
+
+ align:start position:0%
+now as you know glycerol is metabolized
+in two steps first we have a glycerol
+
+ align:start position:0%
+in two steps first we have a glycerol
+ 
+
+ align:start position:0%
+in two steps first we have a glycerol
+kinase that's going to form a glycerol
+
+ align:start position:0%
+kinase that's going to form a glycerol
+ 
+
+ align:start position:0%
+kinase that's going to form a glycerol
+three phosphate as shown here and then
+
+ align:start position:0%
+three phosphate as shown here and then
+ 
+
+ align:start position:0%
+three phosphate as shown here and then
+we're going to use a dehydrogenase that
+
+ align:start position:0%
+we're going to use a dehydrogenase that
+ 
+
+ align:start position:0%
+we're going to use a dehydrogenase that
+uses NAD to oxidize the second carbon of
+
+ align:start position:0%
+uses NAD to oxidize the second carbon of
+ 
+
+ align:start position:0%
+uses NAD to oxidize the second carbon of
+glycerol to dihydro acetone phosphate
+
+ align:start position:0%
+glycerol to dihydro acetone phosphate
+ 
+
+ align:start position:0%
+glycerol to dihydro acetone phosphate
+then it can enter
+
+ align:start position:0%
+then it can enter
+ 
+
+ align:start position:0%
+then it can enter
+glycolysis very conveniently right here
+
+ align:start position:0%
+glycolysis very conveniently right here
+ 
+
+ align:start position:0%
+glycolysis very conveniently right here
+and then it's going to continue getting
+
+ align:start position:0%
+and then it's going to continue getting
+ 
+
+ align:start position:0%
+and then it's going to continue getting
+metabolized towards pyrovate and atil
+
+ align:start position:0%
+metabolized towards pyrovate and atil
+ 
+
+ align:start position:0%
+metabolized towards pyrovate and atil
+COA as as we've seen
+
+ align:start position:0%
+COA as as we've seen
+ 
+
+ align:start position:0%
+COA as as we've seen
+before now the second carbon and
+
+ align:start position:0%
+before now the second carbon and
+ 
+
+ align:start position:0%
+before now the second carbon and
+glycerol is C2 right here I'm going to
+
+ align:start position:0%
+glycerol is C2 right here I'm going to
+ 
+
+ align:start position:0%
+glycerol is C2 right here I'm going to
+mark it with a
+
+ align:start position:0%
+mark it with a
+ 
+
+ align:start position:0%
+mark it with a
+blue
+
+ align:start position:0%
+blue
+ 
+
+ align:start position:0%
+blue
+square so this carbon is right here and
+
+ align:start position:0%
+square so this carbon is right here and
+ 
+
+ align:start position:0%
+square so this carbon is right here and
+it's going to end up right
+
+ align:start position:0%
+it's going to end up right
+ 
+
+ align:start position:0%
+it's going to end up right
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+now this second carbon in diydrone
+
+ align:start position:0%
+now this second carbon in diydrone
+ 
+
+ align:start position:0%
+now this second carbon in diydrone
+phosphate it's going to be the second
+
+ align:start position:0%
+phosphate it's going to be the second
+ 
+
+ align:start position:0%
+phosphate it's going to be the second
+carbon in gap and then second carbon
+
+ align:start position:0%
+carbon in gap and then second carbon
+ 
+
+ align:start position:0%
+carbon in gap and then second carbon
+here here
+
+ align:start position:0%
+here here
+ 
+
+ align:start position:0%
+here here
+here isn't this
+
+ align:start position:0%
+here isn't this
+ 
+
+ align:start position:0%
+here isn't this
+fun then the second carbon in pyate now
+
+ align:start position:0%
+fun then the second carbon in pyate now
+ 
+
+ align:start position:0%
+fun then the second carbon in pyate now
+once the pyate decarbox silat then it's
+
+ align:start position:0%
+once the pyate decarbox silat then it's
+ 
+
+ align:start position:0%
+once the pyate decarbox silat then it's
+going to be the carbonal of acetyl COA
+
+ align:start position:0%
+going to be the carbonal of acetyl COA
+ 
+
+ align:start position:0%
+going to be the carbonal of acetyl COA
+it's this carbon right here now so far
+
+ align:start position:0%
+it's this carbon right here now so far
+ 
+
+ align:start position:0%
+it's this carbon right here now so far
+this carbon has followed the metabolic
+
+ align:start position:0%
+this carbon has followed the metabolic
+ 
+
+ align:start position:0%
+this carbon has followed the metabolic
+pathway but it has not left yet right as
+
+ align:start position:0%
+pathway but it has not left yet right as
+ 
+
+ align:start position:0%
+pathway but it has not left yet right as
+CO2 now what happens to atil COA it's
+
+ align:start position:0%
+CO2 now what happens to atil COA it's
+ 
+
+ align:start position:0%
+CO2 now what happens to atil COA it's
+going to enter the TCA cycle now let's
+
+ align:start position:0%
+going to enter the TCA cycle now let's
+ 
+
+ align:start position:0%
+going to enter the TCA cycle now let's
+take a look at the TCA cycle as we just
+
+ align:start position:0%
+take a look at the TCA cycle as we just
+ 
+
+ align:start position:0%
+take a look at the TCA cycle as we just
+said we're looking now at the
+
+ align:start position:0%
+said we're looking now at the
+ 
+
+ align:start position:0%
+said we're looking now at the
+carbon the first carbon in AEL COA here
+
+ align:start position:0%
+carbon the first carbon in AEL COA here
+ 
+
+ align:start position:0%
+carbon the first carbon in AEL COA here
+the carbon that has the carbonal group
+
+ align:start position:0%
+the carbon that has the carbonal group
+ 
+
+ align:start position:0%
+the carbon that has the carbonal group
+on so as I've shown here in the TCA
+
+ align:start position:0%
+on so as I've shown here in the TCA
+ 
+
+ align:start position:0%
+on so as I've shown here in the TCA
+cycle the the two carbons in acety COA
+
+ align:start position:0%
+cycle the the two carbons in acety COA
+ 
+
+ align:start position:0%
+cycle the the two carbons in acety COA
+are marked with this red line and they
+
+ align:start position:0%
+are marked with this red line and they
+ 
+
+ align:start position:0%
+are marked with this red line and they
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+enter uh and combine with oxaloacetate
+
+ align:start position:0%
+enter uh and combine with oxaloacetate
+ 
+
+ align:start position:0%
+enter uh and combine with oxaloacetate
+to form citrate then citrate isomerizes
+
+ align:start position:0%
+to form citrate then citrate isomerizes
+ 
+
+ align:start position:0%
+to form citrate then citrate isomerizes
+to isocitrate then we're going to lose a
+
+ align:start position:0%
+to isocitrate then we're going to lose a
+ 
+
+ align:start position:0%
+to isocitrate then we're going to lose a
+CO2 molecule which is this middle guy to
+
+ align:start position:0%
+CO2 molecule which is this middle guy to
+ 
+
+ align:start position:0%
+CO2 molecule which is this middle guy to
+form Alpha ketoglutarate but notice the
+
+ align:start position:0%
+form Alpha ketoglutarate but notice the
+ 
+
+ align:start position:0%
+form Alpha ketoglutarate but notice the
+two carbons from actil COA are still in
+
+ align:start position:0%
+two carbons from actil COA are still in
+ 
+
+ align:start position:0%
+two carbons from actil COA are still in
+the molecule then we're going to lose
+
+ align:start position:0%
+the molecule then we're going to lose
+ 
+
+ align:start position:0%
+the molecule then we're going to lose
+another CO2 is this bottom one to form
+
+ align:start position:0%
+another CO2 is this bottom one to form
+ 
+
+ align:start position:0%
+another CO2 is this bottom one to form
+suil COA but once again the two carbons
+
+ align:start position:0%
+suil COA but once again the two carbons
+ 
+
+ align:start position:0%
+suil COA but once again the two carbons
+that came from a COA are still here so
+
+ align:start position:0%
+that came from a COA are still here so
+ 
+
+ align:start position:0%
+that came from a COA are still here so
+in the first TCA cycle none of the CO2
+
+ align:start position:0%
+in the first TCA cycle none of the CO2
+ 
+
+ align:start position:0%
+in the first TCA cycle none of the CO2
+will contain the label that came from
+
+ align:start position:0%
+will contain the label that came from
+ 
+
+ align:start position:0%
+will contain the label that came from
+the from the
+
+ align:start position:0%
+the from the
+ 
+
+ align:start position:0%
+the from the
+glycerol now as we go through the
+
+ align:start position:0%
+glycerol now as we go through the
+ 
+
+ align:start position:0%
+glycerol now as we go through the
+through the TCA cycle we reach this step
+
+ align:start position:0%
+through the TCA cycle we reach this step
+ 
+
+ align:start position:0%
+through the TCA cycle we reach this step
+where is suxin now here I stopped
+
+ align:start position:0%
+where is suxin now here I stopped
+ 
+
+ align:start position:0%
+where is suxin now here I stopped
+putting this red mark because succinate
+
+ align:start position:0%
+putting this red mark because succinate
+ 
+
+ align:start position:0%
+putting this red mark because succinate
+is a symmetric molecule so therefore if
+
+ align:start position:0%
+is a symmetric molecule so therefore if
+ 
+
+ align:start position:0%
+is a symmetric molecule so therefore if
+these two carbons were coming from atil
+
+ align:start position:0%
+these two carbons were coming from atil
+ 
+
+ align:start position:0%
+these two carbons were coming from atil
+Co at this point they will SC ramble so
+
+ align:start position:0%
+Co at this point they will SC ramble so
+ 
+
+ align:start position:0%
+Co at this point they will SC ramble so
+we won't be able to tell whether it was
+
+ align:start position:0%
+we won't be able to tell whether it was
+ 
+
+ align:start position:0%
+we won't be able to tell whether it was
+these two carbons or these two carbons
+
+ align:start position:0%
+these two carbons or these two carbons
+ 
+
+ align:start position:0%
+these two carbons or these two carbons
+all right now let me backtrack and put
+
+ align:start position:0%
+all right now let me backtrack and put
+ 
+
+ align:start position:0%
+all right now let me backtrack and put
+in the labels so astil COA we have this
+
+ align:start position:0%
+in the labels so astil COA we have this
+ 
+
+ align:start position:0%
+in the labels so astil COA we have this
+carbon came from the C2 of glycerol so
+
+ align:start position:0%
+carbon came from the C2 of glycerol so
+ 
+
+ align:start position:0%
+carbon came from the C2 of glycerol so
+we'll find it in this carbon this carbon
+
+ align:start position:0%
+we'll find it in this carbon this carbon
+ 
+
+ align:start position:0%
+we'll find it in this carbon this carbon
+this carbon this carbon all right now we
+
+ align:start position:0%
+this carbon this carbon all right now we
+ 
+
+ align:start position:0%
+this carbon this carbon all right now we
+get to the succinate step and we said
+
+ align:start position:0%
+get to the succinate step and we said
+ 
+
+ align:start position:0%
+get to the succinate step and we said
+well it was here this would be the
+
+ align:start position:0%
+well it was here this would be the
+ 
+
+ align:start position:0%
+well it was here this would be the
+carbon that corresponds to toxil COA but
+
+ align:start position:0%
+carbon that corresponds to toxil COA but
+ 
+
+ align:start position:0%
+carbon that corresponds to toxil COA but
+because this molecule is symmetric by
+
+ align:start position:0%
+because this molecule is symmetric by
+ 
+
+ align:start position:0%
+because this molecule is symmetric by
+the time we get to the malate step to
+
+ align:start position:0%
+the time we get to the malate step to
+ 
+
+ align:start position:0%
+the time we get to the malate step to
+add this hydroxy group it's going to be
+
+ align:start position:0%
+add this hydroxy group it's going to be
+ 
+
+ align:start position:0%
+add this hydroxy group it's going to be
+to the carbon next to the label or the
+
+ align:start position:0%
+to the carbon next to the label or the
+ 
+
+ align:start position:0%
+to the carbon next to the label or the
+carbon further from the label now
+
+ align:start position:0%
+carbon further from the label now
+ 
+
+ align:start position:0%
+carbon further from the label now
+because the molecule is symmetric we
+
+ align:start position:0%
+because the molecule is symmetric we
+ 
+
+ align:start position:0%
+because the molecule is symmetric we
+can't the the ferase enzyme cannot tell
+
+ align:start position:0%
+can't the the ferase enzyme cannot tell
+ 
+
+ align:start position:0%
+can't the the ferase enzyme cannot tell
+which carbon was labeled and which
+
+ align:start position:0%
+which carbon was labeled and which
+ 
+
+ align:start position:0%
+which carbon was labeled and which
+wasn't so therefore malate is going to
+
+ align:start position:0%
+wasn't so therefore malate is going to
+ 
+
+ align:start position:0%
+wasn't so therefore malate is going to
+be half of the molecules is going to
+
+ align:start position:0%
+be half of the molecules is going to
+ 
+
+ align:start position:0%
+be half of the molecules is going to
+have the label on this carbon and half
+
+ align:start position:0%
+have the label on this carbon and half
+ 
+
+ align:start position:0%
+have the label on this carbon and half
+is going to have the label on this
+
+ align:start position:0%
+is going to have the label on this
+ 
+
+ align:start position:0%
+is going to have the label on this
+carbon so I'm going to write like 1 12
+
+ align:start position:0%
+carbon so I'm going to write like 1 12
+ 
+
+ align:start position:0%
+carbon so I'm going to write like 1 12
+square and 1 12 square similarly when we
+
+ align:start position:0%
+square and 1 12 square similarly when we
+ 
+
+ align:start position:0%
+square and 1 12 square similarly when we
+get to oxaloacetate the label is
+
+ align:start position:0%
+get to oxaloacetate the label is
+ 
+
+ align:start position:0%
+get to oxaloacetate the label is
+distributed half on one uh carboxy group
+
+ align:start position:0%
+distributed half on one uh carboxy group
+ 
+
+ align:start position:0%
+distributed half on one uh carboxy group
+and the other half is going to be on the
+
+ align:start position:0%
+and the other half is going to be on the
+ 
+
+ align:start position:0%
+and the other half is going to be on the
+other carboxy
+
+ align:start position:0%
+other carboxy
+ 
+
+ align:start position:0%
+other carboxy
+group all right now so we've gone
+
+ align:start position:0%
+group all right now so we've gone
+ 
+
+ align:start position:0%
+group all right now so we've gone
+through the TCA cycle once and we have
+
+ align:start position:0%
+through the TCA cycle once and we have
+ 
+
+ align:start position:0%
+through the TCA cycle once and we have
+not lost the carbon that came from the
+
+ align:start position:0%
+not lost the carbon that came from the
+ 
+
+ align:start position:0%
+not lost the carbon that came from the
+glycerol but look what happens when we
+
+ align:start position:0%
+glycerol but look what happens when we
+ 
+
+ align:start position:0%
+glycerol but look what happens when we
+continue the TCA cycle a second time so
+
+ align:start position:0%
+continue the TCA cycle a second time so
+ 
+
+ align:start position:0%
+continue the TCA cycle a second time so
+now let's say we combine with an astil
+
+ align:start position:0%
+now let's say we combine with an astil
+ 
+
+ align:start position:0%
+now let's say we combine with an astil
+COA that doesn't have any label at all
+
+ align:start position:0%
+COA that doesn't have any label at all
+ 
+
+ align:start position:0%
+COA that doesn't have any label at all
+now these two carboxy groups are going
+
+ align:start position:0%
+now these two carboxy groups are going
+ 
+
+ align:start position:0%
+now these two carboxy groups are going
+to be these two carboxy group in citrate
+
+ align:start position:0%
+to be these two carboxy group in citrate
+ 
+
+ align:start position:0%
+to be these two carboxy group in citrate
+and as we
+
+ align:start position:0%
+and as we
+ 
+
+ align:start position:0%
+and as we
+discussed both of these two groups are
+
+ align:start position:0%
+discussed both of these two groups are
+ 
+
+ align:start position:0%
+discussed both of these two groups are
+going to be lost at CO2 in these two
+
+ align:start position:0%
+going to be lost at CO2 in these two
+ 
+
+ align:start position:0%
+going to be lost at CO2 in these two
+steps first is the middle carboxy group
+
+ align:start position:0%
+steps first is the middle carboxy group
+ 
+
+ align:start position:0%
+steps first is the middle carboxy group
+that's being lost here and this other
+
+ align:start position:0%
+that's being lost here and this other
+ 
+
+ align:start position:0%
+that's being lost here and this other
+carboxy is going to be lost at the alpha
+
+ align:start position:0%
+carboxy is going to be lost at the alpha
+ 
+
+ align:start position:0%
+carboxy is going to be lost at the alpha
+ketoglutarate dehydrogenate step so the
+
+ align:start position:0%
+ketoglutarate dehydrogenate step so the
+ 
+
+ align:start position:0%
+ketoglutarate dehydrogenate step so the
+second time we go through the TCA cycle
+
+ align:start position:0%
+second time we go through the TCA cycle
+ 
+
+ align:start position:0%
+second time we go through the TCA cycle
+we lose half of the label at the isocit
+
+ align:start position:0%
+we lose half of the label at the isocit
+ 
+
+ align:start position:0%
+we lose half of the label at the isocit
+dehydrogenate step and half of the label
+
+ align:start position:0%
+dehydrogenate step and half of the label
+ 
+
+ align:start position:0%
+dehydrogenate step and half of the label
+at the alpha kilog glutarate
+
+ align:start position:0%
+at the alpha kilog glutarate
+ 
+
+ align:start position:0%
+at the alpha kilog glutarate
+dehydrogenate step all right so I can
+
+ align:start position:0%
+dehydrogenate step all right so I can
+ 
+
+ align:start position:0%
+dehydrogenate step all right so I can
+I'm going to circle these so to answer
+
+ align:start position:0%
+I'm going to circle these so to answer
+ 
+
+ align:start position:0%
+I'm going to circle these so to answer
+Part B the C2 carbon of glycerol is
+
+ align:start position:0%
+Part B the C2 carbon of glycerol is
+ 
+
+ align:start position:0%
+Part B the C2 carbon of glycerol is
+going to be lost as CO2 in the TCA cycle
+
+ align:start position:0%
+going to be lost as CO2 in the TCA cycle
+ 
+
+ align:start position:0%
+going to be lost as CO2 in the TCA cycle
+but we have to go once through the cycle
+
+ align:start position:0%
+but we have to go once through the cycle
+ 
+
+ align:start position:0%
+but we have to go once through the cycle
+first through which none of the label
+
+ align:start position:0%
+first through which none of the label
+ 
+
+ align:start position:0%
+first through which none of the label
+will be lost and then at the second time
+
+ align:start position:0%
+will be lost and then at the second time
+ 
+
+ align:start position:0%
+will be lost and then at the second time
+first in the isocitrate dehydrogenase
+
+ align:start position:0%
+first in the isocitrate dehydrogenase
+ 
+
+ align:start position:0%
+first in the isocitrate dehydrogenase
+then at the alpha ketoglutarate
+
+ align:start position:0%
+then at the alpha ketoglutarate
+ 
+
+ align:start position:0%
+then at the alpha ketoglutarate
+dehydrogenase we're going to be losing
+
+ align:start position:0%
+dehydrogenase we're going to be losing
+ 
+
+ align:start position:0%
+dehydrogenase we're going to be losing
+the CO2 that came from the C2 carbon of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glycerol as you might imagine glycerol
+
+ align:start position:0%
+glycerol as you might imagine glycerol
+ 
+
+ align:start position:0%
+glycerol as you might imagine glycerol
+can also be used to produce energy in
+
+ align:start position:0%
+can also be used to produce energy in
+ 
+
+ align:start position:0%
+can also be used to produce energy in
+fact some bacteria can grow on glycerol
+
+ align:start position:0%
+fact some bacteria can grow on glycerol
+ 
+
+ align:start position:0%
+fact some bacteria can grow on glycerol
+using no other carbon Source now in part
+
+ align:start position:0%
+using no other carbon Source now in part
+ 
+
+ align:start position:0%
+using no other carbon Source now in part
+C of the problem we're going to explore
+
+ align:start position:0%
+C of the problem we're going to explore
+ 
+
+ align:start position:0%
+C of the problem we're going to explore
+how much energy we can get from one
+
+ align:start position:0%
+how much energy we can get from one
+ 
+
+ align:start position:0%
+how much energy we can get from one
+molecule of glycerol let's first review
+
+ align:start position:0%
+molecule of glycerol let's first review
+ 
+
+ align:start position:0%
+molecule of glycerol let's first review
+the metabolism of
+
+ align:start position:0%
+the metabolism of
+ 
+
+ align:start position:0%
+the metabolism of
+glycerol as we just discussed glycerol
+
+ align:start position:0%
+glycerol as we just discussed glycerol
+ 
+
+ align:start position:0%
+glycerol as we just discussed glycerol
+enters metabolism with glycerol kisee
+
+ align:start position:0%
+enters metabolism with glycerol kisee
+ 
+
+ align:start position:0%
+enters metabolism with glycerol kisee
+which then in two steps becomes dihydro
+
+ align:start position:0%
+which then in two steps becomes dihydro
+ 
+
+ align:start position:0%
+which then in two steps becomes dihydro
+asone phosphate which can enter
+
+ align:start position:0%
+asone phosphate which can enter
+ 
+
+ align:start position:0%
+asone phosphate which can enter
+glycolysis all the way to pyate and then
+
+ align:start position:0%
+glycolysis all the way to pyate and then
+ 
+
+ align:start position:0%
+glycolysis all the way to pyate and then
+atil COA here the pyate dehydrogenase
+
+ align:start position:0%
+atil COA here the pyate dehydrogenase
+ 
+
+ align:start position:0%
+atil COA here the pyate dehydrogenase
+allows us to lose one
+
+ align:start position:0%
+allows us to lose one
+ 
+
+ align:start position:0%
+allows us to lose one
+CO2 and then atil COA will enter the TCA
+
+ align:start position:0%
+CO2 and then atil COA will enter the TCA
+ 
+
+ align:start position:0%
+CO2 and then atil COA will enter the TCA
+cycle where within one cycle we're going
+
+ align:start position:0%
+cycle where within one cycle we're going
+ 
+
+ align:start position:0%
+cycle where within one cycle we're going
+to lose two more co2's so that's a total
+
+ align:start position:0%
+to lose two more co2's so that's a total
+ 
+
+ align:start position:0%
+to lose two more co2's so that's a total
+of three carbons that we lose and that's
+
+ align:start position:0%
+of three carbons that we lose and that's
+ 
+
+ align:start position:0%
+of three carbons that we lose and that's
+exactly how many carbons we have in
+
+ align:start position:0%
+exactly how many carbons we have in
+ 
+
+ align:start position:0%
+exactly how many carbons we have in
+glycerol now what we need to keep track
+
+ align:start position:0%
+glycerol now what we need to keep track
+ 
+
+ align:start position:0%
+glycerol now what we need to keep track
+in order to evaluate how much energy we
+
+ align:start position:0%
+in order to evaluate how much energy we
+ 
+
+ align:start position:0%
+in order to evaluate how much energy we
+get from one molecule of glycerol is
+
+ align:start position:0%
+get from one molecule of glycerol is
+ 
+
+ align:start position:0%
+get from one molecule of glycerol is
+whenever we need to use ATP for example
+
+ align:start position:0%
+whenever we need to use ATP for example
+ 
+
+ align:start position:0%
+whenever we need to use ATP for example
+we need to put in energy or whenever we
+
+ align:start position:0%
+we need to put in energy or whenever we
+ 
+
+ align:start position:0%
+we need to put in energy or whenever we
+generate nadh or fadh2 molecules that we
+
+ align:start position:0%
+generate nadh or fadh2 molecules that we
+ 
+
+ align:start position:0%
+generate nadh or fadh2 molecules that we
+can then take to the electron transport
+
+ align:start position:0%
+can then take to the electron transport
+ 
+
+ align:start position:0%
+can then take to the electron transport
+chain and generate atps out of them so
+
+ align:start position:0%
+chain and generate atps out of them so
+ 
+
+ align:start position:0%
+chain and generate atps out of them so
+I've put together a list of the steps in
+
+ align:start position:0%
+I've put together a list of the steps in
+ 
+
+ align:start position:0%
+I've put together a list of the steps in
+the pathway where the energy balance is
+
+ align:start position:0%
+the pathway where the energy balance is
+ 
+
+ align:start position:0%
+the pathway where the energy balance is
+affected either we need to use energy or
+
+ align:start position:0%
+affected either we need to use energy or
+ 
+
+ align:start position:0%
+affected either we need to use energy or
+regenerating energy in the form of ATP
+
+ align:start position:0%
+regenerating energy in the form of ATP
+ 
+
+ align:start position:0%
+regenerating energy in the form of ATP
+or in the form of Redux co-actors such
+
+ align:start position:0%
+or in the form of Redux co-actors such
+ 
+
+ align:start position:0%
+or in the form of Redux co-actors such
+as NAD and
+
+ align:start position:0%
+as NAD and
+ 
+
+ align:start position:0%
+as NAD and
+fad all right so the first step glycerol
+
+ align:start position:0%
+fad all right so the first step glycerol
+ 
+
+ align:start position:0%
+fad all right so the first step glycerol
+kinas we're going to need to spend one
+
+ align:start position:0%
+kinas we're going to need to spend one
+ 
+
+ align:start position:0%
+kinas we're going to need to spend one
+molecule of ATP so I'm going to put a
+
+ align:start position:0%
+molecule of ATP so I'm going to put a
+ 
+
+ align:start position:0%
+molecule of ATP so I'm going to put a
+minus one here for ATP equivalent now in
+
+ align:start position:0%
+minus one here for ATP equivalent now in
+ 
+
+ align:start position:0%
+minus one here for ATP equivalent now in
+the glycerol three phosphate
+
+ align:start position:0%
+the glycerol three phosphate
+ 
+
+ align:start position:0%
+the glycerol three phosphate
+dehydrogenate step which is shown right
+
+ align:start position:0%
+dehydrogenate step which is shown right
+ 
+
+ align:start position:0%
+dehydrogenate step which is shown right
+here we're generating one molecule of
+
+ align:start position:0%
+here we're generating one molecule of
+ 
+
+ align:start position:0%
+here we're generating one molecule of
+nadh so plus one
+
+ align:start position:0%
+nadh so plus one
+ 
+
+ align:start position:0%
+nadh so plus one
+nadh
+
+ align:start position:0%
+nadh
+ 
+
+ align:start position:0%
+nadh
+now for the purpose of this problem
+
+ align:start position:0%
+now for the purpose of this problem
+ 
+
+ align:start position:0%
+now for the purpose of this problem
+we're going to use the convention in one
+
+ align:start position:0%
+we're going to use the convention in one
+ 
+
+ align:start position:0%
+we're going to use the convention in one
+nadh is worse about 3 ATP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalent now later on in the pathway
+
+ align:start position:0%
+equivalent now later on in the pathway
+ 
+
+ align:start position:0%
+equivalent now later on in the pathway
+we're going to get to the Gap DH step
+
+ align:start position:0%
+we're going to get to the Gap DH step
+ 
+
+ align:start position:0%
+we're going to get to the Gap DH step
+where we generate one more nadh molecule
+
+ align:start position:0%
+where we generate one more nadh molecule
+ 
+
+ align:start position:0%
+where we generate one more nadh molecule
+so Gap d h another nadh molecule that's
+
+ align:start position:0%
+so Gap d h another nadh molecule that's
+ 
+
+ align:start position:0%
+so Gap d h another nadh molecule that's
+equivalent to three
+
+ align:start position:0%
+equivalent to three
+ 
+
+ align:start position:0%
+equivalent to three
+atps now as we're moving ahead we have
+
+ align:start position:0%
+atps now as we're moving ahead we have
+ 
+
+ align:start position:0%
+atps now as we're moving ahead we have
+the phospho glycerate kise step where we
+
+ align:start position:0%
+the phospho glycerate kise step where we
+ 
+
+ align:start position:0%
+the phospho glycerate kise step where we
+generate one ATP and then we have the
+
+ align:start position:0%
+generate one ATP and then we have the
+ 
+
+ align:start position:0%
+generate one ATP and then we have the
+pyrovate K step where generate one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ATP I have these written here so + one
+
+ align:start position:0%
+ATP I have these written here so + one
+ 
+
+ align:start position:0%
+ATP I have these written here so + one
+ATP and + one
+
+ align:start position:0%
+ATP and + one
+ 
+
+ align:start position:0%
+ATP and + one
+ATP now
+
+ align:start position:0%
+ATP now
+ 
+
+ align:start position:0%
+ATP now
+finally we know the pyate is going to be
+
+ align:start position:0%
+finally we know the pyate is going to be
+ 
+
+ align:start position:0%
+finally we know the pyate is going to be
+decarbox by the pyate dehydrogenase and
+
+ align:start position:0%
+decarbox by the pyate dehydrogenase and
+ 
+
+ align:start position:0%
+decarbox by the pyate dehydrogenase and
+here two we're generating one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nadh so plus one
+
+ align:start position:0%
+nadh so plus one
+ 
+
+ align:start position:0%
+nadh so plus one
+nadh that's going to be equivalent to
+
+ align:start position:0%
+nadh that's going to be equivalent to
+ 
+
+ align:start position:0%
+nadh that's going to be equivalent to
+three atps all right and finally the TCA
+
+ align:start position:0%
+three atps all right and finally the TCA
+ 
+
+ align:start position:0%
+three atps all right and finally the TCA
+cycle now we have one molecule of ail
+
+ align:start position:0%
+cycle now we have one molecule of ail
+ 
+
+ align:start position:0%
+cycle now we have one molecule of ail
+COA that enters the TCA
+
+ align:start position:0%
+COA that enters the TCA
+ 
+
+ align:start position:0%
+COA that enters the TCA
+cycle so
+
+ align:start position:0%
+cycle so
+ 
+
+ align:start position:0%
+cycle so
+as you guys know for every molecule of a
+
+ align:start position:0%
+as you guys know for every molecule of a
+ 
+
+ align:start position:0%
+as you guys know for every molecule of a
+COA enter the TCA cycle we're going to
+
+ align:start position:0%
+COA enter the TCA cycle we're going to
+ 
+
+ align:start position:0%
+COA enter the TCA cycle we're going to
+be generating 1 2 three
+
+ align:start position:0%
+be generating 1 2 three
+ 
+
+ align:start position:0%
+be generating 1 2 three
+nadh's one
+
+ align:start position:0%
+nadh's one
+ 
+
+ align:start position:0%
+nadh's one
+fadh2 and one
+
+ align:start position:0%
+fadh2 and one
+ 
+
+ align:start position:0%
+fadh2 and one
+GTP so the tally is three
+
+ align:start position:0%
+GTP so the tally is three
+ 
+
+ align:start position:0%
+GTP so the tally is three
+nadh one
+
+ align:start position:0%
+nadh one
+ 
+
+ align:start position:0%
+nadh one
+fadh2 and one
+
+ align:start position:0%
+fadh2 and one
+ 
+
+ align:start position:0%
+fadh2 and one
+GTP now GTP is equivalent to an ATP
+
+ align:start position:0%
+GTP now GTP is equivalent to an ATP
+ 
+
+ align:start position:0%
+GTP now GTP is equivalent to an ATP
+fadh2 counts as 2 atps and nadh counts
+
+ align:start position:0%
+fadh2 counts as 2 atps and nadh counts
+ 
+
+ align:start position:0%
+fadh2 counts as 2 atps and nadh counts
+as three atps so that's a grand total of
+
+ align:start position:0%
+as three atps so that's a grand total of
+ 
+
+ align:start position:0%
+as three atps so that's a grand total of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+atps so putting all of this together for
+
+ align:start position:0%
+atps so putting all of this together for
+ 
+
+ align:start position:0%
+atps so putting all of this together for
+one molecule of glycerol when fully
+
+ align:start position:0%
+one molecule of glycerol when fully
+ 
+
+ align:start position:0%
+one molecule of glycerol when fully
+metabolized to CO2 we get 22 ATP
+
+ align:start position:0%
+metabolized to CO2 we get 22 ATP
+ 
+
+ align:start position:0%
+metabolized to CO2 we get 22 ATP
+equivalents so that's the final answer
+
+ align:start position:0%
+equivalents so that's the final answer
+ 
+
+ align:start position:0%
+equivalents so that's the final answer
+for part C from one molecule of glycerol
+
+ align:start position:0%
+for part C from one molecule of glycerol
+ 
+
+ align:start position:0%
+for part C from one molecule of glycerol
+we get about 22 ATP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalents in part D of the proc
+
+ align:start position:0%
+equivalents in part D of the proc
+ 
+
+ align:start position:0%
+equivalents in part D of the proc
+problem we're tracing the same labels we
+
+ align:start position:0%
+problem we're tracing the same labels we
+ 
+
+ align:start position:0%
+problem we're tracing the same labels we
+had in part A but instead of tracing
+
+ align:start position:0%
+had in part A but instead of tracing
+ 
+
+ align:start position:0%
+had in part A but instead of tracing
+them to CO2 we're going to trace them to
+
+ align:start position:0%
+them to CO2 we're going to trace them to
+ 
+
+ align:start position:0%
+them to CO2 we're going to trace them to
+the amino acid
+
+ align:start position:0%
+the amino acid
+ 
+
+ align:start position:0%
+the amino acid
+alanine as you know one way to produce
+
+ align:start position:0%
+alanine as you know one way to produce
+ 
+
+ align:start position:0%
+alanine as you know one way to produce
+alanine is by transamination from pyate
+
+ align:start position:0%
+alanine is by transamination from pyate
+ 
+
+ align:start position:0%
+alanine is by transamination from pyate
+since we already tracked the label to
+
+ align:start position:0%
+since we already tracked the label to
+ 
+
+ align:start position:0%
+since we already tracked the label to
+pyrovate we need to know how do we
+
+ align:start position:0%
+pyrovate we need to know how do we
+ 
+
+ align:start position:0%
+pyrovate we need to know how do we
+convert pyrovate into
+
+ align:start position:0%
+convert pyrovate into
+ 
+
+ align:start position:0%
+convert pyrovate into
+alanine let's take a look at that
+
+ align:start position:0%
+alanine let's take a look at that
+ 
+
+ align:start position:0%
+alanine let's take a look at that
+reaction as you know Alpha keto acid
+
+ align:start position:0%
+reaction as you know Alpha keto acid
+ 
+
+ align:start position:0%
+reaction as you know Alpha keto acid
+such as pyrovate can be converted into
+
+ align:start position:0%
+such as pyrovate can be converted into
+ 
+
+ align:start position:0%
+such as pyrovate can be converted into
+amino acids by a transamination reaction
+
+ align:start position:0%
+amino acids by a transamination reaction
+ 
+
+ align:start position:0%
+amino acids by a transamination reaction
+here we're going to use another amino
+
+ align:start position:0%
+here we're going to use another amino
+ 
+
+ align:start position:0%
+here we're going to use another amino
+acid to donate the amino group to the
+
+ align:start position:0%
+acid to donate the amino group to the
+ 
+
+ align:start position:0%
+acid to donate the amino group to the
+alpha keto acid pyrovate to form alanine
+
+ align:start position:0%
+alpha keto acid pyrovate to form alanine
+ 
+
+ align:start position:0%
+alpha keto acid pyrovate to form alanine
+now all these transamination reactions
+
+ align:start position:0%
+now all these transamination reactions
+ 
+
+ align:start position:0%
+now all these transamination reactions
+are catalized by PLP or peroxy 5
+
+ align:start position:0%
+are catalized by PLP or peroxy 5
+ 
+
+ align:start position:0%
+are catalized by PLP or peroxy 5
+phosphate which is a co-actor derived
+
+ align:start position:0%
+phosphate which is a co-actor derived
+ 
+
+ align:start position:0%
+phosphate which is a co-actor derived
+from vitamin
+
+ align:start position:0%
+from vitamin
+ 
+
+ align:start position:0%
+from vitamin
+B6 so what it's left to WR in this
+
+ align:start position:0%
+B6 so what it's left to WR in this
+ 
+
+ align:start position:0%
+B6 so what it's left to WR in this
+transformation is the other pair of
+
+ align:start position:0%
+transformation is the other pair of
+ 
+
+ align:start position:0%
+transformation is the other pair of
+amino acid Alpha keto acid so basically
+
+ align:start position:0%
+amino acid Alpha keto acid so basically
+ 
+
+ align:start position:0%
+amino acid Alpha keto acid so basically
+where is this amino group coming from
+
+ align:start position:0%
+where is this amino group coming from
+ 
+
+ align:start position:0%
+where is this amino group coming from
+typically for most transaminases the
+
+ align:start position:0%
+typically for most transaminases the
+ 
+
+ align:start position:0%
+typically for most transaminases the
+other pair is glutamate Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ketoglutarate so we going to have
+
+ align:start position:0%
+ketoglutarate so we going to have
+ 
+
+ align:start position:0%
+ketoglutarate so we going to have
+glutamate it's going to donate the amino
+
+ align:start position:0%
+glutamate it's going to donate the amino
+ 
+
+ align:start position:0%
+glutamate it's going to donate the amino
+group and in the process going to become
+
+ align:start position:0%
+group and in the process going to become
+ 
+
+ align:start position:0%
+group and in the process going to become
+an alpha keto acid Alpha keto
+
+ align:start position:0%
+an alpha keto acid Alpha keto
+ 
+
+ align:start position:0%
+an alpha keto acid Alpha keto
+glutarate so in this way pyate becomes
+
+ align:start position:0%
+glutarate so in this way pyate becomes
+ 
+
+ align:start position:0%
+glutarate so in this way pyate becomes
+alanine now we were tracked in the label
+
+ align:start position:0%
+alanine now we were tracked in the label
+ 
+
+ align:start position:0%
+alanine now we were tracked in the label
+from this carbon so the carbon that will
+
+ align:start position:0%
+from this carbon so the carbon that will
+ 
+
+ align:start position:0%
+from this carbon so the carbon that will
+be lost at CO2 in the Pate dehydrogenate
+
+ align:start position:0%
+be lost at CO2 in the Pate dehydrogenate
+ 
+
+ align:start position:0%
+be lost at CO2 in the Pate dehydrogenate
+reaction so that is this carbon right
+
+ align:start position:0%
+reaction so that is this carbon right
+ 
+
+ align:start position:0%
+reaction so that is this carbon right
+here in pyate so in the transamination
+
+ align:start position:0%
+here in pyate so in the transamination
+ 
+
+ align:start position:0%
+here in pyate so in the transamination
+reaction this carbon becomes the carboxy
+
+ align:start position:0%
+reaction this carbon becomes the carboxy
+ 
+
+ align:start position:0%
+reaction this carbon becomes the carboxy
+carbon of
+
+ align:start position:0%
+carbon of
+ 
+
+ align:start position:0%
+carbon of
+alanine so if you were to start with a
+
+ align:start position:0%
+alanine so if you were to start with a
+ 
+
+ align:start position:0%
+alanine so if you were to start with a
+glycogen that was labeled at the three
+
+ align:start position:0%
+glycogen that was labeled at the three
+ 
+
+ align:start position:0%
+glycogen that was labeled at the three
+or four uh the carbons three and four
+
+ align:start position:0%
+or four uh the carbons three and four
+ 
+
+ align:start position:0%
+or four uh the carbons three and four
+that label would be l
+
+ align:start position:0%
+that label would be l
+ 
+
+ align:start position:0%
+that label would be l
+as CO2 in the parv dehydrogenase
+
+ align:start position:0%
+as CO2 in the parv dehydrogenase
+ 
+
+ align:start position:0%
+as CO2 in the parv dehydrogenase
+reaction as we saw in part A but also
+
+ align:start position:0%
+reaction as we saw in part A but also
+ 
+
+ align:start position:0%
+reaction as we saw in part A but also
+that label will be incorporated in
+
+ align:start position:0%
+that label will be incorporated in
+ 
+
+ align:start position:0%
+that label will be incorporated in
+alanine at the carboxy group of this
+
+ align:start position:0%
+alanine at the carboxy group of this
+ 
+
+ align:start position:0%
+alanine at the carboxy group of this
+amino
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid Parts E and F of the problem deal
+
+ align:start position:0%
+acid Parts E and F of the problem deal
+ 
+
+ align:start position:0%
+acid Parts E and F of the problem deal
+with chasing labels to the amino acids
+
+ align:start position:0%
+with chasing labels to the amino acids
+ 
+
+ align:start position:0%
+with chasing labels to the amino acids
+glutamate and aspartate now both of
+
+ align:start position:0%
+glutamate and aspartate now both of
+ 
+
+ align:start position:0%
+glutamate and aspartate now both of
+these amino acids have their
+
+ align:start position:0%
+these amino acids have their
+ 
+
+ align:start position:0%
+these amino acids have their
+corresponding Alpha keto acids as part
+
+ align:start position:0%
+corresponding Alpha keto acids as part
+ 
+
+ align:start position:0%
+corresponding Alpha keto acids as part
+of the TCA cycle so let's first take a
+
+ align:start position:0%
+of the TCA cycle so let's first take a
+ 
+
+ align:start position:0%
+of the TCA cycle so let's first take a
+look at this TCA cycle here we have the
+
+ align:start position:0%
+look at this TCA cycle here we have the
+ 
+
+ align:start position:0%
+look at this TCA cycle here we have the
+TCA cycle where I
+
+ align:start position:0%
+TCA cycle where I
+ 
+
+ align:start position:0%
+TCA cycle where I
+highlighted uh Alpha ketoglutarate going
+
+ align:start position:0%
+highlighted uh Alpha ketoglutarate going
+ 
+
+ align:start position:0%
+highlighted uh Alpha ketoglutarate going
+into glutamate through a transamination
+
+ align:start position:0%
+into glutamate through a transamination
+ 
+
+ align:start position:0%
+into glutamate through a transamination
+reaction Alpha ketoglutarate and Alpha
+
+ align:start position:0%
+reaction Alpha ketoglutarate and Alpha
+ 
+
+ align:start position:0%
+reaction Alpha ketoglutarate and Alpha
+keto acid can undergo a PLP catalyzed
+
+ align:start position:0%
+keto acid can undergo a PLP catalyzed
+ 
+
+ align:start position:0%
+keto acid can undergo a PLP catalyzed
+transamination to form glutamate and
+
+ align:start position:0%
+transamination to form glutamate and
+ 
+
+ align:start position:0%
+transamination to form glutamate and
+similarly oxaloacetate and another Alpha
+
+ align:start position:0%
+similarly oxaloacetate and another Alpha
+ 
+
+ align:start position:0%
+similarly oxaloacetate and another Alpha
+keto acid can trans aminate to form
+
+ align:start position:0%
+keto acid can trans aminate to form
+ 
+
+ align:start position:0%
+keto acid can trans aminate to form
+aspartate now in Part B of the problem
+
+ align:start position:0%
+aspartate now in Part B of the problem
+ 
+
+ align:start position:0%
+aspartate now in Part B of the problem
+we are looking at the label present at
+
+ align:start position:0%
+we are looking at the label present at
+ 
+
+ align:start position:0%
+we are looking at the label present at
+Carbon 1 in actil COA have we said that
+
+ align:start position:0%
+Carbon 1 in actil COA have we said that
+ 
+
+ align:start position:0%
+Carbon 1 in actil COA have we said that
+this label will stay inside the
+
+ align:start position:0%
+this label will stay inside the
+ 
+
+ align:start position:0%
+this label will stay inside the
+intermediates of the TCA cycle for the
+
+ align:start position:0%
+intermediates of the TCA cycle for the
+ 
+
+ align:start position:0%
+intermediates of the TCA cycle for the
+whole round
+
+ align:start position:0%
+whole round
+ 
+
+ align:start position:0%
+whole round
+now when this label gets the alpha
+
+ align:start position:0%
+now when this label gets the alpha
+ 
+
+ align:start position:0%
+now when this label gets the alpha
+ketoglutarate it's going to be on this
+
+ align:start position:0%
+ketoglutarate it's going to be on this
+ 
+
+ align:start position:0%
+ketoglutarate it's going to be on this
+carboxy group so in the transamination
+
+ align:start position:0%
+carboxy group so in the transamination
+ 
+
+ align:start position:0%
+carboxy group so in the transamination
+reaction the label it's going to end
+
+ align:start position:0%
+reaction the label it's going to end
+ 
+
+ align:start position:0%
+reaction the label it's going to end
+completely on the furthermost carboxy in
+
+ align:start position:0%
+completely on the furthermost carboxy in
+ 
+
+ align:start position:0%
+completely on the furthermost carboxy in
+glutamate so that takes care of part e
+
+ align:start position:0%
+glutamate so that takes care of part e
+ 
+
+ align:start position:0%
+glutamate so that takes care of part e
+now if we continue uh facing this label
+
+ align:start position:0%
+now if we continue uh facing this label
+ 
+
+ align:start position:0%
+now if we continue uh facing this label
+once we get to the succinate the label
+
+ align:start position:0%
+once we get to the succinate the label
+ 
+
+ align:start position:0%
+once we get to the succinate the label
+is going to split half and
+
+ align:start position:0%
+is going to split half and
+ 
+
+ align:start position:0%
+is going to split half and
+half between these two carboxy groups
+
+ align:start position:0%
+half between these two carboxy groups
+ 
+
+ align:start position:0%
+half between these two carboxy groups
+because we cannot
+
+ align:start position:0%
+because we cannot
+ 
+
+ align:start position:0%
+because we cannot
+tell uh which one because the molecule
+
+ align:start position:0%
+tell uh which one because the molecule
+ 
+
+ align:start position:0%
+tell uh which one because the molecule
+is going to be symmetric similarly for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fumerate and in malate as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so in
+
+ align:start position:0%
+well so in
+ 
+
+ align:start position:0%
+well so in
+oxaloacetate the label is going to be on
+
+ align:start position:0%
+oxaloacetate the label is going to be on
+ 
+
+ align:start position:0%
+oxaloacetate the label is going to be on
+both of the carboxy group half of the
+
+ align:start position:0%
+both of the carboxy group half of the
+ 
+
+ align:start position:0%
+both of the carboxy group half of the
+molecules will have it on one half of
+
+ align:start position:0%
+molecules will have it on one half of
+ 
+
+ align:start position:0%
+molecules will have it on one half of
+the molecules will have it on the other
+
+ align:start position:0%
+the molecules will have it on the other
+ 
+
+ align:start position:0%
+the molecules will have it on the other
+so therefore the aspartate is going to
+
+ align:start position:0%
+so therefore the aspartate is going to
+ 
+
+ align:start position:0%
+so therefore the aspartate is going to
+mirror that label distribution half
+
+ align:start position:0%
+mirror that label distribution half
+ 
+
+ align:start position:0%
+mirror that label distribution half
+label on one carboxy half label on the
+
+ align:start position:0%
+label on one carboxy half label on the
+ 
+
+ align:start position:0%
+label on one carboxy half label on the
+other carboxy so that should answer the
+
+ align:start position:0%
+other carboxy so that should answer the
+ 
+
+ align:start position:0%
+other carboxy so that should answer the
+final part of this problem now I hope
+
+ align:start position:0%
+final part of this problem now I hope
+ 
+
+ align:start position:0%
+final part of this problem now I hope
+this problem gave you a better
+
+ align:start position:0%
+this problem gave you a better
+ 
+
+ align:start position:0%
+this problem gave you a better
+understanding of what it means to chase
+
+ align:start position:0%
+understanding of what it means to chase
+ 
+
+ align:start position:0%
+understanding of what it means to chase
+labels to biochemical Pathways and also
+
+ align:start position:0%
+labels to biochemical Pathways and also
+ 
+
+ align:start position:0%
+labels to biochemical Pathways and also
+the chasing labels can help us better
+
+ align:start position:0%
+the chasing labels can help us better
+ 
+
+ align:start position:0%
+the chasing labels can help us better
+understand the mechanism of biochemical
+
+ align:start position:0%
+understand the mechanism of biochemical
+ 
+
+ align:start position:0%
+understand the mechanism of biochemical
+transformations
\ No newline at end of file
diff --git a/4DX9GM_kZmc.txt b/4DX9GM_kZmc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0323f907e5dbbdd38dce9db7d71afa80574183de
--- /dev/null
+++ b/4DX9GM_kZmc.txt
@@ -0,0 +1,12473 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I'm going to go through a
+
+ align:start position:0%
+ocw.mit.edu I'm going to go through a
+ 
+
+ align:start position:0%
+ocw.mit.edu I'm going to go through a
+number of cases with you today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll have to rely
+
+ align:start position:0%
+so we'll have to rely
+ 
+
+ align:start position:0%
+so we'll have to rely
+on sometimes on this handout sometimes
+
+ align:start position:0%
+on sometimes on this handout sometimes
+ 
+
+ align:start position:0%
+on sometimes on this handout sometimes
+on the slides let me first tell you what
+
+ align:start position:0%
+on the slides let me first tell you what
+ 
+
+ align:start position:0%
+on the slides let me first tell you what
+the handout is
+
+ align:start position:0%
+the handout is
+ 
+
+ align:start position:0%
+the handout is
+contains the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first is an example from Philip Bon's
+
+ align:start position:0%
+first is an example from Philip Bon's
+ 
+
+ align:start position:0%
+first is an example from Philip Bon's
+book lived in
+
+ align:start position:0%
+book lived in
+ 
+
+ align:start position:0%
+book lived in
+architecture this is the housing for
+
+ align:start position:0%
+architecture this is the housing for
+ 
+
+ align:start position:0%
+architecture this is the housing for
+steel workers at Pak near
+
+ align:start position:0%
+steel workers at Pak near
+ 
+
+ align:start position:0%
+steel workers at Pak near
+bordo which budon studied
+
+ align:start position:0%
+bordo which budon studied
+ 
+
+ align:start position:0%
+bordo which budon studied
+after a large after a period of time and
+
+ align:start position:0%
+after a large after a period of time and
+ 
+
+ align:start position:0%
+after a large after a period of time and
+made these
+
+ align:start position:0%
+made these
+ 
+
+ align:start position:0%
+made these
+drawings of the changes that people had
+
+ align:start position:0%
+drawings of the changes that people had
+ 
+
+ align:start position:0%
+drawings of the changes that people had
+made to the original plan which is the
+
+ align:start position:0%
+made to the original plan which is the
+ 
+
+ align:start position:0%
+made to the original plan which is the
+top
+
+ align:start position:0%
+top
+ 
+
+ align:start position:0%
+top
+left the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elevations indicate a couple of things
+
+ align:start position:0%
+elevations indicate a couple of things
+ 
+
+ align:start position:0%
+elevations indicate a couple of things
+because I'm not going to go into any
+
+ align:start position:0%
+because I'm not going to go into any
+ 
+
+ align:start position:0%
+because I'm not going to go into any
+detail about this
+
+ align:start position:0%
+detail about this
+ 
+
+ align:start position:0%
+detail about this
+example um people enclosed the the open
+
+ align:start position:0%
+example um people enclosed the the open
+ 
+
+ align:start position:0%
+example um people enclosed the the open
+porch of koues to make
+
+ align:start position:0%
+porch of koues to make
+ 
+
+ align:start position:0%
+porch of koues to make
+garages they replaced long linear
+
+ align:start position:0%
+garages they replaced long linear
+ 
+
+ align:start position:0%
+garages they replaced long linear
+windows by rectangular Windows of a much
+
+ align:start position:0%
+windows by rectangular Windows of a much
+ 
+
+ align:start position:0%
+windows by rectangular Windows of a much
+more uh oblong
+
+ align:start position:0%
+more uh oblong
+ 
+
+ align:start position:0%
+more uh oblong
+nature arguing that K's windows were not
+
+ align:start position:0%
+nature arguing that K's windows were not
+ 
+
+ align:start position:0%
+nature arguing that K's windows were not
+modern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough and so on and so on when kizzi
+
+ align:start position:0%
+enough and so on and so on when kizzi
+ 
+
+ align:start position:0%
+enough and so on and so on when kizzi
+was asked by Buon about these
+
+ align:start position:0%
+was asked by Buon about these
+ 
+
+ align:start position:0%
+was asked by Buon about these
+changes he said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as if grammatically as possible life is
+
+ align:start position:0%
+as if grammatically as possible life is
+ 
+
+ align:start position:0%
+as if grammatically as possible life is
+more important than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+art but there was no con there was no
+
+ align:start position:0%
+art but there was no con there was no
+ 
+
+ align:start position:0%
+art but there was no con there was no
+indication that he expect Ed or made
+
+ align:start position:0%
+indication that he expect Ed or made
+ 
+
+ align:start position:0%
+indication that he expect Ed or made
+Provisions for changes to take
+
+ align:start position:0%
+Provisions for changes to take
+ 
+
+ align:start position:0%
+Provisions for changes to take
+place he was Central to
+
+ align:start position:0%
+place he was Central to
+ 
+
+ align:start position:0%
+place he was Central to
+modernism that time was captured within
+
+ align:start position:0%
+modernism that time was captured within
+ 
+
+ align:start position:0%
+modernism that time was captured within
+the space of the
+
+ align:start position:0%
+the space of the
+ 
+
+ align:start position:0%
+the space of the
+project he neither looked
+
+ align:start position:0%
+project he neither looked
+ 
+
+ align:start position:0%
+project he neither looked
+forward to changes that could be made
+
+ align:start position:0%
+forward to changes that could be made
+ 
+
+ align:start position:0%
+forward to changes that could be made
+nor did you look back to the possibility
+
+ align:start position:0%
+nor did you look back to the possibility
+ 
+
+ align:start position:0%
+nor did you look back to the possibility
+of history or memory affecting your work
+
+ align:start position:0%
+of history or memory affecting your work
+ 
+
+ align:start position:0%
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+so modernism as I try to indicate on
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+
+ align:start position:0%
+so modernism as I try to indicate on
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
+objects which had no reference backwards
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+
+ align:start position:0%
+of any
+ 
+
+ align:start position:0%
+of any
+Value Kia is a classic example the man
+
+ align:start position:0%
+Value Kia is a classic example the man
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+who denies the 19th century
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+
+ align:start position:0%
+who denies the 19th century
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+ align:start position:0%
+Street
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+
+ align:start position:0%
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+ align:start position:0%
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+forever and then proceeds
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+
+ align:start position:0%
+the steel workers themselves find the
+ 
+
+ align:start position:0%
+the steel workers themselves find the
+capacity to change without the change
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+ align:start position:0%
+capacity to change without the change
+ 
+
+ align:start position:0%
+capacity to change without the change
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+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+premeditated we're going to be looking
+
+ align:start position:0%
+premeditated we're going to be looking
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+
+ align:start position:0%
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+today at the issue of looking
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+forward and what predictable what
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+
+ align:start position:0%
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+unpredictability
+
+ align:start position:0%
+unpredictability
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+means I will make I will use the case of
+MIT on the second and third
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page you will see the plan of MIT from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
+from
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+ align:start position:0%
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+
+ align:start position:0%
+1916 to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+2004 I was discuss Maria
+
+ align:start position:0%
+2004 I was discuss Maria
+ 
+
+ align:start position:0%
+2004 I was discuss Maria
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found next two pages are from Rodrigo
+
+ align:start position:0%
+found next two pages are from Rodrigo
+ 
+
+ align:start position:0%
+found next two pages are from Rodrigo
+Perez D
+
+ align:start position:0%
+Perez D
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+
+ align:start position:0%
+Perez D
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+ align:start position:0%
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+ 
+
+ align:start position:0%
+work arguing
+that systematic adding on to existing
+
+ align:start position:0%
+that systematic adding on to existing
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+
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+that systematic adding on to existing
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+ align:start position:0%
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+
+ align:start position:0%
+buildings is an opportunity for good
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not at the top isn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+Rodrigo Perez de AR a
+
+ align:start position:0%
+Rodrigo Perez de AR a
+ 
+
+ align:start position:0%
+Rodrigo Perez de AR a
+rce he's from he's from Colombia do you
+
+ align:start position:0%
+rce he's from he's from Colombia do you
+ 
+
+ align:start position:0%
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+know him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+not he's a quiet man
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+ align:start position:0%
+not he's a quiet man
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+not he's a quiet man
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+who
+ 
+
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+um uh draws very beautiful
+
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+um uh draws very beautiful
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+
+ align:start position:0%
+um uh draws very beautiful
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+drawings the
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+ align:start position:0%
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+
+ align:start position:0%
+servant in the larger reading list for
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+
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+
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+this class you'll find the reference
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+
+ align:start position:0%
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+it's it's published in architectural
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+London
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+I will show some examples of his
+
+ align:start position:0%
+I will show some examples of his
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+
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+I will show some examples of his
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+ align:start position:0%
+um the next two pages
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+
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+um the next two pages
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+are drawings by Louie khah and Allison
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+
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+are drawings by Louie khah and Allison
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+flows the next few pages are plans of
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+flows the next few pages are plans of
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+European universities from 1961 onwards
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+
+ align:start position:0%
+European universities from 1961 onwards
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
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+
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+1963 all slowly dealing with the
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+
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+ 
+ 
+
+ align:start position:0%
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+okay
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+
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+the reaction after the end of
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+ align:start position:0%
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+ 
+
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+cim was in the hands of a small group of
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+cim was in the hands of a small group of
+ 
+
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+cim was in the hands of a small group of
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+
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+Architects called team
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+
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+Architects called team
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+
+ align:start position:0%
+10 who put forward the
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+
+ align:start position:0%
+10 who put forward the
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+possibility that time could be escaped
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+possibility that time could be escaped
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+from that's my words they didn't write
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+from that's my words they didn't write
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+
+ align:start position:0%
+it Allison pet smithson's team 10
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+
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+ 
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+
+ align:start position:0%
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+ align:start position:0%
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+
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+
+ align:start position:0%
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+ 
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+probability they
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+permanent secondly they were interested
+
+ align:start position:0%
+permanent secondly they were interested
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+in flow in the the the idea that
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+
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+in flow in the the the idea that
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+
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+movement systems particularly those that
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+
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+movement systems particularly those that
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+fundamental Al to the
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+ align:start position:0%
+fundamental Al to the
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+
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+
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+thirdly they try to argue for kind of
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+thirdly they try to argue for kind of
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+ align:start position:0%
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+occasion as it occurred in most Urban
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+
+ align:start position:0%
+words like most Architects do soop
+ 
+
+ align:start position:0%
+words like most Architects do soop
+Plastics is the
+
+ align:start position:0%
+Plastics is the
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+
+ align:start position:0%
+Plastics is the
+invention uh soop Plastics is that word
+
+ align:start position:0%
+invention uh soop Plastics is that word
+ 
+
+ align:start position:0%
+invention uh soop Plastics is that word
+which Embraces what painters like
+
+ align:start position:0%
+which Embraces what painters like
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+
+ align:start position:0%
+which Embraces what painters like
+Richard Hamilton and Eduardo paroi were
+
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+Richard Hamilton and Eduardo paroi were
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+
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+painting um it's interesting how a few
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+
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+architects of the modern movement or the
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+
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+
+ align:start position:0%
+association with painting Frank giri and
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+
+ align:start position:0%
+association with painting Frank giri and
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+
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+
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+ align:start position:0%
+largely in Paris and in
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+
+ align:start position:0%
+largely in Paris and in
+Europe um
+
+ align:start position:0%
+Europe um
+ 
+
+ align:start position:0%
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+so we
+
+ align:start position:0%
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+ 
+
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+
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+are Central to team 10's work we will
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+
+ align:start position:0%
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+
+ align:start position:0%
+look a little bit at Team 10's work but
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+
+ align:start position:0%
+look a little bit at Team 10's work but
+I haven't got the time in this class to
+
+ align:start position:0%
+I haven't got the time in this class to
+ 
+
+ align:start position:0%
+I haven't got the time in this class to
+dorate fully on team 10 and the
+
+ align:start position:0%
+dorate fully on team 10 and the
+ 
+
+ align:start position:0%
+dorate fully on team 10 and the
+architecture of the and urbanistic
+
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+architecture of the and urbanistic
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+
+ align:start position:0%
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+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+um we have to accept that you cannot
+
+ align:start position:0%
+um we have to accept that you cannot
+ 
+
+ align:start position:0%
+um we have to accept that you cannot
+predict the
+
+ align:start position:0%
+predict the
+ 
+
+ align:start position:0%
+predict the
+future
+
+ align:start position:0%
+future
+ 
+
+ align:start position:0%
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+uh there's a book by Paul omod in
+
+ align:start position:0%
+uh there's a book by Paul omod in
+ 
+
+ align:start position:0%
+uh there's a book by Paul omod in
+Englishman called why most things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fail which sets out
+
+ align:start position:0%
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+
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+
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+that we may intend to give to achieve a
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+
+ align:start position:0%
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+
+ align:start position:0%
+particular outcome but the complexity of
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+
+ align:start position:0%
+particular outcome but the complexity of
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+
+ align:start position:0%
+the world world even in apparently
+ 
+
+ align:start position:0%
+the world world even in apparently
+simple situations appears to be so great
+
+ align:start position:0%
+simple situations appears to be so great
+ 
+
+ align:start position:0%
+simple situations appears to be so great
+that it's not within our power to ordain
+
+ align:start position:0%
+that it's not within our power to ordain
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+
+ align:start position:0%
+that it's not within our power to ordain
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+
+ align:start position:0%
+the future he gives the
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+
+ align:start position:0%
+the future he gives the
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+of the world's largest the world's large
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+
+ align:start position:0%
+of the world's largest the world's large
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+companies in the period from 1912 to
+ 
+
+ align:start position:0%
+companies in the period from 1912 to
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+
+ align:start position:0%
+1995 out of the 100 largest industrial
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+1912 how many have survived in 199
+
+ align:start position:0%
+1912 how many have survived in 199
+ 
+
+ align:start position:0%
+1912 how many have survived in 199
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gu there's a good book called The Living
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+company
+
+ align:start position:0%
+company
+ 
+
+ align:start position:0%
+company
+stud company's over 200 years old to
+
+ align:start position:0%
+stud company's over 200 years old to
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+largest 100 disappeared 52% % survive so
+ 
+
+ align:start position:0%
+largest 100 disappeared 52% % survive so
+that means over 80 years you have a 50%
+
+ align:start position:0%
+that means over 80 years you have a 50%
+ 
+
+ align:start position:0%
+that means over 80 years you have a 50%
+chance of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+survival that's more than human beings
+
+ align:start position:0%
+survival that's more than human beings
+ 
+
+ align:start position:0%
+survival that's more than human beings
+yeah good it's pretty good he refers to
+
+ align:start position:0%
+yeah good it's pretty good he refers to
+ 
+
+ align:start position:0%
+yeah good it's pretty good he refers to
+the difference between risk and
+
+ align:start position:0%
+the difference between risk and
+ 
+
+ align:start position:0%
+the difference between risk and
+uncertainty uh risk
+
+ align:start position:0%
+uncertainty uh risk
+ 
+
+ align:start position:0%
+uncertainty uh risk
+being where the options are within a
+
+ align:start position:0%
+being where the options are within a
+ 
+
+ align:start position:0%
+being where the options are within a
+span of certainty such as flipping AC
+
+ align:start position:0%
+span of certainty such as flipping AC
+ 
+
+ align:start position:0%
+span of certainty such as flipping AC
+coin and uncertainty is where the
+
+ align:start position:0%
+coin and uncertainty is where the
+ 
+
+ align:start position:0%
+coin and uncertainty is where the
+options are very unclear such as a man
+
+ align:start position:0%
+options are very unclear such as a man
+ 
+
+ align:start position:0%
+options are very unclear such as a man
+or a couple of men from the moon landing
+
+ align:start position:0%
+or a couple of men from the moon landing
+ 
+
+ align:start position:0%
+or a couple of men from the moon landing
+on the earth which some people believe
+
+ align:start position:0%
+on the earth which some people believe
+ 
+
+ align:start position:0%
+on the earth which some people believe
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+um the difference between risk and
+
+ align:start position:0%
+um the difference between risk and
+ 
+
+ align:start position:0%
+um the difference between risk and
+uncertainty isn't easily discussed in
+
+ align:start position:0%
+uncertainty isn't easily discussed in
+ 
+
+ align:start position:0%
+uncertainty isn't easily discussed in
+the work of the people that I'm going to
+
+ align:start position:0%
+the work of the people that I'm going to
+ 
+
+ align:start position:0%
+the work of the people that I'm going to
+be arguing
+
+ align:start position:0%
+be arguing
+ 
+
+ align:start position:0%
+be arguing
+for uh there's a notion somehow that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the do do how much do you know of this
+
+ align:start position:0%
+the do do how much do you know of this
+ 
+
+ align:start position:0%
+the do do how much do you know of this
+work who knows about the Free University
+
+ align:start position:0%
+work who knows about the Free University
+ 
+
+ align:start position:0%
+work who knows about the Free University
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Berlin one person you're all very
+
+ align:start position:0%
+Berlin one person you're all very
+ 
+
+ align:start position:0%
+Berlin one person you're all very
+ignorant if I might say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we don't teach history
+
+ align:start position:0%
+so we don't teach history
+ 
+
+ align:start position:0%
+so we don't teach history
+properly we don't teach Urban history at
+
+ align:start position:0%
+properly we don't teach Urban history at
+ 
+
+ align:start position:0%
+properly we don't teach Urban history at
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+all I've complained about this for most
+
+ align:start position:0%
+all I've complained about this for most
+ 
+
+ align:start position:0%
+all I've complained about this for most
+of my career and seeing this is the last
+
+ align:start position:0%
+of my career and seeing this is the last
+ 
+
+ align:start position:0%
+of my career and seeing this is the last
+time I have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complain I I'll complain
+
+ align:start position:0%
+complain I I'll complain
+ 
+
+ align:start position:0%
+complain I I'll complain
+finally for for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+record all right we'll talk about the
+
+ align:start position:0%
+record all right we'll talk about the
+ 
+
+ align:start position:0%
+record all right we'll talk about the
+Free University in Bain project by
+
+ align:start position:0%
+Free University in Bain project by
+ 
+
+ align:start position:0%
+Free University in Bain project by
+shadra Woods um let's just list if we
+
+ align:start position:0%
+shadra Woods um let's just list if we
+ 
+
+ align:start position:0%
+shadra Woods um let's just list if we
+can some of the convention
+
+ align:start position:0%
+can some of the convention
+ 
+
+ align:start position:0%
+can some of the convention
+methods of achieving flexibility in
+
+ align:start position:0%
+methods of achieving flexibility in
+ 
+
+ align:start position:0%
+methods of achieving flexibility in
+cities number one land
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+banking you
+
+ align:start position:0%
+banking you
+ 
+
+ align:start position:0%
+banking you
+can endow land with cheap uses farming
+
+ align:start position:0%
+can endow land with cheap uses farming
+ 
+
+ align:start position:0%
+can endow land with cheap uses farming
+parking lots and so on on the grounds
+
+ align:start position:0%
+parking lots and so on on the grounds
+ 
+
+ align:start position:0%
+parking lots and so on on the grounds
+that in future when land becomes more
+
+ align:start position:0%
+that in future when land becomes more
+ 
+
+ align:start position:0%
+that in future when land becomes more
+scarce they will be able to be reused
+
+ align:start position:0%
+scarce they will be able to be reused
+ 
+
+ align:start position:0%
+scarce they will be able to be reused
+without much
+
+ align:start position:0%
+without much
+ 
+
+ align:start position:0%
+without much
+demolition farming is not an option
+
+ align:start position:0%
+demolition farming is not an option
+ 
+
+ align:start position:0%
+demolition farming is not an option
+which has been used in urbanism very
+
+ align:start position:0%
+which has been used in urbanism very
+ 
+
+ align:start position:0%
+which has been used in urbanism very
+much if at
+
+ align:start position:0%
+much if at
+ 
+
+ align:start position:0%
+much if at
+all farming in New York is on Terraces
+
+ align:start position:0%
+all farming in New York is on Terraces
+ 
+
+ align:start position:0%
+all farming in New York is on Terraces
+in high 100 100 ft above the ground or
+
+ align:start position:0%
+in high 100 100 ft above the ground or
+ 
+
+ align:start position:0%
+in high 100 100 ft above the ground or
+th000 ft above the ground
+
+ align:start position:0%
+th000 ft above the ground
+ 
+
+ align:start position:0%
+th000 ft above the ground
+um secondly easement easements
+
+ align:start position:0%
+um secondly easement easements
+ 
+
+ align:start position:0%
+um secondly easement easements
+are rights of
+
+ align:start position:0%
+are rights of
+ 
+
+ align:start position:0%
+are rights of
+way which
+
+ align:start position:0%
+way which
+ 
+
+ align:start position:0%
+way which
+uh can be endowed
+
+ align:start position:0%
+uh can be endowed
+ 
+
+ align:start position:0%
+uh can be endowed
+with um limited
+
+ align:start position:0%
+with um limited
+ 
+
+ align:start position:0%
+with um limited
+use such as on the sides of
+
+ align:start position:0%
+use such as on the sides of
+ 
+
+ align:start position:0%
+use such as on the sides of
+Highways when we spoke about Robert
+
+ align:start position:0%
+Highways when we spoke about Robert
+ 
+
+ align:start position:0%
+Highways when we spoke about Robert
+Moses
+
+ align:start position:0%
+Moses
+ 
+
+ align:start position:0%
+Moses
+I spoke about the lack of his provision
+
+ align:start position:0%
+I spoke about the lack of his provision
+ 
+
+ align:start position:0%
+I spoke about the lack of his provision
+of easements on his
+
+ align:start position:0%
+of easements on his
+ 
+
+ align:start position:0%
+of easements on his
+freeways the cost of providing the
+
+ align:start position:0%
+freeways the cost of providing the
+ 
+
+ align:start position:0%
+freeways the cost of providing the
+easement would have been would have
+
+ align:start position:0%
+easement would have been would have
+ 
+
+ align:start position:0%
+easement would have been would have
+allowed the a the addition of public
+
+ align:start position:0%
+allowed the a the addition of public
+ 
+
+ align:start position:0%
+allowed the a the addition of public
+transportation on these next to these
+
+ align:start position:0%
+transportation on these next to these
+ 
+
+ align:start position:0%
+transportation on these next to these
+roads at a cost which is now estimated
+
+ align:start position:0%
+roads at a cost which is now estimated
+ 
+
+ align:start position:0%
+roads at a cost which is now estimated
+to be a fraction of what it now would
+
+ align:start position:0%
+to be a fraction of what it now would
+ 
+
+ align:start position:0%
+to be a fraction of what it now would
+cost to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you
+
+ align:start position:0%
+so you
+ 
+
+ align:start position:0%
+so you
+allow the possibility of an event taking
+
+ align:start position:0%
+allow the possibility of an event taking
+ 
+
+ align:start position:0%
+allow the possibility of an event taking
+place on land which is easily available
+
+ align:start position:0%
+place on land which is easily available
+ 
+
+ align:start position:0%
+place on land which is easily available
+and costs very little initially but
+
+ align:start position:0%
+and costs very little initially but
+ 
+
+ align:start position:0%
+and costs very little initially but
+increases in value as time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+passes the problem with prediction is
+
+ align:start position:0%
+passes the problem with prediction is
+ 
+
+ align:start position:0%
+passes the problem with prediction is
+that there's a difference between the
+
+ align:start position:0%
+that there's a difference between the
+ 
+
+ align:start position:0%
+that there's a difference between the
+right prediction and excessive
+
+ align:start position:0%
+right prediction and excessive
+ 
+
+ align:start position:0%
+right prediction and excessive
+prediction now not it's between too
+
+ align:start position:0%
+prediction now not it's between too
+ 
+
+ align:start position:0%
+prediction now not it's between too
+little pred too little response and too
+
+ align:start position:0%
+little pred too little response and too
+ 
+
+ align:start position:0%
+little pred too little response and too
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+response prediction costs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+money under most circumstances so you
+
+ align:start position:0%
+money under most circumstances so you
+ 
+
+ align:start position:0%
+money under most circumstances so you
+have to you can also do excessive
+
+ align:start position:0%
+have to you can also do excessive
+ 
+
+ align:start position:0%
+have to you can also do excessive
+prediction I think I showed you a
+
+ align:start position:0%
+prediction I think I showed you a
+ 
+
+ align:start position:0%
+prediction I think I showed you a
+diagram of a South African mining town a
+
+ align:start position:0%
+diagram of a South African mining town a
+ 
+
+ align:start position:0%
+diagram of a South African mining town a
+classic case where the town was designed
+
+ align:start position:0%
+classic case where the town was designed
+ 
+
+ align:start position:0%
+classic case where the town was designed
+so that the Central Business could
+
+ align:start position:0%
+so that the Central Business could
+ 
+
+ align:start position:0%
+so that the Central Business could
+expand the expansion area around the
+
+ align:start position:0%
+expand the expansion area around the
+ 
+
+ align:start position:0%
+expand the expansion area around the
+center of the city was so poorly treated
+
+ align:start position:0%
+center of the city was so poorly treated
+ 
+
+ align:start position:0%
+center of the city was so poorly treated
+so badly landscaped and not landscaped
+
+ align:start position:0%
+so badly landscaped and not landscaped
+ 
+
+ align:start position:0%
+so badly landscaped and not landscaped
+at all it was just
+
+ align:start position:0%
+at all it was just
+ 
+
+ align:start position:0%
+at all it was just
+dirt it in fact cause the Central
+
+ align:start position:0%
+dirt it in fact cause the Central
+ 
+
+ align:start position:0%
+dirt it in fact cause the Central
+Business area not only to grow but to
+
+ align:start position:0%
+Business area not only to grow but to
+ 
+
+ align:start position:0%
+Business area not only to grow but to
+decline in size instead of to
+
+ align:start position:0%
+decline in size instead of to
+ 
+
+ align:start position:0%
+decline in size instead of to
+expand ex leaving land for
+
+ align:start position:0%
+expand ex leaving land for
+ 
+
+ align:start position:0%
+expand ex leaving land for
+expansion is one of the ideas that we
+
+ align:start position:0%
+expansion is one of the ideas that we
+ 
+
+ align:start position:0%
+expansion is one of the ideas that we
+look at a bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carefully you can leave open space for
+
+ align:start position:0%
+carefully you can leave open space for
+ 
+
+ align:start position:0%
+carefully you can leave open space for
+consumption as assuming a coarse grain
+
+ align:start position:0%
+consumption as assuming a coarse grain
+ 
+
+ align:start position:0%
+consumption as assuming a coarse grain
+in your
+
+ align:start position:0%
+in your
+ 
+
+ align:start position:0%
+in your
+town I will show you the example of the
+
+ align:start position:0%
+town I will show you the example of the
+ 
+
+ align:start position:0%
+town I will show you the example of the
+so so Olympics in
+
+ align:start position:0%
+so so Olympics in
+ 
+
+ align:start position:0%
+so so Olympics in
+1988 which built its Olympic Games on
+
+ align:start position:0%
+1988 which built its Olympic Games on
+ 
+
+ align:start position:0%
+1988 which built its Olympic Games on
+the basis
+
+ align:start position:0%
+the basis
+ 
+
+ align:start position:0%
+the basis
+of Fairly large open space
+
+ align:start position:0%
+of Fairly large open space
+ 
+
+ align:start position:0%
+of Fairly large open space
+system who knows the 1988 Olympic
+
+ align:start position:0%
+system who knows the 1988 Olympic
+ 
+
+ align:start position:0%
+system who knows the 1988 Olympic
+Games Were You There not at the game but
+
+ align:start position:0%
+Games Were You There not at the game but
+ 
+
+ align:start position:0%
+Games Were You There not at the game but
+I know the side you know the side yeah
+
+ align:start position:0%
+I know the side you know the side yeah
+ 
+
+ align:start position:0%
+I know the side you know the side yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+it's a classic example of the
+
+ align:start position:0%
+it's a classic example of the
+ 
+
+ align:start position:0%
+it's a classic example of the
+cannibalization of easy access space
+
+ align:start position:0%
+cannibalization of easy access space
+ 
+
+ align:start position:0%
+cannibalization of easy access space
+open space is easy access it's cheap not
+
+ align:start position:0%
+open space is easy access it's cheap not
+ 
+
+ align:start position:0%
+open space is easy access it's cheap not
+cheap in the Public's mind but cheaps in
+
+ align:start position:0%
+cheap in the Public's mind but cheaps in
+ 
+
+ align:start position:0%
+cheap in the Public's mind but cheaps in
+the cheap in the promoter's
+
+ align:start position:0%
+the cheap in the promoter's
+ 
+
+ align:start position:0%
+the cheap in the promoter's
+mind and most of the facilities
+
+ align:start position:0%
+mind and most of the facilities
+ 
+
+ align:start position:0%
+mind and most of the facilities
+including the Olympic Village by cang Wu
+
+ align:start position:0%
+including the Olympic Village by cang Wu
+ 
+
+ align:start position:0%
+including the Olympic Village by cang Wu
+who lives here in
+
+ align:start position:0%
+who lives here in
+ 
+
+ align:start position:0%
+who lives here in
+Cambridge was built on this available
+
+ align:start position:0%
+Cambridge was built on this available
+ 
+
+ align:start position:0%
+Cambridge was built on this available
+land will come to Soul 88 later
+
+ align:start position:0%
+land will come to Soul 88 later
+ 
+
+ align:start position:0%
+land will come to Soul 88 later
+on I'm just running through some of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these there infra infrastructure
+
+ align:start position:0%
+these there infra infrastructure
+ 
+
+ align:start position:0%
+these there infra infrastructure
+flexibility um when we designed the MIT
+
+ align:start position:0%
+flexibility um when we designed the MIT
+ 
+
+ align:start position:0%
+flexibility um when we designed the MIT
+brain and cognitive Sciences building we
+
+ align:start position:0%
+brain and cognitive Sciences building we
+ 
+
+ align:start position:0%
+brain and cognitive Sciences building we
+had to allow for the CX railroad to run
+
+ align:start position:0%
+had to allow for the CX railroad to run
+ 
+
+ align:start position:0%
+had to allow for the CX railroad to run
+underneath the
+
+ align:start position:0%
+underneath the
+ 
+
+ align:start position:0%
+underneath the
+building that meant uh an extraordinary
+
+ align:start position:0%
+building that meant uh an extraordinary
+ 
+
+ align:start position:0%
+building that meant uh an extraordinary
+difference in the kind of building which
+
+ align:start position:0%
+difference in the kind of building which
+ 
+
+ align:start position:0%
+difference in the kind of building which
+we could design
+
+ align:start position:0%
+we could design
+ 
+
+ align:start position:0%
+we could design
+but we calculated that if the
+
+ align:start position:0%
+but we calculated that if the
+ 
+
+ align:start position:0%
+but we calculated that if the
+Aires MIT owns the Aires over the CSX
+
+ align:start position:0%
+Aires MIT owns the Aires over the CSX
+ 
+
+ align:start position:0%
+Aires MIT owns the Aires over the CSX
+railroad about 22 ft or 15 M I'm not
+
+ align:start position:0%
+railroad about 22 ft or 15 M I'm not
+ 
+
+ align:start position:0%
+railroad about 22 ft or 15 M I'm not
+sure which I think it's 22 ft MIT can
+
+ align:start position:0%
+sure which I think it's 22 ft MIT can
+ 
+
+ align:start position:0%
+sure which I think it's 22 ft MIT can
+build 22 ft above the plane of the
+
+ align:start position:0%
+build 22 ft above the plane of the
+ 
+
+ align:start position:0%
+build 22 ft above the plane of the
+railroad we calculated when work working
+
+ align:start position:0%
+railroad we calculated when work working
+ 
+
+ align:start position:0%
+railroad we calculated when work working
+on this that if MIT exercised this
+
+ align:start position:0%
+on this that if MIT exercised this
+ 
+
+ align:start position:0%
+on this that if MIT exercised this
+option and built on the air maximum air
+
+ align:start position:0%
+option and built on the air maximum air
+ 
+
+ align:start position:0%
+option and built on the air maximum air
+rights that the well they they have the
+
+ align:start position:0%
+rights that the well they they have the
+ 
+
+ align:start position:0%
+rights that the well they they have the
+air rights the degree to which they can
+
+ align:start position:0%
+air rights the degree to which they can
+ 
+
+ align:start position:0%
+air rights the degree to which they can
+build vertically will have to be
+
+ align:start position:0%
+build vertically will have to be
+ 
+
+ align:start position:0%
+build vertically will have to be
+sanctioned by the city but we calculated
+
+ align:start position:0%
+sanctioned by the city but we calculated
+ 
+
+ align:start position:0%
+sanctioned by the city but we calculated
+that if MIT wish to expand its campus
+
+ align:start position:0%
+that if MIT wish to expand its campus
+ 
+
+ align:start position:0%
+that if MIT wish to expand its campus
+vertically over the
+
+ align:start position:0%
+vertically over the
+ 
+
+ align:start position:0%
+vertically over the
+airit or will the the the development
+
+ align:start position:0%
+airit or will the the the development
+ 
+
+ align:start position:0%
+airit or will the the the development
+would be worth billions of dollars in
+
+ align:start position:0%
+would be worth billions of dollars in
+ 
+
+ align:start position:0%
+would be worth billions of dollars in
+Cambridge terms of square
+
+ align:start position:0%
+Cambridge terms of square
+ 
+
+ align:start position:0%
+Cambridge terms of square
+footage so imagine the possibility of a
+
+ align:start position:0%
+footage so imagine the possibility of a
+ 
+
+ align:start position:0%
+footage so imagine the possibility of a
+future in which MIT could
+
+ align:start position:0%
+future in which MIT could
+ 
+
+ align:start position:0%
+future in which MIT could
+build above a railway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line fact is that we only Built to the
+
+ align:start position:0%
+line fact is that we only Built to the
+ 
+
+ align:start position:0%
+line fact is that we only Built to the
+height at Cambridge alars in our
+
+ align:start position:0%
+height at Cambridge alars in our
+ 
+
+ align:start position:0%
+height at Cambridge alars in our
+building which was large enough for our
+
+ align:start position:0%
+building which was large enough for our
+ 
+
+ align:start position:0%
+building which was large enough for our
+program
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this friction caused by a movement
+
+ align:start position:0%
+but this friction caused by a movement
+ 
+
+ align:start position:0%
+but this friction caused by a movement
+system Kia's proposition of building
+
+ align:start position:0%
+system Kia's proposition of building
+ 
+
+ align:start position:0%
+system Kia's proposition of building
+under the freeways in
+
+ align:start position:0%
+under the freeways in
+ 
+
+ align:start position:0%
+under the freeways in
+algers is not feasible
+
+ align:start position:0%
+algers is not feasible
+ 
+
+ align:start position:0%
+algers is not feasible
+anymore the noise and pollution caused
+
+ align:start position:0%
+anymore the noise and pollution caused
+ 
+
+ align:start position:0%
+anymore the noise and pollution caused
+by the automobiles would make it
+
+ align:start position:0%
+by the automobiles would make it
+ 
+
+ align:start position:0%
+by the automobiles would make it
+impossible to virtually possible to
+
+ align:start position:0%
+impossible to virtually possible to
+ 
+
+ align:start position:0%
+impossible to virtually possible to
+build under
+
+ align:start position:0%
+build under
+ 
+
+ align:start position:0%
+build under
+freeways one of the dramatic Futures in
+
+ align:start position:0%
+freeways one of the dramatic Futures in
+ 
+
+ align:start position:0%
+freeways one of the dramatic Futures in
+the next few 50 years is going to be to
+
+ align:start position:0%
+the next few 50 years is going to be to
+ 
+
+ align:start position:0%
+the next few 50 years is going to be to
+how to capture the space under elevated
+
+ align:start position:0%
+how to capture the space under elevated
+ 
+
+ align:start position:0%
+how to capture the space under elevated
+freeways all over the world they
+
+ align:start position:0%
+freeways all over the world they
+ 
+
+ align:start position:0%
+freeways all over the world they
+elevated con to considerable
+
+ align:start position:0%
+elevated con to considerable
+ 
+
+ align:start position:0%
+elevated con to considerable
+height because you have to be able to
+
+ align:start position:0%
+height because you have to be able to
+ 
+
+ align:start position:0%
+height because you have to be able to
+pass through with a truck which means
+
+ align:start position:0%
+pass through with a truck which means
+ 
+
+ align:start position:0%
+pass through with a truck which means
+that you have to have ramps which at 1
+
+ align:start position:0%
+that you have to have ramps which at 1
+ 
+
+ align:start position:0%
+that you have to have ramps which at 1
+in 10 or 1 in five depending how steep
+
+ align:start position:0%
+in 10 or 1 in five depending how steep
+ 
+
+ align:start position:0%
+in 10 or 1 in five depending how steep
+you are you can take up a large amount
+
+ align:start position:0%
+you are you can take up a large amount
+ 
+
+ align:start position:0%
+you are you can take up a large amount
+of space
+
+ align:start position:0%
+of space
+ 
+
+ align:start position:0%
+of space
+so I haven't seen a proposition in
+
+ align:start position:0%
+so I haven't seen a proposition in
+ 
+
+ align:start position:0%
+so I haven't seen a proposition in
+recent times anywhere in the world for
+
+ align:start position:0%
+recent times anywhere in the world for
+ 
+
+ align:start position:0%
+recent times anywhere in the world for
+capturing the space under a freeway in
+
+ align:start position:0%
+capturing the space under a freeway in
+ 
+
+ align:start position:0%
+capturing the space under a freeway in
+a in a positive sense we have one SM Mar
+
+ align:start position:0%
+a in a positive sense we have one SM Mar
+ 
+
+ align:start position:0%
+a in a positive sense we have one SM Mar
+student project thesis which you'll see
+
+ align:start position:0%
+student project thesis which you'll see
+ 
+
+ align:start position:0%
+student project thesis which you'll see
+in 3 weeks time which tries to do this
+
+ align:start position:0%
+in 3 weeks time which tries to do this
+ 
+
+ align:start position:0%
+in 3 weeks time which tries to do this
+in Boston with great
+
+ align:start position:0%
+in Boston with great
+ 
+
+ align:start position:0%
+in Boston with great
+difficulty but the
+
+ align:start position:0%
+difficulty but the
+ 
+
+ align:start position:0%
+difficulty but the
+Aires mean that a plane that the
+
+ align:start position:0%
+Aires mean that a plane that the
+ 
+
+ align:start position:0%
+Aires mean that a plane that the
+development above a plane which for the
+
+ align:start position:0%
+development above a plane which for the
+ 
+
+ align:start position:0%
+development above a plane which for the
+moment is used by a railroad or freeway
+
+ align:start position:0%
+moment is used by a railroad or freeway
+ 
+
+ align:start position:0%
+moment is used by a railroad or freeway
+and the development below that
+
+ align:start position:0%
+and the development below that
+ 
+
+ align:start position:0%
+and the development below that
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+even penetrating into the
+
+ align:start position:0%
+even penetrating into the
+ 
+
+ align:start position:0%
+even penetrating into the
+ground options which utopianist have
+
+ align:start position:0%
+ground options which utopianist have
+ 
+
+ align:start position:0%
+ground options which utopianist have
+examined and wondered about
+
+ align:start position:0%
+examined and wondered about
+ 
+
+ align:start position:0%
+examined and wondered about
+uh so we have to include them on our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+list lastly is the question of
+
+ align:start position:0%
+list lastly is the question of
+ 
+
+ align:start position:0%
+list lastly is the question of
+geometry and most of the rest of my talk
+
+ align:start position:0%
+geometry and most of the rest of my talk
+ 
+
+ align:start position:0%
+geometry and most of the rest of my talk
+is going to deal with a with people
+
+ align:start position:0%
+is going to deal with a with people
+ 
+
+ align:start position:0%
+is going to deal with a with people
+who've used the idea of geometry to
+
+ align:start position:0%
+who've used the idea of geometry to
+ 
+
+ align:start position:0%
+who've used the idea of geometry to
+allow for future
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+okay one of the people who argued for
+
+ align:start position:0%
+okay one of the people who argued for
+ 
+
+ align:start position:0%
+okay one of the people who argued for
+the impact of geometry is Maria Zero's
+
+ align:start position:0%
+the impact of geometry is Maria Zero's
+ 
+
+ align:start position:0%
+the impact of geometry is Maria Zero's
+thesis Maria was in this
+
+ align:start position:0%
+thesis Maria was in this
+ 
+
+ align:start position:0%
+thesis Maria was in this
+class and became interested in the idea
+
+ align:start position:0%
+class and became interested in the idea
+ 
+
+ align:start position:0%
+class and became interested in the idea
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+change she wanted to study a city W and
+
+ align:start position:0%
+change she wanted to study a city W and
+ 
+
+ align:start position:0%
+change she wanted to study a city W and
+how make some speculation about how
+
+ align:start position:0%
+how make some speculation about how
+ 
+
+ align:start position:0%
+how make some speculation about how
+Urban transport transformation took
+
+ align:start position:0%
+Urban transport transformation took
+ 
+
+ align:start position:0%
+Urban transport transformation took
+place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she decided after being
+
+ align:start position:0%
+she decided after being
+ 
+
+ align:start position:0%
+she decided after being
+forced to limited
+
+ align:start position:0%
+forced to limited
+ 
+
+ align:start position:0%
+forced to limited
+thesis to take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MIT
+
+ align:start position:0%
+MIT
+ 
+
+ align:start position:0%
+MIT
+MIT shadar Woods the architect of the
+
+ align:start position:0%
+MIT shadar Woods the architect of the
+ 
+
+ align:start position:0%
+MIT shadar Woods the architect of the
+firm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J oh forget the name of the French firm
+
+ align:start position:0%
+J oh forget the name of the French firm
+ 
+
+ align:start position:0%
+J oh forget the name of the French firm
+is an American
+
+ align:start position:0%
+is an American
+ 
+
+ align:start position:0%
+is an American
+architect who you developed the word
+
+ align:start position:0%
+architect who you developed the word
+ 
+
+ align:start position:0%
+architect who you developed the word
+ground scraper as a model of MIT and
+
+ align:start position:0%
+ground scraper as a model of MIT and
+ 
+
+ align:start position:0%
+ground scraper as a model of MIT and
+used as the basis for the design of his
+
+ align:start position:0%
+used as the basis for the design of his
+ 
+
+ align:start position:0%
+used as the basis for the design of his
+free University campus in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Berlin
+
+ align:start position:0%
+Berlin
+ 
+
+ align:start position:0%
+Berlin
+Maria worked in the with the drawings in
+
+ align:start position:0%
+Maria worked in the with the drawings in
+ 
+
+ align:start position:0%
+Maria worked in the with the drawings in
+the MIT archives which had never been
+
+ align:start position:0%
+the MIT archives which had never been
+ 
+
+ align:start position:0%
+the MIT archives which had never been
+looked at
+
+ align:start position:0%
+looked at
+ 
+
+ align:start position:0%
+looked at
+before and made an assessment of the
+
+ align:start position:0%
+before and made an assessment of the
+ 
+
+ align:start position:0%
+before and made an assessment of the
+number of G geometric
+
+ align:start position:0%
+number of G geometric
+ 
+
+ align:start position:0%
+number of G geometric
+configurations that allowed the campus
+
+ align:start position:0%
+configurations that allowed the campus
+ 
+
+ align:start position:0%
+configurations that allowed the campus
+to grow in the way that it
+
+ align:start position:0%
+to grow in the way that it
+ 
+
+ align:start position:0%
+to grow in the way that it
+did I haven't got time to go into this
+
+ align:start position:0%
+did I haven't got time to go into this
+ 
+
+ align:start position:0%
+did I haven't got time to go into this
+detail as as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always why are we so short of
+
+ align:start position:0%
+always why are we so short of
+ 
+
+ align:start position:0%
+always why are we so short of
+time is it because we try to do too
+
+ align:start position:0%
+time is it because we try to do too
+ 
+
+ align:start position:0%
+time is it because we try to do too
+much but if you don't do too much who
+
+ align:start position:0%
+much but if you don't do too much who
+ 
+
+ align:start position:0%
+much but if you don't do too much who
+says what is
+
+ align:start position:0%
+says what is
+ 
+
+ align:start position:0%
+says what is
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+should one take one project like this
+
+ align:start position:0%
+should one take one project like this
+ 
+
+ align:start position:0%
+should one take one project like this
+and spend a semester studying it in
+
+ align:start position:0%
+and spend a semester studying it in
+ 
+
+ align:start position:0%
+and spend a semester studying it in
+detail would you gain more from doing
+
+ align:start position:0%
+detail would you gain more from doing
+ 
+
+ align:start position:0%
+detail would you gain more from doing
+that versus attending a class which
+
+ align:start position:0%
+that versus attending a class which
+ 
+
+ align:start position:0%
+that versus attending a class which
+strives to cover everything in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world you you you made your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choice among our findings six stand
+
+ align:start position:0%
+choice among our findings six stand
+ 
+
+ align:start position:0%
+choice among our findings six stand
+out the existence of an underlying
+
+ align:start position:0%
+out the existence of an underlying
+ 
+
+ align:start position:0%
+out the existence of an underlying
+circulation
+
+ align:start position:0%
+circulation
+ 
+
+ align:start position:0%
+circulation
+system MIT
+
+ align:start position:0%
+system MIT
+ 
+
+ align:start position:0%
+system MIT
+is has a block size of 65 ft in width
+
+ align:start position:0%
+is has a block size of 65 ft in width
+ 
+
+ align:start position:0%
+is has a block size of 65 ft in width
+and a central Corridor most of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time the three kinds of stems
+
+ align:start position:0%
+time the three kinds of stems
+ 
+
+ align:start position:0%
+time the three kinds of stems
+used number three the quality of the
+
+ align:start position:0%
+used number three the quality of the
+ 
+
+ align:start position:0%
+used number three the quality of the
+knuckle whenever a building change
+
+ align:start position:0%
+knuckle whenever a building change
+ 
+
+ align:start position:0%
+knuckle whenever a building change
+directions almost always when there's an
+
+ align:start position:0%
+directions almost always when there's an
+ 
+
+ align:start position:0%
+directions almost always when there's an
+an opportunity to change direction the
+
+ align:start position:0%
+an opportunity to change direction the
+ 
+
+ align:start position:0%
+an opportunity to change direction the
+vertical circulation system of
+
+ align:start position:0%
+vertical circulation system of
+ 
+
+ align:start position:0%
+vertical circulation system of
+elevators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and staircases are contained in the
+
+ align:start position:0%
+and and staircases are contained in the
+ 
+
+ align:start position:0%
+and and staircases are contained in the
+knuckle so she shows that every time a
+
+ align:start position:0%
+knuckle so she shows that every time a
+ 
+
+ align:start position:0%
+knuckle so she shows that every time a
+building changes Direction it is free of
+
+ align:start position:0%
+building changes Direction it is free of
+ 
+
+ align:start position:0%
+building changes Direction it is free of
+having to
+
+ align:start position:0%
+having to
+ 
+
+ align:start position:0%
+having to
+replace the circulation vertical
+
+ align:start position:0%
+replace the circulation vertical
+ 
+
+ align:start position:0%
+replace the circulation vertical
+circulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system it means that the circulation
+
+ align:start position:0%
+system it means that the circulation
+ 
+
+ align:start position:0%
+system it means that the circulation
+system becomes more intense as it is
+
+ align:start position:0%
+system becomes more intense as it is
+ 
+
+ align:start position:0%
+system becomes more intense as it is
+joined to other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems the fully equipped unit section
+
+ align:start position:0%
+systems the fully equipped unit section
+ 
+
+ align:start position:0%
+systems the fully equipped unit section
+from the bouet
+
+ align:start position:0%
+from the bouet
+ 
+
+ align:start position:0%
+from the bouet
+system the courtyards is future free
+
+ align:start position:0%
+system the courtyards is future free
+ 
+
+ align:start position:0%
+system the courtyards is future free
+space I never realized that MIT intend
+
+ align:start position:0%
+space I never realized that MIT intend
+ 
+
+ align:start position:0%
+space I never realized that MIT intend
+ended the courtyard system as an
+
+ align:start position:0%
+ended the courtyard system as an
+ 
+
+ align:start position:0%
+ended the courtyard system as an
+opportunity for building expansion thank
+
+ align:start position:0%
+opportunity for building expansion thank
+ 
+
+ align:start position:0%
+opportunity for building expansion thank
+God they
+
+ align:start position:0%
+God they
+ 
+
+ align:start position:0%
+God they
+haven't
+
+ align:start position:0%
+haven't
+ 
+
+ align:start position:0%
+haven't
+um the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+facades where facades were considered to
+
+ align:start position:0%
+facades where facades were considered to
+ 
+
+ align:start position:0%
+facades where facades were considered to
+be permanent they were built of granite
+
+ align:start position:0%
+be permanent they were built of granite
+ 
+
+ align:start position:0%
+be permanent they were built of granite
+or Limestone where the facades were
+
+ align:start position:0%
+or Limestone where the facades were
+ 
+
+ align:start position:0%
+or Limestone where the facades were
+considered to be temporary they were
+
+ align:start position:0%
+considered to be temporary they were
+ 
+
+ align:start position:0%
+considered to be temporary they were
+built a brick Yellow Brick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+facades so
+
+ align:start position:0%
+facades so
+ 
+
+ align:start position:0%
+facades so
+she
+
+ align:start position:0%
+she
+ 
+
+ align:start position:0%
+she
+argues
+
+ align:start position:0%
+argues
+ 
+
+ align:start position:0%
+argues
+very systematically with a lot of data
+
+ align:start position:0%
+very systematically with a lot of data
+ 
+
+ align:start position:0%
+very systematically with a lot of data
+that there was a kind of
+
+ align:start position:0%
+that there was a kind of
+ 
+
+ align:start position:0%
+that there was a kind of
+DNA in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system not a very profound DNA but a
+
+ align:start position:0%
+system not a very profound DNA but a
+ 
+
+ align:start position:0%
+system not a very profound DNA but a
+very simple DNA which allowed a mighty
+
+ align:start position:0%
+very simple DNA which allowed a mighty
+ 
+
+ align:start position:0%
+very simple DNA which allowed a mighty
+to grow until
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+204 on its own
+
+ align:start position:0%
+204 on its own
+ 
+
+ align:start position:0%
+204 on its own
+land
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our building the brain and cognitive
+
+ align:start position:0%
+our building the brain and cognitive
+ 
+
+ align:start position:0%
+our building the brain and cognitive
+Center is on the other side of Asa
+
+ align:start position:0%
+Center is on the other side of Asa
+ 
+
+ align:start position:0%
+Center is on the other side of Asa
+Street it was the first time
+
+ align:start position:0%
+Street it was the first time
+ 
+
+ align:start position:0%
+Street it was the first time
+a a building not the first time but one
+
+ align:start position:0%
+a a building not the first time but one
+ 
+
+ align:start position:0%
+a a building not the first time but one
+of the first times a major building was
+
+ align:start position:0%
+of the first times a major building was
+ 
+
+ align:start position:0%
+of the first times a major building was
+built outside of the limited
+
+ align:start position:0%
+built outside of the limited
+ 
+
+ align:start position:0%
+built outside of the limited
+campus we proposed a connection an
+
+ align:start position:0%
+campus we proposed a connection an
+ 
+
+ align:start position:0%
+campus we proposed a connection an
+aerial connection from building whatever
+
+ align:start position:0%
+aerial connection from building whatever
+ 
+
+ align:start position:0%
+aerial connection from building whatever
+it is across ver Street to
+
+ align:start position:0%
+it is across ver Street to
+ 
+
+ align:start position:0%
+it is across ver Street to
+a to a place on our SEC the second floor
+
+ align:start position:0%
+a to a place on our SEC the second floor
+ 
+
+ align:start position:0%
+a to a place on our SEC the second floor
+of the brain and cogn centers MIT
+
+ align:start position:0%
+of the brain and cogn centers MIT
+ 
+
+ align:start position:0%
+of the brain and cogn centers MIT
+wouldn't build it we tried very hard to
+
+ align:start position:0%
+wouldn't build it we tried very hard to
+ 
+
+ align:start position:0%
+wouldn't build it we tried very hard to
+get it built in fact the German engineer
+
+ align:start position:0%
+get it built in fact the German engineer
+ 
+
+ align:start position:0%
+get it built in fact the German engineer
+Jo SCH who worked on the Freedom Tower
+
+ align:start position:0%
+Jo SCH who worked on the Freedom Tower
+ 
+
+ align:start position:0%
+Jo SCH who worked on the Freedom Tower
+in New York is probably the best
+
+ align:start position:0%
+in New York is probably the best
+ 
+
+ align:start position:0%
+in New York is probably the best
+structural engineer in the world
+
+ align:start position:0%
+structural engineer in the world
+ 
+
+ align:start position:0%
+structural engineer in the world
+designed the connector but it
+
+ align:start position:0%
+designed the connector but it
+ 
+
+ align:start position:0%
+designed the connector but it
+didn't a might now faces an expansive
+
+ align:start position:0%
+didn't a might now faces an expansive
+ 
+
+ align:start position:0%
+didn't a might now faces an expansive
+possibility which is not as
+
+ align:start position:0%
+possibility which is not as
+ 
+
+ align:start position:0%
+possibility which is not as
+simple as expanding on your own land has
+
+ align:start position:0%
+simple as expanding on your own land has
+ 
+
+ align:start position:0%
+simple as expanding on your own land has
+to deal with Urban infrastructure of a
+
+ align:start position:0%
+to deal with Urban infrastructure of a
+ 
+
+ align:start position:0%
+to deal with Urban infrastructure of a
+much more complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nature another use of
+
+ align:start position:0%
+nature another use of
+ 
+
+ align:start position:0%
+nature another use of
+geometry which we mentioned before is in
+
+ align:start position:0%
+geometry which we mentioned before is in
+ 
+
+ align:start position:0%
+geometry which we mentioned before is in
+the L and Dav was planned for Milton ke
+
+ align:start position:0%
+the L and Dav was planned for Milton ke
+ 
+
+ align:start position:0%
+the L and Dav was planned for Milton ke
+in London one of the mark
+
+ align:start position:0%
+in London one of the mark
+ 
+
+ align:start position:0%
+in London one of the mark
+three New
+
+ align:start position:0%
+three New
+ 
+
+ align:start position:0%
+three New
+Towns you'll remember that the
+
+ align:start position:0%
+Towns you'll remember that the
+ 
+
+ align:start position:0%
+Towns you'll remember that the
+grid is used and the grid is spaced at 1
+
+ align:start position:0%
+grid is used and the grid is spaced at 1
+ 
+
+ align:start position:0%
+grid is used and the grid is spaced at 1
+kilm by 1 kilm not one mile by one
+
+ align:start position:0%
+kilm by 1 kilm not one mile by one
+ 
+
+ align:start position:0%
+kilm by 1 kilm not one mile by one
+mile so that the consequence of the
+
+ align:start position:0%
+mile so that the consequence of the
+ 
+
+ align:start position:0%
+mile so that the consequence of the
+generation of volume within this
+
+ align:start position:0%
+generation of volume within this
+ 
+
+ align:start position:0%
+generation of volume within this
+enclosed grid space would not not be too
+
+ align:start position:0%
+enclosed grid space would not not be too
+ 
+
+ align:start position:0%
+enclosed grid space would not not be too
+large and require great separated inter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interaction some other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas the old premise of Milton K's plan
+
+ align:start position:0%
+ideas the old premise of Milton K's plan
+ 
+
+ align:start position:0%
+ideas the old premise of Milton K's plan
+is summarized as follows the central aim
+
+ align:start position:0%
+is summarized as follows the central aim
+ 
+
+ align:start position:0%
+is summarized as follows the central aim
+of the plan is to arrange these
+
+ align:start position:0%
+of the plan is to arrange these
+ 
+
+ align:start position:0%
+of the plan is to arrange these
+necessary fixed elements transport
+
+ align:start position:0%
+necessary fixed elements transport
+ 
+
+ align:start position:0%
+necessary fixed elements transport
+drainage water supply in a new city so
+
+ align:start position:0%
+drainage water supply in a new city so
+ 
+
+ align:start position:0%
+drainage water supply in a new city so
+as to allow the Great possible scope for
+
+ align:start position:0%
+as to allow the Great possible scope for
+ 
+
+ align:start position:0%
+as to allow the Great possible scope for
+freedom and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change they've it has been planned as
+
+ align:start position:0%
+change they've it has been planned as
+ 
+
+ align:start position:0%
+change they've it has been planned as
+far as possible to allow wide varieties
+
+ align:start position:0%
+far as possible to allow wide varieties
+ 
+
+ align:start position:0%
+far as possible to allow wide varieties
+in patterns of life and the greatest
+
+ align:start position:0%
+in patterns of life and the greatest
+ 
+
+ align:start position:0%
+in patterns of life and the greatest
+possible choice for the
+
+ align:start position:0%
+possible choice for the
+ 
+
+ align:start position:0%
+possible choice for the
+future there are two things in the
+
+ align:start position:0%
+future there are two things in the
+ 
+
+ align:start position:0%
+future there are two things in the
+geometry of the well in the application
+
+ align:start position:0%
+geometry of the well in the application
+ 
+
+ align:start position:0%
+geometry of the well in the application
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+geometry number one is the idea of as I
+
+ align:start position:0%
+geometry number one is the idea of as I
+ 
+
+ align:start position:0%
+geometry number one is the idea of as I
+Dre Drew on the Blackboard of
+
+ align:start position:0%
+Dre Drew on the Blackboard of
+ 
+
+ align:start position:0%
+Dre Drew on the Blackboard of
+recognizing the possibility of a space
+
+ align:start position:0%
+recognizing the possibility of a space
+ 
+
+ align:start position:0%
+recognizing the possibility of a space
+frame system space frame system in
+
+ align:start position:0%
+frame system space frame system in
+ 
+
+ align:start position:0%
+frame system space frame system in
+architecture is a system which spans
+
+ align:start position:0%
+architecture is a system which spans
+ 
+
+ align:start position:0%
+architecture is a system which spans
+distance and allows you to put points on
+
+ align:start position:0%
+distance and allows you to put points on
+ 
+
+ align:start position:0%
+distance and allows you to put points on
+the low load system at any point as
+
+ align:start position:0%
+the low load system at any point as
+ 
+
+ align:start position:0%
+the low load system at any point as
+opposed to point and beam
+
+ align:start position:0%
+opposed to point and beam
+ 
+
+ align:start position:0%
+opposed to point and beam
+system where you can only load the
+
+ align:start position:0%
+system where you can only load the
+ 
+
+ align:start position:0%
+system where you can only load the
+system where there is a column beneath
+
+ align:start position:0%
+system where there is a column beneath
+ 
+
+ align:start position:0%
+system where there is a column beneath
+your your point
+
+ align:start position:0%
+your your point
+ 
+
+ align:start position:0%
+your your point
+so it's a kind of pointless system or
+
+ align:start position:0%
+so it's a kind of pointless system or
+ 
+
+ align:start position:0%
+so it's a kind of pointless system or
+freedom of pointing which allows almost
+
+ align:start position:0%
+freedom of pointing which allows almost
+ 
+
+ align:start position:0%
+freedom of pointing which allows almost
+any kind of change to exist the notion
+
+ align:start position:0%
+any kind of change to exist the notion
+ 
+
+ align:start position:0%
+any kind of change to exist the notion
+of deciding what the maximum amount that
+
+ align:start position:0%
+of deciding what the maximum amount that
+ 
+
+ align:start position:0%
+of deciding what the maximum amount that
+you can allow before the system cripples
+
+ align:start position:0%
+you can allow before the system cripples
+ 
+
+ align:start position:0%
+you can allow before the system cripples
+itself is interesting you have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use mathematical prediction systems like
+
+ align:start position:0%
+use mathematical prediction systems like
+ 
+
+ align:start position:0%
+use mathematical prediction systems like
+the poron distribution who knows what
+
+ align:start position:0%
+the poron distribution who knows what
+ 
+
+ align:start position:0%
+the poron distribution who knows what
+the for on distribution
+
+ align:start position:0%
+the for on distribution
+ 
+
+ align:start position:0%
+the for on distribution
+is you should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know if you're going to design a
+
+ align:start position:0%
+know if you're going to design a
+ 
+
+ align:start position:0%
+know if you're going to design a
+University campus how do you decide or
+
+ align:start position:0%
+University campus how do you decide or
+ 
+
+ align:start position:0%
+University campus how do you decide or
+School room how do you decide on the
+
+ align:start position:0%
+School room how do you decide on the
+ 
+
+ align:start position:0%
+School room how do you decide on the
+size of the distribution of the sizes of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classrooms you
+
+ align:start position:0%
+classrooms you
+ 
+
+ align:start position:0%
+classrooms you
+Architects you're in advanced standing
+
+ align:start position:0%
+Architects you're in advanced standing
+ 
+
+ align:start position:0%
+Architects you're in advanced standing
+at MIT you're doing doctorates you're
+
+ align:start position:0%
+at MIT you're doing doctorates you're
+ 
+
+ align:start position:0%
+at MIT you're doing doctorates you're
+doing kinds of advanced
+
+ align:start position:0%
+doing kinds of advanced
+ 
+
+ align:start position:0%
+doing kinds of advanced
+degrees and if I ask you the simple
+
+ align:start position:0%
+degrees and if I ask you the simple
+ 
+
+ align:start position:0%
+degrees and if I ask you the simple
+proposition that if you had to walk out
+
+ align:start position:0%
+proposition that if you had to walk out
+ 
+
+ align:start position:0%
+proposition that if you had to walk out
+of a and you had and you were in Burma
+
+ align:start position:0%
+of a and you had and you were in Burma
+ 
+
+ align:start position:0%
+of a and you had and you were in Burma
+somewhere and they were decided to build
+
+ align:start position:0%
+somewhere and they were decided to build
+ 
+
+ align:start position:0%
+somewhere and they were decided to build
+a new University how would you decide on
+
+ align:start position:0%
+a new University how would you decide on
+ 
+
+ align:start position:0%
+a new University how would you decide on
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+program without knowing the for on
+
+ align:start position:0%
+program without knowing the for on
+ 
+
+ align:start position:0%
+program without knowing the for on
+distribution University of ma the
+
+ align:start position:0%
+distribution University of ma the
+ 
+
+ align:start position:0%
+distribution University of ma the
+Department of Mathematics at Cambridge
+
+ align:start position:0%
+Department of Mathematics at Cambridge
+ 
+
+ align:start position:0%
+Department of Mathematics at Cambridge
+University a new building is designed on
+
+ align:start position:0%
+University a new building is designed on
+ 
+
+ align:start position:0%
+University a new building is designed on
+the basis of the poron distribution
+
+ align:start position:0%
+the basis of the poron distribution
+ 
+
+ align:start position:0%
+the basis of the poron distribution
+it allocates probability of sizes given
+
+ align:start position:0%
+it allocates probability of sizes given
+ 
+
+ align:start position:0%
+it allocates probability of sizes given
+certain average
+
+ align:start position:0%
+certain average
+ 
+
+ align:start position:0%
+certain average
+rates I'm not trying to be clever I'm
+
+ align:start position:0%
+rates I'm not trying to be clever I'm
+ 
+
+ align:start position:0%
+rates I'm not trying to be clever I'm
+just trying to say
+
+ align:start position:0%
+just trying to say
+ 
+
+ align:start position:0%
+just trying to say
+that there
+
+ align:start position:0%
+that there
+ 
+
+ align:start position:0%
+that there
+are statistical measures which give one
+
+ align:start position:0%
+are statistical measures which give one
+ 
+
+ align:start position:0%
+are statistical measures which give one
+a better prediction about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future one of the best subject I ever
+
+ align:start position:0%
+future one of the best subject I ever
+ 
+
+ align:start position:0%
+future one of the best subject I ever
+studied in graduate school was
+
+ align:start position:0%
+studied in graduate school was
+ 
+
+ align:start position:0%
+studied in graduate school was
+statistics I hated it but it made me
+
+ align:start position:0%
+statistics I hated it but it made me
+ 
+
+ align:start position:0%
+statistics I hated it but it made me
+aware of the fact that you can generate
+
+ align:start position:0%
+aware of the fact that you can generate
+ 
+
+ align:start position:0%
+aware of the fact that you can generate
+knowledge through sampling systems of
+
+ align:start position:0%
+knowledge through sampling systems of
+ 
+
+ align:start position:0%
+knowledge through sampling systems of
+great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacity I was staggered when my
+
+ align:start position:0%
+capacity I was staggered when my
+ 
+
+ align:start position:0%
+capacity I was staggered when my
+professor said the only reason we have
+
+ align:start position:0%
+professor said the only reason we have
+ 
+
+ align:start position:0%
+professor said the only reason we have
+live matches is because we know
+
+ align:start position:0%
+live matches is because we know
+ 
+
+ align:start position:0%
+live matches is because we know
+statistically how many matches
+
+ align:start position:0%
+statistically how many matches
+ 
+
+ align:start position:0%
+statistically how many matches
+fail and we can predict the production
+
+ align:start position:0%
+fail and we can predict the production
+ 
+
+ align:start position:0%
+fail and we can predict the production
+of boxes and matches without any of them
+
+ align:start position:0%
+of boxes and matches without any of them
+ 
+
+ align:start position:0%
+of boxes and matches without any of them
+failing
+
+ align:start position:0%
+failing
+ 
+
+ align:start position:0%
+failing
+or 99%
+
+ align:start position:0%
+or 99%
+ 
+
+ align:start position:0%
+or 99%
+succeeding
+
+ align:start position:0%
+succeeding
+ 
+
+ align:start position:0%
+succeeding
+staggered staggering but a simple
+
+ align:start position:0%
+staggered staggering but a simple
+ 
+
+ align:start position:0%
+staggered staggering but a simple
+observation the pon distribution is one
+
+ align:start position:0%
+observation the pon distribution is one
+ 
+
+ align:start position:0%
+observation the pon distribution is one
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the features of
+
+ align:start position:0%
+the features of
+ 
+
+ align:start position:0%
+the features of
+uh so this the second feature of Milton
+
+ align:start position:0%
+uh so this the second feature of Milton
+ 
+
+ align:start position:0%
+uh so this the second feature of Milton
+kanes in trying
+
+ align:start position:0%
+kanes in trying
+ 
+
+ align:start position:0%
+kanes in trying
+to project the possibility of first of
+
+ align:start position:0%
+to project the possibility of first of
+ 
+
+ align:start position:0%
+to project the possibility of first of
+all diversity and secondly of change is
+
+ align:start position:0%
+all diversity and secondly of change is
+ 
+
+ align:start position:0%
+all diversity and secondly of change is
+to introduce zoning systems based on
+
+ align:start position:0%
+to introduce zoning systems based on
+ 
+
+ align:start position:0%
+to introduce zoning systems based on
+performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dimensions the reason why German zoning
+
+ align:start position:0%
+Dimensions the reason why German zoning
+ 
+
+ align:start position:0%
+Dimensions the reason why German zoning
+started out was because of the
+
+ align:start position:0%
+started out was because of the
+ 
+
+ align:start position:0%
+started out was because of the
+industrial city causing noise and dirt
+
+ align:start position:0%
+industrial city causing noise and dirt
+ 
+
+ align:start position:0%
+industrial city causing noise and dirt
+and fumes and traffic as opposed to the
+
+ align:start position:0%
+and fumes and traffic as opposed to the
+ 
+
+ align:start position:0%
+and fumes and traffic as opposed to the
+quiet Notions that required in a
+
+ align:start position:0%
+quiet Notions that required in a
+ 
+
+ align:start position:0%
+quiet Notions that required in a
+residential
+
+ align:start position:0%
+residential
+ 
+
+ align:start position:0%
+residential
+area if
+
+ align:start position:0%
+area if
+ 
+
+ align:start position:0%
+area if
+today uh a high-tech company produces no
+
+ align:start position:0%
+today uh a high-tech company produces no
+ 
+
+ align:start position:0%
+today uh a high-tech company produces no
+noise no smoke no sound can it not be
+
+ align:start position:0%
+noise no smoke no sound can it not be
+ 
+
+ align:start position:0%
+noise no smoke no sound can it not be
+adjacent to a residential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+building of course I don't know how this
+
+ align:start position:0%
+building of course I don't know how this
+ 
+
+ align:start position:0%
+building of course I don't know how this
+has worked in Wilton KES if I buy a
+
+ align:start position:0%
+has worked in Wilton KES if I buy a
+ 
+
+ align:start position:0%
+has worked in Wilton KES if I buy a
+piece of land and I make a wonderful
+
+ align:start position:0%
+piece of land and I make a wonderful
+ 
+
+ align:start position:0%
+piece of land and I make a wonderful
+garden next to it it has
+
+ align:start position:0%
+garden next to it it has
+ 
+
+ align:start position:0%
+garden next to it it has
+value if the city decides to build a
+
+ align:start position:0%
+value if the city decides to build a
+ 
+
+ align:start position:0%
+value if the city decides to build a
+factory next to it I lose
+
+ align:start position:0%
+factory next to it I lose
+ 
+
+ align:start position:0%
+factory next to it I lose
+value how do you count for that change
+
+ align:start position:0%
+value how do you count for that change
+ 
+
+ align:start position:0%
+value how do you count for that change
+do you repay
+
+ align:start position:0%
+do you repay
+ 
+
+ align:start position:0%
+do you repay
+me I take you to court and say I have
+
+ align:start position:0%
+me I take you to court and say I have
+ 
+
+ align:start position:0%
+me I take you to court and say I have
+rights they say you don't have rights to
+
+ align:start position:0%
+rights they say you don't have rights to
+ 
+
+ align:start position:0%
+rights they say you don't have rights to
+predict to confiscate the rights of of
+
+ align:start position:0%
+predict to confiscate the rights of of
+ 
+
+ align:start position:0%
+predict to confiscate the rights of of
+development so around
+
+ align:start position:0%
+development so around
+ 
+
+ align:start position:0%
+development so around
+you it's a fundamental problem if you
+
+ align:start position:0%
+you it's a fundamental problem if you
+ 
+
+ align:start position:0%
+you it's a fundamental problem if you
+wish to designed for
+
+ align:start position:0%
+wish to designed for
+ 
+
+ align:start position:0%
+wish to designed for
+diversity you can of course write rules
+
+ align:start position:0%
+diversity you can of course write rules
+ 
+
+ align:start position:0%
+diversity you can of course write rules
+saying that a factory will not be within
+
+ align:start position:0%
+saying that a factory will not be within
+ 
+
+ align:start position:0%
+saying that a factory will not be within
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ft but performance Dimensions measure
+
+ align:start position:0%
+ft but performance Dimensions measure
+ 
+
+ align:start position:0%
+ft but performance Dimensions measure
+sound
+
+ align:start position:0%
+sound
+ 
+
+ align:start position:0%
+sound
+noise frequency of
+
+ align:start position:0%
+noise frequency of
+ 
+
+ align:start position:0%
+noise frequency of
+traffic if trucks start working as they
+
+ align:start position:0%
+traffic if trucks start working as they
+ 
+
+ align:start position:0%
+traffic if trucks start working as they
+do in New York at 5:00 in the morning
+
+ align:start position:0%
+do in New York at 5:00 in the morning
+ 
+
+ align:start position:0%
+do in New York at 5:00 in the morning
+and I want to sleep what right do I have
+
+ align:start position:0%
+and I want to sleep what right do I have
+ 
+
+ align:start position:0%
+and I want to sleep what right do I have
+to stop the trucks from off loing at
+
+ align:start position:0%
+to stop the trucks from off loing at
+ 
+
+ align:start position:0%
+to stop the trucks from off loing at
+5:00 in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+morning these are tough
+
+ align:start position:0%
+morning these are tough
+ 
+
+ align:start position:0%
+morning these are tough
+questions and
+
+ align:start position:0%
+questions and
+ 
+
+ align:start position:0%
+questions and
+flexibility simply runs up against some
+
+ align:start position:0%
+flexibility simply runs up against some
+ 
+
+ align:start position:0%
+flexibility simply runs up against some
+of these questions in a very real sense
+
+ align:start position:0%
+of these questions in a very real sense
+ 
+
+ align:start position:0%
+of these questions in a very real sense
+it be interesting to check I need to
+
+ align:start position:0%
+it be interesting to check I need to
+ 
+
+ align:start position:0%
+it be interesting to check I need to
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+to John Deano is one of the designers of
+
+ align:start position:0%
+to John Deano is one of the designers of
+ 
+
+ align:start position:0%
+to John Deano is one of the designers of
+wion King about how this has been
+
+ align:start position:0%
+wion King about how this has been
+ 
+
+ align:start position:0%
+wion King about how this has been
+handled to Rodrigo Perez D who argues in
+
+ align:start position:0%
+handled to Rodrigo Perez D who argues in
+ 
+
+ align:start position:0%
+handled to Rodrigo Perez D who argues in
+favor of keeping existing stock and
+
+ align:start position:0%
+favor of keeping existing stock and
+ 
+
+ align:start position:0%
+favor of keeping existing stock and
+building an architecture of
+
+ align:start position:0%
+building an architecture of
+ 
+
+ align:start position:0%
+building an architecture of
+addition he says
+
+ align:start position:0%
+addition he says
+ 
+
+ align:start position:0%
+addition he says
+urbanistic it has three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+advantages by being a gradual organist
+
+ align:start position:0%
+advantages by being a gradual organist
+ 
+
+ align:start position:0%
+advantages by being a gradual organist
+organized incorporation of Parts into an
+
+ align:start position:0%
+organized incorporation of Parts into an
+ 
+
+ align:start position:0%
+organized incorporation of Parts into an
+existing core it implies the use of a
+
+ align:start position:0%
+existing core it implies the use of a
+ 
+
+ align:start position:0%
+existing core it implies the use of a
+pre-existing structure and by doing so
+
+ align:start position:0%
+pre-existing structure and by doing so
+ 
+
+ align:start position:0%
+pre-existing structure and by doing so
+it extends the likelihood that's being
+
+ align:start position:0%
+it extends the likelihood that's being
+ 
+
+ align:start position:0%
+it extends the likelihood that's being
+in use for a prol long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+secondly it allows for a form of
+
+ align:start position:0%
+secondly it allows for a form of
+ 
+
+ align:start position:0%
+secondly it allows for a form of
+development characterized by its low
+
+ align:start position:0%
+development characterized by its low
+ 
+
+ align:start position:0%
+development characterized by its low
+cost in both social and material terms
+
+ align:start position:0%
+cost in both social and material terms
+ 
+
+ align:start position:0%
+cost in both social and material terms
+I'm not sure that he's right maybe it's
+
+ align:start position:0%
+I'm not sure that he's right maybe it's
+ 
+
+ align:start position:0%
+I'm not sure that he's right maybe it's
+true in Colombia but the cost of
+
+ align:start position:0%
+true in Colombia but the cost of
+ 
+
+ align:start position:0%
+true in Colombia but the cost of
+renewing
+
+ align:start position:0%
+renewing
+ 
+
+ align:start position:0%
+renewing
+buildings such as the buildings around
+
+ align:start position:0%
+buildings such as the buildings around
+ 
+
+ align:start position:0%
+buildings such as the buildings around
+year which have been renewed for high
+
+ align:start position:0%
+year which have been renewed for high
+ 
+
+ align:start position:0%
+year which have been renewed for high
+technology purposes is
+
+ align:start position:0%
+technology purposes is
+ 
+
+ align:start position:0%
+technology purposes is
+extensive it's not automatic that you
+
+ align:start position:0%
+extensive it's not automatic that you
+ 
+
+ align:start position:0%
+extensive it's not automatic that you
+put a if you extend a building you put a
+
+ align:start position:0%
+put a if you extend a building you put a
+ 
+
+ align:start position:0%
+put a if you extend a building you put a
+all you do is put a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bedroom in addition to our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+house and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thirdly he says that this
+
+ align:start position:0%
+thirdly he says that this
+ 
+
+ align:start position:0%
+thirdly he says that this
+process this trans additive
+
+ align:start position:0%
+process this trans additive
+ 
+
+ align:start position:0%
+process this trans additive
+transformation ensures a sense of
+
+ align:start position:0%
+transformation ensures a sense of
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+
+ align:start position:0%
+transformation ensures a sense of
+continuity in the construction of the
+
+ align:start position:0%
+continuity in the construction of the
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+
+ align:start position:0%
+continuity in the construction of the
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+
+ align:start position:0%
+town and a sense of place in both
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+
+ align:start position:0%
+town and a sense of place in both
+historical and spatial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms he goes on and on this is the
+
+ align:start position:0%
+terms he goes on and on this is the
+ 
+
+ align:start position:0%
+terms he goes on and on this is the
+piece from architectural
+
+ align:start position:0%
+piece from architectural
+ 
+
+ align:start position:0%
+piece from architectural
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+
+ align:start position:0%
+design if you can't find the
+ 
+
+ align:start position:0%
+design if you can't find the
+AA little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+book Let's look and I need you to look
+
+ align:start position:0%
+book Let's look and I need you to look
+ 
+
+ align:start position:0%
+book Let's look and I need you to look
+at the your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcript let's look at
+
+ align:start position:0%
+transcript let's look at
+ 
+
+ align:start position:0%
+transcript let's look at
+the development of a systematic campus
+
+ align:start position:0%
+the development of a systematic campus
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+
+ align:start position:0%
+the development of a systematic campus
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the British were very intelligent
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+ align:start position:0%
+in the British were very intelligent
+ 
+
+ align:start position:0%
+in the British were very intelligent
+after the they won the
+
+ align:start position:0%
+after the they won the
+ 
+
+ align:start position:0%
+after the they won the
+war the 3945 War they decided under the
+
+ align:start position:0%
+war the 3945 War they decided under the
+ 
+
+ align:start position:0%
+war the 3945 War they decided under the
+labor government which
+
+ align:start position:0%
+labor government which
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+
+ align:start position:0%
+labor government which
+replaced
+
+ align:start position:0%
+replaced
+ 
+
+ align:start position:0%
+replaced
+Churchill Churchill was interestingly
+
+ align:start position:0%
+Churchill Churchill was interestingly
+ 
+
+ align:start position:0%
+Churchill Churchill was interestingly
+successful as a war leader but hopeless
+
+ align:start position:0%
+successful as a war leader but hopeless
+ 
+
+ align:start position:0%
+successful as a war leader but hopeless
+as a as a as a peace
+
+ align:start position:0%
+as a as a as a peace
+ 
+
+ align:start position:0%
+as a as a as a peace
+leader M Maggi that was equally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopeless she was her big war success was
+
+ align:start position:0%
+hopeless she was her big war success was
+ 
+
+ align:start position:0%
+hopeless she was her big war success was
+the F the Ireland big victory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indeed yeah
+
+ align:start position:0%
+indeed yeah
+ 
+
+ align:start position:0%
+indeed yeah
+anyway we start with the 1961 plan for
+
+ align:start position:0%
+anyway we start with the 1961 plan for
+ 
+
+ align:start position:0%
+anyway we start with the 1961 plan for
+the University of
+
+ align:start position:0%
+the University of
+ 
+
+ align:start position:0%
+the University of
+Sussex this is post post
+
+ align:start position:0%
+Sussex this is post post
+ 
+
+ align:start position:0%
+Sussex this is post post
+45 rebuilding of Education institutions
+
+ align:start position:0%
+45 rebuilding of Education institutions
+ 
+
+ align:start position:0%
+45 rebuilding of Education institutions
+in Europe and I use this data just to
+
+ align:start position:0%
+in Europe and I use this data just to
+ 
+
+ align:start position:0%
+in Europe and I use this data just to
+make an argument about the
+
+ align:start position:0%
+make an argument about the
+ 
+
+ align:start position:0%
+make an argument about the
+change 61 Sussex is a campus plan they
+
+ align:start position:0%
+change 61 Sussex is a campus plan they
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+
+ align:start position:0%
+change 61 Sussex is a campus plan they
+are separate schools they IND individual
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+ align:start position:0%
+are separate schools they IND individual
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+
+ align:start position:0%
+are separate schools they IND individual
+categories individual Enterprises School
+
+ align:start position:0%
+categories individual Enterprises School
+ 
+
+ align:start position:0%
+categories individual Enterprises School
+of mathematics School of humanities and
+
+ align:start position:0%
+of mathematics School of humanities and
+ 
+
+ align:start position:0%
+of mathematics School of humanities and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+on by the University of Lancaster in
+
+ align:start position:0%
+on by the University of Lancaster in
+ 
+
+ align:start position:0%
+on by the University of Lancaster in
+1964 attention starts being paid to the
+
+ align:start position:0%
+1964 attention starts being paid to the
+ 
+
+ align:start position:0%
+1964 attention starts being paid to the
+connecting of
+
+ align:start position:0%
+connecting of
+ 
+
+ align:start position:0%
+connecting of
+places and the system is one in which
+
+ align:start position:0%
+places and the system is one in which
+ 
+
+ align:start position:0%
+places and the system is one in which
+modulus space is connected in a in a
+
+ align:start position:0%
+modulus space is connected in a in a
+ 
+
+ align:start position:0%
+modulus space is connected in a in a
+complex Network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number four the University of East
+
+ align:start position:0%
+number four the University of East
+ 
+
+ align:start position:0%
+number four the University of East
+Anglia in 1961 the plan is now a solid
+
+ align:start position:0%
+Anglia in 1961 the plan is now a solid
+ 
+
+ align:start position:0%
+Anglia in 1961 the plan is now a solid
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+configuration with three with small
+
+ align:start position:0%
+configuration with three with small
+ 
+
+ align:start position:0%
+configuration with three with small
+outgrowths but the whole system is very
+
+ align:start position:0%
+outgrowths but the whole system is very
+ 
+
+ align:start position:0%
+outgrowths but the whole system is very
+much based on a
+
+ align:start position:0%
+much based on a
+ 
+
+ align:start position:0%
+much based on a
+linearity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of number five the University of essic
+
+ align:start position:0%
+of number five the University of essic
+ 
+
+ align:start position:0%
+of number five the University of essic
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1961 tries to take that linearity and
+
+ align:start position:0%
+1961 tries to take that linearity and
+ 
+
+ align:start position:0%
+1961 tries to take that linearity and
+bend it up and
+
+ align:start position:0%
+bend it up and
+ 
+
+ align:start position:0%
+bend it up and
+down by now people are asking questions
+
+ align:start position:0%
+down by now people are asking questions
+ 
+
+ align:start position:0%
+down by now people are asking questions
+of whether
+
+ align:start position:0%
+of whether
+ 
+
+ align:start position:0%
+of whether
+interdisciplinary knowledge systems are
+
+ align:start position:0%
+interdisciplinary knowledge systems are
+ 
+
+ align:start position:0%
+interdisciplinary knowledge systems are
+not taking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hold biology and science or physics and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chemistry so the breakdown of
+
+ align:start position:0%
+chemistry so the breakdown of
+ 
+
+ align:start position:0%
+chemistry so the breakdown of
+conventional
+
+ align:start position:0%
+conventional
+ 
+
+ align:start position:0%
+conventional
+disciplines suggests a kind of grouping
+
+ align:start position:0%
+disciplines suggests a kind of grouping
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+
+ align:start position:0%
+disciplines suggests a kind of grouping
+of and even a future in which this might
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+ align:start position:0%
+of and even a future in which this might
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+
+ align:start position:0%
+of and even a future in which this might
+continue allowing for a switch to the
+
+ align:start position:0%
+continue allowing for a switch to the
+ 
+
+ align:start position:0%
+continue allowing for a switch to the
+next page University of
+
+ align:start position:0%
+next page University of
+ 
+
+ align:start position:0%
+next page University of
+s where you start getting some
+
+ align:start position:0%
+s where you start getting some
+ 
+
+ align:start position:0%
+s where you start getting some
+inclination of the idea of building
+
+ align:start position:0%
+inclination of the idea of building
+ 
+
+ align:start position:0%
+inclination of the idea of building
+modular
+
+ align:start position:0%
+modular
+ 
+
+ align:start position:0%
+modular
+space of various
+
+ align:start position:0%
+space of various
+ 
+
+ align:start position:0%
+space of various
+dimensions the University of Dublin John
+
+ align:start position:0%
+dimensions the University of Dublin John
+ 
+
+ align:start position:0%
+dimensions the University of Dublin John
+car theala
+
+ align:start position:0%
+car theala
+ 
+
+ align:start position:0%
+car theala
+project starts trying to articulate the
+
+ align:start position:0%
+project starts trying to articulate the
+ 
+
+ align:start position:0%
+project starts trying to articulate the
+linearity by having a Central Public
+
+ align:start position:0%
+linearity by having a Central Public
+ 
+
+ align:start position:0%
+linearity by having a Central Public
+spine much like the main Corridor at
+
+ align:start position:0%
+spine much like the main Corridor at
+ 
+
+ align:start position:0%
+spine much like the main Corridor at
+MIT and
+
+ align:start position:0%
+MIT and
+ 
+
+ align:start position:0%
+MIT and
+outgrowth from it depending on the need
+
+ align:start position:0%
+outgrowth from it depending on the need
+ 
+
+ align:start position:0%
+outgrowth from it depending on the need
+to be close to the public versus
+
+ align:start position:0%
+to be close to the public versus
+ 
+
+ align:start position:0%
+to be close to the public versus
+uh versus Space which requires
+
+ align:start position:0%
+uh versus Space which requires
+ 
+
+ align:start position:0%
+uh versus Space which requires
+research
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+privacy we go on to the University of
+
+ align:start position:0%
+privacy we go on to the University of
+ 
+
+ align:start position:0%
+privacy we go on to the University of
+lafra in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1965 which is a major major
+
+ align:start position:0%
+1965 which is a major major
+ 
+
+ align:start position:0%
+1965 which is a major major
+departure now a 50x 50 Cube by 15 ft
+
+ align:start position:0%
+departure now a 50x 50 Cube by 15 ft
+ 
+
+ align:start position:0%
+departure now a 50x 50 Cube by 15 ft
+high is the only element to be designed
+
+ align:start position:0%
+high is the only element to be designed
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+
+ align:start position:0%
+high is the only element to be designed
+in in the University
+
+ align:start position:0%
+in in the University
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+
+ align:start position:0%
+in in the University
+space it will account for 70% of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+campus what does this imply it implies
+
+ align:start position:0%
+campus what does this imply it implies
+ 
+
+ align:start position:0%
+campus what does this imply it implies
+that we maximize the possibility of
+
+ align:start position:0%
+that we maximize the possibility of
+ 
+
+ align:start position:0%
+that we maximize the possibility of
+change every space is endowed with a
+
+ align:start position:0%
+change every space is endowed with a
+ 
+
+ align:start position:0%
+change every space is endowed with a
+service structure so that my office can
+
+ align:start position:0%
+service structure so that my office can
+ 
+
+ align:start position:0%
+service structure so that my office can
+become uh a space
+
+ align:start position:0%
+become uh a space
+ 
+
+ align:start position:0%
+become uh a space
+for research scientist who need
+
+ align:start position:0%
+for research scientist who need
+ 
+
+ align:start position:0%
+for research scientist who need
+specialized heating specialized air
+
+ align:start position:0%
+specialized heating specialized air
+ 
+
+ align:start position:0%
+specialized heating specialized air
+specialized steam specialized
+
+ align:start position:0%
+specialized steam specialized
+ 
+
+ align:start position:0%
+specialized steam specialized
+power if I produce all of this for
+
+ align:start position:0%
+power if I produce all of this for
+ 
+
+ align:start position:0%
+power if I produce all of this for
+everybody we can
+
+ align:start position:0%
+everybody we can
+ 
+
+ align:start position:0%
+everybody we can
+change with maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flexibility do you understand the
+
+ align:start position:0%
+flexibility do you understand the
+ 
+
+ align:start position:0%
+flexibility do you understand the
+idea this is the ultimate measure
+
+ align:start position:0%
+idea this is the ultimate measure
+ 
+
+ align:start position:0%
+idea this is the ultimate measure
+flexibility a
+
+ align:start position:0%
+flexibility a
+ 
+
+ align:start position:0%
+flexibility a
+UNIF an item which has
+
+ align:start position:0%
+UNIF an item which has
+ 
+
+ align:start position:0%
+UNIF an item which has
+infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flexibility in competition for the
+
+ align:start position:0%
+flexibility in competition for the
+ 
+
+ align:start position:0%
+flexibility in competition for the
+University new University of Breman one
+
+ align:start position:0%
+University new University of Breman one
+ 
+
+ align:start position:0%
+University new University of Breman one
+of the competitors had a railway line
+
+ align:start position:0%
+of the competitors had a railway line
+ 
+
+ align:start position:0%
+of the competitors had a railway line
+right through the middle of the campus
+
+ align:start position:0%
+right through the middle of the campus
+ 
+
+ align:start position:0%
+right through the middle of the campus
+with a train with a crane on it and it
+
+ align:start position:0%
+with a train with a crane on it and it
+ 
+
+ align:start position:0%
+with a train with a crane on it and it
+kept on moving the parts modules all
+
+ align:start position:0%
+kept on moving the parts modules all
+ 
+
+ align:start position:0%
+kept on moving the parts modules all
+over the place so if I if my department
+
+ align:start position:0%
+over the place so if I if my department
+ 
+
+ align:start position:0%
+over the place so if I if my department
+grew some modul could be added to the
+
+ align:start position:0%
+grew some modul could be added to the
+ 
+
+ align:start position:0%
+grew some modul could be added to the
+top of our existing
+
+ align:start position:0%
+top of our existing
+ 
+
+ align:start position:0%
+top of our existing
+Department if if we fired off of the
+
+ align:start position:0%
+Department if if we fired off of the
+ 
+
+ align:start position:0%
+Department if if we fired off of the
+Department of architecture the modules
+
+ align:start position:0%
+Department of architecture the modules
+ 
+
+ align:start position:0%
+Department of architecture the modules
+could be
+
+ align:start position:0%
+could be
+ 
+
+ align:start position:0%
+could be
+replaced if you speed that
+
+ align:start position:0%
+replaced if you speed that
+ 
+
+ align:start position:0%
+replaced if you speed that
+up you can imagine coming to your office
+
+ align:start position:0%
+up you can imagine coming to your office
+ 
+
+ align:start position:0%
+up you can imagine coming to your office
+on Monday and have needing a algorithm
+
+ align:start position:0%
+on Monday and have needing a algorithm
+ 
+
+ align:start position:0%
+on Monday and have needing a algorithm
+to explain where you should
+
+ align:start position:0%
+to explain where you should
+ 
+
+ align:start position:0%
+to explain where you should
+be or where you're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be MIT Central Corridor despite the
+
+ align:start position:0%
+be MIT Central Corridor despite the
+ 
+
+ align:start position:0%
+be MIT Central Corridor despite the
+changes has
+
+ align:start position:0%
+changes has
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+
+ align:start position:0%
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+remained in it has a low rate of
+
+ align:start position:0%
+remained in it has a low rate of
+ 
+
+ align:start position:0%
+remained in it has a low rate of
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+ align:start position:0%
+change it should have changed much more
+ 
+
+ align:start position:0%
+change it should have changed much more
+than it has but it's become embedded
+
+ align:start position:0%
+than it has but it's become embedded
+ 
+
+ align:start position:0%
+than it has but it's become embedded
+into the system so that whilst almost
+
+ align:start position:0%
+into the system so that whilst almost
+ 
+
+ align:start position:0%
+into the system so that whilst almost
+every other space at MIT has undergone
+
+ align:start position:0%
+every other space at MIT has undergone
+ 
+
+ align:start position:0%
+every other space at MIT has undergone
+change it hasn't it has the same old
+
+ align:start position:0%
+change it hasn't it has the same old
+ 
+
+ align:start position:0%
+change it hasn't it has the same old
+dull
+
+ align:start position:0%
+dull
+ 
+
+ align:start position:0%
+dull
+administrative instead of building a
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+ align:start position:0%
+administrative instead of building a
+ 
+
+ align:start position:0%
+administrative instead of building a
+cafeteria across the street and it
+
+ align:start position:0%
+cafeteria across the street and it
+ 
+
+ align:start position:0%
+cafeteria across the street and it
+should have jettisoned its
+
+ align:start position:0%
+should have jettisoned its
+ 
+
+ align:start position:0%
+should have jettisoned its
+administrative facilities and used this
+
+ align:start position:0%
+administrative facilities and used this
+ 
+
+ align:start position:0%
+administrative facilities and used this
+major Corridor as a place for real
+
+ align:start position:0%
+major Corridor as a place for real
+ 
+
+ align:start position:0%
+major Corridor as a place for real
+public for exhibitions for eating for
+
+ align:start position:0%
+public for exhibitions for eating for
+ 
+
+ align:start position:0%
+public for exhibitions for eating for
+people coming together he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+didn't he lacked the intelligence or
+
+ align:start position:0%
+didn't he lacked the intelligence or
+ 
+
+ align:start position:0%
+didn't he lacked the intelligence or
+the but so excessive flexibility is very
+
+ align:start position:0%
+the but so excessive flexibility is very
+ 
+
+ align:start position:0%
+the but so excessive flexibility is very
+costly one of the reasons you can't do
+
+ align:start position:0%
+costly one of the reasons you can't do
+ 
+
+ align:start position:0%
+costly one of the reasons you can't do
+Advanced science in the old part of MIT
+
+ align:start position:0%
+Advanced science in the old part of MIT
+ 
+
+ align:start position:0%
+Advanced science in the old part of MIT
+is because the is a lack the
+
+ align:start position:0%
+is because the is a lack the
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+
+ align:start position:0%
+is because the is a lack the
+infrastructure is too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weak the sixth FL of our
+
+ align:start position:0%
+ 
+ 
+
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+ 
+building our building
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+ align:start position:0%
+building our building
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+building our building
+has six
+
+ align:start position:0%
+has six
+ 
+
+ align:start position:0%
+has six
+floors well
+
+ align:start position:0%
+floors well
+ 
+
+ align:start position:0%
+floors well
+I'm the sixth floor is for animals
+
+ align:start position:0%
+I'm the sixth floor is for animals
+ 
+
+ align:start position:0%
+I'm the sixth floor is for animals
+all of animals are generally in
+
+ align:start position:0%
+all of animals are generally in
+ 
+
+ align:start position:0%
+all of animals are generally in
+basement one of the future for building
+
+ align:start position:0%
+basement one of the future for building
+ 
+
+ align:start position:0%
+basement one of the future for building
+University Research facilities given
+
+ align:start position:0%
+University Research facilities given
+ 
+
+ align:start position:0%
+University Research facilities given
+climate
+
+ align:start position:0%
+climate
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+
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+climate
+change in New York un New York
+
+ align:start position:0%
+change in New York un New York
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+
+ align:start position:0%
+change in New York un New York
+University the animal Laboratories in
+
+ align:start position:0%
+University the animal Laboratories in
+ 
+
+ align:start position:0%
+University the animal Laboratories in
+the basement W
+
+ align:start position:0%
+the basement W
+ 
+
+ align:start position:0%
+the basement W
+flattered all the research was
+
+ align:start position:0%
+flattered all the research was
+ 
+
+ align:start position:0%
+flattered all the research was
+lost we put our up in the sky for no
+
+ align:start position:0%
+lost we put our up in the sky for no
+ 
+
+ align:start position:0%
+lost we put our up in the sky for no
+clear
+
+ align:start position:0%
+clear
+ 
+
+ align:start position:0%
+clear
+reasons we thought the animals would be
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+reasons we thought the animals would be
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+
+ align:start position:0%
+reasons we thought the animals would be
+better off up in the air then down in
+
+ align:start position:0%
+better off up in the air then down in
+ 
+
+ align:start position:0%
+better off up in the air then down in
+the basement and nobody
+
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+the basement and nobody
+ 
+
+ align:start position:0%
+the basement and nobody
+disagreed on top of that floor is a
+
+ align:start position:0%
+disagreed on top of that floor is a
+ 
+
+ align:start position:0%
+disagreed on top of that floor is a
+floor of
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+floor of
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+floor of
+machines machines which look like
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+machines machines which look like
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+machines machines which look like
+airplane systems because the building
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+airplane systems because the building
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+
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+needs to be is
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+needs to be is
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+needs to be is
+a is a laboratory
+
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+a is a laboratory
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+
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+a is a laboratory
+which has
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+which has
+ 
+
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+which has
+to account for research which requires
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+to account for research which requires
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+to account for research which requires
+highly specialized vectors of steam
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+highly specialized vectors of steam
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+highly specialized vectors of steam
+light all kinds of elements
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+light all kinds of elements
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+light all kinds of elements
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+depths of about 18 in or 2 ft in places
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+is so dense that you cannot get another
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+is so dense that you cannot get another
+ 
+
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+is so dense that you cannot get another
+pipe through
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+pipe through
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+
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+pipe through
+there if we had been count if MIT would
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+there if we had been count if MIT would
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+
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+have allowed us to account for future
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+have allowed us to account for future
+flexibility we would have made the depth
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+flexibility we would have made the depth
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+flexibility we would have made the depth
+greater than the 18 in of TV it costs
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+greater than the 18 in of TV it costs
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+greater than the 18 in of TV it costs
+money we weren't allowed to plan the
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+money we weren't allowed to plan the
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+
+ align:start position:0%
+money we weren't allowed to plan the
+building with
+
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+building with
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+
+ align:start position:0%
+building with
+any space on the building called TBA to
+
+ align:start position:0%
+any space on the building called TBA to
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+
+ align:start position:0%
+any space on the building called TBA to
+be
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+ align:start position:0%
+be
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+
+ align:start position:0%
+be
+added we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+to it's like packing a aircraft
+
+ align:start position:0%
+to it's like packing a aircraft
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+ align:start position:0%
+to it's like packing a aircraft
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+
+ align:start position:0%
+change internally but anyway let's move
+ 
+
+ align:start position:0%
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+on with this these
+
+ align:start position:0%
+on with this these
+ 
+
+ align:start position:0%
+on with this these
+diagrams got a few minutes
+
+ align:start position:0%
+diagrams got a few minutes
+ 
+
+ align:start position:0%
+diagrams got a few minutes
+left the pottery think belt of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1966 with Cedric price the British
+
+ align:start position:0%
+1966 with Cedric price the British
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+
+ align:start position:0%
+1966 with Cedric price the British
+Architects attempt to do a couple of
+
+ align:start position:0%
+Architects attempt to do a couple of
+ 
+
+ align:start position:0%
+Architects attempt to do a couple of
+things to eliminate the idea of a campus
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+things to eliminate the idea of a campus
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+
+ align:start position:0%
+things to eliminate the idea of a campus
+from having only having separateness
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+from having only having separateness
+ 
+
+ align:start position:0%
+from having only having separateness
+from the rest of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+urbanism he decided to
+
+ align:start position:0%
+urbanism he decided to
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+
+ align:start position:0%
+urbanism he decided to
+reuse the to place this British
+
+ align:start position:0%
+reuse the to place this British
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+
+ align:start position:0%
+reuse the to place this British
+University in an area of suffering
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+University in an area of suffering
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+
+ align:start position:0%
+University in an area of suffering
+economic decline in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Staffordshire he argued
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this embedding of the University
+
+ align:start position:0%
+that this embedding of the University
+ 
+
+ align:start position:0%
+that this embedding of the University
+into the society's needs would
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+ align:start position:0%
+into the society's needs would
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+
+ align:start position:0%
+into the society's needs would
+spontaneously produce a another kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+University such as it would it would
+
+ align:start position:0%
+University such as it would it would
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+
+ align:start position:0%
+University such as it would it would
+stimulate the economy for instance
+
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+stimulate the economy for instance
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+
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+stimulate the economy for instance
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+
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+on instead of building university
+ 
+
+ align:start position:0%
+on instead of building university
+dormitories I showed you a project
+
+ align:start position:0%
+dormitories I showed you a project
+ 
+
+ align:start position:0%
+dormitories I showed you a project
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+New
+
+ align:start position:0%
+New
+ 
+
+ align:start position:0%
+New
+York by the fort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Foundation which attempted to do the
+
+ align:start position:0%
+Foundation which attempted to do the
+ 
+
+ align:start position:0%
+Foundation which attempted to do the
+same thing that instead of building
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+same thing that instead of building
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+same thing that instead of building
+university
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+university
+ 
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+university
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+dormitories create a market for the
+ 
+
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+dormitories create a market for the
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+supply of housing by the poor people
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+
+ align:start position:0%
+supply of housing by the poor people
+around the
+
+ align:start position:0%
+around the
+ 
+
+ align:start position:0%
+around the
+University
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the last of these plans is the most
+
+ align:start position:0%
+the last of these plans is the most
+ 
+
+ align:start position:0%
+the last of these plans is the most
+famous of them it's the Free University
+
+ align:start position:0%
+famous of them it's the Free University
+ 
+
+ align:start position:0%
+famous of them it's the Free University
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bon Shadrick Woods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+writes about this
+
+ align:start position:0%
+writes about this
+ 
+
+ align:start position:0%
+writes about this
+plan we have not we have not begun by
+
+ align:start position:0%
+plan we have not we have not begun by
+ 
+
+ align:start position:0%
+plan we have not we have not begun by
+trying to give fixed points within the
+
+ align:start position:0%
+trying to give fixed points within the
+ 
+
+ align:start position:0%
+trying to give fixed points within the
+system I know they will have this people
+
+ align:start position:0%
+system I know they will have this people
+ 
+
+ align:start position:0%
+system I know they will have this people
+make the identical features not the
+
+ align:start position:0%
+make the identical features not the
+ 
+
+ align:start position:0%
+make the identical features not the
+architect I do not want to make any
+
+ align:start position:0%
+architect I do not want to make any
+ 
+
+ align:start position:0%
+architect I do not want to make any
+symbols to begin with I think that the
+
+ align:start position:0%
+symbols to begin with I think that the
+ 
+
+ align:start position:0%
+symbols to begin with I think that the
+use of the building creates centers of
+
+ align:start position:0%
+use of the building creates centers of
+ 
+
+ align:start position:0%
+use of the building creates centers of
+activity the plan is really an attempt
+
+ align:start position:0%
+activity the plan is really an attempt
+ 
+
+ align:start position:0%
+activity the plan is really an attempt
+not to make Center and so on to begin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with it's interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the implication is that if you give
+
+ align:start position:0%
+that the implication is that if you give
+ 
+
+ align:start position:0%
+that the implication is that if you give
+a a an opportunity for people to arrange
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+ align:start position:0%
+a a an opportunity for people to arrange
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+
+ align:start position:0%
+a a an opportunity for people to arrange
+themselves they will have the capacity
+
+ align:start position:0%
+themselves they will have the capacity
+ 
+
+ align:start position:0%
+themselves they will have the capacity
+to do so in a correct manner or in a
+
+ align:start position:0%
+to do so in a correct manner or in a
+ 
+
+ align:start position:0%
+to do so in a correct manner or in a
+manner that is correct for
+
+ align:start position:0%
+manner that is correct for
+ 
+
+ align:start position:0%
+manner that is correct for
+them this is a time when CH n Chomsky
+
+ align:start position:0%
+them this is a time when CH n Chomsky
+ 
+
+ align:start position:0%
+them this is a time when CH n Chomsky
+was was lecturing
+
+ align:start position:0%
+was was lecturing
+ 
+
+ align:start position:0%
+was was lecturing
+about the innate ability of a child to
+
+ align:start position:0%
+about the innate ability of a child to
+ 
+
+ align:start position:0%
+about the innate ability of a child to
+construct a specific system of
+
+ align:start position:0%
+construct a specific system of
+ 
+
+ align:start position:0%
+construct a specific system of
+interconnection amongst
+
+ align:start position:0%
+interconnection amongst
+ 
+
+ align:start position:0%
+interconnection amongst
+Concepts and conditions of use and
+
+ align:start position:0%
+Concepts and conditions of use and
+ 
+
+ align:start position:0%
+Concepts and conditions of use and
+reference on the basis of of scatter
+
+ align:start position:0%
+reference on the basis of of scatter
+ 
+
+ align:start position:0%
+reference on the basis of of scatter
+scanty and Scattered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evidence is there DNA in human
+
+ align:start position:0%
+evidence is there DNA in human
+ 
+
+ align:start position:0%
+evidence is there DNA in human
+beings which automatically will be able
+
+ align:start position:0%
+beings which automatically will be able
+ 
+
+ align:start position:0%
+beings which automatically will be able
+to create better space than a specialist
+
+ align:start position:0%
+to create better space than a specialist
+ 
+
+ align:start position:0%
+to create better space than a specialist
+guiding them or what combination of the
+
+ align:start position:0%
+guiding them or what combination of the
+ 
+
+ align:start position:0%
+guiding them or what combination of the
+two classical
+
+ align:start position:0%
+two classical
+ 
+
+ align:start position:0%
+two classical
+anarchism what would be the wisdom of
+
+ align:start position:0%
+anarchism what would be the wisdom of
+ 
+
+ align:start position:0%
+anarchism what would be the wisdom of
+the Clow in that sense
+
+ align:start position:0%
+the Clow in that sense
+ 
+
+ align:start position:0%
+the Clow in that sense
+well as I can only judge from from
+
+ align:start position:0%
+well as I can only judge from from
+ 
+
+ align:start position:0%
+well as I can only judge from from
+Shadrick Woods who was a very good
+
+ align:start position:0%
+Shadrick Woods who was a very good
+ 
+
+ align:start position:0%
+Shadrick Woods who was a very good
+architect um this is absolutely
+
+ align:start position:0%
+architect um this is absolutely
+ 
+
+ align:start position:0%
+architect um this is absolutely
+anti-classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the crowd will organize itself as it
+
+ align:start position:0%
+the crowd will organize itself as it
+ 
+
+ align:start position:0%
+the crowd will organize itself as it
+goes along and works and
+
+ align:start position:0%
+goes along and works and
+ 
+
+ align:start position:0%
+goes along and works and
+studies there will be a generation of
+
+ align:start position:0%
+studies there will be a generation of
+ 
+
+ align:start position:0%
+studies there will be a generation of
+space which will be more the result of
+
+ align:start position:0%
+space which will be more the result of
+ 
+
+ align:start position:0%
+space which will be more the result of
+the participation of the people then
+
+ align:start position:0%
+the participation of the people then
+ 
+
+ align:start position:0%
+the participation of the people then
+imposed on them I'm putting it rather
+
+ align:start position:0%
+imposed on them I'm putting it rather
+ 
+
+ align:start position:0%
+imposed on them I'm putting it rather
+crudely the notion that there is a DNA
+
+ align:start position:0%
+crudely the notion that there is a DNA
+ 
+
+ align:start position:0%
+crudely the notion that there is a DNA
+in all human beings according to
+
+ align:start position:0%
+in all human beings according to
+ 
+
+ align:start position:0%
+in all human beings according to
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+
+ align:start position:0%
+Chomsky which allows the child to com
+ 
+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+having been told how to do
+ 
+
+ align:start position:0%
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+
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+ 
+
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+
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+
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+ 
+
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+
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+ 
+
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+
+ align:start position:0%
+as an authority now there's still
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+controversies around whether the DNA of
+ 
+
+ align:start position:0%
+controversies around whether the DNA of
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learning my own position about the Free
+
+ align:start position:0%
+learning my own position about the Free
+ 
+
+ align:start position:0%
+learning my own position about the Free
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+
+ align:start position:0%
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+ 
+
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+
+ align:start position:0%
+history it's been vandalized it's been
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+
+ align:start position:0%
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+
+ align:start position:0%
+destroyed it's had to be
+ 
+
+ align:start position:0%
+destroyed it's had to be
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+it never fulfilled the promise that wood
+ 
+
+ align:start position:0%
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+had for
+
+ align:start position:0%
+had for
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+it so what we see through look through
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+all of these cases from Sussex in
+ 
+
+ align:start position:0%
+all of these cases from Sussex in
+61 where the Armature of separated Camp
+
+ align:start position:0%
+61 where the Armature of separated Camp
+ 
+
+ align:start position:0%
+61 where the Armature of separated Camp
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+
+ align:start position:0%
+items in a
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+dismantled into a
+ 
+
+ align:start position:0%
+dismantled into a
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+system which is almost cybernetic in a
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free associations of networks created a
+
+ align:start position:0%
+free associations of networks created a
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationships the trouble with
+
+ align:start position:0%
+relationships the trouble with
+ 
+
+ align:start position:0%
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+architecture is that it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easy you just can't take a piece of
+
+ align:start position:0%
+easy you just can't take a piece of
+ 
+
+ align:start position:0%
+easy you just can't take a piece of
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+has to have
+
+ align:start position:0%
+has to have
+ 
+
+ align:start position:0%
+has to have
+bearing Acoustics unfortunately means
+
+ align:start position:0%
+bearing Acoustics unfortunately means
+ 
+
+ align:start position:0%
+bearing Acoustics unfortunately means
+that the only way to separate sound is
+
+ align:start position:0%
+that the only way to separate sound is
+ 
+
+ align:start position:0%
+that the only way to separate sound is
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass so University is the last place in
+
+ align:start position:0%
+mass so University is the last place in
+ 
+
+ align:start position:0%
+mass so University is the last place in
+the world to flitter around with stud
+
+ align:start position:0%
+the world to flitter around with stud
+ 
+
+ align:start position:0%
+the world to flitter around with stud
+walls or metal prefabricated metal
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+panels if we had a prefabricated metal
+panel
+
+ align:start position:0%
+panel
+ 
+
+ align:start position:0%
+panel
+uninsulated we wouldn't be able to teach
+
+ align:start position:0%
+uninsulated we wouldn't be able to teach
+ 
+
+ align:start position:0%
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+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
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+class so again the pan distribution
+
+ align:start position:0%
+class so again the pan distribution
+ 
+
+ align:start position:0%
+class so again the pan distribution
+might
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+say might guide one into knowing the
+ 
+
+ align:start position:0%
+say might guide one into knowing the
+frequency of places which need acoustic
+
+ align:start position:0%
+frequency of places which need acoustic
+ 
+
+ align:start position:0%
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+separation versus those that don't in
+
+ align:start position:0%
+separation versus those that don't in
+ 
+
+ align:start position:0%
+separation versus those that don't in
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+of making everything
+
+ align:start position:0%
+of making everything
+ 
+
+ align:start position:0%
+of making everything
+possible a pan distribution would say
+
+ align:start position:0%
+possible a pan distribution would say
+ 
+
+ align:start position:0%
+possible a pan distribution would say
+that the likelihood of wet Laboratories
+
+ align:start position:0%
+that the likelihood of wet Laboratories
+ 
+
+ align:start position:0%
+that the likelihood of wet Laboratories
+occurring in your campus or this and
+
+ align:start position:0%
+occurring in your campus or this and
+ 
+
+ align:start position:0%
+occurring in your campus or this and
+therefore you should only
+
+ align:start position:0%
+therefore you should only
+ 
+
+ align:start position:0%
+therefore you should only
+spend the money on a feasible uh
+
+ align:start position:0%
+spend the money on a feasible uh
+ 
+
+ align:start position:0%
+spend the money on a feasible uh
+solution which requires 70% of your
+
+ align:start position:0%
+solution which requires 70% of your
+ 
+
+ align:start position:0%
+solution which requires 70% of your
+buildings to have this
+
+ align:start position:0%
+buildings to have this
+ 
+
+ align:start position:0%
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+flexibility the stata building has no
+
+ align:start position:0%
+flexibility the stata building has no
+ 
+
+ align:start position:0%
+flexibility the stata building has no
+wet Laboratories in it it has therefore
+
+ align:start position:0%
+wet Laboratories in it it has therefore
+ 
+
+ align:start position:0%
+wet Laboratories in it it has therefore
+it has nothing uh I mean if you knew
+
+ align:start position:0%
+it has nothing uh I mean if you knew
+ 
+
+ align:start position:0%
+it has nothing uh I mean if you knew
+architecture well enough you could look
+
+ align:start position:0%
+architecture well enough you could look
+ 
+
+ align:start position:0%
+architecture well enough you could look
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+
+ align:start position:0%
+at the STA building in our building and
+ 
+
+ align:start position:0%
+at the STA building in our building and
+compare them fundamentally and say the
+
+ align:start position:0%
+compare them fundamentally and say the
+ 
+
+ align:start position:0%
+compare them fundamentally and say the
+one has wet Laboratories the one doesn't
+
+ align:start position:0%
+one has wet Laboratories the one doesn't
+ 
+
+ align:start position:0%
+one has wet Laboratories the one doesn't
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+
+ align:start position:0%
+doesn't have any by looking at the the
+ 
+
+ align:start position:0%
+doesn't have any by looking at the the
+amount of chimneys on the
+
+ align:start position:0%
+amount of chimneys on the
+ 
+
+ align:start position:0%
+amount of chimneys on the
+roof we have every kind of
+
+ align:start position:0%
+roof we have every kind of
+ 
+
+ align:start position:0%
+roof we have every kind of
+Chimney emanating smoke or gas whatever
+
+ align:start position:0%
+Chimney emanating smoke or gas whatever
+ 
+
+ align:start position:0%
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+comes from
+
+ align:start position:0%
+comes from
+ 
+
+ align:start position:0%
+comes from
+MIT U the STA building has nothing it
+
+ align:start position:0%
+MIT U the STA building has nothing it
+ 
+
+ align:start position:0%
+MIT U the STA building has nothing it
+has a flat ceiling roof it's about the
+
+ align:start position:0%
+has a flat ceiling roof it's about the
+ 
+
+ align:start position:0%
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+only flat plane in the
+
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+only flat plane in the
+ 
+
+ align:start position:0%
+only flat plane in the
+building okay
+
+ align:start position:0%
+building okay
+ 
+
+ align:start position:0%
+building okay
+I want to look briefly at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two other
+
+ align:start position:0%
+two other
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+
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+ 
+
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+the by the way there's a piece
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+
+ align:start position:0%
+by William
+ 
+
+ align:start position:0%
+by William
+forcet in
+
+ align:start position:0%
+forcet in
+ 
+
+ align:start position:0%
+forcet in
+the MIT planning Journal of one of two
+
+ align:start position:0%
+the MIT planning Journal of one of two
+ 
+
+ align:start position:0%
+the MIT planning Journal of one of two
+volumes ago on flexible life
+
+ align:start position:0%
+volumes ago on flexible life
+ 
+
+ align:start position:0%
+volumes ago on flexible life
+flexibility
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+flexibility the life cycle options the
+
+ align:start position:0%
+flexibility the life cycle options the
+ 
+
+ align:start position:0%
+flexibility the life cycle options the
+synthesis he talks about he gives
+
+ align:start position:0%
+synthesis he talks about he gives
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+of prediction which is based on
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+estimates of outcome and the costing of
+ 
+
+ align:start position:0%
+estimates of outcome and the costing of
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+
+ align:start position:0%
+the estimates of outcome and the
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+decision which is based
+ 
+
+ align:start position:0%
+decision which is based
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+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+system I'd also recommend that you read
+
+ align:start position:0%
+system I'd also recommend that you read
+ 
+
+ align:start position:0%
+system I'd also recommend that you read
+some something in Kevin Lynch's book
+
+ align:start position:0%
+some something in Kevin Lynch's book
+ 
+
+ align:start position:0%
+some something in Kevin Lynch's book
+what time is this
+
+ align:start position:0%
+what time is this
+ 
+
+ align:start position:0%
+what time is this
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+
+ align:start position:0%
+place for an attempt to in the space
+ 
+
+ align:start position:0%
+place for an attempt to in the space
+time continuum to play around with the
+
+ align:start position:0%
+time continuum to play around with the
+ 
+
+ align:start position:0%
+time continuum to play around with the
+idea of
+
+ align:start position:0%
+idea of
+ 
+
+ align:start position:0%
+idea of
+time is a page in which he goes through
+
+ align:start position:0%
+time is a page in which he goes through
+ 
+
+ align:start position:0%
+time is a page in which he goes through
+a whole number of possibilities of
+
+ align:start position:0%
+a whole number of possibilities of
+ 
+
+ align:start position:0%
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+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
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+
+ align:start position:0%
+time and its implic he doesn't speculate
+ 
+
+ align:start position:0%
+time and its implic he doesn't speculate
+about his implications on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space I'm going to skip a bunch of stuff
+
+ align:start position:0%
+space I'm going to skip a bunch of stuff
+ 
+
+ align:start position:0%
+space I'm going to skip a bunch of stuff
+and end with the last two because we
+
+ align:start position:0%
+and end with the last two because we
+ 
+
+ align:start position:0%
+and end with the last two because we
+won't have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time I'll deal with
+
+ align:start position:0%
+time I'll deal with
+ 
+
+ align:start position:0%
+time I'll deal with
+this mainly through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slides I can't find the right
+
+ align:start position:0%
+slides I can't find the right
+ 
+
+ align:start position:0%
+slides I can't find the right
+place the two cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are the use of temporary environments of
+
+ align:start position:0%
+are the use of temporary environments of
+ 
+
+ align:start position:0%
+are the use of temporary environments of
+a fairly large scale in City
+
+ align:start position:0%
+a fairly large scale in City
+ 
+
+ align:start position:0%
+a fairly large scale in City
+the one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the story of Paris between 1855 in
+
+ align:start position:0%
+the story of Paris between 1855 in
+ 
+
+ align:start position:0%
+the story of Paris between 1855 in
+1900 after the success of the Crystal
+
+ align:start position:0%
+1900 after the success of the Crystal
+ 
+
+ align:start position:0%
+1900 after the success of the Crystal
+Palace exhibition in 1851 in London the
+
+ align:start position:0%
+Palace exhibition in 1851 in London the
+ 
+
+ align:start position:0%
+Palace exhibition in 1851 in London the
+French built an exhibition In
+
+ align:start position:0%
+French built an exhibition In
+ 
+
+ align:start position:0%
+French built an exhibition In
+1855 and almost every 11 years
+
+ align:start position:0%
+1855 and almost every 11 years
+ 
+
+ align:start position:0%
+1855 and almost every 11 years
+afterwards
+
+ align:start position:0%
+afterwards
+ 
+
+ align:start position:0%
+afterwards
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1867 18 1878
+
+ align:start position:0%
+1867 18 1878
+ 
+
+ align:start position:0%
+1867 18 1878
+1889 and
+
+ align:start position:0%
+1889 and
+ 
+
+ align:start position:0%
+1889 and
+1900 it had an exhibition a temporary
+
+ align:start position:0%
+1900 it had an exhibition a temporary
+ 
+
+ align:start position:0%
+1900 it had an exhibition a temporary
+exhibition a major temporary exhibition
+
+ align:start position:0%
+exhibition a major temporary exhibition
+ 
+
+ align:start position:0%
+exhibition a major temporary exhibition
+in the center of Paris just north of the
+
+ align:start position:0%
+in the center of Paris just north of the
+ 
+
+ align:start position:0%
+in the center of Paris just north of the
+S and largely south of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s i I'll go through some of the material
+
+ align:start position:0%
+s i I'll go through some of the material
+ 
+
+ align:start position:0%
+s i I'll go through some of the material
+with the slides
+
+ align:start position:0%
+with the slides
+ 
+
+ align:start position:0%
+with the slides
+but let me read you a quote from the
+
+ align:start position:0%
+but let me read you a quote from the
+ 
+
+ align:start position:0%
+but let me read you a quote from the
+French
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+novelist Jean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jiru about the existence of a temporary
+
+ align:start position:0%
+jiru about the existence of a temporary
+ 
+
+ align:start position:0%
+jiru about the existence of a temporary
+city as opposed in conjunction with a
+
+ align:start position:0%
+city as opposed in conjunction with a
+ 
+
+ align:start position:0%
+city as opposed in conjunction with a
+permanent
+
+ align:start position:0%
+permanent
+ 
+
+ align:start position:0%
+permanent
+City he's talking about the citizens of
+
+ align:start position:0%
+City he's talking about the citizens of
+ 
+
+ align:start position:0%
+City he's talking about the citizens of
+Paris they are delighted by the thought
+
+ align:start position:0%
+Paris they are delighted by the thought
+ 
+
+ align:start position:0%
+Paris they are delighted by the thought
+of reaching this cardboard or plaster
+
+ align:start position:0%
+of reaching this cardboard or plaster
+ 
+
+ align:start position:0%
+of reaching this cardboard or plaster
+City through the permanent Stone site of
+
+ align:start position:0%
+City through the permanent Stone site of
+ 
+
+ align:start position:0%
+City through the permanent Stone site of
+Paris what an extraordinary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea that part of your city is rotating
+
+ align:start position:0%
+idea that part of your city is rotating
+ 
+
+ align:start position:0%
+idea that part of your city is rotating
+at a faster speed than the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parts the Free University of villin has
+
+ align:start position:0%
+parts the Free University of villin has
+ 
+
+ align:start position:0%
+parts the Free University of villin has
+no stone sight it only has
+
+ align:start position:0%
+no stone sight it only has
+ 
+
+ align:start position:0%
+no stone sight it only has
+transparency maybe you need a balance
+
+ align:start position:0%
+transparency maybe you need a balance
+ 
+
+ align:start position:0%
+transparency maybe you need a balance
+between tone Stone sight and carboard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+he goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on they do not come to see a disguised
+
+ align:start position:0%
+on they do not come to see a disguised
+ 
+
+ align:start position:0%
+on they do not come to see a disguised
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+transed
+
+ align:start position:0%
+transed
+ 
+
+ align:start position:0%
+transed
+Paris this is not a the exhibitions are
+
+ align:start position:0%
+Paris this is not a the exhibitions are
+ 
+
+ align:start position:0%
+Paris this is not a the exhibitions are
+not transverses Paris not changed Paris
+
+ align:start position:0%
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+
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+ 
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+trees but it was a signal event because
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+
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+ 
+
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+game that that's the Winter Olympic I'm
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+
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+
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+
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+the Olympic Games really only took off
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+
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+the Olympic Games really only took off
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+
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+ 
+
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+
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+ 
+ 
+
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+alcohol oh it was remarkable it made a
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+alcohol oh it was remarkable it made a
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+
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+
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+
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+
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+presentation and I showed the
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+
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+presentation and I showed the
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+introduction to Linny rell's film as
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+
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+introduction to Linny rell's film as
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+
+ align:start position:0%
+opposed to the 84 Olympic Games in Los
+ 
+
+ align:start position:0%
+opposed to the 84 Olympic Games in Los
+Angeles
+
+ align:start position:0%
+Angeles
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+
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+Angeles
+reenal in case you don't know Denny
+
+ align:start position:0%
+reenal in case you don't know Denny
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+
+ align:start position:0%
+reenal in case you don't know Denny
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+reenal she was the German she was the
+ 
+
+ align:start position:0%
+reenal she was the German she was the
+very cryptic and uh and uh all over the
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+ align:start position:0%
+very cryptic and uh and uh all over the
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+
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+very cryptic and uh and uh all over the
+place
+
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+place
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+
+ align:start position:0%
+place
+German uh filmmaker who made Olympia
+
+ align:start position:0%
+German uh filmmaker who made Olympia
+ 
+
+ align:start position:0%
+German uh filmmaker who made Olympia
+she convinced Gobles and Hitler to
+
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+she convinced Gobles and Hitler to
+ 
+
+ align:start position:0%
+she convinced Gobles and Hitler to
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+ align:start position:0%
+record they were very proud of the fact
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+
+ align:start position:0%
+record they were very proud of the fact
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+
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+that Hollywood couldn't make a film of
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+
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+that Hollywood couldn't make a film of
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+
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+the 32
+ 
+
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+the 32
+games I'll show you some of the first
+
+ align:start position:0%
+games I'll show you some of the first
+ 
+
+ align:start position:0%
+games I'll show you some of the first
+still photographs from the 32 games but
+
+ align:start position:0%
+still photographs from the 32 games but
+ 
+
+ align:start position:0%
+still photographs from the 32 games but
+Hitler said we are going to make a
+
+ align:start position:0%
+Hitler said we are going to make a
+ 
+
+ align:start position:0%
+Hitler said we are going to make a
+film and I could go into some detail
+
+ align:start position:0%
+film and I could go into some detail
+ 
+
+ align:start position:0%
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+about the film but you can still find
+
+ align:start position:0%
+about the film but you can still find
+ 
+
+ align:start position:0%
+about the film but you can still find
+Olympia in the 7 11 not 711 what what is
+
+ align:start position:0%
+Olympia in the 7 11 not 711 what what is
+ 
+
+ align:start position:0%
+Olympia in the 7 11 not 711 what what is
+what what are the local sophisticated
+
+ align:start position:0%
+what what are the local sophisticated
+ 
+
+ align:start position:0%
+what what are the local sophisticated
+local video Outlets here in
+
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+local video Outlets here in
+ 
+
+ align:start position:0%
+local video Outlets here in
+Cambridge I don't know it's all on your
+
+ align:start position:0%
+Cambridge I don't know it's all on your
+ 
+
+ align:start position:0%
+Cambridge I don't know it's all on your
+computer now yeah well if you can find
+
+ align:start position:0%
+computer now yeah well if you can find
+ 
+
+ align:start position:0%
+computer now yeah well if you can find
+it Michael if you can find it on your
+
+ align:start position:0%
+it Michael if you can find it on your
+ 
+
+ align:start position:0%
+it Michael if you can find it on your
+computer find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um let's look at these images I'm sorry
+
+ align:start position:0%
+um let's look at these images I'm sorry
+ 
+
+ align:start position:0%
+um let's look at these images I'm sorry
+I have to show uh I've written about the
+
+ align:start position:0%
+I have to show uh I've written about the
+ 
+
+ align:start position:0%
+I have to show uh I've written about the
+Olympic Games it's in the were reading
+
+ align:start position:0%
+Olympic Games it's in the were reading
+ 
+
+ align:start position:0%
+Olympic Games it's in the were reading
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+uh I went to I've been to two Olympic
+
+ align:start position:0%
+uh I went to I've been to two Olympic
+ 
+
+ align:start position:0%
+uh I went to I've been to two Olympic
+Games this is the last meeting of cim
+
+ align:start position:0%
+Games this is the last meeting of cim
+ 
+
+ align:start position:0%
+Games this is the last meeting of cim
+and the arguments in aut too between the
+
+ align:start position:0%
+and the arguments in aut too between the
+ 
+
+ align:start position:0%
+and the arguments in aut too between the
+closed aesthetic of bbp's building in
+
+ align:start position:0%
+closed aesthetic of bbp's building in
+ 
+
+ align:start position:0%
+closed aesthetic of bbp's building in
+Milan and Jan Carlo's building in Mata
+
+ align:start position:0%
+Milan and Jan Carlo's building in Mata
+ 
+
+ align:start position:0%
+Milan and Jan Carlo's building in Mata
+in the south of Italy I haven't got time
+
+ align:start position:0%
+in the south of Italy I haven't got time
+ 
+
+ align:start position:0%
+in the south of Italy I haven't got time
+to go into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next some of the projects of Team 10
+
+ align:start position:0%
+next some of the projects of Team 10
+ 
+
+ align:start position:0%
+next some of the projects of Team 10
+this is Addison and Peter smithson's
+
+ align:start position:0%
+this is Addison and Peter smithson's
+ 
+
+ align:start position:0%
+this is Addison and Peter smithson's
+project for the golden Lane competition
+
+ align:start position:0%
+project for the golden Lane competition
+ 
+
+ align:start position:0%
+project for the golden Lane competition
+you'll see the drawing indicates an
+
+ align:start position:0%
+you'll see the drawing indicates an
+ 
+
+ align:start position:0%
+you'll see the drawing indicates an
+enormous attempt to create
+
+ align:start position:0%
+enormous attempt to create
+ 
+
+ align:start position:0%
+enormous attempt to create
+maximize
+
+ align:start position:0%
+maximize
+ 
+
+ align:start position:0%
+maximize
+communication almost every level has
+
+ align:start position:0%
+communication almost every level has
+ 
+
+ align:start position:0%
+communication almost every level has
+people on it doing something or
+
+ align:start position:0%
+people on it doing something or
+ 
+
+ align:start position:0%
+people on it doing something or
+other yeah is a building which takes
+
+ align:start position:0%
+other yeah is a building which takes
+ 
+
+ align:start position:0%
+other yeah is a building which takes
+linear form and people are supposed to
+
+ align:start position:0%
+linear form and people are supposed to
+ 
+
+ align:start position:0%
+linear form and people are supposed to
+con
+
+ align:start position:0%
+con
+ 
+
+ align:start position:0%
+con
+to socially condensed to use the Russian
+
+ align:start position:0%
+to socially condensed to use the Russian
+ 
+
+ align:start position:0%
+to socially condensed to use the Russian
+term uh it's absolute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonsense I lived in when I came to
+
+ align:start position:0%
+nonsense I lived in when I came to
+ 
+
+ align:start position:0%
+nonsense I lived in when I came to
+America I lived in under Memorial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Drive it's a skip stop elevator building
+
+ align:start position:0%
+Drive it's a skip stop elevator building
+ 
+
+ align:start position:0%
+Drive it's a skip stop elevator building
+which means that you have three times
+
+ align:start position:0%
+which means that you have three times
+ 
+
+ align:start position:0%
+which means that you have three times
+the volume going into the
+
+ align:start position:0%
+the volume going into the
+ 
+
+ align:start position:0%
+the volume going into the
+elevator I picked up a newspaper every
+
+ align:start position:0%
+elevator I picked up a newspaper every
+ 
+
+ align:start position:0%
+elevator I picked up a newspaper every
+morning uh quite early in the morning
+
+ align:start position:0%
+morning uh quite early in the morning
+ 
+
+ align:start position:0%
+morning uh quite early in the morning
+outside the front of the door I never in
+
+ align:start position:0%
+outside the front of the door I never in
+ 
+
+ align:start position:0%
+outside the front of the door I never in
+10 years ever saw another person in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corridor
+
+ align:start position:0%
+corridor
+ 
+
+ align:start position:0%
+corridor
+next parkel Sheffield one of the
+
+ align:start position:0%
+next parkel Sheffield one of the
+ 
+
+ align:start position:0%
+next parkel Sheffield one of the
+outgrows of this system it's now being
+
+ align:start position:0%
+outgrows of this system it's now being
+ 
+
+ align:start position:0%
+outgrows of this system it's now being
+rehabilitated and changed you can see
+
+ align:start position:0%
+rehabilitated and changed you can see
+ 
+
+ align:start position:0%
+rehabilitated and changed you can see
+again the whole idea
+
+ align:start position:0%
+again the whole idea
+ 
+
+ align:start position:0%
+again the whole idea
+of The
+
+ align:start position:0%
+of The
+ 
+
+ align:start position:0%
+of The
+Pedestrian
+
+ align:start position:0%
+Pedestrian
+ 
+
+ align:start position:0%
+Pedestrian
+sidewalk which is in sidewalk elevated
+
+ align:start position:0%
+sidewalk which is in sidewalk elevated
+ 
+
+ align:start position:0%
+sidewalk which is in sidewalk elevated
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+space is that people will use it
+
+ align:start position:0%
+space is that people will use it
+ 
+
+ align:start position:0%
+space is that people will use it
+to they just too few people in a
+
+ align:start position:0%
+to they just too few people in a
+ 
+
+ align:start position:0%
+to they just too few people in a
+building of this kind in most
+
+ align:start position:0%
+building of this kind in most
+ 
+
+ align:start position:0%
+building of this kind in most
+residential buildings to generate
+
+ align:start position:0%
+residential buildings to generate
+ 
+
+ align:start position:0%
+residential buildings to generate
+enough as if communicating with
+
+ align:start position:0%
+enough as if communicating with
+ 
+
+ align:start position:0%
+enough as if communicating with
+everybody who lives next to you is a
+
+ align:start position:0%
+everybody who lives next to you is a
+ 
+
+ align:start position:0%
+everybody who lives next to you is a
+good idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean it's it's it's it's a strange
+
+ align:start position:0%
+I mean it's it's it's it's a strange
+ 
+
+ align:start position:0%
+I mean it's it's it's it's a strange
+it's a strange notion in our thinking
+
+ align:start position:0%
+it's a strange notion in our thinking
+ 
+
+ align:start position:0%
+it's a strange notion in our thinking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+urbanism that we all
+
+ align:start position:0%
+urbanism that we all
+ 
+
+ align:start position:0%
+urbanism that we all
+Greeks meeting in the Agra to discuss
+
+ align:start position:0%
+Greeks meeting in the Agra to discuss
+ 
+
+ align:start position:0%
+Greeks meeting in the Agra to discuss
+our local
+
+ align:start position:0%
+our local
+ 
+
+ align:start position:0%
+our local
+politics
+
+ align:start position:0%
+politics
+ 
+
+ align:start position:0%
+politics
+uh the all kind we'll come back to this
+
+ align:start position:0%
+uh the all kind we'll come back to this
+ 
+
+ align:start position:0%
+uh the all kind we'll come back to this
+in talking about the Contemporary
+
+ align:start position:0%
+in talking about the Contemporary
+ 
+
+ align:start position:0%
+in talking about the Contemporary
+American City but there's a mistaken
+
+ align:start position:0%
+American City but there's a mistaken
+ 
+
+ align:start position:0%
+American City but there's a mistaken
+notion I think sometimes argued by
+
+ align:start position:0%
+notion I think sometimes argued by
+ 
+
+ align:start position:0%
+notion I think sometimes argued by
+Richard Senate
+
+ align:start position:0%
+Richard Senate
+ 
+
+ align:start position:0%
+Richard Senate
+mistakenly that
+
+ align:start position:0%
+mistakenly that
+ 
+
+ align:start position:0%
+mistakenly that
+uh density of
+
+ align:start position:0%
+uh density of
+ 
+
+ align:start position:0%
+uh density of
+population provides intercourse between
+
+ align:start position:0%
+population provides intercourse between
+ 
+
+ align:start position:0%
+population provides intercourse between
+people in a very spontaneous way yes you
+
+ align:start position:0%
+people in a very spontaneous way yes you
+ 
+
+ align:start position:0%
+people in a very spontaneous way yes you
+can only get married to somebody you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meet and py next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another notion by candidas jich and
+
+ align:start position:0%
+another notion by candidas jich and
+ 
+
+ align:start position:0%
+another notion by candidas jich and
+Shadrick Woods's firm the town of the
+
+ align:start position:0%
+Shadrick Woods's firm the town of the
+ 
+
+ align:start position:0%
+Shadrick Woods's firm the town of the
+extension of tulus
+
+ align:start position:0%
+extension of tulus
+ 
+
+ align:start position:0%
+extension of tulus
+tulus the notion of the web a web is an
+
+ align:start position:0%
+tulus the notion of the web a web is an
+ 
+
+ align:start position:0%
+tulus the notion of the web a web is an
+architect geometric form which is meant
+
+ align:start position:0%
+architect geometric form which is meant
+ 
+
+ align:start position:0%
+architect geometric form which is meant
+to produce important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next per is dark okay this is in your
+
+ align:start position:0%
+next per is dark okay this is in your
+ 
+
+ align:start position:0%
+next per is dark okay this is in your
+handout this is the the story of Shand
+
+ align:start position:0%
+handout this is the the story of Shand
+ 
+
+ align:start position:0%
+handout this is the the story of Shand
+reurbanization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chandigar you start off by
+
+ align:start position:0%
+chandigar you start off by
+ 
+
+ align:start position:0%
+chandigar you start off by
+building a few things over time these
+
+ align:start position:0%
+building a few things over time these
+ 
+
+ align:start position:0%
+building a few things over time these
+get added to and added to and added to
+
+ align:start position:0%
+get added to and added to and added to
+ 
+
+ align:start position:0%
+get added to and added to and added to
+and added to and the plan of the central
+
+ align:start position:0%
+and added to and the plan of the central
+ 
+
+ align:start position:0%
+and added to and the plan of the central
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+Kier changes over time as
+
+ align:start position:0%
+Kier changes over time as
+ 
+
+ align:start position:0%
+Kier changes over time as
+the growth is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+consistent all along so you start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very as I think Lou KH said you I'd like
+
+ align:start position:0%
+very as I think Lou KH said you I'd like
+ 
+
+ align:start position:0%
+very as I think Lou KH said you I'd like
+to build the town in when he was working
+
+ align:start position:0%
+to build the town in when he was working
+ 
+
+ align:start position:0%
+to build the town in when he was working
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+Daka uh first out of mud and bricks and
+
+ align:start position:0%
+Daka uh first out of mud and bricks and
+ 
+
+ align:start position:0%
+Daka uh first out of mud and bricks and
+in the end that it will become a city of
+
+ align:start position:0%
+in the end that it will become a city of
+ 
+
+ align:start position:0%
+in the end that it will become a city of
+gold something like
+
+ align:start position:0%
+gold something like
+ 
+
+ align:start position:0%
+gold something like
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next FIS dark is pro the ultimate goal
+
+ align:start position:0%
+next FIS dark is pro the ultimate goal
+ 
+
+ align:start position:0%
+next FIS dark is pro the ultimate goal
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+to exhaust the center of chandigar by
+
+ align:start position:0%
+to exhaust the center of chandigar by
+ 
+
+ align:start position:0%
+to exhaust the center of chandigar by
+new construction additions that's the
+
+ align:start position:0%
+new construction additions that's the
+ 
+
+ align:start position:0%
+new construction additions that's the
+Secretariat building in the distance and
+
+ align:start position:0%
+Secretariat building in the distance and
+ 
+
+ align:start position:0%
+Secretariat building in the distance and
+in the case of Lou
+
+ align:start position:0%
+in the case of Lou
+ 
+
+ align:start position:0%
+in the case of Lou
+Khan's Central comp Lex in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+daa Dar says
+
+ align:start position:0%
+daa Dar says
+ 
+
+ align:start position:0%
+daa Dar says
+that you can through selective additive
+
+ align:start position:0%
+that you can through selective additive
+ 
+
+ align:start position:0%
+that you can through selective additive
+transformation you can change the city
+
+ align:start position:0%
+transformation you can change the city
+ 
+
+ align:start position:0%
+transformation you can change the city
+and build on existing systems rather
+
+ align:start position:0%
+and build on existing systems rather
+ 
+
+ align:start position:0%
+and build on existing systems rather
+than create something from scratch every
+
+ align:start position:0%
+than create something from scratch every
+ 
+
+ align:start position:0%
+than create something from scratch every
+time in a finished way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next the MIT campus which you all know
+
+ align:start position:0%
+next the MIT campus which you all know
+ 
+
+ align:start position:0%
+next the MIT campus which you all know
+well that's a diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from Maria's thesis the
+
+ align:start position:0%
+from Maria's thesis the
+ 
+
+ align:start position:0%
+from Maria's thesis the
+project for the new University of borham
+
+ align:start position:0%
+project for the new University of borham
+ 
+
+ align:start position:0%
+project for the new University of borham
+in Germany by
+
+ align:start position:0%
+in Germany by
+ 
+
+ align:start position:0%
+in Germany by
+cand Jos and
+
+ align:start position:0%
+cand Jos and
+ 
+
+ align:start position:0%
+cand Jos and
+woods it has no
+
+ align:start position:0%
+woods it has no
+ 
+
+ align:start position:0%
+woods it has no
+elevations on the
+
+ align:start position:0%
+elevations on the
+ 
+
+ align:start position:0%
+elevations on the
+outskirts they are just points of growth
+
+ align:start position:0%
+outskirts they are just points of growth
+ 
+
+ align:start position:0%
+outskirts they are just points of growth
+and expansion they stop expanding with
+
+ align:start position:0%
+and expansion they stop expanding with
+ 
+
+ align:start position:0%
+and expansion they stop expanding with
+the topography
+
+ align:start position:0%
+the topography
+ 
+
+ align:start position:0%
+the topography
+curtails expansion there's a central
+
+ align:start position:0%
+curtails expansion there's a central
+ 
+
+ align:start position:0%
+curtails expansion there's a central
+line through the system but the old idea
+
+ align:start position:0%
+line through the system but the old idea
+ 
+
+ align:start position:0%
+line through the system but the old idea
+is that this is A Spacetime
+
+ align:start position:0%
+is that this is A Spacetime
+ 
+
+ align:start position:0%
+is that this is A Spacetime
+configuration that can change at a speed
+
+ align:start position:0%
+configuration that can change at a speed
+ 
+
+ align:start position:0%
+configuration that can change at a speed
+which is not yet determined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next the University of gor
+
+ align:start position:0%
+next the University of gor
+ 
+
+ align:start position:0%
+next the University of gor
+competition the university is a set of
+
+ align:start position:0%
+competition the university is a set of
+ 
+
+ align:start position:0%
+competition the university is a set of
+spaces colored in red and blue with
+
+ align:start position:0%
+spaces colored in red and blue with
+ 
+
+ align:start position:0%
+spaces colored in red and blue with
+different rates of change forget about
+
+ align:start position:0%
+different rates of change forget about
+ 
+
+ align:start position:0%
+different rates of change forget about
+the one on the right that's the
+
+ align:start position:0%
+the one on the right that's the
+ 
+
+ align:start position:0%
+the one on the right that's the
+University of pava by John Carlo deardo
+
+ align:start position:0%
+University of pava by John Carlo deardo
+ 
+
+ align:start position:0%
+University of pava by John Carlo deardo
+next lafra the 50t by 50t module footy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+serviced next the
+
+ align:start position:0%
+serviced next the
+ 
+
+ align:start position:0%
+serviced next the
+french Paris story in the Olympic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Games this this is the the white space
+
+ align:start position:0%
+Games this this is the the white space
+ 
+
+ align:start position:0%
+Games this this is the the white space
+is the transformed white space of the
+
+ align:start position:0%
+is the transformed white space of the
+ 
+
+ align:start position:0%
+is the transformed white space of the
+center of
+
+ align:start position:0%
+center of
+ 
+
+ align:start position:0%
+center of
+Paris uh from 1855 to 1900 on the right
+
+ align:start position:0%
+Paris uh from 1855 to 1900 on the right
+ 
+
+ align:start position:0%
+Paris uh from 1855 to 1900 on the right
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+various Exposition
+
+ align:start position:0%
+various Exposition
+ 
+
+ align:start position:0%
+various Exposition
+artifacts on the middle at the top is
+
+ align:start position:0%
+artifacts on the middle at the top is
+ 
+
+ align:start position:0%
+artifacts on the middle at the top is
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Pavilion on the
+
+ align:start position:0%
+Pavilion on the
+ 
+
+ align:start position:0%
+Pavilion on the
+Shan 1900 they rebuilt as they are today
+
+ align:start position:0%
+Shan 1900 they rebuilt as they are today
+ 
+
+ align:start position:0%
+Shan 1900 they rebuilt as they are today
+and link to a system across the sand on
+
+ align:start position:0%
+and link to a system across the sand on
+ 
+
+ align:start position:0%
+and link to a system across the sand on
+the south 1867 on the
+
+ align:start position:0%
+the south 1867 on the
+ 
+
+ align:start position:0%
+the south 1867 on the
+left is the perfect around the world
+
+ align:start position:0%
+left is the perfect around the world
+ 
+
+ align:start position:0%
+left is the perfect around the world
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+68 it crosses the sin and the it builds
+
+ align:start position:0%
+68 it crosses the sin and the it builds
+ 
+
+ align:start position:0%
+68 it crosses the sin and the it builds
+the EMP gadir on the on the Left Bank no
+
+ align:start position:0%
+the EMP gadir on the on the Left Bank no
+ 
+
+ align:start position:0%
+the EMP gadir on the on the Left Bank no
+it's on the right Bank in
+
+ align:start position:0%
+it's on the right Bank in
+ 
+
+ align:start position:0%
+it's on the right Bank in
+French uh and so on get the Advent of
+
+ align:start position:0%
+French uh and so on get the Advent of
+ 
+
+ align:start position:0%
+French uh and so on get the Advent of
+the Eiffel Tower
+
+ align:start position:0%
+the Eiffel Tower
+ 
+
+ align:start position:0%
+the Eiffel Tower
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+1889 you have the contrast between the
+
+ align:start position:0%
+1889 you have the contrast between the
+ 
+
+ align:start position:0%
+1889 you have the contrast between the
+the parent temporar of this building and
+
+ align:start position:0%
+the parent temporar of this building and
+ 
+
+ align:start position:0%
+the parent temporar of this building and
+the parent permanence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+1937 this one goes but the Eiffel Tower
+
+ align:start position:0%
+1937 this one goes but the Eiffel Tower
+ 
+
+ align:start position:0%
+1937 this one goes but the Eiffel Tower
+stays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next 1855 and the two buildings
+
+ align:start position:0%
+next 1855 and the two buildings
+ 
+
+ align:start position:0%
+next 1855 and the two buildings
+just west of the
+
+ align:start position:0%
+just west of the
+ 
+
+ align:start position:0%
+just west of the
+blue uh
+
+ align:start position:0%
+blue uh
+ 
+
+ align:start position:0%
+blue uh
+sh continuing years the
+
+ align:start position:0%
+sh continuing years the
+ 
+
+ align:start position:0%
+sh continuing years the
+sh and the two replacement buildings for
+
+ align:start position:0%
+sh and the two replacement buildings for
+ 
+
+ align:start position:0%
+sh and the two replacement buildings for
+the 1900
+
+ align:start position:0%
+the 1900
+ 
+
+ align:start position:0%
+the 1900
+Exposition uh I can't reach with my hand
+
+ align:start position:0%
+Exposition uh I can't reach with my hand
+ 
+
+ align:start position:0%
+Exposition uh I can't reach with my hand
+next the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1867 you over 11 years you see this
+
+ align:start position:0%
+1867 you over 11 years you see this
+ 
+
+ align:start position:0%
+1867 you over 11 years you see this
+cycle every time in the construction of
+
+ align:start position:0%
+cycle every time in the construction of
+ 
+
+ align:start position:0%
+cycle every time in the construction of
+something which is ephemeral then it is
+
+ align:start position:0%
+something which is ephemeral then it is
+ 
+
+ align:start position:0%
+something which is ephemeral then it is
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+1867 being removed
+
+ align:start position:0%
+1867 being removed
+ 
+
+ align:start position:0%
+1867 being removed
+next Del's
+
+ align:start position:0%
+next Del's
+ 
+
+ align:start position:0%
+next Del's
+painting the this painting
+
+ align:start position:0%
+painting the this painting
+ 
+
+ align:start position:0%
+painting the this painting
+has a number of features about the
+
+ align:start position:0%
+has a number of features about the
+ 
+
+ align:start position:0%
+has a number of features about the
+existential condition of the G the tyel
+
+ align:start position:0%
+existential condition of the G the tyel
+ 
+
+ align:start position:0%
+existential condition of the G the tyel
+tower as a symbol in the city and here
+
+ align:start position:0%
+tower as a symbol in the city and here
+ 
+
+ align:start position:0%
+tower as a symbol in the city and here
+is an example of a classical system
+
+ align:start position:0%
+is an example of a classical system
+ 
+
+ align:start position:0%
+is an example of a classical system
+which has much meaning apparent meaning
+
+ align:start position:0%
+which has much meaning apparent meaning
+ 
+
+ align:start position:0%
+which has much meaning apparent meaning
+embedded in it but is easily removable
+
+ align:start position:0%
+embedded in it but is easily removable
+ 
+
+ align:start position:0%
+embedded in it but is easily removable
+as opposed to that you can contrast the
+
+ align:start position:0%
+as opposed to that you can contrast the
+ 
+
+ align:start position:0%
+as opposed to that you can contrast the
+meaning of these two IM items in the
+
+ align:start position:0%
+meaning of these two IM items in the
+ 
+
+ align:start position:0%
+meaning of these two IM items in the
+urban
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system why is the Eiffel Tower still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there it produces more income than any
+
+ align:start position:0%
+there it produces more income than any
+ 
+
+ align:start position:0%
+there it produces more income than any
+other public feature in in
+
+ align:start position:0%
+other public feature in in
+ 
+
+ align:start position:0%
+other public feature in in
+Paris
+
+ align:start position:0%
+Paris
+ 
+
+ align:start position:0%
+Paris
+Paris is the largest tourist city in the
+
+ align:start position:0%
+Paris is the largest tourist city in the
+ 
+
+ align:start position:0%
+Paris is the largest tourist city in the
+world it spends more money per capita on
+
+ align:start position:0%
+world it spends more money per capita on
+ 
+
+ align:start position:0%
+world it spends more money per capita on
+cleaning the city than any other city in
+
+ align:start position:0%
+cleaning the city than any other city in
+ 
+
+ align:start position:0%
+cleaning the city than any other city in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+world city comments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next and the final resolution 1937 with
+
+ align:start position:0%
+next and the final resolution 1937 with
+ 
+
+ align:start position:0%
+next and the final resolution 1937 with
+the two winners are the Russian Pavilion
+
+ align:start position:0%
+the two winners are the Russian Pavilion
+ 
+
+ align:start position:0%
+the two winners are the Russian Pavilion
+and the German
+
+ align:start position:0%
+and the German
+ 
+
+ align:start position:0%
+and the German
+Pavilion
+
+ align:start position:0%
+Pavilion
+ 
+
+ align:start position:0%
+Pavilion
+our friend melnikov's design for the 37
+
+ align:start position:0%
+our friend melnikov's design for the 37
+ 
+
+ align:start position:0%
+our friend melnikov's design for the 37
+Exposition was never built
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next the plan of the original Olympic
+
+ align:start position:0%
+next the plan of the original Olympic
+ 
+
+ align:start position:0%
+next the plan of the original Olympic
+Games the inner core of the Temple of
+
+ align:start position:0%
+Games the inner core of the Temple of
+ 
+
+ align:start position:0%
+Games the inner core of the Temple of
+zus and
+
+ align:start position:0%
+zus and
+ 
+
+ align:start position:0%
+zus and
+Hera and outside the pester the
+
+ align:start position:0%
+Hera and outside the pester the
+ 
+
+ align:start position:0%
+Hera and outside the pester the
+wrestling the gymnasium the bathouses
+
+ align:start position:0%
+wrestling the gymnasium the bathouses
+ 
+
+ align:start position:0%
+wrestling the gymnasium the bathouses
+the guest
+
+ align:start position:0%
+the guest
+ 
+
+ align:start position:0%
+the guest
+house the Hippodrome and the stadium so
+
+ align:start position:0%
+house the Hippodrome and the stadium so
+ 
+
+ align:start position:0%
+house the Hippodrome and the stadium so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the plan for the Olympic Games in Munich
+
+ align:start position:0%
+the plan for the Olympic Games in Munich
+ 
+
+ align:start position:0%
+the plan for the Olympic Games in Munich
+in 19 when was Munich
+
+ align:start position:0%
+in 19 when was Munich
+ 
+
+ align:start position:0%
+in 19 when was Munich
+72 I think 72 68 was Mexico City I used
+
+ align:start position:0%
+72 I think 72 68 was Mexico City I used
+ 
+
+ align:start position:0%
+72 I think 72 68 was Mexico City I used
+to know the dates all but I'm
+
+ align:start position:0%
+to know the dates all but I'm
+ 
+
+ align:start position:0%
+to know the dates all but I'm
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+1896 in
+
+ align:start position:0%
+1896 in
+ 
+
+ align:start position:0%
+1896 in
+Athens
+
+ align:start position:0%
+Athens
+ 
+
+ align:start position:0%
+Athens
+1900 in Paris
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next 194 in the United States which is
+
+ align:start position:0%
+next 194 in the United States which is
+ 
+
+ align:start position:0%
+next 194 in the United States which is
+part of an
+
+ align:start position:0%
+part of an
+ 
+
+ align:start position:0%
+part of an
+international much like Paris in 1900
+
+ align:start position:0%
+international much like Paris in 1900
+ 
+
+ align:start position:0%
+international much like Paris in 1900
+1904 was part of an International
+
+ align:start position:0%
+1904 was part of an International
+ 
+
+ align:start position:0%
+1904 was part of an International
+Festival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year Bushman from South Africa produced
+
+ align:start position:0%
+year Bushman from South Africa produced
+ 
+
+ align:start position:0%
+year Bushman from South Africa produced
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+dance
+
+ align:start position:0%
+dance
+ 
+
+ align:start position:0%
+dance
+Bushman started running in the marathon
+
+ align:start position:0%
+Bushman started running in the marathon
+ 
+
+ align:start position:0%
+Bushman started running in the marathon
+were chased off the course by
+
+ align:start position:0%
+were chased off the course by
+ 
+
+ align:start position:0%
+were chased off the course by
+dogs and didn't
+
+ align:start position:0%
+dogs and didn't
+ 
+
+ align:start position:0%
+dogs and didn't
+finish the whole system
+
+ align:start position:0%
+finish the whole system
+ 
+
+ align:start position:0%
+finish the whole system
+was the
+
+ align:start position:0%
+was the
+ 
+
+ align:start position:0%
+was the
+museum the Museum
+
+ align:start position:0%
+museum the Museum
+ 
+
+ align:start position:0%
+museum the Museum
+of the great wonderful Museum of St
+
+ align:start position:0%
+of the great wonderful Museum of St
+ 
+
+ align:start position:0%
+of the great wonderful Museum of St
+Louis the art museum of St Louis is
+
+ align:start position:0%
+Louis the art museum of St Louis is
+ 
+
+ align:start position:0%
+Louis the art museum of St Louis is
+still based on the site of the original
+
+ align:start position:0%
+still based on the site of the original
+ 
+
+ align:start position:0%
+still based on the site of the original
+Exposition in
+
+ align:start position:0%
+Exposition in
+ 
+
+ align:start position:0%
+Exposition in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+next now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1932 this is one of the wonderful set of
+
+ align:start position:0%
+1932 this is one of the wonderful set of
+ 
+
+ align:start position:0%
+1932 this is one of the wonderful set of
+still photographs taken of the games in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+interesting here we have for the first
+
+ align:start position:0%
+interesting here we have for the first
+ 
+
+ align:start position:0%
+interesting here we have for the first
+time the ReUse of a
+
+ align:start position:0%
+time the ReUse of a
+ 
+
+ align:start position:0%
+time the ReUse of a
+stadium on the left is the vice
+
+ align:start position:0%
+stadium on the left is the vice
+ 
+
+ align:start position:0%
+stadium on the left is the vice
+president of the United States in person
+
+ align:start position:0%
+president of the United States in person
+ 
+
+ align:start position:0%
+president of the United States in person
+Mr Garner I think his name was Ghana at
+
+ align:start position:0%
+Mr Garner I think his name was Ghana at
+ 
+
+ align:start position:0%
+Mr Garner I think his name was Ghana at
+opening of the exhibition in 1984
+
+ align:start position:0%
+opening of the exhibition in 1984
+ 
+
+ align:start position:0%
+opening of the exhibition in 1984
+security is so tight that the President
+
+ align:start position:0%
+security is so tight that the President
+ 
+
+ align:start position:0%
+security is so tight that the President
+Ronald Reagan appears only
+
+ align:start position:0%
+Ronald Reagan appears only
+ 
+
+ align:start position:0%
+Ronald Reagan appears only
+electronically but the building Remains
+
+ align:start position:0%
+electronically but the building Remains
+ 
+
+ align:start position:0%
+electronically but the building Remains
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Same one of the extraordinary things
+
+ align:start position:0%
+Same one of the extraordinary things
+ 
+
+ align:start position:0%
+Same one of the extraordinary things
+well we'll see it in the next slide
+
+ align:start position:0%
+well we'll see it in the next slide
+ 
+
+ align:start position:0%
+well we'll see it in the next slide
+next bin in 36 the flame from the
+
+ align:start position:0%
+next bin in 36 the flame from the
+ 
+
+ align:start position:0%
+next bin in 36 the flame from the
+connection to original
+
+ align:start position:0%
+connection to original
+ 
+
+ align:start position:0%
+connection to original
+area in Greece and arriving in Berlin
+
+ align:start position:0%
+area in Greece and arriving in Berlin
+ 
+
+ align:start position:0%
+area in Greece and arriving in Berlin
+with Hitler on the stadium
+
+ align:start position:0%
+with Hitler on the stadium
+ 
+
+ align:start position:0%
+with Hitler on the stadium
+Podium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next sorry I think that's the wrong
+
+ align:start position:0%
+next sorry I think that's the wrong
+ 
+
+ align:start position:0%
+next sorry I think that's the wrong
+slide on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the slide that's supposed to be on
+
+ align:start position:0%
+the the slide that's supposed to be on
+ 
+
+ align:start position:0%
+the the slide that's supposed to be on
+the left shows the network of the Los
+
+ align:start position:0%
+the left shows the network of the Los
+ 
+
+ align:start position:0%
+the left shows the network of the Los
+Angeles 8 4 32 and 84 Stadium
+
+ align:start position:0%
+Angeles 8 4 32 and 84 Stadium
+ 
+
+ align:start position:0%
+Angeles 8 4 32 and 84 Stadium
+Transportation wise it has worked
+
+ align:start position:0%
+Transportation wise it has worked
+ 
+
+ align:start position:0%
+Transportation wise it has worked
+remarkably well because it allows
+
+ align:start position:0%
+remarkably well because it allows
+ 
+
+ align:start position:0%
+remarkably well because it allows
+distribution of traffic in every 360
+
+ align:start position:0%
+distribution of traffic in every 360
+ 
+
+ align:start position:0%
+distribution of traffic in every 360
+directions 360 Dee
+
+ align:start position:0%
+directions 360 Dee
+ 
+
+ align:start position:0%
+directions 360 Dee
+directions um this is
+
+ align:start position:0%
+directions um this is
+ 
+
+ align:start position:0%
+directions um this is
+spar's project for Hitler for 400,000
+
+ align:start position:0%
+spar's project for Hitler for 400,000
+ 
+
+ align:start position:0%
+spar's project for Hitler for 400,000
+people which would eliminate the Olympic
+
+ align:start position:0%
+people which would eliminate the Olympic
+ 
+
+ align:start position:0%
+people which would eliminate the Olympic
+Games
+
+ align:start position:0%
+Games
+ 
+
+ align:start position:0%
+Games
+configuration and hard be able to
+
+ align:start position:0%
+configuration and hard be able to
+ 
+
+ align:start position:0%
+configuration and hard be able to
+anybody to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next some of the plans this is
+
+ align:start position:0%
+next some of the plans this is
+ 
+
+ align:start position:0%
+next some of the plans this is
+so most of these stadia are built on the
+
+ align:start position:0%
+so most of these stadia are built on the
+ 
+
+ align:start position:0%
+so most of these stadia are built on the
+few on the on
+
+ align:start position:0%
+few on the on
+ 
+
+ align:start position:0%
+few on the on
+Parkland the wonderful olypic Village
+
+ align:start position:0%
+Parkland the wonderful olypic Village
+ 
+
+ align:start position:0%
+Parkland the wonderful olypic Village
+byang at the
+
+ align:start position:0%
+byang at the
+ 
+
+ align:start position:0%
+byang at the
+top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next I just cut out most of the
+
+ align:start position:0%
+next I just cut out most of the
+ 
+
+ align:start position:0%
+next I just cut out most of the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+slides this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is two aspects of the
+
+ align:start position:0%
+is two aspects of the
+ 
+
+ align:start position:0%
+is two aspects of the
+American of the couple of aspects of the
+
+ align:start position:0%
+American of the couple of aspects of the
+ 
+
+ align:start position:0%
+American of the couple of aspects of the
+Olympic Games Olympic games are tempor
+
+ align:start position:0%
+Olympic Games Olympic games are tempor
+ 
+
+ align:start position:0%
+Olympic Games Olympic games are tempor
+events in cities they've been used for
+
+ align:start position:0%
+events in cities they've been used for
+ 
+
+ align:start position:0%
+events in cities they've been used for
+cities like Tokyo to argue for building
+
+ align:start position:0%
+cities like Tokyo to argue for building
+ 
+
+ align:start position:0%
+cities like Tokyo to argue for building
+a freeway system for building new
+
+ align:start position:0%
+a freeway system for building new
+ 
+
+ align:start position:0%
+a freeway system for building new
+housing they've been all been used by
+
+ align:start position:0%
+housing they've been all been used by
+ 
+
+ align:start position:0%
+housing they've been all been used by
+countries like contemporary China Tokyo
+
+ align:start position:0%
+countries like contemporary China Tokyo
+ 
+
+ align:start position:0%
+countries like contemporary China Tokyo
+in 1960 Melbourne in 56 to introduce the
+
+ align:start position:0%
+in 1960 Melbourne in 56 to introduce the
+ 
+
+ align:start position:0%
+in 1960 Melbourne in 56 to introduce the
+city as an as a
+
+ align:start position:0%
+city as an as a
+ 
+
+ align:start position:0%
+city as an as a
+international important place for trade
+
+ align:start position:0%
+international important place for trade
+ 
+
+ align:start position:0%
+international important place for trade
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+psychological satisfaction and so on Los
+
+ align:start position:0%
+psychological satisfaction and so on Los
+ 
+
+ align:start position:0%
+psychological satisfaction and so on Los
+Angeles and the
+
+ align:start position:0%
+Angeles and the
+ 
+
+ align:start position:0%
+Angeles and the
+American Exposition Olympic Games at
+
+ align:start position:0%
+American Exposition Olympic Games at
+ 
+
+ align:start position:0%
+American Exposition Olympic Games at
+olymp at Atlanta and Los Angeles have
+
+ align:start position:0%
+olymp at Atlanta and Los Angeles have
+ 
+
+ align:start position:0%
+olymp at Atlanta and Los Angeles have
+argued that you can use reuse existing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infrastructure that you can capitalize
+
+ align:start position:0%
+infrastructure that you can capitalize
+ 
+
+ align:start position:0%
+infrastructure that you can capitalize
+on the existing resources in already in
+
+ align:start position:0%
+on the existing resources in already in
+ 
+
+ align:start position:0%
+on the existing resources in already in
+the city the 84 games builds no new
+
+ align:start position:0%
+the city the 84 games builds no new
+ 
+
+ align:start position:0%
+the city the 84 games builds no new
+housing the Olympic Village is based on
+
+ align:start position:0%
+housing the Olympic Village is based on
+ 
+
+ align:start position:0%
+housing the Olympic Village is based on
+campus housing in in the University of
+
+ align:start position:0%
+campus housing in in the University of
+ 
+
+ align:start position:0%
+campus housing in in the University of
+Southern California the only build
+
+ align:start position:0%
+Southern California the only build
+ 
+
+ align:start position:0%
+Southern California the only build
+building the only new facility built in
+
+ align:start position:0%
+building the only new facility built in
+ 
+
+ align:start position:0%
+building the only new facility built in
+' 84 is the swimming pool paid for by
+
+ align:start position:0%
+' 84 is the swimming pool paid for by
+ 
+
+ align:start position:0%
+' 84 is the swimming pool paid for by
+McDonald's so there's not only a notion
+
+ align:start position:0%
+McDonald's so there's not only a notion
+ 
+
+ align:start position:0%
+McDonald's so there's not only a notion
+of the private sector playing a role
+
+ align:start position:0%
+of the private sector playing a role
+ 
+
+ align:start position:0%
+of the private sector playing a role
+which the ioc which is a semi
+
+ align:start position:0%
+which the ioc which is a semi
+ 
+
+ align:start position:0%
+which the ioc which is a semi
+fascist organization corrupt as
+
+ align:start position:0%
+fascist organization corrupt as
+ 
+
+ align:start position:0%
+fascist organization corrupt as
+hell
+
+ align:start position:0%
+hell
+ 
+
+ align:start position:0%
+hell
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+controlling the
+
+ align:start position:0%
+controlling the
+ 
+
+ align:start position:0%
+controlling the
+franchise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Los Angeles games is widespread
+
+ align:start position:0%
+the Los Angeles games is widespread
+ 
+
+ align:start position:0%
+the Los Angeles games is widespread
+distributed according to the plan of the
+
+ align:start position:0%
+distributed according to the plan of the
+ 
+
+ align:start position:0%
+distributed according to the plan of the
+town the games in the in
+
+ align:start position:0%
+town the games in the in
+ 
+
+ align:start position:0%
+town the games in the in
+Barcelona are also very tightly
+
+ align:start position:0%
+Barcelona are also very tightly
+ 
+
+ align:start position:0%
+Barcelona are also very tightly
+associated with the major form of the
+
+ align:start position:0%
+associated with the major form of the
+ 
+
+ align:start position:0%
+associated with the major form of the
+city the
+
+ align:start position:0%
+city the
+ 
+
+ align:start position:0%
+city the
+anange
+
+ align:start position:0%
+anange
+ 
+
+ align:start position:0%
+anange
+next just the
+
+ align:start position:0%
+next just the
+ 
+
+ align:start position:0%
+next just the
+Olympic 1928 on the right the American
+
+ align:start position:0%
+Olympic 1928 on the right the American
+ 
+
+ align:start position:0%
+Olympic 1928 on the right the American
+team is housed in a
+
+ align:start position:0%
+team is housed in a
+ 
+
+ align:start position:0%
+team is housed in a
+boat the
+
+ align:start position:0%
+boat the
+ 
+
+ align:start position:0%
+boat the
+ultimate Emeral
+
+ align:start position:0%
+ultimate Emeral
+ 
+
+ align:start position:0%
+ultimate Emeral
+item this is Cape Town I was going to
+
+ align:start position:0%
+item this is Cape Town I was going to
+ 
+
+ align:start position:0%
+item this is Cape Town I was going to
+talk about Cape Town's attempt to use
+
+ align:start position:0%
+talk about Cape Town's attempt to use
+ 
+
+ align:start position:0%
+talk about Cape Town's attempt to use
+racial integration as a social basis for
+
+ align:start position:0%
+racial integration as a social basis for
+ 
+
+ align:start position:0%
+racial integration as a social basis for
+the plan of the Olympic Games they never
+
+ align:start position:0%
+the plan of the Olympic Games they never
+ 
+
+ align:start position:0%
+the plan of the Olympic Games they never
+got they never entered
+
+ align:start position:0%
+got they never entered
+ 
+
+ align:start position:0%
+got they never entered
+next and the the project for the Olympic
+
+ align:start position:0%
+next and the the project for the Olympic
+ 
+
+ align:start position:0%
+next and the the project for the Olympic
+Games in Boston re using the river and
+
+ align:start position:0%
+Games in Boston re using the river and
+ 
+
+ align:start position:0%
+Games in Boston re using the river and
+the university facilities along the
+
+ align:start position:0%
+the university facilities along the
+ 
+
+ align:start position:0%
+the university facilities along the
+river is the core and he has an
+
+ align:start position:0%
+river is the core and he has an
+ 
+
+ align:start position:0%
+river is the core and he has an
+indication of how much the games cost
+
+ align:start position:0%
+indication of how much the games cost
+ 
+
+ align:start position:0%
+indication of how much the games cost
+and the division between the private and
+
+ align:start position:0%
+and the division between the private and
+ 
+
+ align:start position:0%
+and the division between the private and
+public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector
\ No newline at end of file
diff --git a/4PkKI_S9TIQ.txt b/4PkKI_S9TIQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7ed7ecb5ed3b3c2c76af4857503a798f97a9c1ef
--- /dev/null
+++ b/4PkKI_S9TIQ.txt
@@ -0,0 +1,228 @@
+Let's wrap up our discussion of system-level
+interconnect by considering how best to connect
+
+N components that need to send messages to
+one another, e.g., CPUs on a multicore chip.
+
+Today such chips have a handful of cores,
+but soon they may have 100s or 1000s of cores.
+
+We'll build our communications network using
+point-to-point links.
+
+In our analysis, each point-to-point link
+is counted at a cost of 1 hardware unit.
+
+Sending a message across a link requires one
+time unit.
+
+And we'll assume that different links can
+operate in parallel, so more links will mean
+
+more message traffic.
+
+We'll do an asymptotic analysis of the throughput
+(total messages per unit time), latency (worst-case
+
+time to deliver a single message), and hardware
+cost.
+
+In other words, we'll make a rough estimate
+how these quantities change as N grows.
+
+Note that in general the throughput and hardware
+cost are proportional to the number of point-to-point
+
+links.
+
+Our baseline is the backplane bus discussed
+earlier, where all the components share a
+
+single communication channel.
+
+With only a single channel, bus throughput
+is 1 message per unit time and a message can
+
+travel between any two components in one time
+unit.
+
+Since each component has to have an interface
+to the shared channel, the total hardware
+
+cost is O(n).
+
+In a ring network each component sends its
+messages to a single neighbor and the links
+
+are arranged so that its possible to reach
+all components.
+
+There are N links in total, so the throughput
+and cost are both O(n).
+
+The worst case latency is also O(n) since
+a message might have to travel across N-1
+
+links to reach the neighbor that's immediately
+upstream.
+
+Ring topologies are useful when message latency
+isn't important or when most messages are
+
+to the component that's immediately downstream,
+i.e., the components form a processing pipeline.
+
+The most general network topology is when
+every component has a direct link to every
+
+other component.
+
+There are O(N**2) links so the throughput
+and cost are both O(N**2).
+
+And the latency is 1 time unit since each
+destination is directly accessible.
+
+Although expensive, complete graphs offer
+very high throughput with very low latencies.
+
+A variant of the complete graph is the crossbar
+switch where a particular row and column can
+
+be connected to form a link between particular
+A and B components
+
+with the restriction that each row and each
+column can only carry 1 message during each
+
+time unit.
+
+Assume that the first row and first column
+connect to the same component, and so on,
+
+i.e., that the example crossbar switch is
+being used to connect 4 components.
+
+Then there are O(n) messages delivered each
+time unit, with a latency of 1.
+
+There are N**2 switches in the crossbar, so
+the cost is O(N**2) even though there are
+
+only O(n) links.
+
+In mesh networks, components are connected
+to some fixed number of neighboring components,
+
+in either 2 or 3 dimensions.
+
+Hence the total number of links is proportional
+to the number of components, so both throughput
+
+and cost are O(n).
+
+The worst-case latencies for mesh networks
+are proportional to length of the sides, so
+
+the latency is O(sqrt n) for 2D meshes and
+O(cube root n) for 3D meshes.
+
+The orderly layout, constant per-node hardware
+costs, and modest worst-case latency make
+
+2D 4-neighbor meshes a popular choice for
+the current generation of experimental multi-core
+
+processors.
+
+Hypercube and tree networks offer logarithmic
+latencies, which for large N may be faster
+
+than mesh networks.
+
+The original CM-1 Connection Machine designed
+in the 80's used a hypercube network to connect
+
+up to 65,536 very simple processors, each
+connected to 16 neighbors.
+
+Later generations incorporated smaller numbers
+of more sophisticated processors, still connected
+
+by a hypercube network.
+
+In the early 90's the last generation of Connection
+Machines used a tree network, with the clever
+
+innovation that the links towards the root
+of the tree had a higher message capacity.
+
+Here's a summary of the theoretical latencies
+we calculated for the various topologies.
+
+As a reality check, it's important to realize
+that the lower bound on the worst-case distance
+
+between components in our 3-dimensional world
+is O(cube root of N).
+
+In the case of a 2D layout, the worst-case
+distance is O(sqrt N).
+
+Since we know that the time to transmit a
+message is proportional to the distance traveled,
+
+we should modify our latency calculations
+to reflect this physical constraint.
+
+Note that the bus and crossbar involve N connections
+to a single link, so here the lower-bound
+
+on the latency needs to reflect the capacitive
+load added by each connection.
+
+The winner?
+
+Mesh networks avoid the need for longer wires
+as the number of connected components grows
+
+and appear to be an attractive alternative
+for high-capacity communication networks connecting
+
+1000's of processors.
+
+Summarizing our discussion:
+point-to-point links are in common use today
+
+for system-level interconnect, and as a result
+our systems are faster, more reliable, more
+
+energy-efficient and smaller than ever before.
+
+Multi-signal parallel buses are still used
+for very-high-bandwidth connections to memories,
+
+with a lot of very careful engineering to
+avoid the electrical problems observed in
+
+earlier bus implementations.
+
+Wireless connections are in common use to
+connect mobile devices to nearby components
+
+and there has been interesting work on how
+to allow mobile devices to discover what peripherals
+
+are nearby and enable them to connect automatically.
+
+The upcoming generation of multi-core chips
+will have 10's to 100's of processing cores.
+
+There is a lot ongoing research to determine
+which communication topology would offer the
+
+best combination of high communication bandwidth
+and low latency.
+
+The next ten years will be an interesting
+time for on-chip network engineers!
\ No newline at end of file
diff --git a/4RSQTqPjOLw.txt b/4RSQTqPjOLw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6508b2dc9777e90f128270a20b3c9652b7a53bd8
--- /dev/null
+++ b/4RSQTqPjOLw.txt
@@ -0,0 +1,9339 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so welcome to our special class with
+
+ align:start position:0%
+so welcome to our special class with
+ 
+
+ align:start position:0%
+so welcome to our special class with
+half people going for Thanksgiving you
+
+ align:start position:0%
+half people going for Thanksgiving you
+ 
+
+ align:start position:0%
+half people going for Thanksgiving you
+guys are the chosen few so pleased
+
+ align:start position:0%
+guys are the chosen few so pleased
+ 
+
+ align:start position:0%
+guys are the chosen few so pleased
+you're here so I'm just gonna see a
+
+ align:start position:0%
+you're here so I'm just gonna see a
+ 
+
+ align:start position:0%
+you're here so I'm just gonna see a
+little bit about models versus data and
+
+ align:start position:0%
+little bit about models versus data and
+ 
+
+ align:start position:0%
+little bit about models versus data and
+then I'm going to talk about go back to
+
+ align:start position:0%
+then I'm going to talk about go back to
+ 
+
+ align:start position:0%
+then I'm going to talk about go back to
+boundary value problems and talk a
+
+ align:start position:0%
+boundary value problems and talk a
+ 
+
+ align:start position:0%
+boundary value problems and talk a
+little bit about how you handle really
+
+ align:start position:0%
+little bit about how you handle really
+ 
+
+ align:start position:0%
+little bit about how you handle really
+big ones yeah yeah yes and in fact these
+
+ align:start position:0%
+big ones yeah yeah yes and in fact these
+ 
+
+ align:start position:0%
+big ones yeah yeah yes and in fact these
+are even going to be on the video
+
+ align:start position:0%
+are even going to be on the video
+ 
+
+ align:start position:0%
+are even going to be on the video
+because they guide just fix the video so
+
+ align:start position:0%
+because they guide just fix the video so
+ 
+
+ align:start position:0%
+because they guide just fix the video so
+it'll be recorded all right um yeah I'm
+
+ align:start position:0%
+it'll be recorded all right um yeah I'm
+ 
+
+ align:start position:0%
+it'll be recorded all right um yeah I'm
+sorry you said the video was broken last
+
+ align:start position:0%
+sorry you said the video was broken last
+ 
+
+ align:start position:0%
+sorry you said the video was broken last
+time so the recording didn't work all
+
+ align:start position:0%
+time so the recording didn't work all
+ 
+
+ align:start position:0%
+time so the recording didn't work all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so when we're talking about models
+
+ align:start position:0%
+so when we're talking about models
+ 
+
+ align:start position:0%
+so when we're talking about models
+versus data a really critical question
+
+ align:start position:0%
+versus data a really critical question
+ 
+
+ align:start position:0%
+versus data a really critical question
+is whether the model is really
+
+ align:start position:0%
+is whether the model is really
+ 
+
+ align:start position:0%
+is whether the model is really
+consistent in the data or not and how do
+
+ align:start position:0%
+consistent in the data or not and how do
+ 
+
+ align:start position:0%
+consistent in the data or not and how do
+we know this is really true
+
+ align:start position:0%
+we know this is really true
+ 
+
+ align:start position:0%
+we know this is really true
+so we talked about how we can figure out
+
+ align:start position:0%
+so we talked about how we can figure out
+ 
+
+ align:start position:0%
+so we talked about how we can figure out
+some sort of chi-squared maximum that we
+
+ align:start position:0%
+some sort of chi-squared maximum that we
+ 
+
+ align:start position:0%
+some sort of chi-squared maximum that we
+would tolerate so maximum we tolerate we
+
+ align:start position:0%
+would tolerate so maximum we tolerate we
+ 
+
+ align:start position:0%
+would tolerate so maximum we tolerate we
+call it Q capital Q and the lecture
+
+ align:start position:0%
+call it Q capital Q and the lecture
+ 
+
+ align:start position:0%
+call it Q capital Q and the lecture
+before and so we think if we can find
+
+ align:start position:0%
+before and so we think if we can find
+ 
+
+ align:start position:0%
+before and so we think if we can find
+out a chi squared of theta that's less
+
+ align:start position:0%
+out a chi squared of theta that's less
+ 
+
+ align:start position:0%
+out a chi squared of theta that's less
+than this then it's at least plausible
+
+ align:start position:0%
+than this then it's at least plausible
+ 
+
+ align:start position:0%
+than this then it's at least plausible
+that our models true right we're
+
+ align:start position:0%
+that our models true right we're
+ 
+
+ align:start position:0%
+that our models true right we're
+alternatively if all chi squared the
+
+ align:start position:0%
+alternatively if all chi squared the
+ 
+
+ align:start position:0%
+alternatively if all chi squared the
+state is for any value of Thetas are
+
+ align:start position:0%
+state is for any value of Thetas are
+ 
+
+ align:start position:0%
+state is for any value of Thetas are
+greater than Phi squared max then then
+
+ align:start position:0%
+greater than Phi squared max then then
+ 
+
+ align:start position:0%
+greater than Phi squared max then then
+we would say the model is false or
+
+ align:start position:0%
+we would say the model is false or
+ 
+
+ align:start position:0%
+we would say the model is false or
+something else is really wrong with our
+
+ align:start position:0%
+something else is really wrong with our
+ 
+
+ align:start position:0%
+something else is really wrong with our
+experiment right that's that's so that's
+
+ align:start position:0%
+experiment right that's that's so that's
+ 
+
+ align:start position:0%
+experiment right that's that's so that's
+what we say when we saying we have a
+
+ align:start position:0%
+what we say when we saying we have a
+ 
+
+ align:start position:0%
+what we say when we saying we have a
+maximum PI squared that we would
+
+ align:start position:0%
+maximum PI squared that we would
+ 
+
+ align:start position:0%
+maximum PI squared that we would
+tolerate so a critical question with
+
+ align:start position:0%
+tolerate so a critical question with
+ 
+
+ align:start position:0%
+tolerate so a critical question with
+this is whether we really found the very
+
+ align:start position:0%
+this is whether we really found the very
+ 
+
+ align:start position:0%
+this is whether we really found the very
+best fit value of the parameters in in
+
+ align:start position:0%
+best fit value of the parameters in in
+ 
+
+ align:start position:0%
+best fit value of the parameters in in
+some simple
+
+ align:start position:0%
+some simple
+ 
+
+ align:start position:0%
+some simple
+problems you might have linear
+
+ align:start position:0%
+problems you might have linear
+ 
+
+ align:start position:0%
+problems you might have linear
+dependence of the parameters and then
+
+ align:start position:0%
+dependence of the parameters and then
+ 
+
+ align:start position:0%
+dependence of the parameters and then
+there's only one best fit usually as
+
+ align:start position:0%
+there's only one best fit usually as
+ 
+
+ align:start position:0%
+there's only one best fit usually as
+long as you have a non singular set of
+
+ align:start position:0%
+long as you have a non singular set of
+ 
+
+ align:start position:0%
+long as you have a non singular set of
+equations and every one we find there's
+
+ align:start position:0%
+equations and every one we find there's
+ 
+
+ align:start position:0%
+equations and every one we find there's
+no trouble however more commonly you
+
+ align:start position:0%
+no trouble however more commonly you
+ 
+
+ align:start position:0%
+no trouble however more commonly you
+have equations which are singular or
+
+ align:start position:0%
+have equations which are singular or
+ 
+
+ align:start position:0%
+have equations which are singular or
+close to singular and also you normally
+
+ align:start position:0%
+close to singular and also you normally
+ 
+
+ align:start position:0%
+close to singular and also you normally
+have nonlinear dependence between the
+
+ align:start position:0%
+have nonlinear dependence between the
+ 
+
+ align:start position:0%
+have nonlinear dependence between the
+model predictions and the parameters so
+
+ align:start position:0%
+model predictions and the parameters so
+ 
+
+ align:start position:0%
+model predictions and the parameters so
+for example I do kinetics we always care
+
+ align:start position:0%
+for example I do kinetics we always care
+ 
+
+ align:start position:0%
+for example I do kinetics we always care
+about the rate coefficients the case and
+
+ align:start position:0%
+about the rate coefficients the case and
+ 
+
+ align:start position:0%
+about the rate coefficients the case and
+they always come in inside a
+
+ align:start position:0%
+they always come in inside a
+ 
+
+ align:start position:0%
+they always come in inside a
+differential equation right you always
+
+ align:start position:0%
+differential equation right you always
+ 
+
+ align:start position:0%
+differential equation right you always
+have like D concentrations DT is even
+
+ align:start position:0%
+have like D concentrations DT is even
+ 
+
+ align:start position:0%
+have like D concentrations DT is even
+some terms and some of them are you know
+
+ align:start position:0%
+some terms and some of them are you know
+ 
+
+ align:start position:0%
+some terms and some of them are you know
+K concentration I times concentration J
+
+ align:start position:0%
+K concentration I times concentration J
+ 
+
+ align:start position:0%
+K concentration I times concentration J
+whatever one is it okay right you have a
+
+ align:start position:0%
+whatever one is it okay right you have a
+ 
+
+ align:start position:0%
+whatever one is it okay right you have a
+lot of like terms like this by molecular
+
+ align:start position:0%
+lot of like terms like this by molecular
+ 
+
+ align:start position:0%
+lot of like terms like this by molecular
+reaction terms and these K some of them
+
+ align:start position:0%
+reaction terms and these K some of them
+ 
+
+ align:start position:0%
+reaction terms and these K some of them
+I don't know and so these are these
+
+ align:start position:0%
+I don't know and so these are these
+ 
+
+ align:start position:0%
+I don't know and so these are these
+would be one of my Thetas so this video
+
+ align:start position:0%
+would be one of my Thetas so this video
+ 
+
+ align:start position:0%
+would be one of my Thetas so this video
+say 217 would be one of these case I
+
+ align:start position:0%
+say 217 would be one of these case I
+ 
+
+ align:start position:0%
+say 217 would be one of these case I
+wanted to determine and when I have a
+
+ align:start position:0%
+wanted to determine and when I have a
+ 
+
+ align:start position:0%
+wanted to determine and when I have a
+differential equation like this when I
+
+ align:start position:0%
+differential equation like this when I
+ 
+
+ align:start position:0%
+differential equation like this when I
+integrate it the K is always going to
+
+ align:start position:0%
+integrate it the K is always going to
+ 
+
+ align:start position:0%
+integrate it the K is always going to
+come in nonlinearly in the in the
+
+ align:start position:0%
+come in nonlinearly in the in the
+ 
+
+ align:start position:0%
+come in nonlinearly in the in the
+solution right so what I want to
+
+ align:start position:0%
+solution right so what I want to
+ 
+
+ align:start position:0%
+solution right so what I want to
+integrate this solution even in the
+
+ align:start position:0%
+integrate this solution even in the
+ 
+
+ align:start position:0%
+integrate this solution even in the
+simplest case you get things like C of T
+
+ align:start position:0%
+simplest case you get things like C of T
+ 
+
+ align:start position:0%
+simplest case you get things like C of T
+is equal to a e to the negative KT that
+
+ align:start position:0%
+is equal to a e to the negative KT that
+ 
+
+ align:start position:0%
+is equal to a e to the negative KT that
+might be really super simple case if you
+
+ align:start position:0%
+might be really super simple case if you
+ 
+
+ align:start position:0%
+might be really super simple case if you
+have a linear kinetics the K is still
+
+ align:start position:0%
+have a linear kinetics the K is still
+ 
+
+ align:start position:0%
+have a linear kinetics the K is still
+coming in nonlinearly to the predictions
+
+ align:start position:0%
+coming in nonlinearly to the predictions
+ 
+
+ align:start position:0%
+coming in nonlinearly to the predictions
+right and if you have anything
+
+ align:start position:0%
+right and if you have anything
+ 
+
+ align:start position:0%
+right and if you have anything
+complicated you can't even write it down
+
+ align:start position:0%
+complicated you can't even write it down
+ 
+
+ align:start position:0%
+complicated you can't even write it down
+the closed form expression and you have
+
+ align:start position:0%
+the closed form expression and you have
+ 
+
+ align:start position:0%
+the closed form expression and you have
+to integrate with in with a OD 45 or OD
+
+ align:start position:0%
+to integrate with in with a OD 45 or OD
+ 
+
+ align:start position:0%
+to integrate with in with a OD 45 or OD
+1 5s and so the relationship between K
+
+ align:start position:0%
+1 5s and so the relationship between K
+ 
+
+ align:start position:0%
+1 5s and so the relationship between K
+and they and the concentrations that
+
+ align:start position:0%
+and they and the concentrations that
+ 
+
+ align:start position:0%
+and they and the concentrations that
+you've measure can be really complicated
+
+ align:start position:0%
+you've measure can be really complicated
+ 
+
+ align:start position:0%
+you've measure can be really complicated
+so it's always nonlinear am I in a mile
+
+ align:start position:0%
+so it's always nonlinear am I in a mile
+ 
+
+ align:start position:0%
+so it's always nonlinear am I in a mile
+up in my world everything all models are
+
+ align:start position:0%
+up in my world everything all models are
+ 
+
+ align:start position:0%
+up in my world everything all models are
+nonlinear and and I think there's many
+
+ align:start position:0%
+nonlinear and and I think there's many
+ 
+
+ align:start position:0%
+nonlinear and and I think there's many
+other situations like that so if you do
+
+ align:start position:0%
+other situations like that so if you do
+ 
+
+ align:start position:0%
+other situations like that so if you do
+trying to measure a diffusivity you it
+
+ align:start position:0%
+trying to measure a diffusivity you it
+ 
+
+ align:start position:0%
+trying to measure a diffusivity you it
+might be possible to seven experiment
+
+ align:start position:0%
+might be possible to seven experiment
+ 
+
+ align:start position:0%
+might be possible to seven experiment
+where you'd expect a linear dependence
+
+ align:start position:0%
+where you'd expect a linear dependence
+ 
+
+ align:start position:0%
+where you'd expect a linear dependence
+due to something you'd measure in the
+
+ align:start position:0%
+due to something you'd measure in the
+ 
+
+ align:start position:0%
+due to something you'd measure in the
+diffusivity but most likely not
+
+ align:start position:0%
+diffusivity but most likely not
+ 
+
+ align:start position:0%
+diffusivity but most likely not
+so most likely it would come and
+
+ align:start position:0%
+so most likely it would come and
+ 
+
+ align:start position:0%
+so most likely it would come and
+unlimitedly somehow and you'd have to
+
+ align:start position:0%
+unlimitedly somehow and you'd have to
+ 
+
+ align:start position:0%
+unlimitedly somehow and you'd have to
+you'd have some model for it and you'd
+
+ align:start position:0%
+you'd have some model for it and you'd
+ 
+
+ align:start position:0%
+you'd have some model for it and you'd
+have nonlinear dependence between that
+
+ align:start position:0%
+have nonlinear dependence between that
+ 
+
+ align:start position:0%
+have nonlinear dependence between that
+number and the numbers you would measure
+
+ align:start position:0%
+number and the numbers you would measure
+ 
+
+ align:start position:0%
+number and the numbers you would measure
+right and almost all the properties or
+
+ align:start position:0%
+right and almost all the properties or
+ 
+
+ align:start position:0%
+right and almost all the properties or
+like that so because you have a
+
+ align:start position:0%
+like that so because you have a
+ 
+
+ align:start position:0%
+like that so because you have a
+nonlinear dependence then you have to
+
+ align:start position:0%
+nonlinear dependence then you have to
+ 
+
+ align:start position:0%
+nonlinear dependence then you have to
+worry about how many minima do you have
+
+ align:start position:0%
+worry about how many minima do you have
+ 
+
+ align:start position:0%
+worry about how many minima do you have
+in your surface so Chi squared of theta
+
+ align:start position:0%
+in your surface so Chi squared of theta
+ 
+
+ align:start position:0%
+in your surface so Chi squared of theta
+is a nonlinear function of a lot of
+
+ align:start position:0%
+is a nonlinear function of a lot of
+ 
+
+ align:start position:0%
+is a nonlinear function of a lot of
+variables and typically it won't just
+
+ align:start position:0%
+variables and typically it won't just
+ 
+
+ align:start position:0%
+variables and typically it won't just
+have one minimum it'll have a whole lot
+
+ align:start position:0%
+have one minimum it'll have a whole lot
+ 
+
+ align:start position:0%
+have one minimum it'll have a whole lot
+of local minima now one of those is a
+
+ align:start position:0%
+of local minima now one of those is a
+ 
+
+ align:start position:0%
+of local minima now one of those is a
+global minimum and that's the one you
+
+ align:start position:0%
+global minimum and that's the one you
+ 
+
+ align:start position:0%
+global minimum and that's the one you
+sort of want that's the very best
+
+ align:start position:0%
+sort of want that's the very best
+ 
+
+ align:start position:0%
+sort of want that's the very best
+possible fit but you normally won't know
+
+ align:start position:0%
+possible fit but you normally won't know
+ 
+
+ align:start position:0%
+possible fit but you normally won't know
+how many minimum it has and so no matter
+
+ align:start position:0%
+how many minimum it has and so no matter
+ 
+
+ align:start position:0%
+how many minimum it has and so no matter
+how many minima you find you don't know
+
+ align:start position:0%
+how many minima you find you don't know
+ 
+
+ align:start position:0%
+how many minima you find you don't know
+if you're done and you don't know if you
+
+ align:start position:0%
+if you're done and you don't know if you
+ 
+
+ align:start position:0%
+if you're done and you don't know if you
+don't have you really found the best fit
+
+ align:start position:0%
+don't have you really found the best fit
+ 
+
+ align:start position:0%
+don't have you really found the best fit
+okay so just because all the ones you
+
+ align:start position:0%
+okay so just because all the ones you
+ 
+
+ align:start position:0%
+okay so just because all the ones you
+found so far are bigger than chi squared
+
+ align:start position:0%
+found so far are bigger than chi squared
+ 
+
+ align:start position:0%
+found so far are bigger than chi squared
+max you might not be ready to write that
+
+ align:start position:0%
+max you might not be ready to write that
+ 
+
+ align:start position:0%
+max you might not be ready to write that
+article to nature to claim the gloss of
+
+ align:start position:0%
+article to nature to claim the gloss of
+ 
+
+ align:start position:0%
+article to nature to claim the gloss of
+physics are incorrect
+
+ align:start position:0%
+physics are incorrect
+ 
+
+ align:start position:0%
+physics are incorrect
+because you're not sure you really found
+
+ align:start position:0%
+because you're not sure you really found
+ 
+
+ align:start position:0%
+because you're not sure you really found
+the very best fit okay so that's one of
+
+ align:start position:0%
+the very best fit okay so that's one of
+ 
+
+ align:start position:0%
+the very best fit okay so that's one of
+the many problems of trying to figure
+
+ align:start position:0%
+the many problems of trying to figure
+ 
+
+ align:start position:0%
+the many problems of trying to figure
+out if a model and data are really
+
+ align:start position:0%
+out if a model and data are really
+ 
+
+ align:start position:0%
+out if a model and data are really
+consistent now that particular one you
+
+ align:start position:0%
+consistent now that particular one you
+ 
+
+ align:start position:0%
+consistent now that particular one you
+can overcome if you can find a
+
+ align:start position:0%
+can overcome if you can find a
+ 
+
+ align:start position:0%
+can overcome if you can find a
+guaranteed way to find a global optimum
+
+ align:start position:0%
+guaranteed way to find a global optimum
+ 
+
+ align:start position:0%
+guaranteed way to find a global optimum
+to find the very best possible fit there
+
+ align:start position:0%
+to find the very best possible fit there
+ 
+
+ align:start position:0%
+to find the very best possible fit there
+is and some people spend their life
+
+ align:start position:0%
+is and some people spend their life
+ 
+
+ align:start position:0%
+is and some people spend their life
+working on this and one of those people
+
+ align:start position:0%
+working on this and one of those people
+ 
+
+ align:start position:0%
+working on this and one of those people
+is professor Barton in this department
+
+ align:start position:0%
+is professor Barton in this department
+ 
+
+ align:start position:0%
+is professor Barton in this department
+and so he teaches a class how to do this
+
+ align:start position:0%
+and so he teaches a class how to do this
+ 
+
+ align:start position:0%
+and so he teaches a class how to do this
+and there are actually methods to do it
+
+ align:start position:0%
+and there are actually methods to do it
+ 
+
+ align:start position:0%
+and there are actually methods to do it
+so if you want to see the application of
+
+ align:start position:0%
+so if you want to see the application of
+ 
+
+ align:start position:0%
+so if you want to see the application of
+this to kinetic models there's paper by
+
+ align:start position:0%
+this to kinetic models there's paper by
+ 
+
+ align:start position:0%
+this to kinetic models there's paper by
+by me and professor Barton and the lead
+
+ align:start position:0%
+by me and professor Barton and the lead
+ 
+
+ align:start position:0%
+by me and professor Barton and the lead
+author is one of his former students
+
+ align:start position:0%
+author is one of his former students
+ 
+
+ align:start position:0%
+author is one of his former students
+Adam singer and j phys chem and it just
+
+ align:start position:0%
+Adam singer and j phys chem and it just
+ 
+
+ align:start position:0%
+Adam singer and j phys chem and it just
+shows how you can use global
+
+ align:start position:0%
+shows how you can use global
+ 
+
+ align:start position:0%
+shows how you can use global
+optimization to guarantee you have the
+
+ align:start position:0%
+optimization to guarantee you have the
+ 
+
+ align:start position:0%
+optimization to guarantee you have the
+very best possible values the parameters
+
+ align:start position:0%
+very best possible values the parameters
+ 
+
+ align:start position:0%
+very best possible values the parameters
+and then I'll show you what happened so
+
+ align:start position:0%
+and then I'll show you what happened so
+ 
+
+ align:start position:0%
+and then I'll show you what happened so
+this is a case where the experimental
+
+ align:start position:0%
+this is a case where the experimental
+ 
+
+ align:start position:0%
+this is a case where the experimental
+data was measured by one of my students
+
+ align:start position:0%
+data was measured by one of my students
+ 
+
+ align:start position:0%
+data was measured by one of my students
+James Taylor and that's the things with
+
+ align:start position:0%
+James Taylor and that's the things with
+ 
+
+ align:start position:0%
+James Taylor and that's the things with
+the error bars and he did a lot of hard
+
+ align:start position:0%
+the error bars and he did a lot of hard
+ 
+
+ align:start position:0%
+the error bars and he did a lot of hard
+work to make sure he had pretty good
+
+ align:start position:0%
+work to make sure he had pretty good
+ 
+
+ align:start position:0%
+work to make sure he had pretty good
+error bars he really knew what they were
+
+ align:start position:0%
+error bars he really knew what they were
+ 
+
+ align:start position:0%
+error bars he really knew what they were
+and so he had those points so he
+
+ align:start position:0%
+and so he had those points so he
+ 
+
+ align:start position:0%
+and so he had those points so he
+measured a lot of points this measure
+
+ align:start position:0%
+measured a lot of points this measure
+ 
+
+ align:start position:0%
+measured a lot of points this measure
+him a lot of points is a key thing so it
+
+ align:start position:0%
+him a lot of points is a key thing so it
+ 
+
+ align:start position:0%
+him a lot of points is a key thing so it
+means his decrees of freedom is very
+
+ align:start position:0%
+means his decrees of freedom is very
+ 
+
+ align:start position:0%
+means his decrees of freedom is very
+large because he's many many different
+
+ align:start position:0%
+large because he's many many different
+ 
+
+ align:start position:0%
+large because he's many many different
+time points along the way there and he
+
+ align:start position:0%
+time points along the way there and he
+ 
+
+ align:start position:0%
+time points along the way there and he
+has error bars in all of them
+
+ align:start position:0%
+has error bars in all of them
+ 
+
+ align:start position:0%
+has error bars in all of them
+and so because the degrees of freedom
+
+ align:start position:0%
+and so because the degrees of freedom
+ 
+
+ align:start position:0%
+and so because the degrees of freedom
+are very large it actually makes it a
+
+ align:start position:0%
+are very large it actually makes it a
+ 
+
+ align:start position:0%
+are very large it actually makes it a
+very good constraint on on the model it
+
+ align:start position:0%
+very good constraint on on the model it
+ 
+
+ align:start position:0%
+very good constraint on on the model it
+tests it very thoroughly where if you
+
+ align:start position:0%
+tests it very thoroughly where if you
+ 
+
+ align:start position:0%
+tests it very thoroughly where if you
+only measured one point then that's not
+
+ align:start position:0%
+only measured one point then that's not
+ 
+
+ align:start position:0%
+only measured one point then that's not
+a very good constraint now what James
+
+ align:start position:0%
+a very good constraint now what James
+ 
+
+ align:start position:0%
+a very good constraint now what James
+had done and we published a paper in
+
+ align:start position:0%
+had done and we published a paper in
+ 
+
+ align:start position:0%
+had done and we published a paper in
+2004 where he did it where he said you
+
+ align:start position:0%
+2004 where he did it where he said you
+ 
+
+ align:start position:0%
+2004 where he did it where he said you
+know when I do my fits this is what I
+
+ align:start position:0%
+know when I do my fits this is what I
+ 
+
+ align:start position:0%
+know when I do my fits this is what I
+get I get these kind of purple and green
+
+ align:start position:0%
+get I get these kind of purple and green
+ 
+
+ align:start position:0%
+get I get these kind of purple and green
+things and therefore they're all outside
+
+ align:start position:0%
+things and therefore they're all outside
+ 
+
+ align:start position:0%
+things and therefore they're all outside
+the error bars and therefore I published
+
+ align:start position:0%
+the error bars and therefore I published
+ 
+
+ align:start position:0%
+the error bars and therefore I published
+in the journal physical chemistry I
+
+ align:start position:0%
+in the journal physical chemistry I
+ 
+
+ align:start position:0%
+in the journal physical chemistry I
+claim this model is wrong based on my
+
+ align:start position:0%
+claim this model is wrong based on my
+ 
+
+ align:start position:0%
+claim this model is wrong based on my
+experimental data okay so we published
+
+ align:start position:0%
+experimental data okay so we published
+ 
+
+ align:start position:0%
+experimental data okay so we published
+that 2004 was accepted by the referees
+
+ align:start position:0%
+that 2004 was accepted by the referees
+ 
+
+ align:start position:0%
+that 2004 was accepted by the referees
+it's in the literature you can read it
+
+ align:start position:0%
+it's in the literature you can read it
+ 
+
+ align:start position:0%
+it's in the literature you can read it
+don't believe it though because Adam
+
+ align:start position:0%
+don't believe it though because Adam
+ 
+
+ align:start position:0%
+don't believe it though because Adam
+singer went back into global
+
+ align:start position:0%
+singer went back into global
+ 
+
+ align:start position:0%
+singer went back into global
+optimization using the same model and
+
+ align:start position:0%
+optimization using the same model and
+ 
+
+ align:start position:0%
+optimization using the same model and
+his red line goes right through all the
+
+ align:start position:0%
+his red line goes right through all the
+ 
+
+ align:start position:0%
+his red line goes right through all the
+points really well do you see that I've
+
+ align:start position:0%
+points really well do you see that I've
+ 
+
+ align:start position:0%
+points really well do you see that I've
+you see the red line there this red red
+
+ align:start position:0%
+you see the red line there this red red
+ 
+
+ align:start position:0%
+you see the red line there this red red
+curve that's the true best fit and so
+
+ align:start position:0%
+curve that's the true best fit and so
+ 
+
+ align:start position:0%
+curve that's the true best fit and so
+although the fits that James had found
+
+ align:start position:0%
+although the fits that James had found
+ 
+
+ align:start position:0%
+although the fits that James had found
+were all local minima and the
+
+ align:start position:0%
+were all local minima and the
+ 
+
+ align:start position:0%
+were all local minima and the
+chi-squared surface and when he actually
+
+ align:start position:0%
+chi-squared surface and when he actually
+ 
+
+ align:start position:0%
+chi-squared surface and when he actually
+found the really the best fit with Adams
+
+ align:start position:0%
+found the really the best fit with Adams
+ 
+
+ align:start position:0%
+found the really the best fit with Adams
+fancy method then it turns out that
+
+ align:start position:0%
+fancy method then it turns out that
+ 
+
+ align:start position:0%
+fancy method then it turns out that
+actually model matches the data like
+
+ align:start position:0%
+actually model matches the data like
+ 
+
+ align:start position:0%
+actually model matches the data like
+perfectly so that's definitely true so
+
+ align:start position:0%
+perfectly so that's definitely true so
+ 
+
+ align:start position:0%
+perfectly so that's definitely true so
+what we could publish the first time was
+
+ align:start position:0%
+what we could publish the first time was
+ 
+
+ align:start position:0%
+what we could publish the first time was
+completely wrong because we said the
+
+ align:start position:0%
+completely wrong because we said the
+ 
+
+ align:start position:0%
+completely wrong because we said the
+model disproved the data but in fact the
+
+ align:start position:0%
+model disproved the data but in fact the
+ 
+
+ align:start position:0%
+model disproved the data but in fact the
+model proved the data I mean the data
+
+ align:start position:0%
+model proved the data I mean the data
+ 
+
+ align:start position:0%
+model proved the data I mean the data
+prove the model or was completely
+
+ align:start position:0%
+prove the model or was completely
+ 
+
+ align:start position:0%
+prove the model or was completely
+consistent in the model in every way in
+
+ align:start position:0%
+consistent in the model in every way in
+ 
+
+ align:start position:0%
+consistent in the model in every way in
+great detail so so I was all embarrassed
+
+ align:start position:0%
+great detail so so I was all embarrassed
+ 
+
+ align:start position:0%
+great detail so so I was all embarrassed
+so then James also in the same paper had
+
+ align:start position:0%
+so then James also in the same paper had
+ 
+
+ align:start position:0%
+so then James also in the same paper had
+found and they could measure another
+
+ align:start position:0%
+found and they could measure another
+ 
+
+ align:start position:0%
+found and they could measure another
+condition a different a different
+
+ align:start position:0%
+condition a different a different
+ 
+
+ align:start position:0%
+condition a different a different
+slightly different case and actually was
+
+ align:start position:0%
+slightly different case and actually was
+ 
+
+ align:start position:0%
+slightly different case and actually was
+looking a different solvent and in this
+
+ align:start position:0%
+looking a different solvent and in this
+ 
+
+ align:start position:0%
+looking a different solvent and in this
+case he found this green curve is his
+
+ align:start position:0%
+case he found this green curve is his
+ 
+
+ align:start position:0%
+case he found this green curve is his
+best fit and it looked pretty good by I
+
+ align:start position:0%
+best fit and it looked pretty good by I
+ 
+
+ align:start position:0%
+best fit and it looked pretty good by I
+though you can see it's sort of
+
+ align:start position:0%
+though you can see it's sort of
+ 
+
+ align:start position:0%
+though you can see it's sort of
+skittering on the tops of the Erb are
+
+ align:start position:0%
+skittering on the tops of the Erb are
+ 
+
+ align:start position:0%
+skittering on the tops of the Erb are
+bands and so this is one where he said
+
+ align:start position:0%
+bands and so this is one where he said
+ 
+
+ align:start position:0%
+bands and so this is one where he said
+you know we do the statistical test
+
+ align:start position:0%
+you know we do the statistical test
+ 
+
+ align:start position:0%
+you know we do the statistical test
+there's like a 5% chance that you would
+
+ align:start position:0%
+there's like a 5% chance that you would
+ 
+
+ align:start position:0%
+there's like a 5% chance that you would
+measure data like he measured if that
+
+ align:start position:0%
+measure data like he measured if that
+ 
+
+ align:start position:0%
+measure data like he measured if that
+green model was the truth
+
+ align:start position:0%
+green model was the truth
+ 
+
+ align:start position:0%
+green model was the truth
+and so we said some wishy-washy words in
+
+ align:start position:0%
+and so we said some wishy-washy words in
+ 
+
+ align:start position:0%
+and so we said some wishy-washy words in
+the paper basically as we weren't really
+
+ align:start position:0%
+the paper basically as we weren't really
+ 
+
+ align:start position:0%
+the paper basically as we weren't really
+sure if it was giving it was consistent
+
+ align:start position:0%
+sure if it was giving it was consistent
+ 
+
+ align:start position:0%
+sure if it was giving it was consistent
+or not consistent with the data but in
+
+ align:start position:0%
+or not consistent with the data but in
+ 
+
+ align:start position:0%
+or not consistent with the data but in
+that case Adam used his fancy global
+
+ align:start position:0%
+that case Adam used his fancy global
+ 
+
+ align:start position:0%
+that case Adam used his fancy global
+optimization techniques I found that
+
+ align:start position:0%
+optimization techniques I found that
+ 
+
+ align:start position:0%
+optimization techniques I found that
+James is it was actually not that far
+
+ align:start position:0%
+James is it was actually not that far
+ 
+
+ align:start position:0%
+James is it was actually not that far
+from the global optimum and he got the
+
+ align:start position:0%
+from the global optimum and he got the
+ 
+
+ align:start position:0%
+from the global optimum and he got the
+red curve there marked by the red arrow
+
+ align:start position:0%
+red curve there marked by the red arrow
+ 
+
+ align:start position:0%
+red curve there marked by the red arrow
+and that one it looks pretty good it
+
+ align:start position:0%
+and that one it looks pretty good it
+ 
+
+ align:start position:0%
+and that one it looks pretty good it
+actually likes when he goes through the
+
+ align:start position:0%
+actually likes when he goes through the
+ 
+
+ align:start position:0%
+actually likes when he goes through the
+data but it doesn't really do it right
+
+ align:start position:0%
+data but it doesn't really do it right
+ 
+
+ align:start position:0%
+data but it doesn't really do it right
+and found that you know it's the
+
+ align:start position:0%
+and found that you know it's the
+ 
+
+ align:start position:0%
+and found that you know it's the
+confidence intervals only 16% so it's
+
+ align:start position:0%
+confidence intervals only 16% so it's
+ 
+
+ align:start position:0%
+confidence intervals only 16% so it's
+only a 16% chance one chance out of six
+
+ align:start position:0%
+only a 16% chance one chance out of six
+ 
+
+ align:start position:0%
+only a 16% chance one chance out of six
+that James would have measured the data
+
+ align:start position:0%
+that James would have measured the data
+ 
+
+ align:start position:0%
+that James would have measured the data
+he measured if that model was true and
+
+ align:start position:0%
+he measured if that model was true and
+ 
+
+ align:start position:0%
+he measured if that model was true and
+now we're sure that we have the global
+
+ align:start position:0%
+now we're sure that we have the global
+ 
+
+ align:start position:0%
+now we're sure that we have the global
+best fit so now we're like thinking well
+
+ align:start position:0%
+best fit so now we're like thinking well
+ 
+
+ align:start position:0%
+best fit so now we're like thinking well
+you know maybe we should say that the
+
+ align:start position:0%
+you know maybe we should say that the
+ 
+
+ align:start position:0%
+you know maybe we should say that the
+model is not true for this case because
+
+ align:start position:0%
+model is not true for this case because
+ 
+
+ align:start position:0%
+model is not true for this case because
+is it eighty four percent chance it's
+
+ align:start position:0%
+is it eighty four percent chance it's
+ 
+
+ align:start position:0%
+is it eighty four percent chance it's
+not true anyway so so actually we got it
+
+ align:start position:0%
+not true anyway so so actually we got it
+ 
+
+ align:start position:0%
+not true anyway so so actually we got it
+wrong both ways so in the first case we
+
+ align:start position:0%
+wrong both ways so in the first case we
+ 
+
+ align:start position:0%
+wrong both ways so in the first case we
+said that our data disprove the model
+
+ align:start position:0%
+said that our data disprove the model
+ 
+
+ align:start position:0%
+said that our data disprove the model
+and in the second case we said that our
+
+ align:start position:0%
+and in the second case we said that our
+ 
+
+ align:start position:0%
+and in the second case we said that our
+model was pretty good with the data but
+
+ align:start position:0%
+model was pretty good with the data but
+ 
+
+ align:start position:0%
+model was pretty good with the data but
+actually they were both wrong so the one
+
+ align:start position:0%
+actually they were both wrong so the one
+ 
+
+ align:start position:0%
+actually they were both wrong so the one
+was wrong that actually the data did
+
+ align:start position:0%
+was wrong that actually the data did
+ 
+
+ align:start position:0%
+was wrong that actually the data did
+prove the model is correct for the first
+
+ align:start position:0%
+prove the model is correct for the first
+ 
+
+ align:start position:0%
+prove the model is correct for the first
+case and it actually looks looks a
+
+ align:start position:0%
+case and it actually looks looks a
+ 
+
+ align:start position:0%
+case and it actually looks looks a
+little fishy for this second case so
+
+ align:start position:0%
+little fishy for this second case so
+ 
+
+ align:start position:0%
+little fishy for this second case so
+anyway this is just a concrete example
+
+ align:start position:0%
+anyway this is just a concrete example
+ 
+
+ align:start position:0%
+anyway this is just a concrete example
+to make you be a little bit more worried
+
+ align:start position:0%
+to make you be a little bit more worried
+ 
+
+ align:start position:0%
+to make you be a little bit more worried
+about what you do when you do these
+
+ align:start position:0%
+about what you do when you do these
+ 
+
+ align:start position:0%
+about what you do when you do these
+fitting things now there's a variety of
+
+ align:start position:0%
+fitting things now there's a variety of
+ 
+
+ align:start position:0%
+fitting things now there's a variety of
+ways to try to do the least squares
+
+ align:start position:0%
+ways to try to do the least squares
+ 
+
+ align:start position:0%
+ways to try to do the least squares
+fitting to try to find Optima there was
+
+ align:start position:0%
+fitting to try to find Optima there was
+ 
+
+ align:start position:0%
+fitting to try to find Optima there was
+a guy named a car from University of
+
+ align:start position:0%
+a guy named a car from University of
+ 
+
+ align:start position:0%
+a guy named a car from University of
+Minnesota and he published a stochastic
+
+ align:start position:0%
+Minnesota and he published a stochastic
+ 
+
+ align:start position:0%
+Minnesota and he published a stochastic
+way to just try a whole lot of different
+
+ align:start position:0%
+way to just try a whole lot of different
+ 
+
+ align:start position:0%
+way to just try a whole lot of different
+initial guesses and that usually works
+
+ align:start position:0%
+initial guesses and that usually works
+ 
+
+ align:start position:0%
+initial guesses and that usually works
+to find the global minimum but if you
+
+ align:start position:0%
+to find the global minimum but if you
+ 
+
+ align:start position:0%
+to find the global minimum but if you
+really want to have a guaranteed global
+
+ align:start position:0%
+really want to have a guaranteed global
+ 
+
+ align:start position:0%
+really want to have a guaranteed global
+minimum that you're absolutely sure
+
+ align:start position:0%
+minimum that you're absolutely sure
+ 
+
+ align:start position:0%
+minimum that you're absolutely sure
+definitely is a global minimum then then
+
+ align:start position:0%
+definitely is a global minimum then then
+ 
+
+ align:start position:0%
+definitely is a global minimum then then
+you really need to use the global
+
+ align:start position:0%
+you really need to use the global
+ 
+
+ align:start position:0%
+you really need to use the global
+optimization methods and you really
+
+ align:start position:0%
+optimization methods and you really
+ 
+
+ align:start position:0%
+optimization methods and you really
+should talk to presser Barton and for
+
+ align:start position:0%
+should talk to presser Barton and for
+ 
+
+ align:start position:0%
+should talk to presser Barton and for
+these kinetic models he actually has a
+
+ align:start position:0%
+these kinetic models he actually has a
+ 
+
+ align:start position:0%
+these kinetic models he actually has a
+distributed code called G doc that will
+
+ align:start position:0%
+distributed code called G doc that will
+ 
+
+ align:start position:0%
+distributed code called G doc that will
+just find the global optimization as
+
+ align:start position:0%
+just find the global optimization as
+ 
+
+ align:start position:0%
+just find the global optimization as
+long as you don't have too many kinetic
+
+ align:start position:0%
+long as you don't have too many kinetic
+ 
+
+ align:start position:0%
+long as you don't have too many kinetic
+parameters I think if you go out to
+
+ align:start position:0%
+parameters I think if you go out to
+ 
+
+ align:start position:0%
+parameters I think if you go out to
+about six
+
+ align:start position:0%
+about six
+ 
+
+ align:start position:0%
+about six
+around six adjustable parameters who can
+
+ align:start position:0%
+around six adjustable parameters who can
+ 
+
+ align:start position:0%
+around six adjustable parameters who can
+handle if you have more than that then
+
+ align:start position:0%
+handle if you have more than that then
+ 
+
+ align:start position:0%
+handle if you have more than that then
+usually typically not but because a
+
+ align:start position:0%
+usually typically not but because a
+ 
+
+ align:start position:0%
+usually typically not but because a
+probably globalization methods is they
+
+ align:start position:0%
+probably globalization methods is they
+ 
+
+ align:start position:0%
+probably globalization methods is they
+scale exponentially with the number of
+
+ align:start position:0%
+scale exponentially with the number of
+ 
+
+ align:start position:0%
+scale exponentially with the number of
+adjustable parameters so or number of
+
+ align:start position:0%
+adjustable parameters so or number of
+ 
+
+ align:start position:0%
+adjustable parameters so or number of
+things you're trying to optimize it's
+
+ align:start position:0%
+things you're trying to optimize it's
+ 
+
+ align:start position:0%
+things you're trying to optimize it's
+now in the other hand if you have a
+
+ align:start position:0%
+now in the other hand if you have a
+ 
+
+ align:start position:0%
+now in the other hand if you have a
+model that you need to use more than six
+
+ align:start position:0%
+model that you need to use more than six
+ 
+
+ align:start position:0%
+model that you need to use more than six
+adjustable parameters to fit your data
+
+ align:start position:0%
+adjustable parameters to fit your data
+ 
+
+ align:start position:0%
+adjustable parameters to fit your data
+then you might want to try to think of a
+
+ align:start position:0%
+then you might want to try to think of a
+ 
+
+ align:start position:0%
+then you might want to try to think of a
+different experiment because you know I
+
+ align:start position:0%
+different experiment because you know I
+ 
+
+ align:start position:0%
+different experiment because you know I
+don't you know the famous saying is like
+
+ align:start position:0%
+don't you know the famous saying is like
+ 
+
+ align:start position:0%
+don't you know the famous saying is like
+you know we've give me n parameters I
+
+ align:start position:0%
+you know we've give me n parameters I
+ 
+
+ align:start position:0%
+you know we've give me n parameters I
+could fit an elephant so you know if you
+
+ align:start position:0%
+could fit an elephant so you know if you
+ 
+
+ align:start position:0%
+could fit an elephant so you know if you
+have more than six parameters and you're
+
+ align:start position:0%
+have more than six parameters and you're
+ 
+
+ align:start position:0%
+have more than six parameters and you're
+trying to fit some data set probably you
+
+ align:start position:0%
+trying to fit some data set probably you
+ 
+
+ align:start position:0%
+trying to fit some data set probably you
+probably be do it right you'll find a
+
+ align:start position:0%
+probably be do it right you'll find a
+ 
+
+ align:start position:0%
+probably be do it right you'll find a
+fit but it may not really prove anything
+
+ align:start position:0%
+fit but it may not really prove anything
+ 
+
+ align:start position:0%
+fit but it may not really prove anything
+so so so for that point of view
+
+ align:start position:0%
+so so so for that point of view
+ 
+
+ align:start position:0%
+so so so for that point of view
+professor Barton's Code G doc is pretty
+
+ align:start position:0%
+professor Barton's Code G doc is pretty
+ 
+
+ align:start position:0%
+professor Barton's Code G doc is pretty
+convenient for doing this nonlinear
+
+ align:start position:0%
+convenient for doing this nonlinear
+ 
+
+ align:start position:0%
+convenient for doing this nonlinear
+optimization so that's a code for a
+
+ align:start position:0%
+optimization so that's a code for a
+ 
+
+ align:start position:0%
+optimization so that's a code for a
+nonlinear optimization with differential
+
+ align:start position:0%
+nonlinear optimization with differential
+ 
+
+ align:start position:0%
+nonlinear optimization with differential
+equations and embedded and they could be
+
+ align:start position:0%
+equations and embedded and they could be
+ 
+
+ align:start position:0%
+equations and embedded and they could be
+staff and they can be large it doesn't
+
+ align:start position:0%
+staff and they can be large it doesn't
+ 
+
+ align:start position:0%
+staff and they can be large it doesn't
+matter we really managed to just the
+
+ align:start position:0%
+matter we really managed to just the
+ 
+
+ align:start position:0%
+matter we really managed to just the
+number of adjustable parameters yeah for
+
+ align:start position:0%
+number of adjustable parameters yeah for
+ 
+
+ align:start position:0%
+number of adjustable parameters yeah for
+the that's the cost of all right
+
+ align:start position:0%
+the that's the cost of all right
+ 
+
+ align:start position:0%
+the that's the cost of all right
+now there was a really good question
+
+ align:start position:0%
+now there was a really good question
+ 
+
+ align:start position:0%
+now there was a really good question
+that you asked I think in class last
+
+ align:start position:0%
+that you asked I think in class last
+ 
+
+ align:start position:0%
+that you asked I think in class last
+time maybe maybe the time before and it
+
+ align:start position:0%
+time maybe maybe the time before and it
+ 
+
+ align:start position:0%
+time maybe maybe the time before and it
+was what happens so so if so look at
+
+ align:start position:0%
+was what happens so so if so look at
+ 
+
+ align:start position:0%
+was what happens so so if so look at
+different cases you get so one case you
+
+ align:start position:0%
+different cases you get so one case you
+ 
+
+ align:start position:0%
+different cases you get so one case you
+got you know if ty squared theta past
+
+ align:start position:0%
+got you know if ty squared theta past
+ 
+
+ align:start position:0%
+got you know if ty squared theta past
+your best fitting parameters is a lot
+
+ align:start position:0%
+your best fitting parameters is a lot
+ 
+
+ align:start position:0%
+your best fitting parameters is a lot
+bigger than chi squared max then you're
+
+ align:start position:0%
+bigger than chi squared max then you're
+ 
+
+ align:start position:0%
+bigger than chi squared max then you're
+ready to say the model disproves it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that one you're okay if
+
+ align:start position:0%
+all right so that one you're okay if
+ 
+
+ align:start position:0%
+all right so that one you're okay if
+chi-squared of your best fit is is less
+
+ align:start position:0%
+chi-squared of your best fit is is less
+ 
+
+ align:start position:0%
+chi-squared of your best fit is is less
+than or sniffing only less than
+
+ align:start position:0%
+than or sniffing only less than
+ 
+
+ align:start position:0%
+than or sniffing only less than
+chi-squared nuts
+
+ align:start position:0%
+chi-squared nuts
+ 
+
+ align:start position:0%
+chi-squared nuts
+let's meet last much less though really
+
+ align:start position:0%
+let's meet last much less though really
+ 
+
+ align:start position:0%
+let's meet last much less though really
+less not equal then then you're really
+
+ align:start position:0%
+less not equal then then you're really
+ 
+
+ align:start position:0%
+less not equal then then you're really
+happy to say that the model is
+
+ align:start position:0%
+happy to say that the model is
+ 
+
+ align:start position:0%
+happy to say that the model is
+consistent the model of data consists of
+
+ align:start position:0%
+consistent the model of data consists of
+ 
+
+ align:start position:0%
+consistent the model of data consists of
+each other in in this case what you
+
+ align:start position:0%
+each other in in this case what you
+ 
+
+ align:start position:0%
+each other in in this case what you
+would normally do next is determine the
+
+ align:start position:0%
+would normally do next is determine the
+ 
+
+ align:start position:0%
+would normally do next is determine the
+confidence intervals on the Thetas that
+
+ align:start position:0%
+confidence intervals on the Thetas that
+ 
+
+ align:start position:0%
+confidence intervals on the Thetas that
+you adjusted right and if you read the
+
+ align:start position:0%
+you adjusted right and if you read the
+ 
+
+ align:start position:0%
+you adjusted right and if you read the
+chapter and numerical recipes for
+
+ align:start position:0%
+chapter and numerical recipes for
+ 
+
+ align:start position:0%
+chapter and numerical recipes for
+example or some of the notes online they
+
+ align:start position:0%
+example or some of the notes online they
+ 
+
+ align:start position:0%
+example or some of the notes online they
+can tell you how to do this right and so
+
+ align:start position:0%
+can tell you how to do this right and so
+ 
+
+ align:start position:0%
+can tell you how to do this right and so
+that was okay there is okay so the case
+
+ align:start position:0%
+that was okay there is okay so the case
+ 
+
+ align:start position:0%
+that was okay there is okay so the case
+that's really problematic is applying
+
+ align:start position:0%
+that's really problematic is applying
+ 
+
+ align:start position:0%
+that's really problematic is applying
+chi squared theta best and it's less
+
+ align:start position:0%
+chi squared theta best and it's less
+ 
+
+ align:start position:0%
+chi squared theta best and it's less
+than chi-squared max so you think the
+
+ align:start position:0%
+than chi-squared max so you think the
+ 
+
+ align:start position:0%
+than chi-squared max so you think the
+model is consistent with the data but
+
+ align:start position:0%
+model is consistent with the data but
+ 
+
+ align:start position:0%
+model is consistent with the data but
+it's pretty darn close just beta squared
+
+ align:start position:0%
+it's pretty darn close just beta squared
+ 
+
+ align:start position:0%
+it's pretty darn close just beta squared
+max and so then you have to figure out
+
+ align:start position:0%
+max and so then you have to figure out
+ 
+
+ align:start position:0%
+max and so then you have to figure out
+well the weird aspect of this is I now
+
+ align:start position:0%
+well the weird aspect of this is I now
+ 
+
+ align:start position:0%
+well the weird aspect of this is I now
+have there's my famous plot of theta 1
+
+ align:start position:0%
+have there's my famous plot of theta 1
+ 
+
+ align:start position:0%
+have there's my famous plot of theta 1
+to theta 2 have two parameters I'm
+
+ align:start position:0%
+to theta 2 have two parameters I'm
+ 
+
+ align:start position:0%
+to theta 2 have two parameters I'm
+adjusting it 1 theta 2 here's my best
+
+ align:start position:0%
+adjusting it 1 theta 2 here's my best
+ 
+
+ align:start position:0%
+adjusting it 1 theta 2 here's my best
+fit if if PI squared Max and in the
+
+ align:start position:0%
+fit if if PI squared Max and in the
+ 
+
+ align:start position:0%
+fit if if PI squared Max and in the
+curve of constant chi squared max or
+
+ align:start position:0%
+curve of constant chi squared max or
+ 
+
+ align:start position:0%
+curve of constant chi squared max or
+something like this this is pi squared
+
+ align:start position:0%
+something like this this is pi squared
+ 
+
+ align:start position:0%
+something like this this is pi squared
+of theta equals max if it's like that
+
+ align:start position:0%
+of theta equals max if it's like that
+ 
+
+ align:start position:0%
+of theta equals max if it's like that
+then I have some big region of a lot of
+
+ align:start position:0%
+then I have some big region of a lot of
+ 
+
+ align:start position:0%
+then I have some big region of a lot of
+different theta values they give it
+
+ align:start position:0%
+different theta values they give it
+ 
+
+ align:start position:0%
+different theta values they give it
+pretty good fits and I'm happy to draw
+
+ align:start position:0%
+pretty good fits and I'm happy to draw
+ 
+
+ align:start position:0%
+pretty good fits and I'm happy to draw
+confidence intervals like draw lines
+
+ align:start position:0%
+confidence intervals like draw lines
+ 
+
+ align:start position:0%
+confidence intervals like draw lines
+here and here for example let's say
+
+ align:start position:0%
+here and here for example let's say
+ 
+
+ align:start position:0%
+here and here for example let's say
+that's the confidence interval in theta
+
+ align:start position:0%
+that's the confidence interval in theta
+ 
+
+ align:start position:0%
+that's the confidence interval in theta
+1 and I'm all right okay
+
+ align:start position:0%
+1 and I'm all right okay
+ 
+
+ align:start position:0%
+1 and I'm all right okay
+and I might you know it's it's sloped
+
+ align:start position:0%
+and I might you know it's it's sloped
+ 
+
+ align:start position:0%
+and I might you know it's it's sloped
+here so I might want to tell people
+
+ align:start position:0%
+here so I might want to tell people
+ 
+
+ align:start position:0%
+here so I might want to tell people
+about the covariance between theta 1
+
+ align:start position:0%
+about the covariance between theta 1
+ 
+
+ align:start position:0%
+about the covariance between theta 1
+theta 2 all right but but I know what to
+
+ align:start position:0%
+theta 2 all right but but I know what to
+ 
+
+ align:start position:0%
+theta 2 all right but but I know what to
+do it's fine now suppose this is the
+
+ align:start position:0%
+do it's fine now suppose this is the
+ 
+
+ align:start position:0%
+do it's fine now suppose this is the
+case that's like this for
+
+ align:start position:0%
+case that's like this for
+ 
+
+ align:start position:0%
+case that's like this for
+scrutiny best is significantly less than
+
+ align:start position:0%
+scrutiny best is significantly less than
+ 
+
+ align:start position:0%
+scrutiny best is significantly less than
+chi-squared Meadows now suppose instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chi-squared best was very close to
+
+ align:start position:0%
+chi-squared best was very close to
+ 
+
+ align:start position:0%
+chi-squared best was very close to
+squared max so then here's cash mark max
+
+ align:start position:0%
+squared max so then here's cash mark max
+ 
+
+ align:start position:0%
+squared max so then here's cash mark max
+this is quite square to theta equals pi
+
+ align:start position:0%
+this is quite square to theta equals pi
+ 
+
+ align:start position:0%
+this is quite square to theta equals pi
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+max this is that it's a good case here's
+
+ align:start position:0%
+max this is that it's a good case here's
+ 
+
+ align:start position:0%
+max this is that it's a good case here's
+the bad case so in the back case there
+
+ align:start position:0%
+the bad case so in the back case there
+ 
+
+ align:start position:0%
+the bad case so in the back case there
+is some region of Thetas that the models
+
+ align:start position:0%
+is some region of Thetas that the models
+ 
+
+ align:start position:0%
+is some region of Thetas that the models
+consistent with the data but it's very
+
+ align:start position:0%
+consistent with the data but it's very
+ 
+
+ align:start position:0%
+consistent with the data but it's very
+tiny there's a little tiny range of
+
+ align:start position:0%
+tiny there's a little tiny range of
+ 
+
+ align:start position:0%
+tiny there's a little tiny range of
+theta values that are that would make
+
+ align:start position:0%
+theta values that are that would make
+ 
+
+ align:start position:0%
+theta values that are that would make
+the models consistent data now what's
+
+ align:start position:0%
+the models consistent data now what's
+ 
+
+ align:start position:0%
+the models consistent data now what's
+weird about this is that my best fit
+
+ align:start position:0%
+weird about this is that my best fit
+ 
+
+ align:start position:0%
+weird about this is that my best fit
+it's not very good the chi-squared is
+
+ align:start position:0%
+it's not very good the chi-squared is
+ 
+
+ align:start position:0%
+it's not very good the chi-squared is
+almost up to my skysport the maximum
+
+ align:start position:0%
+almost up to my skysport the maximum
+ 
+
+ align:start position:0%
+almost up to my skysport the maximum
+chi-squared i would tolerate so it means
+
+ align:start position:0%
+chi-squared i would tolerate so it means
+ 
+
+ align:start position:0%
+chi-squared i would tolerate so it means
+my deviations between my model and data
+
+ align:start position:0%
+my deviations between my model and data
+ 
+
+ align:start position:0%
+my deviations between my model and data
+are pretty bad like like this plot
+
+ align:start position:0%
+are pretty bad like like this plot
+ 
+
+ align:start position:0%
+are pretty bad like like this plot
+actually okay and so like you know it
+
+ align:start position:0%
+actually okay and so like you know it
+ 
+
+ align:start position:0%
+actually okay and so like you know it
+could it's possible I was little bit
+
+ align:start position:0%
+could it's possible I was little bit
+ 
+
+ align:start position:0%
+could it's possible I was little bit
+unlucky and my dataset is pretty far off
+
+ align:start position:0%
+unlucky and my dataset is pretty far off
+ 
+
+ align:start position:0%
+unlucky and my dataset is pretty far off
+but still within the possible range and
+
+ align:start position:0%
+but still within the possible range and
+ 
+
+ align:start position:0%
+but still within the possible range and
+so maybe the model data are consistent
+
+ align:start position:0%
+so maybe the model data are consistent
+ 
+
+ align:start position:0%
+so maybe the model data are consistent
+but then when I try to compute the
+
+ align:start position:0%
+but then when I try to compute the
+ 
+
+ align:start position:0%
+but then when I try to compute the
+confidence intervals on my parameters
+
+ align:start position:0%
+confidence intervals on my parameters
+ 
+
+ align:start position:0%
+confidence intervals on my parameters
+there's only a really small range of
+
+ align:start position:0%
+there's only a really small range of
+ 
+
+ align:start position:0%
+there's only a really small range of
+parameters that are going to give good
+
+ align:start position:0%
+parameters that are going to give good
+ 
+
+ align:start position:0%
+parameters that are going to give good
+fits here because the best possible fit
+
+ align:start position:0%
+fits here because the best possible fit
+ 
+
+ align:start position:0%
+fits here because the best possible fit
+is this red line there's no there's no
+
+ align:start position:0%
+is this red line there's no there's no
+ 
+
+ align:start position:0%
+is this red line there's no there's no
+about choice in the event of the
+
+ align:start position:0%
+about choice in the event of the
+ 
+
+ align:start position:0%
+about choice in the event of the
+parameters just gonna go through all the
+
+ align:start position:0%
+parameters just gonna go through all the
+ 
+
+ align:start position:0%
+parameters just gonna go through all the
+circles right with this model so now I'm
+
+ align:start position:0%
+circles right with this model so now I'm
+ 
+
+ align:start position:0%
+circles right with this model so now I'm
+like well what's going on here so if I
+
+ align:start position:0%
+like well what's going on here so if I
+ 
+
+ align:start position:0%
+like well what's going on here so if I
+if I went ahead and do it the same way I
+
+ align:start position:0%
+if I went ahead and do it the same way I
+ 
+
+ align:start position:0%
+if I went ahead and do it the same way I
+did before I draw my my confidence
+
+ align:start position:0%
+did before I draw my my confidence
+ 
+
+ align:start position:0%
+did before I draw my my confidence
+intervals like this and say okay say wow
+
+ align:start position:0%
+intervals like this and say okay say wow
+ 
+
+ align:start position:0%
+intervals like this and say okay say wow
+I've done an amazingly great job of
+
+ align:start position:0%
+I've done an amazingly great job of
+ 
+
+ align:start position:0%
+I've done an amazingly great job of
+determining theta1 i never say the one
+
+ align:start position:0%
+determining theta1 i never say the one
+ 
+
+ align:start position:0%
+determining theta1 i never say the one
+very very very precisely and the safer
+
+ align:start position:0%
+very very very precisely and the safer
+ 
+
+ align:start position:0%
+very very very precisely and the safer
+data to here's theta two it's got mean
+
+ align:start position:0%
+data to here's theta two it's got mean
+ 
+
+ align:start position:0%
+data to here's theta two it's got mean
+that range to me and i really done a
+
+ align:start position:0%
+that range to me and i really done a
+ 
+
+ align:start position:0%
+that range to me and i really done a
+great job so you know i'm awesome
+
+ align:start position:0%
+great job so you know i'm awesome
+ 
+
+ align:start position:0%
+great job so you know i'm awesome
+but I'm only awesome because my original
+
+ align:start position:0%
+but I'm only awesome because my original
+ 
+
+ align:start position:0%
+but I'm only awesome because my original
+best fit wasn't very good so this is
+
+ align:start position:0%
+best fit wasn't very good so this is
+ 
+
+ align:start position:0%
+best fit wasn't very good so this is
+like might make you feel a little sick
+
+ align:start position:0%
+like might make you feel a little sick
+ 
+
+ align:start position:0%
+like might make you feel a little sick
+in your stomach if you get ready to
+
+ align:start position:0%
+in your stomach if you get ready to
+ 
+
+ align:start position:0%
+in your stomach if you get ready to
+publish the nature right and then you
+
+ align:start position:0%
+publish the nature right and then you
+ 
+
+ align:start position:0%
+publish the nature right and then you
+and if you're if you're the reviewers
+
+ align:start position:0%
+and if you're if you're the reviewers
+ 
+
+ align:start position:0%
+and if you're if you're the reviewers
+are on their game you might get
+
+ align:start position:0%
+are on their game you might get
+ 
+
+ align:start position:0%
+are on their game you might get
+something really skating jacked for the
+
+ align:start position:0%
+something really skating jacked for the
+ 
+
+ align:start position:0%
+something really skating jacked for the
+reviewers so there's kind of two ways to
+
+ align:start position:0%
+reviewers so there's kind of two ways to
+ 
+
+ align:start position:0%
+reviewers so there's kind of two ways to
+play it at this point
+
+ align:start position:0%
+play it at this point
+ 
+
+ align:start position:0%
+play it at this point
+one way is
+
+ align:start position:0%
+one way is
+ 
+
+ align:start position:0%
+one way is
+you are absolutely sure that your
+
+ align:start position:0%
+you are absolutely sure that your
+ 
+
+ align:start position:0%
+you are absolutely sure that your
+equations are correct you are Sir Isaac
+
+ align:start position:0%
+equations are correct you are Sir Isaac
+ 
+
+ align:start position:0%
+equations are correct you are Sir Isaac
+Newton you have just written the law of
+
+ align:start position:0%
+Newton you have just written the law of
+ 
+
+ align:start position:0%
+Newton you have just written the law of
+gravitation you are measuring the orbits
+
+ align:start position:0%
+gravitation you are measuring the orbits
+ 
+
+ align:start position:0%
+gravitation you are measuring the orbits
+of the moons of Jupiter and you are sure
+
+ align:start position:0%
+of the moons of Jupiter and you are sure
+ 
+
+ align:start position:0%
+of the moons of Jupiter and you are sure
+that your equations are right and so you
+
+ align:start position:0%
+that your equations are right and so you
+ 
+
+ align:start position:0%
+that your equations are right and so you
+know my problem is my my antiquated
+
+ align:start position:0%
+know my problem is my my antiquated
+ 
+
+ align:start position:0%
+know my problem is my my antiquated
+Tellez my telescopes of 1600 or not that
+
+ align:start position:0%
+Tellez my telescopes of 1600 or not that
+ 
+
+ align:start position:0%
+Tellez my telescopes of 1600 or not that
+great and so I think I have maybe maybe
+
+ align:start position:0%
+great and so I think I have maybe maybe
+ 
+
+ align:start position:0%
+great and so I think I have maybe maybe
+I miss estimated my error bars my
+
+ align:start position:0%
+I miss estimated my error bars my
+ 
+
+ align:start position:0%
+I miss estimated my error bars my
+measurements maybe might have some
+
+ align:start position:0%
+measurements maybe might have some
+ 
+
+ align:start position:0%
+measurements maybe might have some
+aberration or something the angles are
+
+ align:start position:0%
+aberration or something the angles are
+ 
+
+ align:start position:0%
+aberration or something the angles are
+off right
+
+ align:start position:0%
+off right
+ 
+
+ align:start position:0%
+off right
+I twist the telescope it looks this
+
+ align:start position:0%
+I twist the telescope it looks this
+ 
+
+ align:start position:0%
+I twist the telescope it looks this
+mislead star moves or something right
+
+ align:start position:0%
+mislead star moves or something right
+ 
+
+ align:start position:0%
+mislead star moves or something right
+okay so that's that's one possible way
+
+ align:start position:0%
+okay so that's that's one possible way
+ 
+
+ align:start position:0%
+okay so that's that's one possible way
+to go is say I really believe the model
+
+ align:start position:0%
+to go is say I really believe the model
+ 
+
+ align:start position:0%
+to go is say I really believe the model
+and so I believe that this is the truth
+
+ align:start position:0%
+and so I believe that this is the truth
+ 
+
+ align:start position:0%
+and so I believe that this is the truth
+and I really believe my chi-squared max
+
+ align:start position:0%
+and I really believe my chi-squared max
+ 
+
+ align:start position:0%
+and I really believe my chi-squared max
+to be what it is and I double checked my
+
+ align:start position:0%
+to be what it is and I double checked my
+ 
+
+ align:start position:0%
+to be what it is and I double checked my
+error bars and I think it's true so I
+
+ align:start position:0%
+error bars and I think it's true so I
+ 
+
+ align:start position:0%
+error bars and I think it's true so I
+think I've done a great job and I should
+
+ align:start position:0%
+think I've done a great job and I should
+ 
+
+ align:start position:0%
+think I've done a great job and I should
+publish it in nature because I determine
+
+ align:start position:0%
+publish it in nature because I determine
+ 
+
+ align:start position:0%
+publish it in nature because I determine
+these parameters with 17 more decimal
+
+ align:start position:0%
+these parameters with 17 more decimal
+ 
+
+ align:start position:0%
+these parameters with 17 more decimal
+places than anybody ever could before
+
+ align:start position:0%
+places than anybody ever could before
+ 
+
+ align:start position:0%
+places than anybody ever could before
+okay so that's one way to look at it the
+
+ align:start position:0%
+okay so that's one way to look at it the
+ 
+
+ align:start position:0%
+okay so that's one way to look at it the
+other way to look at it is what's
+
+ align:start position:0%
+other way to look at it is what's
+ 
+
+ align:start position:0%
+other way to look at it is what's
+recommended the numerical recipes book
+
+ align:start position:0%
+recommended the numerical recipes book
+ 
+
+ align:start position:0%
+recommended the numerical recipes book
+and they say don't use instead of
+
+ align:start position:0%
+and they say don't use instead of
+ 
+
+ align:start position:0%
+and they say don't use instead of
+writing equation to be high squared of
+
+ align:start position:0%
+writing equation to be high squared of
+ 
+
+ align:start position:0%
+writing equation to be high squared of
+theta has to be less than chi-squared
+
+ align:start position:0%
+theta has to be less than chi-squared
+ 
+
+ align:start position:0%
+theta has to be less than chi-squared
+max they say when you're computing the
+
+ align:start position:0%
+max they say when you're computing the
+ 
+
+ align:start position:0%
+max they say when you're computing the
+confidence intervals instead write high
+
+ align:start position:0%
+confidence intervals instead write high
+ 
+
+ align:start position:0%
+confidence intervals instead write high
+squared of theta has to be less than PI
+
+ align:start position:0%
+squared of theta has to be less than PI
+ 
+
+ align:start position:0%
+squared of theta has to be less than PI
+squared best-fit plus I squared nice so
+
+ align:start position:0%
+squared best-fit plus I squared nice so
+ 
+
+ align:start position:0%
+squared best-fit plus I squared nice so
+they say don't use those dinky little
+
+ align:start position:0%
+they say don't use those dinky little
+ 
+
+ align:start position:0%
+they say don't use those dinky little
+circle here draw a nice big line around
+
+ align:start position:0%
+circle here draw a nice big line around
+ 
+
+ align:start position:0%
+circle here draw a nice big line around
+there and and and what is this saying I
+
+ align:start position:0%
+there and and and what is this saying I
+ 
+
+ align:start position:0%
+there and and and what is this saying I
+guess it's the saying is I don't believe
+
+ align:start position:0%
+guess it's the saying is I don't believe
+ 
+
+ align:start position:0%
+guess it's the saying is I don't believe
+that my my poor agreement with model
+
+ align:start position:0%
+that my my poor agreement with model
+ 
+
+ align:start position:0%
+that my my poor agreement with model
+data justifies me to declaring very
+
+ align:start position:0%
+data justifies me to declaring very
+ 
+
+ align:start position:0%
+data justifies me to declaring very
+narrow parameter values so I just used
+
+ align:start position:0%
+narrow parameter values so I just used
+ 
+
+ align:start position:0%
+narrow parameter values so I just used
+the kinds of parameter value confidence
+
+ align:start position:0%
+the kinds of parameter value confidence
+ 
+
+ align:start position:0%
+the kinds of parameter value confidence
+intervals that it would have actually
+
+ align:start position:0%
+intervals that it would have actually
+ 
+
+ align:start position:0%
+intervals that it would have actually
+computed at a priori when I do my
+
+ align:start position:0%
+computed at a priori when I do my
+ 
+
+ align:start position:0%
+computed at a priori when I do my
+experimental design I think that's
+
+ align:start position:0%
+experimental design I think that's
+ 
+
+ align:start position:0%
+experimental design I think that's
+really how well I can determine stuff
+
+ align:start position:0%
+really how well I can determine stuff
+ 
+
+ align:start position:0%
+really how well I can determine stuff
+and and I think there's something is
+
+ align:start position:0%
+and and I think there's something is
+ 
+
+ align:start position:0%
+and and I think there's something is
+wrong that my chrisquared best fit is so
+
+ align:start position:0%
+wrong that my chrisquared best fit is so
+ 
+
+ align:start position:0%
+wrong that my chrisquared best fit is so
+bad maybe I don't do my global
+
+ align:start position:0%
+bad maybe I don't do my global
+ 
+
+ align:start position:0%
+bad maybe I don't do my global
+optimization right and so I have the
+
+ align:start position:0%
+optimization right and so I have the
+ 
+
+ align:start position:0%
+optimization right and so I have the
+wrong parameters maybe
+
+ align:start position:0%
+wrong parameters maybe
+ 
+
+ align:start position:0%
+wrong parameters maybe
+I misunderstood estimated Myer bars and
+
+ align:start position:0%
+I misunderstood estimated Myer bars and
+ 
+
+ align:start position:0%
+I misunderstood estimated Myer bars and
+so my Chi squares are all off maybe I
+
+ align:start position:0%
+so my Chi squares are all off maybe I
+ 
+
+ align:start position:0%
+so my Chi squares are all off maybe I
+don't know what else happened something
+
+ align:start position:0%
+don't know what else happened something
+ 
+
+ align:start position:0%
+don't know what else happened something
+happened and I don't believe on that
+
+ align:start position:0%
+happened and I don't believe on that
+ 
+
+ align:start position:0%
+happened and I don't believe on that
+good so therefore I'm going to quote
+
+ align:start position:0%
+good so therefore I'm going to quote
+ 
+
+ align:start position:0%
+good so therefore I'm going to quote
+much broader confidence intervals which
+
+ align:start position:0%
+much broader confidence intervals which
+ 
+
+ align:start position:0%
+much broader confidence intervals which
+means much less precision in my
+
+ align:start position:0%
+means much less precision in my
+ 
+
+ align:start position:0%
+means much less precision in my
+determination of parameters and that's
+
+ align:start position:0%
+determination of parameters and that's
+ 
+
+ align:start position:0%
+determination of parameters and that's
+what the dimeric are these guys
+
+ align:start position:0%
+what the dimeric are these guys
+ 
+
+ align:start position:0%
+what the dimeric are these guys
+recommend you should do but you know
+
+ align:start position:0%
+recommend you should do but you know
+ 
+
+ align:start position:0%
+recommend you should do but you know
+it's up to you and I see the post way so
+
+ align:start position:0%
+it's up to you and I see the post way so
+ 
+
+ align:start position:0%
+it's up to you and I see the post way so
+in the people on the Nobel Prize for the
+
+ align:start position:0%
+in the people on the Nobel Prize for the
+ 
+
+ align:start position:0%
+in the people on the Nobel Prize for the
+dark energy do you guys know about this
+
+ align:start position:0%
+dark energy do you guys know about this
+ 
+
+ align:start position:0%
+dark energy do you guys know about this
+so have you ever saw that data there so
+
+ align:start position:0%
+so have you ever saw that data there so
+ 
+
+ align:start position:0%
+so have you ever saw that data there so
+that's one where they said they were
+
+ align:start position:0%
+that's one where they said they were
+ 
+
+ align:start position:0%
+that's one where they said they were
+using eye x theory of relativity general
+
+ align:start position:0%
+using eye x theory of relativity general
+ 
+
+ align:start position:0%
+using eye x theory of relativity general
+relativity they say we believe Einstein
+
+ align:start position:0%
+relativity they say we believe Einstein
+ 
+
+ align:start position:0%
+relativity they say we believe Einstein
+we believe the equations true and we're
+
+ align:start position:0%
+we believe the equations true and we're
+ 
+
+ align:start position:0%
+we believe the equations true and we're
+not going to know the fact that it you
+
+ align:start position:0%
+not going to know the fact that it you
+ 
+
+ align:start position:0%
+not going to know the fact that it you
+know the data only matches when you
+
+ align:start position:0%
+know the data only matches when you
+ 
+
+ align:start position:0%
+know the data only matches when you
+choose a certain value of the
+
+ align:start position:0%
+choose a certain value of the
+ 
+
+ align:start position:0%
+choose a certain value of the
+cosmological constant we're just going
+
+ align:start position:0%
+cosmological constant we're just going
+ 
+
+ align:start position:0%
+cosmological constant we're just going
+to go with it and we're reporting that's
+
+ align:start position:0%
+to go with it and we're reporting that's
+ 
+
+ align:start position:0%
+to go with it and we're reporting that's
+the value of the cosmological constant
+
+ align:start position:0%
+the value of the cosmological constant
+ 
+
+ align:start position:0%
+the value of the cosmological constant
+now some other people might say that's
+
+ align:start position:0%
+now some other people might say that's
+ 
+
+ align:start position:0%
+now some other people might say that's
+kind of goofy theory Einstein change of
+
+ align:start position:0%
+kind of goofy theory Einstein change of
+ 
+
+ align:start position:0%
+kind of goofy theory Einstein change of
+mind six times about whether what the
+
+ align:start position:0%
+mind six times about whether what the
+ 
+
+ align:start position:0%
+mind six times about whether what the
+cosmic out cosmological constant in the
+
+ align:start position:0%
+cosmic out cosmological constant in the
+ 
+
+ align:start position:0%
+cosmic out cosmological constant in the
+equation at all so I'm not so confident
+
+ align:start position:0%
+equation at all so I'm not so confident
+ 
+
+ align:start position:0%
+equation at all so I'm not so confident
+and I would yeah we port something
+
+ align:start position:0%
+and I would yeah we port something
+ 
+
+ align:start position:0%
+and I would yeah we port something
+different but they went with her gut
+
+ align:start position:0%
+different but they went with her gut
+ 
+
+ align:start position:0%
+different but they went with her gut
+they said we believe Einstein they went
+
+ align:start position:0%
+they said we believe Einstein they went
+ 
+
+ align:start position:0%
+they said we believe Einstein they went
+with it the Nobel Committee agreed and
+
+ align:start position:0%
+with it the Nobel Committee agreed and
+ 
+
+ align:start position:0%
+with it the Nobel Committee agreed and
+they got the Nimmo price so you know
+
+ align:start position:0%
+they got the Nimmo price so you know
+ 
+
+ align:start position:0%
+they got the Nimmo price so you know
+you're taking your chances the new
+
+ align:start position:0%
+you're taking your chances the new
+ 
+
+ align:start position:0%
+you're taking your chances the new
+recipe guys are more like engineers they
+
+ align:start position:0%
+recipe guys are more like engineers they
+ 
+
+ align:start position:0%
+recipe guys are more like engineers they
+say we don't believe models that watch
+
+ align:start position:0%
+say we don't believe models that watch
+ 
+
+ align:start position:0%
+say we don't believe models that watch
+anyway let's just use a more
+
+ align:start position:0%
+anyway let's just use a more
+ 
+
+ align:start position:0%
+anyway let's just use a more
+conservative confidence intervals any
+
+ align:start position:0%
+conservative confidence intervals any
+ 
+
+ align:start position:0%
+conservative confidence intervals any
+questions about this ok all right so now
+
+ align:start position:0%
+questions about this ok all right so now
+ 
+
+ align:start position:0%
+questions about this ok all right so now
+I've changed topics you know change two
+
+ align:start position:0%
+I've changed topics you know change two
+ 
+
+ align:start position:0%
+I've changed topics you know change two
+operators splitting so if you remember
+
+ align:start position:0%
+operators splitting so if you remember
+ 
+
+ align:start position:0%
+operators splitting so if you remember
+back we're talking about
+
+ align:start position:0%
+back we're talking about
+ 
+
+ align:start position:0%
+back we're talking about
+boundary value problems we're often
+
+ align:start position:0%
+boundary value problems we're often
+ 
+
+ align:start position:0%
+boundary value problems we're often
+trying to solve problems that are like
+
+ align:start position:0%
+trying to solve problems that are like
+ 
+
+ align:start position:0%
+trying to solve problems that are like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is a conservation equation
+
+ align:start position:0%
+right so this is a conservation equation
+ 
+
+ align:start position:0%
+right so this is a conservation equation
+for species in a reacting reacting flow
+
+ align:start position:0%
+for species in a reacting reacting flow
+ 
+
+ align:start position:0%
+for species in a reacting reacting flow
+situation so you have some convection
+
+ align:start position:0%
+situation so you have some convection
+ 
+
+ align:start position:0%
+situation so you have some convection
+you have some diffusion you have some
+
+ align:start position:0%
+you have some diffusion you have some
+ 
+
+ align:start position:0%
+you have some diffusion you have some
+reactions now in my life I have a lot of
+
+ align:start position:0%
+reactions now in my life I have a lot of
+ 
+
+ align:start position:0%
+reactions now in my life I have a lot of
+models I have about 200 species in them
+
+ align:start position:0%
+models I have about 200 species in them
+ 
+
+ align:start position:0%
+models I have about 200 species in them
+so I've this K is 200 different
+
+ align:start position:0%
+so I've this K is 200 different
+ 
+
+ align:start position:0%
+so I've this K is 200 different
+variables and then you have these
+
+ align:start position:0%
+variables and then you have these
+ 
+
+ align:start position:0%
+variables and then you have these
+equations and on top of them you have
+
+ align:start position:0%
+equations and on top of them you have
+ 
+
+ align:start position:0%
+equations and on top of them you have
+the nav your six equations for the
+
+ align:start position:0%
+the nav your six equations for the
+ 
+
+ align:start position:0%
+the nav your six equations for the
+momentum conservation and continuity and
+
+ align:start position:0%
+momentum conservation and continuity and
+ 
+
+ align:start position:0%
+momentum conservation and continuity and
+so this is actually pretty bad set of
+
+ align:start position:0%
+so this is actually pretty bad set of
+ 
+
+ align:start position:0%
+so this is actually pretty bad set of
+equations and typically the chemistry is
+
+ align:start position:0%
+equations and typically the chemistry is
+ 
+
+ align:start position:0%
+equations and typically the chemistry is
+stiff because I have chemistry
+
+ align:start position:0%
+stiff because I have chemistry
+ 
+
+ align:start position:0%
+stiff because I have chemistry
+timescales that'll be like in Pico
+
+ align:start position:0%
+timescales that'll be like in Pico
+ 
+
+ align:start position:0%
+timescales that'll be like in Pico
+seconds sub sub nanosecond timescales
+
+ align:start position:0%
+seconds sub sub nanosecond timescales
+ 
+
+ align:start position:0%
+seconds sub sub nanosecond timescales
+and I'm caring about simulating in my
+
+ align:start position:0%
+and I'm caring about simulating in my
+ 
+
+ align:start position:0%
+and I'm caring about simulating in my
+case maybe I've advanced new engine
+
+ align:start position:0%
+case maybe I've advanced new engine
+ 
+
+ align:start position:0%
+case maybe I've advanced new engine
+burning some fuel and so we're running
+
+ align:start position:0%
+burning some fuel and so we're running
+ 
+
+ align:start position:0%
+burning some fuel and so we're running
+over a simulation of a piston cycle
+
+ align:start position:0%
+over a simulation of a piston cycle
+ 
+
+ align:start position:0%
+over a simulation of a piston cycle
+maybe 10 milliseconds but the chemistry
+
+ align:start position:0%
+maybe 10 milliseconds but the chemistry
+ 
+
+ align:start position:0%
+maybe 10 milliseconds but the chemistry
+sub nanosecond so then you multiply it
+
+ align:start position:0%
+sub nanosecond so then you multiply it
+ 
+
+ align:start position:0%
+sub nanosecond so then you multiply it
+out so that's like I'm going at 10 to
+
+ align:start position:0%
+out so that's like I'm going at 10 to
+ 
+
+ align:start position:0%
+out so that's like I'm going at 10 to
+minus 2 seconds down to 10 to minus 10
+
+ align:start position:0%
+minus 2 seconds down to 10 to minus 10
+ 
+
+ align:start position:0%
+minus 2 seconds down to 10 to minus 10
+seconds so it's a two orders of
+
+ align:start position:0%
+seconds so it's a two orders of
+ 
+
+ align:start position:0%
+seconds so it's a two orders of
+magnitude difference in timescales so
+
+ align:start position:0%
+magnitude difference in timescales so
+ 
+
+ align:start position:0%
+magnitude difference in timescales so
+I'm in a bad way trying to solve this
+
+ align:start position:0%
+I'm in a bad way trying to solve this
+ 
+
+ align:start position:0%
+I'm in a bad way trying to solve this
+equation and I have 200 of these guys
+
+ align:start position:0%
+equation and I have 200 of these guys
+ 
+
+ align:start position:0%
+equation and I have 200 of these guys
+coupled to each other and then I think
+
+ align:start position:0%
+coupled to each other and then I think
+ 
+
+ align:start position:0%
+coupled to each other and then I think
+of what my mesh looks like and I'm
+
+ align:start position:0%
+of what my mesh looks like and I'm
+ 
+
+ align:start position:0%
+of what my mesh looks like and I'm
+trying to simulate it inside the piston
+
+ align:start position:0%
+trying to simulate it inside the piston
+ 
+
+ align:start position:0%
+trying to simulate it inside the piston
+actually I have a moving mesh because
+
+ align:start position:0%
+actually I have a moving mesh because
+ 
+
+ align:start position:0%
+actually I have a moving mesh because
+the Pistons compress a so the equations
+
+ align:start position:0%
+the Pistons compress a so the equations
+ 
+
+ align:start position:0%
+the Pistons compress a so the equations
+are kind of complicated for even what
+
+ align:start position:0%
+are kind of complicated for even what
+ 
+
+ align:start position:0%
+are kind of complicated for even what
+the mesh is doing and then I need a
+
+ align:start position:0%
+the mesh is doing and then I need a
+ 
+
+ align:start position:0%
+the mesh is doing and then I need a
+bunch of mesh points there because the
+
+ align:start position:0%
+bunch of mesh points there because the
+ 
+
+ align:start position:0%
+bunch of mesh points there because the
+do you guys know the Cole MacGrath scale
+
+ align:start position:0%
+do you guys know the Cole MacGrath scale
+ 
+
+ align:start position:0%
+do you guys know the Cole MacGrath scale
+you go to learn this yet now it's a
+
+ align:start position:0%
+you go to learn this yet now it's a
+ 
+
+ align:start position:0%
+you go to learn this yet now it's a
+scale like the minimum Eddy size if you
+
+ align:start position:0%
+scale like the minimum Eddy size if you
+ 
+
+ align:start position:0%
+scale like the minimum Eddy size if you
+have a turbulent flow and that's pretty
+
+ align:start position:0%
+have a turbulent flow and that's pretty
+ 
+
+ align:start position:0%
+have a turbulent flow and that's pretty
+darn small also so it might be submicron
+
+ align:start position:0%
+darn small also so it might be submicron
+ 
+
+ align:start position:0%
+darn small also so it might be submicron
+and so I have length scale that's what
+
+ align:start position:0%
+and so I have length scale that's what
+ 
+
+ align:start position:0%
+and so I have length scale that's what
+let's scale this like you know microns
+
+ align:start position:0%
+let's scale this like you know microns
+ 
+
+ align:start position:0%
+let's scale this like you know microns
+maybe so 10 to minus 6 meters but the
+
+ align:start position:0%
+maybe so 10 to minus 6 meters but the
+ 
+
+ align:start position:0%
+maybe so 10 to minus 6 meters but the
+piston diameter is a couple centimeters
+
+ align:start position:0%
+piston diameter is a couple centimeters
+ 
+
+ align:start position:0%
+piston diameter is a couple centimeters
+so again I have like four orders of
+
+ align:start position:0%
+so again I have like four orders of
+ 
+
+ align:start position:0%
+so again I have like four orders of
+magnitude between the mesh size I need
+
+ align:start position:0%
+magnitude between the mesh size I need
+ 
+
+ align:start position:0%
+magnitude between the mesh size I need
+to resolve the physics
+
+ align:start position:0%
+to resolve the physics
+ 
+
+ align:start position:0%
+to resolve the physics
+and the and the size of the thing so I
+
+ align:start position:0%
+and the and the size of the thing so I
+ 
+
+ align:start position:0%
+and the and the size of the thing so I
+need about 10,000 point across the
+
+ align:start position:0%
+need about 10,000 point across the
+ 
+
+ align:start position:0%
+need about 10,000 point across the
+cylinder but it's a 3d problem so I need
+
+ align:start position:0%
+cylinder but it's a 3d problem so I need
+ 
+
+ align:start position:0%
+cylinder but it's a 3d problem so I need
+10 to the 4 times 10 to the 4th times 10
+
+ align:start position:0%
+10 to the 4 times 10 to the 4th times 10
+ 
+
+ align:start position:0%
+10 to the 4 times 10 to the 4th times 10
+to the 4th so I need 10 to the 12th mesh
+
+ align:start position:0%
+to the 4th so I need 10 to the 12th mesh
+ 
+
+ align:start position:0%
+to the 4th so I need 10 to the 12th mesh
+points and then I have 200 variables
+
+ align:start position:0%
+points and then I have 200 variables
+ 
+
+ align:start position:0%
+points and then I have 200 variables
+state variables at each mesh point so I
+
+ align:start position:0%
+state variables at each mesh point so I
+ 
+
+ align:start position:0%
+state variables at each mesh point so I
+have 10 to the 14th state variables so
+
+ align:start position:0%
+have 10 to the 14th state variables so
+ 
+
+ align:start position:0%
+have 10 to the 14th state variables so
+how much remember you have in your
+
+ align:start position:0%
+how much remember you have in your
+ 
+
+ align:start position:0%
+how much remember you have in your
+computer much RAM yeah probably like 16
+
+ align:start position:0%
+computer much RAM yeah probably like 16
+ 
+
+ align:start position:0%
+computer much RAM yeah probably like 16
+gigabytes they have ten to the ninth ten
+
+ align:start position:0%
+gigabytes they have ten to the ninth ten
+ 
+
+ align:start position:0%
+gigabytes they have ten to the ninth ten
+to the ninth bytes is that right now 10
+
+ align:start position:0%
+to the ninth bytes is that right now 10
+ 
+
+ align:start position:0%
+to the ninth bytes is that right now 10
+no what's key again nice ok so a 10 to
+
+ align:start position:0%
+no what's key again nice ok so a 10 to
+ 
+
+ align:start position:0%
+no what's key again nice ok so a 10 to
+the 10th sorry 10 to the 10th bytes but
+
+ align:start position:0%
+the 10th sorry 10 to the 10th bytes but
+ 
+
+ align:start position:0%
+the 10th sorry 10 to the 10th bytes but
+I have 10 to the 14 state variables so I
+
+ align:start position:0%
+I have 10 to the 14 state variables so I
+ 
+
+ align:start position:0%
+I have 10 to the 14 state variables so I
+have a problem so they need to figure
+
+ align:start position:0%
+have a problem so they need to figure
+ 
+
+ align:start position:0%
+have a problem so they need to figure
+out how you solve it so there's two
+
+ align:start position:0%
+out how you solve it so there's two
+ 
+
+ align:start position:0%
+out how you solve it so there's two
+schools of thought of how to solve these
+
+ align:start position:0%
+schools of thought of how to solve these
+ 
+
+ align:start position:0%
+schools of thought of how to solve these
+equations the school thought which has
+
+ align:start position:0%
+equations the school thought which has
+ 
+
+ align:start position:0%
+equations the school thought which has
+actually been the most successful so far
+
+ align:start position:0%
+actually been the most successful so far
+ 
+
+ align:start position:0%
+actually been the most successful so far
+but is not readily available is to get
+
+ align:start position:0%
+but is not readily available is to get
+ 
+
+ align:start position:0%
+but is not readily available is to get
+the government to build you the biggest
+
+ align:start position:0%
+the government to build you the biggest
+ 
+
+ align:start position:0%
+the government to build you the biggest
+possible computer in the world with as
+
+ align:start position:0%
+possible computer in the world with as
+ 
+
+ align:start position:0%
+possible computer in the world with as
+much memory as possible and then you can
+
+ align:start position:0%
+much memory as possible and then you can
+ 
+
+ align:start position:0%
+much memory as possible and then you can
+actually keep track of your state vector
+
+ align:start position:0%
+actually keep track of your state vector
+ 
+
+ align:start position:0%
+actually keep track of your state vector
+all 10 to the 14th elements and and you
+
+ align:start position:0%
+all 10 to the 14th elements and and you
+ 
+
+ align:start position:0%
+all 10 to the 14th elements and and you
+reserve the this whole computer for
+
+ align:start position:0%
+reserve the this whole computer for
+ 
+
+ align:start position:0%
+reserve the this whole computer for
+yourself for you know a month and just
+
+ align:start position:0%
+yourself for you know a month and just
+ 
+
+ align:start position:0%
+yourself for you know a month and just
+run it and you hear how to parallelize
+
+ align:start position:0%
+run it and you hear how to parallelize
+ 
+
+ align:start position:0%
+run it and you hear how to parallelize
+all the calculations and you just use an
+
+ align:start position:0%
+all the calculations and you just use an
+ 
+
+ align:start position:0%
+all the calculations and you just use an
+explicit solver and so that way it's
+
+ align:start position:0%
+explicit solver and so that way it's
+ 
+
+ align:start position:0%
+explicit solver and so that way it's
+just straightforward all you're doing is
+
+ align:start position:0%
+just straightforward all you're doing is
+ 
+
+ align:start position:0%
+just straightforward all you're doing is
+you're computing you know why T plus
+
+ align:start position:0%
+you're computing you know why T plus
+ 
+
+ align:start position:0%
+you're computing you know why T plus
+delta T is equal to something and it's
+
+ align:start position:0%
+delta T is equal to something and it's
+ 
+
+ align:start position:0%
+delta T is equal to something and it's
+just an explicit formula OD 45 fancy
+
+ align:start position:0%
+just an explicit formula OD 45 fancy
+ 
+
+ align:start position:0%
+just an explicit formula OD 45 fancy
+version of that ok and it's just algebra
+
+ align:start position:0%
+version of that ok and it's just algebra
+ 
+
+ align:start position:0%
+version of that ok and it's just algebra
+and you just add them up and it's no
+
+ align:start position:0%
+and you just add them up and it's no
+ 
+
+ align:start position:0%
+and you just add them up and it's no
+problem but this is a limited limited
+
+ align:start position:0%
+problem but this is a limited limited
+ 
+
+ align:start position:0%
+problem but this is a limited limited
+feasibility thing this only became
+
+ align:start position:0%
+feasibility thing this only became
+ 
+
+ align:start position:0%
+feasibility thing this only became
+possible about three years ago when they
+
+ align:start position:0%
+possible about three years ago when they
+ 
+
+ align:start position:0%
+possible about three years ago when they
+build a computer that actually had
+
+ align:start position:0%
+build a computer that actually had
+ 
+
+ align:start position:0%
+build a computer that actually had
+enough memory to store the state vector
+
+ align:start position:0%
+enough memory to store the state vector
+ 
+
+ align:start position:0%
+enough memory to store the state vector
+it's also if the equations are too stiff
+
+ align:start position:0%
+it's also if the equations are too stiff
+ 
+
+ align:start position:0%
+it's also if the equations are too stiff
+it still doesn't work because the the
+
+ align:start position:0%
+it still doesn't work because the the
+ 
+
+ align:start position:0%
+it still doesn't work because the the
+step size the time step you need to use
+
+ align:start position:0%
+step size the time step you need to use
+ 
+
+ align:start position:0%
+step size the time step you need to use
+is so small so say is 100 picoseconds
+
+ align:start position:0%
+is so small so say is 100 picoseconds
+ 
+
+ align:start position:0%
+is so small so say is 100 picoseconds
+you're trying to get out to a
+
+ align:start position:0%
+you're trying to get out to a
+ 
+
+ align:start position:0%
+you're trying to get out to a
+millisecond so you need 10 to the 8th
+
+ align:start position:0%
+millisecond so you need 10 to the 8th
+ 
+
+ align:start position:0%
+millisecond so you need 10 to the 8th
+something time steps which means you
+
+ align:start position:0%
+something time steps which means you
+ 
+
+ align:start position:0%
+something time steps which means you
+need to use double precision
+
+ align:start position:0%
+need to use double precision
+ 
+
+ align:start position:0%
+need to use double precision
+numbers all the way through but if the
+
+ align:start position:0%
+numbers all the way through but if the
+ 
+
+ align:start position:0%
+numbers all the way through but if the
+computer the government builds you a
+
+ align:start position:0%
+computer the government builds you a
+ 
+
+ align:start position:0%
+computer the government builds you a
+64-bit or 128-bit machine then if you
+
+ align:start position:0%
+64-bit or 128-bit machine then if you
+ 
+
+ align:start position:0%
+64-bit or 128-bit machine then if you
+can do it but it anyway this is like a
+
+ align:start position:0%
+can do it but it anyway this is like a
+ 
+
+ align:start position:0%
+can do it but it anyway this is like a
+very special kind of aversion so now
+
+ align:start position:0%
+very special kind of aversion so now
+ 
+
+ align:start position:0%
+very special kind of aversion so now
+most people including me I don't have
+
+ align:start position:0%
+most people including me I don't have
+ 
+
+ align:start position:0%
+most people including me I don't have
+access to that kind of kind of computer
+
+ align:start position:0%
+access to that kind of kind of computer
+ 
+
+ align:start position:0%
+access to that kind of kind of computer
+power it actually if you want to read
+
+ align:start position:0%
+power it actually if you want to read
+ 
+
+ align:start position:0%
+power it actually if you want to read
+about that there's a woman who does that
+
+ align:start position:0%
+about that there's a woman who does that
+ 
+
+ align:start position:0%
+about that there's a woman who does that
+is Jacqueline Chen and you might want to
+
+ align:start position:0%
+is Jacqueline Chen and you might want to
+ 
+
+ align:start position:0%
+is Jacqueline Chen and you might want to
+look on the internet and see about her
+
+ align:start position:0%
+look on the internet and see about her
+ 
+
+ align:start position:0%
+look on the internet and see about her
+and somehow she became buddies with the
+
+ align:start position:0%
+and somehow she became buddies with the
+ 
+
+ align:start position:0%
+and somehow she became buddies with the
+people in charge of the super computers
+
+ align:start position:0%
+people in charge of the super computers
+ 
+
+ align:start position:0%
+people in charge of the super computers
+and so they're happy to give her a month
+
+ align:start position:0%
+and so they're happy to give her a month
+ 
+
+ align:start position:0%
+and so they're happy to give her a month
+of video the best computer in the world
+
+ align:start position:0%
+of video the best computer in the world
+ 
+
+ align:start position:0%
+of video the best computer in the world
+every year and she runs some awesome
+
+ align:start position:0%
+every year and she runs some awesome
+ 
+
+ align:start position:0%
+every year and she runs some awesome
+really awesome calculation that's
+
+ align:start position:0%
+really awesome calculation that's
+ 
+
+ align:start position:0%
+really awesome calculation that's
+exactly right
+
+ align:start position:0%
+exactly right
+ 
+
+ align:start position:0%
+exactly right
+solves everything as all the state
+
+ align:start position:0%
+solves everything as all the state
+ 
+
+ align:start position:0%
+solves everything as all the state
+variables 10 to the 14th it's fantastic
+
+ align:start position:0%
+variables 10 to the 14th it's fantastic
+ 
+
+ align:start position:0%
+variables 10 to the 14th it's fantastic
+and that's like the currently that's the
+
+ align:start position:0%
+and that's like the currently that's the
+ 
+
+ align:start position:0%
+and that's like the currently that's the
+benchmark for how people test
+
+ align:start position:0%
+benchmark for how people test
+ 
+
+ align:start position:0%
+benchmark for how people test
+approximate methods for how to solving
+
+ align:start position:0%
+approximate methods for how to solving
+ 
+
+ align:start position:0%
+approximate methods for how to solving
+this because then she actually has the
+
+ align:start position:0%
+this because then she actually has the
+ 
+
+ align:start position:0%
+this because then she actually has the
+full solution numerically out converged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this again it's like a limited
+
+ align:start position:0%
+but this again it's like a limited
+ 
+
+ align:start position:0%
+but this again it's like a limited
+applicability so new so a lot of people
+
+ align:start position:0%
+applicability so new so a lot of people
+ 
+
+ align:start position:0%
+applicability so new so a lot of people
+are working on approximation methods to
+
+ align:start position:0%
+are working on approximation methods to
+ 
+
+ align:start position:0%
+are working on approximation methods to
+try to solve this equation if I don't
+
+ align:start position:0%
+try to solve this equation if I don't
+ 
+
+ align:start position:0%
+try to solve this equation if I don't
+have access to such awesome computer
+
+ align:start position:0%
+have access to such awesome computer
+ 
+
+ align:start position:0%
+have access to such awesome computer
+resources and the general idea of them
+
+ align:start position:0%
+resources and the general idea of them
+ 
+
+ align:start position:0%
+resources and the general idea of them
+well the two ideas so one idea is
+
+ align:start position:0%
+well the two ideas so one idea is
+ 
+
+ align:start position:0%
+well the two ideas so one idea is
+somehow get rid of the turbulence ok and
+
+ align:start position:0%
+somehow get rid of the turbulence ok and
+ 
+
+ align:start position:0%
+somehow get rid of the turbulence ok and
+so what they do is they use a match
+
+ align:start position:0%
+so what they do is they use a match
+ 
+
+ align:start position:0%
+so what they do is they use a match
+that's coarser that you know what you
+
+ align:start position:0%
+that's coarser that you know what you
+ 
+
+ align:start position:0%
+that's coarser that you know what you
+would need to resolve the color graphs
+
+ align:start position:0%
+would need to resolve the color graphs
+ 
+
+ align:start position:0%
+would need to resolve the color graphs
+scale and then they use models for what
+
+ align:start position:0%
+scale and then they use models for what
+ 
+
+ align:start position:0%
+scale and then they use models for what
+happens for itty-bitty tiny Eddie's and
+
+ align:start position:0%
+happens for itty-bitty tiny Eddie's and
+ 
+
+ align:start position:0%
+happens for itty-bitty tiny Eddie's and
+those are called sub-grid scale models
+
+ align:start position:0%
+those are called sub-grid scale models
+ 
+
+ align:start position:0%
+those are called sub-grid scale models
+and this whole approach is called large
+
+ align:start position:0%
+and this whole approach is called large
+ 
+
+ align:start position:0%
+and this whole approach is called large
+Eddy simulation and the idea is you keep
+
+ align:start position:0%
+Eddy simulation and the idea is you keep
+ 
+
+ align:start position:0%
+Eddy simulation and the idea is you keep
+track of the large Eddie's the big
+
+ align:start position:0%
+track of the large Eddie's the big
+ 
+
+ align:start position:0%
+track of the large Eddie's the big
+recirculation zones that's modeled
+
+ align:start position:0%
+recirculation zones that's modeled
+ 
+
+ align:start position:0%
+recirculation zones that's modeled
+explicitly but you don't keep track of
+
+ align:start position:0%
+explicitly but you don't keep track of
+ 
+
+ align:start position:0%
+explicitly but you don't keep track of
+all the itty-bitty tiny swirling off
+
+ align:start position:0%
+all the itty-bitty tiny swirling off
+ 
+
+ align:start position:0%
+all the itty-bitty tiny swirling off
+little Eddie's that last for a little
+
+ align:start position:0%
+little Eddie's that last for a little
+ 
+
+ align:start position:0%
+little Eddie's that last for a little
+second a little bit of period of time
+
+ align:start position:0%
+second a little bit of period of time
+ 
+
+ align:start position:0%
+second a little bit of period of time
+before they dissipate because of
+
+ align:start position:0%
+before they dissipate because of
+ 
+
+ align:start position:0%
+before they dissipate because of
+diffusion ok so that's the concept and
+
+ align:start position:0%
+diffusion ok so that's the concept and
+ 
+
+ align:start position:0%
+diffusion ok so that's the concept and
+and there's I don't know half of them
+
+ align:start position:0%
+and there's I don't know half of them
+ 
+
+ align:start position:0%
+and there's I don't know half of them
+all of mechanical engineers who are
+
+ align:start position:0%
+all of mechanical engineers who are
+ 
+
+ align:start position:0%
+all of mechanical engineers who are
+working in larger these simulations are
+
+ align:start position:0%
+working in larger these simulations are
+ 
+
+ align:start position:0%
+working in larger these simulations are
+trying to figure out and do this maybe
+
+ align:start position:0%
+trying to figure out and do this maybe
+ 
+
+ align:start position:0%
+trying to figure out and do this maybe
+Jim is one I don't know no ok but at
+
+ align:start position:0%
+Jim is one I don't know no ok but at
+ 
+
+ align:start position:0%
+Jim is one I don't know no ok but at
+least he knows something probably so
+
+ align:start position:0%
+least he knows something probably so
+ 
+
+ align:start position:0%
+least he knows something probably so
+that's one one whole branch is to try
+
+ align:start position:0%
+that's one one whole branch is to try
+ 
+
+ align:start position:0%
+that's one one whole branch is to try
+get rid of turbulence and basically
+
+ align:start position:0%
+get rid of turbulence and basically
+ 
+
+ align:start position:0%
+get rid of turbulence and basically
+that's trying to reduce
+
+ align:start position:0%
+that's trying to reduce
+ 
+
+ align:start position:0%
+that's trying to reduce
+the the density of mesh I need so trying
+
+ align:start position:0%
+the the density of mesh I need so trying
+ 
+
+ align:start position:0%
+the the density of mesh I need so trying
+to give her this used to spatial mesh
+
+ align:start position:0%
+to give her this used to spatial mesh
+ 
+
+ align:start position:0%
+to give her this used to spatial mesh
+but the other issue is the time and the
+
+ align:start position:0%
+but the other issue is the time and the
+ 
+
+ align:start position:0%
+but the other issue is the time and the
+time a is even worse right because I
+
+ align:start position:0%
+time a is even worse right because I
+ 
+
+ align:start position:0%
+time a is even worse right because I
+said I have 10 to the 8th time points
+
+ align:start position:0%
+said I have 10 to the 8th time points
+ 
+
+ align:start position:0%
+said I have 10 to the 8th time points
+and I only need 10 to the 4th
+
+ align:start position:0%
+and I only need 10 to the 4th
+ 
+
+ align:start position:0%
+and I only need 10 to the 4th
+spatial mesh points in the dimension so
+
+ align:start position:0%
+spatial mesh points in the dimension so
+ 
+
+ align:start position:0%
+spatial mesh points in the dimension so
+in some ways that you know if I could do
+
+ align:start position:0%
+in some ways that you know if I could do
+ 
+
+ align:start position:0%
+in some ways that you know if I could do
+something with a time that really can
+
+ align:start position:0%
+something with a time that really can
+ 
+
+ align:start position:0%
+something with a time that really can
+buy me a lot I have eight orders of
+
+ align:start position:0%
+buy me a lot I have eight orders of
+ 
+
+ align:start position:0%
+buy me a lot I have eight orders of
+magnitude I'd like to try to reduce to
+
+ align:start position:0%
+magnitude I'd like to try to reduce to
+ 
+
+ align:start position:0%
+magnitude I'd like to try to reduce to
+you know three orders maybe dude am I
+
+ align:start position:0%
+you know three orders maybe dude am I
+ 
+
+ align:start position:0%
+you know three orders maybe dude am I
+good that'd be really nice so the that
+
+ align:start position:0%
+good that'd be really nice so the that
+ 
+
+ align:start position:0%
+good that'd be really nice so the that
+idea is to say well let's separate the
+
+ align:start position:0%
+idea is to say well let's separate the
+ 
+
+ align:start position:0%
+idea is to say well let's separate the
+fast timescales from the slow timescales
+
+ align:start position:0%
+fast timescales from the slow timescales
+ 
+
+ align:start position:0%
+fast timescales from the slow timescales
+and in fact all the fast timescales
+
+ align:start position:0%
+and in fact all the fast timescales
+ 
+
+ align:start position:0%
+and in fact all the fast timescales
+mostly are all chemistry particularly
+
+ align:start position:0%
+mostly are all chemistry particularly
+ 
+
+ align:start position:0%
+mostly are all chemistry particularly
+after I changed it large Eddy simulation
+
+ align:start position:0%
+after I changed it large Eddy simulation
+ 
+
+ align:start position:0%
+after I changed it large Eddy simulation
+where I get rid of the really small
+
+ align:start position:0%
+where I get rid of the really small
+ 
+
+ align:start position:0%
+where I get rid of the really small
+spatial scales then the the time scale
+
+ align:start position:0%
+spatial scales then the the time scale
+ 
+
+ align:start position:0%
+spatial scales then the the time scale
+of diffusion over this big match is kind
+
+ align:start position:0%
+of diffusion over this big match is kind
+ 
+
+ align:start position:0%
+of diffusion over this big match is kind
+of slow and so I can just I can go to a
+
+ align:start position:0%
+of slow and so I can just I can go to a
+ 
+
+ align:start position:0%
+of slow and so I can just I can go to a
+time scale that's completely controlled
+
+ align:start position:0%
+time scale that's completely controlled
+ 
+
+ align:start position:0%
+time scale that's completely controlled
+by chemistry so we already told you how
+
+ align:start position:0%
+by chemistry so we already told you how
+ 
+
+ align:start position:0%
+by chemistry so we already told you how
+do you solve stiff differential
+
+ align:start position:0%
+do you solve stiff differential
+ 
+
+ align:start position:0%
+do you solve stiff differential
+equations use the stuffs all right and
+
+ align:start position:0%
+equations use the stuffs all right and
+ 
+
+ align:start position:0%
+equations use the stuffs all right and
+there's special methods they're implicit
+
+ align:start position:0%
+there's special methods they're implicit
+ 
+
+ align:start position:0%
+there's special methods they're implicit
+methods and they're specialized solvers
+
+ align:start position:0%
+methods and they're specialized solvers
+ 
+
+ align:start position:0%
+methods and they're specialized solvers
+and what they do is they allow you to
+
+ align:start position:0%
+and what they do is they allow you to
+ 
+
+ align:start position:0%
+and what they do is they allow you to
+take larger time steps then you would be
+
+ align:start position:0%
+take larger time steps then you would be
+ 
+
+ align:start position:0%
+take larger time steps then you would be
+allowed to use with explicit methods
+
+ align:start position:0%
+allowed to use with explicit methods
+ 
+
+ align:start position:0%
+allowed to use with explicit methods
+where you'd run into numerical
+
+ align:start position:0%
+where you'd run into numerical
+ 
+
+ align:start position:0%
+where you'd run into numerical
+instabilities if you try to use explicit
+
+ align:start position:0%
+instabilities if you try to use explicit
+ 
+
+ align:start position:0%
+instabilities if you try to use explicit
+method with a big time stamp it's much
+
+ align:start position:0%
+method with a big time stamp it's much
+ 
+
+ align:start position:0%
+method with a big time stamp it's much
+bigger than the real physical time scale
+
+ align:start position:0%
+bigger than the real physical time scale
+ 
+
+ align:start position:0%
+bigger than the real physical time scale
+you'll get some crazy oscillation but if
+
+ align:start position:0%
+you'll get some crazy oscillation but if
+ 
+
+ align:start position:0%
+you'll get some crazy oscillation but if
+you use the stiff solvers you can get
+
+ align:start position:0%
+you use the stiff solvers you can get
+ 
+
+ align:start position:0%
+you use the stiff solvers you can get
+away with time such that are much much
+
+ align:start position:0%
+away with time such that are much much
+ 
+
+ align:start position:0%
+away with time such that are much much
+larger than the real physical scale so
+
+ align:start position:0%
+larger than the real physical scale so
+ 
+
+ align:start position:0%
+larger than the real physical scale so
+that allows you to go from 100
+
+ align:start position:0%
+that allows you to go from 100
+ 
+
+ align:start position:0%
+that allows you to go from 100
+picoseconds up to maybe 100 nanoseconds
+
+ align:start position:0%
+picoseconds up to maybe 100 nanoseconds
+ 
+
+ align:start position:0%
+picoseconds up to maybe 100 nanoseconds
+get rid of three orders of magnitude of
+
+ align:start position:0%
+get rid of three orders of magnitude of
+ 
+
+ align:start position:0%
+get rid of three orders of magnitude of
+time step by using a sift solver so
+
+ align:start position:0%
+time step by using a sift solver so
+ 
+
+ align:start position:0%
+time step by using a sift solver so
+that's pretty good three orders
+
+ align:start position:0%
+that's pretty good three orders
+ 
+
+ align:start position:0%
+that's pretty good three orders
+magnitude reduction will go for it it's
+
+ align:start position:0%
+magnitude reduction will go for it it's
+ 
+
+ align:start position:0%
+magnitude reduction will go for it it's
+not only reducing the CPU time
+
+ align:start position:0%
+not only reducing the CPU time
+ 
+
+ align:start position:0%
+not only reducing the CPU time
+potentially but it's even more
+
+ align:start position:0%
+potentially but it's even more
+ 
+
+ align:start position:0%
+potentially but it's even more
+importantly reducing the number of
+
+ align:start position:0%
+importantly reducing the number of
+ 
+
+ align:start position:0%
+importantly reducing the number of
+points you have to save because when you
+
+ align:start position:0%
+points you have to save because when you
+ 
+
+ align:start position:0%
+points you have to save because when you
+run this calculation what Jacquelyn Chen
+
+ align:start position:0%
+run this calculation what Jacquelyn Chen
+ 
+
+ align:start position:0%
+run this calculation what Jacquelyn Chen
+ends up with is a list Y and every X met
+
+ align:start position:0%
+ends up with is a list Y and every X met
+ 
+
+ align:start position:0%
+ends up with is a list Y and every X met
+X X and I am that's that's the output of
+
+ align:start position:0%
+X X and I am that's that's the output of
+ 
+
+ align:start position:0%
+X X and I am that's that's the output of
+her program okay so how big is this
+
+ align:start position:0%
+her program okay so how big is this
+ 
+
+ align:start position:0%
+her program okay so how big is this
+object this is 200
+
+ align:start position:0%
+object this is 200
+ 
+
+ align:start position:0%
+object this is 200
+times 10 to the fourth times boy thank
+
+ align:start position:0%
+times 10 to the fourth times boy thank
+ 
+
+ align:start position:0%
+times 10 to the fourth times boy thank
+Allah for gay right that's that's how
+
+ align:start position:0%
+Allah for gay right that's that's how
+ 
+
+ align:start position:0%
+Allah for gay right that's that's how
+many numbers she's gonna get out of her
+
+ align:start position:0%
+many numbers she's gonna get out of her
+ 
+
+ align:start position:0%
+many numbers she's gonna get out of her
+simulation so actually her biggest
+
+ align:start position:0%
+simulation so actually her biggest
+ 
+
+ align:start position:0%
+simulation so actually her biggest
+problem is not actually solving the
+
+ align:start position:0%
+problem is not actually solving the
+ 
+
+ align:start position:0%
+problem is not actually solving the
+simulation as long as she can get the
+
+ align:start position:0%
+simulation as long as she can get the
+ 
+
+ align:start position:0%
+simulation as long as she can get the
+one month two CPU time she's good she's
+
+ align:start position:0%
+one month two CPU time she's good she's
+ 
+
+ align:start position:0%
+one month two CPU time she's good she's
+got this all her problems had to analyze
+
+ align:start position:0%
+got this all her problems had to analyze
+ 
+
+ align:start position:0%
+got this all her problems had to analyze
+her data because she now she has this
+
+ align:start position:0%
+her data because she now she has this
+ 
+
+ align:start position:0%
+her data because she now she has this
+this much data that she has to figure
+
+ align:start position:0%
+this much data that she has to figure
+ 
+
+ align:start position:0%
+this much data that she has to figure
+out to say something rational about it
+
+ align:start position:0%
+out to say something rational about it
+ 
+
+ align:start position:0%
+out to say something rational about it
+and so she has like a whole army of
+
+ align:start position:0%
+and so she has like a whole army of
+ 
+
+ align:start position:0%
+and so she has like a whole army of
+postdocs whose whole job is trying to
+
+ align:start position:0%
+postdocs whose whole job is trying to
+ 
+
+ align:start position:0%
+postdocs whose whole job is trying to
+invent new data interrogation methods
+
+ align:start position:0%
+invent new data interrogation methods
+ 
+
+ align:start position:0%
+invent new data interrogation methods
+and also this dataset is so large it
+
+ align:start position:0%
+and also this dataset is so large it
+ 
+
+ align:start position:0%
+and also this dataset is so large it
+cannot be stored in a hard disk in fact
+
+ align:start position:0%
+cannot be stored in a hard disk in fact
+ 
+
+ align:start position:0%
+cannot be stored in a hard disk in fact
+he cannot be stored on the biggest
+
+ align:start position:0%
+he cannot be stored on the biggest
+ 
+
+ align:start position:0%
+he cannot be stored on the biggest
+Farmar today this so she has to as the
+
+ align:start position:0%
+Farmar today this so she has to as the
+ 
+
+ align:start position:0%
+Farmar today this so she has to as the
+calculators running sending the data to
+
+ align:start position:0%
+calculators running sending the data to
+ 
+
+ align:start position:0%
+calculators running sending the data to
+different forms of hard disks around the
+
+ align:start position:0%
+different forms of hard disks around the
+ 
+
+ align:start position:0%
+different forms of hard disks around the
+world and filling them completely up and
+
+ align:start position:0%
+world and filling them completely up and
+ 
+
+ align:start position:0%
+world and filling them completely up and
+then say to the next one filling them up
+
+ align:start position:0%
+then say to the next one filling them up
+ 
+
+ align:start position:0%
+then say to the next one filling them up
+so she has fragments of this data set
+
+ align:start position:0%
+so she has fragments of this data set
+ 
+
+ align:start position:0%
+so she has fragments of this data set
+steward all over the place and then she
+
+ align:start position:0%
+steward all over the place and then she
+ 
+
+ align:start position:0%
+steward all over the place and then she
+has to you have to what he could graph
+
+ align:start position:0%
+has to you have to what he could graph
+ 
+
+ align:start position:0%
+has to you have to what he could graph
+she has to like ten special graph
+
+ align:start position:0%
+she has to like ten special graph
+ 
+
+ align:start position:0%
+she has to like ten special graph
+software it looks inside this data farm
+
+ align:start position:0%
+software it looks inside this data farm
+ 
+
+ align:start position:0%
+software it looks inside this data farm
+get some numbers looks inside this data
+
+ align:start position:0%
+get some numbers looks inside this data
+ 
+
+ align:start position:0%
+get some numbers looks inside this data
+part and puts it all together in some
+
+ align:start position:0%
+part and puts it all together in some
+ 
+
+ align:start position:0%
+part and puts it all together in some
+way so that's a pretty hard project okay
+
+ align:start position:0%
+way so that's a pretty hard project okay
+ 
+
+ align:start position:0%
+way so that's a pretty hard project okay
+now if but if I can use a stiff solver I
+
+ align:start position:0%
+now if but if I can use a stiff solver I
+ 
+
+ align:start position:0%
+now if but if I can use a stiff solver I
+don't need to use so many time steps so
+
+ align:start position:0%
+don't need to use so many time steps so
+ 
+
+ align:start position:0%
+don't need to use so many time steps so
+if I can get this down to the fifth at
+
+ align:start position:0%
+if I can get this down to the fifth at
+ 
+
+ align:start position:0%
+if I can get this down to the fifth at
+least I got through the three orders of
+
+ align:start position:0%
+least I got through the three orders of
+ 
+
+ align:start position:0%
+least I got through the three orders of
+magnitude of my data right so now I just
+
+ align:start position:0%
+magnitude of my data right so now I just
+ 
+
+ align:start position:0%
+magnitude of my data right so now I just
+need one day to farm maybe instead of
+
+ align:start position:0%
+need one day to farm maybe instead of
+ 
+
+ align:start position:0%
+need one day to farm maybe instead of
+instead if I you know using all the ones
+
+ align:start position:0%
+instead if I you know using all the ones
+ 
+
+ align:start position:0%
+instead if I you know using all the ones
+that Amazon and Google Ellen or
+
+ align:start position:0%
+that Amazon and Google Ellen or
+ 
+
+ align:start position:0%
+that Amazon and Google Ellen or
+something ok so so this is a pretty big
+
+ align:start position:0%
+something ok so so this is a pretty big
+ 
+
+ align:start position:0%
+something ok so so this is a pretty big
+advantage to do it this way now the
+
+ align:start position:0%
+advantage to do it this way now the
+ 
+
+ align:start position:0%
+advantage to do it this way now the
+disadvantage as you know is solving
+
+ align:start position:0%
+disadvantage as you know is solving
+ 
+
+ align:start position:0%
+disadvantage as you know is solving
+implicit different equations is way more
+
+ align:start position:0%
+implicit different equations is way more
+ 
+
+ align:start position:0%
+implicit different equations is way more
+expensive right because you have to
+
+ align:start position:0%
+expensive right because you have to
+ 
+
+ align:start position:0%
+expensive right because you have to
+solve an implicit nonlinear algebraic
+
+ align:start position:0%
+solve an implicit nonlinear algebraic
+ 
+
+ align:start position:0%
+solve an implicit nonlinear algebraic
+equation at every time step and in this
+
+ align:start position:0%
+equation at every time step and in this
+ 
+
+ align:start position:0%
+equation at every time step and in this
+case it could be pretty complicated
+
+ align:start position:0%
+case it could be pretty complicated
+ 
+
+ align:start position:0%
+case it could be pretty complicated
+equation because if I have this many
+
+ align:start position:0%
+equation because if I have this many
+ 
+
+ align:start position:0%
+equation because if I have this many
+state variables so at 10 to the fourth
+
+ align:start position:0%
+state variables so at 10 to the fourth
+ 
+
+ align:start position:0%
+state variables so at 10 to the fourth
+times 10 to the 4 times 7 4 so 10 to the
+
+ align:start position:0%
+times 10 to the 4 times 7 4 so 10 to the
+ 
+
+ align:start position:0%
+times 10 to the 4 times 7 4 so 10 to the
+12 times 200 so 10 to the 14th at each
+
+ align:start position:0%
+12 times 200 so 10 to the 14th at each
+ 
+
+ align:start position:0%
+12 times 200 so 10 to the 14th at each
+time step that's my current state and
+
+ align:start position:0%
+time step that's my current state and
+ 
+
+ align:start position:0%
+time step that's my current state and
+I'm trying to solve a non-linear
+
+ align:start position:0%
+I'm trying to solve a non-linear
+ 
+
+ align:start position:0%
+I'm trying to solve a non-linear
+algebraic equation 10 to the 14th
+
+ align:start position:0%
+algebraic equation 10 to the 14th
+ 
+
+ align:start position:0%
+algebraic equation 10 to the 14th
+unknowns you need you need pretty good
+
+ align:start position:0%
+unknowns you need you need pretty good
+ 
+
+ align:start position:0%
+unknowns you need you need pretty good
+solver I mean I know backslash is good
+
+ align:start position:0%
+solver I mean I know backslash is good
+ 
+
+ align:start position:0%
+solver I mean I know backslash is good
+and you know solve this stuff but but I
+
+ align:start position:0%
+and you know solve this stuff but but I
+ 
+
+ align:start position:0%
+and you know solve this stuff but but I
+really don't think it's gonna work so
+
+ align:start position:0%
+really don't think it's gonna work so
+ 
+
+ align:start position:0%
+really don't think it's gonna work so
+that's a really serious problem so the
+
+ align:start position:0%
+that's a really serious problem so the
+ 
+
+ align:start position:0%
+that's a really serious problem so the
+next trick is to say ok well I only need
+
+ align:start position:0%
+next trick is to say ok well I only need
+ 
+
+ align:start position:0%
+next trick is to say ok well I only need
+the stiffness is only happening because
+
+ align:start position:0%
+the stiffness is only happening because
+ 
+
+ align:start position:0%
+the stiffness is only happening because
+of the chemistry so I don't I could
+
+ align:start position:0%
+of the chemistry so I don't I could
+ 
+
+ align:start position:0%
+of the chemistry so I don't I could
+solve all of the
+
+ align:start position:0%
+solve all of the
+ 
+
+ align:start position:0%
+solve all of the
+volumes separately so the idea is to
+
+ align:start position:0%
+volumes separately so the idea is to
+ 
+
+ align:start position:0%
+volumes separately so the idea is to
+split the problem up I'm going to solve
+
+ align:start position:0%
+split the problem up I'm going to solve
+ 
+
+ align:start position:0%
+split the problem up I'm going to solve
+the chemistry using a SIF solver only at
+
+ align:start position:0%
+the chemistry using a SIF solver only at
+ 
+
+ align:start position:0%
+the chemistry using a SIF solver only at
+one finite volume at a time and then I'm
+
+ align:start position:0%
+one finite volume at a time and then I'm
+ 
+
+ align:start position:0%
+one finite volume at a time and then I'm
+going to do the transport some other way
+
+ align:start position:0%
+going to do the transport some other way
+ 
+
+ align:start position:0%
+going to do the transport some other way
+so what I'm going to do is I'm going to
+
+ align:start position:0%
+so what I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+so what I'm going to do is I'm going to
+rewrite this equation as my my unknowns
+
+ align:start position:0%
+rewrite this equation as my my unknowns
+ 
+
+ align:start position:0%
+rewrite this equation as my my unknowns
+dy DT is equal to some kind of transport
+
+ align:start position:0%
+dy DT is equal to some kind of transport
+ 
+
+ align:start position:0%
+dy DT is equal to some kind of transport
+term and sometimes reactive term and
+
+ align:start position:0%
+term and sometimes reactive term and
+ 
+
+ align:start position:0%
+term and sometimes reactive term and
+this term is local the oldest in this
+
+ align:start position:0%
+this term is local the oldest in this
+ 
+
+ align:start position:0%
+this term is local the oldest in this
+equation this is really saying dy at
+
+ align:start position:0%
+equation this is really saying dy at
+ 
+
+ align:start position:0%
+equation this is really saying dy at
+position X depends on this at position X
+
+ align:start position:0%
+position X depends on this at position X
+ 
+
+ align:start position:0%
+position X depends on this at position X
+whereas to compute these guys I need to
+
+ align:start position:0%
+whereas to compute these guys I need to
+ 
+
+ align:start position:0%
+whereas to compute these guys I need to
+do finite differences or something from
+
+ align:start position:0%
+do finite differences or something from
+ 
+
+ align:start position:0%
+do finite differences or something from
+adjoining kind of volumes right I have
+
+ align:start position:0%
+adjoining kind of volumes right I have
+ 
+
+ align:start position:0%
+adjoining kind of volumes right I have
+to do fluxes from the adjoining volumes
+
+ align:start position:0%
+to do fluxes from the adjoining volumes
+ 
+
+ align:start position:0%
+to do fluxes from the adjoining volumes
+so these guys are sensitive to not just
+
+ align:start position:0%
+so these guys are sensitive to not just
+ 
+
+ align:start position:0%
+so these guys are sensitive to not just
+to my local value of y at this finite
+
+ align:start position:0%
+to my local value of y at this finite
+ 
+
+ align:start position:0%
+to my local value of y at this finite
+volume but also to the neighboring
+
+ align:start position:0%
+volume but also to the neighboring
+ 
+
+ align:start position:0%
+volume but also to the neighboring
+values of Y but if I don't worry about
+
+ align:start position:0%
+values of Y but if I don't worry about
+ 
+
+ align:start position:0%
+values of Y but if I don't worry about
+them if I break it up I had this local
+
+ align:start position:0%
+them if I break it up I had this local
+ 
+
+ align:start position:0%
+them if I break it up I had this local
+thing and this non-local thing this one
+
+ align:start position:0%
+thing and this non-local thing this one
+ 
+
+ align:start position:0%
+thing and this non-local thing this one
+is local it's stiff this one is
+
+ align:start position:0%
+is local it's stiff this one is
+ 
+
+ align:start position:0%
+is local it's stiff this one is
+non-local but it's not so stiff and it's
+
+ align:start position:0%
+non-local but it's not so stiff and it's
+ 
+
+ align:start position:0%
+non-local but it's not so stiff and it's
+often it's linear or nearly linear
+
+ align:start position:0%
+often it's linear or nearly linear
+ 
+
+ align:start position:0%
+often it's linear or nearly linear
+here's the transport
+
+ align:start position:0%
+here's the transport
+ 
+
+ align:start position:0%
+here's the transport
+terms are mostly linear and so I can use
+
+ align:start position:0%
+terms are mostly linear and so I can use
+ 
+
+ align:start position:0%
+terms are mostly linear and so I can use
+I have specialized solvers that people
+
+ align:start position:0%
+I have specialized solvers that people
+ 
+
+ align:start position:0%
+I have specialized solvers that people
+have worked on for many years for each
+
+ align:start position:0%
+have worked on for many years for each
+ 
+
+ align:start position:0%
+have worked on for many years for each
+of these things so for this for the
+
+ align:start position:0%
+of these things so for this for the
+ 
+
+ align:start position:0%
+of these things so for this for the
+stiff thing I have things like OD 1 5 s
+
+ align:start position:0%
+stiff thing I have things like OD 1 5 s
+ 
+
+ align:start position:0%
+stiff thing I have things like OD 1 5 s
+I have Dae pack and - pack and docile
+
+ align:start position:0%
+I have Dae pack and - pack and docile
+ 
+
+ align:start position:0%
+I have Dae pack and - pack and docile
+and sundials and all those programs that
+
+ align:start position:0%
+and sundials and all those programs that
+ 
+
+ align:start position:0%
+and sundials and all those programs that
+people have written spend a lot of
+
+ align:start position:0%
+people have written spend a lot of
+ 
+
+ align:start position:0%
+people have written spend a lot of
+effort to solve this problem and
+
+ align:start position:0%
+effort to solve this problem and
+ 
+
+ align:start position:0%
+effort to solve this problem and
+similarly there's a whole bunch of
+
+ align:start position:0%
+similarly there's a whole bunch of
+ 
+
+ align:start position:0%
+similarly there's a whole bunch of
+people who spent their whole life trying
+
+ align:start position:0%
+people who spent their whole life trying
+ 
+
+ align:start position:0%
+people who spent their whole life trying
+to solve the convection diffusion
+
+ align:start position:0%
+to solve the convection diffusion
+ 
+
+ align:start position:0%
+to solve the convection diffusion
+problems the non-reacting flow problem
+
+ align:start position:0%
+problems the non-reacting flow problem
+ 
+
+ align:start position:0%
+problems the non-reacting flow problem
+and so I can use specialized solvers
+
+ align:start position:0%
+and so I can use specialized solvers
+ 
+
+ align:start position:0%
+and so I can use specialized solvers
+that they have so I want to split this
+
+ align:start position:0%
+that they have so I want to split this
+ 
+
+ align:start position:0%
+that they have so I want to split this
+up and what I really would like to solve
+
+ align:start position:0%
+up and what I really would like to solve
+ 
+
+ align:start position:0%
+up and what I really would like to solve
+which I'd prefer to solve dy DT equals R
+
+ align:start position:0%
+which I'd prefer to solve dy DT equals R
+ 
+
+ align:start position:0%
+which I'd prefer to solve dy DT equals R
+and dy DT equals T completely separately
+
+ align:start position:0%
+and dy DT equals T completely separately
+ 
+
+ align:start position:0%
+and dy DT equals T completely separately
+if I could because I can use specialized
+
+ align:start position:0%
+if I could because I can use specialized
+ 
+
+ align:start position:0%
+if I could because I can use specialized
+methods or the best for each so now to
+
+ align:start position:0%
+methods or the best for each so now to
+ 
+
+ align:start position:0%
+methods or the best for each so now to
+figure out well this is not really the
+
+ align:start position:0%
+figure out well this is not really the
+ 
+
+ align:start position:0%
+figure out well this is not really the
+real equation because it has both I've
+
+ align:start position:0%
+real equation because it has both I've
+ 
+
+ align:start position:0%
+real equation because it has both I've
+added together how can I handle that so
+
+ align:start position:0%
+added together how can I handle that so
+ 
+
+ align:start position:0%
+added together how can I handle that so
+this operator splitting recipe is solve
+
+ align:start position:0%
+this operator splitting recipe is solve
+ 
+
+ align:start position:0%
+this operator splitting recipe is solve
+dy DT equals 2t for a while and at the
+
+ align:start position:0%
+dy DT equals 2t for a while and at the
+ 
+
+ align:start position:0%
+dy DT equals 2t for a while and at the
+end of this process I'll have y ax t
+
+ align:start position:0%
+end of this process I'll have y ax t
+ 
+
+ align:start position:0%
+end of this process I'll have y ax t
+final and then and so I'm sorry solve
+
+ align:start position:0%
+final and then and so I'm sorry solve
+ 
+
+ align:start position:0%
+final and then and so I'm sorry solve
+this equation with y people going on
+
+ align:start position:0%
+this equation with y people going on
+ 
+
+ align:start position:0%
+this equation with y people going on
+it's the equation system solving
+
+ align:start position:0%
+it's the equation system solving
+ 
+
+ align:start position:0%
+it's the equation system solving
+transport I do some transport for a
+
+ align:start position:0%
+transport I do some transport for a
+ 
+
+ align:start position:0%
+transport I do some transport for a
+while I get some values to the Y then I
+
+ align:start position:0%
+while I get some values to the Y then I
+ 
+
+ align:start position:0%
+while I get some values to the Y then I
+take these guys and I saw the reaction
+
+ align:start position:0%
+take these guys and I saw the reaction
+ 
+
+ align:start position:0%
+take these guys and I saw the reaction
+equation starting from y equals y final
+
+ align:start position:0%
+equation starting from y equals y final
+ 
+
+ align:start position:0%
+equation starting from y equals y final
+array this my duties here okay and I
+
+ align:start position:0%
+array this my duties here okay and I
+ 
+
+ align:start position:0%
+array this my duties here okay and I
+solve this one for a while and I'll get
+
+ align:start position:0%
+solve this one for a while and I'll get
+ 
+
+ align:start position:0%
+solve this one for a while and I'll get
+a different different y y q final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright and this is simple anything says
+
+ align:start position:0%
+alright and this is simple anything says
+ 
+
+ align:start position:0%
+alright and this is simple anything says
+just keep going back and forth boom boom
+
+ align:start position:0%
+just keep going back and forth boom boom
+ 
+
+ align:start position:0%
+just keep going back and forth boom boom
+boom boom boom boom boom boom and in the
+
+ align:start position:0%
+boom boom boom boom boom boom and in the
+ 
+
+ align:start position:0%
+boom boom boom boom boom boom and in the
+limit where I make this T final minus T
+
+ align:start position:0%
+limit where I make this T final minus T
+ 
+
+ align:start position:0%
+limit where I make this T final minus T
+naught to be very small then maybe I
+
+ align:start position:0%
+naught to be very small then maybe I
+ 
+
+ align:start position:0%
+naught to be very small then maybe I
+might expect that they might converge
+
+ align:start position:0%
+might expect that they might converge
+ 
+
+ align:start position:0%
+might expect that they might converge
+the same solution as two as a couple of
+
+ align:start position:0%
+the same solution as two as a couple of
+ 
+
+ align:start position:0%
+the same solution as two as a couple of
+equations alright so that's the concept
+
+ align:start position:0%
+equations alright so that's the concept
+ 
+
+ align:start position:0%
+equations alright so that's the concept
+now if you do it this way it doesn't
+
+ align:start position:0%
+now if you do it this way it doesn't
+ 
+
+ align:start position:0%
+now if you do it this way it doesn't
+work very well
+
+ align:start position:0%
+work very well
+ 
+
+ align:start position:0%
+work very well
+your you need to make the this delta T
+
+ align:start position:0%
+your you need to make the this delta T
+ 
+
+ align:start position:0%
+your you need to make the this delta T
+incredibly small to get any accuracy
+
+ align:start position:0%
+incredibly small to get any accuracy
+ 
+
+ align:start position:0%
+incredibly small to get any accuracy
+however you can do a slightly more
+
+ align:start position:0%
+however you can do a slightly more
+ 
+
+ align:start position:0%
+however you can do a slightly more
+clever version which is I solve dy DT
+
+ align:start position:0%
+clever version which is I solve dy DT
+ 
+
+ align:start position:0%
+clever version which is I solve dy DT
+equals 2t starting from YT not going on
+
+ align:start position:0%
+equals 2t starting from YT not going on
+ 
+
+ align:start position:0%
+equals 2t starting from YT not going on
+and I saw this to give me Y at T plus
+
+ align:start position:0%
+and I saw this to give me Y at T plus
+ 
+
+ align:start position:0%
+and I saw this to give me Y at T plus
+delta T over 2 then I solve dy DT is
+
+ align:start position:0%
+delta T over 2 then I solve dy DT is
+ 
+
+ align:start position:0%
+delta T over 2 then I solve dy DT is
+equal to our starting from Y of T not
+
+ align:start position:0%
+equal to our starting from Y of T not
+ 
+
+ align:start position:0%
+equal to our starting from Y of T not
+equal to Y star
+
+ align:start position:0%
+equal to Y star
+ 
+
+ align:start position:0%
+equal to Y star
+my star and this I integrate out to Y of
+
+ align:start position:0%
+my star and this I integrate out to Y of
+ 
+
+ align:start position:0%
+my star and this I integrate out to Y of
+T plus the full delta T I'll call that Y
+
+ align:start position:0%
+T plus the full delta T I'll call that Y
+ 
+
+ align:start position:0%
+T plus the full delta T I'll call that Y
+double star
+
+ align:start position:0%
+double star
+ 
+
+ align:start position:0%
+double star
+and then I solve this one again and I
+
+ align:start position:0%
+and then I solve this one again and I
+ 
+
+ align:start position:0%
+and then I solve this one again and I
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+starting from wife Tina equals two y
+
+ align:start position:0%
+starting from wife Tina equals two y
+ 
+
+ align:start position:0%
+starting from wife Tina equals two y
+double star and I integrate that out for
+
+ align:start position:0%
+double star and I integrate that out for
+ 
+
+ align:start position:0%
+double star and I integrate that out for
+another delta T over two and this one I
+
+ align:start position:0%
+another delta T over two and this one I
+ 
+
+ align:start position:0%
+another delta T over two and this one I
+called my wife final and that's the one
+
+ align:start position:0%
+called my wife final and that's the one
+ 
+
+ align:start position:0%
+called my wife final and that's the one
+I use so I take a half of a transport
+
+ align:start position:0%
+I use so I take a half of a transport
+ 
+
+ align:start position:0%
+I use so I take a half of a transport
+step sort of like I'm starting to do the
+
+ align:start position:0%
+step sort of like I'm starting to do the
+ 
+
+ align:start position:0%
+step sort of like I'm starting to do the
+transport then I sell you know hold on I
+
+ align:start position:0%
+transport then I sell you know hold on I
+ 
+
+ align:start position:0%
+transport then I sell you know hold on I
+got to my reactions if I do my reaction
+
+ align:start position:0%
+got to my reactions if I do my reaction
+ 
+
+ align:start position:0%
+got to my reactions if I do my reaction
+then I do the other half the transport
+
+ align:start position:0%
+then I do the other half the transport
+ 
+
+ align:start position:0%
+then I do the other half the transport
+after that and you can do the analysis
+
+ align:start position:0%
+after that and you can do the analysis
+ 
+
+ align:start position:0%
+after that and you can do the analysis
+of this it turns out this thing
+
+ align:start position:0%
+of this it turns out this thing
+ 
+
+ align:start position:0%
+of this it turns out this thing
+converges to the true solution of the
+
+ align:start position:0%
+converges to the true solution of the
+ 
+
+ align:start position:0%
+converges to the true solution of the
+coupled equations with second-order
+
+ align:start position:0%
+coupled equations with second-order
+ 
+
+ align:start position:0%
+coupled equations with second-order
+accuracy so it might make this delta T
+
+ align:start position:0%
+accuracy so it might make this delta T
+ 
+
+ align:start position:0%
+accuracy so it might make this delta T
+if I cut it in half
+
+ align:start position:0%
+if I cut it in half
+ 
+
+ align:start position:0%
+if I cut it in half
+the precision increases by a factor for
+
+ align:start position:0%
+the precision increases by a factor for
+ 
+
+ align:start position:0%
+the precision increases by a factor for
+my kind of by factor 10 increase by a
+
+ align:start position:0%
+my kind of by factor 10 increase by a
+ 
+
+ align:start position:0%
+my kind of by factor 10 increase by a
+factor of 100 so this is looking more
+
+ align:start position:0%
+factor of 100 so this is looking more
+ 
+
+ align:start position:0%
+factor of 100 so this is looking more
+promising as a way to do it this is the
+
+ align:start position:0%
+promising as a way to do it this is the
+ 
+
+ align:start position:0%
+promising as a way to do it this is the
+most popular way to do it so this recipe
+
+ align:start position:0%
+most popular way to do it so this recipe
+ 
+
+ align:start position:0%
+most popular way to do it so this recipe
+here for operator splitting
+
+ align:start position:0%
+here for operator splitting
+ 
+
+ align:start position:0%
+here for operator splitting
+it's called Strang splitting named after
+
+ align:start position:0%
+it's called Strang splitting named after
+ 
+
+ align:start position:0%
+it's called Strang splitting named after
+Gil Strang who's a professor in the
+
+ align:start position:0%
+Gil Strang who's a professor in the
+ 
+
+ align:start position:0%
+Gil Strang who's a professor in the
+applied mathematics department here
+
+ align:start position:0%
+applied mathematics department here
+ 
+
+ align:start position:0%
+applied mathematics department here
+former head of Siam the international
+
+ align:start position:0%
+former head of Siam the international
+ 
+
+ align:start position:0%
+former head of Siam the international
+body for Applied Mathematics and also
+
+ align:start position:0%
+body for Applied Mathematics and also
+ 
+
+ align:start position:0%
+body for Applied Mathematics and also
+author of fantastically great linear
+
+ align:start position:0%
+author of fantastically great linear
+ 
+
+ align:start position:0%
+author of fantastically great linear
+algebra textbook which maybe some of you
+
+ align:start position:0%
+algebra textbook which maybe some of you
+ 
+
+ align:start position:0%
+algebra textbook which maybe some of you
+guys I've seen some videos of his so he
+
+ align:start position:0%
+guys I've seen some videos of his so he
+ 
+
+ align:start position:0%
+guys I've seen some videos of his so he
+invented this 1968 I was 5 years old
+
+ align:start position:0%
+invented this 1968 I was 5 years old
+ 
+
+ align:start position:0%
+invented this 1968 I was 5 years old
+yeah he didn't know that his invention
+
+ align:start position:0%
+yeah he didn't know that his invention
+ 
+
+ align:start position:0%
+yeah he didn't know that his invention
+was of any practical use being a
+
+ align:start position:0%
+was of any practical use being a
+ 
+
+ align:start position:0%
+was of any practical use being a
+mathematician so he just publish that
+
+ align:start position:0%
+mathematician so he just publish that
+ 
+
+ align:start position:0%
+mathematician so he just publish that
+paper now in the meantime this paper is
+
+ align:start position:0%
+paper now in the meantime this paper is
+ 
+
+ align:start position:0%
+paper now in the meantime this paper is
+like a citation classic it's like
+
+ align:start position:0%
+like a citation classic it's like
+ 
+
+ align:start position:0%
+like a citation classic it's like
+silently I don't know 20 thousand times
+
+ align:start position:0%
+silently I don't know 20 thousand times
+ 
+
+ align:start position:0%
+silently I don't know 20 thousand times
+he had no idea he never looks at
+
+ align:start position:0%
+he had no idea he never looks at
+ 
+
+ align:start position:0%
+he had no idea he never looks at
+citation list he's a mathematician so so
+
+ align:start position:0%
+citation list he's a mathematician so so
+ 
+
+ align:start position:0%
+citation list he's a mathematician so so
+I was working on this problem and let's
+
+ align:start position:0%
+I was working on this problem and let's
+ 
+
+ align:start position:0%
+I was working on this problem and let's
+see let's back up so we just how they
+
+ align:start position:0%
+see let's back up so we just how they
+ 
+
+ align:start position:0%
+see let's back up so we just how they
+usually solve right we usually solve the
+
+ align:start position:0%
+usually solve right we usually solve the
+ 
+
+ align:start position:0%
+usually solve right we usually solve the
+problems the operator splitting sir
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when we we'd like to solve it this
+
+ align:start position:0%
+and when we we'd like to solve it this
+ 
+
+ align:start position:0%
+and when we we'd like to solve it this
+way because I can use specialized
+
+ align:start position:0%
+way because I can use specialized
+ 
+
+ align:start position:0%
+way because I can use specialized
+solvers I use a transport solver here I
+
+ align:start position:0%
+solvers I use a transport solver here I
+ 
+
+ align:start position:0%
+solvers I use a transport solver here I
+use the stiff solver here this one I can
+
+ align:start position:0%
+use the stiff solver here this one I can
+ 
+
+ align:start position:0%
+use the stiff solver here this one I can
+paralyze because I can do a different OD
+
+ align:start position:0%
+paralyze because I can do a different OD
+ 
+
+ align:start position:0%
+paralyze because I can do a different OD
+solution at each finite volume so if I
+
+ align:start position:0%
+solution at each finite volume so if I
+ 
+
+ align:start position:0%
+solution at each finite volume so if I
+have a big computer a big parallel
+
+ align:start position:0%
+have a big computer a big parallel
+ 
+
+ align:start position:0%
+have a big computer a big parallel
+computer say have 10,000 nodes I can
+
+ align:start position:0%
+computer say have 10,000 nodes I can
+ 
+
+ align:start position:0%
+computer say have 10,000 nodes I can
+solve 10,000 finite volume
+
+ align:start position:0%
+solve 10,000 finite volume
+ 
+
+ align:start position:0%
+solve 10,000 finite volume
+simultaneously in this step so the CPU
+
+ align:start position:0%
+simultaneously in this step so the CPU
+ 
+
+ align:start position:0%
+simultaneously in this step so the CPU
+time is reduced a lot so parallel lines
+
+ align:start position:0%
+time is reduced a lot so parallel lines
+ 
+
+ align:start position:0%
+time is reduced a lot so parallel lines
+is easily so this is this is really
+
+ align:start position:0%
+is easily so this is this is really
+ 
+
+ align:start position:0%
+is easily so this is this is really
+popular this is the main way that people
+
+ align:start position:0%
+popular this is the main way that people
+ 
+
+ align:start position:0%
+popular this is the main way that people
+do do things and then in the ideal case
+
+ align:start position:0%
+do do things and then in the ideal case
+ 
+
+ align:start position:0%
+do do things and then in the ideal case
+you do it with a certain guess of TT
+
+ align:start position:0%
+you do it with a certain guess of TT
+ 
+
+ align:start position:0%
+you do it with a certain guess of TT
+then you try TT divided by 5 and if you
+
+ align:start position:0%
+then you try TT divided by 5 and if you
+ 
+
+ align:start position:0%
+then you try TT divided by 5 and if you
+get the same result then you publish it
+
+ align:start position:0%
+get the same result then you publish it
+ 
+
+ align:start position:0%
+get the same result then you publish it
+ok and you think you've converted your
+
+ align:start position:0%
+ok and you think you've converted your
+ 
+
+ align:start position:0%
+ok and you think you've converted your
+solution however what I've what I found
+
+ align:start position:0%
+solution however what I've what I found
+ 
+
+ align:start position:0%
+solution however what I've what I found
+doing this is I was trying to find
+
+ align:start position:0%
+doing this is I was trying to find
+ 
+
+ align:start position:0%
+doing this is I was trying to find
+flames I'm trying to calculate the
+
+ align:start position:0%
+flames I'm trying to calculate the
+ 
+
+ align:start position:0%
+flames I'm trying to calculate the
+positions of flames and what I found was
+
+ align:start position:0%
+positions of flames and what I found was
+ 
+
+ align:start position:0%
+positions of flames and what I found was
+that with the Delta T's I would try
+
+ align:start position:0%
+that with the Delta T's I would try
+ 
+
+ align:start position:0%
+that with the Delta T's I would try
+sometimes I would get a qualitatively
+
+ align:start position:0%
+sometimes I would get a qualitatively
+ 
+
+ align:start position:0%
+sometimes I would get a qualitatively
+different solution depending on the
+
+ align:start position:0%
+different solution depending on the
+ 
+
+ align:start position:0%
+different solution depending on the
+delta T I chose and so in particular
+
+ align:start position:0%
+delta T I chose and so in particular
+ 
+
+ align:start position:0%
+delta T I chose and so in particular
+what I found was that I was solving
+
+ align:start position:0%
+what I found was that I was solving
+ 
+
+ align:start position:0%
+what I found was that I was solving
+burner flames so I have like a burner
+
+ align:start position:0%
+burner flames so I have like a burner
+ 
+
+ align:start position:0%
+burner flames so I have like a burner
+here flame on top of it like this and
+
+ align:start position:0%
+here flame on top of it like this and
+ 
+
+ align:start position:0%
+here flame on top of it like this and
+there's two importantly different cases
+
+ align:start position:0%
+there's two importantly different cases
+ 
+
+ align:start position:0%
+there's two importantly different cases
+one is where the flame is floating above
+
+ align:start position:0%
+one is where the flame is floating above
+ 
+
+ align:start position:0%
+one is where the flame is floating above
+the burner and one is where the flame
+
+ align:start position:0%
+the burner and one is where the flame
+ 
+
+ align:start position:0%
+the burner and one is where the flame
+kind of goes all the way down and
+
+ align:start position:0%
+kind of goes all the way down and
+ 
+
+ align:start position:0%
+kind of goes all the way down and
+touches the metal and you've probably
+
+ align:start position:0%
+touches the metal and you've probably
+ 
+
+ align:start position:0%
+touches the metal and you've probably
+seen both this case a bunch of burner or
+
+ align:start position:0%
+seen both this case a bunch of burner or
+ 
+
+ align:start position:0%
+seen both this case a bunch of burner or
+something like that sometimes if you get
+
+ align:start position:0%
+something like that sometimes if you get
+ 
+
+ align:start position:0%
+something like that sometimes if you get
+the flow rates high enough the whole
+
+ align:start position:0%
+the flow rates high enough the whole
+ 
+
+ align:start position:0%
+the flow rates high enough the whole
+thing will lift off and be floating
+
+ align:start position:0%
+thing will lift off and be floating
+ 
+
+ align:start position:0%
+thing will lift off and be floating
+there and sometimes if you slow the flow
+
+ align:start position:0%
+there and sometimes if you slow the flow
+ 
+
+ align:start position:0%
+there and sometimes if you slow the flow
+rates down the wood they say that the
+
+ align:start position:0%
+rates down the wood they say that the
+ 
+
+ align:start position:0%
+rates down the wood they say that the
+flame will anchor to to the metal some
+
+ align:start position:0%
+flame will anchor to to the metal some
+ 
+
+ align:start position:0%
+flame will anchor to to the metal some
+piece of the flame actually touch the
+
+ align:start position:0%
+piece of the flame actually touch the
+ 
+
+ align:start position:0%
+piece of the flame actually touch the
+metal usually it's like if you have a
+
+ align:start position:0%
+metal usually it's like if you have a
+ 
+
+ align:start position:0%
+metal usually it's like if you have a
+one time you have a case like this you
+
+ align:start position:0%
+one time you have a case like this you
+ 
+
+ align:start position:0%
+one time you have a case like this you
+have like a metal piece metal piece
+
+ align:start position:0%
+have like a metal piece metal piece
+ 
+
+ align:start position:0%
+have like a metal piece metal piece
+here's your mixture coming in out here's
+
+ align:start position:0%
+here's your mixture coming in out here's
+ 
+
+ align:start position:0%
+here's your mixture coming in out here's
+the air and a lot of times the flame
+
+ align:start position:0%
+the air and a lot of times the flame
+ 
+
+ align:start position:0%
+the air and a lot of times the flame
+will come and touch it'll actually touch
+
+ align:start position:0%
+will come and touch it'll actually touch
+ 
+
+ align:start position:0%
+will come and touch it'll actually touch
+this metal piece here you know a flame
+
+ align:start position:0%
+this metal piece here you know a flame
+ 
+
+ align:start position:0%
+this metal piece here you know a flame
+looks sort of like that
+
+ align:start position:0%
+looks sort of like that
+ 
+
+ align:start position:0%
+looks sort of like that
+have you ever see a flame with this
+
+ align:start position:0%
+have you ever see a flame with this
+ 
+
+ align:start position:0%
+have you ever see a flame with this
+anyway this is a common thing anchor
+
+ align:start position:0%
+anyway this is a common thing anchor
+ 
+
+ align:start position:0%
+anyway this is a common thing anchor
+plane if you just have a slow a slow
+
+ align:start position:0%
+plane if you just have a slow a slow
+ 
+
+ align:start position:0%
+plane if you just have a slow a slow
+speed burner that's what you got you go
+
+ align:start position:0%
+speed burner that's what you got you go
+ 
+
+ align:start position:0%
+speed burner that's what you got you go
+high to speed new burner you make the
+
+ align:start position:0%
+high to speed new burner you make the
+ 
+
+ align:start position:0%
+high to speed new burner you make the
+whole thing lift up and sort of dance
+
+ align:start position:0%
+whole thing lift up and sort of dance
+ 
+
+ align:start position:0%
+whole thing lift up and sort of dance
+around if you look at the flame alright
+
+ align:start position:0%
+around if you look at the flame alright
+ 
+
+ align:start position:0%
+around if you look at the flame alright
+I Pisces same you look at a piece of
+
+ align:start position:0%
+I Pisces same you look at a piece of
+ 
+
+ align:start position:0%
+I Pisces same you look at a piece of
+wood burning
+
+ align:start position:0%
+wood burning
+ 
+
+ align:start position:0%
+wood burning
+if it was burning well the flame we
+
+ align:start position:0%
+if it was burning well the flame we
+ 
+
+ align:start position:0%
+if it was burning well the flame we
+lifted off the wood you'll see a gap
+
+ align:start position:0%
+lifted off the wood you'll see a gap
+ 
+
+ align:start position:0%
+lifted off the wood you'll see a gap
+between the flame and the wood if it's
+
+ align:start position:0%
+between the flame and the wood if it's
+ 
+
+ align:start position:0%
+between the flame and the wood if it's
+not burning that while you can see the
+
+ align:start position:0%
+not burning that while you can see the
+ 
+
+ align:start position:0%
+not burning that while you can see the
+flame bit bit so if I'm actually touch
+
+ align:start position:0%
+flame bit bit so if I'm actually touch
+ 
+
+ align:start position:0%
+flame bit bit so if I'm actually touch
+the pieces of wood okay so that's a very
+
+ align:start position:0%
+the pieces of wood okay so that's a very
+ 
+
+ align:start position:0%
+the pieces of wood okay so that's a very
+important thing for a combustion guy so
+
+ align:start position:0%
+important thing for a combustion guy so
+ 
+
+ align:start position:0%
+important thing for a combustion guy so
+I was really to me this is a big deal so
+
+ align:start position:0%
+I was really to me this is a big deal so
+ 
+
+ align:start position:0%
+I was really to me this is a big deal so
+when I solved it with one choice at TT I
+
+ align:start position:0%
+when I solved it with one choice at TT I
+ 
+
+ align:start position:0%
+when I solved it with one choice at TT I
+get this solution when I saw it with
+
+ align:start position:0%
+get this solution when I saw it with
+ 
+
+ align:start position:0%
+get this solution when I saw it with
+another choice of delta T I get this
+
+ align:start position:0%
+another choice of delta T I get this
+ 
+
+ align:start position:0%
+another choice of delta T I get this
+solution with a nice big gap now they
+
+ align:start position:0%
+solution with a nice big gap now they
+ 
+
+ align:start position:0%
+solution with a nice big gap now they
+both can't be right and so I was a
+
+ align:start position:0%
+both can't be right and so I was a
+ 
+
+ align:start position:0%
+both can't be right and so I was a
+little alarmed because it's like it's
+
+ align:start position:0%
+little alarmed because it's like it's
+ 
+
+ align:start position:0%
+little alarmed because it's like it's
+really different right
+
+ align:start position:0%
+really different right
+ 
+
+ align:start position:0%
+really different right
+so I thought like you know I didn't
+
+ align:start position:0%
+so I thought like you know I didn't
+ 
+
+ align:start position:0%
+so I thought like you know I didn't
+really care that much about the dynamics
+
+ align:start position:0%
+really care that much about the dynamics
+ 
+
+ align:start position:0%
+really care that much about the dynamics
+and my problem I just wanted to make
+
+ align:start position:0%
+and my problem I just wanted to make
+ 
+
+ align:start position:0%
+and my problem I just wanted to make
+sure that the steady-state flame I ended
+
+ align:start position:0%
+sure that the steady-state flame I ended
+ 
+
+ align:start position:0%
+sure that the steady-state flame I ended
+up with was the right one so if you're
+
+ align:start position:0%
+up with was the right one so if you're
+ 
+
+ align:start position:0%
+up with was the right one so if you're
+interested in steady state problems this
+
+ align:start position:0%
+interested in steady state problems this
+ 
+
+ align:start position:0%
+interested in steady state problems this
+is a really important thing you want to
+
+ align:start position:0%
+is a really important thing you want to
+ 
+
+ align:start position:0%
+is a really important thing you want to
+make sure that your solution really
+
+ align:start position:0%
+make sure that your solution really
+ 
+
+ align:start position:0%
+make sure that your solution really
+converges to the true steady state so
+
+ align:start position:0%
+converges to the true steady state so
+ 
+
+ align:start position:0%
+converges to the true steady state so
+when I demonstrate experimentally is
+
+ align:start position:0%
+when I demonstrate experimentally is
+ 
+
+ align:start position:0%
+when I demonstrate experimentally is
+this trying splitting method does not is
+
+ align:start position:0%
+this trying splitting method does not is
+ 
+
+ align:start position:0%
+this trying splitting method does not is
+not reliable to converge the safe state
+
+ align:start position:0%
+not reliable to converge the safe state
+ 
+
+ align:start position:0%
+not reliable to converge the safe state
+now I believe I made the delta T tiny
+
+ align:start position:0%
+now I believe I made the delta T tiny
+ 
+
+ align:start position:0%
+now I believe I made the delta T tiny
+enough probably I would converge to the
+
+ align:start position:0%
+enough probably I would converge to the
+ 
+
+ align:start position:0%
+enough probably I would converge to the
+cry steady-state but I don't know how
+
+ align:start position:0%
+cry steady-state but I don't know how
+ 
+
+ align:start position:0%
+cry steady-state but I don't know how
+tiny you have to go and I can't really
+
+ align:start position:0%
+tiny you have to go and I can't really
+ 
+
+ align:start position:0%
+tiny you have to go and I can't really
+judge my convergence criteria very well
+
+ align:start position:0%
+judge my convergence criteria very well
+ 
+
+ align:start position:0%
+judge my convergence criteria very well
+because at some point adult he suddenly
+
+ align:start position:0%
+because at some point adult he suddenly
+ 
+
+ align:start position:0%
+because at some point adult he suddenly
+jumps from one solution to another
+
+ align:start position:0%
+jumps from one solution to another
+ 
+
+ align:start position:0%
+jumps from one solution to another
+solution that's qualitatively completely
+
+ align:start position:0%
+solution that's qualitatively completely
+ 
+
+ align:start position:0%
+solution that's qualitatively completely
+different and so that the convergence is
+
+ align:start position:0%
+different and so that the convergence is
+ 
+
+ align:start position:0%
+different and so that the convergence is
+not smooth and continuous it's like it's
+
+ align:start position:0%
+not smooth and continuous it's like it's
+ 
+
+ align:start position:0%
+not smooth and continuous it's like it's
+converging converging diverging jumps
+
+ align:start position:0%
+converging converging diverging jumps
+ 
+
+ align:start position:0%
+converging converging diverging jumps
+just have the other solution and I don't
+
+ align:start position:0%
+just have the other solution and I don't
+ 
+
+ align:start position:0%
+just have the other solution and I don't
+know where the jump happens and I don't
+
+ align:start position:0%
+know where the jump happens and I don't
+ 
+
+ align:start position:0%
+know where the jump happens and I don't
+know if I keep going further we'll jump
+
+ align:start position:0%
+know if I keep going further we'll jump
+ 
+
+ align:start position:0%
+know if I keep going further we'll jump
+to something else so this makes me very
+
+ align:start position:0%
+to something else so this makes me very
+ 
+
+ align:start position:0%
+to something else so this makes me very
+loath to publish the paper right so I
+
+ align:start position:0%
+loath to publish the paper right so I
+ 
+
+ align:start position:0%
+loath to publish the paper right so I
+don't know so so I would say I just take
+
+ align:start position:0%
+don't know so so I would say I just take
+ 
+
+ align:start position:0%
+don't know so so I would say I just take
+my dad so I started working on trying to
+
+ align:start position:0%
+my dad so I started working on trying to
+ 
+
+ align:start position:0%
+my dad so I started working on trying to
+fix this splitting the problem was this
+
+ align:start position:0%
+fix this splitting the problem was this
+ 
+
+ align:start position:0%
+fix this splitting the problem was this
+trying is really smart so this his
+
+ align:start position:0%
+trying is really smart so this his
+ 
+
+ align:start position:0%
+trying is really smart so this his
+splitting method is really good it's
+
+ align:start position:0%
+splitting method is really good it's
+ 
+
+ align:start position:0%
+splitting method is really good it's
+stable it's it's pretty accurate it's
+
+ align:start position:0%
+stable it's it's pretty accurate it's
+ 
+
+ align:start position:0%
+stable it's it's pretty accurate it's
+really hard to beat it actually and so I
+
+ align:start position:0%
+really hard to beat it actually and so I
+ 
+
+ align:start position:0%
+really hard to beat it actually and so I
+publish the papers and they weren't that
+
+ align:start position:0%
+publish the papers and they weren't that
+ 
+
+ align:start position:0%
+publish the papers and they weren't that
+good because they really didn't really
+
+ align:start position:0%
+good because they really didn't really
+ 
+
+ align:start position:0%
+good because they really didn't really
+improve it that much but then I had a
+
+ align:start position:0%
+improve it that much but then I had a
+ 
+
+ align:start position:0%
+improve it that much but then I had a
+really smart postdoc named Grace Beth
+
+ align:start position:0%
+really smart postdoc named Grace Beth
+ 
+
+ align:start position:0%
+really smart postdoc named Grace Beth
+now works in the arrow Astro Department
+
+ align:start position:0%
+now works in the arrow Astro Department
+ 
+
+ align:start position:0%
+now works in the arrow Astro Department
+and he came up with a different way to
+
+ align:start position:0%
+and he came up with a different way to
+ 
+
+ align:start position:0%
+and he came up with a different way to
+look at this and he said you know if I
+
+ align:start position:0%
+look at this and he said you know if I
+ 
+
+ align:start position:0%
+look at this and he said you know if I
+have a problem that's like this I can
+
+ align:start position:0%
+have a problem that's like this I can
+ 
+
+ align:start position:0%
+have a problem that's like this I can
+always add some constant to this and
+
+ align:start position:0%
+always add some constant to this and
+ 
+
+ align:start position:0%
+always add some constant to this and
+subtract the same constant from this and
+
+ align:start position:0%
+subtract the same constant from this and
+ 
+
+ align:start position:0%
+subtract the same constant from this and
+I'm really getting the same problem and
+
+ align:start position:0%
+I'm really getting the same problem and
+ 
+
+ align:start position:0%
+I'm really getting the same problem and
+so now the thing is can I cleverly
+
+ align:start position:0%
+so now the thing is can I cleverly
+ 
+
+ align:start position:0%
+so now the thing is can I cleverly
+choose this constant so that for example
+
+ align:start position:0%
+choose this constant so that for example
+ 
+
+ align:start position:0%
+choose this constant so that for example
+my steady-state solution is going to be
+
+ align:start position:0%
+my steady-state solution is going to be
+ 
+
+ align:start position:0%
+my steady-state solution is going to be
+good so how to figure out what cost us
+
+ align:start position:0%
+good so how to figure out what cost us
+ 
+
+ align:start position:0%
+good so how to figure out what cost us
+to choose
+
+ align:start position:0%
+to choose
+ 
+
+ align:start position:0%
+to choose
+and so the methods where you add these
+
+ align:start position:0%
+and so the methods where you add these
+ 
+
+ align:start position:0%
+and so the methods where you add these
+constants are called balancing methods
+
+ align:start position:0%
+constants are called balancing methods
+ 
+
+ align:start position:0%
+constants are called balancing methods
+so he's trying to balance the operator
+
+ align:start position:0%
+so he's trying to balance the operator
+ 
+
+ align:start position:0%
+so he's trying to balance the operator
+splitting scheme and what raise method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very simple bath balancing method this
+
+ align:start position:0%
+very simple bath balancing method this
+ 
+
+ align:start position:0%
+very simple bath balancing method this
+is called simple balancing there we go
+
+ align:start position:0%
+is called simple balancing there we go
+ 
+
+ align:start position:0%
+is called simple balancing there we go
+here we go simple balancing you choose
+
+ align:start position:0%
+here we go simple balancing you choose
+ 
+
+ align:start position:0%
+here we go simple balancing you choose
+to see to be the average of your right
+
+ align:start position:0%
+to see to be the average of your right
+ 
+
+ align:start position:0%
+to see to be the average of your right
+hand side at the last the previous time
+
+ align:start position:0%
+hand side at the last the previous time
+ 
+
+ align:start position:0%
+hand side at the last the previous time
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+okay now the idea here is as you're
+
+ align:start position:0%
+okay now the idea here is as you're
+ 
+
+ align:start position:0%
+okay now the idea here is as you're
+getting close to a steady-state the
+
+ align:start position:0%
+getting close to a steady-state the
+ 
+
+ align:start position:0%
+getting close to a steady-state the
+previous time step is not gonna be that
+
+ align:start position:0%
+previous time step is not gonna be that
+ 
+
+ align:start position:0%
+previous time step is not gonna be that
+much different than the current time
+
+ align:start position:0%
+much different than the current time
+ 
+
+ align:start position:0%
+much different than the current time
+step and so this average number is gonna
+
+ align:start position:0%
+step and so this average number is gonna
+ 
+
+ align:start position:0%
+step and so this average number is gonna
+stay more or less steady as you as you
+
+ align:start position:0%
+stay more or less steady as you as you
+ 
+
+ align:start position:0%
+stay more or less steady as you as you
+get close and so what you're really
+
+ align:start position:0%
+get close and so what you're really
+ 
+
+ align:start position:0%
+get close and so what you're really
+doing is adding the sort of the average
+
+ align:start position:0%
+doing is adding the sort of the average
+ 
+
+ align:start position:0%
+doing is adding the sort of the average
+of these two guys to each of them from
+
+ align:start position:0%
+of these two guys to each of them from
+ 
+
+ align:start position:0%
+of these two guys to each of them from
+the previous step and that has the
+
+ align:start position:0%
+the previous step and that has the
+ 
+
+ align:start position:0%
+the previous step and that has the
+consequence of really changing the
+
+ align:start position:0%
+consequence of really changing the
+ 
+
+ align:start position:0%
+consequence of really changing the
+solution so let me just show you so the
+
+ align:start position:0%
+solution so let me just show you so the
+ 
+
+ align:start position:0%
+solution so let me just show you so the
+left-hand side is what strengths
+
+ align:start position:0%
+left-hand side is what strengths
+ 
+
+ align:start position:0%
+left-hand side is what strengths
+splitting does
+
+ align:start position:0%
+splitting does
+ 
+
+ align:start position:0%
+splitting does
+it's the blue steps are the the blue
+
+ align:start position:0%
+it's the blue steps are the the blue
+ 
+
+ align:start position:0%
+it's the blue steps are the the blue
+steps are the transport and the green
+
+ align:start position:0%
+steps are the transport and the green
+ 
+
+ align:start position:0%
+steps are the transport and the green
+steps are the reaction and what's
+
+ align:start position:0%
+steps are the reaction and what's
+ 
+
+ align:start position:0%
+steps are the reaction and what's
+happening is I did a half a transport
+
+ align:start position:0%
+happening is I did a half a transport
+ 
+
+ align:start position:0%
+happening is I did a half a transport
+staff then I do a reaction the reaction
+
+ align:start position:0%
+staff then I do a reaction the reaction
+ 
+
+ align:start position:0%
+staff then I do a reaction the reaction
+sort of jumps me off the trajectory then
+
+ align:start position:0%
+sort of jumps me off the trajectory then
+ 
+
+ align:start position:0%
+sort of jumps me off the trajectory then
+brings me back when the trajectory then
+
+ align:start position:0%
+brings me back when the trajectory then
+ 
+
+ align:start position:0%
+brings me back when the trajectory then
+overshoots because I do a whole delta T
+
+ align:start position:0%
+overshoots because I do a whole delta T
+ 
+
+ align:start position:0%
+overshoots because I do a whole delta T
+step of reaction and then I have to do a
+
+ align:start position:0%
+step of reaction and then I have to do a
+ 
+
+ align:start position:0%
+step of reaction and then I have to do a
+half step of transport back and so I get
+
+ align:start position:0%
+half step of transport back and so I get
+ 
+
+ align:start position:0%
+half step of transport back and so I get
+from the black one black dot is the
+
+ align:start position:0%
+from the black one black dot is the
+ 
+
+ align:start position:0%
+from the black one black dot is the
+first point and the other black dot is
+
+ align:start position:0%
+first point and the other black dot is
+ 
+
+ align:start position:0%
+first point and the other black dot is
+thickness is what I call my final and
+
+ align:start position:0%
+thickness is what I call my final and
+ 
+
+ align:start position:0%
+thickness is what I call my final and
+that's showing what happens and it just
+
+ align:start position:0%
+that's showing what happens and it just
+ 
+
+ align:start position:0%
+that's showing what happens and it just
+repeats like that over and over again is
+
+ align:start position:0%
+repeats like that over and over again is
+ 
+
+ align:start position:0%
+repeats like that over and over again is
+and it makes sense you if you're close
+
+ align:start position:0%
+and it makes sense you if you're close
+ 
+
+ align:start position:0%
+and it makes sense you if you're close
+to steady-state then if you if I just
+
+ align:start position:0%
+to steady-state then if you if I just
+ 
+
+ align:start position:0%
+to steady-state then if you if I just
+take one of these terms without the
+
+ align:start position:0%
+take one of these terms without the
+ 
+
+ align:start position:0%
+take one of these terms without the
+balancing state of transport it's going
+
+ align:start position:0%
+balancing state of transport it's going
+ 
+
+ align:start position:0%
+balancing state of transport it's going
+to head away from steady state because
+
+ align:start position:0%
+to head away from steady state because
+ 
+
+ align:start position:0%
+to head away from steady state because
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+the transport and the reef and the
+
+ align:start position:0%
+the transport and the reef and the
+ 
+
+ align:start position:0%
+the transport and the reef and the
+reaction are balancing against each
+
+ align:start position:0%
+reaction are balancing against each
+ 
+
+ align:start position:0%
+reaction are balancing against each
+other typically you have something
+
+ align:start position:0%
+other typically you have something
+ 
+
+ align:start position:0%
+other typically you have something
+transporting in and is being consumed by
+
+ align:start position:0%
+transporting in and is being consumed by
+ 
+
+ align:start position:0%
+transporting in and is being consumed by
+the reaction we're son is being created
+
+ align:start position:0%
+the reaction we're son is being created
+ 
+
+ align:start position:0%
+the reaction we're son is being created
+by reaction that's being transporting
+
+ align:start position:0%
+by reaction that's being transporting
+ 
+
+ align:start position:0%
+by reaction that's being transporting
+away and they have opposite signs
+
+ align:start position:0%
+away and they have opposite signs
+ 
+
+ align:start position:0%
+away and they have opposite signs
+if I only put one in that has a certain
+
+ align:start position:0%
+if I only put one in that has a certain
+ 
+
+ align:start position:0%
+if I only put one in that has a certain
+sign then I'm going to move away from
+
+ align:start position:0%
+sign then I'm going to move away from
+ 
+
+ align:start position:0%
+sign then I'm going to move away from
+the steady state and then I need the
+
+ align:start position:0%
+the steady state and then I need the
+ 
+
+ align:start position:0%
+the steady state and then I need the
+other one to bring it back and the
+
+ align:start position:0%
+other one to bring it back and the
+ 
+
+ align:start position:0%
+other one to bring it back and the
+reason why is transporting has trouble
+
+ align:start position:0%
+reason why is transporting has trouble
+ 
+
+ align:start position:0%
+reason why is transporting has trouble
+is it's trying to do these it seen these
+
+ align:start position:0%
+is it's trying to do these it seen these
+ 
+
+ align:start position:0%
+is it's trying to do these it seen these
+huge excursions away from the steady
+
+ align:start position:0%
+huge excursions away from the steady
+ 
+
+ align:start position:0%
+huge excursions away from the steady
+state at each time step with the hope
+
+ align:start position:0%
+state at each time step with the hope
+ 
+
+ align:start position:0%
+state at each time step with the hope
+that it ends up back at this a steam
+
+ align:start position:0%
+that it ends up back at this a steam
+ 
+
+ align:start position:0%
+that it ends up back at this a steam
+right that's the that's always supposed
+
+ align:start position:0%
+right that's the that's always supposed
+ 
+
+ align:start position:0%
+right that's the that's always supposed
+to work out and to second order it does
+
+ align:start position:0%
+to work out and to second order it does
+ 
+
+ align:start position:0%
+to work out and to second order it does
+this because it's pretty clever about
+
+ align:start position:0%
+this because it's pretty clever about
+ 
+
+ align:start position:0%
+this because it's pretty clever about
+how it works but it does it's crazy
+
+ align:start position:0%
+how it works but it does it's crazy
+ 
+
+ align:start position:0%
+how it works but it does it's crazy
+excursions now if you have a nonlinear
+
+ align:start position:0%
+excursions now if you have a nonlinear
+ 
+
+ align:start position:0%
+excursions now if you have a nonlinear
+model the further you excursions from
+
+ align:start position:0%
+model the further you excursions from
+ 
+
+ align:start position:0%
+model the further you excursions from
+the real trajectory
+
+ align:start position:0%
+the real trajectory
+ 
+
+ align:start position:0%
+the real trajectory
+the bigger the error you get so if you
+
+ align:start position:0%
+the bigger the error you get so if you
+ 
+
+ align:start position:0%
+the bigger the error you get so if you
+do the balance method you can see what
+
+ align:start position:0%
+do the balance method you can see what
+ 
+
+ align:start position:0%
+do the balance method you can see what
+happens is that when you get to
+
+ align:start position:0%
+happens is that when you get to
+ 
+
+ align:start position:0%
+happens is that when you get to
+steady-state all the steps are just
+
+ align:start position:0%
+steady-state all the steps are just
+ 
+
+ align:start position:0%
+steady-state all the steps are just
+moving you along the state a trajectory
+
+ align:start position:0%
+moving you along the state a trajectory
+ 
+
+ align:start position:0%
+moving you along the state a trajectory
+they're basically maintaining the steady
+
+ align:start position:0%
+they're basically maintaining the steady
+ 
+
+ align:start position:0%
+they're basically maintaining the steady
+state and that's because I added you
+
+ align:start position:0%
+state and that's because I added you
+ 
+
+ align:start position:0%
+state and that's because I added you
+know it's like transport plus half of
+
+ align:start position:0%
+know it's like transport plus half of
+ 
+
+ align:start position:0%
+know it's like transport plus half of
+transport plus ours and oh there's a
+
+ align:start position:0%
+transport plus ours and oh there's a
+ 
+
+ align:start position:0%
+transport plus ours and oh there's a
+present minus sign here so like that so
+
+ align:start position:0%
+present minus sign here so like that so
+ 
+
+ align:start position:0%
+present minus sign here so like that so
+I'm getting rid of half of my transport
+
+ align:start position:0%
+I'm getting rid of half of my transport
+ 
+
+ align:start position:0%
+I'm getting rid of half of my transport
+and I'm adding in half of this so I've
+
+ align:start position:0%
+and I'm adding in half of this so I've
+ 
+
+ align:start position:0%
+and I'm adding in half of this so I've
+changed before I had dy DT is equal to T
+
+ align:start position:0%
+changed before I had dy DT is equal to T
+ 
+
+ align:start position:0%
+changed before I had dy DT is equal to T
+and now I have dy DT is equal to 1/2 of
+
+ align:start position:0%
+and now I have dy DT is equal to 1/2 of
+ 
+
+ align:start position:0%
+and now I have dy DT is equal to 1/2 of
+T mistake so half of T mine minus F of R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's can't be right it must say this
+
+ align:start position:0%
+and it's can't be right it must say this
+ 
+
+ align:start position:0%
+and it's can't be right it must say this
+I must have a sign maybe this is not
+
+ align:start position:0%
+I must have a sign maybe this is not
+ 
+
+ align:start position:0%
+I must have a sign maybe this is not
+it's not the average it should be - it's
+
+ align:start position:0%
+it's not the average it should be - it's
+ 
+
+ align:start position:0%
+it's not the average it should be - it's
+like that the these hoops should be
+
+ align:start position:0%
+like that the these hoops should be
+ 
+
+ align:start position:0%
+like that the these hoops should be
+added and this is because you're
+
+ align:start position:0%
+added and this is because you're
+ 
+
+ align:start position:0%
+added and this is because you're
+canceled out so basically the only teach
+
+ align:start position:0%
+canceled out so basically the only teach
+ 
+
+ align:start position:0%
+canceled out so basically the only teach
+give me zero which is which should be at
+
+ align:start position:0%
+give me zero which is which should be at
+ 
+
+ align:start position:0%
+give me zero which is which should be at
+a steady state so I'm sorry this is that
+
+ align:start position:0%
+a steady state so I'm sorry this is that
+ 
+
+ align:start position:0%
+a steady state so I'm sorry this is that
+previous slide at the sign room this is
+
+ align:start position:0%
+previous slide at the sign room this is
+ 
+
+ align:start position:0%
+previous slide at the sign room this is
+what happens as the solution if you do
+
+ align:start position:0%
+what happens as the solution if you do
+ 
+
+ align:start position:0%
+what happens as the solution if you do
+Strank splitting on the left you get
+
+ align:start position:0%
+Strank splitting on the left you get
+ 
+
+ align:start position:0%
+Strank splitting on the left you get
+more accuracy as you increase as you cut
+
+ align:start position:0%
+more accuracy as you increase as you cut
+ 
+
+ align:start position:0%
+more accuracy as you increase as you cut
+TT but it's only it's not getting any
+
+ align:start position:0%
+TT but it's only it's not getting any
+ 
+
+ align:start position:0%
+TT but it's only it's not getting any
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+it doesn't matter if it's near steady
+
+ align:start position:0%
+it doesn't matter if it's near steady
+ 
+
+ align:start position:0%
+it doesn't matter if it's near steady
+state or away from steady state it it
+
+ align:start position:0%
+state or away from steady state it it
+ 
+
+ align:start position:0%
+state or away from steady state it it
+treats everything equally strange
+
+ align:start position:0%
+treats everything equally strange
+ 
+
+ align:start position:0%
+treats everything equally strange
+putting in the balance splittings as you
+
+ align:start position:0%
+putting in the balance splittings as you
+ 
+
+ align:start position:0%
+putting in the balance splittings as you
+get to steady state all sudden the urge
+
+ align:start position:0%
+get to steady state all sudden the urge
+ 
+
+ align:start position:0%
+get to steady state all sudden the urge
+drive exponentially you see the
+
+ align:start position:0%
+drive exponentially you see the
+ 
+
+ align:start position:0%
+drive exponentially you see the
+logarithm of the air library tape lot so
+
+ align:start position:0%
+logarithm of the air library tape lot so
+ 
+
+ align:start position:0%
+logarithm of the air library tape lot so
+you get tremendously great convergence
+
+ align:start position:0%
+you get tremendously great convergence
+ 
+
+ align:start position:0%
+you get tremendously great convergence
+to the real steady state once you get
+
+ align:start position:0%
+to the real steady state once you get
+ 
+
+ align:start position:0%
+to the real steady state once you get
+anywhere close to this a state now the
+
+ align:start position:0%
+anywhere close to this a state now the
+ 
+
+ align:start position:0%
+anywhere close to this a state now the
+the cost of this is it because the
+
+ align:start position:0%
+the cost of this is it because the
+ 
+
+ align:start position:0%
+the cost of this is it because the
+formula was just which I has a sign
+
+ align:start position:0%
+formula was just which I has a sign
+ 
+
+ align:start position:0%
+formula was just which I has a sign
+mistake I think it depends on yn it
+
+ align:start position:0%
+mistake I think it depends on yn it
+ 
+
+ align:start position:0%
+mistake I think it depends on yn it
+makes the whole thing numerically more
+
+ align:start position:0%
+makes the whole thing numerically more
+ 
+
+ align:start position:0%
+makes the whole thing numerically more
+unstable because it's like an explicit
+
+ align:start position:0%
+unstable because it's like an explicit
+ 
+
+ align:start position:0%
+unstable because it's like an explicit
+thing we're using what happened in
+
+ align:start position:0%
+thing we're using what happened in
+ 
+
+ align:start position:0%
+thing we're using what happened in
+previous time to correct our equation
+
+ align:start position:0%
+previous time to correct our equation
+ 
+
+ align:start position:0%
+previous time to correct our equation
+for future times and so you get are more
+
+ align:start position:0%
+for future times and so you get are more
+ 
+
+ align:start position:0%
+for future times and so you get are more
+likely to numerical instabilities so
+
+ align:start position:0%
+likely to numerical instabilities so
+ 
+
+ align:start position:0%
+likely to numerical instabilities so
+then reinvented an implicit version of
+
+ align:start position:0%
+then reinvented an implicit version of
+ 
+
+ align:start position:0%
+then reinvented an implicit version of
+that and also a higher order method and
+
+ align:start position:0%
+that and also a higher order method and
+ 
+
+ align:start position:0%
+that and also a higher order method and
+that's called rebalance splitting the
+
+ align:start position:0%
+that's called rebalance splitting the
+ 
+
+ align:start position:0%
+that's called rebalance splitting the
+equation is way too complicated me to
+
+ align:start position:0%
+equation is way too complicated me to
+ 
+
+ align:start position:0%
+equation is way too complicated me to
+write down since I can't even write down
+
+ align:start position:0%
+write down since I can't even write down
+ 
+
+ align:start position:0%
+write down since I can't even write down
+that something minus signs correctly in
+
+ align:start position:0%
+that something minus signs correctly in
+ 
+
+ align:start position:0%
+that something minus signs correctly in
+this one but you're happy to read the
+
+ align:start position:0%
+this one but you're happy to read the
+ 
+
+ align:start position:0%
+this one but you're happy to read the
+paper it's in Siam and he has the
+
+ align:start position:0%
+paper it's in Siam and he has the
+ 
+
+ align:start position:0%
+paper it's in Siam and he has the
+equations for that and we put the second
+
+ align:start position:0%
+equations for that and we put the second
+ 
+
+ align:start position:0%
+equations for that and we put the second
+order one end that's implicit then the
+
+ align:start position:0%
+order one end that's implicit then the
+ 
+
+ align:start position:0%
+order one end that's implicit then the
+thing is just as stable as strike
+
+ align:start position:0%
+thing is just as stable as strike
+ 
+
+ align:start position:0%
+thing is just as stable as strike
+splitting but it also has this great
+
+ align:start position:0%
+splitting but it also has this great
+ 
+
+ align:start position:0%
+splitting but it also has this great
+property that as you cook it close to
+
+ align:start position:0%
+property that as you cook it close to
+ 
+
+ align:start position:0%
+property that as you cook it close to
+tie to state it exponentially converges
+
+ align:start position:0%
+tie to state it exponentially converges
+ 
+
+ align:start position:0%
+tie to state it exponentially converges
+to the solution which is sir like how
+
+ align:start position:0%
+to the solution which is sir like how
+ 
+
+ align:start position:0%
+to the solution which is sir like how
+Newton's method is really so good it's
+
+ align:start position:0%
+Newton's method is really so good it's
+ 
+
+ align:start position:0%
+Newton's method is really so good it's
+sort of like that doesn't you get you
+
+ align:start position:0%
+sort of like that doesn't you get you
+ 
+
+ align:start position:0%
+sort of like that doesn't you get you
+get a lot more decimal places really
+
+ align:start position:0%
+get a lot more decimal places really
+ 
+
+ align:start position:0%
+get a lot more decimal places really
+fast why'd you get close to steady-state
+
+ align:start position:0%
+fast why'd you get close to steady-state
+ 
+
+ align:start position:0%
+fast why'd you get close to steady-state
+all right that's enough enjoy
+
+ align:start position:0%
+all right that's enough enjoy
+ 
+
+ align:start position:0%
+all right that's enough enjoy
+Thanksgiving I posted a bunch of
+
+ align:start position:0%
+Thanksgiving I posted a bunch of
+ 
+
+ align:start position:0%
+Thanksgiving I posted a bunch of
+readings and things about my trop
+
+ align:start position:0%
+readings and things about my trop
+ 
+
+ align:start position:0%
+readings and things about my trop
+Monte Carlo and stochastic stuff we're
+
+ align:start position:0%
+Monte Carlo and stochastic stuff we're
+ 
+
+ align:start position:0%
+Monte Carlo and stochastic stuff we're
+gonna talk about next week and also a
+
+ align:start position:0%
+gonna talk about next week and also a
+ 
+
+ align:start position:0%
+gonna talk about next week and also a
+little bit more about moles versus data
+
+ align:start position:0%
+little bit more about moles versus data
+ 
+
+ align:start position:0%
+little bit more about moles versus data
+so do the reading when you get a chance
+
+ align:start position:0%
+so do the reading when you get a chance
+ 
+
+ align:start position:0%
+so do the reading when you get a chance
+say how your families see how your
+
+ align:start position:0%
+say how your families see how your
+ 
+
+ align:start position:0%
+say how your families see how your
+friends nice time
\ No newline at end of file
diff --git a/4ip-4ai6kN8.txt b/4ip-4ai6kN8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..12fcf7dc78d6385c1f0074e15d2f2c69789d2f4b
--- /dev/null
+++ b/4ip-4ai6kN8.txt
@@ -0,0 +1,11467 @@
+align:start position:0%
+ 
+so who were
+
+ align:start position:0%
+so who were
+ 
+
+ align:start position:0%
+so who were
+that's called a spectrogram good and
+
+ align:start position:0%
+that's called a spectrogram good and
+ 
+
+ align:start position:0%
+that's called a spectrogram good and
+it's a spectrogram of me good morning
+
+ align:start position:0%
+it's a spectrogram of me good morning
+ 
+
+ align:start position:0%
+it's a spectrogram of me good morning
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+okay so it's a spectrum of speech okay
+
+ align:start position:0%
+okay so it's a spectrum of speech okay
+ 
+
+ align:start position:0%
+okay so it's a spectrum of speech okay
+and so we are going to continue today on
+
+ align:start position:0%
+and so we are going to continue today on
+ 
+
+ align:start position:0%
+and so we are going to continue today on
+the topic of understanding developing
+
+ align:start position:0%
+the topic of understanding developing
+ 
+
+ align:start position:0%
+the topic of understanding developing
+methods for understanding how to
+
+ align:start position:0%
+methods for understanding how to
+ 
+
+ align:start position:0%
+methods for understanding how to
+characterize and and understand
+
+ align:start position:0%
+characterize and and understand
+ 
+
+ align:start position:0%
+characterize and and understand
+temporally structured signals so that is
+
+ align:start position:0%
+temporally structured signals so that is
+ 
+
+ align:start position:0%
+temporally structured signals so that is
+the microphone recording of my voice
+
+ align:start position:0%
+the microphone recording of my voice
+ 
+
+ align:start position:0%
+the microphone recording of my voice
+saying a good good morning class and
+
+ align:start position:0%
+saying a good good morning class and
+ 
+
+ align:start position:0%
+saying a good good morning class and
+then this is a spectrogram of that
+
+ align:start position:0%
+then this is a spectrogram of that
+ 
+
+ align:start position:0%
+then this is a spectrogram of that
+signal where at each moment in time you
+
+ align:start position:0%
+signal where at each moment in time you
+ 
+
+ align:start position:0%
+signal where at each moment in time you
+can actually extract the spectral
+
+ align:start position:0%
+can actually extract the spectral
+ 
+
+ align:start position:0%
+can actually extract the spectral
+structure of that signal and you can see
+
+ align:start position:0%
+structure of that signal and you can see
+ 
+
+ align:start position:0%
+structure of that signal and you can see
+that the information in speech signals
+
+ align:start position:0%
+that the information in speech signals
+ 
+
+ align:start position:0%
+that the information in speech signals
+is actually carried in in parts of the
+
+ align:start position:0%
+is actually carried in in parts of the
+ 
+
+ align:start position:0%
+is actually carried in in parts of the
+signal in the way the power and the
+
+ align:start position:0%
+signal in the way the power and the
+ 
+
+ align:start position:0%
+signal in the way the power and the
+signal at different frequencies changes
+
+ align:start position:0%
+signal at different frequencies changes
+ 
+
+ align:start position:0%
+signal at different frequencies changes
+over time okay your ears detect these
+
+ align:start position:0%
+over time okay your ears detect these
+ 
+
+ align:start position:0%
+over time okay your ears detect these
+changes in frequency and translate that
+
+ align:start position:0%
+changes in frequency and translate that
+ 
+
+ align:start position:0%
+changes in frequency and translate that
+into information about what I'm saying
+
+ align:start position:0%
+into information about what I'm saying
+ 
+
+ align:start position:0%
+into information about what I'm saying
+okay and so we're going to today start
+
+ align:start position:0%
+okay and so we're going to today start
+ 
+
+ align:start position:0%
+okay and so we're going to today start
+on a well we sort of started last time
+
+ align:start position:0%
+on a well we sort of started last time
+ 
+
+ align:start position:0%
+on a well we sort of started last time
+but we're really going to get going on
+
+ align:start position:0%
+but we're really going to get going on
+ 
+
+ align:start position:0%
+but we're really going to get going on
+this in the next three lectures we're
+
+ align:start position:0%
+this in the next three lectures we're
+ 
+
+ align:start position:0%
+this in the next three lectures we're
+gonna develop a powerful set of tools
+
+ align:start position:0%
+gonna develop a powerful set of tools
+ 
+
+ align:start position:0%
+gonna develop a powerful set of tools
+for characterizing and understanding the
+
+ align:start position:0%
+for characterizing and understanding the
+ 
+
+ align:start position:0%
+for characterizing and understanding the
+temporal structure of signals okay so
+
+ align:start position:0%
+temporal structure of signals okay so
+ 
+
+ align:start position:0%
+temporal structure of signals okay so
+this is the the gameplan for the next
+
+ align:start position:0%
+this is the the gameplan for the next
+ 
+
+ align:start position:0%
+this is the the gameplan for the next
+three lectures today we're going to
+
+ align:start position:0%
+three lectures today we're going to
+ 
+
+ align:start position:0%
+three lectures today we're going to
+cover a Fourier series complex Fourier
+
+ align:start position:0%
+cover a Fourier series complex Fourier
+ 
+
+ align:start position:0%
+cover a Fourier series complex Fourier
+series we're going to extend that to the
+
+ align:start position:0%
+series we're going to extend that to the
+ 
+
+ align:start position:0%
+series we're going to extend that to the
+idea of the Fourier transform and then
+
+ align:start position:0%
+idea of the Fourier transform and then
+ 
+
+ align:start position:0%
+idea of the Fourier transform and then
+so the Fourier transform is sort of a
+
+ align:start position:0%
+so the Fourier transform is sort of a
+ 
+
+ align:start position:0%
+so the Fourier transform is sort of a
+very general mathematical approach to
+
+ align:start position:0%
+very general mathematical approach to
+ 
+
+ align:start position:0%
+very general mathematical approach to
+understanding that the temporal
+
+ align:start position:0%
+understanding that the temporal
+ 
+
+ align:start position:0%
+understanding that the temporal
+structure of signals that's that's more
+
+ align:start position:0%
+structure of signals that's that's more
+ 
+
+ align:start position:0%
+structure of signals that's that's more
+of a you think of that more in the terms
+
+ align:start position:0%
+of a you think of that more in the terms
+ 
+
+ align:start position:0%
+of a you think of that more in the terms
+of doing in terms of doing analytical
+
+ align:start position:0%
+of doing in terms of doing analytical
+ 
+
+ align:start position:0%
+of doing in terms of doing analytical
+calculations or or or sort of conceptual
+
+ align:start position:0%
+calculations or or or sort of conceptual
+ 
+
+ align:start position:0%
+calculations or or or sort of conceptual
+understanding of what
+
+ align:start position:0%
+understanding of what
+ 
+
+ align:start position:0%
+understanding of what
+Fourier decomposition is but then
+
+ align:start position:0%
+Fourier decomposition is but then
+ 
+
+ align:start position:0%
+Fourier decomposition is but then
+there's a very concrete algorithm for
+
+ align:start position:0%
+there's a very concrete algorithm for
+ 
+
+ align:start position:0%
+there's a very concrete algorithm for
+for characterizing spectral structure of
+
+ align:start position:0%
+for characterizing spectral structure of
+ 
+
+ align:start position:0%
+for characterizing spectral structure of
+signals called the fast Fourier
+
+ align:start position:0%
+signals called the fast Fourier
+ 
+
+ align:start position:0%
+signals called the fast Fourier
+transform and that's one class of
+
+ align:start position:0%
+transform and that's one class of
+ 
+
+ align:start position:0%
+transform and that's one class of
+methods where you sample signals
+
+ align:start position:0%
+methods where you sample signals
+ 
+
+ align:start position:0%
+methods where you sample signals
+discretely in time and get back discrete
+
+ align:start position:0%
+discretely in time and get back discrete
+ 
+
+ align:start position:0%
+discretely in time and get back discrete
+power at discrete frequencies so that's
+
+ align:start position:0%
+power at discrete frequencies so that's
+ 
+
+ align:start position:0%
+power at discrete frequencies so that's
+called a discrete Fourier transform and
+
+ align:start position:0%
+called a discrete Fourier transform and
+ 
+
+ align:start position:0%
+called a discrete Fourier transform and
+most often that's used to compute the
+
+ align:start position:0%
+most often that's used to compute the
+ 
+
+ align:start position:0%
+most often that's used to compute the
+power spectrum of signals and so that's
+
+ align:start position:0%
+power spectrum of signals and so that's
+ 
+
+ align:start position:0%
+power spectrum of signals and so that's
+what we're gonna cover today and then in
+
+ align:start position:0%
+what we're gonna cover today and then in
+ 
+
+ align:start position:0%
+what we're gonna cover today and then in
+the next lecture we're gonna cover a
+
+ align:start position:0%
+the next lecture we're gonna cover a
+ 
+
+ align:start position:0%
+the next lecture we're gonna cover a
+number of topics leading up to spectral
+
+ align:start position:0%
+number of topics leading up to spectral
+ 
+
+ align:start position:0%
+number of topics leading up to spectral
+estimation we're gonna start with the
+
+ align:start position:0%
+estimation we're gonna start with the
+ 
+
+ align:start position:0%
+estimation we're gonna start with the
+convolution theorem which is a really
+
+ align:start position:0%
+convolution theorem which is a really
+ 
+
+ align:start position:0%
+convolution theorem which is a really
+powerful way of understanding the
+
+ align:start position:0%
+powerful way of understanding the
+ 
+
+ align:start position:0%
+powerful way of understanding the
+relationship between convolution in the
+
+ align:start position:0%
+relationship between convolution in the
+ 
+
+ align:start position:0%
+relationship between convolution in the
+time domain and multiplication of things
+
+ align:start position:0%
+time domain and multiplication of things
+ 
+
+ align:start position:0%
+time domain and multiplication of things
+in the frequency domain and and the
+
+ align:start position:0%
+in the frequency domain and and the
+ 
+
+ align:start position:0%
+in the frequency domain and and the
+convolution theorem is really powerful
+
+ align:start position:0%
+convolution theorem is really powerful
+ 
+
+ align:start position:0%
+convolution theorem is really powerful
+allowing you to kind of think about and
+
+ align:start position:0%
+allowing you to kind of think about and
+ 
+
+ align:start position:0%
+allowing you to kind of think about and
+to ative lee understand the spectral
+
+ align:start position:0%
+to ative lee understand the spectral
+ 
+
+ align:start position:0%
+to ative lee understand the spectral
+structure of different kinds of signals
+
+ align:start position:0%
+structure of different kinds of signals
+ 
+
+ align:start position:0%
+structure of different kinds of signals
+that you can build by convolving
+
+ align:start position:0%
+that you can build by convolving
+ 
+
+ align:start position:0%
+that you can build by convolving
+different sort of basic elements so if
+
+ align:start position:0%
+different sort of basic elements so if
+ 
+
+ align:start position:0%
+different sort of basic elements so if
+you understand the Fourier decomposition
+
+ align:start position:0%
+you understand the Fourier decomposition
+ 
+
+ align:start position:0%
+you understand the Fourier decomposition
+of a square pulse and a train of pulses
+
+ align:start position:0%
+of a square pulse and a train of pulses
+ 
+
+ align:start position:0%
+of a square pulse and a train of pulses
+or a Gaussian you can basically just by
+
+ align:start position:0%
+or a Gaussian you can basically just by
+ 
+
+ align:start position:0%
+or a Gaussian you can basically just by
+kind of thinking about it figure out the
+
+ align:start position:0%
+kind of thinking about it figure out the
+ 
+
+ align:start position:0%
+kind of thinking about it figure out the
+spectral structure of a lot of different
+
+ align:start position:0%
+spectral structure of a lot of different
+ 
+
+ align:start position:0%
+spectral structure of a lot of different
+signals by just combining those things
+
+ align:start position:0%
+signals by just combining those things
+ 
+
+ align:start position:0%
+signals by just combining those things
+sort of like Lego blocks it's super cool
+
+ align:start position:0%
+sort of like Lego blocks it's super cool
+ 
+
+ align:start position:0%
+sort of like Lego blocks it's super cool
+we're gonna talk about noise and
+
+ align:start position:0%
+we're gonna talk about noise and
+ 
+
+ align:start position:0%
+we're gonna talk about noise and
+filtering we're going to talk about the
+
+ align:start position:0%
+filtering we're going to talk about the
+ 
+
+ align:start position:0%
+filtering we're going to talk about the
+Shannon Nyquist sampling theorem which
+
+ align:start position:0%
+Shannon Nyquist sampling theorem which
+ 
+
+ align:start position:0%
+Shannon Nyquist sampling theorem which
+tells you how fast you have to sample a
+
+ align:start position:0%
+tells you how fast you have to sample a
+ 
+
+ align:start position:0%
+tells you how fast you have to sample a
+signal in order to perfectly reconstruct
+
+ align:start position:0%
+signal in order to perfectly reconstruct
+ 
+
+ align:start position:0%
+signal in order to perfectly reconstruct
+it it turns out it's really amazing if
+
+ align:start position:0%
+it it turns out it's really amazing if
+ 
+
+ align:start position:0%
+it it turns out it's really amazing if
+you have a signal in time you can sample
+
+ align:start position:0%
+you have a signal in time you can sample
+ 
+
+ align:start position:0%
+you have a signal in time you can sample
+that signal at regular intervals and
+
+ align:start position:0%
+that signal at regular intervals and
+ 
+
+ align:start position:0%
+that signal at regular intervals and
+perfectly reconstruct the signal if that
+
+ align:start position:0%
+perfectly reconstruct the signal if that
+ 
+
+ align:start position:0%
+perfectly reconstruct the signal if that
+signal doesn't have frequency components
+
+ align:start position:0%
+signal doesn't have frequency components
+ 
+
+ align:start position:0%
+signal doesn't have frequency components
+that are too high and so that's captured
+
+ align:start position:0%
+that are too high and so that's captured
+ 
+
+ align:start position:0%
+that are too high and so that's captured
+in this Shannon Nyquist sampling theorem
+
+ align:start position:0%
+in this Shannon Nyquist sampling theorem
+ 
+
+ align:start position:0%
+in this Shannon Nyquist sampling theorem
+that turns out to actually be a topic of
+
+ align:start position:0%
+that turns out to actually be a topic of
+ 
+
+ align:start position:0%
+that turns out to actually be a topic of
+current debate there's a there was a
+
+ align:start position:0%
+current debate there's a there was a
+ 
+
+ align:start position:0%
+current debate there's a there was a
+paper published recently by somebody
+
+ align:start position:0%
+paper published recently by somebody
+ 
+
+ align:start position:0%
+paper published recently by somebody
+claiming to be able to get around the
+
+ align:start position:0%
+claiming to be able to get around the
+ 
+
+ align:start position:0%
+claiming to be able to get around the
+sampling theorem and record neural
+
+ align:start position:0%
+sampling theorem and record neural
+ 
+
+ align:start position:0%
+sampling theorem and record neural
+signals without having to
+
+ align:start position:0%
+signals without having to
+ 
+
+ align:start position:0%
+signals without having to
+guarantee they're the conditions under
+
+ align:start position:0%
+guarantee they're the conditions under
+ 
+
+ align:start position:0%
+guarantee they're the conditions under
+which that Nyquist's Shannon Nyquist
+
+ align:start position:0%
+which that Nyquist's Shannon Nyquist
+ 
+
+ align:start position:0%
+which that Nyquist's Shannon Nyquist
+sampling theorem claims and Marcus
+
+ align:start position:0%
+sampling theorem claims and Marcus
+ 
+
+ align:start position:0%
+sampling theorem claims and Marcus
+Meister wrote a scathing rebuttal to
+
+ align:start position:0%
+Meister wrote a scathing rebuttal to
+ 
+
+ align:start position:0%
+Meister wrote a scathing rebuttal to
+that basically claiming that they're
+
+ align:start position:0%
+that basically claiming that they're
+ 
+
+ align:start position:0%
+that basically claiming that they're
+full of baloney and so you know that
+
+ align:start position:0%
+full of baloney and so you know that
+ 
+
+ align:start position:0%
+full of baloney and so you know that
+those folks who wrote that paper maybe
+
+ align:start position:0%
+those folks who wrote that paper maybe
+ 
+
+ align:start position:0%
+those folks who wrote that paper maybe
+should have taken in this class so
+
+ align:start position:0%
+should have taken in this class so
+ 
+
+ align:start position:0%
+should have taken in this class so
+anyway you don't want to be on the wrong
+
+ align:start position:0%
+anyway you don't want to be on the wrong
+ 
+
+ align:start position:0%
+anyway you don't want to be on the wrong
+end of Marcus Meister's blog post so so
+
+ align:start position:0%
+end of Marcus Meister's blog post so so
+ 
+
+ align:start position:0%
+end of Marcus Meister's blog post so so
+pay attention ok so then we're gonna get
+
+ align:start position:0%
+pay attention ok so then we're gonna get
+ 
+
+ align:start position:0%
+pay attention ok so then we're gonna get
+into spectral estimation then in the
+
+ align:start position:0%
+into spectral estimation then in the
+ 
+
+ align:start position:0%
+into spectral estimation then in the
+last lecture we're going to talk about
+
+ align:start position:0%
+last lecture we're going to talk about
+ 
+
+ align:start position:0%
+last lecture we're going to talk about
+spectrograms we're gonna talk about how
+
+ align:start position:0%
+spectrograms we're gonna talk about how
+ 
+
+ align:start position:0%
+spectrograms we're gonna talk about how
+to compute spectrograms and understand
+
+ align:start position:0%
+to compute spectrograms and understand
+ 
+
+ align:start position:0%
+to compute spectrograms and understand
+really how to take the data and break it
+
+ align:start position:0%
+really how to take the data and break it
+ 
+
+ align:start position:0%
+really how to take the data and break it
+into samples called windowing how to
+
+ align:start position:0%
+into samples called windowing how to
+ 
+
+ align:start position:0%
+into samples called windowing how to
+multiply those samples by what's called
+
+ align:start position:0%
+multiply those samples by what's called
+ 
+
+ align:start position:0%
+multiply those samples by what's called
+a taper to avoid contaminating the
+
+ align:start position:0%
+a taper to avoid contaminating the
+ 
+
+ align:start position:0%
+a taper to avoid contaminating the
+signal with lots of noise that's
+
+ align:start position:0%
+signal with lots of noise that's
+ 
+
+ align:start position:0%
+signal with lots of noise that's
+unnecessary we're gonna understand the
+
+ align:start position:0%
+unnecessary we're gonna understand the
+ 
+
+ align:start position:0%
+unnecessary we're gonna understand the
+idea of time bandwidth product how do
+
+ align:start position:0%
+idea of time bandwidth product how do
+ 
+
+ align:start position:0%
+idea of time bandwidth product how do
+you choose the width of that window to
+
+ align:start position:0%
+you choose the width of that window to
+ 
+
+ align:start position:0%
+you choose the width of that window to
+emphasize different parts of the data
+
+ align:start position:0%
+emphasize different parts of the data
+ 
+
+ align:start position:0%
+emphasize different parts of the data
+and then we're going to end with some
+
+ align:start position:0%
+and then we're going to end with some
+ 
+
+ align:start position:0%
+and then we're going to end with some
+advanced filtering methods that are
+
+ align:start position:0%
+advanced filtering methods that are
+ 
+
+ align:start position:0%
+advanced filtering methods that are
+commonly used to to control different
+
+ align:start position:0%
+commonly used to to control different
+ 
+
+ align:start position:0%
+commonly used to to control different
+frequency components of signals in your
+
+ align:start position:0%
+frequency components of signals in your
+ 
+
+ align:start position:0%
+frequency components of signals in your
+data ok so a bunch of really powerful
+
+ align:start position:0%
+data ok so a bunch of really powerful
+ 
+
+ align:start position:0%
+data ok so a bunch of really powerful
+things here's what we're going to talk
+
+ align:start position:0%
+things here's what we're going to talk
+ 
+
+ align:start position:0%
+things here's what we're going to talk
+about today we're gonna start we're
+
+ align:start position:0%
+about today we're gonna start we're
+ 
+
+ align:start position:0%
+about today we're gonna start we're
+gonna continue with this Fourier series
+
+ align:start position:0%
+gonna continue with this Fourier series
+ 
+
+ align:start position:0%
+gonna continue with this Fourier series
+we started with symmetric functions last
+
+ align:start position:0%
+we started with symmetric functions last
+ 
+
+ align:start position:0%
+we started with symmetric functions last
+time we're going to finish that and then
+
+ align:start position:0%
+time we're going to finish that and then
+ 
+
+ align:start position:0%
+time we're going to finish that and then
+talk about asymmetric functions
+
+ align:start position:0%
+talk about asymmetric functions
+ 
+
+ align:start position:0%
+talk about asymmetric functions
+we're gonna extend that to complex
+
+ align:start position:0%
+we're gonna extend that to complex
+ 
+
+ align:start position:0%
+we're gonna extend that to complex
+Fourier series introduce the Fourier
+
+ align:start position:0%
+Fourier series introduce the Fourier
+ 
+
+ align:start position:0%
+Fourier series introduce the Fourier
+transform the discrete Fourier transform
+
+ align:start position:0%
+transform the discrete Fourier transform
+ 
+
+ align:start position:0%
+transform the discrete Fourier transform
+and this algorithm the fast Fourier
+
+ align:start position:0%
+and this algorithm the fast Fourier
+ 
+
+ align:start position:0%
+and this algorithm the fast Fourier
+transform and then I'm going to show you
+
+ align:start position:0%
+transform and then I'm going to show you
+ 
+
+ align:start position:0%
+transform and then I'm going to show you
+how to compute power spectrum so just to
+
+ align:start position:0%
+how to compute power spectrum so just to
+ 
+
+ align:start position:0%
+how to compute power spectrum so just to
+make it clear all of this stuff is
+
+ align:start position:0%
+make it clear all of this stuff is
+ 
+
+ align:start position:0%
+make it clear all of this stuff is
+basically going to be to teach you how
+
+ align:start position:0%
+basically going to be to teach you how
+ 
+
+ align:start position:0%
+basically going to be to teach you how
+to use one line of matlab ok one
+
+ align:start position:0%
+to use one line of matlab ok one
+ 
+
+ align:start position:0%
+to use one line of matlab ok one
+function FFT ok now the problem is it's
+
+ align:start position:0%
+function FFT ok now the problem is it's
+ 
+
+ align:start position:0%
+function FFT ok now the problem is it's
+really easy to do this wrong ok
+
+ align:start position:0%
+really easy to do this wrong ok
+ 
+
+ align:start position:0%
+really easy to do this wrong ok
+it's really easy to use this but not
+
+ align:start position:0%
+it's really easy to use this but not
+ 
+
+ align:start position:0%
+it's really easy to use this but not
+understand what you're doing and come up
+
+ align:start position:0%
+understand what you're doing and come up
+ 
+
+ align:start position:0%
+understand what you're doing and come up
+with the wrong answer ok so so all of
+
+ align:start position:0%
+with the wrong answer ok so so all of
+ 
+
+ align:start position:0%
+with the wrong answer ok so so all of
+these things that we're going to talk
+
+ align:start position:0%
+these things that we're going to talk
+ 
+
+ align:start position:0%
+these things that we're going to talk
+about today are just the kind of basics
+
+ align:start position:0%
+about today are just the kind of basics
+ 
+
+ align:start position:0%
+about today are just the kind of basics
+that you need to understand in order to
+
+ align:start position:0%
+that you need to understand in order to
+ 
+
+ align:start position:0%
+that you need to understand in order to
+use the
+
+ align:start position:0%
+use the
+ 
+
+ align:start position:0%
+use the
+very powerful function in MATLAB okay
+
+ align:start position:0%
+very powerful function in MATLAB okay
+ 
+
+ align:start position:0%
+very powerful function in MATLAB okay
+all right okay so let's get started so
+
+ align:start position:0%
+all right okay so let's get started so
+ 
+
+ align:start position:0%
+all right okay so let's get started so
+last time we we introduced the idea of a
+
+ align:start position:0%
+last time we we introduced the idea of a
+ 
+
+ align:start position:0%
+last time we we introduced the idea of a
+Fourier series we talked about the idea
+
+ align:start position:0%
+Fourier series we talked about the idea
+ 
+
+ align:start position:0%
+Fourier series we talked about the idea
+that you can approximate any periodic
+
+ align:start position:0%
+that you can approximate any periodic
+ 
+
+ align:start position:0%
+that you can approximate any periodic
+function so here I'm just taking a
+
+ align:start position:0%
+function so here I'm just taking a
+ 
+
+ align:start position:0%
+function so here I'm just taking a
+square wave that alternates between
+
+ align:start position:0%
+square wave that alternates between
+ 
+
+ align:start position:0%
+square wave that alternates between
+positive and negative it's periodic with
+
+ align:start position:0%
+positive and negative it's periodic with
+ 
+
+ align:start position:0%
+positive and negative it's periodic with
+a period capital T so it's a function of
+
+ align:start position:0%
+a period capital T so it's a function of
+ 
+
+ align:start position:0%
+a period capital T so it's a function of
+time it's a it's a even function or a
+
+ align:start position:0%
+time it's a it's a even function or a
+ 
+
+ align:start position:0%
+time it's a it's a even function or a
+symmetric function because you can see
+
+ align:start position:0%
+symmetric function because you can see
+ 
+
+ align:start position:0%
+symmetric function because you can see
+that it's it's basically mirror symmetry
+
+ align:start position:0%
+that it's it's basically mirror symmetry
+ 
+
+ align:start position:0%
+that it's it's basically mirror symmetry
+around the y axis okay it's even because
+
+ align:start position:0%
+around the y axis okay it's even because
+ 
+
+ align:start position:0%
+around the y axis okay it's even because
+even polynomials also have that property
+
+ align:start position:0%
+even polynomials also have that property
+ 
+
+ align:start position:0%
+even polynomials also have that property
+of being symmetric we can approximate
+
+ align:start position:0%
+of being symmetric we can approximate
+ 
+
+ align:start position:0%
+of being symmetric we can approximate
+this this periodic function T as a sum
+
+ align:start position:0%
+this this periodic function T as a sum
+ 
+
+ align:start position:0%
+this this periodic function T as a sum
+of sine waves or cosine waves in this
+
+ align:start position:0%
+of sine waves or cosine waves in this
+ 
+
+ align:start position:0%
+of sine waves or cosine waves in this
+case we can approximate that as a cosine
+
+ align:start position:0%
+case we can approximate that as a cosine
+ 
+
+ align:start position:0%
+case we can approximate that as a cosine
+wave of the same period and the same
+
+ align:start position:0%
+wave of the same period and the same
+ 
+
+ align:start position:0%
+wave of the same period and the same
+amplitude so we can approximate it as as
+
+ align:start position:0%
+amplitude so we can approximate it as as
+ 
+
+ align:start position:0%
+amplitude so we can approximate it as as
+a coefficient times cosine 2 pi F naught
+
+ align:start position:0%
+a coefficient times cosine 2 pi F naught
+ 
+
+ align:start position:0%
+a coefficient times cosine 2 pi F naught
+T where F naught is just 1 over the
+
+ align:start position:0%
+T where F naught is just 1 over the
+ 
+
+ align:start position:0%
+T where F naught is just 1 over the
+period alright so if the period is 1
+
+ align:start position:0%
+period alright so if the period is 1
+ 
+
+ align:start position:0%
+period alright so if the period is 1
+second then the frequency is 1 Hertz 1
+
+ align:start position:0%
+second then the frequency is 1 Hertz 1
+ 
+
+ align:start position:0%
+second then the frequency is 1 Hertz 1
+over 1 second we often use this
+
+ align:start position:0%
+over 1 second we often use this
+ 
+
+ align:start position:0%
+over 1 second we often use this
+different representation of frequency
+
+ align:start position:0%
+different representation of frequency
+ 
+
+ align:start position:0%
+different representation of frequency
+which is usually called Omega which is
+
+ align:start position:0%
+which is usually called Omega which is
+ 
+
+ align:start position:0%
+which is usually called Omega which is
+angular frequency and it's just 2 pi
+
+ align:start position:0%
+angular frequency and it's just 2 pi
+ 
+
+ align:start position:0%
+angular frequency and it's just 2 pi
+times this oscillation frequency and it
+
+ align:start position:0%
+times this oscillation frequency and it
+ 
+
+ align:start position:0%
+times this oscillation frequency and it
+has units of radians per second alright
+
+ align:start position:0%
+has units of radians per second alright
+ 
+
+ align:start position:0%
+has units of radians per second alright
+so we talked about the fact that you can
+
+ align:start position:0%
+so we talked about the fact that you can
+ 
+
+ align:start position:0%
+so we talked about the fact that you can
+approximate this periodic function as a
+
+ align:start position:0%
+approximate this periodic function as a
+ 
+
+ align:start position:0%
+approximate this periodic function as a
+sum of cosines we talked about the idea
+
+ align:start position:0%
+sum of cosines we talked about the idea
+ 
+
+ align:start position:0%
+sum of cosines we talked about the idea
+that you only need to consider cosines
+
+ align:start position:0%
+that you only need to consider cosines
+ 
+
+ align:start position:0%
+that you only need to consider cosines
+that are integer multiples of Omega not
+
+ align:start position:0%
+that are integer multiples of Omega not
+ 
+
+ align:start position:0%
+that are integer multiples of Omega not
+because those are the only cosine
+
+ align:start position:0%
+because those are the only cosine
+ 
+
+ align:start position:0%
+because those are the only cosine
+functions those are the only functions
+
+ align:start position:0%
+functions those are the only functions
+ 
+
+ align:start position:0%
+functions those are the only functions
+that also are periodic at frequency
+
+ align:start position:0%
+that also are periodic at frequency
+ 
+
+ align:start position:0%
+that also are periodic at frequency
+Omega naught right so a function cosine
+
+ align:start position:0%
+Omega naught right so a function cosine
+ 
+
+ align:start position:0%
+Omega naught right so a function cosine
+3 Omega naught T is also periodic at
+
+ align:start position:0%
+3 Omega naught T is also periodic at
+ 
+
+ align:start position:0%
+3 Omega naught T is also periodic at
+frequency Omega naught does that make
+
+ align:start position:0%
+frequency Omega naught does that make
+ 
+
+ align:start position:0%
+frequency Omega naught does that make
+sense ok so now we can approximate any
+
+ align:start position:0%
+sense ok so now we can approximate any
+ 
+
+ align:start position:0%
+sense ok so now we can approximate any
+periodic function in this case any even
+
+ align:start position:0%
+periodic function in this case any even
+ 
+
+ align:start position:0%
+periodic function in this case any even
+or symmetric periodic function
+
+ align:start position:0%
+or symmetric periodic function
+ 
+
+ align:start position:0%
+or symmetric periodic function
+as a sum of cosines of frequency the
+
+ align:start position:0%
+as a sum of cosines of frequency the
+ 
+
+ align:start position:0%
+as a sum of cosines of frequency the
+frequencies that are integer multiples
+
+ align:start position:0%
+frequencies that are integer multiples
+ 
+
+ align:start position:0%
+frequencies that are integer multiples
+of Omega not and each one of those
+
+ align:start position:0%
+of Omega not and each one of those
+ 
+
+ align:start position:0%
+of Omega not and each one of those
+cosines will have a different
+
+ align:start position:0%
+cosines will have a different
+ 
+
+ align:start position:0%
+cosines will have a different
+coefficient so here's an example where
+
+ align:start position:0%
+coefficient so here's an example where
+ 
+
+ align:start position:0%
+coefficient so here's an example where
+I'm approximating this square wave here
+
+ align:start position:0%
+I'm approximating this square wave here
+ 
+
+ align:start position:0%
+I'm approximating this square wave here
+as a sum of cosines of these different
+
+ align:start position:0%
+as a sum of cosines of these different
+ 
+
+ align:start position:0%
+as a sum of cosines of these different
+frequencies and it turns out for a
+
+ align:start position:0%
+frequencies and it turns out for a
+ 
+
+ align:start position:0%
+frequencies and it turns out for a
+square wave you only need the odd
+
+ align:start position:0%
+square wave you only need the odd
+ 
+
+ align:start position:0%
+square wave you only need the odd
+multiples of Omega not so here's what
+
+ align:start position:0%
+multiples of Omega not so here's what
+ 
+
+ align:start position:0%
+multiples of Omega not so here's what
+this approximation looks like for the
+
+ align:start position:0%
+this approximation looks like for the
+ 
+
+ align:start position:0%
+this approximation looks like for the
+case where you only have a single cosine
+
+ align:start position:0%
+case where you only have a single cosine
+ 
+
+ align:start position:0%
+case where you only have a single cosine
+function you can add another cosine of
+
+ align:start position:0%
+function you can add another cosine of
+ 
+
+ align:start position:0%
+function you can add another cosine of
+three Omega naught T and you can see
+
+ align:start position:0%
+three Omega naught T and you can see
+ 
+
+ align:start position:0%
+three Omega naught T and you can see
+that that function starts getting a
+
+ align:start position:0%
+that that function starts getting a
+ 
+
+ align:start position:0%
+that that function starts getting a
+little bit more square you can add a
+
+ align:start position:0%
+little bit more square you can add a
+ 
+
+ align:start position:0%
+little bit more square you can add a
+cosine 5 Omega naught T and as you keep
+
+ align:start position:0%
+cosine 5 Omega naught T and as you keep
+ 
+
+ align:start position:0%
+cosine 5 Omega naught T and as you keep
+adding those things again with the
+
+ align:start position:0%
+adding those things again with the
+ 
+
+ align:start position:0%
+adding those things again with the
+correct coefficients in front of these
+
+ align:start position:0%
+correct coefficients in front of these
+ 
+
+ align:start position:0%
+correct coefficients in front of these
+you can see that the function more and
+
+ align:start position:0%
+you can see that the function more and
+ 
+
+ align:start position:0%
+you can see that the function more and
+more closely approximates the square
+
+ align:start position:0%
+more closely approximates the square
+ 
+
+ align:start position:0%
+more closely approximates the square
+wave that we're trying to yes happy but
+
+ align:start position:0%
+wave that we're trying to yes happy but
+ 
+
+ align:start position:0%
+wave that we're trying to yes happy but
+it just it's in general you need all the
+
+ align:start position:0%
+it just it's in general you need all the
+ 
+
+ align:start position:0%
+it just it's in general you need all the
+multiples but for this particular
+
+ align:start position:0%
+multiples but for this particular
+ 
+
+ align:start position:0%
+multiples but for this particular
+function you only need the odd ones okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here's another example so in this
+
+ align:start position:0%
+okay here's another example so in this
+ 
+
+ align:start position:0%
+okay here's another example so in this
+case work we are summing together cosine
+
+ align:start position:0%
+case work we are summing together cosine
+ 
+
+ align:start position:0%
+case work we are summing together cosine
+functions to approximate a train of
+
+ align:start position:0%
+functions to approximate a train of
+ 
+
+ align:start position:0%
+functions to approximate a train of
+pulses okay so the signal we're trying
+
+ align:start position:0%
+pulses okay so the signal we're trying
+ 
+
+ align:start position:0%
+pulses okay so the signal we're trying
+to approximate here it just has a pulse
+
+ align:start position:0%
+to approximate here it just has a pulse
+ 
+
+ align:start position:0%
+to approximate here it just has a pulse
+every one unit of time one one period
+
+ align:start position:0%
+every one unit of time one one period
+ 
+
+ align:start position:0%
+every one unit of time one one period
+and you can see that to approximate this
+
+ align:start position:0%
+and you can see that to approximate this
+ 
+
+ align:start position:0%
+and you can see that to approximate this
+we can basically just sum up all the
+
+ align:start position:0%
+we can basically just sum up all the
+ 
+
+ align:start position:0%
+we can basically just sum up all the
+cosines of all frequencies n Omega
+
+ align:start position:0%
+cosines of all frequencies n Omega
+ 
+
+ align:start position:0%
+cosines of all frequencies n Omega
+naught and you can see that at time zero
+
+ align:start position:0%
+naught and you can see that at time zero
+ 
+
+ align:start position:0%
+naught and you can see that at time zero
+all of those functions are positive
+
+ align:start position:0%
+all of those functions are positive
+ 
+
+ align:start position:0%
+all of those functions are positive
+right and so all those positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contributions to that sum all add up and
+
+ align:start position:0%
+contributions to that sum all add up and
+ 
+
+ align:start position:0%
+contributions to that sum all add up and
+as you add them up and get a big pink
+
+ align:start position:0%
+as you add them up and get a big pink
+ 
+
+ align:start position:0%
+as you add them up and get a big pink
+that's called constructive interference
+
+ align:start position:0%
+that's called constructive interference
+ 
+
+ align:start position:0%
+that's called constructive interference
+so all those Peaks add up but in this
+
+ align:start position:0%
+so all those Peaks add up but in this
+ 
+
+ align:start position:0%
+so all those Peaks add up but in this
+and and you also get those Peaks all
+
+ align:start position:0%
+and and you also get those Peaks all
+ 
+
+ align:start position:0%
+and and you also get those Peaks all
+adding up one period away right
+
+ align:start position:0%
+adding up one period away right
+ 
+
+ align:start position:0%
+adding up one period away right
+one period of cosine Omega not you can
+
+ align:start position:0%
+one period of cosine Omega not you can
+ 
+
+ align:start position:0%
+one period of cosine Omega not you can
+see they add up again so you can see
+
+ align:start position:0%
+see they add up again so you can see
+ 
+
+ align:start position:0%
+see they add up again so you can see
+this is a periodic function in this in
+
+ align:start position:0%
+this is a periodic function in this in
+ 
+
+ align:start position:0%
+this is a periodic function in this in
+this time window between those Peaks you
+
+ align:start position:0%
+this time window between those Peaks you
+ 
+
+ align:start position:0%
+this time window between those Peaks you
+can see that you have positive peaks of
+
+ align:start position:0%
+can see that you have positive peaks of
+ 
+
+ align:start position:0%
+can see that you have positive peaks of
+some of those cosines negative Peaks
+
+ align:start position:0%
+some of those cosines negative Peaks
+ 
+
+ align:start position:0%
+some of those cosines negative Peaks
+positive negative they just sort of all
+
+ align:start position:0%
+positive negative they just sort of all
+ 
+
+ align:start position:0%
+positive negative they just sort of all
+add up they interfere with with each
+
+ align:start position:0%
+add up they interfere with with each
+ 
+
+ align:start position:0%
+add up they interfere with with each
+other destructively to give you a zero
+
+ align:start position:0%
+other destructively to give you a zero
+ 
+
+ align:start position:0%
+other destructively to give you a zero
+in the intervals between the peaks
+
+ align:start position:0%
+in the intervals between the peaks
+ 
+
+ align:start position:0%
+in the intervals between the peaks
+does that make sense and so basically by
+
+ align:start position:0%
+does that make sense and so basically by
+ 
+
+ align:start position:0%
+does that make sense and so basically by
+choosing the amplitudes of these
+
+ align:start position:0%
+choosing the amplitudes of these
+ 
+
+ align:start position:0%
+choosing the amplitudes of these
+different cosine functions you can
+
+ align:start position:0%
+different cosine functions you can
+ 
+
+ align:start position:0%
+different cosine functions you can
+basically build any arbitrary function
+
+ align:start position:0%
+basically build any arbitrary function
+ 
+
+ align:start position:0%
+basically build any arbitrary function
+periodic function down here that makes
+
+ align:start position:0%
+periodic function down here that makes
+ 
+
+ align:start position:0%
+periodic function down here that makes
+sense okay all right
+
+ align:start position:0%
+sense okay all right
+ 
+
+ align:start position:0%
+sense okay all right
+there's one more element that we need to
+
+ align:start position:0%
+there's one more element that we need to
+ 
+
+ align:start position:0%
+there's one more element that we need to
+add here for our Fourier series for even
+
+ align:start position:0%
+add here for our Fourier series for even
+ 
+
+ align:start position:0%
+add here for our Fourier series for even
+functions anybody have any idea what
+
+ align:start position:0%
+functions anybody have any idea what
+ 
+
+ align:start position:0%
+functions anybody have any idea what
+that is notice here I've shifted this
+
+ align:start position:0%
+that is notice here I've shifted this
+ 
+
+ align:start position:0%
+that is notice here I've shifted this
+function up a little bit so it's not
+
+ align:start position:0%
+function up a little bit so it's not
+ 
+
+ align:start position:0%
+function up a little bit so it's not
+centered at zero a constant term was
+
+ align:start position:0%
+centered at zero a constant term was
+ 
+
+ align:start position:0%
+centered at zero a constant term was
+called a DC term okay we basically take
+
+ align:start position:0%
+called a DC term okay we basically take
+ 
+
+ align:start position:0%
+called a DC term okay we basically take
+the average of that function we add it
+
+ align:start position:0%
+the average of that function we add it
+ 
+
+ align:start position:0%
+the average of that function we add it
+here that's called a DC term okay a
+
+ align:start position:0%
+here that's called a DC term okay a
+ 
+
+ align:start position:0%
+here that's called a DC term okay a
+naught over two is essentially the
+
+ align:start position:0%
+naught over two is essentially the
+ 
+
+ align:start position:0%
+naught over two is essentially the
+average of the function we're trying to
+
+ align:start position:0%
+average of the function we're trying to
+ 
+
+ align:start position:0%
+average of the function we're trying to
+approximate okay all right good we can
+
+ align:start position:0%
+approximate okay all right good we can
+ 
+
+ align:start position:0%
+approximate okay all right good we can
+now write that as a sum why even of T
+
+ align:start position:0%
+now write that as a sum why even of T
+ 
+
+ align:start position:0%
+now write that as a sum why even of T
+equals a naught over two plus a sum over
+
+ align:start position:0%
+equals a naught over two plus a sum over
+ 
+
+ align:start position:0%
+equals a naught over two plus a sum over
+all these different ends of a sub n
+
+ align:start position:0%
+all these different ends of a sub n
+ 
+
+ align:start position:0%
+all these different ends of a sub n
+which is a coefficient times cosine n
+
+ align:start position:0%
+which is a coefficient times cosine n
+ 
+
+ align:start position:0%
+which is a coefficient times cosine n
+Omega naught T Omega naught is 1 over
+
+ align:start position:0%
+Omega naught T Omega naught is 1 over
+ 
+
+ align:start position:0%
+Omega naught T Omega naught is 1 over
+there's 2 pi over this this time
+
+ align:start position:0%
+there's 2 pi over this this time
+ 
+
+ align:start position:0%
+there's 2 pi over this this time
+interval here the periodicity okay all
+
+ align:start position:0%
+interval here the periodicity okay all
+ 
+
+ align:start position:0%
+interval here the periodicity okay all
+right good how do we find those
+
+ align:start position:0%
+right good how do we find those
+ 
+
+ align:start position:0%
+right good how do we find those
+coefficients so I just told you that the
+
+ align:start position:0%
+coefficients so I just told you that the
+ 
+
+ align:start position:0%
+coefficients so I just told you that the
+first coefficient the a naught over 2 is
+
+ align:start position:0%
+first coefficient the a naught over 2 is
+ 
+
+ align:start position:0%
+first coefficient the a naught over 2 is
+just the average of our function T over
+
+ align:start position:0%
+just the average of our function T over
+ 
+
+ align:start position:0%
+just the average of our function T over
+one time window from minus T over 2 to
+
+ align:start position:0%
+one time window from minus T over 2 to
+ 
+
+ align:start position:0%
+one time window from minus T over 2 to
+plus T over 2 it's just the integral of
+
+ align:start position:0%
+plus T over 2 it's just the integral of
+ 
+
+ align:start position:0%
+plus T over 2 it's just the integral of
+that function over one period divided by
+
+ align:start position:0%
+that function over one period divided by
+ 
+
+ align:start position:0%
+that function over one period divided by
+T and that gives you the average which
+
+ align:start position:0%
+T and that gives you the average which
+ 
+
+ align:start position:0%
+T and that gives you the average which
+is a naught over 2 all right any
+
+ align:start position:0%
+is a naught over 2 all right any
+ 
+
+ align:start position:0%
+is a naught over 2 all right any
+questions about that it's pretty
+
+ align:start position:0%
+questions about that it's pretty
+ 
+
+ align:start position:0%
+questions about that it's pretty
+straightforward what about this next
+
+ align:start position:0%
+straightforward what about this next
+ 
+
+ align:start position:0%
+straightforward what about this next
+coefficient a 1 so the a 1 coefficient
+
+ align:start position:0%
+coefficient a 1 so the a 1 coefficient
+ 
+
+ align:start position:0%
+coefficient a 1 so the a 1 coefficient
+is just the overlap of our function y of
+
+ align:start position:0%
+is just the overlap of our function y of
+ 
+
+ align:start position:0%
+is just the overlap of our function y of
+T with
+
+ align:start position:0%
+T with
+ 
+
+ align:start position:0%
+T with
+this cosine okay we're just we're just
+
+ align:start position:0%
+this cosine okay we're just we're just
+ 
+
+ align:start position:0%
+this cosine okay we're just we're just
+multiplying why not
+
+ align:start position:0%
+multiplying why not
+ 
+
+ align:start position:0%
+multiplying why not
+times cosine of Omega naught T
+
+ align:start position:0%
+times cosine of Omega naught T
+ 
+
+ align:start position:0%
+times cosine of Omega naught T
+integrating over time and then
+
+ align:start position:0%
+integrating over time and then
+ 
+
+ align:start position:0%
+integrating over time and then
+multiplying by 2 over T ok so that's
+
+ align:start position:0%
+multiplying by 2 over T ok so that's
+ 
+
+ align:start position:0%
+multiplying by 2 over T ok so that's
+that's the answer
+
+ align:start position:0%
+that's the answer
+ 
+
+ align:start position:0%
+that's the answer
+and I'm gonna explain why that is okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is just a correlation right it's
+
+ align:start position:0%
+that is just a correlation right it's
+ 
+
+ align:start position:0%
+that is just a correlation right it's
+it's just like asking how much - let's
+
+ align:start position:0%
+it's just like asking how much - let's
+ 
+
+ align:start position:0%
+it's just like asking how much - let's
+say we had a neuron with a receptive
+
+ align:start position:0%
+say we had a neuron with a receptive
+ 
+
+ align:start position:0%
+say we had a neuron with a receptive
+field of cosine Omega naught T we're
+
+ align:start position:0%
+field of cosine Omega naught T we're
+ 
+
+ align:start position:0%
+field of cosine Omega naught T we're
+asking how well does our signal overlap
+
+ align:start position:0%
+asking how well does our signal overlap
+ 
+
+ align:start position:0%
+asking how well does our signal overlap
+with that receptive field does that make
+
+ align:start position:0%
+with that receptive field does that make
+ 
+
+ align:start position:0%
+with that receptive field does that make
+sense we're just correlating our signal
+
+ align:start position:0%
+sense we're just correlating our signal
+ 
+
+ align:start position:0%
+sense we're just correlating our signal
+with some basis function with some
+
+ align:start position:0%
+with some basis function with some
+ 
+
+ align:start position:0%
+with some basis function with some
+receptive field and we're asking how
+
+ align:start position:0%
+receptive field and we're asking how
+ 
+
+ align:start position:0%
+receptive field and we're asking how
+much overlap is there okay
+
+ align:start position:0%
+much overlap is there okay
+ 
+
+ align:start position:0%
+much overlap is there okay
+the a2 coefficient is just the overlap
+
+ align:start position:0%
+the a2 coefficient is just the overlap
+ 
+
+ align:start position:0%
+the a2 coefficient is just the overlap
+of the function y with cosine 2 Omega
+
+ align:start position:0%
+of the function y with cosine 2 Omega
+ 
+
+ align:start position:0%
+of the function y with cosine 2 Omega
+naught T and the a sub n coefficient is
+
+ align:start position:0%
+naught T and the a sub n coefficient is
+ 
+
+ align:start position:0%
+naught T and the a sub n coefficient is
+just the overlap with cosine n Omega
+
+ align:start position:0%
+just the overlap with cosine n Omega
+ 
+
+ align:start position:0%
+just the overlap with cosine n Omega
+naught T ok just like that and you can
+
+ align:start position:0%
+naught T ok just like that and you can
+ 
+
+ align:start position:0%
+naught T ok just like that and you can
+see that that this average that we took
+
+ align:start position:0%
+see that that this average that we took
+ 
+
+ align:start position:0%
+see that that this average that we took
+up here just is the generalization of
+
+ align:start position:0%
+up here just is the generalization of
+ 
+
+ align:start position:0%
+up here just is the generalization of
+this - the overlap of our function -
+
+ align:start position:0%
+this - the overlap of our function -
+ 
+
+ align:start position:0%
+this - the overlap of our function -
+cosine 0 Omega naught T cosine 0 Omega
+
+ align:start position:0%
+cosine 0 Omega naught T cosine 0 Omega
+ 
+
+ align:start position:0%
+cosine 0 Omega naught T cosine 0 Omega
+naught T is just 1 right and so this
+
+ align:start position:0%
+naught T is just 1 right and so this
+ 
+
+ align:start position:0%
+naught T is just 1 right and so this
+coefficient a naught is just looks the
+
+ align:start position:0%
+coefficient a naught is just looks the
+ 
+
+ align:start position:0%
+coefficient a naught is just looks the
+same as this
+
+ align:start position:0%
+same as this
+ 
+
+ align:start position:0%
+same as this
+it's just that in this case it turns out
+
+ align:start position:0%
+it's just that in this case it turns out
+ 
+
+ align:start position:0%
+it's just that in this case it turns out
+to be the average of the function okay
+
+ align:start position:0%
+to be the average of the function okay
+ 
+
+ align:start position:0%
+to be the average of the function okay
+any questions about that okay so that is
+
+ align:start position:0%
+any questions about that okay so that is
+ 
+
+ align:start position:0%
+any questions about that okay so that is
+in general how you calculate those
+
+ align:start position:0%
+in general how you calculate those
+ 
+
+ align:start position:0%
+in general how you calculate those
+coefficients so you would literally just
+
+ align:start position:0%
+coefficients so you would literally just
+ 
+
+ align:start position:0%
+coefficients so you would literally just
+take your function multiply it by a
+
+ align:start position:0%
+take your function multiply it by a
+ 
+
+ align:start position:0%
+take your function multiply it by a
+cosine of some frequency integrate it
+
+ align:start position:0%
+cosine of some frequency integrate it
+ 
+
+ align:start position:0%
+cosine of some frequency integrate it
+and that's the answer okay all right
+
+ align:start position:0%
+and that's the answer okay all right
+ 
+
+ align:start position:0%
+and that's the answer okay all right
+let's just take a look at what some of
+
+ align:start position:0%
+let's just take a look at what some of
+ 
+
+ align:start position:0%
+let's just take a look at what some of
+these coefficients are for some really
+
+ align:start position:0%
+these coefficients are for some really
+ 
+
+ align:start position:0%
+these coefficients are for some really
+simple functions okay
+
+ align:start position:0%
+simple functions okay
+ 
+
+ align:start position:0%
+simple functions okay
+so there I've rewritten what each of
+
+ align:start position:0%
+so there I've rewritten what each of
+ 
+
+ align:start position:0%
+so there I've rewritten what each of
+those coefficients is as an integral and
+
+ align:start position:0%
+those coefficients is as an integral and
+ 
+
+ align:start position:0%
+those coefficients is as an integral and
+now let's consider the following
+
+ align:start position:0%
+now let's consider the following
+ 
+
+ align:start position:0%
+now let's consider the following
+function so let's say our function is 1
+
+ align:start position:0%
+function so let's say our function is 1
+ 
+
+ align:start position:0%
+function so let's say our function is 1
+it's just a constant at 1 so you can see
+
+ align:start position:0%
+it's just a constant at 1 so you can see
+ 
+
+ align:start position:0%
+it's just a constant at 1 so you can see
+that this integral right from minus T
+
+ align:start position:0%
+that this integral right from minus T
+ 
+
+ align:start position:0%
+that this integral right from minus T
+over 2 to T over 2 that integral is just
+
+ align:start position:0%
+over 2 to T over 2 that integral is just
+ 
+
+ align:start position:0%
+over 2 to T over 2 that integral is just
+T multiplied by 2 over T gives that
+
+ align:start position:0%
+T multiplied by 2 over T gives that
+ 
+
+ align:start position:0%
+T multiplied by 2 over T gives that
+coefficient is just 2 okay if our
+
+ align:start position:0%
+coefficient is just 2 okay if our
+ 
+
+ align:start position:0%
+coefficient is just 2 okay if our
+function is cosine Omega naught T you
+
+ align:start position:0%
+function is cosine Omega naught T you
+ 
+
+ align:start position:0%
+function is cosine Omega naught T you
+can see that if you put a cosine in here
+
+ align:start position:0%
+can see that if you put a cosine in here
+ 
+
+ align:start position:0%
+can see that if you put a cosine in here
+that averages to 0 if you put a cosine
+
+ align:start position:0%
+that averages to 0 if you put a cosine
+ 
+
+ align:start position:0%
+that averages to 0 if you put a cosine
+in here you get cosine squared the
+
+ align:start position:0%
+in here you get cosine squared the
+ 
+
+ align:start position:0%
+in here you get cosine squared the
+integral of cosine squared is just it's
+
+ align:start position:0%
+integral of cosine squared is just it's
+ 
+
+ align:start position:0%
+integral of cosine squared is just it's
+it's just half of the you know basically
+
+ align:start position:0%
+it's just half of the you know basically
+ 
+
+ align:start position:0%
+it's just half of the you know basically
+the full range so that's just T over 2
+
+ align:start position:0%
+the full range so that's just T over 2
+ 
+
+ align:start position:0%
+the full range so that's just T over 2
+when you multiply by 2 over T you get 1
+
+ align:start position:0%
+when you multiply by 2 over T you get 1
+ 
+
+ align:start position:0%
+when you multiply by 2 over T you get 1
+okay and the coefficient a 2 for a
+
+ align:start position:0%
+okay and the coefficient a 2 for a
+ 
+
+ align:start position:0%
+okay and the coefficient a 2 for a
+function cosine Omega T is 0 because the
+
+ align:start position:0%
+function cosine Omega T is 0 because the
+ 
+
+ align:start position:0%
+function cosine Omega T is 0 because the
+integral of cosine Omega naught T times
+
+ align:start position:0%
+integral of cosine Omega naught T times
+ 
+
+ align:start position:0%
+integral of cosine Omega naught T times
+cosine 2 Omega naught T is 0 ok all
+
+ align:start position:0%
+cosine 2 Omega naught T is 0 ok all
+ 
+
+ align:start position:0%
+cosine 2 Omega naught T is 0 ok all
+right if we have a function cosine 2
+
+ align:start position:0%
+right if we have a function cosine 2
+ 
+
+ align:start position:0%
+right if we have a function cosine 2
+Omega naught T then these coefficients
+
+ align:start position:0%
+Omega naught T then these coefficients
+ 
+
+ align:start position:0%
+Omega naught T then these coefficients
+are 0 and that coefficient is 1 you can
+
+ align:start position:0%
+are 0 and that coefficient is 1 you can
+ 
+
+ align:start position:0%
+are 0 and that coefficient is 1 you can
+see that you have this interesting thing
+
+ align:start position:0%
+see that you have this interesting thing
+ 
+
+ align:start position:0%
+see that you have this interesting thing
+here if your function is cosine Omega
+
+ align:start position:0%
+here if your function is cosine Omega
+ 
+
+ align:start position:0%
+here if your function is cosine Omega
+naught T then the only coefficient
+
+ align:start position:0%
+naught T then the only coefficient
+ 
+
+ align:start position:0%
+naught T then the only coefficient
+that's nonzero is the one that you're
+
+ align:start position:0%
+that's nonzero is the one that you're
+ 
+
+ align:start position:0%
+that's nonzero is the one that you're
+overlapping with cosine Omega naught T
+
+ align:start position:0%
+overlapping with cosine Omega naught T
+ 
+
+ align:start position:0%
+overlapping with cosine Omega naught T
+it's it's this only this first
+
+ align:start position:0%
+it's it's this only this first
+ 
+
+ align:start position:0%
+it's it's this only this first
+coefficient that's nonzero if your
+
+ align:start position:0%
+coefficient that's nonzero if your
+ 
+
+ align:start position:0%
+coefficient that's nonzero if your
+function has frequencies a frequency 2
+
+ align:start position:0%
+function has frequencies a frequency 2
+ 
+
+ align:start position:0%
+function has frequencies a frequency 2
+Omega naught T then the only coefficient
+
+ align:start position:0%
+Omega naught T then the only coefficient
+ 
+
+ align:start position:0%
+Omega naught T then the only coefficient
+that's nonzero is the a two okay so what
+
+ align:start position:0%
+that's nonzero is the a two okay so what
+ 
+
+ align:start position:0%
+that's nonzero is the a two okay so what
+that means is that if the function has
+
+ align:start position:0%
+that means is that if the function has
+ 
+
+ align:start position:0%
+that means is that if the function has
+maximal overlap if it overlaps one of
+
+ align:start position:0%
+maximal overlap if it overlaps one of
+ 
+
+ align:start position:0%
+maximal overlap if it overlaps one of
+those cosines then it has zero overlap
+
+ align:start position:0%
+those cosines then it has zero overlap
+ 
+
+ align:start position:0%
+those cosines then it has zero overlap
+with all the others and we can say that
+
+ align:start position:0%
+with all the others and we can say that
+ 
+
+ align:start position:0%
+with all the others and we can say that
+that set of cosine functions cosine
+
+ align:start position:0%
+that set of cosine functions cosine
+ 
+
+ align:start position:0%
+that set of cosine functions cosine
+Omega naught T cosine 2 Omega naught T
+
+ align:start position:0%
+Omega naught T cosine 2 Omega naught T
+ 
+
+ align:start position:0%
+Omega naught T cosine 2 Omega naught T
+forms what's called an orthogonal basis
+
+ align:start position:0%
+forms what's called an orthogonal basis
+ 
+
+ align:start position:0%
+forms what's called an orthogonal basis
+set we're gonna spend a lot of time
+
+ align:start position:0%
+set we're gonna spend a lot of time
+ 
+
+ align:start position:0%
+set we're gonna spend a lot of time
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+basis set later but I've just gonna
+
+ align:start position:0%
+basis set later but I've just gonna
+ 
+
+ align:start position:0%
+basis set later but I've just gonna
+throw this word out to you so that
+
+ align:start position:0%
+throw this word out to you so that
+ 
+
+ align:start position:0%
+throw this word out to you so that
+you've heard it when I come back to the
+
+ align:start position:0%
+you've heard it when I come back to the
+ 
+
+ align:start position:0%
+you've heard it when I come back to the
+idea of basis sets later you're gonna
+
+ align:start position:0%
+idea of basis sets later you're gonna
+ 
+
+ align:start position:0%
+idea of basis sets later you're gonna
+see this connection okay so the basic
+
+ align:start position:0%
+see this connection okay so the basic
+ 
+
+ align:start position:0%
+see this connection okay so the basic
+idea is that what we're doing is we're
+
+ align:start position:0%
+idea is that what we're doing is we're
+ 
+
+ align:start position:0%
+idea is that what we're doing is we're
+taking our signal which is a vector it's
+
+ align:start position:0%
+taking our signal which is a vector it's
+ 
+
+ align:start position:0%
+taking our signal which is a vector it's
+a set of points in time we can think of
+
+ align:start position:0%
+a set of points in time we can think of
+ 
+
+ align:start position:0%
+a set of points in time we can think of
+that as a vector in a high dimensional
+
+ align:start position:0%
+that as a vector in a high dimensional
+ 
+
+ align:start position:0%
+that as a vector in a high dimensional
+space and we're simply expressing it in
+
+ align:start position:0%
+space and we're simply expressing it in
+ 
+
+ align:start position:0%
+space and we're simply expressing it in
+a new basis set okay of cosines of
+
+ align:start position:0%
+a new basis set okay of cosines of
+ 
+
+ align:start position:0%
+a new basis set okay of cosines of
+different frequencies so each of those
+
+ align:start position:0%
+different frequencies so each of those
+ 
+
+ align:start position:0%
+different frequencies so each of those
+functions cosine n Omega T is like a
+
+ align:start position:0%
+functions cosine n Omega T is like a
+ 
+
+ align:start position:0%
+functions cosine n Omega T is like a
+vector in a basis set our signal like a
+
+ align:start position:0%
+vector in a basis set our signal like a
+ 
+
+ align:start position:0%
+vector in a basis set our signal like a
+vector and what we're doing is when
+
+ align:start position:0%
+vector and what we're doing is when
+ 
+
+ align:start position:0%
+vector and what we're doing is when
+we're doing these projections
+
+ align:start position:0%
+we're doing these projections
+ 
+
+ align:start position:0%
+we're doing these projections
+we're simply computing the projection of
+
+ align:start position:0%
+we're simply computing the projection of
+ 
+
+ align:start position:0%
+we're simply computing the projection of
+our of that vector our signal onto these
+
+ align:start position:0%
+our of that vector our signal onto these
+ 
+
+ align:start position:0%
+our of that vector our signal onto these
+different basis functions these
+
+ align:start position:0%
+different basis functions these
+ 
+
+ align:start position:0%
+different basis functions these
+different basis vectors okay so we're
+
+ align:start position:0%
+different basis vectors okay so we're
+ 
+
+ align:start position:0%
+different basis vectors okay so we're
+just finding the Proficient so that we
+
+ align:start position:0%
+just finding the Proficient so that we
+ 
+
+ align:start position:0%
+just finding the Proficient so that we
+can express our signal as a sum of a
+
+ align:start position:0%
+can express our signal as a sum of a
+ 
+
+ align:start position:0%
+can express our signal as a sum of a
+coefficient times a basis vector plus
+
+ align:start position:0%
+coefficient times a basis vector plus
+ 
+
+ align:start position:0%
+coefficient times a basis vector plus
+another coefficient times another basis
+
+ align:start position:0%
+another coefficient times another basis
+ 
+
+ align:start position:0%
+another coefficient times another basis
+vector and so on okay so for example in
+
+ align:start position:0%
+vector and so on okay so for example in
+ 
+
+ align:start position:0%
+vector and so on okay so for example in
+the simple standard basis where this
+
+ align:start position:0%
+the simple standard basis where this
+ 
+
+ align:start position:0%
+the simple standard basis where this
+vector is 0 1 and that vector is 1 0 you
+
+ align:start position:0%
+vector is 0 1 and that vector is 1 0 you
+ 
+
+ align:start position:0%
+vector is 0 1 and that vector is 1 0 you
+can write down an arbitrary vector as a
+
+ align:start position:0%
+can write down an arbitrary vector as a
+ 
+
+ align:start position:0%
+can write down an arbitrary vector as a
+coefficient times this plus another
+
+ align:start position:0%
+coefficient times this plus another
+ 
+
+ align:start position:0%
+coefficient times this plus another
+coefficient times that that makes sense
+
+ align:start position:0%
+coefficient times that that makes sense
+ 
+
+ align:start position:0%
+coefficient times that that makes sense
+ok and how do we find those coefficients
+
+ align:start position:0%
+ok and how do we find those coefficients
+ 
+
+ align:start position:0%
+ok and how do we find those coefficients
+we just take our vector and dot it onto
+
+ align:start position:0%
+we just take our vector and dot it onto
+ 
+
+ align:start position:0%
+we just take our vector and dot it onto
+each one of these basis vectors X x2
+
+ align:start position:0%
+each one of these basis vectors X x2
+ 
+
+ align:start position:0%
+each one of these basis vectors X x2
+that make sense ok you don't you don't
+
+ align:start position:0%
+that make sense ok you don't you don't
+ 
+
+ align:start position:0%
+that make sense ok you don't you don't
+need to like know this for this section
+
+ align:start position:0%
+need to like know this for this section
+ 
+
+ align:start position:0%
+need to like know this for this section
+ok but we're gonna come back to so I
+
+ align:start position:0%
+ok but we're gonna come back to so I
+ 
+
+ align:start position:0%
+ok but we're gonna come back to so I
+would like you to eventually kind of
+
+ align:start position:0%
+would like you to eventually kind of
+ 
+
+ align:start position:0%
+would like you to eventually kind of
+combine these views of taking signals
+
+ align:start position:0%
+combine these views of taking signals
+ 
+
+ align:start position:0%
+combine these views of taking signals
+and and looking at projections of those
+
+ align:start position:0%
+and and looking at projections of those
+ 
+
+ align:start position:0%
+and and looking at projections of those
+into new basis sets ok and as you know
+
+ align:start position:0%
+into new basis sets ok and as you know
+ 
+
+ align:start position:0%
+into new basis sets ok and as you know
+how you see things depends on how you're
+
+ align:start position:0%
+how you see things depends on how you're
+ 
+
+ align:start position:0%
+how you see things depends on how you're
+looking at them the direction that you
+
+ align:start position:0%
+looking at them the direction that you
+ 
+
+ align:start position:0%
+looking at them the direction that you
+look at them that's what we're doing
+
+ align:start position:0%
+look at them that's what we're doing
+ 
+
+ align:start position:0%
+look at them that's what we're doing
+when we take a signal and we project it
+
+ align:start position:0%
+when we take a signal and we project it
+ 
+
+ align:start position:0%
+when we take a signal and we project it
+onto a function
+
+ align:start position:0%
+onto a function
+ 
+
+ align:start position:0%
+onto a function
+we're taking a particular view of that
+
+ align:start position:0%
+we're taking a particular view of that
+ 
+
+ align:start position:0%
+we're taking a particular view of that
+function okay so so as you know the view
+
+ align:start position:0%
+function okay so so as you know the view
+ 
+
+ align:start position:0%
+function okay so so as you know the view
+you have on something has a big impact
+
+ align:start position:0%
+you have on something has a big impact
+ 
+
+ align:start position:0%
+you have on something has a big impact
+on what you see right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's all we're doing is we're
+
+ align:start position:0%
+so that's all we're doing is we're
+ 
+
+ align:start position:0%
+so that's all we're doing is we're
+taking functions and finding the
+
+ align:start position:0%
+taking functions and finding the
+ 
+
+ align:start position:0%
+taking functions and finding the
+projection on which we can see something
+
+ align:start position:0%
+projection on which we can see something
+ 
+
+ align:start position:0%
+projection on which we can see something
+interesting okay that's it that's all
+
+ align:start position:0%
+interesting okay that's it that's all
+ 
+
+ align:start position:0%
+interesting okay that's it that's all
+spectral analysis is and the particular
+
+ align:start position:0%
+spectral analysis is and the particular
+ 
+
+ align:start position:0%
+spectral analysis is and the particular
+views we're looking at are projections
+
+ align:start position:0%
+views we're looking at are projections
+ 
+
+ align:start position:0%
+views we're looking at are projections
+on two different periodic functions
+
+ align:start position:0%
+on two different periodic functions
+ 
+
+ align:start position:0%
+on two different periodic functions
+okay cosines of different frequencies
+
+ align:start position:0%
+okay cosines of different frequencies
+ 
+
+ align:start position:0%
+okay cosines of different frequencies
+all right and what you find is that for
+
+ align:start position:0%
+all right and what you find is that for
+ 
+
+ align:start position:0%
+all right and what you find is that for
+periodic signals there are certain views
+
+ align:start position:0%
+periodic signals there are certain views
+ 
+
+ align:start position:0%
+periodic signals there are certain views
+where something magically pops out and
+
+ align:start position:0%
+where something magically pops out and
+ 
+
+ align:start position:0%
+where something magically pops out and
+you see what's there that you can't see
+
+ align:start position:0%
+you see what's there that you can't see
+ 
+
+ align:start position:0%
+you see what's there that you can't see
+when you just look at the time domain
+
+ align:start position:0%
+when you just look at the time domain
+ 
+
+ align:start position:0%
+when you just look at the time domain
+okay all right so we we looked at even
+
+ align:start position:0%
+okay all right so we we looked at even
+ 
+
+ align:start position:0%
+okay all right so we we looked at even
+functions or symmetric functions now
+
+ align:start position:0%
+functions or symmetric functions now
+ 
+
+ align:start position:0%
+functions or symmetric functions now
+let's take a look at odd functions or
+
+ align:start position:0%
+let's take a look at odd functions or
+ 
+
+ align:start position:0%
+let's take a look at odd functions or
+anti-symmetric functions these are
+
+ align:start position:0%
+anti-symmetric functions these are
+ 
+
+ align:start position:0%
+anti-symmetric functions these are
+called odd because the odd polynomials
+
+ align:start position:0%
+called odd because the odd polynomials
+ 
+
+ align:start position:0%
+called odd because the odd polynomials
+you know like X cubed looks like this if
+
+ align:start position:0%
+you know like X cubed looks like this if
+ 
+
+ align:start position:0%
+you know like X cubed looks like this if
+it's negative on one side it's positive
+
+ align:start position:0%
+it's negative on one side it's positive
+ 
+
+ align:start position:0%
+it's negative on one side it's positive
+on the other side same here if it's
+
+ align:start position:0%
+on the other side same here if it's
+ 
+
+ align:start position:0%
+on the other side same here if it's
+negative here then it's positive there
+
+ align:start position:0%
+negative here then it's positive there
+ 
+
+ align:start position:0%
+negative here then it's positive there
+okay so we can we can now write down
+
+ align:start position:0%
+okay so we can we can now write down
+ 
+
+ align:start position:0%
+okay so we can we can now write down
+Fourier series for odd or anti-symmetric
+
+ align:start position:0%
+Fourier series for odd or anti-symmetric
+ 
+
+ align:start position:0%
+Fourier series for odd or anti-symmetric
+functions what do you think we're gonna
+
+ align:start position:0%
+functions what do you think we're gonna
+ 
+
+ align:start position:0%
+functions what do you think we're gonna
+use instead of cosines we're gonna use
+
+ align:start position:0%
+use instead of cosines we're gonna use
+ 
+
+ align:start position:0%
+use instead of cosines we're gonna use
+signs because signs symmetric around
+
+ align:start position:0%
+signs because signs symmetric around
+ 
+
+ align:start position:0%
+signs because signs symmetric around
+anti symmetric around the origin okay
+
+ align:start position:0%
+anti symmetric around the origin okay
+ 
+
+ align:start position:0%
+anti symmetric around the origin okay
+and we're still going to consider
+
+ align:start position:0%
+and we're still going to consider
+ 
+
+ align:start position:0%
+and we're still going to consider
+functions that are periodic was period t
+
+ align:start position:0%
+functions that are periodic was period t
+ 
+
+ align:start position:0%
+functions that are periodic was period t
+we can take any anti symmetric function
+
+ align:start position:0%
+we can take any anti symmetric function
+ 
+
+ align:start position:0%
+we can take any anti symmetric function
+and approximate approximate it as a sum
+
+ align:start position:0%
+and approximate approximate it as a sum
+ 
+
+ align:start position:0%
+and approximate approximate it as a sum
+of sine waves of frequency to PI over T
+
+ align:start position:0%
+of sine waves of frequency to PI over T
+ 
+
+ align:start position:0%
+of sine waves of frequency to PI over T
+or again Omega naught all right and
+
+ align:start position:0%
+or again Omega naught all right and
+ 
+
+ align:start position:0%
+or again Omega naught all right and
+integer multiples of that Omega naught
+
+ align:start position:0%
+integer multiples of that Omega naught
+ 
+
+ align:start position:0%
+integer multiples of that Omega naught
+okay all right so again our odd
+
+ align:start position:0%
+okay all right so again our odd
+ 
+
+ align:start position:0%
+okay all right so again our odd
+functions can be approximated as a sum
+
+ align:start position:0%
+functions can be approximated as a sum
+ 
+
+ align:start position:0%
+functions can be approximated as a sum
+of components contributions of different
+
+ align:start position:0%
+of components contributions of different
+ 
+
+ align:start position:0%
+of components contributions of different
+frequencies with a coefficient times
+
+ align:start position:0%
+frequencies with a coefficient times
+ 
+
+ align:start position:0%
+frequencies with a coefficient times
+sine of Omega naught T plus another
+
+ align:start position:0%
+sine of Omega naught T plus another
+ 
+
+ align:start position:0%
+sine of Omega naught T plus another
+coefficient times sine of 2 Omega naught
+
+ align:start position:0%
+coefficient times sine of 2 Omega naught
+ 
+
+ align:start position:0%
+coefficient times sine of 2 Omega naught
+T and so on and we can write that as a
+
+ align:start position:0%
+T and so on and we can write that as a
+ 
+
+ align:start position:0%
+T and so on and we can write that as a
+sum that looks like this so a sum over n
+
+ align:start position:0%
+sum that looks like this so a sum over n
+ 
+
+ align:start position:0%
+sum that looks like this so a sum over n
+from one to infinity a coefficient B sub
+
+ align:start position:0%
+from one to infinity a coefficient B sub
+ 
+
+ align:start position:0%
+from one to infinity a coefficient B sub
+n times sine of n Omega naught T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and why is there no DC term here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good because as an anti-symmetric
+
+ align:start position:0%
+good because as an anti-symmetric
+ 
+
+ align:start position:0%
+good because as an anti-symmetric
+function can't have a DC offset okay
+
+ align:start position:0%
+function can't have a DC offset okay
+ 
+
+ align:start position:0%
+function can't have a DC offset okay
+okay so for arbitrary functions you can
+
+ align:start position:0%
+okay so for arbitrary functions you can
+ 
+
+ align:start position:0%
+okay so for arbitrary functions you can
+write down any arbitrary periodic
+
+ align:start position:0%
+write down any arbitrary periodic
+ 
+
+ align:start position:0%
+write down any arbitrary periodic
+function as the sum of a symmetric part
+
+ align:start position:0%
+function as the sum of a symmetric part
+ 
+
+ align:start position:0%
+function as the sum of a symmetric part
+and an anti-symmetric part so we can
+
+ align:start position:0%
+and an anti-symmetric part so we can
+ 
+
+ align:start position:0%
+and an anti-symmetric part so we can
+write down an arbitrary function as a
+
+ align:start position:0%
+write down an arbitrary function as a
+ 
+
+ align:start position:0%
+write down an arbitrary function as a
+sum of this these cosines plus a sum of
+
+ align:start position:0%
+sum of this these cosines plus a sum of
+ 
+
+ align:start position:0%
+sum of this these cosines plus a sum of
+sine waves okay so that's for a series
+
+ align:start position:0%
+sine waves okay so that's for a series
+ 
+
+ align:start position:0%
+sine waves okay so that's for a series
+any questions about that okay
+
+ align:start position:0%
+any questions about that okay
+ 
+
+ align:start position:0%
+any questions about that okay
+so this is kind of messy and it turns
+
+ align:start position:0%
+so this is kind of messy and it turns
+ 
+
+ align:start position:0%
+so this is kind of messy and it turns
+out that there's a much simpler way of
+
+ align:start position:0%
+out that there's a much simpler way of
+ 
+
+ align:start position:0%
+out that there's a much simpler way of
+writing out functions as sums of
+
+ align:start position:0%
+writing out functions as sums of
+ 
+
+ align:start position:0%
+writing out functions as sums of
+periodic functions okay
+
+ align:start position:0%
+periodic functions okay
+ 
+
+ align:start position:0%
+periodic functions okay
+so rather than using cosines and sines
+
+ align:start position:0%
+so rather than using cosines and sines
+ 
+
+ align:start position:0%
+so rather than using cosines and sines
+we're going to use complex Exponential's
+
+ align:start position:0%
+we're going to use complex Exponential's
+ 
+
+ align:start position:0%
+we're going to use complex Exponential's
+okay and that is what complex fourier
+
+ align:start position:0%
+okay and that is what complex fourier
+ 
+
+ align:start position:0%
+okay and that is what complex fourier
+series does okay all right so let's do
+
+ align:start position:0%
+series does okay all right so let's do
+ 
+
+ align:start position:0%
+series does okay all right so let's do
+that so you probably recall that you can
+
+ align:start position:0%
+that so you probably recall that you can
+ 
+
+ align:start position:0%
+that so you probably recall that you can
+write down a complex exponential e to
+
+ align:start position:0%
+write down a complex exponential e to
+ 
+
+ align:start position:0%
+write down a complex exponential e to
+the I Omega T as a cosine Omega T plus I
+
+ align:start position:0%
+the I Omega T as a cosine Omega T plus I
+ 
+
+ align:start position:0%
+the I Omega T as a cosine Omega T plus I
+sine Omega T all right so e to the I
+
+ align:start position:0%
+sine Omega T all right so e to the I
+ 
+
+ align:start position:0%
+sine Omega T all right so e to the I
+Omega T is just a generalization of
+
+ align:start position:0%
+Omega T is just a generalization of
+ 
+
+ align:start position:0%
+Omega T is just a generalization of
+sines and cosines alright so the way to
+
+ align:start position:0%
+sines and cosines alright so the way to
+ 
+
+ align:start position:0%
+sines and cosines alright so the way to
+think about this is e to the I Omega T
+
+ align:start position:0%
+think about this is e to the I Omega T
+ 
+
+ align:start position:0%
+think about this is e to the I Omega T
+is a complex number if we plot it in
+
+ align:start position:0%
+is a complex number if we plot it in
+ 
+
+ align:start position:0%
+is a complex number if we plot it in
+complex plane where we look at the real
+
+ align:start position:0%
+complex plane where we look at the real
+ 
+
+ align:start position:0%
+complex plane where we look at the real
+part along this axis the imaginary part
+
+ align:start position:0%
+part along this axis the imaginary part
+ 
+
+ align:start position:0%
+part along this axis the imaginary part
+along that axis e to the I Omega T just
+
+ align:start position:0%
+along that axis e to the I Omega T just
+ 
+
+ align:start position:0%
+along that axis e to the I Omega T just
+lives on this circle no matter what
+
+ align:start position:0%
+lives on this circle no matter what
+ 
+
+ align:start position:0%
+lives on this circle no matter what
+Omega T is e to the I Omega T just sits
+
+ align:start position:0%
+Omega T is e to the I Omega T just sits
+ 
+
+ align:start position:0%
+Omega T is e to the I Omega T just sits
+on this circle in the complex plane the
+
+ align:start position:0%
+on this circle in the complex plane the
+ 
+
+ align:start position:0%
+on this circle in the complex plane the
+unit circle in the complex plane
+
+ align:start position:0%
+unit circle in the complex plane
+ 
+
+ align:start position:0%
+unit circle in the complex plane
+e to the I Omega T is a function of time
+
+ align:start position:0%
+e to the I Omega T is a function of time
+ 
+
+ align:start position:0%
+e to the I Omega T is a function of time
+it simply has a real part that looks
+
+ align:start position:0%
+it simply has a real part that looks
+ 
+
+ align:start position:0%
+it simply has a real part that looks
+like cosine so the real part of this as
+
+ align:start position:0%
+like cosine so the real part of this as
+ 
+
+ align:start position:0%
+like cosine so the real part of this as
+you increase T or the phase Omega T is
+
+ align:start position:0%
+you increase T or the phase Omega T is
+ 
+
+ align:start position:0%
+you increase T or the phase Omega T is
+the real part just oscillates
+
+ align:start position:0%
+the real part just oscillates
+ 
+
+ align:start position:0%
+the real part just oscillates
+sinusoidally back and forth like this as
+
+ align:start position:0%
+sinusoidally back and forth like this as
+ 
+
+ align:start position:0%
+sinusoidally back and forth like this as
+a cosine the imaginary part just
+
+ align:start position:0%
+a cosine the imaginary part just
+ 
+
+ align:start position:0%
+a cosine the imaginary part just
+oscillates back and forth as a sine
+
+ align:start position:0%
+oscillates back and forth as a sine
+ 
+
+ align:start position:0%
+oscillates back and forth as a sine
+right and when you put them together
+
+ align:start position:0%
+right and when you put them together
+ 
+
+ align:start position:0%
+right and when you put them together
+something that goes back and forth this
+
+ align:start position:0%
+something that goes back and forth this
+ 
+
+ align:start position:0%
+something that goes back and forth this
+way as a cosine up and down that way as
+
+ align:start position:0%
+way as a cosine up and down that way as
+ 
+
+ align:start position:0%
+way as a cosine up and down that way as
+a sine just traces out a circle so e to
+
+ align:start position:0%
+a sine just traces out a circle so e to
+ 
+
+ align:start position:0%
+a sine just traces out a circle so e to
+the I Omega T traces out a circle in
+
+ align:start position:0%
+the I Omega T traces out a circle in
+ 
+
+ align:start position:0%
+the I Omega T traces out a circle in
+this direction and as time increases it
+
+ align:start position:0%
+this direction and as time increases it
+ 
+
+ align:start position:0%
+this direction and as time increases it
+just goes around and around like this e
+
+ align:start position:0%
+just goes around and around like this e
+ 
+
+ align:start position:0%
+just goes around and around like this e
+to the minus IO T I Omega T just goes
+
+ align:start position:0%
+to the minus IO T I Omega T just goes
+ 
+
+ align:start position:0%
+to the minus IO T I Omega T just goes
+the other way okay that makes sense
+
+ align:start position:0%
+the other way okay that makes sense
+ 
+
+ align:start position:0%
+the other way okay that makes sense
+got to the the real part that's going
+
+ align:start position:0%
+got to the the real part that's going
+ 
+
+ align:start position:0%
+got to the the real part that's going
+like this the imaginary part that's
+
+ align:start position:0%
+like this the imaginary part that's
+ 
+
+ align:start position:0%
+like this the imaginary part that's
+going like this alright and you put
+
+ align:start position:0%
+going like this alright and you put
+ 
+
+ align:start position:0%
+going like this alright and you put
+those together and they just go around
+
+ align:start position:0%
+those together and they just go around
+ 
+
+ align:start position:0%
+those together and they just go around
+in a circle okay so you can see it's a
+
+ align:start position:0%
+in a circle okay so you can see it's a
+ 
+
+ align:start position:0%
+in a circle okay so you can see it's a
+way of combining cosine and sine
+
+ align:start position:0%
+way of combining cosine and sine
+ 
+
+ align:start position:0%
+way of combining cosine and sine
+together in one function okay so what
+
+ align:start position:0%
+together in one function okay so what
+ 
+
+ align:start position:0%
+together in one function okay so what
+we're going to do is we're going to
+
+ align:start position:0%
+we're going to do is we're going to
+ 
+
+ align:start position:0%
+we're going to do is we're going to
+rewrite our Fourier series as instead of
+
+ align:start position:0%
+rewrite our Fourier series as instead of
+ 
+
+ align:start position:0%
+rewrite our Fourier series as instead of
+sines and cosines we're going to stick
+
+ align:start position:0%
+sines and cosines we're going to stick
+ 
+
+ align:start position:0%
+sines and cosines we're going to stick
+in each of the we're going to replace
+
+ align:start position:0%
+in each of the we're going to replace
+ 
+
+ align:start position:0%
+in each of the we're going to replace
+the sines and cosines
+
+ align:start position:0%
+the sines and cosines
+ 
+
+ align:start position:0%
+the sines and cosines
+with e to the I Omega T and e to the
+
+ align:start position:0%
+with e to the I Omega T and e to the
+ 
+
+ align:start position:0%
+with e to the I Omega T and e to the
+minus I Omega T so we're just gonna
+
+ align:start position:0%
+minus I Omega T so we're just gonna
+ 
+
+ align:start position:0%
+minus I Omega T so we're just gonna
+solve these two functions for cosine and
+
+ align:start position:0%
+solve these two functions for cosine and
+ 
+
+ align:start position:0%
+solve these two functions for cosine and
+sine and we're gonna take this and plug
+
+ align:start position:0%
+sine and we're gonna take this and plug
+ 
+
+ align:start position:0%
+sine and we're gonna take this and plug
+it into our our Fourier series and see
+
+ align:start position:0%
+it into our our Fourier series and see
+ 
+
+ align:start position:0%
+it into our our Fourier series and see
+what we get okay so let's do that and
+
+ align:start position:0%
+what we get okay so let's do that and
+ 
+
+ align:start position:0%
+what we get okay so let's do that and
+remember 1 over I is just minus I okay
+
+ align:start position:0%
+remember 1 over I is just minus I okay
+ 
+
+ align:start position:0%
+remember 1 over I is just minus I okay
+so here's our 4s here with our sum of
+
+ align:start position:0%
+so here's our 4s here with our sum of
+ 
+
+ align:start position:0%
+so here's our 4s here with our sum of
+cosines our sum up signs we're just
+
+ align:start position:0%
+cosines our sum up signs we're just
+ 
+
+ align:start position:0%
+cosines our sum up signs we're just
+going to replace those things with the e
+
+ align:start position:0%
+going to replace those things with the e
+ 
+
+ align:start position:0%
+going to replace those things with the e
+to the I Omega T plus e to the minus I
+
+ align:start position:0%
+to the I Omega T plus e to the minus I
+ 
+
+ align:start position:0%
+to the I Omega T plus e to the minus I
+Omega T and so on so there we go
+
+ align:start position:0%
+Omega T and so on so there we go
+ 
+
+ align:start position:0%
+Omega T and so on so there we go
+just replacing that there's a 1/2 there
+
+ align:start position:0%
+just replacing that there's a 1/2 there
+ 
+
+ align:start position:0%
+just replacing that there's a 1/2 there
+okay and now we're just going to do some
+
+ align:start position:0%
+okay and now we're just going to do some
+ 
+
+ align:start position:0%
+okay and now we're just going to do some
+algebra and we're gonna collect e to the
+
+ align:start position:0%
+algebra and we're gonna collect e to the
+ 
+
+ align:start position:0%
+algebra and we're gonna collect e to the
+I Omega T's and e to the minus I Omega
+
+ align:start position:0%
+I Omega T's and e to the minus I Omega
+ 
+
+ align:start position:0%
+I Omega T's and e to the minus I Omega
+T's together and this is what it looks
+
+ align:start position:0%
+T's together and this is what it looks
+ 
+
+ align:start position:0%
+T's together and this is what it looks
+like okay so you can see that what we're
+
+ align:start position:0%
+like okay so you can see that what we're
+ 
+
+ align:start position:0%
+like okay so you can see that what we're
+doing is collecting this into a bunch of
+
+ align:start position:0%
+doing is collecting this into a bunch of
+ 
+
+ align:start position:0%
+doing is collecting this into a bunch of
+terms that have e to the positive I and
+
+ align:start position:0%
+terms that have e to the positive I and
+ 
+
+ align:start position:0%
+terms that have e to the positive I and
+Omega T here and e to the minus I and
+
+ align:start position:0%
+Omega T here and e to the minus I and
+ 
+
+ align:start position:0%
+Omega T here and e to the minus I and
+Omega naught T there okay and now we
+
+ align:start position:0%
+Omega naught T there okay and now we
+ 
+
+ align:start position:0%
+Omega naught T there okay and now we
+have a still a sum of three things so it
+
+ align:start position:0%
+have a still a sum of three things so it
+ 
+
+ align:start position:0%
+have a still a sum of three things so it
+doesn't really look like we've really
+
+ align:start position:0%
+doesn't really look like we've really
+ 
+
+ align:start position:0%
+doesn't really look like we've really
+gotten anywhere right okay but notice
+
+ align:start position:0%
+gotten anywhere right okay but notice
+ 
+
+ align:start position:0%
+gotten anywhere right okay but notice
+something if we just put the minus sign
+
+ align:start position:0%
+something if we just put the minus sign
+ 
+
+ align:start position:0%
+something if we just put the minus sign
+into the N okay then we can combine
+
+ align:start position:0%
+into the N okay then we can combine
+ 
+
+ align:start position:0%
+into the N okay then we can combine
+these two into one sum and this if n is
+
+ align:start position:0%
+these two into one sum and this if n is
+ 
+
+ align:start position:0%
+these two into one sum and this if n is
+zero what is e to the I n Omega T it's
+
+ align:start position:0%
+zero what is e to the I n Omega T it's
+ 
+
+ align:start position:0%
+zero what is e to the I n Omega T it's
+just 1 so we can also write this as
+
+ align:start position:0%
+just 1 so we can also write this as
+ 
+
+ align:start position:0%
+just 1 so we can also write this as
+something eetu the I n Omega T as long
+
+ align:start position:0%
+something eetu the I n Omega T as long
+ 
+
+ align:start position:0%
+something eetu the I n Omega T as long
+as n is zero okay so that's what we do
+
+ align:start position:0%
+as n is zero okay so that's what we do
+ 
+
+ align:start position:0%
+as n is zero okay so that's what we do
+oh and by the way these coefficients
+
+ align:start position:0%
+oh and by the way these coefficients
+ 
+
+ align:start position:0%
+oh and by the way these coefficients
+here we can just rewrite as sums of
+
+ align:start position:0%
+here we can just rewrite as sums of
+ 
+
+ align:start position:0%
+here we can just rewrite as sums of
+those coefficients up there don't worry
+
+ align:start position:0%
+those coefficients up there don't worry
+ 
+
+ align:start position:0%
+those coefficients up there don't worry
+this all looks really complicated by the
+
+ align:start position:0%
+this all looks really complicated by the
+ 
+
+ align:start position:0%
+this all looks really complicated by the
+end it's just oil down to one simple
+
+ align:start position:0%
+end it's just oil down to one simple
+ 
+
+ align:start position:0%
+end it's just oil down to one simple
+thing that's why we're doing this we're
+
+ align:start position:0%
+thing that's why we're doing this we're
+ 
+
+ align:start position:0%
+thing that's why we're doing this we're
+simplifying things okay so when you do
+
+ align:start position:0%
+simplifying things okay so when you do
+ 
+
+ align:start position:0%
+simplifying things okay so when you do
+this when you rewrite this this looks
+
+ align:start position:0%
+this when you rewrite this this looks
+ 
+
+ align:start position:0%
+this when you rewrite this this looks
+like a sum over N equals zero this is a
+
+ align:start position:0%
+like a sum over N equals zero this is a
+ 
+
+ align:start position:0%
+like a sum over N equals zero this is a
+sum over positive ends N equals 1 to
+
+ align:start position:0%
+sum over positive ends N equals 1 to
+ 
+
+ align:start position:0%
+sum over positive ends N equals 1 to
+infinity this is a sum over negative n
+
+ align:start position:0%
+infinity this is a sum over negative n
+ 
+
+ align:start position:0%
+infinity this is a sum over negative n
+this one to minus infinity and all those
+
+ align:start position:0%
+this one to minus infinity and all those
+ 
+
+ align:start position:0%
+this one to minus infinity and all those
+combined into one sum so now we can
+
+ align:start position:0%
+combined into one sum so now we can
+ 
+
+ align:start position:0%
+combined into one sum so now we can
+write down any function y of T as a sum
+
+ align:start position:0%
+write down any function y of T as a sum
+ 
+
+ align:start position:0%
+write down any function y of T as a sum
+over N equals minus infinity to infinity
+
+ align:start position:0%
+over N equals minus infinity to infinity
+ 
+
+ align:start position:0%
+over N equals minus infinity to infinity
+of a coefficient a sub n times e to the
+
+ align:start position:0%
+of a coefficient a sub n times e to the
+ 
+
+ align:start position:0%
+of a coefficient a sub n times e to the
+I and Omega okay so we went from having
+
+ align:start position:0%
+I and Omega okay so we went from having
+ 
+
+ align:start position:0%
+I and Omega okay so we went from having
+this cut this complicated thing that sum
+
+ align:start position:0%
+this cut this complicated thing that sum
+ 
+
+ align:start position:0%
+this cut this complicated thing that sum
+over a constant term sines and cosines
+
+ align:start position:0%
+over a constant term sines and cosines
+ 
+
+ align:start position:0%
+over a constant term sines and cosines
+and we boiled it down to
+
+ align:start position:0%
+and we boiled it down to
+ 
+
+ align:start position:0%
+and we boiled it down to
+a single some that's why these these
+
+ align:start position:0%
+a single some that's why these these
+ 
+
+ align:start position:0%
+a single some that's why these these
+complex exponentials are useful okay
+
+ align:start position:0%
+complex exponentials are useful okay
+ 
+
+ align:start position:0%
+complex exponentials are useful okay
+because we don't have to carry around a
+
+ align:start position:0%
+because we don't have to carry around a
+ 
+
+ align:start position:0%
+because we don't have to carry around a
+bunch of different functions different
+
+ align:start position:0%
+bunch of different functions different
+ 
+
+ align:start position:0%
+bunch of different functions different
+basis functions to describe an arbitrary
+
+ align:start position:0%
+basis functions to describe an arbitrary
+ 
+
+ align:start position:0%
+basis functions to describe an arbitrary
+signal why okay but remember this is
+
+ align:start position:0%
+signal why okay but remember this is
+ 
+
+ align:start position:0%
+signal why okay but remember this is
+just a mathematical trick to hide sines
+
+ align:start position:0%
+just a mathematical trick to hide sines
+ 
+
+ align:start position:0%
+just a mathematical trick to hide sines
+and cosines okay it's a very powerful
+
+ align:start position:0%
+and cosines okay it's a very powerful
+ 
+
+ align:start position:0%
+and cosines okay it's a very powerful
+trick but that's all it's doing is its
+
+ align:start position:0%
+trick but that's all it's doing is its
+ 
+
+ align:start position:0%
+trick but that's all it's doing is its
+hiding sines and cosines okay
+
+ align:start position:0%
+hiding sines and cosines okay
+ 
+
+ align:start position:0%
+hiding sines and cosines okay
+all right so we've replaced our sums
+
+ align:start position:0%
+all right so we've replaced our sums
+ 
+
+ align:start position:0%
+all right so we've replaced our sums
+over cosines and sines where the sum of
+
+ align:start position:0%
+over cosines and sines where the sum of
+ 
+
+ align:start position:0%
+over cosines and sines where the sum of
+complex Exponential's alright remember
+
+ align:start position:0%
+complex Exponential's alright remember
+ 
+
+ align:start position:0%
+complex Exponential's alright remember
+what we're doing here were finding a new
+
+ align:start position:0%
+what we're doing here were finding a new
+ 
+
+ align:start position:0%
+what we're doing here were finding a new
+way of writing down functions okay so
+
+ align:start position:0%
+way of writing down functions okay so
+ 
+
+ align:start position:0%
+way of writing down functions okay so
+what's cool about this what's really
+
+ align:start position:0%
+what's cool about this what's really
+ 
+
+ align:start position:0%
+what's cool about this what's really
+interesting about this is that for some
+
+ align:start position:0%
+interesting about this is that for some
+ 
+
+ align:start position:0%
+interesting about this is that for some
+functions so what we're doing is where
+
+ align:start position:0%
+functions so what we're doing is where
+ 
+
+ align:start position:0%
+functions so what we're doing is where
+we have an arbitrary function y and
+
+ align:start position:0%
+we have an arbitrary function y and
+ 
+
+ align:start position:0%
+we have an arbitrary function y and
+we're writing it down with just some
+
+ align:start position:0%
+we're writing it down with just some
+ 
+
+ align:start position:0%
+we're writing it down with just some
+numbers a sub n okay and what's cool
+
+ align:start position:0%
+numbers a sub n okay and what's cool
+ 
+
+ align:start position:0%
+numbers a sub n okay and what's cool
+about this is that for some functions Y
+
+ align:start position:0%
+about this is that for some functions Y
+ 
+
+ align:start position:0%
+about this is that for some functions Y
+you can describe that function with just
+
+ align:start position:0%
+you can describe that function with just
+ 
+
+ align:start position:0%
+you can describe that function with just
+a few few of these coefficients a okay
+
+ align:start position:0%
+a few few of these coefficients a okay
+ 
+
+ align:start position:0%
+a few few of these coefficients a okay
+does that make sense so let me just show
+
+ align:start position:0%
+does that make sense so let me just show
+ 
+
+ align:start position:0%
+does that make sense so let me just show
+you an example of some functions that
+
+ align:start position:0%
+you an example of some functions that
+ 
+
+ align:start position:0%
+you an example of some functions that
+look really really simple when you
+
+ align:start position:0%
+look really really simple when you
+ 
+
+ align:start position:0%
+look really really simple when you
+rewrite them using these coefficients a
+
+ align:start position:0%
+rewrite them using these coefficients a
+ 
+
+ align:start position:0%
+rewrite them using these coefficients a
+okay so here's here's an example so
+
+ align:start position:0%
+okay so here's here's an example so
+ 
+
+ align:start position:0%
+okay so here's here's an example so
+here's a function of n that has three
+
+ align:start position:0%
+here's a function of n that has three
+ 
+
+ align:start position:0%
+here's a function of n that has three
+numbers a sub minus 1 N equals minus 1
+
+ align:start position:0%
+numbers a sub minus 1 N equals minus 1
+ 
+
+ align:start position:0%
+numbers a sub minus 1 N equals minus 1
+is 1/2 a sub 0 and a sub 1 is 1/2 and
+
+ align:start position:0%
+is 1/2 a sub 0 and a sub 1 is 1/2 and
+ 
+
+ align:start position:0%
+is 1/2 a sub 0 and a sub 1 is 1/2 and
+all the rest of them are zeros so really
+
+ align:start position:0%
+all the rest of them are zeros so really
+ 
+
+ align:start position:0%
+all the rest of them are zeros so really
+we only have two nonzero entries in this
+
+ align:start position:0%
+we only have two nonzero entries in this
+ 
+
+ align:start position:0%
+we only have two nonzero entries in this
+sum so what what function is that it's
+
+ align:start position:0%
+sum so what what function is that it's
+ 
+
+ align:start position:0%
+sum so what what function is that it's
+just a cosine right so right we have
+
+ align:start position:0%
+just a cosine right so right we have
+ 
+
+ align:start position:0%
+just a cosine right so right we have
+let's write this out y equals a sum over
+
+ align:start position:0%
+let's write this out y equals a sum over
+ 
+
+ align:start position:0%
+let's write this out y equals a sum over
+all of these things 1/2 e to the might
+
+ align:start position:0%
+all of these things 1/2 e to the might
+ 
+
+ align:start position:0%
+all of these things 1/2 e to the might
+the first n is minus 1 e to the minus I
+
+ align:start position:0%
+the first n is minus 1 e to the minus I
+ 
+
+ align:start position:0%
+the first n is minus 1 e to the minus I
+Omega naught E
+
+ align:start position:0%
+Omega naught E
+ 
+
+ align:start position:0%
+Omega naught E
+plus 1/2 e to the plus I Omega naught T
+
+ align:start position:0%
+plus 1/2 e to the plus I Omega naught T
+ 
+
+ align:start position:0%
+plus 1/2 e to the plus I Omega naught T
+right we're just writing out that sum
+
+ align:start position:0%
+right we're just writing out that sum
+ 
+
+ align:start position:0%
+right we're just writing out that sum
+and that is just just use sorry I didn't
+
+ align:start position:0%
+and that is just just use sorry I didn't
+ 
+
+ align:start position:0%
+and that is just just use sorry I didn't
+tell you what that that equation was
+
+ align:start position:0%
+tell you what that that equation was
+ 
+
+ align:start position:0%
+tell you what that that equation was
+that's Euler's Euler's equation all
+
+ align:start position:0%
+that's Euler's Euler's equation all
+ 
+
+ align:start position:0%
+that's Euler's Euler's equation all
+right that's just cosine minus I sine
+
+ align:start position:0%
+right that's just cosine minus I sine
+ 
+
+ align:start position:0%
+right that's just cosine minus I sine
+Omega T that is just cosine plus I sine
+
+ align:start position:0%
+Omega T that is just cosine plus I sine
+ 
+
+ align:start position:0%
+Omega T that is just cosine plus I sine
+Omega T the sines cancel right and
+
+ align:start position:0%
+Omega T the sines cancel right and
+ 
+
+ align:start position:0%
+Omega T the sines cancel right and
+you're left with cosine T all right so
+
+ align:start position:0%
+you're left with cosine T all right so
+ 
+
+ align:start position:0%
+you're left with cosine T all right so
+here's this function of time that goes
+
+ align:start position:0%
+here's this function of time that goes
+ 
+
+ align:start position:0%
+here's this function of time that goes
+on infinitely if you wanted to write
+
+ align:start position:0%
+on infinitely if you wanted to write
+ 
+
+ align:start position:0%
+on infinitely if you wanted to write
+down all the values of cosine Omega
+
+ align:start position:0%
+down all the values of cosine Omega
+ 
+
+ align:start position:0%
+down all the values of cosine Omega
+naught T you'd have to write down an
+
+ align:start position:0%
+naught T you'd have to write down an
+ 
+
+ align:start position:0%
+naught T you'd have to write down an
+awful lot of numbers and here we can
+
+ align:start position:0%
+awful lot of numbers and here we can
+ 
+
+ align:start position:0%
+awful lot of numbers and here we can
+write down that same function with two
+
+ align:start position:0%
+write down that same function with two
+ 
+
+ align:start position:0%
+write down that same function with two
+numbers right so this is a very compact
+
+ align:start position:0%
+numbers right so this is a very compact
+ 
+
+ align:start position:0%
+numbers right so this is a very compact
+view of that function of time right okay
+
+ align:start position:0%
+view of that function of time right okay
+ 
+
+ align:start position:0%
+view of that function of time right okay
+here's another function what function do
+
+ align:start position:0%
+here's another function what function do
+ 
+
+ align:start position:0%
+here's another function what function do
+you think that is in time what would be
+
+ align:start position:0%
+you think that is in time what would be
+ 
+
+ align:start position:0%
+you think that is in time what would be
+the time domain equivalent of this set
+
+ align:start position:0%
+the time domain equivalent of this set
+ 
+
+ align:start position:0%
+the time domain equivalent of this set
+of Fourier coefficients good so we're
+
+ align:start position:0%
+of Fourier coefficients good so we're
+ 
+
+ align:start position:0%
+of Fourier coefficients good so we're
+gonna do the same thing just write it
+
+ align:start position:0%
+gonna do the same thing just write it
+ 
+
+ align:start position:0%
+gonna do the same thing just write it
+out all these sums are zero all these
+
+ align:start position:0%
+out all these sums are zero all these
+ 
+
+ align:start position:0%
+out all these sums are zero all these
+components are zero except for two of
+
+ align:start position:0%
+components are zero except for two of
+ 
+
+ align:start position:0%
+components are zero except for two of
+them N equals -2 and N equals plus two
+
+ align:start position:0%
+them N equals -2 and N equals plus two
+ 
+
+ align:start position:0%
+them N equals -2 and N equals plus two
+if you just put those in there as 1/2 e
+
+ align:start position:0%
+if you just put those in there as 1/2 e
+ 
+
+ align:start position:0%
+if you just put those in there as 1/2 e
+to the minus 2 Omega naught T plus 1/2 e
+
+ align:start position:0%
+to the minus 2 Omega naught T plus 1/2 e
+ 
+
+ align:start position:0%
+to the minus 2 Omega naught T plus 1/2 e
+to the plus 2 Omega and that is just if
+
+ align:start position:0%
+to the plus 2 Omega and that is just if
+ 
+
+ align:start position:0%
+to the plus 2 Omega and that is just if
+you write that out those signs cancel
+
+ align:start position:0%
+you write that out those signs cancel
+ 
+
+ align:start position:0%
+you write that out those signs cancel
+and you have cosine 2 Omega naught T ok
+
+ align:start position:0%
+and you have cosine 2 Omega naught T ok
+ 
+
+ align:start position:0%
+and you have cosine 2 Omega naught T ok
+pretty simple right ok how about this
+
+ align:start position:0%
+pretty simple right ok how about this
+ 
+
+ align:start position:0%
+pretty simple right ok how about this
+one this is the remember the A's are
+
+ align:start position:0%
+one this is the remember the A's are
+ 
+
+ align:start position:0%
+one this is the remember the A's are
+complex numbers the ones we were looking
+
+ align:start position:0%
+complex numbers the ones we were looking
+ 
+
+ align:start position:0%
+complex numbers the ones we were looking
+at here had two real numbers here's an
+
+ align:start position:0%
+at here had two real numbers here's an
+ 
+
+ align:start position:0%
+at here had two real numbers here's an
+example where the A's
+
+ align:start position:0%
+example where the A's
+ 
+
+ align:start position:0%
+example where the A's
+our our imaginary one is I over to one
+
+ align:start position:0%
+our our imaginary one is I over to one
+ 
+
+ align:start position:0%
+our our imaginary one is I over to one
+is minus I over to that's what the the
+
+ align:start position:0%
+is minus I over to that's what the the
+ 
+
+ align:start position:0%
+is minus I over to that's what the the
+complex Fourier representation looks
+
+ align:start position:0%
+complex Fourier representation looks
+ 
+
+ align:start position:0%
+complex Fourier representation looks
+like of this function we can just put in
+
+ align:start position:0%
+like of this function we can just put in
+ 
+
+ align:start position:0%
+like of this function we can just put in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+you solve that you can see that the in
+
+ align:start position:0%
+you solve that you can see that the in
+ 
+
+ align:start position:0%
+you solve that you can see that the in
+this case the cosines cancel because
+
+ align:start position:0%
+this case the cosines cancel because
+ 
+
+ align:start position:0%
+this case the cosines cancel because
+this is I over 2 cosine 2 Omega t minus
+
+ align:start position:0%
+this is I over 2 cosine 2 Omega t minus
+ 
+
+ align:start position:0%
+this is I over 2 cosine 2 Omega t minus
+I over 2 cosine 2 Omega T those cancel
+
+ align:start position:0%
+I over 2 cosine 2 Omega T those cancel
+ 
+
+ align:start position:0%
+I over 2 cosine 2 Omega T those cancel
+and you're left with sine 2 Omega naught
+
+ align:start position:0%
+and you're left with sine 2 Omega naught
+ 
+
+ align:start position:0%
+and you're left with sine 2 Omega naught
+T okay so that is what we're a
+
+ align:start position:0%
+T okay so that is what we're a
+ 
+
+ align:start position:0%
+T okay so that is what we're a
+representation of sine 2 Omega T looks
+
+ align:start position:0%
+representation of sine 2 Omega T looks
+ 
+
+ align:start position:0%
+representation of sine 2 Omega T looks
+like ok so functions that have higher
+
+ align:start position:0%
+like ok so functions that have higher
+ 
+
+ align:start position:0%
+like ok so functions that have higher
+frequencies will have nonzero elements
+
+ align:start position:0%
+frequencies will have nonzero elements
+ 
+
+ align:start position:0%
+frequencies will have nonzero elements
+that are further out in n right ok any
+
+ align:start position:0%
+that are further out in n right ok any
+ 
+
+ align:start position:0%
+that are further out in n right ok any
+questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok
+
+ align:start position:0%
+ok
+ 
+
+ align:start position:0%
+ok
+so again this set of functions e to the
+
+ align:start position:0%
+so again this set of functions e to the
+ 
+
+ align:start position:0%
+so again this set of functions e to the
+I n Omega naught T for man or that or
+
+ align:start position:0%
+I n Omega naught T for man or that or
+ 
+
+ align:start position:0%
+I n Omega naught T for man or that or
+thoug g''l orthonormal basis set over
+
+ align:start position:0%
+thoug g''l orthonormal basis set over
+ 
+
+ align:start position:0%
+thoug g''l orthonormal basis set over
+that of one's over that interval that a
+
+ align:start position:0%
+that of one's over that interval that a
+ 
+
+ align:start position:0%
+that of one's over that interval that a
+naught coefficient is just the
+
+ align:start position:0%
+naught coefficient is just the
+ 
+
+ align:start position:0%
+naught coefficient is just the
+projection of our function on to e to
+
+ align:start position:0%
+projection of our function on to e to
+ 
+
+ align:start position:0%
+projection of our function on to e to
+the 0 n equals 0 and that's just the
+
+ align:start position:0%
+the 0 n equals 0 and that's just the
+ 
+
+ align:start position:0%
+the 0 n equals 0 and that's just the
+average okay the a 1 coefficient is just
+
+ align:start position:0%
+average okay the a 1 coefficient is just
+ 
+
+ align:start position:0%
+average okay the a 1 coefficient is just
+the projection of our function e to the
+
+ align:start position:0%
+the projection of our function e to the
+ 
+
+ align:start position:0%
+the projection of our function e to the
+minus I Omega naught T and in general
+
+ align:start position:0%
+minus I Omega naught T and in general
+ 
+
+ align:start position:0%
+minus I Omega naught T and in general
+the M coefficient is just the projection
+
+ align:start position:0%
+the M coefficient is just the projection
+ 
+
+ align:start position:0%
+the M coefficient is just the projection
+of our function onto e to the minus I M
+
+ align:start position:0%
+of our function onto e to the minus I M
+ 
+
+ align:start position:0%
+of our function onto e to the minus I M
+Omega naught T ok and we can take those
+
+ align:start position:0%
+Omega naught T ok and we can take those
+ 
+
+ align:start position:0%
+Omega naught T ok and we can take those
+coefficients plug them into this sum and
+
+ align:start position:0%
+coefficients plug them into this sum and
+ 
+
+ align:start position:0%
+coefficients plug them into this sum and
+reconstruct an arbitrary periodic
+
+ align:start position:0%
+reconstruct an arbitrary periodic
+ 
+
+ align:start position:0%
+reconstruct an arbitrary periodic
+function this y of T ok so we have a way
+
+ align:start position:0%
+function this y of T ok so we have a way
+ 
+
+ align:start position:0%
+function this y of T ok so we have a way
+of taking a function and getting these
+
+ align:start position:0%
+of taking a function and getting these
+ 
+
+ align:start position:0%
+of taking a function and getting these
+complex Fourier coefficients and we have
+
+ align:start position:0%
+complex Fourier coefficients and we have
+ 
+
+ align:start position:0%
+complex Fourier coefficients and we have
+a way of taking those coefficients and
+
+ align:start position:0%
+a way of taking those coefficients and
+ 
+
+ align:start position:0%
+a way of taking those coefficients and
+reconstructing our function this is just
+
+ align:start position:0%
+reconstructing our function this is just
+ 
+
+ align:start position:0%
+reconstructing our function this is just
+a bunch of different views function Y
+
+ align:start position:0%
+a bunch of different views function Y
+ 
+
+ align:start position:0%
+a bunch of different views function Y
+and from all of those different views we
+
+ align:start position:0%
+and from all of those different views we
+ 
+
+ align:start position:0%
+and from all of those different views we
+can reconstruct our function and that's
+
+ align:start position:0%
+can reconstruct our function and that's
+ 
+
+ align:start position:0%
+can reconstruct our function and that's
+all it is
+
+ align:start position:0%
+all it is
+ 
+
+ align:start position:0%
+all it is
+so in general when we do Fourier
+
+ align:start position:0%
+so in general when we do Fourier
+ 
+
+ align:start position:0%
+so in general when we do Fourier
+decomposition in a computer in MATLAB on
+
+ align:start position:0%
+decomposition in a computer in MATLAB on
+ 
+
+ align:start position:0%
+decomposition in a computer in MATLAB on
+real signals that you've sampled in time
+
+ align:start position:0%
+real signals that you've sampled in time
+ 
+
+ align:start position:0%
+real signals that you've sampled in time
+it's always done in this kind of
+
+ align:start position:0%
+it's always done in this kind of
+ 
+
+ align:start position:0%
+it's always done in this kind of
+discrete representation you've got in
+
+ align:start position:0%
+discrete representation you've got in
+ 
+
+ align:start position:0%
+discrete representation you've got in
+this case discrete frequencies when you
+
+ align:start position:0%
+this case discrete frequencies when you
+ 
+
+ align:start position:0%
+this case discrete frequencies when you
+sample signals you've got functions that
+
+ align:start position:0%
+sample signals you've got functions that
+ 
+
+ align:start position:0%
+sample signals you've got functions that
+are discrete in time and this becomes a
+
+ align:start position:0%
+are discrete in time and this becomes a
+ 
+
+ align:start position:0%
+are discrete in time and this becomes a
+sum ok but before we go to the discrete
+
+ align:start position:0%
+sum ok but before we go to the discrete
+ 
+
+ align:start position:0%
+sum ok but before we go to the discrete
+case I just want to show you what this
+
+ align:start position:0%
+case I just want to show you what this
+ 
+
+ align:start position:0%
+case I just want to show you what this
+looks like when we go to the the case of
+
+ align:start position:0%
+looks like when we go to the the case of
+ 
+
+ align:start position:0%
+looks like when we go to the the case of
+arbitrary function
+
+ align:start position:0%
+arbitrary function
+ 
+
+ align:start position:0%
+arbitrary function
+this thing was about representing
+
+ align:start position:0%
+this thing was about representing
+ 
+
+ align:start position:0%
+this thing was about representing
+periodic functions you can only
+
+ align:start position:0%
+periodic functions you can only
+ 
+
+ align:start position:0%
+periodic functions you can only
+represent periodic functions using this
+
+ align:start position:0%
+represent periodic functions using this
+ 
+
+ align:start position:0%
+represent periodic functions using this
+these Fourier series okay but before we
+
+ align:start position:0%
+these Fourier series okay but before we
+ 
+
+ align:start position:0%
+these Fourier series okay but before we
+go on to the Fourier transform algorithm
+
+ align:start position:0%
+go on to the Fourier transform algorithm
+ 
+
+ align:start position:0%
+go on to the Fourier transform algorithm
+and discrete Fourier transforms I just
+
+ align:start position:0%
+and discrete Fourier transforms I just
+ 
+
+ align:start position:0%
+and discrete Fourier transforms I just
+want to show you what this looks like
+
+ align:start position:0%
+want to show you what this looks like
+ 
+
+ align:start position:0%
+want to show you what this looks like
+for the case of arbitrary functions okay
+
+ align:start position:0%
+for the case of arbitrary functions okay
+ 
+
+ align:start position:0%
+for the case of arbitrary functions okay
+and it's just I'm just showing this to
+
+ align:start position:0%
+and it's just I'm just showing this to
+ 
+
+ align:start position:0%
+and it's just I'm just showing this to
+you I don't expect you to be able to
+
+ align:start position:0%
+you I don't expect you to be able to
+ 
+
+ align:start position:0%
+you I don't expect you to be able to
+reproduce any of this but you should see
+
+ align:start position:0%
+reproduce any of this but you should see
+ 
+
+ align:start position:0%
+reproduce any of this but you should see
+what it looks like okay for those of you
+
+ align:start position:0%
+what it looks like okay for those of you
+ 
+
+ align:start position:0%
+what it looks like okay for those of you
+who haven't seen it already okay so what
+
+ align:start position:0%
+who haven't seen it already okay so what
+ 
+
+ align:start position:0%
+who haven't seen it already okay so what
+we're gonna do is go from the case of
+
+ align:start position:0%
+we're gonna do is go from the case of
+ 
+
+ align:start position:0%
+we're gonna do is go from the case of
+periodic functions to non periodic
+
+ align:start position:0%
+periodic functions to non periodic
+ 
+
+ align:start position:0%
+periodic functions to non periodic
+functions and the simplest way to think
+
+ align:start position:0%
+functions and the simplest way to think
+ 
+
+ align:start position:0%
+functions and the simplest way to think
+about that is a periodic function does
+
+ align:start position:0%
+about that is a periodic function does
+ 
+
+ align:start position:0%
+about that is a periodic function does
+something here and then it just does the
+
+ align:start position:0%
+something here and then it just does the
+ 
+
+ align:start position:0%
+something here and then it just does the
+same thing here and then it just does
+
+ align:start position:0%
+same thing here and then it just does
+ 
+
+ align:start position:0%
+same thing here and then it just does
+the same thing here right so how do we
+
+ align:start position:0%
+the same thing here right so how do we
+ 
+
+ align:start position:0%
+the same thing here right so how do we
+go from from this to an arbitrary
+
+ align:start position:0%
+go from from this to an arbitrary
+ 
+
+ align:start position:0%
+go from from this to an arbitrary
+function well we're just going to let
+
+ align:start position:0%
+function well we're just going to let
+ 
+
+ align:start position:0%
+function well we're just going to let
+the period go to infinity okay that
+
+ align:start position:0%
+the period go to infinity okay that
+ 
+
+ align:start position:0%
+the period go to infinity okay that
+makes sense okay but that's actually
+
+ align:start position:0%
+makes sense okay but that's actually
+ 
+
+ align:start position:0%
+makes sense okay but that's actually
+pretty easy we're gonna let t go to
+
+ align:start position:0%
+pretty easy we're gonna let t go to
+ 
+
+ align:start position:0%
+pretty easy we're gonna let t go to
+infinity which means the frequencies are
+
+ align:start position:0%
+infinity which means the frequencies are
+ 
+
+ align:start position:0%
+infinity which means the frequencies are
+two pi Omega naught R two PI over T
+
+ align:start position:0%
+two pi Omega naught R two PI over T
+ 
+
+ align:start position:0%
+two pi Omega naught R two PI over T
+that's going to go to zero right so our
+
+ align:start position:0%
+that's going to go to zero right so our
+ 
+
+ align:start position:0%
+that's going to go to zero right so our
+our steps remember when we had this
+
+ align:start position:0%
+our steps remember when we had this
+ 
+
+ align:start position:0%
+our steps remember when we had this
+discrete Fourier transform here we had
+
+ align:start position:0%
+discrete Fourier transform here we had
+ 
+
+ align:start position:0%
+discrete Fourier transform here we had
+these steps in frequency as a function
+
+ align:start position:0%
+these steps in frequency as a function
+ 
+
+ align:start position:0%
+these steps in frequency as a function
+of N those steps are just going to get
+
+ align:start position:0%
+of N those steps are just going to get
+ 
+
+ align:start position:0%
+of N those steps are just going to get
+infinitely close together the different
+
+ align:start position:0%
+infinitely close together the different
+ 
+
+ align:start position:0%
+infinitely close together the different
+frequency bins okay so that's what we're
+
+ align:start position:0%
+frequency bins okay so that's what we're
+ 
+
+ align:start position:0%
+frequency bins okay so that's what we're
+gonna do now you're going to let those
+
+ align:start position:0%
+gonna do now you're going to let those
+ 
+
+ align:start position:0%
+gonna do now you're going to let those
+frequency steps go to zero and now
+
+ align:start position:0%
+frequency steps go to zero and now
+ 
+
+ align:start position:0%
+frequency steps go to zero and now
+frequency in discrete case the frequency
+
+ align:start position:0%
+frequency in discrete case the frequency
+ 
+
+ align:start position:0%
+frequency in discrete case the frequency
+is just that number that n times Omega
+
+ align:start position:0%
+is just that number that n times Omega
+ 
+
+ align:start position:0%
+is just that number that n times Omega
+naught M times Omega naught well Omega
+
+ align:start position:0%
+naught M times Omega naught well Omega
+ 
+
+ align:start position:0%
+naught M times Omega naught well Omega
+naught is going to 0 but the MS are
+
+ align:start position:0%
+naught is going to 0 but the MS are
+ 
+
+ align:start position:0%
+naught is going to 0 but the MS are
+getting really big so we can just change
+
+ align:start position:0%
+getting really big so we can just change
+ 
+
+ align:start position:0%
+getting really big so we can just change
+we're just going to call that Omega okay
+
+ align:start position:0%
+we're just going to call that Omega okay
+ 
+
+ align:start position:0%
+we're just going to call that Omega okay
+letting you know the Omega nuts are
+
+ align:start position:0%
+letting you know the Omega nuts are
+ 
+
+ align:start position:0%
+letting you know the Omega nuts are
+going to 0 so the MS are getting
+
+ align:start position:0%
+going to 0 so the MS are getting
+ 
+
+ align:start position:0%
+going to 0 so the MS are getting
+infinitely big so we can't really use em
+
+ align:start position:0%
+infinitely big so we can't really use em
+ 
+
+ align:start position:0%
+infinitely big so we can't really use em
+anymore or n to label our frequency
+
+ align:start position:0%
+anymore or n to label our frequency
+ 
+
+ align:start position:0%
+anymore or n to label our frequency
+steps so we're just gonna use Omega okay
+
+ align:start position:0%
+steps so we're just gonna use Omega okay
+ 
+
+ align:start position:0%
+steps so we're just gonna use Omega okay
+we used to call our coefficients our
+
+ align:start position:0%
+we used to call our coefficients our
+ 
+
+ align:start position:0%
+we used to call our coefficients our
+Fourier coefficients we used to label
+
+ align:start position:0%
+Fourier coefficients we used to label
+ 
+
+ align:start position:0%
+Fourier coefficients we used to label
+them with em we can't use em anymore
+
+ align:start position:0%
+them with em we can't use em anymore
+ 
+
+ align:start position:0%
+them with em we can't use em anymore
+because M is getting infinitely big so
+
+ align:start position:0%
+because M is getting infinitely big so
+ 
+
+ align:start position:0%
+because M is getting infinitely big so
+we use it we use this new label Omega so
+
+ align:start position:0%
+we use it we use this new label Omega so
+ 
+
+ align:start position:0%
+we use it we use this new label Omega so
+a sub M becomes a new variable our
+
+ align:start position:0%
+a sub M becomes a new variable our
+ 
+
+ align:start position:0%
+a sub M becomes a new variable our
+Fourier transform labeled by the
+
+ align:start position:0%
+Fourier transform labeled by the
+ 
+
+ align:start position:0%
+Fourier transform labeled by the
+frequency Omega okay and we're just
+
+ align:start position:0%
+frequency Omega okay and we're just
+ 
+
+ align:start position:0%
+frequency Omega okay and we're just
+going to basically just make those
+
+ align:start position:0%
+going to basically just make those
+ 
+
+ align:start position:0%
+going to basically just make those
+replacements in here so the coefficients
+
+ align:start position:0%
+replacements in here so the coefficients
+ 
+
+ align:start position:0%
+replacements in here so the coefficients
+become a function of frequency that's
+
+ align:start position:0%
+become a function of frequency that's
+ 
+
+ align:start position:0%
+become a function of frequency that's
+just an integral remember T is going to
+
+ align:start position:0%
+just an integral remember T is going to
+ 
+
+ align:start position:0%
+just an integral remember T is going to
+infinity now so this has to go from
+
+ align:start position:0%
+infinity now so this has to go from
+ 
+
+ align:start position:0%
+infinity now so this has to go from
+minus infinity to infinity of our
+
+ align:start position:0%
+minus infinity to infinity of our
+ 
+
+ align:start position:0%
+minus infinity to infinity of our
+function y times our basis function and
+
+ align:start position:0%
+function y times our basis function and
+ 
+
+ align:start position:0%
+function y times our basis function and
+instead of e to the I M Omega naught T
+
+ align:start position:0%
+instead of e to the I M Omega naught T
+ 
+
+ align:start position:0%
+instead of e to the I M Omega naught T
+we just replaced mo mega not with Omega
+
+ align:start position:0%
+we just replaced mo mega not with Omega
+ 
+
+ align:start position:0%
+we just replaced mo mega not with Omega
+so e to the minus I Omega T okay and
+
+ align:start position:0%
+so e to the minus I Omega T okay and
+ 
+
+ align:start position:0%
+so e to the minus I Omega T okay and
+that is the Fourier transform okay and
+
+ align:start position:0%
+that is the Fourier transform okay and
+ 
+
+ align:start position:0%
+that is the Fourier transform okay and
+we're just going to do the same
+
+ align:start position:0%
+we're just going to do the same
+ 
+
+ align:start position:0%
+we're just going to do the same
+replacement here
+
+ align:start position:0%
+replacement here
+ 
+
+ align:start position:0%
+replacement here
+but we're instead of summing over n
+
+ align:start position:0%
+but we're instead of summing over n
+ 
+
+ align:start position:0%
+but we're instead of summing over n
+going from minus infinity to infinity we
+
+ align:start position:0%
+going from minus infinity to infinity we
+ 
+
+ align:start position:0%
+going from minus infinity to infinity we
+have to write this as an integral as
+
+ align:start position:0%
+have to write this as an integral as
+ 
+
+ align:start position:0%
+have to write this as an integral as
+well and so that we can reconstruct our
+
+ align:start position:0%
+well and so that we can reconstruct our
+ 
+
+ align:start position:0%
+well and so that we can reconstruct our
+function y of T as an integral of our
+
+ align:start position:0%
+function y of T as an integral of our
+ 
+
+ align:start position:0%
+function y of T as an integral of our
+Fourier coefficients times the e to the
+
+ align:start position:0%
+Fourier coefficients times the e to the
+ 
+
+ align:start position:0%
+Fourier coefficients times the e to the
+I Omega T see that it's the same it's
+
+ align:start position:0%
+I Omega T see that it's the same it's
+ 
+
+ align:start position:0%
+I Omega T see that it's the same it's
+essentially the same thing it's just
+
+ align:start position:0%
+essentially the same thing it's just
+ 
+
+ align:start position:0%
+essentially the same thing it's just
+that we're turning this sum into an
+
+ align:start position:0%
+that we're turning this sum into an
+ 
+
+ align:start position:0%
+that we're turning this sum into an
+integral okay all right so that's called
+
+ align:start position:0%
+integral okay all right so that's called
+ 
+
+ align:start position:0%
+integral okay all right so that's called
+a Fourier transform and that's the
+
+ align:start position:0%
+a Fourier transform and that's the
+ 
+
+ align:start position:0%
+a Fourier transform and that's the
+inverse Fourier transform this from a
+
+ align:start position:0%
+inverse Fourier transform this from a
+ 
+
+ align:start position:0%
+inverse Fourier transform this from a
+function to Fourier coefficients and
+
+ align:start position:0%
+function to Fourier coefficients and
+ 
+
+ align:start position:0%
+function to Fourier coefficients and
+this takes your Fourier coefficients and
+
+ align:start position:0%
+this takes your Fourier coefficients and
+ 
+
+ align:start position:0%
+this takes your Fourier coefficients and
+goes back to your function okay all
+
+ align:start position:0%
+goes back to your function okay all
+ 
+
+ align:start position:0%
+goes back to your function okay all
+right good let me just show you a few
+
+ align:start position:0%
+right good let me just show you a few
+ 
+
+ align:start position:0%
+right good let me just show you a few
+simple examples so let's start let's
+
+ align:start position:0%
+simple examples so let's start let's
+ 
+
+ align:start position:0%
+simple examples so let's start let's
+have a start with a function y of T
+
+ align:start position:0%
+have a start with a function y of T
+ 
+
+ align:start position:0%
+have a start with a function y of T
+equals 1 so it's just a constant what is
+
+ align:start position:0%
+equals 1 so it's just a constant what is
+ 
+
+ align:start position:0%
+equals 1 so it's just a constant what is
+the Fourier transform so let's plug this
+
+ align:start position:0%
+the Fourier transform so let's plug this
+ 
+
+ align:start position:0%
+the Fourier transform so let's plug this
+into here
+
+ align:start position:0%
+into here
+ 
+
+ align:start position:0%
+into here
+okay does anyone know what that integral
+
+ align:start position:0%
+okay does anyone know what that integral
+ 
+
+ align:start position:0%
+okay does anyone know what that integral
+looks like of the integral from minus
+
+ align:start position:0%
+looks like of the integral from minus
+ 
+
+ align:start position:0%
+looks like of the integral from minus
+infinity to infinity of e the minus I
+
+ align:start position:0%
+infinity to infinity of e the minus I
+ 
+
+ align:start position:0%
+infinity to infinity of e the minus I
+Omega T DT integrating over time it's a
+
+ align:start position:0%
+Omega T DT integrating over time it's a
+ 
+
+ align:start position:0%
+Omega T DT integrating over time it's a
+delta function there's only one value of
+
+ align:start position:0%
+delta function there's only one value of
+ 
+
+ align:start position:0%
+delta function there's only one value of
+Omega for which that function is not
+
+ align:start position:0%
+Omega for which that function is not
+ 
+
+ align:start position:0%
+Omega for which that function is not
+zero remember so let's say Omega equals
+
+ align:start position:0%
+zero remember so let's say Omega equals
+ 
+
+ align:start position:0%
+zero remember so let's say Omega equals
+one one you know one Hertz this is just
+
+ align:start position:0%
+one one you know one Hertz this is just
+ 
+
+ align:start position:0%
+one one you know one Hertz this is just
+a bunch of sines and cosines so when you
+
+ align:start position:0%
+a bunch of sines and cosines so when you
+ 
+
+ align:start position:0%
+a bunch of sines and cosines so when you
+integrate over sines and cosines you get
+
+ align:start position:0%
+integrate over sines and cosines you get
+ 
+
+ align:start position:0%
+integrate over sines and cosines you get
+zero integral over time of cosine is
+
+ align:start position:0%
+zero integral over time of cosine is
+ 
+
+ align:start position:0%
+zero integral over time of cosine is
+just zero
+
+ align:start position:0%
+just zero
+ 
+
+ align:start position:0%
+just zero
+but if Omega is zero then what is e to
+
+ align:start position:0%
+but if Omega is zero then what is e to
+ 
+
+ align:start position:0%
+but if Omega is zero then what is e to
+the I Omega T e to the I 0 is 1 and so
+
+ align:start position:0%
+the I Omega T e to the I 0 is 1 and so
+ 
+
+ align:start position:0%
+the I Omega T e to the I 0 is 1 and so
+we're integrating over 1 times DT right
+
+ align:start position:0%
+we're integrating over 1 times DT right
+ 
+
+ align:start position:0%
+we're integrating over 1 times DT right
+and that becomes infinity at Omega
+
+ align:start position:0%
+and that becomes infinity at Omega
+ 
+
+ align:start position:0%
+and that becomes infinity at Omega
+equals zero and that's a delta function
+
+ align:start position:0%
+equals zero and that's a delta function
+ 
+
+ align:start position:0%
+equals zero and that's a delta function
+it's zero everywhere except for at zero
+
+ align:start position:0%
+it's zero everywhere except for at zero
+ 
+
+ align:start position:0%
+it's zero everywhere except for at zero
+so that becomes a delta function this
+
+ align:start position:0%
+so that becomes a delta function this
+ 
+
+ align:start position:0%
+so that becomes a delta function this
+Fourier transform of a constant is a
+
+ align:start position:0%
+Fourier transform of a constant is a
+ 
+
+ align:start position:0%
+Fourier transform of a constant is a
+delta function okay and that's a really
+
+ align:start position:0%
+delta function okay and that's a really
+ 
+
+ align:start position:0%
+delta function okay and that's a really
+it's a really good one to know before
+
+ align:start position:0%
+it's a really good one to know before
+ 
+
+ align:start position:0%
+it's a really good one to know before
+you transform of a constant is a delta
+
+ align:start position:0%
+you transform of a constant is a delta
+ 
+
+ align:start position:0%
+you transform of a constant is a delta
+function okay that's called a Fourier
+
+ align:start position:0%
+function okay that's called a Fourier
+ 
+
+ align:start position:0%
+function okay that's called a Fourier
+transform pair you have a function and
+
+ align:start position:0%
+transform pair you have a function and
+ 
+
+ align:start position:0%
+transform pair you have a function and
+another function one function is the
+
+ align:start position:0%
+another function one function is the
+ 
+
+ align:start position:0%
+another function one function is the
+Fourier transform of the other function
+
+ align:start position:0%
+Fourier transform of the other function
+ 
+
+ align:start position:0%
+Fourier transform of the other function
+that's called a Fourier transform pair
+
+ align:start position:0%
+that's called a Fourier transform pair
+ 
+
+ align:start position:0%
+that's called a Fourier transform pair
+okay so the Fourier transform of a
+
+ align:start position:0%
+okay so the Fourier transform of a
+ 
+
+ align:start position:0%
+okay so the Fourier transform of a
+constant is just a delta function at 0
+
+ align:start position:0%
+constant is just a delta function at 0
+ 
+
+ align:start position:0%
+constant is just a delta function at 0
+you can invert that if you integrate
+
+ align:start position:0%
+you can invert that if you integrate
+ 
+
+ align:start position:0%
+you can invert that if you integrate
+let's just plug that Delta function into
+
+ align:start position:0%
+let's just plug that Delta function into
+ 
+
+ align:start position:0%
+let's just plug that Delta function into
+here if you integrate Delta function
+
+ align:start position:0%
+here if you integrate Delta function
+ 
+
+ align:start position:0%
+here if you integrate Delta function
+times e to the I Omega T you just get e
+
+ align:start position:0%
+times e to the I Omega T you just get e
+ 
+
+ align:start position:0%
+times e to the I Omega T you just get e
+to the I 0 T which is just 1 ok
+
+ align:start position:0%
+to the I 0 T which is just 1 ok
+ 
+
+ align:start position:0%
+to the I 0 T which is just 1 ok
+so we can take the Fourier transform of
+
+ align:start position:0%
+so we can take the Fourier transform of
+ 
+
+ align:start position:0%
+so we can take the Fourier transform of
+one get a delta function interest for
+
+ align:start position:0%
+one get a delta function interest for
+ 
+
+ align:start position:0%
+one get a delta function interest for
+you transform the Delta function and get
+
+ align:start position:0%
+you transform the Delta function and get
+ 
+
+ align:start position:0%
+you transform the Delta function and get
+back one okay all right
+
+ align:start position:0%
+back one okay all right
+ 
+
+ align:start position:0%
+back one okay all right
+how about this function right here this
+
+ align:start position:0%
+how about this function right here this
+ 
+
+ align:start position:0%
+how about this function right here this
+function is e to the I Omega 1 it's it's
+
+ align:start position:0%
+function is e to the I Omega 1 it's it's
+ 
+
+ align:start position:0%
+function is e to the I Omega 1 it's it's
+a sine wave and a cosine wave a complex
+
+ align:start position:0%
+a sine wave and a cosine wave a complex
+ 
+
+ align:start position:0%
+a sine wave and a cosine wave a complex
+sine and cosine at frequency Omega 1
+
+ align:start position:0%
+sine and cosine at frequency Omega 1
+ 
+
+ align:start position:0%
+sine and cosine at frequency Omega 1
+anybody know what the for you so it's
+
+ align:start position:0%
+anybody know what the for you so it's
+ 
+
+ align:start position:0%
+anybody know what the for you so it's
+it's basically you can think of this
+
+ align:start position:0%
+it's basically you can think of this
+ 
+
+ align:start position:0%
+it's basically you can think of this
+okay yeah that's all right answer rather
+
+ align:start position:0%
+okay yeah that's all right answer rather
+ 
+
+ align:start position:0%
+okay yeah that's all right answer rather
+than try to explain it I'll just show
+
+ align:start position:0%
+than try to explain it I'll just show
+ 
+
+ align:start position:0%
+than try to explain it I'll just show
+you so the Fourier transform of this is
+
+ align:start position:0%
+you so the Fourier transform of this is
+ 
+
+ align:start position:0%
+you so the Fourier transform of this is
+to peak at Omega 1 alright and we can
+
+ align:start position:0%
+to peak at Omega 1 alright and we can
+ 
+
+ align:start position:0%
+to peak at Omega 1 alright and we can
+inverse Fourier transform that and
+
+ align:start position:0%
+inverse Fourier transform that and
+ 
+
+ align:start position:0%
+inverse Fourier transform that and
+recover our original function ok so
+
+ align:start position:0%
+recover our original function ok so
+ 
+
+ align:start position:0%
+recover our original function ok so
+those that's those last few slides are
+
+ align:start position:0%
+those that's those last few slides are
+ 
+
+ align:start position:0%
+those that's those last few slides are
+more for the aficionados you don't have
+
+ align:start position:0%
+more for the aficionados you don't have
+ 
+
+ align:start position:0%
+more for the aficionados you don't have
+to know that we're gonna spend time
+
+ align:start position:0%
+to know that we're gonna spend time
+ 
+
+ align:start position:0%
+to know that we're gonna spend time
+looking at the at the discrete versions
+
+ align:start position:0%
+looking at the at the discrete versions
+ 
+
+ align:start position:0%
+looking at the at the discrete versions
+of these things okay all right how about
+
+ align:start position:0%
+of these things okay all right how about
+ 
+
+ align:start position:0%
+of these things okay all right how about
+this case this is a simple case where
+
+ align:start position:0%
+this case this is a simple case where
+ 
+
+ align:start position:0%
+this case this is a simple case where
+you have a function that the Fourier
+
+ align:start position:0%
+you have a function that the Fourier
+ 
+
+ align:start position:0%
+you have a function that the Fourier
+transform of which has a peak at Omega 1
+
+ align:start position:0%
+transform of which has a peak at Omega 1
+ 
+
+ align:start position:0%
+transform of which has a peak at Omega 1
+and a peak at minus Omega 1 the Fourier
+
+ align:start position:0%
+and a peak at minus Omega 1 the Fourier
+ 
+
+ align:start position:0%
+and a peak at minus Omega 1 the Fourier
+transform of the inverse Fourier
+
+ align:start position:0%
+transform of the inverse Fourier
+ 
+
+ align:start position:0%
+transform of the inverse Fourier
+transform of that is just cosine Omega
+
+ align:start position:0%
+transform of that is just cosine Omega
+ 
+
+ align:start position:0%
+transform of that is just cosine Omega
+1t ok so a function a cosine function
+
+ align:start position:0%
+1t ok so a function a cosine function
+ 
+
+ align:start position:0%
+1t ok so a function a cosine function
+with frequency Omega 1 has two peaks one
+
+ align:start position:0%
+with frequency Omega 1 has two peaks one
+ 
+
+ align:start position:0%
+with frequency Omega 1 has two peaks one
+at frequency Omega 1 and another one at
+
+ align:start position:0%
+at frequency Omega 1 and another one at
+ 
+
+ align:start position:0%
+at frequency Omega 1 and another one at
+frequency minus Omega 1 so that looks a
+
+ align:start position:0%
+frequency minus Omega 1 so that looks a
+ 
+
+ align:start position:0%
+frequency minus Omega 1 so that looks a
+lot like the case we just talked about
+
+ align:start position:0%
+lot like the case we just talked about
+ 
+
+ align:start position:0%
+lot like the case we just talked about
+right where we had this complex Fourier
+
+ align:start position:0%
+right where we had this complex Fourier
+ 
+
+ align:start position:0%
+right where we had this complex Fourier
+series and we had a peak at N equals 2
+
+ align:start position:0%
+series and we had a peak at N equals 2
+ 
+
+ align:start position:0%
+series and we had a peak at N equals 2
+and another peak at N equals -2 and the
+
+ align:start position:0%
+and another peak at N equals -2 and the
+ 
+
+ align:start position:0%
+and another peak at N equals -2 and the
+function that gave us that complex
+
+ align:start position:0%
+function that gave us that complex
+ 
+
+ align:start position:0%
+function that gave us that complex
+Fourier series was cosine 2t so that's
+
+ align:start position:0%
+Fourier series was cosine 2t so that's
+ 
+
+ align:start position:0%
+Fourier series was cosine 2t so that's
+just what we have here we have a peak in
+
+ align:start position:0%
+just what we have here we have a peak in
+ 
+
+ align:start position:0%
+just what we have here we have a peak in
+the spectrum at Omega 1 peak at minus
+
+ align:start position:0%
+the spectrum at Omega 1 peak at minus
+ 
+
+ align:start position:0%
+the spectrum at Omega 1 peak at minus
+Omega 1 and that is the Fourier
+
+ align:start position:0%
+Omega 1 and that is the Fourier
+ 
+
+ align:start position:0%
+Omega 1 and that is the Fourier
+decomposition of a function that is
+
+ align:start position:0%
+decomposition of a function that is
+ 
+
+ align:start position:0%
+decomposition of a function that is
+cosine Omega 1t
+
+ align:start position:0%
+cosine Omega 1t
+ 
+
+ align:start position:0%
+cosine Omega 1t
+so it's just like what we saw before for
+
+ align:start position:0%
+so it's just like what we saw before for
+ 
+
+ align:start position:0%
+so it's just like what we saw before for
+the case of the Fourier the complex
+
+ align:start position:0%
+the case of the Fourier the complex
+ 
+
+ align:start position:0%
+the case of the Fourier the complex
+Fourier series alright so that was
+
+ align:start position:0%
+Fourier series alright so that was
+ 
+
+ align:start position:0%
+Fourier series alright so that was
+Fourier transform and now let's talk
+
+ align:start position:0%
+Fourier transform and now let's talk
+ 
+
+ align:start position:0%
+Fourier transform and now let's talk
+about the discrete Fourier transform and
+
+ align:start position:0%
+about the discrete Fourier transform and
+ 
+
+ align:start position:0%
+about the discrete Fourier transform and
+the associated algorithm for computing
+
+ align:start position:0%
+the associated algorithm for computing
+ 
+
+ align:start position:0%
+the associated algorithm for computing
+that very quickly called a fast Fourier
+
+ align:start position:0%
+that very quickly called a fast Fourier
+ 
+
+ align:start position:0%
+that very quickly called a fast Fourier
+transform or FFT okay so you can see
+
+ align:start position:0%
+transform or FFT okay so you can see
+ 
+
+ align:start position:0%
+transform or FFT okay so you can see
+computing these Fourier transforms if
+
+ align:start position:0%
+computing these Fourier transforms if
+ 
+
+ align:start position:0%
+computing these Fourier transforms if
+you were to actually try to compute
+
+ align:start position:0%
+you were to actually try to compute
+ 
+
+ align:start position:0%
+you were to actually try to compute
+Fourier transforms by taking a function
+
+ align:start position:0%
+Fourier transforms by taking a function
+ 
+
+ align:start position:0%
+Fourier transforms by taking a function
+multiplying it by these complex
+
+ align:start position:0%
+multiplying it by these complex
+ 
+
+ align:start position:0%
+multiplying it by these complex
+Exponential's like writing down the
+
+ align:start position:0%
+Exponential's like writing down the
+ 
+
+ align:start position:0%
+Exponential's like writing down the
+value of e to the I Omega T at a bunch
+
+ align:start position:0%
+value of e to the I Omega T at a bunch
+ 
+
+ align:start position:0%
+value of e to the I Omega T at a bunch
+of different omegas and a bunch of
+
+ align:start position:0%
+of different omegas and a bunch of
+ 
+
+ align:start position:0%
+of different omegas and a bunch of
+different ways and then integrating that
+
+ align:start position:0%
+different ways and then integrating that
+ 
+
+ align:start position:0%
+different ways and then integrating that
+numerically that would take forever
+
+ align:start position:0%
+numerically that would take forever
+ 
+
+ align:start position:0%
+numerically that would take forever
+right computationally but it turns out
+
+ align:start position:0%
+right computationally but it turns out
+ 
+
+ align:start position:0%
+right computationally but it turns out
+that there's right so you have to
+
+ align:start position:0%
+that there's right so you have to
+ 
+
+ align:start position:0%
+that there's right so you have to
+compute that integral for it over time
+
+ align:start position:0%
+compute that integral for it over time
+ 
+
+ align:start position:0%
+compute that integral for it over time
+for every Omega that you're interested
+
+ align:start position:0%
+for every Omega that you're interested
+ 
+
+ align:start position:0%
+for every Omega that you're interested
+in all right
+
+ align:start position:0%
+in all right
+ 
+
+ align:start position:0%
+in all right
+but it turns out really really fast
+
+ align:start position:0%
+but it turns out really really fast
+ 
+
+ align:start position:0%
+but it turns out really really fast
+algorithm that you can use for the case
+
+ align:start position:0%
+algorithm that you can use for the case
+ 
+
+ align:start position:0%
+algorithm that you can use for the case
+where you've got functions that are
+
+ align:start position:0%
+where you've got functions that are
+ 
+
+ align:start position:0%
+where you've got functions that are
+sampled in time okay and you want to
+
+ align:start position:0%
+sampled in time okay and you want to
+ 
+
+ align:start position:0%
+sampled in time okay and you want to
+extract the frequencies of that signal
+
+ align:start position:0%
+extract the frequencies of that signal
+ 
+
+ align:start position:0%
+extract the frequencies of that signal
+at a discrete set of frequencies
+
+ align:start position:0%
+at a discrete set of frequencies
+ 
+
+ align:start position:0%
+at a discrete set of frequencies
+okay so let's I'm going to switch from
+
+ align:start position:0%
+okay so let's I'm going to switch from
+ 
+
+ align:start position:0%
+okay so let's I'm going to switch from
+using Omega which is very commonly used
+
+ align:start position:0%
+using Omega which is very commonly used
+ 
+
+ align:start position:0%
+using Omega which is very commonly used
+when you're talking about Fourier
+
+ align:start position:0%
+when you're talking about Fourier
+ 
+
+ align:start position:0%
+when you're talking about Fourier
+transforms to just using F the frequency
+
+ align:start position:0%
+transforms to just using F the frequency
+ 
+
+ align:start position:0%
+transforms to just using F the frequency
+so it's just F is just 2 pi so Omega is
+
+ align:start position:0%
+so it's just F is just 2 pi so Omega is
+ 
+
+ align:start position:0%
+so it's just F is just 2 pi so Omega is
+2 pi F so R here I'm just rewriting the
+
+ align:start position:0%
+2 pi F so R here I'm just rewriting the
+ 
+
+ align:start position:0%
+2 pi F so R here I'm just rewriting the
+Fourier transform and the inverse
+
+ align:start position:0%
+Fourier transform and the inverse
+ 
+
+ align:start position:0%
+Fourier transform and the inverse
+Fourier transform with F rather than
+
+ align:start position:0%
+Fourier transform with F rather than
+ 
+
+ align:start position:0%
+Fourier transform with F rather than
+Omega so we're gonna start using F's now
+
+ align:start position:0%
+Omega so we're gonna start using F's now
+ 
+
+ align:start position:0%
+Omega so we're gonna start using F's now
+for the discrete Fourier transform case
+
+ align:start position:0%
+for the discrete Fourier transform case
+ 
+
+ align:start position:0%
+for the discrete Fourier transform case
+and we're going to consider the case
+
+ align:start position:0%
+and we're going to consider the case
+ 
+
+ align:start position:0%
+and we're going to consider the case
+where we have signals that are sampled
+
+ align:start position:0%
+where we have signals that are sampled
+ 
+
+ align:start position:0%
+where we have signals that are sampled
+at regular intervals delta T ok so here
+
+ align:start position:0%
+at regular intervals delta T ok so here
+ 
+
+ align:start position:0%
+at regular intervals delta T ok so here
+we have a function of time Y of T and
+
+ align:start position:0%
+we have a function of time Y of T and
+ 
+
+ align:start position:0%
+we have a function of time Y of T and
+we're gonna sample that signal at
+
+ align:start position:0%
+we're gonna sample that signal at
+ 
+
+ align:start position:0%
+we're gonna sample that signal at
+regular intervals delta T so this is
+
+ align:start position:0%
+regular intervals delta T so this is
+ 
+
+ align:start position:0%
+regular intervals delta T so this is
+Delta t right
+
+ align:start position:0%
+Delta t right
+ 
+
+ align:start position:0%
+Delta t right
+that time interval there so the sampling
+
+ align:start position:0%
+that time interval there so the sampling
+ 
+
+ align:start position:0%
+that time interval there so the sampling
+rate the sampling frequency is just one
+
+ align:start position:0%
+rate the sampling frequency is just one
+ 
+
+ align:start position:0%
+rate the sampling frequency is just one
+over delta T so the way this works in
+
+ align:start position:0%
+over delta T so the way this works in
+ 
+
+ align:start position:0%
+over delta T so the way this works in
+the Fourier transform algorithm is you
+
+ align:start position:0%
+the Fourier transform algorithm is you
+ 
+
+ align:start position:0%
+the Fourier transform algorithm is you
+just take those samples and you into a
+
+ align:start position:0%
+just take those samples and you into a
+ 
+
+ align:start position:0%
+just take those samples and you into a
+vector in MATLAB okay just some one one
+
+ align:start position:0%
+vector in MATLAB okay just some one one
+ 
+
+ align:start position:0%
+vector in MATLAB okay just some one one
+dimensional array and we're going to
+
+ align:start position:0%
+dimensional array and we're going to
+ 
+
+ align:start position:0%
+dimensional array and we're going to
+imagine that our samples are acquired at
+
+ align:start position:0%
+imagine that our samples are acquired at
+ 
+
+ align:start position:0%
+imagine that our samples are acquired at
+different times and let's lay x minus x
+
+ align:start position:0%
+different times and let's lay x minus x
+ 
+
+ align:start position:0%
+different times and let's lay x minus x
+step eight - seven - six time step zero
+
+ align:start position:0%
+step eight - seven - six time step zero
+ 
+
+ align:start position:0%
+step eight - seven - six time step zero
+is in the middle up to time step seven
+
+ align:start position:0%
+is in the middle up to time step seven
+ 
+
+ align:start position:0%
+is in the middle up to time step seven
+and we're gonna say that n is an even
+
+ align:start position:0%
+and we're gonna say that n is an even
+ 
+
+ align:start position:0%
+and we're gonna say that n is an even
+number that the fast Fourier transform
+
+ align:start position:0%
+number that the fast Fourier transform
+ 
+
+ align:start position:0%
+number that the fast Fourier transform
+works much much faster when n is an even
+
+ align:start position:0%
+works much much faster when n is an even
+ 
+
+ align:start position:0%
+works much much faster when n is an even
+number and it works even faster when N
+
+ align:start position:0%
+number and it works even faster when N
+ 
+
+ align:start position:0%
+number and it works even faster when N
+is a multiple a power of two okay so in
+
+ align:start position:0%
+is a multiple a power of two okay so in
+ 
+
+ align:start position:0%
+is a multiple a power of two okay so in
+this case we have 16 samples it's two to
+
+ align:start position:0%
+this case we have 16 samples it's two to
+ 
+
+ align:start position:0%
+this case we have 16 samples it's two to
+the four should usually try to make your
+
+ align:start position:0%
+the four should usually try to make your
+ 
+
+ align:start position:0%
+the four should usually try to make your
+samples be a power of two okay the
+
+ align:start position:0%
+samples be a power of two okay the
+ 
+
+ align:start position:0%
+samples be a power of two okay the
+number of samples okay so there is our
+
+ align:start position:0%
+number of samples okay so there is our
+ 
+
+ align:start position:0%
+number of samples okay so there is our
+function of time sampled at regular
+
+ align:start position:0%
+function of time sampled at regular
+ 
+
+ align:start position:0%
+function of time sampled at regular
+intervals T so you can see that the team
+
+ align:start position:0%
+intervals T so you can see that the team
+ 
+
+ align:start position:0%
+intervals T so you can see that the team
+in the minimum time in this vector of
+
+ align:start position:0%
+in the minimum time in this vector of
+ 
+
+ align:start position:0%
+in the minimum time in this vector of
+sample points in our function is minus n
+
+ align:start position:0%
+sample points in our function is minus n
+ 
+
+ align:start position:0%
+sample points in our function is minus n
+over 2 delta T okay and that Matt is n
+
+ align:start position:0%
+over 2 delta T okay and that Matt is n
+ 
+
+ align:start position:0%
+over 2 delta T okay and that Matt is n
+over 2 minus 1 times delta T okay and
+
+ align:start position:0%
+over 2 minus 1 times delta T okay and
+ 
+
+ align:start position:0%
+over 2 minus 1 times delta T okay and
+that's what the the MATLAB code would
+
+ align:start position:0%
+that's what the the MATLAB code would
+ 
+
+ align:start position:0%
+that's what the the MATLAB code would
+look like to generate an array of time
+
+ align:start position:0%
+look like to generate an array of time
+ 
+
+ align:start position:0%
+look like to generate an array of time
+values okay
+
+ align:start position:0%
+values okay
+ 
+
+ align:start position:0%
+values okay
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+all right the FFT algorithm returns the
+
+ align:start position:0%
+all right the FFT algorithm returns the
+ 
+
+ align:start position:0%
+all right the FFT algorithm returns the
+Fourier components of that function of
+
+ align:start position:0%
+Fourier components of that function of
+ 
+
+ align:start position:0%
+Fourier components of that function of
+time okay and it returns the Fourier
+
+ align:start position:0%
+time okay and it returns the Fourier
+ 
+
+ align:start position:0%
+time okay and it returns the Fourier
+components in a vector that has the
+
+ align:start position:0%
+components in a vector that has the
+ 
+
+ align:start position:0%
+components in a vector that has the
+negative frequencies on one side and the
+
+ align:start position:0%
+negative frequencies on one side and the
+ 
+
+ align:start position:0%
+negative frequencies on one side and the
+positive frequencies on the other side
+
+ align:start position:0%
+positive frequencies on the other side
+ 
+
+ align:start position:0%
+positive frequencies on the other side
+okay and the constant term here in the
+
+ align:start position:0%
+okay and the constant term here in the
+ 
+
+ align:start position:0%
+okay and the constant term here in the
+middle okay the minimum frequency is n
+
+ align:start position:0%
+middle okay the minimum frequency is n
+ 
+
+ align:start position:0%
+middle okay the minimum frequency is n
+over 2 times Delta F oh I should say it
+
+ align:start position:0%
+over 2 times Delta F oh I should say it
+ 
+
+ align:start position:0%
+over 2 times Delta F oh I should say it
+returns the Fourier components in steps
+
+ align:start position:0%
+returns the Fourier components in steps
+ 
+
+ align:start position:0%
+returns the Fourier components in steps
+of Delta F where Delta F is the sampling
+
+ align:start position:0%
+of Delta F where Delta F is the sampling
+ 
+
+ align:start position:0%
+of Delta F where Delta F is the sampling
+rate divided by the number of time steps
+
+ align:start position:0%
+rate divided by the number of time steps
+ 
+
+ align:start position:0%
+rate divided by the number of time steps
+that you put into it okay don't panic
+
+ align:start position:0%
+that you put into it okay don't panic
+ 
+
+ align:start position:0%
+that you put into it okay don't panic
+this is just like reference I'm showing
+
+ align:start position:0%
+this is just like reference I'm showing
+ 
+
+ align:start position:0%
+this is just like reference I'm showing
+you like what how you put the data in
+
+ align:start position:0%
+you like what how you put the data in
+ 
+
+ align:start position:0%
+you like what how you put the data in
+and how you get the data out okay when
+
+ align:start position:0%
+and how you get the data out okay when
+ 
+
+ align:start position:0%
+and how you get the data out okay when
+you put data into the Fourier transform
+
+ align:start position:0%
+you put data into the Fourier transform
+ 
+
+ align:start position:0%
+you put data into the Fourier transform
+algorithm the FFT algorithm you put in
+
+ align:start position:0%
+algorithm the FFT algorithm you put in
+ 
+
+ align:start position:0%
+algorithm the FFT algorithm you put in
+data that's sampled at times and you
+
+ align:start position:0%
+data that's sampled at times and you
+ 
+
+ align:start position:0%
+data that's sampled at times and you
+have to know what those times are right
+
+ align:start position:0%
+have to know what those times are right
+ 
+
+ align:start position:0%
+have to know what those times are right
+if you want to make a plot of the data
+
+ align:start position:0%
+if you want to make a plot of the data
+ 
+
+ align:start position:0%
+if you want to make a plot of the data
+eat to make an array of time values okay
+
+ align:start position:0%
+eat to make an array of time values okay
+ 
+
+ align:start position:0%
+eat to make an array of time values okay
+and they just go from a team into a t
+
+ align:start position:0%
+and they just go from a team into a t
+ 
+
+ align:start position:0%
+and they just go from a team into a t
+max all right and there's a little piece
+
+ align:start position:0%
+max all right and there's a little piece
+ 
+
+ align:start position:0%
+max all right and there's a little piece
+of MATLAB code that produces that array
+
+ align:start position:0%
+of MATLAB code that produces that array
+ 
+
+ align:start position:0%
+of MATLAB code that produces that array
+of times for you what you get back from
+
+ align:start position:0%
+of times for you what you get back from
+ 
+
+ align:start position:0%
+of times for you what you get back from
+the Fourier transform the FFT an array
+
+ align:start position:0%
+the Fourier transform the FFT an array
+ 
+
+ align:start position:0%
+the Fourier transform the FFT an array
+not of values of the function of time
+
+ align:start position:0%
+not of values of the function of time
+ 
+
+ align:start position:0%
+not of values of the function of time
+but rather an array of Fourier
+
+ align:start position:0%
+but rather an array of Fourier
+ 
+
+ align:start position:0%
+but rather an array of Fourier
+coefficients just like we stuck in into
+
+ align:start position:0%
+coefficients just like we stuck in into
+ 
+
+ align:start position:0%
+coefficients just like we stuck in into
+our you know when we did the free the
+
+ align:start position:0%
+our you know when we did the free the
+ 
+
+ align:start position:0%
+our you know when we did the free the
+complex Fourier series we stuck in a
+
+ align:start position:0%
+complex Fourier series we stuck in a
+ 
+
+ align:start position:0%
+complex Fourier series we stuck in a
+function of T and we get out a list of
+
+ align:start position:0%
+function of T and we get out a list of
+ 
+
+ align:start position:0%
+function of T and we get out a list of
+Fourier coefficients same thing here we
+
+ align:start position:0%
+Fourier coefficients same thing here we
+ 
+
+ align:start position:0%
+Fourier coefficients same thing here we
+put in a function of time okay and we
+
+ align:start position:0%
+put in a function of time okay and we
+ 
+
+ align:start position:0%
+put in a function of time okay and we
+get out Fourier coefficients and the
+
+ align:start position:0%
+get out Fourier coefficients and the
+ 
+
+ align:start position:0%
+get out Fourier coefficients and the
+Fourier coefficients are complex numbers
+
+ align:start position:0%
+Fourier coefficients are complex numbers
+ 
+
+ align:start position:0%
+Fourier coefficients are complex numbers
+associated with different free
+
+ align:start position:0%
+associated with different free
+ 
+
+ align:start position:0%
+associated with different free
+Quincy's know though the let's say the
+
+ align:start position:0%
+Quincy's know though the let's say the
+ 
+
+ align:start position:0%
+Quincy's know though the let's say the
+middle coefficient that you get will be
+
+ align:start position:0%
+middle coefficient that you get will be
+ 
+
+ align:start position:0%
+middle coefficient that you get will be
+the coefficient for the constant term
+
+ align:start position:0%
+the coefficient for the constant term
+ 
+
+ align:start position:0%
+the coefficient for the constant term
+right this coefficient down here will be
+
+ align:start position:0%
+right this coefficient down here will be
+ 
+
+ align:start position:0%
+right this coefficient down here will be
+the coefficient for the minimum
+
+ align:start position:0%
+the coefficient for the minimum
+ 
+
+ align:start position:0%
+the coefficient for the minimum
+frequency and that coefficient will be
+
+ align:start position:0%
+frequency and that coefficient will be
+ 
+
+ align:start position:0%
+frequency and that coefficient will be
+the coefficient for the maximum
+
+ align:start position:0%
+the coefficient for the maximum
+ 
+
+ align:start position:0%
+the coefficient for the maximum
+frequency the most positive frequency
+
+ align:start position:0%
+frequency the most positive frequency
+ 
+
+ align:start position:0%
+frequency the most positive frequency
+okay all right does that make sense
+
+ align:start position:0%
+okay all right does that make sense
+ 
+
+ align:start position:0%
+okay all right does that make sense
+ah okay so I was hoping to just kind of
+
+ align:start position:0%
+ah okay so I was hoping to just kind of
+ 
+
+ align:start position:0%
+ah okay so I was hoping to just kind of
+skip over that for now but but when you
+
+ align:start position:0%
+skip over that for now but but when you
+ 
+
+ align:start position:0%
+skip over that for now but but when you
+do a discrete Fourier transform turns
+
+ align:start position:0%
+do a discrete Fourier transform turns
+ 
+
+ align:start position:0%
+do a discrete Fourier transform turns
+out that the coefficient for the most
+
+ align:start position:0%
+out that the coefficient for the most
+ 
+
+ align:start position:0%
+out that the coefficient for the most
+negative frequency is always exactly the
+
+ align:start position:0%
+negative frequency is always exactly the
+ 
+
+ align:start position:0%
+negative frequency is always exactly the
+same as the coefficient for the most
+
+ align:start position:0%
+same as the coefficient for the most
+ 
+
+ align:start position:0%
+same as the coefficient for the most
+positive frequency okay and so and so
+
+ align:start position:0%
+positive frequency okay and so and so
+ 
+
+ align:start position:0%
+positive frequency okay and so and so
+they're just given in 1 they're both
+
+ align:start position:0%
+they're just given in 1 they're both
+ 
+
+ align:start position:0%
+they're just given in 1 they're both
+given in one element of the array okay
+
+ align:start position:0%
+given in one element of the array okay
+ 
+
+ align:start position:0%
+given in one element of the array okay
+you could replicate that up here right
+
+ align:start position:0%
+you could replicate that up here right
+ 
+
+ align:start position:0%
+you could replicate that up here right
+but it would be pointless and the length
+
+ align:start position:0%
+but it would be pointless and the length
+ 
+
+ align:start position:0%
+but it would be pointless and the length
+of the array would have to be n plus 1
+
+ align:start position:0%
+of the array would have to be n plus 1
+ 
+
+ align:start position:0%
+of the array would have to be n plus 1
+ok yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good that's that it always comes up
+
+ align:start position:0%
+okay good that's that it always comes up
+ 
+
+ align:start position:0%
+okay good that's that it always comes up
+and it's a great question so what we're
+
+ align:start position:0%
+and it's a great question so what we're
+ 
+
+ align:start position:0%
+and it's a great question so what we're
+trying to do is to come up with a way of
+
+ align:start position:0%
+trying to do is to come up with a way of
+ 
+
+ align:start position:0%
+trying to do is to come up with a way of
+representing arbitrary functions right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can represent symmetric functions
+
+ align:start position:0%
+so we can represent symmetric functions
+ 
+
+ align:start position:0%
+so we can represent symmetric functions
+with by summing together a bunch of
+
+ align:start position:0%
+with by summing together a bunch of
+ 
+
+ align:start position:0%
+with by summing together a bunch of
+cosines we can represent anti-symmetric
+
+ align:start position:0%
+cosines we can represent anti-symmetric
+ 
+
+ align:start position:0%
+cosines we can represent anti-symmetric
+functions by summing together a bunch of
+
+ align:start position:0%
+functions by summing together a bunch of
+ 
+
+ align:start position:0%
+functions by summing together a bunch of
+sines
+
+ align:start position:0%
+sines
+ 
+
+ align:start position:0%
+sines
+but if we want to represent an arbitrary
+
+ align:start position:0%
+but if we want to represent an arbitrary
+ 
+
+ align:start position:0%
+but if we want to represent an arbitrary
+function we have to use both cosines and
+
+ align:start position:0%
+function we have to use both cosines and
+ 
+
+ align:start position:0%
+function we have to use both cosines and
+sines right so so we have this trick
+
+ align:start position:0%
+sines right so so we have this trick
+ 
+
+ align:start position:0%
+sines right so so we have this trick
+though where we can instead of using
+
+ align:start position:0%
+though where we can instead of using
+ 
+
+ align:start position:0%
+though where we can instead of using
+sines and cosines using these two
+
+ align:start position:0%
+sines and cosines using these two
+ 
+
+ align:start position:0%
+sines and cosines using these two
+separate functions we can use a single
+
+ align:start position:0%
+separate functions we can use a single
+ 
+
+ align:start position:0%
+separate functions we can use a single
+function which is a complex exponential
+
+ align:start position:0%
+function which is a complex exponential
+ 
+
+ align:start position:0%
+function which is a complex exponential
+to represent things that can be
+
+ align:start position:0%
+to represent things that can be
+ 
+
+ align:start position:0%
+to represent things that can be
+represented by sums of cosines as well
+
+ align:start position:0%
+represented by sums of cosines as well
+ 
+
+ align:start position:0%
+represented by sums of cosines as well
+as things that can be represented as
+
+ align:start position:0%
+as things that can be represented as
+ 
+
+ align:start position:0%
+as things that can be represented as
+sums of sines so arbitrary function okay
+
+ align:start position:0%
+sums of sines so arbitrary function okay
+ 
+
+ align:start position:0%
+sums of sines so arbitrary function okay
+and the reason is because the complex
+
+ align:start position:0%
+and the reason is because the complex
+ 
+
+ align:start position:0%
+and the reason is because the complex
+exponential has both a cosine in it and
+
+ align:start position:0%
+exponential has both a cosine in it and
+ 
+
+ align:start position:0%
+exponential has both a cosine in it and
+a sine right so we can represent a
+
+ align:start position:0%
+a sine right so we can represent a
+ 
+
+ align:start position:0%
+a sine right so we can represent a
+cosine as a complex exponential with a
+
+ align:start position:0%
+cosine as a complex exponential with a
+ 
+
+ align:start position:0%
+cosine as a complex exponential with a
+positive free meaning that it's a
+
+ align:start position:0%
+positive free meaning that it's a
+ 
+
+ align:start position:0%
+positive free meaning that it's a
+complex number that goes around this
+
+ align:start position:0%
+complex number that goes around this
+ 
+
+ align:start position:0%
+complex number that goes around this
+direction plus another function where
+
+ align:start position:0%
+direction plus another function where
+ 
+
+ align:start position:0%
+direction plus another function where
+the complex number is going around in
+
+ align:start position:0%
+the complex number is going around in
+ 
+
+ align:start position:0%
+the complex number is going around in
+this direction so positive frequencies
+
+ align:start position:0%
+this direction so positive frequencies
+ 
+
+ align:start position:0%
+this direction so positive frequencies
+mean as as time in this complex number
+
+ align:start position:0%
+mean as as time in this complex number
+ 
+
+ align:start position:0%
+mean as as time in this complex number
+is going around the unit circle in this
+
+ align:start position:0%
+is going around the unit circle in this
+ 
+
+ align:start position:0%
+is going around the unit circle in this
+direction negative frequencies mean the
+
+ align:start position:0%
+direction negative frequencies mean the
+ 
+
+ align:start position:0%
+direction negative frequencies mean the
+complex number is going around in this
+
+ align:start position:0%
+complex number is going around in this
+ 
+
+ align:start position:0%
+complex number is going around in this
+direction and you can see that in order
+
+ align:start position:0%
+direction and you can see that in order
+ 
+
+ align:start position:0%
+direction and you can see that in order
+to represent a cosine I need to have
+
+ align:start position:0%
+to represent a cosine I need to have
+ 
+
+ align:start position:0%
+to represent a cosine I need to have
+okay so let's see if I can do this
+
+ align:start position:0%
+okay so let's see if I can do this
+ 
+
+ align:start position:0%
+okay so let's see if I can do this
+here's here's my e to the here's my
+
+ align:start position:0%
+here's here's my e to the here's my
+ 
+
+ align:start position:0%
+here's here's my e to the here's my
+frequency going around this way here's
+
+ align:start position:0%
+frequency going around this way here's
+ 
+
+ align:start position:0%
+frequency going around this way here's
+my minus frequency
+
+ align:start position:0%
+my minus frequency
+ 
+
+ align:start position:0%
+my minus frequency
+this way okay and you can see that I can
+
+ align:start position:0%
+this way okay and you can see that I can
+ 
+
+ align:start position:0%
+this way okay and you can see that I can
+represent a cosine if I can make the
+
+ align:start position:0%
+represent a cosine if I can make the
+ 
+
+ align:start position:0%
+represent a cosine if I can make the
+imaginary parts cancel right so if I
+
+ align:start position:0%
+imaginary parts cancel right so if I
+ 
+
+ align:start position:0%
+imaginary parts cancel right so if I
+have one function that's going around
+
+ align:start position:0%
+have one function that's going around
+ 
+
+ align:start position:0%
+have one function that's going around
+like this another function that's going
+
+ align:start position:0%
+like this another function that's going
+ 
+
+ align:start position:0%
+like this another function that's going
+around like if I add them then the
+
+ align:start position:0%
+around like if I add them then the
+ 
+
+ align:start position:0%
+around like if I add them then the
+imaginary part cancels right the the
+
+ align:start position:0%
+imaginary part cancels right the the
+ 
+
+ align:start position:0%
+imaginary part cancels right the the
+sign cancels this Plus this is cosine
+
+ align:start position:0%
+sign cancels this Plus this is cosine
+ 
+
+ align:start position:0%
+sign cancels this Plus this is cosine
+plus cosine I sine minus I sine so the
+
+ align:start position:0%
+plus cosine I sine minus I sine so the
+ 
+
+ align:start position:0%
+plus cosine I sine minus I sine so the
+signs can't the sign cancels and what
+
+ align:start position:0%
+signs can't the sign cancels and what
+ 
+
+ align:start position:0%
+signs can't the sign cancels and what
+I'm left with is a sine so represent a
+
+ align:start position:0%
+I'm left with is a sine so represent a
+ 
+
+ align:start position:0%
+I'm left with is a sine so represent a
+cosine as a sum of a function that has a
+
+ align:start position:0%
+cosine as a sum of a function that has a
+ 
+
+ align:start position:0%
+cosine as a sum of a function that has a
+positive frequency and a negative
+
+ align:start position:0%
+positive frequency and a negative
+ 
+
+ align:start position:0%
+positive frequency and a negative
+frequency you can see that the you can
+
+ align:start position:0%
+frequency you can see that the you can
+ 
+
+ align:start position:0%
+frequency you can see that the you can
+see that the Y component the imaginary
+
+ align:start position:0%
+see that the Y component the imaginary
+ 
+
+ align:start position:0%
+see that the Y component the imaginary
+component cancels and all I'm left with
+
+ align:start position:0%
+component cancels and all I'm left with
+ 
+
+ align:start position:0%
+component cancels and all I'm left with
+is the cosine that's going across like
+
+ align:start position:0%
+is the cosine that's going across like
+ 
+
+ align:start position:0%
+is the cosine that's going across like
+this okay so it's just a mathematical
+
+ align:start position:0%
+this okay so it's just a mathematical
+ 
+
+ align:start position:0%
+this okay so it's just a mathematical
+trick positive and negative frequencies
+
+ align:start position:0%
+trick positive and negative frequencies
+ 
+
+ align:start position:0%
+trick positive and negative frequencies
+are just a mathematical trick to make
+
+ align:start position:0%
+are just a mathematical trick to make
+ 
+
+ align:start position:0%
+are just a mathematical trick to make
+either the the symmetric part of the
+
+ align:start position:0%
+either the the symmetric part of the
+ 
+
+ align:start position:0%
+either the the symmetric part of the
+function or anti-symmetric part of the
+
+ align:start position:0%
+function or anti-symmetric part of the
+ 
+
+ align:start position:0%
+function or anti-symmetric part of the
+function cancel okay so I can I can just
+
+ align:start position:0%
+function cancel okay so I can I can just
+ 
+
+ align:start position:0%
+function cancel okay so I can I can just
+use these positive and negative
+
+ align:start position:0%
+use these positive and negative
+ 
+
+ align:start position:0%
+use these positive and negative
+frequencies to represent any function if
+
+ align:start position:0%
+frequencies to represent any function if
+ 
+
+ align:start position:0%
+frequencies to represent any function if
+I only had positive frequencies I
+
+ align:start position:0%
+I only had positive frequencies I
+ 
+
+ align:start position:0%
+I only had positive frequencies I
+wouldn't be able to represent arbitrary
+
+ align:start position:0%
+wouldn't be able to represent arbitrary
+ 
+
+ align:start position:0%
+wouldn't be able to represent arbitrary
+functions okay
+
+ align:start position:0%
+functions okay
+ 
+
+ align:start position:0%
+functions okay
+so just one more little thing that you
+
+ align:start position:0%
+so just one more little thing that you
+ 
+
+ align:start position:0%
+so just one more little thing that you
+need to know about the FFT algorithm so
+
+ align:start position:0%
+need to know about the FFT algorithm so
+ 
+
+ align:start position:0%
+need to know about the FFT algorithm so
+remember we talked about if you have a
+
+ align:start position:0%
+remember we talked about if you have a
+ 
+
+ align:start position:0%
+remember we talked about if you have a
+function of time negative times are over
+
+ align:start position:0%
+function of time negative times are over
+ 
+
+ align:start position:0%
+function of time negative times are over
+here positive times are over here you
+
+ align:start position:0%
+here positive times are over here you
+ 
+
+ align:start position:0%
+here positive times are over here you
+can put you can sample your function at
+
+ align:start position:0%
+can put you can sample your function at
+ 
+
+ align:start position:0%
+can put you can sample your function at
+different times and put those different
+
+ align:start position:0%
+different times and put those different
+ 
+
+ align:start position:0%
+different times and put those different
+samples into an array before you send
+
+ align:start position:0%
+samples into an array before you send
+ 
+
+ align:start position:0%
+samples into an array before you send
+this array of time samples to the FFT
+
+ align:start position:0%
+this array of time samples to the FFT
+ 
+
+ align:start position:0%
+this array of time samples to the FFT
+algorithm you just need to swap the
+
+ align:start position:0%
+algorithm you just need to swap the
+ 
+
+ align:start position:0%
+algorithm you just need to swap the
+right half of the array with the left
+
+ align:start position:0%
+right half of the array with the left
+ 
+
+ align:start position:0%
+right half of the array with the left
+half of the array using a function
+
+ align:start position:0%
+half of the array using a function
+ 
+
+ align:start position:0%
+half of the array using a function
+called time shifted array don't worry
+
+ align:start position:0%
+called time shifted array don't worry
+ 
+
+ align:start position:0%
+called time shifted array don't worry
+about it it's just the guts of the FFT
+
+ align:start position:0%
+about it it's just the guts of the FFT
+ 
+
+ align:start position:0%
+about it it's just the guts of the FFT
+algorithm wants to have the positive x
+
+ align:start position:0%
+algorithm wants to have the positive x
+ 
+
+ align:start position:0%
+algorithm wants to have the positive x
+in the first half and
+
+ align:start position:0%
+in the first half and
+ 
+
+ align:start position:0%
+in the first half and
+negative times in the second half okay
+
+ align:start position:0%
+negative times in the second half okay
+ 
+
+ align:start position:0%
+negative times in the second half okay
+so you just do this all right then you
+
+ align:start position:0%
+so you just do this all right then you
+ 
+
+ align:start position:0%
+so you just do this all right then you
+run the FFT function on this shifted
+
+ align:start position:0%
+run the FFT function on this shifted
+ 
+
+ align:start position:0%
+run the FFT function on this shifted
+time shifted array and what it spits
+
+ align:start position:0%
+time shifted array and what it spits
+ 
+
+ align:start position:0%
+time shifted array and what it spits
+back is an array with the positive
+
+ align:start position:0%
+back is an array with the positive
+ 
+
+ align:start position:0%
+back is an array with the positive
+frequencies in the first half and the
+
+ align:start position:0%
+frequencies in the first half and the
+ 
+
+ align:start position:0%
+frequencies in the first half and the
+negative frequencies in the second half
+
+ align:start position:0%
+negative frequencies in the second half
+ 
+
+ align:start position:0%
+negative frequencies in the second half
+and you can just swap those back using
+
+ align:start position:0%
+and you can just swap those back using
+ 
+
+ align:start position:0%
+and you can just swap those back using
+the search shift again that is your
+
+ align:start position:0%
+the search shift again that is your
+ 
+
+ align:start position:0%
+the search shift again that is your
+spectrum your spectral your spectral
+
+ align:start position:0%
+spectrum your spectral your spectral
+ 
+
+ align:start position:0%
+spectrum your spectral your spectral
+coefficients your Fourier coefficients
+
+ align:start position:0%
+coefficients your Fourier coefficients
+ 
+
+ align:start position:0%
+coefficients your Fourier coefficients
+of this function okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just MATLAB guts don't worry about it
+
+ align:start position:0%
+just MATLAB guts don't worry about it
+ 
+
+ align:start position:0%
+just MATLAB guts don't worry about it
+okay all right so here's a piece of code
+
+ align:start position:0%
+okay all right so here's a piece of code
+ 
+
+ align:start position:0%
+okay all right so here's a piece of code
+that computes the Fourier coefficients
+
+ align:start position:0%
+that computes the Fourier coefficients
+ 
+
+ align:start position:0%
+that computes the Fourier coefficients
+of a function okay so the first thing
+
+ align:start position:0%
+of a function okay so the first thing
+ 
+
+ align:start position:0%
+of a function okay so the first thing
+we're gonna do is define the number of
+
+ align:start position:0%
+we're gonna do is define the number of
+ 
+
+ align:start position:0%
+we're gonna do is define the number of
+points that we have in our array 2048
+
+ align:start position:0%
+points that we have in our array 2048
+ 
+
+ align:start position:0%
+points that we have in our array 2048
+okay so it's a power of two so the FFT
+
+ align:start position:0%
+okay so it's a power of two so the FFT
+ 
+
+ align:start position:0%
+okay so it's a power of two so the FFT
+algorithm runs fast we're figuring out a
+
+ align:start position:0%
+algorithm runs fast we're figuring out a
+ 
+
+ align:start position:0%
+algorithm runs fast we're figuring out a
+we're gonna write down a delta T in this
+
+ align:start position:0%
+we're gonna write down a delta T in this
+ 
+
+ align:start position:0%
+we're gonna write down a delta T in this
+case it's one millisecond the sampling
+
+ align:start position:0%
+case it's one millisecond the sampling
+ 
+
+ align:start position:0%
+case it's one millisecond the sampling
+rate okay the sampling frequency is just
+
+ align:start position:0%
+rate okay the sampling frequency is just
+ 
+
+ align:start position:0%
+rate okay the sampling frequency is just
+one over delta T so one kilohertz the
+
+ align:start position:0%
+one over delta T so one kilohertz the
+ 
+
+ align:start position:0%
+one over delta T so one kilohertz the
+array of times at which the function is
+
+ align:start position:0%
+array of times at which the function is
+ 
+
+ align:start position:0%
+array of times at which the function is
+just going from minus n over 2 to + n
+
+ align:start position:0%
+just going from minus n over 2 to + n
+ 
+
+ align:start position:0%
+just going from minus n over 2 to + n
+over 2 minus 1 times delta T okay I'm
+
+ align:start position:0%
+over 2 minus 1 times delta T okay I'm
+ 
+
+ align:start position:0%
+over 2 minus 1 times delta T okay I'm
+defining the frequency of a sine wave
+
+ align:start position:0%
+defining the frequency of a sine wave
+ 
+
+ align:start position:0%
+defining the frequency of a sine wave
+and we're now getting the values of that
+
+ align:start position:0%
+and we're now getting the values of that
+ 
+
+ align:start position:0%
+and we're now getting the values of that
+cosine function at those different times
+
+ align:start position:0%
+cosine function at those different times
+ 
+
+ align:start position:0%
+cosine function at those different times
+that makes sense we're taking that
+
+ align:start position:0%
+that makes sense we're taking that
+ 
+
+ align:start position:0%
+that makes sense we're taking that
+function of time and circularly shifting
+
+ align:start position:0%
+function of time and circularly shifting
+ 
+
+ align:start position:0%
+function of time and circularly shifting
+it by half the array so that's the
+
+ align:start position:0%
+it by half the array so that's the
+ 
+
+ align:start position:0%
+it by half the array so that's the
+circularly shifted that the swapped
+
+ align:start position:0%
+circularly shifted that the swapped
+ 
+
+ align:start position:0%
+circularly shifted that the swapped
+values of our function why we stick that
+
+ align:start position:0%
+values of our function why we stick that
+ 
+
+ align:start position:0%
+values of our function why we stick that
+into the FFT function
+
+ align:start position:0%
+into the FFT function
+ 
+
+ align:start position:0%
+into the FFT function
+okay it gives you back the Fourier
+
+ align:start position:0%
+okay it gives you back the Fourier
+ 
+
+ align:start position:0%
+okay it gives you back the Fourier
+coefficients you just swap it again and
+
+ align:start position:0%
+coefficients you just swap it again and
+ 
+
+ align:start position:0%
+coefficients you just swap it again and
+that is the spectrum the Fourier
+
+ align:start position:0%
+that is the spectrum the Fourier
+ 
+
+ align:start position:0%
+that is the spectrum the Fourier
+transform signal okay and now you can
+
+ align:start position:0%
+transform signal okay and now you can
+ 
+
+ align:start position:0%
+transform signal okay and now you can
+write down a vector of frequencies of
+
+ align:start position:0%
+write down a vector of frequencies of
+ 
+
+ align:start position:0%
+write down a vector of frequencies of
+each one of those four eight
+
+ align:start position:0%
+each one of those four eight
+ 
+
+ align:start position:0%
+each one of those four eight
+coefficients okay each one of those
+
+ align:start position:0%
+coefficients okay each one of those
+ 
+
+ align:start position:0%
+coefficients okay each one of those
+ments in that vector Y remember there
+
+ align:start position:0%
+ments in that vector Y remember there
+ 
+
+ align:start position:0%
+ments in that vector Y remember there
+are 2,000 of them now 2048 of them each
+
+ align:start position:0%
+are 2,000 of them now 2048 of them each
+ 
+
+ align:start position:0%
+are 2,000 of them now 2048 of them each
+one of those is the Fourier coefficient
+
+ align:start position:0%
+one of those is the Fourier coefficient
+ 
+
+ align:start position:0%
+one of those is the Fourier coefficient
+of the function we put in at each one of
+
+ align:start position:0%
+of the function we put in at each one of
+ 
+
+ align:start position:0%
+of the function we put in at each one of
+those different frequencies okay that
+
+ align:start position:0%
+those different frequencies okay that
+ 
+
+ align:start position:0%
+those different frequencies okay that
+makes sense okay now let's take a look
+
+ align:start position:0%
+makes sense okay now let's take a look
+ 
+
+ align:start position:0%
+makes sense okay now let's take a look
+at a few examples of what that looks
+
+ align:start position:0%
+at a few examples of what that looks
+ 
+
+ align:start position:0%
+at a few examples of what that looks
+like so here is a function y of Y of T
+
+ align:start position:0%
+like so here is a function y of Y of T
+ 
+
+ align:start position:0%
+like so here is a function y of Y of T
+is cosine 2 pi F naught T where F naught
+
+ align:start position:0%
+is cosine 2 pi F naught T where F naught
+ 
+
+ align:start position:0%
+is cosine 2 pi F naught T where F naught
+is 20 Hertz okay so it's just a cosine
+
+ align:start position:0%
+is 20 Hertz okay so it's just a cosine
+ 
+
+ align:start position:0%
+is 20 Hertz okay so it's just a cosine
+wave you run this code on it and what
+
+ align:start position:0%
+wave you run this code on it and what
+ 
+
+ align:start position:0%
+wave you run this code on it and what
+you get back is an array of complex
+
+ align:start position:0%
+you get back is an array of complex
+ 
+
+ align:start position:0%
+you get back is an array of complex
+numbers it has a real and imaginary part
+
+ align:start position:0%
+numbers it has a real and imaginary part
+ 
+
+ align:start position:0%
+numbers it has a real and imaginary part
+as a function of frequency okay any that
+
+ align:start position:0%
+as a function of frequency okay any that
+ 
+
+ align:start position:0%
+as a function of frequency okay any that
+this cosine function has two peaks as
+
+ align:start position:0%
+this cosine function has two peaks as
+ 
+
+ align:start position:0%
+this cosine function has two peaks as
+promised right it has a peak at plus 20
+
+ align:start position:0%
+promised right it has a peak at plus 20
+ 
+
+ align:start position:0%
+promised right it has a peak at plus 20
+Hertz and a peak at minus 20 Hertz one
+
+ align:start position:0%
+Hertz and a peak at minus 20 Hertz one
+ 
+
+ align:start position:0%
+Hertz and a peak at minus 20 Hertz one
+of those Peaks gives you an e to the I
+
+ align:start position:0%
+of those Peaks gives you an e to the I
+ 
+
+ align:start position:0%
+of those Peaks gives you an e to the I
+goes this way at 20 Hertz the other one
+
+ align:start position:0%
+goes this way at 20 Hertz the other one
+ 
+
+ align:start position:0%
+goes this way at 20 Hertz the other one
+gives you an e to the I Omega T that
+
+ align:start position:0%
+gives you an e to the I Omega T that
+ 
+
+ align:start position:0%
+gives you an e to the I Omega T that
+goes this way at 20 Hertz and when you
+
+ align:start position:0%
+goes this way at 20 Hertz and when you
+ 
+
+ align:start position:0%
+goes this way at 20 Hertz and when you
+add them together if I can do that it
+
+ align:start position:0%
+add them together if I can do that it
+ 
+
+ align:start position:0%
+add them together if I can do that it
+gives you a cosine that goes back and
+
+ align:start position:0%
+gives you a cosine that goes back and
+ 
+
+ align:start position:0%
+gives you a cosine that goes back and
+forth there 20 Hertz that one
+
+ align:start position:0%
+forth there 20 Hertz that one
+ 
+
+ align:start position:0%
+forth there 20 Hertz that one
+okay that's it here's a sine wave y
+
+ align:start position:0%
+okay that's it here's a sine wave y
+ 
+
+ align:start position:0%
+okay that's it here's a sine wave y
+equals sine 2 pi F naught T again at 20
+
+ align:start position:0%
+equals sine 2 pi F naught T again at 20
+ 
+
+ align:start position:0%
+equals sine 2 pi F naught T again at 20
+Hertz you run that code on it it gives
+
+ align:start position:0%
+Hertz you run that code on it it gives
+ 
+
+ align:start position:0%
+Hertz you run that code on it it gives
+you this
+
+ align:start position:0%
+you this
+ 
+
+ align:start position:0%
+you this
+notice that okay
+
+ align:start position:0%
+notice that okay
+ 
+
+ align:start position:0%
+notice that okay
+sorry let me just point out one in this
+
+ align:start position:0%
+sorry let me just point out one in this
+ 
+
+ align:start position:0%
+sorry let me just point out one in this
+case the the peaks are in the real part
+
+ align:start position:0%
+case the the peaks are in the real part
+ 
+
+ align:start position:0%
+case the the peaks are in the real part
+of Y for the sine function that real
+
+ align:start position:0%
+of Y for the sine function that real
+ 
+
+ align:start position:0%
+of Y for the sine function that real
+part is zero and the peaks are in the
+
+ align:start position:0%
+part is zero and the peaks are in the
+ 
+
+ align:start position:0%
+part is zero and the peaks are in the
+imaginary part there's a plus I at minus
+
+ align:start position:0%
+imaginary part there's a plus I at minus
+ 
+
+ align:start position:0%
+imaginary part there's a plus I at minus
+20 I over 2 actually at minus 20 Hertz -
+
+ align:start position:0%
+20 I over 2 actually at minus 20 Hertz -
+ 
+
+ align:start position:0%
+20 I over 2 actually at minus 20 Hertz -
+i at plus 20 Hertz okay and what that
+
+ align:start position:0%
+i at plus 20 Hertz okay and what that
+ 
+
+ align:start position:0%
+i at plus 20 Hertz okay and what that
+does is when you multiply that
+
+ align:start position:0%
+does is when you multiply that
+ 
+
+ align:start position:0%
+does is when you multiply that
+coefficient times e to the I Omega T and
+
+ align:start position:0%
+coefficient times e to the I Omega T and
+ 
+
+ align:start position:0%
+coefficient times e to the I Omega T and
+that coefficient times whatever
+
+ align:start position:0%
+that coefficient times whatever
+ 
+
+ align:start position:0%
+that coefficient times whatever
+whichever the opposite 1 is 1 1 going
+
+ align:start position:0%
+whichever the opposite 1 is 1 1 going
+ 
+
+ align:start position:0%
+whichever the opposite 1 is 1 1 going
+this way the other one going this way
+
+ align:start position:0%
+this way the other one going this way
+ 
+
+ align:start position:0%
+this way the other one going this way
+you can see that the real part now
+
+ align:start position:0%
+you can see that the real part now
+ 
+
+ align:start position:0%
+you can see that the real part now
+cancels and what you're left with is the
+
+ align:start position:0%
+cancels and what you're left with is the
+ 
+
+ align:start position:0%
+cancels and what you're left with is the
+sine part that doesn't cancel and that
+
+ align:start position:0%
+sine part that doesn't cancel and that
+ 
+
+ align:start position:0%
+sine part that doesn't cancel and that
+and that is this this function sine
+
+ align:start position:0%
+and that is this this function sine
+ 
+
+ align:start position:0%
+and that is this this function sine
+Omega T okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's about that
+
+ align:start position:0%
+it's about that
+ 
+
+ align:start position:0%
+it's about that
+that's that's kind of boring we're gonna
+
+ align:start position:0%
+that's that's kind of boring we're gonna
+ 
+
+ align:start position:0%
+that's that's kind of boring we're gonna
+put more interesting functions in here
+
+ align:start position:0%
+put more interesting functions in here
+ 
+
+ align:start position:0%
+put more interesting functions in here
+soon but I just wanted you to see what
+
+ align:start position:0%
+soon but I just wanted you to see what
+ 
+
+ align:start position:0%
+soon but I just wanted you to see what
+this algorithm does on the things that
+
+ align:start position:0%
+this algorithm does on the things that
+ 
+
+ align:start position:0%
+this algorithm does on the things that
+we've been talking about all along okay
+
+ align:start position:0%
+we've been talking about all along okay
+ 
+
+ align:start position:0%
+we've been talking about all along okay
+it gives you exactly what you expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number we can write down any arbitrary
+
+ align:start position:0%
+number we can write down any arbitrary
+ 
+
+ align:start position:0%
+number we can write down any arbitrary
+function as a sum of sines and cosines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means we can write down any
+
+ align:start position:0%
+which means we can write down any
+ 
+
+ align:start position:0%
+which means we can write down any
+arbitrary of function as a sum of these
+
+ align:start position:0%
+arbitrary of function as a sum of these
+ 
+
+ align:start position:0%
+arbitrary of function as a sum of these
+little Peaks and these peaks at
+
+ align:start position:0%
+little Peaks and these peaks at
+ 
+
+ align:start position:0%
+little Peaks and these peaks at
+different frequencies okay does that
+
+ align:start position:0%
+different frequencies okay does that
+ 
+
+ align:start position:0%
+different frequencies okay does that
+make sense so all we have to do is find
+
+ align:start position:0%
+make sense so all we have to do is find
+ 
+
+ align:start position:0%
+make sense so all we have to do is find
+these coefficients these Peaks what
+
+ align:start position:0%
+these coefficients these Peaks what
+ 
+
+ align:start position:0%
+these coefficients these Peaks what
+values of these different Peaks to stick
+
+ align:start position:0%
+values of these different Peaks to stick
+ 
+
+ align:start position:0%
+values of these different Peaks to stick
+in to reconstruct any arbitrary function
+
+ align:start position:0%
+in to reconstruct any arbitrary function
+ 
+
+ align:start position:0%
+in to reconstruct any arbitrary function
+okay and we're gonna do a lot of that in
+
+ align:start position:0%
+okay and we're gonna do a lot of that in
+ 
+
+ align:start position:0%
+okay and we're gonna do a lot of that in
+the next lecture we're going to look at
+
+ align:start position:0%
+the next lecture we're going to look at
+ 
+
+ align:start position:0%
+the next lecture we're going to look at
+what different functions here look like
+
+ align:start position:0%
+what different functions here look like
+ 
+
+ align:start position:0%
+what different functions here look like
+in the Fourier domain okay we're gonna
+
+ align:start position:0%
+in the Fourier domain okay we're gonna
+ 
+
+ align:start position:0%
+in the Fourier domain okay we're gonna
+do that for some seasons like a square
+
+ align:start position:0%
+do that for some seasons like a square
+ 
+
+ align:start position:0%
+do that for some seasons like a square
+pulse for trains of pulses for Gaussian
+
+ align:start position:0%
+pulse for trains of pulses for Gaussian
+ 
+
+ align:start position:0%
+pulse for trains of pulses for Gaussian
+or all kinds of different functions and
+
+ align:start position:0%
+or all kinds of different functions and
+ 
+
+ align:start position:0%
+or all kinds of different functions and
+then that using the convolution theorem
+
+ align:start position:0%
+then that using the convolution theorem
+ 
+
+ align:start position:0%
+then that using the convolution theorem
+you can actually just predict in your
+
+ align:start position:0%
+you can actually just predict in your
+ 
+
+ align:start position:0%
+you can actually just predict in your
+own mind what different combinations of
+
+ align:start position:0%
+own mind what different combinations of
+ 
+
+ align:start position:0%
+own mind what different combinations of
+those functions will look like okay so I
+
+ align:start position:0%
+those functions will look like okay so I
+ 
+
+ align:start position:0%
+those functions will look like okay so I
+want to end by talking about one other
+
+ align:start position:0%
+want to end by talking about one other
+ 
+
+ align:start position:0%
+want to end by talking about one other
+really critical concept called a power
+
+ align:start position:0%
+really critical concept called a power
+ 
+
+ align:start position:0%
+really critical concept called a power
+spectrum okay
+
+ align:start position:0%
+spectrum okay
+ 
+
+ align:start position:0%
+spectrum okay
+it's basically usually what you do when
+
+ align:start position:0%
+it's basically usually what you do when
+ 
+
+ align:start position:0%
+it's basically usually what you do when
+you compute the Fourier transform of a
+
+ align:start position:0%
+you compute the Fourier transform of a
+ 
+
+ align:start position:0%
+you compute the Fourier transform of a
+function is to figure out what the power
+
+ align:start position:0%
+function is to figure out what the power
+ 
+
+ align:start position:0%
+function is to figure out what the power
+spectrum is okay the simple answer is
+
+ align:start position:0%
+spectrum is okay the simple answer is
+ 
+
+ align:start position:0%
+spectrum is okay the simple answer is
+that all you do is you square this thing
+
+ align:start position:0%
+that all you do is you square this thing
+ 
+
+ align:start position:0%
+that all you do is you square this thing
+you take the magnitude squared okay but
+
+ align:start position:0%
+you take the magnitude squared okay but
+ 
+
+ align:start position:0%
+you take the magnitude squared okay but
+I'm gonna build up to that a little bit
+
+ align:start position:0%
+I'm gonna build up to that a little bit
+ 
+
+ align:start position:0%
+I'm gonna build up to that a little bit
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+so it's called the power spectrum but
+
+ align:start position:0%
+so it's called the power spectrum but
+ 
+
+ align:start position:0%
+so it's called the power spectrum but
+first we need to understand what we mean
+
+ align:start position:0%
+first we need to understand what we mean
+ 
+
+ align:start position:0%
+first we need to understand what we mean
+by power okay so we're gonna think about
+
+ align:start position:0%
+by power okay so we're gonna think about
+ 
+
+ align:start position:0%
+by power okay so we're gonna think about
+this in the rest of a simple electrical
+
+ align:start position:0%
+this in the rest of a simple electrical
+ 
+
+ align:start position:0%
+this in the rest of a simple electrical
+circuit let's imagine that this function
+
+ align:start position:0%
+circuit let's imagine that this function
+ 
+
+ align:start position:0%
+circuit let's imagine that this function
+that were computing the Fourier
+
+ align:start position:0%
+that were computing the Fourier
+ 
+
+ align:start position:0%
+that were computing the Fourier
+transform of imagine this function is
+
+ align:start position:0%
+transform of imagine this function is
+ 
+
+ align:start position:0%
+transform of imagine this function is
+voltage that's where this idea comes
+
+ align:start position:0%
+voltage that's where this idea comes
+ 
+
+ align:start position:0%
+voltage that's where this idea comes
+from imagine that this function is the
+
+ align:start position:0%
+from imagine that this function is the
+ 
+
+ align:start position:0%
+from imagine that this function is the
+voltage that you've measured somewhere
+
+ align:start position:0%
+voltage that you've measured somewhere
+ 
+
+ align:start position:0%
+voltage that you've measured somewhere
+in a circuit let's say in this circuit
+
+ align:start position:0%
+in a circuit let's say in this circuit
+ 
+
+ align:start position:0%
+in a circuit let's say in this circuit
+right here or current either way so when
+
+ align:start position:0%
+right here or current either way so when
+ 
+
+ align:start position:0%
+right here or current either way so when
+you have current flowing through this
+
+ align:start position:0%
+you have current flowing through this
+ 
+
+ align:start position:0%
+you have current flowing through this
+circuit you can see that that that sign
+
+ align:start position:0%
+circuit you can see that that that sign
+ 
+
+ align:start position:0%
+circuit you can see that that that sign
+is so that's some oscillatory current
+
+ align:start position:0%
+is so that's some oscillatory current
+ 
+
+ align:start position:0%
+is so that's some oscillatory current
+some cosine that drives current through
+
+ align:start position:0%
+some cosine that drives current through
+ 
+
+ align:start position:0%
+some cosine that drives current through
+this resistor and when current flows
+
+ align:start position:0%
+this resistor and when current flows
+ 
+
+ align:start position:0%
+this resistor and when current flows
+through a resistor it dissipates power
+
+ align:start position:0%
+through a resistor it dissipates power
+ 
+
+ align:start position:0%
+through a resistor it dissipates power
+right and the power dissipated in a
+
+ align:start position:0%
+right and the power dissipated in a
+ 
+
+ align:start position:0%
+right and the power dissipated in a
+resistor is just the current times the
+
+ align:start position:0%
+resistor is just the current times the
+ 
+
+ align:start position:0%
+resistor is just the current times the
+voltage drop across that resistor that
+
+ align:start position:0%
+voltage drop across that resistor that
+ 
+
+ align:start position:0%
+voltage drop across that resistor that
+means that the power
+
+ align:start position:0%
+means that the power
+ 
+
+ align:start position:0%
+means that the power
+now remember Ohm's law tells you that
+
+ align:start position:0%
+now remember Ohm's law tells you that
+ 
+
+ align:start position:0%
+now remember Ohm's law tells you that
+current is just pitch divided by
+
+ align:start position:0%
+current is just pitch divided by
+ 
+
+ align:start position:0%
+current is just pitch divided by
+resistance right so this is V divided by
+
+ align:start position:0%
+resistance right so this is V divided by
+ 
+
+ align:start position:0%
+resistance right so this is V divided by
+R so the power is just V squared divided
+
+ align:start position:0%
+R so the power is just V squared divided
+ 
+
+ align:start position:0%
+R so the power is just V squared divided
+by R so if the voltage is just a sine
+
+ align:start position:0%
+by R so if the voltage is just a sine
+ 
+
+ align:start position:0%
+by R so if the voltage is just a sine
+wave at frequency Omega then V is some
+
+ align:start position:0%
+wave at frequency Omega then V is some
+ 
+
+ align:start position:0%
+wave at frequency Omega then V is some
+efficient some amplitude at that
+
+ align:start position:0%
+efficient some amplitude at that
+ 
+
+ align:start position:0%
+efficient some amplitude at that
+frequency times cosine Omega T right we
+
+ align:start position:0%
+frequency times cosine Omega T right we
+ 
+
+ align:start position:0%
+frequency times cosine Omega T right we
+can write that voltage using Euler's
+
+ align:start position:0%
+can write that voltage using Euler's
+ 
+
+ align:start position:0%
+can write that voltage using Euler's
+equation as one-half e to the minus I
+
+ align:start position:0%
+equation as one-half e to the minus I
+ 
+
+ align:start position:0%
+equation as one-half e to the minus I
+Omega T plus one-half e to the plus I
+
+ align:start position:0%
+Omega T plus one-half e to the plus I
+ 
+
+ align:start position:0%
+Omega T plus one-half e to the plus I
+Omega T and let's calculate the power
+
+ align:start position:0%
+Omega T and let's calculate the power
+ 
+
+ align:start position:0%
+Omega T and let's calculate the power
+associated with that voltage well we
+
+ align:start position:0%
+associated with that voltage well we
+ 
+
+ align:start position:0%
+associated with that voltage well we
+have to average over one cycle of that
+
+ align:start position:0%
+have to average over one cycle of that
+ 
+
+ align:start position:0%
+have to average over one cycle of that
+oscillation so the average power is just
+
+ align:start position:0%
+oscillation so the average power is just
+ 
+
+ align:start position:0%
+oscillation so the average power is just
+given by the square magnitude of the
+
+ align:start position:0%
+given by the square magnitude of the
+ 
+
+ align:start position:0%
+given by the square magnitude of the
+Fourier transform so let's just plug
+
+ align:start position:0%
+Fourier transform so let's just plug
+ 
+
+ align:start position:0%
+Fourier transform so let's just plug
+this into here and what you see is that
+
+ align:start position:0%
+this into here and what you see is that
+ 
+
+ align:start position:0%
+this into here and what you see is that
+the power at a given frequency Omega is
+
+ align:start position:0%
+the power at a given frequency Omega is
+ 
+
+ align:start position:0%
+the power at a given frequency Omega is
+just that coefficient magnitude squared
+
+ align:start position:0%
+just that coefficient magnitude squared
+ 
+
+ align:start position:0%
+just that coefficient magnitude squared
+over resistance
+
+ align:start position:0%
+over resistance
+ 
+
+ align:start position:0%
+over resistance
+times 1/2 e to the minus I Omega T
+
+ align:start position:0%
+times 1/2 e to the minus I Omega T
+ 
+
+ align:start position:0%
+times 1/2 e to the minus I Omega T
+magnitude squared plus 1/2 e to the plus
+
+ align:start position:0%
+magnitude squared plus 1/2 e to the plus
+ 
+
+ align:start position:0%
+magnitude squared plus 1/2 e to the plus
+I over I Omega T magnitude squared and
+
+ align:start position:0%
+I over I Omega T magnitude squared and
+ 
+
+ align:start position:0%
+I over I Omega T magnitude squared and
+that's just equal to 1 over R that
+
+ align:start position:0%
+that's just equal to 1 over R that
+ 
+
+ align:start position:0%
+that's just equal to 1 over R that
+coefficient magnitude squared over 2 ok
+
+ align:start position:0%
+coefficient magnitude squared over 2 ok
+ 
+
+ align:start position:0%
+coefficient magnitude squared over 2 ok
+so you can see that the power dissipated
+
+ align:start position:0%
+so you can see that the power dissipated
+ 
+
+ align:start position:0%
+so you can see that the power dissipated
+by this sinusoidal voltage is just that
+
+ align:start position:0%
+by this sinusoidal voltage is just that
+ 
+
+ align:start position:0%
+by this sinusoidal voltage is just that
+magnitude squared over 2 ok so we can
+
+ align:start position:0%
+magnitude squared over 2 ok so we can
+ 
+
+ align:start position:0%
+magnitude squared over 2 ok so we can
+calculate the power dissipated in any
+
+ align:start position:0%
+calculate the power dissipated in any
+ 
+
+ align:start position:0%
+calculate the power dissipated in any
+resistor simply by summing up this
+
+ align:start position:0%
+resistor simply by summing up this
+ 
+
+ align:start position:0%
+resistor simply by summing up this
+magnitude of all of those coefficients
+
+ align:start position:0%
+magnitude of all of those coefficients
+ 
+
+ align:start position:0%
+magnitude of all of those coefficients
+ok so let's look at that you know a
+
+ align:start position:0%
+ok so let's look at that you know a
+ 
+
+ align:start position:0%
+ok so let's look at that you know a
+little more detail so let's think for a
+
+ align:start position:0%
+little more detail so let's think for a
+ 
+
+ align:start position:0%
+little more detail so let's think for a
+moment about the energy that is
+
+ align:start position:0%
+moment about the energy that is
+ 
+
+ align:start position:0%
+moment about the energy that is
+dissipated by a signal ok so energy is
+
+ align:start position:0%
+dissipated by a signal ok so energy is
+ 
+
+ align:start position:0%
+dissipated by a signal ok so energy is
+just the integral over all right
+
+ align:start position:0%
+just the integral over all right
+ 
+
+ align:start position:0%
+just the integral over all right
+power is per unit time total energy is
+
+ align:start position:0%
+power is per unit time total energy is
+ 
+
+ align:start position:0%
+power is per unit time total energy is
+just the integral of the power over time
+
+ align:start position:0%
+just the integral of the power over time
+ 
+
+ align:start position:0%
+just the integral of the power over time
+so power was just is just equal to V
+
+ align:start position:0%
+so power was just is just equal to V
+ 
+
+ align:start position:0%
+so power was just is just equal to V
+squared over R so I'm just gonna
+
+ align:start position:0%
+squared over R so I'm just gonna
+ 
+
+ align:start position:0%
+squared over R so I'm just gonna
+substitute that in there so the energy
+
+ align:start position:0%
+substitute that in there so the energy
+ 
+
+ align:start position:0%
+substitute that in there so the energy
+of a signal is just 1 over R times the
+
+ align:start position:0%
+of a signal is just 1 over R times the
+ 
+
+ align:start position:0%
+of a signal is just 1 over R times the
+integral of V squared over time right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there's a important theorem in
+
+ align:start position:0%
+now there's a important theorem in
+ 
+
+ align:start position:0%
+now there's a important theorem in
+complex analysis called parseval's
+
+ align:start position:0%
+complex analysis called parseval's
+ 
+
+ align:start position:0%
+complex analysis called parseval's
+theorem that says that the integral over
+
+ align:start position:0%
+theorem that says that the integral over
+ 
+
+ align:start position:0%
+theorem that says that the integral over
+the square of the coefficients in time
+
+ align:start position:0%
+the square of the coefficients in time
+ 
+
+ align:start position:0%
+the square of the coefficients in time
+is just equal to the integral of the
+
+ align:start position:0%
+is just equal to the integral of the
+ 
+
+ align:start position:0%
+is just equal to the integral of the
+square magnitude coefficients in
+
+ align:start position:0%
+square magnitude coefficients in
+ 
+
+ align:start position:0%
+square magnitude coefficients in
+frequency ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what that's saying is that is just the
+
+ align:start position:0%
+what that's saying is that is just the
+ 
+
+ align:start position:0%
+what that's saying is that is just the
+same as the total power and the Sigma or
+
+ align:start position:0%
+same as the total power and the Sigma or
+ 
+
+ align:start position:0%
+same as the total power and the Sigma or
+the total energy in a signal if you
+
+ align:start position:0%
+the total energy in a signal if you
+ 
+
+ align:start position:0%
+the total energy in a signal if you
+represent it in the time domain is just
+
+ align:start position:0%
+represent it in the time domain is just
+ 
+
+ align:start position:0%
+represent it in the time domain is just
+the same as the total energy in the
+
+ align:start position:0%
+the same as the total energy in the
+ 
+
+ align:start position:0%
+the same as the total energy in the
+signal if you look at it in the
+
+ align:start position:0%
+signal if you look at it in the
+ 
+
+ align:start position:0%
+signal if you look at it in the
+frequency domain okay and what that's
+
+ align:start position:0%
+frequency domain okay and what that's
+ 
+
+ align:start position:0%
+frequency domain okay and what that's
+saying is that the sum of all the
+
+ align:start position:0%
+saying is that the sum of all the
+ 
+
+ align:start position:0%
+saying is that the sum of all the
+squared component the squared temporal
+
+ align:start position:0%
+squared component the squared temporal
+ 
+
+ align:start position:0%
+squared component the squared temporal
+components is just equal to the sum of
+
+ align:start position:0%
+components is just equal to the sum of
+ 
+
+ align:start position:0%
+components is just equal to the sum of
+all the squared frequency components
+
+ align:start position:0%
+all the squared frequency components
+ 
+
+ align:start position:0%
+all the squared frequency components
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and what that means is that you can see
+
+ align:start position:0%
+and what that means is that you can see
+ 
+
+ align:start position:0%
+and what that means is that you can see
+that each of these frequency components
+
+ align:start position:0%
+that each of these frequency components
+ 
+
+ align:start position:0%
+that each of these frequency components
+each each component in frequency
+
+ align:start position:0%
+each each component in frequency
+ 
+
+ align:start position:0%
+each each component in frequency
+contributes independently to the power
+
+ align:start position:0%
+contributes independently to the power
+ 
+
+ align:start position:0%
+contributes independently to the power
+in the signal okay what that means is
+
+ align:start position:0%
+in the signal okay what that means is
+ 
+
+ align:start position:0%
+in the signal okay what that means is
+that you can think of so you can think
+
+ align:start position:0%
+that you can think of so you can think
+ 
+
+ align:start position:0%
+that you can think of so you can think
+of the total energy and the signal is
+
+ align:start position:0%
+of the total energy and the signal is
+ 
+
+ align:start position:0%
+of the total energy and the signal is
+just the integral over all frequencies
+
+ align:start position:0%
+just the integral over all frequencies
+ 
+
+ align:start position:0%
+just the integral over all frequencies
+of this quantity here that we call the
+
+ align:start position:0%
+of this quantity here that we call the
+ 
+
+ align:start position:0%
+of this quantity here that we call the
+power spectrum okay and so we'll often
+
+ align:start position:0%
+power spectrum okay and so we'll often
+ 
+
+ align:start position:0%
+power spectrum okay and so we'll often
+take a signal calculate the Fourier
+
+ align:start position:0%
+take a signal calculate the Fourier
+ 
+
+ align:start position:0%
+take a signal calculate the Fourier
+components and plot Erev the Fourier
+
+ align:start position:0%
+components and plot Erev the Fourier
+ 
+
+ align:start position:0%
+components and plot Erev the Fourier
+transform the square magnitude of the
+
+ align:start position:0%
+transform the square magnitude of the
+ 
+
+ align:start position:0%
+transform the square magnitude of the
+Fourier transform and that's called the
+
+ align:start position:0%
+Fourier transform and that's called the
+ 
+
+ align:start position:0%
+Fourier transform and that's called the
+power spectrum
+
+ align:start position:0%
+power spectrum
+ 
+
+ align:start position:0%
+power spectrum
+okay we've art and I've already said
+
+ align:start position:0%
+okay we've art and I've already said
+ 
+
+ align:start position:0%
+okay we've art and I've already said
+it's the total variance of the signal
+
+ align:start position:0%
+it's the total variance of the signal
+ 
+
+ align:start position:0%
+it's the total variance of the signal
+and time is the same as the total
+
+ align:start position:0%
+and time is the same as the total
+ 
+
+ align:start position:0%
+and time is the same as the total
+variance of the signal in the frequency
+
+ align:start position:0%
+variance of the signal in the frequency
+ 
+
+ align:start position:0%
+variance of the signal in the frequency
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+so Mathew people talk about the variant
+
+ align:start position:0%
+so Mathew people talk about the variant
+ 
+
+ align:start position:0%
+so Mathew people talk about the variant
+of a signal and more engineering people
+
+ align:start position:0%
+of a signal and more engineering people
+ 
+
+ align:start position:0%
+of a signal and more engineering people
+talk about the power in the signal but
+
+ align:start position:0%
+talk about the power in the signal but
+ 
+
+ align:start position:0%
+talk about the power in the signal but
+they're really talking about the same
+
+ align:start position:0%
+they're really talking about the same
+ 
+
+ align:start position:0%
+they're really talking about the same
+thing okay so let's take this example
+
+ align:start position:0%
+thing okay so let's take this example
+ 
+
+ align:start position:0%
+thing okay so let's take this example
+that we just looked at and look at the
+
+ align:start position:0%
+that we just looked at and look at the
+ 
+
+ align:start position:0%
+that we just looked at and look at the
+power spectrum okay so that's a code
+
+ align:start position:0%
+power spectrum okay so that's a code
+ 
+
+ align:start position:0%
+power spectrum okay so that's a code
+function as these two peaks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let me just point out one more
+
+ align:start position:0%
+now let me just point out one more
+ 
+
+ align:start position:0%
+now let me just point out one more
+important thing for real functions so in
+
+ align:start position:0%
+important thing for real functions so in
+ 
+
+ align:start position:0%
+important thing for real functions so in
+this class we're only going to be
+
+ align:start position:0%
+this class we're only going to be
+ 
+
+ align:start position:0%
+this class we're only going to be
+talking about real functions of time for
+
+ align:start position:0%
+talking about real functions of time for
+ 
+
+ align:start position:0%
+talking about real functions of time for
+real function the square magnitude of
+
+ align:start position:0%
+real function the square magnitude of
+ 
+
+ align:start position:0%
+real function the square magnitude of
+the Fourier transform is symmetric okay
+
+ align:start position:0%
+the Fourier transform is symmetric okay
+ 
+
+ align:start position:0%
+the Fourier transform is symmetric okay
+so you can see here if there's a peak on
+
+ align:start position:0%
+so you can see here if there's a peak on
+ 
+
+ align:start position:0%
+so you can see here if there's a peak on
+the in the positive frequencies there's
+
+ align:start position:0%
+the in the positive frequencies there's
+ 
+
+ align:start position:0%
+the in the positive frequencies there's
+an equivalent peak in the negative
+
+ align:start position:0%
+an equivalent peak in the negative
+ 
+
+ align:start position:0%
+an equivalent peak in the negative
+frequencies so when we plot the power
+
+ align:start position:0%
+frequencies so when we plot the power
+ 
+
+ align:start position:0%
+frequencies so when we plot the power
+spectrum of a signal we always just plot
+
+ align:start position:0%
+spectrum of a signal we always just plot
+ 
+
+ align:start position:0%
+spectrum of a signal we always just plot
+the positive side okay and so here's
+
+ align:start position:0%
+the positive side okay and so here's
+ 
+
+ align:start position:0%
+the positive side okay and so here's
+what that looks like here is the power
+
+ align:start position:0%
+what that looks like here is the power
+ 
+
+ align:start position:0%
+what that looks like here is the power
+spectrum of a cosine signal okay and
+
+ align:start position:0%
+spectrum of a cosine signal okay and
+ 
+
+ align:start position:0%
+spectrum of a cosine signal okay and
+it's just a single peak so in that case
+
+ align:start position:0%
+it's just a single peak so in that case
+ 
+
+ align:start position:0%
+it's just a single peak so in that case
+it was a cosine at 20 Hertz you get a
+
+ align:start position:0%
+it was a cosine at 20 Hertz you get a
+ 
+
+ align:start position:0%
+it was a cosine at 20 Hertz you get a
+single peak at 20 Hertz right well what
+
+ align:start position:0%
+single peak at 20 Hertz right well what
+ 
+
+ align:start position:0%
+single peak at 20 Hertz right well what
+what does it look like for a sine
+
+ align:start position:0%
+what does it look like for a sine
+ 
+
+ align:start position:0%
+what does it look like for a sine
+function what is the power spectrum of a
+
+ align:start position:0%
+function what is the power spectrum of a
+ 
+
+ align:start position:0%
+function what is the power spectrum of a
+sine function remember in that case it
+
+ align:start position:0%
+sine function remember in that case it
+ 
+
+ align:start position:0%
+sine function remember in that case it
+was the real part was zero and the
+
+ align:start position:0%
+was the real part was zero and the
+ 
+
+ align:start position:0%
+was the real part was zero and the
+imaginary part at a plus peak here and a
+
+ align:start position:0%
+imaginary part at a plus peak here and a
+ 
+
+ align:start position:0%
+imaginary part at a plus peak here and a
+minus peak here what is the spectrum of
+
+ align:start position:0%
+minus peak here what is the spectrum of
+ 
+
+ align:start position:0%
+minus peak here what is the spectrum of
+that look like right the square
+
+ align:start position:0%
+that look like right the square
+ 
+
+ align:start position:0%
+that look like right the square
+magnitude of I is just one right
+
+ align:start position:0%
+magnitude of I is just one right
+ 
+
+ align:start position:0%
+magnitude of I is just one right
+magnitude squared of I is just one so
+
+ align:start position:0%
+magnitude squared of I is just one so
+ 
+
+ align:start position:0%
+magnitude squared of I is just one so
+the power spectrum of a sine function
+
+ align:start position:0%
+the power spectrum of a sine function
+ 
+
+ align:start position:0%
+the power spectrum of a sine function
+looks exactly like this same as cosine
+
+ align:start position:0%
+looks exactly like this same as cosine
+ 
+
+ align:start position:0%
+looks exactly like this same as cosine
+it makes a lot of sense right sine and
+
+ align:start position:0%
+it makes a lot of sense right sine and
+ 
+
+ align:start position:0%
+it makes a lot of sense right sine and
+cosine are exactly the same function
+
+ align:start position:0%
+cosine are exactly the same function
+ 
+
+ align:start position:0%
+cosine are exactly the same function
+one's just shifted as by you know a
+
+ align:start position:0%
+one's just shifted as by you know a
+ 
+
+ align:start position:0%
+one's just shifted as by you know a
+quarter period right so it has to have
+
+ align:start position:0%
+quarter period right so it has to have
+ 
+
+ align:start position:0%
+quarter period right so it has to have
+the same power spectrum it has to have
+
+ align:start position:0%
+the same power spectrum it has to have
+ 
+
+ align:start position:0%
+the same power spectrum it has to have
+the same power okay all right let's take
+
+ align:start position:0%
+the same power okay all right let's take
+ 
+
+ align:start position:0%
+the same power okay all right let's take
+a look at a different function of time
+
+ align:start position:0%
+a look at a different function of time
+ 
+
+ align:start position:0%
+a look at a different function of time
+there's a train of delta function so we
+
+ align:start position:0%
+there's a train of delta function so we
+ 
+
+ align:start position:0%
+there's a train of delta function so we
+just have a bunch of Peaks spaced
+
+ align:start position:0%
+just have a bunch of Peaks spaced
+ 
+
+ align:start position:0%
+just have a bunch of Peaks spaced
+regularly at some period I think it was
+
+ align:start position:0%
+regularly at some period I think it was
+ 
+
+ align:start position:0%
+regularly at some period I think it was
+forget the exact number here but it's
+
+ align:start position:0%
+forget the exact number here but it's
+ 
+
+ align:start position:0%
+forget the exact number here but it's
+around 10-ish Hertz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fourier transform of a train of Delta
+
+ align:start position:0%
+Fourier transform of a train of Delta
+ 
+
+ align:start position:0%
+Fourier transform of a train of Delta
+functions is another train of Delta
+
+ align:start position:0%
+functions is another train of Delta
+ 
+
+ align:start position:0%
+functions is another train of Delta
+functions okay pretty cool the period in
+
+ align:start position:0%
+functions okay pretty cool the period in
+ 
+
+ align:start position:0%
+functions okay pretty cool the period in
+the time domain is delta T the period in
+
+ align:start position:0%
+the time domain is delta T the period in
+ 
+
+ align:start position:0%
+the time domain is delta T the period in
+the Fourier domain is 1 over delta T ok
+
+ align:start position:0%
+the Fourier domain is 1 over delta T ok
+ 
+
+ align:start position:0%
+the Fourier domain is 1 over delta T ok
+that's another really important for you
+
+ align:start position:0%
+that's another really important for you
+ 
+
+ align:start position:0%
+that's another really important for you
+transform pair for you to know
+
+ align:start position:0%
+transform pair for you to know
+ 
+
+ align:start position:0%
+transform pair for you to know
+so the first Fourier transform pair that
+
+ align:start position:0%
+so the first Fourier transform pair that
+ 
+
+ align:start position:0%
+so the first Fourier transform pair that
+you need to know is that a constant in
+
+ align:start position:0%
+you need to know is that a constant in
+ 
+
+ align:start position:0%
+you need to know is that a constant in
+the time domain is a delta function in
+
+ align:start position:0%
+the time domain is a delta function in
+ 
+
+ align:start position:0%
+the time domain is a delta function in
+the frequency domain a delta function in
+
+ align:start position:0%
+the frequency domain a delta function in
+ 
+
+ align:start position:0%
+the frequency domain a delta function in
+the time domain is a constant in the
+
+ align:start position:0%
+the time domain is a constant in the
+ 
+
+ align:start position:0%
+the time domain is a constant in the
+frequency domain a train of Delta
+
+ align:start position:0%
+frequency domain a train of Delta
+ 
+
+ align:start position:0%
+frequency domain a train of Delta
+functions in the train is a train of
+
+ align:start position:0%
+functions in the train is a train of
+ 
+
+ align:start position:0%
+functions in the train is a train of
+functions in the frequency domain and
+
+ align:start position:0%
+functions in the frequency domain and
+ 
+
+ align:start position:0%
+functions in the frequency domain and
+vice versa right and there's a very
+
+ align:start position:0%
+vice versa right and there's a very
+ 
+
+ align:start position:0%
+vice versa right and there's a very
+simple relation between the period and
+
+ align:start position:0%
+simple relation between the period and
+ 
+
+ align:start position:0%
+simple relation between the period and
+the time domain and the period in the
+
+ align:start position:0%
+the time domain and the period in the
+ 
+
+ align:start position:0%
+the time domain and the period in the
+frequency domain what does the power
+
+ align:start position:0%
+frequency domain what does the power
+ 
+
+ align:start position:0%
+frequency domain what does the power
+spectrum of this train of Delta
+
+ align:start position:0%
+spectrum of this train of Delta
+ 
+
+ align:start position:0%
+spectrum of this train of Delta
+functions look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just the square magnitude of this
+
+ align:start position:0%
+it's just the square magnitude of this
+ 
+
+ align:start position:0%
+it's just the square magnitude of this
+right so it just looks like a bunch of
+
+ align:start position:0%
+right so it just looks like a bunch of
+ 
+
+ align:start position:0%
+right so it just looks like a bunch of
+Peaks okay
+
+ align:start position:0%
+Peaks okay
+ 
+
+ align:start position:0%
+Peaks okay
+so here's another function a square wave
+
+ align:start position:0%
+so here's another function a square wave
+ 
+
+ align:start position:0%
+so here's another function a square wave
+this is exactly the same function that
+
+ align:start position:0%
+this is exactly the same function that
+ 
+
+ align:start position:0%
+this is exactly the same function that
+we started with if you look at the
+
+ align:start position:0%
+we started with if you look at the
+ 
+
+ align:start position:0%
+we started with if you look at the
+Fourier transform of the imaginary part
+
+ align:start position:0%
+Fourier transform of the imaginary part
+ 
+
+ align:start position:0%
+Fourier transform of the imaginary part
+is zero the real part has these Peaks so
+
+ align:start position:0%
+is zero the real part has these Peaks so
+ 
+
+ align:start position:0%
+is zero the real part has these Peaks so
+the Fourier transforms
+
+ align:start position:0%
+the Fourier transforms
+ 
+
+ align:start position:0%
+the Fourier transforms
+that you would put in front of your
+
+ align:start position:0%
+that you would put in front of your
+ 
+
+ align:start position:0%
+that you would put in front of your
+different cosines at different
+
+ align:start position:0%
+different cosines at different
+ 
+
+ align:start position:0%
+different cosines at different
+frequencies to represent the square wave
+
+ align:start position:0%
+frequencies to represent the square wave
+ 
+
+ align:start position:0%
+frequencies to represent the square wave
+okay so what it looks like is positive
+
+ align:start position:0%
+okay so what it looks like is positive
+ 
+
+ align:start position:0%
+okay so what it looks like is positive
+peak for the lowest frequency negative
+
+ align:start position:0%
+peak for the lowest frequency negative
+ 
+
+ align:start position:0%
+peak for the lowest frequency negative
+peak for the next harmonic positive peak
+
+ align:start position:0%
+peak for the next harmonic positive peak
+ 
+
+ align:start position:0%
+peak for the next harmonic positive peak
+and and gradually decreasing amplitudes
+
+ align:start position:0%
+and and gradually decreasing amplitudes
+ 
+
+ align:start position:0%
+and and gradually decreasing amplitudes
+okay the power spectrum of this oh and
+
+ align:start position:0%
+okay the power spectrum of this oh and
+ 
+
+ align:start position:0%
+okay the power spectrum of this oh and
+one more point is that if you look at
+
+ align:start position:0%
+one more point is that if you look at
+ 
+
+ align:start position:0%
+one more point is that if you look at
+the Fourier transform of a higher
+
+ align:start position:0%
+the Fourier transform of a higher
+ 
+
+ align:start position:0%
+the Fourier transform of a higher
+frequency square wave you can see that
+
+ align:start position:0%
+frequency square wave you can see that
+ 
+
+ align:start position:0%
+frequency square wave you can see that
+those Peaks move apart okay so you can
+
+ align:start position:0%
+those Peaks move apart okay so you can
+ 
+
+ align:start position:0%
+those Peaks move apart okay so you can
+transform so higher frequencies in the
+
+ align:start position:0%
+transform so higher frequencies in the
+ 
+
+ align:start position:0%
+transform so higher frequencies in the
+time domain stuff happening faster in
+
+ align:start position:0%
+time domain stuff happening faster in
+ 
+
+ align:start position:0%
+time domain stuff happening faster in
+the timing is associated with things
+
+ align:start position:0%
+the timing is associated with things
+ 
+
+ align:start position:0%
+the timing is associated with things
+moving out to higher frequencies in the
+
+ align:start position:0%
+moving out to higher frequencies in the
+ 
+
+ align:start position:0%
+moving out to higher frequencies in the
+frequency domain you can see that the
+
+ align:start position:0%
+frequency domain you can see that the
+ 
+
+ align:start position:0%
+frequency domain you can see that the
+same function higher frequencies has the
+
+ align:start position:0%
+same function higher frequencies has the
+ 
+
+ align:start position:0%
+same function higher frequencies has the
+same Fourier transform but with the
+
+ align:start position:0%
+same Fourier transform but with the
+ 
+
+ align:start position:0%
+same Fourier transform but with the
+components spread out to higher
+
+ align:start position:0%
+components spread out to higher
+ 
+
+ align:start position:0%
+components spread out to higher
+frequencies okay and the power spectrum
+
+ align:start position:0%
+frequencies okay and the power spectrum
+ 
+
+ align:start position:0%
+frequencies okay and the power spectrum
+except this and notice that one more
+
+ align:start position:0%
+except this and notice that one more
+ 
+
+ align:start position:0%
+except this and notice that one more
+final point here is that when you look
+
+ align:start position:0%
+final point here is that when you look
+ 
+
+ align:start position:0%
+final point here is that when you look
+at power spectra often signals can have
+
+ align:start position:0%
+at power spectra often signals can have
+ 
+
+ align:start position:0%
+at power spectra often signals can have
+frequency components that are at that
+
+ align:start position:0%
+frequency components that are at that
+ 
+
+ align:start position:0%
+frequency components that are at that
+are very small so that it's hard to see
+
+ align:start position:0%
+are very small so that it's hard to see
+ 
+
+ align:start position:0%
+are very small so that it's hard to see
+them on a linear scale and so we
+
+ align:start position:0%
+them on a linear scale and so we
+ 
+
+ align:start position:0%
+them on a linear scale and so we
+actually plot them in this method you
+
+ align:start position:0%
+actually plot them in this method you
+ 
+
+ align:start position:0%
+actually plot them in this method you
+plot them in units of decibels and I'll
+
+ align:start position:0%
+plot them in units of decibels and I'll
+ 
+
+ align:start position:0%
+plot them in units of decibels and I'll
+explain what those are the next time but
+
+ align:start position:0%
+explain what those are the next time but
+ 
+
+ align:start position:0%
+explain what those are the next time but
+that's another representation of the
+
+ align:start position:0%
+that's another representation of the
+ 
+
+ align:start position:0%
+that's another representation of the
+power spectrum
+
+ align:start position:0%
+power spectrum
+ 
+
+ align:start position:0%
+power spectrum
+of of a signal okay so that's what we've
+
+ align:start position:0%
+of of a signal okay so that's what we've
+ 
+
+ align:start position:0%
+of of a signal okay so that's what we've
+covered and we're going to continue with
+
+ align:start position:0%
+covered and we're going to continue with
+ 
+
+ align:start position:0%
+covered and we're going to continue with
+the gameplan next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/4oIsQdCjMeE.txt b/4oIsQdCjMeE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c3562af4f4c69378aa2786491a979a9f1588d551
--- /dev/null
+++ b/4oIsQdCjMeE.txt
@@ -0,0 +1,10008 @@
+align:start position:0%
+ 
+chiefly in mind here uh two are coming
+
+ align:start position:0%
+chiefly in mind here uh two are coming
+ 
+
+ align:start position:0%
+chiefly in mind here uh two are coming
+from last time uh I wanted to say just a
+
+ align:start position:0%
+from last time uh I wanted to say just a
+ 
+
+ align:start position:0%
+from last time uh I wanted to say just a
+little more about this neat theorem of
+
+ align:start position:0%
+little more about this neat theorem of
+ 
+
+ align:start position:0%
+little more about this neat theorem of
+Max flow Min cut this was a this was a
+
+ align:start position:0%
+Max flow Min cut this was a this was a
+ 
+
+ align:start position:0%
+Max flow Min cut this was a this was a
+do an example of Duality and a
+
+ align:start position:0%
+do an example of Duality and a
+ 
+
+ align:start position:0%
+do an example of Duality and a
+particularly nice one and uh um chapter
+
+ align:start position:0%
+particularly nice one and uh um chapter
+ 
+
+ align:start position:0%
+particularly nice one and uh um chapter
+7 of the book has uh examples and and
+
+ align:start position:0%
+7 of the book has uh examples and and
+ 
+
+ align:start position:0%
+7 of the book has uh examples and and
+more discussion of that then
+
+ align:start position:0%
+more discussion of that then
+ 
+
+ align:start position:0%
+more discussion of that then
+um you were kind enough to get involved
+
+ align:start position:0%
+um you were kind enough to get involved
+ 
+
+ align:start position:0%
+um you were kind enough to get involved
+in my new uh interest which was well the
+
+ align:start position:0%
+in my new uh interest which was well the
+ 
+
+ align:start position:0%
+in my new uh interest which was well the
+specific question was uh when can I
+
+ align:start position:0%
+specific question was uh when can I
+ 
+
+ align:start position:0%
+specific question was uh when can I
+complete a matrix given some of its
+
+ align:start position:0%
+complete a matrix given some of its
+ 
+
+ align:start position:0%
+complete a matrix given some of its
+entries when can I finish it out to have
+
+ align:start position:0%
+entries when can I finish it out to have
+ 
+
+ align:start position:0%
+entries when can I finish it out to have
+rank one and I have some news so of
+
+ align:start position:0%
+rank one and I have some news so of
+ 
+
+ align:start position:0%
+rank one and I have some news so of
+course I'm eager to tell you about it
+
+ align:start position:0%
+course I'm eager to tell you about it
+ 
+
+ align:start position:0%
+course I'm eager to tell you about it
+and uh and then the
+
+ align:start position:0%
+and uh and then the
+ 
+
+ align:start position:0%
+and uh and then the
+I I realized that it might be a pleasure
+
+ align:start position:0%
+I I realized that it might be a pleasure
+ 
+
+ align:start position:0%
+I I realized that it might be a pleasure
+to talk about Game Theory as another uh
+
+ align:start position:0%
+to talk about Game Theory as another uh
+ 
+
+ align:start position:0%
+to talk about Game Theory as another uh
+two person this is twers game theory
+
+ align:start position:0%
+two person this is twers game theory
+ 
+
+ align:start position:0%
+two person this is twers game theory
+created by uh V
+
+ align:start position:0%
+created by uh V
+ 
+
+ align:start position:0%
+created by uh V
+noyman and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh it's another example of Duality uh
+
+ align:start position:0%
+uh uh it's another example of Duality uh
+ 
+
+ align:start position:0%
+uh uh it's another example of Duality uh
+but uh just coming from somewhere from
+
+ align:start position:0%
+but uh just coming from somewhere from
+ 
+
+ align:start position:0%
+but uh just coming from somewhere from
+such a different source that it wasn't
+
+ align:start position:0%
+such a different source that it wasn't
+ 
+
+ align:start position:0%
+such a different source that it wasn't
+recognized uh for a little while that
+
+ align:start position:0%
+recognized uh for a little while that
+ 
+
+ align:start position:0%
+recognized uh for a little while that
+that it fit the framework okay with Max
+
+ align:start position:0%
+that it fit the framework okay with Max
+ 
+
+ align:start position:0%
+that it fit the framework okay with Max
+flow Min cut I just have this uh uh
+
+ align:start position:0%
+flow Min cut I just have this uh uh
+ 
+
+ align:start position:0%
+flow Min cut I just have this uh uh
+example to mention uh suppose all the
+
+ align:start position:0%
+example to mention uh suppose all the
+ 
+
+ align:start position:0%
+example to mention uh suppose all the
+capacities are
+
+ align:start position:0%
+capacities are
+ 
+
+ align:start position:0%
+capacities are
+one on the edges so on every Edge we can
+
+ align:start position:0%
+one on the edges so on every Edge we can
+ 
+
+ align:start position:0%
+one on the edges so on every Edge we can
+send one um uh unit how well in this
+
+ align:start position:0%
+send one um uh unit how well in this
+ 
+
+ align:start position:0%
+send one um uh unit how well in this
+example let's say how much could I get
+
+ align:start position:0%
+example let's say how much could I get
+ 
+
+ align:start position:0%
+example let's say how much could I get
+from the source to the sink
+
+ align:start position:0%
+from the source to the sink
+ 
+
+ align:start position:0%
+from the source to the sink
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+well along those
+
+ align:start position:0%
+well along those
+ 
+
+ align:start position:0%
+well along those
+edges okay uh oh have I made it so I
+
+ align:start position:0%
+edges okay uh oh have I made it so I
+ 
+
+ align:start position:0%
+edges okay uh oh have I made it so I
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+four could I get four through on
+
+ align:start position:0%
+four could I get four through on
+ 
+
+ align:start position:0%
+four could I get four through on
+that yes I think I
+
+ align:start position:0%
+that yes I think I
+ 
+
+ align:start position:0%
+that yes I think I
+could right because yeah so let me let
+
+ align:start position:0%
+could right because yeah so let me let
+ 
+
+ align:start position:0%
+could right because yeah so let me let
+me uh make it a little harder let me add
+
+ align:start position:0%
+me uh make it a little harder let me add
+ 
+
+ align:start position:0%
+me uh make it a little harder let me add
+another Edge
+
+ align:start position:0%
+another Edge
+ 
+
+ align:start position:0%
+another Edge
+there so hopefully I could get more
+
+ align:start position:0%
+there so hopefully I could get more
+ 
+
+ align:start position:0%
+there so hopefully I could get more
+through but I think I can't I think uh
+
+ align:start position:0%
+through but I think I can't I think uh
+ 
+
+ align:start position:0%
+through but I think I can't I think uh
+that how much could I now get through
+
+ align:start position:0%
+that how much could I now get through
+ 
+
+ align:start position:0%
+that how much could I now get through
+from the source to the sink there are 1
+
+ align:start position:0%
+from the source to the sink there are 1
+ 
+
+ align:start position:0%
+from the source to the sink there are 1
+two 3 four five edges leaving the sink
+
+ align:start position:0%
+two 3 four five edges leaving the sink
+ 
+
+ align:start position:0%
+two 3 four five edges leaving the sink
+and then they go different
+
+ align:start position:0%
+and then they go different
+ 
+
+ align:start position:0%
+and then they go different
+places uh and there could be as we had
+
+ align:start position:0%
+places uh and there could be as we had
+ 
+
+ align:start position:0%
+places uh and there could be as we had
+last time uh uh the the bottleneck could
+
+ align:start position:0%
+last time uh uh the the bottleneck could
+ 
+
+ align:start position:0%
+last time uh uh the the bottleneck could
+be in the middle of the of the path or
+
+ align:start position:0%
+be in the middle of the of the path or
+ 
+
+ align:start position:0%
+be in the middle of the of the path or
+it could be right here at the uh sink
+
+ align:start position:0%
+it could be right here at the uh sink
+ 
+
+ align:start position:0%
+it could be right here at the uh sink
+maybe it is maybe in this case I can
+
+ align:start position:0%
+maybe it is maybe in this case I can
+ 
+
+ align:start position:0%
+maybe it is maybe in this case I can
+only get four I could even
+
+ align:start position:0%
+only get four I could even
+ 
+
+ align:start position:0%
+only get four I could even
+uh yeah I could I think maybe the
+
+ align:start position:0%
+uh yeah I could I think maybe the
+ 
+
+ align:start position:0%
+uh yeah I could I think maybe the
+maximal capacity is
+
+ align:start position:0%
+maximal capacity is
+ 
+
+ align:start position:0%
+maximal capacity is
+four agreed yeah and the cut that that
+
+ align:start position:0%
+four agreed yeah and the cut that that
+ 
+
+ align:start position:0%
+four agreed yeah and the cut that that
+shows me that proves it is actually well
+
+ align:start position:0%
+shows me that proves it is actually well
+ 
+
+ align:start position:0%
+shows me that proves it is actually well
+in this case sort of a degenerate case
+
+ align:start position:0%
+in this case sort of a degenerate case
+ 
+
+ align:start position:0%
+in this case sort of a degenerate case
+the sink is all by himself in the cut so
+
+ align:start position:0%
+the sink is all by himself in the cut so
+ 
+
+ align:start position:0%
+the sink is all by himself in the cut so
+there's a cut of one 2 three and four
+
+ align:start position:0%
+there's a cut of one 2 three and four
+ 
+
+ align:start position:0%
+there's a cut of one 2 three and four
+edges getting through and that's the
+
+ align:start position:0%
+edges getting through and that's the
+ 
+
+ align:start position:0%
+edges getting through and that's the
+maximum flow also
+
+ align:start position:0%
+maximum flow also
+ 
+
+ align:start position:0%
+maximum flow also
+and what I let let me draw the the paths
+
+ align:start position:0%
+and what I let let me draw the the paths
+ 
+
+ align:start position:0%
+and what I let let me draw the the paths
+that that it could follow one set of
+
+ align:start position:0%
+that that it could follow one set of
+ 
+
+ align:start position:0%
+that that it could follow one set of
+paths that it could follow uh let's see
+
+ align:start position:0%
+paths that it could follow uh let's see
+ 
+
+ align:start position:0%
+paths that it could follow uh let's see
+I could send one along this
+
+ align:start position:0%
+I could send one along this
+ 
+
+ align:start position:0%
+I could send one along this
+path and I could send one along this
+
+ align:start position:0%
+path and I could send one along this
+ 
+
+ align:start position:0%
+path and I could send one along this
+this path and one around here and one
+
+ align:start position:0%
+this path and one around here and one
+ 
+
+ align:start position:0%
+this path and one around here and one
+around straight through there
+
+ align:start position:0%
+around straight through there
+ 
+
+ align:start position:0%
+around straight through there
+so those notice that those paths are
+
+ align:start position:0%
+so those notice that those paths are
+ 
+
+ align:start position:0%
+so those notice that those paths are
+disjoint separate paths uh the and they
+
+ align:start position:0%
+disjoint separate paths uh the and they
+ 
+
+ align:start position:0%
+disjoint separate paths uh the and they
+have to be right with the
+
+ align:start position:0%
+have to be right with the
+ 
+
+ align:start position:0%
+have to be right with the
+with with this kind of flow I'm not
+
+ align:start position:0%
+with with this kind of flow I'm not
+ 
+
+ align:start position:0%
+with with this kind of flow I'm not
+going to gain anything by sharing by
+
+ align:start position:0%
+going to gain anything by sharing by
+ 
+
+ align:start position:0%
+going to gain anything by sharing by
+having uh by by sharing an edge with two
+
+ align:start position:0%
+having uh by by sharing an edge with two
+ 
+
+ align:start position:0%
+having uh by by sharing an edge with two
+flows so what I'm trying to say is that
+
+ align:start position:0%
+flows so what I'm trying to say is that
+ 
+
+ align:start position:0%
+flows so what I'm trying to say is that
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+example uh it the max flow equal Min cut
+
+ align:start position:0%
+example uh it the max flow equal Min cut
+ 
+
+ align:start position:0%
+example uh it the max flow equal Min cut
+can be expressed in a really in a
+
+ align:start position:0%
+can be expressed in a really in a
+ 
+
+ align:start position:0%
+can be expressed in a really in a
+different way the ma so what I want to
+
+ align:start position:0%
+different way the ma so what I want to
+ 
+
+ align:start position:0%
+different way the ma so what I want to
+do is restate this for the special case
+
+ align:start position:0%
+do is restate this for the special case
+ 
+
+ align:start position:0%
+do is restate this for the special case
+here as the
+
+ align:start position:0%
+here as the
+ 
+
+ align:start position:0%
+here as the
+maximum number of disjoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pass S2 s Prime source to sync so
+
+ align:start position:0%
+pass S2 s Prime source to sync so
+ 
+
+ align:start position:0%
+pass S2 s Prime source to sync so
+there's an example four disjoint paths
+
+ align:start position:0%
+there's an example four disjoint paths
+ 
+
+ align:start position:0%
+there's an example four disjoint paths
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+one so I'm looking for how many
+
+ align:start position:0%
+one so I'm looking for how many
+ 
+
+ align:start position:0%
+one so I'm looking for how many
+independent paths go from here to here
+
+ align:start position:0%
+independent paths go from here to here
+ 
+
+ align:start position:0%
+independent paths go from here to here
+and it's equal to this the capacity
+
+ align:start position:0%
+and it's equal to this the capacity
+ 
+
+ align:start position:0%
+and it's equal to this the capacity
+across the cut and I would like to find
+
+ align:start position:0%
+across the cut and I would like to find
+ 
+
+ align:start position:0%
+across the cut and I would like to find
+a different uh set of words for that uh
+
+ align:start position:0%
+a different uh set of words for that uh
+ 
+
+ align:start position:0%
+a different uh set of words for that uh
+so what happen this cut suppose I
+
+ align:start position:0%
+so what happen this cut suppose I
+ 
+
+ align:start position:0%
+so what happen this cut suppose I
+actually make such a cut so I'll
+
+ align:start position:0%
+actually make such a cut so I'll
+ 
+
+ align:start position:0%
+actually make such a cut so I'll
+actually use the Eraser to to cut the
+
+ align:start position:0%
+actually use the Eraser to to cut the
+ 
+
+ align:start position:0%
+actually use the Eraser to to cut the
+the uh Network so what does a cut mean
+
+ align:start position:0%
+the uh Network so what does a cut mean
+ 
+
+ align:start position:0%
+the uh Network so what does a cut mean
+it's a it's a a separation of the nodes
+
+ align:start position:0%
+it's a it's a a separation of the nodes
+ 
+
+ align:start position:0%
+it's a it's a a separation of the nodes
+into one group with the source and
+
+ align:start position:0%
+into one group with the source and
+ 
+
+ align:start position:0%
+into one group with the source and
+another group with a sync well sorry
+
+ align:start position:0%
+another group with a sync well sorry
+ 
+
+ align:start position:0%
+another group with a sync well sorry
+that in this example the group with a
+
+ align:start position:0%
+that in this example the group with a
+ 
+
+ align:start position:0%
+that in this example the group with a
+sync is only the sync but nevertheless
+
+ align:start position:0%
+sync is only the sync but nevertheless
+ 
+
+ align:start position:0%
+sync is only the sync but nevertheless
+that's that's a cut and what's what has
+
+ align:start position:0%
+that's that's a cut and what's what has
+ 
+
+ align:start position:0%
+that's that's a cut and what's what has
+that cut
+
+ align:start position:0%
+that cut
+ 
+
+ align:start position:0%
+that cut
+done that cut has separated the source
+
+ align:start position:0%
+done that cut has separated the source
+ 
+
+ align:start position:0%
+done that cut has separated the source
+from the sink it's it's literally cut
+
+ align:start position:0%
+from the sink it's it's literally cut
+ 
+
+ align:start position:0%
+from the sink it's it's literally cut
+the two apart so
+
+ align:start position:0%
+the two apart so
+ 
+
+ align:start position:0%
+the two apart so
+the and the capacity of course is the
+
+ align:start position:0%
+the and the capacity of course is the
+ 
+
+ align:start position:0%
+the and the capacity of course is the
+the across the cut is the number
+
+ align:start position:0%
+the across the cut is the number
+ 
+
+ align:start position:0%
+the across the cut is the number
+of times we clipped an edge so here
+
+ align:start position:0%
+of times we clipped an edge so here
+ 
+
+ align:start position:0%
+of times we clipped an edge so here
+here's what I'm trying to to say the
+
+ align:start position:0%
+here's what I'm trying to to say the
+ 
+
+ align:start position:0%
+here's what I'm trying to to say the
+maximum number of disjoint paths that
+
+ align:start position:0%
+maximum number of disjoint paths that
+ 
+
+ align:start position:0%
+maximum number of disjoint paths that
+measured how much flow we could do
+
+ align:start position:0%
+measured how much flow we could do
+ 
+
+ align:start position:0%
+measured how much flow we could do
+equals the minimum
+
+ align:start position:0%
+equals the minimum
+ 
+
+ align:start position:0%
+equals the minimum
+number of cut of cut of cut
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+split may I use it use a strong verb
+
+ align:start position:0%
+split may I use it use a strong verb
+ 
+
+ align:start position:0%
+split may I use it use a strong verb
+there to split s
+
+ align:start position:0%
+there to split s
+ 
+
+ align:start position:0%
+there to split s
+from S Prime the minimum number number
+
+ align:start position:0%
+from S Prime the minimum number number
+ 
+
+ align:start position:0%
+from S Prime the minimum number number
+of edges that it took to to to
+
+ align:start position:0%
+of edges that it took to to to
+ 
+
+ align:start position:0%
+of edges that it took to to to
+uh uh separate this from this you you
+
+ align:start position:0%
+uh uh separate this from this you you
+ 
+
+ align:start position:0%
+uh uh separate this from this you you
+see that that this is a a restatement
+
+ align:start position:0%
+see that that this is a a restatement
+ 
+
+ align:start position:0%
+see that that this is a a restatement
+and maybe we could think why why I mean
+
+ align:start position:0%
+and maybe we could think why why I mean
+ 
+
+ align:start position:0%
+and maybe we could think why why I mean
+this is as
+
+ align:start position:0%
+this is as
+ 
+
+ align:start position:0%
+this is as
+usual we should see weak Duell so what
+
+ align:start position:0%
+usual we should see weak Duell so what
+ 
+
+ align:start position:0%
+usual we should see weak Duell so what
+would what did weak Duality mean weak
+
+ align:start position:0%
+would what did weak Duality mean weak
+ 
+
+ align:start position:0%
+would what did weak Duality mean weak
+Duality which was usually the easy thing
+
+ align:start position:0%
+Duality which was usually the easy thing
+ 
+
+ align:start position:0%
+Duality which was usually the easy thing
+to to to to see so if I just made
+
+ align:start position:0%
+to to to to see so if I just made
+ 
+
+ align:start position:0%
+to to to to see so if I just made
+suppose I had just made this
+
+ align:start position:0%
+suppose I had just made this
+ 
+
+ align:start position:0%
+suppose I had just made this
+statement that I draw a network and I
+
+ align:start position:0%
+statement that I draw a network and I
+ 
+
+ align:start position:0%
+statement that I draw a network and I
+look at how many separate paths there
+
+ align:start position:0%
+look at how many separate paths there
+ 
+
+ align:start position:0%
+look at how many separate paths there
+are that don't don't share any edges
+
+ align:start position:0%
+are that don't don't share any edges
+ 
+
+ align:start position:0%
+are that don't don't share any edges
+that's what disjoint means from source
+
+ align:start position:0%
+that's what disjoint means from source
+ 
+
+ align:start position:0%
+that's what disjoint means from source
+to sync how many
+
+ align:start position:0%
+to sync how many
+ 
+
+ align:start position:0%
+to sync how many
+paths uh and I looked at the minimum
+
+ align:start position:0%
+paths uh and I looked at the minimum
+ 
+
+ align:start position:0%
+paths uh and I looked at the minimum
+number of edges of cuts that I had to
+
+ align:start position:0%
+number of edges of cuts that I had to
+ 
+
+ align:start position:0%
+number of edges of cuts that I had to
+make to separate the two now it should
+
+ align:start position:0%
+make to separate the two now it should
+ 
+
+ align:start position:0%
+make to separate the two now it should
+weak should be maximum less or equal
+
+ align:start position:0%
+weak should be maximum less or equal
+ 
+
+ align:start position:0%
+weak should be maximum less or equal
+minimum should be easy and remember it's
+
+ align:start position:0%
+minimum should be easy and remember it's
+ 
+
+ align:start position:0%
+minimum should be easy and remember it's
+slightly strange that it it's that
+
+ align:start position:0%
+slightly strange that it it's that
+ 
+
+ align:start position:0%
+slightly strange that it it's that
+direction that's easy of course it's the
+
+ align:start position:0%
+direction that's easy of course it's the
+ 
+
+ align:start position:0%
+direction that's easy of course it's the
+maximum of one thing and the minimum of
+
+ align:start position:0%
+maximum of one thing and the minimum of
+ 
+
+ align:start position:0%
+maximum of one thing and the minimum of
+another why is that easy how do I know
+
+ align:start position:0%
+another why is that easy how do I know
+ 
+
+ align:start position:0%
+another why is that easy how do I know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um that if I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have uh the minimum number of edges to
+
+ align:start position:0%
+have uh the minimum number of edges to
+ 
+
+ align:start position:0%
+have uh the minimum number of edges to
+to if I find it if I find some edges
+
+ align:start position:0%
+to if I find it if I find some edges
+ 
+
+ align:start position:0%
+to if I find it if I find some edges
+that split yeah H how do I know that if
+
+ align:start position:0%
+that split yeah H how do I know that if
+ 
+
+ align:start position:0%
+that split yeah H how do I know that if
+I if I find any
+
+ align:start position:0%
+I if I find any
+ 
+
+ align:start position:0%
+I if I find any
+cut any any any bunch of edges I could
+
+ align:start position:0%
+cut any any any bunch of edges I could
+ 
+
+ align:start position:0%
+cut any any any bunch of edges I could
+snip through that would separate Source
+
+ align:start position:0%
+snip through that would separate Source
+ 
+
+ align:start position:0%
+snip through that would separate Source
+from sync and I count those edges and I
+
+ align:start position:0%
+from sync and I count those edges and I
+ 
+
+ align:start position:0%
+from sync and I count those edges and I
+get K how do I know that the number of
+
+ align:start position:0%
+get K how do I know that the number of
+ 
+
+ align:start position:0%
+get K how do I know that the number of
+PA can't be more than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K yeah yeah if if exactly if each Edge
+
+ align:start position:0%
+K yeah yeah if if exactly if each Edge
+ 
+
+ align:start position:0%
+K yeah yeah if if exactly if each Edge
+if uh if I manage to cut the thing with
+
+ align:start position:0%
+if uh if I manage to cut the thing with
+ 
+
+ align:start position:0%
+if uh if I manage to cut the thing with
+k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there couldn't be more than K
+
+ align:start position:0%
+then there couldn't be more than K
+ 
+
+ align:start position:0%
+then there couldn't be more than K
+disjoint paths because then I wouldn't
+
+ align:start position:0%
+disjoint paths because then I wouldn't
+ 
+
+ align:start position:0%
+disjoint paths because then I wouldn't
+have cut one of
+
+ align:start position:0%
+have cut one of
+ 
+
+ align:start position:0%
+have cut one of
+them let let me say that again just easy
+
+ align:start position:0%
+them let let me say that again just easy
+ 
+
+ align:start position:0%
+them let let me say that again just easy
+uh suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose K
+
+ align:start position:0%
+suppose K
+ 
+
+ align:start position:0%
+suppose K
+Cuts
+
+ align:start position:0%
+Cuts
+ 
+
+ align:start position:0%
+Cuts
+split s from S
+
+ align:start position:0%
+split s from S
+ 
+
+ align:start position:0%
+split s from S
+Prime then can't
+
+ align:start position:0%
+Prime then can't
+ 
+
+ align:start position:0%
+Prime then can't
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+more can't be greater than
+
+ align:start position:0%
+more can't be greater than
+ 
+
+ align:start position:0%
+more can't be greater than
+K disjoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths because if there were more than K
+
+ align:start position:0%
+paths because if there were more than K
+ 
+
+ align:start position:0%
+paths because if there were more than K
+disjoint paths then I didn't cut them
+
+ align:start position:0%
+disjoint paths then I didn't cut them
+ 
+
+ align:start position:0%
+disjoint paths then I didn't cut them
+all and then I haven't separated the
+
+ align:start position:0%
+all and then I haven't separated the
+ 
+
+ align:start position:0%
+all and then I haven't separated the
+source from the sink so that that would
+
+ align:start position:0%
+source from the sink so that that would
+ 
+
+ align:start position:0%
+source from the sink so that that would
+be the reasoning that I take any cut
+
+ align:start position:0%
+be the reasoning that I take any cut
+ 
+
+ align:start position:0%
+be the reasoning that I take any cut
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+works I say okay maybe it took k
+
+ align:start position:0%
+works I say okay maybe it took k
+ 
+
+ align:start position:0%
+works I say okay maybe it took k
+a separate edges to clip but then the
+
+ align:start position:0%
+a separate edges to clip but then the
+ 
+
+ align:start position:0%
+a separate edges to clip but then the
+number of disjoint paths couldn't be
+
+ align:start position:0%
+number of disjoint paths couldn't be
+ 
+
+ align:start position:0%
+number of disjoint paths couldn't be
+larger than K because then if it were
+
+ align:start position:0%
+larger than K because then if it were
+ 
+
+ align:start position:0%
+larger than K because then if it were
+one of those paths isn't getting cut and
+
+ align:start position:0%
+one of those paths isn't getting cut and
+ 
+
+ align:start position:0%
+one of those paths isn't getting cut and
+and uh uh we haven't we haven't
+
+ align:start position:0%
+and uh uh we haven't we haven't
+ 
+
+ align:start position:0%
+and uh uh we haven't we haven't
+separated s from S Prime so that that
+
+ align:start position:0%
+separated s from S Prime so that that
+ 
+
+ align:start position:0%
+separated s from S Prime so that that
+says that any any cut that's
+
+ align:start position:0%
+says that any any cut that's
+ 
+
+ align:start position:0%
+says that any any cut that's
+acceptable is large is at least as large
+
+ align:start position:0%
+acceptable is large is at least as large
+ 
+
+ align:start position:0%
+acceptable is large is at least as large
+as any count of disjoint paths so we
+
+ align:start position:0%
+as any count of disjoint paths so we
+ 
+
+ align:start position:0%
+as any count of disjoint paths so we
+increase the count of disjoint paths up
+
+ align:start position:0%
+increase the count of disjoint paths up
+ 
+
+ align:start position:0%
+increase the count of disjoint paths up
+to its maximum we decrease the number of
+
+ align:start position:0%
+to its maximum we decrease the number of
+ 
+
+ align:start position:0%
+to its maximum we decrease the number of
+cuts to the do the best cutting we can
+
+ align:start position:0%
+cuts to the do the best cutting we can
+ 
+
+ align:start position:0%
+cuts to the do the best cutting we can
+and we have less or equal and the point
+
+ align:start position:0%
+and we have less or equal and the point
+ 
+
+ align:start position:0%
+and we have less or equal and the point
+is we actually have equal and maybe
+
+ align:start position:0%
+is we actually have equal and maybe
+ 
+
+ align:start position:0%
+is we actually have equal and maybe
+here's a way to here's a proof of
+
+ align:start position:0%
+here's a way to here's a proof of
+ 
+
+ align:start position:0%
+here's a way to here's a proof of
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+suppose we have uh well the idea of the
+
+ align:start position:0%
+suppose we have uh well the idea of the
+ 
+
+ align:start position:0%
+suppose we have uh well the idea of the
+proof is that if if uh um that suppose
+
+ align:start position:0%
+proof is that if if uh um that suppose
+ 
+
+ align:start position:0%
+proof is that if if uh um that suppose
+we have a maximum flow yeah I I um this
+
+ align:start position:0%
+we have a maximum flow yeah I I um this
+ 
+
+ align:start position:0%
+we have a maximum flow yeah I I um this
+is in the book and and it's hard to take
+
+ align:start position:0%
+is in the book and and it's hard to take
+ 
+
+ align:start position:0%
+is in the book and and it's hard to take
+in verbally but if we had a maximum flow
+
+ align:start position:0%
+in verbally but if we had a maximum flow
+ 
+
+ align:start position:0%
+in verbally but if we had a maximum flow
+suppose we had the flow as large as
+
+ align:start position:0%
+suppose we had the flow as large as
+ 
+
+ align:start position:0%
+suppose we had the flow as large as
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+then I want to see why some cut of that
+
+ align:start position:0%
+then I want to see why some cut of that
+ 
+
+ align:start position:0%
+then I want to see why some cut of that
+size is holding us up so we have a Max a
+
+ align:start position:0%
+size is holding us up so we have a Max a
+ 
+
+ align:start position:0%
+size is holding us up so we have a Max a
+flow as big as possible then
+
+ align:start position:0%
+flow as big as possible then
+ 
+
+ align:start position:0%
+flow as big as possible then
+I keep with s some edges might some some
+
+ align:start position:0%
+I keep with s some edges might some some
+ 
+
+ align:start position:0%
+I keep with s some edges might some some
+with s some edges I might be able to
+
+ align:start position:0%
+with s some edges I might be able to
+ 
+
+ align:start position:0%
+with s some edges I might be able to
+send more
+
+ align:start position:0%
+send more
+ 
+
+ align:start position:0%
+send more
+to some uh along some edges I might be
+
+ align:start position:0%
+to some uh along some edges I might be
+ 
+
+ align:start position:0%
+to some uh along some edges I might be
+able to send more for example along that
+
+ align:start position:0%
+able to send more for example along that
+ 
+
+ align:start position:0%
+able to send more for example along that
+Ed Edge I could send
+
+ align:start position:0%
+Ed Edge I could send
+ 
+
+ align:start position:0%
+Ed Edge I could send
+more ha that's interesting okay now I'm
+
+ align:start position:0%
+more ha that's interesting okay now I'm
+ 
+
+ align:start position:0%
+more ha that's interesting okay now I'm
+going to I may find another cut here so
+
+ align:start position:0%
+going to I may find another cut here so
+ 
+
+ align:start position:0%
+going to I may find another cut here so
+I I keep I group with the S all the
+
+ align:start position:0%
+I I keep I group with the S all the
+ 
+
+ align:start position:0%
+I I keep I group with the S all the
+nodes to which I could still send one
+
+ align:start position:0%
+nodes to which I could still send one
+ 
+
+ align:start position:0%
+nodes to which I could still send one
+more okay let me see I need I'll use
+
+ align:start position:0%
+more okay let me see I need I'll use
+ 
+
+ align:start position:0%
+more okay let me see I need I'll use
+this so with this I keep th this note
+
+ align:start position:0%
+this so with this I keep th this note
+ 
+
+ align:start position:0%
+this so with this I keep th this note
+because I could still send one more to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that who and then oh yeah this is going
+
+ align:start position:0%
+that who and then oh yeah this is going
+ 
+
+ align:start position:0%
+that who and then oh yeah this is going
+to be tricky because I could s now send
+
+ align:start position:0%
+to be tricky because I could s now send
+ 
+
+ align:start position:0%
+to be tricky because I could s now send
+backwards on this Edge so having sent
+
+ align:start position:0%
+backwards on this Edge so having sent
+ 
+
+ align:start position:0%
+backwards on this Edge so having sent
+these forward I could sent one backwards
+
+ align:start position:0%
+these forward I could sent one backwards
+ 
+
+ align:start position:0%
+these forward I could sent one backwards
+I think I'm not going to get into this
+
+ align:start position:0%
+I think I'm not going to get into this
+ 
+
+ align:start position:0%
+I think I'm not going to get into this
+uh uh uh because I don't want the whole
+
+ align:start position:0%
+uh uh uh because I don't want the whole
+ 
+
+ align:start position:0%
+uh uh uh because I don't want the whole
+lecture to be this rather specific topic
+
+ align:start position:0%
+lecture to be this rather specific topic
+ 
+
+ align:start position:0%
+lecture to be this rather specific topic
+what I wanted my my point is that the we
+
+ align:start position:0%
+what I wanted my my point is that the we
+ 
+
+ align:start position:0%
+what I wanted my my point is that the we
+have these
+
+ align:start position:0%
+have these
+ 
+
+ align:start position:0%
+have these
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+special uh dualities for some special
+
+ align:start position:0%
+special uh dualities for some special
+ 
+
+ align:start position:0%
+special uh dualities for some special
+network
+
+ align:start position:0%
+network
+ 
+
+ align:start position:0%
+network
+problems and that they are special cases
+
+ align:start position:0%
+problems and that they are special cases
+ 
+
+ align:start position:0%
+problems and that they are special cases
+of linear programming I mean what are
+
+ align:start position:0%
+of linear programming I mean what are
+ 
+
+ align:start position:0%
+of linear programming I mean what are
+the equations yeah so here is one final
+
+ align:start position:0%
+the equations yeah so here is one final
+ 
+
+ align:start position:0%
+the equations yeah so here is one final
+question on this what are the equations
+
+ align:start position:0%
+question on this what are the equations
+ 
+
+ align:start position:0%
+question on this what are the equations
+that govern a flow I'm trying to
+
+ align:start position:0%
+that govern a flow I'm trying to
+ 
+
+ align:start position:0%
+that govern a flow I'm trying to
+maximize a
+
+ align:start position:0%
+maximize a
+ 
+
+ align:start position:0%
+maximize a
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+what are the equations that govern a
+
+ align:start position:0%
+what are the equations that govern a
+ 
+
+ align:start position:0%
+what are the equations that govern a
+flow I I want to fit it into linear
+
+ align:start position:0%
+flow I I want to fit it into linear
+ 
+
+ align:start position:0%
+flow I I want to fit it into linear
+programming I want to maximize the flow
+
+ align:start position:0%
+programming I want to maximize the flow
+ 
+
+ align:start position:0%
+programming I want to maximize the flow
+so I have my unknowns are the flow along
+
+ align:start position:0%
+so I have my unknowns are the flow along
+ 
+
+ align:start position:0%
+so I have my unknowns are the flow along
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+Edge then I have some inequalities and I
+
+ align:start position:0%
+Edge then I have some inequalities and I
+ 
+
+ align:start position:0%
+Edge then I have some inequalities and I
+have some equations and if you tell me
+
+ align:start position:0%
+have some equations and if you tell me
+ 
+
+ align:start position:0%
+have some equations and if you tell me
+what those so so I'm I've I've so what
+
+ align:start position:0%
+what those so so I'm I've I've so what
+ 
+
+ align:start position:0%
+what those so so I'm I've I've so what
+what describes an okay flow so so so so
+
+ align:start position:0%
+what describes an okay flow so so so so
+ 
+
+ align:start position:0%
+what describes an okay flow so so so so
+Ma mat to match to match linear
+
+ align:start position:0%
+Ma mat to match to match linear
+ 
+
+ align:start position:0%
+Ma mat to match to match linear
+programming I want to ask you what are
+
+ align:start position:0%
+programming I want to ask you what are
+ 
+
+ align:start position:0%
+programming I want to ask you what are
+the what are the
+
+ align:start position:0%
+the what are the
+ 
+
+ align:start position:0%
+the what are the
+inequalities for a flow so I so I'll
+
+ align:start position:0%
+inequalities for a flow so I so I'll
+ 
+
+ align:start position:0%
+inequalities for a flow so I so I'll
+maximize a
+
+ align:start position:0%
+maximize a
+ 
+
+ align:start position:0%
+maximize a
+flow what are the
+
+ align:start position:0%
+flow what are the
+ 
+
+ align:start position:0%
+flow what are the
+inequalities and what are the
+
+ align:start position:0%
+inequalities and what are the
+ 
+
+ align:start position:0%
+inequalities and what are the
+equations what I mean a flow is is um
+
+ align:start position:0%
+equations what I mean a flow is is um
+ 
+
+ align:start position:0%
+equations what I mean a flow is is um
+the the what are the unknowns here the
+
+ align:start position:0%
+the the what are the unknowns here the
+ 
+
+ align:start position:0%
+the the what are the unknowns here the
+unknowns are let me say what the
+
+ align:start position:0%
+unknowns are let me say what the
+ 
+
+ align:start position:0%
+unknowns are let me say what the
+unknowns are uh x i j is the flow
+
+ align:start position:0%
+unknowns are uh x i j is the flow
+ 
+
+ align:start position:0%
+unknowns are uh x i j is the flow
+from uh I to
+
+ align:start position:0%
+from uh I to
+ 
+
+ align:start position:0%
+from uh I to
+J okay so do you remember that in linear
+
+ align:start position:0%
+J okay so do you remember that in linear
+ 
+
+ align:start position:0%
+J okay so do you remember that in linear
+programming you're maximizing something
+
+ align:start position:0%
+programming you're maximizing something
+ 
+
+ align:start position:0%
+programming you're maximizing something
+but you have certain inequalities now
+
+ align:start position:0%
+but you have certain inequalities now
+ 
+
+ align:start position:0%
+but you have certain inequalities now
+what were the inequalities in this in
+
+ align:start position:0%
+what were the inequalities in this in
+ 
+
+ align:start position:0%
+what were the inequalities in this in
+this flow problem the inequalities were
+
+ align:start position:0%
+this flow problem the inequalities were
+ 
+
+ align:start position:0%
+this flow problem the inequalities were
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+flow couldn't exceed the capacity we we
+
+ align:start position:0%
+flow couldn't exceed the capacity we we
+ 
+
+ align:start position:0%
+flow couldn't exceed the capacity we we
+put a capacity of five seven nine one
+
+ align:start position:0%
+put a capacity of five seven nine one
+ 
+
+ align:start position:0%
+put a capacity of five seven nine one
+Whatever on those edges so on every Edge
+
+ align:start position:0%
+Whatever on those edges so on every Edge
+ 
+
+ align:start position:0%
+Whatever on those edges so on every Edge
+there was a upper bound and now I want
+
+ align:start position:0%
+there was a upper bound and now I want
+ 
+
+ align:start position:0%
+there was a upper bound and now I want
+to say what are the equations that flows
+
+ align:start position:0%
+to say what are the equations that flows
+ 
+
+ align:start position:0%
+to say what are the equations that flows
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+satisfy what what's the
+
+ align:start position:0%
+satisfy what what's the
+ 
+
+ align:start position:0%
+satisfy what what's the
+equation I claim that at every node
+
+ align:start position:0%
+equation I claim that at every node
+ 
+
+ align:start position:0%
+equation I claim that at every node
+we've got an
+
+ align:start position:0%
+we've got an
+ 
+
+ align:start position:0%
+we've got an
+equation at
+
+ align:start position:0%
+equation at
+ 
+
+ align:start position:0%
+equation at
+every at every interior node every node
+
+ align:start position:0%
+every at every interior node every node
+ 
+
+ align:start position:0%
+every at every interior node every node
+other than SNS Prime I have an equation
+
+ align:start position:0%
+other than SNS Prime I have an equation
+ 
+
+ align:start position:0%
+other than SNS Prime I have an equation
+and and what is
+
+ align:start position:0%
+and and what is
+ 
+
+ align:start position:0%
+and and what is
+it it's Kirk's law right Kirk Hof's law
+
+ align:start position:0%
+it it's Kirk's law right Kirk Hof's law
+ 
+
+ align:start position:0%
+it it's Kirk's law right Kirk Hof's law
+so we have the the equations are Kirk
+
+ align:start position:0%
+so we have the the equations are Kirk
+ 
+
+ align:start position:0%
+so we have the the equations are Kirk
+off's current law that's that's my
+
+ align:start position:0%
+off's current law that's that's my
+ 
+
+ align:start position:0%
+off's current law that's that's my
+little point that that we we're coming
+
+ align:start position:0%
+little point that that we we're coming
+ 
+
+ align:start position:0%
+little point that that we we're coming
+around again to the to the uh most
+
+ align:start position:0%
+around again to the to the uh most
+ 
+
+ align:start position:0%
+around again to the to the uh most
+fundamental most fundamental equation
+
+ align:start position:0%
+fundamental most fundamental equation
+ 
+
+ align:start position:0%
+fundamental most fundamental equation
+in Applied Mathematics I I guess I dare
+
+ align:start position:0%
+in Applied Mathematics I I guess I dare
+ 
+
+ align:start position:0%
+in Applied Mathematics I I guess I dare
+say that
+
+ align:start position:0%
+say that
+ 
+
+ align:start position:0%
+say that
+um if you're using current law then you
+
+ align:start position:0%
+um if you're using current law then you
+ 
+
+ align:start position:0%
+um if you're using current law then you
+have to allow negative
+
+ align:start position:0%
+have to allow negative
+ 
+
+ align:start position:0%
+have to allow negative
+flows how does that change if I well
+
+ align:start position:0%
+flows how does that change if I well
+ 
+
+ align:start position:0%
+flows how does that change if I well
+let's see uh so I'm interpreting Kirk
+
+ align:start position:0%
+let's see uh so I'm interpreting Kirk
+ 
+
+ align:start position:0%
+let's see uh so I'm interpreting Kirk
+off's current law as at every node the
+
+ align:start position:0%
+off's current law as at every node the
+ 
+
+ align:start position:0%
+off's current law as at every node the
+flow in equals the flow out you're right
+
+ align:start position:0%
+flow in equals the flow out you're right
+ 
+
+ align:start position:0%
+flow in equals the flow out you're right
+so so there'll be some pluses and
+
+ align:start position:0%
+so so there'll be some pluses and
+ 
+
+ align:start position:0%
+so so there'll be some pluses and
+minuses doesn't that change your
+
+ align:start position:0%
+minuses doesn't that change your
+ 
+
+ align:start position:0%
+minuses doesn't that change your
+inequality so now you have a nonlinear
+
+ align:start position:0%
+inequality so now you have a nonlinear
+ 
+
+ align:start position:0%
+inequality so now you have a nonlinear
+inequality the magnitude of XI has to be
+
+ align:start position:0%
+inequality the magnitude of XI has to be
+ 
+
+ align:start position:0%
+inequality the magnitude of XI has to be
+less than C well let I'll just I'm not
+
+ align:start position:0%
+less than C well let I'll just I'm not
+ 
+
+ align:start position:0%
+less than C well let I'll just I'm not
+even sure in this instance but but
+
+ align:start position:0%
+even sure in this instance but but
+ 
+
+ align:start position:0%
+even sure in this instance but but
+suppose we had what looks like a
+
+ align:start position:0%
+suppose we had what looks like a
+ 
+
+ align:start position:0%
+suppose we had what looks like a
+nonlinear
+
+ align:start position:0%
+nonlinear
+ 
+
+ align:start position:0%
+nonlinear
+inequality turn it into linear
+
+ align:start position:0%
+inequality turn it into linear
+ 
+
+ align:start position:0%
+inequality turn it into linear
+inequalities just that's a very good
+
+ align:start position:0%
+inequalities just that's a very good
+ 
+
+ align:start position:0%
+inequalities just that's a very good
+example of how flexible this is how
+
+ align:start position:0%
+example of how flexible this is how
+ 
+
+ align:start position:0%
+example of how flexible this is how
+could I turn that which certainly looks
+
+ align:start position:0%
+could I turn that which certainly looks
+ 
+
+ align:start position:0%
+could I turn that which certainly looks
+nonlinear into linear
+
+ align:start position:0%
+nonlinear into linear
+ 
+
+ align:start position:0%
+nonlinear into linear
+inequalities double the number I could
+
+ align:start position:0%
+inequalities double the number I could
+ 
+
+ align:start position:0%
+inequalities double the number I could
+double the number right I could leave it
+
+ align:start position:0%
+double the number right I could leave it
+ 
+
+ align:start position:0%
+double the number right I could leave it
+as XI J and add to that minus XI J is
+
+ align:start position:0%
+as XI J and add to that minus XI J is
+ 
+
+ align:start position:0%
+as XI J and add to that minus XI J is
+what would it
+
+ align:start position:0%
+what would it
+ 
+
+ align:start position:0%
+what would it
+be greater than or I forgotten minus CI
+
+ align:start position:0%
+be greater than or I forgotten minus CI
+ 
+
+ align:start position:0%
+be greater than or I forgotten minus CI
+J what what would what would it be if I
+
+ align:start position:0%
+J what what would what would it be if I
+ 
+
+ align:start position:0%
+J what what would what would it be if I
+want if I want XI to be small maybe it
+
+ align:start position:0%
+want if I want XI to be small maybe it
+ 
+
+ align:start position:0%
+want if I want XI to be small maybe it
+would be that would
+
+ align:start position:0%
+would be that would
+ 
+
+ align:start position:0%
+would be that would
+it right and then uh yeah yeah uh so or
+
+ align:start position:0%
+it right and then uh yeah yeah uh so or
+ 
+
+ align:start position:0%
+it right and then uh yeah yeah uh so or
+is that no is
+
+ align:start position:0%
+is that no is
+ 
+
+ align:start position:0%
+is that no is
+it is that right I think you need to I
+
+ align:start position:0%
+it is that right I think you need to I
+ 
+
+ align:start position:0%
+it is that right I think you need to I
+I I don't get rid of that minus no on C
+
+ align:start position:0%
+I I don't get rid of that minus no on C
+ 
+
+ align:start position:0%
+I I don't get rid of that minus no on C
+on C
+
+ align:start position:0%
+on C
+ 
+
+ align:start position:0%
+on C
+maybe minus XI greater equal C J yeah
+
+ align:start position:0%
+maybe minus XI greater equal C J yeah
+ 
+
+ align:start position:0%
+maybe minus XI greater equal C J yeah
+okay okay my point is we could do it and
+
+ align:start position:0%
+okay okay my point is we could do it and
+ 
+
+ align:start position:0%
+okay okay my point is we could do it and
+we'd still have linear programming uh
+
+ align:start position:0%
+we'd still have linear programming uh
+ 
+
+ align:start position:0%
+we'd still have linear programming uh
+double the number of uh constraints but
+
+ align:start position:0%
+double the number of uh constraints but
+ 
+
+ align:start position:0%
+double the number of uh constraints but
+we we'll handle those and the point I
+
+ align:start position:0%
+we we'll handle those and the point I
+ 
+
+ align:start position:0%
+we we'll handle those and the point I
+wanted to make was this key equation
+
+ align:start position:0%
+wanted to make was this key equation
+ 
+
+ align:start position:0%
+wanted to make was this key equation
+kof's current law I don't mean to say
+
+ align:start position:0%
+kof's current law I don't mean to say
+ 
+
+ align:start position:0%
+kof's current law I don't mean to say
+that when we look at all of Applied
+
+ align:start position:0%
+that when we look at all of Applied
+ 
+
+ align:start position:0%
+that when we look at all of Applied
+Mathematics kiru's current law jumps out
+
+ align:start position:0%
+Mathematics kiru's current law jumps out
+ 
+
+ align:start position:0%
+Mathematics kiru's current law jumps out
+uniquely except what jumps out is
+
+ align:start position:0%
+uniquely except what jumps out is
+ 
+
+ align:start position:0%
+uniquely except what jumps out is
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+equations conservation equations in
+
+ align:start position:0%
+equations conservation equations in
+ 
+
+ align:start position:0%
+equations conservation equations in
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+out plus possible
+
+ align:start position:0%
+out plus possible
+ 
+
+ align:start position:0%
+out plus possible
+sources that that's that that so much of
+
+ align:start position:0%
+sources that that's that that so much of
+ 
+
+ align:start position:0%
+sources that that's that that so much of
+Applied Mathematics is that's one of the
+
+ align:start position:0%
+Applied Mathematics is that's one of the
+ 
+
+ align:start position:0%
+Applied Mathematics is that's one of the
+equations to look for then there'll be
+
+ align:start position:0%
+equations to look for then there'll be
+ 
+
+ align:start position:0%
+equations to look for then there'll be
+the equation that describes the
+
+ align:start position:0%
+the equation that describes the
+ 
+
+ align:start position:0%
+the equation that describes the
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+uh the the physics of the problem you
+
+ align:start position:0%
+uh the the physics of the problem you
+ 
+
+ align:start position:0%
+uh the the physics of the problem you
+know what what is the flow how does the
+
+ align:start position:0%
+know what what is the flow how does the
+ 
+
+ align:start position:0%
+know what what is the flow how does the
+flow connect to potentials or something
+
+ align:start position:0%
+flow connect to potentials or something
+ 
+
+ align:start position:0%
+flow connect to potentials or something
+but that that balance equation is always
+
+ align:start position:0%
+but that that balance equation is always
+ 
+
+ align:start position:0%
+but that that balance equation is always
+there okay so that's I I'm I'm going to
+
+ align:start position:0%
+there okay so that's I I'm I'm going to
+ 
+
+ align:start position:0%
+there okay so that's I I'm I'm going to
+stop there with a hope
+
+ align:start position:0%
+stop there with a hope
+ 
+
+ align:start position:0%
+stop there with a hope
+well with a hope that
+
+ align:start position:0%
+well with a hope that
+ 
+
+ align:start position:0%
+well with a hope that
+you find some of those um uh ex special
+
+ align:start position:0%
+you find some of those um uh ex special
+ 
+
+ align:start position:0%
+you find some of those um uh ex special
+cases appealing and then also with the
+
+ align:start position:0%
+cases appealing and then also with the
+ 
+
+ align:start position:0%
+cases appealing and then also with the
+hope that you'll enjoy Game
+
+ align:start position:0%
+hope that you'll enjoy Game
+ 
+
+ align:start position:0%
+hope that you'll enjoy Game
+Theory but I'm really Keen to tell you
+
+ align:start position:0%
+Theory but I'm really Keen to tell you
+ 
+
+ align:start position:0%
+Theory but I'm really Keen to tell you
+about if you'll help me again as you did
+
+ align:start position:0%
+about if you'll help me again as you did
+ 
+
+ align:start position:0%
+about if you'll help me again as you did
+last week you kept me going through this
+
+ align:start position:0%
+last week you kept me going through this
+ 
+
+ align:start position:0%
+last week you kept me going through this
+question let me remind you what that
+
+ align:start position:0%
+question let me remind you what that
+ 
+
+ align:start position:0%
+question let me remind you what that
+question was the question
+
+ align:start position:0%
+question was the question
+ 
+
+ align:start position:0%
+question was the question
+was uh so let
+
+ align:start position:0%
+was uh so let
+ 
+
+ align:start position:0%
+was uh so let
+me put the question here the question
+
+ align:start position:0%
+me put the question here the question
+ 
+
+ align:start position:0%
+me put the question here the question
+was I have a
+
+ align:start position:0%
+was I have a
+ 
+
+ align:start position:0%
+was I have a
+matrix and I'm wondering about which
+
+ align:start position:0%
+matrix and I'm wondering about which
+ 
+
+ align:start position:0%
+matrix and I'm wondering about which
+positions could I give arbitrary
+
+ align:start position:0%
+positions could I give arbitrary
+ 
+
+ align:start position:0%
+positions could I give arbitrary
+values and then complete the Matrix to
+
+ align:start position:0%
+values and then complete the Matrix to
+ 
+
+ align:start position:0%
+values and then complete the Matrix to
+have rank one so this is my so I'm
+
+ align:start position:0%
+have rank one so this is my so I'm
+ 
+
+ align:start position:0%
+have rank one so this is my so I'm
+giving any nonzero values and let's take
+
+ align:start position:0%
+giving any nonzero values and let's take
+ 
+
+ align:start position:0%
+giving any nonzero values and let's take
+an example could let's let me take the
+
+ align:start position:0%
+an example could let's let me take the
+ 
+
+ align:start position:0%
+an example could let's let me take the
+example that I had last time well let me
+
+ align:start position:0%
+example that I had last time well let me
+ 
+
+ align:start position:0%
+example that I had last time well let me
+take this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example could
+
+ align:start position:0%
+example could
+ 
+
+ align:start position:0%
+example could
+I give any any nonzero value values in
+
+ align:start position:0%
+I give any any nonzero value values in
+ 
+
+ align:start position:0%
+I give any any nonzero value values in
+those six
+
+ align:start position:0%
+those six
+ 
+
+ align:start position:0%
+those six
+places and aim
+
+ align:start position:0%
+places and aim
+ 
+
+ align:start position:0%
+places and aim
+for complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is that possible and your answer is
+
+ align:start position:0%
+one is that possible and your answer is
+ 
+
+ align:start position:0%
+one is that possible and your answer is
+no because we have here if if rank one
+
+ align:start position:0%
+no because we have here if if rank one
+ 
+
+ align:start position:0%
+no because we have here if if rank one
+will mean what will rank one mean it'll
+
+ align:start position:0%
+will mean what will rank one mean it'll
+ 
+
+ align:start position:0%
+will mean what will rank one mean it'll
+mean that all 2x two determinant
+
+ align:start position:0%
+mean that all 2x two determinant
+ 
+
+ align:start position:0%
+mean that all 2x two determinant
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+zero and that won't be true here so I
+
+ align:start position:0%
+zero and that won't be true here so I
+ 
+
+ align:start position:0%
+zero and that won't be true here so I
+better take one of those out there or
+
+ align:start position:0%
+better take one of those out there or
+ 
+
+ align:start position:0%
+better take one of those out there or
+let me let me take let me make it a
+
+ align:start position:0%
+let me let me take let me make it a
+ 
+
+ align:start position:0%
+let me let me take let me make it a
+little L obvious by taking that one out
+
+ align:start position:0%
+little L obvious by taking that one out
+ 
+
+ align:start position:0%
+little L obvious by taking that one out
+could I now
+
+ align:start position:0%
+could I now
+ 
+
+ align:start position:0%
+could I now
+complete so now I'm I'm I'm less
+
+ align:start position:0%
+complete so now I'm I'm I'm less
+ 
+
+ align:start position:0%
+complete so now I'm I'm I'm less
+ambitious I'm I'm putting in five
+
+ align:start position:0%
+ambitious I'm I'm putting in five
+ 
+
+ align:start position:0%
+ambitious I'm I'm putting in five
+entries and I'm putting them in this
+
+ align:start position:0%
+entries and I'm putting them in this
+ 
+
+ align:start position:0%
+entries and I'm putting them in this
+position and could I now complete those
+
+ align:start position:0%
+position and could I now complete those
+ 
+
+ align:start position:0%
+position and could I now complete those
+to complete this to rank one and the
+
+ align:start position:0%
+to complete this to rank one and the
+ 
+
+ align:start position:0%
+to complete this to rank one and the
+answer is yes right I could this this
+
+ align:start position:0%
+answer is yes right I could this this
+ 
+
+ align:start position:0%
+answer is yes right I could this this
+would this 2x two would now tell me what
+
+ align:start position:0%
+would this 2x two would now tell me what
+ 
+
+ align:start position:0%
+would this 2x two would now tell me what
+that number had to be this 2 by two
+
+ align:start position:0%
+that number had to be this 2 by two
+ 
+
+ align:start position:0%
+that number had to be this 2 by two
+would tell me what this number had to be
+
+ align:start position:0%
+would tell me what this number had to be
+ 
+
+ align:start position:0%
+would tell me what this number had to be
+if I do it two just this 2 by two would
+
+ align:start position:0%
+if I do it two just this 2 by two would
+ 
+
+ align:start position:0%
+if I do it two just this 2 by two would
+tell me that number this 2 by two would
+
+ align:start position:0%
+tell me that number this 2 by two would
+ 
+
+ align:start position:0%
+tell me that number this 2 by two would
+tell me that number well and you might
+
+ align:start position:0%
+tell me that number well and you might
+ 
+
+ align:start position:0%
+tell me that number well and you might
+say wait a minute this two 2 by two told
+
+ align:start position:0%
+say wait a minute this two 2 by two told
+ 
+
+ align:start position:0%
+say wait a minute this two 2 by two told
+me that number also so maybe it's
+
+ align:start position:0%
+me that number also so maybe it's
+ 
+
+ align:start position:0%
+me that number also so maybe it's
+less uh uh um maybe it's
+
+ align:start position:0%
+less uh uh um maybe it's
+ 
+
+ align:start position:0%
+less uh uh um maybe it's
+uh needs a little bit more thinking so
+
+ align:start position:0%
+uh needs a little bit more thinking so
+ 
+
+ align:start position:0%
+uh needs a little bit more thinking so
+right the way I did it was not
+
+ align:start position:0%
+right the way I did it was not
+ 
+
+ align:start position:0%
+right the way I did it was not
+completely convincing because I would
+
+ align:start position:0%
+completely convincing because I would
+ 
+
+ align:start position:0%
+completely convincing because I would
+said okay do that one then do that one
+
+ align:start position:0%
+said okay do that one then do that one
+ 
+
+ align:start position:0%
+said okay do that one then do that one
+then do that one then do this one and
+
+ align:start position:0%
+then do that one then do this one and
+ 
+
+ align:start position:0%
+then do that one then do this one and
+then you say wait a minute those three
+
+ align:start position:0%
+then you say wait a minute those three
+ 
+
+ align:start position:0%
+then you say wait a minute those three
+were specified that determined that one
+
+ align:start position:0%
+were specified that determined that one
+ 
+
+ align:start position:0%
+were specified that determined that one
+so uh I would need a more convincing
+
+ align:start position:0%
+so uh I would need a more convincing
+ 
+
+ align:start position:0%
+so uh I would need a more convincing
+what would be more convincing can can
+
+ align:start position:0%
+what would be more convincing can can
+ 
+
+ align:start position:0%
+what would be more convincing can can
+you can you give me the a correct uh a
+
+ align:start position:0%
+you can you give me the a correct uh a
+ 
+
+ align:start position:0%
+you can you give me the a correct uh a
+better uh well I could go back to that
+
+ align:start position:0%
+better uh well I could go back to that
+ 
+
+ align:start position:0%
+better uh well I could go back to that
+and do it more carefully but how how do
+
+ align:start position:0%
+and do it more carefully but how how do
+ 
+
+ align:start position:0%
+and do it more carefully but how how do
+you see that that could be completed to
+
+ align:start position:0%
+you see that that could be completed to
+ 
+
+ align:start position:0%
+you see that that could be completed to
+rank
+
+ align:start position:0%
+rank
+ 
+
+ align:start position:0%
+rank
+one rank one will mean that every row is
+
+ align:start position:0%
+one rank one will mean that every row is
+ 
+
+ align:start position:0%
+one rank one will mean that every row is
+a multiple of every other
+
+ align:start position:0%
+a multiple of every other
+ 
+
+ align:start position:0%
+a multiple of every other
+rowo so right right we see that row
+
+ align:start position:0%
+rowo so right right we see that row
+ 
+
+ align:start position:0%
+rowo so right right we see that row
+already set just enough for each
+
+ align:start position:0%
+already set just enough for each
+ 
+
+ align:start position:0%
+already set just enough for each
+row not too many right yeah that's right
+
+ align:start position:0%
+row not too many right yeah that's right
+ 
+
+ align:start position:0%
+row not too many right yeah that's right
+we want to know that just enough and not
+
+ align:start position:0%
+we want to know that just enough and not
+ 
+
+ align:start position:0%
+we want to know that just enough and not
+too many okay so after playing around
+
+ align:start position:0%
+too many okay so after playing around
+ 
+
+ align:start position:0%
+too many okay so after playing around
+with examples like that the conjecture
+
+ align:start position:0%
+with examples like that the conjecture
+ 
+
+ align:start position:0%
+with examples like that the conjecture
+was that the right
+
+ align:start position:0%
+was that the right
+ 
+
+ align:start position:0%
+was that the right
+number to
+
+ align:start position:0%
+number to
+ 
+
+ align:start position:0%
+number to
+specify if this is K by
+
+ align:start position:0%
+specify if this is K by
+ 
+
+ align:start position:0%
+specify if this is K by
+K complete a k by
+
+ align:start position:0%
+K complete a k by
+ 
+
+ align:start position:0%
+K complete a k by
+K so 3x3 in this instance the right
+
+ align:start position:0%
+K so 3x3 in this instance the right
+ 
+
+ align:start position:0%
+K so 3x3 in this instance the right
+number is
+
+ align:start position:0%
+number is
+ 
+
+ align:start position:0%
+number is
+five that's our
+
+ align:start position:0%
+five that's our
+ 
+
+ align:start position:0%
+five that's our
+guess and and
+
+ align:start position:0%
+guess and and
+ 
+
+ align:start position:0%
+guess and and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh the general guess was 2K minus one so
+
+ align:start position:0%
+uh the general guess was 2K minus one so
+ 
+
+ align:start position:0%
+uh the general guess was 2K minus one so
+that's what I want to prove that's what
+
+ align:start position:0%
+that's what I want to prove that's what
+ 
+
+ align:start position:0%
+that's what I want to prove that's what
+I want to prove that that that would be
+
+ align:start position:0%
+I want to prove that that that would be
+ 
+
+ align:start position:0%
+I want to prove that that that would be
+the theorem that uh it's completion rank
+
+ align:start position:0%
+the theorem that uh it's completion rank
+ 
+
+ align:start position:0%
+the theorem that uh it's completion rank
+one completion is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible if and only
+
+ align:start position:0%
+possible if and only
+ 
+
+ align:start position:0%
+possible if and only
+if every
+
+ align:start position:0%
+if every
+ 
+
+ align:start position:0%
+if every
+and I have to check the submatrices too
+
+ align:start position:0%
+and I have to check the submatrices too
+ 
+
+ align:start position:0%
+and I have to check the submatrices too
+every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+submatrix of every submatrix of let's
+
+ align:start position:0%
+submatrix of every submatrix of let's
+ 
+
+ align:start position:0%
+submatrix of every submatrix of let's
+say of order let me call its order K
+
+ align:start position:0%
+say of order let me call its order K
+ 
+
+ align:start position:0%
+say of order let me call its order K
+has less than or equal to 2K minus one
+
+ align:start position:0%
+has less than or equal to 2K minus one
+ 
+
+ align:start position:0%
+has less than or equal to 2K minus one
+specified
+
+ align:start position:0%
+specified
+ 
+
+ align:start position:0%
+specified
+entries specified entries and I'm going
+
+ align:start position:0%
+entries specified entries and I'm going
+ 
+
+ align:start position:0%
+entries specified entries and I'm going
+to specify them
+
+ align:start position:0%
+to specify them
+ 
+
+ align:start position:0%
+to specify them
+nonzeros so that that's that's like a
+
+ align:start position:0%
+nonzeros so that that's that's like a
+ 
+
+ align:start position:0%
+nonzeros so that that's that's like a
+hope a new theorem and and uh
+
+ align:start position:0%
+hope a new theorem and and uh
+ 
+
+ align:start position:0%
+hope a new theorem and and uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh it sort of partly happened because of
+
+ align:start position:0%
+uh it sort of partly happened because of
+ 
+
+ align:start position:0%
+uh it sort of partly happened because of
+the examples that we played with so so
+
+ align:start position:0%
+the examples that we played with so so
+ 
+
+ align:start position:0%
+the examples that we played with so so
+why so does this does this example pass
+
+ align:start position:0%
+why so does this does this example pass
+ 
+
+ align:start position:0%
+why so does this does this example pass
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes moved it over to to where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here the as it
+
+ align:start position:0%
+here the as it
+ 
+
+ align:start position:0%
+here the as it
+is yes but of course when I complete
+
+ align:start position:0%
+is yes but of course when I complete
+ 
+
+ align:start position:0%
+is yes but of course when I complete
+it when I complete it I I can hopefully
+
+ align:start position:0%
+it when I complete it I I can hopefully
+ 
+
+ align:start position:0%
+it when I complete it I I can hopefully
+get it to have rank one and and as you
+
+ align:start position:0%
+get it to have rank one and and as you
+ 
+
+ align:start position:0%
+get it to have rank one and and as you
+say if I looked at igen values they
+
+ align:start position:0%
+say if I looked at igen values they
+ 
+
+ align:start position:0%
+say if I looked at igen values they
+would be zero and zero and whatever that
+
+ align:start position:0%
+would be zero and zero and whatever that
+ 
+
+ align:start position:0%
+would be zero and zero and whatever that
+Trace
+
+ align:start position:0%
+Trace
+ 
+
+ align:start position:0%
+Trace
+is yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah I put in numbers so let me let me
+
+ align:start position:0%
+yeah I put in numbers so let me let me
+ 
+
+ align:start position:0%
+yeah I put in numbers so let me let me
+take a specific
+
+ align:start position:0%
+take a specific
+ 
+
+ align:start position:0%
+take a specific
+case can could I give and you'll see by
+
+ align:start position:0%
+case can could I give and you'll see by
+ 
+
+ align:start position:0%
+case can could I give and you'll see by
+the way I write these numbers in 1 4 7 2
+
+ align:start position:0%
+the way I write these numbers in 1 4 7 2
+ 
+
+ align:start position:0%
+the way I write these numbers in 1 4 7 2
+and 11 now the question is can I
+
+ align:start position:0%
+and 11 now the question is can I
+ 
+
+ align:start position:0%
+and 11 now the question is can I
+complete that Matrix to rank one yeah
+
+ align:start position:0%
+complete that Matrix to rank one yeah
+ 
+
+ align:start position:0%
+complete that Matrix to rank one yeah
+this is very thank you for every
+
+ align:start position:0%
+this is very thank you for every
+ 
+
+ align:start position:0%
+this is very thank you for every
+question you ask improves the way I
+
+ align:start position:0%
+question you ask improves the way I
+ 
+
+ align:start position:0%
+question you ask improves the way I
+think about it so so okay so we would
+
+ align:start position:0%
+think about it so so okay so we would
+ 
+
+ align:start position:0%
+think about it so so okay so we would
+say yep we can do it uh all right I
+
+ align:start position:0%
+say yep we can do it uh all right I
+ 
+
+ align:start position:0%
+say yep we can do it uh all right I
+could do it 2 by two you know I would
+
+ align:start position:0%
+could do it 2 by two you know I would
+ 
+
+ align:start position:0%
+could do it 2 by two you know I would
+see okay what do I need there I need a
+
+ align:start position:0%
+see okay what do I need there I need a
+ 
+
+ align:start position:0%
+see okay what do I need there I need a
+half is that
+
+ align:start position:0%
+half is that
+ 
+
+ align:start position:0%
+half is that
+right and really what I need is that for
+
+ align:start position:0%
+right and really what I need is that for
+ 
+
+ align:start position:0%
+right and really what I need is that for
+that row 147 for this row to be half as
+
+ align:start position:0%
+that row 147 for this row to be half as
+ 
+
+ align:start position:0%
+that row 147 for this row to be half as
+much so this would be seven halves and
+
+ align:start position:0%
+much so this would be seven halves and
+ 
+
+ align:start position:0%
+much so this would be seven halves and
+for this row this row should be in the
+
+ align:start position:0%
+for this row this row should be in the
+ 
+
+ align:start position:0%
+for this row this row should be in the
+ratio 11 to 7 or whatever yeah sorry
+
+ align:start position:0%
+ratio 11 to 7 or whatever yeah sorry
+ 
+
+ align:start position:0%
+ratio 11 to 7 or whatever yeah sorry
+when I said arbitrary numbers I didn't
+
+ align:start position:0%
+when I said arbitrary numbers I didn't
+ 
+
+ align:start position:0%
+when I said arbitrary numbers I didn't
+mean that
+
+ align:start position:0%
+mean that
+ 
+
+ align:start position:0%
+mean that
+arbitrary uh yeah but anyway I could do
+
+ align:start position:0%
+arbitrary uh yeah but anyway I could do
+ 
+
+ align:start position:0%
+arbitrary uh yeah but anyway I could do
+it and you realize why just just to be
+
+ align:start position:0%
+it and you realize why just just to be
+ 
+
+ align:start position:0%
+it and you realize why just just to be
+sure that I can't do it for any five
+
+ align:start position:0%
+sure that I can't do it for any five
+ 
+
+ align:start position:0%
+sure that I can't do it for any five
+suppose I specify those
+
+ align:start position:0%
+suppose I specify those
+ 
+
+ align:start position:0%
+suppose I specify those
+five now I can't complete to rank one
+
+ align:start position:0%
+five now I can't complete to rank one
+ 
+
+ align:start position:0%
+five now I can't complete to rank one
+because I'm lost at the start here if
+
+ align:start position:0%
+because I'm lost at the start here if
+ 
+
+ align:start position:0%
+because I'm lost at the start here if
+I've made those arbitrary then that's a
+
+ align:start position:0%
+I've made those arbitrary then that's a
+ 
+
+ align:start position:0%
+I've made those arbitrary then that's a
+2X two that isn't determinant that isn't
+
+ align:start position:0%
+2X two that isn't determinant that isn't
+ 
+
+ align:start position:0%
+2X two that isn't determinant that isn't
+zero and no way I can fix it I I could
+
+ align:start position:0%
+zero and no way I can fix it I I could
+ 
+
+ align:start position:0%
+zero and no way I can fix it I I could
+make those numbers if if you want it
+
+ align:start position:0%
+make those numbers if if you want it
+ 
+
+ align:start position:0%
+make those numbers if if you want it
+right uh so so that's why I have
+
+ align:start position:0%
+right uh so so that's why I have
+ 
+
+ align:start position:0%
+right uh so so that's why I have
+to in the test has to go not only the
+
+ align:start position:0%
+to in the test has to go not only the
+ 
+
+ align:start position:0%
+to in the test has to go not only the
+big guy but all the smaller ones because
+
+ align:start position:0%
+big guy but all the smaller ones because
+ 
+
+ align:start position:0%
+big guy but all the smaller ones because
+if a smaller one fails my test the
+
+ align:start position:0%
+if a smaller one fails my test the
+ 
+
+ align:start position:0%
+if a smaller one fails my test the
+bigger one might still have only 2K
+
+ align:start position:0%
+bigger one might still have only 2K
+ 
+
+ align:start position:0%
+bigger one might still have only 2K
+minus one five specified entries here
+
+ align:start position:0%
+minus one five specified entries here
+ 
+
+ align:start position:0%
+minus one five specified entries here
+but the smaller if a smaller one messes
+
+ align:start position:0%
+but the smaller if a smaller one messes
+ 
+
+ align:start position:0%
+but the smaller if a smaller one messes
+up then I'm it syns me before I can I've
+
+ align:start position:0%
+up then I'm it syns me before I can I've
+ 
+
+ align:start position:0%
+up then I'm it syns me before I can I've
+got no way to save it okay so uh uh let
+
+ align:start position:0%
+got no way to save it okay so uh uh let
+ 
+
+ align:start position:0%
+got no way to save it okay so uh uh let
+me let me take a
+
+ align:start position:0%
+me let me take a
+ 
+
+ align:start position:0%
+me let me take a
+4x4 just uh so 4x4 I should be allowed
+
+ align:start position:0%
+4x4 just uh so 4x4 I should be allowed
+ 
+
+ align:start position:0%
+4x4 just uh so 4x4 I should be allowed
+seven
+
+ align:start position:0%
+seven
+ 
+
+ align:start position:0%
+seven
+entries and
+
+ align:start position:0%
+entries and
+ 
+
+ align:start position:0%
+entries and
+uh okay now here think through how
+
+ align:start position:0%
+uh okay now here think through how
+ 
+
+ align:start position:0%
+uh okay now here think through how
+suppose I have seven
+
+ align:start position:0%
+suppose I have seven
+ 
+
+ align:start position:0%
+suppose I have seven
+entries how can
+
+ align:start position:0%
+entries how can
+ 
+
+ align:start position:0%
+entries how can
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+complete how can I prove that I can
+
+ align:start position:0%
+complete how can I prove that I can
+ 
+
+ align:start position:0%
+complete how can I prove that I can
+complete so I'm I'm asking um what what
+
+ align:start position:0%
+complete so I'm I'm asking um what what
+ 
+
+ align:start position:0%
+complete so I'm I'm asking um what what
+I'm really talking about now is that
+
+ align:start position:0%
+I'm really talking about now is that
+ 
+
+ align:start position:0%
+I'm really talking about now is that
+math step from doing a bunch of examples
+
+ align:start position:0%
+math step from doing a bunch of examples
+ 
+
+ align:start position:0%
+math step from doing a bunch of examples
+and getting
+
+ align:start position:0%
+and getting
+ 
+
+ align:start position:0%
+and getting
+convinced and getting a
+
+ align:start position:0%
+convinced and getting a
+ 
+
+ align:start position:0%
+convinced and getting a
+proof that's absolutely
+
+ align:start position:0%
+proof that's absolutely
+ 
+
+ align:start position:0%
+proof that's absolutely
+convincing see what I'm trying to say
+
+ align:start position:0%
+convincing see what I'm trying to say
+ 
+
+ align:start position:0%
+convincing see what I'm trying to say
+that I now have to think seven entries
+
+ align:start position:0%
+that I now have to think seven entries
+ 
+
+ align:start position:0%
+that I now have to think seven entries
+any any seven subject to this
+
+ align:start position:0%
+any any seven subject to this
+ 
+
+ align:start position:0%
+any any seven subject to this
+constraint how can I show that it's
+
+ align:start position:0%
+constraint how can I show that it's
+ 
+
+ align:start position:0%
+constraint how can I show that it's
+possible all right can I can let me so
+
+ align:start position:0%
+possible all right can I can let me so
+ 
+
+ align:start position:0%
+possible all right can I can let me so
+actually strictly in this proof I have
+
+ align:start position:0%
+actually strictly in this proof I have
+ 
+
+ align:start position:0%
+actually strictly in this proof I have
+two directions to go but let me let me
+
+ align:start position:0%
+two directions to go but let me let me
+ 
+
+ align:start position:0%
+two directions to go but let me let me
+suppose that this test is passed and I
+
+ align:start position:0%
+suppose that this test is passed and I
+ 
+
+ align:start position:0%
+suppose that this test is passed and I
+have a 4x4 with seven entries that
+
+ align:start position:0%
+have a 4x4 with seven entries that
+ 
+
+ align:start position:0%
+have a 4x4 with seven entries that
+passes that test and I'll conclude that
+
+ align:start position:0%
+passes that test and I'll conclude that
+ 
+
+ align:start position:0%
+passes that test and I'll conclude that
+I can
+
+ align:start position:0%
+I can
+ 
+
+ align:start position:0%
+I can
+complete and then there will be another
+
+ align:start position:0%
+complete and then there will be another
+ 
+
+ align:start position:0%
+complete and then there will be another
+step of the proof that that shows that
+
+ align:start position:0%
+step of the proof that that shows that
+ 
+
+ align:start position:0%
+step of the proof that that shows that
+that condition is necessary but let's do
+
+ align:start position:0%
+that condition is necessary but let's do
+ 
+
+ align:start position:0%
+that condition is necessary but let's do
+the first one way that that's okay I've
+
+ align:start position:0%
+the first one way that that's okay I've
+ 
+
+ align:start position:0%
+the first one way that that's okay I've
+got seven
+
+ align:start position:0%
+got seven
+ 
+
+ align:start position:0%
+got seven
+entries in a 4x4 4x4 seven
+
+ align:start position:0%
+entries in a 4x4 4x4 seven
+ 
+
+ align:start position:0%
+entries in a 4x4 4x4 seven
+entries
+
+ align:start position:0%
+entries
+ 
+
+ align:start position:0%
+entries
+okay and now let's see so my here's my
+
+ align:start position:0%
+okay and now let's see so my here's my
+ 
+
+ align:start position:0%
+okay and now let's see so my here's my
+reasoning one row has to
+
+ align:start position:0%
+reasoning one row has to
+ 
+
+ align:start position:0%
+reasoning one row has to
+have and all the rows couldn't have two
+
+ align:start position:0%
+have and all the rows couldn't have two
+ 
+
+ align:start position:0%
+have and all the rows couldn't have two
+entries right right that would make
+
+ align:start position:0%
+entries right right that would make
+ 
+
+ align:start position:0%
+entries right right that would make
+eight so one row has to
+
+ align:start position:0%
+eight so one row has to
+ 
+
+ align:start position:0%
+eight so one row has to
+have no entries or one okay so I'm
+
+ align:start position:0%
+have no entries or one okay so I'm
+ 
+
+ align:start position:0%
+have no entries or one okay so I'm
+covering all cases so so so one row has
+
+ align:start position:0%
+covering all cases so so so one row has
+ 
+
+ align:start position:0%
+covering all cases so so so one row has
+to have either no entries or one entry
+
+ align:start position:0%
+to have either no entries or one entry
+ 
+
+ align:start position:0%
+to have either no entries or one entry
+right so we can reorder the rows and
+
+ align:start position:0%
+right so we can reorder the rows and
+ 
+
+ align:start position:0%
+right so we can reorder the rows and
+make it the first row in fact then we
+
+ align:start position:0%
+make it the first row in fact then we
+ 
+
+ align:start position:0%
+make it the first row in fact then we
+could reorder The Columns and make it
+
+ align:start position:0%
+could reorder The Columns and make it
+ 
+
+ align:start position:0%
+could reorder The Columns and make it
+the First Column so here's a so so up in
+
+ align:start position:0%
+the First Column so here's a so so up in
+ 
+
+ align:start position:0%
+the First Column so here's a so so up in
+the first row is only one entry and I'll
+
+ align:start position:0%
+the first row is only one entry and I'll
+ 
+
+ align:start position:0%
+the first row is only one entry and I'll
+reorder The Columns that won't change
+
+ align:start position:0%
+reorder The Columns that won't change
+ 
+
+ align:start position:0%
+reorder The Columns that won't change
+anything just to keep our our we're
+
+ align:start position:0%
+anything just to keep our our we're
+ 
+
+ align:start position:0%
+anything just to keep our our we're
+looking like that right there has to be
+
+ align:start position:0%
+looking like that right there has to be
+ 
+
+ align:start position:0%
+looking like that right there has to be
+a row with only one entry because
+
+ align:start position:0%
+a row with only one entry because
+ 
+
+ align:start position:0%
+a row with only one entry because
+there's only seven entries all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together and four rows
+
+ align:start position:0%
+together and four rows
+ 
+
+ align:start position:0%
+together and four rows
+okay there has to be a row either with
+
+ align:start position:0%
+okay there has to be a row either with
+ 
+
+ align:start position:0%
+okay there has to be a row either with
+one or or
+
+ align:start position:0%
+one or or
+ 
+
+ align:start position:0%
+one or or
+with or there could be a row of all
+
+ align:start position:0%
+with or there could be a row of all
+ 
+
+ align:start position:0%
+with or there could be a row of all
+zeros uh with what do I mean by this
+
+ align:start position:0%
+zeros uh with what do I mean by this
+ 
+
+ align:start position:0%
+zeros uh with what do I mean by this
+zero I mean unspecified should I put U
+
+ align:start position:0%
+zero I mean unspecified should I put U
+ 
+
+ align:start position:0%
+zero I mean unspecified should I put U
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+unspecified okay you for unspecified or
+
+ align:start position:0%
+unspecified okay you for unspecified or
+ 
+
+ align:start position:0%
+unspecified okay you for unspecified or
+I could possibly
+
+ align:start position:0%
+I could possibly
+ 
+
+ align:start position:0%
+I could possibly
+have a there could be I could have seven
+
+ align:start position:0%
+have a there could be I could have seven
+ 
+
+ align:start position:0%
+have a there could be I could have seven
+in the whole thing but there would be
+
+ align:start position:0%
+in the whole thing but there would be
+ 
+
+ align:start position:0%
+in the whole thing but there would be
+but let's let's kill
+
+ align:start position:0%
+but let's let's kill
+ 
+
+ align:start position:0%
+but let's let's kill
+this possibility first here okay now now
+
+ align:start position:0%
+this possibility first here okay now now
+ 
+
+ align:start position:0%
+this possibility first here okay now now
+how how could I show now I've got seven
+
+ align:start position:0%
+how how could I show now I've got seven
+ 
+
+ align:start position:0%
+how how could I show now I've got seven
+the seven are still specified but
+
+ align:start position:0%
+the seven are still specified but
+ 
+
+ align:start position:0%
+the seven are still specified but
+they're only in three
+
+ align:start position:0%
+they're only in three
+ 
+
+ align:start position:0%
+they're only in three
+rows okay so what do you think
+
+ align:start position:0%
+rows okay so what do you think
+ 
+
+ align:start position:0%
+rows okay so what do you think
+now uh let's see oh I've got four
+
+ align:start position:0%
+now uh let's see oh I've got four
+ 
+
+ align:start position:0%
+now uh let's see oh I've got four
+columns here now the wonderful thing
+
+ align:start position:0%
+columns here now the wonderful thing
+ 
+
+ align:start position:0%
+columns here now the wonderful thing
+about linear algebra is the relation of
+
+ align:start position:0%
+about linear algebra is the relation of
+ 
+
+ align:start position:0%
+about linear algebra is the relation of
+rows to columns that's what you got to
+
+ align:start position:0%
+rows to columns that's what you got to
+ 
+
+ align:start position:0%
+rows to columns that's what you got to
+keep remembering okay so I still have
+
+ align:start position:0%
+keep remembering okay so I still have
+ 
+
+ align:start position:0%
+keep remembering okay so I still have
+four columns and I've got seven
+
+ align:start position:0%
+four columns and I've got seven
+ 
+
+ align:start position:0%
+four columns and I've got seven
+specified so again I have a column that
+
+ align:start position:0%
+specified so again I have a column that
+ 
+
+ align:start position:0%
+specified so again I have a column that
+has only
+
+ align:start position:0%
+has only
+ 
+
+ align:start position:0%
+has only
+one or or none right because there were
+
+ align:start position:0%
+one or or none right because there were
+ 
+
+ align:start position:0%
+one or or none right because there were
+four columns I've got to put seven x's
+
+ align:start position:0%
+four columns I've got to put seven x's
+ 
+
+ align:start position:0%
+four columns I've got to put seven x's
+in here some column is only going to
+
+ align:start position:0%
+in here some column is only going to
+ 
+
+ align:start position:0%
+in here some column is only going to
+have like One
+
+ align:start position:0%
+have like One
+ 
+
+ align:start position:0%
+have like One
+X and the and the other six are going to
+
+ align:start position:0%
+X and the and the other six are going to
+ 
+
+ align:start position:0%
+X and the and the other six are going to
+be in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so I claim
+
+ align:start position:0%
+here okay so I claim
+ 
+
+ align:start position:0%
+here okay so I claim
+that this totally
+
+ align:start position:0%
+that this totally
+ 
+
+ align:start position:0%
+that this totally
+VI
+
+ align:start position:0%
+VI
+ 
+
+ align:start position:0%
+VI
+that this can't happen because I'm I'm
+
+ align:start position:0%
+that this can't happen because I'm I'm
+ 
+
+ align:start position:0%
+that this can't happen because I'm I'm
+assuming this right I'm assuming
+
+ align:start position:0%
+assuming this right I'm assuming
+ 
+
+ align:start position:0%
+assuming this right I'm assuming
+this let's get the logic straight I'm
+
+ align:start position:0%
+this let's get the logic straight I'm
+ 
+
+ align:start position:0%
+this let's get the logic straight I'm
+proving that if this is true I assume
+
+ align:start position:0%
+proving that if this is true I assume
+ 
+
+ align:start position:0%
+proving that if this is true I assume
+it's true and then show
+
+ align:start position:0%
+it's true and then show
+ 
+
+ align:start position:0%
+it's true and then show
+this show this that's this is the
+
+ align:start position:0%
+this show this that's this is the
+ 
+
+ align:start position:0%
+this show this that's this is the
+direction I'm going okay so I assume
+
+ align:start position:0%
+direction I'm going okay so I assume
+ 
+
+ align:start position:0%
+direction I'm going okay so I assume
+that every not only the big Matrix the
+
+ align:start position:0%
+that every not only the big Matrix the
+ 
+
+ align:start position:0%
+that every not only the big Matrix the
+4x4 had seven nonzeros but every
+
+ align:start position:0%
+4x4 had seven nonzeros but every
+ 
+
+ align:start position:0%
+4x4 had seven nonzeros but every
+submatrix of order K didn't have more
+
+ align:start position:0%
+submatrix of order K didn't have more
+ 
+
+ align:start position:0%
+submatrix of order K didn't have more
+than 2K minus one but here I have a
+
+ align:start position:0%
+than 2K minus one but here I have a
+ 
+
+ align:start position:0%
+than 2K minus one but here I have a
+submatrix it's 3x3 and it's got six so
+
+ align:start position:0%
+submatrix it's 3x3 and it's got six so
+ 
+
+ align:start position:0%
+submatrix it's 3x3 and it's got six so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this that couldn't have happened let me
+
+ align:start position:0%
+this that couldn't have happened let me
+ 
+
+ align:start position:0%
+this that couldn't have happened let me
+come back to
+
+ align:start position:0%
+come back to
+ 
+
+ align:start position:0%
+come back to
+here again I'm going to shoot the same
+
+ align:start position:0%
+here again I'm going to shoot the same
+ 
+
+ align:start position:0%
+here again I'm going to shoot the same
+go the same way here um now what do I
+
+ align:start position:0%
+go the same way here um now what do I
+ 
+
+ align:start position:0%
+go the same way here um now what do I
+want to do I'd like to okay now I have
+
+ align:start position:0%
+want to do I'd like to okay now I have
+ 
+
+ align:start position:0%
+want to do I'd like to okay now I have
+one specified guy that's more reasonable
+
+ align:start position:0%
+one specified guy that's more reasonable
+ 
+
+ align:start position:0%
+one specified guy that's more reasonable
+unspecified unspecified now I look at
+
+ align:start position:0%
+unspecified unspecified now I look at
+ 
+
+ align:start position:0%
+unspecified unspecified now I look at
+the columns okay I've got four
+
+ align:start position:0%
+the columns okay I've got four
+ 
+
+ align:start position:0%
+the columns okay I've got four
+columns so what is what's possible
+
+ align:start position:0%
+columns so what is what's possible
+ 
+
+ align:start position:0%
+columns so what is what's possible
+here uh this column might have two guys
+
+ align:start position:0%
+here uh this column might have two guys
+ 
+
+ align:start position:0%
+here uh this column might have two guys
+it might have this specified and one
+
+ align:start position:0%
+it might have this specified and one
+ 
+
+ align:start position:0%
+it might have this specified and one
+more and unspecified unspecified right
+
+ align:start position:0%
+more and unspecified unspecified right
+ 
+
+ align:start position:0%
+more and unspecified unspecified right
+that that could be or I better have
+
+ align:start position:0%
+that that could be or I better have
+ 
+
+ align:start position:0%
+that that could be or I better have
+another or out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here let's see let's see so I'm starting
+
+ align:start position:0%
+here let's see let's see so I'm starting
+ 
+
+ align:start position:0%
+here let's see let's see so I'm starting
+with these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see what are the other well let me
+
+ align:start position:0%
+let's see what are the other well let me
+ 
+
+ align:start position:0%
+let's see what are the other well let me
+follow this case through first suppose
+
+ align:start position:0%
+follow this case through first suppose
+ 
+
+ align:start position:0%
+follow this case through first suppose
+this is my
+
+ align:start position:0%
+this is my
+ 
+
+ align:start position:0%
+this is my
+situation suppose remember I figured out
+
+ align:start position:0%
+situation suppose remember I figured out
+ 
+
+ align:start position:0%
+situation suppose remember I figured out
+okay one row does have to look like that
+
+ align:start position:0%
+okay one row does have to look like that
+ 
+
+ align:start position:0%
+okay one row does have to look like that
+well don't you have to
+
+ align:start position:0%
+well don't you have to
+ 
+
+ align:start position:0%
+well don't you have to
+have point where you're ring that's what
+
+ align:start position:0%
+have point where you're ring that's what
+ 
+
+ align:start position:0%
+have point where you're ring that's what
+I have to show and and this is so in
+
+ align:start position:0%
+I have to show and and this is so in
+ 
+
+ align:start position:0%
+I have to show and and this is so in
+this this is the good case where I do
+
+ align:start position:0%
+this this is the good case where I do
+ 
+
+ align:start position:0%
+this this is the good case where I do
+all right now what's the what's the deal
+
+ align:start position:0%
+all right now what's the what's the deal
+ 
+
+ align:start position:0%
+all right now what's the what's the deal
+here I have uh it looks like this and
+
+ align:start position:0%
+here I have uh it looks like this and
+ 
+
+ align:start position:0%
+here I have uh it looks like this and
+then how many are specified in here the
+
+ align:start position:0%
+then how many are specified in here the
+ 
+
+ align:start position:0%
+then how many are specified in here the
+remaining five so what's what's up with
+
+ align:start position:0%
+remaining five so what's what's up with
+ 
+
+ align:start position:0%
+remaining five so what's what's up with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+case I apply the theorem for smaller
+
+ align:start position:0%
+case I apply the theorem for smaller
+ 
+
+ align:start position:0%
+case I apply the theorem for smaller
+size and I know I can complete this I
+
+ align:start position:0%
+size and I know I can complete this I
+ 
+
+ align:start position:0%
+size and I know I can complete this I
+can complete the five because it's
+
+ align:start position:0%
+can complete the five because it's
+ 
+
+ align:start position:0%
+can complete the five because it's
+satisfied all its little submatrices of
+
+ align:start position:0%
+satisfied all its little submatrices of
+ 
+
+ align:start position:0%
+satisfied all its little submatrices of
+course were part of the part of the part
+
+ align:start position:0%
+course were part of the part of the part
+ 
+
+ align:start position:0%
+course were part of the part of the part
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+assume and it's got five which is the
+
+ align:start position:0%
+assume and it's got five which is the
+ 
+
+ align:start position:0%
+assume and it's got five which is the
+right number so I can complete it so
+
+ align:start position:0%
+right number so I can complete it so
+ 
+
+ align:start position:0%
+right number so I can complete it so
+somehow I do complete it now of course I
+
+ align:start position:0%
+somehow I do complete it now of course I
+ 
+
+ align:start position:0%
+somehow I do complete it now of course I
+have to just check having
+
+ align:start position:0%
+have to just check having
+ 
+
+ align:start position:0%
+have to just check having
+completed
+
+ align:start position:0%
+completed
+ 
+
+ align:start position:0%
+completed
+um some completed the this to have rank
+
+ align:start position:0%
+um some completed the this to have rank
+ 
+
+ align:start position:0%
+um some completed the this to have rank
+one uh can I now finish the
+
+ align:start position:0%
+one uh can I now finish the
+ 
+
+ align:start position:0%
+one uh can I now finish the
+job so now how do I finish the job
+
+ align:start position:0%
+job so now how do I finish the job
+ 
+
+ align:start position:0%
+job so now how do I finish the job
+here uh knowing that those rows are all
+
+ align:start position:0%
+here uh knowing that those rows are all
+ 
+
+ align:start position:0%
+here uh knowing that those rows are all
+in the same direction those three rows
+
+ align:start position:0%
+in the same direction those three rows
+ 
+
+ align:start position:0%
+in the same direction those three rows
+are multiples of each other in the small
+
+ align:start position:0%
+are multiples of each other in the small
+ 
+
+ align:start position:0%
+are multiples of each other in the small
+one now I have to achieve that in the
+
+ align:start position:0%
+one now I have to achieve that in the
+ 
+
+ align:start position:0%
+one now I have to achieve that in the
+4x4 okay well I guess I see one row
+
+ align:start position:0%
+4x4 okay well I guess I see one row
+ 
+
+ align:start position:0%
+4x4 okay well I guess I see one row
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+set and so now how do I fill in this
+
+ align:start position:0%
+set and so now how do I fill in this
+ 
+
+ align:start position:0%
+set and so now how do I fill in this
+row just the ratio whatever I mean that
+
+ align:start position:0%
+row just the ratio whatever I mean that
+ 
+
+ align:start position:0%
+row just the ratio whatever I mean that
+row set this guy sets the ratio and I
+
+ align:start position:0%
+row set this guy sets the ratio and I
+ 
+
+ align:start position:0%
+row set this guy sets the ratio and I
+can fill it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in and how do I fill that one in again
+
+ align:start position:0%
+in and how do I fill that one in again
+ 
+
+ align:start position:0%
+in and how do I fill that one in again
+this was in this was in a certain ratio
+
+ align:start position:0%
+this was in this was in a certain ratio
+ 
+
+ align:start position:0%
+this was in this was in a certain ratio
+with this one so the last entry has to
+
+ align:start position:0%
+with this one so the last entry has to
+ 
+
+ align:start position:0%
+with this one so the last entry has to
+stay in the same ratio and similarly
+
+ align:start position:0%
+stay in the same ratio and similarly
+ 
+
+ align:start position:0%
+stay in the same ratio and similarly
+here this was in a ratio with this
+
+ align:start position:0%
+here this was in a ratio with this
+ 
+
+ align:start position:0%
+here this was in a ratio with this
+because this was rank one in the in the
+
+ align:start position:0%
+because this was rank one in the in the
+ 
+
+ align:start position:0%
+because this was rank one in the in the
+3X3 and then when I'm given that I'm I'm
+
+ align:start position:0%
+3X3 and then when I'm given that I'm I'm
+ 
+
+ align:start position:0%
+3X3 and then when I'm given that I'm I'm
+given that so actually there's a unique
+
+ align:start position:0%
+given that so actually there's a unique
+ 
+
+ align:start position:0%
+given that so actually there's a unique
+way to
+
+ align:start position:0%
+way to
+ 
+
+ align:start position:0%
+way to
+finish so you could say yep that that
+
+ align:start position:0%
+finish so you could say yep that that
+ 
+
+ align:start position:0%
+finish so you could say yep that that
+was no anybody see that I've got one
+
+ align:start position:0%
+was no anybody see that I've got one
+ 
+
+ align:start position:0%
+was no anybody see that I've got one
+more case to worry
+
+ align:start position:0%
+more case to worry
+ 
+
+ align:start position:0%
+more case to worry
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+I well this this was x u u and then I
+
+ align:start position:0%
+I well this this was x u u and then I
+ 
+
+ align:start position:0%
+I well this this was x u u and then I
+said okay what if my row what if this
+
+ align:start position:0%
+said okay what if my row what if this
+ 
+
+ align:start position:0%
+said okay what if my row what if this
+column has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's
+
+ align:start position:0%
+uh let's
+ 
+
+ align:start position:0%
+uh let's
+see uh yeah what right that's a case I
+
+ align:start position:0%
+see uh yeah what right that's a case I
+ 
+
+ align:start position:0%
+see uh yeah what right that's a case I
+have to worry about what if nothing else
+
+ align:start position:0%
+have to worry about what if nothing else
+ 
+
+ align:start position:0%
+have to worry about what if nothing else
+was specified there why am
+
+ align:start position:0%
+was specified there why am
+ 
+
+ align:start position:0%
+was specified there why am
+I how do I know that that couldn't
+
+ align:start position:0%
+I how do I know that that couldn't
+ 
+
+ align:start position:0%
+I how do I know that that couldn't
+be because then I've got six more in the
+
+ align:start position:0%
+be because then I've got six more in the
+ 
+
+ align:start position:0%
+be because then I've got six more in the
+3X3 which which I assumed I didn't have
+
+ align:start position:0%
+3X3 which which I assumed I didn't have
+ 
+
+ align:start position:0%
+3X3 which which I assumed I didn't have
+okay now what okay I think I've got
+
+ align:start position:0%
+okay now what okay I think I've got
+ 
+
+ align:start position:0%
+okay now what okay I think I've got
+another case to worry about
+
+ align:start position:0%
+another case to worry about
+ 
+
+ align:start position:0%
+another case to worry about
+mathematicians are awful
+
+ align:start position:0%
+mathematicians are awful
+ 
+
+ align:start position:0%
+mathematicians are awful
+worriers all right what else do I have
+
+ align:start position:0%
+worriers all right what else do I have
+ 
+
+ align:start position:0%
+worriers all right what else do I have
+to think of maybe the what if what if
+
+ align:start position:0%
+to think of maybe the what if what if
+ 
+
+ align:start position:0%
+to think of maybe the what if what if
+this had
+
+ align:start position:0%
+this had
+ 
+
+ align:start position:0%
+this had
+more like three or or four now what do I
+
+ align:start position:0%
+more like three or or four now what do I
+ 
+
+ align:start position:0%
+more like three or or four now what do I
+deal how do I deal with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case what I'm hoping for is to find a
+
+ align:start position:0%
+case what I'm hoping for is to find a
+ 
+
+ align:start position:0%
+case what I'm hoping for is to find a
+3X3 that's that's
+
+ align:start position:0%
+3X3 that's that's
+ 
+
+ align:start position:0%
+3X3 that's that's
+okay uh now what's up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here in this case one of those other
+
+ align:start position:0%
+here in this case one of those other
+ 
+
+ align:start position:0%
+here in this case one of those other
+columns only have one one of those other
+
+ align:start position:0%
+columns only have one one of those other
+ 
+
+ align:start position:0%
+columns only have one one of those other
+columns will only have one right one of
+
+ align:start position:0%
+columns will only have one right one of
+ 
+
+ align:start position:0%
+columns will only have one right one of
+those other columns will only have one
+
+ align:start position:0%
+those other columns will only have one
+ 
+
+ align:start position:0%
+those other columns will only have one
+because as I've used up three there's
+
+ align:start position:0%
+because as I've used up three there's
+ 
+
+ align:start position:0%
+because as I've used up three there's
+four four more to specify and only and
+
+ align:start position:0%
+four four more to specify and only and
+ 
+
+ align:start position:0%
+four four more to specify and only and
+three and three columns so so some other
+
+ align:start position:0%
+three and three columns so so some other
+ 
+
+ align:start position:0%
+three and three columns so so some other
+column has got got one easily right okay
+
+ align:start position:0%
+column has got got one easily right okay
+ 
+
+ align:start position:0%
+column has got got one easily right okay
+so suppose a second another column only
+
+ align:start position:0%
+so suppose a second another column only
+ 
+
+ align:start position:0%
+so suppose a second another column only
+has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now what do that like now yeah now
+
+ align:start position:0%
+right now what do that like now yeah now
+ 
+
+ align:start position:0%
+right now what do that like now yeah now
+the good columns to look at are this
+
+ align:start position:0%
+the good columns to look at are this
+ 
+
+ align:start position:0%
+the good columns to look at are this
+this row and that column this row and
+
+ align:start position:0%
+this row and that column this row and
+ 
+
+ align:start position:0%
+this row and that column this row and
+that column I I'll move that column
+
+ align:start position:0%
+that column I I'll move that column
+ 
+
+ align:start position:0%
+that column I I'll move that column
+over or you see
+
+ align:start position:0%
+over or you see
+ 
+
+ align:start position:0%
+over or you see
+out of this row and that column I've
+
+ align:start position:0%
+out of this row and that column I've
+ 
+
+ align:start position:0%
+out of this row and that column I've
+used two so I'm remaining with a
+
+ align:start position:0%
+used two so I'm remaining with a
+ 
+
+ align:start position:0%
+used two so I'm remaining with a
+3X3 I have a 3X3 remaining with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five you see that if I look at this
+
+ align:start position:0%
+five you see that if I look at this
+ 
+
+ align:start position:0%
+five you see that if I look at this
+remaining 3 by3 because this row and
+
+ align:start position:0%
+remaining 3 by3 because this row and
+ 
+
+ align:start position:0%
+remaining 3 by3 because this row and
+column have only used two only specified
+
+ align:start position:0%
+column have only used two only specified
+ 
+
+ align:start position:0%
+column have only used two only specified
+two I have five unspecified ones in this
+
+ align:start position:0%
+two I have five unspecified ones in this
+ 
+
+ align:start position:0%
+two I have five unspecified ones in this
+3x3 I can fit I can complete
+
+ align:start position:0%
+3x3 I can fit I can complete
+ 
+
+ align:start position:0%
+3x3 I can fit I can complete
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+by induction by the is that right
+
+ align:start position:0%
+by induction by the is that right
+ 
+
+ align:start position:0%
+by induction by the is that right
+y right because whatever some some of
+
+ align:start position:0%
+y right because whatever some some of
+ 
+
+ align:start position:0%
+y right because whatever some some of
+those were specified but but a total of
+
+ align:start position:0%
+those were specified but but a total of
+ 
+
+ align:start position:0%
+those were specified but but a total of
+five were specified and I can finish the
+
+ align:start position:0%
+five were specified and I can finish the
+ 
+
+ align:start position:0%
+five were specified and I can finish the
+job on the
+
+ align:start position:0%
+job on the
+ 
+
+ align:start position:0%
+job on the
+3X3 and then uh again I'm
+
+ align:start position:0%
+3X3 and then uh again I'm
+ 
+
+ align:start position:0%
+3X3 and then uh again I'm
+uh then I can finish the complete job
+
+ align:start position:0%
+uh then I can finish the complete job
+ 
+
+ align:start position:0%
+uh then I can finish the complete job
+because now I have a row completely set
+
+ align:start position:0%
+because now I have a row completely set
+ 
+
+ align:start position:0%
+because now I have a row completely set
+and that will set the remaining rows I
+
+ align:start position:0%
+and that will set the remaining rows I
+ 
+
+ align:start position:0%
+and that will set the remaining rows I
+can am I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I've partly convinced you by shouting
+
+ align:start position:0%
+I I've partly convinced you by shouting
+ 
+
+ align:start position:0%
+I I've partly convinced you by shouting
+right but uh but
+
+ align:start position:0%
+right but uh but
+ 
+
+ align:start position:0%
+right but uh but
+uh that's how the the the proof uh
+
+ align:start position:0%
+uh that's how the the the proof uh
+ 
+
+ align:start position:0%
+uh that's how the the the proof uh
+didn't turn out to be too messy and I
+
+ align:start position:0%
+didn't turn out to be too messy and I
+ 
+
+ align:start position:0%
+didn't turn out to be too messy and I
+probably could tighten it up a little
+
+ align:start position:0%
+probably could tighten it up a little
+ 
+
+ align:start position:0%
+probably could tighten it up a little
+bit in in what I've described but that
+
+ align:start position:0%
+bit in in what I've described but that
+ 
+
+ align:start position:0%
+bit in in what I've described but that
+that's sort of
+
+ align:start position:0%
+that's sort of
+ 
+
+ align:start position:0%
+that's sort of
+the the way the proof would have to
+
+ align:start position:0%
+the the way the proof would have to
+ 
+
+ align:start position:0%
+the the way the proof would have to
+argue by induction that that there has
+
+ align:start position:0%
+argue by induction that that there has
+ 
+
+ align:start position:0%
+argue by induction that that there has
+to be a row with only one specified then
+
+ align:start position:0%
+to be a row with only one specified then
+ 
+
+ align:start position:0%
+to be a row with only one specified then
+we check the columns we look at the
+
+ align:start position:0%
+we check the columns we look at the
+ 
+
+ align:start position:0%
+we check the columns we look at the
+possibilities not too many we eventually
+
+ align:start position:0%
+possibilities not too many we eventually
+ 
+
+ align:start position:0%
+possibilities not too many we eventually
+we either rule out some of those
+
+ align:start position:0%
+we either rule out some of those
+ 
+
+ align:start position:0%
+we either rule out some of those
+possibilities or we identify a smaller
+
+ align:start position:0%
+possibilities or we identify a smaller
+ 
+
+ align:start position:0%
+possibilities or we identify a smaller
+Matrix that obeys the rules and then by
+
+ align:start position:0%
+Matrix that obeys the rules and then by
+ 
+
+ align:start position:0%
+Matrix that obeys the rules and then by
+the induction step we can complete that
+
+ align:start position:0%
+the induction step we can complete that
+ 
+
+ align:start position:0%
+the induction step we can complete that
+Matrix and then we finish okay so that's
+
+ align:start position:0%
+Matrix and then we finish okay so that's
+ 
+
+ align:start position:0%
+Matrix and then we finish okay so that's
+that's that and let me tell you
+
+ align:start position:0%
+that's that and let me tell you
+ 
+
+ align:start position:0%
+that's that and let me tell you
+about if if you're willing to go one
+
+ align:start position:0%
+about if if you're willing to go one
+ 
+
+ align:start position:0%
+about if if you're willing to go one
+more minute on this
+
+ align:start position:0%
+more minute on this
+ 
+
+ align:start position:0%
+more minute on this
+question what about completing to rank
+
+ align:start position:0%
+question what about completing to rank
+ 
+
+ align:start position:0%
+question what about completing to rank
+two because of course the trouble is
+
+ align:start position:0%
+two because of course the trouble is
+ 
+
+ align:start position:0%
+two because of course the trouble is
+another bad thing about mathematicians
+
+ align:start position:0%
+another bad thing about mathematicians
+ 
+
+ align:start position:0%
+another bad thing about mathematicians
+once you finish right you get the proof
+
+ align:start position:0%
+once you finish right you get the proof
+ 
+
+ align:start position:0%
+once you finish right you get the proof
+happy you're only happy for about 30
+
+ align:start position:0%
+happy you're only happy for about 30
+ 
+
+ align:start position:0%
+happy you're only happy for about 30
+seconds because then you think of the
+
+ align:start position:0%
+seconds because then you think of the
+ 
+
+ align:start position:0%
+seconds because then you think of the
+next case and it's always harder so now
+
+ align:start position:0%
+next case and it's always harder so now
+ 
+
+ align:start position:0%
+next case and it's always harder so now
+suppose we're trying to complete a
+
+ align:start position:0%
+suppose we're trying to complete a
+ 
+
+ align:start position:0%
+suppose we're trying to complete a
+matrix to rank two
+
+ align:start position:0%
+matrix to rank two
+ 
+
+ align:start position:0%
+matrix to rank two
+all right I'm jumping now to a new
+
+ align:start position:0%
+all right I'm jumping now to a new
+ 
+
+ align:start position:0%
+all right I'm jumping now to a new
+question how many would I expect to
+
+ align:start position:0%
+question how many would I expect to
+ 
+
+ align:start position:0%
+question how many would I expect to
+specify say in a 4x4 say in a 4x4 how
+
+ align:start position:0%
+specify say in a 4x4 say in a 4x4 how
+ 
+
+ align:start position:0%
+specify say in a 4x4 say in a 4x4 how
+many entries would I expect to
+
+ align:start position:0%
+many entries would I expect to
+ 
+
+ align:start position:0%
+many entries would I expect to
+specify here it was 2K minus one seven
+
+ align:start position:0%
+specify here it was 2K minus one seven
+ 
+
+ align:start position:0%
+specify here it was 2K minus one seven
+how many now if I'm going to complete to
+
+ align:start position:0%
+how many now if I'm going to complete to
+ 
+
+ align:start position:0%
+how many now if I'm going to complete to
+rank two that's easier
+
+ align:start position:0%
+rank two that's easier
+ 
+
+ align:start position:0%
+rank two that's easier
+right easier to rank two because then I
+
+ align:start position:0%
+right easier to rank two because then I
+ 
+
+ align:start position:0%
+right easier to rank two because then I
+can have two rows that are quite
+
+ align:start position:0%
+can have two rows that are quite
+ 
+
+ align:start position:0%
+can have two rows that are quite
+different and the others have to be
+
+ align:start position:0%
+different and the others have to be
+ 
+
+ align:start position:0%
+different and the others have to be
+combinations of those so I could have
+
+ align:start position:0%
+combinations of those so I could have
+ 
+
+ align:start position:0%
+combinations of those so I could have
+two rows specified completely
+
+ align:start position:0%
+two rows specified completely
+ 
+
+ align:start position:0%
+two rows specified completely
+differently any
+
+ align:start position:0%
+differently any
+ 
+
+ align:start position:0%
+differently any
+completely I'm using X right for for
+
+ align:start position:0%
+completely I'm using X right for for
+ 
+
+ align:start position:0%
+completely I'm using X right for for
+specified I could specify two rows
+
+ align:start position:0%
+specified I could specify two rows
+ 
+
+ align:start position:0%
+specified I could specify two rows
+arbitrarily now I could
+
+ align:start position:0%
+arbitrarily now I could
+ 
+
+ align:start position:0%
+arbitrarily now I could
+specify two entries in the third row and
+
+ align:start position:0%
+specify two entries in the third row and
+ 
+
+ align:start position:0%
+specify two entries in the third row and
+then do you do you see that I could I
+
+ align:start position:0%
+then do you do you see that I could I
+ 
+
+ align:start position:0%
+then do you do you see that I could I
+could finish the
+
+ align:start position:0%
+could finish the
+ 
+
+ align:start position:0%
+could finish the
+job and keep rank two
+
+ align:start position:0%
+job and keep rank two
+ 
+
+ align:start position:0%
+job and keep rank two
+I I'm what I'm trying to do first is
+
+ align:start position:0%
+I I'm what I'm trying to do first is
+ 
+
+ align:start position:0%
+I I'm what I'm trying to do first is
+guess the right
+
+ align:start position:0%
+guess the right
+ 
+
+ align:start position:0%
+guess the right
+number and I'll do that by assuming that
+
+ align:start position:0%
+number and I'll do that by assuming that
+ 
+
+ align:start position:0%
+number and I'll do that by assuming that
+they're in a nice pattern and and and
+
+ align:start position:0%
+they're in a nice pattern and and and
+ 
+
+ align:start position:0%
+they're in a nice pattern and and and
+see okay how many could I expect to do
+
+ align:start position:0%
+see okay how many could I expect to do
+ 
+
+ align:start position:0%
+see okay how many could I expect to do
+in that pattern okay suppose I'm given
+
+ align:start position:0%
+in that pattern okay suppose I'm given
+ 
+
+ align:start position:0%
+in that pattern okay suppose I'm given
+two complete rows then if I'm given this
+
+ align:start position:0%
+two complete rows then if I'm given this
+ 
+
+ align:start position:0%
+two complete rows then if I'm given this
+row and this row that number and that
+
+ align:start position:0%
+row and this row that number and that
+ 
+
+ align:start position:0%
+row and this row that number and that
+number that tells me what combination of
+
+ align:start position:0%
+number that tells me what combination of
+ 
+
+ align:start position:0%
+number that tells me what combination of
+this row and this row it takes to get
+
+ align:start position:0%
+this row and this row it takes to get
+ 
+
+ align:start position:0%
+this row and this row it takes to get
+these two guys right right I've got two
+
+ align:start position:0%
+these two guys right right I've got two
+ 
+
+ align:start position:0%
+these two guys right right I've got two
+coefficients in that combination so I
+
+ align:start position:0%
+coefficients in that combination so I
+ 
+
+ align:start position:0%
+coefficients in that combination so I
+can get I can take a combination to get
+
+ align:start position:0%
+can get I can take a combination to get
+ 
+
+ align:start position:0%
+can get I can take a combination to get
+these two right and then I better have
+
+ align:start position:0%
+these two right and then I better have
+ 
+
+ align:start position:0%
+these two right and then I better have
+those unsp specified because they're
+
+ align:start position:0%
+those unsp specified because they're
+ 
+
+ align:start position:0%
+those unsp specified because they're
+going to be whatever they come out and
+
+ align:start position:0%
+going to be whatever they come out and
+ 
+
+ align:start position:0%
+going to be whatever they come out and
+similarly
+
+ align:start position:0%
+similarly
+ 
+
+ align:start position:0%
+similarly
+here I can I can uh specify
+
+ align:start position:0%
+here I can I can uh specify
+ 
+
+ align:start position:0%
+here I can I can uh specify
+two and uh some combination of those two
+
+ align:start position:0%
+two and uh some combination of those two
+ 
+
+ align:start position:0%
+two and uh some combination of those two
+rows will match those two and then those
+
+ align:start position:0%
+rows will match those two and then those
+ 
+
+ align:start position:0%
+rows will match those two and then those
+unspecified ones will be filled in I'm
+
+ align:start position:0%
+unspecified ones will be filled in I'm
+ 
+
+ align:start position:0%
+unspecified ones will be filled in I'm
+discovering in a 4x4 case I can I would
+
+ align:start position:0%
+discovering in a 4x4 case I can I would
+ 
+
+ align:start position:0%
+discovering in a 4x4 case I can I would
+think I can spe specify
+
+ align:start position:0%
+think I can spe specify
+ 
+
+ align:start position:0%
+think I can spe specify
+12 and but that's the question here I
+
+ align:start position:0%
+12 and but that's the question here I
+ 
+
+ align:start position:0%
+12 and but that's the question here I
+can those 12 I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specify and of course the right so the
+
+ align:start position:0%
+specify and of course the right so the
+ 
+
+ align:start position:0%
+specify and of course the right so the
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+is can I alwayss like your 2 by two case
+
+ align:start position:0%
+is can I alwayss like your 2 by two case
+ 
+
+ align:start position:0%
+is can I alwayss like your 2 by two case
+with rank one it yes it's
+
+ align:start position:0%
+with rank one it yes it's
+ 
+
+ align:start position:0%
+with rank one it yes it's
+it's okay so I went away thinking well
+
+ align:start position:0%
+it's okay so I went away thinking well
+ 
+
+ align:start position:0%
+it's okay so I went away thinking well
+all right got this proof got the right
+
+ align:start position:0%
+all right got this proof got the right
+ 
+
+ align:start position:0%
+all right got this proof got the right
+number here 12 can't be that hard but
+
+ align:start position:0%
+number here 12 can't be that hard but
+ 
+
+ align:start position:0%
+number here 12 can't be that hard but
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um I came up with a case that I didn't
+
+ align:start position:0%
+um I came up with a case that I didn't
+ 
+
+ align:start position:0%
+um I came up with a case that I didn't
+know how to do it so so this I decided
+
+ align:start position:0%
+know how to do it so so this I decided
+ 
+
+ align:start position:0%
+know how to do it so so this I decided
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is this is so I don't know the I I don't
+
+ align:start position:0%
+is this is so I don't know the I I don't
+ 
+
+ align:start position:0%
+is this is so I don't know the I I don't
+have a proof yet I I should say we I'm
+
+ align:start position:0%
+have a proof yet I I should say we I'm
+ 
+
+ align:start position:0%
+have a proof yet I I should say we I'm
+doing this with a really sharp young guy
+
+ align:start position:0%
+doing this with a really sharp young guy
+ 
+
+ align:start position:0%
+doing this with a really sharp young guy
+named David ingerman he's he's the
+
+ align:start position:0%
+named David ingerman he's he's the
+ 
+
+ align:start position:0%
+named David ingerman he's he's the
+source of ideas here okay so now can I
+
+ align:start position:0%
+source of ideas here okay so now can I
+ 
+
+ align:start position:0%
+source of ideas here okay so now can I
+specify any 12 well let me show you what
+
+ align:start position:0%
+specify any 12 well let me show you what
+ 
+
+ align:start position:0%
+specify any 12 well let me show you what
+I got hung up on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could I specify this is 4x4 I think I
+
+ align:start position:0%
+could I specify this is 4x4 I think I
+ 
+
+ align:start position:0%
+could I specify this is 4x4 I think I
+can specify 12 I was pretty sure but now
+
+ align:start position:0%
+can specify 12 I was pretty sure but now
+ 
+
+ align:start position:0%
+can specify 12 I was pretty sure but now
+suppose my unspecified are the
+
+ align:start position:0%
+suppose my unspecified are the
+ 
+
+ align:start position:0%
+suppose my unspecified are the
+diagonal and I specify all 12 of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys so I specify those 12 numbers and
+
+ align:start position:0%
+guys so I specify those 12 numbers and
+ 
+
+ align:start position:0%
+guys so I specify those 12 numbers and
+these four I could leave blank as a sort
+
+ align:start position:0%
+these four I could leave blank as a sort
+ 
+
+ align:start position:0%
+these four I could leave blank as a sort
+of way to see that those are not
+
+ align:start position:0%
+of way to see that those are not
+ 
+
+ align:start position:0%
+of way to see that those are not
+specified and I want to fill this in to
+
+ align:start position:0%
+specified and I want to fill this in to
+ 
+
+ align:start position:0%
+specified and I want to fill this in to
+have rank two fill complete to rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two well can you interchange rows and
+
+ align:start position:0%
+two well can you interchange rows and
+ 
+
+ align:start position:0%
+two well can you interchange rows and
+columns
+
+ align:start position:0%
+columns
+ 
+
+ align:start position:0%
+columns
+I get in of the second well if
+
+ align:start position:0%
+I get in of the second well if
+ 
+
+ align:start position:0%
+I get in of the second well if
+that's yeah if so done but the trouble
+
+ align:start position:0%
+that's yeah if so done but the trouble
+ 
+
+ align:start position:0%
+that's yeah if so done but the trouble
+is there's a row with only two guys in
+
+ align:start position:0%
+is there's a row with only two guys in
+ 
+
+ align:start position:0%
+is there's a row with only two guys in
+it if I move move it elsewhere it's
+
+ align:start position:0%
+it if I move move it elsewhere it's
+ 
+
+ align:start position:0%
+it if I move move it elsewhere it's
+still I got only two if I move it if I
+
+ align:start position:0%
+still I got only two if I move it if I
+ 
+
+ align:start position:0%
+still I got only two if I move it if I
+move yeah but think I mean this is
+
+ align:start position:0%
+move yeah but think I mean this is
+ 
+
+ align:start position:0%
+move yeah but think I mean this is
+exactly the right question so I move
+
+ align:start position:0%
+exactly the right question so I move
+ 
+
+ align:start position:0%
+exactly the right question so I move
+that row up or down still has two if I
+
+ align:start position:0%
+that row up or down still has two if I
+ 
+
+ align:start position:0%
+that row up or down still has two if I
+change columns what happens on that row
+
+ align:start position:0%
+change columns what happens on that row
+ 
+
+ align:start position:0%
+change columns what happens on that row
+those two are still there they just in
+
+ align:start position:0%
+those two are still there they just in
+ 
+
+ align:start position:0%
+those two are still there they just in
+different columns so that's why this one
+
+ align:start position:0%
+different columns so that's why this one
+ 
+
+ align:start position:0%
+different columns so that's why this one
+was so hard because this has got three
+
+ align:start position:0%
+was so hard because this has got three
+ 
+
+ align:start position:0%
+was so hard because this has got three
+in every Row three in every column and I
+
+ align:start position:0%
+in every Row three in every column and I
+ 
+
+ align:start position:0%
+in every Row three in every column and I
+can't with just simple reordering get
+
+ align:start position:0%
+can't with just simple reordering get
+ 
+
+ align:start position:0%
+can't with just simple reordering get
+out of that fix
+
+ align:start position:0%
+out of that fix
+ 
+
+ align:start position:0%
+out of that fix
+so I couldn't see how to do it frankly
+
+ align:start position:0%
+so I couldn't see how to do it frankly
+ 
+
+ align:start position:0%
+so I couldn't see how to do it frankly
+you know you where do you start I didn't
+
+ align:start position:0%
+you know you where do you start I didn't
+ 
+
+ align:start position:0%
+you know you where do you start I didn't
+have a starting Place
+
+ align:start position:0%
+have a starting Place
+ 
+
+ align:start position:0%
+have a starting Place
+somehow and
+
+ align:start position:0%
+somehow and
+ 
+
+ align:start position:0%
+somehow and
+um let me call these numbers like uh A
+
+ align:start position:0%
+um let me call these numbers like uh A
+ 
+
+ align:start position:0%
+um let me call these numbers like uh A
+and B that we would like to be able to
+
+ align:start position:0%
+and B that we would like to be able to
+ 
+
+ align:start position:0%
+and B that we would like to be able to
+find a b c
+
+ align:start position:0%
+find a b c
+ 
+
+ align:start position:0%
+find a b c
+d okay now yesterday afternoon David
+
+ align:start position:0%
+d okay now yesterday afternoon David
+ 
+
+ align:start position:0%
+d okay now yesterday afternoon David
+convinced me I could we could do this
+
+ align:start position:0%
+convinced me I could we could do this
+ 
+
+ align:start position:0%
+convinced me I could we could do this
+one so I can show you how he what he
+
+ align:start position:0%
+one so I can show you how he what he
+ 
+
+ align:start position:0%
+one so I can show you how he what he
+sold me on here okay how he did it and
+
+ align:start position:0%
+sold me on here okay how he did it and
+ 
+
+ align:start position:0%
+sold me on here okay how he did it and
+then that's only so at this point so
+
+ align:start position:0%
+then that's only so at this point so
+ 
+
+ align:start position:0%
+then that's only so at this point so
+this is again a progress report uh our
+
+ align:start position:0%
+this is again a progress report uh our
+ 
+
+ align:start position:0%
+this is again a progress report uh our
+progress report I think is he figured
+
+ align:start position:0%
+progress report I think is he figured
+ 
+
+ align:start position:0%
+progress report I think is he figured
+out how to do this one this particular
+
+ align:start position:0%
+out how to do this one this particular
+ 
+
+ align:start position:0%
+out how to do this one this particular
+one so I still have we still have the
+
+ align:start position:0%
+one so I still have we still have the
+ 
+
+ align:start position:0%
+one so I still have we still have the
+question of any
+
+ align:start position:0%
+question of any
+ 
+
+ align:start position:0%
+question of any
+12 in a
+
+ align:start position:0%
+12 in a
+ 
+
+ align:start position:0%
+12 in a
+4x4 and then the more general question
+
+ align:start position:0%
+4x4 and then the more general question
+ 
+
+ align:start position:0%
+4x4 and then the more general question
+is so completion so let me complete the
+
+ align:start position:0%
+is so completion so let me complete the
+ 
+
+ align:start position:0%
+is so completion so let me complete the
+the the the theorem completion to rank
+
+ align:start position:0%
+the the the theorem completion to rank
+ 
+
+ align:start position:0%
+the the the theorem completion to rank
+two the number here becomes everything
+
+ align:start position:0%
+two the number here becomes everything
+ 
+
+ align:start position:0%
+two the number here becomes everything
+should is 4 K minus 4 that's the right
+
+ align:start position:0%
+should is 4 K minus 4 that's the right
+ 
+
+ align:start position:0%
+should is 4 K minus 4 that's the right
+number which when K is 4 that's 16us 4
+
+ align:start position:0%
+number which when K is 4 that's 16us 4
+ 
+
+ align:start position:0%
+number which when K is 4 that's 16us 4
+which is our 12 so this was the this is
+
+ align:start position:0%
+which is our 12 so this was the this is
+ 
+
+ align:start position:0%
+which is our 12 so this was the this is
+the the guess conjecture you could say
+
+ align:start position:0%
+the the guess conjecture you could say
+ 
+
+ align:start position:0%
+the the guess conjecture you could say
+completion to rank two is possible if
+
+ align:start position:0%
+completion to rank two is possible if
+ 
+
+ align:start position:0%
+completion to rank two is possible if
+and only if every submatrix of order K
+
+ align:start position:0%
+and only if every submatrix of order K
+ 
+
+ align:start position:0%
+and only if every submatrix of order K
+has no more than 4K minus 4 let let me
+
+ align:start position:0%
+has no more than 4K minus 4 let let me
+ 
+
+ align:start position:0%
+has no more than 4K minus 4 let let me
+check 3x 3x3 what would that say I I'm
+
+ align:start position:0%
+check 3x 3x3 what would that say I I'm
+ 
+
+ align:start position:0%
+check 3x 3x3 what would that say I I'm
+saying that I can complete to rank two
+
+ align:start position:0%
+saying that I can complete to rank two
+ 
+
+ align:start position:0%
+saying that I can complete to rank two
+uh and suppose it was 3x3 how many am I
+
+ align:start position:0%
+uh and suppose it was 3x3 how many am I
+ 
+
+ align:start position:0%
+uh and suppose it was 3x3 how many am I
+specifying just just I'm specifying
+
+ align:start position:0%
+specifying just just I'm specifying
+ 
+
+ align:start position:0%
+specifying just just I'm specifying
+eight now is it true that if I had a 3X3
+
+ align:start position:0%
+eight now is it true that if I had a 3X3
+ 
+
+ align:start position:0%
+eight now is it true that if I had a 3X3
+Matrix and I specify
+
+ align:start position:0%
+Matrix and I specify
+ 
+
+ align:start position:0%
+Matrix and I specify
+eight well how many have I got left only
+
+ align:start position:0%
+eight well how many have I got left only
+ 
+
+ align:start position:0%
+eight well how many have I got left only
+one left can I at rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two just just that that one if we can't
+
+ align:start position:0%
+two just just that that one if we can't
+ 
+
+ align:start position:0%
+two just just that that one if we can't
+do 3x3 well just go and shoot ourselves
+
+ align:start position:0%
+do 3x3 well just go and shoot ourselves
+ 
+
+ align:start position:0%
+do 3x3 well just go and shoot ourselves
+so so uh so
+
+ align:start position:0%
+so so uh so
+ 
+
+ align:start position:0%
+so so uh so
+3x3
+
+ align:start position:0%
+3x3
+ 
+
+ align:start position:0%
+3x3
+3x3 so this is rank two I'm still I'm
+
+ align:start position:0%
+3x3 so this is rank two I'm still I'm
+ 
+
+ align:start position:0%
+3x3 so this is rank two I'm still I'm
+still into the rank two thing if 3x3 and
+
+ align:start position:0%
+still into the rank two thing if 3x3 and
+ 
+
+ align:start position:0%
+still into the rank two thing if 3x3 and
+with eight specified eight X's well put
+
+ align:start position:0%
+with eight specified eight X's well put
+ 
+
+ align:start position:0%
+with eight specified eight X's well put
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+wherever that's eight only one left only
+
+ align:start position:0%
+wherever that's eight only one left only
+ 
+
+ align:start position:0%
+wherever that's eight only one left only
+one one Freedom left but I want to get I
+
+ align:start position:0%
+one one Freedom left but I want to get I
+ 
+
+ align:start position:0%
+one one Freedom left but I want to get I
+only I'm aiming for rank two how do I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Itor yes that's right uh so in terms of
+
+ align:start position:0%
+Itor yes that's right uh so in terms of
+ 
+
+ align:start position:0%
+Itor yes that's right uh so in terms of
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+algebra so this is
+
+ align:start position:0%
+algebra so this is
+ 
+
+ align:start position:0%
+algebra so this is
+unspecified
+
+ align:start position:0%
+unspecified
+ 
+
+ align:start position:0%
+unspecified
+the some combination of that well
+
+ align:start position:0%
+the some combination of that well
+ 
+
+ align:start position:0%
+the some combination of that well
+another a quick way to say it is make
+
+ align:start position:0%
+another a quick way to say it is make
+ 
+
+ align:start position:0%
+another a quick way to say it is make
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+determinant what Zer zero make the
+
+ align:start position:0%
+determinant what Zer zero make the
+ 
+
+ align:start position:0%
+determinant what Zer zero make the
+determinant zero which the whole the 3X3
+
+ align:start position:0%
+determinant zero which the whole the 3X3
+ 
+
+ align:start position:0%
+determinant zero which the whole the 3X3
+if the 3X3 determinant is zero What's
+
+ align:start position:0%
+if the 3X3 determinant is zero What's
+ 
+
+ align:start position:0%
+if the 3X3 determinant is zero What's
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rank less than three
+
+ align:start position:0%
+rank less than three
+ 
+
+ align:start position:0%
+rank less than three
+two take two right does does it have to
+
+ align:start position:0%
+two take two right does does it have to
+ 
+
+ align:start position:0%
+two take two right does does it have to
+be exactly r two no no no no less or
+
+ align:start position:0%
+be exactly r two no no no no less or
+ 
+
+ align:start position:0%
+be exactly r two no no no no less or
+equal rank two yeah less or equal rank
+
+ align:start position:0%
+equal rank two yeah less or equal rank
+ 
+
+ align:start position:0%
+equal rank two yeah less or equal rank
+two yeah yeah yeah I have to achieve
+
+ align:start position:0%
+two yeah yeah yeah I have to achieve
+ 
+
+ align:start position:0%
+two yeah yeah yeah I have to achieve
+rank two but of course if I made if I
+
+ align:start position:0%
+rank two but of course if I made if I
+ 
+
+ align:start position:0%
+rank two but of course if I made if I
+specified stuff you know if I specified
+
+ align:start position:0%
+specified stuff you know if I specified
+ 
+
+ align:start position:0%
+specified stuff you know if I specified
+that row exactly in the same direction
+
+ align:start position:0%
+that row exactly in the same direction
+ 
+
+ align:start position:0%
+that row exactly in the same direction
+as that row then and and all sorts of
+
+ align:start position:0%
+as that row then and and all sorts of
+ 
+
+ align:start position:0%
+as that row then and and all sorts of
+stuff then I could maybe even get lower
+
+ align:start position:0%
+stuff then I could maybe even get lower
+ 
+
+ align:start position:0%
+stuff then I could maybe even get lower
+rank but but I'm shooting here for rank
+
+ align:start position:0%
+rank but but I'm shooting here for rank
+ 
+
+ align:start position:0%
+rank but but I'm shooting here for rank
+two so I'm saying if you give me eight I
+
+ align:start position:0%
+two so I'm saying if you give me eight I
+ 
+
+ align:start position:0%
+two so I'm saying if you give me eight I
+can certainly fill in that ninth what
+
+ align:start position:0%
+can certainly fill in that ninth what
+ 
+
+ align:start position:0%
+can certainly fill in that ninth what
+one way the way we saw it was some
+
+ align:start position:0%
+one way the way we saw it was some
+ 
+
+ align:start position:0%
+one way the way we saw it was some
+combination of that row and that row
+
+ align:start position:0%
+combination of that row and that row
+ 
+
+ align:start position:0%
+combination of that row and that row
+will make those two right and it'll tell
+
+ align:start position:0%
+will make those two right and it'll tell
+ 
+
+ align:start position:0%
+will make those two right and it'll tell
+me what that has to be and just I'm just
+
+ align:start position:0%
+me what that has to be and just I'm just
+ 
+
+ align:start position:0%
+me what that has to be and just I'm just
+saying to say the same thing in another
+
+ align:start position:0%
+saying to say the same thing in another
+ 
+
+ align:start position:0%
+saying to say the same thing in another
+language some number there will make the
+
+ align:start position:0%
+language some number there will make the
+ 
+
+ align:start position:0%
+language some number there will make the
+determinate
+
+ align:start position:0%
+determinate
+ 
+
+ align:start position:0%
+determinate
+zero some number there will make the
+
+ align:start position:0%
+zero some number there will make the
+ 
+
+ align:start position:0%
+zero some number there will make the
+determinate zero so I'm okay but
+
+ align:start position:0%
+determinate zero so I'm okay but
+ 
+
+ align:start position:0%
+determinate zero so I'm okay but
+so 3x3 completing to rank two no problem
+
+ align:start position:0%
+so 3x3 completing to rank two no problem
+ 
+
+ align:start position:0%
+so 3x3 completing to rank two no problem
+but 4x4 with 12 specified completing to
+
+ align:start position:0%
+but 4x4 with 12 specified completing to
+ 
+
+ align:start position:0%
+but 4x4 with 12 specified completing to
+rank two big headache okay so can I show
+
+ align:start position:0%
+rank two big headache okay so can I show
+ 
+
+ align:start position:0%
+rank two big headache okay so can I show
+can I come back to this one now this is
+
+ align:start position:0%
+can I come back to this one now this is
+ 
+
+ align:start position:0%
+can I come back to this one now this is
+my last case that I know
+
+ align:start position:0%
+my last case that I know
+ 
+
+ align:start position:0%
+my last case that I know
+about and then the goal is to get the
+
+ align:start position:0%
+about and then the goal is to get the
+ 
+
+ align:start position:0%
+about and then the goal is to get the
+theorem to work for for rank two
+
+ align:start position:0%
+theorem to work for for rank two
+ 
+
+ align:start position:0%
+theorem to work for for rank two
+completion where this is for okay here
+
+ align:start position:0%
+completion where this is for okay here
+ 
+
+ align:start position:0%
+completion where this is for okay here
+here was the
+
+ align:start position:0%
+here was the
+ 
+
+ align:start position:0%
+here was the
+idea suppose I look at this this and
+
+ align:start position:0%
+idea suppose I look at this this and
+ 
+
+ align:start position:0%
+idea suppose I look at this this and
+this so a
+
+ align:start position:0%
+this so a
+ 
+
+ align:start position:0%
+this so a
+3X3 and I and I I I I certainly have to
+
+ align:start position:0%
+3X3 and I and I I I I certainly have to
+ 
+
+ align:start position:0%
+3X3 and I and I I I I certainly have to
+complete that to rank
+
+ align:start position:0%
+complete that to rank
+ 
+
+ align:start position:0%
+complete that to rank
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+so what'll it take well let's look at
+
+ align:start position:0%
+so what'll it take well let's look at
+ 
+
+ align:start position:0%
+so what'll it take well let's look at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+determinant so I'd like to complete this
+
+ align:start position:0%
+determinant so I'd like to complete this
+ 
+
+ align:start position:0%
+determinant so I'd like to complete this
+so what's the determinant I have to make
+
+ align:start position:0%
+so what's the determinant I have to make
+ 
+
+ align:start position:0%
+so what's the determinant I have to make
+the determinant zero
+
+ align:start position:0%
+the determinant zero
+ 
+
+ align:start position:0%
+the determinant zero
+right if I have a 3X three and I'm
+
+ align:start position:0%
+right if I have a 3X three and I'm
+ 
+
+ align:start position:0%
+right if I have a 3X three and I'm
+trying to get lower rank rank two that
+
+ align:start position:0%
+trying to get lower rank rank two that
+ 
+
+ align:start position:0%
+trying to get lower rank rank two that
+surely means it's singular it's
+
+ align:start position:0%
+surely means it's singular it's
+ 
+
+ align:start position:0%
+surely means it's singular it's
+determinant is zero so so
+
+ align:start position:0%
+determinant is zero so so
+ 
+
+ align:start position:0%
+determinant is zero so so
+uh so the determinant of that will have
+
+ align:start position:0%
+uh so the determinant of that will have
+ 
+
+ align:start position:0%
+uh so the determinant of that will have
+to be zero so what's what is the
+
+ align:start position:0%
+to be zero so what's what is the
+ 
+
+ align:start position:0%
+to be zero so what's what is the
+determin it's a * B time a * B *
+
+ align:start position:0%
+determin it's a * B time a * B *
+ 
+
+ align:start position:0%
+determin it's a * B time a * B *
+something times times uh
+
+ align:start position:0%
+something times times uh
+ 
+
+ align:start position:0%
+something times times uh
+something and then what else how many
+
+ align:start position:0%
+something and then what else how many
+ 
+
+ align:start position:0%
+something and then what else how many
+you remember a 3X3
+
+ align:start position:0%
+you remember a 3X3
+ 
+
+ align:start position:0%
+you remember a 3X3
+determinant what's it going to look like
+
+ align:start position:0%
+determinant what's it going to look like
+ 
+
+ align:start position:0%
+determinant what's it going to look like
+it only involves there's an AB term and
+
+ align:start position:0%
+it only involves there's an AB term and
+ 
+
+ align:start position:0%
+it only involves there's an AB term and
+then there's will be a an a time
+
+ align:start position:0%
+then there's will be a an a time
+ 
+
+ align:start position:0%
+then there's will be a an a time
+something q a * some specified and a b
+
+ align:start position:0%
+something q a * some specified and a b
+ 
+
+ align:start position:0%
+something q a * some specified and a b
+times something
+
+ align:start position:0%
+times something
+ 
+
+ align:start position:0%
+times something
+specified and uh and other constant and
+
+ align:start position:0%
+specified and uh and other constant and
+ 
+
+ align:start position:0%
+specified and uh and other constant and
+other specified terms that don't involve
+
+ align:start position:0%
+other specified terms that don't involve
+ 
+
+ align:start position:0%
+other specified terms that don't involve
+A and B has to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero that's the determinant that's the
+
+ align:start position:0%
+zero that's the determinant that's the
+ 
+
+ align:start position:0%
+zero that's the determinant that's the
+3X3
+
+ align:start position:0%
+3X3
+ 
+
+ align:start position:0%
+3X3
+determinant okay but the thing is it
+
+ align:start position:0%
+determinant okay but the thing is it
+ 
+
+ align:start position:0%
+determinant okay but the thing is it
+involves both A and B
+
+ align:start position:0%
+involves both A and B
+ 
+
+ align:start position:0%
+involves both A and B
+so I mean that's only one of the many
+
+ align:start position:0%
+so I mean that's only one of the many
+ 
+
+ align:start position:0%
+so I mean that's only one of the many
+equations many 3x3 determinants but it's
+
+ align:start position:0%
+equations many 3x3 determinants but it's
+ 
+
+ align:start position:0%
+equations many 3x3 determinants but it's
+the one I want to look at and the other
+
+ align:start position:0%
+the one I want to look at and the other
+ 
+
+ align:start position:0%
+the one I want to look at and the other
+one I want to look at is this one can I
+
+ align:start position:0%
+one I want to look at is this one can I
+ 
+
+ align:start position:0%
+one I want to look at is this one can I
+I'll Circle the another 3x3 that's
+
+ align:start position:0%
+I'll Circle the another 3x3 that's
+ 
+
+ align:start position:0%
+I'll Circle the another 3x3 that's
+interesting in yellow
+
+ align:start position:0%
+interesting in yellow
+ 
+
+ align:start position:0%
+interesting in yellow
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+this I just want to use a and b can I I
+
+ align:start position:0%
+this I just want to use a and b can I I
+ 
+
+ align:start position:0%
+this I just want to use a and b can I I
+want to use
+
+ align:start position:0%
+want to use
+ 
+
+ align:start position:0%
+want to use
+this this and
+
+ align:start position:0%
+this this and
+ 
+
+ align:start position:0%
+this this and
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and no let me
+
+ align:start position:0%
+and no let me
+ 
+
+ align:start position:0%
+and no let me
+see what a where's it gone I haven't got
+
+ align:start position:0%
+see what a where's it gone I haven't got
+ 
+
+ align:start position:0%
+see what a where's it gone I haven't got
+David to help me here I'm looking for
+
+ align:start position:0%
+David to help me here I'm looking for
+ 
+
+ align:start position:0%
+David to help me here I'm looking for
+and and this is that
+
+ align:start position:0%
+and and this is that
+ 
+
+ align:start position:0%
+and and this is that
+right I'm looking for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three no no here this this and this okay
+
+ align:start position:0%
+three no no here this this and this okay
+ 
+
+ align:start position:0%
+three no no here this this and this okay
+there's another 3x3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's determined also has to be zero
+
+ align:start position:0%
+so it's determined also has to be zero
+ 
+
+ align:start position:0%
+so it's determined also has to be zero
+and it involves it's independent because
+
+ align:start position:0%
+and it involves it's independent because
+ 
+
+ align:start position:0%
+and it involves it's independent because
+it involves these three numbers and not
+
+ align:start position:0%
+it involves these three numbers and not
+ 
+
+ align:start position:0%
+it involves these three numbers and not
+these three that were that appeared here
+
+ align:start position:0%
+these three that were that appeared here
+ 
+
+ align:start position:0%
+these three that were that appeared here
+so for this determinant to be zero okay
+
+ align:start position:0%
+so for this determinant to be zero okay
+ 
+
+ align:start position:0%
+so for this determinant to be zero okay
+what's it what's that determinant well
+
+ align:start position:0%
+what's it what's that determinant well
+ 
+
+ align:start position:0%
+what's it what's that determinant well
+again I have an AB it looks just like
+
+ align:start position:0%
+again I have an AB it looks just like
+ 
+
+ align:start position:0%
+again I have an AB it looks just like
+this AB times some other specified thing
+
+ align:start position:0%
+this AB times some other specified thing
+ 
+
+ align:start position:0%
+this AB times some other specified thing
+plus a * some other specified thing Q
+
+ align:start position:0%
+plus a * some other specified thing Q
+ 
+
+ align:start position:0%
+plus a * some other specified thing Q
+Plus B B time some other specified thing
+
+ align:start position:0%
+Plus B B time some other specified thing
+ 
+
+ align:start position:0%
+Plus B B time some other specified thing
+R plus some other specified thing has to
+
+ align:start position:0%
+R plus some other specified thing has to
+ 
+
+ align:start position:0%
+R plus some other specified thing has to
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well out of this I can here's the punch
+
+ align:start position:0%
+well out of this I can here's the punch
+ 
+
+ align:start position:0%
+well out of this I can here's the punch
+line then out of this I can determine A
+
+ align:start position:0%
+line then out of this I can determine A
+ 
+
+ align:start position:0%
+line then out of this I can determine A
+and B they're they're nonlinear
+
+ align:start position:0%
+and B they're they're nonlinear
+ 
+
+ align:start position:0%
+and B they're they're nonlinear
+equations that's a little scary but I
+
+ align:start position:0%
+equations that's a little scary but I
+ 
+
+ align:start position:0%
+equations that's a little scary but I
+can I can uh uh subtract write multiple
+
+ align:start position:0%
+can I can uh uh subtract write multiple
+ 
+
+ align:start position:0%
+can I can uh uh subtract write multiple
+of this equation from this one and kill
+
+ align:start position:0%
+of this equation from this one and kill
+ 
+
+ align:start position:0%
+of this equation from this one and kill
+the ab and then I have a linear equation
+
+ align:start position:0%
+the ab and then I have a linear equation
+ 
+
+ align:start position:0%
+the ab and then I have a linear equation
+connecting A and B so I can solve for a
+
+ align:start position:0%
+connecting A and B so I can solve for a
+ 
+
+ align:start position:0%
+connecting A and B so I can solve for a
+and I can plug in then I get a quadratic
+
+ align:start position:0%
+and I can plug in then I get a quadratic
+ 
+
+ align:start position:0%
+and I can plug in then I get a quadratic
+equation for a which I can Sol it's two
+
+ align:start position:0%
+equation for a which I can Sol it's two
+ 
+
+ align:start position:0%
+equation for a which I can Sol it's two
+solutions and I don't yet know whether
+
+ align:start position:0%
+solutions and I don't yet know whether
+ 
+
+ align:start position:0%
+solutions and I don't yet know whether
+they're both okay and then back to find
+
+ align:start position:0%
+they're both okay and then back to find
+ 
+
+ align:start position:0%
+they're both okay and then back to find
+B in other words this leads to a and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b and a similar discussion starting sort
+
+ align:start position:0%
+b and a similar discussion starting sort
+ 
+
+ align:start position:0%
+b and a similar discussion starting sort
+of symmetrically upwards would would
+
+ align:start position:0%
+of symmetrically upwards would would
+ 
+
+ align:start position:0%
+of symmetrically upwards would would
+lead to CND
+
+ align:start position:0%
+lead to CND
+ 
+
+ align:start position:0%
+lead to CND
+D and I believe that would they would
+
+ align:start position:0%
+D and I believe that would they would
+ 
+
+ align:start position:0%
+D and I believe that would they would
+then be right I I haven't even completed
+
+ align:start position:0%
+then be right I I haven't even completed
+ 
+
+ align:start position:0%
+then be right I I haven't even completed
+that that part but I think it would be
+
+ align:start position:0%
+that that part but I think it would be
+ 
+
+ align:start position:0%
+that that part but I think it would be
+so anyway that's a progress report that
+
+ align:start position:0%
+so anyway that's a progress report that
+ 
+
+ align:start position:0%
+so anyway that's a progress report that
+we now have equations that determine the
+
+ align:start position:0%
+we now have equations that determine the
+ 
+
+ align:start position:0%
+we now have equations that determine the
+ab c and d and we believe that when they
+
+ align:start position:0%
+ab c and d and we believe that when they
+ 
+
+ align:start position:0%
+ab c and d and we believe that when they
+determine the whole thing will have rank
+
+ align:start position:0%
+determine the whole thing will have rank
+ 
+
+ align:start position:0%
+determine the whole thing will have rank
+two and then
+
+ align:start position:0%
+two and then
+ 
+
+ align:start position:0%
+two and then
+we're uh I can't say often run
+
+ align:start position:0%
+we're uh I can't say often run
+ 
+
+ align:start position:0%
+we're uh I can't say often run
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh I don't have a general pattern there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so still uh much to much to think
+
+ align:start position:0%
+so still uh much to much to think
+ 
+
+ align:start position:0%
+so still uh much to much to think
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+here I do want to so that that that's
+
+ align:start position:0%
+here I do want to so that that that's
+ 
+
+ align:start position:0%
+here I do want to so that that that's
+that's uh just I I just thought you
+
+ align:start position:0%
+that's uh just I I just thought you
+ 
+
+ align:start position:0%
+that's uh just I I just thought you
+might like to
+
+ align:start position:0%
+might like to
+ 
+
+ align:start position:0%
+might like to
+see three things about this problem
+
+ align:start position:0%
+see three things about this problem
+ 
+
+ align:start position:0%
+see three things about this problem
+in the rank one case you saw how a final
+
+ align:start position:0%
+in the rank one case you saw how a final
+ 
+
+ align:start position:0%
+in the rank one case you saw how a final
+theorem looks how how a proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could do do do the whole job and what a
+
+ align:start position:0%
+could do do do the whole job and what a
+ 
+
+ align:start position:0%
+could do do do the whole job and what a
+proof consisted of in this case you see
+
+ align:start position:0%
+proof consisted of in this case you see
+ 
+
+ align:start position:0%
+proof consisted of in this case you see
+uh theorem in progress where one case is
+
+ align:start position:0%
+uh theorem in progress where one case is
+ 
+
+ align:start position:0%
+uh theorem in progress where one case is
+clear we've now puzzled out another case
+
+ align:start position:0%
+clear we've now puzzled out another case
+ 
+
+ align:start position:0%
+clear we've now puzzled out another case
+but but in our heads we have the we know
+
+ align:start position:0%
+but but in our heads we have the we know
+ 
+
+ align:start position:0%
+but but in our heads we have the we know
+the job is all cases and we're not going
+
+ align:start position:0%
+the job is all cases and we're not going
+ 
+
+ align:start position:0%
+the job is all cases and we're not going
+to get all cases by by uh exhaustion the
+
+ align:start position:0%
+to get all cases by by uh exhaustion the
+ 
+
+ align:start position:0%
+to get all cases by by uh exhaustion the
+only way we can get it is eventually to
+
+ align:start position:0%
+only way we can get it is eventually to
+ 
+
+ align:start position:0%
+only way we can get it is eventually to
+see a pattern here and we don't see it
+
+ align:start position:0%
+see a pattern here and we don't see it
+ 
+
+ align:start position:0%
+see a pattern here and we don't see it
+yet and now
+
+ align:start position:0%
+yet and now
+ 
+
+ align:start position:0%
+yet and now
+thirdly I just want to say because it
+
+ align:start position:0%
+thirdly I just want to say because it
+ 
+
+ align:start position:0%
+thirdly I just want to say because it
+wouldn't have happened except for this
+
+ align:start position:0%
+wouldn't have happened except for this
+ 
+
+ align:start position:0%
+wouldn't have happened except for this
+giving this
+
+ align:start position:0%
+giving this
+ 
+
+ align:start position:0%
+giving this
+course that do you remember that I made
+
+ align:start position:0%
+course that do you remember that I made
+ 
+
+ align:start position:0%
+course that do you remember that I made
+the remark that I about something I had
+
+ align:start position:0%
+the remark that I about something I had
+ 
+
+ align:start position:0%
+the remark that I about something I had
+not known that if I have a triagonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix and let's assume these are
+
+ align:start position:0%
+matrix and let's assume these are
+ 
+
+ align:start position:0%
+matrix and let's assume these are
+nonzeros so it's a triagonal matrix do
+
+ align:start position:0%
+nonzeros so it's a triagonal matrix do
+ 
+
+ align:start position:0%
+nonzeros so it's a triagonal matrix do
+you remember my remark about its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse probably
+
+ align:start position:0%
+inverse probably
+ 
+
+ align:start position:0%
+inverse probably
+not I
+
+ align:start position:0%
+not I
+ 
+
+ align:start position:0%
+not I
+didn't so in the beginning of the course
+
+ align:start position:0%
+didn't so in the beginning of the course
+ 
+
+ align:start position:0%
+didn't so in the beginning of the course
+we had particular numbers twos and minus
+
+ align:start position:0%
+we had particular numbers twos and minus
+ 
+
+ align:start position:0%
+we had particular numbers twos and minus
+ones and we computed the inverse
+
+ align:start position:0%
+ones and we computed the inverse
+ 
+
+ align:start position:0%
+ones and we computed the inverse
+those those special matrices k and t and
+
+ align:start position:0%
+those those special matrices k and t and
+ 
+
+ align:start position:0%
+those those special matrices k and t and
+so on we we we actually found the
+
+ align:start position:0%
+so on we we we actually found the
+ 
+
+ align:start position:0%
+so on we we we actually found the
+inverse so I thought that was
+
+ align:start position:0%
+inverse so I thought that was
+ 
+
+ align:start position:0%
+inverse so I thought that was
+interesting then those inverses had a
+
+ align:start position:0%
+interesting then those inverses had a
+ 
+
+ align:start position:0%
+interesting then those inverses had a
+special form and then I read that that
+
+ align:start position:0%
+special form and then I read that that
+ 
+
+ align:start position:0%
+special form and then I read that that
+form is always there that and what was
+
+ align:start position:0%
+form is always there that and what was
+ 
+
+ align:start position:0%
+form is always there that and what was
+that form that form was that above the
+
+ align:start position:0%
+that form that form was that above the
+ 
+
+ align:start position:0%
+that form that form was that above the
+on and above the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal so for these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+guys that that was rank
+
+ align:start position:0%
+guys that that was rank
+ 
+
+ align:start position:0%
+guys that that was rank
+one that was so that was the thing that
+
+ align:start position:0%
+one that was so that was the thing that
+ 
+
+ align:start position:0%
+one that was so that was the thing that
+the inverse of a triagonal matrix has
+
+ align:start position:0%
+the inverse of a triagonal matrix has
+ 
+
+ align:start position:0%
+the inverse of a triagonal matrix has
+low rank above the diagonal so above the
+
+ align:start position:0%
+low rank above the diagonal so above the
+ 
+
+ align:start position:0%
+low rank above the diagonal so above the
+diagonal here it's of the form UI *
+
+ align:start position:0%
+diagonal here it's of the form UI *
+ 
+
+ align:start position:0%
+diagonal here it's of the form UI *
+VJ this is the the the in the IJ entry
+
+ align:start position:0%
+VJ this is the the the in the IJ entry
+ 
+
+ align:start position:0%
+VJ this is the the the in the IJ entry
+of the this is T for tri diagonal it's
+
+ align:start position:0%
+of the this is T for tri diagonal it's
+ 
+
+ align:start position:0%
+of the this is T for tri diagonal it's
+inverse the igj entry has its form UI VJ
+
+ align:start position:0%
+inverse the igj entry has its form UI VJ
+ 
+
+ align:start position:0%
+inverse the igj entry has its form UI VJ
+and let's suppose it's symmetric then it
+
+ align:start position:0%
+and let's suppose it's symmetric then it
+ 
+
+ align:start position:0%
+and let's suppose it's symmetric then it
+has low rank above the diagonal it
+
+ align:start position:0%
+has low rank above the diagonal it
+ 
+
+ align:start position:0%
+has low rank above the diagonal it
+doesn't have low rank overall so this is
+
+ align:start position:0%
+doesn't have low rank overall so this is
+ 
+
+ align:start position:0%
+doesn't have low rank overall so this is
+this is a different question from from
+
+ align:start position:0%
+this is a different question from from
+ 
+
+ align:start position:0%
+this is a different question from from
+the completion we were trying to
+
+ align:start position:0%
+the completion we were trying to
+ 
+
+ align:start position:0%
+the completion we were trying to
+complete to have low rank for the whole
+
+ align:start position:0%
+complete to have low rank for the whole
+ 
+
+ align:start position:0%
+complete to have low rank for the whole
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+here the thing's invertible the rank is
+
+ align:start position:0%
+here the thing's invertible the rank is
+ 
+
+ align:start position:0%
+here the thing's invertible the rank is
+full the rank is n but but half of it
+
+ align:start position:0%
+full the rank is n but but half of it
+ 
+
+ align:start position:0%
+full the rank is n but but half of it
+has low rank and the other half
+
+ align:start position:0%
+has low rank and the other half
+ 
+
+ align:start position:0%
+has low rank and the other half
+has has uh entries by by symmetry they
+
+ align:start position:0%
+has has uh entries by by symmetry they
+ 
+
+ align:start position:0%
+has has uh entries by by symmetry they
+must be
+
+ align:start position:0%
+must be
+ 
+
+ align:start position:0%
+must be
+ujv and the total rank is n but the the
+
+ align:start position:0%
+ujv and the total rank is n but the the
+ 
+
+ align:start position:0%
+ujv and the total rank is n but the the
+interesting part was that and new to me
+
+ align:start position:0%
+interesting part was that and new to me
+ 
+
+ align:start position:0%
+interesting part was that and new to me
+was that half of it had rank one yeah I
+
+ align:start position:0%
+was that half of it had rank one yeah I
+ 
+
+ align:start position:0%
+was that half of it had rank one yeah I
+jumped in a question
+
+ align:start position:0%
+jumped in a question
+ 
+
+ align:start position:0%
+jumped in a question
+Lex in his work on noise showed that I'm
+
+ align:start position:0%
+Lex in his work on noise showed that I'm
+ 
+
+ align:start position:0%
+Lex in his work on noise showed that I'm
+not sure where he got it from okay that
+
+ align:start position:0%
+not sure where he got it from okay that
+ 
+
+ align:start position:0%
+not sure where he got it from okay that
+if you take a correlation
+
+ align:start position:0%
+if you take a correlation
+ 
+
+ align:start position:0%
+if you take a correlation
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+absolute okay take a correlation which
+
+ align:start position:0%
+absolute okay take a correlation which
+ 
+
+ align:start position:0%
+absolute okay take a correlation which
+is like this all right yes on the right
+
+ align:start position:0%
+is like this all right yes on the right
+ 
+
+ align:start position:0%
+is like this all right yes on the right
+okay then you get the inverse when you
+
+ align:start position:0%
+okay then you get the inverse when you
+ 
+
+ align:start position:0%
+okay then you get the inverse when you
+do the inverse the correlation comes out
+
+ align:start position:0%
+do the inverse the correlation comes out
+ 
+
+ align:start position:0%
+do the inverse the correlation comes out
+as triagonal okay so there was a
+
+ align:start position:0%
+as triagonal okay so there was a
+ 
+
+ align:start position:0%
+as triagonal okay so there was a
+specific case of importance right and
+
+ align:start position:0%
+specific case of importance right and
+ 
+
+ align:start position:0%
+specific case of importance right and
+and these cases that we did were
+
+ align:start position:0%
+and these cases that we did were
+ 
+
+ align:start position:0%
+and these cases that we did were
+specific cases of importance and I had
+
+ align:start position:0%
+specific cases of importance and I had
+ 
+
+ align:start position:0%
+specific cases of importance and I had
+no idea that sort of this was always
+
+ align:start position:0%
+no idea that sort of this was always
+ 
+
+ align:start position:0%
+no idea that sort of this was always
+happened that uh that uh uh if you had
+
+ align:start position:0%
+happened that uh that uh uh if you had
+ 
+
+ align:start position:0%
+happened that uh that uh uh if you had
+rank one here then the on the other side
+
+ align:start position:0%
+rank one here then the on the other side
+ 
+
+ align:start position:0%
+rank one here then the on the other side
+you had Tri diagonal if you have rank
+
+ align:start position:0%
+you had Tri diagonal if you have rank
+ 
+
+ align:start position:0%
+you had Tri diagonal if you have rank
+two here above the diagonal what do you
+
+ align:start position:0%
+two here above the diagonal what do you
+ 
+
+ align:start position:0%
+two here above the diagonal what do you
+figure then this one will be five
+
+ align:start position:0%
+figure then this one will be five
+ 
+
+ align:start position:0%
+figure then this one will be five
+diagonal so I guess
+
+ align:start position:0%
+diagonal so I guess
+ 
+
+ align:start position:0%
+diagonal so I guess
+now I'm I'm I'm sort of looking for a
+
+ align:start position:0%
+now I'm I'm I'm sort of looking for a
+ 
+
+ align:start position:0%
+now I'm I'm I'm sort of looking for a
+general law there I I I I guess I'm not
+
+ align:start position:0%
+general law there I I I I guess I'm not
+ 
+
+ align:start position:0%
+general law there I I I I guess I'm not
+looking so the the general law is then
+
+ align:start position:0%
+looking so the the general law is then
+ 
+
+ align:start position:0%
+looking so the the general law is then
+known that if we have rank five here
+
+ align:start position:0%
+known that if we have rank five here
+ 
+
+ align:start position:0%
+known that if we have rank five here
+then we then I mean it's a big Matrix
+
+ align:start position:0%
+then we then I mean it's a big Matrix
+ 
+
+ align:start position:0%
+then we then I mean it's a big Matrix
+say rank five above the diagonal
+
+ align:start position:0%
+say rank five above the diagonal
+ 
+
+ align:start position:0%
+say rank five above the diagonal
+completed by symmetry so it'll have the
+
+ align:start position:0%
+completed by symmetry so it'll have the
+ 
+
+ align:start position:0%
+completed by symmetry so it'll have the
+thing will have full rank but the other
+
+ align:start position:0%
+thing will have full rank but the other
+ 
+
+ align:start position:0%
+thing will have full rank but the other
+side the inverse will if I said rank
+
+ align:start position:0%
+side the inverse will if I said rank
+ 
+
+ align:start position:0%
+side the inverse will if I said rank
+five there then it would have one two
+
+ align:start position:0%
+five there then it would have one two
+ 
+
+ align:start position:0%
+five there then it would have one two
+three four five diagonals above the main
+
+ align:start position:0%
+three four five diagonals above the main
+ 
+
+ align:start position:0%
+three four five diagonals above the main
+diagonal and Five Below okay fine what
+
+ align:start position:0%
+diagonal and Five Below okay fine what
+ 
+
+ align:start position:0%
+diagonal and Five Below okay fine what
+do you mean by rank above the Diagon
+
+ align:start position:0%
+do you mean by rank above the Diagon
+ 
+
+ align:start position:0%
+do you mean by rank above the Diagon
+well good question that's what led to
+
+ align:start position:0%
+well good question that's what led to
+ 
+
+ align:start position:0%
+well good question that's what led to
+that's what led us to this crazy stuff
+
+ align:start position:0%
+that's what led us to this crazy stuff
+ 
+
+ align:start position:0%
+that's what led us to this crazy stuff
+what do I mean by rank above the
+
+ align:start position:0%
+what do I mean by rank above the
+ 
+
+ align:start position:0%
+what do I mean by rank above the
+diagonal well I certainly mean that that
+
+ align:start position:0%
+diagonal well I certainly mean that that
+ 
+
+ align:start position:0%
+diagonal well I certainly mean that that
+it if it has the form UI VJ do you who
+
+ align:start position:0%
+it if it has the form UI VJ do you who
+ 
+
+ align:start position:0%
+it if it has the form UI VJ do you who
+asked the question yeah uh I mean I I
+
+ align:start position:0%
+asked the question yeah uh I mean I I
+ 
+
+ align:start position:0%
+asked the question yeah uh I mean I I
+identify immediately a matrix that's
+
+ align:start position:0%
+identify immediately a matrix that's
+ 
+
+ align:start position:0%
+identify immediately a matrix that's
+what I mean by having rank one above the
+
+ align:start position:0%
+what I mean by having rank one above the
+ 
+
+ align:start position:0%
+what I mean by having rank one above the
+diagonal if it if it has a form UI VJ
+
+ align:start position:0%
+diagonal if it if it has a form UI VJ
+ 
+
+ align:start position:0%
+diagonal if it if it has a form UI VJ
+that means it has the form of
+
+ align:start position:0%
+that means it has the form of
+ 
+
+ align:start position:0%
+that means it has the form of
+column you know it it it uh um it's
+
+ align:start position:0%
+column you know it it it uh um it's
+ 
+
+ align:start position:0%
+column you know it it it uh um it's
+that's one column of of uh
+
+ align:start position:0%
+that's one column of of uh
+ 
+
+ align:start position:0%
+that's one column of of uh
+U's U1 U2 u3 times a row of V's V1 V2 V3
+
+ align:start position:0%
+U's U1 U2 u3 times a row of V's V1 V2 V3
+ 
+
+ align:start position:0%
+U's U1 U2 u3 times a row of V's V1 V2 V3
+the entry in that would be UI
+
+ align:start position:0%
+the entry in that would be UI
+ 
+
+ align:start position:0%
+the entry in that would be UI
+VJ and it's a it's a rank one it's a
+
+ align:start position:0%
+VJ and it's a it's a rank one it's a
+ 
+
+ align:start position:0%
+VJ and it's a it's a rank one it's a
+column times a row so I I recognize that
+
+ align:start position:0%
+column times a row so I I recognize that
+ 
+
+ align:start position:0%
+column times a row so I I recognize that
+as a rank one Matrix and I'm seeing it
+
+ align:start position:0%
+as a rank one Matrix and I'm seeing it
+ 
+
+ align:start position:0%
+as a rank one Matrix and I'm seeing it
+here in different uh
+
+ align:start position:0%
+here in different uh
+ 
+
+ align:start position:0%
+here in different uh
+notation so that's what I mean by rank
+
+ align:start position:0%
+notation so that's what I mean by rank
+ 
+
+ align:start position:0%
+notation so that's what I mean by rank
+one Matrix if I completed the whole
+
+ align:start position:0%
+one Matrix if I completed the whole
+ 
+
+ align:start position:0%
+one Matrix if I completed the whole
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+by this pattern I would have rank one
+
+ align:start position:0%
+by this pattern I would have rank one
+ 
+
+ align:start position:0%
+by this pattern I would have rank one
+but symmetry completes it with the
+
+ align:start position:0%
+but symmetry completes it with the
+ 
+
+ align:start position:0%
+but symmetry completes it with the
+opposite pattern and and gives me full
+
+ align:start position:0%
+opposite pattern and and gives me full
+ 
+
+ align:start position:0%
+opposite pattern and and gives me full
+Rank and yeah yeah so that would be the
+
+ align:start position:0%
+Rank and yeah yeah so that would be the
+ 
+
+ align:start position:0%
+Rank and yeah yeah so that would be the
+rank one case yes all right here here's
+
+ align:start position:0%
+rank one case yes all right here here's
+ 
+
+ align:start position:0%
+rank one case yes all right here here's
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+idea here's my idea okay algebra is
+
+ align:start position:0%
+idea here's my idea okay algebra is
+ 
+
+ align:start position:0%
+idea here's my idea okay algebra is
+saying that if we have a certain number
+
+ align:start position:0%
+saying that if we have a certain number
+ 
+
+ align:start position:0%
+saying that if we have a certain number
+of diagonals here we have a certain rank
+
+ align:start position:0%
+of diagonals here we have a certain rank
+ 
+
+ align:start position:0%
+of diagonals here we have a certain rank
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+fine can't beat that okay now
+
+ align:start position:0%
+fine can't beat that okay now
+ 
+
+ align:start position:0%
+fine can't beat that okay now
+but I think there must be behind that
+
+ align:start position:0%
+but I think there must be behind that
+ 
+
+ align:start position:0%
+but I think there must be behind that
+somehow a more general rule that if
+
+ align:start position:0%
+somehow a more general rule that if
+ 
+
+ align:start position:0%
+somehow a more general rule that if
+the if the thing is approximately a band
+
+ align:start position:0%
+the if the thing is approximately a band
+ 
+
+ align:start position:0%
+the if the thing is approximately a band
+Matrix now what does that mean if it
+
+ align:start position:0%
+Matrix now what does that mean if it
+ 
+
+ align:start position:0%
+Matrix now what does that mean if it
+tails off fast you see what I want to do
+
+ align:start position:0%
+tails off fast you see what I want to do
+ 
+
+ align:start position:0%
+tails off fast you see what I want to do
+now is generalize this
+
+ align:start position:0%
+now is generalize this
+ 
+
+ align:start position:0%
+now is generalize this
+to when these are not necessarily
+
+ align:start position:0%
+to when these are not necessarily
+ 
+
+ align:start position:0%
+to when these are not necessarily
+strictly zero and this has strict rank
+
+ align:start position:0%
+strictly zero and this has strict rank
+ 
+
+ align:start position:0%
+strictly zero and this has strict rank
+whatever but I wanted to see it's sort
+
+ align:start position:0%
+whatever but I wanted to see it's sort
+ 
+
+ align:start position:0%
+whatever but I wanted to see it's sort
+of like Heisenberg somehow if this tails
+
+ align:start position:0%
+of like Heisenberg somehow if this tails
+ 
+
+ align:start position:0%
+of like Heisenberg somehow if this tails
+off fast then this has pretty close to
+
+ align:start position:0%
+off fast then this has pretty close to
+ 
+
+ align:start position:0%
+off fast then this has pretty close to
+rank one there's my there's my
+
+ align:start position:0%
+rank one there's my there's my
+ 
+
+ align:start position:0%
+rank one there's my there's my
+conjecture that if I if that that if
+
+ align:start position:0%
+conjecture that if I if that that if
+ 
+
+ align:start position:0%
+conjecture that if I if that that if
+these are
+
+ align:start position:0%
+these are
+ 
+
+ align:start position:0%
+these are
+little then the rank here is near one
+
+ align:start position:0%
+little then the rank here is near one
+ 
+
+ align:start position:0%
+little then the rank here is near one
+okay what does that
+
+ align:start position:0%
+okay what does that
+ 
+
+ align:start position:0%
+okay what does that
+mean I suppose it means that I have a
+
+ align:start position:0%
+mean I suppose it means that I have a
+ 
+
+ align:start position:0%
+mean I suppose it means that I have a
+rank one Matrix plus something small so
+
+ align:start position:0%
+rank one Matrix plus something small so
+ 
+
+ align:start position:0%
+rank one Matrix plus something small so
+there's my conjecture uh unwi ly stated
+
+ align:start position:0%
+there's my conjecture uh unwi ly stated
+ 
+
+ align:start position:0%
+there's my conjecture uh unwi ly stated
+here and imprecisely stated but you see
+
+ align:start position:0%
+here and imprecisely stated but you see
+ 
+
+ align:start position:0%
+here and imprecisely stated but you see
+that the you see it's reasonable right
+
+ align:start position:0%
+that the you see it's reasonable right
+ 
+
+ align:start position:0%
+that the you see it's reasonable right
+and if it's reasonable it's probably
+
+ align:start position:0%
+and if it's reasonable it's probably
+ 
+
+ align:start position:0%
+and if it's reasonable it's probably
+true and and if it's probably true it's
+
+ align:start position:0%
+true and and if it's probably true it's
+ 
+
+ align:start position:0%
+true and and if it's probably true it's
+probably been proved that's the bad
+
+ align:start position:0%
+probably been proved that's the bad
+ 
+
+ align:start position:0%
+probably been proved that's the bad
+point but uh um so that'd be my guess
+
+ align:start position:0%
+point but uh um so that'd be my guess
+ 
+
+ align:start position:0%
+point but uh um so that'd be my guess
+that if I have a matrix that's almost a
+
+ align:start position:0%
+that if I have a matrix that's almost a
+ 
+
+ align:start position:0%
+that if I have a matrix that's almost a
+band Matrix then its inverse is almost
+
+ align:start position:0%
+band Matrix then its inverse is almost
+ 
+
+ align:start position:0%
+band Matrix then its inverse is almost
+um uh a rank almost a low rank uh above
+
+ align:start position:0%
+um uh a rank almost a low rank uh above
+ 
+
+ align:start position:0%
+um uh a rank almost a low rank uh above
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+above the diagonal okay stated that way
+
+ align:start position:0%
+above the diagonal okay stated that way
+ 
+
+ align:start position:0%
+above the diagonal okay stated that way
+it sounds like it's pretty clear so I
+
+ align:start position:0%
+it sounds like it's pretty clear so I
+ 
+
+ align:start position:0%
+it sounds like it's pretty clear so I
+have no idea
+
+ align:start position:0%
+have no idea
+ 
+
+ align:start position:0%
+have no idea
+uh uh whether that that idea whether
+
+ align:start position:0%
+uh uh whether that that idea whether
+ 
+
+ align:start position:0%
+uh uh whether that that idea whether
+whether that concept will be it it may
+
+ align:start position:0%
+whether that concept will be it it may
+ 
+
+ align:start position:0%
+whether that concept will be it it may
+be not not difficult to to pin down but
+
+ align:start position:0%
+be not not difficult to to pin down but
+ 
+
+ align:start position:0%
+be not not difficult to to pin down but
+it's uh it's it's sort of the step from
+
+ align:start position:0%
+it's uh it's it's sort of the step from
+ 
+
+ align:start position:0%
+it's uh it's it's sort of the step from
+algebra to
+
+ align:start position:0%
+algebra to
+ 
+
+ align:start position:0%
+algebra to
+analysis it's algebra when you're
+
+ align:start position:0%
+analysis it's algebra when you're
+ 
+
+ align:start position:0%
+analysis it's algebra when you're
+talking about strict zeros and strict
+
+ align:start position:0%
+talking about strict zeros and strict
+ 
+
+ align:start position:0%
+talking about strict zeros and strict
+rank analysis is when you get you get
+
+ align:start position:0%
+rank analysis is when you get you get
+ 
+
+ align:start position:0%
+rank analysis is when you get you get
+things like near zero and near rank then
+
+ align:start position:0%
+things like near zero and near rank then
+ 
+
+ align:start position:0%
+things like near zero and near rank then
+then it's estimates of uh inequalities
+
+ align:start position:0%
+then it's estimates of uh inequalities
+ 
+
+ align:start position:0%
+then it's estimates of uh inequalities
+you're bounding things and that's sort
+
+ align:start position:0%
+you're bounding things and that's sort
+ 
+
+ align:start position:0%
+you're bounding things and that's sort
+of the difference between those two
+
+ align:start position:0%
+of the difference between those two
+ 
+
+ align:start position:0%
+of the difference between those two
+parts of
+
+ align:start position:0%
+parts of
+ 
+
+ align:start position:0%
+parts of
+mathematics so and most people are sort
+
+ align:start position:0%
+mathematics so and most people are sort
+ 
+
+ align:start position:0%
+mathematics so and most people are sort
+of on one in one side or the other
+
+ align:start position:0%
+of on one in one side or the other
+ 
+
+ align:start position:0%
+of on one in one side or the other
+algebraists are just just have that
+
+ align:start position:0%
+algebraists are just just have that
+ 
+
+ align:start position:0%
+algebraists are just just have that
+Knack of playing with um with um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+combinations and Analysis is more about
+
+ align:start position:0%
+combinations and Analysis is more about
+ 
+
+ align:start position:0%
+combinations and Analysis is more about
+uh if you're given certain bounds on
+
+ align:start position:0%
+uh if you're given certain bounds on
+ 
+
+ align:start position:0%
+uh if you're given certain bounds on
+something what else what what bounds do
+
+ align:start position:0%
+something what else what what bounds do
+ 
+
+ align:start position:0%
+something what else what what bounds do
+those imply on other things okay I'm
+
+ align:start position:0%
+those imply on other things okay I'm
+ 
+
+ align:start position:0%
+those imply on other things okay I'm
+I've taken more than an hour of on this
+
+ align:start position:0%
+I've taken more than an hour of on this
+ 
+
+ align:start position:0%
+I've taken more than an hour of on this
+lecture and uh let's make this
+
+ align:start position:0%
+lecture and uh let's make this
+ 
+
+ align:start position:0%
+lecture and uh let's make this
+then can we take a break and I'm happy
+
+ align:start position:0%
+then can we take a break and I'm happy
+ 
+
+ align:start position:0%
+then can we take a break and I'm happy
+to to uh
+
+ align:start position:0%
+to to uh
+ 
+
+ align:start position:0%
+to to uh
+and and also so I'm going to call this
+
+ align:start position:0%
+and and also so I'm going to call this
+ 
+
+ align:start position:0%
+and and also so I'm going to call this
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+32 will
+
+ align:start position:0%
+32 will
+ 
+
+ align:start position:0%
+32 will
+be concentrate on Game Theory and
+
+ align:start position:0%
+be concentrate on Game Theory and
+ 
+
+ align:start position:0%
+be concentrate on Game Theory and
+um apologize to for
+
+ align:start position:0%
+um apologize to for
+ 
+
+ align:start position:0%
+um apologize to for
+for for a work in progress like that but
+
+ align:start position:0%
+for for a work in progress like that but
+ 
+
+ align:start position:0%
+for for a work in progress like that but
+maybe at Lector 31 when I feel I know
+
+ align:start position:0%
+maybe at Lector 31 when I feel I know
+ 
+
+ align:start position:0%
+maybe at Lector 31 when I feel I know
+you all so well uh you forgive me for uh
+
+ align:start position:0%
+you all so well uh you forgive me for uh
+ 
+
+ align:start position:0%
+you all so well uh you forgive me for uh
+describing something that's incomplete
+
+ align:start position:0%
+describing something that's incomplete
+ 
+
+ align:start position:0%
+describing something that's incomplete
+but uh um but connected to what we've
+
+ align:start position:0%
+but uh um but connected to what we've
+ 
+
+ align:start position:0%
+but uh um but connected to what we've
+been doing okay so
+
+ align:start position:0%
+been doing okay so
+ 
+
+ align:start position:0%
+been doing okay so
+uh comput uh okay you're going at this
+
+ align:start position:0%
+uh comput uh okay you're going at this
+ 
+
+ align:start position:0%
+uh comput uh okay you're going at this
+very hard does it have app why why okay
+
+ align:start position:0%
+very hard does it have app why why okay
+ 
+
+ align:start position:0%
+very hard does it have app why why okay
+why all right fair question right and
+
+ align:start position:0%
+why all right fair question right and
+ 
+
+ align:start position:0%
+why all right fair question right and
+and um what's my
+
+ align:start position:0%
+and um what's my
+ 
+
+ align:start position:0%
+and um what's my
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+well just it's really you're really
+
+ align:start position:0%
+well just it's really you're really
+ 
+
+ align:start position:0%
+well just it's really you're really
+seeing what a mathematician who sort of
+
+ align:start position:0%
+seeing what a mathematician who sort of
+ 
+
+ align:start position:0%
+seeing what a mathematician who sort of
+on the border of pure and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applied what happens I mean uh so so I
+
+ align:start position:0%
+applied what happens I mean uh so so I
+ 
+
+ align:start position:0%
+applied what happens I mean uh so so I
+yes I do hope it has applications and
+
+ align:start position:0%
+yes I do hope it has applications and
+ 
+
+ align:start position:0%
+yes I do hope it has applications and
+and I guess in this final minute here I
+
+ align:start position:0%
+and I guess in this final minute here I
+ 
+
+ align:start position:0%
+and I guess in this final minute here I
+was describing
+
+ align:start position:0%
+was describing
+ 
+
+ align:start position:0%
+was describing
+applica my my coming back to
+
+ align:start position:0%
+applica my my coming back to
+ 
+
+ align:start position:0%
+applica my my coming back to
+Applications cuz cuz a a lot of matrices
+
+ align:start position:0%
+Applications cuz cuz a a lot of matrices
+ 
+
+ align:start position:0%
+Applications cuz cuz a a lot of matrices
+a lot of matrices in in applications are
+
+ align:start position:0%
+a lot of matrices in in applications are
+ 
+
+ align:start position:0%
+a lot of matrices in in applications are
+big on the diagonal and and tail off
+
+ align:start position:0%
+big on the diagonal and and tail off
+ 
+
+ align:start position:0%
+big on the diagonal and and tail off
+talking being bad limited yes that
+
+ align:start position:0%
+talking being bad limited yes that
+ 
+
+ align:start position:0%
+talking being bad limited yes that
+that's right yeah that that exactly I
+
+ align:start position:0%
+that's right yeah that that exactly I
+ 
+
+ align:start position:0%
+that's right yeah that that exactly I
+mean that that's another word that falls
+
+ align:start position:0%
+mean that that's another word that falls
+ 
+
+ align:start position:0%
+mean that that's another word that falls
+into this thing so diagonally dominant
+
+ align:start position:0%
+into this thing so diagonally dominant
+ 
+
+ align:start position:0%
+into this thing so diagonally dominant
+is a is a and and people so you meet a
+
+ align:start position:0%
+is a is a and and people so you meet a
+ 
+
+ align:start position:0%
+is a is a and and people so you meet a
+lot of diagonally dominant matrices that
+
+ align:start position:0%
+lot of diagonally dominant matrices that
+ 
+
+ align:start position:0%
+lot of diagonally dominant matrices that
+they make your life easier and um
+
+ align:start position:0%
+they make your life easier and um
+ 
+
+ align:start position:0%
+they make your life easier and um
+because somehow they're they're better
+
+ align:start position:0%
+because somehow they're they're better
+ 
+
+ align:start position:0%
+because somehow they're they're better
+matrices to deal with they might they're
+
+ align:start position:0%
+matrices to deal with they might they're
+ 
+
+ align:start position:0%
+matrices to deal with they might they're
+probably positive definite because that
+
+ align:start position:0%
+probably positive definite because that
+ 
+
+ align:start position:0%
+probably positive definite because that
+diagonal is so tough that it that it uh
+
+ align:start position:0%
+diagonal is so tough that it that it uh
+ 
+
+ align:start position:0%
+diagonal is so tough that it that it uh
+makes a thing positive definite but then
+
+ align:start position:0%
+makes a thing positive definite but then
+ 
+
+ align:start position:0%
+makes a thing positive definite but then
+you want to say why what what what's the
+
+ align:start position:0%
+you want to say why what what what's the
+ 
+
+ align:start position:0%
+you want to say why what what what's the
+consequence in the inverse yeah so so
+
+ align:start position:0%
+consequence in the inverse yeah so so
+ 
+
+ align:start position:0%
+consequence in the inverse yeah so so
+maybe at this point I'm thinking of
+
+ align:start position:0%
+maybe at this point I'm thinking of
+ 
+
+ align:start position:0%
+maybe at this point I'm thinking of
+applied here but over here it's pure fun
+
+ align:start position:0%
+applied here but over here it's pure fun
+ 
+
+ align:start position:0%
+applied here but over here it's pure fun
+right I mean yeah who knows there could
+
+ align:start position:0%
+right I mean yeah who knows there could
+ 
+
+ align:start position:0%
+right I mean yeah who knows there could
+be an application but I don't require
+
+ align:start position:0%
+be an application but I don't require
+ 
+
+ align:start position:0%
+be an application but I don't require
+that to get excited about it that's
+
+ align:start position:0%
+that to get excited about it that's
+ 
+
+ align:start position:0%
+that to get excited about it that's
+that's the that's the reality I just
+
+ align:start position:0%
+that's the that's the reality I just
+ 
+
+ align:start position:0%
+that's the that's the reality I just
+require a puzzle that I can't see the
+
+ align:start position:0%
+require a puzzle that I can't see the
+ 
+
+ align:start position:0%
+require a puzzle that I can't see the
+way the end to yeah all right good okay
\ No newline at end of file
diff --git a/5L4QfjbK87M.txt b/5L4QfjbK87M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ac41170ac1f3b0ef6833b23d00b414135502cda8
--- /dev/null
+++ b/5L4QfjbK87M.txt
@@ -0,0 +1,2828 @@
+align:start position:0%
+ 
+let's do our check
+
+ align:start position:0%
+let's do our check
+ 
+
+ align:start position:0%
+let's do our check
+um so main
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+if integral of Si star of XT KN SI XT
+
+ align:start position:0%
+if integral of Si star of XT KN SI XT
+ 
+
+ align:start position:0%
+if integral of Si star of XT KN SI XT
+KN DX is equal to 1 at T = to T as we
+
+ align:start position:0%
+KN DX is equal to 1 at T = to T as we
+ 
+
+ align:start position:0%
+KN DX is equal to 1 at T = to T as we
+say that
+
+ align:start position:0%
+say that
+ 
+
+ align:start position:0%
+say that
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+then it must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hold for later times T greater than
+
+ align:start position:0%
+hold for later times T greater than
+ 
+
+ align:start position:0%
+hold for later times T greater than
+T this is what we want to check or
+
+ align:start position:0%
+T this is what we want to check or
+ 
+
+ align:start position:0%
+T this is what we want to check or
+verify or prove now to do it
+
+ align:start position:0%
+verify or prove now to do it
+ 
+
+ align:start position:0%
+verify or prove now to do it
+uh we're going to take our time so it's
+
+ align:start position:0%
+uh we're going to take our time so it's
+ 
+
+ align:start position:0%
+uh we're going to take our time so it's
+not going to happen in five minutes not
+
+ align:start position:0%
+not going to happen in five minutes not
+ 
+
+ align:start position:0%
+not going to happen in five minutes not
+10 minutes um maybe not even half an
+
+ align:start position:0%
+10 minutes um maybe not even half an
+ 
+
+ align:start position:0%
+10 minutes um maybe not even half an
+hour
+
+ align:start position:0%
+hour
+ 
+
+ align:start position:0%
+hour
+um not because it's so difficult it's
+
+ align:start position:0%
+um not because it's so difficult it's
+ 
+
+ align:start position:0%
+um not because it's so difficult it's
+because there's so many things that one
+
+ align:start position:0%
+because there's so many things that one
+ 
+
+ align:start position:0%
+because there's so many things that one
+can say in between that teach you a lot
+
+ align:start position:0%
+can say in between that teach you a lot
+ 
+
+ align:start position:0%
+can say in between that teach you a lot
+about quantum mechanics so we're going
+
+ align:start position:0%
+about quantum mechanics so we're going
+ 
+
+ align:start position:0%
+about quantum mechanics so we're going
+to take our time here um so we're going
+
+ align:start position:0%
+to take our time here um so we're going
+ 
+
+ align:start position:0%
+to take our time here um so we're going
+to first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh rewrite it with better notation so
+
+ align:start position:0%
+uh rewrite it with better notation so
+ 
+
+ align:start position:0%
+uh rewrite it with better notation so
+we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Define row of x and t which is going to
+
+ align:start position:0%
+Define row of x and t which is going to
+ 
+
+ align:start position:0%
+Define row of x and t which is going to
+be called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density and it's nothing else than what
+
+ align:start position:0%
+density and it's nothing else than what
+ 
+
+ align:start position:0%
+density and it's nothing else than what
+you would expect P star of x and t * P
+
+ align:start position:0%
+you would expect P star of x and t * P
+ 
+
+ align:start position:0%
+you would expect P star of x and t * P
+of x and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t it's a probability
+
+ align:start position:0%
+t it's a probability
+ 
+
+ align:start position:0%
+t it's a probability
+density U you know that that has the
+
+ align:start position:0%
+density U you know that that has the
+ 
+
+ align:start position:0%
+density U you know that that has the
+right interpretation is s
+
+ align:start position:0%
+right interpretation is s
+ 
+
+ align:start position:0%
+right interpretation is s
+squared and that's the kind of thing
+
+ align:start position:0%
+squared and that's the kind of thing
+ 
+
+ align:start position:0%
+squared and that's the kind of thing
+that integrated over space gives you the
+
+ align:start position:0%
+that integrated over space gives you the
+ 
+
+ align:start position:0%
+that integrated over space gives you the
+total probability so this is a positive
+
+ align:start position:0%
+total probability so this is a positive
+ 
+
+ align:start position:0%
+total probability so this is a positive
+number given by this quantity is called
+
+ align:start position:0%
+number given by this quantity is called
+ 
+
+ align:start position:0%
+number given by this quantity is called
+the probability density fine what do we
+
+ align:start position:0%
+the probability density fine what do we
+ 
+
+ align:start position:0%
+the probability density fine what do we
+know about this probability density that
+
+ align:start position:0%
+know about this probability density that
+ 
+
+ align:start position:0%
+know about this probability density that
+uh that we're trying to find about its
+
+ align:start position:0%
+uh that we're trying to find about its
+ 
+
+ align:start position:0%
+uh that we're trying to find about its
+integral so Define next n of T to be the
+
+ align:start position:0%
+integral so Define next n of T to be the
+ 
+
+ align:start position:0%
+integral so Define next n of T to be the
+integral of row of x and t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX integrate this probability density
+
+ align:start position:0%
+DX integrate this probability density
+ 
+
+ align:start position:0%
+DX integrate this probability density
+throughout
+
+ align:start position:0%
+throughout
+ 
+
+ align:start position:0%
+throughout
+space and that's going to give you n of
+
+ align:start position:0%
+space and that's going to give you n of
+ 
+
+ align:start position:0%
+space and that's going to give you n of
+T now what do we know we know
+
+ align:start position:0%
+T now what do we know we know
+ 
+
+ align:start position:0%
+T now what do we know we know
+that n of t or let's assume that n of T
+
+ align:start position:0%
+that n of t or let's assume that n of T
+ 
+
+ align:start position:0%
+that n of t or let's assume that n of T
+KN is equal to 1
+
+ align:start position:0%
+KN is equal to 1
+ 
+
+ align:start position:0%
+KN is equal to 1
+n is that normalization it's that total
+
+ align:start position:0%
+n is that normalization it's that total
+ 
+
+ align:start position:0%
+n is that normalization it's that total
+integral of the probability what had to
+
+ align:start position:0%
+integral of the probability what had to
+ 
+
+ align:start position:0%
+integral of the probability what had to
+be equal to one well let's
+
+ align:start position:0%
+be equal to one well let's
+ 
+
+ align:start position:0%
+be equal to one well let's
+assume n at T not is equal to 1 that's
+
+ align:start position:0%
+assume n at T not is equal to 1 that's
+ 
+
+ align:start position:0%
+assume n at T not is equal to 1 that's
+good the question is will the shringer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guarantee that and here's the claim the
+
+ align:start position:0%
+guarantee that and here's the claim the
+ 
+
+ align:start position:0%
+guarantee that and here's the claim the
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+DT is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero will the Shing equation guarantee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if the shinger equation guarantees
+
+ align:start position:0%
+this if the shinger equation guarantees
+ 
+
+ align:start position:0%
+this if the shinger equation guarantees
+that this derivative is indeed zero then
+
+ align:start position:0%
+that this derivative is indeed zero then
+ 
+
+ align:start position:0%
+that this derivative is indeed zero then
+we're in in good business because uh the
+
+ align:start position:0%
+we're in in good business because uh the
+ 
+
+ align:start position:0%
+we're in in good business because uh the
+derivative is zero the value is one we
+
+ align:start position:0%
+derivative is zero the value is one we
+ 
+
+ align:start position:0%
+derivative is zero the value is one we
+remain One Forever yes ask why you
+
+ align:start position:0%
+remain One Forever yes ask why you
+ 
+
+ align:start position:0%
+remain One Forever yes ask why you
+specify for T greater than T
+
+ align:start position:0%
+specify for T greater than T
+ 
+
+ align:start position:0%
+specify for T greater than T
+um well I don't have to specify for T
+
+ align:start position:0%
+um well I don't have to specify for T
+ 
+
+ align:start position:0%
+um well I don't have to specify for T
+greater than T not I could do it uh for
+
+ align:start position:0%
+greater than T not I could do it uh for
+ 
+
+ align:start position:0%
+greater than T not I could do it uh for
+all T different than T not but uh I say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I I say it this way as imagining that
+
+ align:start position:0%
+it I I say it this way as imagining that
+ 
+
+ align:start position:0%
+it I I say it this way as imagining that
+somebody prepared the system at some
+
+ align:start position:0%
+somebody prepared the system at some
+ 
+
+ align:start position:0%
+somebody prepared the system at some
+time T not and maybe the system didn't
+
+ align:start position:0%
+time T not and maybe the system didn't
+ 
+
+ align:start position:0%
+time T not and maybe the system didn't
+exist for other times below now if a
+
+ align:start position:0%
+exist for other times below now if a
+ 
+
+ align:start position:0%
+exist for other times below now if a
+system existed for a long time and you
+
+ align:start position:0%
+system existed for a long time and you
+ 
+
+ align:start position:0%
+system existed for a long time and you
+look at it at T not then certainly the
+
+ align:start position:0%
+look at it at T not then certainly the
+ 
+
+ align:start position:0%
+look at it at T not then certainly the
+sheringer equation should imply that uh
+
+ align:start position:0%
+sheringer equation should imply that uh
+ 
+
+ align:start position:0%
+sheringer equation should imply that uh
+it works later and it works before so so
+
+ align:start position:0%
+it works later and it works before so so
+ 
+
+ align:start position:0%
+it works later and it works before so so
+it's not really necessary but U no loss
+
+ align:start position:0%
+it's not really necessary but U no loss
+ 
+
+ align:start position:0%
+it's not really necessary but U no loss
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generality
+
+ align:start position:0%
+generality
+ 
+
+ align:start position:0%
+generality
+okay so does it will it guarantee that
+
+ align:start position:0%
+okay so does it will it guarantee that
+ 
+
+ align:start position:0%
+okay so does it will it guarantee that
+well that's our thing to do so let's
+
+ align:start position:0%
+well that's our thing to do so let's
+ 
+
+ align:start position:0%
+well that's our thing to do so let's
+begin the work by doing a little bit of
+
+ align:start position:0%
+begin the work by doing a little bit of
+ 
+
+ align:start position:0%
+begin the work by doing a little bit of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+calculation and uh and so what do we
+
+ align:start position:0%
+calculation and uh and so what do we
+ 
+
+ align:start position:0%
+calculation and uh and so what do we
+need to do we need to find the
+
+ align:start position:0%
+need to do we need to find the
+ 
+
+ align:start position:0%
+need to do we need to find the
+derivative of this
+
+ align:start position:0%
+derivative of this
+ 
+
+ align:start position:0%
+derivative of this
+quantity so what is this derivative of n
+
+ align:start position:0%
+quantity so what is this derivative of n
+ 
+
+ align:start position:0%
+quantity so what is this derivative of n
+d n
+
+ align:start position:0%
+d n
+ 
+
+ align:start position:0%
+d n
+DT would be the
+
+ align:start position:0%
+DT would be the
+ 
+
+ align:start position:0%
+DT would be the
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+DDT of
+
+ align:start position:0%
+DDT of
+ 
+
+ align:start position:0%
+DDT of
+row of x and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+DX so I went here and brought in the
+
+ align:start position:0%
+DX so I went here and brought in the
+ 
+
+ align:start position:0%
+DX so I went here and brought in the
+DDT which became a partial derivative
+
+ align:start position:0%
+DDT which became a partial derivative
+ 
+
+ align:start position:0%
+DDT which became a partial derivative
+because out this is just a function of T
+
+ align:start position:0%
+because out this is just a function of T
+ 
+
+ align:start position:0%
+because out this is just a function of T
+but inside here there's a function of t
+
+ align:start position:0%
+but inside here there's a function of t
+ 
+
+ align:start position:0%
+but inside here there's a function of t
+and a function of X so I must make clear
+
+ align:start position:0%
+and a function of X so I must make clear
+ 
+
+ align:start position:0%
+and a function of X so I must make clear
+that I'm just differentiating
+
+ align:start position:0%
+that I'm just differentiating
+ 
+
+ align:start position:0%
+that I'm just differentiating
+T so is DDT of row and now we can write
+
+ align:start position:0%
+T so is DDT of row and now we can write
+ 
+
+ align:start position:0%
+T so is DDT of row and now we can write
+it as integral
+
+ align:start position:0%
+it as integral
+ 
+
+ align:start position:0%
+it as integral
+DX what is row is p star P so we would
+
+ align:start position:0%
+DX what is row is p star P so we would
+ 
+
+ align:start position:0%
+DX what is row is p star P so we would
+have DDT of P
+
+ align:start position:0%
+have DDT of P
+ 
+
+ align:start position:0%
+have DDT of P
+star time
+
+ align:start position:0%
+star time
+ 
+
+ align:start position:0%
+star time
+P plus SI
+
+ align:start position:0%
+P plus SI
+ 
+
+ align:start position:0%
+P plus SI
+star DDT of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and here you see if you were
+
+ align:start position:0%
+okay and here you see if you were
+ 
+
+ align:start position:0%
+okay and here you see if you were
+waiting for that um that the shinger
+
+ align:start position:0%
+waiting for that um that the shinger
+ 
+
+ align:start position:0%
+waiting for that um that the shinger
+equation has to be necessary because we
+
+ align:start position:0%
+equation has to be necessary because we
+ 
+
+ align:start position:0%
+equation has to be necessary because we
+have deep side DT and uh that
+
+ align:start position:0%
+have deep side DT and uh that
+ 
+
+ align:start position:0%
+have deep side DT and uh that
+information is there with the shinger
+
+ align:start position:0%
+information is there with the shinger
+ 
+
+ align:start position:0%
+information is there with the shinger
+equation so
+
+ align:start position:0%
+equation so
+ 
+
+ align:start position:0%
+equation so
+let's do that so what do we have I Bar D
+
+ align:start position:0%
+let's do that so what do we have I Bar D
+ 
+
+ align:start position:0%
+let's do that so what do we have I Bar D
+DT equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H we'll write it like that for the time
+
+ align:start position:0%
+H we'll write it like that for the time
+ 
+
+ align:start position:0%
+H we'll write it like that for the time
+being without copying all what H is that
+
+ align:start position:0%
+being without copying all what H is that
+ 
+
+ align:start position:0%
+being without copying all what H is that
+would take a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and uh from this
+
+ align:start position:0%
+time and uh from this
+ 
+
+ align:start position:0%
+time and uh from this
+equation you can find immediately that
+
+ align:start position:0%
+equation you can find immediately that
+ 
+
+ align:start position:0%
+equation you can find immediately that
+deep s
+
+ align:start position:0%
+deep s
+ 
+
+ align:start position:0%
+deep s
+DT is
+
+ align:start position:0%
+DT is
+ 
+
+ align:start position:0%
+DT is
+minus I over H
+
+ align:start position:0%
+minus I over H
+ 
+
+ align:start position:0%
+minus I over H
+bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H now we need to compx conjugate this
+
+ align:start position:0%
+H now we need to compx conjugate this
+ 
+
+ align:start position:0%
+H now we need to compx conjugate this
+equation and that it's always a little
+
+ align:start position:0%
+equation and that it's always a little
+ 
+
+ align:start position:0%
+equation and that it's always a little
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scary but
+
+ align:start position:0%
+scary but
+ 
+
+ align:start position:0%
+scary but
+um in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact it's um actually the way to do it
+
+ align:start position:0%
+fact it's um actually the way to do it
+ 
+
+ align:start position:0%
+fact it's um actually the way to do it
+is in a way that you never get into
+
+ align:start position:0%
+is in a way that you never get into
+ 
+
+ align:start position:0%
+is in a way that you never get into
+scary or strange things so let me take
+
+ align:start position:0%
+scary or strange things so let me take
+ 
+
+ align:start position:0%
+scary or strange things so let me take
+the complex conjugate of this equation
+
+ align:start position:0%
+the complex conjugate of this equation
+ 
+
+ align:start position:0%
+the complex conjugate of this equation
+here I would have I goes to minus i h
+
+ align:start position:0%
+here I would have I goes to minus i h
+ 
+
+ align:start position:0%
+here I would have I goes to minus i h
+bar and now I would have let me go very
+
+ align:start position:0%
+bar and now I would have let me go very
+ 
+
+ align:start position:0%
+bar and now I would have let me go very
+slow D
+
+ align:start position:0%
+slow D
+ 
+
+ align:start position:0%
+slow D
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+equals and then I'll be simple minded
+
+ align:start position:0%
+equals and then I'll be simple minded
+ 
+
+ align:start position:0%
+equals and then I'll be simple minded
+here I think it's the
+
+ align:start position:0%
+here I think it's the
+ 
+
+ align:start position:0%
+here I think it's the
+best I'll just start the right hand
+
+ align:start position:0%
+best I'll just start the right hand
+ 
+
+ align:start position:0%
+best I'll just start the right hand
+side I start the left hand side and
+
+ align:start position:0%
+side I start the left hand side and
+ 
+
+ align:start position:0%
+side I start the left hand side and
+start the right hand
+
+ align:start position:0%
+start the right hand
+ 
+
+ align:start position:0%
+start the right hand
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+now here the complex conjugate of a
+
+ align:start position:0%
+now here the complex conjugate of a
+ 
+
+ align:start position:0%
+now here the complex conjugate of a
+derivative in this case I want to
+
+ align:start position:0%
+derivative in this case I want to
+ 
+
+ align:start position:0%
+derivative in this case I want to
+clarify what it is it's just the
+
+ align:start position:0%
+clarify what it is it's just the
+ 
+
+ align:start position:0%
+clarify what it is it's just the
+derivative of the complex conjugate so
+
+ align:start position:0%
+derivative of the complex conjugate so
+ 
+
+ align:start position:0%
+derivative of the complex conjugate so
+this is minus I bar DDT of size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star equals H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hat star that's
+
+ align:start position:0%
+hat star that's
+ 
+
+ align:start position:0%
+hat star that's
+fine and From Here If I multiply Again
+
+ align:start position:0%
+fine and From Here If I multiply Again
+ 
+
+ align:start position:0%
+fine and From Here If I multiply Again
+by I ided by H bar we get deep SI star
+
+ align:start position:0%
+by I ided by H bar we get deep SI star
+ 
+
+ align:start position:0%
+by I ided by H bar we get deep SI star
+DT is equal
+
+ align:start position:0%
+DT is equal
+ 
+
+ align:start position:0%
+DT is equal
+to I over H
+
+ align:start position:0%
+to I over H
+ 
+
+ align:start position:0%
+to I over H
+star H
+
+ align:start position:0%
+star H
+ 
+
+ align:start position:0%
+star H
+hat
+
+ align:start position:0%
+hat
+ 
+
+ align:start position:0%
+hat
+star okay
+
+ align:start position:0%
+star okay
+ 
+
+ align:start position:0%
+star okay
+this we
+
+ align:start position:0%
+this we
+ 
+
+ align:start position:0%
+this we
+obtain this useful formula and this
+
+ align:start position:0%
+obtain this useful formula and this
+ 
+
+ align:start position:0%
+obtain this useful formula and this
+useful formula and both go into our
+
+ align:start position:0%
+useful formula and both go into our
+ 
+
+ align:start position:0%
+useful formula and both go into our
+calculation of DN
+
+ align:start position:0%
+calculation of DN
+ 
+
+ align:start position:0%
+calculation of DN
+DT so what do we have here the N
+
+ align:start position:0%
+DT so what do we have here the N
+ 
+
+ align:start position:0%
+DT so what do we have here the N
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+DX and I will put um an i over H bar I
+
+ align:start position:0%
+DX and I will put um an i over H bar I
+ 
+
+ align:start position:0%
+DX and I will put um an i over H bar I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I over H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar look at this term
+
+ align:start position:0%
+bar look at this term
+ 
+
+ align:start position:0%
+bar look at this term
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+you have I over H bar H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star p and the second term involves a d
+
+ align:start position:0%
+star p and the second term involves a d
+ 
+
+ align:start position:0%
+star p and the second term involves a d
+DT that comes with an opposite sign same
+
+ align:start position:0%
+DT that comes with an opposite sign same
+ 
+
+ align:start position:0%
+DT that comes with an opposite sign same
+factor of I over H bar so
+
+ align:start position:0%
+factor of I over H bar so
+ 
+
+ align:start position:0%
+factor of I over H bar so
+minus P
+
+ align:start position:0%
+minus P
+ 
+
+ align:start position:0%
+minus P
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh the virtue of what we've done
+
+ align:start position:0%
+okay so uh the virtue of what we've done
+ 
+
+ align:start position:0%
+okay so uh the virtue of what we've done
+so far is that uh it doesn't look so bad
+
+ align:start position:0%
+so far is that uh it doesn't look so bad
+ 
+
+ align:start position:0%
+so far is that uh it doesn't look so bad
+yet and uh looks relatively clean and uh
+
+ align:start position:0%
+yet and uh looks relatively clean and uh
+ 
+
+ align:start position:0%
+yet and uh looks relatively clean and uh
+it's very suggestive actually so what's
+
+ align:start position:0%
+it's very suggestive actually so what's
+ 
+
+ align:start position:0%
+it's very suggestive actually so what's
+happening we want to show that DN DT is
+
+ align:start position:0%
+happening we want to show that DN DT is
+ 
+
+ align:start position:0%
+happening we want to show that DN DT is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+now are we going to be able to show that
+
+ align:start position:0%
+now are we going to be able to show that
+ 
+
+ align:start position:0%
+now are we going to be able to show that
+simply that do a lot of algebra and say
+
+ align:start position:0%
+simply that do a lot of algebra and say
+ 
+
+ align:start position:0%
+simply that do a lot of algebra and say
+oh it's zero well it's kind of going to
+
+ align:start position:0%
+oh it's zero well it's kind of going to
+ 
+
+ align:start position:0%
+oh it's zero well it's kind of going to
+work that way but we're going to do the
+
+ align:start position:0%
+work that way but we're going to do the
+ 
+
+ align:start position:0%
+work that way but we're going to do the
+work and we're going to get to this DN
+
+ align:start position:0%
+work and we're going to get to this DN
+ 
+
+ align:start position:0%
+work and we're going to get to this DN
+DT being an integral of
+
+ align:start position:0%
+DT being an integral of
+ 
+
+ align:start position:0%
+DT being an integral of
+something and it's just not going to
+
+ align:start position:0%
+something and it's just not going to
+ 
+
+ align:start position:0%
+something and it's just not going to
+look like zero but it will be
+
+ align:start position:0%
+look like zero but it will be
+ 
+
+ align:start position:0%
+look like zero but it will be
+manipulated in such a way that you can
+
+ align:start position:0%
+manipulated in such a way that you can
+ 
+
+ align:start position:0%
+manipulated in such a way that you can
+argue it's zero using the boundary
+
+ align:start position:0%
+argue it's zero using the boundary
+ 
+
+ align:start position:0%
+argue it's zero using the boundary
+condition so it it's kind of interesting
+
+ align:start position:0%
+condition so it it's kind of interesting
+ 
+
+ align:start position:0%
+condition so it it's kind of interesting
+how it's going to work but here
+
+ align:start position:0%
+how it's going to work but here
+ 
+
+ align:start position:0%
+how it's going to work but here
+structurally you see what must happen
+
+ align:start position:0%
+structurally you see what must happen
+ 
+
+ align:start position:0%
+structurally you see what must happen
+for this calculation to succeed so we
+
+ align:start position:0%
+for this calculation to succeed so we
+ 
+
+ align:start position:0%
+for this calculation to succeed so we
+need for this to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero be
+
+ align:start position:0%
+zero be
+ 
+
+ align:start position:0%
+zero be
+zero we
+
+ align:start position:0%
+zero we
+ 
+
+ align:start position:0%
+zero we
+need the following thing to happen the
+
+ align:start position:0%
+need the following thing to happen the
+ 
+
+ align:start position:0%
+need the following thing to happen the
+integral of a
+
+ align:start position:0%
+integral of a
+ 
+
+ align:start position:0%
+integral of a
+hat p
+
+ align:start position:0%
+hat p
+ 
+
+ align:start position:0%
+hat p
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+P be equal to the
+
+ align:start position:0%
+P be equal to the
+ 
+
+ align:start position:0%
+P be equal to the
+integral of P star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H and I should write the
+
+ align:start position:0%
+H and I should write the
+ 
+
+ align:start position:0%
+H and I should write the
+DX's they are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so this would
+
+ align:start position:0%
+there so this would
+ 
+
+ align:start position:0%
+there so this would
+guarantee that d n DT is equal to zero
+
+ align:start position:0%
+guarantee that d n DT is equal to zero
+ 
+
+ align:start position:0%
+guarantee that d n DT is equal to zero
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's a very nice statement um and it's
+
+ align:start position:0%
+that's a very nice statement um and it's
+ 
+
+ align:start position:0%
+that's a very nice statement um and it's
+kind of nice is that right you have one
+
+ align:start position:0%
+kind of nice is that right you have one
+ 
+
+ align:start position:0%
+kind of nice is that right you have one
+function starred one function non
+
+ align:start position:0%
+function starred one function non
+ 
+
+ align:start position:0%
+function starred one function non
+starred once the H is with the function
+
+ align:start position:0%
+starred once the H is with the function
+ 
+
+ align:start position:0%
+starred once the H is with the function
+is to be starred but on the other side
+
+ align:start position:0%
+is to be starred but on the other side
+ 
+
+ align:start position:0%
+is to be starred but on the other side
+of the equation the H is on the other
+
+ align:start position:0%
+of the equation the H is on the other
+ 
+
+ align:start position:0%
+of the equation the H is on the other
+side so you've kind of moved the H from
+
+ align:start position:0%
+side so you've kind of moved the H from
+ 
+
+ align:start position:0%
+side so you've kind of moved the H from
+the complex conjugated function to the
+
+ align:start position:0%
+the complex conjugated function to the
+ 
+
+ align:start position:0%
+the complex conjugated function to the
+non-c complex conjugate function from
+
+ align:start position:0%
+non-c complex conjugate function from
+ 
+
+ align:start position:0%
+non-c complex conjugate function from
+the first function to the second
+
+ align:start position:0%
+the first function to the second
+ 
+
+ align:start position:0%
+the first function to the second
+function and that's a very nice thing to
+
+ align:start position:0%
+function and that's a very nice thing to
+ 
+
+ align:start position:0%
+function and that's a very nice thing to
+demand of the
+
+ align:start position:0%
+demand of the
+ 
+
+ align:start position:0%
+demand of the
+hamiltonian so actually what seems to be
+
+ align:start position:0%
+hamiltonian so actually what seems to be
+ 
+
+ align:start position:0%
+hamiltonian so actually what seems to be
+happening is that this conservation of
+
+ align:start position:0%
+happening is that this conservation of
+ 
+
+ align:start position:0%
+happening is that this conservation of
+probability will work if your
+
+ align:start position:0%
+probability will work if your
+ 
+
+ align:start position:0%
+probability will work if your
+hamiltonian is good enough to do
+
+ align:start position:0%
+hamiltonian is good enough to do
+ 
+
+ align:start position:0%
+hamiltonian is good enough to do
+something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and uh this is a nice formula it's
+
+ align:start position:0%
+this and uh this is a nice formula it's
+ 
+
+ align:start position:0%
+this and uh this is a nice formula it's
+a famous formula
+
+ align:start position:0%
+a famous formula
+ 
+
+ align:start position:0%
+a famous formula
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this thing holds this is
+
+ align:start position:0%
+this thing holds this is
+ 
+
+ align:start position:0%
+this thing holds this is
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+true if
+
+ align:start position:0%
+true if
+ 
+
+ align:start position:0%
+true if
+H is a Herm Mission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Operator so that's a very interesting
+
+ align:start position:0%
+Operator so that's a very interesting
+ 
+
+ align:start position:0%
+Operator so that's a very interesting
+new name that shows up that an operator
+
+ align:start position:0%
+new name that shows up that an operator
+ 
+
+ align:start position:0%
+new name that shows up that an operator
+being her missions
+
+ align:start position:0%
+being her missions
+ 
+
+ align:start position:0%
+being her missions
+so this is what I was promising you that
+
+ align:start position:0%
+so this is what I was promising you that
+ 
+
+ align:start position:0%
+so this is what I was promising you that
+we're going to do this and we're going
+
+ align:start position:0%
+we're going to do this and we're going
+ 
+
+ align:start position:0%
+we're going to do this and we're going
+to be learning all kinds of funny things
+
+ align:start position:0%
+to be learning all kinds of funny things
+ 
+
+ align:start position:0%
+to be learning all kinds of funny things
+as as it happens so what is it uh for a
+
+ align:start position:0%
+as as it happens so what is it uh for a
+ 
+
+ align:start position:0%
+as as it happens so what is it uh for a
+Herm Mission operator well a Herm
+
+ align:start position:0%
+Herm Mission operator well a Herm
+ 
+
+ align:start position:0%
+Herm Mission operator well a Herm
+Mission
+
+ align:start position:0%
+Mission
+ 
+
+ align:start position:0%
+Mission
+operator a Herm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mission
+
+ align:start position:0%
+Mission
+ 
+
+ align:start position:0%
+Mission
+H would actually satisfy the
+
+ align:start position:0%
+H would actually satisfy the
+ 
+
+ align:start position:0%
+H would actually satisfy the
+following actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfy that um the
+
+ align:start position:0%
+satisfy that um the
+ 
+
+ align:start position:0%
+satisfy that um the
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+H SI
+
+ align:start position:0%
+H SI
+ 
+
+ align:start position:0%
+H SI
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+star size 2 is equal to the integral of
+
+ align:start position:0%
+star size 2 is equal to the integral of
+ 
+
+ align:start position:0%
+star size 2 is equal to the integral of
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star h
+
+ align:start position:0%
+star h
+ 
+
+ align:start position:0%
+star h
+2 so the an operator is said to be her
+
+ align:start position:0%
+2 so the an operator is said to be her
+ 
+
+ align:start position:0%
+2 so the an operator is said to be her
+Mission if you can move it from the
+
+ align:start position:0%
+Mission if you can move it from the
+ 
+
+ align:start position:0%
+Mission if you can move it from the
+first part to the second part in this
+
+ align:start position:0%
+first part to the second part in this
+ 
+
+ align:start position:0%
+first part to the second part in this
+sense and with two different
+
+ align:start position:0%
+sense and with two different
+ 
+
+ align:start position:0%
+sense and with two different
+functions so this should be possible to
+
+ align:start position:0%
+functions so this should be possible to
+ 
+
+ align:start position:0%
+functions so this should be possible to
+do if an operator is to be called her
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mission now of course if it holds for
+
+ align:start position:0%
+Mission now of course if it holds for
+ 
+
+ align:start position:0%
+Mission now of course if it holds for
+two arbitrary function functions it
+
+ align:start position:0%
+two arbitrary function functions it
+ 
+
+ align:start position:0%
+two arbitrary function functions it
+holds when the two functions are the
+
+ align:start position:0%
+holds when the two functions are the
+ 
+
+ align:start position:0%
+holds when the two functions are the
+same and it's this case so what we need
+
+ align:start position:0%
+same and it's this case so what we need
+ 
+
+ align:start position:0%
+same and it's this case so what we need
+is a par case of the condition of
+
+ align:start position:0%
+is a par case of the condition of
+ 
+
+ align:start position:0%
+is a par case of the condition of
+hermiticity hermiticity means that the
+
+ align:start position:0%
+hermiticity hermiticity means that the
+ 
+
+ align:start position:0%
+hermiticity hermiticity means that the
+operator does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing any two functions that you put
+
+ align:start position:0%
+thing any two functions that you put
+ 
+
+ align:start position:0%
+thing any two functions that you put
+here this equality is
+
+ align:start position:0%
+here this equality is
+ 
+
+ align:start position:0%
+here this equality is
+true now if you ask yourself how do I
+
+ align:start position:0%
+true now if you ask yourself how do I
+ 
+
+ align:start position:0%
+true now if you ask yourself how do I
+even understand that what allows me to
+
+ align:start position:0%
+even understand that what allows me to
+ 
+
+ align:start position:0%
+even understand that what allows me to
+move the H from one side to the other
+
+ align:start position:0%
+move the H from one side to the other
+ 
+
+ align:start position:0%
+move the H from one side to the other
+we'll see it very soon but it's the fact
+
+ align:start position:0%
+we'll see it very soon but it's the fact
+ 
+
+ align:start position:0%
+we'll see it very soon but it's the fact
+that H has second derivatives and maybe
+
+ align:start position:0%
+that H has second derivatives and maybe
+ 
+
+ align:start position:0%
+that H has second derivatives and maybe
+you can integrate them by parts and move
+
+ align:start position:0%
+you can integrate them by parts and move
+ 
+
+ align:start position:0%
+you can integrate them by parts and move
+the derivatives from the P one to the p
+
+ align:start position:0%
+the derivatives from the P one to the p
+ 
+
+ align:start position:0%
+the derivatives from the P one to the p
+2 and do all kinds of things but you
+
+ align:start position:0%
+2 and do all kinds of things but you
+ 
+
+ align:start position:0%
+2 and do all kinds of things but you
+should try to think at this moment
+
+ align:start position:0%
+should try to think at this moment
+ 
+
+ align:start position:0%
+should try to think at this moment
+structurally what kind of objects you
+
+ align:start position:0%
+structurally what kind of objects you
+ 
+
+ align:start position:0%
+structurally what kind of objects you
+have what kind of properties you have
+
+ align:start position:0%
+have what kind of properties you have
+ 
+
+ align:start position:0%
+have what kind of properties you have
+and the object are this
+
+ align:start position:0%
+and the object are this
+ 
+
+ align:start position:0%
+and the object are this
+operator that controls the time
+
+ align:start position:0%
+operator that controls the time
+ 
+
+ align:start position:0%
+operator that controls the time
+Evolution called the hamiltonian and if
+
+ align:start position:0%
+Evolution called the hamiltonian and if
+ 
+
+ align:start position:0%
+Evolution called the hamiltonian and if
+I want probability interpretation to
+
+ align:start position:0%
+I want probability interpretation to
+ 
+
+ align:start position:0%
+I want probability interpretation to
+make sense we need this equality which
+
+ align:start position:0%
+make sense we need this equality which
+ 
+
+ align:start position:0%
+make sense we need this equality which
+is a consequence of
+
+ align:start position:0%
+is a consequence of
+ 
+
+ align:start position:0%
+is a consequence of
+hermiticity
+
+ align:start position:0%
+hermiticity
+ 
+
+ align:start position:0%
+hermiticity
+now I'll maybe use a little this
+
+ align:start position:0%
+now I'll maybe use a little this
+ 
+
+ align:start position:0%
+now I'll maybe use a little this
+Blackboard haven't used it much before
+
+ align:start position:0%
+Blackboard haven't used it much before
+ 
+
+ align:start position:0%
+Blackboard haven't used it much before
+um in terms of uh Herm Mission operators
+
+ align:start position:0%
+um in terms of uh Herm Mission operators
+ 
+
+ align:start position:0%
+um in terms of uh Herm Mission operators
+I'm almost there with the definition of
+
+ align:start position:0%
+I'm almost there with the definition of
+ 
+
+ align:start position:0%
+I'm almost there with the definition of
+a Herm Mission operator I I haven't
+
+ align:start position:0%
+a Herm Mission operator I I haven't
+ 
+
+ align:start position:0%
+a Herm Mission operator I I haven't
+quite given it to you but let's let's
+
+ align:start position:0%
+quite given it to you but let's let's
+ 
+
+ align:start position:0%
+quite given it to you but let's let's
+state it given that we're already in
+
+ align:start position:0%
+state it given that we're already in
+ 
+
+ align:start position:0%
+state it given that we're already in
+this uh discussion of
+
+ align:start position:0%
+this uh discussion of
+ 
+
+ align:start position:0%
+this uh discussion of
+hermeticity
+
+ align:start position:0%
+hermeticity
+ 
+
+ align:start position:0%
+hermeticity
+so this is what is called a Herm Mission
+
+ align:start position:0%
+so this is what is called a Herm Mission
+ 
+
+ align:start position:0%
+so this is what is called a Herm Mission
+operator does that but in
+
+ align:start position:0%
+operator does that but in
+ 
+
+ align:start position:0%
+operator does that but in
+general in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given an operator
+
+ align:start position:0%
+given an operator
+ 
+
+ align:start position:0%
+given an operator
+t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defines its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conjugate t dager as follows so you have
+
+ align:start position:0%
+conjugate t dager as follows so you have
+ 
+
+ align:start position:0%
+conjugate t dager as follows so you have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+integral of P 1
+
+ align:start position:0%
+integral of P 1
+ 
+
+ align:start position:0%
+integral of P 1
+star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P2 and that must be rearranged until it
+
+ align:start position:0%
+P2 and that must be rearranged until it
+ 
+
+ align:start position:0%
+P2 and that must be rearranged until it
+looks like T
+
+ align:start position:0%
+looks like T
+ 
+
+ align:start position:0%
+looks like T
+dagger P
+
+ align:start position:0%
+dagger P
+ 
+
+ align:start position:0%
+dagger P
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+star p
+
+ align:start position:0%
+star p
+ 
+
+ align:start position:0%
+star p
+2 now these things of are the beginning
+
+ align:start position:0%
+2 now these things of are the beginning
+ 
+
+ align:start position:0%
+2 now these things of are the beginning
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+whole set of ideas that are terribly
+
+ align:start position:0%
+whole set of ideas that are terribly
+ 
+
+ align:start position:0%
+whole set of ideas that are terribly
+important in quantum mechanics her
+
+ align:start position:0%
+important in quantum mechanics her
+ 
+
+ align:start position:0%
+important in quantum mechanics her
+Mission operators their igon values and
+
+ align:start position:0%
+Mission operators their igon values and
+ 
+
+ align:start position:0%
+Mission operators their igon values and
+igen vectors so it's going to take a
+
+ align:start position:0%
+igen vectors so it's going to take a
+ 
+
+ align:start position:0%
+igen vectors so it's going to take a
+little time for you to get accustomed to
+
+ align:start position:0%
+little time for you to get accustomed to
+ 
+
+ align:start position:0%
+little time for you to get accustomed to
+them but this is the beginning you will
+
+ align:start position:0%
+them but this is the beginning you will
+ 
+
+ align:start position:0%
+them but this is the beginning you will
+explore a little bit of these things in
+
+ align:start position:0%
+explore a little bit of these things in
+ 
+
+ align:start position:0%
+explore a little bit of these things in
+future homework and start getting
+
+ align:start position:0%
+future homework and start getting
+ 
+
+ align:start position:0%
+future homework and start getting
+familiar if now it looks very strange
+
+ align:start position:0%
+familiar if now it looks very strange
+ 
+
+ align:start position:0%
+familiar if now it looks very strange
+and UNM motivate that maybe um you will
+
+ align:start position:0%
+and UNM motivate that maybe um you will
+ 
+
+ align:start position:0%
+and UNM motivate that maybe um you will
+see that that will change soon even
+
+ align:start position:0%
+see that that will change soon even
+ 
+
+ align:start position:0%
+see that that will change soon even
+throughout the to today's
+
+ align:start position:0%
+throughout the to today's
+ 
+
+ align:start position:0%
+throughout the to today's
+lecture so this is the hermiss conjugate
+
+ align:start position:0%
+lecture so this is the hermiss conjugate
+ 
+
+ align:start position:0%
+lecture so this is the hermiss conjugate
+so you if you want to calculate the Herm
+
+ align:start position:0%
+so you if you want to calculate the Herm
+ 
+
+ align:start position:0%
+so you if you want to calculate the Herm
+missan conjugate you must start with
+
+ align:start position:0%
+missan conjugate you must start with
+ 
+
+ align:start position:0%
+missan conjugate you must start with
+this thing and start doing manipulations
+
+ align:start position:0%
+this thing and start doing manipulations
+ 
+
+ align:start position:0%
+this thing and start doing manipulations
+to clean up the p 2 have nothing act on
+
+ align:start position:0%
+to clean up the p 2 have nothing act on
+ 
+
+ align:start position:0%
+to clean up the p 2 have nothing act on
+p 2 everything acting on P one and that
+
+ align:start position:0%
+p 2 everything acting on P one and that
+ 
+
+ align:start position:0%
+p 2 everything acting on P one and that
+thing is called the dagger and then
+
+ align:start position:0%
+thing is called the dagger and then
+ 
+
+ align:start position:0%
+thing is called the dagger and then
+finally T is her
+
+ align:start position:0%
+finally T is her
+ 
+
+ align:start position:0%
+finally T is her
+mission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if T dagger is equal to
+
+ align:start position:0%
+if T dagger is equal to
+ 
+
+ align:start position:0%
+if T dagger is equal to
+T so if it's her Mission conjugate is
+
+ align:start position:0%
+T so if it's her Mission conjugate is
+ 
+
+ align:start position:0%
+T so if it's her Mission conjugate is
+itself it's almost like people say a
+
+ align:start position:0%
+itself it's almost like people say a
+ 
+
+ align:start position:0%
+itself it's almost like people say a
+real number is a number whose complex
+
+ align:start position:0%
+real number is a number whose complex
+ 
+
+ align:start position:0%
+real number is a number whose complex
+conjugate is equal to itself so a Herm
+
+ align:start position:0%
+conjugate is equal to itself so a Herm
+ 
+
+ align:start position:0%
+conjugate is equal to itself so a Herm
+Mission op operator is one whose Herm
+
+ align:start position:0%
+Mission op operator is one whose Herm
+ 
+
+ align:start position:0%
+Mission op operator is one whose Herm
+Mission conjugate is equal to itself and
+
+ align:start position:0%
+Mission conjugate is equal to itself and
+ 
+
+ align:start position:0%
+Mission conjugate is equal to itself and
+you see if if T is her Mission well then
+
+ align:start position:0%
+you see if if T is her Mission well then
+ 
+
+ align:start position:0%
+you see if if T is her Mission well then
+it's back to T and T in both places
+
+ align:start position:0%
+it's back to T and T in both places
+ 
+
+ align:start position:0%
+it's back to T and T in both places
+which is what we've been saying here
+
+ align:start position:0%
+which is what we've been saying here
+ 
+
+ align:start position:0%
+which is what we've been saying here
+this is a hermiss
+
+ align:start position:0%
+this is a hermiss
+ 
+
+ align:start position:0%
+this is a hermiss
+operator
\ No newline at end of file
diff --git a/5uTd3WzQulo.txt b/5uTd3WzQulo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..13aff387eeb64db827c218cacbe8a699b456793c
--- /dev/null
+++ b/5uTd3WzQulo.txt
@@ -0,0 +1,4338 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, interactive
+teaching.
+
+Here is a famous graph produced
+by Benjamin bloom and
+
+his students.
+
+So here on this axis is
+student achievement.
+
+So after a course is
+over, students are
+
+tested on the material.
+
+And here's their score.
+
+And this is the percentage
+who attained each score.
+
+So here, they compared three
+methods of teaching, but I'll
+
+just compare two.
+
+So one method is standard
+one-group instruction, say
+
+one-to-30, or today,
+maybe one-to-90.
+
+And here is the histogram, the
+distribution of students'
+
+scores, nicely spread out.
+
+Now, by itself, it
+doesn't say much.
+
+But what's really interesting is
+the distribution base after
+
+the same amount of teaching, but
+done in a tutorial form,
+
+with one-to-one or
+maybe one-to-two.
+
+You can put some quantitative
+figures on this
+
+from Bloom's results.
+
+The average--
+
+so this is one-to-one
+tutoring, one-to-30.
+
+The average tutorial student is
+two sigmas better than the
+
+group students.
+
+In other words, the average
+tutorial student is at the
+
+98th percentile of the ordinary
+teaching group.
+
+So the question is--
+
+the natural question is, how can
+we make group instruction
+
+as effective as tutorial
+instruction?
+
+As Benjamin Bloom says, he says,
+finding such methods
+
+would be an educational
+contribution of
+
+the greatest magnitude.
+
+Because, for example,
+it would change our
+
+notions about human potential.
+
+We'd actually realize, oh,
+actually, there's not that
+
+much innate in what
+people can do.
+
+Most of it is how well they've
+learned, how well
+
+they've been taught.
+
+So the great question--
+
+and it's the title of Bloom's
+paper-- is the search for
+
+methods of group instruction
+as effective
+
+as one-to-one tutoring.
+
+To that end, let's think about
+the following question, which
+
+is, what makes tutoring
+so effective?
+
+So I'm going to ask you that,
+to consider that question in
+
+groups of two and three,
+whatever's sort of convenient
+
+in your region of the room.
+
+So, what makes tutoring
+so effective?
+
+After you discuss, we'll take
+reasons, put them on the
+
+board, and then I'll show you
+methods of group instruction
+
+that may not quite get us all
+the way to tutoring, but that
+
+answer many of the good
+characteristics of tutoring
+
+and bring them into
+group instruction.
+
+OK, so please find one
+or two neighbors.
+
+Introduce yourselves.
+
+You never know.
+
+You might find a teaching
+colleague.
+
+And think about what makes
+tutoring so effective.
+
+OK, so take 30 seconds
+and collect
+
+your thoughts together.
+
+OK, who would like to suggest
+something that your group
+
+thought of?
+
+You don't necessarily have to
+believe it, just something you
+
+discussed and think
+we should share.
+
+Yes?
+
+Could you tell me your name?
+
+AUDIENCE: Elena.
+
+PROFESSOR: Elena.
+
+AUDIENCE: For one-on-one
+tutoring, I imagine there's
+
+less time for misconceptions
+to get
+
+ingrained in your brain.
+
+PROFESSOR: OK, you can nip
+misconceptions in the bud.
+
+Whereas in, for example, group
+instruction, you may not even
+
+know the students have
+a misconception
+
+until the final exam.
+
+Then what do you do?
+
+OK, let's see.
+
+This group, could you
+tell me your name?
+
+AUDIENCE: So we thought--
+
+PROFESSOR: Could you
+tell me your name?
+
+AUDIENCE: Eric.
+
+PROFESSOR: Eric.
+
+AUDIENCE: We thought in a group,
+there's probably a lot
+
+of just dissemination
+of information.
+
+And in one-on-one tutoring, it's
+probably not one person
+
+just telling person two
+a bunch of stuff.
+
+It's going through
+exam problems.
+
+PROFESSOR: Right, OK.
+
+So the contrast in this is
+what does the teaching
+
+situation look like?
+
+In a typical lecture, someone
+may just talk at you for 50
+
+minutes, whereas it's hard to
+imagine a one-on-one tutorial
+
+situation where you walk in for
+your tutorial, and they
+
+just talk at you
+for 50 minutes.
+
+That would seem so odd and so
+counter to all conventions of
+
+human discussion.
+
+It would take a really, really
+disciplined and well-trained
+
+person to sit still for 50
+minutes for that kind of
+
+treatment, so not initially a
+good kind of training either.
+
+OK, so I'll say you cannot
+yammer at the audience for 50
+
+minutes straight.
+
+Yes, can you tell
+me your name?
+
+AUDIENCE: Sorry?
+
+PROFESSOR: Could you
+tell me your name?
+
+AUDIENCE: I'm Whitney.
+
+PROFESSOR: Whitney
+
+AUDIENCE: I think it follows
+from this discussion that
+
+arises between two people that
+the student experiences
+
+validation of what they've
+understood, and it helps build
+
+their confidence.
+
+PROFESSOR: OK, because they're
+talking in a small group, so
+
+they can get validation
+in a safe setting.
+
+Is that?
+
+OK, so it's safe.
+
+It's a safe setting for raising
+ideas maybe that
+
+you're not sure about.
+
+OK, there was one more.
+
+Yeah, can you tell
+me your name?
+
+AUDIENCE: Martin.
+
+PROFESSOR: Martin.
+
+AUDIENCE: Yeah.
+
+With tutoring, it's much easier
+to identify exactly
+
+what the student has trouble
+understanding, and then tailor
+
+the teaching according
+to that.
+
+PROFESSOR: OK, so you can tailor
+the teaching according
+
+to what you find out.
+
+So sort of like the new
+electronic SATs.
+
+According to what you don't
+know or do know, in each
+
+question, they give you
+questions based on your
+
+previous answers at the right
+level of difficulty.
+
+So you can tailor.
+
+Yeah, can you tell
+me your name?
+
+AUDIENCE: Azrael.
+
+PROFESSOR: Azrael, yeah.
+
+AUDIENCE: I think related to
+this, it's very valuable to be
+
+able to tailor your teaching
+style to the student
+
+[INAUDIBLE]
+
+in general, not just specific
+points [INAUDIBLE].
+
+PROFESSOR: OK, you can
+tailor the teaching
+
+style to the student.
+
+If, for example, the
+student is--
+
+for example, suppose you're
+teaching math to somebody
+
+who's an architect.
+
+Well, you can use lots of
+examples that are particular
+
+to something they're totally
+fascinated by.
+
+You can tailor a teaching
+method.
+
+OK, let me get something from
+somewhere back there, in case
+
+I've been neglecting people
+way in the back.
+
+Oh, go ahead.
+
+You guys had your chance.
+
+I'll be back.
+
+Can you tell me your name?
+
+AUDIENCE: Graham.
+
+PROFESSOR: Graham.
+
+AUDIENCE: Just the level of
+engagement, it is impossible
+
+to sit there in a one-on-one
+setting and think about the
+
+music you like [INAUDIBLE]
+
+the subject matter at hand.
+
+PROFESSOR: Right.
+
+OK, so the level of engagement
+is much higher in a tutorial.
+
+So that's the complement
+of this one.
+
+So the student engagement
+is much higher.
+
+Yeah, just as it's hard for a
+teacher in a tutorial setting
+
+to just talk for 50 minutes
+straight, it's also hard for a
+
+student in a tutorial session to
+surf the web for 50 minutes
+
+straight, or use their
+BlackBerry or read the
+
+newspaper or whatever it may be
+that the standard methods
+
+of lecture distraction are.
+
+Yes, can you tell
+me your name?
+
+AUDIENCE: Question about
+the conditions in these
+
+experiments.
+
+So normally in a university
+setting in this country,
+
+tutoring is something that
+students seek out for
+
+themselves.
+
+It's not something that's
+provided in lieu of lecture.
+
+Was that the case in this?
+
+Was it really just that the same
+material was covered in
+
+the same semester and they
+just did it two different
+
+ways, and everybody had
+to go to tutoring?
+
+PROFESSOR: Yeah, so what
+they did was--
+
+I don't think these were
+university students.
+
+I think these were high
+school and even
+
+grade school students.
+
+Yeah.
+
+But what they did was they
+took the same number of
+
+teaching hours, and they either
+taught them in lecture
+
+or they taught them in
+tutorials, one-on-one, or I
+
+think sometimes one-on-two.
+
+AUDIENCE: So in both cases, they
+were required to go to
+
+class, in a sense.
+
+PROFESSOR: Yeah.
+
+I mean, I don't know
+if they actually
+
+went to the big class.
+
+But I'm sure they went to
+the tutorial class.
+
+That's partly of one
+of the differences.
+
+That's number six.
+
+Yes, way in the back.
+
+AUDIENCE: From experience,
+I've found that you know
+
+students don't understand
+something.
+
+You don't why until
+you sit down.
+
+Usually you find there's some
+gaping hole that's quite often
+
+easily plugged.
+
+PROFESSOR: OK.
+
+And how do you find that out?
+
+AUDIENCE: You start asking them,
+what class did you have?
+
+What did you not understand?
+
+And sometimes they'll just
+bubble [? right out, ?]
+
+I never got this one
+key concept.
+
+PROFESSOR: OK, so you can ask
+them questions, specific
+
+questions to figure out what
+they don't know, to diagnose
+
+what they're confused about.
+
+OK, let's take one more, and
+then I'll show you some
+
+methods that hopefully address
+what these characteristics--
+
+these missing characteristics
+of group instruction.
+
+Yes?
+
+AUDIENCE: On one-on-one
+tutoring, for the student who
+
+might not be as into the effort
+[INAUDIBLE] added
+
+pressure, just feeling that
+there are other people
+
+[INAUDIBLE]
+
+student, there's no feeling of
+why I need to learn much more,
+
+[INAUDIBLE].
+
+You don't really prepare
+yourself for anyone else.
+
+PROFESSOR: Right, so the
+method of teaching
+
+automatically adjusts to
+whatever level the student is.
+
+So they're not comparing
+to other people.
+
+They're are actually just
+comparing to what they don't
+
+know right then.
+
+So let's just call it intrinsic
+comparison with the
+
+knowledge, rather than extrinsic
+with other students.
+
+OK, so there's less emotional
+churn as a result of that.
+
+OK, so we could continue
+this list, but this is
+
+an excellent start.
+
+So now, if we look through that
+list, there's several
+
+themes that come out.
+
+I mean, it's hard in a group
+setting to figure out what
+
+students don't know.
+
+It's hard to ask
+them questions.
+
+It's hard to keep
+people engaged.
+
+It's easy to just talk at
+people as a teacher.
+
+So what can we do in group
+teaching to capture as many
+
+characteristics of
+this as we can?
+
+Well, I'll show you methods that
+I divide into four time
+
+scales, ranging from
+short to long.
+
+But before I do that, let me ask
+if there are any questions
+
+on anything so far.
+
+OK.
+
+You were first.
+
+AUDIENCE: How is student
+achievement measured?
+
+Is it just test scores?
+
+PROFESSOR: Yeah, that
+was a test score.
+
+So what they did is, actually
+they gave them a test.
+
+Like, if it was algebra, they
+gave them an algebra test, and
+
+then tested them at the end, and
+at the beginning too, just
+
+to see where they were
+to start with.
+
+AUDIENCE: So were the lectures
+more tailored to just teaching
+
+them algebra, and the tutoring
+was specifically tailored to
+
+doing problems in algebra?
+
+PROFESSOR: Well, the tutoring
+was whatever they needed to do
+
+well on the test.
+
+And the lecturing was hopefully
+
+designed that way too.
+
+But it had all the flaws of, you
+want to teach so students
+
+will do well on your
+final exam.
+
+But what do you do
+when you have 30
+
+diverse students in there?
+
+You had a question too.
+
+AUDIENCE: I was just wondering,
+do we know which of
+
+these particular suggestions
+are the most important, and
+
+which ones might be good?
+
+PROFESSOR: We have some idea.
+
+Good question.
+
+The question is which of these
+is most important, and which
+
+is less important.
+
+Actually, they're all getting
+at something similar.
+
+But there's a middle group in
+there, actually, that they
+
+studied, which was
+mastery learning.
+
+So mastery learning, it's just
+like a programmed instruction.
+
+So the idea is that--
+
+Keller Plan is another
+word for it.
+
+So mastery learning is midway
+between tutoring and group
+
+instruction.
+
+There was one sigma better,
+so 84th percentile.
+
+So mastery learning, you don't
+go on to the new topics until
+
+you pass the mastery exam
+on the previous topic.
+
+So you're always building
+on a solid foundation.
+
+And so you work until you can
+pass the exam, and then you
+
+continue on.
+
+And just by adding that to group
+instruction, you get one
+
+sigma better.
+
+So right away, diagnosing
+misconceptions, you can see,
+
+is quite important.
+
+But there's still another
+one sigma to get.
+
+And so that's, I think,
+what all the rest of
+
+these items are about.
+
+And we do know a lot of stuff
+about how people learn.
+
+One of it is questions.
+
+Questions are essential.
+
+So I'm going to talk
+about that.
+
+But let me just ask again,
+any questions?
+
+OK, good.
+
+This time it worked.
+
+So now, what did I do?
+
+So this is actually
+the first method.
+
+So how long did I wait after
+I said, any questions?
+
+Half a second?
+
+One minute?
+
+No, five seconds.
+
+So the first time, I didn't
+wait five seconds, because
+
+actually a question came up a
+little before five seconds.
+
+But this time, the second time,
+I waited five seconds.
+
+Now, why is that?
+
+So that is the first method.
+
+When you ask a question--
+
+for example, "any questions"
+or "what do you think about
+
+this"-- wait five seconds.
+
+And I'll explain why
+in a second.
+
+But, methods shortest
+to longest.
+
+The reason I divide them by
+shortest to longest is the
+
+shortest ones are
+the easiest to
+
+incorporate into your teaching.
+
+So anytime you teach, if you
+ask a question, wait five
+
+seconds, so the five-second
+time scale.
+
+OK, so why do I wait
+five seconds,
+
+and why not two seconds?
+
+Well, the reason is, think
+about your audience.
+
+Suppose you're talking away at
+them, and all the sudden you
+
+ask a question.
+
+Now, what are they hearing?
+
+So everyone's seen
+Charlie Brown?
+
+So what does Charlie Brown hear
+when he goes to school?
+
+Wah wah wah wah wah wah wah wah
+wah wah wah wah, and all
+
+of a sudden that changes
+and there's a question.
+
+It takes about a second to
+realize that the wah wah wah
+
+has stopped, and you're being
+asked a question.
+
+OK, so one second's gone.
+
+Let's call it that, the
+thumb-- one second.
+
+Now, it takes about another
+second to even figure out what
+
+the question is.
+
+Now you say, oh yeah, there's
+a question being asked.
+
+What did they say?
+
+OK, maybe now let's say it's
+one and a half seconds.
+
+So now we're at somewhere
+between two and three seconds.
+
+Now it takes maybe one or two
+more seconds to figure out
+
+what you're going to
+say about that.
+
+Do I have any thoughts
+about it?
+
+Do I actually have
+any questions?
+
+Do I have a thought about the
+thing they're asking me?
+
+Do I know what the band gap is
+in silicon, whatever the
+
+question may be?
+
+So now we're somewhere between
+four, maybe near five seconds.
+
+And then it maybe takes another
+second to get the
+
+courage up to raise your hand
+and be ready with a sentence.
+
+So now we're at least
+five seconds.
+
+So if you don't wait those five
+seconds, what you'll get
+
+is, you'll be getting a few
+questions, but you'll get
+
+questions from people who
+already thought about the
+
+material, in other words, the
+people who are already at the
+
+98th percentile.
+
+But if you want to bring
+everybody in, and get
+
+everybody thinking about it,
+you really need to wait, so
+
+you don't get questions just
+from the usual suspects.
+
+So wait five seconds.
+
+Now, the mechanism is
+quite important.
+
+If you just say, OK I'm going
+to wait five seconds, you'll
+
+go, any questions.
+
+Oh, done, five seconds is up.
+
+And you'll think five seconds
+is up in about one second.
+
+And why is that?
+
+Well, you're up in front of a
+whole bunch of people, and the
+
+adrenaline will be flowing.
+
+And adrenaline speeds
+up your time sense.
+
+All those stories about people
+who-- like mothers who saw
+
+their kid about to get hit by
+the car, they race out and
+
+grab the kid and the
+car keeps going.
+
+Maybe it screeches to a stop.
+
+They've managed to
+rescue their kid.
+
+Well, they could act much faster
+because adrenaline
+
+makes the time sense
+much sharper.
+
+So your idea of five seconds
+will be more like one second.
+
+There's another reason, which is
+there's this mistaken idea
+
+that if you're not talking,
+you're not teaching.
+
+So you're being paid to teach.
+
+And oh my god, you're
+not saying anything.
+
+That means you must not
+know something.
+
+So you feel insecure, and that
+increases the adrenaline and
+
+only speeds up the time
+problem more.
+
+So to wait five seconds, you
+actually have to count it --
+
+one 1,000, two 1,000, three
+1,000, four 1,000, five 1,000.
+
+And I actually sometimes just
+do it behind my back with my
+
+hand-- one 1,000, two
+1,000, three 1,000,
+
+four 1,000, five 1,000.
+
+And it's not like you have to
+be watching the audience for
+
+the whole five seconds.
+
+It's actually better to wait
+the whole five seconds, and
+
+then choose one of the hands
+that has gone up rather than
+
+the first hand that goes
+up at two seconds.
+
+You say, oh, thank god, somebody
+asked a question.
+
+OK, now my waiting is over.
+
+Well, again, you'll be back
+in the usual suspect soup.
+
+So, first time scale for
+bringing in questions, in
+
+other words, spreading the
+engagement through the class.
+
+Because when people are asking
+questions, they're by
+
+definition engaged.
+
+They're struggling with
+the material.
+
+They're trying to make
+it their own.
+
+Wait five seconds.
+
+OK, the next method.
+
+So the next method is short
+time scale, one minute.
+
+And that is to use a feedback
+sheet at the end of every
+
+teaching session.
+
+So you actually have an example
+of a feedback sheet
+
+that we'll ask you to fill out
+at the end of this session,
+
+which we handed out
+at the beginning.
+
+And the blank versions of that
+sheet will also be on the TLL
+
+website, so you can actually
+download it, print it, and use
+
+it in your own teaching,
+as well as my notes
+
+on how to use it.
+
+But the main point is that at
+the end of the class, you give
+
+the students one or two
+minutes to fill
+
+out a feedback sheet.
+
+And what I've converged on is
+the following three questions
+
+on my feedback sheet, which is,
+what was most confusing?
+
+Basically, what question
+you have that
+
+still wasn't answered.
+
+Second question is, what was
+the most useful or most
+
+useless example or demonstration
+or teaching
+
+method that happened today?
+
+And the third question is,
+any other comments?
+
+So now let me explain why I
+use those three questions.
+
+The first question, these sheets
+are all anonymous.
+
+And it's a chance for someone,
+if they felt a little bit shy
+
+asking questions in front of
+people-- so here in the
+
+tutorial, one of the
+characteristics that was
+
+mentioned was that you don't
+feel nervous about asking a
+
+question, because there's no
+one there, or maybe there's
+
+one other person there.
+
+Whereas in a class of
+30 or 80 or 20, you
+
+may feel a bit nervous.
+
+Well, if you feel a bit nervous,
+you just put your
+
+question on the feedback
+sheet.
+
+And so then at the beginning of
+the next session, I answer
+
+all the questions on the
+feedback sheets.
+
+So it takes me more than one
+minute, but actually not that
+
+much longer.
+
+Because you could
+flip through 100
+
+sheets in about 10 minutes.
+
+You just glance through.
+
+You'll see a bunch of questions
+are repeated.
+
+And you'll say, oh yeah, I do
+really need to explain that.
+
+And at the beginning in the next
+session, just explain all
+
+the important points.
+
+And that has another benefit,
+which is that it links back to
+
+the previous lecture, or the
+previous teaching session.
+
+So now you've made a thread
+between the previous session
+
+and the current one, and you got
+everyone up to speed into
+
+the space where you
+want them to be.
+
+So that's why I use the
+first question.
+
+The second question
+is, what worked?
+
+What didn't work?
+
+And I also had to add, and tell
+me whether it worked or
+
+didn't work.
+
+Because I used to get examples
+saying, that example.
+
+And I didn't know whether they
+loved it or hated it.
+
+So then I said, please
+tell me the sign of
+
+the effect as well.
+
+And then I would know.
+
+I would start to build a model
+of how students think and what
+
+works for them.
+
+So every time, basically, I
+learned that I brought in a
+
+demonstration, there
+was universal love
+
+on the second question.
+
+So I said, OK, that really
+connects with students.
+
+And I would make sure
+to do more of that.
+
+So it was reinforcement for me
+and practice for me at being a
+
+better teacher.
+
+And what you'll find is that as
+you use the sheet more and
+
+more, you get better and better
+at predicting how
+
+students think.
+
+So for example, you're doing
+some discussion on the board,
+
+some examples on derivation.
+
+And the first time you do it,
+maybe you don't know it's not
+
+going to go well.
+
+And then you read the sheet and
+you see, oh my god, I was
+
+a disaster.
+
+30 questions out of 80 all said,
+I didn't understand x.
+
+So now you understand that
+students didn't understand the
+
+way you did it.
+
+Well, now you've built
+a better model of
+
+how students think.
+
+So next time you're doing a
+derivation, what you'll find
+
+is-- at least what I've found
+is in the middle of the
+
+derivation, I'll realize, oh,
+this is not going well.
+
+I'm going to get a
+lot of questions
+
+about this on the sheet.
+
+Oops, but it's to late.
+
+I'm in the middle of the soup.
+
+I can't un-drink the soup.
+
+So I just finish the soup and
+just wait for the questions.
+
+But then after maybe another
+week of using the sheet, you
+
+actually have quite a good
+model of the students.
+
+And now before you start the
+derivation or when you're
+
+planning the lecture, you
+realize, oh yeah, that's not
+
+going to go well.
+
+Let me do it the other
+way, because I
+
+know that works better.
+
+So you'll find your model of the
+students developing more
+
+and more refinements and
+more and more accuracy.
+
+In other words, you're becoming
+
+a more expert teacher.
+
+And then the third question
+on the sheet
+
+is, any other comments?
+
+The reason for that is, it's
+just a free-form space.
+
+And I've actually had students
+say, oh, actually, when you
+
+explained that thing, you
+actually explained it wrong.
+
+I was like, oh that's
+good to know.
+
+So then in the beginning
+of the--
+
+because we did it properly in
+this other class, and here's
+
+the exact reference that you
+maybe didn't know about.
+
+I was like, oh great.
+
+So at the beginning of the next
+class, I say, hey, one of
+
+you guys pointed out a mistake
+I made, and here is the
+
+corrected version.
+
+And people might not be
+willing to say that
+
+personally, because they say,
+oh my god, I don't want to
+
+correct the professor and
+make them feel stupid.
+
+But it's much easier to do
+it on an anonymous sheet.
+
+So I get really useful
+information on that.
+
+And sometimes you can figure out
+who did it, so you could
+
+send an email saying, oh thanks,
+that was useful.
+
+All right.
+
+[LAUGHTER]
+
+PROFESSOR: And it is.
+
+So you may think, oh no, you
+don't want to be corrected.
+
+But actually, after you tell
+the students the following
+
+enough, so it's again
+back to this.
+
+In a group, students feel like,
+oh my god, I don't want
+
+to make a mistake.
+
+So I give them the following
+speech quite often.
+
+Because if you don't
+make mistakes--
+
+I tell them, look, how
+much did you know
+
+when you were born?
+
+Not a hell of a lot.
+
+You couldn't talk.
+
+You couldn't hardly walk.
+
+Well, how do you learn stuff?
+
+Did you just all the sudden
+start walking and talking?
+
+No.
+
+You mangled your grammar.
+
+You put "-ed" at the end of
+every past participle, even
+
+though some don't have that.
+
+And eventually you sorted it
+all out and you stood up
+
+straight and you walked.
+
+So basically, how
+did you learn?
+
+By making mistakes.
+
+So the only way to learn
+is to make mistakes.
+
+So if you don't make any
+mistakes, you will learn--
+
+you'll know as much at the start
+of your class as at the
+
+end of the class.
+
+So you want to make mistakes.
+
+So I tell them that
+a bunch of times.
+
+But if then I'm really
+embarrassed about making
+
+mistakes, then I've defeated the
+whole purpose of telling
+
+students that.
+
+So I actually thank them
+whenever they point out
+
+something that I didn't
+do right.
+
+OK, so that's the second
+time scale.
+
+Now, the third time scale
+is not that much longer.
+
+It's about, let's say,
+four or five minutes.
+
+And it's a question which I'll
+call a conceptual multiple
+
+choice question.
+
+And I'll give you an example.
+
+OK, so here is the question
+that I'll use
+
+to illustrate it.
+
+Here is a pyramid with
+a square base.
+
+And it's B by B. The length of
+one side of the base is B. And
+
+the perpendicular height of
+the pyramid is H. OK, so
+
+what's the volume?
+
+OK, so does everyone understand
+the question?
+
+OK.
+
+Give it a try.
+
+Find your group or one or two.
+
+Any questions--
+
+any confusions about
+the question?
+
+Don't give me any answers just
+yet, but any confusions about
+
+the question?
+
+OK, so find your groups of one
+or two other people, and we'll
+
+discuss that question
+in a couple minutes.
+
+Anyone want to say anything
+about this?
+
+Is there a section I
+haven't heard from?
+
+Yeah, go ahead.
+
+Can you just say your name?
+
+AUDIENCE: Brian.
+
+PROFESSOR: Brian, OK.
+
+So you like D but
+not the others?
+
+OK, can you tell me, for
+example, why you don't like A?
+
+AUDIENCE: Well, because all of
+them just have the wrong
+
+proportionality.
+
+If B increases, then the square
+is going to increase in
+
+area as B squared--
+
+PROFESSOR: Ah, so you would
+like that to B squared.
+
+AUDIENCE: Right.
+
+PROFESSOR: Whereas it's just a
+single B and a single H. OK,
+
+so you don't like that because
+the proportionality is wrong.
+
+It doesn't scale correctly.
+
+So let me put here,
+bad scaling.
+
+What was another problem?
+
+AUDIENCE: It also has
+the wrong units.
+
+PROFESSOR: It has bogus units.
+
+OK, so it has bogus
+dimensions.
+
+AUDIENCE: [INAUDIBLE]
+dimensions.
+
+PROFESSOR: No, they're pretty
+much interchangeable.
+
+I use units to mean meters
+or feet or something, and
+
+dimensions to be things
+like length.
+
+But they're pretty much
+interchangeable in usage.
+
+So bad scaling, bad
+dimensions.
+
+OK, anyone have any
+comments about B?
+
+AUDIENCE: Same.
+
+PROFESSOR: Same problem.
+
+In fact, it's even
+more horrendous.
+
+Well, it starts out OK, I
+mean, at least as far as
+
+dimensions are concerned.
+
+But then what does it do?
+
+This has the wrong dimensions.
+
+That has the right dimensions,
+and then you add them.
+
+That's terrible.
+
+OK, so the dimensions
+are just bogus.
+
+Ah, OK.
+
+Can anyone say anything
+about choice C?
+
+Yeah?
+
+AUDIENCE: If you look at the
+extremes, like if you make H
+
+very small--
+
+PROFESSOR: So if you stop on
+this pyramid and step on it
+
+until H goes to 0, what happens
+to the volume here?
+
+It goes to infinity.
+
+Yeah, it's terrible.
+
+So the extreme cases
+are just bogus.
+
+So it fails that test.
+
+OK, now we're back to
+D. So who likes D?
+
+So we have a few people
+who like D.
+
+[STUDENT CALLS OUT]
+
+[LAUGHTER]
+
+PROFESSOR: OK, go ahead.
+
+You don't like D.
+
+AUDIENCE: No, I don't like D.
+
+PROFESSOR: OK, why not?
+
+[LAUGHTER]
+
+AUDIENCE: It's the volume of
+the box, which has a size
+
+[INAUDIBLE].
+
+PROFESSOR: So this is the volume
+of a box, in other
+
+words, if I had vertical
+sides.
+
+So let me draw vertical
+sides here.
+
+Right, so whereas the pyramid
+has actually got to be less.
+
+Now, it's kind of mysterious
+what this factor here should
+
+be, but it's definitely
+less than 1.
+
+So this is comparison
+with a box.
+
+So it has a good properties,
+and it's a good answer.
+
+It's just not correct.
+
+But that's OK, because it's
+important to realize what's
+
+good about it and what's
+not good about it.
+
+So it satisfies the
+extreme cases.
+
+It satisfies dimensions.
+
+It scales correctly.
+
+Like you pointed out, you want
+B squared, because it's the
+
+area down there.
+
+So it's good.
+
+It's not all good.
+
+Let's call it good mostly.
+
+But as they say, a miss is as
+good as a mile except in
+
+horseshoes and atom bombs.
+
+So good mostly, but
+box comparison.
+
+OK, so let me cross this guy
+out and this guy out
+
+and that guy out.
+
+So what do you conclude
+from that?
+
+They're all wrong.
+
+So here's another multiple
+choice question.
+
+[LAUGHTER]
+
+PROFESSOR: OK, so
+who votes for A?
+
+One of these is definitely
+correct.
+
+[LAUGHTER]
+
+PROFESSOR: No votes for A?
+
+Who votes for B?
+
+Oh, I'm hurt.
+
+I'm hurt.
+
+Well, B is in fact correct.
+
+[LAUGHTER]
+
+PROFESSOR: So every once in a
+while, I throw the students a
+
+curve ball and make all
+the choices wrong.
+
+Now, why would I do that, such
+an evil, dastardly thing?
+
+Well, it's good every once
+in a while to do that.
+
+In fact, I found that out
+experimentally, because the
+
+first time I used this question
+with the students, I
+
+was already using the
+feedback sheets.
+
+And on the feedback sheets, I
+got back tons of love on the
+
+comment sheets.
+
+The students said, oh,
+we love that, having
+
+all the answers wrong.
+
+Don't do it too often, but do
+it every once in a while,
+
+maybe once a month or so.
+
+And that way, they never know
+when it's coming, so they
+
+always have to check
+all the answers.
+
+They can't just do everything
+by elimination.
+
+So it is a very useful
+thing to do.
+
+There are other reasons for it
+too, and if you're curious,
+
+ask me in the questions,
+and I'll explain more
+
+reasons to do it.
+
+But that's already a
+sufficient reason.
+
+OK, so that's method three.
+
+And you see you get a
+bit of discussion.
+
+You get multiple choices.
+
+And what does that allow
+you to do right away?
+
+Well, what was one
+of the problems?
+
+Is, you can find out
+what misconception
+
+students have early.
+
+Point one up there, in
+a tutorial, you can
+
+ask students questions.
+
+Well, why not ask some
+questions in
+
+a big lecture too?
+
+So that's what we just did.
+
+So you can find out.
+
+If 90% of the students get it
+like that, you know you don't
+
+have to say much more
+about the topic.
+
+But if the answers are
+distributed at the monkey
+
+line, 25% for all the answers,
+then you know there's going to
+
+be trouble.
+
+And it's worth actually
+expanding on this point and
+
+the theme that question gets
+across right then in lecture.
+
+So you could make it much more
+tailored to the group of
+
+students you have.
+
+And the students also--
+
+what happens in their
+small groups?
+
+Right, so remember we mentioned
+that in a tutorial,
+
+that it's a safe setting for
+raising questions, whereas a
+
+big group might not be.
+
+Well, what have we done by
+letting everyone work in
+
+groups of two or three?
+
+We've created a whole bunch of
+safe settings for questions.
+
+So the students are free
+to discuss in their
+
+groups of two or three.
+
+And if they can't resolve it
+there, well then they feel
+
+pretty confident that it's
+worthwhile sharing it with the
+
+whole class.
+
+Maybe the whole class
+can learn something
+
+from that as well.
+
+And that has another benefit,
+which is that it gets around
+
+the gender imbalance.
+
+So to illustrate this problem,
+I was once in a
+
+bookstore in New York.
+
+And I was standing in the
+computer section and this
+
+couple walked up the stairs.
+
+And the woman asked the
+man, oh, there's some
+
+big fat book on Java.
+
+And she said, what's Java?
+
+And within a millisecond, not
+batting an eyelid, he said,
+
+oh, it's the fastest search
+engine on the internet, which
+
+is completely rubbish.
+
+[LAUGHTER]
+
+PROFESSOR: It's a programming
+language.
+
+So it has absolutely nothing
+to do with a search engine.
+
+I'm sure no search engine
+is even written in Java.
+
+So it has nothing to do
+with search engines.
+
+So it's a complete lie.
+
+But he said it so fast.
+
+So there's a dichotomy there,
+which is-- generally speaking,
+
+it's called actually male
+answer syndrome.
+
+And the women--
+
+[LAUGHTER]
+
+PROFESSOR: I see all the women
+laughing, or I hear all the
+
+women laughing.
+
+Well, what you'll find is
+generally, men are very
+
+willing to talk about stuff
+they know nothing about,
+
+speaking crudely in extreme
+caricatures, whereas women are
+
+reluctant to talk about stuff
+they even know about.
+
+So if you just ask a question to
+a group just flat out, even
+
+with the five-second wait,
+you're more likely to get
+
+responses from the guys
+than from the girls.
+
+So the way to try to mitigate
+that imbalance is to give
+
+people, first, a safe setting
+for asking questions.
+
+And then people actually
+calibrate to the correct level
+
+about, well, is this
+a reasonable idea?
+
+Is this not a reasonable idea?
+
+Could the people around me
+have good ideas about it?
+
+Is it resolved now?
+
+If
+
+Not, well, it's probably safe to
+raise in a bigger setting.
+
+So you'll actually fix the
+gender imbalance to a large
+
+extent, and balance it out.
+
+So it has lots of benefits
+that you get
+
+from tutorial teaching.
+
+So now I'll show you the last
+one, which we won't actually
+
+do for half an hour.
+
+But I want to sketch out how
+you could do a question for
+
+half an hour.
+
+I'll show you the kind of
+question that works in that
+
+time frame.
+
+So this could be multiple
+choice.
+
+Doesn't have to be, but some
+kind of conceptual question
+
+with lots of discussion.
+
+And often, it may have
+a demonstration.
+
+So let me show you that
+particular question.
+
+So I'm going to use--
+
+I have these guys too, but I
+also have the wood blocks
+
+which I like so much.
+
+So here are two wood blocks cut
+for me by the machine shop
+
+of the Cambridge physics
+department
+
+when I taught there.
+
+So they cut them out of the
+same piece of pine, same
+
+grain, direction, everything.
+
+The only difference is this is
+2 centimeters thick, and
+
+that's 1 centimeter thick.
+
+But They're both a foot long
+and 5 centimeters wide.
+
+So what I'm going to do is I'm
+going to tap this block, and
+
+you'll hear a note.
+
+[TAPS A NOTE ON WOOD BLOCK]
+
+PROFESSOR: Did everyone
+hear the note?
+
+Great.
+
+OK, so now the question is, when
+I tap this block, is the
+
+note going to be higher, the
+same frequency, or lower?
+
+OK, so does everyone understand
+the question?
+
+OK, so discuss with
+your neighbors.
+
+We'll take a vote in about
+a couple minutes.
+
+I won't give you the 10 minutes
+I would normally give
+
+people to discuss and argue.
+
+We'll take a couple reasons,
+then we'll do the experiment.
+
+OK, time to vote.
+
+So, just to sketch out how this
+could actually turn into
+
+a 30-minute question, normally I
+give students about a couple
+
+minutes to think on their own,
+then take a vote, and then set
+
+everyone to argue
+with each other.
+
+I say, in particular, find
+someone who has a different
+
+answer than you, and try to
+convince them of your answer.
+
+So then you get a big
+argument going.
+
+And so then I let that go
+for about 10 minutes.
+
+And then we take another vote.
+
+And then we discuss.
+
+So let's just imagine we've
+skipped forward to the end of
+
+the group discussion,
+and we're going to
+
+take the second vote.
+
+So who thinks the thick block
+will have a higher frequency
+
+than the thin block?
+
+About maybe 20 people.
+
+Who thinks they'll be equal?
+
+About 25.
+
+Who thinks the thick block will
+have a lower frequency?
+
+About 50.
+
+OK, so we have a good spread
+of opinion there.
+
+So now, again, in the scenario
+of the 30-minute question, I
+
+would ask for reasons, just like
+I did here, and I would
+
+just be the scribe.
+
+I would just write down people's
+reasons for A, B, or
+
+C, for greater, equal,
+or less than.
+
+Just make sure I understand
+the reason and
+
+then write it down.
+
+I don't have to agree
+with the reason.
+
+Just make sure I understand it,
+and the person who says it
+
+says, yeah, that's what
+I'm trying to say.
+
+Write it on the board.
+
+Then give people the opportunity
+to say a reason
+
+for any of the others or
+against any of them, or
+
+comment on any reason already
+on the board.
+
+And that can go for another
+10 minutes or so,
+
+sometimes even longer.
+
+And then I ask people, OK, the
+test of science is experiment.
+
+Should we do the experiment?
+
+Should we do the experiment?
+
+AUDIENCE: Yes.
+
+PROFESSOR: OK.
+
+So just to remind you
+of the earlier tone.
+
+[TAPS A NOTE ON WOOD BLOCK]
+
+[TAPS A HIGHER NOTE
+ON WOOD BLOCK]
+
+[LAUGHTER]
+
+PROFESSOR: So the
+ayes have it.
+
+OK, so it turns out to be
+roughly almost a factor of two
+
+higher in frequency, almost
+a full octave.
+
+It's not quite.
+
+If they were infinitely thin,
+and this were twice infinitely
+
+thin, it would be exactly
+a factor of two.
+
+But because they have
+a finite thickness,
+
+it's not quite true.
+
+But that's how xylophones
+work.
+
+In fact, many people have
+reasoned their way to the
+
+correct answer by thinking
+about xylophones.
+
+And many people have reasoned
+their way to the incorrect
+
+answer by thinking about guitar
+strings, which brings
+
+up a very interesting discussion
+you can have.
+
+So what did you notice
+about here?
+
+When I was about to tap
+the second one, could
+
+you hear a pin drop?
+
+[LAUGHTER]
+
+PROFESSOR: Right.
+
+Student engagement
+is much higher,
+
+because people are involved.
+
+But the act of voting commits
+people to a public view.
+
+And they want to know, is this
+right or is this not right?
+
+And the act of voting has
+another benefit, which is that
+
+you get a much better
+error signal.
+
+Whereas, suppose you
+didn't vote.
+
+And suppose you thought, well,
+it could be higher because
+
+it's stiffer.
+
+On the other hand, it's bigger
+wavelengths, so it's lower.
+
+And you sort of both reasons
+in your head.
+
+You're in a superposition
+state.
+
+And then the experiment
+happens--
+
+bing bing bing-- and it's
+higher, and you say, oh yeah,
+
+I knew that.
+
+It was higher because it's
+thicker and stiffer.
+
+So you think actually you
+understood everything, but you
+
+didn't actually figure out,
+well, which of these two
+
+reasons is right and why?
+
+Whereas if you have to publicly
+commit to one answer,
+
+then you get a clearly defined
+signal back about whether that
+
+answer was right or not.
+
+So it's very important to
+make sure people vote.
+
+And at the same time, it's very
+important to make sure
+
+people are not punished
+for voting.
+
+So does it matter in my classes
+whether people get the
+
+vote right or not?
+
+I just want them to vote.
+
+And so then I have to give my
+speech about, it's better to
+
+be wrong than right.
+
+Question?
+
+AUDIENCE: So I've been in lots
+of classes where the professor
+
+asks a question and waits a
+few seconds for people to
+
+raise their hands.
+
+And by the time he's done or
+she's done, there's a third of
+
+the class raising their hand,
+and those the people who had
+
+their hands up first.
+
+So how do you actually
+take that step?
+
+PROFESSOR: Sorry, could you tell
+me what they're doing?
+
+They ask a question.
+
+AUDIENCE: They ask
+a question--
+
+PROFESSOR: Do they let the
+whole class discuss it?
+
+AUDIENCE: Not necessarily.
+
+So that's what you're
+saying is key here?
+
+PROFESSOR: Yeah, it's
+really key to let
+
+the whole class discuss--
+
+so the normal structure for a
+long question like this one
+
+I'll do is I'll make
+sure everyone
+
+understands the question.
+
+And then I'll let people think
+by themselves for a minute or
+
+two, and take a vote after that,
+a straw poll, I call it,
+
+so people don't feel
+it's too weighty.
+
+The reason for that is
+that people have
+
+different learning styles.
+
+And some people want to think
+longer for themself, and some
+
+people want to just start
+talking right away, so I want
+
+to give something
+for everybody.
+
+And then after I take that vote,
+that gives me an idea
+
+where the class is, and it gives
+the class an idea of
+
+where they are, and who
+has different views.
+
+And then they can start arguing
+with each other.
+
+And so now they've had a lot of
+time to actually check what
+
+they all think.
+
+So people will have had
+arguments in their group that
+
+they can't resolve, so they're
+very eager to actually share
+
+the argument.
+
+Whereas if you just ask the
+question without giving people
+
+time to struggle with it, you're
+basically wasting the
+
+effect of the question.
+
+AUDIENCE: So how do you decide
+what level of difficulty for
+
+discussion?
+
+PROFESSOR: This is
+a hard question.
+
+But it's so rich.
+
+It has so many things.
+
+I don't expect most people to
+get the question right.
+
+In fact, when I ask this to
+faculty in physics department,
+
+when I give physics teaching
+seminars, most
+
+people get it wrong.
+
+I won't say all the places where
+that's been true, but
+
+it's been at many universities
+around the world.
+
+So I don't expect
+people to get it
+
+right, and I don't care.
+
+The reason for it is that it
+introduces so many ideas--
+
+about, for example, spring
+models of solids.
+
+We can use musical instruments
+as analogies--
+
+that I think it's worth
+spending even a
+
+whole class on it.
+
+And in fact, one time somebody
+said, well, but a xylophone,
+
+all the things are the
+same thickness and
+
+they're just longer.
+
+How does that work?
+
+And I said, oh, I'm glad
+you asked that.
+
+And I pulled out my daughter's
+xylophone--
+
+she has a baby xylophone--
+
+from my backpack.
+
+And so we analyzed the xylophone
+right there.
+
+So it leads to so many
+interesting things that I'm
+
+willing to spend a whole
+class on it.
+
+So that's how I decide
+how much time
+
+to allocate to something.
+
+If it's a really core idea,
+spend more time on it.
+
+And if it's peripheral, tend to
+spend less time on it or do
+
+a really short question
+on it, if at all.
+
+And then the difficulty--
+
+I like to get questions,
+ideally--
+
+I mean, this one's different
+just because it's so rich--
+
+but ideally where students are
+sort of at 60% correct
+
+thinking by themself,
+maybe 65%, even 70%.
+
+Because even though they may be
+right, that sounds like oh,
+
+they're mostly fine,
+but they may not
+
+know why they're right.
+
+So then in the discussion they
+can solidify their reasons and
+
+maybe get up to 80% or 90%.
+
+Whereas if you've got a question
+where they're 30%
+
+correct to start with, and
+that doesn't have other
+
+redeeming qualities like the
+richness of it, you'll just
+
+propagate noise throughout the
+system, and just basically
+
+wrong ideas will just spread all
+over and you'll spend all
+
+your time correcting those.
+
+So I gauge the difficulty
+based on
+
+trying to hit that mark.
+
+OK, so hopefully you've
+seen, first of all,
+
+that tutorial teaching--
+
+the main points from today--
+
+is much more effective than
+regular teaching as normally
+
+practiced because of these
+characteristics--
+
+generally questioning, feedback,
+instant feedback and
+
+corrective feedback
+right away.
+
+But through a series of methods,
+you can bring many of
+
+the benefits of tutorial
+teaching to your own large
+
+group teaching, which is the
+kind of teaching that most of
+
+us will do, just for
+cost reasons.
+
+So I wish you best of luck
+in all your teaching.
+
+AUDIENCE: Can I just [? get ?]
+one interesting statement?
+
+PROFESSOR: Sure.
+
+AUDIENCE: It's something to
+think about, and faculty often
+
+have difficulty with this.
+
+There's probably a pretty high
+correlation between the amount
+
+of information that you want
+to get through to students,
+
+and the time that it
+takes to do it.
+
+The more questions you ask, the
+less you can get through
+
+the material.
+
+And this constant
+questioning--
+
+PROFESSOR: This constant
+battle.
+
+AUDIENCE: What should I do?
+
+Should I just try to get this
+much information because I
+
+want to ask lots of questions?
+
+Or do I want to get that much
+information through, then I
+
+better not spend too much
+time asking questions?
+
+It's a conundrum.
+
+I think asking questions is
+just a phenomenal way of
+
+learning, but [INAUDIBLE].
+
+PROFESSOR: Yeah, basically
+we teach too much stuff.
+
+And that's the fundamental
+problem.
+
+And so one solution to that is
+to say, look, all the details,
+
+get it from a book.
+
+And in class, we're going to
+do what you can't easily do
+
+from the book, which is
+struggle, argue, reason, and
+
+correct those reasons.
+
+That's hard to do from a book.
+
+So you should use the class
+time for something that's
+
+value added that you
+can't do elsewhere.
+
+So good luck with that.
+
+Please take a minute to fill
+out the feedback sheets.
+
+And as long as no one kicks us
+out, I'll be here as long as
+
+people have questions.
+
+[? COMPUTER: Answers ?]
+
+from lecture seven to questions
+
+generated in lecture six.
+
+PROFESSOR: OK, so questions
+from before.
+
+What are your suggestions for
+someone teaching a course that
+
+they are not expert in at all,
+you know, for the first time?
+
+So I'm a practical man.
+
+I know most people, when they're
+teaching a course,
+
+teaching is not going
+to be their life.
+
+I mean, it is for me,
+but that's unusual.
+
+And if you love teaching,
+that's great.
+
+But probably, your job will be
+dependent on how much research
+
+you do or other activities like
+department committees.
+
+And so you don't want to destroy
+your whole career on
+
+your first course.
+
+By which I mean, just try to
+survive your first course.
+
+Because what you could do the
+first time you're teaching
+
+it-- so the answer
+is, you need to
+
+somehow become an expert.
+
+If you want to teach it
+differently and creatively and
+
+interestingly, you somehow
+need to become an expert.
+
+Now, you could do that by
+spending the whole summer
+
+before really figuring out the
+material from scratch.
+
+And that probably in the long
+term is a good thing.
+
+You'd probably find useful
+results in your
+
+research from it.
+
+But probably you don't have
+that summer to do that.
+
+And so what you need to do is
+kill two birds with one stone
+
+and become an expert by teaching
+it, in which case the
+
+best plan I would recommend is
+just to teach it pretty much
+
+the regular way, with some
+
+interactive changes in lecture.
+
+But just follow the regular
+plan, as much as it sticks in
+
+one's craw.
+
+Because in doing that, first
+of all, you will
+
+be rocking the boat.
+
+So people will accept it
+even if it's not great.
+
+And you'll become an
+expert by the end.
+
+And then the next time you
+teach it, you'll be OK.
+
+Then you you've done that summer
+of thinking, but you've
+
+done it during the class.
+
+So it meant the first class
+didn't go as well as it could.
+
+But it also meant you survived
+and you could order material
+
+for your lab and all the
+other things that
+
+you'd do in the summer.
+
+How do you--
+
+so I like it when you emphasize
+that it's OK to get
+
+the wrong answer.
+
+It's like with the wood blocks,
+I mentioned how,
+
+mostly when I ask this of
+physics professors too, people
+
+get it mostly wrong.
+
+And so I had another example of
+that in Colorado, because I
+
+gave a talk using
+the wood blocks.
+
+So how can you incorporate that
+"it's OK to be wrong, as
+
+long as you learn" attitude
+into class?
+
+One of the best ways is to
+minimize the amount of
+
+grading, and the emphasis
+given to grading.
+
+Grading, basically, as a
+first approximation--
+
+so if I just add two letters,
+it's hard to avoid that.
+
+So grading, when you mark
+someone and you tell them,
+
+bad, A B, C, D, well, the people
+who are getting B's,
+
+C's, and D's, whatever the quote
+bad grades are, you are
+
+actually shaming people.
+
+And in some ways, you are
+degrading their psyche.
+
+So it's not healthy.
+
+So that is one of the political
+barriers to
+
+educational change
+is the importance
+
+that we give to grading.
+
+And I will talk about that
+in the final session.
+
+You may think, oh what about
+the people who get A's?
+
+Well, if you're giving A,
+B, C's, and D's, the
+
+people who get A's.
+
+They may have struggled and were
+thinking, oh my god, will
+
+I get an A?
+
+Will I get an A?
+
+Then they get an A.
+So they go, phew.
+
+But still, they were nervous
+about their learning the whole
+
+time instead of enjoying it
+as much as they could.
+
+And second, there's also
+studies, many studies, which
+
+show that when you reward people
+for things they already
+
+enjoy-- this is totally
+fascinating--
+
+so when you reward people for
+things they already enjoy
+
+doing, their enjoyment drops.
+
+So if you start paying people
+for things that they would
+
+like doing anyway, then they
+don't like it as much.
+
+And you [INAUDIBLE] everyday
+examples of this.
+
+You know if you know anyone
+who's a symphony orchestra
+
+player, they say, oh yeah, the
+best way to start hating music
+
+is to be a professional
+musician.
+
+They love music, and then they
+had to do it for pay, in all
+
+of a sudden they don't like as
+much anymore, not all of a
+
+sudden, but slowly.
+
+So there are many, many
+studies about that--
+
+motivation.
+
+So what you want to do really
+is to find intrinsic
+
+motivation.
+
+And so the difference between
+extrinsic and intrinsic
+
+motivation is fundamental.
+
+And what you want to try to do
+is create the environment
+
+always where the motivation
+is intrinsic, so that the
+
+questions are interesting.
+
+So what that means is you
+don't want to use bad
+
+questions that people don't have
+an interest in, and then
+
+force them to be interested
+because you give them
+
+extrinsic motivation.
+
+That's a fundamental bad choice,
+and then it's being
+
+solved with the fundamental
+wrong approach.
+
+What do you need to do is rather
+than do both of those,
+
+you say, OK, let me find
+interesting questions that
+
+people care about.
+
+And then the intrinsic
+motivation carries people
+
+through, whether they're
+right or wrong.
+
+So that's why I like questions
+like the wood block so much,
+
+because people are just
+actually interested.
+
+They want to know.
+
+They say, oh, that's
+a good question.
+
+I should know that.
+
+Oh, maybe I don't.
+
+OK, well maybe I'll
+learn something.
+
+So the other part of that is,
+if you notice, I didn't use
+
+clickers when we did
+this question.
+
+Partly, it's because clickers
+are expensive and you have a
+
+bunch of logistics to do, and
+then you need probably some
+
+ludicrous Windows program to
+receive the signals, and I
+
+haven't written the Linux
+version for it.
+
+So there's all of
+those issues.
+
+Those are, I would say, not
+the fundamental issue.
+
+The fundamental issue with
+clickers, why I don't like
+
+them, is that they make people
+think they're being spied on.
+
+So even especially if you live
+in a surveillance society,
+
+where actually all your phone
+calls are being spied on,
+
+people might think, well when
+you have clickers, you're
+
+being spied on to know whether
+you got the right answer or
+
+not, and it's going to count
+against you at some point.
+
+So I'm very happy with people
+to just raise their hands.
+
+And that's, in a way, more
+anonymous than a clicker that
+
+belongs to you.
+
+So there are ways of getting
+around that with clickers.
+
+You can to have people trade
+clickers so they know that the
+
+clickers are random.
+
+So you can do things
+like that.
+
+But still, I like the informal
+feel of, yeah,
+
+just raise your hand.
+
+Don't worry.
+
+It's a safe space in
+the classroom.
+
+And I have to say that
+a few times.
+
+But just raise your hand,
+and don't worry.
+
+And I'm not spying on you.
+
+I don't care whether you get
+the right answer or not.
+
+For example, with the wood
+blocks, I expect most people
+
+to get the wrong answer.
+
+That's OK.
+
+We'll learn something
+about it afterwards.
+
+So you do have to work at it,
+but there are things you can
+
+do to keep the class
+[? safe. ?]
+
+There are also things to do,
+which is that never--
+
+it's hard to remember how much
+power you have as the
+
+instructor, and just
+as someone in
+
+a position of authority.
+
+So I might have told you the
+story from when I was a
+
+graduate student, but it's
+worth telling again, if I
+
+haven't, which is that I was
+giving a talk in a group
+
+meeting when I was a
+graduate student.
+
+My adviser got frustrated
+with me because I wasn't
+
+understanding some fundamental
+point, actually about springs.
+
+So to demonstrate it, he kicked
+the table at me and
+
+said, is this acting
+like a spring?
+
+And I was so shocked.
+
+I was just mortified
+for like two days.
+
+I just couldn't believe my
+adviser had done that in front
+
+of everybody else, and thought
+that I must be
+
+idiot and showed it.
+
+So then eventually my fellow
+grad students said, well,
+
+actually he does that only
+when you really cares.
+
+So that's better than people
+just switching off.
+
+So I sort of consoled
+myself with that.
+
+But it did make a real strong
+impression on me, how much
+
+even a small push from someone
+in authority can do.
+
+So it's the same thing in
+lecture, if when someone says
+
+something wrong, if you
+say, oh, why would
+
+you have said that?
+
+Even the slightest hint of that,
+people magnify and will
+
+pick up and be very,
+very sensitive to.
+
+So you have to be really,
+really, really careful not to
+
+let that happen.
+
+So one way is the poker face.
+
+So I practiced the poker face.
+
+So when people are making
+suggestions, for example,
+
+about the wood block, why they
+would act one way or another,
+
+I just make sure I get in a
+different mental state.
+
+The mental state is
+transcription.
+
+So I just want to make
+sure I understand
+
+what people are saying.
+
+And then I just write
+that down.
+
+Now, it's even there you
+have to be careful.
+
+Because you'll understand the
+correct answer quicker than
+
+you will the incorrect answer.
+
+So you have to make sure when
+people are explaining the
+
+correct answer, you don't
+complete it for them.
+
+And then in contrast, when
+people are explaining a wrong
+
+answer, you ask lots of
+questions, because
+
+that too is a signal.
+
+So the poker face is tricky to
+do, but once you master it,
+
+that's one good way of giving
+yourself a pause and not
+
+criticizing people for
+their answers.
+
+So there are various ways, but
+you just have to be careful.
+
+And if you do that regularly,
+you'll find in a week or two,
+
+you've overcome the presumption
+people have that
+
+it's dangerous to
+ask questions.
+
+But you do have to work at it.
+
+Is it possible to incorporate
+mastery learning at the
+
+college level?
+
+So actually, there is
+a very interesting
+
+experiment on that.
+
+And it was done at MIT in
+the 1970s, I believe.
+
+It was called--
+
+so it was called the
+Keller Plan.
+
+I don't know if they did it
+for all courses, but the
+
+physics courses were
+taught this way.
+
+I don't know if only that way,
+or that was an option.
+
+So it was in the 1970s,
+which was a time of--
+
+as people who were here
+then said, it was a
+
+very turbulent time.
+
+And the turbulence actually
+enabled lots of educational
+
+experiments to happen, basically
+the '60s and '70s.
+
+So if you look at, for example,
+the Feynman lectures
+
+were in Caltech in the '60s, the
+Berkeley physics course,
+
+1960s, things like the Keller
+Plan, the free schools at the
+
+school level--
+
+tons of experiments happened
+in the '60s and '70s.
+
+So the Keller Plan
+was one of them.
+
+It was mastery learning.
+
+Students worked on problems, and
+when they were ready for
+
+the next piece, they
+continued.
+
+And from what I can tell,
+it worked pretty well.
+
+But then eventually it got
+killed off by basically
+
+faculty who said, no, I'd rather
+teach and do lectures.
+
+Because what's the point of the
+faculty if the students
+
+can learn really well
+from the books?
+
+So I think the Keller Plan
+was a really good idea.
+
+In school, I learned for five
+years of high school math in
+
+three or four weeks using the
+Keller Plan, compared to the
+
+normal pace in school where you
+spend a whole year doing
+
+trigonometry.
+
+So the Keller Plan is a really,
+really excellent way,
+
+if you have reasonable books.
+
+So now, what are the full
+reasons it died?
+
+I'm not really sure.
+
+I need to check into that.
+
+But people who were around then,
+some of them said, yeah,
+
+just people who wanted to
+perform in lecture were really
+
+sad about the Keller Plan
+and wanted to go
+
+back to the old way.
+
+And so when the political
+currents changed, so did the
+
+Keller Plan.
+
+How do I come up with these rich
+and interesting examples
+
+like the wood blocks,
+and how often do
+
+you incorporate demos?
+
+Well, we'll talk about that
+in Walter Lewin's lecture.
+
+So if you saw Walter Lewin's
+lecture, the one on the
+
+pendulum, he must have had
+four or five different
+
+demonstrations.
+
+They were short, but he had
+many demonstrations.
+
+And questions like this, if I
+had 20 of these, I would use
+
+20 different ones.
+
+So usually I have four or five
+of them that are a good long
+
+time demo that are suitable
+for, say, half
+
+a lecture or longer.
+
+And I use them.
+
+So wherever I can find
+them, I use them.
+
+But not every single demo is
+worth spending 30 to 40
+
+minutes on.
+
+So you have to think about
+whether it teaches core ideas,
+
+how it fits with the goals
+of your course.
+
+So for example, let me talk
+through why I use this one.
+
+Well, one of the goals that I
+want is I want students to be
+
+able to make physical
+models themself.
+
+I don't want them to just be
+able to solve equations that
+
+I've put in front of them.
+
+So normally what you do is you'd
+teach them the bending
+
+beam equation, and then maybe
+you'd show them this, and then
+
+you'd do this in two
+or three minutes.
+
+But actually a much more
+interesting question is not,
+
+what's the solution to the
+bending beam equation when the
+
+beam's twice as thick.
+
+The question is, what physical
+model is responsible for
+
+making sound?
+
+When you hear sound, where
+is it coming from?
+
+When you tap this guy--
+
+[TAPS A NOTE ON WOOD BLOCK]--
+why is it making sound, long
+
+before you're even discussing
+the bending beam equation.
+
+So that question is, to my mind,
+much more interesting.
+
+And so I'm very willing to spend
+more time on that, and
+
+having students develop that
+feel, and have them argue and
+
+realize that there's different
+physical models.
+
+It could be a standing
+wave in the block.
+
+It could be that the
+block is bending.
+
+How do you decide, and how do
+you decide which one you're
+
+going to hear more?
+
+And then for each one, how
+do you figure out how the
+
+frequency's going to change?
+
+So that, because it fits so well
+with the course goals,
+
+spend more time on it.
+
+Why is the stiffness a factor
+of eight bigger?
+
+So that one, anyone who
+wants to know, I will
+
+explain after lecture.
+
+Just come to office hours.
+
+So there's a simple picture
+using wood atoms.
+
+Don't ask what wood atoms are.
+
+How can you incorporate aspects
+of mastery learning
+
+into regular teaching?
+
+Ah, so that's what interactive
+teaching is all about.
+
+So the reason mastery learning
+works so well is that you're
+
+not building castles
+of knowledge on
+
+sand, roughly speaking.
+
+So normally what happens-- so
+the extreme case is Cambridge
+
+in England.
+
+So the teaching system there
+is you have an eight-week
+
+term, and then you have a
+six-week break, and then an
+
+eight-week term, six-week break,
+eight-week term, and
+
+then 16-week break.
+
+So the eight-week term, about
+what we would do in a semester
+
+is compressed into eight weeks,
+just basically straight
+
+dictation and lecture.
+
+And the students have a hard
+time really understanding
+
+everything at that pace, so
+they just take dictation.
+
+And then you're supposed to
+figure everything else out,
+
+integrate it in the
+six-week break.
+
+So the problem with that is that
+it's very inefficient.
+
+It's very inefficient because
+you haven't understood A. And
+
+now B uses A, but A hasn't
+really been understood.
+
+So you're not going to
+understand B. So now you have
+
+A and B not really understood,
+so you just write them down.
+
+Now C comes along using A and
+B, but A and B aren't
+
+understood, so the problem
+compounds.
+
+Whereas with mastery learning,
+only when you understand A do
+
+you go onto B. And also when A
+and B are solid, then you go
+
+onto C. So your knowledge
+castles are robust and strong.
+
+And that's not true with
+most teaching.
+
+So how do you remedy
+that problem?
+
+Well one way is you ask
+questions in lecture.
+
+So here, plan interactivity
+and build
+
+it into your lecture.
+
+So by asking students questions
+you figure out, oh,
+
+if only 20% or 30% or maybe even
+40% of the students knew
+
+the correct answer, and even
+after discussion, you think,
+
+oh, OK, well this is a
+fundamental concept.
+
+Presumably that's why you asked
+the question about it.
+
+But it wasn't mastered.
+
+So better fix it, before
+you go on.
+
+So that builds mastery learning
+into the regular
+
+lecturing process.
+
+And that's one reason
+that interactive
+
+teaching is so effective.
+
+So one of the other questions
+later in the sheets is, is
+
+there evidence that interactive
+teaching is good
+
+and helps people learn?
+
+There is actually
+good evidence.
+
+Maybe I should put some of
+those papers online.
+
+One is by Richard Hake.
+
+He's now retired.
+
+He's physics professor from
+Indiana University.
+
+So what he did is he did a
+sample of physics courses
+
+across the country, intro
+physics courses that included
+
+a total of 6,000 students.
+
+And he asked the instructors
+to describe how they did
+
+everything.
+
+And then everything was
+grouped into either
+
+interactive teaching or
+regular teaching.
+
+And just the scores that
+students got on one particular
+
+exam, which was a force concept
+
+inventory, before and after--
+
+they were given the force
+concept inventory before the
+
+class started and at the end--
+
+they saw how much the
+students improved.
+
+OK, so if you improved 100%--
+
+in other words, suppose you
+started at 20% correct and you
+
+got to 100%--
+
+that was considered
+a 1.0 gain.
+
+If you went from 20% percent
+to 60%, that mean you got
+
+halfway to the maximum possible
+score you could have
+
+gotten, so half of the maximum
+improvement, that
+
+was a gain of 0.5.
+
+So he measured the gain
+for everybody.
+
+So this is the gain on the
+force concept inventory.
+
+And this is the number of
+courses in each area.
+
+So it was roughly like that.
+
+So this was the regular.
+
+So the regular teaching, by the
+way, included fantastic
+
+teachers, people who were rated
+highest lecturer in the
+
+university and had won
+lecturing awards.
+
+And the interactive teaching
+was something like this.
+
+I'll put the paper online so you
+can see the exact graph.
+
+But basically, the worst
+interactive teaching was
+
+better than most of the
+regular teaching.
+
+And the regular teaching
+hardly got
+
+better than 0.2 or 0.3.
+
+So if you wanted any more gain
+than that, you really needed
+
+to do interactive methods.
+
+And I think that is because
+you've incorporated mastery
+
+learning into the curriculum.
+
+OK, what do you do when the
+students are really quite and
+
+won't answer your questions?
+
+Or flip side is, what if only
+the quote 5% usual suspects
+
+are the ones answering
+the questions?
+
+What do you do?
+
+Well, so that is related to the
+question of, are there bad
+
+ways of incorporating
+interactivity?
+
+And there are.
+
+The worst is the following,
+which is--
+
+I'll sort of parody it.
+
+So we're doing relativity,
+or nuclear physics.
+
+E equals MC--
+
+[LAUGHTER]
+
+PROFESSOR: Squared, yeah.
+
+OK.
+
+So you'll find a lot of people
+who normally wouldn't teach
+
+interactively are now, they're
+told or they hear that it's
+
+good to teach interactively and
+ask students questions.
+
+But if you don't have any
+practice in how to do that,
+
+the easiest questions to ask
+are just things like this.
+
+And the problem with
+that is not that
+
+they're asking a question.
+
+It's good to ask a question.
+
+But the problem is that this
+thing, this two, is just a
+
+memorized fact.
+
+So it's possible to answer it
+just by memory, whereas if
+
+there was actually some debate
+about what it should be, you
+
+could ask the students
+the question.
+
+But now, if you just ask people
+question like that, and
+
+you give people no time to
+think, yes, you will get
+
+answers just from the quote top
+5%, the usual suspects.
+
+So to avoid that, what you need
+to do is give people a
+
+chance to think on their own.
+
+So that's one of the interactive
+teaching
+
+techniques, the idea of give
+people a minute or even 30
+
+seconds to think on their own,
+so that you'll get answers
+
+from a wider spectrum of
+people, because they've
+
+checked it out with
+their neighbor.
+
+And they feel safer in
+volunteering and answer or
+
+asking a question about it.
+
+So that's how you avoid two
+things, two problems at once.
+
+You avoid the quiet students,
+because you've given-- those
+
+students are being quiet because
+you've given people a
+
+chance to think.
+
+And you also avoid the problem
+of just the usual people
+
+answering, because you've given
+
+everybody a chance to think.
+
+OK, if we don't really
+understand until we teach,
+
+should we have students teach
+each other in presentations,
+
+or is that not worth the time?
+
+My feeling is that huge big
+presentations and having
+
+students present to each other
+is not so much worth the time.
+
+I mean, it's worth the time of
+the one person who's doing the
+
+presentation.
+
+But that's the main person
+who learns in
+
+that teaching session.
+
+So there are several graduate
+seminars, many I took as a
+
+graduate student, that are
+run the following way.
+
+The professor just sits
+back and each time--
+
+they assign a list of topics,
+and each student volunteers
+
+for one topic to present
+to everybody else.
+
+Now, that is a fantastic way
+to learn one topic in the
+
+entire course.
+
+And it does work for that.
+
+And part of my Ph.D. Came out
+of one of the topics that I
+
+learned from one of those
+courses, because I really
+
+wanted to figure it out.
+
+So it can work.
+
+And it does work in some ways.
+
+But it's not a very efficient
+way, because all the other
+
+people are just basically
+passive.
+
+Yeah, they read the stuff.
+
+But now they're being taught by
+someone who's just barely
+
+mastering the field and is not
+likely to teach interactively
+
+with a large margin of safety.
+
+So it's much better to have
+students teach each other by
+
+having them argue with each
+other on small time scale.
+
+So for example, if you remember
+in the wood blocks, I
+
+said, OK, are you with your
+neighbor about your answer?
+
+Well, now the students are
+trying to teach each other.
+
+Some students think, oh yeah,
+it's due to the bending.
+
+OK, well that turns
+out to be correct.
+
+But can you convince
+your neighbor?
+
+Well, in trying to convince
+your neighbor,
+
+you are doing teaching.
+
+You're trying to figure out,
+what's a way that you can do
+
+it without writing down
+50 equations.
+
+That's exactly what you want
+to do in teaching.
+
+So I think it's a much better
+way, is to build the
+
+interactivity into the class
+for everybody, rather than
+
+having it as a rotating seminar
+where just one person
+
+at a time learns.
+
+In organizing big ideas
+into a tree, there are
+
+often multiple ways--
+
+for example, you can do current
+understanding versus
+
+history, or experiment versus
+theory-- and it's often good
+
+for students to know more than
+one of these organizations.
+
+How do you do that in
+a course design?
+
+Yeah, so unfortunately there's
+only one time dimension.
+
+There's three space
+dimensions, but
+
+only one time dimension.
+
+So the course has to evolve
+in one dimension somehow.
+
+So you need at least
+one organization.
+
+But you're right.
+
+You need other organizations
+as well.
+
+So the way I square that
+circle is as follows.
+
+So let's say time
+goes that way.
+
+So this is unit one.
+
+Let's say it's one technique,
+one mode of reasoning,
+
+dimensional analysis.
+
+Let's say this is another
+mode of reasoning,
+
+conservation, and so on.
+
+So these are units.
+
+And now you have topics.
+
+Well, what I like to do is
+I want to show other
+
+organizations.
+
+And why is that good?
+
+Well, what you're doing
+is you're connecting.
+
+You're building threads
+across.
+
+And you're right.
+
+You definitely want
+to do that.
+
+So what I'll do is I'll find
+problems that can be solved
+
+multiple ways.
+
+Suppose this is, for example,
+a problem about a pendulum.
+
+Well, you can solve a pendulum
+with dimensional analysis.
+
+You can also solve a pendulum
+with conservation laws.
+
+So I'll do it again.
+
+So this way, this method is
+sufficient to solve it mostly.
+
+This method is sufficient,
+but now we're
+
+revisiting the old problem.
+
+So I try to find problems that
+thread through, and maybe then
+
+reappear over here.
+
+So that gives you a cross
+cutting organization.
+
+So you can do that not just with
+problems, but with, for
+
+example, other principles.
+
+For example, the history--
+
+suppose you want to incorporate
+history versus
+
+current understanding.
+
+Well, every time you mention
+history and the importance of
+
+history, you say, oh look,
+there's yet another example
+
+where we learned from history.
+
+We learned it here.
+
+We've learned it in this unit.
+
+So now the students have yet
+another structure to bind the
+
+course together.
+
+This is hard to do the first
+time you teach the course.
+
+What you'll do is this first
+time you teach your course,
+
+well, you'll probably do
+it the regular way.
+
+The second time, you'll maybe
+reorganize it this way.
+
+And the third time you do it,
+you start building all the
+
+bridges across it.
+
+Because that's the only time
+you actually see them too.
+
+What are my thoughts
+on grade inflation?
+
+I wish every grade was an A. So
+I think there isn't enough
+
+of it, because of the studies
+I said before.
+
+So I'll talk about that in
+the penultimate lecture.
+
+I think most of these, yeah, I
+think I've now answered with
+
+other comments or questions
+that are there, except for
+
+one, which I'll save
+for next time.
\ No newline at end of file
diff --git a/62KrMWdX-RU.txt b/62KrMWdX-RU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e99a0e02cf852042ef110c3f5c990c6ca02f388e
--- /dev/null
+++ b/62KrMWdX-RU.txt
@@ -0,0 +1,249 @@
+Hi.
+
+In this video, we're going to
+do standard probability
+
+calculations for normal
+random variables.
+
+We're given that x is standard
+normal with mean 0 and
+
+variance 1.
+
+And y is normal with mean
+one and variance 4.
+
+And we're asked for a couple
+of probabilities.
+
+For the normal CDF, we don't
+have a closed form expression.
+
+And so people generally tabulate
+values and for the
+
+standard normal case.
+
+So if we want little x equal to
+3.49, we just look for 3.4
+
+along the rows and 0.09 along
+the columns, and then pick the
+
+value appropriately.
+
+So for part A, we're asked
+what's the probability that x
+
+is less than equal to 1.5?
+
+That's exactly phi of 1.5
+and we can look that up.
+
+1.5 directly and
+that's 0.9332.
+
+Then were asked, what's the
+probability that x is less
+
+than equal to negative 1?
+
+Notice that negative values
+are not on this table.
+
+And the reason that is is
+because the standard normal is
+
+symmetric around zero.
+
+And we don't really need that.
+
+We just recognize that the area
+in this region is exactly
+
+the area in this region.
+
+And so that's equal to the
+probability that x is greater
+
+than equal to 1.
+
+This is equal to 1 minus
+the probability that x
+
+is less than 1.
+
+And we can put the equal sign
+in here because x is
+
+continuous, it doesn't matter.
+
+And so we're going to get,
+this is equal to 1
+
+minus phi of one.
+
+And we can look up phi
+of 1, which is
+
+1.00, and that's 0.8413.
+
+OK.
+
+For part B, we're asked for
+this distribution of y
+
+minus 1 over 2.
+
+So any linear function
+of a normal random
+
+variable is also normal.
+
+And you can see that by using
+the derived distribution for
+
+linear functions of
+random variables.
+
+So in this case, we only need to
+figure out what's the mean
+
+and the variance of this
+normal random variable.
+
+So the mean in this case, I'm
+going to write that as y over
+
+2 minus 1/2.
+
+ 
+
+The expectation operator
+is linear and so
+
+that's going to be--
+
+ 
+
+and the expectation in
+this case is 1, so
+
+that's going to be 0.
+
+Now the variance.
+
+ 
+
+For the shift, it doesn't
+affect the spread.
+
+And so the variance is exactly
+going to be the same without
+
+the minus 1/2.
+
+And for the constant, you
+can just pull that
+
+out and square it.
+
+ 
+
+And the variance of
+y we know is 4.
+
+And so that's 1/4 times
+4, that's 1.
+
+OK.
+
+So now we know that y
+minus 1 over 2 is
+
+actually standard normal.
+
+ 
+
+Actually for any normal random
+variable, you can follow the
+
+same procedure.
+
+You just subtract its mean,
+which is 1 in this case.
+
+And divide by its standard
+deviation and you will get a
+
+standard normal distribution.
+
+All right, so for part C we want
+the probability that y is
+
+between negative 1 and 1.
+
+So let's try to massage it so
+that we can use the standard
+
+normal table.
+
+And we already know that this
+is standard normal, so let's
+
+subtract both sides
+by negative 1.
+
+ 
+
+And that's equal to--
+
+I'm going to call this standard
+normal z, so that's
+
+easier to write.
+
+And that's equal to negative 1
+less than equal to z, less
+
+than equal to zero.
+
+So we're looking for this
+region, 0, 1, negative 1.
+
+ 
+
+So that's just the probability
+that it's less than zero minus
+
+probability that it's less
+than negative 1.
+
+Well for a standard normal, half
+the mass is below zero
+
+and a half the mass is above.
+
+And so that's just going
+to be 0.5 directly.
+
+And for this, we've already
+computed this for a standard
+
+normal, which was
+x in our case.
+
+And that was 1 minus 0.8413.
+
+Done.
+
+So we basically calculated a few
+standard probabilities for
+
+normal distributions.
+
+And we did that by looking
+them up from the standard
+
+normal table.
\ No newline at end of file
diff --git a/6rOvXGoXoJc.txt b/6rOvXGoXoJc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..43a7e34f74a872ddc5565e57426ad59ee91f6cb7
--- /dev/null
+++ b/6rOvXGoXoJc.txt
@@ -0,0 +1,6619 @@
+align:start position:0%
+ 
+so I guess I will start by first of all
+
+ align:start position:0%
+so I guess I will start by first of all
+ 
+
+ align:start position:0%
+so I guess I will start by first of all
+congratulating you all since the last
+
+ align:start position:0%
+congratulating you all since the last
+ 
+
+ align:start position:0%
+congratulating you all since the last
+time I've seen you you've all
+
+ align:start position:0%
+time I've seen you you've all
+ 
+
+ align:start position:0%
+time I've seen you you've all
+regenerated your intestine so it's like
+
+ align:start position:0%
+regenerated your intestine so it's like
+ 
+
+ align:start position:0%
+regenerated your intestine so it's like
+you're a brand-new person okay so so
+
+ align:start position:0%
+you're a brand-new person okay so so
+ 
+
+ align:start position:0%
+you're a brand-new person okay so so
+there's that I want to start the lecture
+
+ align:start position:0%
+there's that I want to start the lecture
+ 
+
+ align:start position:0%
+there's that I want to start the lecture
+by talking about something I've been
+
+ align:start position:0%
+by talking about something I've been
+ 
+
+ align:start position:0%
+by talking about something I've been
+putting off telling you about which is
+
+ align:start position:0%
+putting off telling you about which is
+ 
+
+ align:start position:0%
+putting off telling you about which is
+the Nobel Prize in Physiology or
+
+ align:start position:0%
+the Nobel Prize in Physiology or
+ 
+
+ align:start position:0%
+the Nobel Prize in Physiology or
+medicine that was awarded this year and
+
+ align:start position:0%
+medicine that was awarded this year and
+ 
+
+ align:start position:0%
+medicine that was awarded this year and
+it was awarded to James Allison and
+
+ align:start position:0%
+it was awarded to James Allison and
+ 
+
+ align:start position:0%
+it was awarded to James Allison and
+tasuku hangzhou for their discovery of a
+
+ align:start position:0%
+tasuku hangzhou for their discovery of a
+ 
+
+ align:start position:0%
+tasuku hangzhou for their discovery of a
+way to harness the immune system to
+
+ align:start position:0%
+way to harness the immune system to
+ 
+
+ align:start position:0%
+way to harness the immune system to
+fight cancer okay and we're gonna talk
+
+ align:start position:0%
+fight cancer okay and we're gonna talk
+ 
+
+ align:start position:0%
+fight cancer okay and we're gonna talk
+about the immune system later in the
+
+ align:start position:0%
+about the immune system later in the
+ 
+
+ align:start position:0%
+about the immune system later in the
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+and it turns out I I will lecture on it
+
+ align:start position:0%
+and it turns out I I will lecture on it
+ 
+
+ align:start position:0%
+and it turns out I I will lecture on it
+and I've actually had immunology and in
+
+ align:start position:0%
+and I've actually had immunology and in
+ 
+
+ align:start position:0%
+and I've actually had immunology and in
+fact I had immunology with James Allison
+
+ align:start position:0%
+fact I had immunology with James Allison
+ 
+
+ align:start position:0%
+fact I had immunology with James Allison
+so I will do my best to channel James
+
+ align:start position:0%
+so I will do my best to channel James
+ 
+
+ align:start position:0%
+so I will do my best to channel James
+Allison when I talk about the immune
+
+ align:start position:0%
+Allison when I talk about the immune
+ 
+
+ align:start position:0%
+Allison when I talk about the immune
+system but what what they won the prize
+
+ align:start position:0%
+system but what what they won the prize
+ 
+
+ align:start position:0%
+system but what what they won the prize
+for is they figured out a way to
+
+ align:start position:0%
+for is they figured out a way to
+ 
+
+ align:start position:0%
+for is they figured out a way to
+essentially release the break on the
+
+ align:start position:0%
+essentially release the break on the
+ 
+
+ align:start position:0%
+essentially release the break on the
+immune system in order to allow the
+
+ align:start position:0%
+immune system in order to allow the
+ 
+
+ align:start position:0%
+immune system in order to allow the
+immune system system to better fight
+
+ align:start position:0%
+immune system system to better fight
+ 
+
+ align:start position:0%
+immune system system to better fight
+cancer okay and this is a technique
+
+ align:start position:0%
+cancer okay and this is a technique
+ 
+
+ align:start position:0%
+cancer okay and this is a technique
+that's been used in the clinic and there
+
+ align:start position:0%
+that's been used in the clinic and there
+ 
+
+ align:start position:0%
+that's been used in the clinic and there
+are currently a number of clinical
+
+ align:start position:0%
+are currently a number of clinical
+ 
+
+ align:start position:0%
+are currently a number of clinical
+trials that are also looking to see
+
+ align:start position:0%
+trials that are also looking to see
+ 
+
+ align:start position:0%
+trials that are also looking to see
+whether this can be used in a variety of
+
+ align:start position:0%
+whether this can be used in a variety of
+ 
+
+ align:start position:0%
+whether this can be used in a variety of
+different cancer types okay so I just
+
+ align:start position:0%
+different cancer types okay so I just
+ 
+
+ align:start position:0%
+different cancer types okay so I just
+wanted to point that out now because
+
+ align:start position:0%
+wanted to point that out now because
+ 
+
+ align:start position:0%
+wanted to point that out now because
+we're talking about cancer and I'll go
+
+ align:start position:0%
+we're talking about cancer and I'll go
+ 
+
+ align:start position:0%
+we're talking about cancer and I'll go
+more into the mechanism is how this
+
+ align:start position:0%
+more into the mechanism is how this
+ 
+
+ align:start position:0%
+more into the mechanism is how this
+works when we start talking about the
+
+ align:start position:0%
+works when we start talking about the
+ 
+
+ align:start position:0%
+works when we start talking about the
+immune system so as I mentioned in the
+
+ align:start position:0%
+immune system so as I mentioned in the
+ 
+
+ align:start position:0%
+immune system so as I mentioned in the
+last lecture cancer is basically a
+
+ align:start position:0%
+last lecture cancer is basically a
+ 
+
+ align:start position:0%
+last lecture cancer is basically a
+progressive loss of tissue organization
+
+ align:start position:0%
+progressive loss of tissue organization
+ 
+
+ align:start position:0%
+progressive loss of tissue organization
+and luckily for us our body has a number
+
+ align:start position:0%
+and luckily for us our body has a number
+ 
+
+ align:start position:0%
+and luckily for us our body has a number
+of different barriers to cells becoming
+
+ align:start position:0%
+of different barriers to cells becoming
+ 
+
+ align:start position:0%
+of different barriers to cells becoming
+cancerous and forming a tumor and so I
+
+ align:start position:0%
+cancerous and forming a tumor and so I
+ 
+
+ align:start position:0%
+cancerous and forming a tumor and so I
+wanted to start out just by having you
+
+ align:start position:0%
+wanted to start out just by having you
+ 
+
+ align:start position:0%
+wanted to start out just by having you
+guys tell me what you feel the barriers
+
+ align:start position:0%
+guys tell me what you feel the barriers
+ 
+
+ align:start position:0%
+guys tell me what you feel the barriers
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+to this process so who has an idea of a
+
+ align:start position:0%
+to this process so who has an idea of a
+ 
+
+ align:start position:0%
+to this process so who has an idea of a
+barrier what are the barriers in place
+
+ align:start position:0%
+barrier what are the barriers in place
+ 
+
+ align:start position:0%
+barrier what are the barriers in place
+by your body to prevent cancer cells
+
+ align:start position:0%
+by your body to prevent cancer cells
+ 
+
+ align:start position:0%
+by your body to prevent cancer cells
+from arising and forming a tumor and for
+
+ align:start position:0%
+from arising and forming a tumor and for
+ 
+
+ align:start position:0%
+from arising and forming a tumor and for
+this process to form a malignant tumor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's that Oh Rachel sorry apoptosis is
+
+ align:start position:0%
+what's that Oh Rachel sorry apoptosis is
+ 
+
+ align:start position:0%
+what's that Oh Rachel sorry apoptosis is
+a good one
+
+ align:start position:0%
+a good one
+ 
+
+ align:start position:0%
+a good one
+right so there's a careful process right
+
+ align:start position:0%
+right so there's a careful process right
+ 
+
+ align:start position:0%
+right so there's a careful process right
+in the in your body to limit how long
+
+ align:start position:0%
+in the in your body to limit how long
+ 
+
+ align:start position:0%
+in the in your body to limit how long
+certain cells are resident in the body
+
+ align:start position:0%
+certain cells are resident in the body
+ 
+
+ align:start position:0%
+certain cells are resident in the body
+and all of this depends on communication
+
+ align:start position:0%
+and all of this depends on communication
+ 
+
+ align:start position:0%
+and all of this depends on communication
+between different cell types in your
+
+ align:start position:0%
+between different cell types in your
+ 
+
+ align:start position:0%
+between different cell types in your
+body so so barriers to tumorigenesis and
+
+ align:start position:0%
+body so so barriers to tumorigenesis and
+ 
+
+ align:start position:0%
+body so so barriers to tumorigenesis and
+one type of signal is a survival signal
+
+ align:start position:0%
+one type of signal is a survival signal
+ 
+
+ align:start position:0%
+one type of signal is a survival signal
+and if a cell is not getting a survival
+
+ align:start position:0%
+and if a cell is not getting a survival
+ 
+
+ align:start position:0%
+and if a cell is not getting a survival
+signal then the cell will undergo
+
+ align:start position:0%
+signal then the cell will undergo
+ 
+
+ align:start position:0%
+signal then the cell will undergo
+apoptosis which is what Rachel was
+
+ align:start position:0%
+apoptosis which is what Rachel was
+ 
+
+ align:start position:0%
+apoptosis which is what Rachel was
+referring to right so one barrier is
+
+ align:start position:0%
+referring to right so one barrier is
+ 
+
+ align:start position:0%
+referring to right so one barrier is
+that there is a highly regulated system
+
+ align:start position:0%
+that there is a highly regulated system
+ 
+
+ align:start position:0%
+that there is a highly regulated system
+of determining whether or not cells
+
+ align:start position:0%
+of determining whether or not cells
+ 
+
+ align:start position:0%
+of determining whether or not cells
+divide and also whether or not cells
+
+ align:start position:0%
+divide and also whether or not cells
+ 
+
+ align:start position:0%
+divide and also whether or not cells
+live okay so there are growth survival
+
+ align:start position:0%
+live okay so there are growth survival
+ 
+
+ align:start position:0%
+live okay so there are growth survival
+signals which means that the decision
+
+ align:start position:0%
+signals which means that the decision
+ 
+
+ align:start position:0%
+signals which means that the decision
+for a cell to sort of go off its rocker
+
+ align:start position:0%
+for a cell to sort of go off its rocker
+ 
+
+ align:start position:0%
+for a cell to sort of go off its rocker
+and just start dividing uncontrollably
+
+ align:start position:0%
+and just start dividing uncontrollably
+ 
+
+ align:start position:0%
+and just start dividing uncontrollably
+is not likely for a normal cell
+
+ align:start position:0%
+is not likely for a normal cell
+ 
+
+ align:start position:0%
+is not likely for a normal cell
+something has to happen to that cell in
+
+ align:start position:0%
+something has to happen to that cell in
+ 
+
+ align:start position:0%
+something has to happen to that cell in
+order to perturb it okay so what are
+
+ align:start position:0%
+order to perturb it okay so what are
+ 
+
+ align:start position:0%
+order to perturb it okay so what are
+some other barriers to sort of forming a
+
+ align:start position:0%
+some other barriers to sort of forming a
+ 
+
+ align:start position:0%
+some other barriers to sort of forming a
+tumor and for that tumor to become
+
+ align:start position:0%
+tumor and for that tumor to become
+ 
+
+ align:start position:0%
+tumor and for that tumor to become
+invasive yes Jeremy yeah so the this
+
+ align:start position:0%
+invasive yes Jeremy yeah so the this
+ 
+
+ align:start position:0%
+invasive yes Jeremy yeah so the this
+cancer cell can't activate the immune
+
+ align:start position:0%
+cancer cell can't activate the immune
+ 
+
+ align:start position:0%
+cancer cell can't activate the immune
+system so you could have some type of
+
+ align:start position:0%
+system so you could have some type of
+ 
+
+ align:start position:0%
+system so you could have some type of
+immuno suppression of the cancer
+
+ align:start position:0%
+immuno suppression of the cancer
+ 
+
+ align:start position:0%
+immuno suppression of the cancer
+and I won't talk about that today but
+
+ align:start position:0%
+and I won't talk about that today but
+ 
+
+ align:start position:0%
+and I won't talk about that today but
+maybe we'll come back and talk about it
+
+ align:start position:0%
+maybe we'll come back and talk about it
+ 
+
+ align:start position:0%
+maybe we'll come back and talk about it
+when we talk about the immune system
+
+ align:start position:0%
+when we talk about the immune system
+ 
+
+ align:start position:0%
+when we talk about the immune system
+okay looking looking at this diagram
+
+ align:start position:0%
+okay looking looking at this diagram
+ 
+
+ align:start position:0%
+okay looking looking at this diagram
+when the cell proceeded when the
+
+ align:start position:0%
+when the cell proceeded when the
+ 
+
+ align:start position:0%
+when the cell proceeded when the
+tumorous proceeds to invasive cancer
+
+ align:start position:0%
+tumorous proceeds to invasive cancer
+ 
+
+ align:start position:0%
+tumorous proceeds to invasive cancer
+what do you think are some barriers to
+
+ align:start position:0%
+what do you think are some barriers to
+ 
+
+ align:start position:0%
+what do you think are some barriers to
+that process happening what are cells
+
+ align:start position:0%
+that process happening what are cells
+ 
+
+ align:start position:0%
+that process happening what are cells
+new normally doing in an organ right the
+
+ align:start position:0%
+new normally doing in an organ right the
+ 
+
+ align:start position:0%
+new normally doing in an organ right the
+cells that line your intestine are they
+
+ align:start position:0%
+cells that line your intestine are they
+ 
+
+ align:start position:0%
+cells that line your intestine are they
+like invading into the surrounding
+
+ align:start position:0%
+like invading into the surrounding
+ 
+
+ align:start position:0%
+like invading into the surrounding
+tissue no Jeremy's shaking his head no
+
+ align:start position:0%
+tissue no Jeremy's shaking his head no
+ 
+
+ align:start position:0%
+tissue no Jeremy's shaking his head no
+right so normally cells don't do that
+
+ align:start position:0%
+right so normally cells don't do that
+ 
+
+ align:start position:0%
+right so normally cells don't do that
+right or certain types of cells do but
+
+ align:start position:0%
+right or certain types of cells do but
+ 
+
+ align:start position:0%
+right or certain types of cells do but
+normally if you have cells that are the
+
+ align:start position:0%
+normally if you have cells that are the
+ 
+
+ align:start position:0%
+normally if you have cells that are the
+lining of an epithelium they're not like
+
+ align:start position:0%
+lining of an epithelium they're not like
+ 
+
+ align:start position:0%
+lining of an epithelium they're not like
+going and going off to a blood vessel
+
+ align:start position:0%
+going and going off to a blood vessel
+ 
+
+ align:start position:0%
+going and going off to a blood vessel
+okay so I'm just going to sort of review
+
+ align:start position:0%
+okay so I'm just going to sort of review
+ 
+
+ align:start position:0%
+okay so I'm just going to sort of review
+sort of the structure of the tissue and
+
+ align:start position:0%
+sort of the structure of the tissue and
+ 
+
+ align:start position:0%
+sort of the structure of the tissue and
+then we'll talk about some of the
+
+ align:start position:0%
+then we'll talk about some of the
+ 
+
+ align:start position:0%
+then we'll talk about some of the
+barriers that prevent this from
+
+ align:start position:0%
+barriers that prevent this from
+ 
+
+ align:start position:0%
+barriers that prevent this from
+happening so I'm drawing a tubular organ
+
+ align:start position:0%
+happening so I'm drawing a tubular organ
+ 
+
+ align:start position:0%
+happening so I'm drawing a tubular organ
+here right this could be the tube of the
+
+ align:start position:0%
+here right this could be the tube of the
+ 
+
+ align:start position:0%
+here right this could be the tube of the
+intestine there would be a lumen inside
+
+ align:start position:0%
+intestine there would be a lumen inside
+ 
+
+ align:start position:0%
+intestine there would be a lumen inside
+here it could be some ductal structure
+
+ align:start position:0%
+here it could be some ductal structure
+ 
+
+ align:start position:0%
+here it could be some ductal structure
+in an organ like a mammary gland it
+
+ align:start position:0%
+in an organ like a mammary gland it
+ 
+
+ align:start position:0%
+in an organ like a mammary gland it
+could be that this is the airway of a
+
+ align:start position:0%
+could be that this is the airway of a
+ 
+
+ align:start position:0%
+could be that this is the airway of a
+lung and there's an epithelial lining
+
+ align:start position:0%
+lung and there's an epithelial lining
+ 
+
+ align:start position:0%
+lung and there's an epithelial lining
+around that airway so these cells here
+
+ align:start position:0%
+around that airway so these cells here
+ 
+
+ align:start position:0%
+around that airway so these cells here
+are forming an epithelial lining and one
+
+ align:start position:0%
+are forming an epithelial lining and one
+ 
+
+ align:start position:0%
+are forming an epithelial lining and one
+important aspect of epithelial biology
+
+ align:start position:0%
+important aspect of epithelial biology
+ 
+
+ align:start position:0%
+important aspect of epithelial biology
+is in mature epithelia they have a floor
+
+ align:start position:0%
+is in mature epithelia they have a floor
+ 
+
+ align:start position:0%
+is in mature epithelia they have a floor
+that the cells stand on okay so this
+
+ align:start position:0%
+that the cells stand on okay so this
+ 
+
+ align:start position:0%
+that the cells stand on okay so this
+structure that I just drew around these
+
+ align:start position:0%
+structure that I just drew around these
+ 
+
+ align:start position:0%
+structure that I just drew around these
+cells in green is known as the basement
+
+ align:start position:0%
+cells in green is known as the basement
+ 
+
+ align:start position:0%
+cells in green is known as the basement
+membrane all right it's the basement
+
+ align:start position:0%
+membrane all right it's the basement
+ 
+
+ align:start position:0%
+membrane all right it's the basement
+because it's kind of the floor that this
+
+ align:start position:0%
+because it's kind of the floor that this
+ 
+
+ align:start position:0%
+because it's kind of the floor that this
+other thing is built on and this
+
+ align:start position:0%
+other thing is built on and this
+ 
+
+ align:start position:0%
+other thing is built on and this
+basement membrane is made out of what is
+
+ align:start position:0%
+basement membrane is made out of what is
+ 
+
+ align:start position:0%
+basement membrane is made out of what is
+known as the extracellular matrix which
+
+ align:start position:0%
+known as the extracellular matrix which
+ 
+
+ align:start position:0%
+known as the extracellular matrix which
+I'll just call matrix right now the
+
+ align:start position:0%
+I'll just call matrix right now the
+ 
+
+ align:start position:0%
+I'll just call matrix right now the
+extracellular matrix are base
+
+ align:start position:0%
+extracellular matrix are base
+ 
+
+ align:start position:0%
+extracellular matrix are base
+Stickley extracellular proteins that
+
+ align:start position:0%
+Stickley extracellular proteins that
+ 
+
+ align:start position:0%
+Stickley extracellular proteins that
+form a meshwork
+
+ align:start position:0%
+form a meshwork
+ 
+
+ align:start position:0%
+form a meshwork
+that forms a rate rigid structure on
+
+ align:start position:0%
+that forms a rate rigid structure on
+ 
+
+ align:start position:0%
+that forms a rate rigid structure on
+which epithelial cells can sit on okay
+
+ align:start position:0%
+which epithelial cells can sit on okay
+ 
+
+ align:start position:0%
+which epithelial cells can sit on okay
+now if we think about what surrounds
+
+ align:start position:0%
+now if we think about what surrounds
+ 
+
+ align:start position:0%
+now if we think about what surrounds
+this organ there's there's also matrix
+
+ align:start position:0%
+this organ there's there's also matrix
+ 
+
+ align:start position:0%
+this organ there's there's also matrix
+proteins and sort of intervening areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is known as connective tissue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so if we think about the cells
+
+ align:start position:0%
+okay and so if we think about the cells
+ 
+
+ align:start position:0%
+okay and so if we think about the cells
+that are the epithelial cells here they
+
+ align:start position:0%
+that are the epithelial cells here they
+ 
+
+ align:start position:0%
+that are the epithelial cells here they
+are in one state and this state is known
+
+ align:start position:0%
+are in one state and this state is known
+ 
+
+ align:start position:0%
+are in one state and this state is known
+as epithelial as I just said so these
+
+ align:start position:0%
+as epithelial as I just said so these
+ 
+
+ align:start position:0%
+as epithelial as I just said so these
+are both alleles epithelial cells have a
+
+ align:start position:0%
+are both alleles epithelial cells have a
+ 
+
+ align:start position:0%
+are both alleles epithelial cells have a
+few properties that are really
+
+ align:start position:0%
+few properties that are really
+ 
+
+ align:start position:0%
+few properties that are really
+distinguishing the first is that they
+
+ align:start position:0%
+distinguishing the first is that they
+ 
+
+ align:start position:0%
+distinguishing the first is that they
+have high intercellular adhesion and the
+
+ align:start position:0%
+have high intercellular adhesion and the
+ 
+
+ align:start position:0%
+have high intercellular adhesion and the
+next is that if you consider their
+
+ align:start position:0%
+next is that if you consider their
+ 
+
+ align:start position:0%
+next is that if you consider their
+relative mobility you know they can
+
+ align:start position:0%
+relative mobility you know they can
+ 
+
+ align:start position:0%
+relative mobility you know they can
+obviously move within the epithelium
+
+ align:start position:0%
+obviously move within the epithelium
+ 
+
+ align:start position:0%
+obviously move within the epithelium
+because we talked about the intestine
+
+ align:start position:0%
+because we talked about the intestine
+ 
+
+ align:start position:0%
+because we talked about the intestine
+and how cells are moving from the base
+
+ align:start position:0%
+and how cells are moving from the base
+ 
+
+ align:start position:0%
+and how cells are moving from the base
+of the crypts up to the villas but in
+
+ align:start position:0%
+of the crypts up to the villas but in
+ 
+
+ align:start position:0%
+of the crypts up to the villas but in
+general these cells aren't moving in and
+
+ align:start position:0%
+general these cells aren't moving in and
+ 
+
+ align:start position:0%
+general these cells aren't moving in and
+out of the organ okay so I would say
+
+ align:start position:0%
+out of the organ okay so I would say
+ 
+
+ align:start position:0%
+out of the organ okay so I would say
+that they have a low migratory potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so these are the epithelial
+
+ align:start position:0%
+okay and so these are the epithelial
+ 
+
+ align:start position:0%
+okay and so these are the epithelial
+cells that are here now there are also
+
+ align:start position:0%
+cells that are here now there are also
+ 
+
+ align:start position:0%
+cells that are here now there are also
+cells that are in this interstitial
+
+ align:start position:0%
+cells that are in this interstitial
+ 
+
+ align:start position:0%
+cells that are in this interstitial
+space and I'll draw they often have this
+
+ align:start position:0%
+space and I'll draw they often have this
+ 
+
+ align:start position:0%
+space and I'll draw they often have this
+highly elongated morphology and these
+
+ align:start position:0%
+highly elongated morphology and these
+ 
+
+ align:start position:0%
+highly elongated morphology and these
+cells are in a fundamentally different
+
+ align:start position:0%
+cells are in a fundamentally different
+ 
+
+ align:start position:0%
+cells are in a fundamentally different
+state okay and this state is known as
+
+ align:start position:0%
+state okay and this state is known as
+ 
+
+ align:start position:0%
+state okay and this state is known as
+mesenchymal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or stromal so this area sort of outside
+
+ align:start position:0%
+or stromal so this area sort of outside
+ 
+
+ align:start position:0%
+or stromal so this area sort of outside
+the organ is also known as the stroma so
+
+ align:start position:0%
+the organ is also known as the stroma so
+ 
+
+ align:start position:0%
+the organ is also known as the stroma so
+there are known as stromal cells in this
+
+ align:start position:0%
+there are known as stromal cells in this
+ 
+
+ align:start position:0%
+there are known as stromal cells in this
+in this location and these cells have
+
+ align:start position:0%
+in this location and these cells have
+ 
+
+ align:start position:0%
+in this location and these cells have
+very different properties than
+
+ align:start position:0%
+very different properties than
+ 
+
+ align:start position:0%
+very different properties than
+epithelial cells and that they have low
+
+ align:start position:0%
+epithelial cells and that they have low
+ 
+
+ align:start position:0%
+epithelial cells and that they have low
+adhesion I should say low cell to cell
+
+ align:start position:0%
+adhesion I should say low cell to cell
+ 
+
+ align:start position:0%
+adhesion I should say low cell to cell
+adhesion and in contrast to these
+
+ align:start position:0%
+adhesion and in contrast to these
+ 
+
+ align:start position:0%
+adhesion and in contrast to these
+epithelial cells these stromal cells as
+
+ align:start position:0%
+epithelial cells these stromal cells as
+ 
+
+ align:start position:0%
+epithelial cells these stromal cells as
+you see in this example up here for
+
+ align:start position:0%
+you see in this example up here for
+ 
+
+ align:start position:0%
+you see in this example up here for
+that's a human neutrophil these stromal
+
+ align:start position:0%
+that's a human neutrophil these stromal
+ 
+
+ align:start position:0%
+that's a human neutrophil these stromal
+cells are highly migratory so that
+
+ align:start position:0%
+cells are highly migratory so that
+ 
+
+ align:start position:0%
+cells are highly migratory so that
+neutrophil is chasing a bacterium and
+
+ align:start position:0%
+neutrophil is chasing a bacterium and
+ 
+
+ align:start position:0%
+neutrophil is chasing a bacterium and
+they'll eventually get it but the movie
+
+ align:start position:0%
+they'll eventually get it but the movie
+ 
+
+ align:start position:0%
+they'll eventually get it but the movie
+will loop and so you'll see it
+
+ align:start position:0%
+will loop and so you'll see it
+ 
+
+ align:start position:0%
+will loop and so you'll see it
+constantly chasing that bacterium okay
+
+ align:start position:0%
+constantly chasing that bacterium okay
+ 
+
+ align:start position:0%
+constantly chasing that bacterium okay
+so some examples of stromal cells would
+
+ align:start position:0%
+so some examples of stromal cells would
+ 
+
+ align:start position:0%
+so some examples of stromal cells would
+be immune cells like this human
+
+ align:start position:0%
+be immune cells like this human
+ 
+
+ align:start position:0%
+be immune cells like this human
+neutrophil and you probably know that
+
+ align:start position:0%
+neutrophil and you probably know that
+ 
+
+ align:start position:0%
+neutrophil and you probably know that
+immune cells have to traverse different
+
+ align:start position:0%
+immune cells have to traverse different
+ 
+
+ align:start position:0%
+immune cells have to traverse different
+organ systems they have to be rapidly
+
+ align:start position:0%
+organ systems they have to be rapidly
+ 
+
+ align:start position:0%
+organ systems they have to be rapidly
+recruited to sites of infection or sites
+
+ align:start position:0%
+recruited to sites of infection or sites
+ 
+
+ align:start position:0%
+recruited to sites of infection or sites
+of injury and so this type of cell has
+
+ align:start position:0%
+of injury and so this type of cell has
+ 
+
+ align:start position:0%
+of injury and so this type of cell has
+is fundamentally different from the
+
+ align:start position:0%
+is fundamentally different from the
+ 
+
+ align:start position:0%
+is fundamentally different from the
+types of cells that line your organs
+
+ align:start position:0%
+types of cells that line your organs
+ 
+
+ align:start position:0%
+types of cells that line your organs
+where you basically need those cells to
+
+ align:start position:0%
+where you basically need those cells to
+ 
+
+ align:start position:0%
+where you basically need those cells to
+stay put okay when considering cancer
+
+ align:start position:0%
+stay put okay when considering cancer
+ 
+
+ align:start position:0%
+stay put okay when considering cancer
+right you have these different types of
+
+ align:start position:0%
+right you have these different types of
+ 
+
+ align:start position:0%
+right you have these different types of
+cells in your body 90% of cancer comes
+
+ align:start position:0%
+cells in your body 90% of cancer comes
+ 
+
+ align:start position:0%
+cells in your body 90% of cancer comes
+from a cell of epithelial origin okay so
+
+ align:start position:0%
+from a cell of epithelial origin okay so
+ 
+
+ align:start position:0%
+from a cell of epithelial origin okay so
+90% of cancers are epithelial and origin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay some other examples of stromal
+
+ align:start position:0%
+okay some other examples of stromal
+ 
+
+ align:start position:0%
+okay some other examples of stromal
+cells are cells like fibroblasts and
+
+ align:start position:0%
+cells are cells like fibroblasts and
+ 
+
+ align:start position:0%
+cells are cells like fibroblasts and
+fibroblasts are cells that secrete and
+
+ align:start position:0%
+fibroblasts are cells that secrete and
+ 
+
+ align:start position:0%
+fibroblasts are cells that secrete and
+remodel the matrix that's in connective
+
+ align:start position:0%
+remodel the matrix that's in connective
+ 
+
+ align:start position:0%
+remodel the matrix that's in connective
+tissue and they're also important for
+
+ align:start position:0%
+tissue and they're also important for
+ 
+
+ align:start position:0%
+tissue and they're also important for
+wound healing and secreting matrix
+
+ align:start position:0%
+wound healing and secreting matrix
+ 
+
+ align:start position:0%
+wound healing and secreting matrix
+during the wound healing process okay so
+
+ align:start position:0%
+during the wound healing process okay so
+ 
+
+ align:start position:0%
+during the wound healing process okay so
+that's just to give you a few examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's come back to this
+
+ align:start position:0%
+okay so now let's come back to this
+ 
+
+ align:start position:0%
+okay so now let's come back to this
+example and talk about how is it what
+
+ align:start position:0%
+example and talk about how is it what
+ 
+
+ align:start position:0%
+example and talk about how is it what
+what happens to get a cell to go all the
+
+ align:start position:0%
+what happens to get a cell to go all the
+ 
+
+ align:start position:0%
+what happens to get a cell to go all the
+way from being a normal epithelial cell
+
+ align:start position:0%
+way from being a normal epithelial cell
+ 
+
+ align:start position:0%
+way from being a normal epithelial cell
+to having this type of behavior where
+
+ align:start position:0%
+to having this type of behavior where
+ 
+
+ align:start position:0%
+to having this type of behavior where
+initially you have growth and a loss of
+
+ align:start position:0%
+initially you have growth and a loss of
+ 
+
+ align:start position:0%
+initially you have growth and a loss of
+the control over growth and survival
+
+ align:start position:0%
+the control over growth and survival
+ 
+
+ align:start position:0%
+the control over growth and survival
+signaling and eventually the cancer can
+
+ align:start position:0%
+signaling and eventually the cancer can
+ 
+
+ align:start position:0%
+signaling and eventually the cancer can
+become what's known as malignant and
+
+ align:start position:0%
+become what's known as malignant and
+ 
+
+ align:start position:0%
+become what's known as malignant and
+what's known so it's a progression and
+
+ align:start position:0%
+what's known so it's a progression and
+ 
+
+ align:start position:0%
+what's known so it's a progression and
+initially you might just get increased
+
+ align:start position:0%
+initially you might just get increased
+ 
+
+ align:start position:0%
+initially you might just get increased
+in cell division and abnormal cell shape
+
+ align:start position:0%
+in cell division and abnormal cell shape
+ 
+
+ align:start position:0%
+in cell division and abnormal cell shape
+which is known as dysplasia and at that
+
+ align:start position:0%
+which is known as dysplasia and at that
+ 
+
+ align:start position:0%
+which is known as dysplasia and at that
+point the it's known as something like
+
+ align:start position:0%
+point the it's known as something like
+ 
+
+ align:start position:0%
+point the it's known as something like
+an adenoma or something that's benign
+
+ align:start position:0%
+an adenoma or something that's benign
+ 
+
+ align:start position:0%
+an adenoma or something that's benign
+but it's this last point here up here
+
+ align:start position:0%
+but it's this last point here up here
+ 
+
+ align:start position:0%
+but it's this last point here up here
+where the cells breach this basement
+
+ align:start position:0%
+where the cells breach this basement
+ 
+
+ align:start position:0%
+where the cells breach this basement
+membrane that's when that happens then
+
+ align:start position:0%
+membrane that's when that happens then
+ 
+
+ align:start position:0%
+membrane that's when that happens then
+the cancer is known as carcinoma and
+
+ align:start position:0%
+the cancer is known as carcinoma and
+ 
+
+ align:start position:0%
+the cancer is known as carcinoma and
+it's on the lignin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so malignant look malignant cancer is
+
+ align:start position:0%
+so malignant look malignant cancer is
+ 
+
+ align:start position:0%
+so malignant look malignant cancer is
+cancer that has breached the basement
+
+ align:start position:0%
+cancer that has breached the basement
+ 
+
+ align:start position:0%
+cancer that has breached the basement
+membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I want to sort of take you
+
+ align:start position:0%
+all right so I want to sort of take you
+ 
+
+ align:start position:0%
+all right so I want to sort of take you
+through the progression of tumorigenesis
+
+ align:start position:0%
+through the progression of tumorigenesis
+ 
+
+ align:start position:0%
+through the progression of tumorigenesis
+and first I'm gonna start with the
+
+ align:start position:0%
+and first I'm gonna start with the
+ 
+
+ align:start position:0%
+and first I'm gonna start with the
+breakdown of this growth survival
+
+ align:start position:0%
+breakdown of this growth survival
+ 
+
+ align:start position:0%
+breakdown of this growth survival
+signaling and I just wanted to remind
+
+ align:start position:0%
+signaling and I just wanted to remind
+ 
+
+ align:start position:0%
+signaling and I just wanted to remind
+you about what we talked about with the
+
+ align:start position:0%
+you about what we talked about with the
+ 
+
+ align:start position:0%
+you about what we talked about with the
+intestine as our model organ and in the
+
+ align:start position:0%
+intestine as our model organ and in the
+ 
+
+ align:start position:0%
+intestine as our model organ and in the
+intestine remember that this is all
+
+ align:start position:0%
+intestine remember that this is all
+ 
+
+ align:start position:0%
+intestine remember that this is all
+regulated by signals between cells and
+
+ align:start position:0%
+regulated by signals between cells and
+ 
+
+ align:start position:0%
+regulated by signals between cells and
+like stem cells and niche cells so the
+
+ align:start position:0%
+like stem cells and niche cells so the
+ 
+
+ align:start position:0%
+like stem cells and niche cells so the
+niche cells are sent sending the stem
+
+ align:start position:0%
+niche cells are sent sending the stem
+ 
+
+ align:start position:0%
+niche cells are sent sending the stem
+cells signals like wints that control
+
+ align:start position:0%
+cells signals like wints that control
+ 
+
+ align:start position:0%
+cells signals like wints that control
+their self-renewal and then it's the
+
+ align:start position:0%
+their self-renewal and then it's the
+ 
+
+ align:start position:0%
+their self-renewal and then it's the
+loss of this signaling that allows these
+
+ align:start position:0%
+loss of this signaling that allows these
+ 
+
+ align:start position:0%
+loss of this signaling that allows these
+cells to eventually undergo apoptosis
+
+ align:start position:0%
+cells to eventually undergo apoptosis
+ 
+
+ align:start position:0%
+cells to eventually undergo apoptosis
+and get shed into the lumen of the
+
+ align:start position:0%
+and get shed into the lumen of the
+ 
+
+ align:start position:0%
+and get shed into the lumen of the
+intestine okay so one of the first steps
+
+ align:start position:0%
+intestine okay so one of the first steps
+ 
+
+ align:start position:0%
+intestine okay so one of the first steps
+in cancer is this breakdown and growth
+
+ align:start position:0%
+in cancer is this breakdown and growth
+ 
+
+ align:start position:0%
+in cancer is this breakdown and growth
+survival signaling so this this first
+
+ align:start position:0%
+survival signaling so this this first
+ 
+
+ align:start position:0%
+survival signaling so this this first
+breakdown is going to enable the cells
+
+ align:start position:0%
+breakdown is going to enable the cells
+ 
+
+ align:start position:0%
+breakdown is going to enable the cells
+to sort of overcome this first barrier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so as I just pointed out
+
+ align:start position:0%
+okay and so as I just pointed out
+ 
+
+ align:start position:0%
+okay and so as I just pointed out
+remember it helps to think of what has
+
+ align:start position:0%
+remember it helps to think of what has
+ 
+
+ align:start position:0%
+remember it helps to think of what has
+to happen in a normal tissue or organ
+
+ align:start position:0%
+to happen in a normal tissue or organ
+ 
+
+ align:start position:0%
+to happen in a normal tissue or organ
+normally the decision whether or not a
+
+ align:start position:0%
+normally the decision whether or not a
+ 
+
+ align:start position:0%
+normally the decision whether or not a
+cell divides or death dies so cell
+
+ align:start position:0%
+cell divides or death dies so cell
+ 
+
+ align:start position:0%
+cell divides or death dies so cell
+division and also death is highly
+
+ align:start position:0%
+division and also death is highly
+ 
+
+ align:start position:0%
+division and also death is highly
+regulated okay and it's regulated by
+
+ align:start position:0%
+regulated okay and it's regulated by
+ 
+
+ align:start position:0%
+regulated okay and it's regulated by
+communication with other cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in cancer this regulation goes awry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and how would this regulation go
+
+ align:start position:0%
+right and how would this regulation go
+ 
+
+ align:start position:0%
+right and how would this regulation go
+awry yeah Jeremy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Jeremy suggested that there could be
+
+ align:start position:0%
+so Jeremy suggested that there could be
+ 
+
+ align:start position:0%
+so Jeremy suggested that there could be
+mutations like oncogenic mutations or
+
+ align:start position:0%
+mutations like oncogenic mutations or
+ 
+
+ align:start position:0%
+mutations like oncogenic mutations or
+tumor suppressor loss that lead to
+
+ align:start position:0%
+tumor suppressor loss that lead to
+ 
+
+ align:start position:0%
+tumor suppressor loss that lead to
+abnormal cell division and death and
+
+ align:start position:0%
+abnormal cell division and death and
+ 
+
+ align:start position:0%
+abnormal cell division and death and
+that is exactly right so you could have
+
+ align:start position:0%
+that is exactly right so you could have
+ 
+
+ align:start position:0%
+that is exactly right so you could have
+uncle genic mutations and these
+
+ align:start position:0%
+uncle genic mutations and these
+ 
+
+ align:start position:0%
+uncle genic mutations and these
+oncogenic mutations they often hyper
+
+ align:start position:0%
+oncogenic mutations they often hyper
+ 
+
+ align:start position:0%
+oncogenic mutations they often hyper
+activate or constitutively activate
+
+ align:start position:0%
+activate or constitutively activate
+ 
+
+ align:start position:0%
+activate or constitutively activate
+these growth signaling pathways that are
+
+ align:start position:0%
+these growth signaling pathways that are
+ 
+
+ align:start position:0%
+these growth signaling pathways that are
+normally downstream of growth factors
+
+ align:start position:0%
+normally downstream of growth factors
+ 
+
+ align:start position:0%
+normally downstream of growth factors
+and receptor tyrosine kinase a--'s and
+
+ align:start position:0%
+and receptor tyrosine kinase a--'s and
+ 
+
+ align:start position:0%
+and receptor tyrosine kinase a--'s and
+if you hyper activate those you reduce
+
+ align:start position:0%
+if you hyper activate those you reduce
+ 
+
+ align:start position:0%
+if you hyper activate those you reduce
+the dependency of the cells on these
+
+ align:start position:0%
+the dependency of the cells on these
+ 
+
+ align:start position:0%
+the dependency of the cells on these
+signals okay so these oncogenic
+
+ align:start position:0%
+signals okay so these oncogenic
+ 
+
+ align:start position:0%
+signals okay so these oncogenic
+mutations can reduce the dependency of
+
+ align:start position:0%
+mutations can reduce the dependency of
+ 
+
+ align:start position:0%
+mutations can reduce the dependency of
+cells on growth factors and growth
+
+ align:start position:0%
+cells on growth factors and growth
+ 
+
+ align:start position:0%
+cells on growth factors and growth
+signals okay but one important point is
+
+ align:start position:0%
+signals okay but one important point is
+ 
+
+ align:start position:0%
+signals okay but one important point is
+that this is not enough okay and you can
+
+ align:start position:0%
+that this is not enough okay and you can
+ 
+
+ align:start position:0%
+that this is not enough okay and you can
+think about this in the case of the
+
+ align:start position:0%
+think about this in the case of the
+ 
+
+ align:start position:0%
+think about this in the case of the
+intestine because if you had an
+
+ align:start position:0%
+intestine because if you had an
+ 
+
+ align:start position:0%
+intestine because if you had an
+oncogenic mutation in one of these cells
+
+ align:start position:0%
+oncogenic mutation in one of these cells
+ 
+
+ align:start position:0%
+oncogenic mutation in one of these cells
+here it might not be as dependent on
+
+ align:start position:0%
+here it might not be as dependent on
+ 
+
+ align:start position:0%
+here it might not be as dependent on
+signals for growth but it doesn't matter
+
+ align:start position:0%
+signals for growth but it doesn't matter
+ 
+
+ align:start position:0%
+signals for growth but it doesn't matter
+because even though you had that
+
+ align:start position:0%
+because even though you had that
+ 
+
+ align:start position:0%
+because even though you had that
+mutation is gonna die and it's gonna
+
+ align:start position:0%
+mutation is gonna die and it's gonna
+ 
+
+ align:start position:0%
+mutation is gonna die and it's gonna
+shed out of the tissue okay and actually
+
+ align:start position:0%
+shed out of the tissue okay and actually
+ 
+
+ align:start position:0%
+shed out of the tissue okay and actually
+what happens in many cases where you
+
+ align:start position:0%
+what happens in many cases where you
+ 
+
+ align:start position:0%
+what happens in many cases where you
+activate a signaling pathway that allows
+
+ align:start position:0%
+activate a signaling pathway that allows
+ 
+
+ align:start position:0%
+activate a signaling pathway that allows
+the cell to in an abnormal way go
+
+ align:start position:0%
+the cell to in an abnormal way go
+ 
+
+ align:start position:0%
+the cell to in an abnormal way go
+through the cell cycle you actually
+
+ align:start position:0%
+through the cell cycle you actually
+ 
+
+ align:start position:0%
+through the cell cycle you actually
+induce a failsafe mechanism at the cell
+
+ align:start position:0%
+induce a failsafe mechanism at the cell
+ 
+
+ align:start position:0%
+induce a failsafe mechanism at the cell
+which causes a cell to undergo a p'
+
+ align:start position:0%
+which causes a cell to undergo a p'
+ 
+
+ align:start position:0%
+which causes a cell to undergo a p'
+ptosis okay so often you get this step
+
+ align:start position:0%
+ptosis okay so often you get this step
+ 
+
+ align:start position:0%
+ptosis okay so often you get this step
+happening and the cell just undergo
+
+ align:start position:0%
+happening and the cell just undergo
+ 
+
+ align:start position:0%
+happening and the cell just undergo
+apoptosis because you've evolved to
+
+ align:start position:0%
+apoptosis because you've evolved to
+ 
+
+ align:start position:0%
+apoptosis because you've evolved to
+protect your organs from this type of
+
+ align:start position:0%
+protect your organs from this type of
+ 
+
+ align:start position:0%
+protect your organs from this type of
+mutation so it's the oncogenic mutation
+
+ align:start position:0%
+mutation so it's the oncogenic mutation
+ 
+
+ align:start position:0%
+mutation so it's the oncogenic mutation
+in collaboration with loss of tumor
+
+ align:start position:0%
+in collaboration with loss of tumor
+ 
+
+ align:start position:0%
+in collaboration with loss of tumor
+suppression and one of the main tumor
+
+ align:start position:0%
+suppression and one of the main tumor
+ 
+
+ align:start position:0%
+suppression and one of the main tumor
+suppressive mechanisms our body has is
+
+ align:start position:0%
+suppressive mechanisms our body has is
+ 
+
+ align:start position:0%
+suppressive mechanisms our body has is
+apoptosis where if the cell is doing
+
+ align:start position:0%
+apoptosis where if the cell is doing
+ 
+
+ align:start position:0%
+apoptosis where if the cell is doing
+something abnormal the cell simply dies
+
+ align:start position:0%
+something abnormal the cell simply dies
+ 
+
+ align:start position:0%
+something abnormal the cell simply dies
+okay so so loss of a tumor suppressor
+
+ align:start position:0%
+okay so so loss of a tumor suppressor
+ 
+
+ align:start position:0%
+okay so so loss of a tumor suppressor
+could be loss of a gene that promotes
+
+ align:start position:0%
+could be loss of a gene that promotes
+ 
+
+ align:start position:0%
+could be loss of a gene that promotes
+apoptosis and in that case if the cell
+
+ align:start position:0%
+apoptosis and in that case if the cell
+ 
+
+ align:start position:0%
+apoptosis and in that case if the cell
+loses that mechanism the cell will avoid
+
+ align:start position:0%
+loses that mechanism the cell will avoid
+ 
+
+ align:start position:0%
+loses that mechanism the cell will avoid
+apoptosis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are it seiz uncle genic
+
+ align:start position:0%
+okay so these are it seiz uncle genic
+ 
+
+ align:start position:0%
+okay so these are it seiz uncle genic
+and the los oncogenic mutations and the
+
+ align:start position:0%
+and the los oncogenic mutations and the
+ 
+
+ align:start position:0%
+and the los oncogenic mutations and the
+loss of tumor suppressors which subverts
+
+ align:start position:0%
+loss of tumor suppressors which subverts
+ 
+
+ align:start position:0%
+loss of tumor suppressors which subverts
+the normal communication between cells
+
+ align:start position:0%
+the normal communication between cells
+ 
+
+ align:start position:0%
+the normal communication between cells
+which is required for normal tissue
+
+ align:start position:0%
+which is required for normal tissue
+ 
+
+ align:start position:0%
+which is required for normal tissue
+homeostasis okay now another example of
+
+ align:start position:0%
+homeostasis okay now another example of
+ 
+
+ align:start position:0%
+homeostasis okay now another example of
+this growth in survival signaling is not
+
+ align:start position:0%
+this growth in survival signaling is not
+ 
+
+ align:start position:0%
+this growth in survival signaling is not
+one which involves necessarily a genetic
+
+ align:start position:0%
+one which involves necessarily a genetic
+ 
+
+ align:start position:0%
+one which involves necessarily a genetic
+change but one that involves changes in
+
+ align:start position:0%
+change but one that involves changes in
+ 
+
+ align:start position:0%
+change but one that involves changes in
+expression and it also involves
+
+ align:start position:0%
+expression and it also involves
+ 
+
+ align:start position:0%
+expression and it also involves
+interaction between the tumor and the
+
+ align:start position:0%
+interaction between the tumor and the
+ 
+
+ align:start position:0%
+interaction between the tumor and the
+surrounding cells of the body okay so
+
+ align:start position:0%
+surrounding cells of the body okay so
+ 
+
+ align:start position:0%
+surrounding cells of the body okay so
+I'm going to tell you a little bit about
+
+ align:start position:0%
+I'm going to tell you a little bit about
+ 
+
+ align:start position:0%
+I'm going to tell you a little bit about
+tumor micro-environment and this is
+
+ align:start position:0%
+tumor micro-environment and this is
+ 
+
+ align:start position:0%
+tumor micro-environment and this is
+something that's important to consider
+
+ align:start position:0%
+something that's important to consider
+ 
+
+ align:start position:0%
+something that's important to consider
+in cancer because you know a tumor in
+
+ align:start position:0%
+in cancer because you know a tumor in
+ 
+
+ align:start position:0%
+in cancer because you know a tumor in
+the body it's not an isolation it's
+
+ align:start position:0%
+the body it's not an isolation it's
+ 
+
+ align:start position:0%
+the body it's not an isolation it's
+surrounded by other cells in your body
+
+ align:start position:0%
+surrounded by other cells in your body
+ 
+
+ align:start position:0%
+surrounded by other cells in your body
+and other things in your body okay like
+
+ align:start position:0%
+and other things in your body okay like
+ 
+
+ align:start position:0%
+and other things in your body okay like
+matrix and so here's a picture showing
+
+ align:start position:0%
+matrix and so here's a picture showing
+ 
+
+ align:start position:0%
+matrix and so here's a picture showing
+you a tumor and the tumor is stained
+
+ align:start position:0%
+you a tumor and the tumor is stained
+ 
+
+ align:start position:0%
+you a tumor and the tumor is stained
+with this membrane protein which is
+
+ align:start position:0%
+with this membrane protein which is
+ 
+
+ align:start position:0%
+with this membrane protein which is
+shown here in the rust color so that's
+
+ align:start position:0%
+shown here in the rust color so that's
+ 
+
+ align:start position:0%
+shown here in the rust color so that's
+the tumor and what's also stained in
+
+ align:start position:0%
+the tumor and what's also stained in
+ 
+
+ align:start position:0%
+the tumor and what's also stained in
+this in this piece of tissue is the DNA
+
+ align:start position:0%
+this in this piece of tissue is the DNA
+ 
+
+ align:start position:0%
+this in this piece of tissue is the DNA
+it's stained in blue and so you see the
+
+ align:start position:0%
+it's stained in blue and so you see the
+ 
+
+ align:start position:0%
+it's stained in blue and so you see the
+nuclei of the tumor cells in there but
+
+ align:start position:0%
+nuclei of the tumor cells in there but
+ 
+
+ align:start position:0%
+nuclei of the tumor cells in there but
+you see all these blue nuclei
+
+ align:start position:0%
+you see all these blue nuclei
+ 
+
+ align:start position:0%
+you see all these blue nuclei
+surrounding the tumor and these are
+
+ align:start position:0%
+surrounding the tumor and these are
+ 
+
+ align:start position:0%
+surrounding the tumor and these are
+stromal cells that are around the tumor
+
+ align:start position:0%
+stromal cells that are around the tumor
+ 
+
+ align:start position:0%
+stromal cells that are around the tumor
+and they've actually been recruited to
+
+ align:start position:0%
+and they've actually been recruited to
+ 
+
+ align:start position:0%
+and they've actually been recruited to
+the tumor by the cancer cells okay so in
+
+ align:start position:0%
+the tumor by the cancer cells okay so in
+ 
+
+ align:start position:0%
+the tumor by the cancer cells okay so in
+what I mean by tumor micro-environment
+
+ align:start position:0%
+what I mean by tumor micro-environment
+ 
+
+ align:start position:0%
+what I mean by tumor micro-environment
+is just a region around the tumor okay
+
+ align:start position:0%
+is just a region around the tumor okay
+ 
+
+ align:start position:0%
+is just a region around the tumor okay
+and so if you have a cancer and you have
+
+ align:start position:0%
+and so if you have a cancer and you have
+ 
+
+ align:start position:0%
+and so if you have a cancer and you have
+a tumor the tumor cells can actually
+
+ align:start position:0%
+a tumor the tumor cells can actually
+ 
+
+ align:start position:0%
+a tumor the tumor cells can actually
+secrete signals which recruit stromal
+
+ align:start position:0%
+secrete signals which recruit stromal
+ 
+
+ align:start position:0%
+secrete signals which recruit stromal
+cells okay so there can be a interaction
+
+ align:start position:0%
+cells okay so there can be a interaction
+ 
+
+ align:start position:0%
+cells okay so there can be a interaction
+where the tumor sends recruitment
+
+ align:start position:0%
+where the tumor sends recruitment
+ 
+
+ align:start position:0%
+where the tumor sends recruitment
+signals that causes stromal cells to
+
+ align:start position:0%
+signals that causes stromal cells to
+ 
+
+ align:start position:0%
+signals that causes stromal cells to
+come by and what the stromal cells can
+
+ align:start position:0%
+come by and what the stromal cells can
+ 
+
+ align:start position:0%
+come by and what the stromal cells can
+do what they do for the tumor and why
+
+ align:start position:0%
+do what they do for the tumor and why
+ 
+
+ align:start position:0%
+do what they do for the tumor and why
+this is beneficial for the tumor is that
+
+ align:start position:0%
+this is beneficial for the tumor is that
+ 
+
+ align:start position:0%
+this is beneficial for the tumor is that
+stromal cells can secrete growth signals
+
+ align:start position:0%
+stromal cells can secrete growth signals
+ 
+
+ align:start position:0%
+stromal cells can secrete growth signals
+or survival signals that promote the
+
+ align:start position:0%
+or survival signals that promote the
+ 
+
+ align:start position:0%
+or survival signals that promote the
+growth of the tumor okay so there can be
+
+ align:start position:0%
+growth of the tumor okay so there can be
+ 
+
+ align:start position:0%
+growth of the tumor okay so there can be
+a reciprocal interaction here where you
+
+ align:start position:0%
+a reciprocal interaction here where you
+ 
+
+ align:start position:0%
+a reciprocal interaction here where you
+get a abnormal conversation between
+
+ align:start position:0%
+get a abnormal conversation between
+ 
+
+ align:start position:0%
+get a abnormal conversation between
+cancer cells and the surrounding stromal
+
+ align:start position:0%
+cancer cells and the surrounding stromal
+ 
+
+ align:start position:0%
+cancer cells and the surrounding stromal
+cells but again this is very similar if
+
+ align:start position:0%
+cells but again this is very similar if
+ 
+
+ align:start position:0%
+cells but again this is very similar if
+you think about it to the way a normal
+
+ align:start position:0%
+you think about it to the way a normal
+ 
+
+ align:start position:0%
+you think about it to the way a normal
+organ works right you you often have
+
+ align:start position:0%
+organ works right you you often have
+ 
+
+ align:start position:0%
+organ works right you you often have
+these signals going between cells and
+
+ align:start position:0%
+these signals going between cells and
+ 
+
+ align:start position:0%
+these signals going between cells and
+that is involved in normal tissue
+
+ align:start position:0%
+that is involved in normal tissue
+ 
+
+ align:start position:0%
+that is involved in normal tissue
+homeostasis what's happening here though
+
+ align:start position:0%
+homeostasis what's happening here though
+ 
+
+ align:start position:0%
+homeostasis what's happening here though
+is abnormal and that the cancer cells
+
+ align:start position:0%
+is abnormal and that the cancer cells
+ 
+
+ align:start position:0%
+is abnormal and that the cancer cells
+are constitutively recruiting these
+
+ align:start position:0%
+are constitutively recruiting these
+ 
+
+ align:start position:0%
+are constitutively recruiting these
+stromal cells just to get this growth
+
+ align:start position:0%
+stromal cells just to get this growth
+ 
+
+ align:start position:0%
+stromal cells just to get this growth
+signal that they're addicted to and
+
+ align:start position:0%
+signal that they're addicted to and
+ 
+
+ align:start position:0%
+signal that they're addicted to and
+because you have just the presence of
+
+ align:start position:0%
+because you have just the presence of
+ 
+
+ align:start position:0%
+because you have just the presence of
+such a loop suggests that these cancer
+
+ align:start position:0%
+such a loop suggests that these cancer
+ 
+
+ align:start position:0%
+such a loop suggests that these cancer
+cells even if they have oncogenic
+
+ align:start position:0%
+cells even if they have oncogenic
+ 
+
+ align:start position:0%
+cells even if they have oncogenic
+mutations and lost have lost tumor
+
+ align:start position:0%
+mutations and lost have lost tumor
+ 
+
+ align:start position:0%
+mutations and lost have lost tumor
+suppressors they are not totally
+
+ align:start position:0%
+suppressors they are not totally
+ 
+
+ align:start position:0%
+suppressors they are not totally
+independent of growth signals they still
+
+ align:start position:0%
+independent of growth signals they still
+ 
+
+ align:start position:0%
+independent of growth signals they still
+to some extent rely on growth signals
+
+ align:start position:0%
+to some extent rely on growth signals
+ 
+
+ align:start position:0%
+to some extent rely on growth signals
+okay so these oncogenic mutations they
+
+ align:start position:0%
+okay so these oncogenic mutations they
+ 
+
+ align:start position:0%
+okay so these oncogenic mutations they
+reduce the dependency on growth signals
+
+ align:start position:0%
+reduce the dependency on growth signals
+ 
+
+ align:start position:0%
+reduce the dependency on growth signals
+but this dependency the dependency on
+
+ align:start position:0%
+but this dependency the dependency on
+ 
+
+ align:start position:0%
+but this dependency the dependency on
+growth signals is not eliminated okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one experiment that showed this was
+
+ align:start position:0%
+and one experiment that showed this was
+ 
+
+ align:start position:0%
+and one experiment that showed this was
+an experiment that was done back in the
+
+ align:start position:0%
+an experiment that was done back in the
+ 
+
+ align:start position:0%
+an experiment that was done back in the
+1950s where patients with a type of skin
+
+ align:start position:0%
+1950s where patients with a type of skin
+ 
+
+ align:start position:0%
+1950s where patients with a type of skin
+cancer basal cell carcinoma were taken
+
+ align:start position:0%
+cancer basal cell carcinoma were taken
+ 
+
+ align:start position:0%
+cancer basal cell carcinoma were taken
+and they had their tumors excised from
+
+ align:start position:0%
+and they had their tumors excised from
+ 
+
+ align:start position:0%
+and they had their tumors excised from
+one part of their body and then the
+
+ align:start position:0%
+one part of their body and then the
+ 
+
+ align:start position:0%
+one part of their body and then the
+tumor was grafted on back onto them to
+
+ align:start position:0%
+tumor was grafted on back onto them to
+ 
+
+ align:start position:0%
+tumor was grafted on back onto them to
+another part of their body distant from
+
+ align:start position:0%
+another part of their body distant from
+ 
+
+ align:start position:0%
+another part of their body distant from
+the original site of the tumor and this
+
+ align:start position:0%
+the original site of the tumor and this
+ 
+
+ align:start position:0%
+the original site of the tumor and this
+grafting experiment was done either with
+
+ align:start position:0%
+grafting experiment was done either with
+ 
+
+ align:start position:0%
+grafting experiment was done either with
+the stromal cells that surrounded the
+
+ align:start position:0%
+the stromal cells that surrounded the
+ 
+
+ align:start position:0%
+the stromal cells that surrounded the
+tumor or the stromal cells surrounding
+
+ align:start position:0%
+tumor or the stromal cells surrounding
+ 
+
+ align:start position:0%
+tumor or the stromal cells surrounding
+the tumor were removed in just the tumor
+
+ align:start position:0%
+the tumor were removed in just the tumor
+ 
+
+ align:start position:0%
+the tumor were removed in just the tumor
+cells were grafted back on to the body
+
+ align:start position:0%
+cells were grafted back on to the body
+ 
+
+ align:start position:0%
+cells were grafted back on to the body
+okay now this experiment probably would
+
+ align:start position:0%
+okay now this experiment probably would
+ 
+
+ align:start position:0%
+okay now this experiment probably would
+not be allowed today but back in the 50s
+
+ align:start position:0%
+not be allowed today but back in the 50s
+ 
+
+ align:start position:0%
+not be allowed today but back in the 50s
+I guess it was legal and so the
+
+ align:start position:0%
+I guess it was legal and so the
+ 
+
+ align:start position:0%
+I guess it was legal and so the
+experimental result is that if you
+
+ align:start position:0%
+experimental result is that if you
+ 
+
+ align:start position:0%
+experimental result is that if you
+graphed the tumor cells with the
+
+ align:start position:0%
+graphed the tumor cells with the
+ 
+
+ align:start position:0%
+graphed the tumor cells with the
+surrounding stroma the tumor was able to
+
+ align:start position:0%
+surrounding stroma the tumor was able to
+ 
+
+ align:start position:0%
+surrounding stroma the tumor was able to
+establish a second tumor or the tumor
+
+ align:start position:0%
+establish a second tumor or the tumor
+ 
+
+ align:start position:0%
+establish a second tumor or the tumor
+cells survived this this grafting
+
+ align:start position:0%
+cells survived this this grafting
+ 
+
+ align:start position:0%
+cells survived this this grafting
+procedure where as tumor cells that were
+
+ align:start position:0%
+procedure where as tumor cells that were
+ 
+
+ align:start position:0%
+procedure where as tumor cells that were
+taken without the stroma underwent cell
+
+ align:start position:0%
+taken without the stroma underwent cell
+ 
+
+ align:start position:0%
+taken without the stroma underwent cell
+death when they were put in a new
+
+ align:start position:0%
+death when they were put in a new
+ 
+
+ align:start position:0%
+death when they were put in a new
+location okay so there's something about
+
+ align:start position:0%
+location okay so there's something about
+ 
+
+ align:start position:0%
+location okay so there's something about
+this specialized micro environment that
+
+ align:start position:0%
+this specialized micro environment that
+ 
+
+ align:start position:0%
+this specialized micro environment that
+the tumor creates for itself that is
+
+ align:start position:0%
+the tumor creates for itself that is
+ 
+
+ align:start position:0%
+the tumor creates for itself that is
+enabling the tumor to grow and survive
+
+ align:start position:0%
+enabling the tumor to grow and survive
+ 
+
+ align:start position:0%
+enabling the tumor to grow and survive
+okay and the model is is that it's
+
+ align:start position:0%
+okay and the model is is that it's
+ 
+
+ align:start position:0%
+okay and the model is is that it's
+because these stromal cells are
+
+ align:start position:0%
+because these stromal cells are
+ 
+
+ align:start position:0%
+because these stromal cells are
+secreting growth factors that these
+
+ align:start position:0%
+secreting growth factors that these
+ 
+
+ align:start position:0%
+secreting growth factors that these
+cancer cells are still dependent on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this dependency on growth signals is
+
+ align:start position:0%
+so this dependency on growth signals is
+ 
+
+ align:start position:0%
+so this dependency on growth signals is
+important clinically because some some
+
+ align:start position:0%
+important clinically because some some
+ 
+
+ align:start position:0%
+important clinically because some some
+types of cancer there is an elevation of
+
+ align:start position:0%
+types of cancer there is an elevation of
+ 
+
+ align:start position:0%
+types of cancer there is an elevation of
+growth factor receptors that are
+
+ align:start position:0%
+growth factor receptors that are
+ 
+
+ align:start position:0%
+growth factor receptors that are
+associated with the cancer and the
+
+ align:start position:0%
+associated with the cancer and the
+ 
+
+ align:start position:0%
+associated with the cancer and the
+famous example of that is in 30% of
+
+ align:start position:0%
+famous example of that is in 30% of
+ 
+
+ align:start position:0%
+famous example of that is in 30% of
+breast cancers there is a growth factor
+
+ align:start position:0%
+breast cancers there is a growth factor
+ 
+
+ align:start position:0%
+breast cancers there is a growth factor
+receptor the her2 receptor which is
+
+ align:start position:0%
+receptor the her2 receptor which is
+ 
+
+ align:start position:0%
+receptor the her2 receptor which is
+overexpressed in the cancer cells okay
+
+ align:start position:0%
+overexpressed in the cancer cells okay
+ 
+
+ align:start position:0%
+overexpressed in the cancer cells okay
+so I just drew a receptor here and I'm
+
+ align:start position:0%
+so I just drew a receptor here and I'm
+ 
+
+ align:start position:0%
+so I just drew a receptor here and I'm
+now talking about the her2 receptor her2
+
+ align:start position:0%
+now talking about the her2 receptor her2
+ 
+
+ align:start position:0%
+now talking about the her2 receptor her2
+stands for human epidermal growth factor
+
+ align:start position:0%
+stands for human epidermal growth factor
+ 
+
+ align:start position:0%
+stands for human epidermal growth factor
+EGF receptor - okay so that's this is a
+
+ align:start position:0%
+EGF receptor - okay so that's this is a
+ 
+
+ align:start position:0%
+EGF receptor - okay so that's this is a
+receptor tyrosine kinase which is a
+
+ align:start position:0%
+receptor tyrosine kinase which is a
+ 
+
+ align:start position:0%
+receptor tyrosine kinase which is a
+transmembrane protein receptor it's
+
+ align:start position:0%
+transmembrane protein receptor it's
+ 
+
+ align:start position:0%
+transmembrane protein receptor it's
+expressed on the surface of the cell and
+
+ align:start position:0%
+expressed on the surface of the cell and
+ 
+
+ align:start position:0%
+expressed on the surface of the cell and
+so about 30% of human breast cancers are
+
+ align:start position:0%
+so about 30% of human breast cancers are
+ 
+
+ align:start position:0%
+so about 30% of human breast cancers are
+her to posit positive which means that
+
+ align:start position:0%
+her to posit positive which means that
+ 
+
+ align:start position:0%
+her to posit positive which means that
+the cancer cells are over expressing
+
+ align:start position:0%
+the cancer cells are over expressing
+ 
+
+ align:start position:0%
+the cancer cells are over expressing
+this receptor tyrosine kinase the fact
+
+ align:start position:0%
+this receptor tyrosine kinase the fact
+ 
+
+ align:start position:0%
+this receptor tyrosine kinase the fact
+that you have these these cancer cells
+
+ align:start position:0%
+that you have these these cancer cells
+ 
+
+ align:start position:0%
+that you have these these cancer cells
+over expressing a growth factor receptor
+
+ align:start position:0%
+over expressing a growth factor receptor
+ 
+
+ align:start position:0%
+over expressing a growth factor receptor
+suggests that the cancer is requires
+
+ align:start position:0%
+suggests that the cancer is requires
+ 
+
+ align:start position:0%
+suggests that the cancer is requires
+some type of growth stimulus in order
+
+ align:start position:0%
+some type of growth stimulus in order
+ 
+
+ align:start position:0%
+some type of growth stimulus in order
+for the cancer to be growing okay and
+
+ align:start position:0%
+for the cancer to be growing okay and
+ 
+
+ align:start position:0%
+for the cancer to be growing okay and
+the fact that this was discovered that
+
+ align:start position:0%
+the fact that this was discovered that
+ 
+
+ align:start position:0%
+the fact that this was discovered that
+30% of breast cancers overexpress her2
+
+ align:start position:0%
+30% of breast cancers overexpress her2
+ 
+
+ align:start position:0%
+30% of breast cancers overexpress her2
+has been used by researchers to develop
+
+ align:start position:0%
+has been used by researchers to develop
+ 
+
+ align:start position:0%
+has been used by researchers to develop
+a treatment for this type of cancer
+
+ align:start position:0%
+a treatment for this type of cancer
+ 
+
+ align:start position:0%
+a treatment for this type of cancer
+that's her2 positive the treatment is
+
+ align:start position:0%
+that's her2 positive the treatment is
+ 
+
+ align:start position:0%
+that's her2 positive the treatment is
+known as Herceptin possibly some of you
+
+ align:start position:0%
+known as Herceptin possibly some of you
+ 
+
+ align:start position:0%
+known as Herceptin possibly some of you
+have heard of this
+
+ align:start position:0%
+have heard of this
+ 
+
+ align:start position:0%
+have heard of this
+it was developed at Genentech and what
+
+ align:start position:0%
+it was developed at Genentech and what
+ 
+
+ align:start position:0%
+it was developed at Genentech and what
+Herceptin is is
+
+ align:start position:0%
+Herceptin is is
+ 
+
+ align:start position:0%
+Herceptin is is
+it's an antibody that was raised against
+
+ align:start position:0%
+it's an antibody that was raised against
+ 
+
+ align:start position:0%
+it's an antibody that was raised against
+the human her2 protein
+
+ align:start position:0%
+the human her2 protein
+ 
+
+ align:start position:0%
+the human her2 protein
+okay so Herceptin is an antibody it
+
+ align:start position:0%
+okay so Herceptin is an antibody it
+ 
+
+ align:start position:0%
+okay so Herceptin is an antibody it
+recognizes her two on the surface of
+
+ align:start position:0%
+recognizes her two on the surface of
+ 
+
+ align:start position:0%
+recognizes her two on the surface of
+these cancer cells and if you you can
+
+ align:start position:0%
+these cancer cells and if you you can
+ 
+
+ align:start position:0%
+these cancer cells and if you you can
+treat patients with this antibody and
+
+ align:start position:0%
+treat patients with this antibody and
+ 
+
+ align:start position:0%
+treat patients with this antibody and
+that antibody binds to the her2 positive
+
+ align:start position:0%
+that antibody binds to the her2 positive
+ 
+
+ align:start position:0%
+that antibody binds to the her2 positive
+cells and either blocks the function of
+
+ align:start position:0%
+cells and either blocks the function of
+ 
+
+ align:start position:0%
+cells and either blocks the function of
+her - or recruits immune cells to kill
+
+ align:start position:0%
+her - or recruits immune cells to kill
+ 
+
+ align:start position:0%
+her - or recruits immune cells to kill
+those cells off okay the exact mechanism
+
+ align:start position:0%
+those cells off okay the exact mechanism
+ 
+
+ align:start position:0%
+those cells off okay the exact mechanism
+I don't believe is known but what is
+
+ align:start position:0%
+I don't believe is known but what is
+ 
+
+ align:start position:0%
+I don't believe is known but what is
+known is that Herceptin has really
+
+ align:start position:0%
+known is that Herceptin has really
+ 
+
+ align:start position:0%
+known is that Herceptin has really
+changed how we're able to treat her to
+
+ align:start position:0%
+changed how we're able to treat her to
+ 
+
+ align:start position:0%
+changed how we're able to treat her to
+positive breast cancers and it's been a
+
+ align:start position:0%
+positive breast cancers and it's been a
+ 
+
+ align:start position:0%
+positive breast cancers and it's been a
+huge success story in the fight against
+
+ align:start position:0%
+huge success story in the fight against
+ 
+
+ align:start position:0%
+huge success story in the fight against
+cancer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we've talked about this
+
+ align:start position:0%
+all right so we've talked about this
+ 
+
+ align:start position:0%
+all right so we've talked about this
+first barrier there barrier to tumor
+
+ align:start position:0%
+first barrier there barrier to tumor
+ 
+
+ align:start position:0%
+first barrier there barrier to tumor
+cells becoming at least semi independent
+
+ align:start position:0%
+cells becoming at least semi independent
+ 
+
+ align:start position:0%
+cells becoming at least semi independent
+of these growth factors and so now I
+
+ align:start position:0%
+of these growth factors and so now I
+ 
+
+ align:start position:0%
+of these growth factors and so now I
+want to talk about other barriers to
+
+ align:start position:0%
+want to talk about other barriers to
+ 
+
+ align:start position:0%
+want to talk about other barriers to
+tumorigenesis right and if you consider
+
+ align:start position:0%
+tumorigenesis right and if you consider
+ 
+
+ align:start position:0%
+tumorigenesis right and if you consider
+an epithelial cell here right even if
+
+ align:start position:0%
+an epithelial cell here right even if
+ 
+
+ align:start position:0%
+an epithelial cell here right even if
+these cells are able to grow they won't
+
+ align:start position:0%
+these cells are able to grow they won't
+ 
+
+ align:start position:0%
+these cells are able to grow they won't
+be able to leave the organ until
+
+ align:start position:0%
+be able to leave the organ until
+ 
+
+ align:start position:0%
+be able to leave the organ until
+something else happens and one thing
+
+ align:start position:0%
+something else happens and one thing
+ 
+
+ align:start position:0%
+something else happens and one thing
+that would need to happen for these
+
+ align:start position:0%
+that would need to happen for these
+ 
+
+ align:start position:0%
+that would need to happen for these
+cells to become malignant and to leave
+
+ align:start position:0%
+cells to become malignant and to leave
+ 
+
+ align:start position:0%
+cells to become malignant and to leave
+the organ that they were initially part
+
+ align:start position:0%
+the organ that they were initially part
+ 
+
+ align:start position:0%
+the organ that they were initially part
+of is for there to be a breakdown in the
+
+ align:start position:0%
+of is for there to be a breakdown in the
+ 
+
+ align:start position:0%
+of is for there to be a breakdown in the
+adhesion between cells so for the next
+
+ align:start position:0%
+adhesion between cells so for the next
+ 
+
+ align:start position:0%
+adhesion between cells so for the next
+few minutes I want to talk about the
+
+ align:start position:0%
+few minutes I want to talk about the
+ 
+
+ align:start position:0%
+few minutes I want to talk about the
+breakdown in cell to cell adhesion okay
+
+ align:start position:0%
+breakdown in cell to cell adhesion okay
+ 
+
+ align:start position:0%
+breakdown in cell to cell adhesion okay
+so how what is what a cancer cell
+
+ align:start position:0%
+so how what is what a cancer cell
+ 
+
+ align:start position:0%
+so how what is what a cancer cell
+basically unstick itself from the cells
+
+ align:start position:0%
+basically unstick itself from the cells
+ 
+
+ align:start position:0%
+basically unstick itself from the cells
+that surround it in order to leave an
+
+ align:start position:0%
+that surround it in order to leave an
+ 
+
+ align:start position:0%
+that surround it in order to leave an
+organ and go somewhere else and for that
+
+ align:start position:0%
+organ and go somewhere else and for that
+ 
+
+ align:start position:0%
+organ and go somewhere else and for that
+to explain that I have to remind you
+
+ align:start position:0%
+to explain that I have to remind you
+ 
+
+ align:start position:0%
+to explain that I have to remind you
+about some of the normal biology of
+
+ align:start position:0%
+about some of the normal biology of
+ 
+
+ align:start position:0%
+about some of the normal biology of
+these epithelial cells which we talked
+
+ align:start position:0%
+these epithelial cells which we talked
+ 
+
+ align:start position:0%
+these epithelial cells which we talked
+about earlier which is that they express
+
+ align:start position:0%
+about earlier which is that they express
+ 
+
+ align:start position:0%
+about earlier which is that they express
+these transmembrane proteins that are
+
+ align:start position:0%
+these transmembrane proteins that are
+ 
+
+ align:start position:0%
+these transmembrane proteins that are
+adhesion proteins okay so normally
+
+ align:start position:0%
+adhesion proteins okay so normally
+ 
+
+ align:start position:0%
+adhesion proteins okay so normally
+epithelial cells have adhesion proteins
+
+ align:start position:0%
+epithelial cells have adhesion proteins
+ 
+
+ align:start position:0%
+epithelial cells have adhesion proteins
+and the famous one for epithelia or one
+
+ align:start position:0%
+and the famous one for epithelia or one
+ 
+
+ align:start position:0%
+and the famous one for epithelia or one
+of the famous ones is called epithelial
+
+ align:start position:0%
+of the famous ones is called epithelial
+ 
+
+ align:start position:0%
+of the famous ones is called epithelial
+or e-cat hiren and ecad hiren is a
+
+ align:start position:0%
+or e-cat hiren and ecad hiren is a
+ 
+
+ align:start position:0%
+or e-cat hiren and ecad hiren is a
+transmembrane protein it has a
+
+ align:start position:0%
+transmembrane protein it has a
+ 
+
+ align:start position:0%
+transmembrane protein it has a
+extracellular domain but rather than
+
+ align:start position:0%
+extracellular domain but rather than
+ 
+
+ align:start position:0%
+extracellular domain but rather than
+that extracellular domain binding to
+
+ align:start position:0%
+that extracellular domain binding to
+ 
+
+ align:start position:0%
+that extracellular domain binding to
+some secreted ligand this extracellular
+
+ align:start position:0%
+some secreted ligand this extracellular
+ 
+
+ align:start position:0%
+some secreted ligand this extracellular
+domain recognizes ich adhere in
+
+ align:start position:0%
+domain recognizes ich adhere in
+ 
+
+ align:start position:0%
+domain recognizes ich adhere in
+molecules on other cells and they stick
+
+ align:start position:0%
+molecules on other cells and they stick
+ 
+
+ align:start position:0%
+molecules on other cells and they stick
+to each
+
+ align:start position:0%
+to each
+ 
+
+ align:start position:0%
+to each
+and it essentially functions like
+
+ align:start position:0%
+and it essentially functions like
+ 
+
+ align:start position:0%
+and it essentially functions like
+cellular velcro okay so the cells link
+
+ align:start position:0%
+cellular velcro okay so the cells link
+ 
+
+ align:start position:0%
+cellular velcro okay so the cells link
+together and they stick to each other
+
+ align:start position:0%
+together and they stick to each other
+ 
+
+ align:start position:0%
+together and they stick to each other
+such that they form a coherent tissue
+
+ align:start position:0%
+such that they form a coherent tissue
+ 
+
+ align:start position:0%
+such that they form a coherent tissue
+okay so the way that cancer cells
+
+ align:start position:0%
+okay so the way that cancer cells
+ 
+
+ align:start position:0%
+okay so the way that cancer cells
+subvert this mechanism of adhesion is
+
+ align:start position:0%
+subvert this mechanism of adhesion is
+ 
+
+ align:start position:0%
+subvert this mechanism of adhesion is
+they have to do something that inhibits
+
+ align:start position:0%
+they have to do something that inhibits
+ 
+
+ align:start position:0%
+they have to do something that inhibits
+ECOD hiren and so cancer cells what what
+
+ align:start position:0%
+ECOD hiren and so cancer cells what what
+ 
+
+ align:start position:0%
+ECOD hiren and so cancer cells what what
+they can do is to decrease this cell T
+
+ align:start position:0%
+they can do is to decrease this cell T
+ 
+
+ align:start position:0%
+they can do is to decrease this cell T
+cell adhesion and I'll tell you how in
+
+ align:start position:0%
+cell adhesion and I'll tell you how in
+ 
+
+ align:start position:0%
+cell adhesion and I'll tell you how in
+just a minute and in addition to
+
+ align:start position:0%
+just a minute and in addition to
+ 
+
+ align:start position:0%
+just a minute and in addition to
+decreasing this cell to cell adhesion
+
+ align:start position:0%
+decreasing this cell to cell adhesion
+ 
+
+ align:start position:0%
+decreasing this cell to cell adhesion
+they can also promote the genes that are
+
+ align:start position:0%
+they can also promote the genes that are
+ 
+
+ align:start position:0%
+they can also promote the genes that are
+involved in motility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we have to understand then how
+
+ align:start position:0%
+okay so we have to understand then how
+ 
+
+ align:start position:0%
+okay so we have to understand then how
+it is a cancer cell would do both of
+
+ align:start position:0%
+it is a cancer cell would do both of
+ 
+
+ align:start position:0%
+it is a cancer cell would do both of
+these things and I'll start with cell to
+
+ align:start position:0%
+these things and I'll start with cell to
+ 
+
+ align:start position:0%
+these things and I'll start with cell to
+cell adhesion and in contrast to what
+
+ align:start position:0%
+cell adhesion and in contrast to what
+ 
+
+ align:start position:0%
+cell adhesion and in contrast to what
+we've talked about with the growth and
+
+ align:start position:0%
+we've talked about with the growth and
+ 
+
+ align:start position:0%
+we've talked about with the growth and
+survival signaling where you have
+
+ align:start position:0%
+survival signaling where you have
+ 
+
+ align:start position:0%
+survival signaling where you have
+mutations that happen in cancer cells
+
+ align:start position:0%
+mutations that happen in cancer cells
+ 
+
+ align:start position:0%
+mutations that happen in cancer cells
+and you basically have an irreversible
+
+ align:start position:0%
+and you basically have an irreversible
+ 
+
+ align:start position:0%
+and you basically have an irreversible
+change to the genome of the cell this
+
+ align:start position:0%
+change to the genome of the cell this
+ 
+
+ align:start position:0%
+change to the genome of the cell this
+change in in the adhesive properties of
+
+ align:start position:0%
+change in in the adhesive properties of
+ 
+
+ align:start position:0%
+change in in the adhesive properties of
+the cell and essentially their cell
+
+ align:start position:0%
+the cell and essentially their cell
+ 
+
+ align:start position:0%
+the cell and essentially their cell
+state right because what you see here if
+
+ align:start position:0%
+state right because what you see here if
+ 
+
+ align:start position:0%
+state right because what you see here if
+a cancer cell is having less adhesion
+
+ align:start position:0%
+a cancer cell is having less adhesion
+ 
+
+ align:start position:0%
+a cancer cell is having less adhesion
+and getting more migratory its switching
+
+ align:start position:0%
+and getting more migratory its switching
+ 
+
+ align:start position:0%
+and getting more migratory its switching
+from an epithelial type of state to a
+
+ align:start position:0%
+from an epithelial type of state to a
+ 
+
+ align:start position:0%
+from an epithelial type of state to a
+mesenchymal type of State okay and what
+
+ align:start position:0%
+mesenchymal type of State okay and what
+ 
+
+ align:start position:0%
+mesenchymal type of State okay and what
+this is called is an epithelial to
+
+ align:start position:0%
+this is called is an epithelial to
+ 
+
+ align:start position:0%
+this is called is an epithelial to
+mesenchymal transition and that is EMT
+
+ align:start position:0%
+mesenchymal transition and that is EMT
+ 
+
+ align:start position:0%
+mesenchymal transition and that is EMT
+for short okay and this EMT is not a
+
+ align:start position:0%
+for short okay and this EMT is not a
+ 
+
+ align:start position:0%
+for short okay and this EMT is not a
+genetic change it's not caused by a
+
+ align:start position:0%
+genetic change it's not caused by a
+ 
+
+ align:start position:0%
+genetic change it's not caused by a
+genetic change but it appears that EMT
+
+ align:start position:0%
+genetic change but it appears that EMT
+ 
+
+ align:start position:0%
+genetic change but it appears that EMT
+results from changes in gene regulation
+
+ align:start position:0%
+results from changes in gene regulation
+ 
+
+ align:start position:0%
+results from changes in gene regulation
+so you can think of it as more of an
+
+ align:start position:0%
+so you can think of it as more of an
+ 
+
+ align:start position:0%
+so you can think of it as more of an
+epigenetic change an epigenetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epigenetic change change in gene
+
+ align:start position:0%
+epigenetic change change in gene
+ 
+
+ align:start position:0%
+epigenetic change change in gene
+expression so there's a change in gene
+
+ align:start position:0%
+expression so there's a change in gene
+ 
+
+ align:start position:0%
+expression so there's a change in gene
+expression such that this can reverse
+
+ align:start position:0%
+expression such that this can reverse
+ 
+
+ align:start position:0%
+expression such that this can reverse
+later on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and there are master regulators of
+
+ align:start position:0%
+okay and there are master regulators of
+ 
+
+ align:start position:0%
+okay and there are master regulators of
+this process which alter gene expression
+
+ align:start position:0%
+this process which alter gene expression
+ 
+
+ align:start position:0%
+this process which alter gene expression
+and so the type of gene that alters gene
+
+ align:start position:0%
+and so the type of gene that alters gene
+ 
+
+ align:start position:0%
+and so the type of gene that alters gene
+expression these are also often called
+
+ align:start position:0%
+expression these are also often called
+ 
+
+ align:start position:0%
+expression these are also often called
+transcription factors and there are
+
+ align:start position:0%
+transcription factors and there are
+ 
+
+ align:start position:0%
+transcription factors and there are
+several transcription factors that are
+
+ align:start position:0%
+several transcription factors that are
+ 
+
+ align:start position:0%
+several transcription factors that are
+master regulators of this EMT process
+
+ align:start position:0%
+master regulators of this EMT process
+ 
+
+ align:start position:0%
+master regulators of this EMT process
+and their names are twist snail another
+
+ align:start position:0%
+and their names are twist snail another
+ 
+
+ align:start position:0%
+and their names are twist snail another
+one's called slug there's an escargot
+
+ align:start position:0%
+one's called slug there's an escargot
+ 
+
+ align:start position:0%
+one's called slug there's an escargot
+you can see this got a little out of
+
+ align:start position:0%
+you can see this got a little out of
+ 
+
+ align:start position:0%
+you can see this got a little out of
+hand and you can tell by the names that
+
+ align:start position:0%
+hand and you can tell by the names that
+ 
+
+ align:start position:0%
+hand and you can tell by the names that
+they probably were not discovered in
+
+ align:start position:0%
+they probably were not discovered in
+ 
+
+ align:start position:0%
+they probably were not discovered in
+humans and in fact these genes were
+
+ align:start position:0%
+humans and in fact these genes were
+ 
+
+ align:start position:0%
+humans and in fact these genes were
+discovered in the same genetic screen
+
+ align:start position:0%
+discovered in the same genetic screen
+ 
+
+ align:start position:0%
+discovered in the same genetic screen
+that I outlined before where Hedgehog
+
+ align:start position:0%
+that I outlined before where Hedgehog
+ 
+
+ align:start position:0%
+that I outlined before where Hedgehog
+was discovered okay so it was a genetic
+
+ align:start position:0%
+was discovered okay so it was a genetic
+ 
+
+ align:start position:0%
+was discovered okay so it was a genetic
+screen and the flies and it was these
+
+ align:start position:0%
+screen and the flies and it was these
+ 
+
+ align:start position:0%
+screen and the flies and it was these
+are genes that affect the embryonic
+
+ align:start position:0%
+are genes that affect the embryonic
+ 
+
+ align:start position:0%
+are genes that affect the embryonic
+development of the fly and I'll show you
+
+ align:start position:0%
+development of the fly and I'll show you
+ 
+
+ align:start position:0%
+development of the fly and I'll show you
+this this view of the fly embryo so this
+
+ align:start position:0%
+this this view of the fly embryo so this
+ 
+
+ align:start position:0%
+this this view of the fly embryo so this
+is an embryo here and you see it's an
+
+ align:start position:0%
+is an embryo here and you see it's an
+ 
+
+ align:start position:0%
+is an embryo here and you see it's an
+epithelial sheet surrounding the yolk
+
+ align:start position:0%
+epithelial sheet surrounding the yolk
+ 
+
+ align:start position:0%
+epithelial sheet surrounding the yolk
+and what happens is in early stages of
+
+ align:start position:0%
+and what happens is in early stages of
+ 
+
+ align:start position:0%
+and what happens is in early stages of
+development a population of cells
+
+ align:start position:0%
+development a population of cells
+ 
+
+ align:start position:0%
+development a population of cells
+expressed the twist gene so that's twist
+
+ align:start position:0%
+expressed the twist gene so that's twist
+ 
+
+ align:start position:0%
+expressed the twist gene so that's twist
+in the dark here and this twist gene
+
+ align:start position:0%
+in the dark here and this twist gene
+ 
+
+ align:start position:0%
+in the dark here and this twist gene
+causes these cells to basically invade
+
+ align:start position:0%
+causes these cells to basically invade
+ 
+
+ align:start position:0%
+causes these cells to basically invade
+into the middle of the embryo okay so
+
+ align:start position:0%
+into the middle of the embryo okay so
+ 
+
+ align:start position:0%
+into the middle of the embryo okay so
+here are the twist cells now going into
+
+ align:start position:0%
+here are the twist cells now going into
+ 
+
+ align:start position:0%
+here are the twist cells now going into
+the inside of the embryo and then the
+
+ align:start position:0%
+the inside of the embryo and then the
+ 
+
+ align:start position:0%
+the inside of the embryo and then the
+cells undergo EMT and they start to
+
+ align:start position:0%
+cells undergo EMT and they start to
+ 
+
+ align:start position:0%
+cells undergo EMT and they start to
+migrate around inside the embryo okay
+
+ align:start position:0%
+migrate around inside the embryo okay
+ 
+
+ align:start position:0%
+migrate around inside the embryo okay
+what this is doing for the fly is that
+
+ align:start position:0%
+what this is doing for the fly is that
+ 
+
+ align:start position:0%
+what this is doing for the fly is that
+these are the cells that are going on to
+
+ align:start position:0%
+these are the cells that are going on to
+ 
+
+ align:start position:0%
+these are the cells that are going on to
+form the muscle okay and if you look at
+
+ align:start position:0%
+form the muscle okay and if you look at
+ 
+
+ align:start position:0%
+form the muscle okay and if you look at
+your neighbor you might notice that
+
+ align:start position:0%
+your neighbor you might notice that
+ 
+
+ align:start position:0%
+your neighbor you might notice that
+their muscles are on the inside of their
+
+ align:start position:0%
+their muscles are on the inside of their
+ 
+
+ align:start position:0%
+their muscles are on the inside of their
+body okay so this this process is
+
+ align:start position:0%
+body okay so this this process is
+ 
+
+ align:start position:0%
+body okay so this this process is
+basically putting
+
+ align:start position:0%
+basically putting
+ 
+
+ align:start position:0%
+basically putting
+these cells by getting them to move its
+
+ align:start position:0%
+these cells by getting them to move its
+ 
+
+ align:start position:0%
+these cells by getting them to move its
+putting the cells in the right place for
+
+ align:start position:0%
+putting the cells in the right place for
+ 
+
+ align:start position:0%
+putting the cells in the right place for
+what they are going to differentiate
+
+ align:start position:0%
+what they are going to differentiate
+ 
+
+ align:start position:0%
+what they are going to differentiate
+into during embryonic development okay
+
+ align:start position:0%
+into during embryonic development okay
+ 
+
+ align:start position:0%
+into during embryonic development okay
+and so but this this process if
+
+ align:start position:0%
+and so but this this process if
+ 
+
+ align:start position:0%
+and so but this this process if
+activated during cancer can allow these
+
+ align:start position:0%
+activated during cancer can allow these
+ 
+
+ align:start position:0%
+activated during cancer can allow these
+cells to be more mobile mobile and to
+
+ align:start position:0%
+cells to be more mobile mobile and to
+ 
+
+ align:start position:0%
+cells to be more mobile mobile and to
+leave one organ and go into another
+
+ align:start position:0%
+leave one organ and go into another
+ 
+
+ align:start position:0%
+leave one organ and go into another
+organ okay so cancer isn't inventing
+
+ align:start position:0%
+organ okay so cancer isn't inventing
+ 
+
+ align:start position:0%
+organ okay so cancer isn't inventing
+anything new here it's corrupting a
+
+ align:start position:0%
+anything new here it's corrupting a
+ 
+
+ align:start position:0%
+anything new here it's corrupting a
+normal program that cells have a need
+
+ align:start position:0%
+normal program that cells have a need
+ 
+
+ align:start position:0%
+normal program that cells have a need
+during development and it's in
+
+ align:start position:0%
+during development and it's in
+ 
+
+ align:start position:0%
+during development and it's in
+activating it at an inappropriate time
+
+ align:start position:0%
+activating it at an inappropriate time
+ 
+
+ align:start position:0%
+activating it at an inappropriate time
+okay so these are all transcription
+
+ align:start position:0%
+okay so these are all transcription
+ 
+
+ align:start position:0%
+okay so these are all transcription
+factors and what they do is they repress
+
+ align:start position:0%
+factors and what they do is they repress
+ 
+
+ align:start position:0%
+factors and what they do is they repress
+the expression or function of kid hearin
+
+ align:start position:0%
+the expression or function of kid hearin
+ 
+
+ align:start position:0%
+the expression or function of kid hearin
+such that the cells are no longer as
+
+ align:start position:0%
+such that the cells are no longer as
+ 
+
+ align:start position:0%
+such that the cells are no longer as
+sticky okay so they basically when these
+
+ align:start position:0%
+sticky okay so they basically when these
+ 
+
+ align:start position:0%
+sticky okay so they basically when these
+transcription factors get turned on
+
+ align:start position:0%
+transcription factors get turned on
+ 
+
+ align:start position:0%
+transcription factors get turned on
+it makes the cells less sticky to each
+
+ align:start position:0%
+it makes the cells less sticky to each
+ 
+
+ align:start position:0%
+it makes the cells less sticky to each
+other and it also promotes their
+
+ align:start position:0%
+other and it also promotes their
+ 
+
+ align:start position:0%
+other and it also promotes their
+migration so it turns on genes that are
+
+ align:start position:0%
+migration so it turns on genes that are
+ 
+
+ align:start position:0%
+migration so it turns on genes that are
+important for migration this process of
+
+ align:start position:0%
+important for migration this process of
+ 
+
+ align:start position:0%
+important for migration this process of
+EMT as I mentioned is reversible and it
+
+ align:start position:0%
+EMT as I mentioned is reversible and it
+ 
+
+ align:start position:0%
+EMT as I mentioned is reversible and it
+also involves interactions between tumor
+
+ align:start position:0%
+also involves interactions between tumor
+ 
+
+ align:start position:0%
+also involves interactions between tumor
+and stromal cells I'll show you an
+
+ align:start position:0%
+and stromal cells I'll show you an
+ 
+
+ align:start position:0%
+and stromal cells I'll show you an
+example of so in the fly embryo one
+
+ align:start position:0%
+example of so in the fly embryo one
+ 
+
+ align:start position:0%
+example of so in the fly embryo one
+thing that's nice about the Flies is you
+
+ align:start position:0%
+thing that's nice about the Flies is you
+ 
+
+ align:start position:0%
+thing that's nice about the Flies is you
+can actually watch this happen live and
+
+ align:start position:0%
+can actually watch this happen live and
+ 
+
+ align:start position:0%
+can actually watch this happen live and
+so I'm gonna show you a movie now
+
+ align:start position:0%
+so I'm gonna show you a movie now
+ 
+
+ align:start position:0%
+so I'm gonna show you a movie now
+showing you the invasion process we're
+
+ align:start position:0%
+showing you the invasion process we're
+ 
+
+ align:start position:0%
+showing you the invasion process we're
+gonna have an embryo here and what I'm
+
+ align:start position:0%
+gonna have an embryo here and what I'm
+ 
+
+ align:start position:0%
+gonna have an embryo here and what I'm
+going to show you is we're looking at
+
+ align:start position:0%
+going to show you is we're looking at
+ 
+
+ align:start position:0%
+going to show you is we're looking at
+the cells that are expressing twist and
+
+ align:start position:0%
+the cells that are expressing twist and
+ 
+
+ align:start position:0%
+the cells that are expressing twist and
+snail and they're on one side of the
+
+ align:start position:0%
+snail and they're on one side of the
+ 
+
+ align:start position:0%
+snail and they're on one side of the
+embryo and I'm going to show you a
+
+ align:start position:0%
+embryo and I'm going to show you a
+ 
+
+ align:start position:0%
+embryo and I'm going to show you a
+section of the embryo that is this
+
+ align:start position:0%
+section of the embryo that is this
+ 
+
+ align:start position:0%
+section of the embryo that is this
+analogous to this okay so when the cells
+
+ align:start position:0%
+analogous to this okay so when the cells
+ 
+
+ align:start position:0%
+analogous to this okay so when the cells
+move inside they're gonna disappear in
+
+ align:start position:0%
+move inside they're gonna disappear in
+ 
+
+ align:start position:0%
+move inside they're gonna disappear in
+this movie okay so when you see like the
+
+ align:start position:0%
+this movie okay so when you see like the
+ 
+
+ align:start position:0%
+this movie okay so when you see like the
+crease in in the embryo that's when the
+
+ align:start position:0%
+crease in in the embryo that's when the
+ 
+
+ align:start position:0%
+crease in in the embryo that's when the
+cells are invading into the middle of
+
+ align:start position:0%
+cells are invading into the middle of
+ 
+
+ align:start position:0%
+cells are invading into the middle of
+the embryo and so the cell outlines are
+
+ align:start position:0%
+the embryo and so the cell outlines are
+ 
+
+ align:start position:0%
+the embryo and so the cell outlines are
+in magenta here
+
+ align:start position:0%
+in magenta here
+ 
+
+ align:start position:0%
+in magenta here
+and what's labeled in green is a type of
+
+ align:start position:0%
+and what's labeled in green is a type of
+ 
+
+ align:start position:0%
+and what's labeled in green is a type of
+motor protein that's involved in the
+
+ align:start position:0%
+motor protein that's involved in the
+ 
+
+ align:start position:0%
+motor protein that's involved in the
+mobility of cells and in this case is
+
+ align:start position:0%
+mobility of cells and in this case is
+ 
+
+ align:start position:0%
+mobility of cells and in this case is
+involved in these cells moving into the
+
+ align:start position:0%
+involved in these cells moving into the
+ 
+
+ align:start position:0%
+involved in these cells moving into the
+interior of the embryo so here you see
+
+ align:start position:0%
+interior of the embryo so here you see
+ 
+
+ align:start position:0%
+interior of the embryo so here you see
+the motor protein appearing and that's
+
+ align:start position:0%
+the motor protein appearing and that's
+ 
+
+ align:start position:0%
+the motor protein appearing and that's
+when these cells are going to dive into
+
+ align:start position:0%
+when these cells are going to dive into
+ 
+
+ align:start position:0%
+when these cells are going to dive into
+the embryo right so it's almost like a
+
+ align:start position:0%
+the embryo right so it's almost like a
+ 
+
+ align:start position:0%
+the embryo right so it's almost like a
+waterfall these cells are like moving
+
+ align:start position:0%
+waterfall these cells are like moving
+ 
+
+ align:start position:0%
+waterfall these cells are like moving
+into the inside of the embryo through
+
+ align:start position:0%
+into the inside of the embryo through
+ 
+
+ align:start position:0%
+into the inside of the embryo through
+this process of imagination and
+
+ align:start position:0%
+this process of imagination and
+ 
+
+ align:start position:0%
+this process of imagination and
+subsequently EMT there it goes again
+
+ align:start position:0%
+subsequently EMT there it goes again
+ 
+
+ align:start position:0%
+subsequently EMT there it goes again
+you can see the cells are now on the
+
+ align:start position:0%
+you can see the cells are now on the
+ 
+
+ align:start position:0%
+you can see the cells are now on the
+inside okay
+
+ align:start position:0%
+inside okay
+ 
+
+ align:start position:0%
+inside okay
+so this process of EMT also involves
+
+ align:start position:0%
+so this process of EMT also involves
+ 
+
+ align:start position:0%
+so this process of EMT also involves
+interactions between the cancer cells
+
+ align:start position:0%
+interactions between the cancer cells
+ 
+
+ align:start position:0%
+interactions between the cancer cells
+and the stroma and that's illustrated
+
+ align:start position:0%
+and the stroma and that's illustrated
+ 
+
+ align:start position:0%
+and the stroma and that's illustrated
+here because what you can see what's
+
+ align:start position:0%
+here because what you can see what's
+ 
+
+ align:start position:0%
+here because what you can see what's
+being labeled here you can see the
+
+ align:start position:0%
+being labeled here you can see the
+ 
+
+ align:start position:0%
+being labeled here you can see the
+nuclei of the cells but these cells at
+
+ align:start position:0%
+nuclei of the cells but these cells at
+ 
+
+ align:start position:0%
+nuclei of the cells but these cells at
+the edge of the tumor are up regulating
+
+ align:start position:0%
+the edge of the tumor are up regulating
+ 
+
+ align:start position:0%
+the edge of the tumor are up regulating
+this gene which is an alpha beta
+
+ align:start position:0%
+this gene which is an alpha beta
+ 
+
+ align:start position:0%
+this gene which is an alpha beta
+integral which I'll mention in just a
+
+ align:start position:0%
+integral which I'll mention in just a
+ 
+
+ align:start position:0%
+integral which I'll mention in just a
+minute and this is getting up regulated
+
+ align:start position:0%
+minute and this is getting up regulated
+ 
+
+ align:start position:0%
+minute and this is getting up regulated
+right where the tumor contacts the
+
+ align:start position:0%
+right where the tumor contacts the
+ 
+
+ align:start position:0%
+right where the tumor contacts the
+stroma and this gene alpha beta
+
+ align:start position:0%
+stroma and this gene alpha beta
+ 
+
+ align:start position:0%
+stroma and this gene alpha beta
+integrand is a gene that's associated
+
+ align:start position:0%
+integrand is a gene that's associated
+ 
+
+ align:start position:0%
+integrand is a gene that's associated
+with motility and EMT so in that slide
+
+ align:start position:0%
+with motility and EMT so in that slide
+ 
+
+ align:start position:0%
+with motility and EMT so in that slide
+here one gene involved in motility
+
+ align:start position:0%
+here one gene involved in motility
+ 
+
+ align:start position:0%
+here one gene involved in motility
+as a class of genes called integrins
+
+ align:start position:0%
+as a class of genes called integrins
+ 
+
+ align:start position:0%
+as a class of genes called integrins
+okay and so this also results from the
+
+ align:start position:0%
+okay and so this also results from the
+ 
+
+ align:start position:0%
+okay and so this also results from the
+signaling between the tumor and the
+
+ align:start position:0%
+signaling between the tumor and the
+ 
+
+ align:start position:0%
+signaling between the tumor and the
+surrounding cells and again this is not
+
+ align:start position:0%
+surrounding cells and again this is not
+ 
+
+ align:start position:0%
+surrounding cells and again this is not
+something that cancer created this is
+
+ align:start position:0%
+something that cancer created this is
+ 
+
+ align:start position:0%
+something that cancer created this is
+what happens during wound healing
+
+ align:start position:0%
+what happens during wound healing
+ 
+
+ align:start position:0%
+what happens during wound healing
+so during wound healing if you injure
+
+ align:start position:0%
+so during wound healing if you injure
+ 
+
+ align:start position:0%
+so during wound healing if you injure
+yourself the the wound recruits immune
+
+ align:start position:0%
+yourself the the wound recruits immune
+ 
+
+ align:start position:0%
+yourself the the wound recruits immune
+cells and the immune cells signal to the
+
+ align:start position:0%
+cells and the immune cells signal to the
+ 
+
+ align:start position:0%
+cells and the immune cells signal to the
+surrounding skin or epithelial cells to
+
+ align:start position:0%
+surrounding skin or epithelial cells to
+ 
+
+ align:start position:0%
+surrounding skin or epithelial cells to
+undergo EMT in order to close and fill
+
+ align:start position:0%
+undergo EMT in order to close and fill
+ 
+
+ align:start position:0%
+undergo EMT in order to close and fill
+in the wound okay so this is a natural
+
+ align:start position:0%
+in the wound okay so this is a natural
+ 
+
+ align:start position:0%
+in the wound okay so this is a natural
+process that happens in your body that
+
+ align:start position:0%
+process that happens in your body that
+ 
+
+ align:start position:0%
+process that happens in your body that
+is simply getting corrupted by cancer
+
+ align:start position:0%
+is simply getting corrupted by cancer
+ 
+
+ align:start position:0%
+is simply getting corrupted by cancer
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so now let's talk about this
+
+ align:start position:0%
+all right so now let's talk about this
+ 
+
+ align:start position:0%
+all right so now let's talk about this
+last step of motility so this is now how
+
+ align:start position:0%
+last step of motility so this is now how
+ 
+
+ align:start position:0%
+last step of motility so this is now how
+the cells would break out and move away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright let's come back to this movie
+
+ align:start position:0%
+alright let's come back to this movie
+ 
+
+ align:start position:0%
+alright let's come back to this movie
+here there are a few things I want you
+
+ align:start position:0%
+here there are a few things I want you
+ 
+
+ align:start position:0%
+here there are a few things I want you
+to notice about this movie the first is
+
+ align:start position:0%
+to notice about this movie the first is
+ 
+
+ align:start position:0%
+to notice about this movie the first is
+holy that cell is moving ok and so
+
+ align:start position:0%
+holy that cell is moving ok and so
+ 
+
+ align:start position:0%
+holy that cell is moving ok and so
+so like the first aspect of this is
+
+ align:start position:0%
+so like the first aspect of this is
+ 
+
+ align:start position:0%
+so like the first aspect of this is
+because the cell is moving it suggests
+
+ align:start position:0%
+because the cell is moving it suggests
+ 
+
+ align:start position:0%
+because the cell is moving it suggests
+that there's some sort of force being
+
+ align:start position:0%
+that there's some sort of force being
+ 
+
+ align:start position:0%
+that there's some sort of force being
+generated okay so there is the cell is
+
+ align:start position:0%
+generated okay so there is the cell is
+ 
+
+ align:start position:0%
+generated okay so there is the cell is
+generating force and I'm not talking
+
+ align:start position:0%
+generating force and I'm not talking
+ 
+
+ align:start position:0%
+generating force and I'm not talking
+about like some type of mystical Jedi
+
+ align:start position:0%
+about like some type of mystical Jedi
+ 
+
+ align:start position:0%
+about like some type of mystical Jedi
+force I'm talking about the mass times
+
+ align:start position:0%
+force I'm talking about the mass times
+ 
+
+ align:start position:0%
+force I'm talking about the mass times
+acceleration force okay so like a
+
+ align:start position:0%
+acceleration force okay so like a
+ 
+
+ align:start position:0%
+acceleration force okay so like a
+physical force okay the second thing I
+
+ align:start position:0%
+physical force okay the second thing I
+ 
+
+ align:start position:0%
+physical force okay the second thing I
+want to point out about this movie is
+
+ align:start position:0%
+want to point out about this movie is
+ 
+
+ align:start position:0%
+want to point out about this movie is
+that you see that bacterium and it's
+
+ align:start position:0%
+that you see that bacterium and it's
+ 
+
+ align:start position:0%
+that you see that bacterium and it's
+moving around this cell is able to
+
+ align:start position:0%
+moving around this cell is able to
+ 
+
+ align:start position:0%
+moving around this cell is able to
+follow that bacterium so the cell and
+
+ align:start position:0%
+follow that bacterium so the cell and
+ 
+
+ align:start position:0%
+follow that bacterium so the cell and
+the fourth generation process is very
+
+ align:start position:0%
+the fourth generation process is very
+ 
+
+ align:start position:0%
+the fourth generation process is very
+responsive to the signals that that cell
+
+ align:start position:0%
+responsive to the signals that that cell
+ 
+
+ align:start position:0%
+responsive to the signals that that cell
+is getting okay so the cell is
+
+ align:start position:0%
+is getting okay so the cell is
+ 
+
+ align:start position:0%
+is getting okay so the cell is
+generating force and this force is
+
+ align:start position:0%
+generating force and this force is
+ 
+
+ align:start position:0%
+generating force and this force is
+responsive to signals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for the remaining part of the
+
+ align:start position:0%
+okay so for the remaining part of the
+ 
+
+ align:start position:0%
+okay so for the remaining part of the
+lecture I basically just want to tell
+
+ align:start position:0%
+lecture I basically just want to tell
+ 
+
+ align:start position:0%
+lecture I basically just want to tell
+you about how it is that the cell
+
+ align:start position:0%
+you about how it is that the cell
+ 
+
+ align:start position:0%
+you about how it is that the cell
+generates the force required to move
+
+ align:start position:0%
+generates the force required to move
+ 
+
+ align:start position:0%
+generates the force required to move
+itself around and it involves a
+
+ align:start position:0%
+itself around and it involves a
+ 
+
+ align:start position:0%
+itself around and it involves a
+particular type of protein it's a
+
+ align:start position:0%
+particular type of protein it's a
+ 
+
+ align:start position:0%
+particular type of protein it's a
+component of the cytoskeleton and we've
+
+ align:start position:0%
+component of the cytoskeleton and we've
+ 
+
+ align:start position:0%
+component of the cytoskeleton and we've
+talked about microtubules and the
+
+ align:start position:0%
+talked about microtubules and the
+ 
+
+ align:start position:0%
+talked about microtubules and the
+microtubule cytoskeleton in its role in
+
+ align:start position:0%
+microtubule cytoskeleton in its role in
+ 
+
+ align:start position:0%
+microtubule cytoskeleton in its role in
+segregating the chromosome but there are
+
+ align:start position:0%
+segregating the chromosome but there are
+ 
+
+ align:start position:0%
+segregating the chromosome but there are
+other cytoskeletal systems that the cell
+
+ align:start position:0%
+other cytoskeletal systems that the cell
+ 
+
+ align:start position:0%
+other cytoskeletal systems that the cell
+has and one is called the actin
+
+ align:start position:0%
+has and one is called the actin
+ 
+
+ align:start position:0%
+has and one is called the actin
+cytoskeleton which is showed on the side
+
+ align:start position:0%
+cytoskeleton which is showed on the side
+ 
+
+ align:start position:0%
+cytoskeleton which is showed on the side
+above and actin the actin cytoskeleton
+
+ align:start position:0%
+above and actin the actin cytoskeleton
+ 
+
+ align:start position:0%
+above and actin the actin cytoskeleton
+is a system that is a biopolymer in the
+
+ align:start position:0%
+is a system that is a biopolymer in the
+ 
+
+ align:start position:0%
+is a system that is a biopolymer in the
+cell so this is a biopolymer like
+
+ align:start position:0%
+cell so this is a biopolymer like
+ 
+
+ align:start position:0%
+cell so this is a biopolymer like
+microtubules and actin is a gene and the
+
+ align:start position:0%
+microtubules and actin is a gene and the
+ 
+
+ align:start position:0%
+microtubules and actin is a gene and the
+actin gene encodes for a protein the
+
+ align:start position:0%
+actin gene encodes for a protein the
+ 
+
+ align:start position:0%
+actin gene encodes for a protein the
+actin protein and when the actin protein
+
+ align:start position:0%
+actin protein and when the actin protein
+ 
+
+ align:start position:0%
+actin protein and when the actin protein
+is made in the cell it start out as
+
+ align:start position:0%
+is made in the cell it start out as
+ 
+
+ align:start position:0%
+is made in the cell it start out as
+being just a sink a single globular
+
+ align:start position:0%
+being just a sink a single globular
+ 
+
+ align:start position:0%
+being just a sink a single globular
+protein okay and when the actin is in
+
+ align:start position:0%
+protein okay and when the actin is in
+ 
+
+ align:start position:0%
+protein okay and when the actin is in
+this state it is called globular or g
+
+ align:start position:0%
+this state it is called globular or g
+ 
+
+ align:start position:0%
+this state it is called globular or g
+actin okay but these subunits these
+
+ align:start position:0%
+actin okay but these subunits these
+ 
+
+ align:start position:0%
+actin okay but these subunits these
+proteins can come together and form a
+
+ align:start position:0%
+proteins can come together and form a
+ 
+
+ align:start position:0%
+proteins can come together and form a
+polymer so they can go from being
+
+ align:start position:0%
+polymer so they can go from being
+ 
+
+ align:start position:0%
+polymer so they can go from being
+individual isolated proteins to forming
+
+ align:start position:0%
+individual isolated proteins to forming
+ 
+
+ align:start position:0%
+individual isolated proteins to forming
+a polymer that forms a long skinny
+
+ align:start position:0%
+a polymer that forms a long skinny
+ 
+
+ align:start position:0%
+a polymer that forms a long skinny
+filament okay and the this form of the
+
+ align:start position:0%
+filament okay and the this form of the
+ 
+
+ align:start position:0%
+filament okay and the this form of the
+protein that's forming a biopolymer is
+
+ align:start position:0%
+protein that's forming a biopolymer is
+ 
+
+ align:start position:0%
+protein that's forming a biopolymer is
+known as filamentous or f-actin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and these are long skinny filaments
+
+ align:start position:0%
+okay and these are long skinny filaments
+ 
+
+ align:start position:0%
+okay and these are long skinny filaments
+they can be hundreds of nanometers even
+
+ align:start position:0%
+they can be hundreds of nanometers even
+ 
+
+ align:start position:0%
+they can be hundreds of nanometers even
+microns in length so hundreds of
+
+ align:start position:0%
+microns in length so hundreds of
+ 
+
+ align:start position:0%
+microns in length so hundreds of
+nanometers long and the filament width
+
+ align:start position:0%
+nanometers long and the filament width
+ 
+
+ align:start position:0%
+nanometers long and the filament width
+is about 10 nanometers okay so I'm just
+
+ align:start position:0%
+is about 10 nanometers okay so I'm just
+ 
+
+ align:start position:0%
+is about 10 nanometers okay so I'm just
+trying to give you a sense of dimensions
+
+ align:start position:0%
+trying to give you a sense of dimensions
+ 
+
+ align:start position:0%
+trying to give you a sense of dimensions
+that this is a long skinny filament that
+
+ align:start position:0%
+that this is a long skinny filament that
+ 
+
+ align:start position:0%
+that this is a long skinny filament that
+the cell can assemble and it assembles
+
+ align:start position:0%
+the cell can assemble and it assembles
+ 
+
+ align:start position:0%
+the cell can assemble and it assembles
+into these dense mesh works which you
+
+ align:start position:0%
+into these dense mesh works which you
+ 
+
+ align:start position:0%
+into these dense mesh works which you
+can see in the slide up here right so
+
+ align:start position:0%
+can see in the slide up here right so
+ 
+
+ align:start position:0%
+can see in the slide up here right so
+this is the leading edge of the cell so
+
+ align:start position:0%
+this is the leading edge of the cell so
+ 
+
+ align:start position:0%
+this is the leading edge of the cell so
+the cell will be migrating this way and
+
+ align:start position:0%
+the cell will be migrating this way and
+ 
+
+ align:start position:0%
+the cell will be migrating this way and
+what you see in this in this cell is
+
+ align:start position:0%
+what you see in this in this cell is
+ 
+
+ align:start position:0%
+what you see in this in this cell is
+this densely branched network and these
+
+ align:start position:0%
+this densely branched network and these
+ 
+
+ align:start position:0%
+this densely branched network and these
+are all actin filaments okay so you get
+
+ align:start position:0%
+are all actin filaments okay so you get
+ 
+
+ align:start position:0%
+are all actin filaments okay so you get
+this huge dense forest of actin
+
+ align:start position:0%
+this huge dense forest of actin
+ 
+
+ align:start position:0%
+this huge dense forest of actin
+filaments that's right at the edge of
+
+ align:start position:0%
+filaments that's right at the edge of
+ 
+
+ align:start position:0%
+filaments that's right at the edge of
+the cell that is moving forward okay one
+
+ align:start position:0%
+the cell that is moving forward okay one
+ 
+
+ align:start position:0%
+the cell that is moving forward okay one
+thing I want to point out is like all
+
+ align:start position:0%
+thing I want to point out is like all
+ 
+
+ align:start position:0%
+thing I want to point out is like all
+things in biology this is not a one-way
+
+ align:start position:0%
+things in biology this is not a one-way
+ 
+
+ align:start position:0%
+things in biology this is not a one-way
+street
+
+ align:start position:0%
+street
+ 
+
+ align:start position:0%
+street
+and so these bio polymers are very
+
+ align:start position:0%
+and so these bio polymers are very
+ 
+
+ align:start position:0%
+and so these bio polymers are very
+dynamic meaning they can undergo
+
+ align:start position:0%
+dynamic meaning they can undergo
+ 
+
+ align:start position:0%
+dynamic meaning they can undergo
+assembly and disassembly and they can do
+
+ align:start position:0%
+assembly and disassembly and they can do
+ 
+
+ align:start position:0%
+assembly and disassembly and they can do
+so on the timescale of seconds one last
+
+ align:start position:0%
+so on the timescale of seconds one last
+ 
+
+ align:start position:0%
+so on the timescale of seconds one last
+thing I want to point out about the
+
+ align:start position:0%
+thing I want to point out about the
+ 
+
+ align:start position:0%
+thing I want to point out about the
+actin filament is there's a polarity to
+
+ align:start position:0%
+actin filament is there's a polarity to
+ 
+
+ align:start position:0%
+actin filament is there's a polarity to
+the filament such that there's a end
+
+ align:start position:0%
+the filament such that there's a end
+ 
+
+ align:start position:0%
+the filament such that there's a end
+known as the plus end where growth is
+
+ align:start position:0%
+known as the plus end where growth is
+ 
+
+ align:start position:0%
+known as the plus end where growth is
+favored and there's an end known as the
+
+ align:start position:0%
+favored and there's an end known as the
+ 
+
+ align:start position:0%
+favored and there's an end known as the
+minus end where there's often d
+
+ align:start position:0%
+minus end where there's often d
+ 
+
+ align:start position:0%
+minus end where there's often d
+polymerization so you can get a
+
+ align:start position:0%
+polymerization so you can get a
+ 
+
+ align:start position:0%
+polymerization so you can get a
+directional growth of the filament so
+
+ align:start position:0%
+directional growth of the filament so
+ 
+
+ align:start position:0%
+directional growth of the filament so
+this is where growth happens and so in
+
+ align:start position:0%
+this is where growth happens and so in
+ 
+
+ align:start position:0%
+this is where growth happens and so in
+this network that you're looking at the
+
+ align:start position:0%
+this network that you're looking at the
+ 
+
+ align:start position:0%
+this network that you're looking at the
+way that actin is oriented so I'm going
+
+ align:start position:0%
+way that actin is oriented so I'm going
+ 
+
+ align:start position:0%
+way that actin is oriented so I'm going
+to draw just a cell here you have this
+
+ align:start position:0%
+to draw just a cell here you have this
+ 
+
+ align:start position:0%
+to draw just a cell here you have this
+dense meshwork of actin and in this
+
+ align:start position:0%
+dense meshwork of actin and in this
+ 
+
+ align:start position:0%
+dense meshwork of actin and in this
+meshwork there's a polarity to the way
+
+ align:start position:0%
+meshwork there's a polarity to the way
+ 
+
+ align:start position:0%
+meshwork there's a polarity to the way
+the actin filaments are oriented so the
+
+ align:start position:0%
+the actin filaments are oriented so the
+ 
+
+ align:start position:0%
+the actin filaments are oriented so the
+cell is migrating this way and the plus
+
+ align:start position:0%
+cell is migrating this way and the plus
+ 
+
+ align:start position:0%
+cell is migrating this way and the plus
+ends of the actin filaments are facing
+
+ align:start position:0%
+ends of the actin filaments are facing
+ 
+
+ align:start position:0%
+ends of the actin filaments are facing
+out right at the surface and the minus
+
+ align:start position:0%
+out right at the surface and the minus
+ 
+
+ align:start position:0%
+out right at the surface and the minus
+ends are back here
+
+ align:start position:0%
+ends are back here
+ 
+
+ align:start position:0%
+ends are back here
+okay and so what you have when the cell
+
+ align:start position:0%
+okay and so what you have when the cell
+ 
+
+ align:start position:0%
+okay and so what you have when the cell
+is migrating is you have this biopolymer
+
+ align:start position:0%
+is migrating is you have this biopolymer
+ 
+
+ align:start position:0%
+is migrating is you have this biopolymer
+Network that's growing on this end but
+
+ align:start position:0%
+Network that's growing on this end but
+ 
+
+ align:start position:0%
+Network that's growing on this end but
+shrinking on the other end and that
+
+ align:start position:0%
+shrinking on the other end and that
+ 
+
+ align:start position:0%
+shrinking on the other end and that
+allows the cell to generate a constant
+
+ align:start position:0%
+allows the cell to generate a constant
+ 
+
+ align:start position:0%
+allows the cell to generate a constant
+per true civ force okay so it's the
+
+ align:start position:0%
+per true civ force okay so it's the
+ 
+
+ align:start position:0%
+per true civ force okay so it's the
+growth of actin filaments the growth of
+
+ align:start position:0%
+growth of actin filaments the growth of
+ 
+
+ align:start position:0%
+growth of actin filaments the growth of
+of f-actin which generates a protrusion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no if we consider the whole process of
+
+ align:start position:0%
+no if we consider the whole process of
+ 
+
+ align:start position:0%
+no if we consider the whole process of
+cell migration what you can see is that
+
+ align:start position:0%
+cell migration what you can see is that
+ 
+
+ align:start position:0%
+cell migration what you can see is that
+initially you're gonna push the cell
+
+ align:start position:0%
+initially you're gonna push the cell
+ 
+
+ align:start position:0%
+initially you're gonna push the cell
+membrane forward okay so you get a
+
+ align:start position:0%
+membrane forward okay so you get a
+ 
+
+ align:start position:0%
+membrane forward okay so you get a
+protrusion it pushes it forward that's
+
+ align:start position:0%
+protrusion it pushes it forward that's
+ 
+
+ align:start position:0%
+protrusion it pushes it forward that's
+often called a lamellipodia
+
+ align:start position:0%
+often called a lamellipodia
+ 
+
+ align:start position:0%
+often called a lamellipodia
+or a pseudo pod and so this sort of part
+
+ align:start position:0%
+or a pseudo pod and so this sort of part
+ 
+
+ align:start position:0%
+or a pseudo pod and so this sort of part
+of the cell moves forward but in order
+
+ align:start position:0%
+of the cell moves forward but in order
+ 
+
+ align:start position:0%
+of the cell moves forward but in order
+for the cell to have a net motion
+
+ align:start position:0%
+for the cell to have a net motion
+ 
+
+ align:start position:0%
+for the cell to have a net motion
+forward it then has to stabilize that
+
+ align:start position:0%
+forward it then has to stabilize that
+ 
+
+ align:start position:0%
+forward it then has to stabilize that
+protrusion and it stabilizes the
+
+ align:start position:0%
+protrusion and it stabilizes the
+ 
+
+ align:start position:0%
+protrusion and it stabilizes the
+protrusion by adhering to the substrate
+
+ align:start position:0%
+protrusion by adhering to the substrate
+ 
+
+ align:start position:0%
+protrusion by adhering to the substrate
+so right now we're just considering a
+
+ align:start position:0%
+so right now we're just considering a
+ 
+
+ align:start position:0%
+so right now we're just considering a
+cell moving on a flat substrate and so
+
+ align:start position:0%
+cell moving on a flat substrate and so
+ 
+
+ align:start position:0%
+cell moving on a flat substrate and so
+the way it attaches to the substrate is
+
+ align:start position:0%
+the way it attaches to the substrate is
+ 
+
+ align:start position:0%
+the way it attaches to the substrate is
+through cell matrix adhesion and this
+
+ align:start position:0%
+through cell matrix adhesion and this
+ 
+
+ align:start position:0%
+through cell matrix adhesion and this
+cell matrix adhesion is mediated by
+
+ align:start position:0%
+cell matrix adhesion is mediated by
+ 
+
+ align:start position:0%
+cell matrix adhesion is mediated by
+another type of adhesion receptor known
+
+ align:start position:0%
+another type of adhesion receptor known
+ 
+
+ align:start position:0%
+another type of adhesion receptor known
+as an integral okay so the cell pushes
+
+ align:start position:0%
+as an integral okay so the cell pushes
+ 
+
+ align:start position:0%
+as an integral okay so the cell pushes
+forward anchors itself
+
+ align:start position:0%
+forward anchors itself
+ 
+
+ align:start position:0%
+forward anchors itself
+on the substrate pulls its body along
+
+ align:start position:0%
+on the substrate pulls its body along
+ 
+
+ align:start position:0%
+on the substrate pulls its body along
+and then just repeats that cycle over
+
+ align:start position:0%
+and then just repeats that cycle over
+ 
+
+ align:start position:0%
+and then just repeats that cycle over
+and over again so the the best way I can
+
+ align:start position:0%
+and over again so the the best way I can
+ 
+
+ align:start position:0%
+and over again so the the best way I can
+illustrate this is if you think about it
+
+ align:start position:0%
+illustrate this is if you think about it
+ 
+
+ align:start position:0%
+illustrate this is if you think about it
+right you get your protrusion you get
+
+ align:start position:0%
+right you get your protrusion you get
+ 
+
+ align:start position:0%
+right you get your protrusion you get
+your elbow out you put down you anchor
+
+ align:start position:0%
+your elbow out you put down you anchor
+ 
+
+ align:start position:0%
+your elbow out you put down you anchor
+right and it's just a repeated cycle and
+
+ align:start position:0%
+right and it's just a repeated cycle and
+ 
+
+ align:start position:0%
+right and it's just a repeated cycle and
+it's able to migrate across the
+
+ align:start position:0%
+it's able to migrate across the
+ 
+
+ align:start position:0%
+it's able to migrate across the
+substrate
+
+ align:start position:0%
+substrate
+ 
+
+ align:start position:0%
+substrate
+so it's kind of like a frontal tow
+
+ align:start position:0%
+so it's kind of like a frontal tow
+ 
+
+ align:start position:0%
+so it's kind of like a frontal tow
+mechanism okay you have cycles of
+
+ align:start position:0%
+mechanism okay you have cycles of
+ 
+
+ align:start position:0%
+mechanism okay you have cycles of
+protrusion you generate traction and
+
+ align:start position:0%
+protrusion you generate traction and
+ 
+
+ align:start position:0%
+protrusion you generate traction and
+then you pull in order to translocate
+
+ align:start position:0%
+then you pull in order to translocate
+ 
+
+ align:start position:0%
+then you pull in order to translocate
+okay and so that's how cells are
+
+ align:start position:0%
+okay and so that's how cells are
+ 
+
+ align:start position:0%
+okay and so that's how cells are
+migrating and in 2d oh this is just
+
+ align:start position:0%
+migrating and in 2d oh this is just
+ 
+
+ align:start position:0%
+migrating and in 2d oh this is just
+showing you that cells can pull on stuff
+
+ align:start position:0%
+showing you that cells can pull on stuff
+ 
+
+ align:start position:0%
+showing you that cells can pull on stuff
+so this not all cells migrate in this
+
+ align:start position:0%
+so this not all cells migrate in this
+ 
+
+ align:start position:0%
+so this not all cells migrate in this
+way I just wanted to say that
+
+ align:start position:0%
+way I just wanted to say that
+ 
+
+ align:start position:0%
+way I just wanted to say that
+so in 3d cells have other mechanisms to
+
+ align:start position:0%
+so in 3d cells have other mechanisms to
+ 
+
+ align:start position:0%
+so in 3d cells have other mechanisms to
+migrate that de-emphasize this traction
+
+ align:start position:0%
+migrate that de-emphasize this traction
+ 
+
+ align:start position:0%
+migrate that de-emphasize this traction
+mechanism that cells have okay so you
+
+ align:start position:0%
+mechanism that cells have okay so you
+ 
+
+ align:start position:0%
+mechanism that cells have okay so you
+can get rid of all the integrins that a
+
+ align:start position:0%
+can get rid of all the integrins that a
+ 
+
+ align:start position:0%
+can get rid of all the integrins that a
+cell has and they're still able to
+
+ align:start position:0%
+cell has and they're still able to
+ 
+
+ align:start position:0%
+cell has and they're still able to
+migrate and that's because 2d emphasizes
+
+ align:start position:0%
+migrate and that's because 2d emphasizes
+ 
+
+ align:start position:0%
+migrate and that's because 2d emphasizes
+the role of adhesion but if you confine
+
+ align:start position:0%
+the role of adhesion but if you confine
+ 
+
+ align:start position:0%
+the role of adhesion but if you confine
+the cell then the cells are able to
+
+ align:start position:0%
+the cell then the cells are able to
+ 
+
+ align:start position:0%
+the cell then the cells are able to
+migrate
+
+ align:start position:0%
+migrate
+ 
+
+ align:start position:0%
+migrate
+so what's shown here are cells that are
+
+ align:start position:0%
+so what's shown here are cells that are
+ 
+
+ align:start position:0%
+so what's shown here are cells that are
+not confined this is a confined cell in
+
+ align:start position:0%
+not confined this is a confined cell in
+ 
+
+ align:start position:0%
+not confined this is a confined cell in
+a micropipette and you can see it's the
+
+ align:start position:0%
+a micropipette and you can see it's the
+ 
+
+ align:start position:0%
+a micropipette and you can see it's the
+same type of cell but the cell can
+
+ align:start position:0%
+same type of cell but the cell can
+ 
+
+ align:start position:0%
+same type of cell but the cell can
+migrate in confinement but it can't
+
+ align:start position:0%
+migrate in confinement but it can't
+ 
+
+ align:start position:0%
+migrate in confinement but it can't
+migrate outside of confinement okay so
+
+ align:start position:0%
+migrate outside of confinement okay so
+ 
+
+ align:start position:0%
+migrate outside of confinement okay so
+in this sense the cell is migrating
+
+ align:start position:0%
+in this sense the cell is migrating
+ 
+
+ align:start position:0%
+in this sense the cell is migrating
+through a different mode and you can
+
+ align:start position:0%
+through a different mode and you can
+ 
+
+ align:start position:0%
+through a different mode and you can
+kind of thinking it you can think of it
+
+ align:start position:0%
+kind of thinking it you can think of it
+ 
+
+ align:start position:0%
+kind of thinking it you can think of it
+as the cells doing some type of Chimney
+
+ align:start position:0%
+as the cells doing some type of Chimney
+ 
+
+ align:start position:0%
+as the cells doing some type of Chimney
+maneuver so it's able to kind of like
+
+ align:start position:0%
+maneuver so it's able to kind of like
+ 
+
+ align:start position:0%
+maneuver so it's able to kind of like
+get in a confined environment push out
+
+ align:start position:0%
+get in a confined environment push out
+ 
+
+ align:start position:0%
+get in a confined environment push out
+against its surroundings and that's how
+
+ align:start position:0%
+against its surroundings and that's how
+ 
+
+ align:start position:0%
+against its surroundings and that's how
+the cell then is able to generate
+
+ align:start position:0%
+the cell then is able to generate
+ 
+
+ align:start position:0%
+the cell then is able to generate
+traction in the absence of an integral
+
+ align:start position:0%
+traction in the absence of an integral
+ 
+
+ align:start position:0%
+traction in the absence of an integral
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+all right great so we are set for now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/6wPHoFjnYXI.txt b/6wPHoFjnYXI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..13d75d00dc67e39ae1ad19d9c880165c16ccc6b7
--- /dev/null
+++ b/6wPHoFjnYXI.txt
@@ -0,0 +1,5099 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right thoughts important
+
+ align:start position:0%
+ocw.mit.edu all right thoughts important
+ 
+
+ align:start position:0%
+ocw.mit.edu all right thoughts important
+Concepts through the week principal AES
+
+ align:start position:0%
+Concepts through the week principal AES
+ 
+
+ align:start position:0%
+Concepts through the week principal AES
+principal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AES
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another one Dynamic versus static
+
+ align:start position:0%
+another one Dynamic versus static
+ 
+
+ align:start position:0%
+another one Dynamic versus static
+balances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right another one
+
+ align:start position:0%
+right another one
+ 
+
+ align:start position:0%
+right another one
+symetry symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is in the context of things like
+
+ align:start position:0%
+this is in the context of things like
+ 
+
+ align:start position:0%
+this is in the context of things like
+the mass moment of inertia Matrix yes
+
+ align:start position:0%
+the mass moment of inertia Matrix yes
+ 
+
+ align:start position:0%
+the mass moment of inertia Matrix yes
+parallel AIS the parallel AIS theem okay
+
+ align:start position:0%
+parallel AIS the parallel AIS theem okay
+ 
+
+ align:start position:0%
+parallel AIS the parallel AIS theem okay
+we haven't done much with it yet but
+
+ align:start position:0%
+we haven't done much with it yet but
+ 
+
+ align:start position:0%
+we haven't done much with it yet but
+we're going to come back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it all
+
+ align:start position:0%
+it all
+ 
+
+ align:start position:0%
+it all
+right all right pretty good list we only
+
+ align:start position:0%
+right all right pretty good list we only
+ 
+
+ align:start position:0%
+right all right pretty good list we only
+had one
+
+ align:start position:0%
+had one
+ 
+
+ align:start position:0%
+had one
+lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamic and static balancing let's talk
+
+ align:start position:0%
+Dynamic and static balancing let's talk
+ 
+
+ align:start position:0%
+Dynamic and static balancing let's talk
+about that for a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if let's talk about static balancing
+
+ align:start position:0%
+if let's talk about static balancing
+ 
+
+ align:start position:0%
+if let's talk about static balancing
+tell me what's are features of static
+
+ align:start position:0%
+tell me what's are features of static
+ 
+
+ align:start position:0%
+tell me what's are features of static
+balancing how can you you have a quiz
+
+ align:start position:0%
+balancing how can you you have a quiz
+ 
+
+ align:start position:0%
+balancing how can you you have a quiz
+problem it's on the final you have an
+
+ align:start position:0%
+problem it's on the final you have an
+ 
+
+ align:start position:0%
+problem it's on the final you have an
+object and an axis about which it's
+
+ align:start position:0%
+object and an axis about which it's
+ 
+
+ align:start position:0%
+object and an axis about which it's
+spinning and you're act asked is this
+
+ align:start position:0%
+spinning and you're act asked is this
+ 
+
+ align:start position:0%
+spinning and you're act asked is this
+statically balanced or not
+
+ align:start position:0%
+statically balanced or not
+ 
+
+ align:start position:0%
+statically balanced or not
+how what would you look for Christina
+
+ align:start position:0%
+how what would you look for Christina
+ 
+
+ align:start position:0%
+how what would you look for Christina
+g g needs to be the ceris so the another
+
+ align:start position:0%
+g g needs to be the ceris so the another
+ 
+
+ align:start position:0%
+g g needs to be the ceris so the another
+way of saying that is the axis must the
+
+ align:start position:0%
+way of saying that is the axis must the
+ 
+
+ align:start position:0%
+way of saying that is the axis must the
+axis of rotation must pass through G is
+
+ align:start position:0%
+axis of rotation must pass through G is
+ 
+
+ align:start position:0%
+axis of rotation must pass through G is
+that what you're trying to say the
+
+ align:start position:0%
+that what you're trying to say the
+ 
+
+ align:start position:0%
+that what you're trying to say the
+center of mass okay everybody agree
+
+ align:start position:0%
+center of mass okay everybody agree
+ 
+
+ align:start position:0%
+center of mass okay everybody agree
+about that all right now if I
+
+ align:start position:0%
+about that all right now if I
+ 
+
+ align:start position:0%
+about that all right now if I
+have weird shaped object I know where
+
+ align:start position:0%
+have weird shaped object I know where
+ 
+
+ align:start position:0%
+have weird shaped object I know where
+the center of mass is and I stick the
+
+ align:start position:0%
+the center of mass is and I stick the
+ 
+
+ align:start position:0%
+the center of mass is and I stick the
+axis of rotation at any angle it all
+
+ align:start position:0%
+axis of rotation at any angle it all
+ 
+
+ align:start position:0%
+axis of rotation at any angle it all
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+it is it statically balanced regardless
+
+ align:start position:0%
+it is it statically balanced regardless
+ 
+
+ align:start position:0%
+it is it statically balanced regardless
+of the where I have the axis of rotation
+
+ align:start position:0%
+of the where I have the axis of rotation
+ 
+
+ align:start position:0%
+of the where I have the axis of rotation
+passing through the center of mass yes I
+
+ align:start position:0%
+passing through the center of mass yes I
+ 
+
+ align:start position:0%
+passing through the center of mass yes I
+hear a yes how about there other people
+
+ align:start position:0%
+hear a yes how about there other people
+ 
+
+ align:start position:0%
+hear a yes how about there other people
+okay so how do you I think that's
+
+ align:start position:0%
+okay so how do you I think that's
+ 
+
+ align:start position:0%
+okay so how do you I think that's
+probably right but how do you test it
+
+ align:start position:0%
+probably right but how do you test it
+ 
+
+ align:start position:0%
+probably right but how do you test it
+how do you test to see how it's a simple
+
+ align:start position:0%
+how do you test to see how it's a simple
+ 
+
+ align:start position:0%
+how do you test to see how it's a simple
+test you can form to see if something is
+
+ align:start position:0%
+test you can form to see if something is
+ 
+
+ align:start position:0%
+test you can form to see if something is
+statically balanced see if it goes to a
+
+ align:start position:0%
+statically balanced see if it goes to a
+ 
+
+ align:start position:0%
+statically balanced see if it goes to a
+low point right so you make the axis
+
+ align:start position:0%
+low point right so you make the axis
+ 
+
+ align:start position:0%
+low point right so you make the axis
+that you're rotating about
+
+ align:start position:0%
+that you're rotating about
+ 
+
+ align:start position:0%
+that you're rotating about
+horizontal and see if the thing seeks a
+
+ align:start position:0%
+horizontal and see if the thing seeks a
+ 
+
+ align:start position:0%
+horizontal and see if the thing seeks a
+low point because if it does it's
+
+ align:start position:0%
+low point because if it does it's
+ 
+
+ align:start position:0%
+low point because if it does it's
+telling you
+
+ align:start position:0%
+telling you
+ 
+
+ align:start position:0%
+telling you
+that what about the center of mass it's
+
+ align:start position:0%
+that what about the center of mass it's
+ 
+
+ align:start position:0%
+that what about the center of mass it's
+not going he's not going through the
+
+ align:start position:0%
+not going he's not going through the
+ 
+
+ align:start position:0%
+not going he's not going through the
+axis to go to a low point it means the
+
+ align:start position:0%
+axis to go to a low point it means the
+ 
+
+ align:start position:0%
+axis to go to a low point it means the
+center of mass is somewhere below that
+
+ align:start position:0%
+center of mass is somewhere below that
+ 
+
+ align:start position:0%
+center of mass is somewhere below that
+axis has beenin right so but any axis at
+
+ align:start position:0%
+axis has beenin right so but any axis at
+ 
+
+ align:start position:0%
+axis has beenin right so but any axis at
+all long as it's through G you are
+
+ align:start position:0%
+all long as it's through G you are
+ 
+
+ align:start position:0%
+all long as it's through G you are
+statically balanced okay Dynamic
+
+ align:start position:0%
+statically balanced okay Dynamic
+ 
+
+ align:start position:0%
+statically balanced okay Dynamic
+balancing what are the what's what would
+
+ align:start position:0%
+balancing what are the what's what would
+ 
+
+ align:start position:0%
+balancing what are the what's what would
+you look for on an object you said is
+
+ align:start position:0%
+you look for on an object you said is
+ 
+
+ align:start position:0%
+you look for on an object you said is
+this dynamic Al balanced or not what
+
+ align:start position:0%
+this dynamic Al balanced or not what
+ 
+
+ align:start position:0%
+this dynamic Al balanced or not what
+kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties there would be no unbalanced
+
+ align:start position:0%
+properties there would be no unbalanced
+ 
+
+ align:start position:0%
+properties there would be no unbalanced
+torqus if you decided to rotate it okay
+
+ align:start position:0%
+torqus if you decided to rotate it okay
+ 
+
+ align:start position:0%
+torqus if you decided to rotate it okay
+so you're looking for no unbalanced
+
+ align:start position:0%
+so you're looking for no unbalanced
+ 
+
+ align:start position:0%
+so you're looking for no unbalanced
+torqus doesn't like if if the object is
+
+ align:start position:0%
+torqus doesn't like if if the object is
+ 
+
+ align:start position:0%
+torqus doesn't like if if the object is
+rotating about the axis that you have it
+
+ align:start position:0%
+rotating about the axis that you have it
+ 
+
+ align:start position:0%
+rotating about the axis that you have it
+on you won't need to supply an extra
+
+ align:start position:0%
+on you won't need to supply an extra
+ 
+
+ align:start position:0%
+on you won't need to supply an extra
+torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to want to keep it Balan okay I I it's
+
+ align:start position:0%
+to want to keep it Balan okay I I it's
+ 
+
+ align:start position:0%
+to want to keep it Balan okay I I it's
+pretty convincing off the AIS it's
+
+ align:start position:0%
+pretty convincing off the AIS it's
+ 
+
+ align:start position:0%
+pretty convincing off the AIS it's
+rotating okay but you put in that last
+
+ align:start position:0%
+rotating okay but you put in that last
+ 
+
+ align:start position:0%
+rotating okay but you put in that last
+caveat then it's about then it's getting
+
+ align:start position:0%
+caveat then it's about then it's getting
+ 
+
+ align:start position:0%
+caveat then it's about then it's getting
+pretty correct can there be a torque on
+
+ align:start position:0%
+pretty correct can there be a torque on
+ 
+
+ align:start position:0%
+pretty correct can there be a torque on
+it that's not balanced and have it be
+
+ align:start position:0%
+it that's not balanced and have it be
+ 
+
+ align:start position:0%
+it that's not balanced and have it be
+dynamically balanced well yeah which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one you have a torque that's in the axis
+
+ align:start position:0%
+one you have a torque that's in the axis
+ 
+
+ align:start position:0%
+one you have a torque that's in the axis
+of Spin and around the axis of rotation
+
+ align:start position:0%
+of Spin and around the axis of rotation
+ 
+
+ align:start position:0%
+of Spin and around the axis of rotation
+and that torque will cause what to
+
+ align:start position:0%
+and that torque will cause what to
+ 
+
+ align:start position:0%
+and that torque will cause what to
+happen cause the rot rate to change
+
+ align:start position:0%
+happen cause the rot rate to change
+ 
+
+ align:start position:0%
+happen cause the rot rate to change
+right that that puts energy into the
+
+ align:start position:0%
+right that that puts energy into the
+ 
+
+ align:start position:0%
+right that that puts energy into the
+system and accelerates it and it's a
+
+ align:start position:0%
+system and accelerates it and it's a
+ 
+
+ align:start position:0%
+system and accelerates it and it's a
+torque that's in the direction of spin
+
+ align:start position:0%
+torque that's in the direction of spin
+ 
+
+ align:start position:0%
+torque that's in the direction of spin
+that doesn't cause Dynamic imbalances
+
+ align:start position:0%
+that doesn't cause Dynamic imbalances
+ 
+
+ align:start position:0%
+that doesn't cause Dynamic imbalances
+but a torque that is other than in the
+
+ align:start position:0%
+but a torque that is other than in the
+ 
+
+ align:start position:0%
+but a torque that is other than in the
+direction of
+
+ align:start position:0%
+direction of
+ 
+
+ align:start position:0%
+direction of
+spin that's what that's what a dynamic
+
+ align:start position:0%
+spin that's what that's what a dynamic
+ 
+
+ align:start position:0%
+spin that's what that's what a dynamic
+imbalance is so what are some other ways
+
+ align:start position:0%
+imbalance is so what are some other ways
+ 
+
+ align:start position:0%
+imbalance is so what are some other ways
+you can say this in terms of uh things
+
+ align:start position:0%
+you can say this in terms of uh things
+ 
+
+ align:start position:0%
+you can say this in terms of uh things
+like evidence of if let's say I give you
+
+ align:start position:0%
+like evidence of if let's say I give you
+ 
+
+ align:start position:0%
+like evidence of if let's say I give you
+H and I give you Omega
+
+ align:start position:0%
+H and I give you Omega
+ 
+
+ align:start position:0%
+H and I give you Omega
+how can you just tell by looking at
+
+ align:start position:0%
+how can you just tell by looking at
+ 
+
+ align:start position:0%
+how can you just tell by looking at
+those two things I give you the angular
+
+ align:start position:0%
+those two things I give you the angular
+ 
+
+ align:start position:0%
+those two things I give you the angular
+momentum and I give you this bin how can
+
+ align:start position:0%
+momentum and I give you this bin how can
+ 
+
+ align:start position:0%
+momentum and I give you this bin how can
+you tell instantly whether or not it is
+
+ align:start position:0%
+you tell instantly whether or not it is
+ 
+
+ align:start position:0%
+you tell instantly whether or not it is
+dynamically
+
+ align:start position:0%
+dynamically
+ 
+
+ align:start position:0%
+dynamically
+balanced the components in the same dire
+
+ align:start position:0%
+balanced the components in the same dire
+ 
+
+ align:start position:0%
+balanced the components in the same dire
+so if you're saying if H and Omega are
+
+ align:start position:0%
+so if you're saying if H and Omega are
+ 
+
+ align:start position:0%
+so if you're saying if H and Omega are
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the our align they just have to be
+
+ align:start position:0%
+the our align they just have to be
+ 
+
+ align:start position:0%
+the our align they just have to be
+parallel if they're aligned you do not
+
+ align:start position:0%
+parallel if they're aligned you do not
+ 
+
+ align:start position:0%
+parallel if they're aligned you do not
+have any Dynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imbalance okay that sound right yeah
+
+ align:start position:0%
+imbalance okay that sound right yeah
+ 
+
+ align:start position:0%
+imbalance okay that sound right yeah
+doesn't matter if they're parallel or
+
+ align:start position:0%
+doesn't matter if they're parallel or
+ 
+
+ align:start position:0%
+doesn't matter if they're parallel or
+anti- parallel does it anti mean just
+
+ align:start position:0%
+anti- parallel does it anti mean just
+ 
+
+ align:start position:0%
+anti- parallel does it anti mean just
+opposite senses uh I think that would be
+
+ align:start position:0%
+opposite senses uh I think that would be
+ 
+
+ align:start position:0%
+opposite senses uh I think that would be
+really hard to do I don't know if any I
+
+ align:start position:0%
+really hard to do I don't know if any I
+ 
+
+ align:start position:0%
+really hard to do I don't know if any I
+don't think you can I don't think you
+
+ align:start position:0%
+don't think you can I don't think you
+ 
+
+ align:start position:0%
+don't think you can I don't think you
+can make a system that has angular
+
+ align:start position:0%
+can make a system that has angular
+ 
+
+ align:start position:0%
+can make a system that has angular
+momentum that is negative it's actually
+
+ align:start position:0%
+momentum that is negative it's actually
+ 
+
+ align:start position:0%
+momentum that is negative it's actually
+opposite the direction of the rotation
+
+ align:start position:0%
+opposite the direction of the rotation
+ 
+
+ align:start position:0%
+opposite the direction of the rotation
+rate I don't think it I don't think our
+
+ align:start position:0%
+rate I don't think it I don't think our
+ 
+
+ align:start position:0%
+rate I don't think it I don't think our
+universe supports that physics but
+
+ align:start position:0%
+universe supports that physics but
+ 
+
+ align:start position:0%
+universe supports that physics but
+anyway I think in any case they're
+
+ align:start position:0%
+anyway I think in any case they're
+ 
+
+ align:start position:0%
+anyway I think in any case they're
+aligned you're okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right let's move on so
+
+ align:start position:0%
+okay all right let's move on so
+ 
+
+ align:start position:0%
+okay all right let's move on so
+um today we're going to actually just
+
+ align:start position:0%
+um today we're going to actually just
+ 
+
+ align:start position:0%
+um today we're going to actually just
+have you work a couple problems and you
+
+ align:start position:0%
+have you work a couple problems and you
+ 
+
+ align:start position:0%
+have you work a couple problems and you
+really are going to work in groups and
+
+ align:start position:0%
+really are going to work in groups and
+ 
+
+ align:start position:0%
+really are going to work in groups and
+when you finish one of the groups is
+
+ align:start position:0%
+when you finish one of the groups is
+ 
+
+ align:start position:0%
+when you finish one of the groups is
+going to come up and fill in the blanks
+
+ align:start position:0%
+going to come up and fill in the blanks
+ 
+
+ align:start position:0%
+going to come up and fill in the blanks
+on the of the answer to the problem and
+
+ align:start position:0%
+on the of the answer to the problem and
+ 
+
+ align:start position:0%
+on the of the answer to the problem and
+we'll talk about it and we're going to
+
+ align:start position:0%
+we'll talk about it and we're going to
+ 
+
+ align:start position:0%
+we'll talk about it and we're going to
+work two problems and they have to do
+
+ align:start position:0%
+work two problems and they have to do
+ 
+
+ align:start position:0%
+work two problems and they have to do
+with things that
+
+ align:start position:0%
+with things that
+ 
+
+ align:start position:0%
+with things that
+spin and as a quick
+
+ align:start position:0%
+spin and as a quick
+ 
+
+ align:start position:0%
+spin and as a quick
+review just of information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so the
+
+ align:start position:0%
+this so the
+ 
+
+ align:start position:0%
+this so the
+problem is a simple one it's basically
+
+ align:start position:0%
+problem is a simple one it's basically
+ 
+
+ align:start position:0%
+problem is a simple one it's basically
+this and I decided to lubricate it and I
+
+ align:start position:0%
+this and I decided to lubricate it and I
+ 
+
+ align:start position:0%
+this and I decided to lubricate it and I
+and it made the wood swell and so now it
+
+ align:start position:0%
+and it made the wood swell and so now it
+ 
+
+ align:start position:0%
+and it made the wood swell and so now it
+won't spin at all actually unless I let
+
+ align:start position:0%
+won't spin at all actually unless I let
+ 
+
+ align:start position:0%
+won't spin at all actually unless I let
+the axis spin so it's just this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem the axis passes through the
+
+ align:start position:0%
+problem the axis passes through the
+ 
+
+ align:start position:0%
+problem the axis passes through the
+center of mass
+
+ align:start position:0%
+center of mass
+ 
+
+ align:start position:0%
+center of mass
+and it looks just like this and I've got
+
+ align:start position:0%
+and it looks just like this and I've got
+ 
+
+ align:start position:0%
+and it looks just like this and I've got
+an X axis aligned with the axis of the
+
+ align:start position:0%
+an X axis aligned with the axis of the
+ 
+
+ align:start position:0%
+an X axis aligned with the axis of the
+rod the Z is this way and the spin is
+
+ align:start position:0%
+rod the Z is this way and the spin is
+ 
+
+ align:start position:0%
+rod the Z is this way and the spin is
+Cap Omega and the uh iner the mass
+
+ align:start position:0%
+Cap Omega and the uh iner the mass
+ 
+
+ align:start position:0%
+Cap Omega and the uh iner the mass
+moment of inertia Matrix for this
+
+ align:start position:0%
+moment of inertia Matrix for this
+ 
+
+ align:start position:0%
+moment of inertia Matrix for this
+problem about G and our axis is passing
+
+ align:start position:0%
+problem about G and our axis is passing
+ 
+
+ align:start position:0%
+problem about G and our axis is passing
+through G so Mass moment of inertia
+
+ align:start position:0%
+through G so Mass moment of inertia
+ 
+
+ align:start position:0%
+through G so Mass moment of inertia
+Matrix times Omega gives you H so here's
+
+ align:start position:0%
+Matrix times Omega gives you H so here's
+ 
+
+ align:start position:0%
+Matrix times Omega gives you H so here's
+the mass moment of inertia Matrix
+
+ align:start position:0%
+the mass moment of inertia Matrix
+ 
+
+ align:start position:0%
+the mass moment of inertia Matrix
+I claim is going to be
+
+ align:start position:0%
+I claim is going to be
+ 
+
+ align:start position:0%
+I claim is going to be
+diagonal and the test of that can you
+
+ align:start position:0%
+diagonal and the test of that can you
+ 
+
+ align:start position:0%
+diagonal and the test of that can you
+tell me whether or not I've chosen axes
+
+ align:start position:0%
+tell me whether or not I've chosen axes
+ 
+
+ align:start position:0%
+tell me whether or not I've chosen axes
+that just from symmetry you know are
+
+ align:start position:0%
+that just from symmetry you know are
+ 
+
+ align:start position:0%
+that just from symmetry you know are
+will be principal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis what do you
+
+ align:start position:0%
+axis what do you
+ 
+
+ align:start position:0%
+axis what do you
+think cular yeah so one axis that's an
+
+ align:start position:0%
+think cular yeah so one axis that's an
+ 
+
+ align:start position:0%
+think cular yeah so one axis that's an
+axis of symmetry is down the down the
+
+ align:start position:0%
+axis of symmetry is down the down the
+ 
+
+ align:start position:0%
+axis of symmetry is down the down the
+shaft so that's guaranteed to be one if
+
+ align:start position:0%
+shaft so that's guaranteed to be one if
+ 
+
+ align:start position:0%
+shaft so that's guaranteed to be one if
+I chosen one like that and any other
+
+ align:start position:0%
+I chosen one like that and any other
+ 
+
+ align:start position:0%
+I chosen one like that and any other
+orthogonal pair after that doesn't
+
+ align:start position:0%
+orthogonal pair after that doesn't
+ 
+
+ align:start position:0%
+orthogonal pair after that doesn't
+matter which way or Orient them will'll
+
+ align:start position:0%
+matter which way or Orient them will'll
+ 
+
+ align:start position:0%
+matter which way or Orient them will'll
+also be so I've got one up and one into
+
+ align:start position:0%
+also be so I've got one up and one into
+ 
+
+ align:start position:0%
+also be so I've got one up and one into
+the board so those are principal axes
+
+ align:start position:0%
+the board so those are principal axes
+ 
+
+ align:start position:0%
+the board so those are principal axes
+for this object so it's going to be
+
+ align:start position:0%
+for this object so it's going to be
+ 
+
+ align:start position:0%
+for this object so it's going to be
+diagonal and in fact it looks it's uh Mr
+
+ align:start position:0%
+diagonal and in fact it looks it's uh Mr
+ 
+
+ align:start position:0%
+diagonal and in fact it looks it's uh Mr
+2 over 2 ml2 over 12 and ml2 over 12
+
+ align:start position:0%
+2 over 2 ml2 over 12 and ml2 over 12
+ 
+
+ align:start position:0%
+2 over 2 ml2 over 12 and ml2 over 12
+when you work it out and if you look up
+
+ align:start position:0%
+when you work it out and if you look up
+ 
+
+ align:start position:0%
+when you work it out and if you look up
+in the book most books for SL what they
+
+ align:start position:0%
+in the book most books for SL what they
+ 
+
+ align:start position:0%
+in the book most books for SL what they
+call slender rods will say that this
+
+ align:start position:0%
+call slender rods will say that this
+ 
+
+ align:start position:0%
+call slender rods will say that this
+first term is zero and that's because
+
+ align:start position:0%
+first term is zero and that's because
+ 
+
+ align:start position:0%
+first term is zero and that's because
+saying L is a lot bigger than R the
+
+ align:start position:0%
+saying L is a lot bigger than R the
+ 
+
+ align:start position:0%
+saying L is a lot bigger than R the
+radius of this thing and so Mr r s is a
+
+ align:start position:0%
+radius of this thing and so Mr r s is a
+ 
+
+ align:start position:0%
+radius of this thing and so Mr r s is a
+pretty small number so it's its energy
+
+ align:start position:0%
+pretty small number so it's its energy
+ 
+
+ align:start position:0%
+pretty small number so it's its energy
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+rotation spinning this way is not very
+
+ align:start position:0%
+rotation spinning this way is not very
+ 
+
+ align:start position:0%
+rotation spinning this way is not very
+big or its angular momentum but its
+
+ align:start position:0%
+big or its angular momentum but its
+ 
+
+ align:start position:0%
+big or its angular momentum but its
+angular momentum spinning like this is
+
+ align:start position:0%
+angular momentum spinning like this is
+ 
+
+ align:start position:0%
+angular momentum spinning like this is
+much much larger because you have much
+
+ align:start position:0%
+much much larger because you have much
+ 
+
+ align:start position:0%
+much much larger because you have much
+greater Mr Mr squar okay so you can
+
+ align:start position:0%
+greater Mr Mr squar okay so you can
+ 
+
+ align:start position:0%
+greater Mr Mr squar okay so you can
+leave for the purpose of this problem
+
+ align:start position:0%
+leave for the purpose of this problem
+ 
+
+ align:start position:0%
+leave for the purpose of this problem
+you can treat this as zero and in your
+
+ align:start position:0%
+you can treat this as zero and in your
+ 
+
+ align:start position:0%
+you can treat this as zero and in your
+groups I want you to come up with the
+
+ align:start position:0%
+groups I want you to come up with the
+ 
+
+ align:start position:0%
+groups I want you to come up with the
+Omega Vector H and dhdt so get do get in
+
+ align:start position:0%
+Omega Vector H and dhdt so get do get in
+ 
+
+ align:start position:0%
+Omega Vector H and dhdt so get do get in
+groups talk about it you've got a few
+
+ align:start position:0%
+groups talk about it you've got a few
+ 
+
+ align:start position:0%
+groups talk about it you've got a few
+minutes to do this this one's pretty
+
+ align:start position:0%
+minutes to do this this one's pretty
+ 
+
+ align:start position:0%
+minutes to do this this one's pretty
+straightforward then you can do another
+
+ align:start position:0%
+straightforward then you can do another
+ 
+
+ align:start position:0%
+straightforward then you can do another
+one that's harder so warm up and you
+
+ align:start position:0%
+one that's harder so warm up and you
+ 
+
+ align:start position:0%
+one that's harder so warm up and you
+find a group to work in and you're going
+
+ align:start position:0%
+find a group to work in and you're going
+ 
+
+ align:start position:0%
+find a group to work in and you're going
+to work a couple of problems this got a
+
+ align:start position:0%
+to work a couple of problems this got a
+ 
+
+ align:start position:0%
+to work a couple of problems this got a
+group feels pretty good about their
+
+ align:start position:0%
+group feels pretty good about their
+ 
+
+ align:start position:0%
+group feels pretty good about their
+answer yes all
+
+ align:start position:0%
+answer yes all
+ 
+
+ align:start position:0%
+answer yes all
+right WR it up come up fill in the uh
+
+ align:start position:0%
+right WR it up come up fill in the uh
+ 
+
+ align:start position:0%
+right WR it up come up fill in the uh
+Omega H and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dhdt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay can everybody see
+
+ align:start position:0%
+okay can everybody see
+ 
+
+ align:start position:0%
+okay can everybody see
+it so you have a z component only for
+
+ align:start position:0%
+it so you have a z component only for
+ 
+
+ align:start position:0%
+it so you have a z component only for
+the Omega a z component K hat only for
+
+ align:start position:0%
+the Omega a z component K hat only for
+ 
+
+ align:start position:0%
+the Omega a z component K hat only for
+eight H and it's I Omega izz Omega and
+
+ align:start position:0%
+eight H and it's I Omega izz Omega and
+ 
+
+ align:start position:0%
+eight H and it's I Omega izz Omega and
+dhdt the only variable here is Omega and
+
+ align:start position:0%
+dhdt the only variable here is Omega and
+ 
+
+ align:start position:0%
+dhdt the only variable here is Omega and
+you get an Omega
+
+ align:start position:0%
+you get an Omega
+ 
+
+ align:start position:0%
+you get an Omega
+Dot and there's no
+
+ align:start position:0%
+Dot and there's no
+ 
+
+ align:start position:0%
+Dot and there's no
+dkdt is zero because it doesn't change
+
+ align:start position:0%
+dkdt is zero because it doesn't change
+ 
+
+ align:start position:0%
+dkdt is zero because it doesn't change
+direction any questions about
+
+ align:start position:0%
+direction any questions about
+ 
+
+ align:start position:0%
+direction any questions about
+this yes um I was a little bit confused
+
+ align:start position:0%
+this yes um I was a little bit confused
+ 
+
+ align:start position:0%
+this yes um I was a little bit confused
+about how we knew like the I K in the H
+
+ align:start position:0%
+about how we knew like the I K in the H
+ 
+
+ align:start position:0%
+about how we knew like the I K in the H
+term is it just because it's only I on
+
+ align:start position:0%
+term is it just because it's only I on
+ 
+
+ align:start position:0%
+term is it just because it's only I on
+the top J the bottom so the convention I
+
+ align:start position:0%
+the top J the bottom so the convention I
+ 
+
+ align:start position:0%
+the top J the bottom so the convention I
+if I understand your question correctly
+
+ align:start position:0%
+if I understand your question correctly
+ 
+
+ align:start position:0%
+if I understand your question correctly
+the convention when you write out the H
+
+ align:start position:0%
+the convention when you write out the H
+ 
+
+ align:start position:0%
+the convention when you write out the H
+Vector is it's the result of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplying the three components of the
+
+ align:start position:0%
+multiplying the three components of the
+ 
+
+ align:start position:0%
+multiplying the three components of the
+spin this is the piece in the I
+
+ align:start position:0%
+spin this is the piece in the I
+ 
+
+ align:start position:0%
+spin this is the piece in the I
+Direction J Direction K Direction when
+
+ align:start position:0%
+Direction J Direction K Direction when
+ 
+
+ align:start position:0%
+Direction J Direction K Direction when
+you multiply these out you get
+
+ align:start position:0%
+you multiply these out you get
+ 
+
+ align:start position:0%
+you multiply these out you get
+three results Vector time so this one is
+
+ align:start position:0%
+three results Vector time so this one is
+ 
+
+ align:start position:0%
+three results Vector time so this one is
+HX and it is in the I the second one
+
+ align:start position:0%
+HX and it is in the I the second one
+ 
+
+ align:start position:0%
+HX and it is in the I the second one
+from this times the row middle row gives
+
+ align:start position:0%
+from this times the row middle row gives
+ 
+
+ align:start position:0%
+from this times the row middle row gives
+you Hy and it's in the J and the third
+
+ align:start position:0%
+you Hy and it's in the J and the third
+ 
+
+ align:start position:0%
+you Hy and it's in the J and the third
+one this Vector times these three in the
+
+ align:start position:0%
+one this Vector times these three in the
+ 
+
+ align:start position:0%
+one this Vector times these three in the
+bottom row give you HZ in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K so I thought when I know it could be
+
+ align:start position:0%
+K so I thought when I know it could be
+ 
+
+ align:start position:0%
+K so I thought when I know it could be
+completely wrong but like multiplication
+
+ align:start position:0%
+completely wrong but like multiplication
+ 
+
+ align:start position:0%
+completely wrong but like multiplication
+you multip like this this this and then
+
+ align:start position:0%
+you multip like this this this and then
+ 
+
+ align:start position:0%
+you multip like this this this and then
+this like you so we have
+
+ align:start position:0%
+this like you so we have
+ 
+
+ align:start position:0%
+this like you so we have
+uh capital a capital b capital c terms
+
+ align:start position:0%
+uh capital a capital b capital c terms
+ 
+
+ align:start position:0%
+uh capital a capital b capital c terms
+in the first row so you do like this and
+
+ align:start position:0%
+in the first row so you do like this and
+ 
+
+ align:start position:0%
+in the first row so you do like this and
+you have a capital little a little B
+
+ align:start position:0%
+you have a capital little a little B
+ 
+
+ align:start position:0%
+you have a capital little a little B
+little C terms in this one when you
+
+ align:start position:0%
+little C terms in this one when you
+ 
+
+ align:start position:0%
+little C terms in this one when you
+multiply this times this you get a A
+
+ align:start position:0%
+multiply this times this you get a A
+ 
+
+ align:start position:0%
+multiply this times this you get a A
+plus BB Plus c c
+
+ align:start position:0%
+plus BB Plus c c
+ 
+
+ align:start position:0%
+plus BB Plus c c
+yeah so that's my question so if you
+
+ align:start position:0%
+yeah so that's my question so if you
+ 
+
+ align:start position:0%
+yeah so that's my question so if you
+have like the Omega X is an I hat Omega
+
+ align:start position:0%
+have like the Omega X is an I hat Omega
+ 
+
+ align:start position:0%
+have like the Omega X is an I hat Omega
+Y is in J hat Omega Z is K hat like how
+
+ align:start position:0%
+Y is in J hat Omega Z is K hat like how
+ 
+
+ align:start position:0%
+Y is in J hat Omega Z is K hat like how
+if you're multiplying like this do you
+
+ align:start position:0%
+if you're multiplying like this do you
+ 
+
+ align:start position:0%
+if you're multiplying like this do you
+get only I hats on the top of the yeah
+
+ align:start position:0%
+get only I hats on the top of the yeah
+ 
+
+ align:start position:0%
+get only I hats on the top of the yeah
+well it's because this isn't just a
+
+ align:start position:0%
+well it's because this isn't just a
+ 
+
+ align:start position:0%
+well it's because this isn't just a
+matrix this is actually a
+
+ align:start position:0%
+matrix this is actually a
+ 
+
+ align:start position:0%
+matrix this is actually a
+tensor and we didn't we haven't gone
+
+ align:start position:0%
+tensor and we didn't we haven't gone
+ 
+
+ align:start position:0%
+tensor and we didn't we haven't gone
+into kind of messy tensor notation but
+
+ align:start position:0%
+into kind of messy tensor notation but
+ 
+
+ align:start position:0%
+into kind of messy tensor notation but
+so you're just being told a convention
+
+ align:start position:0%
+so you're just being told a convention
+ 
+
+ align:start position:0%
+so you're just being told a convention
+here and that is because this is a
+
+ align:start position:0%
+here and that is because this is a
+ 
+
+ align:start position:0%
+here and that is because this is a
+vector being multiplied by a tensor the
+
+ align:start position:0%
+vector being multiplied by a tensor the
+ 
+
+ align:start position:0%
+vector being multiplied by a tensor the
+result what even though this is i j
+
+ align:start position:0%
+result what even though this is i j
+ 
+
+ align:start position:0%
+result what even though this is i j
+k Omega x i times this first term in
+
+ align:start position:0%
+k Omega x i times this first term in
+ 
+
+ align:start position:0%
+k Omega x i times this first term in
+this tensor gives you an it gives you an
+
+ align:start position:0%
+this tensor gives you an it gives you an
+ 
+
+ align:start position:0%
+this tensor gives you an it gives you an
+i back Omega y j times this one gives
+
+ align:start position:0%
+i back Omega y j times this one gives
+ 
+
+ align:start position:0%
+i back Omega y j times this one gives
+you an i back Omega z k times that gives
+
+ align:start position:0%
+you an i back Omega z k times that gives
+ 
+
+ align:start position:0%
+you an i back Omega z k times that gives
+you an i back okay that's what I was
+
+ align:start position:0%
+you an i back okay that's what I was
+ 
+
+ align:start position:0%
+you an i back okay that's what I was
+really and that's a great question
+
+ align:start position:0%
+really and that's a great question
+ 
+
+ align:start position:0%
+really and that's a great question
+because it was wasn't obvious we didn't
+
+ align:start position:0%
+because it was wasn't obvious we didn't
+ 
+
+ align:start position:0%
+because it was wasn't obvious we didn't
+do the full tensor mathematics we just
+
+ align:start position:0%
+do the full tensor mathematics we just
+ 
+
+ align:start position:0%
+do the full tensor mathematics we just
+gave you a result and by definition this
+
+ align:start position:0%
+gave you a result and by definition this
+ 
+
+ align:start position:0%
+gave you a result and by definition this
+row times that is in the I Direction J
+
+ align:start position:0%
+row times that is in the I Direction J
+ 
+
+ align:start position:0%
+row times that is in the I Direction J
+Direction K Direction great question
+
+ align:start position:0%
+Direction K Direction great question
+ 
+
+ align:start position:0%
+Direction K Direction great question
+okay okay so let let's go on the harder
+
+ align:start position:0%
+okay okay so let let's go on the harder
+ 
+
+ align:start position:0%
+okay okay so let let's go on the harder
+problem so you're great at that
+
+ align:start position:0%
+problem so you're great at that
+ 
+
+ align:start position:0%
+problem so you're great at that
+one where we're going to do this one now
+
+ align:start position:0%
+one where we're going to do this one now
+ 
+
+ align:start position:0%
+one where we're going to do this one now
+so this uh so we just did this problem
+
+ align:start position:0%
+so this uh so we just did this problem
+ 
+
+ align:start position:0%
+so this uh so we just did this problem
+all right now we want to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+all right and so the
+
+ align:start position:0%
+all right and so the
+ 
+
+ align:start position:0%
+all right and so the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+same I Matrix
+
+ align:start position:0%
+same I Matrix
+ 
+
+ align:start position:0%
+same I Matrix
+is used
+
+ align:start position:0%
+is used
+ 
+
+ align:start position:0%
+is used
+here it's this one and you can let that
+
+ align:start position:0%
+here it's this one and you can let that
+ 
+
+ align:start position:0%
+here it's this one and you can let that
+term be zero because the coordinate
+
+ align:start position:0%
+term be zero because the coordinate
+ 
+
+ align:start position:0%
+term be zero because the coordinate
+system that has been defined on this
+
+ align:start position:0%
+system that has been defined on this
+ 
+
+ align:start position:0%
+system that has been defined on this
+object is x z y into the board but the
+
+ align:start position:0%
+object is x z y into the board but the
+ 
+
+ align:start position:0%
+object is x z y into the board but the
+direction of spin now is like that we'll
+
+ align:start position:0%
+direction of spin now is like that we'll
+ 
+
+ align:start position:0%
+direction of spin now is like that we'll
+call it cap Omega again but it's in that
+
+ align:start position:0%
+call it cap Omega again but it's in that
+ 
+
+ align:start position:0%
+call it cap Omega again but it's in that
+direction and these are 45 degree angles
+
+ align:start position:0%
+direction and these are 45 degree angles
+ 
+
+ align:start position:0%
+direction and these are 45 degree angles
+for the purposes of this problem so uh
+
+ align:start position:0%
+for the purposes of this problem so uh
+ 
+
+ align:start position:0%
+for the purposes of this problem so uh
+that's s cosine of 45 < tk2
+
+ align:start position:0%
+that's s cosine of 45 < tk2
+ 
+
+ align:start position:0%
+that's s cosine of 45 < tk2
+over2 so now what's
+
+ align:start position:0%
+over2 so now what's
+ 
+
+ align:start position:0%
+over2 so now what's
+Omega what's H and what's dhdt so work
+
+ align:start position:0%
+Omega what's H and what's dhdt so work
+ 
+
+ align:start position:0%
+Omega what's H and what's dhdt so work
+in your groups and sort that one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out you ready to go we can be okay go
+
+ align:start position:0%
+out you ready to go we can be okay go
+ 
+
+ align:start position:0%
+out you ready to go we can be okay go
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll probably do this
+
+ align:start position:0%
+we'll probably do this
+ 
+
+ align:start position:0%
+we'll probably do this
+occasionally and I'm I'll say it again I
+
+ align:start position:0%
+occasionally and I'm I'll say it again I
+ 
+
+ align:start position:0%
+occasionally and I'm I'll say it again I
+have no intention of embarrassing you at
+
+ align:start position:0%
+have no intention of embarrassing you at
+ 
+
+ align:start position:0%
+have no intention of embarrassing you at
+the board so the practice will be you
+
+ align:start position:0%
+the board so the practice will be you
+ 
+
+ align:start position:0%
+the board so the practice will be you
+put your answer up you sit down and then
+
+ align:start position:0%
+put your answer up you sit down and then
+ 
+
+ align:start position:0%
+put your answer up you sit down and then
+we talk about it it's not about you it's
+
+ align:start position:0%
+we talk about it it's not about you it's
+ 
+
+ align:start position:0%
+we talk about it it's not about you it's
+about what's on the board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no put the whole thing up yep and if you
+
+ align:start position:0%
+no put the whole thing up yep and if you
+ 
+
+ align:start position:0%
+no put the whole thing up yep and if you
+want to use that big piece of chalk it
+
+ align:start position:0%
+want to use that big piece of chalk it
+ 
+
+ align:start position:0%
+want to use that big piece of chalk it
+shows better just to your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's talk about Omega first how
+
+ align:start position:0%
+okay so let's talk about Omega first how
+ 
+
+ align:start position:0%
+okay so let's talk about Omega first how
+do you figure uh we have a minus < tk2
+
+ align:start position:0%
+do you figure uh we have a minus < tk2
+ 
+
+ align:start position:0%
+do you figure uh we have a minus < tk2
+over2 here can't see that minus < tk2
+
+ align:start position:0%
+over2 here can't see that minus < tk2
+ 
+
+ align:start position:0%
+over2 here can't see that minus < tk2
+over2 Omega i 0 root2 over2 Omega K are
+
+ align:start position:0%
+over2 Omega i 0 root2 over2 Omega K are
+ 
+
+ align:start position:0%
+over2 Omega i 0 root2 over2 Omega K are
+people feel good about that any
+
+ align:start position:0%
+people feel good about that any
+ 
+
+ align:start position:0%
+people feel good about that any
+differences all right so this thing this
+
+ align:start position:0%
+differences all right so this thing this
+ 
+
+ align:start position:0%
+differences all right so this thing this
+Omega that spin clearly has components
+
+ align:start position:0%
+Omega that spin clearly has components
+ 
+
+ align:start position:0%
+Omega that spin clearly has components
+that are like that and like this so this
+
+ align:start position:0%
+that are like that and like this so this
+ 
+
+ align:start position:0%
+that are like that and like this so this
+is your Z piece and your I piece and it
+
+ align:start position:0%
+is your Z piece and your I piece and it
+ 
+
+ align:start position:0%
+is your Z piece and your I piece and it
+is indeed in the minus IAT Direction so
+
+ align:start position:0%
+is indeed in the minus IAT Direction so
+ 
+
+ align:start position:0%
+is indeed in the minus IAT Direction so
+that seems okay and H would be some I
+
+ align:start position:0%
+that seems okay and H would be some I
+ 
+
+ align:start position:0%
+that seems okay and H would be some I
+that the I times
+
+ align:start position:0%
+that the I times
+ 
+
+ align:start position:0%
+that the I times
+Omega and the first term if you'll take
+
+ align:start position:0%
+Omega and the first term if you'll take
+ 
+
+ align:start position:0%
+Omega and the first term if you'll take
+that upper left term as zero then you
+
+ align:start position:0%
+that upper left term as zero then you
+ 
+
+ align:start position:0%
+that upper left term as zero then you
+don't get anything the second term you
+
+ align:start position:0%
+don't get anything the second term you
+ 
+
+ align:start position:0%
+don't get anything the second term you
+don't get anything how so how do how do
+
+ align:start position:0%
+don't get anything how so how do how do
+ 
+
+ align:start position:0%
+don't get anything how so how do how do
+you feel about the angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum any
+
+ align:start position:0%
+momentum any
+ 
+
+ align:start position:0%
+momentum any
+differences okay and the
+
+ align:start position:0%
+differences okay and the
+ 
+
+ align:start position:0%
+differences okay and the
+dhdt uh you take the time derivative of
+
+ align:start position:0%
+dhdt uh you take the time derivative of
+ 
+
+ align:start position:0%
+dhdt uh you take the time derivative of
+this thing you got an Omega dot okay
+
+ align:start position:0%
+this thing you got an Omega dot okay
+ 
+
+ align:start position:0%
+this thing you got an Omega dot okay
+that looks okay as far as it goes but
+
+ align:start position:0%
+that looks okay as far as it goes but
+ 
+
+ align:start position:0%
+that looks okay as far as it goes but
+any other
+
+ align:start position:0%
+any other
+ 
+
+ align:start position:0%
+any other
+thoughts the so K dot is not Zer okay so
+
+ align:start position:0%
+thoughts the so K dot is not Zer okay so
+ 
+
+ align:start position:0%
+thoughts the so K dot is not Zer okay so
+you're saying K hat is changing with
+
+ align:start position:0%
+you're saying K hat is changing with
+ 
+
+ align:start position:0%
+you're saying K hat is changing with
+time yeah and let's think about that so
+
+ align:start position:0%
+time yeah and let's think about that so
+ 
+
+ align:start position:0%
+time yeah and let's think about that so
+it's that's this piece here this is
+
+ align:start position:0%
+it's that's this piece here this is
+ 
+
+ align:start position:0%
+it's that's this piece here this is
+Omega z k
+
+ align:start position:0%
+Omega z k
+ 
+
+ align:start position:0%
+Omega z k
+hat and as this thing goes around that
+
+ align:start position:0%
+hat and as this thing goes around that
+ 
+
+ align:start position:0%
+hat and as this thing goes around that
+unit Vector is doing this right so you
+
+ align:start position:0%
+unit Vector is doing this right so you
+ 
+
+ align:start position:0%
+unit Vector is doing this right so you
+need a dek a DT so do you want to give
+
+ align:start position:0%
+need a dek a DT so do you want to give
+ 
+
+ align:start position:0%
+need a dek a DT so do you want to give
+somebody else give me the second term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here ml
+
+ align:start position:0%
+here ml
+ 
+
+ align:start position:0%
+here ml
+2 time Omega
+
+ align:start position:0%
+2 time Omega
+ 
+
+ align:start position:0%
+2 time Omega
+s because you have the changing
+
+ align:start position:0%
+s because you have the changing
+ 
+
+ align:start position:0%
+s because you have the changing
+direction in your principal axes
+
+ align:start position:0%
+direction in your principal axes
+ 
+
+ align:start position:0%
+direction in your principal axes
+mhm and that's going to be time two okay
+
+ align:start position:0%
+mhm and that's going to be time two okay
+ 
+
+ align:start position:0%
+mhm and that's going to be time two okay
+this is RO omeg Square okay and then
+
+ align:start position:0%
+this is RO omeg Square okay and then
+ 
+
+ align:start position:0%
+this is RO omeg Square okay and then
+what about the < tk2 over2 yeah you
+
+ align:start position:0%
+what about the < tk2 over2 yeah you
+ 
+
+ align:start position:0%
+what about the < tk2 over2 yeah you
+have got a square that too right that'
+
+ align:start position:0%
+have got a square that too right that'
+ 
+
+ align:start position:0%
+have got a square that too right that'
+be squ as well that gives you a
+
+ align:start position:0%
+be squ as well that gives you a
+ 
+
+ align:start position:0%
+be squ as well that gives you a
+half okay and that's that's 12 and
+
+ align:start position:0%
+half okay and that's that's 12 and
+ 
+
+ align:start position:0%
+half okay and that's that's 12 and
+that positive positive yes started out
+
+ align:start position:0%
+that positive positive yes started out
+ 
+
+ align:start position:0%
+that positive positive yes started out
+with a negative
+
+ align:start position:0%
+with a negative
+ 
+
+ align:start position:0%
+with a negative
+but k i cross K is minus J * A minus
+
+ align:start position:0%
+but k i cross K is minus J * A minus
+ 
+
+ align:start position:0%
+but k i cross K is minus J * A minus
+gives you the plus right so this looks
+
+ align:start position:0%
+gives you the plus right so this looks
+ 
+
+ align:start position:0%
+gives you the plus right so this looks
+like this comes out uh ml^ s Omega s j
+
+ align:start position:0%
+like this comes out uh ml^ s Omega s j
+ 
+
+ align:start position:0%
+like this comes out uh ml^ s Omega s j
+hat over 24 I think like that that term
+
+ align:start position:0%
+hat over 24 I think like that that term
+ 
+
+ align:start position:0%
+hat over 24 I think like that that term
+now uh okay and people good with that
+
+ align:start position:0%
+now uh okay and people good with that
+ 
+
+ align:start position:0%
+now uh okay and people good with that
+now so just to remind you
+
+ align:start position:0%
+now so just to remind you
+ 
+
+ align:start position:0%
+now so just to remind you
+um when I was doing these problem when I
+
+ align:start position:0%
+um when I was doing these problem when I
+ 
+
+ align:start position:0%
+um when I was doing these problem when I
+first had to teach this course a few
+
+ align:start position:0%
+first had to teach this course a few
+ 
+
+ align:start position:0%
+first had to teach this course a few
+years ago and I was trying to figure out
+
+ align:start position:0%
+years ago and I was trying to figure out
+ 
+
+ align:start position:0%
+years ago and I was trying to figure out
+you know easy way to teach this and how
+
+ align:start position:0%
+you know easy way to teach this and how
+ 
+
+ align:start position:0%
+you know easy way to teach this and how
+to do these problems I got myself all
+
+ align:start position:0%
+to do these problems I got myself all
+ 
+
+ align:start position:0%
+to do these problems I got myself all
+confused trying to figure out okay which
+
+ align:start position:0%
+confused trying to figure out okay which
+ 
+
+ align:start position:0%
+confused trying to figure out okay which
+components of the rotation Vector are
+
+ align:start position:0%
+components of the rotation Vector are
+ 
+
+ align:start position:0%
+components of the rotation Vector are
+rotating and what do I have to cross
+
+ align:start position:0%
+rotating and what do I have to cross
+ 
+
+ align:start position:0%
+rotating and what do I have to cross
+into it to get the answer and in fact
+
+ align:start position:0%
+into it to get the answer and in fact
+ 
+
+ align:start position:0%
+into it to get the answer and in fact
+you don't have to make it anywhere near
+
+ align:start position:0%
+you don't have to make it anywhere near
+ 
+
+ align:start position:0%
+you don't have to make it anywhere near
+that hard and let's uh take a quick look
+
+ align:start position:0%
+that hard and let's uh take a quick look
+ 
+
+ align:start position:0%
+that hard and let's uh take a quick look
+at something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here H is ml s over
+
+ align:start position:0%
+here H is ml s over
+ 
+
+ align:start position:0%
+here H is ml s over
+12 < tk2 over
+
+ align:start position:0%
+12 < tk2 over
+ 
+
+ align:start position:0%
+12 < tk2 over
+2 where H go < tk2 over to Omega K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hat H is a rotating
+
+ align:start position:0%
+hat H is a rotating
+ 
+
+ align:start position:0%
+hat H is a rotating
+Vector the
+
+ align:start position:0%
+Vector the
+ 
+
+ align:start position:0%
+Vector the
+derivative of a rotating
+
+ align:start position:0%
+derivative of a rotating
+ 
+
+ align:start position:0%
+derivative of a rotating
+Vector in an inertial
+
+ align:start position:0%
+Vector in an inertial
+ 
+
+ align:start position:0%
+Vector in an inertial
+frame is the derivative
+
+ align:start position:0%
+frame is the derivative
+ 
+
+ align:start position:0%
+frame is the derivative
+of that rotating Vector in the rotating
+
+ align:start position:0%
+of that rotating Vector in the rotating
+ 
+
+ align:start position:0%
+of that rotating Vector in the rotating
+frame which is the same thing as saying
+
+ align:start position:0%
+frame which is the same thing as saying
+ 
+
+ align:start position:0%
+frame which is the same thing as saying
+that Omega is zero that's the change in
+
+ align:start position:0%
+that Omega is zero that's the change in
+ 
+
+ align:start position:0%
+that Omega is zero that's the change in
+length of the vector plus Omega cross H
+
+ align:start position:0%
+length of the vector plus Omega cross H
+ 
+
+ align:start position:0%
+length of the vector plus Omega cross H
+Let's test that and to see if that that
+
+ align:start position:0%
+Let's test that and to see if that that
+ 
+
+ align:start position:0%
+Let's test that and to see if that that
+gives us the right answer this
+
+ align:start position:0%
+gives us the right answer this
+ 
+
+ align:start position:0%
+gives us the right answer this
+derivative gives you all that does is
+
+ align:start position:0%
+derivative gives you all that does is
+ 
+
+ align:start position:0%
+derivative gives you all that does is
+gives you the Theta the Omega dot back
+
+ align:start position:0%
+gives you the Theta the Omega dot back
+ 
+
+ align:start position:0%
+gives you the Theta the Omega dot back
+right that's that first term and the
+
+ align:start position:0%
+right that's that first term and the
+ 
+
+ align:start position:0%
+right that's that first term and the
+second term should just then look like
+
+ align:start position:0%
+second term should just then look like
+ 
+
+ align:start position:0%
+second term should just then look like
+uh your Omega which is Omega < tk2
+
+ align:start position:0%
+uh your Omega which is Omega < tk2
+ 
+
+ align:start position:0%
+uh your Omega which is Omega < tk2
+minus root 2 over 2 cap Omega I plus <
+
+ align:start position:0%
+minus root 2 over 2 cap Omega I plus <
+ 
+
+ align:start position:0%
+minus root 2 over 2 cap Omega I plus <
+tk2 over 2 cap Omega
+
+ align:start position:0%
+tk2 over 2 cap Omega
+ 
+
+ align:start position:0%
+tk2 over 2 cap Omega
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+cross a bunch of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constants times K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the k cross K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms are zero the I cross
+
+ align:start position:0%
+terms are zero the I cross
+ 
+
+ align:start position:0%
+terms are zero the I cross
+K minus J and so you get < tk2 over2 * <
+
+ align:start position:0%
+K minus J and so you get < tk2 over2 * <
+ 
+
+ align:start position:0%
+K minus J and so you get < tk2 over2 * <
+tk2 over2 you get uh in you just get
+
+ align:start position:0%
+tk2 over2 you get uh in you just get
+ 
+
+ align:start position:0%
+tk2 over2 you get uh in you just get
+what's in h here multiplied byun2 over2
+
+ align:start position:0%
+what's in h here multiplied byun2 over2
+ 
+
+ align:start position:0%
+what's in h here multiplied byun2 over2
+Omega hat and you get back
+
+ align:start position:0%
+Omega hat and you get back
+ 
+
+ align:start position:0%
+Omega hat and you get back
+exactly these two
+
+ align:start position:0%
+exactly these two
+ 
+
+ align:start position:0%
+exactly these two
+terms so it's that easy you know it's
+
+ align:start position:0%
+terms so it's that easy you know it's
+ 
+
+ align:start position:0%
+terms so it's that easy you know it's
+just the derivative of rotating Vector
+
+ align:start position:0%
+just the derivative of rotating Vector
+ 
+
+ align:start position:0%
+just the derivative of rotating Vector
+just doing Omega cross H is the easiest
+
+ align:start position:0%
+just doing Omega cross H is the easiest
+ 
+
+ align:start position:0%
+just doing Omega cross H is the easiest
+way to deal with
+
+ align:start position:0%
+way to deal with
+ 
+
+ align:start position:0%
+way to deal with
+that derivative of the rotating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+piece and any rotating Vector you can
+
+ align:start position:0%
+piece and any rotating Vector you can
+ 
+
+ align:start position:0%
+piece and any rotating Vector you can
+take his time derivative that way all
+
+ align:start position:0%
+take his time derivative that way all
+ 
+
+ align:start position:0%
+take his time derivative that way all
+right we've got a few minutes uh I want
+
+ align:start position:0%
+right we've got a few minutes uh I want
+ 
+
+ align:start position:0%
+right we've got a few minutes uh I want
+actually any other questions about this
+
+ align:start position:0%
+actually any other questions about this
+ 
+
+ align:start position:0%
+actually any other questions about this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+problem you in physics most of the
+
+ align:start position:0%
+problem you in physics most of the
+ 
+
+ align:start position:0%
+problem you in physics most of the
+problems you've worked before were it
+
+ align:start position:0%
+problems you've worked before were it
+ 
+
+ align:start position:0%
+problems you've worked before were it
+involved rotation are planer we call
+
+ align:start position:0%
+involved rotation are planer we call
+ 
+
+ align:start position:0%
+involved rotation are planer we call
+planer motion problems the axis of spin
+
+ align:start position:0%
+planer motion problems the axis of spin
+ 
+
+ align:start position:0%
+planer motion problems the axis of spin
+was always perpendicular to the plane
+
+ align:start position:0%
+was always perpendicular to the plane
+ 
+
+ align:start position:0%
+was always perpendicular to the plane
+and the rest of the problem was confined
+
+ align:start position:0%
+and the rest of the problem was confined
+ 
+
+ align:start position:0%
+and the rest of the problem was confined
+to the plane you know so hockey pucks
+
+ align:start position:0%
+to the plane you know so hockey pucks
+ 
+
+ align:start position:0%
+to the plane you know so hockey pucks
+sliding along and stuff like that and
+
+ align:start position:0%
+sliding along and stuff like that and
+ 
+
+ align:start position:0%
+sliding along and stuff like that and
+the but it was always assumed that the
+
+ align:start position:0%
+the but it was always assumed that the
+ 
+
+ align:start position:0%
+the but it was always assumed that the
+axis of uh rotation was perpendicular to
+
+ align:start position:0%
+axis of uh rotation was perpendicular to
+ 
+
+ align:start position:0%
+axis of uh rotation was perpendicular to
+the plane and that the angular momentum
+
+ align:start position:0%
+the plane and that the angular momentum
+ 
+
+ align:start position:0%
+the plane and that the angular momentum
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+parallel so this is actually this these
+
+ align:start position:0%
+parallel so this is actually this these
+ 
+
+ align:start position:0%
+parallel so this is actually this these
+are this is a 3D problem this is a 3D
+
+ align:start position:0%
+are this is a 3D problem this is a 3D
+ 
+
+ align:start position:0%
+are this is a 3D problem this is a 3D
+Dynamics problem as soon as is that H
+
+ align:start position:0%
+Dynamics problem as soon as is that H
+ 
+
+ align:start position:0%
+Dynamics problem as soon as is that H
+and the Omega are different directions
+
+ align:start position:0%
+and the Omega are different directions
+ 
+
+ align:start position:0%
+and the Omega are different directions
+you can come up with torqus in all three
+
+ align:start position:0%
+you can come up with torqus in all three
+ 
+
+ align:start position:0%
+you can come up with torqus in all three
+directions right
+
+ align:start position:0%
+directions right
+ 
+
+ align:start position:0%
+directions right
+okay all right is
+
+ align:start position:0%
+okay all right is
+ 
+
+ align:start position:0%
+okay all right is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so any other questions about this and if
+
+ align:start position:0%
+so any other questions about this and if
+ 
+
+ align:start position:0%
+so any other questions about this and if
+not I want to talk about something that
+
+ align:start position:0%
+not I want to talk about something that
+ 
+
+ align:start position:0%
+not I want to talk about something that
+was on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+here's this this this is the one problem
+
+ align:start position:0%
+here's this this this is the one problem
+ 
+
+ align:start position:0%
+here's this this this is the one problem
+on the quiz that gave more conceptual
+
+ align:start position:0%
+on the quiz that gave more conceptual
+ 
+
+ align:start position:0%
+on the quiz that gave more conceptual
+difficulty than any other single problem
+
+ align:start position:0%
+difficulty than any other single problem
+ 
+
+ align:start position:0%
+difficulty than any other single problem
+you know people made mistakes on other
+
+ align:start position:0%
+you know people made mistakes on other
+ 
+
+ align:start position:0%
+you know people made mistakes on other
+problems but got into conceptual trouble
+
+ align:start position:0%
+problems but got into conceptual trouble
+ 
+
+ align:start position:0%
+problems but got into conceptual trouble
+with this problem remember you had a
+
+ align:start position:0%
+with this problem remember you had a
+ 
+
+ align:start position:0%
+with this problem remember you had a
+vehicle driving up a bridge and the
+
+ align:start position:0%
+vehicle driving up a bridge and the
+ 
+
+ align:start position:0%
+vehicle driving up a bridge and the
+bridge could be changing has some
+
+ align:start position:0%
+bridge could be changing has some
+ 
+
+ align:start position:0%
+bridge could be changing has some
+angular rate and it has some angular
+
+ align:start position:0%
+angular rate and it has some angular
+ 
+
+ align:start position:0%
+angular rate and it has some angular
+acceleration and we said to keep the
+
+ align:start position:0%
+acceleration and we said to keep the
+ 
+
+ align:start position:0%
+acceleration and we said to keep the
+problem simple that you could treat this
+
+ align:start position:0%
+problem simple that you could treat this
+ 
+
+ align:start position:0%
+problem simple that you could treat this
+as a particle and that really means you
+
+ align:start position:0%
+as a particle and that really means you
+ 
+
+ align:start position:0%
+as a particle and that really means you
+didn't have to deal with angular
+
+ align:start position:0%
+didn't have to deal with angular
+ 
+
+ align:start position:0%
+didn't have to deal with angular
+momentum I Omega for the object it's
+
+ align:start position:0%
+momentum I Omega for the object it's
+ 
+
+ align:start position:0%
+momentum I Omega for the object it's
+treated like a
+
+ align:start position:0%
+treated like a
+ 
+
+ align:start position:0%
+treated like a
+particle and one of the where
+
+ align:start position:0%
+particle and one of the where
+ 
+
+ align:start position:0%
+particle and one of the where
+people got where the confusion came from
+
+ align:start position:0%
+people got where the confusion came from
+ 
+
+ align:start position:0%
+people got where the confusion came from
+was in figuring out fre B
+
+ align:start position:0%
+was in figuring out fre B
+ 
+
+ align:start position:0%
+was in figuring out fre B
+diagrams you're told in the problem the
+
+ align:start position:0%
+diagrams you're told in the problem the
+ 
+
+ align:start position:0%
+diagrams you're told in the problem the
+language is something like the action of
+
+ align:start position:0%
+language is something like the action of
+ 
+
+ align:start position:0%
+language is something like the action of
+the tires on the road result in a net
+
+ align:start position:0%
+the tires on the road result in a net
+ 
+
+ align:start position:0%
+the tires on the road result in a net
+force up the incline called
+
+ align:start position:0%
+force up the incline called
+ 
+
+ align:start position:0%
+force up the incline called
+T and we didn't call it friction we
+
+ align:start position:0%
+T and we didn't call it friction we
+ 
+
+ align:start position:0%
+T and we didn't call it friction we
+didn't say anything but
+
+ align:start position:0%
+didn't say anything but
+ 
+
+ align:start position:0%
+didn't say anything but
+people a number of people got confused
+
+ align:start position:0%
+people a number of people got confused
+ 
+
+ align:start position:0%
+people a number of people got confused
+about what's that have to do with
+
+ align:start position:0%
+about what's that have to do with
+ 
+
+ align:start position:0%
+about what's that have to do with
+friction how does friction come into
+
+ align:start position:0%
+friction how does friction come into
+ 
+
+ align:start position:0%
+friction how does friction come into
+this okay so let's do the free body
+
+ align:start position:0%
+this okay so let's do the free body
+ 
+
+ align:start position:0%
+this okay so let's do the free body
+diagram for this thing so tell me what's
+
+ align:start position:0%
+diagram for this thing so tell me what's
+ 
+
+ align:start position:0%
+diagram for this thing so tell me what's
+here's my car tell me what to put on the
+
+ align:start position:0%
+here's my car tell me what to put on the
+ 
+
+ align:start position:0%
+here's my car tell me what to put on the
+free body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram wait okay mg all right so you
+
+ align:start position:0%
+diagram wait okay mg all right so you
+ 
+
+ align:start position:0%
+diagram wait okay mg all right so you
+got an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next a norm Force okay that's going this
+
+ align:start position:0%
+next a norm Force okay that's going this
+ 
+
+ align:start position:0%
+next a norm Force okay that's going this
+way we'll call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it got T
+
+ align:start position:0%
+it got T
+ 
+
+ align:start position:0%
+it got T
+okay now what about the tires on the
+
+ align:start position:0%
+okay now what about the tires on the
+ 
+
+ align:start position:0%
+okay now what about the tires on the
+road what about
+
+ align:start position:0%
+road what about
+ 
+
+ align:start position:0%
+road what about
+friction pardon that's T that is T so
+
+ align:start position:0%
+friction pardon that's T that is T so
+ 
+
+ align:start position:0%
+friction pardon that's T that is T so
+you think of the free body diagram you
+
+ align:start position:0%
+you think of the free body diagram you
+ 
+
+ align:start position:0%
+you think of the free body diagram you
+just say what are all the possible
+
+ align:start position:0%
+just say what are all the possible
+ 
+
+ align:start position:0%
+just say what are all the possible
+sources of external force on this thing
+
+ align:start position:0%
+sources of external force on this thing
+ 
+
+ align:start position:0%
+sources of external force on this thing
+and they come from Gravity a body Force
+
+ align:start position:0%
+and they come from Gravity a body Force
+ 
+
+ align:start position:0%
+and they come from Gravity a body Force
+and then other things that are in
+
+ align:start position:0%
+and then other things that are in
+ 
+
+ align:start position:0%
+and then other things that are in
+contact with it and the wheels are in
+
+ align:start position:0%
+contact with it and the wheels are in
+ 
+
+ align:start position:0%
+contact with it and the wheels are in
+contact with the road and through the
+
+ align:start position:0%
+contact with the road and through the
+ 
+
+ align:start position:0%
+contact with the road and through the
+wheels you get the normal force and
+
+ align:start position:0%
+wheels you get the normal force and
+ 
+
+ align:start position:0%
+wheels you get the normal force and
+through the wheels you get any Act of
+
+ align:start position:0%
+through the wheels you get any Act of
+ 
+
+ align:start position:0%
+through the wheels you get any Act of
+friction so that is the that's the total
+
+ align:start position:0%
+friction so that is the that's the total
+ 
+
+ align:start position:0%
+friction so that is the that's the total
+net friction
+
+ align:start position:0%
+net friction
+ 
+
+ align:start position:0%
+net friction
+Force
+
+ align:start position:0%
+Force
+ 
+
+ align:start position:0%
+Force
+so and then once you got that far you
+
+ align:start position:0%
+so and then once you got that far you
+ 
+
+ align:start position:0%
+so and then once you got that far you
+were asked to come up with an equation
+
+ align:start position:0%
+were asked to come up with an equation
+ 
+
+ align:start position:0%
+were asked to come up with an equation
+of motion in this
+
+ align:start position:0%
+of motion in this
+ 
+
+ align:start position:0%
+of motion in this
+direction in the uh direction of the
+
+ align:start position:0%
+direction in the uh direction of the
+ 
+
+ align:start position:0%
+direction in the uh direction of the
+bridge and how do you so when you go to
+
+ align:start position:0%
+bridge and how do you so when you go to
+ 
+
+ align:start position:0%
+bridge and how do you so when you go to
+get an equation of motion you say the
+
+ align:start position:0%
+get an equation of motion you say the
+ 
+
+ align:start position:0%
+get an equation of motion you say the
+sum of the external forces is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to and we'll make these in the X
+
+ align:start position:0%
+to and we'll make these in the X
+ 
+
+ align:start position:0%
+to and we'll make these in the X
+Direction here is the mass times the
+
+ align:start position:0%
+Direction here is the mass times the
+ 
+
+ align:start position:0%
+Direction here is the mass times the
+acceleration in the X Direction and how
+
+ align:start position:0%
+acceleration in the X Direction and how
+ 
+
+ align:start position:0%
+acceleration in the X Direction and how
+would what terms
+
+ align:start position:0%
+would what terms
+ 
+
+ align:start position:0%
+would what terms
+appear
+
+ align:start position:0%
+appear
+ 
+
+ align:start position:0%
+appear
+pardon well those are the forces they're
+
+ align:start position:0%
+pardon well those are the forces they're
+ 
+
+ align:start position:0%
+pardon well those are the forces they're
+on the other side I want you to come up
+
+ align:start position:0%
+on the other side I want you to come up
+ 
+
+ align:start position:0%
+on the other side I want you to come up
+with the acceleration you need to come
+
+ align:start position:0%
+with the acceleration you need to come
+ 
+
+ align:start position:0%
+with the acceleration you need to come
+up with the acceleration
+
+ align:start position:0%
+up with the acceleration
+ 
+
+ align:start position:0%
+up with the acceleration
+terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pardon so this probably most most easily
+
+ align:start position:0%
+pardon so this probably most most easily
+ 
+
+ align:start position:0%
+pardon so this probably most most easily
+to Think Through I think in terms of R
+
+ align:start position:0%
+to Think Through I think in terms of R
+ 
+
+ align:start position:0%
+to Think Through I think in terms of R
+and Theta and polar coordinates because
+
+ align:start position:0%
+and Theta and polar coordinates because
+ 
+
+ align:start position:0%
+and Theta and polar coordinates because
+you've been you've worked dozens of
+
+ align:start position:0%
+you've been you've worked dozens of
+ 
+
+ align:start position:0%
+you've been you've worked dozens of
+times with the complete acceleration of
+
+ align:start position:0%
+times with the complete acceleration of
+ 
+
+ align:start position:0%
+times with the complete acceleration of
+something in a rotating system and this
+
+ align:start position:0%
+something in a rotating system and this
+ 
+
+ align:start position:0%
+something in a rotating system and this
+is a rotating
+
+ align:start position:0%
+is a rotating
+ 
+
+ align:start position:0%
+is a rotating
+system polar coordinates is a pretty
+
+ align:start position:0%
+system polar coordinates is a pretty
+ 
+
+ align:start position:0%
+system polar coordinates is a pretty
+easy good way to do this problem so uh
+
+ align:start position:0%
+easy good way to do this problem so uh
+ 
+
+ align:start position:0%
+easy good way to do this problem so uh
+what are the accelerations in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+R well I do it in terms of well I do it
+
+ align:start position:0%
+R well I do it in terms of well I do it
+ 
+
+ align:start position:0%
+R well I do it in terms of well I do it
+in terms of R and Theta you given a
+
+ align:start position:0%
+in terms of R and Theta you given a
+ 
+
+ align:start position:0%
+in terms of R and Theta you given a
+Theta Dot and a Theta double dot and x
+
+ align:start position:0%
+Theta Dot and a Theta double dot and x
+ 
+
+ align:start position:0%
+Theta Dot and a Theta double dot and x
+and R amount up to
+
+ align:start position:0%
+and R amount up to
+ 
+
+ align:start position:0%
+and R amount up to
+the same thing but I if you call it R
+
+ align:start position:0%
+the same thing but I if you call it R
+ 
+
+ align:start position:0%
+the same thing but I if you call it R
+you'll recognize the terms in your
+
+ align:start position:0%
+you'll recognize the terms in your
+ 
+
+ align:start position:0%
+you'll recognize the terms in your
+acceleration equation so what are the
+
+ align:start position:0%
+acceleration equation so what are the
+ 
+
+ align:start position:0%
+acceleration equation so what are the
+accelerations in the
+
+ align:start position:0%
+accelerations in the
+ 
+
+ align:start position:0%
+accelerations in the
+Direction up the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and those are all in the all it in
+
+ align:start position:0%
+okay and those are all in the all it in
+ 
+
+ align:start position:0%
+okay and those are all in the all it in
+the eye Direction and then if you looked
+
+ align:start position:0%
+the eye Direction and then if you looked
+ 
+
+ align:start position:0%
+the eye Direction and then if you looked
+at that that you obviously could replace
+
+ align:start position:0%
+at that that you obviously could replace
+ 
+
+ align:start position:0%
+at that that you obviously could replace
+rouble dot with X double dot r with X if
+
+ align:start position:0%
+rouble dot with X double dot r with X if
+ 
+
+ align:start position:0%
+rouble dot with X double dot r with X if
+you make your
+
+ align:start position:0%
+you make your
+ 
+
+ align:start position:0%
+you make your
+origin
+
+ align:start position:0%
+origin
+ 
+
+ align:start position:0%
+origin
+here you probably would it's the point
+
+ align:start position:0%
+here you probably would it's the point
+ 
+
+ align:start position:0%
+here you probably would it's the point
+of rotation so that is your that's the
+
+ align:start position:0%
+of rotation so that is your that's the
+ 
+
+ align:start position:0%
+of rotation so that is your that's the
+mass times the acceleration in the
+
+ align:start position:0%
+mass times the acceleration in the
+ 
+
+ align:start position:0%
+mass times the acceleration in the
+direction travel and it's got to be
+
+ align:start position:0%
+direction travel and it's got to be
+ 
+
+ align:start position:0%
+direction travel and it's got to be
+equal to T and minus
+
+ align:start position:0%
+equal to T and minus
+ 
+
+ align:start position:0%
+equal to T and minus
+mg sin Theta probably right and that's
+
+ align:start position:0%
+mg sin Theta probably right and that's
+ 
+
+ align:start position:0%
+mg sin Theta probably right and that's
+one equation of motion you're going to
+
+ align:start position:0%
+one equation of motion you're going to
+ 
+
+ align:start position:0%
+one equation of motion you're going to
+did another equation of motion in the
+
+ align:start position:0%
+did another equation of motion in the
+ 
+
+ align:start position:0%
+did another equation of motion in the
+Theta do theta hat Direction because
+
+ align:start position:0%
+Theta do theta hat Direction because
+ 
+
+ align:start position:0%
+Theta do theta hat Direction because
+what other what accelerations are
+
+ align:start position:0%
+what other what accelerations are
+ 
+
+ align:start position:0%
+what other what accelerations are
+present in this direction in the y j
+
+ align:start position:0%
+present in this direction in the y j
+ 
+
+ align:start position:0%
+present in this direction in the y j
+hat Thea double dot Theta double dot
+
+ align:start position:0%
+hat Thea double dot Theta double dot
+ 
+
+ align:start position:0%
+hat Thea double dot Theta double dot
+your oil Arian one yeah what
+
+ align:start position:0%
+your oil Arian one yeah what
+ 
+
+ align:start position:0%
+your oil Arian one yeah what
+else so the sum of the forces in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y so they are in terms of polar
+
+ align:start position:0%
+Y so they are in terms of polar
+ 
+
+ align:start position:0%
+Y so they are in terms of polar
+coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms well somebody said this one first
+
+ align:start position:0%
+terms well somebody said this one first
+ 
+
+ align:start position:0%
+terms well somebody said this one first
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+two Thea dot is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+right 2 Theta dot r dot and that's in
+
+ align:start position:0%
+right 2 Theta dot r dot and that's in
+ 
+
+ align:start position:0%
+right 2 Theta dot r dot and that's in
+the J Direction and now you've got now
+
+ align:start position:0%
+the J Direction and now you've got now
+ 
+
+ align:start position:0%
+the J Direction and now you've got now
+you can work the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so how would you go about doing
+
+ align:start position:0%
+problem so how would you go about doing
+ 
+
+ align:start position:0%
+problem so how would you go about doing
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+problem where you can't treat it as a
+
+ align:start position:0%
+problem where you can't treat it as a
+ 
+
+ align:start position:0%
+problem where you can't treat it as a
+particle any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+longer and we've graduated to
+
+ align:start position:0%
+longer and we've graduated to
+ 
+
+ align:start position:0%
+longer and we've graduated to
+that because we've been doing we've been
+
+ align:start position:0%
+that because we've been doing we've been
+ 
+
+ align:start position:0%
+that because we've been doing we've been
+doing angular momentum stuff with mass
+
+ align:start position:0%
+doing angular momentum stuff with mass
+ 
+
+ align:start position:0%
+doing angular momentum stuff with mass
+moment of inertia matrices so now you uh
+
+ align:start position:0%
+moment of inertia matrices so now you uh
+ 
+
+ align:start position:0%
+moment of inertia matrices so now you uh
+you want to do this more as a
+
+ align:start position:0%
+you want to do this more as a
+ 
+
+ align:start position:0%
+you want to do this more as a
+full-fledged Dynamics problem taking
+
+ align:start position:0%
+full-fledged Dynamics problem taking
+ 
+
+ align:start position:0%
+full-fledged Dynamics problem taking
+into consideration that so how do you
+
+ align:start position:0%
+into consideration that so how do you
+ 
+
+ align:start position:0%
+into consideration that so how do you
+what is the mass what do you have to
+
+ align:start position:0%
+what is the mass what do you have to
+ 
+
+ align:start position:0%
+what is the mass what do you have to
+modify the do to modify
+
+ align:start position:0%
+modify the do to modify
+ 
+
+ align:start position:0%
+modify the do to modify
+our free body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram here's my simplified vehicle
+
+ align:start position:0%
+diagram here's my simplified vehicle
+ 
+
+ align:start position:0%
+diagram here's my simplified vehicle
+what are the forces on it that you need
+
+ align:start position:0%
+what are the forces on it that you need
+ 
+
+ align:start position:0%
+what are the forces on it that you need
+to deal
+
+ align:start position:0%
+to deal
+ 
+
+ align:start position:0%
+to deal
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so you can add need two because you
+
+ align:start position:0%
+yeah so you can add need two because you
+ 
+
+ align:start position:0%
+yeah so you can add need two because you
+got two wheels on this thing and so
+
+ align:start position:0%
+got two wheels on this thing and so
+ 
+
+ align:start position:0%
+got two wheels on this thing and so
+there's axle one here so you're going to
+
+ align:start position:0%
+there's axle one here so you're going to
+ 
+
+ align:start position:0%
+there's axle one here so you're going to
+one here and then one here I say call
+
+ align:start position:0%
+one here and then one here I say call
+ 
+
+ align:start position:0%
+one here and then one here I say call
+this one N1 N2 what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else the same so you got a g somewhere
+
+ align:start position:0%
+else the same so you got a g somewhere
+ 
+
+ align:start position:0%
+else the same so you got a g somewhere
+and so you still have an mg
+
+ align:start position:0%
+and so you still have an mg
+ 
+
+ align:start position:0%
+and so you still have an mg
+term what other external
+
+ align:start position:0%
+term what other external
+ 
+
+ align:start position:0%
+term what other external
+forces t t but now T is a
+
+ align:start position:0%
+forces t t but now T is a
+ 
+
+ align:start position:0%
+forces t t but now T is a
+problem so I was I gave you before it's
+
+ align:start position:0%
+problem so I was I gave you before it's
+ 
+
+ align:start position:0%
+problem so I was I gave you before it's
+the t is the total net force but that's
+
+ align:start position:0%
+the t is the total net force but that's
+ 
+
+ align:start position:0%
+the t is the total net force but that's
+not adequate in this problem any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+longer yeah so we're going to have have
+
+ align:start position:0%
+longer yeah so we're going to have have
+ 
+
+ align:start position:0%
+longer yeah so we're going to have have
+end up having a friction Force that's
+
+ align:start position:0%
+end up having a friction Force that's
+ 
+
+ align:start position:0%
+end up having a friction Force that's
+applied you know
+
+ align:start position:0%
+applied you know
+ 
+
+ align:start position:0%
+applied you know
+here F1 and another one applied here FS2
+
+ align:start position:0%
+here F1 and another one applied here FS2
+ 
+
+ align:start position:0%
+here F1 and another one applied here FS2
+and F1 plus F2 would be t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how many unknowns do we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have well it looks like four here plus
+
+ align:start position:0%
+have well it looks like four here plus
+ 
+
+ align:start position:0%
+have well it looks like four here plus
+any motion stuff that you have to solve
+
+ align:start position:0%
+any motion stuff that you have to solve
+ 
+
+ align:start position:0%
+any motion stuff that you have to solve
+for so how many equations of motion can
+
+ align:start position:0%
+for so how many equations of motion can
+ 
+
+ align:start position:0%
+for so how many equations of motion can
+you write remember you get one equation
+
+ align:start position:0%
+you write remember you get one equation
+ 
+
+ align:start position:0%
+you write remember you get one equation
+for every Vector component Direction so
+
+ align:start position:0%
+for every Vector component Direction so
+ 
+
+ align:start position:0%
+for every Vector component Direction so
+XYZ gives you three components and you
+
+ align:start position:0%
+XYZ gives you three components and you
+ 
+
+ align:start position:0%
+XYZ gives you three components and you
+could conceivably rewrite three
+
+ align:start position:0%
+could conceivably rewrite three
+ 
+
+ align:start position:0%
+could conceivably rewrite three
+equations so tell me the relevant
+
+ align:start position:0%
+equations so tell me the relevant
+ 
+
+ align:start position:0%
+equations so tell me the relevant
+equations of motion that we could come
+
+ align:start position:0%
+equations of motion that we could come
+ 
+
+ align:start position:0%
+equations of motion that we could come
+up with for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem some forces in X some of forces
+
+ align:start position:0%
+problem some forces in X some of forces
+ 
+
+ align:start position:0%
+problem some forces in X some of forces
+in y okay I I argue a sum of forces in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X that's still true yep sum of forces in
+
+ align:start position:0%
+X that's still true yep sum of forces in
+ 
+
+ align:start position:0%
+X that's still true yep sum of forces in
+y you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said is this
+
+ align:start position:0%
+said is this
+ 
+
+ align:start position:0%
+said is this
+zero no because that bridge is moving
+
+ align:start position:0%
+zero no because that bridge is moving
+ 
+
+ align:start position:0%
+zero no because that bridge is moving
+okay what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else okay and how do you do that sum of
+
+ align:start position:0%
+else okay and how do you do that sum of
+ 
+
+ align:start position:0%
+else okay and how do you do that sum of
+the torqus in what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction well
+
+ align:start position:0%
+direction well
+ 
+
+ align:start position:0%
+direction well
+no yeah I mean you could excuse me I
+
+ align:start position:0%
+no yeah I mean you could excuse me I
+ 
+
+ align:start position:0%
+no yeah I mean you could excuse me I
+shouldn't say that the um do you have
+
+ align:start position:0%
+shouldn't say that the um do you have
+ 
+
+ align:start position:0%
+shouldn't say that the um do you have
+more than one torque term you can work
+
+ align:start position:0%
+more than one torque term you can work
+ 
+
+ align:start position:0%
+more than one torque term you can work
+with here more than one torque
+
+ align:start position:0%
+with here more than one torque
+ 
+
+ align:start position:0%
+with here more than one torque
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes how's
+
+ align:start position:0%
+yes yes how's
+ 
+
+ align:start position:0%
+yes yes how's
+that so let's just think through these
+
+ align:start position:0%
+that so let's just think through these
+ 
+
+ align:start position:0%
+that so let's just think through these
+things so you could have a torque you
+
+ align:start position:0%
+things so you could have a torque you
+ 
+
+ align:start position:0%
+things so you could have a torque you
+could have a torque in the this is
+
+ align:start position:0%
+could have a torque in the this is
+ 
+
+ align:start position:0%
+could have a torque in the this is
+XY Z out of the board you could have a z
+
+ align:start position:0%
+XY Z out of the board you could have a z
+ 
+
+ align:start position:0%
+XY Z out of the board you could have a z
+torque making this thing trying to pitch
+
+ align:start position:0%
+torque making this thing trying to pitch
+ 
+
+ align:start position:0%
+torque making this thing trying to pitch
+up and
+
+ align:start position:0%
+up and
+ 
+
+ align:start position:0%
+up and
+down uh you could have an X torque
+
+ align:start position:0%
+down uh you could have an X torque
+ 
+
+ align:start position:0%
+down uh you could have an X torque
+making it trying to roll over but we
+
+ align:start position:0%
+making it trying to roll over but we
+ 
+
+ align:start position:0%
+making it trying to roll over but we
+don't have any information in that
+
+ align:start position:0%
+don't have any information in that
+ 
+
+ align:start position:0%
+don't have any information in that
+direction and it's strained and we could
+
+ align:start position:0%
+direction and it's strained and we could
+ 
+
+ align:start position:0%
+direction and it's strained and we could
+have a y torque making it try to go like
+
+ align:start position:0%
+have a y torque making it try to go like
+ 
+
+ align:start position:0%
+have a y torque making it try to go like
+that and we don't have any much
+
+ align:start position:0%
+that and we don't have any much
+ 
+
+ align:start position:0%
+that and we don't have any much
+information there so it seems like we've
+
+ align:start position:0%
+information there so it seems like we've
+ 
+
+ align:start position:0%
+information there so it seems like we've
+got an A Z torque equation that we could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write and that's a one seems like we got
+
+ align:start position:0%
+write and that's a one seems like we got
+ 
+
+ align:start position:0%
+write and that's a one seems like we got
+three equations sum of forces is X sum
+
+ align:start position:0%
+three equations sum of forces is X sum
+ 
+
+ align:start position:0%
+three equations sum of forces is X sum
+of forces Y and a torque in the Z
+
+ align:start position:0%
+of forces Y and a torque in the Z
+ 
+
+ align:start position:0%
+of forces Y and a torque in the Z
+and doesn't seem like quite enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's as far as I've gotten with it
+
+ align:start position:0%
+and that's as far as I've gotten with it
+ 
+
+ align:start position:0%
+and that's as far as I've gotten with it
+I just thought of this on the way over
+
+ align:start position:0%
+I just thought of this on the way over
+ 
+
+ align:start position:0%
+I just thought of this on the way over
+here okay so I'd said i' I'd sit down
+
+ align:start position:0%
+here okay so I'd said i' I'd sit down
+ 
+
+ align:start position:0%
+here okay so I'd said i' I'd sit down
+and start working this out and trying to
+
+ align:start position:0%
+and start working this out and trying to
+ 
+
+ align:start position:0%
+and start working this out and trying to
+figure out okay where's my fourth
+
+ align:start position:0%
+figure out okay where's my fourth
+ 
+
+ align:start position:0%
+figure out okay where's my fourth
+equation going to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from and I'm not exactly sure quite
+
+ align:start position:0%
+from and I'm not exactly sure quite
+ 
+
+ align:start position:0%
+from and I'm not exactly sure quite
+yet but that generally I'd go about
+
+ align:start position:0%
+yet but that generally I'd go about
+ 
+
+ align:start position:0%
+yet but that generally I'd go about
+setting it up like that and start
+
+ align:start position:0%
+setting it up like that and start
+ 
+
+ align:start position:0%
+setting it up like that and start
+working those things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay any other questions or
+
+ align:start position:0%
+out okay any other questions or
+ 
+
+ align:start position:0%
+out okay any other questions or
+questions about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quiz we're done early
\ No newline at end of file
diff --git a/7FOFBqw1gMs.txt b/7FOFBqw1gMs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..36d57b4aea269c35df513e03619f23674172b6e6
--- /dev/null
+++ b/7FOFBqw1gMs.txt
@@ -0,0 +1,9805 @@
+align:start position:0%
+ 
+hello can people hear me in the back are
+
+ align:start position:0%
+hello can people hear me in the back are
+ 
+
+ align:start position:0%
+hello can people hear me in the back are
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+good okay so uh welcome to the last
+
+ align:start position:0%
+good okay so uh welcome to the last
+ 
+
+ align:start position:0%
+good okay so uh welcome to the last
+lecture of 604 oh no 61200 yeah um I'm
+
+ align:start position:0%
+lecture of 604 oh no 61200 yeah um I'm
+ 
+
+ align:start position:0%
+lecture of 604 oh no 61200 yeah um I'm
+I'm totally sayane I can remember which
+
+ align:start position:0%
+I'm totally sayane I can remember which
+ 
+
+ align:start position:0%
+I'm totally sayane I can remember which
+class I'm teaching uh welcome you made
+
+ align:start position:0%
+class I'm teaching uh welcome you made
+ 
+
+ align:start position:0%
+class I'm teaching uh welcome you made
+it through the semester well
+
+ align:start position:0%
+it through the semester well
+ 
+
+ align:start position:0%
+it through the semester well
+done uh okay so for today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material we are going to you know wrap
+
+ align:start position:0%
+material we are going to you know wrap
+ 
+
+ align:start position:0%
+material we are going to you know wrap
+up our discussion of
+
+ align:start position:0%
+up our discussion of
+ 
+
+ align:start position:0%
+up our discussion of
+probability and in particular we will be
+
+ align:start position:0%
+probability and in particular we will be
+ 
+
+ align:start position:0%
+probability and in particular we will be
+discussing uh tail bounds so you know uh
+
+ align:start position:0%
+discussing uh tail bounds so you know uh
+ 
+
+ align:start position:0%
+discussing uh tail bounds so you know uh
+what happens if you have a a random
+
+ align:start position:0%
+what happens if you have a a random
+ 
+
+ align:start position:0%
+what happens if you have a a random
+variable like what is the probability
+
+ align:start position:0%
+variable like what is the probability
+ 
+
+ align:start position:0%
+variable like what is the probability
+that this random variable is like very
+
+ align:start position:0%
+that this random variable is like very
+ 
+
+ align:start position:0%
+that this random variable is like very
+large or very small like you know very
+
+ align:start position:0%
+large or very small like you know very
+ 
+
+ align:start position:0%
+large or very small like you know very
+different from from its expectation
+
+ align:start position:0%
+different from from its expectation
+ 
+
+ align:start position:0%
+different from from its expectation
+okay uh so let's start with a a bit a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+review uh
+
+ align:start position:0%
+review uh
+ 
+
+ align:start position:0%
+review uh
+variance okay so I think we uh saw from
+
+ align:start position:0%
+variance okay so I think we uh saw from
+ 
+
+ align:start position:0%
+variance okay so I think we uh saw from
+the last not last lecture two lectures
+
+ align:start position:0%
+the last not last lecture two lectures
+ 
+
+ align:start position:0%
+the last not last lecture two lectures
+ago possibly uh so the variance of a
+
+ align:start position:0%
+ago possibly uh so the variance of a
+ 
+
+ align:start position:0%
+ago possibly uh so the variance of a
+random variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R uh is defined to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation of uh R minus the
+
+ align:start position:0%
+expectation of uh R minus the
+ 
+
+ align:start position:0%
+expectation of uh R minus the
+expectation of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay uh and the standard deviation is
+
+ align:start position:0%
+okay uh and the standard deviation is
+ 
+
+ align:start position:0%
+okay uh and the standard deviation is
+just the square root of that you know if
+
+ align:start position:0%
+just the square root of that you know if
+ 
+
+ align:start position:0%
+just the square root of that you know if
+you've uh taken you know stats or
+
+ align:start position:0%
+you've uh taken you know stats or
+ 
+
+ align:start position:0%
+you've uh taken you know stats or
+anything like that that's probably uh
+
+ align:start position:0%
+anything like that that's probably uh
+ 
+
+ align:start position:0%
+anything like that that's probably uh
+you know something that you've seen more
+
+ align:start position:0%
+you know something that you've seen more
+ 
+
+ align:start position:0%
+you know something that you've seen more
+more often than
+
+ align:start position:0%
+more often than
+ 
+
+ align:start position:0%
+more often than
+variance uh another you know not a
+
+ align:start position:0%
+variance uh another you know not a
+ 
+
+ align:start position:0%
+variance uh another you know not a
+definition but another useful formula an
+
+ align:start position:0%
+definition but another useful formula an
+ 
+
+ align:start position:0%
+definition but another useful formula an
+equivalent formulation of this is that
+
+ align:start position:0%
+equivalent formulation of this is that
+ 
+
+ align:start position:0%
+equivalent formulation of this is that
+the variance of r
+
+ align:start position:0%
+the variance of r
+ 
+
+ align:start position:0%
+the variance of r
+is also equal to the
+
+ align:start position:0%
+is also equal to the
+ 
+
+ align:start position:0%
+is also equal to the
+expectation of r
+
+ align:start position:0%
+expectation of r
+ 
+
+ align:start position:0%
+expectation of r
+s minus the square of the expectation of
+
+ align:start position:0%
+s minus the square of the expectation of
+ 
+
+ align:start position:0%
+s minus the square of the expectation of
+R okay uh so not the definition but it's
+
+ align:start position:0%
+R okay uh so not the definition but it's
+ 
+
+ align:start position:0%
+R okay uh so not the definition but it's
+equivalent and uh I think in recitation
+
+ align:start position:0%
+equivalent and uh I think in recitation
+ 
+
+ align:start position:0%
+equivalent and uh I think in recitation
+perhaps you uh you proved this um this
+
+ align:start position:0%
+perhaps you uh you proved this um this
+ 
+
+ align:start position:0%
+perhaps you uh you proved this um this
+this formula is is a particularly useful
+
+ align:start position:0%
+this formula is is a particularly useful
+ 
+
+ align:start position:0%
+this formula is is a particularly useful
+one for what we're going to be doing
+
+ align:start position:0%
+one for what we're going to be doing
+ 
+
+ align:start position:0%
+one for what we're going to be doing
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+okay uh we also saw that uh you know
+
+ align:start position:0%
+okay uh we also saw that uh you know
+ 
+
+ align:start position:0%
+okay uh we also saw that uh you know
+Varian is linear subject to uh you know
+
+ align:start position:0%
+Varian is linear subject to uh you know
+ 
+
+ align:start position:0%
+Varian is linear subject to uh you know
+certain constraints does anybody
+
+ align:start position:0%
+certain constraints does anybody
+ 
+
+ align:start position:0%
+certain constraints does anybody
+remember what uh what you need for for
+
+ align:start position:0%
+remember what uh what you need for for
+ 
+
+ align:start position:0%
+remember what uh what you need for for
+variance to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+Independence okay so if you
+
+ align:start position:0%
+Independence okay so if you
+ 
+
+ align:start position:0%
+Independence okay so if you
+have R1
+
+ align:start position:0%
+have R1
+ 
+
+ align:start position:0%
+have R1
+R2 RN are
+
+ align:start position:0%
+R2 RN are
+ 
+
+ align:start position:0%
+R2 RN are
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+then uh the variance of the sum is the
+
+ align:start position:0%
+then uh the variance of the sum is the
+ 
+
+ align:start position:0%
+then uh the variance of the sum is the
+sum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops uh is that the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraint is it
+
+ align:start position:0%
+constraint is it
+ 
+
+ align:start position:0%
+constraint is it
+correct who who believes this statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disbelieves who's who's still
+
+ align:start position:0%
+disbelieves who's who's still
+ 
+
+ align:start position:0%
+disbelieves who's who's still
+asleep oh okay maybe we'll we'll give it
+
+ align:start position:0%
+asleep oh okay maybe we'll we'll give it
+ 
+
+ align:start position:0%
+asleep oh okay maybe we'll we'll give it
+a few minutes for people to wake
+
+ align:start position:0%
+a few minutes for people to wake
+ 
+
+ align:start position:0%
+a few minutes for people to wake
+up uh okay um well this is a correct
+
+ align:start position:0%
+up uh okay um well this is a correct
+ 
+
+ align:start position:0%
+up uh okay um well this is a correct
+statement uh however there's something
+
+ align:start position:0%
+statement uh however there's something
+ 
+
+ align:start position:0%
+statement uh however there's something
+uh slightly stronger that we can say we
+
+ align:start position:0%
+uh slightly stronger that we can say we
+ 
+
+ align:start position:0%
+uh slightly stronger that we can say we
+can weaken this this condition right we
+
+ align:start position:0%
+can weaken this this condition right we
+ 
+
+ align:start position:0%
+can weaken this this condition right we
+don't need Mutual Independence what do
+
+ align:start position:0%
+don't need Mutual Independence what do
+ 
+
+ align:start position:0%
+don't need Mutual Independence what do
+we actually need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pair ways Independence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so if we have a bunch of
+
+ align:start position:0%
+yeah okay so if we have a bunch of
+ 
+
+ align:start position:0%
+yeah okay so if we have a bunch of
+Parise independent random variables we
+
+ align:start position:0%
+Parise independent random variables we
+ 
+
+ align:start position:0%
+Parise independent random variables we
+want to find the variance of their sum
+
+ align:start position:0%
+want to find the variance of their sum
+ 
+
+ align:start position:0%
+want to find the variance of their sum
+we can instead just sum the variances
+
+ align:start position:0%
+we can instead just sum the variances
+ 
+
+ align:start position:0%
+we can instead just sum the variances
+okay so another very useful fact uh
+
+ align:start position:0%
+okay so another very useful fact uh
+ 
+
+ align:start position:0%
+okay so another very useful fact uh
+hopefully you proved it already in
+
+ align:start position:0%
+hopefully you proved it already in
+ 
+
+ align:start position:0%
+hopefully you proved it already in
+recitations so we don't need to go over
+
+ align:start position:0%
+recitations so we don't need to go over
+ 
+
+ align:start position:0%
+recitations so we don't need to go over
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+proof uh but these uh well
+
+ align:start position:0%
+proof uh but these uh well
+ 
+
+ align:start position:0%
+proof uh but these uh well
+these two formulas are going to be quite
+
+ align:start position:0%
+these two formulas are going to be quite
+ 
+
+ align:start position:0%
+these two formulas are going to be quite
+useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now time for the first of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tailbones so before I uh give you the
+
+ align:start position:0%
+tailbones so before I uh give you the
+ 
+
+ align:start position:0%
+tailbones so before I uh give you the
+bound uh let's let's think about an
+
+ align:start position:0%
+bound uh let's let's think about an
+ 
+
+ align:start position:0%
+bound uh let's let's think about an
+example so looking at this room uh
+
+ align:start position:0%
+example so looking at this room uh
+ 
+
+ align:start position:0%
+example so looking at this room uh
+suppose I pick a random student and uh
+
+ align:start position:0%
+suppose I pick a random student and uh
+ 
+
+ align:start position:0%
+suppose I pick a random student and uh
+you know let the random variable R be
+
+ align:start position:0%
+you know let the random variable R be
+ 
+
+ align:start position:0%
+you know let the random variable R be
+the the row that the the randomly picked
+
+ align:start position:0%
+the the row that the the randomly picked
+ 
+
+ align:start position:0%
+the the row that the the randomly picked
+student is is sitting in okay so
+
+ align:start position:0%
+student is is sitting in okay so
+ 
+
+ align:start position:0%
+student is is sitting in okay so
+guesstimate that this is about uh you
+
+ align:start position:0%
+guesstimate that this is about uh you
+ 
+
+ align:start position:0%
+guesstimate that this is about uh you
+know the expectation of R is about eight
+
+ align:start position:0%
+know the expectation of R is about eight
+ 
+
+ align:start position:0%
+know the expectation of R is about eight
+so so pick random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+student R is the row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for uh those of you who aren't
+
+ align:start position:0%
+okay so for uh those of you who aren't
+ 
+
+ align:start position:0%
+okay so for uh those of you who aren't
+in the room those of you who are
+
+ align:start position:0%
+in the room those of you who are
+ 
+
+ align:start position:0%
+in the room those of you who are
+watching the video uh what does that
+
+ align:start position:0%
+watching the video uh what does that
+ 
+
+ align:start position:0%
+watching the video uh what does that
+tell them about uh the probability that
+
+ align:start position:0%
+tell them about uh the probability that
+ 
+
+ align:start position:0%
+tell them about uh the probability that
+R is at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+16 so what's the probability that a
+
+ align:start position:0%
+16 so what's the probability that a
+ 
+
+ align:start position:0%
+16 so what's the probability that a
+randomly selected student is sit sitting
+
+ align:start position:0%
+randomly selected student is sit sitting
+ 
+
+ align:start position:0%
+randomly selected student is sit sitting
+in the last five rows I think there 21
+
+ align:start position:0%
+in the last five rows I think there 21
+ 
+
+ align:start position:0%
+in the last five rows I think there 21
+rows here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah does anybody have any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea so maybe I should label this as an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah one minus the CDF okay so the
+
+ align:start position:0%
+yeah one minus the CDF okay so the
+ 
+
+ align:start position:0%
+yeah one minus the CDF okay so the
+people watching the uh watching the
+
+ align:start position:0%
+people watching the uh watching the
+ 
+
+ align:start position:0%
+people watching the uh watching the
+video can't I assume they can't see the
+
+ align:start position:0%
+video can't I assume they can't see the
+ 
+
+ align:start position:0%
+video can't I assume they can't see the
+room so they don't know what the CD
+
+ align:start position:0%
+room so they don't know what the CD
+ 
+
+ align:start position:0%
+room so they don't know what the CD
+is right the only information they
+
+ align:start position:0%
+is right the only information they
+ 
+
+ align:start position:0%
+is right the only information they
+know is that the expectation is
+
+ align:start position:0%
+know is that the expectation is
+ 
+
+ align:start position:0%
+know is that the expectation is
+eight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh can we find the variance from
+
+ align:start position:0%
+yeah oh can we find the variance from
+ 
+
+ align:start position:0%
+yeah oh can we find the variance from
+that and then see how far away we are uh
+
+ align:start position:0%
+that and then see how far away we are uh
+ 
+
+ align:start position:0%
+that and then see how far away we are uh
+no that uh requires more information
+
+ align:start position:0%
+no that uh requires more information
+ 
+
+ align:start position:0%
+no that uh requires more information
+right like we we need to know a little
+
+ align:start position:0%
+right like we we need to know a little
+ 
+
+ align:start position:0%
+right like we we need to know a little
+bit more about uh about what's going on
+
+ align:start position:0%
+bit more about uh about what's going on
+ 
+
+ align:start position:0%
+bit more about uh about what's going on
+right like we we need to you know
+
+ align:start position:0%
+right like we we need to you know
+ 
+
+ align:start position:0%
+right like we we need to you know
+somehow figure out you know the
+
+ align:start position:0%
+somehow figure out you know the
+ 
+
+ align:start position:0%
+somehow figure out you know the
+expectation of R minus 8 squar so like
+
+ align:start position:0%
+expectation of R minus 8 squar so like
+ 
+
+ align:start position:0%
+expectation of R minus 8 squar so like
+we need to know something more about R
+
+ align:start position:0%
+we need to know something more about R
+ 
+
+ align:start position:0%
+we need to know something more about R
+than than just its
+
+ align:start position:0%
+than than just its
+ 
+
+ align:start position:0%
+than than just its
+expectation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes there're 21 so 0 through
+
+ align:start position:0%
+yeah yes there're 21 so 0 through
+ 
+
+ align:start position:0%
+yeah yes there're 21 so 0 through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah can we assume that it's uniformally
+
+ align:start position:0%
+yeah can we assume that it's uniformally
+ 
+
+ align:start position:0%
+yeah can we assume that it's uniformally
+distributed uh no and in fact it it is
+
+ align:start position:0%
+distributed uh no and in fact it it is
+ 
+
+ align:start position:0%
+distributed uh no and in fact it it is
+not uh there seem to be
+
+ align:start position:0%
+not uh there seem to be
+ 
+
+ align:start position:0%
+not uh there seem to be
+you know more students towards the front
+
+ align:start position:0%
+you know more students towards the front
+ 
+
+ align:start position:0%
+you know more students towards the front
+than than towards the back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so your intuition is great though
+
+ align:start position:0%
+yeah so your intuition is great though
+ 
+
+ align:start position:0%
+yeah so your intuition is great though
+right so um well we're using the
+
+ align:start position:0%
+right so um well we're using the
+ 
+
+ align:start position:0%
+right so um well we're using the
+observation that uh that you know 16 is
+
+ align:start position:0%
+observation that uh that you know 16 is
+ 
+
+ align:start position:0%
+observation that uh that you know 16 is
+is twice 8 right we're we're also using
+
+ align:start position:0%
+is twice 8 right we're we're also using
+ 
+
+ align:start position:0%
+is twice 8 right we're we're also using
+the observation that uh you know the
+
+ align:start position:0%
+the observation that uh you know the
+ 
+
+ align:start position:0%
+the observation that uh you know the
+rows are numbered 0 through 20 like
+
+ align:start position:0%
+rows are numbered 0 through 20 like
+ 
+
+ align:start position:0%
+rows are numbered 0 through 20 like
+they're they're non
+
+ align:start position:0%
+they're they're non
+ 
+
+ align:start position:0%
+they're they're non
+negative okay so what
+
+ align:start position:0%
+negative okay so what
+ 
+
+ align:start position:0%
+negative okay so what
+happens if you know more than half of
+
+ align:start position:0%
+happens if you know more than half of
+ 
+
+ align:start position:0%
+happens if you know more than half of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+students are sitting in the back five
+
+ align:start position:0%
+students are sitting in the back five
+ 
+
+ align:start position:0%
+students are sitting in the back five
+rows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does that tell us about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation well if if more than half of
+
+ align:start position:0%
+expectation well if if more than half of
+ 
+
+ align:start position:0%
+expectation well if if more than half of
+the students you know give us R is is at
+
+ align:start position:0%
+the students you know give us R is is at
+ 
+
+ align:start position:0%
+the students you know give us R is is at
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+16 right that tells us that the
+
+ align:start position:0%
+16 right that tells us that the
+ 
+
+ align:start position:0%
+16 right that tells us that the
+expectation should be at least
+
+ align:start position:0%
+expectation should be at least
+ 
+
+ align:start position:0%
+expectation should be at least
+eight right or sorry more than
+
+ align:start position:0%
+eight right or sorry more than
+ 
+
+ align:start position:0%
+eight right or sorry more than
+eight if if more than half of the
+
+ align:start position:0%
+eight if if more than half of the
+ 
+
+ align:start position:0%
+eight if if more than half of the
+students are in the back okay so the
+
+ align:start position:0%
+students are in the back okay so the
+ 
+
+ align:start position:0%
+students are in the back okay so the
+converse of
+
+ align:start position:0%
+converse of
+ 
+
+ align:start position:0%
+converse of
+that is that there are at most half of
+
+ align:start position:0%
+that is that there are at most half of
+ 
+
+ align:start position:0%
+that is that there are at most half of
+the students in the back five
+
+ align:start position:0%
+the students in the back five
+ 
+
+ align:start position:0%
+the students in the back five
+rows okay so let's try and formalize
+
+ align:start position:0%
+rows okay so let's try and formalize
+ 
+
+ align:start position:0%
+rows okay so let's try and formalize
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+intuition so this is what's known as
+
+ align:start position:0%
+intuition so this is what's known as
+ 
+
+ align:start position:0%
+intuition so this is what's known as
+Markov in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equality uh so let R be a non- negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable uh then the
+
+ align:start position:0%
+variable uh then the
+ 
+
+ align:start position:0%
+variable uh then the
+probability that R is greater than or
+
+ align:start position:0%
+probability that R is greater than or
+ 
+
+ align:start position:0%
+probability that R is greater than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+X is less than or equal to the
+
+ align:start position:0%
+X is less than or equal to the
+ 
+
+ align:start position:0%
+X is less than or equal to the
+expectation of
+
+ align:start position:0%
+expectation of
+ 
+
+ align:start position:0%
+expectation of
+r divided by
+
+ align:start position:0%
+r divided by
+ 
+
+ align:start position:0%
+r divided by
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+okay so for the example that we just saw
+
+ align:start position:0%
+okay so for the example that we just saw
+ 
+
+ align:start position:0%
+okay so for the example that we just saw
+right the probability that uh R is at
+
+ align:start position:0%
+right the probability that uh R is at
+ 
+
+ align:start position:0%
+right the probability that uh R is at
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+16 it's at most the expectation which is
+
+ align:start position:0%
+16 it's at most the expectation which is
+ 
+
+ align:start position:0%
+16 it's at most the expectation which is
+8 ID 16 so that gives us 1
+
+ align:start position:0%
+8 ID 16 so that gives us 1
+ 
+
+ align:start position:0%
+8 ID 16 so that gives us 1
+12 okay does the uh does the statement
+
+ align:start position:0%
+12 okay does the uh does the statement
+ 
+
+ align:start position:0%
+12 okay does the uh does the statement
+make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people so basically it's saying that you
+
+ align:start position:0%
+people so basically it's saying that you
+ 
+
+ align:start position:0%
+people so basically it's saying that you
+know you can't have too many super large
+
+ align:start position:0%
+know you can't have too many super large
+ 
+
+ align:start position:0%
+know you can't have too many super large
+values because that would push the
+
+ align:start position:0%
+values because that would push the
+ 
+
+ align:start position:0%
+values because that would push the
+expectation up too
+
+ align:start position:0%
+expectation up too
+ 
+
+ align:start position:0%
+expectation up too
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+okay so how could we prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this any ideas how do we formalize the
+
+ align:start position:0%
+this any ideas how do we formalize the
+ 
+
+ align:start position:0%
+this any ideas how do we formalize the
+intuition that we were just talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about let's try let's try using the law
+
+ align:start position:0%
+about let's try let's try using the law
+ 
+
+ align:start position:0%
+about let's try let's try using the law
+of total expectation
+
+ align:start position:0%
+of total expectation
+ 
+
+ align:start position:0%
+of total expectation
+so how can we write the expectation of
+
+ align:start position:0%
+so how can we write the expectation of
+ 
+
+ align:start position:0%
+so how can we write the expectation of
+R what might we condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on we don't have too many events that we
+
+ align:start position:0%
+on we don't have too many events that we
+ 
+
+ align:start position:0%
+on we don't have too many events that we
+can work with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right which of them might be useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody so let's try let's try
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditioning on X greater than oh wait
+
+ align:start position:0%
+conditioning on X greater than oh wait
+ 
+
+ align:start position:0%
+conditioning on X greater than oh wait
+was it
+
+ align:start position:0%
+was it
+ 
+
+ align:start position:0%
+was it
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+uh yeah R greater than or equal
+
+ align:start position:0%
+uh yeah R greater than or equal
+ 
+
+ align:start position:0%
+uh yeah R greater than or equal
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+okay so what does the law of total
+
+ align:start position:0%
+okay so what does the law of total
+ 
+
+ align:start position:0%
+okay so what does the law of total
+expectation tell
+
+ align:start position:0%
+expectation tell
+ 
+
+ align:start position:0%
+expectation tell
+us well this is going to be the
+
+ align:start position:0%
+us well this is going to be the
+ 
+
+ align:start position:0%
+us well this is going to be the
+expectation of our conditioned on R
+
+ align:start position:0%
+expectation of our conditioned on R
+ 
+
+ align:start position:0%
+expectation of our conditioned on R
+being greater than x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplied by the probability that R is
+
+ align:start position:0%
+multiplied by the probability that R is
+ 
+
+ align:start position:0%
+multiplied by the probability that R is
+greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x okay
+
+ align:start position:0%
+x okay
+ 
+
+ align:start position:0%
+x okay
+plus the
+
+ align:start position:0%
+plus the
+ 
+
+ align:start position:0%
+plus the
+expectation are conditioned on R less
+
+ align:start position:0%
+expectation are conditioned on R less
+ 
+
+ align:start position:0%
+expectation are conditioned on R less
+than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x times that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability okay do people remember that
+
+ align:start position:0%
+probability okay do people remember that
+ 
+
+ align:start position:0%
+probability okay do people remember that
+that coming back hopefully yes no maybe
+
+ align:start position:0%
+that coming back hopefully yes no maybe
+ 
+
+ align:start position:0%
+that coming back hopefully yes no maybe
+few
+
+ align:start position:0%
+few
+ 
+
+ align:start position:0%
+few
+nods
+
+ align:start position:0%
+nods
+ 
+
+ align:start position:0%
+nods
+okay so what do we know about each of
+
+ align:start position:0%
+okay so what do we know about each of
+ 
+
+ align:start position:0%
+okay so what do we know about each of
+these values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's start with this one can anybody
+
+ align:start position:0%
+let's start with this one can anybody
+ 
+
+ align:start position:0%
+let's start with this one can anybody
+bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+yeah yeah it's at least X if you
+
+ align:start position:0%
+yeah yeah it's at least X if you
+ 
+
+ align:start position:0%
+yeah yeah it's at least X if you
+conditioned on R being at least X right
+
+ align:start position:0%
+conditioned on R being at least X right
+ 
+
+ align:start position:0%
+conditioned on R being at least X right
+the expectation of R is is also going to
+
+ align:start position:0%
+the expectation of R is is also going to
+ 
+
+ align:start position:0%
+the expectation of R is is also going to
+be at least X right every outcome is at
+
+ align:start position:0%
+be at least X right every outcome is at
+ 
+
+ align:start position:0%
+be at least X right every outcome is at
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+X okay
+
+ align:start position:0%
+X okay
+ 
+
+ align:start position:0%
+X okay
+so this is going to be at least x
+
+ align:start position:0%
+so this is going to be at least x
+ 
+
+ align:start position:0%
+so this is going to be at least x
+times well this is the probability that
+
+ align:start position:0%
+times well this is the probability that
+ 
+
+ align:start position:0%
+times well this is the probability that
+that we're looking for so let's just
+
+ align:start position:0%
+that we're looking for so let's just
+ 
+
+ align:start position:0%
+that we're looking for so let's just
+write it out as it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what about the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line what do we know about this
+
+ align:start position:0%
+line what do we know about this
+ 
+
+ align:start position:0%
+line what do we know about this
+expectation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah is it one minus the expectation uh
+
+ align:start position:0%
+yeah is it one minus the expectation uh
+ 
+
+ align:start position:0%
+yeah is it one minus the expectation uh
+of the other one uh no so the the
+
+ align:start position:0%
+of the other one uh no so the the
+ 
+
+ align:start position:0%
+of the other one uh no so the the
+probability is one minus the uh the
+
+ align:start position:0%
+probability is one minus the uh the
+ 
+
+ align:start position:0%
+probability is one minus the uh the
+other probability uh the expectation
+
+ align:start position:0%
+other probability uh the expectation
+ 
+
+ align:start position:0%
+other probability uh the expectation
+does not work like that though
+
+ align:start position:0%
+does not work like that though
+ 
+
+ align:start position:0%
+does not work like that though
+yeah it is at most X that is true um
+
+ align:start position:0%
+yeah it is at most X that is true um
+ 
+
+ align:start position:0%
+yeah it is at most X that is true um
+we're actually looking for a lower bound
+
+ align:start position:0%
+we're actually looking for a lower bound
+ 
+
+ align:start position:0%
+we're actually looking for a lower bound
+though
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so at least Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay right we know that that R is always
+
+ align:start position:0%
+okay right we know that that R is always
+ 
+
+ align:start position:0%
+okay right we know that that R is always
+non
+
+ align:start position:0%
+non
+ 
+
+ align:start position:0%
+non
+negative so you know conditioning on
+
+ align:start position:0%
+negative so you know conditioning on
+ 
+
+ align:start position:0%
+negative so you know conditioning on
+anything R is still always going to be
+
+ align:start position:0%
+anything R is still always going to be
+ 
+
+ align:start position:0%
+anything R is still always going to be
+non- negative so it's expectation has to
+
+ align:start position:0%
+non- negative so it's expectation has to
+ 
+
+ align:start position:0%
+non- negative so it's expectation has to
+be non-
+
+ align:start position:0%
+be non-
+ 
+
+ align:start position:0%
+be non-
+negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we we can drop this this is just
+
+ align:start position:0%
+okay so we we can drop this this is just
+ 
+
+ align:start position:0%
+okay so we we can drop this this is just
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+zero now we've got the expectation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R is at
+
+ align:start position:0%
+R is at
+ 
+
+ align:start position:0%
+R is at
+least x times the probability that R is
+
+ align:start position:0%
+least x times the probability that R is
+ 
+
+ align:start position:0%
+least x times the probability that R is
+at least
+
+ align:start position:0%
+at least
+ 
+
+ align:start position:0%
+at least
+X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we can just move this x to the
+
+ align:start position:0%
+okay now we can just move this x to the
+ 
+
+ align:start position:0%
+okay now we can just move this x to the
+other side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assuming X is not negative if x is
+
+ align:start position:0%
+assuming X is not negative if x is
+ 
+
+ align:start position:0%
+assuming X is not negative if x is
+negative then it's a it's a very silly
+
+ align:start position:0%
+negative then it's a it's a very silly
+ 
+
+ align:start position:0%
+negative then it's a it's a very silly
+question so you know or sorry assuming X
+
+ align:start position:0%
+question so you know or sorry assuming X
+ 
+
+ align:start position:0%
+question so you know or sorry assuming X
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+positive okay are people happy with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof do anybody have any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another form of marov which you uh
+
+ align:start position:0%
+so another form of marov which you uh
+ 
+
+ align:start position:0%
+so another form of marov which you uh
+May often encounter is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following so the probability that R is
+
+ align:start position:0%
+following so the probability that R is
+ 
+
+ align:start position:0%
+following so the probability that R is
+at least uh C c times its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation is at most one over
+
+ align:start position:0%
+expectation is at most one over
+ 
+
+ align:start position:0%
+expectation is at most one over
+C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for any positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C so essentially equivalent statement
+
+ align:start position:0%
+C so essentially equivalent statement
+ 
+
+ align:start position:0%
+C so essentially equivalent statement
+just you know you might sometimes see it
+
+ align:start position:0%
+just you know you might sometimes see it
+ 
+
+ align:start position:0%
+just you know you might sometimes see it
+in this form
+
+ align:start position:0%
+in this form
+ 
+
+ align:start position:0%
+in this form
+instead
+
+ align:start position:0%
+instead
+ 
+
+ align:start position:0%
+instead
+okay so let's take a look at a couple
+
+ align:start position:0%
+okay so let's take a look at a couple
+ 
+
+ align:start position:0%
+okay so let's take a look at a couple
+more examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose or is uh the test score of a
+
+ align:start position:0%
+suppose or is uh the test score of a
+ 
+
+ align:start position:0%
+suppose or is uh the test score of a
+randomly chosen student instead of the
+
+ align:start position:0%
+randomly chosen student instead of the
+ 
+
+ align:start position:0%
+randomly chosen student instead of the
+road that they're sitting in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh suppose that these are all
+
+ align:start position:0%
+okay and uh suppose that these are all
+ 
+
+ align:start position:0%
+okay and uh suppose that these are all
+in the range uh
+
+ align:start position:0%
+in the range uh
+ 
+
+ align:start position:0%
+in the range uh
+say 30 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100% okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh can we use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+marov to bound the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability that R is at least say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+90% how might we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that h
+
+ align:start position:0%
+that h
+ 
+
+ align:start position:0%
+that h
+sorry I completely forgot to give you
+
+ align:start position:0%
+sorry I completely forgot to give you
+ 
+
+ align:start position:0%
+sorry I completely forgot to give you
+the expectation the answer is
+
+ align:start position:0%
+the expectation the answer is
+ 
+
+ align:start position:0%
+the expectation the answer is
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay now can you do
+
+ align:start position:0%
+uh okay now can you do
+ 
+
+ align:start position:0%
+uh okay now can you do
+it hopefully it's a little bit easier
+
+ align:start position:0%
+it hopefully it's a little bit easier
+ 
+
+ align:start position:0%
+it hopefully it's a little bit easier
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm yeah so find the value of C such
+
+ align:start position:0%
+mhm yeah so find the value of C such
+ 
+
+ align:start position:0%
+mhm yeah so find the value of C such
+that c c * 75 is
+
+ align:start position:0%
+that c c * 75 is
+ 
+
+ align:start position:0%
+that c c * 75 is
+90 uh
+
+ align:start position:0%
+90 uh
+ 
+
+ align:start position:0%
+90 uh
+so I guess 75 over or 90 divided
+
+ align:start position:0%
+so I guess 75 over or 90 divided
+ 
+
+ align:start position:0%
+so I guess 75 over or 90 divided
+75 that's what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.2 is that right
+
+ align:start position:0%
+1.2 is that right
+ 
+
+ align:start position:0%
+1.2 is that right
+uh 75 is 5 by 15 right 90 is 6 by 15
+
+ align:start position:0%
+uh 75 is 5 by 15 right 90 is 6 by 15
+ 
+
+ align:start position:0%
+uh 75 is 5 by 15 right 90 is 6 by 15
+okay nice arithmetic score okay so then
+
+ align:start position:0%
+okay nice arithmetic score okay so then
+ 
+
+ align:start position:0%
+okay nice arithmetic score okay so then
+uh using
+
+ align:start position:0%
+uh using
+ 
+
+ align:start position:0%
+uh using
+uh this formulation here we
+
+ align:start position:0%
+uh this formulation here we
+ 
+
+ align:start position:0%
+uh this formulation here we
+have the
+
+ align:start position:0%
+have the
+ 
+
+ align:start position:0%
+have the
+probability that R is at least uh you
+
+ align:start position:0%
+probability that R is at least uh you
+ 
+
+ align:start position:0%
+probability that R is at least uh you
+know 1.2 times
+
+ align:start position:0%
+know 1.2 times
+ 
+
+ align:start position:0%
+know 1.2 times
+uh expectation of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is at most 1 divid
+
+ align:start position:0%
+is at most 1 divid
+ 
+
+ align:start position:0%
+is at most 1 divid
+1.2 okay so this is going to be you know
+
+ align:start position:0%
+1.2 okay so this is going to be you know
+ 
+
+ align:start position:0%
+1.2 okay so this is going to be you know
+something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+83%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay people reasonably happy with
+
+ align:start position:0%
+okay people reasonably happy with
+ 
+
+ align:start position:0%
+okay people reasonably happy with
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh the question is um can we
+
+ align:start position:0%
+yeah oh the question is um can we
+ 
+
+ align:start position:0%
+yeah oh the question is um can we
+explain the difference between these two
+
+ align:start position:0%
+explain the difference between these two
+ 
+
+ align:start position:0%
+explain the difference between these two
+formulations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry uh so yeah essentially there is no
+
+ align:start position:0%
+sorry uh so yeah essentially there is no
+ 
+
+ align:start position:0%
+sorry uh so yeah essentially there is no
+difference like there're just uh you
+
+ align:start position:0%
+difference like there're just uh you
+ 
+
+ align:start position:0%
+difference like there're just uh you
+know different ways of of thinking about
+
+ align:start position:0%
+know different ways of of thinking about
+ 
+
+ align:start position:0%
+know different ways of of thinking about
+uh thinking about the bound you can
+
+ align:start position:0%
+uh thinking about the bound you can
+ 
+
+ align:start position:0%
+uh thinking about the bound you can
+either think about bounding it in terms
+
+ align:start position:0%
+either think about bounding it in terms
+ 
+
+ align:start position:0%
+either think about bounding it in terms
+of some you know absolute threshold or
+
+ align:start position:0%
+of some you know absolute threshold or
+ 
+
+ align:start position:0%
+of some you know absolute threshold or
+you can think about it as like in terms
+
+ align:start position:0%
+you can think about it as like in terms
+ 
+
+ align:start position:0%
+you can think about it as like in terms
+of some you know relative threshold like
+
+ align:start position:0%
+of some you know relative threshold like
+ 
+
+ align:start position:0%
+of some you know relative threshold like
+you know multiply the uh the expectation
+
+ align:start position:0%
+you know multiply the uh the expectation
+ 
+
+ align:start position:0%
+you know multiply the uh the expectation
+by some by some scaling Factor okay so
+
+ align:start position:0%
+by some by some scaling Factor okay so
+ 
+
+ align:start position:0%
+by some by some scaling Factor okay so
+you know depending on on which of them
+
+ align:start position:0%
+you know depending on on which of them
+ 
+
+ align:start position:0%
+you know depending on on which of them
+feels more natural to you uh we could
+
+ align:start position:0%
+feels more natural to you uh we could
+ 
+
+ align:start position:0%
+feels more natural to you uh we could
+also used the first formulation to say
+
+ align:start position:0%
+also used the first formulation to say
+ 
+
+ align:start position:0%
+also used the first formulation to say
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+probability that R is greater than
+
+ align:start position:0%
+probability that R is greater than
+ 
+
+ align:start position:0%
+probability that R is greater than
+90 greater than or equal to is going to
+
+ align:start position:0%
+90 greater than or equal to is going to
+ 
+
+ align:start position:0%
+90 greater than or equal to is going to
+be at most uh 75 over
+
+ align:start position:0%
+be at most uh 75 over
+ 
+
+ align:start position:0%
+be at most uh 75 over
+90 which you know same thing
+
+ align:start position:0%
+90 which you know same thing
+ 
+
+ align:start position:0%
+90 which you know same thing
+83% okay so either of them Works they
+
+ align:start position:0%
+83% okay so either of them Works they
+ 
+
+ align:start position:0%
+83% okay so either of them Works they
+both give the same answer they're
+
+ align:start position:0%
+both give the same answer they're
+ 
+
+ align:start position:0%
+both give the same answer they're
+equivalent formulations it's just you
+
+ align:start position:0%
+equivalent formulations it's just you
+ 
+
+ align:start position:0%
+equivalent formulations it's just you
+know whichever one you find easier to
+
+ align:start position:0%
+know whichever one you find easier to
+ 
+
+ align:start position:0%
+know whichever one you find easier to
+think about question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes exactly okay so the question was uh
+
+ align:start position:0%
+yes exactly okay so the question was uh
+ 
+
+ align:start position:0%
+yes exactly okay so the question was uh
+we don't just have a non- negative
+
+ align:start position:0%
+we don't just have a non- negative
+ 
+
+ align:start position:0%
+we don't just have a non- negative
+random variable R right we we've
+
+ align:start position:0%
+random variable R right we we've
+ 
+
+ align:start position:0%
+random variable R right we we've
+actually got an even stronger bound R is
+
+ align:start position:0%
+actually got an even stronger bound R is
+ 
+
+ align:start position:0%
+actually got an even stronger bound R is
+at least 30 not just at least zero okay
+
+ align:start position:0%
+at least 30 not just at least zero okay
+ 
+
+ align:start position:0%
+at least 30 not just at least zero okay
+so can we leverage that to get an even
+
+ align:start position:0%
+so can we leverage that to get an even
+ 
+
+ align:start position:0%
+so can we leverage that to get an even
+stronger
+
+ align:start position:0%
+stronger
+ 
+
+ align:start position:0%
+stronger
+bound okay so how could we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that well let's try def finding
+
+ align:start position:0%
+that well let's try def finding
+ 
+
+ align:start position:0%
+that well let's try def finding
+different random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+so let R Prime be Rus
+
+ align:start position:0%
+so let R Prime be Rus
+ 
+
+ align:start position:0%
+so let R Prime be Rus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is another random variable
+
+ align:start position:0%
+okay so this is another random variable
+ 
+
+ align:start position:0%
+okay so this is another random variable
+right we're just going to take our
+
+ align:start position:0%
+right we're just going to take our
+ 
+
+ align:start position:0%
+right we're just going to take our
+original R we're going to subtract 30 um
+
+ align:start position:0%
+original R we're going to subtract 30 um
+ 
+
+ align:start position:0%
+original R we're going to subtract 30 um
+we're not going to do this to people's
+
+ align:start position:0%
+we're not going to do this to people's
+ 
+
+ align:start position:0%
+we're not going to do this to people's
+exam scores in reality don't don't worry
+
+ align:start position:0%
+exam scores in reality don't don't worry
+ 
+
+ align:start position:0%
+exam scores in reality don't don't worry
+uh but that this makes the the minimum
+
+ align:start position:0%
+uh but that this makes the the minimum
+ 
+
+ align:start position:0%
+uh but that this makes the the minimum
+exam score zero
+
+ align:start position:0%
+exam score zero
+ 
+
+ align:start position:0%
+exam score zero
+right so the hope is that you know now
+
+ align:start position:0%
+right so the hope is that you know now
+ 
+
+ align:start position:0%
+right so the hope is that you know now
+we're kind of satisfying the condition
+
+ align:start position:0%
+we're kind of satisfying the condition
+ 
+
+ align:start position:0%
+we're kind of satisfying the condition
+to to markov's uh inequality like more
+
+ align:start position:0%
+to to markov's uh inequality like more
+ 
+
+ align:start position:0%
+to to markov's uh inequality like more
+tightly so hopefully marov will give us
+
+ align:start position:0%
+tightly so hopefully marov will give us
+ 
+
+ align:start position:0%
+tightly so hopefully marov will give us
+a tighter bound okay so what bound does
+
+ align:start position:0%
+a tighter bound okay so what bound does
+ 
+
+ align:start position:0%
+a tighter bound okay so what bound does
+it give us now what is the
+
+ align:start position:0%
+it give us now what is the
+ 
+
+ align:start position:0%
+it give us now what is the
+probability that R is at least 90
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what is that in terms of R Prime
+
+ align:start position:0%
+well what is that in terms of R Prime
+ 
+
+ align:start position:0%
+well what is that in terms of R Prime
+what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+event
+
+ align:start position:0%
+event
+ 
+
+ align:start position:0%
+event
+yeah yeah so this is the same event and
+
+ align:start position:0%
+yeah yeah so this is the same event and
+ 
+
+ align:start position:0%
+yeah yeah so this is the same event and
+so the same
+
+ align:start position:0%
+so the same
+ 
+
+ align:start position:0%
+so the same
+probability that R Prime is at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+60 now what happens when we apply Markov
+
+ align:start position:0%
+60 now what happens when we apply Markov
+ 
+
+ align:start position:0%
+60 now what happens when we apply Markov
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this well this is going to be at
+
+ align:start position:0%
+this well this is going to be at
+ 
+
+ align:start position:0%
+this well this is going to be at
+most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the expectation of RP Prime
+
+ align:start position:0%
+right the expectation of RP Prime
+ 
+
+ align:start position:0%
+right the expectation of RP Prime
+ID
+
+ align:start position:0%
+ID
+ 
+
+ align:start position:0%
+ID
+60 what is the expectation of R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime yeah 45
+
+ align:start position:0%
+Prime yeah 45
+ 
+
+ align:start position:0%
+Prime yeah 45
+yeah so this is going to be the
+
+ align:start position:0%
+yeah so this is going to be the
+ 
+
+ align:start position:0%
+yeah so this is going to be the
+expectation of R uh minus
+
+ align:start position:0%
+expectation of R uh minus
+ 
+
+ align:start position:0%
+expectation of R uh minus
+30 / 60 which is the expectation so
+
+ align:start position:0%
+30 / 60 which is the expectation so
+ 
+
+ align:start position:0%
+30 / 60 which is the expectation so
+linearity of expectation we can pull
+
+ align:start position:0%
+linearity of expectation we can pull
+ 
+
+ align:start position:0%
+linearity of expectation we can pull
+this or like we can you know split this
+
+ align:start position:0%
+this or like we can you know split this
+ 
+
+ align:start position:0%
+this or like we can you know split this
+into two expectations so this is the
+
+ align:start position:0%
+into two expectations so this is the
+ 
+
+ align:start position:0%
+into two expectations so this is the
+expectation of
+
+ align:start position:0%
+expectation of
+ 
+
+ align:start position:0%
+expectation of
+R minus the expectation of 30 there's
+
+ align:start position:0%
+R minus the expectation of 30 there's
+ 
+
+ align:start position:0%
+R minus the expectation of 30 there's
+you know not really any Randomness
+
+ align:start position:0%
+you know not really any Randomness
+ 
+
+ align:start position:0%
+you know not really any Randomness
+involved there it's just
+
+ align:start position:0%
+involved there it's just
+ 
+
+ align:start position:0%
+involved there it's just
+30 over 60 right so this is
+
+ align:start position:0%
+30 over 60 right so this is
+ 
+
+ align:start position:0%
+30 over 60 right so this is
+45 over 60
+
+ align:start position:0%
+45 over 60
+ 
+
+ align:start position:0%
+45 over 60
+okay does that make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody so now instead of this bound
+
+ align:start position:0%
+everybody so now instead of this bound
+ 
+
+ align:start position:0%
+everybody so now instead of this bound
+of uh you know it's it's at most 83% now
+
+ align:start position:0%
+of uh you know it's it's at most 83% now
+ 
+
+ align:start position:0%
+of uh you know it's it's at most 83% now
+we've got the better bound it's at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+75%
+
+ align:start position:0%
+75%
+ 
+
+ align:start position:0%
+75%
+okay so by shifting our random variable
+
+ align:start position:0%
+okay so by shifting our random variable
+ 
+
+ align:start position:0%
+okay so by shifting our random variable
+we've managed to get a tighter bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the probability that R is at most
+
+ align:start position:0%
+about the probability that R is at most
+ 
+
+ align:start position:0%
+about the probability that R is at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah mhm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that that's kind of what we're doing
+
+ align:start position:0%
+so that that's kind of what we're doing
+ 
+
+ align:start position:0%
+so that that's kind of what we're doing
+right the the the question was uh in the
+
+ align:start position:0%
+right the the the question was uh in the
+ 
+
+ align:start position:0%
+right the the the question was uh in the
+proof of Markov right we're assuming
+
+ align:start position:0%
+proof of Markov right we're assuming
+ 
+
+ align:start position:0%
+proof of Markov right we're assuming
+that the lower bound is zero uh here
+
+ align:start position:0%
+that the lower bound is zero uh here
+ 
+
+ align:start position:0%
+that the lower bound is zero uh here
+we've got a lower bound of 30 instead so
+
+ align:start position:0%
+we've got a lower bound of 30 instead so
+ 
+
+ align:start position:0%
+we've got a lower bound of 30 instead so
+do we need to do something more
+
+ align:start position:0%
+do we need to do something more
+ 
+
+ align:start position:0%
+do we need to do something more
+complicated the answer is no we don't
+
+ align:start position:0%
+complicated the answer is no we don't
+ 
+
+ align:start position:0%
+complicated the answer is no we don't
+have to but if we do it gives us a
+
+ align:start position:0%
+have to but if we do it gives us a
+ 
+
+ align:start position:0%
+have to but if we do it gives us a
+stronger result so that's what we've
+
+ align:start position:0%
+stronger result so that's what we've
+ 
+
+ align:start position:0%
+stronger result so that's what we've
+done here but we don't have to do it
+
+ align:start position:0%
+done here but we don't have to do it
+ 
+
+ align:start position:0%
+done here but we don't have to do it
+right because zero is still a valid
+
+ align:start position:0%
+right because zero is still a valid
+ 
+
+ align:start position:0%
+right because zero is still a valid
+lower bound right we could still say we
+
+ align:start position:0%
+lower bound right we could still say we
+ 
+
+ align:start position:0%
+lower bound right we could still say we
+could say that the co- domain of R is 0
+
+ align:start position:0%
+could say that the co- domain of R is 0
+ 
+
+ align:start position:0%
+could say that the co- domain of R is 0
+to 100 instead of 30 to 100 even even if
+
+ align:start position:0%
+to 100 instead of 30 to 100 even even if
+ 
+
+ align:start position:0%
+to 100 instead of 30 to 100 even even if
+the range stays
+
+ align:start position:0%
+the range stays
+ 
+
+ align:start position:0%
+the range stays
+unchanged okay so it's still a non-
+
+ align:start position:0%
+unchanged okay so it's still a non-
+ 
+
+ align:start position:0%
+unchanged okay so it's still a non-
+negative random variable so we're still
+
+ align:start position:0%
+negative random variable so we're still
+ 
+
+ align:start position:0%
+negative random variable so we're still
+allowed to apply marov to it it's just
+
+ align:start position:0%
+allowed to apply marov to it it's just
+ 
+
+ align:start position:0%
+allowed to apply marov to it it's just
+that you know doing it on r instead of R
+
+ align:start position:0%
+that you know doing it on r instead of R
+ 
+
+ align:start position:0%
+that you know doing it on r instead of R
+Prime gives us a weaker
+
+ align:start position:0%
+Prime gives us a weaker
+ 
+
+ align:start position:0%
+Prime gives us a weaker
+result okay does that make sense to
+
+ align:start position:0%
+result okay does that make sense to
+ 
+
+ align:start position:0%
+result okay does that make sense to
+everybody another question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so the question is what do I mean by
+
+ align:start position:0%
+uh so the question is what do I mean by
+ 
+
+ align:start position:0%
+uh so the question is what do I mean by
+by a tighter bound when when we shift R
+
+ align:start position:0%
+by a tighter bound when when we shift R
+ 
+
+ align:start position:0%
+by a tighter bound when when we shift R
+uh so tighter in the sense that it is
+
+ align:start position:0%
+uh so tighter in the sense that it is
+ 
+
+ align:start position:0%
+uh so tighter in the sense that it is
+stronger right so uh r at least 30
+
+ align:start position:0%
+stronger right so uh r at least 30
+ 
+
+ align:start position:0%
+stronger right so uh r at least 30
+implies that R is at least zero so r r
+
+ align:start position:0%
+implies that R is at least zero so r r
+ 
+
+ align:start position:0%
+implies that R is at least zero so r r
+at least 30 is a stronger condition than
+
+ align:start position:0%
+at least 30 is a stronger condition than
+ 
+
+ align:start position:0%
+at least 30 is a stronger condition than
+than r at least zero
+
+ align:start position:0%
+than r at least zero
+ 
+
+ align:start position:0%
+than r at least zero
+okay so that that's what I mean by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tighter uh so the the difference right
+
+ align:start position:0%
+tighter uh so the the difference right
+ 
+
+ align:start position:0%
+tighter uh so the the difference right
+is how we're applying marov right uh we
+
+ align:start position:0%
+is how we're applying marov right uh we
+ 
+
+ align:start position:0%
+is how we're applying marov right uh we
+are in the first case we're applying
+
+ align:start position:0%
+are in the first case we're applying
+ 
+
+ align:start position:0%
+are in the first case we're applying
+marov to R directly in the second case
+
+ align:start position:0%
+marov to R directly in the second case
+ 
+
+ align:start position:0%
+marov to R directly in the second case
+we are creating a new random
+
+ align:start position:0%
+we are creating a new random
+ 
+
+ align:start position:0%
+we are creating a new random
+variable uh and we're applying marov to
+
+ align:start position:0%
+variable uh and we're applying marov to
+ 
+
+ align:start position:0%
+variable uh and we're applying marov to
+that and you know because uh you know
+
+ align:start position:0%
+that and you know because uh you know
+ 
+
+ align:start position:0%
+that and you know because uh you know
+we've got a a stronger condition like
+
+ align:start position:0%
+we've got a a stronger condition like
+ 
+
+ align:start position:0%
+we've got a a stronger condition like
+the the marov markov's um what do you
+
+ align:start position:0%
+the the marov markov's um what do you
+ 
+
+ align:start position:0%
+the the marov markov's um what do you
+call it precondition is is tight
+
+ align:start position:0%
+call it precondition is is tight
+ 
+
+ align:start position:0%
+call it precondition is is tight
+now uh we can get a a stronger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh could it go higher than 83%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay so we will get to that in a
+
+ align:start position:0%
+uh okay so we will get to that in a
+ 
+
+ align:start position:0%
+uh okay so we will get to that in a
+moment the the question is you know if
+
+ align:start position:0%
+moment the the question is you know if
+ 
+
+ align:start position:0%
+moment the the question is you know if
+we're in a different
+
+ align:start position:0%
+we're in a different
+ 
+
+ align:start position:0%
+we're in a different
+situation uh could shifting it give us
+
+ align:start position:0%
+situation uh could shifting it give us
+ 
+
+ align:start position:0%
+situation uh could shifting it give us
+something that's higher than
+
+ align:start position:0%
+something that's higher than
+ 
+
+ align:start position:0%
+something that's higher than
+83% and the answer is yes
+
+ align:start position:0%
+83% and the answer is yes
+ 
+
+ align:start position:0%
+83% and the answer is yes
+is right in the case where we've applied
+
+ align:start position:0%
+is right in the case where we've applied
+ 
+
+ align:start position:0%
+is right in the case where we've applied
+Markov incorrectly the first time then
+
+ align:start position:0%
+Markov incorrectly the first time then
+ 
+
+ align:start position:0%
+Markov incorrectly the first time then
+yes but uh you know if we've applied
+
+ align:start position:0%
+yes but uh you know if we've applied
+ 
+
+ align:start position:0%
+yes but uh you know if we've applied
+Markov correctly then uh you know the
+
+ align:start position:0%
+Markov correctly then uh you know the
+ 
+
+ align:start position:0%
+Markov correctly then uh you know the
+first is a valid bound right
+
+ align:start position:0%
+first is a valid bound right
+ 
+
+ align:start position:0%
+first is a valid bound right
+right so you know we we could in
+
+ align:start position:0%
+right so you know we we could in
+ 
+
+ align:start position:0%
+right so you know we we could in
+principle improve it but uh you know
+
+ align:start position:0%
+principle improve it but uh you know
+ 
+
+ align:start position:0%
+principle improve it but uh you know
+we're not going to do any worse by you
+
+ align:start position:0%
+we're not going to do any worse by you
+ 
+
+ align:start position:0%
+we're not going to do any worse by you
+know imposing tighter
+
+ align:start position:0%
+know imposing tighter
+ 
+
+ align:start position:0%
+know imposing tighter
+conditions does that like at least kind
+
+ align:start position:0%
+conditions does that like at least kind
+ 
+
+ align:start position:0%
+conditions does that like at least kind
+of intuitively make sense I'll give you
+
+ align:start position:0%
+of intuitively make sense I'll give you
+ 
+
+ align:start position:0%
+of intuitively make sense I'll give you
+a more complete answer in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment any more questions about this
+
+ align:start position:0%
+moment any more questions about this
+ 
+
+ align:start position:0%
+moment any more questions about this
+before we move on to the next
+
+ align:start position:0%
+before we move on to the next
+ 
+
+ align:start position:0%
+before we move on to the next
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes
+
+ align:start position:0%
+yeah yes
+ 
+
+ align:start position:0%
+yeah yes
+it is a good thing uh so the the
+
+ align:start position:0%
+it is a good thing uh so the the
+ 
+
+ align:start position:0%
+it is a good thing uh so the the
+question is is it a good thing that the
+
+ align:start position:0%
+question is is it a good thing that the
+ 
+
+ align:start position:0%
+question is is it a good thing that the
+75% is smaller than the
+
+ align:start position:0%
+75% is smaller than the
+ 
+
+ align:start position:0%
+75% is smaller than the
+83% uh yes we are looking for an upper
+
+ align:start position:0%
+83% uh yes we are looking for an upper
+ 
+
+ align:start position:0%
+83% uh yes we are looking for an upper
+bound on the probability right so a
+
+ align:start position:0%
+bound on the probability right so a
+ 
+
+ align:start position:0%
+bound on the probability right so a
+smaller upper bound is a stronger
+
+ align:start position:0%
+smaller upper bound is a stronger
+ 
+
+ align:start position:0%
+smaller upper bound is a stronger
+condition so that's that's better it's
+
+ align:start position:0%
+condition so that's that's better it's
+ 
+
+ align:start position:0%
+condition so that's that's better it's
+um it's a it's a stronger bound you want
+
+ align:start position:0%
+um it's a it's a stronger bound you want
+ 
+
+ align:start position:0%
+um it's a it's a stronger bound you want
+a smaller upper or AER so that they're
+
+ align:start position:0%
+a smaller upper or AER so that they're
+ 
+
+ align:start position:0%
+a smaller upper or AER so that they're
+the same smaller upper bounds are
+
+ align:start position:0%
+the same smaller upper bounds are
+ 
+
+ align:start position:0%
+the same smaller upper bounds are
+stronger upper bounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so like less than or equal to 83%
+
+ align:start position:0%
+yeah so like less than or equal to 83%
+ 
+
+ align:start position:0%
+yeah so like less than or equal to 83%
+implies less than or equal to uh sorry
+
+ align:start position:0%
+implies less than or equal to uh sorry
+ 
+
+ align:start position:0%
+implies less than or equal to uh sorry
+less than or equal to 75% implies less
+
+ align:start position:0%
+less than or equal to 75% implies less
+ 
+
+ align:start position:0%
+less than or equal to 75% implies less
+than or equal to to 83% so 75 is is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stronger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay have people had enough time to
+
+ align:start position:0%
+okay okay have people had enough time to
+ 
+
+ align:start position:0%
+okay okay have people had enough time to
+think about the probability that R is at
+
+ align:start position:0%
+think about the probability that R is at
+ 
+
+ align:start position:0%
+think about the probability that R is at
+most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+65 how might we use marov to figure this
+
+ align:start position:0%
+65 how might we use marov to figure this
+ 
+
+ align:start position:0%
+65 how might we use marov to figure this
+one out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so R greater than or equal to 66 so
+
+ align:start position:0%
+okay so R greater than or equal to 66 so
+ 
+
+ align:start position:0%
+okay so R greater than or equal to 66 so
+if we assume integer
+
+ align:start position:0%
+if we assume integer
+ 
+
+ align:start position:0%
+if we assume integer
+scores
+
+ align:start position:0%
+scores
+ 
+
+ align:start position:0%
+scores
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um and what does marov tell us about
+
+ align:start position:0%
+um and what does marov tell us about
+ 
+
+ align:start position:0%
+um and what does marov tell us about
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the probability that R
+
+ align:start position:0%
+well the probability that R
+ 
+
+ align:start position:0%
+well the probability that R
+is at least
+
+ align:start position:0%
+is at least
+ 
+
+ align:start position:0%
+is at least
+66 right is going to be at most 75 over
+
+ align:start position:0%
+66 right is going to be at most 75 over
+ 
+
+ align:start position:0%
+66 right is going to be at most 75 over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+which is bigger than
+
+ align:start position:0%
+which is bigger than
+ 
+
+ align:start position:0%
+which is bigger than
+one so applying marov does not tell us
+
+ align:start position:0%
+one so applying marov does not tell us
+ 
+
+ align:start position:0%
+one so applying marov does not tell us
+anything useful it tells us that this is
+
+ align:start position:0%
+anything useful it tells us that this is
+ 
+
+ align:start position:0%
+anything useful it tells us that this is
+a probability that's that's bounded by
+
+ align:start position:0%
+a probability that's that's bounded by
+ 
+
+ align:start position:0%
+a probability that's that's bounded by
+one which we already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knew so it is a good idea it's not quite
+
+ align:start position:0%
+knew so it is a good idea it's not quite
+ 
+
+ align:start position:0%
+knew so it is a good idea it's not quite
+what we want here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what if instead of uh you know
+
+ align:start position:0%
+so what if instead of uh you know
+ 
+
+ align:start position:0%
+so what if instead of uh you know
+fiddling with the event we fiddle with r
+
+ align:start position:0%
+fiddling with the event we fiddle with r
+ 
+
+ align:start position:0%
+fiddling with the event we fiddle with r
+again kind of similar to what we did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah exactly so we're going to flip
+
+ align:start position:0%
+yeah yeah exactly so we're going to flip
+ 
+
+ align:start position:0%
+yeah yeah exactly so we're going to flip
+R right so we're going to define a new
+
+ align:start position:0%
+R right so we're going to define a new
+ 
+
+ align:start position:0%
+R right so we're going to define a new
+random variable let's say s equals
+
+ align:start position:0%
+random variable let's say s equals
+ 
+
+ align:start position:0%
+random variable let's say s equals
+100 minus r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now the probability that R is at
+
+ align:start position:0%
+okay so now the probability that R is at
+ 
+
+ align:start position:0%
+okay so now the probability that R is at
+most
+
+ align:start position:0%
+most
+ 
+
+ align:start position:0%
+most
+65 is the probability that s is at least
+
+ align:start position:0%
+65 is the probability that s is at least
+ 
+
+ align:start position:0%
+65 is the probability that s is at least
+what 100 minus 65
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay can we apply Markov to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm seeing some nods does anybody want
+
+ align:start position:0%
+I'm seeing some nods does anybody want
+ 
+
+ align:start position:0%
+I'm seeing some nods does anybody want
+to do that and spare me the trouble of
+
+ align:start position:0%
+to do that and spare me the trouble of
+ 
+
+ align:start position:0%
+to do that and spare me the trouble of
+doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arithmetic nobody sadness okay
+
+ align:start position:0%
+arithmetic nobody sadness okay
+ 
+
+ align:start position:0%
+arithmetic nobody sadness okay
+uh well what does Markov say well it's
+
+ align:start position:0%
+uh well what does Markov say well it's
+ 
+
+ align:start position:0%
+uh well what does Markov say well it's
+at most the expectation of
+
+ align:start position:0%
+at most the expectation of
+ 
+
+ align:start position:0%
+at most the expectation of
+X oh sorry
+
+ align:start position:0%
+X oh sorry
+ 
+
+ align:start position:0%
+X oh sorry
+s divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+35 okay what is the expectation of s
+
+ align:start position:0%
+35 okay what is the expectation of s
+ 
+
+ align:start position:0%
+35 okay what is the expectation of s
+well using linearity in the same way
+
+ align:start position:0%
+well using linearity in the same way
+ 
+
+ align:start position:0%
+well using linearity in the same way
+that we did a moment
+
+ align:start position:0%
+that we did a moment
+ 
+
+ align:start position:0%
+that we did a moment
+ago this is going to be equal to uh what
+
+ align:start position:0%
+ago this is going to be equal to uh what
+ 
+
+ align:start position:0%
+ago this is going to be equal to uh what
+100 minus the expectation of R which is
+
+ align:start position:0%
+100 minus the expectation of R which is
+ 
+
+ align:start position:0%
+100 minus the expectation of R which is
+75 over 35 so that's 25 over 35 this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+57s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so does does that make sense to
+
+ align:start position:0%
+okay so does does that make sense to
+ 
+
+ align:start position:0%
+okay so does does that make sense to
+everybody there is at most a 57th chance
+
+ align:start position:0%
+everybody there is at most a 57th chance
+ 
+
+ align:start position:0%
+everybody there is at most a 57th chance
+that you uh did worse than
+
+ align:start position:0%
+that you uh did worse than
+ 
+
+ align:start position:0%
+that you uh did worse than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now perhaps not terribly realistic
+
+ align:start position:0%
+okay now perhaps not terribly realistic
+ 
+
+ align:start position:0%
+okay now perhaps not terribly realistic
+in terms of exam scores but uh you know
+
+ align:start position:0%
+in terms of exam scores but uh you know
+ 
+
+ align:start position:0%
+in terms of exam scores but uh you know
+what if say some of the students did so
+
+ align:start position:0%
+what if say some of the students did so
+ 
+
+ align:start position:0%
+what if say some of the students did so
+badly that they got scores that are less
+
+ align:start position:0%
+badly that they got scores that are less
+ 
+
+ align:start position:0%
+badly that they got scores that are less
+than zero like maybe you've got uh you
+
+ align:start position:0%
+than zero like maybe you've got uh you
+ 
+
+ align:start position:0%
+than zero like maybe you've got uh you
+know R is in the range you know minus 30
+
+ align:start position:0%
+know R is in the range you know minus 30
+ 
+
+ align:start position:0%
+know R is in the range you know minus 30
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay same deal expectation of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+75 uh question or
+
+ align:start position:0%
+75 uh question or
+ 
+
+ align:start position:0%
+75 uh question or
+um sorry um okay so what can we say
+
+ align:start position:0%
+um sorry um okay so what can we say
+ 
+
+ align:start position:0%
+um sorry um okay so what can we say
+about the probability that R uh is at
+
+ align:start position:0%
+about the probability that R uh is at
+ 
+
+ align:start position:0%
+about the probability that R uh is at
+least uh say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+90 mhm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah exactly so the observation was
+
+ align:start position:0%
+yeah exactly so the observation was
+ 
+
+ align:start position:0%
+yeah exactly so the observation was
+right if we try to apply marov to this
+
+ align:start position:0%
+right if we try to apply marov to this
+ 
+
+ align:start position:0%
+right if we try to apply marov to this
+maybe I should call it a different call
+
+ align:start position:0%
+maybe I should call it a different call
+ 
+
+ align:start position:0%
+maybe I should call it a different call
+it something different let's call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t so if we try to apply Markov to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T right it's going to be the same thing
+
+ align:start position:0%
+T right it's going to be the same thing
+ 
+
+ align:start position:0%
+T right it's going to be the same thing
+as as when we applied Markov to R before
+
+ align:start position:0%
+as as when we applied Markov to R before
+ 
+
+ align:start position:0%
+as as when we applied Markov to R before
+it'll give us a bound of of 83% the
+
+ align:start position:0%
+it'll give us a bound of of 83% the
+ 
+
+ align:start position:0%
+it'll give us a bound of of 83% the
+problem is that that's wrong that does
+
+ align:start position:0%
+problem is that that's wrong that does
+ 
+
+ align:start position:0%
+problem is that that's wrong that does
+it t does not satisfy the precondition
+
+ align:start position:0%
+it t does not satisfy the precondition
+ 
+
+ align:start position:0%
+it t does not satisfy the precondition
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+Markov okay so what we want to do
+
+ align:start position:0%
+Markov okay so what we want to do
+ 
+
+ align:start position:0%
+Markov okay so what we want to do
+instead is
+
+ align:start position:0%
+instead is
+ 
+
+ align:start position:0%
+instead is
+toine T Prime = t +
+
+ align:start position:0%
+toine T Prime = t +
+ 
+
+ align:start position:0%
+toine T Prime = t +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay and now if we apply Markov to T
+
+ align:start position:0%
+okay and now if we apply Markov to T
+ 
+
+ align:start position:0%
+okay and now if we apply Markov to T
+Prime what do we get so the probability
+
+ align:start position:0%
+Prime what do we get so the probability
+ 
+
+ align:start position:0%
+Prime what do we get so the probability
+that uh T is greater than
+
+ align:start position:0%
+that uh T is greater than
+ 
+
+ align:start position:0%
+that uh T is greater than
+90 is the probability
+
+ align:start position:0%
+90 is the probability
+ 
+
+ align:start position:0%
+90 is the probability
+that t Prime is at least
+
+ align:start position:0%
+that t Prime is at least
+ 
+
+ align:start position:0%
+that t Prime is at least
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay and by Mark of this is going to be
+
+ align:start position:0%
+okay and by Mark of this is going to be
+ 
+
+ align:start position:0%
+okay and by Mark of this is going to be
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+expectation of T
+
+ align:start position:0%
+expectation of T
+ 
+
+ align:start position:0%
+expectation of T
+Prime over
+
+ align:start position:0%
+Prime over
+ 
+
+ align:start position:0%
+Prime over
+120 okay and you know same deal as
+
+ align:start position:0%
+120 okay and you know same deal as
+ 
+
+ align:start position:0%
+120 okay and you know same deal as
+before linearity here gives us uh 75 +
+
+ align:start position:0%
+before linearity here gives us uh 75 +
+ 
+
+ align:start position:0%
+before linearity here gives us uh 75 +
+30 over
+
+ align:start position:0%
+30 over
+ 
+
+ align:start position:0%
+30 over
+120 105 over 120 that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+78 is that
+
+ align:start position:0%
+78 is that
+ 
+
+ align:start position:0%
+78 is that
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay so in this case we do get a you
+
+ align:start position:0%
+okay so in this case we do get a you
+ 
+
+ align:start position:0%
+okay so in this case we do get a you
+know in some sense a weaker bound than
+
+ align:start position:0%
+know in some sense a weaker bound than
+ 
+
+ align:start position:0%
+know in some sense a weaker bound than
+we would have gotten by applying Markov
+
+ align:start position:0%
+we would have gotten by applying Markov
+ 
+
+ align:start position:0%
+we would have gotten by applying Markov
+to to t you know directly but you know
+
+ align:start position:0%
+to to t you know directly but you know
+ 
+
+ align:start position:0%
+to to t you know directly but you know
+applying Markov to T directly doesn't
+
+ align:start position:0%
+applying Markov to T directly doesn't
+ 
+
+ align:start position:0%
+applying Markov to T directly doesn't
+actually work this you know looks weaker
+
+ align:start position:0%
+actually work this you know looks weaker
+ 
+
+ align:start position:0%
+actually work this you know looks weaker
+but it's a correct bound okay so
+
+ align:start position:0%
+but it's a correct bound okay so
+ 
+
+ align:start position:0%
+but it's a correct bound okay so
+hopefully that answers your question
+
+ align:start position:0%
+hopefully that answers your question
+ 
+
+ align:start position:0%
+hopefully that answers your question
+more fully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay does anybody have any
+
+ align:start position:0%
+okay does anybody have any
+ 
+
+ align:start position:0%
+okay does anybody have any
+questions so even though we couldn't
+
+ align:start position:0%
+questions so even though we couldn't
+ 
+
+ align:start position:0%
+questions so even though we couldn't
+apply Markov directly to T we can create
+
+ align:start position:0%
+apply Markov directly to T we can create
+ 
+
+ align:start position:0%
+apply Markov directly to T we can create
+a new random variable T Prime to which
+
+ align:start position:0%
+a new random variable T Prime to which
+ 
+
+ align:start position:0%
+a new random variable T Prime to which
+marov does
+
+ align:start position:0%
+marov does
+ 
+
+ align:start position:0%
+marov does
+apply MH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+uh so using the lower bound of 30 making
+
+ align:start position:0%
+uh so using the lower bound of 30 making
+ 
+
+ align:start position:0%
+uh so using the lower bound of 30 making
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the the statement stronger for for t for
+
+ align:start position:0%
+the the statement stronger for for t for
+ 
+
+ align:start position:0%
+the the statement stronger for for t for
+S oh for S uh which one was s uh s here
+
+ align:start position:0%
+S oh for S uh which one was s uh s here
+ 
+
+ align:start position:0%
+S oh for S uh which one was s uh s here
+um so that does not really help us in
+
+ align:start position:0%
+um so that does not really help us in
+ 
+
+ align:start position:0%
+um so that does not really help us in
+this case um because that kind of
+
+ align:start position:0%
+this case um because that kind of
+ 
+
+ align:start position:0%
+this case um because that kind of
+corresponds to uh an upper
+
+ align:start position:0%
+corresponds to uh an upper
+ 
+
+ align:start position:0%
+corresponds to uh an upper
+bound right rather than rather than the
+
+ align:start position:0%
+bound right rather than rather than the
+ 
+
+ align:start position:0%
+bound right rather than rather than the
+lower bound uh and you know upper bounds
+
+ align:start position:0%
+lower bound uh and you know upper bounds
+ 
+
+ align:start position:0%
+lower bound uh and you know upper bounds
+don't really appear in in the proof of
+
+ align:start position:0%
+don't really appear in in the proof of
+ 
+
+ align:start position:0%
+don't really appear in in the proof of
+Markov like we're not really using them
+
+ align:start position:0%
+Markov like we're not really using them
+ 
+
+ align:start position:0%
+Markov like we're not really using them
+in any way so you know imposing a
+
+ align:start position:0%
+in any way so you know imposing a
+ 
+
+ align:start position:0%
+in any way so you know imposing a
+stronger upper bound doesn't really
+
+ align:start position:0%
+stronger upper bound doesn't really
+ 
+
+ align:start position:0%
+stronger upper bound doesn't really
+doesn't really help okay does does that
+
+ align:start position:0%
+doesn't really help okay does does that
+ 
+
+ align:start position:0%
+doesn't really help okay does does that
+kind of answer your question okay
+
+ align:start position:0%
+kind of answer your question okay
+ 
+
+ align:start position:0%
+kind of answer your question okay
+cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh okay is it always the case that
+
+ align:start position:0%
+yeah uh okay is it always the case that
+ 
+
+ align:start position:0%
+yeah uh okay is it always the case that
+the best lower bound appears or sorry
+
+ align:start position:0%
+the best lower bound appears or sorry
+ 
+
+ align:start position:0%
+the best lower bound appears or sorry
+the best upper bound I guess appears uh
+
+ align:start position:0%
+the best upper bound I guess appears uh
+ 
+
+ align:start position:0%
+the best upper bound I guess appears uh
+when uh when the the range actually
+
+ align:start position:0%
+when uh when the the range actually
+ 
+
+ align:start position:0%
+when uh when the the range actually
+includes
+
+ align:start position:0%
+includes
+ 
+
+ align:start position:0%
+includes
+zero um essentially yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay as far as correct bounds go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so I guess there's a question of like
+
+ align:start position:0%
+so I guess there's a question of like
+ 
+
+ align:start position:0%
+so I guess there's a question of like
+morally why do we need this this non-
+
+ align:start position:0%
+morally why do we need this this non-
+ 
+
+ align:start position:0%
+morally why do we need this this non-
+negativity um
+
+ align:start position:0%
+negativity um
+ 
+
+ align:start position:0%
+negativity um
+and perhaps a very simple illustrative
+
+ align:start position:0%
+and perhaps a very simple illustrative
+ 
+
+ align:start position:0%
+and perhaps a very simple illustrative
+example is suppose we have the random
+
+ align:start position:0%
+example is suppose we have the random
+ 
+
+ align:start position:0%
+example is suppose we have the random
+variable R which is uh plus or minus one
+
+ align:start position:0%
+variable R which is uh plus or minus one
+ 
+
+ align:start position:0%
+variable R which is uh plus or minus one
+depending on you know a Fair coin flip
+
+ align:start position:0%
+depending on you know a Fair coin flip
+ 
+
+ align:start position:0%
+depending on you know a Fair coin flip
+okay so it's it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform on positive one and negative
+
+ align:start position:0%
+uniform on positive one and negative
+ 
+
+ align:start position:0%
+uniform on positive one and negative
+1 okay so if we try to apply Markov to
+
+ align:start position:0%
+1 okay so if we try to apply Markov to
+ 
+
+ align:start position:0%
+1 okay so if we try to apply Markov to
+to that
+
+ align:start position:0%
+to that
+ 
+
+ align:start position:0%
+to that
+corly
+
+ align:start position:0%
+corly
+ 
+
+ align:start position:0%
+corly
+right what does that tell us about the
+
+ align:start position:0%
+right what does that tell us about the
+ 
+
+ align:start position:0%
+right what does that tell us about the
+probability that R is greater
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than2 well if we try to apply marov
+
+ align:start position:0%
+than2 well if we try to apply marov
+ 
+
+ align:start position:0%
+than2 well if we try to apply marov
+directly right the expectation of R is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so you know no matter what we put
+
+ align:start position:0%
+zero so you know no matter what we put
+ 
+
+ align:start position:0%
+zero so you know no matter what we put
+here marov would try to tell us that you
+
+ align:start position:0%
+here marov would try to tell us that you
+ 
+
+ align:start position:0%
+here marov would try to tell us that you
+know the probability is at most
+
+ align:start position:0%
+know the probability is at most
+ 
+
+ align:start position:0%
+know the probability is at most
+zero okay that is clearly rubbish right
+
+ align:start position:0%
+zero okay that is clearly rubbish right
+ 
+
+ align:start position:0%
+zero okay that is clearly rubbish right
+because you know R can be greater than
+
+ align:start position:0%
+because you know R can be greater than
+ 
+
+ align:start position:0%
+because you know R can be greater than
+1/2 R takes value one with probability
+
+ align:start position:0%
+1/2 R takes value one with probability
+ 
+
+ align:start position:0%
+1/2 R takes value one with probability
+1/2
+
+ align:start position:0%
+1/2
+ 
+
+ align:start position:0%
+1/2
+okay so basically our proof uh where was
+
+ align:start position:0%
+okay so basically our proof uh where was
+ 
+
+ align:start position:0%
+okay so basically our proof uh where was
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so if we if we get rid of the non-
+
+ align:start position:0%
+here so if we if we get rid of the non-
+ 
+
+ align:start position:0%
+here so if we if we get rid of the non-
+negativity constraint then this no
+
+ align:start position:0%
+negativity constraint then this no
+ 
+
+ align:start position:0%
+negativity constraint then this no
+longer
+
+ align:start position:0%
+longer
+ 
+
+ align:start position:0%
+longer
+works right we can't kind of discard
+
+ align:start position:0%
+works right we can't kind of discard
+ 
+
+ align:start position:0%
+works right we can't kind of discard
+This this term because that zero you
+
+ align:start position:0%
+This this term because that zero you
+ 
+
+ align:start position:0%
+This this term because that zero you
+know if we don't know that the the
+
+ align:start position:0%
+know if we don't know that the the
+ 
+
+ align:start position:0%
+know if we don't know that the the
+random variable is non negative we could
+
+ align:start position:0%
+random variable is non negative we could
+ 
+
+ align:start position:0%
+random variable is non negative we could
+in principle have a have a negative
+
+ align:start position:0%
+in principle have a have a negative
+ 
+
+ align:start position:0%
+in principle have a have a negative
+value there which you know we we we
+
+ align:start position:0%
+value there which you know we we we
+ 
+
+ align:start position:0%
+value there which you know we we we
+can't get rid of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so another
+
+ align:start position:0%
+okay so another
+ 
+
+ align:start position:0%
+okay so another
+question is Markov tight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in other
+
+ align:start position:0%
+so in other
+ 
+
+ align:start position:0%
+so in other
+words can we make a stronger statement
+
+ align:start position:0%
+words can we make a stronger statement
+ 
+
+ align:start position:0%
+words can we make a stronger statement
+than what marov tells us you know out of
+
+ align:start position:0%
+than what marov tells us you know out of
+ 
+
+ align:start position:0%
+than what marov tells us you know out of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+tin just with you know the information
+
+ align:start position:0%
+tin just with you know the information
+ 
+
+ align:start position:0%
+tin just with you know the information
+that we we have the mean and we have a
+
+ align:start position:0%
+that we we have the mean and we have a
+ 
+
+ align:start position:0%
+that we we have the mean and we have a
+non- negative random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable is there anything stronger that
+
+ align:start position:0%
+variable is there anything stronger that
+ 
+
+ align:start position:0%
+variable is there anything stronger that
+we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say who thinks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes couple of tentative hands who thinks
+
+ align:start position:0%
+yes couple of tentative hands who thinks
+ 
+
+ align:start position:0%
+yes couple of tentative hands who thinks
+no uh couple of less tentative tons who
+
+ align:start position:0%
+no uh couple of less tentative tons who
+ 
+
+ align:start position:0%
+no uh couple of less tentative tons who
+has no
+
+ align:start position:0%
+has no
+ 
+
+ align:start position:0%
+has no
+idea okay well let's let's think about
+
+ align:start position:0%
+idea okay well let's let's think about
+ 
+
+ align:start position:0%
+idea okay well let's let's think about
+some some uh simple examples then okay
+
+ align:start position:0%
+some some uh simple examples then okay
+ 
+
+ align:start position:0%
+some some uh simple examples then okay
+so let's go back to the uh cell phone
+
+ align:start position:0%
+so let's go back to the uh cell phone
+ 
+
+ align:start position:0%
+so let's go back to the uh cell phone
+check problem from uh was it last week
+
+ align:start position:0%
+check problem from uh was it last week
+ 
+
+ align:start position:0%
+check problem from uh was it last week
+don't remember which of the lectures
+
+ align:start position:0%
+don't remember which of the lectures
+ 
+
+ align:start position:0%
+don't remember which of the lectures
+last week Tuesday Thursday both both
+
+ align:start position:0%
+last week Tuesday Thursday both both
+ 
+
+ align:start position:0%
+last week Tuesday Thursday both both
+okay okay so if we consider the Lazy
+
+ align:start position:0%
+okay okay so if we consider the Lazy
+ 
+
+ align:start position:0%
+okay okay so if we consider the Lazy
+Susan version
+
+ align:start position:0%
+Susan version
+ 
+
+ align:start position:0%
+Susan version
+right and we let R be the number
+
+ align:start position:0%
+right and we let R be the number
+ 
+
+ align:start position:0%
+right and we let R be the number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+who get their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phone okay so this is the Lazy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Susan
+
+ align:start position:0%
+Susan
+ 
+
+ align:start position:0%
+Susan
+uh how could we use Markov to bound the
+
+ align:start position:0%
+uh how could we use Markov to bound the
+ 
+
+ align:start position:0%
+uh how could we use Markov to bound the
+probability that everybody gets their
+
+ align:start position:0%
+probability that everybody gets their
+ 
+
+ align:start position:0%
+probability that everybody gets their
+phone back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if everybody gets their phone back
+
+ align:start position:0%
+so if everybody gets their phone back
+ 
+
+ align:start position:0%
+so if everybody gets their phone back
+right that's R equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n what does marov tell us about this
+
+ align:start position:0%
+n what does marov tell us about this
+ 
+
+ align:start position:0%
+n what does marov tell us about this
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah it's the most one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n why is that well the expectation of R
+
+ align:start position:0%
+n why is that well the expectation of R
+ 
+
+ align:start position:0%
+n why is that well the expectation of R
+is one as we saw last week right the
+
+ align:start position:0%
+is one as we saw last week right the
+ 
+
+ align:start position:0%
+is one as we saw last week right the
+bound we're looking at is
+
+ align:start position:0%
+bound we're looking at is
+ 
+
+ align:start position:0%
+bound we're looking at is
+n okay so there's at most a one and
+
+ align:start position:0%
+n okay so there's at most a one and
+ 
+
+ align:start position:0%
+n okay so there's at most a one and
+probability that everybody gets their
+
+ align:start position:0%
+probability that everybody gets their
+ 
+
+ align:start position:0%
+probability that everybody gets their
+phone
+
+ align:start position:0%
+phone
+ 
+
+ align:start position:0%
+phone
+back what is the actual probability that
+
+ align:start position:0%
+back what is the actual probability that
+ 
+
+ align:start position:0%
+back what is the actual probability that
+everybody gets their phone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+yeah yeah the actual probability is 1/ n
+
+ align:start position:0%
+yeah yeah the actual probability is 1/ n
+ 
+
+ align:start position:0%
+yeah yeah the actual probability is 1/ n
+so this is tight okay we can't say
+
+ align:start position:0%
+so this is tight okay we can't say
+ 
+
+ align:start position:0%
+so this is tight okay we can't say
+anything stronger than marov without
+
+ align:start position:0%
+anything stronger than marov without
+ 
+
+ align:start position:0%
+anything stronger than marov without
+additional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information okay does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense so if we know something else about
+
+ align:start position:0%
+sense so if we know something else about
+ 
+
+ align:start position:0%
+sense so if we know something else about
+our distribution then we might be able
+
+ align:start position:0%
+our distribution then we might be able
+ 
+
+ align:start position:0%
+our distribution then we might be able
+to say something more but if all we know
+
+ align:start position:0%
+to say something more but if all we know
+ 
+
+ align:start position:0%
+to say something more but if all we know
+is the expectation and the the non-
+
+ align:start position:0%
+is the expectation and the the non-
+ 
+
+ align:start position:0%
+is the expectation and the the non-
+negativity then Markov is the best that
+
+ align:start position:0%
+negativity then Markov is the best that
+ 
+
+ align:start position:0%
+negativity then Markov is the best that
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay on the other hand you know suppose
+
+ align:start position:0%
+okay on the other hand you know suppose
+ 
+
+ align:start position:0%
+okay on the other hand you know suppose
+suppose we're permuting all of the
+
+ align:start position:0%
+suppose we're permuting all of the
+ 
+
+ align:start position:0%
+suppose we're permuting all of the
+phones instead of you know putting them
+
+ align:start position:0%
+phones instead of you know putting them
+ 
+
+ align:start position:0%
+phones instead of you know putting them
+on the Lazy
+
+ align:start position:0%
+on the Lazy
+ 
+
+ align:start position:0%
+on the Lazy
+Susan Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case what does marov tell us
+
+ align:start position:0%
+so in this case what does marov tell us
+ 
+
+ align:start position:0%
+so in this case what does marov tell us
+about the uh probability that everybody
+
+ align:start position:0%
+about the uh probability that everybody
+ 
+
+ align:start position:0%
+about the uh probability that everybody
+gets their phone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back it's still one over n right we've
+
+ align:start position:0%
+back it's still one over n right we've
+ 
+
+ align:start position:0%
+back it's still one over n right we've
+still got uh a non- negative random
+
+ align:start position:0%
+still got uh a non- negative random
+ 
+
+ align:start position:0%
+still got uh a non- negative random
+variable with the same mean we're still
+
+ align:start position:0%
+variable with the same mean we're still
+ 
+
+ align:start position:0%
+variable with the same mean we're still
+looking at the same threshold right so
+
+ align:start position:0%
+looking at the same threshold right so
+ 
+
+ align:start position:0%
+looking at the same threshold right so
+marov gives us the same bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what is the actual probability that
+
+ align:start position:0%
+okay what is the actual probability that
+ 
+
+ align:start position:0%
+okay what is the actual probability that
+everybody gets their phone back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that's that's exactly when you have
+
+ align:start position:0%
+well that's that's exactly when you have
+ 
+
+ align:start position:0%
+well that's that's exactly when you have
+the identity permutation right you've
+
+ align:start position:0%
+the identity permutation right you've
+ 
+
+ align:start position:0%
+the identity permutation right you've
+got n factorial possible permutations
+
+ align:start position:0%
+got n factorial possible permutations
+ 
+
+ align:start position:0%
+got n factorial possible permutations
+one of them gives everybody's phone
+
+ align:start position:0%
+one of them gives everybody's phone
+ 
+
+ align:start position:0%
+one of them gives everybody's phone
+back so what we're looking for is
+
+ align:start position:0%
+back so what we're looking for is
+ 
+
+ align:start position:0%
+back so what we're looking for is
+actually one/ n
+
+ align:start position:0%
+actually one/ n
+ 
+
+ align:start position:0%
+actually one/ n
+factorial okay so so marov is is very
+
+ align:start position:0%
+factorial okay so so marov is is very
+ 
+
+ align:start position:0%
+factorial okay so so marov is is very
+much not tight in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the next question is what can we
+
+ align:start position:0%
+okay so the next question is what can we
+ 
+
+ align:start position:0%
+okay so the next question is what can we
+say if we do have more information about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh about a random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable so suppose we know the
+
+ align:start position:0%
+variable so suppose we know the
+ 
+
+ align:start position:0%
+variable so suppose we know the
+variance okay so the variance of those
+
+ align:start position:0%
+variance okay so the variance of those
+ 
+
+ align:start position:0%
+variance okay so the variance of those
+two distributions is very different
+
+ align:start position:0%
+two distributions is very different
+ 
+
+ align:start position:0%
+two distributions is very different
+right uh in the case where we put the
+
+ align:start position:0%
+right uh in the case where we put the
+ 
+
+ align:start position:0%
+right uh in the case where we put the
+the phones on the Lazy Susan we've got a
+
+ align:start position:0%
+the phones on the Lazy Susan we've got a
+ 
+
+ align:start position:0%
+the phones on the Lazy Susan we've got a
+very high variance in the case where we
+
+ align:start position:0%
+very high variance in the case where we
+ 
+
+ align:start position:0%
+very high variance in the case where we
+have a random permutation it's much
+
+ align:start position:0%
+have a random permutation it's much
+ 
+
+ align:start position:0%
+have a random permutation it's much
+lower okay so maybe the variance can
+
+ align:start position:0%
+lower okay so maybe the variance can
+ 
+
+ align:start position:0%
+lower okay so maybe the variance can
+tell us you know
+
+ align:start position:0%
+tell us you know
+ 
+
+ align:start position:0%
+tell us you know
+more about these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities okay so this is a
+
+ align:start position:0%
+probabilities okay so this is a
+ 
+
+ align:start position:0%
+probabilities okay so this is a
+different tail bound uh due to Chubby
+
+ align:start position:0%
+different tail bound uh due to Chubby
+ 
+
+ align:start position:0%
+different tail bound uh due to Chubby
+Chev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+probability that R minus the expectation
+
+ align:start position:0%
+probability that R minus the expectation
+ 
+
+ align:start position:0%
+probability that R minus the expectation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+R uh you know an absolute value is at
+
+ align:start position:0%
+R uh you know an absolute value is at
+ 
+
+ align:start position:0%
+R uh you know an absolute value is at
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+X is less than or equal to the variance
+
+ align:start position:0%
+X is less than or equal to the variance
+ 
+
+ align:start position:0%
+X is less than or equal to the variance
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x^2 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so note that we no longer require non-
+
+ align:start position:0%
+so note that we no longer require non-
+ 
+
+ align:start position:0%
+so note that we no longer require non-
+negativity here we just require
+
+ align:start position:0%
+negativity here we just require
+ 
+
+ align:start position:0%
+negativity here we just require
+information about the
+
+ align:start position:0%
+information about the
+ 
+
+ align:start position:0%
+information about the
+variance okay and well the mean we have
+
+ align:start position:0%
+variance okay and well the mean we have
+ 
+
+ align:start position:0%
+variance okay and well the mean we have
+to uh we have to compute it relative to
+
+ align:start position:0%
+to uh we have to compute it relative to
+ 
+
+ align:start position:0%
+to uh we have to compute it relative to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+okay so but but R can be any random
+
+ align:start position:0%
+okay so but but R can be any random
+ 
+
+ align:start position:0%
+okay so but but R can be any random
+variable we're we're no longer
+
+ align:start position:0%
+variable we're we're no longer
+ 
+
+ align:start position:0%
+variable we're we're no longer
+constrained to to looking at non-
+
+ align:start position:0%
+constrained to to looking at non-
+ 
+
+ align:start position:0%
+constrained to to looking at non-
+negative ones it can be anything we just
+
+ align:start position:0%
+negative ones it can be anything we just
+ 
+
+ align:start position:0%
+negative ones it can be anything we just
+have to compute the variance
+
+ align:start position:0%
+have to compute the variance
+ 
+
+ align:start position:0%
+have to compute the variance
+okay how might we prove chubby shvs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inequality any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas is that a hand or a stretch
+
+ align:start position:0%
+ideas is that a hand or a stretch
+ 
+
+ align:start position:0%
+ideas is that a hand or a stretch
+yeah yeah so we're we're going to prove
+
+ align:start position:0%
+yeah yeah so we're we're going to prove
+ 
+
+ align:start position:0%
+yeah yeah so we're we're going to prove
+Chev using
+
+ align:start position:0%
+Chev using
+ 
+
+ align:start position:0%
+Chev using
+marov okay so in order to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+marov what do we need well we need an
+
+ align:start position:0%
+marov what do we need well we need an
+ 
+
+ align:start position:0%
+marov what do we need well we need an
+all negative random variable
+
+ align:start position:0%
+all negative random variable
+ 
+
+ align:start position:0%
+all negative random variable
+okay so kind of similar to what we were
+
+ align:start position:0%
+okay so kind of similar to what we were
+ 
+
+ align:start position:0%
+okay so kind of similar to what we were
+doing earlier with shifting our random
+
+ align:start position:0%
+doing earlier with shifting our random
+ 
+
+ align:start position:0%
+doing earlier with shifting our random
+variable we're going to define a new
+
+ align:start position:0%
+variable we're going to define a new
+ 
+
+ align:start position:0%
+variable we're going to define a new
+random variable that we can then apply
+
+ align:start position:0%
+random variable that we can then apply
+ 
+
+ align:start position:0%
+random variable that we can then apply
+Markov to and that should give us this
+
+ align:start position:0%
+Markov to and that should give us this
+ 
+
+ align:start position:0%
+Markov to and that should give us this
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay does that make sense to
+
+ align:start position:0%
+okay does that make sense to
+ 
+
+ align:start position:0%
+okay does that make sense to
+everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh variance of R sorry thank
+
+ align:start position:0%
+yeah oh variance of R sorry thank
+ 
+
+ align:start position:0%
+yeah oh variance of R sorry thank
+you yes variance of X does not make any
+
+ align:start position:0%
+you yes variance of X does not make any
+ 
+
+ align:start position:0%
+you yes variance of X does not make any
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what might be a useful random
+
+ align:start position:0%
+okay so what might be a useful random
+ 
+
+ align:start position:0%
+okay so what might be a useful random
+variable that we can apply Markov
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to well maybe here's a way we can kind
+
+ align:start position:0%
+to well maybe here's a way we can kind
+ 
+
+ align:start position:0%
+to well maybe here's a way we can kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+cheat
+
+ align:start position:0%
+cheat
+ 
+
+ align:start position:0%
+cheat
+uh in markov's inequality what's the
+
+ align:start position:0%
+uh in markov's inequality what's the
+ 
+
+ align:start position:0%
+uh in markov's inequality what's the
+bound that we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the bound should be the expectation of
+
+ align:start position:0%
+the bound should be the expectation of
+ 
+
+ align:start position:0%
+the bound should be the expectation of
+our random variable
+
+ align:start position:0%
+our random variable
+ 
+
+ align:start position:0%
+our random variable
+right so can we Define a random variable
+
+ align:start position:0%
+right so can we Define a random variable
+ 
+
+ align:start position:0%
+right so can we Define a random variable
+whose expectation is the variance of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah exactly so R Prime equals R
+
+ align:start position:0%
+yeah yeah exactly so R Prime equals R
+ 
+
+ align:start position:0%
+yeah yeah exactly so R Prime equals R
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation
+
+ align:start position:0%
+expectation
+ 
+
+ align:start position:0%
+expectation
+squared okay
+
+ align:start position:0%
+squared okay
+ 
+
+ align:start position:0%
+squared okay
+so this is non- negative right it's it's
+
+ align:start position:0%
+so this is non- negative right it's it's
+ 
+
+ align:start position:0%
+so this is non- negative right it's it's
+a square of some
+
+ align:start position:0%
+a square of some
+ 
+
+ align:start position:0%
+a square of some
+value uh its expectation you know by
+
+ align:start position:0%
+value uh its expectation you know by
+ 
+
+ align:start position:0%
+value uh its expectation you know by
+definition is the variance of
+
+ align:start position:0%
+definition is the variance of
+ 
+
+ align:start position:0%
+definition is the variance of
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+okay and also if we kind of squint right
+
+ align:start position:0%
+okay and also if we kind of squint right
+ 
+
+ align:start position:0%
+okay and also if we kind of squint right
+we can fiddle around with this to you
+
+ align:start position:0%
+we can fiddle around with this to you
+ 
+
+ align:start position:0%
+we can fiddle around with this to you
+know actually threshold R Prime instead
+
+ align:start position:0%
+know actually threshold R Prime instead
+ 
+
+ align:start position:0%
+know actually threshold R Prime instead
+of this absolute value thing that we've
+
+ align:start position:0%
+of this absolute value thing that we've
+ 
+
+ align:start position:0%
+of this absolute value thing that we've
+got here how do we do
+
+ align:start position:0%
+got here how do we do
+ 
+
+ align:start position:0%
+got here how do we do
+that well we just Square the stuff in
+
+ align:start position:0%
+that well we just Square the stuff in
+ 
+
+ align:start position:0%
+that well we just Square the stuff in
+the absolute value right as the same
+
+ align:start position:0%
+the absolute value right as the same
+ 
+
+ align:start position:0%
+the absolute value right as the same
+square as if we didn't have the absolute
+
+ align:start position:0%
+square as if we didn't have the absolute
+ 
+
+ align:start position:0%
+square as if we didn't have the absolute
+value okay so the
+
+ align:start position:0%
+value okay so the
+ 
+
+ align:start position:0%
+value okay so the
+probability that R minus its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation greater than or equal to
+
+ align:start position:0%
+expectation greater than or equal to
+ 
+
+ align:start position:0%
+expectation greater than or equal to
+x equals the
+
+ align:start position:0%
+x equals the
+ 
+
+ align:start position:0%
+x equals the
+probability that R
+
+ align:start position:0%
+probability that R
+ 
+
+ align:start position:0%
+probability that R
+Prime is greater than or equal to
+
+ align:start position:0%
+Prime is greater than or equal to
+ 
+
+ align:start position:0%
+Prime is greater than or equal to
+x^2 right because those are exactly the
+
+ align:start position:0%
+x^2 right because those are exactly the
+ 
+
+ align:start position:0%
+x^2 right because those are exactly the
+same event
+
+ align:start position:0%
+same event
+ 
+
+ align:start position:0%
+same event
+okay they're the same event so they have
+
+ align:start position:0%
+okay they're the same event so they have
+ 
+
+ align:start position:0%
+okay they're the same event so they have
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+probability and now this looks like
+
+ align:start position:0%
+probability and now this looks like
+ 
+
+ align:start position:0%
+probability and now this looks like
+something we can apply Markov to okay
+
+ align:start position:0%
+something we can apply Markov to okay
+ 
+
+ align:start position:0%
+something we can apply Markov to okay
+less than or equal to the
+
+ align:start position:0%
+less than or equal to the
+ 
+
+ align:start position:0%
+less than or equal to the
+expectation of R Prime
+
+ align:start position:0%
+expectation of R Prime
+ 
+
+ align:start position:0%
+expectation of R Prime
+oops divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x^2 okay does that make sense to
+
+ align:start position:0%
+x^2 okay does that make sense to
+ 
+
+ align:start position:0%
+x^2 okay does that make sense to
+everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take a look at an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example so let's look at those test
+
+ align:start position:0%
+example so let's look at those test
+ 
+
+ align:start position:0%
+example so let's look at those test
+scores
+
+ align:start position:0%
+scores
+ 
+
+ align:start position:0%
+scores
+again oops sorry my bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so our same deal we've got test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scores
+
+ align:start position:0%
+scores
+ 
+
+ align:start position:0%
+scores
+expectation is what did we have 70 75
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+75 and say that that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance is
+
+ align:start position:0%
+variance is
+ 
+
+ align:start position:0%
+variance is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay so now what can we
+
+ align:start position:0%
+okay so now what can we
+ 
+
+ align:start position:0%
+okay so now what can we
+say about the probability that R is uh
+
+ align:start position:0%
+say about the probability that R is uh
+ 
+
+ align:start position:0%
+say about the probability that R is uh
+most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+65 any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas how how could we how could we
+
+ align:start position:0%
+ideas how how could we how could we
+ 
+
+ align:start position:0%
+ideas how how could we how could we
+apply treby Chef to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this that doesn't quite look like the
+
+ align:start position:0%
+this that doesn't quite look like the
+ 
+
+ align:start position:0%
+this that doesn't quite look like the
+theorem statement right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we can observe that this is at most
+
+ align:start position:0%
+but we can observe that this is at most
+ 
+
+ align:start position:0%
+but we can observe that this is at most
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+probability that R is at most
+
+ align:start position:0%
+probability that R is at most
+ 
+
+ align:start position:0%
+probability that R is at most
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+or R is greater than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay right if we take the union of two
+
+ align:start position:0%
+okay right if we take the union of two
+ 
+
+ align:start position:0%
+okay right if we take the union of two
+events that Union has you know at least
+
+ align:start position:0%
+events that Union has you know at least
+ 
+
+ align:start position:0%
+events that Union has you know at least
+the probability ility of one of those
+
+ align:start position:0%
+the probability ility of one of those
+ 
+
+ align:start position:0%
+the probability ility of one of those
+two con constituent
+
+ align:start position:0%
+two con constituent
+ 
+
+ align:start position:0%
+two con constituent
+events so this is only increasing the
+
+ align:start position:0%
+events so this is only increasing the
+ 
+
+ align:start position:0%
+events so this is only increasing the
+probability if we add in this this extra
+
+ align:start position:0%
+probability if we add in this this extra
+ 
+
+ align:start position:0%
+probability if we add in this this extra
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know extra half of the
+
+ align:start position:0%
+know extra half of the
+ 
+
+ align:start position:0%
+know extra half of the
+event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and what do we know about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability how could we rewrite that in
+
+ align:start position:0%
+probability how could we rewrite that in
+ 
+
+ align:start position:0%
+probability how could we rewrite that in
+a nicer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+exactly so this is just saying R
+
+ align:start position:0%
+exactly so this is just saying R
+ 
+
+ align:start position:0%
+exactly so this is just saying R
+deviates from its mean by at least 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we've got it in the form
+
+ align:start position:0%
+okay so now we've got it in the form
+ 
+
+ align:start position:0%
+okay so now we've got it in the form
+that chubby CHF
+
+ align:start position:0%
+that chubby CHF
+ 
+
+ align:start position:0%
+that chubby CHF
+likes so we can apply chabby
+
+ align:start position:0%
+likes so we can apply chabby
+ 
+
+ align:start position:0%
+likes so we can apply chabby
+Chev this is at most variance of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r divided
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by uh our threshold is 10 yeah 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squ okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+25 over 100
+
+ align:start position:0%
+25 over 100
+ 
+
+ align:start position:0%
+25 over 100
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+one4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we've got a much stronger bound this
+
+ align:start position:0%
+now we've got a much stronger bound this
+ 
+
+ align:start position:0%
+now we've got a much stronger bound this
+time than we did earlier Yeah question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah okay so explain this
+
+ align:start position:0%
+ah okay so explain this
+ 
+
+ align:start position:0%
+ah okay so explain this
+equality okay uh so R less than or equal
+
+ align:start position:0%
+equality okay uh so R less than or equal
+ 
+
+ align:start position:0%
+equality okay uh so R less than or equal
+to 65 or R greater than or equal to
+
+ align:start position:0%
+to 65 or R greater than or equal to
+ 
+
+ align:start position:0%
+to 65 or R greater than or equal to
+85 um we could rewrite this as you know
+
+ align:start position:0%
+85 um we could rewrite this as you know
+ 
+
+ align:start position:0%
+85 um we could rewrite this as you know
+R minus uh well r -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+75 is uh less than or equal to -10 and
+
+ align:start position:0%
+75 is uh less than or equal to -10 and
+ 
+
+ align:start position:0%
+75 is uh less than or equal to -10 and
+this one is r - 75
+
+ align:start position:0%
+this one is r - 75
+ 
+
+ align:start position:0%
+this one is r - 75
+greater than or equal to positive
+
+ align:start position:0%
+greater than or equal to positive
+ 
+
+ align:start position:0%
+greater than or equal to positive
+10 okay um so you know if you absolute
+
+ align:start position:0%
+10 okay um so you know if you absolute
+ 
+
+ align:start position:0%
+10 okay um so you know if you absolute
+value both of these you know they're
+
+ align:start position:0%
+value both of these you know they're
+ 
+
+ align:start position:0%
+value both of these you know they're
+both you know greater than greater than
+
+ align:start position:0%
+both you know greater than greater than
+ 
+
+ align:start position:0%
+both you know greater than greater than
+or equal to 10 okay does does that kind
+
+ align:start position:0%
+or equal to 10 okay does does that kind
+ 
+
+ align:start position:0%
+or equal to 10 okay does does that kind
+of make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any other questions about uh about
+
+ align:start position:0%
+okay any other questions about uh about
+ 
+
+ align:start position:0%
+okay any other questions about uh about
+this this example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so because we have more information than
+
+ align:start position:0%
+so because we have more information than
+ 
+
+ align:start position:0%
+so because we have more information than
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+had here right we can get a stronger
+
+ align:start position:0%
+had here right we can get a stronger
+ 
+
+ align:start position:0%
+had here right we can get a stronger
+bound okay knowing the variance helps us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out so equivalently we could you know
+
+ align:start position:0%
+out so equivalently we could you know
+ 
+
+ align:start position:0%
+out so equivalently we could you know
+rephrase this in terms of uh you know
+
+ align:start position:0%
+rephrase this in terms of uh you know
+ 
+
+ align:start position:0%
+rephrase this in terms of uh you know
+standard
+
+ align:start position:0%
+standard
+ 
+
+ align:start position:0%
+standard
+deviations uh um where would be a good
+
+ align:start position:0%
+deviations uh um where would be a good
+ 
+
+ align:start position:0%
+deviations uh um where would be a good
+place to write
+
+ align:start position:0%
+place to write
+ 
+
+ align:start position:0%
+place to write
+this how about
+
+ align:start position:0%
+this how about
+ 
+
+ align:start position:0%
+this how about
+here so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability of
+
+ align:start position:0%
+probability of
+ 
+
+ align:start position:0%
+probability of
+being at least two standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviations from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean is at most
+
+ align:start position:0%
+mean is at most
+ 
+
+ align:start position:0%
+mean is at most
+1/4 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anybody have any objections to that
+
+ align:start position:0%
+does anybody have any objections to that
+ 
+
+ align:start position:0%
+does anybody have any objections to that
+last statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you've uh taken a stats class you
+
+ align:start position:0%
+so if you've uh taken a stats class you
+ 
+
+ align:start position:0%
+so if you've uh taken a stats class you
+probably heard something very different
+
+ align:start position:0%
+probably heard something very different
+ 
+
+ align:start position:0%
+probably heard something very different
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that oh nobody nobody's taken
+
+ align:start position:0%
+that oh nobody nobody's taken
+ 
+
+ align:start position:0%
+that oh nobody nobody's taken
+stats that's good high school stats is
+
+ align:start position:0%
+stats that's good high school stats is
+ 
+
+ align:start position:0%
+stats that's good high school stats is
+terrible um um oh that's on camera um
+
+ align:start position:0%
+terrible um um oh that's on camera um
+ 
+
+ align:start position:0%
+terrible um um oh that's on camera um
+never mind stats are great just uh it's
+
+ align:start position:0%
+never mind stats are great just uh it's
+ 
+
+ align:start position:0%
+never mind stats are great just uh it's
+it's good that that you've saved it for
+
+ align:start position:0%
+it's good that that you've saved it for
+ 
+
+ align:start position:0%
+it's good that that you've saved it for
+University instead of doing it in high
+
+ align:start position:0%
+University instead of doing it in high
+ 
+
+ align:start position:0%
+University instead of doing it in high
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+um okay so yeah if if you're looking at
+
+ align:start position:0%
+um okay so yeah if if you're looking at
+ 
+
+ align:start position:0%
+um okay so yeah if if you're looking at
+a a you know a normal distribution right
+
+ align:start position:0%
+a a you know a normal distribution right
+ 
+
+ align:start position:0%
+a a you know a normal distribution right
+you actually have a much a much better
+
+ align:start position:0%
+you actually have a much a much better
+ 
+
+ align:start position:0%
+you actually have a much a much better
+bound than than 1/4 it's something like
+
+ align:start position:0%
+bound than than 1/4 it's something like
+ 
+
+ align:start position:0%
+bound than than 1/4 it's something like
+you know a few
+
+ align:start position:0%
+you know a few
+ 
+
+ align:start position:0%
+you know a few
+percent okay uh so why is
+
+ align:start position:0%
+percent okay uh so why is
+ 
+
+ align:start position:0%
+percent okay uh so why is
+that any ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well for normal distribution right we
+
+ align:start position:0%
+well for normal distribution right we
+ 
+
+ align:start position:0%
+well for normal distribution right we
+know a lot more about the uh about the
+
+ align:start position:0%
+know a lot more about the uh about the
+ 
+
+ align:start position:0%
+know a lot more about the uh about the
+random variable than just its
+
+ align:start position:0%
+random variable than just its
+ 
+
+ align:start position:0%
+random variable than just its
+variance okay so if we know more even
+
+ align:start position:0%
+variance okay so if we know more even
+ 
+
+ align:start position:0%
+variance okay so if we know more even
+more about a random variable than its
+
+ align:start position:0%
+more about a random variable than its
+ 
+
+ align:start position:0%
+more about a random variable than its
+variance it turns out we can make even
+
+ align:start position:0%
+variance it turns out we can make even
+ 
+
+ align:start position:0%
+variance it turns out we can make even
+stronger
+
+ align:start position:0%
+stronger
+ 
+
+ align:start position:0%
+stronger
+statements okay just like adding in the
+
+ align:start position:0%
+statements okay just like adding in the
+ 
+
+ align:start position:0%
+statements okay just like adding in the
+variance was an upgrade from marov let's
+
+ align:start position:0%
+variance was an upgrade from marov let's
+ 
+
+ align:start position:0%
+variance was an upgrade from marov let's
+see how we can upgrade this again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what's upal distrib oh what's a
+
+ align:start position:0%
+yeah what's upal distrib oh what's a
+ 
+
+ align:start position:0%
+yeah what's upal distrib oh what's a
+normal distribution uh think of a normal
+
+ align:start position:0%
+normal distribution uh think of a normal
+ 
+
+ align:start position:0%
+normal distribution uh think of a normal
+distribution as um you know number of
+
+ align:start position:0%
+distribution as um you know number of
+ 
+
+ align:start position:0%
+distribution as um you know number of
+heads if you flip a whole bunch of coins
+
+ align:start position:0%
+heads if you flip a whole bunch of coins
+ 
+
+ align:start position:0%
+heads if you flip a whole bunch of coins
+it's that's not quite it but you know
+
+ align:start position:0%
+it's that's not quite it but you know
+ 
+
+ align:start position:0%
+it's that's not quite it but you know
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+speaking good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cutch oh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah as I just said if you flip
+
+ align:start position:0%
+okay so yeah as I just said if you flip
+ 
+
+ align:start position:0%
+okay so yeah as I just said if you flip
+a whole bunch of coins let your random
+
+ align:start position:0%
+a whole bunch of coins let your random
+ 
+
+ align:start position:0%
+a whole bunch of coins let your random
+variable R be the the number of heads
+
+ align:start position:0%
+variable R be the the number of heads
+ 
+
+ align:start position:0%
+variable R be the the number of heads
+right uh you know a lot more about uh
+
+ align:start position:0%
+right uh you know a lot more about uh
+ 
+
+ align:start position:0%
+right uh you know a lot more about uh
+about this random variable than just its
+
+ align:start position:0%
+about this random variable than just its
+ 
+
+ align:start position:0%
+about this random variable than just its
+variance right you're you can decompose
+
+ align:start position:0%
+variance right you're you can decompose
+ 
+
+ align:start position:0%
+variance right you're you can decompose
+the random variable into a sum of a
+
+ align:start position:0%
+the random variable into a sum of a
+ 
+
+ align:start position:0%
+the random variable into a sum of a
+whole bunch of
+
+ align:start position:0%
+whole bunch of
+ 
+
+ align:start position:0%
+whole bunch of
+indicators okay and all of those
+
+ align:start position:0%
+indicators okay and all of those
+ 
+
+ align:start position:0%
+indicators okay and all of those
+indicators are mutually
+
+ align:start position:0%
+indicators are mutually
+ 
+
+ align:start position:0%
+indicators are mutually
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um in order to use chubby Chev right you
+
+ align:start position:0%
+um in order to use chubby Chev right you
+ 
+
+ align:start position:0%
+um in order to use chubby Chev right you
+don't need Mutual Independence right if
+
+ align:start position:0%
+don't need Mutual Independence right if
+ 
+
+ align:start position:0%
+don't need Mutual Independence right if
+you had something of that form you just
+
+ align:start position:0%
+you had something of that form you just
+ 
+
+ align:start position:0%
+you had something of that form you just
+need parir wise Independence right like
+
+ align:start position:0%
+need parir wise Independence right like
+ 
+
+ align:start position:0%
+need parir wise Independence right like
+you need to compute the
+
+ align:start position:0%
+you need to compute the
+ 
+
+ align:start position:0%
+you need to compute the
+variance okay
+
+ align:start position:0%
+variance okay
+ 
+
+ align:start position:0%
+variance okay
+but if on top of that you have mutual
+
+ align:start position:0%
+but if on top of that you have mutual
+ 
+
+ align:start position:0%
+but if on top of that you have mutual
+Independence it turns out you can do a
+
+ align:start position:0%
+Independence it turns out you can do a
+ 
+
+ align:start position:0%
+Independence it turns out you can do a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+better okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh T1 T2
+
+ align:start position:0%
+uh T1 T2
+ 
+
+ align:start position:0%
+uh T1 T2
+T3 up to TN are mutually independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+variables and uh well let's say in
+
+ align:start position:0%
+variables and uh well let's say in
+ 
+
+ align:start position:0%
+variables and uh well let's say in
+addition they're
+
+ align:start position:0%
+addition they're
+ 
+
+ align:start position:0%
+addition they're
+bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay and the random variable we actually
+
+ align:start position:0%
+okay and the random variable we actually
+ 
+
+ align:start position:0%
+okay and the random variable we actually
+care about is T which is their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then oh and uh say we've also got some
+
+ align:start position:0%
+then oh and uh say we've also got some
+ 
+
+ align:start position:0%
+then oh and uh say we've also got some
+threshold C which is at least
+
+ align:start position:0%
+threshold C which is at least
+ 
+
+ align:start position:0%
+threshold C which is at least
+one uh the probability
+
+ align:start position:0%
+one uh the probability
+ 
+
+ align:start position:0%
+one uh the probability
+that t is at least c times its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation uh close that as well less
+
+ align:start position:0%
+expectation uh close that as well less
+ 
+
+ align:start position:0%
+expectation uh close that as well less
+than or equal to e to the
+
+ align:start position:0%
+than or equal to e to the
+ 
+
+ align:start position:0%
+than or equal to e to the
+negative C log of C minus C +
+
+ align:start position:0%
+negative C log of C minus C +
+ 
+
+ align:start position:0%
+negative C log of C minus C +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+times uh the
+
+ align:start position:0%
+times uh the
+ 
+
+ align:start position:0%
+times uh the
+expectation of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a little bit of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mouthful but what exactly is going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so basically marov was saying right
+
+ align:start position:0%
+here so basically marov was saying right
+ 
+
+ align:start position:0%
+here so basically marov was saying right
+uh that the the probability that you you
+
+ align:start position:0%
+uh that the the probability that you you
+ 
+
+ align:start position:0%
+uh that the the probability that you you
+know deviate from from the mean by a
+
+ align:start position:0%
+know deviate from from the mean by a
+ 
+
+ align:start position:0%
+know deviate from from the mean by a
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+amount uh it's at most you
+
+ align:start position:0%
+amount uh it's at most you
+ 
+
+ align:start position:0%
+amount uh it's at most you
+know it's at most linear in in you know
+
+ align:start position:0%
+know it's at most linear in in you know
+ 
+
+ align:start position:0%
+know it's at most linear in in you know
+how how far you're you're you're
+
+ align:start position:0%
+how how far you're you're you're
+ 
+
+ align:start position:0%
+how how far you're you're you're
+deviating okay Chev said it's uh you
+
+ align:start position:0%
+deviating okay Chev said it's uh you
+ 
+
+ align:start position:0%
+deviating okay Chev said it's uh you
+know at most quadratic this is saying
+
+ align:start position:0%
+know at most quadratic this is saying
+ 
+
+ align:start position:0%
+know at most quadratic this is saying
+it's at most exponential or like inverse
+
+ align:start position:0%
+it's at most exponential or like inverse
+ 
+
+ align:start position:0%
+it's at most exponential or like inverse
+exponential okay so you have a much
+
+ align:start position:0%
+exponential okay so you have a much
+ 
+
+ align:start position:0%
+exponential okay so you have a much
+stronger condition that gives you a much
+
+ align:start position:0%
+stronger condition that gives you a much
+ 
+
+ align:start position:0%
+stronger condition that gives you a much
+stronger bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh and how could we prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it not like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe a proof sketch we we won't go
+
+ align:start position:0%
+maybe a proof sketch we we won't go
+ 
+
+ align:start position:0%
+maybe a proof sketch we we won't go
+through the entire proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what what tools do we have already
+
+ align:start position:0%
+so what what tools do we have already
+ 
+
+ align:start position:0%
+so what what tools do we have already
+what might we be able to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what happens if we apply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Markov how can we apply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Markov in order to use Markov right we
+
+ align:start position:0%
+Markov in order to use Markov right we
+ 
+
+ align:start position:0%
+Markov in order to use Markov right we
+need a non- negative random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable so in order to prove chubby
+
+ align:start position:0%
+variable so in order to prove chubby
+ 
+
+ align:start position:0%
+variable so in order to prove chubby
+right we uh you know took a square that
+
+ align:start position:0%
+right we uh you know took a square that
+ 
+
+ align:start position:0%
+right we uh you know took a square that
+made something non-
+
+ align:start position:0%
+made something non-
+ 
+
+ align:start position:0%
+made something non-
+negative what might be a reasonable
+
+ align:start position:0%
+negative what might be a reasonable
+ 
+
+ align:start position:0%
+negative what might be a reasonable
+thing to try in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+yeah add
+
+ align:start position:0%
+yeah add
+ 
+
+ align:start position:0%
+yeah add
+one uh okay so
+
+ align:start position:0%
+one uh okay so
+ 
+
+ align:start position:0%
+one uh okay so
+look at t + one instead of uh instead of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T so that's actually going to that's not
+
+ align:start position:0%
+T so that's actually going to that's not
+ 
+
+ align:start position:0%
+T so that's actually going to that's not
+going to help us right T is already the
+
+ align:start position:0%
+going to help us right T is already the
+ 
+
+ align:start position:0%
+going to help us right T is already the
+sum of a bunch of non- negative random
+
+ align:start position:0%
+sum of a bunch of non- negative random
+ 
+
+ align:start position:0%
+sum of a bunch of non- negative random
+variables so it's already non- negative
+
+ align:start position:0%
+variables so it's already non- negative
+ 
+
+ align:start position:0%
+variables so it's already non- negative
+right like we're we're not looking to
+
+ align:start position:0%
+right like we're we're not looking to
+ 
+
+ align:start position:0%
+right like we're we're not looking to
+you know turn a non- negative or sorry
+
+ align:start position:0%
+you know turn a non- negative or sorry
+ 
+
+ align:start position:0%
+you know turn a non- negative or sorry
+turn an arbitrary random variable into a
+
+ align:start position:0%
+turn an arbitrary random variable into a
+ 
+
+ align:start position:0%
+turn an arbitrary random variable into a
+non negative one we are trying to find a
+
+ align:start position:0%
+non negative one we are trying to find a
+ 
+
+ align:start position:0%
+non negative one we are trying to find a
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+useful uh non- negative random
+
+ align:start position:0%
+useful uh non- negative random
+ 
+
+ align:start position:0%
+useful uh non- negative random
+variable okay
+
+ align:start position:0%
+variable okay
+ 
+
+ align:start position:0%
+variable okay
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah take the log of both sides close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens if we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponentiate
+
+ align:start position:0%
+exponentiate
+ 
+
+ align:start position:0%
+exponentiate
+so take T Prime equals c to the T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we know about t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we're taking something that's at
+
+ align:start position:0%
+well we're taking something that's at
+ 
+
+ align:start position:0%
+well we're taking something that's at
+least one right or you know raising it
+
+ align:start position:0%
+least one right or you know raising it
+ 
+
+ align:start position:0%
+least one right or you know raising it
+to some positive power well some non-
+
+ align:start position:0%
+to some positive power well some non-
+ 
+
+ align:start position:0%
+to some positive power well some non-
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so T Prime is a non negative random
+
+ align:start position:0%
+okay so T Prime is a non negative random
+ 
+
+ align:start position:0%
+okay so T Prime is a non negative random
+variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do we know anything more about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah it's at least one
+
+ align:start position:0%
+it yeah it's at least one
+ 
+
+ align:start position:0%
+it yeah it's at least one
+yeah so maybe we try applying markup to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay so now we've got a random
+
+ align:start position:0%
+this okay so now we've got a random
+ 
+
+ align:start position:0%
+this okay so now we've got a random
+variable that takes values in the range
+
+ align:start position:0%
+variable that takes values in the range
+ 
+
+ align:start position:0%
+variable that takes values in the range
+from 0 to uh C the n c the N minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay now how could we rewrite this
+
+ align:start position:0%
+okay now how could we rewrite this
+ 
+
+ align:start position:0%
+okay now how could we rewrite this
+condition T greater than or equal to C
+
+ align:start position:0%
+condition T greater than or equal to C
+ 
+
+ align:start position:0%
+condition T greater than or equal to C
+* expectation of T in terms of T Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well because C is at least one
+
+ align:start position:0%
+well because C is at least one
+ 
+
+ align:start position:0%
+well because C is at least one
+right exponentiation is
+
+ align:start position:0%
+right exponentiation is
+ 
+
+ align:start position:0%
+right exponentiation is
+monotone so this is the same as you know
+
+ align:start position:0%
+monotone so this is the same as you know
+ 
+
+ align:start position:0%
+monotone so this is the same as you know
+C to the T greater than or equal to uh C
+
+ align:start position:0%
+C to the T greater than or equal to uh C
+ 
+
+ align:start position:0%
+C to the T greater than or equal to uh C
+to the C *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we don't have too much time so
+
+ align:start position:0%
+okay and we don't have too much time so
+ 
+
+ align:start position:0%
+okay and we don't have too much time so
+I think I will refer you to the book if
+
+ align:start position:0%
+I think I will refer you to the book if
+ 
+
+ align:start position:0%
+I think I will refer you to the book if
+you are interested but the the main idea
+
+ align:start position:0%
+you are interested but the the main idea
+ 
+
+ align:start position:0%
+you are interested but the the main idea
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+is this step here
+
+ align:start position:0%
+is this step here
+ 
+
+ align:start position:0%
+is this step here
+okay you take the random variable you
+
+ align:start position:0%
+okay you take the random variable you
+ 
+
+ align:start position:0%
+okay you take the random variable you
+care about and you exponentiate
+
+ align:start position:0%
+care about and you exponentiate
+ 
+
+ align:start position:0%
+care about and you exponentiate
+it okay and then if you apply apply
+
+ align:start position:0%
+it okay and then if you apply apply
+ 
+
+ align:start position:0%
+it okay and then if you apply apply
+Markov to that right it actually gives
+
+ align:start position:0%
+Markov to that right it actually gives
+ 
+
+ align:start position:0%
+Markov to that right it actually gives
+you a much stronger bound like you know
+
+ align:start position:0%
+you a much stronger bound like you know
+ 
+
+ align:start position:0%
+you a much stronger bound like you know
+if you're if you're using the the mutal
+
+ align:start position:0%
+if you're if you're using the the mutal
+ 
+
+ align:start position:0%
+if you're if you're using the the mutal
+independence of all of the component
+
+ align:start position:0%
+independence of all of the component
+ 
+
+ align:start position:0%
+independence of all of the component
+random variables
+
+ align:start position:0%
+random variables
+ 
+
+ align:start position:0%
+random variables
+right this will give you a much stronger
+
+ align:start position:0%
+right this will give you a much stronger
+ 
+
+ align:start position:0%
+right this will give you a much stronger
+bound than uh than even Shoff okay so I
+
+ align:start position:0%
+bound than uh than even Shoff okay so I
+ 
+
+ align:start position:0%
+bound than uh than even Shoff okay so I
+promised you last week that uh you know
+
+ align:start position:0%
+promised you last week that uh you know
+ 
+
+ align:start position:0%
+promised you last week that uh you know
+we would revisit the uh the coin tosses
+
+ align:start position:0%
+we would revisit the uh the coin tosses
+ 
+
+ align:start position:0%
+we would revisit the uh the coin tosses
+so let's do that
+
+ align:start position:0%
+so let's do that
+ 
+
+ align:start position:0%
+so let's do that
+briefly okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose R is the
+
+ align:start position:0%
+suppose R is the
+ 
+
+ align:start position:0%
+suppose R is the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+heads uh if you flip end coins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you recall we were looking at
+
+ align:start position:0%
+okay so if you recall we were looking at
+ 
+
+ align:start position:0%
+okay so if you recall we were looking at
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+probability that R is uh equal to you
+
+ align:start position:0%
+probability that R is uh equal to you
+ 
+
+ align:start position:0%
+probability that R is uh equal to you
+know n
+
+ align:start position:0%
+know n
+ 
+
+ align:start position:0%
+know n
+over4
+
+ align:start position:0%
+over4
+ 
+
+ align:start position:0%
+over4
+before okay so or maybe
+
+ align:start position:0%
+before okay so or maybe
+ 
+
+ align:start position:0%
+before okay so or maybe
+equivalently three over
+
+ align:start position:0%
+equivalently three over
+ 
+
+ align:start position:0%
+equivalently three over
+4 might be a better way to
+
+ align:start position:0%
+4 might be a better way to
+ 
+
+ align:start position:0%
+4 might be a better way to
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+analogize okay and I promised you that
+
+ align:start position:0%
+analogize okay and I promised you that
+ 
+
+ align:start position:0%
+analogize okay and I promised you that
+we would
+
+ align:start position:0%
+we would
+ 
+
+ align:start position:0%
+we would
+revisit this probability R greater than
+
+ align:start position:0%
+revisit this probability R greater than
+ 
+
+ align:start position:0%
+revisit this probability R greater than
+or equal to 3 n /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what happens if we apply
+
+ align:start position:0%
+okay now what happens if we apply
+ 
+
+ align:start position:0%
+okay now what happens if we apply
+uh each of our three tail bounds to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R well first what happens with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Markov so let's call this p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p is at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what well the probability that R is at
+
+ align:start position:0%
+what well the probability that R is at
+ 
+
+ align:start position:0%
+what well the probability that R is at
+least you know some
+
+ align:start position:0%
+least you know some
+ 
+
+ align:start position:0%
+least you know some
+threshold it's going to be the
+
+ align:start position:0%
+threshold it's going to be the
+ 
+
+ align:start position:0%
+threshold it's going to be the
+expectation of
+
+ align:start position:0%
+expectation of
+ 
+
+ align:start position:0%
+expectation of
+r divided by this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+threshold okay what's the expectation of
+
+ align:start position:0%
+threshold okay what's the expectation of
+ 
+
+ align:start position:0%
+threshold okay what's the expectation of
+R and over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+okay so this is going to be 2/3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about chubby
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shf so similar to what we did with the
+
+ align:start position:0%
+shf so similar to what we did with the
+ 
+
+ align:start position:0%
+shf so similar to what we did with the
+first chbby Chev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example right p is going to be at most
+
+ align:start position:0%
+example right p is going to be at most
+ 
+
+ align:start position:0%
+example right p is going to be at most
+the probability that uh R differs from
+
+ align:start position:0%
+the probability that uh R differs from
+ 
+
+ align:start position:0%
+the probability that uh R differs from
+its it expectation in either
+
+ align:start position:0%
+its it expectation in either
+ 
+
+ align:start position:0%
+its it expectation in either
+direction right by
+
+ align:start position:0%
+direction right by
+ 
+
+ align:start position:0%
+direction right by
+n/4
+
+ align:start position:0%
+n/4
+ 
+
+ align:start position:0%
+n/4
+okay so what does that give us uh
+
+ align:start position:0%
+okay so what does that give us uh
+ 
+
+ align:start position:0%
+okay so what does that give us uh
+probability R minus let's say over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+uh greater than or equal to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over4 is at most
+
+ align:start position:0%
+over4 is at most
+ 
+
+ align:start position:0%
+over4 is at most
+bar of
+
+ align:start position:0%
+bar of
+ 
+
+ align:start position:0%
+bar of
+r divided by uh n over 4^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s okay so what is the uh what is the
+
+ align:start position:0%
+s okay so what is the uh what is the
+ 
+
+ align:start position:0%
+s okay so what is the uh what is the
+variance of r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember we've got a sum of a bunch of
+
+ align:start position:0%
+remember we've got a sum of a bunch of
+ 
+
+ align:start position:0%
+remember we've got a sum of a bunch of
+indicators right they're all mutually
+
+ align:start position:0%
+indicators right they're all mutually
+ 
+
+ align:start position:0%
+indicators right they're all mutually
+independent so the variance is
+
+ align:start position:0%
+independent so the variance is
+ 
+
+ align:start position:0%
+independent so the variance is
+linear what's the variance of a single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indicator
+
+ align:start position:0%
+indicator
+ 
+
+ align:start position:0%
+indicator
+nobody yeah
+
+ align:start position:0%
+nobody yeah
+ 
+
+ align:start position:0%
+nobody yeah
+yeah n over four oh for for R not for a
+
+ align:start position:0%
+yeah n over four oh for for R not for a
+ 
+
+ align:start position:0%
+yeah n over four oh for for R not for a
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay so n over 4 / n^2 over
+
+ align:start position:0%
+okay so n over 4 / n^2 over
+ 
+
+ align:start position:0%
+okay so n over 4 / n^2 over
+16 equal 4
+
+ align:start position:0%
+16 equal 4
+ 
+
+ align:start position:0%
+16 equal 4
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay so much better right much better
+
+ align:start position:0%
+okay so much better right much better
+ 
+
+ align:start position:0%
+okay so much better right much better
+than the 2/3 we just
+
+ align:start position:0%
+than the 2/3 we just
+ 
+
+ align:start position:0%
+than the 2/3 we just
+got what happens if we use turnoff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any
+
+ align:start position:0%
+okay any
+ 
+
+ align:start position:0%
+okay any
+ideas
+
+ align:start position:0%
+ideas
+ 
+
+ align:start position:0%
+ideas
+yeah plug in three halves for C so c
+
+ align:start position:0%
+yeah plug in three halves for C so c
+ 
+
+ align:start position:0%
+yeah plug in three halves for C so c
+equal 3
+
+ align:start position:0%
+equal 3
+ 
+
+ align:start position:0%
+equal 3
+Hales okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay um why don't I uh put TR off
+
+ align:start position:0%
+uh okay um why don't I uh put TR off
+ 
+
+ align:start position:0%
+uh okay um why don't I uh put TR off
+back up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and what does that give us
+
+ align:start position:0%
+okay and what does that give us
+ 
+
+ align:start position:0%
+okay and what does that give us
+probability that uh R is is at least 3es
+
+ align:start position:0%
+probability that uh R is is at least 3es
+ 
+
+ align:start position:0%
+probability that uh R is is at least 3es
+time expectation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R is less than or equal to e to the
+
+ align:start position:0%
+R is less than or equal to e to the
+ 
+
+ align:start position:0%
+R is less than or equal to e to the
+minus is it C log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C minus C + 1 so this is a constant
+
+ align:start position:0%
+C minus C + 1 so this is a constant
+ 
+
+ align:start position:0%
+C minus C + 1 so this is a constant
+times the expectation of
+
+ align:start position:0%
+times the expectation of
+ 
+
+ align:start position:0%
+times the expectation of
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+okay so the expectation of r R is n
+
+ align:start position:0%
+okay so the expectation of r R is n
+ 
+
+ align:start position:0%
+okay so the expectation of r R is n
+/2 right this is a constant so we've got
+
+ align:start position:0%
+/2 right this is a constant so we've got
+ 
+
+ align:start position:0%
+/2 right this is a constant so we've got
+something that's exponential or inverse
+
+ align:start position:0%
+something that's exponential or inverse
+ 
+
+ align:start position:0%
+something that's exponential or inverse
+exponential in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh e to the minus order
+
+ align:start position:0%
+uh e to the minus order
+ 
+
+ align:start position:0%
+uh e to the minus order
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so marov gives us gave us a really
+
+ align:start position:0%
+okay so marov gives us gave us a really
+ 
+
+ align:start position:0%
+okay so marov gives us gave us a really
+bad found chabby Chev you know
+
+ align:start position:0%
+bad found chabby Chev you know
+ 
+
+ align:start position:0%
+bad found chabby Chev you know
+linear pretty reasonable turn off gives
+
+ align:start position:0%
+linear pretty reasonable turn off gives
+ 
+
+ align:start position:0%
+linear pretty reasonable turn off gives
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+exponential okay so that's all we have
+
+ align:start position:0%
+exponential okay so that's all we have
+ 
+
+ align:start position:0%
+exponential okay so that's all we have
+time for today sorry I went a little bit
+
+ align:start position:0%
+time for today sorry I went a little bit
+ 
+
+ align:start position:0%
+time for today sorry I went a little bit
+overtime uh it's been a pleasure
+
+ align:start position:0%
+overtime uh it's been a pleasure
+ 
+
+ align:start position:0%
+overtime uh it's been a pleasure
+teaching you all this semester um and uh
+
+ align:start position:0%
+teaching you all this semester um and uh
+ 
+
+ align:start position:0%
+teaching you all this semester um and uh
+let's see we have uh the rest of our
+
+ align:start position:0%
+let's see we have uh the rest of our
+ 
+
+ align:start position:0%
+let's see we have uh the rest of our
+instructors and at least one ta hello
+
+ align:start position:0%
+instructors and at least one ta hello
+ 
+
+ align:start position:0%
+instructors and at least one ta hello
+Lily uh yeah if anything went wrong it
+
+ align:start position:0%
+Lily uh yeah if anything went wrong it
+ 
+
+ align:start position:0%
+Lily uh yeah if anything went wrong it
+was probably my fault um anything that
+
+ align:start position:0%
+was probably my fault um anything that
+ 
+
+ align:start position:0%
+was probably my fault um anything that
+went right uh you have your Tas to thank
+
+ align:start position:0%
+went right uh you have your Tas to thank
+ 
+
+ align:start position:0%
+went right uh you have your Tas to thank
+for it um including Lily ly Lily's
+
+ align:start position:0%
+for it um including Lily ly Lily's
+ 
+
+ align:start position:0%
+for it um including Lily ly Lily's
+amazing um so yeah perhaps I will see
+
+ align:start position:0%
+amazing um so yeah perhaps I will see
+ 
+
+ align:start position:0%
+amazing um so yeah perhaps I will see
+some of you uh next term in uh in 61 121
+
+ align:start position:0%
+some of you uh next term in uh in 61 121
+ 
+
+ align:start position:0%
+some of you uh next term in uh in 61 121
+um good luck on the final make sure you
+
+ align:start position:0%
+um good luck on the final make sure you
+ 
+
+ align:start position:0%
+um good luck on the final make sure you
+take the right one uh thanks for being
+
+ align:start position:0%
+take the right one uh thanks for being
+ 
+
+ align:start position:0%
+take the right one uh thanks for being
+students in this class it's been lots of
+
+ align:start position:0%
+students in this class it's been lots of
+ 
+
+ align:start position:0%
+students in this class it's been lots of
+fun yeah
+
+ align:start position:0%
+fun yeah
+ 
+
+ align:start position:0%
+fun yeah
+[Applause]
\ No newline at end of file
diff --git a/88fqFjfxgwI.txt b/88fqFjfxgwI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..19e44e4e90bd350765765525d57f32ee833b7ddc
--- /dev/null
+++ b/88fqFjfxgwI.txt
@@ -0,0 +1,2289 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So the way that I
+envision recitations going is
+
+I'll start off kind of reviewing
+some of the points,
+
+some of the high points from
+lectures, might go into detail
+
+on some of the more
+important topics.
+
+And this is also a time for
+you to ask questions.
+
+There's only 25-30 of you here,
+so you should feel a
+
+little bit more comfortable
+asking questions.
+
+And there are no stupid
+questions here.
+
+For the most part, you're all
+beginners at programming.
+
+Am I wrong?
+
+Has anyone programmed
+here before?
+
+OK.
+
+So presumably, none of you have
+any experience with what
+
+we're talking about.
+
+And so if you ask a question, no
+matter how basic you think
+
+it is, it's not stupid.
+
+Because everyone's been there,
+including me and the professor
+
+when we started programing.
+
+And we've made, ourselves,
+really stupid mistakes too.
+
+So.
+
+That said.
+
+We started out by talking
+about the purpose of the
+
+class, which is to teach you
+how to take problems, real
+
+world problems, break them down,
+abstract them, and divvy
+
+them up so that you can solve
+them with a computer.
+
+And when we talk about computer,
+we're talking about
+
+a very simple model where--
+
+and this is the only time you'll
+see anything related to
+
+hardware in this class.
+
+When we talk about a computer,
+we're talking about something
+
+very simple with a CPU and
+memory and maybe some input
+
+and output.
+
+All right.
+
+And when we talk about programs,
+these are sequences
+
+of instructions that are loaded
+into the computer's
+
+memory which can be divided up
+into little cells like this.
+
+All right.
+
+And what they might
+look like is--
+
+This actually doesn't mean
+anything, but it's just, you
+
+know, for the sake
+of demonstration.
+
+This is what a computer
+would see.
+
+As the CPU starts running
+a program, it looks at
+
+whatever's in this memory
+location and says, this is an
+
+instruction I can handle,
+so I'm gonna go do this.
+
+So this might be like add
+two numbers together
+
+and produce a result.
+
+Something very simple,
+very basic.
+
+And as it moves along in a
+straight line fashion, it just
+
+executes this instruction,
+this instruction, this
+
+instruction, et cetera,
+et cetera.
+
+The problem is is that while
+the computer is perfectly
+
+happy to look at this, this
+is gibberish to us.
+
+And most people, most sane
+people, if they're actually
+
+looking at computer code,
+can't decipher this.
+
+So this is where programming
+languages come in.
+
+We can move up a level.
+
+We can abstract away from this,
+and maybe say something
+
+like this stands for --
+
+move a number into a register
+or something like that.
+
+You don't have to know
+what this means.
+
+All you have to know is that
+this is a little bit more
+
+readable than this.
+
+And it represents an instruction
+that the computer
+
+can understand.
+
+The problem is that even at this
+level, this is still very
+
+atomic and very low level, and
+really you can't understand
+
+what's going on.
+
+So--
+
+just so I can fill this in.
+
+We move into say, I'm gonna say
+x is equal to 1 and I'm
+
+gonna add x plus 5 and
+then multiply by 2.
+
+This is a lot easier for
+us to understand.
+
+And this is what we're talking
+about when we're talking about
+
+any sort of programming
+language that we'll be
+
+studying in this course.
+
+And we're studying Python.
+
+So there are hundreds of
+languages that allow you to
+
+express these concepts in
+a form similar to that.
+
+And all it does is it allows us
+to talk to the computer in
+
+this language.
+
+So everyone good with that?
+
+Cool?
+
+All right.
+
+So when we have these
+programming languages, they're
+
+put together in specific ways.
+
+So does everyone remember
+the term syntax?
+
+Can anyone tell me what it meant
+or means in terms of
+
+programming languages?
+
+AUDIENCE: I could guess.
+
+It is the way that the
+string is structured?
+
+PROFESSOR: Yeah.
+
+It's the way the parts of the
+language are put together.
+
+So let's say that I take a
+very simple statement.
+
+I'm taking a variable
+plus this variable.
+
+This is a valid piece of
+syntax for Python, for
+
+example, or, say, arithmetic,
+or a bunch
+
+of different languages.
+
+So this is good.
+
+I can't write.
+
+On the other hand, if we say
+variable variable plus, this
+
+isn't valid in Python,
+for example.
+
+It might be valid in another
+language, but the syntax of
+
+Python won't allow this.
+
+So this is bad syntax.
+
+So.
+
+All right.
+
+So is everyone kind of
+understand what syntax is?
+
+All right.
+
+What about static semantics?
+
+Talked about that in class.
+
+Can anyone give me kind of a
+rough view of what that is?
+
+Can I choose someone?
+
+All right.
+
+When we talk about static
+semantics, we're talking about
+
+syntactically valid statements
+that mean something.
+
+So let's say that I have
+variable a is equal to 5 and b
+
+is equal to 2.
+
+A statement that's syntactically
+correct and is
+
+also meaningful with respect to
+static semantics could be
+
+something like a divided
+by 2, right.
+
+Or a divided by b.
+
+They're valid statements
+syntactically.
+
+And we know that 5 divided by
+2 or a divided by b, they're
+
+both numbers.
+
+They mean something.
+
+On the other hand, let's
+say that I had this.
+
+I'm gonna say that this variable
+d is a string 'foo'.
+
+All right.
+
+This c divided by d where c is
+a number and d is a string,
+
+that's something that's
+not meaningful, right.
+
+What does a number divided
+by a string mean?
+
+Nothing.
+
+So that's what we're talking
+about with static semantics.
+
+So bad.
+
+These two aspects of computer
+programs are pretty easy to
+
+check for a compiler interpreter
+because they're
+
+pretty explicit rules, right.
+
+The part that we spend most
+of our time in is
+
+the semantic part.
+
+And this is where the syntax
+checks out, the statements are
+
+meaningful in and of themselves,
+but the program as
+
+a whole, or the whole kind
+of recipe, doesn't work.
+
+So as an example, so this,
+as we know is fine.
+
+That's correct.
+
+But let's say we have this.
+
+So a is 6, c is 0.
+
+I do that, what's
+6 divided by 0?
+
+It's an error.
+
+But syntactically
+this is fine.
+
+And by static semantics,
+this is fine.
+
+So this is the type of thing
+we're talking about with the
+
+semantic aspects of a program.
+
+Does it work properly?
+
+And before I jump into Python,
+one tip to keep in mind is
+
+that when you're writing
+programs and you're trying to
+
+do your problem sets, your
+program is very explicit.
+
+It's not ambiguous.
+
+So a program will do what
+you tell it to do and
+
+no more and no less.
+
+And a statement doesn't
+mean two things.
+
+So like if I make the statement
+in English, I cannot
+
+say enough good things or
+recommend this person highly
+
+enough, if you write that out
+that can be considered a
+
+statement with two different
+meanings.
+
+One of them is not too
+complimentary.
+
+All right.
+
+So when you're writing your
+programs, if it's not doing
+
+what you think it's doing, one
+of the skills that you need to
+
+learn throughout the semester is
+to be able to read the code
+
+and try to follow along in your
+mind what's going on.
+
+It's not magic.
+
+OK.
+
+So now we're at Python.
+
+We're past kind of the generic
+
+introductory scaffolding stuff.
+
+Now we're onto something that's
+actually gonna be
+
+meaningful for you for the
+next 12, 13, 14 weeks.
+
+All right.
+
+So Python is a general
+purpose language.
+
+It's used for all sorts of
+things, web development, small
+
+device development, desktop
+programs, et cetera.
+
+It's an interpreted language,
+which means that if I have a
+
+program, blah, blah, blah, blah,
+then Python executes it
+
+for me straight away.
+
+Some languages, compiled
+languages, have to go through
+
+a compiler, and then you
+have to run them.
+
+All right.
+
+It's an extra step.
+
+The nice thing about having an
+interpreted language is that
+
+as you may changes to the code,
+you can instantly see
+
+what's going on with
+your program.
+
+So.
+
+See.
+
+It's got a very simple syntax.
+
+And it's also very widely used
+and has been getting--
+
+more and more people have
+started using it, oh, for the
+
+past, say, 15 years.
+
+So.
+
+10 years ago when I first heard
+about it, it was kind of
+
+like this little
+cute language.
+
+Now it's kind of blossomed into
+this wonderful language
+
+that everyone uses and loves.
+
+So.
+
+Programs in Python, and in all
+languages, are sequences of
+
+expressions.
+
+So this is getting
+back to syntax.
+
+And these expressions, they are
+composed of operands and
+
+operators and functions.
+
+So let's say, for example,
+this is an expression.
+
+This is a variable name.
+
+This is the assignment
+operator, and
+
+this is a string literal.
+
+When I say operand, what
+I'm referring to are
+
+things in the language.
+
+That's what a literal
+and a variable are.
+
+And then if I say operator, this
+is something that does
+
+something to things.
+
+So it's--
+
+this is an example of what we
+call an assignment operator.
+
+What it does is it says, take
+what I'm referring to my right
+
+hand side here, create a name
+called myvar, and say that
+
+every time that I reference
+myvar, I get this value.
+
+We'll talk more about
+that later on.
+
+Um.
+
+Let's see.
+
+Where am I going?
+
+So one important thing to know
+about Python is that
+
+everything--
+
+so these things--
+
+are objects.
+
+For now, you don't have to get
+too familiar with what an
+
+object is just--
+
+if you know anything, especially
+for the first quiz,
+
+this is something to know.
+
+These objects, they
+have types, right.
+
+So some types that we have
+in Python are ints.
+
+What are examples of
+ints or integers?
+
+What?
+
+AUDIENCE: 7.
+
+PROFESSOR: Yeah.
+
+Just rattle a few off.
+
+So 7, 0, negative
+1, 2, et cetera.
+
+Now there's another number
+type, floats, right.
+
+So this is what we normally
+think of as real numbers.
+
+But when you're talking about
+real numbers on the computer,
+
+they are kind of dicey to deal
+with-- and we'll actually
+
+cover that later on in the
+semester when we talk about
+
+kind of the inexactness
+of these.
+
+But for now, just know that
+these are numbers with like
+
+decimal points.
+
+All right.
+
+OK.
+
+Where am I going next?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Actually,
+syntactically, yes.
+
+So one thing that you might
+encounter when you're dealing
+
+with your programs-- this is
+kind of off on a tangent--
+
+is when you say assign a number
+to a variable, when you
+
+have a literal like this number
+here, 0, Python infers
+
+what type you're
+talking about.
+
+So in this case, it's gonna
+create a number, and it's
+
+gonna call it a type integer.
+
+All right.
+
+If it sees this, it's gonna
+create this variable, and it's
+
+gonna have a type of float.
+
+Now, it might seem like
+something minor to you right
+
+now, but when you start doing
+some of the math on problem
+
+set one, if you divide by an
+integer, you might run into
+
+problems, right, because in
+computer-land 5 integer
+
+divided by 2 integer
+is equal to 2.
+
+Whereas in the real world,
+it's equal to that.
+
+So just be aware when you're
+working with numbers that you
+
+need to be aware of their type,
+all right, especially
+
+when you're talking about the
+different operations you can
+
+do on them.
+
+So.
+
+So for these number types, you
+have addition, subtraction,
+
+multiplication, division.
+
+For integers, exponentiation,
+which is
+
+represented by two asterisks.
+
+And for integers, modulo.
+
+And then for floats
+plus, minus, same
+
+thing except no modulo.
+
+All right.
+
+So back to the list.
+
+AUDIENCE: Can I ask
+a quick question?
+
+PROFESSOR: Yes.
+
+AUDIENCE: Could you explain
+why like maybe briefly 5
+
+divided by 2 is 2?
+
+You said in computer-land,
+like what?
+
+Is it doing some sort
+of weird rounding?
+
+Or like why, why is that
+different than--?
+
+PROFESSOR: This is because
+the type of the
+
+variable is an integer.
+
+And when you say something is
+an integer, you're talking
+
+about only these
+numbers, right.
+
+So 2 and a 1/2 as an integer
+doesn't exist.
+
+It only exists as a float.
+
+But when you have an operand
+like this that takes two
+
+numbers on both sides, if both
+numbers are integers, this
+
+produces a result that
+is an integer.
+
+So when you have these math
+operators, these produce a
+
+result, right.
+
+So that result has
+a type as well.
+
+Because I can take that
+result and I say c is
+
+equal to 5 and 1/2.
+
+C is now a variable
+in the language.
+
+That means that it has
+to have a type.
+
+And Python says that because I
+did this operation with two
+
+integers, I'm gonna give it
+a type as an integer.
+
+And the closest representation
+to 2 and 1/2 in
+
+integer terms is 2.
+
+AUDIENCE: I thought it
+would round up to 3.
+
+I assumed that it would round
+up to [UNINTELLIGIBLE].
+
+PROFESSOR: Oh, yeah.
+
+You're talking about
+a separate issue.
+
+It's not necessarily that it's
+closest, but it truncates.
+
+AUDIENCE: OK.
+
+PROFESSOR: So when
+it converts--
+
+yeah, it just truncates
+the decimal.
+
+AUDIENCE: What happens if you
+have 5 divided by 2--
+
+[UNINTELLIGIBLE]?
+
+PROFESSOR: So when you get into
+stuff like that, Python's
+
+gonna look at, see it's an
+integer and a float, and--
+
+this is something that we're
+gonna have to actually test
+
+out when I turn on
+the computer.
+
+It should convert to a float,
+but it might not.
+
+So.
+
+We'll test that out, actually.
+
+That's one of the nice things
+about Python is that if you
+
+have a question like that,
+you can test it out
+
+instantaneously.
+
+So remind me ints divided
+by float, and
+
+we'll demonstrate it.
+
+OK.
+
+All right.
+
+So another data type, string.
+
+Anyone know what a string
+is or can tell me?
+
+Shout it out.
+
+Pantomime it.
+
+AUDIENCE: Sequence
+of characters.
+
+PROFESSOR: OK.
+
+So it's something like this.
+
+All right.
+
+And you can--
+
+does anyone mind if
+I erase this?
+
+So in Python, you can specify
+strings a couple ways.
+
+One is with single quotes
+on the sides.
+
+And the other is with
+double quotes.
+
+This is useful, for example,
+if you need to embed quotes
+
+inside a string.
+
+So if I need to, say, have this
+as a quoted string, I
+
+would have single quotes on the
+outside and then double
+
+quotes on the inside,
+or vice versa.
+
+I could do double quotes
+and then single quotes.
+
+The point is that Python needs
+to know when and where the
+
+string starts and where
+the string ends.
+
+We good?
+
+All right.
+
+AUDIENCE: [UNINTELLIGIBLE].
+
+PROFESSOR: So if you put that?
+
+If you write this, Python's
+gonna call that a string.
+
+It's a string that contains
+the character two, though.
+
+All right.
+
+I guess you're asking
+because of the input
+
+with the problem set?
+
+AUDIENCE: --divide that by a
+string, by an integer that
+
+would [UNINTELLIGIBLE].
+
+PROFESSOR: So in your program,
+there's a point where you have
+
+to enter in numbers
+for problem set 1.
+
+Oh, you didn't start?
+
+Well there is a place where
+you have to enter numbers.
+
+So raw_input, for example, is
+gonna return a variable, and
+
+the type of this is
+gonna be a string.
+
+So if you need to use it as an
+integer or as a float, you can
+
+convert it.
+
+So now this is an integer, and
+you can do math with it.
+
+Or you can also say--
+
+Does that make sense?
+
+That's something that'll be
+useful in your problem set.
+
+So just FYI.
+
+All right.
+
+Another data type, Boolean.
+
+Does anyone know what
+a Boolean is?
+
+AUDIENCE: [UNINTELLIGIBLE].
+
+PROFESSOR: What's that?
+
+AUDIENCE: It's like an
+if-then statement?
+
+PROFESSOR: It has to
+do with if-then
+
+statements, but it's a variable.
+
+It's a type that only has two
+values, true or false.
+
+OK.
+
+And we'll talk about this, all
+of these, when I start talking
+
+about operations on them.
+
+Last one that you need to know
+of right now is the none type.
+
+The way to think about none
+is that it's sort
+
+of like dark matter.
+
+It's there.
+
+We know it's there.
+
+It holds a place, but we can't
+do anything with it.
+
+It's there just so that you know
+that there's a variable
+
+that should refer to something
+but that something doesn't
+
+exactly exist.
+
+OK.
+
+You'll see more of it.
+
+But it's nothing,
+but it's there.
+
+And then later on
+in the semester,
+
+there's other data types.
+
+I mean, there's a lot of data
+types, but these are the big
+
+ones that you need to
+know right now.
+
+Other data types that we might
+look at are lists, tuples, and
+
+dictionaries.
+
+These are other major data
+types in Python.
+
+You don't need to know them
+right now 'cause Professor
+
+Guttag will go over
+them in lecture.
+
+But just keep them
+in your brain.
+
+OK.
+
+So we've already talked about
+the operations that we can do
+
+on numbers.
+
+We can also do operations
+on strings.
+
+So we can do something
+called concatenation.
+
+So concatenation is just
+a big word for
+
+sticking two things together.
+
+So if I have s1 and s2 and I
+want to concatenate them to
+
+together, I use the
+plus operator.
+
+So the other thing, too, that I
+want to point out is that we
+
+have a plus operator for ints.
+
+We got a plus operator
+for float.
+
+We've got one for strings.
+
+I don't think they work for
+bools, but they work for lists
+
+and tuples.
+
+This is what's known as an
+overloaded operator.
+
+So it changes shape or changes
+its behavior depending on the
+
+data types of its operands.
+
+So that's why when you're
+dividing an ints by a float,
+
+some languages will convert
+it to a float for you.
+
+Other languages will
+convert to an ints.
+
+It's something that varies.
+
+That's why I'm not sure of
+my answer right now.
+
+So.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: No.
+
+If your computer blows
+up in your face,
+
+then that's an issue.
+
+That's a separate issue.
+
+All right.
+
+So some other operations that
+we have, and they relate to
+
+Booleans, are comparison
+operations.
+
+What these mean are these take
+two operands and compare them.
+
+So if I want to see if--
+
+if I say a less than b and a is
+2 and b is 3, then this is
+
+gonna return true.
+
+The value of this expression
+becomes true.
+
+And if I say a greater than
+b, obviously it's
+
+gonna be false, right.
+
+And all of these operators
+work in
+
+basically the same way.
+
+They take two operations,
+and they give you a
+
+Boolean value back.
+
+All right.
+
+Any questions on that?
+
+AUDIENCE: So are Boolean values
+always true or false?
+
+PROFESSOR: Always
+true or false.
+
+And I'm actually gonna
+get to that now.
+
+So Boolean values-- and this is
+kind of the last major one
+
+we're gonna talk about--
+
+have three operators,
+AND, OR, and NOT.
+
+Actually, these should
+be lowercase.
+
+These, AND and OR, take two
+operands, NOT takes one.
+
+And what they do is if you have
+something like a is true,
+
+b is true, c is false, if you
+say like a AND b, then this
+
+entire expression is gonna
+return true, right.
+
+If I say a AND c, this
+will be false.
+
+AND returns true, if and only
+if both operands are true,
+
+false otherwise.
+
+If you say a OR c, OR returns
+true if both operands or one
+
+operand is true.
+
+So if any of them are true
+or both are true.
+
+If they're both false, then
+it returns false.
+
+And NOT, all this does is if I
+say NOT a, it'll return false.
+
+It reverses it.
+
+Now we can combine
+these together.
+
+So these are very simple
+expressions, but we can also
+
+combine them.
+
+So we can say like a
+AND b OR c, right.
+
+So if both a amd b are true,
+then this becomes true.
+
+And then this entire expression
+becomes true if
+
+this part is true or
+this part is true.
+
+So you can build up pretty
+complicated expressions.
+
+And then the way that they
+relate to these logical
+
+operators is, remember, these
+take numbers on either side
+
+and they produce
+Boolean values.
+
+So if I have--
+
+I can say d is less than e.
+
+This is gonna give me a Boolean
+value, right, which I
+
+can then use the AND operator
+on and I can say--
+
+So what this does is it says if
+d is less than e and e is
+
+less than f, then return true.
+
+This, by the way, would check to
+see that these numbers are
+
+in order, so 3, 4, 5, as
+opposed to 5, 4, 3.
+
+So is everyone good
+on all that?
+
+Did I lose anyone?
+
+No questions?
+
+All right.
+
+So the last couple of things and
+then I'm gonna turn on the
+
+computer and actually walk
+through some code with you and
+
+we'll be done for the day.
+
+So this is kind of the crash
+course in basic syntax for our
+
+basic types for Python.
+
+So there were three--
+
+So what we have now is a way to
+create programs that run in
+
+a straight line, right.
+
+So can anyone give me kind of a
+synopsis of what a straight
+
+line program is?
+
+AUDIENCE: Go down
+line by line.
+
+PROFESSOR: What's that?
+
+AUDIENCE: Everything one--
+go down line by line.
+
+PROFESSOR: Go down line by
+line, do everything once.
+
+All right.
+
+The problem is that this
+doesn't allow us to do
+
+anything, right.
+
+So we have branching.
+
+This is implemented
+by something
+
+called an IF statement.
+
+Now, the way you use an
+IF statement is--
+
+all right.
+
+This is the full version
+of the IF statement.
+
+It's saying, if this condition
+is true, I'm gonna execute the
+
+code in this block.
+
+If this condition is true, if
+this condition is false and
+
+this condition is true,
+then I'm gonna
+
+execute the code here.
+
+And if none of those
+were true, then I
+
+execute what's here.
+
+You don't need to have an ELIF,
+and you don't need to
+
+have an ELSE.
+
+You can just have an IF
+or an IF and an ELSE.
+
+So the three versions
+of this branching--
+
+Now when I, just by way of
+explanation, when I draw like
+
+a line like that, I'm talking
+about a block of code.
+
+Can anyone tell me how Python
+represents blocks of code?
+
+AUDIENCE: Indents?
+
+PROFESSOR: Yeah.
+
+So indentation, right.
+
+We kind of talked about
+that on Thursday.
+
+So blocks of code are chunks
+of code that belong kind of
+
+logically together.
+
+So what this saying is that if I
+execute this, all this block
+
+is gonna get executed, all this
+block is going to get
+
+executed, et cetera.
+
+So if I were to represent this
+pictorially, then this is kind
+
+of the main part of the program
+and then this is the
+
+if statement and the block.
+
+And then it goes back
+to whatever code
+
+is down here, right.
+
+If I represent this
+pictorially, this
+
+would be the true part.
+
+So this part of code,
+this would be else.
+
+And then this part would
+be multiple excursions.
+
+So it would look a little
+bit like a tree.
+
+All right.
+
+So different branches for the
+different bits of code.
+
+Is everyone puzzled on that?
+
+Or anyone puzzled on that?
+
+OK.
+
+And there was a last
+bit of flow control
+
+that we talked about.
+
+What was it?
+
+So if we want to do something
+multiple times?
+
+AUDIENCE: Iterations or loops
+
+PROFESSOR: Iterations
+or loops, right.
+
+So it's called a loop because
+it looks like a loop in the
+
+code, right.
+
+And there's two variants.
+
+There's a WHILE loop and
+there's a FOR loop.
+
+A FOR loop is when you want
+to iterate over a
+
+finite set of elements.
+
+So what this FOR loop does is
+it says I'm gonna take--
+
+this is the range function,
+so we'll talk about this
+
+a little bit later.
+
+But all it does is it gives me
+all the numbers from 1 to 9.
+
+It goes 1 past.
+
+So.
+
+But you don't need to
+know it just yet.
+
+What this is telling Python,
+though, is that we're gonna
+
+execute this block of code
+9 times, all right.
+
+And on each iteration through
+this block of code, we're
+
+gonna set i to 1, and then set
+it to 2, set it to 3, 4, 5, 6,
+
+7, 8, 9, 10.
+
+Anyone lost by that?
+
+We'll see an example of
+it pretty shortly.
+
+And then the last one
+is a WHILE loop.
+
+A WHILE loop executes as long
+as a condition is true.
+
+So it's useful--
+
+don't want to do that.
+
+It's useful when you're not
+necessarily iterating over
+
+this finite set of elements or
+you don't necessarily know how
+
+many times you need to execute
+a specific loop.
+
+You just know that you need to
+keep executing this code while
+
+something is true.
+
+And we'll see an example
+of that pretty quickly.
+
+So I basically shotgun blasted a
+whole bunch of stuff at you.
+
+Is there anything that people
+want me to touch on before I
+
+pull down the screen and we
+start looking at code?
+
+All right.
+
+So has everyone been able
+to get Python set up?
+
+All right.
+
+So you'll know that this is
+the editor window, right.
+
+So what we use to edit
+longer scripts in?
+
+And you know that this is
+the interactive prompt.
+
+Before I forget, let's see what
+happens if I divide the
+
+integer 5 by the float 2.
+
+So Python does what you would
+hope it would do.
+
+It turns it into a float.
+
+If I do this, though,
+it gives me 2.
+
+All right.
+
+So it's an easy way to test.
+
+So we've got two chunks
+of code here that
+
+I want to go over.
+
+One of them, you've
+already seen.
+
+It's the program that tries
+to find the cube root of a
+
+perfect cube.
+
+And why don't we just walk
+through it and read the code?
+
+All right.
+
+So here's that raw_input
+function
+
+that I told you about.
+
+Now, it's gonna take a string
+and it's gonna print the
+
+string out on the screen
+and it's gonna
+
+say enter an integer.
+
+And, comment this out.
+
+So let's enter--
+
+what's a perfect cube?
+
+All right, the return type of
+raw_input is a string, right.
+
+So that int will convert to x.
+
+Now, here's an example of
+a loop, the WHILE loop.
+
+And because we don't have
+knowledge of what the user's
+
+gonna input when the program
+is run, a while loop is an
+
+appropriate kind of control
+loop to use, right.
+
+Because we can test a condition
+where our guess,
+
+which is what's represented by
+ans, if we cube it, is it
+
+still less than x.
+
+All right.
+
+I explained that a little
+bit incorrectly.
+
+What we're doing here is we're
+making a guess, and we're
+
+calling it ans right now,
+and we're gonna set it
+
+initially to zero.
+
+And then we're gonna enter
+this WHILE loop and we're
+
+gonna say we're gonna take
+answer and we're gonna
+
+multiply it three times.
+
+We're gonna cube it.
+
+And if the value of ans cubed
+is less than whatever input
+
+the user gave us, then we're
+gonna keep looping.
+
+And on each loop, we're gonna
+increase the value of our
+
+guess for ans, right.
+
+And if it turns out that x is a
+perfect cube, eventually, by
+
+just iterating through all the
+integers from 1 to whatever,
+
+whatever the cube root of x is,
+we will find the answer.
+
+And we'll know we find the
+answer because answer cubed is
+
+going be less than x.
+
+Now, can anyone tell me
+why we have abs here?
+
+AUDIENCE: The absolute value.
+
+PROFESSOR: Right.
+
+So let's say that the user
+entered in like negative 27.
+
+It still has a cube, right.
+
+It's still negative 3.
+
+But the way that we set up our
+loop, if we were to take this
+
+out, the program would just
+continue executing forever.
+
+Well, for actually a very,
+very long time, but--
+
+the universe would die
+before this finished.
+
+So we have this absolute
+value here.
+
+Is anyone puzzled by this?
+
+Do I need to belabor
+the point?
+
+OK.
+
+So eventually I've entered
+27 and we can actually--
+
+a good way to kind of check
+ourselves is to print out
+
+diagnostic input.
+
+So if guess is 1, that's not--
+
+1 cubed is obviously not 27.
+
+2 cubed is not 27.
+
+3 cubed is 27.
+
+And when we get to that point,
+we leave the loop.
+
+And now we're down in
+this bit of code.
+
+All right.
+
+Now, because we're asking for
+cube roots, we need to check
+
+the condition for when the--
+
+sorry, I'm kind of
+mixed up here.
+
+Sorry.
+
+So when we exit the WHILE loop,
+if we've had a number
+
+that's not a perfect cube, then
+we know that the value
+
+the answer stopped on is not
+going to equal the cube of it,
+
+by way of explanation.
+
+So my last guess
+3 cubed is 27.
+
+Let's run it again.
+
+Let's say that I
+have 20, right.
+
+So what happens is
+it gets to 4.
+
+So 4 cubed is 64, right.
+
+That's obviously not 28.
+
+And that's what this
+condition checks.
+
+And so it knows that if it gets
+to that point, it's not a
+
+perfect cube.
+
+Now, this ELIF statement here
+says, OK, so if this turns out
+
+to be true, that means that
+it wasn't a perfect cube.
+
+But let's say that it was a
+perfect cube, this will be
+
+true, and Python will then start
+to look at this and say,
+
+well, let's look at this if
+condition, or actually--
+
+I'm sorry.
+
+This condition will be false if
+it's a perfect cube, right.
+
+And Python will say, OK, look
+at the next part of the
+
+IF-ELIF statement and will say,
+well, was x less than 0?
+
+What it's doing here, it's
+checking whether or not we've
+
+entered a negative
+number or not.
+
+So if we enter negative 27, what
+it would do is it would
+
+to enter this branch, and then
+it would negate whatever
+
+answer it got.
+
+Because we found the answer
+for a positive
+
+perfect cube, right.
+
+Did I break it?
+
+We are having technical
+difficulties.
+
+Oh, OK.
+
+I'm not sure what
+happened there.
+
+So anyway.
+
+So we go about trying to find
+the cube root of 27, which is
+
+the absolute value of 27.
+
+And we, of course, find it.
+
+It's 3.
+
+But then because we've entered
+a negative number, Python's
+
+gonna enter this branch and
+negate whatever answer we got.
+
+Because we know that in order
+for it to be negative, then it
+
+would have to have been a
+negative number, right.
+
+Is anyone lost?
+
+Everyone good?
+
+AUDIENCE: Do you need an
+exclamation mark for the--?
+
+PROFESSOR: Oh, this one?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: So this is one of
+the comparison operators.
+
+This stands for not equal to.
+
+So if I have--
+
+do a little Python work here--
+if I have a is equal to 5 and
+
+b is equal to 6, if I say a is
+double equal, that's gonna
+
+check and see if they're
+the same value.
+
+Obviously, they're not, so
+it's gonna return false.
+
+On the other hand, if I say
+not equal-- or bang equal
+
+sometimes we call--
+
+this will return true.
+
+OK.
+
+Any other questions?
+
+AUDIENCE: The one that you did
+28 for, shouldn't it not print
+
+the cube root of 28 is 4?
+
+PROFESSOR: Oh.
+
+Yeah.
+
+So yeah.
+
+Should it be indented?
+
+Because if we indented
+here, right, then
+
+what's gonna happen?
+
+It's only gonna print
+out the cube root
+
+for negative numbers.
+
+So what--
+
+what's that?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Well, again, if we
+put an ELSE statement, then it
+
+won't print out the cube root
+for negative numbers.
+
+What we could do, and this is
+kind of a hackish way, is
+
+write it like this.
+
+But that's kind of ugly,
+right, because you're
+
+repeating yourself.
+
+And one thing about computer
+programmers is that we are the
+
+laziest people on the
+face of the earth.
+
+Like, we'll spend 20 hours
+writing a program to do
+
+something in five minutes that
+we could have originally done
+
+in 10 minutes.
+
+It's just our nature.
+
+So anyway.
+
+So we're repeating ourselves.
+
+And while I'm speaking,
+this is the
+
+solution I came up with.
+
+If I were to go back and rewrite
+this, I'd probably
+
+make it a little bit
+less convoluted.
+
+So maybe, let's try this.
+
+So we're gonna check if we
+were successful, and then
+
+we're gonna check if
+x is less than 0.
+
+Now we're not repeating
+ourselves.
+
+And we catch all the cases.
+
+So let's make sure that my fix
+works because oftentimes when
+
+you write programs, you'll
+introduced bugs of your own.
+
+So we've tested when
+it is a cube.
+
+Let's test it when it's not.
+
+OK.
+
+So there we fixed it, I think.
+
+One thing about computer
+programs is that this is a
+
+very simple case, but for
+longer, more complicated
+
+programs, it's almost
+impossible to get
+
+out all of the bugs.
+
+But in this case, pretty
+confident that we were
+
+successful, right.
+
+So does anyone else have
+any other questions
+
+on this bit, right?
+
+All right.
+
+The last thing that I'm gonna go
+over is something called a
+
+fizzbuzz program.
+
+This is just a silly
+little program.
+
+This is the English
+specification.
+
+And this is kind of a first
+instance of where we're gonna
+
+take English and kind of break
+it down into code, figure out
+
+how to break it up, chunk it
+up, and abstract it into
+
+something that actually works.
+
+So the problem is to write a
+program the prints the numbers
+
+from 1 to 100, but for multiples
+of three, print fizz
+
+instead of the number.
+
+And for multiples of
+5, print buzz.
+
+And if there are multiples are
+both 3 and 5, print fizzbuzz.
+
+So if it says numbers from 1 to
+100, when you see something
+
+like this when you're trying
+to figure out how to write
+
+your programs, the first thing
+that should go off in your
+
+mind is, I probably need a for
+loop because I'm iterating
+
+over a set of numbers.
+
+So we happen to know the
+numbers 1 to 100.
+
+And here's a range
+function again.
+
+And we'll talk about range
+next week most likely.
+
+And all we're gonna do is first
+we're gonna get the
+
+string value of this number.
+
+So remember how earlier you
+asked if, or one of the
+
+students asked, if we had a
+number in the string, if that
+
+was a number or not?
+
+So like this.
+
+That's what that STR
+function does.
+
+So if I have a variable a is
+equal to 1, I can say s is
+
+equal to STR a, and s is
+now gonna be that.
+
+All right.
+
+And then what I'm gonna do here
+is I'm gonna check the
+
+integer value, so i, and
+see if it's evenly
+
+divisible by 3 or 5.
+
+And the way that I
+checked that is I
+
+use a modulo operator.
+
+That's what that percent
+sign is.
+
+What this operator does is it
+takes two integer values and
+
+it returns the remainder after
+you've divided the left
+
+integer by the right integer.
+
+So if I have 6 modulo 3,
+what's that gonna be?
+
+It should be 0, right, because
+you can divide 6 evenly by 3.
+
+The other hand, if I say 5
+modulo 3, then that's going to
+
+be 2, right.
+
+Yeah, I had to think about
+it for a second.
+
+OK.
+
+So that's all this does.
+
+And these are two expressions
+that return a
+
+Boolean value, right.
+
+Because this modulo operation
+is gonna return an integer,
+
+and I'm gonna use the equality
+operator to compare it to a
+
+number, another integer, 0,
+and that's gonna give me a
+
+Boolean value.
+
+This expression also gives
+me a Boolean value.
+
+And then I'm gonna combine
+them into--
+
+using the or operator
+for Boolean values--
+
+into a larger expression.
+
+And then if this is true, then
+I know that I'm gonna have to
+
+at lease print fizz,
+buzz, or fizzbuzz.
+
+Because I'm not gonna print
+the number, right, because
+
+it's a multiple of 3 or 5.
+
+And so all this code does is
+just figures out if it's
+
+evenly divisible by 3, then
+I know I print fizz.
+
+So I'm gonna concatenate my
+final string onto it.
+
+And then if it's evenly
+divisible by 5, then I know I
+
+need to print buzz.
+
+So then I'm gonna attach
+buzz onto my output.
+
+And then I'm just gonna print
+whatever I'm left over with.
+
+So to see this in action
+because we are way out
+
+of time right now.
+
+So 1, 2, fizz, 4, buzz,
+6, fizz, 7, 8.
+
+Then we have fizzbuzz for 15.
+
+So it seems to work.
+
+Everyone follow that?
+
+We good?
+
+So I'm done for this
+recitation.
\ No newline at end of file
diff --git a/8Dxo4LPK_9w.txt b/8Dxo4LPK_9w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1d9be36ebeecd8096d3d175562881227730a5c1
--- /dev/null
+++ b/8Dxo4LPK_9w.txt
@@ -0,0 +1,540 @@
+PROFESSOR: That's how
+it looks, a resonance.
+
+You can see it basically
+in the phase shift.
+
+And great increase of the
+phase of almost minutely pi
+
+over a very small
+change of energy.
+
+And it should [INAUDIBLE]
+with a very big [INAUDIBLE]..
+
+So this is how it looks.
+
+And I want to now
+proceed, after if there
+
+are some questions,
+of how do we search
+
+for residences a little
+more mathematically rather
+
+than plotting them.
+
+How could I write an
+equation for a resonance.
+
+Cannot say, oh, the
+phase changes fast.
+
+Well, that's not a very
+nice way of saying it.
+
+It's good.
+
+It's intuitive.
+
+But we should be
+able to do better.
+
+So how do I find resonances?
+
+So let's model
+resonances a little bit.
+
+How do we find resonances?
+
+So let's model this behavior.
+
+By that is writing
+a formula that
+
+is simple enough that seems
+to capture what's happening.
+
+And that formula's
+going to inspire
+
+us to think of resonances
+perhaps a little more clearly.
+
+So suppose you have a
+resonance near k equal alpha.
+
+I claim the following
+formula would be a good way
+
+to represent the resonance?
+
+We would say that tan
+delta is equal to beta
+
+over alpha minus k.
+
+Or-- yeah, we would say that.
+
+[INAUDIBLE] Or if you wish,
+delta is tan minus 1 of beta
+
+over alpha minus k.
+
+Why is that reasonable?
+
+It's a little surprising,
+but not that surprising.
+
+You see that-- delta is
+equal to minus pi over 2.
+
+The tangent of delta
+goes to infinity.
+
+So there's something
+going on here in which you
+
+have this property.
+
+So let's plot this.
+
+So let's plot beta
+over alpha minus k.
+
+You need a clock
+to understand this.
+
+So this is k, and we're
+plotting this quantity.
+
+Well, it's going to go
+crazy at k equal alpha.
+
+That we know.
+
+When k is less than
+alpha, I'm going
+
+to assume that alpha
+and beta are positive.
+
+They both have units of k.
+
+And when k is less than
+alpha-- we begin here--
+
+then this denominator
+is positive,
+
+the numerator is positive,
+ratio is positive.
+
+It's small, maybe.
+
+And then suddenly,
+when k reaches alpha
+
+it goes to infinity.
+
+So it's going to be like that.
+
+Now, it actually
+is true that when
+
+k differs by alpha by
+beta, it reaches value 1.
+
+So here is alpha minus beta.
+
+That point it reaches value 1.
+
+So if I want this
+thing to be very sharp,
+
+I need beta to be small
+so that it's little
+
+until it reaches beta within--
+
+distance beta within alpha,
+and then it shoots up.
+
+So I want beta to be
+small for sharp behavior.
+
+On the other hand here,
+it goes the other way.
+
+It goes from minus
+infinity back to 0,
+
+and has value minus
+1 at alpha plus beta.
+
+So within minus beta, and
+beta off of the center
+
+alpha, most of
+the things happen.
+
+If we plot now the
+tangent of this,
+
+or the arctangent of this, tan
+minus 1 of beta, alpha minus k,
+
+well, if the tangent of
+an angle is very little,
+
+the angle can be taken
+to be very little.
+
+At this point, it
+will reach pi over 2,
+
+so the angle is little,
+will go to pi over 2,
+
+and then quickly becomes
+larger than pi over 2,
+
+you're thinking tangents.
+
+So the tangent is going up,
+is blowing up at pi over 2.
+
+Then continuously, it
+goes to minus pi over 2,
+
+and then continuously goes
+to 0 so it reaches pi.
+
+So this is the
+behavior of delta.
+
+Delta is this tan minus
+1 of beta over that.
+
+And delta is doing
+the right thing.
+
+It's doing this
+kind of behavior.
+
+There is a shift.
+
+I could add a constant
+here to produce this shift,
+
+but it's not important
+at this moment.
+
+The resonance is
+doing this thing,
+
+up to a total shift
+of pi that doesn't
+
+change the tangent of an angle.
+
+So this is one way
+of modeling what's
+
+happening to the phase
+shift near our resonance.
+
+So let's explore
+it a little more.
+
+I can do a couple
+of calculations.
+
+For example, I can compute
+what is d delta dk at k
+
+equals alpha.
+
+That's should be
+a nice quantity.
+
+Is a derivative of the face.
+
+At the resonance,
+at the position
+
+alpha of the resonance.
+
+So here's delta, here
+is k, and there's
+
+the derivative of this k.
+
+And how should it be?
+
+Well, basically, the
+phase changes by amount pi
+
+over a distance beta or 2 beta.
+
+So this must be a
+number divided by beta.
+
+You can calculate this
+derivative from this equation.
+
+It's a nice exercise.
+
+It's actually just 1 over beta.
+
+That's a result. 1 over beta.
+
+The other quantity that
+is nice to understand
+
+is how does this
+scattering amplitude
+
+behave near the resonance.
+
+So what is the
+value of as squared?
+
+Oh, that's the absolute
+value of psi s squared,
+
+which is sine squared delta.
+
+That's the same
+thing as As squared.
+
+Well, you know what is
+the tangent of delta?
+
+A little trigonometric play
+should be able to do it,
+
+and can give you the
+sin squared delta.
+
+And here is the answer.
+
+It's beta squared over
+beta squared plus alpha
+
+minus k squared.
+
+Kind of a nice,
+almost bell shape.
+
+Of course, it's polynomial,
+but it looks a little
+
+like just a nice symmetric
+shape around alpha equal k.
+
+Now, this division is so famous
+it has been given a name.
+
+It's called the
+Breit-Wigner distribution.
+
+Breit-Wigner.
+
+But it's described as the
+Breit-Wigner distribution,
+
+and it's usually referring
+to terms of energy.
+
+Of energy, not momentum.
+
+So-- and it's--
+
+what should happen to
+scattering amplitude in general
+
+when you have a resonance.
+
+So the way to do
+this calculation now
+
+is to say, well, what
+is alpha minus k?
+
+Let's try to relate it to the
+energy minus the energy at k
+
+equal alpha.
+
+Well, this is h
+squared k squared
+
+over 2 m minus h squared
+alpha squared over 2 m,
+
+which is h squared over 2 m,
+k squared minus alpha squared.
+
+On the other hand, I have
+here alpha minus k squared.
+
+I don't have k squared
+minus alpha squared.
+
+So-- approximations.
+
+if the resonance is narrow
+enough, if beta is small,
+
+let's do an approximation.
+
+We do h squared over--
+
+everybody knows
+this approximation,
+
+shouldn't be afraid of doing it.
+
+It's alpha-- how
+could I write it--
+
+k minus alpha
+times k plus alpha.
+
+And the approximation is that
+all the interesting thing
+
+comes from the difference
+between k and alpha,
+
+how close k is to alpha.
+
+So when k is close to
+alpha, all the dependence
+
+is going to be here.
+
+This is going to be about 2
+alpha when k is near alpha.
+
+And if it's a little
+more than that,
+
+it doesn't matter,
+because it's [INAUDIBLE]..
+
+So this could be
+approximated to 2 alpha,
+
+and therefore this becomes h
+squared alpha over m times k
+
+minus alpha.
+
+So that's a little help.
+
+Then size of s squared,
+doing a little more
+
+of algebra with the
+constants there.
+
+Probably you want to
+do it with two lines.
+
+It's tricky.
+
+It's really simple.
+
+It's always written
+in this form--
+
+1 over 4 gamma squared over
+e minus e alpha squared
+
+plus 1 over four gamma
+squared, and that's
+
+the so-called
+Breit-Wigner distribution.
+
+And gamma is a
+funny constant here.
+
+We'll try to
+understand it better.
+
+2 alpha beta h squared over m.
+
+It has to be something that
+depends on alpha and beta,
+
+because after all,
+we weren't modeling
+
+the resonance with alpha beta.
+
+So this curve is very famous.
+
+That's the distribution of
+the scattering amplitude
+
+over energies whenever
+you have a resonance.
+
+So we should plot it.
+
+You have an e alpha.
+
+You have an e alpha
+plus gamma over 2
+
+and e alpha minus gamma over 2.
+
+But the energy minus e alpha
+is equal to the gamma over 2,
+
+you get the gamma squared over
+4 so the total amplitude goes
+
+down to 1/2 of the
+usual amplitudes.
+
+When the energy is equal
+to e alpha, you get 1.
+
+1 for psi s squared.
+
+But when the energy differs
+from e alpha by gamma over 2,
+
+you get half.
+
+So-- actually, I'm not
+sure of the deflection
+
+point, where it is.
+
+Probably not there.
+
+Or is it there?
+
+I don't know.
+
+I drew it as if it is there.
+
+So that's the distribution, and
+the width over here is gamma.
+
+So gamma is called the
+width at half power,
+
+or at half intensity.
+
+Yeah.
+
+Width-- the half width
+of the distribution.
\ No newline at end of file
diff --git a/8MyPd4F7y54.txt b/8MyPd4F7y54.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e57871b25a1b44ba18d390b8e6433ada40325e91
--- /dev/null
+++ b/8MyPd4F7y54.txt
@@ -0,0 +1,8451 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu the end of the last class I
+
+ align:start position:0%
+ocw.mit.edu the end of the last class I
+ 
+
+ align:start position:0%
+ocw.mit.edu the end of the last class I
+mentioned that
+
+ align:start position:0%
+mentioned that
+ 
+
+ align:start position:0%
+mentioned that
+uh this invasion of the end brain by
+
+ align:start position:0%
+uh this invasion of the end brain by
+ 
+
+ align:start position:0%
+uh this invasion of the end brain by
+visual Pathways uh we know that mostly
+
+ align:start position:0%
+visual Pathways uh we know that mostly
+ 
+
+ align:start position:0%
+visual Pathways uh we know that mostly
+it even though there was a direct
+
+ align:start position:0%
+it even though there was a direct
+ 
+
+ align:start position:0%
+it even though there was a direct
+pathway it was very small the one
+
+ align:start position:0%
+pathway it was very small the one
+ 
+
+ align:start position:0%
+pathway it was very small the one
+through the genicular body very small
+
+ align:start position:0%
+through the genicular body very small
+ 
+
+ align:start position:0%
+through the genicular body very small
+early on major Roots into the end braan
+
+ align:start position:0%
+early on major Roots into the end braan
+ 
+
+ align:start position:0%
+early on major Roots into the end braan
+came they began at the tectum also the
+
+ align:start position:0%
+came they began at the tectum also the
+ 
+
+ align:start position:0%
+came they began at the tectum also the
+pretectal area which projected into
+
+ align:start position:0%
+pretectal area which projected into
+ 
+
+ align:start position:0%
+pretectal area which projected into
+thalamic areas which then projected to
+
+ align:start position:0%
+thalamic areas which then projected to
+ 
+
+ align:start position:0%
+thalamic areas which then projected to
+the end brain and so I'm asking I asked
+
+ align:start position:0%
+the end brain and so I'm asking I asked
+ 
+
+ align:start position:0%
+the end brain and so I'm asking I asked
+there at the end of the class what what
+
+ align:start position:0%
+there at the end of the class what what
+ 
+
+ align:start position:0%
+there at the end of the class what what
+what were the Adaptive advantages of
+
+ align:start position:0%
+what were the Adaptive advantages of
+ 
+
+ align:start position:0%
+what were the Adaptive advantages of
+that why would it invade the
+
+ align:start position:0%
+that why would it invade the
+ 
+
+ align:start position:0%
+that why would it invade the
+inbre
+
+ align:start position:0%
+inbre
+ 
+
+ align:start position:0%
+inbre
+uh and first I I try to give an
+
+ align:start position:0%
+uh and first I I try to give an
+ 
+
+ align:start position:0%
+uh and first I I try to give an
+anatomical answer it's a it's a way to
+
+ align:start position:0%
+anatomical answer it's a it's a way to
+ 
+
+ align:start position:0%
+anatomical answer it's a it's a way to
+provide better information to this trium
+
+ align:start position:0%
+provide better information to this trium
+ 
+
+ align:start position:0%
+provide better information to this trium
+remember visual information could reach
+
+ align:start position:0%
+remember visual information could reach
+ 
+
+ align:start position:0%
+remember visual information could reach
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+striatum uh directly from the older
+
+ align:start position:0%
+striatum uh directly from the older
+ 
+
+ align:start position:0%
+striatum uh directly from the older
+phals but those structures weren't
+
+ align:start position:0%
+phals but those structures weren't
+ 
+
+ align:start position:0%
+phals but those structures weren't
+precisely
+
+ align:start position:0%
+precisely
+ 
+
+ align:start position:0%
+precisely
+topographic you know and the striatum
+
+ align:start position:0%
+topographic you know and the striatum
+ 
+
+ align:start position:0%
+topographic you know and the striatum
+wasn't a structure that made really good
+
+ align:start position:0%
+wasn't a structure that made really good
+ 
+
+ align:start position:0%
+wasn't a structure that made really good
+topography as easy to form in evolution
+
+ align:start position:0%
+topography as easy to form in evolution
+ 
+
+ align:start position:0%
+topography as easy to form in evolution
+now that's my
+
+ align:start position:0%
+now that's my
+ 
+
+ align:start position:0%
+now that's my
+interpretation obviously it that
+
+ align:start position:0%
+interpretation obviously it that
+ 
+
+ align:start position:0%
+interpretation obviously it that
+happened mostly in the cortex in the
+
+ align:start position:0%
+happened mostly in the cortex in the
+ 
+
+ align:start position:0%
+happened mostly in the cortex in the
+cortex you you you get this highly
+
+ align:start position:0%
+cortex you you you get this highly
+ 
+
+ align:start position:0%
+cortex you you you get this highly
+topographic mapping of the visual world
+
+ align:start position:0%
+topographic mapping of the visual world
+ 
+
+ align:start position:0%
+topographic mapping of the visual world
+and those Pathways came by way of the
+
+ align:start position:0%
+and those Pathways came by way of the
+ 
+
+ align:start position:0%
+and those Pathways came by way of the
+midbrain and directly from the
+
+ align:start position:0%
+midbrain and directly from the
+ 
+
+ align:start position:0%
+midbrain and directly from the
+geniculate
+
+ align:start position:0%
+geniculate
+ 
+
+ align:start position:0%
+geniculate
+body so that enabled a lot better Acuity
+
+ align:start position:0%
+body so that enabled a lot better Acuity
+ 
+
+ align:start position:0%
+body so that enabled a lot better Acuity
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the learning that the end brain was
+
+ align:start position:0%
+for the learning that the end brain was
+ 
+
+ align:start position:0%
+for the learning that the end brain was
+capable of especially by means of its
+
+ align:start position:0%
+capable of especially by means of its
+ 
+
+ align:start position:0%
+capable of especially by means of its
+Pathways to where two different places
+
+ align:start position:0%
+Pathways to where two different places
+ 
+
+ align:start position:0%
+Pathways to where two different places
+to the striatum rehabit
+
+ align:start position:0%
+to the striatum rehabit
+ 
+
+ align:start position:0%
+to the striatum rehabit
+learning and to the hippocampal
+
+ align:start position:0%
+learning and to the hippocampal
+ 
+
+ align:start position:0%
+learning and to the hippocampal
+formation we're learning about where Lo
+
+ align:start position:0%
+formation we're learning about where Lo
+ 
+
+ align:start position:0%
+formation we're learning about where Lo
+locations of the animal in the
+
+ align:start position:0%
+locations of the animal in the
+ 
+
+ align:start position:0%
+locations of the animal in the
+environment not the locations of other
+
+ align:start position:0%
+environment not the locations of other
+ 
+
+ align:start position:0%
+environment not the locations of other
+animals the location of the animal whose
+
+ align:start position:0%
+animals the location of the animal whose
+ 
+
+ align:start position:0%
+animals the location of the animal whose
+brain we're talking about okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the cognitive functions
+
+ align:start position:0%
+so the cognitive functions
+ 
+
+ align:start position:0%
+so the cognitive functions
+were that root to the hippocampus for
+
+ align:start position:0%
+were that root to the hippocampus for
+ 
+
+ align:start position:0%
+were that root to the hippocampus for
+Place information is a major part of our
+
+ align:start position:0%
+Place information is a major part of our
+ 
+
+ align:start position:0%
+Place information is a major part of our
+cognitive ability our memory
+
+ align:start position:0%
+cognitive ability our memory
+ 
+
+ align:start position:0%
+cognitive ability our memory
+formation but also another kind of
+
+ align:start position:0%
+formation but also another kind of
+ 
+
+ align:start position:0%
+formation but also another kind of
+memory it provided a visual root to the
+
+ align:start position:0%
+memory it provided a visual root to the
+ 
+
+ align:start position:0%
+memory it provided a visual root to the
+amydala which is really part of the
+
+ align:start position:0%
+amydala which is really part of the
+ 
+
+ align:start position:0%
+amydala which is really part of the
+striatum in the way I see it sort of a
+
+ align:start position:0%
+striatum in the way I see it sort of a
+ 
+
+ align:start position:0%
+striatum in the way I see it sort of a
+at least a sort of a codal output of a
+
+ align:start position:0%
+at least a sort of a codal output of a
+ 
+
+ align:start position:0%
+at least a sort of a codal output of a
+striatum it functions like a
+
+ align:start position:0%
+striatum it functions like a
+ 
+
+ align:start position:0%
+striatum it functions like a
+striatum
+
+ align:start position:0%
+striatum
+ 
+
+ align:start position:0%
+striatum
+for the learning of avoidance and
+
+ align:start position:0%
+for the learning of avoidance and
+ 
+
+ align:start position:0%
+for the learning of avoidance and
+approach okay and then also binocular
+
+ align:start position:0%
+approach okay and then also binocular
+ 
+
+ align:start position:0%
+approach okay and then also binocular
+vision which we won't talk very much
+
+ align:start position:0%
+vision which we won't talk very much
+ 
+
+ align:start position:0%
+vision which we won't talk very much
+about now but that was important too
+
+ align:start position:0%
+about now but that was important too
+ 
+
+ align:start position:0%
+about now but that was important too
+because the neocortex made made possible
+
+ align:start position:0%
+because the neocortex made made possible
+ 
+
+ align:start position:0%
+because the neocortex made made possible
+a lot better binocular vision by
+
+ align:start position:0%
+a lot better binocular vision by
+ 
+
+ align:start position:0%
+a lot better binocular vision by
+especially stereoptic
+
+ align:start position:0%
+especially stereoptic
+ 
+
+ align:start position:0%
+especially stereoptic
+stereopsis slight difference in the
+
+ align:start position:0%
+stereopsis slight difference in the
+ 
+
+ align:start position:0%
+stereopsis slight difference in the
+visual image from the two eyes because
+
+ align:start position:0%
+visual image from the two eyes because
+ 
+
+ align:start position:0%
+visual image from the two eyes because
+the information from right eye and left
+
+ align:start position:0%
+the information from right eye and left
+ 
+
+ align:start position:0%
+the information from right eye and left
+eye is kept separate all the way up to
+
+ align:start position:0%
+eye is kept separate all the way up to
+ 
+
+ align:start position:0%
+eye is kept separate all the way up to
+the cortex where then you can combine
+
+ align:start position:0%
+the cortex where then you can combine
+ 
+
+ align:start position:0%
+the cortex where then you can combine
+that information get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depth at the end of that chapter 20 I
+
+ align:start position:0%
+depth at the end of that chapter 20 I
+ 
+
+ align:start position:0%
+depth at the end of that chapter 20 I
+mentioned I believe it's in chapter 20 I
+
+ align:start position:0%
+mentioned I believe it's in chapter 20 I
+ 
+
+ align:start position:0%
+mentioned I believe it's in chapter 20 I
+mentioned some of the expansions and
+
+ align:start position:0%
+mentioned some of the expansions and
+ 
+
+ align:start position:0%
+mentioned some of the expansions and
+specializations of the visual
+
+ align:start position:0%
+specializations of the visual
+ 
+
+ align:start position:0%
+specializations of the visual
+system mainly mid-brain tectum
+
+ align:start position:0%
+system mainly mid-brain tectum
+ 
+
+ align:start position:0%
+system mainly mid-brain tectum
+and the phm cortical projections of the
+
+ align:start position:0%
+and the phm cortical projections of the
+ 
+
+ align:start position:0%
+and the phm cortical projections of the
+visual system the midbrain Tech the
+
+ align:start position:0%
+visual system the midbrain Tech the
+ 
+
+ align:start position:0%
+visual system the midbrain Tech the
+these are the two major structures and
+
+ align:start position:0%
+these are the two major structures and
+ 
+
+ align:start position:0%
+these are the two major structures and
+we're going to look at that
+
+ align:start position:0%
+we're going to look at that
+ 
+
+ align:start position:0%
+we're going to look at that
+today uh just one second here uh and
+
+ align:start position:0%
+today uh just one second here uh and
+ 
+
+ align:start position:0%
+today uh just one second here uh and
+we'll be talking a lot more about
+
+ align:start position:0%
+we'll be talking a lot more about
+ 
+
+ align:start position:0%
+we'll be talking a lot more about
+transcortical Pathways in the following
+
+ align:start position:0%
+transcortical Pathways in the following
+ 
+
+ align:start position:0%
+transcortical Pathways in the following
+class and then I don't deal in the book
+
+ align:start position:0%
+class and then I don't deal in the book
+ 
+
+ align:start position:0%
+class and then I don't deal in the book
+with the tremendous differences among
+
+ align:start position:0%
+with the tremendous differences among
+ 
+
+ align:start position:0%
+with the tremendous differences among
+animals in retinas you develop many
+
+ align:start position:0%
+animals in retinas you develop many
+ 
+
+ align:start position:0%
+animals in retinas you develop many
+retinal specializations and
+
+ align:start position:0%
+retinal specializations and
+ 
+
+ align:start position:0%
+retinal specializations and
+animals you don't need larger eyes just
+
+ align:start position:0%
+animals you don't need larger eyes just
+ 
+
+ align:start position:0%
+animals you don't need larger eyes just
+to get a larger retina and get more
+
+ align:start position:0%
+to get a larger retina and get more
+ 
+
+ align:start position:0%
+to get a larger retina and get more
+retinal gangling cills and more Acuity
+
+ align:start position:0%
+retinal gangling cills and more Acuity
+ 
+
+ align:start position:0%
+retinal gangling cills and more Acuity
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+way what else you need large eyes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for bring in more light why do you buy a
+
+ align:start position:0%
+for bring in more light why do you buy a
+ 
+
+ align:start position:0%
+for bring in more light why do you buy a
+camera with a big lens rather than a
+
+ align:start position:0%
+camera with a big lens rather than a
+ 
+
+ align:start position:0%
+camera with a big lens rather than a
+small lens brings in more light okay if
+
+ align:start position:0%
+small lens brings in more light okay if
+ 
+
+ align:start position:0%
+small lens brings in more light okay if
+you want to get a camera that can take
+
+ align:start position:0%
+you want to get a camera that can take
+ 
+
+ align:start position:0%
+you want to get a camera that can take
+pictures in very dim light get a camera
+
+ align:start position:0%
+pictures in very dim light get a camera
+ 
+
+ align:start position:0%
+pictures in very dim light get a camera
+with a very large lens opening
+
+ align:start position:0%
+with a very large lens opening
+ 
+
+ align:start position:0%
+with a very large lens opening
+like f1.8 or something like that it'll
+
+ align:start position:0%
+like f1.8 or something like that it'll
+ 
+
+ align:start position:0%
+like f1.8 or something like that it'll
+take in a lot of light okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question excellent question we we we
+
+ align:start position:0%
+question excellent question we we we
+ 
+
+ align:start position:0%
+question excellent question we we we
+know that animals with forward-looking
+
+ align:start position:0%
+know that animals with forward-looking
+ 
+
+ align:start position:0%
+know that animals with forward-looking
+eyes they're usually
+
+ align:start position:0%
+eyes they're usually
+ 
+
+ align:start position:0%
+eyes they're usually
+predators and primates and primates are
+
+ align:start position:0%
+predators and primates and primates are
+ 
+
+ align:start position:0%
+predators and primates and primates are
+usually Predators too but not all of
+
+ align:start position:0%
+usually Predators too but not all of
+ 
+
+ align:start position:0%
+usually Predators too but not all of
+them some of them have fruit Gathering
+
+ align:start position:0%
+them some of them have fruit Gathering
+ 
+
+ align:start position:0%
+them some of them have fruit Gathering
+primates but they also need good biner
+
+ align:start position:0%
+primates but they also need good biner
+ 
+
+ align:start position:0%
+primates but they also need good biner
+Vision so they have forward- facing eyes
+
+ align:start position:0%
+Vision so they have forward- facing eyes
+ 
+
+ align:start position:0%
+Vision so they have forward- facing eyes
+too uh but what about the animals with
+
+ align:start position:0%
+too uh but what about the animals with
+ 
+
+ align:start position:0%
+too uh but what about the animals with
+these eyes that like the the hamster
+
+ align:start position:0%
+these eyes that like the the hamster
+ 
+
+ align:start position:0%
+these eyes that like the the hamster
+it's got eyes that look 60° out and 30°
+
+ align:start position:0%
+it's got eyes that look 60° out and 30°
+ 
+
+ align:start position:0%
+it's got eyes that look 60° out and 30°
+up Horizon that's way their eyes look
+
+ align:start position:0%
+up Horizon that's way their eyes look
+ 
+
+ align:start position:0%
+up Horizon that's way their eyes look
+that's the natural position of the eyes
+
+ align:start position:0%
+that's the natural position of the eyes
+ 
+
+ align:start position:0%
+that's the natural position of the eyes
+I've measured it in the hamster but it's
+
+ align:start position:0%
+I've measured it in the hamster but it's
+ 
+
+ align:start position:0%
+I've measured it in the hamster but it's
+pretty similar in other little
+
+ align:start position:0%
+pretty similar in other little
+ 
+
+ align:start position:0%
+pretty similar in other little
+rodents they do have an area of
+
+ align:start position:0%
+rodents they do have an area of
+ 
+
+ align:start position:0%
+rodents they do have an area of
+binocular vision there's about at least
+
+ align:start position:0%
+binocular vision there's about at least
+ 
+
+ align:start position:0%
+binocular vision there's about at least
+30° overlap okay and in that Central
+
+ align:start position:0%
+30° overlap okay and in that Central
+ 
+
+ align:start position:0%
+30° overlap okay and in that Central
+area which the center of it is 30° above
+
+ align:start position:0%
+area which the center of it is 30° above
+ 
+
+ align:start position:0%
+area which the center of it is 30° above
+okay they do have binocular vision okay
+
+ align:start position:0%
+okay they do have binocular vision okay
+ 
+
+ align:start position:0%
+okay they do have binocular vision okay
+and they but it's pretty rudimentary
+
+ align:start position:0%
+and they but it's pretty rudimentary
+ 
+
+ align:start position:0%
+and they but it's pretty rudimentary
+compared to the primates and also they
+
+ align:start position:0%
+compared to the primates and also they
+ 
+
+ align:start position:0%
+compared to the primates and also they
+don't have the High Acuity that primates
+
+ align:start position:0%
+don't have the High Acuity that primates
+ 
+
+ align:start position:0%
+don't have the High Acuity that primates
+have but it's still important for them
+
+ align:start position:0%
+have but it's still important for them
+ 
+
+ align:start position:0%
+have but it's still important for them
+but I've looked at hamster Behavior a
+
+ align:start position:0%
+but I've looked at hamster Behavior a
+ 
+
+ align:start position:0%
+but I've looked at hamster Behavior a
+lot and they they
+
+ align:start position:0%
+lot and they they
+ 
+
+ align:start position:0%
+lot and they they
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+things 5T or even 2 fet and 30 ft away
+
+ align:start position:0%
+things 5T or even 2 fet and 30 ft away
+ 
+
+ align:start position:0%
+things 5T or even 2 fet and 30 ft away
+they don't discriminate very well you
+
+ align:start position:0%
+they don't discriminate very well you
+ 
+
+ align:start position:0%
+they don't discriminate very well you
+know but for things near them they
+
+ align:start position:0%
+know but for things near them they
+ 
+
+ align:start position:0%
+know but for things near them they
+definitely can judge Vision they won't
+
+ align:start position:0%
+definitely can judge Vision they won't
+ 
+
+ align:start position:0%
+definitely can judge Vision they won't
+leap sometimes they do but usually they
+
+ align:start position:0%
+leap sometimes they do but usually they
+ 
+
+ align:start position:0%
+leap sometimes they do but usually they
+won't
+
+ align:start position:0%
+won't
+ 
+
+ align:start position:0%
+won't
+jump into places that are too dangerous
+
+ align:start position:0%
+jump into places that are too dangerous
+ 
+
+ align:start position:0%
+jump into places that are too dangerous
+because they're too high they can see
+
+ align:start position:0%
+because they're too high they can see
+ 
+
+ align:start position:0%
+because they're too high they can see
+the depth well enough it doesn't mean
+
+ align:start position:0%
+the depth well enough it doesn't mean
+ 
+
+ align:start position:0%
+the depth well enough it doesn't mean
+stereopsis cues though it could just be
+
+ align:start position:0%
+stereopsis cues though it could just be
+ 
+
+ align:start position:0%
+stereopsis cues though it could just be
+the the uh various other cues like when
+
+ align:start position:0%
+the the uh various other cues like when
+ 
+
+ align:start position:0%
+the the uh various other cues like when
+they move their head The Parallax that
+
+ align:start position:0%
+they move their head The Parallax that
+ 
+
+ align:start position:0%
+they move their head The Parallax that
+you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there's various cues to depth but if
+
+ align:start position:0%
+uh there's various cues to depth but if
+ 
+
+ align:start position:0%
+uh there's various cues to depth but if
+you study sensation perception class
+
+ align:start position:0%
+you study sensation perception class
+ 
+
+ align:start position:0%
+you study sensation perception class
+here at the MIT you'll learn about
+
+ align:start position:0%
+here at the MIT you'll learn about
+ 
+
+ align:start position:0%
+here at the MIT you'll learn about
+multiple different different various
+
+ align:start position:0%
+multiple different different various
+ 
+
+ align:start position:0%
+multiple different different various
+cues for depth okay that don't involve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stereopsis all right so now we want to
+
+ align:start position:0%
+stereopsis all right so now we want to
+ 
+
+ align:start position:0%
+stereopsis all right so now we want to
+look at the retinal
+
+ align:start position:0%
+look at the retinal
+ 
+
+ align:start position:0%
+look at the retinal
+projections it's a pattern you find in
+
+ align:start position:0%
+projections it's a pattern you find in
+ 
+
+ align:start position:0%
+projections it's a pattern you find in
+all the mammals and I should add that
+
+ align:start position:0%
+all the mammals and I should add that
+ 
+
+ align:start position:0%
+all the mammals and I should add that
+it's really similar in all of the
+
+ align:start position:0%
+it's really similar in all of the
+ 
+
+ align:start position:0%
+it's really similar in all of the
+vertebrates okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is the picture I showed in the last
+
+ align:start position:0%
+this is the picture I showed in the last
+ 
+
+ align:start position:0%
+this is the picture I showed in the last
+class the sort of a cartoon of the optic
+
+ align:start position:0%
+class the sort of a cartoon of the optic
+ 
+
+ align:start position:0%
+class the sort of a cartoon of the optic
+the main optic tract and the accessory
+
+ align:start position:0%
+the main optic tract and the accessory
+ 
+
+ align:start position:0%
+the main optic tract and the accessory
+optic tract here just showing so now we
+
+ align:start position:0%
+optic tract here just showing so now we
+ 
+
+ align:start position:0%
+optic tract here just showing so now we
+want to look at a little more detail of
+
+ align:start position:0%
+want to look at a little more detail of
+ 
+
+ align:start position:0%
+want to look at a little more detail of
+the layout of that system from
+
+ align:start position:0%
+the layout of that system from
+ 
+
+ align:start position:0%
+the layout of that system from
+supermatic nucleus to the two geniculate
+
+ align:start position:0%
+supermatic nucleus to the two geniculate
+ 
+
+ align:start position:0%
+supermatic nucleus to the two geniculate
+nuclei pretectal region where there's
+
+ align:start position:0%
+nuclei pretectal region where there's
+ 
+
+ align:start position:0%
+nuclei pretectal region where there's
+several nuclei where they terminate
+
+ align:start position:0%
+several nuclei where they terminate
+ 
+
+ align:start position:0%
+several nuclei where they terminate
+Superior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cicular so we look at the retinal
+
+ align:start position:0%
+cicular so we look at the retinal
+ 
+
+ align:start position:0%
+cicular so we look at the retinal
+projection in vertebrates the layout of
+
+ align:start position:0%
+projection in vertebrates the layout of
+ 
+
+ align:start position:0%
+projection in vertebrates the layout of
+the optic track and we'll look at them
+
+ align:start position:0%
+the optic track and we'll look at them
+ 
+
+ align:start position:0%
+the optic track and we'll look at them
+in several different ways of looking at
+
+ align:start position:0%
+in several different ways of looking at
+ 
+
+ align:start position:0%
+in several different ways of looking at
+it we'll talk about species differences
+
+ align:start position:0%
+it we'll talk about species differences
+ 
+
+ align:start position:0%
+it we'll talk about species differences
+in relative size of structures because
+
+ align:start position:0%
+in relative size of structures because
+ 
+
+ align:start position:0%
+in relative size of structures because
+qu qualitatively they all have the same
+
+ align:start position:0%
+qu qualitatively they all have the same
+ 
+
+ align:start position:0%
+qu qualitatively they all have the same
+basic
+
+ align:start position:0%
+basic
+ 
+
+ align:start position:0%
+basic
+layout but there are large species
+
+ align:start position:0%
+layout but there are large species
+ 
+
+ align:start position:0%
+layout but there are large species
+differences in relative sizes as well as
+
+ align:start position:0%
+differences in relative sizes as well as
+ 
+
+ align:start position:0%
+differences in relative sizes as well as
+in the eyes are different too so you
+
+ align:start position:0%
+in the eyes are different too so you
+ 
+
+ align:start position:0%
+in the eyes are different too so you
+have different different amount
+
+ align:start position:0%
+have different different amount
+ 
+
+ align:start position:0%
+have different different amount
+different levels of accuity Invision are
+
+ align:start position:0%
+different levels of accuity Invision are
+ 
+
+ align:start position:0%
+different levels of accuity Invision are
+possible in these different species
+
+ align:start position:0%
+possible in these different species
+ 
+
+ align:start position:0%
+possible in these different species
+we'll look a little bit at the at
+
+ align:start position:0%
+we'll look a little bit at the at
+ 
+
+ align:start position:0%
+we'll look a little bit at the at
+architectural differences especially in
+
+ align:start position:0%
+architectural differences especially in
+ 
+
+ align:start position:0%
+architectural differences especially in
+the genicular body and in the optic
+
+ align:start position:0%
+the genicular body and in the optic
+ 
+
+ align:start position:0%
+the genicular body and in the optic
+tectum
+
+ align:start position:0%
+tectum
+ 
+
+ align:start position:0%
+tectum
+so we'll look at lamination in the
+
+ align:start position:0%
+so we'll look at lamination in the
+ 
+
+ align:start position:0%
+so we'll look at lamination in the
+midbrain
+
+ align:start position:0%
+midbrain
+ 
+
+ align:start position:0%
+midbrain
+tectum we'll also look at lamination in
+
+ align:start position:0%
+tectum we'll also look at lamination in
+ 
+
+ align:start position:0%
+tectum we'll also look at lamination in
+the geniculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body and finally we'll look at
+
+ align:start position:0%
+body and finally we'll look at
+ 
+
+ align:start position:0%
+body and finally we'll look at
+topography and I know when you first get
+
+ align:start position:0%
+topography and I know when you first get
+ 
+
+ align:start position:0%
+topography and I know when you first get
+all this you get a little overwhelmed by
+
+ align:start position:0%
+all this you get a little overwhelmed by
+ 
+
+ align:start position:0%
+all this you get a little overwhelmed by
+all the structures and everything so I'm
+
+ align:start position:0%
+all the structures and everything so I'm
+ 
+
+ align:start position:0%
+all the structures and everything so I'm
+not asking you to memorize the
+
+ align:start position:0%
+not asking you to memorize the
+ 
+
+ align:start position:0%
+not asking you to memorize the
+topography but I want you to see I will
+
+ align:start position:0%
+topography but I want you to see I will
+ 
+
+ align:start position:0%
+topography but I want you to see I will
+present it to you in a way that does
+
+ align:start position:0%
+present it to you in a way that does
+ 
+
+ align:start position:0%
+present it to you in a way that does
+make it pretty easy to learn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and these are the questions I put
+
+ align:start position:0%
+okay and these are the questions I put
+ 
+
+ align:start position:0%
+okay and these are the questions I put
+in the list of questions I put online
+
+ align:start position:0%
+in the list of questions I put online
+ 
+
+ align:start position:0%
+in the list of questions I put online
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you these are things we've dealt with
+
+ align:start position:0%
+you these are things we've dealt with
+ 
+
+ align:start position:0%
+you these are things we've dealt with
+before these two questions let's just
+
+ align:start position:0%
+before these two questions let's just
+ 
+
+ align:start position:0%
+before these two questions let's just
+see if any of you have an idea about
+
+ align:start position:0%
+see if any of you have an idea about
+ 
+
+ align:start position:0%
+see if any of you have an idea about
+this first of all what's the first
+
+ align:start position:0%
+this first of all what's the first
+ 
+
+ align:start position:0%
+this first of all what's the first
+structure reached by the accents from
+
+ align:start position:0%
+structure reached by the accents from
+ 
+
+ align:start position:0%
+structure reached by the accents from
+the retinal gang
+
+ align:start position:0%
+the retinal gang
+ 
+
+ align:start position:0%
+the retinal gang
+cells Gan cells project through the
+
+ align:start position:0%
+cells Gan cells project through the
+ 
+
+ align:start position:0%
+cells Gan cells project through the
+nerve we start calling at the tract when
+
+ align:start position:0%
+nerve we start calling at the tract when
+ 
+
+ align:start position:0%
+nerve we start calling at the tract when
+it joins with the rest of the dianon so
+
+ align:start position:0%
+it joins with the rest of the dianon so
+ 
+
+ align:start position:0%
+it joins with the rest of the dianon so
+what's the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure exactly supermatic nucleus
+
+ align:start position:0%
+structure exactly supermatic nucleus
+ 
+
+ align:start position:0%
+structure exactly supermatic nucleus
+right above the crossing of the accent
+
+ align:start position:0%
+right above the crossing of the accent
+ 
+
+ align:start position:0%
+right above the crossing of the accent
+so it's got to be the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one it's part of the hypothalamus
+
+ align:start position:0%
+one it's part of the hypothalamus
+ 
+
+ align:start position:0%
+one it's part of the hypothalamus
+definitely
+
+ align:start position:0%
+definitely
+ 
+
+ align:start position:0%
+definitely
+okay the area in front of that region we
+
+ align:start position:0%
+okay the area in front of that region we
+ 
+
+ align:start position:0%
+okay the area in front of that region we
+call preoptic area of the
+
+ align:start position:0%
+call preoptic area of the
+ 
+
+ align:start position:0%
+call preoptic area of the
+hypothalamus because it's in front of
+
+ align:start position:0%
+hypothalamus because it's in front of
+ 
+
+ align:start position:0%
+hypothalamus because it's in front of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opticis actually we talk about the
+
+ align:start position:0%
+opticis actually we talk about the
+ 
+
+ align:start position:0%
+opticis actually we talk about the
+anterior hypothalamic nucleus and then
+
+ align:start position:0%
+anterior hypothalamic nucleus and then
+ 
+
+ align:start position:0%
+anterior hypothalamic nucleus and then
+the preoptic nucleus so I modify my
+
+ align:start position:0%
+the preoptic nucleus so I modify my
+ 
+
+ align:start position:0%
+the preoptic nucleus so I modify my
+first statement a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit so the four brain subdivision you've
+
+ align:start position:0%
+bit so the four brain subdivision you've
+ 
+
+ align:start position:0%
+bit so the four brain subdivision you've
+just named it's the
+
+ align:start position:0%
+just named it's the
+ 
+
+ align:start position:0%
+just named it's the
+hypothalamus and the major terminal
+
+ align:start position:0%
+hypothalamus and the major terminal
+ 
+
+ align:start position:0%
+hypothalamus and the major terminal
+nucleus in that subdivision is the super
+
+ align:start position:0%
+nucleus in that subdivision is the super
+ 
+
+ align:start position:0%
+nucleus in that subdivision is the super
+I nucleus now remember there there's
+
+ align:start position:0%
+I nucleus now remember there there's
+ 
+
+ align:start position:0%
+I nucleus now remember there there's
+some spill over there too uh that I
+
+ align:start position:0%
+some spill over there too uh that I
+ 
+
+ align:start position:0%
+some spill over there too uh that I
+showed you last time it does project bit
+
+ align:start position:0%
+showed you last time it does project bit
+ 
+
+ align:start position:0%
+showed you last time it does project bit
+to immediately adjoining parts of the
+
+ align:start position:0%
+to immediately adjoining parts of the
+ 
+
+ align:start position:0%
+to immediately adjoining parts of the
+hypothalamus but we know most about that
+
+ align:start position:0%
+hypothalamus but we know most about that
+ 
+
+ align:start position:0%
+hypothalamus but we know most about that
+supermatic nucleus it's very little
+
+ align:start position:0%
+supermatic nucleus it's very little
+ 
+
+ align:start position:0%
+supermatic nucleus it's very little
+known about the functions of the sparse
+
+ align:start position:0%
+known about the functions of the sparse
+ 
+
+ align:start position:0%
+known about the functions of the sparse
+projections people tend to think that
+
+ align:start position:0%
+projections people tend to think that
+ 
+
+ align:start position:0%
+projections people tend to think that
+they don't play any major roles it's why
+
+ align:start position:0%
+they don't play any major roles it's why
+ 
+
+ align:start position:0%
+they don't play any major roles it's why
+they're so
+
+ align:start position:0%
+they're so
+ 
+
+ align:start position:0%
+they're so
+sparse uh
+
+ align:start position:0%
+sparse uh
+ 
+
+ align:start position:0%
+sparse uh
+I'm not convinced of
+
+ align:start position:0%
+I'm not convinced of
+ 
+
+ align:start position:0%
+I'm not convinced of
+that uh they could play important roles
+
+ align:start position:0%
+that uh they could play important roles
+ 
+
+ align:start position:0%
+that uh they could play important roles
+you uh
+
+ align:start position:0%
+you uh
+ 
+
+ align:start position:0%
+you uh
+but the one thing that makes me doubt it
+
+ align:start position:0%
+but the one thing that makes me doubt it
+ 
+
+ align:start position:0%
+but the one thing that makes me doubt it
+a little bit is just that there's
+
+ align:start position:0%
+a little bit is just that there's
+ 
+
+ align:start position:0%
+a little bit is just that there's
+variability when I study the retinal
+
+ align:start position:0%
+variability when I study the retinal
+ 
+
+ align:start position:0%
+variability when I study the retinal
+projections in a number of different
+
+ align:start position:0%
+projections in a number of different
+ 
+
+ align:start position:0%
+projections in a number of different
+hamsters I do get differences in these
+
+ align:start position:0%
+hamsters I do get differences in these
+ 
+
+ align:start position:0%
+hamsters I do get differences in these
+very sparse
+
+ align:start position:0%
+very sparse
+ 
+
+ align:start position:0%
+very sparse
+projections some animals I see more some
+
+ align:start position:0%
+projections some animals I see more some
+ 
+
+ align:start position:0%
+projections some animals I see more some
+I see less but they're always there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the next question is what's the
+
+ align:start position:0%
+okay the next question is what's the
+ 
+
+ align:start position:0%
+okay the next question is what's the
+major difference in the nature of the
+
+ align:start position:0%
+major difference in the nature of the
+ 
+
+ align:start position:0%
+major difference in the nature of the
+projections of the dorsal Thalamus on
+
+ align:start position:0%
+projections of the dorsal Thalamus on
+ 
+
+ align:start position:0%
+projections of the dorsal Thalamus on
+the one hand and the ventral Thalamus or
+
+ align:start position:0%
+the one hand and the ventral Thalamus or
+ 
+
+ align:start position:0%
+the one hand and the ventral Thalamus or
+the epithalamus that is after you go
+
+ align:start position:0%
+the epithalamus that is after you go
+ 
+
+ align:start position:0%
+the epithalamus that is after you go
+past the supermatic inuse the accents go
+
+ align:start position:0%
+past the supermatic inuse the accents go
+ 
+
+ align:start position:0%
+past the supermatic inuse the accents go
+up the side of the dlon and they reach
+
+ align:start position:0%
+up the side of the dlon and they reach
+ 
+
+ align:start position:0%
+up the side of the dlon and they reach
+the sub Talus just above the
+
+ align:start position:0%
+the sub Talus just above the
+ 
+
+ align:start position:0%
+the sub Talus just above the
+hypothalamus then they reach the dorsal
+
+ align:start position:0%
+hypothalamus then they reach the dorsal
+ 
+
+ align:start position:0%
+hypothalamus then they reach the dorsal
+Thalamus then they reach the
+
+ align:start position:0%
+Thalamus then they reach the
+ 
+
+ align:start position:0%
+Thalamus then they reach the
+epithalamus the pretectal nuclei in the
+
+ align:start position:0%
+epithalamus the pretectal nuclei in the
+ 
+
+ align:start position:0%
+epithalamus the pretectal nuclei in the
+epithalamus so there's a big difference
+
+ align:start position:0%
+epithalamus so there's a big difference
+ 
+
+ align:start position:0%
+epithalamus so there's a big difference
+though in the nature of the projections
+
+ align:start position:0%
+though in the nature of the projections
+ 
+
+ align:start position:0%
+though in the nature of the projections
+of the dorsal Thalamus and those other
+
+ align:start position:0%
+of the dorsal Thalamus and those other
+ 
+
+ align:start position:0%
+of the dorsal Thalamus and those other
+groups what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difference exactly biggest difference is
+
+ align:start position:0%
+difference exactly biggest difference is
+ 
+
+ align:start position:0%
+difference exactly biggest difference is
+what she just said the dorsal phalance
+
+ align:start position:0%
+what she just said the dorsal phalance
+ 
+
+ align:start position:0%
+what she just said the dorsal phalance
+and all the major cell GR
+
+ align:start position:0%
+and all the major cell GR
+ 
+
+ align:start position:0%
+and all the major cell GR
+the the at least the Neo Thalamus that
+
+ align:start position:0%
+the the at least the Neo Thalamus that
+ 
+
+ align:start position:0%
+the the at least the Neo Thalamus that
+more recent but we think we of the
+
+ align:start position:0%
+more recent but we think we of the
+ 
+
+ align:start position:0%
+more recent but we think we of the
+dorsal Thalamus like the lateral
+
+ align:start position:0%
+dorsal Thalamus like the lateral
+ 
+
+ align:start position:0%
+dorsal Thalamus like the lateral
+genicular body but the same thing holds
+
+ align:start position:0%
+genicular body but the same thing holds
+ 
+
+ align:start position:0%
+genicular body but the same thing holds
+true for the ventral nucleus mediodorsal
+
+ align:start position:0%
+true for the ventral nucleus mediodorsal
+ 
+
+ align:start position:0%
+true for the ventral nucleus mediodorsal
+nucleus uh medial genicular body IT
+
+ align:start position:0%
+nucleus uh medial genicular body IT
+ 
+
+ align:start position:0%
+nucleus uh medial genicular body IT
+projects to Cortex okay mainly to
+
+ align:start position:0%
+projects to Cortex okay mainly to
+ 
+
+ align:start position:0%
+projects to Cortex okay mainly to
+neocortex it goes to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+embran some neurons some accents will
+
+ align:start position:0%
+embran some neurons some accents will
+ 
+
+ align:start position:0%
+embran some neurons some accents will
+have collaterals in the them on their
+
+ align:start position:0%
+have collaterals in the them on their
+ 
+
+ align:start position:0%
+have collaterals in the them on their
+way to the end braan but the major
+
+ align:start position:0%
+way to the end braan but the major
+ 
+
+ align:start position:0%
+way to the end braan but the major
+projections to the end braan those other
+
+ align:start position:0%
+projections to the end braan those other
+ 
+
+ align:start position:0%
+projections to the end braan those other
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+subs and epip Palms don't project to the
+
+ align:start position:0%
+subs and epip Palms don't project to the
+ 
+
+ align:start position:0%
+subs and epip Palms don't project to the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+braan I mean there were
+
+ align:start position:0%
+braan I mean there were
+ 
+
+ align:start position:0%
+braan I mean there were
+reports you know that they do but modern
+
+ align:start position:0%
+reports you know that they do but modern
+ 
+
+ align:start position:0%
+reports you know that they do but modern
+techniques have never been able to
+
+ align:start position:0%
+techniques have never been able to
+ 
+
+ align:start position:0%
+techniques have never been able to
+verify that they don't project to
+
+ align:start position:0%
+verify that they don't project to
+ 
+
+ align:start position:0%
+verify that they don't project to
+neocortex in
+
+ align:start position:0%
+neocortex in
+ 
+
+ align:start position:0%
+neocortex in
+fact besides some ascending
+
+ align:start position:0%
+fact besides some ascending
+ 
+
+ align:start position:0%
+fact besides some ascending
+projections they have a lot of
+
+ align:start position:0%
+projections they have a lot of
+ 
+
+ align:start position:0%
+projections they have a lot of
+descending
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projections okay so that's the major
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difference okay now I last time I
+
+ align:start position:0%
+difference okay now I last time I
+ 
+
+ align:start position:0%
+difference okay now I last time I
+mention the
+
+ align:start position:0%
+mention the
+ 
+
+ align:start position:0%
+mention the
+epithalamus as a codl most
+
+ align:start position:0%
+epithalamus as a codl most
+ 
+
+ align:start position:0%
+epithalamus as a codl most
+dianic segment or
+
+ align:start position:0%
+dianic segment or
+ 
+
+ align:start position:0%
+dianic segment or
+neuromere it includes cell groups where
+
+ align:start position:0%
+neuromere it includes cell groups where
+ 
+
+ align:start position:0%
+neuromere it includes cell groups where
+the optic track as dense terminations so
+
+ align:start position:0%
+the optic track as dense terminations so
+ 
+
+ align:start position:0%
+the optic track as dense terminations so
+again what do we call those areas of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+termination we call them by we call them
+
+ align:start position:0%
+termination we call them by we call them
+ 
+
+ align:start position:0%
+termination we call them by we call them
+certain nuclei depending on where they
+
+ align:start position:0%
+certain nuclei depending on where they
+ 
+
+ align:start position:0%
+certain nuclei depending on where they
+are they're in
+
+ align:start position:0%
+are they're in
+ 
+
+ align:start position:0%
+are they're in
+front of the tectum so we call them
+
+ align:start position:0%
+front of the tectum so we call them
+ 
+
+ align:start position:0%
+front of the tectum so we call them
+prector okay it doesn't they are rather
+
+ align:start position:0%
+prector okay it doesn't they are rather
+ 
+
+ align:start position:0%
+prector okay it doesn't they are rather
+different these different groups and
+
+ align:start position:0%
+different these different groups and
+ 
+
+ align:start position:0%
+different these different groups and
+they have different functions but we
+
+ align:start position:0%
+they have different functions but we
+ 
+
+ align:start position:0%
+they have different functions but we
+lump them together because they're all
+
+ align:start position:0%
+lump them together because they're all
+ 
+
+ align:start position:0%
+lump them together because they're all
+in that same region call them the
+
+ align:start position:0%
+in that same region call them the
+ 
+
+ align:start position:0%
+in that same region call them the
+pretectal nuclei okay so this is two
+
+ align:start position:0%
+pretectal nuclei okay so this is two
+ 
+
+ align:start position:0%
+pretectal nuclei okay so this is two
+ways to look at don't worry I'll blow
+
+ align:start position:0%
+ways to look at don't worry I'll blow
+ 
+
+ align:start position:0%
+ways to look at don't worry I'll blow
+these up but here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crosssection of the level through the
+
+ align:start position:0%
+crosssection of the level through the
+ 
+
+ align:start position:0%
+crosssection of the level through the
+Dippin this is actually behind the optic
+
+ align:start position:0%
+Dippin this is actually behind the optic
+ 
+
+ align:start position:0%
+Dippin this is actually behind the optic
+kais but you see the optic tract
+
+ align:start position:0%
+kais but you see the optic tract
+ 
+
+ align:start position:0%
+kais but you see the optic tract
+covering most of the dianon or tween
+
+ align:start position:0%
+covering most of the dianon or tween
+ 
+
+ align:start position:0%
+covering most of the dianon or tween
+brain at this level the pretectum up
+
+ align:start position:0%
+brain at this level the pretectum up
+ 
+
+ align:start position:0%
+brain at this level the pretectum up
+here dorsal thamus with the lateral
+
+ align:start position:0%
+here dorsal thamus with the lateral
+ 
+
+ align:start position:0%
+here dorsal thamus with the lateral
+geniculate nucleus right there here's
+
+ align:start position:0%
+geniculate nucleus right there here's
+ 
+
+ align:start position:0%
+geniculate nucleus right there here's
+the subthalamus with the ventral nucleus
+
+ align:start position:0%
+the subthalamus with the ventral nucleus
+ 
+
+ align:start position:0%
+the subthalamus with the ventral nucleus
+of the genicular body there there's
+
+ align:start position:0%
+of the genicular body there there's
+ 
+
+ align:start position:0%
+of the genicular body there there's
+hypothalamus okay this is behind the
+
+ align:start position:0%
+hypothalamus okay this is behind the
+ 
+
+ align:start position:0%
+hypothalamus okay this is behind the
+opticis and the optic track C goes
+
+ align:start position:0%
+opticis and the optic track C goes
+ 
+
+ align:start position:0%
+opticis and the optic track C goes
+covers all these that's why that area is
+
+ align:start position:0%
+covers all these that's why that area is
+ 
+
+ align:start position:0%
+covers all these that's why that area is
+sometimes called optic balance just
+
+ align:start position:0%
+sometimes called optic balance just
+ 
+
+ align:start position:0%
+sometimes called optic balance just
+because the aons of the optic track
+
+ align:start position:0%
+because the aons of the optic track
+ 
+
+ align:start position:0%
+because the aons of the optic track
+cover
+
+ align:start position:0%
+cover
+ 
+
+ align:start position:0%
+cover
+it and then these are the subdivisions
+
+ align:start position:0%
+it and then these are the subdivisions
+ 
+
+ align:start position:0%
+it and then these are the subdivisions
+written as the names for
+
+ align:start position:0%
+written as the names for
+ 
+
+ align:start position:0%
+written as the names for
+their the
+
+ align:start position:0%
+their the
+ 
+
+ align:start position:0%
+their the
+neuromeres now we know hypothalamus is
+
+ align:start position:0%
+neuromeres now we know hypothalamus is
+ 
+
+ align:start position:0%
+neuromeres now we know hypothalamus is
+actually two or three different neurom
+
+ align:start position:0%
+actually two or three different neurom
+ 
+
+ align:start position:0%
+actually two or three different neurom
+mirors and then we call this the ventral
+
+ align:start position:0%
+mirors and then we call this the ventral
+ 
+
+ align:start position:0%
+mirors and then we call this the ventral
+Talus then in the adult we call it sub
+
+ align:start position:0%
+Talus then in the adult we call it sub
+ 
+
+ align:start position:0%
+Talus then in the adult we call it sub
+Talus then the dorsal pelis then the
+
+ align:start position:0%
+Talus then the dorsal pelis then the
+ 
+
+ align:start position:0%
+Talus then the dorsal pelis then the
+epis okay but now there's another way to
+
+ align:start position:0%
+epis okay but now there's another way to
+ 
+
+ align:start position:0%
+epis okay but now there's another way to
+look at the track that I use for
+
+ align:start position:0%
+look at the track that I use for
+ 
+
+ align:start position:0%
+look at the track that I use for
+teaching purposes but I think it's very
+
+ align:start position:0%
+teaching purposes but I think it's very
+ 
+
+ align:start position:0%
+teaching purposes but I think it's very
+useful I just take the track all the way
+
+ align:start position:0%
+useful I just take the track all the way
+ 
+
+ align:start position:0%
+useful I just take the track all the way
+from the supermatic nucleus all the way
+
+ align:start position:0%
+from the supermatic nucleus all the way
+ 
+
+ align:start position:0%
+from the supermatic nucleus all the way
+to the tectum just stretch it out okay
+
+ align:start position:0%
+to the tectum just stretch it out okay
+ 
+
+ align:start position:0%
+to the tectum just stretch it out okay
+so you
+
+ align:start position:0%
+so you
+ 
+
+ align:start position:0%
+so you
+see the retina would be way off here to
+
+ align:start position:0%
+see the retina would be way off here to
+ 
+
+ align:start position:0%
+see the retina would be way off here to
+the left off the screen there to the
+
+ align:start position:0%
+the left off the screen there to the
+ 
+
+ align:start position:0%
+the left off the screen there to the
+left there's the super chiasmatic
+
+ align:start position:0%
+left there's the super chiasmatic
+ 
+
+ align:start position:0%
+left there's the super chiasmatic
+nucleus it's more commonly abbreviated
+
+ align:start position:0%
+nucleus it's more commonly abbreviated
+ 
+
+ align:start position:0%
+nucleus it's more commonly abbreviated
+scn here we call it just but could be
+
+ align:start position:0%
+scn here we call it just but could be
+ 
+
+ align:start position:0%
+scn here we call it just but could be
+done either way and then I just follow
+
+ align:start position:0%
+done either way and then I just follow
+ 
+
+ align:start position:0%
+done either way and then I just follow
+the accents straighten out the tract
+
+ align:start position:0%
+the accents straighten out the tract
+ 
+
+ align:start position:0%
+the accents straighten out the tract
+okay and I show what happens to them the
+
+ align:start position:0%
+okay and I show what happens to them the
+ 
+
+ align:start position:0%
+okay and I show what happens to them the
+longest ones make it to the superior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cicular where they no longer travel
+
+ align:start position:0%
+cicular where they no longer travel
+ 
+
+ align:start position:0%
+cicular where they no longer travel
+mainly at the surface the rest of the
+
+ align:start position:0%
+mainly at the surface the rest of the
+ 
+
+ align:start position:0%
+mainly at the surface the rest of the
+tract is mainly at the surface there are
+
+ align:start position:0%
+tract is mainly at the surface there are
+ 
+
+ align:start position:0%
+tract is mainly at the surface there are
+some that travel internally we call that
+
+ align:start position:0%
+some that travel internally we call that
+ 
+
+ align:start position:0%
+some that travel internally we call that
+the internal optic track but there's
+
+ align:start position:0%
+the internal optic track but there's
+ 
+
+ align:start position:0%
+the internal optic track but there's
+smaller numbers of accents that do that
+
+ align:start position:0%
+smaller numbers of accents that do that
+ 
+
+ align:start position:0%
+smaller numbers of accents that do that
+the main ones travel to the surface
+
+ align:start position:0%
+the main ones travel to the surface
+ 
+
+ align:start position:0%
+the main ones travel to the surface
+except when they get the sphere
+
+ align:start position:0%
+except when they get the sphere
+ 
+
+ align:start position:0%
+except when they get the sphere
+calculus actually they do travel at the
+
+ align:start position:0%
+calculus actually they do travel at the
+ 
+
+ align:start position:0%
+calculus actually they do travel at the
+surface of the culus early in
+
+ align:start position:0%
+surface of the culus early in
+ 
+
+ align:start position:0%
+surface of the culus early in
+development when they first get
+
+ align:start position:0%
+development when they first get
+ 
+
+ align:start position:0%
+development when they first get
+there so then how do they end
+
+ align:start position:0%
+there so then how do they end
+ 
+
+ align:start position:0%
+there so then how do they end
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+down below those superficial layers what
+
+ align:start position:0%
+down below those superficial layers what
+ 
+
+ align:start position:0%
+down below those superficial layers what
+has to happen they're on the
+
+ align:start position:0%
+has to happen they're on the
+ 
+
+ align:start position:0%
+has to happen they're on the
+surface and then they're not with
+
+ align:start position:0%
+surface and then they're not with
+ 
+
+ align:start position:0%
+surface and then they're not with
+further development either the axons
+
+ align:start position:0%
+further development either the axons
+ 
+
+ align:start position:0%
+further development either the axons
+that were on the surface have to die off
+
+ align:start position:0%
+that were on the surface have to die off
+ 
+
+ align:start position:0%
+that were on the surface have to die off
+or the cells in the calculus migrate up
+
+ align:start position:0%
+or the cells in the calculus migrate up
+ 
+
+ align:start position:0%
+or the cells in the calculus migrate up
+through them they're still migrating
+
+ align:start position:0%
+through them they're still migrating
+ 
+
+ align:start position:0%
+through them they're still migrating
+when this tract is farming and the
+
+ align:start position:0%
+when this tract is farming and the
+ 
+
+ align:start position:0%
+when this tract is farming and the
+latter interpretation appears to be
+
+ align:start position:0%
+latter interpretation appears to be
+ 
+
+ align:start position:0%
+latter interpretation appears to be
+true because you do see cell migrations
+
+ align:start position:0%
+true because you do see cell migrations
+ 
+
+ align:start position:0%
+true because you do see cell migrations
+going up to the superficial gray
+
+ align:start position:0%
+going up to the superficial gray
+ 
+
+ align:start position:0%
+going up to the superficial gray
+occurring after the first accents have
+
+ align:start position:0%
+occurring after the first accents have
+ 
+
+ align:start position:0%
+occurring after the first accents have
+reached there and when you look with
+
+ align:start position:0%
+reached there and when you look with
+ 
+
+ align:start position:0%
+reached there and when you look with
+stains that are capable of seeing
+
+ align:start position:0%
+stains that are capable of seeing
+ 
+
+ align:start position:0%
+stains that are capable of seeing
+degeneration occurring you don't see a
+
+ align:start position:0%
+degeneration occurring you don't see a
+ 
+
+ align:start position:0%
+degeneration occurring you don't see a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+degeneration okay so we think it's it's
+
+ align:start position:0%
+degeneration okay so we think it's it's
+ 
+
+ align:start position:0%
+degeneration okay so we think it's it's
+actually doe with the cell migration
+
+ align:start position:0%
+actually doe with the cell migration
+ 
+
+ align:start position:0%
+actually doe with the cell migration
+okay now here you see them it looks like
+
+ align:start position:0%
+okay now here you see them it looks like
+ 
+
+ align:start position:0%
+okay now here you see them it looks like
+they're branching off let let's do it
+
+ align:start position:0%
+they're branching off let let's do it
+ 
+
+ align:start position:0%
+they're branching off let let's do it
+this way here's that first picture again
+
+ align:start position:0%
+this way here's that first picture again
+ 
+
+ align:start position:0%
+this way here's that first picture again
+where I blow it up but it's the same
+
+ align:start position:0%
+where I blow it up but it's the same
+ 
+
+ align:start position:0%
+where I blow it up but it's the same
+thing and I point out here ventral
+
+ align:start position:0%
+thing and I point out here ventral
+ 
+
+ align:start position:0%
+thing and I point out here ventral
+Thalamus is not the ventral nucleus of
+
+ align:start position:0%
+Thalamus is not the ventral nucleus of
+ 
+
+ align:start position:0%
+Thalamus is not the ventral nucleus of
+the dorsal pamus it's really subthalamus
+
+ align:start position:0%
+the dorsal pamus it's really subthalamus
+ 
+
+ align:start position:0%
+the dorsal pamus it's really subthalamus
+okay the vental nucleus is this nucleus
+
+ align:start position:0%
+okay the vental nucleus is this nucleus
+ 
+
+ align:start position:0%
+okay the vental nucleus is this nucleus
+right up in here part of the dorsal
+
+ align:start position:0%
+right up in here part of the dorsal
+ 
+
+ align:start position:0%
+right up in here part of the dorsal
+pal so here I just show the places the
+
+ align:start position:0%
+pal so here I just show the places the
+ 
+
+ align:start position:0%
+pal so here I just show the places the
+optic crack terminates you see the
+
+ align:start position:0%
+optic crack terminates you see the
+ 
+
+ align:start position:0%
+optic crack terminates you see the
+dorsal part of the lateral genicular
+
+ align:start position:0%
+dorsal part of the lateral genicular
+ 
+
+ align:start position:0%
+dorsal part of the lateral genicular
+body now remember this is a road
+
+ align:start position:0%
+body now remember this is a road
+ 
+
+ align:start position:0%
+body now remember this is a road
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lp is not huge but it's the rest of the
+
+ align:start position:0%
+lp is not huge but it's the rest of the
+ 
+
+ align:start position:0%
+lp is not huge but it's the rest of the
+lateral phalam besides the genicular
+
+ align:start position:0%
+lateral phalam besides the genicular
+ 
+
+ align:start position:0%
+lateral phalam besides the genicular
+bodies you have lateral thalamic nuclei
+
+ align:start position:0%
+bodies you have lateral thalamic nuclei
+ 
+
+ align:start position:0%
+bodies you have lateral thalamic nuclei
+the the medial geniculate is another
+
+ align:start position:0%
+the the medial geniculate is another
+ 
+
+ align:start position:0%
+the the medial geniculate is another
+lateral thalamic
+
+ align:start position:0%
+lateral thalamic
+ 
+
+ align:start position:0%
+lateral thalamic
+nucleus
+
+ align:start position:0%
+nucleus
+ 
+
+ align:start position:0%
+nucleus
+uh here is a
+
+ align:start position:0%
+uh here is a
+ 
+
+ align:start position:0%
+uh here is a
+human 12 weeks post conception okay
+
+ align:start position:0%
+human 12 weeks post conception okay
+ 
+
+ align:start position:0%
+human 12 weeks post conception okay
+okay so 3mon human
+
+ align:start position:0%
+okay so 3mon human
+ 
+
+ align:start position:0%
+okay so 3mon human
+fetus there's the rodent
+
+ align:start position:0%
+fetus there's the rodent
+ 
+
+ align:start position:0%
+fetus there's the rodent
+adult here's the human
+
+ align:start position:0%
+adult here's the human
+ 
+
+ align:start position:0%
+adult here's the human
+Fus the
+
+ align:start position:0%
+Fus the
+ 
+
+ align:start position:0%
+Fus the
+adult human FS doesn't look like this at
+
+ align:start position:0%
+adult human FS doesn't look like this at
+ 
+
+ align:start position:0%
+adult human FS doesn't look like this at
+all okay I just want to point out that
+
+ align:start position:0%
+all okay I just want to point out that
+ 
+
+ align:start position:0%
+all okay I just want to point out that
+it's really the same as the
+
+ align:start position:0%
+it's really the same as the
+ 
+
+ align:start position:0%
+it's really the same as the
+rod in fact the embryo looks very
+
+ align:start position:0%
+rod in fact the embryo looks very
+ 
+
+ align:start position:0%
+rod in fact the embryo looks very
+similar okay but then it changes why
+
+ align:start position:0%
+similar okay but then it changes why
+ 
+
+ align:start position:0%
+similar okay but then it changes why
+anybody figure that
+
+ align:start position:0%
+anybody figure that
+ 
+
+ align:start position:0%
+anybody figure that
+out what happens to the human fals
+
+ align:start position:0%
+out what happens to the human fals
+ 
+
+ align:start position:0%
+out what happens to the human fals
+development after that first 3 months of
+
+ align:start position:0%
+development after that first 3 months of
+ 
+
+ align:start position:0%
+development after that first 3 months of
+Life the brain of a 3 month human fetus
+
+ align:start position:0%
+Life the brain of a 3 month human fetus
+ 
+
+ align:start position:0%
+Life the brain of a 3 month human fetus
+is pretty
+
+ align:start position:0%
+is pretty
+ 
+
+ align:start position:0%
+is pretty
+similar to a hamster just after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+birth but then something continues
+
+ align:start position:0%
+birth but then something continues
+ 
+
+ align:start position:0%
+birth but then something continues
+developing in the hamster in both the
+
+ align:start position:0%
+developing in the hamster in both the
+ 
+
+ align:start position:0%
+developing in the hamster in both the
+hamster and human but mostly in human
+
+ align:start position:0%
+hamster and human but mostly in human
+ 
+
+ align:start position:0%
+hamster and human but mostly in human
+after that first three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+months that means by the way the hamster
+
+ align:start position:0%
+months that means by the way the hamster
+ 
+
+ align:start position:0%
+months that means by the way the hamster
+at the human at 3 months postconception
+
+ align:start position:0%
+at the human at 3 months postconception
+ 
+
+ align:start position:0%
+at the human at 3 months postconception
+is like an early postnatal hamster and
+
+ align:start position:0%
+is like an early postnatal hamster and
+ 
+
+ align:start position:0%
+is like an early postnatal hamster and
+the hamster is born in the 16th day of
+
+ align:start position:0%
+the hamster is born in the 16th day of
+ 
+
+ align:start position:0%
+the hamster is born in the 16th day of
+gestation just to give you some times
+
+ align:start position:0%
+gestation just to give you some times
+ 
+
+ align:start position:0%
+gestation just to give you some times
+but anyway what
+
+ align:start position:0%
+but anyway what
+ 
+
+ align:start position:0%
+but anyway what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+this nucleus n labeled NL here the
+
+ align:start position:0%
+this nucleus n labeled NL here the
+ 
+
+ align:start position:0%
+this nucleus n labeled NL here the
+lateral nucleus nucleus lateralis this
+
+ align:start position:0%
+lateral nucleus nucleus lateralis this
+ 
+
+ align:start position:0%
+lateral nucleus nucleus lateralis this
+is the posterior part of nucleus
+
+ align:start position:0%
+is the posterior part of nucleus
+ 
+
+ align:start position:0%
+is the posterior part of nucleus
+lateralis okay that grows and grows and
+
+ align:start position:0%
+lateralis okay that grows and grows and
+ 
+
+ align:start position:0%
+lateralis okay that grows and grows and
+grows and in primates it really gets
+
+ align:start position:0%
+grows and in primates it really gets
+ 
+
+ align:start position:0%
+grows and in primates it really gets
+huge and we change its name we call only
+
+ align:start position:0%
+huge and we change its name we call only
+ 
+
+ align:start position:0%
+huge and we change its name we call only
+part of it the lateral posterior nucleus
+
+ align:start position:0%
+part of it the lateral posterior nucleus
+ 
+
+ align:start position:0%
+part of it the lateral posterior nucleus
+like we call the whole thing in rodents
+
+ align:start position:0%
+like we call the whole thing in rodents
+ 
+
+ align:start position:0%
+like we call the whole thing in rodents
+the rest of it we call the
+
+ align:start position:0%
+the rest of it we call the
+ 
+
+ align:start position:0%
+the rest of it we call the
+pulvinar which means pillow
+
+ align:start position:0%
+pulvinar which means pillow
+ 
+
+ align:start position:0%
+pulvinar which means pillow
+the pillow because it's bulging out so
+
+ align:start position:0%
+the pillow because it's bulging out so
+ 
+
+ align:start position:0%
+the pillow because it's bulging out so
+much because the cortex IT projects
+
+ align:start position:0%
+much because the cortex IT projects
+ 
+
+ align:start position:0%
+much because the cortex IT projects
+to even though it's there real early it
+
+ align:start position:0%
+to even though it's there real early it
+ 
+
+ align:start position:0%
+to even though it's there real early it
+expands so
+
+ align:start position:0%
+expands so
+ 
+
+ align:start position:0%
+expands so
+much and
+
+ align:start position:0%
+much and
+ 
+
+ align:start position:0%
+much and
+Thalamus you know a lot of people that
+
+ align:start position:0%
+Thalamus you know a lot of people that
+ 
+
+ align:start position:0%
+Thalamus you know a lot of people that
+talk about cortex just think the sensory
+
+ align:start position:0%
+talk about cortex just think the sensory
+ 
+
+ align:start position:0%
+talk about cortex just think the sensory
+input comes to it then you go from one
+
+ align:start position:0%
+input comes to it then you go from one
+ 
+
+ align:start position:0%
+input comes to it then you go from one
+region to the other in the cortex then
+
+ align:start position:0%
+region to the other in the cortex then
+ 
+
+ align:start position:0%
+region to the other in the cortex then
+you go out through the motor cortex not
+
+ align:start position:0%
+you go out through the motor cortex not
+ 
+
+ align:start position:0%
+you go out through the motor cortex not
+a very good accurate picture even though
+
+ align:start position:0%
+a very good accurate picture even though
+ 
+
+ align:start position:0%
+a very good accurate picture even though
+the majority of people in this building
+
+ align:start position:0%
+the majority of people in this building
+ 
+
+ align:start position:0%
+the majority of people in this building
+think like that that's not really a good
+
+ align:start position:0%
+think like that that's not really a good
+ 
+
+ align:start position:0%
+think like that that's not really a good
+picture connections of the cortex so
+
+ align:start position:0%
+picture connections of the cortex so
+ 
+
+ align:start position:0%
+picture connections of the cortex so
+we'll be dealing with that including
+
+ align:start position:0%
+we'll be dealing with that including
+ 
+
+ align:start position:0%
+we'll be dealing with that including
+some next next class but we'll continue
+
+ align:start position:0%
+some next next class but we'll continue
+ 
+
+ align:start position:0%
+some next next class but we'll continue
+dealing with it for the other
+
+ align:start position:0%
+dealing with it for the other
+ 
+
+ align:start position:0%
+dealing with it for the other
+systems all right so that's what happens
+
+ align:start position:0%
+systems all right so that's what happens
+ 
+
+ align:start position:0%
+systems all right so that's what happens
+otherwise this this at this
+
+ align:start position:0%
+otherwise this this at this
+ 
+
+ align:start position:0%
+otherwise this this at this
+stage these pictures are pretty similar
+
+ align:start position:0%
+stage these pictures are pretty similar
+ 
+
+ align:start position:0%
+stage these pictures are pretty similar
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+remember those
+
+ align:start position:0%
+remember those
+ 
+
+ align:start position:0%
+remember those
+divisions
+
+ align:start position:0%
+divisions
+ 
+
+ align:start position:0%
+divisions
+here happen because here an even earli
+
+ align:start position:0%
+here happen because here an even earli
+ 
+
+ align:start position:0%
+here happen because here an even earli
+very early embryon embryo where I show a
+
+ align:start position:0%
+very early embryon embryo where I show a
+ 
+
+ align:start position:0%
+very early embryon embryo where I show a
+side view with the segments remember the
+
+ align:start position:0%
+side view with the segments remember the
+ 
+
+ align:start position:0%
+side view with the segments remember the
+seven ROM mirors here then a little
+
+ align:start position:0%
+seven ROM mirors here then a little
+ 
+
+ align:start position:0%
+seven ROM mirors here then a little
+segment we call the ismos and then the
+
+ align:start position:0%
+segment we call the ismos and then the
+ 
+
+ align:start position:0%
+segment we call the ismos and then the
+midbrain which is a pretty big segment
+
+ align:start position:0%
+midbrain which is a pretty big segment
+ 
+
+ align:start position:0%
+midbrain which is a pretty big segment
+and then the
+
+ align:start position:0%
+and then the
+ 
+
+ align:start position:0%
+and then the
+epipal with the pretectal farming area
+
+ align:start position:0%
+epipal with the pretectal farming area
+ 
+
+ align:start position:0%
+epipal with the pretectal farming area
+farming here the vanela farming here and
+
+ align:start position:0%
+farming here the vanela farming here and
+ 
+
+ align:start position:0%
+farming here the vanela farming here and
+then dorsal thalamus
+
+ align:start position:0%
+then dorsal thalamus
+ 
+
+ align:start position:0%
+then dorsal thalamus
+ventral Thalamus or
+
+ align:start position:0%
+ventral Thalamus or
+ 
+
+ align:start position:0%
+ventral Thalamus or
+subthalamus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypothalamus which is actually turns out
+
+ align:start position:0%
+hypothalamus which is actually turns out
+ 
+
+ align:start position:0%
+hypothalamus which is actually turns out
+to be several
+
+ align:start position:0%
+to be several
+ 
+
+ align:start position:0%
+to be several
+subdivisions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then these are the questions we
+
+ align:start position:0%
+okay so then these are the questions we
+ 
+
+ align:start position:0%
+okay so then these are the questions we
+want to answer now I want you to be able
+
+ align:start position:0%
+want to answer now I want you to be able
+ 
+
+ align:start position:0%
+want to answer now I want you to be able
+to name the five main optic track
+
+ align:start position:0%
+to name the five main optic track
+ 
+
+ align:start position:0%
+to name the five main optic track
+termination areas in the order they're
+
+ align:start position:0%
+termination areas in the order they're
+ 
+
+ align:start position:0%
+termination areas in the order they're
+reached by the optic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+track so here they are they're already
+
+ align:start position:0%
+track so here they are they're already
+ 
+
+ align:start position:0%
+track so here they are they're already
+pass the
+
+ align:start position:0%
+pass the
+ 
+
+ align:start position:0%
+pass the
+supermatic then you have the two
+
+ align:start position:0%
+supermatic then you have the two
+ 
+
+ align:start position:0%
+supermatic then you have the two
+geniculate bodies then they get to the
+
+ align:start position:0%
+geniculate bodies then they get to the
+ 
+
+ align:start position:0%
+geniculate bodies then they get to the
+pretectal area here I show them on this
+
+ align:start position:0%
+pretectal area here I show them on this
+ 
+
+ align:start position:0%
+pretectal area here I show them on this
+picture and then finally they they turn
+
+ align:start position:0%
+picture and then finally they they turn
+ 
+
+ align:start position:0%
+picture and then finally they they turn
+codly and they get to the spir click so
+
+ align:start position:0%
+codly and they get to the spir click so
+ 
+
+ align:start position:0%
+codly and they get to the spir click so
+those are the areas one supermatic two
+
+ align:start position:0%
+those are the areas one supermatic two
+ 
+
+ align:start position:0%
+those are the areas one supermatic two
+three four and then five Superior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clickers and then I ask what addition
+
+ align:start position:0%
+clickers and then I ask what addition
+ 
+
+ align:start position:0%
+clickers and then I ask what addition
+areas receive sparse retinal projections
+
+ align:start position:0%
+areas receive sparse retinal projections
+ 
+
+ align:start position:0%
+areas receive sparse retinal projections
+well I already talked about some near
+
+ align:start position:0%
+well I already talked about some near
+ 
+
+ align:start position:0%
+well I already talked about some near
+the supermatic nucleus but there's some
+
+ align:start position:0%
+the supermatic nucleus but there's some
+ 
+
+ align:start position:0%
+the supermatic nucleus but there's some
+other sparse projections in the
+
+ align:start position:0%
+other sparse projections in the
+ 
+
+ align:start position:0%
+other sparse projections in the
+phalance that are somewhat variable from
+
+ align:start position:0%
+phalance that are somewhat variable from
+ 
+
+ align:start position:0%
+phalance that are somewhat variable from
+animal to animal at least among the
+
+ align:start position:0%
+animal to animal at least among the
+ 
+
+ align:start position:0%
+animal to animal at least among the
+hamsters that I've studied I suspect
+
+ align:start position:0%
+hamsters that I've studied I suspect
+ 
+
+ align:start position:0%
+hamsters that I've studied I suspect
+it's true of other species too and that
+
+ align:start position:0%
+it's true of other species too and that
+ 
+
+ align:start position:0%
+it's true of other species too and that
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+be projections to the lp nucleus here
+
+ align:start position:0%
+be projections to the lp nucleus here
+ 
+
+ align:start position:0%
+be projections to the lp nucleus here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so and there are other little
+
+ align:start position:0%
+so and there are other little
+ 
+
+ align:start position:0%
+so and there are other little
+projections near the main projections
+
+ align:start position:0%
+projections near the main projections
+ 
+
+ align:start position:0%
+projections near the main projections
+that are also a little bit variable and
+
+ align:start position:0%
+that are also a little bit variable and
+ 
+
+ align:start position:0%
+that are also a little bit variable and
+then I say inputs from the right and
+
+ align:start position:0%
+then I say inputs from the right and
+ 
+
+ align:start position:0%
+then I say inputs from the right and
+left eyes terminate in different
+
+ align:start position:0%
+left eyes terminate in different
+ 
+
+ align:start position:0%
+left eyes terminate in different
+areas a separation that's especially
+
+ align:start position:0%
+areas a separation that's especially
+ 
+
+ align:start position:0%
+areas a separation that's especially
+important for creating binocular
+
+ align:start position:0%
+important for creating binocular
+ 
+
+ align:start position:0%
+important for creating binocular
+disparity cues for depth for perceiving
+
+ align:start position:0%
+disparity cues for depth for perceiving
+ 
+
+ align:start position:0%
+disparity cues for depth for perceiving
+depth visually visual object so describe
+
+ align:start position:0%
+depth visually visual object so describe
+ 
+
+ align:start position:0%
+depth visually visual object so describe
+the appearance of the distinct areas in
+
+ align:start position:0%
+the appearance of the distinct areas in
+ 
+
+ align:start position:0%
+the appearance of the distinct areas in
+the dianon of a small rodent and of a
+
+ align:start position:0%
+the dianon of a small rodent and of a
+ 
+
+ align:start position:0%
+the dianon of a small rodent and of a
+monkey so here we're talking about the
+
+ align:start position:0%
+monkey so here we're talking about the
+ 
+
+ align:start position:0%
+monkey so here we're talking about the
+layers in the genicular body so in this
+
+ align:start position:0%
+layers in the genicular body so in this
+ 
+
+ align:start position:0%
+layers in the genicular body so in this
+picture that stretched out optic tract I
+
+ align:start position:0%
+picture that stretched out optic tract I
+ 
+
+ align:start position:0%
+picture that stretched out optic tract I
+show
+
+ align:start position:0%
+show
+ 
+
+ align:start position:0%
+show
+that so there's the supermatic then they
+
+ align:start position:0%
+that so there's the supermatic then they
+ 
+
+ align:start position:0%
+that so there's the supermatic then they
+reach the sub pamus this is the lateral
+
+ align:start position:0%
+reach the sub pamus this is the lateral
+ 
+
+ align:start position:0%
+reach the sub pamus this is the lateral
+genicular body ventral
+
+ align:start position:0%
+genicular body ventral
+ 
+
+ align:start position:0%
+genicular body ventral
+portion often abbreviated just LG
+
+ align:start position:0%
+portion often abbreviated just LG
+ 
+
+ align:start position:0%
+portion often abbreviated just LG
+V and it's also abbreviated lgn B
+
+ align:start position:0%
+V and it's also abbreviated lgn B
+ 
+
+ align:start position:0%
+V and it's also abbreviated lgn B
+lateral genicular nucleus vental
+
+ align:start position:0%
+lateral genicular nucleus vental
+ 
+
+ align:start position:0%
+lateral genicular nucleus vental
+part but notice here these are accents
+
+ align:start position:0%
+part but notice here these are accents
+ 
+
+ align:start position:0%
+part but notice here these are accents
+from the controlateral eye that I'm
+
+ align:start position:0%
+from the controlateral eye that I'm
+ 
+
+ align:start position:0%
+from the controlateral eye that I'm
+drawing I show a little area separated
+
+ align:start position:0%
+drawing I show a little area separated
+ 
+
+ align:start position:0%
+drawing I show a little area separated
+here by the dash lines in both the
+
+ align:start position:0%
+here by the dash lines in both the
+ 
+
+ align:start position:0%
+here by the dash lines in both the
+vental and dorsal genicular bodies where
+
+ align:start position:0%
+vental and dorsal genicular bodies where
+ 
+
+ align:start position:0%
+vental and dorsal genicular bodies where
+those accents don't
+
+ align:start position:0%
+those accents don't
+ 
+
+ align:start position:0%
+those accents don't
+go they don't go there because they're
+
+ align:start position:0%
+go they don't go there because they're
+ 
+
+ align:start position:0%
+go they don't go there because they're
+getting input from the outer eye okay
+
+ align:start position:0%
+getting input from the outer eye okay
+ 
+
+ align:start position:0%
+getting input from the outer eye okay
+it's a laminated structure not so
+
+ align:start position:0%
+it's a laminated structure not so
+ 
+
+ align:start position:0%
+it's a laminated structure not so
+obvious in the rodent but when you go to
+
+ align:start position:0%
+obvious in the rodent but when you go to
+ 
+
+ align:start position:0%
+obvious in the rodent but when you go to
+other animals like here's a four layer
+
+ align:start position:0%
+other animals like here's a four layer
+ 
+
+ align:start position:0%
+other animals like here's a four layer
+geniculate body which you find in some
+
+ align:start position:0%
+geniculate body which you find in some
+ 
+
+ align:start position:0%
+geniculate body which you find in some
+species then you find that the
+
+ align:start position:0%
+species then you find that the
+ 
+
+ align:start position:0%
+species then you find that the
+controlateral eye is projecting to the
+
+ align:start position:0%
+controlateral eye is projecting to the
+ 
+
+ align:start position:0%
+controlateral eye is projecting to the
+outermost the layer nearest the optic
+
+ align:start position:0%
+outermost the layer nearest the optic
+ 
+
+ align:start position:0%
+outermost the layer nearest the optic
+tract then it skips a layer and then it
+
+ align:start position:0%
+tract then it skips a layer and then it
+ 
+
+ align:start position:0%
+tract then it skips a layer and then it
+projects to the next layer and then not
+
+ align:start position:0%
+projects to the next layer and then not
+ 
+
+ align:start position:0%
+projects to the next layer and then not
+to the last l so it projects to one and
+
+ align:start position:0%
+to the last l so it projects to one and
+ 
+
+ align:start position:0%
+to the last l so it projects to one and
+three not to two and
+
+ align:start position:0%
+three not to two and
+ 
+
+ align:start position:0%
+three not to two and
+four and then in primates like the
+
+ align:start position:0%
+four and then in primates like the
+ 
+
+ align:start position:0%
+four and then in primates like the
+monkeys not all primates but at least
+
+ align:start position:0%
+monkeys not all primates but at least
+ 
+
+ align:start position:0%
+monkeys not all primates but at least
+monkeys
+
+ align:start position:0%
+monkeys
+ 
+
+ align:start position:0%
+monkeys
+and the Apes and humans you have six
+
+ align:start position:0%
+and the Apes and humans you have six
+ 
+
+ align:start position:0%
+and the Apes and humans you have six
+layers sometimes you see seven in some
+
+ align:start position:0%
+layers sometimes you see seven in some
+ 
+
+ align:start position:0%
+layers sometimes you see seven in some
+parts of the genic body usually we
+
+ align:start position:0%
+parts of the genic body usually we
+ 
+
+ align:start position:0%
+parts of the genic body usually we
+number six number them as six so we'll
+
+ align:start position:0%
+number six number them as six so we'll
+ 
+
+ align:start position:0%
+number six number them as six so we'll
+see that then the axons go through and
+
+ align:start position:0%
+see that then the axons go through and
+ 
+
+ align:start position:0%
+see that then the axons go through and
+over the lp lateral posterior nucleus
+
+ align:start position:0%
+over the lp lateral posterior nucleus
+ 
+
+ align:start position:0%
+over the lp lateral posterior nucleus
+that is the rest of the lateral Palance
+
+ align:start position:0%
+that is the rest of the lateral Palance
+ 
+
+ align:start position:0%
+that is the rest of the lateral Palance
+that part that grows so big in humans
+
+ align:start position:0%
+that part that grows so big in humans
+ 
+
+ align:start position:0%
+that part that grows so big in humans
+and I show a few terminations there it's
+
+ align:start position:0%
+and I show a few terminations there it's
+ 
+
+ align:start position:0%
+and I show a few terminations there it's
+somewhat
+
+ align:start position:0%
+somewhat
+ 
+
+ align:start position:0%
+somewhat
+variable but they are there they're
+
+ align:start position:0%
+variable but they are there they're
+ 
+
+ align:start position:0%
+variable but they are there they're
+sparse
+
+ align:start position:0%
+sparse
+ 
+
+ align:start position:0%
+sparse
+determinations
+
+ align:start position:0%
+determinations
+ 
+
+ align:start position:0%
+determinations
+okay again we don't
+
+ align:start position:0%
+okay again we don't
+ 
+
+ align:start position:0%
+okay again we don't
+know what those
+
+ align:start position:0%
+know what those
+ 
+
+ align:start position:0%
+know what those
+do maybe we don't need to know because
+
+ align:start position:0%
+do maybe we don't need to know because
+ 
+
+ align:start position:0%
+do maybe we don't need to know because
+those same
+
+ align:start position:0%
+those same
+ 
+
+ align:start position:0%
+those same
+neurons where those sparse projections
+
+ align:start position:0%
+neurons where those sparse projections
+ 
+
+ align:start position:0%
+neurons where those sparse projections
+occur get very heavy visual
+
+ align:start position:0%
+occur get very heavy visual
+ 
+
+ align:start position:0%
+occur get very heavy visual
+input but coming from the
+
+ align:start position:0%
+input but coming from the
+ 
+
+ align:start position:0%
+input but coming from the
+calculus not directly from the rtin
+
+ align:start position:0%
+calculus not directly from the rtin
+ 
+
+ align:start position:0%
+calculus not directly from the rtin
+one of the ideas about how the
+
+ align:start position:0%
+one of the ideas about how the
+ 
+
+ align:start position:0%
+one of the ideas about how the
+geniculate body appeared was just that
+
+ align:start position:0%
+geniculate body appeared was just that
+ 
+
+ align:start position:0%
+geniculate body appeared was just that
+these sparse scattered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projections that if some reduction of
+
+ align:start position:0%
+projections that if some reduction of
+ 
+
+ align:start position:0%
+projections that if some reduction of
+the calculus occurred they just sprouted
+
+ align:start position:0%
+the calculus occurred they just sprouted
+ 
+
+ align:start position:0%
+the calculus occurred they just sprouted
+more there and that was adapted to have
+
+ align:start position:0%
+more there and that was adapted to have
+ 
+
+ align:start position:0%
+more there and that was adapted to have
+a shorter root to the cortex so the
+
+ align:start position:0%
+a shorter root to the cortex so the
+ 
+
+ align:start position:0%
+a shorter root to the cortex so the
+genicular body evolved but be that as it
+
+ align:start position:0%
+genicular body evolved but be that as it
+ 
+
+ align:start position:0%
+genicular body evolved but be that as it
+may be the next structure then is the
+
+ align:start position:0%
+may be the next structure then is the
+ 
+
+ align:start position:0%
+may be the next structure then is the
+pretectal area and then finally
+
+ align:start position:0%
+pretectal area and then finally
+ 
+
+ align:start position:0%
+pretectal area and then finally
+spiculus or Optic
+
+ align:start position:0%
+spiculus or Optic
+ 
+
+ align:start position:0%
+spiculus or Optic
+tectum but for mammals we usually use
+
+ align:start position:0%
+tectum but for mammals we usually use
+ 
+
+ align:start position:0%
+tectum but for mammals we usually use
+the term spirit
+
+ align:start position:0%
+the term spirit
+ 
+
+ align:start position:0%
+the term spirit
+cicular all right so let's look at the
+
+ align:start position:0%
+cicular all right so let's look at the
+ 
+
+ align:start position:0%
+cicular all right so let's look at the
+geniculate body now we'll look at
+
+ align:start position:0%
+geniculate body now we'll look at
+ 
+
+ align:start position:0%
+geniculate body now we'll look at
+animals you know with this kind of layer
+
+ align:start position:0%
+animals you know with this kind of layer
+ 
+
+ align:start position:0%
+animals you know with this kind of layer
+but even more the here's the geniculate
+
+ align:start position:0%
+but even more the here's the geniculate
+ 
+
+ align:start position:0%
+but even more the here's the geniculate
+body of a monkey it's similar to a
+
+ align:start position:0%
+body of a monkey it's similar to a
+ 
+
+ align:start position:0%
+body of a monkey it's similar to a
+picture a color picture I took from
+
+ align:start position:0%
+picture a color picture I took from
+ 
+
+ align:start position:0%
+picture a color picture I took from
+Hubble David
+
+ align:start position:0%
+Hubble David
+ 
+
+ align:start position:0%
+Hubble David
+Hubble uh
+
+ align:start position:0%
+Hubble uh
+ 
+
+ align:start position:0%
+Hubble uh
+and from a book that he has online that
+
+ align:start position:0%
+and from a book that he has online that
+ 
+
+ align:start position:0%
+and from a book that he has online that
+anybody can
+
+ align:start position:0%
+anybody can
+ 
+
+ align:start position:0%
+anybody can
+download very nice book unfortunately
+
+ align:start position:0%
+download very nice book unfortunately
+ 
+
+ align:start position:0%
+download very nice book unfortunately
+David died just
+
+ align:start position:0%
+David died just
+ 
+
+ align:start position:0%
+David died just
+recently uh but he was a very productive
+
+ align:start position:0%
+recently uh but he was a very productive
+ 
+
+ align:start position:0%
+recently uh but he was a very productive
+visual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neuroscientist who did many studies of
+
+ align:start position:0%
+neuroscientist who did many studies of
+ 
+
+ align:start position:0%
+neuroscientist who did many studies of
+both cat and
+
+ align:start position:0%
+both cat and
+ 
+
+ align:start position:0%
+both cat and
+monkey uh genicular stride system
+
+ align:start position:0%
+monkey uh genicular stride system
+ 
+
+ align:start position:0%
+monkey uh genicular stride system
+working mostly in visual
+
+ align:start position:0%
+working mostly in visual
+ 
+
+ align:start position:0%
+working mostly in visual
+cortex he did the work with ton weasel
+
+ align:start position:0%
+cortex he did the work with ton weasel
+ 
+
+ align:start position:0%
+cortex he did the work with ton weasel
+who's retired now but has been had a
+
+ align:start position:0%
+who's retired now but has been had a
+ 
+
+ align:start position:0%
+who's retired now but has been had a
+position at Rockefeller University for
+
+ align:start position:0%
+position at Rockefeller University for
+ 
+
+ align:start position:0%
+position at Rockefeller University for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+last quite a few years after he left
+
+ align:start position:0%
+last quite a few years after he left
+ 
+
+ align:start position:0%
+last quite a few years after he left
+Harvard from his work with
+
+ align:start position:0%
+Harvard from his work with
+ 
+
+ align:start position:0%
+Harvard from his work with
+hu but here it shows you how they number
+
+ align:start position:0%
+hu but here it shows you how they number
+ 
+
+ align:start position:0%
+hu but here it shows you how they number
+these uh oh yeah how where did this
+
+ align:start position:0%
+these uh oh yeah how where did this
+ 
+
+ align:start position:0%
+these uh oh yeah how where did this
+horseshoe shape come from that's not
+
+ align:start position:0%
+horseshoe shape come from that's not
+ 
+
+ align:start position:0%
+horseshoe shape come from that's not
+what I'm showing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+can you figure that
+
+ align:start position:0%
+can you figure that
+ 
+
+ align:start position:0%
+can you figure that
+out let's go back to the embryo it
+
+ align:start position:0%
+out let's go back to the embryo it
+ 
+
+ align:start position:0%
+out let's go back to the embryo it
+looked like
+
+ align:start position:0%
+looked like
+ 
+
+ align:start position:0%
+looked like
+this monkey the
+
+ align:start position:0%
+this monkey the
+ 
+
+ align:start position:0%
+this monkey the
+same this structure here grew and grew
+
+ align:start position:0%
+same this structure here grew and grew
+ 
+
+ align:start position:0%
+same this structure here grew and grew
+and grew so this structure got
+
+ align:start position:0%
+and grew so this structure got
+ 
+
+ align:start position:0%
+and grew so this structure got
+pushed this
+
+ align:start position:0%
+pushed this
+ 
+
+ align:start position:0%
+pushed this
+way okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and the pulvinar in growing so
+
+ align:start position:0%
+so and the pulvinar in growing so
+ 
+
+ align:start position:0%
+so and the pulvinar in growing so
+big uh
+
+ align:start position:0%
+big uh
+ 
+
+ align:start position:0%
+big uh
+the thalamus in front of it also grew
+
+ align:start position:0%
+the thalamus in front of it also grew
+ 
+
+ align:start position:0%
+the thalamus in front of it also grew
+and so this thing that's on the side of
+
+ align:start position:0%
+and so this thing that's on the side of
+ 
+
+ align:start position:0%
+and so this thing that's on the side of
+the thalamus here do right here side of
+
+ align:start position:0%
+the thalamus here do right here side of
+ 
+
+ align:start position:0%
+the thalamus here do right here side of
+the phalus got pushed over like that and
+
+ align:start position:0%
+the phalus got pushed over like that and
+ 
+
+ align:start position:0%
+the phalus got pushed over like that and
+it also get got rotated so the genicular
+
+ align:start position:0%
+it also get got rotated so the genicular
+ 
+
+ align:start position:0%
+it also get got rotated so the genicular
+body ends up on the back of the
+
+ align:start position:0%
+body ends up on the back of the
+ 
+
+ align:start position:0%
+body ends up on the back of the
+phal so it goes that way and gets so
+
+ align:start position:0%
+phal so it goes that way and gets so
+ 
+
+ align:start position:0%
+phal so it goes that way and gets so
+this becomes like that and the optic
+
+ align:start position:0%
+this becomes like that and the optic
+ 
+
+ align:start position:0%
+this becomes like that and the optic
+crack which was out here is now under
+
+ align:start position:0%
+crack which was out here is now under
+ 
+
+ align:start position:0%
+crack which was out here is now under
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+means this is the optic track
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface those are the axon the tissue
+
+ align:start position:0%
+surface those are the axon the tissue
+ 
+
+ align:start position:0%
+surface those are the axon the tissue
+is torn off here but that's where the
+
+ align:start position:0%
+is torn off here but that's where the
+ 
+
+ align:start position:0%
+is torn off here but that's where the
+optic tract is but it's exactly top
+
+ align:start position:0%
+optic tract is but it's exactly top
+ 
+
+ align:start position:0%
+optic tract is but it's exactly top
+topologically it's the same as as this
+
+ align:start position:0%
+topologically it's the same as as this
+ 
+
+ align:start position:0%
+topologically it's the same as as this
+this picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you have you see the way they
+
+ align:start position:0%
+and then you have you see the way they
+ 
+
+ align:start position:0%
+and then you have you see the way they
+number them they always start numbering
+
+ align:start position:0%
+number them they always start numbering
+ 
+
+ align:start position:0%
+number them they always start numbering
+them nearest the optic
+
+ align:start position:0%
+them nearest the optic
+ 
+
+ align:start position:0%
+them nearest the optic
+tract so one two notice the first two
+
+ align:start position:0%
+tract so one two notice the first two
+ 
+
+ align:start position:0%
+tract so one two notice the first two
+layers are larger
+
+ align:start position:0%
+layers are larger
+ 
+
+ align:start position:0%
+layers are larger
+cells and then the smaller cell layers
+
+ align:start position:0%
+cells and then the smaller cell layers
+ 
+
+ align:start position:0%
+cells and then the smaller cell layers
+or paral cellular
+
+ align:start position:0%
+or paral cellular
+ 
+
+ align:start position:0%
+or paral cellular
+layers 3 four five and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six and again you have half of them they
+
+ align:start position:0%
+six and again you have half of them they
+ 
+
+ align:start position:0%
+six and again you have half of them they
+getting ipol in contr leral input and
+
+ align:start position:0%
+getting ipol in contr leral input and
+ 
+
+ align:start position:0%
+getting ipol in contr leral input and
+the other half are getting exal almost
+
+ align:start position:0%
+the other half are getting exal almost
+ 
+
+ align:start position:0%
+the other half are getting exal almost
+always the contralateral ey is
+
+ align:start position:0%
+always the contralateral ey is
+ 
+
+ align:start position:0%
+always the contralateral ey is
+projecting to the surface layer and to
+
+ align:start position:0%
+projecting to the surface layer and to
+ 
+
+ align:start position:0%
+projecting to the surface layer and to
+the last layer
+
+ align:start position:0%
+the last layer
+ 
+
+ align:start position:0%
+the last layer
+here and to one of these middle layers
+
+ align:start position:0%
+here and to one of these middle layers
+ 
+
+ align:start position:0%
+here and to one of these middle layers
+okay it varies a little bit among
+
+ align:start position:0%
+okay it varies a little bit among
+ 
+
+ align:start position:0%
+okay it varies a little bit among
+species here's a
+
+ align:start position:0%
+species here's a
+ 
+
+ align:start position:0%
+species here's a
+human and this is a human that uh
+
+ align:start position:0%
+human and this is a human that uh
+ 
+
+ align:start position:0%
+human and this is a human that uh
+picture that was donated to me by a
+
+ align:start position:0%
+picture that was donated to me by a
+ 
+
+ align:start position:0%
+picture that was donated to me by a
+former student who developed a silver
+
+ align:start position:0%
+former student who developed a silver
+ 
+
+ align:start position:0%
+former student who developed a silver
+stain that stained cell bodies gives you
+
+ align:start position:0%
+stain that stained cell bodies gives you
+ 
+
+ align:start position:0%
+stain that stained cell bodies gives you
+very high contrast picture this happens
+
+ align:start position:0%
+very high contrast picture this happens
+ 
+
+ align:start position:0%
+very high contrast picture this happens
+to be from a human case who had a
+
+ align:start position:0%
+to be from a human case who had a
+ 
+
+ align:start position:0%
+to be from a human case who had a
+pathology of one eye so the cells in
+
+ align:start position:0%
+pathology of one eye so the cells in
+ 
+
+ align:start position:0%
+pathology of one eye so the cells in
+the of the ipsilat ey that gets
+
+ align:start position:0%
+the of the ipsilat ey that gets
+ 
+
+ align:start position:0%
+the of the ipsilat ey that gets
+ipsilateral projections the cells are
+
+ align:start position:0%
+ipsilateral projections the cells are
+ 
+
+ align:start position:0%
+ipsilateral projections the cells are
+have shriveled a bit okay so this is one
+
+ align:start position:0%
+have shriveled a bit okay so this is one
+ 
+
+ align:start position:0%
+have shriveled a bit okay so this is one
+of the magnos cellular layers
+
+ align:start position:0%
+of the magnos cellular layers
+ 
+
+ align:start position:0%
+of the magnos cellular layers
+here and then here's the other
+
+ align:start position:0%
+here and then here's the other
+ 
+
+ align:start position:0%
+here and then here's the other
+controlateral layer and the last
+
+ align:start position:0%
+controlateral layer and the last
+ 
+
+ align:start position:0%
+controlateral layer and the last
+controlateral layer these are the layers
+
+ align:start position:0%
+controlateral layer these are the layers
+ 
+
+ align:start position:0%
+controlateral layer these are the layers
+getting IAL
+
+ align:start position:0%
+getting IAL
+ 
+
+ align:start position:0%
+getting IAL
+projections most of the other magnos
+
+ align:start position:0%
+projections most of the other magnos
+ 
+
+ align:start position:0%
+projections most of the other magnos
+layer we don't see
+
+ align:start position:0%
+layer we don't see
+ 
+
+ align:start position:0%
+layer we don't see
+here okay all of these cells
+
+ align:start position:0%
+here okay all of these cells
+ 
+
+ align:start position:0%
+here okay all of these cells
+here are all parts of that lateral
+
+ align:start position:0%
+here are all parts of that lateral
+ 
+
+ align:start position:0%
+here are all parts of that lateral
+Thalamus the pulvinar nucleus and
+
+ align:start position:0%
+Thalamus the pulvinar nucleus and
+ 
+
+ align:start position:0%
+Thalamus the pulvinar nucleus and
+there's a small part of it they call the
+
+ align:start position:0%
+there's a small part of it they call the
+ 
+
+ align:start position:0%
+there's a small part of it they call the
+the part that's the inferior pul
+
+ align:start position:0%
+the part that's the inferior pul
+ 
+
+ align:start position:0%
+the part that's the inferior pul
+pulvinar is similar to LP of the
+
+ align:start position:0%
+pulvinar is similar to LP of the
+ 
+
+ align:start position:0%
+pulvinar is similar to LP of the
+loaden and often they do name an LP too
+
+ align:start position:0%
+loaden and often they do name an LP too
+ 
+
+ align:start position:0%
+loaden and often they do name an LP too
+but it's the homology is not not always
+
+ align:start position:0%
+but it's the homology is not not always
+ 
+
+ align:start position:0%
+but it's the homology is not not always
+that clear okay so this is a picture
+
+ align:start position:0%
+that clear okay so this is a picture
+ 
+
+ align:start position:0%
+that clear okay so this is a picture
+from a very famous neuroanatomist in the
+
+ align:start position:0%
+from a very famous neuroanatomist in the
+ 
+
+ align:start position:0%
+from a very famous neuroanatomist in the
+early part of the 20th century lro
+
+ align:start position:0%
+early part of the 20th century lro
+ 
+
+ align:start position:0%
+early part of the 20th century lro
+Clark who didn't have access
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to beautiful optics for taking low power
+
+ align:start position:0%
+to beautiful optics for taking low power
+ 
+
+ align:start position:0%
+to beautiful optics for taking low power
+pictures and all that so he drew them
+
+ align:start position:0%
+pictures and all that so he drew them
+ 
+
+ align:start position:0%
+pictures and all that so he drew them
+and he drew these beautiful pictures in
+
+ align:start position:0%
+and he drew these beautiful pictures in
+ 
+
+ align:start position:0%
+and he drew these beautiful pictures in
+this case of many
+
+ align:start position:0%
+this case of many
+ 
+
+ align:start position:0%
+this case of many
+different uh primates and at that
+
+ align:start position:0%
+different uh primates and at that
+ 
+
+ align:start position:0%
+different uh primates and at that
+time they thought the Treo might be the
+
+ align:start position:0%
+time they thought the Treo might be the
+ 
+
+ align:start position:0%
+time they thought the Treo might be the
+most primitive primate it turns out to
+
+ align:start position:0%
+most primitive primate it turns out to
+ 
+
+ align:start position:0%
+most primitive primate it turns out to
+be similar to very primitive primates
+
+ align:start position:0%
+be similar to very primitive primates
+ 
+
+ align:start position:0%
+be similar to very primitive primates
+but it's actually an Inc
+
+ align:start position:0%
+but it's actually an Inc
+ 
+
+ align:start position:0%
+but it's actually an Inc
+work but you see the different patterns
+
+ align:start position:0%
+work but you see the different patterns
+ 
+
+ align:start position:0%
+work but you see the different patterns
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+lamination that occur in these different
+
+ align:start position:0%
+lamination that occur in these different
+ 
+
+ align:start position:0%
+lamination that occur in these different
+animals okay they don't all have
+
+ align:start position:0%
+animals okay they don't all have
+ 
+
+ align:start position:0%
+animals okay they don't all have
+identical
+
+ align:start position:0%
+identical
+ 
+
+ align:start position:0%
+identical
+structures okay
+
+ align:start position:0%
+structures okay
+ 
+
+ align:start position:0%
+structures okay
+binocular separation
+
+ align:start position:0%
+binocular separation
+ 
+
+ align:start position:0%
+binocular separation
+the anatomy underlying that binocular
+
+ align:start position:0%
+the anatomy underlying that binocular
+ 
+
+ align:start position:0%
+the anatomy underlying that binocular
+separation in the brain has evolved
+
+ align:start position:0%
+separation in the brain has evolved
+ 
+
+ align:start position:0%
+separation in the brain has evolved
+differently in different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+animals in these pictures
+
+ align:start position:0%
+animals in these pictures
+ 
+
+ align:start position:0%
+animals in these pictures
+the the old world monkey the greenon is
+
+ align:start position:0%
+the the old world monkey the greenon is
+ 
+
+ align:start position:0%
+the the old world monkey the greenon is
+is most similar to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+human this particular this picture here
+
+ align:start position:0%
+human this particular this picture here
+ 
+
+ align:start position:0%
+human this particular this picture here
+is fairly close and level to that
+
+ align:start position:0%
+is fairly close and level to that
+ 
+
+ align:start position:0%
+is fairly close and level to that
+picture the the
+
+ align:start position:0%
+picture the the
+ 
+
+ align:start position:0%
+picture the the
+photograph okay so now I want to go to
+
+ align:start position:0%
+photograph okay so now I want to go to
+ 
+
+ align:start position:0%
+photograph okay so now I want to go to
+the rodent which they're usually using
+
+ align:start position:0%
+the rodent which they're usually using
+ 
+
+ align:start position:0%
+the rodent which they're usually using
+in laboratory work uh for lot of the
+
+ align:start position:0%
+in laboratory work uh for lot of the
+ 
+
+ align:start position:0%
+in laboratory work uh for lot of the
+studies of many
+
+ align:start position:0%
+studies of many
+ 
+
+ align:start position:0%
+studies of many
+systems and
+
+ align:start position:0%
+systems and
+ 
+
+ align:start position:0%
+systems and
+uh I want to I use side views and I show
+
+ align:start position:0%
+uh I want to I use side views and I show
+ 
+
+ align:start position:0%
+uh I want to I use side views and I show
+the op here here's a very simplified
+
+ align:start position:0%
+the op here here's a very simplified
+ 
+
+ align:start position:0%
+the op here here's a very simplified
+picture of it the outline here is a
+
+ align:start position:0%
+picture of it the outline here is a
+ 
+
+ align:start position:0%
+picture of it the outline here is a
+fairly accurate view a side view of the
+
+ align:start position:0%
+fairly accurate view a side view of the
+ 
+
+ align:start position:0%
+fairly accurate view a side view of the
+the upper brain stem of a hamster so you
+
+ align:start position:0%
+the upper brain stem of a hamster so you
+ 
+
+ align:start position:0%
+the upper brain stem of a hamster so you
+see the inferior calculus and spheri
+
+ align:start position:0%
+see the inferior calculus and spheri
+ 
+
+ align:start position:0%
+see the inferior calculus and spheri
+culus of the midbrain
+
+ align:start position:0%
+culus of the midbrain
+ 
+
+ align:start position:0%
+culus of the midbrain
+here this is all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+palus the dorsal palus would be all
+
+ align:start position:0%
+palus the dorsal palus would be all
+ 
+
+ align:start position:0%
+palus the dorsal palus would be all
+through here but the geniculate body
+
+ align:start position:0%
+through here but the geniculate body
+ 
+
+ align:start position:0%
+through here but the geniculate body
+here way out at the
+
+ align:start position:0%
+here way out at the
+ 
+
+ align:start position:0%
+here way out at the
+edge can here's the two parts dorsal and
+
+ align:start position:0%
+edge can here's the two parts dorsal and
+ 
+
+ align:start position:0%
+edge can here's the two parts dorsal and
+dental
+
+ align:start position:0%
+dental
+ 
+
+ align:start position:0%
+dental
+nuclei now remember I showed you I said
+
+ align:start position:0%
+nuclei now remember I showed you I said
+ 
+
+ align:start position:0%
+nuclei now remember I showed you I said
+that the lateral gen the ventral nucleus
+
+ align:start position:0%
+that the lateral gen the ventral nucleus
+ 
+
+ align:start position:0%
+that the lateral gen the ventral nucleus
+lateral geniculate is really subus well
+
+ align:start position:0%
+lateral geniculate is really subus well
+ 
+
+ align:start position:0%
+lateral geniculate is really subus well
+most of the sub remember it's a curv
+
+ align:start position:0%
+most of the sub remember it's a curv
+ 
+
+ align:start position:0%
+most of the sub remember it's a curv
+structure so this is at the lateral Edge
+
+ align:start position:0%
+structure so this is at the lateral Edge
+ 
+
+ align:start position:0%
+structure so this is at the lateral Edge
+so it's much higher up but then as we
+
+ align:start position:0%
+so it's much higher up but then as we
+ 
+
+ align:start position:0%
+so it's much higher up but then as we
+went deeper into the thalamus it would
+
+ align:start position:0%
+went deeper into the thalamus it would
+ 
+
+ align:start position:0%
+went deeper into the thalamus it would
+be way down here
+
+ align:start position:0%
+be way down here
+ 
+
+ align:start position:0%
+be way down here
+okay and what I show here is a little
+
+ align:start position:0%
+okay and what I show here is a little
+ 
+
+ align:start position:0%
+okay and what I show here is a little
+schematic of one little bundle of optic
+
+ align:start position:0%
+schematic of one little bundle of optic
+ 
+
+ align:start position:0%
+schematic of one little bundle of optic
+tract ACC coming from the kism up the
+
+ align:start position:0%
+tract ACC coming from the kism up the
+ 
+
+ align:start position:0%
+tract ACC coming from the kism up the
+side I don't show the
+
+ align:start position:0%
+side I don't show the
+ 
+
+ align:start position:0%
+side I don't show the
+terminations in the superism itic
+
+ align:start position:0%
+terminations in the superism itic
+ 
+
+ align:start position:0%
+terminations in the superism itic
+nucleus because those are different
+
+ align:start position:0%
+nucleus because those are different
+ 
+
+ align:start position:0%
+nucleus because those are different
+axons but I show that
+
+ align:start position:0%
+axons but I show that
+ 
+
+ align:start position:0%
+axons but I show that
+axons that go to the genicular body are
+
+ align:start position:0%
+axons that go to the genicular body are
+ 
+
+ align:start position:0%
+axons that go to the genicular body are
+usually branches of optic trct accents
+
+ align:start position:0%
+usually branches of optic trct accents
+ 
+
+ align:start position:0%
+usually branches of optic trct accents
+that go further that go to the tectum
+
+ align:start position:0%
+that go further that go to the tectum
+ 
+
+ align:start position:0%
+that go further that go to the tectum
+and often the pretectum as
+
+ align:start position:0%
+and often the pretectum as
+ 
+
+ align:start position:0%
+and often the pretectum as
+well I also
+
+ align:start position:0%
+well I also
+ 
+
+ align:start position:0%
+well I also
+show where the major input to the lp
+
+ align:start position:0%
+show where the major input to the lp
+ 
+
+ align:start position:0%
+show where the major input to the lp
+that provides the lp with visual
+
+ align:start position:0%
+that provides the lp with visual
+ 
+
+ align:start position:0%
+that provides the lp with visual
+information doesn't come from the retina
+
+ align:start position:0%
+information doesn't come from the retina
+ 
+
+ align:start position:0%
+information doesn't come from the retina
+even though there are a few projections
+
+ align:start position:0%
+even though there are a few projections
+ 
+
+ align:start position:0%
+even though there are a few projections
+there they come from the superficial or
+
+ align:start position:0%
+there they come from the superficial or
+ 
+
+ align:start position:0%
+there they come from the superficial or
+visual layers of the
+
+ align:start position:0%
+visual layers of the
+ 
+
+ align:start position:0%
+visual layers of the
+spiculus and IT projects both LP and to
+
+ align:start position:0%
+spiculus and IT projects both LP and to
+ 
+
+ align:start position:0%
+spiculus and IT projects both LP and to
+the outer layer of the lateral the
+
+ align:start position:0%
+the outer layer of the lateral the
+ 
+
+ align:start position:0%
+the outer layer of the lateral the
+ventral nucleus of the lateral genicular
+
+ align:start position:0%
+ventral nucleus of the lateral genicular
+ 
+
+ align:start position:0%
+ventral nucleus of the lateral genicular
+body so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I here's the question that I want to
+
+ align:start position:0%
+uh I here's the question that I want to
+ 
+
+ align:start position:0%
+uh I here's the question that I want to
+answer next the there are accents that
+
+ align:start position:0%
+answer next the there are accents that
+ 
+
+ align:start position:0%
+answer next the there are accents that
+leave the main optic cact and terminate
+
+ align:start position:0%
+leave the main optic cact and terminate
+ 
+
+ align:start position:0%
+leave the main optic cact and terminate
+in these small cell groups there up to
+
+ align:start position:0%
+in these small cell groups there up to
+ 
+
+ align:start position:0%
+in these small cell groups there up to
+three of
+
+ align:start position:0%
+three of
+ 
+
+ align:start position:0%
+three of
+them they're described as what kind of
+
+ align:start position:0%
+them they're described as what kind of
+ 
+
+ align:start position:0%
+them they're described as what kind of
+optic
+
+ align:start position:0%
+optic
+ 
+
+ align:start position:0%
+optic
+track the word is accessory optic track
+
+ align:start position:0%
+track the word is accessory optic track
+ 
+
+ align:start position:0%
+track the word is accessory optic track
+and this is a anatomical reconstruction
+
+ align:start position:0%
+and this is a anatomical reconstruction
+ 
+
+ align:start position:0%
+and this is a anatomical reconstruction
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+hamster uh where I had labeled the
+
+ align:start position:0%
+hamster uh where I had labeled the
+ 
+
+ align:start position:0%
+hamster uh where I had labeled the
+axons all of the
+
+ align:start position:0%
+axons all of the
+ 
+
+ align:start position:0%
+axons all of the
+axons that I
+
+ align:start position:0%
+axons that I
+ 
+
+ align:start position:0%
+axons that I
+could which is most of
+
+ align:start position:0%
+could which is most of
+ 
+
+ align:start position:0%
+could which is most of
+them so I get the entire optic TR and I
+
+ align:start position:0%
+them so I get the entire optic TR and I
+ 
+
+ align:start position:0%
+them so I get the entire optic TR and I
+I put together Ser this is done from
+
+ align:start position:0%
+I put together Ser this is done from
+ 
+
+ align:start position:0%
+I put together Ser this is done from
+serial sections so you know the sections
+
+ align:start position:0%
+serial sections so you know the sections
+ 
+
+ align:start position:0%
+serial sections so you know the sections
+were actually like this but pretty close
+
+ align:start position:0%
+were actually like this but pretty close
+ 
+
+ align:start position:0%
+were actually like this but pretty close
+together okay and I then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reconstructed the entire optic track
+
+ align:start position:0%
+reconstructed the entire optic track
+ 
+
+ align:start position:0%
+reconstructed the entire optic track
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+km to
+
+ align:start position:0%
+km to
+ 
+
+ align:start position:0%
+km to
+culas and this particular brain with the
+
+ align:start position:0%
+culas and this particular brain with the
+ 
+
+ align:start position:0%
+culas and this particular brain with the
+I was using degenerating X stains for
+
+ align:start position:0%
+I was using degenerating X stains for
+ 
+
+ align:start position:0%
+I was using degenerating X stains for
+degeneration I didn't get a good picture
+
+ align:start position:0%
+degeneration I didn't get a good picture
+ 
+
+ align:start position:0%
+degeneration I didn't get a good picture
+of the super kais nucleus so like most
+
+ align:start position:0%
+of the super kais nucleus so like most
+ 
+
+ align:start position:0%
+of the super kais nucleus so like most
+scientists I never lie with the data I
+
+ align:start position:0%
+scientists I never lie with the data I
+ 
+
+ align:start position:0%
+scientists I never lie with the data I
+present I don't show it okay but in fact
+
+ align:start position:0%
+present I don't show it okay but in fact
+ 
+
+ align:start position:0%
+present I don't show it okay but in fact
+with other techniques I could see it and
+
+ align:start position:0%
+with other techniques I could see it and
+ 
+
+ align:start position:0%
+with other techniques I could see it and
+it's right
+
+ align:start position:0%
+it's right
+ 
+
+ align:start position:0%
+it's right
+here all right and what I'm showing here
+
+ align:start position:0%
+here all right and what I'm showing here
+ 
+
+ align:start position:0%
+here all right and what I'm showing here
+is the accessory optic tract axons and
+
+ align:start position:0%
+is the accessory optic tract axons and
+ 
+
+ align:start position:0%
+is the accessory optic tract axons and
+you can see why they're called accessory
+
+ align:start position:0%
+you can see why they're called accessory
+ 
+
+ align:start position:0%
+you can see why they're called accessory
+optic tract they leave that main track
+
+ align:start position:0%
+optic tract they leave that main track
+ 
+
+ align:start position:0%
+optic tract they leave that main track
+that goes all the way from km to culas
+
+ align:start position:0%
+that goes all the way from km to culas
+ 
+
+ align:start position:0%
+that goes all the way from km to culas
+here here's some that leave just just
+
+ align:start position:0%
+here here's some that leave just just
+ 
+
+ align:start position:0%
+here here's some that leave just just
+below the cereal peduncle and they
+
+ align:start position:0%
+below the cereal peduncle and they
+ 
+
+ align:start position:0%
+below the cereal peduncle and they
+travel codly and they terminate medial
+
+ align:start position:0%
+travel codly and they terminate medial
+ 
+
+ align:start position:0%
+travel codly and they terminate medial
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+peduncle right there to a nucleus that
+
+ align:start position:0%
+peduncle right there to a nucleus that
+ 
+
+ align:start position:0%
+peduncle right there to a nucleus that
+sort of hugs the medial side of the of
+
+ align:start position:0%
+sort of hugs the medial side of the of
+ 
+
+ align:start position:0%
+sort of hugs the medial side of the of
+the substantia and the coped unle
+
+ align:start position:0%
+the substantia and the coped unle
+ 
+
+ align:start position:0%
+the substantia and the coped unle
+and others do just travel codly below
+
+ align:start position:0%
+and others do just travel codly below
+ 
+
+ align:start position:0%
+and others do just travel codly below
+the phus here they just sort of peel off
+
+ align:start position:0%
+the phus here they just sort of peel off
+ 
+
+ align:start position:0%
+the phus here they just sort of peel off
+at the level of the ventrolateral
+
+ align:start position:0%
+at the level of the ventrolateral
+ 
+
+ align:start position:0%
+at the level of the ventrolateral
+genicular body and they terminate in a
+
+ align:start position:0%
+genicular body and they terminate in a
+ 
+
+ align:start position:0%
+genicular body and they terminate in a
+little nucleus here and some
+
+ align:start position:0%
+little nucleus here and some
+ 
+
+ align:start position:0%
+little nucleus here and some
+accents go down this way and get to this
+
+ align:start position:0%
+accents go down this way and get to this
+ 
+
+ align:start position:0%
+accents go down this way and get to this
+other way there's even some accents
+
+ align:start position:0%
+other way there's even some accents
+ 
+
+ align:start position:0%
+other way there's even some accents
+going in the other direction that's
+
+ align:start position:0%
+going in the other direction that's
+ 
+
+ align:start position:0%
+going in the other direction that's
+called the trans peduncular tract and
+
+ align:start position:0%
+called the trans peduncular tract and
+ 
+
+ align:start position:0%
+called the trans peduncular tract and
+then finally here's a little tract that
+
+ align:start position:0%
+then finally here's a little tract that
+ 
+
+ align:start position:0%
+then finally here's a little tract that
+goes from the pretectal area it leaves
+
+ align:start position:0%
+goes from the pretectal area it leaves
+ 
+
+ align:start position:0%
+goes from the pretectal area it leaves
+the main tract seems to go down to the
+
+ align:start position:0%
+the main tract seems to go down to the
+ 
+
+ align:start position:0%
+the main tract seems to go down to the
+lateral termin nucleus but it has
+
+ align:start position:0%
+lateral termin nucleus but it has
+ 
+
+ align:start position:0%
+lateral termin nucleus but it has
+another little nucleus there way out at
+
+ align:start position:0%
+another little nucleus there way out at
+ 
+
+ align:start position:0%
+another little nucleus there way out at
+the lateral edge of the
+
+ align:start position:0%
+the lateral edge of the
+ 
+
+ align:start position:0%
+the lateral edge of the
+pretectal so that's the accessory optic
+
+ align:start position:0%
+pretectal so that's the accessory optic
+ 
+
+ align:start position:0%
+pretectal so that's the accessory optic
+track very interesting system because
+
+ align:start position:0%
+track very interesting system because
+ 
+
+ align:start position:0%
+track very interesting system because
+all the cells in that tract respond to
+
+ align:start position:0%
+all the cells in that tract respond to
+ 
+
+ align:start position:0%
+all the cells in that tract respond to
+movement of the whole scene across the
+
+ align:start position:0%
+movement of the whole scene across the
+ 
+
+ align:start position:0%
+movement of the whole scene across the
+retina work no matter where you are in
+
+ align:start position:0%
+retina work no matter where you are in
+ 
+
+ align:start position:0%
+retina work no matter where you are in
+the retina you can the cells will detect
+
+ align:start position:0%
+the retina you can the cells will detect
+ 
+
+ align:start position:0%
+the retina you can the cells will detect
+movement in the same direction so when
+
+ align:start position:0%
+movement in the same direction so when
+ 
+
+ align:start position:0%
+movement in the same direction so when
+does that happen when the whole animal
+
+ align:start position:0%
+does that happen when the whole animal
+ 
+
+ align:start position:0%
+does that happen when the whole animal
+starts to fall it happens when the
+
+ align:start position:0%
+starts to fall it happens when the
+ 
+
+ align:start position:0%
+starts to fall it happens when the
+animal's locomoting and so there's
+
+ align:start position:0%
+animal's locomoting and so there's
+ 
+
+ align:start position:0%
+animal's locomoting and so there's
+streaming of the visual World Past his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eyes and it functions as a kind
+
+ align:start position:0%
+eyes and it functions as a kind
+ 
+
+ align:start position:0%
+eyes and it functions as a kind
+of it does the same kind of functions
+
+ align:start position:0%
+of it does the same kind of functions
+ 
+
+ align:start position:0%
+of it does the same kind of functions
+that the distributor system does okay
+
+ align:start position:0%
+that the distributor system does okay
+ 
+
+ align:start position:0%
+that the distributor system does okay
+but it gives
+
+ align:start position:0%
+but it gives
+ 
+
+ align:start position:0%
+but it gives
+visual signals to indicate changes in
+
+ align:start position:0%
+visual signals to indicate changes in
+ 
+
+ align:start position:0%
+visual signals to indicate changes in
+head Direction and eye Direction okay
+
+ align:start position:0%
+head Direction and eye Direction okay
+ 
+
+ align:start position:0%
+head Direction and eye Direction okay
+very important for uh locomotion
+
+ align:start position:0%
+very important for uh locomotion
+ 
+
+ align:start position:0%
+very important for uh locomotion
+and very important if you need to keep
+
+ align:start position:0%
+and very important if you need to keep
+ 
+
+ align:start position:0%
+and very important if you need to keep
+track of your of head position all
+
+ align:start position:0%
+track of your of head position all
+ 
+
+ align:start position:0%
+track of your of head position all
+right so then I just want to show you
+
+ align:start position:0%
+right so then I just want to show you
+ 
+
+ align:start position:0%
+right so then I just want to show you
+that that what that
+
+ align:start position:0%
+that that what that
+ 
+
+ align:start position:0%
+that that what that
+reconstruction uh is doing by taking
+
+ align:start position:0%
+reconstruction uh is doing by taking
+ 
+
+ align:start position:0%
+reconstruction uh is doing by taking
+photographs of a similar brain now here
+
+ align:start position:0%
+photographs of a similar brain now here
+ 
+
+ align:start position:0%
+photographs of a similar brain now here
+I didn't label it here I did so here you
+
+ align:start position:0%
+I didn't label it here I did so here you
+ 
+
+ align:start position:0%
+I didn't label it here I did so here you
+can see because of the way I've shaped
+
+ align:start position:0%
+can see because of the way I've shaped
+ 
+
+ align:start position:0%
+can see because of the way I've shaped
+the light you can see major tracks cuz
+
+ align:start position:0%
+the light you can see major tracks cuz
+ 
+
+ align:start position:0%
+the light you can see major tracks cuz
+they're wider that's the lateral Factory
+
+ align:start position:0%
+they're wider that's the lateral Factory
+ 
+
+ align:start position:0%
+they're wider that's the lateral Factory
+track there's the optic
+
+ align:start position:0%
+track there's the optic
+ 
+
+ align:start position:0%
+track there's the optic
+track there's a pathway carrying
+
+ align:start position:0%
+track there's a pathway carrying
+ 
+
+ align:start position:0%
+track there's a pathway carrying
+auditory input from H brain up to the
+
+ align:start position:0%
+auditory input from H brain up to the
+ 
+
+ align:start position:0%
+auditory input from H brain up to the
+inferior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculus there's the bundle one of you
+
+ align:start position:0%
+calculus there's the bundle one of you
+ 
+
+ align:start position:0%
+calculus there's the bundle one of you
+see these two bundles here we cut those
+
+ align:start position:0%
+see these two bundles here we cut those
+ 
+
+ align:start position:0%
+see these two bundles here we cut those
+when we remove the cerebellum those are
+
+ align:start position:0%
+when we remove the cerebellum those are
+ 
+
+ align:start position:0%
+when we remove the cerebellum those are
+the cerebella pedes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there's hypothal down below and
+
+ align:start position:0%
+okay there's hypothal down below and
+ 
+
+ align:start position:0%
+okay there's hypothal down below and
+there's where I
+
+ align:start position:0%
+there's where I
+ 
+
+ align:start position:0%
+there's where I
+uh when I remove the brain I tore the
+
+ align:start position:0%
+uh when I remove the brain I tore the
+ 
+
+ align:start position:0%
+uh when I remove the brain I tore the
+pituitary off right there okay that
+
+ align:start position:0%
+pituitary off right there okay that
+ 
+
+ align:start position:0%
+pituitary off right there okay that
+would be the mammary bodies at the codal
+
+ align:start position:0%
+would be the mammary bodies at the codal
+ 
+
+ align:start position:0%
+would be the mammary bodies at the codal
+end of the hypothal so here I've labeled
+
+ align:start position:0%
+end of the hypothal so here I've labeled
+ 
+
+ align:start position:0%
+end of the hypothal so here I've labeled
+them and I've labeled a few other
+
+ align:start position:0%
+them and I've labeled a few other
+ 
+
+ align:start position:0%
+them and I've labeled a few other
+structures so this structure here it's
+
+ align:start position:0%
+structures so this structure here it's
+ 
+
+ align:start position:0%
+structures so this structure here it's
+not bamus it's part of the end brain
+
+ align:start position:0%
+not bamus it's part of the end brain
+ 
+
+ align:start position:0%
+not bamus it's part of the end brain
+it's Corpus
+
+ align:start position:0%
+it's Corpus
+ 
+
+ align:start position:0%
+it's Corpus
+triot then I show you exactly where the
+
+ align:start position:0%
+triot then I show you exactly where the
+ 
+
+ align:start position:0%
+triot then I show you exactly where the
+geniculate body is
+
+ align:start position:0%
+geniculate body is
+ 
+
+ align:start position:0%
+geniculate body is
+is I know you say well how what do you
+
+ align:start position:0%
+is I know you say well how what do you
+ 
+
+ align:start position:0%
+is I know you say well how what do you
+mean exactly because I can see the
+
+ align:start position:0%
+mean exactly because I can see the
+ 
+
+ align:start position:0%
+mean exactly because I can see the
+Shadows there I can see them there I
+
+ align:start position:0%
+Shadows there I can see them there I
+ 
+
+ align:start position:0%
+Shadows there I can see them there I
+know that that's exactly the edge of the
+
+ align:start position:0%
+know that that's exactly the edge of the
+ 
+
+ align:start position:0%
+know that that's exactly the edge of the
+dorsal nucleus and this is the vental
+
+ align:start position:0%
+dorsal nucleus and this is the vental
+ 
+
+ align:start position:0%
+dorsal nucleus and this is the vental
+nucleus right below it there's the optic
+
+ align:start position:0%
+nucleus right below it there's the optic
+ 
+
+ align:start position:0%
+nucleus right below it there's the optic
+tract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypothalamus this big bundle here that
+
+ align:start position:0%
+hypothalamus this big bundle here that
+ 
+
+ align:start position:0%
+hypothalamus this big bundle here that
+emerges from behind the optic
+
+ align:start position:0%
+emerges from behind the optic
+ 
+
+ align:start position:0%
+emerges from behind the optic
+track those accents are course ing
+
+ align:start position:0%
+track those accents are course ing
+ 
+
+ align:start position:0%
+track those accents are course ing
+through the Corpus trium here but in the
+
+ align:start position:0%
+through the Corpus trium here but in the
+ 
+
+ align:start position:0%
+through the Corpus trium here but in the
+rodent they're all they're all separated
+
+ align:start position:0%
+rodent they're all they're all separated
+ 
+
+ align:start position:0%
+rodent they're all they're all separated
+a whole bunch of little separate bundles
+
+ align:start position:0%
+a whole bunch of little separate bundles
+ 
+
+ align:start position:0%
+a whole bunch of little separate bundles
+that collect in form the peduncle comes
+
+ align:start position:0%
+that collect in form the peduncle comes
+ 
+
+ align:start position:0%
+that collect in form the peduncle comes
+along the side of the dlon and then
+
+ align:start position:0%
+along the side of the dlon and then
+ 
+
+ align:start position:0%
+along the side of the dlon and then
+passes right on into the pontine region
+
+ align:start position:0%
+passes right on into the pontine region
+ 
+
+ align:start position:0%
+passes right on into the pontine region
+here and then when we study auditory
+
+ align:start position:0%
+here and then when we study auditory
+ 
+
+ align:start position:0%
+here and then when we study auditory
+system we'll learn that this is called
+
+ align:start position:0%
+system we'll learn that this is called
+ 
+
+ align:start position:0%
+system we'll learn that this is called
+the lateral liscus and that bump right
+
+ align:start position:0%
+the lateral liscus and that bump right
+ 
+
+ align:start position:0%
+the lateral liscus and that bump right
+there behind the Celler pet unes that's
+
+ align:start position:0%
+there behind the Celler pet unes that's
+ 
+
+ align:start position:0%
+there behind the Celler pet unes that's
+the clear nucleus and there's the stump
+
+ align:start position:0%
+the clear nucleus and there's the stump
+ 
+
+ align:start position:0%
+the clear nucleus and there's the stump
+of the eighth nerve right
+
+ align:start position:0%
+of the eighth nerve right
+ 
+
+ align:start position:0%
+of the eighth nerve right
+there so you one way is to to learn this
+
+ align:start position:0%
+there so you one way is to to learn this
+ 
+
+ align:start position:0%
+there so you one way is to to learn this
+stuff is to you know study
+
+ align:start position:0%
+stuff is to you know study
+ 
+
+ align:start position:0%
+stuff is to you know study
+reconstructions like this look at these
+
+ align:start position:0%
+reconstructions like this look at these
+ 
+
+ align:start position:0%
+reconstructions like this look at these
+photographs and try to learn to pick out
+
+ align:start position:0%
+photographs and try to learn to pick out
+ 
+
+ align:start position:0%
+photographs and try to learn to pick out
+the structures right now you should be
+
+ align:start position:0%
+the structures right now you should be
+ 
+
+ align:start position:0%
+the structures right now you should be
+able this is midbrain you should know
+
+ align:start position:0%
+able this is midbrain you should know
+ 
+
+ align:start position:0%
+able this is midbrain you should know
+what the calculi are you should know the
+
+ align:start position:0%
+what the calculi are you should know the
+ 
+
+ align:start position:0%
+what the calculi are you should know the
+optic tract and the
+
+ align:start position:0%
+optic tract and the
+ 
+
+ align:start position:0%
+optic tract and the
+hypothalamus
+
+ align:start position:0%
+hypothalamus
+ 
+
+ align:start position:0%
+hypothalamus
+here if I've already told you I've
+
+ align:start position:0%
+here if I've already told you I've
+ 
+
+ align:start position:0%
+here if I've already told you I've
+removed the hemispheres and the
+
+ align:start position:0%
+removed the hemispheres and the
+ 
+
+ align:start position:0%
+removed the hemispheres and the
+cerebellum then you know this has got to
+
+ align:start position:0%
+cerebellum then you know this has got to
+ 
+
+ align:start position:0%
+cerebellum then you know this has got to
+be below the hemispheres and there's
+
+ align:start position:0%
+be below the hemispheres and there's
+ 
+
+ align:start position:0%
+be below the hemispheres and there's
+only one big structure like that it's go
+
+ align:start position:0%
+only one big structure like that it's go
+ 
+
+ align:start position:0%
+only one big structure like that it's go
+the stum
+
+ align:start position:0%
+the stum
+ 
+
+ align:start position:0%
+the stum
+okay so one way is to cover those up and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in the book you can it's done so you
+
+ align:start position:0%
+uh in the book you can it's done so you
+ 
+
+ align:start position:0%
+uh in the book you can it's done so you
+can just put a piece of paper and still
+
+ align:start position:0%
+can just put a piece of paper and still
+ 
+
+ align:start position:0%
+can just put a piece of paper and still
+see the line for the labels okay I want
+
+ align:start position:0%
+see the line for the labels okay I want
+ 
+
+ align:start position:0%
+see the line for the labels okay I want
+you to do that in your book cover up the
+
+ align:start position:0%
+you to do that in your book cover up the
+ 
+
+ align:start position:0%
+you to do that in your book cover up the
+labels and see if you can learn them
+
+ align:start position:0%
+labels and see if you can learn them
+ 
+
+ align:start position:0%
+labels and see if you can learn them
+learn what these structures are on this
+
+ align:start position:0%
+learn what these structures are on this
+ 
+
+ align:start position:0%
+learn what these structures are on this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+uh this kind of picture and this kind of
+
+ align:start position:0%
+uh this kind of picture and this kind of
+ 
+
+ align:start position:0%
+uh this kind of picture and this kind of
+reconstruction were very important to me
+
+ align:start position:0%
+reconstruction were very important to me
+ 
+
+ align:start position:0%
+reconstruction were very important to me
+from a lot for a lot of the experiments
+
+ align:start position:0%
+from a lot for a lot of the experiments
+ 
+
+ align:start position:0%
+from a lot for a lot of the experiments
+I did because I needed to do
+
+ align:start position:0%
+I did because I needed to do
+ 
+
+ align:start position:0%
+I did because I needed to do
+neurosurgery where I would open up the
+
+ align:start position:0%
+neurosurgery where I would open up the
+ 
+
+ align:start position:0%
+neurosurgery where I would open up the
+brain of course I would only see a small
+
+ align:start position:0%
+brain of course I would only see a small
+ 
+
+ align:start position:0%
+brain of course I would only see a small
+part but I learned the landmark so well
+
+ align:start position:0%
+part but I learned the landmark so well
+ 
+
+ align:start position:0%
+part but I learned the landmark so well
+that I could open it up and also using
+
+ align:start position:0%
+that I could open it up and also using
+ 
+
+ align:start position:0%
+that I could open it up and also using
+blood vessels I could see these
+
+ align:start position:0%
+blood vessels I could see these
+ 
+
+ align:start position:0%
+blood vessels I could see these
+structures and see the boundaries that
+
+ align:start position:0%
+structures and see the boundaries that
+ 
+
+ align:start position:0%
+structures and see the boundaries that
+way I could make injections or even
+
+ align:start position:0%
+way I could make injections or even
+ 
+
+ align:start position:0%
+way I could make injections or even
+lesions in just small
+
+ align:start position:0%
+lesions in just small
+ 
+
+ align:start position:0%
+lesions in just small
+regions all right this is another
+
+ align:start position:0%
+regions all right this is another
+ 
+
+ align:start position:0%
+regions all right this is another
+somewhat easier view where I have the
+
+ align:start position:0%
+somewhat easier view where I have the
+ 
+
+ align:start position:0%
+somewhat easier view where I have the
+adult brain on the left and the brain of
+
+ align:start position:0%
+adult brain on the left and the brain of
+ 
+
+ align:start position:0%
+adult brain on the left and the brain of
+a newborn on the right and here I've
+
+ align:start position:0%
+a newborn on the right and here I've
+ 
+
+ align:start position:0%
+a newborn on the right and here I've
+just labeled major parts of the
+
+ align:start position:0%
+just labeled major parts of the
+ 
+
+ align:start position:0%
+just labeled major parts of the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+Factory B NE
+
+ align:start position:0%
+Factory B NE
+ 
+
+ align:start position:0%
+Factory B NE
+cortex Superior calculi inferior
+
+ align:start position:0%
+cortex Superior calculi inferior
+ 
+
+ align:start position:0%
+cortex Superior calculi inferior
+calculi
+
+ align:start position:0%
+calculi
+ 
+
+ align:start position:0%
+calculi
+cerebellum and the Medela
+
+ align:start position:0%
+cerebellum and the Medela
+ 
+
+ align:start position:0%
+cerebellum and the Medela
+blada the codal part of the hindbrain
+
+ align:start position:0%
+blada the codal part of the hindbrain
+ 
+
+ align:start position:0%
+blada the codal part of the hindbrain
+the Ral part of the hind brain is
+
+ align:start position:0%
+the Ral part of the hind brain is
+ 
+
+ align:start position:0%
+the Ral part of the hind brain is
+underneath the cerebellum cerebellum is
+
+ align:start position:0%
+underneath the cerebellum cerebellum is
+ 
+
+ align:start position:0%
+underneath the cerebellum cerebellum is
+part of it but what I want you to note
+
+ align:start position:0%
+part of it but what I want you to note
+ 
+
+ align:start position:0%
+part of it but what I want you to note
+here look at the cerebellum here in the
+
+ align:start position:0%
+here look at the cerebellum here in the
+ 
+
+ align:start position:0%
+here look at the cerebellum here in the
+baby it's just this tiny little collar
+
+ align:start position:0%
+baby it's just this tiny little collar
+ 
+
+ align:start position:0%
+baby it's just this tiny little collar
+behind the inferior
+
+ align:start position:0%
+behind the inferior
+ 
+
+ align:start position:0%
+behind the inferior
+cus it's mainly
+
+ align:start position:0%
+cus it's mainly
+ 
+
+ align:start position:0%
+cus it's mainly
+developing with huge numbers of cell
+
+ align:start position:0%
+developing with huge numbers of cell
+ 
+
+ align:start position:0%
+developing with huge numbers of cell
+migrations from the romic lip to the hbr
+
+ align:start position:0%
+migrations from the romic lip to the hbr
+ 
+
+ align:start position:0%
+migrations from the romic lip to the hbr
+just developing in the newborn
+
+ align:start position:0%
+just developing in the newborn
+ 
+
+ align:start position:0%
+just developing in the newborn
+hamster it's born remember at a stage
+
+ align:start position:0%
+hamster it's born remember at a stage
+ 
+
+ align:start position:0%
+hamster it's born remember at a stage
+it's like a 2 and 1/2 to 3mon human
+
+ align:start position:0%
+it's like a 2 and 1/2 to 3mon human
+ 
+
+ align:start position:0%
+it's like a 2 and 1/2 to 3mon human
+fetus which means that a 2 and 1/2 month
+
+ align:start position:0%
+fetus which means that a 2 and 1/2 month
+ 
+
+ align:start position:0%
+fetus which means that a 2 and 1/2 month
+human fetus looks just like this
+
+ align:start position:0%
+human fetus looks just like this
+ 
+
+ align:start position:0%
+human fetus looks just like this
+too cerebellum grows mostly after that
+
+ align:start position:0%
+too cerebellum grows mostly after that
+ 
+
+ align:start position:0%
+too cerebellum grows mostly after that
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so one way to study that
+
+ align:start position:0%
+okay so one way to study that
+ 
+
+ align:start position:0%
+okay so one way to study that
+just use the book and make yourself a
+
+ align:start position:0%
+just use the book and make yourself a
+ 
+
+ align:start position:0%
+just use the book and make yourself a
+card and cover those up and make sure
+
+ align:start position:0%
+card and cover those up and make sure
+ 
+
+ align:start position:0%
+card and cover those up and make sure
+you know what all those pointers are
+
+ align:start position:0%
+you know what all those pointers are
+ 
+
+ align:start position:0%
+you know what all those pointers are
+pointing towards this one should be the
+
+ align:start position:0%
+pointing towards this one should be the
+ 
+
+ align:start position:0%
+pointing towards this one should be the
+easiest this one will be a little
+
+ align:start position:0%
+easiest this one will be a little
+ 
+
+ align:start position:0%
+easiest this one will be a little
+harder all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right can somebody tell me what e
+
+ align:start position:0%
+right can somebody tell me what e
+ 
+
+ align:start position:0%
+right can somebody tell me what e
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+optic crack and what about what about
+
+ align:start position:0%
+optic crack and what about what about
+ 
+
+ align:start position:0%
+optic crack and what about what about
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+hypothalamus uh can anybody do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c p right cereal cerebral pedon p means
+
+ align:start position:0%
+c p right cereal cerebral pedon p means
+ 
+
+ align:start position:0%
+c p right cereal cerebral pedon p means
+cereal it's
+
+ align:start position:0%
+cereal it's
+ 
+
+ align:start position:0%
+cereal it's
+always it's it's always the abbreviation
+
+ align:start position:0%
+always it's it's always the abbreviation
+ 
+
+ align:start position:0%
+always it's it's always the abbreviation
+for Cal pet unle is PE and I didn't
+
+ align:start position:0%
+for Cal pet unle is PE and I didn't
+ 
+
+ align:start position:0%
+for Cal pet unle is PE and I didn't
+label the PS
+
+ align:start position:0%
+label the PS
+ 
+
+ align:start position:0%
+label the PS
+but this would be the ponts right
+
+ align:start position:0%
+but this would be the ponts right
+ 
+
+ align:start position:0%
+but this would be the ponts right
+there this is the trapezoid body which I
+
+ align:start position:0%
+there this is the trapezoid body which I
+ 
+
+ align:start position:0%
+there this is the trapezoid body which I
+don't name Co
+
+ align:start position:0%
+don't name Co
+ 
+
+ align:start position:0%
+don't name Co
+nucleus cerebel
+
+ align:start position:0%
+nucleus cerebel
+ 
+
+ align:start position:0%
+nucleus cerebel
+peduncle and latal liscus but I just
+
+ align:start position:0%
+peduncle and latal liscus but I just
+ 
+
+ align:start position:0%
+peduncle and latal liscus but I just
+labeled the ones here
+
+ align:start position:0%
+labeled the ones here
+ 
+
+ align:start position:0%
+labeled the ones here
+that you know we might put a a diagram
+
+ align:start position:0%
+that you know we might put a a diagram
+ 
+
+ align:start position:0%
+that you know we might put a a diagram
+like this we wouldn't put all those
+
+ align:start position:0%
+like this we wouldn't put all those
+ 
+
+ align:start position:0%
+like this we wouldn't put all those
+things but we might ask you to do a give
+
+ align:start position:0%
+things but we might ask you to do a give
+ 
+
+ align:start position:0%
+things but we might ask you to do a give
+you a bunch of terms and say well which
+
+ align:start position:0%
+you a bunch of terms and say well which
+ 
+
+ align:start position:0%
+you a bunch of terms and say well which
+one goes with each of these letters you
+
+ align:start position:0%
+one goes with each of these letters you
+ 
+
+ align:start position:0%
+one goes with each of these letters you
+know so if you're at least familiar with
+
+ align:start position:0%
+know so if you're at least familiar with
+ 
+
+ align:start position:0%
+know so if you're at least familiar with
+it you would be able to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay and then here the same thing
+
+ align:start position:0%
+that okay and then here the same thing
+ 
+
+ align:start position:0%
+that okay and then here the same thing
+here I've covered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up just name them off for me what's
+
+ align:start position:0%
+up just name them off for me what's
+ 
+
+ align:start position:0%
+up just name them off for me what's
+that what's
+
+ align:start position:0%
+that what's
+ 
+
+ align:start position:0%
+that what's
+this okay or Cal hemisphere either one
+
+ align:start position:0%
+this okay or Cal hemisphere either one
+ 
+
+ align:start position:0%
+this okay or Cal hemisphere either one
+would be proper what's
+
+ align:start position:0%
+would be proper what's
+ 
+
+ align:start position:0%
+would be proper what's
+that okay notice most of it
+
+ align:start position:0%
+that okay notice most of it
+ 
+
+ align:start position:0%
+that okay notice most of it
+exposed here here only part of it's
+
+ align:start position:0%
+exposed here here only part of it's
+ 
+
+ align:start position:0%
+exposed here here only part of it's
+exposed and in most animals with an
+
+ align:start position:0%
+exposed and in most animals with an
+ 
+
+ align:start position:0%
+exposed and in most animals with an
+either bigger bigger hemospheres you
+
+ align:start position:0%
+either bigger bigger hemospheres you
+ 
+
+ align:start position:0%
+either bigger bigger hemospheres you
+don't even see the membrane from a dors
+
+ align:start position:0%
+don't even see the membrane from a dors
+ 
+
+ align:start position:0%
+don't even see the membrane from a dors
+of view like that okay and this
+
+ align:start position:0%
+of view like that okay and this
+ 
+
+ align:start position:0%
+of view like that okay and this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+cerebellum
+
+ align:start position:0%
+cerebellum
+ 
+
+ align:start position:0%
+cerebellum
+this CLE hind brain or medel BL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I'm asking you another question here
+
+ align:start position:0%
+oh I'm asking you another question here
+ 
+
+ align:start position:0%
+oh I'm asking you another question here
+about naming the structures I said what
+
+ align:start position:0%
+about naming the structures I said what
+ 
+
+ align:start position:0%
+about naming the structures I said what
+would make this more difficult during a
+
+ align:start position:0%
+would make this more difficult during a
+ 
+
+ align:start position:0%
+would make this more difficult during a
+Neurosurgical
+
+ align:start position:0%
+Neurosurgical
+ 
+
+ align:start position:0%
+Neurosurgical
+procedure think about
+
+ align:start position:0%
+procedure think about
+ 
+
+ align:start position:0%
+procedure think about
+it in a Neurosurgical procedure you
+
+ align:start position:0%
+it in a Neurosurgical procedure you
+ 
+
+ align:start position:0%
+it in a Neurosurgical procedure you
+don't expose such a huge amount of the
+
+ align:start position:0%
+don't expose such a huge amount of the
+ 
+
+ align:start position:0%
+don't expose such a huge amount of the
+brain you only can you know you want to
+
+ align:start position:0%
+brain you only can you know you want to
+ 
+
+ align:start position:0%
+brain you only can you know you want to
+make a
+
+ align:start position:0%
+make a
+ 
+
+ align:start position:0%
+make a
+smaller window as possible so you don't
+
+ align:start position:0%
+smaller window as possible so you don't
+ 
+
+ align:start position:0%
+smaller window as possible so you don't
+damage so much
+
+ align:start position:0%
+damage so much
+ 
+
+ align:start position:0%
+damage so much
+tissue so that's the first
+
+ align:start position:0%
+tissue so that's the first
+ 
+
+ align:start position:0%
+tissue so that's the first
+problem and the second thing is there's
+
+ align:start position:0%
+problem and the second thing is there's
+ 
+
+ align:start position:0%
+problem and the second thing is there's
+a lot of blood
+
+ align:start position:0%
+a lot of blood
+ 
+
+ align:start position:0%
+a lot of blood
+vessels in fact you have to be very
+
+ align:start position:0%
+vessels in fact you have to be very
+ 
+
+ align:start position:0%
+vessels in fact you have to be very
+careful not to go through any really big
+
+ align:start position:0%
+careful not to go through any really big
+ 
+
+ align:start position:0%
+careful not to go through any really big
+ones because you'll get so much bleeding
+
+ align:start position:0%
+ones because you'll get so much bleeding
+ 
+
+ align:start position:0%
+ones because you'll get so much bleeding
+that you'll be spending all your time
+
+ align:start position:0%
+that you'll be spending all your time
+ 
+
+ align:start position:0%
+that you'll be spending all your time
+stopping the bleeding and you do spend a
+
+ align:start position:0%
+stopping the bleeding and you do spend a
+ 
+
+ align:start position:0%
+stopping the bleeding and you do spend a
+lot of time doing that neuros
+
+ align:start position:0%
+lot of time doing that neuros
+ 
+
+ align:start position:0%
+lot of time doing that neuros
+surgery although now we have a method to
+
+ align:start position:0%
+surgery although now we have a method to
+ 
+
+ align:start position:0%
+surgery although now we have a method to
+apply that does stop the bleeding of all
+
+ align:start position:0%
+apply that does stop the bleeding of all
+ 
+
+ align:start position:0%
+apply that does stop the bleeding of all
+the smaller
+
+ align:start position:0%
+the smaller
+ 
+
+ align:start position:0%
+the smaller
+vessels just not the huge ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay look at these other pictures for
+
+ align:start position:0%
+okay look at these other pictures for
+ 
+
+ align:start position:0%
+okay look at these other pictures for
+next time and just see if you can figure
+
+ align:start position:0%
+next time and just see if you can figure
+ 
+
+ align:start position:0%
+next time and just see if you can figure
+out what's exposed okay I use different
+
+ align:start position:0%
+out what's exposed okay I use different
+ 
+
+ align:start position:0%
+out what's exposed okay I use different
+lights lighting just so you this is that
+
+ align:start position:0%
+lights lighting just so you this is that
+ 
+
+ align:start position:0%
+lights lighting just so you this is that
+same kind of brain stem that you see
+
+ align:start position:0%
+same kind of brain stem that you see
+ 
+
+ align:start position:0%
+same kind of brain stem that you see
+here with the hemispheres
+
+ align:start position:0%
+here with the hemispheres
+ 
+
+ align:start position:0%
+here with the hemispheres
+removed and you can see various
+
+ align:start position:0%
+removed and you can see various
+ 
+
+ align:start position:0%
+removed and you can see various
+structures here I've done a little more
+
+ align:start position:0%
+structures here I've done a little more
+ 
+
+ align:start position:0%
+structures here I've done a little more
+removal up front here let see if you can
+
+ align:start position:0%
+removal up front here let see if you can
+ 
+
+ align:start position:0%
+removal up front here let see if you can
+figure out what those things are now I
+
+ align:start position:0%
+figure out what those things are now I
+ 
+
+ align:start position:0%
+figure out what those things are now I
+do name a lot of them in the book I
+
+ align:start position:0%
+do name a lot of them in the book I
+ 
+
+ align:start position:0%
+do name a lot of them in the book I
+don't think I show all these pictures in
+
+ align:start position:0%
+don't think I show all these pictures in
+ 
+
+ align:start position:0%
+don't think I show all these pictures in
+the book but you I wanted you to see how
+
+ align:start position:0%
+the book but you I wanted you to see how
+ 
+
+ align:start position:0%
+the book but you I wanted you to see how
+by if you adjust the light a little bit
+
+ align:start position:0%
+by if you adjust the light a little bit
+ 
+
+ align:start position:0%
+by if you adjust the light a little bit
+you can actually see boundaries like
+
+ align:start position:0%
+you can actually see boundaries like
+ 
+
+ align:start position:0%
+you can actually see boundaries like
+look at this one there's the
+
+ align:start position:0%
+look at this one there's the
+ 
+
+ align:start position:0%
+look at this one there's the
+spiculus there's the pretective if you
+
+ align:start position:0%
+spiculus there's the pretective if you
+ 
+
+ align:start position:0%
+spiculus there's the pretective if you
+look at this one even clearer there's
+
+ align:start position:0%
+look at this one even clearer there's
+ 
+
+ align:start position:0%
+look at this one even clearer there's
+the boundary between spiculus and
+
+ align:start position:0%
+the boundary between spiculus and
+ 
+
+ align:start position:0%
+the boundary between spiculus and
+pretectum and look at how clear this
+
+ align:start position:0%
+pretectum and look at how clear this
+ 
+
+ align:start position:0%
+pretectum and look at how clear this
+boundary is and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one pretectal areia
+
+ align:start position:0%
+one pretectal areia
+ 
+
+ align:start position:0%
+one pretectal areia
+LP geniculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body that is the bundle carrying
+
+ align:start position:0%
+body that is the bundle carrying
+ 
+
+ align:start position:0%
+body that is the bundle carrying
+information from the amydala which we
+
+ align:start position:0%
+information from the amydala which we
+ 
+
+ align:start position:0%
+information from the amydala which we
+will be studying soon
+
+ align:start position:0%
+will be studying soon
+ 
+
+ align:start position:0%
+will be studying soon
+okay and this just shows what it looks
+
+ align:start position:0%
+okay and this just shows what it looks
+ 
+
+ align:start position:0%
+okay and this just shows what it looks
+like in a the embryo when it just the
+
+ align:start position:0%
+like in a the embryo when it just the
+ 
+
+ align:start position:0%
+like in a the embryo when it just the
+accents have first Grown back to the
+
+ align:start position:0%
+accents have first Grown back to the
+ 
+
+ align:start position:0%
+accents have first Grown back to the
+tectum very straight pathway back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detecton
+
+ align:start position:0%
+detecton
+ 
+
+ align:start position:0%
+detecton
+and we'll next time we will start in
+
+ align:start position:0%
+and we'll next time we will start in
+ 
+
+ align:start position:0%
+and we'll next time we will start in
+this area and talk about the midbrain a
+
+ align:start position:0%
+this area and talk about the midbrain a
+ 
+
+ align:start position:0%
+this area and talk about the midbrain a
+little more just to look at these
+
+ align:start position:0%
+little more just to look at these
+ 
+
+ align:start position:0%
+little more just to look at these
+pictures but they're in the book uh
+
+ align:start position:0%
+pictures but they're in the book uh
+ 
+
+ align:start position:0%
+pictures but they're in the book uh
+they'll give you a chance to ask about
+
+ align:start position:0%
+they'll give you a chance to ask about
+ 
+
+ align:start position:0%
+they'll give you a chance to ask about
+and uh we'll go through some of these
+
+ align:start position:0%
+and uh we'll go through some of these
+ 
+
+ align:start position:0%
+and uh we'll go through some of these
+before we go on to the Endra
+
+ align:start position:0%
+before we go on to the Endra
+ 
+
+ align:start position:0%
+before we go on to the Endra
+okay
\ No newline at end of file
diff --git a/8umr89M6YgQ.txt b/8umr89M6YgQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d48cf7817e38fe2bf711f2c3cf33bd34fa450e7e
--- /dev/null
+++ b/8umr89M6YgQ.txt
@@ -0,0 +1,1963 @@
+align:start position:0%
+ 
+let's talk a little bit
+
+ align:start position:0%
+let's talk a little bit
+ 
+
+ align:start position:0%
+let's talk a little bit
+more about some of the parameters that
+
+ align:start position:0%
+more about some of the parameters that
+ 
+
+ align:start position:0%
+more about some of the parameters that
+govern the chemical reactions
+
+ align:start position:0%
+govern the chemical reactions
+ 
+
+ align:start position:0%
+govern the chemical reactions
+in a cell and indeed any chemical
+
+ align:start position:0%
+in a cell and indeed any chemical
+ 
+
+ align:start position:0%
+in a cell and indeed any chemical
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+all chemical reactions are governed by
+
+ align:start position:0%
+all chemical reactions are governed by
+ 
+
+ align:start position:0%
+all chemical reactions are governed by
+something called
+
+ align:start position:0%
+something called
+ 
+
+ align:start position:0%
+something called
+free or usable energy
+
+ align:start position:0%
+free or usable energy
+ 
+
+ align:start position:0%
+free or usable energy
+so let us write that reactions
+
+ align:start position:0%
+so let us write that reactions
+ 
+
+ align:start position:0%
+so let us write that reactions
+are governed by free energy
+
+ align:start position:0%
+are governed by free energy
+ 
+
+ align:start position:0%
+are governed by free energy
+where free really means usable and this
+
+ align:start position:0%
+where free really means usable and this
+ 
+
+ align:start position:0%
+where free really means usable and this
+free energy gets a special symbol
+
+ align:start position:0%
+free energy gets a special symbol
+ 
+
+ align:start position:0%
+free energy gets a special symbol
+it is called g and the difference
+
+ align:start position:0%
+it is called g and the difference
+ 
+
+ align:start position:0%
+it is called g and the difference
+in free energy is what's really
+
+ align:start position:0%
+in free energy is what's really
+ 
+
+ align:start position:0%
+in free energy is what's really
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+and so we write delta g delta g
+
+ align:start position:0%
+and so we write delta g delta g
+ 
+
+ align:start position:0%
+and so we write delta g delta g
+comes from a key thermodynamic equation
+
+ align:start position:0%
+comes from a key thermodynamic equation
+ 
+
+ align:start position:0%
+comes from a key thermodynamic equation
+such that the difference in the free
+
+ align:start position:0%
+such that the difference in the free
+ 
+
+ align:start position:0%
+such that the difference in the free
+energy of a reaction
+
+ align:start position:0%
+energy of a reaction
+ 
+
+ align:start position:0%
+energy of a reaction
+has to do with a difference in enthalpy
+
+ align:start position:0%
+has to do with a difference in enthalpy
+ 
+
+ align:start position:0%
+has to do with a difference in enthalpy
+or total energy minus
+
+ align:start position:0%
+or total energy minus
+ 
+
+ align:start position:0%
+or total energy minus
+temperature times the difference
+
+ align:start position:0%
+temperature times the difference
+ 
+
+ align:start position:0%
+temperature times the difference
+in useless energy so this is the
+
+ align:start position:0%
+in useless energy so this is the
+ 
+
+ align:start position:0%
+in useless energy so this is the
+free energy this is the total energy
+
+ align:start position:0%
+free energy this is the total energy
+ 
+
+ align:start position:0%
+free energy this is the total energy
+and this is the temperature multiplied
+
+ align:start position:0%
+and this is the temperature multiplied
+ 
+
+ align:start position:0%
+and this is the temperature multiplied
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+the unusable or free the unusable
+
+ align:start position:0%
+the unusable or free the unusable
+ 
+
+ align:start position:0%
+the unusable or free the unusable
+energy or entropy
+
+ align:start position:0%
+energy or entropy
+ 
+
+ align:start position:0%
+energy or entropy
+okay so this delta g minus delta equals
+
+ align:start position:0%
+okay so this delta g minus delta equals
+ 
+
+ align:start position:0%
+okay so this delta g minus delta equals
+delta h minus t delta
+
+ align:start position:0%
+delta h minus t delta
+ 
+
+ align:start position:0%
+delta h minus t delta
+s is an equation that you should have
+
+ align:start position:0%
+s is an equation that you should have
+ 
+
+ align:start position:0%
+s is an equation that you should have
+seen
+
+ align:start position:0%
+seen
+ 
+
+ align:start position:0%
+seen
+and at least know the terms associated
+
+ align:start position:0%
+and at least know the terms associated
+ 
+
+ align:start position:0%
+and at least know the terms associated
+when we think about a chemical reaction
+
+ align:start position:0%
+when we think about a chemical reaction
+ 
+
+ align:start position:0%
+when we think about a chemical reaction
+such that some reactants can either
+
+ align:start position:0%
+such that some reactants can either
+ 
+
+ align:start position:0%
+such that some reactants can either
+become products reactants becoming
+
+ align:start position:0%
+become products reactants becoming
+ 
+
+ align:start position:0%
+become products reactants becoming
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+or products can become
+
+ align:start position:0%
+or products can become
+ 
+
+ align:start position:0%
+or products can become
+what were reactants so chemical
+
+ align:start position:0%
+what were reactants so chemical
+ 
+
+ align:start position:0%
+what were reactants so chemical
+reactions can go in both directions
+
+ align:start position:0%
+reactions can go in both directions
+ 
+
+ align:start position:0%
+reactions can go in both directions
+there are three things that can happen
+
+ align:start position:0%
+there are three things that can happen
+ 
+
+ align:start position:0%
+there are three things that can happen
+to free energy during this reaction
+
+ align:start position:0%
+to free energy during this reaction
+ 
+
+ align:start position:0%
+to free energy during this reaction
+either one way or the other delta g
+
+ align:start position:0%
+either one way or the other delta g
+ 
+
+ align:start position:0%
+either one way or the other delta g
+can be negative in which case
+
+ align:start position:0%
+can be negative in which case
+ 
+
+ align:start position:0%
+can be negative in which case
+energy is released during the reaction
+
+ align:start position:0%
+energy is released during the reaction
+ 
+
+ align:start position:0%
+energy is released during the reaction
+and the reaction may
+
+ align:start position:0%
+and the reaction may
+ 
+
+ align:start position:0%
+and the reaction may
+proceed it may even be spontaneous
+
+ align:start position:0%
+proceed it may even be spontaneous
+ 
+
+ align:start position:0%
+proceed it may even be spontaneous
+on the other hand delta g might be
+
+ align:start position:0%
+on the other hand delta g might be
+ 
+
+ align:start position:0%
+on the other hand delta g might be
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+delta g might be positive in which case
+
+ align:start position:0%
+delta g might be positive in which case
+ 
+
+ align:start position:0%
+delta g might be positive in which case
+energy is required in order for the
+
+ align:start position:0%
+energy is required in order for the
+ 
+
+ align:start position:0%
+energy is required in order for the
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+to proceed and the third possibility is
+
+ align:start position:0%
+to proceed and the third possibility is
+ 
+
+ align:start position:0%
+to proceed and the third possibility is
+that delta g is
+
+ align:start position:0%
+that delta g is
+ 
+
+ align:start position:0%
+that delta g is
+zero and if delta g is zero
+
+ align:start position:0%
+zero and if delta g is zero
+ 
+
+ align:start position:0%
+zero and if delta g is zero
+the reaction is said to be at
+
+ align:start position:0%
+the reaction is said to be at
+ 
+
+ align:start position:0%
+the reaction is said to be at
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+where the reactants
+
+ align:start position:0%
+where the reactants
+ 
+
+ align:start position:0%
+where the reactants
+become products at the same rate as the
+
+ align:start position:0%
+become products at the same rate as the
+ 
+
+ align:start position:0%
+become products at the same rate as the
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+go back and become reactants
+
+ align:start position:0%
+go back and become reactants
+ 
+
+ align:start position:0%
+go back and become reactants
+so everything is kind of in balance
+
+ align:start position:0%
+so everything is kind of in balance
+ 
+
+ align:start position:0%
+so everything is kind of in balance
+those are your three
+
+ align:start position:0%
+those are your three
+ 
+
+ align:start position:0%
+those are your three
+possibilities and it's important to
+
+ align:start position:0%
+possibilities and it's important to
+ 
+
+ align:start position:0%
+possibilities and it's important to
+think about them
+
+ align:start position:0%
+think about them
+ 
+
+ align:start position:0%
+think about them
+for all biological chemical reactions
+
+ align:start position:0%
+for all biological chemical reactions
+ 
+
+ align:start position:0%
+for all biological chemical reactions
+so here i'm going to lay it out for you
+
+ align:start position:0%
+so here i'm going to lay it out for you
+ 
+
+ align:start position:0%
+so here i'm going to lay it out for you
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+and think about free energy and reaction
+
+ align:start position:0%
+and think about free energy and reaction
+ 
+
+ align:start position:0%
+and think about free energy and reaction
+kinetics
+
+ align:start position:0%
+kinetics
+ 
+
+ align:start position:0%
+kinetics
+for here substrate becoming products
+
+ align:start position:0%
+for here substrate becoming products
+ 
+
+ align:start position:0%
+for here substrate becoming products
+reactants or substrate ros used
+
+ align:start position:0%
+reactants or substrate ros used
+ 
+
+ align:start position:0%
+reactants or substrate ros used
+interchangeably
+
+ align:start position:0%
+interchangeably
+ 
+
+ align:start position:0%
+interchangeably
+free energy as defined for you
+
+ align:start position:0%
+free energy as defined for you
+ 
+
+ align:start position:0%
+free energy as defined for you
+and here energy release
+
+ align:start position:0%
+and here energy release
+ 
+
+ align:start position:0%
+and here energy release
+when delta g is negative these reactions
+
+ align:start position:0%
+when delta g is negative these reactions
+ 
+
+ align:start position:0%
+when delta g is negative these reactions
+can also be called exogonic and they may
+
+ align:start position:0%
+can also be called exogonic and they may
+ 
+
+ align:start position:0%
+can also be called exogonic and they may
+occur spontaneously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the flip endergonic reactions
+
+ align:start position:0%
+the flip endergonic reactions
+ 
+
+ align:start position:0%
+the flip endergonic reactions
+require energy to proceed where delta g
+
+ align:start position:0%
+require energy to proceed where delta g
+ 
+
+ align:start position:0%
+require energy to proceed where delta g
+is positive and delta g
+
+ align:start position:0%
+is positive and delta g
+ 
+
+ align:start position:0%
+is positive and delta g
+zero the reaction is at equilibrium
+
+ align:start position:0%
+zero the reaction is at equilibrium
+ 
+
+ align:start position:0%
+zero the reaction is at equilibrium
+the production of the products
+
+ align:start position:0%
+the production of the products
+ 
+
+ align:start position:0%
+the production of the products
+is the same as the back reaction to the
+
+ align:start position:0%
+is the same as the back reaction to the
+ 
+
+ align:start position:0%
+is the same as the back reaction to the
+production or the regeneration of the
+
+ align:start position:0%
+production or the regeneration of the
+ 
+
+ align:start position:0%
+production or the regeneration of the
+reactants
+
+ align:start position:0%
+reactants
+ 
+
+ align:start position:0%
+reactants
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can portray the thermodynamics
+
+ align:start position:0%
+we can portray the thermodynamics
+ 
+
+ align:start position:0%
+we can portray the thermodynamics
+the free energy changes
+
+ align:start position:0%
+the free energy changes
+ 
+
+ align:start position:0%
+the free energy changes
+using various graphs and
+
+ align:start position:0%
+using various graphs and
+ 
+
+ align:start position:0%
+using various graphs and
+delta g negative reactions typically are
+
+ align:start position:0%
+delta g negative reactions typically are
+ 
+
+ align:start position:0%
+delta g negative reactions typically are
+shown
+
+ align:start position:0%
+shown
+ 
+
+ align:start position:0%
+shown
+as the the schematic as a ball rolling
+
+ align:start position:0%
+as the the schematic as a ball rolling
+ 
+
+ align:start position:0%
+as the the schematic as a ball rolling
+down a hill
+
+ align:start position:0%
+down a hill
+ 
+
+ align:start position:0%
+down a hill
+or you can draw a graph where you can
+
+ align:start position:0%
+or you can draw a graph where you can
+ 
+
+ align:start position:0%
+or you can draw a graph where you can
+see that if you plot energy
+
+ align:start position:0%
+see that if you plot energy
+ 
+
+ align:start position:0%
+see that if you plot energy
+against time you see that there's a
+
+ align:start position:0%
+against time you see that there's a
+ 
+
+ align:start position:0%
+against time you see that there's a
+certain amount of energy released as the
+
+ align:start position:0%
+certain amount of energy released as the
+ 
+
+ align:start position:0%
+certain amount of energy released as the
+products are formed
+
+ align:start position:0%
+products are formed
+ 
+
+ align:start position:0%
+products are formed
+and the flip where delta g is positive
+
+ align:start position:0%
+and the flip where delta g is positive
+ 
+
+ align:start position:0%
+and the flip where delta g is positive
+when you need energy for the reaction to
+
+ align:start position:0%
+when you need energy for the reaction to
+ 
+
+ align:start position:0%
+when you need energy for the reaction to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+then you see that the amount of energy
+
+ align:start position:0%
+then you see that the amount of energy
+ 
+
+ align:start position:0%
+then you see that the amount of energy
+required
+
+ align:start position:0%
+required
+ 
+
+ align:start position:0%
+required
+is a positive input that has to be that
+
+ align:start position:0%
+is a positive input that has to be that
+ 
+
+ align:start position:0%
+is a positive input that has to be that
+has to take place
+
+ align:start position:0%
+has to take place
+ 
+
+ align:start position:0%
+has to take place
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there is a catch here
+
+ align:start position:0%
+but there is a catch here
+ 
+
+ align:start position:0%
+but there is a catch here
+i mentioned that even if delta g is
+
+ align:start position:0%
+i mentioned that even if delta g is
+ 
+
+ align:start position:0%
+i mentioned that even if delta g is
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+sometimes a reaction will not proceed
+
+ align:start position:0%
+sometimes a reaction will not proceed
+ 
+
+ align:start position:0%
+sometimes a reaction will not proceed
+it needs a little push before it will
+
+ align:start position:0%
+it needs a little push before it will
+ 
+
+ align:start position:0%
+it needs a little push before it will
+proceed
+
+ align:start position:0%
+proceed
+ 
+
+ align:start position:0%
+proceed
+and the little push is energy and it's
+
+ align:start position:0%
+and the little push is energy and it's
+ 
+
+ align:start position:0%
+and the little push is energy and it's
+called activation energy
+
+ align:start position:0%
+called activation energy
+ 
+
+ align:start position:0%
+called activation energy
+so we can write you may need
+
+ align:start position:0%
+so we can write you may need
+ 
+
+ align:start position:0%
+so we can write you may need
+activation energy even
+
+ align:start position:0%
+activation energy even
+ 
+
+ align:start position:0%
+activation energy even
+with delta g negative less than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is called an energy barrier you can
+
+ align:start position:0%
+this is called an energy barrier you can
+ 
+
+ align:start position:0%
+this is called an energy barrier you can
+think of it as a ball
+
+ align:start position:0%
+think of it as a ball
+ 
+
+ align:start position:0%
+think of it as a ball
+sitting at the top of a hill and the
+
+ align:start position:0%
+sitting at the top of a hill and the
+ 
+
+ align:start position:0%
+sitting at the top of a hill and the
+ball really could roll down the hill
+
+ align:start position:0%
+ball really could roll down the hill
+ 
+
+ align:start position:0%
+ball really could roll down the hill
+but it has to get out of the little
+
+ align:start position:0%
+but it has to get out of the little
+ 
+
+ align:start position:0%
+but it has to get out of the little
+hollow that it's in before it can do so
+
+ align:start position:0%
+hollow that it's in before it can do so
+ 
+
+ align:start position:0%
+hollow that it's in before it can do so
+getting out of the little hollow so the
+
+ align:start position:0%
+getting out of the little hollow so the
+ 
+
+ align:start position:0%
+getting out of the little hollow so the
+ball can roll down the hill
+
+ align:start position:0%
+ball can roll down the hill
+ 
+
+ align:start position:0%
+ball can roll down the hill
+is the activation energy of a chemical
+
+ align:start position:0%
+is the activation energy of a chemical
+ 
+
+ align:start position:0%
+is the activation energy of a chemical
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+this can be a real barrier to getting
+
+ align:start position:0%
+this can be a real barrier to getting
+ 
+
+ align:start position:0%
+this can be a real barrier to getting
+chemical reactions to go
+
+ align:start position:0%
+chemical reactions to go
+ 
+
+ align:start position:0%
+chemical reactions to go
+and there is a whole class of substances
+
+ align:start position:0%
+and there is a whole class of substances
+ 
+
+ align:start position:0%
+and there is a whole class of substances
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+bring this activation energy down and
+
+ align:start position:0%
+bring this activation energy down and
+ 
+
+ align:start position:0%
+bring this activation energy down and
+allow reactions to proceed
+
+ align:start position:0%
+allow reactions to proceed
+ 
+
+ align:start position:0%
+allow reactions to proceed
+these are called catalysts
+
+ align:start position:0%
+these are called catalysts
+ 
+
+ align:start position:0%
+these are called catalysts
+and they are the things that will get
+
+ align:start position:0%
+and they are the things that will get
+ 
+
+ align:start position:0%
+and they are the things that will get
+your ball out of the hollow that will
+
+ align:start position:0%
+your ball out of the hollow that will
+ 
+
+ align:start position:0%
+your ball out of the hollow that will
+get you over the activation energy hump
+
+ align:start position:0%
+get you over the activation energy hump
+ 
+
+ align:start position:0%
+get you over the activation energy hump
+and allow the reaction to proceed so
+
+ align:start position:0%
+and allow the reaction to proceed so
+ 
+
+ align:start position:0%
+and allow the reaction to proceed so
+catalysts are a class of chemicals
+
+ align:start position:0%
+catalysts are a class of chemicals
+ 
+
+ align:start position:0%
+catalysts are a class of chemicals
+that decrease activation
+
+ align:start position:0%
+that decrease activation
+ 
+
+ align:start position:0%
+that decrease activation
+energy and they're found all over
+
+ align:start position:0%
+energy and they're found all over
+ 
+
+ align:start position:0%
+energy and they're found all over
+chemistry
+
+ align:start position:0%
+chemistry
+ 
+
+ align:start position:0%
+chemistry
+but in life they are defined by a
+
+ align:start position:0%
+but in life they are defined by a
+ 
+
+ align:start position:0%
+but in life they are defined by a
+particular class of biological molecules
+
+ align:start position:0%
+particular class of biological molecules
+ 
+
+ align:start position:0%
+particular class of biological molecules
+that are the enzymes enzymes
+
+ align:start position:0%
+that are the enzymes enzymes
+ 
+
+ align:start position:0%
+that are the enzymes enzymes
+are a hugely important class of
+
+ align:start position:0%
+are a hugely important class of
+ 
+
+ align:start position:0%
+are a hugely important class of
+biological molecules
+
+ align:start position:0%
+biological molecules
+ 
+
+ align:start position:0%
+biological molecules
+and enzymes are biological catalysts
+
+ align:start position:0%
+and enzymes are biological catalysts
+ 
+
+ align:start position:0%
+and enzymes are biological catalysts
+i'll write a couple more things on the
+
+ align:start position:0%
+i'll write a couple more things on the
+ 
+
+ align:start position:0%
+i'll write a couple more things on the
+board and then we'll look at a slide or
+
+ align:start position:0%
+board and then we'll look at a slide or
+ 
+
+ align:start position:0%
+board and then we'll look at a slide or
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+enzymes are very cool because they're
+
+ align:start position:0%
+enzymes are very cool because they're
+ 
+
+ align:start position:0%
+enzymes are very cool because they're
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+for every reaction there are thousands
+
+ align:start position:0%
+for every reaction there are thousands
+ 
+
+ align:start position:0%
+for every reaction there are thousands
+and thousands of enzymes in our bodies
+
+ align:start position:0%
+and thousands of enzymes in our bodies
+ 
+
+ align:start position:0%
+and thousands of enzymes in our bodies
+each of them responsible for pushing a
+
+ align:start position:0%
+each of them responsible for pushing a
+ 
+
+ align:start position:0%
+each of them responsible for pushing a
+particular chemical reaction
+
+ align:start position:0%
+particular chemical reaction
+ 
+
+ align:start position:0%
+particular chemical reaction
+over the activation energy hump
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can write that enzymes are
+
+ align:start position:0%
+so we can write that enzymes are
+ 
+
+ align:start position:0%
+so we can write that enzymes are
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+for each chemical reaction
+
+ align:start position:0%
+for each chemical reaction
+ 
+
+ align:start position:0%
+for each chemical reaction
+each metabolic process in the cell
+
+ align:start position:0%
+each metabolic process in the cell
+ 
+
+ align:start position:0%
+each metabolic process in the cell
+and key to this is that they do not
+
+ align:start position:0%
+and key to this is that they do not
+ 
+
+ align:start position:0%
+and key to this is that they do not
+change the value of delta g they rather
+
+ align:start position:0%
+change the value of delta g they rather
+ 
+
+ align:start position:0%
+change the value of delta g they rather
+speed up the rate of the reaction
+
+ align:start position:0%
+speed up the rate of the reaction
+ 
+
+ align:start position:0%
+speed up the rate of the reaction
+so they do not change delta g
+
+ align:start position:0%
+so they do not change delta g
+ 
+
+ align:start position:0%
+so they do not change delta g
+but speed up reaction rate
+
+ align:start position:0%
+but speed up reaction rate
+ 
+
+ align:start position:0%
+but speed up reaction rate
+how fast it goes the notion of enzymes
+
+ align:start position:0%
+how fast it goes the notion of enzymes
+ 
+
+ align:start position:0%
+how fast it goes the notion of enzymes
+is something that is shown on this slide
+
+ align:start position:0%
+is something that is shown on this slide
+ 
+
+ align:start position:0%
+is something that is shown on this slide
+the enzyme is a molecule and it has
+
+ align:start position:0%
+the enzyme is a molecule and it has
+ 
+
+ align:start position:0%
+the enzyme is a molecule and it has
+a particular place where the substrate
+
+ align:start position:0%
+a particular place where the substrate
+ 
+
+ align:start position:0%
+a particular place where the substrate
+or the reactants
+
+ align:start position:0%
+or the reactants
+ 
+
+ align:start position:0%
+or the reactants
+can bind this is called the active site
+
+ align:start position:0%
+can bind this is called the active site
+ 
+
+ align:start position:0%
+can bind this is called the active site
+and in the schematic the substrate
+
+ align:start position:0%
+and in the schematic the substrate
+ 
+
+ align:start position:0%
+and in the schematic the substrate
+comes and binds to the enzyme and forms
+
+ align:start position:0%
+comes and binds to the enzyme and forms
+ 
+
+ align:start position:0%
+comes and binds to the enzyme and forms
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+enzyme substrate complex and the
+
+ align:start position:0%
+enzyme substrate complex and the
+ 
+
+ align:start position:0%
+enzyme substrate complex and the
+substrate pretty much
+
+ align:start position:0%
+substrate pretty much
+ 
+
+ align:start position:0%
+substrate pretty much
+fits in a particular part of the enzyme
+
+ align:start position:0%
+fits in a particular part of the enzyme
+ 
+
+ align:start position:0%
+fits in a particular part of the enzyme
+once the substrate is inside the enzyme
+
+ align:start position:0%
+once the substrate is inside the enzyme
+ 
+
+ align:start position:0%
+once the substrate is inside the enzyme
+or bound to the enzyme then various
+
+ align:start position:0%
+or bound to the enzyme then various
+ 
+
+ align:start position:0%
+or bound to the enzyme then various
+changes happen that push the substrate
+
+ align:start position:0%
+changes happen that push the substrate
+ 
+
+ align:start position:0%
+changes happen that push the substrate
+over the activation energy barrier and
+
+ align:start position:0%
+over the activation energy barrier and
+ 
+
+ align:start position:0%
+over the activation energy barrier and
+allow the product
+
+ align:start position:0%
+allow the product
+ 
+
+ align:start position:0%
+allow the product
+to form once the product's formed
+
+ align:start position:0%
+to form once the product's formed
+ 
+
+ align:start position:0%
+to form once the product's formed
+it's released from the enzyme and the
+
+ align:start position:0%
+it's released from the enzyme and the
+ 
+
+ align:start position:0%
+it's released from the enzyme and the
+enzyme is free
+
+ align:start position:0%
+enzyme is free
+ 
+
+ align:start position:0%
+enzyme is free
+to be a catalyst again for that chemical
+
+ align:start position:0%
+to be a catalyst again for that chemical
+ 
+
+ align:start position:0%
+to be a catalyst again for that chemical
+reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as we discussed chemical reactions are
+
+ align:start position:0%
+as we discussed chemical reactions are
+ 
+
+ align:start position:0%
+as we discussed chemical reactions are
+reversible and so you can see
+
+ align:start position:0%
+reversible and so you can see
+ 
+
+ align:start position:0%
+reversible and so you can see
+that there are places where the reaction
+
+ align:start position:0%
+that there are places where the reaction
+ 
+
+ align:start position:0%
+that there are places where the reaction
+could proceed backwards
+
+ align:start position:0%
+could proceed backwards
+ 
+
+ align:start position:0%
+could proceed backwards
+although it may not usually do so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the specificity of enzymes is really
+
+ align:start position:0%
+the specificity of enzymes is really
+ 
+
+ align:start position:0%
+the specificity of enzymes is really
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+on this slide you can see um two
+
+ align:start position:0%
+on this slide you can see um two
+ 
+
+ align:start position:0%
+on this slide you can see um two
+enzymes and these are depicted in a
+
+ align:start position:0%
+enzymes and these are depicted in a
+ 
+
+ align:start position:0%
+enzymes and these are depicted in a
+various
+
+ align:start position:0%
+various
+ 
+
+ align:start position:0%
+various
+in a specific structural way so that you
+
+ align:start position:0%
+in a specific structural way so that you
+ 
+
+ align:start position:0%
+in a specific structural way so that you
+can see how the
+
+ align:start position:0%
+can see how the
+ 
+
+ align:start position:0%
+can see how the
+protein is folded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the left hand side is the structure
+
+ align:start position:0%
+on the left hand side is the structure
+ 
+
+ align:start position:0%
+on the left hand side is the structure
+of an enzyme called
+
+ align:start position:0%
+of an enzyme called
+ 
+
+ align:start position:0%
+of an enzyme called
+cellulase it breaks down
+
+ align:start position:0%
+cellulase it breaks down
+ 
+
+ align:start position:0%
+cellulase it breaks down
+cellulose which is the carbohydrate
+
+ align:start position:0%
+cellulose which is the carbohydrate
+ 
+
+ align:start position:0%
+cellulose which is the carbohydrate
+of plants it's in grass it's one of the
+
+ align:start position:0%
+of plants it's in grass it's one of the
+ 
+
+ align:start position:0%
+of plants it's in grass it's one of the
+reasons
+
+ align:start position:0%
+reasons
+ 
+
+ align:start position:0%
+reasons
+that that you cannot you and i
+
+ align:start position:0%
+that that you cannot you and i
+ 
+
+ align:start position:0%
+that that you cannot you and i
+cannot eat grass okay we do not have
+
+ align:start position:0%
+cannot eat grass okay we do not have
+ 
+
+ align:start position:0%
+cannot eat grass okay we do not have
+this enzyme called cellulase
+
+ align:start position:0%
+this enzyme called cellulase
+ 
+
+ align:start position:0%
+this enzyme called cellulase
+okay some organisms do and they're able
+
+ align:start position:0%
+okay some organisms do and they're able
+ 
+
+ align:start position:0%
+okay some organisms do and they're able
+to break down grass
+
+ align:start position:0%
+to break down grass
+ 
+
+ align:start position:0%
+to break down grass
+and to use the um the sugars that come
+
+ align:start position:0%
+and to use the um the sugars that come
+ 
+
+ align:start position:0%
+and to use the um the sugars that come
+from cellulose
+
+ align:start position:0%
+from cellulose
+ 
+
+ align:start position:0%
+from cellulose
+on the right hand side is an enzyme
+
+ align:start position:0%
+on the right hand side is an enzyme
+ 
+
+ align:start position:0%
+on the right hand side is an enzyme
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+amylase amylase breaks down
+
+ align:start position:0%
+amylase amylase breaks down
+ 
+
+ align:start position:0%
+amylase amylase breaks down
+bonds in polymers
+
+ align:start position:0%
+bonds in polymers
+ 
+
+ align:start position:0%
+bonds in polymers
+of glucose that are found in starch
+
+ align:start position:0%
+of glucose that are found in starch
+ 
+
+ align:start position:0%
+of glucose that are found in starch
+you and i have this enzyme and so we can
+
+ align:start position:0%
+you and i have this enzyme and so we can
+ 
+
+ align:start position:0%
+you and i have this enzyme and so we can
+break down starch
+
+ align:start position:0%
+break down starch
+ 
+
+ align:start position:0%
+break down starch
+and use this as a source of energy
+
+ align:start position:0%
+and use this as a source of energy
+ 
+
+ align:start position:0%
+and use this as a source of energy
+these two enzymes have very similar
+
+ align:start position:0%
+these two enzymes have very similar
+ 
+
+ align:start position:0%
+these two enzymes have very similar
+specificity
+
+ align:start position:0%
+specificity
+ 
+
+ align:start position:0%
+specificity
+the cellulase breaks down these beta 1
+
+ align:start position:0%
+the cellulase breaks down these beta 1
+ 
+
+ align:start position:0%
+the cellulase breaks down these beta 1
+4 bonds between glucose monomers
+
+ align:start position:0%
+4 bonds between glucose monomers
+ 
+
+ align:start position:0%
+4 bonds between glucose monomers
+in cellulose and the amylase breaks down
+
+ align:start position:0%
+in cellulose and the amylase breaks down
+ 
+
+ align:start position:0%
+in cellulose and the amylase breaks down
+a slightly different bond called an
+
+ align:start position:0%
+a slightly different bond called an
+ 
+
+ align:start position:0%
+a slightly different bond called an
+alpha 1 4 bond in starch
+
+ align:start position:0%
+alpha 1 4 bond in starch
+ 
+
+ align:start position:0%
+alpha 1 4 bond in starch
+the bonds are similar but they're
+
+ align:start position:0%
+the bonds are similar but they're
+ 
+
+ align:start position:0%
+the bonds are similar but they're
+different enough
+
+ align:start position:0%
+different enough
+ 
+
+ align:start position:0%
+different enough
+that you need separate enzymes in order
+
+ align:start position:0%
+that you need separate enzymes in order
+ 
+
+ align:start position:0%
+that you need separate enzymes in order
+to break them down
+
+ align:start position:0%
+to break them down
+ 
+
+ align:start position:0%
+to break them down
+and these enzyme differences are the
+
+ align:start position:0%
+and these enzyme differences are the
+ 
+
+ align:start position:0%
+and these enzyme differences are the
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+that you can or cannot eat grass and
+
+ align:start position:0%
+that you can or cannot eat grass and
+ 
+
+ align:start position:0%
+that you can or cannot eat grass and
+they demonstrate this notion
+
+ align:start position:0%
+they demonstrate this notion
+ 
+
+ align:start position:0%
+they demonstrate this notion
+of enzyme specificity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want you to take a few minutes now
+
+ align:start position:0%
+i want you to take a few minutes now
+ 
+
+ align:start position:0%
+i want you to take a few minutes now
+to look at the assignment the exercises
+
+ align:start position:0%
+to look at the assignment the exercises
+ 
+
+ align:start position:0%
+to look at the assignment the exercises
+that have to do with free energy
+
+ align:start position:0%
+that have to do with free energy
+ 
+
+ align:start position:0%
+that have to do with free energy
+and practice some of these concepts that
+
+ align:start position:0%
+and practice some of these concepts that
+ 
+
+ align:start position:0%
+and practice some of these concepts that
+we've just discussed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/9J_VCHpvMbY.txt b/9J_VCHpvMbY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c5a6cca28da7a55b1c67be5a1c5cdd8af6bd652f
--- /dev/null
+++ b/9J_VCHpvMbY.txt
@@ -0,0 +1,723 @@
+align:start position:0%
+ 
+hi welcome back to recitation we've been
+
+ align:start position:0%
+hi welcome back to recitation we've been
+ 
+
+ align:start position:0%
+hi welcome back to recitation we've been
+talking about applications of
+
+ align:start position:0%
+talking about applications of
+ 
+
+ align:start position:0%
+talking about applications of
+integration including finding the areas
+
+ align:start position:0%
+integration including finding the areas
+ 
+
+ align:start position:0%
+integration including finding the areas
+between curves so I have here a nice
+
+ align:start position:0%
+between curves so I have here a nice
+ 
+
+ align:start position:0%
+between curves so I have here a nice
+little region that I like I think it's
+
+ align:start position:0%
+little region that I like I think it's
+ 
+
+ align:start position:0%
+little region that I like I think it's
+kind of cute so so it's the region
+
+ align:start position:0%
+kind of cute so so it's the region
+ 
+
+ align:start position:0%
+kind of cute so so it's the region
+between yal sinx and yal cosine X and
+
+ align:start position:0%
+between yal sinx and yal cosine X and
+ 
+
+ align:start position:0%
+between yal sinx and yal cosine X and
+and you know those those two curves
+
+ align:start position:0%
+and you know those those two curves
+ 
+
+ align:start position:0%
+and you know those those two curves
+cross each other over and over again
+
+ align:start position:0%
+cross each other over and over again
+ 
+
+ align:start position:0%
+cross each other over and over again
+they they repr each so just I'm just
+
+ align:start position:0%
+they they repr each so just I'm just
+ 
+
+ align:start position:0%
+they they repr each so just I'm just
+interested in the in the region between
+
+ align:start position:0%
+interested in the in the region between
+ 
+
+ align:start position:0%
+interested in the in the region between
+the the two consecutive points where
+
+ align:start position:0%
+the the two consecutive points where
+ 
+
+ align:start position:0%
+the the two consecutive points where
+they cross so so here you know so at pi
+
+ align:start position:0%
+they cross so so here you know so at pi
+ 
+
+ align:start position:0%
+they cross so so here you know so at pi
+over 4 we have Sin xals Sin pi over4
+
+ align:start position:0%
+over 4 we have Sin xals Sin pi over4
+ 
+
+ align:start position:0%
+over 4 we have Sin xals Sin pi over4
+equals cosine pi over 4 and and at 5 Pi
+
+ align:start position:0%
+equals cosine pi over 4 and and at 5 Pi
+ 
+
+ align:start position:0%
+equals cosine pi over 4 and and at 5 Pi
+over4 they're also equal again down in
+
+ align:start position:0%
+over4 they're also equal again down in
+ 
+
+ align:start position:0%
+over4 they're also equal again down in
+the third quadrant there um so so the
+
+ align:start position:0%
+the third quadrant there um so so the
+ 
+
+ align:start position:0%
+the third quadrant there um so so the
+question is to to compute the the area
+
+ align:start position:0%
+question is to to compute the the area
+ 
+
+ align:start position:0%
+question is to to compute the the area
+of of this region that they that they
+
+ align:start position:0%
+of of this region that they that they
+ 
+
+ align:start position:0%
+of of this region that they that they
+bound between those two points so why
+
+ align:start position:0%
+bound between those two points so why
+ 
+
+ align:start position:0%
+bound between those two points so why
+don't you take a couple minutes work
+
+ align:start position:0%
+don't you take a couple minutes work
+ 
+
+ align:start position:0%
+don't you take a couple minutes work
+through that come back and we can work
+
+ align:start position:0%
+through that come back and we can work
+ 
+
+ align:start position:0%
+through that come back and we can work
+through it
+
+ align:start position:0%
+through it
+ 
+
+ align:start position:0%
+through it
+together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right welcome back so from this
+
+ align:start position:0%
+all right welcome back so from this
+ 
+
+ align:start position:0%
+all right welcome back so from this
+picture it's it's pretty easy to see
+
+ align:start position:0%
+picture it's it's pretty easy to see
+ 
+
+ align:start position:0%
+picture it's it's pretty easy to see
+what the region of integration is I mean
+
+ align:start position:0%
+what the region of integration is I mean
+ 
+
+ align:start position:0%
+what the region of integration is I mean
+what the bounds on X will be as we said
+
+ align:start position:0%
+what the bounds on X will be as we said
+ 
+
+ align:start position:0%
+what the bounds on X will be as we said
+X has to go the the left I mean you
+
+ align:start position:0%
+X has to go the the left I mean you
+ 
+
+ align:start position:0%
+X has to go the the left I mean you
+could let me sorry let me start over you
+
+ align:start position:0%
+could let me sorry let me start over you
+ 
+
+ align:start position:0%
+could let me sorry let me start over you
+could do any two consecutive
+
+ align:start position:0%
+could do any two consecutive
+ 
+
+ align:start position:0%
+could do any two consecutive
+intersection points you want right the
+
+ align:start position:0%
+intersection points you want right the
+ 
+
+ align:start position:0%
+intersection points you want right the
+area is the same in any case because of
+
+ align:start position:0%
+area is the same in any case because of
+ 
+
+ align:start position:0%
+area is the same in any case because of
+the symmetry of these two functions so
+
+ align:start position:0%
+the symmetry of these two functions so
+ 
+
+ align:start position:0%
+the symmetry of these two functions so
+okay but but the first two that are easy
+
+ align:start position:0%
+okay but but the first two that are easy
+ 
+
+ align:start position:0%
+okay but but the first two that are easy
+easiest for me to find are are this pi
+
+ align:start position:0%
+easiest for me to find are are this pi
+ 
+
+ align:start position:0%
+easiest for me to find are are this pi
+over4 and this 5 Pi over4 so I'm going
+
+ align:start position:0%
+over4 and this 5 Pi over4 so I'm going
+ 
+
+ align:start position:0%
+over4 and this 5 Pi over4 so I'm going
+to do those two if you wanted you could
+
+ align:start position:0%
+to do those two if you wanted you could
+ 
+
+ align:start position:0%
+to do those two if you wanted you could
+have done it with with you know a
+
+ align:start position:0%
+have done it with with you know a
+ 
+
+ align:start position:0%
+have done it with with you know a
+different pair of consecutive points um
+
+ align:start position:0%
+different pair of consecutive points um
+ 
+
+ align:start position:0%
+different pair of consecutive points um
+but once we've agreed that that sort of
+
+ align:start position:0%
+but once we've agreed that that sort of
+ 
+
+ align:start position:0%
+but once we've agreed that that sort of
+these first two are the ones I'm going
+
+ align:start position:0%
+these first two are the ones I'm going
+ 
+
+ align:start position:0%
+these first two are the ones I'm going
+to do okay then it's easy I know that
+
+ align:start position:0%
+to do okay then it's easy I know that
+ 
+
+ align:start position:0%
+to do okay then it's easy I know that
+they're pi over4 and 5 Pi over4 so
+
+ align:start position:0%
+they're pi over4 and 5 Pi over4 so
+ 
+
+ align:start position:0%
+they're pi over4 and 5 Pi over4 so
+that's the the interval over which I'm
+
+ align:start position:0%
+that's the the interval over which I'm
+ 
+
+ align:start position:0%
+that's the the interval over which I'm
+going to be integrating and then what I
+
+ align:start position:0%
+going to be integrating and then what I
+ 
+
+ align:start position:0%
+going to be integrating and then what I
+want to do is just view this region as
+
+ align:start position:0%
+want to do is just view this region as
+ 
+
+ align:start position:0%
+want to do is just view this region as
+cut into a lot of little rectangles and
+
+ align:start position:0%
+cut into a lot of little rectangles and
+ 
+
+ align:start position:0%
+cut into a lot of little rectangles and
+I want to integrate the the height the
+
+ align:start position:0%
+I want to integrate the the height the
+ 
+
+ align:start position:0%
+I want to integrate the the height the
+of that of those rectangles in order to
+
+ align:start position:0%
+of that of those rectangles in order to
+ 
+
+ align:start position:0%
+of that of those rectangles in order to
+get the area of the whole region um so
+
+ align:start position:0%
+get the area of the whole region um so
+ 
+
+ align:start position:0%
+get the area of the whole region um so
+in this case the upper curve is yal sinx
+
+ align:start position:0%
+in this case the upper curve is yal sinx
+ 
+
+ align:start position:0%
+in this case the upper curve is yal sinx
+and the lower curve is yal cosine of x
+
+ align:start position:0%
+and the lower curve is yal cosine of x
+ 
+
+ align:start position:0%
+and the lower curve is yal cosine of x
+so the height of a little you know if I
+
+ align:start position:0%
+so the height of a little you know if I
+ 
+
+ align:start position:0%
+so the height of a little you know if I
+draw in a little rectangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here the height of that rectangle is
+
+ align:start position:0%
+here the height of that rectangle is
+ 
+
+ align:start position:0%
+here the height of that rectangle is
+going to be sinx minus cosine X its
+
+ align:start position:0%
+going to be sinx minus cosine X its
+ 
+
+ align:start position:0%
+going to be sinx minus cosine X its
+width is DX and then I add them all up
+
+ align:start position:0%
+width is DX and then I add them all up
+ 
+
+ align:start position:0%
+width is DX and then I add them all up
+by integrating so the
+
+ align:start position:0%
+by integrating so the
+ 
+
+ align:start position:0%
+by integrating so the
+area is just the
+
+ align:start position:0%
+area is just the
+ 
+
+ align:start position:0%
+area is just the
+integral from pi over
+
+ align:start position:0%
+integral from pi over
+ 
+
+ align:start position:0%
+integral from pi over
+4 to 5 piun over4
+
+ align:start position:0%
+4 to 5 piun over4
+ 
+
+ align:start position:0%
+4 to 5 piun over4
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+sinx minus cosine X DX top minus bottom
+
+ align:start position:0%
+sinx minus cosine X DX top minus bottom
+ 
+
+ align:start position:0%
+sinx minus cosine X DX top minus bottom
+to get the height if you did it
+
+ align:start position:0%
+to get the height if you did it
+ 
+
+ align:start position:0%
+to get the height if you did it
+backwards if you wrote cosine minus s
+
+ align:start position:0%
+backwards if you wrote cosine minus s
+ 
+
+ align:start position:0%
+backwards if you wrote cosine minus s
+what you would get is exactly the
+
+ align:start position:0%
+what you would get is exactly the
+ 
+
+ align:start position:0%
+what you would get is exactly the
+negative of the area so it's all right
+
+ align:start position:0%
+negative of the area so it's all right
+ 
+
+ align:start position:0%
+negative of the area so it's all right
+from pi over 4 to 5 pi over 4 okay so
+
+ align:start position:0%
+from pi over 4 to 5 pi over 4 okay so
+ 
+
+ align:start position:0%
+from pi over 4 to 5 pi over 4 okay so
+now we just have to integrate this right
+
+ align:start position:0%
+now we just have to integrate this right
+ 
+
+ align:start position:0%
+now we just have to integrate this right
+so integral of sign the function whose
+
+ align:start position:0%
+so integral of sign the function whose
+ 
+
+ align:start position:0%
+so integral of sign the function whose
+derivative is s is
+
+ align:start position:0%
+derivative is s is
+ 
+
+ align:start position:0%
+derivative is s is
+minus cosine X and the function whose
+
+ align:start position:0%
+minus cosine X and the function whose
+ 
+
+ align:start position:0%
+minus cosine X and the function whose
+derivative is cosine is s so it's
+
+ align:start position:0%
+derivative is cosine is s so it's
+ 
+
+ align:start position:0%
+derivative is cosine is s so it's
+minus sin x
+
+ align:start position:0%
+minus sin x
+ 
+
+ align:start position:0%
+minus sin x
+between pi over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 5 pi over 4 and okay so so now we just
+
+ align:start position:0%
+4 5 pi over 4 and okay so so now we just
+ 
+
+ align:start position:0%
+4 5 pi over 4 and okay so so now we just
+have to plug in the values so this is
+
+ align:start position:0%
+have to plug in the values so this is
+ 
+
+ align:start position:0%
+have to plug in the values so this is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+cosine 5i
+
+ align:start position:0%
+cosine 5i
+ 
+
+ align:start position:0%
+cosine 5i
+4us s
+
+ align:start position:0%
+4us s
+ 
+
+ align:start position:0%
+4us s
+5 Pi
+
+ align:start position:0%
+5 Pi
+ 
+
+ align:start position:0%
+5 Pi
+4 minus
+
+ align:start position:0%
+4 minus
+ 
+
+ align:start position:0%
+4 minus
+minus cosine pi over
+
+ align:start position:0%
+minus cosine pi over
+ 
+
+ align:start position:0%
+minus cosine pi over
+4 minus
+
+ align:start position:0%
+4 minus
+ 
+
+ align:start position:0%
+4 minus
+s pi over 4 and I'm sure you can work
+
+ align:start position:0%
+s pi over 4 and I'm sure you can work
+ 
+
+ align:start position:0%
+s pi over 4 and I'm sure you can work
+out for yourself that this is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to two * the squ of two if I haven't
+
+ align:start position:0%
+to two * the squ of two if I haven't
+ 
+
+ align:start position:0%
+to two * the squ of two if I haven't
+botched anything
+
+ align:start position:0%
+botched anything
+ 
+
+ align:start position:0%
+botched anything
+terribly so I'll end there
\ No newline at end of file
diff --git a/9QwiP6glJfw.txt b/9QwiP6glJfw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..196a15f28f1720b97cd76c0773262d0f3ff85275
--- /dev/null
+++ b/9QwiP6glJfw.txt
@@ -0,0 +1,427 @@
+align:start position:0%
+ 
+okay this is where we were teaching the
+
+ align:start position:0%
+okay this is where we were teaching the
+ 
+
+ align:start position:0%
+okay this is where we were teaching the
+class this is the new ESG kitchen um
+
+ align:start position:0%
+class this is the new ESG kitchen um
+ 
+
+ align:start position:0%
+class this is the new ESG kitchen um
+well we don't use it only for this class
+
+ align:start position:0%
+well we don't use it only for this class
+ 
+
+ align:start position:0%
+well we don't use it only for this class
+it's a community uh kitchen so all the
+
+ align:start position:0%
+it's a community uh kitchen so all the
+ 
+
+ align:start position:0%
+it's a community uh kitchen so all the
+students in the community can use it and
+
+ align:start position:0%
+students in the community can use it and
+ 
+
+ align:start position:0%
+students in the community can use it and
+on Friday we have a community lunch uh
+
+ align:start position:0%
+on Friday we have a community lunch uh
+ 
+
+ align:start position:0%
+on Friday we have a community lunch uh
+so one or two students or uh staff
+
+ align:start position:0%
+so one or two students or uh staff
+ 
+
+ align:start position:0%
+so one or two students or uh staff
+members cook for uh everybody else and
+
+ align:start position:0%
+members cook for uh everybody else and
+ 
+
+ align:start position:0%
+members cook for uh everybody else and
+and this is where where we usually eat
+
+ align:start position:0%
+and this is where where we usually eat
+ 
+
+ align:start position:0%
+and this is where where we usually eat
+all together but for the speak Italian
+
+ align:start position:0%
+all together but for the speak Italian
+ 
+
+ align:start position:0%
+all together but for the speak Italian
+with your mouthful seminar we were using
+
+ align:start position:0%
+with your mouthful seminar we were using
+ 
+
+ align:start position:0%
+with your mouthful seminar we were using
+this board whenever we needed to discuss
+
+ align:start position:0%
+this board whenever we needed to discuss
+ 
+
+ align:start position:0%
+this board whenever we needed to discuss
+some grammar some vocabulary right now
+
+ align:start position:0%
+some grammar some vocabulary right now
+ 
+
+ align:start position:0%
+some grammar some vocabulary right now
+there is some Physics problem that's
+
+ align:start position:0%
+there is some Physics problem that's
+ 
+
+ align:start position:0%
+there is some Physics problem that's
+good because they're my
+
+ align:start position:0%
+good because they're my
+ 
+
+ align:start position:0%
+good because they're my
+students so I know that they have solved
+
+ align:start position:0%
+students so I know that they have solved
+ 
+
+ align:start position:0%
+students so I know that they have solved
+the problem set um and I also had a
+
+ align:start position:0%
+the problem set um and I also had a
+ 
+
+ align:start position:0%
+the problem set um and I also had a
+portable
+
+ align:start position:0%
+portable
+ 
+
+ align:start position:0%
+portable
+whiteboard in case um we needed to have
+
+ align:start position:0%
+whiteboard in case um we needed to have
+ 
+
+ align:start position:0%
+whiteboard in case um we needed to have
+uh to to visualize some of the uh
+
+ align:start position:0%
+uh to to visualize some of the uh
+ 
+
+ align:start position:0%
+uh to to visualize some of the uh
+grammar for example while we were
+
+ align:start position:0%
+grammar for example while we were
+ 
+
+ align:start position:0%
+grammar for example while we were
+cooking so this is the common Lounge um
+
+ align:start position:0%
+cooking so this is the common Lounge um
+ 
+
+ align:start position:0%
+cooking so this is the common Lounge um
+it's well right now there is nobody
+
+ align:start position:0%
+it's well right now there is nobody
+ 
+
+ align:start position:0%
+it's well right now there is nobody
+around because uh it's a holiday but uh
+
+ align:start position:0%
+around because uh it's a holiday but uh
+ 
+
+ align:start position:0%
+around because uh it's a holiday but uh
+usually there are students at every time
+
+ align:start position:0%
+usually there are students at every time
+ 
+
+ align:start position:0%
+usually there are students at every time
+of the day or night it's open
+
+ align:start position:0%
+of the day or night it's open
+ 
+
+ align:start position:0%
+of the day or night it's open
+24/7 and the students come here to work
+
+ align:start position:0%
+24/7 and the students come here to work
+ 
+
+ align:start position:0%
+24/7 and the students come here to work
+on problem sets together or just
+
+ align:start position:0%
+on problem sets together or just
+ 
+
+ align:start position:0%
+on problem sets together or just
+sometimes socialize we have a piano we
+
+ align:start position:0%
+sometimes socialize we have a piano we
+ 
+
+ align:start position:0%
+sometimes socialize we have a piano we
+might have somebody play playing the
+
+ align:start position:0%
+might have somebody play playing the
+ 
+
+ align:start position:0%
+might have somebody play playing the
+piano while the others are solving
+
+ align:start position:0%
+piano while the others are solving
+ 
+
+ align:start position:0%
+piano while the others are solving
+problems at the
+
+ align:start position:0%
+problems at the
+ 
+
+ align:start position:0%
+problems at the
+board and then we have our classrooms on
+
+ align:start position:0%
+board and then we have our classrooms on
+ 
+
+ align:start position:0%
+board and then we have our classrooms on
+both sides of the hallway I can show you
+
+ align:start position:0%
+both sides of the hallway I can show you
+ 
+
+ align:start position:0%
+both sides of the hallway I can show you
+yeah so this is the classroom where I
+
+ align:start position:0%
+yeah so this is the classroom where I
+ 
+
+ align:start position:0%
+yeah so this is the classroom where I
+usually teach physics and as you can see
+
+ align:start position:0%
+usually teach physics and as you can see
+ 
+
+ align:start position:0%
+usually teach physics and as you can see
+it's pretty small we have about um 10 12
+
+ align:start position:0%
+it's pretty small we have about um 10 12
+ 
+
+ align:start position:0%
+it's pretty small we have about um 10 12
+seats it's very different from um the
+
+ align:start position:0%
+seats it's very different from um the
+ 
+
+ align:start position:0%
+seats it's very different from um the
+classrooms in the regular curriculum
+
+ align:start position:0%
+classrooms in the regular curriculum
+ 
+
+ align:start position:0%
+classrooms in the regular curriculum
+where you might take physics but with
+
+ align:start position:0%
+where you might take physics but with
+ 
+
+ align:start position:0%
+where you might take physics but with
+another few hundred students um here
+
+ align:start position:0%
+another few hundred students um here
+ 
+
+ align:start position:0%
+another few hundred students um here
+everybody knows each other by name so
+
+ align:start position:0%
+everybody knows each other by name so
+ 
+
+ align:start position:0%
+everybody knows each other by name so
+they can really work together and um
+
+ align:start position:0%
+they can really work together and um
+ 
+
+ align:start position:0%
+they can really work together and um
+well I use the board so part of my
+
+ align:start position:0%
+well I use the board so part of my
+ 
+
+ align:start position:0%
+well I use the board so part of my
+classes are still lecture style but then
+
+ align:start position:0%
+classes are still lecture style but then
+ 
+
+ align:start position:0%
+classes are still lecture style but then
+we work in groups as you can see from
+
+ align:start position:0%
+we work in groups as you can see from
+ 
+
+ align:start position:0%
+we work in groups as you can see from
+the structure of the table we have
+
+ align:start position:0%
+the structure of the table we have
+ 
+
+ align:start position:0%
+the structure of the table we have
+chairs all around um so apart from the
+
+ align:start position:0%
+chairs all around um so apart from the
+ 
+
+ align:start position:0%
+chairs all around um so apart from the
+main board I also use portable
+
+ align:start position:0%
+main board I also use portable
+ 
+
+ align:start position:0%
+main board I also use portable
+whiteboards um and the idea is that
+
+ align:start position:0%
+whiteboards um and the idea is that
+ 
+
+ align:start position:0%
+whiteboards um and the idea is that
+during the class we can split and um
+
+ align:start position:0%
+during the class we can split and um
+ 
+
+ align:start position:0%
+during the class we can split and um
+solve problems in groups or of two or
+
+ align:start position:0%
+solve problems in groups or of two or
+ 
+
+ align:start position:0%
+solve problems in groups or of two or
+three people which makes it much more
+
+ align:start position:0%
+three people which makes it much more
+ 
+
+ align:start position:0%
+three people which makes it much more
+Interactive
\ No newline at end of file
diff --git a/9T9EMayW-GA.txt b/9T9EMayW-GA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0c956211033969b957a74ca8e4659f5f2c436b96
--- /dev/null
+++ b/9T9EMayW-GA.txt
@@ -0,0 +1,14952 @@
+align:start position:0%
+ 
+we have some administrative things today
+
+ align:start position:0%
+we have some administrative things today
+ 
+
+ align:start position:0%
+we have some administrative things today
+there are uh first of all there are two
+
+ align:start position:0%
+there are uh first of all there are two
+ 
+
+ align:start position:0%
+there are uh first of all there are two
+handouts 34 and 35 we've got the lecture
+
+ align:start position:0%
+handouts 34 and 35 we've got the lecture
+ 
+
+ align:start position:0%
+handouts 34 and 35 we've got the lecture
+notes and I'm handing out the solutions
+
+ align:start position:0%
+notes and I'm handing out the solutions
+ 
+
+ align:start position:0%
+notes and I'm handing out the solutions
+to homework number four and homework
+
+ align:start position:0%
+to homework number four and homework
+ 
+
+ align:start position:0%
+to homework number four and homework
+number four is going back so you can
+
+ align:start position:0%
+number four is going back so you can
+ 
+
+ align:start position:0%
+number four is going back so you can
+pick up homework number four it's in the
+
+ align:start position:0%
+pick up homework number four it's in the
+ 
+
+ align:start position:0%
+pick up homework number four it's in the
+orange folder in the back there and uh
+
+ align:start position:0%
+orange folder in the back there and uh
+ 
+
+ align:start position:0%
+orange folder in the back there and uh
+some reminders or announcements um these
+
+ align:start position:0%
+some reminders or announcements um these
+ 
+
+ align:start position:0%
+some reminders or announcements um these
+will appear on the website today so uh
+
+ align:start position:0%
+will appear on the website today so uh
+ 
+
+ align:start position:0%
+will appear on the website today so uh
+but just to remind you your uh written
+
+ align:start position:0%
+but just to remind you your uh written
+ 
+
+ align:start position:0%
+but just to remind you your uh written
+reports are are due here on uh Thursday
+
+ align:start position:0%
+reports are are due here on uh Thursday
+ 
+
+ align:start position:0%
+reports are are due here on uh Thursday
+December 9th in
+
+ align:start position:0%
+December 9th in
+ 
+
+ align:start position:0%
+December 9th in
+class um I have come up with a a
+
+ align:start position:0%
+class um I have come up with a a
+ 
+
+ align:start position:0%
+class um I have come up with a a
+schedule for the presenters for the
+
+ align:start position:0%
+schedule for the presenters for the
+ 
+
+ align:start position:0%
+schedule for the presenters for the
+people doing oral presentations that's
+
+ align:start position:0%
+people doing oral presentations that's
+ 
+
+ align:start position:0%
+people doing oral presentations that's
+shown here uh we have two uh lecture
+
+ align:start position:0%
+shown here uh we have two uh lecture
+ 
+
+ align:start position:0%
+shown here uh we have two uh lecture
+periods that we're dedicated to oral
+
+ align:start position:0%
+periods that we're dedicated to oral
+ 
+
+ align:start position:0%
+periods that we're dedicated to oral
+presentations the last two lectures of
+
+ align:start position:0%
+presentations the last two lectures of
+ 
+
+ align:start position:0%
+presentations the last two lectures of
+this term so on uh December 7th uh we
+
+ align:start position:0%
+this term so on uh December 7th uh we
+ 
+
+ align:start position:0%
+this term so on uh December 7th uh we
+have uh four speakers and these are the
+
+ align:start position:0%
+have uh four speakers and these are the
+ 
+
+ align:start position:0%
+have uh four speakers and these are the
+four speakers I have chosen for December
+
+ align:start position:0%
+four speakers I have chosen for December
+ 
+
+ align:start position:0%
+four speakers I have chosen for December
+7th um and your presentation time should
+
+ align:start position:0%
+7th um and your presentation time should
+ 
+
+ align:start position:0%
+7th um and your presentation time should
+be of your actual presentation should be
+
+ align:start position:0%
+be of your actual presentation should be
+ 
+
+ align:start position:0%
+be of your actual presentation should be
+about 16
+
+ align:start position:0%
+about 16
+ 
+
+ align:start position:0%
+about 16
+minutes and then beyond that we'll leave
+
+ align:start position:0%
+minutes and then beyond that we'll leave
+ 
+
+ align:start position:0%
+minutes and then beyond that we'll leave
+three minutes for questions and answers
+
+ align:start position:0%
+three minutes for questions and answers
+ 
+
+ align:start position:0%
+three minutes for questions and answers
+uh period so it's a short Q&A and that's
+
+ align:start position:0%
+uh period so it's a short Q&A and that's
+ 
+
+ align:start position:0%
+uh period so it's a short Q&A and that's
+for each talk so I'll make each talk
+
+ align:start position:0%
+for each talk so I'll make each talk
+ 
+
+ align:start position:0%
+for each talk so I'll make each talk
+about 20 minutes and we'll have four
+
+ align:start position:0%
+about 20 minutes and we'll have four
+ 
+
+ align:start position:0%
+about 20 minutes and we'll have four
+people in one period so that should work
+
+ align:start position:0%
+people in one period so that should work
+ 
+
+ align:start position:0%
+people in one period so that should work
+out fine uh and the same thing on
+
+ align:start position:0%
+out fine uh and the same thing on
+ 
+
+ align:start position:0%
+out fine uh and the same thing on
+December 9th these are the four speakers
+
+ align:start position:0%
+December 9th these are the four speakers
+ 
+
+ align:start position:0%
+December 9th these are the four speakers
+that I have chosen for December 9th um
+
+ align:start position:0%
+that I have chosen for December 9th um
+ 
+
+ align:start position:0%
+that I have chosen for December 9th um
+and uh uh pretty much approved all the
+
+ align:start position:0%
+and uh uh pretty much approved all the
+ 
+
+ align:start position:0%
+and uh uh pretty much approved all the
+the topics if you don't if you're not
+
+ align:start position:0%
+the topics if you don't if you're not
+ 
+
+ align:start position:0%
+the topics if you don't if you're not
+sure your topics are approved go on the
+
+ align:start position:0%
+sure your topics are approved go on the
+ 
+
+ align:start position:0%
+sure your topics are approved go on the
+website and I have an indication whether
+
+ align:start position:0%
+website and I have an indication whether
+ 
+
+ align:start position:0%
+website and I have an indication whether
+it's been approved or changed
+
+ align:start position:0%
+it's been approved or changed
+ 
+
+ align:start position:0%
+it's been approved or changed
+um if you need help you're going to be
+
+ align:start position:0%
+um if you need help you're going to be
+ 
+
+ align:start position:0%
+um if you need help you're going to be
+graded for those of you who are doing
+
+ align:start position:0%
+graded for those of you who are doing
+ 
+
+ align:start position:0%
+graded for those of you who are doing
+the oral presentations you're graded on
+
+ align:start position:0%
+the oral presentations you're graded on
+ 
+
+ align:start position:0%
+the oral presentations you're graded on
+two things um same as the written but a
+
+ align:start position:0%
+two things um same as the written but a
+ 
+
+ align:start position:0%
+two things um same as the written but a
+slightly different is you're graded on
+
+ align:start position:0%
+slightly different is you're graded on
+ 
+
+ align:start position:0%
+slightly different is you're graded on
+the presentation you know itself which
+
+ align:start position:0%
+the presentation you know itself which
+ 
+
+ align:start position:0%
+the presentation you know itself which
+includes your oral presentation as well
+
+ align:start position:0%
+includes your oral presentation as well
+ 
+
+ align:start position:0%
+includes your oral presentation as well
+as your slides so you need to provide
+
+ align:start position:0%
+as your slides so you need to provide
+ 
+
+ align:start position:0%
+as your slides so you need to provide
+handouts the same way that I I give out
+
+ align:start position:0%
+handouts the same way that I I give out
+ 
+
+ align:start position:0%
+handouts the same way that I I give out
+handouts to every lecture not as long
+
+ align:start position:0%
+handouts to every lecture not as long
+ 
+
+ align:start position:0%
+handouts to every lecture not as long
+because you're only speaking for 16
+
+ align:start position:0%
+because you're only speaking for 16
+ 
+
+ align:start position:0%
+because you're only speaking for 16
+minutes um but if you need any help
+
+ align:start position:0%
+minutes um but if you need any help
+ 
+
+ align:start position:0%
+minutes um but if you need any help
+making Xerox copies you don't have
+
+ align:start position:0%
+making Xerox copies you don't have
+ 
+
+ align:start position:0%
+making Xerox copies you don't have
+access to a copy or you don't need to
+
+ align:start position:0%
+access to a copy or you don't need to
+ 
+
+ align:start position:0%
+access to a copy or you don't need to
+pay to make those zerox copies my
+
+ align:start position:0%
+pay to make those zerox copies my
+ 
+
+ align:start position:0%
+pay to make those zerox copies my
+assistant if you uh send her the um PDF
+
+ align:start position:0%
+assistant if you uh send her the um PDF
+ 
+
+ align:start position:0%
+assistant if you uh send her the um PDF
+F or the U PowerPoint file preferably or
+
+ align:start position:0%
+F or the U PowerPoint file preferably or
+ 
+
+ align:start position:0%
+F or the U PowerPoint file preferably or
+if you can bring her a hard copy uh of
+
+ align:start position:0%
+if you can bring her a hard copy uh of
+ 
+
+ align:start position:0%
+if you can bring her a hard copy uh of
+your presentation um she'll make the uh
+
+ align:start position:0%
+your presentation um she'll make the uh
+ 
+
+ align:start position:0%
+your presentation um she'll make the uh
+make the enough ZX copies for the rest
+
+ align:start position:0%
+make the enough ZX copies for the rest
+ 
+
+ align:start position:0%
+make the enough ZX copies for the rest
+of the class you need to give her some
+
+ align:start position:0%
+of the class you need to give her some
+ 
+
+ align:start position:0%
+of the class you need to give her some
+time though to do that so do uh make
+
+ align:start position:0%
+time though to do that so do uh make
+ 
+
+ align:start position:0%
+time though to do that so do uh make
+sure you get her that the day before so
+
+ align:start position:0%
+sure you get her that the day before so
+ 
+
+ align:start position:0%
+sure you get her that the day before so
+she is so she has time and her hours are
+
+ align:start position:0%
+she is so she has time and her hours are
+ 
+
+ align:start position:0%
+she is so she has time and her hours are
+8:00 a.m. to 6:00 p.m. uh to uh 2: p.m.
+
+ align:start position:0%
+8:00 a.m. to 6:00 p.m. uh to uh 2: p.m.
+ 
+
+ align:start position:0%
+8:00 a.m. to 6:00 p.m. uh to uh 2: p.m.
+8 8 to 2 so um make sure you get her
+
+ align:start position:0%
+8 8 to 2 so um make sure you get her
+ 
+
+ align:start position:0%
+8 8 to 2 so um make sure you get her
+that the day before if you want help
+
+ align:start position:0%
+that the day before if you want help
+ 
+
+ align:start position:0%
+that the day before if you want help
+making Xerox
+
+ align:start position:0%
+making Xerox
+ 
+
+ align:start position:0%
+making Xerox
+copies and the second component of your
+
+ align:start position:0%
+copies and the second component of your
+ 
+
+ align:start position:0%
+copies and the second component of your
+grade of course is on the technical
+
+ align:start position:0%
+grade of course is on the technical
+ 
+
+ align:start position:0%
+grade of course is on the technical
+content um so one one part of your grade
+
+ align:start position:0%
+content um so one one part of your grade
+ 
+
+ align:start position:0%
+content um so one one part of your grade
+is on the presentation and that includes
+
+ align:start position:0%
+is on the presentation and that includes
+ 
+
+ align:start position:0%
+is on the presentation and that includes
+the quality of your graphics and the
+
+ align:start position:0%
+the quality of your graphics and the
+ 
+
+ align:start position:0%
+the quality of your graphics and the
+quality of your handouts and and the the
+
+ align:start position:0%
+quality of your handouts and and the the
+ 
+
+ align:start position:0%
+quality of your handouts and and the the
+second part is on the actual technical
+
+ align:start position:0%
+second part is on the actual technical
+ 
+
+ align:start position:0%
+second part is on the actual technical
+content the depth and to see that you
+
+ align:start position:0%
+content the depth and to see that you
+ 
+
+ align:start position:0%
+content the depth and to see that you
+read adequate number of references that
+
+ align:start position:0%
+read adequate number of references that
+ 
+
+ align:start position:0%
+read adequate number of references that
+you understand the material and that you
+
+ align:start position:0%
+you understand the material and that you
+ 
+
+ align:start position:0%
+you understand the material and that you
+can present it same thing for written
+
+ align:start position:0%
+can present it same thing for written
+ 
+
+ align:start position:0%
+can present it same thing for written
+reports the only difference is you won't
+
+ align:start position:0%
+reports the only difference is you won't
+ 
+
+ align:start position:0%
+reports the only difference is you won't
+be gred on your speaking because you
+
+ align:start position:0%
+be gred on your speaking because you
+ 
+
+ align:start position:0%
+be gred on your speaking because you
+won't be speaking but for the written
+
+ align:start position:0%
+won't be speaking but for the written
+ 
+
+ align:start position:0%
+won't be speaking but for the written
+report you'll be graded both on
+
+ align:start position:0%
+report you'll be graded both on
+ 
+
+ align:start position:0%
+report you'll be graded both on
+technical content as well as on the
+
+ align:start position:0%
+technical content as well as on the
+ 
+
+ align:start position:0%
+technical content as well as on the
+presentation how how nicely did you lay
+
+ align:start position:0%
+presentation how how nicely did you lay
+ 
+
+ align:start position:0%
+presentation how how nicely did you lay
+out the report how well is it sectioned
+
+ align:start position:0%
+out the report how well is it sectioned
+ 
+
+ align:start position:0%
+out the report how well is it sectioned
+um are the references clear and easy to
+
+ align:start position:0%
+um are the references clear and easy to
+ 
+
+ align:start position:0%
+um are the references clear and easy to
+read do you have good good graphs or are
+
+ align:start position:0%
+read do you have good good graphs or are
+ 
+
+ align:start position:0%
+read do you have good good graphs or are
+the graphs impossible to read things
+
+ align:start position:0%
+the graphs impossible to read things
+ 
+
+ align:start position:0%
+the graphs impossible to read things
+like that so both aspects uh will be
+
+ align:start position:0%
+like that so both aspects uh will be
+ 
+
+ align:start position:0%
+like that so both aspects uh will be
+part of it and all this this information
+
+ align:start position:0%
+part of it and all this this information
+ 
+
+ align:start position:0%
+part of it and all this this information
+will be posted on the web but this gives
+
+ align:start position:0%
+will be posted on the web but this gives
+ 
+
+ align:start position:0%
+will be posted on the web but this gives
+you an idea of when you need to prepare
+
+ align:start position:0%
+you an idea of when you need to prepare
+ 
+
+ align:start position:0%
+you an idea of when you need to prepare
+yourself um so here this is where we are
+
+ align:start position:0%
+yourself um so here this is where we are
+ 
+
+ align:start position:0%
+yourself um so here this is where we are
+right now um on November 23rd this is
+
+ align:start position:0%
+right now um on November 23rd this is
+ 
+
+ align:start position:0%
+right now um on November 23rd this is
+the the Thanksgiving holidays coming up
+
+ align:start position:0%
+the the Thanksgiving holidays coming up
+ 
+
+ align:start position:0%
+the the Thanksgiving holidays coming up
+on Thursday won't have a class Thursday
+
+ align:start position:0%
+on Thursday won't have a class Thursday
+ 
+
+ align:start position:0%
+on Thursday won't have a class Thursday
+today we're finishing up chapter 10 on
+
+ align:start position:0%
+today we're finishing up chapter 10 on
+ 
+
+ align:start position:0%
+today we're finishing up chapter 10 on
+etching um and then we'll move on we
+
+ align:start position:0%
+etching um and then we'll move on we
+ 
+
+ align:start position:0%
+etching um and then we'll move on we
+have two more formal lectures that I'll
+
+ align:start position:0%
+have two more formal lectures that I'll
+ 
+
+ align:start position:0%
+have two more formal lectures that I'll
+be giving uh there'll be one on suicides
+
+ align:start position:0%
+be giving uh there'll be one on suicides
+ 
+
+ align:start position:0%
+be giving uh there'll be one on suicides
+and contacts and novel gate materials
+
+ align:start position:0%
+and contacts and novel gate materials
+ 
+
+ align:start position:0%
+and contacts and novel gate materials
+and then they'll uh on growth and
+
+ align:start position:0%
+and then they'll uh on growth and
+ 
+
+ align:start position:0%
+and then they'll uh on growth and
+processing of strain silicon and silicon
+
+ align:start position:0%
+processing of strain silicon and silicon
+ 
+
+ align:start position:0%
+processing of strain silicon and silicon
+geranium on December 2nd and then you
+
+ align:start position:0%
+geranium on December 2nd and then you
+ 
+
+ align:start position:0%
+geranium on December 2nd and then you
+you folks will start speaking on the 7th
+
+ align:start position:0%
+you folks will start speaking on the 7th
+ 
+
+ align:start position:0%
+you folks will start speaking on the 7th
+uh and and finish up on the 9th and your
+
+ align:start position:0%
+uh and and finish up on the 9th and your
+ 
+
+ align:start position:0%
+uh and and finish up on the 9th and your
+written reports again are due in class
+
+ align:start position:0%
+written reports again are due in class
+ 
+
+ align:start position:0%
+written reports again are due in class
+on that final Thursday December
+
+ align:start position:0%
+on that final Thursday December
+ 
+
+ align:start position:0%
+on that final Thursday December
+9th anybody have any questions or
+
+ align:start position:0%
+9th anybody have any questions or
+ 
+
+ align:start position:0%
+9th anybody have any questions or
+anything about the uh the final report
+
+ align:start position:0%
+anything about the uh the final report
+ 
+
+ align:start position:0%
+anything about the uh the final report
+or the
+
+ align:start position:0%
+or the
+ 
+
+ align:start position:0%
+or the
+schedule send me an email if you have
+
+ align:start position:0%
+schedule send me an email if you have
+ 
+
+ align:start position:0%
+schedule send me an email if you have
+any any questions about
+
+ align:start position:0%
+any any questions about
+ 
+
+ align:start position:0%
+any any questions about
+it okay so let's go on to today's uh
+
+ align:start position:0%
+it okay so let's go on to today's uh
+ 
+
+ align:start position:0%
+it okay so let's go on to today's uh
+today's
+
+ align:start position:0%
+today's
+ 
+
+ align:start position:0%
+today's
+notes and uh we're um each time each
+
+ align:start position:0%
+notes and uh we're um each time each
+ 
+
+ align:start position:0%
+notes and uh we're um each time each
+chapter now you notice we're going
+
+ align:start position:0%
+chapter now you notice we're going
+ 
+
+ align:start position:0%
+chapter now you notice we're going
+through a little more rapidly as we
+
+ align:start position:0%
+through a little more rapidly as we
+ 
+
+ align:start position:0%
+through a little more rapidly as we
+finish up this will uh be the last
+
+ align:start position:0%
+finish up this will uh be the last
+ 
+
+ align:start position:0%
+finish up this will uh be the last
+formal chapter of reading that you'll
+
+ align:start position:0%
+formal chapter of reading that you'll
+ 
+
+ align:start position:0%
+formal chapter of reading that you'll
+have in this class there'll be a little
+
+ align:start position:0%
+have in this class there'll be a little
+ 
+
+ align:start position:0%
+have in this class there'll be a little
+bit U on pilicides you'll have to read
+
+ align:start position:0%
+bit U on pilicides you'll have to read
+ 
+
+ align:start position:0%
+bit U on pilicides you'll have to read
+and then the last uh lecture I uh
+
+ align:start position:0%
+and then the last uh lecture I uh
+ 
+
+ align:start position:0%
+and then the last uh lecture I uh
+there's nothing written up on it so you
+
+ align:start position:0%
+there's nothing written up on it so you
+ 
+
+ align:start position:0%
+there's nothing written up on it so you
+just come to lecture so hopefully you're
+
+ align:start position:0%
+just come to lecture so hopefully you're
+ 
+
+ align:start position:0%
+just come to lecture so hopefully you're
+finishing up reading chapter uh 10 on on
+
+ align:start position:0%
+finishing up reading chapter uh 10 on on
+ 
+
+ align:start position:0%
+finishing up reading chapter uh 10 on on
+etching um what I'm showing here on the
+
+ align:start position:0%
+etching um what I'm showing here on the
+ 
+
+ align:start position:0%
+etching um what I'm showing here on the
+first slide of handout number 34 is kind
+
+ align:start position:0%
+first slide of handout number 34 is kind
+ 
+
+ align:start position:0%
+first slide of handout number 34 is kind
+of a summary of what we talked about
+
+ align:start position:0%
+of a summary of what we talked about
+ 
+
+ align:start position:0%
+of a summary of what we talked about
+last time as far as plasma etching and
+
+ align:start position:0%
+last time as far as plasma etching and
+ 
+
+ align:start position:0%
+last time as far as plasma etching and
+the various mechanisms
+
+ align:start position:0%
+the various mechanisms
+ 
+
+ align:start position:0%
+the various mechanisms
+um there are certain characteristics
+
+ align:start position:0%
+um there are certain characteristics
+ 
+
+ align:start position:0%
+um there are certain characteristics
+which we said were important uh for
+
+ align:start position:0%
+which we said were important uh for
+ 
+
+ align:start position:0%
+which we said were important uh for
+example uh the pressure of the chamber
+
+ align:start position:0%
+example uh the pressure of the chamber
+ 
+
+ align:start position:0%
+example uh the pressure of the chamber
+in which you're etching uh the energy of
+
+ align:start position:0%
+in which you're etching uh the energy of
+ 
+
+ align:start position:0%
+in which you're etching uh the energy of
+the species um and these end up
+
+ align:start position:0%
+the species um and these end up
+ 
+
+ align:start position:0%
+the species um and these end up
+affecting things like selectivity and
+
+ align:start position:0%
+affecting things like selectivity and
+ 
+
+ align:start position:0%
+affecting things like selectivity and
+isotropy uh at the top of the list of
+
+ align:start position:0%
+isotropy uh at the top of the list of
+ 
+
+ align:start position:0%
+isotropy uh at the top of the list of
+the type of etching are the most
+
+ align:start position:0%
+the type of etching are the most
+ 
+
+ align:start position:0%
+the type of etching are the most
+physical etching processes here like
+
+ align:start position:0%
+physical etching processes here like
+ 
+
+ align:start position:0%
+physical etching processes here like
+sputter etching or ion beam Milling it's
+
+ align:start position:0%
+sputter etching or ion beam Milling it's
+ 
+
+ align:start position:0%
+sputter etching or ion beam Milling it's
+pretty much purely physical there's not
+
+ align:start position:0%
+pretty much purely physical there's not
+ 
+
+ align:start position:0%
+pretty much purely physical there's not
+a lot of chemical reactions going on if
+
+ align:start position:0%
+a lot of chemical reactions going on if
+ 
+
+ align:start position:0%
+a lot of chemical reactions going on if
+you go to the very bottom type of
+
+ align:start position:0%
+you go to the very bottom type of
+ 
+
+ align:start position:0%
+you go to the very bottom type of
+etching which is wet chemical etching is
+
+ align:start position:0%
+etching which is wet chemical etching is
+ 
+
+ align:start position:0%
+etching which is wet chemical etching is
+entirely wet there is no physical
+
+ align:start position:0%
+entirely wet there is no physical
+ 
+
+ align:start position:0%
+entirely wet there is no physical
+bombardment and everything in between
+
+ align:start position:0%
+bombardment and everything in between
+ 
+
+ align:start position:0%
+bombardment and everything in between
+has a has a certain component of both
+
+ align:start position:0%
+has a has a certain component of both
+ 
+
+ align:start position:0%
+has a has a certain component of both
+chemical processes and physical uh
+
+ align:start position:0%
+chemical processes and physical uh
+ 
+
+ align:start position:0%
+chemical processes and physical uh
+processes going
+
+ align:start position:0%
+processes going
+ 
+
+ align:start position:0%
+processes going
+on and these arrows point to the
+
+ align:start position:0%
+on and these arrows point to the
+ 
+
+ align:start position:0%
+on and these arrows point to the
+direction in which the uh the quantity
+
+ align:start position:0%
+direction in which the uh the quantity
+ 
+
+ align:start position:0%
+direction in which the uh the quantity
+increases so anisotropy which is so if
+
+ align:start position:0%
+increases so anisotropy which is so if
+ 
+
+ align:start position:0%
+increases so anisotropy which is so if
+the edge to be more vertical than it is
+
+ align:start position:0%
+the edge to be more vertical than it is
+ 
+
+ align:start position:0%
+the edge to be more vertical than it is
+horizontal increases as you go from wet
+
+ align:start position:0%
+horizontal increases as you go from wet
+ 
+
+ align:start position:0%
+horizontal increases as you go from wet
+chemical which is very isotropic all if
+
+ align:start position:0%
+chemical which is very isotropic all if
+ 
+
+ align:start position:0%
+chemical which is very isotropic all if
+you go to splutter etching it's very
+
+ align:start position:0%
+you go to splutter etching it's very
+ 
+
+ align:start position:0%
+you go to splutter etching it's very
+anisotropic so anisotropy increases in
+
+ align:start position:0%
+anisotropic so anisotropy increases in
+ 
+
+ align:start position:0%
+anisotropic so anisotropy increases in
+this Direction selectivity is very poor
+
+ align:start position:0%
+this Direction selectivity is very poor
+ 
+
+ align:start position:0%
+this Direction selectivity is very poor
+or very low for sputter etching you can
+
+ align:start position:0%
+or very low for sputter etching you can
+ 
+
+ align:start position:0%
+or very low for sputter etching you can
+you can sputter everything anything and
+
+ align:start position:0%
+you can sputter everything anything and
+ 
+
+ align:start position:0%
+you can sputter everything anything and
+The Sputter rates are are not very
+
+ align:start position:0%
+The Sputter rates are are not very
+ 
+
+ align:start position:0%
+The Sputter rates are are not very
+different among the elements selectivity
+
+ align:start position:0%
+different among the elements selectivity
+ 
+
+ align:start position:0%
+different among the elements selectivity
+increas is going down so reactive ion
+
+ align:start position:0%
+increas is going down so reactive ion
+ 
+
+ align:start position:0%
+increas is going down so reactive ion
+etching is less selective plasma etching
+
+ align:start position:0%
+etching is less selective plasma etching
+ 
+
+ align:start position:0%
+etching is less selective plasma etching
+is more selective and what chemical
+
+ align:start position:0%
+is more selective and what chemical
+ 
+
+ align:start position:0%
+is more selective and what chemical
+etching tends to be the most selective
+
+ align:start position:0%
+etching tends to be the most selective
+ 
+
+ align:start position:0%
+etching tends to be the most selective
+selectivity increase in this direction
+
+ align:start position:0%
+selectivity increase in this direction
+ 
+
+ align:start position:0%
+selectivity increase in this direction
+in general the energy of the process
+
+ align:start position:0%
+in general the energy of the process
+ 
+
+ align:start position:0%
+in general the energy of the process
+increases going from the bottom to the
+
+ align:start position:0%
+increases going from the bottom to the
+ 
+
+ align:start position:0%
+increases going from the bottom to the
+top so there's more energetics involved
+
+ align:start position:0%
+top so there's more energetics involved
+ 
+
+ align:start position:0%
+top so there's more energetics involved
+in sputter etching uh the particles can
+
+ align:start position:0%
+in sputter etching uh the particles can
+ 
+
+ align:start position:0%
+in sputter etching uh the particles can
+come down with hundreds of electron
+
+ align:start position:0%
+come down with hundreds of electron
+ 
+
+ align:start position:0%
+come down with hundreds of electron
+volts and knock off um knockoff atoms on
+
+ align:start position:0%
+volts and knock off um knockoff atoms on
+ 
+
+ align:start position:0%
+volts and knock off um knockoff atoms on
+the surface so these these processes
+
+ align:start position:0%
+the surface so these these processes
+ 
+
+ align:start position:0%
+the surface so these these processes
+tend to be more
+
+ align:start position:0%
+tend to be more
+ 
+
+ align:start position:0%
+tend to be more
+energetic and the pressure of the system
+
+ align:start position:0%
+energetic and the pressure of the system
+ 
+
+ align:start position:0%
+energetic and the pressure of the system
+um here uh is is tends to be uh lowest
+
+ align:start position:0%
+um here uh is is tends to be uh lowest
+ 
+
+ align:start position:0%
+um here uh is is tends to be uh lowest
+here and then sort of increasing as you
+
+ align:start position:0%
+here and then sort of increasing as you
+ 
+
+ align:start position:0%
+here and then sort of increasing as you
+go uh from here this type of sputter
+
+ align:start position:0%
+go uh from here this type of sputter
+ 
+
+ align:start position:0%
+go uh from here this type of sputter
+etching to pla to uh say plasma
+
+ align:start position:0%
+etching to pla to uh say plasma
+ 
+
+ align:start position:0%
+etching to pla to uh say plasma
+etching so that's just what we talked
+
+ align:start position:0%
+etching so that's just what we talked
+ 
+
+ align:start position:0%
+etching so that's just what we talked
+about last time by way of mechanisms
+
+ align:start position:0%
+about last time by way of mechanisms
+ 
+
+ align:start position:0%
+about last time by way of mechanisms
+today I wanted to give some specific
+
+ align:start position:0%
+today I wanted to give some specific
+ 
+
+ align:start position:0%
+today I wanted to give some specific
+examples and I want to emphasize gate
+
+ align:start position:0%
+examples and I want to emphasize gate
+ 
+
+ align:start position:0%
+examples and I want to emphasize gate
+etching issues and I'll talk a little
+
+ align:start position:0%
+etching issues and I'll talk a little
+ 
+
+ align:start position:0%
+etching issues and I'll talk a little
+bit about uh modeling the the uh
+
+ align:start position:0%
+bit about uh modeling the the uh
+ 
+
+ align:start position:0%
+bit about uh modeling the the uh
+mechanics of how people model etge
+
+ align:start position:0%
+mechanics of how people model etge
+ 
+
+ align:start position:0%
+mechanics of how people model etge
+processes the uh on slide two this is is
+
+ align:start position:0%
+processes the uh on slide two this is is
+ 
+
+ align:start position:0%
+processes the uh on slide two this is is
+a chart or it's half of the chart that I
+
+ align:start position:0%
+a chart or it's half of the chart that I
+ 
+
+ align:start position:0%
+a chart or it's half of the chart that I
+took directly from chapter 10 in your
+
+ align:start position:0%
+took directly from chapter 10 in your
+ 
+
+ align:start position:0%
+took directly from chapter 10 in your
+text and what it shows is um a series of
+
+ align:start position:0%
+text and what it shows is um a series of
+ 
+
+ align:start position:0%
+text and what it shows is um a series of
+common materials and some typical
+
+ align:start position:0%
+common materials and some typical
+ 
+
+ align:start position:0%
+common materials and some typical
+etchants um that are used and then some
+
+ align:start position:0%
+etchants um that are used and then some
+ 
+
+ align:start position:0%
+etchants um that are used and then some
+comments about each of these um etchants
+
+ align:start position:0%
+comments about each of these um etchants
+ 
+
+ align:start position:0%
+comments about each of these um etchants
+for example uh a very common way of
+
+ align:start position:0%
+for example uh a very common way of
+ 
+
+ align:start position:0%
+for example uh a very common way of
+etching polyic
+
+ align:start position:0%
+etching polyic
+ 
+
+ align:start position:0%
+etching polyic
+uh in a generic way is to use sf6 or
+
+ align:start position:0%
+uh in a generic way is to use sf6 or
+ 
+
+ align:start position:0%
+uh in a generic way is to use sf6 or
+cf4 uh what are the characteristics of
+
+ align:start position:0%
+cf4 uh what are the characteristics of
+ 
+
+ align:start position:0%
+cf4 uh what are the characteristics of
+that type of edch well it tends to be
+
+ align:start position:0%
+that type of edch well it tends to be
+ 
+
+ align:start position:0%
+that type of edch well it tends to be
+isotropic or near
+
+ align:start position:0%
+isotropic or near
+ 
+
+ align:start position:0%
+isotropic or near
+isotropic um and not very good uh
+
+ align:start position:0%
+isotropic um and not very good uh
+ 
+
+ align:start position:0%
+isotropic um and not very good uh
+selectivity over si2 so if you hit the
+
+ align:start position:0%
+selectivity over si2 so if you hit the
+ 
+
+ align:start position:0%
+selectivity over si2 so if you hit the
+once you hit the S2 you continue etching
+
+ align:start position:0%
+once you hit the S2 you continue etching
+ 
+
+ align:start position:0%
+once you hit the S2 you continue etching
+so this is a general purpose etch you
+
+ align:start position:0%
+so this is a general purpose etch you
+ 
+
+ align:start position:0%
+so this is a general purpose etch you
+might use if you're trying to strip off
+
+ align:start position:0%
+might use if you're trying to strip off
+ 
+
+ align:start position:0%
+might use if you're trying to strip off
+some poly off the back of the wafer or
+
+ align:start position:0%
+some poly off the back of the wafer or
+ 
+
+ align:start position:0%
+some poly off the back of the wafer or
+something probably not something you
+
+ align:start position:0%
+something probably not something you
+ 
+
+ align:start position:0%
+something probably not something you
+might use if you need uh anot an
+
+ align:start position:0%
+might use if you need uh anot an
+ 
+
+ align:start position:0%
+might use if you need uh anot an
+isotropy or something like that
+
+ align:start position:0%
+isotropy or something like that
+ 
+
+ align:start position:0%
+isotropy or something like that
+um the uh a more anisotropic edch but
+
+ align:start position:0%
+um the uh a more anisotropic edch but
+ 
+
+ align:start position:0%
+um the uh a more anisotropic edch but
+also very not not very selective to sio2
+
+ align:start position:0%
+also very not not very selective to sio2
+ 
+
+ align:start position:0%
+also very not not very selective to sio2
+would be a mixture of cf4 and hydrogen
+
+ align:start position:0%
+would be a mixture of cf4 and hydrogen
+ 
+
+ align:start position:0%
+would be a mixture of cf4 and hydrogen
+or or chf3 some of these fron
+
+ align:start position:0%
+or or chf3 some of these fron
+ 
+
+ align:start position:0%
+or or chf3 some of these fron
+types um you can mix cf4 with oxygen I
+
+ align:start position:0%
+types um you can mix cf4 with oxygen I
+ 
+
+ align:start position:0%
+types um you can mix cf4 with oxygen I
+think we showed last time an example of
+
+ align:start position:0%
+think we showed last time an example of
+ 
+
+ align:start position:0%
+think we showed last time an example of
+the chemistry of this it's uh isotropic
+
+ align:start position:0%
+the chemistry of this it's uh isotropic
+ 
+
+ align:start position:0%
+the chemistry of this it's uh isotropic
+generally reasonably isotropic but is
+
+ align:start position:0%
+generally reasonably isotropic but is
+ 
+
+ align:start position:0%
+generally reasonably isotropic but is
+more selective to
+
+ align:start position:0%
+more selective to
+ 
+
+ align:start position:0%
+more selective to
+sio2 again A lot of times you're etching
+
+ align:start position:0%
+sio2 again A lot of times you're etching
+ 
+
+ align:start position:0%
+sio2 again A lot of times you're etching
+Poly on top of oxide some dialectric and
+
+ align:start position:0%
+Poly on top of oxide some dialectric and
+ 
+
+ align:start position:0%
+Poly on top of oxide some dialectric and
+so you the selectivity of the edge of
+
+ align:start position:0%
+so you the selectivity of the edge of
+ 
+
+ align:start position:0%
+so you the selectivity of the edge of
+the polysilicon edge to the S2 is very
+
+ align:start position:0%
+the polysilicon edge to the S2 is very
+ 
+
+ align:start position:0%
+the polysilicon edge to the S2 is very
+important the most uh the most commonly
+
+ align:start position:0%
+important the most uh the most commonly
+ 
+
+ align:start position:0%
+important the most uh the most commonly
+used etchant gases today for poly
+
+ align:start position:0%
+used etchant gases today for poly
+ 
+
+ align:start position:0%
+used etchant gases today for poly
+silicon and we'll talk about this when
+
+ align:start position:0%
+silicon and we'll talk about this when
+ 
+
+ align:start position:0%
+silicon and we'll talk about this when
+we talk about gate etching are hbr and
+
+ align:start position:0%
+we talk about gate etching are hbr and
+ 
+
+ align:start position:0%
+we talk about gate etching are hbr and
+chlorine or some combination of hbr
+
+ align:start position:0%
+chlorine or some combination of hbr
+ 
+
+ align:start position:0%
+chlorine or some combination of hbr
+chlorine and oxygen these tend to be
+
+ align:start position:0%
+chlorine and oxygen these tend to be
+ 
+
+ align:start position:0%
+chlorine and oxygen these tend to be
+very anisotropic so you can get very
+
+ align:start position:0%
+very anisotropic so you can get very
+ 
+
+ align:start position:0%
+very anisotropic so you can get very
+well-defined sidewalls and most of them
+
+ align:start position:0%
+well-defined sidewalls and most of them
+ 
+
+ align:start position:0%
+well-defined sidewalls and most of them
+are reasonably selective compared to si2
+
+ align:start position:0%
+are reasonably selective compared to si2
+ 
+
+ align:start position:0%
+are reasonably selective compared to si2
+you can get with hbr and O2 combinations
+
+ align:start position:0%
+you can get with hbr and O2 combinations
+ 
+
+ align:start position:0%
+you can get with hbr and O2 combinations
+you can get up to 100 to one selectivity
+
+ align:start position:0%
+you can get up to 100 to one selectivity
+ 
+
+ align:start position:0%
+you can get up to 100 to one selectivity
+uh depending on the the
+
+ align:start position:0%
+uh depending on the the
+ 
+
+ align:start position:0%
+uh depending on the the
+etcher um if you're using if you want ET
+
+ align:start position:0%
+etcher um if you're using if you want ET
+ 
+
+ align:start position:0%
+etcher um if you're using if you want ET
+single Crystal silicon use exactly the
+
+ align:start position:0%
+single Crystal silicon use exactly the
+ 
+
+ align:start position:0%
+single Crystal silicon use exactly the
+same etch and to use for um poly Crystal
+
+ align:start position:0%
+same etch and to use for um poly Crystal
+ 
+
+ align:start position:0%
+same etch and to use for um poly Crystal
+and silicon in general there's not a big
+
+ align:start position:0%
+and silicon in general there's not a big
+ 
+
+ align:start position:0%
+and silicon in general there's not a big
+difference between the
+
+ align:start position:0%
+difference between the
+ 
+
+ align:start position:0%
+difference between the
+two si uh if you need to chch oxide here
+
+ align:start position:0%
+two si uh if you need to chch oxide here
+ 
+
+ align:start position:0%
+two si uh if you need to chch oxide here
+you can um ET sf6 interesting any of the
+
+ align:start position:0%
+you can um ET sf6 interesting any of the
+ 
+
+ align:start position:0%
+you can um ET sf6 interesting any of the
+fluorinated species will will help you
+
+ align:start position:0%
+fluorinated species will will help you
+ 
+
+ align:start position:0%
+fluorinated species will will help you
+with etching oxide notice sf6 was also
+
+ align:start position:0%
+with etching oxide notice sf6 was also
+ 
+
+ align:start position:0%
+with etching oxide notice sf6 was also
+listed as etching poly so that means
+
+ align:start position:0%
+listed as etching poly so that means
+ 
+
+ align:start position:0%
+listed as etching poly so that means
+it's not a very not a very itive
+
+ align:start position:0%
+it's not a very not a very itive
+ 
+
+ align:start position:0%
+it's not a very not a very itive
+Edge um and isotropic etches include a
+
+ align:start position:0%
+Edge um and isotropic etches include a
+ 
+
+ align:start position:0%
+Edge um and isotropic etches include a
+variety of the frons like C2 F6 and C3
+
+ align:start position:0%
+variety of the frons like C2 F6 and C3
+ 
+
+ align:start position:0%
+variety of the frons like C2 F6 and C3
+f8 um they are somewhat selective over
+
+ align:start position:0%
+f8 um they are somewhat selective over
+ 
+
+ align:start position:0%
+f8 um they are somewhat selective over
+silicon when do we etch oxide in in a
+
+ align:start position:0%
+silicon when do we etch oxide in in a
+ 
+
+ align:start position:0%
+silicon when do we etch oxide in in a
+moss process for example we're often
+
+ align:start position:0%
+moss process for example we're often
+ 
+
+ align:start position:0%
+moss process for example we're often
+etching oxide when we're opening up
+
+ align:start position:0%
+etching oxide when we're opening up
+ 
+
+ align:start position:0%
+etching oxide when we're opening up
+contact holes so we have an you know we
+
+ align:start position:0%
+contact holes so we have an you know we
+ 
+
+ align:start position:0%
+contact holes so we have an you know we
+have an interlayer dialectric of some
+
+ align:start position:0%
+have an interlayer dialectric of some
+ 
+
+ align:start position:0%
+have an interlayer dialectric of some
+sort maybe one or 2,000 anes we need to
+
+ align:start position:0%
+sort maybe one or 2,000 anes we need to
+ 
+
+ align:start position:0%
+sort maybe one or 2,000 anes we need to
+get through it uh and with reasonably
+
+ align:start position:0%
+get through it uh and with reasonably
+ 
+
+ align:start position:0%
+get through it uh and with reasonably
+good control of the sidewalls we also
+
+ align:start position:0%
+good control of the sidewalls we also
+ 
+
+ align:start position:0%
+good control of the sidewalls we also
+need to stop on the Silicon you don't
+
+ align:start position:0%
+need to stop on the Silicon you don't
+ 
+
+ align:start position:0%
+need to stop on the Silicon you don't
+want to etch away your Source drains so
+
+ align:start position:0%
+want to etch away your Source drains so
+ 
+
+ align:start position:0%
+want to etch away your Source drains so
+and isotropy and selectivity are also
+
+ align:start position:0%
+and isotropy and selectivity are also
+ 
+
+ align:start position:0%
+and isotropy and selectivity are also
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+important silicon
+
+ align:start position:0%
+important silicon
+ 
+
+ align:start position:0%
+important silicon
+nitride um there are some isotropic
+
+ align:start position:0%
+nitride um there are some isotropic
+ 
+
+ align:start position:0%
+nitride um there are some isotropic
+etches like cf4 and O2 um an anisotropic
+
+ align:start position:0%
+etches like cf4 and O2 um an anisotropic
+ 
+
+ align:start position:0%
+etches like cf4 and O2 um an anisotropic
+etch cf4 and H2 it's this one is
+
+ align:start position:0%
+etch cf4 and H2 it's this one is
+ 
+
+ align:start position:0%
+etch cf4 and H2 it's this one is
+selective over silicon so it'll stop on
+
+ align:start position:0%
+selective over silicon so it'll stop on
+ 
+
+ align:start position:0%
+selective over silicon so it'll stop on
+Silicon but not over si2 uh and
+
+ align:start position:0%
+Silicon but not over si2 uh and
+ 
+
+ align:start position:0%
+Silicon but not over si2 uh and
+sometimes you have stacks consisting of
+
+ align:start position:0%
+sometimes you have stacks consisting of
+ 
+
+ align:start position:0%
+sometimes you have stacks consisting of
+oxide and nitride and you need to Edge
+
+ align:start position:0%
+oxide and nitride and you need to Edge
+ 
+
+ align:start position:0%
+oxide and nitride and you need to Edge
+one of the two um selectivity
+
+ align:start position:0%
+one of the two um selectivity
+ 
+
+ align:start position:0%
+one of the two um selectivity
+selectively so it gets a little tricky
+
+ align:start position:0%
+selectively so it gets a little tricky
+ 
+
+ align:start position:0%
+selectively so it gets a little tricky
+uh you need to pick the etchant and the
+
+ align:start position:0%
+uh you need to pick the etchant and the
+ 
+
+ align:start position:0%
+uh you need to pick the etchant and the
+reactor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carefully what are some other materials
+
+ align:start position:0%
+carefully what are some other materials
+ 
+
+ align:start position:0%
+carefully what are some other materials
+so those are the more common ones maybe
+
+ align:start position:0%
+so those are the more common ones maybe
+ 
+
+ align:start position:0%
+so those are the more common ones maybe
+a little less common but things that you
+
+ align:start position:0%
+a little less common but things that you
+ 
+
+ align:start position:0%
+a little less common but things that you
+do have to etch often uh in plasmas are
+
+ align:start position:0%
+do have to etch often uh in plasmas are
+ 
+
+ align:start position:0%
+do have to etch often uh in plasmas are
+for example aluminum wiring or aluminum
+
+ align:start position:0%
+for example aluminum wiring or aluminum
+ 
+
+ align:start position:0%
+for example aluminum wiring or aluminum
+contacts need to be etched it's very uh
+
+ align:start position:0%
+contacts need to be etched it's very uh
+ 
+
+ align:start position:0%
+contacts need to be etched it's very uh
+common to use chlorinated species like
+
+ align:start position:0%
+common to use chlorinated species like
+ 
+
+ align:start position:0%
+common to use chlorinated species like
+chlorine or
+
+ align:start position:0%
+chlorine or
+ 
+
+ align:start position:0%
+chlorine or
+chcl3 or a mixture of chlorine and
+
+ align:start position:0%
+chcl3 or a mixture of chlorine and
+ 
+
+ align:start position:0%
+chcl3 or a mixture of chlorine and
+nitrogen um uh chlorine itself can be uh
+
+ align:start position:0%
+nitrogen um uh chlorine itself can be uh
+ 
+
+ align:start position:0%
+nitrogen um uh chlorine itself can be uh
+somewhat isotropic and uh some of these
+
+ align:start position:0%
+somewhat isotropic and uh some of these
+ 
+
+ align:start position:0%
+somewhat isotropic and uh some of these
+other gases are are more
+
+ align:start position:0%
+other gases are are more
+ 
+
+ align:start position:0%
+other gases are are more
+anisotropic tungsten um can be etched uh
+
+ align:start position:0%
+anisotropic tungsten um can be etched uh
+ 
+
+ align:start position:0%
+anisotropic tungsten um can be etched uh
+in sf6 uh or chlorine so you notice a
+
+ align:start position:0%
+in sf6 uh or chlorine so you notice a
+ 
+
+ align:start position:0%
+in sf6 uh or chlorine so you notice a
+lot of the metals these are all metals
+
+ align:start position:0%
+lot of the metals these are all metals
+ 
+
+ align:start position:0%
+lot of the metals these are all metals
+are attacked by
+
+ align:start position:0%
+are attacked by
+ 
+
+ align:start position:0%
+are attacked by
+chlorine uh which isn't too unusual if
+
+ align:start position:0%
+chlorine uh which isn't too unusual if
+ 
+
+ align:start position:0%
+chlorine uh which isn't too unusual if
+you if you know a common wet metal
+
+ align:start position:0%
+you if you know a common wet metal
+ 
+
+ align:start position:0%
+you if you know a common wet metal
+etchant is hydrogen chloride H
+
+ align:start position:0%
+etchant is hydrogen chloride H
+ 
+
+ align:start position:0%
+etchant is hydrogen chloride H
+HCL um so um again etching Titanium or
+
+ align:start position:0%
+HCL um so um again etching Titanium or
+ 
+
+ align:start position:0%
+HCL um so um again etching Titanium or
+Ty nitride these are very common tion
+
+ align:start position:0%
+Ty nitride these are very common tion
+ 
+
+ align:start position:0%
+Ty nitride these are very common tion
+chlorine or um mixtures of chlorine with
+
+ align:start position:0%
+chlorine or um mixtures of chlorine with
+ 
+
+ align:start position:0%
+chlorine or um mixtures of chlorine with
+hydrocarbons fer resist an important
+
+ align:start position:0%
+hydrocarbons fer resist an important
+ 
+
+ align:start position:0%
+hydrocarbons fer resist an important
+thing we need to be able to not etch or
+
+ align:start position:0%
+thing we need to be able to not etch or
+ 
+
+ align:start position:0%
+thing we need to be able to not etch or
+P you know pattern uh so much as uh you
+
+ align:start position:0%
+P you know pattern uh so much as uh you
+ 
+
+ align:start position:0%
+P you know pattern uh so much as uh you
+you typically uh want to strip it uh so
+
+ align:start position:0%
+you typically uh want to strip it uh so
+ 
+
+ align:start position:0%
+you typically uh want to strip it uh so
+an ashing step would include uh an
+
+ align:start position:0%
+an ashing step would include uh an
+ 
+
+ align:start position:0%
+an ashing step would include uh an
+oxygen plasma which which reacts um with
+
+ align:start position:0%
+oxygen plasma which which reacts um with
+ 
+
+ align:start position:0%
+oxygen plasma which which reacts um with
+the photo resist the hydrocarbons and
+
+ align:start position:0%
+the photo resist the hydrocarbons and
+ 
+
+ align:start position:0%
+the photo resist the hydrocarbons and
+removes the photo resist and the nice
+
+ align:start position:0%
+removes the photo resist and the nice
+ 
+
+ align:start position:0%
+removes the photo resist and the nice
+thing about O2 plasma is it's very
+
+ align:start position:0%
+thing about O2 plasma is it's very
+ 
+
+ align:start position:0%
+thing about O2 plasma is it's very
+selective it doesn't etch too much of
+
+ align:start position:0%
+selective it doesn't etch too much of
+ 
+
+ align:start position:0%
+selective it doesn't etch too much of
+any it doesn't etch n nitride does an ex
+
+ align:start position:0%
+any it doesn't etch n nitride does an ex
+ 
+
+ align:start position:0%
+any it doesn't etch n nitride does an ex
+oxide it will Etch A little bit of
+
+ align:start position:0%
+oxide it will Etch A little bit of
+ 
+
+ align:start position:0%
+oxide it will Etch A little bit of
+silicon by oxidation that is it'll
+
+ align:start position:0%
+silicon by oxidation that is it'll
+ 
+
+ align:start position:0%
+silicon by oxidation that is it'll
+oxidize a little bit of a surface
+
+ align:start position:0%
+oxidize a little bit of a surface
+ 
+
+ align:start position:0%
+oxidize a little bit of a surface
+silicon and then if you happen to do an
+
+ align:start position:0%
+silicon and then if you happen to do an
+ 
+
+ align:start position:0%
+silicon and then if you happen to do an
+HF dip that'll get removed so it has a
+
+ align:start position:0%
+HF dip that'll get removed so it has a
+ 
+
+ align:start position:0%
+HF dip that'll get removed so it has a
+small amount of silicon removal by an
+
+ align:start position:0%
+small amount of silicon removal by an
+ 
+
+ align:start position:0%
+small amount of silicon removal by an
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+process so again that's uh on page three
+
+ align:start position:0%
+process so again that's uh on page three
+ 
+
+ align:start position:0%
+process so again that's uh on page three
+that's that's the second half of the
+
+ align:start position:0%
+that's that's the second half of the
+ 
+
+ align:start position:0%
+that's that's the second half of the
+chart I took directly from chapter 10 in
+
+ align:start position:0%
+chart I took directly from chapter 10 in
+ 
+
+ align:start position:0%
+chart I took directly from chapter 10 in
+your textbook some common
+
+ align:start position:0%
+your textbook some common
+ 
+
+ align:start position:0%
+your textbook some common
+etchants now I wanted to go uh here on
+
+ align:start position:0%
+etchants now I wanted to go uh here on
+ 
+
+ align:start position:0%
+etchants now I wanted to go uh here on
+on um on slide four I wanted to go
+
+ align:start position:0%
+on um on slide four I wanted to go
+ 
+
+ align:start position:0%
+on um on slide four I wanted to go
+through some um etching challenges in in
+
+ align:start position:0%
+through some um etching challenges in in
+ 
+
+ align:start position:0%
+through some um etching challenges in in
+Moss frontend processing uh from the
+
+ align:start position:0%
+Moss frontend processing uh from the
+ 
+
+ align:start position:0%
+Moss frontend processing uh from the
+last 5 years or so and I'll talk about a
+
+ align:start position:0%
+last 5 years or so and I'll talk about a
+ 
+
+ align:start position:0%
+last 5 years or so and I'll talk about a
+couple of them one is uh for example um
+
+ align:start position:0%
+couple of them one is uh for example um
+ 
+
+ align:start position:0%
+couple of them one is uh for example um
+we've talked about in the past uh Dam a
+
+ align:start position:0%
+we've talked about in the past uh Dam a
+ 
+
+ align:start position:0%
+we've talked about in the past uh Dam a
+dynamic Random Access Memory uh there
+
+ align:start position:0%
+dynamic Random Access Memory uh there
+ 
+
+ align:start position:0%
+dynamic Random Access Memory uh there
+are different ways of storing the charge
+
+ align:start position:0%
+are different ways of storing the charge
+ 
+
+ align:start position:0%
+are different ways of storing the charge
+uh in that memory uh you need to make a
+
+ align:start position:0%
+uh in that memory uh you need to make a
+ 
+
+ align:start position:0%
+uh in that memory uh you need to make a
+capacitor of some sort uh on which you
+
+ align:start position:0%
+capacitor of some sort uh on which you
+ 
+
+ align:start position:0%
+capacitor of some sort uh on which you
+store charge and that is your bit
+
+ align:start position:0%
+store charge and that is your bit
+ 
+
+ align:start position:0%
+store charge and that is your bit
+whether there's charge there or non
+
+ align:start position:0%
+whether there's charge there or non
+ 
+
+ align:start position:0%
+whether there's charge there or non
+charge there tells you whether you have
+
+ align:start position:0%
+charge there tells you whether you have
+ 
+
+ align:start position:0%
+charge there tells you whether you have
+a one or a zero um this capacitor you
+
+ align:start position:0%
+a one or a zero um this capacitor you
+ 
+
+ align:start position:0%
+a one or a zero um this capacitor you
+might think well let's just put a
+
+ align:start position:0%
+might think well let's just put a
+ 
+
+ align:start position:0%
+might think well let's just put a
+capacitor on the substrate we all know
+
+ align:start position:0%
+capacitor on the substrate we all know
+ 
+
+ align:start position:0%
+capacitor on the substrate we all know
+how to make an MLs capacitor but the
+
+ align:start position:0%
+how to make an MLs capacitor but the
+ 
+
+ align:start position:0%
+how to make an MLs capacitor but the
+problem is to make very high density
+
+ align:start position:0%
+problem is to make very high density
+ 
+
+ align:start position:0%
+problem is to make very high density
+damps you can't just make a capacitor
+
+ align:start position:0%
+damps you can't just make a capacitor
+ 
+
+ align:start position:0%
+damps you can't just make a capacitor
+flat on the Silicon substrate you can
+
+ align:start position:0%
+flat on the Silicon substrate you can
+ 
+
+ align:start position:0%
+flat on the Silicon substrate you can
+but then it takes up too much area so
+
+ align:start position:0%
+but then it takes up too much area so
+ 
+
+ align:start position:0%
+but then it takes up too much area so
+people have all different types of ways
+
+ align:start position:0%
+people have all different types of ways
+ 
+
+ align:start position:0%
+people have all different types of ways
+people are thinking of ways of stacking
+
+ align:start position:0%
+people are thinking of ways of stacking
+ 
+
+ align:start position:0%
+people are thinking of ways of stacking
+the capacitor on top of the transistor
+
+ align:start position:0%
+the capacitor on top of the transistor
+ 
+
+ align:start position:0%
+the capacitor on top of the transistor
+that's one method a stacked capacitor
+
+ align:start position:0%
+that's one method a stacked capacitor
+ 
+
+ align:start position:0%
+that's one method a stacked capacitor
+topology another method is take the
+
+ align:start position:0%
+topology another method is take the
+ 
+
+ align:start position:0%
+topology another method is take the
+capacitor and bury it down in the
+
+ align:start position:0%
+capacitor and bury it down in the
+ 
+
+ align:start position:0%
+capacitor and bury it down in the
+substrate somewhere so you can get a
+
+ align:start position:0%
+substrate somewhere so you can get a
+ 
+
+ align:start position:0%
+substrate somewhere so you can get a
+smaller area for your damp cell you can
+
+ align:start position:0%
+smaller area for your damp cell you can
+ 
+
+ align:start position:0%
+smaller area for your damp cell you can
+pack more memory on a given ship and
+
+ align:start position:0%
+pack more memory on a given ship and
+ 
+
+ align:start position:0%
+pack more memory on a given ship and
+then uh you'll have uh you'll have uh
+
+ align:start position:0%
+then uh you'll have uh you'll have uh
+ 
+
+ align:start position:0%
+then uh you'll have uh you'll have uh
+you know much higher performance so this
+
+ align:start position:0%
+you know much higher performance so this
+ 
+
+ align:start position:0%
+you know much higher performance so this
+is an example where you might need to
+
+ align:start position:0%
+is an example where you might need to
+ 
+
+ align:start position:0%
+is an example where you might need to
+etge down into a a silicon substrate to
+
+ align:start position:0%
+etge down into a a silicon substrate to
+ 
+
+ align:start position:0%
+etge down into a a silicon substrate to
+make a trench prior to making a
+
+ align:start position:0%
+make a trench prior to making a
+ 
+
+ align:start position:0%
+make a trench prior to making a
+capacitor this is just an example where
+
+ align:start position:0%
+capacitor this is just an example where
+ 
+
+ align:start position:0%
+capacitor this is just an example where
+you have edged a trench that looks like
+
+ align:start position:0%
+you have edged a trench that looks like
+ 
+
+ align:start position:0%
+you have edged a trench that looks like
+this um lined it with oxide and then uh
+
+ align:start position:0%
+this um lined it with oxide and then uh
+ 
+
+ align:start position:0%
+this um lined it with oxide and then uh
+filled it up with polysilicon to make
+
+ align:start position:0%
+filled it up with polysilicon to make
+ 
+
+ align:start position:0%
+filled it up with polysilicon to make
+one of the plates of the um of the
+
+ align:start position:0%
+one of the plates of the um of the
+ 
+
+ align:start position:0%
+one of the plates of the um of the
+electrode the other plate of electrode
+
+ align:start position:0%
+electrode the other plate of electrode
+ 
+
+ align:start position:0%
+electrode the other plate of electrode
+could be the surrounding silicon
+
+ align:start position:0%
+could be the surrounding silicon
+ 
+
+ align:start position:0%
+could be the surrounding silicon
+material um so so and I took this out of
+
+ align:start position:0%
+material um so so and I took this out of
+ 
+
+ align:start position:0%
+material um so so and I took this out of
+the IBM Journal of research and
+
+ align:start position:0%
+the IBM Journal of research and
+ 
+
+ align:start position:0%
+the IBM Journal of research and
+development just off the web if you want
+
+ align:start position:0%
+development just off the web if you want
+ 
+
+ align:start position:0%
+development just off the web if you want
+to look at that in more detail but so we
+
+ align:start position:0%
+to look at that in more detail but so we
+ 
+
+ align:start position:0%
+to look at that in more detail but so we
+need to make very high aspect ratio
+
+ align:start position:0%
+need to make very high aspect ratio
+ 
+
+ align:start position:0%
+need to make very high aspect ratio
+edges uh for these trenches and we also
+
+ align:start position:0%
+edges uh for these trenches and we also
+ 
+
+ align:start position:0%
+edges uh for these trenches and we also
+need to care about the damage that we do
+
+ align:start position:0%
+need to care about the damage that we do
+ 
+
+ align:start position:0%
+need to care about the damage that we do
+to the Silicon because it's going to be
+
+ align:start position:0%
+to the Silicon because it's going to be
+ 
+
+ align:start position:0%
+to the Silicon because it's going to be
+part of a capacitor so we want it to
+
+ align:start position:0%
+part of a capacitor so we want it to
+ 
+
+ align:start position:0%
+part of a capacitor so we want it to
+have smooth surfaces and things so that
+
+ align:start position:0%
+have smooth surfaces and things so that
+ 
+
+ align:start position:0%
+have smooth surfaces and things so that
+we don't break down the oxide and we get
+
+ align:start position:0%
+we don't break down the oxide and we get
+ 
+
+ align:start position:0%
+we don't break down the oxide and we get
+we get a good electrical performance uh
+
+ align:start position:0%
+we get a good electrical performance uh
+ 
+
+ align:start position:0%
+we get a good electrical performance uh
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+capacitor in fact let's see let's take a
+
+ align:start position:0%
+capacitor in fact let's see let's take a
+ 
+
+ align:start position:0%
+capacitor in fact let's see let's take a
+look here at at page five I took this
+
+ align:start position:0%
+look here at at page five I took this
+ 
+
+ align:start position:0%
+look here at at page five I took this
+from the 20 3
+
+ align:start position:0%
+from the 20 3
+ 
+
+ align:start position:0%
+from the 20 3
+itrs uh table 73 this is just for um
+
+ align:start position:0%
+itrs uh table 73 this is just for um
+ 
+
+ align:start position:0%
+itrs uh table 73 this is just for um
+dram trench capacitors what are some of
+
+ align:start position:0%
+dram trench capacitors what are some of
+ 
+
+ align:start position:0%
+dram trench capacitors what are some of
+the technology requirements we're
+
+ align:start position:0%
+the technology requirements we're
+ 
+
+ align:start position:0%
+the technology requirements we're
+looking at of a long term here going
+
+ align:start position:0%
+looking at of a long term here going
+ 
+
+ align:start position:0%
+looking at of a long term here going
+from um 2010 all the way out to 2020 or
+
+ align:start position:0%
+from um 2010 all the way out to 2020 or
+ 
+
+ align:start position:0%
+from um 2010 all the way out to 2020 or
+2018 what are people expect they might
+
+ align:start position:0%
+2018 what are people expect they might
+ 
+
+ align:start position:0%
+2018 what are people expect they might
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+need um well here there are uh some
+
+ align:start position:0%
+need um well here there are uh some
+ 
+
+ align:start position:0%
+need um well here there are uh some
+indications here of of characteristics
+
+ align:start position:0%
+indications here of of characteristics
+ 
+
+ align:start position:0%
+indications here of of characteristics
+they have things called the trench
+
+ align:start position:0%
+they have things called the trench
+ 
+
+ align:start position:0%
+they have things called the trench
+structure how it will be shaped maybe
+
+ align:start position:0%
+structure how it will be shaped maybe
+ 
+
+ align:start position:0%
+structure how it will be shaped maybe
+more like an upside down bottle
+
+ align:start position:0%
+more like an upside down bottle
+ 
+
+ align:start position:0%
+more like an upside down bottle
+um the circumference of the trench uh
+
+ align:start position:0%
+um the circumference of the trench uh
+ 
+
+ align:start position:0%
+um the circumference of the trench uh
+the trench surfus roughting roughening
+
+ align:start position:0%
+the trench surfus roughting roughening
+ 
+
+ align:start position:0%
+the trench surfus roughting roughening
+Factor um the uh effective oxide
+
+ align:start position:0%
+Factor um the uh effective oxide
+ 
+
+ align:start position:0%
+Factor um the uh effective oxide
+thickness that people will be using in
+
+ align:start position:0%
+thickness that people will be using in
+ 
+
+ align:start position:0%
+thickness that people will be using in
+that trench uh capacitor just to give
+
+ align:start position:0%
+that trench uh capacitor just to give
+ 
+
+ align:start position:0%
+that trench uh capacitor just to give
+you an idea uh in nanometers here we're
+
+ align:start position:0%
+you an idea uh in nanometers here we're
+ 
+
+ align:start position:0%
+you an idea uh in nanometers here we're
+talking about several nanometers maybe
+
+ align:start position:0%
+talking about several nanometers maybe
+ 
+
+ align:start position:0%
+talking about several nanometers maybe
+two nanometers scaling even thinner and
+
+ align:start position:0%
+two nanometers scaling even thinner and
+ 
+
+ align:start position:0%
+two nanometers scaling even thinner and
+thinner um the trench depth in microns
+
+ align:start position:0%
+thinner um the trench depth in microns
+ 
+
+ align:start position:0%
+thinner um the trench depth in microns
+uh for this would be a 30 for a 35 fto
+
+ align:start position:0%
+uh for this would be a 30 for a 35 fto
+ 
+
+ align:start position:0%
+uh for this would be a 30 for a 35 fto
+farad uh capacitor just as an example
+
+ align:start position:0%
+farad uh capacitor just as an example
+ 
+
+ align:start position:0%
+farad uh capacitor just as an example
+how deep will we have to etch um uh
+
+ align:start position:0%
+how deep will we have to etch um uh
+ 
+
+ align:start position:0%
+how deep will we have to etch um uh
+reasonably deep somewhere between five
+
+ align:start position:0%
+reasonably deep somewhere between five
+ 
+
+ align:start position:0%
+reasonably deep somewhere between five
+to seven microns is what people are
+
+ align:start position:0%
+to seven microns is what people are
+ 
+
+ align:start position:0%
+to seven microns is what people are
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+doing aspect ratio so remember we talked
+
+ align:start position:0%
+doing aspect ratio so remember we talked
+ 
+
+ align:start position:0%
+doing aspect ratio so remember we talked
+about aspect ratio as being an important
+
+ align:start position:0%
+about aspect ratio as being an important
+ 
+
+ align:start position:0%
+about aspect ratio as being an important
+attribute of our capabilities for
+
+ align:start position:0%
+attribute of our capabilities for
+ 
+
+ align:start position:0%
+attribute of our capabilities for
+etching well here so here is the trench
+
+ align:start position:0%
+etching well here so here is the trench
+ 
+
+ align:start position:0%
+etching well here so here is the trench
+depth divided by its width we're talking
+
+ align:start position:0%
+depth divided by its width we're talking
+ 
+
+ align:start position:0%
+depth divided by its width we're talking
+about very high aspect ratios that are
+
+ align:start position:0%
+about very high aspect ratios that are
+ 
+
+ align:start position:0%
+about very high aspect ratios that are
+increasing and they're also quite large
+
+ align:start position:0%
+increasing and they're also quite large
+ 
+
+ align:start position:0%
+increasing and they're also quite large
+in 2010 which is a ways off we're
+
+ align:start position:0%
+in 2010 which is a ways off we're
+ 
+
+ align:start position:0%
+in 2010 which is a ways off we're
+reaching aspect ratio is on the order of
+
+ align:start position:0%
+reaching aspect ratio is on the order of
+ 
+
+ align:start position:0%
+reaching aspect ratio is on the order of
+100 and beyond that going even higher
+
+ align:start position:0%
+100 and beyond that going even higher
+ 
+
+ align:start position:0%
+100 and beyond that going even higher
+and you notice Beyond 100 there the um
+
+ align:start position:0%
+and you notice Beyond 100 there the um
+ 
+
+ align:start position:0%
+and you notice Beyond 100 there the um
+cells are all marked red uh indicating
+
+ align:start position:0%
+cells are all marked red uh indicating
+ 
+
+ align:start position:0%
+cells are all marked red uh indicating
+that in that range um people don't
+
+ align:start position:0%
+that in that range um people don't
+ 
+
+ align:start position:0%
+that in that range um people don't
+really know yet how to etch such deep
+
+ align:start position:0%
+really know yet how to etch such deep
+ 
+
+ align:start position:0%
+really know yet how to etch such deep
+aspect ratio um 100 to one um so new
+
+ align:start position:0%
+aspect ratio um 100 to one um so new
+ 
+
+ align:start position:0%
+aspect ratio um 100 to one um so new
+technology is going to have to be
+
+ align:start position:0%
+technology is going to have to be
+ 
+
+ align:start position:0%
+technology is going to have to be
+developed in order to do
+
+ align:start position:0%
+developed in order to do
+ 
+
+ align:start position:0%
+developed in order to do
+that uh they have some indications here
+
+ align:start position:0%
+that uh they have some indications here
+ 
+
+ align:start position:0%
+that uh they have some indications here
+also of what the upper electrode might
+
+ align:start position:0%
+also of what the upper electrode might
+ 
+
+ align:start position:0%
+also of what the upper electrode might
+be made of uh it seems to be metal the
+
+ align:start position:0%
+be made of uh it seems to be metal the
+ 
+
+ align:start position:0%
+be made of uh it seems to be metal the
+dialectric material uh people are
+
+ align:start position:0%
+dialectric material uh people are
+ 
+
+ align:start position:0%
+dialectric material uh people are
+talking about using uh High case again
+
+ align:start position:0%
+talking about using uh High case again
+ 
+
+ align:start position:0%
+talking about using uh High case again
+you're trying to store a fair amount of
+
+ align:start position:0%
+you're trying to store a fair amount of
+ 
+
+ align:start position:0%
+you're trying to store a fair amount of
+charge in a small space you can do that
+
+ align:start position:0%
+charge in a small space you can do that
+ 
+
+ align:start position:0%
+charge in a small space you can do that
+with a um a higher dialectric constant
+
+ align:start position:0%
+with a um a higher dialectric constant
+ 
+
+ align:start position:0%
+with a um a higher dialectric constant
+the bottom uh electrode um could be a
+
+ align:start position:0%
+the bottom uh electrode um could be a
+ 
+
+ align:start position:0%
+the bottom uh electrode um could be a
+combination of silicon and metals uh as
+
+ align:start position:0%
+combination of silicon and metals uh as
+ 
+
+ align:start position:0%
+combination of silicon and metals uh as
+well so just just give you an idea what
+
+ align:start position:0%
+well so just just give you an idea what
+ 
+
+ align:start position:0%
+well so just just give you an idea what
+kind of trenches one needs to etch and
+
+ align:start position:0%
+kind of trenches one needs to etch and
+ 
+
+ align:start position:0%
+kind of trenches one needs to etch and
+this increase in the aspect ratio uh is
+
+ align:start position:0%
+this increase in the aspect ratio uh is
+ 
+
+ align:start position:0%
+this increase in the aspect ratio uh is
+um you know is is pretty amazing in
+
+ align:start position:0%
+um you know is is pretty amazing in
+ 
+
+ align:start position:0%
+um you know is is pretty amazing in
+terms of what tech what technology
+
+ align:start position:0%
+terms of what tech what technology
+ 
+
+ align:start position:0%
+terms of what tech what technology
+requirements are going to be imposed on
+
+ align:start position:0%
+requirements are going to be imposed on
+ 
+
+ align:start position:0%
+requirements are going to be imposed on
+uh on Advanced etching techniques
+
+ align:start position:0%
+uh on Advanced etching techniques
+ 
+
+ align:start position:0%
+uh on Advanced etching techniques
+okay so that's one example uh if I move
+
+ align:start position:0%
+okay so that's one example uh if I move
+ 
+
+ align:start position:0%
+okay so that's one example uh if I move
+on to slide six uh we not only have to
+
+ align:start position:0%
+on to slide six uh we not only have to
+ 
+
+ align:start position:0%
+on to slide six uh we not only have to
+etch silicon into the the single Crystal
+
+ align:start position:0%
+etch silicon into the the single Crystal
+ 
+
+ align:start position:0%
+etch silicon into the the single Crystal
+material but we also have to etch
+
+ align:start position:0%
+material but we also have to etch
+ 
+
+ align:start position:0%
+material but we also have to etch
+silicon when we're etching the gate and
+
+ align:start position:0%
+silicon when we're etching the gate and
+ 
+
+ align:start position:0%
+silicon when we're etching the gate and
+uh in fact etching the gate is becoming
+
+ align:start position:0%
+uh in fact etching the gate is becoming
+ 
+
+ align:start position:0%
+uh in fact etching the gate is becoming
+more and more complicated this is an
+
+ align:start position:0%
+more and more complicated this is an
+ 
+
+ align:start position:0%
+more and more complicated this is an
+example on slide six of what etching
+
+ align:start position:0%
+example on slide six of what etching
+ 
+
+ align:start position:0%
+example on slide six of what etching
+what we call a compound gate or a gate
+
+ align:start position:0%
+what we call a compound gate or a gate
+ 
+
+ align:start position:0%
+what we call a compound gate or a gate
+that that that already has a gate stack
+
+ align:start position:0%
+that that that already has a gate stack
+ 
+
+ align:start position:0%
+that that that already has a gate stack
+or already has several materials um that
+
+ align:start position:0%
+or already has several materials um that
+ 
+
+ align:start position:0%
+or already has several materials um that
+it consists of uh and I apologize this
+
+ align:start position:0%
+it consists of uh and I apologize this
+ 
+
+ align:start position:0%
+it consists of uh and I apologize this
+is not a very good sem um I took this
+
+ align:start position:0%
+is not a very good sem um I took this
+ 
+
+ align:start position:0%
+is not a very good sem um I took this
+off the website again from that IBM
+
+ align:start position:0%
+off the website again from that IBM
+ 
+
+ align:start position:0%
+off the website again from that IBM
+article um and what it is is on on the
+
+ align:start position:0%
+article um and what it is is on on the
+ 
+
+ align:start position:0%
+article um and what it is is on on the
+very top there is photo resist that has
+
+ align:start position:0%
+very top there is photo resist that has
+ 
+
+ align:start position:0%
+very top there is photo resist that has
+been etched that has been patterned I
+
+ align:start position:0%
+been etched that has been patterned I
+ 
+
+ align:start position:0%
+been etched that has been patterned I
+should say then there is a layer of
+
+ align:start position:0%
+should say then there is a layer of
+ 
+
+ align:start position:0%
+should say then there is a layer of
+tungsten pilicide that has been etched
+
+ align:start position:0%
+tungsten pilicide that has been etched
+ 
+
+ align:start position:0%
+tungsten pilicide that has been etched
+and then there's a layer below it of
+
+ align:start position:0%
+and then there's a layer below it of
+ 
+
+ align:start position:0%
+and then there's a layer below it of
+polycrystal and silicon that's been
+
+ align:start position:0%
+polycrystal and silicon that's been
+ 
+
+ align:start position:0%
+polycrystal and silicon that's been
+etched down to say the oxide uh down to
+
+ align:start position:0%
+etched down to say the oxide uh down to
+ 
+
+ align:start position:0%
+etched down to say the oxide uh down to
+the gate oxide and when presented with
+
+ align:start position:0%
+the gate oxide and when presented with
+ 
+
+ align:start position:0%
+the gate oxide and when presented with
+something like this you have to think
+
+ align:start position:0%
+something like this you have to think
+ 
+
+ align:start position:0%
+something like this you have to think
+about using two different types uh after
+
+ align:start position:0%
+about using two different types uh after
+ 
+
+ align:start position:0%
+about using two different types uh after
+you um uh pattern your photo resist and
+
+ align:start position:0%
+you um uh pattern your photo resist and
+ 
+
+ align:start position:0%
+you um uh pattern your photo resist and
+you develop it and you're ready to etch
+
+ align:start position:0%
+you develop it and you're ready to etch
+ 
+
+ align:start position:0%
+you develop it and you're ready to etch
+it you underneath you have two different
+
+ align:start position:0%
+it you underneath you have two different
+ 
+
+ align:start position:0%
+it you underneath you have two different
+types of layers you need to etch a
+
+ align:start position:0%
+types of layers you need to etch a
+ 
+
+ align:start position:0%
+types of layers you need to etch a
+pilicide layer in this example which was
+
+ align:start position:0%
+pilicide layer in this example which was
+ 
+
+ align:start position:0%
+pilicide layer in this example which was
+pre-existing uh as a uniform layer it
+
+ align:start position:0%
+pre-existing uh as a uniform layer it
+ 
+
+ align:start position:0%
+pre-existing uh as a uniform layer it
+has to be etched and then you need to
+
+ align:start position:0%
+has to be etched and then you need to
+ 
+
+ align:start position:0%
+has to be etched and then you need to
+stop on the silicon and then switch
+
+ align:start position:0%
+stop on the silicon and then switch
+ 
+
+ align:start position:0%
+stop on the silicon and then switch
+gases to etch the poly silicon
+
+ align:start position:0%
+gases to etch the poly silicon
+ 
+
+ align:start position:0%
+gases to etch the poly silicon
+underneath now this gets a little tricky
+
+ align:start position:0%
+underneath now this gets a little tricky
+ 
+
+ align:start position:0%
+underneath now this gets a little tricky
+so you have two different Edge gases
+
+ align:start position:0%
+so you have two different Edge gases
+ 
+
+ align:start position:0%
+so you have two different Edge gases
+that doesn't sound too bad you have an
+
+ align:start position:0%
+that doesn't sound too bad you have an
+ 
+
+ align:start position:0%
+that doesn't sound too bad you have an
+edge gas to etge the poly the tungsten
+
+ align:start position:0%
+edge gas to etge the poly the tungsten
+ 
+
+ align:start position:0%
+edge gas to etge the poly the tungsten
+silicide and another series of gases you
+
+ align:start position:0%
+silicide and another series of gases you
+ 
+
+ align:start position:0%
+silicide and another series of gases you
+used to etch the
+
+ align:start position:0%
+used to etch the
+ 
+
+ align:start position:0%
+used to etch the
+polysilicon um one problem though you
+
+ align:start position:0%
+polysilicon um one problem though you
+ 
+
+ align:start position:0%
+polysilicon um one problem though you
+can come across uh for example tungsten
+
+ align:start position:0%
+can come across uh for example tungsten
+ 
+
+ align:start position:0%
+can come across uh for example tungsten
+pilicides uh may not be super pure it
+
+ align:start position:0%
+pilicides uh may not be super pure it
+ 
+
+ align:start position:0%
+pilicides uh may not be super pure it
+may have some oxides incorporated into
+
+ align:start position:0%
+may have some oxides incorporated into
+ 
+
+ align:start position:0%
+may have some oxides incorporated into
+it um uh and uh this these these oxides
+
+ align:start position:0%
+it um uh and uh this these these oxides
+ 
+
+ align:start position:0%
+it um uh and uh this these these oxides
+won't etch if the chch and uh is highly
+
+ align:start position:0%
+won't etch if the chch and uh is highly
+ 
+
+ align:start position:0%
+won't etch if the chch and uh is highly
+selective to oxide so if you're using a
+
+ align:start position:0%
+selective to oxide so if you're using a
+ 
+
+ align:start position:0%
+selective to oxide so if you're using a
+single etch gas that is very selective
+
+ align:start position:0%
+single etch gas that is very selective
+ 
+
+ align:start position:0%
+single etch gas that is very selective
+to oxide say is what you might want to
+
+ align:start position:0%
+to oxide say is what you might want to
+ 
+
+ align:start position:0%
+to oxide say is what you might want to
+do for the poly that same ET gas might
+
+ align:start position:0%
+do for the poly that same ET gas might
+ 
+
+ align:start position:0%
+do for the poly that same ET gas might
+not do very well in the tungsten
+
+ align:start position:0%
+not do very well in the tungsten
+ 
+
+ align:start position:0%
+not do very well in the tungsten
+pilicide and uh what happens when you
+
+ align:start position:0%
+pilicide and uh what happens when you
+ 
+
+ align:start position:0%
+pilicide and uh what happens when you
+use an etching gas that is very
+
+ align:start position:0%
+use an etching gas that is very
+ 
+
+ align:start position:0%
+use an etching gas that is very
+selective to oxide and you don't do a
+
+ align:start position:0%
+selective to oxide and you don't do a
+ 
+
+ align:start position:0%
+selective to oxide and you don't do a
+breakthrough if you have any native
+
+ align:start position:0%
+breakthrough if you have any native
+ 
+
+ align:start position:0%
+breakthrough if you have any native
+oxide on top of that structure and you
+
+ align:start position:0%
+oxide on top of that structure and you
+ 
+
+ align:start position:0%
+oxide on top of that structure and you
+don't break through it you'll end up
+
+ align:start position:0%
+don't break through it you'll end up
+ 
+
+ align:start position:0%
+don't break through it you'll end up
+with something called R grass um and
+
+ align:start position:0%
+with something called R grass um and
+ 
+
+ align:start position:0%
+with something called R grass um and
+it's called grass because it looks like
+
+ align:start position:0%
+it's called grass because it looks like
+ 
+
+ align:start position:0%
+it's called grass because it looks like
+grass in the sem let me on the next
+
+ align:start position:0%
+grass in the sem let me on the next
+ 
+
+ align:start position:0%
+grass in the sem let me on the next
+slide I'll show you a picture of
+
+ align:start position:0%
+slide I'll show you a picture of
+ 
+
+ align:start position:0%
+slide I'll show you a picture of
+grass on page on slide
+
+ align:start position:0%
+grass on page on slide
+ 
+
+ align:start position:0%
+grass on page on slide
+seven um this is an example of an
+
+ align:start position:0%
+seven um this is an example of an
+ 
+
+ align:start position:0%
+seven um this is an example of an
+extreme case of Rie grass and you have a
+
+ align:start position:0%
+extreme case of Rie grass and you have a
+ 
+
+ align:start position:0%
+extreme case of Rie grass and you have a
+flat substrate down to which you have
+
+ align:start position:0%
+flat substrate down to which you have
+ 
+
+ align:start position:0%
+flat substrate down to which you have
+etched
+
+ align:start position:0%
+etched
+ 
+
+ align:start position:0%
+etched
+um and sometimes it's called
+
+ align:start position:0%
+um and sometimes it's called
+ 
+
+ align:start position:0%
+um and sometimes it's called
+micromasking and what happened in
+
+ align:start position:0%
+micromasking and what happened in
+ 
+
+ align:start position:0%
+micromasking and what happened in
+etchant was used to etch this gate
+
+ align:start position:0%
+etchant was used to etch this gate
+ 
+
+ align:start position:0%
+etchant was used to etch this gate
+whatever this material is and etent was
+
+ align:start position:0%
+whatever this material is and etent was
+ 
+
+ align:start position:0%
+whatever this material is and etent was
+used that had a very high selectivity of
+
+ align:start position:0%
+used that had a very high selectivity of
+ 
+
+ align:start position:0%
+used that had a very high selectivity of
+oxide um and there were apparently small
+
+ align:start position:0%
+oxide um and there were apparently small
+ 
+
+ align:start position:0%
+oxide um and there were apparently small
+say oxide inclusions uh at the surface
+
+ align:start position:0%
+say oxide inclusions uh at the surface
+ 
+
+ align:start position:0%
+say oxide inclusions uh at the surface
+of the wafer when when the etch was
+
+ align:start position:0%
+of the wafer when when the etch was
+ 
+
+ align:start position:0%
+of the wafer when when the etch was
+started uh that didn't get fully removed
+
+ align:start position:0%
+started uh that didn't get fully removed
+ 
+
+ align:start position:0%
+started uh that didn't get fully removed
+and so those small oxide areas will act
+
+ align:start position:0%
+and so those small oxide areas will act
+ 
+
+ align:start position:0%
+and so those small oxide areas will act
+like little micro masks they wer were
+
+ align:start position:0%
+like little micro masks they wer were
+ 
+
+ align:start position:0%
+like little micro masks they wer were
+not intentionally put there but there's
+
+ align:start position:0%
+not intentionally put there but there's
+ 
+
+ align:start position:0%
+not intentionally put there but there's
+just a little bit of oxide here and
+
+ align:start position:0%
+just a little bit of oxide here and
+ 
+
+ align:start position:0%
+just a little bit of oxide here and
+there um that the so a breakthrough etch
+
+ align:start position:0%
+there um that the so a breakthrough etch
+ 
+
+ align:start position:0%
+there um that the so a breakthrough etch
+wasn't used as a result if the if the
+
+ align:start position:0%
+wasn't used as a result if the if the
+ 
+
+ align:start position:0%
+wasn't used as a result if the if the
+etch that you're using is highly
+
+ align:start position:0%
+etch that you're using is highly
+ 
+
+ align:start position:0%
+etch that you're using is highly
+selective to oxide it'll never etch it
+
+ align:start position:0%
+selective to oxide it'll never etch it
+ 
+
+ align:start position:0%
+selective to oxide it'll never etch it
+and instead you end up with little posts
+
+ align:start position:0%
+and instead you end up with little posts
+ 
+
+ align:start position:0%
+and instead you end up with little posts
+uh which look like little little blades
+
+ align:start position:0%
+uh which look like little little blades
+ 
+
+ align:start position:0%
+uh which look like little little blades
+of grass um the solution to this is well
+
+ align:start position:0%
+of grass um the solution to this is well
+ 
+
+ align:start position:0%
+of grass um the solution to this is well
+you could say well don't use an ed
+
+ align:start position:0%
+you could say well don't use an ed
+ 
+
+ align:start position:0%
+you could say well don't use an ed
+that's so selective to oxide but you if
+
+ align:start position:0%
+that's so selective to oxide but you if
+ 
+
+ align:start position:0%
+that's so selective to oxide but you if
+you want to stop on S2 you wouldn't want
+
+ align:start position:0%
+you want to stop on S2 you wouldn't want
+ 
+
+ align:start position:0%
+you want to stop on S2 you wouldn't want
+to do that the solution is the very
+
+ align:start position:0%
+to do that the solution is the very
+ 
+
+ align:start position:0%
+to do that the solution is the very
+first part of your Edge step should be a
+
+ align:start position:0%
+first part of your Edge step should be a
+ 
+
+ align:start position:0%
+first part of your Edge step should be a
+breakthrough Edge where you make sure
+
+ align:start position:0%
+breakthrough Edge where you make sure
+ 
+
+ align:start position:0%
+breakthrough Edge where you make sure
+you break through all the native oxide
+
+ align:start position:0%
+you break through all the native oxide
+ 
+
+ align:start position:0%
+you break through all the native oxide
+and then you continue on down so it gets
+
+ align:start position:0%
+and then you continue on down so it gets
+ 
+
+ align:start position:0%
+and then you continue on down so it gets
+a little tricky um when you start um
+
+ align:start position:0%
+a little tricky um when you start um
+ 
+
+ align:start position:0%
+a little tricky um when you start um
+etching multiple materials or when when
+
+ align:start position:0%
+etching multiple materials or when when
+ 
+
+ align:start position:0%
+etching multiple materials or when when
+uh you uh you have to think about the
+
+ align:start position:0%
+uh you uh you have to think about the
+ 
+
+ align:start position:0%
+uh you uh you have to think about the
+fact that there may be materials on the
+
+ align:start position:0%
+fact that there may be materials on the
+ 
+
+ align:start position:0%
+fact that there may be materials on the
+wafer you don't know
+
+ align:start position:0%
+wafer you don't know
+ 
+
+ align:start position:0%
+wafer you don't know
+about Native silicon dioxide may be
+
+ align:start position:0%
+about Native silicon dioxide may be
+ 
+
+ align:start position:0%
+about Native silicon dioxide may be
+there even if you didn't put it there it
+
+ align:start position:0%
+there even if you didn't put it there it
+ 
+
+ align:start position:0%
+there even if you didn't put it there it
+grows there automatically on the wafer
+
+ align:start position:0%
+grows there automatically on the wafer
+ 
+
+ align:start position:0%
+grows there automatically on the wafer
+so you have to remember that you do get
+
+ align:start position:0%
+so you have to remember that you do get
+ 
+
+ align:start position:0%
+so you have to remember that you do get
+it off the surface before you use a
+
+ align:start position:0%
+it off the surface before you use a
+ 
+
+ align:start position:0%
+it off the surface before you use a
+highly selective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Edge um on slide eight what I've done is
+
+ align:start position:0%
+Edge um on slide eight what I've done is
+ 
+
+ align:start position:0%
+Edge um on slide eight what I've done is
+I've I've listed some what I call
+
+ align:start position:0%
+I've I've listed some what I call
+ 
+
+ align:start position:0%
+I've I've listed some what I call
+etching challenges in MOS front and
+
+ align:start position:0%
+etching challenges in MOS front and
+ 
+
+ align:start position:0%
+etching challenges in MOS front and
+processing as they apply to gate etching
+
+ align:start position:0%
+processing as they apply to gate etching
+ 
+
+ align:start position:0%
+processing as they apply to gate etching
+uh and uh logic logic devices in
+
+ align:start position:0%
+uh and uh logic logic devices in
+ 
+
+ align:start position:0%
+uh and uh logic logic devices in
+particular uh this is a um on the
+
+ align:start position:0%
+particular uh this is a um on the
+ 
+
+ align:start position:0%
+particular uh this is a um on the
+left-and side is a tem micrograph I
+
+ align:start position:0%
+left-and side is a tem micrograph I
+ 
+
+ align:start position:0%
+left-and side is a tem micrograph I
+think I showed this the very beginning
+
+ align:start position:0%
+think I showed this the very beginning
+ 
+
+ align:start position:0%
+think I showed this the very beginning
+and several times throughout the course
+
+ align:start position:0%
+and several times throughout the course
+ 
+
+ align:start position:0%
+and several times throughout the course
+just to give you an idea of of what a
+
+ align:start position:0%
+just to give you an idea of of what a
+ 
+
+ align:start position:0%
+just to give you an idea of of what a
+device uh five years ago or so might
+
+ align:start position:0%
+device uh five years ago or so might
+ 
+
+ align:start position:0%
+device uh five years ago or so might
+have looked like this is a fairly larger
+
+ align:start position:0%
+have looked like this is a fairly larger
+ 
+
+ align:start position:0%
+have looked like this is a fairly larger
+technology by today's standards but it's
+
+ align:start position:0%
+technology by today's standards but it's
+ 
+
+ align:start position:0%
+technology by today's standards but it's
+it's I think it's a point a quarter
+
+ align:start position:0%
+it's I think it's a point a quarter
+ 
+
+ align:start position:0%
+it's I think it's a point a quarter
+Micron or something like that uh Channel
+
+ align:start position:0%
+Micron or something like that uh Channel
+ 
+
+ align:start position:0%
+Micron or something like that uh Channel
+length technology here is a polycrystal
+
+ align:start position:0%
+length technology here is a polycrystal
+ 
+
+ align:start position:0%
+length technology here is a polycrystal
+silicon gate there's a thin layer
+
+ align:start position:0%
+silicon gate there's a thin layer
+ 
+
+ align:start position:0%
+silicon gate there's a thin layer
+underneath which is the gate oxide
+
+ align:start position:0%
+underneath which is the gate oxide
+ 
+
+ align:start position:0%
+underneath which is the gate oxide
+separates the gate uh from the channel
+
+ align:start position:0%
+separates the gate uh from the channel
+ 
+
+ align:start position:0%
+separates the gate uh from the channel
+and on top there is a layer which is
+
+ align:start position:0%
+and on top there is a layer which is
+ 
+
+ align:start position:0%
+and on top there is a layer which is
+pilicide now that was put there
+
+ align:start position:0%
+pilicide now that was put there
+ 
+
+ align:start position:0%
+pilicide now that was put there
+afterwards in this case so the gate was
+
+ align:start position:0%
+afterwards in this case so the gate was
+ 
+
+ align:start position:0%
+afterwards in this case so the gate was
+first etched and then um metal was put
+
+ align:start position:0%
+first etched and then um metal was put
+ 
+
+ align:start position:0%
+first etched and then um metal was put
+down and then was reacted with the gate
+
+ align:start position:0%
+down and then was reacted with the gate
+ 
+
+ align:start position:0%
+down and then was reacted with the gate
+and the source strain in in a pilicide
+
+ align:start position:0%
+and the source strain in in a pilicide
+ 
+
+ align:start position:0%
+and the source strain in in a pilicide
+or salicide process we'll talk about
+
+ align:start position:0%
+or salicide process we'll talk about
+ 
+
+ align:start position:0%
+or salicide process we'll talk about
+that next lecture when we talk about
+
+ align:start position:0%
+that next lecture when we talk about
+ 
+
+ align:start position:0%
+that next lecture when we talk about
+silicide so you didn't have to etge
+
+ align:start position:0%
+silicide so you didn't have to etge
+ 
+
+ align:start position:0%
+silicide so you didn't have to etge
+through the through this this was
+
+ align:start position:0%
+through the through this this was
+ 
+
+ align:start position:0%
+through the through this this was
+reacted um later on but what do we care
+
+ align:start position:0%
+reacted um later on but what do we care
+ 
+
+ align:start position:0%
+reacted um later on but what do we care
+about well in this picture um first we
+
+ align:start position:0%
+about well in this picture um first we
+ 
+
+ align:start position:0%
+about well in this picture um first we
+need to control the gate length Or the
+
+ align:start position:0%
+need to control the gate length Or the
+ 
+
+ align:start position:0%
+need to control the gate length Or the
+critical Dimension sometimes called the
+
+ align:start position:0%
+critical Dimension sometimes called the
+ 
+
+ align:start position:0%
+critical Dimension sometimes called the
+CD the gate length is is defined between
+
+ align:start position:0%
+CD the gate length is is defined between
+ 
+
+ align:start position:0%
+CD the gate length is is defined between
+from this point to this point so this
+
+ align:start position:0%
+from this point to this point so this
+ 
+
+ align:start position:0%
+from this point to this point so this
+this width or length if you so to speak
+
+ align:start position:0%
+this width or length if you so to speak
+ 
+
+ align:start position:0%
+this width or length if you so to speak
+of the polysilicon needs to be
+
+ align:start position:0%
+of the polysilicon needs to be
+ 
+
+ align:start position:0%
+of the polysilicon needs to be
+controlled exactly on on all um on all
+
+ align:start position:0%
+controlled exactly on on all um on all
+ 
+
+ align:start position:0%
+controlled exactly on on all um on all
+areas of of the Chip And all areas of
+
+ align:start position:0%
+areas of of the Chip And all areas of
+ 
+
+ align:start position:0%
+areas of of the Chip And all areas of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+wafer the sidewall profile what do I
+
+ align:start position:0%
+wafer the sidewall profile what do I
+ 
+
+ align:start position:0%
+wafer the sidewall profile what do I
+mean by that well this profile going
+
+ align:start position:0%
+mean by that well this profile going
+ 
+
+ align:start position:0%
+mean by that well this profile going
+from the very top down here has to be
+
+ align:start position:0%
+from the very top down here has to be
+ 
+
+ align:start position:0%
+from the very top down here has to be
+controlled you usually want it vertical
+
+ align:start position:0%
+controlled you usually want it vertical
+ 
+
+ align:start position:0%
+controlled you usually want it vertical
+you don't usually want it splay out like
+
+ align:start position:0%
+you don't usually want it splay out like
+ 
+
+ align:start position:0%
+you don't usually want it splay out like
+this you don't want it retrograded like
+
+ align:start position:0%
+this you don't want it retrograded like
+ 
+
+ align:start position:0%
+this you don't want it retrograded like
+this you don't want it straight with a
+
+ align:start position:0%
+this you don't want it straight with a
+ 
+
+ align:start position:0%
+this you don't want it straight with a
+little foot at the bottom you want it
+
+ align:start position:0%
+little foot at the bottom you want it
+ 
+
+ align:start position:0%
+little foot at the bottom you want it
+perfectly vertical and stop that sounds
+
+ align:start position:0%
+perfectly vertical and stop that sounds
+ 
+
+ align:start position:0%
+perfectly vertical and stop that sounds
+kind of trivial but it's not
+
+ align:start position:0%
+kind of trivial but it's not
+ 
+
+ align:start position:0%
+kind of trivial but it's not
+easy um for various reasons uh
+
+ align:start position:0%
+easy um for various reasons uh
+ 
+
+ align:start position:0%
+easy um for various reasons uh
+selectivity we care about as we're
+
+ align:start position:0%
+selectivity we care about as we're
+ 
+
+ align:start position:0%
+selectivity we care about as we're
+etching this polysilicon we don't want
+
+ align:start position:0%
+etching this polysilicon we don't want
+ 
+
+ align:start position:0%
+etching this polysilicon we don't want
+to etch away the resist that that would
+
+ align:start position:0%
+to etch away the resist that that would
+ 
+
+ align:start position:0%
+to etch away the resist that that would
+be masking it on top or whatever mask
+
+ align:start position:0%
+be masking it on top or whatever mask
+ 
+
+ align:start position:0%
+be masking it on top or whatever mask
+material we're using if we're using a
+
+ align:start position:0%
+material we're using if we're using a
+ 
+
+ align:start position:0%
+material we're using if we're using a
+hard mask of si2 so selectivity to the
+
+ align:start position:0%
+hard mask of si2 so selectivity to the
+ 
+
+ align:start position:0%
+hard mask of si2 so selectivity to the
+etge material uh to the masking material
+
+ align:start position:0%
+etge material uh to the masking material
+ 
+
+ align:start position:0%
+etge material uh to the masking material
+is very important
+
+ align:start position:0%
+is very important
+ 
+
+ align:start position:0%
+is very important
+that's one type of selectivity
+
+ align:start position:0%
+that's one type of selectivity
+ 
+
+ align:start position:0%
+that's one type of selectivity
+selectivity to the gate dialectric down
+
+ align:start position:0%
+selectivity to the gate dialectric down
+ 
+
+ align:start position:0%
+selectivity to the gate dialectric down
+here in this um di is is a dialectric
+
+ align:start position:0%
+here in this um di is is a dialectric
+ 
+
+ align:start position:0%
+here in this um di is is a dialectric
+material probably a high K that's
+
+ align:start position:0%
+material probably a high K that's
+ 
+
+ align:start position:0%
+material probably a high K that's
+probably 1 to 2 nmet thick we need to
+
+ align:start position:0%
+probably 1 to 2 nmet thick we need to
+ 
+
+ align:start position:0%
+probably 1 to 2 nmet thick we need to
+stop instantly immediately as soon as we
+
+ align:start position:0%
+stop instantly immediately as soon as we
+ 
+
+ align:start position:0%
+stop instantly immediately as soon as we
+hit it automatically and not go through
+
+ align:start position:0%
+hit it automatically and not go through
+ 
+
+ align:start position:0%
+hit it automatically and not go through
+it and not not uh you know not over Edge
+
+ align:start position:0%
+it and not not uh you know not over Edge
+ 
+
+ align:start position:0%
+it and not not uh you know not over Edge
+too much so uh this is a real issue
+
+ align:start position:0%
+too much so uh this is a real issue
+ 
+
+ align:start position:0%
+too much so uh this is a real issue
+getting uh a chemical selectivity at the
+
+ align:start position:0%
+getting uh a chemical selectivity at the
+ 
+
+ align:start position:0%
+getting uh a chemical selectivity at the
+same time as getting good sidewall
+
+ align:start position:0%
+same time as getting good sidewall
+ 
+
+ align:start position:0%
+same time as getting good sidewall
+profile uh I just mentioned the fact
+
+ align:start position:0%
+profile uh I just mentioned the fact
+ 
+
+ align:start position:0%
+profile uh I just mentioned the fact
+that native oxide is often present on
+
+ align:start position:0%
+that native oxide is often present on
+ 
+
+ align:start position:0%
+that native oxide is often present on
+the polysilicon we have to use a
+
+ align:start position:0%
+the polysilicon we have to use a
+ 
+
+ align:start position:0%
+the polysilicon we have to use a
+breakthrough etch as the initial step of
+
+ align:start position:0%
+breakthrough etch as the initial step of
+ 
+
+ align:start position:0%
+breakthrough etch as the initial step of
+etching otherwise we'll have all kinds
+
+ align:start position:0%
+etching otherwise we'll have all kinds
+ 
+
+ align:start position:0%
+etching otherwise we'll have all kinds
+of um grass
+
+ align:start position:0%
+of um grass
+ 
+
+ align:start position:0%
+of um grass
+problems uh there can be impact of
+
+ align:start position:0%
+problems uh there can be impact of
+ 
+
+ align:start position:0%
+problems uh there can be impact of
+different dopen if you if the dope if
+
+ align:start position:0%
+different dopen if you if the dope if
+ 
+
+ align:start position:0%
+different dopen if you if the dope if
+the gate is doped prior to etching which
+
+ align:start position:0%
+the gate is doped prior to etching which
+ 
+
+ align:start position:0%
+the gate is doped prior to etching which
+it can be if you put down insitu doped
+
+ align:start position:0%
+it can be if you put down insitu doped
+ 
+
+ align:start position:0%
+it can be if you put down insitu doped
+polysilicon the edch rate for a boron or
+
+ align:start position:0%
+polysilicon the edch rate for a boron or
+ 
+
+ align:start position:0%
+polysilicon the edch rate for a boron or
+heavily phosphorous dope poly may be
+
+ align:start position:0%
+heavily phosphorous dope poly may be
+ 
+
+ align:start position:0%
+heavily phosphorous dope poly may be
+different from and it may have different
+
+ align:start position:0%
+different from and it may have different
+ 
+
+ align:start position:0%
+different from and it may have different
+Edge
+
+ align:start position:0%
+Edge
+ 
+
+ align:start position:0%
+Edge
+characteristics um than that of unop so
+
+ align:start position:0%
+characteristics um than that of unop so
+ 
+
+ align:start position:0%
+characteristics um than that of unop so
+you need to take that into account and
+
+ align:start position:0%
+you need to take that into account and
+ 
+
+ align:start position:0%
+you need to take that into account and
+we also mentioned at the very beginning
+
+ align:start position:0%
+we also mentioned at the very beginning
+ 
+
+ align:start position:0%
+we also mentioned at the very beginning
+of the last lecture gate dialectric
+
+ align:start position:0%
+of the last lecture gate dialectric
+ 
+
+ align:start position:0%
+of the last lecture gate dialectric
+damage due to the antenna effect what is
+
+ align:start position:0%
+damage due to the antenna effect what is
+ 
+
+ align:start position:0%
+damage due to the antenna effect what is
+that was you have ions coming down being
+
+ align:start position:0%
+that was you have ions coming down being
+ 
+
+ align:start position:0%
+that was you have ions coming down being
+collected by the gate where do they go
+
+ align:start position:0%
+collected by the gate where do they go
+ 
+
+ align:start position:0%
+collected by the gate where do they go
+well they go they don't go through the
+
+ align:start position:0%
+well they go they don't go through the
+ 
+
+ align:start position:0%
+well they go they don't go through the
+field oxide because that's too thick
+
+ align:start position:0%
+field oxide because that's too thick
+ 
+
+ align:start position:0%
+field oxide because that's too thick
+they get shuttled down the gate and they
+
+ align:start position:0%
+they get shuttled down the gate and they
+ 
+
+ align:start position:0%
+they get shuttled down the gate and they
+go try to um the current tends to go
+
+ align:start position:0%
+go try to um the current tends to go
+ 
+
+ align:start position:0%
+go try to um the current tends to go
+through the gate oxide you have to be
+
+ align:start position:0%
+through the gate oxide you have to be
+ 
+
+ align:start position:0%
+through the gate oxide you have to be
+careful that you don't um put too much
+
+ align:start position:0%
+careful that you don't um put too much
+ 
+
+ align:start position:0%
+careful that you don't um put too much
+current through your gate oxide and
+
+ align:start position:0%
+current through your gate oxide and
+ 
+
+ align:start position:0%
+current through your gate oxide and
+damage it so those are some basic issues
+
+ align:start position:0%
+damage it so those are some basic issues
+ 
+
+ align:start position:0%
+damage it so those are some basic issues
+issues when it comes to poly gate
+
+ align:start position:0%
+issues when it comes to poly gate
+ 
+
+ align:start position:0%
+issues when it comes to poly gate
+etching here's an here's an example on
+
+ align:start position:0%
+etching here's an here's an example on
+ 
+
+ align:start position:0%
+etching here's an here's an example on
+slide nine of a gate etcher it's a
+
+ align:start position:0%
+slide nine of a gate etcher it's a
+ 
+
+ align:start position:0%
+slide nine of a gate etcher it's a
+little bit older technology now but at
+
+ align:start position:0%
+little bit older technology now but at
+ 
+
+ align:start position:0%
+little bit older technology now but at
+the time it was designed by a company
+
+ align:start position:0%
+the time it was designed by a company
+ 
+
+ align:start position:0%
+the time it was designed by a company
+called lamb to be dedicated to um uh
+
+ align:start position:0%
+called lamb to be dedicated to um uh
+ 
+
+ align:start position:0%
+called lamb to be dedicated to um uh
+gate etching only it's called the TCP
+
+ align:start position:0%
+gate etching only it's called the TCP
+ 
+
+ align:start position:0%
+gate etching only it's called the TCP
+9400 um It's relatively low pressure low
+
+ align:start position:0%
+9400 um It's relatively low pressure low
+ 
+
+ align:start position:0%
+9400 um It's relatively low pressure low
+bias high density
+
+ align:start position:0%
+bias high density
+ 
+
+ align:start position:0%
+bias high density
+plasma um has a mechanical clamp truck
+
+ align:start position:0%
+plasma um has a mechanical clamp truck
+ 
+
+ align:start position:0%
+plasma um has a mechanical clamp truck
+remember we talked about the importance
+
+ align:start position:0%
+remember we talked about the importance
+ 
+
+ align:start position:0%
+remember we talked about the importance
+of controlling the temperature of the
+
+ align:start position:0%
+of controlling the temperature of the
+ 
+
+ align:start position:0%
+of controlling the temperature of the
+edge to cool the wafer it's got helium
+
+ align:start position:0%
+edge to cool the wafer it's got helium
+ 
+
+ align:start position:0%
+edge to cool the wafer it's got helium
+on the backside this is an example of a
+
+ align:start position:0%
+on the backside this is an example of a
+ 
+
+ align:start position:0%
+on the backside this is an example of a
+wafer that's front end processing only
+
+ align:start position:0%
+wafer that's front end processing only
+ 
+
+ align:start position:0%
+wafer that's front end processing only
+so no metals are allowed to be go into
+
+ align:start position:0%
+so no metals are allowed to be go into
+ 
+
+ align:start position:0%
+so no metals are allowed to be go into
+the into the uh tool and it you can get
+
+ align:start position:0%
+the into the uh tool and it you can get
+ 
+
+ align:start position:0%
+the into the uh tool and it you can get
+an etch rate of the What's called the
+
+ align:start position:0%
+an etch rate of the What's called the
+ 
+
+ align:start position:0%
+an etch rate of the What's called the
+main etch that's pretty fast in fact
+
+ align:start position:0%
+main etch that's pretty fast in fact
+ 
+
+ align:start position:0%
+main etch that's pretty fast in fact
+higher than you probably need in most
+
+ align:start position:0%
+higher than you probably need in most
+ 
+
+ align:start position:0%
+higher than you probably need in most
+etches today uh the height of the poly
+
+ align:start position:0%
+etches today uh the height of the poly
+ 
+
+ align:start position:0%
+etches today uh the height of the poly
+today is probably only a th000 Anum and
+
+ align:start position:0%
+today is probably only a th000 Anum and
+ 
+
+ align:start position:0%
+today is probably only a th000 Anum and
+this goes at at uh 320 nanometers per
+
+ align:start position:0%
+this goes at at uh 320 nanometers per
+ 
+
+ align:start position:0%
+this goes at at uh 320 nanometers per
+minute so quite uh quite efficient
+
+ align:start position:0%
+minute so quite uh quite efficient
+ 
+
+ align:start position:0%
+minute so quite uh quite efficient
+etching for poly Gates and can give you
+
+ align:start position:0%
+etching for poly Gates and can give you
+ 
+
+ align:start position:0%
+etching for poly Gates and can give you
+the kind of profile shape and activity
+
+ align:start position:0%
+the kind of profile shape and activity
+ 
+
+ align:start position:0%
+the kind of profile shape and activity
+that you
+
+ align:start position:0%
+that you
+ 
+
+ align:start position:0%
+that you
+need if we go on to SL slide 10 this is
+
+ align:start position:0%
+need if we go on to SL slide 10 this is
+ 
+
+ align:start position:0%
+need if we go on to SL slide 10 this is
+just an example of a recipe if we were
+
+ align:start position:0%
+just an example of a recipe if we were
+ 
+
+ align:start position:0%
+just an example of a recipe if we were
+to use that lamb TCP 9400 gate eter uh I
+
+ align:start position:0%
+to use that lamb TCP 9400 gate eter uh I
+ 
+
+ align:start position:0%
+to use that lamb TCP 9400 gate eter uh I
+took this off the Stanford uh website
+
+ align:start position:0%
+took this off the Stanford uh website
+ 
+
+ align:start position:0%
+took this off the Stanford uh website
+this is an actual recipe that they have
+
+ align:start position:0%
+this is an actual recipe that they have
+ 
+
+ align:start position:0%
+this is an actual recipe that they have
+published um showing the individual
+
+ align:start position:0%
+published um showing the individual
+ 
+
+ align:start position:0%
+published um showing the individual
+steps that you would need to use just to
+
+ align:start position:0%
+steps that you would need to use just to
+ 
+
+ align:start position:0%
+steps that you would need to use just to
+give you an idea of some of the
+
+ align:start position:0%
+give you an idea of some of the
+ 
+
+ align:start position:0%
+give you an idea of some of the
+complexity of this etch process now each
+
+ align:start position:0%
+complexity of this etch process now each
+ 
+
+ align:start position:0%
+complexity of this etch process now each
+step they're numbered here 1 through
+
+ align:start position:0%
+step they're numbered here 1 through
+ 
+
+ align:start position:0%
+step they're numbered here 1 through
+nine corresponds to a different time
+
+ align:start position:0%
+nine corresponds to a different time
+ 
+
+ align:start position:0%
+nine corresponds to a different time
+sequence um you know uh different step
+
+ align:start position:0%
+sequence um you know uh different step
+ 
+
+ align:start position:0%
+sequence um you know uh different step
+in the time sequence for the edge so the
+
+ align:start position:0%
+in the time sequence for the edge so the
+ 
+
+ align:start position:0%
+in the time sequence for the edge so the
+very first step label number one um
+
+ align:start position:0%
+very first step label number one um
+ 
+
+ align:start position:0%
+very first step label number one um
+you're adjusting uh the Gap uh which is
+
+ align:start position:0%
+you're adjusting uh the Gap uh which is
+ 
+
+ align:start position:0%
+you're adjusting uh the Gap uh which is
+a parameter inside the tool U the
+
+ align:start position:0%
+a parameter inside the tool U the
+ 
+
+ align:start position:0%
+a parameter inside the tool U the
+pressure is being stabilized at 13 milor
+
+ align:start position:0%
+pressure is being stabilized at 13 milor
+ 
+
+ align:start position:0%
+pressure is being stabilized at 13 milor
+uh automatically by the computer uh and
+
+ align:start position:0%
+uh automatically by the computer uh and
+ 
+
+ align:start position:0%
+uh automatically by the computer uh and
+you're setting up um to uh flow some of
+
+ align:start position:0%
+you're setting up um to uh flow some of
+ 
+
+ align:start position:0%
+you're setting up um to uh flow some of
+your initial gas you're flowing C2 F6 um
+
+ align:start position:0%
+your initial gas you're flowing C2 F6 um
+ 
+
+ align:start position:0%
+your initial gas you're flowing C2 F6 um
+and once you've stabilized U after 20
+
+ align:start position:0%
+and once you've stabilized U after 20
+ 
+
+ align:start position:0%
+and once you've stabilized U after 20
+seconds you go on to the next step
+
+ align:start position:0%
+seconds you go on to the next step
+ 
+
+ align:start position:0%
+seconds you go on to the next step
+okay so the next step is uh step number
+
+ align:start position:0%
+okay so the next step is uh step number
+ 
+
+ align:start position:0%
+okay so the next step is uh step number
+two you're clamping the wafer
+
+ align:start position:0%
+two you're clamping the wafer
+ 
+
+ align:start position:0%
+two you're clamping the wafer
+mechanically to the chuck to get good um
+
+ align:start position:0%
+mechanically to the chuck to get good um
+ 
+
+ align:start position:0%
+mechanically to the chuck to get good um
+you know uh uh control of the
+
+ align:start position:0%
+you know uh uh control of the
+ 
+
+ align:start position:0%
+you know uh uh control of the
+temperature and um you have uh you know
+
+ align:start position:0%
+temperature and um you have uh you know
+ 
+
+ align:start position:0%
+temperature and um you have uh you know
+certain characteristics in that
+
+ align:start position:0%
+certain characteristics in that
+ 
+
+ align:start position:0%
+certain characteristics in that
+step uh so that lasts about 20 seconds
+
+ align:start position:0%
+step uh so that lasts about 20 seconds
+ 
+
+ align:start position:0%
+step uh so that lasts about 20 seconds
+the next is step three is the first etch
+
+ align:start position:0%
+the next is step three is the first etch
+ 
+
+ align:start position:0%
+the next is step three is the first etch
+remember we mentioned when you're using
+
+ align:start position:0%
+remember we mentioned when you're using
+ 
+
+ align:start position:0%
+remember we mentioned when you're using
+a gas that's highly selective you need
+
+ align:start position:0%
+a gas that's highly selective you need
+ 
+
+ align:start position:0%
+a gas that's highly selective you need
+to first start out with a breakthrough
+
+ align:start position:0%
+to first start out with a breakthrough
+ 
+
+ align:start position:0%
+to first start out with a breakthrough
+etch to get through the native oxide
+
+ align:start position:0%
+etch to get through the native oxide
+ 
+
+ align:start position:0%
+etch to get through the native oxide
+here you're etching for about 10 seconds
+
+ align:start position:0%
+here you're etching for about 10 seconds
+ 
+
+ align:start position:0%
+here you're etching for about 10 seconds
+seconds um based on and you you edge
+
+ align:start position:0%
+seconds um based on and you you edge
+ 
+
+ align:start position:0%
+seconds um based on and you you edge
+just for based on time you're flowing C2
+
+ align:start position:0%
+just for based on time you're flowing C2
+ 
+
+ align:start position:0%
+just for based on time you're flowing C2
+F6 uh Al together with uh I guess that's
+
+ align:start position:0%
+F6 uh Al together with uh I guess that's
+ 
+
+ align:start position:0%
+F6 uh Al together with uh I guess that's
+the only thing you're flowing and you've
+
+ align:start position:0%
+the only thing you're flowing and you've
+ 
+
+ align:start position:0%
+the only thing you're flowing and you've
+got um RF power on the top and bottom
+
+ align:start position:0%
+got um RF power on the top and bottom
+ 
+
+ align:start position:0%
+got um RF power on the top and bottom
+250 and 40 watts and your pressure is 13
+
+ align:start position:0%
+250 and 40 watts and your pressure is 13
+ 
+
+ align:start position:0%
+250 and 40 watts and your pressure is 13
+millor so this should break through any
+
+ align:start position:0%
+millor so this should break through any
+ 
+
+ align:start position:0%
+millor so this should break through any
+native oxide for about 10
+
+ align:start position:0%
+native oxide for about 10
+ 
+
+ align:start position:0%
+native oxide for about 10
+seconds um and then the next step is
+
+ align:start position:0%
+seconds um and then the next step is
+ 
+
+ align:start position:0%
+seconds um and then the next step is
+four you need to stabilize the gas flows
+
+ align:start position:0%
+four you need to stabilize the gas flows
+ 
+
+ align:start position:0%
+four you need to stabilize the gas flows
+before the main Edge the main Edge is
+
+ align:start position:0%
+before the main Edge the main Edge is
+ 
+
+ align:start position:0%
+before the main Edge the main Edge is
+The Edge that's going to etge the
+
+ align:start position:0%
+The Edge that's going to etge the
+ 
+
+ align:start position:0%
+The Edge that's going to etge the
+polysilicon so you turn on different
+
+ align:start position:0%
+polysilicon so you turn on different
+ 
+
+ align:start position:0%
+polysilicon so you turn on different
+gases you turn off the C2 F6 you turn on
+
+ align:start position:0%
+gases you turn off the C2 F6 you turn on
+ 
+
+ align:start position:0%
+gases you turn off the C2 F6 you turn on
+the chlorine mixture of chlorine and hbr
+
+ align:start position:0%
+the chlorine mixture of chlorine and hbr
+ 
+
+ align:start position:0%
+the chlorine mixture of chlorine and hbr
+and oxygen that's what we call the main
+
+ align:start position:0%
+and oxygen that's what we call the main
+ 
+
+ align:start position:0%
+and oxygen that's what we call the main
+Edge that's going to do most of the work
+
+ align:start position:0%
+Edge that's going to do most of the work
+ 
+
+ align:start position:0%
+Edge that's going to do most of the work
+in getting you through the polycrystal
+
+ align:start position:0%
+in getting you through the polycrystal
+ 
+
+ align:start position:0%
+in getting you through the polycrystal
+and silicon uh so you're just
+
+ align:start position:0%
+and silicon uh so you're just
+ 
+
+ align:start position:0%
+and silicon uh so you're just
+stabilizing at this point you notice
+
+ align:start position:0%
+stabilizing at this point you notice
+ 
+
+ align:start position:0%
+stabilizing at this point you notice
+there's no power on the top and bottom
+
+ align:start position:0%
+there's no power on the top and bottom
+ 
+
+ align:start position:0%
+there's no power on the top and bottom
+electrodes so you're not actually the
+
+ align:start position:0%
+electrodes so you're not actually the
+ 
+
+ align:start position:0%
+electrodes so you're not actually the
+Plasma's not on so you don't you're not
+
+ align:start position:0%
+Plasma's not on so you don't you're not
+ 
+
+ align:start position:0%
+Plasma's not on so you don't you're not
+lighting a plasma you're just
+
+ align:start position:0%
+lighting a plasma you're just
+ 
+
+ align:start position:0%
+lighting a plasma you're just
+stabilizing the flows through the
+
+ align:start position:0%
+stabilizing the flows through the
+ 
+
+ align:start position:0%
+stabilizing the flows through the
+chamber and that takes a while uh in
+
+ align:start position:0%
+chamber and that takes a while uh in
+ 
+
+ align:start position:0%
+chamber and that takes a while uh in
+this condition in this particular case
+
+ align:start position:0%
+this condition in this particular case
+ 
+
+ align:start position:0%
+this condition in this particular case
+stabilization step is about 20 seconds
+
+ align:start position:0%
+stabilization step is about 20 seconds
+ 
+
+ align:start position:0%
+stabilization step is about 20 seconds
+just gives you time to get the chamber
+
+ align:start position:0%
+just gives you time to get the chamber
+ 
+
+ align:start position:0%
+just gives you time to get the chamber
+get the old gases purged out from the uh
+
+ align:start position:0%
+get the old gases purged out from the uh
+ 
+
+ align:start position:0%
+get the old gases purged out from the uh
+prior Edge which was um the Breakthrough
+
+ align:start position:0%
+prior Edge which was um the Breakthrough
+ 
+
+ align:start position:0%
+prior Edge which was um the Breakthrough
+Edge and get the new ones purged in and
+
+ align:start position:0%
+Edge and get the new ones purged in and
+ 
+
+ align:start position:0%
+Edge and get the new ones purged in and
+establish your pressure of 10 millor
+
+ align:start position:0%
+establish your pressure of 10 millor
+ 
+
+ align:start position:0%
+establish your pressure of 10 millor
+then you actually do the main Edge so
+
+ align:start position:0%
+then you actually do the main Edge so
+ 
+
+ align:start position:0%
+then you actually do the main Edge so
+here you turn the Plasma on by turning
+
+ align:start position:0%
+here you turn the Plasma on by turning
+ 
+
+ align:start position:0%
+here you turn the Plasma on by turning
+the power onto the top and bottom
+
+ align:start position:0%
+the power onto the top and bottom
+ 
+
+ align:start position:0%
+the power onto the top and bottom
+electrodes so the plasma is now lit and
+
+ align:start position:0%
+electrodes so the plasma is now lit and
+ 
+
+ align:start position:0%
+electrodes so the plasma is now lit and
+you're actually etching here for a time
+
+ align:start position:0%
+you're actually etching here for a time
+ 
+
+ align:start position:0%
+you're actually etching here for a time
+of in this particular example 60 seconds
+
+ align:start position:0%
+of in this particular example 60 seconds
+ 
+
+ align:start position:0%
+of in this particular example 60 seconds
+You etge by time so it's a 60c etch uh
+
+ align:start position:0%
+You etge by time so it's a 60c etch uh
+ 
+
+ align:start position:0%
+You etge by time so it's a 60c etch uh
+and then you move to the last
+
+ align:start position:0%
+and then you move to the last
+ 
+
+ align:start position:0%
+and then you move to the last
+stabilization now and and you're
+
+ align:start position:0%
+stabilization now and and you're
+ 
+
+ align:start position:0%
+stabilization now and and you're
+stabilizing to get ready for What's
+
+ align:start position:0%
+stabilizing to get ready for What's
+ 
+
+ align:start position:0%
+stabilizing to get ready for What's
+called the overetch so there's a
+
+ align:start position:0%
+called the overetch so there's a
+ 
+
+ align:start position:0%
+called the overetch so there's a
+breakthrough edch to get through the
+
+ align:start position:0%
+breakthrough edch to get through the
+ 
+
+ align:start position:0%
+breakthrough edch to get through the
+native oxide there's a main edch which
+
+ align:start position:0%
+native oxide there's a main edch which
+ 
+
+ align:start position:0%
+native oxide there's a main edch which
+does most the work now the over etch is
+
+ align:start position:0%
+does most the work now the over etch is
+ 
+
+ align:start position:0%
+does most the work now the over etch is
+the amount of time you need remember
+
+ align:start position:0%
+the amount of time you need remember
+ 
+
+ align:start position:0%
+the amount of time you need remember
+where you pretty much hit the bottom but
+
+ align:start position:0%
+where you pretty much hit the bottom but
+ 
+
+ align:start position:0%
+where you pretty much hit the bottom but
+you may have stringers or other things
+
+ align:start position:0%
+you may have stringers or other things
+ 
+
+ align:start position:0%
+you may have stringers or other things
+uh so the over typically has to have
+
+ align:start position:0%
+uh so the over typically has to have
+ 
+
+ align:start position:0%
+uh so the over typically has to have
+even greater selectivity than the main
+
+ align:start position:0%
+even greater selectivity than the main
+ 
+
+ align:start position:0%
+even greater selectivity than the main
+edch and so the overetch in this example
+
+ align:start position:0%
+edch and so the overetch in this example
+ 
+
+ align:start position:0%
+edch and so the overetch in this example
+you notice they remove the chlorine so
+
+ align:start position:0%
+you notice they remove the chlorine so
+ 
+
+ align:start position:0%
+you notice they remove the chlorine so
+the chlorine flow which was 40 CCM has
+
+ align:start position:0%
+the chlorine flow which was 40 CCM has
+ 
+
+ align:start position:0%
+the chlorine flow which was 40 CCM has
+been removed and you just have hbr and
+
+ align:start position:0%
+been removed and you just have hbr and
+ 
+
+ align:start position:0%
+been removed and you just have hbr and
+O2 this gives you a much higher
+
+ align:start position:0%
+O2 this gives you a much higher
+ 
+
+ align:start position:0%
+O2 this gives you a much higher
+selectivity maybe not as good of an etch
+
+ align:start position:0%
+selectivity maybe not as good of an etch
+ 
+
+ align:start position:0%
+selectivity maybe not as good of an etch
+rate uh but it does have very high
+
+ align:start position:0%
+rate uh but it does have very high
+ 
+
+ align:start position:0%
+rate uh but it does have very high
+selectivity um so that you will not
+
+ align:start position:0%
+selectivity um so that you will not
+ 
+
+ align:start position:0%
+selectivity um so that you will not
+break through that oxide and then you do
+
+ align:start position:0%
+break through that oxide and then you do
+ 
+
+ align:start position:0%
+break through that oxide and then you do
+the over Etch in this step where you
+
+ align:start position:0%
+the over Etch in this step where you
+ 
+
+ align:start position:0%
+the over Etch in this step where you
+light the plasma for 30 seconds uh using
+
+ align:start position:0%
+light the plasma for 30 seconds uh using
+ 
+
+ align:start position:0%
+light the plasma for 30 seconds uh using
+just a mixture of hbr and
+
+ align:start position:0%
+just a mixture of hbr and
+ 
+
+ align:start position:0%
+just a mixture of hbr and
+O2 you then unclamp the wafer the plasma
+
+ align:start position:0%
+O2 you then unclamp the wafer the plasma
+ 
+
+ align:start position:0%
+O2 you then unclamp the wafer the plasma
+goes off after those 30 seconds you
+
+ align:start position:0%
+goes off after those 30 seconds you
+ 
+
+ align:start position:0%
+goes off after those 30 seconds you
+unclamp the wafer and then you end and
+
+ align:start position:0%
+unclamp the wafer and then you end and
+ 
+
+ align:start position:0%
+unclamp the wafer and then you end and
+you're ready to
+
+ align:start position:0%
+you're ready to
+ 
+
+ align:start position:0%
+you're ready to
+unload so you know it's it's all
+
+ align:start position:0%
+unload so you know it's it's all
+ 
+
+ align:start position:0%
+unload so you know it's it's all
+computer controlled um you have in this
+
+ align:start position:0%
+computer controlled um you have in this
+ 
+
+ align:start position:0%
+computer controlled um you have in this
+example of just etching poly silic you
+
+ align:start position:0%
+example of just etching poly silic you
+ 
+
+ align:start position:0%
+example of just etching poly silic you
+have three types of etches a
+
+ align:start position:0%
+have three types of etches a
+ 
+
+ align:start position:0%
+have three types of etches a
+breakthrough a man and an over etch have
+
+ align:start position:0%
+breakthrough a man and an over etch have
+ 
+
+ align:start position:0%
+breakthrough a man and an over etch have
+stabilization steps in between uh and uh
+
+ align:start position:0%
+stabilization steps in between uh and uh
+ 
+
+ align:start position:0%
+stabilization steps in between uh and uh
+this this is an example and then you
+
+ align:start position:0%
+this this is an example and then you
+ 
+
+ align:start position:0%
+this this is an example and then you
+come out and you look at your etch rate
+
+ align:start position:0%
+come out and you look at your etch rate
+ 
+
+ align:start position:0%
+come out and you look at your etch rate
+and your sidewall profile and you see
+
+ align:start position:0%
+and your sidewall profile and you see
+ 
+
+ align:start position:0%
+and your sidewall profile and you see
+how it looks most etches as we said end
+
+ align:start position:0%
+how it looks most etches as we said end
+ 
+
+ align:start position:0%
+how it looks most etches as we said end
+up leaving a sidewall polymer that's
+
+ align:start position:0%
+up leaving a sidewall polymer that's
+ 
+
+ align:start position:0%
+up leaving a sidewall polymer that's
+either um like a hydrocarbon based or it
+
+ align:start position:0%
+either um like a hydrocarbon based or it
+ 
+
+ align:start position:0%
+either um like a hydrocarbon based or it
+might be a glass based like an oxide
+
+ align:start position:0%
+might be a glass based like an oxide
+ 
+
+ align:start position:0%
+might be a glass based like an oxide
+like based material that is what's
+
+ align:start position:0%
+like based material that is what's
+ 
+
+ align:start position:0%
+like based material that is what's
+responsible remember it's the inhibitor
+
+ align:start position:0%
+responsible remember it's the inhibitor
+ 
+
+ align:start position:0%
+responsible remember it's the inhibitor
+layer that keeps you from etching
+
+ align:start position:0%
+layer that keeps you from etching
+ 
+
+ align:start position:0%
+layer that keeps you from etching
+sideways that's what gives you such
+
+ align:start position:0%
+sideways that's what gives you such
+ 
+
+ align:start position:0%
+sideways that's what gives you such
+perfectly vertical side walls you must
+
+ align:start position:0%
+perfectly vertical side walls you must
+ 
+
+ align:start position:0%
+perfectly vertical side walls you must
+have that inhibitor layer the question
+
+ align:start position:0%
+have that inhibitor layer the question
+ 
+
+ align:start position:0%
+have that inhibitor layer the question
+is what do you do with that inhibitor
+
+ align:start position:0%
+is what do you do with that inhibitor
+ 
+
+ align:start position:0%
+is what do you do with that inhibitor
+layer now that it's on your wafer every
+
+ align:start position:0%
+layer now that it's on your wafer every
+ 
+
+ align:start position:0%
+layer now that it's on your wafer every
+single gate has some goop whatever it
+
+ align:start position:0%
+single gate has some goop whatever it
+ 
+
+ align:start position:0%
+single gate has some goop whatever it
+might be sidewall junk uh polymer
+
+ align:start position:0%
+might be sidewall junk uh polymer
+ 
+
+ align:start position:0%
+might be sidewall junk uh polymer
+whatever you want to call it you need to
+
+ align:start position:0%
+whatever you want to call it you need to
+ 
+
+ align:start position:0%
+whatever you want to call it you need to
+do a post Ed cleanup process after that
+
+ align:start position:0%
+do a post Ed cleanup process after that
+ 
+
+ align:start position:0%
+do a post Ed cleanup process after that
+because that inhibitor layer is there uh
+
+ align:start position:0%
+because that inhibitor layer is there uh
+ 
+
+ align:start position:0%
+because that inhibitor layer is there uh
+if you go into a Tem or something you
+
+ align:start position:0%
+if you go into a Tem or something you
+ 
+
+ align:start position:0%
+if you go into a Tem or something you
+can see it what you'll see is or maybe
+
+ align:start position:0%
+can see it what you'll see is or maybe
+ 
+
+ align:start position:0%
+can see it what you'll see is or maybe
+even in an SCM you'll see your
+
+ align:start position:0%
+even in an SCM you'll see your
+ 
+
+ align:start position:0%
+even in an SCM you'll see your
+polysilicon gate and you'll see some
+
+ align:start position:0%
+polysilicon gate and you'll see some
+ 
+
+ align:start position:0%
+polysilicon gate and you'll see some
+material maybe that looks like this some
+
+ align:start position:0%
+material maybe that looks like this some
+ 
+
+ align:start position:0%
+material maybe that looks like this some
+maybe amorphous looking material very
+
+ align:start position:0%
+maybe amorphous looking material very
+ 
+
+ align:start position:0%
+maybe amorphous looking material very
+thin it might only be uh 20 angstroms
+
+ align:start position:0%
+thin it might only be uh 20 angstroms
+ 
+
+ align:start position:0%
+thin it might only be uh 20 angstroms
+something like that it's very thin
+
+ align:start position:0%
+something like that it's very thin
+ 
+
+ align:start position:0%
+something like that it's very thin
+thickness may vary from top to bottom
+
+ align:start position:0%
+thickness may vary from top to bottom
+ 
+
+ align:start position:0%
+thickness may vary from top to bottom
+whatever but that's that's an inhibitor
+
+ align:start position:0%
+whatever but that's that's an inhibitor
+ 
+
+ align:start position:0%
+whatever but that's that's an inhibitor
+layer um that is what gave you that
+
+ align:start position:0%
+layer um that is what gave you that
+ 
+
+ align:start position:0%
+layer um that is what gave you that
+sidewall but typically it's removed by
+
+ align:start position:0%
+sidewall but typically it's removed by
+ 
+
+ align:start position:0%
+sidewall but typically it's removed by
+either an HF dip or HF combined with
+
+ align:start position:0%
+either an HF dip or HF combined with
+ 
+
+ align:start position:0%
+either an HF dip or HF combined with
+piranha
+
+ align:start position:0%
+piranha
+ 
+
+ align:start position:0%
+piranha
+if it's um some kind of hydrocarbon you
+
+ align:start position:0%
+if it's um some kind of hydrocarbon you
+ 
+
+ align:start position:0%
+if it's um some kind of hydrocarbon you
+need the extra piranha uh these are
+
+ align:start position:0%
+need the extra piranha uh these are
+ 
+
+ align:start position:0%
+need the extra piranha uh these are
+typically not things you want to leave
+
+ align:start position:0%
+typically not things you want to leave
+ 
+
+ align:start position:0%
+typically not things you want to leave
+on there they can introduce contaminants
+
+ align:start position:0%
+on there they can introduce contaminants
+ 
+
+ align:start position:0%
+on there they can introduce contaminants
+in in subsequent
+
+ align:start position:0%
+in in subsequent
+ 
+
+ align:start position:0%
+in in subsequent
+steps so you have to do a cleanup
+
+ align:start position:0%
+steps so you have to do a cleanup
+ 
+
+ align:start position:0%
+steps so you have to do a cleanup
+process okay so that's just an example
+
+ align:start position:0%
+process okay so that's just an example
+ 
+
+ align:start position:0%
+process okay so that's just an example
+of using a dedicated gate etcher of how
+
+ align:start position:0%
+of using a dedicated gate etcher of how
+ 
+
+ align:start position:0%
+of using a dedicated gate etcher of how
+you would etch a polysilicon gate um
+
+ align:start position:0%
+you would etch a polysilicon gate um
+ 
+
+ align:start position:0%
+you would etch a polysilicon gate um
+let's just talk about a couple of the
+
+ align:start position:0%
+let's just talk about a couple of the
+ 
+
+ align:start position:0%
+let's just talk about a couple of the
+characteristics people often see and if
+
+ align:start position:0%
+characteristics people often see and if
+ 
+
+ align:start position:0%
+characteristics people often see and if
+you do gate itching this is what you
+
+ align:start position:0%
+you do gate itching this is what you
+ 
+
+ align:start position:0%
+you do gate itching this is what you
+will be up against um here's an example
+
+ align:start position:0%
+will be up against um here's an example
+ 
+
+ align:start position:0%
+will be up against um here's an example
+of what's called notching at the bottom
+
+ align:start position:0%
+of what's called notching at the bottom
+ 
+
+ align:start position:0%
+of what's called notching at the bottom
+of the polysilicon gate it's probably a
+
+ align:start position:0%
+of the polysilicon gate it's probably a
+ 
+
+ align:start position:0%
+of the polysilicon gate it's probably a
+little bit hard to see this is not the
+
+ align:start position:0%
+little bit hard to see this is not the
+ 
+
+ align:start position:0%
+little bit hard to see this is not the
+greatest micrograph these are SCM
+
+ align:start position:0%
+greatest micrograph these are SCM
+ 
+
+ align:start position:0%
+greatest micrograph these are SCM
+cross-sections these line widths from
+
+ align:start position:0%
+cross-sections these line widths from
+ 
+
+ align:start position:0%
+cross-sections these line widths from
+here to here is Nally 02 microns from
+
+ align:start position:0%
+here to here is Nally 02 microns from
+ 
+
+ align:start position:0%
+here to here is Nally 02 microns from
+this point to that point so it's a
+
+ align:start position:0%
+this point to that point so it's a
+ 
+
+ align:start position:0%
+this point to that point so it's a
+polysilicon uh line uh and this is using
+
+ align:start position:0%
+polysilicon uh line uh and this is using
+ 
+
+ align:start position:0%
+polysilicon uh line uh and this is using
+a sort of a standard flow rate and
+
+ align:start position:0%
+a sort of a standard flow rate and
+ 
+
+ align:start position:0%
+a sort of a standard flow rate and
+here's where they modified the flow rate
+
+ align:start position:0%
+here's where they modified the flow rate
+ 
+
+ align:start position:0%
+here's where they modified the flow rate
+making a little bit higher and if you
+
+ align:start position:0%
+making a little bit higher and if you
+ 
+
+ align:start position:0%
+making a little bit higher and if you
+notice the the gate looks sort of
+
+ align:start position:0%
+notice the the gate looks sort of
+ 
+
+ align:start position:0%
+notice the the gate looks sort of
+straight and then it goes down it kind
+
+ align:start position:0%
+straight and then it goes down it kind
+ 
+
+ align:start position:0%
+straight and then it goes down it kind
+of goes in at the bottom like a little
+
+ align:start position:0%
+of goes in at the bottom like a little
+ 
+
+ align:start position:0%
+of goes in at the bottom like a little
+Notch um this is considered to be
+
+ align:start position:0%
+Notch um this is considered to be
+ 
+
+ align:start position:0%
+Notch um this is considered to be
+undesirable in in many cases you
+
+ align:start position:0%
+undesirable in in many cases you
+ 
+
+ align:start position:0%
+undesirable in in many cases you
+typically want the gate sidewall to go
+
+ align:start position:0%
+typically want the gate sidewall to go
+ 
+
+ align:start position:0%
+typically want the gate sidewall to go
+straight
+
+ align:start position:0%
+straight
+ 
+
+ align:start position:0%
+straight
+down why would you not want the gate to
+
+ align:start position:0%
+down why would you not want the gate to
+ 
+
+ align:start position:0%
+down why would you not want the gate to
+be notched um well there's some examples
+
+ align:start position:0%
+be notched um well there's some examples
+ 
+
+ align:start position:0%
+be notched um well there's some examples
+uh of what it might do let's say your
+
+ align:start position:0%
+uh of what it might do let's say your
+ 
+
+ align:start position:0%
+uh of what it might do let's say your
+gate did go in like this so you have it
+
+ align:start position:0%
+gate did go in like this so you have it
+ 
+
+ align:start position:0%
+gate did go in like this so you have it
+vertical and then it kind of I'm going
+
+ align:start position:0%
+vertical and then it kind of I'm going
+ 
+
+ align:start position:0%
+vertical and then it kind of I'm going
+to make it worse I'll make the notch
+
+ align:start position:0%
+to make it worse I'll make the notch
+ 
+
+ align:start position:0%
+to make it worse I'll make the notch
+look really bad so um it might look like
+
+ align:start position:0%
+look really bad so um it might look like
+ 
+
+ align:start position:0%
+look really bad so um it might look like
+that down here and something like that
+
+ align:start position:0%
+that down here and something like that
+ 
+
+ align:start position:0%
+that down here and something like that
+well the problem with notching like that
+
+ align:start position:0%
+well the problem with notching like that
+ 
+
+ align:start position:0%
+well the problem with notching like that
+is uh when you go to do your iron
+
+ align:start position:0%
+is uh when you go to do your iron
+ 
+
+ align:start position:0%
+is uh when you go to do your iron
+implant depending on what angle I'm
+
+ align:start position:0%
+implant depending on what angle I'm
+ 
+
+ align:start position:0%
+implant depending on what angle I'm
+going to implant the source and drain
+
+ align:start position:0%
+going to implant the source and drain
+ 
+
+ align:start position:0%
+going to implant the source and drain
+depending on what angle and how bad the
+
+ align:start position:0%
+depending on what angle and how bad the
+ 
+
+ align:start position:0%
+depending on what angle and how bad the
+um the uh notching is your IR implant
+
+ align:start position:0%
+um the uh notching is your IR implant
+ 
+
+ align:start position:0%
+um the uh notching is your IR implant
+might end up looking like
+
+ align:start position:0%
+might end up looking like
+ 
+
+ align:start position:0%
+might end up looking like
+this so there might be a little region
+
+ align:start position:0%
+this so there might be a little region
+ 
+
+ align:start position:0%
+this so there might be a little region
+on either side where you don't get the
+
+ align:start position:0%
+on either side where you don't get the
+ 
+
+ align:start position:0%
+on either side where you don't get the
+source and drain extensions don't
+
+ align:start position:0%
+source and drain extensions don't
+ 
+
+ align:start position:0%
+source and drain extensions don't
+actually get implanted and where there's
+
+ align:start position:0%
+actually get implanted and where there's
+ 
+
+ align:start position:0%
+actually get implanted and where there's
+no gate okay now you say well I just do
+
+ align:start position:0%
+no gate okay now you say well I just do
+ 
+
+ align:start position:0%
+no gate okay now you say well I just do
+a high enough temperature anal and then
+
+ align:start position:0%
+a high enough temperature anal and then
+ 
+
+ align:start position:0%
+a high enough temperature anal and then
+this arsenic will move right it'll will
+
+ align:start position:0%
+this arsenic will move right it'll will
+ 
+
+ align:start position:0%
+this arsenic will move right it'll will
+probably overlap you'll probably be okay
+
+ align:start position:0%
+probably overlap you'll probably be okay
+ 
+
+ align:start position:0%
+probably overlap you'll probably be okay
+but what if it doesn't you can't go un
+
+ align:start position:0%
+but what if it doesn't you can't go un
+ 
+
+ align:start position:0%
+but what if it doesn't you can't go un
+probably uh and and if that Notch is not
+
+ align:start position:0%
+probably uh and and if that Notch is not
+ 
+
+ align:start position:0%
+probably uh and and if that Notch is not
+well controlled um you can end up with
+
+ align:start position:0%
+well controlled um you can end up with
+ 
+
+ align:start position:0%
+well controlled um you can end up with
+you know all kinds of High series
+
+ align:start position:0%
+you know all kinds of High series
+ 
+
+ align:start position:0%
+you know all kinds of High series
+resistance in that region so people
+
+ align:start position:0%
+resistance in that region so people
+ 
+
+ align:start position:0%
+resistance in that region so people
+typically don't want to notch because it
+
+ align:start position:0%
+typically don't want to notch because it
+ 
+
+ align:start position:0%
+typically don't want to notch because it
+ends up affecting what happens to the
+
+ align:start position:0%
+ends up affecting what happens to the
+ 
+
+ align:start position:0%
+ends up affecting what happens to the
+iron implant because remember this poly
+
+ align:start position:0%
+iron implant because remember this poly
+ 
+
+ align:start position:0%
+iron implant because remember this poly
+that you're forming this gate is the
+
+ align:start position:0%
+that you're forming this gate is the
+ 
+
+ align:start position:0%
+that you're forming this gate is the
+mask for your next step which is going
+
+ align:start position:0%
+mask for your next step which is going
+ 
+
+ align:start position:0%
+mask for your next step which is going
+to be implant the source and drain
+
+ align:start position:0%
+to be implant the source and drain
+ 
+
+ align:start position:0%
+to be implant the source and drain
+extensions um so this is an example of
+
+ align:start position:0%
+extensions um so this is an example of
+ 
+
+ align:start position:0%
+extensions um so this is an example of
+how they got rid of the notch this Notch
+
+ align:start position:0%
+how they got rid of the notch this Notch
+ 
+
+ align:start position:0%
+how they got rid of the notch this Notch
+is not as bad or doesn't look as
+
+ align:start position:0%
+is not as bad or doesn't look as
+ 
+
+ align:start position:0%
+is not as bad or doesn't look as
+dramatic as the one I drew on the board
+
+ align:start position:0%
+dramatic as the one I drew on the board
+ 
+
+ align:start position:0%
+dramatic as the one I drew on the board
+uh they got rid of it by just changing
+
+ align:start position:0%
+uh they got rid of it by just changing
+ 
+
+ align:start position:0%
+uh they got rid of it by just changing
+um a few things they Chang the pressure
+
+ align:start position:0%
+um a few things they Chang the pressure
+ 
+
+ align:start position:0%
+um a few things they Chang the pressure
+and the flow rate and they're able to
+
+ align:start position:0%
+and the flow rate and they're able to
+ 
+
+ align:start position:0%
+and the flow rate and they're able to
+get a more vertical type of sidewall so
+
+ align:start position:0%
+get a more vertical type of sidewall so
+ 
+
+ align:start position:0%
+get a more vertical type of sidewall so
+if you have to do poly silken Gates you
+
+ align:start position:0%
+if you have to do poly silken Gates you
+ 
+
+ align:start position:0%
+if you have to do poly silken Gates you
+find yourself twiddling a lot of the
+
+ align:start position:0%
+find yourself twiddling a lot of the
+ 
+
+ align:start position:0%
+find yourself twiddling a lot of the
+knobs the pressures the flow rates and
+
+ align:start position:0%
+knobs the pressures the flow rates and
+ 
+
+ align:start position:0%
+knobs the pressures the flow rates and
+things like that until you get a shape
+
+ align:start position:0%
+things like that until you get a shape
+ 
+
+ align:start position:0%
+things like that until you get a shape
+um that you're happy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with uh this is another here on slide 12
+
+ align:start position:0%
+with uh this is another here on slide 12
+ 
+
+ align:start position:0%
+with uh this is another here on slide 12
+is another article I took out of
+
+ align:start position:0%
+is another article I took out of
+ 
+
+ align:start position:0%
+is another article I took out of
+literature uh it's an older paper it's
+
+ align:start position:0%
+literature uh it's an older paper it's
+ 
+
+ align:start position:0%
+literature uh it's an older paper it's
+from applied physics letterers
+
+ align:start position:0%
+from applied physics letterers
+ 
+
+ align:start position:0%
+from applied physics letterers
+and uh what they're making uh a point
+
+ align:start position:0%
+and uh what they're making uh a point
+ 
+
+ align:start position:0%
+and uh what they're making uh a point
+here has to do with something called gas
+
+ align:start position:0%
+here has to do with something called gas
+ 
+
+ align:start position:0%
+here has to do with something called gas
+resonance time in the plasma eter uh
+
+ align:start position:0%
+resonance time in the plasma eter uh
+ 
+
+ align:start position:0%
+resonance time in the plasma eter uh
+this resonance time um concept is also
+
+ align:start position:0%
+this resonance time um concept is also
+ 
+
+ align:start position:0%
+this resonance time um concept is also
+important if you're if you're growing th
+
+ align:start position:0%
+important if you're if you're growing th
+ 
+
+ align:start position:0%
+important if you're if you're growing th
+films uh so it also is important in
+
+ align:start position:0%
+films uh so it also is important in
+ 
+
+ align:start position:0%
+films uh so it also is important in
+reactors and things what it what it is
+
+ align:start position:0%
+reactors and things what it what it is
+ 
+
+ align:start position:0%
+reactors and things what it what it is
+has to do is sort of the amount of time
+
+ align:start position:0%
+has to do is sort of the amount of time
+ 
+
+ align:start position:0%
+has to do is sort of the amount of time
+here in seconds or fraction of a second
+
+ align:start position:0%
+here in seconds or fraction of a second
+ 
+
+ align:start position:0%
+here in seconds or fraction of a second
+effectively that that gas a volume of
+
+ align:start position:0%
+effectively that that gas a volume of
+ 
+
+ align:start position:0%
+effectively that that gas a volume of
+gas is is occupies uh the um the plasma
+
+ align:start position:0%
+gas is is occupies uh the um the plasma
+ 
+
+ align:start position:0%
+gas is is occupies uh the um the plasma
+etcher itself so and you you can see
+
+ align:start position:0%
+etcher itself so and you you can see
+ 
+
+ align:start position:0%
+etcher itself so and you you can see
+that resonance time increases so it goes
+
+ align:start position:0%
+that resonance time increases so it goes
+ 
+
+ align:start position:0%
+that resonance time increases so it goes
+up uh with each one of these lines as I
+
+ align:start position:0%
+up uh with each one of these lines as I
+ 
+
+ align:start position:0%
+up uh with each one of these lines as I
+go to higher and higher pressure or it
+
+ align:start position:0%
+go to higher and higher pressure or it
+ 
+
+ align:start position:0%
+go to higher and higher pressure or it
+decreases as I go to lower flows um and
+
+ align:start position:0%
+decreases as I go to lower flows um and
+ 
+
+ align:start position:0%
+decreases as I go to lower flows um and
+um as I go to lower pressures and um as
+
+ align:start position:0%
+um as I go to lower pressures and um as
+ 
+
+ align:start position:0%
+um as I go to lower pressures and um as
+I increase uh the flow rate it goes down
+
+ align:start position:0%
+I increase uh the flow rate it goes down
+ 
+
+ align:start position:0%
+I increase uh the flow rate it goes down
+so you're flowing through faster now why
+
+ align:start position:0%
+so you're flowing through faster now why
+ 
+
+ align:start position:0%
+so you're flowing through faster now why
+would we care about the gas resonance
+
+ align:start position:0%
+would we care about the gas resonance
+ 
+
+ align:start position:0%
+would we care about the gas resonance
+time well we do care about it because
+
+ align:start position:0%
+time well we do care about it because
+ 
+
+ align:start position:0%
+time well we do care about it because
+the amount of time the gas the fresh gas
+
+ align:start position:0%
+the amount of time the gas the fresh gas
+ 
+
+ align:start position:0%
+the amount of time the gas the fresh gas
+is sort of Resident has to do with the
+
+ align:start position:0%
+is sort of Resident has to do with the
+ 
+
+ align:start position:0%
+is sort of Resident has to do with the
+amount of time the gas is available to
+
+ align:start position:0%
+amount of time the gas is available to
+ 
+
+ align:start position:0%
+amount of time the gas is available to
+actually do etching um and if you if you
+
+ align:start position:0%
+actually do etching um and if you if you
+ 
+
+ align:start position:0%
+actually do etching um and if you if you
+have a very long resonance time uh
+
+ align:start position:0%
+have a very long resonance time uh
+ 
+
+ align:start position:0%
+have a very long resonance time uh
+byproducts can develop you know actually
+
+ align:start position:0%
+byproducts can develop you know actually
+ 
+
+ align:start position:0%
+byproducts can develop you know actually
+after all these etch reactions are
+
+ align:start position:0%
+after all these etch reactions are
+ 
+
+ align:start position:0%
+after all these etch reactions are
+chemical reactions they they evolve
+
+ align:start position:0%
+chemical reactions they they evolve
+ 
+
+ align:start position:0%
+chemical reactions they they evolve
+byproducts those byproducts can then sit
+
+ align:start position:0%
+byproducts those byproducts can then sit
+ 
+
+ align:start position:0%
+byproducts those byproducts can then sit
+and develop there for period of
+
+ align:start position:0%
+and develop there for period of
+ 
+
+ align:start position:0%
+and develop there for period of
+fractions of a second and those
+
+ align:start position:0%
+fractions of a second and those
+ 
+
+ align:start position:0%
+fractions of a second and those
+byproducts can then end up affecting the
+
+ align:start position:0%
+byproducts can then end up affecting the
+ 
+
+ align:start position:0%
+byproducts can then end up affecting the
+etch or the sidewall polymer formation
+
+ align:start position:0%
+etch or the sidewall polymer formation
+ 
+
+ align:start position:0%
+etch or the sidewall polymer formation
+or things like that so resonance time is
+
+ align:start position:0%
+or things like that so resonance time is
+ 
+
+ align:start position:0%
+or things like that so resonance time is
+ends up being an important parameter the
+
+ align:start position:0%
+ends up being an important parameter the
+ 
+
+ align:start position:0%
+ends up being an important parameter the
+way people control it as well they
+
+ align:start position:0%
+way people control it as well they
+ 
+
+ align:start position:0%
+way people control it as well they
+either up the flow rate the total gas
+
+ align:start position:0%
+either up the flow rate the total gas
+ 
+
+ align:start position:0%
+either up the flow rate the total gas
+flow rate or they change the pressure in
+
+ align:start position:0%
+flow rate or they change the pressure in
+ 
+
+ align:start position:0%
+flow rate or they change the pressure in
+some ways um uh in in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tool here's just an example from that
+
+ align:start position:0%
+tool here's just an example from that
+ 
+
+ align:start position:0%
+tool here's just an example from that
+same paper on an example of what happens
+
+ align:start position:0%
+same paper on an example of what happens
+ 
+
+ align:start position:0%
+same paper on an example of what happens
+as a function of the Silicon Edge rate
+
+ align:start position:0%
+as a function of the Silicon Edge rate
+ 
+
+ align:start position:0%
+as a function of the Silicon Edge rate
+as a function of uh a flow rate so
+
+ align:start position:0%
+as a function of uh a flow rate so
+ 
+
+ align:start position:0%
+as a function of uh a flow rate so
+here's um etch rate in nanometers per
+
+ align:start position:0%
+here's um etch rate in nanometers per
+ 
+
+ align:start position:0%
+here's um etch rate in nanometers per
+minute and uh this is a particular um
+
+ align:start position:0%
+minute and uh this is a particular um
+ 
+
+ align:start position:0%
+minute and uh this is a particular um
+silicon etch what they're using is
+
+ align:start position:0%
+silicon etch what they're using is
+ 
+
+ align:start position:0%
+silicon etch what they're using is
+chlorine very common um and this was the
+
+ align:start position:0%
+chlorine very common um and this was the
+ 
+
+ align:start position:0%
+chlorine very common um and this was the
+so so-called their present etching
+
+ align:start position:0%
+so so-called their present etching
+ 
+
+ align:start position:0%
+so so-called their present etching
+technique uh when when they had um uh
+
+ align:start position:0%
+technique uh when when they had um uh
+ 
+
+ align:start position:0%
+technique uh when when they had um uh
+using a high gas flow rate uh and a
+
+ align:start position:0%
+using a high gas flow rate uh and a
+ 
+
+ align:start position:0%
+using a high gas flow rate uh and a
+conventional etching technique so it
+
+ align:start position:0%
+conventional etching technique so it
+ 
+
+ align:start position:0%
+conventional etching technique so it
+also when you change the resonance time
+
+ align:start position:0%
+also when you change the resonance time
+ 
+
+ align:start position:0%
+also when you change the resonance time
+uh increasing it uh is going to uh uh
+
+ align:start position:0%
+uh increasing it uh is going to uh uh
+ 
+
+ align:start position:0%
+uh increasing it uh is going to uh uh
+change the um the etch rate so in this
+
+ align:start position:0%
+change the um the etch rate so in this
+ 
+
+ align:start position:0%
+change the um the etch rate so in this
+case a shorter gas residence time
+
+ align:start position:0%
+case a shorter gas residence time
+ 
+
+ align:start position:0%
+case a shorter gas residence time
+increases the um Edge rate so they incre
+
+ align:start position:0%
+increases the um Edge rate so they incre
+ 
+
+ align:start position:0%
+increases the um Edge rate so they incre
+I'm sorry increase the flow means the uh
+
+ align:start position:0%
+I'm sorry increase the flow means the uh
+ 
+
+ align:start position:0%
+I'm sorry increase the flow means the uh
+the amount of time any any volume of
+
+ align:start position:0%
+the amount of time any any volume of
+ 
+
+ align:start position:0%
+the amount of time any any volume of
+gases in the reactor is is shorter and
+
+ align:start position:0%
+gases in the reactor is is shorter and
+ 
+
+ align:start position:0%
+gases in the reactor is is shorter and
+why because it increases availability of
+
+ align:start position:0%
+why because it increases availability of
+ 
+
+ align:start position:0%
+why because it increases availability of
+neutral etent speed species you have the
+
+ align:start position:0%
+neutral etent speed species you have the
+ 
+
+ align:start position:0%
+neutral etent speed species you have the
+unreacted ENT coming in
+
+ align:start position:0%
+unreacted ENT coming in
+ 
+
+ align:start position:0%
+unreacted ENT coming in
+faster and it helps and it also reduces
+
+ align:start position:0%
+faster and it helps and it also reduces
+ 
+
+ align:start position:0%
+faster and it helps and it also reduces
+the concentration of this the reaction
+
+ align:start position:0%
+the concentration of this the reaction
+ 
+
+ align:start position:0%
+the concentration of this the reaction
+byproducts because again these are all
+
+ align:start position:0%
+byproducts because again these are all
+ 
+
+ align:start position:0%
+byproducts because again these are all
+chemical reactions if you want a
+
+ align:start position:0%
+chemical reactions if you want a
+ 
+
+ align:start position:0%
+chemical reactions if you want a
+reaction for a chemical reactant to go
+
+ align:start position:0%
+reaction for a chemical reactant to go
+ 
+
+ align:start position:0%
+reaction for a chemical reactant to go
+faster you put in the reactants faster
+
+ align:start position:0%
+faster you put in the reactants faster
+ 
+
+ align:start position:0%
+faster you put in the reactants faster
+and you remove the B products um rapidly
+
+ align:start position:0%
+and you remove the B products um rapidly
+ 
+
+ align:start position:0%
+and you remove the B products um rapidly
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+well so not only does it affect etch
+
+ align:start position:0%
+well so not only does it affect etch
+ 
+
+ align:start position:0%
+well so not only does it affect etch
+rate but changing things like pressure
+
+ align:start position:0%
+rate but changing things like pressure
+ 
+
+ align:start position:0%
+rate but changing things like pressure
+also affect um the shape of what you get
+
+ align:start position:0%
+also affect um the shape of what you get
+ 
+
+ align:start position:0%
+also affect um the shape of what you get
+here's an example on uh slide 14 uh from
+
+ align:start position:0%
+here's an example on uh slide 14 uh from
+ 
+
+ align:start position:0%
+here's an example on uh slide 14 uh from
+that same article of three different
+
+ align:start position:0%
+that same article of three different
+ 
+
+ align:start position:0%
+that same article of three different
+pressures um here we're at t tour um to
+
+ align:start position:0%
+pressures um here we're at t tour um to
+ 
+
+ align:start position:0%
+pressures um here we're at t tour um to
+try to define a polysilicon gate uh one
+
+ align:start position:0%
+try to define a polysilicon gate uh one
+ 
+
+ align:start position:0%
+try to define a polysilicon gate uh one
+I'm sorry 10 millor one millor and 0.1
+
+ align:start position:0%
+I'm sorry 10 millor one millor and 0.1
+ 
+
+ align:start position:0%
+I'm sorry 10 millor one millor and 0.1
+so we're going down here each Case by
+
+ align:start position:0%
+so we're going down here each Case by
+ 
+
+ align:start position:0%
+so we're going down here each Case by
+order of magnitude and pressure um we're
+
+ align:start position:0%
+order of magnitude and pressure um we're
+ 
+
+ align:start position:0%
+order of magnitude and pressure um we're
+using lower pressure at high flows you
+
+ align:start position:0%
+using lower pressure at high flows you
+ 
+
+ align:start position:0%
+using lower pressure at high flows you
+notice we get more anisotropic etching
+
+ align:start position:0%
+notice we get more anisotropic etching
+ 
+
+ align:start position:0%
+notice we get more anisotropic etching
+and less notching at least when using
+
+ align:start position:0%
+and less notching at least when using
+ 
+
+ align:start position:0%
+and less notching at least when using
+this particular uh chlorine polycylic so
+
+ align:start position:0%
+this particular uh chlorine polycylic so
+ 
+
+ align:start position:0%
+this particular uh chlorine polycylic so
+here at 10
+
+ align:start position:0%
+here at 10
+ 
+
+ align:start position:0%
+here at 10
+millor um and you get a a fairly um
+
+ align:start position:0%
+millor um and you get a a fairly um
+ 
+
+ align:start position:0%
+millor um and you get a a fairly um
+isotropic atch it's not totally
+
+ align:start position:0%
+isotropic atch it's not totally
+ 
+
+ align:start position:0%
+isotropic atch it's not totally
+isotropic but you notice it's etching
+
+ align:start position:0%
+isotropic but you notice it's etching
+ 
+
+ align:start position:0%
+isotropic but you notice it's etching
+sideways as well as vertically and how
+
+ align:start position:0%
+sideways as well as vertically and how
+ 
+
+ align:start position:0%
+sideways as well as vertically and how
+can I tell because this is my photo
+
+ align:start position:0%
+can I tell because this is my photo
+ 
+
+ align:start position:0%
+can I tell because this is my photo
+resist and it's undercut on the left and
+
+ align:start position:0%
+resist and it's undercut on the left and
+ 
+
+ align:start position:0%
+resist and it's undercut on the left and
+right side so the line is a lot narrower
+
+ align:start position:0%
+right side so the line is a lot narrower
+ 
+
+ align:start position:0%
+right side so the line is a lot narrower
+than what had been
+
+ align:start position:0%
+than what had been
+ 
+
+ align:start position:0%
+than what had been
+designed there's a little bit uh better
+
+ align:start position:0%
+designed there's a little bit uh better
+ 
+
+ align:start position:0%
+designed there's a little bit uh better
+is an isotropy at a lower pressure at
+
+ align:start position:0%
+is an isotropy at a lower pressure at
+ 
+
+ align:start position:0%
+is an isotropy at a lower pressure at
+one notor but we still have now we've
+
+ align:start position:0%
+one notor but we still have now we've
+ 
+
+ align:start position:0%
+one notor but we still have now we've
+developed a little Notch at the bottom
+
+ align:start position:0%
+developed a little Notch at the bottom
+ 
+
+ align:start position:0%
+developed a little Notch at the bottom
+which isn't again that's not considered
+
+ align:start position:0%
+which isn't again that's not considered
+ 
+
+ align:start position:0%
+which isn't again that's not considered
+to be good good finally we have um the
+
+ align:start position:0%
+to be good good finally we have um the
+ 
+
+ align:start position:0%
+to be good good finally we have um the
+lowest resonance time or the lowest
+
+ align:start position:0%
+lowest resonance time or the lowest
+ 
+
+ align:start position:0%
+lowest resonance time or the lowest
+pressure here at at 0.1 millor this uh
+
+ align:start position:0%
+pressure here at at 0.1 millor this uh
+ 
+
+ align:start position:0%
+pressure here at at 0.1 millor this uh
+paper demonstrates very vertical
+
+ align:start position:0%
+paper demonstrates very vertical
+ 
+
+ align:start position:0%
+paper demonstrates very vertical
+sidewalls and no undercutting so this is
+
+ align:start position:0%
+sidewalls and no undercutting so this is
+ 
+
+ align:start position:0%
+sidewalls and no undercutting so this is
+a reasonable uh would be a very
+
+ align:start position:0%
+a reasonable uh would be a very
+ 
+
+ align:start position:0%
+a reasonable uh would be a very
+considered a very good quality Edge you
+
+ align:start position:0%
+considered a very good quality Edge you
+ 
+
+ align:start position:0%
+considered a very good quality Edge you
+may be able to make one device with this
+
+ align:start position:0%
+may be able to make one device with this
+ 
+
+ align:start position:0%
+may be able to make one device with this
+Edge I'm not saying this Edge won't work
+
+ align:start position:0%
+Edge I'm not saying this Edge won't work
+ 
+
+ align:start position:0%
+Edge I'm not saying this Edge won't work
+but from a manufacturing point of view
+
+ align:start position:0%
+but from a manufacturing point of view
+ 
+
+ align:start position:0%
+but from a manufacturing point of view
+how do I control how do I control my
+
+ align:start position:0%
+how do I control how do I control my
+ 
+
+ align:start position:0%
+how do I control how do I control my
+line withd on my critical Dimension it's
+
+ align:start position:0%
+line withd on my critical Dimension it's
+ 
+
+ align:start position:0%
+line withd on my critical Dimension it's
+not well controlled at all um so this
+
+ align:start position:0%
+not well controlled at all um so this
+ 
+
+ align:start position:0%
+not well controlled at all um so this
+would not be considered a manufacturable
+
+ align:start position:0%
+would not be considered a manufacturable
+ 
+
+ align:start position:0%
+would not be considered a manufacturable
+type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process there's another consideration so
+
+ align:start position:0%
+process there's another consideration so
+ 
+
+ align:start position:0%
+process there's another consideration so
+we we talked a lot about uh we care
+
+ align:start position:0%
+we we talked a lot about uh we care
+ 
+
+ align:start position:0%
+we we talked a lot about uh we care
+about the etch rate and and the shape of
+
+ align:start position:0%
+about the etch rate and and the shape of
+ 
+
+ align:start position:0%
+about the etch rate and and the shape of
+the sidewall because that affects how
+
+ align:start position:0%
+the sidewall because that affects how
+ 
+
+ align:start position:0%
+the sidewall because that affects how
+we're going to implant it and do other
+
+ align:start position:0%
+we're going to implant it and do other
+ 
+
+ align:start position:0%
+we're going to implant it and do other
+things um a huge consideration anytime
+
+ align:start position:0%
+things um a huge consideration anytime
+ 
+
+ align:start position:0%
+things um a huge consideration anytime
+you are etching features this is not
+
+ align:start position:0%
+you are etching features this is not
+ 
+
+ align:start position:0%
+you are etching features this is not
+just true of a polysilicon gate but I'm
+
+ align:start position:0%
+just true of a polysilicon gate but I'm
+ 
+
+ align:start position:0%
+just true of a polysilicon gate but I'm
+giving the example for a polysilicon
+
+ align:start position:0%
+giving the example for a polysilicon
+ 
+
+ align:start position:0%
+giving the example for a polysilicon
+gate uh is uh so gate Ed as the example
+
+ align:start position:0%
+gate uh is uh so gate Ed as the example
+ 
+
+ align:start position:0%
+gate uh is uh so gate Ed as the example
+is the topography um and and so what
+
+ align:start position:0%
+is the topography um and and so what
+ 
+
+ align:start position:0%
+is the topography um and and so what
+what's the problem well highly
+
+ align:start position:0%
+what's the problem well highly
+ 
+
+ align:start position:0%
+what's the problem well highly
+anisotropic etching so etching that is
+
+ align:start position:0%
+anisotropic etching so etching that is
+ 
+
+ align:start position:0%
+anisotropic etching so etching that is
+only down only vertical doesn't etch
+
+ align:start position:0%
+only down only vertical doesn't etch
+ 
+
+ align:start position:0%
+only down only vertical doesn't etch
+sideways is required to achieve good
+
+ align:start position:0%
+sideways is required to achieve good
+ 
+
+ align:start position:0%
+sideways is required to achieve good
+control we just said that over the gate
+
+ align:start position:0%
+control we just said that over the gate
+ 
+
+ align:start position:0%
+control we just said that over the gate
+length and the shape but um unless you
+
+ align:start position:0%
+length and the shape but um unless you
+ 
+
+ align:start position:0%
+length and the shape but um unless you
+have a long overetch uh that you do at
+
+ align:start position:0%
+have a long overetch uh that you do at
+ 
+
+ align:start position:0%
+have a long overetch uh that you do at
+the end of of a step you can get
+
+ align:start position:0%
+the end of of a step you can get
+ 
+
+ align:start position:0%
+the end of of a step you can get
+stringers left behind and let's just
+
+ align:start position:0%
+stringers left behind and let's just
+ 
+
+ align:start position:0%
+stringers left behind and let's just
+show um an example here so on the left
+
+ align:start position:0%
+show um an example here so on the left
+ 
+
+ align:start position:0%
+show um an example here so on the left
+I'm showing where we've etched through
+
+ align:start position:0%
+I'm showing where we've etched through
+ 
+
+ align:start position:0%
+I'm showing where we've etched through
+polysilicon there was no topog on the
+
+ align:start position:0%
+polysilicon there was no topog on the
+ 
+
+ align:start position:0%
+polysilicon there was no topog on the
+original part of the wafer it which is
+
+ align:start position:0%
+original part of the wafer it which is
+ 
+
+ align:start position:0%
+original part of the wafer it which is
+flat so I have photo resist and I Ed
+
+ align:start position:0%
+flat so I have photo resist and I Ed
+ 
+
+ align:start position:0%
+flat so I have photo resist and I Ed
+polyic and isotropically everything
+
+ align:start position:0%
+polyic and isotropically everything
+ 
+
+ align:start position:0%
+polyic and isotropically everything
+looks very good now what's happened on
+
+ align:start position:0%
+looks very good now what's happened on
+ 
+
+ align:start position:0%
+looks very good now what's happened on
+the right well on the right hand side I
+
+ align:start position:0%
+the right well on the right hand side I
+ 
+
+ align:start position:0%
+the right well on the right hand side I
+had some initial topography so I had a
+
+ align:start position:0%
+had some initial topography so I had a
+ 
+
+ align:start position:0%
+had some initial topography so I had a
+step that looks like this okay so as a
+
+ align:start position:0%
+step that looks like this okay so as a
+ 
+
+ align:start position:0%
+step that looks like this okay so as a
+result of having that step the
+
+ align:start position:0%
+result of having that step the
+ 
+
+ align:start position:0%
+result of having that step the
+polysilicon overlayer which is shown by
+
+ align:start position:0%
+polysilicon overlayer which is shown by
+ 
+
+ align:start position:0%
+polysilicon overlayer which is shown by
+this sort of stippled region the
+
+ align:start position:0%
+this sort of stippled region the
+ 
+
+ align:start position:0%
+this sort of stippled region the
+polysilicon went over everything okay so
+
+ align:start position:0%
+polysilicon went over everything okay so
+ 
+
+ align:start position:0%
+polysilicon went over everything okay so
+uh the polysilicon in this region is
+
+ align:start position:0%
+uh the polysilicon in this region is
+ 
+
+ align:start position:0%
+uh the polysilicon in this region is
+actually thicker than it is in the flat
+
+ align:start position:0%
+actually thicker than it is in the flat
+ 
+
+ align:start position:0%
+actually thicker than it is in the flat
+portion
+
+ align:start position:0%
+portion
+ 
+
+ align:start position:0%
+portion
+so by the time I clear the gate and I
+
+ align:start position:0%
+so by the time I clear the gate and I
+ 
+
+ align:start position:0%
+so by the time I clear the gate and I
+just hit this oxide right here I have
+
+ align:start position:0%
+just hit this oxide right here I have
+ 
+
+ align:start position:0%
+just hit this oxide right here I have
+left behind a Stringer because I haven't
+
+ align:start position:0%
+left behind a Stringer because I haven't
+ 
+
+ align:start position:0%
+left behind a Stringer because I haven't
+etched long enough because the poly
+
+ align:start position:0%
+etched long enough because the poly
+ 
+
+ align:start position:0%
+etched long enough because the poly
+silic thickness was thicker in this
+
+ align:start position:0%
+silic thickness was thicker in this
+ 
+
+ align:start position:0%
+silic thickness was thicker in this
+region and remember I'm only etching
+
+ align:start position:0%
+region and remember I'm only etching
+ 
+
+ align:start position:0%
+region and remember I'm only etching
+vertically it's not going sideways um so
+
+ align:start position:0%
+vertically it's not going sideways um so
+ 
+
+ align:start position:0%
+vertically it's not going sideways um so
+this Stringer is considered to be
+
+ align:start position:0%
+this Stringer is considered to be
+ 
+
+ align:start position:0%
+this Stringer is considered to be
+undesirable because it's now an extra
+
+ align:start position:0%
+undesirable because it's now an extra
+ 
+
+ align:start position:0%
+undesirable because it's now an extra
+gate electrode or it's an extra thing
+
+ align:start position:0%
+gate electrode or it's an extra thing
+ 
+
+ align:start position:0%
+gate electrode or it's an extra thing
+you didn't want in your circuit uh how
+
+ align:start position:0%
+you didn't want in your circuit uh how
+ 
+
+ align:start position:0%
+you didn't want in your circuit uh how
+do I get rid of it well you say just
+
+ align:start position:0%
+do I get rid of it well you say just
+ 
+
+ align:start position:0%
+do I get rid of it well you say just
+keep on itching keep the uh go to do an
+
+ align:start position:0%
+keep on itching keep the uh go to do an
+ 
+
+ align:start position:0%
+keep on itching keep the uh go to do an
+over etch so even though I I I finished
+
+ align:start position:0%
+over etch so even though I I I finished
+ 
+
+ align:start position:0%
+over etch so even though I I I finished
+etching the poly gate and I'm done in
+
+ align:start position:0%
+etching the poly gate and I'm done in
+ 
+
+ align:start position:0%
+etching the poly gate and I'm done in
+this region I'm not done over here so
+
+ align:start position:0%
+this region I'm not done over here so
+ 
+
+ align:start position:0%
+this region I'm not done over here so
+you keep it in and you keep banging on
+
+ align:start position:0%
+you keep it in and you keep banging on
+ 
+
+ align:start position:0%
+you keep it in and you keep banging on
+the top of that Stringer until it
+
+ align:start position:0%
+the top of that Stringer until it
+ 
+
+ align:start position:0%
+the top of that Stringer until it
+finally goes down to
+
+ align:start position:0%
+finally goes down to
+ 
+
+ align:start position:0%
+finally goes down to
+zero uh so you need a very long overed
+
+ align:start position:0%
+zero uh so you need a very long overed
+ 
+
+ align:start position:0%
+zero uh so you need a very long overed
+whenever you have um surface topography
+
+ align:start position:0%
+whenever you have um surface topography
+ 
+
+ align:start position:0%
+whenever you have um surface topography
+uh in order to get rid of stringers
+
+ align:start position:0%
+uh in order to get rid of stringers
+ 
+
+ align:start position:0%
+uh in order to get rid of stringers
+what's the disadvantage of a long over
+
+ align:start position:0%
+what's the disadvantage of a long over
+ 
+
+ align:start position:0%
+what's the disadvantage of a long over
+well you might break through your oxide
+
+ align:start position:0%
+well you might break through your oxide
+ 
+
+ align:start position:0%
+well you might break through your oxide
+because you're still beating on that
+
+ align:start position:0%
+because you're still beating on that
+ 
+
+ align:start position:0%
+because you're still beating on that
+oxide so unless you have really good
+
+ align:start position:0%
+oxide so unless you have really good
+ 
+
+ align:start position:0%
+oxide so unless you have really good
+selectivity as you're beating the
+
+ align:start position:0%
+selectivity as you're beating the
+ 
+
+ align:start position:0%
+selectivity as you're beating the
+Stringer down and getting rid of the
+
+ align:start position:0%
+Stringer down and getting rid of the
+ 
+
+ align:start position:0%
+Stringer down and getting rid of the
+Stringer you could be destroying the
+
+ align:start position:0%
+Stringer you could be destroying the
+ 
+
+ align:start position:0%
+Stringer you could be destroying the
+oxide what's the other bad thing well
+
+ align:start position:0%
+oxide what's the other bad thing well
+ 
+
+ align:start position:0%
+oxide what's the other bad thing well
+you're um your overetch may not be
+
+ align:start position:0%
+you're um your overetch may not be
+ 
+
+ align:start position:0%
+you're um your overetch may not be
+perfectly anisotropic it may be etching
+
+ align:start position:0%
+perfectly anisotropic it may be etching
+ 
+
+ align:start position:0%
+perfectly anisotropic it may be etching
+sideways a little bit on the gate so
+
+ align:start position:0%
+sideways a little bit on the gate so
+ 
+
+ align:start position:0%
+sideways a little bit on the gate so
+unless it's perfectly anisotropic you'll
+
+ align:start position:0%
+unless it's perfectly anisotropic you'll
+ 
+
+ align:start position:0%
+unless it's perfectly anisotropic you'll
+have that so there's always a balance uh
+
+ align:start position:0%
+have that so there's always a balance uh
+ 
+
+ align:start position:0%
+have that so there's always a balance uh
+with over it so this is why you will
+
+ align:start position:0%
+with over it so this is why you will
+ 
+
+ align:start position:0%
+with over it so this is why you will
+find people say if you want to get the
+
+ align:start position:0%
+find people say if you want to get the
+ 
+
+ align:start position:0%
+find people say if you want to get the
+finest patterns your wafer should be
+
+ align:start position:0%
+finest patterns your wafer should be
+ 
+
+ align:start position:0%
+finest patterns your wafer should be
+completely flat you should have no
+
+ align:start position:0%
+completely flat you should have no
+ 
+
+ align:start position:0%
+completely flat you should have no
+topography because if you have a
+
+ align:start position:0%
+topography because if you have a
+ 
+
+ align:start position:0%
+topography because if you have a
+completely flat wafer you never have to
+
+ align:start position:0%
+completely flat wafer you never have to
+ 
+
+ align:start position:0%
+completely flat wafer you never have to
+work about stringers you etch down you
+
+ align:start position:0%
+work about stringers you etch down you
+ 
+
+ align:start position:0%
+work about stringers you etch down you
+stop on the layer below and you stop
+
+ align:start position:0%
+stop on the layer below and you stop
+ 
+
+ align:start position:0%
+stop on the layer below and you stop
+period your over Etch in that case is
+
+ align:start position:0%
+period your over Etch in that case is
+ 
+
+ align:start position:0%
+period your over Etch in that case is
+only dictated by the non-uniformity in
+
+ align:start position:0%
+only dictated by the non-uniformity in
+ 
+
+ align:start position:0%
+only dictated by the non-uniformity in
+the film across the wafer as we talked
+
+ align:start position:0%
+the film across the wafer as we talked
+ 
+
+ align:start position:0%
+the film across the wafer as we talked
+about before non-uniformity etch rate
+
+ align:start position:0%
+about before non-uniformity etch rate
+ 
+
+ align:start position:0%
+about before non-uniformity etch rate
+now we have another requirement on
+
+ align:start position:0%
+now we have another requirement on
+ 
+
+ align:start position:0%
+now we have another requirement on
+overetch I have to not only take into
+
+ align:start position:0%
+overetch I have to not only take into
+ 
+
+ align:start position:0%
+overetch I have to not only take into
+account non-uniformity across the wafer
+
+ align:start position:0%
+account non-uniformity across the wafer
+ 
+
+ align:start position:0%
+account non-uniformity across the wafer
+but if I have topography and I have an
+
+ align:start position:0%
+but if I have topography and I have an
+ 
+
+ align:start position:0%
+but if I have topography and I have an
+anisotropic hch I have to get rid of
+
+ align:start position:0%
+anisotropic hch I have to get rid of
+ 
+
+ align:start position:0%
+anisotropic hch I have to get rid of
+stringers um so you will see the
+
+ align:start position:0%
+stringers um so you will see the
+ 
+
+ align:start position:0%
+stringers um so you will see the
+topography uh on Modern devices as they
+
+ align:start position:0%
+topography uh on Modern devices as they
+ 
+
+ align:start position:0%
+topography uh on Modern devices as they
+get smaller and smaller everything has
+
+ align:start position:0%
+get smaller and smaller everything has
+ 
+
+ align:start position:0%
+get smaller and smaller everything has
+to be smoother and smoother that's why
+
+ align:start position:0%
+to be smoother and smoother that's why
+ 
+
+ align:start position:0%
+to be smoother and smoother that's why
+people went away from Locos right Locos
+
+ align:start position:0%
+people went away from Locos right Locos
+ 
+
+ align:start position:0%
+people went away from Locos right Locos
+creates this big hump on the wafer
+
+ align:start position:0%
+creates this big hump on the wafer
+ 
+
+ align:start position:0%
+creates this big hump on the wafer
+people don't like that we do shallow
+
+ align:start position:0%
+people don't like that we do shallow
+ 
+
+ align:start position:0%
+people don't like that we do shallow
+trench which creates a perfectly flat
+
+ align:start position:0%
+trench which creates a perfectly flat
+ 
+
+ align:start position:0%
+trench which creates a perfectly flat
+wafer that way I can pattern a very very
+
+ align:start position:0%
+wafer that way I can pattern a very very
+ 
+
+ align:start position:0%
+wafer that way I can pattern a very very
+fine line and I don't have to worry
+
+ align:start position:0%
+fine line and I don't have to worry
+ 
+
+ align:start position:0%
+fine line and I don't have to worry
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stringers uh slide 16 is is from a
+
+ align:start position:0%
+stringers uh slide 16 is is from a
+ 
+
+ align:start position:0%
+stringers uh slide 16 is is from a
+different text it has another example of
+
+ align:start position:0%
+different text it has another example of
+ 
+
+ align:start position:0%
+different text it has another example of
+stringer formation maybe this
+
+ align:start position:0%
+stringer formation maybe this
+ 
+
+ align:start position:0%
+stringer formation maybe this
+cross-section might be easier for you to
+
+ align:start position:0%
+cross-section might be easier for you to
+ 
+
+ align:start position:0%
+cross-section might be easier for you to
+see um so uh here's an example at where
+
+ align:start position:0%
+see um so uh here's an example at where
+ 
+
+ align:start position:0%
+see um so uh here's an example at where
+I have a field oxide so the field oxide
+
+ align:start position:0%
+I have a field oxide so the field oxide
+ 
+
+ align:start position:0%
+I have a field oxide so the field oxide
+has a certain step height to it shown
+
+ align:start position:0%
+has a certain step height to it shown
+ 
+
+ align:start position:0%
+has a certain step height to it shown
+here and I have and of course when you
+
+ align:start position:0%
+here and I have and of course when you
+ 
+
+ align:start position:0%
+here and I have and of course when you
+deposit the polysilicon it gets
+
+ align:start position:0%
+deposit the polysilicon it gets
+ 
+
+ align:start position:0%
+deposit the polysilicon it gets
+deposited everywhere on the wafer so
+
+ align:start position:0%
+deposited everywhere on the wafer so
+ 
+
+ align:start position:0%
+deposited everywhere on the wafer so
+this cross-hatched region is the poly
+
+ align:start position:0%
+this cross-hatched region is the poly
+ 
+
+ align:start position:0%
+this cross-hatched region is the poly
+that I want to pattern and this is the
+
+ align:start position:0%
+that I want to pattern and this is the
+ 
+
+ align:start position:0%
+that I want to pattern and this is the
+photo resist after it's been developed
+
+ align:start position:0%
+photo resist after it's been developed
+ 
+
+ align:start position:0%
+photo resist after it's been developed
+and patterned okay now step B here I put
+
+ align:start position:0%
+and patterned okay now step B here I put
+ 
+
+ align:start position:0%
+and patterned okay now step B here I put
+it into the etcher and I use the
+
+ align:start position:0%
+it into the etcher and I use the
+ 
+
+ align:start position:0%
+it into the etcher and I use the
+photoresist as a mass to etch the poly
+
+ align:start position:0%
+photoresist as a mass to etch the poly
+ 
+
+ align:start position:0%
+photoresist as a mass to etch the poly
+so this looks good I have very nice
+
+ align:start position:0%
+so this looks good I have very nice
+ 
+
+ align:start position:0%
+so this looks good I have very nice
+sidewalls and I stop on the oxide uh but
+
+ align:start position:0%
+sidewalls and I stop on the oxide uh but
+ 
+
+ align:start position:0%
+sidewalls and I stop on the oxide uh but
+what happens well in this region right
+
+ align:start position:0%
+what happens well in this region right
+ 
+
+ align:start position:0%
+what happens well in this region right
+here right look at the thickness of this
+
+ align:start position:0%
+here right look at the thickness of this
+ 
+
+ align:start position:0%
+here right look at the thickness of this
+gate material where it goes over the
+
+ align:start position:0%
+gate material where it goes over the
+ 
+
+ align:start position:0%
+gate material where it goes over the
+step the PO the thickness from this
+
+ align:start position:0%
+step the PO the thickness from this
+ 
+
+ align:start position:0%
+step the PO the thickness from this
+point of the top to the very bottom is
+
+ align:start position:0%
+point of the top to the very bottom is
+ 
+
+ align:start position:0%
+point of the top to the very bottom is
+almost twice what the thickness is in
+
+ align:start position:0%
+almost twice what the thickness is in
+ 
+
+ align:start position:0%
+almost twice what the thickness is in
+the flat region so as a result once I've
+
+ align:start position:0%
+the flat region so as a result once I've
+ 
+
+ align:start position:0%
+the flat region so as a result once I've
+cleared the flats I still have this
+
+ align:start position:0%
+cleared the flats I still have this
+ 
+
+ align:start position:0%
+cleared the flats I still have this
+little Notch of material that's unetched
+
+ align:start position:0%
+little Notch of material that's unetched
+ 
+
+ align:start position:0%
+little Notch of material that's unetched
+that's sitting there because my etch
+
+ align:start position:0%
+that's sitting there because my etch
+ 
+
+ align:start position:0%
+that's sitting there because my etch
+only etches vertically if the edch had
+
+ align:start position:0%
+only etches vertically if the edch had
+ 
+
+ align:start position:0%
+only etches vertically if the edch had
+itched sideways then you wouldn't
+
+ align:start position:0%
+itched sideways then you wouldn't
+ 
+
+ align:start position:0%
+itched sideways then you wouldn't
+wouldn't have to worry about that Notch
+
+ align:start position:0%
+wouldn't have to worry about that Notch
+ 
+
+ align:start position:0%
+wouldn't have to worry about that Notch
+so an isotropic edch don't doesn't tend
+
+ align:start position:0%
+so an isotropic edch don't doesn't tend
+ 
+
+ align:start position:0%
+so an isotropic edch don't doesn't tend
+to give you stringers or Stringer for
+
+ align:start position:0%
+to give you stringers or Stringer for
+ 
+
+ align:start position:0%
+to give you stringers or Stringer for
+Stringer formation is not such a big
+
+ align:start position:0%
+Stringer formation is not such a big
+ 
+
+ align:start position:0%
+Stringer formation is not such a big
+deal but if it's anisotropic it is so
+
+ align:start position:0%
+deal but if it's anisotropic it is so
+ 
+
+ align:start position:0%
+deal but if it's anisotropic it is so
+what we do is you continue in Step C
+
+ align:start position:0%
+what we do is you continue in Step C
+ 
+
+ align:start position:0%
+what we do is you continue in Step C
+with an overetch you continue to beat
+
+ align:start position:0%
+with an overetch you continue to beat
+ 
+
+ align:start position:0%
+with an overetch you continue to beat
+down on this and you know introduce an
+
+ align:start position:0%
+down on this and you know introduce an
+ 
+
+ align:start position:0%
+down on this and you know introduce an
+extra 50% of an overed to get rid of the
+
+ align:start position:0%
+extra 50% of an overed to get rid of the
+ 
+
+ align:start position:0%
+extra 50% of an overed to get rid of the
+stringers if you leave the stringers in
+
+ align:start position:0%
+stringers if you leave the stringers in
+ 
+
+ align:start position:0%
+stringers if you leave the stringers in
+place you'll have shorts on your devices
+
+ align:start position:0%
+place you'll have shorts on your devices
+ 
+
+ align:start position:0%
+place you'll have shorts on your devices
+because then you have the this poly
+
+ align:start position:0%
+because then you have the this poly
+ 
+
+ align:start position:0%
+because then you have the this poly
+going all the way around the field you
+
+ align:start position:0%
+going all the way around the field you
+ 
+
+ align:start position:0%
+going all the way around the field you
+can short The Source Trin to the gate
+
+ align:start position:0%
+can short The Source Trin to the gate
+ 
+
+ align:start position:0%
+can short The Source Trin to the gate
+and you get all kinds of problems now
+
+ align:start position:0%
+and you get all kinds of problems now
+ 
+
+ align:start position:0%
+and you get all kinds of problems now
+this is drawn by a cartoon or by an
+
+ align:start position:0%
+this is drawn by a cartoon or by an
+ 
+
+ align:start position:0%
+this is drawn by a cartoon or by an
+illustrator so it's very easy it doesn't
+
+ align:start position:0%
+illustrator so it's very easy it doesn't
+ 
+
+ align:start position:0%
+illustrator so it's very easy it doesn't
+show any detrimental effect of the
+
+ align:start position:0%
+show any detrimental effect of the
+ 
+
+ align:start position:0%
+show any detrimental effect of the
+overage in practice overetching to
+
+ align:start position:0%
+overage in practice overetching to
+ 
+
+ align:start position:0%
+overage in practice overetching to
+remove stringers almost always has some
+
+ align:start position:0%
+remove stringers almost always has some
+ 
+
+ align:start position:0%
+remove stringers almost always has some
+a little detrimental effect and so the
+
+ align:start position:0%
+a little detrimental effect and so the
+ 
+
+ align:start position:0%
+a little detrimental effect and so the
+name of the game is trying to control
+
+ align:start position:0%
+name of the game is trying to control
+ 
+
+ align:start position:0%
+name of the game is trying to control
+your topography so you minimize your
+
+ align:start position:0%
+your topography so you minimize your
+ 
+
+ align:start position:0%
+your topography so you minimize your
+overetch so you don't have to um destroy
+
+ align:start position:0%
+overetch so you don't have to um destroy
+ 
+
+ align:start position:0%
+overetch so you don't have to um destroy
+the structure by overetching too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much so let's look at slide 17 this is
+
+ align:start position:0%
+much so let's look at slide 17 this is
+ 
+
+ align:start position:0%
+much so let's look at slide 17 this is
+an example of uh on that paper that
+
+ align:start position:0%
+an example of uh on that paper that
+ 
+
+ align:start position:0%
+an example of uh on that paper that
+article from IBM on the effects of
+
+ align:start position:0%
+article from IBM on the effects of
+ 
+
+ align:start position:0%
+article from IBM on the effects of
+topography on gate conductor yield with
+
+ align:start position:0%
+topography on gate conductor yield with
+ 
+
+ align:start position:0%
+topography on gate conductor yield with
+respect to shorting as I mentioned if
+
+ align:start position:0%
+respect to shorting as I mentioned if
+ 
+
+ align:start position:0%
+respect to shorting as I mentioned if
+you end up with stringers the gate can
+
+ align:start position:0%
+you end up with stringers the gate can
+ 
+
+ align:start position:0%
+you end up with stringers the gate can
+be shorted to the source and drain so
+
+ align:start position:0%
+be shorted to the source and drain so
+ 
+
+ align:start position:0%
+be shorted to the source and drain so
+here's an example um and they they edged
+
+ align:start position:0%
+here's an example um and they they edged
+ 
+
+ align:start position:0%
+here's an example um and they they edged
+here 21 Wafers or so 20 Wafers and the
+
+ align:start position:0%
+here 21 Wafers or so 20 Wafers and the
+ 
+
+ align:start position:0%
+here 21 Wafers or so 20 Wafers and the
+percent yield so if you have a high
+
+ align:start position:0%
+percent yield so if you have a high
+ 
+
+ align:start position:0%
+percent yield so if you have a high
+yield it means you don't have gate to
+
+ align:start position:0%
+yield it means you don't have gate to
+ 
+
+ align:start position:0%
+yield it means you don't have gate to
+sour strin shorts if you have a low
+
+ align:start position:0%
+sour strin shorts if you have a low
+ 
+
+ align:start position:0%
+sour strin shorts if you have a low
+yield it means you have shorts between
+
+ align:start position:0%
+yield it means you have shorts between
+ 
+
+ align:start position:0%
+yield it means you have shorts between
+the gate and the source drain so this
+
+ align:start position:0%
+the gate and the source drain so this
+ 
+
+ align:start position:0%
+the gate and the source drain so this
+wafer had no topography so they etched
+
+ align:start position:0%
+wafer had no topography so they etched
+ 
+
+ align:start position:0%
+wafer had no topography so they etched
+the gates on perfectly flat Wafers and
+
+ align:start position:0%
+the gates on perfectly flat Wafers and
+ 
+
+ align:start position:0%
+the gates on perfectly flat Wafers and
+the yield was very high it was like 90%
+
+ align:start position:0%
+the yield was very high it was like 90%
+ 
+
+ align:start position:0%
+the yield was very high it was like 90%
+for these five Wafers uh now they
+
+ align:start position:0%
+for these five Wafers uh now they
+ 
+
+ align:start position:0%
+for these five Wafers uh now they
+introduced at the field loide or
+
+ align:start position:0%
+introduced at the field loide or
+ 
+
+ align:start position:0%
+introduced at the field loide or
+somewhere they introduced a 50 nmet step
+
+ align:start position:0%
+somewhere they introduced a 50 nmet step
+ 
+
+ align:start position:0%
+somewhere they introduced a 50 nmet step
+you can see the the yield goes down a
+
+ align:start position:0%
+you can see the the yield goes down a
+ 
+
+ align:start position:0%
+you can see the the yield goes down a
+little bit not too bad though so they
+
+ align:start position:0%
+little bit not too bad though so they
+ 
+
+ align:start position:0%
+little bit not too bad though so they
+have more shorts and here if you
+
+ align:start position:0%
+have more shorts and here if you
+ 
+
+ align:start position:0%
+have more shorts and here if you
+introduce 100 nanometer step on this
+
+ align:start position:0%
+introduce 100 nanometer step on this
+ 
+
+ align:start position:0%
+introduce 100 nanometer step on this
+particular gate Edge you get a yield of
+
+ align:start position:0%
+particular gate Edge you get a yield of
+ 
+
+ align:start position:0%
+particular gate Edge you get a yield of
+only 30% so 70% of devices are shorted
+
+ align:start position:0%
+only 30% so 70% of devices are shorted
+ 
+
+ align:start position:0%
+only 30% so 70% of devices are shorted
+so this means you're getting a lot of
+
+ align:start position:0%
+so this means you're getting a lot of
+ 
+
+ align:start position:0%
+so this means you're getting a lot of
+stringers forming so you can look
+
+ align:start position:0%
+stringers forming so you can look
+ 
+
+ align:start position:0%
+stringers forming so you can look
+stringers you know visually in the
+
+ align:start position:0%
+stringers you know visually in the
+ 
+
+ align:start position:0%
+stringers you know visually in the
+microscope with a temm or an sem or you
+
+ align:start position:0%
+microscope with a temm or an sem or you
+ 
+
+ align:start position:0%
+microscope with a temm or an sem or you
+can look at them with special test
+
+ align:start position:0%
+can look at them with special test
+ 
+
+ align:start position:0%
+can look at them with special test
+structures where you look at your your
+
+ align:start position:0%
+structures where you look at your your
+ 
+
+ align:start position:0%
+structures where you look at your your
+shorting and your yield so this is an
+
+ align:start position:0%
+shorting and your yield so this is an
+ 
+
+ align:start position:0%
+shorting and your yield so this is an
+example where you would say for this
+
+ align:start position:0%
+example where you would say for this
+ 
+
+ align:start position:0%
+example where you would say for this
+particular gate Edge process that the um
+
+ align:start position:0%
+particular gate Edge process that the um
+ 
+
+ align:start position:0%
+particular gate Edge process that the um
+uh 100 nmet step is too much you need to
+
+ align:start position:0%
+uh 100 nmet step is too much you need to
+ 
+
+ align:start position:0%
+uh 100 nmet step is too much you need to
+reduce your step height and not produce
+
+ align:start position:0%
+reduce your step height and not produce
+ 
+
+ align:start position:0%
+reduce your step height and not produce
+such an Abrupt step uh otherwise you
+
+ align:start position:0%
+such an Abrupt step uh otherwise you
+ 
+
+ align:start position:0%
+such an Abrupt step uh otherwise you
+need to increase your OverWatch time or
+
+ align:start position:0%
+need to increase your OverWatch time or
+ 
+
+ align:start position:0%
+need to increase your OverWatch time or
+do something uh but the yield so
+
+ align:start position:0%
+do something uh but the yield so
+ 
+
+ align:start position:0%
+do something uh but the yield so
+stringers are really a big issue and
+
+ align:start position:0%
+stringers are really a big issue and
+ 
+
+ align:start position:0%
+stringers are really a big issue and
+it's it's a always a trade-off between
+
+ align:start position:0%
+it's it's a always a trade-off between
+ 
+
+ align:start position:0%
+it's it's a always a trade-off between
+their remov removal and uh sort of you
+
+ align:start position:0%
+their remov removal and uh sort of you
+ 
+
+ align:start position:0%
+their remov removal and uh sort of you
+know messing up the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure here on slide uh 18 I just
+
+ align:start position:0%
+structure here on slide uh 18 I just
+ 
+
+ align:start position:0%
+structure here on slide uh 18 I just
+showed you some I've shown some ways
+
+ align:start position:0%
+showed you some I've shown some ways
+ 
+
+ align:start position:0%
+showed you some I've shown some ways
+where where we can calculate uh overg
+
+ align:start position:0%
+where where we can calculate uh overg
+ 
+
+ align:start position:0%
+where where we can calculate uh overg
+requirements based on the topography one
+
+ align:start position:0%
+requirements based on the topography one
+ 
+
+ align:start position:0%
+requirements based on the topography one
+might have uh during gate etching so
+
+ align:start position:0%
+might have uh during gate etching so
+ 
+
+ align:start position:0%
+might have uh during gate etching so
+here's an example uh on this particular
+
+ align:start position:0%
+here's an example uh on this particular
+ 
+
+ align:start position:0%
+here's an example uh on this particular
+figure where I'm showing you a field
+
+ align:start position:0%
+figure where I'm showing you a field
+ 
+
+ align:start position:0%
+figure where I'm showing you a field
+oxide uh remember we said the field
+
+ align:start position:0%
+oxide uh remember we said the field
+ 
+
+ align:start position:0%
+oxide uh remember we said the field
+oxide might have a certain height which
+
+ align:start position:0%
+oxide might have a certain height which
+ 
+
+ align:start position:0%
+oxide might have a certain height which
+we're calling t subf o x the thickness
+
+ align:start position:0%
+we're calling t subf o x the thickness
+ 
+
+ align:start position:0%
+we're calling t subf o x the thickness
+of the field
+
+ align:start position:0%
+of the field
+ 
+
+ align:start position:0%
+of the field
+oxide um and it has a certain angle that
+
+ align:start position:0%
+oxide um and it has a certain angle that
+ 
+
+ align:start position:0%
+oxide um and it has a certain angle that
+it's made it's been etched so it's not
+
+ align:start position:0%
+it's made it's been etched so it's not
+ 
+
+ align:start position:0%
+it's made it's been etched so it's not
+perfectly straight up and down it has a
+
+ align:start position:0%
+perfectly straight up and down it has a
+ 
+
+ align:start position:0%
+perfectly straight up and down it has a
+certain angle Theta that it makes with
+
+ align:start position:0%
+certain angle Theta that it makes with
+ 
+
+ align:start position:0%
+certain angle Theta that it makes with
+respect to the substrate so that's your
+
+ align:start position:0%
+respect to the substrate so that's your
+ 
+
+ align:start position:0%
+respect to the substrate so that's your
+field oxide and this black region on top
+
+ align:start position:0%
+field oxide and this black region on top
+ 
+
+ align:start position:0%
+field oxide and this black region on top
+is meant to represent the polysilicon so
+
+ align:start position:0%
+is meant to represent the polysilicon so
+ 
+
+ align:start position:0%
+is meant to represent the polysilicon so
+remember polysilicon is always deposited
+
+ align:start position:0%
+remember polysilicon is always deposited
+ 
+
+ align:start position:0%
+remember polysilicon is always deposited
+everywhere across the
+
+ align:start position:0%
+everywhere across the
+ 
+
+ align:start position:0%
+everywhere across the
+chip um so the black region is the
+
+ align:start position:0%
+chip um so the black region is the
+ 
+
+ align:start position:0%
+chip um so the black region is the
+thickness of the poly now you notice
+
+ align:start position:0%
+thickness of the poly now you notice
+ 
+
+ align:start position:0%
+thickness of the poly now you notice
+that on the sloped portion the thickness
+
+ align:start position:0%
+that on the sloped portion the thickness
+ 
+
+ align:start position:0%
+that on the sloped portion the thickness
+of the poly from here to here is given
+
+ align:start position:0%
+of the poly from here to here is given
+ 
+
+ align:start position:0%
+of the poly from here to here is given
+by T poly times the cosine Theta uh
+
+ align:start position:0%
+by T poly times the cosine Theta uh
+ 
+
+ align:start position:0%
+by T poly times the cosine Theta uh
+right so that it's it's thicker here um
+
+ align:start position:0%
+right so that it's it's thicker here um
+ 
+
+ align:start position:0%
+right so that it's it's thicker here um
+than it is than it is here it's just
+
+ align:start position:0%
+than it is than it is here it's just
+ 
+
+ align:start position:0%
+than it is than it is here it's just
+just by
+
+ align:start position:0%
+just by
+ 
+
+ align:start position:0%
+just by
+geometry so the thicker portion of the
+
+ align:start position:0%
+geometry so the thicker portion of the
+ 
+
+ align:start position:0%
+geometry so the thicker portion of the
+poly here means that you need to
+
+ align:start position:0%
+poly here means that you need to
+ 
+
+ align:start position:0%
+poly here means that you need to
+increase in order to get clear all the
+
+ align:start position:0%
+increase in order to get clear all the
+ 
+
+ align:start position:0%
+increase in order to get clear all the
+poly and to avoid forming a Stringer
+
+ align:start position:0%
+poly and to avoid forming a Stringer
+ 
+
+ align:start position:0%
+poly and to avoid forming a Stringer
+down here you need to increase the EDG
+
+ align:start position:0%
+down here you need to increase the EDG
+ 
+
+ align:start position:0%
+down here you need to increase the EDG
+taon and in fact this this formula gives
+
+ align:start position:0%
+taon and in fact this this formula gives
+ 
+
+ align:start position:0%
+taon and in fact this this formula gives
+you here for this particular um
+
+ align:start position:0%
+you here for this particular um
+ 
+
+ align:start position:0%
+you here for this particular um
+topography gives you an example a
+
+ align:start position:0%
+topography gives you an example a
+ 
+
+ align:start position:0%
+topography gives you an example a
+calculation of the over uh here in in
+
+ align:start position:0%
+calculation of the over uh here in in
+ 
+
+ align:start position:0%
+calculation of the over uh here in in
+percent uh that you would need uh for
+
+ align:start position:0%
+percent uh that you would need uh for
+ 
+
+ align:start position:0%
+percent uh that you would need uh for
+this topography and it's 1/ cosine Theta
+
+ align:start position:0%
+this topography and it's 1/ cosine Theta
+ 
+
+ align:start position:0%
+this topography and it's 1/ cosine Theta
+that quantity minus 1 * 100% so if you
+
+ align:start position:0%
+that quantity minus 1 * 100% so if you
+ 
+
+ align:start position:0%
+that quantity minus 1 * 100% so if you
+have a sidewall angle of 45 Dees so this
+
+ align:start position:0%
+have a sidewall angle of 45 Dees so this
+ 
+
+ align:start position:0%
+have a sidewall angle of 45 Dees so this
+particular example says 45 degrees just
+
+ align:start position:0%
+particular example says 45 degrees just
+ 
+
+ align:start position:0%
+particular example says 45 degrees just
+because of this um we need about a 40%
+
+ align:start position:0%
+because of this um we need about a 40%
+ 
+
+ align:start position:0%
+because of this um we need about a 40%
+poly overedge time to avoid stringers so
+
+ align:start position:0%
+poly overedge time to avoid stringers so
+ 
+
+ align:start position:0%
+poly overedge time to avoid stringers so
+what do people do well either you have
+
+ align:start position:0%
+what do people do well either you have
+ 
+
+ align:start position:0%
+what do people do well either you have
+no topography you keep it very flat you
+
+ align:start position:0%
+no topography you keep it very flat you
+ 
+
+ align:start position:0%
+no topography you keep it very flat you
+bury your field loide and that's called
+
+ align:start position:0%
+bury your field loide and that's called
+ 
+
+ align:start position:0%
+bury your field loide and that's called
+a shallow trench or if you are going to
+
+ align:start position:0%
+a shallow trench or if you are going to
+ 
+
+ align:start position:0%
+a shallow trench or if you are going to
+have a little bit of topography you make
+
+ align:start position:0%
+have a little bit of topography you make
+ 
+
+ align:start position:0%
+have a little bit of topography you make
+it you kind of ramp the Angles and you
+
+ align:start position:0%
+it you kind of ramp the Angles and you
+ 
+
+ align:start position:0%
+it you kind of ramp the Angles and you
+make very shallow ramps you don't have
+
+ align:start position:0%
+make very shallow ramps you don't have
+ 
+
+ align:start position:0%
+make very shallow ramps you don't have
+anything really abrupt um so that you
+
+ align:start position:0%
+anything really abrupt um so that you
+ 
+
+ align:start position:0%
+anything really abrupt um so that you
+know depending on this angle you have to
+
+ align:start position:0%
+know depending on this angle you have to
+ 
+
+ align:start position:0%
+know depending on this angle you have to
+adjust your overed time otherwise you'll
+
+ align:start position:0%
+adjust your overed time otherwise you'll
+ 
+
+ align:start position:0%
+adjust your overed time otherwise you'll
+end up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stringers um sometimes by the way here
+
+ align:start position:0%
+stringers um sometimes by the way here
+ 
+
+ align:start position:0%
+stringers um sometimes by the way here
+on slide 19 sometimes I've been calling
+
+ align:start position:0%
+on slide 19 sometimes I've been calling
+ 
+
+ align:start position:0%
+on slide 19 sometimes I've been calling
+these things stringers stringers is the
+
+ align:start position:0%
+these things stringers stringers is the
+ 
+
+ align:start position:0%
+these things stringers stringers is the
+derogatory term Stringer usually means
+
+ align:start position:0%
+derogatory term Stringer usually means
+ 
+
+ align:start position:0%
+derogatory term Stringer usually means
+something that was left behind that you
+
+ align:start position:0%
+something that was left behind that you
+ 
+
+ align:start position:0%
+something that was left behind that you
+didn't want there um Sometimes some a
+
+ align:start position:0%
+didn't want there um Sometimes some a
+ 
+
+ align:start position:0%
+didn't want there um Sometimes some a
+Stringer is something we want in fact
+
+ align:start position:0%
+Stringer is something we want in fact
+ 
+
+ align:start position:0%
+Stringer is something we want in fact
+it's called when we want it we we give
+
+ align:start position:0%
+it's called when we want it we we give
+ 
+
+ align:start position:0%
+it's called when we want it we we give
+it a a positive name we call it a
+
+ align:start position:0%
+it a a positive name we call it a
+ 
+
+ align:start position:0%
+it a a positive name we call it a
+sidewall spacer so we often use
+
+ align:start position:0%
+sidewall spacer so we often use
+ 
+
+ align:start position:0%
+sidewall spacer so we often use
+anisotropic etches uh without an
+
+ align:start position:0%
+anisotropic etches uh without an
+ 
+
+ align:start position:0%
+anisotropic etches uh without an
+overetch to get a sidewall spacer
+
+ align:start position:0%
+overetch to get a sidewall spacer
+ 
+
+ align:start position:0%
+overetch to get a sidewall spacer
+intentionally here's an example of an
+
+ align:start position:0%
+intentionally here's an example of an
+ 
+
+ align:start position:0%
+intentionally here's an example of an
+intentional production of a Stringer uh
+
+ align:start position:0%
+intentional production of a Stringer uh
+ 
+
+ align:start position:0%
+intentional production of a Stringer uh
+we have a substrate we put one film on
+
+ align:start position:0%
+we have a substrate we put one film on
+ 
+
+ align:start position:0%
+we have a substrate we put one film on
+it could be polysilicon that we have now
+
+ align:start position:0%
+it could be polysilicon that we have now
+ 
+
+ align:start position:0%
+it could be polysilicon that we have now
+patterned with a very sharp step we put
+
+ align:start position:0%
+patterned with a very sharp step we put
+ 
+
+ align:start position:0%
+patterned with a very sharp step we put
+a second film on where we adjust the
+
+ align:start position:0%
+a second film on where we adjust the
+ 
+
+ align:start position:0%
+a second film on where we adjust the
+height or the thickness I should say of
+
+ align:start position:0%
+height or the thickness I should say of
+ 
+
+ align:start position:0%
+height or the thickness I should say of
+the second film to be about oh just the
+
+ align:start position:0%
+the second film to be about oh just the
+ 
+
+ align:start position:0%
+the second film to be about oh just the
+right thickness so that um after I've
+
+ align:start position:0%
+right thickness so that um after I've
+ 
+
+ align:start position:0%
+right thickness so that um after I've
+done a purely vertical or purely
+
+ align:start position:0%
+done a purely vertical or purely
+ 
+
+ align:start position:0%
+done a purely vertical or purely
+anisotropic etch when I'm done I have a
+
+ align:start position:0%
+anisotropic etch when I'm done I have a
+ 
+
+ align:start position:0%
+anisotropic etch when I'm done I have a
+sidewall spacer forming so this material
+
+ align:start position:0%
+sidewall spacer forming so this material
+ 
+
+ align:start position:0%
+sidewall spacer forming so this material
+is Left Behind the nice thing about it
+
+ align:start position:0%
+is Left Behind the nice thing about it
+ 
+
+ align:start position:0%
+is Left Behind the nice thing about it
+is it is self-aligned so I didn't have
+
+ align:start position:0%
+is it is self-aligned so I didn't have
+ 
+
+ align:start position:0%
+is it is self-aligned so I didn't have
+to put another mask down in order to p
+
+ align:start position:0%
+to put another mask down in order to p
+ 
+
+ align:start position:0%
+to put another mask down in order to p
+and do photo lithography to pattern this
+
+ align:start position:0%
+and do photo lithography to pattern this
+ 
+
+ align:start position:0%
+and do photo lithography to pattern this
+all you have to do is have a step in
+
+ align:start position:0%
+all you have to do is have a step in
+ 
+
+ align:start position:0%
+all you have to do is have a step in
+your film number one you put another
+
+ align:start position:0%
+your film number one you put another
+ 
+
+ align:start position:0%
+your film number one you put another
+film down you clear the whole thing with
+
+ align:start position:0%
+film down you clear the whole thing with
+ 
+
+ align:start position:0%
+film down you clear the whole thing with
+a vertical etch and bingo right on the
+
+ align:start position:0%
+a vertical etch and bingo right on the
+ 
+
+ align:start position:0%
+a vertical etch and bingo right on the
+sidewall self-aligned to it is uh a
+
+ align:start position:0%
+sidewall self-aligned to it is uh a
+ 
+
+ align:start position:0%
+sidewall self-aligned to it is uh a
+spacer layer in facts that's exactly how
+
+ align:start position:0%
+spacer layer in facts that's exactly how
+ 
+
+ align:start position:0%
+spacer layer in facts that's exactly how
+spacer layers are formed in modern
+
+ align:start position:0%
+spacer layers are formed in modern
+ 
+
+ align:start position:0%
+spacer layers are formed in modern
+mosfets the polyg gate is etched
+
+ align:start position:0%
+mosfets the polyg gate is etched
+ 
+
+ align:start position:0%
+mosfets the polyg gate is etched
+vertically a certain thickness of
+
+ align:start position:0%
+vertically a certain thickness of
+ 
+
+ align:start position:0%
+vertically a certain thickness of
+nitride or oxide is put down it's etched
+
+ align:start position:0%
+nitride or oxide is put down it's etched
+ 
+
+ align:start position:0%
+nitride or oxide is put down it's etched
+anisotropically and you end up with a
+
+ align:start position:0%
+anisotropically and you end up with a
+ 
+
+ align:start position:0%
+anisotropically and you end up with a
+sidewall spacer so stringers so to speak
+
+ align:start position:0%
+sidewall spacer so stringers so to speak
+ 
+
+ align:start position:0%
+sidewall spacer so stringers so to speak
+are not necessarily bad um usually the
+
+ align:start position:0%
+are not necessarily bad um usually the
+ 
+
+ align:start position:0%
+are not necessarily bad um usually the
+word Stringer means something left
+
+ align:start position:0%
+word Stringer means something left
+ 
+
+ align:start position:0%
+word Stringer means something left
+behind that you don't want but if you do
+
+ align:start position:0%
+behind that you don't want but if you do
+ 
+
+ align:start position:0%
+behind that you don't want but if you do
+want it you call it a sidewall spacer
+
+ align:start position:0%
+want it you call it a sidewall spacer
+ 
+
+ align:start position:0%
+want it you call it a sidewall spacer
+and the width of the spacer which is
+
+ align:start position:0%
+and the width of the spacer which is
+ 
+
+ align:start position:0%
+and the width of the spacer which is
+from this point here to that point there
+
+ align:start position:0%
+from this point here to that point there
+ 
+
+ align:start position:0%
+from this point here to that point there
+that sort of the lateral Dimension is a
+
+ align:start position:0%
+that sort of the lateral Dimension is a
+ 
+
+ align:start position:0%
+that sort of the lateral Dimension is a
+function of how long you did etch and
+
+ align:start position:0%
+function of how long you did etch and
+ 
+
+ align:start position:0%
+function of how long you did etch and
+how over how much overetch you did as
+
+ align:start position:0%
+how over how much overetch you did as
+ 
+
+ align:start position:0%
+how over how much overetch you did as
+well as um the thickness of film two
+
+ align:start position:0%
+well as um the thickness of film two
+ 
+
+ align:start position:0%
+well as um the thickness of film two
+relative to the thickness of film one in
+
+ align:start position:0%
+relative to the thickness of film one in
+ 
+
+ align:start position:0%
+relative to the thickness of film one in
+this example so you can adjust all of
+
+ align:start position:0%
+this example so you can adjust all of
+ 
+
+ align:start position:0%
+this example so you can adjust all of
+those to uh create different width
+
+ align:start position:0%
+those to uh create different width
+ 
+
+ align:start position:0%
+those to uh create different width
+spacers that's a very critical process
+
+ align:start position:0%
+spacers that's a very critical process
+ 
+
+ align:start position:0%
+spacers that's a very critical process
+uh in modern tech
+
+ align:start position:0%
+uh in modern tech
+ 
+
+ align:start position:0%
+uh in modern tech
+technology now this slide actually I
+
+ align:start position:0%
+technology now this slide actually I
+ 
+
+ align:start position:0%
+technology now this slide actually I
+apologize is not in your handouts this
+
+ align:start position:0%
+apologize is not in your handouts this
+ 
+
+ align:start position:0%
+apologize is not in your handouts this
+on page 20 there's two slides here that
+
+ align:start position:0%
+on page 20 there's two slides here that
+ 
+
+ align:start position:0%
+on page 20 there's two slides here that
+that the next couple of three slides are
+
+ align:start position:0%
+that the next couple of three slides are
+ 
+
+ align:start position:0%
+that the next couple of three slides are
+not on your handout uh I don't well no
+
+ align:start position:0%
+not on your handout uh I don't well no
+ 
+
+ align:start position:0%
+not on your handout uh I don't well no
+this one is it's the next two after that
+
+ align:start position:0%
+this one is it's the next two after that
+ 
+
+ align:start position:0%
+this one is it's the next two after that
+that are not uh and if you need the
+
+ align:start position:0%
+that are not uh and if you need the
+ 
+
+ align:start position:0%
+that are not uh and if you need the
+up-to-date handout that they're all
+
+ align:start position:0%
+up-to-date handout that they're all
+ 
+
+ align:start position:0%
+up-to-date handout that they're all
+posted on the web so you can get the
+
+ align:start position:0%
+posted on the web so you can get the
+ 
+
+ align:start position:0%
+posted on the web so you can get the
+PDFs yourself I wanted to is list here
+
+ align:start position:0%
+PDFs yourself I wanted to is list here
+ 
+
+ align:start position:0%
+PDFs yourself I wanted to is list here
+on slide 20 a couple of new issues for
+
+ align:start position:0%
+on slide 20 a couple of new issues for
+ 
+
+ align:start position:0%
+on slide 20 a couple of new issues for
+gate etching and pattering that have
+
+ align:start position:0%
+gate etching and pattering that have
+ 
+
+ align:start position:0%
+gate etching and pattering that have
+come up in the last say three to five
+
+ align:start position:0%
+come up in the last say three to five
+ 
+
+ align:start position:0%
+come up in the last say three to five
+years that you're going to hear more and
+
+ align:start position:0%
+years that you're going to hear more and
+ 
+
+ align:start position:0%
+years that you're going to hear more and
+more about
+
+ align:start position:0%
+more about
+ 
+
+ align:start position:0%
+more about
+uh in the year 2000 this is what people
+
+ align:start position:0%
+uh in the year 2000 this is what people
+ 
+
+ align:start position:0%
+uh in the year 2000 this is what people
+were concerned about they were concerned
+
+ align:start position:0%
+were concerned about they were concerned
+ 
+
+ align:start position:0%
+were concerned about they were concerned
+about etching poly making it vertical
+
+ align:start position:0%
+about etching poly making it vertical
+ 
+
+ align:start position:0%
+about etching poly making it vertical
+maintaining a critical dimension of say
+
+ align:start position:0%
+maintaining a critical dimension of say
+ 
+
+ align:start position:0%
+maintaining a critical dimension of say
+0.18 nanometers .18 microns rather and
+
+ align:start position:0%
+0.18 nanometers .18 microns rather and
+ 
+
+ align:start position:0%
+0.18 nanometers .18 microns rather and
+they were etching through only
+
+ align:start position:0%
+they were etching through only
+ 
+
+ align:start position:0%
+they were etching through only
+polysilicon and putting a putting a
+
+ align:start position:0%
+polysilicon and putting a putting a
+ 
+
+ align:start position:0%
+polysilicon and putting a putting a
+silicide strap on top after after the
+
+ align:start position:0%
+silicide strap on top after after the
+ 
+
+ align:start position:0%
+silicide strap on top after after the
+gate Edge had been completed so that was
+
+ align:start position:0%
+gate Edge had been completed so that was
+ 
+
+ align:start position:0%
+gate Edge had been completed so that was
+the what I should s call the more
+
+ align:start position:0%
+the what I should s call the more
+ 
+
+ align:start position:0%
+the what I should s call the more
+traditional or conventional
+
+ align:start position:0%
+traditional or conventional
+ 
+
+ align:start position:0%
+traditional or conventional
+technology uh what are people doing
+
+ align:start position:0%
+technology uh what are people doing
+ 
+
+ align:start position:0%
+technology uh what are people doing
+these days well people these days are
+
+ align:start position:0%
+these days well people these days are
+ 
+
+ align:start position:0%
+these days well people these days are
+not just doing this for one thing the
+
+ align:start position:0%
+not just doing this for one thing the
+ 
+
+ align:start position:0%
+not just doing this for one thing the
+gates are a lot narrower look at uh
+
+ align:start position:0%
+gates are a lot narrower look at uh
+ 
+
+ align:start position:0%
+gates are a lot narrower look at uh
+today's Gates people are instead of uh
+
+ align:start position:0%
+today's Gates people are instead of uh
+ 
+
+ align:start position:0%
+today's Gates people are instead of uh
+um doing something like um uh 200
+
+ align:start position:0%
+um doing something like um uh 200
+ 
+
+ align:start position:0%
+um doing something like um uh 200
+nanometers we're down to 70 or 80
+
+ align:start position:0%
+nanometers we're down to 70 or 80
+ 
+
+ align:start position:0%
+nanometers we're down to 70 or 80
+nanometers so the dimensions have shrunk
+
+ align:start position:0%
+nanometers so the dimensions have shrunk
+ 
+
+ align:start position:0%
+nanometers so the dimensions have shrunk
+quite a bit and people are doing what
+
+ align:start position:0%
+quite a bit and people are doing what
+ 
+
+ align:start position:0%
+quite a bit and people are doing what
+they call fully silicided Gates so
+
+ align:start position:0%
+they call fully silicided Gates so
+ 
+
+ align:start position:0%
+they call fully silicided Gates so
+instead of just reacting the polysilicon
+
+ align:start position:0%
+instead of just reacting the polysilicon
+ 
+
+ align:start position:0%
+instead of just reacting the polysilicon
+just at the very top of the gate people
+
+ align:start position:0%
+just at the very top of the gate people
+ 
+
+ align:start position:0%
+just at the very top of the gate people
+are actually putting down enough metal
+
+ align:start position:0%
+are actually putting down enough metal
+ 
+
+ align:start position:0%
+are actually putting down enough metal
+and reacting it at the right temperature
+
+ align:start position:0%
+and reacting it at the right temperature
+ 
+
+ align:start position:0%
+and reacting it at the right temperature
+that the metal reacts all the way to the
+
+ align:start position:0%
+that the metal reacts all the way to the
+ 
+
+ align:start position:0%
+that the metal reacts all the way to the
+very bottom in this case on the bottom
+
+ align:start position:0%
+very bottom in this case on the bottom
+ 
+
+ align:start position:0%
+very bottom in this case on the bottom
+would be nickel
+
+ align:start position:0%
+would be nickel
+ 
+
+ align:start position:0%
+would be nickel
+pilicide uh this was formed by
+
+ align:start position:0%
+pilicide uh this was formed by
+ 
+
+ align:start position:0%
+pilicide uh this was formed by
+depositing nickel and reacting it at 450
+
+ align:start position:0%
+depositing nickel and reacting it at 450
+ 
+
+ align:start position:0%
+depositing nickel and reacting it at 450
+all the way to the bottom so there's no
+
+ align:start position:0%
+all the way to the bottom so there's no
+ 
+
+ align:start position:0%
+all the way to the bottom so there's no
+polysilicon left because these days
+
+ align:start position:0%
+polysilicon left because these days
+ 
+
+ align:start position:0%
+polysilicon left because these days
+people don't want polysilicon Gates
+
+ align:start position:0%
+people don't want polysilicon Gates
+ 
+
+ align:start position:0%
+people don't want polysilicon Gates
+polysilicon is a great material to etch
+
+ align:start position:0%
+polysilicon is a great material to etch
+ 
+
+ align:start position:0%
+polysilicon is a great material to etch
+it's highly compatible chemically with
+
+ align:start position:0%
+it's highly compatible chemically with
+ 
+
+ align:start position:0%
+it's highly compatible chemically with
+oxide um but it it has um gate depletion
+
+ align:start position:0%
+oxide um but it it has um gate depletion
+ 
+
+ align:start position:0%
+oxide um but it it has um gate depletion
+problems it doesn't have enough carriers
+
+ align:start position:0%
+problems it doesn't have enough carriers
+ 
+
+ align:start position:0%
+problems it doesn't have enough carriers
+in it polysilicon what's the highest you
+
+ align:start position:0%
+in it polysilicon what's the highest you
+ 
+
+ align:start position:0%
+in it polysilicon what's the highest you
+can dope polysilicon well maybe 1 to 5 *
+
+ align:start position:0%
+can dope polysilicon well maybe 1 to 5 *
+ 
+
+ align:start position:0%
+can dope polysilicon well maybe 1 to 5 *
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+20 so that that that limits your uh
+
+ align:start position:0%
+20 so that that that limits your uh
+ 
+
+ align:start position:0%
+20 so that that that limits your uh
+resistivity and it limits your your gate
+
+ align:start position:0%
+resistivity and it limits your your gate
+ 
+
+ align:start position:0%
+resistivity and it limits your your gate
+depletion people want to use Metals
+
+ align:start position:0%
+depletion people want to use Metals
+ 
+
+ align:start position:0%
+depletion people want to use Metals
+what's the concentration of electrons in
+
+ align:start position:0%
+what's the concentration of electrons in
+ 
+
+ align:start position:0%
+what's the concentration of electrons in
+a metal know 10 22 or 10 23 it's huge
+
+ align:start position:0%
+a metal know 10 22 or 10 23 it's huge
+ 
+
+ align:start position:0%
+a metal know 10 22 or 10 23 it's huge
+it's three or is a magnitude higher so
+
+ align:start position:0%
+it's three or is a magnitude higher so
+ 
+
+ align:start position:0%
+it's three or is a magnitude higher so
+we need more electrons or more holes
+
+ align:start position:0%
+we need more electrons or more holes
+ 
+
+ align:start position:0%
+we need more electrons or more holes
+more carriers in our gates these days
+
+ align:start position:0%
+more carriers in our gates these days
+ 
+
+ align:start position:0%
+more carriers in our gates these days
+the way we do it is we take poly and you
+
+ align:start position:0%
+the way we do it is we take poly and you
+ 
+
+ align:start position:0%
+the way we do it is we take poly and you
+convert it completely to pilicide this
+
+ align:start position:0%
+convert it completely to pilicide this
+ 
+
+ align:start position:0%
+convert it completely to pilicide this
+is called a fully silicided process this
+
+ align:start position:0%
+is called a fully silicided process this
+ 
+
+ align:start position:0%
+is called a fully silicided process this
+is only in research there's a lot of of
+
+ align:start position:0%
+is only in research there's a lot of of
+ 
+
+ align:start position:0%
+is only in research there's a lot of of
+issues with doing this here's an example
+
+ align:start position:0%
+issues with doing this here's an example
+ 
+
+ align:start position:0%
+issues with doing this here's an example
+where they tried to do the suiciding
+
+ align:start position:0%
+where they tried to do the suiciding
+ 
+
+ align:start position:0%
+where they tried to do the suiciding
+with Cobalt in the upper uh micrograph
+
+ align:start position:0%
+with Cobalt in the upper uh micrograph
+ 
+
+ align:start position:0%
+with Cobalt in the upper uh micrograph
+upper SCM micrograph here it didn't work
+
+ align:start position:0%
+upper SCM micrograph here it didn't work
+ 
+
+ align:start position:0%
+upper SCM micrograph here it didn't work
+too well as you can see the Cobalt went
+
+ align:start position:0%
+too well as you can see the Cobalt went
+ 
+
+ align:start position:0%
+too well as you can see the Cobalt went
+down in it didn't make it to the bottom
+
+ align:start position:0%
+down in it didn't make it to the bottom
+ 
+
+ align:start position:0%
+down in it didn't make it to the bottom
+in fact what happens the the Silicon got
+
+ align:start position:0%
+in fact what happens the the Silicon got
+ 
+
+ align:start position:0%
+in fact what happens the the Silicon got
+sucked up in the and next time we'll
+
+ align:start position:0%
+sucked up in the and next time we'll
+ 
+
+ align:start position:0%
+sucked up in the and next time we'll
+talk about pilicide reactions the
+
+ align:start position:0%
+talk about pilicide reactions the
+ 
+
+ align:start position:0%
+talk about pilicide reactions the
+Silicon was actually moving and you
+
+ align:start position:0%
+Silicon was actually moving and you
+ 
+
+ align:start position:0%
+Silicon was actually moving and you
+ended up with a big void so you had no
+
+ align:start position:0%
+ended up with a big void so you had no
+ 
+
+ align:start position:0%
+ended up with a big void so you had no
+gate in this example so this particular
+
+ align:start position:0%
+gate in this example so this particular
+ 
+
+ align:start position:0%
+gate in this example so this particular
+paper was just showing uh I took from uh
+
+ align:start position:0%
+paper was just showing uh I took from uh
+ 
+
+ align:start position:0%
+paper was just showing uh I took from uh
+a few months ago at the vsi conference
+
+ align:start position:0%
+a few months ago at the vsi conference
+ 
+
+ align:start position:0%
+a few months ago at the vsi conference
+in why nickel pilicide works much better
+
+ align:start position:0%
+in why nickel pilicide works much better
+ 
+
+ align:start position:0%
+in why nickel pilicide works much better
+for fully suiciding than does Cobalt
+
+ align:start position:0%
+for fully suiciding than does Cobalt
+ 
+
+ align:start position:0%
+for fully suiciding than does Cobalt
+pilicide which leaves behind uh vo so
+
+ align:start position:0%
+pilicide which leaves behind uh vo so
+ 
+
+ align:start position:0%
+pilicide which leaves behind uh vo so
+there's an example not only are we
+
+ align:start position:0%
+there's an example not only are we
+ 
+
+ align:start position:0%
+there's an example not only are we
+etching poly silan Gates these days we
+
+ align:start position:0%
+etching poly silan Gates these days we
+ 
+
+ align:start position:0%
+etching poly silan Gates these days we
+may end up piling them completely um
+
+ align:start position:0%
+may end up piling them completely um
+ 
+
+ align:start position:0%
+may end up piling them completely um
+that's people are considering there's
+
+ align:start position:0%
+that's people are considering there's
+ 
+
+ align:start position:0%
+that's people are considering there's
+another type of process called which I'm
+
+ align:start position:0%
+another type of process called which I'm
+ 
+
+ align:start position:0%
+another type of process called which I'm
+picturing here on the lower left called
+
+ align:start position:0%
+picturing here on the lower left called
+ 
+
+ align:start position:0%
+picturing here on the lower left called
+a damine replacement gate process and
+
+ align:start position:0%
+a damine replacement gate process and
+ 
+
+ align:start position:0%
+a damine replacement gate process and
+here's an example of a gate where um I
+
+ align:start position:0%
+here's an example of a gate where um I
+ 
+
+ align:start position:0%
+here's an example of a gate where um I
+have Ty nitride so this material uh well
+
+ align:start position:0%
+have Ty nitride so this material uh well
+ 
+
+ align:start position:0%
+have Ty nitride so this material uh well
+it's got tungsten on the top that's the
+
+ align:start position:0%
+it's got tungsten on the top that's the
+ 
+
+ align:start position:0%
+it's got tungsten on the top that's the
+bright material and this sort of gray
+
+ align:start position:0%
+bright material and this sort of gray
+ 
+
+ align:start position:0%
+bright material and this sort of gray
+material is a thin layer of Ty
+
+ align:start position:0%
+material is a thin layer of Ty
+ 
+
+ align:start position:0%
+material is a thin layer of Ty
+nitride and the gate dialectric is half
+
+ align:start position:0%
+nitride and the gate dialectric is half
+ 
+
+ align:start position:0%
+nitride and the gate dialectric is half
+mum dioxide which is down here this is
+
+ align:start position:0%
+mum dioxide which is down here this is
+ 
+
+ align:start position:0%
+mum dioxide which is down here this is
+on a silicon germanium uh type of high
+
+ align:start position:0%
+on a silicon germanium uh type of high
+ 
+
+ align:start position:0%
+on a silicon germanium uh type of high
+Mobility transistor that was also
+
+ align:start position:0%
+Mobility transistor that was also
+ 
+
+ align:start position:0%
+Mobility transistor that was also
+published about six months ago doesn't
+
+ align:start position:0%
+published about six months ago doesn't
+ 
+
+ align:start position:0%
+published about six months ago doesn't
+look anything like a polysilicon gate so
+
+ align:start position:0%
+look anything like a polysilicon gate so
+ 
+
+ align:start position:0%
+look anything like a polysilicon gate so
+not only um are we fully suiciding the
+
+ align:start position:0%
+not only um are we fully suiciding the
+ 
+
+ align:start position:0%
+not only um are we fully suiciding the
+gates but sometimes we're actually
+
+ align:start position:0%
+gates but sometimes we're actually
+ 
+
+ align:start position:0%
+gates but sometimes we're actually
+replacing the polysilicon with another
+
+ align:start position:0%
+replacing the polysilicon with another
+ 
+
+ align:start position:0%
+replacing the polysilicon with another
+material with a gate uh a metal material
+
+ align:start position:0%
+material with a gate uh a metal material
+ 
+
+ align:start position:0%
+material with a gate uh a metal material
+and Ty nitrite is a very popular one so
+
+ align:start position:0%
+and Ty nitrite is a very popular one so
+ 
+
+ align:start position:0%
+and Ty nitrite is a very popular one so
+gate itching is evolving from not only
+
+ align:start position:0%
+gate itching is evolving from not only
+ 
+
+ align:start position:0%
+gate itching is evolving from not only
+having to etge poly and stop on
+
+ align:start position:0%
+having to etge poly and stop on
+ 
+
+ align:start position:0%
+having to etge poly and stop on
+dialectric but now we may have to etge
+
+ align:start position:0%
+dialectric but now we may have to etge
+ 
+
+ align:start position:0%
+dialectric but now we may have to etge
+Metals so lots of new technologies are
+
+ align:start position:0%
+Metals so lots of new technologies are
+ 
+
+ align:start position:0%
+Metals so lots of new technologies are
+being developed uh over the last two or
+
+ align:start position:0%
+being developed uh over the last two or
+ 
+
+ align:start position:0%
+being developed uh over the last two or
+three years and will continue to be
+
+ align:start position:0%
+three years and will continue to be
+ 
+
+ align:start position:0%
+three years and will continue to be
+developed to uh to push the technology
+
+ align:start position:0%
+developed to uh to push the technology
+ 
+
+ align:start position:0%
+developed to uh to push the technology
+forward so it's these next two slides I
+
+ align:start position:0%
+forward so it's these next two slides I
+ 
+
+ align:start position:0%
+forward so it's these next two slides I
+apologize are not in your handouts 21
+
+ align:start position:0%
+apologize are not in your handouts 21
+ 
+
+ align:start position:0%
+apologize are not in your handouts 21
+and 22 but they are on the website so
+
+ align:start position:0%
+and 22 but they are on the website so
+ 
+
+ align:start position:0%
+and 22 but they are on the website so
+you can download the PDF file um how did
+
+ align:start position:0%
+you can download the PDF file um how did
+ 
+
+ align:start position:0%
+you can download the PDF file um how did
+they make I just wanted to show you this
+
+ align:start position:0%
+they make I just wanted to show you this
+ 
+
+ align:start position:0%
+they make I just wanted to show you this
+lower left how does one make a gate that
+
+ align:start position:0%
+lower left how does one make a gate that
+ 
+
+ align:start position:0%
+lower left how does one make a gate that
+looks anything like this just to give
+
+ align:start position:0%
+looks anything like this just to give
+ 
+
+ align:start position:0%
+looks anything like this just to give
+you an
+
+ align:start position:0%
+you an
+ 
+
+ align:start position:0%
+you an
+idea well this is the way you do it um
+
+ align:start position:0%
+idea well this is the way you do it um
+ 
+
+ align:start position:0%
+idea well this is the way you do it um
+uh again this was of this particular uh
+
+ align:start position:0%
+uh again this was of this particular uh
+ 
+
+ align:start position:0%
+uh again this was of this particular uh
+example I took from iedm of 2002 people
+
+ align:start position:0%
+example I took from iedm of 2002 people
+ 
+
+ align:start position:0%
+example I took from iedm of 2002 people
+um make uh use the ordinary process to
+
+ align:start position:0%
+um make uh use the ordinary process to
+ 
+
+ align:start position:0%
+um make uh use the ordinary process to
+make a polysilicon gate so you put down
+
+ align:start position:0%
+make a polysilicon gate so you put down
+ 
+
+ align:start position:0%
+make a polysilicon gate so you put down
+poly you etch it you make your sidewall
+
+ align:start position:0%
+poly you etch it you make your sidewall
+ 
+
+ align:start position:0%
+poly you etch it you make your sidewall
+spacers so that's just like what we've
+
+ align:start position:0%
+spacers so that's just like what we've
+ 
+
+ align:start position:0%
+spacers so that's just like what we've
+learned about in this course and here is
+
+ align:start position:0%
+learned about in this course and here is
+ 
+
+ align:start position:0%
+learned about in this course and here is
+a a very short Channel mosfet here's a
+
+ align:start position:0%
+a a very short Channel mosfet here's a
+ 
+
+ align:start position:0%
+a a very short Channel mosfet here's a
+very long Channel mosfet now at the end
+
+ align:start position:0%
+very long Channel mosfet now at the end
+ 
+
+ align:start position:0%
+very long Channel mosfet now at the end
+of defining your mosfets you put down
+
+ align:start position:0%
+of defining your mosfets you put down
+ 
+
+ align:start position:0%
+of defining your mosfets you put down
+this gray material and you put it
+
+ align:start position:0%
+this gray material and you put it
+ 
+
+ align:start position:0%
+this gray material and you put it
+everywhere very thick so you put down a
+
+ align:start position:0%
+everywhere very thick so you put down a
+ 
+
+ align:start position:0%
+everywhere very thick so you put down a
+dialectric and then you CMP it down so
+
+ align:start position:0%
+dialectric and then you CMP it down so
+ 
+
+ align:start position:0%
+dialectric and then you CMP it down so
+you have dialectric that's been cmpd and
+
+ align:start position:0%
+you have dialectric that's been cmpd and
+ 
+
+ align:start position:0%
+you have dialectric that's been cmpd and
+flattened it's been flattened down just
+
+ align:start position:0%
+flattened it's been flattened down just
+ 
+
+ align:start position:0%
+flattened it's been flattened down just
+so it stops the the uh polishing stops
+
+ align:start position:0%
+so it stops the the uh polishing stops
+ 
+
+ align:start position:0%
+so it stops the the uh polishing stops
+just around this height okay now what
+
+ align:start position:0%
+just around this height okay now what
+ 
+
+ align:start position:0%
+just around this height okay now what
+you do is you the polysilicon is then
+
+ align:start position:0%
+you do is you the polysilicon is then
+ 
+
+ align:start position:0%
+you do is you the polysilicon is then
+wet chemically etched and removed so you
+
+ align:start position:0%
+wet chemically etched and removed so you
+ 
+
+ align:start position:0%
+wet chemically etched and removed so you
+etch out with an etchant that that digs
+
+ align:start position:0%
+etch out with an etchant that that digs
+ 
+
+ align:start position:0%
+etch out with an etchant that that digs
+out the poly um and if you want you can
+
+ align:start position:0%
+out the poly um and if you want you can
+ 
+
+ align:start position:0%
+out the poly um and if you want you can
+even dig out the gate oxide replace it
+
+ align:start position:0%
+even dig out the gate oxide replace it
+ 
+
+ align:start position:0%
+even dig out the gate oxide replace it
+with a high K so so this is what's
+
+ align:start position:0%
+with a high K so so this is what's
+ 
+
+ align:start position:0%
+with a high K so so this is what's
+called a replacement gate process so I'm
+
+ align:start position:0%
+called a replacement gate process so I'm
+ 
+
+ align:start position:0%
+called a replacement gate process so I'm
+actually I use poly to ex your poly you
+
+ align:start position:0%
+actually I use poly to ex your poly you
+ 
+
+ align:start position:0%
+actually I use poly to ex your poly you
+put down cwall spacers you go through
+
+ align:start position:0%
+put down cwall spacers you go through
+ 
+
+ align:start position:0%
+put down cwall spacers you go through
+the high temperature anal and why would
+
+ align:start position:0%
+the high temperature anal and why would
+ 
+
+ align:start position:0%
+the high temperature anal and why would
+anyone want to do this you put down poly
+
+ align:start position:0%
+anyone want to do this you put down poly
+ 
+
+ align:start position:0%
+anyone want to do this you put down poly
+you pattern it and then later on you're
+
+ align:start position:0%
+you pattern it and then later on you're
+ 
+
+ align:start position:0%
+you pattern it and then later on you're
+going to remove it sounds kind of crazy
+
+ align:start position:0%
+going to remove it sounds kind of crazy
+ 
+
+ align:start position:0%
+going to remove it sounds kind of crazy
+why didn't you just put the metal down
+
+ align:start position:0%
+why didn't you just put the metal down
+ 
+
+ align:start position:0%
+why didn't you just put the metal down
+to begin with but does anybody have any
+
+ align:start position:0%
+to begin with but does anybody have any
+ 
+
+ align:start position:0%
+to begin with but does anybody have any
+ideas on why you might want to use poly
+
+ align:start position:0%
+ideas on why you might want to use poly
+ 
+
+ align:start position:0%
+ideas on why you might want to use poly
+and then stick the metal in at the very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end well there's a couple reasons one
+
+ align:start position:0%
+end well there's a couple reasons one
+ 
+
+ align:start position:0%
+end well there's a couple reasons one
+reason is p we know how to etch poly
+
+ align:start position:0%
+reason is p we know how to etch poly
+ 
+
+ align:start position:0%
+reason is p we know how to etch poly
+perfectly right we've spent the last 20
+
+ align:start position:0%
+perfectly right we've spent the last 20
+ 
+
+ align:start position:0%
+perfectly right we've spent the last 20
+years getting perfectly vertical
+
+ align:start position:0%
+years getting perfectly vertical
+ 
+
+ align:start position:0%
+years getting perfectly vertical
+sidewalls so people know how to etch it
+
+ align:start position:0%
+sidewalls so people know how to etch it
+ 
+
+ align:start position:0%
+sidewalls so people know how to etch it
+that's one reason the second reason is
+
+ align:start position:0%
+that's one reason the second reason is
+ 
+
+ align:start position:0%
+that's one reason the second reason is
+poly can go up to very high temperatures
+
+ align:start position:0%
+poly can go up to very high temperatures
+ 
+
+ align:start position:0%
+poly can go up to very high temperatures
+what do I have to do in this process
+
+ align:start position:0%
+what do I have to do in this process
+ 
+
+ align:start position:0%
+what do I have to do in this process
+after you put the gate down you have to
+
+ align:start position:0%
+after you put the gate down you have to
+ 
+
+ align:start position:0%
+after you put the gate down you have to
+implant the sore drains and you have to
+
+ align:start position:0%
+implant the sore drains and you have to
+ 
+
+ align:start position:0%
+implant the sore drains and you have to
+anal them typically at a th000 degrees
+
+ align:start position:0%
+anal them typically at a th000 degrees
+ 
+
+ align:start position:0%
+anal them typically at a th000 degrees
+these days for 10 seconds or 1050 there
+
+ align:start position:0%
+these days for 10 seconds or 1050 there
+ 
+
+ align:start position:0%
+these days for 10 seconds or 1050 there
+aren't too many metals you can pop up to
+
+ align:start position:0%
+aren't too many metals you can pop up to
+ 
+
+ align:start position:0%
+aren't too many metals you can pop up to
+1050 and not either melt them most
+
+ align:start position:0%
+1050 and not either melt them most
+ 
+
+ align:start position:0%
+1050 and not either melt them most
+metals will melt or if you don't melt
+
+ align:start position:0%
+metals will melt or if you don't melt
+ 
+
+ align:start position:0%
+metals will melt or if you don't melt
+them they could undergo dramatic uh
+
+ align:start position:0%
+them they could undergo dramatic uh
+ 
+
+ align:start position:0%
+them they could undergo dramatic uh
+phase transformation some of them could
+
+ align:start position:0%
+phase transformation some of them could
+ 
+
+ align:start position:0%
+phase transformation some of them could
+diffuse into the wafer and cause
+
+ align:start position:0%
+diffuse into the wafer and cause
+ 
+
+ align:start position:0%
+diffuse into the wafer and cause
+problems with deep levels so metals are
+
+ align:start position:0%
+problems with deep levels so metals are
+ 
+
+ align:start position:0%
+problems with deep levels so metals are
+not considered very good to have at high
+
+ align:start position:0%
+not considered very good to have at high
+ 
+
+ align:start position:0%
+not considered very good to have at high
+temperatures so this is a way of using
+
+ align:start position:0%
+temperatures so this is a way of using
+ 
+
+ align:start position:0%
+temperatures so this is a way of using
+poly as a dummy we know exactly how to
+
+ align:start position:0%
+poly as a dummy we know exactly how to
+ 
+
+ align:start position:0%
+poly as a dummy we know exactly how to
+pattern it the only problem with it it
+
+ align:start position:0%
+pattern it the only problem with it it
+ 
+
+ align:start position:0%
+pattern it the only problem with it it
+just doesn't have enough carriers well
+
+ align:start position:0%
+just doesn't have enough carriers well
+ 
+
+ align:start position:0%
+just doesn't have enough carriers well
+we'll put it in the process so we won't
+
+ align:start position:0%
+we'll put it in the process so we won't
+ 
+
+ align:start position:0%
+we'll put it in the process so we won't
+change the process till the very end
+
+ align:start position:0%
+change the process till the very end
+ 
+
+ align:start position:0%
+change the process till the very end
+we'll etch it out um I don't know how
+
+ align:start position:0%
+we'll etch it out um I don't know how
+ 
+
+ align:start position:0%
+we'll etch it out um I don't know how
+manufacturable I don't believe anyone is
+
+ align:start position:0%
+manufacturable I don't believe anyone is
+ 
+
+ align:start position:0%
+manufacturable I don't believe anyone is
+manufacturing products this was just
+
+ align:start position:0%
+manufacturing products this was just
+ 
+
+ align:start position:0%
+manufacturing products this was just
+published in research about two years
+
+ align:start position:0%
+published in research about two years
+ 
+
+ align:start position:0%
+published in research about two years
+ago it is a kind of a neat idea so after
+
+ align:start position:0%
+ago it is a kind of a neat idea so after
+ 
+
+ align:start position:0%
+ago it is a kind of a neat idea so after
+after You' removed this and you open
+
+ align:start position:0%
+after You' removed this and you open
+ 
+
+ align:start position:0%
+after You' removed this and you open
+this hole well then you have an open
+
+ align:start position:0%
+this hole well then you have an open
+ 
+
+ align:start position:0%
+this hole well then you have an open
+hole you can put down your high k um you
+
+ align:start position:0%
+hole you can put down your high k um you
+ 
+
+ align:start position:0%
+hole you can put down your high k um you
+know your haum dioxide you can put down
+
+ align:start position:0%
+know your haum dioxide you can put down
+ 
+
+ align:start position:0%
+know your haum dioxide you can put down
+your Ty nitride by sputtering and a
+
+ align:start position:0%
+your Ty nitride by sputtering and a
+ 
+
+ align:start position:0%
+your Ty nitride by sputtering and a
+Tungsten cap and then maybe some capping
+
+ align:start position:0%
+Tungsten cap and then maybe some capping
+ 
+
+ align:start position:0%
+Tungsten cap and then maybe some capping
+layer of dialectric and CMP the whole
+
+ align:start position:0%
+layer of dialectric and CMP the whole
+ 
+
+ align:start position:0%
+layer of dialectric and CMP the whole
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+down so that's how they got in that last
+
+ align:start position:0%
+down so that's how they got in that last
+ 
+
+ align:start position:0%
+down so that's how they got in that last
+picture that's how they got that uh
+
+ align:start position:0%
+picture that's how they got that uh
+ 
+
+ align:start position:0%
+picture that's how they got that uh
+replacement gate uh in fact this slide
+
+ align:start position:0%
+replacement gate uh in fact this slide
+ 
+
+ align:start position:0%
+replacement gate uh in fact this slide
+22 was also not in your handout but this
+
+ align:start position:0%
+22 was also not in your handout but this
+ 
+
+ align:start position:0%
+22 was also not in your handout but this
+is what it looks like on uh in a TM
+
+ align:start position:0%
+is what it looks like on uh in a TM
+ 
+
+ align:start position:0%
+is what it looks like on uh in a TM
+cross-section in a 50 nmet mosset where
+
+ align:start position:0%
+cross-section in a 50 nmet mosset where
+ 
+
+ align:start position:0%
+cross-section in a 50 nmet mosset where
+they removed the poly they dug it out
+
+ align:start position:0%
+they removed the poly they dug it out
+ 
+
+ align:start position:0%
+they removed the poly they dug it out
+they put in this very dark black layer
+
+ align:start position:0%
+they put in this very dark black layer
+ 
+
+ align:start position:0%
+they put in this very dark black layer
+of half dioxide so that is your gate
+
+ align:start position:0%
+of half dioxide so that is your gate
+ 
+
+ align:start position:0%
+of half dioxide so that is your gate
+dialectric um the Ty nitride is next a
+
+ align:start position:0%
+dialectric um the Ty nitride is next a
+ 
+
+ align:start position:0%
+dialectric um the Ty nitride is next a
+very thin layer that is your gate
+
+ align:start position:0%
+very thin layer that is your gate
+ 
+
+ align:start position:0%
+very thin layer that is your gate
+material um they then have tungsten that
+
+ align:start position:0%
+material um they then have tungsten that
+ 
+
+ align:start position:0%
+material um they then have tungsten that
+they fill it up with so they have uh the
+
+ align:start position:0%
+they fill it up with so they have uh the
+ 
+
+ align:start position:0%
+they fill it up with so they have uh the
+tungsten material which is a little bit
+
+ align:start position:0%
+tungsten material which is a little bit
+ 
+
+ align:start position:0%
+tungsten material which is a little bit
+more um uh environmentally friendly or
+
+ align:start position:0%
+more um uh environmentally friendly or
+ 
+
+ align:start position:0%
+more um uh environmentally friendly or
+it's an easier material to work with to
+
+ align:start position:0%
+it's an easier material to work with to
+ 
+
+ align:start position:0%
+it's an easier material to work with to
+fill up the plug so that's an example uh
+
+ align:start position:0%
+fill up the plug so that's an example uh
+ 
+
+ align:start position:0%
+fill up the plug so that's an example uh
+where the poly was completely removed
+
+ align:start position:0%
+where the poly was completely removed
+ 
+
+ align:start position:0%
+where the poly was completely removed
+so new types of things have to be done
+
+ align:start position:0%
+so new types of things have to be done
+ 
+
+ align:start position:0%
+so new types of things have to be done
+uh with uh uh forming uh Gates these
+
+ align:start position:0%
+uh with uh uh forming uh Gates these
+ 
+
+ align:start position:0%
+uh with uh uh forming uh Gates these
+days okay let me move on here uh now on
+
+ align:start position:0%
+days okay let me move on here uh now on
+ 
+
+ align:start position:0%
+days okay let me move on here uh now on
+slide 23 I I'll move away from the gate
+
+ align:start position:0%
+slide 23 I I'll move away from the gate
+ 
+
+ align:start position:0%
+slide 23 I I'll move away from the gate
+etching and talk a little bit I'll spend
+
+ align:start position:0%
+etching and talk a little bit I'll spend
+ 
+
+ align:start position:0%
+etching and talk a little bit I'll spend
+a few minutes about modeling and
+
+ align:start position:0%
+a few minutes about modeling and
+ 
+
+ align:start position:0%
+a few minutes about modeling and
+simulation um there's a lot of
+
+ align:start position:0%
+simulation um there's a lot of
+ 
+
+ align:start position:0%
+simulation um there's a lot of
+similarity between the models that we
+
+ align:start position:0%
+similarity between the models that we
+ 
+
+ align:start position:0%
+similarity between the models that we
+introduced for deposition the last
+
+ align:start position:0%
+introduced for deposition the last
+ 
+
+ align:start position:0%
+introduced for deposition the last
+couple of lectures that were in chapter
+
+ align:start position:0%
+couple of lectures that were in chapter
+ 
+
+ align:start position:0%
+couple of lectures that were in chapter
+nine and the etching
+
+ align:start position:0%
+nine and the etching
+ 
+
+ align:start position:0%
+nine and the etching
+models um and why is that well well both
+
+ align:start position:0%
+models um and why is that well well both
+ 
+
+ align:start position:0%
+models um and why is that well well both
+deposition and etching use incoming
+
+ align:start position:0%
+deposition and etching use incoming
+ 
+
+ align:start position:0%
+deposition and etching use incoming
+chemical or neutral uh species and ion
+
+ align:start position:0%
+chemical or neutral uh species and ion
+ 
+
+ align:start position:0%
+chemical or neutral uh species and ion
+fluxes and they have a lot of very
+
+ align:start position:0%
+fluxes and they have a lot of very
+ 
+
+ align:start position:0%
+fluxes and they have a lot of very
+similar processes the difference is when
+
+ align:start position:0%
+similar processes the difference is when
+ 
+
+ align:start position:0%
+similar processes the difference is when
+you're depositing the species come down
+
+ align:start position:0%
+you're depositing the species come down
+ 
+
+ align:start position:0%
+you're depositing the species come down
+they move around and they stick they
+
+ align:start position:0%
+they move around and they stick they
+ 
+
+ align:start position:0%
+they move around and they stick they
+react in some way the deposit when
+
+ align:start position:0%
+react in some way the deposit when
+ 
+
+ align:start position:0%
+react in some way the deposit when
+you're etching they come down they move
+
+ align:start position:0%
+you're etching they come down they move
+ 
+
+ align:start position:0%
+you're etching they come down they move
+around they have a chemical reaction but
+
+ align:start position:0%
+around they have a chemical reaction but
+ 
+
+ align:start position:0%
+around they have a chemical reaction but
+they actually remove material so one can
+
+ align:start position:0%
+they actually remove material so one can
+ 
+
+ align:start position:0%
+they actually remove material so one can
+be considered mathematically the inverse
+
+ align:start position:0%
+be considered mathematically the inverse
+ 
+
+ align:start position:0%
+be considered mathematically the inverse
+of the other but um because in math you
+
+ align:start position:0%
+of the other but um because in math you
+ 
+
+ align:start position:0%
+of the other but um because in math you
+can just change the sign from positive
+
+ align:start position:0%
+can just change the sign from positive
+ 
+
+ align:start position:0%
+can just change the sign from positive
+to negative in a computer program
+
+ align:start position:0%
+to negative in a computer program
+ 
+
+ align:start position:0%
+to negative in a computer program
+you can use very much uh similar uh
+
+ align:start position:0%
+you can use very much uh similar uh
+ 
+
+ align:start position:0%
+you can use very much uh similar uh
+methodologies to model uh etching so
+
+ align:start position:0%
+methodologies to model uh etching so
+ 
+
+ align:start position:0%
+methodologies to model uh etching so
+here's an an example of of things uh
+
+ align:start position:0%
+here's an an example of of things uh
+ 
+
+ align:start position:0%
+here's an an example of of things uh
+that might take place um during etching
+
+ align:start position:0%
+that might take place um during etching
+ 
+
+ align:start position:0%
+that might take place um during etching
+you have ionic species coming down you
+
+ align:start position:0%
+you have ionic species coming down you
+ 
+
+ align:start position:0%
+you have ionic species coming down you
+have things coming down and being
+
+ align:start position:0%
+have things coming down and being
+ 
+
+ align:start position:0%
+have things coming down and being
+sputtered away and um um you may have
+
+ align:start position:0%
+sputtered away and um um you may have
+ 
+
+ align:start position:0%
+sputtered away and um um you may have
+things coming down and being emitted or
+
+ align:start position:0%
+things coming down and being emitted or
+ 
+
+ align:start position:0%
+things coming down and being emitted or
+desorbed so a lot of these uh fluxes the
+
+ align:start position:0%
+desorbed so a lot of these uh fluxes the
+ 
+
+ align:start position:0%
+desorbed so a lot of these uh fluxes the
+whole flux equation uh is very much
+
+ align:start position:0%
+whole flux equation uh is very much
+ 
+
+ align:start position:0%
+whole flux equation uh is very much
+analogous between uh deposition and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itching here on slide 24 um just like in
+
+ align:start position:0%
+itching here on slide 24 um just like in
+ 
+
+ align:start position:0%
+itching here on slide 24 um just like in
+the case of
+
+ align:start position:0%
+the case of
+ 
+
+ align:start position:0%
+the case of
+deposition um the etch rate is
+
+ align:start position:0%
+deposition um the etch rate is
+ 
+
+ align:start position:0%
+deposition um the etch rate is
+proportional to the net flux arriving at
+
+ align:start position:0%
+proportional to the net flux arriving at
+ 
+
+ align:start position:0%
+proportional to the net flux arriving at
+a point remember we said the deposition
+
+ align:start position:0%
+a point remember we said the deposition
+ 
+
+ align:start position:0%
+a point remember we said the deposition
+was proportional to the net flux the
+
+ align:start position:0%
+was proportional to the net flux the
+ 
+
+ align:start position:0%
+was proportional to the net flux the
+flux in minus the flux out well the etch
+
+ align:start position:0%
+flux in minus the flux out well the etch
+ 
+
+ align:start position:0%
+flux in minus the flux out well the etch
+rate is often proportional to net flux
+
+ align:start position:0%
+rate is often proportional to net flux
+ 
+
+ align:start position:0%
+rate is often proportional to net flux
+so we have the same kind of situation
+
+ align:start position:0%
+so we have the same kind of situation
+ 
+
+ align:start position:0%
+so we have the same kind of situation
+you have a wafer which has a certain
+
+ align:start position:0%
+you have a wafer which has a certain
+ 
+
+ align:start position:0%
+you have a wafer which has a certain
+pattern surface you form a virtual
+
+ align:start position:0%
+pattern surface you form a virtual
+ 
+
+ align:start position:0%
+pattern surface you form a virtual
+dashed uh plane above it with and you
+
+ align:start position:0%
+dashed uh plane above it with and you
+ 
+
+ align:start position:0%
+dashed uh plane above it with and you
+look at the distribution the angular
+
+ align:start position:0%
+look at the distribution the angular
+ 
+
+ align:start position:0%
+look at the distribution the angular
+distribution uh of the species arriving
+
+ align:start position:0%
+distribution uh of the species arriving
+ 
+
+ align:start position:0%
+distribution uh of the species arriving
+just above the surface on that Dash
+
+ align:start position:0%
+just above the surface on that Dash
+ 
+
+ align:start position:0%
+just above the surface on that Dash
+plane uh if you have a chemical etching
+
+ align:start position:0%
+plane uh if you have a chemical etching
+ 
+
+ align:start position:0%
+plane uh if you have a chemical etching
+species that that is something that's
+
+ align:start position:0%
+species that that is something that's
+ 
+
+ align:start position:0%
+species that that is something that's
+neutral that is not ionized uh you
+
+ align:start position:0%
+neutral that is not ionized uh you
+ 
+
+ align:start position:0%
+neutral that is not ionized uh you
+assume you have an isotropic arrival
+
+ align:start position:0%
+assume you have an isotropic arrival
+ 
+
+ align:start position:0%
+assume you have an isotropic arrival
+distribution so you put a cosine Theta
+
+ align:start position:0%
+distribution so you put a cosine Theta
+ 
+
+ align:start position:0%
+distribution so you put a cosine Theta
+to uh to the N where n equals 1 for a
+
+ align:start position:0%
+to uh to the N where n equals 1 for a
+ 
+
+ align:start position:0%
+to uh to the N where n equals 1 for a
+chemical species if you have an ionic
+
+ align:start position:0%
+chemical species if you have an ionic
+ 
+
+ align:start position:0%
+chemical species if you have an ionic
+species it can be accelerated towards
+
+ align:start position:0%
+species it can be accelerated towards
+ 
+
+ align:start position:0%
+species it can be accelerated towards
+the surface it can arrive very uh much
+
+ align:start position:0%
+the surface it can arrive very uh much
+ 
+
+ align:start position:0%
+the surface it can arrive very uh much
+with a vertical orientation and here we
+
+ align:start position:0%
+with a vertical orientation and here we
+ 
+
+ align:start position:0%
+with a vertical orientation and here we
+for etching we put in cosine Theta the N
+
+ align:start position:0%
+for etching we put in cosine Theta the N
+ 
+
+ align:start position:0%
+for etching we put in cosine Theta the N
+where n could vary between 10 and 100 or
+
+ align:start position:0%
+where n could vary between 10 and 100 or
+ 
+
+ align:start position:0%
+where n could vary between 10 and 100 or
+something like that remember the higher
+
+ align:start position:0%
+something like that remember the higher
+ 
+
+ align:start position:0%
+something like that remember the higher
+the value of n much more vertical the
+
+ align:start position:0%
+the value of n much more vertical the
+ 
+
+ align:start position:0%
+the value of n much more vertical the
+distribution um in the deposition case
+
+ align:start position:0%
+distribution um in the deposition case
+ 
+
+ align:start position:0%
+distribution um in the deposition case
+remember we had the concept of a
+
+ align:start position:0%
+remember we had the concept of a
+ 
+
+ align:start position:0%
+remember we had the concept of a
+sticking coefficient uh well we use uh
+
+ align:start position:0%
+sticking coefficient uh well we use uh
+ 
+
+ align:start position:0%
+sticking coefficient uh well we use uh
+very much that same concept um we when
+
+ align:start position:0%
+very much that same concept um we when
+ 
+
+ align:start position:0%
+very much that same concept um we when
+we're etching we say an ionized species
+
+ align:start position:0%
+we're etching we say an ionized species
+ 
+
+ align:start position:0%
+we're etching we say an ionized species
+usually sticks where it's
+
+ align:start position:0%
+usually sticks where it's
+ 
+
+ align:start position:0%
+usually sticks where it's
+lands um and it's going to react and
+
+ align:start position:0%
+lands um and it's going to react and
+ 
+
+ align:start position:0%
+lands um and it's going to react and
+itch while a reactive neutral species
+
+ align:start position:0%
+itch while a reactive neutral species
+ 
+
+ align:start position:0%
+itch while a reactive neutral species
+may have a low SC value it might bounce
+
+ align:start position:0%
+may have a low SC value it might bounce
+ 
+
+ align:start position:0%
+may have a low SC value it might bounce
+around before it finally reacts and
+
+ align:start position:0%
+around before it finally reacts and
+ 
+
+ align:start position:0%
+around before it finally reacts and
+etches off the
+
+ align:start position:0%
+etches off the
+ 
+
+ align:start position:0%
+etches off the
+surface uh as far as the physical
+
+ align:start position:0%
+surface uh as far as the physical
+ 
+
+ align:start position:0%
+surface uh as far as the physical
+component of etching like sputtering the
+
+ align:start position:0%
+component of etching like sputtering the
+ 
+
+ align:start position:0%
+component of etching like sputtering the
+sputtering yield has the same angular
+
+ align:start position:0%
+sputtering yield has the same angular
+ 
+
+ align:start position:0%
+sputtering yield has the same angular
+dependence that we used in the
+
+ align:start position:0%
+dependence that we used in the
+ 
+
+ align:start position:0%
+dependence that we used in the
+deposition case so again very similar uh
+
+ align:start position:0%
+deposition case so again very similar uh
+ 
+
+ align:start position:0%
+deposition case so again very similar uh
+process going on when we include
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sputtering so slide 20 um 25 I'm showing
+
+ align:start position:0%
+sputtering so slide 20 um 25 I'm showing
+ 
+
+ align:start position:0%
+sputtering so slide 20 um 25 I'm showing
+What's called the linear etch
+
+ align:start position:0%
+What's called the linear etch
+ 
+
+ align:start position:0%
+What's called the linear etch
+model um there have been some very
+
+ align:start position:0%
+model um there have been some very
+ 
+
+ align:start position:0%
+model um there have been some very
+specific models in developed uh here I
+
+ align:start position:0%
+specific models in developed uh here I
+ 
+
+ align:start position:0%
+specific models in developed uh here I
+just want to give a sort of a general
+
+ align:start position:0%
+just want to give a sort of a general
+ 
+
+ align:start position:0%
+just want to give a sort of a general
+purpose etch models a couple of them
+
+ align:start position:0%
+purpose etch models a couple of them
+ 
+
+ align:start position:0%
+purpose etch models a couple of them
+which can be applied uh
+
+ align:start position:0%
+which can be applied uh
+ 
+
+ align:start position:0%
+which can be applied uh
+broadly the so-called linear model
+
+ align:start position:0%
+broadly the so-called linear model
+ 
+
+ align:start position:0%
+broadly the so-called linear model
+assumes that there are chemical and
+
+ align:start position:0%
+assumes that there are chemical and
+ 
+
+ align:start position:0%
+assumes that there are chemical and
+physical components that act
+
+ align:start position:0%
+physical components that act
+ 
+
+ align:start position:0%
+physical components that act
+independently so they're not
+
+ align:start position:0%
+independently so they're not
+ 
+
+ align:start position:0%
+independently so they're not
+linked um uh they're independent of each
+
+ align:start position:0%
+linked um uh they're independent of each
+ 
+
+ align:start position:0%
+linked um uh they're independent of each
+other and in this case we have um a an
+
+ align:start position:0%
+other and in this case we have um a an
+ 
+
+ align:start position:0%
+other and in this case we have um a an
+etch rate that is given by just a of two
+
+ align:start position:0%
+etch rate that is given by just a of two
+ 
+
+ align:start position:0%
+etch rate that is given by just a of two
+terms uh one term that has to do with a
+
+ align:start position:0%
+terms uh one term that has to do with a
+ 
+
+ align:start position:0%
+terms uh one term that has to do with a
+chemical uh flux F subc what the
+
+ align:start position:0%
+chemical uh flux F subc what the
+ 
+
+ align:start position:0%
+chemical uh flux F subc what the
+chemical flux onto the surface at any
+
+ align:start position:0%
+chemical flux onto the surface at any
+ 
+
+ align:start position:0%
+chemical flux onto the surface at any
+point and another term that is
+
+ align:start position:0%
+point and another term that is
+ 
+
+ align:start position:0%
+point and another term that is
+proportional to fepi the ionic
+
+ align:start position:0%
+proportional to fepi the ionic
+ 
+
+ align:start position:0%
+proportional to fepi the ionic
+flux in front of each one of these
+
+ align:start position:0%
+flux in front of each one of these
+ 
+
+ align:start position:0%
+flux in front of each one of these
+fluxes is a k Factor uh Ki and KF these
+
+ align:start position:0%
+fluxes is a k Factor uh Ki and KF these
+ 
+
+ align:start position:0%
+fluxes is a k Factor uh Ki and KF these
+are relative rate constants for the two
+
+ align:start position:0%
+are relative rate constants for the two
+ 
+
+ align:start position:0%
+are relative rate constants for the two
+components uh usually you use these as
+
+ align:start position:0%
+components uh usually you use these as
+ 
+
+ align:start position:0%
+components uh usually you use these as
+fitting parameters uh if I have a large
+
+ align:start position:0%
+fitting parameters uh if I have a large
+ 
+
+ align:start position:0%
+fitting parameters uh if I have a large
+Ki I have a lot of ionic component um
+
+ align:start position:0%
+Ki I have a lot of ionic component um
+ 
+
+ align:start position:0%
+Ki I have a lot of ionic component um
+whereas if I have a large KF would be
+
+ align:start position:0%
+whereas if I have a large KF would be
+ 
+
+ align:start position:0%
+whereas if I have a large KF would be
+more of a chemical
+
+ align:start position:0%
+more of a chemical
+ 
+
+ align:start position:0%
+more of a chemical
+component um what is that uh the
+
+ align:start position:0%
+component um what is that uh the
+ 
+
+ align:start position:0%
+component um what is that uh the
+physical component can be due to purely
+
+ align:start position:0%
+physical component can be due to purely
+ 
+
+ align:start position:0%
+physical component can be due to purely
+physical sputtering for example like we
+
+ align:start position:0%
+physical sputtering for example like we
+ 
+
+ align:start position:0%
+physical sputtering for example like we
+talked about before or it actually can
+
+ align:start position:0%
+talked about before or it actually can
+ 
+
+ align:start position:0%
+talked about before or it actually can
+be some ion enhanced mechanism uh in the
+
+ align:start position:0%
+be some ion enhanced mechanism uh in the
+ 
+
+ align:start position:0%
+be some ion enhanced mechanism uh in the
+regime where the chemical flux is not
+
+ align:start position:0%
+regime where the chemical flux is not
+ 
+
+ align:start position:0%
+regime where the chemical flux is not
+limiting the ion etching so this is a an
+
+ align:start position:0%
+limiting the ion etching so this is a an
+ 
+
+ align:start position:0%
+limiting the ion etching so this is a an
+a linear etch model with independent
+
+ align:start position:0%
+a linear etch model with independent
+ 
+
+ align:start position:0%
+a linear etch model with independent
+chemical and physical uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components here's just an example of
+
+ align:start position:0%
+components here's just an example of
+ 
+
+ align:start position:0%
+components here's just an example of
+some simulations remember Speedy I said
+
+ align:start position:0%
+some simulations remember Speedy I said
+ 
+
+ align:start position:0%
+some simulations remember Speedy I said
+was a topography simulator does both
+
+ align:start position:0%
+was a topography simulator does both
+ 
+
+ align:start position:0%
+was a topography simulator does both
+deposition and
+
+ align:start position:0%
+deposition and
+ 
+
+ align:start position:0%
+deposition and
+etching um here on on slide 26 I have
+
+ align:start position:0%
+etching um here on on slide 26 I have
+ 
+
+ align:start position:0%
+etching um here on on slide 26 I have
+some Speedy simulations using the linear
+
+ align:start position:0%
+some Speedy simulations using the linear
+ 
+
+ align:start position:0%
+some Speedy simulations using the linear
+Edge model and uh we have a b and c well
+
+ align:start position:0%
+Edge model and uh we have a b and c well
+ 
+
+ align:start position:0%
+Edge model and uh we have a b and c well
+what we're doing uh each one of these
+
+ align:start position:0%
+what we're doing uh each one of these
+ 
+
+ align:start position:0%
+what we're doing uh each one of these
+Contours again represents the shape of
+
+ align:start position:0%
+Contours again represents the shape of
+ 
+
+ align:start position:0%
+Contours again represents the shape of
+the edge surface at a given time so
+
+ align:start position:0%
+the edge surface at a given time so
+ 
+
+ align:start position:0%
+the edge surface at a given time so
+we're looking at snapshots in time here
+
+ align:start position:0%
+we're looking at snapshots in time here
+ 
+
+ align:start position:0%
+we're looking at snapshots in time here
+I am I have a edge mask it looks like
+
+ align:start position:0%
+I am I have a edge mask it looks like
+ 
+
+ align:start position:0%
+I am I have a edge mask it looks like
+this so this is my masking material on
+
+ align:start position:0%
+this so this is my masking material on
+ 
+
+ align:start position:0%
+this so this is my masking material on
+the surface and I'm etching into the
+
+ align:start position:0%
+the surface and I'm etching into the
+ 
+
+ align:start position:0%
+the surface and I'm etching into the
+Silicon or into the film below
+
+ align:start position:0%
+Silicon or into the film below
+ 
+
+ align:start position:0%
+Silicon or into the film below
+here I have n equals 1 uh and so for my
+
+ align:start position:0%
+here I have n equals 1 uh and so for my
+ 
+
+ align:start position:0%
+here I have n equals 1 uh and so for my
+chemical flux angular distribution so
+
+ align:start position:0%
+chemical flux angular distribution so
+ 
+
+ align:start position:0%
+chemical flux angular distribution so
+it's going to give you a fairly uh
+
+ align:start position:0%
+it's going to give you a fairly uh
+ 
+
+ align:start position:0%
+it's going to give you a fairly uh
+isotropic uh type of uh of etch you see
+
+ align:start position:0%
+isotropic uh type of uh of etch you see
+ 
+
+ align:start position:0%
+isotropic uh type of uh of etch you see
+you're etching laterally this Dimension
+
+ align:start position:0%
+you're etching laterally this Dimension
+ 
+
+ align:start position:0%
+you're etching laterally this Dimension
+just about the same as you etch
+
+ align:start position:0%
+just about the same as you etch
+ 
+
+ align:start position:0%
+just about the same as you etch
+vertically so there's an isotropic type
+
+ align:start position:0%
+vertically so there's an isotropic type
+ 
+
+ align:start position:0%
+vertically so there's an isotropic type
+of edge here's um where you have n
+
+ align:start position:0%
+of edge here's um where you have n
+ 
+
+ align:start position:0%
+of edge here's um where you have n
+equals 80 uh for the ionic uh flux
+
+ align:start position:0%
+equals 80 uh for the ionic uh flux
+ 
+
+ align:start position:0%
+equals 80 uh for the ionic uh flux
+angular distribution and you end up with
+
+ align:start position:0%
+angular distribution and you end up with
+ 
+
+ align:start position:0%
+angular distribution and you end up with
+very vertical etching it's um basically
+
+ align:start position:0%
+very vertical etching it's um basically
+ 
+
+ align:start position:0%
+very vertical etching it's um basically
+everything's coming straight down
+
+ align:start position:0%
+everything's coming straight down
+ 
+
+ align:start position:0%
+everything's coming straight down
+and etching there's not much lateral
+
+ align:start position:0%
+and etching there's not much lateral
+ 
+
+ align:start position:0%
+and etching there's not much lateral
+etching so this is all chemical etching
+
+ align:start position:0%
+etching so this is all chemical etching
+ 
+
+ align:start position:0%
+etching so this is all chemical etching
+the ion flux of zero all physical
+
+ align:start position:0%
+the ion flux of zero all physical
+ 
+
+ align:start position:0%
+the ion flux of zero all physical
+etching in this case and here's a 50/50
+
+ align:start position:0%
+etching in this case and here's a 50/50
+ 
+
+ align:start position:0%
+etching in this case and here's a 50/50
+I have half chemical and um half
+
+ align:start position:0%
+I have half chemical and um half
+ 
+
+ align:start position:0%
+I have half chemical and um half
+physical fluxes of both and you can see
+
+ align:start position:0%
+physical fluxes of both and you can see
+ 
+
+ align:start position:0%
+physical fluxes of both and you can see
+it it etches a little bit laterally and
+
+ align:start position:0%
+it it etches a little bit laterally and
+ 
+
+ align:start position:0%
+it it etches a little bit laterally and
+and a certain amount vertically so you
+
+ align:start position:0%
+and a certain amount vertically so you
+ 
+
+ align:start position:0%
+and a certain amount vertically so you
+can generate a variety of edge profiles
+
+ align:start position:0%
+can generate a variety of edge profiles
+ 
+
+ align:start position:0%
+can generate a variety of edge profiles
+using a relatively simple um model with
+
+ align:start position:0%
+using a relatively simple um model with
+ 
+
+ align:start position:0%
+using a relatively simple um model with
+only uh you know maybe three or four
+
+ align:start position:0%
+only uh you know maybe three or four
+ 
+
+ align:start position:0%
+only uh you know maybe three or four
+parameters uh and then you can fit this
+
+ align:start position:0%
+parameters uh and then you can fit this
+ 
+
+ align:start position:0%
+parameters uh and then you can fit this
+to what you actually see in your uh
+
+ align:start position:0%
+to what you actually see in your uh
+ 
+
+ align:start position:0%
+to what you actually see in your uh
+actual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+etches the second type of model which is
+
+ align:start position:0%
+etches the second type of model which is
+ 
+
+ align:start position:0%
+etches the second type of model which is
+quite different that's shown here on
+
+ align:start position:0%
+quite different that's shown here on
+ 
+
+ align:start position:0%
+quite different that's shown here on
+slide 27 is called a saturation uh-
+
+ align:start position:0%
+slide 27 is called a saturation uh-
+ 
+
+ align:start position:0%
+slide 27 is called a saturation uh-
+absorption type of edge model um because
+
+ align:start position:0%
+absorption type of edge model um because
+ 
+
+ align:start position:0%
+absorption type of edge model um because
+the fact very often uh this is used when
+
+ align:start position:0%
+the fact very often uh this is used when
+ 
+
+ align:start position:0%
+the fact very often uh this is used when
+the chemical or the neutral etching and
+
+ align:start position:0%
+the chemical or the neutral etching and
+ 
+
+ align:start position:0%
+the chemical or the neutral etching and
+the ion etching or the physical etch
+
+ align:start position:0%
+the ion etching or the physical etch
+ 
+
+ align:start position:0%
+the ion etching or the physical etch
+components are coupled so when one of
+
+ align:start position:0%
+components are coupled so when one of
+ 
+
+ align:start position:0%
+components are coupled so when one of
+these affects the other when you have a
+
+ align:start position:0%
+these affects the other when you have a
+ 
+
+ align:start position:0%
+these affects the other when you have a
+synergistic effect which know is often
+
+ align:start position:0%
+synergistic effect which know is often
+ 
+
+ align:start position:0%
+synergistic effect which know is often
+the case especially when you have side
+
+ align:start position:0%
+the case especially when you have side
+ 
+
+ align:start position:0%
+the case especially when you have side
+wall inhibitor layers or something um
+
+ align:start position:0%
+wall inhibitor layers or something um
+ 
+
+ align:start position:0%
+wall inhibitor layers or something um
+you need to use this type of model so
+
+ align:start position:0%
+you need to use this type of model so
+ 
+
+ align:start position:0%
+you need to use this type of model so
+here's an example um let's say you need
+
+ align:start position:0%
+here's an example um let's say you need
+ 
+
+ align:start position:0%
+here's an example um let's say you need
+an ion flux to remove an inhibitor layer
+
+ align:start position:0%
+an ion flux to remove an inhibitor layer
+ 
+
+ align:start position:0%
+an ion flux to remove an inhibitor layer
+that is formed by uh chemical etching so
+
+ align:start position:0%
+that is formed by uh chemical etching so
+ 
+
+ align:start position:0%
+that is formed by uh chemical etching so
+instead of a linear model where these
+
+ align:start position:0%
+instead of a linear model where these
+ 
+
+ align:start position:0%
+instead of a linear model where these
+two just added up linearly these add
+
+ align:start position:0%
+two just added up linearly these add
+ 
+
+ align:start position:0%
+two just added up linearly these add
+sort of like uh resistors in parallel so
+
+ align:start position:0%
+sort of like uh resistors in parallel so
+ 
+
+ align:start position:0%
+sort of like uh resistors in parallel so
+to speak or capacitors in series if
+
+ align:start position:0%
+to speak or capacitors in series if
+ 
+
+ align:start position:0%
+to speak or capacitors in series if
+you're electrical engineer The Edge rate
+
+ align:start position:0%
+you're electrical engineer The Edge rate
+ 
+
+ align:start position:0%
+you're electrical engineer The Edge rate
+is just given by the inverse one over
+
+ align:start position:0%
+is just given by the inverse one over
+ 
+
+ align:start position:0%
+is just given by the inverse one over
+the sum of 1 K fi plus 1 SC FC so
+
+ align:start position:0%
+the sum of 1 K fi plus 1 SC FC so
+ 
+
+ align:start position:0%
+the sum of 1 K fi plus 1 SC FC so
+there's a one over a chemical flux and
+
+ align:start position:0%
+there's a one over a chemical flux and
+ 
+
+ align:start position:0%
+there's a one over a chemical flux and
+one over an ionic
+
+ align:start position:0%
+one over an ionic
+ 
+
+ align:start position:0%
+one over an ionic
+flux if you plot this equation what does
+
+ align:start position:0%
+flux if you plot this equation what does
+ 
+
+ align:start position:0%
+flux if you plot this equation what does
+it look like here's here's the overall
+
+ align:start position:0%
+it look like here's here's the overall
+ 
+
+ align:start position:0%
+it look like here's here's the overall
+Ed rate as a function of now I'm
+
+ align:start position:0%
+Ed rate as a function of now I'm
+ 
+
+ align:start position:0%
+Ed rate as a function of now I'm
+plotting as a function of the ion flux
+
+ align:start position:0%
+plotting as a function of the ion flux
+ 
+
+ align:start position:0%
+plotting as a function of the ion flux
+um times K subi so it's a function of
+
+ align:start position:0%
+um times K subi so it's a function of
+ 
+
+ align:start position:0%
+um times K subi so it's a function of
+this quantity so it goes up um and and
+
+ align:start position:0%
+this quantity so it goes up um and and
+ 
+
+ align:start position:0%
+this quantity so it goes up um and and
+in the the parameter here is the
+
+ align:start position:0%
+in the the parameter here is the
+ 
+
+ align:start position:0%
+in the the parameter here is the
+chemical flux SC so if either flux is
+
+ align:start position:0%
+chemical flux SC so if either flux is
+ 
+
+ align:start position:0%
+chemical flux SC so if either flux is
+zero so if SC is zero I get zero H rate
+
+ align:start position:0%
+zero so if SC is zero I get zero H rate
+ 
+
+ align:start position:0%
+zero so if SC is zero I get zero H rate
+regardless of what my ion flux is you
+
+ align:start position:0%
+regardless of what my ion flux is you
+ 
+
+ align:start position:0%
+regardless of what my ion flux is you
+need both chemical and the ionic flux um
+
+ align:start position:0%
+need both chemical and the ionic flux um
+ 
+
+ align:start position:0%
+need both chemical and the ionic flux um
+uh so if either flux is zero the overall
+
+ align:start position:0%
+uh so if either flux is zero the overall
+ 
+
+ align:start position:0%
+uh so if either flux is zero the overall
+tra is zero because both of them are
+
+ align:start position:0%
+tra is zero because both of them are
+ 
+
+ align:start position:0%
+tra is zero because both of them are
+required to Edge the material and you
+
+ align:start position:0%
+required to Edge the material and you
+ 
+
+ align:start position:0%
+required to Edge the material and you
+end up with these sort of saturating
+
+ align:start position:0%
+end up with these sort of saturating
+ 
+
+ align:start position:0%
+end up with these sort of saturating
+type of Curves here's for a chemical
+
+ align:start position:0%
+type of Curves here's for a chemical
+ 
+
+ align:start position:0%
+type of Curves here's for a chemical
+flux of 0. five uh as I increase the ion
+
+ align:start position:0%
+flux of 0. five uh as I increase the ion
+ 
+
+ align:start position:0%
+flux of 0. five uh as I increase the ion
+flux you increase the etch rate until
+
+ align:start position:0%
+flux you increase the etch rate until
+ 
+
+ align:start position:0%
+flux you increase the etch rate until
+some point it sort of saturates and it's
+
+ align:start position:0%
+some point it sort of saturates and it's
+ 
+
+ align:start position:0%
+some point it sort of saturates and it's
+no longer a function of of ion flux and
+
+ align:start position:0%
+no longer a function of of ion flux and
+ 
+
+ align:start position:0%
+no longer a function of of ion flux and
+that's it's limited by then by the
+
+ align:start position:0%
+that's it's limited by then by the
+ 
+
+ align:start position:0%
+that's it's limited by then by the
+chemical process so you have a series of
+
+ align:start position:0%
+chemical process so you have a series of
+ 
+
+ align:start position:0%
+chemical process so you have a series of
+the saturating curves it sort of looks
+
+ align:start position:0%
+the saturating curves it sort of looks
+ 
+
+ align:start position:0%
+the saturating curves it sort of looks
+like transistor characteristics because
+
+ align:start position:0%
+like transistor characteristics because
+ 
+
+ align:start position:0%
+like transistor characteristics because
+you have two things controlling it uh
+
+ align:start position:0%
+you have two things controlling it uh
+ 
+
+ align:start position:0%
+you have two things controlling it uh
+both the chemical flux and the ionic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux um so basically this is that same
+
+ align:start position:0%
+flux um so basically this is that same
+ 
+
+ align:start position:0%
+flux um so basically this is that same
+plot I just showed the edge rate tends
+
+ align:start position:0%
+plot I just showed the edge rate tends
+ 
+
+ align:start position:0%
+plot I just showed the edge rate tends
+to saturate when one component gets too
+
+ align:start position:0%
+to saturate when one component gets too
+ 
+
+ align:start position:0%
+to saturate when one component gets too
+large relative to the other so you're
+
+ align:start position:0%
+large relative to the other so you're
+ 
+
+ align:start position:0%
+large relative to the other so you're
+always rate limited by the slower of the
+
+ align:start position:0%
+always rate limited by the slower of the
+ 
+
+ align:start position:0%
+always rate limited by the slower of the
+two series processes either the chemical
+
+ align:start position:0%
+two series processes either the chemical
+ 
+
+ align:start position:0%
+two series processes either the chemical
+etch rate or the ionic edch rate this is
+
+ align:start position:0%
+etch rate or the ionic edch rate this is
+ 
+
+ align:start position:0%
+etch rate or the ionic edch rate this is
+a very generalized approach again it can
+
+ align:start position:0%
+a very generalized approach again it can
+ 
+
+ align:start position:0%
+a very generalized approach again it can
+be broadly applicable and you can use it
+
+ align:start position:0%
+be broadly applicable and you can use it
+ 
+
+ align:start position:0%
+be broadly applicable and you can use it
+to fit um a lot of of different uh Edge
+
+ align:start position:0%
+to fit um a lot of of different uh Edge
+ 
+
+ align:start position:0%
+to fit um a lot of of different uh Edge
+models with again with relatively small
+
+ align:start position:0%
+models with again with relatively small
+ 
+
+ align:start position:0%
+models with again with relatively small
+number of parameters maybe three to four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters on slide 29 I'm showing a
+
+ align:start position:0%
+parameters on slide 29 I'm showing a
+ 
+
+ align:start position:0%
+parameters on slide 29 I'm showing a
+speedy simulation again where we have
+
+ align:start position:0%
+speedy simulation again where we have
+ 
+
+ align:start position:0%
+speedy simulation again where we have
+equal chemical and ionic components and
+
+ align:start position:0%
+equal chemical and ionic components and
+ 
+
+ align:start position:0%
+equal chemical and ionic components and
+you notice what you get is reasonably
+
+ align:start position:0%
+you notice what you get is reasonably
+ 
+
+ align:start position:0%
+you notice what you get is reasonably
+anisotropic etching there's a little bit
+
+ align:start position:0%
+anisotropic etching there's a little bit
+ 
+
+ align:start position:0%
+anisotropic etching there's a little bit
+of lateral etching here down at the
+
+ align:start position:0%
+of lateral etching here down at the
+ 
+
+ align:start position:0%
+of lateral etching here down at the
+bottom um and why is that well because
+
+ align:start position:0%
+bottom um and why is that well because
+ 
+
+ align:start position:0%
+bottom um and why is that well because
+in order to continue etching you need an
+
+ align:start position:0%
+in order to continue etching you need an
+ 
+
+ align:start position:0%
+in order to continue etching you need an
+ion flux to remove the inhibitor layer
+
+ align:start position:0%
+ion flux to remove the inhibitor layer
+ 
+
+ align:start position:0%
+ion flux to remove the inhibitor layer
+uh or whatever it is and that ion flux
+
+ align:start position:0%
+uh or whatever it is and that ion flux
+ 
+
+ align:start position:0%
+uh or whatever it is and that ion flux
+tends to be very vertical uh because we
+
+ align:start position:0%
+tends to be very vertical uh because we
+ 
+
+ align:start position:0%
+tends to be very vertical uh because we
+have a large n value in this case and so
+
+ align:start position:0%
+have a large n value in this case and so
+ 
+
+ align:start position:0%
+have a large n value in this case and so
+the sidewall inhibitor is not removed
+
+ align:start position:0%
+the sidewall inhibitor is not removed
+ 
+
+ align:start position:0%
+the sidewall inhibitor is not removed
+the inhibitor layer is not removed on
+
+ align:start position:0%
+the inhibitor layer is not removed on
+ 
+
+ align:start position:0%
+the inhibitor layer is not removed on
+the sidewalls but it's only removed on
+
+ align:start position:0%
+the sidewalls but it's only removed on
+ 
+
+ align:start position:0%
+the sidewalls but it's only removed on
+the flat surfaces if you change this end
+
+ align:start position:0%
+the flat surfaces if you change this end
+ 
+
+ align:start position:0%
+the flat surfaces if you change this end
+direction you'll start to see a little
+
+ align:start position:0%
+direction you'll start to see a little
+ 
+
+ align:start position:0%
+direction you'll start to see a little
+more lateral etching if you change the N
+
+ align:start position:0%
+more lateral etching if you change the N
+ 
+
+ align:start position:0%
+more lateral etching if you change the N
+number rather uh which that the N will
+
+ align:start position:0%
+number rather uh which that the N will
+ 
+
+ align:start position:0%
+number rather uh which that the N will
+determine sort of the angle of the
+
+ align:start position:0%
+determine sort of the angle of the
+ 
+
+ align:start position:0%
+determine sort of the angle of the
+cosine Theta to the end dependence and
+
+ align:start position:0%
+cosine Theta to the end dependence and
+ 
+
+ align:start position:0%
+cosine Theta to the end dependence and
+then the uh you'll get a little bit more
+
+ align:start position:0%
+then the uh you'll get a little bit more
+ 
+
+ align:start position:0%
+then the uh you'll get a little bit more
+um lateral etching so there's an example
+
+ align:start position:0%
+um lateral etching so there's an example
+ 
+
+ align:start position:0%
+um lateral etching so there's an example
+of uh for equal chemical and ion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components okay so I just want to
+
+ align:start position:0%
+components okay so I just want to
+ 
+
+ align:start position:0%
+components okay so I just want to
+summarize um what we've done in chapter
+
+ align:start position:0%
+summarize um what we've done in chapter
+ 
+
+ align:start position:0%
+summarize um what we've done in chapter
+10 on plasma etching um we there's a lot
+
+ align:start position:0%
+10 on plasma etching um we there's a lot
+ 
+
+ align:start position:0%
+10 on plasma etching um we there's a lot
+of important issues some of the key ones
+
+ align:start position:0%
+of important issues some of the key ones
+ 
+
+ align:start position:0%
+of important issues some of the key ones
+we've covered are the select itivity
+
+ align:start position:0%
+we've covered are the select itivity
+ 
+
+ align:start position:0%
+we've covered are the select itivity
+with respect to the layer below you plus
+
+ align:start position:0%
+with respect to the layer below you plus
+ 
+
+ align:start position:0%
+with respect to the layer below you plus
+the selectivity with with the layer
+
+ align:start position:0%
+the selectivity with with the layer
+ 
+
+ align:start position:0%
+the selectivity with with the layer
+above you or the mask uh the
+
+ align:start position:0%
+above you or the mask uh the
+ 
+
+ align:start position:0%
+above you or the mask uh the
+directionality of the edge how much do
+
+ align:start position:0%
+directionality of the edge how much do
+ 
+
+ align:start position:0%
+directionality of the edge how much do
+you direct vert edch vertically versus
+
+ align:start position:0%
+you direct vert edch vertically versus
+ 
+
+ align:start position:0%
+you direct vert edch vertically versus
+laterally and the shape of the profile
+
+ align:start position:0%
+laterally and the shape of the profile
+ 
+
+ align:start position:0%
+laterally and the shape of the profile
+on the side
+
+ align:start position:0%
+on the side
+ 
+
+ align:start position:0%
+on the side
+wall they tend to be two components of
+
+ align:start position:0%
+wall they tend to be two components of
+ 
+
+ align:start position:0%
+wall they tend to be two components of
+etching there's a chemical one uh that
+
+ align:start position:0%
+etching there's a chemical one uh that
+ 
+
+ align:start position:0%
+etching there's a chemical one uh that
+is reactive neutral species or free
+
+ align:start position:0%
+is reactive neutral species or free
+ 
+
+ align:start position:0%
+is reactive neutral species or free
+radicals there's a physical component
+
+ align:start position:0%
+radicals there's a physical component
+ 
+
+ align:start position:0%
+radicals there's a physical component
+which is just du to the ions being
+
+ align:start position:0%
+which is just du to the ions being
+ 
+
+ align:start position:0%
+which is just du to the ions being
+accelerate towards the surface and
+
+ align:start position:0%
+accelerate towards the surface and
+ 
+
+ align:start position:0%
+accelerate towards the surface and
+reacting or sputtering off um components
+
+ align:start position:0%
+reacting or sputtering off um components
+ 
+
+ align:start position:0%
+reacting or sputtering off um components
+from the wafer
+
+ align:start position:0%
+from the wafer
+ 
+
+ align:start position:0%
+from the wafer
+these can be completely independent and
+
+ align:start position:0%
+these can be completely independent and
+ 
+
+ align:start position:0%
+these can be completely independent and
+then we use the linear model or they can
+
+ align:start position:0%
+then we use the linear model or they can
+ 
+
+ align:start position:0%
+then we use the linear model or they can
+act in in a series in a synergistic
+
+ align:start position:0%
+act in in a series in a synergistic
+ 
+
+ align:start position:0%
+act in in a series in a synergistic
+matter uh Manner and what we would use
+
+ align:start position:0%
+matter uh Manner and what we would use
+ 
+
+ align:start position:0%
+matter uh Manner and what we would use
+the the last Model that we showed uh
+
+ align:start position:0%
+the the last Model that we showed uh
+ 
+
+ align:start position:0%
+the the last Model that we showed uh
+topography on the wafer uh can really
+
+ align:start position:0%
+topography on the wafer uh can really
+ 
+
+ align:start position:0%
+topography on the wafer uh can really
+increase the selectivity
+
+ align:start position:0%
+increase the selectivity
+ 
+
+ align:start position:0%
+increase the selectivity
+requirements um it makes the patterning
+
+ align:start position:0%
+requirements um it makes the patterning
+ 
+
+ align:start position:0%
+requirements um it makes the patterning
+of fine features and stopping on thin
+
+ align:start position:0%
+of fine features and stopping on thin
+ 
+
+ align:start position:0%
+of fine features and stopping on thin
+layers very difficult uh of course
+
+ align:start position:0%
+layers very difficult uh of course
+ 
+
+ align:start position:0%
+layers very difficult uh of course
+lithography is impacted as well by the
+
+ align:start position:0%
+lithography is impacted as well by the
+ 
+
+ align:start position:0%
+lithography is impacted as well by the
+presence of topography because of the
+
+ align:start position:0%
+presence of topography because of the
+ 
+
+ align:start position:0%
+presence of topography because of the
+depth of focus but all modern processes
+
+ align:start position:0%
+depth of focus but all modern processes
+ 
+
+ align:start position:0%
+depth of focus but all modern processes
+seek to minimize topography so people
+
+ align:start position:0%
+seek to minimize topography so people
+ 
+
+ align:start position:0%
+seek to minimize topography so people
+have moved away from uh field oxides
+
+ align:start position:0%
+have moved away from uh field oxides
+ 
+
+ align:start position:0%
+have moved away from uh field oxides
+that go up or that go down you want fil
+
+ align:start position:0%
+that go up or that go down you want fil
+ 
+
+ align:start position:0%
+that go up or that go down you want fil
+oxide that's completely flat with the
+
+ align:start position:0%
+oxide that's completely flat with the
+ 
+
+ align:start position:0%
+oxide that's completely flat with the
+surface so you you see shallow trench
+
+ align:start position:0%
+surface so you you see shallow trench
+ 
+
+ align:start position:0%
+surface so you you see shallow trench
+isolation um there are uh special
+
+ align:start position:0%
+isolation um there are uh special
+ 
+
+ align:start position:0%
+isolation um there are uh special
+highdensity plasma eters have been
+
+ align:start position:0%
+highdensity plasma eters have been
+ 
+
+ align:start position:0%
+highdensity plasma eters have been
+developed to use uh chemicals like hbr
+
+ align:start position:0%
+developed to use uh chemicals like hbr
+ 
+
+ align:start position:0%
+developed to use uh chemicals like hbr
+chlorine and oxygen combined together
+
+ align:start position:0%
+chlorine and oxygen combined together
+ 
+
+ align:start position:0%
+chlorine and oxygen combined together
+specifically for gate etching to control
+
+ align:start position:0%
+specifically for gate etching to control
+ 
+
+ align:start position:0%
+specifically for gate etching to control
+the selectivity so you can stop on the
+
+ align:start position:0%
+the selectivity so you can stop on the
+ 
+
+ align:start position:0%
+the selectivity so you can stop on the
+gate dialectric and to control the shape
+
+ align:start position:0%
+gate dialectric and to control the shape
+ 
+
+ align:start position:0%
+gate dialectric and to control the shape
+of the sidewall profile at the same time
+
+ align:start position:0%
+of the sidewall profile at the same time
+ 
+
+ align:start position:0%
+of the sidewall profile at the same time
+you minimize damage to the underlying um
+
+ align:start position:0%
+you minimize damage to the underlying um
+ 
+
+ align:start position:0%
+you minimize damage to the underlying um
+structures and the underlying gate
+
+ align:start position:0%
+structures and the underlying gate
+ 
+
+ align:start position:0%
+structures and the underlying gate
+oxide the uh models I've talked about
+
+ align:start position:0%
+oxide the uh models I've talked about
+ 
+
+ align:start position:0%
+oxide the uh models I've talked about
+here for etching are fairly uh what I
+
+ align:start position:0%
+here for etching are fairly uh what I
+ 
+
+ align:start position:0%
+here for etching are fairly uh what I
+would call
+
+ align:start position:0%
+would call
+ 
+
+ align:start position:0%
+would call
+empirical uh if you want more predictive
+
+ align:start position:0%
+empirical uh if you want more predictive
+ 
+
+ align:start position:0%
+empirical uh if you want more predictive
+or more physically accurate models of
+
+ align:start position:0%
+or more physically accurate models of
+ 
+
+ align:start position:0%
+or more physically accurate models of
+plasma etching uh uh Professor swin used
+
+ align:start position:0%
+plasma etching uh uh Professor swin used
+ 
+
+ align:start position:0%
+plasma etching uh uh Professor swin used
+to teach class I'm not sure he's
+
+ align:start position:0%
+to teach class I'm not sure he's
+ 
+
+ align:start position:0%
+to teach class I'm not sure he's
+presently teaching it on really on all
+
+ align:start position:0%
+presently teaching it on really on all
+ 
+
+ align:start position:0%
+presently teaching it on really on all
+the details of plasma etching is an
+
+ align:start position:0%
+the details of plasma etching is an
+ 
+
+ align:start position:0%
+the details of plasma etching is an
+entire field in and of itself we've only
+
+ align:start position:0%
+entire field in and of itself we've only
+ 
+
+ align:start position:0%
+entire field in and of itself we've only
+been able to give it two lectures and
+
+ align:start position:0%
+been able to give it two lectures and
+ 
+
+ align:start position:0%
+been able to give it two lectures and
+one chapter of your textbook um so these
+
+ align:start position:0%
+one chapter of your textbook um so these
+ 
+
+ align:start position:0%
+one chapter of your textbook um so these
+models while helpful to people uh that
+
+ align:start position:0%
+models while helpful to people uh that
+ 
+
+ align:start position:0%
+models while helpful to people uh that
+we have now you know people to to these
+
+ align:start position:0%
+we have now you know people to to these
+ 
+
+ align:start position:0%
+we have now you know people to to these
+topography simulators like Speedy it's
+
+ align:start position:0%
+topography simulators like Speedy it's
+ 
+
+ align:start position:0%
+topography simulators like Speedy it's
+not going to give you the same level of
+
+ align:start position:0%
+not going to give you the same level of
+ 
+
+ align:start position:0%
+not going to give you the same level of
+uh chemical understanding if you had a
+
+ align:start position:0%
+uh chemical understanding if you had a
+ 
+
+ align:start position:0%
+uh chemical understanding if you had a
+full-blown model of the etching again
+
+ align:start position:0%
+full-blown model of the etching again
+ 
+
+ align:start position:0%
+full-blown model of the etching again
+it's it's fairly empirical we're fitting
+
+ align:start position:0%
+it's it's fairly empirical we're fitting
+ 
+
+ align:start position:0%
+it's it's fairly empirical we're fitting
+Curves in in speedy and we're fitting
+
+ align:start position:0%
+Curves in in speedy and we're fitting
+ 
+
+ align:start position:0%
+Curves in in speedy and we're fitting
+the shape but gives you some idea of
+
+ align:start position:0%
+the shape but gives you some idea of
+ 
+
+ align:start position:0%
+the shape but gives you some idea of
+what's really go of what's going on if
+
+ align:start position:0%
+what's really go of what's going on if
+ 
+
+ align:start position:0%
+what's really go of what's going on if
+you want more details uh there are other
+
+ align:start position:0%
+you want more details uh there are other
+ 
+
+ align:start position:0%
+you want more details uh there are other
+more detailed classes um you can take
+
+ align:start position:0%
+more detailed classes um you can take
+ 
+
+ align:start position:0%
+more detailed classes um you can take
+okay before we finish up let me just
+
+ align:start position:0%
+okay before we finish up let me just
+ 
+
+ align:start position:0%
+okay before we finish up let me just
+remind people if you came in late that
+
+ align:start position:0%
+remind people if you came in late that
+ 
+
+ align:start position:0%
+remind people if you came in late that
+um we have set the schedule uh after
+
+ align:start position:0%
+um we have set the schedule uh after
+ 
+
+ align:start position:0%
+um we have set the schedule uh after
+today is Thanksgiving there is no that's
+
+ align:start position:0%
+today is Thanksgiving there is no that's
+ 
+
+ align:start position:0%
+today is Thanksgiving there is no that's
+a holiday there's no class next week
+
+ align:start position:0%
+a holiday there's no class next week
+ 
+
+ align:start position:0%
+a holiday there's no class next week
+we'll talk about suicides and and novel
+
+ align:start position:0%
+we'll talk about suicides and and novel
+ 
+
+ align:start position:0%
+we'll talk about suicides and and novel
+gate materials after that we'll talk
+
+ align:start position:0%
+gate materials after that we'll talk
+ 
+
+ align:start position:0%
+gate materials after that we'll talk
+about strange silic and then you guys
+
+ align:start position:0%
+about strange silic and then you guys
+ 
+
+ align:start position:0%
+about strange silic and then you guys
+start talking I've picked the first four
+
+ align:start position:0%
+start talking I've picked the first four
+ 
+
+ align:start position:0%
+start talking I've picked the first four
+speakers here for the reports you have
+
+ align:start position:0%
+speakers here for the reports you have
+ 
+
+ align:start position:0%
+speakers here for the reports you have
+to speak for 16 minutes and then I have
+
+ align:start position:0%
+to speak for 16 minutes and then I have
+ 
+
+ align:start position:0%
+to speak for 16 minutes and then I have
+three questions of uh three U minutes
+
+ align:start position:0%
+three questions of uh three U minutes
+ 
+
+ align:start position:0%
+three questions of uh three U minutes
+for questions and answers on the seventh
+
+ align:start position:0%
+for questions and answers on the seventh
+ 
+
+ align:start position:0%
+for questions and answers on the seventh
+and on the 9th these are the speak
+
+ align:start position:0%
+and on the 9th these are the speak
+ 
+
+ align:start position:0%
+and on the 9th these are the speak
+people speaking on the 9th if you're
+
+ align:start position:0%
+people speaking on the 9th if you're
+ 
+
+ align:start position:0%
+people speaking on the 9th if you're
+doing a written report you must bring it
+
+ align:start position:0%
+doing a written report you must bring it
+ 
+
+ align:start position:0%
+doing a written report you must bring it
+to class on Thursday December 9th that's
+
+ align:start position:0%
+to class on Thursday December 9th that's
+ 
+
+ align:start position:0%
+to class on Thursday December 9th that's
+the last you can hand it in and this
+
+ align:start position:0%
+the last you can hand it in and this
+ 
+
+ align:start position:0%
+the last you can hand it in and this
+will be posted this list uh on on the
+
+ align:start position:0%
+will be posted this list uh on on the
+ 
+
+ align:start position:0%
+will be posted this list uh on on the
+website okay thanks
+
+ align:start position:0%
+website okay thanks
+ 
+
+ align:start position:0%
+website okay thanks
+great
\ No newline at end of file
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+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Now what I'm going
+to do is, I'm going to turn
+
+and start producer theory, OK,
+which will not be in the exam,
+
+but be the next subject
+to the course.
+
+OK, and we're going to spend a
+little bit longer on this.
+
+So what we've been doing so
+far is saying, look, we
+
+introduced the course with
+supply and demand curves,
+
+elasticities, all that.
+
+Hint, all that's on
+the exam too.
+
+OK, and all that.
+
+Then we say, well gee,
+where do supply and
+
+demand curves come from?
+
+Well, demand curves come from
+utility maximization.
+
+And we talked about how where
+indifference curves come from,
+
+how the tangency with the budget
+constraints leads to
+
+the demand curve.
+
+That's where demand
+curves come from.
+
+We talked about what underlies
+demand curves is income and
+
+substitution effects.
+
+OK, now let's come
+to supply curves.
+
+What underlies supply curves?
+
+Now on the one hand, this will
+be much easier than demand
+
+curves, because a lot of
+the logic is the same.
+
+So we can march more quickly
+through the analysis, because
+
+it's basically the same kind
+of tangency of curves with
+
+straight lines that yield supply
+curves that we've seen
+
+with consumer theory.
+
+On the other hand, supply
+curves are a ton harder,
+
+because now we don't
+just have the
+
+price as given to consumers.
+
+The suppliers actually
+make up the price.
+
+With consumers, we said the
+price -- you just went to the
+
+store. you're given a price.
+
+And you choose what to
+buy at those prices.
+
+Well, who set those prices?
+
+Producers do.
+
+And that's what determines the
+underlying supply curve.
+
+So life gets a little bit more
+difficult with producers.
+
+And that's why I'll probably
+spend about twice as many
+
+lectures talking about producer
+theory as we've spent
+
+talking about consumer theory.
+
+Now, let's go to the basics.
+
+The basics are, just as we had
+consumers making decisions, we
+
+thought of a consumer as
+somebody choosing across a
+
+bundle of goods, pizza versus
+movies, now we're going to
+
+think of a producer very simply
+as a black box, where
+
+inputs go in and outputs
+come out.
+
+So think of the firm.
+
+Let's think of a firm,
+a producer, as
+
+just some black box.
+
+We're literally thinking
+a flow chart.
+
+You've got inputs that go in
+and outputs that come out.
+
+And that black box, that firm,
+just as individuals have a
+
+simple goal which is to maximize
+their utility,
+
+producers have a simple
+goal which is to
+
+maximize their profits.
+
+And profits are defined as
+revenue minus cost. OK?
+
+Producers are these black boxes,
+where their goal is to
+
+maximize their profits, which is
+revenue minus cost. And the
+
+key to maximizing profits
+is efficient production.
+
+The key to maximizing profits
+is going to be to produce
+
+goods as efficiently
+as possible.
+
+OK, so profit maximization
+requires production
+
+efficiency.
+
+To maximize your profits, you
+need to produce as efficiently
+
+as possible.
+
+Now, you might ask yourself,
+gee, I can read about all
+
+these companies that have
+executive corporate jets, and
+
+the guys in these lavish
+lifestyles, and that doesn't
+
+seem very efficient
+production.
+
+I'll come back to that.
+
+OK, in a couple of lectures,
+we'll talk about do firms
+
+actually maximize profits, and
+whether they do or not.
+
+But for now, let's take as
+a given that they do.
+
+OK, just as it is a given that
+consumers maximize utility,
+
+let's take as a given that firms
+maximize their profits.
+
+OK?
+
+Now, to decide how to
+efficiently produce goods,
+
+we're going to turn
+and today discuss
+
+firm production functions.
+
+OK, today, we'll focus on
+production functions.
+
+That's essentially the
+technology by which a firm
+
+takes inputs, or what we call
+factors of production, and
+
+turns them into outputs,
+is through
+
+this production function.
+
+So just like your utility
+function is a tool for which
+
+we take bundles of goods and
+turn them into happiness, a
+
+production function is a tool
+for which we take bundles of
+
+inputs and turn them
+into outputs.
+
+OK, but something that's a
+little easier to understand
+
+this, you could think of a
+factory where stuff comes in,
+
+and think of a belt, a
+mechanical belt, going through
+
+and stuff goes in and other
+stuff comes out.
+
+You could think of that
+production function.
+
+We're going to think about two
+different kinds of inputs that
+
+firms are going to use.
+
+Once again, to make life easy,
+we're going to assume firms
+
+only use two kinds of inputs.
+
+Later, we'll expand this, but
+from mostly intuition you can
+
+get from thinking about
+this-- two kinds of
+
+inputs, labor and capital.
+
+Labor and capital are the two
+kinds of inputs firms use.
+
+Labor is clear.
+
+It's just hours of labor,
+hours of work.
+
+OK?
+
+It's just hours of work
+in production.
+
+Capital is a lot trickier.
+
+And we'll spend a lot of time
+this semester struggling with
+
+what capital really means.
+
+Basically for now, think of
+capital as everything else
+
+that goes into production, the
+machines, the buildings, the
+
+land, everything.
+
+Think of capital as everything
+else that goes into
+
+production.
+
+So basically, when you produce
+stuff, you produce it with
+
+workers working with stuff.
+
+Capital's the stuff.
+
+Now, this capital is sort of a
+composite of everything else
+
+that goes into production.
+
+And once again, we'll add some
+more detail on this later.
+
+OK, and the output is
+some output, q.
+
+That's the units
+of production.
+
+That's the output that is
+produced by the firm.
+
+So basically, we can think of a
+production function is q is
+
+some function of l and k.
+
+That's a production function,
+that the output you produce as
+
+your firm--
+
+and by the way, we're going to
+use little q to represent a
+
+firm's output, and big Q to
+represent market output.
+
+OK, so little q, and if I slip
+in this, yell at me, OK?
+
+But we're going to try to
+consistently use little q to
+
+represent a given firm's output,
+and big Q to be the
+
+market's output--
+
+So little q is some function of
+the amount of workers you
+
+have and the amount of
+capital you use.
+
+Now, the important distinction
+we're going to make here is
+
+between variable versus
+fixed inputs.
+
+Variable versus fixed inputs
+is an important distinction
+
+we're going to draw.
+
+Variable inputs are inputs that
+are easily changed, like
+
+how many hours somebody works.
+
+In principle, you could just
+have some work five hours one
+
+day, one hour the next day, 10
+hours the day after that.
+
+It's easy to change
+hours of work.
+
+So that's a variable input.
+
+Fixed inputs are things which
+are harder to change quickly,
+
+like the size of the building
+that the workers
+
+are building in.
+
+Once that building's built, it's
+pretty hard to change it.
+
+You can't like lop off 2/3 of it
+on one day and add it back
+
+the next day.
+
+OK, that's more of
+the fixed inputs.
+
+And this will lead to a critical
+distinction for
+
+production theory, which
+is the short run
+
+versus the long run.
+
+The short run versus
+the long run.
+
+The long run is the
+period over which
+
+all inputs are variable.
+
+The short run is a period over
+which some inputs are fixed.
+
+Let me say it again, it's
+very important.
+
+The short run is the
+period over which
+
+some inputs are fixed.
+
+The long run is the
+period over which
+
+all inputs are variable.
+
+Now, what does that mean?
+
+I can't tell you.
+
+OK?
+
+I can tell you that, clearly,
+tomorrow is the short run.
+
+Clearly, you can't vary all
+your inputs over one day.
+
+And probably next month
+is the short run.
+
+And probably even next year
+is the short run.
+
+There's a lot of inputs that it
+takes more than a month to
+
+change, or a year to change.
+
+On the other hand, 10 years from
+now is almost certainly
+
+the long run.
+
+There's very few inputs to
+production you can't change
+
+over a 10-year period.
+
+So we know a day are
+the short run.
+
+And we know 10 years
+is the long run.
+
+We don't really know where
+the transition is, but in
+
+substance that doesn't
+matter for you guys.
+
+What matters is the definition
+of short run, long run.
+
+When someone asks you what the
+long run is, you say it's the
+
+period of time over which
+all inputs are variable.
+
+That's what matters.
+
+So it doesn't matter if
+you define it in days
+
+or months or years.
+
+It's a theoretical concept,
+which the break from the short
+
+run to the long run is the break
+between when some inputs
+
+are fixed and all inputs
+are variable.
+
+OK?
+
+Now of course, once again
+this is tricky.
+
+And economists recognize
+this subtlety.
+
+A lot of times, economists will
+talk about quasi-fixed
+
+factors of production, which are
+things which could change
+
+in between the short run
+and the long run.
+
+So for instance, take labor.
+
+OK, we'll talk about labor as a
+variable unit of production
+
+you can change in
+the short run.
+
+But in fact, we know in
+practice you can't.
+
+Most jobs, you can't ask the
+guys to come for an hour one
+
+day, and 10 hours the next day,
+five hours the day after
+
+that, maybe some jobs like
+hourly construction.
+
+But most jobs you guys will
+have, OK, your labor isn't
+
+that variable.
+
+We're typically on some kind of
+
+reasonably set work schedule.
+
+Now that work schedule
+can evolve.
+
+OK, but it can't change
+day by day.
+
+None of us are going to have
+jobs where they're going to
+
+say, look, work two hours
+today, 12 hours the
+
+next day, et cetera.
+
+OK, we're all going to have
+jobs with a fairly smooth
+
+distribution.
+
+There'll be peaks and valleys,
+but a fairly smooth
+
+distribution of our
+labor effort.
+
+So really, truly, there's very
+few inputs which are truly
+
+perfectly variable.
+
+OK?
+
+Just like there are no inputs
+which are truly perfectly
+
+fixed, but for the purposes of
+this model, let's think about
+
+labor as a variable input.
+
+Let's think about labor as being
+like hourly labor, like
+
+hourly construction, OK?
+
+And let's think about capital as
+being a fixed input, like a
+
+building that you can't pare
+down or rebuild overnight, but
+
+over a 10-year period you can.
+
+OK?
+
+Questions about that?
+
+Once again, we talked about
+simplifying assumptions at the
+
+beginning of the semester.
+
+This is our set of simplifying
+assumptions.
+
+Simplifying assumptions are that
+firms produce goods with
+
+two inputs, labor and capital,
+that labor is variable, which
+
+means you can change it minute
+to minute or day to day, and
+
+capital is fixed, which means
+you can only change
+
+it in the long run.
+
+OK?
+
+All right, so armed with that,
+let's now talk about how firms
+
+make short-run production
+decisions.
+
+And once again, these are
+a lot of assumptions.
+
+But at the end of the day, I'm
+going to be able to teach you
+
+in a couple of lectures how
+firms make decisions.
+
+And I'm going to be
+about 80% right.
+
+So that's pretty good.
+
+OK, so there are some
+assumptions, but we're going
+
+to go a long way with
+these assumptions.
+
+So let's start by considering
+the short run, and considering
+
+that period of time over
+which labor is variable
+
+but capital is fixed.
+
+Labor is variable but
+capital is fixed.
+
+That is, you have a given plant,
+but you can adjust how
+
+many workers you use every
+day in that plant.
+
+And now the firm has to decide,
+given that that plant
+
+exists, how many workers
+should I hire
+
+to produce my good?
+
+How many workers should I
+hire to produce my good?
+
+And the key concept that's going
+to determine that is
+
+something we'll call the
+marginal product of labor,
+
+which is the change in total
+output resulting from the next
+
+unit of labor used--
+
+that is, delta q, delta l--
+
+is the marginal product
+of labor.
+
+It's going to be the change in
+total output from another unit
+
+of labor, once again holding
+capital constant because
+
+that's fixed.
+
+So really, it's really at a
+given k bar, but that's
+
+implicit in the fact
+it's the short run.
+
+So the given level of capital,
+what is the change in output
+
+for another unit of labor?
+
+And once we get to the short
+run, I shouldn't
+
+have to write this.
+
+If I tell you short run, you
+should know this is true.
+
+But technically, we would
+write that out.
+
+Now, what we're going to do here
+is we're typically going
+
+to assume this--
+
+hint, hint--
+
+if you're comfortable with
+consumer theory, this is like
+
+marginal utility.
+
+Marginal product is like
+marginal utility.
+
+Just as the marginal utility was
+your utility from another
+
+unit of one good, holding the
+other good fixed, marginal
+
+product is the marginal
+production from another unit
+
+of an input, holding the
+other input fixed.
+
+So just sort of a parallel
+to keep in mind.
+
+And just as we've assumed and
+discussed the intuition for
+
+diminishing marginal utility,
+we're going to typically
+
+assume diminishing
+marginal product.
+
+So we're going to assume
+diminishing marginal product.
+
+That is, from a given level of
+labor, the next worker you add
+
+increases your total product by
+less than the previous one.
+
+Now once again, just like we
+have a non- satiation rule in
+
+utility, we're not going
+to say the next
+
+worker doesn't help.
+
+Every worker helps.
+
+But every worker helps less and
+less and less, just like
+
+every pizza means less and
+less and less to you.
+
+Now, the trick here, once again,
+this is like consumer
+
+theory, only more subtle.
+
+With consumer theory, it's
+pretty clear that once you had
+
+one pizza, clearly, the second
+pizza means less.
+
+And once you've seen one movie,
+your first-place prize,
+
+the movie you most want to see,
+clearly the next movie
+
+you want to see means
+a little bit less.
+
+Producer theory is a
+little more subtle.
+
+And you can imagine ranges over
+which more workers help.
+
+They can work together.
+
+So that actually two workers
+can do more than twice what
+
+one worker can do.
+
+And we'll talk about that.
+
+But we're going to focus in the
+main on ranges over which
+
+each additional worker does
+less and less and less.
+
+And the reason is because,
+to remember, this
+
+is less than two--
+
+Yeah?
+
+AUDIENCE: Is there going to
+be a point where actually
+
+additional workers won't do
+anything, because of like
+
+constrain to the amounts
+of other inputs?
+
+PROFESSOR: Once again, we're not
+going to get-- just like
+
+there's a point at which extra
+pizza will make you barf--
+
+OK, we're assuming we don't
+get to that point.
+
+But yes, technically of course,
+at some point more is
+
+not better.
+
+At some point, extra workers
+just sit around.
+
+And so I agree.
+
+So basically, it's
+a little tricky.
+
+You could imagine an initial
+range where more
+
+workers would help.
+
+Then there's the main range
+we'll focus on each additional
+
+worker does less and
+less and less.
+
+And you could imagine that
+running out, which is a worker
+
+does nothing.
+
+But let's just now assume
+we don't get there.
+
+So basically, what's
+the intuition?
+
+Now the intuition for in
+utility theory, for
+
+diminishing marginal utility,
+I thought was pretty easy,
+
+which is each pizza
+means less.
+
+The intuition for why each
+worker does less, I find a
+
+little bit harder.
+
+You could say, well, gee, why
+should one worker do less than
+
+the next worker?
+
+Why shouldn't the next worker
+do less than the first?
+
+And the key is this
+part, that we're
+
+holding capital constant.
+
+The reason each worker does less
+is because they only have
+
+the same amount of stuff
+to work with.
+
+And the classic example we
+use here is the example
+
+of digging a hole.
+
+You go to dig a hole and your
+capital's a shovel.
+
+And let's say for some reason
+the shovels are out, so you
+
+can't get another shovel
+for a while.
+
+OK, so there's one shovel.
+
+So you have one worker digging
+a hole, then the next worker
+
+comes along and that's where
+he can help because he can
+
+spell the first worker.
+
+And maybe the next worker's just
+as good because he can
+
+work more hours, but probably
+it's a little bit less good.
+
+But certainly by the time you
+add a fourth and a fifth and a
+
+sixth person, with one shovel,
+they probably each help
+
+because they can rotate
+and rest each other.
+
+But certainly the sixth person
+is not going to help dig the
+
+hole as much as that second
+person did, or the third, or
+
+fourth, or fifth person, because
+only one shovel.
+
+So they can share a little
+bit and share the
+
+burden a little bit.
+
+But at some point each
+additional worker helps less
+
+because they have to share
+the same shovel.
+
+So that's what diminishing
+marginal product is, because
+
+capital's fixed.
+
+With a certain amount of capital
+to work with, each
+
+additional worker just
+can't help as
+
+much as the one before.
+
+Now eventually, you can
+add more shovels.
+
+And you could have
+wheelbarrows.
+
+So some people could run the
+wheelbarrows, some people
+
+could run the shovels.
+
+But that's the long run.
+
+In the short run, there's the
+one shovel, so each additional
+
+worker does less good.
+
+And that's the intuition.
+
+Once again, not as clean as with
+consumption, where it's
+
+easy to see each additional
+pizza is worth less, because
+
+you could imagine the second
+worker might actually help.
+
+They could rest, et cetera,
+and you could imagine
+
+eventually the ninth worker does
+nothing because there's
+
+nothing left to do.
+
+But let's focus on that range
+where it's intuitive.
+
+We're staying between the second
+and sixth worker, which
+
+is when a worker would help,
+but they help less
+
+and less and less.
+
+OK, and that's the diminishing
+marginal product.
+
+Questions about that?
+
+That's short-run production.
+
+And we're going to come
+back to this.
+
+But I just want to introduce
+these concepts.
+
+Now let's talk about long-run
+production.
+
+Now in the long run, all
+inputs are variable.
+
+That's how we defined
+the long run.
+
+So now a firm doesn't just
+choose how many workers to
+
+hire, or how many hours
+of labor to buy.
+
+It chooses both l and k, and
+has to trade them off, just
+
+like you chose both pizzas
+and movies and had
+
+to trade them off.
+
+So the long-run production
+theory is the same, basically
+
+the same mechanics,
+as utility theory.
+
+There's a production function.
+
+You have two inputs.
+
+You trade them off.
+
+Just like you're a consumer.
+
+You have two goods to consume.
+
+You trade them off.
+
+The difference is going to be
+that ultimately production is
+
+going to self--
+
+the difference is, when you
+decide how to trade them off
+
+as a consumer, you're given
+a budget constraint.
+
+The difference with production
+is the budget constraint is
+
+going to be itself determined
+by the same system.
+
+So you're not only going to
+develop your production
+
+function, but you're going to
+develop your budget constraint
+
+and, you're going
+to decide both.
+
+It's a little bit funky
+but we'll get to it.
+
+But for now, let's just think
+about the parallels to
+
+consumer theory, and think about
+a production function
+
+which is q--
+
+little q--
+
+is the square root
+of k times l.
+
+That same functional form I used
+with pizza and movies,
+
+where utility is the square root
+of pizza times movies.
+
+Now I'm going to say what you
+produce of your good is the
+
+square root of k times l.
+
+Now let's go to figure 8-3.
+
+And what we see here is, if
+you're trading off k and l and
+
+deciding to produce, then you
+get what's called isoquants.
+
+Isoquants are the parallel
+to indifference curves.
+
+Once again, this is all
+the same mechanics.
+
+Just as there were sets of goods
+across which you were
+
+indifferent, two pizzas and one
+movie versus one pizza and
+
+two movies.
+
+Isoquants are sets of
+inputs along which
+
+production is the same.
+
+So along a given isoquant,
+q is fixed.
+
+Each of those isoquants is a
+different level of q, but they
+
+show how you can vary k and l
+to get the same amount of q.
+
+So producing q equals
+square root of 2.
+
+I can use two units of capital
+and one unit of labor, or one
+
+unit of capital and
+two of labor.
+
+So I can choose lots of
+combinations of k and l along
+
+that isoquant to produce a
+given amount of output.
+
+And isoquants have all the
+same features as in
+
+indifference curves.
+
+The further out the better
+because you're producing more.
+
+They can't cross.
+
+All the same set of things we
+have in the indifference
+
+curves are true with
+isoquants as well.
+
+And they slope downwards because
+there's a trade off
+
+between capital and labor.
+
+Now, what's going to determine
+the slope of an isoquant?
+
+Can someone tell me
+what determines
+
+the slope of an isoquant?
+
+What determines if isoquants
+are steep or shallow?
+
+Well, what determines the slope
+of a indifference curve?
+
+Yes, go ahead.
+
+AUDIENCE: It's based on the
+ratio of how much labor is
+
+worth versus capital?
+
+PROFESSOR: Right, and what
+do we call that?
+
+What determines how much they're
+worth from each other?
+
+What determines the slope
+of a indifference curve?
+
+The marginal rate of
+substitution, it was the
+
+substitutability
+between goods.
+
+Likewise, the substitutability
+between labor and capital will
+
+determine the slope of
+these isoquants.
+
+So to see an example, let's do
+an extreme example here.
+
+Let's consider goods that are
+perfectly substitutable.
+
+So like, I don't know, just like
+a Harvard undergraduate
+
+and a beanie baby.
+
+OK, perfectly substitutable.
+
+Figure 8-4a shows the
+case of perfectly
+
+substitutable inputs.
+
+In that case, you would have a
+linear isoquant, because what
+
+that would mean is you don't
+care if you have three capital
+
+and one labor, or three
+labor and one capital.
+
+You don't care.
+
+You don't care if you have two
+labor and two capital, or
+
+three labor and one capital,
+as long as you
+
+get a total of four.
+
+That's all that matters.
+
+They're perfectly substitutable
+inputs, which
+
+would say that it would be
+something like q equals k plus
+
+l would be the case
+of perfectly
+
+substitutable inputs.
+
+You don't care if it's k or l,
+you just care about the total.
+
+That'd be perfectly
+substitutable inputs.
+
+That would be a linear
+isoquant.
+
+OK, on the other hand, let's
+think about goods which are
+
+not at all substitutable like
+cereal and cereal boxes.
+
+The cereal wouldn't be any
+good unless you have a
+
+box to put it in.
+
+The box doesn't do anything
+unless you have
+
+cereal to put in it.
+
+That would be like in 8-4b.
+
+8-4b would show you
+non-substitutable inputs where
+
+basically, given the amount of
+one input, it doesn't matter
+
+how much you have
+of the other.
+
+So for example, if you take
+these-- these we often call
+
+non-substitutable isoquants--
+
+Leontief production functions.
+
+Leontief production function,
+for Wassily Leontief, some old
+
+economist.
+
+And basically, the Leontief
+production function is that
+
+your production, q equals the
+Min of k and l, is the
+
+Leontief production function.
+
+So given how much k you have,
+given you have 10 cereal
+
+boxes, once you have 10 chunks
+of cereal, it doesn't matter
+
+if you have 10, 11,
+12, 1 million.
+
+You only have 10 cereal boxes.
+
+So given an amount of k, then
+it doesn't matter how much l
+
+you have. Once you get to the
+amount of l you need to fill
+
+the cereal boxes, it doesn't
+matter, and vice versa.
+
+So basically, they're perfectly
+non-substitutable.
+
+So all that determines your
+output is which you
+
+have the least of.
+
+OK, so substitutabilities
+determine the slope of the
+
+isoquants and of this
+production function.
+
+Now in general, we'll be
+in between these cases.
+
+There'll be some
+substitutability.
+
+Goods won't be perfectly
+substitutable, but they'll be
+
+somewhat substitutable.
+
+So in general, we'll be in
+between these cases.
+
+And more generally, just as the
+slope of the indifference
+
+curve is the marginal rate of
+substitution, the slope of the
+
+isoquant we will call the
+marginal rate of technical
+
+substitution.
+
+The marginal rate of technical
+substitution-- the rate at
+
+which you can substitute one
+input for another in a
+
+production function is the
+marginal rate of technical
+
+substitution--
+
+which we'll define as delta k,
+delta l for a given q bar, the
+
+rate at which you can
+trade off k for l
+
+to hold q bar fixed.
+
+Now, as with marginal rate of
+substitution, the marginal
+
+rate of technical substitution
+will
+
+change along the isoquant.
+
+So if you go to figure 8-5,
+here we've drawn a typical
+
+isoquant for the production
+function q equals square root
+
+of k times l.
+
+So the production function
+is q equals the square
+
+root of k times l.
+
+And here's a isoquant.
+
+This is the isoquant
+of all combinations
+
+which produce two units.
+
+This is the q equals
+2 isoquant.
+
+Now, unlike utility--
+remember utility?--
+
+we said where u equals
+2 was meaningless.
+
+Utility was an ordinal concept,
+
+not a cardinal concept.
+
+Here, quantity is meaningful.
+
+If you produce four, you would
+have only produced twice as
+
+much as if you produced two.
+
+We can care about both the
+ordinality and the cardinality
+
+of these outcomes.
+
+So we can say, what are the
+combinations of inputs which
+
+lead you to produce two units?
+
+What's all these combinations
+of inputs?
+
+So whereas you can have one unit
+of labor and four units
+
+of capital, two of each, or four
+units of labor and one
+
+unit of capital, all
+will produce two
+
+units of the output.
+
+And what you can see is that the
+marginal rate of technical
+
+substitution varies.
+
+So for instance, when we start
+with four units of capital and
+
+one unit of labor, and we think
+about adding a second
+
+unit of labor, then the marginal
+rate of technical
+
+substitution is minus 2.
+
+That is, one unit of labor is
+worth two units of capital.
+
+In other words, we can produce
+the same amount of widgets of
+
+q, but if we replace two units
+of capital with one unit of
+
+labor, so at that point we're
+very capital-intensive, and
+
+that unit of labor
+is very valuable.
+
+On the other hand, now if you
+imagine we're down at 4-1, at
+
+the third point--
+
+we are probably using
+a, b, c--
+
+now we're at the third point,
+where you have we have four
+
+units of labor and one
+unit of capital.
+
+Now, if you'd be willing to
+give up two units of labor
+
+just to get one unit of capital,
+that's the marginal
+
+rate of technical substitution
+is now minus 1/2.
+
+When you're very
+labor-intensive, you'd be
+
+happy to give up a lot of labor
+to get a little capital.
+
+Once again, the principle of
+diminishing marginal product,
+
+just like the principle of
+diminishing marginal utility,
+
+implies that the marginal rate
+of technical substitution is
+
+going to be falling as you
+go down the isoquant.
+
+Just like the marginal rate of
+substitution fell as you went
+
+down the indifference curve, the
+marginal rate of technical
+
+substitution is going to fall
+as you go down the isoquant.
+
+And why is this?
+
+Once again it's because of
+this diminishing marginal
+
+productivity.
+
+That is, as you add more and
+more labor, given capital,
+
+each unit of labor can
+do less and less.
+
+And likewise, as you add more
+and more capital, given an
+
+amount of workers to use it,
+each unit of capital can do
+
+less and less.
+
+So it's a very different
+approach, but gets you the
+
+same answer, which is with
+consumption, each piece does
+
+less and less for you, but we
+can see that as consumers.
+
+Here's the notions of labor,
+each worker does less and less
+
+for you, holding
+capital fixed.
+
+And each machine by the same
+logic, if you have one guy in
+
+the hole, it doesn't
+matter how many
+
+shovels you throw there.
+
+He still is only one guy.
+
+So each machines is doing less
+and less by the same logic.
+
+And those diminishing marginal
+products lead to this
+
+decreasing marginal rate of
+technical substitution as you
+
+move along the isoquant.
+
+That's about the most technical
+statement I'll make
+
+all semester.
+
+OK, questions about that, about
+what's going on here?
+
+That's production theory.
+
+That's what you need to know
+to know basically how firms
+
+produce things.
+
+Now, what we're going to do
+is, now take this basic
+
+production theory, and turn it
+into actually understanding
+
+how firms make decisions
+on how much to produce.
+
+But before we do that, I want
+to talk about one other
+
+concept, which is very important
+for thinking about
+
+production theory.
+
+And it comes back to these
+assumptions that we make which
+
+might be a little bit
+unrealistic, which is the
+
+concept of returns to scale.
+
+The concept of returns
+to scale.
+
+So here the question is, what
+happens if we increase all
+
+inputs proportionally?
+
+Return to scale.
+
+By scale, I mean, what if we
+just double everything, twice
+
+as much labor and twice
+as much capital.
+
+That's an increase in scale,
+increasing all inputs
+
+proportionally, twice as much
+labor, twice as much capital,
+
+half as much labor, half
+as much capital.
+
+So a change in scale is an equal
+increase or decrease in
+
+all inputs?
+
+Equal proportional.
+
+So what happens if we increase
+all inputs, increase or
+
+decrease proportionally?
+
+And this is an interesting case,
+because it's like, OK,
+
+what if we just make the
+firm half as big?
+
+What happens?
+
+Well, the answer is,
+it depends on
+
+the production process.
+
+Some production processes will
+exhibit what we call constant
+
+returns to scale.
+
+This is a convenient form.
+
+It's convenient because the way
+constant returns to scale
+
+works is, it says that f of
+2l, 2k, is equal to 2
+
+times f of l, k.
+
+That is, if it's constant, you
+can just pull the 2 out.
+
+Doubling the inputs leads to
+doubling the outputs, which
+
+equals to 2q, I'll write here.
+
+Doubling the inputs equals
+doubling the outputs.
+
+So if I have twice as much labor
+and capital, that's the
+
+same as twice producing what I
+had with the original labor
+
+and capital which will get me
+twice the original production.
+
+That's the constant
+returns to scale.
+
+So every time I double my firm,
+I get exactly twice as
+
+much stuff out.
+
+We can contrast that with
+increasing returns to scale,
+
+IRS, which says that f of 2l,
+2k, is greater than 2
+
+times f of l, k.
+
+Or it's greater than 2q.
+
+That is, when I double my firm,
+I produce more than
+
+twice as much stuff.
+
+That'd be increasing
+returns to scale.
+
+On the other hand, we could also
+have decreasing returns
+
+to scale, which not surprisingly
+means that f of
+
+2l, 2k, is less than 2 times
+f of l, k, or less than 2q.
+
+That would be decreasing returns
+to scale, which is
+
+when I double my firm I get less
+than twice as much stuff.
+
+Can anyone give me an example or
+some reason why returns to
+
+scale is going to be increasing
+or decreasing?
+
+Think about firms out there.
+
+Give me some that, by returns to
+scale, would be increasing
+
+or decreasing, any examples
+you can think of.
+
+There's no right answer here.
+
+Yeah.
+
+Go ahead, on the end.
+
+AUDIENCE: Oh, if you're mining
+something, you can only get to
+
+stuff at one time, so having
+more equipment and more people
+
+doesn't mean you can
+get more out of it?
+
+PROFESSOR: Right, so if there's
+a limited resource,
+
+you could imagine decreasing
+returns to scale.
+
+Good.
+
+What else?
+
+Yeah.
+
+AUDIENCE: If the company gets
+harder to manage, that could
+
+be decreasing returns
+to scale?
+
+PROFESSOR: Right, exactly.
+
+If you're an entrepreneur,
+you've got a great idea, but
+
+it turns out that idea only
+works if you really are
+
+hands-on about it.
+
+You're not Mark Zuckerberg, who
+can just farm the thing
+
+out, it's really your idea.
+
+And you've got to be there.
+
+Then after it expands and
+you lose control of the
+
+production, it might not be as
+effective because you're not
+
+there making it happen.
+
+Any ideas why return--
+
+Yeah.
+
+AUDIENCE: If you or
+[UNINTELLIGIBLE]
+
+PROFESSOR: So that's
+an example of
+
+increasing returns to scale.
+
+Increasing returns to scale
+would be, gee, maybe if I'm
+
+bigger, I can get a better
+deal on the inputs.
+
+But that's not quite right,
+because we haven't really got
+
+into prices yet.
+
+I'm looking-- that's really
+a market response--
+
+I'm looking for a more
+technological story, a
+
+technological story of
+increasing returns.
+
+Go ahead.
+
+AUDIENCE: If you're bigger, you
+can hire a specialist to
+
+do work, like a manager
+who can [INAUDIBLE]
+
+PROFESSOR: Exactly.
+
+So it's the opposite, which is,
+let's say you have an idea
+
+which is pretty good, but
+in fact it's replicable.
+
+And right now, you're trying
+to manage some guys.
+
+And then all of a sudden, when
+you get twice as big, you
+
+bring other people in who can
+effectively replicate your
+
+idea, and really expand it
+in a very effective way.
+
+You can have increasing
+returns to scale.
+
+Now, so an example of what that
+looks like, if you go to
+
+the last page in the handout,
+figure 8-6a shows constant
+
+returns to scale.
+
+So let's start with
+8-6a, that's
+
+constant returns to scale.
+
+So here-- and these are
+from the textbook--
+
+for example, when we doubled the
+inputs from 100 labor, 100
+
+capital, to 200 labor, 200
+capital, you doubled output.
+
+Those are constant returns
+to scale isoquants.
+
+The last page shows
+decreasing and
+
+increasing returns to scale.
+
+So for instance, tobacco is an
+example of decreasing returns
+
+to scale, because there's only
+so much leaf that you have
+
+that you can produce.
+
+So here, when you double the
+inputs from 100 to 200, your
+
+output only goes from
+100 to 142.
+
+OK, and if you want to double
+the 200 units, you've got to
+
+go way the heck up
+there on inputs.
+
+On the other hand, primary metal
+production is something
+
+where you can have increasing
+returns to scale, because
+
+there's such high costs of
+building a plant that once
+
+it's built, so just like I said,
+gee, in fact that second
+
+digger of the hole might
+actually make it more
+
+productive.
+
+Once that plant's built, there's
+one worker banging
+
+around the plant, a second
+worker adds a huge amount to
+
+productivity because they
+can specialize.
+
+Basically, increasing returns to
+scale is going to come from
+
+specialization.
+
+So if you build this big plant
+to build primary, to build
+
+steel, one worker in that plant
+is no good, because he's
+
+got to pour the steel,
+then run over and
+
+cool it down, et cetera.
+
+Once you have two, they can
+specialize, and three, they
+
+can specialize more.
+
+You might think of something
+like that would have
+
+increasing returns to scale
+through specialization.
+
+And that's illustrated here,
+where doubling the inputs
+
+actually leads to more than
+doubling the output.
+
+Now we're going to talk
+about all these cases.
+
+Typically, economists are
+suspicious of increasing
+
+returns to scale.
+
+Anybody, anybody who ever has an
+IPO, whoever starts a firm
+
+will always tell you
+that they have
+
+increasing returns to scale.
+
+Well, we say, I've got a great
+idea and the bigger, the more,
+
+the better it's going to be.
+
+And they're generally wrong.
+
+Generally, we think of
+increasing returns to scale as
+
+being like a free lunch.
+
+And we don't like free lunches,
+we economists.
+
+We think, gee, if it's really
+increasing returns to scale,
+
+you would have already
+expanded there.
+
+OK, if it's really such a good
+idea to get bigger, why aren't
+
+you bigger already?
+
+Now, it doesn't mean you can--
+
+Yeah.
+
+AUDIENCE: Well, they
+need capital.
+
+PROFESSOR: Well, they need
+capital, and so that would be
+
+their argument.
+
+And that's great.
+
+And typically, they're wrong.
+
+But that would be why you would
+argue that they need
+
+capital to get bigger.
+
+So typically, we like decreasing
+returns to scale.
+
+That's going to be our
+sort of default
+
+assumption of the world.
+
+In other words, here's a way to
+think about it, think about
+
+we're dealing with mature firms.
+We're modeling, for
+
+instance, mature firms.
+
+We think that for mature firms,
+at least, there's not
+
+increasing returns to scale,
+because in a mature firm they
+
+would have hit that
+point already.
+
+Now they're on the
+decreasing part.
+
+So that's where we're
+going to focus for
+
+the rest of the semester.
+
+OK, let me stop there.
+
+And good luck tomorrow night.
+
+And we'll come back
+to talk more about
+
+production on Wednesday.
\ No newline at end of file
diff --git a/AWU3lTs9KJA.txt b/AWU3lTs9KJA.txt
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index 0000000000000000000000000000000000000000..03e88379da0474166f466adbbfe66df7d7b73fb7
--- /dev/null
+++ b/AWU3lTs9KJA.txt
@@ -0,0 +1,10267 @@
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+ocw.mit.edu so we have a an interesting
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+ocw.mit.edu so we have a an interesting
+ 
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+ocw.mit.edu so we have a an interesting
+um class today we're going to be taking
+
+ align:start position:0%
+um class today we're going to be taking
+ 
+
+ align:start position:0%
+um class today we're going to be taking
+this V curve that we've uh so
+
+ align:start position:0%
+this V curve that we've uh so
+ 
+
+ align:start position:0%
+this V curve that we've uh so
+laboriously uh set up and understood
+
+ align:start position:0%
+laboriously uh set up and understood
+ 
+
+ align:start position:0%
+laboriously uh set up and understood
+sorry about that and now we will uh
+
+ align:start position:0%
+sorry about that and now we will uh
+ 
+
+ align:start position:0%
+sorry about that and now we will uh
+subject to it to illumination um so
+
+ align:start position:0%
+subject to it to illumination um so
+ 
+
+ align:start position:0%
+subject to it to illumination um so
+that's the essence of our lecture today
+
+ align:start position:0%
+that's the essence of our lecture today
+ 
+
+ align:start position:0%
+that's the essence of our lecture today
+the diode under illumination and uh as
+
+ align:start position:0%
+the diode under illumination and uh as
+ 
+
+ align:start position:0%
+the diode under illumination and uh as
+part of today's lecture we have some
+
+ align:start position:0%
+part of today's lecture we have some
+ 
+
+ align:start position:0%
+part of today's lecture we have some
+wonderful little kits over there in the
+
+ align:start position:0%
+wonderful little kits over there in the
+ 
+
+ align:start position:0%
+wonderful little kits over there in the
+corner where we'll actually be testing
+
+ align:start position:0%
+corner where we'll actually be testing
+ 
+
+ align:start position:0%
+corner where we'll actually be testing
+IV curves of solar cells um so I hope uh
+
+ align:start position:0%
+IV curves of solar cells um so I hope uh
+ 
+
+ align:start position:0%
+IV curves of solar cells um so I hope uh
+some of you brought the computers today
+
+ align:start position:0%
+some of you brought the computers today
+ 
+
+ align:start position:0%
+some of you brought the computers today
+and if not we have some extras up here
+
+ align:start position:0%
+and if not we have some extras up here
+ 
+
+ align:start position:0%
+and if not we have some extras up here
+as well use so again just to situate
+
+ align:start position:0%
+as well use so again just to situate
+ 
+
+ align:start position:0%
+as well use so again just to situate
+ourselves you're here on fundamentals uh
+
+ align:start position:0%
+ourselves you're here on fundamentals uh
+ 
+
+ align:start position:0%
+ourselves you're here on fundamentals uh
+we're approaching the
+
+ align:start position:0%
+we're approaching the
+ 
+
+ align:start position:0%
+we're approaching the
+end of our fundamental section but we
+
+ align:start position:0%
+end of our fundamental section but we
+ 
+
+ align:start position:0%
+end of our fundamental section but we
+still have a few really important
+
+ align:start position:0%
+still have a few really important
+ 
+
+ align:start position:0%
+still have a few really important
+lectures to get through after we get
+
+ align:start position:0%
+lectures to get through after we get
+ 
+
+ align:start position:0%
+lectures to get through after we get
+through the fundamentals we'll be in a
+
+ align:start position:0%
+through the fundamentals we'll be in a
+ 
+
+ align:start position:0%
+through the fundamentals we'll be in a
+good position to understand the
+
+ align:start position:0%
+good position to understand the
+ 
+
+ align:start position:0%
+good position to understand the
+different Technologies and finally the
+
+ align:start position:0%
+different Technologies and finally the
+ 
+
+ align:start position:0%
+different Technologies and finally the
+cross cutting themes and our goal is to
+
+ align:start position:0%
+cross cutting themes and our goal is to
+ 
+
+ align:start position:0%
+cross cutting themes and our goal is to
+at least for the fundamentals to
+
+ align:start position:0%
+at least for the fundamentals to
+ 
+
+ align:start position:0%
+at least for the fundamentals to
+understand solar cell conversion
+
+ align:start position:0%
+understand solar cell conversion
+ 
+
+ align:start position:0%
+understand solar cell conversion
+efficiency which is the ratio of output
+
+ align:start position:0%
+efficiency which is the ratio of output
+ 
+
+ align:start position:0%
+efficiency which is the ratio of output
+to input energy and for most solar cells
+
+ align:start position:0%
+to input energy and for most solar cells
+ 
+
+ align:start position:0%
+to input energy and for most solar cells
+this breaks down to the following
+
+ align:start position:0%
+this breaks down to the following
+ 
+
+ align:start position:0%
+this breaks down to the following
+progression from the solar Spectrum to
+
+ align:start position:0%
+progression from the solar Spectrum to
+ 
+
+ align:start position:0%
+progression from the solar Spectrum to
+charge collection and we're going to be
+
+ align:start position:0%
+charge collection and we're going to be
+ 
+
+ align:start position:0%
+charge collection and we're going to be
+focusing on charge separation
+
+ align:start position:0%
+focusing on charge separation
+ 
+
+ align:start position:0%
+focusing on charge separation
+incorporating elements of uh either side
+
+ align:start position:0%
+incorporating elements of uh either side
+ 
+
+ align:start position:0%
+incorporating elements of uh either side
+but mostly focus on charge separation
+
+ align:start position:0%
+but mostly focus on charge separation
+ 
+
+ align:start position:0%
+but mostly focus on charge separation
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+reminding everybody of course that the
+
+ align:start position:0%
+reminding everybody of course that the
+ 
+
+ align:start position:0%
+reminding everybody of course that the
+total system efficiency is the product
+
+ align:start position:0%
+total system efficiency is the product
+ 
+
+ align:start position:0%
+total system efficiency is the product
+of each individual efficiency and if any
+
+ align:start position:0%
+of each individual efficiency and if any
+ 
+
+ align:start position:0%
+of each individual efficiency and if any
+one of these is low the efficiency for
+
+ align:start position:0%
+one of these is low the efficiency for
+ 
+
+ align:start position:0%
+one of these is low the efficiency for
+the entire system is low and since folks
+
+ align:start position:0%
+the entire system is low and since folks
+ 
+
+ align:start position:0%
+the entire system is low and since folks
+are tired of looking at this chart by
+
+ align:start position:0%
+are tired of looking at this chart by
+ 
+
+ align:start position:0%
+are tired of looking at this chart by
+now every single lecture I intend to
+
+ align:start position:0%
+now every single lecture I intend to
+ 
+
+ align:start position:0%
+now every single lecture I intend to
+introduce something new that follows a
+
+ align:start position:0%
+introduce something new that follows a
+ 
+
+ align:start position:0%
+introduce something new that follows a
+similar pattern uh does anybody
+
+ align:start position:0%
+similar pattern uh does anybody
+ 
+
+ align:start position:0%
+similar pattern uh does anybody
+recognize what this is
+
+ align:start position:0%
+recognize what this is
+ 
+
+ align:start position:0%
+recognize what this is
+about so you have over here um some H2O
+
+ align:start position:0%
+about so you have over here um some H2O
+ 
+
+ align:start position:0%
+about so you have over here um some H2O
+uh leading to an going into an oxygen
+
+ align:start position:0%
+uh leading to an going into an oxygen
+ 
+
+ align:start position:0%
+uh leading to an going into an oxygen
+evolving complex and light is coming in
+
+ align:start position:0%
+evolving complex and light is coming in
+ 
+
+ align:start position:0%
+evolving complex and light is coming in
+essentially exciting up an electron
+
+ align:start position:0%
+essentially exciting up an electron
+ 
+
+ align:start position:0%
+essentially exciting up an electron
+which is being stored in some form of
+
+ align:start position:0%
+which is being stored in some form of
+ 
+
+ align:start position:0%
+which is being stored in some form of
+chemical energy what is that
+
+ align:start position:0%
+chemical energy what is that
+ 
+
+ align:start position:0%
+chemical energy what is that
+photosynthesis right and uh just like a
+
+ align:start position:0%
+photosynthesis right and uh just like a
+ 
+
+ align:start position:0%
+photosynthesis right and uh just like a
+solar cell the photosynthetic uh uh
+
+ align:start position:0%
+solar cell the photosynthetic uh uh
+ 
+
+ align:start position:0%
+solar cell the photosynthetic uh uh
+photosynthesis uh conversion efficiency
+
+ align:start position:0%
+photosynthesis uh conversion efficiency
+ 
+
+ align:start position:0%
+photosynthesis uh conversion efficiency
+of the entire system is dictated by the
+
+ align:start position:0%
+of the entire system is dictated by the
+ 
+
+ align:start position:0%
+of the entire system is dictated by the
+efficiency of each individual part
+
+ align:start position:0%
+efficiency of each individual part
+ 
+
+ align:start position:0%
+efficiency of each individual part
+roughly it can be broken down into this
+
+ align:start position:0%
+roughly it can be broken down into this
+ 
+
+ align:start position:0%
+roughly it can be broken down into this
+little pie chart up here the total
+
+ align:start position:0%
+little pie chart up here the total
+ 
+
+ align:start position:0%
+little pie chart up here the total
+system efficiency in blue is somewhere
+
+ align:start position:0%
+system efficiency in blue is somewhere
+ 
+
+ align:start position:0%
+system efficiency in blue is somewhere
+depending on the plant somewhere between
+
+ align:start position:0%
+depending on the plant somewhere between
+ 
+
+ align:start position:0%
+depending on the plant somewhere between
+around 1% uh maybe as high as 7 or 8%
+
+ align:start position:0%
+around 1% uh maybe as high as 7 or 8%
+ 
+
+ align:start position:0%
+around 1% uh maybe as high as 7 or 8%
+depending on very specialized plants
+
+ align:start position:0%
+depending on very specialized plants
+ 
+
+ align:start position:0%
+depending on very specialized plants
+that are experts at converting sunlight
+
+ align:start position:0%
+that are experts at converting sunlight
+ 
+
+ align:start position:0%
+that are experts at converting sunlight
+into uh usable chemical energy and uh
+
+ align:start position:0%
+into uh usable chemical energy and uh
+ 
+
+ align:start position:0%
+into uh usable chemical energy and uh
+that in part is largely due to Optical
+
+ align:start position:0%
+that in part is largely due to Optical
+ 
+
+ align:start position:0%
+that in part is largely due to Optical
+losses if you can see the absorption
+
+ align:start position:0%
+losses if you can see the absorption
+ 
+
+ align:start position:0%
+losses if you can see the absorption
+spectrum of chlorophyll of the different
+
+ align:start position:0%
+spectrum of chlorophyll of the different
+ 
+
+ align:start position:0%
+spectrum of chlorophyll of the different
+types of chlorophyll here um you'll see
+
+ align:start position:0%
+types of chlorophyll here um you'll see
+ 
+
+ align:start position:0%
+types of chlorophyll here um you'll see
+large portions of the solar spectrum
+
+ align:start position:0%
+large portions of the solar spectrum
+ 
+
+ align:start position:0%
+large portions of the solar spectrum
+that go
+
+ align:start position:0%
+that go
+ 
+
+ align:start position:0%
+that go
+underutilized so um again another system
+
+ align:start position:0%
+underutilized so um again another system
+ 
+
+ align:start position:0%
+underutilized so um again another system
+that's similar to a solar cell that uh
+
+ align:start position:0%
+that's similar to a solar cell that uh
+ 
+
+ align:start position:0%
+that's similar to a solar cell that uh
+the uh total system efficiency is the
+
+ align:start position:0%
+the uh total system efficiency is the
+ 
+
+ align:start position:0%
+the uh total system efficiency is the
+product of each individual component
+
+ align:start position:0%
+product of each individual component
+ 
+
+ align:start position:0%
+product of each individual component
+going along here all right right so uh
+
+ align:start position:0%
+going along here all right right so uh
+ 
+
+ align:start position:0%
+going along here all right right so uh
+now what we're going to do is just
+
+ align:start position:0%
+now what we're going to do is just
+ 
+
+ align:start position:0%
+now what we're going to do is just
+quickly revisit the diode in the dark
+
+ align:start position:0%
+quickly revisit the diode in the dark
+ 
+
+ align:start position:0%
+quickly revisit the diode in the dark
+and construct the energy band diagram
+
+ align:start position:0%
+and construct the energy band diagram
+ 
+
+ align:start position:0%
+and construct the energy band diagram
+for p injunction in the dark uh each of
+
+ align:start position:0%
+for p injunction in the dark uh each of
+ 
+
+ align:start position:0%
+for p injunction in the dark uh each of
+you should have on your desk uh these
+
+ align:start position:0%
+you should have on your desk uh these
+ 
+
+ align:start position:0%
+you should have on your desk uh these
+sheets oh we don't have them on the
+
+ align:start position:0%
+sheets oh we don't have them on the
+ 
+
+ align:start position:0%
+sheets oh we don't have them on the
+desks we need to pass those out we need
+
+ align:start position:0%
+desks we need to pass those out we need
+ 
+
+ align:start position:0%
+desks we need to pass those out we need
+to pass those out um so we should have
+
+ align:start position:0%
+to pass those out um so we should have
+ 
+
+ align:start position:0%
+to pass those out um so we should have
+uh sheets that describe the U uh
+
+ align:start position:0%
+uh sheets that describe the U uh
+ 
+
+ align:start position:0%
+uh sheets that describe the U uh
+essentially the the equivalent circuit
+
+ align:start position:0%
+essentially the the equivalent circuit
+ 
+
+ align:start position:0%
+essentially the the equivalent circuit
+diagram uh the IV characteristics and
+
+ align:start position:0%
+diagram uh the IV characteristics and
+ 
+
+ align:start position:0%
+diagram uh the IV characteristics and
+the energy band diagram for our P
+
+ align:start position:0%
+the energy band diagram for our P
+ 
+
+ align:start position:0%
+the energy band diagram for our P
+injunction in the dark we laboriously
+
+ align:start position:0%
+injunction in the dark we laboriously
+ 
+
+ align:start position:0%
+injunction in the dark we laboriously
+filled this out last class class we're
+
+ align:start position:0%
+filled this out last class class we're
+ 
+
+ align:start position:0%
+filled this out last class class we're
+just going to refresh ourselves to make
+
+ align:start position:0%
+just going to refresh ourselves to make
+ 
+
+ align:start position:0%
+just going to refresh ourselves to make
+sure we're all on the same page and redo
+
+ align:start position:0%
+sure we're all on the same page and redo
+ 
+
+ align:start position:0%
+sure we're all on the same page and redo
+it this class right at the beginning
+
+ align:start position:0%
+it this class right at the beginning
+ 
+
+ align:start position:0%
+it this class right at the beginning
+because it's that important thank you
+
+ align:start position:0%
+because it's that important thank you
+ 
+
+ align:start position:0%
+because it's that important thank you
+thank you thank you for those who came
+
+ align:start position:0%
+thank you thank you for those who came
+ 
+
+ align:start position:0%
+thank you thank you for those who came
+to our office hours and for those who
+
+ align:start position:0%
+to our office hours and for those who
+ 
+
+ align:start position:0%
+to our office hours and for those who
+came to the recitations and we really uh
+
+ align:start position:0%
+came to the recitations and we really uh
+ 
+
+ align:start position:0%
+came to the recitations and we really uh
+tried to to get this across uh for those
+
+ align:start position:0%
+tried to to get this across uh for those
+ 
+
+ align:start position:0%
+tried to to get this across uh for those
+who are still struggling uh let's make
+
+ align:start position:0%
+who are still struggling uh let's make
+ 
+
+ align:start position:0%
+who are still struggling uh let's make
+sure that you get this uh sometime
+
+ align:start position:0%
+sure that you get this uh sometime
+ 
+
+ align:start position:0%
+sure that you get this uh sometime
+between now and say the next two weeks
+
+ align:start position:0%
+between now and say the next two weeks
+ 
+
+ align:start position:0%
+between now and say the next two weeks
+because this will feature prominently on
+
+ align:start position:0%
+because this will feature prominently on
+ 
+
+ align:start position:0%
+because this will feature prominently on
+the exam um and it's pretty important
+
+ align:start position:0%
+the exam um and it's pretty important
+ 
+
+ align:start position:0%
+the exam um and it's pretty important
+for understanding how a solar cell works
+
+ align:start position:0%
+for understanding how a solar cell works
+ 
+
+ align:start position:0%
+for understanding how a solar cell works
+so if you would uh not mind working
+
+ align:start position:0%
+so if you would uh not mind working
+ 
+
+ align:start position:0%
+so if you would uh not mind working
+directly with your partner the person
+
+ align:start position:0%
+directly with your partner the person
+ 
+
+ align:start position:0%
+directly with your partner the person
+who's sitting directly next to you uh
+
+ align:start position:0%
+who's sitting directly next to you uh
+ 
+
+ align:start position:0%
+who's sitting directly next to you uh
+let's walk through the uh diode in the
+
+ align:start position:0%
+let's walk through the uh diode in the
+ 
+
+ align:start position:0%
+let's walk through the uh diode in the
+dark and construct the energy band
+
+ align:start position:0%
+dark and construct the energy band
+ 
+
+ align:start position:0%
+dark and construct the energy band
+diagrams for the diode in the dark uh
+
+ align:start position:0%
+diagrams for the diode in the dark uh
+ 
+
+ align:start position:0%
+diagrams for the diode in the dark uh
+I'll walk you through it as soon as
+
+ align:start position:0%
+I'll walk you through it as soon as
+ 
+
+ align:start position:0%
+I'll walk you through it as soon as
+you're done maybe I'll give you uh 3
+
+ align:start position:0%
+you're done maybe I'll give you uh 3
+ 
+
+ align:start position:0%
+you're done maybe I'll give you uh 3
+minutes to complete that and then we'll
+
+ align:start position:0%
+minutes to complete that and then we'll
+ 
+
+ align:start position:0%
+minutes to complete that and then we'll
+uh progress to the diode under
+
+ align:start position:0%
+uh progress to the diode under
+ 
+
+ align:start position:0%
+uh progress to the diode under
+illumination should be a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fun good I see convergence among several
+
+ align:start position:0%
+fun good I see convergence among several
+ 
+
+ align:start position:0%
+fun good I see convergence among several
+of you so let's uh move
+
+ align:start position:0%
+of you so let's uh move
+ 
+
+ align:start position:0%
+of you so let's uh move
+forward uh just to review quickly um the
+
+ align:start position:0%
+forward uh just to review quickly um the
+ 
+
+ align:start position:0%
+forward uh just to review quickly um the
+way I I typically think about it if we
+
+ align:start position:0%
+way I I typically think about it if we
+ 
+
+ align:start position:0%
+way I I typically think about it if we
+start out from the model circuit right
+
+ align:start position:0%
+start out from the model circuit right
+ 
+
+ align:start position:0%
+start out from the model circuit right
+here we have our p and Junction we have
+
+ align:start position:0%
+here we have our p and Junction we have
+ 
+
+ align:start position:0%
+here we have our p and Junction we have
+our space charge region also known as a
+
+ align:start position:0%
+our space charge region also known as a
+ 
+
+ align:start position:0%
+our space charge region also known as a
+quasi neutral region also known as the
+
+ align:start position:0%
+quasi neutral region also known as the
+ 
+
+ align:start position:0%
+quasi neutral region also known as the
+depletion zone so we have this uh region
+
+ align:start position:0%
+depletion zone so we have this uh region
+ 
+
+ align:start position:0%
+depletion zone so we have this uh region
+right here uh that represents the space
+
+ align:start position:0%
+right here uh that represents the space
+ 
+
+ align:start position:0%
+right here uh that represents the space
+charge region now we have uh so this is
+
+ align:start position:0%
+charge region now we have uh so this is
+ 
+
+ align:start position:0%
+charge region now we have uh so this is
+in the dark uh now we have the energy
+
+ align:start position:0%
+in the dark uh now we have the energy
+ 
+
+ align:start position:0%
+in the dark uh now we have the energy
+band diagram shown right here where this
+
+ align:start position:0%
+band diagram shown right here where this
+ 
+
+ align:start position:0%
+band diagram shown right here where this
+dashed Blue Line represents the chemical
+
+ align:start position:0%
+dashed Blue Line represents the chemical
+ 
+
+ align:start position:0%
+dashed Blue Line represents the chemical
+potential also called the firmy energy
+
+ align:start position:0%
+potential also called the firmy energy
+ 
+
+ align:start position:0%
+potential also called the firmy energy
+uh throughout the entire uh uh device
+
+ align:start position:0%
+uh throughout the entire uh uh device
+ 
+
+ align:start position:0%
+uh throughout the entire uh uh device
+right here in cross-section and just to
+
+ align:start position:0%
+right here in cross-section and just to
+ 
+
+ align:start position:0%
+right here in cross-section and just to
+be very very clear we've so far
+
+ align:start position:0%
+be very very clear we've so far
+ 
+
+ align:start position:0%
+be very very clear we've so far
+described the solar cell as light coming
+
+ align:start position:0%
+described the solar cell as light coming
+ 
+
+ align:start position:0%
+described the solar cell as light coming
+through the top and now we've rotated
+
+ align:start position:0%
+through the top and now we've rotated
+ 
+
+ align:start position:0%
+through the top and now we've rotated
+this structure by 90° to represent the p
+
+ align:start position:0%
+this structure by 90° to represent the p
+ 
+
+ align:start position:0%
+this structure by 90° to represent the p
+and Jun and that's been a little
+
+ align:start position:0%
+and Jun and that's been a little
+ 
+
+ align:start position:0%
+and Jun and that's been a little
+confusing for some folks so just to be
+
+ align:start position:0%
+confusing for some folks so just to be
+ 
+
+ align:start position:0%
+confusing for some folks so just to be
+totally clear in a device like this one
+
+ align:start position:0%
+totally clear in a device like this one
+ 
+
+ align:start position:0%
+totally clear in a device like this one
+if it were subject to illumination um
+
+ align:start position:0%
+if it were subject to illumination um
+ 
+
+ align:start position:0%
+if it were subject to illumination um
+you would have light coming in from the
+
+ align:start position:0%
+you would have light coming in from the
+ 
+
+ align:start position:0%
+you would have light coming in from the
+side right either from the P side or
+
+ align:start position:0%
+side right either from the P side or
+ 
+
+ align:start position:0%
+side right either from the P side or
+from the N side so to transfer this into
+
+ align:start position:0%
+from the N side so to transfer this into
+ 
+
+ align:start position:0%
+from the N side so to transfer this into
+what we've seen so far where the solar
+
+ align:start position:0%
+what we've seen so far where the solar
+ 
+
+ align:start position:0%
+what we've seen so far where the solar
+cell devic is facing up toward the sun
+
+ align:start position:0%
+cell devic is facing up toward the sun
+ 
+
+ align:start position:0%
+cell devic is facing up toward the sun
+you'd have to rotate this by 90° right
+
+ align:start position:0%
+you'd have to rotate this by 90° right
+ 
+
+ align:start position:0%
+you'd have to rotate this by 90° right
+just to make sure we're all clear with
+
+ align:start position:0%
+just to make sure we're all clear with
+ 
+
+ align:start position:0%
+just to make sure we're all clear with
+orientations good so we have the fir
+
+ align:start position:0%
+orientations good so we have the fir
+ 
+
+ align:start position:0%
+orientations good so we have the fir
+energy right here uh the drift and
+
+ align:start position:0%
+energy right here uh the drift and
+ 
+
+ align:start position:0%
+energy right here uh the drift and
+diffusion currents for electrons
+
+ align:start position:0%
+diffusion currents for electrons
+ 
+
+ align:start position:0%
+diffusion currents for electrons
+electron diffusion electron drift there
+
+ align:start position:0%
+electron diffusion electron drift there
+ 
+
+ align:start position:0%
+electron diffusion electron drift there
+is a an abundance of electrons over here
+
+ align:start position:0%
+is a an abundance of electrons over here
+ 
+
+ align:start position:0%
+is a an abundance of electrons over here
+in the N type side and so they want to
+
+ align:start position:0%
+in the N type side and so they want to
+ 
+
+ align:start position:0%
+in the N type side and so they want to
+diffuse over to the ptype that's why the
+
+ align:start position:0%
+diffuse over to the ptype that's why the
+ 
+
+ align:start position:0%
+diffuse over to the ptype that's why the
+diffusion current is pointing left once
+
+ align:start position:0%
+diffusion current is pointing left once
+ 
+
+ align:start position:0%
+diffusion current is pointing left once
+they do to a certain degree they set up
+
+ align:start position:0%
+they do to a certain degree they set up
+ 
+
+ align:start position:0%
+they do to a certain degree they set up
+a field the electrons and holes the
+
+ align:start position:0%
+a field the electrons and holes the
+ 
+
+ align:start position:0%
+a field the electrons and holes the
+mobile charges set up a field and that
+
+ align:start position:0%
+mobile charges set up a field and that
+ 
+
+ align:start position:0%
+mobile charges set up a field and that
+creates a drift current uh that
+
+ align:start position:0%
+creates a drift current uh that
+ 
+
+ align:start position:0%
+creates a drift current uh that
+counteracts the fusion and once these
+
+ align:start position:0%
+counteracts the fusion and once these
+ 
+
+ align:start position:0%
+counteracts the fusion and once these
+two are in equilibrium there's no
+
+ align:start position:0%
+two are in equilibrium there's no
+ 
+
+ align:start position:0%
+two are in equilibrium there's no
+current flowing through our device
+
+ align:start position:0%
+current flowing through our device
+ 
+
+ align:start position:0%
+current flowing through our device
+that's why current is equal to zero
+
+ align:start position:0%
+that's why current is equal to zero
+ 
+
+ align:start position:0%
+that's why current is equal to zero
+right here and there's also no potential
+
+ align:start position:0%
+right here and there's also no potential
+ 
+
+ align:start position:0%
+right here and there's also no potential
+difference because the firmy energy the
+
+ align:start position:0%
+difference because the firmy energy the
+ 
+
+ align:start position:0%
+difference because the firmy energy the
+chemical potential is the same on either
+
+ align:start position:0%
+chemical potential is the same on either
+ 
+
+ align:start position:0%
+chemical potential is the same on either
+side of that device and so the voltage
+
+ align:start position:0%
+side of that device and so the voltage
+ 
+
+ align:start position:0%
+side of that device and so the voltage
+output of that solar cell would also be
+
+ align:start position:0%
+output of that solar cell would also be
+ 
+
+ align:start position:0%
+output of that solar cell would also be
+zero we when we forward bias our device
+
+ align:start position:0%
+zero we when we forward bias our device
+ 
+
+ align:start position:0%
+zero we when we forward bias our device
+um now we're forcing a separation of or
+
+ align:start position:0%
+um now we're forcing a separation of or
+ 
+
+ align:start position:0%
+um now we're forcing a separation of or
+or we're forcing a separation of the
+
+ align:start position:0%
+or we're forcing a separation of the
+ 
+
+ align:start position:0%
+or we're forcing a separation of the
+chemical potential on either side of the
+
+ align:start position:0%
+chemical potential on either side of the
+ 
+
+ align:start position:0%
+chemical potential on either side of the
+device um if you connected this to an
+
+ align:start position:0%
+device um if you connected this to an
+ 
+
+ align:start position:0%
+device um if you connected this to an
+external circuit um the electrons would
+
+ align:start position:0%
+external circuit um the electrons would
+ 
+
+ align:start position:0%
+external circuit um the electrons would
+want to flow from this side to that side
+
+ align:start position:0%
+want to flow from this side to that side
+ 
+
+ align:start position:0%
+want to flow from this side to that side
+um but uh since we're forcing uh this
+
+ align:start position:0%
+um but uh since we're forcing uh this
+ 
+
+ align:start position:0%
+um but uh since we're forcing uh this
+condition here with the battery uh we
+
+ align:start position:0%
+condition here with the battery uh we
+ 
+
+ align:start position:0%
+condition here with the battery uh we
+are reducing the barrier height here uh
+
+ align:start position:0%
+are reducing the barrier height here uh
+ 
+
+ align:start position:0%
+are reducing the barrier height here uh
+electrons can now diffuse over from the
+
+ align:start position:0%
+electrons can now diffuse over from the
+ 
+
+ align:start position:0%
+electrons can now diffuse over from the
+N type into the ptype side uh and they
+
+ align:start position:0%
+N type into the ptype side uh and they
+ 
+
+ align:start position:0%
+N type into the ptype side uh and they
+do and the diffusion current increases
+
+ align:start position:0%
+do and the diffusion current increases
+ 
+
+ align:start position:0%
+do and the diffusion current increases
+and that's why we have a current now a
+
+ align:start position:0%
+and that's why we have a current now a
+ 
+
+ align:start position:0%
+and that's why we have a current now a
+positive value we've defined uh the
+
+ align:start position:0%
+positive value we've defined uh the
+ 
+
+ align:start position:0%
+positive value we've defined uh the
+electrons traveling to the left as being
+
+ align:start position:0%
+electrons traveling to the left as being
+ 
+
+ align:start position:0%
+electrons traveling to the left as being
+a positive current we have uh now
+
+ align:start position:0%
+a positive current we have uh now
+ 
+
+ align:start position:0%
+a positive current we have uh now
+electrons traveling from the N type uh
+
+ align:start position:0%
+electrons traveling from the N type uh
+ 
+
+ align:start position:0%
+electrons traveling from the N type uh
+to the ptype material when we reverse
+
+ align:start position:0%
+to the ptype material when we reverse
+ 
+
+ align:start position:0%
+to the ptype material when we reverse
+bias our device notice the separation of
+
+ align:start position:0%
+bias our device notice the separation of
+ 
+
+ align:start position:0%
+bias our device notice the separation of
+the firm energies again we have uh here
+
+ align:start position:0%
+the firm energies again we have uh here
+ 
+
+ align:start position:0%
+the firm energies again we have uh here
+uh one sign of voltage because the right
+
+ align:start position:0%
+uh one sign of voltage because the right
+ 
+
+ align:start position:0%
+uh one sign of voltage because the right
+side is higher than the left and now the
+
+ align:start position:0%
+side is higher than the left and now the
+ 
+
+ align:start position:0%
+side is higher than the left and now the
+right side is lower than the left so our
+
+ align:start position:0%
+right side is lower than the left so our
+ 
+
+ align:start position:0%
+right side is lower than the left so our
+voltage sign flips from right to left
+
+ align:start position:0%
+voltage sign flips from right to left
+ 
+
+ align:start position:0%
+voltage sign flips from right to left
+over here from positive to negative
+
+ align:start position:0%
+over here from positive to negative
+ 
+
+ align:start position:0%
+over here from positive to negative
+values so notice the voltage and now the
+
+ align:start position:0%
+values so notice the voltage and now the
+ 
+
+ align:start position:0%
+values so notice the voltage and now the
+current as well the drift current will
+
+ align:start position:0%
+current as well the drift current will
+ 
+
+ align:start position:0%
+current as well the drift current will
+uh outweigh the diffusion current in
+
+ align:start position:0%
+uh outweigh the diffusion current in
+ 
+
+ align:start position:0%
+uh outweigh the diffusion current in
+this particular case uh because now the
+
+ align:start position:0%
+this particular case uh because now the
+ 
+
+ align:start position:0%
+this particular case uh because now the
+uh barrier for electrons to diffuse from
+
+ align:start position:0%
+uh barrier for electrons to diffuse from
+ 
+
+ align:start position:0%
+uh barrier for electrons to diffuse from
+the end to the P type is very large
+
+ align:start position:0%
+the end to the P type is very large
+ 
+
+ align:start position:0%
+the end to the P type is very large
+they'll have difficulty going from that
+
+ align:start position:0%
+they'll have difficulty going from that
+ 
+
+ align:start position:0%
+they'll have difficulty going from that
+side to that side whereas the drift
+
+ align:start position:0%
+side to that side whereas the drift
+ 
+
+ align:start position:0%
+side to that side whereas the drift
+current is is uh larger because of the
+
+ align:start position:0%
+current is is uh larger because of the
+ 
+
+ align:start position:0%
+current is is uh larger because of the
+larger electric field and as a result
+
+ align:start position:0%
+larger electric field and as a result
+ 
+
+ align:start position:0%
+larger electric field and as a result
+the drift current will dominate and so
+
+ align:start position:0%
+the drift current will dominate and so
+ 
+
+ align:start position:0%
+the drift current will dominate and so
+now instead of electrons flowing from n
+
+ align:start position:0%
+now instead of electrons flowing from n
+ 
+
+ align:start position:0%
+now instead of electrons flowing from n
+type to ptype where we had defined as
+
+ align:start position:0%
+type to ptype where we had defined as
+ 
+
+ align:start position:0%
+type to ptype where we had defined as
+positive current electrons are flowing
+
+ align:start position:0%
+positive current electrons are flowing
+ 
+
+ align:start position:0%
+positive current electrons are flowing
+from ptype to n type in net which we
+
+ align:start position:0%
+from ptype to n type in net which we
+ 
+
+ align:start position:0%
+from ptype to n type in net which we
+Define as negative current and that's
+
+ align:start position:0%
+Define as negative current and that's
+ 
+
+ align:start position:0%
+Define as negative current and that's
+why our current has changed signs over
+
+ align:start position:0%
+why our current has changed signs over
+ 
+
+ align:start position:0%
+why our current has changed signs over
+here notice that we're in positive
+
+ align:start position:0%
+here notice that we're in positive
+ 
+
+ align:start position:0%
+here notice that we're in positive
+current territory and over here notice
+
+ align:start position:0%
+current territory and over here notice
+ 
+
+ align:start position:0%
+current territory and over here notice
+we're in negative current
+
+ align:start position:0%
+we're in negative current
+ 
+
+ align:start position:0%
+we're in negative current
+territory also you'll notice the width
+
+ align:start position:0%
+territory also you'll notice the width
+ 
+
+ align:start position:0%
+territory also you'll notice the width
+of the space charge region changing as
+
+ align:start position:0%
+of the space charge region changing as
+ 
+
+ align:start position:0%
+of the space charge region changing as
+we forward and reverse bias our device
+
+ align:start position:0%
+we forward and reverse bias our device
+ 
+
+ align:start position:0%
+we forward and reverse bias our device
+as the barrier height decreases we have
+
+ align:start position:0%
+as the barrier height decreases we have
+ 
+
+ align:start position:0%
+as the barrier height decreases we have
+a decrease of the built-in electric
+
+ align:start position:0%
+a decrease of the built-in electric
+ 
+
+ align:start position:0%
+a decrease of the built-in electric
+field we have a decrease of the amount
+
+ align:start position:0%
+field we have a decrease of the amount
+ 
+
+ align:start position:0%
+field we have a decrease of the amount
+of charge on either side of the junction
+
+ align:start position:0%
+of charge on either side of the junction
+ 
+
+ align:start position:0%
+of charge on either side of the junction
+uh that's why the depletion with
+
+ align:start position:0%
+uh that's why the depletion with
+ 
+
+ align:start position:0%
+uh that's why the depletion with
+decreases and the opposite happens here
+
+ align:start position:0%
+decreases and the opposite happens here
+ 
+
+ align:start position:0%
+decreases and the opposite happens here
+under reverse bias so uh getting to the
+
+ align:start position:0%
+under reverse bias so uh getting to the
+ 
+
+ align:start position:0%
+under reverse bias so uh getting to the
+point where you can set up a p
+
+ align:start position:0%
+point where you can set up a p
+ 
+
+ align:start position:0%
+point where you can set up a p
+injunction and understand how drift and
+
+ align:start position:0%
+injunction and understand how drift and
+ 
+
+ align:start position:0%
+injunction and understand how drift and
+and diffusion currents come into being
+
+ align:start position:0%
+and diffusion currents come into being
+ 
+
+ align:start position:0%
+and diffusion currents come into being
+in the first place and then being able
+
+ align:start position:0%
+in the first place and then being able
+ 
+
+ align:start position:0%
+in the first place and then being able
+to bias your solar or your bias your
+
+ align:start position:0%
+to bias your solar or your bias your
+ 
+
+ align:start position:0%
+to bias your solar or your bias your
+diode under different conditions is a
+
+ align:start position:0%
+diode under different conditions is a
+ 
+
+ align:start position:0%
+diode under different conditions is a
+really important fundamental skill uh
+
+ align:start position:0%
+really important fundamental skill uh
+ 
+
+ align:start position:0%
+really important fundamental skill uh
+for uh understanding solar cell works
+
+ align:start position:0%
+for uh understanding solar cell works
+ 
+
+ align:start position:0%
+for uh understanding solar cell works
+question on the forward and reverse bias
+
+ align:start position:0%
+question on the forward and reverse bias
+ 
+
+ align:start position:0%
+question on the forward and reverse bias
+is the firing energy actually continuous
+
+ align:start position:0%
+is the firing energy actually continuous
+ 
+
+ align:start position:0%
+is the firing energy actually continuous
+or does it actually make a jum uh so the
+
+ align:start position:0%
+or does it actually make a jum uh so the
+ 
+
+ align:start position:0%
+or does it actually make a jum uh so the
+uh firy energy um which we Define here
+
+ align:start position:0%
+uh firy energy um which we Define here
+ 
+
+ align:start position:0%
+uh firy energy um which we Define here
+as as as the chemical potential notice
+
+ align:start position:0%
+as as as the chemical potential notice
+ 
+
+ align:start position:0%
+as as as the chemical potential notice
+we're avoiding talking about what's
+
+ align:start position:0%
+we're avoiding talking about what's
+ 
+
+ align:start position:0%
+we're avoiding talking about what's
+happening here in the middle until a
+
+ align:start position:0%
+happening here in the middle until a
+ 
+
+ align:start position:0%
+happening here in the middle until a
+couple of lectures from now um that gets
+
+ align:start position:0%
+couple of lectures from now um that gets
+ 
+
+ align:start position:0%
+couple of lectures from now um that gets
+into a a gray Zone where we talk about
+
+ align:start position:0%
+into a a gray Zone where we talk about
+ 
+
+ align:start position:0%
+into a a gray Zone where we talk about
+quasi energies we'll get to that in a
+
+ align:start position:0%
+quasi energies we'll get to that in a
+ 
+
+ align:start position:0%
+quasi energies we'll get to that in a
+minute maybe a couple of lectures but
+
+ align:start position:0%
+minute maybe a couple of lectures but
+ 
+
+ align:start position:0%
+minute maybe a couple of lectures but
+yes the firy energy in the extreme uh
+
+ align:start position:0%
+yes the firy energy in the extreme uh
+ 
+
+ align:start position:0%
+yes the firy energy in the extreme uh
+sides right here near the contacts so
+
+ align:start position:0%
+sides right here near the contacts so
+ 
+
+ align:start position:0%
+sides right here near the contacts so
+you're contacting your device over here
+
+ align:start position:0%
+you're contacting your device over here
+ 
+
+ align:start position:0%
+you're contacting your device over here
+you're contacting your device over here
+
+ align:start position:0%
+you're contacting your device over here
+ 
+
+ align:start position:0%
+you're contacting your device over here
+those those fir energies are different
+
+ align:start position:0%
+those those fir energies are different
+ 
+
+ align:start position:0%
+those those fir energies are different
+on an an absolute energy scale so there
+
+ align:start position:0%
+on an an absolute energy scale so there
+ 
+
+ align:start position:0%
+on an an absolute energy scale so there
+is uh an energy difference when you're
+
+ align:start position:0%
+is uh an energy difference when you're
+ 
+
+ align:start position:0%
+is uh an energy difference when you're
+driving the electrons from one side to
+
+ align:start position:0%
+driving the electrons from one side to
+ 
+
+ align:start position:0%
+driving the electrons from one side to
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other notice in this case right here you
+
+ align:start position:0%
+other notice in this case right here you
+ 
+
+ align:start position:0%
+other notice in this case right here you
+would think that the electrons would
+
+ align:start position:0%
+would think that the electrons would
+ 
+
+ align:start position:0%
+would think that the electrons would
+want to travel through an external
+
+ align:start position:0%
+want to travel through an external
+ 
+
+ align:start position:0%
+want to travel through an external
+circuit to come back to this side
+
+ align:start position:0%
+circuit to come back to this side
+ 
+
+ align:start position:0%
+circuit to come back to this side
+because their energy is higher in this
+
+ align:start position:0%
+because their energy is higher in this
+ 
+
+ align:start position:0%
+because their energy is higher in this
+side and lower over here but we're not
+
+ align:start position:0%
+side and lower over here but we're not
+ 
+
+ align:start position:0%
+side and lower over here but we're not
+uh we're not Illuminating the solar cell
+
+ align:start position:0%
+uh we're not Illuminating the solar cell
+ 
+
+ align:start position:0%
+uh we're not Illuminating the solar cell
+yet we're biasing it using a battery uh
+
+ align:start position:0%
+yet we're biasing it using a battery uh
+ 
+
+ align:start position:0%
+yet we're biasing it using a battery uh
+and this is why uh we have current flow
+
+ align:start position:0%
+and this is why uh we have current flow
+ 
+
+ align:start position:0%
+and this is why uh we have current flow
+coming from this side into that side
+
+ align:start position:0%
+coming from this side into that side
+ 
+
+ align:start position:0%
+coming from this side into that side
+we're essentially forcing the electrons
+
+ align:start position:0%
+we're essentially forcing the electrons
+ 
+
+ align:start position:0%
+we're essentially forcing the electrons
+from the N type into the ptype material
+
+ align:start position:0%
+from the N type into the ptype material
+ 
+
+ align:start position:0%
+from the N type into the ptype material
+we're pushing them up that hill with a
+
+ align:start position:0%
+we're pushing them up that hill with a
+ 
+
+ align:start position:0%
+we're pushing them up that hill with a
+battery and that's why we have this
+
+ align:start position:0%
+battery and that's why we have this
+ 
+
+ align:start position:0%
+battery and that's why we have this
+diffusion current um uh dominating in
+
+ align:start position:0%
+diffusion current um uh dominating in
+ 
+
+ align:start position:0%
+diffusion current um uh dominating in
+the dark in the dark so we have a
+
+ align:start position:0%
+the dark in the dark so we have a
+ 
+
+ align:start position:0%
+the dark in the dark so we have a
+current flowing from right to left in
+
+ align:start position:0%
+current flowing from right to left in
+ 
+
+ align:start position:0%
+current flowing from right to left in
+the illuminated case um we'll have all
+
+ align:start position:0%
+the illuminated case um we'll have all
+ 
+
+ align:start position:0%
+the illuminated case um we'll have all
+of our carriers traveling from left to
+
+ align:start position:0%
+of our carriers traveling from left to
+ 
+
+ align:start position:0%
+of our carriers traveling from left to
+right um and in the dark this is the
+
+ align:start position:0%
+right um and in the dark this is the
+ 
+
+ align:start position:0%
+right um and in the dark this is the
+only case in which we have carriers
+
+ align:start position:0%
+only case in which we have carriers
+ 
+
+ align:start position:0%
+only case in which we have carriers
+traveling from uh right to left and it's
+
+ align:start position:0%
+traveling from uh right to left and it's
+ 
+
+ align:start position:0%
+traveling from uh right to left and it's
+happening because we're using that
+
+ align:start position:0%
+happening because we're using that
+ 
+
+ align:start position:0%
+happening because we're using that
+battery in the dark
+
+ align:start position:0%
+battery in the dark
+ 
+
+ align:start position:0%
+battery in the dark
+uh to change the uh chemical potential
+
+ align:start position:0%
+uh to change the uh chemical potential
+ 
+
+ align:start position:0%
+uh to change the uh chemical potential
+on other side which in effect reduces
+
+ align:start position:0%
+on other side which in effect reduces
+ 
+
+ align:start position:0%
+on other side which in effect reduces
+this barrier height and allows carriers
+
+ align:start position:0%
+this barrier height and allows carriers
+ 
+
+ align:start position:0%
+this barrier height and allows carriers
+to diffuse from the N type and the ptype
+
+ align:start position:0%
+to diffuse from the N type and the ptype
+ 
+
+ align:start position:0%
+to diffuse from the N type and the ptype
+so you can think about it as uh forcing
+
+ align:start position:0%
+so you can think about it as uh forcing
+ 
+
+ align:start position:0%
+so you can think about it as uh forcing
+carriers up the junction right and this
+
+ align:start position:0%
+carriers up the junction right and this
+ 
+
+ align:start position:0%
+carriers up the junction right and this
+is a very useful technique because in
+
+ align:start position:0%
+is a very useful technique because in
+ 
+
+ align:start position:0%
+is a very useful technique because in
+effect what it's doing in a real device
+
+ align:start position:0%
+effect what it's doing in a real device
+ 
+
+ align:start position:0%
+effect what it's doing in a real device
+when you have a two-dimensional device
+
+ align:start position:0%
+when you have a two-dimensional device
+ 
+
+ align:start position:0%
+when you have a two-dimensional device
+with in homogeneities uh the current
+
+ align:start position:0%
+with in homogeneities uh the current
+ 
+
+ align:start position:0%
+with in homogeneities uh the current
+will travel through the weakest point of
+
+ align:start position:0%
+will travel through the weakest point of
+ 
+
+ align:start position:0%
+will travel through the weakest point of
+that P Junction wherever the barrier
+
+ align:start position:0%
+that P Junction wherever the barrier
+ 
+
+ align:start position:0%
+that P Junction wherever the barrier
+height is lowest current will begin
+
+ align:start position:0%
+height is lowest current will begin
+ 
+
+ align:start position:0%
+height is lowest current will begin
+crowding through that spot and so it's a
+
+ align:start position:0%
+crowding through that spot and so it's a
+ 
+
+ align:start position:0%
+crowding through that spot and so it's a
+way of probing or testing uh the the
+
+ align:start position:0%
+way of probing or testing uh the the
+ 
+
+ align:start position:0%
+way of probing or testing uh the the
+quality of your Junction characteristic
+
+ align:start position:0%
+quality of your Junction characteristic
+ 
+
+ align:start position:0%
+quality of your Junction characteristic
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+dark okay so this is uh these this is a
+
+ align:start position:0%
+dark okay so this is uh these this is a
+ 
+
+ align:start position:0%
+dark okay so this is uh these this is a
+basic of of the basics of of p and
+
+ align:start position:0%
+basic of of the basics of of p and
+ 
+
+ align:start position:0%
+basic of of the basics of of p and
+Junction in the dark let's flip our page
+
+ align:start position:0%
+Junction in the dark let's flip our page
+ 
+
+ align:start position:0%
+Junction in the dark let's flip our page
+over and now let's try to imagine what
+
+ align:start position:0%
+over and now let's try to imagine what
+ 
+
+ align:start position:0%
+over and now let's try to imagine what
+will happen under illuminated conditions
+
+ align:start position:0%
+will happen under illuminated conditions
+ 
+
+ align:start position:0%
+will happen under illuminated conditions
+and let's start out in a very simple
+
+ align:start position:0%
+and let's start out in a very simple
+ 
+
+ align:start position:0%
+and let's start out in a very simple
+case we'll assume that the principle of
+
+ align:start position:0%
+case we'll assume that the principle of
+ 
+
+ align:start position:0%
+case we'll assume that the principle of
+superposition applies here that the
+
+ align:start position:0%
+superposition applies here that the
+ 
+
+ align:start position:0%
+superposition applies here that the
+photo excited carriers in other words
+
+ align:start position:0%
+photo excited carriers in other words
+ 
+
+ align:start position:0%
+photo excited carriers in other words
+when light shines into our device I'm
+
+ align:start position:0%
+when light shines into our device I'm
+ 
+
+ align:start position:0%
+when light shines into our device I'm
+looking at this one right now this one
+
+ align:start position:0%
+looking at this one right now this one
+ 
+
+ align:start position:0%
+looking at this one right now this one
+right here and lights coming in and
+
+ align:start position:0%
+right here and lights coming in and
+ 
+
+ align:start position:0%
+right here and lights coming in and
+generating electron whole pairs
+
+ align:start position:0%
+generating electron whole pairs
+ 
+
+ align:start position:0%
+generating electron whole pairs
+essentially exciting electrons across
+
+ align:start position:0%
+essentially exciting electrons across
+ 
+
+ align:start position:0%
+essentially exciting electrons across
+the band Gap like we described in
+
+ align:start position:0%
+the band Gap like we described in
+ 
+
+ align:start position:0%
+the band Gap like we described in
+lecture three so we have uh carriers now
+
+ align:start position:0%
+lecture three so we have uh carriers now
+ 
+
+ align:start position:0%
+lecture three so we have uh carriers now
+being excited across the band Gap what
+
+ align:start position:0%
+being excited across the band Gap what
+ 
+
+ align:start position:0%
+being excited across the band Gap what
+will happen to those electrons now that
+
+ align:start position:0%
+will happen to those electrons now that
+ 
+
+ align:start position:0%
+will happen to those electrons now that
+they're in the conduction band where
+
+ align:start position:0%
+they're in the conduction band where
+ 
+
+ align:start position:0%
+they're in the conduction band where
+will they want to
+
+ align:start position:0%
+will they want to
+ 
+
+ align:start position:0%
+will they want to
+go to the right right okay so what
+
+ align:start position:0%
+go to the right right okay so what
+ 
+
+ align:start position:0%
+go to the right right okay so what
+you'll do is set up what's called an
+
+ align:start position:0%
+you'll do is set up what's called an
+ 
+
+ align:start position:0%
+you'll do is set up what's called an
+illumination current notice now at the
+
+ align:start position:0%
+illumination current notice now at the
+ 
+
+ align:start position:0%
+illumination current notice now at the
+bottom of of the second uh row here you
+
+ align:start position:0%
+bottom of of the second uh row here you
+ 
+
+ align:start position:0%
+bottom of of the second uh row here you
+have electron diffusion electron drift
+
+ align:start position:0%
+have electron diffusion electron drift
+ 
+
+ align:start position:0%
+have electron diffusion electron drift
+and Ill current ill stand for
+
+ align:start position:0%
+and Ill current ill stand for
+ 
+
+ align:start position:0%
+and Ill current ill stand for
+illumination current so you have a third
+
+ align:start position:0%
+illumination current so you have a third
+ 
+
+ align:start position:0%
+illumination current so you have a third
+Arrow here that will have to be
+
+ align:start position:0%
+Arrow here that will have to be
+ 
+
+ align:start position:0%
+Arrow here that will have to be
+implemented in some way and that will uh
+
+ align:start position:0%
+implemented in some way and that will uh
+ 
+
+ align:start position:0%
+implemented in some way and that will uh
+by the principle of superposition you
+
+ align:start position:0%
+by the principle of superposition you
+ 
+
+ align:start position:0%
+by the principle of superposition you
+should think what happens to your IV
+
+ align:start position:0%
+should think what happens to your IV
+ 
+
+ align:start position:0%
+should think what happens to your IV
+curve as well so let's make an estimate
+
+ align:start position:0%
+curve as well so let's make an estimate
+ 
+
+ align:start position:0%
+curve as well so let's make an estimate
+of what we think should happen then I'll
+
+ align:start position:0%
+of what we think should happen then I'll
+ 
+
+ align:start position:0%
+of what we think should happen then I'll
+confer some notes and then we'll measure
+
+ align:start position:0%
+confer some notes and then we'll measure
+ 
+
+ align:start position:0%
+confer some notes and then we'll measure
+what actually does happen under
+
+ align:start position:0%
+what actually does happen under
+ 
+
+ align:start position:0%
+what actually does happen under
+illumination so I'm going give it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shot what does forward and reverse bias
+
+ align:start position:0%
+shot what does forward and reverse bias
+ 
+
+ align:start position:0%
+shot what does forward and reverse bias
+mean when there's no battery this is a
+
+ align:start position:0%
+mean when there's no battery this is a
+ 
+
+ align:start position:0%
+mean when there's no battery this is a
+very interesting question so once you
+
+ align:start position:0%
+very interesting question so once you
+ 
+
+ align:start position:0%
+very interesting question so once you
+start illuminating your solar cell
+
+ align:start position:0%
+start illuminating your solar cell
+ 
+
+ align:start position:0%
+start illuminating your solar cell
+device and you start injecting carriers
+
+ align:start position:0%
+device and you start injecting carriers
+ 
+
+ align:start position:0%
+device and you start injecting carriers
+into it um the uh what will happen is
+
+ align:start position:0%
+into it um the uh what will happen is
+ 
+
+ align:start position:0%
+into it um the uh what will happen is
+very naturally this uh this band
+
+ align:start position:0%
+very naturally this uh this band
+ 
+
+ align:start position:0%
+very naturally this uh this band
+alignment that you see right here this
+
+ align:start position:0%
+alignment that you see right here this
+ 
+
+ align:start position:0%
+alignment that you see right here this
+band diagram will begin to shift toward
+
+ align:start position:0%
+band diagram will begin to shift toward
+ 
+
+ align:start position:0%
+band diagram will begin to shift toward
+the forward bias condition rationale
+
+ align:start position:0%
+the forward bias condition rationale
+ 
+
+ align:start position:0%
+the forward bias condition rationale
+you'll be generating carriers they'll be
+
+ align:start position:0%
+you'll be generating carriers they'll be
+ 
+
+ align:start position:0%
+you'll be generating carriers they'll be
+swept over into this region here one way
+
+ align:start position:0%
+swept over into this region here one way
+ 
+
+ align:start position:0%
+swept over into this region here one way
+to think about it is that you'll be
+
+ align:start position:0%
+to think about it is that you'll be
+ 
+
+ align:start position:0%
+to think about it is that you'll be
+increasing the number of electrons over
+
+ align:start position:0%
+increasing the number of electrons over
+ 
+
+ align:start position:0%
+increasing the number of electrons over
+here and the number of holes over here
+
+ align:start position:0%
+here and the number of holes over here
+ 
+
+ align:start position:0%
+here and the number of holes over here
+which will naturally cause the uh the
+
+ align:start position:0%
+which will naturally cause the uh the
+ 
+
+ align:start position:0%
+which will naturally cause the uh the
+energy of those electrons to increase on
+
+ align:start position:0%
+energy of those electrons to increase on
+ 
+
+ align:start position:0%
+energy of those electrons to increase on
+the side the chemical potential on the
+
+ align:start position:0%
+the side the chemical potential on the
+ 
+
+ align:start position:0%
+the side the chemical potential on the
+sides increase so one way to think about
+
+ align:start position:0%
+sides increase so one way to think about
+ 
+
+ align:start position:0%
+sides increase so one way to think about
+it is as you're illuminating your solar
+
+ align:start position:0%
+it is as you're illuminating your solar
+ 
+
+ align:start position:0%
+it is as you're illuminating your solar
+cell more and more and more you're
+
+ align:start position:0%
+cell more and more and more you're
+ 
+
+ align:start position:0%
+cell more and more and more you're
+forcing a forward bias condition on your
+
+ align:start position:0%
+forcing a forward bias condition on your
+ 
+
+ align:start position:0%
+forcing a forward bias condition on your
+device to get the solar cell to go into
+
+ align:start position:0%
+device to get the solar cell to go into
+ 
+
+ align:start position:0%
+device to get the solar cell to go into
+reverse bias you really do need to bias
+
+ align:start position:0%
+reverse bias you really do need to bias
+ 
+
+ align:start position:0%
+reverse bias you really do need to bias
+your device you physically need to to
+
+ align:start position:0%
+your device you physically need to to
+ 
+
+ align:start position:0%
+your device you physically need to to
+bias
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yes so um when I when I mentioned
+
+ align:start position:0%
+it yes so um when I when I mentioned
+ 
+
+ align:start position:0%
+it yes so um when I when I mentioned
+illumination current here we're really
+
+ align:start position:0%
+illumination current here we're really
+ 
+
+ align:start position:0%
+illumination current here we're really
+talking about the electron illumination
+
+ align:start position:0%
+talking about the electron illumination
+ 
+
+ align:start position:0%
+talking about the electron illumination
+current right where what what direction
+
+ align:start position:0%
+current right where what what direction
+ 
+
+ align:start position:0%
+current right where what what direction
+of travel the electrons are taking
+
+ align:start position:0%
+of travel the electrons are taking
+ 
+
+ align:start position:0%
+of travel the electrons are taking
+inside of our system so uh yes the
+
+ align:start position:0%
+inside of our system so uh yes the
+ 
+
+ align:start position:0%
+inside of our system so uh yes the
+electrons would be traveling from uh
+
+ align:start position:0%
+electrons would be traveling from uh
+ 
+
+ align:start position:0%
+electrons would be traveling from uh
+left to right very astute observation Uh
+
+ align:start position:0%
+left to right very astute observation Uh
+ 
+
+ align:start position:0%
+left to right very astute observation Uh
+current is generally described as a flow
+
+ align:start position:0%
+current is generally described as a flow
+ 
+
+ align:start position:0%
+current is generally described as a flow
+of positive charge and in the absence of
+
+ align:start position:0%
+of positive charge and in the absence of
+ 
+
+ align:start position:0%
+of positive charge and in the absence of
+a definer or um say electrons or holes
+
+ align:start position:0%
+a definer or um say electrons or holes
+ 
+
+ align:start position:0%
+a definer or um say electrons or holes
+uh you rightly could assume that it
+
+ align:start position:0%
+uh you rightly could assume that it
+ 
+
+ align:start position:0%
+uh you rightly could assume that it
+would be the flow of positive charges
+
+ align:start position:0%
+would be the flow of positive charges
+ 
+
+ align:start position:0%
+would be the flow of positive charges
+we're assuming electrons are flowing
+
+ align:start position:0%
+we're assuming electrons are flowing
+ 
+
+ align:start position:0%
+we're assuming electrons are flowing
+here and the alumination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current good all right so so this is
+
+ align:start position:0%
+current good all right so so this is
+ 
+
+ align:start position:0%
+current good all right so so this is
+very positive I see everybody has uh
+
+ align:start position:0%
+very positive I see everybody has uh
+ 
+
+ align:start position:0%
+very positive I see everybody has uh
+settled on the the notion that
+
+ align:start position:0%
+settled on the the notion that
+ 
+
+ align:start position:0%
+settled on the the notion that
+illumination will shift our IV curve
+
+ align:start position:0%
+illumination will shift our IV curve
+ 
+
+ align:start position:0%
+illumination will shift our IV curve
+down because of the way we've defined
+
+ align:start position:0%
+down because of the way we've defined
+ 
+
+ align:start position:0%
+down because of the way we've defined
+current that if current flows from left
+
+ align:start position:0%
+current that if current flows from left
+ 
+
+ align:start position:0%
+current that if current flows from left
+to right that lands Us in negative
+
+ align:start position:0%
+to right that lands Us in negative
+ 
+
+ align:start position:0%
+to right that lands Us in negative
+current territory so that that makes
+
+ align:start position:0%
+current territory so that that makes
+ 
+
+ align:start position:0%
+current territory so that that makes
+sense if we shine light on our system
+
+ align:start position:0%
+sense if we shine light on our system
+ 
+
+ align:start position:0%
+sense if we shine light on our system
+and we have electrons flowing from left
+
+ align:start position:0%
+and we have electrons flowing from left
+ 
+
+ align:start position:0%
+and we have electrons flowing from left
+to right here uh that'll put us into
+
+ align:start position:0%
+to right here uh that'll put us into
+ 
+
+ align:start position:0%
+to right here uh that'll put us into
+negative territory so that shifts the
+
+ align:start position:0%
+negative territory so that shifts the
+ 
+
+ align:start position:0%
+negative territory so that shifts the
+entire thing down and we would add an
+
+ align:start position:0%
+entire thing down and we would add an
+ 
+
+ align:start position:0%
+entire thing down and we would add an
+illumination current an arrow pointing
+
+ align:start position:0%
+illumination current an arrow pointing
+ 
+
+ align:start position:0%
+illumination current an arrow pointing
+to the right right here which would mean
+
+ align:start position:0%
+to the right right here which would mean
+ 
+
+ align:start position:0%
+to the right right here which would mean
+that we would have current flowing
+
+ align:start position:0%
+that we would have current flowing
+ 
+
+ align:start position:0%
+that we would have current flowing
+through our device but there's still no
+
+ align:start position:0%
+through our device but there's still no
+ 
+
+ align:start position:0%
+through our device but there's still no
+difference in the chemical potential on
+
+ align:start position:0%
+difference in the chemical potential on
+ 
+
+ align:start position:0%
+difference in the chemical potential on
+either side there's still no difference
+
+ align:start position:0%
+either side there's still no difference
+ 
+
+ align:start position:0%
+either side there's still no difference
+in firmy energy in the P type and the N
+
+ align:start position:0%
+in firmy energy in the P type and the N
+ 
+
+ align:start position:0%
+in firmy energy in the P type and the N
+type which means our voltage is equal to
+
+ align:start position:0%
+type which means our voltage is equal to
+ 
+
+ align:start position:0%
+type which means our voltage is equal to
+zero which means we're intersecting uh
+
+ align:start position:0%
+zero which means we're intersecting uh
+ 
+
+ align:start position:0%
+zero which means we're intersecting uh
+the the y- axis right here and our
+
+ align:start position:0%
+the the y- axis right here and our
+ 
+
+ align:start position:0%
+the the y- axis right here and our
+little X should be marked uh right down
+
+ align:start position:0%
+little X should be marked uh right down
+ 
+
+ align:start position:0%
+little X should be marked uh right down
+here so it's really just a super
+
+ align:start position:0%
+here so it's really just a super
+ 
+
+ align:start position:0%
+here so it's really just a super
+position great okay now what happens if
+
+ align:start position:0%
+position great okay now what happens if
+ 
+
+ align:start position:0%
+position great okay now what happens if
+we forward bias our device um either uh
+
+ align:start position:0%
+we forward bias our device um either uh
+ 
+
+ align:start position:0%
+we forward bias our device um either uh
+U either because we're we're adding a
+
+ align:start position:0%
+U either because we're we're adding a
+ 
+
+ align:start position:0%
+U either because we're we're adding a
+resistor in series uh to our our solar
+
+ align:start position:0%
+resistor in series uh to our our solar
+ 
+
+ align:start position:0%
+resistor in series uh to our our solar
+cell uh so instead of a battery there
+
+ align:start position:0%
+cell uh so instead of a battery there
+ 
+
+ align:start position:0%
+cell uh so instead of a battery there
+you would replace that with a resistor
+
+ align:start position:0%
+you would replace that with a resistor
+ 
+
+ align:start position:0%
+you would replace that with a resistor
+um or if we're applying a bias voltage
+
+ align:start position:0%
+um or if we're applying a bias voltage
+ 
+
+ align:start position:0%
+um or if we're applying a bias voltage
+as well we could also do that under
+
+ align:start position:0%
+as well we could also do that under
+ 
+
+ align:start position:0%
+as well we could also do that under
+illumination so we'd still have the
+
+ align:start position:0%
+illumination so we'd still have the
+ 
+
+ align:start position:0%
+illumination so we'd still have the
+illumination current right and we'd
+
+ align:start position:0%
+illumination current right and we'd
+ 
+
+ align:start position:0%
+illumination current right and we'd
+through superposition shift this entire
+
+ align:start position:0%
+through superposition shift this entire
+ 
+
+ align:start position:0%
+through superposition shift this entire
+curve down we'd be operating somewhere
+
+ align:start position:0%
+curve down we'd be operating somewhere
+ 
+
+ align:start position:0%
+curve down we'd be operating somewhere
+in this um quadrant right there right so
+
+ align:start position:0%
+in this um quadrant right there right so
+ 
+
+ align:start position:0%
+in this um quadrant right there right so
+this we call a fourth quadrant typically
+
+ align:start position:0%
+this we call a fourth quadrant typically
+ 
+
+ align:start position:0%
+this we call a fourth quadrant typically
+1 2 3 4 fourth qu quadrant this is where
+
+ align:start position:0%
+1 2 3 4 fourth qu quadrant this is where
+ 
+
+ align:start position:0%
+1 2 3 4 fourth qu quadrant this is where
+Power is coming out of the solar cell
+
+ align:start position:0%
+Power is coming out of the solar cell
+ 
+
+ align:start position:0%
+Power is coming out of the solar cell
+device because if we imagine instead of
+
+ align:start position:0%
+device because if we imagine instead of
+ 
+
+ align:start position:0%
+device because if we imagine instead of
+having a battery there we have a
+
+ align:start position:0%
+having a battery there we have a
+ 
+
+ align:start position:0%
+having a battery there we have a
+resistor you will the electrons will
+
+ align:start position:0%
+resistor you will the electrons will
+ 
+
+ align:start position:0%
+resistor you will the electrons will
+travel from the N type material through
+
+ align:start position:0%
+travel from the N type material through
+ 
+
+ align:start position:0%
+travel from the N type material through
+that external load to get to the ptype
+
+ align:start position:0%
+that external load to get to the ptype
+ 
+
+ align:start position:0%
+that external load to get to the ptype
+material where their chemical potential
+
+ align:start position:0%
+material where their chemical potential
+ 
+
+ align:start position:0%
+material where their chemical potential
+is lower right because they'll they'll
+
+ align:start position:0%
+is lower right because they'll they'll
+ 
+
+ align:start position:0%
+is lower right because they'll they'll
+desire to minimize their free energy and
+
+ align:start position:0%
+desire to minimize their free energy and
+ 
+
+ align:start position:0%
+desire to minimize their free energy and
+as a result they'll deposit that power
+
+ align:start position:0%
+as a result they'll deposit that power
+ 
+
+ align:start position:0%
+as a result they'll deposit that power
+across that resistor across that
+
+ align:start position:0%
+across that resistor across that
+ 
+
+ align:start position:0%
+across that resistor across that
+external load in order to get back to
+
+ align:start position:0%
+external load in order to get back to
+ 
+
+ align:start position:0%
+external load in order to get back to
+this other side because that's the only
+
+ align:start position:0%
+this other side because that's the only
+ 
+
+ align:start position:0%
+this other side because that's the only
+path uh that they can travel easily
+
+ align:start position:0%
+path uh that they can travel easily
+ 
+
+ align:start position:0%
+path uh that they can travel easily
+right and so this entire curve shifts
+
+ align:start position:0%
+right and so this entire curve shifts
+ 
+
+ align:start position:0%
+right and so this entire curve shifts
+down you have your red X somewhere in
+
+ align:start position:0%
+down you have your red X somewhere in
+ 
+
+ align:start position:0%
+down you have your red X somewhere in
+this quadrant over here and uh Power is
+
+ align:start position:0%
+this quadrant over here and uh Power is
+ 
+
+ align:start position:0%
+this quadrant over here and uh Power is
+Flowing uh out of the solar cell across
+
+ align:start position:0%
+Flowing uh out of the solar cell across
+ 
+
+ align:start position:0%
+Flowing uh out of the solar cell across
+that external load so on the next slide
+
+ align:start position:0%
+that external load so on the next slide
+ 
+
+ align:start position:0%
+that external load so on the next slide
+pretty much everything is right except
+
+ align:start position:0%
+pretty much everything is right except
+ 
+
+ align:start position:0%
+pretty much everything is right except
+that meula I forgot to replace the
+
+ align:start position:0%
+that meula I forgot to replace the
+ 
+
+ align:start position:0%
+that meula I forgot to replace the
+battery up there with a little resistor
+
+ align:start position:0%
+battery up there with a little resistor
+ 
+
+ align:start position:0%
+battery up there with a little resistor
+so you want to correct that in your
+
+ align:start position:0%
+so you want to correct that in your
+ 
+
+ align:start position:0%
+so you want to correct that in your
+notes instead of having the little
+
+ align:start position:0%
+notes instead of having the little
+ 
+
+ align:start position:0%
+notes instead of having the little
+batteries up there uh you can replace
+
+ align:start position:0%
+batteries up there uh you can replace
+ 
+
+ align:start position:0%
+batteries up there uh you can replace
+those with resistors or a resistor in
+
+ align:start position:0%
+those with resistors or a resistor in
+ 
+
+ align:start position:0%
+those with resistors or a resistor in
+series with a battery if you prefer um
+
+ align:start position:0%
+series with a battery if you prefer um
+ 
+
+ align:start position:0%
+series with a battery if you prefer um
+uh since uh depending on on the
+
+ align:start position:0%
+uh since uh depending on on the
+ 
+
+ align:start position:0%
+uh since uh depending on on the
+illumination condition the intensity we
+
+ align:start position:0%
+illumination condition the intensity we
+ 
+
+ align:start position:0%
+illumination condition the intensity we
+may have natural forward bias condition
+
+ align:start position:0%
+may have natural forward bias condition
+ 
+
+ align:start position:0%
+may have natural forward bias condition
+we may need to apply a bias voltage okay
+
+ align:start position:0%
+we may need to apply a bias voltage okay
+ 
+
+ align:start position:0%
+we may need to apply a bias voltage okay
+so we have RV characteristic like this
+
+ align:start position:0%
+so we have RV characteristic like this
+ 
+
+ align:start position:0%
+so we have RV characteristic like this
+we have a red x uh under forward bias
+
+ align:start position:0%
+we have a red x uh under forward bias
+ 
+
+ align:start position:0%
+we have a red x uh under forward bias
+conditions in the fourth quadrant
+
+ align:start position:0%
+conditions in the fourth quadrant
+ 
+
+ align:start position:0%
+conditions in the fourth quadrant
+denoting that power would be flowing out
+
+ align:start position:0%
+denoting that power would be flowing out
+ 
+
+ align:start position:0%
+denoting that power would be flowing out
+of this solar cell device under these
+
+ align:start position:0%
+of this solar cell device under these
+ 
+
+ align:start position:0%
+of this solar cell device under these
+conditions and now uh the bias is
+
+ align:start position:0%
+conditions and now uh the bias is
+ 
+
+ align:start position:0%
+conditions and now uh the bias is
+inverted we have reverse bias conditions
+
+ align:start position:0%
+inverted we have reverse bias conditions
+ 
+
+ align:start position:0%
+inverted we have reverse bias conditions
+and notice that the current is still has
+
+ align:start position:0%
+and notice that the current is still has
+ 
+
+ align:start position:0%
+and notice that the current is still has
+the same sign so the current is negative
+
+ align:start position:0%
+the same sign so the current is negative
+ 
+
+ align:start position:0%
+the same sign so the current is negative
+here negative here and negative here so
+
+ align:start position:0%
+here negative here and negative here so
+ 
+
+ align:start position:0%
+here negative here and negative here so
+the current is the net current is always
+
+ align:start position:0%
+the current is the net current is always
+ 
+
+ align:start position:0%
+the current is the net current is always
+flowing in in the same direction in all
+
+ align:start position:0%
+flowing in in the same direction in all
+ 
+
+ align:start position:0%
+flowing in in the same direction in all
+cases because we have this illumination
+
+ align:start position:0%
+cases because we have this illumination
+ 
+
+ align:start position:0%
+cases because we have this illumination
+current because we have this generation
+
+ align:start position:0%
+current because we have this generation
+ 
+
+ align:start position:0%
+current because we have this generation
+of carriers inside of the material
+
+ align:start position:0%
+of carriers inside of the material
+ 
+
+ align:start position:0%
+of carriers inside of the material
+that's pretty cool that wasn't the case
+
+ align:start position:0%
+that's pretty cool that wasn't the case
+ 
+
+ align:start position:0%
+that's pretty cool that wasn't the case
+when we had the device in the dark here
+
+ align:start position:0%
+when we had the device in the dark here
+ 
+
+ align:start position:0%
+when we had the device in the dark here
+in in forward bias conditions we're
+
+ align:start position:0%
+in in forward bias conditions we're
+ 
+
+ align:start position:0%
+in in forward bias conditions we're
+actually forcing carriers from the N
+
+ align:start position:0%
+actually forcing carriers from the N
+ 
+
+ align:start position:0%
+actually forcing carriers from the N
+type material into the ptype material
+
+ align:start position:0%
+type material into the ptype material
+ 
+
+ align:start position:0%
+type material into the ptype material
+right but under illumination now we have
+
+ align:start position:0%
+right but under illumination now we have
+ 
+
+ align:start position:0%
+right but under illumination now we have
+all of our carriers traveling from uh
+
+ align:start position:0%
+all of our carriers traveling from uh
+ 
+
+ align:start position:0%
+all of our carriers traveling from uh
+the P type into the N type what's
+
+ align:start position:0%
+the P type into the N type what's
+ 
+
+ align:start position:0%
+the P type into the N type what's
+varying is uh the potential uh with that
+
+ align:start position:0%
+varying is uh the potential uh with that
+ 
+
+ align:start position:0%
+varying is uh the potential uh with that
+the carrier have and of course the total
+
+ align:start position:0%
+the carrier have and of course the total
+ 
+
+ align:start position:0%
+the carrier have and of course the total
+amount of current as you forward bias
+
+ align:start position:0%
+amount of current as you forward bias
+ 
+
+ align:start position:0%
+amount of current as you forward bias
+more and more and more this um downhill
+
+ align:start position:0%
+more and more and more this um downhill
+ 
+
+ align:start position:0%
+more and more and more this um downhill
+slope here decreases right so there's
+
+ align:start position:0%
+slope here decreases right so there's
+ 
+
+ align:start position:0%
+slope here decreases right so there's
+less of a driving force for the carriers
+
+ align:start position:0%
+less of a driving force for the carriers
+ 
+
+ align:start position:0%
+less of a driving force for the carriers
+to be going from the P type to the N
+
+ align:start position:0%
+to be going from the P type to the N
+ 
+
+ align:start position:0%
+to be going from the P type to the N
+type and that's why the current approach
+
+ align:start position:0%
+type and that's why the current approach
+ 
+
+ align:start position:0%
+type and that's why the current approach
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero eventually at some point if you
+
+ align:start position:0%
+zero eventually at some point if you
+ 
+
+ align:start position:0%
+zero eventually at some point if you
+keep forward biasing here the current
+
+ align:start position:0%
+keep forward biasing here the current
+ 
+
+ align:start position:0%
+keep forward biasing here the current
+will be zero there will be no net
+
+ align:start position:0%
+will be zero there will be no net
+ 
+
+ align:start position:0%
+will be zero there will be no net
+current flow right because there will be
+
+ align:start position:0%
+current flow right because there will be
+ 
+
+ align:start position:0%
+current flow right because there will be
+no driving force for the carriers to go
+
+ align:start position:0%
+no driving force for the carriers to go
+ 
+
+ align:start position:0%
+no driving force for the carriers to go
+from the P type into the N type there
+
+ align:start position:0%
+from the P type into the N type there
+ 
+
+ align:start position:0%
+from the P type into the N type there
+will be no more built-in field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind of cool okay so now we're beginning
+
+ align:start position:0%
+kind of cool okay so now we're beginning
+ 
+
+ align:start position:0%
+kind of cool okay so now we're beginning
+to wrap our heads around uh what's
+
+ align:start position:0%
+to wrap our heads around uh what's
+ 
+
+ align:start position:0%
+to wrap our heads around uh what's
+happening to the electrons and holes
+
+ align:start position:0%
+happening to the electrons and holes
+ 
+
+ align:start position:0%
+happening to the electrons and holes
+during solar cell operation um let me
+
+ align:start position:0%
+during solar cell operation um let me
+ 
+
+ align:start position:0%
+during solar cell operation um let me
+put a little bit of mathematics to this
+
+ align:start position:0%
+put a little bit of mathematics to this
+ 
+
+ align:start position:0%
+put a little bit of mathematics to this
+uh these are your IV curves the blue is
+
+ align:start position:0%
+uh these are your IV curves the blue is
+ 
+
+ align:start position:0%
+uh these are your IV curves the blue is
+in the dark and the red is under
+
+ align:start position:0%
+in the dark and the red is under
+ 
+
+ align:start position:0%
+in the dark and the red is under
+illumination and uh we're focused on
+
+ align:start position:0%
+illumination and uh we're focused on
+ 
+
+ align:start position:0%
+illumination and uh we're focused on
+this fourth quadrant right here because
+
+ align:start position:0%
+this fourth quadrant right here because
+ 
+
+ align:start position:0%
+this fourth quadrant right here because
+this is a quadrant which power is coming
+
+ align:start position:0%
+this is a quadrant which power is coming
+ 
+
+ align:start position:0%
+this is a quadrant which power is coming
+out of our solar cell device which
+
+ align:start position:0%
+out of our solar cell device which
+ 
+
+ align:start position:0%
+out of our solar cell device which
+usable Power is coming out that we can
+
+ align:start position:0%
+usable Power is coming out that we can
+ 
+
+ align:start position:0%
+usable Power is coming out that we can
+power an external load why
+
+ align:start position:0%
+power an external load why
+ 
+
+ align:start position:0%
+power an external load why
+well first off the voltage is such that
+
+ align:start position:0%
+well first off the voltage is such that
+ 
+
+ align:start position:0%
+well first off the voltage is such that
+we can power an external load we have
+
+ align:start position:0%
+we can power an external load we have
+ 
+
+ align:start position:0%
+we can power an external load we have
+charge separation the electrons are
+
+ align:start position:0%
+charge separation the electrons are
+ 
+
+ align:start position:0%
+charge separation the electrons are
+accumulated over here and they have
+
+ align:start position:0%
+accumulated over here and they have
+ 
+
+ align:start position:0%
+accumulated over here and they have
+higher potential than they do on the
+
+ align:start position:0%
+higher potential than they do on the
+ 
+
+ align:start position:0%
+higher potential than they do on the
+other side which means that there's
+
+ align:start position:0%
+other side which means that there's
+ 
+
+ align:start position:0%
+other side which means that there's
+there's an incentive for them to go
+
+ align:start position:0%
+there's an incentive for them to go
+ 
+
+ align:start position:0%
+there's an incentive for them to go
+through the external circuit deposit
+
+ align:start position:0%
+through the external circuit deposit
+ 
+
+ align:start position:0%
+through the external circuit deposit
+their their power across that external
+
+ align:start position:0%
+their their power across that external
+ 
+
+ align:start position:0%
+their their power across that external
+load to get back to this other side
+
+ align:start position:0%
+load to get back to this other side
+ 
+
+ align:start position:0%
+load to get back to this other side
+where their potential is lower right so
+
+ align:start position:0%
+where their potential is lower right so
+ 
+
+ align:start position:0%
+where their potential is lower right so
+the voltage is favorable and the current
+
+ align:start position:0%
+the voltage is favorable and the current
+ 
+
+ align:start position:0%
+the voltage is favorable and the current
+is also favorable because now we have
+
+ align:start position:0%
+is also favorable because now we have
+ 
+
+ align:start position:0%
+is also favorable because now we have
+light coming in and this uh uh this
+
+ align:start position:0%
+light coming in and this uh uh this
+ 
+
+ align:start position:0%
+light coming in and this uh uh this
+generation current is driving the
+
+ align:start position:0%
+generation current is driving the
+ 
+
+ align:start position:0%
+generation current is driving the
+carriers or or is creating carriers here
+
+ align:start position:0%
+carriers or or is creating carriers here
+ 
+
+ align:start position:0%
+carriers or or is creating carriers here
+in the P type that can then be driven
+
+ align:start position:0%
+in the P type that can then be driven
+ 
+
+ align:start position:0%
+in the P type that can then be driven
+toward the N type because of the
+
+ align:start position:0%
+toward the N type because of the
+ 
+
+ align:start position:0%
+toward the N type because of the
+built-in field so the conditions are
+
+ align:start position:0%
+built-in field so the conditions are
+ 
+
+ align:start position:0%
+built-in field so the conditions are
+just right under illuminated forward
+
+ align:start position:0%
+just right under illuminated forward
+ 
+
+ align:start position:0%
+just right under illuminated forward
+bias conditions to drive power through
+
+ align:start position:0%
+bias conditions to drive power through
+ 
+
+ align:start position:0%
+bias conditions to drive power through
+our external load under all other
+
+ align:start position:0%
+our external load under all other
+ 
+
+ align:start position:0%
+our external load under all other
+conditions of operations of the solar
+
+ align:start position:0%
+conditions of operations of the solar
+ 
+
+ align:start position:0%
+conditions of operations of the solar
+cell we're putting power into the device
+
+ align:start position:0%
+cell we're putting power into the device
+ 
+
+ align:start position:0%
+cell we're putting power into the device
+not getting power out of it this fourth
+
+ align:start position:0%
+not getting power out of it this fourth
+ 
+
+ align:start position:0%
+not getting power out of it this fourth
+quadrant over here this forward bias
+
+ align:start position:0%
+quadrant over here this forward bias
+ 
+
+ align:start position:0%
+quadrant over here this forward bias
+illuminated case is the only case in
+
+ align:start position:0%
+illuminated case is the only case in
+ 
+
+ align:start position:0%
+illuminated case is the only case in
+which power is coming usable Powers
+
+ align:start position:0%
+which power is coming usable Powers
+ 
+
+ align:start position:0%
+which power is coming usable Powers
+coming out of our solar cell that we can
+
+ align:start position:0%
+coming out of our solar cell that we can
+ 
+
+ align:start position:0%
+coming out of our solar cell that we can
+use so that's why we focus on this
+
+ align:start position:0%
+use so that's why we focus on this
+ 
+
+ align:start position:0%
+use so that's why we focus on this
+fourth quadrant right here the
+
+ align:start position:0%
+fourth quadrant right here the
+ 
+
+ align:start position:0%
+fourth quadrant right here the
+illuminated IV curve is to first order
+
+ align:start position:0%
+illuminated IV curve is to first order
+ 
+
+ align:start position:0%
+illuminated IV curve is to first order
+is just your dark IV curve with a superp
+
+ align:start position:0%
+is just your dark IV curve with a superp
+ 
+
+ align:start position:0%
+is just your dark IV curve with a superp
+position which we call the illumination
+
+ align:start position:0%
+position which we call the illumination
+ 
+
+ align:start position:0%
+position which we call the illumination
+current I sub L and that's what shifts
+
+ align:start position:0%
+current I sub L and that's what shifts
+ 
+
+ align:start position:0%
+current I sub L and that's what shifts
+our entire curve down by this Isabel
+
+ align:start position:0%
+our entire curve down by this Isabel
+ 
+
+ align:start position:0%
+our entire curve down by this Isabel
+right here so this is subel that one
+
+ align:start position:0%
+right here so this is subel that one
+ 
+
+ align:start position:0%
+right here so this is subel that one
+right there or that one right
+
+ align:start position:0%
+right there or that one right
+ 
+
+ align:start position:0%
+right there or that one right
+there kind of cool all right uh what do
+
+ align:start position:0%
+there kind of cool all right uh what do
+ 
+
+ align:start position:0%
+there kind of cool all right uh what do
+we think will happen if our light
+
+ align:start position:0%
+we think will happen if our light
+ 
+
+ align:start position:0%
+we think will happen if our light
+intensity goes down by a factor of
+
+ align:start position:0%
+intensity goes down by a factor of
+ 
+
+ align:start position:0%
+intensity goes down by a factor of
+two so now if if if the amount of
+
+ align:start position:0%
+two so now if if if the amount of
+ 
+
+ align:start position:0%
+two so now if if if the amount of
+sunlight falling on our solar cell drops
+
+ align:start position:0%
+sunlight falling on our solar cell drops
+ 
+
+ align:start position:0%
+sunlight falling on our solar cell drops
+by a half what will happen what do we
+
+ align:start position:0%
+by a half what will happen what do we
+ 
+
+ align:start position:0%
+by a half what will happen what do we
+predict will happen based on this right
+
+ align:start position:0%
+predict will happen based on this right
+ 
+
+ align:start position:0%
+predict will happen based on this right
+here the Curve will shift the red Curve
+
+ align:start position:0%
+here the Curve will shift the red Curve
+ 
+
+ align:start position:0%
+here the Curve will shift the red Curve
+will shift up by about half right
+
+ align:start position:0%
+will shift up by about half right
+ 
+
+ align:start position:0%
+will shift up by about half right
+because the illumination current is now
+
+ align:start position:0%
+because the illumination current is now
+ 
+
+ align:start position:0%
+because the illumination current is now
+cut in
+
+ align:start position:0%
+cut in
+ 
+
+ align:start position:0%
+cut in
+half what will happen to the voltage
+
+ align:start position:0%
+half what will happen to the voltage
+ 
+
+ align:start position:0%
+half what will happen to the voltage
+intersect right
+
+ align:start position:0%
+intersect right
+ 
+
+ align:start position:0%
+intersect right
+here what is the relation between
+
+ align:start position:0%
+here what is the relation between
+ 
+
+ align:start position:0%
+here what is the relation between
+voltage and
+
+ align:start position:0%
+voltage and
+ 
+
+ align:start position:0%
+voltage and
+current it's a logarithmic relation
+
+ align:start position:0%
+current it's a logarithmic relation
+ 
+
+ align:start position:0%
+current it's a logarithmic relation
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so it won't necessarily be cut in
+
+ align:start position:0%
+so it won't necessarily be cut in
+ 
+
+ align:start position:0%
+so it won't necessarily be cut in
+half right but it'll be cut by whatever
+
+ align:start position:0%
+half right but it'll be cut by whatever
+ 
+
+ align:start position:0%
+half right but it'll be cut by whatever
+this would be here log of log of two so
+
+ align:start position:0%
+this would be here log of log of two so
+ 
+
+ align:start position:0%
+this would be here log of log of two so
+um okay so we have we're beginning to
+
+ align:start position:0%
+um okay so we have we're beginning to
+ 
+
+ align:start position:0%
+um okay so we have we're beginning to
+develop an intuitive understanding of
+
+ align:start position:0%
+develop an intuitive understanding of
+ 
+
+ align:start position:0%
+develop an intuitive understanding of
+where electrons are flowing inside of
+
+ align:start position:0%
+where electrons are flowing inside of
+ 
+
+ align:start position:0%
+where electrons are flowing inside of
+our solar cells in the dark and under
+
+ align:start position:0%
+our solar cells in the dark and under
+ 
+
+ align:start position:0%
+our solar cells in the dark and under
+Illumination in the dark is important
+
+ align:start position:0%
+Illumination in the dark is important
+ 
+
+ align:start position:0%
+Illumination in the dark is important
+because we can test our devices in the
+
+ align:start position:0%
+because we can test our devices in the
+ 
+
+ align:start position:0%
+because we can test our devices in the
+dark and we can still learn a lot about
+
+ align:start position:0%
+dark and we can still learn a lot about
+ 
+
+ align:start position:0%
+dark and we can still learn a lot about
+our solar cell device characteristics in
+
+ align:start position:0%
+our solar cell device characteristics in
+ 
+
+ align:start position:0%
+our solar cell device characteristics in
+the dark as well we can under forward
+
+ align:start position:0%
+the dark as well we can under forward
+ 
+
+ align:start position:0%
+the dark as well we can under forward
+bias conditions in the dark we can force
+
+ align:start position:0%
+bias conditions in the dark we can force
+ 
+
+ align:start position:0%
+bias conditions in the dark we can force
+carriers from our uh from one side of
+
+ align:start position:0%
+carriers from our uh from one side of
+ 
+
+ align:start position:0%
+carriers from our uh from one side of
+the junction to the other the wrong way
+
+ align:start position:0%
+the junction to the other the wrong way
+ 
+
+ align:start position:0%
+the junction to the other the wrong way
+and probe for weaknesses in the P
+
+ align:start position:0%
+and probe for weaknesses in the P
+ 
+
+ align:start position:0%
+and probe for weaknesses in the P
+Junction region so that's helpful um and
+
+ align:start position:0%
+Junction region so that's helpful um and
+ 
+
+ align:start position:0%
+Junction region so that's helpful um and
+uh in the illumination condition
+
+ align:start position:0%
+uh in the illumination condition
+ 
+
+ align:start position:0%
+uh in the illumination condition
+obviously we're testing the total amount
+
+ align:start position:0%
+obviously we're testing the total amount
+ 
+
+ align:start position:0%
+obviously we're testing the total amount
+of power that's coming out of our device
+
+ align:start position:0%
+of power that's coming out of our device
+ 
+
+ align:start position:0%
+of power that's coming out of our device
+so again this is uh very useful because
+
+ align:start position:0%
+so again this is uh very useful because
+ 
+
+ align:start position:0%
+so again this is uh very useful because
+it's off of this red curve here that we
+
+ align:start position:0%
+it's off of this red curve here that we
+ 
+
+ align:start position:0%
+it's off of this red curve here that we
+Define the efficiency or the performance
+
+ align:start position:0%
+Define the efficiency or the performance
+ 
+
+ align:start position:0%
+Define the efficiency or the performance
+of the solar cell so what I'll ask folks
+
+ align:start position:0%
+of the solar cell so what I'll ask folks
+ 
+
+ align:start position:0%
+of the solar cell so what I'll ask folks
+to do now is to um uh we'll we'll begin
+
+ align:start position:0%
+to do now is to um uh we'll we'll begin
+ 
+
+ align:start position:0%
+to do now is to um uh we'll we'll begin
+passing around these little tools and
+
+ align:start position:0%
+passing around these little tools and
+ 
+
+ align:start position:0%
+passing around these little tools and
+I'll ask David Bernie needleman to come
+
+ align:start position:0%
+I'll ask David Bernie needleman to come
+ 
+
+ align:start position:0%
+I'll ask David Bernie needleman to come
+up to the front uh David is our our lab
+
+ align:start position:0%
+up to the front uh David is our our lab
+ 
+
+ align:start position:0%
+up to the front uh David is our our lab
+Guru he's the one who uh helped build
+
+ align:start position:0%
+Guru he's the one who uh helped build
+ 
+
+ align:start position:0%
+Guru he's the one who uh helped build
+these really was a driving force behind
+
+ align:start position:0%
+these really was a driving force behind
+ 
+
+ align:start position:0%
+these really was a driving force behind
+getting them built uh these are IV
+
+ align:start position:0%
+getting them built uh these are IV
+ 
+
+ align:start position:0%
+getting them built uh these are IV
+testers that will allow you to measure
+
+ align:start position:0%
+testers that will allow you to measure
+ 
+
+ align:start position:0%
+testers that will allow you to measure
+the current voltage characteristics of
+
+ align:start position:0%
+the current voltage characteristics of
+ 
+
+ align:start position:0%
+the current voltage characteristics of
+solar cells uh right here in class and
+
+ align:start position:0%
+solar cells uh right here in class and
+ 
+
+ align:start position:0%
+solar cells uh right here in class and
+uh he's going to well we'll pass them
+
+ align:start position:0%
+uh he's going to well we'll pass them
+ 
+
+ align:start position:0%
+uh he's going to well we'll pass them
+out while he maybe he comes to the front
+
+ align:start position:0%
+out while he maybe he comes to the front
+ 
+
+ align:start position:0%
+out while he maybe he comes to the front
+here and explains how they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work so now that we have the basic IV
+
+ align:start position:0%
+work so now that we have the basic IV
+ 
+
+ align:start position:0%
+work so now that we have the basic IV
+curves rolling in what I'd like you to
+
+ align:start position:0%
+curves rolling in what I'd like you to
+ 
+
+ align:start position:0%
+curves rolling in what I'd like you to
+do is modify the height or the intensity
+
+ align:start position:0%
+do is modify the height or the intensity
+ 
+
+ align:start position:0%
+do is modify the height or the intensity
+of the light and the easiest way to
+
+ align:start position:0%
+of the light and the easiest way to
+ 
+
+ align:start position:0%
+of the light and the easiest way to
+modify the intensity of the light is to
+
+ align:start position:0%
+modify the intensity of the light is to
+ 
+
+ align:start position:0%
+modify the intensity of the light is to
+move the uh light position up and down
+
+ align:start position:0%
+move the uh light position up and down
+ 
+
+ align:start position:0%
+move the uh light position up and down
+right so uh modify the intensity of the
+
+ align:start position:0%
+right so uh modify the intensity of the
+ 
+
+ align:start position:0%
+right so uh modify the intensity of the
+light and see how this IV curve changes
+
+ align:start position:0%
+light and see how this IV curve changes
+ 
+
+ align:start position:0%
+light and see how this IV curve changes
+note the uh y-axis scale which might uh
+
+ align:start position:0%
+note the uh y-axis scale which might uh
+ 
+
+ align:start position:0%
+note the uh y-axis scale which might uh
+might change as well it might rescale uh
+
+ align:start position:0%
+might change as well it might rescale uh
+ 
+
+ align:start position:0%
+might change as well it might rescale uh
+depending on the condition uh but note
+
+ align:start position:0%
+depending on the condition uh but note
+ 
+
+ align:start position:0%
+depending on the condition uh but note
+the y-axis scale and see how the um uh
+
+ align:start position:0%
+the y-axis scale and see how the um uh
+ 
+
+ align:start position:0%
+the y-axis scale and see how the um uh
+The Intercept of the of the y axis is
+
+ align:start position:0%
+The Intercept of the of the y axis is
+ 
+
+ align:start position:0%
+The Intercept of the of the y axis is
+changed with illumination intensity give
+
+ align:start position:0%
+changed with illumination intensity give
+ 
+
+ align:start position:0%
+changed with illumination intensity give
+that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shot all right
+
+ align:start position:0%
+shot all right
+ 
+
+ align:start position:0%
+shot all right
+folks why don't we uh why don't we
+
+ align:start position:0%
+folks why don't we uh why don't we
+ 
+
+ align:start position:0%
+folks why don't we uh why don't we
+Circle back real quick um this has been
+
+ align:start position:0%
+Circle back real quick um this has been
+ 
+
+ align:start position:0%
+Circle back real quick um this has been
+a good experiment I uh am very much uh
+
+ align:start position:0%
+a good experiment I uh am very much uh
+ 
+
+ align:start position:0%
+a good experiment I uh am very much uh
+in favor of multitasking and browsing so
+
+ align:start position:0%
+in favor of multitasking and browsing so
+ 
+
+ align:start position:0%
+in favor of multitasking and browsing so
+if you want to keep your experiment
+
+ align:start position:0%
+if you want to keep your experiment
+ 
+
+ align:start position:0%
+if you want to keep your experiment
+running over the course of the remainder
+
+ align:start position:0%
+running over the course of the remainder
+ 
+
+ align:start position:0%
+running over the course of the remainder
+the lecture I will certainly have
+
+ align:start position:0%
+the lecture I will certainly have
+ 
+
+ align:start position:0%
+the lecture I will certainly have
+nothing opposed to uh testing a few
+
+ align:start position:0%
+nothing opposed to uh testing a few
+ 
+
+ align:start position:0%
+nothing opposed to uh testing a few
+different elimination conditions and if
+
+ align:start position:0%
+different elimination conditions and if
+ 
+
+ align:start position:0%
+different elimination conditions and if
+there's anything really really important
+
+ align:start position:0%
+there's anything really really important
+ 
+
+ align:start position:0%
+there's anything really really important
+I'm going to emphasize this is really
+
+ align:start position:0%
+I'm going to emphasize this is really
+ 
+
+ align:start position:0%
+I'm going to emphasize this is really
+important wake up folks um the I sub L
+
+ align:start position:0%
+important wake up folks um the I sub L
+ 
+
+ align:start position:0%
+important wake up folks um the I sub L
+just to really recap here we have this
+
+ align:start position:0%
+just to really recap here we have this
+ 
+
+ align:start position:0%
+just to really recap here we have this
+ideal di equation the illumination
+
+ align:start position:0%
+ideal di equation the illumination
+ 
+
+ align:start position:0%
+ideal di equation the illumination
+current coming in from our light source
+
+ align:start position:0%
+current coming in from our light source
+ 
+
+ align:start position:0%
+current coming in from our light source
+and in our little setup how many
+
+ align:start position:0%
+and in our little setup how many
+ 
+
+ align:start position:0%
+and in our little setup how many
+batteries did you see
+
+ align:start position:0%
+batteries did you see
+ 
+
+ align:start position:0%
+batteries did you see
+there look closer how many batteries do
+
+ align:start position:0%
+there look closer how many batteries do
+ 
+
+ align:start position:0%
+there look closer how many batteries do
+you see total in our in our setup look
+
+ align:start position:0%
+you see total in our in our setup look
+ 
+
+ align:start position:0%
+you see total in our in our setup look
+at especially at that light source two
+
+ align:start position:0%
+at especially at that light source two
+ 
+
+ align:start position:0%
+at especially at that light source two
+of them right there's a 9vt and a 1.5
+
+ align:start position:0%
+of them right there's a 9vt and a 1.5
+ 
+
+ align:start position:0%
+of them right there's a 9vt and a 1.5
+volt all right so one of them is
+
+ align:start position:0%
+volt all right so one of them is
+ 
+
+ align:start position:0%
+volt all right so one of them is
+powering the light source and uh we have
+
+ align:start position:0%
+powering the light source and uh we have
+ 
+
+ align:start position:0%
+powering the light source and uh we have
+um as well bias uh to the solar cell
+
+ align:start position:0%
+um as well bias uh to the solar cell
+ 
+
+ align:start position:0%
+um as well bias uh to the solar cell
+device right so we have a bit of a
+
+ align:start position:0%
+device right so we have a bit of a
+ 
+
+ align:start position:0%
+device right so we have a bit of a
+combination of the last two uh slides
+
+ align:start position:0%
+combination of the last two uh slides
+ 
+
+ align:start position:0%
+combination of the last two uh slides
+right in this case we had the in the
+
+ align:start position:0%
+right in this case we had the in the
+ 
+
+ align:start position:0%
+right in this case we had the in the
+dark we were biasing our solar cell
+
+ align:start position:0%
+dark we were biasing our solar cell
+ 
+
+ align:start position:0%
+dark we were biasing our solar cell
+using the battery and under illumination
+
+ align:start position:0%
+using the battery and under illumination
+ 
+
+ align:start position:0%
+using the battery and under illumination
+conditions uh the light itself was
+
+ align:start position:0%
+conditions uh the light itself was
+ 
+
+ align:start position:0%
+conditions uh the light itself was
+causing the solar cell to become forward
+
+ align:start position:0%
+causing the solar cell to become forward
+ 
+
+ align:start position:0%
+causing the solar cell to become forward
+biased but we can add a battery to sweep
+
+ align:start position:0%
+biased but we can add a battery to sweep
+ 
+
+ align:start position:0%
+biased but we can add a battery to sweep
+the uh the bias condition of the device
+
+ align:start position:0%
+the uh the bias condition of the device
+ 
+
+ align:start position:0%
+the uh the bias condition of the device
+right so even though we have a natural
+
+ align:start position:0%
+right so even though we have a natural
+ 
+
+ align:start position:0%
+right so even though we have a natural
+biasing of the of the solar cell By the
+
+ align:start position:0%
+biasing of the of the solar cell By the
+ 
+
+ align:start position:0%
+biasing of the of the solar cell By the
+Light we can force the solar cell under
+
+ align:start position:0%
+Light we can force the solar cell under
+ 
+
+ align:start position:0%
+Light we can force the solar cell under
+different operating conditions with the
+
+ align:start position:0%
+different operating conditions with the
+ 
+
+ align:start position:0%
+different operating conditions with the
+battery and so that's effectively what's
+
+ align:start position:0%
+battery and so that's effectively what's
+ 
+
+ align:start position:0%
+battery and so that's effectively what's
+happening right here is you have a
+
+ align:start position:0%
+happening right here is you have a
+ 
+
+ align:start position:0%
+happening right here is you have a
+combination of
+
+ align:start position:0%
+combination of
+ 
+
+ align:start position:0%
+combination of
+both uh uh simple scenarios that we just
+
+ align:start position:0%
+both uh uh simple scenarios that we just
+ 
+
+ align:start position:0%
+both uh uh simple scenarios that we just
+looked at and uh we're building on on
+
+ align:start position:0%
+looked at and uh we're building on on
+ 
+
+ align:start position:0%
+looked at and uh we're building on on
+those components to really understand uh
+
+ align:start position:0%
+those components to really understand uh
+ 
+
+ align:start position:0%
+those components to really understand uh
+the larger system um why might that be
+
+ align:start position:0%
+the larger system um why might that be
+ 
+
+ align:start position:0%
+the larger system um why might that be
+important or why might that be realistic
+
+ align:start position:0%
+important or why might that be realistic
+ 
+
+ align:start position:0%
+important or why might that be realistic
+well uh the light itself is biasing that
+
+ align:start position:0%
+well uh the light itself is biasing that
+ 
+
+ align:start position:0%
+well uh the light itself is biasing that
+particular solar cell device but that
+
+ align:start position:0%
+particular solar cell device but that
+ 
+
+ align:start position:0%
+particular solar cell device but that
+solar cell might be connected in series
+
+ align:start position:0%
+solar cell might be connected in series
+ 
+
+ align:start position:0%
+solar cell might be connected in series
+with a bunch of other solar cells in a
+
+ align:start position:0%
+with a bunch of other solar cells in a
+ 
+
+ align:start position:0%
+with a bunch of other solar cells in a
+module right and those other solar cells
+
+ align:start position:0%
+module right and those other solar cells
+ 
+
+ align:start position:0%
+module right and those other solar cells
+might be biasing that one uh solar cell
+
+ align:start position:0%
+might be biasing that one uh solar cell
+ 
+
+ align:start position:0%
+might be biasing that one uh solar cell
+so uh that's why we we we have to think
+
+ align:start position:0%
+so uh that's why we we we have to think
+ 
+
+ align:start position:0%
+so uh that's why we we we have to think
+about uh the solar cell device both from
+
+ align:start position:0%
+about uh the solar cell device both from
+ 
+
+ align:start position:0%
+about uh the solar cell device both from
+the perspective of of what bias
+
+ align:start position:0%
+the perspective of of what bias
+ 
+
+ align:start position:0%
+the perspective of of what bias
+condition is it under what illumination
+
+ align:start position:0%
+condition is it under what illumination
+ 
+
+ align:start position:0%
+condition is it under what illumination
+is it under and of course what's
+
+ align:start position:0%
+is it under and of course what's
+ 
+
+ align:start position:0%
+is it under and of course what's
+happening around it is it just powering
+
+ align:start position:0%
+happening around it is it just powering
+ 
+
+ align:start position:0%
+happening around it is it just powering
+external load are there is there a
+
+ align:start position:0%
+external load are there is there a
+ 
+
+ align:start position:0%
+external load are there is there a
+battery connected in series to it are
+
+ align:start position:0%
+battery connected in series to it are
+ 
+
+ align:start position:0%
+battery connected in series to it are
+there other solar cells connected in
+
+ align:start position:0%
+there other solar cells connected in
+ 
+
+ align:start position:0%
+there other solar cells connected in
+series with it okay yes Ashley so I I
+
+ align:start position:0%
+series with it okay yes Ashley so I I
+ 
+
+ align:start position:0%
+series with it okay yes Ashley so I I
+don't understand still why having a load
+
+ align:start position:0%
+don't understand still why having a load
+ 
+
+ align:start position:0%
+don't understand still why having a load
+would bias the device yeah so let's
+
+ align:start position:0%
+would bias the device yeah so let's
+ 
+
+ align:start position:0%
+would bias the device yeah so let's
+imagine uh under illumination conditions
+
+ align:start position:0%
+imagine uh under illumination conditions
+ 
+
+ align:start position:0%
+imagine uh under illumination conditions
+right here what I'm going to do very
+
+ align:start position:0%
+right here what I'm going to do very
+ 
+
+ align:start position:0%
+right here what I'm going to do very
+very quickly is replace this battery um
+
+ align:start position:0%
+very quickly is replace this battery um
+ 
+
+ align:start position:0%
+very quickly is replace this battery um
+manually in my slides if PowerPoint auto
+
+ align:start position:0%
+manually in my slides if PowerPoint auto
+ 
+
+ align:start position:0%
+manually in my slides if PowerPoint auto
+save will allow me with a resistor so um
+
+ align:start position:0%
+save will allow me with a resistor so um
+ 
+
+ align:start position:0%
+save will allow me with a resistor so um
+if you'll excuse my quick uh
+
+ align:start position:0%
+if you'll excuse my quick uh
+ 
+
+ align:start position:0%
+if you'll excuse my quick uh
+introduction here of the
+
+ align:start position:0%
+introduction here of the
+ 
+
+ align:start position:0%
+introduction here of the
+resistor now um sorry about the little
+
+ align:start position:0%
+resistor now um sorry about the little
+ 
+
+ align:start position:0%
+resistor now um sorry about the little
+artistic uh license okay so now I have
+
+ align:start position:0%
+artistic uh license okay so now I have
+ 
+
+ align:start position:0%
+artistic uh license okay so now I have
+my resistor here and um my illumination
+
+ align:start position:0%
+my resistor here and um my illumination
+ 
+
+ align:start position:0%
+my resistor here and um my illumination
+is coming into the device uh from say
+
+ align:start position:0%
+is coming into the device uh from say
+ 
+
+ align:start position:0%
+is coming into the device uh from say
+one of the sides is generating electron
+
+ align:start position:0%
+one of the sides is generating electron
+ 
+
+ align:start position:0%
+one of the sides is generating electron
+ho pairs I have a a multiplicity of
+
+ align:start position:0%
+ho pairs I have a a multiplicity of
+ 
+
+ align:start position:0%
+ho pairs I have a a multiplicity of
+electrons that have now gone down the
+
+ align:start position:0%
+electrons that have now gone down the
+ 
+
+ align:start position:0%
+electrons that have now gone down the
+hill right it's more energetically
+
+ align:start position:0%
+hill right it's more energetically
+ 
+
+ align:start position:0%
+hill right it's more energetically
+favorable for these electrons to be on
+
+ align:start position:0%
+favorable for these electrons to be on
+ 
+
+ align:start position:0%
+favorable for these electrons to be on
+the other side and what has that done
+
+ align:start position:0%
+the other side and what has that done
+ 
+
+ align:start position:0%
+the other side and what has that done
+that's raised the chemical potential
+
+ align:start position:0%
+that's raised the chemical potential
+ 
+
+ align:start position:0%
+that's raised the chemical potential
+this side it's difficult for them to get
+
+ align:start position:0%
+this side it's difficult for them to get
+ 
+
+ align:start position:0%
+this side it's difficult for them to get
+back the other way um it's not
+
+ align:start position:0%
+back the other way um it's not
+ 
+
+ align:start position:0%
+back the other way um it's not
+impossible but it could be more easy for
+
+ align:start position:0%
+impossible but it could be more easy for
+ 
+
+ align:start position:0%
+impossible but it could be more easy for
+them to flow through an external circuit
+
+ align:start position:0%
+them to flow through an external circuit
+ 
+
+ align:start position:0%
+them to flow through an external circuit
+to get back to the other side and as
+
+ align:start position:0%
+to get back to the other side and as
+ 
+
+ align:start position:0%
+to get back to the other side and as
+they flow through that external circuit
+
+ align:start position:0%
+they flow through that external circuit
+ 
+
+ align:start position:0%
+they flow through that external circuit
+they're depositing their energy across
+
+ align:start position:0%
+they're depositing their energy across
+ 
+
+ align:start position:0%
+they're depositing their energy across
+that external circuit what energy well
+
+ align:start position:0%
+that external circuit what energy well
+ 
+
+ align:start position:0%
+that external circuit what energy well
+it's the potential difference from this
+
+ align:start position:0%
+it's the potential difference from this
+ 
+
+ align:start position:0%
+it's the potential difference from this
+side to that
+
+ align:start position:0%
+side to that
+ 
+
+ align:start position:0%
+side to that
+side so that's why the solar cell can be
+
+ align:start position:0%
+side so that's why the solar cell can be
+ 
+
+ align:start position:0%
+side so that's why the solar cell can be
+thought of as under as in fored byas
+
+ align:start position:0%
+thought of as under as in fored byas
+ 
+
+ align:start position:0%
+thought of as under as in fored byas
+conditions under illumination with an
+
+ align:start position:0%
+conditions under illumination with an
+ 
+
+ align:start position:0%
+conditions under illumination with an
+external load attached to it of course
+
+ align:start position:0%
+external load attached to it of course
+ 
+
+ align:start position:0%
+external load attached to it of course
+the load has to be well matched to the
+
+ align:start position:0%
+the load has to be well matched to the
+ 
+
+ align:start position:0%
+the load has to be well matched to the
+uh output of the solar cell device and
+
+ align:start position:0%
+uh output of the solar cell device and
+ 
+
+ align:start position:0%
+uh output of the solar cell device and
+is the biasing because there's a voltage
+
+ align:start position:0%
+is the biasing because there's a voltage
+ 
+
+ align:start position:0%
+is the biasing because there's a voltage
+drop across the resistor uh yes the
+
+ align:start position:0%
+drop across the resistor uh yes the
+ 
+
+ align:start position:0%
+drop across the resistor uh yes the
+biasing is because you have a shift in
+
+ align:start position:0%
+biasing is because you have a shift in
+ 
+
+ align:start position:0%
+biasing is because you have a shift in
+the chemical potential of this side up
+
+ align:start position:0%
+the chemical potential of this side up
+ 
+
+ align:start position:0%
+the chemical potential of this side up
+relative to you have a shift of the N
+
+ align:start position:0%
+relative to you have a shift of the N
+ 
+
+ align:start position:0%
+relative to you have a shift of the N
+type side higher than the ptype side
+
+ align:start position:0%
+type side higher than the ptype side
+ 
+
+ align:start position:0%
+type side higher than the ptype side
+that's a bias anytime you have a
+
+ align:start position:0%
+that's a bias anytime you have a
+ 
+
+ align:start position:0%
+that's a bias anytime you have a
+difference in the chemical potential in
+
+ align:start position:0%
+difference in the chemical potential in
+ 
+
+ align:start position:0%
+difference in the chemical potential in
+one terminal versus the other terminal
+
+ align:start position:0%
+one terminal versus the other terminal
+ 
+
+ align:start position:0%
+one terminal versus the other terminal
+of your solar cell you have a bias
+
+ align:start position:0%
+of your solar cell you have a bias
+ 
+
+ align:start position:0%
+of your solar cell you have a bias
+whether that's generated by light
+
+ align:start position:0%
+whether that's generated by light
+ 
+
+ align:start position:0%
+whether that's generated by light
+whether that's generated by a battery
+
+ align:start position:0%
+whether that's generated by a battery
+ 
+
+ align:start position:0%
+whether that's generated by a battery
+right whether it's the energy input to
+
+ align:start position:0%
+right whether it's the energy input to
+ 
+
+ align:start position:0%
+right whether it's the energy input to
+create that bias is coming from the Sun
+
+ align:start position:0%
+create that bias is coming from the Sun
+ 
+
+ align:start position:0%
+create that bias is coming from the Sun
+or if it's coming from an external
+
+ align:start position:0%
+or if it's coming from an external
+ 
+
+ align:start position:0%
+or if it's coming from an external
+battery uh that's a matter of of detail
+
+ align:start position:0%
+battery uh that's a matter of of detail
+ 
+
+ align:start position:0%
+battery uh that's a matter of of detail
+so okay so is the Sun for biasing yes
+
+ align:start position:0%
+so okay so is the Sun for biasing yes
+ 
+
+ align:start position:0%
+so okay so is the Sun for biasing yes
+one can think about this as talking I
+
+ align:start position:0%
+one can think about this as talking I
+ 
+
+ align:start position:0%
+one can think about this as talking I
+conf between light and like okay oh so
+
+ align:start position:0%
+conf between light and like okay oh so
+ 
+
+ align:start position:0%
+conf between light and like okay oh so
+the LED in this case could forward bias
+
+ align:start position:0%
+the LED in this case could forward bias
+ 
+
+ align:start position:0%
+the LED in this case could forward bias
+your device too I mean it's just photons
+
+ align:start position:0%
+your device too I mean it's just photons
+ 
+
+ align:start position:0%
+your device too I mean it's just photons
+photons are are forward biasing the
+
+ align:start position:0%
+photons are are forward biasing the
+ 
+
+ align:start position:0%
+photons are are forward biasing the
+device yeah so then can Sun ever reverse
+
+ align:start position:0%
+device yeah so then can Sun ever reverse
+ 
+
+ align:start position:0%
+device yeah so then can Sun ever reverse
+bias no that would be very difficult um
+
+ align:start position:0%
+bias no that would be very difficult um
+ 
+
+ align:start position:0%
+bias no that would be very difficult um
+what you could what you could do though
+
+ align:start position:0%
+what you could what you could do though
+ 
+
+ align:start position:0%
+what you could what you could do though
+is have a bunch of solar cells connected
+
+ align:start position:0%
+is have a bunch of solar cells connected
+ 
+
+ align:start position:0%
+is have a bunch of solar cells connected
+in series with this one right that are
+
+ align:start position:0%
+in series with this one right that are
+ 
+
+ align:start position:0%
+in series with this one right that are
+producing forward power you could shade
+
+ align:start position:0%
+producing forward power you could shade
+ 
+
+ align:start position:0%
+producing forward power you could shade
+this device and then power could be
+
+ align:start position:0%
+this device and then power could be
+ 
+
+ align:start position:0%
+this device and then power could be
+flowing backward through it right in
+
+ align:start position:0%
+flowing backward through it right in
+ 
+
+ align:start position:0%
+flowing backward through it right in
+other words it could be in the dark
+
+ align:start position:0%
+other words it could be in the dark
+ 
+
+ align:start position:0%
+other words it could be in the dark
+right here in a dark condition and you
+
+ align:start position:0%
+right here in a dark condition and you
+ 
+
+ align:start position:0%
+right here in a dark condition and you
+could be in a reverse bias condition
+
+ align:start position:0%
+could be in a reverse bias condition
+ 
+
+ align:start position:0%
+could be in a reverse bias condition
+just because of uh the way the other
+
+ align:start position:0%
+just because of uh the way the other
+ 
+
+ align:start position:0%
+just because of uh the way the other
+solar cells around it are behaving if
+
+ align:start position:0%
+solar cells around it are behaving if
+ 
+
+ align:start position:0%
+solar cells around it are behaving if
+you have a shaded solar cell for example
+
+ align:start position:0%
+you have a shaded solar cell for example
+ 
+
+ align:start position:0%
+you have a shaded solar cell for example
+a module so imagine a seagull lands and
+
+ align:start position:0%
+a module so imagine a seagull lands and
+ 
+
+ align:start position:0%
+a module so imagine a seagull lands and
+kind of covers up one of the cells um
+
+ align:start position:0%
+kind of covers up one of the cells um
+ 
+
+ align:start position:0%
+kind of covers up one of the cells um
+that will be under reverse bias um and
+
+ align:start position:0%
+that will be under reverse bias um and
+ 
+
+ align:start position:0%
+that will be under reverse bias um and
+that that could present problem if the
+
+ align:start position:0%
+that that could present problem if the
+ 
+
+ align:start position:0%
+that that could present problem if the
+uh solar cell can't withstand uh the
+
+ align:start position:0%
+uh solar cell can't withstand uh the
+ 
+
+ align:start position:0%
+uh solar cell can't withstand uh the
+reverse bias not this is a very ideal
+
+ align:start position:0%
+reverse bias not this is a very ideal
+ 
+
+ align:start position:0%
+reverse bias not this is a very ideal
+condition what happens in the real world
+
+ align:start position:0%
+condition what happens in the real world
+ 
+
+ align:start position:0%
+condition what happens in the real world
+is that at some reverse bias condition
+
+ align:start position:0%
+is that at some reverse bias condition
+ 
+
+ align:start position:0%
+is that at some reverse bias condition
+you just have biased it so much that
+
+ align:start position:0%
+you just have biased it so much that
+ 
+
+ align:start position:0%
+you just have biased it so much that
+electrons will be able to Tunnel through
+
+ align:start position:0%
+electrons will be able to Tunnel through
+ 
+
+ align:start position:0%
+electrons will be able to Tunnel through
+from the P type into the N type right
+
+ align:start position:0%
+from the P type into the N type right
+ 
+
+ align:start position:0%
+from the P type into the N type right
+here the electrons in the veence band
+
+ align:start position:0%
+here the electrons in the veence band
+ 
+
+ align:start position:0%
+here the electrons in the veence band
+will be able to Tunnel through into the
+
+ align:start position:0%
+will be able to Tunnel through into the
+ 
+
+ align:start position:0%
+will be able to Tunnel through into the
+conduction band and what happens this IV
+
+ align:start position:0%
+conduction band and what happens this IV
+ 
+
+ align:start position:0%
+conduction band and what happens this IV
+curve is it goes Zoom begins dropping so
+
+ align:start position:0%
+curve is it goes Zoom begins dropping so
+ 
+
+ align:start position:0%
+curve is it goes Zoom begins dropping so
+if the solar cell uh reverse bias uh uh
+
+ align:start position:0%
+if the solar cell uh reverse bias uh uh
+ 
+
+ align:start position:0%
+if the solar cell uh reverse bias uh uh
+see the reverse bias current um or the
+
+ align:start position:0%
+see the reverse bias current um or the
+ 
+
+ align:start position:0%
+see the reverse bias current um or the
+current at reverse bias voltage is not
+
+ align:start position:0%
+current at reverse bias voltage is not
+ 
+
+ align:start position:0%
+current at reverse bias voltage is not
+low enough in other words if the P
+
+ align:start position:0%
+low enough in other words if the P
+ 
+
+ align:start position:0%
+low enough in other words if the P
+injunction is not strong enough you
+
+ align:start position:0%
+injunction is not strong enough you
+ 
+
+ align:start position:0%
+injunction is not strong enough you
+could have a catastrophic failure of
+
+ align:start position:0%
+could have a catastrophic failure of
+ 
+
+ align:start position:0%
+could have a catastrophic failure of
+your module with by just shading one of
+
+ align:start position:0%
+your module with by just shading one of
+ 
+
+ align:start position:0%
+your module with by just shading one of
+your cell thankfully this is one of the
+
+ align:start position:0%
+your cell thankfully this is one of the
+ 
+
+ align:start position:0%
+your cell thankfully this is one of the
+testings that are done uh with the solar
+
+ align:start position:0%
+testings that are done uh with the solar
+ 
+
+ align:start position:0%
+testings that are done uh with the solar
+simulator to prevent that failure mode
+
+ align:start position:0%
+simulator to prevent that failure mode
+ 
+
+ align:start position:0%
+simulator to prevent that failure mode
+okay all right I'll I'll entertain
+
+ align:start position:0%
+okay all right I'll I'll entertain
+ 
+
+ align:start position:0%
+okay all right I'll I'll entertain
+deeper Dives with questions I'll try to
+
+ align:start position:0%
+deeper Dives with questions I'll try to
+ 
+
+ align:start position:0%
+deeper Dives with questions I'll try to
+keep the lecture focused on the broader
+
+ align:start position:0%
+keep the lecture focused on the broader
+ 
+
+ align:start position:0%
+keep the lecture focused on the broader
+General topics but if somebody is
+
+ align:start position:0%
+General topics but if somebody is
+ 
+
+ align:start position:0%
+General topics but if somebody is
+interested in in uh in learning more I'm
+
+ align:start position:0%
+interested in in uh in learning more I'm
+ 
+
+ align:start position:0%
+interested in in uh in learning more I'm
+happy to kind of dive into there all
+
+ align:start position:0%
+happy to kind of dive into there all
+ 
+
+ align:start position:0%
+happy to kind of dive into there all
+right so um readings are strong
+
+ align:start position:0%
+right so um readings are strong
+ 
+
+ align:start position:0%
+right so um readings are strong
+encouraged I have uh interacted with
+
+ align:start position:0%
+encouraged I have uh interacted with
+ 
+
+ align:start position:0%
+encouraged I have uh interacted with
+several of you Joe has interacted with
+
+ align:start position:0%
+several of you Joe has interacted with
+ 
+
+ align:start position:0%
+several of you Joe has interacted with
+probably three n uh ending the number of
+
+ align:start position:0%
+probably three n uh ending the number of
+ 
+
+ align:start position:0%
+probably three n uh ending the number of
+people I've interacted with so far um
+
+ align:start position:0%
+people I've interacted with so far um
+ 
+
+ align:start position:0%
+people I've interacted with so far um
+and really try to uh impart the wisdom
+
+ align:start position:0%
+and really try to uh impart the wisdom
+ 
+
+ align:start position:0%
+and really try to uh impart the wisdom
+of p and Junction so uh please please
+
+ align:start position:0%
+of p and Junction so uh please please
+ 
+
+ align:start position:0%
+of p and Junction so uh please please
+please come to us if if still things are
+
+ align:start position:0%
+please come to us if if still things are
+ 
+
+ align:start position:0%
+please come to us if if still things are
+going over your head you should be able
+
+ align:start position:0%
+going over your head you should be able
+ 
+
+ align:start position:0%
+going over your head you should be able
+to explain to your uh roommates uh
+
+ align:start position:0%
+to explain to your uh roommates uh
+ 
+
+ align:start position:0%
+to explain to your uh roommates uh
+exactly what is going on in a p
+
+ align:start position:0%
+exactly what is going on in a p
+ 
+
+ align:start position:0%
+exactly what is going on in a p
+injunction Define parameters that
+
+ align:start position:0%
+injunction Define parameters that
+ 
+
+ align:start position:0%
+injunction Define parameters that
+determine solar cell efficiency so now
+
+ align:start position:0%
+determine solar cell efficiency so now
+ 
+
+ align:start position:0%
+determine solar cell efficiency so now
+we have a qualitative sense about where
+
+ align:start position:0%
+we have a qualitative sense about where
+ 
+
+ align:start position:0%
+we have a qualitative sense about where
+current is Flowing where electrons are
+
+ align:start position:0%
+current is Flowing where electrons are
+ 
+
+ align:start position:0%
+current is Flowing where electrons are
+moving around um what defines uh the
+
+ align:start position:0%
+moving around um what defines uh the
+ 
+
+ align:start position:0%
+moving around um what defines uh the
+power output how the power output is
+
+ align:start position:0%
+power output how the power output is
+ 
+
+ align:start position:0%
+power output how the power output is
+changing with illumination condition
+
+ align:start position:0%
+changing with illumination condition
+ 
+
+ align:start position:0%
+changing with illumination condition
+we're getting an intuitive sense of all
+
+ align:start position:0%
+we're getting an intuitive sense of all
+ 
+
+ align:start position:0%
+we're getting an intuitive sense of all
+of this let's start putting some discret
+
+ align:start position:0%
+of this let's start putting some discret
+ 
+
+ align:start position:0%
+of this let's start putting some discret
+variables to all of that um and there
+
+ align:start position:0%
+variables to all of that um and there
+ 
+
+ align:start position:0%
+variables to all of that um and there
+are a bunch of of of two-letter or
+
+ align:start position:0%
+are a bunch of of of two-letter or
+ 
+
+ align:start position:0%
+are a bunch of of of two-letter or
+three-letter acronyms with some
+
+ align:start position:0%
+three-letter acronyms with some
+ 
+
+ align:start position:0%
+three-letter acronyms with some
+subscripts here that uh we'll get to
+
+ align:start position:0%
+subscripts here that uh we'll get to
+ 
+
+ align:start position:0%
+subscripts here that uh we'll get to
+know uh we'll become very familiar with
+
+ align:start position:0%
+know uh we'll become very familiar with
+ 
+
+ align:start position:0%
+know uh we'll become very familiar with
+over the next few lectures so um How is
+
+ align:start position:0%
+over the next few lectures so um How is
+ 
+
+ align:start position:0%
+over the next few lectures so um How is
+solar cell conversion efficiency
+
+ align:start position:0%
+solar cell conversion efficiency
+ 
+
+ align:start position:0%
+solar cell conversion efficiency
+determinated determined from that
+
+ align:start position:0%
+determinated determined from that
+ 
+
+ align:start position:0%
+determinated determined from that
+illuminated IV curve that's our first
+
+ align:start position:0%
+illuminated IV curve that's our first
+ 
+
+ align:start position:0%
+illuminated IV curve that's our first
+question and um what I'm going to do is
+
+ align:start position:0%
+question and um what I'm going to do is
+ 
+
+ align:start position:0%
+question and um what I'm going to do is
+start with our uh solar cell IV curve
+
+ align:start position:0%
+start with our uh solar cell IV curve
+ 
+
+ align:start position:0%
+start with our uh solar cell IV curve
+right here this is just the fourth
+
+ align:start position:0%
+right here this is just the fourth
+ 
+
+ align:start position:0%
+right here this is just the fourth
+quadrant okay so notice the current
+
+ align:start position:0%
+quadrant okay so notice the current
+ 
+
+ align:start position:0%
+quadrant okay so notice the current
+starts at zero and goes to some negative
+
+ align:start position:0%
+starts at zero and goes to some negative
+ 
+
+ align:start position:0%
+starts at zero and goes to some negative
+values so we're looking in the fourth
+
+ align:start position:0%
+values so we're looking in the fourth
+ 
+
+ align:start position:0%
+values so we're looking in the fourth
+quadrant voltage is going from zero to
+
+ align:start position:0%
+quadrant voltage is going from zero to
+ 
+
+ align:start position:0%
+quadrant voltage is going from zero to
+positive value so again fourth quadrant
+
+ align:start position:0%
+positive value so again fourth quadrant
+ 
+
+ align:start position:0%
+positive value so again fourth quadrant
+we have our uh our ideal diode equation
+
+ align:start position:0%
+we have our uh our ideal diode equation
+ 
+
+ align:start position:0%
+we have our uh our ideal diode equation
+here and oh notice one thing I just
+
+ align:start position:0%
+here and oh notice one thing I just
+ 
+
+ align:start position:0%
+here and oh notice one thing I just
+changed I to J what just happened well I
+
+ align:start position:0%
+changed I to J what just happened well I
+ 
+
+ align:start position:0%
+changed I to J what just happened well I
+and J look very similar but uh they're
+
+ align:start position:0%
+and J look very similar but uh they're
+ 
+
+ align:start position:0%
+and J look very similar but uh they're
+in fact two different variables um most
+
+ align:start position:0%
+in fact two different variables um most
+ 
+
+ align:start position:0%
+in fact two different variables um most
+often PV research will report a current
+
+ align:start position:0%
+often PV research will report a current
+ 
+
+ align:start position:0%
+often PV research will report a current
+density in other words a current per
+
+ align:start position:0%
+density in other words a current per
+ 
+
+ align:start position:0%
+density in other words a current per
+unit area instead of the actual current
+
+ align:start position:0%
+unit area instead of the actual current
+ 
+
+ align:start position:0%
+unit area instead of the actual current
+coming out of the solar cell device so
+
+ align:start position:0%
+coming out of the solar cell device so
+ 
+
+ align:start position:0%
+coming out of the solar cell device so
+what you've been measuring here off of
+
+ align:start position:0%
+what you've been measuring here off of
+ 
+
+ align:start position:0%
+what you've been measuring here off of
+the off of the deck has been current
+
+ align:start position:0%
+the off of the deck has been current
+ 
+
+ align:start position:0%
+the off of the deck has been current
+total current output from that device
+
+ align:start position:0%
+total current output from that device
+ 
+
+ align:start position:0%
+total current output from that device
+and it might be a really tiny number and
+
+ align:start position:0%
+and it might be a really tiny number and
+ 
+
+ align:start position:0%
+and it might be a really tiny number and
+it might be difficult to compare against
+
+ align:start position:0%
+it might be difficult to compare against
+ 
+
+ align:start position:0%
+it might be difficult to compare against
+other size devices and so what solar
+
+ align:start position:0%
+other size devices and so what solar
+ 
+
+ align:start position:0%
+other size devices and so what solar
+cell researchers often do is they say
+
+ align:start position:0%
+cell researchers often do is they say
+ 
+
+ align:start position:0%
+cell researchers often do is they say
+okay let's normalize the current by the
+
+ align:start position:0%
+okay let's normalize the current by the
+ 
+
+ align:start position:0%
+okay let's normalize the current by the
+area to get a current density and we'll
+
+ align:start position:0%
+area to get a current density and we'll
+ 
+
+ align:start position:0%
+area to get a current density and we'll
+call current density J and we'll call
+
+ align:start position:0%
+call current density J and we'll call
+ 
+
+ align:start position:0%
+call current density J and we'll call
+current I right so if we're calculating
+
+ align:start position:0%
+current I right so if we're calculating
+ 
+
+ align:start position:0%
+current I right so if we're calculating
+power we'll have to use I I we have to
+
+ align:start position:0%
+power we'll have to use I I we have to
+ 
+
+ align:start position:0%
+power we'll have to use I I we have to
+multiply I * V but if we're just looking
+
+ align:start position:0%
+multiply I * V but if we're just looking
+ 
+
+ align:start position:0%
+multiply I * V but if we're just looking
+at uh one solar cell versus another uh
+
+ align:start position:0%
+at uh one solar cell versus another uh
+ 
+
+ align:start position:0%
+at uh one solar cell versus another uh
+we can use J as a very convenient way of
+
+ align:start position:0%
+we can use J as a very convenient way of
+ 
+
+ align:start position:0%
+we can use J as a very convenient way of
+comparing one solar cell versus another
+
+ align:start position:0%
+comparing one solar cell versus another
+ 
+
+ align:start position:0%
+comparing one solar cell versus another
+cool okay so um the illuminated AV curve
+
+ align:start position:0%
+cool okay so um the illuminated AV curve
+ 
+
+ align:start position:0%
+cool okay so um the illuminated AV curve
+looks something like this right it's in
+
+ align:start position:0%
+looks something like this right it's in
+ 
+
+ align:start position:0%
+looks something like this right it's in
+the fourth quadrant it goes out a
+
+ align:start position:0%
+the fourth quadrant it goes out a
+ 
+
+ align:start position:0%
+the fourth quadrant it goes out a
+certain amount then it curves up we just
+
+ align:start position:0%
+certain amount then it curves up we just
+ 
+
+ align:start position:0%
+certain amount then it curves up we just
+determined that uh here in class and
+
+ align:start position:0%
+determined that uh here in class and
+ 
+
+ align:start position:0%
+determined that uh here in class and
+that's essentially the ideal diet
+
+ align:start position:0%
+that's essentially the ideal diet
+ 
+
+ align:start position:0%
+that's essentially the ideal diet
+equation with a superposition term this
+
+ align:start position:0%
+equation with a superposition term this
+ 
+
+ align:start position:0%
+equation with a superposition term this
+J sub L right there so um let's parse
+
+ align:start position:0%
+J sub L right there so um let's parse
+ 
+
+ align:start position:0%
+J sub L right there so um let's parse
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+we have the Y intercept over here at the
+
+ align:start position:0%
+we have the Y intercept over here at the
+ 
+
+ align:start position:0%
+we have the Y intercept over here at the
+Y intercept there is maximum current
+
+ align:start position:0%
+Y intercept there is maximum current
+ 
+
+ align:start position:0%
+Y intercept there is maximum current
+flowing through the circuit but no power
+
+ align:start position:0%
+flowing through the circuit but no power
+ 
+
+ align:start position:0%
+flowing through the circuit but no power
+because voltage is equal to zero so
+
+ align:start position:0%
+because voltage is equal to zero so
+ 
+
+ align:start position:0%
+because voltage is equal to zero so
+remember the firmy energy is the same on
+
+ align:start position:0%
+remember the firmy energy is the same on
+ 
+
+ align:start position:0%
+remember the firmy energy is the same on
+either side the chemical potential is
+
+ align:start position:0%
+either side the chemical potential is
+ 
+
+ align:start position:0%
+either side the chemical potential is
+the same on either side of the device so
+
+ align:start position:0%
+the same on either side of the device so
+ 
+
+ align:start position:0%
+the same on either side of the device so
+there's no uh energy gain of the
+
+ align:start position:0%
+there's no uh energy gain of the
+ 
+
+ align:start position:0%
+there's no uh energy gain of the
+electron traveling through the external
+
+ align:start position:0%
+electron traveling through the external
+ 
+
+ align:start position:0%
+electron traveling through the external
+circuit but uh there's a maximum current
+
+ align:start position:0%
+circuit but uh there's a maximum current
+ 
+
+ align:start position:0%
+circuit but uh there's a maximum current
+uh and no power flowing through that
+
+ align:start position:0%
+uh and no power flowing through that
+ 
+
+ align:start position:0%
+uh and no power flowing through that
+external circuit because there's no
+
+ align:start position:0%
+external circuit because there's no
+ 
+
+ align:start position:0%
+external circuit because there's no
+potential to be dropped across the
+
+ align:start position:0%
+potential to be dropped across the
+ 
+
+ align:start position:0%
+potential to be dropped across the
+external resistor the opposite happens
+
+ align:start position:0%
+external resistor the opposite happens
+ 
+
+ align:start position:0%
+external resistor the opposite happens
+over here at this point called VOC which
+
+ align:start position:0%
+over here at this point called VOC which
+ 
+
+ align:start position:0%
+over here at this point called VOC which
+we'll call open circuit voltage the OC
+
+ align:start position:0%
+we'll call open circuit voltage the OC
+ 
+
+ align:start position:0%
+we'll call open circuit voltage the OC
+stands for open circuit V voltage open
+
+ align:start position:0%
+stands for open circuit V voltage open
+ 
+
+ align:start position:0%
+stands for open circuit V voltage open
+circuit voltage is just as you would
+
+ align:start position:0%
+circuit voltage is just as you would
+ 
+
+ align:start position:0%
+circuit voltage is just as you would
+think it is uh when your solar cell is
+
+ align:start position:0%
+think it is uh when your solar cell is
+ 
+
+ align:start position:0%
+think it is uh when your solar cell is
+in an open circuit when you say you took
+
+ align:start position:0%
+in an open circuit when you say you took
+ 
+
+ align:start position:0%
+in an open circuit when you say you took
+a SC pair of scissors please don't do
+
+ align:start position:0%
+a SC pair of scissors please don't do
+ 
+
+ align:start position:0%
+a SC pair of scissors please don't do
+this and cut the leads so that your
+
+ align:start position:0%
+this and cut the leads so that your
+ 
+
+ align:start position:0%
+this and cut the leads so that your
+solar cell wasn't uh uh outputting the
+
+ align:start position:0%
+solar cell wasn't uh uh outputting the
+ 
+
+ align:start position:0%
+solar cell wasn't uh uh outputting the
+current through an external load there
+
+ align:start position:0%
+current through an external load there
+ 
+
+ align:start position:0%
+current through an external load there
+would be a a bias voltage built up
+
+ align:start position:0%
+would be a a bias voltage built up
+ 
+
+ align:start position:0%
+would be a a bias voltage built up
+across the the P and the end side of the
+
+ align:start position:0%
+across the the P and the end side of the
+ 
+
+ align:start position:0%
+across the the P and the end side of the
+solar cell and it would be the maximum
+
+ align:start position:0%
+solar cell and it would be the maximum
+ 
+
+ align:start position:0%
+solar cell and it would be the maximum
+voltage that could be supported by that
+
+ align:start position:0%
+voltage that could be supported by that
+ 
+
+ align:start position:0%
+voltage that could be supported by that
+solar cell device under illumination
+
+ align:start position:0%
+solar cell device under illumination
+ 
+
+ align:start position:0%
+solar cell device under illumination
+conditions that's the open circuit
+
+ align:start position:0%
+conditions that's the open circuit
+ 
+
+ align:start position:0%
+conditions that's the open circuit
+voltage open circuit because there's no
+
+ align:start position:0%
+voltage open circuit because there's no
+ 
+
+ align:start position:0%
+voltage open circuit because there's no
+current again traveling through the
+
+ align:start position:0%
+current again traveling through the
+ 
+
+ align:start position:0%
+current again traveling through the
+external circuit that's why current is
+
+ align:start position:0%
+external circuit that's why current is
+ 
+
+ align:start position:0%
+external circuit that's why current is
+zero right open circuit and voltage um
+
+ align:start position:0%
+zero right open circuit and voltage um
+ 
+
+ align:start position:0%
+zero right open circuit and voltage um
+because this is well it's interesting
+
+ align:start position:0%
+because this is well it's interesting
+ 
+
+ align:start position:0%
+because this is well it's interesting
+point because it's the maximum voltage
+
+ align:start position:0%
+point because it's the maximum voltage
+ 
+
+ align:start position:0%
+point because it's the maximum voltage
+here uh represented in the fourth
+
+ align:start position:0%
+here uh represented in the fourth
+ 
+
+ align:start position:0%
+here uh represented in the fourth
+quadrant and somewhere in between uh the
+
+ align:start position:0%
+quadrant and somewhere in between uh the
+ 
+
+ align:start position:0%
+quadrant and somewhere in between uh the
+point of open circuit voltage and short
+
+ align:start position:0%
+point of open circuit voltage and short
+ 
+
+ align:start position:0%
+point of open circuit voltage and short
+circuit current short circuit current
+
+ align:start position:0%
+circuit current short circuit current
+ 
+
+ align:start position:0%
+circuit current short circuit current
+again because you're short circu in your
+
+ align:start position:0%
+again because you're short circu in your
+ 
+
+ align:start position:0%
+again because you're short circu in your
+device current is flowing through but
+
+ align:start position:0%
+device current is flowing through but
+ 
+
+ align:start position:0%
+device current is flowing through but
+there's no resistor there's no external
+
+ align:start position:0%
+there's no resistor there's no external
+ 
+
+ align:start position:0%
+there's no resistor there's no external
+load there's no power being deposited on
+
+ align:start position:0%
+load there's no power being deposited on
+ 
+
+ align:start position:0%
+load there's no power being deposited on
+external load somewhere between these
+
+ align:start position:0%
+external load somewhere between these
+ 
+
+ align:start position:0%
+external load somewhere between these
+two extreme conditions where there's no
+
+ align:start position:0%
+two extreme conditions where there's no
+ 
+
+ align:start position:0%
+two extreme conditions where there's no
+power flowing through the external
+
+ align:start position:0%
+power flowing through the external
+ 
+
+ align:start position:0%
+power flowing through the external
+circuit you have a maximum power point
+
+ align:start position:0%
+circuit you have a maximum power point
+ 
+
+ align:start position:0%
+circuit you have a maximum power point
+where there is a power being deposited
+
+ align:start position:0%
+where there is a power being deposited
+ 
+
+ align:start position:0%
+where there is a power being deposited
+across your external circuit and a lot
+
+ align:start position:0%
+across your external circuit and a lot
+ 
+
+ align:start position:0%
+across your external circuit and a lot
+of it right that's the maximum power
+
+ align:start position:0%
+of it right that's the maximum power
+ 
+
+ align:start position:0%
+of it right that's the maximum power
+point this is a point at which the solar
+
+ align:start position:0%
+point this is a point at which the solar
+ 
+
+ align:start position:0%
+point this is a point at which the solar
+cell is producing the maximum amount of
+
+ align:start position:0%
+cell is producing the maximum amount of
+ 
+
+ align:start position:0%
+cell is producing the maximum amount of
+power output and to represent that uh
+
+ align:start position:0%
+power output and to represent that uh
+ 
+
+ align:start position:0%
+power output and to represent that uh
+slightly differently what I've done so
+
+ align:start position:0%
+slightly differently what I've done so
+ 
+
+ align:start position:0%
+slightly differently what I've done so
+if I were to take current times voltage
+
+ align:start position:0%
+if I were to take current times voltage
+ 
+
+ align:start position:0%
+if I were to take current times voltage
+right here using fourth quadrant data my
+
+ align:start position:0%
+right here using fourth quadrant data my
+ 
+
+ align:start position:0%
+right here using fourth quadrant data my
+power would be a negative number why
+
+ align:start position:0%
+power would be a negative number why
+ 
+
+ align:start position:0%
+power would be a negative number why
+because vol is positive but current is a
+
+ align:start position:0%
+because vol is positive but current is a
+ 
+
+ align:start position:0%
+because vol is positive but current is a
+negative number right so I multiply a
+
+ align:start position:0%
+negative number right so I multiply a
+ 
+
+ align:start position:0%
+negative number right so I multiply a
+positive and negative number together
+
+ align:start position:0%
+positive and negative number together
+ 
+
+ align:start position:0%
+positive and negative number together
+get a negative number and that just
+
+ align:start position:0%
+get a negative number and that just
+ 
+
+ align:start position:0%
+get a negative number and that just
+sounds weird who talks about power
+
+ align:start position:0%
+sounds weird who talks about power
+ 
+
+ align:start position:0%
+sounds weird who talks about power
+outputs from solar cells being negative
+
+ align:start position:0%
+outputs from solar cells being negative
+ 
+
+ align:start position:0%
+outputs from solar cells being negative
+uh it almost sounds like power is going
+
+ align:start position:0%
+uh it almost sounds like power is going
+ 
+
+ align:start position:0%
+uh it almost sounds like power is going
+into the device so uh this is another
+
+ align:start position:0%
+into the device so uh this is another
+ 
+
+ align:start position:0%
+into the device so uh this is another
+convention that you're going to have to
+
+ align:start position:0%
+convention that you're going to have to
+ 
+
+ align:start position:0%
+convention that you're going to have to
+get used to is looking at the IV curve
+
+ align:start position:0%
+get used to is looking at the IV curve
+ 
+
+ align:start position:0%
+get used to is looking at the IV curve
+in the first quadrant so all we've done
+
+ align:start position:0%
+in the first quadrant so all we've done
+ 
+
+ align:start position:0%
+in the first quadrant so all we've done
+is taken the y- AIS and multiply by
+
+ align:start position:0%
+is taken the y- AIS and multiply by
+ 
+
+ align:start position:0%
+is taken the y- AIS and multiply by
+negative 1 so we flipped it up
+
+ align:start position:0%
+negative 1 so we flipped it up
+ 
+
+ align:start position:0%
+negative 1 so we flipped it up
+right so bear with me here it's it's
+
+ align:start position:0%
+right so bear with me here it's it's
+ 
+
+ align:start position:0%
+right so bear with me here it's it's
+it's a bit tricky to keep all this in
+
+ align:start position:0%
+it's a bit tricky to keep all this in
+ 
+
+ align:start position:0%
+it's a bit tricky to keep all this in
+your Ram but uh here's our short circuit
+
+ align:start position:0%
+your Ram but uh here's our short circuit
+ 
+
+ align:start position:0%
+your Ram but uh here's our short circuit
+current point now here's our open
+
+ align:start position:0%
+current point now here's our open
+ 
+
+ align:start position:0%
+current point now here's our open
+circuit voltage Point our IV curve now
+
+ align:start position:0%
+circuit voltage Point our IV curve now
+ 
+
+ align:start position:0%
+circuit voltage Point our IV curve now
+is pointed down before it was going up
+
+ align:start position:0%
+is pointed down before it was going up
+ 
+
+ align:start position:0%
+is pointed down before it was going up
+because we were in the fourth quadrant
+
+ align:start position:0%
+because we were in the fourth quadrant
+ 
+
+ align:start position:0%
+because we were in the fourth quadrant
+now we flipped essentially just done a
+
+ align:start position:0%
+now we flipped essentially just done a
+ 
+
+ align:start position:0%
+now we flipped essentially just done a
+we we've we've done a flip vertical if
+
+ align:start position:0%
+we we've we've done a flip vertical if
+ 
+
+ align:start position:0%
+we we've we've done a flip vertical if
+you will on our I curve and we have uh
+
+ align:start position:0%
+you will on our I curve and we have uh
+ 
+
+ align:start position:0%
+you will on our I curve and we have uh
+our Uh current increasing here going to
+
+ align:start position:0%
+our Uh current increasing here going to
+ 
+
+ align:start position:0%
+our Uh current increasing here going to
+higher Vias voltages now we can take the
+
+ align:start position:0%
+higher Vias voltages now we can take the
+ 
+
+ align:start position:0%
+higher Vias voltages now we can take the
+product of the voltage and the current
+
+ align:start position:0%
+product of the voltage and the current
+ 
+
+ align:start position:0%
+product of the voltage and the current
+to determine the power and we obtain a
+
+ align:start position:0%
+to determine the power and we obtain a
+ 
+
+ align:start position:0%
+to determine the power and we obtain a
+curve that looks very much like this
+
+ align:start position:0%
+curve that looks very much like this
+ 
+
+ align:start position:0%
+curve that looks very much like this
+blue curve right here that you can see
+
+ align:start position:0%
+blue curve right here that you can see
+ 
+
+ align:start position:0%
+blue curve right here that you can see
+and the maximum power point is truth in
+
+ align:start position:0%
+and the maximum power point is truth in
+ 
+
+ align:start position:0%
+and the maximum power point is truth in
+advertising it's act to maximum power
+
+ align:start position:0%
+advertising it's act to maximum power
+ 
+
+ align:start position:0%
+advertising it's act to maximum power
+it's where this blue curve reaches a
+
+ align:start position:0%
+it's where this blue curve reaches a
+ 
+
+ align:start position:0%
+it's where this blue curve reaches a
+maximum that is the maximum power point
+
+ align:start position:0%
+maximum that is the maximum power point
+ 
+
+ align:start position:0%
+maximum that is the maximum power point
+of the solar cell device that is where
+
+ align:start position:0%
+of the solar cell device that is where
+ 
+
+ align:start position:0%
+of the solar cell device that is where
+the solar cell is outputting the maximum
+
+ align:start position:0%
+the solar cell is outputting the maximum
+ 
+
+ align:start position:0%
+the solar cell is outputting the maximum
+amount of power and so at this maximum
+
+ align:start position:0%
+amount of power and so at this maximum
+ 
+
+ align:start position:0%
+amount of power and so at this maximum
+power point there is a voltage and a
+
+ align:start position:0%
+power point there is a voltage and a
+ 
+
+ align:start position:0%
+power point there is a voltage and a
+current associated with it that you can
+
+ align:start position:0%
+current associated with it that you can
+ 
+
+ align:start position:0%
+current associated with it that you can
+read right off the IV curve and this we
+
+ align:start position:0%
+read right off the IV curve and this we
+ 
+
+ align:start position:0%
+read right off the IV curve and this we
+call JMP or current density at the
+
+ align:start position:0%
+call JMP or current density at the
+ 
+
+ align:start position:0%
+call JMP or current density at the
+maximum power point and V MP which is
+
+ align:start position:0%
+maximum power point and V MP which is
+ 
+
+ align:start position:0%
+maximum power point and V MP which is
+the voltage at the maximum power
+
+ align:start position:0%
+the voltage at the maximum power
+ 
+
+ align:start position:0%
+the voltage at the maximum power
+point so so far we've learned uh
+
+ align:start position:0%
+point so so far we've learned uh
+ 
+
+ align:start position:0%
+point so so far we've learned uh
+essentially four variables here we have
+
+ align:start position:0%
+essentially four variables here we have
+ 
+
+ align:start position:0%
+essentially four variables here we have
+our JSC our VOC and our JMP and our VMP
+
+ align:start position:0%
+our JSC our VOC and our JMP and our VMP
+ 
+
+ align:start position:0%
+our JSC our VOC and our JMP and our VMP
+at that data point right
+
+ align:start position:0%
+at that data point right
+ 
+
+ align:start position:0%
+at that data point right
+there questions since I know you have
+
+ align:start position:0%
+there questions since I know you have
+ 
+
+ align:start position:0%
+there questions since I know you have
+them Ure that the device is working the
+
+ align:start position:0%
+them Ure that the device is working the
+ 
+
+ align:start position:0%
+them Ure that the device is working the
+maximum
+
+ align:start position:0%
+maximum
+ 
+
+ align:start position:0%
+maximum
+PowerPoint uh does an external voltage
+
+ align:start position:0%
+PowerPoint uh does an external voltage
+ 
+
+ align:start position:0%
+PowerPoint uh does an external voltage
+have to be applied to it so to to ensure
+
+ align:start position:0%
+have to be applied to it so to to ensure
+ 
+
+ align:start position:0%
+have to be applied to it so to to ensure
+that the solar cell device is operating
+
+ align:start position:0%
+that the solar cell device is operating
+ 
+
+ align:start position:0%
+that the solar cell device is operating
+right here um a couple of things need to
+
+ align:start position:0%
+right here um a couple of things need to
+ 
+
+ align:start position:0%
+right here um a couple of things need to
+happen you need to have the right
+
+ align:start position:0%
+happen you need to have the right
+ 
+
+ align:start position:0%
+happen you need to have the right
+illumination conditions and and you need
+
+ align:start position:0%
+illumination conditions and and you need
+ 
+
+ align:start position:0%
+illumination conditions and and you need
+to have the right load so the two need
+
+ align:start position:0%
+to have the right load so the two need
+ 
+
+ align:start position:0%
+to have the right load so the two need
+to be matched to each other absolutely
+
+ align:start position:0%
+to be matched to each other absolutely
+ 
+
+ align:start position:0%
+to be matched to each other absolutely
+and that's where some of the Power
+
+ align:start position:0%
+and that's where some of the Power
+ 
+
+ align:start position:0%
+and that's where some of the Power
+Electronics come into play yeah yeah
+
+ align:start position:0%
+Electronics come into play yeah yeah
+ 
+
+ align:start position:0%
+Electronics come into play yeah yeah
+last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem we assumed that output voltage
+
+ align:start position:0%
+problem we assumed that output voltage
+ 
+
+ align:start position:0%
+problem we assumed that output voltage
+would be B Gap 0.5 Vols yeah is that a
+
+ align:start position:0%
+would be B Gap 0.5 Vols yeah is that a
+ 
+
+ align:start position:0%
+would be B Gap 0.5 Vols yeah is that a
+general safe assumption for aign
+
+ align:start position:0%
+general safe assumption for aign
+ 
+
+ align:start position:0%
+general safe assumption for aign
+solar yeah so it's very interesting
+
+ align:start position:0%
+solar yeah so it's very interesting
+ 
+
+ align:start position:0%
+solar yeah so it's very interesting
+question um regarding the homework
+
+ align:start position:0%
+question um regarding the homework
+ 
+
+ align:start position:0%
+question um regarding the homework
+question I'm going to repeat it so that
+
+ align:start position:0%
+question I'm going to repeat it so that
+ 
+
+ align:start position:0%
+question I'm going to repeat it so that
+the microphone can hear it um the
+
+ align:start position:0%
+the microphone can hear it um the
+ 
+
+ align:start position:0%
+the microphone can hear it um the
+homework uh question the last the last
+
+ align:start position:0%
+homework uh question the last the last
+ 
+
+ align:start position:0%
+homework uh question the last the last
+uh homework there was one question that
+
+ align:start position:0%
+uh homework there was one question that
+ 
+
+ align:start position:0%
+uh homework there was one question that
+inquired uh assume that the voltage at
+
+ align:start position:0%
+inquired uh assume that the voltage at
+ 
+
+ align:start position:0%
+inquired uh assume that the voltage at
+the maximum power point is the band Gap
+
+ align:start position:0%
+the maximum power point is the band Gap
+ 
+
+ align:start position:0%
+the maximum power point is the band Gap
+uh voltage equivalent minus 0.5 volts
+
+ align:start position:0%
+uh voltage equivalent minus 0.5 volts
+ 
+
+ align:start position:0%
+uh voltage equivalent minus 0.5 volts
+and uh the rationale for that assumption
+
+ align:start position:0%
+and uh the rationale for that assumption
+ 
+
+ align:start position:0%
+and uh the rationale for that assumption
+is as follows the open circuit voltage
+
+ align:start position:0%
+is as follows the open circuit voltage
+ 
+
+ align:start position:0%
+is as follows the open circuit voltage
+this point is generally between 0.35 and
+
+ align:start position:0%
+this point is generally between 0.35 and
+ 
+
+ align:start position:0%
+this point is generally between 0.35 and
+0.4 volts minus the band gap or lower
+
+ align:start position:0%
+0.4 volts minus the band gap or lower
+ 
+
+ align:start position:0%
+0.4 volts minus the band gap or lower
+than the bang Gap so you have the bang
+
+ align:start position:0%
+than the bang Gap so you have the bang
+ 
+
+ align:start position:0%
+than the bang Gap so you have the bang
+Gap energy minus 0.4 volts and I can
+
+ align:start position:0%
+Gap energy minus 0.4 volts and I can
+ 
+
+ align:start position:0%
+Gap energy minus 0.4 volts and I can
+show you a very nice little paper that
+
+ align:start position:0%
+show you a very nice little paper that
+ 
+
+ align:start position:0%
+show you a very nice little paper that
+describes why that is essentially has to
+
+ align:start position:0%
+describes why that is essentially has to
+ 
+
+ align:start position:0%
+describes why that is essentially has to
+do in part with the losses inside of the
+
+ align:start position:0%
+do in part with the losses inside of the
+ 
+
+ align:start position:0%
+do in part with the losses inside of the
+solar cell thermodynamic limits of
+
+ align:start position:0%
+solar cell thermodynamic limits of
+ 
+
+ align:start position:0%
+solar cell thermodynamic limits of
+conversion inside of the solar cell
+
+ align:start position:0%
+conversion inside of the solar cell
+ 
+
+ align:start position:0%
+conversion inside of the solar cell
+device then what we've done is we've
+
+ align:start position:0%
+device then what we've done is we've
+ 
+
+ align:start position:0%
+device then what we've done is we've
+done another another additional
+
+ align:start position:0%
+done another another additional
+ 
+
+ align:start position:0%
+done another another additional
+discounting from the vocc to the maximum
+
+ align:start position:0%
+discounting from the vocc to the maximum
+ 
+
+ align:start position:0%
+discounting from the vocc to the maximum
+PowerPoint which we've assumed is around
+
+ align:start position:0%
+PowerPoint which we've assumed is around
+ 
+
+ align:start position:0%
+PowerPoint which we've assumed is around
+0.1 maybe2 volts uh notice the shape of
+
+ align:start position:0%
+0.1 maybe2 volts uh notice the shape of
+ 
+
+ align:start position:0%
+0.1 maybe2 volts uh notice the shape of
+the IV curve right here the maximum
+
+ align:start position:0%
+the IV curve right here the maximum
+ 
+
+ align:start position:0%
+the IV curve right here the maximum
+PowerPoint is interesting because the
+
+ align:start position:0%
+PowerPoint is interesting because the
+ 
+
+ align:start position:0%
+PowerPoint is interesting because the
+voltage at the maximum power point is
+
+ align:start position:0%
+voltage at the maximum power point is
+ 
+
+ align:start position:0%
+voltage at the maximum power point is
+almost the vocc in a good device and the
+
+ align:start position:0%
+almost the vocc in a good device and the
+ 
+
+ align:start position:0%
+almost the vocc in a good device and the
+current at the maximum power point is
+
+ align:start position:0%
+current at the maximum power point is
+ 
+
+ align:start position:0%
+current at the maximum power point is
+almost JSC but not
+
+ align:start position:0%
+almost JSC but not
+ 
+
+ align:start position:0%
+almost JSC but not
+quite right so uh the discounting from
+
+ align:start position:0%
+quite right so uh the discounting from
+ 
+
+ align:start position:0%
+quite right so uh the discounting from
+the vocc to the maximum PowerPoint
+
+ align:start position:0%
+the vocc to the maximum PowerPoint
+ 
+
+ align:start position:0%
+the vocc to the maximum PowerPoint
+voltage is not that much as is the
+
+ align:start position:0%
+voltage is not that much as is the
+ 
+
+ align:start position:0%
+voltage is not that much as is the
+discounting from the short circuit
+
+ align:start position:0%
+discounting from the short circuit
+ 
+
+ align:start position:0%
+discounting from the short circuit
+current to the maximum power point in a
+
+ align:start position:0%
+current to the maximum power point in a
+ 
+
+ align:start position:0%
+current to the maximum power point in a
+good device in a bad device uh this
+
+ align:start position:0%
+good device in a bad device uh this
+ 
+
+ align:start position:0%
+good device in a bad device uh this
+maximum PowerPoint here could be dragged
+
+ align:start position:0%
+maximum PowerPoint here could be dragged
+ 
+
+ align:start position:0%
+maximum PowerPoint here could be dragged
+all the way down here you could have an
+
+ align:start position:0%
+all the way down here you could have an
+ 
+
+ align:start position:0%
+all the way down here you could have an
+IV curve that looked something more like
+
+ align:start position:0%
+IV curve that looked something more like
+ 
+
+ align:start position:0%
+IV curve that looked something more like
+this instead almost like a resistor at
+
+ align:start position:0%
+this instead almost like a resistor at
+ 
+
+ align:start position:0%
+this instead almost like a resistor at
+which point um the maximum power output
+
+ align:start position:0%
+which point um the maximum power output
+ 
+
+ align:start position:0%
+which point um the maximum power output
+would be a lot less a lot less than
+
+ align:start position:0%
+would be a lot less a lot less than
+ 
+
+ align:start position:0%
+would be a lot less a lot less than
+what's shown here in the blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve cool all right so let's uh
+
+ align:start position:0%
+curve cool all right so let's uh
+ 
+
+ align:start position:0%
+curve cool all right so let's uh
+continue moving on um the efficiency of
+
+ align:start position:0%
+continue moving on um the efficiency of
+ 
+
+ align:start position:0%
+continue moving on um the efficiency of
+the solar cell Ada uh this Greek letter
+
+ align:start position:0%
+the solar cell Ada uh this Greek letter
+ 
+
+ align:start position:0%
+the solar cell Ada uh this Greek letter
+Ada is our power out versus Power in our
+
+ align:start position:0%
+Ada is our power out versus Power in our
+ 
+
+ align:start position:0%
+Ada is our power out versus Power in our
+power in is the illumination intensity
+
+ align:start position:0%
+power in is the illumination intensity
+ 
+
+ align:start position:0%
+power in is the illumination intensity
+given in units of watts per meter squar
+
+ align:start position:0%
+given in units of watts per meter squar
+ 
+
+ align:start position:0%
+given in units of watts per meter squar
+so we calculated this in our very first
+
+ align:start position:0%
+so we calculated this in our very first
+ 
+
+ align:start position:0%
+so we calculated this in our very first
+homework assignment and realized that
+
+ align:start position:0%
+homework assignment and realized that
+ 
+
+ align:start position:0%
+homework assignment and realized that
+the am 1.5 spectrum is around 1,000
+
+ align:start position:0%
+the am 1.5 spectrum is around 1,000
+ 
+
+ align:start position:0%
+the am 1.5 spectrum is around 1,000
+watts per met squ so that's our input
+
+ align:start position:0%
+watts per met squ so that's our input
+ 
+
+ align:start position:0%
+watts per met squ so that's our input
+power right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here our output power is the voltage at
+
+ align:start position:0%
+here our output power is the voltage at
+ 
+
+ align:start position:0%
+here our output power is the voltage at
+the maximum power point times whoopsie
+
+ align:start position:0%
+the maximum power point times whoopsie
+ 
+
+ align:start position:0%
+the maximum power point times whoopsie
+times the current at the maximum power
+
+ align:start position:0%
+times the current at the maximum power
+ 
+
+ align:start position:0%
+times the current at the maximum power
+point not the current density the
+
+ align:start position:0%
+point not the current density the
+ 
+
+ align:start position:0%
+point not the current density the
+current at the maximum power point so
+
+ align:start position:0%
+current at the maximum power point so
+ 
+
+ align:start position:0%
+current at the maximum power point so
+take this current density and multiply
+
+ align:start position:0%
+take this current density and multiply
+ 
+
+ align:start position:0%
+take this current density and multiply
+by area that's effectively the the units
+
+ align:start position:0%
+by area that's effectively the the units
+ 
+
+ align:start position:0%
+by area that's effectively the the units
+work out better that way um so it would
+
+ align:start position:0%
+work out better that way um so it would
+ 
+
+ align:start position:0%
+work out better that way um so it would
+be either V * I at the maximum power
+
+ align:start position:0%
+be either V * I at the maximum power
+ 
+
+ align:start position:0%
+be either V * I at the maximum power
+point or V * J * the area at the area of
+
+ align:start position:0%
+point or V * J * the area at the area of
+ 
+
+ align:start position:0%
+point or V * J * the area at the area of
+the device the area of the solar cell at
+
+ align:start position:0%
+the device the area of the solar cell at
+ 
+
+ align:start position:0%
+the device the area of the solar cell at
+the maximum power point and that's the
+
+ align:start position:0%
+the maximum power point and that's the
+ 
+
+ align:start position:0%
+the maximum power point and that's the
+total power
+
+ align:start position:0%
+total power
+ 
+
+ align:start position:0%
+total power
+out actually yeah yeah so um as long as
+
+ align:start position:0%
+out actually yeah yeah so um as long as
+ 
+
+ align:start position:0%
+out actually yeah yeah so um as long as
+the units are are in units of watts per
+
+ align:start position:0%
+the units are are in units of watts per
+ 
+
+ align:start position:0%
+the units are are in units of watts per
+meter squared yeah down here if this is
+
+ align:start position:0%
+meter squared yeah down here if this is
+ 
+
+ align:start position:0%
+meter squared yeah down here if this is
+not total Watts but watts per meter
+
+ align:start position:0%
+not total Watts but watts per meter
+ 
+
+ align:start position:0%
+not total Watts but watts per meter
+squar you could still use current
+
+ align:start position:0%
+squar you could still use current
+ 
+
+ align:start position:0%
+squar you could still use current
+density um that would those units would
+
+ align:start position:0%
+density um that would those units would
+ 
+
+ align:start position:0%
+density um that would those units would
+still work out so be be very careful
+
+ align:start position:0%
+still work out so be be very careful
+ 
+
+ align:start position:0%
+still work out so be be very careful
+whether you use total uh Power in or
+
+ align:start position:0%
+whether you use total uh Power in or
+ 
+
+ align:start position:0%
+whether you use total uh Power in or
+normalized by unit area power right just
+
+ align:start position:0%
+normalized by unit area power right just
+ 
+
+ align:start position:0%
+normalized by unit area power right just
+keep track of your units don't do like
+
+ align:start position:0%
+keep track of your units don't do like
+ 
+
+ align:start position:0%
+keep track of your units don't do like
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+professor um okay so we have efficiency
+
+ align:start position:0%
+professor um okay so we have efficiency
+ 
+
+ align:start position:0%
+professor um okay so we have efficiency
+here as power out versus Power in the
+
+ align:start position:0%
+here as power out versus Power in the
+ 
+
+ align:start position:0%
+here as power out versus Power in the
+power out being the maximum PowerPoint
+
+ align:start position:0%
+power out being the maximum PowerPoint
+ 
+
+ align:start position:0%
+power out being the maximum PowerPoint
+power and the power in being the
+
+ align:start position:0%
+power and the power in being the
+ 
+
+ align:start position:0%
+power and the power in being the
+illumination from the Sun now we're
+
+ align:start position:0%
+illumination from the Sun now we're
+ 
+
+ align:start position:0%
+illumination from the Sun now we're
+really talking this is starting to get
+
+ align:start position:0%
+really talking this is starting to get
+ 
+
+ align:start position:0%
+really talking this is starting to get
+interesting because it's beginning to
+
+ align:start position:0%
+interesting because it's beginning to
+ 
+
+ align:start position:0%
+interesting because it's beginning to
+click pieces from lecture number two
+
+ align:start position:0%
+click pieces from lecture number two
+ 
+
+ align:start position:0%
+click pieces from lecture number two
+coming together with what we're seeing
+
+ align:start position:0%
+coming together with what we're seeing
+ 
+
+ align:start position:0%
+coming together with what we're seeing
+now so this is a solar cell output power
+
+ align:start position:0%
+now so this is a solar cell output power
+ 
+
+ align:start position:0%
+now so this is a solar cell output power
+at the maximum power point and sunlight
+
+ align:start position:0%
+at the maximum power point and sunlight
+ 
+
+ align:start position:0%
+at the maximum power point and sunlight
+coming in okay so what I'm going to do
+
+ align:start position:0%
+coming in okay so what I'm going to do
+ 
+
+ align:start position:0%
+coming in okay so what I'm going to do
+next is um I'm going to take this
+
+ align:start position:0%
+next is um I'm going to take this
+ 
+
+ align:start position:0%
+next is um I'm going to take this
+maximum PowerPoint I'm going to draw a
+
+ align:start position:0%
+maximum PowerPoint I'm going to draw a
+ 
+
+ align:start position:0%
+maximum PowerPoint I'm going to draw a
+box that ends that starts at the origin
+
+ align:start position:0%
+box that ends that starts at the origin
+ 
+
+ align:start position:0%
+box that ends that starts at the origin
+here and the other uh the other the
+
+ align:start position:0%
+here and the other uh the other the
+ 
+
+ align:start position:0%
+here and the other uh the other the
+opposite uh the kitty corner corner of
+
+ align:start position:0%
+opposite uh the kitty corner corner of
+ 
+
+ align:start position:0%
+opposite uh the kitty corner corner of
+my box is going to end at the maximum
+
+ align:start position:0%
+my box is going to end at the maximum
+ 
+
+ align:start position:0%
+my box is going to end at the maximum
+PowerPoint so I'll have some rectal
+
+ align:start position:0%
+PowerPoint so I'll have some rectal
+ 
+
+ align:start position:0%
+PowerPoint so I'll have some rectal
+linear shape that will comprise the
+
+ align:start position:0%
+linear shape that will comprise the
+ 
+
+ align:start position:0%
+linear shape that will comprise the
+maximum PowerPoint and0 0 the origin as
+
+ align:start position:0%
+maximum PowerPoint and0 0 the origin as
+ 
+
+ align:start position:0%
+maximum PowerPoint and0 0 the origin as
+two of its uh corners and that box looks
+
+ align:start position:0%
+two of its uh corners and that box looks
+ 
+
+ align:start position:0%
+two of its uh corners and that box looks
+like this blue one right here the area
+
+ align:start position:0%
+like this blue one right here the area
+ 
+
+ align:start position:0%
+like this blue one right here the area
+of that box is JMP time
+
+ align:start position:0%
+of that box is JMP time
+ 
+
+ align:start position:0%
+of that box is JMP time
+VMP okay and notice I have another box
+
+ align:start position:0%
+VMP okay and notice I have another box
+ 
+
+ align:start position:0%
+VMP okay and notice I have another box
+around here I have this uh clear box
+
+ align:start position:0%
+around here I have this uh clear box
+ 
+
+ align:start position:0%
+around here I have this uh clear box
+that starts uh at the VOC uh point and
+
+ align:start position:0%
+that starts uh at the VOC uh point and
+ 
+
+ align:start position:0%
+that starts uh at the VOC uh point and
+the JSC point and now I have have two
+
+ align:start position:0%
+the JSC point and now I have have two
+ 
+
+ align:start position:0%
+the JSC point and now I have have two
+rectilinear shapes this blue one and the
+
+ align:start position:0%
+rectilinear shapes this blue one and the
+ 
+
+ align:start position:0%
+rectilinear shapes this blue one and the
+clear one right here the bigger one the
+
+ align:start position:0%
+clear one right here the bigger one the
+ 
+
+ align:start position:0%
+clear one right here the bigger one the
+bigger one has an area of JC time
+
+ align:start position:0%
+bigger one has an area of JC time
+ 
+
+ align:start position:0%
+bigger one has an area of JC time
+vo and I'm going to define a parameter
+
+ align:start position:0%
+vo and I'm going to define a parameter
+ 
+
+ align:start position:0%
+vo and I'm going to define a parameter
+called Phill factor which will be the
+
+ align:start position:0%
+called Phill factor which will be the
+ 
+
+ align:start position:0%
+called Phill factor which will be the
+ratio of these two areas the ratio of
+
+ align:start position:0%
+ratio of these two areas the ratio of
+ 
+
+ align:start position:0%
+ratio of these two areas the ratio of
+those two boxes the VMP * JMP divided by
+
+ align:start position:0%
+those two boxes the VMP * JMP divided by
+ 
+
+ align:start position:0%
+those two boxes the VMP * JMP divided by
+the VOC JSC if this is one which is
+
+ align:start position:0%
+the VOC JSC if this is one which is
+ 
+
+ align:start position:0%
+the VOC JSC if this is one which is
+virtually impossible to do but if this
+
+ align:start position:0%
+virtually impossible to do but if this
+ 
+
+ align:start position:0%
+virtually impossible to do but if this
+were one it would mean that these two
+
+ align:start position:0%
+were one it would mean that these two
+ 
+
+ align:start position:0%
+were one it would mean that these two
+boxes were the same size and the current
+
+ align:start position:0%
+boxes were the same size and the current
+ 
+
+ align:start position:0%
+boxes were the same size and the current
+and voltage at the maximum power points
+
+ align:start position:0%
+and voltage at the maximum power points
+ 
+
+ align:start position:0%
+and voltage at the maximum power points
+would be the current and voltage uh
+
+ align:start position:0%
+would be the current and voltage uh
+ 
+
+ align:start position:0%
+would be the current and voltage uh
+under short circuit and open circuit
+
+ align:start position:0%
+under short circuit and open circuit
+ 
+
+ align:start position:0%
+under short circuit and open circuit
+conditions respectively in real life the
+
+ align:start position:0%
+conditions respectively in real life the
+ 
+
+ align:start position:0%
+conditions respectively in real life the
+uh uh this blue box is smaller than the
+
+ align:start position:0%
+uh uh this blue box is smaller than the
+ 
+
+ align:start position:0%
+uh uh this blue box is smaller than the
+this clear box right over here and so uh
+
+ align:start position:0%
+this clear box right over here and so uh
+ 
+
+ align:start position:0%
+this clear box right over here and so uh
+the JMP VMP product is less than the JSC
+
+ align:start position:0%
+the JMP VMP product is less than the JSC
+ 
+
+ align:start position:0%
+the JMP VMP product is less than the JSC
+vocc product and by consequence as well
+
+ align:start position:0%
+vocc product and by consequence as well
+ 
+
+ align:start position:0%
+vocc product and by consequence as well
+the JMP is less than JSC v&p is less
+
+ align:start position:0%
+the JMP is less than JSC v&p is less
+ 
+
+ align:start position:0%
+the JMP is less than JSC v&p is less
+than uh V so the ratio of the two boxes
+
+ align:start position:0%
+than uh V so the ratio of the two boxes
+ 
+
+ align:start position:0%
+than uh V so the ratio of the two boxes
+is defined as the fill Factor The Fill
+
+ align:start position:0%
+is defined as the fill Factor The Fill
+ 
+
+ align:start position:0%
+is defined as the fill Factor The Fill
+Factor indicates the quality of your
+
+ align:start position:0%
+Factor indicates the quality of your
+ 
+
+ align:start position:0%
+Factor indicates the quality of your
+diode if your fill factor is very poor
+
+ align:start position:0%
+diode if your fill factor is very poor
+ 
+
+ align:start position:0%
+diode if your fill factor is very poor
+that means that that sun right over
+
+ align:start position:0%
+that means that that sun right over
+ 
+
+ align:start position:0%
+that means that that sun right over
+there denotes the maximum power point is
+
+ align:start position:0%
+there denotes the maximum power point is
+ 
+
+ align:start position:0%
+there denotes the maximum power point is
+being dragged toward the origin that
+
+ align:start position:0%
+being dragged toward the origin that
+ 
+
+ align:start position:0%
+being dragged toward the origin that
+means that the area of this blue box is
+
+ align:start position:0%
+means that the area of this blue box is
+ 
+
+ align:start position:0%
+means that the area of this blue box is
+growing smaller relative to the area of
+
+ align:start position:0%
+growing smaller relative to the area of
+ 
+
+ align:start position:0%
+growing smaller relative to the area of
+this clear box The Fill factor is going
+
+ align:start position:0%
+this clear box The Fill factor is going
+ 
+
+ align:start position:0%
+this clear box The Fill factor is going
+down that means you're filling less of
+
+ align:start position:0%
+down that means you're filling less of
+ 
+
+ align:start position:0%
+down that means you're filling less of
+this maximum square box function defined
+
+ align:start position:0%
+this maximum square box function defined
+ 
+
+ align:start position:0%
+this maximum square box function defined
+by vjc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh we have defined efficiency as
+
+ align:start position:0%
+okay so uh we have defined efficiency as
+ 
+
+ align:start position:0%
+okay so uh we have defined efficiency as
+uh Power out divided by power in power
+
+ align:start position:0%
+uh Power out divided by power in power
+ 
+
+ align:start position:0%
+uh Power out divided by power in power
+out being the current voltage product at
+
+ align:start position:0%
+out being the current voltage product at
+ 
+
+ align:start position:0%
+out being the current voltage product at
+the maximum power point divided by the
+
+ align:start position:0%
+the maximum power point divided by the
+ 
+
+ align:start position:0%
+the maximum power point divided by the
+solar instulation fill Factor being
+
+ align:start position:0%
+solar instulation fill Factor being
+ 
+
+ align:start position:0%
+solar instulation fill Factor being
+defined as the U ratio of VMP imp
+
+ align:start position:0%
+defined as the U ratio of VMP imp
+ 
+
+ align:start position:0%
+defined as the U ratio of VMP imp
+product divided by VOC uh ISC product uh
+
+ align:start position:0%
+product divided by VOC uh ISC product uh
+ 
+
+ align:start position:0%
+product divided by VOC uh ISC product uh
+notice that here I've written this in
+
+ align:start position:0%
+notice that here I've written this in
+ 
+
+ align:start position:0%
+notice that here I've written this in
+terms of total current here in terms of
+
+ align:start position:0%
+terms of total current here in terms of
+ 
+
+ align:start position:0%
+terms of total current here in terms of
+current density uh the area is
+
+ align:start position:0%
+current density uh the area is
+ 
+
+ align:start position:0%
+current density uh the area is
+essentially just cancel out because you
+
+ align:start position:0%
+essentially just cancel out because you
+ 
+
+ align:start position:0%
+essentially just cancel out because you
+have an area in the numerator and
+
+ align:start position:0%
+have an area in the numerator and
+ 
+
+ align:start position:0%
+have an area in the numerator and
+denominator they cancel these ratios
+
+ align:start position:0%
+denominator they cancel these ratios
+ 
+
+ align:start position:0%
+denominator they cancel these ratios
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+identical thus we obtain an expression
+
+ align:start position:0%
+identical thus we obtain an expression
+ 
+
+ align:start position:0%
+identical thus we obtain an expression
+for the efficiency in terms of fill
+
+ align:start position:0%
+for the efficiency in terms of fill
+ 
+
+ align:start position:0%
+for the efficiency in terms of fill
+Factor vo and ISC simply by using this
+
+ align:start position:0%
+Factor vo and ISC simply by using this
+ 
+
+ align:start position:0%
+Factor vo and ISC simply by using this
+fill factor definition right here what
+
+ align:start position:0%
+fill factor definition right here what
+ 
+
+ align:start position:0%
+fill factor definition right here what
+I've done is I've multiplied this side
+
+ align:start position:0%
+I've done is I've multiplied this side
+ 
+
+ align:start position:0%
+I've done is I've multiplied this side
+of the equation let's just focus right
+
+ align:start position:0%
+of the equation let's just focus right
+ 
+
+ align:start position:0%
+of the equation let's just focus right
+here where we have fil Factor equals VMP
+
+ align:start position:0%
+here where we have fil Factor equals VMP
+ 
+
+ align:start position:0%
+here where we have fil Factor equals VMP
+* / VC I I've moved the uh denominator
+
+ align:start position:0%
+* / VC I I've moved the uh denominator
+ 
+
+ align:start position:0%
+* / VC I I've moved the uh denominator
+up to the side over here multiplied it
+
+ align:start position:0%
+up to the side over here multiplied it
+ 
+
+ align:start position:0%
+up to the side over here multiplied it
+by fi factor and that's my
+
+ align:start position:0%
+by fi factor and that's my
+ 
+
+ align:start position:0%
+by fi factor and that's my
+now I go back to that top equation I say
+
+ align:start position:0%
+now I go back to that top equation I say
+ 
+
+ align:start position:0%
+now I go back to that top equation I say
+my VMP is now going to be substituted by
+
+ align:start position:0%
+my VMP is now going to be substituted by
+ 
+
+ align:start position:0%
+my VMP is now going to be substituted by
+a fill Factor time VOC * ISC and that's
+
+ align:start position:0%
+a fill Factor time VOC * ISC and that's
+ 
+
+ align:start position:0%
+a fill Factor time VOC * ISC and that's
+how I get to this equation right here
+
+ align:start position:0%
+how I get to this equation right here
+ 
+
+ align:start position:0%
+how I get to this equation right here
+why why do I go through the effort of
+
+ align:start position:0%
+why why do I go through the effort of
+ 
+
+ align:start position:0%
+why why do I go through the effort of
+this little numerical manipulation I do
+
+ align:start position:0%
+this little numerical manipulation I do
+ 
+
+ align:start position:0%
+this little numerical manipulation I do
+it because these parameters right here
+
+ align:start position:0%
+it because these parameters right here
+ 
+
+ align:start position:0%
+it because these parameters right here
+are fairly easy to measure using the
+
+ align:start position:0%
+are fairly easy to measure using the
+ 
+
+ align:start position:0%
+are fairly easy to measure using the
+solar simulator that you just put
+
+ align:start position:0%
+solar simulator that you just put
+ 
+
+ align:start position:0%
+solar simulator that you just put
+together right so I can measure the
+
+ align:start position:0%
+together right so I can measure the
+ 
+
+ align:start position:0%
+together right so I can measure the
+point at which uh my voltage is at open
+
+ align:start position:0%
+point at which uh my voltage is at open
+ 
+
+ align:start position:0%
+point at which uh my voltage is at open
+circuit condition I can measure the
+
+ align:start position:0%
+circuit condition I can measure the
+ 
+
+ align:start position:0%
+circuit condition I can measure the
+current uh at Short Circuit condition
+
+ align:start position:0%
+current uh at Short Circuit condition
+ 
+
+ align:start position:0%
+current uh at Short Circuit condition
+and simply by taking the ratio of those
+
+ align:start position:0%
+and simply by taking the ratio of those
+ 
+
+ align:start position:0%
+and simply by taking the ratio of those
+boxes I can determine what my fill
+
+ align:start position:0%
+boxes I can determine what my fill
+ 
+
+ align:start position:0%
+boxes I can determine what my fill
+factor is as well and these break down
+
+ align:start position:0%
+factor is as well and these break down
+ 
+
+ align:start position:0%
+factor is as well and these break down
+roughly into uh uh the the the the
+
+ align:start position:0%
+roughly into uh uh the the the the
+ 
+
+ align:start position:0%
+roughly into uh uh the the the the
+current is going to be a function
+
+ align:start position:0%
+current is going to be a function
+ 
+
+ align:start position:0%
+current is going to be a function
+roughly I again them really painting
+
+ align:start position:0%
+roughly I again them really painting
+ 
+
+ align:start position:0%
+roughly I again them really painting
+broad brush Strokes here the current is
+
+ align:start position:0%
+broad brush Strokes here the current is
+ 
+
+ align:start position:0%
+broad brush Strokes here the current is
+going to be roughly a function of
+
+ align:start position:0%
+going to be roughly a function of
+ 
+
+ align:start position:0%
+going to be roughly a function of
+Illumination condition and bulk material
+
+ align:start position:0%
+Illumination condition and bulk material
+ 
+
+ align:start position:0%
+Illumination condition and bulk material
+quality the VOC will be roughly a
+
+ align:start position:0%
+quality the VOC will be roughly a
+ 
+
+ align:start position:0%
+quality the VOC will be roughly a
+function of the interface the diode
+
+ align:start position:0%
+function of the interface the diode
+ 
+
+ align:start position:0%
+function of the interface the diode
+characteristics and the fill factor is
+
+ align:start position:0%
+characteristics and the fill factor is
+ 
+
+ align:start position:0%
+characteristics and the fill factor is
+going to be a function of the interface
+
+ align:start position:0%
+going to be a function of the interface
+ 
+
+ align:start position:0%
+going to be a function of the interface
+di characteristics but also of the
+
+ align:start position:0%
+di characteristics but also of the
+ 
+
+ align:start position:0%
+di characteristics but also of the
+resistances within the device and so
+
+ align:start position:0%
+resistances within the device and so
+ 
+
+ align:start position:0%
+resistances within the device and so
+from an engineering point of view we
+
+ align:start position:0%
+from an engineering point of view we
+ 
+
+ align:start position:0%
+from an engineering point of view we
+break the solar cell output down into
+
+ align:start position:0%
+break the solar cell output down into
+ 
+
+ align:start position:0%
+break the solar cell output down into
+these three parameters so that we can
+
+ align:start position:0%
+these three parameters so that we can
+ 
+
+ align:start position:0%
+these three parameters so that we can
+better understand uh what's going wrong
+
+ align:start position:0%
+better understand uh what's going wrong
+ 
+
+ align:start position:0%
+better understand uh what's going wrong
+with our solar cell if we have
+
+ align:start position:0%
+with our solar cell if we have
+ 
+
+ align:start position:0%
+with our solar cell if we have
+everything lumped in terms of VMP it
+
+ align:start position:0%
+everything lumped in terms of VMP it
+ 
+
+ align:start position:0%
+everything lumped in terms of VMP it
+becomes a little bit more obscure to
+
+ align:start position:0%
+becomes a little bit more obscure to
+ 
+
+ align:start position:0%
+becomes a little bit more obscure to
+figure out what exactly is going wrong
+
+ align:start position:0%
+figure out what exactly is going wrong
+ 
+
+ align:start position:0%
+figure out what exactly is going wrong
+with our solar cell device Ashley how do
+
+ align:start position:0%
+with our solar cell device Ashley how do
+ 
+
+ align:start position:0%
+with our solar cell device Ashley how do
+you I guess the fill Factor also an
+
+ align:start position:0%
+you I guess the fill Factor also an
+ 
+
+ align:start position:0%
+you I guess the fill Factor also an
+easily measurable parameter so the fill
+
+ align:start position:0%
+easily measurable parameter so the fill
+ 
+
+ align:start position:0%
+easily measurable parameter so the fill
+Factor you would measure essentially by
+
+ align:start position:0%
+Factor you would measure essentially by
+ 
+
+ align:start position:0%
+Factor you would measure essentially by
+uh doing the little analysis we just did
+
+ align:start position:0%
+uh doing the little analysis we just did
+ 
+
+ align:start position:0%
+uh doing the little analysis we just did
+right here yeah exactly so you'd have to
+
+ align:start position:0%
+right here yeah exactly so you'd have to
+ 
+
+ align:start position:0%
+right here yeah exactly so you'd have to
+do a voltage current sweep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm coolness okay so we have um an
+
+ align:start position:0%
+mhm coolness okay so we have um an
+ 
+
+ align:start position:0%
+mhm coolness okay so we have um an
+expression for efficiency in terms of
+
+ align:start position:0%
+expression for efficiency in terms of
+ 
+
+ align:start position:0%
+expression for efficiency in terms of
+fill Factor VOC ISC and uh our incoming
+
+ align:start position:0%
+fill Factor VOC ISC and uh our incoming
+ 
+
+ align:start position:0%
+fill Factor VOC ISC and uh our incoming
+uh Power so power out this right here
+
+ align:start position:0%
+uh Power so power out this right here
+ 
+
+ align:start position:0%
+uh Power so power out this right here
+again is power out divid by power
+
+ align:start position:0%
+again is power out divid by power
+ 
+
+ align:start position:0%
+again is power out divid by power
+in why does efficiency matter why why do
+
+ align:start position:0%
+in why does efficiency matter why why do
+ 
+
+ align:start position:0%
+in why does efficiency matter why why do
+we why do we care so much about
+
+ align:start position:0%
+we why do we care so much about
+ 
+
+ align:start position:0%
+we why do we care so much about
+efficiency well um the conversion
+
+ align:start position:0%
+efficiency well um the conversion
+ 
+
+ align:start position:0%
+efficiency well um the conversion
+efficiency determines the area of solar
+
+ align:start position:0%
+efficiency determines the area of solar
+ 
+
+ align:start position:0%
+efficiency determines the area of solar
+cells needed to produce a certain Peak
+
+ align:start position:0%
+cells needed to produce a certain Peak
+ 
+
+ align:start position:0%
+cells needed to produce a certain Peak
+power or to think of it differently the
+
+ align:start position:0%
+power or to think of it differently the
+ 
+
+ align:start position:0%
+power or to think of it differently the
+area of solar panels that is necessary
+
+ align:start position:0%
+area of solar panels that is necessary
+ 
+
+ align:start position:0%
+area of solar panels that is necessary
+to produce a certain energy per unit
+
+ align:start position:0%
+to produce a certain energy per unit
+ 
+
+ align:start position:0%
+to produce a certain energy per unit
+time and uh many cost scale with area
+
+ align:start position:0%
+time and uh many cost scale with area
+ 
+
+ align:start position:0%
+time and uh many cost scale with area
+you have glass encapsulant the absorber
+
+ align:start position:0%
+you have glass encapsulant the absorber
+ 
+
+ align:start position:0%
+you have glass encapsulant the absorber
+materials within the solar cell devices
+
+ align:start position:0%
+materials within the solar cell devices
+ 
+
+ align:start position:0%
+materials within the solar cell devices
+themselves the metals that are used to
+
+ align:start position:0%
+themselves the metals that are used to
+ 
+
+ align:start position:0%
+themselves the metals that are used to
+make contacts uh the labor that's used
+
+ align:start position:0%
+make contacts uh the labor that's used
+ 
+
+ align:start position:0%
+make contacts uh the labor that's used
+to install the panels if you have larger
+
+ align:start position:0%
+to install the panels if you have larger
+ 
+
+ align:start position:0%
+to install the panels if you have larger
+panel area you need more labor to
+
+ align:start position:0%
+panel area you need more labor to
+ 
+
+ align:start position:0%
+panel area you need more labor to
+install it the aluminum and rack and
+
+ align:start position:0%
+install it the aluminum and rack and
+ 
+
+ align:start position:0%
+install it the aluminum and rack and
+framing materials that go into uh
+
+ align:start position:0%
+framing materials that go into uh
+ 
+
+ align:start position:0%
+framing materials that go into uh
+holding the panels up in the field uh
+
+ align:start position:0%
+holding the panels up in the field uh
+ 
+
+ align:start position:0%
+holding the panels up in the field uh
+either on a roof or out in the field so
+
+ align:start position:0%
+either on a roof or out in the field so
+ 
+
+ align:start position:0%
+either on a roof or out in the field so
+um efficiency affects pretty much
+
+ align:start position:0%
+um efficiency affects pretty much
+ 
+
+ align:start position:0%
+um efficiency affects pretty much
+everything but the inverter and possibly
+
+ align:start position:0%
+everything but the inverter and possibly
+ 
+
+ align:start position:0%
+everything but the inverter and possibly
+some of the soft costs of the project
+
+ align:start position:0%
+some of the soft costs of the project
+ 
+
+ align:start position:0%
+some of the soft costs of the project
+that includes the architect and uh the
+
+ align:start position:0%
+that includes the architect and uh the
+ 
+
+ align:start position:0%
+that includes the architect and uh the
+people who you pay to handle the money
+
+ align:start position:0%
+people who you pay to handle the money
+ 
+
+ align:start position:0%
+people who you pay to handle the money
+um financing so uh the lawyers perhaps
+
+ align:start position:0%
+um financing so uh the lawyers perhaps
+ 
+
+ align:start position:0%
+um financing so uh the lawyers perhaps
+so pretty much all of uh all of the real
+
+ align:start position:0%
+so pretty much all of uh all of the real
+ 
+
+ align:start position:0%
+so pretty much all of uh all of the real
+material and labor costs are scaling
+
+ align:start position:0%
+material and labor costs are scaling
+ 
+
+ align:start position:0%
+material and labor costs are scaling
+with area uh and so efficiency
+
+ align:start position:0%
+with area uh and so efficiency
+ 
+
+ align:start position:0%
+with area uh and so efficiency
+determines that to a large degree and
+
+ align:start position:0%
+determines that to a large degree and
+ 
+
+ align:start position:0%
+determines that to a large degree and
+hence it's a highly leveraged way to the
+
+ align:start position:0%
+hence it's a highly leveraged way to the
+ 
+
+ align:start position:0%
+hence it's a highly leveraged way to the
+cost of solar energy if you do a
+
+ align:start position:0%
+cost of solar energy if you do a
+ 
+
+ align:start position:0%
+cost of solar energy if you do a
+sensitivity analysis which you will do
+
+ align:start position:0%
+sensitivity analysis which you will do
+ 
+
+ align:start position:0%
+sensitivity analysis which you will do
+in the second and third parts of the
+
+ align:start position:0%
+in the second and third parts of the
+ 
+
+ align:start position:0%
+in the second and third parts of the
+class and look at the cost of solar and
+
+ align:start position:0%
+class and look at the cost of solar and
+ 
+
+ align:start position:0%
+class and look at the cost of solar and
+how it scales with efficiency you'll see
+
+ align:start position:0%
+how it scales with efficiency you'll see
+ 
+
+ align:start position:0%
+how it scales with efficiency you'll see
+that efficiency is one of the
+
+ align:start position:0%
+that efficiency is one of the
+ 
+
+ align:start position:0%
+that efficiency is one of the
+determining factors for cost in a solar
+
+ align:start position:0%
+determining factors for cost in a solar
+ 
+
+ align:start position:0%
+determining factors for cost in a solar
+cell device and that's why we focus on
+
+ align:start position:0%
+cell device and that's why we focus on
+ 
+
+ align:start position:0%
+cell device and that's why we focus on
+it a lot to put into perspective if the
+
+ align:start position:0%
+it a lot to put into perspective if the
+ 
+
+ align:start position:0%
+it a lot to put into perspective if the
+efficiency up there is determined by the
+
+ align:start position:0%
+efficiency up there is determined by the
+ 
+
+ align:start position:0%
+efficiency up there is determined by the
+output power versus the input power if
+
+ align:start position:0%
+output power versus the input power if
+ 
+
+ align:start position:0%
+output power versus the input power if
+we had 100% conversion uh efficiency
+
+ align:start position:0%
+we had 100% conversion uh efficiency
+ 
+
+ align:start position:0%
+we had 100% conversion uh efficiency
+which is impossible to achieve
+
+ align:start position:0%
+which is impossible to achieve
+ 
+
+ align:start position:0%
+which is impossible to achieve
+thermodynamically impossible to achieve
+
+ align:start position:0%
+thermodynamically impossible to achieve
+ 
+
+ align:start position:0%
+thermodynamically impossible to achieve
+we would produce a certain amount of
+
+ align:start position:0%
+we would produce a certain amount of
+ 
+
+ align:start position:0%
+we would produce a certain amount of
+energy per unit time or certain amount
+
+ align:start position:0%
+energy per unit time or certain amount
+ 
+
+ align:start position:0%
+energy per unit time or certain amount
+of peak power with this panel right
+
+ align:start position:0%
+of peak power with this panel right
+ 
+
+ align:start position:0%
+of peak power with this panel right
+there say that's the size of our field
+
+ align:start position:0%
+there say that's the size of our field
+ 
+
+ align:start position:0%
+there say that's the size of our field
+installation if we had a 33% efficiency
+
+ align:start position:0%
+installation if we had a 33% efficiency
+ 
+
+ align:start position:0%
+installation if we had a 33% efficiency
+cell which is closer to space grade
+
+ align:start position:0%
+cell which is closer to space grade
+ 
+
+ align:start position:0%
+cell which is closer to space grade
+solar cells we'd need three times that
+
+ align:start position:0%
+solar cells we'd need three times that
+ 
+
+ align:start position:0%
+solar cells we'd need three times that
+area so three times the encapsulant
+
+ align:start position:0%
+area so three times the encapsulant
+ 
+
+ align:start position:0%
+area so three times the encapsulant
+three times the glass three times the
+
+ align:start position:0%
+three times the glass three times the
+ 
+
+ align:start position:0%
+three times the glass three times the
+labor to install it and if we had a
+
+ align:start position:0%
+labor to install it and if we had a
+ 
+
+ align:start position:0%
+labor to install it and if we had a
+20% efficiency say uh high-end but but
+
+ align:start position:0%
+20% efficiency say uh high-end but but
+ 
+
+ align:start position:0%
+20% efficiency say uh high-end but but
+still uh commercial uh solar module not
+
+ align:start position:0%
+still uh commercial uh solar module not
+ 
+
+ align:start position:0%
+still uh commercial uh solar module not
+something you'd need to get from NASA
+
+ align:start position:0%
+something you'd need to get from NASA
+ 
+
+ align:start position:0%
+something you'd need to get from NASA
+but something that you could uh buy uh
+
+ align:start position:0%
+but something that you could uh buy uh
+ 
+
+ align:start position:0%
+but something that you could uh buy uh
+from a a supplier you would need five
+
+ align:start position:0%
+from a a supplier you would need five
+ 
+
+ align:start position:0%
+from a a supplier you would need five
+times that area whereas if you had a 10%
+
+ align:start position:0%
+times that area whereas if you had a 10%
+ 
+
+ align:start position:0%
+times that area whereas if you had a 10%
+efficiency module which is more
+
+ align:start position:0%
+efficiency module which is more
+ 
+
+ align:start position:0%
+efficiency module which is more
+approaching the area of some relatively
+
+ align:start position:0%
+approaching the area of some relatively
+ 
+
+ align:start position:0%
+approaching the area of some relatively
+inexpensive uh solar cells you would
+
+ align:start position:0%
+inexpensive uh solar cells you would
+ 
+
+ align:start position:0%
+inexpensive uh solar cells you would
+need 10 times that area so if you're
+
+ align:start position:0%
+need 10 times that area so if you're
+ 
+
+ align:start position:0%
+need 10 times that area so if you're
+doing a cost analysis this is why
+
+ align:start position:0%
+doing a cost analysis this is why
+ 
+
+ align:start position:0%
+doing a cost analysis this is why
+efficiency matters it might still be
+
+ align:start position:0%
+efficiency matters it might still be
+ 
+
+ align:start position:0%
+efficiency matters it might still be
+cheaper to use this instead of to use
+
+ align:start position:0%
+cheaper to use this instead of to use
+ 
+
+ align:start position:0%
+cheaper to use this instead of to use
+this over here might very well be more
+
+ align:start position:0%
+this over here might very well be more
+ 
+
+ align:start position:0%
+this over here might very well be more
+expensive when you do the math and
+
+ align:start position:0%
+expensive when you do the math and
+ 
+
+ align:start position:0%
+expensive when you do the math and
+figure out how much it cost to deposit
+
+ align:start position:0%
+figure out how much it cost to deposit
+ 
+
+ align:start position:0%
+figure out how much it cost to deposit
+those materials with a very low food
+
+ align:start position:0%
+those materials with a very low food
+ 
+
+ align:start position:0%
+those materials with a very low food
+foot deposition process and very high
+
+ align:start position:0%
+foot deposition process and very high
+ 
+
+ align:start position:0%
+foot deposition process and very high
+cost it might still be but it might not
+
+ align:start position:0%
+cost it might still be but it might not
+ 
+
+ align:start position:0%
+cost it might still be but it might not
+the material cost might end up whopping
+
+ align:start position:0%
+the material cost might end up whopping
+ 
+
+ align:start position:0%
+the material cost might end up whopping
+you and so a simple equation that
+
+ align:start position:0%
+you and so a simple equation that
+ 
+
+ align:start position:0%
+you and so a simple equation that
+calculates all these parameters in the
+
+ align:start position:0%
+calculates all these parameters in the
+ 
+
+ align:start position:0%
+calculates all these parameters in the
+material costs the module efficiency uh
+
+ align:start position:0%
+material costs the module efficiency uh
+ 
+
+ align:start position:0%
+material costs the module efficiency uh
+essentially the material and wafer costs
+
+ align:start position:0%
+essentially the material and wafer costs
+ 
+
+ align:start position:0%
+essentially the material and wafer costs
+are being calculated in dollars per
+
+ align:start position:0%
+are being calculated in dollars per
+ 
+
+ align:start position:0%
+are being calculated in dollars per
+meter squared they're saying how many
+
+ align:start position:0%
+meter squared they're saying how many
+ 
+
+ align:start position:0%
+meter squared they're saying how many
+dollars go into producing a meter
+
+ align:start position:0%
+dollars go into producing a meter
+ 
+
+ align:start position:0%
+dollars go into producing a meter
+squared of this material and the
+
+ align:start position:0%
+squared of this material and the
+ 
+
+ align:start position:0%
+squared of this material and the
+efficiency is over here and this is just
+
+ align:start position:0%
+efficiency is over here and this is just
+ 
+
+ align:start position:0%
+efficiency is over here and this is just
+a very simple uh uh back of the envelope
+
+ align:start position:0%
+a very simple uh uh back of the envelope
+ 
+
+ align:start position:0%
+a very simple uh uh back of the envelope
+calculation type of way of of of
+
+ align:start position:0%
+calculation type of way of of of
+ 
+
+ align:start position:0%
+calculation type of way of of of
+estimating the cost of a solar system so
+
+ align:start position:0%
+estimating the cost of a solar system so
+ 
+
+ align:start position:0%
+estimating the cost of a solar system so
+if you say okay I'm I'm willing to pay
+
+ align:start position:0%
+if you say okay I'm I'm willing to pay
+ 
+
+ align:start position:0%
+if you say okay I'm I'm willing to pay
+uh more for a higher efficiency cell
+
+ align:start position:0%
+uh more for a higher efficiency cell
+ 
+
+ align:start position:0%
+uh more for a higher efficiency cell
+because I'm using less area uh you can
+
+ align:start position:0%
+because I'm using less area uh you can
+ 
+
+ align:start position:0%
+because I'm using less area uh you can
+use this type of calculation uh to get
+
+ align:start position:0%
+use this type of calculation uh to get
+ 
+
+ align:start position:0%
+use this type of calculation uh to get
+to the the answer quickly it's not a
+
+ align:start position:0%
+to the the answer quickly it's not a
+ 
+
+ align:start position:0%
+to the the answer quickly it's not a
+levelized cost of electricity analysis
+
+ align:start position:0%
+levelized cost of electricity analysis
+ 
+
+ align:start position:0%
+levelized cost of electricity analysis
+it's not using discounted Capital flows
+
+ align:start position:0%
+it's not using discounted Capital flows
+ 
+
+ align:start position:0%
+it's not using discounted Capital flows
+and so forth which we'll get to later on
+
+ align:start position:0%
+and so forth which we'll get to later on
+ 
+
+ align:start position:0%
+and so forth which we'll get to later on
+in class this is a really backof the
+
+ align:start position:0%
+in class this is a really backof the
+ 
+
+ align:start position:0%
+in class this is a really backof the
+envelope engineering approach to
+
+ align:start position:0%
+envelope engineering approach to
+ 
+
+ align:start position:0%
+envelope engineering approach to
+estimating cost of a solar
+
+ align:start position:0%
+estimating cost of a solar
+ 
+
+ align:start position:0%
+estimating cost of a solar
+system um so I think this is a great
+
+ align:start position:0%
+system um so I think this is a great
+ 
+
+ align:start position:0%
+system um so I think this is a great
+place to stop uh and if anybody has a
+
+ align:start position:0%
+place to stop uh and if anybody has a
+ 
+
+ align:start position:0%
+place to stop uh and if anybody has a
+pitch concerning their project ideas
+
+ align:start position:0%
+pitch concerning their project ideas
+ 
+
+ align:start position:0%
+pitch concerning their project ideas
+class project ideas I'd like to invite
+
+ align:start position:0%
+class project ideas I'd like to invite
+ 
+
+ align:start position:0%
+class project ideas I'd like to invite
+them to the front now um the class
+
+ align:start position:0%
+them to the front now um the class
+ 
+
+ align:start position:0%
+them to the front now um the class
+project mind you is really the Capstone
+
+ align:start position:0%
+project mind you is really the Capstone
+ 
+
+ align:start position:0%
+project mind you is really the Capstone
+of this class 266 267 so if you have an
+
+ align:start position:0%
+of this class 266 267 so if you have an
+ 
+
+ align:start position:0%
+of this class 266 267 so if you have an
+idea a fun idea for a class project I'd
+
+ align:start position:0%
+idea a fun idea for a class project I'd
+ 
+
+ align:start position:0%
+idea a fun idea for a class project I'd
+invite you to give a pitch up here at
+
+ align:start position:0%
+invite you to give a pitch up here at
+ 
+
+ align:start position:0%
+invite you to give a pitch up here at
+the front of class or you're welcome to
+
+ align:start position:0%
+the front of class or you're welcome to
+ 
+
+ align:start position:0%
+the front of class or you're welcome to
+uh send on an email to the class ler
\ No newline at end of file
diff --git a/AfQxyVuLeCs.txt b/AfQxyVuLeCs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..880fa419eba32dae27cd4217c14914993f0c1cf7
--- /dev/null
+++ b/AfQxyVuLeCs.txt
@@ -0,0 +1,1985 @@
+So, one question to ask
+ourselves is,
+
+what is engineering?
+How do we define,
+
+what is engineering?
+Well, the definition I like to
+
+use is one put forth by Steve
+Senturia, one of our professors
+
+who is now retired.
+He defined engineering to be
+
+the purposeful use of science.
+All right, so what is 6.002
+
+about?
+So, 6.002 is a first course in
+
+engineering.
+And I like to view 6.002 as the
+
+gainful employment of Maxwell's
+equations.
+
+Many of you have seen Maxwell's
+equations before.
+
+Most of you should have.
+And they are hard stuff.
+
+6.002 is all about teaching you
+how to simplify our lives,
+
+make things simple.
+So, if you can gainfully employ
+
+Maxwell's equations,
+gainfully employ the facts of
+
+nature to build very interesting
+systems.
+
+So let me show you how the
+transition is made.
+
+So, there's a world around us,
+nature, so we made some
+
+observations in nature.
+We make measurements,
+
+and we can write down large
+tables of measurements.
+
+So, for example,
+we can take objects and measure
+
+the voltage across them,
+and look at the resulting
+
+current through the elements.
+So, we may end up getting a
+
+bunch of values such as
+[CHALKBOARD].
+
+So, we start out life with
+making measurements on what
+
+exists.
+And we build a bunch of tables.
+
+Now, we could directly take
+these tables,
+
+and based on observations of
+these tables,
+
+we could go ahead and build
+very interesting engineering
+
+systems that help us out in
+day-to-day lives.
+
+But that's incredibly hard.
+Imagine having to resort to a
+
+set of tables to do any kind of
+useful work.
+
+So what we do as engineers,
+we first layer a level of
+
+abstraction.
+We look at all the data,
+
+and somehow layer abstraction
+such that we can simplify or
+
+much more succinctly put in a
+simple equation or a simple
+
+statement what these numbers are
+telling us.
+
+OK, so for example,
+our physics laws,
+
+so laws of physics for example
+are simply abstractions,
+
+the laws of abstractions.
+So, these sets of numbers can
+
+be codified by Ohm's law,
+for example,
+
+V is equal to RI,
+the voltage current,
+
+relates to the resistance of
+the object.
+
+So, V is equal to RI is a law
+that succinctly describes a set
+
+of experiments,
+and replaces a large number of
+
+tables with a very simple
+statement.
+
+You could call this the law,
+or you could call it an
+
+abstraction.
+OK so you see laws of physics,
+
+call them abstractions of
+physics if you like.
+
+Similarly, there are Maxwell's
+equations and so on and so
+
+forth.
+So, this is what is.
+
+This is what's out there.
+OK, and a law as an abstraction
+
+describe the properties of
+nature, as we see it,
+
+in some succinct form.
+Now, if you want to go and
+
+build useful things,
+we could take these
+
+abstractions,
+take Maxwell's equations,
+
+and go and build things.
+But it's hard.
+
+It's really,
+really hard.
+
+And what you learn in,
+at MIT is this place is all
+
+about simplifying things.
+Take complicated things,
+
+build layers of abstraction,
+and simplify things so that we
+
+can build useful systems.
+Even in 6.002 we start life by
+
+making a huge leap from
+Maxwell's equations to a couple
+
+of very, very simple laws.
+OK, I'm going to show you that
+
+leap that we will make today.
+So, the first abstraction that
+
+we layer is called the lump
+circuit abstraction.
+
+OK, in the lump circuit
+abstraction, what we do is we
+
+make a set of simplifications
+that allows us to view a set of
+
+objects as discrete or lumped
+elements.
+
+So, we may, I will define
+voltage sources.
+
+We'll define resistors.
+We'll define capacitors,
+
+and so on.
+OK, and I'm going to make the
+
+jump, and show you how we make
+the jump in a few minutes.
+
+So, on that sort of
+abstraction, we then layer yet
+
+another abstract layer.
+And let me call that the
+
+amplifier abstraction.
+OK, remember,
+
+here we are absolutely down and
+dirty.
+
+We are setting the probes,
+measuring objects,
+
+and building huge tables.
+We abstracted things into
+
+simple laws, and life got a
+little better.
+
+OK, I'm going to show you can
+abstract things further out and
+
+build discrete objects,
+and, you could build even more
+
+interesting components called
+amplifiers and begin playing
+
+around with amplifiers.
+OK, so when you are using
+
+amplifiers, you don't really
+have to worry about the details
+
+of Maxwell's equations.
+OK, I'll give you some very
+
+simple abstract rules of
+behavior for an amplifier,
+
+and you can go build very
+interesting systems without
+
+really, really knowing how
+Maxwell's equations applies to
+
+that because you will be working
+at this abstract layer.
+
+However, since you're
+engineers, and you are good at
+
+building such systems,
+it's very important for you to
+
+understand how we make this leap
+from the laws of physics into
+
+some of our very primitive
+engineering abstractions.
+
+So, once we make the amplified
+abstraction in 6.002,
+
+by the way, 6.002 starts here.
+We start from the laws of
+
+physics and then proceed all the
+way out.
+
+So, once we talk about
+amplifiers we will take two
+
+pads.
+On the amplifier,
+
+you will build the next
+abstraction called the digital
+
+abstraction.
+OK, and with the digital
+
+abstraction, we will build new
+elements such as inverters and
+
+combinational gates,
+OK?
+
+So, notice we are building
+bigger, and bigger things,
+
+which have more and more
+complicated behavior inside
+
+them, but which are very simple
+to describe, right?
+
+So, following the digital
+abstraction, we will superimpose
+
+the combinational logic
+abstraction on top of that,
+
+and define functional blocks
+that look like this:
+
+some inputs,
+some function,
+
+some outputs.
+The next abstraction on top of
+
+that will be the clock digital
+abstraction, where we will have
+
+some notion of time introduced
+into the system.
+
+There will be a clock,
+and this will be some function.
+
+And there will be a clock that
+introduces time into the sort of
+
+logic values that functions
+operate upon.
+
+Following that,
+the next level of abstraction
+
+that we build is called
+instruction set abstraction.
+
+OK, now you begin to see things
+that consumers get to look at.
+
+Can someone give me an example
+of, or name an instruction set,
+
+or instruction set abstraction?
+Bingo.
+
+So, x86 is one set of
+abstractions.
+
+And in fact,
+in many universities,
+
+education could well start just
+by saying, OK,
+
+here's an abstraction.
+These are the x86 instructions,
+
+OK?
+Some MIT gurus have designed
+
+this awesome little
+microprocessor,
+
+OK?
+So you just worry about,
+
+you take this abstraction layer
+here, the assembly instructions,
+
+and you go and build systems on
+top of that.
+
+OK, so this is an abstraction
+layer called the x86 layer.
+
+There are other abstraction
+layers.
+
+In 6.004, you will learn about,
+I believe, the alpha or the
+
+beta, OK, and various other
+abstractions at this point.
+
+So, 6.002 kind of goes until
+here.
+
+6.002 takes me from the world
+of physics all the way to the
+
+world of interesting analog and
+digital systems.
+
+OK, 004, the course on
+computation structures,
+
+will show you how to build
+computers all the way from
+
+simple digital objects all the
+way to big systems.
+
+Following that,
+you learn about language
+
+abstractions,
+Java, C, and other languages,
+
+and that's in 6.002.
+And there are several other
+
+courses that will cover that.
+Following this,
+
+you learn about software system
+abstractions,
+
+and software systems,
+you will learn about operating
+
+systems.
+Any example of an operating
+
+system abstraction that people
+know out there?
+
+What's that?
+Linux.
+
+What else?
+I'm just wondering how long
+
+I'll have to go before I hear
+what I want to hear.
+
+[LAUGHTER] OK,
+so we have a bunch of software
+
+systems.
+So, if we have a bunch of
+
+software systems,
+these are nothing but
+
+abstractions.
+Linux simply implies a set of
+
+system calls that the programs
+must adhere to.
+
+Windows is another set of
+system calls.
+
+That's it.
+And see how much money they
+
+made out of it?
+OK, it's all about abstraction
+
+layers, that all start from
+nature.
+
+All right?
+Build abstraction upon
+
+abstraction upon abstraction
+upon abstraction,
+
+and someone out here are lots
+of dollars.
+
+OK, so based on these
+abstractions,
+
+we can then build useful things
+for human beings.
+
+We can build very useful
+things, video games,
+
+so we can send space shuttles
+up, and a whole bunch of other
+
+systems.
+But it's based on these
+
+abstraction layers.
+What's unique about education
+
+at MIT?
+What's unique about 6.002 and
+
+EECS?
+Is to my knowledge,
+
+there are not many other places
+in the world where you will get
+
+an education in everything going
+all the way from nature to how
+
+to build very complicated analog
+and digital systems.
+
+OK, we will show you layer upon
+layer upon layer upon layer,
+
+peel away the onion until you
+are down to raw nature,
+
+OK, through Maxwell's
+equations.
+
+So, 6.002, 004,
+this is 033,
+
+OK, 6.170, and so on.
+OK, the whole EECS is about
+
+building abstraction layers,
+one on top of the other.
+
+So that's one path.
+There's the analog path.
+
+The analog path would take an
+amplifier, and build an
+
+abstraction layer called the
+op-amp.
+
+See how similar they all look?
+You know the amplifier,
+
+the inverter of the digital
+world, and the operational
+
+amplifier in the analog world,
+just different ways of looking
+
+at the same devices.
+So, to build an analog system,
+
+to build an operational
+amplifier, and then,
+
+here we go end up building a
+whole bunch of different
+
+interesting analog system
+components.
+
+OK, and these components might
+look like oscillators.
+
+They might look like filters.
+OK, they look like power
+
+supplies, a whole bunch of very
+interesting abstract components,
+
+which pulled together can then
+give you the next set of
+
+systems.
+And these systems might be
+
+toasters, or say for example
+other analog systems like the
+
+various control systems for
+various power plants and so on
+
+and so forth,
+and ultimately,
+
+fun and dollars.
+OK, so 6.002 is about going
+
+from physics all the way to this
+point.
+
+We will build interesting
+analog systems,
+
+and take you up to interesting
+digital system components,
+
+from which 004 will take you
+all the way to building computer
+
+architectures.
+So that, in a nutshell,
+
+kind of gives you a feel for
+the space of EECS.
+
+OK, this chart here is almost a
+vignette of what EECS at MIT is
+
+all about.
+And this is the world according
+
+to Agarwal, because he's
+teaching 002.
+
+OK, so this is 6.002,
+and the rest of EECS is
+
+somewhere out there.
+OK, so I'm going to do now is
+
+throughout this course;
+I want you to think about which
+
+part in this vignette we are in.
+So, right now,
+
+I'm going to start here and
+take you here.
+
+OK, and as you get closer and
+closer, things get simpler,
+
+and simpler,
+and simpler.
+
+Still, the final abstractions
+are pedal, brake,
+
+steering wheel.
+I mean, that's the abstraction
+
+to play a game,
+right, four or five very simple
+
+interfaces, and that's all you
+need to know.
+
+And everybody in the world can
+play stuff.
+
+So remember,
+this stuff is complicated.
+
+This stuff is very,
+very simple.
+
+OK, and the more we build
+abstractions and come to this
+
+side, things get simpler and
+simpler.
+
+So, a large part of what I'll
+cover today is make the biggest
+
+simplification.
+The biggest simplification we
+
+will make his go from Maxwell's
+equation to some very,
+
+very simple algebraic rules.
+OK, I did Maxwell's equations
+
+myself.
+And I tell you,
+
+they were very interesting
+stuff but complicated.
+
+I can't imagine building
+efficient systems using
+
+Maxwell's equations.
+So, let's take an example,
+
+OK?
+So, let's say I have a battery.
+
+Just switch to page three of
+your course notes.
+
+And let's say I connect that to
+a bulb.
+
+OK, and this is a wire.
+And, the battery supplies some
+
+voltage, V, and I ask you a
+simple question.
+
+What is the current through the
+bulb?
+
+OK, so here is something that I
+can build using objects.
+
+I can pick a round from stores
+and so on.
+
+And I can collect them up in
+this way, and ask the question,
+
+what is the current,
+I?
+
+Now, if all you've done is
+learn about Maxwell's equations,
+
+you can roll up your sleeves
+and say, ah-ha!
+
+The first step is to write down
+all of Maxwell's equations,
+
+and you can say,
+del cross E is minus del and go
+
+on, and on, and on,
+OK, and write out all of
+
+Maxwell's equations and say,
+now how do I get from there to
+
+here?
+OK, it's very good.
+
+You can do it.
+OK, you can do it,
+
+but it's very complicated.
+OK, so instead,
+
+what you're going to do is take
+the easy way.
+
+So, what I want to remind you
+is that this course is actually
+
+very easy.
+OK remember,
+
+we're going to be building
+abstraction upon abstraction to
+
+make your lives easier.
+If you think your lives are
+
+getting more complicated,
+then you are not using
+
+intuition enough.
+OK, just remember the big I
+
+word.
+It's all about making things
+
+simple.
+OK, so let me give you an
+
+analogy.
+So, suppose you have an object.
+
+OK, and I apply a force to the
+object.
+
+It's an analogy,
+OK to get some insight into how
+
+to do this.
+So, I say here's an object.
+
+I apply a force,
+and I ask you the question.
+
+What is the acceleration of the
+object when I apply a force,
+
+F?
+So, how would you do it?
+
+OK, and eighth,
+or ninth, or tenth grader can
+
+do this.
+OK, they would ask me,
+
+what's the mass of the object?
+OK, I ask you what is the
+
+acceleration?
+You would turn around and ask
+
+me, what is the mass of the
+object?
+
+I tell you, the mass of the
+object is M.
+
+And then you say,
+oh sure, A is F divided by M,
+
+done.
+It's as simple as that.
+
+OK, I could have gone into all
+kinds of differential equations
+
+and so on to figure that out,
+but you asked me for the mass.
+
+And you gave me the answer,
+A is F divided by M.
+
+So, you ignored a bunch of
+things.
+
+You ignored the shape of the
+object.
+
+You ignored its color.
+You ignored its temperature.
+
+OK, and you ignored the soft or
+hard or whatever.
+
+OK, you ignored a whole bunch
+of things.
+
+You were focused on one thing.
+OK, you're focused on its mass.
+
+And, it turns out that the
+process really was developed
+
+from a set of simplifications.
+That is called,
+
+does anybody remember this?
+Point mass simplification.
+
+OK, so, in physics,
+you've done this before.
+
+OK, you've simplified your
+lives by viewing objects as
+
+having a mass at a point,
+and force is acting at that
+
+point.
+OK, M is that property of the
+
+object that is of interest to
+you.
+
+This process is called,
+in physics, point mass
+
+discretization.
+OK, now using an analogy,
+
+and I'm going to show you a
+similar simple process to do the
+
+problem with the light bulb.
+OK, so take my light bulb
+
+again,
+
+And I focus on the filament of
+the light bulb.
+
+OK, all I care about is the
+current flowing through the
+
+light bulb.
+OK, I don't care about whether
+
+the filament is twisted,
+whether it's hot.
+
+I don't care about its shape.
+I don't care about its color.
+
+All I care about is the
+current.
+
+OK, so to do that,
+what we can do here at a very
+
+high level is since we just need
+the current and don't care about
+
+a bunch of other properties,
+we will simply replace the bulb
+
+with a discrete object called a
+resistor.
+
+So the discrete object is a
+resistor, much like the point
+
+mass simplification that we did
+earlier that replaced the bulb
+
+filament with a object called a
+resistor, a discrete object
+
+called a resistor.
+Or a lump object called
+
+resister, and put a value next
+to it just like the mass for the
+
+object, a resistance value,
+R.
+
+OK, now what I can do is in the
+same manner, replace the battery
+
+with an object called a battery
+object, and connect that here,
+
+the voltage,
+V, applied to it.
+
+V falls across the resistor,
+and I get my I simply from
+
+Ohm's law as we divide by R.
+So, notice here,
+
+to replace this complicated
+bulb, this really twisty,
+
+weird old thing with this
+discreet thing called a
+
+resistor, and its only property
+of interest was its resistance
+
+value, R, direct analogy to what
+we did there.
+
+So, since R represents the only
+property of interest,
+
+we can simply ignore all the
+other things.
+
+So, notice here,
+we've done things the simple
+
+way.
+And remember,
+
+in EE, in the electrical
+engineering, we do things the
+
+simple way.
+OK, we could go the hard route
+
+and do Maxwell's equations,
+and get PhD's in physics,
+
+and so on.
+But out here,
+
+we are looking to do useful,
+interesting systems in the
+
+simplest way that we can.
+OK, we do things a simple way.
+
+All right, so we just did this,
+and boom, I found out what the
+
+current was.
+Now, I cheated a little bit.
+
+I've cheated a little bit.
+R is a lumped abstraction for
+
+the bulb.
+So, you look at this resistor
+
+here.
+That is simply a placeholder.
+
+It's a stand-in for this
+complicated thing called a bulb.
+
+It's a discreet object.
+It's a lumped object,
+
+and represents the bulb.
+Now, so most of 6.002 will take
+
+off from here,
+OK, and that's it.
+
+To very simple stuff,
+like V is equal to IR,
+
+it's a simple high school
+algebra to take off in that
+
+direction.
+But before we go there,
+
+it's important to understand,
+why was it that we were able to
+
+make the simplification?
+OK, we did something else.
+
+Something's going on under the
+covers here.
+
+On the one hand,
+I say let's use Maxwell's,
+
+and then I jump out and say,
+hey, we can just use this
+
+simple thing.
+I did something that allowed me
+
+to go from here to here.
+And you need to understand why
+
+I did that and how I did that.
+Understand it once,
+
+and then you won't have to need
+that information again.
+
+You just need to understand it.
+So, let's take a closer look at
+
+the bulb filament,
+and look at what we really did.
+
+So, here's my filament,
+A, and let's say that the
+
+surface area here,
+I label that SA,
+
+and the one down here SB,
+my voltage, V,
+
+applied there,
+and this is what I call my
+
+black box that I've replaced
+with a resistor.
+
+Notice that,
+in order for this to work,
+
+V and I need to be defined.
+So I needs to be defined,
+
+and V needs to be defined.
+OK, if I give you a random
+
+object, and I don't tell you
+anything else about the object,
+
+it's not clear I can do that.
+OK, if it's a much more general
+
+situation, I have to write down
+Maxwell's equations,
+
+and this is what I would write
+down.
+
+Write down J dot dS as a
+function of the coordinate here
+
+integrated over the area minus,
+OK, I would have to start from
+
+there from one of Maxwell's
+equations.
+
+All right, notice that this
+becomes IA, and this becomes IB
+
+in our simplification.
+But, if I don't tell you
+
+anything else,
+you have to start from here.
+
+You will have some varying
+current here by point.
+
+You might have some other
+current coming out here because
+
+I may have some charge buildup
+happening inside.
+
+If charge is building up inside
+the filament;
+
+then I would have to put del q
+by del t out here,
+
+right, the current in minus the
+current out must equal charge
+
+buildup.
+Whoa, where is this and where
+
+is that?
+So this is reality.
+
+This is really,
+really what I have to do.
+
+But how did I get there?
+How did I get there?
+
+The key answer is,
+as engineers,
+
+when in doubt we simplify.
+Remember, we are engineers.
+
+Our goal in life is to build
+interesting systems.
+
+OK and some are motivated by
+money.
+
+OK, so our goal is to build
+interesting systems and do good
+
+to humanity.
+So, as long as we can build a
+
+good light bulb,
+we are happy.
+
+So what we can do is we can
+say, look, all I care about is
+
+building interesting systems.
+So I can say,
+
+hey, this stuff is too hard.
+Let's make the assumption that
+
+all the systems that we will
+consider will have this thing be
+
+zero.
+OK, in other words,
+
+if I take a complete object,
+if I take an element like a
+
+resistor or a capacitor,
+the box around the entire
+
+element, OK, and I want to just
+deal with those systems in which
+
+this thing is zero.
+You can come and beat me up and
+
+say, but why?
+Why not?
+
+Why am I doing this?
+And I am saying the world is
+
+arbitrary.
+I'm an engineer;
+
+I want to build good systems.
+By making this simplification,
+
+I eliminate this squiggle
+thing, and so on.
+
+I don't want to deal with it.
+I want to make my life simple.
+
+So this is gone to zero
+because, why?
+
+Because I have said that in the
+future I will only deal with
+
+those elements for which this is
+true.
+
+I'm going to discipline myself.
+I'm going to discipline myself
+
+to only deal with those systems.
+OK, Maxwell is turning around
+
+and, you know,
+mad at me and all that stuff,
+
+but tough.
+So this, what I've said about
+
+making a simplification here,
+and this is one of the
+
+simplifications I'm making.
+And I give a name to the
+
+simplification.
+And that's called the lumped
+
+matter discipline.
+OK, so I'm saying I will only
+
+deal with elements for which if
+I put a black box around it,
+
+this is going to be true.
+And if this is going to be
+
+true, then notice,
+there is no charge buildup.
+
+Current in must equal current
+out.
+
+Ah-ha!
+So this becomes IA.
+
+This becomes IB.
+Yes.
+
+OK, I can now deal with IA's
+and IB's.
+
+And IB and IA are equal because
+this is zero.
+
+Notice that there is a whole
+bunch of depth here in the jump
+
+from here to here.
+As MIT graduates,
+
+you really, really need to
+understand why it is that we
+
+made that jump,
+and then go and use that,
+
+and do cool things.
+All right, this allows us to
+
+define I.
+We have a unique I associated
+
+with an element for the current
+through the element.
+
+We still have to worry about B,
+and I won't go through that in
+
+detail.
+The course notes have some
+
+discussion of that and so does
+the textbook.
+
+So V, AB is defined when del
+phi B, the rate of change of
+
+magnetic flux is zero.
+So, if I take the element and I
+
+take any region outside the
+element, this must be true.
+
+And you say,
+why should that be true?
+
+That's not true in general.
+Absolutely.
+
+It's not true in general.
+But I, because I choose to,
+
+I going to deal with only those
+elements.
+
+I will discipline myself.
+But these are only those
+
+elements for which this is true,
+and this is true.
+
+I'm going to limit my world.
+I'm going to create a play
+
+field for myself.
+You want to play;
+
+follow my rules.
+OK, and that's called the
+
+lumped matter discipline.
+So once you say that I'm going
+
+to adhere to the lump matter
+discipline, and this is true
+
+inside your elements.
+This is true outside the
+
+elements.
+You can define VA and VB,
+
+and good things happen to you.
+OK, let me show you a few
+
+examples of lumped elements.
+But remember,
+
+a large part of what we're
+doing is based on these two
+
+assumptions.
+And to just go through the
+
+background on that,
+I would encourage you to go to
+
+chapter 1 of your course notes
+and read through just as how
+
+this came about,
+that comes about.
+
+So, by doing that by adhering
+to a lumped matter discipline,
+
+we can now lump objects.
+We could lump a bulb into a
+
+resistor.
+OK, so to be clear,
+
+a certain number of lumped
+objects, and now,
+
+the universe is going to be
+comprised into lumped objects.
+
+OK, so before this,
+when he went home,
+
+we talked about eggs,
+and omelets,
+
+and light bulbs,
+and switches,
+
+but once you come to MIT,
+and after you've taken 6.002,
+
+you begin talking about lumped
+elements, you know,
+
+resistors, voltage sources,
+capacitors, little inky-dinky
+
+objects that follow the lumped
+matter discipline.
+
+OK, they stick to very simple
+rules, and the math that you
+
+have to do to analyze them is
+incredibly simple.
+
+What could be simpler than V is
+equal to IR?
+
+So, let me give you an example
+of interesting lumped elements,
+
+and then show you a couple of
+really nasty lumped elements.
+
+OK.
+
+OK, so what you see out here,
+so we characterize lumped
+
+elements by the VI
+characteristics.
+
+OK, you apply voltage,
+measure the current.
+
+OK, so what I can do is I can
+plot I here, and V here,
+
+and see what it looks like.
+OK, I can characterize elements
+
+by their VI relationship.
+And there are a bunch of
+
+elements that I can create based
+on the VI relationship.
+
+So let me show you a few
+examples.
+
+So for the resistor,
+since V is directly
+
+proportional to I,
+and R is a constant,
+
+I get a straight line.
+That's the I axis,
+
+the V axis, and this is the
+resistor.
+
+What I actually have is a
+variable resistor,
+
+so I'm going to change the
+resistance value,
+
+R, and the curve will also
+change slope.
+
+OK, I changed the value of R
+because it's a variable
+
+resistor, and the changes slope
+because my R is different.
+
+OK, next, let me go to a fixed
+resistor, and this guy here on
+
+the screen to your left is a
+fixed resistor.
+
+And you see that its IV
+characteristic is a line of a
+
+given slope, 1 by R,
+and that's it.
+
+I can't change it.
+Number three,
+
+I have another lumped element
+called a Zener diode that you
+
+will see in the fourth week of
+this class, and the
+
+characteristics for the Zener
+diode look like this:
+
+IV.
+If my voltage goes across the
+
+Zener diode goes up slightly,
+the current shoots up.
+
+But if the voltage becomes
+negative I don't have any
+
+current flowing into it until
+the voltage passes on the
+
+threshold, at which point my
+current begins to build up.
+
+OK, so I can increase the
+voltage a little bit,
+
+and it can show that the
+current starts building up
+
+again.
+So that's another interesting
+
+lumped element called a Zener
+diode.
+
+Let's switch to the next one
+called a diode.
+
+So a diode looks like this:
+IV.
+
+As the voltage across the diode
+becomes positive,
+
+around .6 volts,
+or thereabout,
+
+the current begins to shoot up.
+But when the voltage is below
+
+that threshold of .6,
+then my current is almost zero.
+
+It's another lumped element
+called a diode.
+
+And you will begin using these
+elements in your 002 lives to
+
+build interesting systems.
+The next example is a
+
+thermistor.
+A thermistor is a resistor
+
+whose resistance varies with
+temperature.
+
+OK, so this is a very expensive
+little hairdryer,
+
+and what I'm going to do is
+blow some hot air at my
+
+resistor, and you're going to
+see that its value is going to
+
+change depending on how much I
+heat it.
+
+So as it cools down,
+let me cool it down,
+
+so you can see it's coming
+down.
+
+I can zap it again.
+I could do this all day.
+
+This is so much fun.
+OK, so that's another
+
+interesting lumped element.
+As the temperature rises,
+
+its resistance changes.
+The next thing is called a
+
+photo resistor.
+It's a resistor.
+
+It used to be a resistor;
+Lorenzo?
+
+Oh OK, that's fine.
+So this is a photo resistor.
+
+And notice that it almost
+behaves like an open circuit.
+
+But what I'm going to do is
+shine some light on it.
+
+When I shine light on it,
+it begins to conduct and
+
+becomes a resistor of some
+value.
+
+There you go.
+OK, so that's a photo resistor.
+
+So now I'm going to show you a
+battery.
+
+Notice we did talk about
+batteries before.
+
+I'll show you a battery.
+So before you show a battery,
+
+just thinking your own minds,
+what should the IV
+
+characteristic of a battery look
+like?
+
+IV.
+A battery supplies a constant
+
+voltage.
+You know your little cell,
+
+the AA battery,
+1.5 volts?
+
+So, think of what the IV
+characteristic of a battery
+
+should look like for three
+seconds before it shows you.
+
+This is the one I showed,
+Lorenzo?.
+
+It's a straight line.
+This is a good battery.
+
+It's a straight,
+vertical line,
+
+but says that the voltage is
+1.5 volts, or thereabouts.
+
+No matter what current it
+supplies as an ideal voltage
+
+source, it has a fixed voltage,
+V, and no matter what the
+
+current going through is.
+Now, I'll show you a dud,
+
+a bad battery,
+and this is what the bad
+
+battery looks like.
+So, many of you have had your
+
+car batteries die on you.
+When you go to the store,
+
+they check your batteries.
+They use exactly this
+
+principle, that dead batteries
+have resistance.
+
+By the way, you see slopes
+here.
+
+You're thinking of resistance.
+OK, they can use this property
+
+to figure out that your battery
+is dead.
+
+So that's a dead battery.
+And finally,
+
+let me show you a bulb.
+We started with a bulb,
+
+and so I need to end,
+OK, we started with a bulb,
+
+so I need to end with a bulb.
+And what you will see is that a
+
+bulb simply behaves like a
+resistor.
+
+Its IV curve is going to look
+like this.
+
+OK, notice this is my bulb.
+And guess what,
+
+it behaves like a resistor.
+It's a very interesting kind of
+
+resistor, so I won't go into
+details for now.
+
+But notice its IV
+characteristic behaves like a
+
+resistor.
+OK, so those are some pretty
+
+standard lumped elements.
+You deal with a lot more sets
+
+of lumped elements,
+switches, MOSFETs,
+
+capacitors, inductors,
+a bunch of other fun stuff.
+
+But before we do that,
+what I wanted to tell you,
+
+don't go berserk on this
+abstraction binge.
+
+Too much of anything is bad for
+you.
+
+So what I'm going to show you
+is, abstractions or models are
+
+only valid provided you work
+within a set of constraints.
+
+Notice, we have already had
+this tacit handshake which said
+
+that we follow the discipline.
+Even after we follow the
+
+discipline, there are ranges to
+how well physical elements can
+
+behave like ideal lumped
+elements.
+
+OK, for example,
+what we will do is show you the
+
+resistor.
+And it's going to look like a
+
+resistor.
+And I'm going to keep
+
+increasing the voltage around
+it.
+
+OK, what's going to happen at
+some point?
+
+I just keep doing that.
+If it's an ideal element,
+
+if you're a theorist,
+you say, oh yeah,
+
+the curve will keep extending
+until I reach infinity.
+
+But this is a practical
+resistor, so people out here can
+
+cover your eyes or something.
+OK, so you're abstraction can't
+
+predict that.
+All it says is the current is
+
+an amp.
+It can't predict the heat,
+
+light, or the smell.
+In the laboratory,
+
+even, you get the smell.
+You know what somebody has just
+
+done.
+So that's one example of the
+
+lumped abstraction breaking
+down.
+
+So, if I really believe that my
+own BS, anything is a lumped
+
+element.
+So here's a pickle.
+
+A pickle is a lumped element.
+I can choose it as a lumped
+
+resistor.
+But this is a very interesting
+
+lumped resistor.
+Don't try this at home.
+
+This is a standard pickle into
+which you are pumping 110 V AC.
+
+I promise you,
+this is a standard pickle.
+
+So, it has a fixed resistance,
+but your lumped abstraction
+
+cannot predict the nice light
+and sound effect.
+
+OK, so the last two or three
+minutes what I want to do,
+
+so remember,
+don't get carried away by
+
+abstractions.
+There are limits.
+
+OK, you can't predict
+everything.
+
+OK, that's the smell of a
+pickle.
+
+OK, so let me give you a
+preview of some upcoming
+
+attractions, and show you one
+more quick simplification in the
+
+last few minutes.
+So what we can do,
+
+once we build these lumped
+elements, we can connect them in
+
+circuits.
+OK, so I can build a circuit,
+
+of the sort.
+So here's a voltage source with
+
+a bunch of resistors.
+I can connect them with wires
+
+and build a circuit of the sort.
+One interesting question we can
+
+ask ourselves is,
+under the lumped matter
+
+discipline, what can we say
+about the voltages?
+
+OK, if I go around the loop,
+provided my world adheres to
+
+the lumped matter discipline,
+what can I say about the
+
+voltages around this loop?
+Ah-ha, Maxwell again,
+
+right?
+So, I can write Maxwell's
+
+appropriate equation to solve
+that.
+
+OK, voltages have something to
+do with E and your integral of E
+
+dot dl and all of that stuff,
+right?
+
+So this is the appropriate
+Maxwell's equations to use.
+
+And I want to find out what
+happens here.
+
+Now remember,
+under LMD, I made the
+
+assumption.
+OK, my world,
+
+my playground,
+has del phi B by del t being
+
+zero.
+The rate of change of flux is
+
+zero.
+So, under these circumstances,
+
+I can write this.
+I can break up this line
+
+integral into three parts across
+the voltage source and across
+
+the two resistors and write that
+down.
+
+OK, and then when I can do,
+is now that the right-hand side
+
+is zero, I can simply take this.
+And I know that E dot dl across
+
+this element is simply VCA.
+This is VAB,
+
+and this is VBC equals zero.
+OK, so when I make the
+
+assumption that del phi B by del
+t is zero, and I go around this
+
+loop, apply Maxwell's equations,
+what do I find?
+
+I find that the sum of the
+voltages, VCA plus VAB plus VBC,
+
+is zero.
+That's fantastic.
+
+So now, I could say hasta la
+vista to this baby here.
+
+And I can focus on this guy and
+say, Maxwell's equations,
+
+this thing with squiggles and
+dels and all that stuff,
+
+can be simplified to the sum of
+the voltages across a set of
+
+elements in a loop in a circuit
+is zero.
+
+OK, and this is called
+Kirchhoff's first first law,
+
+KVL.
+OK, similarly,
+
+in recitation section,
+you'll see the application of
+
+Kirchhoff's current law,
+which comes from this be equal
+
+to zero, and all the currents
+coming into a node being zero.
+
+So, KVL and KCl directly come
+out of the lumped matter
+
+discipline.
+And you can use those to solve
+
+circuits like this.
\ No newline at end of file
diff --git a/AmOVEZRyryk.txt b/AmOVEZRyryk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7579564098ab08d920b93fe7876419624430ad35
--- /dev/null
+++ b/AmOVEZRyryk.txt
@@ -0,0 +1,115 @@
+align:start position:0%
+ 
+well I like to eat and cook and I like
+
+ align:start position:0%
+well I like to eat and cook and I like
+ 
+
+ align:start position:0%
+well I like to eat and cook and I like
+to learn different languages and I also
+
+ align:start position:0%
+to learn different languages and I also
+ 
+
+ align:start position:0%
+to learn different languages and I also
+noticed that the students were curious
+
+ align:start position:0%
+noticed that the students were curious
+ 
+
+ align:start position:0%
+noticed that the students were curious
+about my background my cultural
+
+ align:start position:0%
+about my background my cultural
+ 
+
+ align:start position:0%
+about my background my cultural
+background so I thought it would be nice
+
+ align:start position:0%
+background so I thought it would be nice
+ 
+
+ align:start position:0%
+background so I thought it would be nice
+to organize a seminar in which I could
+
+ align:start position:0%
+to organize a seminar in which I could
+ 
+
+ align:start position:0%
+to organize a seminar in which I could
+teach a little bit of Italian and then
+
+ align:start position:0%
+teach a little bit of Italian and then
+ 
+
+ align:start position:0%
+teach a little bit of Italian and then
+we just renovated the common kitchen so
+
+ align:start position:0%
+we just renovated the common kitchen so
+ 
+
+ align:start position:0%
+we just renovated the common kitchen so
+at tsg we also have this very nice big
+
+ align:start position:0%
+at tsg we also have this very nice big
+ 
+
+ align:start position:0%
+at tsg we also have this very nice big
+kitchen available for the whole
+
+ align:start position:0%
+kitchen available for the whole
+ 
+
+ align:start position:0%
+kitchen available for the whole
+community and I thought well maybe I can
+
+ align:start position:0%
+community and I thought well maybe I can
+ 
+
+ align:start position:0%
+community and I thought well maybe I can
+combine the two things and have a
+
+ align:start position:0%
+combine the two things and have a
+ 
+
+ align:start position:0%
+combine the two things and have a
+language course with the practice that's
+
+ align:start position:0%
+language course with the practice that's
+ 
+
+ align:start position:0%
+language course with the practice that's
+a with a real sort of immersion in the
+
+ align:start position:0%
+a with a real sort of immersion in the
+ 
+
+ align:start position:0%
+a with a real sort of immersion in the
+language and the culture
\ No newline at end of file
diff --git a/AqXOYgpbMBM.txt b/AqXOYgpbMBM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9dcd9ea75efd501cca26765b552f5dcf372058b7
--- /dev/null
+++ b/AqXOYgpbMBM.txt
@@ -0,0 +1,1107 @@
+align:start position:0%
+ 
+hi there welcome back to recitation in
+
+ align:start position:0%
+hi there welcome back to recitation in
+ 
+
+ align:start position:0%
+hi there welcome back to recitation in
+lecture you've been learning about when
+
+ align:start position:0%
+lecture you've been learning about when
+ 
+
+ align:start position:0%
+lecture you've been learning about when
+vectors are
+
+ align:start position:0%
+vectors are
+ 
+
+ align:start position:0%
+vectors are
+dependent when they span a space what a
+
+ align:start position:0%
+dependent when they span a space what a
+ 
+
+ align:start position:0%
+dependent when they span a space what a
+basis is what a dimension of a vector
+
+ align:start position:0%
+basis is what a dimension of a vector
+ 
+
+ align:start position:0%
+basis is what a dimension of a vector
+space is and the problem for today is
+
+ align:start position:0%
+space is and the problem for today is
+ 
+
+ align:start position:0%
+space is and the problem for today is
+exactly about that we have a vector
+
+ align:start position:0%
+exactly about that we have a vector
+ 
+
+ align:start position:0%
+exactly about that we have a vector
+space that is given it's spanned by
+
+ align:start position:0%
+space that is given it's spanned by
+ 
+
+ align:start position:0%
+space that is given it's spanned by
+these four vectors and we're asked to
+
+ align:start position:0%
+these four vectors and we're asked to
+ 
+
+ align:start position:0%
+these four vectors and we're asked to
+find the dimension of that vector space
+
+ align:start position:0%
+find the dimension of that vector space
+ 
+
+ align:start position:0%
+find the dimension of that vector space
+and the basis for it well why don't you
+
+ align:start position:0%
+and the basis for it well why don't you
+ 
+
+ align:start position:0%
+and the basis for it well why don't you
+hit pause on the video and work on it
+
+ align:start position:0%
+hit pause on the video and work on it
+ 
+
+ align:start position:0%
+hit pause on the video and work on it
+for a while and I'll come back in a
+
+ align:start position:0%
+for a while and I'll come back in a
+ 
+
+ align:start position:0%
+for a while and I'll come back in a
+little bit to help you out with it all
+
+ align:start position:0%
+little bit to help you out with it all
+ 
+
+ align:start position:0%
+little bit to help you out with it all
+right we're back let's work on it well
+
+ align:start position:0%
+right we're back let's work on it well
+ 
+
+ align:start position:0%
+right we're back let's work on it well
+so we need to find the dimension and the
+
+ align:start position:0%
+so we need to find the dimension and the
+ 
+
+ align:start position:0%
+so we need to find the dimension and the
+basis remember what the dimension is
+
+ align:start position:0%
+basis remember what the dimension is
+ 
+
+ align:start position:0%
+basis remember what the dimension is
+it's simply the number of vectors in a
+
+ align:start position:0%
+it's simply the number of vectors in a
+ 
+
+ align:start position:0%
+it's simply the number of vectors in a
+basis for the vector space so actually
+
+ align:start position:0%
+basis for the vector space so actually
+ 
+
+ align:start position:0%
+basis for the vector space so actually
+the problems is backwards we want to
+
+ align:start position:0%
+the problems is backwards we want to
+ 
+
+ align:start position:0%
+the problems is backwards we want to
+find the basis for the space first and
+
+ align:start position:0%
+find the basis for the space first and
+ 
+
+ align:start position:0%
+find the basis for the space first and
+then find the dimension all right all
+
+ align:start position:0%
+then find the dimension all right all
+ 
+
+ align:start position:0%
+then find the dimension all right all
+right first here and second here all
+
+ align:start position:0%
+right first here and second here all
+ 
+
+ align:start position:0%
+right first here and second here all
+right so we want to find a basis for the
+
+ align:start position:0%
+right so we want to find a basis for the
+ 
+
+ align:start position:0%
+right so we want to find a basis for the
+vector space spanned by these four
+
+ align:start position:0%
+vector space spanned by these four
+ 
+
+ align:start position:0%
+vector space spanned by these four
+vectors all right so you might be
+
+ align:start position:0%
+vectors all right so you might be
+ 
+
+ align:start position:0%
+vectors all right so you might be
+tempted to just say that a basis for
+
+ align:start position:0%
+tempted to just say that a basis for
+ 
+
+ align:start position:0%
+tempted to just say that a basis for
+this vector space is those four vectors
+
+ align:start position:0%
+this vector space is those four vectors
+ 
+
+ align:start position:0%
+this vector space is those four vectors
+because they span the vector space but
+
+ align:start position:0%
+because they span the vector space but
+ 
+
+ align:start position:0%
+because they span the vector space but
+there's another thing that a basis has
+
+ align:start position:0%
+there's another thing that a basis has
+ 
+
+ align:start position:0%
+there's another thing that a basis has
+to satisfy and it is the elements of the
+
+ align:start position:0%
+to satisfy and it is the elements of the
+ 
+
+ align:start position:0%
+to satisfy and it is the elements of the
+basis have to be linearly independent
+
+ align:start position:0%
+basis have to be linearly independent
+ 
+
+ align:start position:0%
+basis have to be linearly independent
+and we don't know that these are so we
+
+ align:start position:0%
+and we don't know that these are so we
+ 
+
+ align:start position:0%
+and we don't know that these are so we
+have to check how do we check that four
+
+ align:start position:0%
+have to check how do we check that four
+ 
+
+ align:start position:0%
+have to check how do we check that four
+vectors are linearly independent
+
+ align:start position:0%
+vectors are linearly independent
+ 
+
+ align:start position:0%
+vectors are linearly independent
+well there's a couple of different ways
+
+ align:start position:0%
+well there's a couple of different ways
+ 
+
+ align:start position:0%
+well there's a couple of different ways
+but here's what we're going to do we're
+
+ align:start position:0%
+but here's what we're going to do we're
+ 
+
+ align:start position:0%
+but here's what we're going to do we're
+going to put these vectors as rows of a
+
+ align:start position:0%
+going to put these vectors as rows of a
+ 
+
+ align:start position:0%
+going to put these vectors as rows of a
+matrix and then we'll do elimination and
+
+ align:start position:0%
+matrix and then we'll do elimination and
+ 
+
+ align:start position:0%
+matrix and then we'll do elimination and
+when we get to the end the rows that
+
+ align:start position:0%
+when we get to the end the rows that
+ 
+
+ align:start position:0%
+when we get to the end the rows that
+have pivots are the independent ones so
+
+ align:start position:0%
+have pivots are the independent ones so
+ 
+
+ align:start position:0%
+have pivots are the independent ones so
+let's do that
+
+ align:start position:0%
+let's do that
+ 
+
+ align:start position:0%
+let's do that
+1 1 s 2 0 minus 1 1 2 0 minus 4 1 0 1 3
+
+ align:start position:0%
+1 1 s 2 0 minus 1 1 2 0 minus 4 1 0 1 3
+ 
+
+ align:start position:0%
+1 1 s 2 0 minus 1 1 2 0 minus 4 1 0 1 3
+plus 3 2
+
+ align:start position:0%
+plus 3 2
+ 
+
+ align:start position:0%
+plus 3 2
+- 3 0 minus 2 0 all right by now you
+
+ align:start position:0%
+- 3 0 minus 2 0 all right by now you
+ 
+
+ align:start position:0%
+- 3 0 minus 2 0 all right by now you
+must have done elimination a million
+
+ align:start position:0%
+must have done elimination a million
+ 
+
+ align:start position:0%
+must have done elimination a million
+times so I'll go a little bit faster 1 X
+
+ align:start position:0%
+times so I'll go a little bit faster 1 X
+ 
+
+ align:start position:0%
+times so I'll go a little bit faster 1 X
+2 X 1 0 1 0 + 2 - 4 - this one's already
+
+ align:start position:0%
+2 X 1 0 1 0 + 2 - 4 - this one's already
+ 
+
+ align:start position:0%
+2 X 1 0 1 0 + 2 - 4 - this one's already
+done 1 3 - 3 - 2 - 2 3 - 2 0 + 4 - 2 & 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right one more step 1 1 - 2 0 - 1
+
+ align:start position:0%
+all right one more step 1 1 - 2 0 - 1
+ 
+
+ align:start position:0%
+all right one more step 1 1 - 2 0 - 1
+all these are done 0 1 2 x 4 2 0 1 minus
+
+ align:start position:0%
+all these are done 0 1 2 x 4 2 0 1 minus
+ 
+
+ align:start position:0%
+all these are done 0 1 2 x 4 2 0 1 minus
+1 is 0 3 minus 2 is 1 - 3 + 4 is 1 2
+
+ align:start position:0%
+1 is 0 3 minus 2 is 1 - 3 + 4 is 1 2
+ 
+
+ align:start position:0%
+1 is 0 3 minus 2 is 1 - 3 + 4 is 1 2
+minus 2 is 0 1 minus 1 is 0 - 2 again
+
+ align:start position:0%
+minus 2 is 0 1 minus 1 is 0 - 2 again
+ 
+
+ align:start position:0%
+minus 2 is 0 1 minus 1 is 0 - 2 again
+and 0 oh you can see where this is going
+
+ align:start position:0%
+and 0 oh you can see where this is going
+ 
+
+ align:start position:0%
+and 0 oh you can see where this is going
+in the next step this row is going to
+
+ align:start position:0%
+in the next step this row is going to
+ 
+
+ align:start position:0%
+in the next step this row is going to
+disappear 1 1 minus 2 0 minus 1 0 1 - 2
+
+ align:start position:0%
+disappear 1 1 minus 2 0 minus 1 0 1 - 2
+ 
+
+ align:start position:0%
+disappear 1 1 minus 2 0 minus 1 0 1 - 2
+0 0 1 1 0 0 0 0 0 0 all right we're done
+
+ align:start position:0%
+0 0 1 1 0 0 0 0 0 0 all right we're done
+ 
+
+ align:start position:0%
+0 0 1 1 0 0 0 0 0 0 all right we're done
+with elimination and so let's circle our
+
+ align:start position:0%
+with elimination and so let's circle our
+ 
+
+ align:start position:0%
+with elimination and so let's circle our
+pivots and here our pivots we have three
+
+ align:start position:0%
+pivots and here our pivots we have three
+ 
+
+ align:start position:0%
+pivots and here our pivots we have three
+pivots and so these three rows are
+
+ align:start position:0%
+pivots and so these three rows are
+ 
+
+ align:start position:0%
+pivots and so these three rows are
+linearly independent
+
+ align:start position:0%
+linearly independent
+ 
+
+ align:start position:0%
+linearly independent
+now and in fact these rows still span
+
+ align:start position:0%
+now and in fact these rows still span
+ 
+
+ align:start position:0%
+now and in fact these rows still span
+the same space that the initial four
+
+ align:start position:0%
+the same space that the initial four
+ 
+
+ align:start position:0%
+the same space that the initial four
+rows did because when you do elimination
+
+ align:start position:0%
+rows did because when you do elimination
+ 
+
+ align:start position:0%
+rows did because when you do elimination
+all that you're doing is recombining
+
+ align:start position:0%
+all that you're doing is recombining
+ 
+
+ align:start position:0%
+all that you're doing is recombining
+your rows while by doing linear
+
+ align:start position:0%
+your rows while by doing linear
+ 
+
+ align:start position:0%
+your rows while by doing linear
+combinations of them so for example your
+
+ align:start position:0%
+combinations of them so for example your
+ 
+
+ align:start position:0%
+combinations of them so for example your
+first rows stay the same throughout your
+
+ align:start position:0%
+first rows stay the same throughout your
+ 
+
+ align:start position:0%
+first rows stay the same throughout your
+second row was replaced by Row 2 minus
+
+ align:start position:0%
+second row was replaced by Row 2 minus
+ 
+
+ align:start position:0%
+second row was replaced by Row 2 minus
+Row 1 but it's really still spanning the
+
+ align:start position:0%
+Row 1 but it's really still spanning the
+ 
+
+ align:start position:0%
+Row 1 but it's really still spanning the
+same space and it goes on and then the
+
+ align:start position:0%
+same space and it goes on and then the
+ 
+
+ align:start position:0%
+same space and it goes on and then the
+fourth row it turns out was useless
+
+ align:start position:0%
+fourth row it turns out was useless
+ 
+
+ align:start position:0%
+fourth row it turns out was useless
+you only need to the first three so the
+
+ align:start position:0%
+you only need to the first three so the
+ 
+
+ align:start position:0%
+you only need to the first three so the
+elements for a basis well they will be
+
+ align:start position:0%
+elements for a basis well they will be
+ 
+
+ align:start position:0%
+elements for a basis well they will be
+these three let me write that basis 1 5
+
+ align:start position:0%
+these three let me write that basis 1 5
+ 
+
+ align:start position:0%
+these three let me write that basis 1 5
+minus 2 0 minus 1 4 2 0 0 1 1 0 could
+
+ align:start position:0%
+minus 2 0 minus 1 4 2 0 0 1 1 0 could
+ 
+
+ align:start position:0%
+minus 2 0 minus 1 4 2 0 0 1 1 0 could
+you have used the first three rows yes
+
+ align:start position:0%
+you have used the first three rows yes
+ 
+
+ align:start position:0%
+you have used the first three rows yes
+you could you can't always do that
+
+ align:start position:0%
+you could you can't always do that
+ 
+
+ align:start position:0%
+you could you can't always do that
+sometimes in elimination you have to
+
+ align:start position:0%
+sometimes in elimination you have to
+ 
+
+ align:start position:0%
+sometimes in elimination you have to
+switch rows because there's a zero where
+
+ align:start position:0%
+switch rows because there's a zero where
+ 
+
+ align:start position:0%
+switch rows because there's a zero where
+a pivot should be when that happens you
+
+ align:start position:0%
+a pivot should be when that happens you
+ 
+
+ align:start position:0%
+a pivot should be when that happens you
+have to use these three or you have to
+
+ align:start position:0%
+have to use these three or you have to
+ 
+
+ align:start position:0%
+have to use these three or you have to
+keep track of which row you switched to
+
+ align:start position:0%
+keep track of which row you switched to
+ 
+
+ align:start position:0%
+keep track of which row you switched to
+go back and use the initial ones but
+
+ align:start position:0%
+go back and use the initial ones but
+ 
+
+ align:start position:0%
+go back and use the initial ones but
+it's really safe to use these ones and
+
+ align:start position:0%
+it's really safe to use these ones and
+ 
+
+ align:start position:0%
+it's really safe to use these ones and
+also they're simpler than the ones that
+
+ align:start position:0%
+also they're simpler than the ones that
+ 
+
+ align:start position:0%
+also they're simpler than the ones that
+you started with so why not the other
+
+ align:start position:0%
+you started with so why not the other
+ 
+
+ align:start position:0%
+you started with so why not the other
+question that we had was what is the
+
+ align:start position:0%
+question that we had was what is the
+ 
+
+ align:start position:0%
+question that we had was what is the
+dimension of the vector space well this
+
+ align:start position:0%
+dimension of the vector space well this
+ 
+
+ align:start position:0%
+dimension of the vector space well this
+is the easy part the dimension of the
+
+ align:start position:0%
+is the easy part the dimension of the
+ 
+
+ align:start position:0%
+is the easy part the dimension of the
+vector space is 1 2 3 and that solves
+
+ align:start position:0%
+vector space is 1 2 3 and that solves
+ 
+
+ align:start position:0%
+vector space is 1 2 3 and that solves
+the problem but there's one more thing
+
+ align:start position:0%
+the problem but there's one more thing
+ 
+
+ align:start position:0%
+the problem but there's one more thing
+that I want to tell you I told you that
+
+ align:start position:0%
+that I want to tell you I told you that
+ 
+
+ align:start position:0%
+that I want to tell you I told you that
+there's a couple of ways to find out
+
+ align:start position:0%
+there's a couple of ways to find out
+ 
+
+ align:start position:0%
+there's a couple of ways to find out
+which of those four vectors are linearly
+
+ align:start position:0%
+which of those four vectors are linearly
+ 
+
+ align:start position:0%
+which of those four vectors are linearly
+independent and the one that I used was
+
+ align:start position:0%
+independent and the one that I used was
+ 
+
+ align:start position:0%
+independent and the one that I used was
+I put them in two rows and performed
+
+ align:start position:0%
+I put them in two rows and performed
+ 
+
+ align:start position:0%
+I put them in two rows and performed
+elimination and picked out the rows that
+
+ align:start position:0%
+elimination and picked out the rows that
+ 
+
+ align:start position:0%
+elimination and picked out the rows that
+have pivots on them another way to do it
+
+ align:start position:0%
+have pivots on them another way to do it
+ 
+
+ align:start position:0%
+have pivots on them another way to do it
+is to write the initial vectors as
+
+ align:start position:0%
+is to write the initial vectors as
+ 
+
+ align:start position:0%
+is to write the initial vectors as
+columns of the matrix and then perform
+
+ align:start position:0%
+columns of the matrix and then perform
+ 
+
+ align:start position:0%
+columns of the matrix and then perform
+elimination that also works and as you
+
+ align:start position:0%
+elimination that also works and as you
+ 
+
+ align:start position:0%
+elimination that also works and as you
+know because you're only working with
+
+ align:start position:0%
+know because you're only working with
+ 
+
+ align:start position:0%
+know because you're only working with
+the transpose of this matrix you can get
+
+ align:start position:0%
+the transpose of this matrix you can get
+ 
+
+ align:start position:0%
+the transpose of this matrix you can get
+the same number of pivots let's go over
+
+ align:start position:0%
+the same number of pivots let's go over
+ 
+
+ align:start position:0%
+the same number of pivots let's go over
+here where I have the same while the
+
+ align:start position:0%
+here where I have the same while the
+ 
+
+ align:start position:0%
+here where I have the same while the
+transpose of that matrix I have the same
+
+ align:start position:0%
+transpose of that matrix I have the same
+ 
+
+ align:start position:0%
+transpose of that matrix I have the same
+vectors but now written as columns my
+
+ align:start position:0%
+vectors but now written as columns my
+ 
+
+ align:start position:0%
+vectors but now written as columns my
+for initial vector is written as columns
+
+ align:start position:0%
+for initial vector is written as columns
+ 
+
+ align:start position:0%
+for initial vector is written as columns
+and here I have
+
+ align:start position:0%
+and here I have
+ 
+
+ align:start position:0%
+and here I have
+performed elimination and this is the
+
+ align:start position:0%
+performed elimination and this is the
+ 
+
+ align:start position:0%
+performed elimination and this is the
+final result let me circle the pivots
+
+ align:start position:0%
+final result let me circle the pivots
+ 
+
+ align:start position:0%
+final result let me circle the pivots
+again here they are three which is going
+
+ align:start position:0%
+again here they are three which is going
+ 
+
+ align:start position:0%
+again here they are three which is going
+to give me three independent three
+
+ align:start position:0%
+to give me three independent three
+ 
+
+ align:start position:0%
+to give me three independent three
+linearly independent vectors and hence
+
+ align:start position:0%
+linearly independent vectors and hence
+ 
+
+ align:start position:0%
+linearly independent vectors and hence
+three elements of the basis and hence
+
+ align:start position:0%
+three elements of the basis and hence
+ 
+
+ align:start position:0%
+three elements of the basis and hence
+dimension three for the vector space but
+
+ align:start position:0%
+dimension three for the vector space but
+ 
+
+ align:start position:0%
+dimension three for the vector space but
+I can no longer use these three these
+
+ align:start position:0%
+I can no longer use these three these
+ 
+
+ align:start position:0%
+I can no longer use these three these
+three columns as elements of the basis
+
+ align:start position:0%
+three columns as elements of the basis
+ 
+
+ align:start position:0%
+three columns as elements of the basis
+because when I did elimination I changed
+
+ align:start position:0%
+because when I did elimination I changed
+ 
+
+ align:start position:0%
+because when I did elimination I changed
+the column space so the column space of
+
+ align:start position:0%
+the column space so the column space of
+ 
+
+ align:start position:0%
+the column space so the column space of
+this vector of this matrix is not the
+
+ align:start position:0%
+this vector of this matrix is not the
+ 
+
+ align:start position:0%
+this vector of this matrix is not the
+same as the column space of the
+
+ align:start position:0%
+same as the column space of the
+ 
+
+ align:start position:0%
+same as the column space of the
+eliminated version so I cannot use these
+
+ align:start position:0%
+eliminated version so I cannot use these
+ 
+
+ align:start position:0%
+eliminated version so I cannot use these
+in fact if you look at them can probably
+
+ align:start position:0%
+in fact if you look at them can probably
+ 
+
+ align:start position:0%
+in fact if you look at them can probably
+understand that they're not going to
+
+ align:start position:0%
+understand that they're not going to
+ 
+
+ align:start position:0%
+understand that they're not going to
+span the same space as these because all
+
+ align:start position:0%
+span the same space as these because all
+ 
+
+ align:start position:0%
+span the same space as these because all
+that I have done here are zeros and I
+
+ align:start position:0%
+that I have done here are zeros and I
+ 
+
+ align:start position:0%
+that I have done here are zeros and I
+get a lot more than just zeros in the
+
+ align:start position:0%
+get a lot more than just zeros in the
+ 
+
+ align:start position:0%
+get a lot more than just zeros in the
+last two entries of the vectors so what
+
+ align:start position:0%
+last two entries of the vectors so what
+ 
+
+ align:start position:0%
+last two entries of the vectors so what
+I need to do is the pivots are in the
+
+ align:start position:0%
+I need to do is the pivots are in the
+ 
+
+ align:start position:0%
+I need to do is the pivots are in the
+first second and third columns I need to
+
+ align:start position:0%
+first second and third columns I need to
+ 
+
+ align:start position:0%
+first second and third columns I need to
+use these three columns as my basis I'll
+
+ align:start position:0%
+use these three columns as my basis I'll
+ 
+
+ align:start position:0%
+use these three columns as my basis I'll
+just write bases down here and that will
+
+ align:start position:0%
+just write bases down here and that will
+ 
+
+ align:start position:0%
+just write bases down here and that will
+work too so see I have produced two
+
+ align:start position:0%
+work too so see I have produced two
+ 
+
+ align:start position:0%
+work too so see I have produced two
+different basis for the same vector
+
+ align:start position:0%
+different basis for the same vector
+ 
+
+ align:start position:0%
+different basis for the same vector
+space which is totally fine you can pick
+
+ align:start position:0%
+space which is totally fine you can pick
+ 
+
+ align:start position:0%
+space which is totally fine you can pick
+the basis that you prefer all right
+
+ align:start position:0%
+the basis that you prefer all right
+ 
+
+ align:start position:0%
+the basis that you prefer all right
+we're done thank you
\ No newline at end of file
diff --git a/BGug_49cGYw.txt b/BGug_49cGYw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6592a23088176894f5aa3c50ede7e66f4872201e
--- /dev/null
+++ b/BGug_49cGYw.txt
@@ -0,0 +1,8923 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today I'd like to continue the
+
+ align:start position:0%
+hi today I'd like to continue the
+ 
+
+ align:start position:0%
+hi today I'd like to continue the
+discussion of root Locust techniques
+
+ align:start position:0%
+discussion of root Locust techniques
+ 
+
+ align:start position:0%
+discussion of root Locust techniques
+that we started in the last session as
+
+ align:start position:0%
+that we started in the last session as
+ 
+
+ align:start position:0%
+that we started in the last session as
+you recall root Locust is one of the two
+
+ align:start position:0%
+you recall root Locust is one of the two
+ 
+
+ align:start position:0%
+you recall root Locust is one of the two
+principal methods that we're going to
+
+ align:start position:0%
+principal methods that we're going to
+ 
+
+ align:start position:0%
+principal methods that we're going to
+use to evaluate the stability of
+
+ align:start position:0%
+use to evaluate the stability of
+ 
+
+ align:start position:0%
+use to evaluate the stability of
+feedback systems the advantage of this
+
+ align:start position:0%
+feedback systems the advantage of this
+ 
+
+ align:start position:0%
+feedback systems the advantage of this
+technique along with the second
+
+ align:start position:0%
+technique along with the second
+ 
+
+ align:start position:0%
+technique along with the second
+technique which we'll introduce later is
+
+ align:start position:0%
+technique which we'll introduce later is
+ 
+
+ align:start position:0%
+technique which we'll introduce later is
+that it gives us a way to start with
+
+ align:start position:0%
+that it gives us a way to start with
+ 
+
+ align:start position:0%
+that it gives us a way to start with
+readily identifi identifiable quantities
+
+ align:start position:0%
+readily identifi identifiable quantities
+ 
+
+ align:start position:0%
+readily identifi identifiable quantities
+in particular the loop transmission of
+
+ align:start position:0%
+in particular the loop transmission of
+ 
+
+ align:start position:0%
+in particular the loop transmission of
+the feedback system and by rather
+
+ align:start position:0%
+the feedback system and by rather
+ 
+
+ align:start position:0%
+the feedback system and by rather
+straightforward analytic manipulations
+
+ align:start position:0%
+straightforward analytic manipulations
+ 
+
+ align:start position:0%
+straightforward analytic manipulations
+determine the closed loop transfer
+
+ align:start position:0%
+determine the closed loop transfer
+ 
+
+ align:start position:0%
+determine the closed loop transfer
+function or at least the important
+
+ align:start position:0%
+function or at least the important
+ 
+
+ align:start position:0%
+function or at least the important
+features of the closed loop transfer
+
+ align:start position:0%
+features of the closed loop transfer
+ 
+
+ align:start position:0%
+features of the closed loop transfer
+function we also find out that in
+
+ align:start position:0%
+function we also find out that in
+ 
+
+ align:start position:0%
+function we also find out that in
+addition to getting a binary answer to
+
+ align:start position:0%
+addition to getting a binary answer to
+ 
+
+ align:start position:0%
+addition to getting a binary answer to
+the stability problem in other words are
+
+ align:start position:0%
+the stability problem in other words are
+ 
+
+ align:start position:0%
+the stability problem in other words are
+there any poles of the closed loop
+
+ align:start position:0%
+there any poles of the closed loop
+ 
+
+ align:start position:0%
+there any poles of the closed loop
+transfer function in the right half of
+
+ align:start position:0%
+transfer function in the right half of
+ 
+
+ align:start position:0%
+transfer function in the right half of
+the S
+
+ align:start position:0%
+the S
+ 
+
+ align:start position:0%
+the S
+plane we're also able to get a very good
+
+ align:start position:0%
+plane we're also able to get a very good
+ 
+
+ align:start position:0%
+plane we're also able to get a very good
+analog measure of relative stability in
+
+ align:start position:0%
+analog measure of relative stability in
+ 
+
+ align:start position:0%
+analog measure of relative stability in
+other words we can find out how close
+
+ align:start position:0%
+other words we can find out how close
+ 
+
+ align:start position:0%
+other words we can find out how close
+our system is to instability we can tell
+
+ align:start position:0%
+our system is to instability we can tell
+ 
+
+ align:start position:0%
+our system is to instability we can tell
+once we've determined that our system is
+
+ align:start position:0%
+once we've determined that our system is
+ 
+
+ align:start position:0%
+once we've determined that our system is
+stable what the damping ratio of the
+
+ align:start position:0%
+stable what the damping ratio of the
+ 
+
+ align:start position:0%
+stable what the damping ratio of the
+dominant closed loop pole pair is and in
+
+ align:start position:0%
+dominant closed loop pole pair is and in
+ 
+
+ align:start position:0%
+dominant closed loop pole pair is and in
+fact you can determine many other
+
+ align:start position:0%
+fact you can determine many other
+ 
+
+ align:start position:0%
+fact you can determine many other
+features of the Clos Loop response that
+
+ align:start position:0%
+features of the Clos Loop response that
+ 
+
+ align:start position:0%
+features of the Clos Loop response that
+we might be interested
+
+ align:start position:0%
+we might be interested
+ 
+
+ align:start position:0%
+we might be interested
+in if you recall last time we in fact
+
+ align:start position:0%
+in if you recall last time we in fact
+ 
+
+ align:start position:0%
+in if you recall last time we in fact
+looked at a root Locus diagram remember
+
+ align:start position:0%
+looked at a root Locus diagram remember
+ 
+
+ align:start position:0%
+looked at a root Locus diagram remember
+that we present the results of root
+
+ align:start position:0%
+that we present the results of root
+ 
+
+ align:start position:0%
+that we present the results of root
+Locus analysis in a root Locus
+
+ align:start position:0%
+Locus analysis in a root Locus
+ 
+
+ align:start position:0%
+Locus analysis in a root Locus
+diagram and we started with a
+
+ align:start position:0%
+diagram and we started with a
+ 
+
+ align:start position:0%
+diagram and we started with a
+particularly simple system in particular
+
+ align:start position:0%
+particularly simple system in particular
+ 
+
+ align:start position:0%
+particularly simple system in particular
+we started with a system that had two
+
+ align:start position:0%
+we started with a system that had two
+ 
+
+ align:start position:0%
+we started with a system that had two
+poles associated with the loop
+
+ align:start position:0%
+poles associated with the loop
+ 
+
+ align:start position:0%
+poles associated with the loop
+transmission and no zeros both of those
+
+ align:start position:0%
+transmission and no zeros both of those
+ 
+
+ align:start position:0%
+transmission and no zeros both of those
+poles were located on the negative real
+
+ align:start position:0%
+poles were located on the negative real
+ 
+
+ align:start position:0%
+poles were located on the negative real
+axis at Min -1 over to a and min-1 over
+
+ align:start position:0%
+axis at Min -1 over to a and min-1 over
+ 
+
+ align:start position:0%
+axis at Min -1 over to a and min-1 over
+to B we then went ahead
+
+ align:start position:0%
+to B we then went ahead
+ 
+
+ align:start position:0%
+to B we then went ahead
+and wrote an expression for the closed
+
+ align:start position:0%
+and wrote an expression for the closed
+ 
+
+ align:start position:0%
+and wrote an expression for the closed
+loop transfer function and focused our
+
+ align:start position:0%
+loop transfer function and focused our
+ 
+
+ align:start position:0%
+loop transfer function and focused our
+attention on the characteristic equation
+
+ align:start position:0%
+attention on the characteristic equation
+ 
+
+ align:start position:0%
+attention on the characteristic equation
+in particular the denominator of the
+
+ align:start position:0%
+in particular the denominator of the
+ 
+
+ align:start position:0%
+in particular the denominator of the
+closed loop transfer function we were
+
+ align:start position:0%
+closed loop transfer function we were
+ 
+
+ align:start position:0%
+closed loop transfer function we were
+then able to solve that characteristic
+
+ align:start position:0%
+then able to solve that characteristic
+ 
+
+ align:start position:0%
+then able to solve that characteristic
+equation solve the root for the roots of
+
+ align:start position:0%
+equation solve the root for the roots of
+ 
+
+ align:start position:0%
+equation solve the root for the roots of
+that characteristic equation by setting
+
+ align:start position:0%
+that characteristic equation by setting
+ 
+
+ align:start position:0%
+that characteristic equation by setting
+it equal to zero and since the roots of
+
+ align:start position:0%
+it equal to zero and since the roots of
+ 
+
+ align:start position:0%
+it equal to zero and since the roots of
+the characteristic equation are the
+
+ align:start position:0%
+the characteristic equation are the
+ 
+
+ align:start position:0%
+the characteristic equation are the
+poles of the system closed loop transfer
+
+ align:start position:0%
+poles of the system closed loop transfer
+ 
+
+ align:start position:0%
+poles of the system closed loop transfer
+function we could determine how the
+
+ align:start position:0%
+function we could determine how the
+ 
+
+ align:start position:0%
+function we could determine how the
+closed loop transfer function poles
+
+ align:start position:0%
+closed loop transfer function poles
+ 
+
+ align:start position:0%
+closed loop transfer function poles
+varied in particular as we changed a fot
+
+ align:start position:0%
+varied in particular as we changed a fot
+ 
+
+ align:start position:0%
+varied in particular as we changed a fot
+for the system recall that a fot is the
+
+ align:start position:0%
+for the system recall that a fot is the
+ 
+
+ align:start position:0%
+for the system recall that a fot is the
+magnitude of the low frequency Loop
+
+ align:start position:0%
+magnitude of the low frequency Loop
+ 
+
+ align:start position:0%
+magnitude of the low frequency Loop
+transmission of the system when we
+
+ align:start position:0%
+transmission of the system when we
+ 
+
+ align:start position:0%
+transmission of the system when we
+perform that calculation Again by
+
+ align:start position:0%
+perform that calculation Again by
+ 
+
+ align:start position:0%
+perform that calculation Again by
+directly factoring the characteristic
+
+ align:start position:0%
+directly factoring the characteristic
+ 
+
+ align:start position:0%
+directly factoring the characteristic
+equation we found that the closed loop
+
+ align:start position:0%
+equation we found that the closed loop
+ 
+
+ align:start position:0%
+equation we found that the closed loop
+poles start very close to the location
+
+ align:start position:0%
+poles start very close to the location
+ 
+
+ align:start position:0%
+poles start very close to the location
+of the loop transmission poles for small
+
+ align:start position:0%
+of the loop transmission poles for small
+ 
+
+ align:start position:0%
+of the loop transmission poles for small
+values of a f in this particular system
+
+ align:start position:0%
+values of a f in this particular system
+ 
+
+ align:start position:0%
+values of a f in this particular system
+and then as a f inre increases the two
+
+ align:start position:0%
+and then as a f inre increases the two
+ 
+
+ align:start position:0%
+and then as a f inre increases the two
+poles the two closed loop poles move
+
+ align:start position:0%
+poles the two closed loop poles move
+ 
+
+ align:start position:0%
+poles the two closed loop poles move
+closer together and finally become
+
+ align:start position:0%
+closer together and finally become
+ 
+
+ align:start position:0%
+closer together and finally become
+coincident on the negative real axis at
+
+ align:start position:0%
+coincident on the negative real axis at
+ 
+
+ align:start position:0%
+coincident on the negative real axis at
+a location that's actually the
+
+ align:start position:0%
+a location that's actually the
+ 
+
+ align:start position:0%
+a location that's actually the
+arithmetic mean of the two Loop
+
+ align:start position:0%
+arithmetic mean of the two Loop
+ 
+
+ align:start position:0%
+arithmetic mean of the two Loop
+transmission pole
+
+ align:start position:0%
+transmission pole
+ 
+
+ align:start position:0%
+transmission pole
+locations further increases in a fnot
+
+ align:start position:0%
+locations further increases in a fnot
+ 
+
+ align:start position:0%
+locations further increases in a fnot
+beyond that necessary to get the two
+
+ align:start position:0%
+beyond that necessary to get the two
+ 
+
+ align:start position:0%
+beyond that necessary to get the two
+poles coincident result in the two poles
+
+ align:start position:0%
+poles coincident result in the two poles
+ 
+
+ align:start position:0%
+poles coincident result in the two poles
+branching off the real axis and getting
+
+ align:start position:0%
+branching off the real axis and getting
+ 
+
+ align:start position:0%
+branching off the real axis and getting
+an increasingly large imaginary
+
+ align:start position:0%
+an increasingly large imaginary
+ 
+
+ align:start position:0%
+an increasingly large imaginary
+portion as the two closed loop Pooles
+
+ align:start position:0%
+portion as the two closed loop Pooles
+ 
+
+ align:start position:0%
+portion as the two closed loop Pooles
+become a complex conjugate pair with an
+
+ align:start position:0%
+become a complex conjugate pair with an
+ 
+
+ align:start position:0%
+become a complex conjugate pair with an
+increasingly large imaginary component
+
+ align:start position:0%
+increasingly large imaginary component
+ 
+
+ align:start position:0%
+increasingly large imaginary component
+the real part stays fixed and so as a
+
+ align:start position:0%
+the real part stays fixed and so as a
+ 
+
+ align:start position:0%
+the real part stays fixed and so as a
+fnot increases why the two complex
+
+ align:start position:0%
+fnot increases why the two complex
+ 
+
+ align:start position:0%
+fnot increases why the two complex
+conjugate poles move off North and South
+
+ align:start position:0%
+conjugate poles move off North and South
+ 
+
+ align:start position:0%
+conjugate poles move off North and South
+in the S plane of course they have to be
+
+ align:start position:0%
+in the S plane of course they have to be
+ 
+
+ align:start position:0%
+in the S plane of course they have to be
+symmetrical with respect to the real
+
+ align:start position:0%
+symmetrical with respect to the real
+ 
+
+ align:start position:0%
+symmetrical with respect to the real
+axis since this is corresponds to the
+
+ align:start position:0%
+axis since this is corresponds to the
+ 
+
+ align:start position:0%
+axis since this is corresponds to the
+pole locations for a physically
+
+ align:start position:0%
+pole locations for a physically
+ 
+
+ align:start position:0%
+pole locations for a physically
+realizable system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we found that we were able to
+
+ align:start position:0%
+we found that we were able to
+ 
+
+ align:start position:0%
+we found that we were able to
+determine the closed loop pole locations
+
+ align:start position:0%
+determine the closed loop pole locations
+ 
+
+ align:start position:0%
+determine the closed loop pole locations
+for our second order system by directly
+
+ align:start position:0%
+for our second order system by directly
+ 
+
+ align:start position:0%
+for our second order system by directly
+factoring the characteristic equation
+
+ align:start position:0%
+factoring the characteristic equation
+ 
+
+ align:start position:0%
+factoring the characteristic equation
+unfortunately that operation becomes
+
+ align:start position:0%
+unfortunately that operation becomes
+ 
+
+ align:start position:0%
+unfortunately that operation becomes
+tedious for anything other than first
+
+ align:start position:0%
+tedious for anything other than first
+ 
+
+ align:start position:0%
+tedious for anything other than first
+and second order systems and so today
+
+ align:start position:0%
+and second order systems and so today
+ 
+
+ align:start position:0%
+and second order systems and so today
+we'd like to look at the way we can
+
+ align:start position:0%
+we'd like to look at the way we can
+ 
+
+ align:start position:0%
+we'd like to look at the way we can
+construct the root Locust diagram
+
+ align:start position:0%
+construct the root Locust diagram
+ 
+
+ align:start position:0%
+construct the root Locust diagram
+without having to directly Factor the
+
+ align:start position:0%
+without having to directly Factor the
+ 
+
+ align:start position:0%
+without having to directly Factor the
+characteristic
+
+ align:start position:0%
+characteristic
+ 
+
+ align:start position:0%
+characteristic
+equation we call we have a standard
+
+ align:start position:0%
+equation we call we have a standard
+ 
+
+ align:start position:0%
+equation we call we have a standard
+topology which has a forward path
+
+ align:start position:0%
+topology which has a forward path
+ 
+
+ align:start position:0%
+topology which has a forward path
+transmission a of s and a feedback path
+
+ align:start position:0%
+transmission a of s and a feedback path
+ 
+
+ align:start position:0%
+transmission a of s and a feedback path
+transmission F of
+
+ align:start position:0%
+transmission F of
+ 
+
+ align:start position:0%
+transmission F of
+s when we write a closed loop transfer
+
+ align:start position:0%
+s when we write a closed loop transfer
+ 
+
+ align:start position:0%
+s when we write a closed loop transfer
+function for the system we of course
+
+ align:start position:0%
+function for the system we of course
+ 
+
+ align:start position:0%
+function for the system we of course
+find out that capital A of s the input
+
+ align:start position:0%
+find out that capital A of s the input
+ 
+
+ align:start position:0%
+find out that capital A of s the input
+to Output transfer function is simply
+
+ align:start position:0%
+to Output transfer function is simply
+ 
+
+ align:start position:0%
+to Output transfer function is simply
+equal to the forward path transmission
+
+ align:start position:0%
+equal to the forward path transmission
+ 
+
+ align:start position:0%
+equal to the forward path transmission
+over 1 minus the loop transmission we're
+
+ align:start position:0%
+over 1 minus the loop transmission we're
+ 
+
+ align:start position:0%
+over 1 minus the loop transmission we're
+not particularly worried initially about
+
+ align:start position:0%
+not particularly worried initially about
+ 
+
+ align:start position:0%
+not particularly worried initially about
+the location of zeros or initial
+
+ align:start position:0%
+the location of zeros or initial
+ 
+
+ align:start position:0%
+the location of zeros or initial
+considerations with root Locust
+
+ align:start position:0%
+considerations with root Locust
+ 
+
+ align:start position:0%
+considerations with root Locust
+techniques will focus only on how we
+
+ align:start position:0%
+techniques will focus only on how we
+ 
+
+ align:start position:0%
+techniques will focus only on how we
+find the poles of the system
+
+ align:start position:0%
+find the poles of the system
+ 
+
+ align:start position:0%
+find the poles of the system
+consequently we'll look only at the
+
+ align:start position:0%
+consequently we'll look only at the
+ 
+
+ align:start position:0%
+consequently we'll look only at the
+characteristic equation which we recall
+
+ align:start position:0%
+characteristic equation which we recall
+ 
+
+ align:start position:0%
+characteristic equation which we recall
+is one minus the loop transmission that
+
+ align:start position:0%
+is one minus the loop transmission that
+ 
+
+ align:start position:0%
+is one minus the loop transmission that
+characteristic equation is of course
+
+ align:start position:0%
+characteristic equation is of course
+ 
+
+ align:start position:0%
+characteristic equation is of course
+common for any system with uh equal
+
+ align:start position:0%
+common for any system with uh equal
+ 
+
+ align:start position:0%
+common for any system with uh equal
+values for the AF product remember that
+
+ align:start position:0%
+values for the AF product remember that
+ 
+
+ align:start position:0%
+values for the AF product remember that
+the zeros of closed loop transfer
+
+ align:start position:0%
+the zeros of closed loop transfer
+ 
+
+ align:start position:0%
+the zeros of closed loop transfer
+function are dependent on how Dynamics
+
+ align:start position:0%
+function are dependent on how Dynamics
+ 
+
+ align:start position:0%
+function are dependent on how Dynamics
+are distributed between the forward path
+
+ align:start position:0%
+are distributed between the forward path
+ 
+
+ align:start position:0%
+are distributed between the forward path
+and the feedback path but the poles of a
+
+ align:start position:0%
+and the feedback path but the poles of a
+ 
+
+ align:start position:0%
+and the feedback path but the poles of a
+closed loop transfer function are
+
+ align:start position:0%
+closed loop transfer function are
+ 
+
+ align:start position:0%
+closed loop transfer function are
+dependent only on the AF product well
+
+ align:start position:0%
+dependent only on the AF product well
+ 
+
+ align:start position:0%
+dependent only on the AF product well
+when we calculate the characteristic
+
+ align:start position:0%
+when we calculate the characteristic
+ 
+
+ align:start position:0%
+when we calculate the characteristic
+equation or one minus the loop
+
+ align:start position:0%
+equation or one minus the loop
+ 
+
+ align:start position:0%
+equation or one minus the loop
+transmission it's simply 1 plus a of s f
+
+ align:start position:0%
+transmission it's simply 1 plus a of s f
+ 
+
+ align:start position:0%
+transmission it's simply 1 plus a of s f
+of s recalling that the loop
+
+ align:start position:0%
+of s recalling that the loop
+ 
+
+ align:start position:0%
+of s recalling that the loop
+transmission is minus a of s f of s then
+
+ align:start position:0%
+transmission is minus a of s f of s then
+ 
+
+ align:start position:0%
+transmission is minus a of s f of s then
+we conclude that the poles of the closed
+
+ align:start position:0%
+we conclude that the poles of the closed
+ 
+
+ align:start position:0%
+we conclude that the poles of the closed
+loop transfer function capital A of s
+
+ align:start position:0%
+loop transfer function capital A of s
+ 
+
+ align:start position:0%
+loop transfer function capital A of s
+occur when 1 plus a of s F of s equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z we may choose to express the AF
+
+ align:start position:0%
+z we may choose to express the AF
+ 
+
+ align:start position:0%
+z we may choose to express the AF
+product as being equal to a fot times
+
+ align:start position:0%
+product as being equal to a fot times
+ 
+
+ align:start position:0%
+product as being equal to a fot times
+some G of s where we've included all of
+
+ align:start position:0%
+some G of s where we've included all of
+ 
+
+ align:start position:0%
+some G of s where we've included all of
+the frequency dependent portions of the
+
+ align:start position:0%
+the frequency dependent portions of the
+ 
+
+ align:start position:0%
+the frequency dependent portions of the
+loop Transmission in G of s and
+
+ align:start position:0%
+loop Transmission in G of s and
+ 
+
+ align:start position:0%
+loop Transmission in G of s and
+furthermore we'll choose to write G of s
+
+ align:start position:0%
+furthermore we'll choose to write G of s
+ 
+
+ align:start position:0%
+furthermore we'll choose to write G of s
+in a form such that g of0 is equal to
+
+ align:start position:0%
+in a form such that g of0 is equal to
+ 
+
+ align:start position:0%
+in a form such that g of0 is equal to
+one we'll normalize G of s so that the
+
+ align:start position:0%
+one we'll normalize G of s so that the
+ 
+
+ align:start position:0%
+one we'll normalize G of s so that the
+DC value of G of s is one in that case
+
+ align:start position:0%
+DC value of G of s is one in that case
+ 
+
+ align:start position:0%
+DC value of G of s is one in that case
+the quantity a fnot has the physical
+
+ align:start position:0%
+the quantity a fnot has the physical
+ 
+
+ align:start position:0%
+the quantity a fnot has the physical
+interpretation of being the magnitude of
+
+ align:start position:0%
+interpretation of being the magnitude of
+ 
+
+ align:start position:0%
+interpretation of being the magnitude of
+the DC Loop
+
+ align:start position:0%
+the DC Loop
+ 
+
+ align:start position:0%
+the DC Loop
+transmission suppose we'd like to
+
+ align:start position:0%
+transmission suppose we'd like to
+ 
+
+ align:start position:0%
+transmission suppose we'd like to
+perform a test suppose we're told
+
+ align:start position:0%
+perform a test suppose we're told
+ 
+
+ align:start position:0%
+perform a test suppose we're told
+that a particular system has a closed
+
+ align:start position:0%
+that a particular system has a closed
+ 
+
+ align:start position:0%
+that a particular system has a closed
+loop pole at a point in the S plane
+
+ align:start position:0%
+loop pole at a point in the S plane
+ 
+
+ align:start position:0%
+loop pole at a point in the S plane
+S1 and we' like to check to see if
+
+ align:start position:0%
+S1 and we' like to check to see if
+ 
+
+ align:start position:0%
+S1 and we' like to check to see if
+that's really true well that's easy to
+
+ align:start position:0%
+that's really true well that's easy to
+ 
+
+ align:start position:0%
+that's really true well that's easy to
+do if we're to close loop pole the
+
+ align:start position:0%
+do if we're to close loop pole the
+ 
+
+ align:start position:0%
+do if we're to close loop pole the
+characteristic equation the denominator
+
+ align:start position:0%
+characteristic equation the denominator
+ 
+
+ align:start position:0%
+characteristic equation the denominator
+of any transfer function for the system
+
+ align:start position:0%
+of any transfer function for the system
+ 
+
+ align:start position:0%
+of any transfer function for the system
+must in fact be equal to zero that's
+
+ align:start position:0%
+must in fact be equal to zero that's
+ 
+
+ align:start position:0%
+must in fact be equal to zero that's
+what we mean by a poll the denominator
+
+ align:start position:0%
+what we mean by a poll the denominator
+ 
+
+ align:start position:0%
+what we mean by a poll the denominator
+goes to zero consequently the transfer
+
+ align:start position:0%
+goes to zero consequently the transfer
+ 
+
+ align:start position:0%
+goes to zero consequently the transfer
+function in question becomes
+
+ align:start position:0%
+function in question becomes
+ 
+
+ align:start position:0%
+function in question becomes
+infinite so if we we are in fact at a
+
+ align:start position:0%
+infinite so if we we are in fact at a
+ 
+
+ align:start position:0%
+infinite so if we we are in fact at a
+poll of capital A of s the quantity 1+ a
+
+ align:start position:0%
+poll of capital A of s the quantity 1+ a
+ 
+
+ align:start position:0%
+poll of capital A of s the quantity 1+ a
+f time G of S1 must be equal to zero we
+
+ align:start position:0%
+f time G of S1 must be equal to zero we
+ 
+
+ align:start position:0%
+f time G of S1 must be equal to zero we
+can rearrange and recognize that that
+
+ align:start position:0%
+can rearrange and recognize that that
+ 
+
+ align:start position:0%
+can rearrange and recognize that that
+tells us that a FN time G of S1 must be
+
+ align:start position:0%
+tells us that a FN time G of S1 must be
+ 
+
+ align:start position:0%
+tells us that a FN time G of S1 must be
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus1 since a f g of s in general is a
+
+ align:start position:0%
+minus1 since a f g of s in general is a
+ 
+
+ align:start position:0%
+minus1 since a f g of s in general is a
+complex number we have to satisfy two
+
+ align:start position:0%
+complex number we have to satisfy two
+ 
+
+ align:start position:0%
+complex number we have to satisfy two
+conditions simultaneously to make it
+
+ align:start position:0%
+conditions simultaneously to make it
+ 
+
+ align:start position:0%
+conditions simultaneously to make it
+equal to minus1 in particular the
+
+ align:start position:0%
+equal to minus1 in particular the
+ 
+
+ align:start position:0%
+equal to minus1 in particular the
+magnitude of a f * G of s evaluated at
+
+ align:start position:0%
+magnitude of a f * G of s evaluated at
+ 
+
+ align:start position:0%
+magnitude of a f * G of s evaluated at
+the point s equal S1 must be equal to
+
+ align:start position:0%
+the point s equal S1 must be equal to
+ 
+
+ align:start position:0%
+the point s equal S1 must be equal to
+one and simultaneously the angle of the
+
+ align:start position:0%
+one and simultaneously the angle of the
+ 
+
+ align:start position:0%
+one and simultaneously the angle of the
+transfer function a f g of s evaluated
+
+ align:start position:0%
+transfer function a f g of s evaluated
+ 
+
+ align:start position:0%
+transfer function a f g of s evaluated
+the point S1 has to be equal to an odd
+
+ align:start position:0%
+the point S1 has to be equal to an odd
+ 
+
+ align:start position:0%
+the point S1 has to be equal to an odd
+multiple of
+
+ align:start position:0%
+multiple of
+ 
+
+ align:start position:0%
+multiple of
+180° however since we've chosen to
+
+ align:start position:0%
+180° however since we've chosen to
+ 
+
+ align:start position:0%
+180° however since we've chosen to
+include all of the Dynamics of our Loop
+
+ align:start position:0%
+include all of the Dynamics of our Loop
+ 
+
+ align:start position:0%
+include all of the Dynamics of our Loop
+Transmission in the quantity G of s the
+
+ align:start position:0%
+Transmission in the quantity G of s the
+ 
+
+ align:start position:0%
+Transmission in the quantity G of s the
+angle condition reduces to Simply Having
+
+ align:start position:0%
+angle condition reduces to Simply Having
+ 
+
+ align:start position:0%
+angle condition reduces to Simply Having
+the angle of G of S1 being equal to an
+
+ align:start position:0%
+the angle of G of S1 being equal to an
+ 
+
+ align:start position:0%
+the angle of G of S1 being equal to an
+odd multiple of 1880 de where we
+
+ align:start position:0%
+odd multiple of 1880 de where we
+ 
+
+ align:start position:0%
+odd multiple of 1880 de where we
+recognize in this expression n as an
+
+ align:start position:0%
+recognize in this expression n as an
+ 
+
+ align:start position:0%
+recognize in this expression n as an
+integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just to refresh your memory recall that
+
+ align:start position:0%
+just to refresh your memory recall that
+ 
+
+ align:start position:0%
+just to refresh your memory recall that
+if we go into the S plane and want to
+
+ align:start position:0%
+if we go into the S plane and want to
+ 
+
+ align:start position:0%
+if we go into the S plane and want to
+evaluate the Val a function of s at some
+
+ align:start position:0%
+evaluate the Val a function of s at some
+ 
+
+ align:start position:0%
+evaluate the Val a function of s at some
+point in the S plane suppose this is the
+
+ align:start position:0%
+point in the S plane suppose this is the
+ 
+
+ align:start position:0%
+point in the S plane suppose this is the
+point of Interest
+
+ align:start position:0%
+point of Interest
+ 
+
+ align:start position:0%
+point of Interest
+S1 and we're trying to check and see if
+
+ align:start position:0%
+S1 and we're trying to check and see if
+ 
+
+ align:start position:0%
+S1 and we're trying to check and see if
+that point S1 in fact satisfies the
+
+ align:start position:0%
+that point S1 in fact satisfies the
+ 
+
+ align:start position:0%
+that point S1 in fact satisfies the
+conditions for being a pole of capital A
+
+ align:start position:0%
+conditions for being a pole of capital A
+ 
+
+ align:start position:0%
+conditions for being a pole of capital A
+of s we can do the following we draw
+
+ align:start position:0%
+of s we can do the following we draw
+ 
+
+ align:start position:0%
+of s we can do the following we draw
+vectors from the poles and
+
+ align:start position:0%
+vectors from the poles and
+ 
+
+ align:start position:0%
+vectors from the poles and
+Zer of the AF
+
+ align:start position:0%
+Zer of the AF
+ 
+
+ align:start position:0%
+Zer of the AF
+product or of the G product to the point
+
+ align:start position:0%
+product or of the G product to the point
+ 
+
+ align:start position:0%
+product or of the G product to the point
+in question here we have
+
+ align:start position:0%
+in question here we have
+ 
+
+ align:start position:0%
+in question here we have
+shown one real axis pole of G ofs uh two
+
+ align:start position:0%
+shown one real axis pole of G ofs uh two
+ 
+
+ align:start position:0%
+shown one real axis pole of G ofs uh two
+complex conjugate a complex conjugate
+
+ align:start position:0%
+complex conjugate a complex conjugate
+ 
+
+ align:start position:0%
+complex conjugate a complex conjugate
+pole pair of G ofs and a single zero of
+
+ align:start position:0%
+pole pair of G ofs and a single zero of
+ 
+
+ align:start position:0%
+pole pair of G ofs and a single zero of
+G ofs if we now try to evaluate G of s
+
+ align:start position:0%
+G ofs if we now try to evaluate G of s
+ 
+
+ align:start position:0%
+G ofs if we now try to evaluate G of s
+at the point S1 what we do is draw
+
+ align:start position:0%
+at the point S1 what we do is draw
+ 
+
+ align:start position:0%
+at the point S1 what we do is draw
+vectors from the poles and the zero
+
+ align:start position:0%
+vectors from the poles and the zero
+ 
+
+ align:start position:0%
+vectors from the poles and the zero
+of G of s to the point S1 and I've
+
+ align:start position:0%
+of G of s to the point S1 and I've
+ 
+
+ align:start position:0%
+of G of s to the point S1 and I've
+showed that for the three
+
+ align:start position:0%
+showed that for the three
+ 
+
+ align:start position:0%
+showed that for the three
+poles and for the
+
+ align:start position:0%
+poles and for the
+ 
+
+ align:start position:0%
+poles and for the
+zero and we can evaluate the angle and
+
+ align:start position:0%
+zero and we can evaluate the angle and
+ 
+
+ align:start position:0%
+zero and we can evaluate the angle and
+the magnitude associated with those
+
+ align:start position:0%
+the magnitude associated with those
+ 
+
+ align:start position:0%
+the magnitude associated with those
+vectors in particular let's call this
+
+ align:start position:0%
+vectors in particular let's call this
+ 
+
+ align:start position:0%
+vectors in particular let's call this
+angle Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and similarly the length of this
+
+ align:start position:0%
+1 and similarly the length of this
+ 
+
+ align:start position:0%
+1 and similarly the length of this
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+L1 and let's call this this angle Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 and let's call this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle theta
+
+ align:start position:0%
+angle theta
+ 
+
+ align:start position:0%
+angle theta
+3 and let's call this angle Theta 4 and
+
+ align:start position:0%
+3 and let's call this angle Theta 4 and
+ 
+
+ align:start position:0%
+3 and let's call this angle Theta 4 and
+recall that this angle we
+
+ align:start position:0%
+recall that this angle we
+ 
+
+ align:start position:0%
+recall that this angle we
+evaluate like
+
+ align:start position:0%
+evaluate like
+ 
+
+ align:start position:0%
+evaluate like
+this so Theta 4 is a an angle greater
+
+ align:start position:0%
+this so Theta 4 is a an angle greater
+ 
+
+ align:start position:0%
+this so Theta 4 is a an angle greater
+actually than 270 degrees as I've shown
+
+ align:start position:0%
+actually than 270 degrees as I've shown
+ 
+
+ align:start position:0%
+actually than 270 degrees as I've shown
+it similarly let's remember that the
+
+ align:start position:0%
+it similarly let's remember that the
+ 
+
+ align:start position:0%
+it similarly let's remember that the
+lengths of the other vectors are L2 L3
+
+ align:start position:0%
+lengths of the other vectors are L2 L3
+ 
+
+ align:start position:0%
+lengths of the other vectors are L2 L3
+in here and L4 for the fourth
+
+ align:start position:0%
+in here and L4 for the fourth
+ 
+
+ align:start position:0%
+in here and L4 for the fourth
+vector and we can then evaluate the
+
+ align:start position:0%
+vector and we can then evaluate the
+ 
+
+ align:start position:0%
+vector and we can then evaluate the
+angle of G of
+
+ align:start position:0%
+angle of G of
+ 
+
+ align:start position:0%
+angle of G of
+s for values of s equal to
+
+ align:start position:0%
+s for values of s equal to
+ 
+
+ align:start position:0%
+s for values of s equal to
+S1 as being equal simply to the sum of
+
+ align:start position:0%
+S1 as being equal simply to the sum of
+ 
+
+ align:start position:0%
+S1 as being equal simply to the sum of
+all the angles associated with the
+
+ align:start position:0%
+all the angles associated with the
+ 
+
+ align:start position:0%
+all the angles associated with the
+vectors from Zer in this case we only
+
+ align:start position:0%
+vectors from Zer in this case we only
+ 
+
+ align:start position:0%
+vectors from Zer in this case we only
+have one of them so that's Theta 1 and
+
+ align:start position:0%
+have one of them so that's Theta 1 and
+ 
+
+ align:start position:0%
+have one of them so that's Theta 1 and
+we subtract from that sum the angles
+
+ align:start position:0%
+we subtract from that sum the angles
+ 
+
+ align:start position:0%
+we subtract from that sum the angles
+associated with the vectors from all of
+
+ align:start position:0%
+associated with the vectors from all of
+ 
+
+ align:start position:0%
+associated with the vectors from all of
+the poles of the function in particular
+
+ align:start position:0%
+the poles of the function in particular
+ 
+
+ align:start position:0%
+the poles of the function in particular
+in our case minus Theta 2 minus theta 3
+
+ align:start position:0%
+in our case minus Theta 2 minus theta 3
+ 
+
+ align:start position:0%
+in our case minus Theta 2 minus theta 3
+minus Theta 4 since those are the angles
+
+ align:start position:0%
+minus Theta 4 since those are the angles
+ 
+
+ align:start position:0%
+minus Theta 4 since those are the angles
+associated with the three poles of G of
+
+ align:start position:0%
+associated with the three poles of G of
+ 
+
+ align:start position:0%
+associated with the three poles of G of
+s similarly the magnitude of our
+
+ align:start position:0%
+s similarly the magnitude of our
+ 
+
+ align:start position:0%
+s similarly the magnitude of our
+transfer function is within a constant
+
+ align:start position:0%
+transfer function is within a constant
+ 
+
+ align:start position:0%
+transfer function is within a constant
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+proportionality equal to the product of
+
+ align:start position:0%
+proportionality equal to the product of
+ 
+
+ align:start position:0%
+proportionality equal to the product of
+the lengths of the vectors from all of
+
+ align:start position:0%
+the lengths of the vectors from all of
+ 
+
+ align:start position:0%
+the lengths of the vectors from all of
+the zeros to the point in question
+
+ align:start position:0%
+the zeros to the point in question
+ 
+
+ align:start position:0%
+the zeros to the point in question
+question in our system again we have
+
+ align:start position:0%
+question in our system again we have
+ 
+
+ align:start position:0%
+question in our system again we have
+only one zero so that's L1 divided by
+
+ align:start position:0%
+only one zero so that's L1 divided by
+ 
+
+ align:start position:0%
+only one zero so that's L1 divided by
+the product of the lengths of the
+
+ align:start position:0%
+the product of the lengths of the
+ 
+
+ align:start position:0%
+the product of the lengths of the
+vectors from all the PO poles of the
+
+ align:start position:0%
+vectors from all the PO poles of the
+ 
+
+ align:start position:0%
+vectors from all the PO poles of the
+transfer function to the point in
+
+ align:start position:0%
+transfer function to the point in
+ 
+
+ align:start position:0%
+transfer function to the point in
+question so in our case with three poles
+
+ align:start position:0%
+question so in our case with three poles
+ 
+
+ align:start position:0%
+question so in our case with three poles
+we have the product L2 * L3 *
+
+ align:start position:0%
+we have the product L2 * L3 *
+ 
+
+ align:start position:0%
+we have the product L2 * L3 *
+L4 well all we have to do then if we are
+
+ align:start position:0%
+L4 well all we have to do then if we are
+ 
+
+ align:start position:0%
+L4 well all we have to do then if we are
+interested in finding out whether a
+
+ align:start position:0%
+interested in finding out whether a
+ 
+
+ align:start position:0%
+interested in finding out whether a
+particular Point S1 in fact corresponds
+
+ align:start position:0%
+particular Point S1 in fact corresponds
+ 
+
+ align:start position:0%
+particular Point S1 in fact corresponds
+to a closed loop pole of capital A of s
+
+ align:start position:0%
+to a closed loop pole of capital A of s
+ 
+
+ align:start position:0%
+to a closed loop pole of capital A of s
+is to evaluate the function G of of S1
+
+ align:start position:0%
+is to evaluate the function G of of S1
+ 
+
+ align:start position:0%
+is to evaluate the function G of of S1
+or in particular a f time G of S1 and
+
+ align:start position:0%
+or in particular a f time G of S1 and
+ 
+
+ align:start position:0%
+or in particular a f time G of S1 and
+see if that product is equal to
+
+ align:start position:0%
+see if that product is equal to
+ 
+
+ align:start position:0%
+see if that product is equal to
+minus1 usually the most powerful test
+
+ align:start position:0%
+minus1 usually the most powerful test
+ 
+
+ align:start position:0%
+minus1 usually the most powerful test
+involves the angle condition remember
+
+ align:start position:0%
+involves the angle condition remember
+ 
+
+ align:start position:0%
+involves the angle condition remember
+that we're going to construct a root
+
+ align:start position:0%
+that we're going to construct a root
+ 
+
+ align:start position:0%
+that we're going to construct a root
+Locus diagram starting with the poles
+
+ align:start position:0%
+Locus diagram starting with the poles
+ 
+
+ align:start position:0%
+Locus diagram starting with the poles
+and zeros of the loop
+
+ align:start position:0%
+and zeros of the loop
+ 
+
+ align:start position:0%
+and zeros of the loop
+transmission and then find out how the
+
+ align:start position:0%
+transmission and then find out how the
+ 
+
+ align:start position:0%
+transmission and then find out how the
+closed loop poles change location as a
+
+ align:start position:0%
+closed loop poles change location as a
+ 
+
+ align:start position:0%
+closed loop poles change location as a
+function of a fnot as a function of the
+
+ align:start position:0%
+function of a fnot as a function of the
+ 
+
+ align:start position:0%
+function of a fnot as a function of the
+DC magnitude of the loop
+
+ align:start position:0%
+DC magnitude of the loop
+ 
+
+ align:start position:0%
+DC magnitude of the loop
+transmission since we're constructing
+
+ align:start position:0%
+transmission since we're constructing
+ 
+
+ align:start position:0%
+transmission since we're constructing
+our root Locus diagram as a function of
+
+ align:start position:0%
+our root Locus diagram as a function of
+ 
+
+ align:start position:0%
+our root Locus diagram as a function of
+a FN we can always find a value of a KN
+
+ align:start position:0%
+a FN we can always find a value of a KN
+ 
+
+ align:start position:0%
+a FN we can always find a value of a KN
+FN which will make the magnitude
+
+ align:start position:0%
+FN which will make the magnitude
+ 
+
+ align:start position:0%
+FN which will make the magnitude
+condition be satisfied consequently the
+
+ align:start position:0%
+condition be satisfied consequently the
+ 
+
+ align:start position:0%
+condition be satisfied consequently the
+uh part of this development that really
+
+ align:start position:0%
+uh part of this development that really
+ 
+
+ align:start position:0%
+uh part of this development that really
+gives us Leverage is the angle condition
+
+ align:start position:0%
+gives us Leverage is the angle condition
+ 
+
+ align:start position:0%
+gives us Leverage is the angle condition
+and so what we ought to do as a general
+
+ align:start position:0%
+and so what we ought to do as a general
+ 
+
+ align:start position:0%
+and so what we ought to do as a general
+test
+
+ align:start position:0%
+test
+ 
+
+ align:start position:0%
+test
+is look in the S plane for points where
+
+ align:start position:0%
+is look in the S plane for points where
+ 
+
+ align:start position:0%
+is look in the S plane for points where
+the angle condition is satisfied in
+
+ align:start position:0%
+the angle condition is satisfied in
+ 
+
+ align:start position:0%
+the angle condition is satisfied in
+other words where for points where G of
+
+ align:start position:0%
+other words where for points where G of
+ 
+
+ align:start position:0%
+other words where for points where G of
+s has an angle that's equal to an odd
+
+ align:start position:0%
+s has an angle that's equal to an odd
+ 
+
+ align:start position:0%
+s has an angle that's equal to an odd
+multiple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+180° that condition has been exploited
+
+ align:start position:0%
+180° that condition has been exploited
+ 
+
+ align:start position:0%
+180° that condition has been exploited
+to develop a number of rules that help
+
+ align:start position:0%
+to develop a number of rules that help
+ 
+
+ align:start position:0%
+to develop a number of rules that help
+us sketch rapidly and and accurately the
+
+ align:start position:0%
+us sketch rapidly and and accurately the
+ 
+
+ align:start position:0%
+us sketch rapidly and and accurately the
+root Locust diagram for a system I'd
+
+ align:start position:0%
+root Locust diagram for a system I'd
+ 
+
+ align:start position:0%
+root Locust diagram for a system I'd
+like to point out at the outset that
+
+ align:start position:0%
+like to point out at the outset that
+ 
+
+ align:start position:0%
+like to point out at the outset that
+there's little universality among
+
+ align:start position:0%
+there's little universality among
+ 
+
+ align:start position:0%
+there's little universality among
+authors and and on the on the specifics
+
+ align:start position:0%
+authors and and on the on the specifics
+ 
+
+ align:start position:0%
+authors and and on the on the specifics
+of these rules some people feel that
+
+ align:start position:0%
+of these rules some people feel that
+ 
+
+ align:start position:0%
+of these rules some people feel that
+there are a greater number of them
+
+ align:start position:0%
+there are a greater number of them
+ 
+
+ align:start position:0%
+there are a greater number of them
+required others feel there's there are
+
+ align:start position:0%
+required others feel there's there are
+ 
+
+ align:start position:0%
+required others feel there's there are
+fewer I've seen some developments that
+
+ align:start position:0%
+fewer I've seen some developments that
+ 
+
+ align:start position:0%
+fewer I've seen some developments that
+state only three or four rules I've seen
+
+ align:start position:0%
+state only three or four rules I've seen
+ 
+
+ align:start position:0%
+state only three or four rules I've seen
+other developments where there are as
+
+ align:start position:0%
+other developments where there are as
+ 
+
+ align:start position:0%
+other developments where there are as
+many as 15 rules drawn out and I happen
+
+ align:start position:0%
+many as 15 rules drawn out and I happen
+ 
+
+ align:start position:0%
+many as 15 rules drawn out and I happen
+to have chosen eight which are my own
+
+ align:start position:0%
+to have chosen eight which are my own
+ 
+
+ align:start position:0%
+to have chosen eight which are my own
+favorites and I feel that that they give
+
+ align:start position:0%
+favorites and I feel that that they give
+ 
+
+ align:start position:0%
+favorites and I feel that that they give
+us a good handle on quickly constructing
+
+ align:start position:0%
+us a good handle on quickly constructing
+ 
+
+ align:start position:0%
+us a good handle on quickly constructing
+a root Locust diagram but again I
+
+ align:start position:0%
+a root Locust diagram but again I
+ 
+
+ align:start position:0%
+a root Locust diagram but again I
+emphasize that you can velop rules of
+
+ align:start position:0%
+emphasize that you can velop rules of
+ 
+
+ align:start position:0%
+emphasize that you can velop rules of
+your own by going back to our real
+
+ align:start position:0%
+your own by going back to our real
+ 
+
+ align:start position:0%
+your own by going back to our real
+consideration which is that the a fot G
+
+ align:start position:0%
+consideration which is that the a fot G
+ 
+
+ align:start position:0%
+consideration which is that the a fot G
+ofs product has to be equal to minus one
+
+ align:start position:0%
+ofs product has to be equal to minus one
+ 
+
+ align:start position:0%
+ofs product has to be equal to minus one
+at a pole of capital A of
+
+ align:start position:0%
+at a pole of capital A of
+ 
+
+ align:start position:0%
+at a pole of capital A of
+s the rules are given in considerable
+
+ align:start position:0%
+s the rules are given in considerable
+ 
+
+ align:start position:0%
+s the rules are given in considerable
+detail in the text and I haven't written
+
+ align:start position:0%
+detail in the text and I haven't written
+ 
+
+ align:start position:0%
+detail in the text and I haven't written
+them out in that sort of detail here but
+
+ align:start position:0%
+them out in that sort of detail here but
+ 
+
+ align:start position:0%
+them out in that sort of detail here but
+what I'd like to do is explain the rules
+
+ align:start position:0%
+what I'd like to do is explain the rules
+ 
+
+ align:start position:0%
+what I'd like to do is explain the rules
+you can read them at your leisure and
+
+ align:start position:0%
+you can read them at your leisure and
+ 
+
+ align:start position:0%
+you can read them at your leisure and
+then also illustrate the ones that we've
+
+ align:start position:0%
+then also illustrate the ones that we've
+ 
+
+ align:start position:0%
+then also illustrate the ones that we've
+already seen in our second order system
+
+ align:start position:0%
+already seen in our second order system
+ 
+
+ align:start position:0%
+already seen in our second order system
+the first rule involves the number of
+
+ align:start position:0%
+the first rule involves the number of
+ 
+
+ align:start position:0%
+the first rule involves the number of
+branches and in particular the number of
+
+ align:start position:0%
+branches and in particular the number of
+ 
+
+ align:start position:0%
+branches and in particular the number of
+branches in a root Locus diagram is
+
+ align:start position:0%
+branches in a root Locus diagram is
+ 
+
+ align:start position:0%
+branches in a root Locus diagram is
+equal to the number of poles of capital
+
+ align:start position:0%
+equal to the number of poles of capital
+ 
+
+ align:start position:0%
+equal to the number of poles of capital
+of of the loop transmission the number
+
+ align:start position:0%
+of of the loop transmission the number
+ 
+
+ align:start position:0%
+of of the loop transmission the number
+of poles of the AF
+
+ align:start position:0%
+of poles of the AF
+ 
+
+ align:start position:0%
+of poles of the AF
+product that's simply a statement of the
+
+ align:start position:0%
+product that's simply a statement of the
+ 
+
+ align:start position:0%
+product that's simply a statement of the
+fact that feedback doesn't add any modes
+
+ align:start position:0%
+fact that feedback doesn't add any modes
+ 
+
+ align:start position:0%
+fact that feedback doesn't add any modes
+of energy storage to the system and so
+
+ align:start position:0%
+of energy storage to the system and so
+ 
+
+ align:start position:0%
+of energy storage to the system and so
+if we have three poles in the Loop
+
+ align:start position:0%
+if we have three poles in the Loop
+ 
+
+ align:start position:0%
+if we have three poles in the Loop
+transmission if we have three
+
+ align:start position:0%
+transmission if we have three
+ 
+
+ align:start position:0%
+transmission if we have three
+independent methods of energy storage in
+
+ align:start position:0%
+independent methods of energy storage in
+ 
+
+ align:start position:0%
+independent methods of energy storage in
+the system then in fact all closed loop
+
+ align:start position:0%
+the system then in fact all closed loop
+ 
+
+ align:start position:0%
+the system then in fact all closed loop
+transfer functions also have those three
+
+ align:start position:0%
+transfer functions also have those three
+ 
+
+ align:start position:0%
+transfer functions also have those three
+modes of energy
+
+ align:start position:0%
+modes of energy
+ 
+
+ align:start position:0%
+modes of energy
+storage the second part of rule one
+
+ align:start position:0%
+storage the second part of rule one
+ 
+
+ align:start position:0%
+storage the second part of rule one
+involves the location of the closed loop
+
+ align:start position:0%
+involves the location of the closed loop
+ 
+
+ align:start position:0%
+involves the location of the closed loop
+roots or the closed loop poles for very
+
+ align:start position:0%
+roots or the closed loop poles for very
+ 
+
+ align:start position:0%
+roots or the closed loop poles for very
+large and for very small values of the a
+
+ align:start position:0%
+large and for very small values of the a
+ 
+
+ align:start position:0%
+large and for very small values of the a
+FN product in particular satisfaction of
+
+ align:start position:0%
+FN product in particular satisfaction of
+ 
+
+ align:start position:0%
+FN product in particular satisfaction of
+the magnitude condition this becomes a
+
+ align:start position:0%
+the magnitude condition this becomes a
+ 
+
+ align:start position:0%
+the magnitude condition this becomes a
+little embarrassing since I had
+
+ align:start position:0%
+little embarrassing since I had
+ 
+
+ align:start position:0%
+little embarrassing since I had
+mentioned that the real leverage comes
+
+ align:start position:0%
+mentioned that the real leverage comes
+ 
+
+ align:start position:0%
+mentioned that the real leverage comes
+out of the angle condition and
+
+ align:start position:0%
+out of the angle condition and
+ 
+
+ align:start position:0%
+out of the angle condition and
+unfortunately the first rule is really
+
+ align:start position:0%
+unfortunately the first rule is really
+ 
+
+ align:start position:0%
+unfortunately the first rule is really
+proved using the magnitude condition if
+
+ align:start position:0%
+proved using the magnitude condition if
+ 
+
+ align:start position:0%
+proved using the magnitude condition if
+we rearrange the magnitude condition the
+
+ align:start position:0%
+we rearrange the magnitude condition the
+ 
+
+ align:start position:0%
+we rearrange the magnitude condition the
+magnitude of G of s must be equal to one
+
+ align:start position:0%
+magnitude of G of s must be equal to one
+ 
+
+ align:start position:0%
+magnitude of G of s must be equal to one
+over the a FN product in order to be at
+
+ align:start position:0%
+over the a FN product in order to be at
+ 
+
+ align:start position:0%
+over the a FN product in order to be at
+a point which is a closed loop pole of
+
+ align:start position:0%
+a point which is a closed loop pole of
+ 
+
+ align:start position:0%
+a point which is a closed loop pole of
+capital
+
+ align:start position:0%
+capital
+ 
+
+ align:start position:0%
+capital
+a uh suppose we have a very very small a
+
+ align:start position:0%
+a uh suppose we have a very very small a
+ 
+
+ align:start position:0%
+a uh suppose we have a very very small a
+FN product in order to satisfy the
+
+ align:start position:0%
+FN product in order to satisfy the
+ 
+
+ align:start position:0%
+FN product in order to satisfy the
+magnitude condition
+
+ align:start position:0%
+magnitude condition
+ 
+
+ align:start position:0%
+magnitude condition
+G of s must be very very large in other
+
+ align:start position:0%
+G of s must be very very large in other
+ 
+
+ align:start position:0%
+G of s must be very very large in other
+words we have to be very close to a pole
+
+ align:start position:0%
+words we have to be very close to a pole
+ 
+
+ align:start position:0%
+words we have to be very close to a pole
+of G of s or correspondingly to a pole
+
+ align:start position:0%
+of G of s or correspondingly to a pole
+ 
+
+ align:start position:0%
+of G of s or correspondingly to a pole
+of the loop transmission so our branches
+
+ align:start position:0%
+of the loop transmission so our branches
+ 
+
+ align:start position:0%
+of the loop transmission so our branches
+the branches of our root Locus diagram
+
+ align:start position:0%
+the branches of our root Locus diagram
+ 
+
+ align:start position:0%
+the branches of our root Locus diagram
+start at the poles of the loop
+
+ align:start position:0%
+start at the poles of the loop
+ 
+
+ align:start position:0%
+start at the poles of the loop
+transmission similarly when we have very
+
+ align:start position:0%
+transmission similarly when we have very
+ 
+
+ align:start position:0%
+transmission similarly when we have very
+large values of a
+
+ align:start position:0%
+large values of a
+ 
+
+ align:start position:0%
+large values of a
+f uh let's see for a f not very large
+
+ align:start position:0%
+f uh let's see for a f not very large
+ 
+
+ align:start position:0%
+f uh let's see for a f not very large
+the magnitude of G of s has to be very
+
+ align:start position:0%
+the magnitude of G of s has to be very
+ 
+
+ align:start position:0%
+the magnitude of G of s has to be very
+small in other words we have to be close
+
+ align:start position:0%
+small in other words we have to be close
+ 
+
+ align:start position:0%
+small in other words we have to be close
+to a zero of G of s so the branches
+
+ align:start position:0%
+to a zero of G of s so the branches
+ 
+
+ align:start position:0%
+to a zero of G of s so the branches
+start at poles of the loop transmission
+
+ align:start position:0%
+start at poles of the loop transmission
+ 
+
+ align:start position:0%
+start at poles of the loop transmission
+and end at zeros of the loop
+
+ align:start position:0%
+and end at zeros of the loop
+ 
+
+ align:start position:0%
+and end at zeros of the loop
+transmission where starting and ending
+
+ align:start position:0%
+transmission where starting and ending
+ 
+
+ align:start position:0%
+transmission where starting and ending
+are defined respectively by small values
+
+ align:start position:0%
+are defined respectively by small values
+ 
+
+ align:start position:0%
+are defined respectively by small values
+of a FN and large values of a
+
+ align:start position:0%
+of a FN and large values of a
+ 
+
+ align:start position:0%
+of a FN and large values of a
+FN we've seen that
+
+ align:start position:0%
+FN we've seen that
+ 
+
+ align:start position:0%
+FN we've seen that
+behavior in our second order system uh
+
+ align:start position:0%
+behavior in our second order system uh
+ 
+
+ align:start position:0%
+behavior in our second order system uh
+recall here we had Loop transmission
+
+ align:start position:0%
+recall here we had Loop transmission
+ 
+
+ align:start position:0%
+recall here we had Loop transmission
+poles at the two x locations we used
+
+ align:start position:0%
+poles at the two x locations we used
+ 
+
+ align:start position:0%
+poles at the two x locations we used
+usually indicate Loop transmission poles
+
+ align:start position:0%
+usually indicate Loop transmission poles
+ 
+
+ align:start position:0%
+usually indicate Loop transmission poles
+and zeros for reference points in our
+
+ align:start position:0%
+and zeros for reference points in our
+ 
+
+ align:start position:0%
+and zeros for reference points in our
+root Locus diagram and recall that the
+
+ align:start position:0%
+root Locus diagram and recall that the
+ 
+
+ align:start position:0%
+root Locus diagram and recall that the
+closed loop pole started at this
+
+ align:start position:0%
+closed loop pole started at this
+ 
+
+ align:start position:0%
+closed loop pole started at this
+location for vanishingly small values of
+
+ align:start position:0%
+location for vanishingly small values of
+ 
+
+ align:start position:0%
+location for vanishingly small values of
+a FN and then as a FN got very
+
+ align:start position:0%
+a FN and then as a FN got very
+ 
+
+ align:start position:0%
+a FN and then as a FN got very
+large why the poles went off as or the
+
+ align:start position:0%
+large why the poles went off as or the
+ 
+
+ align:start position:0%
+large why the poles went off as or the
+branches the closed loop poles left the
+
+ align:start position:0%
+branches the closed loop poles left the
+ 
+
+ align:start position:0%
+branches the closed loop poles left the
+S plane as shown well our statement of
+
+ align:start position:0%
+S plane as shown well our statement of
+ 
+
+ align:start position:0%
+S plane as shown well our statement of
+rule one says that they end up the
+
+ align:start position:0%
+rule one says that they end up the
+ 
+
+ align:start position:0%
+rule one says that they end up the
+branches must terminate at zeros for
+
+ align:start position:0%
+branches must terminate at zeros for
+ 
+
+ align:start position:0%
+branches must terminate at zeros for
+very large values of of the AF product
+
+ align:start position:0%
+very large values of of the AF product
+ 
+
+ align:start position:0%
+very large values of of the AF product
+or of a f and here in fact we have a
+
+ align:start position:0%
+or of a f and here in fact we have a
+ 
+
+ align:start position:0%
+or of a f and here in fact we have a
+second order Loop Transmission in other
+
+ align:start position:0%
+second order Loop Transmission in other
+ 
+
+ align:start position:0%
+second order Loop Transmission in other
+words the denominator polinomial is
+
+ align:start position:0%
+words the denominator polinomial is
+ 
+
+ align:start position:0%
+words the denominator polinomial is
+second order in
+
+ align:start position:0%
+second order in
+ 
+
+ align:start position:0%
+second order in
+s and that function goes to zero or the
+
+ align:start position:0%
+s and that function goes to zero or the
+ 
+
+ align:start position:0%
+s and that function goes to zero or the
+the loop transmission goes to zero for
+
+ align:start position:0%
+the loop transmission goes to zero for
+ 
+
+ align:start position:0%
+the loop transmission goes to zero for
+very large values of s and in fact it
+
+ align:start position:0%
+very large values of s and in fact it
+ 
+
+ align:start position:0%
+very large values of s and in fact it
+goes to zero for large values of s as s^
+
+ align:start position:0%
+goes to zero for large values of s as s^
+ 
+
+ align:start position:0%
+goes to zero for large values of s as s^
+s in other words our Loop Transmission
+
+ align:start position:0%
+s in other words our Loop Transmission
+ 
+
+ align:start position:0%
+s in other words our Loop Transmission
+in addition to having two poles at S =
+
+ align:start position:0%
+in addition to having two poles at S =
+ 
+
+ align:start position:0%
+in addition to having two poles at S =
+-1/ T A and S Min - one over T B has two
+
+ align:start position:0%
+-1/ T A and S Min - one over T B has two
+ 
+
+ align:start position:0%
+-1/ T A and S Min - one over T B has two
+zeros at
+
+ align:start position:0%
+zeros at
+ 
+
+ align:start position:0%
+zeros at
+infinity and so uh in this case the
+
+ align:start position:0%
+infinity and so uh in this case the
+ 
+
+ align:start position:0%
+infinity and so uh in this case the
+branches leave the S plane we can
+
+ align:start position:0%
+branches leave the S plane we can
+ 
+
+ align:start position:0%
+branches leave the S plane we can
+consider that as really terminating on
+
+ align:start position:0%
+consider that as really terminating on
+ 
+
+ align:start position:0%
+consider that as really terminating on
+zeros of the loop transmission which
+
+ align:start position:0%
+zeros of the loop transmission which
+ 
+
+ align:start position:0%
+zeros of the loop transmission which
+happen to be located at Infinity one of
+
+ align:start position:0%
+happen to be located at Infinity one of
+ 
+
+ align:start position:0%
+happen to be located at Infinity one of
+the rules that we'll get later on
+
+ align:start position:0%
+the rules that we'll get later on
+ 
+
+ align:start position:0%
+the rules that we'll get later on
+effectively tells us what direction is
+
+ align:start position:0%
+effectively tells us what direction is
+ 
+
+ align:start position:0%
+effectively tells us what direction is
+infinity for a specific Loop
+
+ align:start position:0%
+infinity for a specific Loop
+ 
+
+ align:start position:0%
+infinity for a specific Loop
+transmission that's another important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Point rule two deals with the behavior
+
+ align:start position:0%
+Point rule two deals with the behavior
+ 
+
+ align:start position:0%
+Point rule two deals with the behavior
+on the real
+
+ align:start position:0%
+on the real
+ 
+
+ align:start position:0%
+on the real
+axis and what I've shown here is an S
+
+ align:start position:0%
+axis and what I've shown here is an S
+ 
+
+ align:start position:0%
+axis and what I've shown here is an S
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram suppose we're concerned with the
+
+ align:start position:0%
+diagram suppose we're concerned with the
+ 
+
+ align:start position:0%
+diagram suppose we're concerned with the
+portions of the real axis where branches
+
+ align:start position:0%
+portions of the real axis where branches
+ 
+
+ align:start position:0%
+portions of the real axis where branches
+of the root Locus diagram can exist and
+
+ align:start position:0%
+of the root Locus diagram can exist and
+ 
+
+ align:start position:0%
+of the root Locus diagram can exist and
+in fact must exist suppose we'd like to
+
+ align:start position:0%
+in fact must exist suppose we'd like to
+ 
+
+ align:start position:0%
+in fact must exist suppose we'd like to
+test some part of the real axis possibly
+
+ align:start position:0%
+test some part of the real axis possibly
+ 
+
+ align:start position:0%
+test some part of the real axis possibly
+here to see if that's a possible
+
+ align:start position:0%
+here to see if that's a possible
+ 
+
+ align:start position:0%
+here to see if that's a possible
+location for a branch of the root Locus
+
+ align:start position:0%
+location for a branch of the root Locus
+ 
+
+ align:start position:0%
+location for a branch of the root Locus
+diagram we evaluate the angle of the
+
+ align:start position:0%
+diagram we evaluate the angle of the
+ 
+
+ align:start position:0%
+diagram we evaluate the angle of the
+loop transmission or the angle of G of s
+
+ align:start position:0%
+loop transmission or the angle of G of s
+ 
+
+ align:start position:0%
+loop transmission or the angle of G of s
+at that point and of course we've
+
+ align:start position:0%
+at that point and of course we've
+ 
+
+ align:start position:0%
+at that point and of course we've
+assumed that I have show I'm showing in
+
+ align:start position:0%
+assumed that I have show I'm showing in
+ 
+
+ align:start position:0%
+assumed that I have show I'm showing in
+the diagram the poles and the zeros of G
+
+ align:start position:0%
+the diagram the poles and the zeros of G
+ 
+
+ align:start position:0%
+the diagram the poles and the zeros of G
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+s and when I evaluate the angle of this
+
+ align:start position:0%
+s and when I evaluate the angle of this
+ 
+
+ align:start position:0%
+s and when I evaluate the angle of this
+function I of course draw vectors from
+
+ align:start position:0%
+function I of course draw vectors from
+ 
+
+ align:start position:0%
+function I of course draw vectors from
+the poles and the zeros to the point in
+
+ align:start position:0%
+the poles and the zeros to the point in
+ 
+
+ align:start position:0%
+the poles and the zeros to the point in
+question and let's see for every real
+
+ align:start position:0%
+question and let's see for every real
+ 
+
+ align:start position:0%
+question and let's see for every real
+axis Pole or zero to my right I get a
+
+ align:start position:0%
+axis Pole or zero to my right I get a
+ 
+
+ align:start position:0%
+axis Pole or zero to my right I get a
+net 180° the angle of a vector from this
+
+ align:start position:0%
+net 180° the angle of a vector from this
+ 
+
+ align:start position:0%
+net 180° the angle of a vector from this
+zero to this point is 180° similarly the
+
+ align:start position:0%
+zero to this point is 180° similarly the
+ 
+
+ align:start position:0%
+zero to this point is 180° similarly the
+angle of of a vector from this pole to
+
+ align:start position:0%
+angle of of a vector from this pole to
+ 
+
+ align:start position:0%
+angle of of a vector from this pole to
+this point is minus 180 degre or the net
+
+ align:start position:0%
+this point is minus 180 degre or the net
+ 
+
+ align:start position:0%
+this point is minus 180 degre or the net
+angle since that's a denominator term uh
+
+ align:start position:0%
+angle since that's a denominator term uh
+ 
+
+ align:start position:0%
+angle since that's a denominator term uh
+but every real axis Pole or zero to my
+
+ align:start position:0%
+but every real axis Pole or zero to my
+ 
+
+ align:start position:0%
+but every real axis Pole or zero to my
+right contributes a net 180
+
+ align:start position:0%
+right contributes a net 180
+ 
+
+ align:start position:0%
+right contributes a net 180
+de real axis poles or zeros to the left
+
+ align:start position:0%
+de real axis poles or zeros to the left
+ 
+
+ align:start position:0%
+de real axis poles or zeros to the left
+of the point in question contribute
+
+ align:start position:0%
+of the point in question contribute
+ 
+
+ align:start position:0%
+of the point in question contribute
+nothing to the angle when I draw a
+
+ align:start position:0%
+nothing to the angle when I draw a
+ 
+
+ align:start position:0%
+nothing to the angle when I draw a
+vector from this pole for example to
+
+ align:start position:0%
+vector from this pole for example to
+ 
+
+ align:start position:0%
+vector from this pole for example to
+this point why the angle associated with
+
+ align:start position:0%
+this point why the angle associated with
+ 
+
+ align:start position:0%
+this point why the angle associated with
+that Vector is zero similarly complex
+
+ align:start position:0%
+that Vector is zero similarly complex
+ 
+
+ align:start position:0%
+that Vector is zero similarly complex
+conjugate poles or zeros have angles
+
+ align:start position:0%
+conjugate poles or zeros have angles
+ 
+
+ align:start position:0%
+conjugate poles or zeros have angles
+which sum to a multiple of
+
+ align:start position:0%
+which sum to a multiple of
+ 
+
+ align:start position:0%
+which sum to a multiple of
+360° a given complex conjugate pair has
+
+ align:start position:0%
+360° a given complex conjugate pair has
+ 
+
+ align:start position:0%
+360° a given complex conjugate pair has
+an angle which sums to precisely 360°
+
+ align:start position:0%
+an angle which sums to precisely 360°
+ 
+
+ align:start position:0%
+an angle which sums to precisely 360°
+consider the contribution from this
+
+ align:start position:0%
+consider the contribution from this
+ 
+
+ align:start position:0%
+consider the contribution from this
+complex conjugate zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pair this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle
+
+ align:start position:0%
+angle
+ 
+
+ align:start position:0%
+angle
+plus this angle sum to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+360° well fine the condition then is
+
+ align:start position:0%
+360° well fine the condition then is
+ 
+
+ align:start position:0%
+360° well fine the condition then is
+simply that in order to have an odd
+
+ align:start position:0%
+simply that in order to have an odd
+ 
+
+ align:start position:0%
+simply that in order to have an odd
+multiple of 180 degrees in other words
+
+ align:start position:0%
+multiple of 180 degrees in other words
+ 
+
+ align:start position:0%
+multiple of 180 degrees in other words
+to have a minus sign associated with G
+
+ align:start position:0%
+to have a minus sign associated with G
+ 
+
+ align:start position:0%
+to have a minus sign associated with G
+of s we must have an OD number of poles
+
+ align:start position:0%
+of s we must have an OD number of poles
+ 
+
+ align:start position:0%
+of s we must have an OD number of poles
+and Zer to the right of us on the real
+
+ align:start position:0%
+and Zer to the right of us on the real
+ 
+
+ align:start position:0%
+and Zer to the right of us on the real
+axis since each one of those poles and
+
+ align:start position:0%
+axis since each one of those poles and
+ 
+
+ align:start position:0%
+axis since each one of those poles and
+zeros contributes a net 180° to the
+
+ align:start position:0%
+zeros contributes a net 180° to the
+ 
+
+ align:start position:0%
+zeros contributes a net 180° to the
+angle of G of s consequently the only
+
+ align:start position:0%
+angle of G of s consequently the only
+ 
+
+ align:start position:0%
+angle of G of s consequently the only
+way we can have an odd multiple of 180
+
+ align:start position:0%
+way we can have an odd multiple of 180
+ 
+
+ align:start position:0%
+way we can have an odd multiple of 180
+Dees is to have an odd number of poles
+
+ align:start position:0%
+Dees is to have an odd number of poles
+ 
+
+ align:start position:0%
+Dees is to have an odd number of poles
+and zeros to our right and so in this
+
+ align:start position:0%
+and zeros to our right and so in this
+ 
+
+ align:start position:0%
+and zeros to our right and so in this
+particular situation for this
+
+ align:start position:0%
+particular situation for this
+ 
+
+ align:start position:0%
+particular situation for this
+particular pole and
+
+ align:start position:0%
+particular pole and
+ 
+
+ align:start position:0%
+particular pole and
+zero configuration of G of s this this
+
+ align:start position:0%
+zero configuration of G of s this this
+ 
+
+ align:start position:0%
+zero configuration of G of s this this
+portion of the real axis will have
+
+ align:start position:0%
+portion of the real axis will have
+ 
+
+ align:start position:0%
+portion of the real axis will have
+branches there are three poles and zeros
+
+ align:start position:0%
+branches there are three poles and zeros
+ 
+
+ align:start position:0%
+branches there are three poles and zeros
+to our right similarly this
+
+ align:start position:0%
+to our right similarly this
+ 
+
+ align:start position:0%
+to our right similarly this
+portion will have a branch or branches
+
+ align:start position:0%
+portion will have a branch or branches
+ 
+
+ align:start position:0%
+portion will have a branch or branches
+there are again uh one an odd number of
+
+ align:start position:0%
+there are again uh one an odd number of
+ 
+
+ align:start position:0%
+there are again uh one an odd number of
+zeros in this case to our
+
+ align:start position:0%
+zeros in this case to our
+ 
+
+ align:start position:0%
+zeros in this case to our
+right rule three deals with the behavior
+
+ align:start position:0%
+right rule three deals with the behavior
+ 
+
+ align:start position:0%
+right rule three deals with the behavior
+on portions of the real axis where the
+
+ align:start position:0%
+on portions of the real axis where the
+ 
+
+ align:start position:0%
+on portions of the real axis where the
+branches exist we've determined Those
+
+ align:start position:0%
+branches exist we've determined Those
+ 
+
+ align:start position:0%
+branches exist we've determined Those
+portions from rule two and if in fact
+
+ align:start position:0%
+portions from rule two and if in fact
+ 
+
+ align:start position:0%
+portions from rule two and if in fact
+there are portions of the real axis
+
+ align:start position:0%
+there are portions of the real axis
+ 
+
+ align:start position:0%
+there are portions of the real axis
+between either two pairs of poles we saw
+
+ align:start position:0%
+between either two pairs of poles we saw
+ 
+
+ align:start position:0%
+between either two pairs of poles we saw
+an example of that when we were
+
+ align:start position:0%
+an example of that when we were
+ 
+
+ align:start position:0%
+an example of that when we were
+discussing rule two or between two
+
+ align:start position:0%
+discussing rule two or between two
+ 
+
+ align:start position:0%
+discussing rule two or between two
+zeros why there have to be two separate
+
+ align:start position:0%
+zeros why there have to be two separate
+ 
+
+ align:start position:0%
+zeros why there have to be two separate
+branches in those locations in other
+
+ align:start position:0%
+branches in those locations in other
+ 
+
+ align:start position:0%
+branches in those locations in other
+words we've said that branches start at
+
+ align:start position:0%
+words we've said that branches start at
+ 
+
+ align:start position:0%
+words we've said that branches start at
+poles of the loop transmission and
+
+ align:start position:0%
+poles of the loop transmission and
+ 
+
+ align:start position:0%
+poles of the loop transmission and
+consequently if there are two poles and
+
+ align:start position:0%
+consequently if there are two poles and
+ 
+
+ align:start position:0%
+consequently if there are two poles and
+if the real axis between them as here uh
+
+ align:start position:0%
+if the real axis between them as here uh
+ 
+
+ align:start position:0%
+if the real axis between them as here uh
+has branches on it there must be two
+
+ align:start position:0%
+has branches on it there must be two
+ 
+
+ align:start position:0%
+has branches on it there must be two
+branches and the only thing that can
+
+ align:start position:0%
+branches and the only thing that can
+ 
+
+ align:start position:0%
+branches and the only thing that can
+happen as a FN increases these branches
+
+ align:start position:0%
+happen as a FN increases these branches
+ 
+
+ align:start position:0%
+happen as a FN increases these branches
+recall start at the poles of G ofs or
+
+ align:start position:0%
+recall start at the poles of G ofs or
+ 
+
+ align:start position:0%
+recall start at the poles of G ofs or
+the poles of the loop transmission for
+
+ align:start position:0%
+the poles of the loop transmission for
+ 
+
+ align:start position:0%
+the poles of the loop transmission for
+small values of a f as we increase a FN
+
+ align:start position:0%
+small values of a f as we increase a FN
+ 
+
+ align:start position:0%
+small values of a f as we increase a FN
+the two branches come together but they
+
+ align:start position:0%
+the two branches come together but they
+ 
+
+ align:start position:0%
+the two branches come together but they
+must eventually leave the real axis so
+
+ align:start position:0%
+must eventually leave the real axis so
+ 
+
+ align:start position:0%
+must eventually leave the real axis so
+that they can reach zeros somewhere and
+
+ align:start position:0%
+that they can reach zeros somewhere and
+ 
+
+ align:start position:0%
+that they can reach zeros somewhere and
+consequently they must break away from
+
+ align:start position:0%
+consequently they must break away from
+ 
+
+ align:start position:0%
+consequently they must break away from
+the real axis at some point between the
+
+ align:start position:0%
+the real axis at some point between the
+ 
+
+ align:start position:0%
+the real axis at some point between the
+two poles similarly if there are two
+
+ align:start position:0%
+two poles similarly if there are two
+ 
+
+ align:start position:0%
+two poles similarly if there are two
+zeros surrounding a portion of the real
+
+ align:start position:0%
+zeros surrounding a portion of the real
+ 
+
+ align:start position:0%
+zeros surrounding a portion of the real
+axis where branches exist for some value
+
+ align:start position:0%
+axis where branches exist for some value
+ 
+
+ align:start position:0%
+axis where branches exist for some value
+of a FN the branches must enter the real
+
+ align:start position:0%
+of a FN the branches must enter the real
+ 
+
+ align:start position:0%
+of a FN the branches must enter the real
+axis and then head off toward those two
+
+ align:start position:0%
+axis and then head off toward those two
+ 
+
+ align:start position:0%
+axis and then head off toward those two
+zeros for larger values of a f and so
+
+ align:start position:0%
+zeros for larger values of a f and so
+ 
+
+ align:start position:0%
+zeros for larger values of a f and so
+there has to have to be either Breakaway
+
+ align:start position:0%
+there has to have to be either Breakaway
+ 
+
+ align:start position:0%
+there has to have to be either Breakaway
+points between two pairs of poles where
+
+ align:start position:0%
+points between two pairs of poles where
+ 
+
+ align:start position:0%
+points between two pairs of poles where
+branches exist or entry points to the
+
+ align:start position:0%
+branches exist or entry points to the
+ 
+
+ align:start position:0%
+branches exist or entry points to the
+real axis between two pairs of zeros
+
+ align:start position:0%
+real axis between two pairs of zeros
+ 
+
+ align:start position:0%
+real axis between two pairs of zeros
+where branches exist and we can solve
+
+ align:start position:0%
+where branches exist and we can solve
+ 
+
+ align:start position:0%
+where branches exist and we can solve
+for the location of those entry points
+
+ align:start position:0%
+for the location of those entry points
+ 
+
+ align:start position:0%
+for the location of those entry points
+by considering an equation DG of s by DS
+
+ align:start position:0%
+by considering an equation DG of s by DS
+ 
+
+ align:start position:0%
+by considering an equation DG of s by DS
+equals z let me point out that it's not
+
+ align:start position:0%
+equals z let me point out that it's not
+ 
+
+ align:start position:0%
+equals z let me point out that it's not
+always necessary to solve precisely for
+
+ align:start position:0%
+always necessary to solve precisely for
+ 
+
+ align:start position:0%
+always necessary to solve precisely for
+such entry or Breakaway points in fact
+
+ align:start position:0%
+such entry or Breakaway points in fact
+ 
+
+ align:start position:0%
+such entry or Breakaway points in fact
+my own feeling is that a very real
+
+ align:start position:0%
+my own feeling is that a very real
+ 
+
+ align:start position:0%
+my own feeling is that a very real
+benefit of a root Locus technique is
+
+ align:start position:0%
+benefit of a root Locus technique is
+ 
+
+ align:start position:0%
+benefit of a root Locus technique is
+that it gives us a way to very quickly
+
+ align:start position:0%
+that it gives us a way to very quickly
+ 
+
+ align:start position:0%
+that it gives us a way to very quickly
+sketch important features of a loop
+
+ align:start position:0%
+sketch important features of a loop
+ 
+
+ align:start position:0%
+sketch important features of a loop
+transmission or of a closed loop
+
+ align:start position:0%
+transmission or of a closed loop
+ 
+
+ align:start position:0%
+transmission or of a closed loop
+transfer function and therefore very
+
+ align:start position:0%
+transfer function and therefore very
+ 
+
+ align:start position:0%
+transfer function and therefore very
+very frequently we're not interested in
+
+ align:start position:0%
+very frequently we're not interested in
+ 
+
+ align:start position:0%
+very frequently we're not interested in
+exact numerical results we get enough
+
+ align:start position:0%
+exact numerical results we get enough
+ 
+
+ align:start position:0%
+exact numerical results we get enough
+feeling for what's going on on by by
+
+ align:start position:0%
+feeling for what's going on on by by
+ 
+
+ align:start position:0%
+feeling for what's going on on by by
+approximate techniques however if we are
+
+ align:start position:0%
+approximate techniques however if we are
+ 
+
+ align:start position:0%
+approximate techniques however if we are
+interested in getting precise numerical
+
+ align:start position:0%
+interested in getting precise numerical
+ 
+
+ align:start position:0%
+interested in getting precise numerical
+results one of the things we might need
+
+ align:start position:0%
+results one of the things we might need
+ 
+
+ align:start position:0%
+results one of the things we might need
+to know is are the Breakaway points we
+
+ align:start position:0%
+to know is are the Breakaway points we
+ 
+
+ align:start position:0%
+to know is are the Breakaway points we
+can get that from the equation that I've
+
+ align:start position:0%
+can get that from the equation that I've
+ 
+
+ align:start position:0%
+can get that from the equation that I've
+indicated again we've seen this behavior
+
+ align:start position:0%
+indicated again we've seen this behavior
+ 
+
+ align:start position:0%
+indicated again we've seen this behavior
+in our second order system notice that
+
+ align:start position:0%
+in our second order system notice that
+ 
+
+ align:start position:0%
+in our second order system notice that
+here we have uh the two branches coming
+
+ align:start position:0%
+here we have uh the two branches coming
+ 
+
+ align:start position:0%
+here we have uh the two branches coming
+together the real axis in this region
+
+ align:start position:0%
+together the real axis in this region
+ 
+
+ align:start position:0%
+together the real axis in this region
+must in fact be a possible must contain
+
+ align:start position:0%
+must in fact be a possible must contain
+ 
+
+ align:start position:0%
+must in fact be a possible must contain
+branches of of the root Locust diagram
+
+ align:start position:0%
+branches of of the root Locust diagram
+ 
+
+ align:start position:0%
+branches of of the root Locust diagram
+since there's an odd number of of poles
+
+ align:start position:0%
+since there's an odd number of of poles
+ 
+
+ align:start position:0%
+since there's an odd number of of poles
+and zeros to our right in particular
+
+ align:start position:0%
+and zeros to our right in particular
+ 
+
+ align:start position:0%
+and zeros to our right in particular
+there's one pole to our right on the
+
+ align:start position:0%
+there's one pole to our right on the
+ 
+
+ align:start position:0%
+there's one pole to our right on the
+real axis uh the two branches come
+
+ align:start position:0%
+real axis uh the two branches come
+ 
+
+ align:start position:0%
+real axis uh the two branches come
+together they break away the Breakaway
+
+ align:start position:0%
+together they break away the Breakaway
+ 
+
+ align:start position:0%
+together they break away the Breakaway
+is at right angles and that's always the
+
+ align:start position:0%
+is at right angles and that's always the
+ 
+
+ align:start position:0%
+is at right angles and that's always the
+case Breakaway or re-entry to the real
+
+ align:start position:0%
+case Breakaway or re-entry to the real
+ 
+
+ align:start position:0%
+case Breakaway or re-entry to the real
+axis is always at right angles to the
+
+ align:start position:0%
+axis is always at right angles to the
+ 
+
+ align:start position:0%
+axis is always at right angles to the
+axis all the branches May curve
+
+ align:start position:0%
+axis all the branches May curve
+ 
+
+ align:start position:0%
+axis all the branches May curve
+immediately after leaving the real axis
+
+ align:start position:0%
+immediately after leaving the real axis
+ 
+
+ align:start position:0%
+immediately after leaving the real axis
+so the Breakaway occurs at right angles
+
+ align:start position:0%
+so the Breakaway occurs at right angles
+ 
+
+ align:start position:0%
+so the Breakaway occurs at right angles
+if we went through the G ofs that
+
+ align:start position:0%
+if we went through the G ofs that
+ 
+
+ align:start position:0%
+if we went through the G ofs that
+corresponds to this example and solved
+
+ align:start position:0%
+corresponds to this example and solved
+ 
+
+ align:start position:0%
+corresponds to this example and solved
+for break away points we would find that
+
+ align:start position:0%
+for break away points we would find that
+ 
+
+ align:start position:0%
+for break away points we would find that
+it was in fact at the arithmetic mean of
+
+ align:start position:0%
+it was in fact at the arithmetic mean of
+ 
+
+ align:start position:0%
+it was in fact at the arithmetic mean of
+the loop transmission pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+locations rule four uh has to do with
+
+ align:start position:0%
+locations rule four uh has to do with
+ 
+
+ align:start position:0%
+locations rule four uh has to do with
+the average distance of branches from
+
+ align:start position:0%
+the average distance of branches from
+ 
+
+ align:start position:0%
+the average distance of branches from
+the imaginary axis and in particular it
+
+ align:start position:0%
+the imaginary axis and in particular it
+ 
+
+ align:start position:0%
+the imaginary axis and in particular it
+tells us that if the number of poles
+
+ align:start position:0%
+tells us that if the number of poles
+ 
+
+ align:start position:0%
+tells us that if the number of poles
+associated with the loop transmission
+
+ align:start position:0%
+associated with the loop transmission
+ 
+
+ align:start position:0%
+associated with the loop transmission
+which I'll denote by capital P capital P
+
+ align:start position:0%
+which I'll denote by capital P capital P
+ 
+
+ align:start position:0%
+which I'll denote by capital P capital P
+is a number of poles of the loop
+
+ align:start position:0%
+is a number of poles of the loop
+ 
+
+ align:start position:0%
+is a number of poles of the loop
+transmission capital Z is the number of
+
+ align:start position:0%
+transmission capital Z is the number of
+ 
+
+ align:start position:0%
+transmission capital Z is the number of
+zeros associated with Loop transmission
+
+ align:start position:0%
+zeros associated with Loop transmission
+ 
+
+ align:start position:0%
+zeros associated with Loop transmission
+if the number of poles of the loop
+
+ align:start position:0%
+if the number of poles of the loop
+ 
+
+ align:start position:0%
+if the number of poles of the loop
+transmission exceeds the number of zeros
+
+ align:start position:0%
+transmission exceeds the number of zeros
+ 
+
+ align:start position:0%
+transmission exceeds the number of zeros
+by two or more then the average distance
+
+ align:start position:0%
+by two or more then the average distance
+ 
+
+ align:start position:0%
+by two or more then the average distance
+of all closed loop poles from the real
+
+ align:start position:0%
+of all closed loop poles from the real
+ 
+
+ align:start position:0%
+of all closed loop poles from the real
+axis remains
+
+ align:start position:0%
+axis remains
+ 
+
+ align:start position:0%
+axis remains
+constant the proof of this is an
+
+ align:start position:0%
+constant the proof of this is an
+ 
+
+ align:start position:0%
+constant the proof of this is an
+algebraic one I do it in the book and I
+
+ align:start position:0%
+algebraic one I do it in the book and I
+ 
+
+ align:start position:0%
+algebraic one I do it in the book and I
+won't do it here we've again seen that
+
+ align:start position:0%
+won't do it here we've again seen that
+ 
+
+ align:start position:0%
+won't do it here we've again seen that
+behavior in our sample second order
+
+ align:start position:0%
+behavior in our sample second order
+ 
+
+ align:start position:0%
+behavior in our sample second order
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+here again the average distance of the
+
+ align:start position:0%
+here again the average distance of the
+ 
+
+ align:start position:0%
+here again the average distance of the
+two Loop transmission poles from the
+
+ align:start position:0%
+two Loop transmission poles from the
+ 
+
+ align:start position:0%
+two Loop transmission poles from the
+imaginary axis is the quantity shown
+
+ align:start position:0%
+imaginary axis is the quantity shown
+ 
+
+ align:start position:0%
+imaginary axis is the quantity shown
+since our closed loop poles start for
+
+ align:start position:0%
+since our closed loop poles start for
+ 
+
+ align:start position:0%
+since our closed loop poles start for
+small values of a f at these two
+
+ align:start position:0%
+small values of a f at these two
+ 
+
+ align:start position:0%
+small values of a f at these two
+locations that tells us that as the
+
+ align:start position:0%
+locations that tells us that as the
+ 
+
+ align:start position:0%
+locations that tells us that as the
+branches move that average has to be
+
+ align:start position:0%
+branches move that average has to be
+ 
+
+ align:start position:0%
+branches move that average has to be
+maintained and in fact what that implies
+
+ align:start position:0%
+maintained and in fact what that implies
+ 
+
+ align:start position:0%
+maintained and in fact what that implies
+is something we didn't get readily from
+
+ align:start position:0%
+is something we didn't get readily from
+ 
+
+ align:start position:0%
+is something we didn't get readily from
+the algebraic development we had already
+
+ align:start position:0%
+the algebraic development we had already
+ 
+
+ align:start position:0%
+the algebraic development we had already
+performed although we could have gotten
+
+ align:start position:0%
+performed although we could have gotten
+ 
+
+ align:start position:0%
+performed although we could have gotten
+it what it says is that when we
+
+ align:start position:0%
+it what it says is that when we
+ 
+
+ align:start position:0%
+it what it says is that when we
+have achieved a value of a f knot that
+
+ align:start position:0%
+have achieved a value of a f knot that
+ 
+
+ align:start position:0%
+have achieved a value of a f knot that
+gets us to move a given distance inward
+
+ align:start position:0%
+gets us to move a given distance inward
+ 
+
+ align:start position:0%
+gets us to move a given distance inward
+from this Loop transmission pole this
+
+ align:start position:0%
+from this Loop transmission pole this
+ 
+
+ align:start position:0%
+from this Loop transmission pole this
+branch has moved by precisely the same
+
+ align:start position:0%
+branch has moved by precisely the same
+ 
+
+ align:start position:0%
+branch has moved by precisely the same
+distance inward from this closed loop or
+
+ align:start position:0%
+distance inward from this closed loop or
+ 
+
+ align:start position:0%
+distance inward from this closed loop or
+this Loop transmission pole location so
+
+ align:start position:0%
+this Loop transmission pole location so
+ 
+
+ align:start position:0%
+this Loop transmission pole location so
+as these branches move they have to move
+
+ align:start position:0%
+as these branches move they have to move
+ 
+
+ align:start position:0%
+as these branches move they have to move
+symmetrically
+
+ align:start position:0%
+symmetrically
+ 
+
+ align:start position:0%
+symmetrically
+we of course find out that that
+
+ align:start position:0%
+we of course find out that that
+ 
+
+ align:start position:0%
+we of course find out that that
+condition is maintained as we get to
+
+ align:start position:0%
+condition is maintained as we get to
+ 
+
+ align:start position:0%
+condition is maintained as we get to
+complex conjugate pole pairs because
+
+ align:start position:0%
+complex conjugate pole pairs because
+ 
+
+ align:start position:0%
+complex conjugate pole pairs because
+again the average distance this distance
+
+ align:start position:0%
+again the average distance this distance
+ 
+
+ align:start position:0%
+again the average distance this distance
+plus this distance ided two equals this
+
+ align:start position:0%
+plus this distance ided two equals this
+ 
+
+ align:start position:0%
+plus this distance ided two equals this
+distance plus this distance divided
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two rule number five basically deals
+
+ align:start position:0%
+two rule number five basically deals
+ 
+
+ align:start position:0%
+two rule number five basically deals
+with what direction is Infinity uh as
+
+ align:start position:0%
+with what direction is Infinity uh as
+ 
+
+ align:start position:0%
+with what direction is Infinity uh as
+I'd mentioned in the discussion of rule
+
+ align:start position:0%
+I'd mentioned in the discussion of rule
+ 
+
+ align:start position:0%
+I'd mentioned in the discussion of rule
+number one in particular we're
+
+ align:start position:0%
+number one in particular we're
+ 
+
+ align:start position:0%
+number one in particular we're
+interested in the ASM tootes that the
+
+ align:start position:0%
+interested in the ASM tootes that the
+ 
+
+ align:start position:0%
+interested in the ASM tootes that the
+branches make for large values of a
+
+ align:start position:0%
+branches make for large values of a
+ 
+
+ align:start position:0%
+branches make for large values of a
+fnot and the way we evaluate that is as
+
+ align:start position:0%
+fnot and the way we evaluate that is as
+ 
+
+ align:start position:0%
+fnot and the way we evaluate that is as
+follows consider a root Locus diagram
+
+ align:start position:0%
+follows consider a root Locus diagram
+ 
+
+ align:start position:0%
+follows consider a root Locus diagram
+and let's suppose we want to evaluate
+
+ align:start position:0%
+and let's suppose we want to evaluate
+ 
+
+ align:start position:0%
+and let's suppose we want to evaluate
+the angle associated with G of s when
+
+ align:start position:0%
+the angle associated with G of s when
+ 
+
+ align:start position:0%
+the angle associated with G of s when
+we're very far from the origin in other
+
+ align:start position:0%
+we're very far from the origin in other
+ 
+
+ align:start position:0%
+we're very far from the origin in other
+words let's consider what happens when
+
+ align:start position:0%
+words let's consider what happens when
+ 
+
+ align:start position:0%
+words let's consider what happens when
+we're evaluating the angle of G of s
+
+ align:start position:0%
+we're evaluating the angle of G of s
+ 
+
+ align:start position:0%
+we're evaluating the angle of G of s
+somewhere out
+
+ align:start position:0%
+somewhere out
+ 
+
+ align:start position:0%
+somewhere out
+here as we look from our test point back
+
+ align:start position:0%
+here as we look from our test point back
+ 
+
+ align:start position:0%
+here as we look from our test point back
+toward the finite s plane why all the
+
+ align:start position:0%
+toward the finite s plane why all the
+ 
+
+ align:start position:0%
+toward the finite s plane why all the
+poles and zeros associated with G of s
+
+ align:start position:0%
+poles and zeros associated with G of s
+ 
+
+ align:start position:0%
+poles and zeros associated with G of s
+make just about the same angle the
+
+ align:start position:0%
+make just about the same angle the
+ 
+
+ align:start position:0%
+make just about the same angle the
+vectors to all of those poles make just
+
+ align:start position:0%
+vectors to all of those poles make just
+ 
+
+ align:start position:0%
+vectors to all of those poles make just
+about the same angle with the real axis
+
+ align:start position:0%
+about the same angle with the real axis
+ 
+
+ align:start position:0%
+about the same angle with the real axis
+in other words when we're evaluating the
+
+ align:start position:0%
+in other words when we're evaluating the
+ 
+
+ align:start position:0%
+in other words when we're evaluating the
+angle way up there uh it doesn't matter
+
+ align:start position:0%
+angle way up there uh it doesn't matter
+ 
+
+ align:start position:0%
+angle way up there uh it doesn't matter
+much which of these poles are zeros we
+
+ align:start position:0%
+much which of these poles are zeros we
+ 
+
+ align:start position:0%
+much which of these poles are zeros we
+draw the vector from the angle is just
+
+ align:start position:0%
+draw the vector from the angle is just
+ 
+
+ align:start position:0%
+draw the vector from the angle is just
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+same and consequently the angle of G of
+
+ align:start position:0%
+same and consequently the angle of G of
+ 
+
+ align:start position:0%
+same and consequently the angle of G of
+s evaluated at a point far from the
+
+ align:start position:0%
+s evaluated at a point far from the
+ 
+
+ align:start position:0%
+s evaluated at a point far from the
+origin is equal
+
+ align:start position:0%
+origin is equal
+ 
+
+ align:start position:0%
+origin is equal
+to or must satisfy the condition such
+
+ align:start position:0%
+to or must satisfy the condition such
+ 
+
+ align:start position:0%
+to or must satisfy the condition such
+that Z * Theta Theta is the angle of
+
+ align:start position:0%
+that Z * Theta Theta is the angle of
+ 
+
+ align:start position:0%
+that Z * Theta Theta is the angle of
+course z is the number of zeros minus P
+
+ align:start position:0%
+course z is the number of zeros minus P
+ 
+
+ align:start position:0%
+course z is the number of zeros minus P
+* Theta p is the number of poles must
+
+ align:start position:0%
+* Theta p is the number of poles must
+ 
+
+ align:start position:0%
+* Theta p is the number of poles must
+equal an odd multiple of 180 degre
+
+ align:start position:0%
+equal an odd multiple of 180 degre
+ 
+
+ align:start position:0%
+equal an odd multiple of 180 degre
+we can solve that equation to determine
+
+ align:start position:0%
+we can solve that equation to determine
+ 
+
+ align:start position:0%
+we can solve that equation to determine
+Theta and that gives us the ASM totic
+
+ align:start position:0%
+Theta and that gives us the ASM totic
+ 
+
+ align:start position:0%
+Theta and that gives us the ASM totic
+behavior of the branches far from the
+
+ align:start position:0%
+behavior of the branches far from the
+ 
+
+ align:start position:0%
+behavior of the branches far from the
+origin if we did that we'd get the Theta
+
+ align:start position:0%
+origin if we did that we'd get the Theta
+ 
+
+ align:start position:0%
+origin if we did that we'd get the Theta
+has to be equal to an odd multiple of
+
+ align:start position:0%
+has to be equal to an odd multiple of
+ 
+
+ align:start position:0%
+has to be equal to an odd multiple of
+180° actually over Z minus P this really
+
+ align:start position:0%
+180° actually over Z minus P this really
+ 
+
+ align:start position:0%
+180° actually over Z minus P this really
+isn't an error however because we're
+
+ align:start position:0%
+isn't an error however because we're
+ 
+
+ align:start position:0%
+isn't an error however because we're
+going to allow n to take on all possible
+
+ align:start position:0%
+going to allow n to take on all possible
+ 
+
+ align:start position:0%
+going to allow n to take on all possible
+integral values both positive and
+
+ align:start position:0%
+integral values both positive and
+ 
+
+ align:start position:0%
+integral values both positive and
+negative by convention since most
+
+ align:start position:0%
+negative by convention since most
+ 
+
+ align:start position:0%
+negative by convention since most
+systems have more poles in their Loop
+
+ align:start position:0%
+systems have more poles in their Loop
+ 
+
+ align:start position:0%
+systems have more poles in their Loop
+trans Mission than zeros reflecting the
+
+ align:start position:0%
+trans Mission than zeros reflecting the
+ 
+
+ align:start position:0%
+trans Mission than zeros reflecting the
+fact that that the world is basically
+
+ align:start position:0%
+fact that that the world is basically
+ 
+
+ align:start position:0%
+fact that that the world is basically
+low pass in nature we choose to write
+
+ align:start position:0%
+low pass in nature we choose to write
+ 
+
+ align:start position:0%
+low pass in nature we choose to write
+the denominator in a way that it becomes
+
+ align:start position:0%
+the denominator in a way that it becomes
+ 
+
+ align:start position:0%
+the denominator in a way that it becomes
+positive so we write the denominator as
+
+ align:start position:0%
+positive so we write the denominator as
+ 
+
+ align:start position:0%
+positive so we write the denominator as
+P minus Z we've already seen that
+
+ align:start position:0%
+P minus Z we've already seen that
+ 
+
+ align:start position:0%
+P minus Z we've already seen that
+behavior again in the one root Locus
+
+ align:start position:0%
+behavior again in the one root Locus
+ 
+
+ align:start position:0%
+behavior again in the one root Locus
+diagram that we've
+
+ align:start position:0%
+diagram that we've
+ 
+
+ align:start position:0%
+diagram that we've
+constructed here we have two poles
+
+ align:start position:0%
+constructed here we have two poles
+ 
+
+ align:start position:0%
+constructed here we have two poles
+capital P is 2 Z is zero and so if we
+
+ align:start position:0%
+capital P is 2 Z is zero and so if we
+ 
+
+ align:start position:0%
+capital P is 2 Z is zero and so if we
+took uh n equal to zero and solved for
+
+ align:start position:0%
+took uh n equal to zero and solved for
+ 
+
+ align:start position:0%
+took uh n equal to zero and solved for
+the Ang Les of the ASM tootes we'd find
+
+ align:start position:0%
+the Ang Les of the ASM tootes we'd find
+ 
+
+ align:start position:0%
+the Ang Les of the ASM tootes we'd find
+out that those angles were or that angle
+
+ align:start position:0%
+out that those angles were or that angle
+ 
+
+ align:start position:0%
+out that those angles were or that angle
+was 180° divided by 2 in other words
+
+ align:start position:0%
+was 180° divided by 2 in other words
+ 
+
+ align:start position:0%
+was 180° divided by 2 in other words
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+90° similarly when we allowed n to be
+
+ align:start position:0%
+90° similarly when we allowed n to be
+ 
+
+ align:start position:0%
+90° similarly when we allowed n to be
+equal to 1 we'd find that the angle was
+
+ align:start position:0%
+equal to 1 we'd find that the angle was
+ 
+
+ align:start position:0%
+equal to 1 we'd find that the angle was
+3 *
+
+ align:start position:0%
+3 *
+ 
+
+ align:start position:0%
+3 *
+180° ided 2 or
+
+ align:start position:0%
+180° ided 2 or
+ 
+
+ align:start position:0%
+180° ided 2 or
+270° so that gets us an as ASM toote in
+
+ align:start position:0%
+270° so that gets us an as ASM toote in
+ 
+
+ align:start position:0%
+270° so that gets us an as ASM toote in
+this direction similarly if we allowed n
+
+ align:start position:0%
+this direction similarly if we allowed n
+ 
+
+ align:start position:0%
+this direction similarly if we allowed n
+to take on larger Val values we just get
+
+ align:start position:0%
+to take on larger Val values we just get
+ 
+
+ align:start position:0%
+to take on larger Val values we just get
+cyclical values would repeat the 90° and
+
+ align:start position:0%
+cyclical values would repeat the 90° and
+ 
+
+ align:start position:0%
+cyclical values would repeat the 90° and
+270° that we've already seen so there's
+
+ align:start position:0%
+270° that we've already seen so there's
+ 
+
+ align:start position:0%
+270° that we've already seen so there's
+no further information gained from that
+
+ align:start position:0%
+no further information gained from that
+ 
+
+ align:start position:0%
+no further information gained from that
+in this particular system the branches
+
+ align:start position:0%
+in this particular system the branches
+ 
+
+ align:start position:0%
+in this particular system the branches
+coincide with the ASM tootes uh as soon
+
+ align:start position:0%
+coincide with the ASM tootes uh as soon
+ 
+
+ align:start position:0%
+coincide with the ASM tootes uh as soon
+as the branches leave the real axis that
+
+ align:start position:0%
+as the branches leave the real axis that
+ 
+
+ align:start position:0%
+as the branches leave the real axis that
+isn't always the case of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course the second part of rule five
+
+ align:start position:0%
+course the second part of rule five
+ 
+
+ align:start position:0%
+course the second part of rule five
+really tells us where the asmm tootes
+
+ align:start position:0%
+really tells us where the asmm tootes
+ 
+
+ align:start position:0%
+really tells us where the asmm tootes
+intersect the real axis
+
+ align:start position:0%
+intersect the real axis
+ 
+
+ align:start position:0%
+intersect the real axis
+and that intersection by an algebraic
+
+ align:start position:0%
+and that intersection by an algebraic
+ 
+
+ align:start position:0%
+and that intersection by an algebraic
+development simply comes at the sum of
+
+ align:start position:0%
+development simply comes at the sum of
+ 
+
+ align:start position:0%
+development simply comes at the sum of
+the real part of the poles of G of s
+
+ align:start position:0%
+the real part of the poles of G of s
+ 
+
+ align:start position:0%
+the real part of the poles of G of s
+minus the sum of the real part of the
+
+ align:start position:0%
+minus the sum of the real part of the
+ 
+
+ align:start position:0%
+minus the sum of the real part of the
+zeros of G of s once again divided by
+
+ align:start position:0%
+zeros of G of s once again divided by
+ 
+
+ align:start position:0%
+zeros of G of s once again divided by
+the number of poles minus the number of
+
+ align:start position:0%
+the number of poles minus the number of
+ 
+
+ align:start position:0%
+the number of poles minus the number of
+zeros associated with the loop
+
+ align:start position:0%
+zeros associated with the loop
+ 
+
+ align:start position:0%
+zeros associated with the loop
+transmission so this again we could
+
+ align:start position:0%
+transmission so this again we could
+ 
+
+ align:start position:0%
+transmission so this again we could
+check for our particular system we have
+
+ align:start position:0%
+check for our particular system we have
+ 
+
+ align:start position:0%
+check for our particular system we have
+simply Two Poles uh so if we add the
+
+ align:start position:0%
+simply Two Poles uh so if we add the
+ 
+
+ align:start position:0%
+simply Two Poles uh so if we add the
+real parts of the poles divide by two we
+
+ align:start position:0%
+real parts of the poles divide by two we
+ 
+
+ align:start position:0%
+real parts of the poles divide by two we
+end up with the ASM toote intersection
+
+ align:start position:0%
+end up with the ASM toote intersection
+ 
+
+ align:start position:0%
+end up with the ASM toote intersection
+being at the average distance of the
+
+ align:start position:0%
+being at the average distance of the
+ 
+
+ align:start position:0%
+being at the average distance of the
+poles from the imaginary axis the poles
+
+ align:start position:0%
+poles from the imaginary axis the poles
+ 
+
+ align:start position:0%
+poles from the imaginary axis the poles
+of G of s from the imaginary
+
+ align:start position:0%
+of G of s from the imaginary
+ 
+
+ align:start position:0%
+of G of s from the imaginary
+axis rule six tells us the angle that a
+
+ align:start position:0%
+axis rule six tells us the angle that a
+ 
+
+ align:start position:0%
+axis rule six tells us the angle that a
+branch makes uh either leaving a complex
+
+ align:start position:0%
+branch makes uh either leaving a complex
+ 
+
+ align:start position:0%
+branch makes uh either leaving a complex
+conjugate pole for small values of a KN
+
+ align:start position:0%
+conjugate pole for small values of a KN
+ 
+
+ align:start position:0%
+conjugate pole for small values of a KN
+F KN or entering a complex conjugate
+
+ align:start position:0%
+F KN or entering a complex conjugate
+ 
+
+ align:start position:0%
+F KN or entering a complex conjugate
+zero for very large Val values of a FN
+
+ align:start position:0%
+zero for very large Val values of a FN
+ 
+
+ align:start position:0%
+zero for very large Val values of a FN
+in other words if we were interested in
+
+ align:start position:0%
+in other words if we were interested in
+ 
+
+ align:start position:0%
+in other words if we were interested in
+how the branches of the root Locus
+
+ align:start position:0%
+how the branches of the root Locus
+ 
+
+ align:start position:0%
+how the branches of the root Locus
+diagram eventually reached this zero for
+
+ align:start position:0%
+diagram eventually reached this zero for
+ 
+
+ align:start position:0%
+diagram eventually reached this zero for
+very large values of a fnot a branch
+
+ align:start position:0%
+very large values of a fnot a branch
+ 
+
+ align:start position:0%
+very large values of a fnot a branch
+might come into that point uh from
+
+ align:start position:0%
+might come into that point uh from
+ 
+
+ align:start position:0%
+might come into that point uh from
+somewhere in the S plane for
+
+ align:start position:0%
+somewhere in the S plane for
+ 
+
+ align:start position:0%
+somewhere in the S plane for
+sufficiently large values of a fnot and
+
+ align:start position:0%
+sufficiently large values of a fnot and
+ 
+
+ align:start position:0%
+sufficiently large values of a fnot and
+if we were interested in this angle in
+
+ align:start position:0%
+if we were interested in this angle in
+ 
+
+ align:start position:0%
+if we were interested in this angle in
+other words the angle that that Branch
+
+ align:start position:0%
+other words the angle that that Branch
+ 
+
+ align:start position:0%
+other words the angle that that Branch
+had at the time it entered or for the
+
+ align:start position:0%
+had at the time it entered or for the
+ 
+
+ align:start position:0%
+had at the time it entered or for the
+value of a fnot uh when it enters that
+
+ align:start position:0%
+value of a fnot uh when it enters that
+ 
+
+ align:start position:0%
+value of a fnot uh when it enters that
+zero or reaches that zero in particular
+
+ align:start position:0%
+zero or reaches that zero in particular
+ 
+
+ align:start position:0%
+zero or reaches that zero in particular
+this angle why we can determine that
+
+ align:start position:0%
+this angle why we can determine that
+ 
+
+ align:start position:0%
+this angle why we can determine that
+angle by simply evaluating the angle uh
+
+ align:start position:0%
+angle by simply evaluating the angle uh
+ 
+
+ align:start position:0%
+angle by simply evaluating the angle uh
+from all of the poles of G of s taking
+
+ align:start position:0%
+from all of the poles of G of s taking
+ 
+
+ align:start position:0%
+from all of the poles of G of s taking
+the sum of
+
+ align:start position:0%
+the sum of
+ 
+
+ align:start position:0%
+the sum of
+180° plus the angle from all of the
+
+ align:start position:0%
+180° plus the angle from all of the
+ 
+
+ align:start position:0%
+180° plus the angle from all of the
+poles of G of s to the zero in question
+
+ align:start position:0%
+poles of G of s to the zero in question
+ 
+
+ align:start position:0%
+poles of G of s to the zero in question
+minus the angle from all of the other
+
+ align:start position:0%
+minus the angle from all of the other
+ 
+
+ align:start position:0%
+minus the angle from all of the other
+zeros of G of s to the zero in question
+
+ align:start position:0%
+zeros of G of s to the zero in question
+ 
+
+ align:start position:0%
+zeros of G of s to the zero in question
+so this is simply a way of satisfying
+
+ align:start position:0%
+so this is simply a way of satisfying
+ 
+
+ align:start position:0%
+so this is simply a way of satisfying
+the odd multiple of
+
+ align:start position:0%
+the odd multiple of
+ 
+
+ align:start position:0%
+the odd multiple of
+180° at a point in the S plane we can do
+
+ align:start position:0%
+180° at a point in the S plane we can do
+ 
+
+ align:start position:0%
+180° at a point in the S plane we can do
+the same thing if we ask at what angle
+
+ align:start position:0%
+the same thing if we ask at what angle
+ 
+
+ align:start position:0%
+the same thing if we ask at what angle
+does a branch depart a complex conjugate
+
+ align:start position:0%
+does a branch depart a complex conjugate
+ 
+
+ align:start position:0%
+does a branch depart a complex conjugate
+pole for small values of a f you simply
+
+ align:start position:0%
+pole for small values of a f you simply
+ 
+
+ align:start position:0%
+pole for small values of a f you simply
+keep track of the arithmetic you find
+
+ align:start position:0%
+keep track of the arithmetic you find
+ 
+
+ align:start position:0%
+keep track of the arithmetic you find
+out that's
+
+ align:start position:0%
+out that's
+ 
+
+ align:start position:0%
+out that's
+180° plus the sum of the angles when we
+
+ align:start position:0%
+180° plus the sum of the angles when we
+ 
+
+ align:start position:0%
+180° plus the sum of the angles when we
+draw vectors from all of the zeros of
+
+ align:start position:0%
+draw vectors from all of the zeros of
+ 
+
+ align:start position:0%
+draw vectors from all of the zeros of
+the loop transmission to the pole in
+
+ align:start position:0%
+the loop transmission to the pole in
+ 
+
+ align:start position:0%
+the loop transmission to the pole in
+question minus the sum of the angles
+
+ align:start position:0%
+question minus the sum of the angles
+ 
+
+ align:start position:0%
+question minus the sum of the angles
+when we draw vectors from all of the
+
+ align:start position:0%
+when we draw vectors from all of the
+ 
+
+ align:start position:0%
+when we draw vectors from all of the
+poles of the loop transmission to the
+
+ align:start position:0%
+poles of the loop transmission to the
+ 
+
+ align:start position:0%
+poles of the loop transmission to the
+pole in question as to say proving that
+
+ align:start position:0%
+pole in question as to say proving that
+ 
+
+ align:start position:0%
+pole in question as to say proving that
+relationship uh simply involves keeping
+
+ align:start position:0%
+relationship uh simply involves keeping
+ 
+
+ align:start position:0%
+relationship uh simply involves keeping
+books to ensure that we have a net angle
+
+ align:start position:0%
+books to ensure that we have a net angle
+ 
+
+ align:start position:0%
+books to ensure that we have a net angle
+of 180
+
+ align:start position:0%
+of 180
+ 
+
+ align:start position:0%
+of 180
+degrees rule seven is a powerful one
+
+ align:start position:0%
+degrees rule seven is a powerful one
+ 
+
+ align:start position:0%
+degrees rule seven is a powerful one
+which allows us quite often to very
+
+ align:start position:0%
+which allows us quite often to very
+ 
+
+ align:start position:0%
+which allows us quite often to very
+rapidly sketch certain important
+
+ align:start position:0%
+rapidly sketch certain important
+ 
+
+ align:start position:0%
+rapidly sketch certain important
+features of the closed loop transfer
+
+ align:start position:0%
+features of the closed loop transfer
+ 
+
+ align:start position:0%
+features of the closed loop transfer
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+in particular what it tells us is that
+
+ align:start position:0%
+in particular what it tells us is that
+ 
+
+ align:start position:0%
+in particular what it tells us is that
+we have a system which includes a
+
+ align:start position:0%
+we have a system which includes a
+ 
+
+ align:start position:0%
+we have a system which includes a
+collection of poles quite near the
+
+ align:start position:0%
+collection of poles quite near the
+ 
+
+ align:start position:0%
+collection of poles quite near the
+origin relative to some others we're
+
+ align:start position:0%
+origin relative to some others we're
+ 
+
+ align:start position:0%
+origin relative to some others we're
+able to ignore the remote poles and in
+
+ align:start position:0%
+able to ignore the remote poles and in
+ 
+
+ align:start position:0%
+able to ignore the remote poles and in
+fact remote zeros when we're interested
+
+ align:start position:0%
+fact remote zeros when we're interested
+ 
+
+ align:start position:0%
+fact remote zeros when we're interested
+in the behavior of the root Locust
+
+ align:start position:0%
+in the behavior of the root Locust
+ 
+
+ align:start position:0%
+in the behavior of the root Locust
+diagram near the
+
+ align:start position:0%
+diagram near the
+ 
+
+ align:start position:0%
+diagram near the
+origin we can see how that works Suppose
+
+ align:start position:0%
+origin we can see how that works Suppose
+ 
+
+ align:start position:0%
+origin we can see how that works Suppose
+there are a collection of of poles and
+
+ align:start position:0%
+there are a collection of of poles and
+ 
+
+ align:start position:0%
+there are a collection of of poles and
+zeros associated with the loop
+
+ align:start position:0%
+zeros associated with the loop
+ 
+
+ align:start position:0%
+zeros associated with the loop
+transmission that are somewhere down
+
+ align:start position:0%
+transmission that are somewhere down
+ 
+
+ align:start position:0%
+transmission that are somewhere down
+near the
+
+ align:start position:0%
+near the
+ 
+
+ align:start position:0%
+near the
+origin and then there are some
+
+ align:start position:0%
+origin and then there are some
+ 
+
+ align:start position:0%
+origin and then there are some
+additional ones at much higher
+
+ align:start position:0%
+additional ones at much higher
+ 
+
+ align:start position:0%
+additional ones at much higher
+frequencies or much further from the
+
+ align:start position:0%
+frequencies or much further from the
+ 
+
+ align:start position:0%
+frequencies or much further from the
+origin possibly out here this very
+
+ align:start position:0%
+origin possibly out here this very
+ 
+
+ align:start position:0%
+origin possibly out here this very
+frequently happens when we look at at
+
+ align:start position:0%
+frequently happens when we look at at
+ 
+
+ align:start position:0%
+frequently happens when we look at at
+the behavior for example of a transistor
+
+ align:start position:0%
+the behavior for example of a transistor
+ 
+
+ align:start position:0%
+the behavior for example of a transistor
+amplifier an operational amplifier where
+
+ align:start position:0%
+amplifier an operational amplifier where
+ 
+
+ align:start position:0%
+amplifier an operational amplifier where
+there are certain poles possibly those
+
+ align:start position:0%
+there are certain poles possibly those
+ 
+
+ align:start position:0%
+there are certain poles possibly those
+due to collector to base capacitance or
+
+ align:start position:0%
+due to collector to base capacitance or
+ 
+
+ align:start position:0%
+due to collector to base capacitance or
+intentional capacitors that we've added
+
+ align:start position:0%
+intentional capacitors that we've added
+ 
+
+ align:start position:0%
+intentional capacitors that we've added
+to the Circuit that are relatively low
+
+ align:start position:0%
+to the Circuit that are relatively low
+ 
+
+ align:start position:0%
+to the Circuit that are relatively low
+frequency in in nature and there may be
+
+ align:start position:0%
+frequency in in nature and there may be
+ 
+
+ align:start position:0%
+frequency in in nature and there may be
+some zeros at relatively low frequencies
+
+ align:start position:0%
+some zeros at relatively low frequencies
+ 
+
+ align:start position:0%
+some zeros at relatively low frequencies
+as well well and then very frequently
+
+ align:start position:0%
+as well well and then very frequently
+ 
+
+ align:start position:0%
+as well well and then very frequently
+there are other much higher frequency
+
+ align:start position:0%
+there are other much higher frequency
+ 
+
+ align:start position:0%
+there are other much higher frequency
+poles and possibly zeros typically
+
+ align:start position:0%
+poles and possibly zeros typically
+ 
+
+ align:start position:0%
+poles and possibly zeros typically
+occurring out at about Omega T the gain
+
+ align:start position:0%
+occurring out at about Omega T the gain
+ 
+
+ align:start position:0%
+occurring out at about Omega T the gain
+bandwidth product for the transistor and
+
+ align:start position:0%
+bandwidth product for the transistor and
+ 
+
+ align:start position:0%
+bandwidth product for the transistor and
+so this sort of a a pattern very
+
+ align:start position:0%
+so this sort of a a pattern very
+ 
+
+ align:start position:0%
+so this sort of a a pattern very
+frequently exists in electronic
+
+ align:start position:0%
+frequently exists in electronic
+ 
+
+ align:start position:0%
+frequently exists in electronic
+amplifiers similarly uh we can find this
+
+ align:start position:0%
+amplifiers similarly uh we can find this
+ 
+
+ align:start position:0%
+amplifiers similarly uh we can find this
+sort of thing in a mechanical system
+
+ align:start position:0%
+sort of thing in a mechanical system
+ 
+
+ align:start position:0%
+sort of thing in a mechanical system
+there may be certain poles due to the
+
+ align:start position:0%
+there may be certain poles due to the
+ 
+
+ align:start position:0%
+there may be certain poles due to the
+energy storage in lump masses and
+
+ align:start position:0%
+energy storage in lump masses and
+ 
+
+ align:start position:0%
+energy storage in lump masses and
+springs in the system and then we get
+
+ align:start position:0%
+springs in the system and then we get
+ 
+
+ align:start position:0%
+springs in the system and then we get
+into much higher frequency poles poles
+
+ align:start position:0%
+into much higher frequency poles poles
+ 
+
+ align:start position:0%
+into much higher frequency poles poles
+much more remote from the axxis that
+
+ align:start position:0%
+much more remote from the axxis that
+ 
+
+ align:start position:0%
+much more remote from the axxis that
+have to do with things like mechanical
+
+ align:start position:0%
+have to do with things like mechanical
+ 
+
+ align:start position:0%
+have to do with things like mechanical
+resonances in the system so this this
+
+ align:start position:0%
+resonances in the system so this this
+ 
+
+ align:start position:0%
+resonances in the system so this this
+kind of a situation exists quite
+
+ align:start position:0%
+kind of a situation exists quite
+ 
+
+ align:start position:0%
+kind of a situation exists quite
+frequently in feedback systems of
+
+ align:start position:0%
+frequently in feedback systems of
+ 
+
+ align:start position:0%
+frequently in feedback systems of
+Interest well to see why we might be
+
+ align:start position:0%
+Interest well to see why we might be
+ 
+
+ align:start position:0%
+Interest well to see why we might be
+able to ignore remote poles and zeros
+
+ align:start position:0%
+able to ignore remote poles and zeros
+ 
+
+ align:start position:0%
+able to ignore remote poles and zeros
+when we evaluate the or look for the
+
+ align:start position:0%
+when we evaluate the or look for the
+ 
+
+ align:start position:0%
+when we evaluate the or look for the
+branches in the vicinity of the origin
+
+ align:start position:0%
+branches in the vicinity of the origin
+ 
+
+ align:start position:0%
+branches in the vicinity of the origin
+suppose we had found out that this
+
+ align:start position:0%
+suppose we had found out that this
+ 
+
+ align:start position:0%
+suppose we had found out that this
+particular point in fact satisfied the
+
+ align:start position:0%
+particular point in fact satisfied the
+ 
+
+ align:start position:0%
+particular point in fact satisfied the
+conditions necessary to be on a branch
+
+ align:start position:0%
+conditions necessary to be on a branch
+ 
+
+ align:start position:0%
+conditions necessary to be on a branch
+in the absence of these higher frequency
+
+ align:start position:0%
+in the absence of these higher frequency
+ 
+
+ align:start position:0%
+in the absence of these higher frequency
+poles in other words when we evaluated
+
+ align:start position:0%
+poles in other words when we evaluated
+ 
+
+ align:start position:0%
+poles in other words when we evaluated
+the net angle
+
+ align:start position:0%
+the net angle
+ 
+
+ align:start position:0%
+the net angle
+associated with all of these poles and
+
+ align:start position:0%
+associated with all of these poles and
+ 
+
+ align:start position:0%
+associated with all of these poles and
+zeros we'd find out that the net angle
+
+ align:start position:0%
+zeros we'd find out that the net angle
+ 
+
+ align:start position:0%
+zeros we'd find out that the net angle
+evaluated at this point was an odd
+
+ align:start position:0%
+evaluated at this point was an odd
+ 
+
+ align:start position:0%
+evaluated at this point was an odd
+multiple of
+
+ align:start position:0%
+multiple of
+ 
+
+ align:start position:0%
+multiple of
+180° we now ask how does that change if
+
+ align:start position:0%
+180° we now ask how does that change if
+ 
+
+ align:start position:0%
+180° we now ask how does that change if
+we consider the remote poles well we
+
+ align:start position:0%
+we consider the remote poles well we
+ 
+
+ align:start position:0%
+we consider the remote poles well we
+draw some vectors from the remote poles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the net angular contribution from
+
+ align:start position:0%
+but the net angular contribution from
+ 
+
+ align:start position:0%
+but the net angular contribution from
+those remote poles is quite small this
+
+ align:start position:0%
+those remote poles is quite small this
+ 
+
+ align:start position:0%
+those remote poles is quite small this
+angle is small and in fact the complex
+
+ align:start position:0%
+angle is small and in fact the complex
+ 
+
+ align:start position:0%
+angle is small and in fact the complex
+conjugate pair sum to a very small angle
+
+ align:start position:0%
+conjugate pair sum to a very small angle
+ 
+
+ align:start position:0%
+conjugate pair sum to a very small angle
+while one of these angles is quite large
+
+ align:start position:0%
+while one of these angles is quite large
+ 
+
+ align:start position:0%
+while one of these angles is quite large
+the sum of these two angles is very
+
+ align:start position:0%
+the sum of these two angles is very
+ 
+
+ align:start position:0%
+the sum of these two angles is very
+small so the remote poles don't change
+
+ align:start position:0%
+small so the remote poles don't change
+ 
+
+ align:start position:0%
+small so the remote poles don't change
+the net angle of G of s very much
+
+ align:start position:0%
+the net angle of G of s very much
+ 
+
+ align:start position:0%
+the net angle of G of s very much
+evaluated at this point and we can make
+
+ align:start position:0%
+evaluated at this point and we can make
+ 
+
+ align:start position:0%
+evaluated at this point and we can make
+up for that very small change by simply
+
+ align:start position:0%
+up for that very small change by simply
+ 
+
+ align:start position:0%
+up for that very small change by simply
+relocating our Branch a tiny amount
+
+ align:start position:0%
+relocating our Branch a tiny amount
+ 
+
+ align:start position:0%
+relocating our Branch a tiny amount
+recognizing that moving our test point a
+
+ align:start position:0%
+recognizing that moving our test point a
+ 
+
+ align:start position:0%
+recognizing that moving our test point a
+very small amount has a tremendous
+
+ align:start position:0%
+very small amount has a tremendous
+ 
+
+ align:start position:0%
+very small amount has a tremendous
+effect on the angles associated with the
+
+ align:start position:0%
+effect on the angles associated with the
+ 
+
+ align:start position:0%
+effect on the angles associated with the
+vectors from these local poles and zeros
+
+ align:start position:0%
+vectors from these local poles and zeros
+ 
+
+ align:start position:0%
+vectors from these local poles and zeros
+consequently the conclusion that that
+
+ align:start position:0%
+consequently the conclusion that that
+ 
+
+ align:start position:0%
+consequently the conclusion that that
+the remote poles and zeros don't really
+
+ align:start position:0%
+the remote poles and zeros don't really
+ 
+
+ align:start position:0%
+the remote poles and zeros don't really
+contribute very much to the behavior of
+
+ align:start position:0%
+contribute very much to the behavior of
+ 
+
+ align:start position:0%
+contribute very much to the behavior of
+the root Locus diagram in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vicinity rule 8 is simply a restatement
+
+ align:start position:0%
+vicinity rule 8 is simply a restatement
+ 
+
+ align:start position:0%
+vicinity rule 8 is simply a restatement
+of the magnitude condition in other
+
+ align:start position:0%
+of the magnitude condition in other
+ 
+
+ align:start position:0%
+of the magnitude condition in other
+words once we found a point S1 in the S
+
+ align:start position:0%
+words once we found a point S1 in the S
+ 
+
+ align:start position:0%
+words once we found a point S1 in the S
+plane where the angle condition is
+
+ align:start position:0%
+plane where the angle condition is
+ 
+
+ align:start position:0%
+plane where the angle condition is
+satisfied the value of a knot fnot
+
+ align:start position:0%
+satisfied the value of a knot fnot
+ 
+
+ align:start position:0%
+satisfied the value of a knot fnot
+necessary to get us to that point on the
+
+ align:start position:0%
+necessary to get us to that point on the
+ 
+
+ align:start position:0%
+necessary to get us to that point on the
+root Locus branch is simply equal to one
+
+ align:start position:0%
+root Locus branch is simply equal to one
+ 
+
+ align:start position:0%
+root Locus branch is simply equal to one
+over the or the magnitude of 1 over G of
+
+ align:start position:0%
+over the or the magnitude of 1 over G of
+ 
+
+ align:start position:0%
+over the or the magnitude of 1 over G of
+G evaluated at that
+
+ align:start position:0%
+G evaluated at that
+ 
+
+ align:start position:0%
+G evaluated at that
+point well with that
+
+ align:start position:0%
+point well with that
+ 
+
+ align:start position:0%
+point well with that
+as a statement of the rules that we're
+
+ align:start position:0%
+as a statement of the rules that we're
+ 
+
+ align:start position:0%
+as a statement of the rules that we're
+going to use to draw root Locust
+
+ align:start position:0%
+going to use to draw root Locust
+ 
+
+ align:start position:0%
+going to use to draw root Locust
+diagrams I'd like to begin to look at
+
+ align:start position:0%
+diagrams I'd like to begin to look at
+ 
+
+ align:start position:0%
+diagrams I'd like to begin to look at
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+simple pole zero possibilities for Loop
+
+ align:start position:0%
+simple pole zero possibilities for Loop
+ 
+
+ align:start position:0%
+simple pole zero possibilities for Loop
+transmissions and then see the
+
+ align:start position:0%
+transmissions and then see the
+ 
+
+ align:start position:0%
+transmissions and then see the
+corresponding root Locust diagrams the
+
+ align:start position:0%
+corresponding root Locust diagrams the
+ 
+
+ align:start position:0%
+corresponding root Locust diagrams the
+simplest possible case is of course the
+
+ align:start position:0%
+simplest possible case is of course the
+ 
+
+ align:start position:0%
+simplest possible case is of course the
+first order system that has one Loop
+
+ align:start position:0%
+first order system that has one Loop
+ 
+
+ align:start position:0%
+first order system that has one Loop
+transmission pole on the negative real
+
+ align:start position:0%
+transmission pole on the negative real
+ 
+
+ align:start position:0%
+transmission pole on the negative real
+axis so here we have one located let's
+
+ align:start position:0%
+axis so here we have one located let's
+ 
+
+ align:start position:0%
+axis so here we have one located let's
+say at a point minus one over to
+
+ align:start position:0%
+say at a point minus one over to
+ 
+
+ align:start position:0%
+say at a point minus one over to
+a about the only rule we need here is
+
+ align:start position:0%
+a about the only rule we need here is
+ 
+
+ align:start position:0%
+a about the only rule we need here is
+rule number one it tells us that the
+
+ align:start position:0%
+rule number one it tells us that the
+ 
+
+ align:start position:0%
+rule number one it tells us that the
+negative real axis to the left of that
+
+ align:start position:0%
+negative real axis to the left of that
+ 
+
+ align:start position:0%
+negative real axis to the left of that
+Loop transmission pole uh is is a
+
+ align:start position:0%
+Loop transmission pole uh is is a
+ 
+
+ align:start position:0%
+Loop transmission pole uh is is a
+possible location for a branch of the
+
+ align:start position:0%
+possible location for a branch of the
+ 
+
+ align:start position:0%
+possible location for a branch of the
+root Locus diagram and furthermore there
+
+ align:start position:0%
+root Locus diagram and furthermore there
+ 
+
+ align:start position:0%
+root Locus diagram and furthermore there
+is only one branch associated with the
+
+ align:start position:0%
+is only one branch associated with the
+ 
+
+ align:start position:0%
+is only one branch associated with the
+root Locus diagram and so combining
+
+ align:start position:0%
+root Locus diagram and so combining
+ 
+
+ align:start position:0%
+root Locus diagram and so combining
+those two facts tells us that the root
+
+ align:start position:0%
+those two facts tells us that the root
+ 
+
+ align:start position:0%
+those two facts tells us that the root
+Locus diagram simply starts here for
+
+ align:start position:0%
+Locus diagram simply starts here for
+ 
+
+ align:start position:0%
+Locus diagram simply starts here for
+very small values of a f ends at a zero
+
+ align:start position:0%
+very small values of a f ends at a zero
+ 
+
+ align:start position:0%
+very small values of a f ends at a zero
+at Infinity which happens to in this
+
+ align:start position:0%
+at Infinity which happens to in this
+ 
+
+ align:start position:0%
+at Infinity which happens to in this
+case lie out along the negative real
+
+ align:start position:0%
+case lie out along the negative real
+ 
+
+ align:start position:0%
+case lie out along the negative real
+axis since we have one pole if we uh
+
+ align:start position:0%
+axis since we have one pole if we uh
+ 
+
+ align:start position:0%
+axis since we have one pole if we uh
+calculate an ASM toote for example we
+
+ align:start position:0%
+calculate an ASM toote for example we
+ 
+
+ align:start position:0%
+calculate an ASM toote for example we
+find that the ASM toote lies at minus
+
+ align:start position:0%
+find that the ASM toote lies at minus
+ 
+
+ align:start position:0%
+find that the ASM toote lies at minus
+180° so we get the branch traveling out
+
+ align:start position:0%
+180° so we get the branch traveling out
+ 
+
+ align:start position:0%
+180° so we get the branch traveling out
+the negative real axis like so for
+
+ align:start position:0%
+the negative real axis like so for
+ 
+
+ align:start position:0%
+the negative real axis like so for
+increasing a
+
+ align:start position:0%
+increasing a
+ 
+
+ align:start position:0%
+increasing a
+fot I think it's worth pointing out how
+
+ align:start position:0%
+fot I think it's worth pointing out how
+ 
+
+ align:start position:0%
+fot I think it's worth pointing out how
+that car responds with an earlier
+
+ align:start position:0%
+that car responds with an earlier
+ 
+
+ align:start position:0%
+that car responds with an earlier
+development that we've done we looked at
+
+ align:start position:0%
+development that we've done we looked at
+ 
+
+ align:start position:0%
+development that we've done we looked at
+the single pole case when we started our
+
+ align:start position:0%
+the single pole case when we started our
+ 
+
+ align:start position:0%
+the single pole case when we started our
+discussion of the D dynamics of feedback
+
+ align:start position:0%
+discussion of the D dynamics of feedback
+ 
+
+ align:start position:0%
+discussion of the D dynamics of feedback
+systems and uh in fact under under those
+
+ align:start position:0%
+systems and uh in fact under under those
+ 
+
+ align:start position:0%
+systems and uh in fact under under those
+conditions we started with an a of s
+
+ align:start position:0%
+conditions we started with an a of s
+ 
+
+ align:start position:0%
+conditions we started with an a of s
+that was equal to a KN over a single
+
+ align:start position:0%
+that was equal to a KN over a single
+ 
+
+ align:start position:0%
+that was equal to a KN over a single
+pole a single real axis pole and we
+
+ align:start position:0%
+pole a single real axis pole and we
+ 
+
+ align:start position:0%
+pole a single real axis pole and we
+assumed that F was frequency independent
+
+ align:start position:0%
+assumed that F was frequency independent
+ 
+
+ align:start position:0%
+assumed that F was frequency independent
+and equal to F when we calculated the
+
+ align:start position:0%
+and equal to F when we calculated the
+ 
+
+ align:start position:0%
+and equal to F when we calculated the
+closed loop transfer function we
+
+ align:start position:0%
+closed loop transfer function we
+ 
+
+ align:start position:0%
+closed loop transfer function we
+determined that capital A of s was
+
+ align:start position:0%
+determined that capital A of s was
+ 
+
+ align:start position:0%
+determined that capital A of s was
+simply equal to 1 over FN time 1/ to as
+
+ align:start position:0%
+simply equal to 1 over FN time 1/ to as
+ 
+
+ align:start position:0%
+simply equal to 1 over FN time 1/ to as
+/ a f plus 1/ a f + one certainly as we
+
+ align:start position:0%
+/ a f plus 1/ a f + one certainly as we
+ 
+
+ align:start position:0%
+/ a f plus 1/ a f + one certainly as we
+increase the a fot product the condition
+
+ align:start position:0%
+increase the a fot product the condition
+ 
+
+ align:start position:0%
+increase the a fot product the condition
+under which we construct our root Locus
+
+ align:start position:0%
+under which we construct our root Locus
+ 
+
+ align:start position:0%
+under which we construct our root Locus
+diagram the single closed loop pole
+
+ align:start position:0%
+diagram the single closed loop pole
+ 
+
+ align:start position:0%
+diagram the single closed loop pole
+simply moves toward higher frequencies
+
+ align:start position:0%
+simply moves toward higher frequencies
+ 
+
+ align:start position:0%
+simply moves toward higher frequencies
+in other words the coefficient
+
+ align:start position:0%
+in other words the coefficient
+ 
+
+ align:start position:0%
+in other words the coefficient
+associated with the S term becomes
+
+ align:start position:0%
+associated with the S term becomes
+ 
+
+ align:start position:0%
+associated with the S term becomes
+smaller and smaller and smaller in the
+
+ align:start position:0%
+smaller and smaller and smaller in the
+ 
+
+ align:start position:0%
+smaller and smaller and smaller in the
+denominator so we get the behavior that
+
+ align:start position:0%
+denominator so we get the behavior that
+ 
+
+ align:start position:0%
+denominator so we get the behavior that
+we've
+
+ align:start position:0%
+we've
+ 
+
+ align:start position:0%
+we've
+indicated the second order case we've
+
+ align:start position:0%
+indicated the second order case we've
+ 
+
+ align:start position:0%
+indicated the second order case we've
+looked at in considerable detail and so
+
+ align:start position:0%
+looked at in considerable detail and so
+ 
+
+ align:start position:0%
+looked at in considerable detail and so
+I won't look at that again a somewhat
+
+ align:start position:0%
+I won't look at that again a somewhat
+ 
+
+ align:start position:0%
+I won't look at that again a somewhat
+more inter Behavior exists when we
+
+ align:start position:0%
+more inter Behavior exists when we
+ 
+
+ align:start position:0%
+more inter Behavior exists when we
+consider the third order a third order
+
+ align:start position:0%
+consider the third order a third order
+ 
+
+ align:start position:0%
+consider the third order a third order
+system in other words a loop
+
+ align:start position:0%
+system in other words a loop
+ 
+
+ align:start position:0%
+system in other words a loop
+transmission that has three real axis
+
+ align:start position:0%
+transmission that has three real axis
+ 
+
+ align:start position:0%
+transmission that has three real axis
+poles associated with it with it our
+
+ align:start position:0%
+poles associated with it with it our
+ 
+
+ align:start position:0%
+poles associated with it with it our
+rule number one tells us that this
+
+ align:start position:0%
+rule number one tells us that this
+ 
+
+ align:start position:0%
+rule number one tells us that this
+region of the real axis where we have
+
+ align:start position:0%
+region of the real axis where we have
+ 
+
+ align:start position:0%
+region of the real axis where we have
+one pole to the right uh includes
+
+ align:start position:0%
+one pole to the right uh includes
+ 
+
+ align:start position:0%
+one pole to the right uh includes
+contains branches and that this portion
+
+ align:start position:0%
+contains branches and that this portion
+ 
+
+ align:start position:0%
+contains branches and that this portion
+of the real axis uh includes a branch
+
+ align:start position:0%
+of the real axis uh includes a branch
+ 
+
+ align:start position:0%
+of the real axis uh includes a branch
+furthermore we that there there has to
+
+ align:start position:0%
+furthermore we that there there has to
+ 
+
+ align:start position:0%
+furthermore we that there there has to
+be a breakaway Point uh in this region
+
+ align:start position:0%
+be a breakaway Point uh in this region
+ 
+
+ align:start position:0%
+be a breakaway Point uh in this region
+since here we have a branch or a pair of
+
+ align:start position:0%
+since here we have a branch or a pair of
+ 
+
+ align:start position:0%
+since here we have a branch or a pair of
+branches existing between two poles on
+
+ align:start position:0%
+branches existing between two poles on
+ 
+
+ align:start position:0%
+branches existing between two poles on
+the real axis so there has to be a
+
+ align:start position:0%
+the real axis so there has to be a
+ 
+
+ align:start position:0%
+the real axis so there has to be a
+breakaway somewhere between them we'd
+
+ align:start position:0%
+breakaway somewhere between them we'd
+ 
+
+ align:start position:0%
+breakaway somewhere between them we'd
+actually expect let's see that that
+
+ align:start position:0%
+actually expect let's see that that
+ 
+
+ align:start position:0%
+actually expect let's see that that
+Breakaway uh would have to be a little
+
+ align:start position:0%
+Breakaway uh would have to be a little
+ 
+
+ align:start position:0%
+Breakaway uh would have to be a little
+bit to the right of the midpoint if we
+
+ align:start position:0%
+bit to the right of the midpoint if we
+ 
+
+ align:start position:0%
+bit to the right of the midpoint if we
+keep track of the average distance
+
+ align:start position:0%
+keep track of the average distance
+ 
+
+ align:start position:0%
+keep track of the average distance
+because we recognize that this branch is
+
+ align:start position:0%
+because we recognize that this branch is
+ 
+
+ align:start position:0%
+because we recognize that this branch is
+continuously moving to the left
+
+ align:start position:0%
+continuously moving to the left
+ 
+
+ align:start position:0%
+continuously moving to the left
+consequently we'd anticipate that the
+
+ align:start position:0%
+consequently we'd anticipate that the
+ 
+
+ align:start position:0%
+consequently we'd anticipate that the
+Breakaway would have to be just a little
+
+ align:start position:0%
+Breakaway would have to be just a little
+ 
+
+ align:start position:0%
+Breakaway would have to be just a little
+bit to the right of the midpoint here in
+
+ align:start position:0%
+bit to the right of the midpoint here in
+ 
+
+ align:start position:0%
+bit to the right of the midpoint here in
+order to keep the average distance from
+
+ align:start position:0%
+order to keep the average distance from
+ 
+
+ align:start position:0%
+order to keep the average distance from
+the imaginary axis a constant so we
+
+ align:start position:0%
+the imaginary axis a constant so we
+ 
+
+ align:start position:0%
+the imaginary axis a constant so we
+might get a breakaway somewhere in
+
+ align:start position:0%
+might get a breakaway somewhere in
+ 
+
+ align:start position:0%
+might get a breakaway somewhere in
+here we also can calculate the angles of
+
+ align:start position:0%
+here we also can calculate the angles of
+ 
+
+ align:start position:0%
+here we also can calculate the angles of
+the ASM tootes which is useful in this
+
+ align:start position:0%
+the ASM tootes which is useful in this
+ 
+
+ align:start position:0%
+the ASM tootes which is useful in this
+case we have three poles and no zeros
+
+ align:start position:0%
+case we have three poles and no zeros
+ 
+
+ align:start position:0%
+case we have three poles and no zeros
+and consequently we would find expect
+
+ align:start position:0%
+and consequently we would find expect
+ 
+
+ align:start position:0%
+and consequently we would find expect
+ASM tootes at plus 60° 180° / 3 at 180
+
+ align:start position:0%
+ASM tootes at plus 60° 180° / 3 at 180
+ 
+
+ align:start position:0%
+ASM tootes at plus 60° 180° / 3 at 180
+de which is
+
+ align:start position:0%
+de which is
+ 
+
+ align:start position:0%
+de which is
+540° /
+
+ align:start position:0%
+540° /
+ 
+
+ align:start position:0%
+540° /
+3 and let's see we'd also expect U
+
+ align:start position:0%
+3 and let's see we'd also expect U
+ 
+
+ align:start position:0%
+3 and let's see we'd also expect U
+another ASM toote at
+
+ align:start position:0%
+another ASM toote at
+ 
+
+ align:start position:0%
+another ASM toote at
+270° uh for this particular system in
+
+ align:start position:0%
+270° uh for this particular system in
+ 
+
+ align:start position:0%
+270° uh for this particular system in
+other in other words I'm sorry at 300°
+
+ align:start position:0%
+other in other words I'm sorry at 300°
+ 
+
+ align:start position:0%
+other in other words I'm sorry at 300°
+at minus 60° that's
+
+ align:start position:0%
+at minus 60° that's
+ 
+
+ align:start position:0%
+at minus 60° that's
+900° divided 3 so uh we'd anticipate for
+
+ align:start position:0%
+900° divided 3 so uh we'd anticipate for
+ 
+
+ align:start position:0%
+900° divided 3 so uh we'd anticipate for
+large values of a f that there'd be as
+
+ align:start position:0%
+large values of a f that there'd be as
+ 
+
+ align:start position:0%
+large values of a f that there'd be as
+asmp tootes at plus and minus 60° and at
+
+ align:start position:0%
+asmp tootes at plus and minus 60° and at
+ 
+
+ align:start position:0%
+asmp tootes at plus and minus 60° and at
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+180° and the asmp tootes intersect
+
+ align:start position:0%
+180° and the asmp tootes intersect
+ 
+
+ align:start position:0%
+180° and the asmp tootes intersect
+somewhere on the negative part of the S
+
+ align:start position:0%
+somewhere on the negative part of the S
+ 
+
+ align:start position:0%
+somewhere on the negative part of the S
+plane since the real parts of all of
+
+ align:start position:0%
+plane since the real parts of all of
+ 
+
+ align:start position:0%
+plane since the real parts of all of
+these poles are negative and putting
+
+ align:start position:0%
+these poles are negative and putting
+ 
+
+ align:start position:0%
+these poles are negative and putting
+those things together we conclude that
+
+ align:start position:0%
+those things together we conclude that
+ 
+
+ align:start position:0%
+those things together we conclude that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+behavior might be something as follows
+
+ align:start position:0%
+behavior might be something as follows
+ 
+
+ align:start position:0%
+behavior might be something as follows
+these branches eventually getting into
+
+ align:start position:0%
+these branches eventually getting into
+ 
+
+ align:start position:0%
+these branches eventually getting into
+the right into the right half plane
+
+ align:start position:0%
+the right into the right half plane
+ 
+
+ align:start position:0%
+the right into the right half plane
+inlying system of course this third
+
+ align:start position:0%
+inlying system of course this third
+ 
+
+ align:start position:0%
+inlying system of course this third
+order system can become unstable for
+
+ align:start position:0%
+order system can become unstable for
+ 
+
+ align:start position:0%
+order system can become unstable for
+sufficiently large values of a
+
+ align:start position:0%
+sufficiently large values of a
+ 
+
+ align:start position:0%
+sufficiently large values of a
+f and ultimately we get ASM tootes of
+
+ align:start position:0%
+f and ultimately we get ASM tootes of
+ 
+
+ align:start position:0%
+f and ultimately we get ASM tootes of
+plus or minus 60° associated with those
+
+ align:start position:0%
+plus or minus 60° associated with those
+ 
+
+ align:start position:0%
+plus or minus 60° associated with those
+that complex conjugate pair of
+
+ align:start position:0%
+that complex conjugate pair of
+ 
+
+ align:start position:0%
+that complex conjugate pair of
+branches it's interesting to point out a
+
+ align:start position:0%
+branches it's interesting to point out a
+ 
+
+ align:start position:0%
+branches it's interesting to point out a
+special case that we've investigated
+
+ align:start position:0%
+special case that we've investigated
+ 
+
+ align:start position:0%
+special case that we've investigated
+earlier of this three pole situation in
+
+ align:start position:0%
+earlier of this three pole situation in
+ 
+
+ align:start position:0%
+earlier of this three pole situation in
+particular one where we have three
+
+ align:start position:0%
+particular one where we have three
+ 
+
+ align:start position:0%
+particular one where we have three
+coincident poles if you recall we looked
+
+ align:start position:0%
+coincident poles if you recall we looked
+ 
+
+ align:start position:0%
+coincident poles if you recall we looked
+at this situation when we discussed the
+
+ align:start position:0%
+at this situation when we discussed the
+ 
+
+ align:start position:0%
+at this situation when we discussed the
+possibility for in stability in feedback
+
+ align:start position:0%
+possibility for in stability in feedback
+ 
+
+ align:start position:0%
+possibility for in stability in feedback
+systems and in that case the root Locus
+
+ align:start position:0%
+systems and in that case the root Locus
+ 
+
+ align:start position:0%
+systems and in that case the root Locus
+diagram is somewhat degenerate and in
+
+ align:start position:0%
+diagram is somewhat degenerate and in
+ 
+
+ align:start position:0%
+diagram is somewhat degenerate and in
+fact the branches immediately parallel
+
+ align:start position:0%
+fact the branches immediately parallel
+ 
+
+ align:start position:0%
+fact the branches immediately parallel
+the asmp tootes or lie along the ASM
+
+ align:start position:0%
+the asmp tootes or lie along the ASM
+ 
+
+ align:start position:0%
+the asmp tootes or lie along the ASM
+tootes
+
+ align:start position:0%
+tootes
+ 
+
+ align:start position:0%
+tootes
+and look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and in fact if we keep track of the
+
+ align:start position:0%
+this and in fact if we keep track of the
+ 
+
+ align:start position:0%
+this and in fact if we keep track of the
+arithmetic involved if this is
+
+ align:start position:0%
+arithmetic involved if this is
+ 
+
+ align:start position:0%
+arithmetic involved if this is
+60° uh and this point is minus1 over to
+
+ align:start position:0%
+60° uh and this point is minus1 over to
+ 
+
+ align:start position:0%
+60° uh and this point is minus1 over to
+then the
+
+ align:start position:0%
+then the
+ 
+
+ align:start position:0%
+then the
+this Branch crosses in the right into
+
+ align:start position:0%
+this Branch crosses in the right into
+ 
+
+ align:start position:0%
+this Branch crosses in the right into
+the right half plane at S = Plus J Ric 3
+
+ align:start position:0%
+the right half plane at S = Plus J Ric 3
+ 
+
+ align:start position:0%
+the right half plane at S = Plus J Ric 3
+over to since this angle is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+60° we can also use as an aid to
+
+ align:start position:0%
+60° we can also use as an aid to
+ 
+
+ align:start position:0%
+60° we can also use as an aid to
+constructing more accurate root Locus
+
+ align:start position:0%
+constructing more accurate root Locus
+ 
+
+ align:start position:0%
+constructing more accurate root Locus
+diagrams if we feel the need to do that
+
+ align:start position:0%
+diagrams if we feel the need to do that
+ 
+
+ align:start position:0%
+diagrams if we feel the need to do that
+some rather simple arithmetic
+
+ align:start position:0%
+some rather simple arithmetic
+ 
+
+ align:start position:0%
+some rather simple arithmetic
+calculations and I'd like to illustrate
+
+ align:start position:0%
+calculations and I'd like to illustrate
+ 
+
+ align:start position:0%
+calculations and I'd like to illustrate
+that in closing let's consider an AF ofs
+
+ align:start position:0%
+that in closing let's consider an AF ofs
+ 
+
+ align:start position:0%
+that in closing let's consider an AF ofs
+F of s that includes three poles in
+
+ align:start position:0%
+F of s that includes three poles in
+ 
+
+ align:start position:0%
+F of s that includes three poles in
+particular we have a fnot over three
+
+ align:start position:0%
+particular we have a fnot over three
+ 
+
+ align:start position:0%
+particular we have a fnot over three
+real axis poles one located with a time
+
+ align:start position:0%
+real axis poles one located with a time
+ 
+
+ align:start position:0%
+real axis poles one located with a time
+constant of 1 second in other words at s
+
+ align:start position:0%
+constant of 1 second in other words at s
+ 
+
+ align:start position:0%
+constant of 1 second in other words at s
+equal minus1 another one located with a
+
+ align:start position:0%
+equal minus1 another one located with a
+ 
+
+ align:start position:0%
+equal minus1 another one located with a
+time constant of a half a second at s
+
+ align:start position:0%
+time constant of a half a second at s
+ 
+
+ align:start position:0%
+time constant of a half a second at s
+equal min-2 and finally the third real
+
+ align:start position:0%
+equal min-2 and finally the third real
+ 
+
+ align:start position:0%
+equal min-2 and finally the third real
+axis pole with a with a time constant of
+
+ align:start position:0%
+axis pole with a with a time constant of
+ 
+
+ align:start position:0%
+axis pole with a with a time constant of
+a tenth of a second located at s equal
+
+ align:start position:0%
+a tenth of a second located at s equal
+ 
+
+ align:start position:0%
+a tenth of a second located at s equal
+minus1 and I have that one done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so fairly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accurately here in other words we show
+
+ align:start position:0%
+accurately here in other words we show
+ 
+
+ align:start position:0%
+accurately here in other words we show
+the loop transmission pole locations at
+
+ align:start position:0%
+the loop transmission pole locations at
+ 
+
+ align:start position:0%
+the loop transmission pole locations at
+s equal minus1 s = -2 and S = -10 we've
+
+ align:start position:0%
+s equal minus1 s = -2 and S = -10 we've
+ 
+
+ align:start position:0%
+s equal minus1 s = -2 and S = -10 we've
+already looked at some of the features
+
+ align:start position:0%
+already looked at some of the features
+ 
+
+ align:start position:0%
+already looked at some of the features
+of this sort of a diagram uh in
+
+ align:start position:0%
+of this sort of a diagram uh in
+ 
+
+ align:start position:0%
+of this sort of a diagram uh in
+particular branches exist between these
+
+ align:start position:0%
+particular branches exist between these
+ 
+
+ align:start position:0%
+particular branches exist between these
+two poles uh and to the left of the
+
+ align:start position:0%
+two poles uh and to the left of the
+ 
+
+ align:start position:0%
+two poles uh and to the left of the
+third Loop transmission pole the asmm
+
+ align:start position:0%
+third Loop transmission pole the asmm
+ 
+
+ align:start position:0%
+third Loop transmission pole the asmm
+tootes are at plus andus 60° and at
+
+ align:start position:0%
+tootes are at plus andus 60° and at
+ 
+
+ align:start position:0%
+tootes are at plus andus 60° and at
+180° uh for this particular case the ASM
+
+ align:start position:0%
+180° uh for this particular case the ASM
+ 
+
+ align:start position:0%
+180° uh for this particular case the ASM
+tootes intersect the real axis at Min -1
+
+ align:start position:0%
+tootes intersect the real axis at Min -1
+ 
+
+ align:start position:0%
+tootes intersect the real axis at Min -1
+-2 that that gives us minus 3 and
+
+ align:start position:0%
+-2 that that gives us minus 3 and
+ 
+
+ align:start position:0%
+-2 that that gives us minus 3 and
+another minus 10 in other words
+
+ align:start position:0%
+another minus 10 in other words
+ 
+
+ align:start position:0%
+another minus 10 in other words
+-3 divided by the number of poles which
+
+ align:start position:0%
+-3 divided by the number of poles which
+ 
+
+ align:start position:0%
+-3 divided by the number of poles which
+is three so the ASM tootes intersect the
+
+ align:start position:0%
+is three so the ASM tootes intersect the
+ 
+
+ align:start position:0%
+is three so the ASM tootes intersect the
+real axis
+
+ align:start position:0%
+real axis
+ 
+
+ align:start position:0%
+real axis
+at -4 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A3 and using that information we can
+
+ align:start position:0%
+A3 and using that information we can
+ 
+
+ align:start position:0%
+A3 and using that information we can
+begin to sketch the behavior of our root
+
+ align:start position:0%
+begin to sketch the behavior of our root
+ 
+
+ align:start position:0%
+begin to sketch the behavior of our root
+Locus
+
+ align:start position:0%
+Locus
+ 
+
+ align:start position:0%
+Locus
+diagram note that if we totally ignore
+
+ align:start position:0%
+diagram note that if we totally ignore
+ 
+
+ align:start position:0%
+diagram note that if we totally ignore
+the third pole we have this rule that
+
+ align:start position:0%
+the third pole we have this rule that
+ 
+
+ align:start position:0%
+the third pole we have this rule that
+says we can ignore remote poles and
+
+ align:start position:0%
+says we can ignore remote poles and
+ 
+
+ align:start position:0%
+says we can ignore remote poles and
+zeros when we're interested in the
+
+ align:start position:0%
+zeros when we're interested in the
+ 
+
+ align:start position:0%
+zeros when we're interested in the
+behavior near the origin if we totally
+
+ align:start position:0%
+behavior near the origin if we totally
+ 
+
+ align:start position:0%
+behavior near the origin if we totally
+ignore the third pole we'd anticipate
+
+ align:start position:0%
+ignore the third pole we'd anticipate
+ 
+
+ align:start position:0%
+ignore the third pole we'd anticipate
+that Breakaway would occur at the
+
+ align:start position:0%
+that Breakaway would occur at the
+ 
+
+ align:start position:0%
+that Breakaway would occur at the
+arithmetic mean of the location of these
+
+ align:start position:0%
+arithmetic mean of the location of these
+ 
+
+ align:start position:0%
+arithmetic mean of the location of these
+two Loop transmission poles that's what
+
+ align:start position:0%
+two Loop transmission poles that's what
+ 
+
+ align:start position:0%
+two Loop transmission poles that's what
+happens in only the two- pole
+
+ align:start position:0%
+happens in only the two- pole
+ 
+
+ align:start position:0%
+happens in only the two- pole
+case uh that would tell us that
+
+ align:start position:0%
+case uh that would tell us that
+ 
+
+ align:start position:0%
+case uh that would tell us that
+Breakaway would occur at minus
+
+ align:start position:0%
+Breakaway would occur at minus
+ 
+
+ align:start position:0%
+Breakaway would occur at minus
+1.5 on the negative real axis if we
+
+ align:start position:0%
+1.5 on the negative real axis if we
+ 
+
+ align:start position:0%
+1.5 on the negative real axis if we
+actually do a an exact calculation of
+
+ align:start position:0%
+actually do a an exact calculation of
+ 
+
+ align:start position:0%
+actually do a an exact calculation of
+the Breakaway point we find that it
+
+ align:start position:0%
+the Breakaway point we find that it
+ 
+
+ align:start position:0%
+the Breakaway point we find that it
+really occurs at minus
+
+ align:start position:0%
+really occurs at minus
+ 
+
+ align:start position:0%
+really occurs at minus
+1.47 so in this particular system where
+
+ align:start position:0%
+1.47 so in this particular system where
+ 
+
+ align:start position:0%
+1.47 so in this particular system where
+we have two poles located within a
+
+ align:start position:0%
+we have two poles located within a
+ 
+
+ align:start position:0%
+we have two poles located within a
+distance of two units of the origin a
+
+ align:start position:0%
+distance of two units of the origin a
+ 
+
+ align:start position:0%
+distance of two units of the origin a
+third Pole located 10 units from the
+
+ align:start position:0%
+third Pole located 10 units from the
+ 
+
+ align:start position:0%
+third Pole located 10 units from the
+origin we find out that we could predict
+
+ align:start position:0%
+origin we find out that we could predict
+ 
+
+ align:start position:0%
+origin we find out that we could predict
+Breakaway very accurately totally
+
+ align:start position:0%
+Breakaway very accurately totally
+ 
+
+ align:start position:0%
+Breakaway very accurately totally
+ignoring the third
+
+ align:start position:0%
+ignoring the third
+ 
+
+ align:start position:0%
+ignoring the third
+pole we can get some other important
+
+ align:start position:0%
+pole we can get some other important
+ 
+
+ align:start position:0%
+pole we can get some other important
+features of the diagram if we're
+
+ align:start position:0%
+features of the diagram if we're
+ 
+
+ align:start position:0%
+features of the diagram if we're
+interested in that by using rather
+
+ align:start position:0%
+interested in that by using rather
+ 
+
+ align:start position:0%
+interested in that by using rather
+simple numerical techniques for example
+
+ align:start position:0%
+simple numerical techniques for example
+ 
+
+ align:start position:0%
+simple numerical techniques for example
+we talked about Ralph or the Ralph
+
+ align:start position:0%
+we talked about Ralph or the Ralph
+ 
+
+ align:start position:0%
+we talked about Ralph or the Ralph
+Criterion last time and we found that
+
+ align:start position:0%
+Criterion last time and we found that
+ 
+
+ align:start position:0%
+Criterion last time and we found that
+that was a a rather simple numerical
+
+ align:start position:0%
+that was a a rather simple numerical
+ 
+
+ align:start position:0%
+that was a a rather simple numerical
+method that would allow us to determine
+
+ align:start position:0%
+method that would allow us to determine
+ 
+
+ align:start position:0%
+method that would allow us to determine
+the number of closed loop poles of the
+
+ align:start position:0%
+the number of closed loop poles of the
+ 
+
+ align:start position:0%
+the number of closed loop poles of the
+transfer function fun in the right half
+
+ align:start position:0%
+transfer function fun in the right half
+ 
+
+ align:start position:0%
+transfer function fun in the right half
+plane another way to use that as I
+
+ align:start position:0%
+plane another way to use that as I
+ 
+
+ align:start position:0%
+plane another way to use that as I
+indicate in the book and I believe you
+
+ align:start position:0%
+indicate in the book and I believe you
+ 
+
+ align:start position:0%
+indicate in the book and I believe you
+tried with with some of the homework
+
+ align:start position:0%
+tried with with some of the homework
+ 
+
+ align:start position:0%
+tried with with some of the homework
+problems last time is to determine for
+
+ align:start position:0%
+problems last time is to determine for
+ 
+
+ align:start position:0%
+problems last time is to determine for
+example what value of a fot will result
+
+ align:start position:0%
+example what value of a fot will result
+ 
+
+ align:start position:0%
+example what value of a fot will result
+in a complex conjugate pair of poles
+
+ align:start position:0%
+in a complex conjugate pair of poles
+ 
+
+ align:start position:0%
+in a complex conjugate pair of poles
+lying on the imaginary axis if we do
+
+ align:start position:0%
+lying on the imaginary axis if we do
+ 
+
+ align:start position:0%
+lying on the imaginary axis if we do
+that development we can determine the
+
+ align:start position:0%
+that development we can determine the
+ 
+
+ align:start position:0%
+that development we can determine the
+value of a fnot which gets the closed
+
+ align:start position:0%
+value of a fnot which gets the closed
+ 
+
+ align:start position:0%
+value of a fnot which gets the closed
+loop poles to these two points and
+
+ align:start position:0%
+loop poles to these two points and
+ 
+
+ align:start position:0%
+loop poles to these two points and
+furthermore we can also determine the
+
+ align:start position:0%
+furthermore we can also determine the
+ 
+
+ align:start position:0%
+furthermore we can also determine the
+imaginary component when the poles cross
+
+ align:start position:0%
+imaginary component when the poles cross
+ 
+
+ align:start position:0%
+imaginary component when the poles cross
+into the right half plane and we perform
+
+ align:start position:0%
+into the right half plane and we perform
+ 
+
+ align:start position:0%
+into the right half plane and we perform
+that calculation we find that these
+
+ align:start position:0%
+that calculation we find that these
+ 
+
+ align:start position:0%
+that calculation we find that these
+branches cross into the right half plane
+
+ align:start position:0%
+branches cross into the right half plane
+ 
+
+ align:start position:0%
+branches cross into the right half plane
+at points plus and minus J
+
+ align:start position:0%
+at points plus and minus J
+ 
+
+ align:start position:0%
+at points plus and minus J
+5.65 furthermore the value of a FN
+
+ align:start position:0%
+5.65 furthermore the value of a FN
+ 
+
+ align:start position:0%
+5.65 furthermore the value of a FN
+necessary to get a pair of complex
+
+ align:start position:0%
+necessary to get a pair of complex
+ 
+
+ align:start position:0%
+necessary to get a pair of complex
+conjugate poles in the right half plane
+
+ align:start position:0%
+conjugate poles in the right half plane
+ 
+
+ align:start position:0%
+conjugate poles in the right half plane
+in other words to make this third order
+
+ align:start position:0%
+in other words to make this third order
+ 
+
+ align:start position:0%
+in other words to make this third order
+system unstable is an a f value of
+
+ align:start position:0%
+system unstable is an a f value of
+ 
+
+ align:start position:0%
+system unstable is an a f value of
+19.8 we can also uh use rather simple
+
+ align:start position:0%
+19.8 we can also uh use rather simple
+ 
+
+ align:start position:0%
+19.8 we can also uh use rather simple
+algebraic manipulations to determine
+
+ align:start position:0%
+algebraic manipulations to determine
+ 
+
+ align:start position:0%
+algebraic manipulations to determine
+other important features of the diagram
+
+ align:start position:0%
+other important features of the diagram
+ 
+
+ align:start position:0%
+other important features of the diagram
+or as a design aid for example we might
+
+ align:start position:0%
+or as a design aid for example we might
+ 
+
+ align:start position:0%
+or as a design aid for example we might
+we recognize that we have one degree of
+
+ align:start position:0%
+we recognize that we have one degree of
+ 
+
+ align:start position:0%
+we recognize that we have one degree of
+freedom in this particular development
+
+ align:start position:0%
+freedom in this particular development
+ 
+
+ align:start position:0%
+freedom in this particular development
+the only thing we're able to control is
+
+ align:start position:0%
+the only thing we're able to control is
+ 
+
+ align:start position:0%
+the only thing we're able to control is
+the a FN product we're constructing the
+
+ align:start position:0%
+the a FN product we're constructing the
+ 
+
+ align:start position:0%
+the a FN product we're constructing the
+root Locust diagram as a function of a
+
+ align:start position:0%
+root Locust diagram as a function of a
+ 
+
+ align:start position:0%
+root Locust diagram as a function of a
+FN and that's the single degree of
+
+ align:start position:0%
+FN and that's the single degree of
+ 
+
+ align:start position:0%
+FN and that's the single degree of
+Freedom that we have so we might be able
+
+ align:start position:0%
+Freedom that we have so we might be able
+ 
+
+ align:start position:0%
+Freedom that we have so we might be able
+to we expect that we'd be able to
+
+ align:start position:0%
+to we expect that we'd be able to
+ 
+
+ align:start position:0%
+to we expect that we'd be able to
+control one feature of the closed loop
+
+ align:start position:0%
+control one feature of the closed loop
+ 
+
+ align:start position:0%
+control one feature of the closed loop
+response for example uh we might choose
+
+ align:start position:0%
+response for example uh we might choose
+ 
+
+ align:start position:0%
+response for example uh we might choose
+to fix the location of the real axis
+
+ align:start position:0%
+to fix the location of the real axis
+ 
+
+ align:start position:0%
+to fix the location of the real axis
+closed loop pole that's not a
+
+ align:start position:0%
+closed loop pole that's not a
+ 
+
+ align:start position:0%
+closed loop pole that's not a
+particularly useful constraint but it's
+
+ align:start position:0%
+particularly useful constraint but it's
+ 
+
+ align:start position:0%
+particularly useful constraint but it's
+at least one
+
+ align:start position:0%
+at least one
+ 
+
+ align:start position:0%
+at least one
+possibility another one which is
+
+ align:start position:0%
+possibility another one which is
+ 
+
+ align:start position:0%
+possibility another one which is
+probably a more useful constraint might
+
+ align:start position:0%
+probably a more useful constraint might
+ 
+
+ align:start position:0%
+probably a more useful constraint might
+be to exercise our one degree of freedom
+
+ align:start position:0%
+be to exercise our one degree of freedom
+ 
+
+ align:start position:0%
+be to exercise our one degree of freedom
+in order to set the damping ratio of the
+
+ align:start position:0%
+in order to set the damping ratio of the
+ 
+
+ align:start position:0%
+in order to set the damping ratio of the
+complex conjugate pole pair in other
+
+ align:start position:0%
+complex conjugate pole pair in other
+ 
+
+ align:start position:0%
+complex conjugate pole pair in other
+words we recognize that as we increase a
+
+ align:start position:0%
+words we recognize that as we increase a
+ 
+
+ align:start position:0%
+words we recognize that as we increase a
+FN our closed loop poles Move Along
+
+ align:start position:0%
+FN our closed loop poles Move Along
+ 
+
+ align:start position:0%
+FN our closed loop poles Move Along
+these branches and suppose that I would
+
+ align:start position:0%
+these branches and suppose that I would
+ 
+
+ align:start position:0%
+these branches and suppose that I would
+like to design for a given damping ratio
+
+ align:start position:0%
+like to design for a given damping ratio
+ 
+
+ align:start position:0%
+like to design for a given damping ratio
+associated with the Clos Loop pole pair
+
+ align:start position:0%
+associated with the Clos Loop pole pair
+ 
+
+ align:start position:0%
+associated with the Clos Loop pole pair
+these this closed loop pole pair
+
+ align:start position:0%
+these this closed loop pole pair
+ 
+
+ align:start position:0%
+these this closed loop pole pair
+certainly dominates performance since
+
+ align:start position:0%
+certainly dominates performance since
+ 
+
+ align:start position:0%
+certainly dominates performance since
+it's the pole pair closest to the
+
+ align:start position:0%
+it's the pole pair closest to the
+ 
+
+ align:start position:0%
+it's the pole pair closest to the
+imaginary Axis or closest to the origin
+
+ align:start position:0%
+imaginary Axis or closest to the origin
+ 
+
+ align:start position:0%
+imaginary Axis or closest to the origin
+and much closer than the Third
+
+ align:start position:0%
+and much closer than the Third
+ 
+
+ align:start position:0%
+and much closer than the Third
+well what we can do is write the
+
+ align:start position:0%
+well what we can do is write the
+ 
+
+ align:start position:0%
+well what we can do is write the
+polinomial the characteristic equation
+
+ align:start position:0%
+polinomial the characteristic equation
+ 
+
+ align:start position:0%
+polinomial the characteristic equation
+of the closed loop transfer function and
+
+ align:start position:0%
+of the closed loop transfer function and
+ 
+
+ align:start position:0%
+of the closed loop transfer function and
+if for example we'd like to set up for a
+
+ align:start position:0%
+if for example we'd like to set up for a
+ 
+
+ align:start position:0%
+if for example we'd like to set up for a
+damping ratio of 0.5 in other words
+
+ align:start position:0%
+damping ratio of 0.5 in other words
+ 
+
+ align:start position:0%
+damping ratio of 0.5 in other words
+these branches 60° from the real axis
+
+ align:start position:0%
+these branches 60° from the real axis
+ 
+
+ align:start position:0%
+these branches 60° from the real axis
+that implies a given relationship among
+
+ align:start position:0%
+that implies a given relationship among
+ 
+
+ align:start position:0%
+that implies a given relationship among
+the coefficients of the characteristic
+
+ align:start position:0%
+the coefficients of the characteristic
+ 
+
+ align:start position:0%
+the coefficients of the characteristic
+equation and we can use rather simple
+
+ align:start position:0%
+equation and we can use rather simple
+ 
+
+ align:start position:0%
+equation and we can use rather simple
+algebraic manipulations to determine the
+
+ align:start position:0%
+algebraic manipulations to determine the
+ 
+
+ align:start position:0%
+algebraic manipulations to determine the
+value of a FN that matches those
+
+ align:start position:0%
+value of a FN that matches those
+ 
+
+ align:start position:0%
+value of a FN that matches those
+conditions I I do that in the book when
+
+ align:start position:0%
+conditions I I do that in the book when
+ 
+
+ align:start position:0%
+conditions I I do that in the book when
+we go through that development we find
+
+ align:start position:0%
+we go through that development we find
+ 
+
+ align:start position:0%
+we go through that development we find
+out that this
+
+ align:start position:0%
+out that this
+ 
+
+ align:start position:0%
+out that this
+system has a closed loop damping ratio
+
+ align:start position:0%
+system has a closed loop damping ratio
+ 
+
+ align:start position:0%
+system has a closed loop damping ratio
+for the dominant pole pair of 0.5 for an
+
+ align:start position:0%
+for the dominant pole pair of 0.5 for an
+ 
+
+ align:start position:0%
+for the dominant pole pair of 0.5 for an
+a fnot of only
+
+ align:start position:0%
+a fnot of only
+ 
+
+ align:start position:0%
+a fnot of only
+2.2 so in this particular system we find
+
+ align:start position:0%
+2.2 so in this particular system we find
+ 
+
+ align:start position:0%
+2.2 so in this particular system we find
+out that if we'd like to maintain a
+
+ align:start position:0%
+out that if we'd like to maintain a
+ 
+
+ align:start position:0%
+out that if we'd like to maintain a
+reasonable amount of damping where
+
+ align:start position:0%
+reasonable amount of damping where
+ 
+
+ align:start position:0%
+reasonable amount of damping where
+reasonable amount of damping might be a
+
+ align:start position:0%
+reasonable amount of damping might be a
+ 
+
+ align:start position:0%
+reasonable amount of damping might be a
+damping ratio for the dominant pole pair
+
+ align:start position:0%
+damping ratio for the dominant pole pair
+ 
+
+ align:start position:0%
+damping ratio for the dominant pole pair
+of greater than than 0.5 we can only
+
+ align:start position:0%
+of greater than than 0.5 we can only
+ 
+
+ align:start position:0%
+of greater than than 0.5 we can only
+achieve an A F product of 2.2 or a
+
+ align:start position:0%
+achieve an A F product of 2.2 or a
+ 
+
+ align:start position:0%
+achieve an A F product of 2.2 or a
+desensitivity by our original definition
+
+ align:start position:0%
+desensitivity by our original definition
+ 
+
+ align:start position:0%
+desensitivity by our original definition
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+3.2 next time we'll look from a root
+
+ align:start position:0%
+3.2 next time we'll look from a root
+ 
+
+ align:start position:0%
+3.2 next time we'll look from a root
+Locust Point of View at how we might be
+
+ align:start position:0%
+Locust Point of View at how we might be
+ 
+
+ align:start position:0%
+Locust Point of View at how we might be
+able to improve that situation what
+
+ align:start position:0%
+able to improve that situation what
+ 
+
+ align:start position:0%
+able to improve that situation what
+should we do to certain kinds of
+
+ align:start position:0%
+should we do to certain kinds of
+ 
+
+ align:start position:0%
+should we do to certain kinds of
+feedback systems in order to increase
+
+ align:start position:0%
+feedback systems in order to increase
+ 
+
+ align:start position:0%
+feedback systems in order to increase
+the desensitivity we can obtain before
+
+ align:start position:0%
+the desensitivity we can obtain before
+ 
+
+ align:start position:0%
+the desensitivity we can obtain before
+we reach a given degree of instability
+
+ align:start position:0%
+we reach a given degree of instability
+ 
+
+ align:start position:0%
+we reach a given degree of instability
+thank you
\ No newline at end of file
diff --git a/BK1afo-GMag.txt b/BK1afo-GMag.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bdd981953e95f9fa056dd8e89cfa6e42dd9ec9e8
--- /dev/null
+++ b/BK1afo-GMag.txt
@@ -0,0 +1,7211 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu the thing we have to talk
+
+ align:start position:0%
+ocw.mit.edu the thing we have to talk
+ 
+
+ align:start position:0%
+ocw.mit.edu the thing we have to talk
+about here is multicellular
+
+ align:start position:0%
+about here is multicellular
+ 
+
+ align:start position:0%
+about here is multicellular
+life cells although we can think of them
+
+ align:start position:0%
+life cells although we can think of them
+ 
+
+ align:start position:0%
+life cells although we can think of them
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+entities are generally not the unit of a
+
+ align:start position:0%
+entities are generally not the unit of a
+ 
+
+ align:start position:0%
+entities are generally not the unit of a
+whole organism there are many organisms
+
+ align:start position:0%
+whole organism there are many organisms
+ 
+
+ align:start position:0%
+whole organism there are many organisms
+whose unit is a single cell but the
+
+ align:start position:0%
+whose unit is a single cell but the
+ 
+
+ align:start position:0%
+whose unit is a single cell but the
+really interesting ones are the ones
+
+ align:start position:0%
+really interesting ones are the ones
+ 
+
+ align:start position:0%
+really interesting ones are the ones
+that have got lots of
+
+ align:start position:0%
+that have got lots of
+ 
+
+ align:start position:0%
+that have got lots of
+cells and so life has developed in a way
+
+ align:start position:0%
+cells and so life has developed in a way
+ 
+
+ align:start position:0%
+cells and so life has developed in a way
+that most organisms are multicellular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can pose the question of why that
+
+ align:start position:0%
+and we can pose the question of why that
+ 
+
+ align:start position:0%
+and we can pose the question of why that
+might be you know my trite phrase well
+
+ align:start position:0%
+might be you know my trite phrase well
+ 
+
+ align:start position:0%
+might be you know my trite phrase well
+it's more interesting is actually a very
+
+ align:start position:0%
+it's more interesting is actually a very
+ 
+
+ align:start position:0%
+it's more interesting is actually a very
+poor answer there's a much better answer
+
+ align:start position:0%
+poor answer there's a much better answer
+ 
+
+ align:start position:0%
+poor answer there's a much better answer
+and that is if you have something made
+
+ align:start position:0%
+and that is if you have something made
+ 
+
+ align:start position:0%
+and that is if you have something made
+of lots of cells different parts of that
+
+ align:start position:0%
+of lots of cells different parts of that
+ 
+
+ align:start position:0%
+of lots of cells different parts of that
+organism can specialize and do different
+
+ align:start position:0%
+organism can specialize and do different
+ 
+
+ align:start position:0%
+organism can specialize and do different
+things and so you can get a
+
+ align:start position:0%
+things and so you can get a
+ 
+
+ align:start position:0%
+things and so you can get a
+diversification of function with which
+
+ align:start position:0%
+diversification of function with which
+ 
+
+ align:start position:0%
+diversification of function with which
+allows the organism to colonize new
+
+ align:start position:0%
+allows the organism to colonize new
+ 
+
+ align:start position:0%
+allows the organism to colonize new
+parts of the earth interact with its
+
+ align:start position:0%
+parts of the earth interact with its
+ 
+
+ align:start position:0%
+parts of the earth interact with its
+environment in different ways interact
+
+ align:start position:0%
+environment in different ways interact
+ 
+
+ align:start position:0%
+environment in different ways interact
+with other members of its species in
+
+ align:start position:0%
+with other members of its species in
+ 
+
+ align:start position:0%
+with other members of its species in
+different ways and it does become allow
+
+ align:start position:0%
+different ways and it does become allow
+ 
+
+ align:start position:0%
+different ways and it does become allow
+a much greater complexity of life so I
+
+ align:start position:0%
+a much greater complexity of life so I
+ 
+
+ align:start position:0%
+a much greater complexity of life so I
+would say the answer I would give you is
+
+ align:start position:0%
+would say the answer I would give you is
+ 
+
+ align:start position:0%
+would say the answer I would give you is
+it allows new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evolve and greater
+
+ align:start position:0%
+evolve and greater
+ 
+
+ align:start position:0%
+evolve and greater
+complexity of life to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+develop if we consider the human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adult and look and see what we're made
+
+ align:start position:0%
+adult and look and see what we're made
+ 
+
+ align:start position:0%
+adult and look and see what we're made
+of we contain about 400 different kinds
+
+ align:start position:0%
+of we contain about 400 different kinds
+ 
+
+ align:start position:0%
+of we contain about 400 different kinds
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+cells we can call those cell types
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where each cell
+
+ align:start position:0%
+where each cell
+ 
+
+ align:start position:0%
+where each cell
+type has a specialized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function those
+
+ align:start position:0%
+function those
+ 
+
+ align:start position:0%
+function those
+cells are organized together and they're
+
+ align:start position:0%
+cells are organized together and they're
+ 
+
+ align:start position:0%
+cells are organized together and they're
+located in specific
+
+ align:start position:0%
+located in specific
+ 
+
+ align:start position:0%
+located in specific
+places so the cell types are organized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+groups they are organized into
+
+ align:start position:0%
+groups they are organized into
+ 
+
+ align:start position:0%
+groups they are organized into
+three-dimensional structures one of the
+
+ align:start position:0%
+three-dimensional structures one of the
+ 
+
+ align:start position:0%
+three-dimensional structures one of the
+things that is most interesting about
+
+ align:start position:0%
+things that is most interesting about
+ 
+
+ align:start position:0%
+things that is most interesting about
+living organisms is that they're
+
+ align:start position:0%
+living organisms is that they're
+ 
+
+ align:start position:0%
+living organisms is that they're
+3D think of it if we were all sitting
+
+ align:start position:0%
+3D think of it if we were all sitting
+ 
+
+ align:start position:0%
+3D think of it if we were all sitting
+there as flat sheets you know you get
+
+ align:start position:0%
+there as flat sheets you know you get
+ 
+
+ align:start position:0%
+there as flat sheets you know you get
+the idea the 3D is
+
+ align:start position:0%
+the idea the 3D is
+ 
+
+ align:start position:0%
+the idea the 3D is
+extraordinary and it's one of the things
+
+ align:start position:0%
+extraordinary and it's one of the things
+ 
+
+ align:start position:0%
+extraordinary and it's one of the things
+that being multicellular allows you to
+
+ align:start position:0%
+that being multicellular allows you to
+ 
+
+ align:start position:0%
+that being multicellular allows you to
+do so cells are organized into groups
+
+ align:start position:0%
+do so cells are organized into groups
+ 
+
+ align:start position:0%
+do so cells are organized into groups
+they are organized into 3D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structures and this notion of groups of
+
+ align:start position:0%
+structures and this notion of groups of
+ 
+
+ align:start position:0%
+structures and this notion of groups of
+cells and
+
+ align:start position:0%
+cells and
+ 
+
+ align:start position:0%
+cells and
+structures is that they work together
+
+ align:start position:0%
+structures is that they work together
+ 
+
+ align:start position:0%
+structures is that they work together
+groups of cells arranged in a certain
+
+ align:start position:0%
+groups of cells arranged in a certain
+ 
+
+ align:start position:0%
+groups of cells arranged in a certain
+way work together to form a a ho an
+
+ align:start position:0%
+way work together to form a a ho an
+ 
+
+ align:start position:0%
+way work together to form a a ho an
+organ that has got an even greater
+
+ align:start position:0%
+organ that has got an even greater
+ 
+
+ align:start position:0%
+organ that has got an even greater
+specialized
+
+ align:start position:0%
+specialized
+ 
+
+ align:start position:0%
+specialized
+function so these work together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to make
+
+ align:start position:0%
+to make
+ 
+
+ align:start position:0%
+to make
+organs and in particular as we'll talk
+
+ align:start position:0%
+organs and in particular as we'll talk
+ 
+
+ align:start position:0%
+organs and in particular as we'll talk
+about next time it's the groups of cells
+
+ align:start position:0%
+about next time it's the groups of cells
+ 
+
+ align:start position:0%
+about next time it's the groups of cells
+and their 3D structures which makes the
+
+ align:start position:0%
+and their 3D structures which makes the
+ 
+
+ align:start position:0%
+and their 3D structures which makes the
+organs and the organs themselves can be
+
+ align:start position:0%
+organs and the organs themselves can be
+ 
+
+ align:start position:0%
+organs and the organs themselves can be
+organized into Super structures called
+
+ align:start position:0%
+organized into Super structures called
+ 
+
+ align:start position:0%
+organized into Super structures called
+organ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems and we'll work on all of these
+
+ align:start position:0%
+systems and we'll work on all of these
+ 
+
+ align:start position:0%
+systems and we'll work on all of these
+things over the next couple of
+
+ align:start position:0%
+things over the next couple of
+ 
+
+ align:start position:0%
+things over the next couple of
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+today we're going to talk about cell
+
+ align:start position:0%
+today we're going to talk about cell
+ 
+
+ align:start position:0%
+today we're going to talk about cell
+type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is before I'm I'm thinking if I should
+
+ align:start position:0%
+is before I'm I'm thinking if I should
+ 
+
+ align:start position:0%
+is before I'm I'm thinking if I should
+show you a slide first or if I should
+
+ align:start position:0%
+show you a slide first or if I should
+ 
+
+ align:start position:0%
+show you a slide first or if I should
+write this on the board let me show you
+
+ align:start position:0%
+write this on the board let me show you
+ 
+
+ align:start position:0%
+write this on the board let me show you
+a slide first because I want these next
+
+ align:start position:0%
+a slide first because I want these next
+ 
+
+ align:start position:0%
+a slide first because I want these next
+two boards to follow one from another
+
+ align:start position:0%
+two boards to follow one from another
+ 
+
+ align:start position:0%
+two boards to follow one from another
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right different cells oh oh there we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay different cell types these are
+
+ align:start position:0%
+okay different cell types these are
+ 
+
+ align:start position:0%
+okay different cell types these are
+micrographs of different cell types here
+
+ align:start position:0%
+micrographs of different cell types here
+ 
+
+ align:start position:0%
+micrographs of different cell types here
+are red blood cells which regulate
+
+ align:start position:0%
+are red blood cells which regulate
+ 
+
+ align:start position:0%
+are red blood cells which regulate
+oxygen transport spatar involved in rep
+
+ align:start position:0%
+oxygen transport spatar involved in rep
+ 
+
+ align:start position:0%
+oxygen transport spatar involved in rep
+reproduction and neurons involved in
+
+ align:start position:0%
+reproduction and neurons involved in
+ 
+
+ align:start position:0%
+reproduction and neurons involved in
+communication each of them has got the
+
+ align:start position:0%
+communication each of them has got the
+ 
+
+ align:start position:0%
+communication each of them has got the
+basic cellular functions that we've
+
+ align:start position:0%
+basic cellular functions that we've
+ 
+
+ align:start position:0%
+basic cellular functions that we've
+talked about over the last lectures but
+
+ align:start position:0%
+talked about over the last lectures but
+ 
+
+ align:start position:0%
+talked about over the last lectures but
+each of them is obviously
+
+ align:start position:0%
+each of them is obviously
+ 
+
+ align:start position:0%
+each of them is obviously
+morphologically different they look
+
+ align:start position:0%
+morphologically different they look
+ 
+
+ align:start position:0%
+morphologically different they look
+different and they carry out different
+
+ align:start position:0%
+different and they carry out different
+ 
+
+ align:start position:0%
+different and they carry out different
+functions the cell types get organized
+
+ align:start position:0%
+functions the cell types get organized
+ 
+
+ align:start position:0%
+functions the cell types get organized
+in specific ways this is a really really
+
+ align:start position:0%
+in specific ways this is a really really
+ 
+
+ align:start position:0%
+in specific ways this is a really really
+extraordinary example which is the
+
+ align:start position:0%
+extraordinary example which is the
+ 
+
+ align:start position:0%
+extraordinary example which is the
+retina of your eye the light sensitive
+
+ align:start position:0%
+retina of your eye the light sensitive
+ 
+
+ align:start position:0%
+retina of your eye the light sensitive
+part of your eye which contains a number
+
+ align:start position:0%
+part of your eye which contains a number
+ 
+
+ align:start position:0%
+part of your eye which contains a number
+of different kinds of cells and these
+
+ align:start position:0%
+of different kinds of cells and these
+ 
+
+ align:start position:0%
+of different kinds of cells and these
+cells are organized in layers and so
+
+ align:start position:0%
+cells are organized in layers and so
+ 
+
+ align:start position:0%
+cells are organized in layers and so
+they're colorcoded here and you can see
+
+ align:start position:0%
+they're colorcoded here and you can see
+ 
+
+ align:start position:0%
+they're colorcoded here and you can see
+the different layers are grouped
+
+ align:start position:0%
+the different layers are grouped
+ 
+
+ align:start position:0%
+the different layers are grouped
+together but then the different layers
+
+ align:start position:0%
+together but then the different layers
+ 
+
+ align:start position:0%
+together but then the different layers
+communicate with one
+
+ align:start position:0%
+communicate with one
+ 
+
+ align:start position:0%
+communicate with one
+another and this communication and this
+
+ align:start position:0%
+another and this communication and this
+ 
+
+ align:start position:0%
+another and this communication and this
+organization is key you can have all the
+
+ align:start position:0%
+organization is key you can have all the
+ 
+
+ align:start position:0%
+organization is key you can have all the
+different cell types in the retina but
+
+ align:start position:0%
+different cell types in the retina but
+ 
+
+ align:start position:0%
+different cell types in the retina but
+if they're not arranged in this rigid
+
+ align:start position:0%
+if they're not arranged in this rigid
+ 
+
+ align:start position:0%
+if they're not arranged in this rigid
+structure or in this specific structure
+
+ align:start position:0%
+structure or in this specific structure
+ 
+
+ align:start position:0%
+structure or in this specific structure
+the retina doesn't
+
+ align:start position:0%
+the retina doesn't
+ 
+
+ align:start position:0%
+the retina doesn't
+function 3D structures we'll talk next
+
+ align:start position:0%
+function 3D structures we'll talk next
+ 
+
+ align:start position:0%
+function 3D structures we'll talk next
+time about engineering structure out of
+
+ align:start position:0%
+time about engineering structure out of
+ 
+
+ align:start position:0%
+time about engineering structure out of
+cells and the heart is one thing you
+
+ align:start position:0%
+cells and the heart is one thing you
+ 
+
+ align:start position:0%
+cells and the heart is one thing you
+have to think about engineering the only
+
+ align:start position:0%
+have to think about engineering the only
+ 
+
+ align:start position:0%
+have to think about engineering the only
+raw material that you have to use for
+
+ align:start position:0%
+raw material that you have to use for
+ 
+
+ align:start position:0%
+raw material that you have to use for
+the engineering is cells and so how do
+
+ align:start position:0%
+the engineering is cells and so how do
+ 
+
+ align:start position:0%
+the engineering is cells and so how do
+you get something that looks like a
+
+ align:start position:0%
+you get something that looks like a
+ 
+
+ align:start position:0%
+you get something that looks like a
+human heart and carries out the
+
+ align:start position:0%
+human heart and carries out the
+ 
+
+ align:start position:0%
+human heart and carries out the
+exquisitely regulated pumping function
+
+ align:start position:0%
+exquisitely regulated pumping function
+ 
+
+ align:start position:0%
+exquisitely regulated pumping function
+of the heart
+
+ align:start position:0%
+of the heart
+ 
+
+ align:start position:0%
+of the heart
+and here's another one that I'll touch
+
+ align:start position:0%
+and here's another one that I'll touch
+ 
+
+ align:start position:0%
+and here's another one that I'll touch
+on which is the question of
+
+ align:start position:0%
+on which is the question of
+ 
+
+ align:start position:0%
+on which is the question of
+position it's not that we just are made
+
+ align:start position:0%
+position it's not that we just are made
+ 
+
+ align:start position:0%
+position it's not that we just are made
+up of lots of different kinds of cells
+
+ align:start position:0%
+up of lots of different kinds of cells
+ 
+
+ align:start position:0%
+up of lots of different kinds of cells
+that are grouped together in organs it's
+
+ align:start position:0%
+that are grouped together in organs it's
+ 
+
+ align:start position:0%
+that are grouped together in organs it's
+that they're also positioned in the
+
+ align:start position:0%
+that they're also positioned in the
+ 
+
+ align:start position:0%
+that they're also positioned in the
+correct place and in this plasticized
+
+ align:start position:0%
+correct place and in this plasticized
+ 
+
+ align:start position:0%
+correct place and in this plasticized
+human actually I think it's a fully
+
+ align:start position:0%
+human actually I think it's a fully
+ 
+
+ align:start position:0%
+human actually I think it's a fully
+plastic human if you open up the cavity
+
+ align:start position:0%
+plastic human if you open up the cavity
+ 
+
+ align:start position:0%
+plastic human if you open up the cavity
+and look into the abdomen you can see
+
+ align:start position:0%
+and look into the abdomen you can see
+ 
+
+ align:start position:0%
+and look into the abdomen you can see
+these organs that are arranged packed so
+
+ align:start position:0%
+these organs that are arranged packed so
+ 
+
+ align:start position:0%
+these organs that are arranged packed so
+beautifully like this it's no accident
+
+ align:start position:0%
+beautifully like this it's no accident
+ 
+
+ align:start position:0%
+beautifully like this it's no accident
+they get there because they're told to
+
+ align:start position:0%
+they get there because they're told to
+ 
+
+ align:start position:0%
+they get there because they're told to
+get there there is a process that
+
+ align:start position:0%
+get there there is a process that
+ 
+
+ align:start position:0%
+get there there is a process that
+positions the organs in the precise way
+
+ align:start position:0%
+positions the organs in the precise way
+ 
+
+ align:start position:0%
+positions the organs in the precise way
+and if they're positioned incorrectly
+
+ align:start position:0%
+and if they're positioned incorrectly
+ 
+
+ align:start position:0%
+and if they're positioned incorrectly
+there are medical consequences which are
+
+ align:start position:0%
+there are medical consequences which are
+ 
+
+ align:start position:0%
+there are medical consequences which are
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+severe all right so all of these things
+
+ align:start position:0%
+severe all right so all of these things
+ 
+
+ align:start position:0%
+severe all right so all of these things
+we need to think about but let's go back
+
+ align:start position:0%
+we need to think about but let's go back
+ 
+
+ align:start position:0%
+we need to think about but let's go back
+to the board and you will recognize this
+
+ align:start position:0%
+to the board and you will recognize this
+ 
+
+ align:start position:0%
+to the board and you will recognize this
+diagram which is pivotal for what we're
+
+ align:start position:0%
+diagram which is pivotal for what we're
+ 
+
+ align:start position:0%
+diagram which is pivotal for what we're
+going to talk about
+
+ align:start position:0%
+going to talk about
+ 
+
+ align:start position:0%
+going to talk about
+today here is a mantra that I've
+
+ align:start position:0%
+today here is a mantra that I've
+ 
+
+ align:start position:0%
+today here is a mantra that I've
+mentioned before and you need to know
+
+ align:start position:0%
+mentioned before and you need to know
+ 
+
+ align:start position:0%
+mentioned before and you need to know
+and really need to understand this all
+
+ align:start position:0%
+and really need to understand this all
+ 
+
+ align:start position:0%
+and really need to understand this all
+cells contain the same set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes Professor Jax will give you one
+
+ align:start position:0%
+genes Professor Jax will give you one
+ 
+
+ align:start position:0%
+genes Professor Jax will give you one
+exception to this rule but it's the
+
+ align:start position:0%
+exception to this rule but it's the
+ 
+
+ align:start position:0%
+exception to this rule but it's the
+exception all cells in your body body
+
+ align:start position:0%
+exception all cells in your body body
+ 
+
+ align:start position:0%
+exception all cells in your body body
+contain the same set of
+
+ align:start position:0%
+contain the same set of
+ 
+
+ align:start position:0%
+contain the same set of
+genes but not all those genes are used
+
+ align:start position:0%
+genes but not all those genes are used
+ 
+
+ align:start position:0%
+genes but not all those genes are used
+in every cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type but each cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type
+
+ align:start position:0%
+type
+ 
+
+ align:start position:0%
+type
+uses and you know the word expresses now
+
+ align:start position:0%
+uses and you know the word expresses now
+ 
+
+ align:start position:0%
+uses and you know the word expresses now
+each cell type
+
+ align:start position:0%
+each cell type
+ 
+
+ align:start position:0%
+each cell type
+expresses a
+
+ align:start position:0%
+expresses a
+ 
+
+ align:start position:0%
+expresses a
+subset and it's a unique sub well let me
+
+ align:start position:0%
+subset and it's a unique sub well let me
+ 
+
+ align:start position:0%
+subset and it's a unique sub well let me
+put unique in parentheses and you'll
+
+ align:start position:0%
+put unique in parentheses and you'll
+ 
+
+ align:start position:0%
+put unique in parentheses and you'll
+you'll see what I mean a unique subset
+
+ align:start position:0%
+you'll see what I mean a unique subset
+ 
+
+ align:start position:0%
+you'll see what I mean a unique subset
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genome and this set of genes and the
+
+ align:start position:0%
+genome and this set of genes and the
+ 
+
+ align:start position:0%
+genome and this set of genes and the
+products of those genes make the cell
+
+ align:start position:0%
+products of those genes make the cell
+ 
+
+ align:start position:0%
+products of those genes make the cell
+type what it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the products of those genes usually
+
+ align:start position:0%
+is the products of those genes usually
+ 
+
+ align:start position:0%
+is the products of those genes usually
+proteins and some rnas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give the cell type its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function so there are two cories here
+
+ align:start position:0%
+function so there are two cories here
+ 
+
+ align:start position:0%
+function so there are two cories here
+one you have to understand how the
+
+ align:start position:0%
+one you have to understand how the
+ 
+
+ align:start position:0%
+one you have to understand how the
+expression of genes is controlled and
+
+ align:start position:0%
+expression of genes is controlled and
+ 
+
+ align:start position:0%
+expression of genes is controlled and
+that is pivotal to this list and two
+
+ align:start position:0%
+that is pivotal to this list and two
+ 
+
+ align:start position:0%
+that is pivotal to this list and two
+this set of genes that makes each cell
+
+ align:start position:0%
+this set of genes that makes each cell
+ 
+
+ align:start position:0%
+this set of genes that makes each cell
+type the set of active genes that makes
+
+ align:start position:0%
+type the set of active genes that makes
+ 
+
+ align:start position:0%
+type the set of active genes that makes
+each cell type what it is forms a kind
+
+ align:start position:0%
+each cell type what it is forms a kind
+ 
+
+ align:start position:0%
+each cell type what it is forms a kind
+of a combinatorial code for a cell type
+
+ align:start position:0%
+of a combinatorial code for a cell type
+ 
+
+ align:start position:0%
+of a combinatorial code for a cell type
+so let's just write this down so control
+
+ align:start position:0%
+so let's just write this down so control
+ 
+
+ align:start position:0%
+so let's just write this down so control
+of gene expression is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crucial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there is a combinatorial code of
+
+ align:start position:0%
+and there is a combinatorial code of
+ 
+
+ align:start position:0%
+and there is a combinatorial code of
+gene expression for each cell type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a combinatorial code of expressed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes for each cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type you will not find this notion of a
+
+ align:start position:0%
+type you will not find this notion of a
+ 
+
+ align:start position:0%
+type you will not find this notion of a
+combinatorial code in your book but I
+
+ align:start position:0%
+combinatorial code in your book but I
+ 
+
+ align:start position:0%
+combinatorial code in your book but I
+think if you talk to any life scientist
+
+ align:start position:0%
+think if you talk to any life scientist
+ 
+
+ align:start position:0%
+think if you talk to any life scientist
+who's doing research right now they
+
+ align:start position:0%
+who's doing research right now they
+ 
+
+ align:start position:0%
+who's doing research right now they
+would agree that that is the correct way
+
+ align:start position:0%
+would agree that that is the correct way
+ 
+
+ align:start position:0%
+would agree that that is the correct way
+to be thinking about cell type so let's
+
+ align:start position:0%
+to be thinking about cell type so let's
+ 
+
+ align:start position:0%
+to be thinking about cell type so let's
+explore this a bit more and let's write
+
+ align:start position:0%
+explore this a bit more and let's write
+ 
+
+ align:start position:0%
+explore this a bit more and let's write
+out three different cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types and I'm going to introduce the
+
+ align:start position:0%
+types and I'm going to introduce the
+ 
+
+ align:start position:0%
+types and I'm going to introduce the
+word here self
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fate and both cell type and cell fate
+
+ align:start position:0%
+fate and both cell type and cell fate
+ 
+
+ align:start position:0%
+fate and both cell type and cell fate
+can be used interchangeably with the
+
+ align:start position:0%
+can be used interchangeably with the
+ 
+
+ align:start position:0%
+can be used interchangeably with the
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+function and let's pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neurons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+muscle and the epidermis which is the
+
+ align:start position:0%
+muscle and the epidermis which is the
+ 
+
+ align:start position:0%
+muscle and the epidermis which is the
+outer layer of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skin and let's consider the genes that
+
+ align:start position:0%
+skin and let's consider the genes that
+ 
+
+ align:start position:0%
+skin and let's consider the genes that
+are present in each cell type and let's
+
+ align:start position:0%
+are present in each cell type and let's
+ 
+
+ align:start position:0%
+are present in each cell type and let's
+consider the genes that are expressed in
+
+ align:start position:0%
+consider the genes that are expressed in
+ 
+
+ align:start position:0%
+consider the genes that are expressed in
+each cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type the genes that are present in each
+
+ align:start position:0%
+type the genes that are present in each
+ 
+
+ align:start position:0%
+type the genes that are present in each
+cell type as I've just told you are the
+
+ align:start position:0%
+cell type as I've just told you are the
+ 
+
+ align:start position:0%
+cell type as I've just told you are the
+same and so
+
+ align:start position:0%
+same and so
+ 
+
+ align:start position:0%
+same and so
+let's make them A B C D and
+
+ align:start position:0%
+let's make them A B C D and
+ 
+
+ align:start position:0%
+let's make them A B C D and
+E and each of those genes is present in
+
+ align:start position:0%
+E and each of those genes is present in
+ 
+
+ align:start position:0%
+E and each of those genes is present in
+each of these cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types but only some of them are used and
+
+ align:start position:0%
+types but only some of them are used and
+ 
+
+ align:start position:0%
+types but only some of them are used and
+so let's say in the neurons
+
+ align:start position:0%
+so let's say in the neurons
+ 
+
+ align:start position:0%
+so let's say in the neurons
+a B and E are used in muscle a c and d
+
+ align:start position:0%
+a B and E are used in muscle a c and d
+ 
+
+ align:start position:0%
+a B and E are used in muscle a c and d
+and a b and c in
+
+ align:start position:0%
+and a b and c in
+ 
+
+ align:start position:0%
+and a b and c in
+epidermis okay so look at what I've
+
+ align:start position:0%
+epidermis okay so look at what I've
+ 
+
+ align:start position:0%
+epidermis okay so look at what I've
+written there and you can pick out some
+
+ align:start position:0%
+written there and you can pick out some
+ 
+
+ align:start position:0%
+written there and you can pick out some
+patterns you can pick out a gene that is
+
+ align:start position:0%
+patterns you can pick out a gene that is
+ 
+
+ align:start position:0%
+patterns you can pick out a gene that is
+expressed in all of the cell types so
+
+ align:start position:0%
+expressed in all of the cell types so
+ 
+
+ align:start position:0%
+expressed in all of the cell types so
+Gene
+
+ align:start position:0%
+Gene
+ 
+
+ align:start position:0%
+Gene
+a is expressed in all of the cell types
+
+ align:start position:0%
+a is expressed in all of the cell types
+ 
+
+ align:start position:0%
+a is expressed in all of the cell types
+and Gene a exemplifies a gene that we
+
+ align:start position:0%
+and Gene a exemplifies a gene that we
+ 
+
+ align:start position:0%
+and Gene a exemplifies a gene that we
+term ubiquitously expressed sometimes
+
+ align:start position:0%
+term ubiquitously expressed sometimes
+ 
+
+ align:start position:0%
+term ubiquitously expressed sometimes
+termed a housekeeping Gene I really
+
+ align:start position:0%
+termed a housekeeping Gene I really
+ 
+
+ align:start position:0%
+termed a housekeeping Gene I really
+dislike that term but you will see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so ubiquitously
+
+ align:start position:0%
+it so ubiquitously
+ 
+
+ align:start position:0%
+it so ubiquitously
+expressed maybe you'll see
+
+ align:start position:0%
+expressed maybe you'll see
+ 
+
+ align:start position:0%
+expressed maybe you'll see
+housekeeping you can come to office ours
+
+ align:start position:0%
+housekeeping you can come to office ours
+ 
+
+ align:start position:0%
+housekeeping you can come to office ours
+and I'll tell you why I hate that term
+
+ align:start position:0%
+and I'll tell you why I hate that term
+ 
+
+ align:start position:0%
+and I'll tell you why I hate that term
+and then you can pick out a gene which
+
+ align:start position:0%
+and then you can pick out a gene which
+ 
+
+ align:start position:0%
+and then you can pick out a gene which
+is expressed in some of the cell types
+
+ align:start position:0%
+is expressed in some of the cell types
+ 
+
+ align:start position:0%
+is expressed in some of the cell types
+but not others so let's look at B here
+
+ align:start position:0%
+but not others so let's look at B here
+ 
+
+ align:start position:0%
+but not others so let's look at B here
+has B expressed in the neurons and the
+
+ align:start position:0%
+has B expressed in the neurons and the
+ 
+
+ align:start position:0%
+has B expressed in the neurons and the
+epidermis but not in the
+
+ align:start position:0%
+epidermis but not in the
+ 
+
+ align:start position:0%
+epidermis but not in the
+muscle and B would be referred to and
+
+ align:start position:0%
+muscle and B would be referred to and
+ 
+
+ align:start position:0%
+muscle and B would be referred to and
+actually C is the same way isn't it C is
+
+ align:start position:0%
+actually C is the same way isn't it C is
+ 
+
+ align:start position:0%
+actually C is the same way isn't it C is
+in muscle and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epidermis B and C would be referred to
+
+ align:start position:0%
+epidermis B and C would be referred to
+ 
+
+ align:start position:0%
+epidermis B and C would be referred to
+as genes with restricted
+
+ align:start position:0%
+as genes with restricted
+ 
+
+ align:start position:0%
+as genes with restricted
+expression so B and C would have
+
+ align:start position:0%
+expression so B and C would have
+ 
+
+ align:start position:0%
+expression so B and C would have
+restricted
+
+ align:start position:0%
+restricted
+ 
+
+ align:start position:0%
+restricted
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+expression and then there's two genes
+
+ align:start position:0%
+expression and then there's two genes
+ 
+
+ align:start position:0%
+expression and then there's two genes
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+e and D which are only expressed in one
+
+ align:start position:0%
+e and D which are only expressed in one
+ 
+
+ align:start position:0%
+e and D which are only expressed in one
+of the their own cell type in neurons or
+
+ align:start position:0%
+of the their own cell type in neurons or
+ 
+
+ align:start position:0%
+of the their own cell type in neurons or
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+muscle so d and e would be cell type
+
+ align:start position:0%
+muscle so d and e would be cell type
+ 
+
+ align:start position:0%
+muscle so d and e would be cell type
+specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes and from this simple example you
+
+ align:start position:0%
+genes and from this simple example you
+ 
+
+ align:start position:0%
+genes and from this simple example you
+you can see a number of things firstly
+
+ align:start position:0%
+you can see a number of things firstly
+ 
+
+ align:start position:0%
+you can see a number of things firstly
+you can get a combinatorial code that is
+
+ align:start position:0%
+you can get a combinatorial code that is
+ 
+
+ align:start position:0%
+you can get a combinatorial code that is
+specific for a cell type without any
+
+ align:start position:0%
+specific for a cell type without any
+ 
+
+ align:start position:0%
+specific for a cell type without any
+genes that are specifically expressed in
+
+ align:start position:0%
+genes that are specifically expressed in
+ 
+
+ align:start position:0%
+genes that are specifically expressed in
+the cell type if you look in the
+
+ align:start position:0%
+the cell type if you look in the
+ 
+
+ align:start position:0%
+the cell type if you look in the
+epidermis example A B and C are
+
+ align:start position:0%
+epidermis example A B and C are
+ 
+
+ align:start position:0%
+epidermis example A B and C are
+expressed none of them are cell type
+
+ align:start position:0%
+expressed none of them are cell type
+ 
+
+ align:start position:0%
+expressed none of them are cell type
+specific but nonetheless they give the
+
+ align:start position:0%
+specific but nonetheless they give the
+ 
+
+ align:start position:0%
+specific but nonetheless they give the
+combinatorial code that is the epidermis
+
+ align:start position:0%
+combinatorial code that is the epidermis
+ 
+
+ align:start position:0%
+combinatorial code that is the epidermis
+and then the other examples of each got
+
+ align:start position:0%
+and then the other examples of each got
+ 
+
+ align:start position:0%
+and then the other examples of each got
+a cell type specific
+
+ align:start position:0%
+a cell type specific
+ 
+
+ align:start position:0%
+a cell type specific
+Gene what does a combinatorial code
+
+ align:start position:0%
+Gene what does a combinatorial code
+ 
+
+ align:start position:0%
+Gene what does a combinatorial code
+really look like well to be honest we
+
+ align:start position:0%
+really look like well to be honest we
+ 
+
+ align:start position:0%
+really look like well to be honest we
+don't actually know there's no cell type
+
+ align:start position:0%
+don't actually know there's no cell type
+ 
+
+ align:start position:0%
+don't actually know there's no cell type
+for which the combinatorial code has
+
+ align:start position:0%
+for which the combinatorial code has
+ 
+
+ align:start position:0%
+for which the combinatorial code has
+been worked out but you know now there
+
+ align:start position:0%
+been worked out but you know now there
+ 
+
+ align:start position:0%
+been worked out but you know now there
+are about 20,000 human genes and
+
+ align:start position:0%
+are about 20,000 human genes and
+ 
+
+ align:start position:0%
+are about 20,000 human genes and
+probably about half of them are
+
+ align:start position:0%
+probably about half of them are
+ 
+
+ align:start position:0%
+probably about half of them are
+expressed in most cell types so the
+
+ align:start position:0%
+expressed in most cell types so the
+ 
+
+ align:start position:0%
+expressed in most cell types so the
+combinatorial code for any given cell
+
+ align:start position:0%
+combinatorial code for any given cell
+ 
+
+ align:start position:0%
+combinatorial code for any given cell
+type is going to be thousands and
+
+ align:start position:0%
+type is going to be thousands and
+ 
+
+ align:start position:0%
+type is going to be thousands and
+thousands of genes which are expressed
+
+ align:start position:0%
+thousands of genes which are expressed
+ 
+
+ align:start position:0%
+thousands of genes which are expressed
+or not expressed and which are also
+
+ align:start position:0%
+or not expressed and which are also
+ 
+
+ align:start position:0%
+or not expressed and which are also
+expressed at different levels and we
+
+ align:start position:0%
+expressed at different levels and we
+ 
+
+ align:start position:0%
+expressed at different levels and we
+have to take that into account so really
+
+ align:start position:0%
+have to take that into account so really
+ 
+
+ align:start position:0%
+have to take that into account so really
+finding the combinatorial code is
+
+ align:start position:0%
+finding the combinatorial code is
+ 
+
+ align:start position:0%
+finding the combinatorial code is
+incredibly difficult and we don't know
+
+ align:start position:0%
+incredibly difficult and we don't know
+ 
+
+ align:start position:0%
+incredibly difficult and we don't know
+any for any cell type but the notion is
+
+ align:start position:0%
+any for any cell type but the notion is
+ 
+
+ align:start position:0%
+any for any cell type but the notion is
+exactly the same I want to remind you
+
+ align:start position:0%
+exactly the same I want to remind you
+ 
+
+ align:start position:0%
+exactly the same I want to remind you
+here with this diagram that the control
+
+ align:start position:0%
+here with this diagram that the control
+ 
+
+ align:start position:0%
+here with this diagram that the control
+of gene expression to give you the final
+
+ align:start position:0%
+of gene expression to give you the final
+ 
+
+ align:start position:0%
+of gene expression to give you the final
+expressed product can be anywhere all
+
+ align:start position:0%
+expressed product can be anywhere all
+ 
+
+ align:start position:0%
+expressed product can be anywhere all
+the way from chromatin structure through
+
+ align:start position:0%
+the way from chromatin structure through
+ 
+
+ align:start position:0%
+the way from chromatin structure through
+transcription all the way through
+
+ align:start position:0%
+transcription all the way through
+ 
+
+ align:start position:0%
+transcription all the way through
+protein processing modification and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+localization good
+
+ align:start position:0%
+localization good
+ 
+
+ align:start position:0%
+localization good
+all right so now we have a framework by
+
+ align:start position:0%
+all right so now we have a framework by
+ 
+
+ align:start position:0%
+all right so now we have a framework by
+which we can think of what a cell type
+
+ align:start position:0%
+which we can think of what a cell type
+ 
+
+ align:start position:0%
+which we can think of what a cell type
+is and the question of course that
+
+ align:start position:0%
+is and the question of course that
+ 
+
+ align:start position:0%
+is and the question of course that
+you're asking is so how does that
+
+ align:start position:0%
+you're asking is so how does that
+ 
+
+ align:start position:0%
+you're asking is so how does that
+combinatorial code get expressed in each
+
+ align:start position:0%
+combinatorial code get expressed in each
+ 
+
+ align:start position:0%
+combinatorial code get expressed in each
+of the cell types let's pose that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question how does a cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type express its code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's a couple of
+
+ align:start position:0%
+and there's a couple of
+ 
+
+ align:start position:0%
+and there's a couple of
+answers the global answer that I'm going
+
+ align:start position:0%
+answers the global answer that I'm going
+ 
+
+ align:start position:0%
+answers the global answer that I'm going
+to give you to this question is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stepwise and let's have
+
+ align:start position:0%
+stepwise and let's have
+ 
+
+ align:start position:0%
+stepwise and let's have
+stepwise answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one the
+
+ align:start position:0%
+one the
+ 
+
+ align:start position:0%
+one the
+idea and we can do this I'm going to do
+
+ align:start position:0%
+idea and we can do this I'm going to do
+ 
+
+ align:start position:0%
+idea and we can do this I'm going to do
+this two ways I'm actually going to do
+
+ align:start position:0%
+this two ways I'm actually going to do
+ 
+
+ align:start position:0%
+this two ways I'm actually going to do
+this no I'm not going to do this two
+
+ align:start position:0%
+this no I'm not going to do this two
+ 
+
+ align:start position:0%
+this no I'm not going to do this two
+ways before we get
+
+ align:start position:0%
+ways before we get
+ 
+
+ align:start position:0%
+ways before we get
+there this is a great slide which will
+
+ align:start position:0%
+there this is a great slide which will
+ 
+
+ align:start position:0%
+there this is a great slide which will
+show you two things one it will show you
+
+ align:start position:0%
+show you two things one it will show you
+ 
+
+ align:start position:0%
+show you two things one it will show you
+the expression patterns of two different
+
+ align:start position:0%
+the expression patterns of two different
+ 
+
+ align:start position:0%
+the expression patterns of two different
+genes in the whole organism so here is a
+
+ align:start position:0%
+genes in the whole organism so here is a
+ 
+
+ align:start position:0%
+genes in the whole organism so here is a
+gene called myod I've shown this to you
+
+ align:start position:0%
+gene called myod I've shown this to you
+ 
+
+ align:start position:0%
+gene called myod I've shown this to you
+before that is cell type specific it's
+
+ align:start position:0%
+before that is cell type specific it's
+ 
+
+ align:start position:0%
+before that is cell type specific it's
+just expressed in these kind of Chevron
+
+ align:start position:0%
+just expressed in these kind of Chevron
+ 
+
+ align:start position:0%
+just expressed in these kind of Chevron
+shaped things which are the developing
+
+ align:start position:0%
+shaped things which are the developing
+ 
+
+ align:start position:0%
+shaped things which are the developing
+skeletal muscles the voluntary muscle
+
+ align:start position:0%
+skeletal muscles the voluntary muscle
+ 
+
+ align:start position:0%
+skeletal muscles the voluntary muscle
+and here are a couple of genes that are
+
+ align:start position:0%
+and here are a couple of genes that are
+ 
+
+ align:start position:0%
+and here are a couple of genes that are
+expressed in large regions of the
+
+ align:start position:0%
+expressed in large regions of the
+ 
+
+ align:start position:0%
+expressed in large regions of the
+developing animal and you can see
+
+ align:start position:0%
+developing animal and you can see
+ 
+
+ align:start position:0%
+developing animal and you can see
+they're expressed because of these
+
+ align:start position:0%
+they're expressed because of these
+ 
+
+ align:start position:0%
+they're expressed because of these
+colors that are there and the colors are
+
+ align:start position:0%
+colors that are there and the colors are
+ 
+
+ align:start position:0%
+colors that are there and the colors are
+indicative of where the RNA for that
+
+ align:start position:0%
+indicative of where the RNA for that
+ 
+
+ align:start position:0%
+indicative of where the RNA for that
+Gene is the technique that allows you to
+
+ align:start position:0%
+Gene is the technique that allows you to
+ 
+
+ align:start position:0%
+Gene is the technique that allows you to
+look in a whole animal and ask where the
+
+ align:start position:0%
+look in a whole animal and ask where the
+ 
+
+ align:start position:0%
+look in a whole animal and ask where the
+rnas for particular genes are found is
+
+ align:start position:0%
+rnas for particular genes are found is
+ 
+
+ align:start position:0%
+rnas for particular genes are found is
+called incu
+
+ align:start position:0%
+called incu
+ 
+
+ align:start position:0%
+called incu
+hybridization up here at the top of the
+
+ align:start position:0%
+hybridization up here at the top of the
+ 
+
+ align:start position:0%
+hybridization up here at the top of the
+screen
+
+ align:start position:0%
+screen
+ 
+
+ align:start position:0%
+screen
+and the idea is that you take animals
+
+ align:start position:0%
+and the idea is that you take animals
+ 
+
+ align:start position:0%
+and the idea is that you take animals
+here I've said embryos developing
+
+ align:start position:0%
+here I've said embryos developing
+ 
+
+ align:start position:0%
+here I've said embryos developing
+animals and you fix them which means you
+
+ align:start position:0%
+animals and you fix them which means you
+ 
+
+ align:start position:0%
+animals and you fix them which means you
+kill them and you permeabilize them you
+
+ align:start position:0%
+kill them and you permeabilize them you
+ 
+
+ align:start position:0%
+kill them and you permeabilize them you
+make holes in them and then you use the
+
+ align:start position:0%
+make holes in them and then you use the
+ 
+
+ align:start position:0%
+make holes in them and then you use the
+principles of base pairing where you
+
+ align:start position:0%
+principles of base pairing where you
+ 
+
+ align:start position:0%
+principles of base pairing where you
+look and see where the RNA is using a
+
+ align:start position:0%
+look and see where the RNA is using a
+ 
+
+ align:start position:0%
+look and see where the RNA is using a
+probe which is an anti-sense RNA for a
+
+ align:start position:0%
+probe which is an anti-sense RNA for a
+ 
+
+ align:start position:0%
+probe which is an anti-sense RNA for a
+particular Gene of interest and you
+
+ align:start position:0%
+particular Gene of interest and you
+ 
+
+ align:start position:0%
+particular Gene of interest and you
+label this anti-sense RNA you mix it
+
+ align:start position:0%
+label this anti-sense RNA you mix it
+ 
+
+ align:start position:0%
+label this anti-sense RNA you mix it
+with the embryo that's got holes in or
+
+ align:start position:0%
+with the embryo that's got holes in or
+ 
+
+ align:start position:0%
+with the embryo that's got holes in or
+the animal that's got holes where the
+
+ align:start position:0%
+the animal that's got holes where the
+ 
+
+ align:start position:0%
+the animal that's got holes where the
+RNA for Gene X is it will base pair to
+
+ align:start position:0%
+RNA for Gene X is it will base pair to
+ 
+
+ align:start position:0%
+RNA for Gene X is it will base pair to
+your anti-sense probe you then wash out
+
+ align:start position:0%
+your anti-sense probe you then wash out
+ 
+
+ align:start position:0%
+your anti-sense probe you then wash out
+the extra and you look and see where the
+
+ align:start position:0%
+the extra and you look and see where the
+ 
+
+ align:start position:0%
+the extra and you look and see where the
+color that comes from the label is and
+
+ align:start position:0%
+color that comes from the label is and
+ 
+
+ align:start position:0%
+color that comes from the label is and
+that color tells you where the RNA for a
+
+ align:start position:0%
+that color tells you where the RNA for a
+ 
+
+ align:start position:0%
+that color tells you where the RNA for a
+particular Gene is so these colors in
+
+ align:start position:0%
+particular Gene is so these colors in
+ 
+
+ align:start position:0%
+particular Gene is so these colors in
+this developing animal tell you where
+
+ align:start position:0%
+this developing animal tell you where
+ 
+
+ align:start position:0%
+this developing animal tell you where
+particular rnas are it's a very powerful
+
+ align:start position:0%
+particular rnas are it's a very powerful
+ 
+
+ align:start position:0%
+particular rnas are it's a very powerful
+technique and it allows us to figure out
+
+ align:start position:0%
+technique and it allows us to figure out
+ 
+
+ align:start position:0%
+technique and it allows us to figure out
+which genes are
+
+ align:start position:0%
+which genes are
+ 
+
+ align:start position:0%
+which genes are
+type specific and which genes are more
+
+ align:start position:0%
+type specific and which genes are more
+ 
+
+ align:start position:0%
+type specific and which genes are more
+generally
+
+ align:start position:0%
+generally
+ 
+
+ align:start position:0%
+generally
+expressed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's look at your first handout
+
+ align:start position:0%
+okay let's look at your first handout
+ 
+
+ align:start position:0%
+okay let's look at your first handout
+and I'm going to write it on the board
+
+ align:start position:0%
+and I'm going to write it on the board
+ 
+
+ align:start position:0%
+and I'm going to write it on the board
+as well because this is really important
+
+ align:start position:0%
+as well because this is really important
+ 
+
+ align:start position:0%
+as well because this is really important
+and you're going to need to know this
+
+ align:start position:0%
+and you're going to need to know this
+ 
+
+ align:start position:0%
+and you're going to need to know this
+for this lecture and when we get to stem
+
+ align:start position:0%
+for this lecture and when we get to stem
+ 
+
+ align:start position:0%
+for this lecture and when we get to stem
+cells as
+
+ align:start position:0%
+cells as
+ 
+
+ align:start position:0%
+cells as
+well so you can look on the screen you
+
+ align:start position:0%
+well so you can look on the screen you
+ 
+
+ align:start position:0%
+well so you can look on the screen you
+can look on your handout and I would
+
+ align:start position:0%
+can look on your handout and I would
+ 
+
+ align:start position:0%
+can look on your handout and I would
+suggest you write it as well the notion
+
+ align:start position:0%
+suggest you write it as well the notion
+ 
+
+ align:start position:0%
+suggest you write it as well the notion
+when we're thinking about cell type is
+
+ align:start position:0%
+when we're thinking about cell type is
+ 
+
+ align:start position:0%
+when we're thinking about cell type is
+that we start off with cells that don't
+
+ align:start position:0%
+that we start off with cells that don't
+ 
+
+ align:start position:0%
+that we start off with cells that don't
+know who they are and they're called
+
+ align:start position:0%
+know who they are and they're called
+ 
+
+ align:start position:0%
+know who they are and they're called
+uncommitted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells they are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+undecided and as they go through
+
+ align:start position:0%
+undecided and as they go through
+ 
+
+ align:start position:0%
+undecided and as they go through
+life they get some inputs we'll be vague
+
+ align:start position:0%
+life they get some inputs we'll be vague
+ 
+
+ align:start position:0%
+life they get some inputs we'll be vague
+about those they're up there I'm not
+
+ align:start position:0%
+about those they're up there I'm not
+ 
+
+ align:start position:0%
+about those they're up there I'm not
+going to write them here and at that
+
+ align:start position:0%
+going to write them here and at that
+ 
+
+ align:start position:0%
+going to write them here and at that
+point they become emitted
+
+ align:start position:0%
+point they become emitted
+ 
+
+ align:start position:0%
+point they become emitted
+cells they're sometimes called
+
+ align:start position:0%
+cells they're sometimes called
+ 
+
+ align:start position:0%
+cells they're sometimes called
+determined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and at this point the cells have
+
+ align:start position:0%
+cells and at this point the cells have
+ 
+
+ align:start position:0%
+cells and at this point the cells have
+decided what they're going to
+
+ align:start position:0%
+decided what they're going to
+ 
+
+ align:start position:0%
+decided what they're going to
+become and later on those committed or
+
+ align:start position:0%
+become and later on those committed or
+ 
+
+ align:start position:0%
+become and later on those committed or
+determined cells will go on and they
+
+ align:start position:0%
+determined cells will go on and they
+ 
+
+ align:start position:0%
+determined cells will go on and they
+will become differentiated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells where they have their final fate
+
+ align:start position:0%
+cells where they have their final fate
+ 
+
+ align:start position:0%
+cells where they have their final fate
+or their final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function there's a Time metric on
+
+ align:start position:0%
+function there's a Time metric on
+ 
+
+ align:start position:0%
+function there's a Time metric on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+progression and the notion really is
+
+ align:start position:0%
+progression and the notion really is
+ 
+
+ align:start position:0%
+progression and the notion really is
+that as cells go through this decision
+
+ align:start position:0%
+that as cells go through this decision
+ 
+
+ align:start position:0%
+that as cells go through this decision
+making process they change which genes
+
+ align:start position:0%
+making process they change which genes
+ 
+
+ align:start position:0%
+making process they change which genes
+they are expressing such that at the
+
+ align:start position:0%
+they are expressing such that at the
+ 
+
+ align:start position:0%
+they are expressing such that at the
+culmination but if you think about this
+
+ align:start position:0%
+culmination but if you think about this
+ 
+
+ align:start position:0%
+culmination but if you think about this
+or come and talk to me you'll find it's
+
+ align:start position:0%
+or come and talk to me you'll find it's
+ 
+
+ align:start position:0%
+or come and talk to me you'll find it's
+more complicated at the culmination they
+
+ align:start position:0%
+more complicated at the culmination they
+ 
+
+ align:start position:0%
+more complicated at the culmination they
+will be expressing their combinatorial
+
+ align:start position:0%
+will be expressing their combinatorial
+ 
+
+ align:start position:0%
+will be expressing their combinatorial
+code uncommitted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells as they transition to committed
+
+ align:start position:0%
+cells as they transition to committed
+ 
+
+ align:start position:0%
+cells as they transition to committed
+cells activate a set of genes that I'm
+
+ align:start position:0%
+cells activate a set of genes that I'm
+ 
+
+ align:start position:0%
+cells activate a set of genes that I'm
+going to call regulatory genes they're
+
+ align:start position:0%
+going to call regulatory genes they're
+ 
+
+ align:start position:0%
+going to call regulatory genes they're
+the transcription factors the
+
+ align:start position:0%
+the transcription factors the
+ 
+
+ align:start position:0%
+the transcription factors the
+translation factors the protein
+
+ align:start position:0%
+translation factors the protein
+ 
+
+ align:start position:0%
+translation factors the protein
+processing factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these regulatory genes will then go
+
+ align:start position:0%
+and these regulatory genes will then go
+ 
+
+ align:start position:0%
+and these regulatory genes will then go
+and activate a set of
+
+ align:start position:0%
+and activate a set of
+ 
+
+ align:start position:0%
+and activate a set of
+genes that I'll call affector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes and the affector genes are the
+
+ align:start position:0%
+genes and the affector genes are the
+ 
+
+ align:start position:0%
+genes and the affector genes are the
+ones that are actually carrying out the
+
+ align:start position:0%
+ones that are actually carrying out the
+ 
+
+ align:start position:0%
+ones that are actually carrying out the
+function of the cell they are the globin
+
+ align:start position:0%
+function of the cell they are the globin
+ 
+
+ align:start position:0%
+function of the cell they are the globin
+that's carrying the oxygen around the
+
+ align:start position:0%
+that's carrying the oxygen around the
+ 
+
+ align:start position:0%
+that's carrying the oxygen around the
+body they are the neurofilaments that
+
+ align:start position:0%
+body they are the neurofilaments that
+ 
+
+ align:start position:0%
+body they are the neurofilaments that
+are making the neurons long and strong
+
+ align:start position:0%
+are making the neurons long and strong
+ 
+
+ align:start position:0%
+are making the neurons long and strong
+and able to transmit a signal they are
+
+ align:start position:0%
+and able to transmit a signal they are
+ 
+
+ align:start position:0%
+and able to transmit a signal they are
+the Keratin which make hair cells able
+
+ align:start position:0%
+the Keratin which make hair cells able
+ 
+
+ align:start position:0%
+the Keratin which make hair cells able
+to secrete the hair that actually you
+
+ align:start position:0%
+to secrete the hair that actually you
+ 
+
+ align:start position:0%
+to secrete the hair that actually you
+see so the affector genes are the
+
+ align:start position:0%
+see so the affector genes are the
+ 
+
+ align:start position:0%
+see so the affector genes are the
+functioning the
+
+ align:start position:0%
+functioning the
+ 
+
+ align:start position:0%
+functioning the
+functional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mediators and it's this mix of
+
+ align:start position:0%
+mediators and it's this mix of
+ 
+
+ align:start position:0%
+mediators and it's this mix of
+regulatory genes which I've written as R
+
+ align:start position:0%
+regulatory genes which I've written as R
+ 
+
+ align:start position:0%
+regulatory genes which I've written as R
+and effed genes which I've written
+
+ align:start position:0%
+and effed genes which I've written
+ 
+
+ align:start position:0%
+and effed genes which I've written
+written as e which form the
+
+ align:start position:0%
+written as e which form the
+ 
+
+ align:start position:0%
+written as e which form the
+combinatorial
+
+ align:start position:0%
+combinatorial
+ 
+
+ align:start position:0%
+combinatorial
+code for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell okay so that's one answer and you
+
+ align:start position:0%
+cell okay so that's one answer and you
+ 
+
+ align:start position:0%
+cell okay so that's one answer and you
+have more up there which we'll come to
+
+ align:start position:0%
+have more up there which we'll come to
+ 
+
+ align:start position:0%
+have more up there which we'll come to
+in a moment but let me give you another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+answer it's also the same answer step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wise but this answer has to do with the
+
+ align:start position:0%
+wise but this answer has to do with the
+ 
+
+ align:start position:0%
+wise but this answer has to do with the
+history of an organism I've avoided
+
+ align:start position:0%
+history of an organism I've avoided
+ 
+
+ align:start position:0%
+history of an organism I've avoided
+talking about embryos until now because
+
+ align:start position:0%
+talking about embryos until now because
+ 
+
+ align:start position:0%
+talking about embryos until now because
+I wanted you to think about the outcome
+
+ align:start position:0%
+I wanted you to think about the outcome
+ 
+
+ align:start position:0%
+I wanted you to think about the outcome
+the cell types but actually all of this
+
+ align:start position:0%
+the cell types but actually all of this
+ 
+
+ align:start position:0%
+the cell types but actually all of this
+starts cell type formation starts right
+
+ align:start position:0%
+starts cell type formation starts right
+ 
+
+ align:start position:0%
+starts cell type formation starts right
+at the beginning of an organism's
+
+ align:start position:0%
+at the beginning of an organism's
+ 
+
+ align:start position:0%
+at the beginning of an organism's
+life when two haid cells the egg and the
+
+ align:start position:0%
+life when two haid cells the egg and the
+ 
+
+ align:start position:0%
+life when two haid cells the egg and the
+sperm
+
+ align:start position:0%
+sperm
+ 
+
+ align:start position:0%
+sperm
+magically get together and join to form
+
+ align:start position:0%
+magically get together and join to form
+ 
+
+ align:start position:0%
+magically get together and join to form
+a diploid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zygote this zygote which is also a
+
+ align:start position:0%
+zygote this zygote which is also a
+ 
+
+ align:start position:0%
+zygote this zygote which is also a
+single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell is itself a magical cell because it
+
+ align:start position:0%
+cell is itself a magical cell because it
+ 
+
+ align:start position:0%
+cell is itself a magical cell because it
+contains all the information necessary
+
+ align:start position:0%
+contains all the information necessary
+ 
+
+ align:start position:0%
+contains all the information necessary
+to form whatever organism is going to be
+
+ align:start position:0%
+to form whatever organism is going to be
+ 
+
+ align:start position:0%
+to form whatever organism is going to be
+the outcome
+
+ align:start position:0%
+the outcome
+ 
+
+ align:start position:0%
+the outcome
+the zygote goes on to form an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+embryo also
+
+ align:start position:0%
+embryo also
+ 
+
+ align:start position:0%
+embryo also
+diploid that contains many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and the embryo goes on to form the
+
+ align:start position:0%
+cells and the embryo goes on to form the
+ 
+
+ align:start position:0%
+cells and the embryo goes on to form the
+diploid
+
+ align:start position:0%
+diploid
+ 
+
+ align:start position:0%
+diploid
+adult
+
+ align:start position:0%
+adult
+ 
+
+ align:start position:0%
+adult
+also with many cells and in humans there
+
+ align:start position:0%
+also with many cells and in humans there
+ 
+
+ align:start position:0%
+also with many cells and in humans there
+are about 10 to the 14th
+
+ align:start position:0%
+are about 10 to the 14th
+ 
+
+ align:start position:0%
+are about 10 to the 14th
+cells in a human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adult and during this
+
+ align:start position:0%
+adult and during this
+ 
+
+ align:start position:0%
+adult and during this
+process of two single cells two dying
+
+ align:start position:0%
+process of two single cells two dying
+ 
+
+ align:start position:0%
+process of two single cells two dying
+cells the egg and the sperm are cells
+
+ align:start position:0%
+cells the egg and the sperm are cells
+ 
+
+ align:start position:0%
+cells the egg and the sperm are cells
+with a very finite lifetime when those
+
+ align:start position:0%
+with a very finite lifetime when those
+ 
+
+ align:start position:0%
+with a very finite lifetime when those
+cells fuse with one another and we're
+
+ align:start position:0%
+cells fuse with one another and we're
+ 
+
+ align:start position:0%
+cells fuse with one another and we're
+not going to talk about this any more
+
+ align:start position:0%
+not going to talk about this any more
+ 
+
+ align:start position:0%
+not going to talk about this any more
+than than than this discussion because
+
+ align:start position:0%
+than than than this discussion because
+ 
+
+ align:start position:0%
+than than than this discussion because
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+constraints when they refuse to form the
+
+ align:start position:0%
+constraints when they refuse to form the
+ 
+
+ align:start position:0%
+constraints when they refuse to form the
+zygote there is an extraordinary process
+
+ align:start position:0%
+zygote there is an extraordinary process
+ 
+
+ align:start position:0%
+zygote there is an extraordinary process
+where the zygote is now resurrected in
+
+ align:start position:0%
+where the zygote is now resurrected in
+ 
+
+ align:start position:0%
+where the zygote is now resurrected in
+its life and it has the capacity to give
+
+ align:start position:0%
+its life and it has the capacity to give
+ 
+
+ align:start position:0%
+its life and it has the capacity to give
+rise to the whole
+
+ align:start position:0%
+rise to the whole
+ 
+
+ align:start position:0%
+rise to the whole
+organism what happens during this
+
+ align:start position:0%
+organism what happens during this
+ 
+
+ align:start position:0%
+organism what happens during this
+process well firstly I've pointed out
+
+ align:start position:0%
+process well firstly I've pointed out
+ 
+
+ align:start position:0%
+process well firstly I've pointed out
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+divide there's a lot of cell division
+
+ align:start position:0%
+divide there's a lot of cell division
+ 
+
+ align:start position:0%
+divide there's a lot of cell division
+and that's really key to getting
+
+ align:start position:0%
+and that's really key to getting
+ 
+
+ align:start position:0%
+and that's really key to getting
+different cell types you have to have
+
+ align:start position:0%
+different cell types you have to have
+ 
+
+ align:start position:0%
+different cell types you have to have
+something to work with and as they
+
+ align:start position:0%
+something to work with and as they
+ 
+
+ align:start position:0%
+something to work with and as they
+divide they become different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+according to the list on the screen and
+
+ align:start position:0%
+according to the list on the screen and
+ 
+
+ align:start position:0%
+according to the list on the screen and
+on the board above the egg the
+
+ align:start position:0%
+on the board above the egg the
+ 
+
+ align:start position:0%
+on the board above the egg the
+sperm in fact are differentiated
+
+ align:start position:0%
+sperm in fact are differentiated
+ 
+
+ align:start position:0%
+sperm in fact are differentiated
+cells but let's start with the zygote
+
+ align:start position:0%
+cells but let's start with the zygote
+ 
+
+ align:start position:0%
+cells but let's start with the zygote
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+undetermined or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncommitted and undifferentiated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm using determined and committed
+
+ align:start position:0%
+and I'm using determined and committed
+ 
+
+ align:start position:0%
+and I'm using determined and committed
+deliberately interchangeably so you get
+
+ align:start position:0%
+deliberately interchangeably so you get
+ 
+
+ align:start position:0%
+deliberately interchangeably so you get
+the idea that the terms are
+
+ align:start position:0%
+the idea that the terms are
+ 
+
+ align:start position:0%
+the idea that the terms are
+interchangeable so the zygote is
+
+ align:start position:0%
+interchangeable so the zygote is
+ 
+
+ align:start position:0%
+interchangeable so the zygote is
+undetermined and
+
+ align:start position:0%
+undetermined and
+ 
+
+ align:start position:0%
+undetermined and
+undifferentiated and as it goes through
+
+ align:start position:0%
+undifferentiated and as it goes through
+ 
+
+ align:start position:0%
+undifferentiated and as it goes through
+its embryonic stage determination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+starts and
+
+ align:start position:0%
+starts and
+ 
+
+ align:start position:0%
+starts and
+continues into the adult and later
+
+ align:start position:0%
+continues into the adult and later
+ 
+
+ align:start position:0%
+continues into the adult and later
+during late stages of embryogenesis and
+
+ align:start position:0%
+during late stages of embryogenesis and
+ 
+
+ align:start position:0%
+during late stages of embryogenesis and
+into the adult cells differentiate and
+
+ align:start position:0%
+into the adult cells differentiate and
+ 
+
+ align:start position:0%
+into the adult cells differentiate and
+become their final thing so
+
+ align:start position:0%
+become their final thing so
+ 
+
+ align:start position:0%
+become their final thing so
+determination starts in the embryo and
+
+ align:start position:0%
+determination starts in the embryo and
+ 
+
+ align:start position:0%
+determination starts in the embryo and
+sometime later the process of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiation starts and
+
+ align:start position:0%
+differentiation starts and
+ 
+
+ align:start position:0%
+differentiation starts and
+continues and so that's a second way of
+
+ align:start position:0%
+continues and so that's a second way of
+ 
+
+ align:start position:0%
+continues and so that's a second way of
+actually writing out the stepwise
+
+ align:start position:0%
+actually writing out the stepwise
+ 
+
+ align:start position:0%
+actually writing out the stepwise
+phenomenon of how cells become different
+
+ align:start position:0%
+phenomenon of how cells become different
+ 
+
+ align:start position:0%
+phenomenon of how cells become different
+from one another and how different cell
+
+ align:start position:0%
+from one another and how different cell
+ 
+
+ align:start position:0%
+from one another and how different cell
+types are formed
+
+ align:start position:0%
+types are formed
+ 
+
+ align:start position:0%
+types are formed
+let's take a look at some slides here
+
+ align:start position:0%
+let's take a look at some slides here
+ 
+
+ align:start position:0%
+let's take a look at some slides here
+and let's take a look at a couple of
+
+ align:start position:0%
+and let's take a look at a couple of
+ 
+
+ align:start position:0%
+and let's take a look at a couple of
+movies this is a movie of the first few
+
+ align:start position:0%
+movies this is a movie of the first few
+ 
+
+ align:start position:0%
+movies this is a movie of the first few
+weeks of human development and what
+
+ align:start position:0%
+weeks of human development and what
+ 
+
+ align:start position:0%
+weeks of human development and what
+you'll be able to see from this is the
+
+ align:start position:0%
+you'll be able to see from this is the
+ 
+
+ align:start position:0%
+you'll be able to see from this is the
+enormous increase in size of a human
+
+ align:start position:0%
+enormous increase in size of a human
+ 
+
+ align:start position:0%
+enormous increase in size of a human
+embryo that's coupled with cell division
+
+ align:start position:0%
+embryo that's coupled with cell division
+ 
+
+ align:start position:0%
+embryo that's coupled with cell division
+and also with cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determination and it's going to play
+
+ align:start position:0%
+determination and it's going to play
+ 
+
+ align:start position:0%
+determination and it's going to play
+again and what you can see up until
+
+ align:start position:0%
+again and what you can see up until
+ 
+
+ align:start position:0%
+again and what you can see up until
+about day 56 we all had very nice tails
+
+ align:start position:0%
+about day 56 we all had very nice tails
+ 
+
+ align:start position:0%
+about day 56 we all had very nice tails
+and then they disappeared unlike other
+
+ align:start position:0%
+and then they disappeared unlike other
+ 
+
+ align:start position:0%
+and then they disappeared unlike other
+animals but all of these are taken at
+
+ align:start position:0%
+animals but all of these are taken at
+ 
+
+ align:start position:0%
+animals but all of these are taken at
+the same scale and so you can get a
+
+ align:start position:0%
+the same scale and so you can get a
+ 
+
+ align:start position:0%
+the same scale and so you can get a
+sense of the huge amount of cell
+
+ align:start position:0%
+sense of the huge amount of cell
+ 
+
+ align:start position:0%
+sense of the huge amount of cell
+division that's going on during these
+
+ align:start position:0%
+division that's going on during these
+ 
+
+ align:start position:0%
+division that's going on during these
+first few weeks of
+
+ align:start position:0%
+first few weeks of
+ 
+
+ align:start position:0%
+first few weeks of
+Life here's a second one this is a zebra
+
+ align:start position:0%
+Life here's a second one this is a zebra
+ 
+
+ align:start position:0%
+Life here's a second one this is a zebra
+fish embryo and I want you to watch this
+
+ align:start position:0%
+fish embryo and I want you to watch this
+ 
+
+ align:start position:0%
+fish embryo and I want you to watch this
+embryo as it develops very rapidly much
+
+ align:start position:0%
+embryo as it develops very rapidly much
+ 
+
+ align:start position:0%
+embryo as it develops very rapidly much
+more rapidly than a human during the
+
+ align:start position:0%
+more rapidly than a human during the
+ 
+
+ align:start position:0%
+more rapidly than a human during the
+first 19 hours of development
+
+ align:start position:0%
+first 19 hours of development
+ 
+
+ align:start position:0%
+first 19 hours of development
+the fish embryo is kind of like a
+
+ align:start position:0%
+the fish embryo is kind of like a
+ 
+
+ align:start position:0%
+the fish embryo is kind of like a
+chicken embryo there's a big cell called
+
+ align:start position:0%
+chicken embryo there's a big cell called
+ 
+
+ align:start position:0%
+chicken embryo there's a big cell called
+a Yol cell and on top of this Yol cell
+
+ align:start position:0%
+a Yol cell and on top of this Yol cell
+ 
+
+ align:start position:0%
+a Yol cell and on top of this Yol cell
+sits a little other cell which is the
+
+ align:start position:0%
+sits a little other cell which is the
+ 
+
+ align:start position:0%
+sits a little other cell which is the
+embryo itself and it's this little top
+
+ align:start position:0%
+embryo itself and it's this little top
+ 
+
+ align:start position:0%
+embryo itself and it's this little top
+cell here it's already divided to give
+
+ align:start position:0%
+cell here it's already divided to give
+ 
+
+ align:start position:0%
+cell here it's already divided to give
+rise to two cells from which the embryo
+
+ align:start position:0%
+rise to two cells from which the embryo
+ 
+
+ align:start position:0%
+rise to two cells from which the embryo
+is going to arise and so as you watch
+
+ align:start position:0%
+is going to arise and so as you watch
+ 
+
+ align:start position:0%
+is going to arise and so as you watch
+the movie you'll see these two cells
+
+ align:start position:0%
+the movie you'll see these two cells
+ 
+
+ align:start position:0%
+the movie you'll see these two cells
+dividing into four into eight and so on
+
+ align:start position:0%
+dividing into four into eight and so on
+ 
+
+ align:start position:0%
+dividing into four into eight and so on
+and then you'll be able to see the
+
+ align:start position:0%
+and then you'll be able to see the
+ 
+
+ align:start position:0%
+and then you'll be able to see the
+beginnings of the fish emerge and I'll
+
+ align:start position:0%
+beginnings of the fish emerge and I'll
+ 
+
+ align:start position:0%
+beginnings of the fish emerge and I'll
+play it a couple of times and point out
+
+ align:start position:0%
+play it a couple of times and point out
+ 
+
+ align:start position:0%
+play it a couple of times and point out
+some things to you here's the cell
+
+ align:start position:0%
+some things to you here's the cell
+ 
+
+ align:start position:0%
+some things to you here's the cell
+division taking place it's not as rapid
+
+ align:start position:0%
+division taking place it's not as rapid
+ 
+
+ align:start position:0%
+division taking place it's not as rapid
+as this but it's of course a very rapid
+
+ align:start position:0%
+as this but it's of course a very rapid
+ 
+
+ align:start position:0%
+as this but it's of course a very rapid
+process and now you have a little cap of
+
+ align:start position:0%
+process and now you have a little cap of
+ 
+
+ align:start position:0%
+process and now you have a little cap of
+cells on the Yol and Watch What Happens
+
+ align:start position:0%
+cells on the Yol and Watch What Happens
+ 
+
+ align:start position:0%
+cells on the Yol and Watch What Happens
+that cap of cells spreads out to cover
+
+ align:start position:0%
+that cap of cells spreads out to cover
+ 
+
+ align:start position:0%
+that cap of cells spreads out to cover
+up the Yoke and a lot of cells move to
+
+ align:start position:0%
+up the Yoke and a lot of cells move to
+ 
+
+ align:start position:0%
+up the Yoke and a lot of cells move to
+that side of the embryo the right hand
+
+ align:start position:0%
+that side of the embryo the right hand
+ 
+
+ align:start position:0%
+that side of the embryo the right hand
+side of the screen here's the eye
+
+ align:start position:0%
+side of the screen here's the eye
+ 
+
+ align:start position:0%
+side of the screen here's the eye
+emerging and the brain and here are the
+
+ align:start position:0%
+emerging and the brain and here are the
+ 
+
+ align:start position:0%
+emerging and the brain and here are the
+muscles of the fish and let's watch it
+
+ align:start position:0%
+muscles of the fish and let's watch it
+ 
+
+ align:start position:0%
+muscles of the fish and let's watch it
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+Isn't that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool okay so let me stop it here at this
+
+ align:start position:0%
+cool okay so let me stop it here at this
+ 
+
+ align:start position:0%
+cool okay so let me stop it here at this
+stage you've got several hundred cells
+
+ align:start position:0%
+stage you've got several hundred cells
+ 
+
+ align:start position:0%
+stage you've got several hundred cells
+that are sitting on top of this Yol cell
+
+ align:start position:0%
+that are sitting on top of this Yol cell
+ 
+
+ align:start position:0%
+that are sitting on top of this Yol cell
+this pointer seems to have died but
+
+ align:start position:0%
+this pointer seems to have died but
+ 
+
+ align:start position:0%
+this pointer seems to have died but
+they're sitting on top of the Yol cell
+
+ align:start position:0%
+they're sitting on top of the Yol cell
+ 
+
+ align:start position:0%
+they're sitting on top of the Yol cell
+and you'll be able to see when I start
+
+ align:start position:0%
+and you'll be able to see when I start
+ 
+
+ align:start position:0%
+and you'll be able to see when I start
+the movie again how those cells spread
+
+ align:start position:0%
+the movie again how those cells spread
+ 
+
+ align:start position:0%
+the movie again how those cells spread
+out to cover and they are actively doing
+
+ align:start position:0%
+out to cover and they are actively doing
+ 
+
+ align:start position:0%
+out to cover and they are actively doing
+it they know to do it they actively
+
+ align:start position:0%
+it they know to do it they actively
+ 
+
+ align:start position:0%
+it they know to do it they actively
+spread out to cover the surface of the
+
+ align:start position:0%
+spread out to cover the surface of the
+ 
+
+ align:start position:0%
+spread out to cover the surface of the
+embryo and then actively a group of them
+
+ align:start position:0%
+embryo and then actively a group of them
+ 
+
+ align:start position:0%
+embryo and then actively a group of them
+moves to one side of the embryo to form
+
+ align:start position:0%
+moves to one side of the embryo to form
+ 
+
+ align:start position:0%
+moves to one side of the embryo to form
+most of the embryo including all the
+
+ align:start position:0%
+most of the embryo including all the
+ 
+
+ align:start position:0%
+most of the embryo including all the
+nervous system the muscles the
+
+ align:start position:0%
+nervous system the muscles the
+ 
+
+ align:start position:0%
+nervous system the muscles the
+intestines and so on so let's start it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again okay there you can see these cells
+
+ align:start position:0%
+again okay there you can see these cells
+ 
+
+ align:start position:0%
+again okay there you can see these cells
+spreading out they've spread it out to
+
+ align:start position:0%
+spreading out they've spread it out to
+ 
+
+ align:start position:0%
+spreading out they've spread it out to
+this they've spread out to this point
+
+ align:start position:0%
+this they've spread out to this point
+ 
+
+ align:start position:0%
+this they've spread out to this point
+let's let them spread out some more here
+
+ align:start position:0%
+let's let them spread out some more here
+ 
+
+ align:start position:0%
+let's let them spread out some more here
+they are they've completely closed up
+
+ align:start position:0%
+they are they've completely closed up
+ 
+
+ align:start position:0%
+they are they've completely closed up
+the Yol and if we stop now you'll see on
+
+ align:start position:0%
+the Yol and if we stop now you'll see on
+ 
+
+ align:start position:0%
+the Yol and if we stop now you'll see on
+the right right hand side of the screen
+
+ align:start position:0%
+the right right hand side of the screen
+ 
+
+ align:start position:0%
+the right right hand side of the screen
+there's a much thicker group of cells
+
+ align:start position:0%
+there's a much thicker group of cells
+ 
+
+ align:start position:0%
+there's a much thicker group of cells
+there are thousands and thousands of
+
+ align:start position:0%
+there are thousands and thousands of
+ 
+
+ align:start position:0%
+there are thousands and thousands of
+cells now that are there now at this
+
+ align:start position:0%
+cells now that are there now at this
+ 
+
+ align:start position:0%
+cells now that are there now at this
+point if you look at gene expression in
+
+ align:start position:0%
+point if you look at gene expression in
+ 
+
+ align:start position:0%
+point if you look at gene expression in
+the embryo you can pick out many
+
+ align:start position:0%
+the embryo you can pick out many
+ 
+
+ align:start position:0%
+the embryo you can pick out many
+different regions of the future brain
+
+ align:start position:0%
+different regions of the future brain
+ 
+
+ align:start position:0%
+different regions of the future brain
+you can pick out the future intestines
+
+ align:start position:0%
+you can pick out the future intestines
+ 
+
+ align:start position:0%
+you can pick out the future intestines
+and the future muscles but there is no
+
+ align:start position:0%
+and the future muscles but there is no
+ 
+
+ align:start position:0%
+and the future muscles but there is no
+differentiation at this point the cells
+
+ align:start position:0%
+differentiation at this point the cells
+ 
+
+ align:start position:0%
+differentiation at this point the cells
+do not know the cells have not finished
+
+ align:start position:0%
+do not know the cells have not finished
+ 
+
+ align:start position:0%
+do not know the cells have not finished
+becoming what they're becoming and here
+
+ align:start position:0%
+becoming what they're becoming and here
+ 
+
+ align:start position:0%
+becoming what they're becoming and here
+as we go on a bit
+
+ align:start position:0%
+as we go on a bit
+ 
+
+ align:start position:0%
+as we go on a bit
+more okay here is the
+
+ align:start position:0%
+more okay here is the
+ 
+
+ align:start position:0%
+more okay here is the
+eye up front and these bumps of the
+
+ align:start position:0%
+eye up front and these bumps of the
+ 
+
+ align:start position:0%
+eye up front and these bumps of the
+brain and then these little Chevron
+
+ align:start position:0%
+brain and then these little Chevron
+ 
+
+ align:start position:0%
+brain and then these little Chevron
+shaped things there are the future
+
+ align:start position:0%
+shaped things there are the future
+ 
+
+ align:start position:0%
+shaped things there are the future
+muscles your fish filet and there is the
+
+ align:start position:0%
+muscles your fish filet and there is the
+ 
+
+ align:start position:0%
+muscles your fish filet and there is the
+fish moving on okay it's really a
+
+ align:start position:0%
+fish moving on okay it's really a
+ 
+
+ align:start position:0%
+fish moving on okay it's really a
+fantastic
+
+ align:start position:0%
+fantastic
+ 
+
+ align:start position:0%
+fantastic
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+okay very good let's go back to the
+
+ align:start position:0%
+okay very good let's go back to the
+ 
+
+ align:start position:0%
+okay very good let's go back to the
+board and talk about this more
+
+ align:start position:0%
+board and talk about this more
+ 
+
+ align:start position:0%
+board and talk about this more
+theoretically we've sort of answered a
+
+ align:start position:0%
+theoretically we've sort of answered a
+ 
+
+ align:start position:0%
+theoretically we've sort of answered a
+question here how does a cell type
+
+ align:start position:0%
+question here how does a cell type
+ 
+
+ align:start position:0%
+question here how does a cell type
+express it its code well not all at once
+
+ align:start position:0%
+express it its code well not all at once
+ 
+
+ align:start position:0%
+express it its code well not all at once
+over time and over a series of many
+
+ align:start position:0%
+over time and over a series of many
+ 
+
+ align:start position:0%
+over time and over a series of many
+steps but that's not actually the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer and so let's rephrase the
+
+ align:start position:0%
+answer and so let's rephrase the
+ 
+
+ align:start position:0%
+answer and so let's rephrase the
+question to make it a little more
+
+ align:start position:0%
+question to make it a little more
+ 
+
+ align:start position:0%
+question to make it a little more
+precise and I've rephrased it by asking
+
+ align:start position:0%
+precise and I've rephrased it by asking
+ 
+
+ align:start position:0%
+precise and I've rephrased it by asking
+what tells a specific cell type to
+
+ align:start position:0%
+what tells a specific cell type to
+ 
+
+ align:start position:0%
+what tells a specific cell type to
+express its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code what tells a specific cell type to
+
+ align:start position:0%
+code what tells a specific cell type to
+ 
+
+ align:start position:0%
+code what tells a specific cell type to
+express its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code and the answer is this is not going
+
+ align:start position:0%
+code and the answer is this is not going
+ 
+
+ align:start position:0%
+code and the answer is this is not going
+to be really helpful to you but it will
+
+ align:start position:0%
+to be really helpful to you but it will
+ 
+
+ align:start position:0%
+to be really helpful to you but it will
+in a moment the answer is that there are
+
+ align:start position:0%
+in a moment the answer is that there are
+ 
+
+ align:start position:0%
+in a moment the answer is that there are
+a bunch of inputs okay there are a bunch
+
+ align:start position:0%
+a bunch of inputs okay there are a bunch
+ 
+
+ align:start position:0%
+a bunch of inputs okay there are a bunch
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+instructions that the cell
+
+ align:start position:0%
+instructions that the cell
+ 
+
+ align:start position:0%
+instructions that the cell
+gets okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's write this out in a kind of
+
+ align:start position:0%
+and let's write this out in a kind of
+ 
+
+ align:start position:0%
+and let's write this out in a kind of
+theoretical way we'll get to the
+
+ align:start position:0%
+theoretical way we'll get to the
+ 
+
+ align:start position:0%
+theoretical way we'll get to the
+molecules in a moment here again are our
+
+ align:start position:0%
+molecules in a moment here again are our
+ 
+
+ align:start position:0%
+molecules in a moment here again are our
+uncommitted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and they can be exposed to a
+
+ align:start position:0%
+cells and they can be exposed to a
+ 
+
+ align:start position:0%
+cells and they can be exposed to a
+number of different molecules the inputs
+
+ align:start position:0%
+number of different molecules the inputs
+ 
+
+ align:start position:0%
+number of different molecules the inputs
+let me just you know come clean here the
+
+ align:start position:0%
+let me just you know come clean here the
+ 
+
+ align:start position:0%
+let me just you know come clean here the
+inputs are specific molecules and as
+
+ align:start position:0%
+inputs are specific molecules and as
+ 
+
+ align:start position:0%
+inputs are specific molecules and as
+you'll see in a moment they all have got
+
+ align:start position:0%
+you'll see in a moment they all have got
+ 
+
+ align:start position:0%
+you'll see in a moment they all have got
+something to do with cell signaling or
+
+ align:start position:0%
+something to do with cell signaling or
+ 
+
+ align:start position:0%
+something to do with cell signaling or
+regulating gene
+
+ align:start position:0%
+regulating gene
+ 
+
+ align:start position:0%
+regulating gene
+expression these UNC lied cells can be
+
+ align:start position:0%
+expression these UNC lied cells can be
+ 
+
+ align:start position:0%
+expression these UNC lied cells can be
+exposed to many different inputs let's
+
+ align:start position:0%
+exposed to many different inputs let's
+ 
+
+ align:start position:0%
+exposed to many different inputs let's
+take three different
+
+ align:start position:0%
+take three different
+ 
+
+ align:start position:0%
+take three different
+inputs we'll call them input one two and
+
+ align:start position:0%
+inputs we'll call them input one two and
+ 
+
+ align:start position:0%
+inputs we'll call them input one two and
+three and these inputs through many
+
+ align:start position:0%
+three and these inputs through many
+ 
+
+ align:start position:0%
+three and these inputs through many
+steps and changes in gene
+
+ align:start position:0%
+steps and changes in gene
+ 
+
+ align:start position:0%
+steps and changes in gene
+expression and the inputs can be
+
+ align:start position:0%
+expression and the inputs can be
+ 
+
+ align:start position:0%
+expression and the inputs can be
+composite they don't have to be a single
+
+ align:start position:0%
+composite they don't have to be a single
+ 
+
+ align:start position:0%
+composite they don't have to be a single
+thing we'll take those cells into
+
+ align:start position:0%
+thing we'll take those cells into
+ 
+
+ align:start position:0%
+thing we'll take those cells into
+differentiated cell type one cell type
+
+ align:start position:0%
+differentiated cell type one cell type
+ 
+
+ align:start position:0%
+differentiated cell type one cell type
+two or cell type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three and cell type one you know to
+
+ align:start position:0%
+three and cell type one you know to
+ 
+
+ align:start position:0%
+three and cell type one you know to
+belabor this we'll express code one cell
+
+ align:start position:0%
+belabor this we'll express code one cell
+ 
+
+ align:start position:0%
+belabor this we'll express code one cell
+type two code two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc as these decisions are made similar
+
+ align:start position:0%
+Etc as these decisions are made similar
+ 
+
+ align:start position:0%
+Etc as these decisions are made similar
+to the kinds ofc decisions we've looked
+
+ align:start position:0%
+to the kinds ofc decisions we've looked
+ 
+
+ align:start position:0%
+to the kinds ofc decisions we've looked
+at in Biochemistry previously there can
+
+ align:start position:0%
+at in Biochemistry previously there can
+ 
+
+ align:start position:0%
+at in Biochemistry previously there can
+be interactions and so it may be that as
+
+ align:start position:0%
+be interactions and so it may be that as
+ 
+
+ align:start position:0%
+be interactions and so it may be that as
+cell type one develops it's actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inhibits the formation of cell type
+
+ align:start position:0%
+inhibits the formation of cell type
+ 
+
+ align:start position:0%
+inhibits the formation of cell type
+2 and cell type two in turn might be an
+
+ align:start position:0%
+2 and cell type two in turn might be an
+ 
+
+ align:start position:0%
+2 and cell type two in turn might be an
+inhibitor of the formation of cell type
+
+ align:start position:0%
+inhibitor of the formation of cell type
+ 
+
+ align:start position:0%
+inhibitor of the formation of cell type
+three so there are interactions between
+
+ align:start position:0%
+three so there are interactions between
+ 
+
+ align:start position:0%
+three so there are interactions between
+cells so the inputs
+
+ align:start position:0%
+cells so the inputs
+ 
+
+ align:start position:0%
+cells so the inputs
+can be composite they can comp composed
+
+ align:start position:0%
+can be composite they can comp composed
+ 
+
+ align:start position:0%
+can be composite they can comp composed
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+several
+
+ align:start position:0%
+several
+ 
+
+ align:start position:0%
+several
+molecules factors if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like and there's cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk just like the cross talk between
+
+ align:start position:0%
+talk just like the cross talk between
+ 
+
+ align:start position:0%
+talk just like the cross talk between
+the receptors that we talked about in
+
+ align:start position:0%
+the receptors that we talked about in
+ 
+
+ align:start position:0%
+the receptors that we talked about in
+cell cell signaling and that's not
+
+ align:start position:0%
+cell cell signaling and that's not
+ 
+
+ align:start position:0%
+cell cell signaling and that's not
+surprising ring because in fact the
+
+ align:start position:0%
+surprising ring because in fact the
+ 
+
+ align:start position:0%
+surprising ring because in fact the
+inputs include cell cell signaling
+
+ align:start position:0%
+inputs include cell cell signaling
+ 
+
+ align:start position:0%
+inputs include cell cell signaling
+molecules those lians and receptors that
+
+ align:start position:0%
+molecules those lians and receptors that
+ 
+
+ align:start position:0%
+molecules those lians and receptors that
+we spoke about previously so what are
+
+ align:start position:0%
+we spoke about previously so what are
+ 
+
+ align:start position:0%
+we spoke about previously so what are
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs and they're
+
+ align:start position:0%
+inputs and they're
+ 
+
+ align:start position:0%
+inputs and they're
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+one are signals that act between
+
+ align:start position:0%
+one are signals that act between
+ 
+
+ align:start position:0%
+one are signals that act between
+cells just like we've been talking about
+
+ align:start position:0%
+cells just like we've been talking about
+ 
+
+ align:start position:0%
+cells just like we've been talking about
+in cell biology cell cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signaling and wherever you talk about
+
+ align:start position:0%
+signaling and wherever you talk about
+ 
+
+ align:start position:0%
+signaling and wherever you talk about
+cell cell
+
+ align:start position:0%
+cell cell
+ 
+
+ align:start position:0%
+cell cell
+signaling it is implicit that you're
+
+ align:start position:0%
+signaling it is implicit that you're
+ 
+
+ align:start position:0%
+signaling it is implicit that you're
+talking about interactions between
+
+ align:start position:0%
+talking about interactions between
+ 
+
+ align:start position:0%
+talking about interactions between
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lians which in development are sometimes
+
+ align:start position:0%
+lians which in development are sometimes
+ 
+
+ align:start position:0%
+lians which in development are sometimes
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induces act on the receptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outcome is to change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sate this is a subset of the signaling
+
+ align:start position:0%
+Sate this is a subset of the signaling
+ 
+
+ align:start position:0%
+Sate this is a subset of the signaling
+interactions we talked about previously
+
+ align:start position:0%
+interactions we talked about previously
+ 
+
+ align:start position:0%
+interactions we talked about previously
+where the response here the response
+
+ align:start position:0%
+where the response here the response
+ 
+
+ align:start position:0%
+where the response here the response
+previously was manifold the response
+
+ align:start position:0%
+previously was manifold the response
+ 
+
+ align:start position:0%
+previously was manifold the response
+here would be to change
+
+ align:start position:0%
+here would be to change
+ 
+
+ align:start position:0%
+here would be to change
+sulfate but there's a second kind of
+
+ align:start position:0%
+sulfate but there's a second kind of
+ 
+
+ align:start position:0%
+sulfate but there's a second kind of
+input and those are the molecules that
+
+ align:start position:0%
+input and those are the molecules that
+ 
+
+ align:start position:0%
+input and those are the molecules that
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+autonomous also referred to as being
+
+ align:start position:0%
+autonomous also referred to as being
+ 
+
+ align:start position:0%
+autonomous also referred to as being
+inherited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factors and referred to in development
+
+ align:start position:0%
+factors and referred to in development
+ 
+
+ align:start position:0%
+factors and referred to in development
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinants and these
+
+ align:start position:0%
+determinants and these
+ 
+
+ align:start position:0%
+determinants and these
+determinants this is what cell
+
+ align:start position:0%
+determinants this is what cell
+ 
+
+ align:start position:0%
+determinants this is what cell
+autonomous means act within cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so they are not going to be lians
+
+ align:start position:0%
+and so they are not going to be lians
+ 
+
+ align:start position:0%
+and so they are not going to be lians
+and receptors they will be things for
+
+ align:start position:0%
+and receptors they will be things for
+ 
+
+ align:start position:0%
+and receptors they will be things for
+example like transcription
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+furthermore both determinants and
+
+ align:start position:0%
+furthermore both determinants and
+ 
+
+ align:start position:0%
+furthermore both determinants and
+inducers can act in a concentration
+
+ align:start position:0%
+inducers can act in a concentration
+ 
+
+ align:start position:0%
+inducers can act in a concentration
+dependent way so that a small amount
+
+ align:start position:0%
+dependent way so that a small amount
+ 
+
+ align:start position:0%
+dependent way so that a small amount
+would give you one
+
+ align:start position:0%
+would give you one
+ 
+
+ align:start position:0%
+would give you one
+sulfate and a larger amount would give
+
+ align:start position:0%
+sulfate and a larger amount would give
+ 
+
+ align:start position:0%
+sulfate and a larger amount would give
+you a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sulfate so can be concentration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dependent and in the cases where a
+
+ align:start position:0%
+dependent and in the cases where a
+ 
+
+ align:start position:0%
+dependent and in the cases where a
+signal or a determinant is concentration
+
+ align:start position:0%
+signal or a determinant is concentration
+ 
+
+ align:start position:0%
+signal or a determinant is concentration
+dependent it gets a special name it's
+
+ align:start position:0%
+dependent it gets a special name it's
+ 
+
+ align:start position:0%
+dependent it gets a special name it's
+referred to as a
+
+ align:start position:0%
+referred to as a
+ 
+
+ align:start position:0%
+referred to as a
+morphogen for historical not
+
+ align:start position:0%
+morphogen for historical not
+ 
+
+ align:start position:0%
+morphogen for historical not
+particularly logical reasons but if you
+
+ align:start position:0%
+particularly logical reasons but if you
+ 
+
+ align:start position:0%
+particularly logical reasons but if you
+see the term you'll
+
+ align:start position:0%
+see the term you'll
+ 
+
+ align:start position:0%
+see the term you'll
+know and finally before we go to some
+
+ align:start position:0%
+know and finally before we go to some
+ 
+
+ align:start position:0%
+know and finally before we go to some
+slides one can find groups of these
+
+ align:start position:0%
+slides one can find groups of these
+ 
+
+ align:start position:0%
+slides one can find groups of these
+inputs groups of these regulatory
+
+ align:start position:0%
+inputs groups of these regulatory
+ 
+
+ align:start position:0%
+inputs groups of these regulatory
+molecules so all of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs all of these are the regulatory
+
+ align:start position:0%
+inputs all of these are the regulatory
+ 
+
+ align:start position:0%
+inputs all of these are the regulatory
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+regulatory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factors and they can act spatially in a
+
+ align:start position:0%
+factors and they can act spatially in a
+ 
+
+ align:start position:0%
+factors and they can act spatially in a
+group so you can find regions of the
+
+ align:start position:0%
+group so you can find regions of the
+ 
+
+ align:start position:0%
+group so you can find regions of the
+developing embryo where there are groups
+
+ align:start position:0%
+developing embryo where there are groups
+ 
+
+ align:start position:0%
+developing embryo where there are groups
+of these molecules acting together and
+
+ align:start position:0%
+of these molecules acting together and
+ 
+
+ align:start position:0%
+of these molecules acting together and
+where you find these groups that
+
+ align:start position:0%
+where you find these groups that
+ 
+
+ align:start position:0%
+where you find these groups that
+particular region of the embryo may have
+
+ align:start position:0%
+particular region of the embryo may have
+ 
+
+ align:start position:0%
+particular region of the embryo may have
+a powerful effect in influencing the
+
+ align:start position:0%
+a powerful effect in influencing the
+ 
+
+ align:start position:0%
+a powerful effect in influencing the
+cells which form around it and that
+
+ align:start position:0%
+cells which form around it and that
+ 
+
+ align:start position:0%
+cells which form around it and that
+region that group of of factors in one
+
+ align:start position:0%
+region that group of of factors in one
+ 
+
+ align:start position:0%
+region that group of of factors in one
+region that can influence its
+
+ align:start position:0%
+region that can influence its
+ 
+
+ align:start position:0%
+region that can influence its
+surroundings is called an
+
+ align:start position:0%
+surroundings is called an
+ 
+
+ align:start position:0%
+surroundings is called an
+organizer so groups of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signals which are
+
+ align:start position:0%
+signals which are
+ 
+
+ align:start position:0%
+signals which are
+localized that is in one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place in one group of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells can influence the surrounding
+
+ align:start position:0%
+cells can influence the surrounding
+ 
+
+ align:start position:0%
+cells can influence the surrounding
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and is termed an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organizer and there are many
+
+ align:start position:0%
+organizer and there are many
+ 
+
+ align:start position:0%
+organizer and there are many
+organizers in the body both in the
+
+ align:start position:0%
+organizers in the body both in the
+ 
+
+ align:start position:0%
+organizers in the body both in the
+embryo and in ourselves as we'll discuss
+
+ align:start position:0%
+embryo and in ourselves as we'll discuss
+ 
+
+ align:start position:0%
+embryo and in ourselves as we'll discuss
+when we talk about stem
+
+ align:start position:0%
+when we talk about stem
+ 
+
+ align:start position:0%
+when we talk about stem
+cells examples of organizers I'll show
+
+ align:start position:0%
+cells examples of organizers I'll show
+ 
+
+ align:start position:0%
+cells examples of organizers I'll show
+you in a moment there's something called
+
+ align:start position:0%
+you in a moment there's something called
+ 
+
+ align:start position:0%
+you in a moment there's something called
+the span organizer which is very famous
+
+ align:start position:0%
+the span organizer which is very famous
+ 
+
+ align:start position:0%
+the span organizer which is very famous
+and some of you may have leared about
+
+ align:start position:0%
+and some of you may have leared about
+ 
+
+ align:start position:0%
+and some of you may have leared about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+previously and then there are regions
+
+ align:start position:0%
+previously and then there are regions
+ 
+
+ align:start position:0%
+previously and then there are regions
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+example in the forbrain the developing
+
+ align:start position:0%
+example in the forbrain the developing
+ 
+
+ align:start position:0%
+example in the forbrain the developing
+cerebrum where there is an organizer
+
+ align:start position:0%
+cerebrum where there is an organizer
+ 
+
+ align:start position:0%
+cerebrum where there is an organizer
+that actually tells the different parts
+
+ align:start position:0%
+that actually tells the different parts
+ 
+
+ align:start position:0%
+that actually tells the different parts
+of you're developing higher cortical
+
+ align:start position:0%
+of you're developing higher cortical
+ 
+
+ align:start position:0%
+of you're developing higher cortical
+function to form so let's look at some
+
+ align:start position:0%
+function to form so let's look at some
+ 
+
+ align:start position:0%
+function to form so let's look at some
+slides and some of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+handouts and I drew these for you
+
+ align:start position:0%
+handouts and I drew these for you
+ 
+
+ align:start position:0%
+handouts and I drew these for you
+because I thought it was really
+
+ align:start position:0%
+because I thought it was really
+ 
+
+ align:start position:0%
+because I thought it was really
+important that you got them here's
+
+ align:start position:0%
+important that you got them here's
+ 
+
+ align:start position:0%
+important that you got them here's
+localized
+
+ align:start position:0%
+localized
+ 
+
+ align:start position:0%
+localized
+determinance localized Regulators called
+
+ align:start position:0%
+determinance localized Regulators called
+ 
+
+ align:start position:0%
+determinance localized Regulators called
+determinant and you see the idea here
+
+ align:start position:0%
+determinant and you see the idea here
+ 
+
+ align:start position:0%
+determinant and you see the idea here
+this is important this isn't on the
+
+ align:start position:0%
+this is important this isn't on the
+ 
+
+ align:start position:0%
+this is important this isn't on the
+board here's the Mother
+
+ align:start position:0%
+board here's the Mother
+ 
+
+ align:start position:0%
+board here's the Mother
+cell with these boxes where these boxes
+
+ align:start position:0%
+cell with these boxes where these boxes
+ 
+
+ align:start position:0%
+cell with these boxes where these boxes
+represent some kind of regulatory factor
+
+ align:start position:0%
+represent some kind of regulatory factor
+ 
+
+ align:start position:0%
+represent some kind of regulatory factor
+and you can see I've drawn them on one
+
+ align:start position:0%
+and you can see I've drawn them on one
+ 
+
+ align:start position:0%
+and you can see I've drawn them on one
+side of the cell such that when that
+
+ align:start position:0%
+side of the cell such that when that
+ 
+
+ align:start position:0%
+side of the cell such that when that
+cell divides one of the does doesn't get
+
+ align:start position:0%
+cell divides one of the does doesn't get
+ 
+
+ align:start position:0%
+cell divides one of the does doesn't get
+them and one of them does and if the
+
+ align:start position:0%
+them and one of them does and if the
+ 
+
+ align:start position:0%
+them and one of them does and if the
+boxes are regulatory factors the
+
+ align:start position:0%
+boxes are regulatory factors the
+ 
+
+ align:start position:0%
+boxes are regulatory factors the
+daughter cell that gets them will go on
+
+ align:start position:0%
+daughter cell that gets them will go on
+ 
+
+ align:start position:0%
+daughter cell that gets them will go on
+to do something different than the one
+
+ align:start position:0%
+to do something different than the one
+ 
+
+ align:start position:0%
+to do something different than the one
+that doesn't and you can get two
+
+ align:start position:0%
+that doesn't and you can get two
+ 
+
+ align:start position:0%
+that doesn't and you can get two
+different cell types coming out of this
+
+ align:start position:0%
+different cell types coming out of this
+ 
+
+ align:start position:0%
+different cell types coming out of this
+and I've listed examples of the many
+
+ align:start position:0%
+and I've listed examples of the many
+ 
+
+ align:start position:0%
+and I've listed examples of the many
+different kinds of factors that can be
+
+ align:start position:0%
+different kinds of factors that can be
+ 
+
+ align:start position:0%
+different kinds of factors that can be
+determinance here's a real
+
+ align:start position:0%
+determinance here's a real
+ 
+
+ align:start position:0%
+determinance here's a real
+example this is an early worm embrio
+
+ align:start position:0%
+example this is an early worm embrio
+ 
+
+ align:start position:0%
+example this is an early worm embrio
+remember I told you about Professor
+
+ align:start position:0%
+remember I told you about Professor
+ 
+
+ align:start position:0%
+remember I told you about Professor
+horvitz who got the Nobel Prize for
+
+ align:start position:0%
+horvitz who got the Nobel Prize for
+ 
+
+ align:start position:0%
+horvitz who got the Nobel Prize for
+discovering cell death Pro cesses this
+
+ align:start position:0%
+discovering cell death Pro cesses this
+ 
+
+ align:start position:0%
+discovering cell death Pro cesses this
+is the same animal he works on and on
+
+ align:start position:0%
+is the same animal he works on and on
+ 
+
+ align:start position:0%
+is the same animal he works on and on
+the top
+
+ align:start position:0%
+the top
+ 
+
+ align:start position:0%
+the top
+panels are nuclei stained in blue with
+
+ align:start position:0%
+panels are nuclei stained in blue with
+ 
+
+ align:start position:0%
+panels are nuclei stained in blue with
+this die called dappy here's the zygote
+
+ align:start position:0%
+this die called dappy here's the zygote
+ 
+
+ align:start position:0%
+this die called dappy here's the zygote
+here's the two cell embryo and the 32
+
+ align:start position:0%
+here's the two cell embryo and the 32
+ 
+
+ align:start position:0%
+here's the two cell embryo and the 32
+cell embryo and you can see that there's
+
+ align:start position:0%
+cell embryo and you can see that there's
+ 
+
+ align:start position:0%
+cell embryo and you can see that there's
+a nucleus in every cell okay on the
+
+ align:start position:0%
+a nucleus in every cell okay on the
+ 
+
+ align:start position:0%
+a nucleus in every cell okay on the
+bottom are some determinants that are
+
+ align:start position:0%
+bottom are some determinants that are
+ 
+
+ align:start position:0%
+bottom are some determinants that are
+called P granules P granules are
+
+ align:start position:0%
+called P granules P granules are
+ 
+
+ align:start position:0%
+called P granules P granules are
+Composites of protein and RNA and they
+
+ align:start position:0%
+Composites of protein and RNA and they
+ 
+
+ align:start position:0%
+Composites of protein and RNA and they
+are Regulators of where the future germs
+
+ align:start position:0%
+are Regulators of where the future germs
+ 
+
+ align:start position:0%
+are Regulators of where the future germs
+cells will form the future egg and sperm
+
+ align:start position:0%
+cells will form the future egg and sperm
+ 
+
+ align:start position:0%
+cells will form the future egg and sperm
+look how these ger look how these P
+
+ align:start position:0%
+look how these ger look how these P
+ 
+
+ align:start position:0%
+look how these ger look how these P
+granules segregate during development
+
+ align:start position:0%
+granules segregate during development
+ 
+
+ align:start position:0%
+granules segregate during development
+here they are on one side of the embryo
+
+ align:start position:0%
+here they are on one side of the embryo
+ 
+
+ align:start position:0%
+here they are on one side of the embryo
+even in the zygote and then the zygote
+
+ align:start position:0%
+even in the zygote and then the zygote
+ 
+
+ align:start position:0%
+even in the zygote and then the zygote
+splits look one of the two cells gets
+
+ align:start position:0%
+splits look one of the two cells gets
+ 
+
+ align:start position:0%
+splits look one of the two cells gets
+them all and the other does nothing and
+
+ align:start position:0%
+them all and the other does nothing and
+ 
+
+ align:start position:0%
+them all and the other does nothing and
+at the 32 cell stage there is one cell
+
+ align:start position:0%
+at the 32 cell stage there is one cell
+ 
+
+ align:start position:0%
+at the 32 cell stage there is one cell
+out of 32 that has all of the P granules
+
+ align:start position:0%
+out of 32 that has all of the P granules
+ 
+
+ align:start position:0%
+out of 32 that has all of the P granules
+and they've been excluded or degraded
+
+ align:start position:0%
+and they've been excluded or degraded
+ 
+
+ align:start position:0%
+and they've been excluded or degraded
+from the rest of the embryo okay and
+
+ align:start position:0%
+from the rest of the embryo okay and
+ 
+
+ align:start position:0%
+from the rest of the embryo okay and
+that is a really beautiful example
+
+ align:start position:0%
+that is a really beautiful example
+ 
+
+ align:start position:0%
+that is a really beautiful example
+perhaps the most beautiful example of
+
+ align:start position:0%
+perhaps the most beautiful example of
+ 
+
+ align:start position:0%
+perhaps the most beautiful example of
+determinant
+
+ align:start position:0%
+determinant
+ 
+
+ align:start position:0%
+determinant
+segregating here's another one the
+
+ align:start position:0%
+segregating here's another one the
+ 
+
+ align:start position:0%
+segregating here's another one the
+signaling effect is secreted by
+
+ align:start position:0%
+signaling effect is secreted by
+ 
+
+ align:start position:0%
+signaling effect is secreted by
+neighboring cells uncommitted cells over
+
+ align:start position:0%
+neighboring cells uncommitted cells over
+ 
+
+ align:start position:0%
+neighboring cells uncommitted cells over
+time will do something there's enough
+
+ align:start position:0%
+time will do something there's enough
+ 
+
+ align:start position:0%
+time will do something there's enough
+transcription factors and Regulatory
+
+ align:start position:0%
+transcription factors and Regulatory
+ 
+
+ align:start position:0%
+transcription factors and Regulatory
+factors in all cells that over time
+
+ align:start position:0%
+factors in all cells that over time
+ 
+
+ align:start position:0%
+factors in all cells that over time
+they'll go on to differentiate into
+
+ align:start position:0%
+they'll go on to differentiate into
+ 
+
+ align:start position:0%
+they'll go on to differentiate into
+something if they're normal cells but
+
+ align:start position:0%
+something if they're normal cells but
+ 
+
+ align:start position:0%
+something if they're normal cells but
+here's a signaling cell telling an
+
+ align:start position:0%
+here's a signaling cell telling an
+ 
+
+ align:start position:0%
+here's a signaling cell telling an
+uncommitted cell to activate a signaling
+
+ align:start position:0%
+uncommitted cell to activate a signaling
+ 
+
+ align:start position:0%
+uncommitted cell to activate a signaling
+pathway and go on and make cell type two
+
+ align:start position:0%
+pathway and go on and make cell type two
+ 
+
+ align:start position:0%
+pathway and go on and make cell type two
+okay and these are the inducers which
+
+ align:start position:0%
+okay and these are the inducers which
+ 
+
+ align:start position:0%
+okay and these are the inducers which
+are lians binding to receptors and
+
+ align:start position:0%
+are lians binding to receptors and
+ 
+
+ align:start position:0%
+are lians binding to receptors and
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+sulfate these signaling Pathways can act
+
+ align:start position:0%
+sulfate these signaling Pathways can act
+ 
+
+ align:start position:0%
+sulfate these signaling Pathways can act
+in a concentration dependent
+
+ align:start position:0%
+in a concentration dependent
+ 
+
+ align:start position:0%
+in a concentration dependent
+way as seen on that
+
+ align:start position:0%
+way as seen on that
+ 
+
+ align:start position:0%
+way as seen on that
+screen and here is the notion of a
+
+ align:start position:0%
+screen and here is the notion of a
+ 
+
+ align:start position:0%
+screen and here is the notion of a
+morphogen where High liand concentration
+
+ align:start position:0%
+morphogen where High liand concentration
+ 
+
+ align:start position:0%
+morphogen where High liand concentration
+will give an output of cell type two and
+
+ align:start position:0%
+will give an output of cell type two and
+ 
+
+ align:start position:0%
+will give an output of cell type two and
+low Lian concentration an output of cell
+
+ align:start position:0%
+low Lian concentration an output of cell
+ 
+
+ align:start position:0%
+low Lian concentration an output of cell
+type 3 and we touched on how this works
+
+ align:start position:0%
+type 3 and we touched on how this works
+ 
+
+ align:start position:0%
+type 3 and we touched on how this works
+molecularly previously it's not well
+
+ align:start position:0%
+molecularly previously it's not well
+ 
+
+ align:start position:0%
+molecularly previously it's not well
+understood and is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complicated this is the most famous
+
+ align:start position:0%
+complicated this is the most famous
+ 
+
+ align:start position:0%
+complicated this is the most famous
+example of cells that can go on and tell
+
+ align:start position:0%
+example of cells that can go on and tell
+ 
+
+ align:start position:0%
+example of cells that can go on and tell
+other cells what to become it's a group
+
+ align:start position:0%
+other cells what to become it's a group
+ 
+
+ align:start position:0%
+other cells what to become it's a group
+of cells that was termed the organizer
+
+ align:start position:0%
+of cells that was termed the organizer
+ 
+
+ align:start position:0%
+of cells that was termed the organizer
+before it was clear that there were
+
+ align:start position:0%
+before it was clear that there were
+ 
+
+ align:start position:0%
+before it was clear that there were
+actually lots of organizers and the
+
+ align:start position:0%
+actually lots of organizers and the
+ 
+
+ align:start position:0%
+actually lots of organizers and the
+organizer was defined by a graduate
+
+ align:start position:0%
+organizer was defined by a graduate
+ 
+
+ align:start position:0%
+organizer was defined by a graduate
+student Hilda Mangold together with her
+
+ align:start position:0%
+student Hilda Mangold together with her
+ 
+
+ align:start position:0%
+student Hilda Mangold together with her
+advisor hunt spaman Mangold
+
+ align:start position:0%
+advisor hunt spaman Mangold
+ 
+
+ align:start position:0%
+advisor hunt spaman Mangold
+unfortunately went on and and was killed
+
+ align:start position:0%
+unfortunately went on and and was killed
+ 
+
+ align:start position:0%
+unfortunately went on and and was killed
+in an explosion Shaman went on to get
+
+ align:start position:0%
+in an explosion Shaman went on to get
+ 
+
+ align:start position:0%
+in an explosion Shaman went on to get
+the first Nobel Prize for developmental
+
+ align:start position:0%
+the first Nobel Prize for developmental
+ 
+
+ align:start position:0%
+the first Nobel Prize for developmental
+biology in 1935 it's never seemed Fair
+
+ align:start position:0%
+biology in 1935 it's never seemed Fair
+ 
+
+ align:start position:0%
+biology in 1935 it's never seemed Fair
+it isn't fair anyway um that was the
+
+ align:start position:0%
+it isn't fair anyway um that was the
+ 
+
+ align:start position:0%
+it isn't fair anyway um that was the
+that is the sad story Shan was the
+
+ align:start position:0%
+that is the sad story Shan was the
+ 
+
+ align:start position:0%
+that is the sad story Shan was the
+preeminent developmental biologist in
+
+ align:start position:0%
+preeminent developmental biologist in
+ 
+
+ align:start position:0%
+preeminent developmental biologist in
+the 1920s and this is the finding that
+
+ align:start position:0%
+the 1920s and this is the finding that
+ 
+
+ align:start position:0%
+the 1920s and this is the finding that
+Dr Mangold made she took an embryo and
+
+ align:start position:0%
+Dr Mangold made she took an embryo and
+ 
+
+ align:start position:0%
+Dr Mangold made she took an embryo and
+she removed from the embryo
+
+ align:start position:0%
+she removed from the embryo
+ 
+
+ align:start position:0%
+she removed from the embryo
+see not only do you see my calendar you
+
+ align:start position:0%
+see not only do you see my calendar you
+ 
+
+ align:start position:0%
+see not only do you see my calendar you
+get an insight into the rest of my life
+
+ align:start position:0%
+get an insight into the rest of my life
+ 
+
+ align:start position:0%
+get an insight into the rest of my life
+okay my husband is a professor over at
+
+ align:start position:0%
+okay my husband is a professor over at
+ 
+
+ align:start position:0%
+okay my husband is a professor over at
+that other
+
+ align:start position:0%
+that other
+ 
+
+ align:start position:0%
+that other
+university
+
+ align:start position:0%
+university
+ 
+
+ align:start position:0%
+university
+so we have competing teaching schedules
+
+ align:start position:0%
+so we have competing teaching schedules
+ 
+
+ align:start position:0%
+so we have competing teaching schedules
+today all right so Dr Mangold took a
+
+ align:start position:0%
+today all right so Dr Mangold took a
+ 
+
+ align:start position:0%
+today all right so Dr Mangold took a
+group of cells from the future back of
+
+ align:start position:0%
+group of cells from the future back of
+ 
+
+ align:start position:0%
+group of cells from the future back of
+the embryo we'll talk about this next
+
+ align:start position:0%
+the embryo we'll talk about this next
+ 
+
+ align:start position:0%
+the embryo we'll talk about this next
+time and she transplanted them into
+
+ align:start position:0%
+time and she transplanted them into
+ 
+
+ align:start position:0%
+time and she transplanted them into
+another embryo she transplanted them
+
+ align:start position:0%
+another embryo she transplanted them
+ 
+
+ align:start position:0%
+another embryo she transplanted them
+into the belly so she took back cells
+
+ align:start position:0%
+into the belly so she took back cells
+ 
+
+ align:start position:0%
+into the belly so she took back cells
+and put them in the future belly of a
+
+ align:start position:0%
+and put them in the future belly of a
+ 
+
+ align:start position:0%
+and put them in the future belly of a
+host embryo so there's a donor and a
+
+ align:start position:0%
+host embryo so there's a donor and a
+ 
+
+ align:start position:0%
+host embryo so there's a donor and a
+host and she could see the difference
+
+ align:start position:0%
+host and she could see the difference
+ 
+
+ align:start position:0%
+host and she could see the difference
+between these embryos because they had
+
+ align:start position:0%
+between these embryos because they had
+ 
+
+ align:start position:0%
+between these embryos because they had
+different pigmentation they were
+
+ align:start position:0%
+different pigmentation they were
+ 
+
+ align:start position:0%
+different pigmentation they were
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+colors and then she let them go on and
+
+ align:start position:0%
+colors and then she let them go on and
+ 
+
+ align:start position:0%
+colors and then she let them go on and
+develop and this was a hugely difficult
+
+ align:start position:0%
+develop and this was a hugely difficult
+ 
+
+ align:start position:0%
+develop and this was a hugely difficult
+experiment in those days for technical
+
+ align:start position:0%
+experiment in those days for technical
+ 
+
+ align:start position:0%
+experiment in those days for technical
+reasons but over a period of a couple of
+
+ align:start position:0%
+reasons but over a period of a couple of
+ 
+
+ align:start position:0%
+reasons but over a period of a couple of
+months these embryos developed and what
+
+ align:start position:0%
+months these embryos developed and what
+ 
+
+ align:start position:0%
+months these embryos developed and what
+she found was this peculiar embryo which
+
+ align:start position:0%
+she found was this peculiar embryo which
+ 
+
+ align:start position:0%
+she found was this peculiar embryo which
+is a conjoined twin
+
+ align:start position:0%
+is a conjoined twin
+ 
+
+ align:start position:0%
+is a conjoined twin
+and she could show by looking to see
+
+ align:start position:0%
+and she could show by looking to see
+ 
+
+ align:start position:0%
+and she could show by looking to see
+where the cells she had transplanted in
+
+ align:start position:0%
+where the cells she had transplanted in
+ 
+
+ align:start position:0%
+where the cells she had transplanted in
+were that there was this host embryo
+
+ align:start position:0%
+were that there was this host embryo
+ 
+
+ align:start position:0%
+were that there was this host embryo
+that was made of all the original host
+
+ align:start position:0%
+that was made of all the original host
+ 
+
+ align:start position:0%
+that was made of all the original host
+tissue and there was another embryo
+
+ align:start position:0%
+tissue and there was another embryo
+ 
+
+ align:start position:0%
+tissue and there was another embryo
+joined to it in this
+
+ align:start position:0%
+joined to it in this
+ 
+
+ align:start position:0%
+joined to it in this
+orientation but that only a little bit
+
+ align:start position:0%
+orientation but that only a little bit
+ 
+
+ align:start position:0%
+orientation but that only a little bit
+of the second embryo actually came from
+
+ align:start position:0%
+of the second embryo actually came from
+ 
+
+ align:start position:0%
+of the second embryo actually came from
+the donor
+
+ align:start position:0%
+the donor
+ 
+
+ align:start position:0%
+the donor
+cells most of the second embryo came
+
+ align:start position:0%
+cells most of the second embryo came
+ 
+
+ align:start position:0%
+cells most of the second embryo came
+from the host cells and this was epipal
+
+ align:start position:0%
+from the host cells and this was epipal
+ 
+
+ align:start position:0%
+from the host cells and this was epipal
+because she could understand that those
+
+ align:start position:0%
+because she could understand that those
+ 
+
+ align:start position:0%
+because she could understand that those
+donor cells had told the host tissue to
+
+ align:start position:0%
+donor cells had told the host tissue to
+ 
+
+ align:start position:0%
+donor cells had told the host tissue to
+make another embryo it was an
+
+ align:start position:0%
+make another embryo it was an
+ 
+
+ align:start position:0%
+make another embryo it was an
+extraordinary unprecedented finding and
+
+ align:start position:0%
+extraordinary unprecedented finding and
+ 
+
+ align:start position:0%
+extraordinary unprecedented finding and
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+gave the notion that cells can tell
+
+ align:start position:0%
+gave the notion that cells can tell
+ 
+
+ align:start position:0%
+gave the notion that cells can tell
+other cells what to become does this
+
+ align:start position:0%
+other cells what to become does this
+ 
+
+ align:start position:0%
+other cells what to become does this
+happen in other animals for sure this is
+
+ align:start position:0%
+happen in other animals for sure this is
+ 
+
+ align:start position:0%
+happen in other animals for sure this is
+from a colleague of mine Jerry Thompson
+
+ align:start position:0%
+from a colleague of mine Jerry Thompson
+ 
+
+ align:start position:0%
+from a colleague of mine Jerry Thompson
+who made these conjoined twinned frog
+
+ align:start position:0%
+who made these conjoined twinned frog
+ 
+
+ align:start position:0%
+who made these conjoined twinned frog
+embryos by organizer
+
+ align:start position:0%
+embryos by organizer
+ 
+
+ align:start position:0%
+embryos by organizer
+transplants does it happen in humans it
+
+ align:start position:0%
+transplants does it happen in humans it
+ 
+
+ align:start position:0%
+transplants does it happen in humans it
+does conjoin twins come from we believe
+
+ align:start position:0%
+does conjoin twins come from we believe
+ 
+
+ align:start position:0%
+does conjoin twins come from we believe
+organizers that have split and have
+
+ align:start position:0%
+organizers that have split and have
+ 
+
+ align:start position:0%
+organizers that have split and have
+given rise to two embryos which don't
+
+ align:start position:0%
+given rise to two embryos which don't
+ 
+
+ align:start position:0%
+given rise to two embryos which don't
+separate properly from one
+
+ align:start position:0%
+separate properly from one
+ 
+
+ align:start position:0%
+separate properly from one
+another okay and we will stop there and
+
+ align:start position:0%
+another okay and we will stop there and
+ 
+
+ align:start position:0%
+another okay and we will stop there and
+continue
+
+ align:start position:0%
+continue
+ 
+
+ align:start position:0%
+continue
+on Monday
\ No newline at end of file
diff --git a/BZwdYmPS5f8.txt b/BZwdYmPS5f8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1ccad6f670bb1e45ac5ed3c105ed1ce938e75b29
--- /dev/null
+++ b/BZwdYmPS5f8.txt
@@ -0,0 +1,1947 @@
+align:start position:0%
+ 
+hi open course whereare Learners we've
+
+ align:start position:0%
+hi open course whereare Learners we've
+ 
+
+ align:start position:0%
+hi open course whereare Learners we've
+gotten to the part of the first lecture
+
+ align:start position:0%
+gotten to the part of the first lecture
+ 
+
+ align:start position:0%
+gotten to the part of the first lecture
+where the technical difficulties made it
+
+ align:start position:0%
+where the technical difficulties made it
+ 
+
+ align:start position:0%
+where the technical difficulties made it
+little too hard to follow what was
+
+ align:start position:0%
+little too hard to follow what was
+ 
+
+ align:start position:0%
+little too hard to follow what was
+happening there so I'm going to uh
+
+ align:start position:0%
+happening there so I'm going to uh
+ 
+
+ align:start position:0%
+happening there so I'm going to uh
+re-record what we all did as the opening
+
+ align:start position:0%
+re-record what we all did as the opening
+ 
+
+ align:start position:0%
+re-record what we all did as the opening
+of the class to begin go ahead and go to
+
+ align:start position:0%
+of the class to begin go ahead and go to
+ 
+
+ align:start position:0%
+of the class to begin go ahead and go to
+the URL on the screen right now this is
+
+ align:start position:0%
+the URL on the screen right now this is
+ 
+
+ align:start position:0%
+the URL on the screen right now this is
+a project from Google called collab that
+
+ align:start position:0%
+a project from Google called collab that
+ 
+
+ align:start position:0%
+a project from Google called collab that
+allows you to run Python scripts
+
+ align:start position:0%
+allows you to run Python scripts
+ 
+
+ align:start position:0%
+allows you to run Python scripts
+including music 21 in your own browser
+
+ align:start position:0%
+including music 21 in your own browser
+ 
+
+ align:start position:0%
+including music 21 in your own browser
+without installing anything on your
+
+ align:start position:0%
+without installing anything on your
+ 
+
+ align:start position:0%
+without installing anything on your
+computer
+
+ align:start position:0%
+computer
+ 
+
+ align:start position:0%
+computer
+so so go ahead and click this play
+
+ align:start position:0%
+so so go ahead and click this play
+ 
+
+ align:start position:0%
+so so go ahead and click this play
+button you're going to see a warning
+
+ align:start position:0%
+button you're going to see a warning
+ 
+
+ align:start position:0%
+button you're going to see a warning
+that uh Google didn't write this
+
+ align:start position:0%
+that uh Google didn't write this
+ 
+
+ align:start position:0%
+that uh Google didn't write this
+notebook I did U it's I think it's
+
+ align:start position:0%
+notebook I did U it's I think it's
+ 
+
+ align:start position:0%
+notebook I did U it's I think it's
+pretty safe what it does is it installs
+
+ align:start position:0%
+pretty safe what it does is it installs
+ 
+
+ align:start position:0%
+pretty safe what it does is it installs
+the latest version of music 21 and Muse
+
+ align:start position:0%
+the latest version of music 21 and Muse
+ 
+
+ align:start position:0%
+the latest version of music 21 and Muse
+score and some other software needed to
+
+ align:start position:0%
+score and some other software needed to
+ 
+
+ align:start position:0%
+score and some other software needed to
+uh run some of the tools we're going to
+
+ align:start position:0%
+uh run some of the tools we're going to
+ 
+
+ align:start position:0%
+uh run some of the tools we're going to
+be using without installing python on
+
+ align:start position:0%
+be using without installing python on
+ 
+
+ align:start position:0%
+be using without installing python on
+your computer Google already has a copy
+
+ align:start position:0%
+your computer Google already has a copy
+ 
+
+ align:start position:0%
+your computer Google already has a copy
+of Music 21 but this just uh brings you
+
+ align:start position:0%
+of Music 21 but this just uh brings you
+ 
+
+ align:start position:0%
+of Music 21 but this just uh brings you
+to the latest
+
+ align:start position:0%
+to the latest
+ 
+
+ align:start position:0%
+to the latest
+version and go ahead and pause and we'll
+
+ align:start position:0%
+version and go ahead and pause and we'll
+ 
+
+ align:start position:0%
+version and go ahead and pause and we'll
+come back after it's all installed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome back I hope that the cells
+
+ align:start position:0%
+welcome back I hope that the cells
+ 
+
+ align:start position:0%
+welcome back I hope that the cells
+aren't um running anymore so we can
+
+ align:start position:0%
+aren't um running anymore so we can
+ 
+
+ align:start position:0%
+aren't um running anymore so we can
+start uh coming in if you've never used
+
+ align:start position:0%
+start uh coming in if you've never used
+ 
+
+ align:start position:0%
+start uh coming in if you've never used
+a Jupiter notebook or another online
+
+ align:start position:0%
+a Jupiter notebook or another online
+ 
+
+ align:start position:0%
+a Jupiter notebook or another online
+collaborative environment the important
+
+ align:start position:0%
+collaborative environment the important
+ 
+
+ align:start position:0%
+collaborative environment the important
+thing that you're going to need is to be
+
+ align:start position:0%
+thing that you're going to need is to be
+ 
+
+ align:start position:0%
+thing that you're going to need is to be
+clicking into these cells the gray ones
+
+ align:start position:0%
+clicking into these cells the gray ones
+ 
+
+ align:start position:0%
+clicking into these cells the gray ones
+are where U type and the uh ones with a
+
+ align:start position:0%
+are where U type and the uh ones with a
+ 
+
+ align:start position:0%
+are where U type and the uh ones with a
+white or black background are the ones
+
+ align:start position:0%
+white or black background are the ones
+ 
+
+ align:start position:0%
+white or black background are the ones
+where uh output's coming out in order to
+
+ align:start position:0%
+where uh output's coming out in order to
+ 
+
+ align:start position:0%
+where uh output's coming out in order to
+run a cell you just type shift and
+
+ align:start position:0%
+run a cell you just type shift and
+ 
+
+ align:start position:0%
+run a cell you just type shift and
+return or shift and enter so what we're
+
+ align:start position:0%
+return or shift and enter so what we're
+ 
+
+ align:start position:0%
+return or shift and enter so what we're
+going to do is I'm just going to um
+
+ align:start position:0%
+going to do is I'm just going to um
+ 
+
+ align:start position:0%
+going to do is I'm just going to um
+click into this cell and hit shift enter
+
+ align:start position:0%
+click into this cell and hit shift enter
+ 
+
+ align:start position:0%
+click into this cell and hit shift enter
+and this will make sure that music 21
+
+ align:start position:0%
+and this will make sure that music 21
+ 
+
+ align:start position:0%
+and this will make sure that music 21
+actually works sometimes the first time
+
+ align:start position:0%
+actually works sometimes the first time
+ 
+
+ align:start position:0%
+actually works sometimes the first time
+you show a score it um it doesn't work
+
+ align:start position:0%
+you show a score it um it doesn't work
+ 
+
+ align:start position:0%
+you show a score it um it doesn't work
+as well and on some browsers this will
+
+ align:start position:0%
+as well and on some browsers this will
+ 
+
+ align:start position:0%
+as well and on some browsers this will
+work um you can listen to a score
+
+ align:start position:0%
+work um you can listen to a score
+ 
+
+ align:start position:0%
+work um you can listen to a score
+and we's see if this works or
+
+ align:start position:0%
+and we's see if this works or
+ 
+
+ align:start position:0%
+and we's see if this works or
+not there we go and now we're ready to
+
+ align:start position:0%
+not there we go and now we're ready to
+ 
+
+ align:start position:0%
+not there we go and now we're ready to
+actually begin uh we're not going to
+
+ align:start position:0%
+actually begin uh we're not going to
+ 
+
+ align:start position:0%
+actually begin uh we're not going to
+generate with AI today we'll write our
+
+ align:start position:0%
+generate with AI today we'll write our
+ 
+
+ align:start position:0%
+generate with AI today we'll write our
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+scores so with you're with me we're
+
+ align:start position:0%
+scores so with you're with me we're
+ 
+
+ align:start position:0%
+scores so with you're with me we're
+going to start uh anything where you're
+
+ align:start position:0%
+going to start uh anything where you're
+ 
+
+ align:start position:0%
+going to start uh anything where you're
+doing a python session by importing the
+
+ align:start position:0%
+doing a python session by importing the
+ 
+
+ align:start position:0%
+doing a python session by importing the
+code that's useful and for this one it's
+
+ align:start position:0%
+code that's useful and for this one it's
+ 
+
+ align:start position:0%
+code that's useful and for this one it's
+uh the music21 toolkit so we're going to
+
+ align:start position:0%
+uh the music21 toolkit so we're going to
+ 
+
+ align:start position:0%
+uh the music21 toolkit so we're going to
+import everything from it if you're
+
+ align:start position:0%
+import everything from it if you're
+ 
+
+ align:start position:0%
+import everything from it if you're
+somebody who done a lot of python and
+
+ align:start position:0%
+somebody who done a lot of python and
+ 
+
+ align:start position:0%
+somebody who done a lot of python and
+cares about things like polluting your
+
+ align:start position:0%
+cares about things like polluting your
+ 
+
+ align:start position:0%
+cares about things like polluting your
+namespace you can do individual mod
+
+ align:start position:0%
+namespace you can do individual mod
+ 
+
+ align:start position:0%
+namespace you can do individual mod
+modules but I'm always going to do it as
+
+ align:start position:0%
+modules but I'm always going to do it as
+ 
+
+ align:start position:0%
+modules but I'm always going to do it as
+if we have all the parts of Music 21 at
+
+ align:start position:0%
+if we have all the parts of Music 21 at
+ 
+
+ align:start position:0%
+if we have all the parts of Music 21 at
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fingertips so we're going to load a
+
+ align:start position:0%
+fingertips so we're going to load a
+ 
+
+ align:start position:0%
+fingertips so we're going to load a
+Corral by Johan Johan Sebastian Bach
+
+ align:start position:0%
+Corral by Johan Johan Sebastian Bach
+ 
+
+ align:start position:0%
+Corral by Johan Johan Sebastian Bach
+it's a shortest Corral called bwv 66.6
+
+ align:start position:0%
+it's a shortest Corral called bwv 66.6
+ 
+
+ align:start position:0%
+it's a shortest Corral called bwv 66.6
+so first I'll create a variable call it
+
+ align:start position:0%
+so first I'll create a variable call it
+ 
+
+ align:start position:0%
+so first I'll create a variable call it
+boach and we'll use the Corpus tool from
+
+ align:start position:0%
+boach and we'll use the Corpus tool from
+ 
+
+ align:start position:0%
+boach and we'll use the Corpus tool from
+music 21 and it's parse function to load
+
+ align:start position:0%
+music 21 and it's parse function to load
+ 
+
+ align:start position:0%
+music 21 and it's parse function to load
+in Bach bwv 6 6.6 I'll hit shift enter
+
+ align:start position:0%
+in Bach bwv 6 6.6 I'll hit shift enter
+ 
+
+ align:start position:0%
+in Bach bwv 6 6.6 I'll hit shift enter
+and it's assigned to boach and we can
+
+ align:start position:0%
+and it's assigned to boach and we can
+ 
+
+ align:start position:0%
+and it's assigned to boach and we can
+call the method show on it to see the
+
+ align:start position:0%
+call the method show on it to see the
+ 
+
+ align:start position:0%
+call the method show on it to see the
+score of that Yep looks like a crow by
+
+ align:start position:0%
+score of that Yep looks like a crow by
+ 
+
+ align:start position:0%
+score of that Yep looks like a crow by
+Bach and you can see that has soprano
+
+ align:start position:0%
+Bach and you can see that has soprano
+ 
+
+ align:start position:0%
+Bach and you can see that has soprano
+Alto tenor base and we can get the alter
+
+ align:start position:0%
+Alto tenor base and we can get the alter
+ 
+
+ align:start position:0%
+Alto tenor base and we can get the alter
+part by saying um bach. Parts square
+
+ align:start position:0%
+part by saying um bach. Parts square
+ 
+
+ align:start position:0%
+part by saying um bach. Parts square
+brackets open Alto and we'll just show
+
+ align:start position:0%
+brackets open Alto and we'll just show
+ 
+
+ align:start position:0%
+brackets open Alto and we'll just show
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes looks like the Alto part now we'll
+
+ align:start position:0%
+yes looks like the Alto part now we'll
+ 
+
+ align:start position:0%
+yes looks like the Alto part now we'll
+get the soprano part and assign it to a
+
+ align:start position:0%
+get the soprano part and assign it to a
+ 
+
+ align:start position:0%
+get the soprano part and assign it to a
+variable sop for soprano and we'll just
+
+ align:start position:0%
+variable sop for soprano and we'll just
+ 
+
+ align:start position:0%
+variable sop for soprano and we'll just
+do that instead this time we'll get it
+
+ align:start position:0%
+do that instead this time we'll get it
+ 
+
+ align:start position:0%
+do that instead this time we'll get it
+by doing the part number and so it's the
+
+ align:start position:0%
+by doing the part number and so it's the
+ 
+
+ align:start position:0%
+by doing the part number and so it's the
+first part and so in Python that means
+
+ align:start position:0%
+first part and so in Python that means
+ 
+
+ align:start position:0%
+first part and so in Python that means
+it's part zero Parts zero and one of the
+
+ align:start position:0%
+it's part zero Parts zero and one of the
+ 
+
+ align:start position:0%
+it's part zero Parts zero and one of the
+things that we do in music 21 is when
+
+ align:start position:0%
+things that we do in music 21 is when
+ 
+
+ align:start position:0%
+things that we do in music 21 is when
+something is in a programmer
+
+ align:start position:0%
+something is in a programmer
+ 
+
+ align:start position:0%
+something is in a programmer
+rule we follow um the conventions of
+
+ align:start position:0%
+rule we follow um the conventions of
+ 
+
+ align:start position:0%
+rule we follow um the conventions of
+programming where everything starts with
+
+ align:start position:0%
+programming where everything starts with
+ 
+
+ align:start position:0%
+programming where everything starts with
+zero and when we're in musician space
+
+ align:start position:0%
+zero and when we're in musician space
+ 
+
+ align:start position:0%
+zero and when we're in musician space
+such as talking about measures we don't
+
+ align:start position:0%
+such as talking about measures we don't
+ 
+
+ align:start position:0%
+such as talking about measures we don't
+subtract one from the measure number or
+
+ align:start position:0%
+subtract one from the measure number or
+ 
+
+ align:start position:0%
+subtract one from the measure number or
+anything like that so if we wanted to
+
+ align:start position:0%
+anything like that so if we wanted to
+ 
+
+ align:start position:0%
+anything like that so if we wanted to
+just see measures 3 through five
+
+ align:start position:0%
+just see measures 3 through five
+ 
+
+ align:start position:0%
+just see measures 3 through five
+inclusive of the soprano part we could
+
+ align:start position:0%
+inclusive of the soprano part we could
+ 
+
+ align:start position:0%
+inclusive of the soprano part we could
+do something like that
+
+ align:start position:0%
+do something like that
+ 
+
+ align:start position:0%
+do something like that
+oops or we could type the word measure
+
+ align:start position:0%
+oops or we could type the word measure
+ 
+
+ align:start position:0%
+oops or we could type the word measure
+properly and then we'll get that measure
+
+ align:start position:0%
+properly and then we'll get that measure
+ 
+
+ align:start position:0%
+properly and then we'll get that measure
+just gets a single measure this one got
+
+ align:start position:0%
+just gets a single measure this one got
+ 
+
+ align:start position:0%
+just gets a single measure this one got
+that great and um in fact we'll use the
+
+ align:start position:0%
+that great and um in fact we'll use the
+ 
+
+ align:start position:0%
+that great and um in fact we'll use the
+measure thing now and we'll get in
+
+ align:start position:0%
+measure thing now and we'll get in
+ 
+
+ align:start position:0%
+measure thing now and we'll get in
+measure five the zero first second note
+
+ align:start position:0%
+measure five the zero first second note
+ 
+
+ align:start position:0%
+measure five the zero first second note
+the one with the forada on it and so
+
+ align:start position:0%
+the one with the forada on it and so
+ 
+
+ align:start position:0%
+the one with the forada on it and so
+we'll call it C because it's a c
+
+ align:start position:0%
+we'll call it C because it's a c
+ 
+
+ align:start position:0%
+we'll call it C because it's a c
+actually it's a C sharp but um well
+
+ align:start position:0%
+actually it's a C sharp but um well
+ 
+
+ align:start position:0%
+actually it's a C sharp but um well
+we'll see why not and so we'll get notes
+
+ align:start position:0%
+we'll see why not and so we'll get notes
+ 
+
+ align:start position:0%
+we'll see why not and so we'll get notes
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+two if we called it C
+
+ align:start position:0%
+two if we called it C
+ 
+
+ align:start position:0%
+two if we called it C
+then everything after this would be a
+
+ align:start position:0%
+then everything after this would be a
+ 
+
+ align:start position:0%
+then everything after this would be a
+common so that doesn't work so we'll
+
+ align:start position:0%
+common so that doesn't work so we'll
+ 
+
+ align:start position:0%
+common so that doesn't work so we'll
+just call it c um and now what we can do
+
+ align:start position:0%
+just call it c um and now what we can do
+ 
+
+ align:start position:0%
+just call it c um and now what we can do
+is manipulate it change its style it's
+
+ align:start position:0%
+is manipulate it change its style it's
+ 
+
+ align:start position:0%
+is manipulate it change its style it's
+color to
+
+ align:start position:0%
+color to
+ 
+
+ align:start position:0%
+color to
+red and now when I show the soprano part
+
+ align:start position:0%
+red and now when I show the soprano part
+ 
+
+ align:start position:0%
+red and now when I show the soprano part
+because uh they're all linked to each
+
+ align:start position:0%
+because uh they're all linked to each
+ 
+
+ align:start position:0%
+because uh they're all linked to each
+other we should see yep there's a note
+
+ align:start position:0%
+other we should see yep there's a note
+ 
+
+ align:start position:0%
+other we should see yep there's a note
+that's in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Red so that's how we can manipulate a
+
+ align:start position:0%
+Red so that's how we can manipulate a
+ 
+
+ align:start position:0%
+Red so that's how we can manipulate a
+score and now let's see how we can do
+
+ align:start position:0%
+score and now let's see how we can do
+ 
+
+ align:start position:0%
+score and now let's see how we can do
+some analytical functions on things so
+
+ align:start position:0%
+some analytical functions on things so
+ 
+
+ align:start position:0%
+some analytical functions on things so
+let's do Baka analyze and we'll analyze
+
+ align:start position:0%
+let's do Baka analyze and we'll analyze
+ 
+
+ align:start position:0%
+let's do Baka analyze and we'll analyze
+the key of the
+
+ align:start position:0%
+the key of the
+ 
+
+ align:start position:0%
+the key of the
+piece and it says it returns a key
+
+ align:start position:0%
+piece and it says it returns a key
+ 
+
+ align:start position:0%
+piece and it says it returns a key
+object that says it's in F minor and one
+
+ align:start position:0%
+object that says it's in F minor and one
+ 
+
+ align:start position:0%
+object that says it's in F minor and one
+of the things I really want to emphasize
+
+ align:start position:0%
+of the things I really want to emphasize
+ 
+
+ align:start position:0%
+of the things I really want to emphasize
+is always go back and do the smell test
+
+ align:start position:0%
+is always go back and do the smell test
+ 
+
+ align:start position:0%
+is always go back and do the smell test
+is this true ises it look like baloney
+
+ align:start position:0%
+is this true ises it look like baloney
+ 
+
+ align:start position:0%
+is this true ises it look like baloney
+and we can kind of see well begins in a
+
+ align:start position:0%
+and we can kind of see well begins in a
+ 
+
+ align:start position:0%
+and we can kind of see well begins in a
+but it does have three Sharps and at the
+
+ align:start position:0%
+but it does have three Sharps and at the
+ 
+
+ align:start position:0%
+but it does have three Sharps and at the
+end yep there is an FP in the base so
+
+ align:start position:0%
+end yep there is an FP in the base so
+ 
+
+ align:start position:0%
+end yep there is an FP in the base so
+looks kind of like F major but yeah okay
+
+ align:start position:0%
+looks kind of like F major but yeah okay
+ 
+
+ align:start position:0%
+looks kind of like F major but yeah okay
+here some F minor okay it kind of passes
+
+ align:start position:0%
+here some F minor okay it kind of passes
+ 
+
+ align:start position:0%
+here some F minor okay it kind of passes
+the spell tests and we'll see why that's
+
+ align:start position:0%
+the spell tests and we'll see why that's
+ 
+
+ align:start position:0%
+the spell tests and we'll see why that's
+so important in just a little bit but it
+
+ align:start position:0%
+so important in just a little bit but it
+ 
+
+ align:start position:0%
+so important in just a little bit but it
+did seem like it was beginning in a so
+
+ align:start position:0%
+did seem like it was beginning in a so
+ 
+
+ align:start position:0%
+did seem like it was beginning in a so
+we can just analyze a portion of that so
+
+ align:start position:0%
+we can just analyze a portion of that so
+ 
+
+ align:start position:0%
+we can just analyze a portion of that so
+we'll do B measures zero because we want
+
+ align:start position:0%
+we'll do B measures zero because we want
+ 
+
+ align:start position:0%
+we'll do B measures zero because we want
+the pickup measure and two and we'll
+
+ align:start position:0%
+the pickup measure and two and we'll
+ 
+
+ align:start position:0%
+the pickup measure and two and we'll
+analyze the of just that
+
+ align:start position:0%
+analyze the of just that
+ 
+
+ align:start position:0%
+analyze the of just that
+passage uh does seem to start in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+major let's do something that seems
+
+ align:start position:0%
+major let's do something that seems
+ 
+
+ align:start position:0%
+major let's do something that seems
+pretty simple let's count the number of
+
+ align:start position:0%
+pretty simple let's count the number of
+ 
+
+ align:start position:0%
+pretty simple let's count the number of
+notes in the piece so we can just do Len
+
+ align:start position:0%
+notes in the piece so we can just do Len
+ 
+
+ align:start position:0%
+notes in the piece so we can just do Len
+bach. notes that just gets uh all the
+
+ align:start position:0%
+bach. notes that just gets uh all the
+ 
+
+ align:start position:0%
+bach. notes that just gets uh all the
+notes the piece in another language
+
+ align:start position:0%
+notes the piece in another language
+ 
+
+ align:start position:0%
+notes the piece in another language
+would be bl. notes. length and I don't
+
+ align:start position:0%
+would be bl. notes. length and I don't
+ 
+
+ align:start position:0%
+would be bl. notes. length and I don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+um I don't know how many notes are in
+
+ align:start position:0%
+um I don't know how many notes are in
+ 
+
+ align:start position:0%
+um I don't know how many notes are in
+the piece but I'm pretty sure it's more
+
+ align:start position:0%
+the piece but I'm pretty sure it's more
+ 
+
+ align:start position:0%
+the piece but I'm pretty sure it's more
+than zero and the Reas reason for this
+
+ align:start position:0%
+than zero and the Reas reason for this
+ 
+
+ align:start position:0%
+than zero and the Reas reason for this
+is that music 21 and most ways of
+
+ align:start position:0%
+is that music 21 and most ways of
+ 
+
+ align:start position:0%
+is that music 21 and most ways of
+conceiving music on the computer don't
+
+ align:start position:0%
+conceiving music on the computer don't
+ 
+
+ align:start position:0%
+conceiving music on the computer don't
+think of the score as having notes the
+
+ align:start position:0%
+think of the score as having notes the
+ 
+
+ align:start position:0%
+think of the score as having notes the
+score has Parts the parts have measures
+
+ align:start position:0%
+score has Parts the parts have measures
+ 
+
+ align:start position:0%
+score has Parts the parts have measures
+and the measures have notes so what we
+
+ align:start position:0%
+and the measures have notes so what we
+ 
+
+ align:start position:0%
+and the measures have notes so what we
+could do is get the length of Bach Parts
+
+ align:start position:0%
+could do is get the length of Bach Parts
+ 
+
+ align:start position:0%
+could do is get the length of Bach Parts
+one measure two do notes and see okay
+
+ align:start position:0%
+one measure two do notes and see okay
+ 
+
+ align:start position:0%
+one measure two do notes and see okay
+that passes the smell test so what we
+
+ align:start position:0%
+that passes the smell test so what we
+ 
+
+ align:start position:0%
+that passes the smell test so what we
+can do instead is we can use something
+
+ align:start position:0%
+can do instead is we can use something
+ 
+
+ align:start position:0%
+can do instead is we can use something
+called recurse so we'll get the bach.
+
+ align:start position:0%
+called recurse so we'll get the bach.
+ 
+
+ align:start position:0%
+called recurse so we'll get the bach.
+recurse that's a function or a method
+
+ align:start position:0%
+recurse that's a function or a method
+ 
+
+ align:start position:0%
+recurse that's a function or a method
+and we get the notes on that and what
+
+ align:start position:0%
+and we get the notes on that and what
+ 
+
+ align:start position:0%
+and we get the notes on that and what
+recurse says is open up every box you
+
+ align:start position:0%
+recurse says is open up every box you
+ 
+
+ align:start position:0%
+recurse says is open up every box you
+get to a part open it up look inside for
+
+ align:start position:0%
+get to a part open it up look inside for
+ 
+
+ align:start position:0%
+get to a part open it up look inside for
+measures open it up and keep going until
+
+ align:start position:0%
+measures open it up and keep going until
+ 
+
+ align:start position:0%
+measures open it up and keep going until
+you find
+
+ align:start position:0%
+you find
+ 
+
+ align:start position:0%
+you find
+notes and 165 notes that seems to pass
+
+ align:start position:0%
+notes and 165 notes that seems to pass
+ 
+
+ align:start position:0%
+notes and 165 notes that seems to pass
+the smell test to
+
+ align:start position:0%
+the smell test to
+ 
+
+ align:start position:0%
+the smell test to
+me right now we've been working with
+
+ align:start position:0%
+me right now we've been working with
+ 
+
+ align:start position:0%
+me right now we've been working with
+this as a series of of parts that are
+
+ align:start position:0%
+this as a series of of parts that are
+ 
+
+ align:start position:0%
+this as a series of of parts that are
+not connected to each other but of
+
+ align:start position:0%
+not connected to each other but of
+ 
+
+ align:start position:0%
+not connected to each other but of
+course there are chords in there also
+
+ align:start position:0%
+course there are chords in there also
+ 
+
+ align:start position:0%
+course there are chords in there also
+but if we do um B Dot and here's another
+
+ align:start position:0%
+but if we do um B Dot and here's another
+ 
+
+ align:start position:0%
+but if we do um B Dot and here's another
+way you can say recurse I want to
+
+ align:start position:0%
+way you can say recurse I want to
+ 
+
+ align:start position:0%
+way you can say recurse I want to
+recurse and get everything that's a
+
+ align:start position:0%
+recurse and get everything that's a
+ 
+
+ align:start position:0%
+recurse and get everything that's a
+chord there are no chords in this piece
+
+ align:start position:0%
+chord there are no chords in this piece
+ 
+
+ align:start position:0%
+chord there are no chords in this piece
+so we have to create some chords using
+
+ align:start position:0%
+so we have to create some chords using
+ 
+
+ align:start position:0%
+so we have to create some chords using
+the chordify method so we'll say core
+
+ align:start position:0%
+the chordify method so we'll say core
+ 
+
+ align:start position:0%
+the chordify method so we'll say core
+for chords equals buck. chordify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now if we
+
+ align:start position:0%
+and now if we
+ 
+
+ align:start position:0%
+and now if we
+show the cified
+
+ align:start position:0%
+show the cified
+ 
+
+ align:start position:0%
+show the cified
+method and we can see that some of these
+
+ align:start position:0%
+method and we can see that some of these
+ 
+
+ align:start position:0%
+method and we can see that some of these
+notes are way too low to be read
+
+ align:start position:0%
+notes are way too low to be read
+ 
+
+ align:start position:0%
+notes are way too low to be read
+properly and they have duplicated notes
+
+ align:start position:0%
+properly and they have duplicated notes
+ 
+
+ align:start position:0%
+properly and they have duplicated notes
+and things and over the course of the
+
+ align:start position:0%
+and things and over the course of the
+ 
+
+ align:start position:0%
+and things and over the course of the
+semester we'll find ways that we can
+
+ align:start position:0%
+semester we'll find ways that we can
+ 
+
+ align:start position:0%
+semester we'll find ways that we can
+make this a lot more representable
+
+ align:start position:0%
+make this a lot more representable
+ 
+
+ align:start position:0%
+make this a lot more representable
+including things like getting rid of
+
+ align:start position:0%
+including things like getting rid of
+ 
+
+ align:start position:0%
+including things like getting rid of
+passing tones and other things that
+
+ align:start position:0%
+passing tones and other things that
+ 
+
+ align:start position:0%
+passing tones and other things that
+disturb looking at the chords but for
+
+ align:start position:0%
+disturb looking at the chords but for
+ 
+
+ align:start position:0%
+disturb looking at the chords but for
+now we can look at chord chord for the
+
+ align:start position:0%
+now we can look at chord chord for the
+ 
+
+ align:start position:0%
+now we can look at chord chord for the
+chords the number of chords in that and
+
+ align:start position:0%
+chords the number of chords in that and
+ 
+
+ align:start position:0%
+chords the number of chords in that and
+see that yep that looks like a
+
+ align:start position:0%
+see that yep that looks like a
+ 
+
+ align:start position:0%
+see that yep that looks like a
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+number so I hope that gives you a taste
+
+ align:start position:0%
+number so I hope that gives you a taste
+ 
+
+ align:start position:0%
+number so I hope that gives you a taste
+of some of what we're going to be doing
+
+ align:start position:0%
+of some of what we're going to be doing
+ 
+
+ align:start position:0%
+of some of what we're going to be doing
+over the course of the semester of this
+
+ align:start position:0%
+over the course of the semester of this
+ 
+
+ align:start position:0%
+over the course of the semester of this
+class now we've gone very fast through a
+
+ align:start position:0%
+class now we've gone very fast through a
+ 
+
+ align:start position:0%
+class now we've gone very fast through a
+bunch of things but don't worry because
+
+ align:start position:0%
+bunch of things but don't worry because
+ 
+
+ align:start position:0%
+bunch of things but don't worry because
+we're going to lock all those things up
+
+ align:start position:0%
+we're going to lock all those things up
+ 
+
+ align:start position:0%
+we're going to lock all those things up
+cify is going to be locked up anal
+
+ align:start position:0%
+cify is going to be locked up anal
+ 
+
+ align:start position:0%
+cify is going to be locked up anal
+analyze key is going to be locked up and
+
+ align:start position:0%
+analyze key is going to be locked up and
+ 
+
+ align:start position:0%
+analyze key is going to be locked up and
+what mean that means that it won't be
+
+ align:start position:0%
+what mean that means that it won't be
+ 
+
+ align:start position:0%
+what mean that means that it won't be
+available to be used in the rest of the
+
+ align:start position:0%
+available to be used in the rest of the
+ 
+
+ align:start position:0%
+available to be used in the rest of the
+class until it's unlocked again the way
+
+ align:start position:0%
+class until it's unlocked again the way
+ 
+
+ align:start position:0%
+class until it's unlocked again the way
+this class is going to work is all these
+
+ align:start position:0%
+this class is going to work is all these
+ 
+
+ align:start position:0%
+this class is going to work is all these
+analytical tools all these ways of
+
+ align:start position:0%
+analytical tools all these ways of
+ 
+
+ align:start position:0%
+analytical tools all these ways of
+conceiving a score will Begin by being
+
+ align:start position:0%
+conceiving a score will Begin by being
+ 
+
+ align:start position:0%
+conceiving a score will Begin by being
+locked and then you'll do an assignment
+
+ align:start position:0%
+locked and then you'll do an assignment
+ 
+
+ align:start position:0%
+locked and then you'll do an assignment
+either as a problem set or as uh in in
+
+ align:start position:0%
+either as a problem set or as uh in in
+ 
+
+ align:start position:0%
+either as a problem set or as uh in in
+class assignment where we'll figure out
+
+ align:start position:0%
+class assignment where we'll figure out
+ 
+
+ align:start position:0%
+class assignment where we'll figure out
+how does this work what what are the
+
+ align:start position:0%
+how does this work what what are the
+ 
+
+ align:start position:0%
+how does this work what what are the
+ways of doing this and then once you've
+
+ align:start position:0%
+ways of doing this and then once you've
+ 
+
+ align:start position:0%
+ways of doing this and then once you've
+designed your own algorithm for doing
+
+ align:start position:0%
+designed your own algorithm for doing
+ 
+
+ align:start position:0%
+designed your own algorithm for doing
+these things you can either continue to
+
+ align:start position:0%
+these things you can either continue to
+ 
+
+ align:start position:0%
+these things you can either continue to
+use your own algorithm or you will have
+
+ align:start position:0%
+use your own algorithm or you will have
+ 
+
+ align:start position:0%
+use your own algorithm or you will have
+unlocked the music 21 version of the
+
+ align:start position:0%
+unlocked the music 21 version of the
+ 
+
+ align:start position:0%
+unlocked the music 21 version of the
+algorithm and from then on you can use
+
+ align:start position:0%
+algorithm and from then on you can use
+ 
+
+ align:start position:0%
+algorithm and from then on you can use
+that instead so we're going to just be
+
+ align:start position:0%
+that instead so we're going to just be
+ 
+
+ align:start position:0%
+that instead so we're going to just be
+building up knowledge little by little
+
+ align:start position:0%
+building up knowledge little by little
+ 
+
+ align:start position:0%
+building up knowledge little by little
+until we have
+
+ align:start position:0%
+until we have
+ 
+
+ align:start position:0%
+until we have
+everything one of the things that as an
+
+ align:start position:0%
+everything one of the things that as an
+ 
+
+ align:start position:0%
+everything one of the things that as an
+open courseware learner you won't have
+
+ align:start position:0%
+open courseware learner you won't have
+ 
+
+ align:start position:0%
+open courseware learner you won't have
+access to
+
+ align:start position:0%
+access to
+ 
+
+ align:start position:0%
+access to
+is the extremely valuable things that
+
+ align:start position:0%
+is the extremely valuable things that
+ 
+
+ align:start position:0%
+is the extremely valuable things that
+happened outside of class yes coming to
+
+ align:start position:0%
+happened outside of class yes coming to
+ 
+
+ align:start position:0%
+happened outside of class yes coming to
+office hours but mostly with students
+
+ align:start position:0%
+office hours but mostly with students
+ 
+
+ align:start position:0%
+office hours but mostly with students
+helping each other giving each other
+
+ align:start position:0%
+helping each other giving each other
+ 
+
+ align:start position:0%
+helping each other giving each other
+inspiration for projects they could do
+
+ align:start position:0%
+inspiration for projects they could do
+ 
+
+ align:start position:0%
+inspiration for projects they could do
+and helping them through some of the
+
+ align:start position:0%
+and helping them through some of the
+ 
+
+ align:start position:0%
+and helping them through some of the
+more difficult parts of the class so I
+
+ align:start position:0%
+more difficult parts of the class so I
+ 
+
+ align:start position:0%
+more difficult parts of the class so I
+encourage you if you can find somebody
+
+ align:start position:0%
+encourage you if you can find somebody
+ 
+
+ align:start position:0%
+encourage you if you can find somebody
+else online who's also taking the course
+
+ align:start position:0%
+else online who's also taking the course
+ 
+
+ align:start position:0%
+else online who's also taking the course
+or somebody who has taken it in the past
+
+ align:start position:0%
+or somebody who has taken it in the past
+ 
+
+ align:start position:0%
+or somebody who has taken it in the past
+and get to know them that will give you
+
+ align:start position:0%
+and get to know them that will give you
+ 
+
+ align:start position:0%
+and get to know them that will give you
+a lot more of the experience that the
+
+ align:start position:0%
+a lot more of the experience that the
+ 
+
+ align:start position:0%
+a lot more of the experience that the
+students had at MIT when they were
+
+ align:start position:0%
+students had at MIT when they were
+ 
+
+ align:start position:0%
+students had at MIT when they were
+taking the class in
+
+ align:start position:0%
+taking the class in
+ 
+
+ align:start position:0%
+taking the class in
+person I'm so glad that you've chosen to
+
+ align:start position:0%
+person I'm so glad that you've chosen to
+ 
+
+ align:start position:0%
+person I'm so glad that you've chosen to
+take your time to learn about the
+
+ align:start position:0%
+take your time to learn about the
+ 
+
+ align:start position:0%
+take your time to learn about the
+fascinating world of Music Theory and
+
+ align:start position:0%
+fascinating world of Music Theory and
+ 
+
+ align:start position:0%
+fascinating world of Music Theory and
+music analysis with a computer and I
+
+ align:start position:0%
+music analysis with a computer and I
+ 
+
+ align:start position:0%
+music analysis with a computer and I
+look forward to seeing you again from
+
+ align:start position:0%
+look forward to seeing you again from
+ 
+
+ align:start position:0%
+look forward to seeing you again from
+time to time in this course
\ No newline at end of file
diff --git a/C42jXQLc_Jo.txt b/C42jXQLc_Jo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9de1c5037e769940d3f1abad9876388734bbf2f5
--- /dev/null
+++ b/C42jXQLc_Jo.txt
@@ -0,0 +1,15363 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so um module systems and
+
+ align:start position:0%
+ocw.mit.edu so um module systems and
+ 
+
+ align:start position:0%
+ocw.mit.edu so um module systems and
+reliability uh what we're going to do is
+
+ align:start position:0%
+reliability uh what we're going to do is
+ 
+
+ align:start position:0%
+reliability uh what we're going to do is
+talk about how we go from the cells uh
+
+ align:start position:0%
+talk about how we go from the cells uh
+ 
+
+ align:start position:0%
+talk about how we go from the cells uh
+or from the uh films uh to full modules
+
+ align:start position:0%
+or from the uh films uh to full modules
+ 
+
+ align:start position:0%
+or from the uh films uh to full modules
+and finally to systems so our first
+
+ align:start position:0%
+and finally to systems so our first
+ 
+
+ align:start position:0%
+and finally to systems so our first
+learning objective is to describe more
+
+ align:start position:0%
+learning objective is to describe more
+ 
+
+ align:start position:0%
+learning objective is to describe more
+or less the DNA or anatomy of a PV
+
+ align:start position:0%
+or less the DNA or anatomy of a PV
+ 
+
+ align:start position:0%
+or less the DNA or anatomy of a PV
+module uh this will be a bit of a prep
+
+ align:start position:0%
+module uh this will be a bit of a prep
+ 
+
+ align:start position:0%
+module uh this will be a bit of a prep
+for the visit to fronhofer CSE where
+
+ align:start position:0%
+for the visit to fronhofer CSE where
+ 
+
+ align:start position:0%
+for the visit to fronhofer CSE where
+we'll get to see uh the labs and see all
+
+ align:start position:0%
+we'll get to see uh the labs and see all
+ 
+
+ align:start position:0%
+we'll get to see uh the labs and see all
+the materials that go into a PV module
+
+ align:start position:0%
+the materials that go into a PV module
+ 
+
+ align:start position:0%
+the materials that go into a PV module
+so just establishing some definitions up
+
+ align:start position:0%
+so just establishing some definitions up
+ 
+
+ align:start position:0%
+so just establishing some definitions up
+front so we're all speaking the same
+
+ align:start position:0%
+front so we're all speaking the same
+ 
+
+ align:start position:0%
+front so we're all speaking the same
+language um you start out with either a
+
+ align:start position:0%
+language um you start out with either a
+ 
+
+ align:start position:0%
+language um you start out with either a
+film right if you're depositing a thin
+
+ align:start position:0%
+film right if you're depositing a thin
+ 
+
+ align:start position:0%
+film right if you're depositing a thin
+film material uh which is uh usually div
+
+ align:start position:0%
+film material uh which is uh usually div
+ 
+
+ align:start position:0%
+film material uh which is uh usually div
+into discret devices using laser
+
+ align:start position:0%
+into discret devices using laser
+ 
+
+ align:start position:0%
+into discret devices using laser
+processing um or you can start out with
+
+ align:start position:0%
+processing um or you can start out with
+ 
+
+ align:start position:0%
+processing um or you can start out with
+a discrete wafer which has been
+
+ align:start position:0%
+a discrete wafer which has been
+ 
+
+ align:start position:0%
+a discrete wafer which has been
+processed into a cell the module is the
+
+ align:start position:0%
+processed into a cell the module is the
+ 
+
+ align:start position:0%
+processed into a cell the module is the
+combination of many of these cells uh
+
+ align:start position:0%
+combination of many of these cells uh
+ 
+
+ align:start position:0%
+combination of many of these cells uh
+shown very generically right here
+
+ align:start position:0%
+shown very generically right here
+ 
+
+ align:start position:0%
+shown very generically right here
+without the interconnects because you
+
+ align:start position:0%
+without the interconnects because you
+ 
+
+ align:start position:0%
+without the interconnects because you
+can uh tie up the cells together in
+
+ align:start position:0%
+can uh tie up the cells together in
+ 
+
+ align:start position:0%
+can uh tie up the cells together in
+parallel or in series depending on uh on
+
+ align:start position:0%
+parallel or in series depending on uh on
+ 
+
+ align:start position:0%
+parallel or in series depending on uh on
+on on what sort of voltage and current
+
+ align:start position:0%
+on on what sort of voltage and current
+ 
+
+ align:start position:0%
+on on what sort of voltage and current
+outputs you desire from your module and
+
+ align:start position:0%
+outputs you desire from your module and
+ 
+
+ align:start position:0%
+outputs you desire from your module and
+then finally the modules are situated
+
+ align:start position:0%
+then finally the modules are situated
+ 
+
+ align:start position:0%
+then finally the modules are situated
+together in an array uh that showing a
+
+ align:start position:0%
+together in an array uh that showing a
+ 
+
+ align:start position:0%
+together in an array uh that showing a
+combination of six modules forming that
+
+ align:start position:0%
+combination of six modules forming that
+ 
+
+ align:start position:0%
+combination of six modules forming that
+array array right there and as you can
+
+ align:start position:0%
+array array right there and as you can
+ 
+
+ align:start position:0%
+array array right there and as you can
+see modules are typically this size
+
+ align:start position:0%
+see modules are typically this size
+ 
+
+ align:start position:0%
+see modules are typically this size
+right here right they're U usually about
+
+ align:start position:0%
+right here right they're U usually about
+ 
+
+ align:start position:0%
+right here right they're U usually about
+this size or even a little larger um
+
+ align:start position:0%
+this size or even a little larger um
+ 
+
+ align:start position:0%
+this size or even a little larger um
+they're rather heavy so you get a sense
+
+ align:start position:0%
+they're rather heavy so you get a sense
+ 
+
+ align:start position:0%
+they're rather heavy so you get a sense
+it's uh they're not extremely light
+
+ align:start position:0%
+it's uh they're not extremely light
+ 
+
+ align:start position:0%
+it's uh they're not extremely light
+majority of that mass is coming from the
+
+ align:start position:0%
+majority of that mass is coming from the
+ 
+
+ align:start position:0%
+majority of that mass is coming from the
+glass in the front some from the
+
+ align:start position:0%
+glass in the front some from the
+ 
+
+ align:start position:0%
+glass in the front some from the
+aluminum as well and they're comprised
+
+ align:start position:0%
+aluminum as well and they're comprised
+ 
+
+ align:start position:0%
+aluminum as well and they're comprised
+of many materials if you uh were to take
+
+ align:start position:0%
+of many materials if you uh were to take
+ 
+
+ align:start position:0%
+of many materials if you uh were to take
+this apart which will actually see the
+
+ align:start position:0%
+this apart which will actually see the
+ 
+
+ align:start position:0%
+this apart which will actually see the
+individual components that front up for
+
+ align:start position:0%
+individual components that front up for
+ 
+
+ align:start position:0%
+individual components that front up for
+CSE you notice that there are many
+
+ align:start position:0%
+CSE you notice that there are many
+ 
+
+ align:start position:0%
+CSE you notice that there are many
+materials involved in making one of
+
+ align:start position:0%
+materials involved in making one of
+ 
+
+ align:start position:0%
+materials involved in making one of
+these modules uh from the back skinin
+
+ align:start position:0%
+these modules uh from the back skinin
+ 
+
+ align:start position:0%
+these modules uh from the back skinin
+materials the junction box the aluminum
+
+ align:start position:0%
+materials the junction box the aluminum
+ 
+
+ align:start position:0%
+materials the junction box the aluminum
+framing on the side the glass in the
+
+ align:start position:0%
+framing on the side the glass in the
+ 
+
+ align:start position:0%
+framing on the side the glass in the
+front uh the encapsulate materials that
+
+ align:start position:0%
+front uh the encapsulate materials that
+ 
+
+ align:start position:0%
+front uh the encapsulate materials that
+fuse everything together that bind
+
+ align:start position:0%
+fuse everything together that bind
+ 
+
+ align:start position:0%
+fuse everything together that bind
+everything and the cells uh the solar
+
+ align:start position:0%
+everything and the cells uh the solar
+ 
+
+ align:start position:0%
+everything and the cells uh the solar
+cell devices themselves so our first
+
+ align:start position:0%
+cell devices themselves so our first
+ 
+
+ align:start position:0%
+cell devices themselves so our first
+step is to walk through the anatomy of a
+
+ align:start position:0%
+step is to walk through the anatomy of a
+ 
+
+ align:start position:0%
+step is to walk through the anatomy of a
+module at least in theory so that when
+
+ align:start position:0%
+module at least in theory so that when
+ 
+
+ align:start position:0%
+module at least in theory so that when
+we actually see it at frer CSE we'll
+
+ align:start position:0%
+we actually see it at frer CSE we'll
+ 
+
+ align:start position:0%
+we actually see it at frer CSE we'll
+have a better sense of what we're
+
+ align:start position:0%
+have a better sense of what we're
+ 
+
+ align:start position:0%
+have a better sense of what we're
+looking at yep Ashley here's what
+
+ align:start position:0%
+looking at yep Ashley here's what
+ 
+
+ align:start position:0%
+looking at yep Ashley here's what
+determines the that specific size we've
+
+ align:start position:0%
+determines the that specific size we've
+ 
+
+ align:start position:0%
+determines the that specific size we've
+already talked about you know the pseudo
+
+ align:start position:0%
+already talked about you know the pseudo
+ 
+
+ align:start position:0%
+already talked about you know the pseudo
+square and how you have to balance those
+
+ align:start position:0%
+square and how you have to balance those
+ 
+
+ align:start position:0%
+square and how you have to balance those
+the two different cost parameters but
+
+ align:start position:0%
+the two different cost parameters but
+ 
+
+ align:start position:0%
+the two different cost parameters but
+why that size specifically like why that
+
+ align:start position:0%
+why that size specifically like why that
+ 
+
+ align:start position:0%
+why that size specifically like why that
+size specifically we're going to get to
+
+ align:start position:0%
+size specifically we're going to get to
+ 
+
+ align:start position:0%
+size specifically we're going to get to
+that in a few slides um it comes as you
+
+ align:start position:0%
+that in a few slides um it comes as you
+ 
+
+ align:start position:0%
+that in a few slides um it comes as you
+probably guess from some historical
+
+ align:start position:0%
+probably guess from some historical
+ 
+
+ align:start position:0%
+probably guess from some historical
+reasons okay um so some of some basic uh
+
+ align:start position:0%
+reasons okay um so some of some basic uh
+ 
+
+ align:start position:0%
+reasons okay um so some of some basic uh
+principles about solar modules there's
+
+ align:start position:0%
+principles about solar modules there's
+ 
+
+ align:start position:0%
+principles about solar modules there's
+there's quite a diversity of modules
+
+ align:start position:0%
+there's quite a diversity of modules
+ 
+
+ align:start position:0%
+there's quite a diversity of modules
+when you look at them uh these are
+
+ align:start position:0%
+when you look at them uh these are
+ 
+
+ align:start position:0%
+when you look at them uh these are
+examples just within one company uh just
+
+ align:start position:0%
+examples just within one company uh just
+ 
+
+ align:start position:0%
+examples just within one company uh just
+to to to highlight uh what you the range
+
+ align:start position:0%
+to to to highlight uh what you the range
+ 
+
+ align:start position:0%
+to to to highlight uh what you the range
+of module types that you might see
+
+ align:start position:0%
+of module types that you might see
+ 
+
+ align:start position:0%
+of module types that you might see
+right here you can see in this
+
+ align:start position:0%
+right here you can see in this
+ 
+
+ align:start position:0%
+right here you can see in this
+particular module uh there's very little
+
+ align:start position:0%
+particular module uh there's very little
+ 
+
+ align:start position:0%
+particular module uh there's very little
+anti-reflective coating on the glass so
+
+ align:start position:0%
+anti-reflective coating on the glass so
+ 
+
+ align:start position:0%
+anti-reflective coating on the glass so
+you're able to look through the front
+
+ align:start position:0%
+you're able to look through the front
+ 
+
+ align:start position:0%
+you're able to look through the front
+glass and see some white spaces in
+
+ align:start position:0%
+glass and see some white spaces in
+ 
+
+ align:start position:0%
+glass and see some white spaces in
+between the cells we know from the
+
+ align:start position:0%
+between the cells we know from the
+ 
+
+ align:start position:0%
+between the cells we know from the
+lecture on Crystal and silicon PV that
+
+ align:start position:0%
+lecture on Crystal and silicon PV that
+ 
+
+ align:start position:0%
+lecture on Crystal and silicon PV that
+when you see these little gaps in
+
+ align:start position:0%
+when you see these little gaps in
+ 
+
+ align:start position:0%
+when you see these little gaps in
+between the cells those are pseudo
+
+ align:start position:0%
+between the cells those are pseudo
+ 
+
+ align:start position:0%
+between the cells those are pseudo
+squares right those are those round uh
+
+ align:start position:0%
+squares right those are those round uh
+ 
+
+ align:start position:0%
+squares right those are those round uh
+ingots of Shuki silicon that have been
+
+ align:start position:0%
+ingots of Shuki silicon that have been
+ 
+
+ align:start position:0%
+ingots of Shuki silicon that have been
+sliced into Wafers and then the edges
+
+ align:start position:0%
+sliced into Wafers and then the edges
+ 
+
+ align:start position:0%
+sliced into Wafers and then the edges
+have been shaven off and you have that
+
+ align:start position:0%
+have been shaven off and you have that
+ 
+
+ align:start position:0%
+have been shaven off and you have that
+stop sign type pattern of a solar cell
+
+ align:start position:0%
+stop sign type pattern of a solar cell
+ 
+
+ align:start position:0%
+stop sign type pattern of a solar cell
+right um so that that way you know okay
+
+ align:start position:0%
+right um so that that way you know okay
+ 
+
+ align:start position:0%
+right um so that that way you know okay
+these are single Crystal and cells right
+
+ align:start position:0%
+these are single Crystal and cells right
+ 
+
+ align:start position:0%
+these are single Crystal and cells right
+lined up in a module together and
+
+ align:start position:0%
+lined up in a module together and
+ 
+
+ align:start position:0%
+lined up in a module together and
+there's very little anti-reflective
+
+ align:start position:0%
+there's very little anti-reflective
+ 
+
+ align:start position:0%
+there's very little anti-reflective
+coating on the glass which means that
+
+ align:start position:0%
+coating on the glass which means that
+ 
+
+ align:start position:0%
+coating on the glass which means that
+you're losing a fair amount due to
+
+ align:start position:0%
+you're losing a fair amount due to
+ 
+
+ align:start position:0%
+you're losing a fair amount due to
+reflectance the module on the right hand
+
+ align:start position:0%
+reflectance the module on the right hand
+ 
+
+ align:start position:0%
+reflectance the module on the right hand
+side right here has uh that uh the ENT
+
+ align:start position:0%
+side right here has uh that uh the ENT
+ 
+
+ align:start position:0%
+side right here has uh that uh the ENT
+reflection coating on the glass it could
+
+ align:start position:0%
+reflection coating on the glass it could
+ 
+
+ align:start position:0%
+reflection coating on the glass it could
+be uh an index of refraction uh gradient
+
+ align:start position:0%
+be uh an index of refraction uh gradient
+ 
+
+ align:start position:0%
+be uh an index of refraction uh gradient
+gradient to absorb more of the light it
+
+ align:start position:0%
+gradient to absorb more of the light it
+ 
+
+ align:start position:0%
+gradient to absorb more of the light it
+could also be uh surface texturing to
+
+ align:start position:0%
+could also be uh surface texturing to
+ 
+
+ align:start position:0%
+could also be uh surface texturing to
+scatter the light and trap it by total
+
+ align:start position:0%
+scatter the light and trap it by total
+ 
+
+ align:start position:0%
+scatter the light and trap it by total
+internal reflection once it gets inside
+
+ align:start position:0%
+internal reflection once it gets inside
+ 
+
+ align:start position:0%
+internal reflection once it gets inside
+um there's a few different ways uh that
+
+ align:start position:0%
+um there's a few different ways uh that
+ 
+
+ align:start position:0%
+um there's a few different ways uh that
+that one can do that usually the film
+
+ align:start position:0%
+that one can do that usually the film
+ 
+
+ align:start position:0%
+that one can do that usually the film
+coding is is the most common and uh here
+
+ align:start position:0%
+coding is is the most common and uh here
+ 
+
+ align:start position:0%
+coding is is the most common and uh here
+on the on the left hand side we have a
+
+ align:start position:0%
+on the on the left hand side we have a
+ 
+
+ align:start position:0%
+on the on the left hand side we have a
+similar uh subcell component but much
+
+ align:start position:0%
+similar uh subcell component but much
+ 
+
+ align:start position:0%
+similar uh subcell component but much
+larger module comprised of a larger
+
+ align:start position:0%
+larger module comprised of a larger
+ 
+
+ align:start position:0%
+larger module comprised of a larger
+number of cells with a a higher power
+
+ align:start position:0%
+number of cells with a a higher power
+ 
+
+ align:start position:0%
+number of cells with a a higher power
+output and uh we can see quite a wide
+
+ align:start position:0%
+output and uh we can see quite a wide
+ 
+
+ align:start position:0%
+output and uh we can see quite a wide
+variance of of different types of
+
+ align:start position:0%
+variance of of different types of
+ 
+
+ align:start position:0%
+variance of of different types of
+modules that'll be an important message
+
+ align:start position:0%
+modules that'll be an important message
+ 
+
+ align:start position:0%
+modules that'll be an important message
+in a few um the Water Rinse Cycle really
+
+ align:start position:0%
+in a few um the Water Rinse Cycle really
+ 
+
+ align:start position:0%
+in a few um the Water Rinse Cycle really
+depends on where you're at like for the
+
+ align:start position:0%
+depends on where you're at like for the
+ 
+
+ align:start position:0%
+depends on where you're at like for the
+module on my roof we just leave them up
+
+ align:start position:0%
+module on my roof we just leave them up
+ 
+
+ align:start position:0%
+module on my roof we just leave them up
+here in New England it's it's pretty
+
+ align:start position:0%
+here in New England it's it's pretty
+ 
+
+ align:start position:0%
+here in New England it's it's pretty
+much okay uh if we did have trees that
+
+ align:start position:0%
+much okay uh if we did have trees that
+ 
+
+ align:start position:0%
+much okay uh if we did have trees that
+deposited leaves nearby we'd have to
+
+ align:start position:0%
+deposited leaves nearby we'd have to
+ 
+
+ align:start position:0%
+deposited leaves nearby we'd have to
+clean it off uh in the fall uh but we
+
+ align:start position:0%
+clean it off uh in the fall uh but we
+ 
+
+ align:start position:0%
+clean it off uh in the fall uh but we
+don't uh if you're mounting modules in
+
+ align:start position:0%
+don't uh if you're mounting modules in
+ 
+
+ align:start position:0%
+don't uh if you're mounting modules in
+the Middle East where that fine grain
+
+ align:start position:0%
+the Middle East where that fine grain
+ 
+
+ align:start position:0%
+the Middle East where that fine grain
+sand exists and the if you're within 10
+
+ align:start position:0%
+sand exists and the if you're within 10
+ 
+
+ align:start position:0%
+sand exists and the if you're within 10
+kilometers from the coast where you have
+
+ align:start position:0%
+kilometers from the coast where you have
+ 
+
+ align:start position:0%
+kilometers from the coast where you have
+the salt and the sea water in the air uh
+
+ align:start position:0%
+the salt and the sea water in the air uh
+ 
+
+ align:start position:0%
+the salt and the sea water in the air uh
+you can get this uh really hard to
+
+ align:start position:0%
+you can get this uh really hard to
+ 
+
+ align:start position:0%
+you can get this uh really hard to
+remove uh sand caking the modules and
+
+ align:start position:0%
+remove uh sand caking the modules and
+ 
+
+ align:start position:0%
+remove uh sand caking the modules and
+you would have to clean them much more
+
+ align:start position:0%
+you would have to clean them much more
+ 
+
+ align:start position:0%
+you would have to clean them much more
+frequently uh than this as matter of
+
+ align:start position:0%
+frequently uh than this as matter of
+ 
+
+ align:start position:0%
+frequently uh than this as matter of
+fact I believe the numbers are in Abu
+
+ align:start position:0%
+fact I believe the numbers are in Abu
+ 
+
+ align:start position:0%
+fact I believe the numbers are in Abu
+Dhabi right outside of um one of the uh
+
+ align:start position:0%
+Dhabi right outside of um one of the uh
+ 
+
+ align:start position:0%
+Dhabi right outside of um one of the uh
+one the capital of one of the Emirates
+
+ align:start position:0%
+one the capital of one of the Emirates
+ 
+
+ align:start position:0%
+one the capital of one of the Emirates
+in in uh the UAE uh if you were to just
+
+ align:start position:0%
+in in uh the UAE uh if you were to just
+ 
+
+ align:start position:0%
+in in uh the UAE uh if you were to just
+leave your modules out near the ocean uh
+
+ align:start position:0%
+leave your modules out near the ocean uh
+ 
+
+ align:start position:0%
+leave your modules out near the ocean uh
+near the desert you would have a 40%
+
+ align:start position:0%
+near the desert you would have a 40%
+ 
+
+ align:start position:0%
+near the desert you would have a 40%
+drop in module output over a
+
+ align:start position:0%
+drop in module output over a
+ 
+
+ align:start position:0%
+drop in module output over a
+month right so that's what happens in
+
+ align:start position:0%
+month right so that's what happens in
+ 
+
+ align:start position:0%
+month right so that's what happens in
+certain environments uh in certain
+
+ align:start position:0%
+certain environments uh in certain
+ 
+
+ align:start position:0%
+certain environments uh in certain
+others like uh New England were more uh
+
+ align:start position:0%
+others like uh New England were more uh
+ 
+
+ align:start position:0%
+others like uh New England were more uh
+I say more buffered in that regard we
+
+ align:start position:0%
+I say more buffered in that regard we
+ 
+
+ align:start position:0%
+I say more buffered in that regard we
+have have frequent rain and we don't
+
+ align:start position:0%
+have have frequent rain and we don't
+ 
+
+ align:start position:0%
+have have frequent rain and we don't
+have the the dust coming from any nearby
+
+ align:start position:0%
+have the the dust coming from any nearby
+ 
+
+ align:start position:0%
+have the the dust coming from any nearby
+desert um typically there are no moving
+
+ align:start position:0%
+desert um typically there are no moving
+ 
+
+ align:start position:0%
+desert um typically there are no moving
+parts and typically there's a 20 to 30y
+
+ align:start position:0%
+parts and typically there's a 20 to 30y
+ 
+
+ align:start position:0%
+parts and typically there's a 20 to 30y
+year manufacturer warranty some of the
+
+ align:start position:0%
+year manufacturer warranty some of the
+ 
+
+ align:start position:0%
+year manufacturer warranty some of the
+newer materials that have been less
+
+ align:start position:0%
+newer materials that have been less
+ 
+
+ align:start position:0%
+newer materials that have been less
+tested might give say a 10-year
+
+ align:start position:0%
+tested might give say a 10-year
+ 
+
+ align:start position:0%
+tested might give say a 10-year
+manufacturers warranty and have to
+
+ align:start position:0%
+manufacturers warranty and have to
+ 
+
+ align:start position:0%
+manufacturers warranty and have to
+offset uh the risk in years 10 to 20 by
+
+ align:start position:0%
+offset uh the risk in years 10 to 20 by
+ 
+
+ align:start position:0%
+offset uh the risk in years 10 to 20 by
+um by uh uh lowering the cost up front
+
+ align:start position:0%
+um by uh uh lowering the cost up front
+ 
+
+ align:start position:0%
+um by uh uh lowering the cost up front
+or lowering the price up front so we
+
+ align:start position:0%
+or lowering the price up front so we
+ 
+
+ align:start position:0%
+or lowering the price up front so we
+have uh some Basics about solar modules
+
+ align:start position:0%
+have uh some Basics about solar modules
+ 
+
+ align:start position:0%
+have uh some Basics about solar modules
+uh just to to situate ourselves let's
+
+ align:start position:0%
+uh just to to situate ourselves let's
+ 
+
+ align:start position:0%
+uh just to to situate ourselves let's
+dive into the module d since this is uh
+
+ align:start position:0%
+dive into the module d since this is uh
+ 
+
+ align:start position:0%
+dive into the module d since this is uh
+where where the rubber hits the road um
+
+ align:start position:0%
+where where the rubber hits the road um
+ 
+
+ align:start position:0%
+where where the rubber hits the road um
+I'm going to show this to you in theory
+
+ align:start position:0%
+I'm going to show this to you in theory
+ 
+
+ align:start position:0%
+I'm going to show this to you in theory
+and then we're going to see uh roles
+
+ align:start position:0%
+and then we're going to see uh roles
+ 
+
+ align:start position:0%
+and then we're going to see uh roles
+reams of these uh module iner materials
+
+ align:start position:0%
+reams of these uh module iner materials
+ 
+
+ align:start position:0%
+reams of these uh module iner materials
+when we visit fraer so uh we start with
+
+ align:start position:0%
+when we visit fraer so uh we start with
+ 
+
+ align:start position:0%
+when we visit fraer so uh we start with
+the solar cells themselves these are
+
+ align:start position:0%
+the solar cells themselves these are
+ 
+
+ align:start position:0%
+the solar cells themselves these are
+these little blue uh objects right there
+
+ align:start position:0%
+these little blue uh objects right there
+ 
+
+ align:start position:0%
+these little blue uh objects right there
+um typically these cells are already
+
+ align:start position:0%
+um typically these cells are already
+ 
+
+ align:start position:0%
+um typically these cells are already
+strung together at that point they have
+
+ align:start position:0%
+strung together at that point they have
+ 
+
+ align:start position:0%
+strung together at that point they have
+contact metalization uh on on the front
+
+ align:start position:0%
+contact metalization uh on on the front
+ 
+
+ align:start position:0%
+contact metalization uh on on the front
+side which we deposit say for example by
+
+ align:start position:0%
+side which we deposit say for example by
+ 
+
+ align:start position:0%
+side which we deposit say for example by
+screen printing which you've done in the
+
+ align:start position:0%
+screen printing which you've done in the
+ 
+
+ align:start position:0%
+screen printing which you've done in the
+lab downstairs and then you string them
+
+ align:start position:0%
+lab downstairs and then you string them
+ 
+
+ align:start position:0%
+lab downstairs and then you string them
+together using a machine called a tabber
+
+ align:start position:0%
+together using a machine called a tabber
+ 
+
+ align:start position:0%
+together using a machine called a tabber
+Stringer to connect one cell to the next
+
+ align:start position:0%
+Stringer to connect one cell to the next
+ 
+
+ align:start position:0%
+Stringer to connect one cell to the next
+essentially the front of one cell to the
+
+ align:start position:0%
+essentially the front of one cell to the
+ 
+
+ align:start position:0%
+essentially the front of one cell to the
+back of the next and they're all lined
+
+ align:start position:0%
+back of the next and they're all lined
+ 
+
+ align:start position:0%
+back of the next and they're all lined
+up like that and you deposit layers of
+
+ align:start position:0%
+up like that and you deposit layers of
+ 
+
+ align:start position:0%
+up like that and you deposit layers of
+Eva which is um ethyl vinyl acetate uh
+
+ align:start position:0%
+Eva which is um ethyl vinyl acetate uh
+ 
+
+ align:start position:0%
+Eva which is um ethyl vinyl acetate uh
+this is typically the encapsulate
+
+ align:start position:0%
+this is typically the encapsulate
+ 
+
+ align:start position:0%
+this is typically the encapsulate
+material used it's shown in red right
+
+ align:start position:0%
+material used it's shown in red right
+ 
+
+ align:start position:0%
+material used it's shown in red right
+here in this drawing it's the
+
+ align:start position:0%
+here in this drawing it's the
+ 
+
+ align:start position:0%
+here in this drawing it's the
+encapsulate material used uh for uh
+
+ align:start position:0%
+encapsulate material used uh for uh
+ 
+
+ align:start position:0%
+encapsulate material used uh for uh
+Crystal and silicon PV on the back side
+
+ align:start position:0%
+Crystal and silicon PV on the back side
+ 
+
+ align:start position:0%
+Crystal and silicon PV on the back side
+there's a a sheet of material called
+
+ align:start position:0%
+there's a a sheet of material called
+ 
+
+ align:start position:0%
+there's a a sheet of material called
+tedlar despite it being drawn in yellow
+
+ align:start position:0%
+tedlar despite it being drawn in yellow
+ 
+
+ align:start position:0%
+tedlar despite it being drawn in yellow
+right there it's the white skin material
+
+ align:start position:0%
+right there it's the white skin material
+ 
+
+ align:start position:0%
+right there it's the white skin material
+here it's this white
+
+ align:start position:0%
+here it's this white
+ 
+
+ align:start position:0%
+here it's this white
+material right around
+
+ align:start position:0%
+material right around
+ 
+
+ align:start position:0%
+material right around
+here and we have the glass in the front
+
+ align:start position:0%
+here and we have the glass in the front
+ 
+
+ align:start position:0%
+here and we have the glass in the front
+side and typically it's low iron glass
+
+ align:start position:0%
+side and typically it's low iron glass
+ 
+
+ align:start position:0%
+side and typically it's low iron glass
+so it can transmit the ultraviolet light
+
+ align:start position:0%
+so it can transmit the ultraviolet light
+ 
+
+ align:start position:0%
+so it can transmit the ultraviolet light
+uh or a large portion of it um to give
+
+ align:start position:0%
+uh or a large portion of it um to give
+ 
+
+ align:start position:0%
+uh or a large portion of it um to give
+better blue response to your solar cells
+
+ align:start position:0%
+better blue response to your solar cells
+ 
+
+ align:start position:0%
+better blue response to your solar cells
+so you're capturing a larger portion of
+
+ align:start position:0%
+so you're capturing a larger portion of
+ 
+
+ align:start position:0%
+so you're capturing a larger portion of
+the solar
+
+ align:start position:0%
+the solar
+ 
+
+ align:start position:0%
+the solar
+Spectrum okay so we have uh the
+
+ align:start position:0%
+Spectrum okay so we have uh the
+ 
+
+ align:start position:0%
+Spectrum okay so we have uh the
+different components right there um one
+
+ align:start position:0%
+different components right there um one
+ 
+
+ align:start position:0%
+different components right there um one
+little piece of trivia about Eva uh for
+
+ align:start position:0%
+little piece of trivia about Eva uh for
+ 
+
+ align:start position:0%
+little piece of trivia about Eva uh for
+the chemist in the room uh what do you
+
+ align:start position:0%
+the chemist in the room uh what do you
+ 
+
+ align:start position:0%
+the chemist in the room uh what do you
+think this would decompose into um let
+
+ align:start position:0%
+think this would decompose into um let
+ 
+
+ align:start position:0%
+think this would decompose into um let
+me uh just uh give you a little hand
+
+ align:start position:0%
+me uh just uh give you a little hand
+ 
+
+ align:start position:0%
+me uh just uh give you a little hand
+here if you had
+
+ align:start position:0%
+here if you had
+ 
+
+ align:start position:0%
+here if you had
+some uh let's
+
+ align:start position:0%
+some uh let's
+ 
+
+ align:start position:0%
+some uh let's
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+um right so these represent uh methyl
+
+ align:start position:0%
+um right so these represent uh methyl
+ 
+
+ align:start position:0%
+um right so these represent uh methyl
+groups hydrogens uh carbon carbon carbon
+
+ align:start position:0%
+groups hydrogens uh carbon carbon carbon
+ 
+
+ align:start position:0%
+groups hydrogens uh carbon carbon carbon
+double bonded to an oxygen anybody
+
+ align:start position:0%
+double bonded to an oxygen anybody
+ 
+
+ align:start position:0%
+double bonded to an oxygen anybody
+recognize yeah yeah so um if you're if
+
+ align:start position:0%
+recognize yeah yeah so um if you're if
+ 
+
+ align:start position:0%
+recognize yeah yeah so um if you're if
+you're looking at the decomposition of
+
+ align:start position:0%
+you're looking at the decomposition of
+ 
+
+ align:start position:0%
+you're looking at the decomposition of
+this uh little uh group right here you
+
+ align:start position:0%
+this uh little uh group right here you
+ 
+
+ align:start position:0%
+this uh little uh group right here you
+could easily Envision it decomposing
+
+ align:start position:0%
+could easily Envision it decomposing
+ 
+
+ align:start position:0%
+could easily Envision it decomposing
+into acetic acid uh from the name
+
+ align:start position:0%
+into acetic acid uh from the name
+ 
+
+ align:start position:0%
+into acetic acid uh from the name
+ethinyl acetate right so uh if you have
+
+ align:start position:0%
+ethinyl acetate right so uh if you have
+ 
+
+ align:start position:0%
+ethinyl acetate right so uh if you have
+um a thin fill material that could react
+
+ align:start position:0%
+um a thin fill material that could react
+ 
+
+ align:start position:0%
+um a thin fill material that could react
+with the encapsulant you could decompose
+
+ align:start position:0%
+with the encapsulant you could decompose
+ 
+
+ align:start position:0%
+with the encapsulant you could decompose
+your encapsulant and cause a degradation
+
+ align:start position:0%
+your encapsulant and cause a degradation
+ 
+
+ align:start position:0%
+your encapsulant and cause a degradation
+um of of not only the the encapsulant
+
+ align:start position:0%
+um of of not only the the encapsulant
+ 
+
+ align:start position:0%
+um of of not only the the encapsulant
+itself which would block some of the
+
+ align:start position:0%
+itself which would block some of the
+ 
+
+ align:start position:0%
+itself which would block some of the
+light going through but of the solar
+
+ align:start position:0%
+light going through but of the solar
+ 
+
+ align:start position:0%
+light going through but of the solar
+cell absorber material too um so that's
+
+ align:start position:0%
+cell absorber material too um so that's
+ 
+
+ align:start position:0%
+cell absorber material too um so that's
+why in many thin fil materials uh there
+
+ align:start position:0%
+why in many thin fil materials uh there
+ 
+
+ align:start position:0%
+why in many thin fil materials uh there
+are other encapsulants used like PVB
+
+ align:start position:0%
+are other encapsulants used like PVB
+ 
+
+ align:start position:0%
+are other encapsulants used like PVB
+right polyvinyl butol and some folks are
+
+ align:start position:0%
+right polyvinyl butol and some folks are
+ 
+
+ align:start position:0%
+right polyvinyl butol and some folks are
+even talking about getting away from
+
+ align:start position:0%
+even talking about getting away from
+ 
+
+ align:start position:0%
+even talking about getting away from
+glass and Eva all together and just
+
+ align:start position:0%
+glass and Eva all together and just
+ 
+
+ align:start position:0%
+glass and Eva all together and just
+putting down um I say an organic uh
+
+ align:start position:0%
+putting down um I say an organic uh
+ 
+
+ align:start position:0%
+putting down um I say an organic uh
+resin type material maybe a very hard um
+
+ align:start position:0%
+resin type material maybe a very hard um
+ 
+
+ align:start position:0%
+resin type material maybe a very hard um
+uh polymeric material that could be used
+
+ align:start position:0%
+uh polymeric material that could be used
+ 
+
+ align:start position:0%
+uh polymeric material that could be used
+in a floor in a clean room let's say
+
+ align:start position:0%
+in a floor in a clean room let's say
+ 
+
+ align:start position:0%
+in a floor in a clean room let's say
+yeah is the low iron content of the
+
+ align:start position:0%
+yeah is the low iron content of the
+ 
+
+ align:start position:0%
+yeah is the low iron content of the
+glass also important to prevent
+
+ align:start position:0%
+glass also important to prevent
+ 
+
+ align:start position:0%
+glass also important to prevent
+impurities getting into the we pass that
+
+ align:start position:0%
+impurities getting into the we pass that
+ 
+
+ align:start position:0%
+impurities getting into the we pass that
+so uh the question was is a low iron
+
+ align:start position:0%
+so uh the question was is a low iron
+ 
+
+ align:start position:0%
+so uh the question was is a low iron
+content in the glass also useful for
+
+ align:start position:0%
+content in the glass also useful for
+ 
+
+ align:start position:0%
+content in the glass also useful for
+preventing impurities from getting in um
+
+ align:start position:0%
+preventing impurities from getting in um
+ 
+
+ align:start position:0%
+preventing impurities from getting in um
+I would say if you're
+
+ align:start position:0%
+I would say if you're
+ 
+
+ align:start position:0%
+I would say if you're
+producing see the the diffusivity and
+
+ align:start position:0%
+producing see the the diffusivity and
+ 
+
+ align:start position:0%
+producing see the the diffusivity and
+solubility of impurities in a solid
+
+ align:start position:0%
+solubility of impurities in a solid
+ 
+
+ align:start position:0%
+solubility of impurities in a solid
+typically follow boltzman statistics
+
+ align:start position:0%
+typically follow boltzman statistics
+ 
+
+ align:start position:0%
+typically follow boltzman statistics
+meaning they increase exponentially with
+
+ align:start position:0%
+meaning they increase exponentially with
+ 
+
+ align:start position:0%
+meaning they increase exponentially with
+temperature it's it's an entropy driven
+
+ align:start position:0%
+temperature it's it's an entropy driven
+ 
+
+ align:start position:0%
+temperature it's it's an entropy driven
+effect and uh as a result of being at
+
+ align:start position:0%
+effect and uh as a result of being at
+ 
+
+ align:start position:0%
+effect and uh as a result of being at
+room temperature the transmission or the
+
+ align:start position:0%
+room temperature the transmission or the
+ 
+
+ align:start position:0%
+room temperature the transmission or the
+diffusivity and hence the solubility of
+
+ align:start position:0%
+diffusivity and hence the solubility of
+ 
+
+ align:start position:0%
+diffusivity and hence the solubility of
+iron inside of the bulk silicon is very
+
+ align:start position:0%
+iron inside of the bulk silicon is very
+ 
+
+ align:start position:0%
+iron inside of the bulk silicon is very
+low um and even over 20year span uh the
+
+ align:start position:0%
+low um and even over 20year span uh the
+ 
+
+ align:start position:0%
+low um and even over 20year span uh the
+total diffusion length of the iron from
+
+ align:start position:0%
+total diffusion length of the iron from
+ 
+
+ align:start position:0%
+total diffusion length of the iron from
+the glass into the Silicon would be
+
+ align:start position:0%
+the glass into the Silicon would be
+ 
+
+ align:start position:0%
+the glass into the Silicon would be
+rather small now point taken if you were
+
+ align:start position:0%
+rather small now point taken if you were
+ 
+
+ align:start position:0%
+rather small now point taken if you were
+to say create a quartz tube to do your
+
+ align:start position:0%
+to say create a quartz tube to do your
+ 
+
+ align:start position:0%
+to say create a quartz tube to do your
+phosphorous diffusion at 800 degre C or
+
+ align:start position:0%
+phosphorous diffusion at 800 degre C or
+ 
+
+ align:start position:0%
+phosphorous diffusion at 800 degre C or
+850° C um and you had iron inside of
+
+ align:start position:0%
+850° C um and you had iron inside of
+ 
+
+ align:start position:0%
+850° C um and you had iron inside of
+that quartz tube then it could very
+
+ align:start position:0%
+that quartz tube then it could very
+ 
+
+ align:start position:0%
+that quartz tube then it could very
+easily diffuse into your wafer so it is
+
+ align:start position:0%
+easily diffuse into your wafer so it is
+ 
+
+ align:start position:0%
+easily diffuse into your wafer so it is
+important to to be considerate of of
+
+ align:start position:0%
+important to to be considerate of of
+ 
+
+ align:start position:0%
+important to to be considerate of of
+impurities and the effects thereof but
+
+ align:start position:0%
+impurities and the effects thereof but
+ 
+
+ align:start position:0%
+impurities and the effects thereof but
+uh at low temperatures close to room
+
+ align:start position:0%
+uh at low temperatures close to room
+ 
+
+ align:start position:0%
+uh at low temperatures close to room
+temperature there's very little risk of
+
+ align:start position:0%
+temperature there's very little risk of
+ 
+
+ align:start position:0%
+temperature there's very little risk of
+it moving around good so um tedlar this
+
+ align:start position:0%
+it moving around good so um tedlar this
+ 
+
+ align:start position:0%
+it moving around good so um tedlar this
+back skin material right here forms uh
+
+ align:start position:0%
+back skin material right here forms uh
+ 
+
+ align:start position:0%
+back skin material right here forms uh
+an almost impenetrable back layer you
+
+ align:start position:0%
+an almost impenetrable back layer you
+ 
+
+ align:start position:0%
+an almost impenetrable back layer you
+might want to put little asteris around
+
+ align:start position:0%
+might want to put little asteris around
+ 
+
+ align:start position:0%
+might want to put little asteris around
+uh sorry a little uh quotes around
+
+ align:start position:0%
+uh sorry a little uh quotes around
+ 
+
+ align:start position:0%
+uh sorry a little uh quotes around
+impenetrable nothing is absolutely
+
+ align:start position:0%
+impenetrable nothing is absolutely
+ 
+
+ align:start position:0%
+impenetrable nothing is absolutely
+impenetrable but uh there is it is a
+
+ align:start position:0%
+impenetrable but uh there is it is a
+ 
+
+ align:start position:0%
+impenetrable but uh there is it is a
+very tough tough material if you were to
+
+ align:start position:0%
+very tough tough material if you were to
+ 
+
+ align:start position:0%
+very tough tough material if you were to
+take a piece of tedlar and try to break
+
+ align:start position:0%
+take a piece of tedlar and try to break
+ 
+
+ align:start position:0%
+take a piece of tedlar and try to break
+it try to rip it or tear it um even the
+
+ align:start position:0%
+it try to rip it or tear it um even the
+ 
+
+ align:start position:0%
+it try to rip it or tear it um even the
+strongest in the class would be
+
+ align:start position:0%
+strongest in the class would be
+ 
+
+ align:start position:0%
+strongest in the class would be
+challenged in that regard uh and we'll
+
+ align:start position:0%
+challenged in that regard uh and we'll
+ 
+
+ align:start position:0%
+challenged in that regard uh and we'll
+have a chance to do that at frown hoofer
+
+ align:start position:0%
+have a chance to do that at frown hoofer
+ 
+
+ align:start position:0%
+have a chance to do that at frown hoofer
+um the aluminum frame provides rigidity
+
+ align:start position:0%
+um the aluminum frame provides rigidity
+ 
+
+ align:start position:0%
+um the aluminum frame provides rigidity
+right so the mechanical engineers in the
+
+ align:start position:0%
+right so the mechanical engineers in the
+ 
+
+ align:start position:0%
+right so the mechanical engineers in the
+room um would understand that the
+
+ align:start position:0%
+room um would understand that the
+ 
+
+ align:start position:0%
+room um would understand that the
+bending mode of this glass right or the
+
+ align:start position:0%
+bending mode of this glass right or the
+ 
+
+ align:start position:0%
+bending mode of this glass right or the
+twist um is prevented by these uh rigid
+
+ align:start position:0%
+twist um is prevented by these uh rigid
+ 
+
+ align:start position:0%
+twist um is prevented by these uh rigid
+aluminum uh extruded aluminum components
+
+ align:start position:0%
+aluminum uh extruded aluminum components
+ 
+
+ align:start position:0%
+aluminum uh extruded aluminum components
+right here in the back right and you can
+
+ align:start position:0%
+right here in the back right and you can
+ 
+
+ align:start position:0%
+right here in the back right and you can
+see that a lot of the mass is
+
+ align:start position:0%
+see that a lot of the mass is
+ 
+
+ align:start position:0%
+see that a lot of the mass is
+concentrated away from uh this the the
+
+ align:start position:0%
+concentrated away from uh this the the
+ 
+
+ align:start position:0%
+concentrated away from uh this the the
+the the centroid right uh which results
+
+ align:start position:0%
+the the centroid right uh which results
+ 
+
+ align:start position:0%
+the the centroid right uh which results
+in a larger stiffness prevention of of
+
+ align:start position:0%
+in a larger stiffness prevention of of
+ 
+
+ align:start position:0%
+in a larger stiffness prevention of of
+bending larger bending moment second
+
+ align:start position:0%
+bending larger bending moment second
+ 
+
+ align:start position:0%
+bending larger bending moment second
+moment if you will okay so there's a
+
+ align:start position:0%
+moment if you will okay so there's a
+ 
+
+ align:start position:0%
+moment if you will okay so there's a
+fair amount of mechanical engineering
+
+ align:start position:0%
+fair amount of mechanical engineering
+ 
+
+ align:start position:0%
+fair amount of mechanical engineering
+that goes into the design uh because you
+
+ align:start position:0%
+that goes into the design uh because you
+ 
+
+ align:start position:0%
+that goes into the design uh because you
+want to minimize commodity material
+
+ align:start position:0%
+want to minimize commodity material
+ 
+
+ align:start position:0%
+want to minimize commodity material
+costs you want to minimize the amount of
+
+ align:start position:0%
+costs you want to minimize the amount of
+ 
+
+ align:start position:0%
+costs you want to minimize the amount of
+materials that go into the module but
+
+ align:start position:0%
+materials that go into the module but
+ 
+
+ align:start position:0%
+materials that go into the module but
+you still want it to last for 20 years
+
+ align:start position:0%
+you still want it to last for 20 years
+ 
+
+ align:start position:0%
+you still want it to last for 20 years
+you still want it to be resistant to
+
+ align:start position:0%
+you still want it to be resistant to
+ 
+
+ align:start position:0%
+you still want it to be resistant to
+snow loads to wind loads you don't want
+
+ align:start position:0%
+snow loads to wind loads you don't want
+ 
+
+ align:start position:0%
+snow loads to wind loads you don't want
+to break and you don't want to make good
+
+ align:start position:0%
+to break and you don't want to make good
+ 
+
+ align:start position:0%
+to break and you don't want to make good
+on your 20-year warranty that costs you
+
+ align:start position:0%
+on your 20-year warranty that costs you
+ 
+
+ align:start position:0%
+on your 20-year warranty that costs you
+money as
+
+ align:start position:0%
+money as
+ 
+
+ align:start position:0%
+money as
+manufacturer so the circuit design in
+
+ align:start position:0%
+manufacturer so the circuit design in
+ 
+
+ align:start position:0%
+manufacturer so the circuit design in
+most modules follows something very
+
+ align:start position:0%
+most modules follows something very
+ 
+
+ align:start position:0%
+most modules follows something very
+similar to this now what you see when
+
+ align:start position:0%
+similar to this now what you see when
+ 
+
+ align:start position:0%
+similar to this now what you see when
+you glance at this what what you should
+
+ align:start position:0%
+you glance at this what what you should
+ 
+
+ align:start position:0%
+you glance at this what what you should
+be looking is you here are the context
+
+ align:start position:0%
+be looking is you here are the context
+ 
+
+ align:start position:0%
+be looking is you here are the context
+those those are the leads coming out of
+
+ align:start position:0%
+those those are the leads coming out of
+ 
+
+ align:start position:0%
+those those are the leads coming out of
+the module they're essentially these uh
+
+ align:start position:0%
+the module they're essentially these uh
+ 
+
+ align:start position:0%
+the module they're essentially these uh
+leads coming out in the back in the
+
+ align:start position:0%
+leads coming out in the back in the
+ 
+
+ align:start position:0%
+leads coming out in the back in the
+junction box you want to turn it around
+
+ align:start position:0%
+junction box you want to turn it around
+ 
+
+ align:start position:0%
+junction box you want to turn it around
+again here we go so here are the module
+
+ align:start position:0%
+again here we go so here are the module
+ 
+
+ align:start position:0%
+again here we go so here are the module
+leads coming out and the question is how
+
+ align:start position:0%
+leads coming out and the question is how
+ 
+
+ align:start position:0%
+leads coming out and the question is how
+do I String together the cells inside of
+
+ align:start position:0%
+do I String together the cells inside of
+ 
+
+ align:start position:0%
+do I String together the cells inside of
+my module how do I String together these
+
+ align:start position:0%
+my module how do I String together these
+ 
+
+ align:start position:0%
+my module how do I String together these
+cells right in here to provide the
+
+ align:start position:0%
+cells right in here to provide the
+ 
+
+ align:start position:0%
+cells right in here to provide the
+greatest value to the customer do I
+
+ align:start position:0%
+greatest value to the customer do I
+ 
+
+ align:start position:0%
+greatest value to the customer do I
+connect them all in series and make just
+
+ align:start position:0%
+connect them all in series and make just
+ 
+
+ align:start position:0%
+connect them all in series and make just
+one long snaky uh electronic path do I
+
+ align:start position:0%
+one long snaky uh electronic path do I
+ 
+
+ align:start position:0%
+one long snaky uh electronic path do I
+connect them all in parallel that would
+
+ align:start position:0%
+connect them all in parallel that would
+ 
+
+ align:start position:0%
+connect them all in parallel that would
+require a lot of wiring um or do I some
+
+ align:start position:0%
+require a lot of wiring um or do I some
+ 
+
+ align:start position:0%
+require a lot of wiring um or do I some
+do I do something in between and if you
+
+ align:start position:0%
+do I do something in between and if you
+ 
+
+ align:start position:0%
+do I do something in between and if you
+were to come up close to here and
+
+ align:start position:0%
+were to come up close to here and
+ 
+
+ align:start position:0%
+were to come up close to here and
+inspect it what you would see is that
+
+ align:start position:0%
+inspect it what you would see is that
+ 
+
+ align:start position:0%
+inspect it what you would see is that
+you have uh strings in parallel right so
+
+ align:start position:0%
+you have uh strings in parallel right so
+ 
+
+ align:start position:0%
+you have uh strings in parallel right so
+you have a one going from here down and
+
+ align:start position:0%
+you have a one going from here down and
+ 
+
+ align:start position:0%
+you have a one going from here down and
+around that's one two and three right
+
+ align:start position:0%
+around that's one two and three right
+ 
+
+ align:start position:0%
+around that's one two and three right
+three of these strings and um they're
+
+ align:start position:0%
+three of these strings and um they're
+ 
+
+ align:start position:0%
+three of these strings and um they're
+connected those three strings are
+
+ align:start position:0%
+connected those three strings are
+ 
+
+ align:start position:0%
+connected those three strings are
+connected in parallel and each string is
+
+ align:start position:0%
+connected in parallel and each string is
+ 
+
+ align:start position:0%
+connected in parallel and each string is
+comprised of uh several uh solar cells
+
+ align:start position:0%
+comprised of uh several uh solar cells
+ 
+
+ align:start position:0%
+comprised of uh several uh solar cells
+now for historical reasons the Crystal
+
+ align:start position:0%
+now for historical reasons the Crystal
+ 
+
+ align:start position:0%
+now for historical reasons the Crystal
+and silicon solar cell modules have
+
+ align:start position:0%
+and silicon solar cell modules have
+ 
+
+ align:start position:0%
+and silicon solar cell modules have
+typically had strings of around 36 cells
+
+ align:start position:0%
+typically had strings of around 36 cells
+ 
+
+ align:start position:0%
+typically had strings of around 36 cells
+connected in series um what this does is
+
+ align:start position:0%
+connected in series um what this does is
+ 
+
+ align:start position:0%
+connected in series um what this does is
+it yields a maximum PowerPoint voltage
+
+ align:start position:0%
+it yields a maximum PowerPoint voltage
+ 
+
+ align:start position:0%
+it yields a maximum PowerPoint voltage
+somewhere in the range of 17 to 18 volts
+
+ align:start position:0%
+somewhere in the range of 17 to 18 volts
+ 
+
+ align:start position:0%
+somewhere in the range of 17 to 18 volts
+if you remember the voc's of your solar
+
+ align:start position:0%
+if you remember the voc's of your solar
+ 
+
+ align:start position:0%
+if you remember the voc's of your solar
+cells and the maximum PowerPoint voltage
+
+ align:start position:0%
+cells and the maximum PowerPoint voltage
+ 
+
+ align:start position:0%
+cells and the maximum PowerPoint voltage
+of your solar cells or somewhere around
+
+ align:start position:0%
+of your solar cells or somewhere around
+ 
+
+ align:start position:0%
+of your solar cells or somewhere around
+0.5 um and uh so you take 36 cells
+
+ align:start position:0%
+0.5 um and uh so you take 36 cells
+ 
+
+ align:start position:0%
+0.5 um and uh so you take 36 cells
+divide by two or multiply by 0.5 if you
+
+ align:start position:0%
+divide by two or multiply by 0.5 if you
+ 
+
+ align:start position:0%
+divide by two or multiply by 0.5 if you
+will and you're Landing somewhere in
+
+ align:start position:0%
+will and you're Landing somewhere in
+ 
+
+ align:start position:0%
+will and you're Landing somewhere in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Ballpark and what that does is it
+
+ align:start position:0%
+Ballpark and what that does is it
+ 
+
+ align:start position:0%
+Ballpark and what that does is it
+enables you to hit even under lower
+
+ align:start position:0%
+enables you to hit even under lower
+ 
+
+ align:start position:0%
+enables you to hit even under lower
+light conditions the over potential
+
+ align:start position:0%
+light conditions the over potential
+ 
+
+ align:start position:0%
+light conditions the over potential
+needed to charge a a rechargeable
+
+ align:start position:0%
+needed to charge a a rechargeable
+ 
+
+ align:start position:0%
+needed to charge a a rechargeable
+battery so if it a 12vt battery um and
+
+ align:start position:0%
+battery so if it a 12vt battery um and
+ 
+
+ align:start position:0%
+battery so if it a 12vt battery um and
+the voltage output of the battery is
+
+ align:start position:0%
+the voltage output of the battery is
+ 
+
+ align:start position:0%
+the voltage output of the battery is
+between say 12 and kind of dropping down
+
+ align:start position:0%
+between say 12 and kind of dropping down
+ 
+
+ align:start position:0%
+between say 12 and kind of dropping down
+to 10 before it starts using its utility
+
+ align:start position:0%
+to 10 before it starts using its utility
+ 
+
+ align:start position:0%
+to 10 before it starts using its utility
+when you try to start your car and it
+
+ align:start position:0%
+when you try to start your car and it
+ 
+
+ align:start position:0%
+when you try to start your car and it
+just turns it doesn't really turn over
+
+ align:start position:0%
+just turns it doesn't really turn over
+ 
+
+ align:start position:0%
+just turns it doesn't really turn over
+and you can't start your engine it's
+
+ align:start position:0%
+and you can't start your engine it's
+ 
+
+ align:start position:0%
+and you can't start your engine it's
+probably because the voltage in your
+
+ align:start position:0%
+probably because the voltage in your
+ 
+
+ align:start position:0%
+probably because the voltage in your
+battery has dropped to about uh 10 volts
+
+ align:start position:0%
+battery has dropped to about uh 10 volts
+ 
+
+ align:start position:0%
+battery has dropped to about uh 10 volts
+um the over potential needed to charge
+
+ align:start position:0%
+um the over potential needed to charge
+ 
+
+ align:start position:0%
+um the over potential needed to charge
+it 13 plus um that's what you're hitting
+
+ align:start position:0%
+it 13 plus um that's what you're hitting
+ 
+
+ align:start position:0%
+it 13 plus um that's what you're hitting
+with with the string and uh that's for
+
+ align:start position:0%
+with with the string and uh that's for
+ 
+
+ align:start position:0%
+with with the string and uh that's for
+historical reasons why we had this
+
+ align:start position:0%
+historical reasons why we had this
+ 
+
+ align:start position:0%
+historical reasons why we had this
+number of cells connected together um as
+
+ align:start position:0%
+number of cells connected together um as
+ 
+
+ align:start position:0%
+number of cells connected together um as
+grid tide systems become more common
+
+ align:start position:0%
+grid tide systems become more common
+ 
+
+ align:start position:0%
+grid tide systems become more common
+though um this constraint is being
+
+ align:start position:0%
+though um this constraint is being
+ 
+
+ align:start position:0%
+though um this constraint is being
+reduced right we have about over 90% of
+
+ align:start position:0%
+reduced right we have about over 90% of
+ 
+
+ align:start position:0%
+reduced right we have about over 90% of
+all of our solar modules today are
+
+ align:start position:0%
+all of our solar modules today are
+ 
+
+ align:start position:0%
+all of our solar modules today are
+connected to the grid including the ones
+
+ align:start position:0%
+connected to the grid including the ones
+ 
+
+ align:start position:0%
+connected to the grid including the ones
+in my home so when I'm not there and
+
+ align:start position:0%
+in my home so when I'm not there and
+ 
+
+ align:start position:0%
+in my home so when I'm not there and
+it's producing excess electricity it's
+
+ align:start position:0%
+it's producing excess electricity it's
+ 
+
+ align:start position:0%
+it's producing excess electricity it's
+pumping it into the grid and maybe we're
+
+ align:start position:0%
+pumping it into the grid and maybe we're
+ 
+
+ align:start position:0%
+pumping it into the grid and maybe we're
+using some of my electrons here I don't
+
+ align:start position:0%
+using some of my electrons here I don't
+ 
+
+ align:start position:0%
+using some of my electrons here I don't
+know um so as grid tide systems become
+
+ align:start position:0%
+know um so as grid tide systems become
+ 
+
+ align:start position:0%
+know um so as grid tide systems become
+more common um you you care less about
+
+ align:start position:0%
+more common um you you care less about
+ 
+
+ align:start position:0%
+more common um you you care less about
+me the over potential requirements for a
+
+ align:start position:0%
+me the over potential requirements for a
+ 
+
+ align:start position:0%
+me the over potential requirements for a
+battery you care more about matching the
+
+ align:start position:0%
+battery you care more about matching the
+ 
+
+ align:start position:0%
+battery you care more about matching the
+output of your solar module with
+
+ align:start position:0%
+output of your solar module with
+ 
+
+ align:start position:0%
+output of your solar module with
+whatever inverter technology you're
+
+ align:start position:0%
+whatever inverter technology you're
+ 
+
+ align:start position:0%
+whatever inverter technology you're
+using to convert the DC power into AC
+
+ align:start position:0%
+using to convert the DC power into AC
+ 
+
+ align:start position:0%
+using to convert the DC power into AC
+power number two why do they spec the
+
+ align:start position:0%
+power number two why do they spec the
+ 
+
+ align:start position:0%
+power number two why do they spec the
+modules that size you notice that I
+
+ align:start position:0%
+modules that size you notice that I
+ 
+
+ align:start position:0%
+modules that size you notice that I
+could lift it just barely I'm a
+
+ align:start position:0%
+could lift it just barely I'm a
+ 
+
+ align:start position:0%
+could lift it just barely I'm a
+university Professor I sit in my chair
+
+ align:start position:0%
+university Professor I sit in my chair
+ 
+
+ align:start position:0%
+university Professor I sit in my chair
+and think most of the time uh a person
+
+ align:start position:0%
+and think most of the time uh a person
+ 
+
+ align:start position:0%
+and think most of the time uh a person
+uh you know somebody strong out there in
+
+ align:start position:0%
+uh you know somebody strong out there in
+ 
+
+ align:start position:0%
+uh you know somebody strong out there in
+the field mounting modules say if if
+
+ align:start position:0%
+the field mounting modules say if if
+ 
+
+ align:start position:0%
+the field mounting modules say if if
+Jessica in the back were module
+
+ align:start position:0%
+Jessica in the back were module
+ 
+
+ align:start position:0%
+Jessica in the back were module
+installer she could lift this no problem
+
+ align:start position:0%
+installer she could lift this no problem
+ 
+
+ align:start position:0%
+installer she could lift this no problem
+probably with her pinky finger and
+
+ align:start position:0%
+probably with her pinky finger and
+ 
+
+ align:start position:0%
+probably with her pinky finger and
+that's why there bite-sized right
+
+ align:start position:0%
+that's why there bite-sized right
+ 
+
+ align:start position:0%
+that's why there bite-sized right
+they're they're a single person liftable
+
+ align:start position:0%
+they're they're a single person liftable
+ 
+
+ align:start position:0%
+they're they're a single person liftable
+uh installable modules you can't make
+
+ align:start position:0%
+uh installable modules you can't make
+ 
+
+ align:start position:0%
+uh installable modules you can't make
+them too big or else you start needing
+
+ align:start position:0%
+them too big or else you start needing
+ 
+
+ align:start position:0%
+them too big or else you start needing
+cranes uh which of course has its own
+
+ align:start position:0%
+cranes uh which of course has its own
+ 
+
+ align:start position:0%
+cranes uh which of course has its own
+benefits for large field installations
+
+ align:start position:0%
+benefits for large field installations
+ 
+
+ align:start position:0%
+benefits for large field installations
+wouldn't really make sense with our
+
+ align:start position:0%
+wouldn't really make sense with our
+ 
+
+ align:start position:0%
+wouldn't really make sense with our
+current mode of installation on
+
+ align:start position:0%
+current mode of installation on
+ 
+
+ align:start position:0%
+current mode of installation on
+residential yeah the um so if you had a
+
+ align:start position:0%
+residential yeah the um so if you had a
+ 
+
+ align:start position:0%
+residential yeah the um so if you had a
+battery if you were powering a or
+
+ align:start position:0%
+battery if you were powering a or
+ 
+
+ align:start position:0%
+battery if you were powering a or
+charging a battery with this the module
+
+ align:start position:0%
+charging a battery with this the module
+ 
+
+ align:start position:0%
+charging a battery with this the module
+you also wouldn't want to have too many
+
+ align:start position:0%
+you also wouldn't want to have too many
+ 
+
+ align:start position:0%
+you also wouldn't want to have too many
+volts right I guess maybe that's a
+
+ align:start position:0%
+volts right I guess maybe that's a
+ 
+
+ align:start position:0%
+volts right I guess maybe that's a
+really basic Electronics question yeah
+
+ align:start position:0%
+really basic Electronics question yeah
+ 
+
+ align:start position:0%
+really basic Electronics question yeah
+so the question is can you can can you
+
+ align:start position:0%
+so the question is can you can can you
+ 
+
+ align:start position:0%
+so the question is can you can can you
+can you uh do you benefit by having
+
+ align:start position:0%
+can you uh do you benefit by having
+ 
+
+ align:start position:0%
+can you uh do you benefit by having
+larger over potential uh when when
+
+ align:start position:0%
+larger over potential uh when when
+ 
+
+ align:start position:0%
+larger over potential uh when when
+recharging a battery um while I'm not a
+
+ align:start position:0%
+recharging a battery um while I'm not a
+ 
+
+ align:start position:0%
+recharging a battery um while I'm not a
+battery expert uh so I'll definitely
+
+ align:start position:0%
+battery expert uh so I'll definitely
+ 
+
+ align:start position:0%
+battery expert uh so I'll definitely
+caution on this I would imagine uh that
+
+ align:start position:0%
+caution on this I would imagine uh that
+ 
+
+ align:start position:0%
+caution on this I would imagine uh that
+there would be some law of diminishing
+
+ align:start position:0%
+there would be some law of diminishing
+ 
+
+ align:start position:0%
+there would be some law of diminishing
+returns you would be limited in terms of
+
+ align:start position:0%
+returns you would be limited in terms of
+ 
+
+ align:start position:0%
+returns you would be limited in terms of
+the recharge rate not by the over
+
+ align:start position:0%
+the recharge rate not by the over
+ 
+
+ align:start position:0%
+the recharge rate not by the over
+potential but by by some other component
+
+ align:start position:0%
+potential but by by some other component
+ 
+
+ align:start position:0%
+potential but by by some other component
+like the electrolyte diffusivity let's
+
+ align:start position:0%
+like the electrolyte diffusivity let's
+ 
+
+ align:start position:0%
+like the electrolyte diffusivity let's
+say uh inside of your system uh as an
+
+ align:start position:0%
+say uh inside of your system uh as an
+ 
+
+ align:start position:0%
+say uh inside of your system uh as an
+example but I would I would defer that
+
+ align:start position:0%
+example but I would I would defer that
+ 
+
+ align:start position:0%
+example but I would I would defer that
+to the battery experts my impression
+
+ align:start position:0%
+to the battery experts my impression
+ 
+
+ align:start position:0%
+to the battery experts my impression
+though is that you get a lot of
+
+ align:start position:0%
+though is that you get a lot of
+ 
+
+ align:start position:0%
+though is that you get a lot of
+diminishing
+
+ align:start position:0%
+diminishing
+ 
+
+ align:start position:0%
+diminishing
+returns um packing fraction in the
+
+ align:start position:0%
+returns um packing fraction in the
+ 
+
+ align:start position:0%
+returns um packing fraction in the
+modules so we talked about the different
+
+ align:start position:0%
+modules so we talked about the different
+ 
+
+ align:start position:0%
+modules so we talked about the different
+uh cell sizes um if you're processing
+
+ align:start position:0%
+uh cell sizes um if you're processing
+ 
+
+ align:start position:0%
+uh cell sizes um if you're processing
+discret cells um the higher packing
+
+ align:start position:0%
+discret cells um the higher packing
+ 
+
+ align:start position:0%
+discret cells um the higher packing
+fraction enables lower glass and
+
+ align:start position:0%
+fraction enables lower glass and
+ 
+
+ align:start position:0%
+fraction enables lower glass and
+capsulin and cost per Watt peak uh the
+
+ align:start position:0%
+capsulin and cost per Watt peak uh the
+ 
+
+ align:start position:0%
+capsulin and cost per Watt peak uh the
+lower packing fraction you get to play
+
+ align:start position:0%
+lower packing fraction you get to play
+ 
+
+ align:start position:0%
+lower packing fraction you get to play
+some games with Optical concentration uh
+
+ align:start position:0%
+some games with Optical concentration uh
+ 
+
+ align:start position:0%
+some games with Optical concentration uh
+for here for instance if you have space
+
+ align:start position:0%
+for here for instance if you have space
+ 
+
+ align:start position:0%
+for here for instance if you have space
+between your cells uh you can uh have a
+
+ align:start position:0%
+between your cells uh you can uh have a
+ 
+
+ align:start position:0%
+between your cells uh you can uh have a
+diffuse luran scatterer in the back
+
+ align:start position:0%
+diffuse luran scatterer in the back
+ 
+
+ align:start position:0%
+diffuse luran scatterer in the back
+which uh will reflect the light at a
+
+ align:start position:0%
+which uh will reflect the light at a
+ 
+
+ align:start position:0%
+which uh will reflect the light at a
+different angle uh scattering it and
+
+ align:start position:0%
+different angle uh scattering it and
+ 
+
+ align:start position:0%
+different angle uh scattering it and
+that light could be trapped by total
+
+ align:start position:0%
+that light could be trapped by total
+ 
+
+ align:start position:0%
+that light could be trapped by total
+internal reflection inside of the glass
+
+ align:start position:0%
+internal reflection inside of the glass
+ 
+
+ align:start position:0%
+internal reflection inside of the glass
+if the angle um reaching the glass is
+
+ align:start position:0%
+if the angle um reaching the glass is
+ 
+
+ align:start position:0%
+if the angle um reaching the glass is
+say 15° or greater so you can play some
+
+ align:start position:0%
+say 15° or greater so you can play some
+ 
+
+ align:start position:0%
+say 15° or greater so you can play some
+games there uh that's why the tedlar
+
+ align:start position:0%
+games there uh that's why the tedlar
+ 
+
+ align:start position:0%
+games there uh that's why the tedlar
+back skin being white is typically used
+
+ align:start position:0%
+back skin being white is typically used
+ 
+
+ align:start position:0%
+back skin being white is typically used
+in most solar modules right so that we
+
+ align:start position:0%
+in most solar modules right so that we
+ 
+
+ align:start position:0%
+in most solar modules right so that we
+scatter or we reflect and then scatter
+
+ align:start position:0%
+scatter or we reflect and then scatter
+ 
+
+ align:start position:0%
+scatter or we reflect and then scatter
+and then trap the light that comes in in
+
+ align:start position:0%
+and then trap the light that comes in in
+ 
+
+ align:start position:0%
+and then trap the light that comes in in
+between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells so to put this into another um you
+
+ align:start position:0%
+cells so to put this into another um you
+ 
+
+ align:start position:0%
+cells so to put this into another um you
+know just a another fancier
+
+ align:start position:0%
+know just a another fancier
+ 
+
+ align:start position:0%
+know just a another fancier
+threedimensional framework we have our
+
+ align:start position:0%
+threedimensional framework we have our
+ 
+
+ align:start position:0%
+threedimensional framework we have our
+interconnected cells we have our
+
+ align:start position:0%
+interconnected cells we have our
+ 
+
+ align:start position:0%
+interconnected cells we have our
+encapsulin above and below the
+
+ align:start position:0%
+encapsulin above and below the
+ 
+
+ align:start position:0%
+encapsulin above and below the
+encapsulant material is an interesting
+
+ align:start position:0%
+encapsulant material is an interesting
+ 
+
+ align:start position:0%
+encapsulant material is an interesting
+thing it's solid at room temperature but
+
+ align:start position:0%
+thing it's solid at room temperature but
+ 
+
+ align:start position:0%
+thing it's solid at room temperature but
+it begins to flow at around 15075 de C
+
+ align:start position:0%
+it begins to flow at around 15075 de C
+ 
+
+ align:start position:0%
+it begins to flow at around 15075 de C
+which means um you you you if you've
+
+ align:start position:0%
+which means um you you you if you've
+ 
+
+ align:start position:0%
+which means um you you you if you've
+ever seen if you ever put a a plastic
+
+ align:start position:0%
+ever seen if you ever put a a plastic
+ 
+
+ align:start position:0%
+ever seen if you ever put a a plastic
+bottle in the oven and you've noticed
+
+ align:start position:0%
+bottle in the oven and you've noticed
+ 
+
+ align:start position:0%
+bottle in the oven and you've noticed
+how it begins to melt and sag and droop
+
+ align:start position:0%
+how it begins to melt and sag and droop
+ 
+
+ align:start position:0%
+how it begins to melt and sag and droop
+um that that's essentially the type of
+
+ align:start position:0%
+um that that's essentially the type of
+ 
+
+ align:start position:0%
+um that that's essentially the type of
+flow that you would experience inside of
+
+ align:start position:0%
+flow that you would experience inside of
+ 
+
+ align:start position:0%
+flow that you would experience inside of
+this encapsulate material and it flows
+
+ align:start position:0%
+this encapsulate material and it flows
+ 
+
+ align:start position:0%
+this encapsulate material and it flows
+around the cells and it fuses them
+
+ align:start position:0%
+around the cells and it fuses them
+ 
+
+ align:start position:0%
+around the cells and it fuses them
+together with the glass on top uh and
+
+ align:start position:0%
+together with the glass on top uh and
+ 
+
+ align:start position:0%
+together with the glass on top uh and
+they stick together once they cool down
+
+ align:start position:0%
+they stick together once they cool down
+ 
+
+ align:start position:0%
+they stick together once they cool down
+to room temperature um that forms what's
+
+ align:start position:0%
+to room temperature um that forms what's
+ 
+
+ align:start position:0%
+to room temperature um that forms what's
+called a laminate because now you have
+
+ align:start position:0%
+called a laminate because now you have
+ 
+
+ align:start position:0%
+called a laminate because now you have
+the the um the back skin the frame isn't
+
+ align:start position:0%
+the the um the back skin the frame isn't
+ 
+
+ align:start position:0%
+the the um the back skin the frame isn't
+shown right here um you have the back
+
+ align:start position:0%
+shown right here um you have the back
+ 
+
+ align:start position:0%
+shown right here um you have the back
+skin material you have the encapsulant
+
+ align:start position:0%
+skin material you have the encapsulant
+ 
+
+ align:start position:0%
+skin material you have the encapsulant
+the cells the encapsulant on the other
+
+ align:start position:0%
+the cells the encapsulant on the other
+ 
+
+ align:start position:0%
+the cells the encapsulant on the other
+side and your glass on the front side
+
+ align:start position:0%
+side and your glass on the front side
+ 
+
+ align:start position:0%
+side and your glass on the front side
+right all together forming a nice stack
+
+ align:start position:0%
+right all together forming a nice stack
+ 
+
+ align:start position:0%
+right all together forming a nice stack
+of materials and they're stuck together
+
+ align:start position:0%
+of materials and they're stuck together
+ 
+
+ align:start position:0%
+of materials and they're stuck together
+Bound by the encapsulant that's called
+
+ align:start position:0%
+Bound by the encapsulant that's called
+ 
+
+ align:start position:0%
+Bound by the encapsulant that's called
+called the laminate it's it doesn't
+
+ align:start position:0%
+called the laminate it's it doesn't
+ 
+
+ align:start position:0%
+called the laminate it's it doesn't
+resist bending very well or twist very
+
+ align:start position:0%
+resist bending very well or twist very
+ 
+
+ align:start position:0%
+resist bending very well or twist very
+well because it doesn't yet have the
+
+ align:start position:0%
+well because it doesn't yet have the
+ 
+
+ align:start position:0%
+well because it doesn't yet have the
+frame on it but it certainly can be
+
+ align:start position:0%
+frame on it but it certainly can be
+ 
+
+ align:start position:0%
+frame on it but it certainly can be
+transported around a factory and moved
+
+ align:start position:0%
+transported around a factory and moved
+ 
+
+ align:start position:0%
+transported around a factory and moved
+from one station to another without risk
+
+ align:start position:0%
+from one station to another without risk
+ 
+
+ align:start position:0%
+from one station to another without risk
+of saying the cells falling out um
+
+ align:start position:0%
+of saying the cells falling out um
+ 
+
+ align:start position:0%
+of saying the cells falling out um
+they're they're pretty well fused there
+
+ align:start position:0%
+they're they're pretty well fused there
+ 
+
+ align:start position:0%
+they're they're pretty well fused there
+um in terms of of moving to New
+
+ align:start position:0%
+um in terms of of moving to New
+ 
+
+ align:start position:0%
+um in terms of of moving to New
+materials there's a lot of work right
+
+ align:start position:0%
+materials there's a lot of work right
+ 
+
+ align:start position:0%
+materials there's a lot of work right
+now to squeeze the commodity costs out
+
+ align:start position:0%
+now to squeeze the commodity costs out
+ 
+
+ align:start position:0%
+now to squeeze the commodity costs out
+of solar module manufacturing if you
+
+ align:start position:0%
+of solar module manufacturing if you
+ 
+
+ align:start position:0%
+of solar module manufacturing if you
+look at the percentage of cost of
+
+ align:start position:0%
+look at the percentage of cost of
+ 
+
+ align:start position:0%
+look at the percentage of cost of
+commodity materials in the Solar module
+
+ align:start position:0%
+commodity materials in the Solar module
+ 
+
+ align:start position:0%
+commodity materials in the Solar module
+is quite high and so people are focusing
+
+ align:start position:0%
+is quite high and so people are focusing
+ 
+
+ align:start position:0%
+is quite high and so people are focusing
+on new types of transparent front
+
+ align:start position:0%
+on new types of transparent front
+ 
+
+ align:start position:0%
+on new types of transparent front
+surface materials that let the light in
+
+ align:start position:0%
+surface materials that let the light in
+ 
+
+ align:start position:0%
+surface materials that let the light in
+glass Replacements right you could
+
+ align:start position:0%
+glass Replacements right you could
+ 
+
+ align:start position:0%
+glass Replacements right you could
+Envision uh um you you we have many
+
+ align:start position:0%
+Envision uh um you you we have many
+ 
+
+ align:start position:0%
+Envision uh um you you we have many
+examples of really hard resistant
+
+ align:start position:0%
+examples of really hard resistant
+ 
+
+ align:start position:0%
+examples of really hard resistant
+polymeric materials in our daily lives
+
+ align:start position:0%
+polymeric materials in our daily lives
+ 
+
+ align:start position:0%
+polymeric materials in our daily lives
+people are looking into those the
+
+ align:start position:0%
+people are looking into those the
+ 
+
+ align:start position:0%
+people are looking into those the
+encapsulant materials ethinyl acetate is
+
+ align:start position:0%
+encapsulant materials ethinyl acetate is
+ 
+
+ align:start position:0%
+encapsulant materials ethinyl acetate is
+fairly expensive and there aren't that
+
+ align:start position:0%
+fairly expensive and there aren't that
+ 
+
+ align:start position:0%
+fairly expensive and there aren't that
+many companies that manufacture it and
+
+ align:start position:0%
+many companies that manufacture it and
+ 
+
+ align:start position:0%
+many companies that manufacture it and
+so people are looking to options to
+
+ align:start position:0%
+so people are looking to options to
+ 
+
+ align:start position:0%
+so people are looking to options to
+replace it uh tedlar even more so that
+
+ align:start position:0%
+replace it uh tedlar even more so that
+ 
+
+ align:start position:0%
+replace it uh tedlar even more so that
+back skin material although the
+
+ align:start position:0%
+back skin material although the
+ 
+
+ align:start position:0%
+back skin material although the
+challenge there is a lot harder a lot
+
+ align:start position:0%
+challenge there is a lot harder a lot
+ 
+
+ align:start position:0%
+challenge there is a lot harder a lot
+tougher no intendo it's a really strong
+
+ align:start position:0%
+tougher no intendo it's a really strong
+ 
+
+ align:start position:0%
+tougher no intendo it's a really strong
+material um and uh a lot of our uh
+
+ align:start position:0%
+material um and uh a lot of our uh
+ 
+
+ align:start position:0%
+material um and uh a lot of our uh
+Modern Chemistry or or chemical
+
+ align:start position:0%
+Modern Chemistry or or chemical
+ 
+
+ align:start position:0%
+Modern Chemistry or or chemical
+engineering goes into making and
+
+ align:start position:0%
+engineering goes into making and
+ 
+
+ align:start position:0%
+engineering goes into making and
+designing it and then finally finding
+
+ align:start position:0%
+designing it and then finally finding
+ 
+
+ align:start position:0%
+designing it and then finally finding
+some replacement for the frame uh people
+
+ align:start position:0%
+some replacement for the frame uh people
+ 
+
+ align:start position:0%
+some replacement for the frame uh people
+are talking about frameless modules that
+
+ align:start position:0%
+are talking about frameless modules that
+ 
+
+ align:start position:0%
+are talking about frameless modules that
+means taking off this aluminum piece
+
+ align:start position:0%
+means taking off this aluminum piece
+ 
+
+ align:start position:0%
+means taking off this aluminum piece
+right here on the side and just leaving
+
+ align:start position:0%
+right here on the side and just leaving
+ 
+
+ align:start position:0%
+right here on the side and just leaving
+the laminate and somehow providing the
+
+ align:start position:0%
+the laminate and somehow providing the
+ 
+
+ align:start position:0%
+the laminate and somehow providing the
+mechanical rigidity to the laminate uh
+
+ align:start position:0%
+mechanical rigidity to the laminate uh
+ 
+
+ align:start position:0%
+mechanical rigidity to the laminate uh
+and avoiding the cost of the extruded
+
+ align:start position:0%
+and avoiding the cost of the extruded
+ 
+
+ align:start position:0%
+and avoiding the cost of the extruded
+aluminum components so a lot of work
+
+ align:start position:0%
+aluminum components so a lot of work
+ 
+
+ align:start position:0%
+aluminum components so a lot of work
+going in uh in module
+
+ align:start position:0%
+going in uh in module
+ 
+
+ align:start position:0%
+going in uh in module
+Design This is a picture of folks
+
+ align:start position:0%
+Design This is a picture of folks
+ 
+
+ align:start position:0%
+Design This is a picture of folks
+mounting the aluminum framing onto the
+
+ align:start position:0%
+mounting the aluminum framing onto the
+ 
+
+ align:start position:0%
+mounting the aluminum framing onto the
+module uh these are uh these are uh
+
+ align:start position:0%
+module uh these are uh these are uh
+ 
+
+ align:start position:0%
+module uh these are uh these are uh
+essentially U large look like steel
+
+ align:start position:0%
+essentially U large look like steel
+ 
+
+ align:start position:0%
+essentially U large look like steel
+components that are pushing the aluminum
+
+ align:start position:0%
+components that are pushing the aluminum
+ 
+
+ align:start position:0%
+components that are pushing the aluminum
+into the module and uh making sure that
+
+ align:start position:0%
+into the module and uh making sure that
+ 
+
+ align:start position:0%
+into the module and uh making sure that
+there's a snug fit between the aluminum
+
+ align:start position:0%
+there's a snug fit between the aluminum
+ 
+
+ align:start position:0%
+there's a snug fit between the aluminum
+and the module itself as you can see by
+
+ align:start position:0%
+and the module itself as you can see by
+ 
+
+ align:start position:0%
+and the module itself as you can see by
+the size and shapes of these cells that
+
+ align:start position:0%
+the size and shapes of these cells that
+ 
+
+ align:start position:0%
+the size and shapes of these cells that
+gives you an indication of what company
+
+ align:start position:0%
+gives you an indication of what company
+ 
+
+ align:start position:0%
+gives you an indication of what company
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+is um module technology there's there's
+
+ align:start position:0%
+is um module technology there's there's
+ 
+
+ align:start position:0%
+is um module technology there's there's
+uh some work as well going into replace
+
+ align:start position:0%
+uh some work as well going into replace
+ 
+
+ align:start position:0%
+uh some work as well going into replace
+replacing let's see here we go uh
+
+ align:start position:0%
+replacing let's see here we go uh
+ 
+
+ align:start position:0%
+replacing let's see here we go uh
+replacing the tabing stringing step
+
+ align:start position:0%
+replacing the tabing stringing step
+ 
+
+ align:start position:0%
+replacing the tabing stringing step
+right so this is a machine that tabs and
+
+ align:start position:0%
+right so this is a machine that tabs and
+ 
+
+ align:start position:0%
+right so this is a machine that tabs and
+strings the cells to one another we'll
+
+ align:start position:0%
+strings the cells to one another we'll
+ 
+
+ align:start position:0%
+strings the cells to one another we'll
+see one at frown Hopper it's really
+
+ align:start position:0%
+see one at frown Hopper it's really
+ 
+
+ align:start position:0%
+see one at frown Hopper it's really
+impressive When You See It Go but it's
+
+ align:start position:0%
+impressive When You See It Go but it's
+ 
+
+ align:start position:0%
+impressive When You See It Go but it's
+also quite expensive um and so if you
+
+ align:start position:0%
+also quite expensive um and so if you
+ 
+
+ align:start position:0%
+also quite expensive um and so if you
+can get rid of the tabing stringy
+
+ align:start position:0%
+can get rid of the tabing stringy
+ 
+
+ align:start position:0%
+can get rid of the tabing stringy
+imagine just lying up the little cells
+
+ align:start position:0%
+imagine just lying up the little cells
+ 
+
+ align:start position:0%
+imagine just lying up the little cells
+like cookies on a cookie sheet and they
+
+ align:start position:0%
+like cookies on a cookie sheet and they
+ 
+
+ align:start position:0%
+like cookies on a cookie sheet and they
+all are interconnected by contact with
+
+ align:start position:0%
+all are interconnected by contact with
+ 
+
+ align:start position:0%
+all are interconnected by contact with
+whatever Back skin material is on the
+
+ align:start position:0%
+whatever Back skin material is on the
+ 
+
+ align:start position:0%
+whatever Back skin material is on the
+back that is printed let's say with a
+
+ align:start position:0%
+back that is printed let's say with a
+ 
+
+ align:start position:0%
+back that is printed let's say with a
+circuitry already you would wind up in a
+
+ align:start position:0%
+circuitry already you would wind up in a
+ 
+
+ align:start position:0%
+circuitry already you would wind up in a
+situation like this where you have your
+
+ align:start position:0%
+situation like this where you have your
+ 
+
+ align:start position:0%
+situation like this where you have your
+cells and direct contact with some
+
+ align:start position:0%
+cells and direct contact with some
+ 
+
+ align:start position:0%
+cells and direct contact with some
+printed circuitry on your back boom boom
+
+ align:start position:0%
+printed circuitry on your back boom boom
+ 
+
+ align:start position:0%
+printed circuitry on your back boom boom
+boom boom boom and you're off and
+
+ align:start position:0%
+boom boom boom and you're off and
+ 
+
+ align:start position:0%
+boom boom boom and you're off and
+running in this particular case you see
+
+ align:start position:0%
+running in this particular case you see
+ 
+
+ align:start position:0%
+running in this particular case you see
+this these little white dots here um the
+
+ align:start position:0%
+this these little white dots here um the
+ 
+
+ align:start position:0%
+this these little white dots here um the
+grid pattern on that cell is a radial
+
+ align:start position:0%
+grid pattern on that cell is a radial
+ 
+
+ align:start position:0%
+grid pattern on that cell is a radial
+spider pattern that emanates a spider
+
+ align:start position:0%
+spider pattern that emanates a spider
+ 
+
+ align:start position:0%
+spider pattern that emanates a spider
+web pattern that emanates from that
+
+ align:start position:0%
+web pattern that emanates from that
+ 
+
+ align:start position:0%
+web pattern that emanates from that
+Central Point collects current from
+
+ align:start position:0%
+Central Point collects current from
+ 
+
+ align:start position:0%
+Central Point collects current from
+nearby essentially an area about that
+
+ align:start position:0%
+nearby essentially an area about that
+ 
+
+ align:start position:0%
+nearby essentially an area about that
+big is collected let's say by that
+
+ align:start position:0%
+big is collected let's say by that
+ 
+
+ align:start position:0%
+big is collected let's say by that
+little point right there and then
+
+ align:start position:0%
+little point right there and then
+ 
+
+ align:start position:0%
+little point right there and then
+there's a hole drilled through the solar
+
+ align:start position:0%
+there's a hole drilled through the solar
+ 
+
+ align:start position:0%
+there's a hole drilled through the solar
+cell where the metal is wrapping through
+
+ align:start position:0%
+cell where the metal is wrapping through
+ 
+
+ align:start position:0%
+cell where the metal is wrapping through
+to the back and that's where it's making
+
+ align:start position:0%
+to the back and that's where it's making
+ 
+
+ align:start position:0%
+to the back and that's where it's making
+contact with the backside right there
+
+ align:start position:0%
+contact with the backside right there
+ 
+
+ align:start position:0%
+contact with the backside right there
+and then there are other regions of the
+
+ align:start position:0%
+and then there are other regions of the
+ 
+
+ align:start position:0%
+and then there are other regions of the
+solar cell that are uh are making
+
+ align:start position:0%
+solar cell that are uh are making
+ 
+
+ align:start position:0%
+solar cell that are uh are making
+contact with the the the bulk the base
+
+ align:start position:0%
+contact with the the the bulk the base
+ 
+
+ align:start position:0%
+contact with the the the bulk the base
+if you will so you have both of your n
+
+ align:start position:0%
+if you will so you have both of your n
+ 
+
+ align:start position:0%
+if you will so you have both of your n
+and your P type contacts on the back
+
+ align:start position:0%
+and your P type contacts on the back
+ 
+
+ align:start position:0%
+and your P type contacts on the back
+side of your solar cell and that's
+
+ align:start position:0%
+side of your solar cell and that's
+ 
+
+ align:start position:0%
+side of your solar cell and that's
+what's shown in this drawing uh so there
+
+ align:start position:0%
+what's shown in this drawing uh so there
+ 
+
+ align:start position:0%
+what's shown in this drawing uh so there
+are attempts as well to put all of the
+
+ align:start position:0%
+are attempts as well to put all of the
+ 
+
+ align:start position:0%
+are attempts as well to put all of the
+contacts or connect the contacts onto
+
+ align:start position:0%
+contacts or connect the contacts onto
+ 
+
+ align:start position:0%
+contacts or connect the contacts onto
+the back to enable this monolithic uh
+
+ align:start position:0%
+the back to enable this monolithic uh
+ 
+
+ align:start position:0%
+the back to enable this monolithic uh
+manufacturing yes how is that
+
+ align:start position:0%
+manufacturing yes how is that
+ 
+
+ align:start position:0%
+manufacturing yes how is that
+short okay so um how's that not a short
+
+ align:start position:0%
+short okay so um how's that not a short
+ 
+
+ align:start position:0%
+short okay so um how's that not a short
+let me show you how that would not not
+
+ align:start position:0%
+let me show you how that would not not
+ 
+
+ align:start position:0%
+let me show you how that would not not
+be a
+
+ align:start position:0%
+be a
+ 
+
+ align:start position:0%
+be a
+short what I'm going to do is attempt to
+
+ align:start position:0%
+short what I'm going to do is attempt to
+ 
+
+ align:start position:0%
+short what I'm going to do is attempt to
+draw uh two different cell designs that
+
+ align:start position:0%
+draw uh two different cell designs that
+ 
+
+ align:start position:0%
+draw uh two different cell designs that
+um could lead to not
+
+ align:start position:0%
+um could lead to not
+ 
+
+ align:start position:0%
+um could lead to not
+shorting one cell design that could lead
+
+ align:start position:0%
+shorting one cell design that could lead
+ 
+
+ align:start position:0%
+shorting one cell design that could lead
+to not shorting would be let's say this
+
+ align:start position:0%
+to not shorting would be let's say this
+ 
+
+ align:start position:0%
+to not shorting would be let's say this
+would be our front surface um our base
+
+ align:start position:0%
+would be our front surface um our base
+ 
+
+ align:start position:0%
+would be our front surface um our base
+is I'm going to draw it flat here on the
+
+ align:start position:0%
+is I'm going to draw it flat here on the
+ 
+
+ align:start position:0%
+is I'm going to draw it flat here on the
+back just for Simplicity but it could be
+
+ align:start position:0%
+back just for Simplicity but it could be
+ 
+
+ align:start position:0%
+back just for Simplicity but it could be
+textured as well um I'm going to call
+
+ align:start position:0%
+textured as well um I'm going to call
+ 
+
+ align:start position:0%
+textured as well um I'm going to call
+this uh lightly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doped uh lightly doped semiconductor
+
+ align:start position:0%
+doped uh lightly doped semiconductor
+ 
+
+ align:start position:0%
+doped uh lightly doped semiconductor
+material and then I could have heavily
+
+ align:start position:0%
+material and then I could have heavily
+ 
+
+ align:start position:0%
+material and then I could have heavily
+doped um uh let's say U this would be
+
+ align:start position:0%
+doped um uh let's say U this would be
+ 
+
+ align:start position:0%
+doped um uh let's say U this would be
+I'm going to I'm going to exaggerate
+
+ align:start position:0%
+I'm going to I'm going to exaggerate
+ 
+
+ align:start position:0%
+I'm going to I'm going to exaggerate
+here just for for effect this could be
+
+ align:start position:0%
+here just for for effect this could be
+ 
+
+ align:start position:0%
+here just for for effect this could be
+my positively my my heavily n type doped
+
+ align:start position:0%
+my positively my my heavily n type doped
+ 
+
+ align:start position:0%
+my positively my my heavily n type doped
+material this could be my heavily ptype
+
+ align:start position:0%
+material this could be my heavily ptype
+ 
+
+ align:start position:0%
+material this could be my heavily ptype
+doped material so I'm drawing p+ n plus
+
+ align:start position:0%
+doped material so I'm drawing p+ n plus
+ 
+
+ align:start position:0%
+doped material so I'm drawing p+ n plus
+another n plus another p+ right so I
+
+ align:start position:0%
+another n plus another p+ right so I
+ 
+
+ align:start position:0%
+another n plus another p+ right so I
+have um charge separation occurring at
+
+ align:start position:0%
+have um charge separation occurring at
+ 
+
+ align:start position:0%
+have um charge separation occurring at
+these regions right here and then
+
+ align:start position:0%
+these regions right here and then
+ 
+
+ align:start position:0%
+these regions right here and then
+contacts on the other side this is my
+
+ align:start position:0%
+contacts on the other side this is my
+ 
+
+ align:start position:0%
+contacts on the other side this is my
+electron contact this is my ho contact
+
+ align:start position:0%
+electron contact this is my ho contact
+ 
+
+ align:start position:0%
+electron contact this is my ho contact
+this is my electron contact this is my
+
+ align:start position:0%
+this is my electron contact this is my
+ 
+
+ align:start position:0%
+this is my electron contact this is my
+ho contact and now what's happening is
+
+ align:start position:0%
+ho contact and now what's happening is
+ 
+
+ align:start position:0%
+ho contact and now what's happening is
+charge separate or photo excited
+
+ align:start position:0%
+charge separate or photo excited
+ 
+
+ align:start position:0%
+charge separate or photo excited
+carriers are being generated in here but
+
+ align:start position:0%
+carriers are being generated in here but
+ 
+
+ align:start position:0%
+carriers are being generated in here but
+the field that separates them is all in
+
+ align:start position:0%
+the field that separates them is all in
+ 
+
+ align:start position:0%
+the field that separates them is all in
+the back and so now the carriers are
+
+ align:start position:0%
+the back and so now the carriers are
+ 
+
+ align:start position:0%
+the back and so now the carriers are
+being separated electrons being
+
+ align:start position:0%
+being separated electrons being
+ 
+
+ align:start position:0%
+being separated electrons being
+collected by the dark or shaded rather
+
+ align:start position:0%
+collected by the dark or shaded rather
+ 
+
+ align:start position:0%
+collected by the dark or shaded rather
+the shaded areas and the holes being
+
+ align:start position:0%
+the shaded areas and the holes being
+ 
+
+ align:start position:0%
+the shaded areas and the holes being
+collected by these unshaded contacts
+
+ align:start position:0%
+collected by these unshaded contacts
+ 
+
+ align:start position:0%
+collected by these unshaded contacts
+here in the back and if I'm clever about
+
+ align:start position:0%
+here in the back and if I'm clever about
+ 
+
+ align:start position:0%
+here in the back and if I'm clever about
+my contact positioning right here I have
+
+ align:start position:0%
+my contact positioning right here I have
+ 
+
+ align:start position:0%
+my contact positioning right here I have
+a kind of an interdigitated P or
+
+ align:start position:0%
+a kind of an interdigitated P or
+ 
+
+ align:start position:0%
+a kind of an interdigitated P or
+electron and whole collectors right I'm
+
+ align:start position:0%
+electron and whole collectors right I'm
+ 
+
+ align:start position:0%
+electron and whole collectors right I'm
+able to uh collect both without having
+
+ align:start position:0%
+able to uh collect both without having
+ 
+
+ align:start position:0%
+able to uh collect both without having
+any sort of shunting another design
+
+ align:start position:0%
+any sort of shunting another design
+ 
+
+ align:start position:0%
+any sort of shunting another design
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+be let's see so this is called an in
+
+ align:start position:0%
+be let's see so this is called an in
+ 
+
+ align:start position:0%
+be let's see so this is called an in
+digitated back contact structure or
+
+ align:start position:0%
+digitated back contact structure or
+ 
+
+ align:start position:0%
+digitated back contact structure or
+IBC um actually less relevant in that in
+
+ align:start position:0%
+IBC um actually less relevant in that in
+ 
+
+ align:start position:0%
+IBC um actually less relevant in that in
+in in this particular case in most in
+
+ align:start position:0%
+in in this particular case in most in
+ 
+
+ align:start position:0%
+in in this particular case in most in
+most in digitated back Conta cells it's
+
+ align:start position:0%
+most in digitated back Conta cells it's
+ 
+
+ align:start position:0%
+most in digitated back Conta cells it's
+it's actually an N type silicon lightly
+
+ align:start position:0%
+it's actually an N type silicon lightly
+ 
+
+ align:start position:0%
+it's actually an N type silicon lightly
+doped n type silicon just because Point
+
+ align:start position:0%
+doped n type silicon just because Point
+ 
+
+ align:start position:0%
+doped n type silicon just because Point
+defects tend to have smaller capture
+
+ align:start position:0%
+defects tend to have smaller capture
+ 
+
+ align:start position:0%
+defects tend to have smaller capture
+cross-section an N type silicon and
+
+ align:start position:0%
+cross-section an N type silicon and
+ 
+
+ align:start position:0%
+cross-section an N type silicon and
+ptype silicon so minority care lifetime
+
+ align:start position:0%
+ptype silicon so minority care lifetime
+ 
+
+ align:start position:0%
+ptype silicon so minority care lifetime
+tends to be larger another uh cell
+
+ align:start position:0%
+tends to be larger another uh cell
+ 
+
+ align:start position:0%
+tends to be larger another uh cell
+design again looking in cross-section
+
+ align:start position:0%
+design again looking in cross-section
+ 
+
+ align:start position:0%
+design again looking in cross-section
+you might have uh here this being your
+
+ align:start position:0%
+you might have uh here this being your
+ 
+
+ align:start position:0%
+you might have uh here this being your
+solar cell um you could add texture but
+
+ align:start position:0%
+solar cell um you could add texture but
+ 
+
+ align:start position:0%
+solar cell um you could add texture but
+I'm emitting it just for for Simplicity
+
+ align:start position:0%
+I'm emitting it just for for Simplicity
+ 
+
+ align:start position:0%
+I'm emitting it just for for Simplicity
+uh now let's see we um we drill a hole
+
+ align:start position:0%
+uh now let's see we um we drill a hole
+ 
+
+ align:start position:0%
+uh now let's see we um we drill a hole
+using a laser right here so we have a
+
+ align:start position:0%
+using a laser right here so we have a
+ 
+
+ align:start position:0%
+using a laser right here so we have a
+very thin hole um of course the in three
+
+ align:start position:0%
+very thin hole um of course the in three
+ 
+
+ align:start position:0%
+very thin hole um of course the in three
+dimensions there's mechanical rigidity
+
+ align:start position:0%
+dimensions there's mechanical rigidity
+ 
+
+ align:start position:0%
+dimensions there's mechanical rigidity
+by the bulk of the material in the other
+
+ align:start position:0%
+by the bulk of the material in the other
+ 
+
+ align:start position:0%
+by the bulk of the material in the other
+dimension but we have this whole drilled
+
+ align:start position:0%
+dimension but we have this whole drilled
+ 
+
+ align:start position:0%
+dimension but we have this whole drilled
+through and we can make about 18,000 of
+
+ align:start position:0%
+through and we can make about 18,000 of
+ 
+
+ align:start position:0%
+through and we can make about 18,000 of
+these holes in about 6 seconds with
+
+ align:start position:0%
+these holes in about 6 seconds with
+ 
+
+ align:start position:0%
+these holes in about 6 seconds with
+modern Laser Technology so it's really
+
+ align:start position:0%
+modern Laser Technology so it's really
+ 
+
+ align:start position:0%
+modern Laser Technology so it's really
+not that hard and and and in to to make
+
+ align:start position:0%
+not that hard and and and in to to make
+ 
+
+ align:start position:0%
+not that hard and and and in to to make
+this uh happen although a lot of
+
+ align:start position:0%
+this uh happen although a lot of
+ 
+
+ align:start position:0%
+this uh happen although a lot of
+engineering effort is is put into it but
+
+ align:start position:0%
+engineering effort is is put into it but
+ 
+
+ align:start position:0%
+engineering effort is is put into it but
+it is possible and then you could have
+
+ align:start position:0%
+it is possible and then you could have
+ 
+
+ align:start position:0%
+it is possible and then you could have
+your contact metalization say for
+
+ align:start position:0%
+your contact metalization say for
+ 
+
+ align:start position:0%
+your contact metalization say for
+electrons right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here um you could have the PN
+
+ align:start position:0%
+here um you could have the PN
+ 
+
+ align:start position:0%
+here um you could have the PN
+Junction like
+
+ align:start position:0%
+Junction like
+ 
+
+ align:start position:0%
+Junction like
+this so This Here could be your n Plus
+
+ align:start position:0%
+this so This Here could be your n Plus
+ 
+
+ align:start position:0%
+this so This Here could be your n Plus
+material again n plus material this by
+
+ align:start position:0%
+material again n plus material this by
+ 
+
+ align:start position:0%
+material again n plus material this by
+uh effect would also be and you could
+
+ align:start position:0%
+uh effect would also be and you could
+ 
+
+ align:start position:0%
+uh effect would also be and you could
+have your P materials over here um and
+
+ align:start position:0%
+have your P materials over here um and
+ 
+
+ align:start position:0%
+have your P materials over here um and
+you can make contact to the back right
+
+ align:start position:0%
+you can make contact to the back right
+ 
+
+ align:start position:0%
+you can make contact to the back right
+here and contact to the back right here
+
+ align:start position:0%
+here and contact to the back right here
+ 
+
+ align:start position:0%
+here and contact to the back right here
+and as long as there's no uh short or
+
+ align:start position:0%
+and as long as there's no uh short or
+ 
+
+ align:start position:0%
+and as long as there's no uh short or
+metal short between the electron and
+
+ align:start position:0%
+metal short between the electron and
+ 
+
+ align:start position:0%
+metal short between the electron and
+hole you say for example you generate an
+
+ align:start position:0%
+hole you say for example you generate an
+ 
+
+ align:start position:0%
+hole you say for example you generate an
+electron hole pair here the electron
+
+ align:start position:0%
+electron hole pair here the electron
+ 
+
+ align:start position:0%
+electron hole pair here the electron
+goes up to here it goes through the
+
+ align:start position:0%
+goes up to here it goes through the
+ 
+
+ align:start position:0%
+goes up to here it goes through the
+metal to the back and gets pulled out
+
+ align:start position:0%
+metal to the back and gets pulled out
+ 
+
+ align:start position:0%
+metal to the back and gets pulled out
+and the hole goes to this contact over
+
+ align:start position:0%
+and the hole goes to this contact over
+ 
+
+ align:start position:0%
+and the hole goes to this contact over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and that's how you separate the charges
+
+ align:start position:0%
+and that's how you separate the charges
+ 
+
+ align:start position:0%
+and that's how you separate the charges
+so this would be an example of uh an
+
+ align:start position:0%
+so this would be an example of uh an
+ 
+
+ align:start position:0%
+so this would be an example of uh an
+emitter wrap through or metal wrap
+
+ align:start position:0%
+emitter wrap through or metal wrap
+ 
+
+ align:start position:0%
+emitter wrap through or metal wrap
+through uh device
+
+ align:start position:0%
+through uh device
+ 
+
+ align:start position:0%
+through uh device
+technology also shown mwt metal wrap
+
+ align:start position:0%
+technology also shown mwt metal wrap
+ 
+
+ align:start position:0%
+technology also shown mwt metal wrap
+through um so we have at least two
+
+ align:start position:0%
+through um so we have at least two
+ 
+
+ align:start position:0%
+through um so we have at least two
+different device geometries and and many
+
+ align:start position:0%
+different device geometries and and many
+ 
+
+ align:start position:0%
+different device geometries and and many
+more many more device architectures that
+
+ align:start position:0%
+more many more device architectures that
+ 
+
+ align:start position:0%
+more many more device architectures that
+could fit in with this uh Future Vision
+
+ align:start position:0%
+could fit in with this uh Future Vision
+ 
+
+ align:start position:0%
+could fit in with this uh Future Vision
+the problem right now is that the
+
+ align:start position:0%
+the problem right now is that the
+ 
+
+ align:start position:0%
+the problem right now is that the
+printed uh back skin materials cost
+
+ align:start position:0%
+printed uh back skin materials cost
+ 
+
+ align:start position:0%
+printed uh back skin materials cost
+about five times more than the
+
+ align:start position:0%
+about five times more than the
+ 
+
+ align:start position:0%
+about five times more than the
+non-printed ones just because they're
+
+ align:start position:0%
+non-printed ones just because they're
+ 
+
+ align:start position:0%
+non-printed ones just because they're
+very low scale uh people haven't inv
+
+ align:start position:0%
+very low scale uh people haven't inv
+ 
+
+ align:start position:0%
+very low scale uh people haven't inv
+investigated it much so anytime you
+
+ align:start position:0%
+investigated it much so anytime you
+ 
+
+ align:start position:0%
+investigated it much so anytime you
+introduce a new technology into the
+
+ align:start position:0%
+introduce a new technology into the
+ 
+
+ align:start position:0%
+introduce a new technology into the
+market you'll hear it over and over
+
+ align:start position:0%
+market you'll hear it over and over
+ 
+
+ align:start position:0%
+market you'll hear it over and over
+again in these Innovation and
+
+ align:start position:0%
+again in these Innovation and
+ 
+
+ align:start position:0%
+again in these Innovation and
+Entrepreneurship classes here at MIT you
+
+ align:start position:0%
+Entrepreneurship classes here at MIT you
+ 
+
+ align:start position:0%
+Entrepreneurship classes here at MIT you
+have to be significantly better than the
+
+ align:start position:0%
+have to be significantly better than the
+ 
+
+ align:start position:0%
+have to be significantly better than the
+competition if you're only a little bit
+
+ align:start position:0%
+competition if you're only a little bit
+ 
+
+ align:start position:0%
+competition if you're only a little bit
+better you face an enormous barrier to
+
+ align:start position:0%
+better you face an enormous barrier to
+ 
+
+ align:start position:0%
+better you face an enormous barrier to
+entry because you have the rest of the
+
+ align:start position:0%
+entry because you have the rest of the
+ 
+
+ align:start position:0%
+entry because you have the rest of the
+industry pedaling Along on their
+
+ align:start position:0%
+industry pedaling Along on their
+ 
+
+ align:start position:0%
+industry pedaling Along on their
+bicycles in a huge pelaton benefiting
+
+ align:start position:0%
+bicycles in a huge pelaton benefiting
+ 
+
+ align:start position:0%
+bicycles in a huge pelaton benefiting
+from each other's Drafting and you're on
+
+ align:start position:0%
+from each other's Drafting and you're on
+ 
+
+ align:start position:0%
+from each other's Drafting and you're on
+your own bike facing your own headwinds
+
+ align:start position:0%
+your own bike facing your own headwinds
+ 
+
+ align:start position:0%
+your own bike facing your own headwinds
+right trying to build everything up your
+
+ align:start position:0%
+right trying to build everything up your
+ 
+
+ align:start position:0%
+right trying to build everything up your
+own Factory your own expertise it's
+
+ align:start position:0%
+own Factory your own expertise it's
+ 
+
+ align:start position:0%
+own Factory your own expertise it's
+challenging but not to say I'm I'm not
+
+ align:start position:0%
+challenging but not to say I'm I'm not
+ 
+
+ align:start position:0%
+challenging but not to say I'm I'm not
+putting trying to put put a damper on
+
+ align:start position:0%
+putting trying to put put a damper on
+ 
+
+ align:start position:0%
+putting trying to put put a damper on
+Innovation I'm just trying to qualify
+
+ align:start position:0%
+Innovation I'm just trying to qualify
+ 
+
+ align:start position:0%
+Innovation I'm just trying to qualify
+the areas of greatest opportunity and
+
+ align:start position:0%
+the areas of greatest opportunity and
+ 
+
+ align:start position:0%
+the areas of greatest opportunity and
+lowest resistance to to change but go
+
+ align:start position:0%
+lowest resistance to to change but go
+ 
+
+ align:start position:0%
+lowest resistance to to change but go
+ahead prove me wrong make make a
+
+ align:start position:0%
+ahead prove me wrong make make a
+ 
+
+ align:start position:0%
+ahead prove me wrong make make a
+difference um the uh with with without
+
+ align:start position:0%
+difference um the uh with with without
+ 
+
+ align:start position:0%
+difference um the uh with with without
+that sort of Headstrong uh mentality of
+
+ align:start position:0%
+that sort of Headstrong uh mentality of
+ 
+
+ align:start position:0%
+that sort of Headstrong uh mentality of
+gosh I know I have something here and
+
+ align:start position:0%
+gosh I know I have something here and
+ 
+
+ align:start position:0%
+gosh I know I have something here and
+I'm just going to prove the world that I
+
+ align:start position:0%
+I'm just going to prove the world that I
+ 
+
+ align:start position:0%
+I'm just going to prove the world that I
+have it we wouldn't have for example the
+
+ align:start position:0%
+have it we wouldn't have for example the
+ 
+
+ align:start position:0%
+have it we wouldn't have for example the
+Pilkington plate glass process working
+
+ align:start position:0%
+Pilkington plate glass process working
+ 
+
+ align:start position:0%
+Pilkington plate glass process working
+or float glass process sorry um we'd
+
+ align:start position:0%
+or float glass process sorry um we'd
+ 
+
+ align:start position:0%
+or float glass process sorry um we'd
+still probably be pouring and grinding
+
+ align:start position:0%
+still probably be pouring and grinding
+ 
+
+ align:start position:0%
+still probably be pouring and grinding
+and polishing our panes of glass and
+
+ align:start position:0%
+and polishing our panes of glass and
+ 
+
+ align:start position:0%
+and polishing our panes of glass and
+they'd be very expensive um that was a a
+
+ align:start position:0%
+they'd be very expensive um that was a a
+ 
+
+ align:start position:0%
+they'd be very expensive um that was a a
+a little side story but it took them
+
+ align:start position:0%
+a little side story but it took them
+ 
+
+ align:start position:0%
+a little side story but it took them
+about 10 years to develop the the float
+
+ align:start position:0%
+about 10 years to develop the the float
+ 
+
+ align:start position:0%
+about 10 years to develop the the float
+glass process inside of a company owned
+
+ align:start position:0%
+glass process inside of a company owned
+ 
+
+ align:start position:0%
+glass process inside of a company owned
+by a family as opposed to publicly
+
+ align:start position:0%
+by a family as opposed to publicly
+ 
+
+ align:start position:0%
+by a family as opposed to publicly
+traded company so they could continue
+
+ align:start position:0%
+traded company so they could continue
+ 
+
+ align:start position:0%
+traded company so they could continue
+losing money over a long period of time
+
+ align:start position:0%
+losing money over a long period of time
+ 
+
+ align:start position:0%
+losing money over a long period of time
+until they perfected it once they got it
+
+ align:start position:0%
+until they perfected it once they got it
+ 
+
+ align:start position:0%
+until they perfected it once they got it
+right the whole world copied it but it
+
+ align:start position:0%
+right the whole world copied it but it
+ 
+
+ align:start position:0%
+right the whole world copied it but it
+took 10 years of of good investment for
+
+ align:start position:0%
+took 10 years of of good investment for
+ 
+
+ align:start position:0%
+took 10 years of of good investment for
+them to get it right all right um let's
+
+ align:start position:0%
+them to get it right all right um let's
+ 
+
+ align:start position:0%
+them to get it right all right um let's
+move on uh we're going to talk about
+
+ align:start position:0%
+move on uh we're going to talk about
+ 
+
+ align:start position:0%
+move on uh we're going to talk about
+module spec sheets here um you when you
+
+ align:start position:0%
+module spec sheets here um you when you
+ 
+
+ align:start position:0%
+module spec sheets here um you when you
+came into class today you should have
+
+ align:start position:0%
+came into class today you should have
+ 
+
+ align:start position:0%
+came into class today you should have
+picked up one of
+
+ align:start position:0%
+picked up one of
+ 
+
+ align:start position:0%
+picked up one of
+these uh this is an example of a First
+
+ align:start position:0%
+these uh this is an example of a First
+ 
+
+ align:start position:0%
+these uh this is an example of a First
+Solar module spec sheet um what it does
+
+ align:start position:0%
+Solar module spec sheet um what it does
+ 
+
+ align:start position:0%
+Solar module spec sheet um what it does
+hits you front and center the company
+
+ align:start position:0%
+hits you front and center the company
+ 
+
+ align:start position:0%
+hits you front and center the company
+name for solar uh FS Series 3 that's the
+
+ align:start position:0%
+name for solar uh FS Series 3 that's the
+ 
+
+ align:start position:0%
+name for solar uh FS Series 3 that's the
+name of the module and PV module so uh
+
+ align:start position:0%
+name of the module and PV module so uh
+ 
+
+ align:start position:0%
+name of the module and PV module so uh
+it gives you the mechanical description
+
+ align:start position:0%
+it gives you the mechanical description
+ 
+
+ align:start position:0%
+it gives you the mechanical description
+the size the weight um and then on the
+
+ align:start position:0%
+the size the weight um and then on the
+ 
+
+ align:start position:0%
+the size the weight um and then on the
+back it gives you all the technical
+
+ align:start position:0%
+back it gives you all the technical
+ 
+
+ align:start position:0%
+back it gives you all the technical
+parameters that you've wanted so on the
+
+ align:start position:0%
+parameters that you've wanted so on the
+ 
+
+ align:start position:0%
+parameters that you've wanted so on the
+back side of the let's see we'll go to
+
+ align:start position:0%
+back side of the let's see we'll go to
+ 
+
+ align:start position:0%
+back side of the let's see we'll go to
+the go to the First Solar spec okay well
+
+ align:start position:0%
+the go to the First Solar spec okay well
+ 
+
+ align:start position:0%
+the go to the First Solar spec okay well
+um on your spec sheet right here you can
+
+ align:start position:0%
+um on your spec sheet right here you can
+ 
+
+ align:start position:0%
+um on your spec sheet right here you can
+look at some of the parameters there's
+
+ align:start position:0%
+look at some of the parameters there's
+ 
+
+ align:start position:0%
+look at some of the parameters there's
+power at the maximum PowerPoint voltage
+
+ align:start position:0%
+power at the maximum PowerPoint voltage
+ 
+
+ align:start position:0%
+power at the maximum PowerPoint voltage
+and current at the maximum PowerPoint um
+
+ align:start position:0%
+and current at the maximum PowerPoint um
+ 
+
+ align:start position:0%
+and current at the maximum PowerPoint um
+the vocc the ISC and so forth you have a
+
+ align:start position:0%
+the vocc the ISC and so forth you have a
+ 
+
+ align:start position:0%
+the vocc the ISC and so forth you have a
+bunch of different parameters including
+
+ align:start position:0%
+bunch of different parameters including
+ 
+
+ align:start position:0%
+bunch of different parameters including
+the temperature uh sensitivity right how
+
+ align:start position:0%
+the temperature uh sensitivity right how
+ 
+
+ align:start position:0%
+the temperature uh sensitivity right how
+much does the power degrade with
+
+ align:start position:0%
+much does the power degrade with
+ 
+
+ align:start position:0%
+much does the power degrade with
+increasing temperature so all of these
+
+ align:start position:0%
+increasing temperature so all of these
+ 
+
+ align:start position:0%
+increasing temperature so all of these
+things we studied in class and now when
+
+ align:start position:0%
+things we studied in class and now when
+ 
+
+ align:start position:0%
+things we studied in class and now when
+you pick up the spec sheet you're a pro
+
+ align:start position:0%
+you pick up the spec sheet you're a pro
+ 
+
+ align:start position:0%
+you pick up the spec sheet you're a pro
+you look at it you're like oh yeah I
+
+ align:start position:0%
+you look at it you're like oh yeah I
+ 
+
+ align:start position:0%
+you look at it you're like oh yeah I
+know what that does I know what that
+
+ align:start position:0%
+know what that does I know what that
+ 
+
+ align:start position:0%
+know what that does I know what that
+means I know how to model the the energy
+
+ align:start position:0%
+means I know how to model the the energy
+ 
+
+ align:start position:0%
+means I know how to model the the energy
+output of the system and um and that's
+
+ align:start position:0%
+output of the system and um and that's
+ 
+
+ align:start position:0%
+output of the system and um and that's
+essentially what the engineers do when
+
+ align:start position:0%
+essentially what the engineers do when
+ 
+
+ align:start position:0%
+essentially what the engineers do when
+they pick up a spec sheet uh they read
+
+ align:start position:0%
+they pick up a spec sheet uh they read
+ 
+
+ align:start position:0%
+they pick up a spec sheet uh they read
+it and then they input those parameters
+
+ align:start position:0%
+it and then they input those parameters
+ 
+
+ align:start position:0%
+it and then they input those parameters
+into their computer models and they can
+
+ align:start position:0%
+into their computer models and they can
+ 
+
+ align:start position:0%
+into their computer models and they can
+predict how this these modules will
+
+ align:start position:0%
+predict how this these modules will
+ 
+
+ align:start position:0%
+predict how this these modules will
+perform out in the field at a given
+
+ align:start position:0%
+perform out in the field at a given
+ 
+
+ align:start position:0%
+perform out in the field at a given
+location okay and so you have a variety
+
+ align:start position:0%
+location okay and so you have a variety
+ 
+
+ align:start position:0%
+location okay and so you have a variety
+of different spec sheets these are the
+
+ align:start position:0%
+of different spec sheets these are the
+ 
+
+ align:start position:0%
+of different spec sheets these are the
+the modules that are on my roof uh
+
+ align:start position:0%
+the modules that are on my roof uh
+ 
+
+ align:start position:0%
+the modules that are on my roof uh
+they're sharp 187 watt modules um you
+
+ align:start position:0%
+they're sharp 187 watt modules um you
+ 
+
+ align:start position:0%
+they're sharp 187 watt modules um you
+have for example uh right here an
+
+ align:start position:0%
+have for example uh right here an
+ 
+
+ align:start position:0%
+have for example uh right here an
+example of an evergreen solar module
+
+ align:start position:0%
+example of an evergreen solar module
+ 
+
+ align:start position:0%
+example of an evergreen solar module
+let's let's spend a minute here looking
+
+ align:start position:0%
+let's let's spend a minute here looking
+ 
+
+ align:start position:0%
+let's let's spend a minute here looking
+a little more deeply um these modules
+
+ align:start position:0%
+a little more deeply um these modules
+ 
+
+ align:start position:0%
+a little more deeply um these modules
+these solar modules are the same size
+
+ align:start position:0%
+these solar modules are the same size
+ 
+
+ align:start position:0%
+these solar modules are the same size
+but they're three different uh three
+
+ align:start position:0%
+but they're three different uh three
+ 
+
+ align:start position:0%
+but they're three different uh three
+different Power outputs and I think we
+
+ align:start position:0%
+different Power outputs and I think we
+ 
+
+ align:start position:0%
+different Power outputs and I think we
+went through this already right we have
+
+ align:start position:0%
+went through this already right we have
+ 
+
+ align:start position:0%
+went through this already right we have
+good cells medium cells and bad cells
+
+ align:start position:0%
+good cells medium cells and bad cells
+ 
+
+ align:start position:0%
+good cells medium cells and bad cells
+and they're Bend together in the
+
+ align:start position:0%
+and they're Bend together in the
+ 
+
+ align:start position:0%
+and they're Bend together in the
+different modules so that they can
+
+ align:start position:0%
+different modules so that they can
+ 
+
+ align:start position:0%
+different modules so that they can
+extract the maximum price from the
+
+ align:start position:0%
+extract the maximum price from the
+ 
+
+ align:start position:0%
+extract the maximum price from the
+consumer right so that's why you have
+
+ align:start position:0%
+consumer right so that's why you have
+ 
+
+ align:start position:0%
+consumer right so that's why you have
+the three different uh ratings of power
+
+ align:start position:0%
+the three different uh ratings of power
+ 
+
+ align:start position:0%
+the three different uh ratings of power
+for three different types of modules
+
+ align:start position:0%
+for three different types of modules
+ 
+
+ align:start position:0%
+for three different types of modules
+with essentially the same form factor
+
+ align:start position:0%
+with essentially the same form factor
+ 
+
+ align:start position:0%
+with essentially the same form factor
+the same size and weight they're just
+
+ align:start position:0%
+the same size and weight they're just
+ 
+
+ align:start position:0%
+the same size and weight they're just
+different quality
+
+ align:start position:0%
+different quality
+ 
+
+ align:start position:0%
+different quality
+cells yep so that's that's that
+
+ align:start position:0%
+cells yep so that's that's that
+ 
+
+ align:start position:0%
+cells yep so that's that's that
+temperature coefficients
+
+ align:start position:0%
+temperature coefficients
+ 
+
+ align:start position:0%
+temperature coefficients
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+forth okay um one thing to note right
+
+ align:start position:0%
+forth okay um one thing to note right
+ 
+
+ align:start position:0%
+forth okay um one thing to note right
+here is uh on the back sides of your
+
+ align:start position:0%
+here is uh on the back sides of your
+ 
+
+ align:start position:0%
+here is uh on the back sides of your
+modules you typically have a little
+
+ align:start position:0%
+modules you typically have a little
+ 
+
+ align:start position:0%
+modules you typically have a little
+diagram that shows you how to
+
+ align:start position:0%
+diagram that shows you how to
+ 
+
+ align:start position:0%
+diagram that shows you how to
+interconnect one module to the next and
+
+ align:start position:0%
+interconnect one module to the next and
+ 
+
+ align:start position:0%
+interconnect one module to the next and
+those are the cables that are used uh to
+
+ align:start position:0%
+those are the cables that are used uh to
+ 
+
+ align:start position:0%
+those are the cables that are used uh to
+do the interconnection there are some
+
+ align:start position:0%
+do the interconnection there are some
+ 
+
+ align:start position:0%
+do the interconnection there are some
+companies trying to get fancy right now
+
+ align:start position:0%
+companies trying to get fancy right now
+ 
+
+ align:start position:0%
+companies trying to get fancy right now
+and saying well you know instead of uh
+
+ align:start position:0%
+and saying well you know instead of uh
+ 
+
+ align:start position:0%
+and saying well you know instead of uh
+interconnecting and then uh affixing the
+
+ align:start position:0%
+interconnecting and then uh affixing the
+ 
+
+ align:start position:0%
+interconnecting and then uh affixing the
+modules separately why don't we just
+
+ align:start position:0%
+modules separately why don't we just
+ 
+
+ align:start position:0%
+modules separately why don't we just
+make these modules that kind of click
+
+ align:start position:0%
+make these modules that kind of click
+ 
+
+ align:start position:0%
+make these modules that kind of click
+together and part of the clicking
+
+ align:start position:0%
+together and part of the clicking
+ 
+
+ align:start position:0%
+together and part of the clicking
+process is the interconnection
+
+ align:start position:0%
+process is the interconnection
+ 
+
+ align:start position:0%
+process is the interconnection
+electrically and the other part
+
+ align:start position:0%
+electrically and the other part
+ 
+
+ align:start position:0%
+electrically and the other part
+obviously is the mechanical rigidity so
+
+ align:start position:0%
+obviously is the mechanical rigidity so
+ 
+
+ align:start position:0%
+obviously is the mechanical rigidity so
+there there's certainly room for
+
+ align:start position:0%
+there there's certainly room for
+ 
+
+ align:start position:0%
+there there's certainly room for
+optimization on module
+
+ align:start position:0%
+optimization on module
+ 
+
+ align:start position:0%
+optimization on module
+design yeah Jessica when they're sold
+
+ align:start position:0%
+design yeah Jessica when they're sold
+ 
+
+ align:start position:0%
+design yeah Jessica when they're sold
+when the modules are sold they're
+
+ align:start position:0%
+when the modules are sold they're
+ 
+
+ align:start position:0%
+when the modules are sold they're
+advertised for their voltage at maximum
+
+ align:start position:0%
+advertised for their voltage at maximum
+ 
+
+ align:start position:0%
+advertised for their voltage at maximum
+power what's the software that we should
+
+ align:start position:0%
+power what's the software that we should
+ 
+
+ align:start position:0%
+power what's the software that we should
+use I'm actually using this from another
+
+ align:start position:0%
+use I'm actually using this from another
+ 
+
+ align:start position:0%
+use I'm actually using this from another
+class what's the software that we should
+
+ align:start position:0%
+class what's the software that we should
+ 
+
+ align:start position:0%
+class what's the software that we should
+use to use that maximum power point
+
+ align:start position:0%
+use to use that maximum power point
+ 
+
+ align:start position:0%
+use to use that maximum power point
+voltage into translate that into what
+
+ align:start position:0%
+voltage into translate that into what
+ 
+
+ align:start position:0%
+voltage into translate that into what
+it's actually going to be you know hours
+
+ align:start position:0%
+it's actually going to be you know hours
+ 
+
+ align:start position:0%
+it's actually going to be you know hours
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+something okay so um
+
+ align:start position:0%
+something okay so um
+ 
+
+ align:start position:0%
+something okay so um
+the the question became how do I go from
+
+ align:start position:0%
+the the question became how do I go from
+ 
+
+ align:start position:0%
+the the question became how do I go from
+a module spec sheet like this um with
+
+ align:start position:0%
+a module spec sheet like this um with
+ 
+
+ align:start position:0%
+a module spec sheet like this um with
+with this data right here and translate
+
+ align:start position:0%
+with this data right here and translate
+ 
+
+ align:start position:0%
+with this data right here and translate
+that into number of kilowatt hours
+
+ align:start position:0%
+that into number of kilowatt hours
+ 
+
+ align:start position:0%
+that into number of kilowatt hours
+produced per unit time a day a year um
+
+ align:start position:0%
+produced per unit time a day a year um
+ 
+
+ align:start position:0%
+produced per unit time a day a year um
+at a given site location the best
+
+ align:start position:0%
+at a given site location the best
+ 
+
+ align:start position:0%
+at a given site location the best
+program that I know of to to to that
+
+ align:start position:0%
+program that I know of to to to that
+ 
+
+ align:start position:0%
+program that I know of to to to that
+encompasses all of this would be a
+
+ align:start position:0%
+encompasses all of this would be a
+ 
+
+ align:start position:0%
+encompasses all of this would be a
+program called PV Watts produced by enal
+
+ align:start position:0%
+program called PV Watts produced by enal
+ 
+
+ align:start position:0%
+program called PV Watts produced by enal
+PV Watts Al together and uh you can look
+
+ align:start position:0%
+PV Watts Al together and uh you can look
+ 
+
+ align:start position:0%
+PV Watts Al together and uh you can look
+it up you can use it online and you can
+
+ align:start position:0%
+it up you can use it online and you can
+ 
+
+ align:start position:0%
+it up you can use it online and you can
+input uh your specific mod module spec
+
+ align:start position:0%
+input uh your specific mod module spec
+ 
+
+ align:start position:0%
+input uh your specific mod module spec
+parameters into the uh into the program
+
+ align:start position:0%
+parameters into the uh into the program
+ 
+
+ align:start position:0%
+parameters into the uh into the program
+now that said we have a lot of the tools
+
+ align:start position:0%
+now that said we have a lot of the tools
+ 
+
+ align:start position:0%
+now that said we have a lot of the tools
+to do the estimates ourselves if you uh
+
+ align:start position:0%
+to do the estimates ourselves if you uh
+ 
+
+ align:start position:0%
+to do the estimates ourselves if you uh
+ruffle back to homework I think it was
+
+ align:start position:0%
+ruffle back to homework I think it was
+ 
+
+ align:start position:0%
+ruffle back to homework I think it was
+homework number two uh we calculated the
+
+ align:start position:0%
+homework number two uh we calculated the
+ 
+
+ align:start position:0%
+homework number two uh we calculated the
+output of a solar system based on uh the
+
+ align:start position:0%
+output of a solar system based on uh the
+ 
+
+ align:start position:0%
+output of a solar system based on uh the
+module spec parameters and so now that
+
+ align:start position:0%
+module spec parameters and so now that
+ 
+
+ align:start position:0%
+module spec parameters and so now that
+we we uh can pick up a module spec sheet
+
+ align:start position:0%
+we we uh can pick up a module spec sheet
+ 
+
+ align:start position:0%
+we we uh can pick up a module spec sheet
+and read it in a bit more detail we can
+
+ align:start position:0%
+and read it in a bit more detail we can
+ 
+
+ align:start position:0%
+and read it in a bit more detail we can
+perform those estimates a little bit
+
+ align:start position:0%
+perform those estimates a little bit
+ 
+
+ align:start position:0%
+perform those estimates a little bit
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+accurately y
+
+ align:start position:0%
+accurately y
+ 
+
+ align:start position:0%
+accurately y
+firstar panel is a lot
+
+ align:start position:0%
+firstar panel is a lot
+ 
+
+ align:start position:0%
+firstar panel is a lot
+there yep so is there reason why First
+
+ align:start position:0%
+there yep so is there reason why First
+ 
+
+ align:start position:0%
+there yep so is there reason why First
+Solar goes smaller cells yeah so uh why
+
+ align:start position:0%
+Solar goes smaller cells yeah so uh why
+ 
+
+ align:start position:0%
+Solar goes smaller cells yeah so uh why
+why is this First Solar module the fs
+
+ align:start position:0%
+why is this First Solar module the fs
+ 
+
+ align:start position:0%
+why is this First Solar module the fs
+Series 3 module a little smaller than
+
+ align:start position:0%
+Series 3 module a little smaller than
+ 
+
+ align:start position:0%
+Series 3 module a little smaller than
+some of the Crystal and silicon modules
+
+ align:start position:0%
+some of the Crystal and silicon modules
+ 
+
+ align:start position:0%
+some of the Crystal and silicon modules
+four thin film deposition especially for
+
+ align:start position:0%
+four thin film deposition especially for
+ 
+
+ align:start position:0%
+four thin film deposition especially for
+this uh closed space sublimation process
+
+ align:start position:0%
+this uh closed space sublimation process
+ 
+
+ align:start position:0%
+this uh closed space sublimation process
+that for solar uses um you're limited in
+
+ align:start position:0%
+that for solar uses um you're limited in
+ 
+
+ align:start position:0%
+that for solar uses um you're limited in
+terms of the deposition area by the
+
+ align:start position:0%
+terms of the deposition area by the
+ 
+
+ align:start position:0%
+terms of the deposition area by the
+uniformity of that position over a large
+
+ align:start position:0%
+uniformity of that position over a large
+ 
+
+ align:start position:0%
+uniformity of that position over a large
+uh uh region so if you're sputtering the
+
+ align:start position:0%
+uh uh region so if you're sputtering the
+ 
+
+ align:start position:0%
+uh uh region so if you're sputtering the
+material uh it's typically related to to
+
+ align:start position:0%
+material uh it's typically related to to
+ 
+
+ align:start position:0%
+material uh it's typically related to to
+the size of your Target and the distance
+
+ align:start position:0%
+the size of your Target and the distance
+ 
+
+ align:start position:0%
+the size of your Target and the distance
+to your substrate um that will limit the
+
+ align:start position:0%
+to your substrate um that will limit the
+ 
+
+ align:start position:0%
+to your substrate um that will limit the
+maximum size that you can deposit
+
+ align:start position:0%
+maximum size that you can deposit
+ 
+
+ align:start position:0%
+maximum size that you can deposit
+uniformly and you probably want to
+
+ align:start position:0%
+uniformly and you probably want to
+ 
+
+ align:start position:0%
+uniformly and you probably want to
+deposit to within plus or minus 2% let's
+
+ align:start position:0%
+deposit to within plus or minus 2% let's
+ 
+
+ align:start position:0%
+deposit to within plus or minus 2% let's
+say maybe 5% I'm not extremely privy to
+
+ align:start position:0%
+say maybe 5% I'm not extremely privy to
+ 
+
+ align:start position:0%
+say maybe 5% I'm not extremely privy to
+the precise tolerances in the PV
+
+ align:start position:0%
+the precise tolerances in the PV
+ 
+
+ align:start position:0%
+the precise tolerances in the PV
+industry in terms of thin film thickness
+
+ align:start position:0%
+industry in terms of thin film thickness
+ 
+
+ align:start position:0%
+industry in terms of thin film thickness
+variation but that would be my my um my
+
+ align:start position:0%
+variation but that would be my my um my
+ 
+
+ align:start position:0%
+variation but that would be my my um my
+estimate um and in terms of these
+
+ align:start position:0%
+estimate um and in terms of these
+ 
+
+ align:start position:0%
+estimate um and in terms of these
+thermal evaporation processes again it's
+
+ align:start position:0%
+thermal evaporation processes again it's
+ 
+
+ align:start position:0%
+thermal evaporation processes again it's
+uh it's how the machine is designed so I
+
+ align:start position:0%
+uh it's how the machine is designed so I
+ 
+
+ align:start position:0%
+uh it's how the machine is designed so I
+imagine you could probably go bigger um
+
+ align:start position:0%
+imagine you could probably go bigger um
+ 
+
+ align:start position:0%
+imagine you could probably go bigger um
+um is it cost effective question mark
+
+ align:start position:0%
+um is it cost effective question mark
+ 
+
+ align:start position:0%
+um is it cost effective question mark
+somebody at First Solar most obviously
+
+ align:start position:0%
+somebody at First Solar most obviously
+ 
+
+ align:start position:0%
+somebody at First Solar most obviously
+did the cost analysis and said that this
+
+ align:start position:0%
+did the cost analysis and said that this
+ 
+
+ align:start position:0%
+did the cost analysis and said that this
+is the optimum between a variety of
+
+ align:start position:0%
+is the optimum between a variety of
+ 
+
+ align:start position:0%
+is the optimum between a variety of
+different factors between
+
+ align:start position:0%
+different factors between
+ 
+
+ align:start position:0%
+different factors between
+manufacturability and ease of
+
+ align:start position:0%
+manufacturability and ease of
+ 
+
+ align:start position:0%
+manufacturability and ease of
+installation yeah don't put efficiency
+
+ align:start position:0%
+installation yeah don't put efficiency
+ 
+
+ align:start position:0%
+installation yeah don't put efficiency
+on the sheet is there a reason why they
+
+ align:start position:0%
+on the sheet is there a reason why they
+ 
+
+ align:start position:0%
+on the sheet is there a reason why they
+don't put efficiency on the sheet well
+
+ align:start position:0%
+don't put efficiency on the sheet well
+ 
+
+ align:start position:0%
+don't put efficiency on the sheet well
+you could probably very easily calculate
+
+ align:start position:0%
+you could probably very easily calculate
+ 
+
+ align:start position:0%
+you could probably very easily calculate
+the efficiency right um there are two
+
+ align:start position:0%
+the efficiency right um there are two
+ 
+
+ align:start position:0%
+the efficiency right um there are two
+types of module efficiencies um there's
+
+ align:start position:0%
+types of module efficiencies um there's
+ 
+
+ align:start position:0%
+types of module efficiencies um there's
+what's called uh total area efficiency
+
+ align:start position:0%
+what's called uh total area efficiency
+ 
+
+ align:start position:0%
+what's called uh total area efficiency
+where you take the total area of your
+
+ align:start position:0%
+where you take the total area of your
+ 
+
+ align:start position:0%
+where you take the total area of your
+module all the way up to the aluminum
+
+ align:start position:0%
+module all the way up to the aluminum
+ 
+
+ align:start position:0%
+module all the way up to the aluminum
+frame and calculate that as your area so
+
+ align:start position:0%
+frame and calculate that as your area so
+ 
+
+ align:start position:0%
+frame and calculate that as your area so
+you take your power your maximum power
+
+ align:start position:0%
+you take your power your maximum power
+ 
+
+ align:start position:0%
+you take your power your maximum power
+uh rated at am 1.5 Sun conditions and
+
+ align:start position:0%
+uh rated at am 1.5 Sun conditions and
+ 
+
+ align:start position:0%
+uh rated at am 1.5 Sun conditions and
+divided by the area there's also um a
+
+ align:start position:0%
+divided by the area there's also um a
+ 
+
+ align:start position:0%
+divided by the area there's also um a
+variety of other uh less um
+
+ align:start position:0%
+variety of other uh less um
+ 
+
+ align:start position:0%
+variety of other uh less um
+straightforward ways of calculating
+
+ align:start position:0%
+straightforward ways of calculating
+ 
+
+ align:start position:0%
+straightforward ways of calculating
+efficiency some of which take the active
+
+ align:start position:0%
+efficiency some of which take the active
+ 
+
+ align:start position:0%
+efficiency some of which take the active
+area of the cells only others uh exclude
+
+ align:start position:0%
+area of the cells only others uh exclude
+ 
+
+ align:start position:0%
+area of the cells only others uh exclude
+the frame right and so the module
+
+ align:start position:0%
+the frame right and so the module
+ 
+
+ align:start position:0%
+the frame right and so the module
+efficiency um is not extremely
+
+ align:start position:0%
+efficiency um is not extremely
+ 
+
+ align:start position:0%
+efficiency um is not extremely
+straightforward parameter it has to be
+
+ align:start position:0%
+straightforward parameter it has to be
+ 
+
+ align:start position:0%
+straightforward parameter it has to be
+specified based on what areas is uh is
+
+ align:start position:0%
+specified based on what areas is uh is
+ 
+
+ align:start position:0%
+specified based on what areas is uh is
+assumed that would be my estimate for
+
+ align:start position:0%
+assumed that would be my estimate for
+ 
+
+ align:start position:0%
+assumed that would be my estimate for
+why they didn't put it right on here and
+
+ align:start position:0%
+why they didn't put it right on here and
+ 
+
+ align:start position:0%
+why they didn't put it right on here and
+secondly I mean their module efficiency
+
+ align:start position:0%
+secondly I mean their module efficiency
+ 
+
+ align:start position:0%
+secondly I mean their module efficiency
+if you do the math that one probably
+
+ align:start position:0%
+if you do the math that one probably
+ 
+
+ align:start position:0%
+if you do the math that one probably
+turns out to be somewhere between 11 and
+
+ align:start position:0%
+turns out to be somewhere between 11 and
+ 
+
+ align:start position:0%
+turns out to be somewhere between 11 and
+11.5% now they're hitting 12 or so um
+
+ align:start position:0%
+11.5% now they're hitting 12 or so um
+ 
+
+ align:start position:0%
+11.5% now they're hitting 12 or so um
+that's not a very high number compared
+
+ align:start position:0%
+that's not a very high number compared
+ 
+
+ align:start position:0%
+that's not a very high number compared
+to say a crystal and silicon module and
+
+ align:start position:0%
+to say a crystal and silicon module and
+ 
+
+ align:start position:0%
+to say a crystal and silicon module and
+so it wouldn't be it's probably
+
+ align:start position:0%
+so it wouldn't be it's probably
+ 
+
+ align:start position:0%
+so it wouldn't be it's probably
+something they advertise on their on
+
+ align:start position:0%
+something they advertise on their on
+ 
+
+ align:start position:0%
+something they advertise on their on
+their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spec um describe how PV module power
+
+ align:start position:0%
+spec um describe how PV module power
+ 
+
+ align:start position:0%
+spec um describe how PV module power
+output is affected by the cell mismatch
+
+ align:start position:0%
+output is affected by the cell mismatch
+ 
+
+ align:start position:0%
+output is affected by the cell mismatch
+losses warning I'm going to lose some of
+
+ align:start position:0%
+losses warning I'm going to lose some of
+ 
+
+ align:start position:0%
+losses warning I'm going to lose some of
+you on this uh those of you without uh
+
+ align:start position:0%
+you on this uh those of you without uh
+ 
+
+ align:start position:0%
+you on this uh those of you without uh
+very strong uh electrical engineering or
+
+ align:start position:0%
+very strong uh electrical engineering or
+ 
+
+ align:start position:0%
+very strong uh electrical engineering or
+physics background I I'm going to pick
+
+ align:start position:0%
+physics background I I'm going to pick
+ 
+
+ align:start position:0%
+physics background I I'm going to pick
+you up at Point number three um so plan
+
+ align:start position:0%
+you up at Point number three um so plan
+ 
+
+ align:start position:0%
+you up at Point number three um so plan
+a flag right here uh we'll come back to
+
+ align:start position:0%
+a flag right here uh we'll come back to
+ 
+
+ align:start position:0%
+a flag right here uh we'll come back to
+it but for those who care to follow
+
+ align:start position:0%
+it but for those who care to follow
+ 
+
+ align:start position:0%
+it but for those who care to follow
+along um this is this is some really fun
+
+ align:start position:0%
+along um this is this is some really fun
+ 
+
+ align:start position:0%
+along um this is this is some really fun
+stuff that can get into why we want to
+
+ align:start position:0%
+stuff that can get into why we want to
+ 
+
+ align:start position:0%
+stuff that can get into why we want to
+match our cells properly in terms of
+
+ align:start position:0%
+match our cells properly in terms of
+ 
+
+ align:start position:0%
+match our cells properly in terms of
+their outputs right so the total current
+
+ align:start position:0%
+their outputs right so the total current
+ 
+
+ align:start position:0%
+their outputs right so the total current
+output this is the ideal diode equation
+
+ align:start position:0%
+output this is the ideal diode equation
+ 
+
+ align:start position:0%
+output this is the ideal diode equation
+all without all the fancy two diode
+
+ align:start position:0%
+all without all the fancy two diode
+ 
+
+ align:start position:0%
+all without all the fancy two diode
+model you know recombination the space
+
+ align:start position:0%
+model you know recombination the space
+ 
+
+ align:start position:0%
+model you know recombination the space
+charge region Rec combination the bulk
+
+ align:start position:0%
+charge region Rec combination the bulk
+ 
+
+ align:start position:0%
+charge region Rec combination the bulk
+without the series resistance and shunt
+
+ align:start position:0%
+without the series resistance and shunt
+ 
+
+ align:start position:0%
+without the series resistance and shunt
+resistance just a very simple um
+
+ align:start position:0%
+resistance just a very simple um
+ 
+
+ align:start position:0%
+resistance just a very simple um
+explanation of of the ideal di model
+
+ align:start position:0%
+explanation of of the ideal di model
+ 
+
+ align:start position:0%
+explanation of of the ideal di model
+what we're doing is we're our m is the
+
+ align:start position:0%
+what we're doing is we're our m is the
+ 
+
+ align:start position:0%
+what we're doing is we're our m is the
+number of cells in parallel and our N is
+
+ align:start position:0%
+number of cells in parallel and our N is
+ 
+
+ align:start position:0%
+number of cells in parallel and our N is
+a number of cells in series so we go
+
+ align:start position:0%
+a number of cells in series so we go
+ 
+
+ align:start position:0%
+a number of cells in series so we go
+back to our equivalent circuit diagrams
+
+ align:start position:0%
+back to our equivalent circuit diagrams
+ 
+
+ align:start position:0%
+back to our equivalent circuit diagrams
+where we have two say voltage current
+
+ align:start position:0%
+where we have two say voltage current
+ 
+
+ align:start position:0%
+where we have two say voltage current
+sources that are connected in series if
+
+ align:start position:0%
+sources that are connected in series if
+ 
+
+ align:start position:0%
+sources that are connected in series if
+you connect those two in series now the
+
+ align:start position:0%
+you connect those two in series now the
+ 
+
+ align:start position:0%
+you connect those two in series now the
+voltage will add right so the effective
+
+ align:start position:0%
+voltage will add right so the effective
+ 
+
+ align:start position:0%
+voltage will add right so the effective
+voltage across the entire system if you
+
+ align:start position:0%
+voltage across the entire system if you
+ 
+
+ align:start position:0%
+voltage across the entire system if you
+draw a black box around your two
+
+ align:start position:0%
+draw a black box around your two
+ 
+
+ align:start position:0%
+draw a black box around your two
+individual voltage producers the
+
+ align:start position:0%
+individual voltage producers the
+ 
+
+ align:start position:0%
+individual voltage producers the
+effective voltage across the entire
+
+ align:start position:0%
+effective voltage across the entire
+ 
+
+ align:start position:0%
+effective voltage across the entire
+system will be voltage 1 plus voltage
+
+ align:start position:0%
+system will be voltage 1 plus voltage
+ 
+
+ align:start position:0%
+system will be voltage 1 plus voltage
+two in series right um the currents now
+
+ align:start position:0%
+two in series right um the currents now
+ 
+
+ align:start position:0%
+two in series right um the currents now
+if you think about the current you can
+
+ align:start position:0%
+if you think about the current you can
+ 
+
+ align:start position:0%
+if you think about the current you can
+think of current the first order as this
+
+ align:start position:0%
+think of current the first order as this
+ 
+
+ align:start position:0%
+think of current the first order as this
+as this River trying to flow through a
+
+ align:start position:0%
+as this River trying to flow through a
+ 
+
+ align:start position:0%
+as this River trying to flow through a
+river of electrons trying to flow
+
+ align:start position:0%
+river of electrons trying to flow
+ 
+
+ align:start position:0%
+river of electrons trying to flow
+through your your circuit if there's any
+
+ align:start position:0%
+through your your circuit if there's any
+ 
+
+ align:start position:0%
+through your your circuit if there's any
+bottleneck somewhere that's going to
+
+ align:start position:0%
+bottleneck somewhere that's going to
+ 
+
+ align:start position:0%
+bottleneck somewhere that's going to
+limit the the current that can flow
+
+ align:start position:0%
+limit the the current that can flow
+ 
+
+ align:start position:0%
+limit the the current that can flow
+through the entire circuit um so the the
+
+ align:start position:0%
+through the entire circuit um so the the
+ 
+
+ align:start position:0%
+through the entire circuit um so the the
+current the combined current is going to
+
+ align:start position:0%
+current the combined current is going to
+ 
+
+ align:start position:0%
+current the combined current is going to
+be limited by the worst performer um in
+
+ align:start position:0%
+be limited by the worst performer um in
+ 
+
+ align:start position:0%
+be limited by the worst performer um in
+mathematical terms it would be the
+
+ align:start position:0%
+mathematical terms it would be the
+ 
+
+ align:start position:0%
+mathematical terms it would be the
+harmonic mean one over effective current
+
+ align:start position:0%
+harmonic mean one over effective current
+ 
+
+ align:start position:0%
+harmonic mean one over effective current
+would be one over current 1 plus one
+
+ align:start position:0%
+would be one over current 1 plus one
+ 
+
+ align:start position:0%
+would be one over current 1 plus one
+over current two right so um what we see
+
+ align:start position:0%
+over current two right so um what we see
+ 
+
+ align:start position:0%
+over current two right so um what we see
+here is if we have a number of cells
+
+ align:start position:0%
+here is if we have a number of cells
+ 
+
+ align:start position:0%
+here is if we have a number of cells
+connected in parallel um now instead of
+
+ align:start position:0%
+connected in parallel um now instead of
+ 
+
+ align:start position:0%
+connected in parallel um now instead of
+having to connected in series like this
+
+ align:start position:0%
+having to connected in series like this
+ 
+
+ align:start position:0%
+having to connected in series like this
+you connect them in parallel now the
+
+ align:start position:0%
+you connect them in parallel now the
+ 
+
+ align:start position:0%
+you connect them in parallel now the
+currents are adding and the voltage will
+
+ align:start position:0%
+currents are adding and the voltage will
+ 
+
+ align:start position:0%
+currents are adding and the voltage will
+be limited by the worst performer
+
+ align:start position:0%
+be limited by the worst performer
+ 
+
+ align:start position:0%
+be limited by the worst performer
+because the potential across both is
+
+ align:start position:0%
+because the potential across both is
+ 
+
+ align:start position:0%
+because the potential across both is
+going to be limited by whatever the
+
+ align:start position:0%
+going to be limited by whatever the
+ 
+
+ align:start position:0%
+going to be limited by whatever the
+lowest potential is so
+
+ align:start position:0%
+lowest potential is so
+ 
+
+ align:start position:0%
+lowest potential is so
+when we connect in parallel we add
+
+ align:start position:0%
+when we connect in parallel we add
+ 
+
+ align:start position:0%
+when we connect in parallel we add
+currents and when we connect in series
+
+ align:start position:0%
+currents and when we connect in series
+ 
+
+ align:start position:0%
+currents and when we connect in series
+we add voltages that's a very simple way
+
+ align:start position:0%
+we add voltages that's a very simple way
+ 
+
+ align:start position:0%
+we add voltages that's a very simple way
+to think about it and that's why we have
+
+ align:start position:0%
+to think about it and that's why we have
+ 
+
+ align:start position:0%
+to think about it and that's why we have
+the M appearing here up up top uh if you
+
+ align:start position:0%
+the M appearing here up up top uh if you
+ 
+
+ align:start position:0%
+the M appearing here up up top uh if you
+have a number of cells connected in
+
+ align:start position:0%
+have a number of cells connected in
+ 
+
+ align:start position:0%
+have a number of cells connected in
+parallel you will essentially be
+
+ align:start position:0%
+parallel you will essentially be
+ 
+
+ align:start position:0%
+parallel you will essentially be
+multiplying the illuminated current of
+
+ align:start position:0%
+multiplying the illuminated current of
+ 
+
+ align:start position:0%
+multiplying the illuminated current of
+one cell by whatever M it is and if you
+
+ align:start position:0%
+one cell by whatever M it is and if you
+ 
+
+ align:start position:0%
+one cell by whatever M it is and if you
+have uh a number of cells connected in
+
+ align:start position:0%
+have uh a number of cells connected in
+ 
+
+ align:start position:0%
+have uh a number of cells connected in
+series that will impact the
+
+ align:start position:0%
+series that will impact the
+ 
+
+ align:start position:0%
+series that will impact the
+voltage okay so um that's an expression
+
+ align:start position:0%
+voltage okay so um that's an expression
+ 
+
+ align:start position:0%
+voltage okay so um that's an expression
+that uh is useful for uh n and M number
+
+ align:start position:0%
+that uh is useful for uh n and M number
+ 
+
+ align:start position:0%
+that uh is useful for uh n and M number
+of identical cells identical cells
+
+ align:start position:0%
+of identical cells identical cells
+ 
+
+ align:start position:0%
+of identical cells identical cells
+connected in either series or parallel
+
+ align:start position:0%
+connected in either series or parallel
+ 
+
+ align:start position:0%
+connected in either series or parallel
+respectively and in practice if we have
+
+ align:start position:0%
+respectively and in practice if we have
+ 
+
+ align:start position:0%
+respectively and in practice if we have
+uh bad performers in the bunch if we
+
+ align:start position:0%
+uh bad performers in the bunch if we
+ 
+
+ align:start position:0%
+uh bad performers in the bunch if we
+have one cell that's performing worse
+
+ align:start position:0%
+have one cell that's performing worse
+ 
+
+ align:start position:0%
+have one cell that's performing worse
+than another either because it is
+
+ align:start position:0%
+than another either because it is
+ 
+
+ align:start position:0%
+than another either because it is
+intrinsically worse it is a defective
+
+ align:start position:0%
+intrinsically worse it is a defective
+ 
+
+ align:start position:0%
+intrinsically worse it is a defective
+cell that somehow got in there or became
+
+ align:start position:0%
+cell that somehow got in there or became
+ 
+
+ align:start position:0%
+cell that somehow got in there or became
+defective during use or it's a temporary
+
+ align:start position:0%
+defective during use or it's a temporary
+ 
+
+ align:start position:0%
+defective during use or it's a temporary
+effect maybe a seagull just landed on
+
+ align:start position:0%
+effect maybe a seagull just landed on
+ 
+
+ align:start position:0%
+effect maybe a seagull just landed on
+top of that cell and is shading it right
+
+ align:start position:0%
+top of that cell and is shading it right
+ 
+
+ align:start position:0%
+top of that cell and is shading it right
+um so whatever the reason is temporary
+
+ align:start position:0%
+um so whatever the reason is temporary
+ 
+
+ align:start position:0%
+um so whatever the reason is temporary
+or permanent um that uh cell number two
+
+ align:start position:0%
+or permanent um that uh cell number two
+ 
+
+ align:start position:0%
+or permanent um that uh cell number two
+now is is is a is a bad apple um and so
+
+ align:start position:0%
+now is is is a is a bad apple um and so
+ 
+
+ align:start position:0%
+now is is is a is a bad apple um and so
+if we're looking at parallel mismatches
+
+ align:start position:0%
+if we're looking at parallel mismatches
+ 
+
+ align:start position:0%
+if we're looking at parallel mismatches
+we take what we know about cells and
+
+ align:start position:0%
+we take what we know about cells and
+ 
+
+ align:start position:0%
+we take what we know about cells and
+parallel okay the voltage is limited by
+
+ align:start position:0%
+parallel okay the voltage is limited by
+ 
+
+ align:start position:0%
+parallel okay the voltage is limited by
+the worst performer and we look at the
+
+ align:start position:0%
+the worst performer and we look at the
+ 
+
+ align:start position:0%
+the worst performer and we look at the
+individual IV curves of the good and the
+
+ align:start position:0%
+individual IV curves of the good and the
+ 
+
+ align:start position:0%
+individual IV curves of the good and the
+bad cell this is the good cell right
+
+ align:start position:0%
+bad cell this is the good cell right
+ 
+
+ align:start position:0%
+bad cell this is the good cell right
+here this
+
+ align:start position:0%
+here this
+ 
+
+ align:start position:0%
+here this
+curve there right and so this now is
+
+ align:start position:0%
+curve there right and so this now is
+ 
+
+ align:start position:0%
+curve there right and so this now is
+being positive power essentially power
+
+ align:start position:0%
+being positive power essentially power
+ 
+
+ align:start position:0%
+being positive power essentially power
+coming out of the solar cell is plotted
+
+ align:start position:0%
+coming out of the solar cell is plotted
+ 
+
+ align:start position:0%
+coming out of the solar cell is plotted
+in the first quadrant we have uh a lot
+
+ align:start position:0%
+in the first quadrant we have uh a lot
+ 
+
+ align:start position:0%
+in the first quadrant we have uh a lot
+of power coming out and a large voltage
+
+ align:start position:0%
+of power coming out and a large voltage
+ 
+
+ align:start position:0%
+of power coming out and a large voltage
+for our good cell here's our bad cell
+
+ align:start position:0%
+for our good cell here's our bad cell
+ 
+
+ align:start position:0%
+for our good cell here's our bad cell
+right there right so slightly lower
+
+ align:start position:0%
+right there right so slightly lower
+ 
+
+ align:start position:0%
+right there right so slightly lower
+current output uh given by the the
+
+ align:start position:0%
+current output uh given by the the
+ 
+
+ align:start position:0%
+current output uh given by the the
+logarithmic effect and the um the
+
+ align:start position:0%
+logarithmic effect and the um the
+ 
+
+ align:start position:0%
+logarithmic effect and the um the
+voltage is lower significantly lower
+
+ align:start position:0%
+voltage is lower significantly lower
+ 
+
+ align:start position:0%
+voltage is lower significantly lower
+than say the good cell and so the
+
+ align:start position:0%
+than say the good cell and so the
+ 
+
+ align:start position:0%
+than say the good cell and so the
+combined output right here the current
+
+ align:start position:0%
+combined output right here the current
+ 
+
+ align:start position:0%
+combined output right here the current
+at Short Circuit current conditions is
+
+ align:start position:0%
+at Short Circuit current conditions is
+ 
+
+ align:start position:0%
+at Short Circuit current conditions is
+going to be the sum of the good and the
+
+ align:start position:0%
+going to be the sum of the good and the
+ 
+
+ align:start position:0%
+going to be the sum of the good and the
+bad so that's there the voltage is going
+
+ align:start position:0%
+bad so that's there the voltage is going
+ 
+
+ align:start position:0%
+bad so that's there the voltage is going
+to be the harmonic mean so limited by
+
+ align:start position:0%
+to be the harmonic mean so limited by
+ 
+
+ align:start position:0%
+to be the harmonic mean so limited by
+the the worst
+
+ align:start position:0%
+the the worst
+ 
+
+ align:start position:0%
+the the worst
+performer that's uh how uh low voltage
+
+ align:start position:0%
+performer that's uh how uh low voltage
+ 
+
+ align:start position:0%
+performer that's uh how uh low voltage
+cells can really mess up parallel
+
+ align:start position:0%
+cells can really mess up parallel
+ 
+
+ align:start position:0%
+cells can really mess up parallel
+strings so for example this set of of of
+
+ align:start position:0%
+strings so for example this set of of of
+ 
+
+ align:start position:0%
+strings so for example this set of of of
+two rows of cells this one right here uh
+
+ align:start position:0%
+two rows of cells this one right here uh
+ 
+
+ align:start position:0%
+two rows of cells this one right here uh
+which is all connected in series is
+
+ align:start position:0%
+which is all connected in series is
+ 
+
+ align:start position:0%
+which is all connected in series is
+connected in parallel to this one and
+
+ align:start position:0%
+connected in parallel to this one and
+ 
+
+ align:start position:0%
+connected in parallel to this one and
+this one right and so if one of these
+
+ align:start position:0%
+this one right and so if one of these
+ 
+
+ align:start position:0%
+this one right and so if one of these
+one of these three uh subsets of cells
+
+ align:start position:0%
+one of these three uh subsets of cells
+ 
+
+ align:start position:0%
+one of these three uh subsets of cells
+has a lower voltage than the others the
+
+ align:start position:0%
+has a lower voltage than the others the
+ 
+
+ align:start position:0%
+has a lower voltage than the others the
+combined voltage output of the of the
+
+ align:start position:0%
+combined voltage output of the of the
+ 
+
+ align:start position:0%
+combined voltage output of the of the
+entire module will be lower lower
+
+ align:start position:0%
+entire module will be lower lower
+ 
+
+ align:start position:0%
+entire module will be lower lower
+similarly now we've put them in series
+
+ align:start position:0%
+similarly now we've put them in series
+ 
+
+ align:start position:0%
+similarly now we've put them in series
+uh if we have a bad cell that's
+
+ align:start position:0%
+uh if we have a bad cell that's
+ 
+
+ align:start position:0%
+uh if we have a bad cell that's
+producing less current than the good
+
+ align:start position:0%
+producing less current than the good
+ 
+
+ align:start position:0%
+producing less current than the good
+cell and notice that they same open
+
+ align:start position:0%
+cell and notice that they same open
+ 
+
+ align:start position:0%
+cell and notice that they same open
+circuit voltage now just for uh just for
+
+ align:start position:0%
+circuit voltage now just for uh just for
+ 
+
+ align:start position:0%
+circuit voltage now just for uh just for
+a say the the the thought experiment
+
+ align:start position:0%
+a say the the the thought experiment
+ 
+
+ align:start position:0%
+a say the the the thought experiment
+here in the classroom um typically if a
+
+ align:start position:0%
+here in the classroom um typically if a
+ 
+
+ align:start position:0%
+here in the classroom um typically if a
+cell is performing worse than current it
+
+ align:start position:0%
+cell is performing worse than current it
+ 
+
+ align:start position:0%
+cell is performing worse than current it
+will also have a lower voltage but just
+
+ align:start position:0%
+will also have a lower voltage but just
+ 
+
+ align:start position:0%
+will also have a lower voltage but just
+for the thought experiment right here we
+
+ align:start position:0%
+for the thought experiment right here we
+ 
+
+ align:start position:0%
+for the thought experiment right here we
+have um bad cell good cell bad cell has
+
+ align:start position:0%
+have um bad cell good cell bad cell has
+ 
+
+ align:start position:0%
+have um bad cell good cell bad cell has
+half the current of the good cell so the
+
+ align:start position:0%
+half the current of the good cell so the
+ 
+
+ align:start position:0%
+half the current of the good cell so the
+voltage output in series is going to be
+
+ align:start position:0%
+voltage output in series is going to be
+ 
+
+ align:start position:0%
+voltage output in series is going to be
+the addition of the two boom boom and
+
+ align:start position:0%
+the addition of the two boom boom and
+ 
+
+ align:start position:0%
+the addition of the two boom boom and
+you're up to here but the current output
+
+ align:start position:0%
+you're up to here but the current output
+ 
+
+ align:start position:0%
+you're up to here but the current output
+will be limited by the worst performer
+
+ align:start position:0%
+will be limited by the worst performer
+ 
+
+ align:start position:0%
+will be limited by the worst performer
+and again the combined output of this uh
+
+ align:start position:0%
+and again the combined output of this uh
+ 
+
+ align:start position:0%
+and again the combined output of this uh
+set of cells connected in series is
+
+ align:start position:0%
+set of cells connected in series is
+ 
+
+ align:start position:0%
+set of cells connected in series is
+going to be right around here and So
+
+ align:start position:0%
+going to be right around here and So
+ 
+
+ align:start position:0%
+going to be right around here and So
+based on your cell performance if you
+
+ align:start position:0%
+based on your cell performance if you
+ 
+
+ align:start position:0%
+based on your cell performance if you
+know that my Vol if if you know that
+
+ align:start position:0%
+know that my Vol if if you know that
+ 
+
+ align:start position:0%
+know that my Vol if if you know that
+your voltage has a certain variance in
+
+ align:start position:0%
+your voltage has a certain variance in
+ 
+
+ align:start position:0%
+your voltage has a certain variance in
+your manufacturing line and your current
+
+ align:start position:0%
+your manufacturing line and your current
+ 
+
+ align:start position:0%
+your manufacturing line and your current
+has a certain variance in your
+
+ align:start position:0%
+has a certain variance in your
+ 
+
+ align:start position:0%
+has a certain variance in your
+manufacturing line that might entice you
+
+ align:start position:0%
+manufacturing line that might entice you
+ 
+
+ align:start position:0%
+manufacturing line that might entice you
+to string together your cells in one way
+
+ align:start position:0%
+to string together your cells in one way
+ 
+
+ align:start position:0%
+to string together your cells in one way
+or another right depending on on how you
+
+ align:start position:0%
+or another right depending on on how you
+ 
+
+ align:start position:0%
+or another right depending on on how you
+want to mitigate your
+
+ align:start position:0%
+want to mitigate your
+ 
+
+ align:start position:0%
+want to mitigate your
+losses shaded cells so up to now
+
+ align:start position:0%
+losses shaded cells so up to now
+ 
+
+ align:start position:0%
+losses shaded cells so up to now
+everybody kind of gets based on on on on
+
+ align:start position:0%
+everybody kind of gets based on on on on
+ 
+
+ align:start position:0%
+everybody kind of gets based on on on on
+kof's laws and so forth from from
+
+ align:start position:0%
+kof's laws and so forth from from
+ 
+
+ align:start position:0%
+kof's laws and so forth from from
+equivalent circuit diagram so we're
+
+ align:start position:0%
+equivalent circuit diagram so we're
+ 
+
+ align:start position:0%
+equivalent circuit diagram so we're
+we're rolling now we're going to get to
+
+ align:start position:0%
+we're rolling now we're going to get to
+ 
+
+ align:start position:0%
+we're rolling now we're going to get to
+shaded cells and here's where uh it
+
+ align:start position:0%
+shaded cells and here's where uh it
+ 
+
+ align:start position:0%
+shaded cells and here's where uh it
+becomes a little bit more difficult to
+
+ align:start position:0%
+becomes a little bit more difficult to
+ 
+
+ align:start position:0%
+becomes a little bit more difficult to
+understand absent the reading in in that
+
+ align:start position:0%
+understand absent the reading in in that
+ 
+
+ align:start position:0%
+understand absent the reading in in that
+book over there did everybody get a
+
+ align:start position:0%
+book over there did everybody get a
+ 
+
+ align:start position:0%
+book over there did everybody get a
+chance to see the blue book did it make
+
+ align:start position:0%
+chance to see the blue book did it make
+ 
+
+ align:start position:0%
+chance to see the blue book did it make
+its rounds over here no didn't why don't
+
+ align:start position:0%
+its rounds over here no didn't why don't
+ 
+
+ align:start position:0%
+its rounds over here no didn't why don't
+we pass the uh the Blue Book around Omar
+
+ align:start position:0%
+we pass the uh the Blue Book around Omar
+ 
+
+ align:start position:0%
+we pass the uh the Blue Book around Omar
+over there I and get a chance to see it
+
+ align:start position:0%
+over there I and get a chance to see it
+ 
+
+ align:start position:0%
+over there I and get a chance to see it
+yet we're going to consider that we have
+
+ align:start position:0%
+yet we're going to consider that we have
+ 
+
+ align:start position:0%
+yet we're going to consider that we have
+10 identical solar cells connected in
+
+ align:start position:0%
+10 identical solar cells connected in
+ 
+
+ align:start position:0%
+10 identical solar cells connected in
+series and this one over here is shaded
+
+ align:start position:0%
+series and this one over here is shaded
+ 
+
+ align:start position:0%
+series and this one over here is shaded
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+now so uh this is described I believe in
+
+ align:start position:0%
+now so uh this is described I believe in
+ 
+
+ align:start position:0%
+now so uh this is described I believe in
+figure 5.7 in the book one with the
+
+ align:start position:0%
+figure 5.7 in the book one with the
+ 
+
+ align:start position:0%
+figure 5.7 in the book one with the
+green little tab we've assumed that the
+
+ align:start position:0%
+green little tab we've assumed that the
+ 
+
+ align:start position:0%
+green little tab we've assumed that the
+combined IV characteristic of the N good
+
+ align:start position:0%
+combined IV characteristic of the N good
+ 
+
+ align:start position:0%
+combined IV characteristic of the N good
+cells is this one right
+
+ align:start position:0%
+cells is this one right
+ 
+
+ align:start position:0%
+cells is this one right
+here and the one bad cell is this right
+
+ align:start position:0%
+here and the one bad cell is this right
+ 
+
+ align:start position:0%
+here and the one bad cell is this right
+here right so it's a little bit of a uh
+
+ align:start position:0%
+here right so it's a little bit of a uh
+ 
+
+ align:start position:0%
+here right so it's a little bit of a uh
+say a strange IV characteristic and um
+
+ align:start position:0%
+say a strange IV characteristic and um
+ 
+
+ align:start position:0%
+say a strange IV characteristic and um
+what happens next if you combine the two
+
+ align:start position:0%
+what happens next if you combine the two
+ 
+
+ align:start position:0%
+what happens next if you combine the two
+in series and you use the same protocol
+
+ align:start position:0%
+in series and you use the same protocol
+ 
+
+ align:start position:0%
+in series and you use the same protocol
+that we've done so far the voltage will
+
+ align:start position:0%
+that we've done so far the voltage will
+ 
+
+ align:start position:0%
+that we've done so far the voltage will
+add so whatever voltage gain right here
+
+ align:start position:0%
+add so whatever voltage gain right here
+ 
+
+ align:start position:0%
+add so whatever voltage gain right here
+has been added over here but the current
+
+ align:start position:0%
+has been added over here but the current
+ 
+
+ align:start position:0%
+has been added over here but the current
+is going to be limited by the worst
+
+ align:start position:0%
+is going to be limited by the worst
+ 
+
+ align:start position:0%
+is going to be limited by the worst
+performer which happens to be this uh
+
+ align:start position:0%
+performer which happens to be this uh
+ 
+
+ align:start position:0%
+performer which happens to be this uh
+solar cell right here and so the
+
+ align:start position:0%
+solar cell right here and so the
+ 
+
+ align:start position:0%
+solar cell right here and so the
+combined output is going to be lower
+
+ align:start position:0%
+combined output is going to be lower
+ 
+
+ align:start position:0%
+combined output is going to be lower
+significantly lower than uh than those
+
+ align:start position:0%
+significantly lower than uh than those
+ 
+
+ align:start position:0%
+significantly lower than uh than those
+of the good cells and that's what
+
+ align:start position:0%
+of the good cells and that's what
+ 
+
+ align:start position:0%
+of the good cells and that's what
+happens when one cell in a string is
+
+ align:start position:0%
+happens when one cell in a string is
+ 
+
+ align:start position:0%
+happens when one cell in a string is
+shaded if there aren't any fancy
+
+ align:start position:0%
+shaded if there aren't any fancy
+ 
+
+ align:start position:0%
+shaded if there aren't any fancy
+Electronics to allow the current to
+
+ align:start position:0%
+Electronics to allow the current to
+ 
+
+ align:start position:0%
+Electronics to allow the current to
+bypass it furthermore this amount of
+
+ align:start position:0%
+bypass it furthermore this amount of
+ 
+
+ align:start position:0%
+bypass it furthermore this amount of
+power will be dissipated in the bad cell
+
+ align:start position:0%
+power will be dissipated in the bad cell
+ 
+
+ align:start position:0%
+power will be dissipated in the bad cell
+when the string is short
+
+ align:start position:0%
+when the string is short
+ 
+
+ align:start position:0%
+when the string is short
+circuited it can change a bit when you
+
+ align:start position:0%
+circuited it can change a bit when you
+ 
+
+ align:start position:0%
+circuited it can change a bit when you
+start uh moving toward operating
+
+ align:start position:0%
+start uh moving toward operating
+ 
+
+ align:start position:0%
+start uh moving toward operating
+conditions but it's a sizable amount of
+
+ align:start position:0%
+conditions but it's a sizable amount of
+ 
+
+ align:start position:0%
+conditions but it's a sizable amount of
+power being dumped into that bad cell
+
+ align:start position:0%
+power being dumped into that bad cell
+ 
+
+ align:start position:0%
+power being dumped into that bad cell
+and in in in practice that cell is
+
+ align:start position:0%
+and in in in practice that cell is
+ 
+
+ align:start position:0%
+and in in in practice that cell is
+reverse biased let me show you using uh
+
+ align:start position:0%
+reverse biased let me show you using uh
+ 
+
+ align:start position:0%
+reverse biased let me show you using uh
+our wonderful ppcd ROM
+
+ align:start position:0%
+our wonderful ppcd ROM
+ 
+
+ align:start position:0%
+our wonderful ppcd ROM
+um exactly why that
+
+ align:start position:0%
+um exactly why that
+ 
+
+ align:start position:0%
+um exactly why that
+is so here we have two solar cells
+
+ align:start position:0%
+is so here we have two solar cells
+ 
+
+ align:start position:0%
+is so here we have two solar cells
+connected in series and they're both
+
+ align:start position:0%
+connected in series and they're both
+ 
+
+ align:start position:0%
+connected in series and they're both
+producing an equal amount of uh of
+
+ align:start position:0%
+producing an equal amount of uh of
+ 
+
+ align:start position:0%
+producing an equal amount of uh of
+current because they have an equal
+
+ align:start position:0%
+current because they have an equal
+ 
+
+ align:start position:0%
+current because they have an equal
+number of these yellow arrows incident
+
+ align:start position:0%
+number of these yellow arrows incident
+ 
+
+ align:start position:0%
+number of these yellow arrows incident
+on them and they're equal in every other
+
+ align:start position:0%
+on them and they're equal in every other
+ 
+
+ align:start position:0%
+on them and they're equal in every other
+aspect so it's still a thought
+
+ align:start position:0%
+aspect so it's still a thought
+ 
+
+ align:start position:0%
+aspect so it's still a thought
+experiment right now um the current that
+
+ align:start position:0%
+experiment right now um the current that
+ 
+
+ align:start position:0%
+experiment right now um the current that
+is cycling through this circuit in the
+
+ align:start position:0%
+is cycling through this circuit in the
+ 
+
+ align:start position:0%
+is cycling through this circuit in the
+external circuit right here uh is the
+
+ align:start position:0%
+external circuit right here uh is the
+ 
+
+ align:start position:0%
+external circuit right here uh is the
+strength of the magnitude of that
+
+ align:start position:0%
+strength of the magnitude of that
+ 
+
+ align:start position:0%
+strength of the magnitude of that
+current is being indicated by the color
+
+ align:start position:0%
+current is being indicated by the color
+ 
+
+ align:start position:0%
+current is being indicated by the color
+in this particular case it's very bright
+
+ align:start position:0%
+in this particular case it's very bright
+ 
+
+ align:start position:0%
+in this particular case it's very bright
+it's bright green it indicates a lot of
+
+ align:start position:0%
+it's bright green it indicates a lot of
+ 
+
+ align:start position:0%
+it's bright green it indicates a lot of
+current is flowing through it so up to
+
+ align:start position:0%
+current is flowing through it so up to
+ 
+
+ align:start position:0%
+current is flowing through it so up to
+now every everything makes sense this is
+
+ align:start position:0%
+now every everything makes sense this is
+ 
+
+ align:start position:0%
+now every everything makes sense this is
+in short circuit conditions so there's
+
+ align:start position:0%
+in short circuit conditions so there's
+ 
+
+ align:start position:0%
+in short circuit conditions so there's
+no voltage there's no potential across
+
+ align:start position:0%
+no voltage there's no potential across
+ 
+
+ align:start position:0%
+no voltage there's no potential across
+either cell it's in short circuit
+
+ align:start position:0%
+either cell it's in short circuit
+ 
+
+ align:start position:0%
+either cell it's in short circuit
+conditions and current is flowing
+
+ align:start position:0%
+conditions and current is flowing
+ 
+
+ align:start position:0%
+conditions and current is flowing
+through this circuit right here now I'm
+
+ align:start position:0%
+through this circuit right here now I'm
+ 
+
+ align:start position:0%
+through this circuit right here now I'm
+going to mismatch the two cells I'm
+
+ align:start position:0%
+going to mismatch the two cells I'm
+ 
+
+ align:start position:0%
+going to mismatch the two cells I'm
+going to exchange one of the cells for a
+
+ align:start position:0%
+going to exchange one of the cells for a
+ 
+
+ align:start position:0%
+going to exchange one of the cells for a
+a bad
+
+ align:start position:0%
+a bad
+ 
+
+ align:start position:0%
+a bad
+apple okay first off I I know just from
+
+ align:start position:0%
+apple okay first off I I know just from
+ 
+
+ align:start position:0%
+apple okay first off I I know just from
+uh what we've been talking about so far
+
+ align:start position:0%
+uh what we've been talking about so far
+ 
+
+ align:start position:0%
+uh what we've been talking about so far
+that the current is limited by the worst
+
+ align:start position:0%
+that the current is limited by the worst
+ 
+
+ align:start position:0%
+that the current is limited by the worst
+performer that the current flowing
+
+ align:start position:0%
+performer that the current flowing
+ 
+
+ align:start position:0%
+performer that the current flowing
+through the external circuit is now
+
+ align:start position:0%
+through the external circuit is now
+ 
+
+ align:start position:0%
+through the external circuit is now
+going to be lower and the first order
+
+ align:start position:0%
+going to be lower and the first order
+ 
+
+ align:start position:0%
+going to be lower and the first order
+it's it's more or less approximate to
+
+ align:start position:0%
+it's it's more or less approximate to
+ 
+
+ align:start position:0%
+it's it's more or less approximate to
+what uh the current is in this bad cell
+
+ align:start position:0%
+what uh the current is in this bad cell
+ 
+
+ align:start position:0%
+what uh the current is in this bad cell
+so the bad cell right here which is
+
+ align:start position:0%
+so the bad cell right here which is
+ 
+
+ align:start position:0%
+so the bad cell right here which is
+indicated by the the two arrows now
+
+ align:start position:0%
+indicated by the the two arrows now
+ 
+
+ align:start position:0%
+indicated by the the two arrows now
+instead of the four right this shaded
+
+ align:start position:0%
+instead of the four right this shaded
+ 
+
+ align:start position:0%
+instead of the four right this shaded
+cell right here is producing less
+
+ align:start position:0%
+cell right here is producing less
+ 
+
+ align:start position:0%
+cell right here is producing less
+current and so I know based on what
+
+ align:start position:0%
+current and so I know based on what
+ 
+
+ align:start position:0%
+current and so I know based on what
+we've talked about so far that the
+
+ align:start position:0%
+we've talked about so far that the
+ 
+
+ align:start position:0%
+we've talked about so far that the
+combined current output of the entire
+
+ align:start position:0%
+combined current output of the entire
+ 
+
+ align:start position:0%
+combined current output of the entire
+circuit is going to be approximately
+
+ align:start position:0%
+circuit is going to be approximately
+ 
+
+ align:start position:0%
+circuit is going to be approximately
+this one so hence you see a darker uh
+
+ align:start position:0%
+this one so hence you see a darker uh
+ 
+
+ align:start position:0%
+this one so hence you see a darker uh
+color represented the same color that's
+
+ align:start position:0%
+color represented the same color that's
+ 
+
+ align:start position:0%
+color represented the same color that's
+flowing through the
+
+ align:start position:0%
+flowing through the
+ 
+
+ align:start position:0%
+flowing through the
+cell so what happens to the large amount
+
+ align:start position:0%
+cell so what happens to the large amount
+ 
+
+ align:start position:0%
+cell so what happens to the large amount
+of current that's being generated inside
+
+ align:start position:0%
+of current that's being generated inside
+ 
+
+ align:start position:0%
+of current that's being generated inside
+of this one it's that cell still has the
+
+ align:start position:0%
+of this one it's that cell still has the
+ 
+
+ align:start position:0%
+of this one it's that cell still has the
+capacity to produce a large amount of
+
+ align:start position:0%
+capacity to produce a large amount of
+ 
+
+ align:start position:0%
+capacity to produce a large amount of
+current where is it going well some of
+
+ align:start position:0%
+current where is it going well some of
+ 
+
+ align:start position:0%
+current where is it going well some of
+that current is going through is is is
+
+ align:start position:0%
+that current is going through is is is
+ 
+
+ align:start position:0%
+that current is going through is is is
+going through the cell right here
+
+ align:start position:0%
+going through the cell right here
+ 
+
+ align:start position:0%
+going through the cell right here
+forward biasing it which would result in
+
+ align:start position:0%
+forward biasing it which would result in
+ 
+
+ align:start position:0%
+forward biasing it which would result in
+a negative bias or reverse bias of the
+
+ align:start position:0%
+a negative bias or reverse bias of the
+ 
+
+ align:start position:0%
+a negative bias or reverse bias of the
+bad cell because the uh the potential
+
+ align:start position:0%
+bad cell because the uh the potential
+ 
+
+ align:start position:0%
+bad cell because the uh the potential
+across this combined system still has to
+
+ align:start position:0%
+across this combined system still has to
+ 
+
+ align:start position:0%
+across this combined system still has to
+be zero you're in short circuit
+
+ align:start position:0%
+be zero you're in short circuit
+ 
+
+ align:start position:0%
+be zero you're in short circuit
+conditions so the potential here has to
+
+ align:start position:0%
+conditions so the potential here has to
+ 
+
+ align:start position:0%
+conditions so the potential here has to
+be equal to the potential there so what
+
+ align:start position:0%
+be equal to the potential there so what
+ 
+
+ align:start position:0%
+be equal to the potential there so what
+I've effectively done is I've reverse
+
+ align:start position:0%
+I've effectively done is I've reverse
+ 
+
+ align:start position:0%
+I've effectively done is I've reverse
+biased my bad
+
+ align:start position:0%
+biased my bad
+ 
+
+ align:start position:0%
+biased my bad
+cell and we'll get to why that's a
+
+ align:start position:0%
+cell and we'll get to why that's a
+ 
+
+ align:start position:0%
+cell and we'll get to why that's a
+problem later on those who are
+
+ align:start position:0%
+problem later on those who are
+ 
+
+ align:start position:0%
+problem later on those who are
+electrical engineers can already begin
+
+ align:start position:0%
+electrical engineers can already begin
+ 
+
+ align:start position:0%
+electrical engineers can already begin
+Conjuring up ideas of reverse bias
+
+ align:start position:0%
+Conjuring up ideas of reverse bias
+ 
+
+ align:start position:0%
+Conjuring up ideas of reverse bias
+breakdown but we'll get to uh we'll
+
+ align:start position:0%
+breakdown but we'll get to uh we'll
+ 
+
+ align:start position:0%
+breakdown but we'll get to uh we'll
+explain why it is why why reverse bias
+
+ align:start position:0%
+explain why it is why why reverse bias
+ 
+
+ align:start position:0%
+explain why it is why why reverse bias
+is bad in a few now if you had a series
+
+ align:start position:0%
+is bad in a few now if you had a series
+ 
+
+ align:start position:0%
+is bad in a few now if you had a series
+of these cells connected a bunch of
+
+ align:start position:0%
+of these cells connected a bunch of
+ 
+
+ align:start position:0%
+of these cells connected a bunch of
+these cells connected in series and they
+
+ align:start position:0%
+these cells connected in series and they
+ 
+
+ align:start position:0%
+these cells connected in series and they
+were all producing copious amounts of
+
+ align:start position:0%
+were all producing copious amounts of
+ 
+
+ align:start position:0%
+were all producing copious amounts of
+juice and you had One Bad Apple in your
+
+ align:start position:0%
+juice and you had One Bad Apple in your
+ 
+
+ align:start position:0%
+juice and you had One Bad Apple in your
+string you would be dumping a
+
+ align:start position:0%
+string you would be dumping a
+ 
+
+ align:start position:0%
+string you would be dumping a
+considerable amount of power across that
+
+ align:start position:0%
+considerable amount of power across that
+ 
+
+ align:start position:0%
+considerable amount of power across that
+or you could be dumping a considerable
+
+ align:start position:0%
+or you could be dumping a considerable
+ 
+
+ align:start position:0%
+or you could be dumping a considerable
+amount of power across that one cell and
+
+ align:start position:0%
+amount of power across that one cell and
+ 
+
+ align:start position:0%
+amount of power across that one cell and
+that's where um this graph right here
+
+ align:start position:0%
+that's where um this graph right here
+ 
+
+ align:start position:0%
+that's where um this graph right here
+comes from the power dissipated within
+
+ align:start position:0%
+comes from the power dissipated within
+ 
+
+ align:start position:0%
+comes from the power dissipated within
+the bad cell and that's a problem
+
+ align:start position:0%
+the bad cell and that's a problem
+ 
+
+ align:start position:0%
+the bad cell and that's a problem
+because if there's any weakness in the
+
+ align:start position:0%
+because if there's any weakness in the
+ 
+
+ align:start position:0%
+because if there's any weakness in the
+PN Junction of that bad cell and you're
+
+ align:start position:0%
+PN Junction of that bad cell and you're
+ 
+
+ align:start position:0%
+PN Junction of that bad cell and you're
+reverse biasing it you're going to be
+
+ align:start position:0%
+reverse biasing it you're going to be
+ 
+
+ align:start position:0%
+reverse biasing it you're going to be
+flooding a lot of current through that
+
+ align:start position:0%
+flooding a lot of current through that
+ 
+
+ align:start position:0%
+flooding a lot of current through that
+one little spot which means that that
+
+ align:start position:0%
+one little spot which means that that
+ 
+
+ align:start position:0%
+one little spot which means that that
+spot's going to heat up and it's going
+
+ align:start position:0%
+spot's going to heat up and it's going
+ 
+
+ align:start position:0%
+spot's going to heat up and it's going
+to form a hot spot which has the
+
+ align:start position:0%
+to form a hot spot which has the
+ 
+
+ align:start position:0%
+to form a hot spot which has the
+potential to get very hot and we know
+
+ align:start position:0%
+potential to get very hot and we know
+ 
+
+ align:start position:0%
+potential to get very hot and we know
+that the encapsulant materials flow at
+
+ align:start position:0%
+that the encapsulant materials flow at
+ 
+
+ align:start position:0%
+that the encapsulant materials flow at
+around 150 to 175 C and some other
+
+ align:start position:0%
+around 150 to 175 C and some other
+ 
+
+ align:start position:0%
+around 150 to 175 C and some other
+material failures can occur above that
+
+ align:start position:0%
+material failures can occur above that
+ 
+
+ align:start position:0%
+material failures can occur above that
+so um hot spots are bad um if you
+
+ align:start position:0%
+so um hot spots are bad um if you
+ 
+
+ align:start position:0%
+so um hot spots are bad um if you
+reverse bias your devices um you can
+
+ align:start position:0%
+reverse bias your devices um you can
+ 
+
+ align:start position:0%
+reverse bias your devices um you can
+enter what's called a breakdown regime
+
+ align:start position:0%
+enter what's called a breakdown regime
+ 
+
+ align:start position:0%
+enter what's called a breakdown regime
+uh that essentially is is is is driven
+
+ align:start position:0%
+uh that essentially is is is is driven
+ 
+
+ align:start position:0%
+uh that essentially is is is is driven
+often times in a real solar cell by
+
+ align:start position:0%
+often times in a real solar cell by
+ 
+
+ align:start position:0%
+often times in a real solar cell by
+isolated points in your say weaknesses
+
+ align:start position:0%
+isolated points in your say weaknesses
+ 
+
+ align:start position:0%
+isolated points in your say weaknesses
+in the PN Junction where current is
+
+ align:start position:0%
+in the PN Junction where current is
+ 
+
+ align:start position:0%
+in the PN Junction where current is
+going to flow and that leads to the
+
+ align:start position:0%
+going to flow and that leads to the
+ 
+
+ align:start position:0%
+going to flow and that leads to the
+Hotpot failure I just mentioned here's
+
+ align:start position:0%
+Hotpot failure I just mentioned here's
+ 
+
+ align:start position:0%
+Hotpot failure I just mentioned here's
+um thermographic Imaging not using the
+
+ align:start position:0%
+um thermographic Imaging not using the
+ 
+
+ align:start position:0%
+um thermographic Imaging not using the
+fancy camera that we have downstairs
+
+ align:start position:0%
+fancy camera that we have downstairs
+ 
+
+ align:start position:0%
+fancy camera that we have downstairs
+using a much
+
+ align:start position:0%
+using a much
+ 
+
+ align:start position:0%
+using a much
+simpler camera out in the field lower
+
+ align:start position:0%
+simpler camera out in the field lower
+ 
+
+ align:start position:0%
+simpler camera out in the field lower
+cost it's uh these are high enough
+
+ align:start position:0%
+cost it's uh these are high enough
+ 
+
+ align:start position:0%
+cost it's uh these are high enough
+temperature variances to be able to
+
+ align:start position:0%
+temperature variances to be able to
+ 
+
+ align:start position:0%
+temperature variances to be able to
+detect using pretty low tech technology
+
+ align:start position:0%
+detect using pretty low tech technology
+ 
+
+ align:start position:0%
+detect using pretty low tech technology
+it's not a small amount of current going
+
+ align:start position:0%
+it's not a small amount of current going
+ 
+
+ align:start position:0%
+it's not a small amount of current going
+through a solar cell these are large
+
+ align:start position:0%
+through a solar cell these are large
+ 
+
+ align:start position:0%
+through a solar cell these are large
+massive amounts of current going through
+
+ align:start position:0%
+massive amounts of current going through
+ 
+
+ align:start position:0%
+massive amounts of current going through
+defective cells in the field and so you
+
+ align:start position:0%
+defective cells in the field and so you
+ 
+
+ align:start position:0%
+defective cells in the field and so you
+can use these um you can use these
+
+ align:start position:0%
+can use these um you can use these
+ 
+
+ align:start position:0%
+can use these um you can use these
+cameras to visualize the underperforming
+
+ align:start position:0%
+cameras to visualize the underperforming
+ 
+
+ align:start position:0%
+cameras to visualize the underperforming
+cells inside of modules and that's
+
+ align:start position:0%
+cells inside of modules and that's
+ 
+
+ align:start position:0%
+cells inside of modules and that's
+pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nifty all right so we planted that flag
+
+ align:start position:0%
+nifty all right so we planted that flag
+ 
+
+ align:start position:0%
+nifty all right so we planted that flag
+and let's come back to it um we're going
+
+ align:start position:0%
+and let's come back to it um we're going
+ 
+
+ align:start position:0%
+and let's come back to it um we're going
+to describe how microinverters and micro
+
+ align:start position:0%
+to describe how microinverters and micro
+ 
+
+ align:start position:0%
+to describe how microinverters and micro
+Electronics can improve module
+
+ align:start position:0%
+Electronics can improve module
+ 
+
+ align:start position:0%
+Electronics can improve module
+performance output um even if you didn't
+
+ align:start position:0%
+performance output um even if you didn't
+ 
+
+ align:start position:0%
+performance output um even if you didn't
+follow all the detail of the explanation
+
+ align:start position:0%
+follow all the detail of the explanation
+ 
+
+ align:start position:0%
+follow all the detail of the explanation
+until now you can appreciate the fact
+
+ align:start position:0%
+until now you can appreciate the fact
+ 
+
+ align:start position:0%
+until now you can appreciate the fact
+that a bad apple a bad solar cell uh
+
+ align:start position:0%
+that a bad apple a bad solar cell uh
+ 
+
+ align:start position:0%
+that a bad apple a bad solar cell uh
+connected in series or in parallel with
+
+ align:start position:0%
+connected in series or in parallel with
+ 
+
+ align:start position:0%
+connected in series or in parallel with
+the rest of them can cause the combined
+
+ align:start position:0%
+the rest of them can cause the combined
+ 
+
+ align:start position:0%
+the rest of them can cause the combined
+output of the module to be lower and so
+
+ align:start position:0%
+output of the module to be lower and so
+ 
+
+ align:start position:0%
+output of the module to be lower and so
+we're going to talk about how
+
+ align:start position:0%
+we're going to talk about how
+ 
+
+ align:start position:0%
+we're going to talk about how
+microelectronics and eventually
+
+ align:start position:0%
+microelectronics and eventually
+ 
+
+ align:start position:0%
+microelectronics and eventually
+microinverters can help resolve that
+
+ align:start position:0%
+microinverters can help resolve that
+ 
+
+ align:start position:0%
+microinverters can help resolve that
+either on a cell level or on a larger
+
+ align:start position:0%
+either on a cell level or on a larger
+ 
+
+ align:start position:0%
+either on a cell level or on a larger
+modu to module level the simple
+
+ align:start position:0%
+modu to module level the simple
+ 
+
+ align:start position:0%
+modu to module level the simple
+principle of a bypass diode of a cell is
+
+ align:start position:0%
+principle of a bypass diode of a cell is
+ 
+
+ align:start position:0%
+principle of a bypass diode of a cell is
+this if if the if the reverse bias
+
+ align:start position:0%
+this if if the if the reverse bias
+ 
+
+ align:start position:0%
+this if if the if the reverse bias
+current comes too large instead of
+
+ align:start position:0%
+current comes too large instead of
+ 
+
+ align:start position:0%
+current comes too large instead of
+forcing the current to flow through the
+
+ align:start position:0%
+forcing the current to flow through the
+ 
+
+ align:start position:0%
+forcing the current to flow through the
+bad cell you can force it to flow around
+
+ align:start position:0%
+bad cell you can force it to flow around
+ 
+
+ align:start position:0%
+bad cell you can force it to flow around
+um a bypass diode and therefore it it it
+
+ align:start position:0%
+um a bypass diode and therefore it it it
+ 
+
+ align:start position:0%
+um a bypass diode and therefore it it it
+it it short circuits it leaves a cell
+
+ align:start position:0%
+it it short circuits it leaves a cell
+ 
+
+ align:start position:0%
+it it short circuits it leaves a cell
+out of the circuit right the the current
+
+ align:start position:0%
+out of the circuit right the the current
+ 
+
+ align:start position:0%
+out of the circuit right the the current
+is Flowing around it and so you result
+
+ align:start position:0%
+is Flowing around it and so you result
+ 
+
+ align:start position:0%
+is Flowing around it and so you result
+in less of a degradation of your module
+
+ align:start position:0%
+in less of a degradation of your module
+ 
+
+ align:start position:0%
+in less of a degradation of your module
+to put it uh from an equivalent IV curve
+
+ align:start position:0%
+to put it uh from an equivalent IV curve
+ 
+
+ align:start position:0%
+to put it uh from an equivalent IV curve
+perspective instead of adding this IV
+
+ align:start position:0%
+perspective instead of adding this IV
+ 
+
+ align:start position:0%
+perspective instead of adding this IV
+curve here with the rest of them you're
+
+ align:start position:0%
+curve here with the rest of them you're
+ 
+
+ align:start position:0%
+curve here with the rest of them you're
+simply moving the current around it so
+
+ align:start position:0%
+simply moving the current around it so
+ 
+
+ align:start position:0%
+simply moving the current around it so
+you'd have the end good cells and and
+
+ align:start position:0%
+you'd have the end good cells and and
+ 
+
+ align:start position:0%
+you'd have the end good cells and and
+that's it end of story the 10th cell
+
+ align:start position:0%
+that's it end of story the 10th cell
+ 
+
+ align:start position:0%
+that's it end of story the 10th cell
+would just be taken out of your circuit
+
+ align:start position:0%
+would just be taken out of your circuit
+ 
+
+ align:start position:0%
+would just be taken out of your circuit
+it would be pushed
+
+ align:start position:0%
+it would be pushed
+ 
+
+ align:start position:0%
+it would be pushed
+aside okay so uh on a cell level that
+
+ align:start position:0%
+aside okay so uh on a cell level that
+ 
+
+ align:start position:0%
+aside okay so uh on a cell level that
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+um skip over a couple of these I think
+
+ align:start position:0%
+um skip over a couple of these I think
+ 
+
+ align:start position:0%
+um skip over a couple of these I think
+on a module level as well it can make a
+
+ align:start position:0%
+on a module level as well it can make a
+ 
+
+ align:start position:0%
+on a module level as well it can make a
+lot of sense and here it it really does
+
+ align:start position:0%
+lot of sense and here it it really does
+ 
+
+ align:start position:0%
+lot of sense and here it it really does
+because you're um the uh shading losses
+
+ align:start position:0%
+because you're um the uh shading losses
+ 
+
+ align:start position:0%
+because you're um the uh shading losses
+on a module level tend to be more severe
+
+ align:start position:0%
+on a module level tend to be more severe
+ 
+
+ align:start position:0%
+on a module level tend to be more severe
+you could have for example a tree in the
+
+ align:start position:0%
+you could have for example a tree in the
+ 
+
+ align:start position:0%
+you could have for example a tree in the
+wrong place or a telephone pole
+
+ align:start position:0%
+wrong place or a telephone pole
+ 
+
+ align:start position:0%
+wrong place or a telephone pole
+somewhere uh shading one particular
+
+ align:start position:0%
+somewhere uh shading one particular
+ 
+
+ align:start position:0%
+somewhere uh shading one particular
+module in an array an array of modules
+
+ align:start position:0%
+module in an array an array of modules
+ 
+
+ align:start position:0%
+module in an array an array of modules
+on my roof for example there are 12
+
+ align:start position:0%
+on my roof for example there are 12
+ 
+
+ align:start position:0%
+on my roof for example there are 12
+sharp 187 right so if you have uh a
+
+ align:start position:0%
+sharp 187 right so if you have uh a
+ 
+
+ align:start position:0%
+sharp 187 right so if you have uh a
+series of these modules up on the roof
+
+ align:start position:0%
+series of these modules up on the roof
+ 
+
+ align:start position:0%
+series of these modules up on the roof
+um you can cause the current to
+
+ align:start position:0%
+um you can cause the current to
+ 
+
+ align:start position:0%
+um you can cause the current to
+circumvent one of the modules that's
+
+ align:start position:0%
+circumvent one of the modules that's
+ 
+
+ align:start position:0%
+circumvent one of the modules that's
+underperforming again using the bypass
+
+ align:start position:0%
+underperforming again using the bypass
+ 
+
+ align:start position:0%
+underperforming again using the bypass
+diodes and those are fairly standard in
+
+ align:start position:0%
+diodes and those are fairly standard in
+ 
+
+ align:start position:0%
+diodes and those are fairly standard in
+most of the junction boxes so inside of
+
+ align:start position:0%
+most of the junction boxes so inside of
+ 
+
+ align:start position:0%
+most of the junction boxes so inside of
+here there is uh some very simple
+
+ align:start position:0%
+here there is uh some very simple
+ 
+
+ align:start position:0%
+here there is uh some very simple
+Electronics to prevent uh the modules
+
+ align:start position:0%
+Electronics to prevent uh the modules
+ 
+
+ align:start position:0%
+Electronics to prevent uh the modules
+from becoming power syns and perhaps
+
+ align:start position:0%
+from becoming power syns and perhaps
+ 
+
+ align:start position:0%
+from becoming power syns and perhaps
+even drawing power from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um okay so uh
+
+ align:start position:0%
+okay um okay so uh
+ 
+
+ align:start position:0%
+okay um okay so uh
+microinverters some people say well
+
+ align:start position:0%
+microinverters some people say well
+ 
+
+ align:start position:0%
+microinverters some people say well
+instead of just managing power on a DC
+
+ align:start position:0%
+instead of just managing power on a DC
+ 
+
+ align:start position:0%
+instead of just managing power on a DC
+basis and either dealing with the
+
+ align:start position:0%
+basis and either dealing with the
+ 
+
+ align:start position:0%
+basis and either dealing with the
+mismatch loss or cutting bad apples out
+
+ align:start position:0%
+mismatch loss or cutting bad apples out
+ 
+
+ align:start position:0%
+mismatch loss or cutting bad apples out
+of the circuit altogether let's do
+
+ align:start position:0%
+of the circuit altogether let's do
+ 
+
+ align:start position:0%
+of the circuit altogether let's do
+something even better let's try to to
+
+ align:start position:0%
+something even better let's try to to
+ 
+
+ align:start position:0%
+something even better let's try to to
+put this in in in uh childhood education
+
+ align:start position:0%
+put this in in in uh childhood education
+ 
+
+ align:start position:0%
+put this in in in uh childhood education
+terms let's let every module perform up
+
+ align:start position:0%
+terms let's let every module perform up
+ 
+
+ align:start position:0%
+terms let's let every module perform up
+to their most to the greatest potential
+
+ align:start position:0%
+to their most to the greatest potential
+ 
+
+ align:start position:0%
+to their most to the greatest potential
+and then everybody is happy right so
+
+ align:start position:0%
+and then everybody is happy right so
+ 
+
+ align:start position:0%
+and then everybody is happy right so
+we're going to convert the power
+
+ align:start position:0%
+we're going to convert the power
+ 
+
+ align:start position:0%
+we're going to convert the power
+directly on the back of the module into
+
+ align:start position:0%
+directly on the back of the module into
+ 
+
+ align:start position:0%
+directly on the back of the module into
+AC alternating current and then we're
+
+ align:start position:0%
+AC alternating current and then we're
+ 
+
+ align:start position:0%
+AC alternating current and then we're
+going to use Electronics from there to
+
+ align:start position:0%
+going to use Electronics from there to
+ 
+
+ align:start position:0%
+going to use Electronics from there to
+essentially add the add the uh uh
+
+ align:start position:0%
+essentially add the add the uh uh
+ 
+
+ align:start position:0%
+essentially add the add the uh uh
+currents together once we have defined
+
+ align:start position:0%
+currents together once we have defined
+ 
+
+ align:start position:0%
+currents together once we have defined
+the voltage at 120 volts at alternating
+
+ align:start position:0%
+the voltage at 120 volts at alternating
+ 
+
+ align:start position:0%
+the voltage at 120 volts at alternating
+current and uh and the advantage of that
+
+ align:start position:0%
+current and uh and the advantage of that
+ 
+
+ align:start position:0%
+current and uh and the advantage of that
+is that if something if one module is
+
+ align:start position:0%
+is that if something if one module is
+ 
+
+ align:start position:0%
+is that if something if one module is
+underperforming instead of contri zero
+
+ align:start position:0%
+underperforming instead of contri zero
+ 
+
+ align:start position:0%
+underperforming instead of contri zero
+it's now contributing some fraction if
+
+ align:start position:0%
+it's now contributing some fraction if
+ 
+
+ align:start position:0%
+it's now contributing some fraction if
+the mismatch was small enough not to
+
+ align:start position:0%
+the mismatch was small enough not to
+ 
+
+ align:start position:0%
+the mismatch was small enough not to
+trip any of the bypass diodes but still
+
+ align:start position:0%
+trip any of the bypass diodes but still
+ 
+
+ align:start position:0%
+trip any of the bypass diodes but still
+degrade the power of the overall system
+
+ align:start position:0%
+degrade the power of the overall system
+ 
+
+ align:start position:0%
+degrade the power of the overall system
+now you're able to recover you're able
+
+ align:start position:0%
+now you're able to recover you're able
+ 
+
+ align:start position:0%
+now you're able to recover you're able
+to allow that good module to perform up
+
+ align:start position:0%
+to allow that good module to perform up
+ 
+
+ align:start position:0%
+to allow that good module to perform up
+to its true potential instead of being
+
+ align:start position:0%
+to its true potential instead of being
+ 
+
+ align:start position:0%
+to its true potential instead of being
+dragged down by the others and so the
+
+ align:start position:0%
+dragged down by the others and so the
+ 
+
+ align:start position:0%
+dragged down by the others and so the
+microinverter companies that are uh
+
+ align:start position:0%
+microinverter companies that are uh
+ 
+
+ align:start position:0%
+microinverter companies that are uh
+proposing and and actually marketing and
+
+ align:start position:0%
+proposing and and actually marketing and
+ 
+
+ align:start position:0%
+proposing and and actually marketing and
+selling modules that apply the
+
+ align:start position:0%
+selling modules that apply the
+ 
+
+ align:start position:0%
+selling modules that apply the
+electronics directly in the back of the
+
+ align:start position:0%
+electronics directly in the back of the
+ 
+
+ align:start position:0%
+electronics directly in the back of the
+solar panels have the advantage of being
+
+ align:start position:0%
+solar panels have the advantage of being
+ 
+
+ align:start position:0%
+solar panels have the advantage of being
+able to eek out several additional
+
+ align:start position:0%
+able to eek out several additional
+ 
+
+ align:start position:0%
+able to eek out several additional
+percent of total power from the from the
+
+ align:start position:0%
+percent of total power from the from the
+ 
+
+ align:start position:0%
+percent of total power from the from the
+array from the system the disadvantage
+
+ align:start position:0%
+array from the system the disadvantage
+ 
+
+ align:start position:0%
+array from the system the disadvantage
+of Distributing these microinverter
+
+ align:start position:0%
+of Distributing these microinverter
+ 
+
+ align:start position:0%
+of Distributing these microinverter
+components over every single module
+
+ align:start position:0%
+components over every single module
+ 
+
+ align:start position:0%
+components over every single module
+is a lot of them cost money you have to
+
+ align:start position:0%
+is a lot of them cost money you have to
+ 
+
+ align:start position:0%
+is a lot of them cost money you have to
+make a lot of them they cost money
+
+ align:start position:0%
+make a lot of them they cost money
+ 
+
+ align:start position:0%
+make a lot of them they cost money
+they're costly and meantime between
+
+ align:start position:0%
+they're costly and meantime between
+ 
+
+ align:start position:0%
+they're costly and meantime between
+failures increases right potentially
+
+ align:start position:0%
+failures increases right potentially
+ 
+
+ align:start position:0%
+failures increases right potentially
+potentially um so if you if you have an
+
+ align:start position:0%
+potentially um so if you if you have an
+ 
+
+ align:start position:0%
+potentially um so if you if you have an
+inverter how many people know how long
+
+ align:start position:0%
+inverter how many people know how long
+ 
+
+ align:start position:0%
+inverter how many people know how long
+an inverter lasts before it needs to be
+
+ align:start position:0%
+an inverter lasts before it needs to be
+ 
+
+ align:start position:0%
+an inverter lasts before it needs to be
+replaced
+
+ align:start position:0%
+replaced
+ 
+
+ align:start position:0%
+replaced
+typically five to 10 years now it's it's
+
+ align:start position:0%
+typically five to 10 years now it's it's
+ 
+
+ align:start position:0%
+typically five to 10 years now it's it's
+up to say 7 to 12 but yeah somewhere in
+
+ align:start position:0%
+up to say 7 to 12 but yeah somewhere in
+ 
+
+ align:start position:0%
+up to say 7 to 12 but yeah somewhere in
+that range less than the 20 to 30 year
+
+ align:start position:0%
+that range less than the 20 to 30 year
+ 
+
+ align:start position:0%
+that range less than the 20 to 30 year
+LIF of your of your array and so now if
+
+ align:start position:0%
+LIF of your of your array and so now if
+ 
+
+ align:start position:0%
+LIF of your of your array and so now if
+you have these distributed little
+
+ align:start position:0%
+you have these distributed little
+ 
+
+ align:start position:0%
+you have these distributed little
+inverters across every solar panel uh
+
+ align:start position:0%
+inverters across every solar panel uh
+ 
+
+ align:start position:0%
+inverters across every solar panel uh
+and they Fizz out after a certain amount
+
+ align:start position:0%
+and they Fizz out after a certain amount
+ 
+
+ align:start position:0%
+and they Fizz out after a certain amount
+of time you have to go somebody has to
+
+ align:start position:0%
+of time you have to go somebody has to
+ 
+
+ align:start position:0%
+of time you have to go somebody has to
+go up there and replace them first
+
+ align:start position:0%
+go up there and replace them first
+ 
+
+ align:start position:0%
+go up there and replace them first
+identify where they where they went down
+
+ align:start position:0%
+identify where they where they went down
+ 
+
+ align:start position:0%
+identify where they where they went down
+and then replace them so microinverter
+
+ align:start position:0%
+and then replace them so microinverter
+ 
+
+ align:start position:0%
+and then replace them so microinverter
+longevity is an important part of
+
+ align:start position:0%
+longevity is an important part of
+ 
+
+ align:start position:0%
+longevity is an important part of
+reducing risk and marketing inverters so
+
+ align:start position:0%
+reducing risk and marketing inverters so
+ 
+
+ align:start position:0%
+reducing risk and marketing inverters so
+the microinverter community is helping
+
+ align:start position:0%
+the microinverter community is helping
+ 
+
+ align:start position:0%
+the microinverter community is helping
+to push or improve the quality of
+
+ align:start position:0%
+to push or improve the quality of
+ 
+
+ align:start position:0%
+to push or improve the quality of
+inverters over the entire solar Spectrum
+
+ align:start position:0%
+inverters over the entire solar Spectrum
+ 
+
+ align:start position:0%
+inverters over the entire solar Spectrum
+which is kind of cool yeah what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+so my understanding from reie Ram who's
+
+ align:start position:0%
+so my understanding from reie Ram who's
+ 
+
+ align:start position:0%
+so my understanding from reie Ram who's
+actually down in in arpa right now um
+
+ align:start position:0%
+actually down in in arpa right now um
+ 
+
+ align:start position:0%
+actually down in in arpa right now um
+he's a professor at MIT who's been been
+
+ align:start position:0%
+he's a professor at MIT who's been been
+ 
+
+ align:start position:0%
+he's a professor at MIT who's been been
+assisting uh the doe over the past
+
+ align:start position:0%
+assisting uh the doe over the past
+ 
+
+ align:start position:0%
+assisting uh the doe over the past
+couple of years um many uh most failure
+
+ align:start position:0%
+couple of years um many uh most failure
+ 
+
+ align:start position:0%
+couple of years um many uh most failure
+and inverters relates to the Power
+
+ align:start position:0%
+and inverters relates to the Power
+ 
+
+ align:start position:0%
+and inverters relates to the Power
+Electronics itself and the high-speed
+
+ align:start position:0%
+Electronics itself and the high-speed
+ 
+
+ align:start position:0%
+Electronics itself and the high-speed
+switchers that are used that's my
+
+ align:start position:0%
+switchers that are used that's my
+ 
+
+ align:start position:0%
+switchers that are used that's my
+understanding um I could uh I could look
+
+ align:start position:0%
+understanding um I could uh I could look
+ 
+
+ align:start position:0%
+understanding um I could uh I could look
+into that a little bit more and get you
+
+ align:start position:0%
+into that a little bit more and get you
+ 
+
+ align:start position:0%
+into that a little bit more and get you
+more details about precise inverter
+
+ align:start position:0%
+more details about precise inverter
+ 
+
+ align:start position:0%
+more details about precise inverter
+failure modes uh but uh that is that is
+
+ align:start position:0%
+failure modes uh but uh that is that is
+ 
+
+ align:start position:0%
+failure modes uh but uh that is that is
+my rudimentary understanding from
+
+ align:start position:0%
+my rudimentary understanding from
+ 
+
+ align:start position:0%
+my rudimentary understanding from
+discussions with him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um sorry my screen is still cracked it's
+
+ align:start position:0%
+um sorry my screen is still cracked it's
+ 
+
+ align:start position:0%
+um sorry my screen is still cracked it's
+going to be fixed tonight um advantages
+
+ align:start position:0%
+going to be fixed tonight um advantages
+ 
+
+ align:start position:0%
+going to be fixed tonight um advantages
+of integrated Power Electronics maximum
+
+ align:start position:0%
+of integrated Power Electronics maximum
+ 
+
+ align:start position:0%
+of integrated Power Electronics maximum
+PowerPoint tracking disadvantages okay
+
+ align:start position:0%
+PowerPoint tracking disadvantages okay
+ 
+
+ align:start position:0%
+PowerPoint tracking disadvantages okay
+yeah okay and so it's it's still a
+
+ align:start position:0%
+yeah okay and so it's it's still a
+ 
+
+ align:start position:0%
+yeah okay and so it's it's still a
+relatively Hot Topic there there was an
+
+ align:start position:0%
+relatively Hot Topic there there was an
+ 
+
+ align:start position:0%
+relatively Hot Topic there there was an
+RPA call uh for improved Power
+
+ align:start position:0%
+RPA call uh for improved Power
+ 
+
+ align:start position:0%
+RPA call uh for improved Power
+Electronics across uh solar and other
+
+ align:start position:0%
+Electronics across uh solar and other
+ 
+
+ align:start position:0%
+Electronics across uh solar and other
+Industries um and there is some
+
+ align:start position:0%
+Industries um and there is some
+ 
+
+ align:start position:0%
+Industries um and there is some
+discussion in the PV Community as to how
+
+ align:start position:0%
+discussion in the PV Community as to how
+ 
+
+ align:start position:0%
+discussion in the PV Community as to how
+much to adopt this new technology
+
+ align:start position:0%
+much to adopt this new technology
+ 
+
+ align:start position:0%
+much to adopt this new technology
+especially in residential systems so
+
+ align:start position:0%
+especially in residential systems so
+ 
+
+ align:start position:0%
+especially in residential systems so
+Trends um in in installations in general
+
+ align:start position:0%
+Trends um in in installations in general
+ 
+
+ align:start position:0%
+Trends um in in installations in general
+uh in the past um installations were uh
+
+ align:start position:0%
+uh in the past um installations were uh
+ 
+
+ align:start position:0%
+uh in the past um installations were uh
+heavily labor intensive uh there is now
+
+ align:start position:0%
+heavily labor intensive uh there is now
+ 
+
+ align:start position:0%
+heavily labor intensive uh there is now
+a large amount of pre-assembly done
+
+ align:start position:0%
+a large amount of pre-assembly done
+ 
+
+ align:start position:0%
+a large amount of pre-assembly done
+before the modules hit the roof uh but
+
+ align:start position:0%
+before the modules hit the roof uh but
+ 
+
+ align:start position:0%
+before the modules hit the roof uh but
+there's still a sizable number of
+
+ align:start position:0%
+there's still a sizable number of
+ 
+
+ align:start position:0%
+there's still a sizable number of
+components that go into every single
+
+ align:start position:0%
+components that go into every single
+ 
+
+ align:start position:0%
+components that go into every single
+solar module and um that takes time to
+
+ align:start position:0%
+solar module and um that takes time to
+ 
+
+ align:start position:0%
+solar module and um that takes time to
+mount everything out there in the field
+
+ align:start position:0%
+mount everything out there in the field
+ 
+
+ align:start position:0%
+mount everything out there in the field
+uh so what are some other you know what
+
+ align:start position:0%
+uh so what are some other you know what
+ 
+
+ align:start position:0%
+uh so what are some other you know what
+is what is the the dream of any solar uh
+
+ align:start position:0%
+is what is the the dream of any solar uh
+ 
+
+ align:start position:0%
+is what is the the dream of any solar uh
+installer is to get this roll of
+
+ align:start position:0%
+installer is to get this roll of
+ 
+
+ align:start position:0%
+installer is to get this roll of
+material that just unrolls unfurls onto
+
+ align:start position:0%
+material that just unrolls unfurls onto
+ 
+
+ align:start position:0%
+material that just unrolls unfurls onto
+the roof and using a staple gun bang
+
+ align:start position:0%
+the roof and using a staple gun bang
+ 
+
+ align:start position:0%
+the roof and using a staple gun bang
+bang bang bang bang or a nail gun
+
+ align:start position:0%
+bang bang bang bang or a nail gun
+ 
+
+ align:start position:0%
+bang bang bang bang or a nail gun
+everything is is is locked down it's
+
+ align:start position:0%
+everything is is is locked down it's
+ 
+
+ align:start position:0%
+everything is is is locked down it's
+lightweight it doesn't underperform when
+
+ align:start position:0%
+lightweight it doesn't underperform when
+ 
+
+ align:start position:0%
+lightweight it doesn't underperform when
+um when uh it it gets too warm uh these
+
+ align:start position:0%
+um when uh it it gets too warm uh these
+ 
+
+ align:start position:0%
+um when uh it it gets too warm uh these
+are all the specs that would constitute
+
+ align:start position:0%
+are all the specs that would constitute
+ 
+
+ align:start position:0%
+are all the specs that would constitute
+say an ideal solar module we don't get
+
+ align:start position:0%
+say an ideal solar module we don't get
+ 
+
+ align:start position:0%
+say an ideal solar module we don't get
+that lucky we have to make compromises
+
+ align:start position:0%
+that lucky we have to make compromises
+ 
+
+ align:start position:0%
+that lucky we have to make compromises
+in reality and um say for example on my
+
+ align:start position:0%
+in reality and um say for example on my
+ 
+
+ align:start position:0%
+in reality and um say for example on my
+roof there was a soft spot on the roof
+
+ align:start position:0%
+roof there was a soft spot on the roof
+ 
+
+ align:start position:0%
+roof there was a soft spot on the roof
+that had to be worked around uh the
+
+ align:start position:0%
+that had to be worked around uh the
+ 
+
+ align:start position:0%
+that had to be worked around uh the
+structur engineer had to be called back
+
+ align:start position:0%
+structur engineer had to be called back
+ 
+
+ align:start position:0%
+structur engineer had to be called back
+and evaluate and figure out whether or
+
+ align:start position:0%
+and evaluate and figure out whether or
+ 
+
+ align:start position:0%
+and evaluate and figure out whether or
+not it needed reinforcement and so forth
+
+ align:start position:0%
+not it needed reinforcement and so forth
+ 
+
+ align:start position:0%
+not it needed reinforcement and so forth
+so we're we're we're still far away in
+
+ align:start position:0%
+so we're we're we're still far away in
+ 
+
+ align:start position:0%
+so we're we're we're still far away in
+terms of where we need to be for solar
+
+ align:start position:0%
+terms of where we need to be for solar
+ 
+
+ align:start position:0%
+terms of where we need to be for solar
+installations to really be uh truly low
+
+ align:start position:0%
+installations to really be uh truly low
+ 
+
+ align:start position:0%
+installations to really be uh truly low
+cost uh and a lot of it has to do with
+
+ align:start position:0%
+cost uh and a lot of it has to do with
+ 
+
+ align:start position:0%
+cost uh and a lot of it has to do with
+the balance of system
+
+ align:start position:0%
+the balance of system
+ 
+
+ align:start position:0%
+the balance of system
+design um so I I mentioned a few
+
+ align:start position:0%
+design um so I I mentioned a few
+ 
+
+ align:start position:0%
+design um so I I mentioned a few
+companies are are attempting to uh
+
+ align:start position:0%
+companies are are attempting to uh
+ 
+
+ align:start position:0%
+companies are are attempting to uh
+integrate the the connections into this
+
+ align:start position:0%
+integrate the the connections into this
+ 
+
+ align:start position:0%
+integrate the the connections into this
+fasile click uh uh lock mechanism um
+
+ align:start position:0%
+fasile click uh uh lock mechanism um
+ 
+
+ align:start position:0%
+fasile click uh uh lock mechanism um
+there have been patents filed I think
+
+ align:start position:0%
+there have been patents filed I think
+ 
+
+ align:start position:0%
+there have been patents filed I think
+since the 1990s on this probably even
+
+ align:start position:0%
+since the 1990s on this probably even
+ 
+
+ align:start position:0%
+since the 1990s on this probably even
+earlier um more recently uh some
+
+ align:start position:0%
+earlier um more recently uh some
+ 
+
+ align:start position:0%
+earlier um more recently uh some
+companies have marketed a product in
+
+ align:start position:0%
+companies have marketed a product in
+ 
+
+ align:start position:0%
+companies have marketed a product in
+this regard and of course that increases
+
+ align:start position:0%
+this regard and of course that increases
+ 
+
+ align:start position:0%
+this regard and of course that increases
+the uh the facility of installation
+
+ align:start position:0%
+the uh the facility of installation
+ 
+
+ align:start position:0%
+the uh the facility of installation
+there's even a few that are selling uh I
+
+ align:start position:0%
+there's even a few that are selling uh I
+ 
+
+ align:start position:0%
+there's even a few that are selling uh I
+think it was a keynet lows and uh for a
+
+ align:start position:0%
+think it was a keynet lows and uh for a
+ 
+
+ align:start position:0%
+think it was a keynet lows and uh for a
+Time BP Solar was selling at Home Depot
+
+ align:start position:0%
+Time BP Solar was selling at Home Depot
+ 
+
+ align:start position:0%
+Time BP Solar was selling at Home Depot
+uh there are examples of companies
+
+ align:start position:0%
+uh there are examples of companies
+ 
+
+ align:start position:0%
+uh there are examples of companies
+beginning to Market their product at
+
+ align:start position:0%
+beginning to Market their product at
+ 
+
+ align:start position:0%
+beginning to Market their product at
+hardware stores question could youing
+
+ align:start position:0%
+hardware stores question could youing
+ 
+
+ align:start position:0%
+hardware stores question could youing
+included in balance of systems yes so
+
+ align:start position:0%
+included in balance of systems yes so
+ 
+
+ align:start position:0%
+included in balance of systems yes so
+balance of systems um is defined as
+
+ align:start position:0%
+balance of systems um is defined as
+ 
+
+ align:start position:0%
+balance of systems um is defined as
+everything beyond the module so that
+
+ align:start position:0%
+everything beyond the module so that
+ 
+
+ align:start position:0%
+everything beyond the module so that
+would include the wiring the the framing
+
+ align:start position:0%
+would include the wiring the the framing
+ 
+
+ align:start position:0%
+would include the wiring the the framing
+the racking the inverter um yes that
+
+ align:start position:0%
+the racking the inverter um yes that
+ 
+
+ align:start position:0%
+the racking the inverter um yes that
+that is that is balance of systems
+
+ align:start position:0%
+that is that is balance of systems
+ 
+
+ align:start position:0%
+that is that is balance of systems
+excellent question excellent
+
+ align:start position:0%
+excellent question excellent
+ 
+
+ align:start position:0%
+excellent question excellent
+question so um we're going to talk about
+
+ align:start position:0%
+question so um we're going to talk about
+ 
+
+ align:start position:0%
+question so um we're going to talk about
+some of the tests that the PB module
+
+ align:start position:0%
+some of the tests that the PB module
+ 
+
+ align:start position:0%
+some of the tests that the PB module
+must pass to ensure reliable
+
+ align:start position:0%
+must pass to ensure reliable
+ 
+
+ align:start position:0%
+must pass to ensure reliable
+multi-decade service life in the field
+
+ align:start position:0%
+multi-decade service life in the field
+ 
+
+ align:start position:0%
+multi-decade service life in the field
+and some of the shortcomings of the
+
+ align:start position:0%
+and some of the shortcomings of the
+ 
+
+ align:start position:0%
+and some of the shortcomings of the
+tests uh I'm going to motivate this by
+
+ align:start position:0%
+tests uh I'm going to motivate this by
+ 
+
+ align:start position:0%
+tests uh I'm going to motivate this by
+saying um uh there's there's reason to
+
+ align:start position:0%
+saying um uh there's there's reason to
+ 
+
+ align:start position:0%
+saying um uh there's there's reason to
+be concerned uh in the early days of the
+
+ align:start position:0%
+be concerned uh in the early days of the
+ 
+
+ align:start position:0%
+be concerned uh in the early days of the
+indust indry about performance and
+
+ align:start position:0%
+indust indry about performance and
+ 
+
+ align:start position:0%
+indust indry about performance and
+reliability this was a study done by
+
+ align:start position:0%
+reliability this was a study done by
+ 
+
+ align:start position:0%
+reliability this was a study done by
+Arie Jacobson uh the group that's
+
+ align:start position:0%
+Arie Jacobson uh the group that's
+ 
+
+ align:start position:0%
+Arie Jacobson uh the group that's
+working with the World Bank will be as
+
+ align:start position:0%
+working with the World Bank will be as
+ 
+
+ align:start position:0%
+working with the World Bank will be as
+well working with Arie Jacobson uh on
+
+ align:start position:0%
+well working with Arie Jacobson uh on
+ 
+
+ align:start position:0%
+well working with Arie Jacobson uh on
+their class project uh he's a professor
+
+ align:start position:0%
+their class project uh he's a professor
+ 
+
+ align:start position:0%
+their class project uh he's a professor
+at hul University in California uh
+
+ align:start position:0%
+at hul University in California uh
+ 
+
+ align:start position:0%
+at hul University in California uh
+during his PhD with Dan camon and
+
+ align:start position:0%
+during his PhD with Dan camon and
+ 
+
+ align:start position:0%
+during his PhD with Dan camon and
+Berkeley uh he did an audit of rated
+
+ align:start position:0%
+Berkeley uh he did an audit of rated
+ 
+
+ align:start position:0%
+Berkeley uh he did an audit of rated
+versus actual power outputs of solar
+
+ align:start position:0%
+versus actual power outputs of solar
+ 
+
+ align:start position:0%
+versus actual power outputs of solar
+modules in the field of Kenya in Africa
+
+ align:start position:0%
+modules in the field of Kenya in Africa
+ 
+
+ align:start position:0%
+modules in the field of Kenya in Africa
+and found uh rather large discrepancy
+
+ align:start position:0%
+and found uh rather large discrepancy
+ 
+
+ align:start position:0%
+and found uh rather large discrepancy
+between what was promised and what was
+
+ align:start position:0%
+between what was promised and what was
+ 
+
+ align:start position:0%
+between what was promised and what was
+actually delivered this is a great
+
+ align:start position:0%
+actually delivered this is a great
+ 
+
+ align:start position:0%
+actually delivered this is a great
+example of um field work being done good
+
+ align:start position:0%
+example of um field work being done good
+ 
+
+ align:start position:0%
+example of um field work being done good
+old-fashioned detective work that leads
+
+ align:start position:0%
+old-fashioned detective work that leads
+ 
+
+ align:start position:0%
+old-fashioned detective work that leads
+to changes in the industry um that got a
+
+ align:start position:0%
+to changes in the industry um that got a
+ 
+
+ align:start position:0%
+to changes in the industry um that got a
+number of the underperformers to improve
+
+ align:start position:0%
+number of the underperformers to improve
+ 
+
+ align:start position:0%
+number of the underperformers to improve
+their their product so I I mentioned uh
+
+ align:start position:0%
+their their product so I I mentioned uh
+ 
+
+ align:start position:0%
+their their product so I I mentioned uh
+you know there there was there's a
+
+ align:start position:0%
+you know there there was there's a
+ 
+
+ align:start position:0%
+you know there there was there's a
+question of of the customer am I getting
+
+ align:start position:0%
+question of of the customer am I getting
+ 
+
+ align:start position:0%
+question of of the customer am I getting
+the real value that I've been promised
+
+ align:start position:0%
+the real value that I've been promised
+ 
+
+ align:start position:0%
+the real value that I've been promised
+uh especially in the absence of
+
+ align:start position:0%
+uh especially in the absence of
+ 
+
+ align:start position:0%
+uh especially in the absence of
+independent monitoring if you're not
+
+ align:start position:0%
+independent monitoring if you're not
+ 
+
+ align:start position:0%
+independent monitoring if you're not
+actively measuring the power output and
+
+ align:start position:0%
+actively measuring the power output and
+ 
+
+ align:start position:0%
+actively measuring the power output and
+recording it um there's always that
+
+ align:start position:0%
+recording it um there's always that
+ 
+
+ align:start position:0%
+recording it um there's always that
+question lingering so module testing and
+
+ align:start position:0%
+question lingering so module testing and
+ 
+
+ align:start position:0%
+question lingering so module testing and
+reliability is is meant to ensure
+
+ align:start position:0%
+reliability is is meant to ensure
+ 
+
+ align:start position:0%
+reliability is is meant to ensure
+product quality and output quality
+
+ align:start position:0%
+product quality and output quality
+ 
+
+ align:start position:0%
+product quality and output quality
+secondly it's safety I mentioned these
+
+ align:start position:0%
+secondly it's safety I mentioned these
+ 
+
+ align:start position:0%
+secondly it's safety I mentioned these
+thermographic cameras this is an example
+
+ align:start position:0%
+thermographic cameras this is an example
+ 
+
+ align:start position:0%
+thermographic cameras this is an example
+on an array of you know Hot Spot it's
+
+ align:start position:0%
+on an array of you know Hot Spot it's
+ 
+
+ align:start position:0%
+on an array of you know Hot Spot it's
+not too hot right now it's 36 degrees or
+
+ align:start position:0%
+not too hot right now it's 36 degrees or
+ 
+
+ align:start position:0%
+not too hot right now it's 36 degrees or
+so but everything else is down around 15
+
+ align:start position:0%
+so but everything else is down around 15
+ 
+
+ align:start position:0%
+so but everything else is down around 15
+if you imagine this being on a sunny day
+
+ align:start position:0%
+if you imagine this being on a sunny day
+ 
+
+ align:start position:0%
+if you imagine this being on a sunny day
+um a really sunny day this could uh this
+
+ align:start position:0%
+um a really sunny day this could uh this
+ 
+
+ align:start position:0%
+um a really sunny day this could uh this
+hot spot potentially could be getting up
+
+ align:start position:0%
+hot spot potentially could be getting up
+ 
+
+ align:start position:0%
+hot spot potentially could be getting up
+uh much higher uh so that's obviously of
+
+ align:start position:0%
+uh much higher uh so that's obviously of
+ 
+
+ align:start position:0%
+uh much higher uh so that's obviously of
+concern and um there's as well uh
+
+ align:start position:0%
+concern and um there's as well uh
+ 
+
+ align:start position:0%
+concern and um there's as well uh
+hotspots or or or heat that can be
+
+ align:start position:0%
+hotspots or or or heat that can be
+ 
+
+ align:start position:0%
+hotspots or or or heat that can be
+generated from the junction box on on
+
+ align:start position:0%
+generated from the junction box on on
+ 
+
+ align:start position:0%
+generated from the junction box on on
+the back um this contains a fair amount
+
+ align:start position:0%
+the back um this contains a fair amount
+ 
+
+ align:start position:0%
+the back um this contains a fair amount
+of electronics again and if there is uh
+
+ align:start position:0%
+of electronics again and if there is uh
+ 
+
+ align:start position:0%
+of electronics again and if there is uh
+some failure of the electronics inside
+
+ align:start position:0%
+some failure of the electronics inside
+ 
+
+ align:start position:0%
+some failure of the electronics inside
+of here you could have the combined
+
+ align:start position:0%
+of here you could have the combined
+ 
+
+ align:start position:0%
+of here you could have the combined
+power output of the entire module arcing
+
+ align:start position:0%
+power output of the entire module arcing
+ 
+
+ align:start position:0%
+power output of the entire module arcing
+right through a given component back
+
+ align:start position:0%
+right through a given component back
+ 
+
+ align:start position:0%
+right through a given component back
+here causing Sparks to fly and this is
+
+ align:start position:0%
+here causing Sparks to fly and this is
+ 
+
+ align:start position:0%
+here causing Sparks to fly and this is
+where this Photon International article
+
+ align:start position:0%
+where this Photon International article
+ 
+
+ align:start position:0%
+where this Photon International article
+from 2009 comes in where um they say uh
+
+ align:start position:0%
+from 2009 comes in where um they say uh
+ 
+
+ align:start position:0%
+from 2009 comes in where um they say uh
+it's extremely important the upshot of
+
+ align:start position:0%
+it's extremely important the upshot of
+ 
+
+ align:start position:0%
+it's extremely important the upshot of
+the entire article I I gave it to you in
+
+ align:start position:0%
+the entire article I I gave it to you in
+ 
+
+ align:start position:0%
+the entire article I I gave it to you in
+its entirety but the upshot is
+
+ align:start position:0%
+its entirety but the upshot is
+ 
+
+ align:start position:0%
+its entirety but the upshot is
+let's not play with fire meaning let's
+
+ align:start position:0%
+let's not play with fire meaning let's
+ 
+
+ align:start position:0%
+let's not play with fire meaning let's
+make sure that the safety standards of
+
+ align:start position:0%
+make sure that the safety standards of
+ 
+
+ align:start position:0%
+make sure that the safety standards of
+solar modules are really up to spec so
+
+ align:start position:0%
+solar modules are really up to spec so
+ 
+
+ align:start position:0%
+solar modules are really up to spec so
+that the risk of something
+
+ align:start position:0%
+that the risk of something
+ 
+
+ align:start position:0%
+that the risk of something
+catastrophically bad happening is
+
+ align:start position:0%
+catastrophically bad happening is
+ 
+
+ align:start position:0%
+catastrophically bad happening is
+negligible right because there's nothing
+
+ align:start position:0%
+negligible right because there's nothing
+ 
+
+ align:start position:0%
+negligible right because there's nothing
+worse for a nent industry than to have
+
+ align:start position:0%
+worse for a nent industry than to have
+ 
+
+ align:start position:0%
+worse for a nent industry than to have
+some uh dare I say it Fukushima
+
+ align:start position:0%
+some uh dare I say it Fukushima
+ 
+
+ align:start position:0%
+some uh dare I say it Fukushima
+equivalent occur right on on some very
+
+ align:start position:0%
+equivalent occur right on on some very
+ 
+
+ align:start position:0%
+equivalent occur right on on some very
+high-profile event that causes public
+
+ align:start position:0%
+high-profile event that causes public
+ 
+
+ align:start position:0%
+high-profile event that causes public
+opinion to sway against it so uh making
+
+ align:start position:0%
+opinion to sway against it so uh making
+ 
+
+ align:start position:0%
+opinion to sway against it so uh making
+sure that modules are safe is of most
+
+ align:start position:0%
+sure that modules are safe is of most
+ 
+
+ align:start position:0%
+sure that modules are safe is of most
+importance to preserving the positive
+
+ align:start position:0%
+importance to preserving the positive
+ 
+
+ align:start position:0%
+importance to preserving the positive
+image of solar and that's what this
+
+ align:start position:0%
+image of solar and that's what this
+ 
+
+ align:start position:0%
+image of solar and that's what this
+article here is is meant to convey and
+
+ align:start position:0%
+article here is is meant to convey and
+ 
+
+ align:start position:0%
+article here is is meant to convey and
+you're welcome to read it in detail it
+
+ align:start position:0%
+you're welcome to read it in detail it
+ 
+
+ align:start position:0%
+you're welcome to read it in detail it
+cites one particular example where that
+
+ align:start position:0%
+cites one particular example where that
+ 
+
+ align:start position:0%
+cites one particular example where that
+didn't happen and it did lead to a a
+
+ align:start position:0%
+didn't happen and it did lead to a a
+ 
+
+ align:start position:0%
+didn't happen and it did lead to a a
+little PR U uh event uh well justified
+
+ align:start position:0%
+little PR U uh event uh well justified
+ 
+
+ align:start position:0%
+little PR U uh event uh well justified
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+fact um shown here are a series of tests
+
+ align:start position:0%
+fact um shown here are a series of tests
+ 
+
+ align:start position:0%
+fact um shown here are a series of tests
+that one can conduct with uh solar
+
+ align:start position:0%
+that one can conduct with uh solar
+ 
+
+ align:start position:0%
+that one can conduct with uh solar
+modules um I showed a list of different
+
+ align:start position:0%
+modules um I showed a list of different
+ 
+
+ align:start position:0%
+modules um I showed a list of different
+um of IC tests standardized uh um
+
+ align:start position:0%
+um of IC tests standardized uh um
+ 
+
+ align:start position:0%
+um of IC tests standardized uh um
+protocols these are a series of tests
+
+ align:start position:0%
+protocols these are a series of tests
+ 
+
+ align:start position:0%
+protocols these are a series of tests
+typically between uh say 12 and 20 that
+
+ align:start position:0%
+typically between uh say 12 and 20 that
+ 
+
+ align:start position:0%
+typically between uh say 12 and 20 that
+uh represent a battery of tests for the
+
+ align:start position:0%
+uh represent a battery of tests for the
+ 
+
+ align:start position:0%
+uh represent a battery of tests for the
+solar module and if they pass it they
+
+ align:start position:0%
+solar module and if they pass it they
+ 
+
+ align:start position:0%
+solar module and if they pass it they
+are IEC certified and you'll see on the
+
+ align:start position:0%
+are IEC certified and you'll see on the
+ 
+
+ align:start position:0%
+are IEC certified and you'll see on the
+back of certain spec sheets like this
+
+ align:start position:0%
+back of certain spec sheets like this
+ 
+
+ align:start position:0%
+back of certain spec sheets like this
+one from First Solar right here the
+
+ align:start position:0%
+one from First Solar right here the
+ 
+
+ align:start position:0%
+one from First Solar right here the
+different uh testing agencies that have
+
+ align:start position:0%
+different uh testing agencies that have
+ 
+
+ align:start position:0%
+different uh testing agencies that have
+certified the module right these little
+
+ align:start position:0%
+certified the module right these little
+ 
+
+ align:start position:0%
+certified the module right these little
+uh logos represented so it says uh it's
+
+ align:start position:0%
+uh logos represented so it says uh it's
+ 
+
+ align:start position:0%
+uh logos represented so it says uh it's
+UL certified uh C Mark uh certified
+
+ align:start position:0%
+UL certified uh C Mark uh certified
+ 
+
+ align:start position:0%
+UL certified uh C Mark uh certified
+according to I spec
+
+ align:start position:0%
+according to I spec
+ 
+
+ align:start position:0%
+according to I spec
+61646 that's the one right up there at
+
+ align:start position:0%
+61646 that's the one right up there at
+ 
+
+ align:start position:0%
+61646 that's the one right up there at
+the top and so forth so specification or
+
+ align:start position:0%
+the top and so forth so specification or
+ 
+
+ align:start position:0%
+the top and so forth so specification or
+or or certification is very important
+
+ align:start position:0%
+or or certification is very important
+ 
+
+ align:start position:0%
+or or certification is very important
+what happens during testing well we'll
+
+ align:start position:0%
+what happens during testing well we'll
+ 
+
+ align:start position:0%
+what happens during testing well we'll
+see it because when I designed the front
+
+ align:start position:0%
+see it because when I designed the front
+ 
+
+ align:start position:0%
+see it because when I designed the front
+offer CSC Labs uh we designed it Roland
+
+ align:start position:0%
+offer CSC Labs uh we designed it Roland
+ 
+
+ align:start position:0%
+offer CSC Labs uh we designed it Roland
+Schindler and I with the I tests in mind
+
+ align:start position:0%
+Schindler and I with the I tests in mind
+ 
+
+ align:start position:0%
+Schindler and I with the I tests in mind
+so each of the pieces of equipment out
+
+ align:start position:0%
+so each of the pieces of equipment out
+ 
+
+ align:start position:0%
+so each of the pieces of equipment out
+there are to test one component of the I
+
+ align:start position:0%
+there are to test one component of the I
+ 
+
+ align:start position:0%
+there are to test one component of the I
+test um included in the test is
+
+ align:start position:0%
+test um included in the test is
+ 
+
+ align:start position:0%
+test um included in the test is
+environmental cycling where you take a
+
+ align:start position:0%
+environmental cycling where you take a
+ 
+
+ align:start position:0%
+environmental cycling where you take a
+module inside of this what looks like an
+
+ align:start position:0%
+module inside of this what looks like an
+ 
+
+ align:start position:0%
+module inside of this what looks like an
+oven and heats it up cools it down Heats
+
+ align:start position:0%
+oven and heats it up cools it down Heats
+ 
+
+ align:start position:0%
+oven and heats it up cools it down Heats
+it up cools it down or maintains a high
+
+ align:start position:0%
+it up cools it down or maintains a high
+ 
+
+ align:start position:0%
+it up cools it down or maintains a high
+temperature with high humidity different
+
+ align:start position:0%
+temperature with high humidity different
+ 
+
+ align:start position:0%
+temperature with high humidity different
+types of environmental Chambers do
+
+ align:start position:0%
+types of environmental Chambers do
+ 
+
+ align:start position:0%
+types of environmental Chambers do
+different things but they're meant to
+
+ align:start position:0%
+different things but they're meant to
+ 
+
+ align:start position:0%
+different things but they're meant to
+simulate an accelerated uh aging process
+
+ align:start position:0%
+simulate an accelerated uh aging process
+ 
+
+ align:start position:0%
+simulate an accelerated uh aging process
+again since most diffusion processes are
+
+ align:start position:0%
+again since most diffusion processes are
+ 
+
+ align:start position:0%
+again since most diffusion processes are
+driven by boltzman statistics there's an
+
+ align:start position:0%
+driven by boltzman statistics there's an
+ 
+
+ align:start position:0%
+driven by boltzman statistics there's an
+exponential increase with exponentially
+
+ align:start position:0%
+exponential increase with exponentially
+ 
+
+ align:start position:0%
+exponential increase with exponentially
+increasing temp or with increasing
+
+ align:start position:0%
+increasing temp or with increasing
+ 
+
+ align:start position:0%
+increasing temp or with increasing
+temperature and hence we can simulate
+
+ align:start position:0%
+temperature and hence we can simulate
+ 
+
+ align:start position:0%
+temperature and hence we can simulate
+accelerated degradation at higher
+
+ align:start position:0%
+accelerated degradation at higher
+ 
+
+ align:start position:0%
+accelerated degradation at higher
+temperatures so it's not uncommon that
+
+ align:start position:0%
+temperatures so it's not uncommon that
+ 
+
+ align:start position:0%
+temperatures so it's not uncommon that
+you hear about 8585 tests which mean 85°
+
+ align:start position:0%
+you hear about 8585 tests which mean 85°
+ 
+
+ align:start position:0%
+you hear about 8585 tests which mean 85°
+C at 85% humidity right so that is that
+
+ align:start position:0%
+C at 85% humidity right so that is that
+ 
+
+ align:start position:0%
+C at 85% humidity right so that is that
+is a massive jungle we we don't have
+
+ align:start position:0%
+is a massive jungle we we don't have
+ 
+
+ align:start position:0%
+is a massive jungle we we don't have
+thankfully uh places on Earth like that
+
+ align:start position:0%
+thankfully uh places on Earth like that
+ 
+
+ align:start position:0%
+thankfully uh places on Earth like that
+the maximum temperatures are at around
+
+ align:start position:0%
+the maximum temperatures are at around
+ 
+
+ align:start position:0%
+the maximum temperatures are at around
+45 50 55 degre C typically in in those
+
+ align:start position:0%
+45 50 55 degre C typically in in those
+ 
+
+ align:start position:0%
+45 50 55 degre C typically in in those
+cases very dry but in here 85° C it's
+
+ align:start position:0%
+cases very dry but in here 85° C it's
+ 
+
+ align:start position:0%
+cases very dry but in here 85° C it's
+still below the boiling point of water
+
+ align:start position:0%
+still below the boiling point of water
+ 
+
+ align:start position:0%
+still below the boiling point of water
+very high humidity and the humidity if
+
+ align:start position:0%
+very high humidity and the humidity if
+ 
+
+ align:start position:0%
+very high humidity and the humidity if
+there is any place for the humidity to
+
+ align:start position:0%
+there is any place for the humidity to
+ 
+
+ align:start position:0%
+there is any place for the humidity to
+go inside the module if you have any
+
+ align:start position:0%
+go inside the module if you have any
+ 
+
+ align:start position:0%
+go inside the module if you have any
+failure of your encapsulate material or
+
+ align:start position:0%
+failure of your encapsulate material or
+ 
+
+ align:start position:0%
+failure of your encapsulate material or
+can get inside it will and it'll begin
+
+ align:start position:0%
+can get inside it will and it'll begin
+ 
+
+ align:start position:0%
+can get inside it will and it'll begin
+degrading your module you'll see the
+
+ align:start position:0%
+degrading your module you'll see the
+ 
+
+ align:start position:0%
+degrading your module you'll see the
+power output decrease and after 3 months
+
+ align:start position:0%
+power output decrease and after 3 months
+ 
+
+ align:start position:0%
+power output decrease and after 3 months
+uh subjected to that sort of torture if
+
+ align:start position:0%
+uh subjected to that sort of torture if
+ 
+
+ align:start position:0%
+uh subjected to that sort of torture if
+the module is poorly designed uh often
+
+ align:start position:0%
+the module is poorly designed uh often
+ 
+
+ align:start position:0%
+the module is poorly designed uh often
+times it will fail now some of the
+
+ align:start position:0%
+times it will fail now some of the
+ 
+
+ align:start position:0%
+times it will fail now some of the
+shortcomings of these tests these those
+
+ align:start position:0%
+shortcomings of these tests these those
+ 
+
+ align:start position:0%
+shortcomings of these tests these those
+uh those that humidity uh cycle isn't
+
+ align:start position:0%
+uh those that humidity uh cycle isn't
+ 
+
+ align:start position:0%
+uh those that humidity uh cycle isn't
+necessarily uh with the module uh
+
+ align:start position:0%
+necessarily uh with the module uh
+ 
+
+ align:start position:0%
+necessarily uh with the module uh
+experiencing an applied bias voltage so
+
+ align:start position:0%
+experiencing an applied bias voltage so
+ 
+
+ align:start position:0%
+experiencing an applied bias voltage so
+if there's any electrom migration effect
+
+ align:start position:0%
+if there's any electrom migration effect
+ 
+
+ align:start position:0%
+if there's any electrom migration effect
+uh you might not detect it with that so
+
+ align:start position:0%
+uh you might not detect it with that so
+ 
+
+ align:start position:0%
+uh you might not detect it with that so
+there are people designing new forms of
+
+ align:start position:0%
+there are people designing new forms of
+ 
+
+ align:start position:0%
+there are people designing new forms of
+tests that will uh probe other failure
+
+ align:start position:0%
+tests that will uh probe other failure
+ 
+
+ align:start position:0%
+tests that will uh probe other failure
+modes other degradation mechanisms that
+
+ align:start position:0%
+modes other degradation mechanisms that
+ 
+
+ align:start position:0%
+modes other degradation mechanisms that
+aren't necessarily captured in these IC
+
+ align:start position:0%
+aren't necessarily captured in these IC
+ 
+
+ align:start position:0%
+aren't necessarily captured in these IC
+tests do you have a question no no
+
+ align:start position:0%
+tests do you have a question no no
+ 
+
+ align:start position:0%
+tests do you have a question no no
+question okay yeah over here what is the
+
+ align:start position:0%
+question okay yeah over here what is the
+ 
+
+ align:start position:0%
+question okay yeah over here what is the
+degradation by Water by water yes so
+
+ align:start position:0%
+degradation by Water by water yes so
+ 
+
+ align:start position:0%
+degradation by Water by water yes so
+water humidity um it typically what
+
+ align:start position:0%
+water humidity um it typically what
+ 
+
+ align:start position:0%
+water humidity um it typically what
+happens is in the laminate itself um
+
+ align:start position:0%
+happens is in the laminate itself um
+ 
+
+ align:start position:0%
+happens is in the laminate itself um
+there will be some part at the edge that
+
+ align:start position:0%
+there will be some part at the edge that
+ 
+
+ align:start position:0%
+there will be some part at the edge that
+water can get in not always but in in
+
+ align:start position:0%
+water can get in not always but in in
+ 
+
+ align:start position:0%
+water can get in not always but in in
+the poorly designed ones yes and so the
+
+ align:start position:0%
+the poorly designed ones yes and so the
+ 
+
+ align:start position:0%
+the poorly designed ones yes and so the
+water can get in and begin diffusing in
+
+ align:start position:0%
+water can get in and begin diffusing in
+ 
+
+ align:start position:0%
+water can get in and begin diffusing in
+right uh into the module so so if you
+
+ align:start position:0%
+right uh into the module so so if you
+ 
+
+ align:start position:0%
+right uh into the module so so if you
+have a thin fil material that uh reacts
+
+ align:start position:0%
+have a thin fil material that uh reacts
+ 
+
+ align:start position:0%
+have a thin fil material that uh reacts
+with water you might degrade the actual
+
+ align:start position:0%
+with water you might degrade the actual
+ 
+
+ align:start position:0%
+with water you might degrade the actual
+absorber layer itself if you have a
+
+ align:start position:0%
+absorber layer itself if you have a
+ 
+
+ align:start position:0%
+absorber layer itself if you have a
+silicon device um the water could react
+
+ align:start position:0%
+silicon device um the water could react
+ 
+
+ align:start position:0%
+silicon device um the water could react
+with the metal and cause it to
+
+ align:start position:0%
+with the metal and cause it to
+ 
+
+ align:start position:0%
+with the metal and cause it to
+corrode right cause it to oxidize in
+
+ align:start position:0%
+corrode right cause it to oxidize in
+ 
+
+ align:start position:0%
+corrode right cause it to oxidize in
+other words um and so the and of course
+
+ align:start position:0%
+other words um and so the and of course
+ 
+
+ align:start position:0%
+other words um and so the and of course
+in reacting with the ethyl vinyl acetate
+
+ align:start position:0%
+in reacting with the ethyl vinyl acetate
+ 
+
+ align:start position:0%
+in reacting with the ethyl vinyl acetate
+it can cause the encapsulant to
+
+ align:start position:0%
+it can cause the encapsulant to
+ 
+
+ align:start position:0%
+it can cause the encapsulant to
+delaminate from the
+
+ align:start position:0%
+delaminate from the
+ 
+
+ align:start position:0%
+delaminate from the
+cells and tear apart and so you see this
+
+ align:start position:0%
+cells and tear apart and so you see this
+ 
+
+ align:start position:0%
+cells and tear apart and so you see this
+discoloration of the module um those are
+
+ align:start position:0%
+discoloration of the module um those are
+ 
+
+ align:start position:0%
+discoloration of the module um those are
+some of the failure modes that can occur
+
+ align:start position:0%
+some of the failure modes that can occur
+ 
+
+ align:start position:0%
+some of the failure modes that can occur
+when water gets in through the side if
+
+ align:start position:0%
+when water gets in through the side if
+ 
+
+ align:start position:0%
+when water gets in through the side if
+it manag to permeate the um encapsulant
+
+ align:start position:0%
+it manag to permeate the um encapsulant
+ 
+
+ align:start position:0%
+it manag to permeate the um encapsulant
+materials themselves those sorts of
+
+ align:start position:0%
+materials themselves those sorts of
+ 
+
+ align:start position:0%
+materials themselves those sorts of
+effects can occur directly as opposed to
+
+ align:start position:0%
+effects can occur directly as opposed to
+ 
+
+ align:start position:0%
+effects can occur directly as opposed to
+coming in through the sides another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questiona
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yep so they presumably test some
+
+ align:start position:0%
+yes yep so they presumably test some
+ 
+
+ align:start position:0%
+yes yep so they presumably test some
+small fraction of the modules and then
+
+ align:start position:0%
+small fraction of the modules and then
+ 
+
+ align:start position:0%
+small fraction of the modules and then
+if those modules pass the test which
+
+ align:start position:0%
+if those modules pass the test which
+ 
+
+ align:start position:0%
+if those modules pass the test which
+takes several months to conduct uh and
+
+ align:start position:0%
+takes several months to conduct uh and
+ 
+
+ align:start position:0%
+takes several months to conduct uh and
+that's why there's a large barrier for
+
+ align:start position:0%
+that's why there's a large barrier for
+ 
+
+ align:start position:0%
+that's why there's a large barrier for
+module Innovation uh
+
+ align:start position:0%
+module Innovation uh
+ 
+
+ align:start position:0%
+module Innovation uh
+but if they pass those tests then they
+
+ align:start position:0%
+but if they pass those tests then they
+ 
+
+ align:start position:0%
+but if they pass those tests then they
+assume that every module is yes so uh
+
+ align:start position:0%
+assume that every module is yes so uh
+ 
+
+ align:start position:0%
+assume that every module is yes so uh
+there there are a series of of of I
+
+ align:start position:0%
+there there are a series of of of I
+ 
+
+ align:start position:0%
+there there are a series of of of I
+would say um definitions of what
+
+ align:start position:0%
+would say um definitions of what
+ 
+
+ align:start position:0%
+would say um definitions of what
+constitutes a major alteration to the
+
+ align:start position:0%
+constitutes a major alteration to the
+ 
+
+ align:start position:0%
+constitutes a major alteration to the
+process so if you majorly alter your
+
+ align:start position:0%
+process so if you majorly alter your
+ 
+
+ align:start position:0%
+process so if you majorly alter your
+process then you have to get your module
+
+ align:start position:0%
+process then you have to get your module
+ 
+
+ align:start position:0%
+process then you have to get your module
+recertified um but if uh if you stay
+
+ align:start position:0%
+recertified um but if uh if you stay
+ 
+
+ align:start position:0%
+recertified um but if uh if you stay
+within those bounds then you can
+
+ align:start position:0%
+within those bounds then you can
+ 
+
+ align:start position:0%
+within those bounds then you can
+continue uh uh selling under the old
+
+ align:start position:0%
+continue uh uh selling under the old
+ 
+
+ align:start position:0%
+continue uh uh selling under the old
+certification um it's not too dissimilar
+
+ align:start position:0%
+certification um it's not too dissimilar
+ 
+
+ align:start position:0%
+certification um it's not too dissimilar
+to say uh the way our food is tested by
+
+ align:start position:0%
+to say uh the way our food is tested by
+ 
+
+ align:start position:0%
+to say uh the way our food is tested by
+the FDA uh it's not every single hand
+
+ align:start position:0%
+the FDA uh it's not every single hand
+ 
+
+ align:start position:0%
+the FDA uh it's not every single hand
+hamburger um it's it's a it's a spot
+
+ align:start position:0%
+hamburger um it's it's a it's a spot
+ 
+
+ align:start position:0%
+hamburger um it's it's a it's a spot
+test um in this particular case these
+
+ align:start position:0%
+test um in this particular case these
+ 
+
+ align:start position:0%
+test um in this particular case these
+are uh examples of the newest uh
+
+ align:start position:0%
+are uh examples of the newest uh
+ 
+
+ align:start position:0%
+are uh examples of the newest uh
+Technologies to come off the line and
+
+ align:start position:0%
+Technologies to come off the line and
+ 
+
+ align:start position:0%
+Technologies to come off the line and
+you get a couple of chances to pass um
+
+ align:start position:0%
+you get a couple of chances to pass um
+ 
+
+ align:start position:0%
+you get a couple of chances to pass um
+if you fail the first one it's not the
+
+ align:start position:0%
+if you fail the first one it's not the
+ 
+
+ align:start position:0%
+if you fail the first one it's not the
+end of the world uh it just means that
+
+ align:start position:0%
+end of the world uh it just means that
+ 
+
+ align:start position:0%
+end of the world uh it just means that
+you have to pass the next time or else
+
+ align:start position:0%
+you have to pass the next time or else
+ 
+
+ align:start position:0%
+you have to pass the next time or else
+you have a stain on your record um and
+
+ align:start position:0%
+you have a stain on your record um and
+ 
+
+ align:start position:0%
+you have a stain on your record um and
+many of the companies now have their own
+
+ align:start position:0%
+many of the companies now have their own
+ 
+
+ align:start position:0%
+many of the companies now have their own
+uh facilities to do these tests inhouse
+
+ align:start position:0%
+uh facilities to do these tests inhouse
+ 
+
+ align:start position:0%
+uh facilities to do these tests inhouse
+they still send them out to the
+
+ align:start position:0%
+they still send them out to the
+ 
+
+ align:start position:0%
+they still send them out to the
+certified testing bodies that are
+
+ align:start position:0%
+certified testing bodies that are
+ 
+
+ align:start position:0%
+certified testing bodies that are
+independent to get the final seal of
+
+ align:start position:0%
+independent to get the final seal of
+ 
+
+ align:start position:0%
+independent to get the final seal of
+approval but they know fairly well
+
+ align:start position:0%
+approval but they know fairly well
+ 
+
+ align:start position:0%
+approval but they know fairly well
+before they send them out are we going
+
+ align:start position:0%
+before they send them out are we going
+ 
+
+ align:start position:0%
+before they send them out are we going
+to pass or not in your early days it was
+
+ align:start position:0%
+to pass or not in your early days it was
+ 
+
+ align:start position:0%
+to pass or not in your early days it was
+you always had to hold on to the seat of
+
+ align:start position:0%
+you always had to hold on to the seat of
+ 
+
+ align:start position:0%
+you always had to hold on to the seat of
+your pants because you never quite knew
+
+ align:start position:0%
+your pants because you never quite knew
+ 
+
+ align:start position:0%
+your pants because you never quite knew
+what was going to happen when test
+
+ align:start position:0%
+what was going to happen when test
+ 
+
+ align:start position:0%
+what was going to happen when test
+results came back um but now um it's
+
+ align:start position:0%
+results came back um but now um it's
+ 
+
+ align:start position:0%
+results came back um but now um it's
+it's it's much better uh much more
+
+ align:start position:0%
+it's it's much better uh much more
+ 
+
+ align:start position:0%
+it's it's much better uh much more
+predictable and my favorite test out of
+
+ align:start position:0%
+predictable and my favorite test out of
+ 
+
+ align:start position:0%
+predictable and my favorite test out of
+all the ones in there there're are
+
+ align:start position:0%
+all the ones in there there're are
+ 
+
+ align:start position:0%
+all the ones in there there're are
+number uh if if you imagine a dozen to
+
+ align:start position:0%
+number uh if if you imagine a dozen to
+ 
+
+ align:start position:0%
+number uh if if you imagine a dozen to
+20 tests uh from Illuminating it and
+
+ align:start position:0%
+20 tests uh from Illuminating it and
+ 
+
+ align:start position:0%
+20 tests uh from Illuminating it and
+measuring the power output um one of my
+
+ align:start position:0%
+measuring the power output um one of my
+ 
+
+ align:start position:0%
+measuring the power output um one of my
+favorite tests involves a hail gun um so
+
+ align:start position:0%
+favorite tests involves a hail gun um so
+ 
+
+ align:start position:0%
+favorite tests involves a hail gun um so
+the the similar manner to how uh the the
+
+ align:start position:0%
+the the similar manner to how uh the the
+ 
+
+ align:start position:0%
+the the similar manner to how uh the the
+FAA tests wind Shields of planes and and
+
+ align:start position:0%
+FAA tests wind Shields of planes and and
+ 
+
+ align:start position:0%
+FAA tests wind Shields of planes and and
+and and plane engines by uh shooting
+
+ align:start position:0%
+and and plane engines by uh shooting
+ 
+
+ align:start position:0%
+and and plane engines by uh shooting
+Frozen chickens or turkeys at them uh in
+
+ align:start position:0%
+Frozen chickens or turkeys at them uh in
+ 
+
+ align:start position:0%
+Frozen chickens or turkeys at them uh in
+this particular case we're shooting
+
+ align:start position:0%
+this particular case we're shooting
+ 
+
+ align:start position:0%
+this particular case we're shooting
+Frozen balls of water at the modules and
+
+ align:start position:0%
+Frozen balls of water at the modules and
+ 
+
+ align:start position:0%
+Frozen balls of water at the modules and
+seeing if they crack um that's one of
+
+ align:start position:0%
+seeing if they crack um that's one of
+ 
+
+ align:start position:0%
+seeing if they crack um that's one of
+the ones uh you can Envision as well an
+
+ align:start position:0%
+the ones uh you can Envision as well an
+ 
+
+ align:start position:0%
+the ones uh you can Envision as well an
+immersion test underwater uh combined
+
+ align:start position:0%
+immersion test underwater uh combined
+ 
+
+ align:start position:0%
+immersion test underwater uh combined
+with bending to see if uh if if there's
+
+ align:start position:0%
+with bending to see if uh if if there's
+ 
+
+ align:start position:0%
+with bending to see if uh if if there's
+any uh failure in the module so we uh
+
+ align:start position:0%
+any uh failure in the module so we uh
+ 
+
+ align:start position:0%
+any uh failure in the module so we uh
+they are tested quite extensively using
+
+ align:start position:0%
+they are tested quite extensively using
+ 
+
+ align:start position:0%
+they are tested quite extensively using
+these protocols and the objective is to
+
+ align:start position:0%
+these protocols and the objective is to
+ 
+
+ align:start position:0%
+these protocols and the objective is to
+ensure quality and safety to the
+
+ align:start position:0%
+ensure quality and safety to the
+ 
+
+ align:start position:0%
+ensure quality and safety to the
+consumer what's the tough
+
+ align:start position:0%
+consumer what's the tough
+ 
+
+ align:start position:0%
+consumer what's the tough
+this top right oh top right over here
+
+ align:start position:0%
+this top right oh top right over here
+ 
+
+ align:start position:0%
+this top right oh top right over here
+this is a mechanical loading test um
+
+ align:start position:0%
+this is a mechanical loading test um
+ 
+
+ align:start position:0%
+this is a mechanical loading test um
+what it appears to be uh where uh you
+
+ align:start position:0%
+what it appears to be uh where uh you
+ 
+
+ align:start position:0%
+what it appears to be uh where uh you
+you just exert um what is typically that
+
+ align:start position:0%
+you just exert um what is typically that
+ 
+
+ align:start position:0%
+you just exert um what is typically that
+that's what it appears to be in this
+
+ align:start position:0%
+that's what it appears to be in this
+ 
+
+ align:start position:0%
+that's what it appears to be in this
+particular case I could be wrong but um
+
+ align:start position:0%
+particular case I could be wrong but um
+ 
+
+ align:start position:0%
+particular case I could be wrong but um
+my understanding is that the this module
+
+ align:start position:0%
+my understanding is that the this module
+ 
+
+ align:start position:0%
+my understanding is that the this module
+is constrained on the edges right now
+
+ align:start position:0%
+is constrained on the edges right now
+ 
+
+ align:start position:0%
+is constrained on the edges right now
+and that there's a load being uh pushed
+
+ align:start position:0%
+and that there's a load being uh pushed
+ 
+
+ align:start position:0%
+and that there's a load being uh pushed
+down in the center um you could also
+
+ align:start position:0%
+down in the center um you could also
+ 
+
+ align:start position:0%
+down in the center um you could also
+Envision a sandbag test where you uh
+
+ align:start position:0%
+Envision a sandbag test where you uh
+ 
+
+ align:start position:0%
+Envision a sandbag test where you uh
+load physical sandbags um there is uh
+
+ align:start position:0%
+load physical sandbags um there is uh
+ 
+
+ align:start position:0%
+load physical sandbags um there is uh
+there are variety of of different types
+
+ align:start position:0%
+there are variety of of different types
+ 
+
+ align:start position:0%
+there are variety of of different types
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variants yep okay so that comes from the
+
+ align:start position:0%
+variants yep okay so that comes from the
+ 
+
+ align:start position:0%
+variants yep okay so that comes from the
+First Solar um spec sheet describe the
+
+ align:start position:0%
+First Solar um spec sheet describe the
+ 
+
+ align:start position:0%
+First Solar um spec sheet describe the
+differences between various types of PV
+
+ align:start position:0%
+differences between various types of PV
+ 
+
+ align:start position:0%
+differences between various types of PV
+systems since we're running short on
+
+ align:start position:0%
+systems since we're running short on
+ 
+
+ align:start position:0%
+systems since we're running short on
+time this is a bit of a repeat from uh
+
+ align:start position:0%
+time this is a bit of a repeat from uh
+ 
+
+ align:start position:0%
+time this is a bit of a repeat from uh
+what we talked about uh the very first
+
+ align:start position:0%
+what we talked about uh the very first
+ 
+
+ align:start position:0%
+what we talked about uh the very first
+day in class the non-tracking the
+
+ align:start position:0%
+day in class the non-tracking the
+ 
+
+ align:start position:0%
+day in class the non-tracking the
+tracking um so I'm going to fly through
+
+ align:start position:0%
+tracking um so I'm going to fly through
+ 
+
+ align:start position:0%
+tracking um so I'm going to fly through
+that into grid tied and Standalone right
+
+ align:start position:0%
+that into grid tied and Standalone right
+ 
+
+ align:start position:0%
+that into grid tied and Standalone right
+so grid tied and Standalone systems is
+
+ align:start position:0%
+so grid tied and Standalone systems is
+ 
+
+ align:start position:0%
+so grid tied and Standalone systems is
+very straightforward if if you have a
+
+ align:start position:0%
+very straightforward if if you have a
+ 
+
+ align:start position:0%
+very straightforward if if you have a
+system that is tied to the grid somehow
+
+ align:start position:0%
+system that is tied to the grid somehow
+ 
+
+ align:start position:0%
+system that is tied to the grid somehow
+it has to be able to interface with the
+
+ align:start position:0%
+it has to be able to interface with the
+ 
+
+ align:start position:0%
+it has to be able to interface with the
+grid let me go to that in a second um
+
+ align:start position:0%
+grid let me go to that in a second um
+ 
+
+ align:start position:0%
+grid let me go to that in a second um
+here so if you're having a grid tied
+
+ align:start position:0%
+here so if you're having a grid tied
+ 
+
+ align:start position:0%
+here so if you're having a grid tied
+system that means that your house or or
+
+ align:start position:0%
+system that means that your house or or
+ 
+
+ align:start position:0%
+system that means that your house or or
+or solar array whatever it is that's
+
+ align:start position:0%
+or solar array whatever it is that's
+ 
+
+ align:start position:0%
+or solar array whatever it is that's
+producing the electricity uh has to be
+
+ align:start position:0%
+producing the electricity uh has to be
+ 
+
+ align:start position:0%
+producing the electricity uh has to be
+tied to the grid and interface with it
+
+ align:start position:0%
+tied to the grid and interface with it
+ 
+
+ align:start position:0%
+tied to the grid and interface with it
+since the uh electricity is alternating
+
+ align:start position:0%
+since the uh electricity is alternating
+ 
+
+ align:start position:0%
+since the uh electricity is alternating
+current uh there has to be a device to
+
+ align:start position:0%
+current uh there has to be a device to
+ 
+
+ align:start position:0%
+current uh there has to be a device to
+convert the the direct current power
+
+ align:start position:0%
+convert the the direct current power
+ 
+
+ align:start position:0%
+convert the the direct current power
+into alternating current and that's
+
+ align:start position:0%
+into alternating current and that's
+ 
+
+ align:start position:0%
+into alternating current and that's
+called the inverter we've already
+
+ align:start position:0%
+called the inverter we've already
+ 
+
+ align:start position:0%
+called the inverter we've already
+touched upon that a few times over
+
+ align:start position:0%
+touched upon that a few times over
+ 
+
+ align:start position:0%
+touched upon that a few times over
+today's class and these objects are um
+
+ align:start position:0%
+today's class and these objects are um
+ 
+
+ align:start position:0%
+today's class and these objects are um
+range in size for the ones in the house
+
+ align:start position:0%
+range in size for the ones in the house
+ 
+
+ align:start position:0%
+range in size for the ones in the house
+you could find inverters that are about
+
+ align:start position:0%
+you could find inverters that are about
+ 
+
+ align:start position:0%
+you could find inverters that are about
+y big right that can handle a few
+
+ align:start position:0%
+y big right that can handle a few
+ 
+
+ align:start position:0%
+y big right that can handle a few
+kilowatts uh the ones that are handling
+
+ align:start position:0%
+kilowatts uh the ones that are handling
+ 
+
+ align:start position:0%
+kilowatts uh the ones that are handling
+these large solar field installations or
+
+ align:start position:0%
+these large solar field installations or
+ 
+
+ align:start position:0%
+these large solar field installations or
+segments thereof um let me find a large
+
+ align:start position:0%
+segments thereof um let me find a large
+ 
+
+ align:start position:0%
+segments thereof um let me find a large
+solar field installation for here we go
+
+ align:start position:0%
+solar field installation for here we go
+ 
+
+ align:start position:0%
+solar field installation for here we go
+here are pictures some pictures of large
+
+ align:start position:0%
+here are pictures some pictures of large
+ 
+
+ align:start position:0%
+here are pictures some pictures of large
+solar field installation this is the
+
+ align:start position:0%
+solar field installation this is the
+ 
+
+ align:start position:0%
+solar field installation this is the
+road these little green dots are trees
+
+ align:start position:0%
+road these little green dots are trees
+ 
+
+ align:start position:0%
+road these little green dots are trees
+that's a big field installation right
+
+ align:start position:0%
+that's a big field installation right
+ 
+
+ align:start position:0%
+that's a big field installation right
+there um those inverters are are are
+
+ align:start position:0%
+there um those inverters are are are
+ 
+
+ align:start position:0%
+there um those inverters are are are
+Warehouse can be uh much larger sized
+
+ align:start position:0%
+Warehouse can be uh much larger sized
+ 
+
+ align:start position:0%
+Warehouse can be uh much larger sized
+right uh than the smaller ones that
+
+ align:start position:0%
+right uh than the smaller ones that
+ 
+
+ align:start position:0%
+right uh than the smaller ones that
+you'd find in your
+
+ align:start position:0%
+you'd find in your
+ 
+
+ align:start position:0%
+you'd find in your
+house um and so listing the major
+
+ align:start position:0%
+house um and so listing the major
+ 
+
+ align:start position:0%
+house um and so listing the major
+balance the system components um the PV
+
+ align:start position:0%
+balance the system components um the PV
+ 
+
+ align:start position:0%
+balance the system components um the PV
+array would be connected to the grid VI
+
+ align:start position:0%
+array would be connected to the grid VI
+ 
+
+ align:start position:0%
+array would be connected to the grid VI
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+inverter um the Excess power would be
+
+ align:start position:0%
+inverter um the Excess power would be
+ 
+
+ align:start position:0%
+inverter um the Excess power would be
+sent to the grid causing the meter to
+
+ align:start position:0%
+sent to the grid causing the meter to
+ 
+
+ align:start position:0%
+sent to the grid causing the meter to
+spin backward which is a very gratifying
+
+ align:start position:0%
+spin backward which is a very gratifying
+ 
+
+ align:start position:0%
+spin backward which is a very gratifying
+observation from a homeowner's point of
+
+ align:start position:0%
+observation from a homeowner's point of
+ 
+
+ align:start position:0%
+observation from a homeowner's point of
+view or at at the very least a rate
+
+ align:start position:0%
+view or at at the very least a rate
+ 
+
+ align:start position:0%
+view or at at the very least a rate
+payer utility payers point of view um
+
+ align:start position:0%
+payer utility payers point of view um
+ 
+
+ align:start position:0%
+payer utility payers point of view um
+the uh the act of sending the power back
+
+ align:start position:0%
+the uh the act of sending the power back
+ 
+
+ align:start position:0%
+the uh the act of sending the power back
+to the grid is uh a bit of free riding
+
+ align:start position:0%
+to the grid is uh a bit of free riding
+ 
+
+ align:start position:0%
+to the grid is uh a bit of free riding
+right because I'm not paying for the
+
+ align:start position:0%
+right because I'm not paying for the
+ 
+
+ align:start position:0%
+right because I'm not paying for the
+grid I'm a consumer but I'm getting
+
+ align:start position:0%
+grid I'm a consumer but I'm getting
+ 
+
+ align:start position:0%
+grid I'm a consumer but I'm getting
+credit for the electricity I put back in
+
+ align:start position:0%
+credit for the electricity I put back in
+ 
+
+ align:start position:0%
+credit for the electricity I put back in
+the grid but I'm not helping to maintain
+
+ align:start position:0%
+the grid but I'm not helping to maintain
+ 
+
+ align:start position:0%
+the grid but I'm not helping to maintain
+the grid necessarily I'm paying some
+
+ align:start position:0%
+the grid necessarily I'm paying some
+ 
+
+ align:start position:0%
+the grid necessarily I'm paying some
+transmission and distribution costs on
+
+ align:start position:0%
+transmission and distribution costs on
+ 
+
+ align:start position:0%
+transmission and distribution costs on
+my utility bill um but that's
+
+ align:start position:0%
+my utility bill um but that's
+ 
+
+ align:start position:0%
+my utility bill um but that's
+essentially the same cost that everyone
+
+ align:start position:0%
+essentially the same cost that everyone
+ 
+
+ align:start position:0%
+essentially the same cost that everyone
+else is paying uh utility companies have
+
+ align:start position:0%
+else is paying uh utility companies have
+ 
+
+ align:start position:0%
+else is paying uh utility companies have
+begun getting wise about that and have
+
+ align:start position:0%
+begun getting wise about that and have
+ 
+
+ align:start position:0%
+begun getting wise about that and have
+begun leveraging sech charges based on
+
+ align:start position:0%
+begun leveraging sech charges based on
+ 
+
+ align:start position:0%
+begun leveraging sech charges based on
+the input of solar electricity into the
+
+ align:start position:0%
+the input of solar electricity into the
+ 
+
+ align:start position:0%
+the input of solar electricity into the
+grid which I now pay so I'm no longer a
+
+ align:start position:0%
+grid which I now pay so I'm no longer a
+ 
+
+ align:start position:0%
+grid which I now pay so I'm no longer a
+free rider I was for a little bit um so
+
+ align:start position:0%
+free rider I was for a little bit um so
+ 
+
+ align:start position:0%
+free rider I was for a little bit um so
+mounted onto the roof of the ground if
+
+ align:start position:0%
+mounted onto the roof of the ground if
+ 
+
+ align:start position:0%
+mounted onto the roof of the ground if
+you mount the solar panels you need
+
+ align:start position:0%
+you mount the solar panels you need
+ 
+
+ align:start position:0%
+you mount the solar panels you need
+racking and framing materials that's
+
+ align:start position:0%
+racking and framing materials that's
+ 
+
+ align:start position:0%
+racking and framing materials that's
+also balance the
+
+ align:start position:0%
+also balance the
+ 
+
+ align:start position:0%
+also balance the
+systems okay so uh check check check
+
+ align:start position:0%
+systems okay so uh check check check
+ 
+
+ align:start position:0%
+systems okay so uh check check check
+check you typically have as well a
+
+ align:start position:0%
+check you typically have as well a
+ 
+
+ align:start position:0%
+check you typically have as well a
+circuit breaker uh or just a very simple
+
+ align:start position:0%
+circuit breaker uh or just a very simple
+ 
+
+ align:start position:0%
+circuit breaker uh or just a very simple
+lever that disconnects the solar panel
+
+ align:start position:0%
+lever that disconnects the solar panel
+ 
+
+ align:start position:0%
+lever that disconnects the solar panel
+from the grid why is that important the
+
+ align:start position:0%
+from the grid why is that important the
+ 
+
+ align:start position:0%
+from the grid why is that important the
+utility companies know that on my house
+
+ align:start position:0%
+utility companies know that on my house
+ 
+
+ align:start position:0%
+utility companies know that on my house
+in Cambridge there is a solar array and
+
+ align:start position:0%
+in Cambridge there is a solar array and
+ 
+
+ align:start position:0%
+in Cambridge there is a solar array and
+that that array is connected to the grid
+
+ align:start position:0%
+that that array is connected to the grid
+ 
+
+ align:start position:0%
+that that array is connected to the grid
+let's imagine a tree falls in the power
+
+ align:start position:0%
+let's imagine a tree falls in the power
+ 
+
+ align:start position:0%
+let's imagine a tree falls in the power
+lines and during the next storm and the
+
+ align:start position:0%
+lines and during the next storm and the
+ 
+
+ align:start position:0%
+lines and during the next storm and the
+utility crew has to go out there to
+
+ align:start position:0%
+utility crew has to go out there to
+ 
+
+ align:start position:0%
+utility crew has to go out there to
+repair it during the day they know that
+
+ align:start position:0%
+repair it during the day they know that
+ 
+
+ align:start position:0%
+repair it during the day they know that
+although the rest of the grid is down
+
+ align:start position:0%
+although the rest of the grid is down
+ 
+
+ align:start position:0%
+although the rest of the grid is down
+there's that one little power center on
+
+ align:start position:0%
+there's that one little power center on
+ 
+
+ align:start position:0%
+there's that one little power center on
+my house that's uh injecting power into
+
+ align:start position:0%
+my house that's uh injecting power into
+ 
+
+ align:start position:0%
+my house that's uh injecting power into
+the grid and so they'll come along to my
+
+ align:start position:0%
+the grid and so they'll come along to my
+ 
+
+ align:start position:0%
+the grid and so they'll come along to my
+house disconnect the solar panels from
+
+ align:start position:0%
+house disconnect the solar panels from
+ 
+
+ align:start position:0%
+house disconnect the solar panels from
+the grid they'll go to my neighbors
+
+ align:start position:0%
+the grid they'll go to my neighbors
+ 
+
+ align:start position:0%
+the grid they'll go to my neighbors
+disconnect theirs as well go to the
+
+ align:start position:0%
+disconnect theirs as well go to the
+ 
+
+ align:start position:0%
+disconnect theirs as well go to the
+person across the street who also has
+
+ align:start position:0%
+person across the street who also has
+ 
+
+ align:start position:0%
+person across the street who also has
+solar panels disconnect them then go to
+
+ align:start position:0%
+solar panels disconnect them then go to
+ 
+
+ align:start position:0%
+solar panels disconnect them then go to
+work on the utility line so that's why
+
+ align:start position:0%
+work on the utility line so that's why
+ 
+
+ align:start position:0%
+work on the utility line so that's why
+the external uh
+
+ align:start position:0%
+the external uh
+ 
+
+ align:start position:0%
+the external uh
+uh uh circuit breaker is very important
+
+ align:start position:0%
+uh uh circuit breaker is very important
+ 
+
+ align:start position:0%
+uh uh circuit breaker is very important
+back to inverters um modern efficiencies
+
+ align:start position:0%
+back to inverters um modern efficiencies
+ 
+
+ align:start position:0%
+back to inverters um modern efficiencies
+of the inverter component range between
+
+ align:start position:0%
+of the inverter component range between
+ 
+
+ align:start position:0%
+of the inverter component range between
+94 and 97% typical um record inverter
+
+ align:start position:0%
+94 and 97% typical um record inverter
+ 
+
+ align:start position:0%
+94 and 97% typical um record inverter
+efficiencies up to 99% have been
+
+ align:start position:0%
+efficiencies up to 99% have been
+ 
+
+ align:start position:0%
+efficiencies up to 99% have been
+demonstrated
+
+ align:start position:0%
+demonstrated
+ 
+
+ align:start position:0%
+demonstrated
+um and they all have what's called
+
+ align:start position:0%
+um and they all have what's called
+ 
+
+ align:start position:0%
+um and they all have what's called
+maximum PowerPoint tracking which means
+
+ align:start position:0%
+maximum PowerPoint tracking which means
+ 
+
+ align:start position:0%
+maximum PowerPoint tracking which means
+that they will be able to sense what the
+
+ align:start position:0%
+that they will be able to sense what the
+ 
+
+ align:start position:0%
+that they will be able to sense what the
+combined output is of the array on your
+
+ align:start position:0%
+combined output is of the array on your
+ 
+
+ align:start position:0%
+combined output is of the array on your
+roof and adjust the uh the the the the
+
+ align:start position:0%
+roof and adjust the uh the the the the
+ 
+
+ align:start position:0%
+roof and adjust the uh the the the the
+resistance in the circuit to match the
+
+ align:start position:0%
+resistance in the circuit to match the
+ 
+
+ align:start position:0%
+resistance in the circuit to match the
+maximum power point and that way you're
+
+ align:start position:0%
+maximum power point and that way you're
+ 
+
+ align:start position:0%
+maximum power point and that way you're
+producing the maximum amount of power
+
+ align:start position:0%
+producing the maximum amount of power
+ 
+
+ align:start position:0%
+producing the maximum amount of power
+that you could be potentially under any
+
+ align:start position:0%
+that you could be potentially under any
+ 
+
+ align:start position:0%
+that you could be potentially under any
+given illumination condition so a lot of
+
+ align:start position:0%
+given illumination condition so a lot of
+ 
+
+ align:start position:0%
+given illumination condition so a lot of
+fancy Electronics goes into the inverter
+
+ align:start position:0%
+fancy Electronics goes into the inverter
+ 
+
+ align:start position:0%
+fancy Electronics goes into the inverter
+I really have to um I really have to
+
+ align:start position:0%
+I really have to um I really have to
+ 
+
+ align:start position:0%
+I really have to um I really have to
+give them a lot of respect in that
+
+ align:start position:0%
+give them a lot of respect in that
+ 
+
+ align:start position:0%
+give them a lot of respect in that
+regard typically 5 to seven maybe even
+
+ align:start position:0%
+regard typically 5 to seven maybe even
+ 
+
+ align:start position:0%
+regard typically 5 to seven maybe even
+10 year manufacturer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+warranty and um the mounting methods we
+
+ align:start position:0%
+warranty and um the mounting methods we
+ 
+
+ align:start position:0%
+warranty and um the mounting methods we
+talked about mounting and racking um
+
+ align:start position:0%
+talked about mounting and racking um
+ 
+
+ align:start position:0%
+talked about mounting and racking um
+this type was fairly common in the early
+
+ align:start position:0%
+this type was fairly common in the early
+ 
+
+ align:start position:0%
+this type was fairly common in the early
+days of solar we had these uh field
+
+ align:start position:0%
+days of solar we had these uh field
+ 
+
+ align:start position:0%
+days of solar we had these uh field
+installations especially built on hills
+
+ align:start position:0%
+installations especially built on hills
+ 
+
+ align:start position:0%
+installations especially built on hills
+in California um would say most common
+
+ align:start position:0%
+in California um would say most common
+ 
+
+ align:start position:0%
+in California um would say most common
+Now is really just mounting directly on
+
+ align:start position:0%
+Now is really just mounting directly on
+ 
+
+ align:start position:0%
+Now is really just mounting directly on
+a roof often times flat uh for large
+
+ align:start position:0%
+a roof often times flat uh for large
+ 
+
+ align:start position:0%
+a roof often times flat uh for large
+field installations one AIS trackers are
+
+ align:start position:0%
+field installations one AIS trackers are
+ 
+
+ align:start position:0%
+field installations one AIS trackers are
+are very common nowadays tracking as a
+
+ align:start position:0%
+are very common nowadays tracking as a
+ 
+
+ align:start position:0%
+are very common nowadays tracking as a
+function of time of day and then
+
+ align:start position:0%
+function of time of day and then
+ 
+
+ align:start position:0%
+function of time of day and then
+manually adjusting the entire array uh
+
+ align:start position:0%
+manually adjusting the entire array uh
+ 
+
+ align:start position:0%
+manually adjusting the entire array uh
+for season if need be so the grid tide
+
+ align:start position:0%
+for season if need be so the grid tide
+ 
+
+ align:start position:0%
+for season if need be so the grid tide
+systems causing meters to spin backward
+
+ align:start position:0%
+systems causing meters to spin backward
+ 
+
+ align:start position:0%
+systems causing meters to spin backward
+again very gratifying and um this is an
+
+ align:start position:0%
+again very gratifying and um this is an
+ 
+
+ align:start position:0%
+again very gratifying and um this is an
+example of my utility bill um where you
+
+ align:start position:0%
+example of my utility bill um where you
+ 
+
+ align:start position:0%
+example of my utility bill um where you
+have a balance of
+
+ align:start position:0%
+have a balance of
+ 
+
+ align:start position:0%
+have a balance of
+$163 negative um so they're giving me
+
+ align:start position:0%
+$163 negative um so they're giving me
+ 
+
+ align:start position:0%
+$163 negative um so they're giving me
+credit over the course of a year uh in
+
+ align:start position:0%
+credit over the course of a year uh in
+ 
+
+ align:start position:0%
+credit over the course of a year uh in
+the winter time this was an example of a
+
+ align:start position:0%
+the winter time this was an example of a
+ 
+
+ align:start position:0%
+the winter time this was an example of a
+month in December when a lot of snow
+
+ align:start position:0%
+month in December when a lot of snow
+ 
+
+ align:start position:0%
+month in December when a lot of snow
+happened and uh the panels were covered
+
+ align:start position:0%
+happened and uh the panels were covered
+ 
+
+ align:start position:0%
+happened and uh the panels were covered
+for quite a while or at least partially
+
+ align:start position:0%
+for quite a while or at least partially
+ 
+
+ align:start position:0%
+for quite a while or at least partially
+shaded by the snow for a while right um
+
+ align:start position:0%
+shaded by the snow for a while right um
+ 
+
+ align:start position:0%
+shaded by the snow for a while right um
+and we drew power from the Grid on net
+
+ align:start position:0%
+and we drew power from the Grid on net
+ 
+
+ align:start position:0%
+and we drew power from the Grid on net
+that month but in all the other months
+
+ align:start position:0%
+that month but in all the other months
+ 
+
+ align:start position:0%
+that month but in all the other months
+we unet produced power and negative
+
+ align:start position:0%
+we unet produced power and negative
+ 
+
+ align:start position:0%
+we unet produced power and negative
+numbers aren't shown on the scale here
+
+ align:start position:0%
+numbers aren't shown on the scale here
+ 
+
+ align:start position:0%
+numbers aren't shown on the scale here
+but uh if they were shown you'd see uh
+
+ align:start position:0%
+but uh if they were shown you'd see uh
+ 
+
+ align:start position:0%
+but uh if they were shown you'd see uh
+probably a greater negative value in the
+
+ align:start position:0%
+probably a greater negative value in the
+ 
+
+ align:start position:0%
+probably a greater negative value in the
+summertime in other words we're
+
+ align:start position:0%
+summertime in other words we're
+ 
+
+ align:start position:0%
+summertime in other words we're
+producing a lot of power in the summer
+
+ align:start position:0%
+producing a lot of power in the summer
+ 
+
+ align:start position:0%
+producing a lot of power in the summer
+more sun and at the end of the year they
+
+ align:start position:0%
+more sun and at the end of the year they
+ 
+
+ align:start position:0%
+more sun and at the end of the year they
+draw a line at the bottom and they say
+
+ align:start position:0%
+draw a line at the bottom and they say
+ 
+
+ align:start position:0%
+draw a line at the bottom and they say
+did you owe us money no all right great
+
+ align:start position:0%
+did you owe us money no all right great
+ 
+
+ align:start position:0%
+did you owe us money no all right great
+if you if we owed you money tough luck
+
+ align:start position:0%
+if you if we owed you money tough luck
+ 
+
+ align:start position:0%
+if you if we owed you money tough luck
+um if if we're zero then everybody's
+
+ align:start position:0%
+um if if we're zero then everybody's
+ 
+
+ align:start position:0%
+um if if we're zero then everybody's
+happy uh so we typically produce more
+
+ align:start position:0%
+happy uh so we typically produce more
+ 
+
+ align:start position:0%
+happy uh so we typically produce more
+electricity than we consume in our in
+
+ align:start position:0%
+electricity than we consume in our in
+ 
+
+ align:start position:0%
+electricity than we consume in our in
+our house and that's an example of what
+
+ align:start position:0%
+our house and that's an example of what
+ 
+
+ align:start position:0%
+our house and that's an example of what
+happens on a practical level um off grid
+
+ align:start position:0%
+happens on a practical level um off grid
+ 
+
+ align:start position:0%
+happens on a practical level um off grid
+PV systems just ever so briefly
+
+ align:start position:0%
+PV systems just ever so briefly
+ 
+
+ align:start position:0%
+PV systems just ever so briefly
+um so uh let's imagine that you're uh
+
+ align:start position:0%
+um so uh let's imagine that you're uh
+ 
+
+ align:start position:0%
+um so uh let's imagine that you're uh
+running some illicit business and you
+
+ align:start position:0%
+running some illicit business and you
+ 
+
+ align:start position:0%
+running some illicit business and you
+want to be off grid or uh let's imagine
+
+ align:start position:0%
+want to be off grid or uh let's imagine
+ 
+
+ align:start position:0%
+want to be off grid or uh let's imagine
+that you're uh instead uh let's let's a
+
+ align:start position:0%
+that you're uh instead uh let's let's a
+ 
+
+ align:start position:0%
+that you're uh instead uh let's let's a
+more realistic example let's say that
+
+ align:start position:0%
+more realistic example let's say that
+ 
+
+ align:start position:0%
+more realistic example let's say that
+you're um afraid of the next power
+
+ align:start position:0%
+you're um afraid of the next power
+ 
+
+ align:start position:0%
+you're um afraid of the next power
+outage of being out of power for the
+
+ align:start position:0%
+outage of being out of power for the
+ 
+
+ align:start position:0%
+outage of being out of power for the
+next s to 10 days after the the storm
+
+ align:start position:0%
+next s to 10 days after the the storm
+ 
+
+ align:start position:0%
+next s to 10 days after the the storm
+passes through your house and you want
+
+ align:start position:0%
+passes through your house and you want
+ 
+
+ align:start position:0%
+passes through your house and you want
+to isolate yourself from the grid if
+
+ align:start position:0%
+to isolate yourself from the grid if
+ 
+
+ align:start position:0%
+to isolate yourself from the grid if
+need be you would want to have a charge
+
+ align:start position:0%
+need be you would want to have a charge
+ 
+
+ align:start position:0%
+need be you would want to have a charge
+controller that would be able to uh
+
+ align:start position:0%
+controller that would be able to uh
+ 
+
+ align:start position:0%
+controller that would be able to uh
+distribute the power to the DC loads or
+
+ align:start position:0%
+distribute the power to the DC loads or
+ 
+
+ align:start position:0%
+distribute the power to the DC loads or
+to batteries to store them um and then
+
+ align:start position:0%
+to batteries to store them um and then
+ 
+
+ align:start position:0%
+to batteries to store them um and then
+the inverter going to the AC loads or to
+
+ align:start position:0%
+the inverter going to the AC loads or to
+ 
+
+ align:start position:0%
+the inverter going to the AC loads or to
+the grid thereafter um so it is possible
+
+ align:start position:0%
+the grid thereafter um so it is possible
+ 
+
+ align:start position:0%
+the grid thereafter um so it is possible
+to architect A system that is uh
+
+ align:start position:0%
+to architect A system that is uh
+ 
+
+ align:start position:0%
+to architect A system that is uh
+semi-autonomous but it does require more
+
+ align:start position:0%
+semi-autonomous but it does require more
+ 
+
+ align:start position:0%
+semi-autonomous but it does require more
+components and more cost
+
+ align:start position:0%
+components and more cost
+ 
+
+ align:start position:0%
+components and more cost
+right and I just wanted to emphasize one
+
+ align:start position:0%
+right and I just wanted to emphasize one
+ 
+
+ align:start position:0%
+right and I just wanted to emphasize one
+thing as we we close up life is really
+
+ align:start position:0%
+thing as we we close up life is really
+ 
+
+ align:start position:0%
+thing as we we close up life is really
+good as an installer right now if we
+
+ align:start position:0%
+good as an installer right now if we
+ 
+
+ align:start position:0%
+good as an installer right now if we
+flashed back to four or five years ago
+
+ align:start position:0%
+flashed back to four or five years ago
+ 
+
+ align:start position:0%
+flashed back to four or five years ago
+life would have been really good as a a
+
+ align:start position:0%
+life would have been really good as a a
+ 
+
+ align:start position:0%
+life would have been really good as a a
+solar uh panel producer especially if
+
+ align:start position:0%
+solar uh panel producer especially if
+ 
+
+ align:start position:0%
+solar uh panel producer especially if
+you were involved in the feed stock
+
+ align:start position:0%
+you were involved in the feed stock
+ 
+
+ align:start position:0%
+you were involved in the feed stock
+industry but now the prices of modules
+
+ align:start position:0%
+industry but now the prices of modules
+ 
+
+ align:start position:0%
+industry but now the prices of modules
+have been severely
+
+ align:start position:0%
+have been severely
+ 
+
+ align:start position:0%
+have been severely
+squeezed by lowcost competition from
+
+ align:start position:0%
+squeezed by lowcost competition from
+ 
+
+ align:start position:0%
+squeezed by lowcost competition from
+overseas and the pricing of modules is
+
+ align:start position:0%
+overseas and the pricing of modules is
+ 
+
+ align:start position:0%
+overseas and the pricing of modules is
+around $13 per Watt peak this is some of
+
+ align:start position:0%
+around $13 per Watt peak this is some of
+ 
+
+ align:start position:0%
+around $13 per Watt peak this is some of
+the the the lowest cost uh uh lowest
+
+ align:start position:0%
+the the the lowest cost uh uh lowest
+ 
+
+ align:start position:0%
+the the the lowest cost uh uh lowest
+price modules that are out there right
+
+ align:start position:0%
+price modules that are out there right
+ 
+
+ align:start position:0%
+price modules that are out there right
+now and the price of installing the
+
+ align:start position:0%
+now and the price of installing the
+ 
+
+ align:start position:0%
+now and the price of installing the
+system on your roof here in the US is
+
+ align:start position:0%
+system on your roof here in the US is
+ 
+
+ align:start position:0%
+system on your roof here in the US is
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+$520 who's pocketing the
+
+ align:start position:0%
+$520 who's pocketing the
+ 
+
+ align:start position:0%
+$520 who's pocketing the
+$4.20 who gets to keep that
+
+ align:start position:0%
+$4.20 who gets to keep that
+ 
+
+ align:start position:0%
+$4.20 who gets to keep that
+money is it the installer or the module
+
+ align:start position:0%
+money is it the installer or the module
+ 
+
+ align:start position:0%
+money is it the installer or the module
+producer it's got to be the installer
+
+ align:start position:0%
+producer it's got to be the installer
+ 
+
+ align:start position:0%
+producer it's got to be the installer
+right and who's suffering right now in
+
+ align:start position:0%
+right and who's suffering right now in
+ 
+
+ align:start position:0%
+right and who's suffering right now in
+in the industry no matter where you are
+
+ align:start position:0%
+in the industry no matter where you are
+ 
+
+ align:start position:0%
+in the industry no matter where you are
+us China Germany who's suffering right
+
+ align:start position:0%
+us China Germany who's suffering right
+ 
+
+ align:start position:0%
+us China Germany who's suffering right
+now the module producers right the
+
+ align:start position:0%
+now the module producers right the
+ 
+
+ align:start position:0%
+now the module producers right the
+people manufacturing this stuff right
+
+ align:start position:0%
+people manufacturing this stuff right
+ 
+
+ align:start position:0%
+people manufacturing this stuff right
+here all right which brings me to my
+
+ align:start position:0%
+here all right which brings me to my
+ 
+
+ align:start position:0%
+here all right which brings me to my
+current topic of the day everybody
+
+ align:start position:0%
+current topic of the day everybody
+ 
+
+ align:start position:0%
+current topic of the day everybody
+picked up this one right here this Green
+
+ align:start position:0%
+picked up this one right here this Green
+ 
+
+ align:start position:0%
+picked up this one right here this Green
+Tech media article this is really
+
+ align:start position:0%
+Tech media article this is really
+ 
+
+ align:start position:0%
+Tech media article this is really
+current November 8th that was two days
+
+ align:start position:0%
+current November 8th that was two days
+ 
+
+ align:start position:0%
+current November 8th that was two days
+ago uh Eric wof he's uh higher up there
+
+ align:start position:0%
+ago uh Eric wof he's uh higher up there
+ 
+
+ align:start position:0%
+ago uh Eric wof he's uh higher up there
+in Green Tech media and he's writing
+
+ align:start position:0%
+in Green Tech media and he's writing
+ 
+
+ align:start position:0%
+in Green Tech media and he's writing
+about the China us trade War uh that's
+
+ align:start position:0%
+about the China us trade War uh that's
+ 
+
+ align:start position:0%
+about the China us trade War uh that's
+evolving
+
+ align:start position:0%
+evolving
+ 
+
+ align:start position:0%
+evolving
+pitting within the US pitting the module
+
+ align:start position:0%
+pitting within the US pitting the module
+ 
+
+ align:start position:0%
+pitting within the US pitting the module
+manufacturers against the
+
+ align:start position:0%
+manufacturers against the
+ 
+
+ align:start position:0%
+manufacturers against the
+installers right so the installers these
+
+ align:start position:0%
+installers right so the installers these
+ 
+
+ align:start position:0%
+installers right so the installers these
+guys who are pocketing a lot of money
+
+ align:start position:0%
+guys who are pocketing a lot of money
+ 
+
+ align:start position:0%
+guys who are pocketing a lot of money
+right now are saying no no no no no let
+
+ align:start position:0%
+right now are saying no no no no no let
+ 
+
+ align:start position:0%
+right now are saying no no no no no let
+the Chinese modules come in it's great
+
+ align:start position:0%
+the Chinese modules come in it's great
+ 
+
+ align:start position:0%
+the Chinese modules come in it's great
+for it's it's it keeps are are cost low
+
+ align:start position:0%
+for it's it's it keeps are are cost low
+ 
+
+ align:start position:0%
+for it's it's it keeps are are cost low
+the folks who are manufacturing the
+
+ align:start position:0%
+the folks who are manufacturing the
+ 
+
+ align:start position:0%
+the folks who are manufacturing the
+modules on the other hand are saying
+
+ align:start position:0%
+modules on the other hand are saying
+ 
+
+ align:start position:0%
+modules on the other hand are saying
+well wait a second uh they got uh unfair
+
+ align:start position:0%
+well wait a second uh they got uh unfair
+ 
+
+ align:start position:0%
+well wait a second uh they got uh unfair
+uh treatment by their government and the
+
+ align:start position:0%
+uh treatment by their government and the
+ 
+
+ align:start position:0%
+uh treatment by their government and the
+Chinese module manufacturers in turn are
+
+ align:start position:0%
+Chinese module manufacturers in turn are
+ 
+
+ align:start position:0%
+Chinese module manufacturers in turn are
+saying well it's not only us who are
+
+ align:start position:0%
+saying well it's not only us who are
+ 
+
+ align:start position:0%
+saying well it's not only us who are
+getting subsidies from the government
+
+ align:start position:0%
+getting subsidies from the government
+ 
+
+ align:start position:0%
+getting subsidies from the government
+look at yourselves you got subsidies too
+
+ align:start position:0%
+look at yourselves you got subsidies too
+ 
+
+ align:start position:0%
+look at yourselves you got subsidies too
+and the US manufacturers say well well
+
+ align:start position:0%
+and the US manufacturers say well well
+ 
+
+ align:start position:0%
+and the US manufacturers say well well
+you got more subsidies than we did so
+
+ align:start position:0%
+you got more subsidies than we did so
+ 
+
+ align:start position:0%
+you got more subsidies than we did so
+it's it's evolving into a little bit of
+
+ align:start position:0%
+it's it's evolving into a little bit of
+ 
+
+ align:start position:0%
+it's it's evolving into a little bit of
+a a complex situation there are some
+
+ align:start position:0%
+a a complex situation there are some
+ 
+
+ align:start position:0%
+a a complex situation there are some
+people trying to cut through all of that
+
+ align:start position:0%
+people trying to cut through all of that
+ 
+
+ align:start position:0%
+people trying to cut through all of that
+and say with very simplistic messages um
+
+ align:start position:0%
+and say with very simplistic messages um
+ 
+
+ align:start position:0%
+and say with very simplistic messages um
+free trade or certain other people
+
+ align:start position:0%
+free trade or certain other people
+ 
+
+ align:start position:0%
+free trade or certain other people
+saying made in USA is important or other
+
+ align:start position:0%
+saying made in USA is important or other
+ 
+
+ align:start position:0%
+saying made in USA is important or other
+people saying um this is unfair for one
+
+ align:start position:0%
+people saying um this is unfair for one
+ 
+
+ align:start position:0%
+people saying um this is unfair for one
+reason or another but it's important to
+
+ align:start position:0%
+reason or another but it's important to
+ 
+
+ align:start position:0%
+reason or another but it's important to
+really understand the complexity of
+
+ align:start position:0%
+really understand the complexity of
+ 
+
+ align:start position:0%
+really understand the complexity of
+what's going on in the context of a
+
+ align:start position:0%
+what's going on in the context of a
+ 
+
+ align:start position:0%
+what's going on in the context of a
+dynamically changing market right the
+
+ align:start position:0%
+dynamically changing market right the
+ 
+
+ align:start position:0%
+dynamically changing market right the
+the market is changing quite uh quite a
+
+ align:start position:0%
+the market is changing quite uh quite a
+ 
+
+ align:start position:0%
+the market is changing quite uh quite a
+lot in the past the module prices and I
+
+ align:start position:0%
+lot in the past the module prices and I
+ 
+
+ align:start position:0%
+lot in the past the module prices and I
+say past recent past as in a year ago
+
+ align:start position:0%
+say past recent past as in a year ago
+ 
+
+ align:start position:0%
+say past recent past as in a year ago
+module prices were upward of of 250 $3
+
+ align:start position:0%
+module prices were upward of of 250 $3
+ 
+
+ align:start position:0%
+module prices were upward of of 250 $3
+per Watt peak right it's only in the
+
+ align:start position:0%
+per Watt peak right it's only in the
+ 
+
+ align:start position:0%
+per Watt peak right it's only in the
+over Supply condition created within the
+
+ align:start position:0%
+over Supply condition created within the
+ 
+
+ align:start position:0%
+over Supply condition created within the
+last year and a half where the module
+
+ align:start position:0%
+last year and a half where the module
+ 
+
+ align:start position:0%
+last year and a half where the module
+prices have dropped precipitously down
+
+ align:start position:0%
+prices have dropped precipitously down
+ 
+
+ align:start position:0%
+prices have dropped precipitously down
+to a dollar and that happens when you're
+
+ align:start position:0%
+to a dollar and that happens when you're
+ 
+
+ align:start position:0%
+to a dollar and that happens when you're
+in an over Supply
+
+ align:start position:0%
+in an over Supply
+ 
+
+ align:start position:0%
+in an over Supply
+condition whereas these uh um you know
+
+ align:start position:0%
+condition whereas these uh um you know
+ 
+
+ align:start position:0%
+condition whereas these uh um you know
+these these these installation prices
+
+ align:start position:0%
+these these these installation prices
+ 
+
+ align:start position:0%
+these these these installation prices
+really haven't budged too much they're
+
+ align:start position:0%
+really haven't budged too much they're
+ 
+
+ align:start position:0%
+really haven't budged too much they're
+enjoying the fact that this in an over
+
+ align:start position:0%
+enjoying the fact that this in an over
+ 
+
+ align:start position:0%
+enjoying the fact that this in an over
+Supply condition and there's still a
+
+ align:start position:0%
+Supply condition and there's still a
+ 
+
+ align:start position:0%
+Supply condition and there's still a
+market for their modules
+
+ align:start position:0%
+market for their modules
+ 
+
+ align:start position:0%
+market for their modules
+so it's complex we'll explore the some
+
+ align:start position:0%
+so it's complex we'll explore the some
+ 
+
+ align:start position:0%
+so it's complex we'll explore the some
+of the issues uh some of the complex
+
+ align:start position:0%
+of the issues uh some of the complex
+ 
+
+ align:start position:0%
+of the issues uh some of the complex
+issues uh in our next few classes and
+
+ align:start position:0%
+issues uh in our next few classes and
+ 
+
+ align:start position:0%
+issues uh in our next few classes and
+we'll dive into that in detail a leave
+
+ align:start position:0%
+we'll dive into that in detail a leave
+ 
+
+ align:start position:0%
+we'll dive into that in detail a leave
+for you to study on your own life cycle
+
+ align:start position:0%
+for you to study on your own life cycle
+ 
+
+ align:start position:0%
+for you to study on your own life cycle
+analysis it's very important life cycle
+
+ align:start position:0%
+analysis it's very important life cycle
+ 
+
+ align:start position:0%
+analysis it's very important life cycle
+analysis in in a nutshell really depends
+
+ align:start position:0%
+analysis in in a nutshell really depends
+ 
+
+ align:start position:0%
+analysis in in a nutshell really depends
+on what you consider in your analysis
+
+ align:start position:0%
+on what you consider in your analysis
+ 
+
+ align:start position:0%
+on what you consider in your analysis
+right where you draw the box and uh at
+
+ align:start position:0%
+right where you draw the box and uh at
+ 
+
+ align:start position:0%
+right where you draw the box and uh at
+the end of the day module recycling is
+
+ align:start position:0%
+the end of the day module recycling is
+ 
+
+ align:start position:0%
+the end of the day module recycling is
+going to be important as well uh uh for
+
+ align:start position:0%
+going to be important as well uh uh for
+ 
+
+ align:start position:0%
+going to be important as well uh uh for
+determining the ultimate uh impact in
+
+ align:start position:0%
+determining the ultimate uh impact in
+ 
+
+ align:start position:0%
+determining the ultimate uh impact in
+both in terms of CO2 impact energy
+
+ align:start position:0%
+both in terms of CO2 impact energy
+ 
+
+ align:start position:0%
+both in terms of CO2 impact energy
+payback and environmental impact of PV
+
+ align:start position:0%
+payback and environmental impact of PV
+ 
+
+ align:start position:0%
+payback and environmental impact of PV
+in the long run so I'll leave you with
+
+ align:start position:0%
+in the long run so I'll leave you with
+ 
+
+ align:start position:0%
+in the long run so I'll leave you with
+those thoughts and we'll see us on
+
+ align:start position:0%
+those thoughts and we'll see us on
+ 
+
+ align:start position:0%
+those thoughts and we'll see us on
+Tuesday e
\ No newline at end of file
diff --git a/C95294_vvQY.txt b/C95294_vvQY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..653276656d4d99726eb88d4d0cca908f0a88e181
--- /dev/null
+++ b/C95294_vvQY.txt
@@ -0,0 +1,4720 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+So we've been talking about
+predicting structure proteins.
+
+At the end of the
+last lecture we
+
+started to talk a little bit
+about predicting interactions,
+
+and that's going to be the
+focus of today's lecture.
+
+And we identified a couple of
+different possible prediction
+
+challenges.
+
+One was quantitative
+predictions of what
+
+happens when you make specific
+mutations in a known protein
+
+complex.
+
+We talked about
+trying to predict
+
+the structure of, say,
+just a pair of proteins,
+
+and then trying to do that
+on the global scale for all
+
+known proteins.
+
+And so last time,
+if you recall, we
+
+thought that initially maybe
+this would be a simple problem.
+
+We have proteins of known
+structure with a complex.
+
+Structure of the
+complex is also known.
+
+And we want to make predictions
+as to the change in affinity
+
+when there's a
+specific mutation made.
+
+In principle, this
+should be easy
+
+because we have all those
+different formulations
+
+for the potential
+energy function.
+
+And so if we figure out what
+the local structural changes are
+
+that are due to the insertion
+or deletion of some side chain,
+
+then we should be
+able to predict
+
+the change in the
+potential energy,
+
+and therefore the change in
+the energy of the complex.
+
+But in fact, it
+turned out that it
+
+was very, very hard to do that.
+
+And so this plot compared--
+the black circles
+
+were the prediction
+algorithms for this problem,
+
+compared to just simply
+a substitution matrix,
+
+the BLOSUM substitution matrix
+defined in terms of the area
+
+under the curve for
+beneficial mutations
+
+and deleterious mutations.
+
+And you can see that very,
+very few of the black dots
+
+get far away from what is the
+really simple default model.
+
+A lot of them do worse.
+
+So OK, well maybe that's
+not such a simple problem
+
+because it requires a highly
+quantitative prediction.
+
+Maybe we'll do
+better just trying
+
+to predict which
+proteins interact at all.
+
+And so that's going to be
+the focus of today's lecture.
+
+Now, that also had
+a problem, right?
+
+Because even if I know the
+structure of two proteins,
+
+I don't know necessarily
+what surfaces
+
+of those proteins interact.
+
+And so I have to
+figure out this docking
+
+problem of which part
+of protein A interacts
+
+with which part of protein B.
+
+That's the beginning
+of my problem,
+
+and then I have to make a
+series of subsequent decisions.
+
+So I'm going to
+have to figure out
+
+for any potential
+partner of my protein,
+
+I need to figure out
+the docking problem,
+
+the relative
+position orientation.
+
+Now, in this little
+cartoon, it's
+
+shown as a completely
+static protein that
+
+approaches another
+static protein.
+
+The only thing that's changing
+is the relative coordinates.
+
+But of course, there
+will be local changes
+
+in confirmation, perhaps
+even global ones.
+
+And so we need to be able
+to make some estimates as
+
+to what those structural
+rearrangements will
+
+be when the two
+proteins interact.
+
+And then after we've
+come up with our best
+
+estimate of the
+structural rearrangements,
+
+only then can we come up with
+an estimate of the energy
+
+interaction and
+decide whether it's
+
+better than some threshold.
+
+OK.
+
+So one of the problems that's
+pretty obvious from this
+
+is that this kind of
+approach in principle,
+
+if we do it rigorously
+through all the steps,
+
+would be extremely slow.
+
+Now, another part that's perhaps
+a little bit less obvious
+
+is that it's going to be very
+prone to false positives.
+
+And why do you
+think that might be?
+
+What am I not taking
+into account here?
+
+AUDIENCE: Are you
+not taking into
+
+account the desolvation
+[INAUDIBLE].
+
+PROFESSOR: So one
+answer is I'm not
+
+taking account of
+the desolvation,
+
+but in fact, I can do that.
+
+Right?
+
+So some of the potential
+energy functions
+
+we looked at, the
+statistician's version rather
+
+than the physicist's
+makes it pretty easy
+
+to incorporate the desolvation.
+
+Any other thoughts as to what
+I'm not taking into account?
+
+What other protein
+should I be considering
+
+when I'm considering
+an interaction problem?
+
+So I've isolated, in
+this case, two proteins.
+
+I'm saying, in a universe
+where these are the only two
+
+proteins that exist, will
+they have a favorable energy
+
+interaction?
+
+What I really need to know is
+whether that energy interaction
+
+is more favorable than all
+the competing interactions
+
+that they could have.
+
+So even if I find something
+that's potentially
+
+a good interaction, it may
+not be the best possible
+
+interaction.
+
+And if I consider then the
+concentration of this protein
+
+and the concentration of
+all the other molecules
+
+out there that have
+a higher affinity,
+
+then it could turn out
+that this is actually
+
+a rather poor substrate
+for my protein, a rather
+
+poor interaction partner.
+
+So we have that false
+positive problem.
+
+OK.
+
+But let's focus on the
+computational efficiency
+
+problem, because
+that's at least one
+
+that we can come up with
+some nice algorithms
+
+to try to solve.
+
+So what we want to do is try
+to limit our search space.
+
+If I want to figure out--
+I have a query protein
+
+and I want to ask, what
+does it interact with,
+
+instead of trying to do
+the pairwise comparison
+
+of this protein with every
+other protein in the database,
+
+and doing very precise
+structural calculations on all
+
+of those, maybe
+there's some way that I
+
+can prefilter the
+set of proteins
+
+that it might interact with.
+
+And that's what we're
+going to look at.
+
+So we're going to try
+to officially choose
+
+potential partners
+before we're doing
+
+any structural comparison.
+
+And then once we
+have those partners,
+
+we're going to try
+to avoid having
+
+to do detailed calculations
+until we have a relatively
+
+high degree of confidence that
+these proteins could interact
+
+by other criteria.
+
+And we're going to look at two
+papers that describe algorithms
+
+for solving this
+problem, and they're
+
+both uploaded to the website.
+
+The first thing
+that we'll look at
+
+is called PRISM that actually
+uses structural calculations.
+
+And then we'll look
+at PrePPI, which
+
+deals with everything
+purely at-- without actually
+
+explicitly calculating
+the structures.
+
+OK.
+
+So what does PRISM do?
+
+Well, it's based on
+the notion that there
+
+are a limited number
+of architectures
+
+that we could look at for
+which proteins can interact.
+
+And so if we can identify
+those architectures,
+
+then we can try to figure
+out whether a protein is
+
+a potential partner
+of another one
+
+before we do the detailed,
+costly calculations.
+
+In addition, in
+those architectures,
+
+not all amino acids
+are going to be equal,
+
+but there are going
+to be some that
+
+contribute more to the
+energy than others.
+
+And so by identifying
+those critical residues,
+
+we can once again focus
+our computational energy
+
+on those complexes that are
+most likely to be important.
+
+OK.
+
+So it has these two components--
+a rigid-body structural
+
+comparison.
+
+So that's that two
+proteins are not
+
+changing their own
+coordinates, they're
+
+just being brought together
+in different conformations.
+
+And then once the proteins
+have passed a series of checks,
+
+then we allow for
+flexible refinement using
+
+the kinds of energies we looked
+at in the previous lectures
+
+to decide how high affinity
+this complex could be.
+
+And the critical
+thing is that we're
+
+going to make some of
+these early decisions
+
+after the rigid-body comparison
+using structural similarity,
+
+evolutionary conservation,
+and particularly
+
+looking at these regions
+that are called hotspots.
+
+These are sites where most of
+the free energy of interaction
+
+occurs during an interface.
+
+So it's not, as I said,
+uniformly distributed.
+
+So I showed you this
+slide last time.
+
+It shows chymotrypsin in a
+light gray and its interaction
+
+with some protein partners.
+
+These two share some global
+similarity to each other,
+
+whereas this partner is
+quite different from either
+
+of these two globally.
+
+But you can see that
+at the interface,
+
+it's actually quite similar.
+
+And so this gives you hope that
+even if you can't find a direct
+
+homologue-- so if you
+were trying to figure out,
+
+what does this protein
+in yellow interact with,
+
+and you searched the database
+and you couldn't find anything
+
+that was its
+structural homologue,
+
+but if you could figure
+out to look for homologues
+
+of the lower regions
+that interact,
+
+you might be able to figure out
+that it interacts with the same
+
+protein as this
+one and this one.
+
+OK.
+
+So what about this
+idea of hotspots?
+
+And this was an
+idea that was first
+
+developed in 1995 by this
+paper, Clackson and Wells,
+
+where they were looking at the
+interaction of a cell surface
+
+receptor with its
+ligand approaching.
+
+And they did
+systematic mutagenesis
+
+across the surface
+of the interface
+
+to see when I mutate any
+single amino acid to alanine,
+
+how much it affects the
+energy of interaction.
+
+What they found was things
+were highly non-uniform.
+
+So this lower curve shows
+the change in free energy
+
+when you mutate particular
+individual amino acids
+
+to alanine.
+
+And you can see there are
+big losses of free energy
+
+at some places, and
+other places there's
+
+almost no change in the
+free energy binding.
+
+In a few places you
+actually get a benefit
+
+from mutating a side
+chain to alanine.
+
+So in this particular
+case, and it's
+
+held up over many,
+many cases then,
+
+the free energy of binding is
+not uniform across the surface,
+
+but it's distributed in what
+has been called hotspots.
+
+So here is a structure
+of the human growth
+
+hormone and its receptor.
+
+And in red are the
+few amino acids that
+
+contribute very, very large
+amounts-- more than one
+
+and a half kcals per mole--
+to the energy of interaction.
+
+And it doesn't correspond
+with any simple structural
+
+parameter.
+
+So it's not the amino acids
+that have the biggest surface
+
+area, for example, or
+anything like that.
+
+So it's not trivial to figure
+out what these regions are,
+
+although there are some
+prediction algorithms.
+
+So there are studies,
+and subsequent ones
+
+have indicated that roughly
+10% of the amino acids
+
+at the interface
+are the ones that
+
+have the biggest contribution.
+
+There are some trends, but
+none of these are hard rules.
+
+These tend to be rich in
+these three amino acids--
+
+tryptophan, arginine,
+and tyrosine.
+
+If you might imagine,
+these are regions
+
+of the protein that are
+highly complimentary.
+
+So there'll be a patch
+on one side that's
+
+a hotspot matching
+up with another patch
+
+on the other protein
+that's also a hotspot.
+
+And it's kind of
+an interesting note
+
+that around these regions
+where the hotspots occur,
+
+there are other amino
+acids that exclude solvent
+
+from the interface.
+
+And they call that an o-ring.
+
+So these are some
+of the features that
+
+tend to occur with
+protein interfaces.
+
+So in this PRISM algorithm,
+what they do is the following.
+
+They start off with a
+template-- two proteins that
+
+are known to interact-- and
+they define the interface simply
+
+by close approach of
+amino acids in one
+
+chain to amino
+acids in the other.
+
+So in this case,
+shown in these balls
+
+are regions of the
+proteins that interact.
+
+And then they isolate
+the interfacial residues.
+
+Ignore the rest of the
+protein, because we
+
+said that the parts that
+interact in different proteins
+
+could be homologous even
+if the global structures
+
+of the proteins are not, right?
+
+So we're going to do our
+structural similarity
+
+calculations purely on
+the interface residues
+
+and not on the entire structure.
+
+So then with that
+template, you can then
+
+look at lots of proteins
+and see whether they
+
+have any structural match
+to pieces that interact.
+
+So here they've identified
+this protein, ASPP2,
+
+which has structural homology
+to I kappa b at the interface.
+
+Although globally
+it's quite different.
+
+And now, once they have this
+potential partner for NF kappa
+
+b, this ASPP2,
+they're going to test
+
+whether there's a
+good structural match,
+
+whether specifically
+in the regions
+
+that are hotspots-- they have
+an algorithm for predicting
+
+hotspots-- whether the
+match is good, whether it's
+
+sequence conservation
+at those hotspots.
+
+And only then do they
+do the refinement
+
+to do the flexible
+refinement of the type
+
+that we looked at in the
+previous lecture, energy
+
+minimization, and
+other approaches
+
+to figure out what the
+best possible structure
+
+of this complex
+would be, and then
+
+what it's free energy would be.
+
+So here's their
+description of the problem.
+
+They have template
+proteins and targets.
+
+They do a structure alignment.
+
+They asked whether it
+passes some thresholds.
+
+These are very, very
+fast calculations to do.
+
+And only if they pass
+these fast calculations
+
+do you do more
+detailed calculations.
+
+And finally, only
+if it passes this
+
+do you do the very
+computationally expensive
+
+refinement.
+
+And then one critical thing to
+remember from this algorithm
+
+is that it doesn't require
+the template and its query
+
+to be perfectly
+matched in structure.
+
+In fact, the elements of the
+structure at the interface
+
+could come from different
+parts of the chain.
+
+So they don't take into
+account the chain order.
+
+So if I had a beta sheet
+structure in one protein that
+
+looks like this, in my
+query these two proteins
+
+could be very
+indirectly connected.
+
+I don't care that there's a
+huge gap in the insertion.
+
+I just care that locally
+at the interface,
+
+one protein looks a
+lot like the other.
+
+There was a question
+in the back.
+
+AUDIENCE: How do you search
+a database for 3d structures?
+
+Are you just looking
+at all the [INAUDIBLE]?
+
+PROFESSOR: That's right.
+
+So the question was,
+how do you search
+
+a database for 3D structure?
+
+You do structural
+similarity comparisons
+
+that are based on
+the 3D coordinates.
+
+The simplest way to do it,
+but not the most efficient,
+
+is to find the rigid-body
+superpositions that
+
+minimize the root mean
+squared deviation, which
+
+was a metric we gave in one
+of the previous lectures.
+
+There are faster things
+you can do as well.
+
+You could imagine that you could
+look at certain global features
+
+of elements of secondary
+structure and so on.
+
+And there's been a lot of work
+making those algorithms very
+
+fast.
+
+Other questions?
+
+Good question.
+
+So they give an
+example in their papers
+
+that starting off with this
+known structural complex,
+
+cyclin-dependent kinase, the
+cyclin, and p27, the inhibitor.
+
+And then looking for
+structural matches.
+
+So we can identify this
+potential structure match.
+
+You refined it, get an
+energy of interaction.
+
+Try another one that has no
+global structural similarity.
+
+Again, once it passes
+all the checks,
+
+you compute the
+refinement and the energy.
+
+And similarly with this side.
+
+And so from this
+initial complex,
+
+where we had these
+two proteins which
+
+were known to interact in the
+PDP they can make predictions
+
+that these other proteins are
+likely to interact even though,
+
+again, at the global
+level, there's
+
+very little sequence similarity.
+
+Is that clear?
+
+OK.
+
+So the advantage of this
+is that it eventually
+
+does do these structural
+refinements that
+
+allow us to figure out
+the best match between two
+
+potential interacting proteins.
+
+But that's also its
+weakness because that
+
+takes a lot of
+computational time.
+
+So this other approach called
+PrePPI never actually does
+
+those structural refinements
+of the type we talked about
+
+in the previous lecture.
+
+So if so, how does it
+figure out whether the two
+
+proteins are likely to interact?
+
+So this is their schematic,
+and we'll go through the steps.
+
+So you start off with
+two query proteins
+
+that you want to know
+if they interact.
+
+And you do sequence
+similarity to a database
+
+of known structures.
+
+So you find sequence
+homologues to those proteins.
+
+And so they call
+those homology models.
+
+MA and MB.
+
+And now they look through the
+database for all the structural
+
+homologues, not
+sequence homologues,
+
+but structural
+homologues of MA and MB.
+
+So they get a
+series of neighbors
+
+that they call NA 1
+through n and NB 1 to n.
+
+So these are the neighbors
+of these homologues.
+
+And they asked whether
+any of these neighbors,
+
+anything in this row,
+anything in this row,
+
+are known to interact.
+
+And that potential
+interaction then
+
+could be a model for the
+interaction of the query,
+
+right?
+
+So far so good.
+
+Then they do a
+sequence alignment.
+
+They sequence
+alignment of MA and MB,
+
+which are the known structural
+homologues of the queries,
+
+and the two proteins that
+are known to interact.
+
+And so now they've got
+this potential model
+
+for the interaction of the
+queries made up of two proteins
+
+of known structure that have
+homologues that are known
+
+to interact.
+
+OK?
+
+So it's two steps removed
+from the actual interaction.
+
+Now, while their
+figure says that they
+
+do a structural
+superposition, that's
+
+not, in fact, what they do.
+
+If you look at it carefully,
+it's a sequence analysis.
+
+And I'll take you through
+the steps in a second.
+
+So they mean structured
+in a rather loose way.
+
+So they're only doing
+sequence comparisons here.
+
+They're never actually
+building a homology model
+
+for the queries.
+
+OK
+
+So this figure comes
+from the supplement
+
+where, for some
+mysterious reason,
+
+they've changed all
+the nomenclature.
+
+So things that previously
+were called NA and NB
+
+have now been called TA and TB.
+
+Take what you get.
+
+So this is a pair of
+interacting proteins
+
+where the structure of
+the interaction is known.
+
+And they're structural
+neighbors of NA and NB,
+
+which you don't know whether
+they interact or not.
+
+They identify interacting
+residues in this structure.
+
+That's why it's represented by
+these black lines connecting
+
+blue dots.
+
+So these are
+interacting residues
+
+from the two template proteins
+and neighbors NA and NB.
+
+And they asked whether the
+amino acids in MA and MB
+
+also are good matches
+for this interface.
+
+And they have a number of
+criteria for doing that.
+
+So they come up
+with five measures.
+
+The first of those measures
+is a structural similarity
+
+between these MA proteins and
+the MA and MB and NA and NB.
+
+Then similarity-- OK, similarity
+is the structural similarity.
+
+Then they asked, how many of the
+amino acids at this interface,
+
+and what fraction of the
+amino acids at the interface
+
+can be aligned?
+
+So this is a sequence-based
+alignment of MA
+
+and-- well, it's here called TA,
+but was previously called MA.
+
+Just to make life complicated.
+
+So this is the
+sequence-based alignment.
+
+These are they interacting
+residues, all the blue ones
+
+in the structure of
+TA and TB interacting.
+
+And they asked, what
+fraction and what number
+
+of these amino acids are aligned
+in this sequence alignment?
+
+So here they come
+up with a number.
+
+In this case, I guess, it's
+four amino acids in this-- four
+
+pairs, I should say, of the
+amino acids-- one, two, three,
+
+and four, indicated
+by these four lines--
+
+are both interacting in the
+structure of the complex
+
+and can be aligned to
+sequences in MA and MB.
+
+And then they use
+these other algorithms
+
+that are based primarily
+on machine learning
+
+looking at protein
+interfaces to decide
+
+whether the sequence of the
+amino acids that are going
+
+to sit at those places
+in the interface
+
+are likely to be residues that
+typically occur at interfaces.
+
+So this is the
+kind of statistics
+
+that I showed you before
+from those old papers that
+
+said 10% of the amino acids
+are in these hotspots.
+
+Certain kinds of amino
+acids are predominant there.
+
+So the number of algorithms,
+and they list a bunch,
+
+that they use to
+come up with a score
+
+to decide whether these
+residues, in fact, are
+
+statistically likely
+to be good matches.
+
+So they have these criteria
+and they decide then
+
+that some fraction of the amino
+acids at this interface in MA
+
+and MB are likely to
+be reasonable ones
+
+to be at the interface.
+
+So with all that
+done, they then use
+
+all of these different scores
+with a Bayesian classifier,
+
+and we'll talk a
+little bit later
+
+in this lecture and
+probably the next lecture
+
+as well as to what a
+Bayesian classifier is.
+
+But they plug all
+those scores in that
+
+they've derived
+from these proteins
+
+to decide whether
+these two proteins are
+
+likely to interact.
+
+So the advantage
+of this approach
+
+is it's extremely fast.
+
+Everything we've talked
+about are very, very quick
+
+calculations.
+
+Even the structural
+alignments are fast.
+
+The sequence alignments,
+of course, are.
+
+So we get through the whole
+database very quickly.
+
+So they've actually computed the
+potential attraction partners
+
+of every pair of proteins in
+various genomes based solely
+
+on these alignments.
+
+The disadvantage-- so what's
+the disadvantage of this method?
+
+AUDIENCE: Can't get a
+de novo interaction?
+
+PROFESSOR: We can't get
+any de novo interaction,
+
+so if there's no neighboring
+structures that interact,
+
+they'll never come up with it.
+
+So that's an important point.
+
+And then the other problem
+is, because it doesn't
+
+have the structural
+refinement, it's
+
+given up on that
+slow calculation,
+
+so also loses a lot of
+potential specificity.
+
+All the conformational
+changes that can occur
+
+will be lost to an
+algorithm like this.
+
+So we have these two
+competing approaches.
+
+Yes, questions in the back.
+
+AUDIENCE: Couldn't this method
+actually be used as an input
+
+to, say, a refinement
+step, for example?
+
+PROFESSOR: The
+question was, could you
+
+use this kind of approach as an
+input to the refinement step?
+
+And absolutely one could.
+
+Is there another
+question back there?
+
+Other questions?
+
+All right.
+
+So we're going to take a slight
+turn here in the course lecture
+
+and move away from a purely
+computational approach
+
+and actually look at how
+interaction measurements are
+
+made.
+
+One of the big changes
+of the last decade or so
+
+is that we've gone from an era
+when interactions were measured
+
+pairwise to interactions
+being measured in bulk.
+
+So through high
+throughput measurements.
+
+And we'll see that that leads
+us to some statistical problems
+
+which eventually bring us back
+to some computational issues
+
+as well.
+
+So if you want to measure
+all the proteins that
+
+interact in an
+organism, turns out
+
+to be, obviously,
+very difficult.
+
+One big advance that's
+helped with this
+
+is the idea of tagging proteins
+and using mass spectrometry
+
+to figure out what
+they interact with.
+
+So in these two sets
+of papers, which
+
+were some of the early
+ones being done in yeast,
+
+they took one protein at a
+time and attached a tag to it.
+
+And I'll talk about exactly
+what those tags are,
+
+but those are labels
+that allow you
+
+to attach it to a solid support.
+
+And then by attaching
+to a solid support,
+
+you could then
+purify any proteins
+
+that stuck to protein one here.
+
+And then after you purify them,
+you can run them out on a gel,
+
+cut them out, and
+figure out what
+
+the identity of those
+interacting proteins
+
+were by mass spec.
+
+So this sounds very
+labor intensive,
+
+but it's still a lot faster than
+anything that came before it.
+
+And with this
+approach, they were
+
+able to go through
+entire genomes,
+
+proteomes I should
+say, and figure out
+
+all the interacting partners
+for very, very large fractions
+
+of all the proteins there.
+
+So with this approach,
+what kinds of proteins
+
+do you think are likely
+to be false positives?
+
+Any thoughts?
+
+Yes.
+
+AUDIENCE: Proteins
+stuck on the column that
+
+has nothing to do with
+interaction [INAUDIBLE].
+
+PROFESSOR: Exactly.
+
+So one thing that can
+be quite problematic
+
+are proteins that
+stick to the column
+
+regardless of which
+protein you put there.
+
+And we'll see an approach
+to getting rid of that.
+
+Other kinds of problems?
+
+A variant of that.
+
+Thoughts?
+
+What about proteins
+that tend to stick
+
+to other proteins
+non-specifically, right?
+
+Those are going to be
+quite problematic too.
+
+And what are the
+likely false negatives
+
+in an approach like this?
+
+The proteins that really do
+interact with the blue one
+
+but aren't picked up.
+
+Yes.
+
+AUDIENCE: Weak interaction
+partners [INAUDIBLE]
+
+PROFESSOR: Weak interaction
+partners, things,
+
+particularly with
+short half lives.
+
+Because you do a lot
+of washing, so it's
+
+going to be dependent
+on half-life.
+
+Very good.
+
+What else?
+
+Yeah.
+
+AUDIENCE: Maybe something
+that interacts in tag region?
+
+PROFESSOR: Something interacts
+in the tag region, right.
+
+So something
+interacts right around
+
+here would be lost because this
+would sterically interfere.
+
+Very good.
+
+Anything else?
+
+What about the
+concentration of proteins.
+
+How does that influence
+whether they show up here?
+
+All right.
+
+So if I have a very high
+concentration protein,
+
+it may interact even though
+naturally it doesn't.
+
+They never see each other.
+
+They're in different
+compartments.
+
+But when [INAUDIBLE]
+and do this.
+
+But low abundance
+proteins are going
+
+to be quite problematic because
+there'll be very little of them
+
+in these complexes compared to
+the high abundance proteins.
+
+It won't be detected
+by this method.
+
+They will never get to
+the mass spec, and so on.
+
+So we've got both false
+positives and false negatives
+
+in these approaches.
+
+Now, one of the
+things that came up
+
+was proteins that stick
+non-specifically to the column.
+
+And there was a
+clever approach in one
+
+of these early papers that
+got picked up to avoid that.
+
+And this is called tandem
+affinity purification,
+
+or TAP-tags.
+
+And the idea is the following.
+
+We have some gene.
+
+And we use homologous
+recombination--
+
+this was done in
+yeast where this
+
+is easy-- to insert
+this sequence, which
+
+codes for the following.
+
+A piece of protein of
+no particular function,
+
+as far as anyone
+knows, a spacer,
+
+followed by this
+calmodulin-binding protein,
+
+followed by a protease
+recognition site,
+
+and then by protein A.
+
+So once this protein
+gets expressed--
+
+and it gets expressed
+in it's native levels
+
+because you're inserting
+this into the genome.
+
+So it's not on an
+exogenous promoter.
+
+It's in its normal position.
+
+Whatever that protein
+was, then has it
+
+as C terminus all these pieces.
+
+So how does that help?
+
+In the purification, we start
+with something, IgG IGG,
+
+that binds to protein
+A. So now that's
+
+what attaches us to
+the solid support.
+
+And attached to
+the solid support
+
+will be all those things
+that are nonspecific binders.
+
+And so if I have some
+nonspecific binder that
+
+just likes my solid
+support, it'll be here.
+
+Nonspecific.
+
+And if I just acid washed
+everything off the column
+
+and ran my gels with that,
+or boiled it off in SDS,
+
+I would get the
+nonspecific protein too.
+
+But what they do instead
+is they instead cleave here
+
+with a very specific protease
+that recognizes this site.
+
+It's called a tobacco
+etch virus protease.
+
+It has a very long
+recognition sequence.
+
+You can make sure it doesn't cut
+anywhere in any other protein.
+
+And so now, instead of
+alluding non-specifically
+
+with acid or detergent, you
+allude specifically with TEV,
+
+and then this part of the
+protein will fall off.
+
+And then you do a
+second purification
+
+that relies on this
+piece of the protein.
+
+So you pull out only
+the things that you
+
+want that have the CBP,
+the calmodulin binding
+
+protein, by having different
+kind of solid support
+
+that has calmodulin
+attached to it.
+
+And so through this
+process, you can get rid
+
+of a lot of nonspecific binders.
+
+It doesn't help you with
+the false negatives, right?
+
+You've made the wash
+conditions even harsher
+
+so you're going to
+lose more proteins.
+
+But you'll pick up
+fewer false positives.
+
+And then finally, the last
+purification procedure actually
+
+uses EGTA, which is
+a chelating agent.
+
+So this interaction
+between CBP and calmodulin
+
+depends on calcium.
+
+EGTA sucks the calcium
+out of that interaction.
+
+And so it's, again, a very
+specific way of alluding rather
+
+nonspecific one, like heat,
+salt, acid, or detergent.
+
+So this has been one technology,
+affinity purification
+
+followed by mass spec, that's
+given us a lot of information
+
+on protein-protein interactions.
+
+And a computing
+technology that's
+
+also contributed quite a lot
+is called yeast two-hybrid.
+
+So in this approach,
+you have a reporter gene
+
+that normally is not
+going to be transcribed.
+
+It has at a design DNA binding
+site, a DNA binding protein,
+
+and your bait protein.
+
+And you want to figure
+out every protein that
+
+can interact with this prey.
+
+So the prey now is attached
+to an activation domain.
+
+If these two proteins
+don't interact,
+
+the activation domain never
+gets recruited to this reporter,
+
+there's no transcription.
+
+But if the green protein and
+the blue protein interact,
+
+then the activation
+domain is going
+
+to be recruited to
+this promoter and it's
+
+going to turn on transcription,
+and then you'll get a signal.
+
+So what are some of the
+advantages of this approach?
+
+It doesn't require you
+to purify anything.
+
+So it should be
+much more sensitive
+
+to low abundance proteins.
+
+So that's definitely
+an advantage.
+
+It'll pick up a lot of those
+transient interactions.
+
+You may not get
+continuous activation,
+
+but you'll get
+transient activation.
+
+And if you've set the
+conditions up properly,
+
+you can pick up the
+transient activation.
+
+But it has its own biases,
+so none of these techniques
+
+are going to be perfect.
+
+It's going to be
+biased against proteins
+
+that don't express well.
+
+This is, as the name implies,
+typically done in yeast.
+
+So if you have human
+proteins and you express them
+
+in yeast, or plant proteins
+that you express in yeast,
+
+there could be some proteins
+that just will not express well
+
+in that organism.
+
+What else can be a problem?
+
+Some proteins don't do
+well in the nucleus, right?
+
+So if you're interested
+in interactions
+
+with membrane
+proteins, it's going
+
+to be very hard to get them
+to express in the nucleus,
+
+and therefore, you'll never
+pick up those interactions.
+
+OK.
+
+So we've got these two
+different technologies--
+
+the affinity capture mass
+spec and the two-hybrid.
+
+Questions on those technologies?
+
+Yes.
+
+AUDIENCE: Could
+another control be
+
+for the mass spec
+purification just
+
+to subtract out everything
+that alludes non-specifically.
+
+PROFESSOR: The question was,
+could you subtract out anything
+
+that's nonspecific.
+
+And yes, if you've
+got what you might
+
+call frequent flyers,
+proteins that show up
+
+in every single
+purification, then you
+
+can simply ignore those.
+
+And that is often done.
+
+So that'll help you
+with things that
+
+are very nonspecific
+for the surface.
+
+What's more of a
+problem are proteins
+
+that have some affinity
+for your protein
+
+x but are not really
+highly specific for it.
+
+So they tend to bind in
+certain kinds of patches.
+
+Those would be
+harder to figure out
+
+because they won't
+stick to everything.
+
+Good question.
+
+Other questions?
+
+All right.
+
+So we've got these
+different technologies.
+
+What we'd really
+like to be able do
+
+is we know that there are
+problems in each approach.
+
+We'd like to be able to compute
+the probability that two
+
+proteins interact
+based on the data.
+
+So now we're turning back to the
+more mathematical computational
+
+approaches.
+
+So if we just consider
+one experiment-- and we're
+
+going to talk about
+gold standard.
+
+So what's a gold standard?
+
+It's a set of proteins that we
+have extremely high confidence
+
+interact because it was analyzed
+by some other technology.
+
+Not two-hybrid, non-affinity
+capture mass spec, but much,
+
+much more direct interactions.
+
+By physical measurements,
+maybe the structural work.
+
+So the number of
+criteria that go into it.
+
+So we have this
+gold standard data
+
+set where we know the proteins
+definitely interact, and we
+
+have our experiment.
+
+So clearly anything
+in the overlap,
+
+we can count as true
+positives, right?
+
+We detected it.
+
+It's in the database
+of gold standards.
+
+And things that are in the
+gold standard that we missed
+
+are obviously false negatives.
+
+We report them as
+non-interacting,
+
+but in fact they do.
+
+The question is, how much
+of this is true positive?
+
+Everything that's detected
+in the experiment but we
+
+have no information
+for it in the database.
+
+So that could be for one
+of two reasons, right?
+
+That could be that they
+really don't interact.
+
+Or it could be that
+no one's measured it.
+
+The whole point
+of this experiment
+
+is to find new things.
+
+So is there any way to estimate
+what fraction of all the things
+
+that are unique to this
+experiment are true positives,
+
+and what fraction
+are false positives?
+
+Those we'd like to
+try to figure out.
+
+Now, if we just
+had one experiment,
+
+that would be very challenging.
+
+But what happens when
+we've got two experiments?
+
+So we have these two affinity
+capture mass spec experiments,
+
+or maybe affinity capture
+mass spec and a two-hybrid.
+
+So now let's think about
+the overlap of those two
+
+experiments with
+the gold standard.
+
+So I've got this region of
+overlap between experiment 1
+
+and experiment 2,
+and then this region
+
+that's overlapping
+between all three things.
+
+Experiment 1, experiment
+2, and the gold standard.
+
+So these clearly are
+two positives, right?
+
+They're high confidence
+because I picked them up
+
+in both experiments, and
+they're in the gold standard.
+
+What about all these things
+in what I've labeled here
+
+region 2?
+
+Well, if we believe that
+these two experiments are
+
+independent of each
+other in a rigorous way--
+
+so let's say one's a
+two-hybrid and one's
+
+an affinity capture mass spec,
+there's no particular reason
+
+that the false
+positives for one would
+
+be false positives in the other.
+
+In that case, I can
+call this region 2
+
+my consensus true positives.
+
+I have a very high
+confidence that these
+
+are true interactors.
+
+Everyone buy that?
+
+Seem reasonable?
+
+OK.
+
+So here's where
+the trick comes in.
+
+What fraction of all these
+consensus true positives
+
+are picked up in
+the gold standard?
+
+This ratio, right?
+
+Region 1 over region 2.
+
+OK.
+
+So now I've got this region
+of things that are picked up--
+
+the true positives from
+this experiment, then
+
+the gold standard.
+
+And then I've got this region
+that's unique to experiment 2
+
+and it's going to be some
+mix of true positives
+
+and false positives.
+
+And the authors of this
+paper that are cited here
+
+make the following argument.
+
+We're going to assume
+that the ratio of I to II
+
+is the same as the
+ratio of III to IV.
+
+So the fraction of
+consensus true positives
+
+that are picked-- these are
+independent experiments.
+
+So the fraction
+of true positives
+
+that are picked up
+in the gold standard
+
+is going to be constant,
+whether they're in the consensus
+
+or not.
+
+So the fraction at
+ratio of I to II
+
+is going to be the same
+as the ratio of III to IV.
+
+So by that then, I can figure
+out how much of this region
+
+consists of true
+positives and how much
+
+consists of false positives.
+
+Everyone buy that?
+
+Yeah.
+
+AUDIENCE: Can I check--
+are we not saying
+
+that the gold standard
+represents all true positives?
+
+PROFESSOR: Correct.
+
+Well, we're saying that the
+gold standard consists of things
+
+that we know to interact--
+
+AUDIENCE: But there may be more.
+
+PROFESSOR: But
+there may be more.
+
+And the goal of our experiment
+is to find those other ones.
+
+All right.
+
+So if you accept that premise,
+which seems plausible,
+
+then you can compute what
+fraction of all the things
+
+that are picked up in
+each of these experiments
+
+are likely to be true positives.
+
+So drum roll please.
+
+It turns out that the
+number's not that high.
+
+So the fraction of
+things in the consensus
+
+was 347 out of almost 2000.
+
+And if you do the math
+then, what you end up with
+
+is that the true
+fraction in this region,
+
+for which we have no
+data, is 1,123 out of--
+
+and the false piece in this
+is going to be almost 15,000.
+
+And they went ahead and
+did this for a number
+
+of different
+experiments and computed
+
+the fraction of derived false
+positives for these data--
+
+might be a little bit hard
+to see on this screen.
+
+But the numbers range
+from 50% false positives
+
+to, in some cases, over
+90% false positives.
+
+That's a little
+disturbing, right?
+
+So these technologies are good
+at picking up interactions,
+
+but there's reason
+to be very skeptical.
+
+OK.
+
+So now we've got
+a serious problem,
+
+because how are we
+going to figure out
+
+which of these interactions
+to trust when we know
+
+that a very, very large fraction
+of them are false positives?
+
+So what could you do?
+
+Well, you could take only
+the little bit of overlap.
+
+You could say, I have that Venn
+diagram-- method 1, method 2.
+
+They did agree on
+a bunch of things.
+
+So I could take only those.
+
+That obviously
+throws away a lot.
+
+Someone else suggested we could
+throw away the sticky proteins,
+
+right?
+
+So maybe there are
+nonspecific proteins
+
+that don't show up
+in every experiment,
+
+but they show up in a
+very, very large fraction
+
+of all experiments.
+
+Maybe I toss those out.
+
+That's another possibility.
+
+But what we really
+want to do is actually
+
+come up with a
+probability estimate.
+
+To not have to make
+a hard decision,
+
+but come up with an
+estimate of the probability
+
+that things interact
+based on all the data.
+
+So how do we go
+about doing that?
+
+So first of all, what happens
+if you just require a consensus?
+
+So this plot shows
+accuracy and coverage
+
+of the gold standard for
+individual experiments
+
+with different thresholds for
+deciding what's interacting,
+
+different cutoffs and things.
+
+So the individual
+experiments are shown here.
+
+And then if you
+acquire two methods
+
+to pick something up, or three
+methods to pick something up,
+
+you can get better and
+better in your accuracy.
+
+This is a log-log plot.
+
+So if you require
+three methods to agree
+
+before you call something
+a true positive,
+
+you can get up to-- I'm not
+sure exactly what this is,
+
+but 80%, 90% possibly.
+
+Right?
+
+But look at where
+you at the y-axis.
+
+You'd only get
+about less than 1%
+
+coverage of the gold standard.
+
+So that's not a great approach.
+
+So what we really
+want to do, as I said,
+
+is to try to estimate the
+probability that proteins
+
+interact given all of
+our available data.
+
+And the data could be
+specific experiments.
+
+Say the two different
+mass spec experiments
+
+we just referred to.
+
+Or as we'll see a
+little bit later
+
+in this lecture and possibly
+the next one, other kinds
+
+of extraneous data that are not
+direct physical measurements
+
+of interaction, but
+might give us confidence
+
+that things interact based
+on similarity in annotation,
+
+or similarity in gene
+expression, and so on.
+
+And we'll get into
+details of that.
+
+OK.
+
+So to do this, we need
+to have a little bit
+
+of a refresher on
+Bayesian statistics.
+
+So I want to measure
+the probability
+
+that an interaction is true
+given the available data.
+
+Right?
+
+And I can estimate that based
+on the probability of observing
+
+the data for things
+that I know to be true
+
+and these prior estimates.
+
+So what's the prior probability
+that an interaction is true
+
+and the prior probability of
+observing a particular data
+
+set.
+
+Now, this by itself isn't
+really that helpful.
+
+I haven't told you yet how
+to calculate any of the terms
+
+on the right.
+
+But bear with me.
+
+If I want to decide
+the likelihood
+
+that a protein interacts--
+how likely is it?
+
+Is it more likely that
+it interacts or not?
+
+I can compute this ratio.
+
+The probability
+that the interaction
+
+is true given the data
+over the probability
+
+an interaction is
+false given the data.
+
+That's the likelihood ratio.
+
+So by this formula, I then
+cancel out this probability
+
+of the data, the prior
+probability of the data.
+
+And if I had a way
+of calculating this,
+
+and we'll get to it in
+a second, then if it's
+
+more likely than not to
+be a true interaction,
+
+I can call it an interaction,
+right, if it's less likely.
+
+So if this ratio
+is greater than 1,
+
+I accept it as a
+true interaction.
+
+If this ratio is less
+than 1, then I reject it.
+
+OK.
+
+So now our challenge
+is to figure out
+
+how to compute these terms.
+
+One more thing to note
+is if all I want to do
+
+is be able to rank every
+interaction by this likelihood
+
+ratio, rather than coming
+up with a hard threshold,
+
+then I actually don't
+need all these terms.
+
+So this is the likelihood ratio.
+
+I can convert it to a log space.
+
+So it's going to be the
+sum of these two terms.
+
+And if I'm simply
+ranking everything
+
+by this log likelihood
+ratio, this term
+
+is the same for
+every interaction.
+
+It's just composed of
+prior probabilities.
+
+So it's not going to
+affect the ranking at all.
+
+Any questions on that?
+
+Is that clear?
+
+Good.
+
+So if I just want to come
+up with a ranking function,
+
+all I need to do--
+all-- I need to do
+
+is to be able to estimate
+the probability of observing
+
+data for true interactions and
+the probability of observing
+
+that set of data for
+false interactions.
+
+Everybody buy that?
+
+Yes, please.
+
+AUDIENCE: When you say
+that prior probability is
+
+the same for all
+interactions, we're
+
+saying we're assuming the same
+prior probability for all,
+
+or is this [INAUDIBLE]?
+
+PROFESSOR: That's
+its definition.
+
+We mean, what is the prior
+probability that proteins
+
+interact versus the
+prior probability?
+
+So it's independent of the
+proteins that we're looking at.
+
+Other questions?
+
+All right.
+
+So we need a way of
+computing this piece
+
+of all the things
+we've looked at before.
+
+So how do we get an estimate
+of the probability observing
+
+a particular
+configuration of the data?
+
+Meaning, I detect
+it in experiment 1
+
+and not in experiment
+2, but in experiment 3.
+
+What's the probability of that
+given it's a true interaction?
+
+So that's what we're going
+to dive into right now.
+
+OK.
+
+So one thing we could
+do to make life simpler,
+
+and then we'll remove
+this simplification later,
+
+but let's, for the time being,
+assume that all of my data
+
+are independent.
+
+So the two-hybrid is going
+to have completely different
+
+mistakes than the affinity
+capture mass spec.
+
+So those two data
+sets are going to be
+
+completely independent
+of each other.
+
+So I can write this as a product
+of a particular observation--
+
+a particular mass
+spec experiment
+
+and a particular two-hybrid
+experiment for true attractions
+
+and false interactions.
+
+So it's the product
+of the probability
+
+that a particular experiment
+would detect an interaction
+
+if the interaction is
+true over the probability
+
+that that particular
+experiment would detect it
+
+if there was no interaction.
+
+I'm just going to multiply
+all of those probabilities.
+
+Yes.
+
+AUDIENCE: [INAUDIBLE].
+
+This is one interaction pair?
+
+PROFESSOR: That's right.
+
+AUDIENCE: And you
+take the product
+
+over all the interaction
+pairs within one
+
+run of the experiment.
+
+Is that correct?
+
+PROFESSOR: If I
+want to determine
+
+whether a particular
+interaction pair--
+
+I want to compute
+this log likelihood
+
+ratio, or this,
+actually, ranking ratio,
+
+because I've thrown
+away the priors.
+
+I want to compute this ranking
+ratio for a particular pair.
+
+So I've got protein
+A and protein B.
+
+And I want to determine
+whether I believe
+
+it to be more likely
+to interact or not,
+
+and rank it with all
+the others, right?
+
+So I'm doing this for
+a pair of proteins now.
+
+So far so good?
+
+Now, for that pair
+of proteins, I
+
+have a series of observations,
+or lack of observations, right?
+
+I have a whole bunch
+of experiments.
+
+This experiment detected
+it, that experiment
+
+didn't detect it, this one did.
+
+So what's the probability
+of these proteins--
+
+these A and B really interact
+given that yes, no, yes
+
+in my experiments?
+
+And then for new protein,
+it might be no, no, yes,
+
+and what I want to figure out
+the probability for this pair.
+
+AUDIENCE: So is the scale
+of the big letter M,
+
+is it on the order of like 10
+experiments, 100 experiments,
+
+or thousands of experiments?
+
+PROFESSOR: Ah.
+
+So the question is,
+what's the scale of this.
+
+So obviously, that's going to
+depend on what kind of data
+
+I bring in, but in
+these cases, it's small.
+
+So we have a handful of these
+high throughput experiments
+
+over entire genomes
+and proteomes.
+
+So there's not to be a lot.
+
+So in some of
+these early papers,
+
+there were four
+interaction experiments
+
+that they were looking at.
+
+Now the numbers might
+be a little bit bigger,
+
+but not significantly greater.
+
+All right.
+
+So now to compute this, we
+need a set of gold standards.
+
+But now we don't just need gold
+standard positive interactions,
+
+proteins that we know
+really do interact.
+
+We also need proteins that we
+know really don't interact.
+
+Because I want to compute the
+probability of an observation
+
+given that some interaction
+is definitely wrong.
+
+So precisely how I
+compute these terms
+
+is going to depend
+on the kinds of data.
+
+The experiments I've
+just been talking about,
+
+these high throughput
+mass spec, which
+
+were the ones which we looked
+at the ratio of the consensus,
+
+true positives, and estimated
+that 96% of all the data
+
+were possibly in error.
+
+The details of how to do
+those calculations are here.
+
+I leave you to look that
+up if you're interested.
+
+But now what we're
+going to do is
+
+we're going to see how, if
+we were to rank interactions
+
+based on this term,
+we can avoid having
+
+to throw out most of our data.
+
+So we said if we require all
+the experiments to agree,
+
+we're going to have
+very, very low coverage.
+
+Now we're instead going
+to rank everything
+
+based on this likelihood
+ratio, or something
+
+derived from the
+likelihood ratio.
+
+So in this paper
+where they were simply
+
+looking at the
+protein-protein interaction
+
+data sets to compute
+these interactions,
+
+they ranked everything based on
+that ranking function we just
+
+described.
+
+And then as you
+vary your threshold,
+
+you can figure out how many
+true positives you have
+
+and how many false positives
+you have in the gold standard.
+
+True interactors and
+false interactors.
+
+And you can compute
+this curve, right?
+
+For any particular value
+of that ranking ratio,
+
+what's my sensitivity and
+what's my specificity?
+
+Are you clear what
+this plot means?
+
+And here they've
+plotted the values
+
+for individual experiments.
+
+And this is the value for
+an independent database
+
+of gold standard interactions.
+
+And so now, where
+do they come up
+
+with their true positives
+and their false positives?
+
+A lot of this is going to depend
+on how representative those
+
+are.
+
+And all these numbers
+are subject to revision
+
+if you decide that the true
+positives and false positives
+
+that people are using
+are not accurate enough.
+
+So they used two well annotated
+databases of interactions.
+
+One from MIPS and one from SGD.
+
+And you can play those
+off against each other
+
+as the database
+of true positives.
+
+In some ways, that's
+the easier thing
+
+because people like to report
+that proteins interact.
+
+They tend not to like to report
+the proteins don't interact.
+
+You don't see a lot of
+nature papers saying protein
+
+x doesn't interact
+with protein y.
+
+So how are you going
+to figure out, then,
+
+what are your true negatives?
+
+So the strategies
+that they used-- well,
+
+one possibility is they're
+annotated to be in complexes,
+
+and those complexes are
+different from each other.
+
+That's not bad, right?
+
+But it's not a guarantee either.
+
+Or this is a little bit better.
+
+They're annotated to be in
+different parts of the cell.
+
+Of course, if those
+annotations aren't perfect,
+
+low concentrations, you
+could still be wrong.
+
+Or that they have
+anti-correlated gene
+
+expression.
+
+I kind of like this one.
+
+So it's one thing to be not
+correlated, but if you're
+
+anti-correlated, seems
+pretty suggestive
+
+that these two proteins are
+never in a complex together.
+
+Again, it's no guarantee
+because, as we'll talk about
+
+in some detail later,
+RNA levels are not
+
+very good predictors
+of protein levels.
+
+But if you apply enough
+of these criteria,
+
+you can come up with
+a set of proteins
+
+that you have fairly
+high confidence really
+
+don't interact.
+
+You combine that with
+the databases of proteins
+
+with very high confidence
+that they do interact,
+
+and you can get the true
+positives and false positives
+
+that you need for this analysis.
+
+all right.
+
+So that's a way of
+combining some information.
+
+We're going to see a
+generalization of that
+
+called Bayesian networks.
+
+We've mentioned this
+already in at least
+
+two different
+contexts, and it'll
+
+come up again later
+in the course as well.
+
+So these are very
+general methods
+
+for reasoning probabilistically.
+
+We will see them
+in the context here
+
+of predicting interactions.
+
+We'll see them later in the
+context of gene regulation
+
+and signaling as well.
+
+What we fundamentally need
+to do a Bayesian network
+
+is a graphical structure that
+represents our understanding
+
+what the relationship is
+between causes and effects.
+
+And a set of
+probabilities that allow
+
+us to compute things
+on this network.
+
+We'll show you examples where
+those networks are derived
+
+from our prior understanding
+of the problem,
+
+but also ones where the
+structure of the network
+
+is learned from the data.
+
+And we're going to see
+two primary contexts.
+
+First we have this question
+of whether proteins interact.
+
+That's what we've just
+been talking about.
+
+So here are four experiments,
+the in vitro pulldown
+
+experiments and yeast
+two-hybrid experiments,
+
+that give us relatively
+independent information
+
+about whether proteins interact.
+
+And we're going to
+look at a paper that
+
+used those data with
+a Bayesian network
+
+to compute the probability that
+two proteins really do interact
+
+based on the combination
+of all the data,
+
+rather than throwing out
+anything that doesn't fall
+
+in the overlap, which could
+be a very, very small number.
+
+And then later on
+we'll see examples
+
+of using Bayesian networks to
+understand biological networks.
+
+So this might be a set
+of transcription factors
+
+that are regulating a set of
+differentially expressed genes.
+
+And the structure of
+the graphical network
+
+for a Bayesian network
+has a lot of similarities
+
+to the way we normally
+think about transcriptional
+
+regulatory networks.
+
+So there's sort of a
+natural way of transferring
+
+our regulatory problem into
+a graphical network problem.
+
+But we're going to focus
+on these prediction
+
+problems for protein-protein
+interactions first.
+
+Now, if I just want to compute
+the probability of detecting
+
+an interaction in various
+experiments, given that it's
+
+true or false, I
+could explicitly
+
+compute that probability.
+
+And we saw examples
+of that just now.
+
+But some of these
+Bayesian network problems
+
+become much, much
+too large to do that.
+
+This is a little tiny
+piece of a Bayesian network
+
+that is supposed to
+represent I believe
+
+it's transcriptional
+regulatory network.
+
+You could never possibly
+write down all of the terms
+
+in this probability, where every
+node could, in principle depend
+
+on every other node
+in the network.
+
+It would just be a
+ridiculously large problem.
+
+In fact, how large would it be
+if I've got N binary variables,
+
+my gene is on or off, my
+interaction is true or false,
+
+I have 2 to the N
+possible states?
+
+Right?
+
+And the only constraint
+I have, in principle,
+
+is that all the probabilities
+have to add up to one.
+
+So I have 2 to the N minus 1.
+
+2 to the N minus 1 possible
+variables that I need to set.
+
+So that's a ridiculously
+large number in most contexts.
+
+So how do Bayesian networks
+help us solve this problem?
+
+Well, we represent
+our understanding
+
+of the problem in a
+graphical structure
+
+where we have
+causes and effects.
+
+And there'll be a direct arrow
+from a cause to an effect.
+
+I don't always know the cause.
+
+So in our context,
+we were trying
+
+to figure out whether
+two proteins interact.
+
+What do we measure?
+
+We actually don't
+measure interactions.
+
+We measure the result of a
+particular experiment, which
+
+is a combination of
+whether interacted
+
+and all sorts of noise
+that we've just discussed.
+
+So the effects that we observe
+are detected in experiment one
+
+or detected in experiment two.
+
+The cause is, did
+it interact or not?
+
+So the cause is hidden,
+the effects are observed.
+
+Now, in the case we
+were looking at before,
+
+we treated all
+these probabilities
+
+as being independent.
+
+But we might know something
+about the structure
+
+of our experiments, the kinds
+of experiments we're doing,
+
+that might lead us to have
+a different structure.
+
+So we could have an
+interaction that gives rise
+
+to all different kinds of data.
+
+But depending on whether
+the protein's a membrane
+
+protein or highly
+expressed, it might
+
+influence the results
+of certain experiments
+
+and not influence the
+results of others, right?
+
+So like a two-hybrid
+would be very biased
+
+by which one of these?
+
+The membrane, right?
+
+And then the affinity
+capture mass spec
+
+could be very
+influenced by proteins
+
+that are expressed at very
+high levels or very low levels.
+
+If we assume that all the
+interactions are independent,
+
+then we multiply probabilities.
+
+And we'll go into
+more detail, but this
+
+is what we're looking
+at up until now.
+
+In cases where we believe that
+all the observations are not
+
+independent, then
+we're not going
+
+to simply multiply things.
+
+We'll see there's
+a more precise way
+
+of computing the probabilities.
+
+Now in this case, I've drawn
+the graphical structure
+
+because I believe that
+I know what's going on.
+
+But in the more general
+case that we'll look at,
+
+we'll actually derive the
+structure from the data.
+
+One of the nice things
+about Bayesian networks
+
+is that it removes the
+need to have all 2 to the N
+
+minus 1 possible parameters,
+because it tells us there
+
+are certain
+independence conditions.
+
+So node is independent of its
+ancestors given its parents.
+
+What does that mean?
+
+If I'm trying to reason
+about the expression of one
+
+of the genes down here, and I
+know that this transcription
+
+factor is on, I
+don't really care
+
+what the probability is
+that any particular parent
+
+of that transcription
+factor is on, right?
+
+So I don't need to know anything
+of transcription factor B1
+
+if I know the state of B2.
+
+If this is on, then
+that's the only thing
+
+that's going to affect whether
+it's turning on these genes,
+
+regardless of what the
+activation state of its parent
+
+was.
+
+Is that clear?
+
+Yes.
+
+AUDIENCE: The
+slide's saying TF B1.
+
+[INAUDIBLE] TF B2?
+
+It says TF A1.
+
+PROFESSOR: Yeah, sorry.
+
+That should say TF B1.
+
+Thank you.
+
+OK.
+
+So we'll do a little example.
+
+It's admission season
+both for graduate school
+
+and undergraduate.
+
+So let's do a little
+toy example where
+
+we're going to get rid of
+the admissions committees
+
+and just do
+automated admissions.
+
+So we're going to collect
+various data about students,
+
+and then we're going to
+build a Bayesian network.
+
+And that network
+is going to decide
+
+whether to admit students
+into this simplified version.
+
+And the only information that
+will go into our decision
+
+will be the grades on the
+transcript and the GREs.
+
+Hopefully that's not the case.
+
+And we believe
+that certain things
+
+influenced your
+grades and your GREs.
+
+Whether or not the
+student is smart
+
+certainly should
+have some influence,
+
+but also the great
+inflation at their school
+
+will have some influence.
+
+So a prediction problem
+in a Bayesian network
+
+is going from the
+causes to the effects.
+
+So if I want to predict
+whether a student's admitted,
+
+I only need to look upstream.
+
+So we want to predict-- we
+observe the things on the top.
+
+Say, grades and
+GREs, and we want
+
+to predict whether this student
+should be admitted or not.
+
+There's another problem called
+an inference problem, which
+
+is when we observe
+the effect and we
+
+want to make inferences
+about the causes.
+
+So an example of that would
+be, you apply for an internship
+
+and they say, oh,
+she's a student at MIT.
+
+I bet she's smart.
+
+Right?
+
+They're doing an
+inference problem.
+
+We'll leave it for you to decide
+whether you and your colleagues
+
+are as smart as everyone
+thinks, but hopefully you are.
+
+OK.
+
+So we've got these two
+different kinds of problems.
+
+We've got prediction
+problems from top to bottom,
+
+and inference problems
+from bottom to top.
+
+And we're going to talk about
+conditional probability.
+
+So if I've got some very
+small piece of this network
+
+with just two nodes,
+I could write out
+
+all the possible probabilities
+for any pair of those nodes.
+
+So the probability that
+a student is not smart
+
+given that that student has
+low grades, the probability
+
+that the student is not smart
+given that the student has
+
+good grades, and so on, for all
+possible pairwise comparisons.
+
+Or I could write this as a
+conditional probability, which
+
+tends to be an easier way
+to think about the problem.
+
+What's the conditional
+probability of a student
+
+being smart given that
+they've got good grades
+
+or given that they
+have bad grades?
+
+They have the same information.
+
+For this one, I need
+additional information
+
+about the total probability of
+students being smart or not.
+
+And the total number of
+variables, as I said,
+
+in either case is the same.
+
+So these are completely
+interchangeable,
+
+but it's a lot easier to reason
+with conditional probabilities
+
+than with the joint
+probability tables.
+
+Those we'll see in a second.
+
+So as I've said, you don't
+need a full probability table
+
+for a Bayesian network.
+
+You don't need two N to
+the minus 1 variables.
+
+And the fundamental
+reason for that
+
+is that the joint
+probability is only
+
+going to depend on the parents.
+
+So in this toy example,
+the GRE scores over here
+
+are not dependent
+on grade inflation.
+
+Now, that all
+hopefully makes sense.
+
+Questions?
+
+Bayesian networks get
+a little murky next,
+
+so I'm going to try to
+give you into-- oh, yes.
+
+Question, please.
+
+AUDIENCE: You said that
+the parents don't affect
+
+their children, but if grade
+inflation affects the grades,
+
+how does that
+influence-- will that
+
+influence the grade [INAUDIBLE]?
+
+PROFESSOR: Sorry, can you
+say the question again?
+
+AUDIENCE: I guess
+I'm just confused
+
+by this particular example.
+
+What do you mean by
+the joint probability?
+
+The joint probability of what?
+
+PROFESSOR: So if I
+want to figure out
+
+the probability of some
+particular configuration of all
+
+the nodes in my network,
+I don't necessarily
+
+need to consider
+all possibilities.
+
+Because for example,
+if I want to consider
+
+all of the joint
+probability samples
+
+with settings for the GREs,
+whether the student had
+
+good GRE scores
+or not, that's not
+
+going be influenced by the
+student's school's grade
+
+inflation policies.
+
+AUDIENCE: But wouldn't the
+grades be influenced by the--
+
+PROFESSOR: But the
+grades would be.
+
+That's right.
+
+So some of the
+variables I can remove
+
+and others-- some of the
+joint probability statements
+
+I don't need to worry
+about and others I do.
+
+And which ones I
+need to consider
+
+is determined by
+the graph structure.
+
+Yes.
+
+AUDIENCE: How is the graph
+structure determined?
+
+PROFESSOR: OK.
+
+So how is the graph
+structure determined?
+
+So it's determined
+in one of two ways.
+
+I can draw it in advance because
+I believe that I know something
+
+about my setting, I believe
+that these data are independent.
+
+Then it has that
+structure like this.
+
+Cause and a bunch of
+independent effects.
+
+Or perhaps I claim to know that
+actually two of these things
+
+have a common parent as well.
+
+In some cases I know.
+
+We'll also talk about how
+to learn the structure
+
+from the data, which is
+the more common setting
+
+in regulatory networks.
+
+So in these kinds
+of problems when
+
+trying to decide
+how to integrate
+
+different proteomic data
+sets, typically people
+
+make arbitrary decisions
+about what the structure
+
+is based on their
+knowledge of the system.
+
+But if you're trying to figure
+out de novo which proteins
+
+interact with which, which
+proteins regulate which genes,
+
+then you have to learn
+it from the data.
+
+And we'll talk about how
+to do that in a second.
+
+Great questions.
+
+Any other questions?
+
+Anything in the quiet
+half of the room?
+
+OK.
+
+So as I said, this
+part of it, I think
+
+you can usually
+come up with cases
+
+that give you fairly
+good intuition.
+
+One of the things that is true
+in these Bayesian networks
+
+which most people find a
+little bit surprising at first
+
+is something called
+explaining away.
+
+So let's look at this
+Bayesian network.
+
+I go outside and I
+detect that things
+
+are slippery on the grass.
+
+So that could be for
+a lot of reasons,
+
+but one possible reason
+is that the grass is wet.
+
+OK.
+
+What are the causes of
+the grass being wet?
+
+Well, it could have
+rained or the sprinklers
+
+might have been on.
+
+And depending on this
+as an example-- so
+
+a lot of the Bayesian networks
+were developed in Stanford
+
+by Judea Pearl and colleagues.
+
+And of course, in California
+it doesn't rain that often.
+
+So there the season is a strong
+determiner of these things.
+
+Not so much around here.
+
+So in this example
+that they like to do,
+
+so does the
+probability that it's
+
+raining depend on whether
+the sprinkler is on or not?
+
+Now, the answer
+should be no, right?
+
+I mean, in reality, when
+you think about-- there's
+
+no causal relationship
+between the sprinkler being on
+
+and the rain.
+
+But in fact, when we're
+reasoning over these networks,
+
+we actually are influenced.
+
+In a probabilistic model,
+if I know that it's raining,
+
+and I know the grass
+is wet, then what
+
+do I think about the
+sprinkler being on?
+
+Do I think it's just as likely?
+
+No, I think it's
+less likely, right?
+
+If I go outside and see the
+grass is wet, there are clouds,
+
+the rain is coming
+down, is the sprinkler
+
+likely to be on or not?
+
+It's likely to be off, right?
+
+So there's no
+causal relationship,
+
+but there's the probabilistic
+relationship through the graph
+
+structure.
+
+And that's called
+explaining away.
+
+And you can take a whole
+course on how to understand
+
+which relationships you
+can detect and which not.
+
+This is not the place
+to try to go into that,
+
+but I hope you'll be
+familiar with this problem.
+
+And I'll try to give
+you a toy example that
+
+makes it a little bit
+more obvious in terms
+
+of the equations
+where this comes from.
+
+So imagine this very silly game
+where we play, we toss coins.
+
+We toss a coin twice.
+
+And if it turns up heads
+both times, you get a point.
+
+If it turns up tails both
+times, you get a point.
+
+But if one's a head and one's a
+tail, you don't get any points.
+
+Now, does the probability that I
+tossed a head on the first time
+
+depend on whether I toss
+a tail on the second time?
+
+So causally,
+obviously not, right?
+
+First of all, it
+happened earlier in time.
+
+And secondly, the coin tosses
+are completely independent.
+
+But what happens when
+I know the outcome?
+
+What if I know
+what score you got?
+
+So if I know your score,
+then is the probability
+
+that I tossed the
+heads on the first time
+
+independent of whether I got
+a tail on the second time?
+
+What do you think?
+
+How many people think
+it is independent then?
+
+How many people think
+it's not independent.
+
+Very good.
+
+It's not independent.
+
+And obviously, here's
+the math to prove it,
+
+but your intuition
+does the same thing.
+
+So what's the probability
+that I tossed a head
+
+on the second time
+given that I got a one,
+
+I scored, and I tossed a
+tail on the first time?
+
+Obviously, it's zero, right?
+
+So here's the
+probability of getting
+
+a head in the first
+time and scoring one,
+
+and tails on the second
+time is exactly zero.
+
+So that's called
+explaining away.
+
+You can reduce your
+belief in certain parents
+
+based on what you know
+about the children.
+
+Think of this coin toss
+example or the rain
+
+in California and
+the sprinklers.
+
+All right.
+
+So as this come
+up several times,
+
+how do we obtain the
+Bayesian network structure?
+
+There are two problems that
+we need to be able to solve.
+
+We need to be able to
+learn the structure,
+
+and we need to be able to
+learn these probability tables.
+
+If we know structure, how
+do we get the probabilities?
+
+Well, we need to identify
+some objective function we're
+
+going to try to optimize,
+and then choose values
+
+for all probability
+distributions that
+
+optimize that
+objective function.
+
+And that's the
+kind of thing we've
+
+been doing all along, just
+like in the Gibbs sampler.
+
+We need some objective
+function or protein structure.
+
+We need some objective
+function that we're
+
+going to try to optimize.
+
+So there are two common
+ones that are used a lot.
+
+There's maximum likelihood
+and the maximum posterior.
+
+So maximum likelihood is defined
+as the set of param-- theta
+
+is all the parameters, all
+the probability distributions,
+
+the probability of getting a
+score of one given that you had
+
+heads and tails,
+whatever it may be.
+
+The probability of
+getting admitted
+
+given that you had certain
+GREs and certain grades.
+
+So we want to find
+the set of parameters,
+
+all those probability
+distributions, that
+
+maximize this.
+
+The probability of the
+data, our training data,
+
+given those parameters.
+
+That's a pretty obvious one.
+
+And the maximum posterior
+includes some of our beliefs
+
+about the prior
+probability of the data
+
+and the prior probability
+of the parameters.
+
+This is a little
+bit less intuitive
+
+because you have
+to ask, well, where
+
+do those numbers come from?
+
+And that, again, is a
+whole course unto itself.
+
+OK.
+
+Now, how do you find
+these parameters?
+
+Again, it's the kinds
+of search problems
+
+that we've looked at before,
+various kinds of hill climbing.
+
+So gradient descent,
+expectation maximization,
+
+Gibbs sampling, which
+you've looked at explicitly.
+
+And again, the full
+details of how to do that
+
+are outside of our scope today.
+
+OK.
+
+So in our example of
+this coin toss game,
+
+we would use one of
+these two functions
+
+to try to decide what's
+the probability of getting
+
+heads or tails for
+any given score.
+
+That's what the kinds
+of parameters are.
+
+Now, the structure
+problem actually
+
+turns out to be
+really, really hard,
+
+because there are a very
+exponentially large number
+
+of potential structures
+to draw from.
+
+And unless you've got
+some prior knowledge,
+
+it can be impossible, depending
+on how much data you have,
+
+to actually build
+this structure.
+
+So there are many algorithms
+that have been proposed.
+
+And a lot of our
+settings, we're going
+
+to use some kind
+of prior knowledge
+
+to reduce the search space.
+
+So if we're trying to talk
+about transcriptional regulatory
+
+networks, it's very common
+to assume that there are only
+
+some kinds of nodes that can be
+causes and other kinds of nodes
+
+that can be effects, right?
+
+So in gene expression
+it would be effect,
+
+and then you would
+limit your causes
+
+to only be
+transcription factors.
+
+It would generally be signaling
+molecules or something
+
+like that, and not allow all
+20,000 genes to be causes
+
+and all 20,000
+genes to be effects.
+
+So there are lot of
+resources to learn more
+
+about Bayesian networks.
+
+As I said, you can have
+whole courses on this.
+
+I think there are a lot of
+good tutorials at this website.
+
+I've also put in the notes
+a little toy example for you
+
+to work through all the
+probabilities, which I think,
+
+in the interest of time, we
+won't go through in detail.
+
+All right.
+
+So to motivate what we're going
+to do in the next lecture,
+
+I just want to talk
+about other kinds of data
+
+that you could bring to bear
+on this problem of predicting
+
+which proteins interact.
+
+We'll see, then,
+how that gets fed
+
+into an interaction
+Bayesian network
+
+to make the predictions.
+
+So we've talked about affinity
+capture and two-hybrid,
+
+but what other
+kinds of data could
+
+we use to predict the
+probability interaction?
+
+Well, one thing you could use
+would be gene expression data.
+
+And the idea is that if
+two proteins interact,
+
+they should be present in the
+cell at the same time, right?
+
+So we talked about
+this a little bit.
+
+If they're
+anti-correlated, it seems
+
+very unlikely they interact.
+
+What about if they're
+correlated, but not perfectly
+
+correlated?
+
+So here's a plot that shows
+a histogram of proteins that
+
+are known to interact, proteins
+that are known not to interact.
+
+So empty circles are known
+interacting proteins,
+
+the dark circles are
+non-interacting proteins,
+
+and the other ones are based
+on the experimental data.
+
+And the distance here
+is the difference
+
+between expression profiles.
+
+And we'll talk in coming lecture
+about exactly how to compute
+
+distance between
+expression profiles.
+
+But the further to the right
+it is, the less similar
+
+the expression profiles
+are across large data sets.
+
+So what you see
+is the interacting
+
+proteins tend to be shifted
+more to the left, more
+
+similar expression profiles
+than the non-interacting ones.
+
+But what do you
+notice about this?
+
+There's no way to
+draw a line and say,
+
+everything to the right
+of this is in one class
+
+and everything to the
+left is another, right?
+
+So by itself, it's not
+going to get us very far.
+
+There are plenty of
+non-interacting proteins
+
+that have very highly correlated
+gene expression and plenty
+
+of interacting proteins
+that have poorly
+
+correlated gene expression.
+
+So it's a trend, not a rule.
+
+Now, what about evolution?
+
+So if I look over many, many
+organisms, I might expect what?
+
+The proteins that
+interact with each other
+
+are going to appear in
+the same species, right?
+
+So let's look at
+these two cases.
+
+We've got a bunch of--
+eight different genomes.
+
+And I've got gene 1 and gene 2,
+which I suspect might interact,
+
+and gene 3 and gene 4, which
+I suspect might interact.
+
+Now, looking at
+these two patterns
+
+of evolution, which one
+do we have more confidence
+
+in that it interacts?
+
+The red one or the green one?
+
+So what do we notice about
+the difference between them?
+
+What's true of the red one
+compared to the green one?
+
+Yeah.
+
+AUDIENCE: The red one is only
+in one branch of the tree.
+
+PROFESSOR: The red one is
+only one branch in the tree
+
+and the green one
+is scattered across.
+
+So let's take a vote.
+
+Do we believe that
+the red one is
+
+better evidence of
+interaction or the green one
+
+is better evidence
+of interaction?
+
+Red?
+
+Green?
+
+Can I have an advocate of green.
+
+Someone explain their rationale?
+
+Anyone in the quiet
+side of the room?
+
+All right, Ed.
+
+AUDIENCE: Because red is only
+on one branch of the tree,
+
+I'd expect that
+they're naturally more
+
+correlated with each other.
+
+They have less--
+they appear together
+
+in [INAUDIBLE] so I'd
+expect [INAUDIBLE].
+
+PROFESSOR: OK.
+
+So the argument is that red only
+occurs in one part of the tree.
+
+And so there could be a
+very simple explanation
+
+for all the reds being in one
+part of the tree and one not,
+
+which would be a single
+loss and gain event.
+
+Right?
+
+Somewhere early
+on, perhaps here,
+
+I gain those two proteins.
+
+And then they're inherited
+throughout the genome,
+
+like most of genes get
+inherited throughout the genome.
+
+Whereas here, we've
+got independent events
+
+of gain and loss.
+
+And at each one of these
+independent events,
+
+we're getting them
+moving jointly, either
+
+in or out of the genome.
+
+So there's more
+evidence for green
+
+to be interacting than red.
+
+Everyone buy that?
+
+Even some of the
+advocates of red?
+
+Questions?
+
+Yes.
+
+AUDIENCE: Could there be a
+way of either objectively
+
+or mathematically
+[INAUDIBLE] that way,
+
+or is it just the
+reasoning [INAUDIBLE]?
+
+PROFESSOR: One can do
+the statistics on it
+
+with known ones, right?
+
+I think that's
+probably the best way.
+
+And we'll actually see that
+in one of these papers that
+
+uses-- well,
+actually, now I don't
+
+recall whether they
+use this co-evolution.
+
+But yeah, there are
+plenty of papers
+
+that actually have done
+the statistics on that.
+
+So it is supported.
+
+And a related kind
+of question is
+
+what's called the
+Rosetta Stone approach.
+
+Unfortunately, of
+the term Rosetta
+
+gets used far too much
+in computational biology.
+
+So this has nothing to
+do with the other Rosetta
+
+that we've been talking about.
+
+And this has to do
+with how often you
+
+find the same pair of genes in
+the same genome versus split up
+
+in different genomes.
+
+OK.
+
+So what we're going to
+look at next time then
+
+is an approach that
+combines these kinds of data
+
+with the protein interaction
+physical measurements
+
+through the two-hybrid and the
+affinity capture mass spec that
+
+actually uses the Bayesian
+networks we talked
+
+about this time to predict
+whether two proteins are
+
+likely to interact based on
+all of the available data.
+
+These evolutionary arguments,
+the [? sentiality ?] arguments,
+
+and then the interaction data.
+
+Any final questions?
+
+OK, see you next time.
\ No newline at end of file
diff --git a/CxAkraYlBuE.txt b/CxAkraYlBuE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2e6157da2bcc79b50d0bdeb3293f6f64f8822143
--- /dev/null
+++ b/CxAkraYlBuE.txt
@@ -0,0 +1,10067 @@
+align:start position:0%
+ 
+we are
+
+ align:start position:0%
+we are
+ 
+
+ align:start position:0%
+we are
+we are going to be leaving the territory
+
+ align:start position:0%
+we are going to be leaving the territory
+ 
+
+ align:start position:0%
+we are going to be leaving the territory
+of uh some of some of you have had high
+
+ align:start position:0%
+of uh some of some of you have had high
+ 
+
+ align:start position:0%
+of uh some of some of you have had high
+school chemistry we're going to be
+
+ align:start position:0%
+school chemistry we're going to be
+ 
+
+ align:start position:0%
+school chemistry we're going to be
+starting to leave that territory
+
+ align:start position:0%
+starting to leave that territory
+ 
+
+ align:start position:0%
+starting to leave that territory
+and get into some of the things i talked
+
+ align:start position:0%
+and get into some of the things i talked
+ 
+
+ align:start position:0%
+and get into some of the things i talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+before that you may have never seen so
+
+ align:start position:0%
+before that you may have never seen so
+ 
+
+ align:start position:0%
+before that you may have never seen so
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+um today we'll be talking about
+
+ align:start position:0%
+um today we'll be talking about
+ 
+
+ align:start position:0%
+um today we'll be talking about
+semiconductors
+
+ align:start position:0%
+semiconductors
+ 
+
+ align:start position:0%
+semiconductors
+right and what happens when you take all
+
+ align:start position:0%
+right and what happens when you take all
+ 
+
+ align:start position:0%
+right and what happens when you take all
+these atomic orbitals
+
+ align:start position:0%
+these atomic orbitals
+ 
+
+ align:start position:0%
+these atomic orbitals
+and you put them into a solid um
+
+ align:start position:0%
+and you put them into a solid um
+ 
+
+ align:start position:0%
+and you put them into a solid um
+and and then by the end of the week
+
+ align:start position:0%
+and and then by the end of the week
+ 
+
+ align:start position:0%
+and and then by the end of the week
+we'll talk about metals
+
+ align:start position:0%
+we'll talk about metals
+ 
+
+ align:start position:0%
+we'll talk about metals
+and then next week we're going to talk
+
+ align:start position:0%
+and then next week we're going to talk
+ 
+
+ align:start position:0%
+and then next week we're going to talk
+about crystals right so that's what's
+
+ align:start position:0%
+about crystals right so that's what's
+ 
+
+ align:start position:0%
+about crystals right so that's what's
+coming
+
+ align:start position:0%
+coming
+ 
+
+ align:start position:0%
+coming
+before we get into uh uh um
+
+ align:start position:0%
+before we get into uh uh um
+ 
+
+ align:start position:0%
+before we get into uh uh um
+semiconductors and and solids
+
+ align:start position:0%
+semiconductors and and solids
+ 
+
+ align:start position:0%
+semiconductors and and solids
+there's one type of bonding we covered
+
+ align:start position:0%
+there's one type of bonding we covered
+ 
+
+ align:start position:0%
+there's one type of bonding we covered
+but i didn't put the stats up on the
+
+ align:start position:0%
+but i didn't put the stats up on the
+ 
+
+ align:start position:0%
+but i didn't put the stats up on the
+on the column so i just wanted to kind
+
+ align:start position:0%
+on the column so i just wanted to kind
+ 
+
+ align:start position:0%
+on the column so i just wanted to kind
+of make sure that we
+
+ align:start position:0%
+of make sure that we
+ 
+
+ align:start position:0%
+of make sure that we
+finish that and that was hydrogen
+
+ align:start position:0%
+finish that and that was hydrogen
+ 
+
+ align:start position:0%
+finish that and that was hydrogen
+bonding
+
+ align:start position:0%
+bonding
+ 
+
+ align:start position:0%
+bonding
+and there's a little video you know
+
+ align:start position:0%
+and there's a little video you know
+ 
+
+ align:start position:0%
+and there's a little video you know
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+we're not going to go into all the
+
+ align:start position:0%
+we're not going to go into all the
+ 
+
+ align:start position:0%
+we're not going to go into all the
+amazing properties of water but if
+
+ align:start position:0%
+amazing properties of water but if
+ 
+
+ align:start position:0%
+amazing properties of water but if
+you're interested
+
+ align:start position:0%
+you're interested
+ 
+
+ align:start position:0%
+you're interested
+this is a really cool website that talks
+
+ align:start position:0%
+this is a really cool website that talks
+ 
+
+ align:start position:0%
+this is a really cool website that talks
+about all the anomalies
+
+ align:start position:0%
+about all the anomalies
+ 
+
+ align:start position:0%
+about all the anomalies
+of water and and many of water's
+
+ align:start position:0%
+of water and and many of water's
+ 
+
+ align:start position:0%
+of water and and many of water's
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+are anomalous and much of the reason for
+
+ align:start position:0%
+are anomalous and much of the reason for
+ 
+
+ align:start position:0%
+are anomalous and much of the reason for
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is the last type of bonding we talked
+
+ align:start position:0%
+is the last type of bonding we talked
+ 
+
+ align:start position:0%
+is the last type of bonding we talked
+about intermolecular bonds we talked
+
+ align:start position:0%
+about intermolecular bonds we talked
+ 
+
+ align:start position:0%
+about intermolecular bonds we talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+last friday which is the hydrogen bond
+
+ align:start position:0%
+last friday which is the hydrogen bond
+ 
+
+ align:start position:0%
+last friday which is the hydrogen bond
+so remember
+
+ align:start position:0%
+so remember
+ 
+
+ align:start position:0%
+so remember
+our table i just wanted to fill out the
+
+ align:start position:0%
+our table i just wanted to fill out the
+ 
+
+ align:start position:0%
+our table i just wanted to fill out the
+table because i didn't fill out the
+
+ align:start position:0%
+table because i didn't fill out the
+ 
+
+ align:start position:0%
+table because i didn't fill out the
+table right
+
+ align:start position:0%
+table right
+ 
+
+ align:start position:0%
+table right
+that's the type of bond and the model
+
+ align:start position:0%
+that's the type of bond and the model
+ 
+
+ align:start position:0%
+that's the type of bond and the model
+was some kind of
+
+ align:start position:0%
+was some kind of
+ 
+
+ align:start position:0%
+was some kind of
+you know electronegative um
+
+ align:start position:0%
+you know electronegative um
+ 
+
+ align:start position:0%
+you know electronegative um
+it was some kind of highly
+
+ align:start position:0%
+it was some kind of highly
+ 
+
+ align:start position:0%
+it was some kind of highly
+electronegative atom like a
+
+ align:start position:0%
+electronegative atom like a
+ 
+
+ align:start position:0%
+electronegative atom like a
+was oxygen or nitrogen or fluorine
+
+ align:start position:0%
+was oxygen or nitrogen or fluorine
+ 
+
+ align:start position:0%
+was oxygen or nitrogen or fluorine
+so that you drew a lot of charge off of
+
+ align:start position:0%
+so that you drew a lot of charge off of
+ 
+
+ align:start position:0%
+so that you drew a lot of charge off of
+that hydrogen
+
+ align:start position:0%
+that hydrogen
+ 
+
+ align:start position:0%
+that hydrogen
+and you left it uh with a really strong
+
+ align:start position:0%
+and you left it uh with a really strong
+ 
+
+ align:start position:0%
+and you left it uh with a really strong
+delta plus
+
+ align:start position:0%
+delta plus
+ 
+
+ align:start position:0%
+delta plus
+so that it could then bond to some
+
+ align:start position:0%
+so that it could then bond to some
+ 
+
+ align:start position:0%
+so that it could then bond to some
+other atom it might be the same atom by
+
+ align:start position:0%
+other atom it might be the same atom by
+ 
+
+ align:start position:0%
+other atom it might be the same atom by
+the way it was in the cases that we
+
+ align:start position:0%
+the way it was in the cases that we
+ 
+
+ align:start position:0%
+the way it was in the cases that we
+you know that we talked about i'll just
+
+ align:start position:0%
+you know that we talked about i'll just
+ 
+
+ align:start position:0%
+you know that we talked about i'll just
+use the same atom because we used
+
+ align:start position:0%
+use the same atom because we used
+ 
+
+ align:start position:0%
+use the same atom because we used
+hf and h2o so then it would be the o or
+
+ align:start position:0%
+hf and h2o so then it would be the o or
+ 
+
+ align:start position:0%
+hf and h2o so then it would be the o or
+the f
+
+ align:start position:0%
+the f
+ 
+
+ align:start position:0%
+the f
+but it's to a lone pair right on that
+
+ align:start position:0%
+but it's to a lone pair right on that
+ 
+
+ align:start position:0%
+but it's to a lone pair right on that
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+that that was the hydrogen bond and the
+
+ align:start position:0%
+that that was the hydrogen bond and the
+ 
+
+ align:start position:0%
+that that was the hydrogen bond and the
+range
+
+ align:start position:0%
+range
+ 
+
+ align:start position:0%
+range
+of attraction is in
+
+ align:start position:0%
+of attraction is in
+ 
+
+ align:start position:0%
+of attraction is in
+kilojoules per mole of bonds
+
+ align:start position:0%
+kilojoules per mole of bonds
+ 
+
+ align:start position:0%
+kilojoules per mole of bonds
+is something like let's see 10
+
+ align:start position:0%
+is something like let's see 10
+ 
+
+ align:start position:0%
+is something like let's see 10
+to 40. so it's pretty strong you know
+
+ align:start position:0%
+to 40. so it's pretty strong you know
+ 
+
+ align:start position:0%
+to 40. so it's pretty strong you know
+compared to some of the weaker things
+
+ align:start position:0%
+compared to some of the weaker things
+ 
+
+ align:start position:0%
+compared to some of the weaker things
+like london
+
+ align:start position:0%
+like london
+ 
+
+ align:start position:0%
+like london
+the hydrogen bond can be pretty strong
+
+ align:start position:0%
+the hydrogen bond can be pretty strong
+ 
+
+ align:start position:0%
+the hydrogen bond can be pretty strong
+and one of these the examples that
+
+ align:start position:0%
+and one of these the examples that
+ 
+
+ align:start position:0%
+and one of these the examples that
+is the classic example would be
+
+ align:start position:0%
+is the classic example would be
+ 
+
+ align:start position:0%
+is the classic example would be
+hydrogen hydrogen
+
+ align:start position:0%
+hydrogen hydrogen
+ 
+
+ align:start position:0%
+hydrogen hydrogen
+there's the hydrogen bond right there
+
+ align:start position:0%
+there's the hydrogen bond right there
+ 
+
+ align:start position:0%
+there's the hydrogen bond right there
+you see hydrogen bond
+
+ align:start position:0%
+you see hydrogen bond
+ 
+
+ align:start position:0%
+you see hydrogen bond
+between another oxygen with itch
+
+ align:start position:0%
+between another oxygen with itch
+ 
+
+ align:start position:0%
+between another oxygen with itch
+hydrogens
+
+ align:start position:0%
+hydrogens
+ 
+
+ align:start position:0%
+hydrogens
+as well now we talked about how water is
+
+ align:start position:0%
+as well now we talked about how water is
+ 
+
+ align:start position:0%
+as well now we talked about how water is
+so special
+
+ align:start position:0%
+so special
+ 
+
+ align:start position:0%
+so special
+because in the case of water not only
+
+ align:start position:0%
+because in the case of water not only
+ 
+
+ align:start position:0%
+because in the case of water not only
+do i have exactly two hydrogens in each
+
+ align:start position:0%
+do i have exactly two hydrogens in each
+ 
+
+ align:start position:0%
+do i have exactly two hydrogens in each
+molecule that i've
+
+ align:start position:0%
+molecule that i've
+ 
+
+ align:start position:0%
+molecule that i've
+caused this strong delta plus but i've
+
+ align:start position:0%
+caused this strong delta plus but i've
+ 
+
+ align:start position:0%
+caused this strong delta plus but i've
+also got two lone pairs
+
+ align:start position:0%
+also got two lone pairs
+ 
+
+ align:start position:0%
+also got two lone pairs
+so the numbers work right in hf that's
+
+ align:start position:0%
+so the numbers work right in hf that's
+ 
+
+ align:start position:0%
+so the numbers work right in hf that's
+also a hydrogen bonded
+
+ align:start position:0%
+also a hydrogen bonded
+ 
+
+ align:start position:0%
+also a hydrogen bonded
+it can hydrogen bond to itself right but
+
+ align:start position:0%
+it can hydrogen bond to itself right but
+ 
+
+ align:start position:0%
+it can hydrogen bond to itself right but
+i've got three lone pairs on each f and
+
+ align:start position:0%
+i've got three lone pairs on each f and
+ 
+
+ align:start position:0%
+i've got three lone pairs on each f and
+only one hydrogen that i've taken that
+
+ align:start position:0%
+only one hydrogen that i've taken that
+ 
+
+ align:start position:0%
+only one hydrogen that i've taken that
+charge away from so you still get the
+
+ align:start position:0%
+charge away from so you still get the
+ 
+
+ align:start position:0%
+charge away from so you still get the
+hydrogen bonding but this is the
+
+ align:start position:0%
+hydrogen bonding but this is the
+ 
+
+ align:start position:0%
+hydrogen bonding but this is the
+beautiful balance
+
+ align:start position:0%
+beautiful balance
+ 
+
+ align:start position:0%
+beautiful balance
+oh and there's a video showing water
+
+ align:start position:0%
+oh and there's a video showing water
+ 
+
+ align:start position:0%
+oh and there's a video showing water
+bonded to each other there it is oh
+
+ align:start position:0%
+bonded to each other there it is oh
+ 
+
+ align:start position:0%
+bonded to each other there it is oh
+because there's nothing like just
+
+ align:start position:0%
+because there's nothing like just
+ 
+
+ align:start position:0%
+because there's nothing like just
+imagining what a hydrogen bond looks
+
+ align:start position:0%
+imagining what a hydrogen bond looks
+ 
+
+ align:start position:0%
+imagining what a hydrogen bond looks
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+and so of course a hydrogen bond well
+
+ align:start position:0%
+and so of course a hydrogen bond well
+ 
+
+ align:start position:0%
+and so of course a hydrogen bond well
+okay charges oh it's french pole
+
+ align:start position:0%
+okay charges oh it's french pole
+ 
+
+ align:start position:0%
+okay charges oh it's french pole
+right okay oh that's what it looks like
+
+ align:start position:0%
+right okay oh that's what it looks like
+ 
+
+ align:start position:0%
+right okay oh that's what it looks like
+it really if you could get down there it
+
+ align:start position:0%
+it really if you could get down there it
+ 
+
+ align:start position:0%
+it really if you could get down there it
+would be a ray of a laser beam
+
+ align:start position:0%
+would be a ray of a laser beam
+ 
+
+ align:start position:0%
+would be a ray of a laser beam
+light it says
+
+ align:start position:0%
+light it says
+ 
+
+ align:start position:0%
+light it says
+hydrogen and that's
+
+ align:start position:0%
+hydrogen and that's
+ 
+
+ align:start position:0%
+hydrogen and that's
+and and there it is and this is what's
+
+ align:start position:0%
+and and there it is and this is what's
+ 
+
+ align:start position:0%
+and and there it is and this is what's
+going on in the liquid right and they're
+
+ align:start position:0%
+going on in the liquid right and they're
+ 
+
+ align:start position:0%
+going on in the liquid right and they're
+kind of seeing each other
+
+ align:start position:0%
+kind of seeing each other
+ 
+
+ align:start position:0%
+kind of seeing each other
+and they're talking in there but they
+
+ align:start position:0%
+and they're talking in there but they
+ 
+
+ align:start position:0%
+and they're talking in there but they
+feel this strong
+
+ align:start position:0%
+feel this strong
+ 
+
+ align:start position:0%
+feel this strong
+strong hydrogen bond okay and that's
+
+ align:start position:0%
+strong hydrogen bond okay and that's
+ 
+
+ align:start position:0%
+strong hydrogen bond okay and that's
+happening all over the place and in a
+
+ align:start position:0%
+happening all over the place and in a
+ 
+
+ align:start position:0%
+happening all over the place and in a
+liquid
+
+ align:start position:0%
+liquid
+ 
+
+ align:start position:0%
+liquid
+they are making and breaking all the
+
+ align:start position:0%
+they are making and breaking all the
+ 
+
+ align:start position:0%
+they are making and breaking all the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah because well it depends right
+
+ align:start position:0%
+yeah yeah because well it depends right
+ 
+
+ align:start position:0%
+yeah yeah because well it depends right
+it depends it's a great question
+
+ align:start position:0%
+it depends it's a great question
+ 
+
+ align:start position:0%
+it depends it's a great question
+why do they separate right well they
+
+ align:start position:0%
+why do they separate right well they
+ 
+
+ align:start position:0%
+why do they separate right well they
+don't in
+
+ align:start position:0%
+don't in
+ 
+
+ align:start position:0%
+don't in
+ice right so in ice i mean you know they
+
+ align:start position:0%
+ice right so in ice i mean you know they
+ 
+
+ align:start position:0%
+ice right so in ice i mean you know they
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+but a nice it's a solid so they're sort
+
+ align:start position:0%
+but a nice it's a solid so they're sort
+ 
+
+ align:start position:0%
+but a nice it's a solid so they're sort
+of locked in
+
+ align:start position:0%
+of locked in
+ 
+
+ align:start position:0%
+of locked in
+right and and so in there you're gonna
+
+ align:start position:0%
+right and and so in there you're gonna
+ 
+
+ align:start position:0%
+right and and so in there you're gonna
+have pretty much each water molecule has
+
+ align:start position:0%
+have pretty much each water molecule has
+ 
+
+ align:start position:0%
+have pretty much each water molecule has
+four look at this it's you know from
+
+ align:start position:0%
+four look at this it's you know from
+ 
+
+ align:start position:0%
+four look at this it's you know from
+vesper right
+
+ align:start position:0%
+vesper right
+ 
+
+ align:start position:0%
+vesper right
+four possible four possible bonds you
+
+ align:start position:0%
+four possible four possible bonds you
+ 
+
+ align:start position:0%
+four possible four possible bonds you
+can make
+
+ align:start position:0%
+can make
+ 
+
+ align:start position:0%
+can make
+tetrahedral would sort of but there's
+
+ align:start position:0%
+tetrahedral would sort of but there's
+ 
+
+ align:start position:0%
+tetrahedral would sort of but there's
+actually lots of ways you can orient
+
+ align:start position:0%
+actually lots of ways you can orient
+ 
+
+ align:start position:0%
+actually lots of ways you can orient
+them in a solid so there's many forms of
+
+ align:start position:0%
+them in a solid so there's many forms of
+ 
+
+ align:start position:0%
+them in a solid so there's many forms of
+ice 12
+
+ align:start position:0%
+ice 12
+ 
+
+ align:start position:0%
+ice 12
+different ways to make a solid of ice
+
+ align:start position:0%
+different ways to make a solid of ice
+ 
+
+ align:start position:0%
+different ways to make a solid of ice
+right but but see
+
+ align:start position:0%
+right but but see
+ 
+
+ align:start position:0%
+right but but see
+here goes in tight
+
+ align:start position:0%
+here goes in tight
+ 
+
+ align:start position:0%
+here goes in tight
+so so here in the liquid at room
+
+ align:start position:0%
+so so here in the liquid at room
+ 
+
+ align:start position:0%
+so so here in the liquid at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+with the laser beams they're coming in
+
+ align:start position:0%
+with the laser beams they're coming in
+ 
+
+ align:start position:0%
+with the laser beams they're coming in
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and they're bonding but they have enough
+
+ align:start position:0%
+and they're bonding but they have enough
+ 
+
+ align:start position:0%
+and they're bonding but they have enough
+energy to break the bond too
+
+ align:start position:0%
+energy to break the bond too
+ 
+
+ align:start position:0%
+energy to break the bond too
+so they stick and they unstick because
+
+ align:start position:0%
+so they stick and they unstick because
+ 
+
+ align:start position:0%
+so they stick and they unstick because
+there's enough thermal energy in the
+
+ align:start position:0%
+there's enough thermal energy in the
+ 
+
+ align:start position:0%
+there's enough thermal energy in the
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+to continuously break them and remake
+
+ align:start position:0%
+to continuously break them and remake
+ 
+
+ align:start position:0%
+to continuously break them and remake
+them that's what that's when it's a
+
+ align:start position:0%
+them that's what that's when it's a
+ 
+
+ align:start position:0%
+them that's what that's when it's a
+liquid
+
+ align:start position:0%
+liquid
+ 
+
+ align:start position:0%
+liquid
+when is it a liquid versus a gas right
+
+ align:start position:0%
+when is it a liquid versus a gas right
+ 
+
+ align:start position:0%
+when is it a liquid versus a gas right
+the boiling point remember
+
+ align:start position:0%
+the boiling point remember
+ 
+
+ align:start position:0%
+the boiling point remember
+that is a proxy we talked about last
+
+ align:start position:0%
+that is a proxy we talked about last
+ 
+
+ align:start position:0%
+that is a proxy we talked about last
+friday that is a proxy for
+
+ align:start position:0%
+friday that is a proxy for
+ 
+
+ align:start position:0%
+friday that is a proxy for
+the bonding strength between these
+
+ align:start position:0%
+the bonding strength between these
+ 
+
+ align:start position:0%
+the bonding strength between these
+molecules right
+
+ align:start position:0%
+molecules right
+ 
+
+ align:start position:0%
+molecules right
+if it's a stronger bonding then the
+
+ align:start position:0%
+if it's a stronger bonding then the
+ 
+
+ align:start position:0%
+if it's a stronger bonding then the
+boiling point will be higher and higher
+
+ align:start position:0%
+boiling point will be higher and higher
+ 
+
+ align:start position:0%
+boiling point will be higher and higher
+oh water should have boiled at a much
+
+ align:start position:0%
+oh water should have boiled at a much
+ 
+
+ align:start position:0%
+oh water should have boiled at a much
+lower temperature
+
+ align:start position:0%
+lower temperature
+ 
+
+ align:start position:0%
+lower temperature
+if it didn't have this very special
+
+ align:start position:0%
+if it didn't have this very special
+ 
+
+ align:start position:0%
+if it didn't have this very special
+hydrogen bond which is not
+
+ align:start position:0%
+hydrogen bond which is not
+ 
+
+ align:start position:0%
+hydrogen bond which is not
+a dipole dipole people try to people try
+
+ align:start position:0%
+a dipole dipole people try to people try
+ 
+
+ align:start position:0%
+a dipole dipole people try to people try
+to write the the physics of the hydrogen
+
+ align:start position:0%
+to write the the physics of the hydrogen
+ 
+
+ align:start position:0%
+to write the the physics of the hydrogen
+bond as one over r cubed that is not
+
+ align:start position:0%
+bond as one over r cubed that is not
+ 
+
+ align:start position:0%
+bond as one over r cubed that is not
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+it is not just as simple as it's another
+
+ align:start position:0%
+it is not just as simple as it's another
+ 
+
+ align:start position:0%
+it is not just as simple as it's another
+dipole-dipole-type interaction
+
+ align:start position:0%
+dipole-dipole-type interaction
+ 
+
+ align:start position:0%
+dipole-dipole-type interaction
+it's complicated complicated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember we had covalent bonds were
+
+ align:start position:0%
+remember we had covalent bonds were
+ 
+
+ align:start position:0%
+remember we had covalent bonds were
+complicated too
+
+ align:start position:0%
+complicated too
+ 
+
+ align:start position:0%
+complicated too
+so we're not going to put a simple one
+
+ align:start position:0%
+so we're not going to put a simple one
+ 
+
+ align:start position:0%
+so we're not going to put a simple one
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+r something dependents for the hydrogen
+
+ align:start position:0%
+r something dependents for the hydrogen
+ 
+
+ align:start position:0%
+r something dependents for the hydrogen
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+okay good question okay now
+
+ align:start position:0%
+okay good question okay now
+ 
+
+ align:start position:0%
+okay good question okay now
+uh all right so that's an intermolecular
+
+ align:start position:0%
+uh all right so that's an intermolecular
+ 
+
+ align:start position:0%
+uh all right so that's an intermolecular
+now we're going to move on to
+
+ align:start position:0%
+now we're going to move on to
+ 
+
+ align:start position:0%
+now we're going to move on to
+solids that was our last intermolecular
+
+ align:start position:0%
+solids that was our last intermolecular
+ 
+
+ align:start position:0%
+solids that was our last intermolecular
+interaction oh but there's before i do
+
+ align:start position:0%
+interaction oh but there's before i do
+ 
+
+ align:start position:0%
+interaction oh but there's before i do
+there's actually
+
+ align:start position:0%
+there's actually
+ 
+
+ align:start position:0%
+there's actually
+an example question i put there that you
+
+ align:start position:0%
+an example question i put there that you
+ 
+
+ align:start position:0%
+an example question i put there that you
+could now answer
+
+ align:start position:0%
+could now answer
+ 
+
+ align:start position:0%
+could now answer
+which this is actually i just want to
+
+ align:start position:0%
+which this is actually i just want to
+ 
+
+ align:start position:0%
+which this is actually i just want to
+show you the type of okay so we cover
+
+ align:start position:0%
+show you the type of okay so we cover
+ 
+
+ align:start position:0%
+show you the type of okay so we cover
+all these intermolecular bonds
+
+ align:start position:0%
+all these intermolecular bonds
+ 
+
+ align:start position:0%
+all these intermolecular bonds
+here's a question from a quiz last year
+
+ align:start position:0%
+here's a question from a quiz last year
+ 
+
+ align:start position:0%
+here's a question from a quiz last year
+lists the intermolecular forces in each
+
+ align:start position:0%
+lists the intermolecular forces in each
+ 
+
+ align:start position:0%
+lists the intermolecular forces in each
+substance
+
+ align:start position:0%
+substance
+ 
+
+ align:start position:0%
+substance
+right methane and then you got that
+
+ align:start position:0%
+right methane and then you got that
+ 
+
+ align:start position:0%
+right methane and then you got that
+ch3oh right and then you got the ch3cl
+
+ align:start position:0%
+ch3oh right and then you got the ch3cl
+ 
+
+ align:start position:0%
+ch3oh right and then you got the ch3cl
+right and and so you can do this now
+
+ align:start position:0%
+right and and so you can do this now
+ 
+
+ align:start position:0%
+right and and so you can do this now
+because for methane
+
+ align:start position:0%
+because for methane
+ 
+
+ align:start position:0%
+because for methane
+all you got is london it's not a polar
+
+ align:start position:0%
+all you got is london it's not a polar
+ 
+
+ align:start position:0%
+all you got is london it's not a polar
+molecule all you got is london
+
+ align:start position:0%
+molecule all you got is london
+ 
+
+ align:start position:0%
+molecule all you got is london
+there's no hydrogen bonding right
+
+ align:start position:0%
+there's no hydrogen bonding right
+ 
+
+ align:start position:0%
+there's no hydrogen bonding right
+but for ch3oh
+
+ align:start position:0%
+but for ch3oh
+ 
+
+ align:start position:0%
+but for ch3oh
+do you have hydrogen bonding yeah
+
+ align:start position:0%
+do you have hydrogen bonding yeah
+ 
+
+ align:start position:0%
+do you have hydrogen bonding yeah
+you do because if you draw because you
+
+ align:start position:0%
+you do because if you draw because you
+ 
+
+ align:start position:0%
+you do because if you draw because you
+got an h that's had the
+
+ align:start position:0%
+got an h that's had the
+ 
+
+ align:start position:0%
+got an h that's had the
+the charge taken from it by oxygen a
+
+ align:start position:0%
+the charge taken from it by oxygen a
+ 
+
+ align:start position:0%
+the charge taken from it by oxygen a
+highly electronegative atom
+
+ align:start position:0%
+highly electronegative atom
+ 
+
+ align:start position:0%
+highly electronegative atom
+and then and then you've got lone pairs
+
+ align:start position:0%
+and then and then you've got lone pairs
+ 
+
+ align:start position:0%
+and then and then you've got lone pairs
+on that same oxygen so you can hydrogen
+
+ align:start position:0%
+on that same oxygen so you can hydrogen
+ 
+
+ align:start position:0%
+on that same oxygen so you can hydrogen
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+and you've also got london
+
+ align:start position:0%
+and you've also got london
+ 
+
+ align:start position:0%
+and you've also got london
+right now is that it is there anything
+
+ align:start position:0%
+right now is that it is there anything
+ 
+
+ align:start position:0%
+right now is that it is there anything
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+ch3oh what else is is there any other
+
+ align:start position:0%
+ch3oh what else is is there any other
+ 
+
+ align:start position:0%
+ch3oh what else is is there any other
+type of bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the last question you need to ask
+
+ align:start position:0%
+well the last question you need to ask
+ 
+
+ align:start position:0%
+well the last question you need to ask
+is is there a dipole moment
+
+ align:start position:0%
+is is there a dipole moment
+ 
+
+ align:start position:0%
+is is there a dipole moment
+in the molecule because if that molecule
+
+ align:start position:0%
+in the molecule because if that molecule
+ 
+
+ align:start position:0%
+in the molecule because if that molecule
+had a permanent dipole
+
+ align:start position:0%
+had a permanent dipole
+ 
+
+ align:start position:0%
+had a permanent dipole
+then there's another type of
+
+ align:start position:0%
+then there's another type of
+ 
+
+ align:start position:0%
+then there's another type of
+intermolecular interaction like we
+
+ align:start position:0%
+intermolecular interaction like we
+ 
+
+ align:start position:0%
+intermolecular interaction like we
+talked about
+
+ align:start position:0%
+talked about
+ 
+
+ align:start position:0%
+talked about
+dipole-dipole so you'd have three right
+
+ align:start position:0%
+dipole-dipole so you'd have three right
+ 
+
+ align:start position:0%
+dipole-dipole so you'd have three right
+and for ch3cl well there
+
+ align:start position:0%
+and for ch3cl well there
+ 
+
+ align:start position:0%
+and for ch3cl well there
+you you also you know that for ch3cl
+
+ align:start position:0%
+you you also you know that for ch3cl
+ 
+
+ align:start position:0%
+you you also you know that for ch3cl
+you're going to have a dipole moment
+
+ align:start position:0%
+you're going to have a dipole moment
+ 
+
+ align:start position:0%
+you're going to have a dipole moment
+remember we compare dipole moments and
+
+ align:start position:0%
+remember we compare dipole moments and
+ 
+
+ align:start position:0%
+remember we compare dipole moments and
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+and if you have a dipole moment in a
+
+ align:start position:0%
+and if you have a dipole moment in a
+ 
+
+ align:start position:0%
+and if you have a dipole moment in a
+molecule then that dipole moment can
+
+ align:start position:0%
+molecule then that dipole moment can
+ 
+
+ align:start position:0%
+molecule then that dipole moment can
+talk to another
+
+ align:start position:0%
+talk to another
+ 
+
+ align:start position:0%
+talk to another
+dipole moment and be interacting with it
+
+ align:start position:0%
+dipole moment and be interacting with it
+ 
+
+ align:start position:0%
+dipole moment and be interacting with it
+so that's a kind of bond
+
+ align:start position:0%
+so that's a kind of bond
+ 
+
+ align:start position:0%
+so that's a kind of bond
+and is that it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+london london is always there
+
+ align:start position:0%
+london london is always there
+ 
+
+ align:start position:0%
+london london is always there
+it's always there you've also got london
+
+ align:start position:0%
+it's always there you've also got london
+ 
+
+ align:start position:0%
+it's always there you've also got london
+don't forget
+
+ align:start position:0%
+don't forget
+ 
+
+ align:start position:0%
+don't forget
+right so you'd have dipole dipole plus
+
+ align:start position:0%
+right so you'd have dipole dipole plus
+ 
+
+ align:start position:0%
+right so you'd have dipole dipole plus
+london here
+
+ align:start position:0%
+london here
+ 
+
+ align:start position:0%
+london here
+right dipole dipole london and hydrogen
+
+ align:start position:0%
+right dipole dipole london and hydrogen
+ 
+
+ align:start position:0%
+right dipole dipole london and hydrogen
+just london right so this is what this
+
+ align:start position:0%
+just london right so this is what this
+ 
+
+ align:start position:0%
+just london right so this is what this
+is the kind of way i want
+
+ align:start position:0%
+is the kind of way i want
+ 
+
+ align:start position:0%
+is the kind of way i want
+and you might be able to think about
+
+ align:start position:0%
+and you might be able to think about
+ 
+
+ align:start position:0%
+and you might be able to think about
+well what would a trend like you know
+
+ align:start position:0%
+well what would a trend like you know
+ 
+
+ align:start position:0%
+well what would a trend like you know
+if you think about like okay well if a
+
+ align:start position:0%
+if you think about like okay well if a
+ 
+
+ align:start position:0%
+if you think about like okay well if a
+molecule just has london
+
+ align:start position:0%
+molecule just has london
+ 
+
+ align:start position:0%
+molecule just has london
+then what does london depend on
+
+ align:start position:0%
+then what does london depend on
+ 
+
+ align:start position:0%
+then what does london depend on
+right well it depends on the
+
+ align:start position:0%
+right well it depends on the
+ 
+
+ align:start position:0%
+right well it depends on the
+polarizability
+
+ align:start position:0%
+polarizability
+ 
+
+ align:start position:0%
+polarizability
+of the charge so that could be something
+
+ align:start position:0%
+of the charge so that could be something
+ 
+
+ align:start position:0%
+of the charge so that could be something
+with acid it depends on the size because
+
+ align:start position:0%
+with acid it depends on the size because
+ 
+
+ align:start position:0%
+with acid it depends on the size because
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+tells you how much i say well what about
+
+ align:start position:0%
+tells you how much i say well what about
+ 
+
+ align:start position:0%
+tells you how much i say well what about
+sih4 compared to ch4
+
+ align:start position:0%
+sih4 compared to ch4
+ 
+
+ align:start position:0%
+sih4 compared to ch4
+sih which is going to be you know more
+
+ align:start position:0%
+sih which is going to be you know more
+ 
+
+ align:start position:0%
+sih which is going to be you know more
+strongly bonded
+
+ align:start position:0%
+strongly bonded
+ 
+
+ align:start position:0%
+strongly bonded
+right you can answer that because you
+
+ align:start position:0%
+right you can answer that because you
+ 
+
+ align:start position:0%
+right you can answer that because you
+know the only force there is london
+
+ align:start position:0%
+know the only force there is london
+ 
+
+ align:start position:0%
+know the only force there is london
+and you know for london it's how much
+
+ align:start position:0%
+and you know for london it's how much
+ 
+
+ align:start position:0%
+and you know for london it's how much
+contact area you have is going to be one
+
+ align:start position:0%
+contact area you have is going to be one
+ 
+
+ align:start position:0%
+contact area you have is going to be one
+of the factors the more contact
+
+ align:start position:0%
+of the factors the more contact
+ 
+
+ align:start position:0%
+of the factors the more contact
+the more chances these things can get
+
+ align:start position:0%
+the more chances these things can get
+ 
+
+ align:start position:0%
+the more chances these things can get
+close enough and polarized
+
+ align:start position:0%
+close enough and polarized
+ 
+
+ align:start position:0%
+close enough and polarized
+right and then polarizability would be
+
+ align:start position:0%
+right and then polarizability would be
+ 
+
+ align:start position:0%
+right and then polarizability would be
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+good okay all right now we're going on
+
+ align:start position:0%
+good okay all right now we're going on
+ 
+
+ align:start position:0%
+good okay all right now we're going on
+to solids
+
+ align:start position:0%
+to solids
+ 
+
+ align:start position:0%
+to solids
+now the big picture is
+
+ align:start position:0%
+now the big picture is
+ 
+
+ align:start position:0%
+now the big picture is
+pretty awesome if you look at the big
+
+ align:start position:0%
+pretty awesome if you look at the big
+ 
+
+ align:start position:0%
+pretty awesome if you look at the big
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+we have done the electronic structure of
+
+ align:start position:0%
+we have done the electronic structure of
+ 
+
+ align:start position:0%
+we have done the electronic structure of
+atoms and
+
+ align:start position:0%
+atoms and
+ 
+
+ align:start position:0%
+atoms and
+molecules right so we've gone through
+
+ align:start position:0%
+molecules right so we've gone through
+ 
+
+ align:start position:0%
+molecules right so we've gone through
+and we worked our way through the bore
+
+ align:start position:0%
+and we worked our way through the bore
+ 
+
+ align:start position:0%
+and we worked our way through the bore
+atom the atomic model
+
+ align:start position:0%
+atom the atomic model
+ 
+
+ align:start position:0%
+atom the atomic model
+quantum numbers aufbau what happens when
+
+ align:start position:0%
+quantum numbers aufbau what happens when
+ 
+
+ align:start position:0%
+quantum numbers aufbau what happens when
+you go from one electron to many
+
+ align:start position:0%
+you go from one electron to many
+ 
+
+ align:start position:0%
+you go from one electron to many
+and octet stability which is lewis and
+
+ align:start position:0%
+and octet stability which is lewis and
+ 
+
+ align:start position:0%
+and octet stability which is lewis and
+vesper
+
+ align:start position:0%
+vesper
+ 
+
+ align:start position:0%
+vesper
+we have also now talked about how
+
+ align:start position:0%
+we have also now talked about how
+ 
+
+ align:start position:0%
+we have also now talked about how
+molecules come together in different
+
+ align:start position:0%
+molecules come together in different
+ 
+
+ align:start position:0%
+molecules come together in different
+ways how the atoms come together in the
+
+ align:start position:0%
+ways how the atoms come together in the
+ 
+
+ align:start position:0%
+ways how the atoms come together in the
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and how the molecules come together in
+
+ align:start position:0%
+and how the molecules come together in
+ 
+
+ align:start position:0%
+and how the molecules come together in
+different ways right dipole dipole
+
+ align:start position:0%
+different ways right dipole dipole
+ 
+
+ align:start position:0%
+different ways right dipole dipole
+london dispersion hydrogen bonding right
+
+ align:start position:0%
+london dispersion hydrogen bonding right
+ 
+
+ align:start position:0%
+london dispersion hydrogen bonding right
+and then there's these forms of
+
+ align:start position:0%
+and then there's these forms of
+ 
+
+ align:start position:0%
+and then there's these forms of
+aggregation gas liquid and solid and of
+
+ align:start position:0%
+aggregation gas liquid and solid and of
+ 
+
+ align:start position:0%
+aggregation gas liquid and solid and of
+course we're excited about this
+
+ align:start position:0%
+course we're excited about this
+ 
+
+ align:start position:0%
+course we're excited about this
+so i put my little emoji there
+
+ align:start position:0%
+so i put my little emoji there
+ 
+
+ align:start position:0%
+so i put my little emoji there
+right because that's what we're gonna do
+
+ align:start position:0%
+right because that's what we're gonna do
+ 
+
+ align:start position:0%
+right because that's what we're gonna do
+now we're actually gonna
+
+ align:start position:0%
+now we're actually gonna
+ 
+
+ align:start position:0%
+now we're actually gonna
+take we talked a little bit about solids
+
+ align:start position:0%
+take we talked a little bit about solids
+ 
+
+ align:start position:0%
+take we talked a little bit about solids
+already but now we're to take
+
+ align:start position:0%
+already but now we're to take
+ 
+
+ align:start position:0%
+already but now we're to take
+the electronic structure that we've
+
+ align:start position:0%
+the electronic structure that we've
+ 
+
+ align:start position:0%
+the electronic structure that we've
+built up
+
+ align:start position:0%
+built up
+ 
+
+ align:start position:0%
+built up
+right these orbitals and we're going to
+
+ align:start position:0%
+right these orbitals and we're going to
+ 
+
+ align:start position:0%
+right these orbitals and we're going to
+make solids out of them
+
+ align:start position:0%
+make solids out of them
+ 
+
+ align:start position:0%
+make solids out of them
+okay so this is the week where
+
+ align:start position:0%
+okay so this is the week where
+ 
+
+ align:start position:0%
+okay so this is the week where
+these are the next two weeks right where
+
+ align:start position:0%
+these are the next two weeks right where
+ 
+
+ align:start position:0%
+these are the next two weeks right where
+we're going to talk a lot about
+
+ align:start position:0%
+we're going to talk a lot about
+ 
+
+ align:start position:0%
+we're going to talk a lot about
+solids and this week
+
+ align:start position:0%
+solids and this week
+ 
+
+ align:start position:0%
+solids and this week
+this week okay this week
+
+ align:start position:0%
+this week okay this week
+ 
+
+ align:start position:0%
+this week okay this week
+we're going to do the electronic
+
+ align:start position:0%
+we're going to do the electronic
+ 
+
+ align:start position:0%
+we're going to do the electronic
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+and next week
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to do adams so that's our
+
+ align:start position:0%
+we're going to do adams so that's our
+ 
+
+ align:start position:0%
+we're going to do adams so that's our
+plan
+
+ align:start position:0%
+plan
+ 
+
+ align:start position:0%
+plan
+right and next week friday we're going
+
+ align:start position:0%
+right and next week friday we're going
+ 
+
+ align:start position:0%
+right and next week friday we're going
+to break a bunch of stuff with parents
+
+ align:start position:0%
+to break a bunch of stuff with parents
+ 
+
+ align:start position:0%
+to break a bunch of stuff with parents
+so so this week we're going to what do
+
+ align:start position:0%
+so so this week we're going to what do
+ 
+
+ align:start position:0%
+so so this week we're going to what do
+electrons do in solids
+
+ align:start position:0%
+electrons do in solids
+ 
+
+ align:start position:0%
+electrons do in solids
+next week how do atoms arrange in solids
+
+ align:start position:0%
+next week how do atoms arrange in solids
+ 
+
+ align:start position:0%
+next week how do atoms arrange in solids
+and together that gives us so much
+
+ align:start position:0%
+and together that gives us so much
+ 
+
+ align:start position:0%
+and together that gives us so much
+understanding
+
+ align:start position:0%
+understanding
+ 
+
+ align:start position:0%
+understanding
+of how chemistry affects properties in
+
+ align:start position:0%
+of how chemistry affects properties in
+ 
+
+ align:start position:0%
+of how chemistry affects properties in
+solids
+
+ align:start position:0%
+solids
+ 
+
+ align:start position:0%
+solids
+okay so that's the big picture now
+
+ align:start position:0%
+okay so that's the big picture now
+ 
+
+ align:start position:0%
+okay so that's the big picture now
+here's the thing
+
+ align:start position:0%
+here's the thing
+ 
+
+ align:start position:0%
+here's the thing
+why does that matter well because so
+
+ align:start position:0%
+why does that matter well because so
+ 
+
+ align:start position:0%
+why does that matter well because so
+many properties can vary by
+
+ align:start position:0%
+many properties can vary by
+ 
+
+ align:start position:0%
+many properties can vary by
+so much depending on what i just said
+
+ align:start position:0%
+so much depending on what i just said
+ 
+
+ align:start position:0%
+so much depending on what i just said
+how does chemistry affect properties in
+
+ align:start position:0%
+how does chemistry affect properties in
+ 
+
+ align:start position:0%
+how does chemistry affect properties in
+solids well
+
+ align:start position:0%
+solids well
+ 
+
+ align:start position:0%
+solids well
+it's it's complicated but look at this
+
+ align:start position:0%
+it's it's complicated but look at this
+ 
+
+ align:start position:0%
+it's it's complicated but look at this
+variation
+
+ align:start position:0%
+variation
+ 
+
+ align:start position:0%
+variation
+28 orders of magnitude of conductivity
+
+ align:start position:0%
+28 orders of magnitude of conductivity
+ 
+
+ align:start position:0%
+28 orders of magnitude of conductivity
+electrical conductivity
+
+ align:start position:0%
+electrical conductivity
+ 
+
+ align:start position:0%
+electrical conductivity
+28 orders of magnitude that's a lot of
+
+ align:start position:0%
+28 orders of magnitude that's a lot of
+ 
+
+ align:start position:0%
+28 orders of magnitude that's a lot of
+zeros
+
+ align:start position:0%
+zeros
+ 
+
+ align:start position:0%
+zeros
+10 minus these are the electrical
+
+ align:start position:0%
+10 minus these are the electrical
+ 
+
+ align:start position:0%
+10 minus these are the electrical
+conductivities of different
+
+ align:start position:0%
+conductivities of different
+ 
+
+ align:start position:0%
+conductivities of different
+atoms right different uh
+
+ align:start position:0%
+atoms right different uh
+ 
+
+ align:start position:0%
+atoms right different uh
+materials and you can see that
+
+ align:start position:0%
+materials and you can see that
+ 
+
+ align:start position:0%
+materials and you can see that
+it's going to depend on what you have
+
+ align:start position:0%
+it's going to depend on what you have
+ 
+
+ align:start position:0%
+it's going to depend on what you have
+but it's also going to depend
+
+ align:start position:0%
+but it's also going to depend
+ 
+
+ align:start position:0%
+but it's also going to depend
+on so that's the chemistry but it's also
+
+ align:start position:0%
+on so that's the chemistry but it's also
+ 
+
+ align:start position:0%
+on so that's the chemistry but it's also
+going to depend on the bonding
+
+ align:start position:0%
+going to depend on the bonding
+ 
+
+ align:start position:0%
+going to depend on the bonding
+it's going to depend on how the
+
+ align:start position:0%
+it's going to depend on how the
+ 
+
+ align:start position:0%
+it's going to depend on how the
+electronic structure comes together
+
+ align:start position:0%
+electronic structure comes together
+ 
+
+ align:start position:0%
+electronic structure comes together
+and it's going to depend on how the
+
+ align:start position:0%
+and it's going to depend on how the
+ 
+
+ align:start position:0%
+and it's going to depend on how the
+atoms come together that is what will
+
+ align:start position:0%
+atoms come together that is what will
+ 
+
+ align:start position:0%
+atoms come together that is what will
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+28 orders of magnitude that has a lot of
+
+ align:start position:0%
+28 orders of magnitude that has a lot of
+ 
+
+ align:start position:0%
+28 orders of magnitude that has a lot of
+variation
+
+ align:start position:0%
+variation
+ 
+
+ align:start position:0%
+variation
+right so we're going to start by
+
+ align:start position:0%
+right so we're going to start by
+ 
+
+ align:start position:0%
+right so we're going to start by
+thinking about how electrons
+
+ align:start position:0%
+thinking about how electrons
+ 
+
+ align:start position:0%
+thinking about how electrons
+see these solids that's how we're going
+
+ align:start position:0%
+see these solids that's how we're going
+ 
+
+ align:start position:0%
+see these solids that's how we're going
+to start
+
+ align:start position:0%
+to start
+ 
+
+ align:start position:0%
+to start
+now the thing is that these good old
+
+ align:start position:0%
+now the thing is that these good old
+ 
+
+ align:start position:0%
+now the thing is that these good old
+days these good old days
+
+ align:start position:0%
+days these good old days
+ 
+
+ align:start position:0%
+days these good old days
+of molecular orbital theory are going to
+
+ align:start position:0%
+of molecular orbital theory are going to
+ 
+
+ align:start position:0%
+of molecular orbital theory are going to
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+they're gonna have to end today no
+
+ align:start position:0%
+they're gonna have to end today no
+ 
+
+ align:start position:0%
+they're gonna have to end today no
+they're not ending for like quizzes
+
+ align:start position:0%
+they're not ending for like quizzes
+ 
+
+ align:start position:0%
+they're not ending for like quizzes
+and exams don't forget about them but
+
+ align:start position:0%
+and exams don't forget about them but
+ 
+
+ align:start position:0%
+and exams don't forget about them but
+we gotta move on because this is just
+
+ align:start position:0%
+we gotta move on because this is just
+ 
+
+ align:start position:0%
+we gotta move on because this is just
+two atoms
+
+ align:start position:0%
+two atoms
+ 
+
+ align:start position:0%
+two atoms
+two atoms but what happens when we have
+
+ align:start position:0%
+two atoms but what happens when we have
+ 
+
+ align:start position:0%
+two atoms but what happens when we have
+like a solid right how many atoms do we
+
+ align:start position:0%
+like a solid right how many atoms do we
+ 
+
+ align:start position:0%
+like a solid right how many atoms do we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+we got a lot we got a lot so let's go
+
+ align:start position:0%
+we got a lot we got a lot so let's go
+ 
+
+ align:start position:0%
+we got a lot we got a lot so let's go
+i'll go here okay now you know
+
+ align:start position:0%
+i'll go here okay now you know
+ 
+
+ align:start position:0%
+i'll go here okay now you know
+if you look if you think about that
+
+ align:start position:0%
+if you look if you think about that
+ 
+
+ align:start position:0%
+if you look if you think about that
+picture that was our p
+
+ align:start position:0%
+picture that was our p
+ 
+
+ align:start position:0%
+picture that was our p
+i'm going to take 1s orbitals
+
+ align:start position:0%
+i'm going to take 1s orbitals
+ 
+
+ align:start position:0%
+i'm going to take 1s orbitals
+and let's just think about this for a
+
+ align:start position:0%
+and let's just think about this for a
+ 
+
+ align:start position:0%
+and let's just think about this for a
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+if you take 1s orbitals and you make and
+
+ align:start position:0%
+if you take 1s orbitals and you make and
+ 
+
+ align:start position:0%
+if you take 1s orbitals and you make and
+you have 2 atoms
+
+ align:start position:0%
+you have 2 atoms
+ 
+
+ align:start position:0%
+you have 2 atoms
+that come together well they're gonna
+
+ align:start position:0%
+that come together well they're gonna
+ 
+
+ align:start position:0%
+that come together well they're gonna
+you know do just what you see there
+
+ align:start position:0%
+you know do just what you see there
+ 
+
+ align:start position:0%
+you know do just what you see there
+where you've got your 1s and your 1s
+
+ align:start position:0%
+where you've got your 1s and your 1s
+ 
+
+ align:start position:0%
+where you've got your 1s and your 1s
+and i'm even going to fill these up in
+
+ align:start position:0%
+and i'm even going to fill these up in
+ 
+
+ align:start position:0%
+and i'm even going to fill these up in
+the sigma and sigma star
+
+ align:start position:0%
+the sigma and sigma star
+ 
+
+ align:start position:0%
+the sigma and sigma star
+so that would be like two 1s orbitals
+
+ align:start position:0%
+so that would be like two 1s orbitals
+ 
+
+ align:start position:0%
+so that would be like two 1s orbitals
+that i have either okay so up here i
+
+ align:start position:0%
+that i have either okay so up here i
+ 
+
+ align:start position:0%
+that i have either okay so up here i
+took
+
+ align:start position:0%
+took
+ 
+
+ align:start position:0%
+took
+one it was a positive and i subtracted
+
+ align:start position:0%
+one it was a positive and i subtracted
+ 
+
+ align:start position:0%
+one it was a positive and i subtracted
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and here i took one and i added one
+
+ align:start position:0%
+and here i took one and i added one
+ 
+
+ align:start position:0%
+and here i took one and i added one
+and remember this gave us this
+
+ align:start position:0%
+and remember this gave us this
+ 
+
+ align:start position:0%
+and remember this gave us this
+and this and this gave us the bonding
+
+ align:start position:0%
+and this and this gave us the bonding
+ 
+
+ align:start position:0%
+and this and this gave us the bonding
+orbital right
+
+ align:start position:0%
+orbital right
+ 
+
+ align:start position:0%
+orbital right
+bonding antibonding it all came from
+
+ align:start position:0%
+bonding antibonding it all came from
+ 
+
+ align:start position:0%
+bonding antibonding it all came from
+lcao
+
+ align:start position:0%
+lcao
+ 
+
+ align:start position:0%
+lcao
+lcao is a linear combination of atomic
+
+ align:start position:0%
+lcao is a linear combination of atomic
+ 
+
+ align:start position:0%
+lcao is a linear combination of atomic
+orbitals that's the theory we use to
+
+ align:start position:0%
+orbitals that's the theory we use to
+ 
+
+ align:start position:0%
+orbitals that's the theory we use to
+build up our mo theory
+
+ align:start position:0%
+build up our mo theory
+ 
+
+ align:start position:0%
+build up our mo theory
+right but now we got to go a lot further
+
+ align:start position:0%
+right but now we got to go a lot further
+ 
+
+ align:start position:0%
+right but now we got to go a lot further
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so i'm going to because i don't want to
+
+ align:start position:0%
+so i'm going to because i don't want to
+ 
+
+ align:start position:0%
+so i'm going to because i don't want to
+keep adding things
+
+ align:start position:0%
+keep adding things
+ 
+
+ align:start position:0%
+keep adding things
+here and here it gets complicated right
+
+ align:start position:0%
+here and here it gets complicated right
+ 
+
+ align:start position:0%
+here and here it gets complicated right
+i'm trying to find
+
+ align:start position:0%
+i'm trying to find
+ 
+
+ align:start position:0%
+i'm trying to find
+the the mos for more and more and more
+
+ align:start position:0%
+the the mos for more and more and more
+ 
+
+ align:start position:0%
+the the mos for more and more and more
+atoms
+
+ align:start position:0%
+atoms
+ 
+
+ align:start position:0%
+atoms
+because i got to put a whole lot into my
+
+ align:start position:0%
+because i got to put a whole lot into my
+ 
+
+ align:start position:0%
+because i got to put a whole lot into my
+solid right
+
+ align:start position:0%
+solid right
+ 
+
+ align:start position:0%
+solid right
+so i'm going to write them on the just
+
+ align:start position:0%
+so i'm going to write them on the just
+ 
+
+ align:start position:0%
+so i'm going to write them on the just
+on one side right if i write
+
+ align:start position:0%
+on one side right if i write
+ 
+
+ align:start position:0%
+on one side right if i write
+the two here like that
+
+ align:start position:0%
+the two here like that
+ 
+
+ align:start position:0%
+the two here like that
+and that would be sigma and sigma star
+
+ align:start position:0%
+and that would be sigma and sigma star
+ 
+
+ align:start position:0%
+and that would be sigma and sigma star
+then you know what i'm talking about i'm
+
+ align:start position:0%
+then you know what i'm talking about i'm
+ 
+
+ align:start position:0%
+then you know what i'm talking about i'm
+taking the two and i'm combining them in
+
+ align:start position:0%
+taking the two and i'm combining them in
+ 
+
+ align:start position:0%
+taking the two and i'm combining them in
+two different ways
+
+ align:start position:0%
+two different ways
+ 
+
+ align:start position:0%
+two different ways
+but what if i had three well see if i
+
+ align:start position:0%
+but what if i had three well see if i
+ 
+
+ align:start position:0%
+but what if i had three well see if i
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+three so i've got three s orbitals now
+
+ align:start position:0%
+three so i've got three s orbitals now
+ 
+
+ align:start position:0%
+three so i've got three s orbitals now
+right so if i've got three s orbitals
+
+ align:start position:0%
+right so if i've got three s orbitals
+ 
+
+ align:start position:0%
+right so if i've got three s orbitals
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+if you think about it i could also add
+
+ align:start position:0%
+if you think about it i could also add
+ 
+
+ align:start position:0%
+if you think about it i could also add
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+like that that would be a very nice
+
+ align:start position:0%
+like that that would be a very nice
+ 
+
+ align:start position:0%
+like that that would be a very nice
+bonding orbital right if you add them
+
+ align:start position:0%
+bonding orbital right if you add them
+ 
+
+ align:start position:0%
+bonding orbital right if you add them
+you see that they're
+
+ align:start position:0%
+you see that they're
+ 
+
+ align:start position:0%
+you see that they're
+they're going to have the same kind of
+
+ align:start position:0%
+they're going to have the same kind of
+ 
+
+ align:start position:0%
+they're going to have the same kind of
+really nice body but i could also
+
+ align:start position:0%
+really nice body but i could also
+ 
+
+ align:start position:0%
+really nice body but i could also
+subtract one in the middle
+
+ align:start position:0%
+subtract one in the middle
+ 
+
+ align:start position:0%
+subtract one in the middle
+and if i did that so i had a plus
+
+ align:start position:0%
+and if i did that so i had a plus
+ 
+
+ align:start position:0%
+and if i did that so i had a plus
+minus plus there right so those are the
+
+ align:start position:0%
+minus plus there right so those are the
+ 
+
+ align:start position:0%
+minus plus there right so those are the
+signs right
+
+ align:start position:0%
+signs right
+ 
+
+ align:start position:0%
+signs right
+plus s minus s plus s then
+
+ align:start position:0%
+plus s minus s plus s then
+ 
+
+ align:start position:0%
+plus s minus s plus s then
+you can see that in between those as i
+
+ align:start position:0%
+you can see that in between those as i
+ 
+
+ align:start position:0%
+you can see that in between those as i
+add these together you have nodes
+
+ align:start position:0%
+add these together you have nodes
+ 
+
+ align:start position:0%
+add these together you have nodes
+right so like this is not going to look
+
+ align:start position:0%
+right so like this is not going to look
+ 
+
+ align:start position:0%
+right so like this is not going to look
+very like a very happy bonding situation
+
+ align:start position:0%
+very like a very happy bonding situation
+ 
+
+ align:start position:0%
+very like a very happy bonding situation
+i'm going to have something in there
+
+ align:start position:0%
+i'm going to have something in there
+ 
+
+ align:start position:0%
+i'm going to have something in there
+and then something in there that's what
+
+ align:start position:0%
+and then something in there that's what
+ 
+
+ align:start position:0%
+and then something in there that's what
+that's going to look like as i bring
+
+ align:start position:0%
+that's going to look like as i bring
+ 
+
+ align:start position:0%
+that's going to look like as i bring
+them closer and try to add them
+
+ align:start position:0%
+them closer and try to add them
+ 
+
+ align:start position:0%
+them closer and try to add them
+i made two nodes here well there's one
+
+ align:start position:0%
+i made two nodes here well there's one
+ 
+
+ align:start position:0%
+i made two nodes here well there's one
+other way you could do this and we know
+
+ align:start position:0%
+other way you could do this and we know
+ 
+
+ align:start position:0%
+other way you could do this and we know
+that the number of molecular orbitals
+
+ align:start position:0%
+that the number of molecular orbitals
+ 
+
+ align:start position:0%
+that the number of molecular orbitals
+has to equal
+
+ align:start position:0%
+has to equal
+ 
+
+ align:start position:0%
+has to equal
+the number of atomic orbitals right we
+
+ align:start position:0%
+the number of atomic orbitals right we
+ 
+
+ align:start position:0%
+the number of atomic orbitals right we
+know that so
+
+ align:start position:0%
+know that so
+ 
+
+ align:start position:0%
+know that so
+there's one more that we need because i
+
+ align:start position:0%
+there's one more that we need because i
+ 
+
+ align:start position:0%
+there's one more that we need because i
+started with three s's
+
+ align:start position:0%
+started with three s's
+ 
+
+ align:start position:0%
+started with three s's
+and you can kind of see that right you
+
+ align:start position:0%
+and you can kind of see that right you
+ 
+
+ align:start position:0%
+and you can kind of see that right you
+can see that because if i had
+
+ align:start position:0%
+can see that because if i had
+ 
+
+ align:start position:0%
+can see that because if i had
+a plus and a plus
+
+ align:start position:0%
+a plus and a plus
+ 
+
+ align:start position:0%
+a plus and a plus
+if i had done it that way or maybe the
+
+ align:start position:0%
+if i had done it that way or maybe the
+ 
+
+ align:start position:0%
+if i had done it that way or maybe the
+other way right maybe this was
+
+ align:start position:0%
+other way right maybe this was
+ 
+
+ align:start position:0%
+other way right maybe this was
+over there but you see i got a i got a
+
+ align:start position:0%
+over there but you see i got a i got a
+ 
+
+ align:start position:0%
+over there but you see i got a i got a
+little bonding going on in here between
+
+ align:start position:0%
+little bonding going on in here between
+ 
+
+ align:start position:0%
+little bonding going on in here between
+them and i got an anti-bonding there
+
+ align:start position:0%
+them and i got an anti-bonding there
+ 
+
+ align:start position:0%
+them and i got an anti-bonding there
+it's almost like it kind of cancels out
+
+ align:start position:0%
+it's almost like it kind of cancels out
+ 
+
+ align:start position:0%
+it's almost like it kind of cancels out
+so you could imagine that that
+
+ align:start position:0%
+so you could imagine that that
+ 
+
+ align:start position:0%
+so you could imagine that that
+combination of s orbitals if i add and
+
+ align:start position:0%
+combination of s orbitals if i add and
+ 
+
+ align:start position:0%
+combination of s orbitals if i add and
+subtract them this way it's going to be
+
+ align:start position:0%
+subtract them this way it's going to be
+ 
+
+ align:start position:0%
+subtract them this way it's going to be
+somewhere right in the middle
+
+ align:start position:0%
+somewhere right in the middle
+ 
+
+ align:start position:0%
+somewhere right in the middle
+right maybe not so bonding maybe not so
+
+ align:start position:0%
+right maybe not so bonding maybe not so
+ 
+
+ align:start position:0%
+right maybe not so bonding maybe not so
+antibody
+
+ align:start position:0%
+antibody
+ 
+
+ align:start position:0%
+antibody
+okay good all right well let's do four
+
+ align:start position:0%
+okay good all right well let's do four
+ 
+
+ align:start position:0%
+okay good all right well let's do four
+so if i had four if i started with four
+
+ align:start position:0%
+so if i had four if i started with four
+ 
+
+ align:start position:0%
+so if i had four if i started with four
+this is like four hydrogen atoms let's
+
+ align:start position:0%
+this is like four hydrogen atoms let's
+ 
+
+ align:start position:0%
+this is like four hydrogen atoms let's
+say although i'm not filling it yet
+
+ align:start position:0%
+say although i'm not filling it yet
+ 
+
+ align:start position:0%
+say although i'm not filling it yet
+but so four 1s orbitals well now
+
+ align:start position:0%
+but so four 1s orbitals well now
+ 
+
+ align:start position:0%
+but so four 1s orbitals well now
+you see i could do this i can add them
+
+ align:start position:0%
+you see i could do this i can add them
+ 
+
+ align:start position:0%
+you see i could do this i can add them
+all up
+
+ align:start position:0%
+all up
+ 
+
+ align:start position:0%
+all up
+and get this super awesome bonding state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i could also alternate them
+
+ align:start position:0%
+well i could also alternate them
+ 
+
+ align:start position:0%
+well i could also alternate them
+so that everything is anti-bonding
+
+ align:start position:0%
+so that everything is anti-bonding
+ 
+
+ align:start position:0%
+so that everything is anti-bonding
+look at that right these are going to
+
+ align:start position:0%
+look at that right these are going to
+ 
+
+ align:start position:0%
+look at that right these are going to
+cancel as you bring them together
+
+ align:start position:0%
+cancel as you bring them together
+ 
+
+ align:start position:0%
+cancel as you bring them together
+and you're going to get antibonding
+
+ align:start position:0%
+and you're going to get antibonding
+ 
+
+ align:start position:0%
+and you're going to get antibonding
+antibonding right
+
+ align:start position:0%
+antibonding right
+ 
+
+ align:start position:0%
+antibonding right
+but there's also two other options
+
+ align:start position:0%
+but there's also two other options
+ 
+
+ align:start position:0%
+but there's also two other options
+because in tight
+
+ align:start position:0%
+because in tight
+ 
+
+ align:start position:0%
+because in tight
+that are in between right here i can add
+
+ align:start position:0%
+that are in between right here i can add
+ 
+
+ align:start position:0%
+that are in between right here i can add
+two and then subtract two and you can
+
+ align:start position:0%
+two and then subtract two and you can
+ 
+
+ align:start position:0%
+two and then subtract two and you can
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+these would these are both negative and
+
+ align:start position:0%
+these would these are both negative and
+ 
+
+ align:start position:0%
+these would these are both negative and
+as they come together they're going to
+
+ align:start position:0%
+as they come together they're going to
+ 
+
+ align:start position:0%
+as they come together they're going to
+overlap constructively so will these but
+
+ align:start position:0%
+overlap constructively so will these but
+ 
+
+ align:start position:0%
+overlap constructively so will these but
+in the middle here
+
+ align:start position:0%
+in the middle here
+ 
+
+ align:start position:0%
+in the middle here
+they're going to be kind of destructive
+
+ align:start position:0%
+they're going to be kind of destructive
+ 
+
+ align:start position:0%
+they're going to be kind of destructive
+interference right destructive
+
+ align:start position:0%
+interference right destructive
+ 
+
+ align:start position:0%
+interference right destructive
+and so you're going to have this one
+
+ align:start position:0%
+and so you're going to have this one
+ 
+
+ align:start position:0%
+and so you're going to have this one
+node in between
+
+ align:start position:0%
+node in between
+ 
+
+ align:start position:0%
+node in between
+but in general you can imagine this will
+
+ align:start position:0%
+but in general you can imagine this will
+ 
+
+ align:start position:0%
+but in general you can imagine this will
+be more bonding
+
+ align:start position:0%
+be more bonding
+ 
+
+ align:start position:0%
+be more bonding
+than anti-bonding right so we draw it
+
+ align:start position:0%
+than anti-bonding right so we draw it
+ 
+
+ align:start position:0%
+than anti-bonding right so we draw it
+down below the middle
+
+ align:start position:0%
+down below the middle
+ 
+
+ align:start position:0%
+down below the middle
+whereas up here you could also imagine
+
+ align:start position:0%
+whereas up here you could also imagine
+ 
+
+ align:start position:0%
+whereas up here you could also imagine
+something like this
+
+ align:start position:0%
+something like this
+ 
+
+ align:start position:0%
+something like this
+where you start with a plus and you put
+
+ align:start position:0%
+where you start with a plus and you put
+ 
+
+ align:start position:0%
+where you start with a plus and you put
+two minuses in there
+
+ align:start position:0%
+two minuses in there
+ 
+
+ align:start position:0%
+two minuses in there
+and a plus over there is it just adding
+
+ align:start position:0%
+and a plus over there is it just adding
+ 
+
+ align:start position:0%
+and a plus over there is it just adding
+and subtracting it's just i'm taking lco
+
+ align:start position:0%
+and subtracting it's just i'm taking lco
+ 
+
+ align:start position:0%
+and subtracting it's just i'm taking lco
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+and moving it to more than two orbitals
+
+ align:start position:0%
+and moving it to more than two orbitals
+ 
+
+ align:start position:0%
+and moving it to more than two orbitals
+okay but that that so now you see that
+
+ align:start position:0%
+okay but that that so now you see that
+ 
+
+ align:start position:0%
+okay but that that so now you see that
+you can actually understand this from
+
+ align:start position:0%
+you can actually understand this from
+ 
+
+ align:start position:0%
+you can actually understand this from
+the number of nodes right
+
+ align:start position:0%
+the number of nodes right
+ 
+
+ align:start position:0%
+the number of nodes right
+this is like three nodes
+
+ align:start position:0%
+this is like three nodes
+ 
+
+ align:start position:0%
+this is like three nodes
+this is two two nodes over there
+
+ align:start position:0%
+this is two two nodes over there
+ 
+
+ align:start position:0%
+this is two two nodes over there
+this is one node
+
+ align:start position:0%
+this is one node
+ 
+
+ align:start position:0%
+this is one node
+and zero nodes this is exactly the
+
+ align:start position:0%
+and zero nodes this is exactly the
+ 
+
+ align:start position:0%
+and zero nodes this is exactly the
+kind of thing we talked about already
+
+ align:start position:0%
+kind of thing we talked about already
+ 
+
+ align:start position:0%
+kind of thing we talked about already
+but for only two orbitals now we're just
+
+ align:start position:0%
+but for only two orbitals now we're just
+ 
+
+ align:start position:0%
+but for only two orbitals now we're just
+continuing it along
+
+ align:start position:0%
+continuing it along
+ 
+
+ align:start position:0%
+continuing it along
+okay you can see why the good old days
+
+ align:start position:0%
+okay you can see why the good old days
+ 
+
+ align:start position:0%
+okay you can see why the good old days
+are over because
+
+ align:start position:0%
+are over because
+ 
+
+ align:start position:0%
+are over because
+see now we got to jump this up a level
+
+ align:start position:0%
+see now we got to jump this up a level
+ 
+
+ align:start position:0%
+see now we got to jump this up a level
+and we got to think how many s orbitals
+
+ align:start position:0%
+and we got to think how many s orbitals
+ 
+
+ align:start position:0%
+and we got to think how many s orbitals
+do i have in a typical piece of matter
+
+ align:start position:0%
+do i have in a typical piece of matter
+ 
+
+ align:start position:0%
+do i have in a typical piece of matter
+how many do you think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take a guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly but take a chunk of
+
+ align:start position:0%
+roughly but take a chunk of
+ 
+
+ align:start position:0%
+roughly but take a chunk of
+hydrogen this big how many how many how
+
+ align:start position:0%
+hydrogen this big how many how many how
+ 
+
+ align:start position:0%
+hydrogen this big how many how many how
+many atoms do i have
+
+ align:start position:0%
+many atoms do i have
+ 
+
+ align:start position:0%
+many atoms do i have
+a mole exactly that's why we invented
+
+ align:start position:0%
+a mole exactly that's why we invented
+ 
+
+ align:start position:0%
+a mole exactly that's why we invented
+the mole
+
+ align:start position:0%
+the mole
+ 
+
+ align:start position:0%
+the mole
+so that we could count big numbers by
+
+ align:start position:0%
+so that we could count big numbers by
+ 
+
+ align:start position:0%
+so that we could count big numbers by
+just saying one
+
+ align:start position:0%
+just saying one
+ 
+
+ align:start position:0%
+just saying one
+one mole but if i have a mole then i've
+
+ align:start position:0%
+one mole but if i have a mole then i've
+ 
+
+ align:start position:0%
+one mole but if i have a mole then i've
+got like 10 to the 24th of these
+
+ align:start position:0%
+got like 10 to the 24th of these
+ 
+
+ align:start position:0%
+got like 10 to the 24th of these
+i just went to four i just went to four
+
+ align:start position:0%
+i just went to four i just went to four
+ 
+
+ align:start position:0%
+i just went to four i just went to four
+right but it just keeps on going so
+
+ align:start position:0%
+right but it just keeps on going so
+ 
+
+ align:start position:0%
+right but it just keeps on going so
+april does this
+
+ align:start position:0%
+april does this
+ 
+
+ align:start position:0%
+april does this
+so here's like okay one okay
+
+ align:start position:0%
+so here's like okay one okay
+ 
+
+ align:start position:0%
+so here's like okay one okay
+orbital of atom oh i labeled that well
+
+ align:start position:0%
+orbital of atom oh i labeled that well
+ 
+
+ align:start position:0%
+orbital of atom oh i labeled that well
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+bonding antibonding orbitals of
+
+ align:start position:0%
+bonding antibonding orbitals of
+ 
+
+ align:start position:0%
+bonding antibonding orbitals of
+molecules and then you see okay there's
+
+ align:start position:0%
+molecules and then you see okay there's
+ 
+
+ align:start position:0%
+molecules and then you see okay there's
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+there's four five you keep on going
+
+ align:start position:0%
+there's four five you keep on going
+ 
+
+ align:start position:0%
+there's four five you keep on going
+okay they got a little tired and then
+
+ align:start position:0%
+okay they got a little tired and then
+ 
+
+ align:start position:0%
+okay they got a little tired and then
+they wrote 30
+
+ align:start position:0%
+they wrote 30
+ 
+
+ align:start position:0%
+they wrote 30
+30 30 orbitals
+
+ align:start position:0%
+30 30 orbitals
+ 
+
+ align:start position:0%
+30 30 orbitals
+30 is still way way far away see but
+
+ align:start position:0%
+30 is still way way far away see but
+ 
+
+ align:start position:0%
+30 is still way way far away see but
+if you had 30 s orbitals you might still
+
+ align:start position:0%
+if you had 30 s orbitals you might still
+ 
+
+ align:start position:0%
+if you had 30 s orbitals you might still
+be able to kind of see them
+
+ align:start position:0%
+be able to kind of see them
+ 
+
+ align:start position:0%
+be able to kind of see them
+see these lines discreetly remember this
+
+ align:start position:0%
+see these lines discreetly remember this
+ 
+
+ align:start position:0%
+see these lines discreetly remember this
+is energy space they might actually
+
+ align:start position:0%
+is energy space they might actually
+ 
+
+ align:start position:0%
+is energy space they might actually
+remember like these energies are really
+
+ align:start position:0%
+remember like these energies are really
+ 
+
+ align:start position:0%
+remember like these energies are really
+important right the lines between the
+
+ align:start position:0%
+important right the lines between the
+ 
+
+ align:start position:0%
+important right the lines between the
+deltas but if you have a mole
+
+ align:start position:0%
+deltas but if you have a mole
+ 
+
+ align:start position:0%
+deltas but if you have a mole
+if you have a mole it looks like one
+
+ align:start position:0%
+if you have a mole it looks like one
+ 
+
+ align:start position:0%
+if you have a mole it looks like one
+continuous set of lines
+
+ align:start position:0%
+continuous set of lines
+ 
+
+ align:start position:0%
+continuous set of lines
+these don't really look discrete anymore
+
+ align:start position:0%
+these don't really look discrete anymore
+ 
+
+ align:start position:0%
+these don't really look discrete anymore
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+these don't look discreet and so
+
+ align:start position:0%
+these don't look discreet and so
+ 
+
+ align:start position:0%
+these don't look discreet and so
+if you have a mole of atoms so if you
+
+ align:start position:0%
+if you have a mole of atoms so if you
+ 
+
+ align:start position:0%
+if you have a mole of atoms so if you
+have a solid
+
+ align:start position:0%
+have a solid
+ 
+
+ align:start position:0%
+have a solid
+we call that that collection
+
+ align:start position:0%
+we call that that collection
+ 
+
+ align:start position:0%
+we call that that collection
+of orbitals that are all stuck in here
+
+ align:start position:0%
+of orbitals that are all stuck in here
+ 
+
+ align:start position:0%
+of orbitals that are all stuck in here
+a band we call that a band
+
+ align:start position:0%
+a band we call that a band
+ 
+
+ align:start position:0%
+a band we call that a band
+okay so if i take now i'm not going to
+
+ align:start position:0%
+okay so if i take now i'm not going to
+ 
+
+ align:start position:0%
+okay so if i take now i'm not going to
+draw
+
+ align:start position:0%
+draw
+ 
+
+ align:start position:0%
+draw
+10 to the 24th 10 to the 24th
+
+ align:start position:0%
+10 to the 24th 10 to the 24th
+ 
+
+ align:start position:0%
+10 to the 24th 10 to the 24th
+s orbitals but pretend
+
+ align:start position:0%
+s orbitals but pretend
+ 
+
+ align:start position:0%
+s orbitals but pretend
+pretend that that's what i have here
+
+ align:start position:0%
+pretend that that's what i have here
+ 
+
+ align:start position:0%
+pretend that that's what i have here
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+what happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what i do is i form a continuum of
+
+ align:start position:0%
+what i do is i form a continuum of
+ 
+
+ align:start position:0%
+what i do is i form a continuum of
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+a continuum of levels for those
+
+ align:start position:0%
+a continuum of levels for those
+ 
+
+ align:start position:0%
+a continuum of levels for those
+electrons and this
+
+ align:start position:0%
+electrons and this
+ 
+
+ align:start position:0%
+electrons and this
+they're so packed together we don't even
+
+ align:start position:0%
+they're so packed together we don't even
+ 
+
+ align:start position:0%
+they're so packed together we don't even
+draw them as lines we can't
+
+ align:start position:0%
+draw them as lines we can't
+ 
+
+ align:start position:0%
+draw them as lines we can't
+right so this is called the 1s
+
+ align:start position:0%
+right so this is called the 1s
+ 
+
+ align:start position:0%
+right so this is called the 1s
+band oh-ho band
+
+ align:start position:0%
+band oh-ho band
+ 
+
+ align:start position:0%
+band oh-ho band
+it's a band it's a band of states
+
+ align:start position:0%
+it's a band it's a band of states
+ 
+
+ align:start position:0%
+it's a band it's a band of states
+it's a band of states that's the 1s band
+
+ align:start position:0%
+it's a band of states that's the 1s band
+ 
+
+ align:start position:0%
+it's a band of states that's the 1s band
+now there's some important rules
+
+ align:start position:0%
+now there's some important rules
+ 
+
+ align:start position:0%
+now there's some important rules
+that are really just the same but we
+
+ align:start position:0%
+that are really just the same but we
+ 
+
+ align:start position:0%
+that are really just the same but we
+follow them here too
+
+ align:start position:0%
+follow them here too
+ 
+
+ align:start position:0%
+follow them here too
+and so i want to emphasize them we've
+
+ align:start position:0%
+and so i want to emphasize them we've
+ 
+
+ align:start position:0%
+and so i want to emphasize them we've
+already learned them for
+
+ align:start position:0%
+already learned them for
+ 
+
+ align:start position:0%
+already learned them for
+molecules they hold for bands and solids
+
+ align:start position:0%
+molecules they hold for bands and solids
+ 
+
+ align:start position:0%
+molecules they hold for bands and solids
+right so so now for example
+
+ align:start position:0%
+right so so now for example
+ 
+
+ align:start position:0%
+right so so now for example
+let's think about this each of these
+
+ align:start position:0%
+let's think about this each of these
+ 
+
+ align:start position:0%
+let's think about this each of these
+orbitals
+
+ align:start position:0%
+orbitals
+ 
+
+ align:start position:0%
+orbitals
+could occupy how many electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two right so i had two electrons
+
+ align:start position:0%
+two right so i had two electrons
+ 
+
+ align:start position:0%
+two right so i had two electrons
+for each s orbital
+
+ align:start position:0%
+for each s orbital
+ 
+
+ align:start position:0%
+for each s orbital
+s orb well you know if you think about
+
+ align:start position:0%
+s orb well you know if you think about
+ 
+
+ align:start position:0%
+s orb well you know if you think about
+that then
+
+ align:start position:0%
+that then
+ 
+
+ align:start position:0%
+that then
+for n atoms for n atoms
+
+ align:start position:0%
+for n atoms for n atoms
+ 
+
+ align:start position:0%
+for n atoms for n atoms
+and here what did i say 10 to the 24th
+
+ align:start position:0%
+and here what did i say 10 to the 24th
+ 
+
+ align:start position:0%
+and here what did i say 10 to the 24th
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+there's one s orbital that comes from
+
+ align:start position:0%
+there's one s orbital that comes from
+ 
+
+ align:start position:0%
+there's one s orbital that comes from
+each atom
+
+ align:start position:0%
+each atom
+ 
+
+ align:start position:0%
+each atom
+so for n atoms then i would have two n
+
+ align:start position:0%
+so for n atoms then i would have two n
+ 
+
+ align:start position:0%
+so for n atoms then i would have two n
+electrons could go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can go can go into
+
+ align:start position:0%
+can go can go into
+ 
+
+ align:start position:0%
+can go can go into
+the 1s band right so if i have
+
+ align:start position:0%
+the 1s band right so if i have
+ 
+
+ align:start position:0%
+the 1s band right so if i have
+oh that makes sense right because i had
+
+ align:start position:0%
+oh that makes sense right because i had
+ 
+
+ align:start position:0%
+oh that makes sense right because i had
+two for each orbital and i had that many
+
+ align:start position:0%
+two for each orbital and i had that many
+ 
+
+ align:start position:0%
+two for each orbital and i had that many
+so if i know how many atoms i have
+
+ align:start position:0%
+so if i know how many atoms i have
+ 
+
+ align:start position:0%
+so if i know how many atoms i have
+right that make up this solid then
+
+ align:start position:0%
+right that make up this solid then
+ 
+
+ align:start position:0%
+right that make up this solid then
+that's how many electrons that band can
+
+ align:start position:0%
+that's how many electrons that band can
+ 
+
+ align:start position:0%
+that's how many electrons that band can
+have in it
+
+ align:start position:0%
+have in it
+ 
+
+ align:start position:0%
+have in it
+all we did is is go from the orbital
+
+ align:start position:0%
+all we did is is go from the orbital
+ 
+
+ align:start position:0%
+all we did is is go from the orbital
+atomic orbital picture to the solid to
+
+ align:start position:0%
+atomic orbital picture to the solid to
+ 
+
+ align:start position:0%
+atomic orbital picture to the solid to
+the mole
+
+ align:start position:0%
+the mole
+ 
+
+ align:start position:0%
+the mole
+right okay why am i saying that well
+
+ align:start position:0%
+right okay why am i saying that well
+ 
+
+ align:start position:0%
+right okay why am i saying that well
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+filling filling is
+
+ align:start position:0%
+filling filling is
+ 
+
+ align:start position:0%
+filling filling is
+incredibly important and it happens in
+
+ align:start position:0%
+incredibly important and it happens in
+ 
+
+ align:start position:0%
+incredibly important and it happens in
+the same way just like it was so
+
+ align:start position:0%
+the same way just like it was so
+ 
+
+ align:start position:0%
+the same way just like it was so
+important for
+
+ align:start position:0%
+important for
+ 
+
+ align:start position:0%
+important for
+molecular orbitals it's also critical
+
+ align:start position:0%
+molecular orbitals it's also critical
+ 
+
+ align:start position:0%
+molecular orbitals it's also critical
+for bands
+
+ align:start position:0%
+for bands
+ 
+
+ align:start position:0%
+for bands
+so filling is like
+
+ align:start position:0%
+so filling is like
+ 
+
+ align:start position:0%
+so filling is like
+mo it's just like in mo's start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lowest energy lowest energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then fill up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know if you think about this if i
+
+ align:start position:0%
+so you know if you think about this if i
+ 
+
+ align:start position:0%
+so you know if you think about this if i
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+now i'm gonna i'm gonna actually say
+
+ align:start position:0%
+now i'm gonna i'm gonna actually say
+ 
+
+ align:start position:0%
+now i'm gonna i'm gonna actually say
+well okay i made the 1s band
+
+ align:start position:0%
+well okay i made the 1s band
+ 
+
+ align:start position:0%
+well okay i made the 1s band
+by combining these orbitals now i'm
+
+ align:start position:0%
+by combining these orbitals now i'm
+ 
+
+ align:start position:0%
+by combining these orbitals now i'm
+going to say what a half
+
+ align:start position:0%
+going to say what a half
+ 
+
+ align:start position:0%
+going to say what a half
+which tells me how to fill it now i have
+
+ align:start position:0%
+which tells me how to fill it now i have
+ 
+
+ align:start position:0%
+which tells me how to fill it now i have
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+so if this is the 1s band if this is the
+
+ align:start position:0%
+so if this is the 1s band if this is the
+ 
+
+ align:start position:0%
+so if this is the 1s band if this is the
+1s
+
+ align:start position:0%
+1s
+ 
+
+ align:start position:0%
+1s
+band and i have
+
+ align:start position:0%
+band and i have
+ 
+
+ align:start position:0%
+band and i have
+hydrogen right
+
+ align:start position:0%
+hydrogen right
+ 
+
+ align:start position:0%
+hydrogen right
+so hydrogen has for each hydrogen
+
+ align:start position:0%
+so hydrogen has for each hydrogen
+ 
+
+ align:start position:0%
+so hydrogen has for each hydrogen
+i've got one electron but i just said
+
+ align:start position:0%
+i've got one electron but i just said
+ 
+
+ align:start position:0%
+i've got one electron but i just said
+that in the 1s band for each atom i
+
+ align:start position:0%
+that in the 1s band for each atom i
+ 
+
+ align:start position:0%
+that in the 1s band for each atom i
+could have put 2 electrons so you know
+
+ align:start position:0%
+could have put 2 electrons so you know
+ 
+
+ align:start position:0%
+could have put 2 electrons so you know
+if this is made of hydrogen
+
+ align:start position:0%
+if this is made of hydrogen
+ 
+
+ align:start position:0%
+if this is made of hydrogen
+that it's half filled which is exactly
+
+ align:start position:0%
+that it's half filled which is exactly
+ 
+
+ align:start position:0%
+that it's half filled which is exactly
+what that picture shows
+
+ align:start position:0%
+what that picture shows
+ 
+
+ align:start position:0%
+what that picture shows
+that's the filling you see it's filled
+
+ align:start position:0%
+that's the filling you see it's filled
+ 
+
+ align:start position:0%
+that's the filling you see it's filled
+halfway the band is filled halfway
+
+ align:start position:0%
+halfway the band is filled halfway
+ 
+
+ align:start position:0%
+halfway the band is filled halfway
+it it's it's like the mo picture
+
+ align:start position:0%
+it it's it's like the mo picture
+ 
+
+ align:start position:0%
+it it's it's like the mo picture
+right but it's not because i've made a
+
+ align:start position:0%
+right but it's not because i've made a
+ 
+
+ align:start position:0%
+right but it's not because i've made a
+continuous band out of it
+
+ align:start position:0%
+continuous band out of it
+ 
+
+ align:start position:0%
+continuous band out of it
+so instead of putting lines here lines
+
+ align:start position:0%
+so instead of putting lines here lines
+ 
+
+ align:start position:0%
+so instead of putting lines here lines
+there and then occupying them with
+
+ align:start position:0%
+there and then occupying them with
+ 
+
+ align:start position:0%
+there and then occupying them with
+arrows
+
+ align:start position:0%
+arrows
+ 
+
+ align:start position:0%
+arrows
+i fill them up with 10 to the 24th ish
+
+ align:start position:0%
+i fill them up with 10 to the 24th ish
+ 
+
+ align:start position:0%
+i fill them up with 10 to the 24th ish
+electrons so we fill bands up like that
+
+ align:start position:0%
+electrons so we fill bands up like that
+ 
+
+ align:start position:0%
+electrons so we fill bands up like that
+and we know that it's half filled
+
+ align:start position:0%
+and we know that it's half filled
+ 
+
+ align:start position:0%
+and we know that it's half filled
+because it's hydrogen
+
+ align:start position:0%
+because it's hydrogen
+ 
+
+ align:start position:0%
+because it's hydrogen
+another thing that we know is
+
+ align:start position:0%
+another thing that we know is
+ 
+
+ align:start position:0%
+another thing that we know is
+that the energy remember this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is also important right
+
+ align:start position:0%
+this is also important right
+ 
+
+ align:start position:0%
+this is also important right
+that that energy
+
+ align:start position:0%
+that that energy
+ 
+
+ align:start position:0%
+that that energy
+is related to interaction
+
+ align:start position:0%
+is related to interaction
+ 
+
+ align:start position:0%
+is related to interaction
+and overlap this is something we talked
+
+ align:start position:0%
+and overlap this is something we talked
+ 
+
+ align:start position:0%
+and overlap this is something we talked
+about interaction
+
+ align:start position:0%
+about interaction
+ 
+
+ align:start position:0%
+about interaction
+and overlap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the orbitals how how much does that
+
+ align:start position:0%
+of the orbitals how how much does that
+ 
+
+ align:start position:0%
+of the orbitals how how much does that
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+go up and down in energy right and
+
+ align:start position:0%
+go up and down in energy right and
+ 
+
+ align:start position:0%
+go up and down in energy right and
+something we talked about
+
+ align:start position:0%
+something we talked about
+ 
+
+ align:start position:0%
+something we talked about
+how much that band goes up and down in
+
+ align:start position:0%
+how much that band goes up and down in
+ 
+
+ align:start position:0%
+how much that band goes up and down in
+energy is just like in the the
+
+ align:start position:0%
+energy is just like in the the
+ 
+
+ align:start position:0%
+energy is just like in the the
+h2 molecule nicely 1s 1s sigma sigma
+
+ align:start position:0%
+h2 molecule nicely 1s 1s sigma sigma
+ 
+
+ align:start position:0%
+h2 molecule nicely 1s 1s sigma sigma
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+how far apart are sigma star in energy
+
+ align:start position:0%
+how far apart are sigma star in energy
+ 
+
+ align:start position:0%
+how far apart are sigma star in energy
+what depends
+
+ align:start position:0%
+what depends
+ 
+
+ align:start position:0%
+what depends
+on the interaction strength and the
+
+ align:start position:0%
+on the interaction strength and the
+ 
+
+ align:start position:0%
+on the interaction strength and the
+overlap between those orbitals
+
+ align:start position:0%
+overlap between those orbitals
+ 
+
+ align:start position:0%
+overlap between those orbitals
+the same is true in solids right same is
+
+ align:start position:0%
+the same is true in solids right same is
+ 
+
+ align:start position:0%
+the same is true in solids right same is
+true in solids so how
+
+ align:start position:0%
+true in solids so how
+ 
+
+ align:start position:0%
+true in solids so how
+what is the width of that band
+
+ align:start position:0%
+what is the width of that band
+ 
+
+ align:start position:0%
+what is the width of that band
+right how spread out over energy is it
+
+ align:start position:0%
+right how spread out over energy is it
+ 
+
+ align:start position:0%
+right how spread out over energy is it
+okay now so there's some ground rules
+
+ align:start position:0%
+okay now so there's some ground rules
+ 
+
+ align:start position:0%
+okay now so there's some ground rules
+now what else can we say okay so there's
+
+ align:start position:0%
+now what else can we say okay so there's
+ 
+
+ align:start position:0%
+now what else can we say okay so there's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+absolute least bonding state
+
+ align:start position:0%
+absolute least bonding state
+ 
+
+ align:start position:0%
+absolute least bonding state
+anti-bonding all the way up there
+
+ align:start position:0%
+anti-bonding all the way up there
+ 
+
+ align:start position:0%
+anti-bonding all the way up there
+the most bonding and then you've got
+
+ align:start position:0%
+the most bonding and then you've got
+ 
+
+ align:start position:0%
+the most bonding and then you've got
+almost infinite number of possibilities
+
+ align:start position:0%
+almost infinite number of possibilities
+ 
+
+ align:start position:0%
+almost infinite number of possibilities
+in between
+
+ align:start position:0%
+in between
+ 
+
+ align:start position:0%
+in between
+right yeah but the thing is
+
+ align:start position:0%
+right yeah but the thing is
+ 
+
+ align:start position:0%
+right yeah but the thing is
+that filling determines
+
+ align:start position:0%
+that filling determines
+ 
+
+ align:start position:0%
+that filling determines
+the properties you you can't just know
+
+ align:start position:0%
+the properties you you can't just know
+ 
+
+ align:start position:0%
+the properties you you can't just know
+the bands or the band structure as it's
+
+ align:start position:0%
+the bands or the band structure as it's
+ 
+
+ align:start position:0%
+the bands or the band structure as it's
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+right but you have to know the filling
+
+ align:start position:0%
+right but you have to know the filling
+ 
+
+ align:start position:0%
+right but you have to know the filling
+and when you have a situation like this
+
+ align:start position:0%
+and when you have a situation like this
+ 
+
+ align:start position:0%
+and when you have a situation like this
+so what let's write this down
+
+ align:start position:0%
+so what let's write this down
+ 
+
+ align:start position:0%
+so what let's write this down
+when you have partial filling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partially filled
+
+ align:start position:0%
+partially filled
+ 
+
+ align:start position:0%
+partially filled
+band is a metal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i will talk about metals on friday
+
+ align:start position:0%
+and i will talk about metals on friday
+ 
+
+ align:start position:0%
+and i will talk about metals on friday
+so we will come back to that concept and
+
+ align:start position:0%
+so we will come back to that concept and
+ 
+
+ align:start position:0%
+so we will come back to that concept and
+the electronic structure of metals
+
+ align:start position:0%
+the electronic structure of metals
+ 
+
+ align:start position:0%
+the electronic structure of metals
+on friday and but today
+
+ align:start position:0%
+on friday and but today
+ 
+
+ align:start position:0%
+on friday and but today
+i want to talk about something else that
+
+ align:start position:0%
+i want to talk about something else that
+ 
+
+ align:start position:0%
+i want to talk about something else that
+happens which is when
+
+ align:start position:0%
+happens which is when
+ 
+
+ align:start position:0%
+happens which is when
+you fill not in the middle of a band
+
+ align:start position:0%
+you fill not in the middle of a band
+ 
+
+ align:start position:0%
+you fill not in the middle of a band
+not in the middle but maybe all the way
+
+ align:start position:0%
+not in the middle but maybe all the way
+ 
+
+ align:start position:0%
+not in the middle but maybe all the way
+up to the top and there's a gap
+
+ align:start position:0%
+up to the top and there's a gap
+ 
+
+ align:start position:0%
+up to the top and there's a gap
+that's a different kind of material so
+
+ align:start position:0%
+that's a different kind of material so
+ 
+
+ align:start position:0%
+that's a different kind of material so
+if filling stops somewhere partially in
+
+ align:start position:0%
+if filling stops somewhere partially in
+ 
+
+ align:start position:0%
+if filling stops somewhere partially in
+the band in the middle of a band if
+
+ align:start position:0%
+the band in the middle of a band if
+ 
+
+ align:start position:0%
+the band in the middle of a band if
+you're filling you're counting
+
+ align:start position:0%
+you're filling you're counting
+ 
+
+ align:start position:0%
+you're filling you're counting
+and and you didn't go all the way up
+
+ align:start position:0%
+and and you didn't go all the way up
+ 
+
+ align:start position:0%
+and and you didn't go all the way up
+then you have a medal
+
+ align:start position:0%
+then you have a medal
+ 
+
+ align:start position:0%
+then you have a medal
+now but the thing is here we've only
+
+ align:start position:0%
+now but the thing is here we've only
+ 
+
+ align:start position:0%
+now but the thing is here we've only
+talked about one kind of band
+
+ align:start position:0%
+talked about one kind of band
+ 
+
+ align:start position:0%
+talked about one kind of band
+this is the s band what but every single
+
+ align:start position:0%
+this is the s band what but every single
+ 
+
+ align:start position:0%
+this is the s band what but every single
+one of these
+
+ align:start position:0%
+one of these
+ 
+
+ align:start position:0%
+one of these
+i can make i can make band look at this
+
+ align:start position:0%
+i can make i can make band look at this
+ 
+
+ align:start position:0%
+i can make i can make band look at this
+i can take
+
+ align:start position:0%
+i can take
+ 
+
+ align:start position:0%
+i can take
+a mole of orbitals and make an s
+
+ align:start position:0%
+a mole of orbitals and make an s
+ 
+
+ align:start position:0%
+a mole of orbitals and make an s
+band like that and then oh that was 1s
+
+ align:start position:0%
+band like that and then oh that was 1s
+ 
+
+ align:start position:0%
+band like that and then oh that was 1s
+here's 2s and look at this i can take
+
+ align:start position:0%
+here's 2s and look at this i can take
+ 
+
+ align:start position:0%
+here's 2s and look at this i can take
+the p electrons and make a p band
+
+ align:start position:0%
+the p electrons and make a p band
+ 
+
+ align:start position:0%
+the p electrons and make a p band
+p 2p band i can do this with every
+
+ align:start position:0%
+p 2p band i can do this with every
+ 
+
+ align:start position:0%
+p 2p band i can do this with every
+single 2s
+
+ align:start position:0%
+single 2s
+ 
+
+ align:start position:0%
+single 2s
+1s right so depending
+
+ align:start position:0%
+1s right so depending
+ 
+
+ align:start position:0%
+1s right so depending
+on a bunch of factors depending on a
+
+ align:start position:0%
+on a bunch of factors depending on a
+ 
+
+ align:start position:0%
+on a bunch of factors depending on a
+bunch of factors
+
+ align:start position:0%
+bunch of factors
+ 
+
+ align:start position:0%
+bunch of factors
+these bands could look different
+
+ align:start position:0%
+these bands could look different
+ 
+
+ align:start position:0%
+these bands could look different
+what does it depend on so this is yeah
+
+ align:start position:0%
+what does it depend on so this is yeah
+ 
+
+ align:start position:0%
+what does it depend on so this is yeah
+so the ba
+
+ align:start position:0%
+so the ba
+ 
+
+ align:start position:0%
+so the ba
+the way these bands are organized right
+
+ align:start position:0%
+the way these bands are organized right
+ 
+
+ align:start position:0%
+the way these bands are organized right
+we know now that
+
+ align:start position:0%
+we know now that
+ 
+
+ align:start position:0%
+we know now that
+that these orbitals will come together
+
+ align:start position:0%
+that these orbitals will come together
+ 
+
+ align:start position:0%
+that these orbitals will come together
+like i've drawn there and there
+
+ align:start position:0%
+like i've drawn there and there
+ 
+
+ align:start position:0%
+like i've drawn there and there
+and form bands what is the distance
+
+ align:start position:0%
+and form bands what is the distance
+ 
+
+ align:start position:0%
+and form bands what is the distance
+between these
+
+ align:start position:0%
+between these
+ 
+
+ align:start position:0%
+between these
+did they did they overlap maybe
+
+ align:start position:0%
+did they did they overlap maybe
+ 
+
+ align:start position:0%
+did they did they overlap maybe
+are they very far in energy right these
+
+ align:start position:0%
+are they very far in energy right these
+ 
+
+ align:start position:0%
+are they very far in energy right these
+things depend
+
+ align:start position:0%
+things depend
+ 
+
+ align:start position:0%
+things depend
+on adam
+
+ align:start position:0%
+on adam
+ 
+
+ align:start position:0%
+on adam
+depends on the atom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the bonding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the structure
+
+ align:start position:0%
+and the structure
+ 
+
+ align:start position:0%
+and the structure
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do those bands look well it depends
+
+ align:start position:0%
+how do those bands look well it depends
+ 
+
+ align:start position:0%
+how do those bands look well it depends
+and we'll be talking about some examples
+
+ align:start position:0%
+and we'll be talking about some examples
+ 
+
+ align:start position:0%
+and we'll be talking about some examples
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+for now i want to focus on that filling
+
+ align:start position:0%
+for now i want to focus on that filling
+ 
+
+ align:start position:0%
+for now i want to focus on that filling
+thing again
+
+ align:start position:0%
+thing again
+ 
+
+ align:start position:0%
+thing again
+on that filling thing what happens
+
+ align:start position:0%
+on that filling thing what happens
+ 
+
+ align:start position:0%
+on that filling thing what happens
+if i you know i just did hi you know if
+
+ align:start position:0%
+if i you know i just did hi you know if
+ 
+
+ align:start position:0%
+if i you know i just did hi you know if
+i fill this 1s
+
+ align:start position:0%
+i fill this 1s
+ 
+
+ align:start position:0%
+i fill this 1s
+up to halfway it's a metal if i keep
+
+ align:start position:0%
+up to halfway it's a metal if i keep
+ 
+
+ align:start position:0%
+up to halfway it's a metal if i keep
+filling keep adding electrons and i fill
+
+ align:start position:0%
+filling keep adding electrons and i fill
+ 
+
+ align:start position:0%
+filling keep adding electrons and i fill
+this up halfway
+
+ align:start position:0%
+this up halfway
+ 
+
+ align:start position:0%
+this up halfway
+it's a metal but if i
+
+ align:start position:0%
+it's a metal but if i
+ 
+
+ align:start position:0%
+it's a metal but if i
+stop filling you know if i fill this
+
+ align:start position:0%
+stop filling you know if i fill this
+ 
+
+ align:start position:0%
+stop filling you know if i fill this
+and then i fill this and then there's
+
+ align:start position:0%
+and then i fill this and then there's
+ 
+
+ align:start position:0%
+and then i fill this and then there's
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+some space in energy and i didn't fill
+
+ align:start position:0%
+some space in energy and i didn't fill
+ 
+
+ align:start position:0%
+some space in energy and i didn't fill
+anymore that's not a metal
+
+ align:start position:0%
+anymore that's not a metal
+ 
+
+ align:start position:0%
+anymore that's not a metal
+that's not a metal so if there's a gap
+
+ align:start position:0%
+that's not a metal so if there's a gap
+ 
+
+ align:start position:0%
+that's not a metal so if there's a gap
+so there can be gaps between bands
+
+ align:start position:0%
+so there can be gaps between bands
+ 
+
+ align:start position:0%
+so there can be gaps between bands
+which i just showed you that's between
+
+ align:start position:0%
+which i just showed you that's between
+ 
+
+ align:start position:0%
+which i just showed you that's between
+an s and a p band
+
+ align:start position:0%
+an s and a p band
+ 
+
+ align:start position:0%
+an s and a p band
+right and then the filling determines
+
+ align:start position:0%
+right and then the filling determines
+ 
+
+ align:start position:0%
+right and then the filling determines
+the properties and they're so
+
+ align:start position:0%
+the properties and they're so
+ 
+
+ align:start position:0%
+the properties and they're so
+important right they're so important so
+
+ align:start position:0%
+important right they're so important so
+ 
+
+ align:start position:0%
+important right they're so important so
+let's talk about that i want to talk
+
+ align:start position:0%
+let's talk about that i want to talk
+ 
+
+ align:start position:0%
+let's talk about that i want to talk
+about these
+
+ align:start position:0%
+about these
+ 
+
+ align:start position:0%
+about these
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+semiconductors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today and wednesday and medals on friday
+
+ align:start position:0%
+today and wednesday and medals on friday
+ 
+
+ align:start position:0%
+today and wednesday and medals on friday
+okay and we're going to see it through
+
+ align:start position:0%
+okay and we're going to see it through
+ 
+
+ align:start position:0%
+okay and we're going to see it through
+the vantage point of these electronic
+
+ align:start position:0%
+the vantage point of these electronic
+ 
+
+ align:start position:0%
+the vantage point of these electronic
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+and the next week we'll see it through
+
+ align:start position:0%
+and the next week we'll see it through
+ 
+
+ align:start position:0%
+and the next week we'll see it through
+the vantage point of atoms
+
+ align:start position:0%
+the vantage point of atoms
+ 
+
+ align:start position:0%
+the vantage point of atoms
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+if you have a gap well you always have
+
+ align:start position:0%
+if you have a gap well you always have
+ 
+
+ align:start position:0%
+if you have a gap well you always have
+gaps the question again comes to filling
+
+ align:start position:0%
+gaps the question again comes to filling
+ 
+
+ align:start position:0%
+gaps the question again comes to filling
+if the filling stops right if the
+
+ align:start position:0%
+if the filling stops right if the
+ 
+
+ align:start position:0%
+if the filling stops right if the
+filling stops
+
+ align:start position:0%
+filling stops
+ 
+
+ align:start position:0%
+filling stops
+uh let me write i want to define this
+
+ align:start position:0%
+uh let me write i want to define this
+ 
+
+ align:start position:0%
+uh let me write i want to define this
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+importantly so if the filling stops
+
+ align:start position:0%
+importantly so if the filling stops
+ 
+
+ align:start position:0%
+importantly so if the filling stops
+then you have this highest occupied
+
+ align:start position:0%
+then you have this highest occupied
+ 
+
+ align:start position:0%
+then you have this highest occupied
+level so let's suppose i have
+
+ align:start position:0%
+level so let's suppose i have
+ 
+
+ align:start position:0%
+level so let's suppose i have
+filling this is some band
+
+ align:start position:0%
+filling this is some band
+ 
+
+ align:start position:0%
+filling this is some band
+and this is some band and this is
+
+ align:start position:0%
+and this is some band and this is
+ 
+
+ align:start position:0%
+and this is some band and this is
+unoccupied
+
+ align:start position:0%
+unoccupied
+ 
+
+ align:start position:0%
+unoccupied
+so unoccupied by electrons
+
+ align:start position:0%
+so unoccupied by electrons
+ 
+
+ align:start position:0%
+so unoccupied by electrons
+this is fully occupied
+
+ align:start position:0%
+this is fully occupied
+ 
+
+ align:start position:0%
+this is fully occupied
+by electrons now
+
+ align:start position:0%
+by electrons now
+ 
+
+ align:start position:0%
+by electrons now
+so what's going to happen well first of
+
+ align:start position:0%
+so what's going to happen well first of
+ 
+
+ align:start position:0%
+so what's going to happen well first of
+all let's just get some
+
+ align:start position:0%
+all let's just get some
+ 
+
+ align:start position:0%
+all let's just get some
+some terms the last band
+
+ align:start position:0%
+some terms the last band
+ 
+
+ align:start position:0%
+some terms the last band
+that i filled the last band that i
+
+ align:start position:0%
+that i filled the last band that i
+ 
+
+ align:start position:0%
+that i filled the last band that i
+filled is called the valence band
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valence band and
+
+ align:start position:0%
+valence band and
+ 
+
+ align:start position:0%
+valence band and
+we use vb for short and
+
+ align:start position:0%
+we use vb for short and
+ 
+
+ align:start position:0%
+we use vb for short and
+the first band that i don't fill is
+
+ align:start position:0%
+the first band that i don't fill is
+ 
+
+ align:start position:0%
+the first band that i don't fill is
+called the conduction band
+
+ align:start position:0%
+called the conduction band
+ 
+
+ align:start position:0%
+called the conduction band
+and as we talk more about these
+
+ align:start position:0%
+and as we talk more about these
+ 
+
+ align:start position:0%
+and as we talk more about these
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+you will see why they're called that
+
+ align:start position:0%
+you will see why they're called that
+ 
+
+ align:start position:0%
+you will see why they're called that
+conduction band
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but for now just just trust me in the in
+
+ align:start position:0%
+but for now just just trust me in the in
+ 
+
+ align:start position:0%
+but for now just just trust me in the in
+the labeling so
+
+ align:start position:0%
+the labeling so
+ 
+
+ align:start position:0%
+the labeling so
+the conduction band and the valence band
+
+ align:start position:0%
+the conduction band and the valence band
+ 
+
+ align:start position:0%
+the conduction band and the valence band
+depend on the filling
+
+ align:start position:0%
+depend on the filling
+ 
+
+ align:start position:0%
+depend on the filling
+because again it's you know it's where i
+
+ align:start position:0%
+because again it's you know it's where i
+ 
+
+ align:start position:0%
+because again it's you know it's where i
+filled two now
+
+ align:start position:0%
+filled two now
+ 
+
+ align:start position:0%
+filled two now
+the top level the very very top level
+
+ align:start position:0%
+the top level the very very top level
+ 
+
+ align:start position:0%
+the top level the very very top level
+out of these 10 to the 24th level
+
+ align:start position:0%
+out of these 10 to the 24th level
+ 
+
+ align:start position:0%
+out of these 10 to the 24th level
+that very top one has a special name
+
+ align:start position:0%
+that very top one has a special name
+ 
+
+ align:start position:0%
+that very top one has a special name
+it's the vb
+
+ align:start position:0%
+it's the vb
+ 
+
+ align:start position:0%
+it's the vb
+maximum that makes sense right it's the
+
+ align:start position:0%
+maximum that makes sense right it's the
+ 
+
+ align:start position:0%
+maximum that makes sense right it's the
+top valence band or the vbn
+
+ align:start position:0%
+top valence band or the vbn
+ 
+
+ align:start position:0%
+top valence band or the vbn
+and the one down here also has a special
+
+ align:start position:0%
+and the one down here also has a special
+ 
+
+ align:start position:0%
+and the one down here also has a special
+name it's the cb
+
+ align:start position:0%
+name it's the cb
+ 
+
+ align:start position:0%
+name it's the cb
+minimum minimum
+
+ align:start position:0%
+minimum minimum
+ 
+
+ align:start position:0%
+minimum minimum
+or cbm
+
+ align:start position:0%
+or cbm
+ 
+
+ align:start position:0%
+or cbm
+so the valence band maximum and the
+
+ align:start position:0%
+so the valence band maximum and the
+ 
+
+ align:start position:0%
+so the valence band maximum and the
+conduction minimum are
+
+ align:start position:0%
+conduction minimum are
+ 
+
+ align:start position:0%
+conduction minimum are
+you know it tells you if you think about
+
+ align:start position:0%
+you know it tells you if you think about
+ 
+
+ align:start position:0%
+you know it tells you if you think about
+it it tells you
+
+ align:start position:0%
+it it tells you
+ 
+
+ align:start position:0%
+it it tells you
+if you subtracted those energies between
+
+ align:start position:0%
+if you subtracted those energies between
+ 
+
+ align:start position:0%
+if you subtracted those energies between
+those parts of the band
+
+ align:start position:0%
+those parts of the band
+ 
+
+ align:start position:0%
+those parts of the band
+you'd get the distance and energy
+
+ align:start position:0%
+you'd get the distance and energy
+ 
+
+ align:start position:0%
+you'd get the distance and energy
+between the two bands right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the conduction band minimum is
+
+ align:start position:0%
+right so the conduction band minimum is
+ 
+
+ align:start position:0%
+right so the conduction band minimum is
+this energy level here
+
+ align:start position:0%
+this energy level here
+ 
+
+ align:start position:0%
+this energy level here
+and the valence band maximum energy now
+
+ align:start position:0%
+and the valence band maximum energy now
+ 
+
+ align:start position:0%
+and the valence band maximum energy now
+remember valence electro it's called the
+
+ align:start position:0%
+remember valence electro it's called the
+ 
+
+ align:start position:0%
+remember valence electro it's called the
+valence band it makes sense because
+
+ align:start position:0%
+valence band it makes sense because
+ 
+
+ align:start position:0%
+valence band it makes sense because
+valence electrons
+
+ align:start position:0%
+valence electrons
+ 
+
+ align:start position:0%
+valence electrons
+remember are those ones as we talked
+
+ align:start position:0%
+remember are those ones as we talked
+ 
+
+ align:start position:0%
+remember are those ones as we talked
+about with lewis where
+
+ align:start position:0%
+about with lewis where
+ 
+
+ align:start position:0%
+about with lewis where
+you're you know you've got kind of the
+
+ align:start position:0%
+you're you know you've got kind of the
+ 
+
+ align:start position:0%
+you're you know you've got kind of the
+bonding and the action and the chemistry
+
+ align:start position:0%
+bonding and the action and the chemistry
+ 
+
+ align:start position:0%
+bonding and the action and the chemistry
+happening and so this is that top most
+
+ align:start position:0%
+happening and so this is that top most
+ 
+
+ align:start position:0%
+happening and so this is that top most
+state of the topmost valence band
+
+ align:start position:0%
+state of the topmost valence band
+ 
+
+ align:start position:0%
+state of the topmost valence band
+all right this is the valence band
+
+ align:start position:0%
+all right this is the valence band
+ 
+
+ align:start position:0%
+all right this is the valence band
+topmost state okay
+
+ align:start position:0%
+topmost state okay
+ 
+
+ align:start position:0%
+topmost state okay
+and there's one more definition we got
+
+ align:start position:0%
+and there's one more definition we got
+ 
+
+ align:start position:0%
+and there's one more definition we got
+to know about this is why we're setting
+
+ align:start position:0%
+to know about this is why we're setting
+ 
+
+ align:start position:0%
+to know about this is why we're setting
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+up which is that that energy difference
+
+ align:start position:0%
+up which is that that energy difference
+ 
+
+ align:start position:0%
+up which is that that energy difference
+here oh
+
+ align:start position:0%
+here oh
+ 
+
+ align:start position:0%
+here oh
+that is really important so
+
+ align:start position:0%
+that is really important so
+ 
+
+ align:start position:0%
+that is really important so
+the energy of the conduction band
+
+ align:start position:0%
+the energy of the conduction band
+ 
+
+ align:start position:0%
+the energy of the conduction band
+minimum
+
+ align:start position:0%
+minimum
+ 
+
+ align:start position:0%
+minimum
+minus the energy of the valence band
+
+ align:start position:0%
+minus the energy of the valence band
+ 
+
+ align:start position:0%
+minus the energy of the valence band
+maximum
+
+ align:start position:0%
+maximum
+ 
+
+ align:start position:0%
+maximum
+is equal to something called the band
+
+ align:start position:0%
+is equal to something called the band
+ 
+
+ align:start position:0%
+is equal to something called the band
+gap
+
+ align:start position:0%
+gap
+ 
+
+ align:start position:0%
+gap
+energy gap it's the band gap
+
+ align:start position:0%
+energy gap it's the band gap
+ 
+
+ align:start position:0%
+energy gap it's the band gap
+band this is an extremely
+
+ align:start position:0%
+band this is an extremely
+ 
+
+ align:start position:0%
+band this is an extremely
+important property of materials
+
+ align:start position:0%
+important property of materials
+ 
+
+ align:start position:0%
+important property of materials
+the electronic band gap okay
+
+ align:start position:0%
+the electronic band gap okay
+ 
+
+ align:start position:0%
+the electronic band gap okay
+what is the energy difference between
+
+ align:start position:0%
+what is the energy difference between
+ 
+
+ align:start position:0%
+what is the energy difference between
+the highest occupied
+
+ align:start position:0%
+the highest occupied
+ 
+
+ align:start position:0%
+the highest occupied
+electrons and the lowest unoccupied
+
+ align:start position:0%
+electrons and the lowest unoccupied
+ 
+
+ align:start position:0%
+electrons and the lowest unoccupied
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+that's what we're talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if
+
+ align:start position:0%
+so if
+ 
+
+ align:start position:0%
+so if
+that filling if that distance okay so
+
+ align:start position:0%
+that filling if that distance okay so
+ 
+
+ align:start position:0%
+that filling if that distance okay so
+here's
+
+ align:start position:0%
+here's
+ 
+
+ align:start position:0%
+here's
+here's an element carbon in the diamond
+
+ align:start position:0%
+here's an element carbon in the diamond
+ 
+
+ align:start position:0%
+here's an element carbon in the diamond
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+and just not purple is filled
+
+ align:start position:0%
+and just not purple is filled
+ 
+
+ align:start position:0%
+and just not purple is filled
+and not purple is not filled so so you
+
+ align:start position:0%
+and not purple is not filled so so you
+ 
+
+ align:start position:0%
+and not purple is not filled so so you
+know that that's the conduction band
+
+ align:start position:0%
+know that that's the conduction band
+ 
+
+ align:start position:0%
+know that that's the conduction band
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and that's the valence band and the band
+
+ align:start position:0%
+and that's the valence band and the band
+ 
+
+ align:start position:0%
+and that's the valence band and the band
+gap which we've just defined here
+
+ align:start position:0%
+gap which we've just defined here
+ 
+
+ align:start position:0%
+gap which we've just defined here
+is the energy difference between those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for diamond it's really large for
+
+ align:start position:0%
+and for diamond it's really large for
+ 
+
+ align:start position:0%
+and for diamond it's really large for
+diamond it's really large
+
+ align:start position:0%
+diamond it's really large
+ 
+
+ align:start position:0%
+diamond it's really large
+so you can see that in fact
+
+ align:start position:0%
+so you can see that in fact
+ 
+
+ align:start position:0%
+so you can see that in fact
+the gap is over if we converted this to
+
+ align:start position:0%
+the gap is over if we converted this to
+ 
+
+ align:start position:0%
+the gap is over if we converted this to
+electron volts it's more than
+
+ align:start position:0%
+electron volts it's more than
+ 
+
+ align:start position:0%
+electron volts it's more than
+is more than five electron volts more
+
+ align:start position:0%
+is more than five electron volts more
+ 
+
+ align:start position:0%
+is more than five electron volts more
+than five electron volts
+
+ align:start position:0%
+than five electron volts
+ 
+
+ align:start position:0%
+than five electron volts
+all right now i mentioned thermal energy
+
+ align:start position:0%
+all right now i mentioned thermal energy
+ 
+
+ align:start position:0%
+all right now i mentioned thermal energy
+in answer to the question about water
+
+ align:start position:0%
+in answer to the question about water
+ 
+
+ align:start position:0%
+in answer to the question about water
+right and room temperature so room
+
+ align:start position:0%
+right and room temperature so room
+ 
+
+ align:start position:0%
+right and room temperature so room
+temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the energy of room temperature if you
+
+ align:start position:0%
+the energy of room temperature if you
+ 
+
+ align:start position:0%
+the energy of room temperature if you
+think about temperature as
+
+ align:start position:0%
+think about temperature as
+ 
+
+ align:start position:0%
+think about temperature as
+as an energy of like vibrational motion
+
+ align:start position:0%
+as an energy of like vibrational motion
+ 
+
+ align:start position:0%
+as an energy of like vibrational motion
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and you can do that right you use
+
+ align:start position:0%
+and you can do that right you use
+ 
+
+ align:start position:0%
+and you can do that right you use
+something called the boltzmann constant
+
+ align:start position:0%
+something called the boltzmann constant
+ 
+
+ align:start position:0%
+something called the boltzmann constant
+and you can get what the room
+
+ align:start position:0%
+and you can get what the room
+ 
+
+ align:start position:0%
+and you can get what the room
+temperature energy is and it's something
+
+ align:start position:0%
+temperature energy is and it's something
+ 
+
+ align:start position:0%
+temperature energy is and it's something
+like 0.025 electron volts
+
+ align:start position:0%
+like 0.025 electron volts
+ 
+
+ align:start position:0%
+like 0.025 electron volts
+seems pretty small so the point is if
+
+ align:start position:0%
+seems pretty small so the point is if
+ 
+
+ align:start position:0%
+seems pretty small so the point is if
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+if that's the energy the thermal energy
+
+ align:start position:0%
+if that's the energy the thermal energy
+ 
+
+ align:start position:0%
+if that's the energy the thermal energy
+i have at room temperature
+
+ align:start position:0%
+i have at room temperature
+ 
+
+ align:start position:0%
+i have at room temperature
+then if my band gap is so much larger
+
+ align:start position:0%
+then if my band gap is so much larger
+ 
+
+ align:start position:0%
+then if my band gap is so much larger
+than that
+
+ align:start position:0%
+than that
+ 
+
+ align:start position:0%
+than that
+is so much larger than that it means
+
+ align:start position:0%
+is so much larger than that it means
+ 
+
+ align:start position:0%
+is so much larger than that it means
+those electrons are always going to be
+
+ align:start position:0%
+those electrons are always going to be
+ 
+
+ align:start position:0%
+those electrons are always going to be
+stuck
+
+ align:start position:0%
+stuck
+ 
+
+ align:start position:0%
+stuck
+they're never going to even in some
+
+ align:start position:0%
+they're never going to even in some
+ 
+
+ align:start position:0%
+they're never going to even in some
+accident
+
+ align:start position:0%
+accident
+ 
+
+ align:start position:0%
+accident
+have enough thermal energy to come up
+
+ align:start position:0%
+have enough thermal energy to come up
+ 
+
+ align:start position:0%
+have enough thermal energy to come up
+and be
+
+ align:start position:0%
+and be
+ 
+
+ align:start position:0%
+and be
+excited yeah we'll talk about this later
+
+ align:start position:0%
+excited yeah we'll talk about this later
+ 
+
+ align:start position:0%
+excited yeah we'll talk about this later
+so they're really stuck and and if if an
+
+ align:start position:0%
+so they're really stuck and and if if an
+ 
+
+ align:start position:0%
+so they're really stuck and and if if an
+electron is in the valence band it can't
+
+ align:start position:0%
+electron is in the valence band it can't
+ 
+
+ align:start position:0%
+electron is in the valence band it can't
+move very well
+
+ align:start position:0%
+move very well
+ 
+
+ align:start position:0%
+move very well
+it can't move it's kind of stuck in
+
+ align:start position:0%
+it can't move it's kind of stuck in
+ 
+
+ align:start position:0%
+it can't move it's kind of stuck in
+those bonds
+
+ align:start position:0%
+those bonds
+ 
+
+ align:start position:0%
+those bonds
+it's kind of stuck in those bonds and so
+
+ align:start position:0%
+it's kind of stuck in those bonds and so
+ 
+
+ align:start position:0%
+it's kind of stuck in those bonds and so
+here if there's electrons all stuck here
+
+ align:start position:0%
+here if there's electrons all stuck here
+ 
+
+ align:start position:0%
+here if there's electrons all stuck here
+and they never have a chance to go up
+
+ align:start position:0%
+and they never have a chance to go up
+ 
+
+ align:start position:0%
+and they never have a chance to go up
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+where they can travel freely this is
+
+ align:start position:0%
+where they can travel freely this is
+ 
+
+ align:start position:0%
+where they can travel freely this is
+really going to be an insulator
+
+ align:start position:0%
+really going to be an insulator
+ 
+
+ align:start position:0%
+really going to be an insulator
+this is not going to carry electrons
+
+ align:start position:0%
+this is not going to carry electrons
+ 
+
+ align:start position:0%
+this is not going to carry electrons
+through the material
+
+ align:start position:0%
+through the material
+ 
+
+ align:start position:0%
+through the material
+so that's an insulator when you have a
+
+ align:start position:0%
+so that's an insulator when you have a
+ 
+
+ align:start position:0%
+so that's an insulator when you have a
+very large band gap like that
+
+ align:start position:0%
+very large band gap like that
+ 
+
+ align:start position:0%
+very large band gap like that
+we call that an insulator
+
+ align:start position:0%
+we call that an insulator
+ 
+
+ align:start position:0%
+we call that an insulator
+okay but see if we compare and this is
+
+ align:start position:0%
+okay but see if we compare and this is
+ 
+
+ align:start position:0%
+okay but see if we compare and this is
+interesting you're just going down
+
+ align:start position:0%
+interesting you're just going down
+ 
+
+ align:start position:0%
+interesting you're just going down
+in the periodic table if you compare
+
+ align:start position:0%
+in the periodic table if you compare
+ 
+
+ align:start position:0%
+in the periodic table if you compare
+diamond to silicon
+
+ align:start position:0%
+diamond to silicon
+ 
+
+ align:start position:0%
+diamond to silicon
+to germanium right well see
+
+ align:start position:0%
+to germanium right well see
+ 
+
+ align:start position:0%
+to germanium right well see
+what happens is the band gap gets
+
+ align:start position:0%
+what happens is the band gap gets
+ 
+
+ align:start position:0%
+what happens is the band gap gets
+smaller i'm still
+
+ align:start position:0%
+smaller i'm still
+ 
+
+ align:start position:0%
+smaller i'm still
+filling them all the way up to the top
+
+ align:start position:0%
+filling them all the way up to the top
+ 
+
+ align:start position:0%
+filling them all the way up to the top
+of a band
+
+ align:start position:0%
+of a band
+ 
+
+ align:start position:0%
+of a band
+so i'm not a metal if i'm a metal
+
+ align:start position:0%
+so i'm not a metal if i'm a metal
+ 
+
+ align:start position:0%
+so i'm not a metal if i'm a metal
+it's because my filling stops somewhere
+
+ align:start position:0%
+it's because my filling stops somewhere
+ 
+
+ align:start position:0%
+it's because my filling stops somewhere
+in the middle of a band
+
+ align:start position:0%
+in the middle of a band
+ 
+
+ align:start position:0%
+in the middle of a band
+so i'm not a metal i'm a semiconductor
+
+ align:start position:0%
+so i'm not a metal i'm a semiconductor
+ 
+
+ align:start position:0%
+so i'm not a metal i'm a semiconductor
+and not an insulator and the reason i'm
+
+ align:start position:0%
+and not an insulator and the reason i'm
+ 
+
+ align:start position:0%
+and not an insulator and the reason i'm
+a semiconductor
+
+ align:start position:0%
+a semiconductor
+ 
+
+ align:start position:0%
+a semiconductor
+is that my band gap is kind of small
+
+ align:start position:0%
+is that my band gap is kind of small
+ 
+
+ align:start position:0%
+is that my band gap is kind of small
+enough so that
+
+ align:start position:0%
+enough so that
+ 
+
+ align:start position:0%
+enough so that
+electrons can kind of jump from here up
+
+ align:start position:0%
+electrons can kind of jump from here up
+ 
+
+ align:start position:0%
+electrons can kind of jump from here up
+to there
+
+ align:start position:0%
+to there
+ 
+
+ align:start position:0%
+to there
+sometimes sometimes
+
+ align:start position:0%
+sometimes sometimes
+ 
+
+ align:start position:0%
+sometimes sometimes
+that's why it's called a semiconductor
+
+ align:start position:0%
+that's why it's called a semiconductor
+ 
+
+ align:start position:0%
+that's why it's called a semiconductor
+there they kind of conduct electrons
+
+ align:start position:0%
+there they kind of conduct electrons
+ 
+
+ align:start position:0%
+there they kind of conduct electrons
+right so the electron
+
+ align:start position:0%
+right so the electron
+ 
+
+ align:start position:0%
+right so the electron
+can get up to the conduction band in a
+
+ align:start position:0%
+can get up to the conduction band in a
+ 
+
+ align:start position:0%
+can get up to the conduction band in a
+semiconductor
+
+ align:start position:0%
+semiconductor
+ 
+
+ align:start position:0%
+semiconductor
+more easily than an insulator and that's
+
+ align:start position:0%
+more easily than an insulator and that's
+ 
+
+ align:start position:0%
+more easily than an insulator and that's
+why it can conduct
+
+ align:start position:0%
+why it can conduct
+ 
+
+ align:start position:0%
+why it can conduct
+electricity much better than an
+
+ align:start position:0%
+electricity much better than an
+ 
+
+ align:start position:0%
+electricity much better than an
+insulator many many many orders of
+
+ align:start position:0%
+insulator many many many orders of
+ 
+
+ align:start position:0%
+insulator many many many orders of
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+but the way that we have talked about
+
+ align:start position:0%
+but the way that we have talked about
+ 
+
+ align:start position:0%
+but the way that we have talked about
+getting electrons
+
+ align:start position:0%
+getting electrons
+ 
+
+ align:start position:0%
+getting electrons
+excited getting electrons excited is
+
+ align:start position:0%
+excited getting electrons excited is
+ 
+
+ align:start position:0%
+excited getting electrons excited is
+with light
+
+ align:start position:0%
+with light
+ 
+
+ align:start position:0%
+with light
+and we can do that for solids too we can
+
+ align:start position:0%
+and we can do that for solids too we can
+ 
+
+ align:start position:0%
+and we can do that for solids too we can
+do the same thing for solids
+
+ align:start position:0%
+do the same thing for solids
+ 
+
+ align:start position:0%
+do the same thing for solids
+right and so if i if i plot
+
+ align:start position:0%
+right and so if i if i plot
+ 
+
+ align:start position:0%
+right and so if i if i plot
+the absorption if i take a solid
+
+ align:start position:0%
+the absorption if i take a solid
+ 
+
+ align:start position:0%
+the absorption if i take a solid
+and i shine light on it there's
+
+ align:start position:0%
+and i shine light on it there's
+ 
+
+ align:start position:0%
+and i shine light on it there's
+something called the absorption
+
+ align:start position:0%
+something called the absorption
+ 
+
+ align:start position:0%
+something called the absorption
+coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the absorption coefficient which is
+
+ align:start position:0%
+the absorption coefficient which is
+ 
+
+ align:start position:0%
+the absorption coefficient which is
+really just
+
+ align:start position:0%
+really just
+ 
+
+ align:start position:0%
+really just
+a measure of how you know
+
+ align:start position:0%
+a measure of how you know
+ 
+
+ align:start position:0%
+a measure of how you know
+how far down into the solid did that
+
+ align:start position:0%
+how far down into the solid did that
+ 
+
+ align:start position:0%
+how far down into the solid did that
+light have to go
+
+ align:start position:0%
+light have to go
+ 
+
+ align:start position:0%
+light have to go
+before some electron got excited by it
+
+ align:start position:0%
+before some electron got excited by it
+ 
+
+ align:start position:0%
+before some electron got excited by it
+how well does it well okay different
+
+ align:start position:0%
+how well does it well okay different
+ 
+
+ align:start position:0%
+how well does it well okay different
+solids can absorb
+
+ align:start position:0%
+solids can absorb
+ 
+
+ align:start position:0%
+solids can absorb
+electrons differently but the main point
+
+ align:start position:0%
+electrons differently but the main point
+ 
+
+ align:start position:0%
+electrons differently but the main point
+is if i plot that versus energy
+
+ align:start position:0%
+is if i plot that versus energy
+ 
+
+ align:start position:0%
+is if i plot that versus energy
+you know for something like silicon
+
+ align:start position:0%
+you know for something like silicon
+ 
+
+ align:start position:0%
+you know for something like silicon
+the band gap of silicon is 1.1 ev
+
+ align:start position:0%
+the band gap of silicon is 1.1 ev
+ 
+
+ align:start position:0%
+the band gap of silicon is 1.1 ev
+so that's what it would look like for
+
+ align:start position:0%
+so that's what it would look like for
+ 
+
+ align:start position:0%
+so that's what it would look like for
+silicon because you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this should be wavelength
+
+ align:start position:0%
+this should be wavelength
+ 
+
+ align:start position:0%
+this should be wavelength
+wavelength because you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because as you get to lower so you know
+
+ align:start position:0%
+because as you get to lower so you know
+ 
+
+ align:start position:0%
+because as you get to lower so you know
+that above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's exactly like for atoms if i shine
+
+ align:start position:0%
+it's exactly like for atoms if i shine
+ 
+
+ align:start position:0%
+it's exactly like for atoms if i shine
+light like remember the bohr model if i
+
+ align:start position:0%
+light like remember the bohr model if i
+ 
+
+ align:start position:0%
+light like remember the bohr model if i
+shine light
+
+ align:start position:0%
+shine light
+ 
+
+ align:start position:0%
+shine light
+on an atom that has enough energy to
+
+ align:start position:0%
+on an atom that has enough energy to
+ 
+
+ align:start position:0%
+on an atom that has enough energy to
+promote it up
+
+ align:start position:0%
+promote it up
+ 
+
+ align:start position:0%
+promote it up
+then it can go right but the difference
+
+ align:start position:0%
+then it can go right but the difference
+ 
+
+ align:start position:0%
+then it can go right but the difference
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is that for silicon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see for silicon that's right there for
+
+ align:start position:0%
+see for silicon that's right there for
+ 
+
+ align:start position:0%
+see for silicon that's right there for
+silicon there's this big empty space
+
+ align:start position:0%
+silicon there's this big empty space
+ 
+
+ align:start position:0%
+silicon there's this big empty space
+with no bands
+
+ align:start position:0%
+with no bands
+ 
+
+ align:start position:0%
+with no bands
+it's just like the atom when there's no
+
+ align:start position:0%
+it's just like the atom when there's no
+ 
+
+ align:start position:0%
+it's just like the atom when there's no
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+i cannot have an electron there
+
+ align:start position:0%
+i cannot have an electron there
+ 
+
+ align:start position:0%
+i cannot have an electron there
+i'm stuck so the electron can be here or
+
+ align:start position:0%
+i'm stuck so the electron can be here or
+ 
+
+ align:start position:0%
+i'm stuck so the electron can be here or
+it can be here
+
+ align:start position:0%
+it can be here
+ 
+
+ align:start position:0%
+it can be here
+and so the light the energy of the light
+
+ align:start position:0%
+and so the light the energy of the light
+ 
+
+ align:start position:0%
+and so the light the energy of the light
+has to be at least the band gap
+
+ align:start position:0%
+has to be at least the band gap
+ 
+
+ align:start position:0%
+has to be at least the band gap
+to get it up at least the band gap to
+
+ align:start position:0%
+to get it up at least the band gap to
+ 
+
+ align:start position:0%
+to get it up at least the band gap to
+get it up
+
+ align:start position:0%
+get it up
+ 
+
+ align:start position:0%
+get it up
+right so what that means is that if i
+
+ align:start position:0%
+right so what that means is that if i
+ 
+
+ align:start position:0%
+right so what that means is that if i
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+so why does this go to zero with with
+
+ align:start position:0%
+so why does this go to zero with with
+ 
+
+ align:start position:0%
+so why does this go to zero with with
+increasing wavelength what it means is
+
+ align:start position:0%
+increasing wavelength what it means is
+ 
+
+ align:start position:0%
+increasing wavelength what it means is
+that if my
+
+ align:start position:0%
+that if my
+ 
+
+ align:start position:0%
+that if my
+valence band looks like this and my
+
+ align:start position:0%
+valence band looks like this and my
+ 
+
+ align:start position:0%
+valence band looks like this and my
+conduction band looks like this
+
+ align:start position:0%
+conduction band looks like this
+ 
+
+ align:start position:0%
+conduction band looks like this
+yeah and now my light is coming and i
+
+ align:start position:0%
+yeah and now my light is coming and i
+ 
+
+ align:start position:0%
+yeah and now my light is coming and i
+want to take an electron and promote it
+
+ align:start position:0%
+want to take an electron and promote it
+ 
+
+ align:start position:0%
+want to take an electron and promote it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+well it cannot be the electron
+
+ align:start position:0%
+well it cannot be the electron
+ 
+
+ align:start position:0%
+well it cannot be the electron
+cannot be cannot exist
+
+ align:start position:0%
+cannot be cannot exist
+ 
+
+ align:start position:0%
+cannot be cannot exist
+in side the band gap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's no states there it's just like
+
+ align:start position:0%
+there's no states there it's just like
+ 
+
+ align:start position:0%
+there's no states there it's just like
+we talked about with atoms
+
+ align:start position:0%
+we talked about with atoms
+ 
+
+ align:start position:0%
+we talked about with atoms
+but now we've got almost infinite states
+
+ align:start position:0%
+but now we've got almost infinite states
+ 
+
+ align:start position:0%
+but now we've got almost infinite states
+here no states there
+
+ align:start position:0%
+here no states there
+ 
+
+ align:start position:0%
+here no states there
+and then again we start with infinite
+
+ align:start position:0%
+and then again we start with infinite
+ 
+
+ align:start position:0%
+and then again we start with infinite
+places where it can be
+
+ align:start position:0%
+places where it can be
+ 
+
+ align:start position:0%
+places where it can be
+right what that means is that if i shine
+
+ align:start position:0%
+right what that means is that if i shine
+ 
+
+ align:start position:0%
+right what that means is that if i shine
+light on it the only way silicon
+
+ align:start position:0%
+light on it the only way silicon
+ 
+
+ align:start position:0%
+light on it the only way silicon
+the only way it can absorb this light is
+
+ align:start position:0%
+the only way it can absorb this light is
+ 
+
+ align:start position:0%
+the only way it can absorb this light is
+if the light has
+
+ align:start position:0%
+if the light has
+ 
+
+ align:start position:0%
+if the light has
+energy greater than the band gap
+
+ align:start position:0%
+energy greater than the band gap
+ 
+
+ align:start position:0%
+energy greater than the band gap
+or wavelength less than the band gap
+
+ align:start position:0%
+or wavelength less than the band gap
+ 
+
+ align:start position:0%
+or wavelength less than the band gap
+that's why
+
+ align:start position:0%
+that's why
+ 
+
+ align:start position:0%
+that's why
+i drew it that way right so it goes to
+
+ align:start position:0%
+i drew it that way right so it goes to
+ 
+
+ align:start position:0%
+i drew it that way right so it goes to
+zero so it's going to absorb in
+
+ align:start position:0%
+zero so it's going to absorb in
+ 
+
+ align:start position:0%
+zero so it's going to absorb in
+wavelength up to a certain point
+
+ align:start position:0%
+wavelength up to a certain point
+ 
+
+ align:start position:0%
+wavelength up to a certain point
+and then if i go higher in wavelength
+
+ align:start position:0%
+and then if i go higher in wavelength
+ 
+
+ align:start position:0%
+and then if i go higher in wavelength
+those are energies that are too small
+
+ align:start position:0%
+those are energies that are too small
+ 
+
+ align:start position:0%
+those are energies that are too small
+it's going to like try to absorb here
+
+ align:start position:0%
+it's going to like try to absorb here
+ 
+
+ align:start position:0%
+it's going to like try to absorb here
+but there's nowhere to absorb to
+
+ align:start position:0%
+but there's nowhere to absorb to
+ 
+
+ align:start position:0%
+but there's nowhere to absorb to
+so it can't right but if it has enough
+
+ align:start position:0%
+so it can't right but if it has enough
+ 
+
+ align:start position:0%
+so it can't right but if it has enough
+energy oh look at this
+
+ align:start position:0%
+energy oh look at this
+ 
+
+ align:start position:0%
+energy oh look at this
+this is also different i could absorb
+
+ align:start position:0%
+this is also different i could absorb
+ 
+
+ align:start position:0%
+this is also different i could absorb
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+or here or here i can take all those
+
+ align:start position:0%
+or here or here i can take all those
+ 
+
+ align:start position:0%
+or here or here i can take all those
+higher energies and absorb
+
+ align:start position:0%
+higher energies and absorb
+ 
+
+ align:start position:0%
+higher energies and absorb
+light kind of continuously
+
+ align:start position:0%
+light kind of continuously
+ 
+
+ align:start position:0%
+light kind of continuously
+unlike in the atom where it could only
+
+ align:start position:0%
+unlike in the atom where it could only
+ 
+
+ align:start position:0%
+unlike in the atom where it could only
+be the level to hop you from n
+
+ align:start position:0%
+be the level to hop you from n
+ 
+
+ align:start position:0%
+be the level to hop you from n
+equals two to n equals four right but
+
+ align:start position:0%
+equals two to n equals four right but
+ 
+
+ align:start position:0%
+equals two to n equals four right but
+here i have
+
+ align:start position:0%
+here i have
+ 
+
+ align:start position:0%
+here i have
+an almost continuous set of states
+
+ align:start position:0%
+an almost continuous set of states
+ 
+
+ align:start position:0%
+an almost continuous set of states
+except in the band gap where i have no
+
+ align:start position:0%
+except in the band gap where i have no
+ 
+
+ align:start position:0%
+except in the band gap where i have no
+states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's what the absorption would look
+
+ align:start position:0%
+so that's what the absorption would look
+ 
+
+ align:start position:0%
+so that's what the absorption would look
+like for silicon
+
+ align:start position:0%
+like for silicon
+ 
+
+ align:start position:0%
+like for silicon
+and if you look at the band gap this
+
+ align:start position:0%
+and if you look at the band gap this
+ 
+
+ align:start position:0%
+and if you look at the band gap this
+very very important quantity
+
+ align:start position:0%
+very very important quantity
+ 
+
+ align:start position:0%
+very very important quantity
+there's carbon there's diamond there's
+
+ align:start position:0%
+there's carbon there's diamond there's
+ 
+
+ align:start position:0%
+there's carbon there's diamond there's
+silicon
+
+ align:start position:0%
+silicon
+ 
+
+ align:start position:0%
+silicon
+there's germanium right and you can see
+
+ align:start position:0%
+there's germanium right and you can see
+ 
+
+ align:start position:0%
+there's germanium right and you can see
+that as you go
+
+ align:start position:0%
+that as you go
+ 
+
+ align:start position:0%
+that as you go
+to heavier and heavier elements
+
+ align:start position:0%
+to heavier and heavier elements
+ 
+
+ align:start position:0%
+to heavier and heavier elements
+you change the gap
+
+ align:start position:0%
+you change the gap
+ 
+
+ align:start position:0%
+you change the gap
+you can understand this from what you
+
+ align:start position:0%
+you can understand this from what you
+ 
+
+ align:start position:0%
+you can understand this from what you
+know about the electron levels in atoms
+
+ align:start position:0%
+know about the electron levels in atoms
+ 
+
+ align:start position:0%
+know about the electron levels in atoms
+because in an atom
+
+ align:start position:0%
+because in an atom
+ 
+
+ align:start position:0%
+because in an atom
+right in an atom remember as a
+
+ align:start position:0%
+right in an atom remember as a
+ 
+
+ align:start position:0%
+right in an atom remember as a
+you know if i get heavier and heavier
+
+ align:start position:0%
+you know if i get heavier and heavier
+ 
+
+ align:start position:0%
+you know if i get heavier and heavier
+those electrons
+
+ align:start position:0%
+those electrons
+ 
+
+ align:start position:0%
+those electrons
+all the way on the outer uh you know the
+
+ align:start position:0%
+all the way on the outer uh you know the
+ 
+
+ align:start position:0%
+all the way on the outer uh you know the
+outer edges of the atom they're more
+
+ align:start position:0%
+outer edges of the atom they're more
+ 
+
+ align:start position:0%
+outer edges of the atom they're more
+weakly
+
+ align:start position:0%
+weakly
+ 
+
+ align:start position:0%
+weakly
+bonded to the atom right they're weaker
+
+ align:start position:0%
+bonded to the atom right they're weaker
+ 
+
+ align:start position:0%
+bonded to the atom right they're weaker
+and weaker and weaker
+
+ align:start position:0%
+and weaker and weaker
+ 
+
+ align:start position:0%
+and weaker and weaker
+right so the energy is higher and higher
+
+ align:start position:0%
+right so the energy is higher and higher
+ 
+
+ align:start position:0%
+right so the energy is higher and higher
+remember it like so it's like instead of
+
+ align:start position:0%
+remember it like so it's like instead of
+ 
+
+ align:start position:0%
+remember it like so it's like instead of
+being these deeper energy levels that
+
+ align:start position:0%
+being these deeper energy levels that
+ 
+
+ align:start position:0%
+being these deeper energy levels that
+have more body
+
+ align:start position:0%
+have more body
+ 
+
+ align:start position:0%
+have more body
+more energy in them lower in energy
+
+ align:start position:0%
+more energy in them lower in energy
+ 
+
+ align:start position:0%
+more energy in them lower in energy
+they're less and less energy
+
+ align:start position:0%
+they're less and less energy
+ 
+
+ align:start position:0%
+they're less and less energy
+right well so you can you can imagine
+
+ align:start position:0%
+right well so you can you can imagine
+ 
+
+ align:start position:0%
+right well so you can you can imagine
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+that those are what you're starting with
+
+ align:start position:0%
+that those are what you're starting with
+ 
+
+ align:start position:0%
+that those are what you're starting with
+those are what you're starting with
+
+ align:start position:0%
+those are what you're starting with
+ 
+
+ align:start position:0%
+those are what you're starting with
+these right these are the atom levels
+
+ align:start position:0%
+these right these are the atom levels
+ 
+
+ align:start position:0%
+these right these are the atom levels
+that you're starting with so if you're
+
+ align:start position:0%
+that you're starting with so if you're
+ 
+
+ align:start position:0%
+that you're starting with so if you're
+going to make your atom
+
+ align:start position:0%
+going to make your atom
+ 
+
+ align:start position:0%
+going to make your atom
+have electrons that are more weakly
+
+ align:start position:0%
+have electrons that are more weakly
+ 
+
+ align:start position:0%
+have electrons that are more weakly
+bound
+
+ align:start position:0%
+bound
+ 
+
+ align:start position:0%
+bound
+with energies that are higher that
+
+ align:start position:0%
+with energies that are higher that
+ 
+
+ align:start position:0%
+with energies that are higher that
+aren't as deep and don't have as much
+
+ align:start position:0%
+aren't as deep and don't have as much
+ 
+
+ align:start position:0%
+aren't as deep and don't have as much
+distance between them
+
+ align:start position:0%
+distance between them
+ 
+
+ align:start position:0%
+distance between them
+right in the energy landscape then the
+
+ align:start position:0%
+right in the energy landscape then the
+ 
+
+ align:start position:0%
+right in the energy landscape then the
+gaps will get smaller
+
+ align:start position:0%
+gaps will get smaller
+ 
+
+ align:start position:0%
+gaps will get smaller
+now that is a very simple picture
+
+ align:start position:0%
+now that is a very simple picture
+ 
+
+ align:start position:0%
+now that is a very simple picture
+a very simple picture of why the gaps
+
+ align:start position:0%
+a very simple picture of why the gaps
+ 
+
+ align:start position:0%
+a very simple picture of why the gaps
+get smaller it happens to work for this
+
+ align:start position:0%
+get smaller it happens to work for this
+ 
+
+ align:start position:0%
+get smaller it happens to work for this
+column
+
+ align:start position:0%
+column
+ 
+
+ align:start position:0%
+column
+right so you know if you look at this
+
+ align:start position:0%
+right so you know if you look at this
+ 
+
+ align:start position:0%
+right so you know if you look at this
+and some people would even call this an
+
+ align:start position:0%
+and some people would even call this an
+ 
+
+ align:start position:0%
+and some people would even call this an
+um a metal because that's such a small
+
+ align:start position:0%
+um a metal because that's such a small
+ 
+
+ align:start position:0%
+um a metal because that's such a small
+gap but i like to call it a
+
+ align:start position:0%
+gap but i like to call it a
+ 
+
+ align:start position:0%
+gap but i like to call it a
+semiconductor
+
+ align:start position:0%
+semiconductor
+ 
+
+ align:start position:0%
+semiconductor
+right but if your gap is zero if your
+
+ align:start position:0%
+right but if your gap is zero if your
+ 
+
+ align:start position:0%
+right but if your gap is zero if your
+band gap is zero
+
+ align:start position:0%
+band gap is zero
+ 
+
+ align:start position:0%
+band gap is zero
+it means there's no gap so
+
+ align:start position:0%
+it means there's no gap so
+ 
+
+ align:start position:0%
+it means there's no gap so
+by definition you're in the middle of a
+
+ align:start position:0%
+by definition you're in the middle of a
+ 
+
+ align:start position:0%
+by definition you're in the middle of a
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+you're somewhere in the middle of a band
+
+ align:start position:0%
+you're somewhere in the middle of a band
+ 
+
+ align:start position:0%
+you're somewhere in the middle of a band
+and if you're in the middle of a band
+
+ align:start position:0%
+and if you're in the middle of a band
+ 
+
+ align:start position:0%
+and if you're in the middle of a band
+you're a medal you didn't fill that band
+
+ align:start position:0%
+you're a medal you didn't fill that band
+ 
+
+ align:start position:0%
+you're a medal you didn't fill that band
+all the way up right
+
+ align:start position:0%
+all the way up right
+ 
+
+ align:start position:0%
+all the way up right
+but if you filled it up and then there's
+
+ align:start position:0%
+but if you filled it up and then there's
+ 
+
+ align:start position:0%
+but if you filled it up and then there's
+a little gap between you and the next
+
+ align:start position:0%
+a little gap between you and the next
+ 
+
+ align:start position:0%
+a little gap between you and the next
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+then you're a semiconductor or if it's
+
+ align:start position:0%
+then you're a semiconductor or if it's
+ 
+
+ align:start position:0%
+then you're a semiconductor or if it's
+much greater
+
+ align:start position:0%
+much greater
+ 
+
+ align:start position:0%
+much greater
+like greater than three electron volts
+
+ align:start position:0%
+like greater than three electron volts
+ 
+
+ align:start position:0%
+like greater than three electron volts
+three and a half electron volts
+
+ align:start position:0%
+three and a half electron volts
+ 
+
+ align:start position:0%
+three and a half electron volts
+then you're an insulator okay
+
+ align:start position:0%
+then you're an insulator okay
+ 
+
+ align:start position:0%
+then you're an insulator okay
+now so you can imagine now why right so
+
+ align:start position:0%
+now so you can imagine now why right so
+ 
+
+ align:start position:0%
+now so you can imagine now why right so
+as the as the interactions get stronger
+
+ align:start position:0%
+as the as the interactions get stronger
+ 
+
+ align:start position:0%
+as the as the interactions get stronger
+you can imagine those distances can get
+
+ align:start position:0%
+you can imagine those distances can get
+ 
+
+ align:start position:0%
+you can imagine those distances can get
+larger
+
+ align:start position:0%
+larger
+ 
+
+ align:start position:0%
+larger
+and so you could have larger and larger
+
+ align:start position:0%
+and so you could have larger and larger
+ 
+
+ align:start position:0%
+and so you could have larger and larger
+gaps which can explain this trend
+
+ align:start position:0%
+gaps which can explain this trend
+ 
+
+ align:start position:0%
+gaps which can explain this trend
+but as i said before where did i put it
+
+ align:start position:0%
+but as i said before where did i put it
+ 
+
+ align:start position:0%
+but as i said before where did i put it
+it depends
+
+ align:start position:0%
+it depends
+ 
+
+ align:start position:0%
+it depends
+not just on the atom and the original
+
+ align:start position:0%
+not just on the atom and the original
+ 
+
+ align:start position:0%
+not just on the atom and the original
+energy levels but on how those bond
+
+ align:start position:0%
+energy levels but on how those bond
+ 
+
+ align:start position:0%
+energy levels but on how those bond
+together and we'll talk about that on
+
+ align:start position:0%
+together and we'll talk about that on
+ 
+
+ align:start position:0%
+together and we'll talk about that on
+wednesday
+
+ align:start position:0%
+wednesday
+ 
+
+ align:start position:0%
+wednesday
+and it also depends on the structure
+
+ align:start position:0%
+and it also depends on the structure
+ 
+
+ align:start position:0%
+and it also depends on the structure
+which we'll talk about next week
+
+ align:start position:0%
+which we'll talk about next week
+ 
+
+ align:start position:0%
+which we'll talk about next week
+so it's not just as simple as that but
+
+ align:start position:0%
+so it's not just as simple as that but
+ 
+
+ align:start position:0%
+so it's not just as simple as that but
+you can understand
+
+ align:start position:0%
+you can understand
+ 
+
+ align:start position:0%
+you can understand
+you know basic trends this way for some
+
+ align:start position:0%
+you know basic trends this way for some
+ 
+
+ align:start position:0%
+you know basic trends this way for some
+of the columns
+
+ align:start position:0%
+of the columns
+ 
+
+ align:start position:0%
+of the columns
+okay now um okay we'll get to that on on
+
+ align:start position:0%
+okay now um okay we'll get to that on on
+ 
+
+ align:start position:0%
+okay now um okay we'll get to that on on
+friday um now the goody bag gives you a
+
+ align:start position:0%
+friday um now the goody bag gives you a
+ 
+
+ align:start position:0%
+friday um now the goody bag gives you a
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+to probe this so what's in the goodie
+
+ align:start position:0%
+to probe this so what's in the goodie
+ 
+
+ align:start position:0%
+to probe this so what's in the goodie
+bag the goodie bag has
+
+ align:start position:0%
+bag the goodie bag has
+ 
+
+ align:start position:0%
+bag the goodie bag has
+a way of measuring conductivity now i
+
+ align:start position:0%
+a way of measuring conductivity now i
+ 
+
+ align:start position:0%
+a way of measuring conductivity now i
+just told you that you cannot get
+
+ align:start position:0%
+just told you that you cannot get
+ 
+
+ align:start position:0%
+just told you that you cannot get
+connectivity unless you have electrons
+
+ align:start position:0%
+connectivity unless you have electrons
+ 
+
+ align:start position:0%
+connectivity unless you have electrons
+that are able to make this jump
+
+ align:start position:0%
+that are able to make this jump
+ 
+
+ align:start position:0%
+that are able to make this jump
+to make this jump they've got to be able
+
+ align:start position:0%
+to make this jump they've got to be able
+ 
+
+ align:start position:0%
+to make this jump they've got to be able
+to go up
+
+ align:start position:0%
+to go up
+ 
+
+ align:start position:0%
+to go up
+from the valence band to the conduction
+
+ align:start position:0%
+from the valence band to the conduction
+ 
+
+ align:start position:0%
+from the valence band to the conduction
+band if they don't
+
+ align:start position:0%
+band if they don't
+ 
+
+ align:start position:0%
+band if they don't
+do that they're not free they're stuck
+
+ align:start position:0%
+do that they're not free they're stuck
+ 
+
+ align:start position:0%
+do that they're not free they're stuck
+in these bonds
+
+ align:start position:0%
+in these bonds
+ 
+
+ align:start position:0%
+in these bonds
+right you got to get them free so they
+
+ align:start position:0%
+right you got to get them free so they
+ 
+
+ align:start position:0%
+right you got to get them free so they
+can roam around
+
+ align:start position:0%
+can roam around
+ 
+
+ align:start position:0%
+can roam around
+and not be stuck in this bond or that
+
+ align:start position:0%
+and not be stuck in this bond or that
+ 
+
+ align:start position:0%
+and not be stuck in this bond or that
+bond right
+
+ align:start position:0%
+bond right
+ 
+
+ align:start position:0%
+bond right
+this measures that this measures that
+
+ align:start position:0%
+this measures that this measures that
+ 
+
+ align:start position:0%
+this measures that this measures that
+right this measures whether electrons
+
+ align:start position:0%
+right this measures whether electrons
+ 
+
+ align:start position:0%
+right this measures whether electrons
+are in the conduction band
+
+ align:start position:0%
+are in the conduction band
+ 
+
+ align:start position:0%
+are in the conduction band
+you've also got some leds and some leds
+
+ align:start position:0%
+you've also got some leds and some leds
+ 
+
+ align:start position:0%
+you've also got some leds and some leds
+and this is the critical piece here why
+
+ align:start position:0%
+and this is the critical piece here why
+ 
+
+ align:start position:0%
+and this is the critical piece here why
+do you have
+
+ align:start position:0%
+do you have
+ 
+
+ align:start position:0%
+do you have
+two kinds of leds because on the one
+
+ align:start position:0%
+two kinds of leds because on the one
+ 
+
+ align:start position:0%
+two kinds of leds because on the one
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+what you're doing i'm giving you a way
+
+ align:start position:0%
+what you're doing i'm giving you a way
+ 
+
+ align:start position:0%
+what you're doing i'm giving you a way
+to excite
+
+ align:start position:0%
+to excite
+ 
+
+ align:start position:0%
+to excite
+electrons so i'm giving you a way
+
+ align:start position:0%
+electrons so i'm giving you a way
+ 
+
+ align:start position:0%
+electrons so i'm giving you a way
+to actually promote electrons so you've
+
+ align:start position:0%
+to actually promote electrons so you've
+ 
+
+ align:start position:0%
+to actually promote electrons so you've
+got 10 to the 24th electrons in this
+
+ align:start position:0%
+got 10 to the 24th electrons in this
+ 
+
+ align:start position:0%
+got 10 to the 24th electrons in this
+valence band
+
+ align:start position:0%
+valence band
+ 
+
+ align:start position:0%
+valence band
+this would be the vb and this would be
+
+ align:start position:0%
+this would be the vb and this would be
+ 
+
+ align:start position:0%
+this would be the vb and this would be
+the cb
+
+ align:start position:0%
+the cb
+ 
+
+ align:start position:0%
+the cb
+and what you're doing is you're shining
+
+ align:start position:0%
+and what you're doing is you're shining
+ 
+
+ align:start position:0%
+and what you're doing is you're shining
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+right with different frequencies which
+
+ align:start position:0%
+right with different frequencies which
+ 
+
+ align:start position:0%
+right with different frequencies which
+means different energies
+
+ align:start position:0%
+means different energies
+ 
+
+ align:start position:0%
+means different energies
+okay that's what the right hand side
+
+ align:start position:0%
+okay that's what the right hand side
+ 
+
+ align:start position:0%
+okay that's what the right hand side
+gives you it gives you
+
+ align:start position:0%
+gives you it gives you
+ 
+
+ align:start position:0%
+gives you it gives you
+different energies of the photons so you
+
+ align:start position:0%
+different energies of the photons so you
+ 
+
+ align:start position:0%
+different energies of the photons so you
+have a way now
+
+ align:start position:0%
+have a way now
+ 
+
+ align:start position:0%
+have a way now
+of shining energy on a semiconductor and
+
+ align:start position:0%
+of shining energy on a semiconductor and
+ 
+
+ align:start position:0%
+of shining energy on a semiconductor and
+that's the second piece
+
+ align:start position:0%
+that's the second piece
+ 
+
+ align:start position:0%
+that's the second piece
+the semiconductor is what an led is
+
+ align:start position:0%
+the semiconductor is what an led is
+ 
+
+ align:start position:0%
+the semiconductor is what an led is
+it's a semiconductor if leds were
+
+ align:start position:0%
+it's a semiconductor if leds were
+ 
+
+ align:start position:0%
+it's a semiconductor if leds were
+insulators they wouldn't work and if
+
+ align:start position:0%
+insulators they wouldn't work and if
+ 
+
+ align:start position:0%
+insulators they wouldn't work and if
+they're metals they wouldn't work
+
+ align:start position:0%
+they're metals they wouldn't work
+ 
+
+ align:start position:0%
+they're metals they wouldn't work
+because the way an led works is actually
+
+ align:start position:0%
+because the way an led works is actually
+ 
+
+ align:start position:0%
+because the way an led works is actually
+just the opposite
+
+ align:start position:0%
+just the opposite
+ 
+
+ align:start position:0%
+just the opposite
+here i'm shining light so that an
+
+ align:start position:0%
+here i'm shining light so that an
+ 
+
+ align:start position:0%
+here i'm shining light so that an
+electron gets promoted and i can measure
+
+ align:start position:0%
+electron gets promoted and i can measure
+ 
+
+ align:start position:0%
+electron gets promoted and i can measure
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+with my my voltmeter but i could also
+
+ align:start position:0%
+with my my voltmeter but i could also
+ 
+
+ align:start position:0%
+with my my voltmeter but i could also
+put electrons in with a current that
+
+ align:start position:0%
+put electrons in with a current that
+ 
+
+ align:start position:0%
+put electrons in with a current that
+gets them up here
+
+ align:start position:0%
+gets them up here
+ 
+
+ align:start position:0%
+gets them up here
+and then they drop down and emit a
+
+ align:start position:0%
+and then they drop down and emit a
+ 
+
+ align:start position:0%
+and then they drop down and emit a
+photon that's what an led is
+
+ align:start position:0%
+photon that's what an led is
+ 
+
+ align:start position:0%
+photon that's what an led is
+right that's what an led is it's just
+
+ align:start position:0%
+right that's what an led is it's just
+ 
+
+ align:start position:0%
+right that's what an led is it's just
+the reverse and so what i've given you
+
+ align:start position:0%
+the reverse and so what i've given you
+ 
+
+ align:start position:0%
+the reverse and so what i've given you
+on the left
+
+ align:start position:0%
+on the left
+ 
+
+ align:start position:0%
+on the left
+are different semiconductors
+
+ align:start position:0%
+are different semiconductors
+ 
+
+ align:start position:0%
+are different semiconductors
+because you see just just like a
+
+ align:start position:0%
+because you see just just like a
+ 
+
+ align:start position:0%
+because you see just just like a
+different you know
+
+ align:start position:0%
+different you know
+ 
+
+ align:start position:0%
+different you know
+if i'm running current through like i am
+
+ align:start position:0%
+if i'm running current through like i am
+ 
+
+ align:start position:0%
+if i'm running current through like i am
+on the right you see those are different
+
+ align:start position:0%
+on the right you see those are different
+ 
+
+ align:start position:0%
+on the right you see those are different
+colors
+
+ align:start position:0%
+colors
+ 
+
+ align:start position:0%
+colors
+that means that i must have different
+
+ align:start position:0%
+that means that i must have different
+ 
+
+ align:start position:0%
+that means that i must have different
+gaps
+
+ align:start position:0%
+gaps
+ 
+
+ align:start position:0%
+gaps
+you know that you know that already from
+
+ align:start position:0%
+you know that you know that already from
+ 
+
+ align:start position:0%
+you know that you know that already from
+the work we did with bohr
+
+ align:start position:0%
+the work we did with bohr
+ 
+
+ align:start position:0%
+the work we did with bohr
+and the color or frequency of light that
+
+ align:start position:0%
+and the color or frequency of light that
+ 
+
+ align:start position:0%
+and the color or frequency of light that
+you could get out of different
+
+ align:start position:0%
+you could get out of different
+ 
+
+ align:start position:0%
+you could get out of different
+transitions
+
+ align:start position:0%
+transitions
+ 
+
+ align:start position:0%
+transitions
+but it's the same here did an electron
+
+ align:start position:0%
+but it's the same here did an electron
+ 
+
+ align:start position:0%
+but it's the same here did an electron
+you know did i put an electron up here
+
+ align:start position:0%
+you know did i put an electron up here
+ 
+
+ align:start position:0%
+you know did i put an electron up here
+and then it fell down and gave off some
+
+ align:start position:0%
+and then it fell down and gave off some
+ 
+
+ align:start position:0%
+and then it fell down and gave off some
+lambda
+
+ align:start position:0%
+lambda
+ 
+
+ align:start position:0%
+lambda
+right that lambda has to equal the
+
+ align:start position:0%
+right that lambda has to equal the
+ 
+
+ align:start position:0%
+right that lambda has to equal the
+difference between
+
+ align:start position:0%
+difference between
+ 
+
+ align:start position:0%
+difference between
+the i mean it just equals the band gap
+
+ align:start position:0%
+the i mean it just equals the band gap
+ 
+
+ align:start position:0%
+the i mean it just equals the band gap
+right it equals the band gap
+
+ align:start position:0%
+right it equals the band gap
+ 
+
+ align:start position:0%
+right it equals the band gap
+because the electron was put up to here
+
+ align:start position:0%
+because the electron was put up to here
+ 
+
+ align:start position:0%
+because the electron was put up to here
+in the cbm and then it drops down to the
+
+ align:start position:0%
+in the cbm and then it drops down to the
+ 
+
+ align:start position:0%
+in the cbm and then it drops down to the
+vbm and it emits a photon that's what's
+
+ align:start position:0%
+vbm and it emits a photon that's what's
+ 
+
+ align:start position:0%
+vbm and it emits a photon that's what's
+happening on the right-hand side but see
+
+ align:start position:0%
+happening on the right-hand side but see
+ 
+
+ align:start position:0%
+happening on the right-hand side but see
+you've also got on the left-hand side
+
+ align:start position:0%
+you've also got on the left-hand side
+ 
+
+ align:start position:0%
+you've also got on the left-hand side
+you've got sensors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's just leds on the left see
+
+ align:start position:0%
+because it's just leds on the left see
+ 
+
+ align:start position:0%
+because it's just leds on the left see
+but if i hook those
+
+ align:start position:0%
+but if i hook those
+ 
+
+ align:start position:0%
+but if i hook those
+up if i hook those up to
+
+ align:start position:0%
+up if i hook those up to
+ 
+
+ align:start position:0%
+up if i hook those up to
+uh the voltmeter well i'm hooking up a
+
+ align:start position:0%
+uh the voltmeter well i'm hooking up a
+ 
+
+ align:start position:0%
+uh the voltmeter well i'm hooking up a
+semiconductor to a voltmeter
+
+ align:start position:0%
+semiconductor to a voltmeter
+ 
+
+ align:start position:0%
+semiconductor to a voltmeter
+so i'm hooking this up and i'm reading
+
+ align:start position:0%
+so i'm hooking this up and i'm reading
+ 
+
+ align:start position:0%
+so i'm hooking this up and i'm reading
+is there any current
+
+ align:start position:0%
+is there any current
+ 
+
+ align:start position:0%
+is there any current
+yeah and the answer in a dark room is no
+
+ align:start position:0%
+yeah and the answer in a dark room is no
+ 
+
+ align:start position:0%
+yeah and the answer in a dark room is no
+unless you make it really really hot
+
+ align:start position:0%
+unless you make it really really hot
+ 
+
+ align:start position:0%
+unless you make it really really hot
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+because you have to go to very high
+
+ align:start position:0%
+because you have to go to very high
+ 
+
+ align:start position:0%
+because you have to go to very high
+temperature but what if i shine light on
+
+ align:start position:0%
+temperature but what if i shine light on
+ 
+
+ align:start position:0%
+temperature but what if i shine light on
+this now
+
+ align:start position:0%
+this now
+ 
+
+ align:start position:0%
+this now
+well if i shine light that has the right
+
+ align:start position:0%
+well if i shine light that has the right
+ 
+
+ align:start position:0%
+well if i shine light that has the right
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+to put electrons up in the in the cbm
+
+ align:start position:0%
+to put electrons up in the in the cbm
+ 
+
+ align:start position:0%
+to put electrons up in the in the cbm
+from the vbm then i'll read something on
+
+ align:start position:0%
+from the vbm then i'll read something on
+ 
+
+ align:start position:0%
+from the vbm then i'll read something on
+the voltmeter
+
+ align:start position:0%
+the voltmeter
+ 
+
+ align:start position:0%
+the voltmeter
+so by giving you different leds on the
+
+ align:start position:0%
+so by giving you different leds on the
+ 
+
+ align:start position:0%
+so by giving you different leds on the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+i'm giving you different band gaps you
+
+ align:start position:0%
+i'm giving you different band gaps you
+ 
+
+ align:start position:0%
+i'm giving you different band gaps you
+have in your hands
+
+ align:start position:0%
+have in your hands
+ 
+
+ align:start position:0%
+have in your hands
+different semiconductor band gaps and by
+
+ align:start position:0%
+different semiconductor band gaps and by
+ 
+
+ align:start position:0%
+different semiconductor band gaps and by
+reading whether
+
+ align:start position:0%
+reading whether
+ 
+
+ align:start position:0%
+reading whether
+there are electrons in here or not you
+
+ align:start position:0%
+there are electrons in here or not you
+ 
+
+ align:start position:0%
+there are electrons in here or not you
+can tell what
+
+ align:start position:0%
+can tell what
+ 
+
+ align:start position:0%
+can tell what
+frequency of light i shined on them so
+
+ align:start position:0%
+frequency of light i shined on them so
+ 
+
+ align:start position:0%
+frequency of light i shined on them so
+they're both
+
+ align:start position:0%
+they're both
+ 
+
+ align:start position:0%
+they're both
+emitters of photons and detectors of
+
+ align:start position:0%
+emitters of photons and detectors of
+ 
+
+ align:start position:0%
+emitters of photons and detectors of
+photons
+
+ align:start position:0%
+photons
+ 
+
+ align:start position:0%
+photons
+and it all comes together because you
+
+ align:start position:0%
+and it all comes together because you
+ 
+
+ align:start position:0%
+and it all comes together because you
+have a semiconductor
+
+ align:start position:0%
+have a semiconductor
+ 
+
+ align:start position:0%
+have a semiconductor
+which happened because you took 10 to
+
+ align:start position:0%
+which happened because you took 10 to
+ 
+
+ align:start position:0%
+which happened because you took 10 to
+the 24 states
+
+ align:start position:0%
+the 24 states
+ 
+
+ align:start position:0%
+the 24 states
+you put them together you had gaps
+
+ align:start position:0%
+you put them together you had gaps
+ 
+
+ align:start position:0%
+you put them together you had gaps
+between them and you filled all the way
+
+ align:start position:0%
+between them and you filled all the way
+ 
+
+ align:start position:0%
+between them and you filled all the way
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+to one of those gaps and that gap was
+
+ align:start position:0%
+to one of those gaps and that gap was
+ 
+
+ align:start position:0%
+to one of those gaps and that gap was
+around one
+
+ align:start position:0%
+around one
+ 
+
+ align:start position:0%
+around one
+or two electron volts we will pick this
+
+ align:start position:0%
+or two electron volts we will pick this
+ 
+
+ align:start position:0%
+or two electron volts we will pick this
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+on friday and go further i mean on
+
+ align:start position:0%
+on friday and go further i mean on
+ 
+
+ align:start position:0%
+on friday and go further i mean on
+wednesday on wednesday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/E2HglWZcfKw.txt b/E2HglWZcfKw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1efee84087cc0a1f56d22083738232eb65aeb682
--- /dev/null
+++ b/E2HglWZcfKw.txt
@@ -0,0 +1,2494 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at ocw dot
+
+MIT dot edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to lecture
+
+number six.
+
+In this lecture I would like
+to discuss with you the
+
+formulation and calculation of
+isoparametric finite elements.
+
+We considered earlier already,
+in lecture four, the
+
+calculation all finite
+element matrices.
+
+But in that lecture we
+considered the generalized
+
+coordinate finite
+element models.
+
+The generalized coordinate
+finite element models were the
+
+first finite elements derived.
+
+However, I now want to discuss
+with you a more general
+
+approach of deriving the
+required interpolation
+
+matrices and element matrices.
+
+And this more general approach
+is the isoparametric finite
+
+element derivation.
+
+The isoparametric finite
+elements that I will be
+
+discussing in this and the
+next lecture are, in my
+
+opinion, the most effective
+elements currently available
+
+for plane stress, plane strain,
+axisymmetric analysis,
+
+three dimensional analysis,
+thick and thin shell analysis.
+
+These elements are being used,
+for example, in the computer
+
+program [? Aldena ?].
+
+They are also used in other
+computer programs and
+
+represent a modern approach
+to the solution
+
+off structure problems.
+
+In this lecture, I would like
+to talk about the derivation
+
+of continuum elements.
+
+In the next lecture we will talk
+about the derivation of
+
+structural elements, [INAUDIBLE]
+and central
+
+elements, beam elements.
+
+The basic concept of
+isoparametric finite element
+
+analysis, is that we interpolate
+the geometry of an
+
+element, and the displacements
+of an element in
+
+exactly the same way.
+
+Let us look at the geometry
+interpolation.
+
+Here you see for three
+dimensional analysis, the
+
+interpolation of the
+x-coordinate within the
+
+element, where we use
+interpolation functions h i.
+
+Of course these interpolation
+functions are unknown and I
+
+will have to show you
+how we derive
+
+them for certain elements.
+
+The x i as a nodal
+point coordinate.
+
+The x i value for i equals 1,
+for example, is nothing else
+
+than the x-coordinate
+of nodal point one.
+
+And so on.
+
+So the x i, the nodal point
+coordinates for all nodes,
+
+they are given, they are input
+in the analysis the way we
+
+have been discussing it in
+the previous lecture.
+
+And if we know the h i, we have
+a direct relationship for
+
+the x-coordinates within the
+element, as a function of the
+
+nodal point coordinates.
+
+Again, I have to show you how
+we obtain the h i functions
+
+for the various elements
+that we are using.
+
+Similarly, for the y
+interpolation and similarly
+
+for the z interpolation.
+
+Having derived the h i functions
+we are using in the
+
+isoparametric finite element,
+the same functions also to
+
+interpolate the displacements.
+
+Notice that we're having here,
+the nodal point displacements
+
+u i, v i, and w i, and here we
+have the same interpolation
+
+functions that we already
+used in the coordinate
+
+interpolations.
+
+And if the number of nodes
+that are used in the
+
+description of the element--
+
+and, in fact, we will see that N
+can be a variable, it can be
+
+equal to three, four, five, up
+to a large number of nodes.
+
+And in practice we generally
+don't go much further than 60.
+
+I mentioned that I want to
+discuss in this lecture
+
+continuum elements.
+
+Well, the continuum elements
+that we addressing ourselves
+
+to are the truss element, the
+two d elements-- plane stress,
+
+plane strain, and axisymmetric
+elements--
+
+and then, the 3 d elements for
+three dimensional and thick
+
+shell analysis.
+
+These are continuum elements.
+
+We call them continuum elements,
+because we only use
+
+u, here u and v, and
+here, u v and w--
+
+the displacements--
+
+to describe the internal
+element displacements.
+
+We're only using the nodal point
+displacements u, u v,
+
+and u v w, for all of the nodal
+points to describe the
+
+internal element
+displacements.
+
+Structure elements, on the
+other hand, also use the
+
+rotations at the nodal point
+theta x, theta y, and theta z,
+
+in order to describe the
+
+deformations within the element.
+
+And I will be discussing
+structural elements in the
+
+next lecture, so, for the
+moment, we do not have any
+
+rotations at the nodes.
+
+Or what we will allow, u v and
+w displacements at the nodes.
+
+Typical examples are given
+on this Viewgraph.
+
+These are elements that are
+available in the computer
+
+program [? Aldena ?].
+
+Here we have a truss element,
+a two-noded truss element.
+
+The only displacement of
+interest in the truss is the
+
+actual displacement here.
+
+Here we have a three-noded
+truss, or cable element.
+
+Here we have a set of two
+dimensional elements.
+
+Notice we have triangular
+elements here, a triangular
+
+element here.
+
+We have here an eight node
+element that is curved.
+
+We can construct curved
+elements in the
+
+isoparametric approach.
+
+And here we have a rectangular,
+eight node
+
+element, straight sides,
+in other words.
+
+These elements are used in plane
+stress, plane strain,
+
+and axisymmetric analysis.
+
+In three dimensional analysis
+we might be talking about--
+
+we might be using--
+
+such elements such as the
+eight node brick.
+
+Each node now has three
+displacements, u, v, and w.
+
+This is here a higher order
+element, where we have, in
+
+addition to the corner nodes,
+we also have mid-side nodes.
+
+You don't need to
+have a mid-side
+
+nodes along all sides.
+
+For example here,
+I did not put a
+
+mid-side node as an example.
+
+In fact we could simply have
+mid-side nodes here, and no
+
+mid-side nodes anywhere else.
+
+I will show you how we
+deconstruct these
+
+interpolation matrices in
+the next few minutes.
+
+Let us consider, as
+a very simple
+
+example, a special case.
+
+And the special case that I
+would like to look at is a
+
+truss element, which
+is two units long.
+
+In other words, the length from
+here to there, is equal
+
+to 1, and similarly the length
+from here to there, is also
+
+equal to one.
+
+I'm describing the element with
+a coordinate r that I set
+
+equal to zero at the midpoint
+of the element, plus one at
+
+the right end and minus
+one at the left end.
+
+This is special geometry and
+we will later on have to
+
+generalize our approach to more
+general geometries where
+
+the length is not equal
+to two and the element
+
+might even be curved.
+
+But for instructive purposes,
+let's look at
+
+this geometry first.
+
+Similarly, for two dimensional
+analysis, I want to look at an
+
+element that has length two this
+direction and length two
+
+that direction.
+
+In other words, a generalization
+of the concept
+
+that we just looked
+at for the truss.
+
+Now we have two dimensions and
+in each dimension we have a
+
+length of two.
+
+I embed into this element
+an rs-coordinate system.
+
+And this coordinate system now
+has its origin here at r
+
+equals zero and s equals zero.
+
+The r-axis bisects this
+side, and the s-axis
+
+bisects this side.
+
+Notice that this is a coordinate
+system that is
+
+embedded into the element.
+
+We also call that the natural
+coordinate system, or the
+
+Isoparametric coordinate
+system.
+
+This element, two by two, would
+lie in space in an x
+
+xy-coordinate system
+as indicated here.
+
+Now for three dimensional
+analysis we would proceed in
+
+the same way, then we would
+consider an element that is
+
+two by two by two
+units long into
+
+each coordinate direction.
+
+And then we would have an
+rs-axis and a t-axis coming
+
+out of the transparency in
+this particular case.
+
+Well, I want to look at the
+truss element, the special
+
+truss element, and the special
+two d element.
+
+And I want to show you how
+we can construct the
+
+interpolation matrices, the
+displacement interpolation
+
+matrices, h i.
+
+These are also the coordinate
+interpolation matrices.
+
+I want to show you how we
+construct them for the special
+
+elements, how we then can
+calculate the strain
+
+displacement interpolation
+matrices
+
+for the special elements.
+
+And then I want to go on and
+show you how we generalize to
+
+concepts to curved elements.
+
+And once we have discussed the
+two dimensional case, I think
+
+you can see yourself how the
+concepts are generalized to
+
+the three dimensional case.
+
+Let's look then at our two-noded
+truss first.
+
+Here we have once more, the
+truss, and we have node one on
+
+the right hand side, node two
+on the left hand side.
+
+Our r-coordinate system starts
+in the middle of the truss.
+
+Notice what we want to obtain
+is that we interpolate our u
+
+displacement via the
+interpolations.
+
+U being equal to h i times u i,
+the h i are the unknowns.
+
+I want to show you how
+we obtain the h i.
+
+The u i are the nodal
+point displacements.
+
+In this particular case it would
+be here, u two and here
+
+we would have u one.
+
+I in other words, goes
+from one to two for
+
+this particular case.
+
+The h i has to be
+a function of r.
+
+For a given r, however, we can
+evaluate the u displacement if
+
+we have u i is given.
+
+In other words, when u one and
+u two are given, then for a
+
+given r, we can evaluate
+directly from this relation
+
+the displacement at
+that point r.
+
+Well, with two nodes, we
+can only have a bi--
+
+only a linear representation
+in the displacements.
+
+The h one, from this relation,
+must be this function.
+
+Because if we look at this, and
+we say let u two be equal
+
+to zero, we would simply
+have that u is
+
+equal to h one u one.
+
+Well, therefore, our h one must
+look this one, because u
+
+one has its full
+strength here.
+
+If we put u one equal to one, we
+would have u is equal to h
+
+one, and this would
+be the variation.
+
+Similarly, for h two, in this
+case, we would have u is equal
+
+to h two u two.
+
+H one is now equal to zero.
+
+If we put you two equal to one,
+as I have done in this
+
+particular case, then our linear
+variation is indicated
+
+as shown here , and
+the function h two
+
+is given right here.
+
+Notice that h two is equal to
+zero when r is equal to one.
+
+And h two is equal to one when
+r is equal to minus 1.
+
+So, this gives us h two.
+
+The two-noded truss, therefore,
+simply has this
+
+description here for the
+displacement and the
+
+coordinates.
+
+Remember that we're using the
+same h i for displacement and
+
+coordinates.
+
+It simply has this description
+where h one and h two are
+
+defined as shown.
+
+Let us now say that we want to
+add another node, that we want
+
+to put another node
+right there.
+
+In other words, we want to go
+from a two-noded description
+
+to a three-noded description.
+
+On one of the earlier
+Viewgraphs, you could see a
+
+three-noded cable element.
+
+Well, the way we proceed in the
+construction of the h i
+
+functions is as follows.
+
+The two-noded element simply
+had this description here.
+
+H one is given as shown
+here on the left
+
+side of the blue line.
+
+H two was simply this.
+
+And we knew that we could do
+no better than a linear
+
+description in displacements
+between two nodes.
+
+However, now we have a third
+node right here.
+
+And a third node means that
+we can use a parabolic
+
+description in displacements.
+
+Now h three must be equal to one
+at the third node and zero
+
+at both sides.
+
+Why?
+
+Well, because, remember we have
+u now equal to h i u I,
+
+where i equals one to three.
+
+And if we put u one equal to
+zero and u to equal to zero,
+
+we simply have u equals h three
+u three, and, therefore,
+
+h three is this function.
+
+I've written it down here when
+r is equal to zero its one
+
+when r is equal to minus 1
+or plus h three is zero.
+
+So this is our h three.
+
+However, if we now look back to
+our earlier description of
+
+h one and h two for the
+two-noded element, we remember
+
+that we had a linear
+variation here.
+
+That we had a linear variation
+here and here.
+
+This one was a linear
+variation of h one--
+
+let me take here the green color
+to show once more what
+
+we are talking about--
+
+that was our linear variation.
+
+And here, this one here was our
+linear variation there.
+
+Well, now with the third node
+there, we recognize that, at
+
+this third node our h two--
+
+our actual h two for the
+three-noded truss--
+
+must be zero here.
+
+H one must be zero here.
+
+Well, how can we make
+it zero here?
+
+We can make it zero by
+subtracting from our two-noded
+
+truss h one, one half of this
+parabolic description.
+
+And that's what I
+have done here.
+
+Similarly, we have to subtract
+it here, because then, what we
+
+are doing is we are taking one
+half off this parabola, and we
+
+are putting it right on here.
+
+This is one half of the
+bottom parabola.
+
+We are putting it on there.
+
+And that brings this point
+back to that point.
+
+Remember this is equal to one.
+
+I want one half as a correction
+here, and that's
+
+why I take one half of one minus
+r squared, to bring this
+
+point back to there.
+
+This total description then,
+this total part--
+
+this part here, all
+of that together--
+
+is our h one for the three-noded
+element, for the
+
+three-noded element.
+
+And similarly, we would
+have four h two.
+
+This total part here is this
+function here for our
+
+three-noded element.
+
+Now the important point that
+I really would like you to
+
+understand is that, we have
+started off with a two-noded
+
+element description--
+
+h one only the linear part, h
+two only the linear part.
+
+We have constructed the
+interpolation function for the
+
+third node, and then we have
+corrected the earlier
+
+two-noded interpolation
+functions via subtracting a
+
+certain part of the third
+interpolation function, in
+
+order to obtain the new
+h one and h two for
+
+the three-noded element.
+
+And this is indeed the actual
+procedure that we can use very
+
+effectively in constructing
+higher order elements.
+
+We are starting off with
+the lower order element
+
+descriptions--
+
+the ones shown here dashed with
+a dashed line, the linear
+
+part only--
+
+and we add in the higher order
+description, and subtract the
+
+correction from the lower
+order description.
+
+The correction has to be
+subtracted to bring this point
+
+back to zero, because h one
+total must now be equal to
+
+zero here, h two total must be
+equal to zero here, and this
+
+way we have constructed our new
+h one and h two for the
+
+three-noded truss element.
+
+Let's look at the four-noded
+element in two dimensions now.
+
+Here we use very similar
+concepts.
+
+These are the four nodes
+for the element.
+
+The description along a side
+is just like we have been
+
+discussing now for the truss,
+linear here and linear here.
+
+Notice h one can directly
+be written down.
+
+It has to be equal to one here
+and zero everywhere else.
+
+This is a function which is
+bilinear and which satisfies
+
+these conditions to be equal
+to one here and.
+
+Zero at the other nodes.
+
+It is a linear variation along
+this side, along this side,
+
+and also across the surface.
+
+In other words, for a given
+value of r, we have a linear
+
+variation across here too.
+
+How do we obtain h two?
+
+Well, we simply have to change
+the signs over here--
+
+the plus signs here-- in
+an appropriate way.
+
+H two shall be equal to one
+here zero at all the other
+
+nodes, while we see that this
+function satisfies these
+
+conditions, let's put in
+r equal to minus 1.
+
+That makes this two, divided
+by four, gives us one half.
+
+S has to be equal to plus
+1 at this point--
+
+you get another two in here--
+
+so h two is equal to one
+right there, and its
+
+zero everywhere else.
+
+Similarly we construct
+h three and h four.
+
+Indeed we can immediately
+observe that these signs--
+
+plus in both cases here, a minus
+here, plus there, minus,
+
+minus, plus, minus-- these signs
+correspond to nothing
+
+else in the signs of the r- and
+s-coordinates of the nodal
+
+point under consideration.
+
+R and s is plus here, you have
+two plus signs here.
+
+R is negative here, you put
+a negative sign here.
+
+But s is positive here, you
+put a plus sign there.
+
+r and s both are negative here,
+so we have two negative
+
+signs here, et cetera.
+
+Let us now see how we construct
+from this basic four
+
+node element, which really
+corresponds to our basic two
+
+node element in the case of
+the truss, how we can
+
+construct higher
+order elements.
+
+Well, we proceed in much the
+same way as in the truss
+
+formulation.
+
+Here we have a four-noded basic
+element and we have
+
+added a fifth node to it.
+
+Now let's look at
+this in detail.
+
+Since we now have added a fifth
+node here, we know that
+
+we can allow a parabolic
+distribution.
+
+In fact, we should allow a
+parabolic distribution of
+
+displacements along the side.
+
+Well, if its a parabola along
+the side for s being plus 1,
+
+we immediately see that
+this function here--
+
+this s equal to plus one, this
+is equal to two, knocks out
+
+that one half, we have
+a one minus r
+
+squared along the side--
+
+just the same function that we
+already had in the truss.
+
+Well, along this direction we
+can only vary things linearly
+
+because we have two nodes only
+in along these directions.
+
+And this is the reason
+why we have to put in
+
+a one plus s here.
+
+The linear variation is
+given by one plus s.
+
+And we also notice that when s
+is equal to minus 1, in other
+
+words, we are looking at this
+side, this function is zero.
+
+When s is equal to plus one,
+as we pointed out earlier,
+
+this function here--
+
+this part and that part--
+
+gives us a one together, and we
+have simply a one minus r
+
+squared along here.
+
+So, here you can see these
+triangles that show the linear
+
+variation along this side.
+
+These parabolas here run really
+across here, but with a
+
+different intensity.
+
+The intensity off the parabola
+goes down linearly from one at
+
+this end, to is zero
+at that end.
+
+This is our h five.
+
+Well, if we have this as our h
+five, we remember that our
+
+original h one of the of the
+four-noded element had a
+
+linear variation along here,
+and also a linear variation
+
+along here.
+
+We will now have to take this
+h one and subtract some
+
+correction from it.
+
+In order to make this point here
+have zero displacement,
+
+four h one.
+
+Well, what we will do is we take
+this h five and subtract
+
+a multiple of h five
+from h one.
+
+In fact, you can see since the
+original h one is equal to one
+
+half here, we simply have to
+subtract one half of this
+
+function to obtain
+the new h one.
+
+And this is what I have done
+on this Viewgraph.
+
+The h one now is the original
+h one that we had.
+
+And we are subtracting one half
+of h five, which is one
+
+half of the parabolic
+distribution, to bring this
+
+point here down to zero
+in displacements.
+
+And that's what we
+have done here.
+
+The resulting function
+then is shown here.
+
+And our h one for the five-noded
+element is shown
+
+right here.
+
+Similarly, for h two--
+
+this is the h two function for
+the five-noded element--
+
+interesting to note that h three
+and h four are for the
+
+five-noded element, the same as
+for the four-noded element.
+
+Because this fifth node lies
+between nodes one and two.
+
+And there is no effect
+along this side and
+
+along this side here--
+
+along that side four h three and
+h four-- so, we have our
+
+original functions also for
+the five-noded element.
+
+Let us look now at a
+
+generalization of this concept.
+
+Here we have a typical
+nine-noded element.
+
+A very effective element for
+many types of applications.
+
+I already show it here in its
+curved form, but think of it,
+
+please, as follows.
+
+This is the x-axis.
+
+This is the r-axis.
+
+S is equal to zero
+along this side.
+
+S is equal to plus one
+along this side.
+
+S is equal to minus
+1 along this side.
+
+R is equal to plus one
+along this side.
+
+R is equal to minus one
+along the side.
+
+And r is zero along this axis.
+
+So, in the r s description,
+in the embedded coordinate
+
+system, this element is still a
+two by two squared element.
+
+Well, if we look then at the
+interpolation functions, for
+
+this element, they
+look as follows.
+
+Now maybe you have difficulty
+seeing all this information,
+
+so, please then refer to the
+study guide where you'll find
+
+this Viewgraph.
+
+For the four-noded element,
+we had these
+
+interpolation functions.
+
+If we want to deal with the
+five-noded element, what we
+
+have to do is, we add this
+interpolation function.
+
+And--
+
+as I pointed out earlier--
+
+we have to correct our
+h one and h two.
+
+But that is all of the
+correction that is required.
+
+H three and h four
+not corrected--
+
+they are blank spots here, they
+are blank spots here.
+
+So, our five-noded element would
+have these interpolation
+
+functions now shown in red.
+
+For if we added a sixth node--
+
+and I now should go back to
+our earlier picture--
+
+if I wanted to add, in addition
+to the fifth node,
+
+also the sixth node.
+
+Well, then, I have to put
+another interpolation function
+
+down here, which now
+is parabolic in s
+
+and linear in r.
+
+And I have to correct h two and
+h three again, these are
+
+the corrections.
+
+So, now I have in green here
+shown to you the interpolation
+
+functions off a six-noded
+element.
+
+And like that we can proceed
+by adding interpolation
+
+functions and correcting
+the earlier constructed
+
+interpolation functions
+as shown.
+
+Like that we can proceed
+to directly obtain the
+
+interpolation functions for
+the five-noded, six-noded,
+
+seven-, eight-, and nine-noded
+element.
+
+In fact, its also important to
+notice that we could have this
+
+node, that node, this node, and
+that node, and just h nine
+
+also added.
+
+We could have, in other words,
+a five-noded element which
+
+looks like this.
+
+It has this node, that one, that
+one, and that one, and
+
+that one in the middle.
+
+Another five-noded element would
+be this one, this one,
+
+this one, this one with
+that node in there.
+
+So there is no necessity in
+having all the nodes below a
+
+certain number.
+
+But we can simply use four
+nodes, and then add whichever
+
+nodes we want to have
+into the element.
+
+This is, then, how we construct
+
+interpolation functions.
+
+And once we had the h i, we
+directly can obtain the h
+
+matrix, the matrix that gives
+the displacements in terms of
+
+the nodal point displacements.
+
+Notice that the h
+matrix really is
+
+constructed from the hi's.
+
+And the elements of
+the b matrix--
+
+the strain displacement
+interpolation matrix--
+
+are the derivatives of
+the h i or zero.
+
+And I will show you an
+example right now.
+
+Because we are using four, we
+are still looking at the
+
+special case of a two by two
+by two element in a truss
+
+case, only this two.
+
+Plane stress, plane strain,
+axisymmetry, two dimensional
+
+analysis, we have
+these two two's.
+
+In other words, we're talking
+about a two by two element.
+
+And in three dimensional
+analysis we would talk about a
+
+two by two by two element.
+
+In these cases, we have x equal
+to r, y equal to s, z
+
+equal to t.
+
+So the strains--
+
+which are derivatives with
+respect to x the actual
+
+physical coordinates--
+
+can also directly be obtained
+by simply taking the
+
+derivative with respect
+to r, and then
+
+similarly for s and t.
+
+Let us look at a four node,
+two dimensional element.
+
+This is really the element
+that we have used in our
+
+earlier example of the
+cantilever analysis.
+
+Here we would simply have
+that u r s, v r s, are
+
+described as shown.
+
+Notice that in the first row we
+are really saying nothing
+
+else than u is a summation
+h i u i.
+
+Where i equals one to
+four because we have
+
+a four-noded element.
+
+H i u i.
+
+In the second row we are really
+saying nothing else
+
+than v being the summation of i
+equals one to four h i v i.
+
+And all I have done is I have
+taken these hi's and assembled
+
+them into a matrix form to
+obtain our h matrix.
+
+This h matrix here--
+
+the entries in that h matrix--
+are dependent on the ordering
+
+that you're using here for u
+one, v one, u two, et cetera.
+
+With this ordering, these
+are the entries.
+
+Notice there are zeroes here,
+because the v degrees of
+
+freedom at the nodes have
+no contribution to the u
+
+displacement in the element.
+
+Well, if we look at the plane
+stress case and want to
+
+construct our b matrix, remember
+the b matrix gives
+
+the strains in terms of the
+nodal point displacements.
+
+And we remember also that our
+epsilon xx is equal to a dy
+
+dx, our epsilon yy is equal to
+dv dy and our gamma xy is
+
+equal to a du dy plus dv dx.
+
+Well, if we recognize
+these facts.
+
+And we also note again that for
+the two by two element, r
+
+is identical to x, s
+is identical to y.
+
+Then, we can obtain the epsilon
+rr or epsilon xx by
+
+simply taking the derivatives of
+the hi's with respect to r.
+
+Notice here, since u is equal
+to the summation of h i u i,
+
+dy dr, which is equal to du dx,
+is nothing else then the
+
+summation of partial
+h i dr u i.
+
+And this part, which runs
+from one to four--
+
+i going from one to four--
+
+I simply put right in there.
+
+I proceed similarly
+for epsilon yy.
+
+Now I'm talking about the v
+displacements, which are
+
+stored after the u
+displacements.
+
+That's why I'm looking
+here at the second
+
+column, the last column.
+
+And here we have dh one ds,
+because we are talking about
+
+the derivative with respect to
+y or with respect to s, which
+
+is the same thing.
+
+So here we have the entries
+for the epsilon ss part.
+
+Now for the strain part, we are
+talking du dy or du ds, dv
+
+dx, dv dr. And all we have to
+do in now is take this term
+
+and put it right in there, and
+take this term and put it
+
+right in there.
+
+And then the last row
+here gives us
+
+the shearing strength.
+
+So this is our b matrix for the
+
+special two by two element.
+
+It is constructed in
+a very simple way.
+
+The h i are known, and if we
+had five or six or seven
+
+nodes, we would proceed in
+exactly the same way.
+
+All we would have to do is
+include additional columns in
+
+the b matrix that would give us
+the appropriate entries for
+
+strains generated by the
+additional nodal point
+
+displacements.
+
+Let us now look how we can
+generalize these concepts to
+
+the element that is not,
+anymore, in the physical x and
+
+y space, two by two element.
+
+In the physical x and y
+space, this element--
+
+four-noded element now--
+
+might look as shown here.
+
+However, what we do is we still
+deal with the r- and
+
+s-coordinate system embedded
+on the element.
+
+We are on s one here, minus one
+s plus one here, r and s
+
+both minus one here, plus
+one here s minus one.
+
+So in the natural coordinate
+space, the rs space, we still
+
+have a two by two element.
+
+The interpolation of the
+displacement therefore--
+
+the interpolation of
+the displacements--
+
+even for the distorted element,
+is exactly still as
+
+shown here.
+
+Provided we are entering
+always with the
+
+appropriate r and s.
+
+H one is a function
+of r and s.
+
+So if we look at a point in
+the general element, if we
+
+look at a point in the general
+element, here, for example, at
+
+such a point.
+
+Because that point has a
+specific r and s value.
+
+And if we want to find the
+displacement at that point,
+
+well, we would have to put the
+r and s value of that point
+
+into h one, h two, h three, h
+four, and that gives us then
+
+the displacement at that point,
+in terms of the nodal
+
+point displacement.
+
+So, the displacement
+interpolation for this element
+
+can still be done in
+the r and s space.
+
+However, difficulties arise--
+
+or additional considerations
+I should say rather--
+
+arise when we talk about
+strains, because the physical
+
+strains that we have to deal
+with are derivatives with
+
+respect to x and y, and
+not r and s anymore.
+
+Well, so what we have to
+do is, use a Jacobian
+
+Transformation.
+
+What we want are the
+derivatives with
+
+respect to x and y.
+
+What we can find easily are
+derivatives with respect to r
+
+and s on the displacements,
+because the displacements are
+
+given in terms of
+r and s values.
+
+So, remember u is equal to some
+of h i u i and the h i is
+
+a function of r and s, so, we
+can directly find derivatives
+
+with respect to r and s of u.
+
+What we cannot find easily are
+derivatives with respect to x.
+
+This is the relationship
+that we use.
+
+It gives us a transformation
+from derivatives of x and y to
+
+derivatives r and s.
+
+A question must immediately be
+in your mind, why do we not
+
+write down directly this
+relationship, which is given
+
+by the [INAUDIBLE].
+
+If we want d dx of
+displacements, why not just
+
+use d dx being equal to d
+dr, dr dx, and so on.
+
+Well, the difficultly
+is that we cannot
+
+find dr dx very easily.
+
+We have x being this function
+of h i x i.
+
+This is the interpolation which
+we have to use now.
+
+I mentioned earlier on the
+first slide that we
+
+interpolate displacement and
+coordinates in the same way.
+
+So, here we have a linear
+interpolation of the
+
+coordinates, from this node
+to that node, and in
+
+between here too.
+
+So we are using this
+interpolation here on the
+
+coordinates.
+
+And we can easily dx dr, but we
+cannot easily find dr dx.
+
+You would have to invert this
+relationship somehow so that
+
+we have r in terms of x.
+
+Well, it is easier, therefore,
+to write this relationship
+
+down, which is really
+the chain rule.
+
+This is also the chain rule, its
+a chain rule the other way
+
+around, which gives d dr being
+equal to d dx, dx dr plus d dy
+
+dy dr, if we multiply
+this out.
+
+And its this relationship that
+we can use effectively.
+
+Well, this relationship in three
+dimensional analysis
+
+would involve a third row
+and third column.
+
+In one dimensional analysis we
+only talk about one by one.
+
+In other words, in one dimension
+analysis for a truss
+
+we just have that entry.
+
+In general we can write it in
+this way, where j is the
+
+Jacobian transformation from the
+xyz-coordinate system to
+
+the rst-coordinate system.
+
+And since we want these
+derivative--
+
+because these derivatives give
+us actual strains, we have to
+
+invert this relationship.
+
+Having constructed then, these
+derivatives in terms of these
+
+derivatives, which we can find
+just as we have done before,
+
+we can now establish the
+b matrix in much
+
+the same way as earlier.
+
+And since we now have h and b
+matrices for an element--
+
+these are a function
+r, s, and t--
+
+we would perform the
+integration.
+
+And now I'm referring to
+the integration of
+
+the stiffness matrix.
+
+Remember k is equal to b,
+transposed cb over the volume.
+
+Now notice that since the b
+matrix that we are using in
+
+here is a function of r and s in
+a two dimensional analysis.
+
+And r runs from minus one to
+plus one, and s runs from
+
+minus one to plus one.
+
+We now have to use a
+transformation also on dv to
+
+integrate over the r s volume.
+
+And that integration--
+
+and that dv element is expressed
+as shown here--
+
+and that is given to us from
+mathematical analysis.
+
+So basically what we are saying
+here is that we are
+
+replacing this integral over
+the physical volume by an
+
+integral minus one to plus one,
+minus one to plus one.
+
+And that signifies from minus
+one to plus one over r and
+
+over s, if we had a three
+dimensional analysis we would
+
+have another integral
+sign here.
+
+B transposed now r and s
+function of r and s, cb,
+
+function of r and s.
+
+And then our dv, now in
+terms of r and s.
+
+So this is how we really
+do things.
+
+And remember this dv here, this
+dv, is that one there.
+
+This integration is effectively
+performed using
+
+numerical integration and
+I will discuss later on.
+
+Let's look once at the Jacobian
+transformation for
+
+some very simple examples--
+
+the Jacobian transformation for
+
+some very simple examples--
+
+just to make things
+a little clearer.
+
+In this case we really have
+taken our two by two element
+
+and we have stretched it
+into the x- and y-axes.
+
+That stretching is giving us a
+three here and a two there
+
+because our two by two element
+has a length of two here, and
+
+six divided by two
+gives us three.
+
+Similarly here we have stretched
+the element by a
+
+factor of two.
+
+This relationship here is,
+in general, calculated--
+
+the j is, in general,
+calculated--
+
+as shown here.
+
+And the result of that, by
+putting these interpolations
+
+into there are these
+values here.
+
+Physically what these mean
+is a stretching, in this
+
+particular case, into
+the x- and y-axis.
+
+Somewhat--
+
+the case where we cannot
+directly--
+
+not easily directly write down
+to j matrix is this one.
+
+Here we would go through the
+actual evaluation the way I
+
+have indicated it.
+
+In other words, we would
+go through this actual
+
+evaluation, substituting from
+here and of course for y also.
+
+And this would be the result
+Notice that we now have a
+
+stretching here of three,
+compression from a two length
+
+to a one length--
+
+therefore we have a one half
+here-- and there's also an
+
+angle change that gives us the
+off-diagonal element here.
+
+Another interesting case here,
+as an example, we have the
+
+same lengths here--
+
+two same lengths here-- but a
+distortion in the element
+
+because this node two
+has come down from
+
+there to its midpoint.
+
+And the resulting Jacobian
+is given here.
+
+Now notice that that Jacobian is
+a function r and s, so the
+
+inverse, which is used in the
+construction of the b matrix
+
+would also be a function
+of r and s.
+
+A particularly interesting case
+is the one where we shift
+
+nodes to advantage.
+
+See here we have
+our original--
+
+our three-noded element that we
+talked about already-- in
+
+the r space now.
+
+Its a truss element.
+
+And let's say that in our actual
+physical space, we have
+
+this node there, the three
+node there, and
+
+the two node there.
+
+The element in the actual
+physical space
+
+has a length of l.
+
+We have taken this node and
+shifted it to the quarter
+
+point of the element, to the
+quarter point of the element.
+
+What I will show you right now
+is that by having done so-- by
+
+having taken this node from its
+midpoint and shift it over
+
+in the actual physical space
+to the quarter point--
+
+we will find that the strain has
+a singularity here of one
+
+over square root x.
+
+This is a very important point
+which can be used in the
+
+analysis of fracture problems,
+because we know that in the
+
+analysis of fracture problems,
+we have a one over square root
+
+x singularity at a crack tip.
+
+And, if we want to predict the
+actual stress there or the
+
+displacement around the crack
+tip, it can be of advantage to
+
+use this fact, shifting nodes to
+quarter points in order to
+
+capture the stress singularity
+more accurately.
+
+Well let me show you then how
+this strain or stress
+
+singularity comes about.
+
+If we look at this element
+here and we use our
+
+interpolation on the
+coordinates, this
+
+would be the result.
+
+Now, notice that we
+have substituted
+
+the x i values here.
+
+X one is zero, x two is l,
+x three is l over four.
+
+We have substituted those values
+and directly come up
+
+with this result.
+
+Well, we can see that
+this indeed is true.
+
+Let's put r equal
+to plus one n.
+
+In other words, the right
+hand side node--
+
+for the right hand side node--
+and we would have a two here
+
+squared, gives us four, goes
+out with that four.
+
+So at i equals plus 1 we have
+x equal to l, which
+
+is correct of course.
+
+Let's put i equal to minus one
+n, we find x is equal to zero.
+
+Let's put i equal to
+zero n we find x is
+
+equal to l over four.
+
+In other words, this has been a
+simple check in that we have
+
+the right interpolation--
+
+geometry interpolation--
+
+for this element.
+
+Our j now is simply, dx
+dr, X is given here.
+
+If you take the differentiation
+of that you
+
+get the two in front that gives
+l over two times one
+
+plus r, this value here,
+in other words.
+
+Then our b matrix is
+constructed by the
+
+inverse of the j--
+
+that is this one--
+
+two times the r derivative of
+the interpolation functions.
+
+Of course here we talk only
+about one strain.
+
+Remember, in the truss, the only
+displacement of concern
+
+is the u displacement and the
+strain is simply epsilon xx, a
+
+strain into this
+direction also.
+
+Well, this is our
+b matrix then.
+
+And if we take our h one,
+two, and three, and we
+
+differentiate these--
+
+as indicated here with respect
+to r-- we directly obtain
+
+these functions here.
+
+If we now recognize that since
+we have x related to r here,
+
+we can also invert this
+relationship.
+
+We can write r in terms of x.
+
+And if we have done so we can
+take that relationship and put
+
+it right in here.
+
+Then we would get
+b in terms of x.
+
+And that's what I
+have done here.
+
+The first line shows simply r in
+terms of x now, and I have
+
+substituted that r value into
+the b matrix and this is there
+
+is the result.
+
+Notice that we have a
+strain singularity.
+
+This is the first
+element here.
+
+The next element--
+
+this is here--
+
+the next element in b matrix,
+and that is the third element
+
+in the b matrix.
+
+Notice that we have in this
+element, that one, and that
+
+one the one over square root
+x, which means that we have
+
+one over square root
+x singularity
+
+at x equal to zero.
+
+Well, this fact is used very
+effectively in fracture
+
+mechanics analysis.
+
+Assume that we have crack here
+and that we want to analyze
+
+the stress conditions
+around that crack.
+
+What we can do is we use now two
+dimension elements, as its
+
+a plane stress situation.
+
+We would put a two dimensional
+triangular element there and
+
+we shift the midpoint nodes.
+
+This is now very small
+here, but I hope
+
+you can still follow.
+
+You shift these midpoint nodes
+to the quarter point, just the
+
+way we have been
+doing it here.
+
+You are putting the third node
+the quarter point and the
+
+result is that at this crack tip
+we have a one over square
+
+root x singularity, using
+this element layout.
+
+And we know that in fact, there
+is a one over square
+
+root x singularity in linear
+fracture mechanics analysis.
+
+And so this is an effective
+way of capturing this
+
+singularity, and has been used
+or is currently being used
+
+very abundantly in practice.
+
+The important point that I
+wanted to make really is that
+
+we can shift nodes in the
+element to our advantage.
+
+But, we really do that in
+specific applications such as
+
+fracture mechanics.
+
+In general we will see later
+when I talk about modeling of
+
+finite element systems, in
+general, it is most effective
+
+to leave the mid-side nodes at
+their physical midpoints.
+
+In other words for an
+eight-noded element, two
+
+dimensional analysis, we would
+put this mid-node in the
+
+physical space also, actually
+at the midpoint.
+
+We would not shift it.
+
+Then the element has good
+convergence characteristics
+
+into all directions and this is
+really how the element is
+
+used most effectively for
+general applications.
+
+However, in specific
+applications, such as fracture
+
+mechanics analysis, it can be
+of advantage to shift these
+
+mid-side nodes to pick up
+certain strain or stress
+
+singularities that
+we know do exist.
+
+Now on the last transparency
+that I wanted to show you, I
+
+wanted to indicate something to
+you that I will be talking
+
+about in later lectures more
+abundantly, namely the fact
+
+that we're using numerical
+integration.
+
+B, for the k matrix as an
+example, is once again now a
+
+function of r and s.
+
+This part here is also a
+function of r and s.
+
+So we have here function
+of r and s.
+
+and we have here also a
+function of r and s.
+
+So this f matrix here is
+a function of r and s.
+
+Notice that the b also includes
+the inversion of the
+
+j, the Jacobian matrix.
+
+It includes the inversion of
+the j, because we had to
+
+construct the x and y and z
+derivatives from the r, s, and
+
+t derivatives.
+
+So, what we do in practical
+analysis is that we use
+
+numerical integration to
+evaluate the k matrix.
+
+I have indicated that here
+schematically, if you look at
+
+this element here.
+
+What we do is, we evaluate the
+f matrix-- this is a matrix.
+
+In two dimensional analysis we
+would only run over i and j.
+
+I is this direction.
+
+J is that direction.
+
+In three dimensional analysis,
+which is in general analysis,
+
+we run i, j, and k this way.
+
+We evaluate the f matrix
+here at specific
+
+points, r, s, and t.
+
+T now being this axis.
+
+And then multiply that f matrix
+by certain weight
+
+constants and sum these
+contributions over all i, j,
+
+and k, in order to obtain an
+accurate enough approximation
+
+to the actual stiffness
+matrix.
+
+The order of approximation
+with which we obtain the
+
+actual stiffness matrix--
+
+or rather how closely the
+numerically calculated
+
+stiffness matrix approximates
+the actual stiffness matrix--
+
+depends on, number one, how many
+integration points we are
+
+using and what kind
+of integration
+
+scheme we are using.
+
+These points here correspond
+to the Gauss numerical
+
+integration.
+
+In this case for two dimensional
+analysis, we would
+
+use a two by two integration.
+
+In other words, i and j would
+both run from one to two.
+
+K is not applicable and we would
+have altogether four
+
+evaluations off the Fs here.
+
+Multiply each of them by
+weighting factors, which has
+
+been derived for us by Gauss
+some long time ago.
+
+And summing up these
+contributions gives us a close
+
+enough approximation
+to the k matrix.
+
+Of course, the question of how
+many points we have to use,
+
+what integration scheme we
+should use, is a very
+
+important one.
+
+We must use enough integration
+points to get a close enough
+
+approximation to the actual
+stiffness matrix and I will be
+
+addressing those questions
+in a later lecture.
+
+This is all I wanted to
+say in this lecture.
+
+Thank you very much for
+your attention.
\ No newline at end of file
diff --git a/E58_lRznkDg.txt b/E58_lRznkDg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..200bf78768ca2993a697f3ec68d9937d92db80d3
--- /dev/null
+++ b/E58_lRznkDg.txt
@@ -0,0 +1,8547 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
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+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu we're going to do the first
+
+ align:start position:0%
+ocw.mit.edu we're going to do the first
+ 
+
+ align:start position:0%
+ocw.mit.edu we're going to do the first
+of three lectures on the last topic
+
+ align:start position:0%
+of three lectures on the last topic
+ 
+
+ align:start position:0%
+of three lectures on the last topic
+we're going to talk about phase diagram
+
+ align:start position:0%
+we're going to talk about phase diagram
+ 
+
+ align:start position:0%
+we're going to talk about phase diagram
+starting today Monday and wrap it up on
+
+ align:start position:0%
+starting today Monday and wrap it up on
+ 
+
+ align:start position:0%
+starting today Monday and wrap it up on
+Wednesday
+
+ align:start position:0%
+Wednesday
+ 
+
+ align:start position:0%
+Wednesday
+um phase diagrams is related to the
+
+ align:start position:0%
+um phase diagrams is related to the
+ 
+
+ align:start position:0%
+um phase diagrams is related to the
+question of stability and sustaining the
+
+ align:start position:0%
+question of stability and sustaining the
+ 
+
+ align:start position:0%
+question of stability and sustaining the
+solid state and we've talked about the
+
+ align:start position:0%
+solid state and we've talked about the
+ 
+
+ align:start position:0%
+solid state and we've talked about the
+behavior of solids and we've used solids
+
+ align:start position:0%
+behavior of solids and we've used solids
+ 
+
+ align:start position:0%
+behavior of solids and we've used solids
+in order to teach the rudiments of
+
+ align:start position:0%
+in order to teach the rudiments of
+ 
+
+ align:start position:0%
+in order to teach the rudiments of
+chemistry but today I want to talk about
+
+ align:start position:0%
+chemistry but today I want to talk about
+ 
+
+ align:start position:0%
+chemistry but today I want to talk about
+the conditions under which solids are
+
+ align:start position:0%
+the conditions under which solids are
+ 
+
+ align:start position:0%
+the conditions under which solids are
+stable and uh what under what conditions
+
+ align:start position:0%
+stable and uh what under what conditions
+ 
+
+ align:start position:0%
+stable and uh what under what conditions
+do solids uh remain stable when they
+
+ align:start position:0%
+do solids uh remain stable when they
+ 
+
+ align:start position:0%
+do solids uh remain stable when they
+become unstable this important in
+
+ align:start position:0%
+become unstable this important in
+ 
+
+ align:start position:0%
+become unstable this important in
+industry for example if you're running a
+
+ align:start position:0%
+industry for example if you're running a
+ 
+
+ align:start position:0%
+industry for example if you're running a
+cast chop you're making Auto Parts you
+
+ align:start position:0%
+cast chop you're making Auto Parts you
+ 
+
+ align:start position:0%
+cast chop you're making Auto Parts you
+want to know what the solidification
+
+ align:start position:0%
+want to know what the solidification
+ 
+
+ align:start position:0%
+want to know what the solidification
+temperature is of a particular alloy
+
+ align:start position:0%
+temperature is of a particular alloy
+ 
+
+ align:start position:0%
+temperature is of a particular alloy
+it's important in failure analysis
+
+ align:start position:0%
+it's important in failure analysis
+ 
+
+ align:start position:0%
+it's important in failure analysis
+something like U the fall of the World
+
+ align:start position:0%
+something like U the fall of the World
+ 
+
+ align:start position:0%
+something like U the fall of the World
+Trade Center looking at the metal
+
+ align:start position:0%
+Trade Center looking at the metal
+ 
+
+ align:start position:0%
+Trade Center looking at the metal
+specimens to determine what was the mode
+
+ align:start position:0%
+specimens to determine what was the mode
+ 
+
+ align:start position:0%
+specimens to determine what was the mode
+of failure the temperature excursions
+
+ align:start position:0%
+of failure the temperature excursions
+ 
+
+ align:start position:0%
+of failure the temperature excursions
+leave a signature a thermal signature
+
+ align:start position:0%
+leave a signature a thermal signature
+ 
+
+ align:start position:0%
+leave a signature a thermal signature
+indicative of the history of what
+
+ align:start position:0%
+indicative of the history of what
+ 
+
+ align:start position:0%
+indicative of the history of what
+happened to that object and by
+
+ align:start position:0%
+happened to that object and by
+ 
+
+ align:start position:0%
+happened to that object and by
+determining whether something went above
+
+ align:start position:0%
+determining whether something went above
+ 
+
+ align:start position:0%
+determining whether something went above
+a certain phase transformation
+
+ align:start position:0%
+a certain phase transformation
+ 
+
+ align:start position:0%
+a certain phase transformation
+temperature we can retrace reconstruct
+
+ align:start position:0%
+temperature we can retrace reconstruct
+ 
+
+ align:start position:0%
+temperature we can retrace reconstruct
+the uh the
+
+ align:start position:0%
+the uh the
+ 
+
+ align:start position:0%
+the uh the
+incident you might say well gee what's
+
+ align:start position:0%
+incident you might say well gee what's
+ 
+
+ align:start position:0%
+incident you might say well gee what's
+the big deal I mean you you look on
+
+ align:start position:0%
+the big deal I mean you you look on
+ 
+
+ align:start position:0%
+the big deal I mean you you look on
+the look up in the tables everybody
+
+ align:start position:0%
+the look up in the tables everybody
+ 
+
+ align:start position:0%
+the look up in the tables everybody
+knows that water boils at 100°
+
+ align:start position:0%
+knows that water boils at 100°
+ 
+
+ align:start position:0%
+knows that water boils at 100°
+Centigrade but maybe it's not so simple
+
+ align:start position:0%
+Centigrade but maybe it's not so simple
+ 
+
+ align:start position:0%
+Centigrade but maybe it's not so simple
+let's say you decide to realize your
+
+ align:start position:0%
+let's say you decide to realize your
+ 
+
+ align:start position:0%
+let's say you decide to realize your
+life's Ambitions and you're going to go
+
+ align:start position:0%
+life's Ambitions and you're going to go
+ 
+
+ align:start position:0%
+life's Ambitions and you're going to go
+climb Mount Everest so you plop down
+
+ align:start position:0%
+climb Mount Everest so you plop down
+ 
+
+ align:start position:0%
+climb Mount Everest so you plop down
+$10,000 you get a permit from the napes
+
+ align:start position:0%
+$10,000 you get a permit from the napes
+ 
+
+ align:start position:0%
+$10,000 you get a permit from the napes
+government the next thing you know
+
+ align:start position:0%
+government the next thing you know
+ 
+
+ align:start position:0%
+government the next thing you know
+you're at base camp 20,000 ft you have a
+
+ align:start position:0%
+you're at base camp 20,000 ft you have a
+ 
+
+ align:start position:0%
+you're at base camp 20,000 ft you have a
+hankering for soft Bo boiled egg so you
+
+ align:start position:0%
+hankering for soft Bo boiled egg so you
+ 
+
+ align:start position:0%
+hankering for soft Bo boiled egg so you
+pitch of campfire put in the
+
+ align:start position:0%
+pitch of campfire put in the
+ 
+
+ align:start position:0%
+pitch of campfire put in the
+eggs 5 minutes 10 minutes 15 minutes
+
+ align:start position:0%
+eggs 5 minutes 10 minutes 15 minutes
+ 
+
+ align:start position:0%
+eggs 5 minutes 10 minutes 15 minutes
+pardon me you want hard boiled eggs you
+
+ align:start position:0%
+pardon me you want hard boiled eggs you
+ 
+
+ align:start position:0%
+pardon me you want hard boiled eggs you
+want hardboiled eggs after 15 minutes
+
+ align:start position:0%
+want hardboiled eggs after 15 minutes
+ 
+
+ align:start position:0%
+want hardboiled eggs after 15 minutes
+you open the eggs they're still
+
+ align:start position:0%
+you open the eggs they're still
+ 
+
+ align:start position:0%
+you open the eggs they're still
+running you get really steamed you 20
+
+ align:start position:0%
+running you get really steamed you 20
+ 
+
+ align:start position:0%
+running you get really steamed you 20
+minutes 25 minutes every time the Yol is
+
+ align:start position:0%
+minutes 25 minutes every time the Yol is
+ 
+
+ align:start position:0%
+minutes 25 minutes every time the Yol is
+still running the white is converted but
+
+ align:start position:0%
+still running the white is converted but
+ 
+
+ align:start position:0%
+still running the white is converted but
+the yolk is still running what's going
+
+ align:start position:0%
+the yolk is still running what's going
+ 
+
+ align:start position:0%
+the yolk is still running what's going
+on well we talked about denaturing the
+
+ align:start position:0%
+on well we talked about denaturing the
+ 
+
+ align:start position:0%
+on well we talked about denaturing the
+white denatures at 65°
+
+ align:start position:0%
+white denatures at 65°
+ 
+
+ align:start position:0%
+white denatures at 65°
+Centigrade but
+
+ align:start position:0%
+Centigrade but
+ 
+
+ align:start position:0%
+Centigrade but
+at 20,000 ft the atmospheric pressure is
+
+ align:start position:0%
+at 20,000 ft the atmospheric pressure is
+ 
+
+ align:start position:0%
+at 20,000 ft the atmospheric pressure is
+reduced to the point that water boils at
+
+ align:start position:0%
+reduced to the point that water boils at
+ 
+
+ align:start position:0%
+reduced to the point that water boils at
+below the denaturing temperature of the
+
+ align:start position:0%
+below the denaturing temperature of the
+ 
+
+ align:start position:0%
+below the denaturing temperature of the
+egg yolk and so you can boil until the
+
+ align:start position:0%
+egg yolk and so you can boil until the
+ 
+
+ align:start position:0%
+egg yolk and so you can boil until the
+end of time and you'll always have
+
+ align:start position:0%
+end of time and you'll always have
+ 
+
+ align:start position:0%
+end of time and you'll always have
+softboiled eggs if you like softboiled
+
+ align:start position:0%
+softboiled eggs if you like softboiled
+ 
+
+ align:start position:0%
+softboiled eggs if you like softboiled
+eggs you cannot screw up you cannot
+
+ align:start position:0%
+eggs you cannot screw up you cannot
+ 
+
+ align:start position:0%
+eggs you cannot screw up you cannot
+screw up okay so what do we know from
+
+ align:start position:0%
+screw up okay so what do we know from
+ 
+
+ align:start position:0%
+screw up okay so what do we know from
+this little anecdote this little
+
+ align:start position:0%
+this little anecdote this little
+ 
+
+ align:start position:0%
+this little anecdote this little
+anecdote is that the boiling point the
+
+ align:start position:0%
+anecdote is that the boiling point the
+ 
+
+ align:start position:0%
+anecdote is that the boiling point the
+boiling point is a function of pressure
+
+ align:start position:0%
+boiling point is a function of pressure
+ 
+
+ align:start position:0%
+boiling point is a function of pressure
+so it's not that simple let's go to
+
+ align:start position:0%
+so it's not that simple let's go to
+ 
+
+ align:start position:0%
+so it's not that simple let's go to
+another place let's go uh let's go under
+
+ align:start position:0%
+another place let's go uh let's go under
+ 
+
+ align:start position:0%
+another place let's go uh let's go under
+the hood of a car one my favorite places
+
+ align:start position:0%
+the hood of a car one my favorite places
+ 
+
+ align:start position:0%
+the hood of a car one my favorite places
+okay so here's what's going on under the
+
+ align:start position:0%
+okay so here's what's going on under the
+ 
+
+ align:start position:0%
+okay so here's what's going on under the
+hood of a car here you've got the
+
+ align:start position:0%
+hood of a car here you've got the
+ 
+
+ align:start position:0%
+hood of a car here you've got the
+engine and inside the engine we have
+
+ align:start position:0%
+engine and inside the engine we have
+ 
+
+ align:start position:0%
+engine and inside the engine we have
+combustion and the combustion gives off
+
+ align:start position:0%
+combustion and the combustion gives off
+ 
+
+ align:start position:0%
+combustion and the combustion gives off
+a huge amount of heat we have to
+
+ align:start position:0%
+a huge amount of heat we have to
+ 
+
+ align:start position:0%
+a huge amount of heat we have to
+dissipate that heat so we have water
+
+ align:start position:0%
+dissipate that heat so we have water
+ 
+
+ align:start position:0%
+dissipate that heat so we have water
+channels running through the engine and
+
+ align:start position:0%
+channels running through the engine and
+ 
+
+ align:start position:0%
+channels running through the engine and
+out to the radiator and the radiator
+
+ align:start position:0%
+out to the radiator and the radiator
+ 
+
+ align:start position:0%
+out to the radiator and the radiator
+cools this water before recirculating it
+
+ align:start position:0%
+cools this water before recirculating it
+ 
+
+ align:start position:0%
+cools this water before recirculating it
+thanks to the action of either fand or
+
+ align:start position:0%
+thanks to the action of either fand or
+ 
+
+ align:start position:0%
+thanks to the action of either fand or
+wind or some kind of movement of
+
+ align:start position:0%
+wind or some kind of movement of
+ 
+
+ align:start position:0%
+wind or some kind of movement of
+air and so what's the principle here the
+
+ align:start position:0%
+air and so what's the principle here the
+ 
+
+ align:start position:0%
+air and so what's the principle here the
+principle here is that inside the
+
+ align:start position:0%
+principle here is that inside the
+ 
+
+ align:start position:0%
+principle here is that inside the
+radiator we've got solid this is the the
+
+ align:start position:0%
+radiator we've got solid this is the the
+ 
+
+ align:start position:0%
+radiator we've got solid this is the the
+rad it's probably made of uh the old
+
+ align:start position:0%
+rad it's probably made of uh the old
+ 
+
+ align:start position:0%
+rad it's probably made of uh the old
+days they made them out of copper but
+
+ align:start position:0%
+days they made them out of copper but
+ 
+
+ align:start position:0%
+days they made them out of copper but
+nowadays they're making more and more of
+
+ align:start position:0%
+nowadays they're making more and more of
+ 
+
+ align:start position:0%
+nowadays they're making more and more of
+them out of aluminum and we have liquid
+
+ align:start position:0%
+them out of aluminum and we have liquid
+ 
+
+ align:start position:0%
+them out of aluminum and we have liquid
+which is the coolant this is the coolant
+
+ align:start position:0%
+which is the coolant this is the coolant
+ 
+
+ align:start position:0%
+which is the coolant this is the coolant
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+water and we have a big delta T here
+
+ align:start position:0%
+water and we have a big delta T here
+ 
+
+ align:start position:0%
+water and we have a big delta T here
+right this is hot this is cool and so we
+
+ align:start position:0%
+right this is hot this is cool and so we
+ 
+
+ align:start position:0%
+right this is hot this is cool and so we
+have a heat flux going in this direction
+
+ align:start position:0%
+have a heat flux going in this direction
+ 
+
+ align:start position:0%
+have a heat flux going in this direction
+and this is working great because the
+
+ align:start position:0%
+and this is working great because the
+ 
+
+ align:start position:0%
+and this is working great because the
+density of water is high and so
+
+ align:start position:0%
+density of water is high and so
+ 
+
+ align:start position:0%
+density of water is high and so
+therefore it's able to transfer heat
+
+ align:start position:0%
+therefore it's able to transfer heat
+ 
+
+ align:start position:0%
+therefore it's able to transfer heat
+very efficiently so this is good this is
+
+ align:start position:0%
+very efficiently so this is good this is
+ 
+
+ align:start position:0%
+very efficiently so this is good this is
+really good what can happen if things go
+
+ align:start position:0%
+really good what can happen if things go
+ 
+
+ align:start position:0%
+really good what can happen if things go
+out of control things go out of control
+
+ align:start position:0%
+out of control things go out of control
+ 
+
+ align:start position:0%
+out of control things go out of control
+and we start to boil and you know that
+
+ align:start position:0%
+and we start to boil and you know that
+ 
+
+ align:start position:0%
+and we start to boil and you know that
+the boiling point of water is more or
+
+ align:start position:0%
+the boiling point of water is more or
+ 
+
+ align:start position:0%
+the boiling point of water is more or
+less 100° Centigrade we're down here
+
+ align:start position:0%
+less 100° Centigrade we're down here
+ 
+
+ align:start position:0%
+less 100° Centigrade we're down here
+we're not at the base camp in Mount
+
+ align:start position:0%
+we're not at the base camp in Mount
+ 
+
+ align:start position:0%
+we're not at the base camp in Mount
+Everest here's what happens when things
+
+ align:start position:0%
+Everest here's what happens when things
+ 
+
+ align:start position:0%
+Everest here's what happens when things
+start to go out of control now we start
+
+ align:start position:0%
+start to go out of control now we start
+ 
+
+ align:start position:0%
+start to go out of control now we start
+to get
+
+ align:start position:0%
+to get
+ 
+
+ align:start position:0%
+to get
+gas bubbles these are the gas bubbles
+
+ align:start position:0%
+gas bubbles these are the gas bubbles
+ 
+
+ align:start position:0%
+gas bubbles these are the gas bubbles
+associated with the boiling of water and
+
+ align:start position:0%
+associated with the boiling of water and
+ 
+
+ align:start position:0%
+associated with the boiling of water and
+now the heat transfer between gas and
+
+ align:start position:0%
+now the heat transfer between gas and
+ 
+
+ align:start position:0%
+now the heat transfer between gas and
+solid between gas and solid is very poor
+
+ align:start position:0%
+solid between gas and solid is very poor
+ 
+
+ align:start position:0%
+solid between gas and solid is very poor
+think about it what's transferring the
+
+ align:start position:0%
+think about it what's transferring the
+ 
+
+ align:start position:0%
+think about it what's transferring the
+heat it's the atoms and the atom density
+
+ align:start position:0%
+heat it's the atoms and the atom density
+ 
+
+ align:start position:0%
+heat it's the atoms and the atom density
+in a gas is sparse SO gas is a very poor
+
+ align:start position:0%
+in a gas is sparse SO gas is a very poor
+ 
+
+ align:start position:0%
+in a gas is sparse SO gas is a very poor
+heat transfer medium so we must avoid
+
+ align:start position:0%
+heat transfer medium so we must avoid
+ 
+
+ align:start position:0%
+heat transfer medium so we must avoid
+boiling if we get boiling then we get
+
+ align:start position:0%
+boiling if we get boiling then we get
+ 
+
+ align:start position:0%
+boiling if we get boiling then we get
+into a thermal runaway situation because
+
+ align:start position:0%
+into a thermal runaway situation because
+ 
+
+ align:start position:0%
+into a thermal runaway situation because
+now we got boiling in the first place
+
+ align:start position:0%
+now we got boiling in the first place
+ 
+
+ align:start position:0%
+now we got boiling in the first place
+cuz the water was too hot but now we're
+
+ align:start position:0%
+cuz the water was too hot but now we're
+ 
+
+ align:start position:0%
+cuz the water was too hot but now we're
+doing a less efficient job of cooling
+
+ align:start position:0%
+doing a less efficient job of cooling
+ 
+
+ align:start position:0%
+doing a less efficient job of cooling
+and it's going to get worse and worse
+
+ align:start position:0%
+and it's going to get worse and worse
+ 
+
+ align:start position:0%
+and it's going to get worse and worse
+and worse until finally boom so what I
+
+ align:start position:0%
+and worse until finally boom so what I
+ 
+
+ align:start position:0%
+and worse until finally boom so what I
+want to do is I want to get my liquid
+
+ align:start position:0%
+want to do is I want to get my liquid
+ 
+
+ align:start position:0%
+want to do is I want to get my liquid
+range I want to tailor the properties of
+
+ align:start position:0%
+range I want to tailor the properties of
+ 
+
+ align:start position:0%
+range I want to tailor the properties of
+the coolant I want a coolant that will
+
+ align:start position:0%
+the coolant I want a coolant that will
+ 
+
+ align:start position:0%
+the coolant I want a coolant that will
+be boil over prooof so if I could raise
+
+ align:start position:0%
+be boil over prooof so if I could raise
+ 
+
+ align:start position:0%
+be boil over prooof so if I could raise
+the boiling point that would make the
+
+ align:start position:0%
+the boiling point that would make the
+ 
+
+ align:start position:0%
+the boiling point that would make the
+car safer to drive under extreme
+
+ align:start position:0%
+car safer to drive under extreme
+ 
+
+ align:start position:0%
+car safer to drive under extreme
+conditions typically what happens is
+
+ align:start position:0%
+conditions typically what happens is
+ 
+
+ align:start position:0%
+conditions typically what happens is
+you're zooming down the highway on a hot
+
+ align:start position:0%
+you're zooming down the highway on a hot
+ 
+
+ align:start position:0%
+you're zooming down the highway on a hot
+summer's day and then there's a some
+
+ align:start position:0%
+summer's day and then there's a some
+ 
+
+ align:start position:0%
+summer's day and then there's a some
+reason to come to an abrupt stop and
+
+ align:start position:0%
+reason to come to an abrupt stop and
+ 
+
+ align:start position:0%
+reason to come to an abrupt stop and
+then there's all that heat to be
+
+ align:start position:0%
+then there's all that heat to be
+ 
+
+ align:start position:0%
+then there's all that heat to be
+dissipated and no more do you get the
+
+ align:start position:0%
+dissipated and no more do you get the
+ 
+
+ align:start position:0%
+dissipated and no more do you get the
+benefit of the motion of the car now
+
+ align:start position:0%
+benefit of the motion of the car now
+ 
+
+ align:start position:0%
+benefit of the motion of the car now
+you're just relying on the fan so what
+
+ align:start position:0%
+you're just relying on the fan so what
+ 
+
+ align:start position:0%
+you're just relying on the fan so what
+can we do if we go to the top of Everest
+
+ align:start position:0%
+can we do if we go to the top of Everest
+ 
+
+ align:start position:0%
+can we do if we go to the top of Everest
+and the pressure goes down and the
+
+ align:start position:0%
+and the pressure goes down and the
+ 
+
+ align:start position:0%
+and the pressure goes down and the
+boiling point Falls could I raise the
+
+ align:start position:0%
+boiling point Falls could I raise the
+ 
+
+ align:start position:0%
+boiling point Falls could I raise the
+boiling point by applying more pressure
+
+ align:start position:0%
+boiling point by applying more pressure
+ 
+
+ align:start position:0%
+boiling point by applying more pressure
+yeah let's put a pressure cap on the
+
+ align:start position:0%
+yeah let's put a pressure cap on the
+ 
+
+ align:start position:0%
+yeah let's put a pressure cap on the
+radiator let's keep the contents of the
+
+ align:start position:0%
+radiator let's keep the contents of the
+ 
+
+ align:start position:0%
+radiator let's keep the contents of the
+radiator high and if you read the top
+
+ align:start position:0%
+radiator high and if you read the top
+ 
+
+ align:start position:0%
+radiator high and if you read the top
+it'll say 15 psi which is one atmosphere
+
+ align:start position:0%
+it'll say 15 psi which is one atmosphere
+ 
+
+ align:start position:0%
+it'll say 15 psi which is one atmosphere
+so I've got one atmosphere here plus an
+
+ align:start position:0%
+so I've got one atmosphere here plus an
+ 
+
+ align:start position:0%
+so I've got one atmosphere here plus an
+extra atmosphere so I'm running at two
+
+ align:start position:0%
+extra atmosphere so I'm running at two
+ 
+
+ align:start position:0%
+extra atmosphere so I'm running at two
+atmospheres pressure so that will raise
+
+ align:start position:0%
+atmospheres pressure so that will raise
+ 
+
+ align:start position:0%
+atmospheres pressure so that will raise
+the boiling point and Stave off the
+
+ align:start position:0%
+the boiling point and Stave off the
+ 
+
+ align:start position:0%
+the boiling point and Stave off the
+dangerous gas Evolution and then I can
+
+ align:start position:0%
+dangerous gas Evolution and then I can
+ 
+
+ align:start position:0%
+dangerous gas Evolution and then I can
+do one more thing instead of running
+
+ align:start position:0%
+do one more thing instead of running
+ 
+
+ align:start position:0%
+do one more thing instead of running
+pure water I will add ethylene
+
+ align:start position:0%
+pure water I will add ethylene
+ 
+
+ align:start position:0%
+pure water I will add ethylene
+glycol I'll add ethylene glycol about 50
+
+ align:start position:0%
+glycol I'll add ethylene glycol about 50
+ 
+
+ align:start position:0%
+glycol I'll add ethylene glycol about 50
+per volume you know this is antifreeze
+
+ align:start position:0%
+per volume you know this is antifreeze
+ 
+
+ align:start position:0%
+per volume you know this is antifreeze
+it gives a freezing point depression
+
+ align:start position:0%
+it gives a freezing point depression
+ 
+
+ align:start position:0%
+it gives a freezing point depression
+we'll talk talk about that next day but
+
+ align:start position:0%
+we'll talk talk about that next day but
+ 
+
+ align:start position:0%
+we'll talk talk about that next day but
+it also gives boiling point elevation so
+
+ align:start position:0%
+it also gives boiling point elevation so
+ 
+
+ align:start position:0%
+it also gives boiling point elevation so
+in the summertime you should always run
+
+ align:start position:0%
+in the summertime you should always run
+ 
+
+ align:start position:0%
+in the summertime you should always run
+with antifreeze because the combination
+
+ align:start position:0%
+with antifreeze because the combination
+ 
+
+ align:start position:0%
+with antifreeze because the combination
+of the pressure cap plus the addition of
+
+ align:start position:0%
+of the pressure cap plus the addition of
+ 
+
+ align:start position:0%
+of the pressure cap plus the addition of
+the glycol raises the boiling point from
+
+ align:start position:0%
+the glycol raises the boiling point from
+ 
+
+ align:start position:0%
+the glycol raises the boiling point from
+212 I'm talking about car so I'm going
+
+ align:start position:0%
+212 I'm talking about car so I'm going
+ 
+
+ align:start position:0%
+212 I'm talking about car so I'm going
+to use Fahrenheit here 212° Fahrenheit
+
+ align:start position:0%
+to use Fahrenheit here 212° Fahrenheit
+ 
+
+ align:start position:0%
+to use Fahrenheit here 212° Fahrenheit
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+265° fahr this buys you a much higher
+
+ align:start position:0%
+265° fahr this buys you a much higher
+ 
+
+ align:start position:0%
+265° fahr this buys you a much higher
+cushion so what are we doing we're
+
+ align:start position:0%
+cushion so what are we doing we're
+ 
+
+ align:start position:0%
+cushion so what are we doing we're
+tailoring this by making the boiling
+
+ align:start position:0%
+tailoring this by making the boiling
+ 
+
+ align:start position:0%
+tailoring this by making the boiling
+point a function of pressure and now I'm
+
+ align:start position:0%
+point a function of pressure and now I'm
+ 
+
+ align:start position:0%
+point a function of pressure and now I'm
+showing you that it's also a function of
+
+ align:start position:0%
+showing you that it's also a function of
+ 
+
+ align:start position:0%
+showing you that it's also a function of
+composition so this whole business of
+
+ align:start position:0%
+composition so this whole business of
+ 
+
+ align:start position:0%
+composition so this whole business of
+solid state stability I hope I'm showing
+
+ align:start position:0%
+solid state stability I hope I'm showing
+ 
+
+ align:start position:0%
+solid state stability I hope I'm showing
+you has a little bit more to it than
+
+ align:start position:0%
+you has a little bit more to it than
+ 
+
+ align:start position:0%
+you has a little bit more to it than
+just looking up the transformation
+
+ align:start position:0%
+just looking up the transformation
+ 
+
+ align:start position:0%
+just looking up the transformation
+temperature on the periodic table or the
+
+ align:start position:0%
+temperature on the periodic table or the
+ 
+
+ align:start position:0%
+temperature on the periodic table or the
+handbook so I want to talk to you for
+
+ align:start position:0%
+handbook so I want to talk to you for
+ 
+
+ align:start position:0%
+handbook so I want to talk to you for
+the next three lectures about phase
+
+ align:start position:0%
+the next three lectures about phase
+ 
+
+ align:start position:0%
+the next three lectures about phase
+diagrams phase diagrams are atlases
+
+ align:start position:0%
+diagrams phase diagrams are atlases
+ 
+
+ align:start position:0%
+diagrams phase diagrams are atlases
+they're Maps they're maps of stability
+
+ align:start position:0%
+they're Maps they're maps of stability
+ 
+
+ align:start position:0%
+they're Maps they're maps of stability
+that answer the question if you specify
+
+ align:start position:0%
+that answer the question if you specify
+ 
+
+ align:start position:0%
+that answer the question if you specify
+pressure composition temperature what
+
+ align:start position:0%
+pressure composition temperature what
+ 
+
+ align:start position:0%
+pressure composition temperature what
+are the stable phases so that's what you
+
+ align:start position:0%
+are the stable phases so that's what you
+ 
+
+ align:start position:0%
+are the stable phases so that's what you
+need to know so let's talk about phase
+
+ align:start position:0%
+need to know so let's talk about phase
+ 
+
+ align:start position:0%
+need to know so let's talk about phase
+diagrams phase
+
+ align:start position:0%
+diagrams phase
+ 
+
+ align:start position:0%
+diagrams phase
+diagrams as stability
+
+ align:start position:0%
+diagrams as stability
+ 
+
+ align:start position:0%
+diagrams as stability
+Maps stability Maps the stability of
+
+ align:start position:0%
+Maps stability Maps the stability of
+ 
+
+ align:start position:0%
+Maps stability Maps the stability of
+what the stability of the state of
+
+ align:start position:0%
+what the stability of the state of
+ 
+
+ align:start position:0%
+what the stability of the state of
+aggregation it's going to tell us if
+
+ align:start position:0%
+aggregation it's going to tell us if
+ 
+
+ align:start position:0%
+aggregation it's going to tell us if
+it's solid liquid gas
+
+ align:start position:0%
+it's solid liquid gas
+ 
+
+ align:start position:0%
+it's solid liquid gas
+and under what
+
+ align:start position:0%
+and under what
+ 
+
+ align:start position:0%
+and under what
+circumstances so let's look at some uh
+
+ align:start position:0%
+circumstances so let's look at some uh
+ 
+
+ align:start position:0%
+circumstances so let's look at some uh
+simple phase diagrams but before we can
+
+ align:start position:0%
+simple phase diagrams but before we can
+ 
+
+ align:start position:0%
+simple phase diagrams but before we can
+do it I need to Define some terms for
+
+ align:start position:0%
+do it I need to Define some terms for
+ 
+
+ align:start position:0%
+do it I need to Define some terms for
+you so first of all let's define the
+
+ align:start position:0%
+you so first of all let's define the
+ 
+
+ align:start position:0%
+you so first of all let's define the
+term phase the phase is a region of a
+
+ align:start position:0%
+term phase the phase is a region of a
+ 
+
+ align:start position:0%
+term phase the phase is a region of a
+substance a region of a substance that
+
+ align:start position:0%
+substance a region of a substance that
+ 
+
+ align:start position:0%
+substance a region of a substance that
+has the following
+
+ align:start position:0%
+has the following
+ 
+
+ align:start position:0%
+has the following
+characteristics
+
+ align:start position:0%
+characteristics
+ 
+
+ align:start position:0%
+characteristics
+uniform and chemical
+
+ align:start position:0%
+uniform and chemical
+ 
+
+ align:start position:0%
+uniform and chemical
+composition it's uniform in chemical
+
+ align:start position:0%
+composition it's uniform in chemical
+ 
+
+ align:start position:0%
+composition it's uniform in chemical
+composition the second thing about it is
+
+ align:start position:0%
+composition the second thing about it is
+ 
+
+ align:start position:0%
+composition the second thing about it is
+that it's physically
+
+ align:start position:0%
+that it's physically
+ 
+
+ align:start position:0%
+that it's physically
+distinct physically distinct and I'll
+
+ align:start position:0%
+distinct physically distinct and I'll
+ 
+
+ align:start position:0%
+distinct physically distinct and I'll
+give you some rich examples I I want put
+
+ align:start position:0%
+give you some rich examples I I want put
+ 
+
+ align:start position:0%
+give you some rich examples I I want put
+this down just to document it and then
+
+ align:start position:0%
+this down just to document it and then
+ 
+
+ align:start position:0%
+this down just to document it and then
+after you see a few examples these words
+
+ align:start position:0%
+after you see a few examples these words
+ 
+
+ align:start position:0%
+after you see a few examples these words
+will mean something to you so it's
+
+ align:start position:0%
+will mean something to you so it's
+ 
+
+ align:start position:0%
+will mean something to you so it's
+physically distinct and uh in the
+
+ align:start position:0%
+physically distinct and uh in the
+ 
+
+ align:start position:0%
+physically distinct and uh in the
+extreme it's mechanically
+
+ align:start position:0%
+extreme it's mechanically
+ 
+
+ align:start position:0%
+extreme it's mechanically
+separable it's mechanically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separable physically distinct and
+
+ align:start position:0%
+separable physically distinct and
+ 
+
+ align:start position:0%
+separable physically distinct and
+mechanically separable so let's look at
+
+ align:start position:0%
+mechanically separable so let's look at
+ 
+
+ align:start position:0%
+mechanically separable so let's look at
+some examples of one phase and two-phase
+
+ align:start position:0%
+some examples of one phase and two-phase
+ 
+
+ align:start position:0%
+some examples of one phase and two-phase
+systems and you this is one of these
+
+ align:start position:0%
+systems and you this is one of these
+ 
+
+ align:start position:0%
+systems and you this is one of these
+days where we we're using symbols to
+
+ align:start position:0%
+days where we we're using symbols to
+ 
+
+ align:start position:0%
+days where we we're using symbols to
+mean multiple meanings I've already used
+
+ align:start position:0%
+mean multiple meanings I've already used
+ 
+
+ align:start position:0%
+mean multiple meanings I've already used
+P to represent pressure if I use P now
+
+ align:start position:0%
+P to represent pressure if I use P now
+ 
+
+ align:start position:0%
+P to represent pressure if I use P now
+to represent number of phases you won't
+
+ align:start position:0%
+to represent number of phases you won't
+ 
+
+ align:start position:0%
+to represent number of phases you won't
+be able to tell one from the other so I
+
+ align:start position:0%
+be able to tell one from the other so I
+ 
+
+ align:start position:0%
+be able to tell one from the other so I
+feel a little bit Western today so I'll
+
+ align:start position:0%
+feel a little bit Western today so I'll
+ 
+
+ align:start position:0%
+feel a little bit Western today so I'll
+make it Circle P so Circle P equals
+
+ align:start position:0%
+make it Circle P so Circle P equals
+ 
+
+ align:start position:0%
+make it Circle P so Circle P equals
+number of phases not to be confused with
+
+ align:start position:0%
+number of phases not to be confused with
+ 
+
+ align:start position:0%
+number of phases not to be confused with
+P which is the pressure so number of
+
+ align:start position:0%
+P which is the pressure so number of
+ 
+
+ align:start position:0%
+P which is the pressure so number of
+phases I designate by Circle P so let's
+
+ align:start position:0%
+phases I designate by Circle P so let's
+ 
+
+ align:start position:0%
+phases I designate by Circle P so let's
+look at some uh simple single phase
+
+ align:start position:0%
+look at some uh simple single phase
+ 
+
+ align:start position:0%
+look at some uh simple single phase
+systems so let's look at P equal 1 P
+
+ align:start position:0%
+systems so let's look at P equal 1 P
+ 
+
+ align:start position:0%
+systems so let's look at P equal 1 P
+equal 1 so how about pure
+
+ align:start position:0%
+equal 1 so how about pure
+ 
+
+ align:start position:0%
+equal 1 so how about pure
+water pure water
+
+ align:start position:0%
+water pure water
+ 
+
+ align:start position:0%
+water pure water
+liquid I have a beaker of water it's
+
+ align:start position:0%
+liquid I have a beaker of water it's
+ 
+
+ align:start position:0%
+liquid I have a beaker of water it's
+uniform and chemical composition
+
+ align:start position:0%
+uniform and chemical composition
+ 
+
+ align:start position:0%
+uniform and chemical composition
+physically distinct mechanically
+
+ align:start position:0%
+physically distinct mechanically
+ 
+
+ align:start position:0%
+physically distinct mechanically
+separable how about uh how about white
+
+ align:start position:0%
+separable how about uh how about white
+ 
+
+ align:start position:0%
+separable how about uh how about white
+gold white gold white gold consists of
+
+ align:start position:0%
+gold white gold white gold consists of
+ 
+
+ align:start position:0%
+gold white gold white gold consists of
+an alloy of certainly gold to which we
+
+ align:start position:0%
+an alloy of certainly gold to which we
+ 
+
+ align:start position:0%
+an alloy of certainly gold to which we
+add silver and we add nickel and these
+
+ align:start position:0%
+add silver and we add nickel and these
+ 
+
+ align:start position:0%
+add silver and we add nickel and these
+are all FCC metals and at the atomistic
+
+ align:start position:0%
+are all FCC metals and at the atomistic
+ 
+
+ align:start position:0%
+are all FCC metals and at the atomistic
+level you have them substituting for one
+
+ align:start position:0%
+level you have them substituting for one
+ 
+
+ align:start position:0%
+level you have them substituting for one
+another on the gold lattice and so I
+
+ align:start position:0%
+another on the gold lattice and so I
+ 
+
+ align:start position:0%
+another on the gold lattice and so I
+have uniform chemical composition I have
+
+ align:start position:0%
+have uniform chemical composition I have
+ 
+
+ align:start position:0%
+have uniform chemical composition I have
+no boundaries there could be grain
+
+ align:start position:0%
+no boundaries there could be grain
+ 
+
+ align:start position:0%
+no boundaries there could be grain
+boundaries but that's different but it
+
+ align:start position:0%
+boundaries but that's different but it
+ 
+
+ align:start position:0%
+boundaries but that's different but it
+the grain boundaries do not represent
+
+ align:start position:0%
+the grain boundaries do not represent
+ 
+
+ align:start position:0%
+the grain boundaries do not represent
+something that is uh a difference in
+
+ align:start position:0%
+something that is uh a difference in
+ 
+
+ align:start position:0%
+something that is uh a difference in
+chemical composition so this is this is
+
+ align:start position:0%
+chemical composition so this is this is
+ 
+
+ align:start position:0%
+chemical composition so this is this is
+pure and this is a solution so if it's a
+
+ align:start position:0%
+pure and this is a solution so if it's a
+ 
+
+ align:start position:0%
+pure and this is a solution so if it's a
+pure material or a solution
+
+ align:start position:0%
+pure material or a solution
+ 
+
+ align:start position:0%
+pure material or a solution
+solution it will qualify a single phase
+
+ align:start position:0%
+solution it will qualify a single phase
+ 
+
+ align:start position:0%
+solution it will qualify a single phase
+okay um let's look so here's a liquid
+
+ align:start position:0%
+okay um let's look so here's a liquid
+ 
+
+ align:start position:0%
+okay um let's look so here's a liquid
+here's a solid let's look at a gas how
+
+ align:start position:0%
+here's a solid let's look at a gas how
+ 
+
+ align:start position:0%
+here's a solid let's look at a gas how
+about air air is a solution of nitrogen
+
+ align:start position:0%
+about air air is a solution of nitrogen
+ 
+
+ align:start position:0%
+about air air is a solution of nitrogen
+oxygen argon increasingly CO2 in the
+
+ align:start position:0%
+oxygen argon increasingly CO2 in the
+ 
+
+ align:start position:0%
+oxygen argon increasingly CO2 in the
+city when you got coal burning for
+
+ align:start position:0%
+city when you got coal burning for
+ 
+
+ align:start position:0%
+city when you got coal burning for
+electric power there's so SO2 oh let's
+
+ align:start position:0%
+electric power there's so SO2 oh let's
+ 
+
+ align:start position:0%
+electric power there's so SO2 oh let's
+not forget our pal nitrous oxide and if
+
+ align:start position:0%
+not forget our pal nitrous oxide and if
+ 
+
+ align:start position:0%
+not forget our pal nitrous oxide and if
+you live near an Alcoa smelter you'll
+
+ align:start position:0%
+you live near an Alcoa smelter you'll
+ 
+
+ align:start position:0%
+you live near an Alcoa smelter you'll
+have cf4 if you live near a magnesium
+
+ align:start position:0%
+have cf4 if you live near a magnesium
+ 
+
+ align:start position:0%
+have cf4 if you live near a magnesium
+smel melter you'll smell chlorine but in
+
+ align:start position:0%
+smel melter you'll smell chlorine but in
+ 
+
+ align:start position:0%
+smel melter you'll smell chlorine but in
+Cambridge mercifully we just have to
+
+ align:start position:0%
+Cambridge mercifully we just have to
+ 
+
+ align:start position:0%
+Cambridge mercifully we just have to
+enjoy these so and this is all single
+
+ align:start position:0%
+enjoy these so and this is all single
+ 
+
+ align:start position:0%
+enjoy these so and this is all single
+phase you don't see the gases settling
+
+ align:start position:0%
+phase you don't see the gases settling
+ 
+
+ align:start position:0%
+phase you don't see the gases settling
+according to density they mix intimately
+
+ align:start position:0%
+according to density they mix intimately
+ 
+
+ align:start position:0%
+according to density they mix intimately
+in all proportions and one more solid uh
+
+ align:start position:0%
+in all proportions and one more solid uh
+ 
+
+ align:start position:0%
+in all proportions and one more solid uh
+calcio
+
+ align:start position:0%
+calcio
+ 
+
+ align:start position:0%
+calcio
+zerconia we talked about this one before
+
+ align:start position:0%
+zerconia we talked about this one before
+ 
+
+ align:start position:0%
+zerconia we talked about this one before
+this is the lime stabilized zerconia for
+
+ align:start position:0%
+this is the lime stabilized zerconia for
+ 
+
+ align:start position:0%
+this is the lime stabilized zerconia for
+oxygen sensors and I'll show you later
+
+ align:start position:0%
+oxygen sensors and I'll show you later
+ 
+
+ align:start position:0%
+oxygen sensors and I'll show you later
+that this is the uh material that's used
+
+ align:start position:0%
+that this is the uh material that's used
+ 
+
+ align:start position:0%
+that this is the uh material that's used
+for uh the faux Diamond this is a solid
+
+ align:start position:0%
+for uh the faux Diamond this is a solid
+ 
+
+ align:start position:0%
+for uh the faux Diamond this is a solid
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+calcium ion sitting on zirconium site so
+
+ align:start position:0%
+calcium ion sitting on zirconium site so
+ 
+
+ align:start position:0%
+calcium ion sitting on zirconium site so
+this is single phase there's no calcium
+
+ align:start position:0%
+this is single phase there's no calcium
+ 
+
+ align:start position:0%
+this is single phase there's no calcium
+Island calcium oxide islands and
+
+ align:start position:0%
+Island calcium oxide islands and
+ 
+
+ align:start position:0%
+Island calcium oxide islands and
+zirconium oxide Islands this is a solid
+
+ align:start position:0%
+zirconium oxide Islands this is a solid
+ 
+
+ align:start position:0%
+zirconium oxide Islands this is a solid
+solution so therefore it's all one phase
+
+ align:start position:0%
+solution so therefore it's all one phase
+ 
+
+ align:start position:0%
+solution so therefore it's all one phase
+now let's contrast that to something
+
+ align:start position:0%
+now let's contrast that to something
+ 
+
+ align:start position:0%
+now let's contrast that to something
+that's two-phase to get a sense of what
+
+ align:start position:0%
+that's two-phase to get a sense of what
+ 
+
+ align:start position:0%
+that's two-phase to get a sense of what
+the difference is so instead of pure
+
+ align:start position:0%
+the difference is so instead of pure
+ 
+
+ align:start position:0%
+the difference is so instead of pure
+water just liquid suppose I have ice
+
+ align:start position:0%
+water just liquid suppose I have ice
+ 
+
+ align:start position:0%
+water just liquid suppose I have ice
+cubes ice cubes in water ice cubes in
+
+ align:start position:0%
+cubes ice cubes in water ice cubes in
+ 
+
+ align:start position:0%
+cubes ice cubes in water ice cubes in
+water it's still pure I didn't change
+
+ align:start position:0%
+water it's still pure I didn't change
+ 
+
+ align:start position:0%
+water it's still pure I didn't change
+the composition but I've got two
+
+ align:start position:0%
+the composition but I've got two
+ 
+
+ align:start position:0%
+the composition but I've got two
+different states I've got two different
+
+ align:start position:0%
+different states I've got two different
+ 
+
+ align:start position:0%
+different states I've got two different
+states I've got a solid state and a
+
+ align:start position:0%
+states I've got a solid state and a
+ 
+
+ align:start position:0%
+states I've got a solid state and a
+liquid state and this fits the fits the
+
+ align:start position:0%
+liquid state and this fits the fits the
+ 
+
+ align:start position:0%
+liquid state and this fits the fits the
+definition in other words the ice
+
+ align:start position:0%
+definition in other words the ice
+ 
+
+ align:start position:0%
+definition in other words the ice
+floating in the water is uniform in
+
+ align:start position:0%
+floating in the water is uniform in
+ 
+
+ align:start position:0%
+floating in the water is uniform in
+chemical composition and it's physically
+
+ align:start position:0%
+chemical composition and it's physically
+ 
+
+ align:start position:0%
+chemical composition and it's physically
+distinct or I can say I can put a
+
+ align:start position:0%
+distinct or I can say I can put a
+ 
+
+ align:start position:0%
+distinct or I can say I can put a
+boundary around it and I can isolate all
+
+ align:start position:0%
+boundary around it and I can isolate all
+ 
+
+ align:start position:0%
+boundary around it and I can isolate all
+of the ice cubes and in fact these are
+
+ align:start position:0%
+of the ice cubes and in fact these are
+ 
+
+ align:start position:0%
+of the ice cubes and in fact these are
+mechanically separable I could pull out
+
+ align:start position:0%
+mechanically separable I could pull out
+ 
+
+ align:start position:0%
+mechanically separable I could pull out
+all of the ice cubes and be left with
+
+ align:start position:0%
+all of the ice cubes and be left with
+ 
+
+ align:start position:0%
+all of the ice cubes and be left with
+only the liquid
+
+ align:start position:0%
+only the liquid
+ 
+
+ align:start position:0%
+only the liquid
+okay solid and liquid two different
+
+ align:start position:0%
+okay solid and liquid two different
+ 
+
+ align:start position:0%
+okay solid and liquid two different
+phases because they're two different
+
+ align:start position:0%
+phases because they're two different
+ 
+
+ align:start position:0%
+phases because they're two different
+states of the same material I think uh
+
+ align:start position:0%
+states of the same material I think uh
+ 
+
+ align:start position:0%
+states of the same material I think uh
+we also looked at milk we looked at milk
+
+ align:start position:0%
+we also looked at milk we looked at milk
+ 
+
+ align:start position:0%
+we also looked at milk we looked at milk
+and milk has fat
+
+ align:start position:0%
+and milk has fat
+ 
+
+ align:start position:0%
+and milk has fat
+globules in the aquous
+
+ align:start position:0%
+globules in the aquous
+ 
+
+ align:start position:0%
+globules in the aquous
+phase in the aquous solution all right
+
+ align:start position:0%
+phase in the aquous solution all right
+ 
+
+ align:start position:0%
+phase in the aquous solution all right
+so I've got fat globules they're very
+
+ align:start position:0%
+so I've got fat globules they're very
+ 
+
+ align:start position:0%
+so I've got fat globules they're very
+tiny and they scatter light but if we
+
+ align:start position:0%
+tiny and they scatter light but if we
+ 
+
+ align:start position:0%
+tiny and they scatter light but if we
+got down to the micro level we could
+
+ align:start position:0%
+got down to the micro level we could
+ 
+
+ align:start position:0%
+got down to the micro level we could
+find these fat globules as something
+
+ align:start position:0%
+find these fat globules as something
+ 
+
+ align:start position:0%
+find these fat globules as something
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+mechanically uh separable physically
+
+ align:start position:0%
+mechanically uh separable physically
+ 
+
+ align:start position:0%
+mechanically uh separable physically
+distinct and of uniform composition and
+
+ align:start position:0%
+distinct and of uniform composition and
+ 
+
+ align:start position:0%
+distinct and of uniform composition and
+different from this so this is two
+
+ align:start position:0%
+different from this so this is two
+ 
+
+ align:start position:0%
+different from this so this is two
+different phases because we have two
+
+ align:start position:0%
+different phases because we have two
+ 
+
+ align:start position:0%
+different phases because we have two
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+compositions we have two different
+
+ align:start position:0%
+compositions we have two different
+ 
+
+ align:start position:0%
+compositions we have two different
+compositions and lastly uh there was the
+
+ align:start position:0%
+compositions and lastly uh there was the
+ 
+
+ align:start position:0%
+compositions and lastly uh there was the
+Visions the Visions cookware the
+
+ align:start position:0%
+Visions the Visions cookware the
+ 
+
+ align:start position:0%
+Visions the Visions cookware the
+pyroceram the Pyro seram that was the
+
+ align:start position:0%
+pyroceram the Pyro seram that was the
+ 
+
+ align:start position:0%
+pyroceram the Pyro seram that was the
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+ceramic the glass ceramic that's 95%
+
+ align:start position:0%
+ceramic the glass ceramic that's 95%
+ 
+
+ align:start position:0%
+ceramic the glass ceramic that's 95%
+crystallin and 5% glassy so which you
+
+ align:start position:0%
+crystallin and 5% glassy so which you
+ 
+
+ align:start position:0%
+crystallin and 5% glassy so which you
+have here is you have a glassy
+
+ align:start position:0%
+have here is you have a glassy
+ 
+
+ align:start position:0%
+have here is you have a glassy
+phase glassy
+
+ align:start position:0%
+phase glassy
+ 
+
+ align:start position:0%
+phase glassy
+Matrix and
+
+ align:start position:0%
+Matrix and
+ 
+
+ align:start position:0%
+Matrix and
+crystallin crystallin
+
+ align:start position:0%
+crystallin crystallin
+ 
+
+ align:start position:0%
+crystallin crystallin
+precipitates okay so again we don't have
+
+ align:start position:0%
+precipitates okay so again we don't have
+ 
+
+ align:start position:0%
+precipitates okay so again we don't have
+a change in composition but we have a
+
+ align:start position:0%
+a change in composition but we have a
+ 
+
+ align:start position:0%
+a change in composition but we have a
+change in order in atomic order so the
+
+ align:start position:0%
+change in order in atomic order so the
+ 
+
+ align:start position:0%
+change in order in atomic order so the
+glassy phase and the devitrified phase
+
+ align:start position:0%
+glassy phase and the devitrified phase
+ 
+
+ align:start position:0%
+glassy phase and the devitrified phase
+so we can actually draw boundaries
+
+ align:start position:0%
+so we can actually draw boundaries
+ 
+
+ align:start position:0%
+so we can actually draw boundaries
+around all the crystallin precipitate so
+
+ align:start position:0%
+around all the crystallin precipitate so
+ 
+
+ align:start position:0%
+around all the crystallin precipitate so
+I I hope this gives you a sense of what
+
+ align:start position:0%
+I I hope this gives you a sense of what
+ 
+
+ align:start position:0%
+I I hope this gives you a sense of what
+what's going on on here the second thing
+
+ align:start position:0%
+what's going on on here the second thing
+ 
+
+ align:start position:0%
+what's going on on here the second thing
+is that uh these phase diagrams are
+
+ align:start position:0%
+is that uh these phase diagrams are
+ 
+
+ align:start position:0%
+is that uh these phase diagrams are
+drawn under conditions called
+
+ align:start position:0%
+drawn under conditions called
+ 
+
+ align:start position:0%
+drawn under conditions called
+equilibrium that's why we talk about
+
+ align:start position:0%
+equilibrium that's why we talk about
+ 
+
+ align:start position:0%
+equilibrium that's why we talk about
+stability so let's define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium equilibrium is a
+
+ align:start position:0%
+equilibrium equilibrium is a
+ 
+
+ align:start position:0%
+equilibrium equilibrium is a
+condition which represents the lowest
+
+ align:start position:0%
+condition which represents the lowest
+ 
+
+ align:start position:0%
+condition which represents the lowest
+energy state of the system the lowest
+
+ align:start position:0%
+energy state of the system the lowest
+ 
+
+ align:start position:0%
+energy state of the system the lowest
+energy state in other words if you take
+
+ align:start position:0%
+energy state in other words if you take
+ 
+
+ align:start position:0%
+energy state in other words if you take
+all of the constituents and give them
+
+ align:start position:0%
+all of the constituents and give them
+ 
+
+ align:start position:0%
+all of the constituents and give them
+infinite time and the energy they need
+
+ align:start position:0%
+infinite time and the energy they need
+ 
+
+ align:start position:0%
+infinite time and the energy they need
+to achieve the lowest energy State this
+
+ align:start position:0%
+to achieve the lowest energy State this
+ 
+
+ align:start position:0%
+to achieve the lowest energy State this
+is where they will get to and we will
+
+ align:start position:0%
+is where they will get to and we will
+ 
+
+ align:start position:0%
+is where they will get to and we will
+know that it's the equilibrium State
+
+ align:start position:0%
+know that it's the equilibrium State
+ 
+
+ align:start position:0%
+know that it's the equilibrium State
+because the properties are invariant
+
+ align:start position:0%
+because the properties are invariant
+ 
+
+ align:start position:0%
+because the properties are invariant
+properties are invariant with time this
+
+ align:start position:0%
+properties are invariant with time this
+ 
+
+ align:start position:0%
+properties are invariant with time this
+is sort of like a steady state but
+
+ align:start position:0%
+is sort of like a steady state but
+ 
+
+ align:start position:0%
+is sort of like a steady state but
+steady state is something that could be
+
+ align:start position:0%
+steady state is something that could be
+ 
+
+ align:start position:0%
+steady state is something that could be
+sort of locked in on the road to
+
+ align:start position:0%
+sort of locked in on the road to
+ 
+
+ align:start position:0%
+sort of locked in on the road to
+stability so this is the ultimate
+
+ align:start position:0%
+stability so this is the ultimate
+ 
+
+ align:start position:0%
+stability so this is the ultimate
+stability as contrasted with
+
+ align:start position:0%
+stability as contrasted with
+ 
+
+ align:start position:0%
+stability as contrasted with
+metastability metastability
+
+ align:start position:0%
+metastability metastability
+ 
+
+ align:start position:0%
+metastability metastability
+is something that's steady state but
+
+ align:start position:0%
+is something that's steady state but
+ 
+
+ align:start position:0%
+is something that's steady state but
+could get Stabler yet and the example of
+
+ align:start position:0%
+could get Stabler yet and the example of
+ 
+
+ align:start position:0%
+could get Stabler yet and the example of
+meta stability is
+
+ align:start position:0%
+meta stability is
+ 
+
+ align:start position:0%
+meta stability is
+Diamond which is not the stable form of
+
+ align:start position:0%
+Diamond which is not the stable form of
+ 
+
+ align:start position:0%
+Diamond which is not the stable form of
+carbon at room temperature but Diamond
+
+ align:start position:0%
+carbon at room temperature but Diamond
+ 
+
+ align:start position:0%
+carbon at room temperature but Diamond
+was formed under different conditions
+
+ align:start position:0%
+was formed under different conditions
+ 
+
+ align:start position:0%
+was formed under different conditions
+and then brought under ambient pressure
+
+ align:start position:0%
+and then brought under ambient pressure
+ 
+
+ align:start position:0%
+and then brought under ambient pressure
+and temperature but the activation
+
+ align:start position:0%
+and temperature but the activation
+ 
+
+ align:start position:0%
+and temperature but the activation
+energy to convert is so high that it
+
+ align:start position:0%
+energy to convert is so high that it
+ 
+
+ align:start position:0%
+energy to convert is so high that it
+stays apparently stable but in point of
+
+ align:start position:0%
+stays apparently stable but in point of
+ 
+
+ align:start position:0%
+stays apparently stable but in point of
+fact it's metastable another one is
+
+ align:start position:0%
+fact it's metastable another one is
+ 
+
+ align:start position:0%
+fact it's metastable another one is
+metallic glass metallic glass we know
+
+ align:start position:0%
+metallic glass metallic glass we know
+ 
+
+ align:start position:0%
+metallic glass metallic glass we know
+that metallic glass was formed under
+
+ align:start position:0%
+that metallic glass was formed under
+ 
+
+ align:start position:0%
+that metallic glass was formed under
+high quench rates if you take metallic
+
+ align:start position:0%
+high quench rates if you take metallic
+ 
+
+ align:start position:0%
+high quench rates if you take metallic
+glass and Heat it moderately you will
+
+ align:start position:0%
+glass and Heat it moderately you will
+ 
+
+ align:start position:0%
+glass and Heat it moderately you will
+give it sufficient activation energy to
+
+ align:start position:0%
+give it sufficient activation energy to
+ 
+
+ align:start position:0%
+give it sufficient activation energy to
+then jump from this glassy state to the
+
+ align:start position:0%
+then jump from this glassy state to the
+ 
+
+ align:start position:0%
+then jump from this glassy state to the
+crystallin state and ultimately achieve
+
+ align:start position:0%
+crystallin state and ultimately achieve
+ 
+
+ align:start position:0%
+crystallin state and ultimately achieve
+its its equilibrium value its
+
+ align:start position:0%
+its its equilibrium value its
+ 
+
+ align:start position:0%
+its its equilibrium value its
+equilibrium value so those are examples
+
+ align:start position:0%
+equilibrium value so those are examples
+ 
+
+ align:start position:0%
+equilibrium value so those are examples
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+uh equilibrium metastability and then
+
+ align:start position:0%
+uh equilibrium metastability and then
+ 
+
+ align:start position:0%
+uh equilibrium metastability and then
+the last thing as you noticed I talked
+
+ align:start position:0%
+the last thing as you noticed I talked
+ 
+
+ align:start position:0%
+the last thing as you noticed I talked
+about pure materials and then
+
+ align:start position:0%
+about pure materials and then
+ 
+
+ align:start position:0%
+about pure materials and then
+multicomponent materials they have
+
+ align:start position:0%
+multicomponent materials they have
+ 
+
+ align:start position:0%
+multicomponent materials they have
+different uh elements that are mixed and
+
+ align:start position:0%
+different uh elements that are mixed and
+ 
+
+ align:start position:0%
+different uh elements that are mixed and
+so we need a counter a metric that uh
+
+ align:start position:0%
+so we need a counter a metric that uh
+ 
+
+ align:start position:0%
+so we need a counter a metric that uh
+details what the level of chemical
+
+ align:start position:0%
+details what the level of chemical
+ 
+
+ align:start position:0%
+details what the level of chemical
+complexity is and for that we call in to
+
+ align:start position:0%
+complexity is and for that we call in to
+ 
+
+ align:start position:0%
+complexity is and for that we call in to
+play a term called
+
+ align:start position:0%
+play a term called
+ 
+
+ align:start position:0%
+play a term called
+component component and it's the measure
+
+ align:start position:0%
+component component and it's the measure
+ 
+
+ align:start position:0%
+component component and it's the measure
+measure of chemical
+
+ align:start position:0%
+measure of chemical
+ 
+
+ align:start position:0%
+measure of chemical
+complexity measure of chemical
+
+ align:start position:0%
+complexity measure of chemical
+ 
+
+ align:start position:0%
+complexity measure of chemical
+complexity what do I mean by that in the
+
+ align:start position:0%
+complexity what do I mean by that in the
+ 
+
+ align:start position:0%
+complexity what do I mean by that in the
+simplest in the simplest terms how many
+
+ align:start position:0%
+simplest in the simplest terms how many
+ 
+
+ align:start position:0%
+simplest in the simplest terms how many
+bottles do I have to pull off the shelf
+
+ align:start position:0%
+bottles do I have to pull off the shelf
+ 
+
+ align:start position:0%
+bottles do I have to pull off the shelf
+to make this thing okay bottles off the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shelf and again this is best best given
+
+ align:start position:0%
+shelf and again this is best best given
+ 
+
+ align:start position:0%
+shelf and again this is best best given
+by uh illustration so I I'll show you a
+
+ align:start position:0%
+by uh illustration so I I'll show you a
+ 
+
+ align:start position:0%
+by uh illustration so I I'll show you a
+mix of components and phases so we'll do
+
+ align:start position:0%
+mix of components and phases so we'll do
+ 
+
+ align:start position:0%
+mix of components and phases so we'll do
+a little Matrix here start on a new
+
+ align:start position:0%
+a little Matrix here start on a new
+ 
+
+ align:start position:0%
+a little Matrix here start on a new
+board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so AC cross the across the top
+
+ align:start position:0%
+so okay so AC cross the across the top
+ 
+
+ align:start position:0%
+so okay so AC cross the across the top
+I'll look at single phase and dual phase
+
+ align:start position:0%
+I'll look at single phase and dual phase
+ 
+
+ align:start position:0%
+I'll look at single phase and dual phase
+and down the column I'll look at one
+
+ align:start position:0%
+and down the column I'll look at one
+ 
+
+ align:start position:0%
+and down the column I'll look at one
+component two component three component
+
+ align:start position:0%
+component two component three component
+ 
+
+ align:start position:0%
+component two component three component
+systems so the simplest is up here one
+
+ align:start position:0%
+systems so the simplest is up here one
+ 
+
+ align:start position:0%
+systems so the simplest is up here one
+one one phase one component so that's
+
+ align:start position:0%
+one one phase one component so that's
+ 
+
+ align:start position:0%
+one one phase one component so that's
+pure water pure water all liquid single
+
+ align:start position:0%
+pure water pure water all liquid single
+ 
+
+ align:start position:0%
+pure water pure water all liquid single
+phase single component you can say but
+
+ align:start position:0%
+phase single component you can say but
+ 
+
+ align:start position:0%
+phase single component you can say but
+don't you need hydrogen and oxygen well
+
+ align:start position:0%
+don't you need hydrogen and oxygen well
+ 
+
+ align:start position:0%
+don't you need hydrogen and oxygen well
+if you if you take one of the thermal
+
+ align:start position:0%
+if you if you take one of the thermal
+ 
+
+ align:start position:0%
+if you if you take one of the thermal
+classes later you'll learn that the
+
+ align:start position:0%
+classes later you'll learn that the
+ 
+
+ align:start position:0%
+classes later you'll learn that the
+hydrogen and oxygen are linked by
+
+ align:start position:0%
+hydrogen and oxygen are linked by
+ 
+
+ align:start position:0%
+hydrogen and oxygen are linked by
+stochiometry so it's still one body off
+
+ align:start position:0%
+stochiometry so it's still one body off
+ 
+
+ align:start position:0%
+stochiometry so it's still one body off
+the shelf there's no variation in the
+
+ align:start position:0%
+the shelf there's no variation in the
+ 
+
+ align:start position:0%
+the shelf there's no variation in the
+hydrogen to oxygen ratio um Diamond even
+
+ align:start position:0%
+hydrogen to oxygen ratio um Diamond even
+ 
+
+ align:start position:0%
+hydrogen to oxygen ratio um Diamond even
+though it's metast stable it is all I
+
+ align:start position:0%
+though it's metast stable it is all I
+ 
+
+ align:start position:0%
+though it's metast stable it is all I
+need is carbon so and it's single phase
+
+ align:start position:0%
+need is carbon so and it's single phase
+ 
+
+ align:start position:0%
+need is carbon so and it's single phase
+there's no change of uh phase across the
+
+ align:start position:0%
+there's no change of uh phase across the
+ 
+
+ align:start position:0%
+there's no change of uh phase across the
+diamond in many cases the diamonds that
+
+ align:start position:0%
+diamond in many cases the diamonds that
+ 
+
+ align:start position:0%
+diamond in many cases the diamonds that
+you will see they're all single Crystal
+
+ align:start position:0%
+you will see they're all single Crystal
+ 
+
+ align:start position:0%
+you will see they're all single Crystal
+don't ever go to the jeweler and ask for
+
+ align:start position:0%
+don't ever go to the jeweler and ask for
+ 
+
+ align:start position:0%
+don't ever go to the jeweler and ask for
+poly Crystal and Diamond it's not going
+
+ align:start position:0%
+poly Crystal and Diamond it's not going
+ 
+
+ align:start position:0%
+poly Crystal and Diamond it's not going
+to be very pretty okay please remember
+
+ align:start position:0%
+to be very pretty okay please remember
+ 
+
+ align:start position:0%
+to be very pretty okay please remember
+that um so let's look at something
+
+ align:start position:0%
+that um so let's look at something
+ 
+
+ align:start position:0%
+that um so let's look at something
+that's now uh two components well that
+
+ align:start position:0%
+that's now uh two components well that
+ 
+
+ align:start position:0%
+that's now uh two components well that
+would be uh calcio zerconia right it's
+
+ align:start position:0%
+would be uh calcio zerconia right it's
+ 
+
+ align:start position:0%
+would be uh calcio zerconia right it's
+one phase it's a single solid solution
+
+ align:start position:0%
+one phase it's a single solid solution
+ 
+
+ align:start position:0%
+one phase it's a single solid solution
+but I needed two bottles I needed a
+
+ align:start position:0%
+but I needed two bottles I needed a
+ 
+
+ align:start position:0%
+but I needed two bottles I needed a
+bottle of calcium oxide and a bottle of
+
+ align:start position:0%
+bottle of calcium oxide and a bottle of
+ 
+
+ align:start position:0%
+bottle of calcium oxide and a bottle of
+zirconium oxide but they mix intimately
+
+ align:start position:0%
+zirconium oxide but they mix intimately
+ 
+
+ align:start position:0%
+zirconium oxide but they mix intimately
+and I have a single phase and then the
+
+ align:start position:0%
+and I have a single phase and then the
+ 
+
+ align:start position:0%
+and I have a single phase and then the
+white gold the white gold is the gold
+
+ align:start position:0%
+white gold the white gold is the gold
+ 
+
+ align:start position:0%
+white gold the white gold is the gold
+the silver and the nickel three
+
+ align:start position:0%
+the silver and the nickel three
+ 
+
+ align:start position:0%
+the silver and the nickel three
+different elements they mix intimately
+
+ align:start position:0%
+different elements they mix intimately
+ 
+
+ align:start position:0%
+different elements they mix intimately
+and they give me a single phase over
+
+ align:start position:0%
+and they give me a single phase over
+ 
+
+ align:start position:0%
+and they give me a single phase over
+here I've got one component so I'm
+
+ align:start position:0%
+here I've got one component so I'm
+ 
+
+ align:start position:0%
+here I've got one component so I'm
+working only with say water so this will
+
+ align:start position:0%
+working only with say water so this will
+ 
+
+ align:start position:0%
+working only with say water so this will
+be the ice
+
+ align:start position:0%
+be the ice
+ 
+
+ align:start position:0%
+be the ice
+ice water or I call it slush ice water
+
+ align:start position:0%
+ice water or I call it slush ice water
+ 
+
+ align:start position:0%
+ice water or I call it slush ice water
+slush two phases and they're in
+
+ align:start position:0%
+slush two phases and they're in
+ 
+
+ align:start position:0%
+slush two phases and they're in
+equilibrium so this is at 0 degrees C
+
+ align:start position:0%
+equilibrium so this is at 0 degrees C
+ 
+
+ align:start position:0%
+equilibrium so this is at 0 degrees C
+and they are stable over time all right
+
+ align:start position:0%
+and they are stable over time all right
+ 
+
+ align:start position:0%
+and they are stable over time all right
+the lowest energy state invariant so the
+
+ align:start position:0%
+the lowest energy state invariant so the
+ 
+
+ align:start position:0%
+the lowest energy state invariant so the
+slush remains stable so you can have
+
+ align:start position:0%
+slush remains stable so you can have
+ 
+
+ align:start position:0%
+slush remains stable so you can have
+Dynamics some of the solid dissolves
+
+ align:start position:0%
+Dynamics some of the solid dissolves
+ 
+
+ align:start position:0%
+Dynamics some of the solid dissolves
+into liquid and some of the liquid
+
+ align:start position:0%
+into liquid and some of the liquid
+ 
+
+ align:start position:0%
+into liquid and some of the liquid
+freezes out as solid but the net change
+
+ align:start position:0%
+freezes out as solid but the net change
+ 
+
+ align:start position:0%
+freezes out as solid but the net change
+is zero stable ice water slush uh second
+
+ align:start position:0%
+is zero stable ice water slush uh second
+ 
+
+ align:start position:0%
+is zero stable ice water slush uh second
+one we saw this we talked about
+
+ align:start position:0%
+one we saw this we talked about
+ 
+
+ align:start position:0%
+one we saw this we talked about
+solubility we looked at the mix of
+
+ align:start position:0%
+solubility we looked at the mix of
+ 
+
+ align:start position:0%
+solubility we looked at the mix of
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+tetrachloride and water two liquids we
+
+ align:start position:0%
+tetrachloride and water two liquids we
+ 
+
+ align:start position:0%
+tetrachloride and water two liquids we
+shake them up and they phase separate
+
+ align:start position:0%
+shake them up and they phase separate
+ 
+
+ align:start position:0%
+shake them up and they phase separate
+I've been using that term phase separate
+
+ align:start position:0%
+I've been using that term phase separate
+ 
+
+ align:start position:0%
+I've been using that term phase separate
+two phases there's an organic phase or
+
+ align:start position:0%
+two phases there's an organic phase or
+ 
+
+ align:start position:0%
+two phases there's an organic phase or
+an if you say a carbon Rich phase a
+
+ align:start position:0%
+an if you say a carbon Rich phase a
+ 
+
+ align:start position:0%
+an if you say a carbon Rich phase a
+non-polar phase and a hydrogen bonded
+
+ align:start position:0%
+non-polar phase and a hydrogen bonded
+ 
+
+ align:start position:0%
+non-polar phase and a hydrogen bonded
+phase so these are emiss they're emiss
+
+ align:start position:0%
+phase so these are emiss they're emiss
+ 
+
+ align:start position:0%
+phase so these are emiss they're emiss
+and I will have two components two
+
+ align:start position:0%
+and I will have two components two
+ 
+
+ align:start position:0%
+and I will have two components two
+phases and then the last one this would
+
+ align:start position:0%
+phases and then the last one this would
+ 
+
+ align:start position:0%
+phases and then the last one this would
+be the visions
+
+ align:start position:0%
+be the visions
+ 
+
+ align:start position:0%
+be the visions
+the Visions because that consisted of
+
+ align:start position:0%
+the Visions because that consisted of
+ 
+
+ align:start position:0%
+the Visions because that consisted of
+lithium oxide
+
+ align:start position:0%
+lithium oxide
+ 
+
+ align:start position:0%
+lithium oxide
+alumina and silica I need to get three
+
+ align:start position:0%
+alumina and silica I need to get three
+ 
+
+ align:start position:0%
+alumina and silica I need to get three
+bottles off the shelf remember I had a
+
+ align:start position:0%
+bottles off the shelf remember I had a
+ 
+
+ align:start position:0%
+bottles off the shelf remember I had a
+network former a network modifier and an
+
+ align:start position:0%
+network former a network modifier and an
+ 
+
+ align:start position:0%
+network former a network modifier and an
+intermediate and that gave me this
+
+ align:start position:0%
+intermediate and that gave me this
+ 
+
+ align:start position:0%
+intermediate and that gave me this
+remarkable uh two-phase mixture that I
+
+ align:start position:0%
+remarkable uh two-phase mixture that I
+ 
+
+ align:start position:0%
+remarkable uh two-phase mixture that I
+triggered the uh exsolution of a
+
+ align:start position:0%
+triggered the uh exsolution of a
+ 
+
+ align:start position:0%
+triggered the uh exsolution of a
+crystallin phase so now I want let's
+
+ align:start position:0%
+crystallin phase so now I want let's
+ 
+
+ align:start position:0%
+crystallin phase so now I want let's
+look at some real examples stability
+
+ align:start position:0%
+look at some real examples stability
+ 
+
+ align:start position:0%
+look at some real examples stability
+Maps so I want to
+
+ align:start position:0%
+Maps so I want to
+ 
+
+ align:start position:0%
+Maps so I want to
+start learn to crawl before we learn to
+
+ align:start position:0%
+start learn to crawl before we learn to
+ 
+
+ align:start position:0%
+start learn to crawl before we learn to
+run so let's look look at simple one so
+
+ align:start position:0%
+run so let's look look at simple one so
+ 
+
+ align:start position:0%
+run so let's look look at simple one so
+we're going to put Cals 1 so this is
+
+ align:start position:0%
+we're going to put Cals 1 so this is
+ 
+
+ align:start position:0%
+we're going to put Cals 1 so this is
+pure materials pure materials Cals 1 one
+
+ align:start position:0%
+pure materials pure materials Cals 1 one
+ 
+
+ align:start position:0%
+pure materials pure materials Cals 1 one
+component and we're going to look at
+
+ align:start position:0%
+component and we're going to look at
+ 
+
+ align:start position:0%
+component and we're going to look at
+since we have C C equals 1 it's fixed
+
+ align:start position:0%
+since we have C C equals 1 it's fixed
+ 
+
+ align:start position:0%
+since we have C C equals 1 it's fixed
+all I have left then we have pressure
+
+ align:start position:0%
+all I have left then we have pressure
+ 
+
+ align:start position:0%
+all I have left then we have pressure
+composition temperature composition is
+
+ align:start position:0%
+composition temperature composition is
+ 
+
+ align:start position:0%
+composition temperature composition is
+fixed because it doesn't vary here so I
+
+ align:start position:0%
+fixed because it doesn't vary here so I
+ 
+
+ align:start position:0%
+fixed because it doesn't vary here so I
+just have to look look at P versus T
+
+ align:start position:0%
+just have to look look at P versus T
+ 
+
+ align:start position:0%
+just have to look look at P versus T
+those are the only variables that I have
+
+ align:start position:0%
+those are the only variables that I have
+ 
+
+ align:start position:0%
+those are the only variables that I have
+to deal with so let's look at at some of
+
+ align:start position:0%
+to deal with so let's look at at some of
+ 
+
+ align:start position:0%
+to deal with so let's look at at some of
+these now the first one I want to look
+
+ align:start position:0%
+these now the first one I want to look
+ 
+
+ align:start position:0%
+these now the first one I want to look
+at is one that you're pretty familiar
+
+ align:start position:0%
+at is one that you're pretty familiar
+ 
+
+ align:start position:0%
+at is one that you're pretty familiar
+with water let's look at the phase
+
+ align:start position:0%
+with water let's look at the phase
+ 
+
+ align:start position:0%
+with water let's look at the phase
+diagram of pure water so we're going to
+
+ align:start position:0%
+diagram of pure water so we're going to
+ 
+
+ align:start position:0%
+diagram of pure water so we're going to
+plot how the phases of water vary over
+
+ align:start position:0%
+plot how the phases of water vary over
+ 
+
+ align:start position:0%
+plot how the phases of water vary over
+pressure and temperature and I'm going
+
+ align:start position:0%
+pressure and temperature and I'm going
+ 
+
+ align:start position:0%
+pressure and temperature and I'm going
+to plot temperature in degrees Celsius
+
+ align:start position:0%
+to plot temperature in degrees Celsius
+ 
+
+ align:start position:0%
+to plot temperature in degrees Celsius
+and I'm going to plot temper excuse me
+
+ align:start position:0%
+and I'm going to plot temper excuse me
+ 
+
+ align:start position:0%
+and I'm going to plot temper excuse me
+pressure and atmospheres although I'll
+
+ align:start position:0%
+pressure and atmospheres although I'll
+ 
+
+ align:start position:0%
+pressure and atmospheres although I'll
+give you the conversion to SI so let me
+
+ align:start position:0%
+give you the conversion to SI so let me
+ 
+
+ align:start position:0%
+give you the conversion to SI so let me
+just put the general diagram on it's
+
+ align:start position:0%
+just put the general diagram on it's
+ 
+
+ align:start position:0%
+just put the general diagram on it's
+sort of a a y-shaped looking diagram so
+
+ align:start position:0%
+sort of a a y-shaped looking diagram so
+ 
+
+ align:start position:0%
+sort of a a y-shaped looking diagram so
+lowest temperature this is where we have
+
+ align:start position:0%
+lowest temperature this is where we have
+ 
+
+ align:start position:0%
+lowest temperature this is where we have
+the solid regime solid water ice the
+
+ align:start position:0%
+the solid regime solid water ice the
+ 
+
+ align:start position:0%
+the solid regime solid water ice the
+highest temperature must be where we
+
+ align:start position:0%
+highest temperature must be where we
+ 
+
+ align:start position:0%
+highest temperature must be where we
+have the gas or water vapor and in
+
+ align:start position:0%
+have the gas or water vapor and in
+ 
+
+ align:start position:0%
+have the gas or water vapor and in
+between we have the
+
+ align:start position:0%
+between we have the
+ 
+
+ align:start position:0%
+between we have the
+liquid and these lines represent the
+
+ align:start position:0%
+liquid and these lines represent the
+ 
+
+ align:start position:0%
+liquid and these lines represent the
+equilibria these lines this one is the
+
+ align:start position:0%
+equilibria these lines this one is the
+ 
+
+ align:start position:0%
+equilibria these lines this one is the
+equilibrium between liquid and Vapor
+
+ align:start position:0%
+equilibrium between liquid and Vapor
+ 
+
+ align:start position:0%
+equilibrium between liquid and Vapor
+liquid and Vapor so this is a liquid
+
+ align:start position:0%
+liquid and Vapor so this is a liquid
+ 
+
+ align:start position:0%
+liquid and Vapor so this is a liquid
+equals Vapor coexistence curve
+
+ align:start position:0%
+equals Vapor coexistence curve
+ 
+
+ align:start position:0%
+equals Vapor coexistence curve
+coexistence curve and it's not a single
+
+ align:start position:0%
+coexistence curve and it's not a single
+ 
+
+ align:start position:0%
+coexistence curve and it's not a single
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+this one here is solid liquid
+
+ align:start position:0%
+this one here is solid liquid
+ 
+
+ align:start position:0%
+this one here is solid liquid
+coexistence curve solid equals uh liquid
+
+ align:start position:0%
+coexistence curve solid equals uh liquid
+ 
+
+ align:start position:0%
+coexistence curve solid equals uh liquid
+coexistence
+
+ align:start position:0%
+coexistence
+ 
+
+ align:start position:0%
+coexistence
+curve now you know some of the data
+
+ align:start position:0%
+curve now you know some of the data
+ 
+
+ align:start position:0%
+curve now you know some of the data
+points on this graph we live at one
+
+ align:start position:0%
+points on this graph we live at one
+ 
+
+ align:start position:0%
+points on this graph we live at one
+atmosphere that's our world the one
+
+ align:start position:0%
+atmosphere that's our world the one
+ 
+
+ align:start position:0%
+atmosphere that's our world the one
+atmosphere isobar so let's put P equals
+
+ align:start position:0%
+atmosphere isobar so let's put P equals
+ 
+
+ align:start position:0%
+atmosphere isobar so let's put P equals
+1 and you know that at one atmosphere
+
+ align:start position:0%
+1 and you know that at one atmosphere
+ 
+
+ align:start position:0%
+1 and you know that at one atmosphere
+pure water freezes at 0° C so that's the
+
+ align:start position:0%
+pure water freezes at 0° C so that's the
+ 
+
+ align:start position:0%
+pure water freezes at 0° C so that's the
+point along the solid liquid coexistence
+
+ align:start position:0%
+point along the solid liquid coexistence
+ 
+
+ align:start position:0%
+point along the solid liquid coexistence
+curve at one atmosphere applied pressure
+
+ align:start position:0%
+curve at one atmosphere applied pressure
+ 
+
+ align:start position:0%
+curve at one atmosphere applied pressure
+and furthermore you know that at sea
+
+ align:start position:0%
+and furthermore you know that at sea
+ 
+
+ align:start position:0%
+and furthermore you know that at sea
+level where we have one atmosphere
+
+ align:start position:0%
+level where we have one atmosphere
+ 
+
+ align:start position:0%
+level where we have one atmosphere
+pressure the liquid turns to Vapor at
+
+ align:start position:0%
+pressure the liquid turns to Vapor at
+ 
+
+ align:start position:0%
+pressure the liquid turns to Vapor at
+100 De C at 100° C so when we go to we
+
+ align:start position:0%
+100 De C at 100° C so when we go to we
+ 
+
+ align:start position:0%
+100 De C at 100° C so when we go to we
+go to Mount Everest we're over here see
+
+ align:start position:0%
+go to Mount Everest we're over here see
+ 
+
+ align:start position:0%
+go to Mount Everest we're over here see
+we're at lower pressure and if we're at
+
+ align:start position:0%
+we're at lower pressure and if we're at
+ 
+
+ align:start position:0%
+we're at lower pressure and if we're at
+lower pressure we're at lower
+
+ align:start position:0%
+lower pressure we're at lower
+ 
+
+ align:start position:0%
+lower pressure we're at lower
+temperature and then if we're in
+
+ align:start position:0%
+temperature and then if we're in
+ 
+
+ align:start position:0%
+temperature and then if we're in
+the radiator the cooling system of the
+
+ align:start position:0%
+the radiator the cooling system of the
+ 
+
+ align:start position:0%
+the radiator the cooling system of the
+car we
+
+ align:start position:0%
+car we
+ 
+
+ align:start position:0%
+car we
+applied higher pressure we trapped in a
+
+ align:start position:0%
+applied higher pressure we trapped in a
+ 
+
+ align:start position:0%
+applied higher pressure we trapped in a
+higher pressure and thereby extended the
+
+ align:start position:0%
+higher pressure and thereby extended the
+ 
+
+ align:start position:0%
+higher pressure and thereby extended the
+temperature range over which the liquid
+
+ align:start position:0%
+temperature range over which the liquid
+ 
+
+ align:start position:0%
+temperature range over which the liquid
+is stable see at two atmospheres the
+
+ align:start position:0%
+is stable see at two atmospheres the
+ 
+
+ align:start position:0%
+is stable see at two atmospheres the
+liquid is stable over a wider range of
+
+ align:start position:0%
+liquid is stable over a wider range of
+ 
+
+ align:start position:0%
+liquid is stable over a wider range of
+temperature at one atmosphere it's what
+
+ align:start position:0%
+temperature at one atmosphere it's what
+ 
+
+ align:start position:0%
+temperature at one atmosphere it's what
+we know one to Excuse Me 0 to 100
+
+ align:start position:0%
+we know one to Excuse Me 0 to 100
+ 
+
+ align:start position:0%
+we know one to Excuse Me 0 to 100
+Celsius and at lower at lower pressures
+
+ align:start position:0%
+Celsius and at lower at lower pressures
+ 
+
+ align:start position:0%
+Celsius and at lower at lower pressures
+it's stable over an even narrower
+
+ align:start position:0%
+it's stable over an even narrower
+ 
+
+ align:start position:0%
+it's stable over an even narrower
+temperature range so the boiling point
+
+ align:start position:0%
+temperature range so the boiling point
+ 
+
+ align:start position:0%
+temperature range so the boiling point
+I'm showing you how it varies as a
+
+ align:start position:0%
+I'm showing you how it varies as a
+ 
+
+ align:start position:0%
+I'm showing you how it varies as a
+function of pressure and down here we
+
+ align:start position:0%
+function of pressure and down here we
+ 
+
+ align:start position:0%
+function of pressure and down here we
+have this is solid equals Vapor
+
+ align:start position:0%
+have this is solid equals Vapor
+ 
+
+ align:start position:0%
+have this is solid equals Vapor
+coexistence curve below a certain
+
+ align:start position:0%
+coexistence curve below a certain
+ 
+
+ align:start position:0%
+coexistence curve below a certain
+pressure you can go directly from solid
+
+ align:start position:0%
+pressure you can go directly from solid
+ 
+
+ align:start position:0%
+pressure you can go directly from solid
+to Vapor if you hang your clothes out on
+
+ align:start position:0%
+to Vapor if you hang your clothes out on
+ 
+
+ align:start position:0%
+to Vapor if you hang your clothes out on
+the clothes line and it's- 20° C and
+
+ align:start position:0%
+the clothes line and it's- 20° C and
+ 
+
+ align:start position:0%
+the clothes line and it's- 20° C and
+first thing that happens is the water
+
+ align:start position:0%
+first thing that happens is the water
+ 
+
+ align:start position:0%
+first thing that happens is the water
+freezes but if you come back hours later
+
+ align:start position:0%
+freezes but if you come back hours later
+ 
+
+ align:start position:0%
+freezes but if you come back hours later
+the clothes are dry what happened did
+
+ align:start position:0%
+the clothes are dry what happened did
+ 
+
+ align:start position:0%
+the clothes are dry what happened did
+somebody come in truck grab all the
+
+ align:start position:0%
+somebody come in truck grab all the
+ 
+
+ align:start position:0%
+somebody come in truck grab all the
+clothes and take them down to the laundr
+
+ align:start position:0%
+clothes and take them down to the laundr
+ 
+
+ align:start position:0%
+clothes and take them down to the laundr
+mat put them into the dryer and then
+
+ align:start position:0%
+mat put them into the dryer and then
+ 
+
+ align:start position:0%
+mat put them into the dryer and then
+come back and hang them on the clothes
+
+ align:start position:0%
+come back and hang them on the clothes
+ 
+
+ align:start position:0%
+come back and hang them on the clothes
+line how did it happen happen went
+
+ align:start position:0%
+line how did it happen happen went
+ 
+
+ align:start position:0%
+line how did it happen happen went
+directly from solid to Vapor this is
+
+ align:start position:0%
+directly from solid to Vapor this is
+ 
+
+ align:start position:0%
+directly from solid to Vapor this is
+sublimation this is
+
+ align:start position:0%
+sublimation this is
+ 
+
+ align:start position:0%
+sublimation this is
+sublimation here liquid goes to Vapor is
+
+ align:start position:0%
+sublimation here liquid goes to Vapor is
+ 
+
+ align:start position:0%
+sublimation here liquid goes to Vapor is
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaporation Vapor goes to liquid is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condensation these are the phase
+
+ align:start position:0%
+condensation these are the phase
+ 
+
+ align:start position:0%
+condensation these are the phase
+Transformations solid goes to liquid you
+
+ align:start position:0%
+Transformations solid goes to liquid you
+ 
+
+ align:start position:0%
+Transformations solid goes to liquid you
+know that's
+
+ align:start position:0%
+know that's
+ 
+
+ align:start position:0%
+know that's
+melting and liquid goes to solid that is
+
+ align:start position:0%
+melting and liquid goes to solid that is
+ 
+
+ align:start position:0%
+melting and liquid goes to solid that is
+solidification and I say that without
+
+ align:start position:0%
+solidification and I say that without
+ 
+
+ align:start position:0%
+solidification and I say that without
+prejudice it it could be to form the
+
+ align:start position:0%
+prejudice it it could be to form the
+ 
+
+ align:start position:0%
+prejudice it it could be to form the
+glassy solid or it could be to form
+
+ align:start position:0%
+glassy solid or it could be to form
+ 
+
+ align:start position:0%
+glassy solid or it could be to form
+the amorphous solid and sublimation
+
+ align:start position:0%
+the amorphous solid and sublimation
+ 
+
+ align:start position:0%
+the amorphous solid and sublimation
+talks about both directions Vapor to
+
+ align:start position:0%
+talks about both directions Vapor to
+ 
+
+ align:start position:0%
+talks about both directions Vapor to
+solid or solid to Vapor is
+
+ align:start position:0%
+solid or solid to Vapor is
+ 
+
+ align:start position:0%
+solid or solid to Vapor is
+sublimation so this is a coexistence
+
+ align:start position:0%
+sublimation so this is a coexistence
+ 
+
+ align:start position:0%
+sublimation so this is a coexistence
+curve so along here we can even put some
+
+ align:start position:0%
+curve so along here we can even put some
+ 
+
+ align:start position:0%
+curve so along here we can even put some
+labels we can put over here single phase
+
+ align:start position:0%
+labels we can put over here single phase
+ 
+
+ align:start position:0%
+labels we can put over here single phase
+over here single phase and over here
+
+ align:start position:0%
+over here single phase and over here
+ 
+
+ align:start position:0%
+over here single phase and over here
+single phase and along these coexistence
+
+ align:start position:0%
+single phase and along these coexistence
+ 
+
+ align:start position:0%
+single phase and along these coexistence
+curves liquid equals Vapor so I have two
+
+ align:start position:0%
+curves liquid equals Vapor so I have two
+ 
+
+ align:start position:0%
+curves liquid equals Vapor so I have two
+phases along all the coexistence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curves along the coexistence curves look
+
+ align:start position:0%
+curves along the coexistence curves look
+ 
+
+ align:start position:0%
+curves along the coexistence curves look
+at this point here that's a curiosity
+
+ align:start position:0%
+at this point here that's a curiosity
+ 
+
+ align:start position:0%
+at this point here that's a curiosity
+isn't it what do I have here according
+
+ align:start position:0%
+isn't it what do I have here according
+ 
+
+ align:start position:0%
+isn't it what do I have here according
+to this diagram I have solid liquid and
+
+ align:start position:0%
+to this diagram I have solid liquid and
+ 
+
+ align:start position:0%
+to this diagram I have solid liquid and
+Vapor in
+
+ align:start position:0%
+Vapor in
+ 
+
+ align:start position:0%
+Vapor in
+equilibrium this
+
+ align:start position:0%
+equilibrium this
+ 
+
+ align:start position:0%
+equilibrium this
+is ice cubes in boiling water ice cubes
+
+ align:start position:0%
+is ice cubes in boiling water ice cubes
+ 
+
+ align:start position:0%
+is ice cubes in boiling water ice cubes
+and boiling water all three phases at
+
+ align:start position:0%
+and boiling water all three phases at
+ 
+
+ align:start position:0%
+and boiling water all three phases at
+this point here and this Point first of
+
+ align:start position:0%
+this point here and this Point first of
+ 
+
+ align:start position:0%
+this point here and this Point first of
+all as you can imagine not to scale
+
+ align:start position:0%
+all as you can imagine not to scale
+ 
+
+ align:start position:0%
+all as you can imagine not to scale
+because some of the features are rather
+
+ align:start position:0%
+because some of the features are rather
+ 
+
+ align:start position:0%
+because some of the features are rather
+subtle and wouldn't be seen if I drew
+
+ align:start position:0%
+subtle and wouldn't be seen if I drew
+ 
+
+ align:start position:0%
+subtle and wouldn't be seen if I drew
+this to scale this is at a very slight
+
+ align:start position:0%
+this to scale this is at a very slight
+ 
+
+ align:start position:0%
+this to scale this is at a very slight
+elevation in temperature it's about 1/
+
+ align:start position:0%
+elevation in temperature it's about 1/
+ 
+
+ align:start position:0%
+elevation in temperature it's about 1/
+100th of a degree above Zer Celsius and
+
+ align:start position:0%
+100th of a degree above Zer Celsius and
+ 
+
+ align:start position:0%
+100th of a degree above Zer Celsius and
+the pressure here is about oh it's it's
+
+ align:start position:0%
+the pressure here is about oh it's it's
+ 
+
+ align:start position:0%
+the pressure here is about oh it's it's
+not about I know what it is it's 4.58
+
+ align:start position:0%
+not about I know what it is it's 4.58
+ 
+
+ align:start position:0%
+not about I know what it is it's 4.58
+millimet I'm going to squeeze that in
+
+ align:start position:0%
+millimet I'm going to squeeze that in
+ 
+
+ align:start position:0%
+millimet I'm going to squeeze that in
+here it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4.58 millim of mercury and you need to
+
+ align:start position:0%
+4.58 millim of mercury and you need to
+ 
+
+ align:start position:0%
+4.58 millim of mercury and you need to
+know that one atmosphere if you remember
+
+ align:start position:0%
+know that one atmosphere if you remember
+ 
+
+ align:start position:0%
+know that one atmosphere if you remember
+torelli and his vacuum tube is 76 CM or
+
+ align:start position:0%
+torelli and his vacuum tube is 76 CM or
+ 
+
+ align:start position:0%
+torelli and his vacuum tube is 76 CM or
+760 millimet of mercury so that's the
+
+ align:start position:0%
+760 millimet of mercury so that's the
+ 
+
+ align:start position:0%
+760 millimet of mercury so that's the
+pressure it's 4.58 millim and so if you
+
+ align:start position:0%
+pressure it's 4.58 millim and so if you
+ 
+
+ align:start position:0%
+pressure it's 4.58 millim and so if you
+were to take water pour it into a beaker
+
+ align:start position:0%
+were to take water pour it into a beaker
+ 
+
+ align:start position:0%
+were to take water pour it into a beaker
+cover the beaker with a some enclosure
+
+ align:start position:0%
+cover the beaker with a some enclosure
+ 
+
+ align:start position:0%
+cover the beaker with a some enclosure
+that allowed you to pump the temperature
+
+ align:start position:0%
+that allowed you to pump the temperature
+ 
+
+ align:start position:0%
+that allowed you to pump the temperature
+down eventually you would reach excuse
+
+ align:start position:0%
+down eventually you would reach excuse
+ 
+
+ align:start position:0%
+down eventually you would reach excuse
+me pump the pressure down eventually you
+
+ align:start position:0%
+me pump the pressure down eventually you
+ 
+
+ align:start position:0%
+me pump the pressure down eventually you
+would reach the pressure at which
+
+ align:start position:0%
+would reach the pressure at which
+ 
+
+ align:start position:0%
+would reach the pressure at which
+water boils at room temperature water
+
+ align:start position:0%
+water boils at room temperature water
+ 
+
+ align:start position:0%
+water boils at room temperature water
+boils at room temperature remember this
+
+ align:start position:0%
+boils at room temperature remember this
+ 
+
+ align:start position:0%
+boils at room temperature remember this
+number 2020 2020 roughly 20° C 20 millim
+
+ align:start position:0%
+number 2020 2020 roughly 20° C 20 millim
+ 
+
+ align:start position:0%
+number 2020 2020 roughly 20° C 20 millim
+of mercury round numbers it's not
+
+ align:start position:0%
+of mercury round numbers it's not
+ 
+
+ align:start position:0%
+of mercury round numbers it's not
+exactly that but it's it's very close so
+
+ align:start position:0%
+exactly that but it's it's very close so
+ 
+
+ align:start position:0%
+exactly that but it's it's very close so
+if you get 20 millimet of mercury you'll
+
+ align:start position:0%
+if you get 20 millimet of mercury you'll
+ 
+
+ align:start position:0%
+if you get 20 millimet of mercury you'll
+have boiling water at room temperature
+
+ align:start position:0%
+have boiling water at room temperature
+ 
+
+ align:start position:0%
+have boiling water at room temperature
+but if you get down a z degrees see just
+
+ align:start position:0%
+but if you get down a z degrees see just
+ 
+
+ align:start position:0%
+but if you get down a z degrees see just
+100th of a degree higher you have all
+
+ align:start position:0%
+100th of a degree higher you have all
+ 
+
+ align:start position:0%
+100th of a degree higher you have all
+three phases ice cubes with water
+
+ align:start position:0%
+three phases ice cubes with water
+ 
+
+ align:start position:0%
+three phases ice cubes with water
+boiling in uh liquid so here we are with
+
+ align:start position:0%
+boiling in uh liquid so here we are with
+ 
+
+ align:start position:0%
+boiling in uh liquid so here we are with
+all of the
+
+ align:start position:0%
+all of the
+ 
+
+ align:start position:0%
+all of the
+all of the different phases and uh oh
+
+ align:start position:0%
+all of the different phases and uh oh
+ 
+
+ align:start position:0%
+all of the different phases and uh oh
+there's last thing I wanted to tell you
+
+ align:start position:0%
+there's last thing I wanted to tell you
+ 
+
+ align:start position:0%
+there's last thing I wanted to tell you
+last thing is you see this slope here
+
+ align:start position:0%
+last thing is you see this slope here
+ 
+
+ align:start position:0%
+last thing is you see this slope here
+see this slope it's negative slope and
+
+ align:start position:0%
+see this slope it's negative slope and
+ 
+
+ align:start position:0%
+see this slope it's negative slope and
+it it kind of puzzles me because when
+
+ align:start position:0%
+it it kind of puzzles me because when
+ 
+
+ align:start position:0%
+it it kind of puzzles me because when
+you look at it normally you'd think you
+
+ align:start position:0%
+you look at it normally you'd think you
+ 
+
+ align:start position:0%
+you look at it normally you'd think you
+see if you go at a at a a constant uh
+
+ align:start position:0%
+see if you go at a at a a constant uh
+ 
+
+ align:start position:0%
+see if you go at a at a a constant uh
+constant temperature let's say we start
+
+ align:start position:0%
+constant temperature let's say we start
+ 
+
+ align:start position:0%
+constant temperature let's say we start
+at 0 degrees and very very low pressure
+
+ align:start position:0%
+at 0 degrees and very very low pressure
+ 
+
+ align:start position:0%
+at 0 degrees and very very low pressure
+so we have something that's a gas and
+
+ align:start position:0%
+so we have something that's a gas and
+ 
+
+ align:start position:0%
+so we have something that's a gas and
+then we press atoms closer and closer
+
+ align:start position:0%
+then we press atoms closer and closer
+ 
+
+ align:start position:0%
+then we press atoms closer and closer
+together and then it says you make a
+
+ align:start position:0%
+together and then it says you make a
+ 
+
+ align:start position:0%
+together and then it says you make a
+solid and then at the constant
+
+ align:start position:0%
+solid and then at the constant
+ 
+
+ align:start position:0%
+solid and then at the constant
+temperature you press the solid atoms
+
+ align:start position:0%
+temperature you press the solid atoms
+ 
+
+ align:start position:0%
+temperature you press the solid atoms
+closer together and it says you make a
+
+ align:start position:0%
+closer together and it says you make a
+ 
+
+ align:start position:0%
+closer together and it says you make a
+liquid again doesn't that sound kind of
+
+ align:start position:0%
+liquid again doesn't that sound kind of
+ 
+
+ align:start position:0%
+liquid again doesn't that sound kind of
+backwards wouldn't you think that you
+
+ align:start position:0%
+backwards wouldn't you think that you
+ 
+
+ align:start position:0%
+backwards wouldn't you think that you
+start with gas atoms far apart then you
+
+ align:start position:0%
+start with gas atoms far apart then you
+ 
+
+ align:start position:0%
+start with gas atoms far apart then you
+move closer you get liquid atoms and you
+
+ align:start position:0%
+move closer you get liquid atoms and you
+ 
+
+ align:start position:0%
+move closer you get liquid atoms and you
+press the liquid atoms and you get a
+
+ align:start position:0%
+press the liquid atoms and you get a
+ 
+
+ align:start position:0%
+press the liquid atoms and you get a
+solid but water is special water is
+
+ align:start position:0%
+solid but water is special water is
+ 
+
+ align:start position:0%
+solid but water is special water is
+special because the bonding in the solid
+
+ align:start position:0%
+special because the bonding in the solid
+ 
+
+ align:start position:0%
+special because the bonding in the solid
+is more open than bonding in the liquid
+
+ align:start position:0%
+is more open than bonding in the liquid
+ 
+
+ align:start position:0%
+is more open than bonding in the liquid
+and I can look at this and say because
+
+ align:start position:0%
+and I can look at this and say because
+ 
+
+ align:start position:0%
+and I can look at this and say because
+when I press from solid to liquid liid
+
+ align:start position:0%
+when I press from solid to liquid liid
+ 
+
+ align:start position:0%
+when I press from solid to liquid liid
+this tells me that the density of the
+
+ align:start position:0%
+this tells me that the density of the
+ 
+
+ align:start position:0%
+this tells me that the density of the
+solid is lower than the density of the
+
+ align:start position:0%
+solid is lower than the density of the
+ 
+
+ align:start position:0%
+solid is lower than the density of the
+liquid I look at that and I say ice
+
+ align:start position:0%
+liquid I look at that and I say ice
+ 
+
+ align:start position:0%
+liquid I look at that and I say ice
+cubes float ice cubes float and there
+
+ align:start position:0%
+cubes float ice cubes float and there
+ 
+
+ align:start position:0%
+cubes float ice cubes float and there
+are other there are other uh systems for
+
+ align:start position:0%
+are other there are other uh systems for
+ 
+
+ align:start position:0%
+are other there are other uh systems for
+which the same happens uh here's silicon
+
+ align:start position:0%
+which the same happens uh here's silicon
+ 
+
+ align:start position:0%
+which the same happens uh here's silicon
+look at silicon here's the phase diagram
+
+ align:start position:0%
+look at silicon here's the phase diagram
+ 
+
+ align:start position:0%
+look at silicon here's the phase diagram
+for silicon pressure versus temperature
+
+ align:start position:0%
+for silicon pressure versus temperature
+ 
+
+ align:start position:0%
+for silicon pressure versus temperature
+you see uh uh down here it's FCC the
+
+ align:start position:0%
+you see uh uh down here it's FCC the
+ 
+
+ align:start position:0%
+you see uh uh down here it's FCC the
+diamond cubic structure and if we go
+
+ align:start position:0%
+diamond cubic structure and if we go
+ 
+
+ align:start position:0%
+diamond cubic structure and if we go
+there's the melting point of silicon we
+
+ align:start position:0%
+there's the melting point of silicon we
+ 
+
+ align:start position:0%
+there's the melting point of silicon we
+go to the liquid it's got more near its
+
+ align:start position:0%
+go to the liquid it's got more near its
+ 
+
+ align:start position:0%
+go to the liquid it's got more near its
+neighbor how many nearest neighbors does
+
+ align:start position:0%
+neighbor how many nearest neighbors does
+ 
+
+ align:start position:0%
+neighbor how many nearest neighbors does
+the solid have it's sp3 hybridized has
+
+ align:start position:0%
+the solid have it's sp3 hybridized has
+ 
+
+ align:start position:0%
+the solid have it's sp3 hybridized has
+four nearest neighbors most liquids have
+
+ align:start position:0%
+four nearest neighbors most liquids have
+ 
+
+ align:start position:0%
+four nearest neighbors most liquids have
+about six nearest neighbors so when you
+
+ align:start position:0%
+about six nearest neighbors so when you
+ 
+
+ align:start position:0%
+about six nearest neighbors so when you
+have these open structures like Silicon
+
+ align:start position:0%
+have these open structures like Silicon
+ 
+
+ align:start position:0%
+have these open structures like Silicon
+geranium the silicate glasses and
+
+ align:start position:0%
+geranium the silicate glasses and
+ 
+
+ align:start position:0%
+geranium the silicate glasses and
+Ice you actually go to a more condensed
+
+ align:start position:0%
+Ice you actually go to a more condensed
+ 
+
+ align:start position:0%
+Ice you actually go to a more condensed
+system when you first liquefy and this
+
+ align:start position:0%
+system when you first liquefy and this
+ 
+
+ align:start position:0%
+system when you first liquefy and this
+is how you skate by the way you know
+
+ align:start position:0%
+is how you skate by the way you know
+ 
+
+ align:start position:0%
+is how you skate by the way you know
+you're down here at one atmosphere about
+
+ align:start position:0%
+you're down here at one atmosphere about
+ 
+
+ align:start position:0%
+you're down here at one atmosphere about
+minus5 degrees C and you put your weight
+
+ align:start position:0%
+minus5 degrees C and you put your weight
+ 
+
+ align:start position:0%
+minus5 degrees C and you put your weight
+on the blades so that's a mass which
+
+ align:start position:0%
+on the blades so that's a mass which
+ 
+
+ align:start position:0%
+on the blades so that's a mass which
+then becomes a force on a small small
+
+ align:start position:0%
+then becomes a force on a small small
+ 
+
+ align:start position:0%
+then becomes a force on a small small
+area which becomes a pressure and then
+
+ align:start position:0%
+area which becomes a pressure and then
+ 
+
+ align:start position:0%
+area which becomes a pressure and then
+that allows you to cross this line so
+
+ align:start position:0%
+that allows you to cross this line so
+ 
+
+ align:start position:0%
+that allows you to cross this line so
+you glide on a thin film of water and if
+
+ align:start position:0%
+you glide on a thin film of water and if
+ 
+
+ align:start position:0%
+you glide on a thin film of water and if
+the temperature gets really cold if it's
+
+ align:start position:0%
+the temperature gets really cold if it's
+ 
+
+ align:start position:0%
+the temperature gets really cold if it's
+down here at around minus 20 and I've
+
+ align:start position:0%
+down here at around minus 20 and I've
+ 
+
+ align:start position:0%
+down here at around minus 20 and I've
+had the pleasure of skating when it's
+
+ align:start position:0%
+had the pleasure of skating when it's
+ 
+
+ align:start position:0%
+had the pleasure of skating when it's
+minus 20 my
+
+ align:start position:0%
+minus 20 my
+ 
+
+ align:start position:0%
+minus 20 my
+mass converted to appropriate pressure
+
+ align:start position:0%
+mass converted to appropriate pressure
+ 
+
+ align:start position:0%
+mass converted to appropriate pressure
+on the blades is not high enough to
+
+ align:start position:0%
+on the blades is not high enough to
+ 
+
+ align:start position:0%
+on the blades is not high enough to
+cross this line and the skating
+
+ align:start position:0%
+cross this line and the skating
+ 
+
+ align:start position:0%
+cross this line and the skating
+experience is very different because now
+
+ align:start position:0%
+experience is very different because now
+ 
+
+ align:start position:0%
+experience is very different because now
+it's just it's just steel blades on ice
+
+ align:start position:0%
+it's just it's just steel blades on ice
+ 
+
+ align:start position:0%
+it's just it's just steel blades on ice
+and it's you don't get traction to put
+
+ align:start position:0%
+and it's you don't get traction to put
+ 
+
+ align:start position:0%
+and it's you don't get traction to put
+it simply you fall okay you fall not
+
+ align:start position:0%
+it simply you fall okay you fall not
+ 
+
+ align:start position:0%
+it simply you fall okay you fall not
+good not good okay so let's let's look
+
+ align:start position:0%
+good not good okay so let's let's look
+ 
+
+ align:start position:0%
+good not good okay so let's let's look
+at a few others if we contrast here this
+
+ align:start position:0%
+at a few others if we contrast here this
+ 
+
+ align:start position:0%
+at a few others if we contrast here this
+is aluminum a simple FCC metal and what
+
+ align:start position:0%
+is aluminum a simple FCC metal and what
+ 
+
+ align:start position:0%
+is aluminum a simple FCC metal and what
+we see with aluminum in this case it's
+
+ align:start position:0%
+we see with aluminum in this case it's
+ 
+
+ align:start position:0%
+we see with aluminum in this case it's
+normal liquid has about six to eight
+
+ align:start position:0%
+normal liquid has about six to eight
+ 
+
+ align:start position:0%
+normal liquid has about six to eight
+nearest neighbors and the solid has 12
+
+ align:start position:0%
+nearest neighbors and the solid has 12
+ 
+
+ align:start position:0%
+nearest neighbors and the solid has 12
+nearest neighbors so the solid is denser
+
+ align:start position:0%
+nearest neighbors so the solid is denser
+ 
+
+ align:start position:0%
+nearest neighbors so the solid is denser
+than the liquid and you see that in the
+
+ align:start position:0%
+than the liquid and you see that in the
+ 
+
+ align:start position:0%
+than the liquid and you see that in the
+face diagram here's nitrogen nitrogen is
+
+ align:start position:0%
+face diagram here's nitrogen nitrogen is
+ 
+
+ align:start position:0%
+face diagram here's nitrogen nitrogen is
+uh let's see what do we have it's at 1
+
+ align:start position:0%
+uh let's see what do we have it's at 1
+ 
+
+ align:start position:0%
+uh let's see what do we have it's at 1
+atmosphere pressure its U uh melting
+
+ align:start position:0%
+atmosphere pressure its U uh melting
+ 
+
+ align:start position:0%
+atmosphere pressure its U uh melting
+point is 63 Kelvin its boiling point is
+
+ align:start position:0%
+point is 63 Kelvin its boiling point is
+ 
+
+ align:start position:0%
+point is 63 Kelvin its boiling point is
+77 Kelvin you remember that because MIT
+
+ align:start position:0%
+77 Kelvin you remember that because MIT
+ 
+
+ align:start position:0%
+77 Kelvin you remember that because MIT
+is 77 Mass AB so nitrogen boils at 77
+
+ align:start position:0%
+is 77 Mass AB so nitrogen boils at 77
+ 
+
+ align:start position:0%
+is 77 Mass AB so nitrogen boils at 77
+Kelvin and the triple point is down here
+
+ align:start position:0%
+Kelvin and the triple point is down here
+ 
+
+ align:start position:0%
+Kelvin and the triple point is down here
+it's it's about 100 of a degree below
+
+ align:start position:0%
+it's it's about 100 of a degree below
+ 
+
+ align:start position:0%
+it's it's about 100 of a degree below
+and it turns out it's about an eighth of
+
+ align:start position:0%
+and it turns out it's about an eighth of
+ 
+
+ align:start position:0%
+and it turns out it's about an eighth of
+an atmosphere pressure this is the
+
+ align:start position:0%
+an atmosphere pressure this is the
+ 
+
+ align:start position:0%
+an atmosphere pressure this is the
+triple point of nitrogen ice in boiling
+
+ align:start position:0%
+triple point of nitrogen ice in boiling
+ 
+
+ align:start position:0%
+triple point of nitrogen ice in boiling
+liquid nitrogen but this has a positive
+
+ align:start position:0%
+liquid nitrogen but this has a positive
+ 
+
+ align:start position:0%
+liquid nitrogen but this has a positive
+slope so this means that the solid
+
+ align:start position:0%
+slope so this means that the solid
+ 
+
+ align:start position:0%
+slope so this means that the solid
+nitrogen ice sinks to the bottom of the
+
+ align:start position:0%
+nitrogen ice sinks to the bottom of the
+ 
+
+ align:start position:0%
+nitrogen ice sinks to the bottom of the
+liquid nitrogen and I thought since it's
+
+ align:start position:0%
+liquid nitrogen and I thought since it's
+ 
+
+ align:start position:0%
+liquid nitrogen and I thought since it's
+Friday maybe we could have just a little
+
+ align:start position:0%
+Friday maybe we could have just a little
+ 
+
+ align:start position:0%
+Friday maybe we could have just a little
+bit of fun here with the liquid nitrogen
+
+ align:start position:0%
+bit of fun here with the liquid nitrogen
+ 
+
+ align:start position:0%
+bit of fun here with the liquid nitrogen
+so I'm going to get dressed first I have
+
+ align:start position:0%
+so I'm going to get dressed first I have
+ 
+
+ align:start position:0%
+so I'm going to get dressed first I have
+to practice safe science I have to set
+
+ align:start position:0%
+to practice safe science I have to set
+ 
+
+ align:start position:0%
+to practice safe science I have to set
+an example for you you see I this year
+
+ align:start position:0%
+an example for you you see I this year
+ 
+
+ align:start position:0%
+an example for you you see I this year
+one of my uh staff Patrick trappa said
+
+ align:start position:0%
+one of my uh staff Patrick trappa said
+ 
+
+ align:start position:0%
+one of my uh staff Patrick trappa said
+why don't you wear a lab coat so I said
+
+ align:start position:0%
+why don't you wear a lab coat so I said
+ 
+
+ align:start position:0%
+why don't you wear a lab coat so I said
+okay try to try to do this
+
+ align:start position:0%
+okay try to try to do this
+ 
+
+ align:start position:0%
+okay try to try to do this
+properly is what which which design
+
+ align:start position:0%
+properly is what which which design
+ 
+
+ align:start position:0%
+properly is what which which design
+house did you go to for this
+
+ align:start position:0%
+house did you go to for this
+ 
+
+ align:start position:0%
+house did you go to for this
+Valentino
+
+ align:start position:0%
+Valentino
+ 
+
+ align:start position:0%
+Valentino
+vers okay so what are we going to do oh
+
+ align:start position:0%
+vers okay so what are we going to do oh
+ 
+
+ align:start position:0%
+vers okay so what are we going to do oh
+we're going to get some nitrogen let's
+
+ align:start position:0%
+we're going to get some nitrogen let's
+ 
+
+ align:start position:0%
+we're going to get some nitrogen let's
+get some nitrogen we'll have some fun
+
+ align:start position:0%
+get some nitrogen we'll have some fun
+ 
+
+ align:start position:0%
+get some nitrogen we'll have some fun
+with so we're going to be working at 77
+
+ align:start position:0%
+with so we're going to be working at 77
+ 
+
+ align:start position:0%
+with so we're going to be working at 77
+Kelvin and for those of you in the back
+
+ align:start position:0%
+Kelvin and for those of you in the back
+ 
+
+ align:start position:0%
+Kelvin and for those of you in the back
+we're going to put this up on the
+
+ align:start position:0%
+we're going to put this up on the
+ 
+
+ align:start position:0%
+we're going to put this up on the
+monitors oh no food in the laboratory so
+
+ align:start position:0%
+monitors oh no food in the laboratory so
+ 
+
+ align:start position:0%
+monitors oh no food in the laboratory so
+let's put that over
+
+ align:start position:0%
+let's put that over
+ 
+
+ align:start position:0%
+let's put that over
+there okay let's pour a little bit of
+
+ align:start position:0%
+there okay let's pour a little bit of
+ 
+
+ align:start position:0%
+there okay let's pour a little bit of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fantastic okay
+
+ align:start position:0%
+fantastic okay
+ 
+
+ align:start position:0%
+fantastic okay
+so see what are we going to so uh first
+
+ align:start position:0%
+so see what are we going to so uh first
+ 
+
+ align:start position:0%
+so see what are we going to so uh first
+thing we'll do is uh let's let's look at
+
+ align:start position:0%
+thing we'll do is uh let's let's look at
+ 
+
+ align:start position:0%
+thing we'll do is uh let's let's look at
+glass transition temperature so I have
+
+ align:start position:0%
+glass transition temperature so I have
+ 
+
+ align:start position:0%
+glass transition temperature so I have
+some uh rubber gloves oh I have to face
+
+ align:start position:0%
+some uh rubber gloves oh I have to face
+ 
+
+ align:start position:0%
+some uh rubber gloves oh I have to face
+uh Craig over this way okay Craig I'm
+
+ align:start position:0%
+uh Craig over this way okay Craig I'm
+ 
+
+ align:start position:0%
+uh Craig over this way okay Craig I'm
+going to do it this so here's some
+
+ align:start position:0%
+going to do it this so here's some
+ 
+
+ align:start position:0%
+going to do it this so here's some
+rubber gloves and so you know you can
+
+ align:start position:0%
+rubber gloves and so you know you can
+ 
+
+ align:start position:0%
+rubber gloves and so you know you can
+hear that they're they're acting elastic
+
+ align:start position:0%
+hear that they're they're acting elastic
+ 
+
+ align:start position:0%
+hear that they're they're acting elastic
+they're above their TG so this is just
+
+ align:start position:0%
+they're above their TG so this is just
+ 
+
+ align:start position:0%
+they're above their TG so this is just
+the calent bonds and what I'm going to
+
+ align:start position:0%
+the calent bonds and what I'm going to
+ 
+
+ align:start position:0%
+the calent bonds and what I'm going to
+do is pour a little bit of nitrogen in
+
+ align:start position:0%
+do is pour a little bit of nitrogen in
+ 
+
+ align:start position:0%
+do is pour a little bit of nitrogen in
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know if you noticed but the
+
+ align:start position:0%
+I don't know if you noticed but the
+ 
+
+ align:start position:0%
+I don't know if you noticed but the
+these gloves are chyal just just in case
+
+ align:start position:0%
+these gloves are chyal just just in case
+ 
+
+ align:start position:0%
+these gloves are chyal just just in case
+you notice I chose CYO
+
+ align:start position:0%
+you notice I chose CYO
+ 
+
+ align:start position:0%
+you notice I chose CYO
+gloves okay so now see so they're below
+
+ align:start position:0%
+gloves okay so now see so they're below
+ 
+
+ align:start position:0%
+gloves okay so now see so they're below
+the glass transition temperature I'm
+
+ align:start position:0%
+the glass transition temperature I'm
+ 
+
+ align:start position:0%
+the glass transition temperature I'm
+sorry Craig I got to here you get that
+
+ align:start position:0%
+sorry Craig I got to here you get that
+ 
+
+ align:start position:0%
+sorry Craig I got to here you get that
+we'll do it one more time okay gone
+
+ align:start position:0%
+we'll do it one more time okay gone
+ 
+
+ align:start position:0%
+we'll do it one more time okay gone
+glass transition temperature also if you
+
+ align:start position:0%
+glass transition temperature also if you
+ 
+
+ align:start position:0%
+glass transition temperature also if you
+wanted to drill the uh um if you wanted
+
+ align:start position:0%
+wanted to drill the uh um if you wanted
+ 
+
+ align:start position:0%
+wanted to drill the uh um if you wanted
+to drill the rubber stopper of course
+
+ align:start position:0%
+to drill the rubber stopper of course
+ 
+
+ align:start position:0%
+to drill the rubber stopper of course
+now you can hear I got to keep doing it
+
+ align:start position:0%
+now you can hear I got to keep doing it
+ 
+
+ align:start position:0%
+now you can hear I got to keep doing it
+this side
+
+ align:start position:0%
+this side
+ 
+
+ align:start position:0%
+this side
+so you can hear that it's it's rubbery
+
+ align:start position:0%
+so you can hear that it's it's rubbery
+ 
+
+ align:start position:0%
+so you can hear that it's it's rubbery
+I'm going to drop it in there let it
+
+ align:start position:0%
+I'm going to drop it in there let it
+ 
+
+ align:start position:0%
+I'm going to drop it in there let it
+mind its own business oh Saran Wrap it's
+
+ align:start position:0%
+mind its own business oh Saran Wrap it's
+ 
+
+ align:start position:0%
+mind its own business oh Saran Wrap it's
+also got glass transition temperature so
+
+ align:start position:0%
+also got glass transition temperature so
+ 
+
+ align:start position:0%
+also got glass transition temperature so
+we can show that getting it into liquid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nitrogen Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you hear how it's flexible now what
+
+ align:start position:0%
+you hear how it's flexible now what
+ 
+
+ align:start position:0%
+you hear how it's flexible now what
+we'll do is we'll put that in
+
+ align:start position:0%
+we'll do is we'll put that in
+ 
+
+ align:start position:0%
+we'll do is we'll put that in
+there okay now you can hear how it
+
+ align:start position:0%
+there okay now you can hear how it
+ 
+
+ align:start position:0%
+there okay now you can hear how it
+changes it's below the glass
+
+ align:start position:0%
+changes it's below the glass
+ 
+
+ align:start position:0%
+changes it's below the glass
+transition I should have been wearing
+
+ align:start position:0%
+transition I should have been wearing
+ 
+
+ align:start position:0%
+transition I should have been wearing
+gloves and all that but you know
+
+ align:start position:0%
+gloves and all that but you know
+ 
+
+ align:start position:0%
+gloves and all that but you know
+forget okay how about protein oh you
+
+ align:start position:0%
+forget okay how about protein oh you
+ 
+
+ align:start position:0%
+forget okay how about protein oh you
+know the other thing we can do other
+
+ align:start position:0%
+know the other thing we can do other
+ 
+
+ align:start position:0%
+know the other thing we can do other
+thing we can do is I want to make some
+
+ align:start position:0%
+thing we can do is I want to make some
+ 
+
+ align:start position:0%
+thing we can do is I want to make some
+liquid oxygen so I don't know can we
+
+ align:start position:0%
+liquid oxygen so I don't know can we
+ 
+
+ align:start position:0%
+liquid oxygen so I don't know can we
+just cut to the to the computer slide
+
+ align:start position:0%
+just cut to the to the computer slide
+ 
+
+ align:start position:0%
+just cut to the to the computer slide
+for a second I want to show people what
+
+ align:start position:0%
+for a second I want to show people what
+ 
+
+ align:start position:0%
+for a second I want to show people what
+we're going to do here with uh this next
+
+ align:start position:0%
+we're going to do here with uh this next
+ 
+
+ align:start position:0%
+we're going to do here with uh this next
+one all right so what I'm going to do is
+
+ align:start position:0%
+one all right so what I'm going to do is
+ 
+
+ align:start position:0%
+one all right so what I'm going to do is
+I'm going to put um a a graduated
+
+ align:start position:0%
+I'm going to put um a a graduated
+ 
+
+ align:start position:0%
+I'm going to put um a a graduated
+cylinder inside fill this with liquid
+
+ align:start position:0%
+cylinder inside fill this with liquid
+ 
+
+ align:start position:0%
+cylinder inside fill this with liquid
+nitrogen and these are the boiling
+
+ align:start position:0%
+nitrogen and these are the boiling
+ 
+
+ align:start position:0%
+nitrogen and these are the boiling
+points of oxygen argon and nitrogen and
+
+ align:start position:0%
+points of oxygen argon and nitrogen and
+ 
+
+ align:start position:0%
+points of oxygen argon and nitrogen and
+nitrogen is at 77 so this is all 77
+
+ align:start position:0%
+nitrogen is at 77 so this is all 77
+ 
+
+ align:start position:0%
+nitrogen is at 77 so this is all 77
+Kelvin but oxygen uh condenses at 90 so
+
+ align:start position:0%
+Kelvin but oxygen uh condenses at 90 so
+ 
+
+ align:start position:0%
+Kelvin but oxygen uh condenses at 90 so
+we're going to make liquid oxygen with a
+
+ align:start position:0%
+we're going to make liquid oxygen with a
+ 
+
+ align:start position:0%
+we're going to make liquid oxygen with a
+little bit of argon ice I'm just going
+
+ align:start position:0%
+little bit of argon ice I'm just going
+ 
+
+ align:start position:0%
+little bit of argon ice I'm just going
+to let it sit there for the balance of
+
+ align:start position:0%
+to let it sit there for the balance of
+ 
+
+ align:start position:0%
+to let it sit there for the balance of
+the lecture and maybe at the end we'll
+
+ align:start position:0%
+the lecture and maybe at the end we'll
+ 
+
+ align:start position:0%
+the lecture and maybe at the end we'll
+see some of the uh liquid oxygen so so
+
+ align:start position:0%
+see some of the uh liquid oxygen so so
+ 
+
+ align:start position:0%
+see some of the uh liquid oxygen so so
+let's just pour
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so we'll let that work and uh
+
+ align:start position:0%
+that okay so we'll let that work and uh
+ 
+
+ align:start position:0%
+that okay so we'll let that work and uh
+oh yeah how about proteins we said they
+
+ align:start position:0%
+oh yeah how about proteins we said they
+ 
+
+ align:start position:0%
+oh yeah how about proteins we said they
+were polymers so let's see if we can do
+
+ align:start position:0%
+were polymers so let's see if we can do
+ 
+
+ align:start position:0%
+were polymers so let's see if we can do
+something with the with the proteins
+
+ align:start position:0%
+something with the with the proteins
+ 
+
+ align:start position:0%
+something with the with the proteins
+here oh yeah we're going to put the
+
+ align:start position:0%
+here oh yeah we're going to put the
+ 
+
+ align:start position:0%
+here oh yeah we're going to put the
+roses in you know they have glass
+
+ align:start position:0%
+roses in you know they have glass
+ 
+
+ align:start position:0%
+roses in you know they have glass
+flowers at Harvard at the at the Museum
+
+ align:start position:0%
+flowers at Harvard at the at the Museum
+ 
+
+ align:start position:0%
+flowers at Harvard at the at the Museum
+fog Museum we have glass flowers here at
+
+ align:start position:0%
+fog Museum we have glass flowers here at
+ 
+
+ align:start position:0%
+fog Museum we have glass flowers here at
+MIT see this okay so this is a rose you
+
+ align:start position:0%
+MIT see this okay so this is a rose you
+ 
+
+ align:start position:0%
+MIT see this okay so this is a rose you
+know it's very soft just nice think
+
+ align:start position:0%
+know it's very soft just nice think
+ 
+
+ align:start position:0%
+know it's very soft just nice think
+watch this okay let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go it's not a kitten come
+
+ align:start position:0%
+go it's not a kitten come
+ 
+
+ align:start position:0%
+go it's not a kitten come
+on maybe it only works on roses maybe we
+
+ align:start position:0%
+on maybe it only works on roses maybe we
+ 
+
+ align:start position:0%
+on maybe it only works on roses maybe we
+should do one more it's got to be a
+
+ align:start position:0%
+should do one more it's got to be a
+ 
+
+ align:start position:0%
+should do one more it's got to be a
+scientist you don't know maybe it's just
+
+ align:start position:0%
+scientist you don't know maybe it's just
+ 
+
+ align:start position:0%
+scientist you don't know maybe it's just
+roses that do this so let's look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one glass transition temperature there
+
+ align:start position:0%
+one glass transition temperature there
+ 
+
+ align:start position:0%
+one glass transition temperature there
+it is okay so we got that going we'll
+
+ align:start position:0%
+it is okay so we got that going we'll
+ 
+
+ align:start position:0%
+it is okay so we got that going we'll
+let the oxygen uh condense and let's see
+
+ align:start position:0%
+let the oxygen uh condense and let's see
+ 
+
+ align:start position:0%
+let the oxygen uh condense and let's see
+let's go back to the computer I think
+
+ align:start position:0%
+let's go back to the computer I think
+ 
+
+ align:start position:0%
+let's go back to the computer I think
+we're going to take a break and go back
+
+ align:start position:0%
+we're going to take a break and go back
+ 
+
+ align:start position:0%
+we're going to take a break and go back
+to some some more learning here ah a a
+
+ align:start position:0%
+to some some more learning here ah a a
+ 
+
+ align:start position:0%
+to some some more learning here ah a a
+ah yeah
+
+ align:start position:0%
+ah yeah
+ 
+
+ align:start position:0%
+ah yeah
+okay so here here are some uh hang on
+
+ align:start position:0%
+okay so here here are some uh hang on
+ 
+
+ align:start position:0%
+okay so here here are some uh hang on
+there's one other one here I think got
+
+ align:start position:0%
+there's one other one here I think got
+ 
+
+ align:start position:0%
+there's one other one here I think got
+out of here all right so we've seen this
+
+ align:start position:0%
+out of here all right so we've seen this
+ 
+
+ align:start position:0%
+out of here all right so we've seen this
+one here's nitrogen with all of its
+
+ align:start position:0%
+one here's nitrogen with all of its
+ 
+
+ align:start position:0%
+one here's nitrogen with all of its
+different uh solid phases nitrogen
+
+ align:start position:0%
+different uh solid phases nitrogen
+ 
+
+ align:start position:0%
+different uh solid phases nitrogen
+actually has different Crystal
+
+ align:start position:0%
+actually has different Crystal
+ 
+
+ align:start position:0%
+actually has different Crystal
+structures and so this diagram shows
+
+ align:start position:0%
+structures and so this diagram shows
+ 
+
+ align:start position:0%
+structures and so this diagram shows
+what's going on as you as you change
+
+ align:start position:0%
+what's going on as you as you change
+ 
+
+ align:start position:0%
+what's going on as you as you change
+pressure at constant temperature here we
+
+ align:start position:0%
+pressure at constant temperature here we
+ 
+
+ align:start position:0%
+pressure at constant temperature here we
+are still down around minus uh 70 Kelvin
+
+ align:start position:0%
+are still down around minus uh 70 Kelvin
+ 
+
+ align:start position:0%
+are still down around minus uh 70 Kelvin
+so there we go from liquid to solid it's
+
+ align:start position:0%
+so there we go from liquid to solid it's
+ 
+
+ align:start position:0%
+so there we go from liquid to solid it's
+hcp and then it becomes simple cubic and
+
+ align:start position:0%
+hcp and then it becomes simple cubic and
+ 
+
+ align:start position:0%
+hcp and then it becomes simple cubic and
+then romic and so on so this property
+
+ align:start position:0%
+then romic and so on so this property
+ 
+
+ align:start position:0%
+then romic and so on so this property
+certain elements have multiple different
+
+ align:start position:0%
+certain elements have multiple different
+ 
+
+ align:start position:0%
+certain elements have multiple different
+um composition excuse me multiple
+
+ align:start position:0%
+um composition excuse me multiple
+ 
+
+ align:start position:0%
+um composition excuse me multiple
+different Crystal structures is called
+
+ align:start position:0%
+different Crystal structures is called
+ 
+
+ align:start position:0%
+different Crystal structures is called
+polymorphism so these are called
+
+ align:start position:0%
+polymorphism so these are called
+ 
+
+ align:start position:0%
+polymorphism so these are called
+different polymorphs you've already
+
+ align:start position:0%
+different polymorphs you've already
+ 
+
+ align:start position:0%
+different polymorphs you've already
+heard that uh iron has in some instances
+
+ align:start position:0%
+heard that uh iron has in some instances
+ 
+
+ align:start position:0%
+heard that uh iron has in some instances
+BCC crystal structure and FCC crystal
+
+ align:start position:0%
+BCC crystal structure and FCC crystal
+ 
+
+ align:start position:0%
+BCC crystal structure and FCC crystal
+structure and the phase diagrams will
+
+ align:start position:0%
+structure and the phase diagrams will
+ 
+
+ align:start position:0%
+structure and the phase diagrams will
+reveal when these transitions occur
+
+ align:start position:0%
+reveal when these transitions occur
+ 
+
+ align:start position:0%
+reveal when these transitions occur
+here's carbon dioxide solid liquid gas
+
+ align:start position:0%
+here's carbon dioxide solid liquid gas
+ 
+
+ align:start position:0%
+here's carbon dioxide solid liquid gas
+it's got a positive slope what's
+
+ align:start position:0%
+it's got a positive slope what's
+ 
+
+ align:start position:0%
+it's got a positive slope what's
+interesting about carbon dioxide is look
+
+ align:start position:0%
+interesting about carbon dioxide is look
+ 
+
+ align:start position:0%
+interesting about carbon dioxide is look
+here the one atmosphere isobar takes you
+
+ align:start position:0%
+here the one atmosphere isobar takes you
+ 
+
+ align:start position:0%
+here the one atmosphere isobar takes you
+directly from solid to gas so it doesn't
+
+ align:start position:0%
+directly from solid to gas so it doesn't
+ 
+
+ align:start position:0%
+directly from solid to gas so it doesn't
+go liquid and that gives it value as a a
+
+ align:start position:0%
+go liquid and that gives it value as a a
+ 
+
+ align:start position:0%
+go liquid and that gives it value as a a
+as a refrigerant because when it uh
+
+ align:start position:0%
+as a refrigerant because when it uh
+ 
+
+ align:start position:0%
+as a refrigerant because when it uh
+gives up its uh enthalpy of uh of
+
+ align:start position:0%
+gives up its uh enthalpy of uh of
+ 
+
+ align:start position:0%
+gives up its uh enthalpy of uh of
+transformation you don't end up with a
+
+ align:start position:0%
+transformation you don't end up with a
+ 
+
+ align:start position:0%
+transformation you don't end up with a
+liquid which can mess up your contents
+
+ align:start position:0%
+liquid which can mess up your contents
+ 
+
+ align:start position:0%
+liquid which can mess up your contents
+and so this is often used in U in
+
+ align:start position:0%
+and so this is often used in U in
+ 
+
+ align:start position:0%
+and so this is often used in U in
+shipping certain materials so we've got
+
+ align:start position:0%
+shipping certain materials so we've got
+ 
+
+ align:start position:0%
+shipping certain materials so we've got
+some here let's play with some dry ice
+
+ align:start position:0%
+some here let's play with some dry ice
+ 
+
+ align:start position:0%
+some here let's play with some dry ice
+there's a great big ice cube here but
+
+ align:start position:0%
+there's a great big ice cube here but
+ 
+
+ align:start position:0%
+there's a great big ice cube here but
+there's some that's already broken off
+
+ align:start position:0%
+there's some that's already broken off
+ 
+
+ align:start position:0%
+there's some that's already broken off
+see so this uh I okay so here we are
+
+ align:start position:0%
+see so this uh I okay so here we are
+ 
+
+ align:start position:0%
+see so this uh I okay so here we are
+this is the big ice cube I guess Craig
+
+ align:start position:0%
+this is the big ice cube I guess Craig
+ 
+
+ align:start position:0%
+this is the big ice cube I guess Craig
+is going to want to see this so let's
+
+ align:start position:0%
+is going to want to see this so let's
+ 
+
+ align:start position:0%
+is going to want to see this so let's
+let's let Craig and the people watch the
+
+ align:start position:0%
+let's let Craig and the people watch the
+ 
+
+ align:start position:0%
+let's let Craig and the people watch the
+video This what I call an ice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cube okay now this is at uh at minus 78°
+
+ align:start position:0%
+cube okay now this is at uh at minus 78°
+ 
+
+ align:start position:0%
+cube okay now this is at uh at minus 78°
+C and so it's it can go directly you're
+
+ align:start position:0%
+C and so it's it can go directly you're
+ 
+
+ align:start position:0%
+C and so it's it can go directly you're
+seeing it it's Sublime um let's see we
+
+ align:start position:0%
+seeing it it's Sublime um let's see we
+ 
+
+ align:start position:0%
+seeing it it's Sublime um let's see we
+can do some things just to prove let's
+
+ align:start position:0%
+can do some things just to prove let's
+ 
+
+ align:start position:0%
+can do some things just to prove let's
+prove that it's going directly from
+
+ align:start position:0%
+prove that it's going directly from
+ 
+
+ align:start position:0%
+prove that it's going directly from
+solid to uh gas so I have some just some
+
+ align:start position:0%
+solid to uh gas so I have some just some
+ 
+
+ align:start position:0%
+solid to uh gas so I have some just some
+plain spring water here non-carbonated
+
+ align:start position:0%
+plain spring water here non-carbonated
+ 
+
+ align:start position:0%
+plain spring water here non-carbonated
+this is flat okay so this is flat I'll
+
+ align:start position:0%
+this is flat okay so this is flat I'll
+ 
+
+ align:start position:0%
+this is flat okay so this is flat I'll
+put that on the edge there for Craig and
+
+ align:start position:0%
+put that on the edge there for Craig and
+ 
+
+ align:start position:0%
+put that on the edge there for Craig and
+then just to show that we're going
+
+ align:start position:0%
+then just to show that we're going
+ 
+
+ align:start position:0%
+then just to show that we're going
+directly I take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay see I'll hold still Craig so
+
+ align:start position:0%
+this okay see I'll hold still Craig so
+ 
+
+ align:start position:0%
+this okay see I'll hold still Craig so
+there we go you see the bubbles coming
+
+ align:start position:0%
+there we go you see the bubbles coming
+ 
+
+ align:start position:0%
+there we go you see the bubbles coming
+off giant bubbles
+
+ align:start position:0%
+off giant bubbles
+ 
+
+ align:start position:0%
+off giant bubbles
+see so we're making CO2 in water and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good I want you to notice something you
+
+ align:start position:0%
+good I want you to notice something you
+ 
+
+ align:start position:0%
+good I want you to notice something you
+know you can buy this bottled WI
+
+ align:start position:0%
+know you can buy this bottled WI
+ 
+
+ align:start position:0%
+know you can buy this bottled WI
+and I don't know if you can see Craig I
+
+ align:start position:0%
+and I don't know if you can see Craig I
+ 
+
+ align:start position:0%
+and I don't know if you can see Craig I
+don't know if you can catch this but you
+
+ align:start position:0%
+don't know if you can catch this but you
+ 
+
+ align:start position:0%
+don't know if you can catch this but you
+see they have these tiny wimpy bubbles
+
+ align:start position:0%
+see they have these tiny wimpy bubbles
+ 
+
+ align:start position:0%
+see they have these tiny wimpy bubbles
+we have big
+
+ align:start position:0%
+we have big
+ 
+
+ align:start position:0%
+we have big
+bubbles we have big
+
+ align:start position:0%
+bubbles we have big
+ 
+
+ align:start position:0%
+bubbles we have big
+bubbles so that's
+
+ align:start position:0%
+bubbles so that's
+ 
+
+ align:start position:0%
+bubbles so that's
+CO2 let's see what else have we got
+
+ align:start position:0%
+CO2 let's see what else have we got
+ 
+
+ align:start position:0%
+CO2 let's see what else have we got
+going let's see if we still have some uh
+
+ align:start position:0%
+going let's see if we still have some uh
+ 
+
+ align:start position:0%
+going let's see if we still have some uh
+uh liquid we've made any liquid oxygen
+
+ align:start position:0%
+uh liquid we've made any liquid oxygen
+ 
+
+ align:start position:0%
+uh liquid we've made any liquid oxygen
+yet oh yeah there's just a little bit he
+
+ align:start position:0%
+yet oh yeah there's just a little bit he
+ 
+
+ align:start position:0%
+yet oh yeah there's just a little bit he
+won't be able to pick it up on the
+
+ align:start position:0%
+won't be able to pick it up on the
+ 
+
+ align:start position:0%
+won't be able to pick it up on the
+camera okay so now the the last thing I
+
+ align:start position:0%
+camera okay so now the the last thing I
+ 
+
+ align:start position:0%
+camera okay so now the the last thing I
+want to do is to go back to the um
+
+ align:start position:0%
+want to do is to go back to the um
+ 
+
+ align:start position:0%
+want to do is to go back to the um
+computer image if we could
+
+ align:start position:0%
+computer image if we could
+ 
+
+ align:start position:0%
+computer image if we could
+please Okay so we've got carbon dioxide
+
+ align:start position:0%
+please Okay so we've got carbon dioxide
+ 
+
+ align:start position:0%
+please Okay so we've got carbon dioxide
+all right here's a couple other phase
+
+ align:start position:0%
+all right here's a couple other phase
+ 
+
+ align:start position:0%
+all right here's a couple other phase
+diagrams zonia I mentioned to you that
+
+ align:start position:0%
+diagrams zonia I mentioned to you that
+ 
+
+ align:start position:0%
+diagrams zonia I mentioned to you that
+zerconia uh this is just pure zerconia
+
+ align:start position:0%
+zerconia uh this is just pure zerconia
+ 
+
+ align:start position:0%
+zerconia uh this is just pure zerconia
+zro2 and what do we find cubic is the
+
+ align:start position:0%
+zro2 and what do we find cubic is the
+ 
+
+ align:start position:0%
+zro2 and what do we find cubic is the
+form that gives you that faux Diamond
+
+ align:start position:0%
+form that gives you that faux Diamond
+ 
+
+ align:start position:0%
+form that gives you that faux Diamond
+but look it's stable only above about
+
+ align:start position:0%
+but look it's stable only above about
+ 
+
+ align:start position:0%
+but look it's stable only above about
+2,000 degre C so if you're going to give
+
+ align:start position:0%
+2,000 degre C so if you're going to give
+ 
+
+ align:start position:0%
+2,000 degre C so if you're going to give
+your sweetheart that uh that faux
+
+ align:start position:0%
+your sweetheart that uh that faux
+ 
+
+ align:start position:0%
+your sweetheart that uh that faux
+Diamond that's going to be too hot it's
+
+ align:start position:0%
+Diamond that's going to be too hot it's
+ 
+
+ align:start position:0%
+Diamond that's going to be too hot it's
+too hot so what we're going to learn
+
+ align:start position:0%
+too hot so what we're going to learn
+ 
+
+ align:start position:0%
+too hot so what we're going to learn
+next day is how to to open up this range
+
+ align:start position:0%
+next day is how to to open up this range
+ 
+
+ align:start position:0%
+next day is how to to open up this range
+of stability the way we opened up the
+
+ align:start position:0%
+of stability the way we opened up the
+ 
+
+ align:start position:0%
+of stability the way we opened up the
+range of liquid stability by adding
+
+ align:start position:0%
+range of liquid stability by adding
+ 
+
+ align:start position:0%
+range of liquid stability by adding
+ethylene glycol to water and see if we
+
+ align:start position:0%
+ethylene glycol to water and see if we
+ 
+
+ align:start position:0%
+ethylene glycol to water and see if we
+can get cubic zirconia stable down to
+
+ align:start position:0%
+can get cubic zirconia stable down to
+ 
+
+ align:start position:0%
+can get cubic zirconia stable down to
+room temperature right but normally it's
+
+ align:start position:0%
+room temperature right but normally it's
+ 
+
+ align:start position:0%
+room temperature right but normally it's
+monoc Clinic then it goes tetragonal It
+
+ align:start position:0%
+monoc Clinic then it goes tetragonal It
+ 
+
+ align:start position:0%
+monoc Clinic then it goes tetragonal It
+goes cubic and it goes liquid and so on
+
+ align:start position:0%
+goes cubic and it goes liquid and so on
+ 
+
+ align:start position:0%
+goes cubic and it goes liquid and so on
+then it even goes Vapor here's carbon at
+
+ align:start position:0%
+then it even goes Vapor here's carbon at
+ 
+
+ align:start position:0%
+then it even goes Vapor here's carbon at
+room temperature over a wide range of
+
+ align:start position:0%
+room temperature over a wide range of
+ 
+
+ align:start position:0%
+room temperature over a wide range of
+pressure is graphite hexagonal close
+
+ align:start position:0%
+pressure is graphite hexagonal close
+ 
+
+ align:start position:0%
+pressure is graphite hexagonal close
+pack then an elevated pressure it
+
+ align:start position:0%
+pack then an elevated pressure it
+ 
+
+ align:start position:0%
+pack then an elevated pressure it
+becomes diamond and here's liquid carbon
+
+ align:start position:0%
+becomes diamond and here's liquid carbon
+ 
+
+ align:start position:0%
+becomes diamond and here's liquid carbon
+it turns out that by judicious choice of
+
+ align:start position:0%
+it turns out that by judicious choice of
+ 
+
+ align:start position:0%
+it turns out that by judicious choice of
+chemistry people at General Electric
+
+ align:start position:0%
+chemistry people at General Electric
+ 
+
+ align:start position:0%
+chemistry people at General Electric
+about 30 years ago reasoned that steel
+
+ align:start position:0%
+about 30 years ago reasoned that steel
+ 
+
+ align:start position:0%
+about 30 years ago reasoned that steel
+consists of carbon and iron and if we
+
+ align:start position:0%
+consists of carbon and iron and if we
+ 
+
+ align:start position:0%
+consists of carbon and iron and if we
+quench steel we end up with carbon in
+
+ align:start position:0%
+quench steel we end up with carbon in
+ 
+
+ align:start position:0%
+quench steel we end up with carbon in
+the iron lattice if we put too much
+
+ align:start position:0%
+the iron lattice if we put too much
+ 
+
+ align:start position:0%
+the iron lattice if we put too much
+carbon the carbon will exsolve as
+
+ align:start position:0%
+carbon the carbon will exsolve as
+ 
+
+ align:start position:0%
+carbon the carbon will exsolve as
+precipitates well if we could exsolve at
+
+ align:start position:0%
+precipitates well if we could exsolve at
+ 
+
+ align:start position:0%
+precipitates well if we could exsolve at
+elevated pressure could we get the
+
+ align:start position:0%
+elevated pressure could we get the
+ 
+
+ align:start position:0%
+elevated pressure could we get the
+carbon to exsolve not as graphite but
+
+ align:start position:0%
+carbon to exsolve not as graphite but
+ 
+
+ align:start position:0%
+carbon to exsolve not as graphite but
+Diamond cubic and they did it they
+
+ align:start position:0%
+Diamond cubic and they did it they
+ 
+
+ align:start position:0%
+Diamond cubic and they did it they
+generated artificial diamonds and one of
+
+ align:start position:0%
+generated artificial diamonds and one of
+ 
+
+ align:start position:0%
+generated artificial diamonds and one of
+the leaders of the team was of course
+
+ align:start position:0%
+the leaders of the team was of course
+ 
+
+ align:start position:0%
+the leaders of the team was of course
+three Alum from MIT whom I met years
+
+ align:start position:0%
+three Alum from MIT whom I met years
+ 
+
+ align:start position:0%
+three Alum from MIT whom I met years
+later on a committee in um Washington in
+
+ align:start position:0%
+later on a committee in um Washington in
+ 
+
+ align:start position:0%
+later on a committee in um Washington in
+connection with the aluminum industry
+
+ align:start position:0%
+connection with the aluminum industry
+ 
+
+ align:start position:0%
+connection with the aluminum industry
+and he told me he was uh um in the team
+
+ align:start position:0%
+and he told me he was uh um in the team
+ 
+
+ align:start position:0%
+and he told me he was uh um in the team
+that went to London to negotiate with
+
+ align:start position:0%
+that went to London to negotiate with
+ 
+
+ align:start position:0%
+that went to London to negotiate with
+deur the big uh South African Diamond
+
+ align:start position:0%
+deur the big uh South African Diamond
+ 
+
+ align:start position:0%
+deur the big uh South African Diamond
+concern they were scared because General
+
+ align:start position:0%
+concern they were scared because General
+ 
+
+ align:start position:0%
+concern they were scared because General
+Electric reported that they could make
+
+ align:start position:0%
+Electric reported that they could make
+ 
+
+ align:start position:0%
+Electric reported that they could make
+artificial diamonds and they General
+
+ align:start position:0%
+artificial diamonds and they General
+ 
+
+ align:start position:0%
+artificial diamonds and they General
+Electric had reported that they could
+
+ align:start position:0%
+Electric had reported that they could
+ 
+
+ align:start position:0%
+Electric had reported that they could
+make large artificial diamonds well
+
+ align:start position:0%
+make large artificial diamonds well
+ 
+
+ align:start position:0%
+make large artificial diamonds well
+large they were trying to make diamond
+
+ align:start position:0%
+large they were trying to make diamond
+ 
+
+ align:start position:0%
+large they were trying to make diamond
+dust they actually had one that was
+
+ align:start position:0%
+dust they actually had one that was
+ 
+
+ align:start position:0%
+dust they actually had one that was
+about 1 millimeter it was Tiny But deers
+
+ align:start position:0%
+about 1 millimeter it was Tiny But deers
+ 
+
+ align:start position:0%
+about 1 millimeter it was Tiny But deers
+was was nervous and uh this is the
+
+ align:start position:0%
+was was nervous and uh this is the
+ 
+
+ align:start position:0%
+was was nervous and uh this is the
+fellow's name was Rod hanaman and he
+
+ align:start position:0%
+fellow's name was Rod hanaman and he
+ 
+
+ align:start position:0%
+fellow's name was Rod hanaman and he
+told me that the thing that scared him
+
+ align:start position:0%
+told me that the thing that scared him
+ 
+
+ align:start position:0%
+told me that the thing that scared him
+most was not sitting down with the Burrs
+
+ align:start position:0%
+most was not sitting down with the Burrs
+ 
+
+ align:start position:0%
+most was not sitting down with the Burrs
+because he had them bluffed the hardest
+
+ align:start position:0%
+because he had them bluffed the hardest
+ 
+
+ align:start position:0%
+because he had them bluffed the hardest
+thing was getting through uh British
+
+ align:start position:0%
+thing was getting through uh British
+ 
+
+ align:start position:0%
+thing was getting through uh British
+Customs because he had this on his
+
+ align:start position:0%
+Customs because he had this on his
+ 
+
+ align:start position:0%
+Customs because he had this on his
+person now if he opens up and they see
+
+ align:start position:0%
+person now if he opens up and they see
+ 
+
+ align:start position:0%
+person now if he opens up and they see
+all of this diamond material and
+
+ align:start position:0%
+all of this diamond material and
+ 
+
+ align:start position:0%
+all of this diamond material and
+remember artificial diamonds don't exist
+
+ align:start position:0%
+remember artificial diamonds don't exist
+ 
+
+ align:start position:0%
+remember artificial diamonds don't exist
+yet so he's going to tell the Customs
+
+ align:start position:0%
+yet so he's going to tell the Customs
+ 
+
+ align:start position:0%
+yet so he's going to tell the Customs
+agent well these are artificial diamonds
+
+ align:start position:0%
+agent well these are artificial diamonds
+ 
+
+ align:start position:0%
+agent well these are artificial diamonds
+I I don't think that's going to work
+
+ align:start position:0%
+I I don't think that's going to work
+ 
+
+ align:start position:0%
+I I don't think that's going to work
+it's there's always the you know what's
+
+ align:start position:0%
+it's there's always the you know what's
+ 
+
+ align:start position:0%
+it's there's always the you know what's
+it the early bird gets the worm but it's
+
+ align:start position:0%
+it the early bird gets the worm but it's
+ 
+
+ align:start position:0%
+it the early bird gets the worm but it's
+the second mouse that gets the cheese so
+
+ align:start position:0%
+the second mouse that gets the cheese so
+ 
+
+ align:start position:0%
+the second mouse that gets the cheese so
+you can be too early sometimes with that
+
+ align:start position:0%
+you can be too early sometimes with that
+ 
+
+ align:start position:0%
+you can be too early sometimes with that
+okay here's bisou here's bisou bismo has
+
+ align:start position:0%
+okay here's bisou here's bisou bismo has
+ 
+
+ align:start position:0%
+okay here's bisou here's bisou bismo has
+a lot of phases look at all the
+
+ align:start position:0%
+a lot of phases look at all the
+ 
+
+ align:start position:0%
+a lot of phases look at all the
+different phases of bismo and look at
+
+ align:start position:0%
+different phases of bismo and look at
+ 
+
+ align:start position:0%
+different phases of bismo and look at
+here what does this tell you about the
+
+ align:start position:0%
+here what does this tell you about the
+ 
+
+ align:start position:0%
+here what does this tell you about the
+solid bismo it will float in liquid
+
+ align:start position:0%
+solid bismo it will float in liquid
+ 
+
+ align:start position:0%
+solid bismo it will float in liquid
+bismuth and then if you go to high
+
+ align:start position:0%
+bismuth and then if you go to high
+ 
+
+ align:start position:0%
+bismuth and then if you go to high
+enough in pressure it compresses here's
+
+ align:start position:0%
+enough in pressure it compresses here's
+ 
+
+ align:start position:0%
+enough in pressure it compresses here's
+sulfur this sulfur is really one
+
+ align:start position:0%
+sulfur this sulfur is really one
+ 
+
+ align:start position:0%
+sulfur this sulfur is really one
+confused
+
+ align:start position:0%
+confused
+ 
+
+ align:start position:0%
+confused
+element look at all the solid phases
+
+ align:start position:0%
+element look at all the solid phases
+ 
+
+ align:start position:0%
+element look at all the solid phases
+look at all the liquid phases sulfur is
+
+ align:start position:0%
+look at all the liquid phases sulfur is
+ 
+
+ align:start position:0%
+look at all the liquid phases sulfur is
+one mess look it so it has allotropes
+
+ align:start position:0%
+one mess look it so it has allotropes
+ 
+
+ align:start position:0%
+one mess look it so it has allotropes
+allotropes are are different bonding
+
+ align:start position:0%
+allotropes are are different bonding
+ 
+
+ align:start position:0%
+allotropes are are different bonding
+forms for example oxygen and exist as
+
+ align:start position:0%
+forms for example oxygen and exist as
+ 
+
+ align:start position:0%
+forms for example oxygen and exist as
+atomic oxygen the molecular oxygen O2
+
+ align:start position:0%
+atomic oxygen the molecular oxygen O2
+ 
+
+ align:start position:0%
+atomic oxygen the molecular oxygen O2
+and O3 which is Ozone so we say that O2
+
+ align:start position:0%
+and O3 which is Ozone so we say that O2
+ 
+
+ align:start position:0%
+and O3 which is Ozone so we say that O2
+and O3 are both allotropes of oxygen
+
+ align:start position:0%
+and O3 are both allotropes of oxygen
+ 
+
+ align:start position:0%
+and O3 are both allotropes of oxygen
+well sulfur has 16 allotropes 16 it
+
+ align:start position:0%
+well sulfur has 16 allotropes 16 it
+ 
+
+ align:start position:0%
+well sulfur has 16 allotropes 16 it
+exists as discrete atoms as the dier
+
+ align:start position:0%
+exists as discrete atoms as the dier
+ 
+
+ align:start position:0%
+exists as discrete atoms as the dier
+this this hex exer the common solid form
+
+ align:start position:0%
+this this hex exer the common solid form
+ 
+
+ align:start position:0%
+this this hex exer the common solid form
+is this eight member uh circular linkage
+
+ align:start position:0%
+is this eight member uh circular linkage
+ 
+
+ align:start position:0%
+is this eight member uh circular linkage
+and then it polymerizes in the
+
+ align:start position:0%
+and then it polymerizes in the
+ 
+
+ align:start position:0%
+and then it polymerizes in the
+Melt so here's the low temperature room
+
+ align:start position:0%
+Melt so here's the low temperature room
+ 
+
+ align:start position:0%
+Melt so here's the low temperature room
+temperature sulfur is romic and at
+
+ align:start position:0%
+temperature sulfur is romic and at
+ 
+
+ align:start position:0%
+temperature sulfur is romic and at
+elevated temperature it goes monoclinic
+
+ align:start position:0%
+elevated temperature it goes monoclinic
+ 
+
+ align:start position:0%
+elevated temperature it goes monoclinic
+it's a solid solid phase transformation
+
+ align:start position:0%
+it's a solid solid phase transformation
+ 
+
+ align:start position:0%
+it's a solid solid phase transformation
+that's what you're seeing in that phase
+
+ align:start position:0%
+that's what you're seeing in that phase
+ 
+
+ align:start position:0%
+that's what you're seeing in that phase
+diagram when you you look back here
+
+ align:start position:0%
+diagram when you you look back here
+ 
+
+ align:start position:0%
+diagram when you you look back here
+that's what all this is there's the
+
+ align:start position:0%
+that's what all this is there's the
+ 
+
+ align:start position:0%
+that's what all this is there's the
+monoc clinic and then the the romic all
+
+ align:start position:0%
+monoc clinic and then the the romic all
+ 
+
+ align:start position:0%
+monoc clinic and then the the romic all
+right and then if you melt it
+
+ align:start position:0%
+right and then if you melt it
+ 
+
+ align:start position:0%
+right and then if you melt it
+um it first it gives the straw colored
+
+ align:start position:0%
+um it first it gives the straw colored
+ 
+
+ align:start position:0%
+um it first it gives the straw colored
+liquid which they call Lambda at 119°
+
+ align:start position:0%
+liquid which they call Lambda at 119°
+ 
+
+ align:start position:0%
+liquid which they call Lambda at 119°
+and around 160 this turns into the the
+
+ align:start position:0%
+and around 160 this turns into the the
+ 
+
+ align:start position:0%
+and around 160 this turns into the the
+Rings start to open up and it turns an
+
+ align:start position:0%
+Rings start to open up and it turns an
+ 
+
+ align:start position:0%
+Rings start to open up and it turns an
+orange color at 160 and then this is uh
+
+ align:start position:0%
+orange color at 160 and then this is uh
+ 
+
+ align:start position:0%
+orange color at 160 and then this is uh
+at some elevated temperature about 200°
+
+ align:start position:0%
+at some elevated temperature about 200°
+ 
+
+ align:start position:0%
+at some elevated temperature about 200°
+C they poured this long polymer sulfur
+
+ align:start position:0%
+C they poured this long polymer sulfur
+ 
+
+ align:start position:0%
+C they poured this long polymer sulfur
+goo into water quenching it and guess
+
+ align:start position:0%
+goo into water quenching it and guess
+ 
+
+ align:start position:0%
+goo into water quenching it and guess
+what you form you form a glass it's
+
+ align:start position:0%
+what you form you form a glass it's
+ 
+
+ align:start position:0%
+what you form you form a glass it's
+plastic sulfur so all of this is
+
+ align:start position:0%
+plastic sulfur so all of this is
+ 
+
+ align:start position:0%
+plastic sulfur so all of this is
+happening as a result of the the
+
+ align:start position:0%
+happening as a result of the the
+ 
+
+ align:start position:0%
+happening as a result of the the
+different phases that are present so
+
+ align:start position:0%
+different phases that are present so
+ 
+
+ align:start position:0%
+different phases that are present so
+this is forming plastic sulfur the last
+
+ align:start position:0%
+this is forming plastic sulfur the last
+ 
+
+ align:start position:0%
+this is forming plastic sulfur the last
+thing I want to tell you about is a this
+
+ align:start position:0%
+thing I want to tell you about is a this
+ 
+
+ align:start position:0%
+thing I want to tell you about is a this
+last phase super critical fluid which is
+
+ align:start position:0%
+last phase super critical fluid which is
+ 
+
+ align:start position:0%
+last phase super critical fluid which is
+a very high temperature high pressure
+
+ align:start position:0%
+a very high temperature high pressure
+ 
+
+ align:start position:0%
+a very high temperature high pressure
+phase where you can't tell a gas from a
+
+ align:start position:0%
+phase where you can't tell a gas from a
+ 
+
+ align:start position:0%
+phase where you can't tell a gas from a
+liquid you can think of it as a highly
+
+ align:start position:0%
+liquid you can think of it as a highly
+ 
+
+ align:start position:0%
+liquid you can think of it as a highly
+compressed gas or a highly rarified
+
+ align:start position:0%
+compressed gas or a highly rarified
+ 
+
+ align:start position:0%
+compressed gas or a highly rarified
+liquid the blondes get far enough apart
+
+ align:start position:0%
+liquid the blondes get far enough apart
+ 
+
+ align:start position:0%
+liquid the blondes get far enough apart
+that the liquid is behaving a little bit
+
+ align:start position:0%
+that the liquid is behaving a little bit
+ 
+
+ align:start position:0%
+that the liquid is behaving a little bit
+differently the solvation properties are
+
+ align:start position:0%
+differently the solvation properties are
+ 
+
+ align:start position:0%
+differently the solvation properties are
+those of a liquid but here's what
+
+ align:start position:0%
+those of a liquid but here's what
+ 
+
+ align:start position:0%
+those of a liquid but here's what
+happens in the supercritical fluid you
+
+ align:start position:0%
+happens in the supercritical fluid you
+ 
+
+ align:start position:0%
+happens in the supercritical fluid you
+have transport properties of a gas so
+
+ align:start position:0%
+have transport properties of a gas so
+ 
+
+ align:start position:0%
+have transport properties of a gas so
+you have something that's liquidlike in
+
+ align:start position:0%
+you have something that's liquidlike in
+ 
+
+ align:start position:0%
+you have something that's liquidlike in
+terms of its ability to solvate things
+
+ align:start position:0%
+terms of its ability to solvate things
+ 
+
+ align:start position:0%
+terms of its ability to solvate things
+but it has gas-like diffusivity gas-like
+
+ align:start position:0%
+but it has gas-like diffusivity gas-like
+ 
+
+ align:start position:0%
+but it has gas-like diffusivity gas-like
+viscosity and this is very very uh much
+
+ align:start position:0%
+viscosity and this is very very uh much
+ 
+
+ align:start position:0%
+viscosity and this is very very uh much
+in the U research agenda these days
+
+ align:start position:0%
+in the U research agenda these days
+ 
+
+ align:start position:0%
+in the U research agenda these days
+using supercritical fluids to attack
+
+ align:start position:0%
+using supercritical fluids to attack
+ 
+
+ align:start position:0%
+using supercritical fluids to attack
+things like um uh toxic waste and so on
+
+ align:start position:0%
+things like um uh toxic waste and so on
+ 
+
+ align:start position:0%
+things like um uh toxic waste and so on
+without having to resort to very
+
+ align:start position:0%
+without having to resort to very
+ 
+
+ align:start position:0%
+without having to resort to very
+aggressive solvents it's no sense going
+
+ align:start position:0%
+aggressive solvents it's no sense going
+ 
+
+ align:start position:0%
+aggressive solvents it's no sense going
+after aggressive toxins when you have to
+
+ align:start position:0%
+after aggressive toxins when you have to
+ 
+
+ align:start position:0%
+after aggressive toxins when you have to
+use aggressive organic solvents but this
+
+ align:start position:0%
+use aggressive organic solvents but this
+ 
+
+ align:start position:0%
+use aggressive organic solvents but this
+will give you something of low polarity
+
+ align:start position:0%
+will give you something of low polarity
+ 
+
+ align:start position:0%
+will give you something of low polarity
+dissolving non-polar things and here's
+
+ align:start position:0%
+dissolving non-polar things and here's
+ 
+
+ align:start position:0%
+dissolving non-polar things and here's
+one that you you use more often than you
+
+ align:start position:0%
+one that you you use more often than you
+ 
+
+ align:start position:0%
+one that you you use more often than you
+know uh decaffeinating coffee uses
+
+ align:start position:0%
+know uh decaffeinating coffee uses
+ 
+
+ align:start position:0%
+know uh decaffeinating coffee uses
+solvent extraction when I was your age
+
+ align:start position:0%
+solvent extraction when I was your age
+ 
+
+ align:start position:0%
+solvent extraction when I was your age
+they actually used this stuff called
+
+ align:start position:0%
+they actually used this stuff called
+ 
+
+ align:start position:0%
+they actually used this stuff called
+methylene chloride I subsequently used
+
+ align:start position:0%
+methylene chloride I subsequently used
+ 
+
+ align:start position:0%
+methylene chloride I subsequently used
+it in stripping paint it's very vicious
+
+ align:start position:0%
+it in stripping paint it's very vicious
+ 
+
+ align:start position:0%
+it in stripping paint it's very vicious
+you see the trick in decaffeinating
+
+ align:start position:0%
+you see the trick in decaffeinating
+ 
+
+ align:start position:0%
+you see the trick in decaffeinating
+coffee is to get the caffeine out but
+
+ align:start position:0%
+coffee is to get the caffeine out but
+ 
+
+ align:start position:0%
+coffee is to get the caffeine out but
+not to brew the coffee you want to
+
+ align:start position:0%
+not to brew the coffee you want to
+ 
+
+ align:start position:0%
+not to brew the coffee you want to
+selectively get the caffeine so now they
+
+ align:start position:0%
+selectively get the caffeine so now they
+ 
+
+ align:start position:0%
+selectively get the caffeine so now they
+use uh super critical carbon dioxide so
+
+ align:start position:0%
+use uh super critical carbon dioxide so
+ 
+
+ align:start position:0%
+use uh super critical carbon dioxide so
+carbon dioxide leeches out the C
+
+ align:start position:0%
+carbon dioxide leeches out the C
+ 
+
+ align:start position:0%
+carbon dioxide leeches out the C
+caffeine but doesn't touch the coffee so
+
+ align:start position:0%
+caffeine but doesn't touch the coffee so
+ 
+
+ align:start position:0%
+caffeine but doesn't touch the coffee so
+you get up into that uh temperature
+
+ align:start position:0%
+you get up into that uh temperature
+ 
+
+ align:start position:0%
+you get up into that uh temperature
+pressure regime leech out the caffeine
+
+ align:start position:0%
+pressure regime leech out the caffeine
+ 
+
+ align:start position:0%
+pressure regime leech out the caffeine
+and then you change temperature and
+
+ align:start position:0%
+and then you change temperature and
+ 
+
+ align:start position:0%
+and then you change temperature and
+pressure and now you have this pregnant
+
+ align:start position:0%
+pressure and now you have this pregnant
+ 
+
+ align:start position:0%
+pressure and now you have this pregnant
+liquor that is exceeding the solubility
+
+ align:start position:0%
+liquor that is exceeding the solubility
+ 
+
+ align:start position:0%
+liquor that is exceeding the solubility
+product and now you exsolve the caffeine
+
+ align:start position:0%
+product and now you exsolve the caffeine
+ 
+
+ align:start position:0%
+product and now you exsolve the caffeine
+and then you reflux the CO2 and that's
+
+ align:start position:0%
+and then you reflux the CO2 and that's
+ 
+
+ align:start position:0%
+and then you reflux the CO2 and that's
+how we we go about uh with the uh coffee
+
+ align:start position:0%
+how we we go about uh with the uh coffee
+ 
+
+ align:start position:0%
+how we we go about uh with the uh coffee
+the last thing I'm going to do uh before
+
+ align:start position:0%
+the last thing I'm going to do uh before
+ 
+
+ align:start position:0%
+the last thing I'm going to do uh before
+I introduce uh someone's going to tell
+
+ align:start position:0%
+I introduce uh someone's going to tell
+ 
+
+ align:start position:0%
+I introduce uh someone's going to tell
+you about some other activities that
+
+ align:start position:0%
+you about some other activities that
+ 
+
+ align:start position:0%
+you about some other activities that
+will happen during IAP is to tell you
+
+ align:start position:0%
+will happen during IAP is to tell you
+ 
+
+ align:start position:0%
+will happen during IAP is to tell you
+about uh I guess this lesson is that
+
+ align:start position:0%
+about uh I guess this lesson is that
+ 
+
+ align:start position:0%
+about uh I guess this lesson is that
+there are no depths uh uh there are no
+
+ align:start position:0%
+there are no depths uh uh there are no
+ 
+
+ align:start position:0%
+there are no depths uh uh there are no
+limits to the depths of human stupidity
+
+ align:start position:0%
+limits to the depths of human stupidity
+ 
+
+ align:start position:0%
+limits to the depths of human stupidity
+um this is this will tie in denaturing
+
+ align:start position:0%
+um this is this will tie in denaturing
+ 
+
+ align:start position:0%
+um this is this will tie in denaturing
+of protein from last day this is a news
+
+ align:start position:0%
+of protein from last day this is a news
+ 
+
+ align:start position:0%
+of protein from last day this is a news
+thing dick Kinga P principle at
+
+ align:start position:0%
+thing dick Kinga P principle at
+ 
+
+ align:start position:0%
+thing dick Kinga P principle at
+Silverton High School said this is in
+
+ align:start position:0%
+Silverton High School said this is in
+ 
+
+ align:start position:0%
+Silverton High School said this is in
+Silverton Oregon and I'm not making this
+
+ align:start position:0%
+Silverton Oregon and I'm not making this
+ 
+
+ align:start position:0%
+Silverton Oregon and I'm not making this
+up said a pep rally stunt that burn
+
+ align:start position:0%
+up said a pep rally stunt that burn
+ 
+
+ align:start position:0%
+up said a pep rally stunt that burn
+Force students won't ever be repeated
+
+ align:start position:0%
+Force students won't ever be repeated
+ 
+
+ align:start position:0%
+Force students won't ever be repeated
+the fource suffered severe burns on
+
+ align:start position:0%
+the fource suffered severe burns on
+ 
+
+ align:start position:0%
+the fource suffered severe burns on
+their buttocks from sitting on blocks of
+
+ align:start position:0%
+their buttocks from sitting on blocks of
+ 
+
+ align:start position:0%
+their buttocks from sitting on blocks of
+dry
+
+ align:start position:0%
+dry
+ 
+
+ align:start position:0%
+dry
+ice the girls were chosen by their
+
+ align:start position:0%
+ice the girls were chosen by their
+ 
+
+ align:start position:0%
+ice the girls were chosen by their
+classmates for a stunt to see who could
+
+ align:start position:0%
+classmates for a stunt to see who could
+ 
+
+ align:start position:0%
+classmates for a stunt to see who could
+sit on the ice the longest the dry ice
+
+ align:start position:0%
+sit on the ice the longest the dry ice
+ 
+
+ align:start position:0%
+sit on the ice the longest the dry ice
+or solid carbon dioxide can be as cold
+
+ align:start position:0%
+or solid carbon dioxide can be as cold
+ 
+
+ align:start position:0%
+or solid carbon dioxide can be as cold
+as 112 Fahrenheit below zero the four
+
+ align:start position:0%
+as 112 Fahrenheit below zero the four
+ 
+
+ align:start position:0%
+as 112 Fahrenheit below zero the four
+were treated at Silverton Hospital Dr
+
+ align:start position:0%
+were treated at Silverton Hospital Dr
+ 
+
+ align:start position:0%
+were treated at Silverton Hospital Dr
+Frank lord said some of the girls may
+
+ align:start position:0%
+Frank lord said some of the girls may
+ 
+
+ align:start position:0%
+Frank lord said some of the girls may
+need skin grafts theyve denatured the
+
+ align:start position:0%
+need skin grafts theyve denatured the
+ 
+
+ align:start position:0%
+need skin grafts theyve denatured the
+proteins this is a quote the truth is
+
+ align:start position:0%
+proteins this is a quote the truth is
+ 
+
+ align:start position:0%
+proteins this is a quote the truth is
+I've never seen any frostbite on this
+
+ align:start position:0%
+I've never seen any frostbite on this
+ 
+
+ align:start position:0%
+I've never seen any frostbite on this
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+anatomy anyways it goes on about how
+
+ align:start position:0%
+anatomy anyways it goes on about how
+ 
+
+ align:start position:0%
+anatomy anyways it goes on about how
+this was tied in with
+
+ align:start position:0%
+this was tied in with
+ 
+
+ align:start position:0%
+this was tied in with
+football homecoming and and some
+
+ align:start position:0%
+football homecoming and and some
+ 
+
+ align:start position:0%
+football homecoming and and some
+somebody just didn't didn't pay
+
+ align:start position:0%
+somebody just didn't didn't pay
+ 
+
+ align:start position:0%
+somebody just didn't didn't pay
+attention
\ No newline at end of file
diff --git a/EXYgISgOw0g.txt b/EXYgISgOw0g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..546a0571c8bd7b2c35afe08f9e638e098ad82fb7
--- /dev/null
+++ b/EXYgISgOw0g.txt
@@ -0,0 +1,851 @@
+align:start position:0%
+ 
+in this video we'll discuss how
+
+ align:start position:0%
+in this video we'll discuss how
+ 
+
+ align:start position:0%
+in this video we'll discuss how
+radiation therapy can be framed as an
+
+ align:start position:0%
+radiation therapy can be framed as an
+ 
+
+ align:start position:0%
+radiation therapy can be framed as an
+optimization problem the data is
+
+ align:start position:0%
+optimization problem the data is
+ 
+
+ align:start position:0%
+optimization problem the data is
+collected in the treatment planning
+
+ align:start position:0%
+collected in the treatment planning
+ 
+
+ align:start position:0%
+collected in the treatment planning
+process which starts from a CT scan like
+
+ align:start position:0%
+process which starts from a CT scan like
+ 
+
+ align:start position:0%
+process which starts from a CT scan like
+the one you see here on the right using
+
+ align:start position:0%
+the one you see here on the right using
+ 
+
+ align:start position:0%
+the one you see here on the right using
+the CT scan a radiation oncologist
+
+ align:start position:0%
+the CT scan a radiation oncologist
+ 
+
+ align:start position:0%
+the CT scan a radiation oncologist
+contours or draws out lines around the
+
+ align:start position:0%
+contours or draws out lines around the
+ 
+
+ align:start position:0%
+contours or draws out lines around the
+tumor and various critical structures in
+
+ align:start position:0%
+tumor and various critical structures in
+ 
+
+ align:start position:0%
+tumor and various critical structures in
+this image the oncologist would contour
+
+ align:start position:0%
+this image the oncologist would contour
+ 
+
+ align:start position:0%
+this image the oncologist would contour
+structures like the parotid glands the
+
+ align:start position:0%
+structures like the parotid glands the
+ 
+
+ align:start position:0%
+structures like the parotid glands the
+largest of the saliva glands and the
+
+ align:start position:0%
+largest of the saliva glands and the
+ 
+
+ align:start position:0%
+largest of the saliva glands and the
+brain then each structure is discretized
+
+ align:start position:0%
+brain then each structure is discretized
+ 
+
+ align:start position:0%
+brain then each structure is discretized
+into voxels or volume elements which are
+
+ align:start position:0%
+into voxels or volume elements which are
+ 
+
+ align:start position:0%
+into voxels or volume elements which are
+typically four millimeters in dimension
+
+ align:start position:0%
+typically four millimeters in dimension
+ 
+
+ align:start position:0%
+typically four millimeters in dimension
+the second image here shows a closer
+
+ align:start position:0%
+the second image here shows a closer
+ 
+
+ align:start position:0%
+the second image here shows a closer
+view of the brain you can see the small
+
+ align:start position:0%
+view of the brain you can see the small
+ 
+
+ align:start position:0%
+view of the brain you can see the small
+squares or voxels here they're
+
+ align:start position:0%
+squares or voxels here they're
+ 
+
+ align:start position:0%
+squares or voxels here they're
+two-dimensional but in reality they
+
+ align:start position:0%
+two-dimensional but in reality they
+ 
+
+ align:start position:0%
+two-dimensional but in reality they
+would be 3-dimensional now we can
+
+ align:start position:0%
+would be 3-dimensional now we can
+ 
+
+ align:start position:0%
+would be 3-dimensional now we can
+compute how much dose each beam lit or
+
+ align:start position:0%
+compute how much dose each beam lit or
+ 
+
+ align:start position:0%
+compute how much dose each beam lit or
+piece of the beam
+
+ align:start position:0%
+piece of the beam
+ 
+
+ align:start position:0%
+piece of the beam
+delivers to each voxel we'll start with
+
+ align:start position:0%
+delivers to each voxel we'll start with
+ 
+
+ align:start position:0%
+delivers to each voxel we'll start with
+a small example suppose we have nine
+
+ align:start position:0%
+a small example suppose we have nine
+ 
+
+ align:start position:0%
+a small example suppose we have nine
+voxels and six beam let's our voxels can
+
+ align:start position:0%
+voxels and six beam let's our voxels can
+ 
+
+ align:start position:0%
+voxels and six beam let's our voxels can
+be categorized into three types the
+
+ align:start position:0%
+be categorized into three types the
+ 
+
+ align:start position:0%
+be categorized into three types the
+tumor voxels which are colored pink here
+
+ align:start position:0%
+tumor voxels which are colored pink here
+ 
+
+ align:start position:0%
+tumor voxels which are colored pink here
+the spinal cord voxel colored dark green
+
+ align:start position:0%
+the spinal cord voxel colored dark green
+ 
+
+ align:start position:0%
+the spinal cord voxel colored dark green
+and other healthy tissue voxels colored
+
+ align:start position:0%
+and other healthy tissue voxels colored
+ 
+
+ align:start position:0%
+and other healthy tissue voxels colored
+light green so we have four tumor voxels
+
+ align:start position:0%
+light green so we have four tumor voxels
+ 
+
+ align:start position:0%
+light green so we have four tumor voxels
+one spinal cord voxel and four other
+
+ align:start position:0%
+one spinal cord voxel and four other
+ 
+
+ align:start position:0%
+one spinal cord voxel and four other
+healthy tissue boxes we have two beams
+
+ align:start position:0%
+healthy tissue boxes we have two beams
+ 
+
+ align:start position:0%
+healthy tissue boxes we have two beams
+that are each split into three beam
+
+ align:start position:0%
+that are each split into three beam
+ 
+
+ align:start position:0%
+that are each split into three beam
+let's beam one is composed of beam let's
+
+ align:start position:0%
+let's beam one is composed of beam let's
+ 
+
+ align:start position:0%
+let's beam one is composed of beam let's
+one two and three and comes in from the
+
+ align:start position:0%
+one two and three and comes in from the
+ 
+
+ align:start position:0%
+one two and three and comes in from the
+right beam two is composed of beam let's
+
+ align:start position:0%
+right beam two is composed of beam let's
+ 
+
+ align:start position:0%
+right beam two is composed of beam let's
+four five and six and comes in from the
+
+ align:start position:0%
+four five and six and comes in from the
+ 
+
+ align:start position:0%
+four five and six and comes in from the
+top our objective is to minimize the
+
+ align:start position:0%
+top our objective is to minimize the
+ 
+
+ align:start position:0%
+top our objective is to minimize the
+total dose to healthy tissue
+
+ align:start position:0%
+total dose to healthy tissue
+ 
+
+ align:start position:0%
+total dose to healthy tissue
+both to the spinal cord and to the other
+
+ align:start position:0%
+both to the spinal cord and to the other
+ 
+
+ align:start position:0%
+both to the spinal cord and to the other
+healthy tissue we have two types of
+
+ align:start position:0%
+healthy tissue we have two types of
+ 
+
+ align:start position:0%
+healthy tissue we have two types of
+constraints the first is that the dose
+
+ align:start position:0%
+constraints the first is that the dose
+ 
+
+ align:start position:0%
+constraints the first is that the dose
+to the tumor voxels must be at least
+
+ align:start position:0%
+to the tumor voxels must be at least
+ 
+
+ align:start position:0%
+to the tumor voxels must be at least
+seven gray
+
+ align:start position:0%
+seven gray
+ 
+
+ align:start position:0%
+seven gray
+which is the unit of measure for
+
+ align:start position:0%
+which is the unit of measure for
+ 
+
+ align:start position:0%
+which is the unit of measure for
+radiation our second constraint is that
+
+ align:start position:0%
+radiation our second constraint is that
+ 
+
+ align:start position:0%
+radiation our second constraint is that
+the dose to the spinal cord voxel can't
+
+ align:start position:0%
+the dose to the spinal cord voxel can't
+ 
+
+ align:start position:0%
+the dose to the spinal cord voxel can't
+be more than five gray since we want to
+
+ align:start position:0%
+be more than five gray since we want to
+ 
+
+ align:start position:0%
+be more than five gray since we want to
+be careful to protect the spinal cord we
+
+ align:start position:0%
+be careful to protect the spinal cord we
+ 
+
+ align:start position:0%
+be careful to protect the spinal cord we
+know the dose that each beam lit gives
+
+ align:start position:0%
+know the dose that each beam lit gives
+ 
+
+ align:start position:0%
+know the dose that each beam lit gives
+to each voxel at unit intensity this
+
+ align:start position:0%
+to each voxel at unit intensity this
+ 
+
+ align:start position:0%
+to each voxel at unit intensity this
+table shows the dose that each beam
+
+ align:start position:0%
+table shows the dose that each beam
+ 
+
+ align:start position:0%
+table shows the dose that each beam
+length and beam one gives to the voxels
+
+ align:start position:0%
+length and beam one gives to the voxels
+ 
+
+ align:start position:0%
+length and beam one gives to the voxels
+remember that this is at unit intensity
+
+ align:start position:0%
+remember that this is at unit intensity
+ 
+
+ align:start position:0%
+remember that this is at unit intensity
+if we double the intensity of the beam
+
+ align:start position:0%
+if we double the intensity of the beam
+ 
+
+ align:start position:0%
+if we double the intensity of the beam
+light we double the doses the dose to
+
+ align:start position:0%
+light we double the doses the dose to
+ 
+
+ align:start position:0%
+light we double the doses the dose to
+each voxel can depend on how far the
+
+ align:start position:0%
+each voxel can depend on how far the
+ 
+
+ align:start position:0%
+each voxel can depend on how far the
+beam that has to travel or the type of
+
+ align:start position:0%
+beam that has to travel or the type of
+ 
+
+ align:start position:0%
+beam that has to travel or the type of
+tissue that the beam light has to travel
+
+ align:start position:0%
+tissue that the beam light has to travel
+ 
+
+ align:start position:0%
+tissue that the beam light has to travel
+through similarly we know the dose that
+
+ align:start position:0%
+through similarly we know the dose that
+ 
+
+ align:start position:0%
+through similarly we know the dose that
+each beam l''m beam 2 gives to each
+
+ align:start position:0%
+each beam l''m beam 2 gives to each
+ 
+
+ align:start position:0%
+each beam l''m beam 2 gives to each
+voxel again at unit intensity the dose
+
+ align:start position:0%
+voxel again at unit intensity the dose
+ 
+
+ align:start position:0%
+voxel again at unit intensity the dose
+depends on the direction of the beam and
+
+ align:start position:0%
+depends on the direction of the beam and
+ 
+
+ align:start position:0%
+depends on the direction of the beam and
+what it travels through putting these
+
+ align:start position:0%
+what it travels through putting these
+ 
+
+ align:start position:0%
+what it travels through putting these
+tables together we can write out our
+
+ align:start position:0%
+tables together we can write out our
+ 
+
+ align:start position:0%
+tables together we can write out our
+optimization problem our decision
+
+ align:start position:0%
+optimization problem our decision
+ 
+
+ align:start position:0%
+optimization problem our decision
+variables are the intensities of each
+
+ align:start position:0%
+variables are the intensities of each
+ 
+
+ align:start position:0%
+variables are the intensities of each
+beam what we'll call them x1 the
+
+ align:start position:0%
+beam what we'll call them x1 the
+ 
+
+ align:start position:0%
+beam what we'll call them x1 the
+intensity for beam lint 1 x2 the
+
+ align:start position:0%
+intensity for beam lint 1 x2 the
+ 
+
+ align:start position:0%
+intensity for beam lint 1 x2 the
+intensity for beam light 2 x3 the
+
+ align:start position:0%
+intensity for beam light 2 x3 the
+ 
+
+ align:start position:0%
+intensity for beam light 2 x3 the
+intensity for beam 1 3 etc all the way
+
+ align:start position:0%
+intensity for beam 1 3 etc all the way
+ 
+
+ align:start position:0%
+intensity for beam 1 3 etc all the way
+up through x6 as we mentioned before our
+
+ align:start position:0%
+up through x6 as we mentioned before our
+ 
+
+ align:start position:0%
+up through x6 as we mentioned before our
+objective is to minimize the total dose
+
+ align:start position:0%
+objective is to minimize the total dose
+ 
+
+ align:start position:0%
+objective is to minimize the total dose
+to the healthy tissue including the
+
+ align:start position:0%
+to the healthy tissue including the
+ 
+
+ align:start position:0%
+to the healthy tissue including the
+spinal cord so we want to minimize the
+
+ align:start position:0%
+spinal cord so we want to minimize the
+ 
+
+ align:start position:0%
+spinal cord so we want to minimize the
+total dose beam lit one gives to healthy
+
+ align:start position:0%
+total dose beam lit one gives to healthy
+ 
+
+ align:start position:0%
+total dose beam lit one gives to healthy
+tissue which is 1 plus 2 times x1 plus
+
+ align:start position:0%
+tissue which is 1 plus 2 times x1 plus
+ 
+
+ align:start position:0%
+tissue which is 1 plus 2 times x1 plus
+the total dose beam what 2 gives to
+
+ align:start position:0%
+the total dose beam what 2 gives to
+ 
+
+ align:start position:0%
+the total dose beam what 2 gives to
+healthy tissue which is 2 plus 2.5 times
+
+ align:start position:0%
+healthy tissue which is 2 plus 2.5 times
+ 
+
+ align:start position:0%
+healthy tissue which is 2 plus 2.5 times
+x2 plus the total dose beam let three
+
+ align:start position:0%
+x2 plus the total dose beam let three
+ 
+
+ align:start position:0%
+x2 plus the total dose beam let three
+gifts to healthy tissue which is 2.5 X 3
+
+ align:start position:0%
+gifts to healthy tissue which is 2.5 X 3
+ 
+
+ align:start position:0%
+gifts to healthy tissue which is 2.5 X 3
+now for beam what's 4 5 & 6 beam what
+
+ align:start position:0%
+now for beam what's 4 5 & 6 beam what
+ 
+
+ align:start position:0%
+now for beam what's 4 5 & 6 beam what
+for just gives one dose to healthy
+
+ align:start position:0%
+for just gives one dose to healthy
+ 
+
+ align:start position:0%
+for just gives one dose to healthy
+tissue beam what 5 2 times X 5 and then
+
+ align:start position:0%
+tissue beam what 5 2 times X 5 and then
+ 
+
+ align:start position:0%
+tissue beam what 5 2 times X 5 and then
+beam lit 6 we have 1 plus 2 plus 1 times
+
+ align:start position:0%
+beam lit 6 we have 1 plus 2 plus 1 times
+ 
+
+ align:start position:0%
+beam lit 6 we have 1 plus 2 plus 1 times
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+now for our constraints first we need to
+
+ align:start position:0%
+now for our constraints first we need to
+ 
+
+ align:start position:0%
+now for our constraints first we need to
+make sure that each voxel of the tumor
+
+ align:start position:0%
+make sure that each voxel of the tumor
+ 
+
+ align:start position:0%
+make sure that each voxel of the tumor
+gets a dose of at least seven let's
+
+ align:start position:0%
+gets a dose of at least seven let's
+ 
+
+ align:start position:0%
+gets a dose of at least seven let's
+start with the first tumor voxel in the
+
+ align:start position:0%
+start with the first tumor voxel in the
+ 
+
+ align:start position:0%
+start with the first tumor voxel in the
+top row so 2 times X 1 plus X 5 needs to
+
+ align:start position:0%
+top row so 2 times X 1 plus X 5 needs to
+ 
+
+ align:start position:0%
+top row so 2 times X 1 plus X 5 needs to
+be greater than or equal to 7 now the
+
+ align:start position:0%
+be greater than or equal to 7 now the
+ 
+
+ align:start position:0%
+be greater than or equal to 7 now the
+tumor voxel in the second row we have X
+
+ align:start position:0%
+tumor voxel in the second row we have X
+ 
+
+ align:start position:0%
+tumor voxel in the second row we have X
+2 plus 2 X 4 also greater than or equal
+
+ align:start position:0%
+2 plus 2 X 4 also greater than or equal
+ 
+
+ align:start position:0%
+2 plus 2 X 4 also greater than or equal
+to 7 now for the two tumor voxels in the
+
+ align:start position:0%
+to 7 now for the two tumor voxels in the
+ 
+
+ align:start position:0%
+to 7 now for the two tumor voxels in the
+bottom row we have 1.5 X 3 plus x4
+
+ align:start position:0%
+bottom row we have 1.5 X 3 plus x4
+ 
+
+ align:start position:0%
+bottom row we have 1.5 X 3 plus x4
+greater than or equal to 7 and 1.5 X 3
+
+ align:start position:0%
+greater than or equal to 7 and 1.5 X 3
+ 
+
+ align:start position:0%
+greater than or equal to 7 and 1.5 X 3
+plus X 5 greater than or equal to 7 then
+
+ align:start position:0%
+plus X 5 greater than or equal to 7 then
+ 
+
+ align:start position:0%
+plus X 5 greater than or equal to 7 then
+for the spinal cord we need to make sure
+
+ align:start position:0%
+for the spinal cord we need to make sure
+ 
+
+ align:start position:0%
+for the spinal cord we need to make sure
+that 2 times X 2 plus 2 times X 5 is
+
+ align:start position:0%
+that 2 times X 2 plus 2 times X 5 is
+ 
+
+ align:start position:0%
+that 2 times X 2 plus 2 times X 5 is
+less than or equal to 5 and lastly we
+
+ align:start position:0%
+less than or equal to 5 and lastly we
+ 
+
+ align:start position:0%
+less than or equal to 5 and lastly we
+just need to make sure that all of our
+
+ align:start position:0%
+just need to make sure that all of our
+ 
+
+ align:start position:0%
+just need to make sure that all of our
+decision variables are non-negative so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they should all be greater than or equal
+
+ align:start position:0%
+they should all be greater than or equal
+ 
+
+ align:start position:0%
+they should all be greater than or equal
+to 0 now that we've set up our
+
+ align:start position:0%
+to 0 now that we've set up our
+ 
+
+ align:start position:0%
+to 0 now that we've set up our
+optimization problem we'll solve it in
+
+ align:start position:0%
+optimization problem we'll solve it in
+ 
+
+ align:start position:0%
+optimization problem we'll solve it in
+libreoffice in the next video
\ No newline at end of file
diff --git a/EXYw8_pnKr0.txt b/EXYw8_pnKr0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..660636a7366626f0d10961673cdf92a4ebbe4cac
--- /dev/null
+++ b/EXYw8_pnKr0.txt
@@ -0,0 +1,8651 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another lecture in my series on Urban
+
+ align:start position:0%
+another lecture in my series on Urban
+ 
+
+ align:start position:0%
+another lecture in my series on Urban
+Energy Systems and policy my name is
+
+ align:start position:0%
+Energy Systems and policy my name is
+ 
+
+ align:start position:0%
+Energy Systems and policy my name is
+David Sue I'm an associate professor of
+
+ align:start position:0%
+David Sue I'm an associate professor of
+ 
+
+ align:start position:0%
+David Sue I'm an associate professor of
+urban studies and planning MIT
+
+ align:start position:0%
+urban studies and planning MIT
+ 
+
+ align:start position:0%
+urban studies and planning MIT
+and this week I want to talk about
+
+ align:start position:0%
+and this week I want to talk about
+ 
+
+ align:start position:0%
+and this week I want to talk about
+cities and buildings and Energy
+
+ align:start position:0%
+cities and buildings and Energy
+ 
+
+ align:start position:0%
+cities and buildings and Energy
+Efficiency
+
+ align:start position:0%
+Efficiency
+ 
+
+ align:start position:0%
+Efficiency
+the class materials or the materials for
+
+ align:start position:0%
+the class materials or the materials for
+ 
+
+ align:start position:0%
+the class materials or the materials for
+class discussion on Tuesday are in the
+
+ align:start position:0%
+class discussion on Tuesday are in the
+ 
+
+ align:start position:0%
+class discussion on Tuesday are in the
+syllabus we'll talk mostly about the
+
+ align:start position:0%
+syllabus we'll talk mostly about the
+ 
+
+ align:start position:0%
+syllabus we'll talk mostly about the
+Makai reading today the first bullet
+
+ align:start position:0%
+Makai reading today the first bullet
+ 
+
+ align:start position:0%
+Makai reading today the first bullet
+point but we'll talk about the other
+
+ align:start position:0%
+point but we'll talk about the other
+ 
+
+ align:start position:0%
+point but we'll talk about the other
+readings in class on Tuesday
+
+ align:start position:0%
+readings in class on Tuesday
+ 
+
+ align:start position:0%
+readings in class on Tuesday
+I don't really want to start with this
+
+ align:start position:0%
+I don't really want to start with this
+ 
+
+ align:start position:0%
+I don't really want to start with this
+quote you may have heard this quote
+
+ align:start position:0%
+quote you may have heard this quote
+ 
+
+ align:start position:0%
+quote you may have heard this quote
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+it's from Winston Churchill it's in a
+
+ align:start position:0%
+it's from Winston Churchill it's in a
+ 
+
+ align:start position:0%
+it's from Winston Churchill it's in a
+speech he gave after the bombing of the
+
+ align:start position:0%
+speech he gave after the bombing of the
+ 
+
+ align:start position:0%
+speech he gave after the bombing of the
+House of Commons after a raid in the
+
+ align:start position:0%
+House of Commons after a raid in the
+ 
+
+ align:start position:0%
+House of Commons after a raid in the
+London Blitz and he says we shaped
+
+ align:start position:0%
+London Blitz and he says we shaped
+ 
+
+ align:start position:0%
+London Blitz and he says we shaped
+buildings and afterwards our buildings
+
+ align:start position:0%
+buildings and afterwards our buildings
+ 
+
+ align:start position:0%
+buildings and afterwards our buildings
+shape us at the time they're discussing
+
+ align:start position:0%
+shape us at the time they're discussing
+ 
+
+ align:start position:0%
+shape us at the time they're discussing
+how or whether to rebuild the House of
+
+ align:start position:0%
+how or whether to rebuild the House of
+ 
+
+ align:start position:0%
+how or whether to rebuild the House of
+Commons after it was hit by a bomb but I
+
+ align:start position:0%
+Commons after it was hit by a bomb but I
+ 
+
+ align:start position:0%
+Commons after it was hit by a bomb but I
+think it's a evocative quote that gets
+
+ align:start position:0%
+think it's a evocative quote that gets
+ 
+
+ align:start position:0%
+think it's a evocative quote that gets
+used quite often to describe what the
+
+ align:start position:0%
+used quite often to describe what the
+ 
+
+ align:start position:0%
+used quite often to describe what the
+influence of buildings on culture is and
+
+ align:start position:0%
+influence of buildings on culture is and
+ 
+
+ align:start position:0%
+influence of buildings on culture is and
+I've had a lifelong Fascination
+
+ align:start position:0%
+I've had a lifelong Fascination
+ 
+
+ align:start position:0%
+I've had a lifelong Fascination
+architecture and so what I want to focus
+
+ align:start position:0%
+architecture and so what I want to focus
+ 
+
+ align:start position:0%
+architecture and so what I want to focus
+on today is how buildings reflect many
+
+ align:start position:0%
+on today is how buildings reflect many
+ 
+
+ align:start position:0%
+on today is how buildings reflect many
+different things Energy Efficiency is
+
+ align:start position:0%
+different things Energy Efficiency is
+ 
+
+ align:start position:0%
+different things Energy Efficiency is
+not usually at the top of anyone's list
+
+ align:start position:0%
+not usually at the top of anyone's list
+ 
+
+ align:start position:0%
+not usually at the top of anyone's list
+of concerns at the same time I hope to
+
+ align:start position:0%
+of concerns at the same time I hope to
+ 
+
+ align:start position:0%
+of concerns at the same time I hope to
+convince you that buildings are an
+
+ align:start position:0%
+convince you that buildings are an
+ 
+
+ align:start position:0%
+convince you that buildings are an
+incredibly important part of our problem
+
+ align:start position:0%
+incredibly important part of our problem
+ 
+
+ align:start position:0%
+incredibly important part of our problem
+that we need to tackle for the energy
+
+ align:start position:0%
+that we need to tackle for the energy
+ 
+
+ align:start position:0%
+that we need to tackle for the energy
+transition and also
+
+ align:start position:0%
+transition and also
+ 
+
+ align:start position:0%
+transition and also
+also argue that there's ways that we can
+
+ align:start position:0%
+also argue that there's ways that we can
+ 
+
+ align:start position:0%
+also argue that there's ways that we can
+shape buildings that will shape our
+
+ align:start position:0%
+shape buildings that will shape our
+ 
+
+ align:start position:0%
+shape buildings that will shape our
+later energy using behaviors
+
+ align:start position:0%
+later energy using behaviors
+ 
+
+ align:start position:0%
+later energy using behaviors
+and so just to give you a few arguments
+
+ align:start position:0%
+and so just to give you a few arguments
+ 
+
+ align:start position:0%
+and so just to give you a few arguments
+about why buildings are so important for
+
+ align:start position:0%
+about why buildings are so important for
+ 
+
+ align:start position:0%
+about why buildings are so important for
+energy use and climate change in terms
+
+ align:start position:0%
+energy use and climate change in terms
+ 
+
+ align:start position:0%
+energy use and climate change in terms
+of operational energy buildings about 35
+
+ align:start position:0%
+of operational energy buildings about 35
+ 
+
+ align:start position:0%
+of operational energy buildings about 35
+percent of the primary energy used in
+
+ align:start position:0%
+percent of the primary energy used in
+ 
+
+ align:start position:0%
+percent of the primary energy used in
+the world they were responsible for
+
+ align:start position:0%
+the world they were responsible for
+ 
+
+ align:start position:0%
+the world they were responsible for
+about 38 of greenhouse gas emissions
+
+ align:start position:0%
+about 38 of greenhouse gas emissions
+ 
+
+ align:start position:0%
+about 38 of greenhouse gas emissions
+worldwide
+
+ align:start position:0%
+worldwide
+ 
+
+ align:start position:0%
+worldwide
+and it's also worth noting that for
+
+ align:start position:0%
+and it's also worth noting that for
+ 
+
+ align:start position:0%
+and it's also worth noting that for
+cities in particular the subject of this
+
+ align:start position:0%
+cities in particular the subject of this
+ 
+
+ align:start position:0%
+cities in particular the subject of this
+course uh buildings are a much higher
+
+ align:start position:0%
+course uh buildings are a much higher
+ 
+
+ align:start position:0%
+course uh buildings are a much higher
+percentage of City emissions in New York
+
+ align:start position:0%
+percentage of City emissions in New York
+ 
+
+ align:start position:0%
+percentage of City emissions in New York
+City buildings represent about 70
+
+ align:start position:0%
+City buildings represent about 70
+ 
+
+ align:start position:0%
+City buildings represent about 70
+percent of the greenhouse gas emissions
+
+ align:start position:0%
+percent of the greenhouse gas emissions
+ 
+
+ align:start position:0%
+percent of the greenhouse gas emissions
+though we also have to kind of be aware
+
+ align:start position:0%
+though we also have to kind of be aware
+ 
+
+ align:start position:0%
+though we also have to kind of be aware
+that you know this is also reflective of
+
+ align:start position:0%
+that you know this is also reflective of
+ 
+
+ align:start position:0%
+that you know this is also reflective of
+as I've said before New York City being
+
+ align:start position:0%
+as I've said before New York City being
+ 
+
+ align:start position:0%
+as I've said before New York City being
+a financial center in Singapore uh
+
+ align:start position:0%
+a financial center in Singapore uh
+ 
+
+ align:start position:0%
+a financial center in Singapore uh
+buildings are only 20 of greenhouse gas
+
+ align:start position:0%
+buildings are only 20 of greenhouse gas
+ 
+
+ align:start position:0%
+buildings are only 20 of greenhouse gas
+emissions because Singapore has a
+
+ align:start position:0%
+emissions because Singapore has a
+ 
+
+ align:start position:0%
+emissions because Singapore has a
+surprisingly large industrial-based uh
+
+ align:start position:0%
+surprisingly large industrial-based uh
+ 
+
+ align:start position:0%
+surprisingly large industrial-based uh
+specifically of uh liquid natural gas
+
+ align:start position:0%
+specifically of uh liquid natural gas
+ 
+
+ align:start position:0%
+specifically of uh liquid natural gas
+processing
+
+ align:start position:0%
+processing
+ 
+
+ align:start position:0%
+processing
+but in terms of embodying energy
+
+ align:start position:0%
+but in terms of embodying energy
+ 
+
+ align:start position:0%
+but in terms of embodying energy
+buildings represent also their
+
+ align:start position:0%
+buildings represent also their
+ 
+
+ align:start position:0%
+buildings represent also their
+construction represents a significant
+
+ align:start position:0%
+construction represents a significant
+ 
+
+ align:start position:0%
+construction represents a significant
+additional portion of their energy use
+
+ align:start position:0%
+additional portion of their energy use
+ 
+
+ align:start position:0%
+additional portion of their energy use
+and greenhouse gas emissions the
+
+ align:start position:0%
+and greenhouse gas emissions the
+ 
+
+ align:start position:0%
+and greenhouse gas emissions the
+building construction industry is
+
+ align:start position:0%
+building construction industry is
+ 
+
+ align:start position:0%
+building construction industry is
+responsible for about five percent of
+
+ align:start position:0%
+responsible for about five percent of
+ 
+
+ align:start position:0%
+responsible for about five percent of
+the primary energy use in the world uh
+
+ align:start position:0%
+the primary energy use in the world uh
+ 
+
+ align:start position:0%
+the primary energy use in the world uh
+10 of emissions
+
+ align:start position:0%
+10 of emissions
+ 
+
+ align:start position:0%
+10 of emissions
+and it's also worth noting that in
+
+ align:start position:0%
+and it's also worth noting that in
+ 
+
+ align:start position:0%
+and it's also worth noting that in
+cities like New York many of the cities
+
+ align:start position:0%
+cities like New York many of the cities
+ 
+
+ align:start position:0%
+cities like New York many of the cities
+that are as many of the buildings that
+
+ align:start position:0%
+that are as many of the buildings that
+ 
+
+ align:start position:0%
+that are as many of the buildings that
+are already there here in 2022 are going
+
+ align:start position:0%
+are already there here in 2022 are going
+ 
+
+ align:start position:0%
+are already there here in 2022 are going
+to be there for our mid-centric Bull in
+
+ align:start position:0%
+to be there for our mid-centric Bull in
+ 
+
+ align:start position:0%
+to be there for our mid-centric Bull in
+2050. so a key part of our challenge for
+
+ align:start position:0%
+2050. so a key part of our challenge for
+ 
+
+ align:start position:0%
+2050. so a key part of our challenge for
+addressing buildings is retrofitting the
+
+ align:start position:0%
+addressing buildings is retrofitting the
+ 
+
+ align:start position:0%
+addressing buildings is retrofitting the
+existing buildings we have new
+
+ align:start position:0%
+existing buildings we have new
+ 
+
+ align:start position:0%
+existing buildings we have new
+construction may be occurring in other
+
+ align:start position:0%
+construction may be occurring in other
+ 
+
+ align:start position:0%
+construction may be occurring in other
+cities that are faster growing but New
+
+ align:start position:0%
+cities that are faster growing but New
+ 
+
+ align:start position:0%
+cities that are faster growing but New
+York City is already quite dense we
+
+ align:start position:0%
+York City is already quite dense we
+ 
+
+ align:start position:0%
+York City is already quite dense we
+actually need to figure out how to
+
+ align:start position:0%
+actually need to figure out how to
+ 
+
+ align:start position:0%
+actually need to figure out how to
+retrofit the millions of buildings we
+
+ align:start position:0%
+retrofit the millions of buildings we
+ 
+
+ align:start position:0%
+retrofit the millions of buildings we
+already have in New York City
+
+ align:start position:0%
+already have in New York City
+ 
+
+ align:start position:0%
+already have in New York City
+it's also important to note that
+
+ align:start position:0%
+it's also important to note that
+ 
+
+ align:start position:0%
+it's also important to note that
+buildings shape our health and we're
+
+ align:start position:0%
+buildings shape our health and we're
+ 
+
+ align:start position:0%
+buildings shape our health and we're
+quite concerned about how buildings
+
+ align:start position:0%
+quite concerned about how buildings
+ 
+
+ align:start position:0%
+quite concerned about how buildings
+affect our health uh this famous
+
+ align:start position:0%
+affect our health uh this famous
+ 
+
+ align:start position:0%
+affect our health uh this famous
+statistic from Lawrence Berkeley
+
+ align:start position:0%
+statistic from Lawrence Berkeley
+ 
+
+ align:start position:0%
+statistic from Lawrence Berkeley
+National Laboratory using the American
+
+ align:start position:0%
+National Laboratory using the American
+ 
+
+ align:start position:0%
+National Laboratory using the American
+timing survey basically asks people how
+
+ align:start position:0%
+timing survey basically asks people how
+ 
+
+ align:start position:0%
+timing survey basically asks people how
+much time do they spend and where and
+
+ align:start position:0%
+much time do they spend and where and
+ 
+
+ align:start position:0%
+much time do they spend and where and
+they find that people spend about 87
+
+ align:start position:0%
+they find that people spend about 87
+ 
+
+ align:start position:0%
+they find that people spend about 87
+percent of their lives and yours and on
+
+ align:start position:0%
+percent of their lives and yours and on
+ 
+
+ align:start position:0%
+percent of their lives and yours and on
+six percent of their time in enclosed
+
+ align:start position:0%
+six percent of their time in enclosed
+ 
+
+ align:start position:0%
+six percent of their time in enclosed
+Vehicles so 93 of their time is
+
+ align:start position:0%
+Vehicles so 93 of their time is
+ 
+
+ align:start position:0%
+Vehicles so 93 of their time is
+essentially spent in spaces that can be
+
+ align:start position:0%
+essentially spent in spaces that can be
+ 
+
+ align:start position:0%
+essentially spent in spaces that can be
+air-conditioned or affected by air
+
+ align:start position:0%
+air-conditioned or affected by air
+ 
+
+ align:start position:0%
+air-conditioned or affected by air
+conditioning
+
+ align:start position:0%
+conditioning
+ 
+
+ align:start position:0%
+conditioning
+of course after three years of covid we
+
+ align:start position:0%
+of course after three years of covid we
+ 
+
+ align:start position:0%
+of course after three years of covid we
+don't probably need to reinforce this
+
+ align:start position:0%
+don't probably need to reinforce this
+ 
+
+ align:start position:0%
+don't probably need to reinforce this
+coin too much but covid and our
+
+ align:start position:0%
+coin too much but covid and our
+ 
+
+ align:start position:0%
+coin too much but covid and our
+concerned about ventilation have
+
+ align:start position:0%
+concerned about ventilation have
+ 
+
+ align:start position:0%
+concerned about ventilation have
+fundamentally affected our desire for
+
+ align:start position:0%
+fundamentally affected our desire for
+ 
+
+ align:start position:0%
+fundamentally affected our desire for
+Real Estate now Recent research from the
+
+ align:start position:0%
+Real Estate now Recent research from the
+ 
+
+ align:start position:0%
+Real Estate now Recent research from the
+San Francisco fed that Paul Krugman has
+
+ align:start position:0%
+San Francisco fed that Paul Krugman has
+ 
+
+ align:start position:0%
+San Francisco fed that Paul Krugman has
+written about is essentially looking at
+
+ align:start position:0%
+written about is essentially looking at
+ 
+
+ align:start position:0%
+written about is essentially looking at
+inflation and the contribution of real
+
+ align:start position:0%
+inflation and the contribution of real
+ 
+
+ align:start position:0%
+inflation and the contribution of real
+estate to inflation and he argued I
+
+ align:start position:0%
+estate to inflation and he argued I
+ 
+
+ align:start position:0%
+estate to inflation and he argued I
+think like convincingly that there's a
+
+ align:start position:0%
+think like convincingly that there's a
+ 
+
+ align:start position:0%
+think like convincingly that there's a
+kind of secular shift in what people
+
+ align:start position:0%
+kind of secular shift in what people
+ 
+
+ align:start position:0%
+kind of secular shift in what people
+want people need more space or Zoom
+
+ align:start position:0%
+want people need more space or Zoom
+ 
+
+ align:start position:0%
+want people need more space or Zoom
+calls for spending their time at home
+
+ align:start position:0%
+calls for spending their time at home
+ 
+
+ align:start position:0%
+calls for spending their time at home
+this ties into the remote work trends
+
+ align:start position:0%
+this ties into the remote work trends
+ 
+
+ align:start position:0%
+this ties into the remote work trends
+that we talked about last week
+
+ align:start position:0%
+that we talked about last week
+ 
+
+ align:start position:0%
+that we talked about last week
+and of course we should not forget that
+
+ align:start position:0%
+and of course we should not forget that
+ 
+
+ align:start position:0%
+and of course we should not forget that
+there's always a crisis or there is a
+
+ align:start position:0%
+there's always a crisis or there is a
+ 
+
+ align:start position:0%
+there's always a crisis or there is a
+increasing crisis in providing
+
+ align:start position:0%
+increasing crisis in providing
+ 
+
+ align:start position:0%
+increasing crisis in providing
+affordable and sufficient housing not
+
+ align:start position:0%
+affordable and sufficient housing not
+ 
+
+ align:start position:0%
+affordable and sufficient housing not
+only in this country and in our major
+
+ align:start position:0%
+only in this country and in our major
+ 
+
+ align:start position:0%
+only in this country and in our major
+cities but in many countries also so
+
+ align:start position:0%
+cities but in many countries also so
+ 
+
+ align:start position:0%
+cities but in many countries also so
+when we think talk about buildings we
+
+ align:start position:0%
+when we think talk about buildings we
+ 
+
+ align:start position:0%
+when we think talk about buildings we
+need to think about what we're trying to
+
+ align:start position:0%
+need to think about what we're trying to
+ 
+
+ align:start position:0%
+need to think about what we're trying to
+provide uh fundamentally is a habitat or
+
+ align:start position:0%
+provide uh fundamentally is a habitat or
+ 
+
+ align:start position:0%
+provide uh fundamentally is a habitat or
+Shelter From the environment
+
+ align:start position:0%
+Shelter From the environment
+ 
+
+ align:start position:0%
+Shelter From the environment
+but how we do that have tremendous
+
+ align:start position:0%
+but how we do that have tremendous
+ 
+
+ align:start position:0%
+but how we do that have tremendous
+implications for our energy use and
+
+ align:start position:0%
+implications for our energy use and
+ 
+
+ align:start position:0%
+implications for our energy use and
+climate goals and so finally what we'll
+
+ align:start position:0%
+climate goals and so finally what we'll
+ 
+
+ align:start position:0%
+climate goals and so finally what we'll
+talk about in this lectures mostly the
+
+ align:start position:0%
+talk about in this lectures mostly the
+ 
+
+ align:start position:0%
+talk about in this lectures mostly the
+Makai reading uh he focuses on how much
+
+ align:start position:0%
+Makai reading uh he focuses on how much
+ 
+
+ align:start position:0%
+Makai reading uh he focuses on how much
+it takes to heat cool and use various
+
+ align:start position:0%
+it takes to heat cool and use various
+ 
+
+ align:start position:0%
+it takes to heat cool and use various
+appliances and we're really trying to
+
+ align:start position:0%
+appliances and we're really trying to
+ 
+
+ align:start position:0%
+appliances and we're really trying to
+get some underlying questions how much
+
+ align:start position:0%
+get some underlying questions how much
+ 
+
+ align:start position:0%
+get some underlying questions how much
+energy is used in buildings how much
+
+ align:start position:0%
+energy is used in buildings how much
+ 
+
+ align:start position:0%
+energy is used in buildings how much
+more efficient and buildings be
+
+ align:start position:0%
+more efficient and buildings be
+ 
+
+ align:start position:0%
+more efficient and buildings be
+what specific activities in buildings
+
+ align:start position:0%
+what specific activities in buildings
+ 
+
+ align:start position:0%
+what specific activities in buildings
+lead to energy use and we will examine
+
+ align:start position:0%
+lead to energy use and we will examine
+ 
+
+ align:start position:0%
+lead to energy use and we will examine
+whether that leads to energy waste and
+
+ align:start position:0%
+whether that leads to energy waste and
+ 
+
+ align:start position:0%
+whether that leads to energy waste and
+finally how can we motivate individual
+
+ align:start position:0%
+finally how can we motivate individual
+ 
+
+ align:start position:0%
+finally how can we motivate individual
+users to save energy in buildings
+
+ align:start position:0%
+users to save energy in buildings
+ 
+
+ align:start position:0%
+users to save energy in buildings
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just to highlight for a moment the role
+
+ align:start position:0%
+just to highlight for a moment the role
+ 
+
+ align:start position:0%
+just to highlight for a moment the role
+of buildings in the economy this is our
+
+ align:start position:0%
+of buildings in the economy this is our
+ 
+
+ align:start position:0%
+of buildings in the economy this is our
+familiar send key diagram the U.S energy
+
+ align:start position:0%
+familiar send key diagram the U.S energy
+ 
+
+ align:start position:0%
+familiar send key diagram the U.S energy
+economy being roughly about 97 quads if
+
+ align:start position:0%
+economy being roughly about 97 quads if
+ 
+
+ align:start position:0%
+economy being roughly about 97 quads if
+you look at the final uses here the
+
+ align:start position:0%
+you look at the final uses here the
+ 
+
+ align:start position:0%
+you look at the final uses here the
+final uses for buildings are generally
+
+ align:start position:0%
+final uses for buildings are generally
+ 
+
+ align:start position:0%
+final uses for buildings are generally
+categorized as residential and
+
+ align:start position:0%
+categorized as residential and
+ 
+
+ align:start position:0%
+categorized as residential and
+Commercial put together
+
+ align:start position:0%
+Commercial put together
+ 
+
+ align:start position:0%
+Commercial put together
+that's about 20 quads which means it's
+
+ align:start position:0%
+that's about 20 quads which means it's
+ 
+
+ align:start position:0%
+that's about 20 quads which means it's
+responsible for about 20 of the total
+
+ align:start position:0%
+responsible for about 20 of the total
+ 
+
+ align:start position:0%
+responsible for about 20 of the total
+energy going into the economy and about
+
+ align:start position:0%
+energy going into the economy and about
+ 
+
+ align:start position:0%
+energy going into the economy and about
+30 percent of our final uses if you take
+
+ align:start position:0%
+30 percent of our final uses if you take
+ 
+
+ align:start position:0%
+30 percent of our final uses if you take
+these two as a proportion of all the
+
+ align:start position:0%
+these two as a proportion of all the
+ 
+
+ align:start position:0%
+these two as a proportion of all the
+various pink boxes representing final
+
+ align:start position:0%
+various pink boxes representing final
+ 
+
+ align:start position:0%
+various pink boxes representing final
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+of course as a proportion of electricity
+
+ align:start position:0%
+of course as a proportion of electricity
+ 
+
+ align:start position:0%
+of course as a proportion of electricity
+use residential commercial buildings
+
+ align:start position:0%
+use residential commercial buildings
+ 
+
+ align:start position:0%
+use residential commercial buildings
+actually tend to use a much larger
+
+ align:start position:0%
+actually tend to use a much larger
+ 
+
+ align:start position:0%
+actually tend to use a much larger
+proportion of the energy it looks like
+
+ align:start position:0%
+proportion of the energy it looks like
+ 
+
+ align:start position:0%
+proportion of the energy it looks like
+north of 70 percent
+
+ align:start position:0%
+north of 70 percent
+ 
+
+ align:start position:0%
+north of 70 percent
+because industrial uses and
+
+ align:start position:0%
+because industrial uses and
+ 
+
+ align:start position:0%
+because industrial uses and
+transportation tend to use fossil fuels
+
+ align:start position:0%
+transportation tend to use fossil fuels
+ 
+
+ align:start position:0%
+transportation tend to use fossil fuels
+like petroleum and natural gas or oil
+
+ align:start position:0%
+like petroleum and natural gas or oil
+ 
+
+ align:start position:0%
+like petroleum and natural gas or oil
+so most electricity that we generate
+
+ align:start position:0%
+so most electricity that we generate
+ 
+
+ align:start position:0%
+so most electricity that we generate
+actually goes into buildings
+
+ align:start position:0%
+actually goes into buildings
+ 
+
+ align:start position:0%
+actually goes into buildings
+and just to highlight what the users
+
+ align:start position:0%
+and just to highlight what the users
+ 
+
+ align:start position:0%
+and just to highlight what the users
+uses of energy are in our buildings this
+
+ align:start position:0%
+uses of energy are in our buildings this
+ 
+
+ align:start position:0%
+uses of energy are in our buildings this
+is a Sankey diagram specifically for
+
+ align:start position:0%
+is a Sankey diagram specifically for
+ 
+
+ align:start position:0%
+is a Sankey diagram specifically for
+buildings specifically for commercial
+
+ align:start position:0%
+buildings specifically for commercial
+ 
+
+ align:start position:0%
+buildings specifically for commercial
+buildings and this is actually a
+
+ align:start position:0%
+buildings and this is actually a
+ 
+
+ align:start position:0%
+buildings and this is actually a
+relatively old report for Pacific
+
+ align:start position:0%
+relatively old report for Pacific
+ 
+
+ align:start position:0%
+relatively old report for Pacific
+Northwest National Labs but I'm guessing
+
+ align:start position:0%
+Northwest National Labs but I'm guessing
+ 
+
+ align:start position:0%
+Northwest National Labs but I'm guessing
+it hasn't changed too much over time and
+
+ align:start position:0%
+it hasn't changed too much over time and
+ 
+
+ align:start position:0%
+it hasn't changed too much over time and
+if you look at this we have input coal
+
+ align:start position:0%
+if you look at this we have input coal
+ 
+
+ align:start position:0%
+if you look at this we have input coal
+natural gas petroleum natural gas this
+
+ align:start position:0%
+natural gas petroleum natural gas this
+ 
+
+ align:start position:0%
+natural gas petroleum natural gas this
+is all going through Electric utilities
+
+ align:start position:0%
+is all going through Electric utilities
+ 
+
+ align:start position:0%
+is all going through Electric utilities
+and these arrows here in the bottom are
+
+ align:start position:0%
+and these arrows here in the bottom are
+ 
+
+ align:start position:0%
+and these arrows here in the bottom are
+natural gas petroleum and biomass going
+
+ align:start position:0%
+natural gas petroleum and biomass going
+ 
+
+ align:start position:0%
+natural gas petroleum and biomass going
+directly into the commercial building
+
+ align:start position:0%
+directly into the commercial building
+ 
+
+ align:start position:0%
+directly into the commercial building
+sector and you can see all the uses here
+
+ align:start position:0%
+sector and you can see all the uses here
+ 
+
+ align:start position:0%
+sector and you can see all the uses here
+on the right we will focus in on this
+
+ align:start position:0%
+on the right we will focus in on this
+ 
+
+ align:start position:0%
+on the right we will focus in on this
+further
+
+ align:start position:0%
+further
+ 
+
+ align:start position:0%
+further
+and if you look at what the total energy
+
+ align:start position:0%
+and if you look at what the total energy
+ 
+
+ align:start position:0%
+and if you look at what the total energy
+that's delivered to commercial customers
+
+ align:start position:0%
+that's delivered to commercial customers
+ 
+
+ align:start position:0%
+that's delivered to commercial customers
+is you can see that it's really a grab
+
+ align:start position:0%
+is you can see that it's really a grab
+ 
+
+ align:start position:0%
+is you can see that it's really a grab
+bag of many different energy uses how
+
+ align:start position:0%
+bag of many different energy uses how
+ 
+
+ align:start position:0%
+bag of many different energy uses how
+half of it looks like electricity half
+
+ align:start position:0%
+half of it looks like electricity half
+ 
+
+ align:start position:0%
+half of it looks like electricity half
+of it looks like fossil fuels that are
+
+ align:start position:0%
+of it looks like fossil fuels that are
+ 
+
+ align:start position:0%
+of it looks like fossil fuels that are
+busted directly on site
+
+ align:start position:0%
+busted directly on site
+ 
+
+ align:start position:0%
+busted directly on site
+you can see that a significant portion
+
+ align:start position:0%
+you can see that a significant portion
+ 
+
+ align:start position:0%
+you can see that a significant portion
+of the uses are for space cooling
+
+ align:start position:0%
+of the uses are for space cooling
+ 
+
+ align:start position:0%
+of the uses are for space cooling
+ventilation lighting Refrigeration
+
+ align:start position:0%
+ventilation lighting Refrigeration
+ 
+
+ align:start position:0%
+ventilation lighting Refrigeration
+office equipment and then all of most of
+
+ align:start position:0%
+office equipment and then all of most of
+ 
+
+ align:start position:0%
+office equipment and then all of most of
+our natural gas goes to do space heating
+
+ align:start position:0%
+our natural gas goes to do space heating
+ 
+
+ align:start position:0%
+our natural gas goes to do space heating
+water heating and other uses and some
+
+ align:start position:0%
+water heating and other uses and some
+ 
+
+ align:start position:0%
+water heating and other uses and some
+cooking the petroleum or coal is still
+
+ align:start position:0%
+cooking the petroleum or coal is still
+ 
+
+ align:start position:0%
+cooking the petroleum or coal is still
+used in many countries but less so in
+
+ align:start position:0%
+used in many countries but less so in
+ 
+
+ align:start position:0%
+used in many countries but less so in
+the United States is almost all entirely
+
+ align:start position:0%
+the United States is almost all entirely
+ 
+
+ align:start position:0%
+the United States is almost all entirely
+going to space Heating and water heating
+
+ align:start position:0%
+going to space Heating and water heating
+ 
+
+ align:start position:0%
+going to space Heating and water heating
+and then there's a portion of biomass
+
+ align:start position:0%
+and then there's a portion of biomass
+ 
+
+ align:start position:0%
+and then there's a portion of biomass
+that's essentially wood stoves which is
+
+ align:start position:0%
+that's essentially wood stoves which is
+ 
+
+ align:start position:0%
+that's essentially wood stoves which is
+this little sliver here and of course we
+
+ align:start position:0%
+this little sliver here and of course we
+ 
+
+ align:start position:0%
+this little sliver here and of course we
+have the smallest liver is unfortunately
+
+ align:start position:0%
+have the smallest liver is unfortunately
+ 
+
+ align:start position:0%
+have the smallest liver is unfortunately
+Renewables now but we hope to perhaps
+
+ align:start position:0%
+Renewables now but we hope to perhaps
+ 
+
+ align:start position:0%
+Renewables now but we hope to perhaps
+increase that as we have energy
+
+ align:start position:0%
+increase that as we have energy
+ 
+
+ align:start position:0%
+increase that as we have energy
+generation in homes occurring at a
+
+ align:start position:0%
+generation in homes occurring at a
+ 
+
+ align:start position:0%
+generation in homes occurring at a
+greater scale with rooftop solar
+
+ align:start position:0%
+greater scale with rooftop solar
+ 
+
+ align:start position:0%
+greater scale with rooftop solar
+if you look at the residential sector
+
+ align:start position:0%
+if you look at the residential sector
+ 
+
+ align:start position:0%
+if you look at the residential sector
+again we have electric utilities here at
+
+ align:start position:0%
+again we have electric utilities here at
+ 
+
+ align:start position:0%
+again we have electric utilities here at
+the top and we have elect Direct
+
+ align:start position:0%
+the top and we have elect Direct
+ 
+
+ align:start position:0%
+the top and we have elect Direct
+Delivery of fuels at the bottom and you
+
+ align:start position:0%
+Delivery of fuels at the bottom and you
+ 
+
+ align:start position:0%
+Delivery of fuels at the bottom and you
+can see if we focus in on residential
+
+ align:start position:0%
+can see if we focus in on residential
+ 
+
+ align:start position:0%
+can see if we focus in on residential
+buildings
+
+ align:start position:0%
+buildings
+ 
+
+ align:start position:0%
+buildings
+from this Pacific Northwest National lab
+
+ align:start position:0%
+from this Pacific Northwest National lab
+ 
+
+ align:start position:0%
+from this Pacific Northwest National lab
+report you can see again that there's
+
+ align:start position:0%
+report you can see again that there's
+ 
+
+ align:start position:0%
+report you can see again that there's
+many different activities occurring in
+
+ align:start position:0%
+many different activities occurring in
+ 
+
+ align:start position:0%
+many different activities occurring in
+buildings space heating cooling lighting
+
+ align:start position:0%
+buildings space heating cooling lighting
+ 
+
+ align:start position:0%
+buildings space heating cooling lighting
+Refrigeration so on
+
+ align:start position:0%
+Refrigeration so on
+ 
+
+ align:start position:0%
+Refrigeration so on
+all these are the same with wood solar
+
+ align:start position:0%
+all these are the same with wood solar
+ 
+
+ align:start position:0%
+all these are the same with wood solar
+is a larger portion of the energy use
+
+ align:start position:0%
+is a larger portion of the energy use
+ 
+
+ align:start position:0%
+is a larger portion of the energy use
+for residential buildings Thanos for
+
+ align:start position:0%
+for residential buildings Thanos for
+ 
+
+ align:start position:0%
+for residential buildings Thanos for
+commercial buildings
+
+ align:start position:0%
+commercial buildings
+ 
+
+ align:start position:0%
+commercial buildings
+but this is to point out that buildings
+
+ align:start position:0%
+but this is to point out that buildings
+ 
+
+ align:start position:0%
+but this is to point out that buildings
+are tightly integrated objects or tools
+
+ align:start position:0%
+are tightly integrated objects or tools
+ 
+
+ align:start position:0%
+are tightly integrated objects or tools
+that have basically been engineered for
+
+ align:start position:0%
+that have basically been engineered for
+ 
+
+ align:start position:0%
+that have basically been engineered for
+lots of different things they provide
+
+ align:start position:0%
+lots of different things they provide
+ 
+
+ align:start position:0%
+lots of different things they provide
+shelter they provide habitat they
+
+ align:start position:0%
+shelter they provide habitat they
+ 
+
+ align:start position:0%
+shelter they provide habitat they
+provide home this is where we do you
+
+ align:start position:0%
+provide home this is where we do you
+ 
+
+ align:start position:0%
+provide home this is where we do you
+know live work play after payment and so
+
+ align:start position:0%
+know live work play after payment and so
+ 
+
+ align:start position:0%
+know live work play after payment and so
+you know we have lots of different uses
+
+ align:start position:0%
+you know we have lots of different uses
+ 
+
+ align:start position:0%
+you know we have lots of different uses
+for trying to accomplish and what we
+
+ align:start position:0%
+for trying to accomplish and what we
+ 
+
+ align:start position:0%
+for trying to accomplish and what we
+want to do is also reduce the energy use
+
+ align:start position:0%
+want to do is also reduce the energy use
+ 
+
+ align:start position:0%
+want to do is also reduce the energy use
+or greenhouse gas emission footprint of
+
+ align:start position:0%
+or greenhouse gas emission footprint of
+ 
+
+ align:start position:0%
+or greenhouse gas emission footprint of
+this sector
+
+ align:start position:0%
+this sector
+ 
+
+ align:start position:0%
+this sector
+just to give you a final kind of sense
+
+ align:start position:0%
+just to give you a final kind of sense
+ 
+
+ align:start position:0%
+just to give you a final kind of sense
+of the importance of buildings if we
+
+ align:start position:0%
+of the importance of buildings if we
+ 
+
+ align:start position:0%
+of the importance of buildings if we
+look back at the Williams NL 2020 deep
+
+ align:start position:0%
+look back at the Williams NL 2020 deep
+ 
+
+ align:start position:0%
+look back at the Williams NL 2020 deep
+decarbonization Pathways or carbon
+
+ align:start position:0%
+decarbonization Pathways or carbon
+ 
+
+ align:start position:0%
+decarbonization Pathways or carbon
+neutral Pathways to the United States
+
+ align:start position:0%
+neutral Pathways to the United States
+ 
+
+ align:start position:0%
+neutral Pathways to the United States
+again we have this 2020 reference case
+
+ align:start position:0%
+again we have this 2020 reference case
+ 
+
+ align:start position:0%
+again we have this 2020 reference case
+this 2050 100 renewable case but if we
+
+ align:start position:0%
+this 2050 100 renewable case but if we
+ 
+
+ align:start position:0%
+this 2050 100 renewable case but if we
+want to achieve decarbonization from 100
+
+ align:start position:0%
+want to achieve decarbonization from 100
+ 
+
+ align:start position:0%
+want to achieve decarbonization from 100
+Renewables we essentially need to
+
+ align:start position:0%
+Renewables we essentially need to
+ 
+
+ align:start position:0%
+Renewables we essentially need to
+decrease our electricity use by half
+
+ align:start position:0%
+decrease our electricity use by half
+ 
+
+ align:start position:0%
+decrease our electricity use by half
+that has to become much more efficient
+
+ align:start position:0%
+that has to become much more efficient
+ 
+
+ align:start position:0%
+that has to become much more efficient
+by use of heat pumps and other more
+
+ align:start position:0%
+by use of heat pumps and other more
+ 
+
+ align:start position:0%
+by use of heat pumps and other more
+efficient Technologies we essentially
+
+ align:start position:0%
+efficient Technologies we essentially
+ 
+
+ align:start position:0%
+efficient Technologies we essentially
+have to eliminate our use of natural gas
+
+ align:start position:0%
+have to eliminate our use of natural gas
+ 
+
+ align:start position:0%
+have to eliminate our use of natural gas
+pipeline into homes we need to actually
+
+ align:start position:0%
+pipeline into homes we need to actually
+ 
+
+ align:start position:0%
+pipeline into homes we need to actually
+increase our electricity
+
+ align:start position:0%
+increase our electricity
+ 
+
+ align:start position:0%
+increase our electricity
+biomass use through electricity mostly
+
+ align:start position:0%
+biomass use through electricity mostly
+ 
+
+ align:start position:0%
+biomass use through electricity mostly
+and again we have to make our homes much
+
+ align:start position:0%
+and again we have to make our homes much
+ 
+
+ align:start position:0%
+and again we have to make our homes much
+much more efficient or make our
+
+ align:start position:0%
+much more efficient or make our
+ 
+
+ align:start position:0%
+much more efficient or make our
+buildings much much more efficient
+
+ align:start position:0%
+buildings much much more efficient
+ 
+
+ align:start position:0%
+buildings much much more efficient
+but the key message to take home here is
+
+ align:start position:0%
+but the key message to take home here is
+ 
+
+ align:start position:0%
+but the key message to take home here is
+we actually have to use half as much
+
+ align:start position:0%
+we actually have to use half as much
+ 
+
+ align:start position:0%
+we actually have to use half as much
+energy and the half that we do use has
+
+ align:start position:0%
+energy and the half that we do use has
+ 
+
+ align:start position:0%
+energy and the half that we do use has
+to become much more efficient
+
+ align:start position:0%
+to become much more efficient
+ 
+
+ align:start position:0%
+to become much more efficient
+so just to give you a sense of how we
+
+ align:start position:0%
+so just to give you a sense of how we
+ 
+
+ align:start position:0%
+so just to give you a sense of how we
+actually lose energy to the environment
+
+ align:start position:0%
+actually lose energy to the environment
+ 
+
+ align:start position:0%
+actually lose energy to the environment
+why are we continually having to heat
+
+ align:start position:0%
+why are we continually having to heat
+ 
+
+ align:start position:0%
+why are we continually having to heat
+and cool our homes there's basically
+
+ align:start position:0%
+and cool our homes there's basically
+ 
+
+ align:start position:0%
+and cool our homes there's basically
+three ways that heat transfer occurs
+
+ align:start position:0%
+three ways that heat transfer occurs
+ 
+
+ align:start position:0%
+three ways that heat transfer occurs
+this is how our heating energy is lost
+
+ align:start position:0%
+this is how our heating energy is lost
+ 
+
+ align:start position:0%
+this is how our heating energy is lost
+or how we call our Heating and load
+
+ align:start position:0%
+or how we call our Heating and load
+ 
+
+ align:start position:0%
+or how we call our Heating and load
+there's three ways that we gain or lose
+
+ align:start position:0%
+there's three ways that we gain or lose
+ 
+
+ align:start position:0%
+there's three ways that we gain or lose
+heat from the house to the environment
+
+ align:start position:0%
+heat from the house to the environment
+ 
+
+ align:start position:0%
+heat from the house to the environment
+it's either ventilation through
+
+ align:start position:0%
+it's either ventilation through
+ 
+
+ align:start position:0%
+it's either ventilation through
+conduction infiltration which is air
+
+ align:start position:0%
+conduction infiltration which is air
+ 
+
+ align:start position:0%
+conduction infiltration which is air
+moving in and out essentially a drafty
+
+ align:start position:0%
+moving in and out essentially a drafty
+ 
+
+ align:start position:0%
+moving in and out essentially a drafty
+door or drafted window loses energy to
+
+ align:start position:0%
+door or drafted window loses energy to
+ 
+
+ align:start position:0%
+door or drafted window loses energy to
+the environment because our warm energy
+
+ align:start position:0%
+the environment because our warm energy
+ 
+
+ align:start position:0%
+the environment because our warm energy
+is being leaked out to the cool
+
+ align:start position:0%
+is being leaked out to the cool
+ 
+
+ align:start position:0%
+is being leaked out to the cool
+environment or if it's hot outside we're
+
+ align:start position:0%
+environment or if it's hot outside we're
+ 
+
+ align:start position:0%
+environment or if it's hot outside we're
+losing the energy we use to cool the air
+
+ align:start position:0%
+losing the energy we use to cool the air
+ 
+
+ align:start position:0%
+losing the energy we use to cool the air
+outside and equilibriates to the
+
+ align:start position:0%
+outside and equilibriates to the
+ 
+
+ align:start position:0%
+outside and equilibriates to the
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+there's conduction which is where the
+
+ align:start position:0%
+there's conduction which is where the
+ 
+
+ align:start position:0%
+there's conduction which is where the
+heat actually is conducted out through
+
+ align:start position:0%
+heat actually is conducted out through
+ 
+
+ align:start position:0%
+heat actually is conducted out through
+materials molecules excite basically the
+
+ align:start position:0%
+materials molecules excite basically the
+ 
+
+ align:start position:0%
+materials molecules excite basically the
+neighboring molecules this is what
+
+ align:start position:0%
+neighboring molecules this is what
+ 
+
+ align:start position:0%
+neighboring molecules this is what
+happens to your external walls and the
+
+ align:start position:0%
+happens to your external walls and the
+ 
+
+ align:start position:0%
+happens to your external walls and the
+ground slab or the roof
+
+ align:start position:0%
+ground slab or the roof
+ 
+
+ align:start position:0%
+ground slab or the roof
+and then radiation this is essentially
+
+ align:start position:0%
+and then radiation this is essentially
+ 
+
+ align:start position:0%
+and then radiation this is essentially
+the process where we do gain some heat
+
+ align:start position:0%
+the process where we do gain some heat
+ 
+
+ align:start position:0%
+the process where we do gain some heat
+let's say from radiation being absorbed
+
+ align:start position:0%
+let's say from radiation being absorbed
+ 
+
+ align:start position:0%
+let's say from radiation being absorbed
+by homes but also we know in our houses
+
+ align:start position:0%
+by homes but also we know in our houses
+ 
+
+ align:start position:0%
+by homes but also we know in our houses
+are warmer than the environment they're
+
+ align:start position:0%
+are warmer than the environment they're
+ 
+
+ align:start position:0%
+are warmer than the environment they're
+radiating heat to the environment and
+
+ align:start position:0%
+radiating heat to the environment and
+ 
+
+ align:start position:0%
+radiating heat to the environment and
+there's a good newspaper that gives a
+
+ align:start position:0%
+there's a good newspaper that gives a
+ 
+
+ align:start position:0%
+there's a good newspaper that gives a
+detailed breakdown for some of these
+
+ align:start position:0%
+detailed breakdown for some of these
+ 
+
+ align:start position:0%
+detailed breakdown for some of these
+fundamental physical mechanisms if
+
+ align:start position:0%
+fundamental physical mechanisms if
+ 
+
+ align:start position:0%
+fundamental physical mechanisms if
+you're more interested in that
+
+ align:start position:0%
+you're more interested in that
+ 
+
+ align:start position:0%
+you're more interested in that
+and the key point that I like that like
+
+ align:start position:0%
+and the key point that I like that like
+ 
+
+ align:start position:0%
+and the key point that I like that like
+high makes is that conduction and
+
+ align:start position:0%
+high makes is that conduction and
+ 
+
+ align:start position:0%
+high makes is that conduction and
+ventilation depend on the temperature
+
+ align:start position:0%
+ventilation depend on the temperature
+ 
+
+ align:start position:0%
+ventilation depend on the temperature
+difference between inside and outside
+
+ align:start position:0%
+difference between inside and outside
+ 
+
+ align:start position:0%
+difference between inside and outside
+temperature our radiation depends on the
+
+ align:start position:0%
+temperature our radiation depends on the
+ 
+
+ align:start position:0%
+temperature our radiation depends on the
+area so you have this kind of basic
+
+ align:start position:0%
+area so you have this kind of basic
+ 
+
+ align:start position:0%
+area so you have this kind of basic
+breakdown of some of the factors
+
+ align:start position:0%
+breakdown of some of the factors
+ 
+
+ align:start position:0%
+breakdown of some of the factors
+involved conduction is area times a u
+
+ align:start position:0%
+involved conduction is area times a u
+ 
+
+ align:start position:0%
+involved conduction is area times a u
+value times the
+
+ align:start position:0%
+value times the
+ 
+
+ align:start position:0%
+value times the
+um difference in temperature times time
+
+ align:start position:0%
+um difference in temperature times time
+ 
+
+ align:start position:0%
+um difference in temperature times time
+ventilation is the volume times the rate
+
+ align:start position:0%
+ventilation is the volume times the rate
+ 
+
+ align:start position:0%
+ventilation is the volume times the rate
+I think that the volume is uh being
+
+ align:start position:0%
+I think that the volume is uh being
+ 
+
+ align:start position:0%
+I think that the volume is uh being
+moved out or sorry the a number of ways
+
+ align:start position:0%
+moved out or sorry the a number of ways
+ 
+
+ align:start position:0%
+moved out or sorry the a number of ways
+energy could be lost times delta T times
+
+ align:start position:0%
+energy could be lost times delta T times
+ 
+
+ align:start position:0%
+energy could be lost times delta T times
+time and radiation is area times solar
+
+ align:start position:0%
+time and radiation is area times solar
+ 
+
+ align:start position:0%
+time and radiation is area times solar
+density of course the way it's written
+
+ align:start position:0%
+density of course the way it's written
+ 
+
+ align:start position:0%
+density of course the way it's written
+here in Makai is to highlight the fact
+
+ align:start position:0%
+here in Makai is to highlight the fact
+ 
+
+ align:start position:0%
+here in Makai is to highlight the fact
+that induction and ventilation both
+
+ align:start position:0%
+that induction and ventilation both
+ 
+
+ align:start position:0%
+that induction and ventilation both
+depend on the delta T the Delta
+
+ align:start position:0%
+depend on the delta T the Delta
+ 
+
+ align:start position:0%
+depend on the delta T the Delta
+temperature times time
+
+ align:start position:0%
+temperature times time
+ 
+
+ align:start position:0%
+temperature times time
+and so this is how Makai basically
+
+ align:start position:0%
+and so this is how Makai basically
+ 
+
+ align:start position:0%
+and so this is how Makai basically
+breaks down how his house lost energy in
+
+ align:start position:0%
+breaks down how his house lost energy in
+ 
+
+ align:start position:0%
+breaks down how his house lost energy in
+2007 and how he tries to tackle this
+
+ align:start position:0%
+2007 and how he tries to tackle this
+ 
+
+ align:start position:0%
+2007 and how he tries to tackle this
+problem of Energy Efficiency he breaks
+
+ align:start position:0%
+problem of Energy Efficiency he breaks
+ 
+
+ align:start position:0%
+problem of Energy Efficiency he breaks
+down the horizontal surfaces to the
+
+ align:start position:0%
+down the horizontal surfaces to the
+ 
+
+ align:start position:0%
+down the horizontal surfaces to the
+roofs the floors vertical surfaces to
+
+ align:start position:0%
+roofs the floors vertical surfaces to
+ 
+
+ align:start position:0%
+roofs the floors vertical surfaces to
+the walls pin walls blade doors windows
+
+ align:start position:0%
+the walls pin walls blade doors windows
+ 
+
+ align:start position:0%
+the walls pin walls blade doors windows
+double blade windows and then calculates
+
+ align:start position:0%
+double blade windows and then calculates
+ 
+
+ align:start position:0%
+double blade windows and then calculates
+the leakiness and this is the number of
+
+ align:start position:0%
+the leakiness and this is the number of
+ 
+
+ align:start position:0%
+the leakiness and this is the number of
+air changes per hour so you can
+
+ align:start position:0%
+air changes per hour so you can
+ 
+
+ align:start position:0%
+air changes per hour so you can
+calculate the meters squared in terms of
+
+ align:start position:0%
+calculate the meters squared in terms of
+ 
+
+ align:start position:0%
+calculate the meters squared in terms of
+area the U value is a indication of the
+
+ align:start position:0%
+area the U value is a indication of the
+ 
+
+ align:start position:0%
+area the U value is a indication of the
+power transfer ending on difference in
+
+ align:start position:0%
+power transfer ending on difference in
+ 
+
+ align:start position:0%
+power transfer ending on difference in
+temperature so it's watts per meter
+
+ align:start position:0%
+temperature so it's watts per meter
+ 
+
+ align:start position:0%
+temperature so it's watts per meter
+Square divided by degrees Celsius and
+
+ align:start position:0%
+Square divided by degrees Celsius and
+ 
+
+ align:start position:0%
+Square divided by degrees Celsius and
+that gives us leakiness if we multiply
+
+ align:start position:0%
+that gives us leakiness if we multiply
+ 
+
+ align:start position:0%
+that gives us leakiness if we multiply
+area times U value of Watts which is the
+
+ align:start position:0%
+area times U value of Watts which is the
+ 
+
+ align:start position:0%
+area times U value of Watts which is the
+power being lost for every degree
+
+ align:start position:0%
+power being lost for every degree
+ 
+
+ align:start position:0%
+power being lost for every degree
+celsius difference
+
+ align:start position:0%
+celsius difference
+ 
+
+ align:start position:0%
+celsius difference
+and it was a ventilation we have the
+
+ align:start position:0%
+and it was a ventilation we have the
+ 
+
+ align:start position:0%
+and it was a ventilation we have the
+number of air changes per hour so we
+
+ align:start position:0%
+number of air changes per hour so we
+ 
+
+ align:start position:0%
+number of air changes per hour so we
+have a volume of 80 meters cubed in the
+
+ align:start position:0%
+have a volume of 80 meters cubed in the
+ 
+
+ align:start position:0%
+have a volume of 80 meters cubed in the
+bedrooms we want to change the air in
+
+ align:start position:0%
+bedrooms we want to change the air in
+ 
+
+ align:start position:0%
+bedrooms we want to change the air in
+there a half every per hour or change
+
+ align:start position:0%
+there a half every per hour or change
+ 
+
+ align:start position:0%
+there a half every per hour or change
+the entire room volume once every two
+
+ align:start position:0%
+the entire room volume once every two
+ 
+
+ align:start position:0%
+the entire room volume once every two
+hours and that gives us leakiness in
+
+ align:start position:0%
+hours and that gives us leakiness in
+ 
+
+ align:start position:0%
+hours and that gives us leakiness in
+terms of what herb degrees Celsius
+
+ align:start position:0%
+terms of what herb degrees Celsius
+ 
+
+ align:start position:0%
+terms of what herb degrees Celsius
+what Makai calculates is that the main
+
+ align:start position:0%
+what Makai calculates is that the main
+ 
+
+ align:start position:0%
+what Makai calculates is that the main
+way is that he loses heat in his house
+
+ align:start position:0%
+way is that he loses heat in his house
+ 
+
+ align:start position:0%
+way is that he loses heat in his house
+in Cambridge the UK which is similar to
+
+ align:start position:0%
+in Cambridge the UK which is similar to
+ 
+
+ align:start position:0%
+in Cambridge the UK which is similar to
+the climate of Boston that is losing
+
+ align:start position:0%
+the climate of Boston that is losing
+ 
+
+ align:start position:0%
+the climate of Boston that is losing
+about 78 percent of its energy through
+
+ align:start position:0%
+about 78 percent of its energy through
+ 
+
+ align:start position:0%
+about 78 percent of its energy through
+conduction and about 22 percent of its
+
+ align:start position:0%
+conduction and about 22 percent of its
+ 
+
+ align:start position:0%
+conduction and about 22 percent of its
+energy through ventilation changes
+
+ align:start position:0%
+energy through ventilation changes
+ 
+
+ align:start position:0%
+energy through ventilation changes
+and so what he does to try to reduce the
+
+ align:start position:0%
+and so what he does to try to reduce the
+ 
+
+ align:start position:0%
+and so what he does to try to reduce the
+energy loss of his house is to add
+
+ align:start position:0%
+energy loss of his house is to add
+ 
+
+ align:start position:0%
+energy loss of his house is to add
+cavity wall insulation he increases the
+
+ align:start position:0%
+cavity wall insulation he increases the
+ 
+
+ align:start position:0%
+cavity wall insulation he increases the
+roof insulation he adds a new storm door
+
+ align:start position:0%
+roof insulation he adds a new storm door
+ 
+
+ align:start position:0%
+roof insulation he adds a new storm door
+and he replaces the back door and window
+
+ align:start position:0%
+and he replaces the back door and window
+ 
+
+ align:start position:0%
+and he replaces the back door and window
+with double glazed windows I want to
+
+ align:start position:0%
+with double glazed windows I want to
+ 
+
+ align:start position:0%
+with double glazed windows I want to
+emphasize here that Energy Efficiency is
+
+ align:start position:0%
+emphasize here that Energy Efficiency is
+ 
+
+ align:start position:0%
+emphasize here that Energy Efficiency is
+not necessarily A high-tech Endeavor it
+
+ align:start position:0%
+not necessarily A high-tech Endeavor it
+ 
+
+ align:start position:0%
+not necessarily A high-tech Endeavor it
+can be a high-tech Endeavor but at the
+
+ align:start position:0%
+can be a high-tech Endeavor but at the
+ 
+
+ align:start position:0%
+can be a high-tech Endeavor but at the
+same time all these things that he does
+
+ align:start position:0%
+same time all these things that he does
+ 
+
+ align:start position:0%
+same time all these things that he does
+in 2007 are fairly simple things this is
+
+ align:start position:0%
+in 2007 are fairly simple things this is
+ 
+
+ align:start position:0%
+in 2007 are fairly simple things this is
+essentially a technology that you can
+
+ align:start position:0%
+essentially a technology that you can
+ 
+
+ align:start position:0%
+essentially a technology that you can
+acquire from your hardware store having
+
+ align:start position:0%
+acquire from your hardware store having
+ 
+
+ align:start position:0%
+acquire from your hardware store having
+said that there are startups that
+
+ align:start position:0%
+said that there are startups that
+ 
+
+ align:start position:0%
+said that there are startups that
+actually drive cars around like the
+
+ align:start position:0%
+actually drive cars around like the
+ 
+
+ align:start position:0%
+actually drive cars around like the
+Google cars that do street view and they
+
+ align:start position:0%
+Google cars that do street view and they
+ 
+
+ align:start position:0%
+Google cars that do street view and they
+actually measure the
+
+ align:start position:0%
+actually measure the
+ 
+
+ align:start position:0%
+actually measure the
+inductive and radiative losses of houses
+
+ align:start position:0%
+inductive and radiative losses of houses
+ 
+
+ align:start position:0%
+inductive and radiative losses of houses
+using infrared cameras or guns and so
+
+ align:start position:0%
+using infrared cameras or guns and so
+ 
+
+ align:start position:0%
+using infrared cameras or guns and so
+you can basically drive around and map
+
+ align:start position:0%
+you can basically drive around and map
+ 
+
+ align:start position:0%
+you can basically drive around and map
+out the city from the street and see
+
+ align:start position:0%
+out the city from the street and see
+ 
+
+ align:start position:0%
+out the city from the street and see
+where people lose energy and there's a
+
+ align:start position:0%
+where people lose energy and there's a
+ 
+
+ align:start position:0%
+where people lose energy and there's a
+number of energy startups I think that
+
+ align:start position:0%
+number of energy startups I think that
+ 
+
+ align:start position:0%
+number of energy startups I think that
+are trying to use that technology to try
+
+ align:start position:0%
+are trying to use that technology to try
+ 
+
+ align:start position:0%
+are trying to use that technology to try
+to identify homes that might be
+
+ align:start position:0%
+to identify homes that might be
+ 
+
+ align:start position:0%
+to identify homes that might be
+to essentially acquire a customer for
+
+ align:start position:0%
+to essentially acquire a customer for
+ 
+
+ align:start position:0%
+to essentially acquire a customer for
+Energy Efficiency
+
+ align:start position:0%
+Energy Efficiency
+ 
+
+ align:start position:0%
+Energy Efficiency
+so just to give you a sense of what's
+
+ align:start position:0%
+so just to give you a sense of what's
+ 
+
+ align:start position:0%
+so just to give you a sense of what's
+possible with Energy Efficiency measures
+
+ align:start position:0%
+possible with Energy Efficiency measures
+ 
+
+ align:start position:0%
+possible with Energy Efficiency measures
+now this is uh from a old report I think
+
+ align:start position:0%
+now this is uh from a old report I think
+ 
+
+ align:start position:0%
+now this is uh from a old report I think
+it's from one of the National Labs and
+
+ align:start position:0%
+it's from one of the National Labs and
+ 
+
+ align:start position:0%
+it's from one of the National Labs and
+this shows actually we have an R value
+
+ align:start position:0%
+this shows actually we have an R value
+ 
+
+ align:start position:0%
+this shows actually we have an R value
+which is a resistance value or one over
+
+ align:start position:0%
+which is a resistance value or one over
+ 
+
+ align:start position:0%
+which is a resistance value or one over
+the U value one over the leakiness
+
+ align:start position:0%
+the U value one over the leakiness
+ 
+
+ align:start position:0%
+the U value one over the leakiness
+and you can see that the Technologies
+
+ align:start position:0%
+and you can see that the Technologies
+ 
+
+ align:start position:0%
+and you can see that the Technologies
+here are basically net energy losers but
+
+ align:start position:0%
+here are basically net energy losers but
+ 
+
+ align:start position:0%
+here are basically net energy losers but
+they are decreasing amounts or
+
+ align:start position:0%
+they are decreasing amounts or
+ 
+
+ align:start position:0%
+they are decreasing amounts or
+increasing amounts of resistance over
+
+ align:start position:0%
+increasing amounts of resistance over
+ 
+
+ align:start position:0%
+increasing amounts of resistance over
+time starting 1970 going from 1990 we
+
+ align:start position:0%
+time starting 1970 going from 1990 we
+ 
+
+ align:start position:0%
+time starting 1970 going from 1990 we
+have very poor single pane windows we
+
+ align:start position:0%
+have very poor single pane windows we
+ 
+
+ align:start position:0%
+have very poor single pane windows we
+get a much better improvement from
+
+ align:start position:0%
+get a much better improvement from
+ 
+
+ align:start position:0%
+get a much better improvement from
+developing windows but we're getting to
+
+ align:start position:0%
+developing windows but we're getting to
+ 
+
+ align:start position:0%
+developing windows but we're getting to
+low e-windows super windows and super
+
+ align:start position:0%
+low e-windows super windows and super
+ 
+
+ align:start position:0%
+low e-windows super windows and super
+windows that are essentially net energy
+
+ align:start position:0%
+windows that are essentially net energy
+ 
+
+ align:start position:0%
+windows that are essentially net energy
+losers but we're decreasing how much
+
+ align:start position:0%
+losers but we're decreasing how much
+ 
+
+ align:start position:0%
+losers but we're decreasing how much
+we're losing in projected time I guess
+
+ align:start position:0%
+we're losing in projected time I guess
+ 
+
+ align:start position:0%
+we're losing in projected time I guess
+after the um in the last 10 years we're
+
+ align:start position:0%
+after the um in the last 10 years we're
+ 
+
+ align:start position:0%
+after the um in the last 10 years we're
+expected to get to a very high
+
+ align:start position:0%
+expected to get to a very high
+ 
+
+ align:start position:0%
+expected to get to a very high
+resistance super windows and so I'm not
+
+ align:start position:0%
+resistance super windows and so I'm not
+ 
+
+ align:start position:0%
+resistance super windows and so I'm not
+quite sure the current state of
+
+ align:start position:0%
+quite sure the current state of
+ 
+
+ align:start position:0%
+quite sure the current state of
+Technology but I suspect that we are
+
+ align:start position:0%
+Technology but I suspect that we are
+ 
+
+ align:start position:0%
+Technology but I suspect that we are
+well above where we were double paying
+
+ align:start position:0%
+well above where we were double paying
+ 
+
+ align:start position:0%
+well above where we were double paying
+with those
+
+ align:start position:0%
+with those
+ 
+
+ align:start position:0%
+with those
+and just to give you a sense of some of
+
+ align:start position:0%
+and just to give you a sense of some of
+ 
+
+ align:start position:0%
+and just to give you a sense of some of
+the r values included in a model model
+
+ align:start position:0%
+the r values included in a model model
+ 
+
+ align:start position:0%
+the r values included in a model model
+building code one area that's I've said
+
+ align:start position:0%
+building code one area that's I've said
+ 
+
+ align:start position:0%
+building code one area that's I've said
+too that local governments and cities
+
+ align:start position:0%
+too that local governments and cities
+ 
+
+ align:start position:0%
+too that local governments and cities
+can actually do a lot of work or you
+
+ align:start position:0%
+can actually do a lot of work or you
+ 
+
+ align:start position:0%
+can actually do a lot of work or you
+implement policies that actually change
+
+ align:start position:0%
+implement policies that actually change
+ 
+
+ align:start position:0%
+implement policies that actually change
+the building stock are there building
+
+ align:start position:0%
+the building stock are there building
+ 
+
+ align:start position:0%
+the building stock are there building
+codes all of our all of our buildings
+
+ align:start position:0%
+codes all of our all of our buildings
+ 
+
+ align:start position:0%
+codes all of our all of our buildings
+have to be built to a fire code and
+
+ align:start position:0%
+have to be built to a fire code and
+ 
+
+ align:start position:0%
+have to be built to a fire code and
+electrical code in the places that have
+
+ align:start position:0%
+electrical code in the places that have
+ 
+
+ align:start position:0%
+electrical code in the places that have
+earthquakes a seismic code these are the
+
+ align:start position:0%
+earthquakes a seismic code these are the
+ 
+
+ align:start position:0%
+earthquakes a seismic code these are the
+fundamental codes that govern how our
+
+ align:start position:0%
+fundamental codes that govern how our
+ 
+
+ align:start position:0%
+fundamental codes that govern how our
+buildings are built in Florida after
+
+ align:start position:0%
+buildings are built in Florida after
+ 
+
+ align:start position:0%
+buildings are built in Florida after
+Hurricane Andrew 1992 it actually
+
+ align:start position:0%
+Hurricane Andrew 1992 it actually
+ 
+
+ align:start position:0%
+Hurricane Andrew 1992 it actually
+developed some of the strongest building
+
+ align:start position:0%
+developed some of the strongest building
+ 
+
+ align:start position:0%
+developed some of the strongest building
+codes in the country because the
+
+ align:start position:0%
+codes in the country because the
+ 
+
+ align:start position:0%
+codes in the country because the
+hurricane revealed that relatively
+
+ align:start position:0%
+hurricane revealed that relatively
+ 
+
+ align:start position:0%
+hurricane revealed that relatively
+simple interventions in the building
+
+ align:start position:0%
+simple interventions in the building
+ 
+
+ align:start position:0%
+simple interventions in the building
+code would result in much better and
+
+ align:start position:0%
+code would result in much better and
+ 
+
+ align:start position:0%
+code would result in much better and
+stronger homes
+
+ align:start position:0%
+stronger homes
+ 
+
+ align:start position:0%
+stronger homes
+but this is also a key area where local
+
+ align:start position:0%
+but this is also a key area where local
+ 
+
+ align:start position:0%
+but this is also a key area where local
+governments and cities have jurisdiction
+
+ align:start position:0%
+governments and cities have jurisdiction
+ 
+
+ align:start position:0%
+governments and cities have jurisdiction
+they are allowed to actually Implement
+
+ align:start position:0%
+they are allowed to actually Implement
+ 
+
+ align:start position:0%
+they are allowed to actually Implement
+building codes in a way that the state
+
+ align:start position:0%
+building codes in a way that the state
+ 
+
+ align:start position:0%
+building codes in a way that the state
+and federal governments cannot so just
+
+ align:start position:0%
+and federal governments cannot so just
+ 
+
+ align:start position:0%
+and federal governments cannot so just
+to give you a sense of the r values in
+
+ align:start position:0%
+to give you a sense of the r values in
+ 
+
+ align:start position:0%
+to give you a sense of the r values in
+model buildings based on what two
+
+ align:start position:0%
+model buildings based on what two
+ 
+
+ align:start position:0%
+model buildings based on what two
+International energy conservation codes
+
+ align:start position:0%
+International energy conservation codes
+ 
+
+ align:start position:0%
+International energy conservation codes
+require there's a there's a code from
+
+ align:start position:0%
+require there's a there's a code from
+ 
+
+ align:start position:0%
+require there's a there's a code from
+2000 there's an upgraded code in 2012
+
+ align:start position:0%
+2000 there's an upgraded code in 2012
+ 
+
+ align:start position:0%
+2000 there's an upgraded code in 2012
+and there's proposed changes further
+
+ align:start position:0%
+and there's proposed changes further
+ 
+
+ align:start position:0%
+and there's proposed changes further
+this has been a key area of research in
+
+ align:start position:0%
+this has been a key area of research in
+ 
+
+ align:start position:0%
+this has been a key area of research in
+the last 10 or 12 years the federal
+
+ align:start position:0%
+the last 10 or 12 years the federal
+ 
+
+ align:start position:0%
+the last 10 or 12 years the federal
+government since the era stimulus and
+
+ align:start position:0%
+government since the era stimulus and
+ 
+
+ align:start position:0%
+government since the era stimulus and
+the Obama Administration has pushed
+
+ align:start position:0%
+the Obama Administration has pushed
+ 
+
+ align:start position:0%
+the Obama Administration has pushed
+building codes very hard to improve very
+
+ align:start position:0%
+building codes very hard to improve very
+ 
+
+ align:start position:0%
+building codes very hard to improve very
+quickly so you can see that the r values
+
+ align:start position:0%
+quickly so you can see that the r values
+ 
+
+ align:start position:0%
+quickly so you can see that the r values
+of ceilings have essentially doubled
+
+ align:start position:0%
+of ceilings have essentially doubled
+ 
+
+ align:start position:0%
+of ceilings have essentially doubled
+from 2000 to the proposed code from this
+
+ align:start position:0%
+from 2000 to the proposed code from this
+ 
+
+ align:start position:0%
+from 2000 to the proposed code from this
+golbossier access paper
+
+ align:start position:0%
+golbossier access paper
+ 
+
+ align:start position:0%
+golbossier access paper
+you can see that above ground walls have
+
+ align:start position:0%
+you can see that above ground walls have
+ 
+
+ align:start position:0%
+you can see that above ground walls have
+essentially tripled in the resistance to
+
+ align:start position:0%
+essentially tripled in the resistance to
+ 
+
+ align:start position:0%
+essentially tripled in the resistance to
+heat losses basement walls have
+
+ align:start position:0%
+heat losses basement walls have
+ 
+
+ align:start position:0%
+heat losses basement walls have
+essentially doubled floors have doubled
+
+ align:start position:0%
+essentially doubled floors have doubled
+ 
+
+ align:start position:0%
+essentially doubled floors have doubled
+roofs have doubles and mass walls have
+
+ align:start position:0%
+roofs have doubles and mass walls have
+ 
+
+ align:start position:0%
+roofs have doubles and mass walls have
+developed a code value for the first
+
+ align:start position:0%
+developed a code value for the first
+ 
+
+ align:start position:0%
+developed a code value for the first
+time these are all ways that when the
+
+ align:start position:0%
+time these are all ways that when the
+ 
+
+ align:start position:0%
+time these are all ways that when the
+local government simply specifies you
+
+ align:start position:0%
+local government simply specifies you
+ 
+
+ align:start position:0%
+local government simply specifies you
+have to build the standard that the
+
+ align:start position:0%
+have to build the standard that the
+ 
+
+ align:start position:0%
+have to build the standard that the
+local development industry and
+
+ align:start position:0%
+local development industry and
+ 
+
+ align:start position:0%
+local development industry and
+contractors have to respond to that
+
+ align:start position:0%
+contractors have to respond to that
+ 
+
+ align:start position:0%
+contractors have to respond to that
+so this is why I had you calculate 15
+
+ align:start position:0%
+so this is why I had you calculate 15
+ 
+
+ align:start position:0%
+so this is why I had you calculate 15
+degree days in the problem set if you
+
+ align:start position:0%
+degree days in the problem set if you
+ 
+
+ align:start position:0%
+degree days in the problem set if you
+look at makai's house he shows that in
+
+ align:start position:0%
+look at makai's house he shows that in
+ 
+
+ align:start position:0%
+look at makai's house he shows that in
+Cambridge which again is similar to the
+
+ align:start position:0%
+Cambridge which again is similar to the
+ 
+
+ align:start position:0%
+Cambridge which again is similar to the
+climate of Boston for the most of the
+
+ align:start position:0%
+climate of Boston for the most of the
+ 
+
+ align:start position:0%
+climate of Boston for the most of the
+year you can see that he's doing Heating
+
+ align:start position:0%
+year you can see that he's doing Heating
+ 
+
+ align:start position:0%
+year you can see that he's doing Heating
+in his house he has 3 200 Degree Days of
+
+ align:start position:0%
+in his house he has 3 200 Degree Days of
+ 
+
+ align:start position:0%
+in his house he has 3 200 Degree Days of
+heating and about 91 degrees of cooling
+
+ align:start position:0%
+heating and about 91 degrees of cooling
+ 
+
+ align:start position:0%
+heating and about 91 degrees of cooling
+required if you look at
+
+ align:start position:0%
+required if you look at
+ 
+
+ align:start position:0%
+required if you look at
+um I think what happens after his Energy
+
+ align:start position:0%
+um I think what happens after his Energy
+ 
+
+ align:start position:0%
+um I think what happens after his Energy
+Efficiency installations he goes to
+
+ align:start position:0%
+Efficiency installations he goes to
+ 
+
+ align:start position:0%
+Efficiency installations he goes to
+about 22 or 2300 degrees days of heating
+
+ align:start position:0%
+about 22 or 2300 degrees days of heating
+ 
+
+ align:start position:0%
+about 22 or 2300 degrees days of heating
+and is unaffected by cooling but this is
+
+ align:start position:0%
+and is unaffected by cooling but this is
+ 
+
+ align:start position:0%
+and is unaffected by cooling but this is
+to say that if you simply change the
+
+ align:start position:0%
+to say that if you simply change the
+ 
+
+ align:start position:0%
+to say that if you simply change the
+base temperature which is what I did
+
+ align:start position:0%
+base temperature which is what I did
+ 
+
+ align:start position:0%
+base temperature which is what I did
+what you did the problem set you can
+
+ align:start position:0%
+what you did the problem set you can
+ 
+
+ align:start position:0%
+what you did the problem set you can
+actually reduce how much time is heating
+
+ align:start position:0%
+actually reduce how much time is heating
+ 
+
+ align:start position:0%
+actually reduce how much time is heating
+which is to say that we measure
+
+ align:start position:0%
+which is to say that we measure
+ 
+
+ align:start position:0%
+which is to say that we measure
+everything against the temperature we'd
+
+ align:start position:0%
+everything against the temperature we'd
+ 
+
+ align:start position:0%
+everything against the temperature we'd
+like to keep our indoor temperature at
+
+ align:start position:0%
+like to keep our indoor temperature at
+ 
+
+ align:start position:0%
+like to keep our indoor temperature at
+so this looks like around 65 degrees and
+
+ align:start position:0%
+so this looks like around 65 degrees and
+ 
+
+ align:start position:0%
+so this looks like around 65 degrees and
+this is about 2 degrees Celsius lower
+
+ align:start position:0%
+this is about 2 degrees Celsius lower
+ 
+
+ align:start position:0%
+this is about 2 degrees Celsius lower
+and you simply change the thermostat
+
+ align:start position:0%
+and you simply change the thermostat
+ 
+
+ align:start position:0%
+and you simply change the thermostat
+setting what you're trying you target
+
+ align:start position:0%
+setting what you're trying you target
+ 
+
+ align:start position:0%
+setting what you're trying you target
+for maintaining indoor temperature you
+
+ align:start position:0%
+for maintaining indoor temperature you
+ 
+
+ align:start position:0%
+for maintaining indoor temperature you
+can actually significantly decrease the
+
+ align:start position:0%
+can actually significantly decrease the
+ 
+
+ align:start position:0%
+can actually significantly decrease the
+amount of heating or cooling required to
+
+ align:start position:0%
+amount of heating or cooling required to
+ 
+
+ align:start position:0%
+amount of heating or cooling required to
+make up that heat loss remember that we
+
+ align:start position:0%
+make up that heat loss remember that we
+ 
+
+ align:start position:0%
+make up that heat loss remember that we
+looked at conduction and radiation
+
+ align:start position:0%
+looked at conduction and radiation
+ 
+
+ align:start position:0%
+looked at conduction and radiation
+dependent on the delta T times time if
+
+ align:start position:0%
+dependent on the delta T times time if
+ 
+
+ align:start position:0%
+dependent on the delta T times time if
+we change simply the delta T that we're
+
+ align:start position:0%
+we change simply the delta T that we're
+ 
+
+ align:start position:0%
+we change simply the delta T that we're
+trying to eat or cool to that we can
+
+ align:start position:0%
+trying to eat or cool to that we can
+ 
+
+ align:start position:0%
+trying to eat or cool to that we can
+reduce a lot of our Heating and Cooling
+
+ align:start position:0%
+reduce a lot of our Heating and Cooling
+ 
+
+ align:start position:0%
+reduce a lot of our Heating and Cooling
+energy use
+
+ align:start position:0%
+energy use
+ 
+
+ align:start position:0%
+energy use
+this is also why there's a very large
+
+ align:start position:0%
+this is also why there's a very large
+ 
+
+ align:start position:0%
+this is also why there's a very large
+push on heat pumps this is a diagram
+
+ align:start position:0%
+push on heat pumps this is a diagram
+ 
+
+ align:start position:0%
+push on heat pumps this is a diagram
+from a book from Randolph and Masters
+
+ align:start position:0%
+from a book from Randolph and Masters
+ 
+
+ align:start position:0%
+from a book from Randolph and Masters
+I mean basically have this very simple
+
+ align:start position:0%
+I mean basically have this very simple
+ 
+
+ align:start position:0%
+I mean basically have this very simple
+diagram that I like it basically shows
+
+ align:start position:0%
+diagram that I like it basically shows
+ 
+
+ align:start position:0%
+diagram that I like it basically shows
+how refrigerator acts as an air
+
+ align:start position:0%
+how refrigerator acts as an air
+ 
+
+ align:start position:0%
+how refrigerator acts as an air
+conditioner but it heats the world where
+
+ align:start position:0%
+conditioner but it heats the world where
+ 
+
+ align:start position:0%
+conditioner but it heats the world where
+air conditioning the space inside a
+
+ align:start position:0%
+air conditioning the space inside a
+ 
+
+ align:start position:0%
+air conditioning the space inside a
+refrigerator and the back of your
+
+ align:start position:0%
+refrigerator and the back of your
+ 
+
+ align:start position:0%
+refrigerator and the back of your
+refrigerator is rejecting heat of course
+
+ align:start position:0%
+refrigerator is rejecting heat of course
+ 
+
+ align:start position:0%
+refrigerator is rejecting heat of course
+we can flip this thing around and we
+
+ align:start position:0%
+we can flip this thing around and we
+ 
+
+ align:start position:0%
+we can flip this thing around and we
+could actually heat cool the outside
+
+ align:start position:0%
+could actually heat cool the outside
+ 
+
+ align:start position:0%
+could actually heat cool the outside
+world and keep the inside of our house
+
+ align:start position:0%
+world and keep the inside of our house
+ 
+
+ align:start position:0%
+world and keep the inside of our house
+this is essentially how a heat pump
+
+ align:start position:0%
+this is essentially how a heat pump
+ 
+
+ align:start position:0%
+this is essentially how a heat pump
+works it's the same thing as a
+
+ align:start position:0%
+works it's the same thing as a
+ 
+
+ align:start position:0%
+works it's the same thing as a
+refrigerator the same thing as an air
+
+ align:start position:0%
+refrigerator the same thing as an air
+ 
+
+ align:start position:0%
+refrigerator the same thing as an air
+conditioner but the key difference in a
+
+ align:start position:0%
+conditioner but the key difference in a
+ 
+
+ align:start position:0%
+conditioner but the key difference in a
+heat pump is you can operate it both
+
+ align:start position:0%
+heat pump is you can operate it both
+ 
+
+ align:start position:0%
+heat pump is you can operate it both
+directions I think I told you the story
+
+ align:start position:0%
+directions I think I told you the story
+ 
+
+ align:start position:0%
+directions I think I told you the story
+before of research I did in Brazil that
+
+ align:start position:0%
+before of research I did in Brazil that
+ 
+
+ align:start position:0%
+before of research I did in Brazil that
+looked at electricity use in informal
+
+ align:start position:0%
+looked at electricity use in informal
+ 
+
+ align:start position:0%
+looked at electricity use in informal
+settlements and informal settlement log
+
+ align:start position:0%
+settlements and informal settlement log
+ 
+
+ align:start position:0%
+settlements and informal settlement log
+tool don't pay for their electricity use
+
+ align:start position:0%
+tool don't pay for their electricity use
+ 
+
+ align:start position:0%
+tool don't pay for their electricity use
+40 of all electricity in Brazil is
+
+ align:start position:0%
+40 of all electricity in Brazil is
+ 
+
+ align:start position:0%
+40 of all electricity in Brazil is
+unpaid for or stolen from the grid and
+
+ align:start position:0%
+unpaid for or stolen from the grid and
+ 
+
+ align:start position:0%
+unpaid for or stolen from the grid and
+so people actually have very little
+
+ align:start position:0%
+so people actually have very little
+ 
+
+ align:start position:0%
+so people actually have very little
+incentive to save energy so people use
+
+ align:start position:0%
+incentive to save energy so people use
+ 
+
+ align:start position:0%
+incentive to save energy so people use
+their refrigerators not only to store
+
+ align:start position:0%
+their refrigerators not only to store
+ 
+
+ align:start position:0%
+their refrigerators not only to store
+food or to even cool their home because
+
+ align:start position:0%
+food or to even cool their home because
+ 
+
+ align:start position:0%
+food or to even cool their home because
+they can just leave the doors open but
+
+ align:start position:0%
+they can just leave the doors open but
+ 
+
+ align:start position:0%
+they can just leave the doors open but
+people actually use refrigerators to dry
+
+ align:start position:0%
+people actually use refrigerators to dry
+ 
+
+ align:start position:0%
+people actually use refrigerators to dry
+clothes they put dry clothes on the hot
+
+ align:start position:0%
+clothes they put dry clothes on the hot
+ 
+
+ align:start position:0%
+clothes they put dry clothes on the hot
+condenser on the back or the heating
+
+ align:start position:0%
+condenser on the back or the heating
+ 
+
+ align:start position:0%
+condenser on the back or the heating
+cool coils or the radiating heat fins
+
+ align:start position:0%
+cool coils or the radiating heat fins
+ 
+
+ align:start position:0%
+cool coils or the radiating heat fins
+and that those actually radiate heat and
+
+ align:start position:0%
+and that those actually radiate heat and
+ 
+
+ align:start position:0%
+and that those actually radiate heat and
+they use them to dry clothes sometimes
+
+ align:start position:0%
+they use them to dry clothes sometimes
+ 
+
+ align:start position:0%
+they use them to dry clothes sometimes
+so there's been a very large push in
+
+ align:start position:0%
+so there's been a very large push in
+ 
+
+ align:start position:0%
+so there's been a very large push in
+policy now to use heat pumps because
+
+ align:start position:0%
+policy now to use heat pumps because
+ 
+
+ align:start position:0%
+policy now to use heat pumps because
+unlike burning fuels correctly you
+
+ align:start position:0%
+unlike burning fuels correctly you
+ 
+
+ align:start position:0%
+unlike burning fuels correctly you
+actually get about four times more
+
+ align:start position:0%
+actually get about four times more
+ 
+
+ align:start position:0%
+actually get about four times more
+energy uh rather four times the heating
+
+ align:start position:0%
+energy uh rather four times the heating
+ 
+
+ align:start position:0%
+energy uh rather four times the heating
+or cooling effect for the same unit of
+
+ align:start position:0%
+or cooling effect for the same unit of
+ 
+
+ align:start position:0%
+or cooling effect for the same unit of
+energy in a heat pump as the Makai book
+
+ align:start position:0%
+energy in a heat pump as the Makai book
+ 
+
+ align:start position:0%
+energy in a heat pump as the Makai book
+explains why heat pumps are uh what
+
+ align:start position:0%
+explains why heat pumps are uh what
+ 
+
+ align:start position:0%
+explains why heat pumps are uh what
+we're talking about in terms of why
+
+ align:start position:0%
+we're talking about in terms of why
+ 
+
+ align:start position:0%
+we're talking about in terms of why
+we're generating more Heating and
+
+ align:start position:0%
+we're generating more Heating and
+ 
+
+ align:start position:0%
+we're generating more Heating and
+Cooling energy has to do with entropy
+
+ align:start position:0%
+Cooling energy has to do with entropy
+ 
+
+ align:start position:0%
+Cooling energy has to do with entropy
+Makai book goes into more detail if
+
+ align:start position:0%
+Makai book goes into more detail if
+ 
+
+ align:start position:0%
+Makai book goes into more detail if
+you're interested in that
+
+ align:start position:0%
+you're interested in that
+ 
+
+ align:start position:0%
+you're interested in that
+to kind of emphasize why we are trying
+
+ align:start position:0%
+to kind of emphasize why we are trying
+ 
+
+ align:start position:0%
+to kind of emphasize why we are trying
+to treat our climate I think
+
+ align:start position:0%
+to treat our climate I think
+ 
+
+ align:start position:0%
+to treat our climate I think
+instinctively we know that the United
+
+ align:start position:0%
+instinctively we know that the United
+ 
+
+ align:start position:0%
+instinctively we know that the United
+States is defined as quite different
+
+ align:start position:0%
+States is defined as quite different
+ 
+
+ align:start position:0%
+States is defined as quite different
+assignment zones we have a marine zone
+
+ align:start position:0%
+assignment zones we have a marine zone
+ 
+
+ align:start position:0%
+assignment zones we have a marine zone
+or almost Mediterranean Zone on the west
+
+ align:start position:0%
+or almost Mediterranean Zone on the west
+ 
+
+ align:start position:0%
+or almost Mediterranean Zone on the west
+coast we have our very hot dry or mixed
+
+ align:start position:0%
+coast we have our very hot dry or mixed
+ 
+
+ align:start position:0%
+coast we have our very hot dry or mixed
+dry environment we have cold or very
+
+ align:start position:0%
+dry environment we have cold or very
+ 
+
+ align:start position:0%
+dry environment we have cold or very
+cold environment that we're in the Upper
+
+ align:start position:0%
+cold environment that we're in the Upper
+ 
+
+ align:start position:0%
+cold environment that we're in the Upper
+Midwest upper west and New England we
+
+ align:start position:0%
+Midwest upper west and New England we
+ 
+
+ align:start position:0%
+Midwest upper west and New England we
+have a mixed humid climate and we have a
+
+ align:start position:0%
+have a mixed humid climate and we have a
+ 
+
+ align:start position:0%
+have a mixed humid climate and we have a
+hot human planet
+
+ align:start position:0%
+hot human planet
+ 
+
+ align:start position:0%
+hot human planet
+the reason why this matters for building
+
+ align:start position:0%
+the reason why this matters for building
+ 
+
+ align:start position:0%
+the reason why this matters for building
+design or building engineering is that
+
+ align:start position:0%
+design or building engineering is that
+ 
+
+ align:start position:0%
+design or building engineering is that
+Engineers actually use charts that are
+
+ align:start position:0%
+Engineers actually use charts that are
+ 
+
+ align:start position:0%
+Engineers actually use charts that are
+called psychometric charts and those are
+
+ align:start position:0%
+called psychometric charts and those are
+ 
+
+ align:start position:0%
+called psychometric charts and those are
+charts that actually detail how
+
+ align:start position:0%
+charts that actually detail how
+ 
+
+ align:start position:0%
+charts that actually detail how
+comfortable people feel in mixes of
+
+ align:start position:0%
+comfortable people feel in mixes of
+ 
+
+ align:start position:0%
+comfortable people feel in mixes of
+humidity and temperature
+
+ align:start position:0%
+humidity and temperature
+ 
+
+ align:start position:0%
+humidity and temperature
+so the reason why we look at these
+
+ align:start position:0%
+so the reason why we look at these
+ 
+
+ align:start position:0%
+so the reason why we look at these
+different climate zones is that we know
+
+ align:start position:0%
+different climate zones is that we know
+ 
+
+ align:start position:0%
+different climate zones is that we know
+our energy use is closely related to the
+
+ align:start position:0%
+our energy use is closely related to the
+ 
+
+ align:start position:0%
+our energy use is closely related to the
+humidity and temperature of the outdoor
+
+ align:start position:0%
+humidity and temperature of the outdoor
+ 
+
+ align:start position:0%
+humidity and temperature of the outdoor
+environment and that's what our
+
+ align:start position:0%
+environment and that's what our
+ 
+
+ align:start position:0%
+environment and that's what our
+buildings are trying to correct for so
+
+ align:start position:0%
+buildings are trying to correct for so
+ 
+
+ align:start position:0%
+buildings are trying to correct for so
+we know that in hot humid environments
+
+ align:start position:0%
+we know that in hot humid environments
+ 
+
+ align:start position:0%
+we know that in hot humid environments
+or hot dry environments we use much more
+
+ align:start position:0%
+or hot dry environments we use much more
+ 
+
+ align:start position:0%
+or hot dry environments we use much more
+air conditioning we may use
+
+ align:start position:0%
+air conditioning we may use
+ 
+
+ align:start position:0%
+air conditioning we may use
+dehumidifiers or air conditioners may
+
+ align:start position:0%
+dehumidifiers or air conditioners may
+ 
+
+ align:start position:0%
+dehumidifiers or air conditioners may
+have to work differently to account for
+
+ align:start position:0%
+have to work differently to account for
+ 
+
+ align:start position:0%
+have to work differently to account for
+this humid environment
+
+ align:start position:0%
+this humid environment
+ 
+
+ align:start position:0%
+this humid environment
+uh the US eia also it defines these
+
+ align:start position:0%
+uh the US eia also it defines these
+ 
+
+ align:start position:0%
+uh the US eia also it defines these
+climate zones in slightly different ways
+
+ align:start position:0%
+climate zones in slightly different ways
+ 
+
+ align:start position:0%
+climate zones in slightly different ways
+but you can see here on the bottom they
+
+ align:start position:0%
+but you can see here on the bottom they
+ 
+
+ align:start position:0%
+but you can see here on the bottom they
+Define their zones in terms of how many
+
+ align:start position:0%
+Define their zones in terms of how many
+ 
+
+ align:start position:0%
+Define their zones in terms of how many
+cooling Degree Days how many heating
+
+ align:start position:0%
+cooling Degree Days how many heating
+ 
+
+ align:start position:0%
+cooling Degree Days how many heating
+Degree Days our buildings use
+
+ align:start position:0%
+Degree Days our buildings use
+ 
+
+ align:start position:0%
+Degree Days our buildings use
+these numbers actually factor into how
+
+ align:start position:0%
+these numbers actually factor into how
+ 
+
+ align:start position:0%
+these numbers actually factor into how
+we measure energy star ratings on
+
+ align:start position:0%
+we measure energy star ratings on
+ 
+
+ align:start position:0%
+we measure energy star ratings on
+buildings because we rate buildings
+
+ align:start position:0%
+buildings because we rate buildings
+ 
+
+ align:start position:0%
+buildings because we rate buildings
+according to how effectively their
+
+ align:start position:0%
+according to how effectively their
+ 
+
+ align:start position:0%
+according to how effectively their
+heating or cooling relative to the
+
+ align:start position:0%
+heating or cooling relative to the
+ 
+
+ align:start position:0%
+heating or cooling relative to the
+environment but we also know that our
+
+ align:start position:0%
+environment but we also know that our
+ 
+
+ align:start position:0%
+environment but we also know that our
+commercial buildings for energy star are
+
+ align:start position:0%
+commercial buildings for energy star are
+ 
+
+ align:start position:0%
+commercial buildings for energy star are
+located in many different environments
+
+ align:start position:0%
+located in many different environments
+ 
+
+ align:start position:0%
+located in many different environments
+so we try to score them differently
+
+ align:start position:0%
+so we try to score them differently
+ 
+
+ align:start position:0%
+so we try to score them differently
+so just to show you the reason why I had
+
+ align:start position:0%
+so just to show you the reason why I had
+ 
+
+ align:start position:0%
+so just to show you the reason why I had
+you look at your appliances briefly is
+
+ align:start position:0%
+you look at your appliances briefly is
+ 
+
+ align:start position:0%
+you look at your appliances briefly is
+that Makai estimates the loads from
+
+ align:start position:0%
+that Makai estimates the loads from
+ 
+
+ align:start position:0%
+that Makai estimates the loads from
+various selected appliances and you can
+
+ align:start position:0%
+various selected appliances and you can
+ 
+
+ align:start position:0%
+various selected appliances and you can
+see it's a pretty simple calculation we
+
+ align:start position:0%
+see it's a pretty simple calculation we
+ 
+
+ align:start position:0%
+see it's a pretty simple calculation we
+have these different categories cooking
+
+ align:start position:0%
+have these different categories cooking
+ 
+
+ align:start position:0%
+have these different categories cooking
+cleaning and cooling they have a power
+
+ align:start position:0%
+cleaning and cooling they have a power
+ 
+
+ align:start position:0%
+cleaning and cooling they have a power
+use which is kilowatts or joules per
+
+ align:start position:0%
+use which is kilowatts or joules per
+ 
+
+ align:start position:0%
+use which is kilowatts or joules per
+second we simply multiply times a unit
+
+ align:start position:0%
+second we simply multiply times a unit
+ 
+
+ align:start position:0%
+second we simply multiply times a unit
+of time here hours and then we get
+
+ align:start position:0%
+of time here hours and then we get
+ 
+
+ align:start position:0%
+of time here hours and then we get
+kilowatt hours which are a measure of
+
+ align:start position:0%
+kilowatt hours which are a measure of
+ 
+
+ align:start position:0%
+kilowatt hours which are a measure of
+energy per person per day and so we just
+
+ align:start position:0%
+energy per person per day and so we just
+ 
+
+ align:start position:0%
+energy per person per day and so we just
+multiply a spreadsheet you can see that
+
+ align:start position:0%
+multiply a spreadsheet you can see that
+ 
+
+ align:start position:0%
+multiply a spreadsheet you can see that
+the largest users of energy are the
+
+ align:start position:0%
+the largest users of energy are the
+ 
+
+ align:start position:0%
+the largest users of energy are the
+tumble dryer the freezer the electric
+
+ align:start position:0%
+tumble dryer the freezer the electric
+ 
+
+ align:start position:0%
+tumble dryer the freezer the electric
+oven and the electric cooker
+
+ align:start position:0%
+oven and the electric cooker
+ 
+
+ align:start position:0%
+oven and the electric cooker
+you can see it on an annual basis for
+
+ align:start position:0%
+you can see it on an annual basis for
+ 
+
+ align:start position:0%
+you can see it on an annual basis for
+two people you get to about 4 500
+
+ align:start position:0%
+two people you get to about 4 500
+ 
+
+ align:start position:0%
+two people you get to about 4 500
+kilowatt hours per person per year
+
+ align:start position:0%
+kilowatt hours per person per year
+ 
+
+ align:start position:0%
+kilowatt hours per person per year
+that's actually relatively low I think
+
+ align:start position:0%
+that's actually relatively low I think
+ 
+
+ align:start position:0%
+that's actually relatively low I think
+in the US the average household uses
+
+ align:start position:0%
+in the US the average household uses
+ 
+
+ align:start position:0%
+in the US the average household uses
+about 14
+
+ align:start position:0%
+about 14
+ 
+
+ align:start position:0%
+about 14
+000 kilowatt hours per person per year
+
+ align:start position:0%
+000 kilowatt hours per person per year
+ 
+
+ align:start position:0%
+000 kilowatt hours per person per year
+so you can see the average electricity
+
+ align:start position:0%
+so you can see the average electricity
+ 
+
+ align:start position:0%
+so you can see the average electricity
+consumption in the United Kingdom and
+
+ align:start position:0%
+consumption in the United Kingdom and
+ 
+
+ align:start position:0%
+consumption in the United Kingdom and
+Tanzania are relatively lower one reason
+
+ align:start position:0%
+Tanzania are relatively lower one reason
+ 
+
+ align:start position:0%
+Tanzania are relatively lower one reason
+for that might be that makai's house has
+
+ align:start position:0%
+for that might be that makai's house has
+ 
+
+ align:start position:0%
+for that might be that makai's house has
+a party wall built quite densely it's a
+
+ align:start position:0%
+a party wall built quite densely it's a
+ 
+
+ align:start position:0%
+a party wall built quite densely it's a
+relatively small home by American
+
+ align:start position:0%
+relatively small home by American
+ 
+
+ align:start position:0%
+relatively small home by American
+Standards
+
+ align:start position:0%
+Standards
+ 
+
+ align:start position:0%
+Standards
+so just to show you what some of the
+
+ align:start position:0%
+so just to show you what some of the
+ 
+
+ align:start position:0%
+so just to show you what some of the
+Technologies are that might help us
+
+ align:start position:0%
+Technologies are that might help us
+ 
+
+ align:start position:0%
+Technologies are that might help us
+understand how we use energy in
+
+ align:start position:0%
+understand how we use energy in
+ 
+
+ align:start position:0%
+understand how we use energy in
+buildings I'm going to show you some of
+
+ align:start position:0%
+buildings I'm going to show you some of
+ 
+
+ align:start position:0%
+buildings I'm going to show you some of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um devices I use to manage my own home
+
+ align:start position:0%
+um devices I use to manage my own home
+ 
+
+ align:start position:0%
+um devices I use to manage my own home
+mostly out of interest and because I
+
+ align:start position:0%
+mostly out of interest and because I
+ 
+
+ align:start position:0%
+mostly out of interest and because I
+like to show students every year with
+
+ align:start position:0%
+like to show students every year with
+ 
+
+ align:start position:0%
+like to show students every year with
+some of these different Technologies
+
+ align:start position:0%
+some of these different Technologies
+ 
+
+ align:start position:0%
+some of these different Technologies
+look like
+
+ align:start position:0%
+look like
+ 
+
+ align:start position:0%
+look like
+okay so just to show you what some of
+
+ align:start position:0%
+okay so just to show you what some of
+ 
+
+ align:start position:0%
+okay so just to show you what some of
+these Technologies I use to match my
+
+ align:start position:0%
+these Technologies I use to match my
+ 
+
+ align:start position:0%
+these Technologies I use to match my
+home look like
+
+ align:start position:0%
+home look like
+ 
+
+ align:start position:0%
+home look like
+I'm going to show you
+
+ align:start position:0%
+I'm going to show you
+ 
+
+ align:start position:0%
+I'm going to show you
+this is a sense monitor this is actually
+
+ align:start position:0%
+this is a sense monitor this is actually
+ 
+
+ align:start position:0%
+this is a sense monitor this is actually
+a small monitor that I installed in my
+
+ align:start position:0%
+a small monitor that I installed in my
+ 
+
+ align:start position:0%
+a small monitor that I installed in my
+electrical panel box and it basically
+
+ align:start position:0%
+electrical panel box and it basically
+ 
+
+ align:start position:0%
+electrical panel box and it basically
+measures the entire energy use going
+
+ align:start position:0%
+measures the entire energy use going
+ 
+
+ align:start position:0%
+measures the entire energy use going
+from the electrical grid into my house
+
+ align:start position:0%
+from the electrical grid into my house
+ 
+
+ align:start position:0%
+from the electrical grid into my house
+you can see this is a typical day from
+
+ align:start position:0%
+you can see this is a typical day from
+ 
+
+ align:start position:0%
+you can see this is a typical day from
+6am to about midnight and you can see
+
+ align:start position:0%
+6am to about midnight and you can see
+ 
+
+ align:start position:0%
+6am to about midnight and you can see
+several different things happening a
+
+ align:start position:0%
+several different things happening a
+ 
+
+ align:start position:0%
+several different things happening a
+first energy use is pretty low and
+
+ align:start position:0%
+first energy use is pretty low and
+ 
+
+ align:start position:0%
+first energy use is pretty low and
+morning before we wake up other measure
+
+ align:start position:0%
+morning before we wake up other measure
+ 
+
+ align:start position:0%
+morning before we wake up other measure
+as you can see when I'm moving here is
+
+ align:start position:0%
+as you can see when I'm moving here is
+ 
+
+ align:start position:0%
+as you can see when I'm moving here is
+the current meter this measures 500
+
+ align:start position:0%
+the current meter this measures 500
+ 
+
+ align:start position:0%
+the current meter this measures 500
+watts going to the house you see these
+
+ align:start position:0%
+watts going to the house you see these
+ 
+
+ align:start position:0%
+watts going to the house you see these
+occasional small Cycles that's probably
+
+ align:start position:0%
+occasional small Cycles that's probably
+ 
+
+ align:start position:0%
+occasional small Cycles that's probably
+the refrigerator cycling just keep the
+
+ align:start position:0%
+the refrigerator cycling just keep the
+ 
+
+ align:start position:0%
+the refrigerator cycling just keep the
+food cool and then we wake up and we
+
+ align:start position:0%
+food cool and then we wake up and we
+ 
+
+ align:start position:0%
+food cool and then we wake up and we
+start running all our appliances things
+
+ align:start position:0%
+start running all our appliances things
+ 
+
+ align:start position:0%
+start running all our appliances things
+go very high that could be the tumble
+
+ align:start position:0%
+go very high that could be the tumble
+ 
+
+ align:start position:0%
+go very high that could be the tumble
+dryer coming out in the morning it could
+
+ align:start position:0%
+dryer coming out in the morning it could
+ 
+
+ align:start position:0%
+dryer coming out in the morning it could
+be a hair dryer coming on and then this
+
+ align:start position:0%
+be a hair dryer coming on and then this
+ 
+
+ align:start position:0%
+be a hair dryer coming on and then this
+is probably a dishwasher load that we
+
+ align:start position:0%
+is probably a dishwasher load that we
+ 
+
+ align:start position:0%
+is probably a dishwasher load that we
+set when I leave for work you can see
+
+ align:start position:0%
+set when I leave for work you can see
+ 
+
+ align:start position:0%
+set when I leave for work you can see
+throughout the day when we're away at
+
+ align:start position:0%
+throughout the day when we're away at
+ 
+
+ align:start position:0%
+throughout the day when we're away at
+work or school our energy use quite low
+
+ align:start position:0%
+work or school our energy use quite low
+ 
+
+ align:start position:0%
+work or school our energy use quite low
+again these are refrigerator cycling
+
+ align:start position:0%
+again these are refrigerator cycling
+ 
+
+ align:start position:0%
+again these are refrigerator cycling
+going through and then you can see we
+
+ align:start position:0%
+going through and then you can see we
+ 
+
+ align:start position:0%
+going through and then you can see we
+get home around 6 pm and we start
+
+ align:start position:0%
+get home around 6 pm and we start
+ 
+
+ align:start position:0%
+get home around 6 pm and we start
+turning on lights turning on cooking
+
+ align:start position:0%
+turning on lights turning on cooking
+ 
+
+ align:start position:0%
+turning on lights turning on cooking
+devices is in our energy go load goes up
+
+ align:start position:0%
+devices is in our energy go load goes up
+ 
+
+ align:start position:0%
+devices is in our energy go load goes up
+quite a high again let me probably run
+
+ align:start position:0%
+quite a high again let me probably run
+ 
+
+ align:start position:0%
+quite a high again let me probably run
+the dishwasher or the uh tumble dryer at
+
+ align:start position:0%
+the dishwasher or the uh tumble dryer at
+ 
+
+ align:start position:0%
+the dishwasher or the uh tumble dryer at
+the end of the day again this is a small
+
+ align:start position:0%
+the end of the day again this is a small
+ 
+
+ align:start position:0%
+the end of the day again this is a small
+box that it goes into the electrical
+
+ align:start position:0%
+box that it goes into the electrical
+ 
+
+ align:start position:0%
+box that it goes into the electrical
+panel gives me a handy dashboard tells
+
+ align:start position:0%
+panel gives me a handy dashboard tells
+ 
+
+ align:start position:0%
+panel gives me a handy dashboard tells
+me how much energy I'm consuming
+
+ align:start position:0%
+me how much energy I'm consuming
+ 
+
+ align:start position:0%
+me how much energy I'm consuming
+relative to my bill much to my
+
+ align:start position:0%
+relative to my bill much to my
+ 
+
+ align:start position:0%
+relative to my bill much to my
+frustration it shows I'm totally average
+
+ align:start position:0%
+frustration it shows I'm totally average
+ 
+
+ align:start position:0%
+frustration it shows I'm totally average
+and how much energy I use compared to
+
+ align:start position:0%
+and how much energy I use compared to
+ 
+
+ align:start position:0%
+and how much energy I use compared to
+other similar homes I use less than
+
+ align:start position:0%
+other similar homes I use less than
+ 
+
+ align:start position:0%
+other similar homes I use less than
+other sense homes in Massachusetts I use
+
+ align:start position:0%
+other sense homes in Massachusetts I use
+ 
+
+ align:start position:0%
+other sense homes in Massachusetts I use
+yet less than most sense homes all over
+
+ align:start position:0%
+yet less than most sense homes all over
+ 
+
+ align:start position:0%
+yet less than most sense homes all over
+the country but you know it gives me
+
+ align:start position:0%
+the country but you know it gives me
+ 
+
+ align:start position:0%
+the country but you know it gives me
+some useful ways to manage my energy use
+
+ align:start position:0%
+some useful ways to manage my energy use
+ 
+
+ align:start position:0%
+some useful ways to manage my energy use
+shows me when pumps or heat goes on and
+
+ align:start position:0%
+shows me when pumps or heat goes on and
+ 
+
+ align:start position:0%
+shows me when pumps or heat goes on and
+off in my house
+
+ align:start position:0%
+off in my house
+ 
+
+ align:start position:0%
+off in my house
+and it also shows me when certain
+
+ align:start position:0%
+and it also shows me when certain
+ 
+
+ align:start position:0%
+and it also shows me when certain
+appliances are on or how much they use
+
+ align:start position:0%
+appliances are on or how much they use
+ 
+
+ align:start position:0%
+appliances are on or how much they use
+for example always on represents the
+
+ align:start position:0%
+for example always on represents the
+ 
+
+ align:start position:0%
+for example always on represents the
+vampire load these are all the Chargers
+
+ align:start position:0%
+vampire load these are all the Chargers
+ 
+
+ align:start position:0%
+vampire load these are all the Chargers
+that are plugged into all the walls all
+
+ align:start position:0%
+that are plugged into all the walls all
+ 
+
+ align:start position:0%
+that are plugged into all the walls all
+the time this is a point that Makai
+
+ align:start position:0%
+the time this is a point that Makai
+ 
+
+ align:start position:0%
+the time this is a point that Makai
+makes but also shows me how much each of
+
+ align:start position:0%
+makes but also shows me how much each of
+ 
+
+ align:start position:0%
+makes but also shows me how much each of
+the AC units use it showed me how much
+
+ align:start position:0%
+the AC units use it showed me how much
+ 
+
+ align:start position:0%
+the AC units use it showed me how much
+that implies on a bill basis shows me
+
+ align:start position:0%
+that implies on a bill basis shows me
+ 
+
+ align:start position:0%
+that implies on a bill basis shows me
+which appliances use the most and shows
+
+ align:start position:0%
+which appliances use the most and shows
+ 
+
+ align:start position:0%
+which appliances use the most and shows
+me ways I could possibly reduce my
+
+ align:start position:0%
+me ways I could possibly reduce my
+ 
+
+ align:start position:0%
+me ways I could possibly reduce my
+energy consumption here you can see that
+
+ align:start position:0%
+energy consumption here you can see that
+ 
+
+ align:start position:0%
+energy consumption here you can see that
+my clothes dryer I off to about 41
+
+ align:start position:0%
+my clothes dryer I off to about 41
+ 
+
+ align:start position:0%
+my clothes dryer I off to about 41
+dollars per year six percent of my
+
+ align:start position:0%
+dollars per year six percent of my
+ 
+
+ align:start position:0%
+dollars per year six percent of my
+electricity use you can see how many how
+
+ align:start position:0%
+electricity use you can see how many how
+ 
+
+ align:start position:0%
+electricity use you can see how many how
+many times or how often I put it on
+
+ align:start position:0%
+many times or how often I put it on
+ 
+
+ align:start position:0%
+many times or how often I put it on
+another device that I use to measure uh
+
+ align:start position:0%
+another device that I use to measure uh
+ 
+
+ align:start position:0%
+another device that I use to measure uh
+manage our home electricity use is a
+
+ align:start position:0%
+manage our home electricity use is a
+ 
+
+ align:start position:0%
+manage our home electricity use is a
+nest thermostat you can see right now
+
+ align:start position:0%
+nest thermostat you can see right now
+ 
+
+ align:start position:0%
+nest thermostat you can see right now
+the downstairs is set for 65 degrees
+
+ align:start position:0%
+the downstairs is set for 65 degrees
+ 
+
+ align:start position:0%
+the downstairs is set for 65 degrees
+upstairs for 63 degrees because it's
+
+ align:start position:0%
+upstairs for 63 degrees because it's
+ 
+
+ align:start position:0%
+upstairs for 63 degrees because it's
+been hot upstairs during the day very
+
+ align:start position:0%
+been hot upstairs during the day very
+ 
+
+ align:start position:0%
+been hot upstairs during the day very
+much if I click on one of these you can
+
+ align:start position:0%
+much if I click on one of these you can
+ 
+
+ align:start position:0%
+much if I click on one of these you can
+see that I have a schedule
+
+ align:start position:0%
+see that I have a schedule
+ 
+
+ align:start position:0%
+see that I have a schedule
+that changes throughout the day
+
+ align:start position:0%
+that changes throughout the day
+ 
+
+ align:start position:0%
+that changes throughout the day
+obviously I wanted to heat it while
+
+ align:start position:0%
+obviously I wanted to heat it while
+ 
+
+ align:start position:0%
+obviously I wanted to heat it while
+we're awake and I'd like to have the
+
+ align:start position:0%
+we're awake and I'd like to have the
+ 
+
+ align:start position:0%
+we're awake and I'd like to have the
+house cold while we're asleep but also
+
+ align:start position:0%
+house cold while we're asleep but also
+ 
+
+ align:start position:0%
+house cold while we're asleep but also
+crucially it's useful that you when you
+
+ align:start position:0%
+crucially it's useful that you when you
+ 
+
+ align:start position:0%
+crucially it's useful that you when you
+go let's say to the airport and you're
+
+ align:start position:0%
+go let's say to the airport and you're
+ 
+
+ align:start position:0%
+go let's say to the airport and you're
+on your way to a trip you realize oh I
+
+ align:start position:0%
+on your way to a trip you realize oh I
+ 
+
+ align:start position:0%
+on your way to a trip you realize oh I
+left the thermostat on I can actually
+
+ align:start position:0%
+left the thermostat on I can actually
+ 
+
+ align:start position:0%
+left the thermostat on I can actually
+turn the energy down my entire house
+
+ align:start position:0%
+turn the energy down my entire house
+ 
+
+ align:start position:0%
+turn the energy down my entire house
+remotely
+
+ align:start position:0%
+remotely
+ 
+
+ align:start position:0%
+remotely
+finally I have rooftop solar panels you
+
+ align:start position:0%
+finally I have rooftop solar panels you
+ 
+
+ align:start position:0%
+finally I have rooftop solar panels you
+can see here in the middle of the day
+
+ align:start position:0%
+can see here in the middle of the day
+ 
+
+ align:start position:0%
+can see here in the middle of the day
+one set of panels that are facing the
+
+ align:start position:0%
+one set of panels that are facing the
+ 
+
+ align:start position:0%
+one set of panels that are facing the
+East are still getting a lot of power
+
+ align:start position:0%
+East are still getting a lot of power
+ 
+
+ align:start position:0%
+East are still getting a lot of power
+but slowly the uh as the sun moves over
+
+ align:start position:0%
+but slowly the uh as the sun moves over
+ 
+
+ align:start position:0%
+but slowly the uh as the sun moves over
+the top of the house or the roof line of
+
+ align:start position:0%
+the top of the house or the roof line of
+ 
+
+ align:start position:0%
+the top of the house or the roof line of
+the house all these panels here on the
+
+ align:start position:0%
+the house all these panels here on the
+ 
+
+ align:start position:0%
+the house all these panels here on the
+right are going to get more energy and
+
+ align:start position:0%
+right are going to get more energy and
+ 
+
+ align:start position:0%
+right are going to get more energy and
+it's kind of cool you can actually see
+
+ align:start position:0%
+it's kind of cool you can actually see
+ 
+
+ align:start position:0%
+it's kind of cool you can actually see
+on a weekly basis how much energy uh the
+
+ align:start position:0%
+on a weekly basis how much energy uh the
+ 
+
+ align:start position:0%
+on a weekly basis how much energy uh the
+how much energy is being used
+
+ align:start position:0%
+how much energy is being used
+ 
+
+ align:start position:0%
+how much energy is being used
+and you can actually see
+
+ align:start position:0%
+and you can actually see
+ 
+
+ align:start position:0%
+and you can actually see
+uh throughout the week I got a nice
+
+ align:start position:0%
+uh throughout the week I got a nice
+ 
+
+ align:start position:0%
+uh throughout the week I got a nice
+sunny day with lots of solar energy
+
+ align:start position:0%
+sunny day with lots of solar energy
+ 
+
+ align:start position:0%
+sunny day with lots of solar energy
+maybe a cloudier day with less solar
+
+ align:start position:0%
+maybe a cloudier day with less solar
+ 
+
+ align:start position:0%
+maybe a cloudier day with less solar
+energy and more Soul energy throughout
+
+ align:start position:0%
+energy and more Soul energy throughout
+ 
+
+ align:start position:0%
+energy and more Soul energy throughout
+the day last few days of the week uh
+
+ align:start position:0%
+the day last few days of the week uh
+ 
+
+ align:start position:0%
+the day last few days of the week uh
+there are fancier setups for people a
+
+ align:start position:0%
+there are fancier setups for people a
+ 
+
+ align:start position:0%
+there are fancier setups for people a
+lot of Engineers uh electrical energy
+
+ align:start position:0%
+lot of Engineers uh electrical energy
+ 
+
+ align:start position:0%
+lot of Engineers uh electrical energy
+and Engineers like to calculate how much
+
+ align:start position:0%
+and Engineers like to calculate how much
+ 
+
+ align:start position:0%
+and Engineers like to calculate how much
+solar is coming to the house and how
+
+ align:start position:0%
+solar is coming to the house and how
+ 
+
+ align:start position:0%
+solar is coming to the house and how
+much they're using I clearly don't have
+
+ align:start position:0%
+much they're using I clearly don't have
+ 
+
+ align:start position:0%
+much they're using I clearly don't have
+all these systems integrated but this is
+
+ align:start position:0%
+all these systems integrated but this is
+ 
+
+ align:start position:0%
+all these systems integrated but this is
+to point out that all the data we need
+
+ align:start position:0%
+to point out that all the data we need
+ 
+
+ align:start position:0%
+to point out that all the data we need
+to manage our Energy Efficiency uses are
+
+ align:start position:0%
+to manage our Energy Efficiency uses are
+ 
+
+ align:start position:0%
+to manage our Energy Efficiency uses are
+much is much easier to get it involves
+
+ align:start position:0%
+much is much easier to get it involves
+ 
+
+ align:start position:0%
+much is much easier to get it involves
+installing one device on my electrical
+
+ align:start position:0%
+installing one device on my electrical
+ 
+
+ align:start position:0%
+installing one device on my electrical
+panel it involves managing my
+
+ align:start position:0%
+panel it involves managing my
+ 
+
+ align:start position:0%
+panel it involves managing my
+thermostats communicating through the
+
+ align:start position:0%
+thermostats communicating through the
+ 
+
+ align:start position:0%
+thermostats communicating through the
+Wi-Fi this is my solar panels
+
+ align:start position:0%
+Wi-Fi this is my solar panels
+ 
+
+ align:start position:0%
+Wi-Fi this is my solar panels
+communicating to the internet and
+
+ align:start position:0%
+communicating to the internet and
+ 
+
+ align:start position:0%
+communicating to the internet and
+sending information to my computer or
+
+ align:start position:0%
+sending information to my computer or
+ 
+
+ align:start position:0%
+sending information to my computer or
+web app
+
+ align:start position:0%
+web app
+ 
+
+ align:start position:0%
+web app
+okay and the last point I want to point
+
+ align:start position:0%
+okay and the last point I want to point
+ 
+
+ align:start position:0%
+okay and the last point I want to point
+out the last point I want to make is
+
+ align:start position:0%
+out the last point I want to make is
+ 
+
+ align:start position:0%
+out the last point I want to make is
+that you know a lot of this information
+
+ align:start position:0%
+that you know a lot of this information
+ 
+
+ align:start position:0%
+that you know a lot of this information
+that you need to measure your energy use
+
+ align:start position:0%
+that you need to measure your energy use
+ 
+
+ align:start position:0%
+that you need to measure your energy use
+is actually on your electricity or
+
+ align:start position:0%
+is actually on your electricity or
+ 
+
+ align:start position:0%
+is actually on your electricity or
+natural gas bills I know we talked in
+
+ align:start position:0%
+natural gas bills I know we talked in
+ 
+
+ align:start position:0%
+natural gas bills I know we talked in
+class about only a third of you get your
+
+ align:start position:0%
+class about only a third of you get your
+ 
+
+ align:start position:0%
+class about only a third of you get your
+bills because the two-thirds of you live
+
+ align:start position:0%
+bills because the two-thirds of you live
+ 
+
+ align:start position:0%
+bills because the two-thirds of you live
+in dorms or let's say share departments
+
+ align:start position:0%
+in dorms or let's say share departments
+ 
+
+ align:start position:0%
+in dorms or let's say share departments
+but if you look at your electricity bill
+
+ align:start position:0%
+but if you look at your electricity bill
+ 
+
+ align:start position:0%
+but if you look at your electricity bill
+for those who get them very carefully
+
+ align:start position:0%
+for those who get them very carefully
+ 
+
+ align:start position:0%
+for those who get them very carefully
+you can see a number of policy
+
+ align:start position:0%
+you can see a number of policy
+ 
+
+ align:start position:0%
+you can see a number of policy
+implications on your bill there's
+
+ align:start position:0%
+implications on your bill there's
+ 
+
+ align:start position:0%
+implications on your bill there's
+various charges for Energy Efficiency
+
+ align:start position:0%
+various charges for Energy Efficiency
+ 
+
+ align:start position:0%
+various charges for Energy Efficiency
+whether or not you access Energy
+
+ align:start position:0%
+whether or not you access Energy
+ 
+
+ align:start position:0%
+whether or not you access Energy
+Efficiency Services there's a delivery
+
+ align:start position:0%
+Efficiency Services there's a delivery
+ 
+
+ align:start position:0%
+Efficiency Services there's a delivery
+charge there's a fuel charge we know all
+
+ align:start position:0%
+charge there's a fuel charge we know all
+ 
+
+ align:start position:0%
+charge there's a fuel charge we know all
+these different charges are changing
+
+ align:start position:0%
+these different charges are changing
+ 
+
+ align:start position:0%
+these different charges are changing
+over time because of our change in
+
+ align:start position:0%
+over time because of our change in
+ 
+
+ align:start position:0%
+over time because of our change in
+energy markets and so I was going I'll
+
+ align:start position:0%
+energy markets and so I was going I'll
+ 
+
+ align:start position:0%
+energy markets and so I was going I'll
+probably show you some bills in class if
+
+ align:start position:0%
+probably show you some bills in class if
+ 
+
+ align:start position:0%
+probably show you some bills in class if
+only because there's privacy
+
+ align:start position:0%
+only because there's privacy
+ 
+
+ align:start position:0%
+only because there's privacy
+implications I don't want to show them
+
+ align:start position:0%
+implications I don't want to show them
+ 
+
+ align:start position:0%
+implications I don't want to show them
+on this video
+
+ align:start position:0%
+on this video
+ 
+
+ align:start position:0%
+on this video
+but let's just think about why buildings
+
+ align:start position:0%
+but let's just think about why buildings
+ 
+
+ align:start position:0%
+but let's just think about why buildings
+again are important in a global sense
+
+ align:start position:0%
+again are important in a global sense
+ 
+
+ align:start position:0%
+again are important in a global sense
+the International Energy agency I did a
+
+ align:start position:0%
+the International Energy agency I did a
+ 
+
+ align:start position:0%
+the International Energy agency I did a
+report in 2020 called tracking buildings
+
+ align:start position:0%
+report in 2020 called tracking buildings
+ 
+
+ align:start position:0%
+report in 2020 called tracking buildings
+and they point out that building energy
+
+ align:start position:0%
+and they point out that building energy
+ 
+
+ align:start position:0%
+and they point out that building energy
+use is not on track to meet our Paris
+
+ align:start position:0%
+use is not on track to meet our Paris
+ 
+
+ align:start position:0%
+use is not on track to meet our Paris
+climate of given goals so we focus on
+
+ align:start position:0%
+climate of given goals so we focus on
+ 
+
+ align:start position:0%
+climate of given goals so we focus on
+different aspects of their report we can
+
+ align:start position:0%
+different aspects of their report we can
+ 
+
+ align:start position:0%
+different aspects of their report we can
+see that lighting has actually been a
+
+ align:start position:0%
+see that lighting has actually been a
+ 
+
+ align:start position:0%
+see that lighting has actually been a
+relative success story we had other
+
+ align:start position:0%
+relative success story we had other
+ 
+
+ align:start position:0%
+relative success story we had other
+forms of lighting and of fluorescent
+
+ align:start position:0%
+forms of lighting and of fluorescent
+ 
+
+ align:start position:0%
+forms of lighting and of fluorescent
+lighting but light emitting diodes LED
+
+ align:start position:0%
+lighting but light emitting diodes LED
+ 
+
+ align:start position:0%
+lighting but light emitting diodes LED
+bulbs have shot up remarkably almost to
+
+ align:start position:0%
+bulbs have shot up remarkably almost to
+ 
+
+ align:start position:0%
+bulbs have shot up remarkably almost to
+about 50 percent of lighting sales uh 20
+
+ align:start position:0%
+about 50 percent of lighting sales uh 20
+ 
+
+ align:start position:0%
+about 50 percent of lighting sales uh 20
+from 2010 to 2018. they're about 50 of
+
+ align:start position:0%
+from 2010 to 2018. they're about 50 of
+ 
+
+ align:start position:0%
+from 2010 to 2018. they're about 50 of
+lighting sales and they are headed for
+
+ align:start position:0%
+lighting sales and they are headed for
+ 
+
+ align:start position:0%
+lighting sales and they are headed for
+about 80 percent that is on track for us
+
+ align:start position:0%
+about 80 percent that is on track for us
+ 
+
+ align:start position:0%
+about 80 percent that is on track for us
+to meet our sustainable development
+
+ align:start position:0%
+to meet our sustainable development
+ 
+
+ align:start position:0%
+to meet our sustainable development
+scenarios or our Paris climate
+
+ align:start position:0%
+scenarios or our Paris climate
+ 
+
+ align:start position:0%
+scenarios or our Paris climate
+agreements
+
+ align:start position:0%
+agreements
+ 
+
+ align:start position:0%
+agreements
+LEDs are a success story because they're
+
+ align:start position:0%
+LEDs are a success story because they're
+ 
+
+ align:start position:0%
+LEDs are a success story because they're
+essentially developed with Government
+
+ align:start position:0%
+essentially developed with Government
+ 
+
+ align:start position:0%
+essentially developed with Government
+research funding but they required
+
+ align:start position:0%
+research funding but they required
+ 
+
+ align:start position:0%
+research funding but they required
+subsidy at the beginning and then as
+
+ align:start position:0%
+subsidy at the beginning and then as
+ 
+
+ align:start position:0%
+subsidy at the beginning and then as
+they are produced in scale they became
+
+ align:start position:0%
+they are produced in scale they became
+ 
+
+ align:start position:0%
+they are produced in scale they became
+much much cheaper I actually bought LED
+
+ align:start position:0%
+much much cheaper I actually bought LED
+ 
+
+ align:start position:0%
+much much cheaper I actually bought LED
+light bulbs in graduate school for I
+
+ align:start position:0%
+light bulbs in graduate school for I
+ 
+
+ align:start position:0%
+light bulbs in graduate school for I
+think about fifty dollars a ball and now
+
+ align:start position:0%
+think about fifty dollars a ball and now
+ 
+
+ align:start position:0%
+think about fifty dollars a ball and now
+these bulbs have the exact same light
+
+ align:start position:0%
+these bulbs have the exact same light
+ 
+
+ align:start position:0%
+these bulbs have the exact same light
+quality as incandescent bulbs or
+
+ align:start position:0%
+quality as incandescent bulbs or
+ 
+
+ align:start position:0%
+quality as incandescent bulbs or
+fluorescent bulbs but now they cost one
+
+ align:start position:0%
+fluorescent bulbs but now they cost one
+ 
+
+ align:start position:0%
+fluorescent bulbs but now they cost one
+dollar or less so LED bulbs are a Energy
+
+ align:start position:0%
+dollar or less so LED bulbs are a Energy
+ 
+
+ align:start position:0%
+dollar or less so LED bulbs are a Energy
+Efficiency success story
+
+ align:start position:0%
+Efficiency success story
+ 
+
+ align:start position:0%
+Efficiency success story
+if you look at building envelopes all
+
+ align:start position:0%
+if you look at building envelopes all
+ 
+
+ align:start position:0%
+if you look at building envelopes all
+the things that Dave Makai did in his
+
+ align:start position:0%
+the things that Dave Makai did in his
+ 
+
+ align:start position:0%
+the things that Dave Makai did in his
+home to try to reduce conduction
+
+ align:start position:0%
+home to try to reduce conduction
+ 
+
+ align:start position:0%
+home to try to reduce conduction
+ventilation and radiative losses you can
+
+ align:start position:0%
+ventilation and radiative losses you can
+ 
+
+ align:start position:0%
+ventilation and radiative losses you can
+see that the EI iea says we are not on
+
+ align:start position:0%
+see that the EI iea says we are not on
+ 
+
+ align:start position:0%
+see that the EI iea says we are not on
+track almost two-thirds of country lack
+
+ align:start position:0%
+track almost two-thirds of country lack
+ 
+
+ align:start position:0%
+track almost two-thirds of country lack
+any mandatory building energy codes
+
+ align:start position:0%
+any mandatory building energy codes
+ 
+
+ align:start position:0%
+any mandatory building energy codes
+meaning that many buildings are not
+
+ align:start position:0%
+meaning that many buildings are not
+ 
+
+ align:start position:0%
+meaning that many buildings are not
+built with any kind of code or any kind
+
+ align:start position:0%
+built with any kind of code or any kind
+ 
+
+ align:start position:0%
+built with any kind of code or any kind
+of Energy Efficiency at all this is
+
+ align:start position:0%
+of Energy Efficiency at all this is
+ 
+
+ align:start position:0%
+of Energy Efficiency at all this is
+similar to the number of buildings that
+
+ align:start position:0%
+similar to the number of buildings that
+ 
+
+ align:start position:0%
+similar to the number of buildings that
+are built with Architects which is only
+
+ align:start position:0%
+are built with Architects which is only
+ 
+
+ align:start position:0%
+are built with Architects which is only
+a small fraction of buildings built in
+
+ align:start position:0%
+a small fraction of buildings built in
+ 
+
+ align:start position:0%
+a small fraction of buildings built in
+the world we know we have a lot of
+
+ align:start position:0%
+the world we know we have a lot of
+ 
+
+ align:start position:0%
+the world we know we have a lot of
+construction that people do themselves
+
+ align:start position:0%
+construction that people do themselves
+ 
+
+ align:start position:0%
+construction that people do themselves
+either do it yourself or informal
+
+ align:start position:0%
+either do it yourself or informal
+ 
+
+ align:start position:0%
+either do it yourself or informal
+settlements but those places are often
+
+ align:start position:0%
+settlements but those places are often
+ 
+
+ align:start position:0%
+settlements but those places are often
+not governed by energy codes so
+
+ align:start position:0%
+not governed by energy codes so
+ 
+
+ align:start position:0%
+not governed by energy codes so
+therefore they're not energy efficient
+
+ align:start position:0%
+therefore they're not energy efficient
+ 
+
+ align:start position:0%
+therefore they're not energy efficient
+and therefore they're not using energy
+
+ align:start position:0%
+and therefore they're not using energy
+ 
+
+ align:start position:0%
+and therefore they're not using energy
+very efficiently in a way that is going
+
+ align:start position:0%
+very efficiently in a way that is going
+ 
+
+ align:start position:0%
+very efficiently in a way that is going
+to help us reach our Paris climate
+
+ align:start position:0%
+to help us reach our Paris climate
+ 
+
+ align:start position:0%
+to help us reach our Paris climate
+agreement goals
+
+ align:start position:0%
+agreement goals
+ 
+
+ align:start position:0%
+agreement goals
+in terms of heating you can see that we
+
+ align:start position:0%
+in terms of heating you can see that we
+ 
+
+ align:start position:0%
+in terms of heating you can see that we
+have fossil fuel based equipment
+
+ align:start position:0%
+have fossil fuel based equipment
+ 
+
+ align:start position:0%
+have fossil fuel based equipment
+conventional electric equipment heat
+
+ align:start position:0%
+conventional electric equipment heat
+ 
+
+ align:start position:0%
+conventional electric equipment heat
+pumps District heat and other renewable
+
+ align:start position:0%
+pumps District heat and other renewable
+ 
+
+ align:start position:0%
+pumps District heat and other renewable
+sources of energy in order to meet our
+
+ align:start position:0%
+sources of energy in order to meet our
+ 
+
+ align:start position:0%
+sources of energy in order to meet our
+sustainable development scenarios we
+
+ align:start position:0%
+sustainable development scenarios we
+ 
+
+ align:start position:0%
+sustainable development scenarios we
+need heat pumps to expand by a factor of
+
+ align:start position:0%
+need heat pumps to expand by a factor of
+ 
+
+ align:start position:0%
+need heat pumps to expand by a factor of
+probably four or five and we need our
+
+ align:start position:0%
+probably four or five and we need our
+ 
+
+ align:start position:0%
+probably four or five and we need our
+use of fossil fuel based equipment like
+
+ align:start position:0%
+use of fossil fuel based equipment like
+ 
+
+ align:start position:0%
+use of fossil fuel based equipment like
+the natural gas coming into our homes
+
+ align:start position:0%
+the natural gas coming into our homes
+ 
+
+ align:start position:0%
+the natural gas coming into our homes
+and spaces now to decrease we need
+
+ align:start position:0%
+and spaces now to decrease we need
+ 
+
+ align:start position:0%
+and spaces now to decrease we need
+conventional electric equipment to
+
+ align:start position:0%
+conventional electric equipment to
+ 
+
+ align:start position:0%
+conventional electric equipment to
+decrease because it's relatively much
+
+ align:start position:0%
+decrease because it's relatively much
+ 
+
+ align:start position:0%
+decrease because it's relatively much
+less efficient than heat pumps District
+
+ align:start position:0%
+less efficient than heat pumps District
+ 
+
+ align:start position:0%
+less efficient than heat pumps District
+heat is not actually predicted to expand
+
+ align:start position:0%
+heat is not actually predicted to expand
+ 
+
+ align:start position:0%
+heat is not actually predicted to expand
+very much and the use of other
+
+ align:start position:0%
+very much and the use of other
+ 
+
+ align:start position:0%
+very much and the use of other
+Renewables and perhaps hydrogen is
+
+ align:start position:0%
+Renewables and perhaps hydrogen is
+ 
+
+ align:start position:0%
+Renewables and perhaps hydrogen is
+expected to expand but the problem is to
+
+ align:start position:0%
+expected to expand but the problem is to
+ 
+
+ align:start position:0%
+expected to expand but the problem is to
+meet our 2050 goals our 2030 goals sorry
+
+ align:start position:0%
+meet our 2050 goals our 2030 goals sorry
+ 
+
+ align:start position:0%
+meet our 2050 goals our 2030 goals sorry
+we are not on track according to the iea
+
+ align:start position:0%
+we are not on track according to the iea
+ 
+
+ align:start position:0%
+we are not on track according to the iea
+in terms of sheet pumps we need more
+
+ align:start position:0%
+in terms of sheet pumps we need more
+ 
+
+ align:start position:0%
+in terms of sheet pumps we need more
+efforts many households purchase heat
+
+ align:start position:0%
+efforts many households purchase heat
+ 
+
+ align:start position:0%
+efforts many households purchase heat
+pumps in 2019 if anything that's
+
+ align:start position:0%
+pumps in 2019 if anything that's
+ 
+
+ align:start position:0%
+pumps in 2019 if anything that's
+probably expanded rapidly with the
+
+ align:start position:0%
+probably expanded rapidly with the
+ 
+
+ align:start position:0%
+probably expanded rapidly with the
+explosion and natural gas prices because
+
+ align:start position:0%
+explosion and natural gas prices because
+ 
+
+ align:start position:0%
+explosion and natural gas prices because
+the war on Ukraine we know heat pump
+
+ align:start position:0%
+the war on Ukraine we know heat pump
+ 
+
+ align:start position:0%
+the war on Ukraine we know heat pump
+sales are going up very quickly some
+
+ align:start position:0%
+sales are going up very quickly some
+ 
+
+ align:start position:0%
+sales are going up very quickly some
+people have said that one of the biggest
+
+ align:start position:0%
+people have said that one of the biggest
+ 
+
+ align:start position:0%
+people have said that one of the biggest
+things we can do to try to reduce
+
+ align:start position:0%
+things we can do to try to reduce
+ 
+
+ align:start position:0%
+things we can do to try to reduce
+Europe's dependent on dependence on
+
+ align:start position:0%
+Europe's dependent on dependence on
+ 
+
+ align:start position:0%
+Europe's dependent on dependence on
+Russian gas
+
+ align:start position:0%
+Russian gas
+ 
+
+ align:start position:0%
+Russian gas
+is to send the heat pumps we need to
+
+ align:start position:0%
+is to send the heat pumps we need to
+ 
+
+ align:start position:0%
+is to send the heat pumps we need to
+manufacture heat pumps as quickly as
+
+ align:start position:0%
+manufacture heat pumps as quickly as
+ 
+
+ align:start position:0%
+manufacture heat pumps as quickly as
+possible but I can tell you from
+
+ align:start position:0%
+possible but I can tell you from
+ 
+
+ align:start position:0%
+possible but I can tell you from
+personal experience my home uses natural
+
+ align:start position:0%
+personal experience my home uses natural
+ 
+
+ align:start position:0%
+personal experience my home uses natural
+gas it is difficult to retrofit a
+
+ align:start position:0%
+gas it is difficult to retrofit a
+ 
+
+ align:start position:0%
+gas it is difficult to retrofit a
+relatively old home with a heat pump or
+
+ align:start position:0%
+relatively old home with a heat pump or
+ 
+
+ align:start position:0%
+relatively old home with a heat pump or
+rather it is not it's not inherently
+
+ align:start position:0%
+rather it is not it's not inherently
+ 
+
+ align:start position:0%
+rather it is not it's not inherently
+difficult but right now even as somebody
+
+ align:start position:0%
+difficult but right now even as somebody
+ 
+
+ align:start position:0%
+difficult but right now even as somebody
+who's very interested in this problem I
+
+ align:start position:0%
+who's very interested in this problem I
+ 
+
+ align:start position:0%
+who's very interested in this problem I
+have a hard time trying to figure out
+
+ align:start position:0%
+have a hard time trying to figure out
+ 
+
+ align:start position:0%
+have a hard time trying to figure out
+how to retrofit my 1925 home with the
+
+ align:start position:0%
+how to retrofit my 1925 home with the
+ 
+
+ align:start position:0%
+how to retrofit my 1925 home with the
+key pump so this is an area where
+
+ align:start position:0%
+key pump so this is an area where
+ 
+
+ align:start position:0%
+key pump so this is an area where
+contractors Architects Engineers
+
+ align:start position:0%
+contractors Architects Engineers
+ 
+
+ align:start position:0%
+contractors Architects Engineers
+um small businesses have a tremendous
+
+ align:start position:0%
+um small businesses have a tremendous
+ 
+
+ align:start position:0%
+um small businesses have a tremendous
+opportunity to increase the adoption of
+
+ align:start position:0%
+opportunity to increase the adoption of
+ 
+
+ align:start position:0%
+opportunity to increase the adoption of
+heat pumps and this is an area where the
+
+ align:start position:0%
+heat pumps and this is an area where the
+ 
+
+ align:start position:0%
+heat pumps and this is an area where the
+inflation reduction act gives a lot of
+
+ align:start position:0%
+inflation reduction act gives a lot of
+ 
+
+ align:start position:0%
+inflation reduction act gives a lot of
+tax incentives for homeowners to
+
+ align:start position:0%
+tax incentives for homeowners to
+ 
+
+ align:start position:0%
+tax incentives for homeowners to
+increase the use of heat pumps which is
+
+ align:start position:0%
+increase the use of heat pumps which is
+ 
+
+ align:start position:0%
+increase the use of heat pumps which is
+why I included that AC Triple E report
+
+ align:start position:0%
+why I included that AC Triple E report
+ 
+
+ align:start position:0%
+why I included that AC Triple E report
+for you to read
+
+ align:start position:0%
+for you to read
+ 
+
+ align:start position:0%
+for you to read
+if you look at cooling efforts cooling
+
+ align:start position:0%
+if you look at cooling efforts cooling
+ 
+
+ align:start position:0%
+if you look at cooling efforts cooling
+efforts uh cooling is actually a big
+
+ align:start position:0%
+efforts uh cooling is actually a big
+ 
+
+ align:start position:0%
+efforts uh cooling is actually a big
+area of concern because we know that not
+
+ align:start position:0%
+area of concern because we know that not
+ 
+
+ align:start position:0%
+area of concern because we know that not
+only is the world getting hotter but
+
+ align:start position:0%
+only is the world getting hotter but
+ 
+
+ align:start position:0%
+only is the world getting hotter but
+lots of places in the world that are
+
+ align:start position:0%
+lots of places in the world that are
+ 
+
+ align:start position:0%
+lots of places in the world that are
+getting richer like sub-Saharan Africa
+
+ align:start position:0%
+getting richer like sub-Saharan Africa
+ 
+
+ align:start position:0%
+getting richer like sub-Saharan Africa
+or southeast Asia India essentially are
+
+ align:start position:0%
+or southeast Asia India essentially are
+ 
+
+ align:start position:0%
+or southeast Asia India essentially are
+relatively hot and humid climates as
+
+ align:start position:0%
+relatively hot and humid climates as
+ 
+
+ align:start position:0%
+relatively hot and humid climates as
+those places get richer and more
+
+ align:start position:0%
+those places get richer and more
+ 
+
+ align:start position:0%
+those places get richer and more
+urbanized there will be greater demand
+
+ align:start position:0%
+urbanized there will be greater demand
+ 
+
+ align:start position:0%
+urbanized there will be greater demand
+for cooling so the energy demand for
+
+ align:start position:0%
+for cooling so the energy demand for
+ 
+
+ align:start position:0%
+for cooling so the energy demand for
+space cooling is actually going up quite
+
+ align:start position:0%
+space cooling is actually going up quite
+ 
+
+ align:start position:0%
+space cooling is actually going up quite
+a bit
+
+ align:start position:0%
+a bit
+ 
+
+ align:start position:0%
+a bit
+there's a space cooling intensity index
+
+ align:start position:0%
+there's a space cooling intensity index
+ 
+
+ align:start position:0%
+there's a space cooling intensity index
+in the sustainable development scenario
+
+ align:start position:0%
+in the sustainable development scenario
+ 
+
+ align:start position:0%
+in the sustainable development scenario
+and we like our space cooling intensity
+
+ align:start position:0%
+and we like our space cooling intensity
+ 
+
+ align:start position:0%
+and we like our space cooling intensity
+index to go down which is the amount of
+
+ align:start position:0%
+index to go down which is the amount of
+ 
+
+ align:start position:0%
+index to go down which is the amount of
+energy we use for cooling the good news
+
+ align:start position:0%
+energy we use for cooling the good news
+ 
+
+ align:start position:0%
+energy we use for cooling the good news
+is if we're going to install air
+
+ align:start position:0%
+is if we're going to install air
+ 
+
+ align:start position:0%
+is if we're going to install air
+conditioning we can simply install a
+
+ align:start position:0%
+conditioning we can simply install a
+ 
+
+ align:start position:0%
+conditioning we can simply install a
+heat pump and get both Heating and
+
+ align:start position:0%
+heat pump and get both Heating and
+ 
+
+ align:start position:0%
+heat pump and get both Heating and
+Cooling benefits and they're relatively
+
+ align:start position:0%
+Cooling benefits and they're relatively
+ 
+
+ align:start position:0%
+Cooling benefits and they're relatively
+more efficient the problem is in order
+
+ align:start position:0%
+more efficient the problem is in order
+ 
+
+ align:start position:0%
+more efficient the problem is in order
+to increase the use of heat pumps again
+
+ align:start position:0%
+to increase the use of heat pumps again
+ 
+
+ align:start position:0%
+to increase the use of heat pumps again
+for cooling we need to make more policy
+
+ align:start position:0%
+for cooling we need to make more policy
+ 
+
+ align:start position:0%
+for cooling we need to make more policy
+effort or more efforts need to be made
+
+ align:start position:0%
+effort or more efforts need to be made
+ 
+
+ align:start position:0%
+effort or more efforts need to be made
+across industry and government
+
+ align:start position:0%
+across industry and government
+ 
+
+ align:start position:0%
+across industry and government
+if you look at appliances and Equipment
+
+ align:start position:0%
+if you look at appliances and Equipment
+ 
+
+ align:start position:0%
+if you look at appliances and Equipment
+Energy Star Energy guide those yellow
+
+ align:start position:0%
+Energy Star Energy guide those yellow
+ 
+
+ align:start position:0%
+Energy Star Energy guide those yellow
+tags on appliances you might buy in the
+
+ align:start position:0%
+tags on appliances you might buy in the
+ 
+
+ align:start position:0%
+tags on appliances you might buy in the
+store energy equipment has become much
+
+ align:start position:0%
+store energy equipment has become much
+ 
+
+ align:start position:0%
+store energy equipment has become much
+more efficient than before partly
+
+ align:start position:0%
+more efficient than before partly
+ 
+
+ align:start position:0%
+more efficient than before partly
+because of changes in technology and
+
+ align:start position:0%
+because of changes in technology and
+ 
+
+ align:start position:0%
+because of changes in technology and
+partly because Energy Efficiency codes
+
+ align:start position:0%
+partly because Energy Efficiency codes
+ 
+
+ align:start position:0%
+partly because Energy Efficiency codes
+have pushed the technology to become
+
+ align:start position:0%
+have pushed the technology to become
+ 
+
+ align:start position:0%
+have pushed the technology to become
+more efficient but in order for us to
+
+ align:start position:0%
+more efficient but in order for us to
+ 
+
+ align:start position:0%
+more efficient but in order for us to
+reach our sustainable development
+
+ align:start position:0%
+reach our sustainable development
+ 
+
+ align:start position:0%
+reach our sustainable development
+scenario in 2030 we still need to make
+
+ align:start position:0%
+scenario in 2030 we still need to make
+ 
+
+ align:start position:0%
+scenario in 2030 we still need to make
+more effort uh demand is being driven by
+
+ align:start position:0%
+more effort uh demand is being driven by
+ 
+
+ align:start position:0%
+more effort uh demand is being driven by
+Rising ownership of connected plug load
+
+ align:start position:0%
+Rising ownership of connected plug load
+ 
+
+ align:start position:0%
+Rising ownership of connected plug load
+devices those are the devices you plug
+
+ align:start position:0%
+devices those are the devices you plug
+ 
+
+ align:start position:0%
+devices those are the devices you plug
+into the wall especially in developing
+
+ align:start position:0%
+into the wall especially in developing
+ 
+
+ align:start position:0%
+into the wall especially in developing
+countries that are becoming wealthier so
+
+ align:start position:0%
+countries that are becoming wealthier so
+ 
+
+ align:start position:0%
+countries that are becoming wealthier so
+we need to try to pass performance
+
+ align:start position:0%
+we need to try to pass performance
+ 
+
+ align:start position:0%
+we need to try to pass performance
+standards that govern how much energy
+
+ align:start position:0%
+standards that govern how much energy
+ 
+
+ align:start position:0%
+standards that govern how much energy
+all of our devices use
+
+ align:start position:0%
+all of our devices use
+ 
+
+ align:start position:0%
+all of our devices use
+and finally you know there's also
+
+ align:start position:0%
+and finally you know there's also
+ 
+
+ align:start position:0%
+and finally you know there's also
+behavioral interventions we can make
+
+ align:start position:0%
+behavioral interventions we can make
+ 
+
+ align:start position:0%
+behavioral interventions we can make
+this is an important thing I want to
+
+ align:start position:0%
+this is an important thing I want to
+ 
+
+ align:start position:0%
+this is an important thing I want to
+touch on today leading into next week's
+
+ align:start position:0%
+touch on today leading into next week's
+ 
+
+ align:start position:0%
+touch on today leading into next week's
+discussion this is a paper by Tyler
+
+ align:start position:0%
+discussion this is a paper by Tyler
+ 
+
+ align:start position:0%
+discussion this is a paper by Tyler
+margettis shazina Atari and David Landy
+
+ align:start position:0%
+margettis shazina Atari and David Landy
+ 
+
+ align:start position:0%
+margettis shazina Atari and David Landy
+that is published in nature in 2019 our
+
+ align:start position:0%
+that is published in nature in 2019 our
+ 
+
+ align:start position:0%
+that is published in nature in 2019 our
+nature energy in 2019 and the headline
+
+ align:start position:0%
+nature energy in 2019 and the headline
+ 
+
+ align:start position:0%
+nature energy in 2019 and the headline
+is simply that simple interventions can
+
+ align:start position:0%
+is simply that simple interventions can
+ 
+
+ align:start position:0%
+is simply that simple interventions can
+correct misperceptions of Home energy
+
+ align:start position:0%
+correct misperceptions of Home energy
+ 
+
+ align:start position:0%
+correct misperceptions of Home energy
+use and the reason why I had you look
+
+ align:start position:0%
+use and the reason why I had you look
+ 
+
+ align:start position:0%
+use and the reason why I had you look
+around your apartments and homes and how
+
+ align:start position:0%
+around your apartments and homes and how
+ 
+
+ align:start position:0%
+around your apartments and homes and how
+much energy things use and try to
+
+ align:start position:0%
+much energy things use and try to
+ 
+
+ align:start position:0%
+much energy things use and try to
+calculate it and really want to look
+
+ align:start position:0%
+calculate it and really want to look
+ 
+
+ align:start position:0%
+calculate it and really want to look
+through Dave MacKay's home is that
+
+ align:start position:0%
+through Dave MacKay's home is that
+ 
+
+ align:start position:0%
+through Dave MacKay's home is that
+people don't have a very good sense
+
+ align:start position:0%
+people don't have a very good sense
+ 
+
+ align:start position:0%
+people don't have a very good sense
+actually how much various appliances use
+
+ align:start position:0%
+actually how much various appliances use
+ 
+
+ align:start position:0%
+actually how much various appliances use
+and if you look at this graph this is
+
+ align:start position:0%
+and if you look at this graph this is
+ 
+
+ align:start position:0%
+and if you look at this graph this is
+the estimate that people give on a
+
+ align:start position:0%
+the estimate that people give on a
+ 
+
+ align:start position:0%
+the estimate that people give on a
+survey a logarithmic scale on the
+
+ align:start position:0%
+survey a logarithmic scale on the
+ 
+
+ align:start position:0%
+survey a logarithmic scale on the
+vertical axis and the actual energy use
+
+ align:start position:0%
+vertical axis and the actual energy use
+ 
+
+ align:start position:0%
+vertical axis and the actual energy use
+of these appliances on the horizontal
+
+ align:start position:0%
+of these appliances on the horizontal
+ 
+
+ align:start position:0%
+of these appliances on the horizontal
+scale also a logarithmic scale which
+
+ align:start position:0%
+scale also a logarithmic scale which
+ 
+
+ align:start position:0%
+scale also a logarithmic scale which
+means that people perfectly predicted
+
+ align:start position:0%
+means that people perfectly predicted
+ 
+
+ align:start position:0%
+means that people perfectly predicted
+the amount of energy use all these
+
+ align:start position:0%
+the amount of energy use all these
+ 
+
+ align:start position:0%
+the amount of energy use all these
+different devices use they'd be right on
+
+ align:start position:0%
+different devices use they'd be right on
+ 
+
+ align:start position:0%
+different devices use they'd be right on
+this dotted line
+
+ align:start position:0%
+this dotted line
+ 
+
+ align:start position:0%
+this dotted line
+but you can see for small devices like
+
+ align:start position:0%
+but you can see for small devices like
+ 
+
+ align:start position:0%
+but you can see for small devices like
+LEDs they actually estimate they use
+
+ align:start position:0%
+LEDs they actually estimate they use
+ 
+
+ align:start position:0%
+LEDs they actually estimate they use
+more than they actually do and for large
+
+ align:start position:0%
+more than they actually do and for large
+ 
+
+ align:start position:0%
+more than they actually do and for large
+devices like a central air conditioner
+
+ align:start position:0%
+devices like a central air conditioner
+ 
+
+ align:start position:0%
+devices like a central air conditioner
+they actually estimate it using less
+
+ align:start position:0%
+they actually estimate it using less
+ 
+
+ align:start position:0%
+they actually estimate it using less
+energy than they actually do or else
+
+ align:start position:0%
+energy than they actually do or else
+ 
+
+ align:start position:0%
+energy than they actually do or else
+they would be on this dotted line
+
+ align:start position:0%
+they would be on this dotted line
+ 
+
+ align:start position:0%
+they would be on this dotted line
+and so the key Point here is that they
+
+ align:start position:0%
+and so the key Point here is that they
+ 
+
+ align:start position:0%
+and so the key Point here is that they
+actually do an experiment where they
+
+ align:start position:0%
+actually do an experiment where they
+ 
+
+ align:start position:0%
+actually do an experiment where they
+target the use of energy use and they
+
+ align:start position:0%
+target the use of energy use and they
+ 
+
+ align:start position:0%
+target the use of energy use and they
+try to develop two interventions first
+
+ align:start position:0%
+try to develop two interventions first
+ 
+
+ align:start position:0%
+try to develop two interventions first
+they try to Target how people respond by
+
+ align:start position:0%
+they try to Target how people respond by
+ 
+
+ align:start position:0%
+they try to Target how people respond by
+just giving people quantitative
+
+ align:start position:0%
+just giving people quantitative
+ 
+
+ align:start position:0%
+just giving people quantitative
+information about the extreme
+
+ align:start position:0%
+information about the extreme
+ 
+
+ align:start position:0%
+information about the extreme
+electricity is they tell they tell
+
+ align:start position:0%
+electricity is they tell they tell
+ 
+
+ align:start position:0%
+electricity is they tell they tell
+people how much a phone charger uses how
+
+ align:start position:0%
+people how much a phone charger uses how
+ 
+
+ align:start position:0%
+people how much a phone charger uses how
+much a clothes dryer use uses and they
+
+ align:start position:0%
+much a clothes dryer use uses and they
+ 
+
+ align:start position:0%
+much a clothes dryer use uses and they
+predict that this is going to help
+
+ align:start position:0%
+predict that this is going to help
+ 
+
+ align:start position:0%
+predict that this is going to help
+people understand or translate their
+
+ align:start position:0%
+people understand or translate their
+ 
+
+ align:start position:0%
+people understand or translate their
+beliefs into energy use into explicit
+
+ align:start position:0%
+beliefs into energy use into explicit
+ 
+
+ align:start position:0%
+beliefs into energy use into explicit
+aspects without necessarily changing
+
+ align:start position:0%
+aspects without necessarily changing
+ 
+
+ align:start position:0%
+aspects without necessarily changing
+their underlying beliefs about energy
+
+ align:start position:0%
+their underlying beliefs about energy
+ 
+
+ align:start position:0%
+their underlying beliefs about energy
+use and that's relevant because we know
+
+ align:start position:0%
+use and that's relevant because we know
+ 
+
+ align:start position:0%
+use and that's relevant because we know
+we have very different beliefs about
+
+ align:start position:0%
+we have very different beliefs about
+ 
+
+ align:start position:0%
+we have very different beliefs about
+energy use and climate
+
+ align:start position:0%
+energy use and climate
+ 
+
+ align:start position:0%
+energy use and climate
+the second thing they do is they target
+
+ align:start position:0%
+the second thing they do is they target
+ 
+
+ align:start position:0%
+the second thing they do is they target
+systematic understanding by supplying a
+
+ align:start position:0%
+systematic understanding by supplying a
+ 
+
+ align:start position:0%
+systematic understanding by supplying a
+simple explicit heuristic rule they say
+
+ align:start position:0%
+simple explicit heuristic rule they say
+ 
+
+ align:start position:0%
+simple explicit heuristic rule they say
+people underestimate the energy by
+
+ align:start position:0%
+people underestimate the energy by
+ 
+
+ align:start position:0%
+people underestimate the energy by
+appliances that change the temperature
+
+ align:start position:0%
+appliances that change the temperature
+ 
+
+ align:start position:0%
+appliances that change the temperature
+perhaps because heat generation and heat
+
+ align:start position:0%
+perhaps because heat generation and heat
+ 
+
+ align:start position:0%
+perhaps because heat generation and heat
+removal may not be as noticeable as
+
+ align:start position:0%
+removal may not be as noticeable as
+ 
+
+ align:start position:0%
+removal may not be as noticeable as
+movement or lighting so therefore they
+
+ align:start position:0%
+movement or lighting so therefore they
+ 
+
+ align:start position:0%
+movement or lighting so therefore they
+give this explicit heuristic this kind
+
+ align:start position:0%
+give this explicit heuristic this kind
+ 
+
+ align:start position:0%
+give this explicit heuristic this kind
+of rule for people to judge energies
+
+ align:start position:0%
+of rule for people to judge energies
+ 
+
+ align:start position:0%
+of rule for people to judge energies
+they say larger appliances that
+
+ align:start position:0%
+they say larger appliances that
+ 
+
+ align:start position:0%
+they say larger appliances that
+primarily heat or cool use a lot more
+
+ align:start position:0%
+primarily heat or cool use a lot more
+ 
+
+ align:start position:0%
+primarily heat or cool use a lot more
+energy than people think they use that's
+
+ align:start position:0%
+energy than people think they use that's
+ 
+
+ align:start position:0%
+energy than people think they use that's
+all they say and they give people these
+
+ align:start position:0%
+all they say and they give people these
+ 
+
+ align:start position:0%
+all they say and they give people these
+two interventions and see how well they
+
+ align:start position:0%
+two interventions and see how well they
+ 
+
+ align:start position:0%
+two interventions and see how well they
+can estimate energy use
+
+ align:start position:0%
+can estimate energy use
+ 
+
+ align:start position:0%
+can estimate energy use
+the reason why that's important is
+
+ align:start position:0%
+the reason why that's important is
+ 
+
+ align:start position:0%
+the reason why that's important is
+because our underlying beliefs about
+
+ align:start position:0%
+because our underlying beliefs about
+ 
+
+ align:start position:0%
+because our underlying beliefs about
+energy and climate may actually shape
+
+ align:start position:0%
+energy and climate may actually shape
+ 
+
+ align:start position:0%
+energy and climate may actually shape
+how well we can actually perceive energy
+
+ align:start position:0%
+how well we can actually perceive energy
+ 
+
+ align:start position:0%
+how well we can actually perceive energy
+use these are all graphs that show the
+
+ align:start position:0%
+use these are all graphs that show the
+ 
+
+ align:start position:0%
+use these are all graphs that show the
+understanding of finds a relatively
+
+ align:start position:0%
+understanding of finds a relatively
+ 
+
+ align:start position:0%
+understanding of finds a relatively
+relative energy use on the horizontal
+
+ align:start position:0%
+relative energy use on the horizontal
+ 
+
+ align:start position:0%
+relative energy use on the horizontal
+axis and to see how they're correlated
+
+ align:start position:0%
+axis and to see how they're correlated
+ 
+
+ align:start position:0%
+axis and to see how they're correlated
+with behavioral Choice accuracy which uh
+
+ align:start position:0%
+with behavioral Choice accuracy which uh
+ 
+
+ align:start position:0%
+with behavioral Choice accuracy which uh
+behavioral choices people use make to
+
+ align:start position:0%
+behavioral choices people use make to
+ 
+
+ align:start position:0%
+behavioral choices people use make to
+change their energy use they see if it
+
+ align:start position:0%
+change their energy use they see if it
+ 
+
+ align:start position:0%
+change their energy use they see if it
+correlates with pro-environmental
+
+ align:start position:0%
+correlates with pro-environmental
+ 
+
+ align:start position:0%
+correlates with pro-environmental
+attitudes they see if it correlates with
+
+ align:start position:0%
+attitudes they see if it correlates with
+ 
+
+ align:start position:0%
+attitudes they see if it correlates with
+climate change beliefs and to see if it
+
+ align:start position:0%
+climate change beliefs and to see if it
+ 
+
+ align:start position:0%
+climate change beliefs and to see if it
+correlates with climate policy support
+
+ align:start position:0%
+correlates with climate policy support
+ 
+
+ align:start position:0%
+correlates with climate policy support
+and you can see that behavioral Choice
+
+ align:start position:0%
+and you can see that behavioral Choice
+ 
+
+ align:start position:0%
+and you can see that behavioral Choice
+accuracy is actually relatively the same
+
+ align:start position:0%
+accuracy is actually relatively the same
+ 
+
+ align:start position:0%
+accuracy is actually relatively the same
+among liberates liberals moderates and
+
+ align:start position:0%
+among liberates liberals moderates and
+ 
+
+ align:start position:0%
+among liberates liberals moderates and
+conservatives but you can see that Pro
+
+ align:start position:0%
+conservatives but you can see that Pro
+ 
+
+ align:start position:0%
+conservatives but you can see that Pro
+enviral attitudes climate change beliefs
+
+ align:start position:0%
+enviral attitudes climate change beliefs
+ 
+
+ align:start position:0%
+enviral attitudes climate change beliefs
+and climate policy support all diverge
+
+ align:start position:0%
+and climate policy support all diverge
+ 
+
+ align:start position:0%
+and climate policy support all diverge
+that's their point of this paper is that
+
+ align:start position:0%
+that's their point of this paper is that
+ 
+
+ align:start position:0%
+that's their point of this paper is that
+if you actually Supply people with both
+
+ align:start position:0%
+if you actually Supply people with both
+ 
+
+ align:start position:0%
+if you actually Supply people with both
+this kind of scale use intervention
+
+ align:start position:0%
+this kind of scale use intervention
+ 
+
+ align:start position:0%
+this kind of scale use intervention
+telling people how much energy
+
+ align:start position:0%
+telling people how much energy
+ 
+
+ align:start position:0%
+telling people how much energy
+appliances use or giving them an
+
+ align:start position:0%
+appliances use or giving them an
+ 
+
+ align:start position:0%
+appliances use or giving them an
+increased understanding of appliances
+
+ align:start position:0%
+increased understanding of appliances
+ 
+
+ align:start position:0%
+increased understanding of appliances
+relative energy use they have different
+
+ align:start position:0%
+relative energy use they have different
+ 
+
+ align:start position:0%
+relative energy use they have different
+implications for who may be listening to
+
+ align:start position:0%
+implications for who may be listening to
+ 
+
+ align:start position:0%
+implications for who may be listening to
+this message and how they might act on
+
+ align:start position:0%
+this message and how they might act on
+ 
+
+ align:start position:0%
+this message and how they might act on
+these beliefs so they argue in this
+
+ align:start position:0%
+these beliefs so they argue in this
+ 
+
+ align:start position:0%
+these beliefs so they argue in this
+paper that if you increase people's
+
+ align:start position:0%
+paper that if you increase people's
+ 
+
+ align:start position:0%
+paper that if you increase people's
+understanding of Appliance development
+
+ align:start position:0%
+understanding of Appliance development
+ 
+
+ align:start position:0%
+understanding of Appliance development
+energy use you may be able to not
+
+ align:start position:0%
+energy use you may be able to not
+ 
+
+ align:start position:0%
+energy use you may be able to not
+necessarily affect their programmable
+
+ align:start position:0%
+necessarily affect their programmable
+ 
+
+ align:start position:0%
+necessarily affect their programmable
+attitudes or the climate change beliefs
+
+ align:start position:0%
+attitudes or the climate change beliefs
+ 
+
+ align:start position:0%
+attitudes or the climate change beliefs
+or their support for climate policies
+
+ align:start position:0%
+or their support for climate policies
+ 
+
+ align:start position:0%
+or their support for climate policies
+but at least you can correct the
+
+ align:start position:0%
+but at least you can correct the
+ 
+
+ align:start position:0%
+but at least you can correct the
+misperceptions of Home energy use
+
+ align:start position:0%
+misperceptions of Home energy use
+ 
+
+ align:start position:0%
+misperceptions of Home energy use
+finally just to kind of touch on the
+
+ align:start position:0%
+finally just to kind of touch on the
+ 
+
+ align:start position:0%
+finally just to kind of touch on the
+help aspect of decarbonization this is a
+
+ align:start position:0%
+help aspect of decarbonization this is a
+ 
+
+ align:start position:0%
+help aspect of decarbonization this is a
+project I'm working on in indoor air
+
+ align:start position:0%
+project I'm working on in indoor air
+ 
+
+ align:start position:0%
+project I'm working on in indoor air
+quality in New York City it's an
+
+ align:start position:0%
+quality in New York City it's an
+ 
+
+ align:start position:0%
+quality in New York City it's an
+interesting project because we're
+
+ align:start position:0%
+interesting project because we're
+ 
+
+ align:start position:0%
+interesting project because we're
+working on a low-income or affordable
+
+ align:start position:0%
+working on a low-income or affordable
+ 
+
+ align:start position:0%
+working on a low-income or affordable
+housing building a subsidized housing
+
+ align:start position:0%
+housing building a subsidized housing
+ 
+
+ align:start position:0%
+housing building a subsidized housing
+building and what the developer or the
+
+ align:start position:0%
+building and what the developer or the
+ 
+
+ align:start position:0%
+building and what the developer or the
+owner is doing is essentially
+
+ align:start position:0%
+owner is doing is essentially
+ 
+
+ align:start position:0%
+owner is doing is essentially
+retrofitting this building to be
+
+ align:start position:0%
+retrofitting this building to be
+ 
+
+ align:start position:0%
+retrofitting this building to be
+decarborized they're upgrading it to
+
+ align:start position:0%
+decarborized they're upgrading it to
+ 
+
+ align:start position:0%
+decarborized they're upgrading it to
+passive house standards meaning they're
+
+ align:start position:0%
+passive house standards meaning they're
+ 
+
+ align:start position:0%
+passive house standards meaning they're
+wrapping the whole building in a highly
+
+ align:start position:0%
+wrapping the whole building in a highly
+ 
+
+ align:start position:0%
+wrapping the whole building in a highly
+efficient envelope and they're
+
+ align:start position:0%
+efficient envelope and they're
+ 
+
+ align:start position:0%
+efficient envelope and they're
+decarbonizing building the building by
+
+ align:start position:0%
+decarbonizing building the building by
+ 
+
+ align:start position:0%
+decarbonizing building the building by
+taking the water heating and the space
+
+ align:start position:0%
+taking the water heating and the space
+ 
+
+ align:start position:0%
+taking the water heating and the space
+heating out and installing basically
+
+ align:start position:0%
+heating out and installing basically
+ 
+
+ align:start position:0%
+heating out and installing basically
+heat pumps of the roof that will push
+
+ align:start position:0%
+heat pumps of the roof that will push
+ 
+
+ align:start position:0%
+heat pumps of the roof that will push
+air down to each of the apartment lines
+
+ align:start position:0%
+air down to each of the apartment lines
+ 
+
+ align:start position:0%
+air down to each of the apartment lines
+through these blue ventilation shops and
+
+ align:start position:0%
+through these blue ventilation shops and
+ 
+
+ align:start position:0%
+through these blue ventilation shops and
+of course when the ventilation or the uh
+
+ align:start position:0%
+of course when the ventilation or the uh
+ 
+
+ align:start position:0%
+of course when the ventilation or the uh
+exhaust air comes out of the apartments
+
+ align:start position:0%
+exhaust air comes out of the apartments
+ 
+
+ align:start position:0%
+exhaust air comes out of the apartments
+it'll come up back to this blue line and
+
+ align:start position:0%
+it'll come up back to this blue line and
+ 
+
+ align:start position:0%
+it'll come up back to this blue line and
+go through the heat exchanger meaning
+
+ align:start position:0%
+go through the heat exchanger meaning
+ 
+
+ align:start position:0%
+go through the heat exchanger meaning
+that all the heat will be captured in
+
+ align:start position:0%
+that all the heat will be captured in
+ 
+
+ align:start position:0%
+that all the heat will be captured in
+the building even if we need to push in
+
+ align:start position:0%
+the building even if we need to push in
+ 
+
+ align:start position:0%
+the building even if we need to push in
+new fresh air for ventilation
+
+ align:start position:0%
+new fresh air for ventilation
+ 
+
+ align:start position:0%
+new fresh air for ventilation
+but we also have to think of the
+
+ align:start position:0%
+but we also have to think of the
+ 
+
+ align:start position:0%
+but we also have to think of the
+implications this has for ventilation
+
+ align:start position:0%
+implications this has for ventilation
+ 
+
+ align:start position:0%
+implications this has for ventilation
+and for health we know that
+
+ align:start position:0%
+and for health we know that
+ 
+
+ align:start position:0%
+and for health we know that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Gas Appliances produce uh uncombusted
+
+ align:start position:0%
+Gas Appliances produce uh uncombusted
+ 
+
+ align:start position:0%
+Gas Appliances produce uh uncombusted
+methane but also particulate matter and
+
+ align:start position:0%
+methane but also particulate matter and
+ 
+
+ align:start position:0%
+methane but also particulate matter and
+have a gas or chemical it may release
+
+ align:start position:0%
+have a gas or chemical it may release
+ 
+
+ align:start position:0%
+have a gas or chemical it may release
+chemicals into living spaces so what
+
+ align:start position:0%
+chemicals into living spaces so what
+ 
+
+ align:start position:0%
+chemicals into living spaces so what
+we're hoping to see in this project is
+
+ align:start position:0%
+we're hoping to see in this project is
+ 
+
+ align:start position:0%
+we're hoping to see in this project is
+by decarbonizing and removing the gas in
+
+ align:start position:0%
+by decarbonizing and removing the gas in
+ 
+
+ align:start position:0%
+by decarbonizing and removing the gas in
+the building we improve air quality
+
+ align:start position:0%
+the building we improve air quality
+ 
+
+ align:start position:0%
+the building we improve air quality
+inside this building and so we put these
+
+ align:start position:0%
+inside this building and so we put these
+ 
+
+ align:start position:0%
+inside this building and so we put these
+air quality sensors and all these points
+
+ align:start position:0%
+air quality sensors and all these points
+ 
+
+ align:start position:0%
+air quality sensors and all these points
+in the building what we are hoping to
+
+ align:start position:0%
+in the building what we are hoping to
+ 
+
+ align:start position:0%
+in the building what we are hoping to
+show
+
+ align:start position:0%
+show
+ 
+
+ align:start position:0%
+show
+is that not only can we decarbonize a
+
+ align:start position:0%
+is that not only can we decarbonize a
+ 
+
+ align:start position:0%
+is that not only can we decarbonize a
+relatively inexpensive or low income
+
+ align:start position:0%
+relatively inexpensive or low income
+ 
+
+ align:start position:0%
+relatively inexpensive or low income
+building if we can decarbonize it we
+
+ align:start position:0%
+building if we can decarbonize it we
+ 
+
+ align:start position:0%
+building if we can decarbonize it we
+also improve people's air quality inside
+
+ align:start position:0%
+also improve people's air quality inside
+ 
+
+ align:start position:0%
+also improve people's air quality inside
+their homes so we're hoping for a triple
+
+ align:start position:0%
+their homes so we're hoping for a triple
+ 
+
+ align:start position:0%
+their homes so we're hoping for a triple
+win and that is applicable to any
+
+ align:start position:0%
+win and that is applicable to any
+ 
+
+ align:start position:0%
+win and that is applicable to any
+building it is relatively cheap that it
+
+ align:start position:0%
+building it is relatively cheap that it
+ 
+
+ align:start position:0%
+building it is relatively cheap that it
+eliminates the greenhouse gas use in
+
+ align:start position:0%
+eliminates the greenhouse gas use in
+ 
+
+ align:start position:0%
+eliminates the greenhouse gas use in
+these buildings and also improves
+
+ align:start position:0%
+these buildings and also improves
+ 
+
+ align:start position:0%
+these buildings and also improves
+People's Health we've been doing a
+
+ align:start position:0%
+People's Health we've been doing a
+ 
+
+ align:start position:0%
+People's Health we've been doing a
+two-year field experiment and we're
+
+ align:start position:0%
+two-year field experiment and we're
+ 
+
+ align:start position:0%
+two-year field experiment and we're
+almost done with it so I'm looking
+
+ align:start position:0%
+almost done with it so I'm looking
+ 
+
+ align:start position:0%
+almost done with it so I'm looking
+forward to sharing the results with you
+
+ align:start position:0%
+forward to sharing the results with you
+ 
+
+ align:start position:0%
+forward to sharing the results with you
+and soon and that concludes our lecture
+
+ align:start position:0%
+and soon and that concludes our lecture
+ 
+
+ align:start position:0%
+and soon and that concludes our lecture
+for today
\ No newline at end of file
diff --git a/F07k0PSQ8xk.txt b/F07k0PSQ8xk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..655b8c590d37a38cbea07ac76fa21e9d0b808be3
--- /dev/null
+++ b/F07k0PSQ8xk.txt
@@ -0,0 +1,2927 @@
+align:start position:0%
+ 
+this week but it's still let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+literally it means how does it go
+
+ align:start position:0%
+literally it means how does it go
+ 
+
+ align:start position:0%
+literally it means how does it go
+so it's it's general
+
+ align:start position:0%
+so it's it's general
+ 
+
+ align:start position:0%
+so it's it's general
+it doesn't matter if i'm talking to one
+
+ align:start position:0%
+it doesn't matter if i'm talking to one
+ 
+
+ align:start position:0%
+it doesn't matter if i'm talking to one
+person or
+
+ align:start position:0%
+person or
+ 
+
+ align:start position:0%
+person or
+more people at a time coming up
+
+ align:start position:0%
+more people at a time coming up
+ 
+
+ align:start position:0%
+more people at a time coming up
+try to say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is it
+
+ align:start position:0%
+what is it
+ 
+
+ align:start position:0%
+what is it
+the festival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it could be it could be a party
+
+ align:start position:0%
+yeah it could be it could be a party
+ 
+
+ align:start position:0%
+yeah it could be it could be a party
+but in this case it's a celebration or a
+
+ align:start position:0%
+but in this case it's a celebration or a
+ 
+
+ align:start position:0%
+but in this case it's a celebration or a
+holiday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+women international women's day oh yeah
+
+ align:start position:0%
+women international women's day oh yeah
+ 
+
+ align:start position:0%
+women international women's day oh yeah
+it's wednesday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's celebrated well everywhere
+
+ align:start position:0%
+so it's celebrated well everywhere
+ 
+
+ align:start position:0%
+so it's celebrated well everywhere
+around the world it's the international
+
+ align:start position:0%
+around the world it's the international
+ 
+
+ align:start position:0%
+around the world it's the international
+international women's day
+
+ align:start position:0%
+international women's day
+ 
+
+ align:start position:0%
+international women's day
+and it's a day when we honor women and
+
+ align:start position:0%
+and it's a day when we honor women and
+ 
+
+ align:start position:0%
+and it's a day when we honor women and
+well we try to remind ourselves that we
+
+ align:start position:0%
+well we try to remind ourselves that we
+ 
+
+ align:start position:0%
+well we try to remind ourselves that we
+need to make a constant action
+
+ align:start position:0%
+need to make a constant action
+ 
+
+ align:start position:0%
+need to make a constant action
+to keep equality
+
+ align:start position:0%
+to keep equality
+ 
+
+ align:start position:0%
+to keep equality
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+to be fair
+
+ align:start position:0%
+to be fair
+ 
+
+ align:start position:0%
+to be fair
+in every aspect of life
+
+ align:start position:0%
+in every aspect of life
+ 
+
+ align:start position:0%
+in every aspect of life
+so i think it's really funny because in
+
+ align:start position:0%
+so i think it's really funny because in
+ 
+
+ align:start position:0%
+so i think it's really funny because in
+the us
+
+ align:start position:0%
+the us
+ 
+
+ align:start position:0%
+the us
+everybody's paying attention to equality
+
+ align:start position:0%
+everybody's paying attention to equality
+ 
+
+ align:start position:0%
+everybody's paying attention to equality
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+there isn't a big celebration for la
+
+ align:start position:0%
+there isn't a big celebration for la
+ 
+
+ align:start position:0%
+there isn't a big celebration for la
+festa de la donna
+
+ align:start position:0%
+festa de la donna
+ 
+
+ align:start position:0%
+festa de la donna
+well in italy it's different since about
+
+ align:start position:0%
+well in italy it's different since about
+ 
+
+ align:start position:0%
+well in italy it's different since about
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+we actually celebrate
+
+ align:start position:0%
+we actually celebrate
+ 
+
+ align:start position:0%
+we actually celebrate
+women's day the conditions of women are
+
+ align:start position:0%
+women's day the conditions of women are
+ 
+
+ align:start position:0%
+women's day the conditions of women are
+worse in italy than here but we still
+
+ align:start position:0%
+worse in italy than here but we still
+ 
+
+ align:start position:0%
+worse in italy than here but we still
+celebrate la festa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today if you were in italy every time
+
+ align:start position:0%
+today if you were in italy every time
+ 
+
+ align:start position:0%
+today if you were in italy every time
+you would meet a woman you would say al
+
+ align:start position:0%
+you would meet a woman you would say al
+ 
+
+ align:start position:0%
+you would meet a woman you would say al
+gory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aubury
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+literally means wishes but it's like
+
+ align:start position:0%
+literally means wishes but it's like
+ 
+
+ align:start position:0%
+literally means wishes but it's like
+felicitations and you can use it in
+
+ align:start position:0%
+felicitations and you can use it in
+ 
+
+ align:start position:0%
+felicitations and you can use it in
+every context it's not just for
+
+ align:start position:0%
+every context it's not just for
+ 
+
+ align:start position:0%
+every context it's not just for
+women's day it's like it's your birthday
+
+ align:start position:0%
+women's day it's like it's your birthday
+ 
+
+ align:start position:0%
+women's day it's like it's your birthday
+aubury new year's eve
+
+ align:start position:0%
+aubury new year's eve
+ 
+
+ align:start position:0%
+aubury new year's eve
+christmas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+and then you can say specifically for
+
+ align:start position:0%
+and then you can say specifically for
+ 
+
+ align:start position:0%
+and then you can say specifically for
+this day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fiesta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes so literally it would mean good
+
+ align:start position:0%
+yeah yes so literally it would mean good
+ 
+
+ align:start position:0%
+yeah yes so literally it would mean good
+celebration of the woman but it means
+
+ align:start position:0%
+celebration of the woman but it means
+ 
+
+ align:start position:0%
+celebration of the woman but it means
+that she would say happy women's day
+
+ align:start position:0%
+that she would say happy women's day
+ 
+
+ align:start position:0%
+that she would say happy women's day
+good so try to say talk together one two
+
+ align:start position:0%
+good so try to say talk together one two
+ 
+
+ align:start position:0%
+good so try to say talk together one two
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at school we learned that the origin of
+
+ align:start position:0%
+at school we learned that the origin of
+ 
+
+ align:start position:0%
+at school we learned that the origin of
+this day
+
+ align:start position:0%
+this day
+ 
+
+ align:start position:0%
+this day
+has the root in two events that happened
+
+ align:start position:0%
+has the root in two events that happened
+ 
+
+ align:start position:0%
+has the root in two events that happened
+outside italy on the 8th of march
+
+ align:start position:0%
+outside italy on the 8th of march
+ 
+
+ align:start position:0%
+outside italy on the 8th of march
+one happened on
+
+ align:start position:0%
+one happened on
+ 
+
+ align:start position:0%
+one happened on
+the 8th of march
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it was a strike
+
+ align:start position:0%
+and it was a strike
+ 
+
+ align:start position:0%
+and it was a strike
+of government workers in new york
+
+ align:start position:0%
+of government workers in new york
+ 
+
+ align:start position:0%
+of government workers in new york
+in the us
+
+ align:start position:0%
+in the us
+ 
+
+ align:start position:0%
+in the us
+and um well apparently after these
+
+ align:start position:0%
+and um well apparently after these
+ 
+
+ align:start position:0%
+and um well apparently after these
+strikes
+
+ align:start position:0%
+strikes
+ 
+
+ align:start position:0%
+strikes
+well these strikes led to the foundation
+
+ align:start position:0%
+well these strikes led to the foundation
+ 
+
+ align:start position:0%
+well these strikes led to the foundation
+of the women
+
+ align:start position:0%
+of the women
+ 
+
+ align:start position:0%
+of the women
+unions
+
+ align:start position:0%
+unions
+ 
+
+ align:start position:0%
+unions
+now i did a little bit of research
+
+ align:start position:0%
+now i did a little bit of research
+ 
+
+ align:start position:0%
+now i did a little bit of research
+and according to some historians this
+
+ align:start position:0%
+and according to some historians this
+ 
+
+ align:start position:0%
+and according to some historians this
+event never happened
+
+ align:start position:0%
+event never happened
+ 
+
+ align:start position:0%
+event never happened
+so is it true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+so let's try and do this to read this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i told you that there was a strike
+
+ align:start position:0%
+and i told you that there was a strike
+ 
+
+ align:start position:0%
+and i told you that there was a strike
+it's a very important word that you need
+
+ align:start position:0%
+it's a very important word that you need
+ 
+
+ align:start position:0%
+it's a very important word that you need
+to learn
+
+ align:start position:0%
+to learn
+ 
+
+ align:start position:0%
+to learn
+strike is chop it off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with one with one piece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you need to know this
+
+ align:start position:0%
+and you need to know this
+ 
+
+ align:start position:0%
+and you need to know this
+word because if you travel to italy i'm
+
+ align:start position:0%
+word because if you travel to italy i'm
+ 
+
+ align:start position:0%
+word because if you travel to italy i'm
+like 99 sure that there would be some
+
+ align:start position:0%
+like 99 sure that there would be some
+ 
+
+ align:start position:0%
+like 99 sure that there would be some
+sort of chaperone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah or some other sort of chaperone
+
+ align:start position:0%
+yes yeah or some other sort of chaperone
+ 
+
+ align:start position:0%
+yes yeah or some other sort of chaperone
+so it's good if you know this word
+
+ align:start position:0%
+so it's good if you know this word
+ 
+
+ align:start position:0%
+so it's good if you know this word
+so i told you that there were two events
+
+ align:start position:0%
+so i told you that there were two events
+ 
+
+ align:start position:0%
+so i told you that there were two events
+that led to the choice of the
+
+ align:start position:0%
+that led to the choice of the
+ 
+
+ align:start position:0%
+that led to the choice of the
+octod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the first event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second one
+
+ align:start position:0%
+the second one
+ 
+
+ align:start position:0%
+the second one
+it's again it's another chopero
+
+ align:start position:0%
+it's again it's another chopero
+ 
+
+ align:start position:0%
+it's again it's another chopero
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+lotto
+
+ align:start position:0%
+lotto
+ 
+
+ align:start position:0%
+lotto
+marzonia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in russia in saint petersburg
+
+ align:start position:0%
+in russia in saint petersburg
+ 
+
+ align:start position:0%
+in russia in saint petersburg
+so women were
+
+ align:start position:0%
+so women were
+ 
+
+ align:start position:0%
+so women were
+protesting
+
+ align:start position:0%
+protesting
+ 
+
+ align:start position:0%
+protesting
+because well it was a very hard period
+
+ align:start position:0%
+because well it was a very hard period
+ 
+
+ align:start position:0%
+because well it was a very hard period
+there was
+
+ align:start position:0%
+there was
+ 
+
+ align:start position:0%
+there was
+the first world war
+
+ align:start position:0%
+the first world war
+ 
+
+ align:start position:0%
+the first world war
+and then there was also the russian
+
+ align:start position:0%
+and then there was also the russian
+ 
+
+ align:start position:0%
+and then there was also the russian
+revolution going on so there were a lot
+
+ align:start position:0%
+revolution going on so there were a lot
+ 
+
+ align:start position:0%
+revolution going on so there were a lot
+of tests and there was like food so they
+
+ align:start position:0%
+of tests and there was like food so they
+ 
+
+ align:start position:0%
+of tests and there was like food so they
+were making this chopero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+bread yes
+
+ align:start position:0%
+bread yes
+ 
+
+ align:start position:0%
+bread yes
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+peace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll chop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in italy we celebrate it in many
+
+ align:start position:0%
+so in italy we celebrate it in many
+ 
+
+ align:start position:0%
+so in italy we celebrate it in many
+different ways but there are a lot of
+
+ align:start position:0%
+different ways but there are a lot of
+ 
+
+ align:start position:0%
+different ways but there are a lot of
+meetings
+
+ align:start position:0%
+meetings
+ 
+
+ align:start position:0%
+meetings
+maybe discussions public discussions but
+
+ align:start position:0%
+maybe discussions public discussions but
+ 
+
+ align:start position:0%
+maybe discussions public discussions but
+then it's also nice because there is
+
+ align:start position:0%
+then it's also nice because there is
+ 
+
+ align:start position:0%
+then it's also nice because there is
+traditional gift a very simple gift that
+
+ align:start position:0%
+traditional gift a very simple gift that
+ 
+
+ align:start position:0%
+traditional gift a very simple gift that
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+give to women in their lives and this
+
+ align:start position:0%
+give to women in their lives and this
+ 
+
+ align:start position:0%
+give to women in their lives and this
+gift is a flower
+
+ align:start position:0%
+gift is a flower
+ 
+
+ align:start position:0%
+gift is a flower
+called mimosa it's a yellow flower
+
+ align:start position:0%
+called mimosa it's a yellow flower
+ 
+
+ align:start position:0%
+called mimosa it's a yellow flower
+so it's a reminder that it's women's day
+
+ align:start position:0%
+so it's a reminder that it's women's day
+ 
+
+ align:start position:0%
+so it's a reminder that it's women's day
+and also it's very nice because it means
+
+ align:start position:0%
+and also it's very nice because it means
+ 
+
+ align:start position:0%
+and also it's very nice because it means
+you think oh it's spring summer spring
+
+ align:start position:0%
+you think oh it's spring summer spring
+ 
+
+ align:start position:0%
+you think oh it's spring summer spring
+this is a stand
+
+ align:start position:0%
+this is a stand
+ 
+
+ align:start position:0%
+this is a stand
+that the italian post office made in the
+
+ align:start position:0%
+that the italian post office made in the
+ 
+
+ align:start position:0%
+that the italian post office made in the
+occasion of bethesda de la donna last
+
+ align:start position:0%
+occasion of bethesda de la donna last
+ 
+
+ align:start position:0%
+occasion of bethesda de la donna last
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+and this is the mimosa flower
+
+ align:start position:0%
+and this is the mimosa flower
+ 
+
+ align:start position:0%
+and this is the mimosa flower
+it's nice it's yellow and it has a very
+
+ align:start position:0%
+it's nice it's yellow and it has a very
+ 
+
+ align:start position:0%
+it's nice it's yellow and it has a very
+sweet smell
+
+ align:start position:0%
+sweet smell
+ 
+
+ align:start position:0%
+sweet smell
+it's a a tree
+
+ align:start position:0%
+it's a a tree
+ 
+
+ align:start position:0%
+it's a a tree
+an albero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this tree is native of australia but
+
+ align:start position:0%
+and this tree is native of australia but
+ 
+
+ align:start position:0%
+and this tree is native of australia but
+we grow it
+
+ align:start position:0%
+we grow it
+ 
+
+ align:start position:0%
+we grow it
+in italy
+
+ align:start position:0%
+in italy
+ 
+
+ align:start position:0%
+in italy
+and particularly the latalot there are a
+
+ align:start position:0%
+and particularly the latalot there are a
+ 
+
+ align:start position:0%
+and particularly the latalot there are a
+lot of mimosa trees
+
+ align:start position:0%
+lot of mimosa trees
+ 
+
+ align:start position:0%
+lot of mimosa trees
+in liguria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you know where liguria is
+
+ align:start position:0%
+do you know where liguria is
+ 
+
+ align:start position:0%
+do you know where liguria is
+so what i was telling you is that we we
+
+ align:start position:0%
+so what i was telling you is that we we
+ 
+
+ align:start position:0%
+so what i was telling you is that we we
+grow a lot of mimosa
+
+ align:start position:0%
+grow a lot of mimosa
+ 
+
+ align:start position:0%
+grow a lot of mimosa
+by the way in english you would say
+
+ align:start position:0%
+by the way in english you would say
+ 
+
+ align:start position:0%
+by the way in english you would say
+acacia it's a certain location it's a
+
+ align:start position:0%
+acacia it's a certain location it's a
+ 
+
+ align:start position:0%
+acacia it's a certain location it's a
+kind of issue
+
+ align:start position:0%
+kind of issue
+ 
+
+ align:start position:0%
+kind of issue
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the vision i was telling you about
+
+ align:start position:0%
+and the vision i was telling you about
+ 
+
+ align:start position:0%
+and the vision i was telling you about
+is called liguria
+
+ align:start position:0%
+is called liguria
+ 
+
+ align:start position:0%
+is called liguria
+and it's here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i've been talking a lot now but it's
+
+ align:start position:0%
+so i've been talking a lot now but it's
+ 
+
+ align:start position:0%
+so i've been talking a lot now but it's
+your turn guys
+
+ align:start position:0%
+your turn guys
+ 
+
+ align:start position:0%
+your turn guys
+i'm also a spectator now it's their turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what did you understand what did they
+
+ align:start position:0%
+what did you understand what did they
+ 
+
+ align:start position:0%
+what did you understand what did they
+say there was the one thing you said you
+
+ align:start position:0%
+say there was the one thing you said you
+ 
+
+ align:start position:0%
+say there was the one thing you said you
+liked doing yeah
+
+ align:start position:0%
+liked doing yeah
+ 
+
+ align:start position:0%
+liked doing yeah
+oh i like food
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes and that's food
+
+ align:start position:0%
+yes and that's food
+ 
+
+ align:start position:0%
+yes and that's food
+so they introduced themselves and they
+
+ align:start position:0%
+so they introduced themselves and they
+ 
+
+ align:start position:0%
+so they introduced themselves and they
+were saying where they come from
+
+ align:start position:0%
+were saying where they come from
+ 
+
+ align:start position:0%
+were saying where they come from
+and then they started discussing about
+
+ align:start position:0%
+and then they started discussing about
+ 
+
+ align:start position:0%
+and then they started discussing about
+what they like
+
+ align:start position:0%
+what they like
+ 
+
+ align:start position:0%
+what they like
+you said you like
+
+ align:start position:0%
+you said you like
+ 
+
+ align:start position:0%
+you said you like
+food
+
+ align:start position:0%
+food
+ 
+
+ align:start position:0%
+food
+i don't remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about they saw each other they're like
+
+ align:start position:0%
+about they saw each other they're like
+ 
+
+ align:start position:0%
+about they saw each other they're like
+oh i'm doing well you're doing well yeah
+
+ align:start position:0%
+oh i'm doing well you're doing well yeah
+ 
+
+ align:start position:0%
+oh i'm doing well you're doing well yeah
+what did you do this weekend
+
+ align:start position:0%
+what did you do this weekend
+ 
+
+ align:start position:0%
+what did you do this weekend
+i slept and
+
+ align:start position:0%
+i slept and
+ 
+
+ align:start position:0%
+i slept and
+did you eat
+
+ align:start position:0%
+did you eat
+ 
+
+ align:start position:0%
+did you eat
+no oh you cooked what are you doing this
+
+ align:start position:0%
+no oh you cooked what are you doing this
+ 
+
+ align:start position:0%
+no oh you cooked what are you doing this
+weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quick pizza
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else did you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is great every italian would
+
+ align:start position:0%
+this is great every italian would
+ 
+
+ align:start position:0%
+this is great every italian would
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+but it was a mix of spanish and italian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+studios
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and everybody would understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for like i am sleeping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+so you use the verb stare
+
+ align:start position:0%
+so you use the verb stare
+ 
+
+ align:start position:0%
+so you use the verb stare
+stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so today we are going to talk a little
+
+ align:start position:0%
+so today we are going to talk a little
+ 
+
+ align:start position:0%
+so today we are going to talk a little
+bit more than usual
+
+ align:start position:0%
+bit more than usual
+ 
+
+ align:start position:0%
+bit more than usual
+i want you to try to talk about
+
+ align:start position:0%
+i want you to try to talk about
+ 
+
+ align:start position:0%
+i want you to try to talk about
+your typical day
+
+ align:start position:0%
+your typical day
+ 
+
+ align:start position:0%
+your typical day
+la nata typically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes surprise hoping that you can okay
+
+ align:start position:0%
+yes surprise hoping that you can okay
+ 
+
+ align:start position:0%
+yes surprise hoping that you can okay
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+so why i didn't say il giorno typical
+
+ align:start position:0%
+so why i didn't say il giorno typical
+ 
+
+ align:start position:0%
+so why i didn't say il giorno typical
+well in general typical would be
+
+ align:start position:0%
+well in general typical would be
+ 
+
+ align:start position:0%
+well in general typical would be
+fine as well
+
+ align:start position:0%
+fine as well
+ 
+
+ align:start position:0%
+fine as well
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we used mostly the word word jornata
+
+ align:start position:0%
+we used mostly the word word jornata
+ 
+
+ align:start position:0%
+we used mostly the word word jornata
+when you want to describe the day
+
+ align:start position:0%
+when you want to describe the day
+ 
+
+ align:start position:0%
+when you want to describe the day
+as something that has a duration
+
+ align:start position:0%
+as something that has a duration
+ 
+
+ align:start position:0%
+as something that has a duration
+while journal is just kind of a date
+
+ align:start position:0%
+while journal is just kind of a date
+ 
+
+ align:start position:0%
+while journal is just kind of a date
+so for example
+
+ align:start position:0%
+so for example
+ 
+
+ align:start position:0%
+so for example
+if i'm
+
+ align:start position:0%
+if i'm
+ 
+
+ align:start position:0%
+if i'm
+meeting you in the morning i can say
+
+ align:start position:0%
+meeting you in the morning i can say
+ 
+
+ align:start position:0%
+meeting you in the morning i can say
+bonjourno
+
+ align:start position:0%
+bonjourno
+ 
+
+ align:start position:0%
+bonjourno
+but then if i want to
+
+ align:start position:0%
+but then if i want to
+ 
+
+ align:start position:0%
+but then if i want to
+wish you have a good day i would say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wants to you don't have to speak italian
+
+ align:start position:0%
+wants to you don't have to speak italian
+ 
+
+ align:start position:0%
+wants to you don't have to speak italian
+you can make a mix of any language
+
+ align:start position:0%
+you can make a mix of any language
+ 
+
+ align:start position:0%
+you can make a mix of any language
+i don't speak chinese
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go shower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes i do a shower
+
+ align:start position:0%
+yes i do a shower
+ 
+
+ align:start position:0%
+yes i do a shower
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and we use the verb fare
+
+ align:start position:0%
+and we use the verb fare
+ 
+
+ align:start position:0%
+and we use the verb fare
+from which we write factcha we use it in
+
+ align:start position:0%
+from which we write factcha we use it in
+ 
+
+ align:start position:0%
+from which we write factcha we use it in
+a lot of different contexts so it's
+
+ align:start position:0%
+a lot of different contexts so it's
+ 
+
+ align:start position:0%
+a lot of different contexts so it's
+really useful facial adoption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is this
+
+ align:start position:0%
+so is this
+ 
+
+ align:start position:0%
+so is this
+feminine masculine singular plural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coffee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then another couple of things
+
+ align:start position:0%
+and then another couple of things
+ 
+
+ align:start position:0%
+and then another couple of things
+that you would do in your journal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a funny word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i usually use the
+
+ align:start position:0%
+i usually use the
+ 
+
+ align:start position:0%
+i usually use the
+washing machine
+
+ align:start position:0%
+washing machine
+ 
+
+ align:start position:0%
+washing machine
+and what we say
+
+ align:start position:0%
+and what we say
+ 
+
+ align:start position:0%
+and what we say
+we say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lava
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a lot of times i get confused when i
+
+ align:start position:0%
+and a lot of times i get confused when i
+ 
+
+ align:start position:0%
+and a lot of times i get confused when i
+speak
+
+ align:start position:0%
+speak
+ 
+
+ align:start position:0%
+speak
+english
+
+ align:start position:0%
+english
+ 
+
+ align:start position:0%
+english
+i tend to say i do the laundry no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right how do you decide
+
+ align:start position:0%
+all right how do you decide
+ 
+
+ align:start position:0%
+all right how do you decide
+on the articles because there's there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e e so there are rules and i wrote them
+
+ align:start position:0%
+e e so there are rules and i wrote them
+ 
+
+ align:start position:0%
+e e so there are rules and i wrote them
+in the blog but
+
+ align:start position:0%
+in the blog but
+ 
+
+ align:start position:0%
+in the blog but
+it takes time to remember the rules so
+
+ align:start position:0%
+it takes time to remember the rules so
+ 
+
+ align:start position:0%
+it takes time to remember the rules so
+the best thing is practice but in this
+
+ align:start position:0%
+the best thing is practice but in this
+ 
+
+ align:start position:0%
+the best thing is practice but in this
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+singular would be amino plural is amici
+
+ align:start position:0%
+singular would be amino plural is amici
+ 
+
+ align:start position:0%
+singular would be amino plural is amici
+it's masculine and it starts with a
+
+ align:start position:0%
+it's masculine and it starts with a
+ 
+
+ align:start position:0%
+it's masculine and it starts with a
+vowel
+
+ align:start position:0%
+vowel
+ 
+
+ align:start position:0%
+vowel
+so for masculine plural you have two
+
+ align:start position:0%
+so for masculine plural you have two
+ 
+
+ align:start position:0%
+so for masculine plural you have two
+options
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since it starts with the vowel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we've been talking a lot about
+
+ align:start position:0%
+but we've been talking a lot about
+ 
+
+ align:start position:0%
+but we've been talking a lot about
+food
+
+ align:start position:0%
+food
+ 
+
+ align:start position:0%
+food
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in italy food plays a very central role
+
+ align:start position:0%
+in italy food plays a very central role
+ 
+
+ align:start position:0%
+in italy food plays a very central role
+so everything
+
+ align:start position:0%
+so everything
+ 
+
+ align:start position:0%
+so everything
+everything revolves around food
+
+ align:start position:0%
+everything revolves around food
+ 
+
+ align:start position:0%
+everything revolves around food
+either manchamo or cucinamo
+
+ align:start position:0%
+either manchamo or cucinamo
+ 
+
+ align:start position:0%
+either manchamo or cucinamo
+or pagliamo di mangiare
+
+ align:start position:0%
+or pagliamo di mangiare
+ 
+
+ align:start position:0%
+or pagliamo di mangiare
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we talk about food what are the main
+
+ align:start position:0%
+we talk about food what are the main
+ 
+
+ align:start position:0%
+we talk about food what are the main
+meals we already heard one
+
+ align:start position:0%
+meals we already heard one
+ 
+
+ align:start position:0%
+meals we already heard one
+conversation
+
+ align:start position:0%
+conversation
+ 
+
+ align:start position:0%
+conversation
+so what is it
+
+ align:start position:0%
+so what is it
+ 
+
+ align:start position:0%
+so what is it
+breakfast yes then we have infrared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it's like a mid-afternoon snack
+
+ align:start position:0%
+yes it's like a mid-afternoon snack
+ 
+
+ align:start position:0%
+yes it's like a mid-afternoon snack
+typically very important
+
+ align:start position:0%
+typically very important
+ 
+
+ align:start position:0%
+typically very important
+usually kids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before dinner and maybe if you're on
+
+ align:start position:0%
+before dinner and maybe if you're on
+ 
+
+ align:start position:0%
+before dinner and maybe if you're on
+vacation you can do it also before lunch
+
+ align:start position:0%
+vacation you can do it also before lunch
+ 
+
+ align:start position:0%
+vacation you can do it also before lunch
+you meet with friends at a bar or at
+
+ align:start position:0%
+you meet with friends at a bar or at
+ 
+
+ align:start position:0%
+you meet with friends at a bar or at
+someone
+
+ align:start position:0%
+someone
+ 
+
+ align:start position:0%
+someone
+house
+
+ align:start position:0%
+house
+ 
+
+ align:start position:0%
+house
+and you drink a glass of wine and you
+
+ align:start position:0%
+and you drink a glass of wine and you
+ 
+
+ align:start position:0%
+and you drink a glass of wine and you
+eat
+
+ align:start position:0%
+eat
+ 
+
+ align:start position:0%
+eat
+chips olives bruschetta
+
+ align:start position:0%
+chips olives bruschetta
+ 
+
+ align:start position:0%
+chips olives bruschetta
+you know some little snacks and this is
+
+ align:start position:0%
+you know some little snacks and this is
+ 
+
+ align:start position:0%
+you know some little snacks and this is
+what we call aperitivo
+
+ align:start position:0%
+what we call aperitivo
+ 
+
+ align:start position:0%
+what we call aperitivo
+and it's really
+
+ align:start position:0%
+and it's really
+ 
+
+ align:start position:0%
+and it's really
+aperitivo
+
+ align:start position:0%
+aperitivo
+ 
+
+ align:start position:0%
+aperitivo
+and it's really fun
+
+ align:start position:0%
+and it's really fun
+ 
+
+ align:start position:0%
+and it's really fun
+it's a fun activity we can't do it here
+
+ align:start position:0%
+it's a fun activity we can't do it here
+ 
+
+ align:start position:0%
+it's a fun activity we can't do it here
+we can do a verity with coke if you're
+
+ align:start position:0%
+we can do a verity with coke if you're
+ 
+
+ align:start position:0%
+we can do a verity with coke if you're
+21.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drink orange juice
+
+ align:start position:0%
+drink orange juice
+ 
+
+ align:start position:0%
+drink orange juice
+but it's a really nice event because you
+
+ align:start position:0%
+but it's a really nice event because you
+ 
+
+ align:start position:0%
+but it's a really nice event because you
+you live you know you finish school or
+
+ align:start position:0%
+you live you know you finish school or
+ 
+
+ align:start position:0%
+you live you know you finish school or
+you finish um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+and you can
+
+ align:start position:0%
+and you can
+ 
+
+ align:start position:0%
+and you can
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as a student it's particularly fun
+
+ align:start position:0%
+and as a student it's particularly fun
+ 
+
+ align:start position:0%
+and as a student it's particularly fun
+because essentially you pay for a glass
+
+ align:start position:0%
+because essentially you pay for a glass
+ 
+
+ align:start position:0%
+because essentially you pay for a glass
+of wine maybe just a few euros and with
+
+ align:start position:0%
+of wine maybe just a few euros and with
+ 
+
+ align:start position:0%
+of wine maybe just a few euros and with
+this glass of wine typically they will
+
+ align:start position:0%
+this glass of wine typically they will
+ 
+
+ align:start position:0%
+this glass of wine typically they will
+give you all kind of food
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sounds perfect yes i like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+china
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we take a typical
+
+ align:start position:0%
+so if we take a typical
+ 
+
+ align:start position:0%
+so if we take a typical
+fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have typically a lot of different
+
+ align:start position:0%
+we have typically a lot of different
+ 
+
+ align:start position:0%
+we have typically a lot of different
+courses right there i listed them here
+
+ align:start position:0%
+courses right there i listed them here
+ 
+
+ align:start position:0%
+courses right there i listed them here
+first time i went to italy with my
+
+ align:start position:0%
+first time i went to italy with my
+ 
+
+ align:start position:0%
+first time i went to italy with my
+husband we were invited for dinner at
+
+ align:start position:0%
+husband we were invited for dinner at
+ 
+
+ align:start position:0%
+husband we were invited for dinner at
+some friend's house
+
+ align:start position:0%
+some friend's house
+ 
+
+ align:start position:0%
+some friend's house
+and so when we started with lanky pasto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we had a nice
+
+ align:start position:0%
+then we had a nice
+ 
+
+ align:start position:0%
+then we had a nice
+dish of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in large quantities so there was a lot
+
+ align:start position:0%
+in large quantities so there was a lot
+ 
+
+ align:start position:0%
+in large quantities so there was a lot
+of pasta
+
+ align:start position:0%
+of pasta
+ 
+
+ align:start position:0%
+of pasta
+so he ate a lot and mike was the guest
+
+ align:start position:0%
+so he ate a lot and mike was the guest
+ 
+
+ align:start position:0%
+so he ate a lot and mike was the guest
+of honor and everybody was telling him
+
+ align:start position:0%
+of honor and everybody was telling him
+ 
+
+ align:start position:0%
+of honor and everybody was telling him
+to manchester
+
+ align:start position:0%
+to manchester
+ 
+
+ align:start position:0%
+to manchester
+that's one dish of pasta second dish of
+
+ align:start position:0%
+that's one dish of pasta second dish of
+ 
+
+ align:start position:0%
+that's one dish of pasta second dish of
+pasta
+
+ align:start position:0%
+pasta
+ 
+
+ align:start position:0%
+pasta
+we need to finish it vanilla we need to
+
+ align:start position:0%
+we need to finish it vanilla we need to
+ 
+
+ align:start position:0%
+we need to finish it vanilla we need to
+finish it
+
+ align:start position:0%
+finish it
+ 
+
+ align:start position:0%
+finish it
+another pasta and then as soon as he
+
+ align:start position:0%
+another pasta and then as soon as he
+ 
+
+ align:start position:0%
+another pasta and then as soon as he
+finished his last piece of pasta
+
+ align:start position:0%
+finished his last piece of pasta
+ 
+
+ align:start position:0%
+finished his last piece of pasta
+everybody said now we can eat it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second course
+
+ align:start position:0%
+second course
+ 
+
+ align:start position:0%
+second course
+typically is pasta rice or soup
+
+ align:start position:0%
+typically is pasta rice or soup
+ 
+
+ align:start position:0%
+typically is pasta rice or soup
+it's a condom
+
+ align:start position:0%
+it's a condom
+ 
+
+ align:start position:0%
+it's a condom
+it can be
+
+ align:start position:0%
+it can be
+ 
+
+ align:start position:0%
+it can be
+some meat
+
+ align:start position:0%
+some meat
+ 
+
+ align:start position:0%
+some meat
+eggs yes
+
+ align:start position:0%
+eggs yes
+ 
+
+ align:start position:0%
+eggs yes
+distechaste
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a side dish
+
+ align:start position:0%
+it's a side dish
+ 
+
+ align:start position:0%
+it's a side dish
+vegetables for example cheese and then
+
+ align:start position:0%
+vegetables for example cheese and then
+ 
+
+ align:start position:0%
+vegetables for example cheese and then
+dolce
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in our classes i don't know if you
+
+ align:start position:0%
+so in our classes i don't know if you
+ 
+
+ align:start position:0%
+so in our classes i don't know if you
+noticed but during the first four weeks
+
+ align:start position:0%
+noticed but during the first four weeks
+ 
+
+ align:start position:0%
+noticed but during the first four weeks
+we were just cooking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then after four weeks
+
+ align:start position:0%
+and then after four weeks
+ 
+
+ align:start position:0%
+and then after four weeks
+and with four weeks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is every time that you take something
+
+ align:start position:0%
+is every time that you take something
+ 
+
+ align:start position:0%
+is every time that you take something
+you mince it
+
+ align:start position:0%
+you mince it
+ 
+
+ align:start position:0%
+you mince it
+you put it together typically you may
+
+ align:start position:0%
+you put it together typically you may
+ 
+
+ align:start position:0%
+you put it together typically you may
+add some
+
+ align:start position:0%
+add some
+ 
+
+ align:start position:0%
+add some
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+bread crumbs maybe one egg so everything
+
+ align:start position:0%
+bread crumbs maybe one egg so everything
+ 
+
+ align:start position:0%
+bread crumbs maybe one egg so everything
+sticks together a little bit of cheese
+
+ align:start position:0%
+sticks together a little bit of cheese
+ 
+
+ align:start position:0%
+sticks together a little bit of cheese
+you make
+
+ align:start position:0%
+you make
+ 
+
+ align:start position:0%
+you make
+some little balls like meatballs
+
+ align:start position:0%
+some little balls like meatballs
+ 
+
+ align:start position:0%
+some little balls like meatballs
+and then you either fry them or you can
+
+ align:start position:0%
+and then you either fry them or you can
+ 
+
+ align:start position:0%
+and then you either fry them or you can
+bake them
+
+ align:start position:0%
+bake them
+ 
+
+ align:start position:0%
+bake them
+or you can cook them at low heat in a
+
+ align:start position:0%
+or you can cook them at low heat in a
+ 
+
+ align:start position:0%
+or you can cook them at low heat in a
+pan maybe you can add some pasade
+
+ align:start position:0%
+pan maybe you can add some pasade
+ 
+
+ align:start position:0%
+pan maybe you can add some pasade
+pomodoro there are a lot of different
+
+ align:start position:0%
+pomodoro there are a lot of different
+ 
+
+ align:start position:0%
+pomodoro there are a lot of different
+qualities so epileptic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/F6H50Hbulbk.txt b/F6H50Hbulbk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..53ee888ee8695521f7a0f42aab4e74e120456dff
--- /dev/null
+++ b/F6H50Hbulbk.txt
@@ -0,0 +1,225 @@
+We now come to a very important
+concept, the concept
+
+of independence of
+random variables.
+
+We are already familiar with the
+notion of independence of
+
+two events.
+
+We have the mathematical
+definition, and the
+
+interpretation is that
+conditional probabilities are
+
+the same as unconditional
+ones.
+
+Intuitively, when you are told
+that B occurred, this does not
+
+change your beliefs about A,
+and so the conditional
+
+probability of A is the same
+as the unconditional
+
+probability.
+
+We have a similar definition
+of independence of a random
+
+variable and an event A. The
+mathematical definition is
+
+that event A and the event that
+X takes on a specific
+
+value, that these two events
+are independent in the
+
+ordinary sense.
+
+So the probability of both of
+these events happening is the
+
+product of their individual
+probabilities.
+
+But we require this to be true
+for all values of little x.
+
+Intuitively, if I tell you that
+A occurred, this is not
+
+going to change the distribution
+of the random
+
+variable x.
+
+This is one interpretation of
+what independence means in
+
+this context.
+
+And this has to be true for all
+values of little x, that
+
+is, when [the]
+
+event occurs, the probabilities
+of any
+
+particular little x [are]
+
+going to be the same as the
+original unconditional
+
+probabilities.
+
+We also have a symmetrical
+interpretation.
+
+If I tell you the value of
+X, then the conditional
+
+probability of event A is
+not going to change.
+
+It's going to be the same as the
+unconditional probability.
+
+And again, this is going to be
+the case for all values of X.
+
+So, no matter what they tell
+you about X, your beliefs
+
+about A are not going
+to change.
+
+We can now move and define the
+notion of independence of two
+
+random variables.
+
+The mathematical definition is
+that the event that X takes on
+
+a value little x and the event
+that Y takes on a value little
+
+y, these two events are
+independent, and this is true
+
+for all possible values of
+little x and little y.
+
+In PMF notation, this
+relation here can be
+
+written in this form.
+
+And basically, the joint PMF
+factors out as a product of
+
+the marginal PMFs of the
+two random variables.
+
+Again, this relation has to be
+true for all possible little x
+
+and little y.
+
+What does independence mean?
+
+When I tell you the value of y,
+and no matter what value I
+
+tell you, your beliefs about
+X will not change.
+
+So that the conditional PMF of
+X given Y is going to be the
+
+same as the unconditional PMF of
+X. And this has to be true
+
+for any values of the arguments
+of these PMFs.
+
+There is also a symmetric
+interpretation, which is that
+
+the conditional PMF of Y given
+X is going to be the same as
+
+the unconditional PMF of Y.
+We have the symmetric
+
+interpretation because, as we
+can see from this definition,
+
+X and Y have symmetric roles.
+
+Finally, we can define the
+notion of independence of
+
+multiple random variables
+by a similar relation.
+
+Here, the definition is for
+the case of three random
+
+variables, but you can imagine
+how the definition for any
+
+finite number of random
+variables will go.
+
+Namely, the joint PMF of all
+the random variables can be
+
+expressed as the product of the
+
+corresponding marginal PMFs.
+
+What is the intuitive
+interpretation of
+
+independence here?
+
+It means that information
+about some of the random
+
+variables will not change your
+beliefs, the probabilities,
+
+about the remaining
+random variables.
+
+Any conditional probabilities
+and any conditional PMFs will
+
+be the same as the unconditional
+ones.
+
+In the real world, independence
+models situations
+
+where each of the random
+variables is generated in a
+
+decoupled manner, in a separate
+probabilistic
+
+experiment.
+
+And these probabilistic
+experiments do not interact
+
+with each other and have no
+common sources of uncertainty.
\ No newline at end of file
diff --git a/FrrTXj13DNk.txt b/FrrTXj13DNk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3aadf23b98dfe41e54d05015d3774de9bed38d5f
--- /dev/null
+++ b/FrrTXj13DNk.txt
@@ -0,0 +1,7795 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so you see that uh I thought
+
+ align:start position:0%
+ocw.mit.edu so you see that uh I thought
+ 
+
+ align:start position:0%
+ocw.mit.edu so you see that uh I thought
+maybe we've got enough uh good
+
+ align:start position:0%
+maybe we've got enough uh good
+ 
+
+ align:start position:0%
+maybe we've got enough uh good
+examples in theory where we need some
+
+ align:start position:0%
+examples in theory where we need some
+ 
+
+ align:start position:0%
+examples in theory where we need some
+practice we need some uh
+
+ align:start position:0%
+practice we need some uh
+ 
+
+ align:start position:0%
+practice we need some uh
+exper experiments with some of the
+
+ align:start position:0%
+exper experiments with some of the
+ 
+
+ align:start position:0%
+exper experiments with some of the
+finite difference methods that we've
+
+ align:start position:0%
+finite difference methods that we've
+ 
+
+ align:start position:0%
+finite difference methods that we've
+spoken about so I created this homework
+
+ align:start position:0%
+spoken about so I created this homework
+ 
+
+ align:start position:0%
+spoken about so I created this homework
+in which you would like choose one of
+
+ align:start position:0%
+in which you would like choose one of
+ 
+
+ align:start position:0%
+in which you would like choose one of
+these uh that we've done well actually
+
+ align:start position:0%
+these uh that we've done well actually
+ 
+
+ align:start position:0%
+these uh that we've done well actually
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+two uh the shinger equation which has
+
+ align:start position:0%
+two uh the shinger equation which has
+ 
+
+ align:start position:0%
+two uh the shinger equation which has
+that imaginary I in there uh we haven't
+
+ align:start position:0%
+that imaginary I in there uh we haven't
+ 
+
+ align:start position:0%
+that imaginary I in there uh we haven't
+spoken about yet so uh but you could um
+
+ align:start position:0%
+spoken about yet so uh but you could um
+ 
+
+ align:start position:0%
+spoken about yet so uh but you could um
+do the kind of fora analysis that we've
+
+ align:start position:0%
+do the kind of fora analysis that we've
+ 
+
+ align:start position:0%
+do the kind of fora analysis that we've
+done for the heat equation but of course
+
+ align:start position:0%
+done for the heat equation but of course
+ 
+
+ align:start position:0%
+done for the heat equation but of course
+it's going to be different because of
+
+ align:start position:0%
+it's going to be different because of
+ 
+
+ align:start position:0%
+it's going to be different because of
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+I we you'll get an e to the minus i k 2
+
+ align:start position:0%
+I we you'll get an e to the minus i k 2
+ 
+
+ align:start position:0%
+I we you'll get an e to the minus i k 2
+T I guess and that means that's a number
+
+ align:start position:0%
+T I guess and that means that's a number
+ 
+
+ align:start position:0%
+T I guess and that means that's a number
+of of uh absolute value one instead of a
+
+ align:start position:0%
+of of uh absolute value one instead of a
+ 
+
+ align:start position:0%
+of of uh absolute value one instead of a
+rapidly
+
+ align:start position:0%
+rapidly
+ 
+
+ align:start position:0%
+rapidly
+decaying uh coefficient okay so my idea
+
+ align:start position:0%
+decaying uh coefficient okay so my idea
+ 
+
+ align:start position:0%
+decaying uh coefficient okay so my idea
+is to choose one of those groups or a
+
+ align:start position:0%
+is to choose one of those groups or a
+ 
+
+ align:start position:0%
+is to choose one of those groups or a
+number five if you want
+
+ align:start position:0%
+number five if you want
+ 
+
+ align:start position:0%
+number five if you want
+and uh Say by next Friday uh just give
+
+ align:start position:0%
+and uh Say by next Friday uh just give
+ 
+
+ align:start position:0%
+and uh Say by next Friday uh just give
+me some
+
+ align:start position:0%
+me some
+ 
+
+ align:start position:0%
+me some
+uh uh experiment with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code in this case you could use well we
+
+ align:start position:0%
+code in this case you could use well we
+ 
+
+ align:start position:0%
+code in this case you could use well we
+have four methods and three of them are
+
+ align:start position:0%
+have four methods and three of them are
+ 
+
+ align:start position:0%
+have four methods and three of them are
+already uh in code and you're welcome to
+
+ align:start position:0%
+already uh in code and you're welcome to
+ 
+
+ align:start position:0%
+already uh in code and you're welcome to
+use those or your own and and I raised
+
+ align:start position:0%
+use those or your own and and I raised
+ 
+
+ align:start position:0%
+use those or your own and and I raised
+questions last time and I'll put this on
+
+ align:start position:0%
+questions last time and I'll put this on
+ 
+
+ align:start position:0%
+questions last time and I'll put this on
+the website with a little more detail so
+
+ align:start position:0%
+the website with a little more detail so
+ 
+
+ align:start position:0%
+the website with a little more detail so
+ju just to give you an idea of what's
+
+ align:start position:0%
+ju just to give you an idea of what's
+ 
+
+ align:start position:0%
+ju just to give you an idea of what's
+coming uh so this is the problem that
+
+ align:start position:0%
+coming uh so this is the problem that
+ 
+
+ align:start position:0%
+coming uh so this is the problem that
+we're in the middle of speaking about
+
+ align:start position:0%
+we're in the middle of speaking about
+ 
+
+ align:start position:0%
+we're in the middle of speaking about
+near the end the mixture of convection
+
+ align:start position:0%
+near the end the mixture of convection
+ 
+
+ align:start position:0%
+near the end the mixture of convection
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+diffusion and this is shringer which is
+
+ align:start position:0%
+diffusion and this is shringer which is
+ 
+
+ align:start position:0%
+diffusion and this is shringer which is
+new this is the advection equation or
+
+ align:start position:0%
+new this is the advection equation or
+ 
+
+ align:start position:0%
+new this is the advection equation or
+the one-way wave equation which we've
+
+ align:start position:0%
+the one-way wave equation which we've
+ 
+
+ align:start position:0%
+the one-way wave equation which we've
+started with and this is what's this
+
+ align:start position:0%
+started with and this is what's this
+ 
+
+ align:start position:0%
+started with and this is what's this
+will be the subject of today's lecture
+
+ align:start position:0%
+will be the subject of today's lecture
+ 
+
+ align:start position:0%
+will be the subject of today's lecture
+and and next time and the best uh
+
+ align:start position:0%
+and and next time and the best uh
+ 
+
+ align:start position:0%
+and and next time and the best uh
+reference I can give as well as the
+
+ align:start position:0%
+reference I can give as well as the
+ 
+
+ align:start position:0%
+reference I can give as well as the
+textbook the applied math book has
+
+ align:start position:0%
+textbook the applied math book has
+ 
+
+ align:start position:0%
+textbook the applied math book has
+uh significant uh discussion of of of
+
+ align:start position:0%
+uh significant uh discussion of of of
+ 
+
+ align:start position:0%
+uh significant uh discussion of of of
+this conservation law but also it was
+
+ align:start position:0%
+this conservation law but also it was
+ 
+
+ align:start position:0%
+this conservation law but also it was
+it's very well presented in the 16920
+
+ align:start position:0%
+it's very well presented in the 16920
+ 
+
+ align:start position:0%
+it's very well presented in the 16920
+lecture notes that are on open
+
+ align:start position:0%
+lecture notes that are on open
+ 
+
+ align:start position:0%
+lecture notes that are on open
+courseware lectures 11 and 12 so I'm I'm
+
+ align:start position:0%
+courseware lectures 11 and 12 so I'm I'm
+ 
+
+ align:start position:0%
+courseware lectures 11 and 12 so I'm I'm
+I'm going to use those as a guide in in
+
+ align:start position:0%
+I'm going to use those as a guide in in
+ 
+
+ align:start position:0%
+I'm going to use those as a guide in in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+lecture anyway we can I thought i' just
+
+ align:start position:0%
+lecture anyway we can I thought i' just
+ 
+
+ align:start position:0%
+lecture anyway we can I thought i' just
+uh uh put that up as uh
+
+ align:start position:0%
+uh uh put that up as uh
+ 
+
+ align:start position:0%
+uh uh put that up as uh
+um you know time to see
+
+ align:start position:0%
+um you know time to see
+ 
+
+ align:start position:0%
+um you know time to see
+what what various difference methods
+
+ align:start position:0%
+what what various difference methods
+ 
+
+ align:start position:0%
+what what various difference methods
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+do and uh and again it'll be on the
+
+ align:start position:0%
+do and uh and again it'll be on the
+ 
+
+ align:start position:0%
+do and uh and again it'll be on the
+website okay then now to to say another
+
+ align:start position:0%
+website okay then now to to say another
+ 
+
+ align:start position:0%
+website okay then now to to say another
+word about this uh this one this
+
+ align:start position:0%
+word about this uh this one this
+ 
+
+ align:start position:0%
+word about this uh this one this
+uh convection diffusion equation
+
+ align:start position:0%
+uh convection diffusion equation
+ 
+
+ align:start position:0%
+uh convection diffusion equation
+so last time I wrote down a difference
+
+ align:start position:0%
+so last time I wrote down a difference
+ 
+
+ align:start position:0%
+so last time I wrote down a difference
+equation very much like
+
+ align:start position:0%
+equation very much like
+ 
+
+ align:start position:0%
+equation very much like
+that except what I wrote down last time
+
+ align:start position:0%
+that except what I wrote down last time
+ 
+
+ align:start position:0%
+that except what I wrote down last time
+was upwinded so that was just
+
+ align:start position:0%
+was upwinded so that was just
+ 
+
+ align:start position:0%
+was upwinded so that was just
+J now it's j minus
+
+ align:start position:0%
+J now it's j minus
+ 
+
+ align:start position:0%
+J now it's j minus
+one and the choice there is not clear
+
+ align:start position:0%
+one and the choice there is not clear
+ 
+
+ align:start position:0%
+one and the choice there is not clear
+this gives us uh higher accuracy of
+
+ align:start position:0%
+this gives us uh higher accuracy of
+ 
+
+ align:start position:0%
+this gives us uh higher accuracy of
+course for
+
+ align:start position:0%
+course for
+ 
+
+ align:start position:0%
+course for
+that X difference because it's centered
+
+ align:start position:0%
+that X difference because it's centered
+ 
+
+ align:start position:0%
+that X difference because it's centered
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J and we still have this centered of
+
+ align:start position:0%
+J and we still have this centered of
+ 
+
+ align:start position:0%
+J and we still have this centered of
+course the second difference is centered
+
+ align:start position:0%
+course the second difference is centered
+ 
+
+ align:start position:0%
+course the second difference is centered
+here so I wrote down here what the uh
+
+ align:start position:0%
+here so I wrote down here what the uh
+ 
+
+ align:start position:0%
+here so I wrote down here what the uh
+coefficients are of the three old values
+
+ align:start position:0%
+coefficients are of the three old values
+ 
+
+ align:start position:0%
+coefficients are of the three old values
+at J + one at J and at J minus one but
+
+ align:start position:0%
+at J + one at J and at J minus one but
+ 
+
+ align:start position:0%
+at J + one at J and at J minus one but
+there's one uh
+
+ align:start position:0%
+there's one uh
+ 
+
+ align:start position:0%
+there's one uh
+important Point
+
+ align:start position:0%
+important Point
+ 
+
+ align:start position:0%
+important Point
+here uh the price for that extra
+
+ align:start position:0%
+here uh the price for that extra
+ 
+
+ align:start position:0%
+here uh the price for that extra
+accuracy was Poss may possibly
+
+ align:start position:0%
+accuracy was Poss may possibly
+ 
+
+ align:start position:0%
+accuracy was Poss may possibly
+be a negative coefficient this could be
+
+ align:start position:0%
+be a negative coefficient this could be
+ 
+
+ align:start position:0%
+be a negative coefficient this could be
+negative or it could be positive it
+
+ align:start position:0%
+negative or it could be positive it
+ 
+
+ align:start position:0%
+negative or it could be positive it
+depends which is more important the
+
+ align:start position:0%
+depends which is more important the
+ 
+
+ align:start position:0%
+depends which is more important the
+small R the the convection part or the
+
+ align:start position:0%
+small R the the convection part or the
+ 
+
+ align:start position:0%
+small R the the convection part or the
+Big R and uh let let me let me uh follow
+
+ align:start position:0%
+Big R and uh let let me let me uh follow
+ 
+
+ align:start position:0%
+Big R and uh let let me let me uh follow
+up so you you remember the price that if
+
+ align:start position:0%
+up so you you remember the price that if
+ 
+
+ align:start position:0%
+up so you you remember the price that if
+if we see a negative
+
+ align:start position:0%
+if we see a negative
+ 
+
+ align:start position:0%
+if we see a negative
+coefficient then we uh have we expect
+
+ align:start position:0%
+coefficient then we uh have we expect
+ 
+
+ align:start position:0%
+coefficient then we uh have we expect
+some oscillations to appear and actually
+
+ align:start position:0%
+some oscillations to appear and actually
+ 
+
+ align:start position:0%
+some oscillations to appear and actually
+they were supposed to appear in figure
+
+ align:start position:0%
+they were supposed to appear in figure
+ 
+
+ align:start position:0%
+they were supposed to appear in figure
+512 but it hasn't been done yet and if
+
+ align:start position:0%
+512 but it hasn't been done yet and if
+ 
+
+ align:start position:0%
+512 but it hasn't been done yet and if
+you would choose this one and do figure
+
+ align:start position:0%
+you would choose this one and do figure
+ 
+
+ align:start position:0%
+you would choose this one and do figure
+512 I'll would be incredibly
+
+ align:start position:0%
+512 I'll would be incredibly
+ 
+
+ align:start position:0%
+512 I'll would be incredibly
+grateful so figure 512 was to show uh
+
+ align:start position:0%
+grateful so figure 512 was to show uh
+ 
+
+ align:start position:0%
+grateful so figure 512 was to show uh
+the evolution of a from a un not uh for
+
+ align:start position:0%
+the evolution of a from a un not uh for
+ 
+
+ align:start position:0%
+the evolution of a from a un not uh for
+the convection
+
+ align:start position:0%
+the convection
+ 
+
+ align:start position:0%
+the convection
+diffusion okay so can I
+
+ align:start position:0%
+diffusion okay so can I
+ 
+
+ align:start position:0%
+diffusion okay so can I
+just do you see that in comparing r with
+
+ align:start position:0%
+just do you see that in comparing r with
+ 
+
+ align:start position:0%
+just do you see that in comparing r with
+r over
+
+ align:start position:0%
+r over
+ 
+
+ align:start position:0%
+r over
+two we're those are dimensionless
+
+ align:start position:0%
+two we're those are dimensionless
+ 
+
+ align:start position:0%
+two we're those are dimensionless
+quantities right can I can I take
+
+ align:start position:0%
+quantities right can I can I take
+ 
+
+ align:start position:0%
+quantities right can I can I take
+another minute to try I'm a total
+
+ align:start position:0%
+another minute to try I'm a total
+ 
+
+ align:start position:0%
+another minute to try I'm a total
+amateur at uh dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis I did always think however
+
+ align:start position:0%
+analysis I did always think however
+ 
+
+ align:start position:0%
+analysis I did always think however
+that Einstein could have proved well not
+
+ align:start position:0%
+that Einstein could have proved well not
+ 
+
+ align:start position:0%
+that Einstein could have proved well not
+maybe proved but could have conjectured
+
+ align:start position:0%
+maybe proved but could have conjectured
+ 
+
+ align:start position:0%
+maybe proved but could have conjectured
+that e was mc^ s the most important
+
+ align:start position:0%
+that e was mc^ s the most important
+ 
+
+ align:start position:0%
+that e was mc^ s the most important
+equation in relativity just by checking
+
+ align:start position:0%
+equation in relativity just by checking
+ 
+
+ align:start position:0%
+equation in relativity just by checking
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dimensions I don't know if that would I
+
+ align:start position:0%
+dimensions I don't know if that would I
+ 
+
+ align:start position:0%
+dimensions I don't know if that would I
+mean right that would like might might
+
+ align:start position:0%
+mean right that would like might might
+ 
+
+ align:start position:0%
+mean right that would like might might
+have occurred to him to realize that mc^
+
+ align:start position:0%
+have occurred to him to realize that mc^
+ 
+
+ align:start position:0%
+have occurred to him to realize that mc^
+s has the dimensions if we wrote those
+
+ align:start position:0%
+s has the dimensions if we wrote those
+ 
+
+ align:start position:0%
+s has the dimensions if we wrote those
+out of
+
+ align:start position:0%
+out of
+ 
+
+ align:start position:0%
+out of
+energy I don't know if that uh put an
+
+ align:start position:0%
+energy I don't know if that uh put an
+ 
+
+ align:start position:0%
+energy I don't know if that uh put an
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+uh into the into the system which
+
+ align:start position:0%
+uh into the into the system which
+ 
+
+ align:start position:0%
+uh into the into the system which
+produced of course that the fact that
+
+ align:start position:0%
+produced of course that the fact that
+ 
+
+ align:start position:0%
+produced of course that the fact that
+and of course there would be a
+
+ align:start position:0%
+and of course there would be a
+ 
+
+ align:start position:0%
+and of course there would be a
+dimensionless constant which amazingly
+
+ align:start position:0%
+dimensionless constant which amazingly
+ 
+
+ align:start position:0%
+dimensionless constant which amazingly
+happens to be
+
+ align:start position:0%
+happens to be
+ 
+
+ align:start position:0%
+happens to be
+one okay so dimensional analysis could
+
+ align:start position:0%
+one okay so dimensional analysis could
+ 
+
+ align:start position:0%
+one okay so dimensional analysis could
+like change the world this won't quite
+
+ align:start position:0%
+like change the world this won't quite
+ 
+
+ align:start position:0%
+like change the world this won't quite
+change the world but a little a little
+
+ align:start position:0%
+change the world but a little a little
+ 
+
+ align:start position:0%
+change the world but a little a little
+touch of of uh something okay so can I
+
+ align:start position:0%
+touch of of uh something okay so can I
+ 
+
+ align:start position:0%
+touch of of uh something okay so can I
+just uh uh you remember that this PE
+
+ align:start position:0%
+just uh uh you remember that this PE
+ 
+
+ align:start position:0%
+just uh uh you remember that this PE
+number and I'll write his name down
+
+ align:start position:0%
+number and I'll write his name down
+ 
+
+ align:start position:0%
+number and I'll write his name down
+again p c e t the peklay number in the
+
+ align:start position:0%
+again p c e t the peklay number in the
+ 
+
+ align:start position:0%
+again p c e t the peklay number in the
+uh differential equation the peklay
+
+ align:start position:0%
+uh differential equation the peklay
+ 
+
+ align:start position:0%
+uh differential equation the peklay
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+was a ratio essentially a ratio of
+
+ align:start position:0%
+was a ratio essentially a ratio of
+ 
+
+ align:start position:0%
+was a ratio essentially a ratio of
+C to D but to get the uh I think we
+
+ align:start position:0%
+C to D but to get the uh I think we
+ 
+
+ align:start position:0%
+C to D but to get the uh I think we
+needed was that what we
+
+ align:start position:0%
+needed was that what we
+ 
+
+ align:start position:0%
+needed was that what we
+needed we needed a we needed a length
+
+ align:start position:0%
+needed we needed a we needed a length
+ 
+
+ align:start position:0%
+needed we needed a we needed a length
+to make it
+
+ align:start position:0%
+to make it
+ 
+
+ align:start position:0%
+to make it
+dimensionless C is the coefficient for C
+
+ align:start position:0%
+dimensionless C is the coefficient for C
+ 
+
+ align:start position:0%
+dimensionless C is the coefficient for C
+over D sort of tells us roughly the
+
+ align:start position:0%
+over D sort of tells us roughly the
+ 
+
+ align:start position:0%
+over D sort of tells us roughly the
+importance of convection and diffusion
+
+ align:start position:0%
+importance of convection and diffusion
+ 
+
+ align:start position:0%
+importance of convection and diffusion
+but we but there's a length scale to be
+
+ align:start position:0%
+but we but there's a length scale to be
+ 
+
+ align:start position:0%
+but we but there's a length scale to be
+included now the cell Peekay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number which I'll just call P I'm just
+
+ align:start position:0%
+number which I'll just call P I'm just
+ 
+
+ align:start position:0%
+number which I'll just call P I'm just
+going to take to be R over R because
+
+ align:start position:0%
+going to take to be R over R because
+ 
+
+ align:start position:0%
+going to take to be R over R because
+those are dimensionals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you see that it's going to play a
+
+ align:start position:0%
+and you see that it's going to play a
+ 
+
+ align:start position:0%
+and you see that it's going to play a
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+here uh let me see I forg uh I think I
+
+ align:start position:0%
+here uh let me see I forg uh I think I
+ 
+
+ align:start position:0%
+here uh let me see I forg uh I think I
+want R over R uh maybe I want a
+
+ align:start position:0%
+want R over R uh maybe I want a
+ 
+
+ align:start position:0%
+want R over R uh maybe I want a
+two just because I would like that to
+
+ align:start position:0%
+two just because I would like that to
+ 
+
+ align:start position:0%
+two just because I would like that to
+I'd like it to come out Simply there
+
+ align:start position:0%
+I'd like it to come out Simply there
+ 
+
+ align:start position:0%
+I'd like it to come out Simply there
+right okay uh so I may put in a two so
+
+ align:start position:0%
+right okay uh so I may put in a two so
+ 
+
+ align:start position:0%
+right okay uh so I may put in a two so
+that R would be two RP where did that
+
+ align:start position:0%
+that R would be two RP where did that
+ 
+
+ align:start position:0%
+that R would be two RP where did that
+two come from by the way I guess it came
+
+ align:start position:0%
+two come from by the way I guess it came
+ 
+
+ align:start position:0%
+two come from by the way I guess it came
+from there right that was the that was
+
+ align:start position:0%
+from there right that was the that was
+ 
+
+ align:start position:0%
+from there right that was the that was
+it came from that minus 12 so probably I
+
+ align:start position:0%
+it came from that minus 12 so probably I
+ 
+
+ align:start position:0%
+it came from that minus 12 so probably I
+want a two there just so that I have a
+
+ align:start position:0%
+want a two there just so that I have a
+ 
+
+ align:start position:0%
+want a two there just so that I have a
+very simple decision of whether
+
+ align:start position:0%
+very simple decision of whether
+ 
+
+ align:start position:0%
+very simple decision of whether
+this uh coefficient is positive or
+
+ align:start position:0%
+this uh coefficient is positive or
+ 
+
+ align:start position:0%
+this uh coefficient is positive or
+negative yeah uh let me so let me put in
+
+ align:start position:0%
+negative yeah uh let me so let me put in
+ 
+
+ align:start position:0%
+negative yeah uh let me so let me put in
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+two okay so r/2 is RP then this this
+
+ align:start position:0%
+two okay so r/2 is RP then this this
+ 
+
+ align:start position:0%
+two okay so r/2 is RP then this this
+quantity is R * P so this is r - R * P
+
+ align:start position:0%
+quantity is R * P so this is r - R * P
+ 
+
+ align:start position:0%
+quantity is R * P so this is r - R * P
+or it's R which we know is okay Time 1
+
+ align:start position:0%
+or it's R which we know is okay Time 1
+ 
+
+ align:start position:0%
+or it's R which we know is okay Time 1
+minus p in other words P smaller than
+
+ align:start position:0%
+minus p in other words P smaller than
+ 
+
+ align:start position:0%
+minus p in other words P smaller than
+one that coefficient all the three
+
+ align:start position:0%
+one that coefficient all the three
+ 
+
+ align:start position:0%
+one that coefficient all the three
+coefficients are positive it's certainly
+
+ align:start position:0%
+coefficients are positive it's certainly
+ 
+
+ align:start position:0%
+coefficients are positive it's certainly
+stable not only stable it can't
+
+ align:start position:0%
+stable not only stable it can't
+ 
+
+ align:start position:0%
+stable not only stable it can't
+oscillate it we can't have uh we're
+
+ align:start position:0%
+oscillate it we can't have uh we're
+ 
+
+ align:start position:0%
+oscillate it we can't have uh we're
+taking a combination of the three old
+
+ align:start position:0%
+taking a combination of the three old
+ 
+
+ align:start position:0%
+taking a combination of the three old
+values and uh oscillations can't show up
+
+ align:start position:0%
+values and uh oscillations can't show up
+ 
+
+ align:start position:0%
+values and uh oscillations can't show up
+okay so just to see what is this then
+
+ align:start position:0%
+okay so just to see what is this then
+ 
+
+ align:start position:0%
+okay so just to see what is this then
+you remember that R is C delta T over
+
+ align:start position:0%
+you remember that R is C delta T over
+ 
+
+ align:start position:0%
+you remember that R is C delta T over
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+and capital r is D delta T over Delta
+
+ align:start position:0%
+and capital r is D delta T over Delta
+ 
+
+ align:start position:0%
+and capital r is D delta T over Delta
+x^2 so just to complete this uh the
+
+ align:start position:0%
+x^2 so just to complete this uh the
+ 
+
+ align:start position:0%
+x^2 so just to complete this uh the
+Delta T's cancel one of the Delta X
+
+ align:start position:0%
+Delta T's cancel one of the Delta X
+ 
+
+ align:start position:0%
+Delta T's cancel one of the Delta X
+cancels the other one comes up so it's C
+
+ align:start position:0%
+cancels the other one comes up so it's C
+ 
+
+ align:start position:0%
+cancels the other one comes up so it's C
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+D and we have a Delta X and A
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so that's why it's called the cell pay
+
+ align:start position:0%
+2 so that's why it's called the cell pay
+ 
+
+ align:start position:0%
+2 so that's why it's called the cell pay
+number because it's the cell size or in
+
+ align:start position:0%
+number because it's the cell size or in
+ 
+
+ align:start position:0%
+number because it's the cell size or in
+my convention half the cell size that uh
+
+ align:start position:0%
+my convention half the cell size that uh
+ 
+
+ align:start position:0%
+my convention half the cell size that uh
+gives the length scale and uh decides
+
+ align:start position:0%
+gives the length scale and uh decides
+ 
+
+ align:start position:0%
+gives the length scale and uh decides
+whether p is so so I'm just going to
+
+ align:start position:0%
+whether p is so so I'm just going to
+ 
+
+ align:start position:0%
+whether p is so so I'm just going to
+write down the conclusion that that the
+
+ align:start position:0%
+write down the conclusion that that the
+ 
+
+ align:start position:0%
+write down the conclusion that that the
+figure should show uh P smaller than
+
+ align:start position:0%
+figure should show uh P smaller than
+ 
+
+ align:start position:0%
+figure should show uh P smaller than
+one that means that this coefficient is
+
+ align:start position:0%
+one that means that this coefficient is
+ 
+
+ align:start position:0%
+one that means that this coefficient is
+also positive so that's positive
+
+ align:start position:0%
+also positive so that's positive
+ 
+
+ align:start position:0%
+also positive so that's positive
+coefficients no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillation and I think you'll see in
+
+ align:start position:0%
+oscillation and I think you'll see in
+ 
+
+ align:start position:0%
+oscillation and I think you'll see in
+the in from the from the output that P
+
+ align:start position:0%
+the in from the from the output that P
+ 
+
+ align:start position:0%
+the in from the from the output that P
+bigger than one produces
+
+ align:start position:0%
+bigger than one produces
+ 
+
+ align:start position:0%
+bigger than one produces
+is oscillation we we don't
+
+ align:start position:0%
+is oscillation we we don't
+ 
+
+ align:start position:0%
+is oscillation we we don't
+like in other words we we really don't
+
+ align:start position:0%
+like in other words we we really don't
+ 
+
+ align:start position:0%
+like in other words we we really don't
+want P larger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and uh uh of course you could say
+
+ align:start position:0%
+one and uh uh of course you could say
+ 
+
+ align:start position:0%
+one and uh uh of course you could say
+well look at P it's got a Delta X in it
+
+ align:start position:0%
+well look at P it's got a Delta X in it
+ 
+
+ align:start position:0%
+well look at P it's got a Delta X in it
+that's not that's not going to be a big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number and and and the method will work
+
+ align:start position:0%
+number and and and the method will work
+ 
+
+ align:start position:0%
+number and and and the method will work
+fine as Delta X and delta T go to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh we're going to do a finite
+
+ align:start position:0%
+but uh we're going to do a finite
+ 
+
+ align:start position:0%
+but uh we're going to do a finite
+calculation and so we're seeing for the
+
+ align:start position:0%
+calculation and so we're seeing for the
+ 
+
+ align:start position:0%
+calculation and so we're seeing for the
+first time like because we have two
+
+ align:start position:0%
+first time like because we have two
+ 
+
+ align:start position:0%
+first time like because we have two
+terms that are not dimensionally
+
+ align:start position:0%
+terms that are not dimensionally
+ 
+
+ align:start position:0%
+terms that are not dimensionally
+identical see and D that
+
+ align:start position:0%
+identical see and D that
+ 
+
+ align:start position:0%
+identical see and D that
+uh in that in that competition between
+
+ align:start position:0%
+uh in that in that competition between
+ 
+
+ align:start position:0%
+uh in that in that competition between
+convection and diffusion the length
+
+ align:start position:0%
+convection and diffusion the length
+ 
+
+ align:start position:0%
+convection and diffusion the length
+scale is crucial and the and the mes
+
+ align:start position:0%
+scale is crucial and the and the mes
+ 
+
+ align:start position:0%
+scale is crucial and the and the mes
+size is crucial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I guess the answer is we can resolve
+
+ align:start position:0%
+so I guess the answer is we can resolve
+ 
+
+ align:start position:0%
+so I guess the answer is we can resolve
+it by taking Delta X small enough and
+
+ align:start position:0%
+it by taking Delta X small enough and
+ 
+
+ align:start position:0%
+it by taking Delta X small enough and
+hopefully that's not a problem but of
+
+ align:start position:0%
+hopefully that's not a problem but of
+ 
+
+ align:start position:0%
+hopefully that's not a problem but of
+course you you know that
+
+ align:start position:0%
+course you you know that
+ 
+
+ align:start position:0%
+course you you know that
+uh there are many physical cases in
+
+ align:start position:0%
+uh there are many physical cases in
+ 
+
+ align:start position:0%
+uh there are many physical cases in
+which uh the diffusion coefficient or
+
+ align:start position:0%
+which uh the diffusion coefficient or
+ 
+
+ align:start position:0%
+which uh the diffusion coefficient or
+the viscosity coefficient the is small
+
+ align:start position:0%
+the viscosity coefficient the is small
+ 
+
+ align:start position:0%
+the viscosity coefficient the is small
+is quite small and uh so getting that
+
+ align:start position:0%
+is quite small and uh so getting that
+ 
+
+ align:start position:0%
+is quite small and uh so getting that
+below one might be hard because this D
+
+ align:start position:0%
+below one might be hard because this D
+ 
+
+ align:start position:0%
+below one might be hard because this D
+could be a very small number
+
+ align:start position:0%
+could be a very small number
+ 
+
+ align:start position:0%
+could be a very small number
+yeah okay so that I
+
+ align:start position:0%
+yeah okay so that I
+ 
+
+ align:start position:0%
+yeah okay so that I
+won't maybe can I also mention on the as
+
+ align:start position:0%
+won't maybe can I also mention on the as
+ 
+
+ align:start position:0%
+won't maybe can I also mention on the as
+something that we haven't done here was
+
+ align:start position:0%
+something that we haven't done here was
+ 
+
+ align:start position:0%
+something that we haven't done here was
+to move uh the the
+
+ align:start position:0%
+to move uh the the
+ 
+
+ align:start position:0%
+to move uh the the
+uh the the second derivative this guy to
+
+ align:start position:0%
+uh the the second derivative this guy to
+ 
+
+ align:start position:0%
+uh the the second derivative this guy to
+to time n
+
+ align:start position:0%
+to time n
+ 
+
+ align:start position:0%
+to time n
++1 make it implicit the the diffusion
+
+ align:start position:0%
++1 make it implicit the the diffusion
+ 
+
+ align:start position:0%
++1 make it implicit the the diffusion
+part one often does that the diffusion
+
+ align:start position:0%
+part one often does that the diffusion
+ 
+
+ align:start position:0%
+part one often does that the diffusion
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the term is the one that's forcing us to
+
+ align:start position:0%
+the term is the one that's forcing us to
+ 
+
+ align:start position:0%
+the term is the one that's forcing us to
+take this uh coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R below a half delta T of order Delta X2
+
+ align:start position:0%
+R below a half delta T of order Delta X2
+ 
+
+ align:start position:0%
+R below a half delta T of order Delta X2
+and the way to avoid that is to move the
+
+ align:start position:0%
+and the way to avoid that is to move the
+ 
+
+ align:start position:0%
+and the way to avoid that is to move the
+VIS City term at least half of it up to
+
+ align:start position:0%
+VIS City term at least half of it up to
+ 
+
+ align:start position:0%
+VIS City term at least half of it up to
+the uh up to the new time okay so that's
+
+ align:start position:0%
+the uh up to the new time okay so that's
+ 
+
+ align:start position:0%
+the uh up to the new time okay so that's
+a third method so we've done
+
+ align:start position:0%
+a third method so we've done
+ 
+
+ align:start position:0%
+a third method so we've done
+upwind last time uh centered explicit
+
+ align:start position:0%
+upwind last time uh centered explicit
+ 
+
+ align:start position:0%
+upwind last time uh centered explicit
+this time but then that's a third one
+
+ align:start position:0%
+this time but then that's a third one
+ 
+
+ align:start position:0%
+this time but then that's a third one
+that's uh has to be looked at okay so
+
+ align:start position:0%
+that's uh has to be looked at okay so
+ 
+
+ align:start position:0%
+that's uh has to be looked at okay so
+those those are that that's where uh
+
+ align:start position:0%
+those those are that that's where uh
+ 
+
+ align:start position:0%
+those those are that that's where uh
+um we stand on linear problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I I'm sort of ready to jump into
+
+ align:start position:0%
+uh I I'm sort of ready to jump into
+ 
+
+ align:start position:0%
+uh I I'm sort of ready to jump into
+nonlinear
+
+ align:start position:0%
+nonlinear
+ 
+
+ align:start position:0%
+nonlinear
+ones recognizing that there well there's
+
+ align:start position:0%
+ones recognizing that there well there's
+ 
+
+ align:start position:0%
+ones recognizing that there well there's
+always more to say about linear ones
+
+ align:start position:0%
+always more to say about linear ones
+ 
+
+ align:start position:0%
+always more to say about linear ones
+what are some of the things that we have
+
+ align:start position:0%
+what are some of the things that we have
+ 
+
+ align:start position:0%
+what are some of the things that we have
+not properly discussed boundary
+
+ align:start position:0%
+not properly discussed boundary
+ 
+
+ align:start position:0%
+not properly discussed boundary
+conditions above
+
+ align:start position:0%
+conditions above
+ 
+
+ align:start position:0%
+conditions above
+all boundary conditions we and we could
+
+ align:start position:0%
+all boundary conditions we and we could
+ 
+
+ align:start position:0%
+all boundary conditions we and we could
+we we could uh do something with those
+
+ align:start position:0%
+we we could uh do something with those
+ 
+
+ align:start position:0%
+we we could uh do something with those
+we could and the notes will uh say more
+
+ align:start position:0%
+we could and the notes will uh say more
+ 
+
+ align:start position:0%
+we could and the notes will uh say more
+about boundary conditions so there are
+
+ align:start position:0%
+about boundary conditions so there are
+ 
+
+ align:start position:0%
+about boundary conditions so there are
+several types of boundary conditions I I
+
+ align:start position:0%
+several types of boundary conditions I I
+ 
+
+ align:start position:0%
+several types of boundary conditions I I
+guess I'm going to say something about
+
+ align:start position:0%
+guess I'm going to say something about
+ 
+
+ align:start position:0%
+guess I'm going to say something about
+them now but this will be a board that
+
+ align:start position:0%
+them now but this will be a board that
+ 
+
+ align:start position:0%
+them now but this will be a board that
+kind of gets covered up so boundary
+
+ align:start position:0%
+kind of gets covered up so boundary
+ 
+
+ align:start position:0%
+kind of gets covered up so boundary
+conditions so what are the different
+
+ align:start position:0%
+conditions so what are the different
+ 
+
+ align:start position:0%
+conditions so what are the different
+types well at a real physical boundary
+
+ align:start position:0%
+types well at a real physical boundary
+ 
+
+ align:start position:0%
+types well at a real physical boundary
+we might have U equal 0 say in heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flow we might hold the boundary it might
+
+ align:start position:0%
+flow we might hold the boundary it might
+ 
+
+ align:start position:0%
+flow we might hold the boundary it might
+be the edge of a freezer or something we
+
+ align:start position:0%
+be the edge of a freezer or something we
+ 
+
+ align:start position:0%
+be the edge of a freezer or something we
+might hold the temperature at zero or or
+
+ align:start position:0%
+might hold the temperature at zero or or
+ 
+
+ align:start position:0%
+might hold the temperature at zero or or
+at some at some given value we might
+
+ align:start position:0%
+at some at some given value we might
+ 
+
+ align:start position:0%
+at some at some given value we might
+prescribe U at a
+
+ align:start position:0%
+prescribe U at a
+ 
+
+ align:start position:0%
+prescribe U at a
+boundary or we might prescribe the
+
+ align:start position:0%
+boundary or we might prescribe the
+ 
+
+ align:start position:0%
+boundary or we might prescribe the
+derivative and just in case we're in
+
+ align:start position:0%
+derivative and just in case we're in
+ 
+
+ align:start position:0%
+derivative and just in case we're in
+several Dimensions I'll better write it
+
+ align:start position:0%
+several Dimensions I'll better write it
+ 
+
+ align:start position:0%
+several Dimensions I'll better write it
+as the outgoing derivative could be
+
+ align:start position:0%
+as the outgoing derivative could be
+ 
+
+ align:start position:0%
+as the outgoing derivative could be
+prescribed say Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are those two types of boundary
+
+ align:start position:0%
+so what are those two types of boundary
+ 
+
+ align:start position:0%
+so what are those two types of boundary
+conditions called one's called absorbing
+
+ align:start position:0%
+conditions called one's called absorbing
+ 
+
+ align:start position:0%
+conditions called one's called absorbing
+an absorbing boundary and the other is
+
+ align:start position:0%
+an absorbing boundary and the other is
+ 
+
+ align:start position:0%
+an absorbing boundary and the other is
+an insulated boundary where uh no heat
+
+ align:start position:0%
+an insulated boundary where uh no heat
+ 
+
+ align:start position:0%
+an insulated boundary where uh no heat
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+through to maintain this heat probably
+
+ align:start position:0%
+through to maintain this heat probably
+ 
+
+ align:start position:0%
+through to maintain this heat probably
+does go through if our if our body is
+
+ align:start position:0%
+does go through if our if our body is
+ 
+
+ align:start position:0%
+does go through if our if our body is
+warm and it's we're holding it at zero
+
+ align:start position:0%
+warm and it's we're holding it at zero
+ 
+
+ align:start position:0%
+warm and it's we're holding it at zero
+on its boundary then heat is going to
+
+ align:start position:0%
+on its boundary then heat is going to
+ 
+
+ align:start position:0%
+on its boundary then heat is going to
+travel out
+
+ align:start position:0%
+travel out
+ 
+
+ align:start position:0%
+travel out
+and in fact as time goes to Infinity
+
+ align:start position:0%
+and in fact as time goes to Infinity
+ 
+
+ align:start position:0%
+and in fact as time goes to Infinity
+we're going to approach a a
+
+ align:start position:0%
+we're going to approach a a
+ 
+
+ align:start position:0%
+we're going to approach a a
+cold a uniformally cold thing here
+
+ align:start position:0%
+cold a uniformally cold thing here
+ 
+
+ align:start position:0%
+cold a uniformally cold thing here
+heat's not allowed to travel out so what
+
+ align:start position:0%
+heat's not allowed to travel out so what
+ 
+
+ align:start position:0%
+heat's not allowed to travel out so what
+will happen as time goes on is it will
+
+ align:start position:0%
+will happen as time goes on is it will
+ 
+
+ align:start position:0%
+will happen as time goes on is it will
+uh um approach a constant the
+
+ align:start position:0%
+uh um approach a constant the
+ 
+
+ align:start position:0%
+uh um approach a constant the
+temperature will approach a constant
+
+ align:start position:0%
+temperature will approach a constant
+ 
+
+ align:start position:0%
+temperature will approach a constant
+because it can't leave and it diffuses
+
+ align:start position:0%
+because it can't leave and it diffuses
+ 
+
+ align:start position:0%
+because it can't leave and it diffuses
+and uh and now I wanted to
+
+ align:start position:0%
+and uh and now I wanted to
+ 
+
+ align:start position:0%
+and uh and now I wanted to
+mention a third type of boundary which
+
+ align:start position:0%
+mention a third type of boundary which
+ 
+
+ align:start position:0%
+mention a third type of boundary which
+is a purely computational boundary we we
+
+ align:start position:0%
+is a purely computational boundary we we
+ 
+
+ align:start position:0%
+is a purely computational boundary we we
+we talked last time about uh Maxwell's
+
+ align:start position:0%
+we talked last time about uh Maxwell's
+ 
+
+ align:start position:0%
+we talked last time about uh Maxwell's
+equations in free space and the big
+
+ align:start position:0%
+equations in free space and the big
+ 
+
+ align:start position:0%
+equations in free space and the big
+application of Maxwell's equations or
+
+ align:start position:0%
+application of Maxwell's equations or
+ 
+
+ align:start position:0%
+application of Maxwell's equations or
+one of the big ones historically has
+
+ align:start position:0%
+one of the big ones historically has
+ 
+
+ align:start position:0%
+one of the big ones historically has
+been to like the exterior of an airplane
+
+ align:start position:0%
+been to like the exterior of an airplane
+ 
+
+ align:start position:0%
+been to like the exterior of an airplane
+to radar or other electromagnetic
+
+ align:start position:0%
+to radar or other electromagnetic
+ 
+
+ align:start position:0%
+to radar or other electromagnetic
+signals so what do we do if we have an
+
+ align:start position:0%
+signals so what do we do if we have an
+ 
+
+ align:start position:0%
+signals so what do we do if we have an
+exterior problem see here I was always
+
+ align:start position:0%
+exterior problem see here I was always
+ 
+
+ align:start position:0%
+exterior problem see here I was always
+thinking about an interior problem you
+
+ align:start position:0%
+thinking about an interior problem you
+ 
+
+ align:start position:0%
+thinking about an interior problem you
+know we're we're inside zero to Zer to L
+
+ align:start position:0%
+know we're we're inside zero to Zer to L
+ 
+
+ align:start position:0%
+know we're we're inside zero to Zer to L
+or something but now what do we do if a
+
+ align:start position:0%
+or something but now what do we do if a
+ 
+
+ align:start position:0%
+or something but now what do we do if a
+region is the outside it's free space
+
+ align:start position:0%
+region is the outside it's free space
+ 
+
+ align:start position:0%
+region is the outside it's free space
+all the way well we have to create a
+
+ align:start position:0%
+all the way well we have to create a
+ 
+
+ align:start position:0%
+all the way well we have to create a
+computational box of some sort so we
+
+ align:start position:0%
+computational box of some sort so we
+ 
+
+ align:start position:0%
+computational box of some sort so we
+create a box in which we
+
+ align:start position:0%
+create a box in which we
+ 
+
+ align:start position:0%
+create a box in which we
+compute but but the boundaries of this
+
+ align:start position:0%
+compute but but the boundaries of this
+ 
+
+ align:start position:0%
+compute but but the boundaries of this
+box the X boundaries of it
+
+ align:start position:0%
+box the X boundaries of it
+ 
+
+ align:start position:0%
+box the X boundaries of it
+are purely artificial they're just
+
+ align:start position:0%
+are purely artificial they're just
+ 
+
+ align:start position:0%
+are purely artificial they're just
+because we can't compute to Infinity so
+
+ align:start position:0%
+because we can't compute to Infinity so
+ 
+
+ align:start position:0%
+because we can't compute to Infinity so
+waves travel in this
+
+ align:start position:0%
+waves travel in this
+ 
+
+ align:start position:0%
+waves travel in this
+box and they travel to the so you see
+
+ align:start position:0%
+box and they travel to the so you see
+ 
+
+ align:start position:0%
+box and they travel to the so you see
+what I mean here here's we're we're
+
+ align:start position:0%
+what I mean here here's we're we're
+ 
+
+ align:start position:0%
+what I mean here here's we're we're
+solving it in all this space except
+
+ align:start position:0%
+solving it in all this space except
+ 
+
+ align:start position:0%
+solving it in all this space except
+that's too much so we we that's a that's
+
+ align:start position:0%
+that's too much so we we that's a that's
+ 
+
+ align:start position:0%
+that's too much so we we that's a that's
+meant to be a very large box not a small
+
+ align:start position:0%
+meant to be a very large box not a small
+ 
+
+ align:start position:0%
+meant to be a very large box not a small
+as large as we can
+
+ align:start position:0%
+as large as we can
+ 
+
+ align:start position:0%
+as large as we can
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+but waves are still going to hit the
+
+ align:start position:0%
+but waves are still going to hit the
+ 
+
+ align:start position:0%
+but waves are still going to hit the
+boundary of that box okay what do we
+
+ align:start position:0%
+boundary of that box okay what do we
+ 
+
+ align:start position:0%
+boundary of that box okay what do we
+choose as boundary condition
+
+ align:start position:0%
+choose as boundary condition
+ 
+
+ align:start position:0%
+choose as boundary condition
+there if we don't want it to reflect
+
+ align:start position:0%
+there if we don't want it to reflect
+ 
+
+ align:start position:0%
+there if we don't want it to reflect
+back because it it's not the real it's
+
+ align:start position:0%
+back because it it's not the real it's
+ 
+
+ align:start position:0%
+back because it it's not the real it's
+not a real boundary so we have to create
+
+ align:start position:0%
+not a real boundary so we have to create
+ 
+
+ align:start position:0%
+not a real boundary so we have to create
+an I'll put ABC for absorbing boundary
+
+ align:start position:0%
+an I'll put ABC for absorbing boundary
+ 
+
+ align:start position:0%
+an I'll put ABC for absorbing boundary
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+absorbing that a is for an absorbing
+
+ align:start position:0%
+absorbing that a is for an absorbing
+ 
+
+ align:start position:0%
+absorbing that a is for an absorbing
+boundary condition that that
+
+ align:start position:0%
+boundary condition that that
+ 
+
+ align:start position:0%
+boundary condition that that
+uh that and and the creation of these
+
+ align:start position:0%
+uh that and and the creation of these
+ 
+
+ align:start position:0%
+uh that and and the creation of these
+boundary conditions is a is an important
+
+ align:start position:0%
+boundary conditions is a is an important
+ 
+
+ align:start position:0%
+boundary conditions is a is an important
+topic within finite
+
+ align:start position:0%
+topic within finite
+ 
+
+ align:start position:0%
+topic within finite
+differences uh for Maxwell's equations
+
+ align:start position:0%
+differences uh for Maxwell's equations
+ 
+
+ align:start position:0%
+differences uh for Maxwell's equations
+uh a a good idea was produced and has
+
+ align:start position:0%
+uh a a good idea was produced and has
+ 
+
+ align:start position:0%
+uh a a good idea was produced and has
+has keeps being developed called
+
+ align:start position:0%
+has keeps being developed called
+ 
+
+ align:start position:0%
+has keeps being developed called
+perfectly matched layer the idea in that
+
+ align:start position:0%
+perfectly matched layer the idea in that
+ 
+
+ align:start position:0%
+perfectly matched layer the idea in that
+perfect Ally matched layer let me just
+
+ align:start position:0%
+perfect Ally matched layer let me just
+ 
+
+ align:start position:0%
+perfect Ally matched layer let me just
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+PML and I haven't seen this so much in
+
+ align:start position:0%
+PML and I haven't seen this so much in
+ 
+
+ align:start position:0%
+PML and I haven't seen this so much in
+other uh application areas the idea with
+
+ align:start position:0%
+other uh application areas the idea with
+ 
+
+ align:start position:0%
+other uh application areas the idea with
+this perfectly matched layer is to
+
+ align:start position:0%
+this perfectly matched layer is to
+ 
+
+ align:start position:0%
+this perfectly matched layer is to
+create a
+
+ align:start position:0%
+create a
+ 
+
+ align:start position:0%
+create a
+artificial um dialectric I guess a
+
+ align:start position:0%
+artificial um dialectric I guess a
+ 
+
+ align:start position:0%
+artificial um dialectric I guess a
+dialectric medium it would be in the in
+
+ align:start position:0%
+dialectric medium it would be in the in
+ 
+
+ align:start position:0%
+dialectric medium it would be in the in
+the electromagnetic case an
+
+ align:start position:0%
+the electromagnetic case an
+ 
+
+ align:start position:0%
+the electromagnetic case an
+artificial uh thin
+
+ align:start position:0%
+artificial uh thin
+ 
+
+ align:start position:0%
+artificial uh thin
+layer which
+
+ align:start position:0%
+layer which
+ 
+
+ align:start position:0%
+layer which
+has just the right properties to stop
+
+ align:start position:0%
+has just the right properties to stop
+ 
+
+ align:start position:0%
+has just the right properties to stop
+the wave and swallow
+
+ align:start position:0%
+the wave and swallow
+ 
+
+ align:start position:0%
+the wave and swallow
+it okay I could I'll put on the website
+
+ align:start position:0%
+it okay I could I'll put on the website
+ 
+
+ align:start position:0%
+it okay I could I'll put on the website
+references to um uh to that it's a
+
+ align:start position:0%
+references to um uh to that it's a
+ 
+
+ align:start position:0%
+references to um uh to that it's a
+bright idea and uh but uh not totally
+
+ align:start position:0%
+bright idea and uh but uh not totally
+ 
+
+ align:start position:0%
+bright idea and uh but uh not totally
+simple and uh when we change difference
+
+ align:start position:0%
+simple and uh when we change difference
+ 
+
+ align:start position:0%
+simple and uh when we change difference
+methods then that perfectly matched
+
+ align:start position:0%
+methods then that perfectly matched
+ 
+
+ align:start position:0%
+methods then that perfectly matched
+layer has to go with it okay
+
+ align:start position:0%
+layer has to go with it okay
+ 
+
+ align:start position:0%
+layer has to go with it okay
+that's my that's the end of my thoughts
+
+ align:start position:0%
+that's my that's the end of my thoughts
+ 
+
+ align:start position:0%
+that's my that's the end of my thoughts
+about linear problems for
+
+ align:start position:0%
+about linear problems for
+ 
+
+ align:start position:0%
+about linear problems for
+now we're coming back of course in a few
+
+ align:start position:0%
+now we're coming back of course in a few
+ 
+
+ align:start position:0%
+now we're coming back of course in a few
+weeks to
+
+ align:start position:0%
+weeks to
+ 
+
+ align:start position:0%
+weeks to
+um to solving large systems large linear
+
+ align:start position:0%
+um to solving large systems large linear
+ 
+
+ align:start position:0%
+um to solving large systems large linear
+systems the kind that we would meet if
+
+ align:start position:0%
+systems the kind that we would meet if
+ 
+
+ align:start position:0%
+systems the kind that we would meet if
+we use an implicit
+
+ align:start position:0%
+we use an implicit
+ 
+
+ align:start position:0%
+we use an implicit
+method or the kind that we meet if we're
+
+ align:start position:0%
+method or the kind that we meet if we're
+ 
+
+ align:start position:0%
+method or the kind that we meet if we're
+solving a steady state problem but for
+
+ align:start position:0%
+solving a steady state problem but for
+ 
+
+ align:start position:0%
+solving a steady state problem but for
+now let me go let me go
+
+ align:start position:0%
+now let me go let me go
+ 
+
+ align:start position:0%
+now let me go let me go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um that model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation and you see right away the
+
+ align:start position:0%
+equation and you see right away the
+ 
+
+ align:start position:0%
+equation and you see right away the
+difference between that equation and
+
+ align:start position:0%
+difference between that equation and
+ 
+
+ align:start position:0%
+difference between that equation and
+the advection equation that had a
+
+ align:start position:0%
+the advection equation that had a
+ 
+
+ align:start position:0%
+the advection equation that had a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+velocity here we have a velocity
+
+ align:start position:0%
+velocity here we have a velocity
+ 
+
+ align:start position:0%
+velocity here we have a velocity
+that so C is minus U I
+
+ align:start position:0%
+that so C is minus U I
+ 
+
+ align:start position:0%
+that so C is minus U I
+guess C is minus think of C uh this U as
+
+ align:start position:0%
+guess C is minus think of C uh this U as
+ 
+
+ align:start position:0%
+guess C is minus think of C uh this U as
+being comparable to minus
+
+ align:start position:0%
+being comparable to minus
+ 
+
+ align:start position:0%
+being comparable to minus
+C so in other words If U is positive I'm
+
+ align:start position:0%
+C so in other words If U is positive I'm
+ 
+
+ align:start position:0%
+C so in other words If U is positive I'm
+now going to have waves going to the
+
+ align:start position:0%
+now going to have waves going to the
+ 
+
+ align:start position:0%
+now going to have waves going to the
+right so let me just put this down U
+
+ align:start position:0%
+right so let me just put this down U
+ 
+
+ align:start position:0%
+right so let me just put this down U
+greater than zero will mean
+
+ align:start position:0%
+greater than zero will mean
+ 
+
+ align:start position:0%
+greater than zero will mean
+waves going to increasing x to the
+
+ align:start position:0%
+waves going to increasing x to the
+ 
+
+ align:start position:0%
+waves going to increasing x to the
+right and the idea will be
+
+ align:start position:0%
+right and the idea will be
+ 
+
+ align:start position:0%
+right and the idea will be
+we have to discuss that
+
+ align:start position:0%
+we have to discuss that
+ 
+
+ align:start position:0%
+we have to discuss that
+problem and as always we would like to
+
+ align:start position:0%
+problem and as always we would like to
+ 
+
+ align:start position:0%
+problem and as always we would like to
+solve it uh analytically find some
+
+ align:start position:0%
+solve it uh analytically find some
+ 
+
+ align:start position:0%
+solve it uh analytically find some
+whatever formulas we
+
+ align:start position:0%
+whatever formulas we
+ 
+
+ align:start position:0%
+whatever formulas we
+can understand what's happening in terms
+
+ align:start position:0%
+can understand what's happening in terms
+ 
+
+ align:start position:0%
+can understand what's happening in terms
+of these characteristic lines because
+
+ align:start position:0%
+of these characteristic lines because
+ 
+
+ align:start position:0%
+of these characteristic lines because
+this when we have one equation and it's
+
+ align:start position:0%
+this when we have one equation and it's
+ 
+
+ align:start position:0%
+this when we have one equation and it's
+and uh one space variable we really
+
+ align:start position:0%
+and uh one space variable we really
+ 
+
+ align:start position:0%
+and uh one space variable we really
+can catch the the essence of the
+
+ align:start position:0%
+can catch the the essence of the
+ 
+
+ align:start position:0%
+can catch the the essence of the
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+by understanding the characteristic
+
+ align:start position:0%
+by understanding the characteristic
+ 
+
+ align:start position:0%
+by understanding the characteristic
+lines and then how do we do it
+
+ align:start position:0%
+lines and then how do we do it
+ 
+
+ align:start position:0%
+lines and then how do we do it
+numerically okay so I before class I
+
+ align:start position:0%
+numerically okay so I before class I
+ 
+
+ align:start position:0%
+numerically okay so I before class I
+wrote just a few equivalent forms of it
+
+ align:start position:0%
+wrote just a few equivalent forms of it
+ 
+
+ align:start position:0%
+wrote just a few equivalent forms of it
+this is an equivalent form and this is
+
+ align:start position:0%
+this is an equivalent form and this is
+ 
+
+ align:start position:0%
+this is an equivalent form and this is
+so to speak the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form this is the form where we see a
+
+ align:start position:0%
+form this is the form where we see a
+ 
+
+ align:start position:0%
+form this is the form where we see a
+Time derivative of U as always
+
+ align:start position:0%
+Time derivative of U as always
+ 
+
+ align:start position:0%
+Time derivative of U as always
+and we see a space derivative of U ^2
+
+ align:start position:0%
+and we see a space derivative of U ^2
+ 
+
+ align:start position:0%
+and we see a space derivative of U ^2
+over 2 which of course produces that but
+
+ align:start position:0%
+over 2 which of course produces that but
+ 
+
+ align:start position:0%
+over 2 which of course produces that but
+somehow this is the quantity it's called
+
+ align:start position:0%
+somehow this is the quantity it's called
+ 
+
+ align:start position:0%
+somehow this is the quantity it's called
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+flux that's uh physically
+
+ align:start position:0%
+flux that's uh physically
+ 
+
+ align:start position:0%
+flux that's uh physically
+meaningful F of U so I've chosen a
+
+ align:start position:0%
+meaningful F of U so I've chosen a
+ 
+
+ align:start position:0%
+meaningful F of U so I've chosen a
+simple flux function U ^2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 and uh so that's the difference
+
+ align:start position:0%
+2 and uh so that's the difference
+ 
+
+ align:start position:0%
+2 and uh so that's the difference
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+but you'll see that the differential
+
+ align:start position:0%
+but you'll see that the differential
+ 
+
+ align:start position:0%
+but you'll see that the differential
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+can produce a multi two solutions at the
+
+ align:start position:0%
+can produce a multi two solutions at the
+ 
+
+ align:start position:0%
+can produce a multi two solutions at the
+same point and we have to
+
+ align:start position:0%
+same point and we have to
+ 
+
+ align:start position:0%
+same point and we have to
+choose in other words the the
+
+ align:start position:0%
+choose in other words the the
+ 
+
+ align:start position:0%
+choose in other words the the
+differential the the solution can become
+
+ align:start position:0%
+differential the the solution can become
+ 
+
+ align:start position:0%
+differential the the solution can become
+discontinuous a perfectly
+
+ align:start position:0%
+discontinuous a perfectly
+ 
+
+ align:start position:0%
+discontinuous a perfectly
+smooth starting
+
+ align:start position:0%
+smooth starting
+ 
+
+ align:start position:0%
+smooth starting
+function after a while
+
+ align:start position:0%
+function after a while
+ 
+
+ align:start position:0%
+function after a while
+this is the essence of the of the
+
+ align:start position:0%
+this is the essence of the of the
+ 
+
+ align:start position:0%
+this is the essence of the of the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+now I have a I might have a smooth
+
+ align:start position:0%
+now I have a I might have a smooth
+ 
+
+ align:start position:0%
+now I have a I might have a smooth
+starting function at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous the solution is constant
+
+ align:start position:0%
+continuous the solution is constant
+ 
+
+ align:start position:0%
+continuous the solution is constant
+along characteristic
+
+ align:start position:0%
+along characteristic
+ 
+
+ align:start position:0%
+along characteristic
+lines but what happens if two
+
+ align:start position:0%
+lines but what happens if two
+ 
+
+ align:start position:0%
+lines but what happens if two
+characteristic lines run into each other
+
+ align:start position:0%
+characteristic lines run into each other
+ 
+
+ align:start position:0%
+characteristic lines run into each other
+I've drawn that possibility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and it'll take a little time to see
+
+ align:start position:0%
+and it'll take a little time to see
+ 
+
+ align:start position:0%
+and it'll take a little time to see
+exactly what's happening but the
+
+ align:start position:0%
+exactly what's happening but the
+ 
+
+ align:start position:0%
+exactly what's happening but the
+characteristics we can see here so the
+
+ align:start position:0%
+characteristics we can see here so the
+ 
+
+ align:start position:0%
+characteristics we can see here so the
+starting values were one up to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point so when the starting value is
+
+ align:start position:0%
+point so when the starting value is
+ 
+
+ align:start position:0%
+point so when the starting value is
+one and the and U is constant along
+
+ align:start position:0%
+one and the and U is constant along
+ 
+
+ align:start position:0%
+one and the and U is constant along
+characteristic lines then U is one and
+
+ align:start position:0%
+characteristic lines then U is one and
+ 
+
+ align:start position:0%
+characteristic lines then U is one and
+those lines it's just like having c
+
+ align:start position:0%
+those lines it's just like having c
+ 
+
+ align:start position:0%
+those lines it's just like having c
+equal to c equal to minus one I guess in
+
+ align:start position:0%
+equal to c equal to minus one I guess in
+ 
+
+ align:start position:0%
+equal to c equal to minus one I guess in
+the in the one-way wave equation we have
+
+ align:start position:0%
+the in the one-way wave equation we have
+ 
+
+ align:start position:0%
+the in the one-way wave equation we have
+a one-way wave going to the right now
+
+ align:start position:0%
+a one-way wave going to the right now
+ 
+
+ align:start position:0%
+a one-way wave going to the right now
+along characteristic lines so U is one
+
+ align:start position:0%
+along characteristic lines so U is one
+ 
+
+ align:start position:0%
+along characteristic lines so U is one
+in all this X in this part of the XT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+right we have to come back to the
+
+ align:start position:0%
+right we have to come back to the
+ 
+
+ align:start position:0%
+right we have to come back to the
+formulas to to confirm what I just said
+
+ align:start position:0%
+formulas to to confirm what I just said
+ 
+
+ align:start position:0%
+formulas to to confirm what I just said
+and then over here at the far
+
+ align:start position:0%
+and then over here at the far
+ 
+
+ align:start position:0%
+and then over here at the far
+right the starting value is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and
+
+ align:start position:0%
+zero and
+ 
+
+ align:start position:0%
+zero and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the characteristics in that case the the
+
+ align:start position:0%
+the characteristics in that case the the
+ 
+
+ align:start position:0%
+the characteristics in that case the the
+velocity the C associated with that is
+
+ align:start position:0%
+velocity the C associated with that is
+ 
+
+ align:start position:0%
+velocity the C associated with that is
+zero so it's a standing it's not moving
+
+ align:start position:0%
+zero so it's a standing it's not moving
+ 
+
+ align:start position:0%
+zero so it's a standing it's not moving
+the characteristics are just straight
+
+ align:start position:0%
+the characteristics are just straight
+ 
+
+ align:start position:0%
+the characteristics are just straight
+lines in the time Direction nothing's
+
+ align:start position:0%
+lines in the time Direction nothing's
+ 
+
+ align:start position:0%
+lines in the time Direction nothing's
+happening right when you think of a
+
+ align:start position:0%
+happening right when you think of a
+ 
+
+ align:start position:0%
+happening right when you think of a
+characteristic that's going straight up
+
+ align:start position:0%
+characteristic that's going straight up
+ 
+
+ align:start position:0%
+characteristic that's going straight up
+it's just carrying in the value of U
+
+ align:start position:0%
+it's just carrying in the value of U
+ 
+
+ align:start position:0%
+it's just carrying in the value of U
+without moving left or right so you
+
+ align:start position:0%
+without moving left or right so you
+ 
+
+ align:start position:0%
+without moving left or right so you
+stays zero so youu is you will be one
+
+ align:start position:0%
+stays zero so youu is you will be one
+ 
+
+ align:start position:0%
+stays zero so youu is you will be one
+here you will be zero here and now
+
+ align:start position:0%
+here you will be zero here and now
+ 
+
+ align:start position:0%
+here you will be zero here and now
+something's happening in here and we
+
+ align:start position:0%
+something's happening in here and we
+ 
+
+ align:start position:0%
+something's happening in here and we
+have to figure out what it
+
+ align:start position:0%
+have to figure out what it
+ 
+
+ align:start position:0%
+have to figure out what it
+is but maybe I can anticipate the main
+
+ align:start position:0%
+is but maybe I can anticipate the main
+ 
+
+ align:start position:0%
+is but maybe I can anticipate the main
+point before any any
+
+ align:start position:0%
+point before any any
+ 
+
+ align:start position:0%
+point before any any
+algebra the the characteristic lines in
+
+ align:start position:0%
+algebra the the characteristic lines in
+ 
+
+ align:start position:0%
+algebra the the characteristic lines in
+the in this
+
+ align:start position:0%
+the in this
+ 
+
+ align:start position:0%
+the in this
+region have a slope somewhere between
+
+ align:start position:0%
+region have a slope somewhere between
+ 
+
+ align:start position:0%
+region have a slope somewhere between
+the slope
+
+ align:start position:0%
+the slope
+ 
+
+ align:start position:0%
+the slope
+one and the slope
+
+ align:start position:0%
+one and the slope
+ 
+
+ align:start position:0%
+one and the slope
+zero you see we're starting let me let
+
+ align:start position:0%
+zero you see we're starting let me let
+ 
+
+ align:start position:0%
+zero you see we're starting let me let
+me graph u z of X so so let me graph u u
+
+ align:start position:0%
+me graph u z of X so so let me graph u u
+ 
+
+ align:start position:0%
+me graph u z of X so so let me graph u u
+u of
+
+ align:start position:0%
+u of
+ 
+
+ align:start position:0%
+u of
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+is let me the key points are zero and
+
+ align:start position:0%
+is let me the key points are zero and
+ 
+
+ align:start position:0%
+is let me the key points are zero and
+one 0 and one so u z of
+
+ align:start position:0%
+one 0 and one so u z of
+ 
+
+ align:start position:0%
+one 0 and one so u z of
+X I start with
+
+ align:start position:0%
+X I start with
+ 
+
+ align:start position:0%
+X I start with
+a with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant initial function the constant
+
+ align:start position:0%
+constant initial function the constant
+ 
+
+ align:start position:0%
+constant initial function the constant
+profile to the left of zero and a
+
+ align:start position:0%
+profile to the left of zero and a
+ 
+
+ align:start position:0%
+profile to the left of zero and a
+constant profile to the right of one and
+
+ align:start position:0%
+constant profile to the right of one and
+ 
+
+ align:start position:0%
+constant profile to the right of one and
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+between okay so it's that it's that
+
+ align:start position:0%
+between okay so it's that it's that
+ 
+
+ align:start position:0%
+between okay so it's that it's that
+starting values that I wrote here 1 1 -
+
+ align:start position:0%
+starting values that I wrote here 1 1 -
+ 
+
+ align:start position:0%
+starting values that I wrote here 1 1 -
+x and Zer are these three
+
+ align:start position:0%
+x and Zer are these three
+ 
+
+ align:start position:0%
+x and Zer are these three
+pieces and then here I'm in the XT plane
+
+ align:start position:0%
+pieces and then here I'm in the XT plane
+ 
+
+ align:start position:0%
+pieces and then here I'm in the XT plane
+where here I'm in the XU plane
+
+ align:start position:0%
+where here I'm in the XU plane
+ 
+
+ align:start position:0%
+where here I'm in the XU plane
+so I drew characteristics and we still
+
+ align:start position:0%
+so I drew characteristics and we still
+ 
+
+ align:start position:0%
+so I drew characteristics and we still
+have to track we have to say more what
+
+ align:start position:0%
+have to track we have to say more what
+ 
+
+ align:start position:0%
+have to track we have to say more what
+characteristics are and understand that
+
+ align:start position:0%
+characteristics are and understand that
+ 
+
+ align:start position:0%
+characteristics are and understand that
+these have slopes in between but you're
+
+ align:start position:0%
+these have slopes in between but you're
+ 
+
+ align:start position:0%
+these have slopes in between but you're
+not surprised because the the values of
+
+ align:start position:0%
+not surprised because the the values of
+ 
+
+ align:start position:0%
+not surprised because the the values of
+you are in between one and zero so they
+
+ align:start position:0%
+you are in between one and zero so they
+ 
+
+ align:start position:0%
+you are in between one and zero so they
+go that way and they meet
+
+ align:start position:0%
+go that way and they meet
+ 
+
+ align:start position:0%
+go that way and they meet
+here so up to time t equal 1
+
+ align:start position:0%
+here so up to time t equal 1
+ 
+
+ align:start position:0%
+here so up to time t equal 1
+characteristics tell everything up to t
+
+ align:start position:0%
+characteristics tell everything up to t
+ 
+
+ align:start position:0%
+characteristics tell everything up to t
+equal one I know that U will be one
+
+ align:start position:0%
+equal one I know that U will be one
+ 
+
+ align:start position:0%
+equal one I know that U will be one
+along these characteristics and when I
+
+ align:start position:0%
+along these characteristics and when I
+ 
+
+ align:start position:0%
+along these characteristics and when I
+find these characteristics U is whatever
+
+ align:start position:0%
+find these characteristics U is whatever
+ 
+
+ align:start position:0%
+find these characteristics U is whatever
+it starts at what and U is zero up all
+
+ align:start position:0%
+it starts at what and U is zero up all
+ 
+
+ align:start position:0%
+it starts at what and U is zero up all
+these characteristics so up to that
+
+ align:start position:0%
+these characteristics so up to that
+ 
+
+ align:start position:0%
+these characteristics so up to that
+time uh algebra the F the differential
+
+ align:start position:0%
+time uh algebra the F the differential
+ 
+
+ align:start position:0%
+time uh algebra the F the differential
+equation is going to be totally
+
+ align:start position:0%
+equation is going to be totally
+ 
+
+ align:start position:0%
+equation is going to be totally
+okay but after that time the
+
+ align:start position:0%
+okay but after that time the
+ 
+
+ align:start position:0%
+okay but after that time the
+differential equation is in difficulty
+
+ align:start position:0%
+differential equation is in difficulty
+ 
+
+ align:start position:0%
+differential equation is in difficulty
+because at that moment T so what's
+
+ align:start position:0%
+because at that moment T so what's
+ 
+
+ align:start position:0%
+because at that moment T so what's
+happening as t as T increases from 0 to
+
+ align:start position:0%
+happening as t as T increases from 0 to
+ 
+
+ align:start position:0%
+happening as t as T increases from 0 to
+one there this is the picture at t equal
+
+ align:start position:0%
+one there this is the picture at t equal
+ 
+
+ align:start position:0%
+one there this is the picture at t equal
+Z the picture at t equal to 1 at t equal
+
+ align:start position:0%
+Z the picture at t equal to 1 at t equal
+ 
+
+ align:start position:0%
+Z the picture at t equal to 1 at t equal
+a half let's say what would be the
+
+ align:start position:0%
+a half let's say what would be the
+ 
+
+ align:start position:0%
+a half let's say what would be the
+picture at t equal to half well this at
+
+ align:start position:0%
+picture at t equal to half well this at
+ 
+
+ align:start position:0%
+picture at t equal to half well this at
+t equal to half this state one has has
+
+ align:start position:0%
+t equal to half this state one has has
+ 
+
+ align:start position:0%
+t equal to half this state one has has
+penetrated this
+
+ align:start position:0%
+penetrated this
+ 
+
+ align:start position:0%
+penetrated this
+far half to to halfway
+
+ align:start position:0%
+far half to to halfway
+ 
+
+ align:start position:0%
+far half to to halfway
+then in here is this uh converging
+
+ align:start position:0%
+then in here is this uh converging
+ 
+
+ align:start position:0%
+then in here is this uh converging
+characteristics that come from a
+
+ align:start position:0%
+characteristics that come from a
+ 
+
+ align:start position:0%
+characteristics that come from a
+linear uh profile and over here it's all
+
+ align:start position:0%
+linear uh profile and over here it's all
+ 
+
+ align:start position:0%
+linear uh profile and over here it's all
+zeros so that zero is still there but
+
+ align:start position:0%
+zeros so that zero is still there but
+ 
+
+ align:start position:0%
+zeros so that zero is still there but
+the you see what's happening this guy is
+
+ align:start position:0%
+the you see what's happening this guy is
+ 
+
+ align:start position:0%
+the you see what's happening this guy is
+the profile is
+
+ align:start position:0%
+the profile is
+ 
+
+ align:start position:0%
+the profile is
+steepening this is at t equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half steeper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we still have the algebra to do but I
+
+ align:start position:0%
+we still have the algebra to do but I
+ 
+
+ align:start position:0%
+we still have the algebra to do but I
+think it's if you the main first thing
+
+ align:start position:0%
+think it's if you the main first thing
+ 
+
+ align:start position:0%
+think it's if you the main first thing
+is to see roughly what's happening then
+
+ align:start position:0%
+is to see roughly what's happening then
+ 
+
+ align:start position:0%
+is to see roughly what's happening then
+at t equal to
+
+ align:start position:0%
+at t equal to
+ 
+
+ align:start position:0%
+at t equal to
+one this is totally steep so this is the
+
+ align:start position:0%
+one this is totally steep so this is the
+ 
+
+ align:start position:0%
+one this is totally steep so this is the
+situation at tal to
+
+ align:start position:0%
+situation at tal to
+ 
+
+ align:start position:0%
+situation at tal to
+1 I have and I could have I could have
+
+ align:start position:0%
+1 I have and I could have I could have
+ 
+
+ align:start position:0%
+1 I have and I could have I could have
+given you that as the initial condition
+
+ align:start position:0%
+given you that as the initial condition
+ 
+
+ align:start position:0%
+given you that as the initial condition
+but I and the 16 920 notes thought okay
+
+ align:start position:0%
+but I and the 16 920 notes thought okay
+ 
+
+ align:start position:0%
+but I and the 16 920 notes thought okay
+let's have a little piece for a while
+
+ align:start position:0%
+let's have a little piece for a while
+ 
+
+ align:start position:0%
+let's have a little piece for a while
+see what those characteristics are doing
+
+ align:start position:0%
+see what those characteristics are doing
+ 
+
+ align:start position:0%
+see what those characteristics are doing
+when they're when they're uh they're
+
+ align:start position:0%
+when they're when they're uh they're
+ 
+
+ align:start position:0%
+when they're when they're uh they're
+converging but they're not
+
+ align:start position:0%
+converging but they're not
+ 
+
+ align:start position:0%
+converging but they're not
+crossing the trouble is after t equal to
+
+ align:start position:0%
+crossing the trouble is after t equal to
+ 
+
+ align:start position:0%
+crossing the trouble is after t equal to
+one they are
+
+ align:start position:0%
+one they are
+ 
+
+ align:start position:0%
+one they are
+crossing and
+
+ align:start position:0%
+crossing and
+ 
+
+ align:start position:0%
+crossing and
+now what's the solution in this re in
+
+ align:start position:0%
+now what's the solution in this re in
+ 
+
+ align:start position:0%
+now what's the solution in this re in
+this cross-hatched rain
+
+ align:start position:0%
+this cross-hatched rain
+ 
+
+ align:start position:0%
+this cross-hatched rain
+region do I follow do I take the value
+
+ align:start position:0%
+region do I follow do I take the value
+ 
+
+ align:start position:0%
+region do I follow do I take the value
+zero that's coming up along these
+
+ align:start position:0%
+zero that's coming up along these
+ 
+
+ align:start position:0%
+zero that's coming up along these
+characteristics do I take the value one
+
+ align:start position:0%
+characteristics do I take the value one
+ 
+
+ align:start position:0%
+characteristics do I take the value one
+that's coming along these
+
+ align:start position:0%
+that's coming along these
+ 
+
+ align:start position:0%
+that's coming along these
+characteristics what's happening in
+
+ align:start position:0%
+characteristics what's happening in
+ 
+
+ align:start position:0%
+characteristics what's happening in
+here so there's a cross-hatched region
+
+ align:start position:0%
+here so there's a cross-hatched region
+ 
+
+ align:start position:0%
+here so there's a cross-hatched region
+there which uh is a big question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mark because my rule of following
+
+ align:start position:0%
+mark because my rule of following
+ 
+
+ align:start position:0%
+mark because my rule of following
+characteristics has led me to two
+
+ align:start position:0%
+characteristics has led me to two
+ 
+
+ align:start position:0%
+characteristics has led me to two
+answers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh we want we want a physically relevant
+
+ align:start position:0%
+uh we want we want a physically relevant
+ 
+
+ align:start position:0%
+uh we want we want a physically relevant
+answer we want uh we're sort of
+
+ align:start position:0%
+answer we want uh we're sort of
+ 
+
+ align:start position:0%
+answer we want uh we're sort of
+expecting and we'll see that this uh
+
+ align:start position:0%
+expecting and we'll see that this uh
+ 
+
+ align:start position:0%
+expecting and we'll see that this uh
+that this um Step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function is a step function I mean we
+
+ align:start position:0%
+function is a step function I mean we
+ 
+
+ align:start position:0%
+function is a step function I mean we
+the answer will be a step function it
+
+ align:start position:0%
+the answer will be a step function it
+ 
+
+ align:start position:0%
+the answer will be a step function it
+will be one and then drop to
+
+ align:start position:0%
+will be one and then drop to
+ 
+
+ align:start position:0%
+will be one and then drop to
+zero along
+
+ align:start position:0%
+zero along
+ 
+
+ align:start position:0%
+zero along
+some path in the XT plane which is not a
+
+ align:start position:0%
+some path in the XT plane which is not a
+ 
+
+ align:start position:0%
+some path in the XT plane which is not a
+characteristic the characteristics are
+
+ align:start position:0%
+characteristic the characteristics are
+ 
+
+ align:start position:0%
+characteristic the characteristics are
+going at
+
+ align:start position:0%
+going at
+ 
+
+ align:start position:0%
+going at
+45° and at
+
+ align:start position:0%
+45° and at
+ 
+
+ align:start position:0%
+45° and at
+90° and
+
+ align:start position:0%
+90° and
+ 
+
+ align:start position:0%
+90° and
+actually it's so this is the region I'm
+
+ align:start position:0%
+actually it's so this is the region I'm
+ 
+
+ align:start position:0%
+actually it's so this is the region I'm
+interested in so can I blow up that
+
+ align:start position:0%
+interested in so can I blow up that
+ 
+
+ align:start position:0%
+interested in so can I blow up that
+region so if I blow up that region which
+
+ align:start position:0%
+region so if I blow up that region which
+ 
+
+ align:start position:0%
+region so if I blow up that region which
+that's where the
+
+ align:start position:0%
+that's where the
+ 
+
+ align:start position:0%
+that's where the
+shocks the shocks are are meeting
+
+ align:start position:0%
+shocks the shocks are are meeting
+ 
+
+ align:start position:0%
+shocks the shocks are are meeting
+everywhere in this in this region this
+
+ align:start position:0%
+everywhere in this in this region this
+ 
+
+ align:start position:0%
+everywhere in this in this region this
+was the point what was that point that I
+
+ align:start position:0%
+was the point what was that point that I
+ 
+
+ align:start position:0%
+was the point what was that point that I
+guess that was the point xal 0 and t
+
+ align:start position:0%
+guess that was the point xal 0 and t
+ 
+
+ align:start position:0%
+guess that was the point xal 0 and t
+equal 1 there okay and the question is
+
+ align:start position:0%
+equal 1 there okay and the question is
+ 
+
+ align:start position:0%
+equal 1 there okay and the question is
+so and I know that I have U equal Z over
+
+ align:start position:0%
+so and I know that I have U equal Z over
+ 
+
+ align:start position:0%
+so and I know that I have U equal Z over
+here here and I know oops U equal 1 over
+
+ align:start position:0%
+here here and I know oops U equal 1 over
+ 
+
+ align:start position:0%
+here here and I know oops U equal 1 over
+here and I know that I have U equal 0
+
+ align:start position:0%
+here and I know that I have U equal 0
+ 
+
+ align:start position:0%
+here and I know that I have U equal 0
+here but the question is where
+
+ align:start position:0%
+here but the question is where
+ 
+
+ align:start position:0%
+here but the question is where
+and well what happens in between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can think of at least two
+
+ align:start position:0%
+you can think of at least two
+ 
+
+ align:start position:0%
+you can think of at least two
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scenarios and one of those is that
+
+ align:start position:0%
+scenarios and one of those is that
+ 
+
+ align:start position:0%
+scenarios and one of those is that
+there's a shock
+
+ align:start position:0%
+there's a shock
+ 
+
+ align:start position:0%
+there's a shock
+line that goes let's say somewhere in
+
+ align:start position:0%
+line that goes let's say somewhere in
+ 
+
+ align:start position:0%
+line that goes let's say somewhere in
+the middle and so that you you stays one
+
+ align:start position:0%
+the middle and so that you you stays one
+ 
+
+ align:start position:0%
+the middle and so that you you stays one
+all the way to that line and drops to
+
+ align:start position:0%
+all the way to that line and drops to
+ 
+
+ align:start position:0%
+all the way to that line and drops to
+zero after it in other words this this
+
+ align:start position:0%
+zero after it in other words this this
+ 
+
+ align:start position:0%
+zero after it in other words this this
+um wall of
+
+ align:start position:0%
+um wall of
+ 
+
+ align:start position:0%
+um wall of
+water travels to the
+
+ align:start position:0%
+water travels to the
+ 
+
+ align:start position:0%
+water travels to the
+right the the shock the discontinuity
+
+ align:start position:0%
+right the the shock the discontinuity
+ 
+
+ align:start position:0%
+right the the shock the discontinuity
+moves
+
+ align:start position:0%
+moves
+ 
+
+ align:start position:0%
+moves
+along uh not necessarily at the speed
+
+ align:start position:0%
+along uh not necessarily at the speed
+ 
+
+ align:start position:0%
+along uh not necessarily at the speed
+that this one this this would be moving
+
+ align:start position:0%
+that this one this this would be moving
+ 
+
+ align:start position:0%
+that this one this this would be moving
+along the speed of one with this
+
+ align:start position:0%
+along the speed of one with this
+ 
+
+ align:start position:0%
+along the speed of one with this
+pushing not stationary either which is
+
+ align:start position:0%
+pushing not stationary either which is
+ 
+
+ align:start position:0%
+pushing not stationary either which is
+what this the right side would like but
+
+ align:start position:0%
+what this the right side would like but
+ 
+
+ align:start position:0%
+what this the right side would like but
+somewhere between so that's a shock line
+
+ align:start position:0%
+somewhere between so that's a shock line
+ 
+
+ align:start position:0%
+somewhere between so that's a shock line
+I just for short call it a
+
+ align:start position:0%
+I just for short call it a
+ 
+
+ align:start position:0%
+I just for short call it a
+shock
+
+ align:start position:0%
+shock
+ 
+
+ align:start position:0%
+shock
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay then there's another possibility
+
+ align:start position:0%
+okay then there's another possibility
+ 
+
+ align:start position:0%
+okay then there's another possibility
+and that will happen in this case
+
+ align:start position:0%
+and that will happen in this case
+ 
+
+ align:start position:0%
+and that will happen in this case
+actually that will happen in this
+
+ align:start position:0%
+actually that will happen in this
+ 
+
+ align:start position:0%
+actually that will happen in this
+case but there is another possibility
+
+ align:start position:0%
+case but there is another possibility
+ 
+
+ align:start position:0%
+case but there is another possibility
+that will happen in other
+
+ align:start position:0%
+that will happen in other
+ 
+
+ align:start position:0%
+that will happen in other
+cases and that would be a
+
+ align:start position:0%
+cases and that would be a
+ 
+
+ align:start position:0%
+cases and that would be a
+fan of
+
+ align:start position:0%
+fan of
+ 
+
+ align:start position:0%
+fan of
+characteristics let let me see that when
+
+ align:start position:0%
+characteristics let let me see that when
+ 
+
+ align:start position:0%
+characteristics let let me see that when
+it comes but I I'm just mentioning it to
+
+ align:start position:0%
+it comes but I I'm just mentioning it to
+ 
+
+ align:start position:0%
+it comes but I I'm just mentioning it to
+say that this business of the shock line
+
+ align:start position:0%
+say that this business of the shock line
+ 
+
+ align:start position:0%
+say that this business of the shock line
+which is what we'll pursue now which
+
+ align:start position:0%
+which is what we'll pursue now which
+ 
+
+ align:start position:0%
+which is what we'll pursue now which
+because it's what happens with this
+
+ align:start position:0%
+because it's what happens with this
+ 
+
+ align:start position:0%
+because it's what happens with this
+problem is not the
+
+ align:start position:0%
+problem is not the
+ 
+
+ align:start position:0%
+problem is not the
+only is not always the the uh the way to
+
+ align:start position:0%
+only is not always the the uh the way to
+ 
+
+ align:start position:0%
+only is not always the the uh the way to
+the way to match the way to deal with a
+
+ align:start position:0%
+the way to match the way to deal with a
+ 
+
+ align:start position:0%
+the way to match the way to deal with a
+a a problem of of lack of information
+
+ align:start position:0%
+a a problem of of lack of information
+ 
+
+ align:start position:0%
+a a problem of of lack of information
+coming from the characteristics okay so
+
+ align:start position:0%
+coming from the characteristics okay so
+ 
+
+ align:start position:0%
+coming from the characteristics okay so
+so I guess our question
+
+ align:start position:0%
+so I guess our question
+ 
+
+ align:start position:0%
+so I guess our question
+is what is that shock line what's the
+
+ align:start position:0%
+is what is that shock line what's the
+ 
+
+ align:start position:0%
+is what is that shock line what's the
+path what's the
+
+ align:start position:0%
+path what's the
+ 
+
+ align:start position:0%
+path what's the
+slope and what what controls it and the
+
+ align:start position:0%
+slope and what what controls it and the
+ 
+
+ align:start position:0%
+slope and what what controls it and the
+answer will be the what control the
+
+ align:start position:0%
+answer will be the what control the
+ 
+
+ align:start position:0%
+answer will be the what control the
+we've run into problems with the
+
+ align:start position:0%
+we've run into problems with the
+ 
+
+ align:start position:0%
+we've run into problems with the
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equation and the way
+
+ align:start position:0%
+equation and the way
+ 
+
+ align:start position:0%
+equation and the way
+to see
+
+ align:start position:0%
+to see
+ 
+
+ align:start position:0%
+to see
+what continues to happen
+
+ align:start position:0%
+what continues to happen
+ 
+
+ align:start position:0%
+what continues to happen
+is to go to the integrated form the
+
+ align:start position:0%
+is to go to the integrated form the
+ 
+
+ align:start position:0%
+is to go to the integrated form the
+integral form of the equation where of
+
+ align:start position:0%
+integral form of the equation where of
+ 
+
+ align:start position:0%
+integral form of the equation where of
+course by taking an integral I've made
+
+ align:start position:0%
+course by taking an integral I've made
+ 
+
+ align:start position:0%
+course by taking an integral I've made
+it I make everything smoother and also I
+
+ align:start position:0%
+it I make everything smoother and also I
+ 
+
+ align:start position:0%
+it I make everything smoother and also I
+preserve the physical law the
+
+ align:start position:0%
+preserve the physical law the
+ 
+
+ align:start position:0%
+preserve the physical law the
+conservation law so this is really the
+
+ align:start position:0%
+conservation law so this is really the
+ 
+
+ align:start position:0%
+conservation law so this is really the
+conservation
+
+ align:start position:0%
+conservation
+ 
+
+ align:start position:0%
+conservation
+law it's conser what is this well let's
+
+ align:start position:0%
+law it's conser what is this well let's
+ 
+
+ align:start position:0%
+law it's conser what is this well let's
+first of all see where it comes from it
+
+ align:start position:0%
+first of all see where it comes from it
+ 
+
+ align:start position:0%
+first of all see where it comes from it
+just comes from
+
+ align:start position:0%
+just comes from
+ 
+
+ align:start position:0%
+just comes from
+integrating this
+
+ align:start position:0%
+integrating this
+ 
+
+ align:start position:0%
+integrating this
+equation with respect to X so I have a
+
+ align:start position:0%
+equation with respect to X so I have a
+ 
+
+ align:start position:0%
+equation with respect to X so I have a
+Time derivative that I keep out here and
+
+ align:start position:0%
+Time derivative that I keep out here and
+ 
+
+ align:start position:0%
+Time derivative that I keep out here and
+but my space derivative is going to
+
+ align:start position:0%
+but my space derivative is going to
+ 
+
+ align:start position:0%
+but my space derivative is going to
+disappear because I'm integrating with
+
+ align:start position:0%
+disappear because I'm integrating with
+ 
+
+ align:start position:0%
+disappear because I'm integrating with
+respect to X so I can call D by DT or
+
+ align:start position:0%
+respect to X so I can call D by DT or
+ 
+
+ align:start position:0%
+respect to X so I can call D by DT or
+partial d by DT the integral of U with
+
+ align:start position:0%
+partial d by DT the integral of U with
+ 
+
+ align:start position:0%
+partial d by DT the integral of U with
+respect to X and I'm integrating from
+
+ align:start position:0%
+respect to X and I'm integrating from
+ 
+
+ align:start position:0%
+respect to X and I'm integrating from
+somewhere from some point to some other
+
+ align:start position:0%
+somewhere from some point to some other
+ 
+
+ align:start position:0%
+somewhere from some point to some other
+point instead of A and B I'll call them
+
+ align:start position:0%
+point instead of A and B I'll call them
+ 
+
+ align:start position:0%
+point instead of A and B I'll call them
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+I really I'm sorry I should say X on the
+
+ align:start position:0%
+I really I'm sorry I should say X on the
+ 
+
+ align:start position:0%
+I really I'm sorry I should say X on the
+left and X on the
+
+ align:start position:0%
+left and X on the
+ 
+
+ align:start position:0%
+left and X on the
+right some point x at the left and some
+
+ align:start position:0%
+right some point x at the left and some
+ 
+
+ align:start position:0%
+right some point x at the left and some
+point x at the
+
+ align:start position:0%
+point x at the
+ 
+
+ align:start position:0%
+point x at the
+right and now I've integrated this one
+
+ align:start position:0%
+right and now I've integrated this one
+ 
+
+ align:start position:0%
+right and now I've integrated this one
+I've I've called This is f of U so I'm
+
+ align:start position:0%
+I've I've called This is f of U so I'm
+ 
+
+ align:start position:0%
+I've I've called This is f of U so I'm
+now thinking of any uh flux
+
+ align:start position:0%
+now thinking of any uh flux
+ 
+
+ align:start position:0%
+now thinking of any uh flux
+function and the integral of course
+
+ align:start position:0%
+function and the integral of course
+ 
+
+ align:start position:0%
+function and the integral of course
+gives me f of U at the upper end minus F
+
+ align:start position:0%
+gives me f of U at the upper end minus F
+ 
+
+ align:start position:0%
+gives me f of U at the upper end minus F
+of U at the lower end okay so that's the
+
+ align:start position:0%
+of U at the lower end okay so that's the
+ 
+
+ align:start position:0%
+of U at the lower end okay so that's the
+conservation law let me write that word
+
+ align:start position:0%
+conservation law let me write that word
+ 
+
+ align:start position:0%
+conservation law let me write that word
+down this is the conservation law what
+
+ align:start position:0%
+down this is the conservation law what
+ 
+
+ align:start position:0%
+down this is the conservation law what
+is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+saying it's saying that the change in
+
+ align:start position:0%
+saying it's saying that the change in
+ 
+
+ align:start position:0%
+saying it's saying that the change in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+quantity in the
+
+ align:start position:0%
+quantity in the
+ 
+
+ align:start position:0%
+quantity in the
+interval is given by if there's any
+
+ align:start position:0%
+interval is given by if there's any
+ 
+
+ align:start position:0%
+interval is given by if there's any
+change any any time derivative the rate
+
+ align:start position:0%
+change any any time derivative the rate
+ 
+
+ align:start position:0%
+change any any time derivative the rate
+of change in the interval
+
+ align:start position:0%
+of change in the interval
+ 
+
+ align:start position:0%
+of change in the interval
+of this of this it's a conservation of
+
+ align:start position:0%
+of this of this it's a conservation of
+ 
+
+ align:start position:0%
+of this of this it's a conservation of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+integral meaning that the that any
+
+ align:start position:0%
+integral meaning that the that any
+ 
+
+ align:start position:0%
+integral meaning that the that any
+change in that integral happens
+
+ align:start position:0%
+change in that integral happens
+ 
+
+ align:start position:0%
+change in that integral happens
+because there's flow going out the right
+
+ align:start position:0%
+because there's flow going out the right
+ 
+
+ align:start position:0%
+because there's flow going out the right
+hand side of the interval or there's
+
+ align:start position:0%
+hand side of the interval or there's
+ 
+
+ align:start position:0%
+hand side of the interval or there's
+flow coming in the left side of the
+
+ align:start position:0%
+flow coming in the left side of the
+ 
+
+ align:start position:0%
+flow coming in the left side of the
+interval so that's why we have a minus
+
+ align:start position:0%
+interval so that's why we have a minus
+ 
+
+ align:start position:0%
+interval so that's why we have a minus
+sign between them so that's a statement
+
+ align:start position:0%
+sign between them so that's a statement
+ 
+
+ align:start position:0%
+sign between them so that's a statement
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+conservation and uh oh there's one more
+
+ align:start position:0%
+conservation and uh oh there's one more
+ 
+
+ align:start position:0%
+conservation and uh oh there's one more
+example that I I'll mention now so let
+
+ align:start position:0%
+example that I I'll mention now so let
+ 
+
+ align:start position:0%
+example that I I'll mention now so let
+me give this a particular equation a
+
+ align:start position:0%
+me give this a particular equation a
+ 
+
+ align:start position:0%
+me give this a particular equation a
+name just because you see it you often
+
+ align:start position:0%
+name just because you see it you often
+ 
+
+ align:start position:0%
+name just because you see it you often
+see it written uh called Burger's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation but
+
+ align:start position:0%
+equation but
+ 
+
+ align:start position:0%
+equation but
+actually the the full name is the inv
+
+ align:start position:0%
+actually the the full name is the inv
+ 
+
+ align:start position:0%
+actually the the full name is the inv
+visive no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+viscosity Berger's equation because it's
+
+ align:start position:0%
+viscosity Berger's equation because it's
+ 
+
+ align:start position:0%
+viscosity Berger's equation because it's
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so just one word about Burger's
+
+ align:start position:0%
+zero so just one word about Burger's
+ 
+
+ align:start position:0%
+zero so just one word about Burger's
+equation so
+
+ align:start position:0%
+equation so
+ 
+
+ align:start position:0%
+equation so
+Burger allowed a uxx term here so he had
+
+ align:start position:0%
+Burger allowed a uxx term here so he had
+ 
+
+ align:start position:0%
+Burger allowed a uxx term here so he had
+uh one of our conve nonlinear
+
+ align:start position:0%
+uh one of our conve nonlinear
+ 
+
+ align:start position:0%
+uh one of our conve nonlinear
+convection and a diffusion
+
+ align:start position:0%
+convection and a diffusion
+ 
+
+ align:start position:0%
+convection and a diffusion
+term and his convection was was this
+
+ align:start position:0%
+term and his convection was was this
+ 
+
+ align:start position:0%
+term and his convection was was this
+simple uh expression
+
+ align:start position:0%
+simple uh expression
+ 
+
+ align:start position:0%
+simple uh expression
+uux it's the kind of thing you see in
+
+ align:start position:0%
+uux it's the kind of thing you see in
+ 
+
+ align:start position:0%
+uux it's the kind of thing you see in
+the nav Stokes equations right the
+
+ align:start position:0%
+the nav Stokes equations right the
+ 
+
+ align:start position:0%
+the nav Stokes equations right the
+nonlinearity in NV stes is sort of in
+
+ align:start position:0%
+nonlinearity in NV stes is sort of in
+ 
+
+ align:start position:0%
+nonlinearity in NV stes is sort of in
+this term of this General sort but this
+
+ align:start position:0%
+this term of this General sort but this
+ 
+
+ align:start position:0%
+this term of this General sort but this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+a major simplification such a
+
+ align:start position:0%
+a major simplification such a
+ 
+
+ align:start position:0%
+a major simplification such a
+simplification that
+
+ align:start position:0%
+simplification that
+ 
+
+ align:start position:0%
+simplification that
+Burgers could solve even though the
+
+ align:start position:0%
+Burgers could solve even though the
+ 
+
+ align:start position:0%
+Burgers could solve even though the
+equation was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonlinear uh well two people at the same
+
+ align:start position:0%
+nonlinear uh well two people at the same
+ 
+
+ align:start position:0%
+nonlinear uh well two people at the same
+time discovered the change of variable
+
+ align:start position:0%
+time discovered the change of variable
+ 
+
+ align:start position:0%
+time discovered the change of variable
+simple little
+
+ align:start position:0%
+simple little
+ 
+
+ align:start position:0%
+simple little
+trick hop and Cole I'll put their names
+
+ align:start position:0%
+trick hop and Cole I'll put their names
+ 
+
+ align:start position:0%
+trick hop and Cole I'll put their names
+down because they had nice short last
+
+ align:start position:0%
+down because they had nice short last
+ 
+
+ align:start position:0%
+down because they had nice short last
+names they both discovered uh in the
+
+ align:start position:0%
+names they both discovered uh in the
+ 
+
+ align:start position:0%
+names they both discovered uh in the
+case of a diffusion term they both
+
+ align:start position:0%
+case of a diffusion term they both
+ 
+
+ align:start position:0%
+case of a diffusion term they both
+discovered a little a change of
+
+ align:start position:0%
+discovered a little a change of
+ 
+
+ align:start position:0%
+discovered a little a change of
+variables that made the equation linear
+
+ align:start position:0%
+variables that made the equation linear
+ 
+
+ align:start position:0%
+variables that made the equation linear
+then they could solve the equation
+
+ align:start position:0%
+then they could solve the equation
+ 
+
+ align:start position:0%
+then they could solve the equation
+that's in the textbook uh in this
+
+ align:start position:0%
+that's in the textbook uh in this
+ 
+
+ align:start position:0%
+that's in the textbook uh in this
+section on conservation laws and then
+
+ align:start position:0%
+section on conservation laws and then
+ 
+
+ align:start position:0%
+section on conservation laws and then
+what then the important thing what the
+
+ align:start position:0%
+what then the important thing what the
+ 
+
+ align:start position:0%
+what then the important thing what the
+burgers could do was let the diffusion
+
+ align:start position:0%
+burgers could do was let the diffusion
+ 
+
+ align:start position:0%
+burgers could do was let the diffusion
+coefficient go to zero so then in the
+
+ align:start position:0%
+coefficient go to zero so then in the
+ 
+
+ align:start position:0%
+coefficient go to zero so then in the
+limit he got the invit burgers equation
+
+ align:start position:0%
+limit he got the invit burgers equation
+ 
+
+ align:start position:0%
+limit he got the invit burgers equation
+the one we're looking at and he could
+
+ align:start position:0%
+the one we're looking at and he could
+ 
+
+ align:start position:0%
+the one we're looking at and he could
+look at the solution and let the limit
+
+ align:start position:0%
+look at the solution and let the limit
+ 
+
+ align:start position:0%
+look at the solution and let the limit
+go to zero
+
+ align:start position:0%
+go to zero
+ 
+
+ align:start position:0%
+go to zero
+and that's another way to figure out
+
+ align:start position:0%
+and that's another way to figure out
+ 
+
+ align:start position:0%
+and that's another way to figure out
+what's the right
+
+ align:start position:0%
+what's the right
+ 
+
+ align:start position:0%
+what's the right
+Solution that's the viscosity method a
+
+ align:start position:0%
+Solution that's the viscosity method a
+ 
+
+ align:start position:0%
+Solution that's the viscosity method a
+fundamental method for finding out when
+
+ align:start position:0%
+fundamental method for finding out when
+ 
+
+ align:start position:0%
+fundamental method for finding out when
+when we run into a problem shocks run
+
+ align:start position:0%
+when we run into a problem shocks run
+ 
+
+ align:start position:0%
+when we run into a problem shocks run
+into each other we don't know which it
+
+ align:start position:0%
+into each other we don't know which it
+ 
+
+ align:start position:0%
+into each other we don't know which it
+what the which what to
+
+ align:start position:0%
+what the which what to
+ 
+
+ align:start position:0%
+what the which what to
+choose one way to find out in in this 1D
+
+ align:start position:0%
+choose one way to find out in in this 1D
+ 
+
+ align:start position:0%
+choose one way to find out in in this 1D
+problem and also in much tougher
+
+ align:start position:0%
+problem and also in much tougher
+ 
+
+ align:start position:0%
+problem and also in much tougher
+nonlinear multi-dimensional problems is
+
+ align:start position:0%
+nonlinear multi-dimensional problems is
+ 
+
+ align:start position:0%
+nonlinear multi-dimensional problems is
+put in a little viscosity
+
+ align:start position:0%
+put in a little viscosity
+ 
+
+ align:start position:0%
+put in a little viscosity
+and and let it be small let it even get
+
+ align:start position:0%
+and and let it be small let it even get
+ 
+
+ align:start position:0%
+and and let it be small let it even get
+smaller then with a little
+
+ align:start position:0%
+smaller then with a little
+ 
+
+ align:start position:0%
+smaller then with a little
+viscosity officially this
+
+ align:start position:0%
+viscosity officially this
+ 
+
+ align:start position:0%
+viscosity officially this
+term in some sense the the the uh this
+
+ align:start position:0%
+term in some sense the the the uh this
+ 
+
+ align:start position:0%
+term in some sense the the the uh this
+term because it's a second derivative is
+
+ align:start position:0%
+term because it's a second derivative is
+ 
+
+ align:start position:0%
+term because it's a second derivative is
+officially mathematically speaking sort
+
+ align:start position:0%
+officially mathematically speaking sort
+ 
+
+ align:start position:0%
+officially mathematically speaking sort
+of dominates this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one as far as I mean this will get
+
+ align:start position:0%
+one as far as I mean this will get
+ 
+
+ align:start position:0%
+one as far as I mean this will get
+produce a smooth solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soltion this term as we know doesn't
+
+ align:start position:0%
+soltion this term as we know doesn't
+ 
+
+ align:start position:0%
+soltion this term as we know doesn't
+smooth the solution just just advs it
+
+ align:start position:0%
+smooth the solution just just advs it
+ 
+
+ align:start position:0%
+smooth the solution just just advs it
+just carries it along but this term will
+
+ align:start position:0%
+just carries it along but this term will
+ 
+
+ align:start position:0%
+just carries it along but this term will
+smooth it so th this is uh the the
+
+ align:start position:0%
+smooth it so th this is uh the the
+ 
+
+ align:start position:0%
+smooth it so th this is uh the the
+dominant term the second derivative no
+
+ align:start position:0%
+dominant term the second derivative no
+ 
+
+ align:start position:0%
+dominant term the second derivative no
+surprise uh
+
+ align:start position:0%
+surprise uh
+ 
+
+ align:start position:0%
+surprise uh
+but so when we introduce that that
+
+ align:start position:0%
+but so when we introduce that that
+ 
+
+ align:start position:0%
+but so when we introduce that that
+Smooths everything we get it we have no
+
+ align:start position:0%
+Smooths everything we get it we have no
+ 
+
+ align:start position:0%
+Smooths everything we get it we have no
+problem to say there is a illusion for
+
+ align:start position:0%
+problem to say there is a illusion for
+ 
+
+ align:start position:0%
+problem to say there is a illusion for
+at least for simpler
+
+ align:start position:0%
+at least for simpler
+ 
+
+ align:start position:0%
+at least for simpler
+models and uh then we can see what
+
+ align:start position:0%
+models and uh then we can see what
+ 
+
+ align:start position:0%
+models and uh then we can see what
+happens when that when that term
+
+ align:start position:0%
+happens when that when that term
+ 
+
+ align:start position:0%
+happens when that when that term
+approaches zero okay so that's another
+
+ align:start position:0%
+approaches zero okay so that's another
+ 
+
+ align:start position:0%
+approaches zero okay so that's another
+method and of course that's kind of what
+
+ align:start position:0%
+method and of course that's kind of what
+ 
+
+ align:start position:0%
+method and of course that's kind of what
+we're doing with finite differences
+
+ align:start position:0%
+we're doing with finite differences
+ 
+
+ align:start position:0%
+we're doing with finite differences
+finite differences if we put in a little
+
+ align:start position:0%
+finite differences if we put in a little
+ 
+
+ align:start position:0%
+finite differences if we put in a little
+viscosity a little second space
+
+ align:start position:0%
+viscosity a little second space
+ 
+
+ align:start position:0%
+viscosity a little second space
+difference and take delta T small enough
+
+ align:start position:0%
+difference and take delta T small enough
+ 
+
+ align:start position:0%
+difference and take delta T small enough
+for stability then we can solve
+
+ align:start position:0%
+for stability then we can solve
+ 
+
+ align:start position:0%
+for stability then we can solve
+it and if we take it very
+
+ align:start position:0%
+it and if we take it very
+ 
+
+ align:start position:0%
+it and if we take it very
+small we should get something close to
+
+ align:start position:0%
+small we should get something close to
+ 
+
+ align:start position:0%
+small we should get something close to
+the invis Limit okay so that's uh that I
+
+ align:start position:0%
+the invis Limit okay so that's uh that I
+ 
+
+ align:start position:0%
+the invis Limit okay so that's uh that I
+was just giving Burger's name to that
+
+ align:start position:0%
+was just giving Burger's name to that
+ 
+
+ align:start position:0%
+was just giving Burger's name to that
+particular example so this isn't the
+
+ align:start position:0%
+particular example so this isn't the
+ 
+
+ align:start position:0%
+particular example so this isn't the
+only example but it's the simplest
+
+ align:start position:0%
+only example but it's the simplest
+ 
+
+ align:start position:0%
+only example but it's the simplest
+example okay another
+
+ align:start position:0%
+example okay another
+ 
+
+ align:start position:0%
+example okay another
+example of conservation laws that
+
+ align:start position:0%
+example of conservation laws that
+ 
+
+ align:start position:0%
+example of conservation laws that
+everybody likes I think
+
+ align:start position:0%
+everybody likes I think
+ 
+
+ align:start position:0%
+everybody likes I think
+is the traffic flow traffic flow in One
+
+ align:start position:0%
+is the traffic flow traffic flow in One
+ 
+
+ align:start position:0%
+is the traffic flow traffic flow in One
+Direction say on the Mass Pike so what's
+
+ align:start position:0%
+Direction say on the Mass Pike so what's
+ 
+
+ align:start position:0%
+Direction say on the Mass Pike so what's
+the equation of traffic flow can I put
+
+ align:start position:0%
+the equation of traffic flow can I put
+ 
+
+ align:start position:0%
+the equation of traffic flow can I put
+that let me put that on a board here and
+
+ align:start position:0%
+that let me put that on a board here and
+ 
+
+ align:start position:0%
+that let me put that on a board here and
+then uh then I have to come back to
+
+ align:start position:0%
+then uh then I have to come back to
+ 
+
+ align:start position:0%
+then uh then I have to come back to
+this okay well I'll put it
+
+ align:start position:0%
+this okay well I'll put it
+ 
+
+ align:start position:0%
+this okay well I'll put it
+here so example two well I don't know if
+
+ align:start position:0%
+here so example two well I don't know if
+ 
+
+ align:start position:0%
+here so example two well I don't know if
+you can call that example one we didn't
+
+ align:start position:0%
+you can call that example one we didn't
+ 
+
+ align:start position:0%
+you can call that example one we didn't
+give it a physical meaning example two
+
+ align:start position:0%
+give it a physical meaning example two
+ 
+
+ align:start position:0%
+give it a physical meaning example two
+will be traffic flow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flow in
+
+ align:start position:0%
+flow in
+ 
+
+ align:start position:0%
+flow in
+1D and what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unknown well it's the thing I've been
+
+ align:start position:0%
+unknown well it's the thing I've been
+ 
+
+ align:start position:0%
+unknown well it's the thing I've been
+calling
+
+ align:start position:0%
+calling
+ 
+
+ align:start position:0%
+calling
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+but uh for traffic flow the natural
+
+ align:start position:0%
+but uh for traffic flow the natural
+ 
+
+ align:start position:0%
+but uh for traffic flow the natural
+unknown is the density of the traffic
+
+ align:start position:0%
+unknown is the density of the traffic
+ 
+
+ align:start position:0%
+unknown is the density of the traffic
+the density of the cars is the car
+
+ align:start position:0%
+the density of the cars is the car
+ 
+
+ align:start position:0%
+the density of the cars is the car
+density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and everybody calls uses Row for density
+
+ align:start position:0%
+and everybody calls uses Row for density
+ 
+
+ align:start position:0%
+and everybody calls uses Row for density
+so can I use row rather than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U and then in the uh in the equation
+
+ align:start position:0%
+U and then in the uh in the equation
+ 
+
+ align:start position:0%
+U and then in the uh in the equation
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+be uh a a a car a velocity that I'll
+
+ align:start position:0%
+be uh a a a car a velocity that I'll
+ 
+
+ align:start position:0%
+be uh a a a car a velocity that I'll
+call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V that's not a new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unknown in fact in fact the velocity
+
+ align:start position:0%
+unknown in fact in fact the velocity
+ 
+
+ align:start position:0%
+unknown in fact in fact the velocity
+experimentally depends or the there's a
+
+ align:start position:0%
+experimentally depends or the there's a
+ 
+
+ align:start position:0%
+experimentally depends or the there's a
+relation the density and the velocity
+
+ align:start position:0%
+relation the density and the velocity
+ 
+
+ align:start position:0%
+relation the density and the velocity
+are by experiments if you run an
+
+ align:start position:0%
+are by experiments if you run an
+ 
+
+ align:start position:0%
+are by experiments if you run an
+experiment on the Mass Pike in heavy
+
+ align:start position:0%
+experiment on the Mass Pike in heavy
+ 
+
+ align:start position:0%
+experiment on the Mass Pike in heavy
+traffic that could be a homework problem
+
+ align:start position:0%
+traffic that could be a homework problem
+ 
+
+ align:start position:0%
+traffic that could be a homework problem
+too to uh find the relation between uh V
+
+ align:start position:0%
+too to uh find the relation between uh V
+ 
+
+ align:start position:0%
+too to uh find the relation between uh V
+and row so I'm going to keep this row as
+
+ align:start position:0%
+and row so I'm going to keep this row as
+ 
+
+ align:start position:0%
+and row so I'm going to keep this row as
+the unknown and imagine that we have
+
+ align:start position:0%
+the unknown and imagine that we have
+ 
+
+ align:start position:0%
+the unknown and imagine that we have
+some experimental velocity V of row and
+
+ align:start position:0%
+some experimental velocity V of row and
+ 
+
+ align:start position:0%
+some experimental velocity V of row and
+and what would we expect I guess we
+
+ align:start position:0%
+and what would we expect I guess we
+ 
+
+ align:start position:0%
+and what would we expect I guess we
+expect that uh as
+
+ align:start position:0%
+expect that uh as
+ 
+
+ align:start position:0%
+expect that uh as
+row uh increase as the density increases
+
+ align:start position:0%
+row uh increase as the density increases
+ 
+
+ align:start position:0%
+row uh increase as the density increases
+what will
+
+ align:start position:0%
+what will
+ 
+
+ align:start position:0%
+what will
+happen as the density
+
+ align:start position:0%
+happen as the density
+ 
+
+ align:start position:0%
+happen as the density
+increases the traffic is going to slow
+
+ align:start position:0%
+increases the traffic is going to slow
+ 
+
+ align:start position:0%
+increases the traffic is going to slow
+down ultimately come to a
+
+ align:start position:0%
+down ultimately come to a
+ 
+
+ align:start position:0%
+down ultimately come to a
+stop where if the density is ex is is
+
+ align:start position:0%
+stop where if the density is ex is is
+ 
+
+ align:start position:0%
+stop where if the density is ex is is
+very small so the the density is zero I
+
+ align:start position:0%
+very small so the the density is zero I
+ 
+
+ align:start position:0%
+very small so the the density is zero I
+we just have a single
+
+ align:start position:0%
+we just have a single
+ 
+
+ align:start position:0%
+we just have a single
+driver the police are not out so he's
+
+ align:start position:0%
+driver the police are not out so he's
+ 
+
+ align:start position:0%
+driver the police are not out so he's
+going you know
+
+ align:start position:0%
+going you know
+ 
+
+ align:start position:0%
+going you know
+Vmax or 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vmax but uh as the as the the uh Road
+
+ align:start position:0%
+Vmax but uh as the as the the uh Road
+ 
+
+ align:start position:0%
+Vmax but uh as the as the the uh Road
+gets crowded the velocity drops and
+
+ align:start position:0%
+gets crowded the velocity drops and
+ 
+
+ align:start position:0%
+gets crowded the velocity drops and
+maybe drops linearly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that would be a possible and not not not
+
+ align:start position:0%
+that would be a possible and not not not
+ 
+
+ align:start position:0%
+that would be a possible and not not not
+that terrible
+
+ align:start position:0%
+that terrible
+ 
+
+ align:start position:0%
+that terrible
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh relation between V and row so what
+
+ align:start position:0%
+uh relation between V and row so what
+ 
+
+ align:start position:0%
+uh relation between V and row so what
+would be the flux function in this
+
+ align:start position:0%
+would be the flux function in this
+ 
+
+ align:start position:0%
+would be the flux function in this
+traffic flow
+
+ align:start position:0%
+traffic flow
+ 
+
+ align:start position:0%
+traffic flow
+problem the conservation law is like
+
+ align:start position:0%
+problem the conservation law is like
+ 
+
+ align:start position:0%
+problem the conservation law is like
+conservation of cars right if we look at
+
+ align:start position:0%
+conservation of cars right if we look at
+ 
+
+ align:start position:0%
+conservation of cars right if we look at
+um a unit you know a certain uh a piece
+
+ align:start position:0%
+um a unit you know a certain uh a piece
+ 
+
+ align:start position:0%
+um a unit you know a certain uh a piece
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+turnpike then the conservation law says
+
+ align:start position:0%
+turnpike then the conservation law says
+ 
+
+ align:start position:0%
+turnpike then the conservation law says
+that the total number of cars
+
+ align:start position:0%
+that the total number of cars
+ 
+
+ align:start position:0%
+that the total number of cars
+inside CH which is this
+
+ align:start position:0%
+inside CH which is this
+ 
+
+ align:start position:0%
+inside CH which is this
+changes by cars
+
+ align:start position:0%
+changes by cars
+ 
+
+ align:start position:0%
+changes by cars
+leaving and by cars
+
+ align:start position:0%
+leaving and by cars
+ 
+
+ align:start position:0%
+leaving and by cars
+entering and so the flux function I
+
+ align:start position:0%
+entering and so the flux function I
+ 
+
+ align:start position:0%
+entering and so the flux function I
+think will be so we have to know like
+
+ align:start position:0%
+think will be so we have to know like
+ 
+
+ align:start position:0%
+think will be so we have to know like
+sort how many cars are
+
+ align:start position:0%
+sort how many cars are
+ 
+
+ align:start position:0%
+sort how many cars are
+leaving and I think the flux function
+
+ align:start position:0%
+leaving and I think the flux function
+ 
+
+ align:start position:0%
+leaving and I think the flux function
+would be probably V * row I think the
+
+ align:start position:0%
+would be probably V * row I think the
+ 
+
+ align:start position:0%
+would be probably V * row I think the
+flux function flux function of row now
+
+ align:start position:0%
+flux function flux function of row now
+ 
+
+ align:start position:0%
+flux function flux function of row now
+is my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unknown I think would be V of row times
+
+ align:start position:0%
+unknown I think would be V of row times
+ 
+
+ align:start position:0%
+unknown I think would be V of row times
+Row the velocity times the density
+
+ align:start position:0%
+Row the velocity times the density
+ 
+
+ align:start position:0%
+Row the velocity times the density
+that's tell me tells me how many cars
+
+ align:start position:0%
+that's tell me tells me how many cars
+ 
+
+ align:start position:0%
+that's tell me tells me how many cars
+are going out okay so I guess what I
+
+ align:start position:0%
+are going out okay so I guess what I
+ 
+
+ align:start position:0%
+are going out okay so I guess what I
+want to say is that we will meet that we
+
+ align:start position:0%
+want to say is that we will meet that we
+ 
+
+ align:start position:0%
+want to say is that we will meet that we
+we we meet in this traffic flow example
+
+ align:start position:0%
+we we meet in this traffic flow example
+ 
+
+ align:start position:0%
+we we meet in this traffic flow example
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+possibilities
+
+ align:start position:0%
+possibilities
+ 
+
+ align:start position:0%
+possibilities
+that we meet them mathematically just
+
+ align:start position:0%
+that we meet them mathematically just
+ 
+
+ align:start position:0%
+that we meet them mathematically just
+the way we meet them in actual
+
+ align:start position:0%
+the way we meet them in actual
+ 
+
+ align:start position:0%
+the way we meet them in actual
+driving
+
+ align:start position:0%
+driving
+ 
+
+ align:start position:0%
+driving
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh a shock so this this shock
+
+ align:start position:0%
+uh a shock so this this shock
+ 
+
+ align:start position:0%
+uh a shock so this this shock
+corresponds to so what's that like stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go this corresponds to I suppose like
+
+ align:start position:0%
+go this corresponds to I suppose like
+ 
+
+ align:start position:0%
+go this corresponds to I suppose like
+meeting a red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+light coming up to a red light the
+
+ align:start position:0%
+light coming up to a red light the
+ 
+
+ align:start position:0%
+light coming up to a red light the
+traffic you know behind normally stops
+
+ align:start position:0%
+traffic you know behind normally stops
+ 
+
+ align:start position:0%
+traffic you know behind normally stops
+has to come has to slow way down and
+
+ align:start position:0%
+has to come has to slow way down and
+ 
+
+ align:start position:0%
+has to come has to slow way down and
+stop then the light turns
+
+ align:start position:0%
+stop then the light turns
+ 
+
+ align:start position:0%
+stop then the light turns
+green the first car takes off the cars
+
+ align:start position:0%
+green the first car takes off the cars
+ 
+
+ align:start position:0%
+green the first car takes off the cars
+begin to spread
+
+ align:start position:0%
+begin to spread
+ 
+
+ align:start position:0%
+begin to spread
+out that's
+
+ align:start position:0%
+out that's
+ 
+
+ align:start position:0%
+out that's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh the solution that I that I have that
+
+ align:start position:0%
+uh the solution that I that I have that
+ 
+
+ align:start position:0%
+uh the solution that I that I have that
+I don't see in this with this uh
+
+ align:start position:0%
+I don't see in this with this uh
+ 
+
+ align:start position:0%
+I don't see in this with this uh
+starting function a a sort of fan of
+
+ align:start position:0%
+starting function a a sort of fan of
+ 
+
+ align:start position:0%
+starting function a a sort of fan of
+cars so so maybe I could write those
+
+ align:start position:0%
+cars so so maybe I could write those
+ 
+
+ align:start position:0%
+cars so so maybe I could write those
+words down shock or a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fan this is the shock is is what happens
+
+ align:start position:0%
+fan this is the shock is is what happens
+ 
+
+ align:start position:0%
+fan this is the shock is is what happens
+when characteristics come together cars
+
+ align:start position:0%
+when characteristics come together cars
+ 
+
+ align:start position:0%
+when characteristics come together cars
+come together the fan is when the
+
+ align:start position:0%
+come together the fan is when the
+ 
+
+ align:start position:0%
+come together the fan is when the
+characteristics fan out
+
+ align:start position:0%
+characteristics fan out
+ 
+
+ align:start position:0%
+characteristics fan out
+actually I could I could illustrate a
+
+ align:start position:0%
+actually I could I could illustrate a
+ 
+
+ align:start position:0%
+actually I could I could illustrate a
+fan here right away suppose I reverse 0
+
+ align:start position:0%
+fan here right away suppose I reverse 0
+ 
+
+ align:start position:0%
+fan here right away suppose I reverse 0
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one just to see what okay so here's my
+
+ align:start position:0%
+one just to see what okay so here's my
+ 
+
+ align:start position:0%
+one just to see what okay so here's my
+this is my X
+
+ align:start position:0%
+this is my X
+ 
+
+ align:start position:0%
+this is my X
+again so here I'm going to I'm going to
+
+ align:start position:0%
+again so here I'm going to I'm going to
+ 
+
+ align:start position:0%
+again so here I'm going to I'm going to
+have u0 to be Z
+
+ align:start position:0%
+have u0 to be Z
+ 
+
+ align:start position:0%
+have u0 to be Z
+now u0 to
+
+ align:start position:0%
+now u0 to
+ 
+
+ align:start position:0%
+now u0 to
+be well I I can even it's called a remon
+
+ align:start position:0%
+be well I I can even it's called a remon
+ 
+
+ align:start position:0%
+be well I I can even it's called a remon
+problem when there are just two values
+
+ align:start position:0%
+problem when there are just two values
+ 
+
+ align:start position:0%
+problem when there are just two values
+here U is one so
+
+ align:start position:0%
+here U is one so
+ 
+
+ align:start position:0%
+here U is one so
+I'm so that the so-called remon problem
+
+ align:start position:0%
+I'm so that the so-called remon problem
+ 
+
+ align:start position:0%
+I'm so that the so-called remon problem
+is the cleanest example of the whole of
+
+ align:start position:0%
+is the cleanest example of the whole of
+ 
+
+ align:start position:0%
+is the cleanest example of the whole of
+the whole conservation law theory when
+
+ align:start position:0%
+the whole conservation law theory when
+ 
+
+ align:start position:0%
+the whole conservation law theory when
+there are just two starting values zero
+
+ align:start position:0%
+there are just two starting values zero
+ 
+
+ align:start position:0%
+there are just two starting values zero
+and one or one and zero and it makes a
+
+ align:start position:0%
+and one or one and zero and it makes a
+ 
+
+ align:start position:0%
+and one or one and zero and it makes a
+big difference one and zero we saw when
+
+ align:start position:0%
+big difference one and zero we saw when
+ 
+
+ align:start position:0%
+big difference one and zero we saw when
+we reach time one we had a one and a
+
+ align:start position:0%
+we reach time one we had a one and a
+ 
+
+ align:start position:0%
+we reach time one we had a one and a
+zero and after that a shock form here
+
+ align:start position:0%
+zero and after that a shock form here
+ 
+
+ align:start position:0%
+zero and after that a shock form here
+zero and one the characteristics here
+
+ align:start position:0%
+zero and one the characteristics here
+ 
+
+ align:start position:0%
+zero and one the characteristics here
+are going as always so U is one
+
+ align:start position:0%
+are going as always so U is one
+ 
+
+ align:start position:0%
+are going as always so U is one
+here characteristics
+
+ align:start position:0%
+here characteristics
+ 
+
+ align:start position:0%
+here characteristics
+here this is staying at zero there's no
+
+ align:start position:0%
+here this is staying at zero there's no
+ 
+
+ align:start position:0%
+here this is staying at zero there's no
+reason to change but here we
+
+ align:start position:0%
+reason to change but here we
+ 
+
+ align:start position:0%
+reason to change but here we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+now a region just like the other one but
+
+ align:start position:0%
+now a region just like the other one but
+ 
+
+ align:start position:0%
+now a region just like the other one but
+with a major difference that now it's u
+
+ align:start position:0%
+with a major difference that now it's u
+ 
+
+ align:start position:0%
+with a major difference that now it's u
+z on the left and one on the right where
+
+ align:start position:0%
+z on the left and one on the right where
+ 
+
+ align:start position:0%
+z on the left and one on the right where
+before it was one on the left and zero
+
+ align:start position:0%
+before it was one on the left and zero
+ 
+
+ align:start position:0%
+before it was one on the left and zero
+on the right and the question is what
+
+ align:start position:0%
+on the right and the question is what
+ 
+
+ align:start position:0%
+on the right and the question is what
+happens in here well you might think a
+
+ align:start position:0%
+happens in here well you might think a
+ 
+
+ align:start position:0%
+happens in here well you might think a
+shock an a a a a step up from zero to
+
+ align:start position:0%
+shock an a a a a step up from zero to
+ 
+
+ align:start position:0%
+shock an a a a a step up from zero to
+one at some point
+
+ align:start position:0%
+one at some point
+ 
+
+ align:start position:0%
+one at some point
+and I would have to agree that you could
+
+ align:start position:0%
+and I would have to agree that you could
+ 
+
+ align:start position:0%
+and I would have to agree that you could
+do that in such a way that you maintain
+
+ align:start position:0%
+do that in such a way that you maintain
+ 
+
+ align:start position:0%
+do that in such a way that you maintain
+the conservation law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that's not what
+
+ align:start position:0%
+but that's not what
+ 
+
+ align:start position:0%
+but that's not what
+happens this is this is going to be a
+
+ align:start position:0%
+happens this is this is going to be a
+ 
+
+ align:start position:0%
+happens this is this is going to be a
+fan in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we're going to have we what we'll
+
+ align:start position:0%
+here we're going to have we what we'll
+ 
+
+ align:start position:0%
+here we're going to have we what we'll
+have as characteristics in here this
+
+ align:start position:0%
+have as characteristics in here this
+ 
+
+ align:start position:0%
+have as characteristics in here this
+will let me draw the profile so the
+
+ align:start position:0%
+will let me draw the profile so the
+ 
+
+ align:start position:0%
+will let me draw the profile so the
+profile is zero there to
+
+ align:start position:0%
+profile is zero there to
+ 
+
+ align:start position:0%
+profile is zero there to
+zero and and at some time then over
+
+ align:start position:0%
+zero and and at some time then over
+ 
+
+ align:start position:0%
+zero and and at some time then over
+here where this characteristic is met
+
+ align:start position:0%
+here where this characteristic is met
+ 
+
+ align:start position:0%
+here where this characteristic is met
+it's one and this is what
+
+ align:start position:0%
+it's one and this is what
+ 
+
+ align:start position:0%
+it's one and this is what
+happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the in instead of getting worse less
+
+ align:start position:0%
+the in instead of getting worse less
+ 
+
+ align:start position:0%
+the in instead of getting worse less
+smooth the solution gets better more
+
+ align:start position:0%
+smooth the solution gets better more
+ 
+
+ align:start position:0%
+smooth the solution gets better more
+smooth when it when the directions is
+
+ align:start position:0%
+smooth when it when the directions is
+ 
+
+ align:start position:0%
+smooth when it when the directions is
+reversed so we see that our problem had
+
+ align:start position:0%
+reversed so we see that our problem had
+ 
+
+ align:start position:0%
+reversed so we see that our problem had
+to be nonlinear a linear problem
+
+ align:start position:0%
+to be nonlinear a linear problem
+ 
+
+ align:start position:0%
+to be nonlinear a linear problem
+couldn't do these two opposite things
+
+ align:start position:0%
+couldn't do these two opposite things
+ 
+
+ align:start position:0%
+couldn't do these two opposite things
+in uh the same thing so here we would
+
+ align:start position:0%
+in uh the same thing so here we would
+ 
+
+ align:start position:0%
+in uh the same thing so here we would
+have a fan and that the characteristics
+
+ align:start position:0%
+have a fan and that the characteristics
+ 
+
+ align:start position:0%
+have a fan and that the characteristics
+go there and it's reflected there okay
+
+ align:start position:0%
+go there and it's reflected there okay
+ 
+
+ align:start position:0%
+go there and it's reflected there okay
+so there's a picture of the phenomena
+
+ align:start position:0%
+so there's a picture of the phenomena
+ 
+
+ align:start position:0%
+so there's a picture of the phenomena
+that we're looking at and would and we
+
+ align:start position:0%
+that we're looking at and would and we
+ 
+
+ align:start position:0%
+that we're looking at and would and we
+would like to see numerically
+
+ align:start position:0%
+would like to see numerically
+ 
+
+ align:start position:0%
+would like to see numerically
+too when I so next
+
+ align:start position:0%
+too when I so next
+ 
+
+ align:start position:0%
+too when I so next
+time I want to
+
+ align:start position:0%
+time I want to
+ 
+
+ align:start position:0%
+time I want to
+find so I can say now what I have to do
+
+ align:start position:0%
+find so I can say now what I have to do
+ 
+
+ align:start position:0%
+find so I can say now what I have to do
+next time one is to to locate the
+
+ align:start position:0%
+next time one is to to locate the
+ 
+
+ align:start position:0%
+next time one is to to locate the
+shock the shock line when there is one
+
+ align:start position:0%
+shock the shock line when there is one
+ 
+
+ align:start position:0%
+shock the shock line when there is one
+and two to
+
+ align:start position:0%
+and two to
+ 
+
+ align:start position:0%
+and two to
+decide how do we decide between shock or
+
+ align:start position:0%
+decide how do we decide between shock or
+ 
+
+ align:start position:0%
+decide how do we decide between shock or
+fan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when when from the point of view of pure
+
+ align:start position:0%
+when when from the point of view of pure
+ 
+
+ align:start position:0%
+when when from the point of view of pure
+conservation we could
+
+ align:start position:0%
+conservation we could
+ 
+
+ align:start position:0%
+conservation we could
+choose but nature makes a choice and one
+
+ align:start position:0%
+choose but nature makes a choice and one
+ 
+
+ align:start position:0%
+choose but nature makes a choice and one
+way to decide make that decision is
+
+ align:start position:0%
+way to decide make that decision is
+ 
+
+ align:start position:0%
+way to decide make that decision is
+Burger's way of putting in a little
+
+ align:start position:0%
+Burger's way of putting in a little
+ 
+
+ align:start position:0%
+Burger's way of putting in a little
+diffusion and letting it get zero go to
+
+ align:start position:0%
+diffusion and letting it get zero go to
+ 
+
+ align:start position:0%
+diffusion and letting it get zero go to
+disappear but we need a direct rule so
+
+ align:start position:0%
+disappear but we need a direct rule so
+ 
+
+ align:start position:0%
+disappear but we need a direct rule so
+we need a direct entropy condition so
+
+ align:start position:0%
+we need a direct entropy condition so
+ 
+
+ align:start position:0%
+we need a direct entropy condition so
+this is going to be uh uh a uh shock
+
+ align:start position:0%
+this is going to be uh uh a uh shock
+ 
+
+ align:start position:0%
+this is going to be uh uh a uh shock
+speed a formula for shock speed s s
+
+ align:start position:0%
+speed a formula for shock speed s s
+ 
+
+ align:start position:0%
+speed a formula for shock speed s s
+equals shock speed we'll
+
+ align:start position:0%
+equals shock speed we'll
+ 
+
+ align:start position:0%
+equals shock speed we'll
+find if there is a shock and number two
+
+ align:start position:0%
+find if there is a shock and number two
+ 
+
+ align:start position:0%
+find if there is a shock and number two
+is going to be this decision is going to
+
+ align:start position:0%
+is going to be this decision is going to
+ 
+
+ align:start position:0%
+is going to be this decision is going to
+be based on a quantity called entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which appears only in nonlinear problems
+
+ align:start position:0%
+which appears only in nonlinear problems
+ 
+
+ align:start position:0%
+which appears only in nonlinear problems
+really okay so that's uh that's a
+
+ align:start position:0%
+really okay so that's uh that's a
+ 
+
+ align:start position:0%
+really okay so that's uh that's a
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+picture which uh these
+
+ align:start position:0%
+picture which uh these
+ 
+
+ align:start position:0%
+picture which uh these
+uh 16920
+
+ align:start position:0%
+uh 16920
+ 
+
+ align:start position:0%
+uh 16920
+notes are a excellent reference for the
+
+ align:start position:0%
+notes are a excellent reference for the
+ 
+
+ align:start position:0%
+notes are a excellent reference for the
+book also and uh Monday's lecture will
+
+ align:start position:0%
+book also and uh Monday's lecture will
+ 
+
+ align:start position:0%
+book also and uh Monday's lecture will
+pick up there so we we can see the two
+
+ align:start position:0%
+pick up there so we we can see the two
+ 
+
+ align:start position:0%
+pick up there so we we can see the two
+the two situations here
+
+ align:start position:0%
+the two situations here
+ 
+
+ align:start position:0%
+the two situations here
+and the question is what do we do at
+
+ align:start position:0%
+and the question is what do we do at
+ 
+
+ align:start position:0%
+and the question is what do we do at
+this point okay see you Monday have a
+
+ align:start position:0%
+this point okay see you Monday have a
+ 
+
+ align:start position:0%
+this point okay see you Monday have a
+good weekend and uh any uh email
+
+ align:start position:0%
+good weekend and uh any uh email
+ 
+
+ align:start position:0%
+good weekend and uh any uh email
+questions about the homework just you
+
+ align:start position:0%
+questions about the homework just you
+ 
+
+ align:start position:0%
+questions about the homework just you
+could send to me or to Andor to maybe
+
+ align:start position:0%
+could send to me or to Andor to maybe
+ 
+
+ align:start position:0%
+could send to me or to Andor to maybe
+and to Mr Cho who will be looking at the
+
+ align:start position:0%
+and to Mr Cho who will be looking at the
+ 
+
+ align:start position:0%
+and to Mr Cho who will be looking at the
+homeworks that come
+
+ align:start position:0%
+homeworks that come
+ 
+
+ align:start position:0%
+homeworks that come
+in good thanks
\ No newline at end of file
diff --git a/FuGcyIynuxg.txt b/FuGcyIynuxg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3d3bc26ebec3367e77ff048aa75de37be2609721
--- /dev/null
+++ b/FuGcyIynuxg.txt
@@ -0,0 +1,12019 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well while people are filing in we can
+
+ align:start position:0%
+well while people are filing in we can
+ 
+
+ align:start position:0%
+well while people are filing in we can
+chat a little bit about the quiz overall
+
+ align:start position:0%
+chat a little bit about the quiz overall
+ 
+
+ align:start position:0%
+chat a little bit about the quiz overall
+I was very very impressed at least with
+
+ align:start position:0%
+I was very very impressed at least with
+ 
+
+ align:start position:0%
+I was very very impressed at least with
+the question one in question to which I
+
+ align:start position:0%
+the question one in question to which I
+ 
+
+ align:start position:0%
+the question one in question to which I
+graded heathen grade in question three
+
+ align:start position:0%
+graded heathen grade in question three
+ 
+
+ align:start position:0%
+graded heathen grade in question three
+so here's all the all the statistics you
+
+ align:start position:0%
+so here's all the all the statistics you
+ 
+
+ align:start position:0%
+so here's all the all the statistics you
+can see that this was a pretty difficult
+
+ align:start position:0%
+can see that this was a pretty difficult
+ 
+
+ align:start position:0%
+can see that this was a pretty difficult
+quiz actually would you agree you have
+
+ align:start position:0%
+quiz actually would you agree you have
+ 
+
+ align:start position:0%
+quiz actually would you agree you have
+evidence to overcome that null
+
+ align:start position:0%
+evidence to overcome that null
+ 
+
+ align:start position:0%
+evidence to overcome that null
+hypothesis that it was a a difficult
+
+ align:start position:0%
+hypothesis that it was a a difficult
+ 
+
+ align:start position:0%
+hypothesis that it was a a difficult
+quiz you know so the average there about
+
+ align:start position:0%
+quiz you know so the average there about
+ 
+
+ align:start position:0%
+quiz you know so the average there about
+78 79 with a fairly fairly widespread
+
+ align:start position:0%
+78 79 with a fairly fairly widespread
+ 
+
+ align:start position:0%
+78 79 with a fairly fairly widespread
+what we will do is post both the quiz
+
+ align:start position:0%
+what we will do is post both the quiz
+ 
+
+ align:start position:0%
+what we will do is post both the quiz
+and the solutions which may be more
+
+ align:start position:0%
+and the solutions which may be more
+ 
+
+ align:start position:0%
+and the solutions which may be more
+interesting to you since you already
+
+ align:start position:0%
+interesting to you since you already
+ 
+
+ align:start position:0%
+interesting to you since you already
+have the quiz and if you do if you do
+
+ align:start position:0%
+have the quiz and if you do if you do
+ 
+
+ align:start position:0%
+have the quiz and if you do if you do
+see anything feel free to chat with us
+
+ align:start position:0%
+see anything feel free to chat with us
+ 
+
+ align:start position:0%
+see anything feel free to chat with us
+about about the question or whatever I
+
+ align:start position:0%
+about about the question or whatever I
+ 
+
+ align:start position:0%
+about about the question or whatever I
+if you're concerned about a point here
+
+ align:start position:0%
+if you're concerned about a point here
+ 
+
+ align:start position:0%
+if you're concerned about a point here
+or a point there I really wouldn't worry
+
+ align:start position:0%
+or a point there I really wouldn't worry
+ 
+
+ align:start position:0%
+or a point there I really wouldn't worry
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+you know where our grading is is we
+
+ align:start position:0%
+you know where our grading is is we
+ 
+
+ align:start position:0%
+you know where our grading is is we
+attempt to be as accurate as possible
+
+ align:start position:0%
+attempt to be as accurate as possible
+ 
+
+ align:start position:0%
+attempt to be as accurate as possible
+but we reserve the right to have a
+
+ align:start position:0%
+but we reserve the right to have a
+ 
+
+ align:start position:0%
+but we reserve the right to have a
+little bit of variation given the nature
+
+ align:start position:0%
+little bit of variation given the nature
+ 
+
+ align:start position:0%
+little bit of variation given the nature
+of the course and in integrating and we
+
+ align:start position:0%
+of the course and in integrating and we
+ 
+
+ align:start position:0%
+of the course and in integrating and we
+will of course be treating everything a
+
+ align:start position:0%
+will of course be treating everything a
+ 
+
+ align:start position:0%
+will of course be treating everything a
+little bit as a mix in you know at the
+
+ align:start position:0%
+little bit as a mix in you know at the
+ 
+
+ align:start position:0%
+little bit as a mix in you know at the
+end from this quiz grade the second quiz
+
+ align:start position:0%
+end from this quiz grade the second quiz
+ 
+
+ align:start position:0%
+end from this quiz grade the second quiz
+grade class participation homeworks all
+
+ align:start position:0%
+grade class participation homeworks all
+ 
+
+ align:start position:0%
+grade class participation homeworks all
+of that so I I think the main thing to
+
+ align:start position:0%
+of that so I I think the main thing to
+ 
+
+ align:start position:0%
+of that so I I think the main thing to
+do is look at the solutions and make
+
+ align:start position:0%
+do is look at the solutions and make
+ 
+
+ align:start position:0%
+do is look at the solutions and make
+sure that you understand at least the
+
+ align:start position:0%
+sure that you understand at least the
+ 
+
+ align:start position:0%
+sure that you understand at least the
+approaches that we took in the solutions
+
+ align:start position:0%
+approaches that we took in the solutions
+ 
+
+ align:start position:0%
+approaches that we took in the solutions
+is not to say that some of the
+
+ align:start position:0%
+is not to say that some of the
+ 
+
+ align:start position:0%
+is not to say that some of the
+approaches that people took on the quiz
+
+ align:start position:0%
+approaches that people took on the quiz
+ 
+
+ align:start position:0%
+approaches that people took on the quiz
+is wrong
+
+ align:start position:0%
+is wrong
+ 
+
+ align:start position:0%
+is wrong
+in fact on problem - I think the biggest
+
+ align:start position:0%
+in fact on problem - I think the biggest
+ 
+
+ align:start position:0%
+in fact on problem - I think the biggest
+thing that we observed is people
+
+ align:start position:0%
+thing that we observed is people
+ 
+
+ align:start position:0%
+thing that we observed is people
+answered the third part if you remember
+
+ align:start position:0%
+answered the third part if you remember
+ 
+
+ align:start position:0%
+answered the third part if you remember
+really the hard way and unfortunately
+
+ align:start position:0%
+really the hard way and unfortunately
+ 
+
+ align:start position:0%
+really the hard way and unfortunately
+you may have burned a fair amount of
+
+ align:start position:0%
+you may have burned a fair amount of
+ 
+
+ align:start position:0%
+you may have burned a fair amount of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+on that with very detailed t-tests and
+
+ align:start position:0%
+on that with very detailed t-tests and
+ 
+
+ align:start position:0%
+on that with very detailed t-tests and
+Neph tests and you know sort of
+
+ align:start position:0%
+Neph tests and you know sort of
+ 
+
+ align:start position:0%
+Neph tests and you know sort of
+complicated hypothesis tests whereas
+
+ align:start position:0%
+complicated hypothesis tests whereas
+ 
+
+ align:start position:0%
+complicated hypothesis tests whereas
+what you had was already the confidence
+
+ align:start position:0%
+what you had was already the confidence
+ 
+
+ align:start position:0%
+what you had was already the confidence
+intervals from Parts A and B that you
+
+ align:start position:0%
+intervals from Parts A and B that you
+ 
+
+ align:start position:0%
+intervals from Parts A and B that you
+could use directly in many cases to make
+
+ align:start position:0%
+could use directly in many cases to make
+ 
+
+ align:start position:0%
+could use directly in many cases to make
+inferences so were there any questions
+
+ align:start position:0%
+inferences so were there any questions
+ 
+
+ align:start position:0%
+inferences so were there any questions
+on the quiz top level not not detailed
+
+ align:start position:0%
+on the quiz top level not not detailed
+ 
+
+ align:start position:0%
+on the quiz top level not not detailed
+okay well take a look at those and again
+
+ align:start position:0%
+okay well take a look at those and again
+ 
+
+ align:start position:0%
+okay well take a look at those and again
+talk to Hayden arrive if more if you
+
+ align:start position:0%
+talk to Hayden arrive if more if you
+ 
+
+ align:start position:0%
+talk to Hayden arrive if more if you
+have any confusions I think is is the
+
+ align:start position:0%
+have any confusions I think is is the
+ 
+
+ align:start position:0%
+have any confusions I think is is the
+main thing okay so here's the plan for
+
+ align:start position:0%
+main thing okay so here's the plan for
+ 
+
+ align:start position:0%
+main thing okay so here's the plan for
+today we started on full factorial
+
+ align:start position:0%
+today we started on full factorial
+ 
+
+ align:start position:0%
+today we started on full factorial
+models design of experiments last time
+
+ align:start position:0%
+models design of experiments last time
+ 
+
+ align:start position:0%
+models design of experiments last time
+I'm gonna pick up where we left off on
+
+ align:start position:0%
+I'm gonna pick up where we left off on
+ 
+
+ align:start position:0%
+I'm gonna pick up where we left off on
+some of that talk a little bit more
+
+ align:start position:0%
+some of that talk a little bit more
+ 
+
+ align:start position:0%
+some of that talk a little bit more
+about the extension of that to
+
+ align:start position:0%
+about the extension of that to
+ 
+
+ align:start position:0%
+about the extension of that to
+generalize to decay experiments the key
+
+ align:start position:0%
+generalize to decay experiments the key
+ 
+
+ align:start position:0%
+generalize to decay experiments the key
+idea here is again picking out
+
+ align:start position:0%
+idea here is again picking out
+ 
+
+ align:start position:0%
+idea here is again picking out
+experimental design points so that you
+
+ align:start position:0%
+experimental design points so that you
+ 
+
+ align:start position:0%
+experimental design points so that you
+can fit particular kinds of models and
+
+ align:start position:0%
+can fit particular kinds of models and
+ 
+
+ align:start position:0%
+can fit particular kinds of models and
+we'll start again with ANOVA for linear
+
+ align:start position:0%
+we'll start again with ANOVA for linear
+ 
+
+ align:start position:0%
+we'll start again with ANOVA for linear
+models and then move on to asking the
+
+ align:start position:0%
+models and then move on to asking the
+ 
+
+ align:start position:0%
+models and then move on to asking the
+question what if a linear model is not
+
+ align:start position:0%
+question what if a linear model is not
+ 
+
+ align:start position:0%
+question what if a linear model is not
+sufficient how do you know if a linear
+
+ align:start position:0%
+sufficient how do you know if a linear
+ 
+
+ align:start position:0%
+sufficient how do you know if a linear
+model is not sufficient how do you check
+
+ align:start position:0%
+model is not sufficient how do you check
+ 
+
+ align:start position:0%
+model is not sufficient how do you check
+for the adequacy of the model form is
+
+ align:start position:0%
+for the adequacy of the model form is
+ 
+
+ align:start position:0%
+for the adequacy of the model form is
+there evidence that you need higher
+
+ align:start position:0%
+there evidence that you need higher
+ 
+
+ align:start position:0%
+there evidence that you need higher
+order terms like a quadratic or other
+
+ align:start position:0%
+order terms like a quadratic or other
+ 
+
+ align:start position:0%
+order terms like a quadratic or other
+curvature so we'll spend the first half
+
+ align:start position:0%
+curvature so we'll spend the first half
+ 
+
+ align:start position:0%
+curvature so we'll spend the first half
+really focused on that and then we'll
+
+ align:start position:0%
+really focused on that and then we'll
+ 
+
+ align:start position:0%
+really focused on that and then we'll
+start moving into some additional issues
+
+ align:start position:0%
+start moving into some additional issues
+ 
+
+ align:start position:0%
+start moving into some additional issues
+in experimental design these ideas of
+
+ align:start position:0%
+in experimental design these ideas of
+ 
+
+ align:start position:0%
+in experimental design these ideas of
+blocks and confounding as well as those
+
+ align:start position:0%
+blocks and confounding as well as those
+ 
+
+ align:start position:0%
+blocks and confounding as well as those
+same issues come out very strongly in
+
+ align:start position:0%
+same issues come out very strongly in
+ 
+
+ align:start position:0%
+same issues come out very strongly in
+fractional factorial designs so we'll
+
+ align:start position:0%
+fractional factorial designs so we'll
+ 
+
+ align:start position:0%
+fractional factorial designs so we'll
+get to that
+
+ align:start position:0%
+get to that
+ 
+
+ align:start position:0%
+get to that
+now I posted on the website reading
+
+ align:start position:0%
+now I posted on the website reading
+ 
+
+ align:start position:0%
+now I posted on the website reading
+assignment the key is probably
+
+ align:start position:0%
+assignment the key is probably
+ 
+
+ align:start position:0%
+assignment the key is probably
+Montgomery Chapter 12 I find that a
+
+ align:start position:0%
+Montgomery Chapter 12 I find that a
+ 
+
+ align:start position:0%
+Montgomery Chapter 12 I find that a
+little bit better description than then
+
+ align:start position:0%
+little bit better description than then
+ 
+
+ align:start position:0%
+little bit better description than then
+may and Spanos but there are some
+
+ align:start position:0%
+may and Spanos but there are some
+ 
+
+ align:start position:0%
+may and Spanos but there are some
+additional topics at the end of the main
+
+ align:start position:0%
+additional topics at the end of the main
+ 
+
+ align:start position:0%
+additional topics at the end of the main
+Spanos chapter that is 713 can't
+
+ align:start position:0%
+Spanos chapter that is 713 can't
+ 
+
+ align:start position:0%
+Spanos chapter that is 713 can't
+remember but it's it's posted on the
+
+ align:start position:0%
+remember but it's it's posted on the
+ 
+
+ align:start position:0%
+remember but it's it's posted on the
+website and so there are some things
+
+ align:start position:0%
+website and so there are some things
+ 
+
+ align:start position:0%
+website and so there are some things
+you'll want to scan and they in Spanish
+
+ align:start position:0%
+you'll want to scan and they in Spanish
+ 
+
+ align:start position:0%
+you'll want to scan and they in Spanish
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+so recall that last time we started
+
+ align:start position:0%
+so recall that last time we started
+ 
+
+ align:start position:0%
+so recall that last time we started
+talking a little bit about the kinds of
+
+ align:start position:0%
+talking a little bit about the kinds of
+ 
+
+ align:start position:0%
+talking a little bit about the kinds of
+models that are associated with
+
+ align:start position:0%
+models that are associated with
+ 
+
+ align:start position:0%
+models that are associated with
+different experimental designs so for
+
+ align:start position:0%
+different experimental designs so for
+ 
+
+ align:start position:0%
+different experimental designs so for
+example we start with sort of this
+
+ align:start position:0%
+example we start with sort of this
+ 
+
+ align:start position:0%
+example we start with sort of this
+simple model it's not the simplest
+
+ align:start position:0%
+simple model it's not the simplest
+ 
+
+ align:start position:0%
+simple model it's not the simplest
+because we already have two factors but
+
+ align:start position:0%
+because we already have two factors but
+ 
+
+ align:start position:0%
+because we already have two factors but
+a very simple two by two or two to the
+
+ align:start position:0%
+a very simple two by two or two to the
+ 
+
+ align:start position:0%
+a very simple two by two or two to the
+two model where again what we've got are
+
+ align:start position:0%
+two model where again what we've got are
+ 
+
+ align:start position:0%
+two model where again what we've got are
+two levels in each of two factors so our
+
+ align:start position:0%
+two levels in each of two factors so our
+ 
+
+ align:start position:0%
+two levels in each of two factors so our
+factors here are X 1 and X 2 and we've
+
+ align:start position:0%
+factors here are X 1 and X 2 and we've
+ 
+
+ align:start position:0%
+factors here are X 1 and X 2 and we've
+got two different levels so we're just
+
+ align:start position:0%
+got two different levels so we're just
+ 
+
+ align:start position:0%
+got two different levels so we're just
+picking the corner points or extremal
+
+ align:start position:0%
+picking the corner points or extremal
+ 
+
+ align:start position:0%
+picking the corner points or extremal
+points for that and we talked last time
+
+ align:start position:0%
+points for that and we talked last time
+ 
+
+ align:start position:0%
+points for that and we talked last time
+about how this can generate a regression
+
+ align:start position:0%
+about how this can generate a regression
+ 
+
+ align:start position:0%
+about how this can generate a regression
+model that has both mean and first order
+
+ align:start position:0%
+model that has both mean and first order
+ 
+
+ align:start position:0%
+model that has both mean and first order
+terms as well as an interaction term we
+
+ align:start position:0%
+terms as well as an interaction term we
+ 
+
+ align:start position:0%
+terms as well as an interaction term we
+also talked about the way that you can
+
+ align:start position:0%
+also talked about the way that you can
+ 
+
+ align:start position:0%
+also talked about the way that you can
+estimate these using contrast and I'm
+
+ align:start position:0%
+estimate these using contrast and I'm
+ 
+
+ align:start position:0%
+estimate these using contrast and I'm
+going to pick up on that a little bit
+
+ align:start position:0%
+going to pick up on that a little bit
+ 
+
+ align:start position:0%
+going to pick up on that a little bit
+where we talk about the effect of
+
+ align:start position:0%
+where we talk about the effect of
+ 
+
+ align:start position:0%
+where we talk about the effect of
+varying x1 the total effect being a
+
+ align:start position:0%
+varying x1 the total effect being a
+ 
+
+ align:start position:0%
+varying x1 the total effect being a
+movement or in the output or an average
+
+ align:start position:0%
+movement or in the output or an average
+ 
+
+ align:start position:0%
+movement or in the output or an average
+movement in the output by a magnitude a
+
+ align:start position:0%
+movement in the output by a magnitude a
+ 
+
+ align:start position:0%
+movement in the output by a magnitude a
+in these coded coefficients for X 1 as
+
+ align:start position:0%
+in these coded coefficients for X 1 as
+ 
+
+ align:start position:0%
+in these coded coefficients for X 1 as
+well as effects for B and the
+
+ align:start position:0%
+well as effects for B and the
+ 
+
+ align:start position:0%
+well as effects for B and the
+interaction effect and basically we're
+
+ align:start position:0%
+interaction effect and basically we're
+ 
+
+ align:start position:0%
+interaction effect and basically we're
+seeing that there is this correspondence
+
+ align:start position:0%
+seeing that there is this correspondence
+ 
+
+ align:start position:0%
+seeing that there is this correspondence
+between a regression approach or a
+
+ align:start position:0%
+between a regression approach or a
+ 
+
+ align:start position:0%
+between a regression approach or a
+contrast approach is a very fast quick
+
+ align:start position:0%
+contrast approach is a very fast quick
+ 
+
+ align:start position:0%
+contrast approach is a very fast quick
+way to estimate these coefficients using
+
+ align:start position:0%
+way to estimate these coefficients using
+ 
+
+ align:start position:0%
+way to estimate these coefficients using
+these these kinds of design of
+
+ align:start position:0%
+these these kinds of design of
+ 
+
+ align:start position:0%
+these these kinds of design of
+experiments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's not good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's very strange all right so a
+
+ align:start position:0%
+that's very strange all right so a
+ 
+
+ align:start position:0%
+that's very strange all right so a
+little bit of the terminology that we we
+
+ align:start position:0%
+little bit of the terminology that we we
+ 
+
+ align:start position:0%
+little bit of the terminology that we we
+talked about just to remind us and then
+
+ align:start position:0%
+talked about just to remind us and then
+ 
+
+ align:start position:0%
+talked about just to remind us and then
+expand on that a little bit there is
+
+ align:start position:0%
+expand on that a little bit there is
+ 
+
+ align:start position:0%
+expand on that a little bit there is
+this notion of a contrast that's going
+
+ align:start position:0%
+this notion of a contrast that's going
+ 
+
+ align:start position:0%
+this notion of a contrast that's going
+to get us to being able to estimate the
+
+ align:start position:0%
+to get us to being able to estimate the
+ 
+
+ align:start position:0%
+to get us to being able to estimate the
+effect of say coefficient coefficient a
+
+ align:start position:0%
+effect of say coefficient coefficient a
+ 
+
+ align:start position:0%
+effect of say coefficient coefficient a
+or beta 1 or beta each of our two main
+
+ align:start position:0%
+or beta 1 or beta each of our two main
+ 
+
+ align:start position:0%
+or beta 1 or beta each of our two main
+effects or the interaction effects and
+
+ align:start position:0%
+effects or the interaction effects and
+ 
+
+ align:start position:0%
+effects or the interaction effects and
+these sort of condensed down tables
+
+ align:start position:0%
+these sort of condensed down tables
+ 
+
+ align:start position:0%
+these sort of condensed down tables
+summarizing the design of your
+
+ align:start position:0%
+summarizing the design of your
+ 
+
+ align:start position:0%
+summarizing the design of your
+experiment a really useful tools for
+
+ align:start position:0%
+experiment a really useful tools for
+ 
+
+ align:start position:0%
+experiment a really useful tools for
+being able to generate these contrasts
+
+ align:start position:0%
+being able to generate these contrasts
+ 
+
+ align:start position:0%
+being able to generate these contrasts
+for being able to identify what the mix
+
+ align:start position:0%
+for being able to identify what the mix
+ 
+
+ align:start position:0%
+for being able to identify what the mix
+of level settings are for each of the
+
+ align:start position:0%
+of level settings are for each of the
+ 
+
+ align:start position:0%
+of level settings are for each of the
+trial runs that we do and so on so a
+
+ align:start position:0%
+trial runs that we do and so on so a
+ 
+
+ align:start position:0%
+trial runs that we do and so on so a
+little bit of terminology again we said
+
+ align:start position:0%
+little bit of terminology again we said
+ 
+
+ align:start position:0%
+little bit of terminology again we said
+this column here the trial column is
+
+ align:start position:0%
+this column here the trial column is
+ 
+
+ align:start position:0%
+this column here the trial column is
+essentially you know our run and we can
+
+ align:start position:0%
+essentially you know our run and we can
+ 
+
+ align:start position:0%
+essentially you know our run and we can
+label them in a shorthand that tells us
+
+ align:start position:0%
+label them in a shorthand that tells us
+ 
+
+ align:start position:0%
+label them in a shorthand that tells us
+what our factor settings are our level
+
+ align:start position:0%
+what our factor settings are our level
+ 
+
+ align:start position:0%
+what our factor settings are our level
+settings are for each of our two factors
+
+ align:start position:0%
+settings are for each of our two factors
+ 
+
+ align:start position:0%
+settings are for each of our two factors
+are X 1 factor and our X 2 factor so the
+
+ align:start position:0%
+are X 1 factor and our X 2 factor so the
+ 
+
+ align:start position:0%
+are X 1 factor and our X 2 factor so the
+first label here is just the low setting
+
+ align:start position:0%
+first label here is just the low setting
+ 
+
+ align:start position:0%
+first label here is just the low setting
+for both of our factors and we'll label
+
+ align:start position:0%
+for both of our factors and we'll label
+ 
+
+ align:start position:0%
+for both of our factors and we'll label
+that with a with a 1 hour high setting
+
+ align:start position:0%
+that with a with a 1 hour high setting
+ 
+
+ align:start position:0%
+that with a with a 1 hour high setting
+for the a factor we label that one with
+
+ align:start position:0%
+for the a factor we label that one with
+ 
+
+ align:start position:0%
+for the a factor we label that one with
+a high setting or A+ sometimes well
+
+ align:start position:0%
+a high setting or A+ sometimes well
+ 
+
+ align:start position:0%
+a high setting or A+ sometimes well
+legal that is a +1 and our low setting
+
+ align:start position:0%
+legal that is a +1 and our low setting
+ 
+
+ align:start position:0%
+legal that is a +1 and our low setting
+then for everything else for B or B
+
+ align:start position:0%
+then for everything else for B or B
+ 
+
+ align:start position:0%
+then for everything else for B or B
+factor here that's where we set that one
+
+ align:start position:0%
+factor here that's where we set that one
+ 
+
+ align:start position:0%
+factor here that's where we set that one
+high and when we set both of them high
+
+ align:start position:0%
+high and when we set both of them high
+ 
+
+ align:start position:0%
+high and when we set both of them high
+that's our our plus setting for the two
+
+ align:start position:0%
+that's our our plus setting for the two
+ 
+
+ align:start position:0%
+that's our our plus setting for the two
+of them now we can also think about what
+
+ align:start position:0%
+of them now we can also think about what
+ 
+
+ align:start position:0%
+of them now we can also think about what
+is the sort of factor level for the
+
+ align:start position:0%
+is the sort of factor level for the
+ 
+
+ align:start position:0%
+is the sort of factor level for the
+interaction and we do that with this
+
+ align:start position:0%
+interaction and we do that with this
+ 
+
+ align:start position:0%
+interaction and we do that with this
+very funky shorthand algebra just saying
+
+ align:start position:0%
+very funky shorthand algebra just saying
+ 
+
+ align:start position:0%
+very funky shorthand algebra just saying
+okay a B is really think of that as a
+
+ align:start position:0%
+okay a B is really think of that as a
+ 
+
+ align:start position:0%
+okay a B is really think of that as a
+multiplication of the a and B factors so
+
+ align:start position:0%
+multiplication of the a and B factors so
+ 
+
+ align:start position:0%
+multiplication of the a and B factors so
+a minus 1 and a minus 1 gives a plus 1
+
+ align:start position:0%
+a minus 1 and a minus 1 gives a plus 1
+ 
+
+ align:start position:0%
+a minus 1 and a minus 1 gives a plus 1
+there and similarly for all of the other
+
+ align:start position:0%
+there and similarly for all of the other
+ 
+
+ align:start position:0%
+there and similarly for all of the other
+columns that generates the level setting
+
+ align:start position:0%
+columns that generates the level setting
+ 
+
+ align:start position:0%
+columns that generates the level setting
+if you will for each of those
+
+ align:start position:0%
+if you will for each of those
+ 
+
+ align:start position:0%
+if you will for each of those
+for each of those combinations now in
+
+ align:start position:0%
+for each of those combinations now in
+ 
+
+ align:start position:0%
+for each of those combinations now in
+the actual experiment of course we're
+
+ align:start position:0%
+the actual experiment of course we're
+ 
+
+ align:start position:0%
+the actual experiment of course we're
+only setting X 1 and X 2 for each of our
+
+ align:start position:0%
+only setting X 1 and X 2 for each of our
+ 
+
+ align:start position:0%
+only setting X 1 and X 2 for each of our
+trials these experimental interaction
+
+ align:start position:0%
+trials these experimental interaction
+ 
+
+ align:start position:0%
+trials these experimental interaction
+columns are essentially giving us
+
+ align:start position:0%
+columns are essentially giving us
+ 
+
+ align:start position:0%
+columns are essentially giving us
+information that we need in order to
+
+ align:start position:0%
+information that we need in order to
+ 
+
+ align:start position:0%
+information that we need in order to
+form the contrast in the shorthand way
+
+ align:start position:0%
+form the contrast in the shorthand way
+ 
+
+ align:start position:0%
+form the contrast in the shorthand way
+of estimating effects as well as we'll
+
+ align:start position:0%
+of estimating effects as well as we'll
+ 
+
+ align:start position:0%
+of estimating effects as well as we'll
+see this a little bit later as well as
+
+ align:start position:0%
+see this a little bit later as well as
+ 
+
+ align:start position:0%
+see this a little bit later as well as
+telling us what the interaction term
+
+ align:start position:0%
+telling us what the interaction term
+ 
+
+ align:start position:0%
+telling us what the interaction term
+should be if we're going to form
+
+ align:start position:0%
+should be if we're going to form
+ 
+
+ align:start position:0%
+should be if we're going to form
+regression including do the regression
+
+ align:start position:0%
+regression including do the regression
+ 
+
+ align:start position:0%
+regression including do the regression
+on the interaction factor so it's pretty
+
+ align:start position:0%
+on the interaction factor so it's pretty
+ 
+
+ align:start position:0%
+on the interaction factor so it's pretty
+funky all intertwined here so something
+
+ align:start position:0%
+funky all intertwined here so something
+ 
+
+ align:start position:0%
+funky all intertwined here so something
+strange in our slides this this is
+
+ align:start position:0%
+strange in our slides this this is
+ 
+
+ align:start position:0%
+strange in our slides this this is
+simply I don't know what that is it's
+
+ align:start position:0%
+simply I don't know what that is it's
+ 
+
+ align:start position:0%
+simply I don't know what that is it's
+supposed to be a dot just a
+
+ align:start position:0%
+supposed to be a dot just a
+ 
+
+ align:start position:0%
+supposed to be a dot just a
+multiplication because now we can say
+
+ align:start position:0%
+multiplication because now we can say
+ 
+
+ align:start position:0%
+multiplication because now we can say
+okay how do we form the contrast between
+
+ align:start position:0%
+okay how do we form the contrast between
+ 
+
+ align:start position:0%
+okay how do we form the contrast between
+our different combinations of settings
+
+ align:start position:0%
+our different combinations of settings
+ 
+
+ align:start position:0%
+our different combinations of settings
+in order to estimate the effect of a and
+
+ align:start position:0%
+in order to estimate the effect of a and
+ 
+
+ align:start position:0%
+in order to estimate the effect of a and
+essentially what we're going to be doing
+
+ align:start position:0%
+essentially what we're going to be doing
+ 
+
+ align:start position:0%
+essentially what we're going to be doing
+is forming the average between the high
+
+ align:start position:0%
+is forming the average between the high
+ 
+
+ align:start position:0%
+is forming the average between the high
+for a this column and this column or the
+
+ align:start position:0%
+for a this column and this column or the
+ 
+
+ align:start position:0%
+for a this column and this column or the
+difference between the average of those
+
+ align:start position:0%
+difference between the average of those
+ 
+
+ align:start position:0%
+difference between the average of those
+two columns and these two settings so
+
+ align:start position:0%
+two columns and these two settings so
+ 
+
+ align:start position:0%
+two columns and these two settings so
+I'm basically forming the contrast in
+
+ align:start position:0%
+I'm basically forming the contrast in
+ 
+
+ align:start position:0%
+I'm basically forming the contrast in
+each case for each factor is the
+
+ align:start position:0%
+each case for each factor is the
+ 
+
+ align:start position:0%
+each case for each factor is the
+difference between the high and the low
+
+ align:start position:0%
+difference between the high and the low
+ 
+
+ align:start position:0%
+difference between the high and the low
+setting and so that's actually why we
+
+ align:start position:0%
+setting and so that's actually why we
+ 
+
+ align:start position:0%
+setting and so that's actually why we
+need the interaction factor so we can we
+
+ align:start position:0%
+need the interaction factor so we can we
+ 
+
+ align:start position:0%
+need the interaction factor so we can we
+can look at the high settings for the
+
+ align:start position:0%
+can look at the high settings for the
+ 
+
+ align:start position:0%
+can look at the high settings for the
+interaction the the a B and the 1 and
+
+ align:start position:0%
+interaction the the a B and the 1 and
+ 
+
+ align:start position:0%
+interaction the the a B and the 1 and
+then the minus a and the minus B where
+
+ align:start position:0%
+then the minus a and the minus B where
+ 
+
+ align:start position:0%
+then the minus a and the minus B where
+are these coming from a much better way
+
+ align:start position:0%
+are these coming from a much better way
+ 
+
+ align:start position:0%
+are these coming from a much better way
+to picture this is if we look at this
+
+ align:start position:0%
+to picture this is if we look at this
+ 
+
+ align:start position:0%
+to picture this is if we look at this
+kind of graphically so what I'm going to
+
+ align:start position:0%
+kind of graphically so what I'm going to
+ 
+
+ align:start position:0%
+kind of graphically so what I'm going to
+do here first is generalize this is a 2
+
+ align:start position:0%
+do here first is generalize this is a 2
+ 
+
+ align:start position:0%
+do here first is generalize this is a 2
+to the 3 design in more general terms we
+
+ align:start position:0%
+to the 3 design in more general terms we
+ 
+
+ align:start position:0%
+to the 3 design in more general terms we
+can do a full factorial with any number
+
+ align:start position:0%
+can do a full factorial with any number
+ 
+
+ align:start position:0%
+can do a full factorial with any number
+of factors and form this sort of
+
+ align:start position:0%
+of factors and form this sort of
+ 
+
+ align:start position:0%
+of factors and form this sort of
+hypercube again with corner points at
+
+ align:start position:0%
+hypercube again with corner points at
+ 
+
+ align:start position:0%
+hypercube again with corner points at
+all komban
+
+ align:start position:0%
+all komban
+ 
+
+ align:start position:0%
+all komban
+of the high and low values or levels for
+
+ align:start position:0%
+of the high and low values or levels for
+ 
+
+ align:start position:0%
+of the high and low values or levels for
+each of our setting and on that
+
+ align:start position:0%
+each of our setting and on that
+ 
+
+ align:start position:0%
+each of our setting and on that
+hypercube so now I've got a factor B
+
+ align:start position:0%
+hypercube so now I've got a factor B
+ 
+
+ align:start position:0%
+hypercube so now I've got a factor B
+factor and C factor this is a nice
+
+ align:start position:0%
+factor and C factor this is a nice
+ 
+
+ align:start position:0%
+factor and C factor this is a nice
+picture performing what that contrast is
+
+ align:start position:0%
+picture performing what that contrast is
+ 
+
+ align:start position:0%
+picture performing what that contrast is
+doing and how we rest amay ting the
+
+ align:start position:0%
+doing and how we rest amay ting the
+ 
+
+ align:start position:0%
+doing and how we rest amay ting the
+average effect of changing one factor at
+
+ align:start position:0%
+average effect of changing one factor at
+ 
+
+ align:start position:0%
+average effect of changing one factor at
+a time on this picture right so just
+
+ align:start position:0%
+a time on this picture right so just
+ 
+
+ align:start position:0%
+a time on this picture right so just
+conceptually and are intuitively if you
+
+ align:start position:0%
+conceptually and are intuitively if you
+ 
+
+ align:start position:0%
+conceptually and are intuitively if you
+were trying to form an estimate of the
+
+ align:start position:0%
+were trying to form an estimate of the
+ 
+
+ align:start position:0%
+were trying to form an estimate of the
+factor effect a associated with some
+
+ align:start position:0%
+factor effect a associated with some
+ 
+
+ align:start position:0%
+factor effect a associated with some
+variable X 1 notice that what we've got
+
+ align:start position:0%
+variable X 1 notice that what we've got
+ 
+
+ align:start position:0%
+variable X 1 notice that what we've got
+at all of these settings on the Left
+
+ align:start position:0%
+at all of these settings on the Left
+ 
+
+ align:start position:0%
+at all of these settings on the Left
+sort of shaded with the blue those are
+
+ align:start position:0%
+sort of shaded with the blue those are
+ 
+
+ align:start position:0%
+sort of shaded with the blue those are
+all low settings for our a factor
+
+ align:start position:0%
+all low settings for our a factor
+ 
+
+ align:start position:0%
+all low settings for our a factor
+I'm varying B and C also but in for all
+
+ align:start position:0%
+I'm varying B and C also but in for all
+ 
+
+ align:start position:0%
+I'm varying B and C also but in for all
+of those I'm holding the a factor at the
+
+ align:start position:0%
+of those I'm holding the a factor at the
+ 
+
+ align:start position:0%
+of those I'm holding the a factor at the
+low value and then similarly on the red
+
+ align:start position:0%
+low value and then similarly on the red
+ 
+
+ align:start position:0%
+low value and then similarly on the red
+side I'm holding the a factor at the
+
+ align:start position:0%
+side I'm holding the a factor at the
+ 
+
+ align:start position:0%
+side I'm holding the a factor at the
+high value in all of those cases may be
+
+ align:start position:0%
+high value in all of those cases may be
+ 
+
+ align:start position:0%
+high value in all of those cases may be
+varying other things too but if I think
+
+ align:start position:0%
+varying other things too but if I think
+ 
+
+ align:start position:0%
+varying other things too but if I think
+that those other effects are basically
+
+ align:start position:0%
+that those other effects are basically
+ 
+
+ align:start position:0%
+that those other effects are basically
+balancing out now what I've got is a
+
+ align:start position:0%
+balancing out now what I've got is a
+ 
+
+ align:start position:0%
+balancing out now what I've got is a
+difference between the a high and the a
+
+ align:start position:0%
+difference between the a high and the a
+ 
+
+ align:start position:0%
+difference between the a high and the a
+low as a net overall estimate of the
+
+ align:start position:0%
+low as a net overall estimate of the
+ 
+
+ align:start position:0%
+low as a net overall estimate of the
+total effect of changing variable x1
+
+ align:start position:0%
+total effect of changing variable x1
+ 
+
+ align:start position:0%
+total effect of changing variable x1
+changing the variable associated with a
+
+ align:start position:0%
+changing the variable associated with a
+ 
+
+ align:start position:0%
+changing the variable associated with a
+and that's all that the contrasts are
+
+ align:start position:0%
+and that's all that the contrasts are
+ 
+
+ align:start position:0%
+and that's all that the contrasts are
+doing they're simply saying ok the the
+
+ align:start position:0%
+doing they're simply saying ok the the
+ 
+
+ align:start position:0%
+doing they're simply saying ok the the
+high contrast is all of the places where
+
+ align:start position:0%
+high contrast is all of the places where
+ 
+
+ align:start position:0%
+high contrast is all of the places where
+a is set high - all of the places where
+
+ align:start position:0%
+a is set high - all of the places where
+ 
+
+ align:start position:0%
+a is set high - all of the places where
+a is set low form that difference recall
+
+ align:start position:0%
+a is set low form that difference recall
+ 
+
+ align:start position:0%
+a is set low form that difference recall
+that we've got I need to take the
+
+ align:start position:0%
+that we've got I need to take the
+ 
+
+ align:start position:0%
+that we've got I need to take the
+average so in each of these cases I've
+
+ align:start position:0%
+average so in each of these cases I've
+ 
+
+ align:start position:0%
+average so in each of these cases I've
+got four points at high and four points
+
+ align:start position:0%
+got four points at high and four points
+ 
+
+ align:start position:0%
+got four points at high and four points
+at low so I'm taking the average and
+
+ align:start position:0%
+at low so I'm taking the average and
+ 
+
+ align:start position:0%
+at low so I'm taking the average and
+taking the difference that's my estimate
+
+ align:start position:0%
+taking the difference that's my estimate
+ 
+
+ align:start position:0%
+taking the difference that's my estimate
+of the total net net effect question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay say that question again I've got
+
+ align:start position:0%
+okay say that question again I've got
+ 
+
+ align:start position:0%
+okay say that question again I've got
+here's AC so so so far what we've done
+
+ align:start position:0%
+here's AC so so so far what we've done
+ 
+
+ align:start position:0%
+here's AC so so so far what we've done
+is only estimated one of the contrasts
+
+ align:start position:0%
+is only estimated one of the contrasts
+ 
+
+ align:start position:0%
+is only estimated one of the contrasts
+it looks like you're actually getting
+
+ align:start position:0%
+it looks like you're actually getting
+ 
+
+ align:start position:0%
+it looks like you're actually getting
+close to estimating a different a
+
+ align:start position:0%
+close to estimating a different a
+ 
+
+ align:start position:0%
+close to estimating a different a
+different term in a model so so what we
+
+ align:start position:0%
+different term in a model so so what we
+ 
+
+ align:start position:0%
+different term in a model so so what we
+did here was just to estimate the a
+
+ align:start position:0%
+did here was just to estimate the a
+ 
+
+ align:start position:0%
+did here was just to estimate the a
+affection I would not also need to do
+
+ align:start position:0%
+affection I would not also need to do
+ 
+
+ align:start position:0%
+affection I would not also need to do
+the same thing for the B effect okay so
+
+ align:start position:0%
+the same thing for the B effect okay so
+ 
+
+ align:start position:0%
+the same thing for the B effect okay so
+that's telling me if I vary x2 and I can
+
+ align:start position:0%
+that's telling me if I vary x2 and I can
+ 
+
+ align:start position:0%
+that's telling me if I vary x2 and I can
+similarly do that for the C effect but
+
+ align:start position:0%
+similarly do that for the C effect but
+ 
+
+ align:start position:0%
+similarly do that for the C effect but
+then there's a question well what if
+
+ align:start position:0%
+then there's a question well what if
+ 
+
+ align:start position:0%
+then there's a question well what if
+there is an interaction between two of
+
+ align:start position:0%
+there is an interaction between two of
+ 
+
+ align:start position:0%
+there is an interaction between two of
+these terms and one can also form a
+
+ align:start position:0%
+these terms and one can also form a
+ 
+
+ align:start position:0%
+these terms and one can also form a
+contrast or an interaction effect and
+
+ align:start position:0%
+contrast or an interaction effect and
+ 
+
+ align:start position:0%
+contrast or an interaction effect and
+maybe this is not exactly what you are
+
+ align:start position:0%
+maybe this is not exactly what you are
+ 
+
+ align:start position:0%
+maybe this is not exactly what you are
+describing but it's getting close to
+
+ align:start position:0%
+describing but it's getting close to
+ 
+
+ align:start position:0%
+describing but it's getting close to
+other ways of combining some of these
+
+ align:start position:0%
+other ways of combining some of these
+ 
+
+ align:start position:0%
+other ways of combining some of these
+effects so it turns out what this does
+
+ align:start position:0%
+effects so it turns out what this does
+ 
+
+ align:start position:0%
+effects so it turns out what this does
+is makes a balanced combination of our
+
+ align:start position:0%
+is makes a balanced combination of our
+ 
+
+ align:start position:0%
+is makes a balanced combination of our
+data points to be able to take advantage
+
+ align:start position:0%
+data points to be able to take advantage
+ 
+
+ align:start position:0%
+data points to be able to take advantage
+of that a B column this is just
+
+ align:start position:0%
+of that a B column this is just
+ 
+
+ align:start position:0%
+of that a B column this is just
+basically taking the high and low
+
+ align:start position:0%
+basically taking the high and low
+ 
+
+ align:start position:0%
+basically taking the high and low
+combinations and forming that estimate
+
+ align:start position:0%
+combinations and forming that estimate
+ 
+
+ align:start position:0%
+combinations and forming that estimate
+of the a/b interaction effect using the
+
+ align:start position:0%
+of the a/b interaction effect using the
+ 
+
+ align:start position:0%
+of the a/b interaction effect using the
+contrast between these between these
+
+ align:start position:0%
+contrast between these between these
+ 
+
+ align:start position:0%
+contrast between these between these
+points now there would also be another
+
+ align:start position:0%
+points now there would also be another
+ 
+
+ align:start position:0%
+points now there would also be another
+contrast for the BC interaction if you
+
+ align:start position:0%
+contrast for the BC interaction if you
+ 
+
+ align:start position:0%
+contrast for the BC interaction if you
+sort of rotated these around and formed
+
+ align:start position:0%
+sort of rotated these around and formed
+ 
+
+ align:start position:0%
+sort of rotated these around and formed
+the plane where you took took the
+
+ align:start position:0%
+the plane where you took took the
+ 
+
+ align:start position:0%
+the plane where you took took the
+high/low combinations of B and C instead
+
+ align:start position:0%
+high/low combinations of B and C instead
+ 
+
+ align:start position:0%
+high/low combinations of B and C instead
+of a and B okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that get at your question a rigidity
+
+ align:start position:0%
+is that get at your question a rigidity
+ 
+
+ align:start position:0%
+is that get at your question a rigidity
+you can always form different
+
+ align:start position:0%
+you can always form different
+ 
+
+ align:start position:0%
+you can always form different
+combinations of things the question is
+
+ align:start position:0%
+combinations of things the question is
+ 
+
+ align:start position:0%
+combinations of things the question is
+what combination do you need in order to
+
+ align:start position:0%
+what combination do you need in order to
+ 
+
+ align:start position:0%
+what combination do you need in order to
+be able to estimate the coefficient in
+
+ align:start position:0%
+be able to estimate the coefficient in
+ 
+
+ align:start position:0%
+be able to estimate the coefficient in
+the model yes I mean I think you can
+
+ align:start position:0%
+the model yes I mean I think you can
+ 
+
+ align:start position:0%
+the model yes I mean I think you can
+generate this that that cross thing is
+
+ align:start position:0%
+generate this that that cross thing is
+ 
+
+ align:start position:0%
+generate this that that cross thing is
+intuitive in the sense only in the sense
+
+ align:start position:0%
+intuitive in the sense only in the sense
+ 
+
+ align:start position:0%
+intuitive in the sense only in the sense
+that it corresponds nicely you can
+
+ align:start position:0%
+that it corresponds nicely you can
+ 
+
+ align:start position:0%
+that it corresponds nicely you can
+generate it once you have this column so
+
+ align:start position:0%
+generate it once you have this column so
+ 
+
+ align:start position:0%
+generate it once you have this column so
+now I can connect up the high points and
+
+ align:start position:0%
+now I can connect up the high points and
+ 
+
+ align:start position:0%
+now I can connect up the high points and
+that would be one plane connect up the
+
+ align:start position:0%
+that would be one plane connect up the
+ 
+
+ align:start position:0%
+that would be one plane connect up the
+low points that's my other plane and
+
+ align:start position:0%
+low points that's my other plane and
+ 
+
+ align:start position:0%
+low points that's my other plane and
+then I take the difference but it's not
+
+ align:start position:0%
+then I take the difference but it's not
+ 
+
+ align:start position:0%
+then I take the difference but it's not
+entirely intuitive why that particular
+
+ align:start position:0%
+entirely intuitive why that particular
+ 
+
+ align:start position:0%
+entirely intuitive why that particular
+combination gives you the estimate of
+
+ align:start position:0%
+combination gives you the estimate of
+ 
+
+ align:start position:0%
+combination gives you the estimate of
+that coefficient I agree with that so
+
+ align:start position:0%
+that coefficient I agree with that so
+ 
+
+ align:start position:0%
+that coefficient I agree with that so
+this is kind of the shorthand that gives
+
+ align:start position:0%
+this is kind of the shorthand that gives
+ 
+
+ align:start position:0%
+this is kind of the shorthand that gives
+the answer in fact I don't have a good
+
+ align:start position:0%
+the answer in fact I don't have a good
+ 
+
+ align:start position:0%
+the answer in fact I don't have a good
+intuitive explanation just looking
+
+ align:start position:0%
+intuitive explanation just looking
+ 
+
+ align:start position:0%
+intuitive explanation just looking
+purely at this picture why that
+
+ align:start position:0%
+purely at this picture why that
+ 
+
+ align:start position:0%
+purely at this picture why that
+estimates the interaction it's the
+
+ align:start position:0%
+estimates the interaction it's the
+ 
+
+ align:start position:0%
+estimates the interaction it's the
+closest I can come is almost in two
+
+ align:start position:0%
+closest I can come is almost in two
+ 
+
+ align:start position:0%
+closest I can come is almost in two
+dimensions instead of three with these
+
+ align:start position:0%
+dimensions instead of three with these
+ 
+
+ align:start position:0%
+dimensions instead of three with these
+interaction plots that we we've drawn
+
+ align:start position:0%
+interaction plots that we we've drawn
+ 
+
+ align:start position:0%
+interaction plots that we we've drawn
+before so the the basic interaction plot
+
+ align:start position:0%
+before so the the basic interaction plot
+ 
+
+ align:start position:0%
+before so the the basic interaction plot
+would look and say if I just have x1 and
+
+ align:start position:0%
+would look and say if I just have x1 and
+ 
+
+ align:start position:0%
+would look and say if I just have x1 and
+x2 values by just drawing as here's my
+
+ align:start position:0%
+x2 values by just drawing as here's my
+ 
+
+ align:start position:0%
+x2 values by just drawing as here's my
+output as I vary x1 from high to low
+
+ align:start position:0%
+output as I vary x1 from high to low
+ 
+
+ align:start position:0%
+output as I vary x1 from high to low
+holding x2 low that would be one effect
+
+ align:start position:0%
+holding x2 low that would be one effect
+ 
+
+ align:start position:0%
+holding x2 low that would be one effect
+if now I let X to be high
+
+ align:start position:0%
+if now I let X to be high
+ 
+
+ align:start position:0%
+if now I let X to be high
+I don't have just an offset but I've got
+
+ align:start position:0%
+I don't have just an offset but I've got
+ 
+
+ align:start position:0%
+I don't have just an offset but I've got
+a different Delta here than here that
+
+ align:start position:0%
+a different Delta here than here that
+ 
+
+ align:start position:0%
+a different Delta here than here that
+means that in combination x1 and x2 work
+
+ align:start position:0%
+means that in combination x1 and x2 work
+ 
+
+ align:start position:0%
+means that in combination x1 and x2 work
+together to do something different than
+
+ align:start position:0%
+together to do something different than
+ 
+
+ align:start position:0%
+together to do something different than
+purely x1 or x2 there is not just purely
+
+ align:start position:0%
+purely x1 or x2 there is not just purely
+ 
+
+ align:start position:0%
+purely x1 or x2 there is not just purely
+an additive a effect in the B effect but
+
+ align:start position:0%
+an additive a effect in the B effect but
+ 
+
+ align:start position:0%
+an additive a effect in the B effect but
+there is an a/b effect and in three
+
+ align:start position:0%
+there is an a/b effect and in three
+ 
+
+ align:start position:0%
+there is an a/b effect and in three
+dimensions so so in two dimensions
+
+ align:start position:0%
+dimensions so so in two dimensions
+ 
+
+ align:start position:0%
+dimensions so so in two dimensions
+essentially what you're doing is looking
+
+ align:start position:0%
+essentially what you're doing is looking
+ 
+
+ align:start position:0%
+essentially what you're doing is looking
+at forming the Delta from this
+
+ align:start position:0%
+at forming the Delta from this
+ 
+
+ align:start position:0%
+at forming the Delta from this
+combination and this combination and
+
+ align:start position:0%
+combination and this combination and
+ 
+
+ align:start position:0%
+combination and this combination and
+saying there is a difference an extra
+
+ align:start position:0%
+saying there is a difference an extra
+ 
+
+ align:start position:0%
+saying there is a difference an extra
+Delta between the two in 3d it's a
+
+ align:start position:0%
+Delta between the two in 3d it's a
+ 
+
+ align:start position:0%
+Delta between the two in 3d it's a
+little harder to to see but I think it's
+
+ align:start position:0%
+little harder to to see but I think it's
+ 
+
+ align:start position:0%
+little harder to to see but I think it's
+doing conceptually that same thing yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I think we did in the two factor so
+
+ align:start position:0%
+oh I think we did in the two factor so
+ 
+
+ align:start position:0%
+oh I think we did in the two factor so
+the four is basically just because I'm
+
+ align:start position:0%
+the four is basically just because I'm
+ 
+
+ align:start position:0%
+the four is basically just because I'm
+taking the average from each of the this
+
+ align:start position:0%
+taking the average from each of the this
+ 
+
+ align:start position:0%
+taking the average from each of the this
+point has four points so I'm just taking
+
+ align:start position:0%
+point has four points so I'm just taking
+ 
+
+ align:start position:0%
+point has four points so I'm just taking
+me the average from that the difference
+
+ align:start position:0%
+me the average from that the difference
+ 
+
+ align:start position:0%
+me the average from that the difference
+from that so the four is coming from the
+
+ align:start position:0%
+from that so the four is coming from the
+ 
+
+ align:start position:0%
+from that so the four is coming from the
+number of points I had in each average
+
+ align:start position:0%
+number of points I had in each average
+ 
+
+ align:start position:0%
+number of points I had in each average
+that's an estimate of the total effect
+
+ align:start position:0%
+that's an estimate of the total effect
+ 
+
+ align:start position:0%
+that's an estimate of the total effect
+then there's one additional subtle point
+
+ align:start position:0%
+then there's one additional subtle point
+ 
+
+ align:start position:0%
+then there's one additional subtle point
+which is how do I get from that factor
+
+ align:start position:0%
+which is how do I get from that factor
+ 
+
+ align:start position:0%
+which is how do I get from that factor
+total of net effect main effect a or
+
+ align:start position:0%
+total of net effect main effect a or
+ 
+
+ align:start position:0%
+total of net effect main effect a or
+interaction effect a B to an estimate of
+
+ align:start position:0%
+interaction effect a B to an estimate of
+ 
+
+ align:start position:0%
+interaction effect a B to an estimate of
+the model coefficient and that's where
+
+ align:start position:0%
+the model coefficient and that's where
+ 
+
+ align:start position:0%
+the model coefficient and that's where
+some scaling comes into play what we've
+
+ align:start position:0%
+some scaling comes into play what we've
+ 
+
+ align:start position:0%
+some scaling comes into play what we've
+done in these pictures is scaled our x1
+
+ align:start position:0%
+done in these pictures is scaled our x1
+ 
+
+ align:start position:0%
+done in these pictures is scaled our x1
+and x2 to a low of minus one and a high
+
+ align:start position:0%
+and x2 to a low of minus one and a high
+ 
+
+ align:start position:0%
+and x2 to a low of minus one and a high
+of one intermediate point of zero so if
+
+ align:start position:0%
+of one intermediate point of zero so if
+ 
+
+ align:start position:0%
+of one intermediate point of zero so if
+then if the total effect here just
+
+ align:start position:0%
+then if the total effect here just
+ 
+
+ align:start position:0%
+then if the total effect here just
+saying let's say this was the the
+
+ align:start position:0%
+saying let's say this was the the
+ 
+
+ align:start position:0%
+saying let's say this was the the
+overall a effect what I'd like is
+
+ align:start position:0%
+overall a effect what I'd like is
+ 
+
+ align:start position:0%
+overall a effect what I'd like is
+something that goes y equals beta naught
+
+ align:start position:0%
+something that goes y equals beta naught
+ 
+
+ align:start position:0%
+something that goes y equals beta naught
+plus beta 1 X 1
+
+ align:start position:0%
+plus beta 1 X 1
+ 
+
+ align:start position:0%
+plus beta 1 X 1
+and so what I've got is a total range in
+
+ align:start position:0%
+and so what I've got is a total range in
+ 
+
+ align:start position:0%
+and so what I've got is a total range in
+X one of two so I have to basically
+
+ align:start position:0%
+X one of two so I have to basically
+ 
+
+ align:start position:0%
+X one of two so I have to basically
+scale this so that I've got a over 2 X 1
+
+ align:start position:0%
+scale this so that I've got a over 2 X 1
+ 
+
+ align:start position:0%
+scale this so that I've got a over 2 X 1
+as X goes from 0 to 1 I've got half of
+
+ align:start position:0%
+as X goes from 0 to 1 I've got half of
+ 
+
+ align:start position:0%
+as X goes from 0 to 1 I've got half of
+the effect and as X goes from 0 to minus
+
+ align:start position:0%
+the effect and as X goes from 0 to minus
+ 
+
+ align:start position:0%
+the effect and as X goes from 0 to minus
+1 I've got the other half of the effect
+
+ align:start position:0%
+1 I've got the other half of the effect
+ 
+
+ align:start position:0%
+1 I've got the other half of the effect
+so that's where beta 1 is equal to the a
+
+ align:start position:0%
+so that's where beta 1 is equal to the a
+ 
+
+ align:start position:0%
+so that's where beta 1 is equal to the a
+over 2 and that's only true again a lot
+
+ align:start position:0%
+over 2 and that's only true again a lot
+ 
+
+ align:start position:0%
+over 2 and that's only true again a lot
+of what I'm saying is only true if we're
+
+ align:start position:0%
+of what I'm saying is only true if we're
+ 
+
+ align:start position:0%
+of what I'm saying is only true if we're
+using the scale coefficients for X 1
+
+ align:start position:0%
+using the scale coefficients for X 1
+ 
+
+ align:start position:0%
+using the scale coefficients for X 1
+from minus 1 to plus 1 and then all this
+
+ align:start position:0%
+from minus 1 to plus 1 and then all this
+ 
+
+ align:start position:0%
+from minus 1 to plus 1 and then all this
+magical shorthand of these column tables
+
+ align:start position:0%
+magical shorthand of these column tables
+ 
+
+ align:start position:0%
+magical shorthand of these column tables
+the multiplication of column tables the
+
+ align:start position:0%
+the multiplication of column tables the
+ 
+
+ align:start position:0%
+the multiplication of column tables the
+formula formation of these contrasts
+
+ align:start position:0%
+formula formation of these contrasts
+ 
+
+ align:start position:0%
+formula formation of these contrasts
+works out really nicely and so that's
+
+ align:start position:0%
+works out really nicely and so that's
+ 
+
+ align:start position:0%
+works out really nicely and so that's
+where you'll look in the literature and
+
+ align:start position:0%
+where you'll look in the literature and
+ 
+
+ align:start position:0%
+where you'll look in the literature and
+there's so much machinery around this
+
+ align:start position:0%
+there's so much machinery around this
+ 
+
+ align:start position:0%
+there's so much machinery around this
+that makes it relatively quick and easy
+
+ align:start position:0%
+that makes it relatively quick and easy
+ 
+
+ align:start position:0%
+that makes it relatively quick and easy
+ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can extend all of this again to
+
+ align:start position:0%
+so we can extend all of this again to
+ 
+
+ align:start position:0%
+so we can extend all of this again to
+beyond 1 factor or 2 factors to 3
+
+ align:start position:0%
+beyond 1 factor or 2 factors to 3
+ 
+
+ align:start position:0%
+beyond 1 factor or 2 factors to 3
+factors or any k factors so we can
+
+ align:start position:0%
+factors or any k factors so we can
+ 
+
+ align:start position:0%
+factors or any k factors so we can
+consider for example a 2 to the third
+
+ align:start position:0%
+consider for example a 2 to the third
+ 
+
+ align:start position:0%
+consider for example a 2 to the third
+experiment where now we have 3 factors
+
+ align:start position:0%
+experiment where now we have 3 factors
+ 
+
+ align:start position:0%
+experiment where now we have 3 factors
+in X 1 X 2 X 3 or going with sort of an
+
+ align:start position:0%
+in X 1 X 2 X 3 or going with sort of an
+ 
+
+ align:start position:0%
+in X 1 X 2 X 3 or going with sort of an
+A effect via the effect and C effect and
+
+ align:start position:0%
+A effect via the effect and C effect and
+ 
+
+ align:start position:0%
+A effect via the effect and C effect and
+then we can just extend this to the
+
+ align:start position:0%
+then we can just extend this to the
+ 
+
+ align:start position:0%
+then we can just extend this to the
+different treatment combinations and
+
+ align:start position:0%
+different treatment combinations and
+ 
+
+ align:start position:0%
+different treatment combinations and
+essentially what we're doing here is
+
+ align:start position:0%
+essentially what we're doing here is
+ 
+
+ align:start position:0%
+essentially what we're doing here is
+formulating every possible corner point
+
+ align:start position:0%
+formulating every possible corner point
+ 
+
+ align:start position:0%
+formulating every possible corner point
+every possible combination of the high
+
+ align:start position:0%
+every possible combination of the high
+ 
+
+ align:start position:0%
+every possible combination of the high
+and low for each of the settings and the
+
+ align:start position:0%
+and low for each of the settings and the
+ 
+
+ align:start position:0%
+and low for each of the settings and the
+same idea applies here I've indicated
+
+ align:start position:0%
+same idea applies here I've indicated
+ 
+
+ align:start position:0%
+same idea applies here I've indicated
+them indicated them with a plus 1 minus
+
+ align:start position:0%
+them indicated them with a plus 1 minus
+ 
+
+ align:start position:0%
+them indicated them with a plus 1 minus
+1 rather than just a plus minus but it's
+
+ align:start position:0%
+1 rather than just a plus minus but it's
+ 
+
+ align:start position:0%
+1 rather than just a plus minus but it's
+exactly the same idea and you can see
+
+ align:start position:0%
+exactly the same idea and you can see
+ 
+
+ align:start position:0%
+exactly the same idea and you can see
+sort of see already lurking here which
+
+ align:start position:0%
+sort of see already lurking here which
+ 
+
+ align:start position:0%
+sort of see already lurking here which
+runs would you use to estimate the C
+
+ align:start position:0%
+runs would you use to estimate the C
+ 
+
+ align:start position:0%
+runs would you use to estimate the C
+effect that one's sort of leaps out at
+
+ align:start position:0%
+effect that one's sort of leaps out at
+ 
+
+ align:start position:0%
+effect that one's sort of leaps out at
+us as we happen to have ordered this
+
+ align:start position:0%
+us as we happen to have ordered this
+ 
+
+ align:start position:0%
+us as we happen to have ordered this
+caught this this table right I would
+
+ align:start position:0%
+caught this this table right I would
+ 
+
+ align:start position:0%
+caught this this table right I would
+average these runs runs 5 6 7 & 8
+
+ align:start position:0%
+average these runs runs 5 6 7 & 8
+ 
+
+ align:start position:0%
+average these runs runs 5 6 7 & 8
+average runs 1 2 3 & 4
+
+ align:start position:0%
+average runs 1 2 3 & 4
+ 
+
+ align:start position:0%
+average runs 1 2 3 & 4
+take the difference in that my estimate
+
+ align:start position:0%
+take the difference in that my estimate
+ 
+
+ align:start position:0%
+take the difference in that my estimate
+of the sea effect now that's the
+
+ align:start position:0%
+of the sea effect now that's the
+ 
+
+ align:start position:0%
+of the sea effect now that's the
+contrast that I would do again for see
+
+ align:start position:0%
+contrast that I would do again for see
+ 
+
+ align:start position:0%
+contrast that I would do again for see
+if I also want to form contrast for the
+
+ align:start position:0%
+if I also want to form contrast for the
+ 
+
+ align:start position:0%
+if I also want to form contrast for the
+other coefficients it's exactly the same
+
+ align:start position:0%
+other coefficients it's exactly the same
+ 
+
+ align:start position:0%
+other coefficients it's exactly the same
+thing but the the table is not quite
+
+ align:start position:0%
+thing but the the table is not quite
+ 
+
+ align:start position:0%
+thing but the the table is not quite
+worrying oriented to make it leap out at
+
+ align:start position:0%
+worrying oriented to make it leap out at
+ 
+
+ align:start position:0%
+worrying oriented to make it leap out at
+me but essentially for the aid contrast
+
+ align:start position:0%
+me but essentially for the aid contrast
+ 
+
+ align:start position:0%
+me but essentially for the aid contrast
+and just forming those for my a a B
+
+ align:start position:0%
+and just forming those for my a a B
+ 
+
+ align:start position:0%
+and just forming those for my a a B
+that's my plus ones all my pluses and
+
+ align:start position:0%
+that's my plus ones all my pluses and
+ 
+
+ align:start position:0%
+that's my plus ones all my pluses and
+all my minus is forming that as my
+
+ align:start position:0%
+all my minus is forming that as my
+ 
+
+ align:start position:0%
+all my minus is forming that as my
+contrast I can very quickly then
+
+ align:start position:0%
+contrast I can very quickly then
+ 
+
+ align:start position:0%
+contrast I can very quickly then
+estimate that main effect using this big
+
+ align:start position:0%
+estimate that main effect using this big
+ 
+
+ align:start position:0%
+estimate that main effect using this big
+column I can also estimate my
+
+ align:start position:0%
+column I can also estimate my
+ 
+
+ align:start position:0%
+column I can also estimate my
+interaction terms we already talked
+
+ align:start position:0%
+interaction terms we already talked
+ 
+
+ align:start position:0%
+interaction terms we already talked
+about an a/b interaction if I have three
+
+ align:start position:0%
+about an a/b interaction if I have three
+ 
+
+ align:start position:0%
+about an a/b interaction if I have three
+model cuffs or three three factors I can
+
+ align:start position:0%
+model cuffs or three three factors I can
+ 
+
+ align:start position:0%
+model cuffs or three three factors I can
+have three-way interactions where
+
+ align:start position:0%
+have three-way interactions where
+ 
+
+ align:start position:0%
+have three-way interactions where
+depending on all of the settings of a B
+
+ align:start position:0%
+depending on all of the settings of a B
+ 
+
+ align:start position:0%
+depending on all of the settings of a B
+and C I might get a little boost up or
+
+ align:start position:0%
+and C I might get a little boost up or
+ 
+
+ align:start position:0%
+and C I might get a little boost up or
+down different than I would just from a
+
+ align:start position:0%
+down different than I would just from a
+ 
+
+ align:start position:0%
+down different than I would just from a
+B C and even different from the boost I
+
+ align:start position:0%
+B C and even different from the boost I
+ 
+
+ align:start position:0%
+B C and even different from the boost I
+got by having a and B in combination I
+
+ align:start position:0%
+got by having a and B in combination I
+ 
+
+ align:start position:0%
+got by having a and B in combination I
+can have these subtle three-way
+
+ align:start position:0%
+can have these subtle three-way
+ 
+
+ align:start position:0%
+can have these subtle three-way
+interactions and you can form the
+
+ align:start position:0%
+interactions and you can form the
+ 
+
+ align:start position:0%
+interactions and you can form the
+contrast and estimate that effect in a
+
+ align:start position:0%
+contrast and estimate that effect in a
+ 
+
+ align:start position:0%
+contrast and estimate that effect in a
+similar fashion using the ABC
+
+ align:start position:0%
+similar fashion using the ABC
+ 
+
+ align:start position:0%
+similar fashion using the ABC
+interaction column and form the contrast
+
+ align:start position:0%
+interaction column and form the contrast
+ 
+
+ align:start position:0%
+interaction column and form the contrast
+using that two steps to get to here one
+
+ align:start position:0%
+using that two steps to get to here one
+ 
+
+ align:start position:0%
+using that two steps to get to here one
+step is how do i generate this column
+
+ align:start position:0%
+step is how do i generate this column
+ 
+
+ align:start position:0%
+step is how do i generate this column
+and then the second step is then using
+
+ align:start position:0%
+and then the second step is then using
+ 
+
+ align:start position:0%
+and then the second step is then using
+that column to form an estimate of the
+
+ align:start position:0%
+that column to form an estimate of the
+ 
+
+ align:start position:0%
+that column to form an estimate of the
+interaction effect so how do we get to
+
+ align:start position:0%
+interaction effect so how do we get to
+ 
+
+ align:start position:0%
+interaction effect so how do we get to
+ABC column by extension of what I told
+
+ align:start position:0%
+ABC column by extension of what I told
+ 
+
+ align:start position:0%
+ABC column by extension of what I told
+you about the a B column how do you
+
+ align:start position:0%
+you about the a B column how do you
+ 
+
+ align:start position:0%
+you about the a B column how do you
+generate that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just multiply it's kind of this
+
+ align:start position:0%
+just multiply it's kind of this
+ 
+
+ align:start position:0%
+just multiply it's kind of this
+multiplication I just take the a B and C
+
+ align:start position:0%
+multiplication I just take the a B and C
+ 
+
+ align:start position:0%
+multiplication I just take the a B and C
+columns 20 twice multiply out those
+
+ align:start position:0%
+columns 20 twice multiply out those
+ 
+
+ align:start position:0%
+columns 20 twice multiply out those
+factors so minus 1 minus 1 minus 1 gives
+
+ align:start position:0%
+factors so minus 1 minus 1 minus 1 gives
+ 
+
+ align:start position:0%
+factors so minus 1 minus 1 minus 1 gives
+me I overrode it there we go it gives me
+
+ align:start position:0%
+me I overrode it there we go it gives me
+ 
+
+ align:start position:0%
+me I overrode it there we go it gives me
+a minus 1 and I similarly do that for
+
+ align:start position:0%
+a minus 1 and I similarly do that for
+ 
+
+ align:start position:0%
+a minus 1 and I similarly do that for
+all of the columns once I have that then
+
+ align:start position:0%
+all of the columns once I have that then
+ 
+
+ align:start position:0%
+all of the columns once I have that then
+then doing the second step is is pretty
+
+ align:start position:0%
+then doing the second step is is pretty
+ 
+
+ align:start position:0%
+then doing the second step is is pretty
+simple to estimate that that contrast
+
+ align:start position:0%
+simple to estimate that that contrast
+ 
+
+ align:start position:0%
+simple to estimate that that contrast
+now we have to be a once we've got the
+
+ align:start position:0%
+now we have to be a once we've got the
+ 
+
+ align:start position:0%
+now we have to be a once we've got the
+contrast just the differences in the
+
+ align:start position:0%
+contrast just the differences in the
+ 
+
+ align:start position:0%
+contrast just the differences in the
+columns then I do have to do a little
+
+ align:start position:0%
+columns then I do have to do a little
+ 
+
+ align:start position:0%
+columns then I do have to do a little
+bit of that normalization actually I
+
+ align:start position:0%
+bit of that normalization actually I
+ 
+
+ align:start position:0%
+bit of that normalization actually I
+probably am not completely consistent
+
+ align:start position:0%
+probably am not completely consistent
+ 
+
+ align:start position:0%
+probably am not completely consistent
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+the contrast is just the differences
+
+ align:start position:0%
+the contrast is just the differences
+ 
+
+ align:start position:0%
+the contrast is just the differences
+between the the points I then have to do
+
+ align:start position:0%
+between the the points I then have to do
+ 
+
+ align:start position:0%
+between the the points I then have to do
+the average over the number of points
+
+ align:start position:0%
+the average over the number of points
+ 
+
+ align:start position:0%
+the average over the number of points
+whoops well two things to form the
+
+ align:start position:0%
+whoops well two things to form the
+ 
+
+ align:start position:0%
+whoops well two things to form the
+estimate of the overall effect first off
+
+ align:start position:0%
+estimate of the overall effect first off
+ 
+
+ align:start position:0%
+estimate of the overall effect first off
+I have to divide by the number of points
+
+ align:start position:0%
+I have to divide by the number of points
+ 
+
+ align:start position:0%
+I have to divide by the number of points
+I had in each of those those contrasts
+
+ align:start position:0%
+I had in each of those those contrasts
+ 
+
+ align:start position:0%
+I had in each of those those contrasts
+which has been basically just 2 to the K
+
+ align:start position:0%
+which has been basically just 2 to the K
+ 
+
+ align:start position:0%
+which has been basically just 2 to the K
+minus 1 right when we had that cube with
+
+ align:start position:0%
+minus 1 right when we had that cube with
+ 
+
+ align:start position:0%
+minus 1 right when we had that cube with
+8 points it was 2 to the 3rd 8 divided
+
+ align:start position:0%
+8 points it was 2 to the 3rd 8 divided
+ 
+
+ align:start position:0%
+8 points it was 2 to the 3rd 8 divided
+by 2 because I'm forming half of the
+
+ align:start position:0%
+by 2 because I'm forming half of the
+ 
+
+ align:start position:0%
+by 2 because I'm forming half of the
+points in one contrast half of the
+
+ align:start position:0%
+points in one contrast half of the
+ 
+
+ align:start position:0%
+points in one contrast half of the
+points in the other and then this end
+
+ align:start position:0%
+points in the other and then this end
+ 
+
+ align:start position:0%
+points in the other and then this end
+which we haven't talked about very much
+
+ align:start position:0%
+which we haven't talked about very much
+ 
+
+ align:start position:0%
+which we haven't talked about very much
+is just the replicants I can do multiple
+
+ align:start position:0%
+is just the replicants I can do multiple
+ 
+
+ align:start position:0%
+is just the replicants I can do multiple
+runs of each experimental point so I can
+
+ align:start position:0%
+runs of each experimental point so I can
+ 
+
+ align:start position:0%
+runs of each experimental point so I can
+also average those in right so it's also
+
+ align:start position:0%
+also average those in right so it's also
+ 
+
+ align:start position:0%
+also average those in right so it's also
+possible that we've gotten more than one
+
+ align:start position:0%
+possible that we've gotten more than one
+ 
+
+ align:start position:0%
+possible that we've gotten more than one
+run at every experimental combination
+
+ align:start position:0%
+run at every experimental combination
+ 
+
+ align:start position:0%
+run at every experimental combination
+point so that's how we can estimate
+
+ align:start position:0%
+point so that's how we can estimate
+ 
+
+ align:start position:0%
+point so that's how we can estimate
+those those effects and then once we
+
+ align:start position:0%
+those those effects and then once we
+ 
+
+ align:start position:0%
+those those effects and then once we
+have that for example here that's how we
+
+ align:start position:0%
+have that for example here that's how we
+ 
+
+ align:start position:0%
+have that for example here that's how we
+get the in the 2 to the 3rd we get a 1/4
+
+ align:start position:0%
+get the in the 2 to the 3rd we get a 1/4
+ 
+
+ align:start position:0%
+get the in the 2 to the 3rd we get a 1/4
+factor that we saw earlier for the 3
+
+ align:start position:0%
+factor that we saw earlier for the 3
+ 
+
+ align:start position:0%
+factor that we saw earlier for the 3
+factor you know cube in
+
+ align:start position:0%
+factor you know cube in
+ 
+
+ align:start position:0%
+factor you know cube in
+three-dimensional space as an estimate
+
+ align:start position:0%
+three-dimensional space as an estimate
+ 
+
+ align:start position:0%
+three-dimensional space as an estimate
+for the overall effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now another point is here I'm
+
+ align:start position:0%
+okay now another point is here I'm
+ 
+
+ align:start position:0%
+okay now another point is here I'm
+talking about estimating our model using
+
+ align:start position:0%
+talking about estimating our model using
+ 
+
+ align:start position:0%
+talking about estimating our model using
+these contrasts and factor effects and
+
+ align:start position:0%
+these contrasts and factor effects and
+ 
+
+ align:start position:0%
+these contrasts and factor effects and
+another approach and probably the
+
+ align:start position:0%
+another approach and probably the
+ 
+
+ align:start position:0%
+another approach and probably the
+approach that you would end up using
+
+ align:start position:0%
+approach that you would end up using
+ 
+
+ align:start position:0%
+approach that you would end up using
+more often if you actually had you know
+
+ align:start position:0%
+more often if you actually had you know
+ 
+
+ align:start position:0%
+more often if you actually had you know
+computers handy is to do over regression
+
+ align:start position:0%
+computers handy is to do over regression
+ 
+
+ align:start position:0%
+computers handy is to do over regression
+right take your data put it in solve the
+
+ align:start position:0%
+right take your data put it in solve the
+ 
+
+ align:start position:0%
+right take your data put it in solve the
+solve the regression equations and
+
+ align:start position:0%
+solve the regression equations and
+ 
+
+ align:start position:0%
+solve the regression equations and
+regress to get your estimate of your
+
+ align:start position:0%
+regress to get your estimate of your
+ 
+
+ align:start position:0%
+regress to get your estimate of your
+coefficients and essentially these big
+
+ align:start position:0%
+coefficients and essentially these big
+ 
+
+ align:start position:0%
+coefficients and essentially these big
+tables that we talked about these
+
+ align:start position:0%
+tables that we talked about these
+ 
+
+ align:start position:0%
+tables that we talked about these
+combinations are still critical and very
+
+ align:start position:0%
+combinations are still critical and very
+ 
+
+ align:start position:0%
+combinations are still critical and very
+very useful because that's basically how
+
+ align:start position:0%
+very useful because that's basically how
+ 
+
+ align:start position:0%
+very useful because that's basically how
+you form the X matrix that describes the
+
+ align:start position:0%
+you form the X matrix that describes the
+ 
+
+ align:start position:0%
+you form the X matrix that describes the
+combinations of all of your factor
+
+ align:start position:0%
+combinations of all of your factor
+ 
+
+ align:start position:0%
+combinations of all of your factor
+levels that you feed into the regression
+
+ align:start position:0%
+levels that you feed into the regression
+ 
+
+ align:start position:0%
+levels that you feed into the regression
+this is your back with your coded values
+
+ align:start position:0%
+this is your back with your coded values
+ 
+
+ align:start position:0%
+this is your back with your coded values
+from minus 1 to plus 1 this is your X
+
+ align:start position:0%
+from minus 1 to plus 1 this is your X
+ 
+
+ align:start position:0%
+from minus 1 to plus 1 this is your X
+matrix right there because what you're
+
+ align:start position:0%
+matrix right there because what you're
+ 
+
+ align:start position:0%
+matrix right there because what you're
+trying to do is estimate a beta naught
+
+ align:start position:0%
+trying to do is estimate a beta naught
+ 
+
+ align:start position:0%
+trying to do is estimate a beta naught
+but you know a beta 1 and the beta 2 and
+
+ align:start position:0%
+but you know a beta 1 and the beta 2 and
+ 
+
+ align:start position:0%
+but you know a beta 1 and the beta 2 and
+a beta 3 oops beta 3 and then also
+
+ align:start position:0%
+a beta 3 oops beta 3 and then also
+ 
+
+ align:start position:0%
+a beta 3 oops beta 3 and then also
+trying to estimate these interaction
+
+ align:start position:0%
+trying to estimate these interaction
+ 
+
+ align:start position:0%
+trying to estimate these interaction
+terms a beta 1 2 a beta 1 3 beta 2 3 and
+
+ align:start position:0%
+terms a beta 1 2 a beta 1 3 beta 2 3 and
+ 
+
+ align:start position:0%
+terms a beta 1 2 a beta 1 3 beta 2 3 and
+even a beta 1 2 3 and so you're
+
+ align:start position:0%
+even a beta 1 2 3 and so you're
+ 
+
+ align:start position:0%
+even a beta 1 2 3 and so you're
+basically fictitiously creating these as
+
+ align:start position:0%
+basically fictitiously creating these as
+ 
+
+ align:start position:0%
+basically fictitiously creating these as
+additional variables for the product of
+
+ align:start position:0%
+additional variables for the product of
+ 
+
+ align:start position:0%
+additional variables for the product of
+X 1 X 2 X 3 in your regression so you
+
+ align:start position:0%
+X 1 X 2 X 3 in your regression so you
+ 
+
+ align:start position:0%
+X 1 X 2 X 3 in your regression so you
+need this this table even if you're
+
+ align:start position:0%
+need this this table even if you're
+ 
+
+ align:start position:0%
+need this this table even if you're
+doing regression in order to be able to
+
+ align:start position:0%
+doing regression in order to be able to
+ 
+
+ align:start position:0%
+doing regression in order to be able to
+set up the regression if you want to
+
+ align:start position:0%
+set up the regression if you want to
+ 
+
+ align:start position:0%
+set up the regression if you want to
+also include these interaction terms in
+
+ align:start position:0%
+also include these interaction terms in
+ 
+
+ align:start position:0%
+also include these interaction terms in
+your regression model you have to create
+
+ align:start position:0%
+your regression model you have to create
+ 
+
+ align:start position:0%
+your regression model you have to create
+sort of fictitious columns of data based
+
+ align:start position:0%
+sort of fictitious columns of data based
+ 
+
+ align:start position:0%
+sort of fictitious columns of data based
+on those interactions the product of
+
+ align:start position:0%
+on those interactions the product of
+ 
+
+ align:start position:0%
+on those interactions the product of
+your three input settings and this is
+
+ align:start position:0%
+your three input settings and this is
+ 
+
+ align:start position:0%
+your three input settings and this is
+basically telling you exactly what those
+
+ align:start position:0%
+basically telling you exactly what those
+ 
+
+ align:start position:0%
+basically telling you exactly what those
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+so this is essentially showing that that
+
+ align:start position:0%
+so this is essentially showing that that
+ 
+
+ align:start position:0%
+so this is essentially showing that that
+same thing I just described in words
+
+ align:start position:0%
+same thing I just described in words
+ 
+
+ align:start position:0%
+same thing I just described in words
+what we're talking about here is
+
+ align:start position:0%
+what we're talking about here is
+ 
+
+ align:start position:0%
+what we're talking about here is
+basically setting up to do the
+
+ align:start position:0%
+basically setting up to do the
+ 
+
+ align:start position:0%
+basically setting up to do the
+pseudo-inverse
+
+ align:start position:0%
+pseudo-inverse
+ 
+
+ align:start position:0%
+pseudo-inverse
+when I've got my data with my X matrix
+
+ align:start position:0%
+when I've got my data with my X matrix
+ 
+
+ align:start position:0%
+when I've got my data with my X matrix
+being my setup of my input conditions
+
+ align:start position:0%
+being my setup of my input conditions
+ 
+
+ align:start position:0%
+being my setup of my input conditions
+and then Y being my output and then beta
+
+ align:start position:0%
+and then Y being my output and then beta
+ 
+
+ align:start position:0%
+and then Y being my output and then beta
+being my vector of coefficients with
+
+ align:start position:0%
+being my vector of coefficients with
+ 
+
+ align:start position:0%
+being my vector of coefficients with
+both the mean the main effects and the
+
+ align:start position:0%
+both the mean the main effects and the
+ 
+
+ align:start position:0%
+both the mean the main effects and the
+interaction effects so I would have to
+
+ align:start position:0%
+interaction effects so I would have to
+ 
+
+ align:start position:0%
+interaction effects so I would have to
+create the column of the X 1 X 2 product
+
+ align:start position:0%
+create the column of the X 1 X 2 product
+ 
+
+ align:start position:0%
+create the column of the X 1 X 2 product
+in order to be able to do that and then
+
+ align:start position:0%
+in order to be able to do that and then
+ 
+
+ align:start position:0%
+in order to be able to do that and then
+you can see again here the relationship
+
+ align:start position:0%
+you can see again here the relationship
+ 
+
+ align:start position:0%
+you can see again here the relationship
+between the contrasts idea and the
+
+ align:start position:0%
+between the contrasts idea and the
+ 
+
+ align:start position:0%
+between the contrasts idea and the
+regression idea that comes out ok
+
+ align:start position:0%
+regression idea that comes out ok
+ 
+
+ align:start position:0%
+regression idea that comes out ok
+relatively clear any questions on that
+
+ align:start position:0%
+relatively clear any questions on that
+ 
+
+ align:start position:0%
+relatively clear any questions on that
+ok so now we've estimated coefficients
+
+ align:start position:0%
+ok so now we've estimated coefficients
+ 
+
+ align:start position:0%
+ok so now we've estimated coefficients
+we've estimated effects either in the
+
+ align:start position:0%
+we've estimated effects either in the
+ 
+
+ align:start position:0%
+we've estimated effects either in the
+regression or the or the contrast
+
+ align:start position:0%
+regression or the or the contrast
+ 
+
+ align:start position:0%
+regression or the or the contrast
+approach a key question is you do that
+
+ align:start position:0%
+approach a key question is you do that
+ 
+
+ align:start position:0%
+approach a key question is you do that
+you get a value for a you know the a
+
+ align:start position:0%
+you get a value for a you know the a
+ 
+
+ align:start position:0%
+you get a value for a you know the a
+effect that's nonzero do you think it's
+
+ align:start position:0%
+effect that's nonzero do you think it's
+ 
+
+ align:start position:0%
+effect that's nonzero do you think it's
+significant or not is it real or not or
+
+ align:start position:0%
+significant or not is it real or not or
+ 
+
+ align:start position:0%
+significant or not is it real or not or
+would you have observed that amount of a
+
+ align:start position:0%
+would you have observed that amount of a
+ 
+
+ align:start position:0%
+would you have observed that amount of a
+by chance alone given random noise in
+
+ align:start position:0%
+by chance alone given random noise in
+ 
+
+ align:start position:0%
+by chance alone given random noise in
+your experiment this is exactly back to
+
+ align:start position:0%
+your experiment this is exactly back to
+ 
+
+ align:start position:0%
+your experiment this is exactly back to
+the ANOVA question that we were asking
+
+ align:start position:0%
+the ANOVA question that we were asking
+ 
+
+ align:start position:0%
+the ANOVA question that we were asking
+earlier I'd like to know the
+
+ align:start position:0%
+earlier I'd like to know the
+ 
+
+ align:start position:0%
+earlier I'd like to know the
+significance of these effects is it
+
+ align:start position:0%
+significance of these effects is it
+ 
+
+ align:start position:0%
+significance of these effects is it
+large enough to give me 90% confidence
+
+ align:start position:0%
+large enough to give me 90% confidence
+ 
+
+ align:start position:0%
+large enough to give me 90% confidence
+or 95% confidence that it's real that it
+
+ align:start position:0%
+or 95% confidence that it's real that it
+ 
+
+ align:start position:0%
+or 95% confidence that it's real that it
+wouldn't have occurred by chance alone
+
+ align:start position:0%
+wouldn't have occurred by chance alone
+ 
+
+ align:start position:0%
+wouldn't have occurred by chance alone
+and so essentially what we want to do is
+
+ align:start position:0%
+and so essentially what we want to do is
+ 
+
+ align:start position:0%
+and so essentially what we want to do is
+run the ANOVA for each of our effects
+
+ align:start position:0%
+run the ANOVA for each of our effects
+ 
+
+ align:start position:0%
+run the ANOVA for each of our effects
+each of our if I have you know three
+
+ align:start position:0%
+each of our if I have you know three
+ 
+
+ align:start position:0%
+each of our if I have you know three
+factors I'd like to know is the main
+
+ align:start position:0%
+factors I'd like to know is the main
+ 
+
+ align:start position:0%
+factors I'd like to know is the main
+effect associated with factor 2 is that
+
+ align:start position:0%
+effect associated with factor 2 is that
+ 
+
+ align:start position:0%
+effect associated with factor 2 is that
+significant I can also do that for
+
+ align:start position:0%
+significant I can also do that for
+ 
+
+ align:start position:0%
+significant I can also do that for
+interaction effects I've and very often
+
+ align:start position:0%
+interaction effects I've and very often
+ 
+
+ align:start position:0%
+interaction effects I've and very often
+you might see large main effects but you
+
+ align:start position:0%
+you might see large main effects but you
+ 
+
+ align:start position:0%
+you might see large main effects but you
+want to ask the question
+
+ align:start position:0%
+want to ask the question
+ 
+
+ align:start position:0%
+want to ask the question
+is there really an interaction between
+
+ align:start position:0%
+is there really an interaction between
+ 
+
+ align:start position:0%
+is there really an interaction between
+these two do I can I think of them as
+
+ align:start position:0%
+these two do I can I think of them as
+ 
+
+ align:start position:0%
+these two do I can I think of them as
+separable coefficients or separable
+
+ align:start position:0%
+separable coefficients or separable
+ 
+
+ align:start position:0%
+separable coefficients or separable
+knobs on my equipment or do I have to
+
+ align:start position:0%
+knobs on my equipment or do I have to
+ 
+
+ align:start position:0%
+knobs on my equipment or do I have to
+think of them as highly coupled I'd like
+
+ align:start position:0%
+think of them as highly coupled I'd like
+ 
+
+ align:start position:0%
+think of them as highly coupled I'd like
+to know the significance of the
+
+ align:start position:0%
+to know the significance of the
+ 
+
+ align:start position:0%
+to know the significance of the
+interaction effect so we essentially
+
+ align:start position:0%
+interaction effect so we essentially
+ 
+
+ align:start position:0%
+interaction effect so we essentially
+just use the ANOVA approach fairly
+
+ align:start position:0%
+just use the ANOVA approach fairly
+ 
+
+ align:start position:0%
+just use the ANOVA approach fairly
+directly but what we're doing is forming
+
+ align:start position:0%
+directly but what we're doing is forming
+ 
+
+ align:start position:0%
+directly but what we're doing is forming
+an estimate of the total deviations
+
+ align:start position:0%
+an estimate of the total deviations
+ 
+
+ align:start position:0%
+an estimate of the total deviations
+associated with that effect the sum of
+
+ align:start position:0%
+associated with that effect the sum of
+ 
+
+ align:start position:0%
+associated with that effect the sum of
+squared deviations which turns out to be
+
+ align:start position:0%
+squared deviations which turns out to be
+ 
+
+ align:start position:0%
+squared deviations which turns out to be
+the contrast squared and then divided by
+
+ align:start position:0%
+the contrast squared and then divided by
+ 
+
+ align:start position:0%
+the contrast squared and then divided by
+the N over 2k
+
+ align:start position:0%
+the N over 2k
+ 
+
+ align:start position:0%
+the N over 2k
+factor there's a homework problem set
+
+ align:start position:0%
+factor there's a homework problem set
+ 
+
+ align:start position:0%
+factor there's a homework problem set
+where you get to help derive why that is
+
+ align:start position:0%
+where you get to help derive why that is
+ 
+
+ align:start position:0%
+where you get to help derive why that is
+true or convince yourself why that is
+
+ align:start position:0%
+true or convince yourself why that is
+ 
+
+ align:start position:0%
+true or convince yourself why that is
+true but essentially you're looking
+
+ align:start position:0%
+true but essentially you're looking
+ 
+
+ align:start position:0%
+true but essentially you're looking
+forward to it I can see but what that
+
+ align:start position:0%
+forward to it I can see but what that
+ 
+
+ align:start position:0%
+forward to it I can see but what that
+lets us do is look again at the total
+
+ align:start position:0%
+lets us do is look again at the total
+ 
+
+ align:start position:0%
+lets us do is look again at the total
+amount of of magnitude of sum of squared
+
+ align:start position:0%
+amount of of magnitude of sum of squared
+ 
+
+ align:start position:0%
+amount of of magnitude of sum of squared
+deviations around a mean associated with
+
+ align:start position:0%
+deviations around a mean associated with
+ 
+
+ align:start position:0%
+deviations around a mean associated with
+that effect and then look at that in
+
+ align:start position:0%
+that effect and then look at that in
+ 
+
+ align:start position:0%
+that effect and then look at that in
+comparison to some estimate of the
+
+ align:start position:0%
+comparison to some estimate of the
+ 
+
+ align:start position:0%
+comparison to some estimate of the
+random noise and do an app test just
+
+ align:start position:0%
+random noise and do an app test just
+ 
+
+ align:start position:0%
+random noise and do an app test just
+like we normally do with ANOVA so you
+
+ align:start position:0%
+like we normally do with ANOVA so you
+ 
+
+ align:start position:0%
+like we normally do with ANOVA so you
+can start to again do that if you've got
+
+ align:start position:0%
+can start to again do that if you've got
+ 
+
+ align:start position:0%
+can start to again do that if you've got
+two effects or 2 factors you would look
+
+ align:start position:0%
+two effects or 2 factors you would look
+ 
+
+ align:start position:0%
+two effects or 2 factors you would look
+for the question it's there something
+
+ align:start position:0%
+for the question it's there something
+ 
+
+ align:start position:0%
+for the question it's there something
+significant in the a effect in the B
+
+ align:start position:0%
+significant in the a effect in the B
+ 
+
+ align:start position:0%
+significant in the a effect in the B
+effect and in the interaction and then
+
+ align:start position:0%
+effect and in the interaction and then
+ 
+
+ align:start position:0%
+effect and in the interaction and then
+the remaining sum of squared deviations
+
+ align:start position:0%
+the remaining sum of squared deviations
+ 
+
+ align:start position:0%
+the remaining sum of squared deviations
+or the residual gives you your error
+
+ align:start position:0%
+or the residual gives you your error
+ 
+
+ align:start position:0%
+or the residual gives you your error
+estimate that you use in the denominator
+
+ align:start position:0%
+estimate that you use in the denominator
+ 
+
+ align:start position:0%
+estimate that you use in the denominator
+and that's that's how you decompose the
+
+ align:start position:0%
+and that's that's how you decompose the
+ 
+
+ align:start position:0%
+and that's that's how you decompose the
+total observed variations so then you
+
+ align:start position:0%
+total observed variations so then you
+ 
+
+ align:start position:0%
+total observed variations so then you
+can form that into an ANOVA table again
+
+ align:start position:0%
+can form that into an ANOVA table again
+ 
+
+ align:start position:0%
+can form that into an ANOVA table again
+looking at the main effects a and B the
+
+ align:start position:0%
+looking at the main effects a and B the
+ 
+
+ align:start position:0%
+looking at the main effects a and B the
+interaction effect and an estimate of
+
+ align:start position:0%
+interaction effect and an estimate of
+ 
+
+ align:start position:0%
+interaction effect and an estimate of
+the error again we get this little funky
+
+ align:start position:0%
+the error again we get this little funky
+ 
+
+ align:start position:0%
+the error again we get this little funky
+cent sign that's supposed to just be a
+
+ align:start position:0%
+cent sign that's supposed to just be a
+ 
+
+ align:start position:0%
+cent sign that's supposed to just be a
+multiplication that's just a little dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where again you're forming estimates of
+
+ align:start position:0%
+where again you're forming estimates of
+ 
+
+ align:start position:0%
+where again you're forming estimates of
+the mean squares and then ratios of
+
+ align:start position:0%
+the mean squares and then ratios of
+ 
+
+ align:start position:0%
+the mean squares and then ratios of
+those and then you do your your F test
+
+ align:start position:0%
+those and then you do your your F test
+ 
+
+ align:start position:0%
+those and then you do your your F test
+to see if the F is higher than that so
+
+ align:start position:0%
+to see if the F is higher than that so
+ 
+
+ align:start position:0%
+to see if the F is higher than that so
+this is one way of looking at it in
+
+ align:start position:0%
+this is one way of looking at it in
+ 
+
+ align:start position:0%
+this is one way of looking at it in
+terms of contrast if instead of forming
+
+ align:start position:0%
+terms of contrast if instead of forming
+ 
+
+ align:start position:0%
+terms of contrast if instead of forming
+contrast you had used the regression and
+
+ align:start position:0%
+contrast you had used the regression and
+ 
+
+ align:start position:0%
+contrast you had used the regression and
+come up with regression coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+associated with each of each of the
+
+ align:start position:0%
+associated with each of each of the
+ 
+
+ align:start position:0%
+associated with each of each of the
+terms you can similarly form the sum of
+
+ align:start position:0%
+terms you can similarly form the sum of
+ 
+
+ align:start position:0%
+terms you can similarly form the sum of
+squares and the mean squares from that
+
+ align:start position:0%
+squares and the mean squares from that
+ 
+
+ align:start position:0%
+squares and the mean squares from that
+from that perspective and in the
+
+ align:start position:0%
+from that perspective and in the
+ 
+
+ align:start position:0%
+from that perspective and in the
+regression form by the way that that
+
+ align:start position:0%
+regression form by the way that that
+ 
+
+ align:start position:0%
+regression form by the way that that
+turns out nicely because it's also gives
+
+ align:start position:0%
+turns out nicely because it's also gives
+ 
+
+ align:start position:0%
+turns out nicely because it's also gives
+you the chance to not subtract off the
+
+ align:start position:0%
+you the chance to not subtract off the
+ 
+
+ align:start position:0%
+you the chance to not subtract off the
+mean from everything but actually
+
+ align:start position:0%
+mean from everything but actually
+ 
+
+ align:start position:0%
+mean from everything but actually
+estimate whether the mean it may be
+
+ align:start position:0%
+estimate whether the mean it may be
+ 
+
+ align:start position:0%
+estimate whether the mean it may be
+significantly different than than zero
+
+ align:start position:0%
+significantly different than than zero
+ 
+
+ align:start position:0%
+significantly different than than zero
+but it's but it's essentially the same
+
+ align:start position:0%
+but it's but it's essentially the same
+ 
+
+ align:start position:0%
+but it's but it's essentially the same
+thing okay so what I've tried to
+
+ align:start position:0%
+thing okay so what I've tried to
+ 
+
+ align:start position:0%
+thing okay so what I've tried to
+convince you here is that you can use
+
+ align:start position:0%
+convince you here is that you can use
+ 
+
+ align:start position:0%
+convince you here is that you can use
+ANOVA to estimate that's a tool we
+
+ align:start position:0%
+ANOVA to estimate that's a tool we
+ 
+
+ align:start position:0%
+ANOVA to estimate that's a tool we
+already know to estimate whether the
+
+ align:start position:0%
+already know to estimate whether the
+ 
+
+ align:start position:0%
+already know to estimate whether the
+effects are significant or not and
+
+ align:start position:0%
+effects are significant or not and
+ 
+
+ align:start position:0%
+effects are significant or not and
+whether you should include that term in
+
+ align:start position:0%
+whether you should include that term in
+ 
+
+ align:start position:0%
+whether you should include that term in
+your model if you don't have enough
+
+ align:start position:0%
+your model if you don't have enough
+ 
+
+ align:start position:0%
+your model if you don't have enough
+evidence that that value the coefficient
+
+ align:start position:0%
+evidence that that value the coefficient
+ 
+
+ align:start position:0%
+evidence that that value the coefficient
+associated with x1 might be nonzero
+
+ align:start position:0%
+associated with x1 might be nonzero
+ 
+
+ align:start position:0%
+associated with x1 might be nonzero
+you're probably better off not including
+
+ align:start position:0%
+you're probably better off not including
+ 
+
+ align:start position:0%
+you're probably better off not including
+it in your model in which case those any
+
+ align:start position:0%
+it in your model in which case those any
+ 
+
+ align:start position:0%
+it in your model in which case those any
+little squiggles that might be there but
+
+ align:start position:0%
+little squiggles that might be there but
+ 
+
+ align:start position:0%
+little squiggles that might be there but
+you're not confident really are there
+
+ align:start position:0%
+you're not confident really are there
+ 
+
+ align:start position:0%
+you're not confident really are there
+contribute to your error term and you
+
+ align:start position:0%
+contribute to your error term and you
+ 
+
+ align:start position:0%
+contribute to your error term and you
+treat them basically as noise rather
+
+ align:start position:0%
+treat them basically as noise rather
+ 
+
+ align:start position:0%
+treat them basically as noise rather
+than trying to fit them okay so let's
+
+ align:start position:0%
+than trying to fit them okay so let's
+ 
+
+ align:start position:0%
+than trying to fit them okay so let's
+let's try this out for an example this
+
+ align:start position:0%
+let's try this out for an example this
+ 
+
+ align:start position:0%
+let's try this out for an example this
+is one of the sets of data that we
+
+ align:start position:0%
+is one of the sets of data that we
+ 
+
+ align:start position:0%
+is one of the sets of data that we
+looked at very early in the term it's
+
+ align:start position:0%
+looked at very early in the term it's
+ 
+
+ align:start position:0%
+looked at very early in the term it's
+the break forming remember the the press
+
+ align:start position:0%
+the break forming remember the the press
+ 
+
+ align:start position:0%
+the break forming remember the the press
+we have either aluminum or stainless
+
+ align:start position:0%
+we have either aluminum or stainless
+ 
+
+ align:start position:0%
+we have either aluminum or stainless
+steel and we've got sort of an angled
+
+ align:start position:0%
+steel and we've got sort of an angled
+ 
+
+ align:start position:0%
+steel and we've got sort of an angled
+press and we're pressing it down into
+
+ align:start position:0%
+press and we're pressing it down into
+ 
+
+ align:start position:0%
+press and we're pressing it down into
+some depth and trying to bend that that
+
+ align:start position:0%
+some depth and trying to bend that that
+ 
+
+ align:start position:0%
+some depth and trying to bend that that
+piece of sheet metal and that was
+
+ align:start position:0%
+piece of sheet metal and that was
+ 
+
+ align:start position:0%
+piece of sheet metal and that was
+actually a designed experiment in fact
+
+ align:start position:0%
+actually a designed experiment in fact
+ 
+
+ align:start position:0%
+actually a designed experiment in fact
+the two factors that we were looking at
+
+ align:start position:0%
+the two factors that we were looking at
+ 
+
+ align:start position:0%
+the two factors that we were looking at
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is how deep the punch goes in and what
+
+ align:start position:0%
+is how deep the punch goes in and what
+ 
+
+ align:start position:0%
+is how deep the punch goes in and what
+the material type was either aluminum or
+
+ align:start position:0%
+the material type was either aluminum or
+ 
+
+ align:start position:0%
+the material type was either aluminum or
+steel and this is just identifying the
+
+ align:start position:0%
+steel and this is just identifying the
+ 
+
+ align:start position:0%
+steel and this is just identifying the
+factor levels that I'm going to
+
+ align:start position:0%
+factor levels that I'm going to
+ 
+
+ align:start position:0%
+factor levels that I'm going to
+associate with with these terms now this
+
+ align:start position:0%
+associate with with these terms now this
+ 
+
+ align:start position:0%
+associate with with these terms now this
+is actually an interesting one because
+
+ align:start position:0%
+is actually an interesting one because
+ 
+
+ align:start position:0%
+is actually an interesting one because
+this is a discrete factor level well
+
+ align:start position:0%
+this is a discrete factor level well
+ 
+
+ align:start position:0%
+this is a discrete factor level well
+this is more of a continuous factor
+
+ align:start position:0%
+this is more of a continuous factor
+ 
+
+ align:start position:0%
+this is more of a continuous factor
+level and you know you'll you'll catch a
+
+ align:start position:0%
+level and you know you'll you'll catch a
+ 
+
+ align:start position:0%
+level and you know you'll you'll catch a
+little bit later there's something a
+
+ align:start position:0%
+little bit later there's something a
+ 
+
+ align:start position:0%
+little bit later there's something a
+little bit odd where we talk about the
+
+ align:start position:0%
+little bit odd where we talk about the
+ 
+
+ align:start position:0%
+little bit odd where we talk about the
+zero factor setting between aluminum and
+
+ align:start position:0%
+zero factor setting between aluminum and
+ 
+
+ align:start position:0%
+zero factor setting between aluminum and
+steel that actually doesn't make any
+
+ align:start position:0%
+steel that actually doesn't make any
+ 
+
+ align:start position:0%
+steel that actually doesn't make any
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+but I can talk about perhaps the zero
+
+ align:start position:0%
+but I can talk about perhaps the zero
+ 
+
+ align:start position:0%
+but I can talk about perhaps the zero
+factor setting of zero point four or
+
+ align:start position:0%
+factor setting of zero point four or
+ 
+
+ align:start position:0%
+factor setting of zero point four or
+five inches halfway between the low and
+
+ align:start position:0%
+five inches halfway between the low and
+ 
+
+ align:start position:0%
+five inches halfway between the low and
+the high of a continuous parameter so I
+
+ align:start position:0%
+the high of a continuous parameter so I
+ 
+
+ align:start position:0%
+the high of a continuous parameter so I
+like this because it's mixing or showing
+
+ align:start position:0%
+like this because it's mixing or showing
+ 
+
+ align:start position:0%
+like this because it's mixing or showing
+that the same tools and technology
+
+ align:start position:0%
+that the same tools and technology
+ 
+
+ align:start position:0%
+that the same tools and technology
+mostly work for both discrete decisions
+
+ align:start position:0%
+mostly work for both discrete decisions
+ 
+
+ align:start position:0%
+mostly work for both discrete decisions
+and design of experiments and continuous
+
+ align:start position:0%
+and design of experiments and continuous
+ 
+
+ align:start position:0%
+and design of experiments and continuous
+ones and we'll see where it doesn't a
+
+ align:start position:0%
+ones and we'll see where it doesn't a
+ 
+
+ align:start position:0%
+ones and we'll see where it doesn't a
+little bit letter later so let's try out
+
+ align:start position:0%
+little bit letter later so let's try out
+ 
+
+ align:start position:0%
+little bit letter later so let's try out
+a very simple designed experiment a two
+
+ align:start position:0%
+a very simple designed experiment a two
+ 
+
+ align:start position:0%
+a very simple designed experiment a two
+to the two factor where the final angle
+
+ align:start position:0%
+to the two factor where the final angle
+ 
+
+ align:start position:0%
+to the two factor where the final angle
+after removing the punch is our output
+
+ align:start position:0%
+after removing the punch is our output
+ 
+
+ align:start position:0%
+after removing the punch is our output
+this is the actual data what we've got
+
+ align:start position:0%
+this is the actual data what we've got
+ 
+
+ align:start position:0%
+this is the actual data what we've got
+is for each of the level settings
+
+ align:start position:0%
+is for each of the level settings
+ 
+
+ align:start position:0%
+is for each of the level settings
+we've got replicas so I'm doing ten
+
+ align:start position:0%
+we've got replicas so I'm doing ten
+ 
+
+ align:start position:0%
+we've got replicas so I'm doing ten
+replicates at each at each test setting
+
+ align:start position:0%
+replicates at each at each test setting
+ 
+
+ align:start position:0%
+replicates at each at each test setting
+of the high and low combination for x1
+
+ align:start position:0%
+of the high and low combination for x1
+ 
+
+ align:start position:0%
+of the high and low combination for x1
+and excellent so I've got four different
+
+ align:start position:0%
+and excellent so I've got four different
+ 
+
+ align:start position:0%
+and excellent so I've got four different
+corners four different combinations ten
+
+ align:start position:0%
+corners four different combinations ten
+ 
+
+ align:start position:0%
+corners four different combinations ten
+replicates and and here's the data for
+
+ align:start position:0%
+replicates and and here's the data for
+ 
+
+ align:start position:0%
+replicates and and here's the data for
+that by the way we'll come back to this
+
+ align:start position:0%
+that by the way we'll come back to this
+ 
+
+ align:start position:0%
+that by the way we'll come back to this
+a little bit later but if this is run
+
+ align:start position:0%
+a little bit later but if this is run
+ 
+
+ align:start position:0%
+a little bit later but if this is run
+number and if those are done in time
+
+ align:start position:0%
+number and if those are done in time
+ 
+
+ align:start position:0%
+number and if those are done in time
+there's actually something a little
+
+ align:start position:0%
+there's actually something a little
+ 
+
+ align:start position:0%
+there's actually something a little
+risky in this experimental design what
+
+ align:start position:0%
+risky in this experimental design what
+ 
+
+ align:start position:0%
+risky in this experimental design what
+if this is foreshadowing - coming back
+
+ align:start position:0%
+if this is foreshadowing - coming back
+ 
+
+ align:start position:0%
+if this is foreshadowing - coming back
+to additional issues of nasty things you
+
+ align:start position:0%
+to additional issues of nasty things you
+ 
+
+ align:start position:0%
+to additional issues of nasty things you
+got to keep in mind when you do design
+
+ align:start position:0%
+got to keep in mind when you do design
+ 
+
+ align:start position:0%
+got to keep in mind when you do design
+of experiments but what if there was
+
+ align:start position:0%
+of experiments but what if there was
+ 
+
+ align:start position:0%
+of experiments but what if there was
+some time degradation
+
+ align:start position:0%
+some time degradation
+ 
+
+ align:start position:0%
+some time degradation
+some time we're in the tool the problem
+
+ align:start position:0%
+some time we're in the tool the problem
+ 
+
+ align:start position:0%
+some time we're in the tool the problem
+is you wouldn't really be able to
+
+ align:start position:0%
+is you wouldn't really be able to
+ 
+
+ align:start position:0%
+is you wouldn't really be able to
+distinguish a time effect from a change
+
+ align:start position:0%
+distinguish a time effect from a change
+ 
+
+ align:start position:0%
+distinguish a time effect from a change
+in the factor settings so one approach
+
+ align:start position:0%
+in the factor settings so one approach
+ 
+
+ align:start position:0%
+in the factor settings so one approach
+that you might if you can cheaply do it
+
+ align:start position:0%
+that you might if you can cheaply do it
+ 
+
+ align:start position:0%
+that you might if you can cheaply do it
+here you might actually have got to make
+
+ align:start position:0%
+here you might actually have got to make
+ 
+
+ align:start position:0%
+here you might actually have got to make
+you know maybe some kind of machine
+
+ align:start position:0%
+you know maybe some kind of machine
+ 
+
+ align:start position:0%
+you know maybe some kind of machine
+setup change and you wouldn't want to do
+
+ align:start position:0%
+setup change and you wouldn't want to do
+ 
+
+ align:start position:0%
+setup change and you wouldn't want to do
+this but you might randomize the order
+
+ align:start position:0%
+this but you might randomize the order
+ 
+
+ align:start position:0%
+this but you might randomize the order
+of your runs in time to sort of block
+
+ align:start position:0%
+of your runs in time to sort of block
+ 
+
+ align:start position:0%
+of your runs in time to sort of block
+against the effect of of time and we'll
+
+ align:start position:0%
+against the effect of of time and we'll
+ 
+
+ align:start position:0%
+against the effect of of time and we'll
+come back to that but but here it's a
+
+ align:start position:0%
+come back to that but but here it's a
+ 
+
+ align:start position:0%
+come back to that but but here it's a
+simple I do all of my Lolo combinations
+
+ align:start position:0%
+simple I do all of my Lolo combinations
+ 
+
+ align:start position:0%
+simple I do all of my Lolo combinations
+first then I did my my low high then my
+
+ align:start position:0%
+first then I did my my low high then my
+ 
+
+ align:start position:0%
+first then I did my my low high then my
+high low and my high high okay so that's
+
+ align:start position:0%
+high low and my high high okay so that's
+ 
+
+ align:start position:0%
+high low and my high high okay so that's
+our data now what we're doing here first
+
+ align:start position:0%
+our data now what we're doing here first
+ 
+
+ align:start position:0%
+our data now what we're doing here first
+off is I'm just going to form the mean I
+
+ align:start position:0%
+off is I'm just going to form the mean I
+ 
+
+ align:start position:0%
+off is I'm just going to form the mean I
+take the the mean of those ten points
+
+ align:start position:0%
+take the the mean of those ten points
+ 
+
+ align:start position:0%
+take the the mean of those ten points
+and that's going to be my Y bar at each
+
+ align:start position:0%
+and that's going to be my Y bar at each
+ 
+
+ align:start position:0%
+and that's going to be my Y bar at each
+of my level settings so I'm sort of
+
+ align:start position:0%
+of my level settings so I'm sort of
+ 
+
+ align:start position:0%
+of my level settings so I'm sort of
+reducing it down from the ten replicates
+
+ align:start position:0%
+reducing it down from the ten replicates
+ 
+
+ align:start position:0%
+reducing it down from the ten replicates
+down to four means so this is my mean at
+
+ align:start position:0%
+down to four means so this is my mean at
+ 
+
+ align:start position:0%
+down to four means so this is my mean at
+each of those four different conditions
+
+ align:start position:0%
+each of those four different conditions
+ 
+
+ align:start position:0%
+each of those four different conditions
+and now I have my my output my Y vector
+
+ align:start position:0%
+and now I have my my output my Y vector
+ 
+
+ align:start position:0%
+and now I have my my output my Y vector
+setting up for a regression as being the
+
+ align:start position:0%
+setting up for a regression as being the
+ 
+
+ align:start position:0%
+setting up for a regression as being the
+observed means what's my X matrix
+
+ align:start position:0%
+observed means what's my X matrix
+ 
+
+ align:start position:0%
+observed means what's my X matrix
+setting up for my my regression oops
+
+ align:start position:0%
+setting up for my my regression oops
+ 
+
+ align:start position:0%
+setting up for my my regression oops
+it's just it's it's based on the level
+
+ align:start position:0%
+it's just it's it's based on the level
+ 
+
+ align:start position:0%
+it's just it's it's based on the level
+settings but notice we also add in that
+
+ align:start position:0%
+settings but notice we also add in that
+ 
+
+ align:start position:0%
+settings but notice we also add in that
+one factor that one factor is basically
+
+ align:start position:0%
+one factor that one factor is basically
+ 
+
+ align:start position:0%
+one factor that one factor is basically
+giving us when I multiply out my matrix
+
+ align:start position:0%
+giving us when I multiply out my matrix
+ 
+
+ align:start position:0%
+giving us when I multiply out my matrix
+that's corresponding to my beta not my
+
+ align:start position:0%
+that's corresponding to my beta not my
+ 
+
+ align:start position:0%
+that's corresponding to my beta not my
+overall mean so that what that's going
+
+ align:start position:0%
+overall mean so that what that's going
+ 
+
+ align:start position:0%
+overall mean so that what that's going
+to do is be able to to sort of add all
+
+ align:start position:0%
+to do is be able to to sort of add all
+ 
+
+ align:start position:0%
+to do is be able to to sort of add all
+of those up divided by four and give me
+
+ align:start position:0%
+of those up divided by four and give me
+ 
+
+ align:start position:0%
+of those up divided by four and give me
+an estimate of the overall grand mean of
+
+ align:start position:0%
+an estimate of the overall grand mean of
+ 
+
+ align:start position:0%
+an estimate of the overall grand mean of
+my output okay
+
+ align:start position:0%
+my output okay
+ 
+
+ align:start position:0%
+my output okay
+and we also create the x1 x2 cross
+
+ align:start position:0%
+and we also create the x1 x2 cross
+ 
+
+ align:start position:0%
+and we also create the x1 x2 cross
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+in order to be able to estimate an
+
+ align:start position:0%
+in order to be able to estimate an
+ 
+
+ align:start position:0%
+in order to be able to estimate an
+interaction term so overall then this
+
+ align:start position:0%
+interaction term so overall then this
+ 
+
+ align:start position:0%
+interaction term so overall then this
+here is my my X matrix I can then solve
+
+ align:start position:0%
+here is my my X matrix I can then solve
+ 
+
+ align:start position:0%
+here is my my X matrix I can then solve
+it now notice we're using the direct
+
+ align:start position:0%
+it now notice we're using the direct
+ 
+
+ align:start position:0%
+it now notice we're using the direct
+inverse and not the pseudo inverse y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember ultimately we've got you know y
+
+ align:start position:0%
+remember ultimately we've got you know y
+ 
+
+ align:start position:0%
+remember ultimately we've got you know y
+equals B beta X that's the model we're
+
+ align:start position:0%
+equals B beta X that's the model we're
+ 
+
+ align:start position:0%
+equals B beta X that's the model we're
+trying to form a beta naught plus beta 1
+
+ align:start position:0%
+trying to form a beta naught plus beta 1
+ 
+
+ align:start position:0%
+trying to form a beta naught plus beta 1
+beta 2 plus an interaction term in this
+
+ align:start position:0%
+beta 2 plus an interaction term in this
+ 
+
+ align:start position:0%
+beta 2 plus an interaction term in this
+approach how many data points do I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fitting into this regression my Y vector
+
+ align:start position:0%
+fitting into this regression my Y vector
+ 
+
+ align:start position:0%
+fitting into this regression my Y vector
+was four data points because it was just
+
+ align:start position:0%
+was four data points because it was just
+ 
+
+ align:start position:0%
+was four data points because it was just
+the means right
+
+ align:start position:0%
+the means right
+ 
+
+ align:start position:0%
+the means right
+how many coefficients for I can exactly
+
+ align:start position:0%
+how many coefficients for I can exactly
+ 
+
+ align:start position:0%
+how many coefficients for I can exactly
+fit my four coefficients and that's why
+
+ align:start position:0%
+fit my four coefficients and that's why
+ 
+
+ align:start position:0%
+fit my four coefficients and that's why
+I can do the direct inverse and when I
+
+ align:start position:0%
+I can do the direct inverse and when I
+ 
+
+ align:start position:0%
+I can do the direct inverse and when I
+do that it directly pops out these
+
+ align:start position:0%
+do that it directly pops out these
+ 
+
+ align:start position:0%
+do that it directly pops out these
+values from my beta coefficients which
+
+ align:start position:0%
+values from my beta coefficients which
+ 
+
+ align:start position:0%
+values from my beta coefficients which
+feed or give me my regression model
+
+ align:start position:0%
+feed or give me my regression model
+ 
+
+ align:start position:0%
+feed or give me my regression model
+what's Epsilon in this model 0 its 0 I
+
+ align:start position:0%
+what's Epsilon in this model 0 its 0 I
+ 
+
+ align:start position:0%
+what's Epsilon in this model 0 its 0 I
+exactly fit my four data points with
+
+ align:start position:0%
+exactly fit my four data points with
+ 
+
+ align:start position:0%
+exactly fit my four data points with
+with my 4 coefficients I don't even have
+
+ align:start position:0%
+with my 4 coefficients I don't even have
+ 
+
+ align:start position:0%
+with my 4 coefficients I don't even have
+any extra data to estimate Epsilon if I
+
+ align:start position:0%
+any extra data to estimate Epsilon if I
+ 
+
+ align:start position:0%
+any extra data to estimate Epsilon if I
+just use the mean values however if I go
+
+ align:start position:0%
+just use the mean values however if I go
+ 
+
+ align:start position:0%
+just use the mean values however if I go
+back and expand out realize I had 10
+
+ align:start position:0%
+back and expand out realize I had 10
+ 
+
+ align:start position:0%
+back and expand out realize I had 10
+replicates at each of those main values
+
+ align:start position:0%
+replicates at each of those main values
+ 
+
+ align:start position:0%
+replicates at each of those main values
+that's one form a one one source of
+
+ align:start position:0%
+that's one form a one one source of
+ 
+
+ align:start position:0%
+that's one form a one one source of
+information about pure replication error
+
+ align:start position:0%
+information about pure replication error
+ 
+
+ align:start position:0%
+information about pure replication error
+that is to say noise factors in in the
+
+ align:start position:0%
+that is to say noise factors in in the
+ 
+
+ align:start position:0%
+that is to say noise factors in in the
+data so in this approach where I just
+
+ align:start position:0%
+data so in this approach where I just
+ 
+
+ align:start position:0%
+data so in this approach where I just
+used the mean and the regression I don't
+
+ align:start position:0%
+used the mean and the regression I don't
+ 
+
+ align:start position:0%
+used the mean and the regression I don't
+have an estimate for Epsilon I would
+
+ align:start position:0%
+have an estimate for Epsilon I would
+ 
+
+ align:start position:0%
+have an estimate for Epsilon I would
+have to look back and form a separate
+
+ align:start position:0%
+have to look back and form a separate
+ 
+
+ align:start position:0%
+have to look back and form a separate
+pool the estimate across my four
+
+ align:start position:0%
+pool the estimate across my four
+ 
+
+ align:start position:0%
+pool the estimate across my four
+experimental data points for for the
+
+ align:start position:0%
+experimental data points for for the
+ 
+
+ align:start position:0%
+experimental data points for for the
+noise variance in the in the system okay
+
+ align:start position:0%
+noise variance in the in the system okay
+ 
+
+ align:start position:0%
+noise variance in the in the system okay
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I thought I had another example okay
+
+ align:start position:0%
+now I thought I had another example okay
+ 
+
+ align:start position:0%
+now I thought I had another example okay
+we'll come back to that so once I've got
+
+ align:start position:0%
+we'll come back to that so once I've got
+ 
+
+ align:start position:0%
+we'll come back to that so once I've got
+the model this is essentially the model
+
+ align:start position:0%
+the model this is essentially the model
+ 
+
+ align:start position:0%
+the model this is essentially the model
+that I have of the true underlying
+
+ align:start position:0%
+that I have of the true underlying
+ 
+
+ align:start position:0%
+that I have of the true underlying
+process again first-order linear plus an
+
+ align:start position:0%
+process again first-order linear plus an
+ 
+
+ align:start position:0%
+process again first-order linear plus an
+interaction plus maybe I have lingering
+
+ align:start position:0%
+interaction plus maybe I have lingering
+ 
+
+ align:start position:0%
+interaction plus maybe I have lingering
+in my head there might still be some
+
+ align:start position:0%
+in my head there might still be some
+ 
+
+ align:start position:0%
+in my head there might still be some
+higher-order quadratic dependence for
+
+ align:start position:0%
+higher-order quadratic dependence for
+ 
+
+ align:start position:0%
+higher-order quadratic dependence for
+example I'm punched out I haven't really
+
+ align:start position:0%
+example I'm punched out I haven't really
+ 
+
+ align:start position:0%
+example I'm punched out I haven't really
+sampled enough to be able to estimate
+
+ align:start position:0%
+sampled enough to be able to estimate
+ 
+
+ align:start position:0%
+sampled enough to be able to estimate
+that and I also have some noise the
+
+ align:start position:0%
+that and I also have some noise the
+ 
+
+ align:start position:0%
+that and I also have some noise the
+model that I have fit right here my Y
+
+ align:start position:0%
+model that I have fit right here my Y
+ 
+
+ align:start position:0%
+model that I have fit right here my Y
+hat estimate includes estimates I guess
+
+ align:start position:0%
+hat estimate includes estimates I guess
+ 
+
+ align:start position:0%
+hat estimate includes estimates I guess
+I should say estimates here for for
+
+ align:start position:0%
+I should say estimates here for for
+ 
+
+ align:start position:0%
+I should say estimates here for for
+these different terms and what we're
+
+ align:start position:0%
+these different terms and what we're
+ 
+
+ align:start position:0%
+these different terms and what we're
+basically saying is we're lumping in
+
+ align:start position:0%
+basically saying is we're lumping in
+ 
+
+ align:start position:0%
+basically saying is we're lumping in
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+all of the errors that might be lurking
+
+ align:start position:0%
+all of the errors that might be lurking
+ 
+
+ align:start position:0%
+all of the errors that might be lurking
+as two effects together one is random
+
+ align:start position:0%
+as two effects together one is random
+ 
+
+ align:start position:0%
+as two effects together one is random
+noise the other is neglected higher
+
+ align:start position:0%
+noise the other is neglected higher
+ 
+
+ align:start position:0%
+noise the other is neglected higher
+order terms
+
+ align:start position:0%
+order terms
+ 
+
+ align:start position:0%
+order terms
+remember these are that's kind of our
+
+ align:start position:0%
+remember these are that's kind of our
+ 
+
+ align:start position:0%
+remember these are that's kind of our
+acronym for higher order terms okay
+
+ align:start position:0%
+acronym for higher order terms okay
+ 
+
+ align:start position:0%
+acronym for higher order terms okay
+question right so what you so the
+
+ align:start position:0%
+question right so what you so the
+ 
+
+ align:start position:0%
+question right so what you so the
+question was what if you add additional
+
+ align:start position:0%
+question was what if you add additional
+ 
+
+ align:start position:0%
+question was what if you add additional
+higher order terms to drive epsilon to
+
+ align:start position:0%
+higher order terms to drive epsilon to
+ 
+
+ align:start position:0%
+higher order terms to drive epsilon to
+zero this is a very good point because
+
+ align:start position:0%
+zero this is a very good point because
+ 
+
+ align:start position:0%
+zero this is a very good point because
+if I don't have any replicates I could
+
+ align:start position:0%
+if I don't have any replicates I could
+ 
+
+ align:start position:0%
+if I don't have any replicates I could
+always add model terms until I finally
+
+ align:start position:0%
+always add model terms until I finally
+ 
+
+ align:start position:0%
+always add model terms until I finally
+get to where I have a perfect fit right
+
+ align:start position:0%
+get to where I have a perfect fit right
+ 
+
+ align:start position:0%
+get to where I have a perfect fit right
+just like we saw with the four data
+
+ align:start position:0%
+just like we saw with the four data
+ 
+
+ align:start position:0%
+just like we saw with the four data
+points and forth in which case my
+
+ align:start position:0%
+points and forth in which case my
+ 
+
+ align:start position:0%
+points and forth in which case my
+residual then is zero but I've added
+
+ align:start position:0%
+residual then is zero but I've added
+ 
+
+ align:start position:0%
+residual then is zero but I've added
+model terms but I also have no way in
+
+ align:start position:0%
+model terms but I also have no way in
+ 
+
+ align:start position:0%
+model terms but I also have no way in
+that case of knowing whether the model
+
+ align:start position:0%
+that case of knowing whether the model
+ 
+
+ align:start position:0%
+that case of knowing whether the model
+terms are significant or not if I have
+
+ align:start position:0%
+terms are significant or not if I have
+ 
+
+ align:start position:0%
+terms are significant or not if I have
+replicates on the other hand then you
+
+ align:start position:0%
+replicates on the other hand then you
+ 
+
+ align:start position:0%
+replicates on the other hand then you
+will almost never if there's any noise
+
+ align:start position:0%
+will almost never if there's any noise
+ 
+
+ align:start position:0%
+will almost never if there's any noise
+in the replicants where the replicates
+
+ align:start position:0%
+in the replicants where the replicates
+ 
+
+ align:start position:0%
+in the replicants where the replicates
+do not lie exactly on top of each other
+
+ align:start position:0%
+do not lie exactly on top of each other
+ 
+
+ align:start position:0%
+do not lie exactly on top of each other
+for every rerun at the same
+
+ align:start position:0%
+for every rerun at the same
+ 
+
+ align:start position:0%
+for every rerun at the same
+then there's no way to drive the
+
+ align:start position:0%
+then there's no way to drive the
+ 
+
+ align:start position:0%
+then there's no way to drive the
+residual to zero because I will have
+
+ align:start position:0%
+residual to zero because I will have
+ 
+
+ align:start position:0%
+residual to zero because I will have
+pure process error at least even if I've
+
+ align:start position:0%
+pure process error at least even if I've
+ 
+
+ align:start position:0%
+pure process error at least even if I've
+added all the model terms I need to
+
+ align:start position:0%
+added all the model terms I need to
+ 
+
+ align:start position:0%
+added all the model terms I need to
+drive model error phot to zero so we've
+
+ align:start position:0%
+drive model error phot to zero so we've
+ 
+
+ align:start position:0%
+drive model error phot to zero so we've
+got actually these two things going on
+
+ align:start position:0%
+got actually these two things going on
+ 
+
+ align:start position:0%
+got actually these two things going on
+we've got two key sources of residuals
+
+ align:start position:0%
+we've got two key sources of residuals
+ 
+
+ align:start position:0%
+we've got two key sources of residuals
+lack of lack of perfection in our model
+
+ align:start position:0%
+lack of lack of perfection in our model
+ 
+
+ align:start position:0%
+lack of lack of perfection in our model
+that we want to talk about how we
+
+ align:start position:0%
+that we want to talk about how we
+ 
+
+ align:start position:0%
+that we want to talk about how we
+distinguish and detect because one of
+
+ align:start position:0%
+distinguish and detect because one of
+ 
+
+ align:start position:0%
+distinguish and detect because one of
+those is letting whether we have an
+
+ align:start position:0%
+those is letting whether we have an
+ 
+
+ align:start position:0%
+those is letting whether we have an
+adequate model form do I have the right
+
+ align:start position:0%
+adequate model form do I have the right
+ 
+
+ align:start position:0%
+adequate model form do I have the right
+terms and enough of the terms in there
+
+ align:start position:0%
+terms and enough of the terms in there
+ 
+
+ align:start position:0%
+terms and enough of the terms in there
+or is there just replication variance
+
+ align:start position:0%
+or is there just replication variance
+ 
+
+ align:start position:0%
+or is there just replication variance
+noise which I can't fit all I can do is
+
+ align:start position:0%
+noise which I can't fit all I can do is
+ 
+
+ align:start position:0%
+noise which I can't fit all I can do is
+estimate the Sigma associated with that
+
+ align:start position:0%
+estimate the Sigma associated with that
+ 
+
+ align:start position:0%
+estimate the Sigma associated with that
+replica noise okay that's the key
+
+ align:start position:0%
+replica noise okay that's the key
+ 
+
+ align:start position:0%
+replica noise okay that's the key
+question that we that we want to to get
+
+ align:start position:0%
+question that we that we want to to get
+ 
+
+ align:start position:0%
+question that we that we want to to get
+to before we get to breaking down the
+
+ align:start position:0%
+to before we get to breaking down the
+ 
+
+ align:start position:0%
+to before we get to breaking down the
+residuals one thing that you should
+
+ align:start position:0%
+residuals one thing that you should
+ 
+
+ align:start position:0%
+residuals one thing that you should
+always do after you fit your model is
+
+ align:start position:0%
+always do after you fit your model is
+ 
+
+ align:start position:0%
+always do after you fit your model is
+actually look at the residuals to see if
+
+ align:start position:0%
+actually look at the residuals to see if
+ 
+
+ align:start position:0%
+actually look at the residuals to see if
+there are trends qualitatively that may
+
+ align:start position:0%
+there are trends qualitatively that may
+ 
+
+ align:start position:0%
+there are trends qualitatively that may
+be missing because that will often give
+
+ align:start position:0%
+be missing because that will often give
+ 
+
+ align:start position:0%
+be missing because that will often give
+you a lot of insight into whether it's a
+
+ align:start position:0%
+you a lot of insight into whether it's a
+ 
+
+ align:start position:0%
+you a lot of insight into whether it's a
+model model structure problem or not and
+
+ align:start position:0%
+model model structure problem or not and
+ 
+
+ align:start position:0%
+model model structure problem or not and
+so for this data what we've actually
+
+ align:start position:0%
+so for this data what we've actually
+ 
+
+ align:start position:0%
+so for this data what we've actually
+done here is look at the residuals
+
+ align:start position:0%
+done here is look at the residuals
+ 
+
+ align:start position:0%
+done here is look at the residuals
+associated with the ten replicates that
+
+ align:start position:0%
+associated with the ten replicates that
+ 
+
+ align:start position:0%
+associated with the ten replicates that
+we've got and what you'll see is first
+
+ align:start position:0%
+we've got and what you'll see is first
+ 
+
+ align:start position:0%
+we've got and what you'll see is first
+off the mean of your residuals had
+
+ align:start position:0%
+off the mean of your residuals had
+ 
+
+ align:start position:0%
+off the mean of your residuals had
+better be zero otherwise you've actually
+
+ align:start position:0%
+better be zero otherwise you've actually
+ 
+
+ align:start position:0%
+better be zero otherwise you've actually
+got a screw-up somewhere in your fit
+
+ align:start position:0%
+got a screw-up somewhere in your fit
+ 
+
+ align:start position:0%
+got a screw-up somewhere in your fit
+just mechanically right but what you
+
+ align:start position:0%
+just mechanically right but what you
+ 
+
+ align:start position:0%
+just mechanically right but what you
+would like to see is essentially the
+
+ align:start position:0%
+would like to see is essentially the
+ 
+
+ align:start position:0%
+would like to see is essentially the
+residuals ought to not depend on the
+
+ align:start position:0%
+residuals ought to not depend on the
+ 
+
+ align:start position:0%
+residuals ought to not depend on the
+level setting or the or the experimental
+
+ align:start position:0%
+level setting or the or the experimental
+ 
+
+ align:start position:0%
+level setting or the or the experimental
+data point especially with continuous
+
+ align:start position:0%
+data point especially with continuous
+ 
+
+ align:start position:0%
+data point especially with continuous
+parameters if what you see is the
+
+ align:start position:0%
+parameters if what you see is the
+ 
+
+ align:start position:0%
+parameters if what you see is the
+residuals versus mall values are very
+
+ align:start position:0%
+residuals versus mall values are very
+ 
+
+ align:start position:0%
+residuals versus mall values are very
+tiny and the residuals for big values
+
+ align:start position:0%
+tiny and the residuals for big values
+ 
+
+ align:start position:0%
+tiny and the residuals for big values
+are really really large that actually
+
+ align:start position:0%
+are really really large that actually
+ 
+
+ align:start position:0%
+are really really large that actually
+violates some of the
+
+ align:start position:0%
+violates some of the
+ 
+
+ align:start position:0%
+violates some of the
+we've made in in the model fitting and
+
+ align:start position:0%
+we've made in in the model fitting and
+ 
+
+ align:start position:0%
+we've made in in the model fitting and
+you might need to go and do a
+
+ align:start position:0%
+you might need to go and do a
+ 
+
+ align:start position:0%
+you might need to go and do a
+transformation of your data perhaps
+
+ align:start position:0%
+transformation of your data perhaps
+ 
+
+ align:start position:0%
+transformation of your data perhaps
+something like a logarithmic
+
+ align:start position:0%
+something like a logarithmic
+ 
+
+ align:start position:0%
+something like a logarithmic
+transformation or some other
+
+ align:start position:0%
+transformation or some other
+ 
+
+ align:start position:0%
+transformation or some other
+transformation of your Y output data
+
+ align:start position:0%
+transformation of your Y output data
+ 
+
+ align:start position:0%
+transformation of your Y output data
+because your residuals are not all in 0
+
+ align:start position:0%
+because your residuals are not all in 0
+ 
+
+ align:start position:0%
+because your residuals are not all in 0
+Sigma squared as we assume the same
+
+ align:start position:0%
+Sigma squared as we assume the same
+ 
+
+ align:start position:0%
+Sigma squared as we assume the same
+variance for each of your data points
+
+ align:start position:0%
+variance for each of your data points
+ 
+
+ align:start position:0%
+variance for each of your data points
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes oh so the the question for folks
+
+ align:start position:0%
+yes yes oh so the the question for folks
+ 
+
+ align:start position:0%
+yes yes oh so the the question for folks
+in Singapore may not have heard that was
+
+ align:start position:0%
+in Singapore may not have heard that was
+ 
+
+ align:start position:0%
+in Singapore may not have heard that was
+was all right aren't there other
+
+ align:start position:0%
+was all right aren't there other
+ 
+
+ align:start position:0%
+was all right aren't there other
+possible sources of residual or error
+
+ align:start position:0%
+possible sources of residual or error
+ 
+
+ align:start position:0%
+possible sources of residual or error
+including for example other factors like
+
+ align:start position:0%
+including for example other factors like
+ 
+
+ align:start position:0%
+including for example other factors like
+an x3 factor that we didn't even
+
+ align:start position:0%
+an x3 factor that we didn't even
+ 
+
+ align:start position:0%
+an x3 factor that we didn't even
+consider is working underneath and
+
+ align:start position:0%
+consider is working underneath and
+ 
+
+ align:start position:0%
+consider is working underneath and
+that's absolutely true those are all
+
+ align:start position:0%
+that's absolutely true those are all
+ 
+
+ align:start position:0%
+that's absolutely true those are all
+potential additional sources of I guess
+
+ align:start position:0%
+potential additional sources of I guess
+ 
+
+ align:start position:0%
+potential additional sources of I guess
+you could look at it it's either model
+
+ align:start position:0%
+you could look at it it's either model
+ 
+
+ align:start position:0%
+you could look at it it's either model
+error or noise what we're doing is
+
+ align:start position:0%
+error or noise what we're doing is
+ 
+
+ align:start position:0%
+error or noise what we're doing is
+treating it all as noise and we'll talk
+
+ align:start position:0%
+treating it all as noise and we'll talk
+ 
+
+ align:start position:0%
+treating it all as noise and we'll talk
+a little bit more about nuisance factors
+
+ align:start position:0%
+a little bit more about nuisance factors
+ 
+
+ align:start position:0%
+a little bit more about nuisance factors
+and how we might walk against that but
+
+ align:start position:0%
+and how we might walk against that but
+ 
+
+ align:start position:0%
+and how we might walk against that but
+essentially we're lumping all of those
+
+ align:start position:0%
+essentially we're lumping all of those
+ 
+
+ align:start position:0%
+essentially we're lumping all of those
+things into just the Sigma squared
+
+ align:start position:0%
+things into just the Sigma squared
+ 
+
+ align:start position:0%
+things into just the Sigma squared
+unless we're explicitly breaking them
+
+ align:start position:0%
+unless we're explicitly breaking them
+ 
+
+ align:start position:0%
+unless we're explicitly breaking them
+out and treating them in our model yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay so you did essentially the
+
+ align:start position:0%
+yes okay so you did essentially the
+ 
+
+ align:start position:0%
+yes okay so you did essentially the
+special case where if you believe really
+
+ align:start position:0%
+special case where if you believe really
+ 
+
+ align:start position:0%
+special case where if you believe really
+the higher order term or even the
+
+ align:start position:0%
+the higher order term or even the
+ 
+
+ align:start position:0%
+the higher order term or even the
+interaction term in our two-by-two let's
+
+ align:start position:0%
+interaction term in our two-by-two let's
+ 
+
+ align:start position:0%
+interaction term in our two-by-two let's
+say I really believe that really is not
+
+ align:start position:0%
+say I really believe that really is not
+ 
+
+ align:start position:0%
+say I really believe that really is not
+any reason for there to be an a/b
+
+ align:start position:0%
+any reason for there to be an a/b
+ 
+
+ align:start position:0%
+any reason for there to be an a/b
+interaction you can use that as
+
+ align:start position:0%
+interaction you can use that as
+ 
+
+ align:start position:0%
+interaction you can use that as
+essentially a replicate and not include
+
+ align:start position:0%
+essentially a replicate and not include
+ 
+
+ align:start position:0%
+essentially a replicate and not include
+that in the model term in which case
+
+ align:start position:0%
+that in the model term in which case
+ 
+
+ align:start position:0%
+that in the model term in which case
+then I've got four data points three
+
+ align:start position:0%
+then I've got four data points three
+ 
+
+ align:start position:0%
+then I've got four data points three
+model terms theta naught beta 1 beta 2
+
+ align:start position:0%
+model terms theta naught beta 1 beta 2
+ 
+
+ align:start position:0%
+model terms theta naught beta 1 beta 2
+and I've got the barest bones of
+
+ align:start position:0%
+and I've got the barest bones of
+ 
+
+ align:start position:0%
+and I've got the barest bones of
+additional data to be able to form an
+
+ align:start position:0%
+additional data to be able to form an
+ 
+
+ align:start position:0%
+additional data to be able to form an
+error estimate so it's basically
+
+ align:start position:0%
+error estimate so it's basically
+ 
+
+ align:start position:0%
+error estimate so it's basically
+treating the interaction as noise
+
+ align:start position:0%
+treating the interaction as noise
+ 
+
+ align:start position:0%
+treating the interaction as noise
+because I don't think that it's real and
+
+ align:start position:0%
+because I don't think that it's real and
+ 
+
+ align:start position:0%
+because I don't think that it's real and
+then you can do you've got just enough
+
+ align:start position:0%
+then you can do you've got just enough
+ 
+
+ align:start position:0%
+then you can do you've got just enough
+to be able to at least ask minimal
+
+ align:start position:0%
+to be able to at least ask minimal
+ 
+
+ align:start position:0%
+to be able to at least ask minimal
+questions about significance one last
+
+ align:start position:0%
+questions about significance one last
+ 
+
+ align:start position:0%
+questions about significance one last
+thing that we always want to do with our
+
+ align:start position:0%
+thing that we always want to do with our
+ 
+
+ align:start position:0%
+thing that we always want to do with our
+residuals is do a quick test or check to
+
+ align:start position:0%
+residuals is do a quick test or check to
+ 
+
+ align:start position:0%
+residuals is do a quick test or check to
+see is it reasonable that to think that
+
+ align:start position:0%
+see is it reasonable that to think that
+ 
+
+ align:start position:0%
+see is it reasonable that to think that
+these things are normally distributed so
+
+ align:start position:0%
+these things are normally distributed so
+ 
+
+ align:start position:0%
+these things are normally distributed so
+you can you know again do a QQ plot and
+
+ align:start position:0%
+you can you know again do a QQ plot and
+ 
+
+ align:start position:0%
+you can you know again do a QQ plot and
+see if there's strong evidence of
+
+ align:start position:0%
+see if there's strong evidence of
+ 
+
+ align:start position:0%
+see if there's strong evidence of
+something strange going on now I said
+
+ align:start position:0%
+something strange going on now I said
+ 
+
+ align:start position:0%
+something strange going on now I said
+here we kind of had to do if I if I used
+
+ align:start position:0%
+here we kind of had to do if I if I used
+ 
+
+ align:start position:0%
+here we kind of had to do if I if I used
+my Y average as my output I can do the
+
+ align:start position:0%
+my Y average as my output I can do the
+ 
+
+ align:start position:0%
+my Y average as my output I can do the
+regression and solve directly you could
+
+ align:start position:0%
+regression and solve directly you could
+ 
+
+ align:start position:0%
+regression and solve directly you could
+also formulate the regression problem
+
+ align:start position:0%
+also formulate the regression problem
+ 
+
+ align:start position:0%
+also formulate the regression problem
+using all of the data and not pre
+
+ align:start position:0%
+using all of the data and not pre
+ 
+
+ align:start position:0%
+using all of the data and not pre
+calculating the average for each of my
+
+ align:start position:0%
+calculating the average for each of my
+ 
+
+ align:start position:0%
+calculating the average for each of my
+four settings in which case we set up
+
+ align:start position:0%
+four settings in which case we set up
+ 
+
+ align:start position:0%
+four settings in which case we set up
+our data a little bit larger I still
+
+ align:start position:0%
+our data a little bit larger I still
+ 
+
+ align:start position:0%
+our data a little bit larger I still
+have my I don't know why it became in
+
+ align:start position:0%
+have my I don't know why it became in
+ 
+
+ align:start position:0%
+have my I don't know why it became in
+the ADA
+
+ align:start position:0%
+the ADA
+ 
+
+ align:start position:0%
+the ADA
+I guess there's my ADA that's still a Y
+
+ align:start position:0%
+I guess there's my ADA that's still a Y
+ 
+
+ align:start position:0%
+I guess there's my ADA that's still a Y
+this is my Y data I still have my X
+
+ align:start position:0%
+this is my Y data I still have my X
+ 
+
+ align:start position:0%
+this is my Y data I still have my X
+which has my main effects and my
+
+ align:start position:0%
+which has my main effects and my
+ 
+
+ align:start position:0%
+which has my main effects and my
+interaction but now each of the
+
+ align:start position:0%
+interaction but now each of the
+ 
+
+ align:start position:0%
+interaction but now each of the
+replicates for example I don't know if
+
+ align:start position:0%
+replicates for example I don't know if
+ 
+
+ align:start position:0%
+replicates for example I don't know if
+you can see it but this is a one one one
+
+ align:start position:0%
+you can see it but this is a one one one
+ 
+
+ align:start position:0%
+you can see it but this is a one one one
+setting and that's one of those outputs
+
+ align:start position:0%
+setting and that's one of those outputs
+ 
+
+ align:start position:0%
+setting and that's one of those outputs
+here's another one one one and the
+
+ align:start position:0%
+here's another one one one and the
+ 
+
+ align:start position:0%
+here's another one one one and the
+output for that particular run in other
+
+ align:start position:0%
+output for that particular run in other
+ 
+
+ align:start position:0%
+output for that particular run in other
+words I have multiple rows in my data I
+
+ align:start position:0%
+words I have multiple rows in my data I
+ 
+
+ align:start position:0%
+words I have multiple rows in my data I
+have ten rows with the same factor
+
+ align:start position:0%
+have ten rows with the same factor
+ 
+
+ align:start position:0%
+have ten rows with the same factor
+settings
+
+ align:start position:0%
+settings
+ 
+
+ align:start position:0%
+settings
+and each one of which has a different
+
+ align:start position:0%
+and each one of which has a different
+ 
+
+ align:start position:0%
+and each one of which has a different
+output Y and now I can set up and do my
+
+ align:start position:0%
+output Y and now I can set up and do my
+ 
+
+ align:start position:0%
+output Y and now I can set up and do my
+regression now I have to use the
+
+ align:start position:0%
+regression now I have to use the
+ 
+
+ align:start position:0%
+regression now I have to use the
+pseudo-inverse
+
+ align:start position:0%
+pseudo-inverse
+ 
+
+ align:start position:0%
+pseudo-inverse
+right because I've got more data than
+
+ align:start position:0%
+right because I've got more data than
+ 
+
+ align:start position:0%
+right because I've got more data than
+I've got coefficients so I'm doing my
+
+ align:start position:0%
+I've got coefficients so I'm doing my
+ 
+
+ align:start position:0%
+I've got coefficients so I'm doing my
+least squares fitting using my pseudo
+
+ align:start position:0%
+least squares fitting using my pseudo
+ 
+
+ align:start position:0%
+least squares fitting using my pseudo
+inverse and what pops out if you
+
+ align:start position:0%
+inverse and what pops out if you
+ 
+
+ align:start position:0%
+inverse and what pops out if you
+actually do that with this data is
+
+ align:start position:0%
+actually do that with this data is
+ 
+
+ align:start position:0%
+actually do that with this data is
+exactly the same beta thank God right
+
+ align:start position:0%
+exactly the same beta thank God right
+ 
+
+ align:start position:0%
+exactly the same beta thank God right
+okay so it's the same estimates of beta
+
+ align:start position:0%
+okay so it's the same estimates of beta
+ 
+
+ align:start position:0%
+okay so it's the same estimates of beta
+as as before now you might also have
+
+ align:start position:0%
+as as before now you might also have
+ 
+
+ align:start position:0%
+as as before now you might also have
+directly a residual based on the
+
+ align:start position:0%
+directly a residual based on the
+ 
+
+ align:start position:0%
+directly a residual based on the
+difference between your predicted Y your
+
+ align:start position:0%
+difference between your predicted Y your
+ 
+
+ align:start position:0%
+difference between your predicted Y your
+Y hat and your actual measured I've got
+
+ align:start position:0%
+Y hat and your actual measured I've got
+ 
+
+ align:start position:0%
+Y hat and your actual measured I've got
+four I've got 40 of those values and I
+
+ align:start position:0%
+four I've got 40 of those values and I
+ 
+
+ align:start position:0%
+four I've got 40 of those values and I
+can use that as my overall estimate for
+
+ align:start position:0%
+can use that as my overall estimate for
+ 
+
+ align:start position:0%
+can use that as my overall estimate for
+my overall residual in that in this case
+
+ align:start position:0%
+my overall residual in that in this case
+ 
+
+ align:start position:0%
+my overall residual in that in this case
+so it sort of pops right out as well and
+
+ align:start position:0%
+so it sort of pops right out as well and
+ 
+
+ align:start position:0%
+so it sort of pops right out as well and
+you can form the same residual so if you
+
+ align:start position:0%
+you can form the same residual so if you
+ 
+
+ align:start position:0%
+you can form the same residual so if you
+actually plot this for the response
+
+ align:start position:0%
+actually plot this for the response
+ 
+
+ align:start position:0%
+actually plot this for the response
+surface for a very simple linear model
+
+ align:start position:0%
+surface for a very simple linear model
+ 
+
+ align:start position:0%
+surface for a very simple linear model
+with interaction this is what you see as
+
+ align:start position:0%
+with interaction this is what you see as
+ 
+
+ align:start position:0%
+with interaction this is what you see as
+you change the material access from your
+
+ align:start position:0%
+you change the material access from your
+ 
+
+ align:start position:0%
+you change the material access from your
+high to low and your depth axis you've
+
+ align:start position:0%
+high to low and your depth axis you've
+ 
+
+ align:start position:0%
+high to low and your depth axis you've
+got kind of this looks like mostly a
+
+ align:start position:0%
+got kind of this looks like mostly a
+ 
+
+ align:start position:0%
+got kind of this looks like mostly a
+slanted plane kind of kind of effect
+
+ align:start position:0%
+slanted plane kind of kind of effect
+ 
+
+ align:start position:0%
+slanted plane kind of kind of effect
+notice that so let me ask you do you
+
+ align:start position:0%
+notice that so let me ask you do you
+ 
+
+ align:start position:0%
+notice that so let me ask you do you
+think there is a significant at the pot
+
+ align:start position:0%
+think there is a significant at the pot
+ 
+
+ align:start position:0%
+think there is a significant at the pot
+do you think there's a significant
+
+ align:start position:0%
+do you think there's a significant
+ 
+
+ align:start position:0%
+do you think there's a significant
+effect from factor X one significant
+
+ align:start position:0%
+effect from factor X one significant
+ 
+
+ align:start position:0%
+effect from factor X one significant
+effect from factor X two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I see some head shaking it looks like
+
+ align:start position:0%
+I see some head shaking it looks like
+ 
+
+ align:start position:0%
+I see some head shaking it looks like
+it's a nice trend there's lots of
+
+ align:start position:0%
+it's a nice trend there's lots of
+ 
+
+ align:start position:0%
+it's a nice trend there's lots of
+movement in the output values sure why
+
+ align:start position:0%
+movement in the output values sure why
+ 
+
+ align:start position:0%
+movement in the output values sure why
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+just looking at this plot I argue you
+
+ align:start position:0%
+just looking at this plot I argue you
+ 
+
+ align:start position:0%
+just looking at this plot I argue you
+can't tell this is just your best fit
+
+ align:start position:0%
+can't tell this is just your best fit
+ 
+
+ align:start position:0%
+can't tell this is just your best fit
+based on your betas but you don't
+
+ align:start position:0%
+based on your betas but you don't
+ 
+
+ align:start position:0%
+based on your betas but you don't
+actually know whether they're
+
+ align:start position:0%
+actually know whether they're
+ 
+
+ align:start position:0%
+actually know whether they're
+significant or not just plotting the
+
+ align:start position:0%
+significant or not just plotting the
+ 
+
+ align:start position:0%
+significant or not just plotting the
+output of your model here's why for
+
+ align:start position:0%
+output of your model here's why for
+ 
+
+ align:start position:0%
+output of your model here's why for
+example if I were to tell you okay at
+
+ align:start position:0%
+example if I were to tell you okay at
+ 
+
+ align:start position:0%
+example if I were to tell you okay at
+this combination of depth and material
+
+ align:start position:0%
+this combination of depth and material
+ 
+
+ align:start position:0%
+this combination of depth and material
+at the plus one plus one
+
+ align:start position:0%
+at the plus one plus one
+ 
+
+ align:start position:0%
+at the plus one plus one
+I actually plotted the 10 different
+
+ align:start position:0%
+I actually plotted the 10 different
+ 
+
+ align:start position:0%
+I actually plotted the 10 different
+values you saw and they all looked like
+
+ align:start position:0%
+values you saw and they all looked like
+ 
+
+ align:start position:0%
+values you saw and they all looked like
+like this and if I plotted the low-low
+
+ align:start position:0%
+like this and if I plotted the low-low
+ 
+
+ align:start position:0%
+like this and if I plotted the low-low
+and they all look like this now you'd
+
+ align:start position:0%
+and they all look like this now you'd
+ 
+
+ align:start position:0%
+and they all look like this now you'd
+start to say yeah my mom will output
+
+ align:start position:0%
+start to say yeah my mom will output
+ 
+
+ align:start position:0%
+start to say yeah my mom will output
+you know there's big separation between
+
+ align:start position:0%
+you know there's big separation between
+ 
+
+ align:start position:0%
+you know there's big separation between
+those two I think that's significant on
+
+ align:start position:0%
+those two I think that's significant on
+ 
+
+ align:start position:0%
+those two I think that's significant on
+the other hand if I plotted and showed
+
+ align:start position:0%
+the other hand if I plotted and showed
+ 
+
+ align:start position:0%
+the other hand if I plotted and showed
+you a scatter around here that was huge
+
+ align:start position:0%
+you a scatter around here that was huge
+ 
+
+ align:start position:0%
+you a scatter around here that was huge
+and a scatter of your actual data points
+
+ align:start position:0%
+and a scatter of your actual data points
+ 
+
+ align:start position:0%
+and a scatter of your actual data points
+around this condition that was also huge
+
+ align:start position:0%
+around this condition that was also huge
+ 
+
+ align:start position:0%
+around this condition that was also huge
+and there was big overlap between the
+
+ align:start position:0%
+and there was big overlap between the
+ 
+
+ align:start position:0%
+and there was big overlap between the
+two now you'd be a little more leery
+
+ align:start position:0%
+two now you'd be a little more leery
+ 
+
+ align:start position:0%
+two now you'd be a little more leery
+right you'd say well that was my best
+
+ align:start position:0%
+right you'd say well that was my best
+ 
+
+ align:start position:0%
+right you'd say well that was my best
+fit but I'm not sure they're they're
+
+ align:start position:0%
+fit but I'm not sure they're they're
+ 
+
+ align:start position:0%
+fit but I'm not sure they're they're
+actually significant so this highlights
+
+ align:start position:0%
+actually significant so this highlights
+ 
+
+ align:start position:0%
+actually significant so this highlights
+again you've got to use the ANOVA as
+
+ align:start position:0%
+again you've got to use the ANOVA as
+ 
+
+ align:start position:0%
+again you've got to use the ANOVA as
+well to be able to decide is there
+
+ align:start position:0%
+well to be able to decide is there
+ 
+
+ align:start position:0%
+well to be able to decide is there
+actually significance to the model
+
+ align:start position:0%
+actually significance to the model
+ 
+
+ align:start position:0%
+actually significance to the model
+coefficient that we were looking at it's
+
+ align:start position:0%
+coefficient that we were looking at it's
+ 
+
+ align:start position:0%
+coefficient that we were looking at it's
+just another another picture this is
+
+ align:start position:0%
+just another another picture this is
+ 
+
+ align:start position:0%
+just another another picture this is
+looking a little bit at the side this is
+
+ align:start position:0%
+looking a little bit at the side this is
+ 
+
+ align:start position:0%
+looking a little bit at the side this is
+pointing out if I believe that the terms
+
+ align:start position:0%
+pointing out if I believe that the terms
+ 
+
+ align:start position:0%
+pointing out if I believe that the terms
+are significant you could sort of ask
+
+ align:start position:0%
+are significant you could sort of ask
+ 
+
+ align:start position:0%
+are significant you could sort of ask
+the question is there an interaction
+
+ align:start position:0%
+the question is there an interaction
+ 
+
+ align:start position:0%
+the question is there an interaction
+effect it looks like there's not quite
+
+ align:start position:0%
+effect it looks like there's not quite
+ 
+
+ align:start position:0%
+effect it looks like there's not quite
+parallelism between these two lines
+
+ align:start position:0%
+parallelism between these two lines
+ 
+
+ align:start position:0%
+parallelism between these two lines
+there may be an AV interaction but I'd
+
+ align:start position:0%
+there may be an AV interaction but I'd
+ 
+
+ align:start position:0%
+there may be an AV interaction but I'd
+also need to ask the question about
+
+ align:start position:0%
+also need to ask the question about
+ 
+
+ align:start position:0%
+also need to ask the question about
+significance on that so that's the key
+
+ align:start position:0%
+significance on that so that's the key
+ 
+
+ align:start position:0%
+significance on that so that's the key
+question the effects of these terms are
+
+ align:start position:0%
+question the effects of these terms are
+ 
+
+ align:start position:0%
+question the effects of these terms are
+they significant or not
+
+ align:start position:0%
+they significant or not
+ 
+
+ align:start position:0%
+they significant or not
+we would do the ANOVA analysis by the
+
+ align:start position:0%
+we would do the ANOVA analysis by the
+ 
+
+ align:start position:0%
+we would do the ANOVA analysis by the
+way the ANOVA and the t-test
+
+ align:start position:0%
+way the ANOVA and the t-test
+ 
+
+ align:start position:0%
+way the ANOVA and the t-test
+it's almost the same in fact I think
+
+ align:start position:0%
+it's almost the same in fact I think
+ 
+
+ align:start position:0%
+it's almost the same in fact I think
+another problem on the problem set is
+
+ align:start position:0%
+another problem on the problem set is
+ 
+
+ align:start position:0%
+another problem on the problem set is
+understanding a little bit the
+
+ align:start position:0%
+understanding a little bit the
+ 
+
+ align:start position:0%
+understanding a little bit the
+relationship between these two ways of
+
+ align:start position:0%
+relationship between these two ways of
+ 
+
+ align:start position:0%
+relationship between these two ways of
+looking at the problem if I were to just
+
+ align:start position:0%
+looking at the problem if I were to just
+ 
+
+ align:start position:0%
+looking at the problem if I were to just
+look at this data and look at the effect
+
+ align:start position:0%
+look at this data and look at the effect
+ 
+
+ align:start position:0%
+look at this data and look at the effect
+of depth only on the aluminum so I'm
+
+ align:start position:0%
+of depth only on the aluminum so I'm
+ 
+
+ align:start position:0%
+of depth only on the aluminum so I'm
+just holding just looking at the
+
+ align:start position:0%
+just holding just looking at the
+ 
+
+ align:start position:0%
+just holding just looking at the
+aluminum parts for the depth of 0.6 and
+
+ align:start position:0%
+aluminum parts for the depth of 0.6 and
+ 
+
+ align:start position:0%
+aluminum parts for the depth of 0.6 and
+the depth of 0.3 there's the spread in
+
+ align:start position:0%
+the depth of 0.3 there's the spread in
+ 
+
+ align:start position:0%
+the depth of 0.3 there's the spread in
+my data I can look and say what's the
+
+ align:start position:0%
+my data I can look and say what's the
+ 
+
+ align:start position:0%
+my data I can look and say what's the
+variation within the test compared to
+
+ align:start position:0%
+variation within the test compared to
+ 
+
+ align:start position:0%
+variation within the test compared to
+the variation between tests I could then
+
+ align:start position:0%
+the variation between tests I could then
+ 
+
+ align:start position:0%
+the variation between tests I could then
+think of that as my F test or I could do
+
+ align:start position:0%
+think of that as my F test or I could do
+ 
+
+ align:start position:0%
+think of that as my F test or I could do
+a pairwise t-test or do a t-test looking
+
+ align:start position:0%
+a pairwise t-test or do a t-test looking
+ 
+
+ align:start position:0%
+a pairwise t-test or do a t-test looking
+at at the difference in the means given
+
+ align:start position:0%
+at at the difference in the means given
+ 
+
+ align:start position:0%
+at at the difference in the means given
+the spread between the two turns out to
+
+ align:start position:0%
+the spread between the two turns out to
+ 
+
+ align:start position:0%
+the spread between the two turns out to
+be the same test gives the same
+
+ align:start position:0%
+be the same test gives the same
+ 
+
+ align:start position:0%
+be the same test gives the same
+significance level whether you do it
+
+ align:start position:0%
+significance level whether you do it
+ 
+
+ align:start position:0%
+significance level whether you do it
+with an F or a T but essentially this is
+
+ align:start position:0%
+with an F or a T but essentially this is
+ 
+
+ align:start position:0%
+with an F or a T but essentially this is
+the same question I was just describing
+
+ align:start position:0%
+the same question I was just describing
+ 
+
+ align:start position:0%
+the same question I was just describing
+qualitatively on the 3d plot looking at
+
+ align:start position:0%
+qualitatively on the 3d plot looking at
+ 
+
+ align:start position:0%
+qualitatively on the 3d plot looking at
+one factor at a time I can ask the
+
+ align:start position:0%
+one factor at a time I can ask the
+ 
+
+ align:start position:0%
+one factor at a time I can ask the
+question do I think the effective depth
+
+ align:start position:0%
+question do I think the effective depth
+ 
+
+ align:start position:0%
+question do I think the effective depth
+is significant this is looking at it
+
+ align:start position:0%
+is significant this is looking at it
+ 
+
+ align:start position:0%
+is significant this is looking at it
+qualitatively I can go and chug and do
+
+ align:start position:0%
+qualitatively I can go and chug and do
+ 
+
+ align:start position:0%
+qualitatively I can go and chug and do
+the ANOVA or the t-test machinery but it
+
+ align:start position:0%
+the ANOVA or the t-test machinery but it
+ 
+
+ align:start position:0%
+the ANOVA or the t-test machinery but it
+gives the same idea I can do the same
+
+ align:start position:0%
+gives the same idea I can do the same
+ 
+
+ align:start position:0%
+gives the same idea I can do the same
+thing for the material effect say if I
+
+ align:start position:0%
+thing for the material effect say if I
+ 
+
+ align:start position:0%
+thing for the material effect say if I
+look at aluminum versus the stainless
+
+ align:start position:0%
+look at aluminum versus the stainless
+ 
+
+ align:start position:0%
+look at aluminum versus the stainless
+steel is that effect significant by the
+
+ align:start position:0%
+steel is that effect significant by the
+ 
+
+ align:start position:0%
+steel is that effect significant by the
+way you can go and chug through and do
+
+ align:start position:0%
+way you can go and chug through and do
+ 
+
+ align:start position:0%
+way you can go and chug through and do
+all of that what do you think are these
+
+ align:start position:0%
+all of that what do you think are these
+ 
+
+ align:start position:0%
+all of that what do you think are these
+factors significant I have high
+
+ align:start position:0%
+factors significant I have high
+ 
+
+ align:start position:0%
+factors significant I have high
+confidence I'm pretty confident that
+
+ align:start position:0%
+confidence I'm pretty confident that
+ 
+
+ align:start position:0%
+confidence I'm pretty confident that
+those are real effects there's a huge
+
+ align:start position:0%
+those are real effects there's a huge
+ 
+
+ align:start position:0%
+those are real effects there's a huge
+spread between these so you know the
+
+ align:start position:0%
+spread between these so you know the
+ 
+
+ align:start position:0%
+spread between these so you know the
+intuition is very clear the interaction
+
+ align:start position:0%
+intuition is very clear the interaction
+ 
+
+ align:start position:0%
+intuition is very clear the interaction
+effect that's a little tricky so we can
+
+ align:start position:0%
+effect that's a little tricky so we can
+ 
+
+ align:start position:0%
+effect that's a little tricky so we can
+go in I would actually want to run the
+
+ align:start position:0%
+go in I would actually want to run the
+ 
+
+ align:start position:0%
+go in I would actually want to run the
+ANOVA test in that case here's my raw
+
+ align:start position:0%
+ANOVA test in that case here's my raw
+ 
+
+ align:start position:0%
+ANOVA test in that case here's my raw
+data there's the model I fit again using
+
+ align:start position:0%
+data there's the model I fit again using
+ 
+
+ align:start position:0%
+data there's the model I fit again using
+the ANOVA table that we saw a minute ago
+
+ align:start position:0%
+the ANOVA table that we saw a minute ago
+ 
+
+ align:start position:0%
+the ANOVA table that we saw a minute ago
+I could by hand form that or I could put
+
+ align:start position:0%
+I could by hand form that or I could put
+ 
+
+ align:start position:0%
+I could by hand form that or I could put
+it in jump and come out with that with
+
+ align:start position:0%
+it in jump and come out with that with
+ 
+
+ align:start position:0%
+it in jump and come out with that with
+the output but now here this is very
+
+ align:start position:0%
+the output but now here this is very
+ 
+
+ align:start position:0%
+the output but now here this is very
+nice because I
+
+ align:start position:0%
+nice because I
+ 
+
+ align:start position:0%
+nice because I
+look and say okay associated with the
+
+ align:start position:0%
+look and say okay associated with the
+ 
+
+ align:start position:0%
+look and say okay associated with the
+mean x1 x2 and the interaction x1 x2
+
+ align:start position:0%
+mean x1 x2 and the interaction x1 x2
+ 
+
+ align:start position:0%
+mean x1 x2 and the interaction x1 x2
+what are the mean squares and the F
+
+ align:start position:0%
+what are the mean squares and the F
+ 
+
+ align:start position:0%
+what are the mean squares and the F
+compared to our estimate of the noise
+
+ align:start position:0%
+compared to our estimate of the noise
+ 
+
+ align:start position:0%
+compared to our estimate of the noise
+remember we had 40 data points I'm
+
+ align:start position:0%
+remember we had 40 data points I'm
+ 
+
+ align:start position:0%
+remember we had 40 data points I'm
+estimating four model coefficients
+
+ align:start position:0%
+estimating four model coefficients
+ 
+
+ align:start position:0%
+estimating four model coefficients
+that's leaving 36 replicate degrees of
+
+ align:start position:0%
+that's leaving 36 replicate degrees of
+ 
+
+ align:start position:0%
+that's leaving 36 replicate degrees of
+freedom so I have a very good estimate
+
+ align:start position:0%
+freedom so I have a very good estimate
+ 
+
+ align:start position:0%
+freedom so I have a very good estimate
+of noise in the system that's the
+
+ align:start position:0%
+of noise in the system that's the
+ 
+
+ align:start position:0%
+of noise in the system that's the
+denominator in all of my F ratios and
+
+ align:start position:0%
+denominator in all of my F ratios and
+ 
+
+ align:start position:0%
+denominator in all of my F ratios and
+I'm seeing apps from 10,000 down to 77
+
+ align:start position:0%
+I'm seeing apps from 10,000 down to 77
+ 
+
+ align:start position:0%
+I'm seeing apps from 10,000 down to 77
+in my F critical for 95 percent
+
+ align:start position:0%
+in my F critical for 95 percent
+ 
+
+ align:start position:0%
+in my F critical for 95 percent
+confidence is 4.1 so it looks like all
+
+ align:start position:0%
+confidence is 4.1 so it looks like all
+ 
+
+ align:start position:0%
+confidence is 4.1 so it looks like all
+of my apps are much bigger than that I
+
+ align:start position:0%
+of my apps are much bigger than that I
+ 
+
+ align:start position:0%
+of my apps are much bigger than that I
+have high confidence that the mean is
+
+ align:start position:0%
+have high confidence that the mean is
+ 
+
+ align:start position:0%
+have high confidence that the mean is
+significant these main effects are
+
+ align:start position:0%
+significant these main effects are
+ 
+
+ align:start position:0%
+significant these main effects are
+significant and the interaction is real
+
+ align:start position:0%
+significant and the interaction is real
+ 
+
+ align:start position:0%
+significant and the interaction is real
+it is bigger than I would expect given
+
+ align:start position:0%
+it is bigger than I would expect given
+ 
+
+ align:start position:0%
+it is bigger than I would expect given
+the noise in the process so I would
+
+ align:start position:0%
+the noise in the process so I would
+ 
+
+ align:start position:0%
+the noise in the process so I would
+accept all of those model terms so so
+
+ align:start position:0%
+accept all of those model terms so so
+ 
+
+ align:start position:0%
+accept all of those model terms so so
+far we use the idea of replicates to ask
+
+ align:start position:0%
+far we use the idea of replicates to ask
+ 
+
+ align:start position:0%
+far we use the idea of replicates to ask
+the significance question we said our
+
+ align:start position:0%
+the significance question we said our
+ 
+
+ align:start position:0%
+the significance question we said our
+residual could have two sources of error
+
+ align:start position:0%
+residual could have two sources of error
+ 
+
+ align:start position:0%
+residual could have two sources of error
+in it one is pure replication noise but
+
+ align:start position:0%
+in it one is pure replication noise but
+ 
+
+ align:start position:0%
+in it one is pure replication noise but
+the other thing that we haven't really
+
+ align:start position:0%
+the other thing that we haven't really
+ 
+
+ align:start position:0%
+the other thing that we haven't really
+is assessed yet is is the model form
+
+ align:start position:0%
+is assessed yet is is the model form
+ 
+
+ align:start position:0%
+is assessed yet is is the model form
+adequate you might still be nervous that
+
+ align:start position:0%
+adequate you might still be nervous that
+ 
+
+ align:start position:0%
+adequate you might still be nervous that
+maybe there's a quadratic relationship
+
+ align:start position:0%
+maybe there's a quadratic relationship
+ 
+
+ align:start position:0%
+maybe there's a quadratic relationship
+between output and the punched out with
+
+ align:start position:0%
+between output and the punched out with
+ 
+
+ align:start position:0%
+between output and the punched out with
+those two data points the best I could
+
+ align:start position:0%
+those two data points the best I could
+ 
+
+ align:start position:0%
+those two data points the best I could
+do is fit a linear model how would you
+
+ align:start position:0%
+do is fit a linear model how would you
+ 
+
+ align:start position:0%
+do is fit a linear model how would you
+possibly check to see if there might be
+
+ align:start position:0%
+possibly check to see if there might be
+ 
+
+ align:start position:0%
+possibly check to see if there might be
+curvature in the model or a quadratic
+
+ align:start position:0%
+curvature in the model or a quadratic
+ 
+
+ align:start position:0%
+curvature in the model or a quadratic
+effect do you have enough data to do
+
+ align:start position:0%
+effect do you have enough data to do
+ 
+
+ align:start position:0%
+effect do you have enough data to do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what there could be a Centrepointe
+
+ align:start position:0%
+what there could be a Centrepointe
+ 
+
+ align:start position:0%
+what there could be a Centrepointe
+let's add a center point let's consider
+
+ align:start position:0%
+let's add a center point let's consider
+ 
+
+ align:start position:0%
+let's add a center point let's consider
+additional experimental center points
+
+ align:start position:0%
+additional experimental center points
+ 
+
+ align:start position:0%
+additional experimental center points
+okay so what you would do then is is run
+
+ align:start position:0%
+okay so what you would do then is is run
+ 
+
+ align:start position:0%
+okay so what you would do then is is run
+some additional things at the center
+
+ align:start position:0%
+some additional things at the center
+ 
+
+ align:start position:0%
+some additional things at the center
+level the zero setting of those two data
+
+ align:start position:0%
+level the zero setting of those two data
+ 
+
+ align:start position:0%
+level the zero setting of those two data
+points and then look at the deviation
+
+ align:start position:0%
+points and then look at the deviation
+ 
+
+ align:start position:0%
+points and then look at the deviation
+between what the linear model suggests
+
+ align:start position:0%
+between what the linear model suggests
+ 
+
+ align:start position:0%
+between what the linear model suggests
+and what the actual data comes up with
+
+ align:start position:0%
+and what the actual data comes up with
+ 
+
+ align:start position:0%
+and what the actual data comes up with
+now you've got to ask significance of
+
+ align:start position:0%
+now you've got to ask significance of
+ 
+
+ align:start position:0%
+now you've got to ask significance of
+the Delta again your model may not be
+
+ align:start position:0%
+the Delta again your model may not be
+ 
+
+ align:start position:0%
+the Delta again your model may not be
+perfect in predicting what that center
+
+ align:start position:0%
+perfect in predicting what that center
+ 
+
+ align:start position:0%
+perfect in predicting what that center
+point is even if there is no curvature
+
+ align:start position:0%
+point is even if there is no curvature
+ 
+
+ align:start position:0%
+point is even if there is no curvature
+in the model because there's noise also
+
+ align:start position:0%
+in the model because there's noise also
+ 
+
+ align:start position:0%
+in the model because there's noise also
+in the model so we have to do two things
+
+ align:start position:0%
+in the model so we have to do two things
+ 
+
+ align:start position:0%
+in the model so we have to do two things
+one is we have to estimate the deviation
+
+ align:start position:0%
+one is we have to estimate the deviation
+ 
+
+ align:start position:0%
+one is we have to estimate the deviation
+from our simpler model the linear model
+
+ align:start position:0%
+from our simpler model the linear model
+ 
+
+ align:start position:0%
+from our simpler model the linear model
+versus the estimation with the quadratic
+
+ align:start position:0%
+versus the estimation with the quadratic
+ 
+
+ align:start position:0%
+versus the estimation with the quadratic
+term that would go through say the
+
+ align:start position:0%
+term that would go through say the
+ 
+
+ align:start position:0%
+term that would go through say the
+center point go through that additional
+
+ align:start position:0%
+center point go through that additional
+ 
+
+ align:start position:0%
+center point go through that additional
+center point and then compare the size
+
+ align:start position:0%
+center point and then compare the size
+ 
+
+ align:start position:0%
+center point and then compare the size
+of that to the natural spread in our
+
+ align:start position:0%
+of that to the natural spread in our
+ 
+
+ align:start position:0%
+of that to the natural spread in our
+data and do essentially an F test or an
+
+ align:start position:0%
+data and do essentially an F test or an
+ 
+
+ align:start position:0%
+data and do essentially an F test or an
+ANOVA test on that quadratic model term
+
+ align:start position:0%
+ANOVA test on that quadratic model term
+ 
+
+ align:start position:0%
+ANOVA test on that quadratic model term
+the same thing bother you about this
+
+ align:start position:0%
+the same thing bother you about this
+ 
+
+ align:start position:0%
+the same thing bother you about this
+picture we can set up and do this center
+
+ align:start position:0%
+picture we can set up and do this center
+ 
+
+ align:start position:0%
+picture we can set up and do this center
+point and run it right so so I'm there
+
+ align:start position:0%
+point and run it right so so I'm there
+ 
+
+ align:start position:0%
+point and run it right so so I'm there
+on the tool I'm setting the depth factor
+
+ align:start position:0%
+on the tool I'm setting the depth factor
+ 
+
+ align:start position:0%
+on the tool I'm setting the depth factor
+that's my x2 factor I guess and I've put
+
+ align:start position:0%
+that's my x2 factor I guess and I've put
+ 
+
+ align:start position:0%
+that's my x2 factor I guess and I've put
+it at zero point four or five inches I
+
+ align:start position:0%
+it at zero point four or five inches I
+ 
+
+ align:start position:0%
+it at zero point four or five inches I
+picked my part I got my aluminum I've
+
+ align:start position:0%
+picked my part I got my aluminum I've
+ 
+
+ align:start position:0%
+picked my part I got my aluminum I've
+got my stainless steel I need my zero
+
+ align:start position:0%
+got my stainless steel I need my zero
+ 
+
+ align:start position:0%
+got my stainless steel I need my zero
+level there is no center point on that
+
+ align:start position:0%
+level there is no center point on that
+ 
+
+ align:start position:0%
+level there is no center point on that
+right so you'd have to actually be very
+
+ align:start position:0%
+right so you'd have to actually be very
+ 
+
+ align:start position:0%
+right so you'd have to actually be very
+careful if you've got only discrete
+
+ align:start position:0%
+careful if you've got only discrete
+ 
+
+ align:start position:0%
+careful if you've got only discrete
+values that don't have some ordering or
+
+ align:start position:0%
+values that don't have some ordering or
+ 
+
+ align:start position:0%
+values that don't have some ordering or
+some continuous degree to them you can't
+
+ align:start position:0%
+some continuous degree to them you can't
+ 
+
+ align:start position:0%
+some continuous degree to them you can't
+do a center point right so what would
+
+ align:start position:0%
+do a center point right so what would
+ 
+
+ align:start position:0%
+do a center point right so what would
+you do in this case
+
+ align:start position:0%
+you do in this case
+ 
+
+ align:start position:0%
+you do in this case
+a physical model it's so complicated
+
+ align:start position:0%
+a physical model it's so complicated
+ 
+
+ align:start position:0%
+a physical model it's so complicated
+that's hopeless we don't have a physical
+
+ align:start position:0%
+that's hopeless we don't have a physical
+ 
+
+ align:start position:0%
+that's hopeless we don't have a physical
+model you might try a physical model
+
+ align:start position:0%
+model you might try a physical model
+ 
+
+ align:start position:0%
+model you might try a physical model
+there's something simpler you could do
+
+ align:start position:0%
+there's something simpler you could do
+ 
+
+ align:start position:0%
+there's something simpler you could do
+still using design of experiments yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just use the simplest point maybe I'm
+
+ align:start position:0%
+just use the simplest point maybe I'm
+ 
+
+ align:start position:0%
+just use the simplest point maybe I'm
+thinking what additional experimental
+
+ align:start position:0%
+thinking what additional experimental
+ 
+
+ align:start position:0%
+thinking what additional experimental
+point should I run to be able to decide
+
+ align:start position:0%
+point should I run to be able to decide
+ 
+
+ align:start position:0%
+point should I run to be able to decide
+if there is an additional curvature
+
+ align:start position:0%
+if there is an additional curvature
+ 
+
+ align:start position:0%
+if there is an additional curvature
+remember we were asking the question is
+
+ align:start position:0%
+remember we were asking the question is
+ 
+
+ align:start position:0%
+remember we were asking the question is
+there curvature or a higher order term
+
+ align:start position:0%
+there curvature or a higher order term
+ 
+
+ align:start position:0%
+there curvature or a higher order term
+associated with what variable just punch
+
+ align:start position:0%
+associated with what variable just punch
+ 
+
+ align:start position:0%
+associated with what variable just punch
+them right so why don't I still pick
+
+ align:start position:0%
+them right so why don't I still pick
+ 
+
+ align:start position:0%
+them right so why don't I still pick
+this but now I can pick data points
+
+ align:start position:0%
+this but now I can pick data points
+ 
+
+ align:start position:0%
+this but now I can pick data points
+right here and I might also pick data
+
+ align:start position:0%
+right here and I might also pick data
+ 
+
+ align:start position:0%
+right here and I might also pick data
+points right here I don't have to pick
+
+ align:start position:0%
+points right here I don't have to pick
+ 
+
+ align:start position:0%
+points right here I don't have to pick
+one center point I could actually pick a
+
+ align:start position:0%
+one center point I could actually pick a
+ 
+
+ align:start position:0%
+one center point I could actually pick a
+couple in fact I could even just do the
+
+ align:start position:0%
+couple in fact I could even just do the
+ 
+
+ align:start position:0%
+couple in fact I could even just do the
+runs right here and say this is what the
+
+ align:start position:0%
+runs right here and say this is what the
+ 
+
+ align:start position:0%
+runs right here and say this is what the
+linear model would predict but if
+
+ align:start position:0%
+linear model would predict but if
+ 
+
+ align:start position:0%
+linear model would predict but if
+there's curvature in my surface then I'm
+
+ align:start position:0%
+there's curvature in my surface then I'm
+ 
+
+ align:start position:0%
+there's curvature in my surface then I'm
+gonna get a deviation just at the
+
+ align:start position:0%
+gonna get a deviation just at the
+ 
+
+ align:start position:0%
+gonna get a deviation just at the
+stainless-steel setting now if I were
+
+ align:start position:0%
+stainless-steel setting now if I were
+ 
+
+ align:start position:0%
+stainless-steel setting now if I were
+careful in trying to keep things
+
+ align:start position:0%
+careful in trying to keep things
+ 
+
+ align:start position:0%
+careful in trying to keep things
+balanced I might do the stainless steel
+
+ align:start position:0%
+balanced I might do the stainless steel
+ 
+
+ align:start position:0%
+balanced I might do the stainless steel
+and and the aluminum and get an estimate
+
+ align:start position:0%
+and and the aluminum and get an estimate
+ 
+
+ align:start position:0%
+and and the aluminum and get an estimate
+across both of those at that deviation
+
+ align:start position:0%
+across both of those at that deviation
+ 
+
+ align:start position:0%
+across both of those at that deviation
+Falls so essentially what we're trying
+
+ align:start position:0%
+Falls so essentially what we're trying
+ 
+
+ align:start position:0%
+Falls so essentially what we're trying
+to do here is add a data point and then
+
+ align:start position:0%
+to do here is add a data point and then
+ 
+
+ align:start position:0%
+to do here is add a data point and then
+look at a lack of fit test in particular
+
+ align:start position:0%
+look at a lack of fit test in particular
+ 
+
+ align:start position:0%
+look at a lack of fit test in particular
+where I want to say is the model error
+
+ align:start position:0%
+where I want to say is the model error
+ 
+
+ align:start position:0%
+where I want to say is the model error
+the deviation because of this extra
+
+ align:start position:0%
+the deviation because of this extra
+ 
+
+ align:start position:0%
+the deviation because of this extra
+higher order term is it explainable by
+
+ align:start position:0%
+higher order term is it explainable by
+ 
+
+ align:start position:0%
+higher order term is it explainable by
+pure replicate variance or is it larger
+
+ align:start position:0%
+pure replicate variance or is it larger
+ 
+
+ align:start position:0%
+pure replicate variance or is it larger
+than that and therefore not explainable
+
+ align:start position:0%
+than that and therefore not explainable
+ 
+
+ align:start position:0%
+than that and therefore not explainable
+by my noise factor if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we've got more deviation because of
+
+ align:start position:0%
+if we've got more deviation because of
+ 
+
+ align:start position:0%
+if we've got more deviation because of
+the of the quadratic term say if I'm
+
+ align:start position:0%
+the of the quadratic term say if I'm
+ 
+
+ align:start position:0%
+the of the quadratic term say if I'm
+adding an x squared in this model and x2
+
+ align:start position:0%
+adding an x squared in this model and x2
+ 
+
+ align:start position:0%
+adding an x squared in this model and x2
+squared term then then I have to kind of
+
+ align:start position:0%
+squared term then then I have to kind of
+ 
+
+ align:start position:0%
+squared term then then I have to kind of
+reject the null hypothesis and so as
+
+ align:start position:0%
+reject the null hypothesis and so as
+ 
+
+ align:start position:0%
+reject the null hypothesis and so as
+I've just got random variance I really
+
+ align:start position:0%
+I've just got random variance I really
+ 
+
+ align:start position:0%
+I've just got random variance I really
+need an extra model term so we can still
+
+ align:start position:0%
+need an extra model term so we can still
+ 
+
+ align:start position:0%
+need an extra model term so we can still
+use the the the basic ANOVA setup so
+
+ align:start position:0%
+use the the the basic ANOVA setup so
+ 
+
+ align:start position:0%
+use the the the basic ANOVA setup so
+this is our our model with higher-order
+
+ align:start position:0%
+this is our our model with higher-order
+ 
+
+ align:start position:0%
+this is our our model with higher-order
+terms you might think about trying to
+
+ align:start position:0%
+terms you might think about trying to
+ 
+
+ align:start position:0%
+terms you might think about trying to
+add to higher order terms I would argue
+
+ align:start position:0%
+add to higher order terms I would argue
+ 
+
+ align:start position:0%
+add to higher order terms I would argue
+if this is the material type it makes no
+
+ align:start position:0%
+if this is the material type it makes no
+ 
+
+ align:start position:0%
+if this is the material type it makes no
+sense to add that term I wouldn't do
+
+ align:start position:0%
+sense to add that term I wouldn't do
+ 
+
+ align:start position:0%
+sense to add that term I wouldn't do
+that that would be bad but if this is
+
+ align:start position:0%
+that that would be bad but if this is
+ 
+
+ align:start position:0%
+that that would be bad but if this is
+associated with the punch depth then I
+
+ align:start position:0%
+associated with the punch depth then I
+ 
+
+ align:start position:0%
+associated with the punch depth then I
+think it does make sense to add the
+
+ align:start position:0%
+think it does make sense to add the
+ 
+
+ align:start position:0%
+think it does make sense to add the
+hypothesis of that and then you check
+
+ align:start position:0%
+hypothesis of that and then you check
+ 
+
+ align:start position:0%
+hypothesis of that and then you check
+for deviation at one or more of those of
+
+ align:start position:0%
+for deviation at one or more of those of
+ 
+
+ align:start position:0%
+for deviation at one or more of those of
+those points and the basic question is
+
+ align:start position:0%
+those points and the basic question is
+ 
+
+ align:start position:0%
+those points and the basic question is
+is asking whether you know beta 2 2 is
+
+ align:start position:0%
+is asking whether you know beta 2 2 is
+ 
+
+ align:start position:0%
+is asking whether you know beta 2 2 is
+equal to 0 or not is it is the effect
+
+ align:start position:0%
+equal to 0 or not is it is the effect
+ 
+
+ align:start position:0%
+equal to 0 or not is it is the effect
+due to that aviation possibly the same
+
+ align:start position:0%
+due to that aviation possibly the same
+ 
+
+ align:start position:0%
+due to that aviation possibly the same
+as noise or not so we can go through and
+
+ align:start position:0%
+as noise or not so we can go through and
+ 
+
+ align:start position:0%
+as noise or not so we can go through and
+do that here's a simple a simple test
+
+ align:start position:0%
+do that here's a simple a simple test
+ 
+
+ align:start position:0%
+do that here's a simple a simple test
+simple example and this is kind of
+
+ align:start position:0%
+simple example and this is kind of
+ 
+
+ align:start position:0%
+simple example and this is kind of
+aggregating what we saw going back and
+
+ align:start position:0%
+aggregating what we saw going back and
+ 
+
+ align:start position:0%
+aggregating what we saw going back and
+in fact some of the earlier can things
+
+ align:start position:0%
+in fact some of the earlier can things
+ 
+
+ align:start position:0%
+in fact some of the earlier can things
+we talked about if I don't have
+
+ align:start position:0%
+we talked about if I don't have
+ 
+
+ align:start position:0%
+we talked about if I don't have
+replicate data what can I do if I just
+
+ align:start position:0%
+replicate data what can I do if I just
+ 
+
+ align:start position:0%
+replicate data what can I do if I just
+do my full factorial for corner point
+
+ align:start position:0%
+do my full factorial for corner point
+ 
+
+ align:start position:0%
+do my full factorial for corner point
+test no replicates and I used the full
+
+ align:start position:0%
+test no replicates and I used the full
+ 
+
+ align:start position:0%
+test no replicates and I used the full
+linear model with interactions
+
+ align:start position:0%
+linear model with interactions
+ 
+
+ align:start position:0%
+linear model with interactions
+I cannot test for significance and I
+
+ align:start position:0%
+I cannot test for significance and I
+ 
+
+ align:start position:0%
+I cannot test for significance and I
+cannot test for lack of fit that's the
+
+ align:start position:0%
+cannot test for lack of fit that's the
+ 
+
+ align:start position:0%
+cannot test for lack of fit that's the
+most bare-bones situation you've got
+
+ align:start position:0%
+most bare-bones situation you've got
+ 
+
+ align:start position:0%
+most bare-bones situation you've got
+I've got a perfect fit but you better be
+
+ align:start position:0%
+I've got a perfect fit but you better be
+ 
+
+ align:start position:0%
+I've got a perfect fit but you better be
+awfully sure that there's not noise
+
+ align:start position:0%
+awfully sure that there's not noise
+ 
+
+ align:start position:0%
+awfully sure that there's not noise
+going on in your model or in your system
+
+ align:start position:0%
+going on in your model or in your system
+ 
+
+ align:start position:0%
+going on in your model or in your system
+so I can even without replicating my
+
+ align:start position:0%
+so I can even without replicating my
+ 
+
+ align:start position:0%
+so I can even without replicating my
+corner points I can still step back and
+
+ align:start position:0%
+corner points I can still step back and
+ 
+
+ align:start position:0%
+corner points I can still step back and
+ask the question about lack of fit by
+
+ align:start position:0%
+ask the question about lack of fit by
+ 
+
+ align:start position:0%
+ask the question about lack of fit by
+adding center points
+
+ align:start position:0%
+adding center points
+ 
+
+ align:start position:0%
+adding center points
+but if I just add one center point one
+
+ align:start position:0%
+but if I just add one center point one
+ 
+
+ align:start position:0%
+but if I just add one center point one
+replicate at the center point
+
+ align:start position:0%
+replicate at the center point
+ 
+
+ align:start position:0%
+replicate at the center point
+can I really ask the question about
+
+ align:start position:0%
+can I really ask the question about
+ 
+
+ align:start position:0%
+can I really ask the question about
+significance of the quadratic term no I
+
+ align:start position:0%
+significance of the quadratic term no I
+ 
+
+ align:start position:0%
+significance of the quadratic term no I
+would be able to perfectly fit the
+
+ align:start position:0%
+would be able to perfectly fit the
+ 
+
+ align:start position:0%
+would be able to perfectly fit the
+quadratic term with that one extra data
+
+ align:start position:0%
+quadratic term with that one extra data
+ 
+
+ align:start position:0%
+quadratic term with that one extra data
+point one extra model coefficient so you
+
+ align:start position:0%
+point one extra model coefficient so you
+ 
+
+ align:start position:0%
+point one extra model coefficient so you
+have to have replicates somewhere in the
+
+ align:start position:0%
+have to have replicates somewhere in the
+ 
+
+ align:start position:0%
+have to have replicates somewhere in the
+system and one typical approach is maybe
+
+ align:start position:0%
+system and one typical approach is maybe
+ 
+
+ align:start position:0%
+system and one typical approach is maybe
+I don't want to have ten replicates at
+
+ align:start position:0%
+I don't want to have ten replicates at
+ 
+
+ align:start position:0%
+I don't want to have ten replicates at
+each of my you know corner points I'm
+
+ align:start position:0%
+each of my you know corner points I'm
+ 
+
+ align:start position:0%
+each of my you know corner points I'm
+just gonna add replicates at my center
+
+ align:start position:0%
+just gonna add replicates at my center
+ 
+
+ align:start position:0%
+just gonna add replicates at my center
+point so now with the addition of center
+
+ align:start position:0%
+point so now with the addition of center
+ 
+
+ align:start position:0%
+point so now with the addition of center
+points to potentially check for
+
+ align:start position:0%
+points to potentially check for
+ 
+
+ align:start position:0%
+points to potentially check for
+curvature and replicates I've got an
+
+ align:start position:0%
+curvature and replicates I've got an
+ 
+
+ align:start position:0%
+curvature and replicates I've got an
+estimate of random or a replica noise
+
+ align:start position:0%
+estimate of random or a replica noise
+ 
+
+ align:start position:0%
+estimate of random or a replica noise
+and deviation from the linear so
+
+ align:start position:0%
+and deviation from the linear so
+ 
+
+ align:start position:0%
+and deviation from the linear so
+together by adding replicates at the
+
+ align:start position:0%
+together by adding replicates at the
+ 
+
+ align:start position:0%
+together by adding replicates at the
+center point you get a lot of power so
+
+ align:start position:0%
+center point you get a lot of power so
+ 
+
+ align:start position:0%
+center point you get a lot of power so
+then you can use the ANOVA approach and
+
+ align:start position:0%
+then you can use the ANOVA approach and
+ 
+
+ align:start position:0%
+then you can use the ANOVA approach and
+this is just working through and saying
+
+ align:start position:0%
+this is just working through and saying
+ 
+
+ align:start position:0%
+this is just working through and saying
+you know I estimate the quadratic term
+
+ align:start position:0%
+you know I estimate the quadratic term
+ 
+
+ align:start position:0%
+you know I estimate the quadratic term
+or the deviation and sum of squared
+
+ align:start position:0%
+or the deviation and sum of squared
+ 
+
+ align:start position:0%
+or the deviation and sum of squared
+deviations from that form an estimate of
+
+ align:start position:0%
+deviations from that form an estimate of
+ 
+
+ align:start position:0%
+deviations from that form an estimate of
+the variance because of that and compare
+
+ align:start position:0%
+the variance because of that and compare
+ 
+
+ align:start position:0%
+the variance because of that and compare
+that to the replication error so I can
+
+ align:start position:0%
+that to the replication error so I can
+ 
+
+ align:start position:0%
+that to the replication error so I can
+say here's just kind of working that out
+
+ align:start position:0%
+say here's just kind of working that out
+ 
+
+ align:start position:0%
+say here's just kind of working that out
+for our example where I've got the
+
+ align:start position:0%
+for our example where I've got the
+ 
+
+ align:start position:0%
+for our example where I've got the
+average of my outputs from the linear
+
+ align:start position:0%
+average of my outputs from the linear
+ 
+
+ align:start position:0%
+average of my outputs from the linear
+model the average at my replicate if my
+
+ align:start position:0%
+model the average at my replicate if my
+ 
+
+ align:start position:0%
+model the average at my replicate if my
+overall grand average is a little
+
+ align:start position:0%
+overall grand average is a little
+ 
+
+ align:start position:0%
+overall grand average is a little
+different than the average coming from
+
+ align:start position:0%
+different than the average coming from
+ 
+
+ align:start position:0%
+different than the average coming from
+my center point replicates that's the
+
+ align:start position:0%
+my center point replicates that's the
+ 
+
+ align:start position:0%
+my center point replicates that's the
+deviation due to the hypothesized
+
+ align:start position:0%
+deviation due to the hypothesized
+ 
+
+ align:start position:0%
+deviation due to the hypothesized
+quadratic term I can form the variance
+
+ align:start position:0%
+quadratic term I can form the variance
+ 
+
+ align:start position:0%
+quadratic term I can form the variance
+of that and then compare that to my
+
+ align:start position:0%
+of that and then compare that to my
+ 
+
+ align:start position:0%
+of that and then compare that to my
+underlying estimate okay and then this
+
+ align:start position:0%
+underlying estimate okay and then this
+ 
+
+ align:start position:0%
+underlying estimate okay and then this
+example I'll let you work through this
+
+ align:start position:0%
+example I'll let you work through this
+ 
+
+ align:start position:0%
+example I'll let you work through this
+is just doing that for a simple run
+
+ align:start position:0%
+is just doing that for a simple run
+ 
+
+ align:start position:0%
+is just doing that for a simple run
+where again I have just one run at each
+
+ align:start position:0%
+where again I have just one run at each
+ 
+
+ align:start position:0%
+where again I have just one run at each
+of the four corner points this is a
+
+ align:start position:0%
+of the four corner points this is a
+ 
+
+ align:start position:0%
+of the four corner points this is a
+different data set by the way this is
+
+ align:start position:0%
+different data set by the way this is
+ 
+
+ align:start position:0%
+different data set by the way this is
+not the break forming anymore and then
+
+ align:start position:0%
+not the break forming anymore and then
+ 
+
+ align:start position:0%
+not the break forming anymore and then
+I've got five replicates here at the
+
+ align:start position:0%
+I've got five replicates here at the
+ 
+
+ align:start position:0%
+I've got five replicates here at the
+center point question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so we are making the assumption here
+
+ align:start position:0%
+yes so we are making the assumption here
+ 
+
+ align:start position:0%
+yes so we are making the assumption here
+and it's the same one we've made pretty
+
+ align:start position:0%
+and it's the same one we've made pretty
+ 
+
+ align:start position:0%
+and it's the same one we've made pretty
+much in most ANOVA analyses that the
+
+ align:start position:0%
+much in most ANOVA analyses that the
+ 
+
+ align:start position:0%
+much in most ANOVA analyses that the
+variance is the same at all
+
+ align:start position:0%
+variance is the same at all
+ 
+
+ align:start position:0%
+variance is the same at all
+run points in other words we have the N
+
+ align:start position:0%
+run points in other words we have the N
+ 
+
+ align:start position:0%
+run points in other words we have the N
+0 Sigma squared assumption where Sigma
+
+ align:start position:0%
+0 Sigma squared assumption where Sigma
+ 
+
+ align:start position:0%
+0 Sigma squared assumption where Sigma
+squared is operative at the center point
+
+ align:start position:0%
+squared is operative at the center point
+ 
+
+ align:start position:0%
+squared is operative at the center point
+as well as all the corner points so this
+
+ align:start position:0%
+as well as all the corner points so this
+ 
+
+ align:start position:0%
+as well as all the corner points so this
+is a neat example where again we're
+
+ align:start position:0%
+is a neat example where again we're
+ 
+
+ align:start position:0%
+is a neat example where again we're
+trying to estimate main effects perhaps
+
+ align:start position:0%
+trying to estimate main effects perhaps
+ 
+
+ align:start position:0%
+trying to estimate main effects perhaps
+interaction effects we've got an a/b
+
+ align:start position:0%
+interaction effects we've got an a/b
+ 
+
+ align:start position:0%
+interaction effects we've got an a/b
+interaction column here now I've also
+
+ align:start position:0%
+interaction column here now I've also
+ 
+
+ align:start position:0%
+interaction column here now I've also
+got it so just using the corner points
+
+ align:start position:0%
+got it so just using the corner points
+ 
+
+ align:start position:0%
+got it so just using the corner points
+we can fit fit a model we can ask the
+
+ align:start position:0%
+we can fit fit a model we can ask the
+ 
+
+ align:start position:0%
+we can fit fit a model we can ask the
+ANOVA question on significance of that
+
+ align:start position:0%
+ANOVA question on significance of that
+ 
+
+ align:start position:0%
+ANOVA question on significance of that
+but I can also form the sum of squares
+
+ align:start position:0%
+but I can also form the sum of squares
+ 
+
+ align:start position:0%
+but I can also form the sum of squares
+due to this quadratic term and use the
+
+ align:start position:0%
+due to this quadratic term and use the
+ 
+
+ align:start position:0%
+due to this quadratic term and use the
+replicate information there to be able
+
+ align:start position:0%
+replicate information there to be able
+ 
+
+ align:start position:0%
+replicate information there to be able
+to form an estimate of the overall
+
+ align:start position:0%
+to form an estimate of the overall
+ 
+
+ align:start position:0%
+to form an estimate of the overall
+process variance and what that lets me
+
+ align:start position:0%
+process variance and what that lets me
+ 
+
+ align:start position:0%
+process variance and what that lets me
+do is form the F test line in here for
+
+ align:start position:0%
+do is form the F test line in here for
+ 
+
+ align:start position:0%
+do is form the F test line in here for
+the quadratic term in addition to the
+
+ align:start position:0%
+the quadratic term in addition to the
+ 
+
+ align:start position:0%
+the quadratic term in addition to the
+a/b and the interaction term and in this
+
+ align:start position:0%
+a/b and the interaction term and in this
+ 
+
+ align:start position:0%
+a/b and the interaction term and in this
+case when I look at that F ratio the sum
+
+ align:start position:0%
+case when I look at that F ratio the sum
+ 
+
+ align:start position:0%
+case when I look at that F ratio the sum
+of squared deviations from the quadratic
+
+ align:start position:0%
+of squared deviations from the quadratic
+ 
+
+ align:start position:0%
+of squared deviations from the quadratic
+estimate versus the linear estimate
+
+ align:start position:0%
+estimate versus the linear estimate
+ 
+
+ align:start position:0%
+estimate versus the linear estimate
+compared to my estimate of noise in the
+
+ align:start position:0%
+compared to my estimate of noise in the
+ 
+
+ align:start position:0%
+compared to my estimate of noise in the
+system I get a very small F well below
+
+ align:start position:0%
+system I get a very small F well below
+ 
+
+ align:start position:0%
+system I get a very small F well below
+the critical and therefore I conclude
+
+ align:start position:0%
+the critical and therefore I conclude
+ 
+
+ align:start position:0%
+the critical and therefore I conclude
+there is no evidence of lack of fit I do
+
+ align:start position:0%
+there is no evidence of lack of fit I do
+ 
+
+ align:start position:0%
+there is no evidence of lack of fit I do
+not include the quadratic term and I
+
+ align:start position:0%
+not include the quadratic term and I
+ 
+
+ align:start position:0%
+not include the quadratic term and I
+stick with the linear model now would
+
+ align:start position:0%
+stick with the linear model now would
+ 
+
+ align:start position:0%
+stick with the linear model now would
+you keep the interaction term same thing
+
+ align:start position:0%
+you keep the interaction term same thing
+ 
+
+ align:start position:0%
+you keep the interaction term same thing
+it's also not significant would you keep
+
+ align:start position:0%
+it's also not significant would you keep
+ 
+
+ align:start position:0%
+it's also not significant would you keep
+the to main effect terms
+
+ align:start position:0%
+the to main effect terms
+ 
+
+ align:start position:0%
+the to main effect terms
+yeah sure those are above the above the
+
+ align:start position:0%
+yeah sure those are above the above the
+ 
+
+ align:start position:0%
+yeah sure those are above the above the
+F naught so I'm happy with those so this
+
+ align:start position:0%
+F naught so I'm happy with those so this
+ 
+
+ align:start position:0%
+F naught so I'm happy with those so this
+is a nice simple data set additive
+
+ align:start position:0%
+is a nice simple data set additive
+ 
+
+ align:start position:0%
+is a nice simple data set additive
+effects no interaction it's kind of the
+
+ align:start position:0%
+effects no interaction it's kind of the
+ 
+
+ align:start position:0%
+effects no interaction it's kind of the
+best for ultimately using the model in a
+
+ align:start position:0%
+best for ultimately using the model in a
+ 
+
+ align:start position:0%
+best for ultimately using the model in a
+in a control kind of setting because I
+
+ align:start position:0%
+in a control kind of setting because I
+ 
+
+ align:start position:0%
+in a control kind of setting because I
+can presumably change and
+
+ align:start position:0%
+can presumably change and
+ 
+
+ align:start position:0%
+can presumably change and
+independently and try to get the output
+
+ align:start position:0%
+independently and try to get the output
+ 
+
+ align:start position:0%
+independently and try to get the output
+that I want I mean you're always you
+
+ align:start position:0%
+that I want I mean you're always you
+ 
+
+ align:start position:0%
+that I want I mean you're always you
+always got to be a little careful and
+
+ align:start position:0%
+always got to be a little careful and
+ 
+
+ align:start position:0%
+always got to be a little careful and
+use exactly that knowledge you know this
+
+ align:start position:0%
+use exactly that knowledge you know this
+ 
+
+ align:start position:0%
+use exactly that knowledge you know this
+was a this was a 95% confidence and if I
+
+ align:start position:0%
+was a this was a 95% confidence and if I
+ 
+
+ align:start position:0%
+was a this was a 95% confidence and if I
+was anywhere near the boundary I might
+
+ align:start position:0%
+was anywhere near the boundary I might
+ 
+
+ align:start position:0%
+was anywhere near the boundary I might
+say well might might I want to include
+
+ align:start position:0%
+say well might might I want to include
+ 
+
+ align:start position:0%
+say well might might I want to include
+that if I wanted to just be 90 percent
+
+ align:start position:0%
+that if I wanted to just be 90 percent
+ 
+
+ align:start position:0%
+that if I wanted to just be 90 percent
+confidence because that's probably
+
+ align:start position:0%
+confidence because that's probably
+ 
+
+ align:start position:0%
+confidence because that's probably
+suggesting that that model term really
+
+ align:start position:0%
+suggesting that that model term really
+ 
+
+ align:start position:0%
+suggesting that that model term really
+does have an effect in this case that
+
+ align:start position:0%
+does have an effect in this case that
+ 
+
+ align:start position:0%
+does have an effect in this case that
+cutoff you know those are very obvious
+
+ align:start position:0%
+cutoff you know those are very obvious
+ 
+
+ align:start position:0%
+cutoff you know those are very obvious
+but in other subtle cases you actually
+
+ align:start position:0%
+but in other subtle cases you actually
+ 
+
+ align:start position:0%
+but in other subtle cases you actually
+have to use some some intuition and
+
+ align:start position:0%
+have to use some some intuition and
+ 
+
+ align:start position:0%
+have to use some some intuition and
+knowledge one one one part of that does
+
+ align:start position:0%
+knowledge one one one part of that does
+ 
+
+ align:start position:0%
+knowledge one one one part of that does
+look at and maybe you're getting at this
+
+ align:start position:0%
+look at and maybe you're getting at this
+ 
+
+ align:start position:0%
+look at and maybe you're getting at this
+a little bit with sensitivity there's
+
+ align:start position:0%
+a little bit with sensitivity there's
+ 
+
+ align:start position:0%
+a little bit with sensitivity there's
+another sensitivity analysis you can do
+
+ align:start position:0%
+another sensitivity analysis you can do
+ 
+
+ align:start position:0%
+another sensitivity analysis you can do
+which which has to do with not the not
+
+ align:start position:0%
+which which has to do with not the not
+ 
+
+ align:start position:0%
+which which has to do with not the not
+tweaking the alpha level the
+
+ align:start position:0%
+tweaking the alpha level the
+ 
+
+ align:start position:0%
+tweaking the alpha level the
+significance level you can tweak that a
+
+ align:start position:0%
+significance level you can tweak that a
+ 
+
+ align:start position:0%
+significance level you can tweak that a
+little bit but you also might ask the
+
+ align:start position:0%
+little bit but you also might ask the
+ 
+
+ align:start position:0%
+little bit but you also might ask the
+question slightly differently about
+
+ align:start position:0%
+question slightly differently about
+ 
+
+ align:start position:0%
+question slightly differently about
+whether the model coefficient is real or
+
+ align:start position:0%
+whether the model coefficient is real or
+ 
+
+ align:start position:0%
+whether the model coefficient is real or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+that's a significance question you can
+
+ align:start position:0%
+that's a significance question you can
+ 
+
+ align:start position:0%
+that's a significance question you can
+also ask the question how big is the
+
+ align:start position:0%
+also ask the question how big is the
+ 
+
+ align:start position:0%
+also ask the question how big is the
+effect is it so big that I would want to
+
+ align:start position:0%
+effect is it so big that I would want to
+ 
+
+ align:start position:0%
+effect is it so big that I would want to
+include it in the model or it's real but
+
+ align:start position:0%
+include it in the model or it's real but
+ 
+
+ align:start position:0%
+include it in the model or it's real but
+it's so tiny compared to my other
+
+ align:start position:0%
+it's so tiny compared to my other
+ 
+
+ align:start position:0%
+it's so tiny compared to my other
+effects that I'm going to neglect it so
+
+ align:start position:0%
+effects that I'm going to neglect it so
+ 
+
+ align:start position:0%
+effects that I'm going to neglect it so
+there is this difference between
+
+ align:start position:0%
+there is this difference between
+ 
+
+ align:start position:0%
+there is this difference between
+significant real and important or not
+
+ align:start position:0%
+significant real and important or not
+ 
+
+ align:start position:0%
+significant real and important or not
+and so that's where your knowledge of
+
+ align:start position:0%
+and so that's where your knowledge of
+ 
+
+ align:start position:0%
+and so that's where your knowledge of
+the process also comes into play and
+
+ align:start position:0%
+the process also comes into play and
+ 
+
+ align:start position:0%
+the process also comes into play and
+whether you might want to include or
+
+ align:start position:0%
+whether you might want to include or
+ 
+
+ align:start position:0%
+whether you might want to include or
+drop model terms okay I think what we'll
+
+ align:start position:0%
+drop model terms okay I think what we'll
+ 
+
+ align:start position:0%
+drop model terms okay I think what we'll
+do is although right actually only go
+
+ align:start position:0%
+do is although right actually only go
+ 
+
+ align:start position:0%
+do is although right actually only go
+for about five more minutes and give you
+
+ align:start position:0%
+for about five more minutes and give you
+ 
+
+ align:start position:0%
+for about five more minutes and give you
+a little bit of a glimpse of blocks and
+
+ align:start position:0%
+a little bit of a glimpse of blocks and
+ 
+
+ align:start position:0%
+a little bit of a glimpse of blocks and
+co-found confounding talk about these
+
+ align:start position:0%
+co-found confounding talk about these
+ 
+
+ align:start position:0%
+co-found confounding talk about these
+nuisance factors a little bit and then
+
+ align:start position:0%
+nuisance factors a little bit and then
+ 
+
+ align:start position:0%
+nuisance factors a little bit and then
+next time we'll come back and dive in
+
+ align:start position:0%
+next time we'll come back and dive in
+ 
+
+ align:start position:0%
+next time we'll come back and dive in
+more on
+
+ align:start position:0%
+more on
+ 
+
+ align:start position:0%
+more on
+fractional factorial designs because
+
+ align:start position:0%
+fractional factorial designs because
+ 
+
+ align:start position:0%
+fractional factorial designs because
+there are some additional design issues
+
+ align:start position:0%
+there are some additional design issues
+ 
+
+ align:start position:0%
+there are some additional design issues
+I've only alluded to in experimental
+
+ align:start position:0%
+I've only alluded to in experimental
+ 
+
+ align:start position:0%
+I've only alluded to in experimental
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+so far we've really just done full
+
+ align:start position:0%
+so far we've really just done full
+ 
+
+ align:start position:0%
+so far we've really just done full
+factorial these corner points and then
+
+ align:start position:0%
+factorial these corner points and then
+ 
+
+ align:start position:0%
+factorial these corner points and then
+also the idea of Centrepointe stacked
+
+ align:start position:0%
+also the idea of Centrepointe stacked
+ 
+
+ align:start position:0%
+also the idea of Centrepointe stacked
+asked the question about curvature but
+
+ align:start position:0%
+asked the question about curvature but
+ 
+
+ align:start position:0%
+asked the question about curvature but
+there may be other factors you know
+
+ align:start position:0%
+there may be other factors you know
+ 
+
+ align:start position:0%
+there may be other factors you know
+maybe there was the temperature in our
+
+ align:start position:0%
+maybe there was the temperature in our
+ 
+
+ align:start position:0%
+maybe there was the temperature in our
+break forming tool that we didn't really
+
+ align:start position:0%
+break forming tool that we didn't really
+ 
+
+ align:start position:0%
+break forming tool that we didn't really
+want to do a design experiment on we're
+
+ align:start position:0%
+want to do a design experiment on we're
+ 
+
+ align:start position:0%
+want to do a design experiment on we're
+not really sure it's important or not
+
+ align:start position:0%
+not really sure it's important or not
+ 
+
+ align:start position:0%
+not really sure it's important or not
+but maybe it's out there there may be
+
+ align:start position:0%
+but maybe it's out there there may be
+ 
+
+ align:start position:0%
+but maybe it's out there there may be
+all these other new synthetic nuisance
+
+ align:start position:0%
+all these other new synthetic nuisance
+ 
+
+ align:start position:0%
+all these other new synthetic nuisance
+factors or nuisance effects they may
+
+ align:start position:0%
+factors or nuisance effects they may
+ 
+
+ align:start position:0%
+factors or nuisance effects they may
+affect the output but I didn't really
+
+ align:start position:0%
+affect the output but I didn't really
+ 
+
+ align:start position:0%
+affect the output but I didn't really
+want to include the effect in the model
+
+ align:start position:0%
+want to include the effect in the model
+ 
+
+ align:start position:0%
+want to include the effect in the model
+and I rather suppress them and for sure
+
+ align:start position:0%
+and I rather suppress them and for sure
+ 
+
+ align:start position:0%
+and I rather suppress them and for sure
+suppress them from making from me making
+
+ align:start position:0%
+suppress them from making from me making
+ 
+
+ align:start position:0%
+suppress them from making from me making
+a mistake and and confusing the effect
+
+ align:start position:0%
+a mistake and and confusing the effect
+ 
+
+ align:start position:0%
+a mistake and and confusing the effect
+of temperature with say the effect of
+
+ align:start position:0%
+of temperature with say the effect of
+ 
+
+ align:start position:0%
+of temperature with say the effect of
+which metal I use so what are the
+
+ align:start position:0%
+which metal I use so what are the
+ 
+
+ align:start position:0%
+which metal I use so what are the
+approaches you can do well in many cases
+
+ align:start position:0%
+approaches you can do well in many cases
+ 
+
+ align:start position:0%
+approaches you can do well in many cases
+I may not be able to run the whole
+
+ align:start position:0%
+I may not be able to run the whole
+ 
+
+ align:start position:0%
+I may not be able to run the whole
+experiment holding that factor constant
+
+ align:start position:0%
+experiment holding that factor constant
+ 
+
+ align:start position:0%
+experiment holding that factor constant
+in general you would really want to make
+
+ align:start position:0%
+in general you would really want to make
+ 
+
+ align:start position:0%
+in general you would really want to make
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+well if temperature affects things I
+
+ align:start position:0%
+well if temperature affects things I
+ 
+
+ align:start position:0%
+well if temperature affects things I
+want to hold the temperature of the tool
+
+ align:start position:0%
+want to hold the temperature of the tool
+ 
+
+ align:start position:0%
+want to hold the temperature of the tool
+as constant as I can try to keep
+
+ align:start position:0%
+as constant as I can try to keep
+ 
+
+ align:start position:0%
+as constant as I can try to keep
+everything else as constant as possible
+
+ align:start position:0%
+everything else as constant as possible
+ 
+
+ align:start position:0%
+everything else as constant as possible
+time can often be an important
+
+ align:start position:0%
+time can often be an important
+ 
+
+ align:start position:0%
+time can often be an important
+substitute for nuisance effects right
+
+ align:start position:0%
+substitute for nuisance effects right
+ 
+
+ align:start position:0%
+substitute for nuisance effects right
+time is going on and other things may be
+
+ align:start position:0%
+time is going on and other things may be
+ 
+
+ align:start position:0%
+time is going on and other things may be
+changing so you can't entirely suppress
+
+ align:start position:0%
+changing so you can't entirely suppress
+ 
+
+ align:start position:0%
+changing so you can't entirely suppress
+potentially all these other nuisance
+
+ align:start position:0%
+potentially all these other nuisance
+ 
+
+ align:start position:0%
+potentially all these other nuisance
+effects but in general you want to keep
+
+ align:start position:0%
+effects but in general you want to keep
+ 
+
+ align:start position:0%
+effects but in general you want to keep
+everything else constant but some cases
+
+ align:start position:0%
+everything else constant but some cases
+ 
+
+ align:start position:0%
+everything else constant but some cases
+you may not be able to hold everything
+
+ align:start position:0%
+you may not be able to hold everything
+ 
+
+ align:start position:0%
+you may not be able to hold everything
+else constant and if you know some of
+
+ align:start position:0%
+else constant and if you know some of
+ 
+
+ align:start position:0%
+else constant and if you know some of
+these factors like temperature perhaps
+
+ align:start position:0%
+these factors like temperature perhaps
+ 
+
+ align:start position:0%
+these factors like temperature perhaps
+you know throughout the day varies in my
+
+ align:start position:0%
+you know throughout the day varies in my
+ 
+
+ align:start position:0%
+you know throughout the day varies in my
+machine shop say then it may be
+
+ align:start position:0%
+machine shop say then it may be
+ 
+
+ align:start position:0%
+machine shop say then it may be
+uncontrollable but it's a known factor
+
+ align:start position:0%
+uncontrollable but it's a known factor
+ 
+
+ align:start position:0%
+uncontrollable but it's a known factor
+in which case I might want to think
+
+ align:start position:0%
+in which case I might want to think
+ 
+
+ align:start position:0%
+in which case I might want to think
+about that and randomize the order of my
+
+ align:start position:0%
+about that and randomize the order of my
+ 
+
+ align:start position:0%
+about that and randomize the order of my
+runs against that so I equally includes
+
+ align:start position:0%
+runs against that so I equally includes
+ 
+
+ align:start position:0%
+runs against that so I equally includes
+some high levels of that nuisance factor
+
+ align:start position:0%
+some high levels of that nuisance factor
+ 
+
+ align:start position:0%
+some high levels of that nuisance factor
+and some low levels of that nuisance
+
+ align:start position:0%
+and some low levels of that nuisance
+ 
+
+ align:start position:0%
+and some low levels of that nuisance
+in each of my other settings I try as
+
+ align:start position:0%
+in each of my other settings I try as
+ 
+
+ align:start position:0%
+in each of my other settings I try as
+much as I can to randomize basically
+
+ align:start position:0%
+much as I can to randomize basically
+ 
+
+ align:start position:0%
+much as I can to randomize basically
+convert that effect from a systemic
+
+ align:start position:0%
+convert that effect from a systemic
+ 
+
+ align:start position:0%
+convert that effect from a systemic
+effect into a random noise effect okay
+
+ align:start position:0%
+effect into a random noise effect okay
+ 
+
+ align:start position:0%
+effect into a random noise effect okay
+in many cases if I can actually pick the
+
+ align:start position:0%
+in many cases if I can actually pick the
+ 
+
+ align:start position:0%
+in many cases if I can actually pick the
+level of temperature it's known and
+
+ align:start position:0%
+level of temperature it's known and
+ 
+
+ align:start position:0%
+level of temperature it's known and
+controllable you can actually design
+
+ align:start position:0%
+controllable you can actually design
+ 
+
+ align:start position:0%
+controllable you can actually design
+your experiment separate out the data
+
+ align:start position:0%
+your experiment separate out the data
+ 
+
+ align:start position:0%
+your experiment separate out the data
+into blocks where in each of the two
+
+ align:start position:0%
+into blocks where in each of the two
+ 
+
+ align:start position:0%
+into blocks where in each of the two
+blocks the nuisance factor is held
+
+ align:start position:0%
+blocks the nuisance factor is held
+ 
+
+ align:start position:0%
+blocks the nuisance factor is held
+constant and what we have the
+
+ align:start position:0%
+constant and what we have the
+ 
+
+ align:start position:0%
+constant and what we have the
+opportunity to do is transform the
+
+ align:start position:0%
+opportunity to do is transform the
+ 
+
+ align:start position:0%
+opportunity to do is transform the
+effect of that nuisance factor into what
+
+ align:start position:0%
+effect of that nuisance factor into what
+ 
+
+ align:start position:0%
+effect of that nuisance factor into what
+would only be a very higher-order
+
+ align:start position:0%
+would only be a very higher-order
+ 
+
+ align:start position:0%
+would only be a very higher-order
+interaction term in our model okay and
+
+ align:start position:0%
+interaction term in our model okay and
+ 
+
+ align:start position:0%
+interaction term in our model okay and
+that's the intuition I want to just give
+
+ align:start position:0%
+that's the intuition I want to just give
+ 
+
+ align:start position:0%
+that's the intuition I want to just give
+you a little bit of a glimpse for and
+
+ align:start position:0%
+you a little bit of a glimpse for and
+ 
+
+ align:start position:0%
+you a little bit of a glimpse for and
+then we'll talk about next time first
+
+ align:start position:0%
+then we'll talk about next time first
+ 
+
+ align:start position:0%
+then we'll talk about next time first
+off if if the thing is controllable we
+
+ align:start position:0%
+off if if the thing is controllable we
+ 
+
+ align:start position:0%
+off if if the thing is controllable we
+would just want to say replicate and
+
+ align:start position:0%
+would just want to say replicate and
+ 
+
+ align:start position:0%
+would just want to say replicate and
+randomize here's an example where we're
+
+ align:start position:0%
+randomize here's an example where we're
+ 
+
+ align:start position:0%
+randomize here's an example where we're
+looking for the hardness of four
+
+ align:start position:0%
+looking for the hardness of four
+ 
+
+ align:start position:0%
+looking for the hardness of four
+different test samples but I'm doing it
+
+ align:start position:0%
+different test samples but I'm doing it
+ 
+
+ align:start position:0%
+different test samples but I'm doing it
+with an indentation Tet test but I've
+
+ align:start position:0%
+with an indentation Tet test but I've
+ 
+
+ align:start position:0%
+with an indentation Tet test but I've
+got four different tips that I'm using
+
+ align:start position:0%
+got four different tips that I'm using
+ 
+
+ align:start position:0%
+got four different tips that I'm using
+for the indentation
+
+ align:start position:0%
+for the indentation
+ 
+
+ align:start position:0%
+for the indentation
+I don't really won't care about the tip
+
+ align:start position:0%
+I don't really won't care about the tip
+ 
+
+ align:start position:0%
+I don't really won't care about the tip
+factor but I'm worried that it might
+
+ align:start position:0%
+factor but I'm worried that it might
+ 
+
+ align:start position:0%
+factor but I'm worried that it might
+might perturb my estimate of the
+
+ align:start position:0%
+might perturb my estimate of the
+ 
+
+ align:start position:0%
+might perturb my estimate of the
+hardness so you can first off basically
+
+ align:start position:0%
+hardness so you can first off basically
+ 
+
+ align:start position:0%
+hardness so you can first off basically
+think of it as I'm just gonna run with
+
+ align:start position:0%
+think of it as I'm just gonna run with
+ 
+
+ align:start position:0%
+think of it as I'm just gonna run with
+all four tips and take the average and
+
+ align:start position:0%
+all four tips and take the average and
+ 
+
+ align:start position:0%
+all four tips and take the average and
+that's my best average of our estimate
+
+ align:start position:0%
+that's my best average of our estimate
+ 
+
+ align:start position:0%
+that's my best average of our estimate
+of the hardness in the four cases so I'm
+
+ align:start position:0%
+of the hardness in the four cases so I'm
+ 
+
+ align:start position:0%
+of the hardness in the four cases so I'm
+just replicating around that nuisance
+
+ align:start position:0%
+just replicating around that nuisance
+ 
+
+ align:start position:0%
+just replicating around that nuisance
+factor not including it in the model
+
+ align:start position:0%
+factor not including it in the model
+ 
+
+ align:start position:0%
+factor not including it in the model
+explicitly but I'm randomizing or or
+
+ align:start position:0%
+explicitly but I'm randomizing or or
+ 
+
+ align:start position:0%
+explicitly but I'm randomizing or or
+replicating around it many cases you
+
+ align:start position:0%
+replicating around it many cases you
+ 
+
+ align:start position:0%
+replicating around it many cases you
+don't have the opportunity it's too
+
+ align:start position:0%
+don't have the opportunity it's too
+ 
+
+ align:start position:0%
+don't have the opportunity it's too
+expensive to do lots of replications and
+
+ align:start position:0%
+expensive to do lots of replications and
+ 
+
+ align:start position:0%
+expensive to do lots of replications and
+what what I want to do is arrange things
+
+ align:start position:0%
+what what I want to do is arrange things
+ 
+
+ align:start position:0%
+what what I want to do is arrange things
+so that if there is a nuisance factor it
+
+ align:start position:0%
+so that if there is a nuisance factor it
+ 
+
+ align:start position:0%
+so that if there is a nuisance factor it
+will have them
+
+ align:start position:0%
+will have them
+ 
+
+ align:start position:0%
+will have them
+least damaging effect on my model so
+
+ align:start position:0%
+least damaging effect on my model so
+ 
+
+ align:start position:0%
+least damaging effect on my model so
+here's my one little Intuit intuitive
+
+ align:start position:0%
+here's my one little Intuit intuitive
+ 
+
+ align:start position:0%
+here's my one little Intuit intuitive
+example suppose we've got this
+
+ align:start position:0%
+example suppose we've got this
+ 
+
+ align:start position:0%
+example suppose we've got this
+two-by-two design so I've got two
+
+ align:start position:0%
+two-by-two design so I've got two
+ 
+
+ align:start position:0%
+two-by-two design so I've got two
+factors two levels doing four runs but
+
+ align:start position:0%
+factors two levels doing four runs but
+ 
+
+ align:start position:0%
+factors two levels doing four runs but
+let's say I have to arrange it where I
+
+ align:start position:0%
+let's say I have to arrange it where I
+ 
+
+ align:start position:0%
+let's say I have to arrange it where I
+do two runs at low temperature and two
+
+ align:start position:0%
+do two runs at low temperature and two
+ 
+
+ align:start position:0%
+do two runs at low temperature and two
+runs at high temperature that's just I'm
+
+ align:start position:0%
+runs at high temperature that's just I'm
+ 
+
+ align:start position:0%
+runs at high temperature that's just I'm
+gonna have to do two runs in the morning
+
+ align:start position:0%
+gonna have to do two runs in the morning
+ 
+
+ align:start position:0%
+gonna have to do two runs in the morning
+two in the afternoon and during the day
+
+ align:start position:0%
+two in the afternoon and during the day
+ 
+
+ align:start position:0%
+two in the afternoon and during the day
+my machine shop heats up that's just the
+
+ align:start position:0%
+my machine shop heats up that's just the
+ 
+
+ align:start position:0%
+my machine shop heats up that's just the
+way it is I gotta live with it which two
+
+ align:start position:0%
+way it is I gotta live with it which two
+ 
+
+ align:start position:0%
+way it is I gotta live with it which two
+runs should I pick to do with the high
+
+ align:start position:0%
+runs should I pick to do with the high
+ 
+
+ align:start position:0%
+runs should I pick to do with the high
+temperature in which to run should I do
+
+ align:start position:0%
+temperature in which to run should I do
+ 
+
+ align:start position:0%
+temperature in which to run should I do
+at the low temperature suppose I did it
+
+ align:start position:0%
+at the low temperature suppose I did it
+ 
+
+ align:start position:0%
+at the low temperature suppose I did it
+like this where this was my low
+
+ align:start position:0%
+like this where this was my low
+ 
+
+ align:start position:0%
+like this where this was my low
+temperature and this was my high
+
+ align:start position:0%
+temperature and this was my high
+ 
+
+ align:start position:0%
+temperature and this was my high
+temperature any problem with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big problem with that if x2 has an
+
+ align:start position:0%
+big problem with that if x2 has an
+ 
+
+ align:start position:0%
+big problem with that if x2 has an
+effect I can't tell whether that's a
+
+ align:start position:0%
+effect I can't tell whether that's a
+ 
+
+ align:start position:0%
+effect I can't tell whether that's a
+temperature effect or an x2 effect
+
+ align:start position:0%
+temperature effect or an x2 effect
+ 
+
+ align:start position:0%
+temperature effect or an x2 effect
+because I did both of my x2 runs at the
+
+ align:start position:0%
+because I did both of my x2 runs at the
+ 
+
+ align:start position:0%
+because I did both of my x2 runs at the
+low temperature and both of my you know
+
+ align:start position:0%
+low temperature and both of my you know
+ 
+
+ align:start position:0%
+low temperature and both of my you know
+high values of x2 but the high
+
+ align:start position:0%
+high values of x2 but the high
+ 
+
+ align:start position:0%
+high values of x2 but the high
+temperature I don't know whether it's a
+
+ align:start position:0%
+temperature I don't know whether it's a
+ 
+
+ align:start position:0%
+temperature I don't know whether it's a
+temperature effect when I form that
+
+ align:start position:0%
+temperature effect when I form that
+ 
+
+ align:start position:0%
+temperature effect when I form that
+contrast or an x2 effect is there a
+
+ align:start position:0%
+contrast or an x2 effect is there a
+ 
+
+ align:start position:0%
+contrast or an x2 effect is there a
+better way to arrange or pick which two
+
+ align:start position:0%
+better way to arrange or pick which two
+ 
+
+ align:start position:0%
+better way to arrange or pick which two
+ones I want to do so that I don't get
+
+ align:start position:0%
+ones I want to do so that I don't get
+ 
+
+ align:start position:0%
+ones I want to do so that I don't get
+confused with the main effects in the
+
+ align:start position:0%
+confused with the main effects in the
+ 
+
+ align:start position:0%
+confused with the main effects in the
+experiment and the intuition here is yes
+
+ align:start position:0%
+experiment and the intuition here is yes
+ 
+
+ align:start position:0%
+experiment and the intuition here is yes
+there is a better approach what if I
+
+ align:start position:0%
+there is a better approach what if I
+ 
+
+ align:start position:0%
+there is a better approach what if I
+pick block one to run the one and a B
+
+ align:start position:0%
+pick block one to run the one and a B
+ 
+
+ align:start position:0%
+pick block one to run the one and a B
+combinations so what if I pick block one
+
+ align:start position:0%
+combinations so what if I pick block one
+ 
+
+ align:start position:0%
+combinations so what if I pick block one
+to run what I say the one in the a b1
+
+ align:start position:0%
+to run what I say the one in the a b1
+ 
+
+ align:start position:0%
+to run what I say the one in the a b1
+and a B notice what's nice about that
+
+ align:start position:0%
+and a B notice what's nice about that
+ 
+
+ align:start position:0%
+and a B notice what's nice about that
+the one in the ad so make that block one
+
+ align:start position:0%
+the one in the ad so make that block one
+ 
+
+ align:start position:0%
+the one in the ad so make that block one
+and make this block to notice that
+
+ align:start position:0%
+and make this block to notice that
+ 
+
+ align:start position:0%
+and make this block to notice that
+neither block is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponding to both high settings or
+
+ align:start position:0%
+corresponding to both high settings or
+ 
+
+ align:start position:0%
+corresponding to both high settings or
+both low settings for either factor when
+
+ align:start position:0%
+both low settings for either factor when
+ 
+
+ align:start position:0%
+both low settings for either factor when
+in fact the block is is actually lining
+
+ align:start position:0%
+in fact the block is is actually lining
+ 
+
+ align:start position:0%
+in fact the block is is actually lining
+up with is the x1x2 interaction factor
+
+ align:start position:0%
+up with is the x1x2 interaction factor
+ 
+
+ align:start position:0%
+up with is the x1x2 interaction factor
+so what we've done is said I'm going to
+
+ align:start position:0%
+so what we've done is said I'm going to
+ 
+
+ align:start position:0%
+so what we've done is said I'm going to
+I don't want to get confused about
+
+ align:start position:0%
+I don't want to get confused about
+ 
+
+ align:start position:0%
+I don't want to get confused about
+whether there's a main effect or this
+
+ align:start position:0%
+whether there's a main effect or this
+ 
+
+ align:start position:0%
+whether there's a main effect or this
+that's nasty nuisance factor is having
+
+ align:start position:0%
+that's nasty nuisance factor is having
+ 
+
+ align:start position:0%
+that's nasty nuisance factor is having
+an effect what I would am willing to do
+
+ align:start position:0%
+an effect what I would am willing to do
+ 
+
+ align:start position:0%
+an effect what I would am willing to do
+is be confused or confound between my
+
+ align:start position:0%
+is be confused or confound between my
+ 
+
+ align:start position:0%
+is be confused or confound between my
+block effect and my interaction effect I
+
+ align:start position:0%
+block effect and my interaction effect I
+ 
+
+ align:start position:0%
+block effect and my interaction effect I
+won't be able to tell if the interaction
+
+ align:start position:0%
+won't be able to tell if the interaction
+ 
+
+ align:start position:0%
+won't be able to tell if the interaction
+is real or not but that's okay I believe
+
+ align:start position:0%
+is real or not but that's okay I believe
+ 
+
+ align:start position:0%
+is real or not but that's okay I believe
+it's not and I'd rather mix in my my
+
+ align:start position:0%
+it's not and I'd rather mix in my my
+ 
+
+ align:start position:0%
+it's not and I'd rather mix in my my
+block factor so this gets to this idea
+
+ align:start position:0%
+block factor so this gets to this idea
+ 
+
+ align:start position:0%
+block factor so this gets to this idea
+of forming patterns or blocking in this
+
+ align:start position:0%
+of forming patterns or blocking in this
+ 
+
+ align:start position:0%
+of forming patterns or blocking in this
+case to confound so that I can detect
+
+ align:start position:0%
+case to confound so that I can detect
+ 
+
+ align:start position:0%
+case to confound so that I can detect
+some things and not others
+
+ align:start position:0%
+some things and not others
+ 
+
+ align:start position:0%
+some things and not others
+and we'll talk more about that next time
+
+ align:start position:0%
+and we'll talk more about that next time
+ 
+
+ align:start position:0%
+and we'll talk more about that next time
+talk a little bit more generally about
+
+ align:start position:0%
+talk a little bit more generally about
+ 
+
+ align:start position:0%
+talk a little bit more generally about
+confounding and this actually leads into
+
+ align:start position:0%
+confounding and this actually leads into
+ 
+
+ align:start position:0%
+confounding and this actually leads into
+the main idea of fractional factorial
+
+ align:start position:0%
+the main idea of fractional factorial
+ 
+
+ align:start position:0%
+the main idea of fractional factorial
+design where I may not want to pick all
+
+ align:start position:0%
+design where I may not want to pick all
+ 
+
+ align:start position:0%
+design where I may not want to pick all
+of my corner points I might subset some
+
+ align:start position:0%
+of my corner points I might subset some
+ 
+
+ align:start position:0%
+of my corner points I might subset some
+of them because I'm willing to be
+
+ align:start position:0%
+of them because I'm willing to be
+ 
+
+ align:start position:0%
+of them because I'm willing to be
+confused about whether there's a fourth
+
+ align:start position:0%
+confused about whether there's a fourth
+ 
+
+ align:start position:0%
+confused about whether there's a fourth
+order factor that's also the same
+
+ align:start position:0%
+order factor that's also the same
+ 
+
+ align:start position:0%
+order factor that's also the same
+detection or same contrast with a second
+
+ align:start position:0%
+detection or same contrast with a second
+ 
+
+ align:start position:0%
+detection or same contrast with a second
+order interaction factor I don't care
+
+ align:start position:0%
+order interaction factor I don't care
+ 
+
+ align:start position:0%
+order interaction factor I don't care
+and therefore if I don't care I can
+
+ align:start position:0%
+and therefore if I don't care I can
+ 
+
+ align:start position:0%
+and therefore if I don't care I can
+actually reduce the number of
+
+ align:start position:0%
+actually reduce the number of
+ 
+
+ align:start position:0%
+actually reduce the number of
+experimental points we want to do so
+
+ align:start position:0%
+experimental points we want to do so
+ 
+
+ align:start position:0%
+experimental points we want to do so
+we'll talk about that next time
\ No newline at end of file
diff --git a/GP8RSRrWtMU.txt b/GP8RSRrWtMU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e5e12c49dcb89ff2e430d5a4e28bc88a31da4bcb
--- /dev/null
+++ b/GP8RSRrWtMU.txt
@@ -0,0 +1,12571 @@
+align:start position:0%
+ 
+so today we are going to be talking
+
+ align:start position:0%
+so today we are going to be talking
+ 
+
+ align:start position:0%
+so today we are going to be talking
+about proton radiography and proton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Imaging so we're starting a series of
+
+ align:start position:0%
+Imaging so we're starting a series of
+ 
+
+ align:start position:0%
+Imaging so we're starting a series of
+three lectures in which we're looking at
+
+ align:start position:0%
+three lectures in which we're looking at
+ 
+
+ align:start position:0%
+three lectures in which we're looking at
+how to use particles as PR in the plasma
+
+ align:start position:0%
+how to use particles as PR in the plasma
+ 
+
+ align:start position:0%
+how to use particles as PR in the plasma
+previously you remember we used
+
+ align:start position:0%
+previously you remember we used
+ 
+
+ align:start position:0%
+previously you remember we used
+electromagnetic radiation and we looked
+
+ align:start position:0%
+electromagnetic radiation and we looked
+ 
+
+ align:start position:0%
+electromagnetic radiation and we looked
+at the emission from the plasma but now
+
+ align:start position:0%
+at the emission from the plasma but now
+ 
+
+ align:start position:0%
+at the emission from the plasma but now
+we're actively pushing particles through
+
+ align:start position:0%
+we're actively pushing particles through
+ 
+
+ align:start position:0%
+we're actively pushing particles through
+the plasma seeing what happens so
+
+ align:start position:0%
+the plasma seeing what happens so
+ 
+
+ align:start position:0%
+the plasma seeing what happens so
+imagine and we'll talk about exactly how
+
+ align:start position:0%
+imagine and we'll talk about exactly how
+ 
+
+ align:start position:0%
+imagine and we'll talk about exactly how
+you do this later on that you have some
+
+ align:start position:0%
+you do this later on that you have some
+ 
+
+ align:start position:0%
+you do this later on that you have some
+source of protons a beam of
+
+ align:start position:0%
+source of protons a beam of
+ 
+
+ align:start position:0%
+source of protons a beam of
+protons with some spread maybe it's
+
+ align:start position:0%
+protons with some spread maybe it's
+ 
+
+ align:start position:0%
+protons with some spread maybe it's
+emitting into four Pi ster agent maybe
+
+ align:start position:0%
+emitting into four Pi ster agent maybe
+ 
+
+ align:start position:0%
+emitting into four Pi ster agent maybe
+it's a tightly focused beam doesn't
+
+ align:start position:0%
+it's a tightly focused beam doesn't
+ 
+
+ align:start position:0%
+it's a tightly focused beam doesn't
+really matter you have plasma
+
+ align:start position:0%
+really matter you have plasma
+ 
+
+ align:start position:0%
+really matter you have plasma
+here and maybe within that plasma you
+
+ align:start position:0%
+here and maybe within that plasma you
+ 
+
+ align:start position:0%
+here and maybe within that plasma you
+have some magnetic fields so you have
+
+ align:start position:0%
+have some magnetic fields so you have
+ 
+
+ align:start position:0%
+have some magnetic fields so you have
+magnetic field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lines maybe look thidal from the point
+
+ align:start position:0%
+lines maybe look thidal from the point
+ 
+
+ align:start position:0%
+lines maybe look thidal from the point
+of view of the protons here so they're
+
+ align:start position:0%
+of view of the protons here so they're
+ 
+
+ align:start position:0%
+of view of the protons here so they're
+looping like
+
+ align:start position:0%
+looping like
+ 
+
+ align:start position:0%
+looping like
+this then as our protons go through here
+
+ align:start position:0%
+this then as our protons go through here
+ 
+
+ align:start position:0%
+this then as our protons go through here
+they're going to feel a
+
+ align:start position:0%
+they're going to feel a
+ 
+
+ align:start position:0%
+they're going to feel a
+force which is is equal to their charge
+
+ align:start position:0%
+force which is is equal to their charge
+ 
+
+ align:start position:0%
+force which is is equal to their charge
+I'll just write as
+
+ align:start position:0%
+I'll just write as
+ 
+
+ align:start position:0%
+I'll just write as
+e b cross
+
+ align:start position:0%
+e b cross
+ 
+
+ align:start position:0%
+e b cross
+B so they've got velocity in this
+
+ align:start position:0%
+B so they've got velocity in this
+ 
+
+ align:start position:0%
+B so they've got velocity in this
+direction for example here the magnetic
+
+ align:start position:0%
+direction for example here the magnetic
+ 
+
+ align:start position:0%
+direction for example here the magnetic
+field is pointing into the page and so
+
+ align:start position:0%
+field is pointing into the page and so
+ 
+
+ align:start position:0%
+field is pointing into the page and so
+the particles are going to feel a force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upwards and these particles here are
+
+ align:start position:0%
+upwards and these particles here are
+ 
+
+ align:start position:0%
+upwards and these particles here are
+going to feel a force
+
+ align:start position:0%
+going to feel a force
+ 
+
+ align:start position:0%
+going to feel a force
+downwards like this and if we put some
+
+ align:start position:0%
+downwards like this and if we put some
+ 
+
+ align:start position:0%
+downwards like this and if we put some
+sort of detector some distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+we should see that our source which
+
+ align:start position:0%
+we should see that our source which
+ 
+
+ align:start position:0%
+we should see that our source which
+maybe was initially uniform so we had a
+
+ align:start position:0%
+maybe was initially uniform so we had a
+ 
+
+ align:start position:0%
+maybe was initially uniform so we had a
+uniform number of protons per centimet
+
+ align:start position:0%
+uniform number of protons per centimet
+ 
+
+ align:start position:0%
+uniform number of protons per centimet
+squared millimet squared now that
+
+ align:start position:0%
+squared millimet squared now that
+ 
+
+ align:start position:0%
+squared millimet squared now that
+uniform intensity is going to be changed
+
+ align:start position:0%
+uniform intensity is going to be changed
+ 
+
+ align:start position:0%
+uniform intensity is going to be changed
+so for example if we draw a little line
+
+ align:start position:0%
+so for example if we draw a little line
+ 
+
+ align:start position:0%
+so for example if we draw a little line
+drawing of intensity over the initial
+
+ align:start position:0%
+drawing of intensity over the initial
+ 
+
+ align:start position:0%
+drawing of intensity over the initial
+intensity in the absence of this
+
+ align:start position:0%
+intensity in the absence of this
+ 
+
+ align:start position:0%
+intensity in the absence of this
+plasma our intensity profile would just
+
+ align:start position:0%
+plasma our intensity profile would just
+ 
+
+ align:start position:0%
+plasma our intensity profile would just
+be one there's nothing to change the
+
+ align:start position:0%
+be one there's nothing to change the
+ 
+
+ align:start position:0%
+be one there's nothing to change the
+intensity but in this case here we can
+
+ align:start position:0%
+intensity but in this case here we can
+ 
+
+ align:start position:0%
+intensity but in this case here we can
+see that this magnetic field
+
+ align:start position:0%
+see that this magnetic field
+ 
+
+ align:start position:0%
+see that this magnetic field
+configuration has created a void it's
+
+ align:start position:0%
+configuration has created a void it's
+ 
+
+ align:start position:0%
+configuration has created a void it's
+pushed the protons outward effectively
+
+ align:start position:0%
+pushed the protons outward effectively
+ 
+
+ align:start position:0%
+pushed the protons outward effectively
+defocus them so we see that we're going
+
+ align:start position:0%
+defocus them so we see that we're going
+ 
+
+ align:start position:0%
+defocus them so we see that we're going
+to have relatively few protons in the
+
+ align:start position:0%
+to have relatively few protons in the
+ 
+
+ align:start position:0%
+to have relatively few protons in the
+middle we're going to have a pile up of
+
+ align:start position:0%
+middle we're going to have a pile up of
+ 
+
+ align:start position:0%
+middle we're going to have a pile up of
+protons at the edge and then far away
+
+ align:start position:0%
+protons at the edge and then far away
+ 
+
+ align:start position:0%
+protons at the edge and then far away
+from the plasma we're just going to have
+
+ align:start position:0%
+from the plasma we're just going to have
+ 
+
+ align:start position:0%
+from the plasma we're just going to have
+our standard fluence of one because
+
+ align:start position:0%
+our standard fluence of one because
+ 
+
+ align:start position:0%
+our standard fluence of one because
+there'll be some particles that just go
+
+ align:start position:0%
+there'll be some particles that just go
+ 
+
+ align:start position:0%
+there'll be some particles that just go
+around the edge here and you know in
+
+ align:start position:0%
+around the edge here and you know in
+ 
+
+ align:start position:0%
+around the edge here and you know in
+this little drawing it's can be nice and
+
+ align:start position:0%
+this little drawing it's can be nice and
+ 
+
+ align:start position:0%
+this little drawing it's can be nice and
+symetric so what this would look like if
+
+ align:start position:0%
+symetric so what this would look like if
+ 
+
+ align:start position:0%
+symetric so what this would look like if
+we looked front
+
+ align:start position:0%
+we looked front
+ 
+
+ align:start position:0%
+we looked front
+on potentially is a bright ring where we
+
+ align:start position:0%
+on potentially is a bright ring where we
+ 
+
+ align:start position:0%
+on potentially is a bright ring where we
+have lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protons and a void in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+center that's the magnetic fields we
+
+ align:start position:0%
+center that's the magnetic fields we
+ 
+
+ align:start position:0%
+center that's the magnetic fields we
+could also have a
+
+ align:start position:0%
+could also have a
+ 
+
+ align:start position:0%
+could also have a
+plasma that has electric Fields as well
+
+ align:start position:0%
+plasma that has electric Fields as well
+ 
+
+ align:start position:0%
+plasma that has electric Fields as well
+and although you know we think electric
+
+ align:start position:0%
+and although you know we think electric
+ 
+
+ align:start position:0%
+and although you know we think electric
+fields are quite
+
+ align:start position:0%
+fields are quite
+ 
+
+ align:start position:0%
+fields are quite
+small due to the B shielding on time
+
+ align:start position:0%
+small due to the B shielding on time
+ 
+
+ align:start position:0%
+small due to the B shielding on time
+scales in HD plasmas where these are
+
+ align:start position:0%
+scales in HD plasmas where these are
+ 
+
+ align:start position:0%
+scales in HD plasmas where these are
+often used the electric Fields can be
+
+ align:start position:0%
+often used the electric Fields can be
+ 
+
+ align:start position:0%
+often used the electric Fields can be
+relatively large because the plasma does
+
+ align:start position:0%
+relatively large because the plasma does
+ 
+
+ align:start position:0%
+relatively large because the plasma does
+not have to be quasy neutral so we could
+
+ align:start position:0%
+not have to be quasy neutral so we could
+ 
+
+ align:start position:0%
+not have to be quasy neutral so we could
+have some sort of electric field like
+
+ align:start position:0%
+have some sort of electric field like
+ 
+
+ align:start position:0%
+have some sort of electric field like
+this and then our electric field would
+
+ align:start position:0%
+this and then our electric field would
+ 
+
+ align:start position:0%
+this and then our electric field would
+also put a force on these
+
+ align:start position:0%
+also put a force on these
+ 
+
+ align:start position:0%
+also put a force on these
+protons in this case I've drawn it in
+
+ align:start position:0%
+protons in this case I've drawn it in
+ 
+
+ align:start position:0%
+protons in this case I've drawn it in
+the same way so the electric field is
+
+ align:start position:0%
+the same way so the electric field is
+ 
+
+ align:start position:0%
+the same way so the electric field is
+pushing the protons out from here so if
+
+ align:start position:0%
+pushing the protons out from here so if
+ 
+
+ align:start position:0%
+pushing the protons out from here so if
+I draw some more protons coming from a
+
+ align:start position:0%
+I draw some more protons coming from a
+ 
+
+ align:start position:0%
+I draw some more protons coming from a
+point source I draw some trajectories
+
+ align:start position:0%
+point source I draw some trajectories
+ 
+
+ align:start position:0%
+point source I draw some trajectories
+going into the plasma
+
+ align:start position:0%
+going into the plasma
+ 
+
+ align:start position:0%
+going into the plasma
+I'll have protons which are being bent
+
+ align:start position:0%
+I'll have protons which are being bent
+ 
+
+ align:start position:0%
+I'll have protons which are being bent
+upwards and
+
+ align:start position:0%
+upwards and
+ 
+
+ align:start position:0%
+upwards and
+downwards like this and so on my
+
+ align:start position:0%
+downwards like this and so on my
+ 
+
+ align:start position:0%
+downwards like this and so on my
+detector I could for example see a very
+
+ align:start position:0%
+detector I could for example see a very
+ 
+
+ align:start position:0%
+detector I could for example see a very
+similar pattern where I have a void in
+
+ align:start position:0%
+similar pattern where I have a void in
+ 
+
+ align:start position:0%
+similar pattern where I have a void in
+the middle I have some regions of
+
+ align:start position:0%
+the middle I have some regions of
+ 
+
+ align:start position:0%
+the middle I have some regions of
+increased fluence on the limbs and then
+
+ align:start position:0%
+increased fluence on the limbs and then
+ 
+
+ align:start position:0%
+increased fluence on the limbs and then
+I have a region where there's
+
+ align:start position:0%
+I have a region where there's
+ 
+
+ align:start position:0%
+I have a region where there's
+undisturbed fluence because I've got
+
+ align:start position:0%
+undisturbed fluence because I've got
+ 
+
+ align:start position:0%
+undisturbed fluence because I've got
+particles which are just going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around so this is a technique called
+
+ align:start position:0%
+around so this is a technique called
+ 
+
+ align:start position:0%
+around so this is a technique called
+proton Imaging it's a way of Imaging
+
+ align:start position:0%
+proton Imaging it's a way of Imaging
+ 
+
+ align:start position:0%
+proton Imaging it's a way of Imaging
+electric and magnetic fields but of
+
+ align:start position:0%
+electric and magnetic fields but of
+ 
+
+ align:start position:0%
+electric and magnetic fields but of
+course uh it feels both the electric and
+
+ align:start position:0%
+course uh it feels both the electric and
+ 
+
+ align:start position:0%
+course uh it feels both the electric and
+the magnetic field so that's one
+
+ align:start position:0%
+the magnetic field so that's one
+ 
+
+ align:start position:0%
+the magnetic field so that's one
+fundamental limitation with it is that
+
+ align:start position:0%
+fundamental limitation with it is that
+ 
+
+ align:start position:0%
+fundamental limitation with it is that
+you're never quite sure whether your
+
+ align:start position:0%
+you're never quite sure whether your
+ 
+
+ align:start position:0%
+you're never quite sure whether your
+deflection is due to electric or
+
+ align:start position:0%
+deflection is due to electric or
+ 
+
+ align:start position:0%
+deflection is due to electric or
+magnetic
+
+ align:start position:0%
+magnetic
+ 
+
+ align:start position:0%
+magnetic
+fields there is a third form of proton
+
+ align:start position:0%
+fields there is a third form of proton
+ 
+
+ align:start position:0%
+fields there is a third form of proton
+Imaging which is technically called
+
+ align:start position:0%
+Imaging which is technically called
+ 
+
+ align:start position:0%
+Imaging which is technically called
+proton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radiography on radiography the
+
+ align:start position:0%
+radiography on radiography the
+ 
+
+ align:start position:0%
+radiography on radiography the
+radiography here is to make you think
+
+ align:start position:0%
+radiography here is to make you think
+ 
+
+ align:start position:0%
+radiography here is to make you think
+about X-rays and x-ray radiography which
+
+ align:start position:0%
+about X-rays and x-ray radiography which
+ 
+
+ align:start position:0%
+about X-rays and x-ray radiography which
+is where you have your beam of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles and you have some very very
+
+ align:start position:0%
+particles and you have some very very
+ 
+
+ align:start position:0%
+particles and you have some very very
+dense plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and because it's so dense these
+
+ align:start position:0%
+here and because it's so dense these
+ 
+
+ align:start position:0%
+here and because it's so dense these
+particles don't stream through it and
+
+ align:start position:0%
+particles don't stream through it and
+ 
+
+ align:start position:0%
+particles don't stream through it and
+just feel the electrical magnetic fields
+
+ align:start position:0%
+just feel the electrical magnetic fields
+ 
+
+ align:start position:0%
+just feel the electrical magnetic fields
+the particles start scattering and
+
+ align:start position:0%
+the particles start scattering and
+ 
+
+ align:start position:0%
+the particles start scattering and
+colliding and maybe they never Escape
+
+ align:start position:0%
+colliding and maybe they never Escape
+ 
+
+ align:start position:0%
+colliding and maybe they never Escape
+out the other side and then on your
+
+ align:start position:0%
+out the other side and then on your
+ 
+
+ align:start position:0%
+out the other side and then on your
+detector you would have similar to an
+
+ align:start position:0%
+detector you would have similar to an
+ 
+
+ align:start position:0%
+detector you would have similar to an
+x-ray an image which for example has a
+
+ align:start position:0%
+x-ray an image which for example has a
+ 
+
+ align:start position:0%
+x-ray an image which for example has a
+region which is a void whether or no
+
+ align:start position:0%
+region which is a void whether or no
+ 
+
+ align:start position:0%
+region which is a void whether or no
+protons and that's because all the
+
+ align:start position:0%
+protons and that's because all the
+ 
+
+ align:start position:0%
+protons and that's because all the
+protons have been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scattered so again this only
+
+ align:start position:0%
+scattered so again this only
+ 
+
+ align:start position:0%
+scattered so again this only
+happens at high
+
+ align:start position:0%
+happens at high
+ 
+
+ align:start position:0%
+happens at high
+densities at lower densities the
+
+ align:start position:0%
+densities at lower densities the
+ 
+
+ align:start position:0%
+densities at lower densities the
+particle should stream through um
+
+ align:start position:0%
+particle should stream through um
+ 
+
+ align:start position:0%
+particle should stream through um
+unfortunately a lot of people call this
+
+ align:start position:0%
+unfortunately a lot of people call this
+ 
+
+ align:start position:0%
+unfortunately a lot of people call this
+proton Imaging technique proton
+
+ align:start position:0%
+proton Imaging technique proton
+ 
+
+ align:start position:0%
+proton Imaging technique proton
+radiography because that's what it was
+
+ align:start position:0%
+radiography because that's what it was
+ 
+
+ align:start position:0%
+radiography because that's what it was
+initially called but it's not a
+
+ align:start position:0%
+initially called but it's not a
+ 
+
+ align:start position:0%
+initially called but it's not a
+radiographic technique radiography
+
+ align:start position:0%
+radiographic technique radiography
+ 
+
+ align:start position:0%
+radiographic technique radiography
+refers to like your beam being
+
+ align:start position:0%
+refers to like your beam being
+ 
+
+ align:start position:0%
+refers to like your beam being
+attenuated by density in the way so it's
+
+ align:start position:0%
+attenuated by density in the way so it's
+ 
+
+ align:start position:0%
+attenuated by density in the way so it's
+not really a right name but you'll see a
+
+ align:start position:0%
+not really a right name but you'll see a
+ 
+
+ align:start position:0%
+not really a right name but you'll see a
+lot of people call this proton
+
+ align:start position:0%
+lot of people call this proton
+ 
+
+ align:start position:0%
+lot of people call this proton
+radiography um some people have been
+
+ align:start position:0%
+radiography um some people have been
+ 
+
+ align:start position:0%
+radiography um some people have been
+trying to call it proton Imaging instead
+
+ align:start position:0%
+trying to call it proton Imaging instead
+ 
+
+ align:start position:0%
+trying to call it proton Imaging instead
+um even in the case where you don't have
+
+ align:start position:0%
+um even in the case where you don't have
+ 
+
+ align:start position:0%
+um even in the case where you don't have
+such a high density you may still end up
+
+ align:start position:0%
+such a high density you may still end up
+ 
+
+ align:start position:0%
+such a high density you may still end up
+with enough density in plasma that it
+
+ align:start position:0%
+with enough density in plasma that it
+ 
+
+ align:start position:0%
+with enough density in plasma that it
+will sort of knock a particle off course
+
+ align:start position:0%
+will sort of knock a particle off course
+ 
+
+ align:start position:0%
+will sort of knock a particle off course
+and that will lead to some sort of
+
+ align:start position:0%
+and that will lead to some sort of
+ 
+
+ align:start position:0%
+and that will lead to some sort of
+blurring so these weak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collisions can lead to blurring of the
+
+ align:start position:0%
+collisions can lead to blurring of the
+ 
+
+ align:start position:0%
+collisions can lead to blurring of the
+image so you may still want to take into
+
+ align:start position:0%
+image so you may still want to take into
+ 
+
+ align:start position:0%
+image so you may still want to take into
+account the collisionality a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit okay and the referen is for this
+
+ align:start position:0%
+bit okay and the referen is for this
+ 
+
+ align:start position:0%
+bit okay and the referen is for this
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+are two
+
+ align:start position:0%
+are two
+ 
+
+ align:start position:0%
+are two
+papers first one is by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kland you can find it in review of
+
+ align:start position:0%
+kland you can find it in review of
+ 
+
+ align:start position:0%
+kland you can find it in review of
+scientific instruments RSI from
+
+ align:start position:0%
+scientific instruments RSI from
+ 
+
+ align:start position:0%
+scientific instruments RSI from
+2012 a lot of the mathematics will be
+
+ align:start position:0%
+2012 a lot of the mathematics will be
+ 
+
+ align:start position:0%
+2012 a lot of the mathematics will be
+using as based off this paper and very
+
+ align:start position:0%
+using as based off this paper and very
+ 
+
+ align:start position:0%
+using as based off this paper and very
+recently there was a review article by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+schaer hasn't been published yet it's on
+
+ align:start position:0%
+schaer hasn't been published yet it's on
+ 
+
+ align:start position:0%
+schaer hasn't been published yet it's on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+archive and that was published last year
+
+ align:start position:0%
+archive and that was published last year
+ 
+
+ align:start position:0%
+archive and that was published last year
+and this review article is really really
+
+ align:start position:0%
+and this review article is really really
+ 
+
+ align:start position:0%
+and this review article is really really
+good at the nitty-gritty of how proton
+
+ align:start position:0%
+good at the nitty-gritty of how proton
+ 
+
+ align:start position:0%
+good at the nitty-gritty of how proton
+rography is actually done and we'll talk
+
+ align:start position:0%
+rography is actually done and we'll talk
+ 
+
+ align:start position:0%
+rography is actually done and we'll talk
+an awful lot or a little bit at least
+
+ align:start position:0%
+an awful lot or a little bit at least
+ 
+
+ align:start position:0%
+an awful lot or a little bit at least
+about how these sources of protons are
+
+ align:start position:0%
+about how these sources of protons are
+ 
+
+ align:start position:0%
+about how these sources of protons are
+made later on but now for the first bit
+
+ align:start position:0%
+made later on but now for the first bit
+ 
+
+ align:start position:0%
+made later on but now for the first bit
+we're just going to assume there is some
+
+ align:start position:0%
+we're just going to assume there is some
+ 
+
+ align:start position:0%
+we're just going to assume there is some
+source of protons so before we get on to
+
+ align:start position:0%
+source of protons so before we get on to
+ 
+
+ align:start position:0%
+source of protons so before we get on to
+a more mathematical treatment of this
+
+ align:start position:0%
+a more mathematical treatment of this
+ 
+
+ align:start position:0%
+a more mathematical treatment of this
+does anyone have any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah absolutely right so at the
+
+ align:start position:0%
+yes yeah absolutely right so at the
+ 
+
+ align:start position:0%
+yes yeah absolutely right so at the
+edges here where they have less distance
+
+ align:start position:0%
+edges here where they have less distance
+ 
+
+ align:start position:0%
+edges here where they have less distance
+travel through you could have something
+
+ align:start position:0%
+travel through you could have something
+ 
+
+ align:start position:0%
+travel through you could have something
+that gets knocked around but still gets
+
+ align:start position:0%
+that gets knocked around but still gets
+ 
+
+ align:start position:0%
+that gets knocked around but still gets
+through but maybe another particle
+
+ align:start position:0%
+through but maybe another particle
+ 
+
+ align:start position:0%
+through but maybe another particle
+traveling a very similar path doesn't
+
+ align:start position:0%
+traveling a very similar path doesn't
+ 
+
+ align:start position:0%
+traveling a very similar path doesn't
+get through and so you'd have you know
+
+ align:start position:0%
+get through and so you'd have you know
+ 
+
+ align:start position:0%
+get through and so you'd have you know
+gray scale you'd have few so just like
+
+ align:start position:0%
+gray scale you'd have few so just like
+ 
+
+ align:start position:0%
+gray scale you'd have few so just like
+was x-rays
+
+ align:start position:0%
+was x-rays
+ 
+
+ align:start position:0%
+was x-rays
+yeah other questions any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online okay so mathematically this does
+
+ align:start position:0%
+online okay so mathematically this does
+ 
+
+ align:start position:0%
+online okay so mathematically this does
+look very similar to shog graphy but
+
+ align:start position:0%
+look very similar to shog graphy but
+ 
+
+ align:start position:0%
+look very similar to shog graphy but
+there are some differences so I'm going
+
+ align:start position:0%
+there are some differences so I'm going
+ 
+
+ align:start position:0%
+there are some differences so I'm going
+to go through the mathematics again so
+
+ align:start position:0%
+to go through the mathematics again so
+ 
+
+ align:start position:0%
+to go through the mathematics again so
+you may notice some similarities some
+
+ align:start position:0%
+you may notice some similarities some
+ 
+
+ align:start position:0%
+you may notice some similarities some
+differences in notation that's all okay
+
+ align:start position:0%
+differences in notation that's all okay
+ 
+
+ align:start position:0%
+differences in notation that's all okay
+um so we're going to start by making
+
+ align:start position:0%
+um so we're going to start by making
+ 
+
+ align:start position:0%
+um so we're going to start by making
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assumptions our first assumption is that
+
+ align:start position:0%
+assumptions our first assumption is that
+ 
+
+ align:start position:0%
+assumptions our first assumption is that
+we have a point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+source in reality this means that if we
+
+ align:start position:0%
+source in reality this means that if we
+ 
+
+ align:start position:0%
+source in reality this means that if we
+have some Source size
+
+ align:start position:0%
+have some Source size
+ 
+
+ align:start position:0%
+have some Source size
+here which has uh a size say d source
+
+ align:start position:0%
+here which has uh a size say d source
+ 
+
+ align:start position:0%
+here which has uh a size say d source
+that has to be much much less than the
+
+ align:start position:0%
+that has to be much much less than the
+ 
+
+ align:start position:0%
+that has to be much much less than the
+length scale the size of our
+
+ align:start position:0%
+length scale the size of our
+ 
+
+ align:start position:0%
+length scale the size of our
+plasma because if that's true we have
+
+ align:start position:0%
+plasma because if that's true we have
+ 
+
+ align:start position:0%
+plasma because if that's true we have
+some finite Source size here and some
+
+ align:start position:0%
+some finite Source size here and some
+ 
+
+ align:start position:0%
+some finite Source size here and some
+very big plasma from the perspective of
+
+ align:start position:0%
+very big plasma from the perspective of
+ 
+
+ align:start position:0%
+very big plasma from the perspective of
+the plasma this will roughly be a point
+
+ align:start position:0%
+the plasma this will roughly be a point
+ 
+
+ align:start position:0%
+the plasma this will roughly be a point
+so we can make this more rigorous by
+
+ align:start position:0%
+so we can make this more rigorous by
+ 
+
+ align:start position:0%
+so we can make this more rigorous by
+introducing a dimensionless parameter
+
+ align:start position:0%
+introducing a dimensionless parameter
+ 
+
+ align:start position:0%
+introducing a dimensionless parameter
+and insisting that parameter is small um
+
+ align:start position:0%
+and insisting that parameter is small um
+ 
+
+ align:start position:0%
+and insisting that parameter is small um
+this is a pretty good
+
+ align:start position:0%
+this is a pretty good
+ 
+
+ align:start position:0%
+this is a pretty good
+approximation um the next thing we need
+
+ align:start position:0%
+approximation um the next thing we need
+ 
+
+ align:start position:0%
+approximation um the next thing we need
+to assume is a uniform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B which is to say that we have the same
+
+ align:start position:0%
+B which is to say that we have the same
+ 
+
+ align:start position:0%
+B which is to say that we have the same
+number of protons coming through every
+
+ align:start position:0%
+number of protons coming through every
+ 
+
+ align:start position:0%
+number of protons coming through every
+little infimal solid angle unit here so
+
+ align:start position:0%
+little infimal solid angle unit here so
+ 
+
+ align:start position:0%
+little infimal solid angle unit here so
+that in the absence of any plasma when I
+
+ align:start position:0%
+that in the absence of any plasma when I
+ 
+
+ align:start position:0%
+that in the absence of any plasma when I
+put my detector here I do in fact get a
+
+ align:start position:0%
+put my detector here I do in fact get a
+ 
+
+ align:start position:0%
+put my detector here I do in fact get a
+nice uniform signal on it so I over i z
+
+ align:start position:0%
+nice uniform signal on it so I over i z
+ 
+
+ align:start position:0%
+nice uniform signal on it so I over i z
+is just one here if my signal is not
+
+ align:start position:0%
+is just one here if my signal is not
+ 
+
+ align:start position:0%
+is just one here if my signal is not
+uniform like this it complicates the
+
+ align:start position:0%
+uniform like this it complicates the
+ 
+
+ align:start position:0%
+uniform like this it complicates the
+interpretation it turns out you can do
+
+ align:start position:0%
+interpretation it turns out you can do
+ 
+
+ align:start position:0%
+interpretation it turns out you can do
+something with a non-uniform uh beam of
+
+ align:start position:0%
+something with a non-uniform uh beam of
+ 
+
+ align:start position:0%
+something with a non-uniform uh beam of
+protons but mathematically it's harder
+
+ align:start position:0%
+protons but mathematically it's harder
+ 
+
+ align:start position:0%
+protons but mathematically it's harder
+so we're going to insist on a uniform
+
+ align:start position:0%
+so we're going to insist on a uniform
+ 
+
+ align:start position:0%
+so we're going to insist on a uniform
+beam so we'll say the gradient of the
+
+ align:start position:0%
+beam so we'll say the gradient of the
+ 
+
+ align:start position:0%
+beam so we'll say the gradient of the
+beam intensity is equal to zero at
+
+ align:start position:0%
+beam intensity is equal to zero at
+ 
+
+ align:start position:0%
+beam intensity is equal to zero at
+least over the target over the plasma I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess okay third approximation we'll
+
+ align:start position:0%
+guess okay third approximation we'll
+ 
+
+ align:start position:0%
+guess okay third approximation we'll
+make is the paraxial approximation
+
+ align:start position:0%
+make is the paraxial approximation
+ 
+
+ align:start position:0%
+make is the paraxial approximation
+from geometric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optics the paraxial approximation is
+
+ align:start position:0%
+optics the paraxial approximation is
+ 
+
+ align:start position:0%
+optics the paraxial approximation is
+basically saying that although these
+
+ align:start position:0%
+basically saying that although these
+ 
+
+ align:start position:0%
+basically saying that although these
+particles are following some path we can
+
+ align:start position:0%
+particles are following some path we can
+ 
+
+ align:start position:0%
+particles are following some path we can
+call DL our detector is relatively
+
+ align:start position:0%
+call DL our detector is relatively
+ 
+
+ align:start position:0%
+call DL our detector is relatively
+small and so most the particles are
+
+ align:start position:0%
+small and so most the particles are
+ 
+
+ align:start position:0%
+small and so most the particles are
+going almost parallel
+
+ align:start position:0%
+going almost parallel
+ 
+
+ align:start position:0%
+going almost parallel
+to DZ hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so this means means we can
+
+ align:start position:0%
+here so this means means we can
+ 
+
+ align:start position:0%
+here so this means means we can
+approximate any path integrals as just
+
+ align:start position:0%
+approximate any path integrals as just
+ 
+
+ align:start position:0%
+approximate any path integrals as just
+integrals in The Zed Direction and this
+
+ align:start position:0%
+integrals in The Zed Direction and this
+ 
+
+ align:start position:0%
+integrals in The Zed Direction and this
+also means we can approximate angles
+
+ align:start position:0%
+also means we can approximate angles
+ 
+
+ align:start position:0%
+also means we can approximate angles
+like tan Alpha be approximately sin
+
+ align:start position:0%
+like tan Alpha be approximately sin
+ 
+
+ align:start position:0%
+like tan Alpha be approximately sin
+Alpha be approximately Alpha this makes
+
+ align:start position:0%
+Alpha be approximately Alpha this makes
+ 
+
+ align:start position:0%
+Alpha be approximately Alpha this makes
+the mathematics very easy as well and
+
+ align:start position:0%
+the mathematics very easy as well and
+ 
+
+ align:start position:0%
+the mathematics very easy as well and
+the final assumption we'll make is that
+
+ align:start position:0%
+the final assumption we'll make is that
+ 
+
+ align:start position:0%
+the final assumption we'll make is that
+our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protons are test
+
+ align:start position:0%
+protons are test
+ 
+
+ align:start position:0%
+protons are test
+particles so you may have seen a test
+
+ align:start position:0%
+particles so you may have seen a test
+ 
+
+ align:start position:0%
+particles so you may have seen a test
+particle formulism
+
+ align:start position:0%
+particle formulism
+ 
+
+ align:start position:0%
+particle formulism
+ISM in some bits of plasma Theory the
+
+ align:start position:0%
+ISM in some bits of plasma Theory the
+ 
+
+ align:start position:0%
+ISM in some bits of plasma Theory the
+idea is your test particle merely
+
+ align:start position:0%
+idea is your test particle merely
+ 
+
+ align:start position:0%
+idea is your test particle merely
+experiences the fields inside your
+
+ align:start position:0%
+experiences the fields inside your
+ 
+
+ align:start position:0%
+experiences the fields inside your
+plasma it doesn't contribute to them so
+
+ align:start position:0%
+plasma it doesn't contribute to them so
+ 
+
+ align:start position:0%
+plasma it doesn't contribute to them so
+the fact that we have this beam of
+
+ align:start position:0%
+the fact that we have this beam of
+ 
+
+ align:start position:0%
+the fact that we have this beam of
+protons streaming through here we assume
+
+ align:start position:0%
+protons streaming through here we assume
+ 
+
+ align:start position:0%
+protons streaming through here we assume
+it has negligible perturbation on the
+
+ align:start position:0%
+it has negligible perturbation on the
+ 
+
+ align:start position:0%
+it has negligible perturbation on the
+plasma itself so we have no deflection
+
+ align:start position:0%
+plasma itself so we have no deflection
+ 
+
+ align:start position:0%
+plasma itself so we have no deflection
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+between protons within the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam
+
+ align:start position:0%
+beam
+ 
+
+ align:start position:0%
+beam
+and this is a statement that the average
+
+ align:start position:0%
+and this is a statement that the average
+ 
+
+ align:start position:0%
+and this is a statement that the average
+potential that the protons are creating
+
+ align:start position:0%
+potential that the protons are creating
+ 
+
+ align:start position:0%
+potential that the protons are creating
+divided by their kinetic energy is much
+
+ align:start position:0%
+divided by their kinetic energy is much
+ 
+
+ align:start position:0%
+divided by their kinetic energy is much
+much less than one that is to say
+
+ align:start position:0%
+much less than one that is to say
+ 
+
+ align:start position:0%
+much less than one that is to say
+they're going so fast that even if they
+
+ align:start position:0%
+they're going so fast that even if they
+ 
+
+ align:start position:0%
+they're going so fast that even if they
+do feel a small electric field that
+
+ align:start position:0%
+do feel a small electric field that
+ 
+
+ align:start position:0%
+do feel a small electric field that
+deflects them slightly it's negligible
+
+ align:start position:0%
+deflects them slightly it's negligible
+ 
+
+ align:start position:0%
+deflects them slightly it's negligible
+because they're moving so fast it
+
+ align:start position:0%
+because they're moving so fast it
+ 
+
+ align:start position:0%
+because they're moving so fast it
+doesn't change their overall proton
+
+ align:start position:0%
+doesn't change their overall proton
+ 
+
+ align:start position:0%
+doesn't change their overall proton
+kinetic energy
+
+ align:start position:0%
+kinetic energy
+ 
+
+ align:start position:0%
+kinetic energy
+here okay any questions on assumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always yeah yeah yeah the paraxial
+
+ align:start position:0%
+always yeah yeah yeah the paraxial
+ 
+
+ align:start position:0%
+always yeah yeah yeah the paraxial
+region takes care of that yeah exactly
+
+ align:start position:0%
+region takes care of that yeah exactly
+ 
+
+ align:start position:0%
+region takes care of that yeah exactly
+but you're right but like we're really
+
+ align:start position:0%
+but you're right but like we're really
+ 
+
+ align:start position:0%
+but you're right but like we're really
+talking about like less than a degree
+
+ align:start position:0%
+talking about like less than a degree
+ 
+
+ align:start position:0%
+talking about like less than a degree
+sub tenders is very very small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the only place is appeared so far
+
+ align:start position:0%
+yeah the only place is appeared so far
+ 
+
+ align:start position:0%
+yeah the only place is appeared so far
+as we've assumed that it's very very
+
+ align:start position:0%
+as we've assumed that it's very very
+ 
+
+ align:start position:0%
+as we've assumed that it's very very
+high so these protons tend to be and
+
+ align:start position:0%
+high so these protons tend to be and
+ 
+
+ align:start position:0%
+high so these protons tend to be and
+we'll get on to the generation mechanism
+
+ align:start position:0%
+we'll get on to the generation mechanism
+ 
+
+ align:start position:0%
+we'll get on to the generation mechanism
+but these tend to be like Mega electron
+
+ align:start position:0%
+but these tend to be like Mega electron
+ 
+
+ align:start position:0%
+but these tend to be like Mega electron
+volt energy protons here so they're much
+
+ align:start position:0%
+volt energy protons here so they're much
+ 
+
+ align:start position:0%
+volt energy protons here so they're much
+much uh um faster than any of the other
+
+ align:start position:0%
+much uh um faster than any of the other
+ 
+
+ align:start position:0%
+much uh um faster than any of the other
+particles in our system generally and
+
+ align:start position:0%
+particles in our system generally and
+ 
+
+ align:start position:0%
+particles in our system generally and
+because you know that the collisionality
+
+ align:start position:0%
+because you know that the collisionality
+ 
+
+ align:start position:0%
+because you know that the collisionality
+the meanf free path uh goes as I'm GNA
+
+ align:start position:0%
+the meanf free path uh goes as I'm GNA
+ 
+
+ align:start position:0%
+the meanf free path uh goes as I'm GNA
+get this right velocity
+
+ align:start position:0%
+get this right velocity
+ 
+
+ align:start position:0%
+get this right velocity
+cubed then these very fast particles
+
+ align:start position:0%
+cubed then these very fast particles
+ 
+
+ align:start position:0%
+cubed then these very fast particles
+here have a very long meanf free path
+
+ align:start position:0%
+here have a very long meanf free path
+ 
+
+ align:start position:0%
+here have a very long meanf free path
+their collisionality is very low so
+
+ align:start position:0%
+their collisionality is very low so
+ 
+
+ align:start position:0%
+their collisionality is very low so
+they're unlikely to collide with any
+
+ align:start position:0%
+they're unlikely to collide with any
+ 
+
+ align:start position:0%
+they're unlikely to collide with any
+particles in the to yeah we'll talk
+
+ align:start position:0%
+particles in the to yeah we'll talk
+ 
+
+ align:start position:0%
+particles in the to yeah we'll talk
+about that yeah no no no it's great yeah
+
+ align:start position:0%
+about that yeah no no no it's great yeah
+ 
+
+ align:start position:0%
+about that yeah no no no it's great yeah
+yeah um for the purposes of this we're
+
+ align:start position:0%
+yeah um for the purposes of this we're
+ 
+
+ align:start position:0%
+yeah um for the purposes of this we're
+going to do it in such a way that we
+
+ align:start position:0%
+going to do it in such a way that we
+ 
+
+ align:start position:0%
+going to do it in such a way that we
+will just solve for the end like there
+
+ align:start position:0%
+will just solve for the end like there
+ 
+
+ align:start position:0%
+will just solve for the end like there
+are some protons with part energy one
+
+ align:start position:0%
+are some protons with part energy one
+ 
+
+ align:start position:0%
+are some protons with part energy one
+and sub protons of energy two and our
+
+ align:start position:0%
+and sub protons of energy two and our
+ 
+
+ align:start position:0%
+and sub protons of energy two and our
+solution is separable and I guess that
+
+ align:start position:0%
+solution is separable and I guess that
+ 
+
+ align:start position:0%
+solution is separable and I guess that
+comes back to here the fact the beam
+
+ align:start position:0%
+comes back to here the fact the beam
+ 
+
+ align:start position:0%
+comes back to here the fact the beam
+doesn't interact with itself but we'll
+
+ align:start position:0%
+doesn't interact with itself but we'll
+ 
+
+ align:start position:0%
+doesn't interact with itself but we'll
+talk a lot about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they're much lighter and so they'll
+
+ align:start position:0%
+yeah they're much lighter and so they'll
+ 
+
+ align:start position:0%
+yeah they're much lighter and so they'll
+scatter more easily but people have
+
+ align:start position:0%
+scatter more easily but people have
+ 
+
+ align:start position:0%
+scatter more easily but people have
+started doing electron Imaging as well
+
+ align:start position:0%
+started doing electron Imaging as well
+ 
+
+ align:start position:0%
+started doing electron Imaging as well
+but then you sort of need like G beams
+
+ align:start position:0%
+but then you sort of need like G beams
+ 
+
+ align:start position:0%
+but then you sort of need like G beams
+and stuff like that so the protons are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better I don't know enough about the
+
+ align:start position:0%
+better I don't know enough about the
+ 
+
+ align:start position:0%
+better I don't know enough about the
+Electron Beam techniques at the moment
+
+ align:start position:0%
+Electron Beam techniques at the moment
+ 
+
+ align:start position:0%
+Electron Beam techniques at the moment
+so a lot of I'm going to show you
+
+ align:start position:0%
+so a lot of I'm going to show you
+ 
+
+ align:start position:0%
+so a lot of I'm going to show you
+through is like very specific detectors
+
+ align:start position:0%
+through is like very specific detectors
+ 
+
+ align:start position:0%
+through is like very specific detectors
+that have been created for protons and I
+
+ align:start position:0%
+that have been created for protons and I
+ 
+
+ align:start position:0%
+that have been created for protons and I
+don't know whether that detective
+
+ align:start position:0%
+don't know whether that detective
+ 
+
+ align:start position:0%
+don't know whether that detective
+technology exists for electrons in the
+
+ align:start position:0%
+technology exists for electrons in the
+ 
+
+ align:start position:0%
+technology exists for electrons in the
+same way so yeah there another question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's very hard to make a columnated
+
+ align:start position:0%
+yeah it's very hard to make a columnated
+ 
+
+ align:start position:0%
+yeah it's very hard to make a columnated
+beam of protons and when we talk about
+
+ align:start position:0%
+beam of protons and when we talk about
+ 
+
+ align:start position:0%
+beam of protons and when we talk about
+the generation mechanisms they tend to
+
+ align:start position:0%
+the generation mechanisms they tend to
+ 
+
+ align:start position:0%
+the generation mechanisms they tend to
+make Point sources or or things with
+
+ align:start position:0%
+make Point sources or or things with
+ 
+
+ align:start position:0%
+make Point sources or or things with
+very small spot sizes so it's a
+
+ align:start position:0%
+very small spot sizes so it's a
+ 
+
+ align:start position:0%
+very small spot sizes so it's a
+technological limitation yeah in the
+
+ align:start position:0%
+technological limitation yeah in the
+ 
+
+ align:start position:0%
+technological limitation yeah in the
+very early days people use particle
+
+ align:start position:0%
+very early days people use particle
+ 
+
+ align:start position:0%
+very early days people use particle
+accelerators to do this but although
+
+ align:start position:0%
+accelerators to do this but although
+ 
+
+ align:start position:0%
+accelerators to do this but although
+particle accelerators can accelerate a
+
+ align:start position:0%
+particle accelerators can accelerate a
+ 
+
+ align:start position:0%
+particle accelerators can accelerate a
+lot of particles to high energy um it's
+
+ align:start position:0%
+lot of particles to high energy um it's
+ 
+
+ align:start position:0%
+lot of particles to high energy um it's
+not enough particles on the time scale
+
+ align:start position:0%
+not enough particles on the time scale
+ 
+
+ align:start position:0%
+not enough particles on the time scale
+of these experiments these experiments
+
+ align:start position:0%
+of these experiments these experiments
+ 
+
+ align:start position:0%
+of these experiments these experiments
+are over in like a nanc and so you need
+
+ align:start position:0%
+are over in like a nanc and so you need
+ 
+
+ align:start position:0%
+are over in like a nanc and so you need
+a very very bright burst of protons and
+
+ align:start position:0%
+a very very bright burst of protons and
+ 
+
+ align:start position:0%
+a very very bright burst of protons and
+it turns out the techniques we have for
+
+ align:start position:0%
+it turns out the techniques we have for
+ 
+
+ align:start position:0%
+it turns out the techniques we have for
+making those bursts of protons make a
+
+ align:start position:0%
+making those bursts of protons make a
+ 
+
+ align:start position:0%
+making those bursts of protons make a
+nice point source yeah was there a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question oh um when you say point source
+
+ align:start position:0%
+question oh um when you say point source
+ 
+
+ align:start position:0%
+question oh um when you say point source
+um you mean like just from a specific
+
+ align:start position:0%
+um you mean like just from a specific
+ 
+
+ align:start position:0%
+um you mean like just from a specific
+one location not like the point source
+
+ align:start position:0%
+one location not like the point source
+ 
+
+ align:start position:0%
+one location not like the point source
+hitting the plasma
+
+ align:start position:0%
+hitting the plasma
+ 
+
+ align:start position:0%
+hitting the plasma
+correct uh sorry could you say that a
+
+ align:start position:0%
+correct uh sorry could you say that a
+ 
+
+ align:start position:0%
+correct uh sorry could you say that a
+different way yeah um so the point
+
+ align:start position:0%
+different way yeah um so the point
+ 
+
+ align:start position:0%
+different way yeah um so the point
+source is the is the beams and when you
+
+ align:start position:0%
+source is the is the beams and when you
+ 
+
+ align:start position:0%
+source is the is the beams and when you
+were talking about the um particle
+
+ align:start position:0%
+were talking about the um particle
+ 
+
+ align:start position:0%
+were talking about the um particle
+acceleration uh said it was coming from
+
+ align:start position:0%
+acceleration uh said it was coming from
+ 
+
+ align:start position:0%
+acceleration uh said it was coming from
+a single area are they still doing that
+
+ align:start position:0%
+a single area are they still doing that
+ 
+
+ align:start position:0%
+a single area are they still doing that
+with like uh however else they're
+
+ align:start position:0%
+with like uh however else they're
+ 
+
+ align:start position:0%
+with like uh however else they're
+generating the protons these days um why
+
+ align:start position:0%
+generating the protons these days um why
+ 
+
+ align:start position:0%
+generating the protons these days um why
+don't we yeah we'll skip over that and
+
+ align:start position:0%
+don't we yeah we'll skip over that and
+ 
+
+ align:start position:0%
+don't we yeah we'll skip over that and
+we'll get to how the protons are being
+
+ align:start position:0%
+we'll get to how the protons are being
+ 
+
+ align:start position:0%
+we'll get to how the protons are being
+generated later and it might make a bit
+
+ align:start position:0%
+generated later and it might make a bit
+ 
+
+ align:start position:0%
+generated later and it might make a bit
+more sense so now you can imagine this
+
+ align:start position:0%
+more sense so now you can imagine this
+ 
+
+ align:start position:0%
+more sense so now you can imagine this
+as a point source that for example is um
+
+ align:start position:0%
+as a point source that for example is um
+ 
+
+ align:start position:0%
+as a point source that for example is um
+emitting protons in every direction I
+
+ align:start position:0%
+emitting protons in every direction I
+ 
+
+ align:start position:0%
+emitting protons in every direction I
+see right it just turns out our plasma
+
+ align:start position:0%
+see right it just turns out our plasma
+ 
+
+ align:start position:0%
+see right it just turns out our plasma
+is only in One Direction and so from the
+
+ align:start position:0%
+is only in One Direction and so from the
+ 
+
+ align:start position:0%
+is only in One Direction and so from the
+point of view of the plasma there's just
+
+ align:start position:0%
+point of view of the plasma there's just
+ 
+
+ align:start position:0%
+point of view of the plasma there's just
+a little point that sending protons it
+
+ align:start position:0%
+a little point that sending protons it
+ 
+
+ align:start position:0%
+a little point that sending protons it
+way but reality that's not exactly
+
+ align:start position:0%
+way but reality that's not exactly
+ 
+
+ align:start position:0%
+way but reality that's not exactly
+happening yeah I see okay thank you
+
+ align:start position:0%
+happening yeah I see okay thank you
+ 
+
+ align:start position:0%
+happening yeah I see okay thank you
+okay any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so let's set up the
+
+ align:start position:0%
+questions okay so let's set up the
+ 
+
+ align:start position:0%
+questions okay so let's set up the
+geometry of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so we've got our point
+
+ align:start position:0%
+problem so we've got our point
+ 
+
+ align:start position:0%
+problem so we've got our point
+source over here we've got our
+
+ align:start position:0%
+source over here we've got our
+ 
+
+ align:start position:0%
+source over here we've got our
+plasma here the distance between the two
+
+ align:start position:0%
+plasma here the distance between the two
+ 
+
+ align:start position:0%
+plasma here the distance between the two
+of these is lowercase
+
+ align:start position:0%
+of these is lowercase
+ 
+
+ align:start position:0%
+of these is lowercase
+L our plasma has has some characteristic
+
+ align:start position:0%
+L our plasma has has some characteristic
+ 
+
+ align:start position:0%
+L our plasma has has some characteristic
+size a here we have a
+
+ align:start position:0%
+size a here we have a
+ 
+
+ align:start position:0%
+size a here we have a
+detector some distance
+
+ align:start position:0%
+detector some distance
+ 
+
+ align:start position:0%
+detector some distance
+away and we'll call that
+
+ align:start position:0%
+away and we'll call that
+ 
+
+ align:start position:0%
+away and we'll call that
+distance capital
+
+ align:start position:0%
+distance capital
+ 
+
+ align:start position:0%
+distance capital
+L within the plasma we have a coordinate
+
+ align:start position:0%
+L within the plasma we have a coordinate
+ 
+
+ align:start position:0%
+L within the plasma we have a coordinate
+system and we label points within the
+
+ align:start position:0%
+system and we label points within the
+ 
+
+ align:start position:0%
+system and we label points within the
+plasma using the position Vector x0 here
+
+ align:start position:0%
+plasma using the position Vector x0 here
+ 
+
+ align:start position:0%
+plasma using the position Vector x0 here
+so if I say if I have a position with a
+
+ align:start position:0%
+so if I say if I have a position with a
+ 
+
+ align:start position:0%
+so if I say if I have a position with a
+Z subscript that's somewhere within the
+
+ align:start position:0%
+Z subscript that's somewhere within the
+ 
+
+ align:start position:0%
+Z subscript that's somewhere within the
+plasma and then on the
+
+ align:start position:0%
+plasma and then on the
+ 
+
+ align:start position:0%
+plasma and then on the
+detector I have a position Vector X so
+
+ align:start position:0%
+detector I have a position Vector X so
+ 
+
+ align:start position:0%
+detector I have a position Vector X so
+what we're going to be doing is looking
+
+ align:start position:0%
+what we're going to be doing is looking
+ 
+
+ align:start position:0%
+what we're going to be doing is looking
+at how the protons are deflected at
+
+ align:start position:0%
+at how the protons are deflected at
+ 
+
+ align:start position:0%
+at how the protons are deflected at
+position x0 and they will end up
+
+ align:start position:0%
+position x0 and they will end up
+ 
+
+ align:start position:0%
+position x0 and they will end up
+somewhere on the detector at X and what
+
+ align:start position:0%
+somewhere on the detector at X and what
+ 
+
+ align:start position:0%
+somewhere on the detector at X and what
+our job is therefore is to link what we
+
+ align:start position:0%
+our job is therefore is to link what we
+ 
+
+ align:start position:0%
+our job is therefore is to link what we
+see on our detector X back to the
+
+ align:start position:0%
+see on our detector X back to the
+ 
+
+ align:start position:0%
+see on our detector X back to the
+properties of the plasma at
+
+ align:start position:0%
+properties of the plasma at
+ 
+
+ align:start position:0%
+properties of the plasma at
+x0 and we can think of a
+
+ align:start position:0%
+x0 and we can think of a
+ 
+
+ align:start position:0%
+x0 and we can think of a
+proton coming out like this and within
+
+ align:start position:0%
+proton coming out like this and within
+ 
+
+ align:start position:0%
+proton coming out like this and within
+the plasma undergoing some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection and it's deflected from its
+
+ align:start position:0%
+deflection and it's deflected from its
+ 
+
+ align:start position:0%
+deflection and it's deflected from its
+original trajectory by an angle Alpha
+
+ align:start position:0%
+original trajectory by an angle Alpha
+ 
+
+ align:start position:0%
+original trajectory by an angle Alpha
+and this Alpha in general can be a
+
+ align:start position:0%
+and this Alpha in general can be a
+ 
+
+ align:start position:0%
+and this Alpha in general can be a
+vector right so we can have an angle in
+
+ align:start position:0%
+vector right so we can have an angle in
+ 
+
+ align:start position:0%
+vector right so we can have an angle in
+this direction and we can have an angle
+
+ align:start position:0%
+this direction and we can have an angle
+ 
+
+ align:start position:0%
+this direction and we can have an angle
+in this direction here and we drawing it
+
+ align:start position:0%
+in this direction here and we drawing it
+ 
+
+ align:start position:0%
+in this direction here and we drawing it
+mostly in 1D but remember the particles
+
+ align:start position:0%
+mostly in 1D but remember the particles
+ 
+
+ align:start position:0%
+mostly in 1D but remember the particles
+be deflected in two Dimensions as
+
+ align:start position:0%
+be deflected in two Dimensions as
+ 
+
+ align:start position:0%
+be deflected in two Dimensions as
+well okay so from this symol geometry we
+
+ align:start position:0%
+well okay so from this symol geometry we
+ 
+
+ align:start position:0%
+well okay so from this symol geometry we
+can already write down what we're going
+
+ align:start position:0%
+can already write down what we're going
+ 
+
+ align:start position:0%
+can already write down what we're going
+to see on the detector X so
+
+ align:start position:0%
+to see on the detector X so
+ 
+
+ align:start position:0%
+to see on the detector X so
+X is a location of a proton which
+
+ align:start position:0%
+X is a location of a proton which
+ 
+
+ align:start position:0%
+X is a location of a proton which
+streamed through the point
+
+ align:start position:0%
+streamed through the point
+ 
+
+ align:start position:0%
+streamed through the point
+x0 and then there's a magnification
+
+ align:start position:0%
+x0 and then there's a magnification
+ 
+
+ align:start position:0%
+x0 and then there's a magnification
+Factor capital L over lowercase L this
+
+ align:start position:0%
+Factor capital L over lowercase L this
+ 
+
+ align:start position:0%
+Factor capital L over lowercase L this
+is just similar triangles this just says
+
+ align:start position:0%
+is just similar triangles this just says
+ 
+
+ align:start position:0%
+is just similar triangles this just says
+in the absence of any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection I will have ended up at this
+
+ align:start position:0%
+deflection I will have ended up at this
+ 
+
+ align:start position:0%
+deflection I will have ended up at this
+Point here and that point is magnified
+
+ align:start position:0%
+Point here and that point is magnified
+ 
+
+ align:start position:0%
+Point here and that point is magnified
+because capital L and lowercase L are
+
+ align:start position:0%
+because capital L and lowercase L are
+ 
+
+ align:start position:0%
+because capital L and lowercase L are
+different so so far this is just what
+
+ align:start position:0%
+different so so far this is just what
+ 
+
+ align:start position:0%
+different so so far this is just what
+you get without any plasma when you put
+
+ align:start position:0%
+you get without any plasma when you put
+ 
+
+ align:start position:0%
+you get without any plasma when you put
+the plasma in of course you get some
+
+ align:start position:0%
+the plasma in of course you get some
+ 
+
+ align:start position:0%
+the plasma in of course you get some
+deflection Alpha and that Alpha is Times
+
+ align:start position:0%
+deflection Alpha and that Alpha is Times
+ 
+
+ align:start position:0%
+deflection Alpha and that Alpha is Times
+by the distance between the plasma and
+
+ align:start position:0%
+by the distance between the plasma and
+ 
+
+ align:start position:0%
+by the distance between the plasma and
+the detector here so again this is just
+
+ align:start position:0%
+the detector here so again this is just
+ 
+
+ align:start position:0%
+the detector here so again this is just
+geometry there's nothing to do with
+
+ align:start position:0%
+geometry there's nothing to do with
+ 
+
+ align:start position:0%
+geometry there's nothing to do with
+plasmas or protons or anything in
+
+ align:start position:0%
+plasmas or protons or anything in
+ 
+
+ align:start position:0%
+plasmas or protons or anything in
+there so just to clarify what of these
+
+ align:start position:0%
+there so just to clarify what of these
+ 
+
+ align:start position:0%
+there so just to clarify what of these
+terms are this is at the
+
+ align:start position:0%
+terms are this is at the
+ 
+
+ align:start position:0%
+terms are this is at the
+detector this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object this term
+
+ align:start position:0%
+object this term
+ 
+
+ align:start position:0%
+object this term
+here is due to the Divergence of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam we wouldn't have this term if we
+
+ align:start position:0%
+beam we wouldn't have this term if we
+ 
+
+ align:start position:0%
+beam we wouldn't have this term if we
+had a columnated beam like we had with
+
+ align:start position:0%
+had a columnated beam like we had with
+ 
+
+ align:start position:0%
+had a columnated beam like we had with
+lasers remember with the laser we
+
+ align:start position:0%
+lasers remember with the laser we
+ 
+
+ align:start position:0%
+lasers remember with the laser we
+started out with a load of rays which
+
+ align:start position:0%
+started out with a load of rays which
+ 
+
+ align:start position:0%
+started out with a load of rays which
+parallel and so this wouldn't have
+
+ align:start position:0%
+parallel and so this wouldn't have
+ 
+
+ align:start position:0%
+parallel and so this wouldn't have
+happened with a columnated beam but we
+
+ align:start position:0%
+happened with a columnated beam but we
+ 
+
+ align:start position:0%
+happened with a columnated beam but we
+don't have that we we got a point source
+
+ align:start position:0%
+don't have that we we got a point source
+ 
+
+ align:start position:0%
+don't have that we we got a point source
+we got a diverging Fe and then finally
+
+ align:start position:0%
+we got a diverging Fe and then finally
+ 
+
+ align:start position:0%
+we got a diverging Fe and then finally
+this is to do with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection so this is liography
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a diverging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typically we set up our system so L low
+
+ align:start position:0%
+typically we set up our system so L low
+ 
+
+ align:start position:0%
+typically we set up our system so L low
+uppercase L upon lowercase L is much
+
+ align:start position:0%
+uppercase L upon lowercase L is much
+ 
+
+ align:start position:0%
+uppercase L upon lowercase L is much
+much larger than one that is to say we
+
+ align:start position:0%
+much larger than one that is to say we
+ 
+
+ align:start position:0%
+much larger than one that is to say we
+have our source we have our
+
+ align:start position:0%
+have our source we have our
+ 
+
+ align:start position:0%
+have our source we have our
+plasma and then quite a long distance
+
+ align:start position:0%
+plasma and then quite a long distance
+ 
+
+ align:start position:0%
+plasma and then quite a long distance
+away we have our detector here remember
+
+ align:start position:0%
+away we have our detector here remember
+ 
+
+ align:start position:0%
+away we have our detector here remember
+this is lowercase L this is uppercase L
+
+ align:start position:0%
+this is lowercase L this is uppercase L
+ 
+
+ align:start position:0%
+this is lowercase L this is uppercase L
+um this is for two reasons firstly the
+
+ align:start position:0%
+um this is for two reasons firstly the
+ 
+
+ align:start position:0%
+um this is for two reasons firstly the
+plasmas tend to be very small and so by
+
+ align:start position:0%
+plasmas tend to be very small and so by
+ 
+
+ align:start position:0%
+plasmas tend to be very small and so by
+setting it up like this we get a massive
+
+ align:start position:0%
+setting it up like this we get a massive
+ 
+
+ align:start position:0%
+setting it up like this we get a massive
+magnification so because we've got these
+
+ align:start position:0%
+magnification so because we've got these
+ 
+
+ align:start position:0%
+magnification so because we've got these
+diverging protons here mapping out over
+
+ align:start position:0%
+diverging protons here mapping out over
+ 
+
+ align:start position:0%
+diverging protons here mapping out over
+there we're going to have a nice big
+
+ align:start position:0%
+there we're going to have a nice big
+ 
+
+ align:start position:0%
+there we're going to have a nice big
+image to look at you know so if this is
+
+ align:start position:0%
+image to look at you know so if this is
+ 
+
+ align:start position:0%
+image to look at you know so if this is
+only 100 microns across maybe on your
+
+ align:start position:0%
+only 100 microns across maybe on your
+ 
+
+ align:start position:0%
+only 100 microns across maybe on your
+image over here it's 10 millimeters
+
+ align:start position:0%
+image over here it's 10 millimeters
+ 
+
+ align:start position:0%
+image over here it's 10 millimeters
+across which is still pretty small but
+
+ align:start position:0%
+across which is still pretty small but
+ 
+
+ align:start position:0%
+across which is still pretty small but
+maybe you can actually see something
+
+ align:start position:0%
+maybe you can actually see something
+ 
+
+ align:start position:0%
+maybe you can actually see something
+under your detector the other reason is
+
+ align:start position:0%
+under your detector the other reason is
+ 
+
+ align:start position:0%
+under your detector the other reason is
+just practical you Cann put your
+
+ align:start position:0%
+just practical you Cann put your
+ 
+
+ align:start position:0%
+just practical you Cann put your
+detector very close to your plasma if
+
+ align:start position:0%
+detector very close to your plasma if
+ 
+
+ align:start position:0%
+detector very close to your plasma if
+this is something like a laser driven
+
+ align:start position:0%
+this is something like a laser driven
+ 
+
+ align:start position:0%
+this is something like a laser driven
+ICF implosion you really don't want to
+
+ align:start position:0%
+ICF implosion you really don't want to
+ 
+
+ align:start position:0%
+ICF implosion you really don't want to
+have your detector close because it will
+
+ align:start position:0%
+have your detector close because it will
+ 
+
+ align:start position:0%
+have your detector close because it will
+get trash you got to put it a long way
+
+ align:start position:0%
+get trash you got to put it a long way
+ 
+
+ align:start position:0%
+get trash you got to put it a long way
+away um so this is typically the regime
+
+ align:start position:0%
+away um so this is typically the regime
+ 
+
+ align:start position:0%
+away um so this is typically the regime
+that we work in and then
+
+ align:start position:0%
+that we work in and then
+ 
+
+ align:start position:0%
+that we work in and then
+as you can see up here that means that
+
+ align:start position:0%
+as you can see up here that means that
+ 
+
+ align:start position:0%
+as you can see up here that means that
+we have a term that looks
+
+ align:start position:0%
+we have a term that looks
+ 
+
+ align:start position:0%
+we have a term that looks
+like x0 1 plus capital L over lowercase
+
+ align:start position:0%
+like x0 1 plus capital L over lowercase
+ 
+
+ align:start position:0%
+like x0 1 plus capital L over lowercase
+L and we can just drop that term there
+
+ align:start position:0%
+L and we can just drop that term there
+ 
+
+ align:start position:0%
+L and we can just drop that term there
+as being small compared to the second
+
+ align:start position:0%
+as being small compared to the second
+ 
+
+ align:start position:0%
+as being small compared to the second
+term and we can then convert that
+
+ align:start position:0%
+term and we can then convert that
+ 
+
+ align:start position:0%
+term and we can then convert that
+equation so that it reads x equal
+
+ align:start position:0%
+equation so that it reads x equal
+ 
+
+ align:start position:0%
+equation so that it reads x equal
+L x0 upon lower case
+
+ align:start position:0%
+L x0 upon lower case
+ 
+
+ align:start position:0%
+L x0 upon lower case
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+Alpha I've just taken the capital L
+
+ align:start position:0%
+Alpha I've just taken the capital L
+ 
+
+ align:start position:0%
+Alpha I've just taken the capital L
+outside the brackets here now we have
+
+ align:start position:0%
+outside the brackets here now we have
+ 
+
+ align:start position:0%
+outside the brackets here now we have
+these two terms inside so this first
+
+ align:start position:0%
+these two terms inside so this first
+ 
+
+ align:start position:0%
+these two terms inside so this first
+term as I said is simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magnification very poorly written and
+
+ align:start position:0%
+magnification very poorly written and
+ 
+
+ align:start position:0%
+magnification very poorly written and
+this second term here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Distortion because the rays are being
+
+ align:start position:0%
+Distortion because the rays are being
+ 
+
+ align:start position:0%
+Distortion because the rays are being
+deflected we didn't have the Distortion
+
+ align:start position:0%
+deflected we didn't have the Distortion
+ 
+
+ align:start position:0%
+deflected we didn't have the Distortion
+this would just be an Imaging system
+
+ align:start position:0%
+this would just be an Imaging system
+ 
+
+ align:start position:0%
+this would just be an Imaging system
+with magnification because the rays are
+
+ align:start position:0%
+with magnification because the rays are
+ 
+
+ align:start position:0%
+with magnification because the rays are
+being deflected we have Distortion and
+
+ align:start position:0%
+being deflected we have Distortion and
+ 
+
+ align:start position:0%
+being deflected we have Distortion and
+because it's Distortion proton Imaging
+
+ align:start position:0%
+because it's Distortion proton Imaging
+ 
+
+ align:start position:0%
+because it's Distortion proton Imaging
+is not
+
+ align:start position:0%
+is not
+ 
+
+ align:start position:0%
+is not
+Imaging so perhaps they should call it
+
+ align:start position:0%
+Imaging so perhaps they should call it
+ 
+
+ align:start position:0%
+Imaging so perhaps they should call it
+proton deflectometry we can argue about
+
+ align:start position:0%
+proton deflectometry we can argue about
+ 
+
+ align:start position:0%
+proton deflectometry we can argue about
+the name for ages but this is not an
+
+ align:start position:0%
+the name for ages but this is not an
+ 
+
+ align:start position:0%
+the name for ages but this is not an
+Imaging technique like quotography if
+
+ align:start position:0%
+Imaging technique like quotography if
+ 
+
+ align:start position:0%
+Imaging technique like quotography if
+you see something on your detect
+
+ align:start position:0%
+you see something on your detect
+ 
+
+ align:start position:0%
+you see something on your detect
+it doesn't have a onetoone
+
+ align:start position:0%
+it doesn't have a onetoone
+ 
+
+ align:start position:0%
+it doesn't have a onetoone
+correspondence with what's going on in
+
+ align:start position:0%
+correspondence with what's going on in
+ 
+
+ align:start position:0%
+correspondence with what's going on in
+the plasma features are enhanced and
+
+ align:start position:0%
+the plasma features are enhanced and
+ 
+
+ align:start position:0%
+the plasma features are enhanced and
+enlarged the void that we were producing
+
+ align:start position:0%
+enlarged the void that we were producing
+ 
+
+ align:start position:0%
+enlarged the void that we were producing
+here that void for example is going to
+
+ align:start position:0%
+here that void for example is going to
+ 
+
+ align:start position:0%
+here that void for example is going to
+be larger than the real size of the
+
+ align:start position:0%
+be larger than the real size of the
+ 
+
+ align:start position:0%
+be larger than the real size of the
+plasma the protons are being pushed
+
+ align:start position:0%
+plasma the protons are being pushed
+ 
+
+ align:start position:0%
+plasma the protons are being pushed
+outwards
+
+ align:start position:0%
+outwards
+ 
+
+ align:start position:0%
+outwards
+okay so mathematically what we're doing
+
+ align:start position:0%
+okay so mathematically what we're doing
+ 
+
+ align:start position:0%
+okay so mathematically what we're doing
+is we're
+
+ align:start position:0%
+is we're
+ 
+
+ align:start position:0%
+is we're
+taking some area inside the plasma D s0
+
+ align:start position:0%
+taking some area inside the plasma D s0
+ 
+
+ align:start position:0%
+taking some area inside the plasma D s0
+which has a certain number of prot
+
+ align:start position:0%
+which has a certain number of prot
+ 
+
+ align:start position:0%
+which has a certain number of prot
+going through
+
+ align:start position:0%
+going through
+ 
+
+ align:start position:0%
+going through
+it and we're mapping that out onto some
+
+ align:start position:0%
+it and we're mapping that out onto some
+ 
+
+ align:start position:0%
+it and we're mapping that out onto some
+area on the detector which does not have
+
+ align:start position:0%
+area on the detector which does not have
+ 
+
+ align:start position:0%
+area on the detector which does not have
+to be anywhere close to the same shape
+
+ align:start position:0%
+to be anywhere close to the same shape
+ 
+
+ align:start position:0%
+to be anywhere close to the same shape
+because of all the deflections going on
+
+ align:start position:0%
+because of all the deflections going on
+ 
+
+ align:start position:0%
+because of all the deflections going on
+inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and that area is just the S so
+
+ align:start position:0%
+here and that area is just the S so
+ 
+
+ align:start position:0%
+here and that area is just the S so
+we're keeping our subscript notation
+
+ align:start position:0%
+we're keeping our subscript notation
+ 
+
+ align:start position:0%
+we're keeping our subscript notation
+here this is the object this is the
+
+ align:start position:0%
+here this is the object this is the
+ 
+
+ align:start position:0%
+here this is the object this is the
+image that's forming here and the way to
+
+ align:start position:0%
+image that's forming here and the way to
+ 
+
+ align:start position:0%
+image that's forming here and the way to
+link these is to say that DS is equal to
+
+ align:start position:0%
+link these is to say that DS is equal to
+ 
+
+ align:start position:0%
+link these is to say that DS is equal to
+the magnitude of this quantity
+
+ align:start position:0%
+the magnitude of this quantity
+ 
+
+ align:start position:0%
+the magnitude of this quantity
+D at
+
+ align:start position:0%
+D at
+ 
+
+ align:start position:0%
+D at
+x0 times DS and this is a quantity that
+
+ align:start position:0%
+x0 times DS and this is a quantity that
+ 
+
+ align:start position:0%
+x0 times DS and this is a quantity that
+some of you may know it's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jacobian and it has the
+
+ align:start position:0%
+Jacobian and it has the
+ 
+
+ align:start position:0%
+Jacobian and it has the
+form partial X and Y over
+
+ align:start position:0%
+form partial X and Y over
+ 
+
+ align:start position:0%
+form partial X and Y over
+partial
+
+ align:start position:0%
+partial
+ 
+
+ align:start position:0%
+partial
+x0 y z of course we haven't told you how
+
+ align:start position:0%
+x0 y z of course we haven't told you how
+ 
+
+ align:start position:0%
+x0 y z of course we haven't told you how
+to calculate that yet but it's going to
+
+ align:start position:0%
+to calculate that yet but it's going to
+ 
+
+ align:start position:0%
+to calculate that yet but it's going to
+be related to this here so this is just
+
+ align:start position:0%
+be related to this here so this is just
+ 
+
+ align:start position:0%
+be related to this here so this is just
+a general statement when you're mapping
+
+ align:start position:0%
+a general statement when you're mapping
+ 
+
+ align:start position:0%
+a general statement when you're mapping
+some area to another area you can do it
+
+ align:start position:0%
+some area to another area you can do it
+ 
+
+ align:start position:0%
+some area to another area you can do it
+using this Jacobian transform um and the
+
+ align:start position:0%
+using this Jacobian transform um and the
+ 
+
+ align:start position:0%
+using this Jacobian transform um and the
+exact way Jacobian transform Works will
+
+ align:start position:0%
+exact way Jacobian transform Works will
+ 
+
+ align:start position:0%
+exact way Jacobian transform Works will
+be related to this and we'll Solve IT
+
+ align:start position:0%
+be related to this and we'll Solve IT
+ 
+
+ align:start position:0%
+be related to this and we'll Solve IT
+explicitly uh sorry the left hand side
+
+ align:start position:0%
+explicitly uh sorry the left hand side
+ 
+
+ align:start position:0%
+explicitly uh sorry the left hand side
+here thank you yes didn't make much
+
+ align:start position:0%
+here thank you yes didn't make much
+ 
+
+ align:start position:0%
+here thank you yes didn't make much
+sense I said it and I guess this is a
+
+ align:start position:0%
+sense I said it and I guess this is a
+ 
+
+ align:start position:0%
+sense I said it and I guess this is a
+vector again but here I've written out
+
+ align:start position:0%
+vector again but here I've written out
+ 
+
+ align:start position:0%
+vector again but here I've written out
+explicitly in terms of the X and Y
+
+ align:start position:0%
+explicitly in terms of the X and Y
+ 
+
+ align:start position:0%
+explicitly in terms of the X and Y
+components um here I just put in this
+
+ align:start position:0%
+components um here I just put in this
+ 
+
+ align:start position:0%
+components um here I just put in this
+more compact Vector notation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay we're going to assume
+
+ align:start position:0%
+questions okay we're going to assume
+ 
+
+ align:start position:0%
+questions okay we're going to assume
+that we can serve particles maybe this
+
+ align:start position:0%
+that we can serve particles maybe this
+ 
+
+ align:start position:0%
+that we can serve particles maybe this
+was another assumption up here that none
+
+ align:start position:0%
+was another assumption up here that none
+ 
+
+ align:start position:0%
+was another assumption up here that none
+of our particles are scattered lost but
+
+ align:start position:0%
+of our particles are scattered lost but
+ 
+
+ align:start position:0%
+of our particles are scattered lost but
+if we conserve the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protons then the intensity on our
+
+ align:start position:0%
+protons then the intensity on our
+ 
+
+ align:start position:0%
+protons then the intensity on our
+detector is going to be equal to the
+
+ align:start position:0%
+detector is going to be equal to the
+ 
+
+ align:start position:0%
+detector is going to be equal to the
+intensity going through the object
+
+ align:start position:0%
+intensity going through the object
+ 
+
+ align:start position:0%
+intensity going through the object
+divided by this
+
+ align:start position:0%
+divided by this
+ 
+
+ align:start position:0%
+divided by this
+jacobia is equivalent statement that
+
+ align:start position:0%
+jacobia is equivalent statement that
+ 
+
+ align:start position:0%
+jacobia is equivalent statement that
+we're conserving the area of this
+
+ align:start position:0%
+we're conserving the area of this
+ 
+
+ align:start position:0%
+we're conserving the area of this
+Jacobian transformation here we're
+
+ align:start position:0%
+Jacobian transformation here we're
+ 
+
+ align:start position:0%
+Jacobian transformation here we're
+conserving intensity here and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trovian is going to be equal to l^2
+
+ align:start position:0%
+trovian is going to be equal to l^2
+ 
+
+ align:start position:0%
+trovian is going to be equal to l^2
+capital l s upon lowercase l s times 1
+
+ align:start position:0%
+capital l s upon lowercase l s times 1
+ 
+
+ align:start position:0%
+capital l s upon lowercase l s times 1
+plus then we start doing a tailor
+
+ align:start position:0%
+plus then we start doing a tailor
+ 
+
+ align:start position:0%
+plus then we start doing a tailor
+expansion uh of this uh equation here
+
+ align:start position:0%
+expansion uh of this uh equation here
+ 
+
+ align:start position:0%
+expansion uh of this uh equation here
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+gradient of alpha plus l s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial alpha x component partial
+
+ align:start position:0%
+partial alpha x component partial
+ 
+
+ align:start position:0%
+partial alpha x component partial
+x0 partial alpha y component partial y z
+
+ align:start position:0%
+x0 partial alpha y component partial y z
+ 
+
+ align:start position:0%
+x0 partial alpha y component partial y z
+and then another term which follows
+
+ align:start position:0%
+and then another term which follows
+ 
+
+ align:start position:0%
+and then another term which follows
+symmetrically from this which is minus
+
+ align:start position:0%
+symmetrically from this which is minus
+ 
+
+ align:start position:0%
+symmetrically from this which is minus
+partial alpha x component partial y0
+
+ align:start position:0%
+partial alpha x component partial y0
+ 
+
+ align:start position:0%
+partial alpha x component partial y0
+partial alpha y component partial
+
+ align:start position:0%
+partial alpha y component partial
+ 
+
+ align:start position:0%
+partial alpha y component partial
+x0 plus some other terms that we're
+
+ align:start position:0%
+x0 plus some other terms that we're
+ 
+
+ align:start position:0%
+x0 plus some other terms that we're
+going to drop as being small here
+
+ align:start position:0%
+going to drop as being small here
+ 
+
+ align:start position:0%
+going to drop as being small here
+there's probably a more compact Vector
+
+ align:start position:0%
+there's probably a more compact Vector
+ 
+
+ align:start position:0%
+there's probably a more compact Vector
+notation for this but I just wanted to
+
+ align:start position:0%
+notation for this but I just wanted to
+ 
+
+ align:start position:0%
+notation for this but I just wanted to
+write it out more explicitly this one is
+
+ align:start position:0%
+write it out more explicitly this one is
+ 
+
+ align:start position:0%
+write it out more explicitly this one is
+clearly just partial alpha x partial X
+
+ align:start position:0%
+clearly just partial alpha x partial X
+ 
+
+ align:start position:0%
+clearly just partial alpha x partial X
+Plus partial alpha y partial Y and these
+
+ align:start position:0%
+Plus partial alpha y partial Y and these
+ 
+
+ align:start position:0%
+Plus partial alpha y partial Y and these
+are all zero subscripts because we're
+
+ align:start position:0%
+are all zero subscripts because we're
+ 
+
+ align:start position:0%
+are all zero subscripts because we're
+doing the derivative inside the plasma
+
+ align:start position:0%
+doing the derivative inside the plasma
+ 
+
+ align:start position:0%
+doing the derivative inside the plasma
+so this is looking at derivatives of how
+
+ align:start position:0%
+so this is looking at derivatives of how
+ 
+
+ align:start position:0%
+so this is looking at derivatives of how
+the angle changes inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the okay so if you can calculate your
+
+ align:start position:0%
+the okay so if you can calculate your
+ 
+
+ align:start position:0%
+the okay so if you can calculate your
+angle Alpha and you might think I can do
+
+ align:start position:0%
+angle Alpha and you might think I can do
+ 
+
+ align:start position:0%
+angle Alpha and you might think I can do
+that if I know the Electric magnetic
+
+ align:start position:0%
+that if I know the Electric magnetic
+ 
+
+ align:start position:0%
+that if I know the Electric magnetic
+fields in my system and you be right
+
+ align:start position:0%
+fields in my system and you be right
+ 
+
+ align:start position:0%
+fields in my system and you be right
+then you can now calculate how alpha
+
+ align:start position:0%
+then you can now calculate how alpha
+ 
+
+ align:start position:0%
+then you can now calculate how alpha
+changes within the plasma how the
+
+ align:start position:0%
+changes within the plasma how the
+ 
+
+ align:start position:0%
+changes within the plasma how the
+protons get distorted and now you can
+
+ align:start position:0%
+protons get distorted and now you can
+ 
+
+ align:start position:0%
+protons get distorted and now you can
+work out what your intensity is compared
+
+ align:start position:0%
+work out what your intensity is compared
+ 
+
+ align:start position:0%
+work out what your intensity is compared
+to your initial intensity and it turns
+
+ align:start position:0%
+to your initial intensity and it turns
+ 
+
+ align:start position:0%
+to your initial intensity and it turns
+out that the sorts of images you get out
+
+ align:start position:0%
+out that the sorts of images you get out
+ 
+
+ align:start position:0%
+out that the sorts of images you get out
+of here there's a very useful
+
+ align:start position:0%
+of here there's a very useful
+ 
+
+ align:start position:0%
+of here there's a very useful
+dimensionless parameter that you can
+
+ align:start position:0%
+dimensionless parameter that you can
+ 
+
+ align:start position:0%
+dimensionless parameter that you can
+write down to characterize the different
+
+ align:start position:0%
+write down to characterize the different
+ 
+
+ align:start position:0%
+write down to characterize the different
+images and this parameter is called the
+
+ align:start position:0%
+images and this parameter is called the
+ 
+
+ align:start position:0%
+images and this parameter is called the
+contrast
+
+ align:start position:0%
+contrast
+ 
+
+ align:start position:0%
+contrast
+parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's written as Mu and it is defined
+
+ align:start position:0%
+and it's written as Mu and it is defined
+ 
+
+ align:start position:0%
+and it's written as Mu and it is defined
+as lowercase L over a lowercase L was
+
+ align:start position:0%
+as lowercase L over a lowercase L was
+ 
+
+ align:start position:0%
+as lowercase L over a lowercase L was
+the distance from the point source to
+
+ align:start position:0%
+the distance from the point source to
+ 
+
+ align:start position:0%
+the distance from the point source to
+the plasma and a is the size of our
+
+ align:start position:0%
+the plasma and a is the size of our
+ 
+
+ align:start position:0%
+the plasma and a is the size of our
+plasma times the modulus of this
+
+ align:start position:0%
+plasma times the modulus of this
+ 
+
+ align:start position:0%
+plasma times the modulus of this
+deflection angle Vector so the size of
+
+ align:start position:0%
+deflection angle Vector so the size of
+ 
+
+ align:start position:0%
+deflection angle Vector so the size of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection and it turns out if you're in
+
+ align:start position:0%
+deflection and it turns out if you're in
+ 
+
+ align:start position:0%
+deflection and it turns out if you're in
+a r regime where this parameter is much
+
+ align:start position:0%
+a r regime where this parameter is much
+ 
+
+ align:start position:0%
+a r regime where this parameter is much
+much less than one then you find out
+
+ align:start position:0%
+much less than one then you find out
+ 
+
+ align:start position:0%
+much less than one then you find out
+that your D your Jacobian here is
+
+ align:start position:0%
+that your D your Jacobian here is
+ 
+
+ align:start position:0%
+that your D your Jacobian here is
+approximately constant and so your
+
+ align:start position:0%
+approximately constant and so your
+ 
+
+ align:start position:0%
+approximately constant and so your
+intensity is approximately constant so
+
+ align:start position:0%
+intensity is approximately constant so
+ 
+
+ align:start position:0%
+intensity is approximately constant so
+we talked about this with shog graphy
+
+ align:start position:0%
+we talked about this with shog graphy
+ 
+
+ align:start position:0%
+we talked about this with shog graphy
+this is a regime where we only have
+
+ align:start position:0%
+this is a regime where we only have
+ 
+
+ align:start position:0%
+this is a regime where we only have
+small intensity variations and when you
+
+ align:start position:0%
+small intensity variations and when you
+ 
+
+ align:start position:0%
+small intensity variations and when you
+have small intensity variations you have
+
+ align:start position:0%
+have small intensity variations you have
+ 
+
+ align:start position:0%
+have small intensity variations you have
+a chance of being able to undo this
+
+ align:start position:0%
+a chance of being able to undo this
+ 
+
+ align:start position:0%
+a chance of being able to undo this
+transformation and work out what the was
+
+ align:start position:0%
+transformation and work out what the was
+ 
+
+ align:start position:0%
+transformation and work out what the was
+and therefore work out something about
+
+ align:start position:0%
+and therefore work out something about
+ 
+
+ align:start position:0%
+and therefore work out something about
+your plasma but if you have a contrast
+
+ align:start position:0%
+your plasma but if you have a contrast
+ 
+
+ align:start position:0%
+your plasma but if you have a contrast
+parameter where mu is about one this
+
+ align:start position:0%
+parameter where mu is about one this
+ 
+
+ align:start position:0%
+parameter where mu is about one this
+corresponds to having your
+
+ align:start position:0%
+corresponds to having your
+ 
+
+ align:start position:0%
+corresponds to having your
+Jacobian uh with
+
+ align:start position:0%
+Jacobian uh with
+ 
+
+ align:start position:0%
+Jacobian uh with
+singularities or with zeros in
+
+ align:start position:0%
+singularities or with zeros in
+ 
+
+ align:start position:0%
+singularities or with zeros in
+it you can see if you have zeros in D
+
+ align:start position:0%
+it you can see if you have zeros in D
+ 
+
+ align:start position:0%
+it you can see if you have zeros in D
+then all of a sudden you're going to
+
+ align:start position:0%
+then all of a sudden you're going to
+ 
+
+ align:start position:0%
+then all of a sudden you're going to
+have your initial intensity over zero
+
+ align:start position:0%
+have your initial intensity over zero
+ 
+
+ align:start position:0%
+have your initial intensity over zero
+your intensity will go to some very very
+
+ align:start position:0%
+your intensity will go to some very very
+ 
+
+ align:start position:0%
+your intensity will go to some very very
+large number and these are the cotic
+
+ align:start position:0%
+large number and these are the cotic
+ 
+
+ align:start position:0%
+large number and these are the cotic
+patterns we talked about in
+
+ align:start position:0%
+patterns we talked about in
+ 
+
+ align:start position:0%
+patterns we talked about in
+chirography
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah I wish I had some more space but
+
+ align:start position:0%
+uh yeah I wish I had some more space but
+ 
+
+ align:start position:0%
+uh yeah I wish I had some more space but
+I don't so well actually uh maybe I have
+
+ align:start position:0%
+I don't so well actually uh maybe I have
+ 
+
+ align:start position:0%
+I don't so well actually uh maybe I have
+just about enough space so in this case
+
+ align:start position:0%
+just about enough space so in this case
+ 
+
+ align:start position:0%
+just about enough space so in this case
+here you can show that your intensity on
+
+ align:start position:0%
+here you can show that your intensity on
+ 
+
+ align:start position:0%
+here you can show that your intensity on
+your detector is equal to your Source
+
+ align:start position:0%
+your detector is equal to your Source
+ 
+
+ align:start position:0%
+your detector is equal to your Source
+intensity uh times one minus
+
+ align:start position:0%
+intensity uh times one minus
+ 
+
+ align:start position:0%
+intensity uh times one minus
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+Divergence of alpha like this and this
+
+ align:start position:0%
+Divergence of alpha like this and this
+ 
+
+ align:start position:0%
+Divergence of alpha like this and this
+is equivalent the equation we came up
+
+ align:start position:0%
+is equivalent the equation we came up
+ 
+
+ align:start position:0%
+is equivalent the equation we came up
+with ography where we've implicitly
+
+ align:start position:0%
+with ography where we've implicitly
+ 
+
+ align:start position:0%
+with ography where we've implicitly
+assumed that all of these terms are very
+
+ align:start position:0%
+assumed that all of these terms are very
+ 
+
+ align:start position:0%
+assumed that all of these terms are very
+small if you look here our contrast
+
+ align:start position:0%
+small if you look here our contrast
+ 
+
+ align:start position:0%
+small if you look here our contrast
+parameter has an L an alpha and an a
+
+ align:start position:0%
+parameter has an L an alpha and an a
+ 
+
+ align:start position:0%
+parameter has an L an alpha and an a
+we've got an L an alpha and this
+
+ align:start position:0%
+we've got an L an alpha and this
+ 
+
+ align:start position:0%
+we've got an L an alpha and this
+gradient is going to be on the order
+
+ align:start position:0%
+gradient is going to be on the order
+ 
+
+ align:start position:0%
+gradient is going to be on the order
+of the size of the plasma like that so
+
+ align:start position:0%
+of the size of the plasma like that so
+ 
+
+ align:start position:0%
+of the size of the plasma like that so
+we've implicitly assumed this contrast
+
+ align:start position:0%
+we've implicitly assumed this contrast
+ 
+
+ align:start position:0%
+we've implicitly assumed this contrast
+parameter is small in order to get this
+
+ align:start position:0%
+parameter is small in order to get this
+ 
+
+ align:start position:0%
+parameter is small in order to get this
+solution and so what we see is we have
+
+ align:start position:0%
+solution and so what we see is we have
+ 
+
+ align:start position:0%
+solution and so what we see is we have
+small variations in intensity it's one
+
+ align:start position:0%
+small variations in intensity it's one
+ 
+
+ align:start position:0%
+small variations in intensity it's one
+minus a very small
+
+ align:start position:0%
+minus a very small
+ 
+
+ align:start position:0%
+minus a very small
+number if we have zeros here then we
+
+ align:start position:0%
+number if we have zeros here then we
+ 
+
+ align:start position:0%
+number if we have zeros here then we
+actually have to solve fully for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d for D everywhere inside the
+
+ align:start position:0%
+d for D everywhere inside the
+ 
+
+ align:start position:0%
+d for D everywhere inside the
+plasma and this is where we start
+
+ align:start position:0%
+plasma and this is where we start
+ 
+
+ align:start position:0%
+plasma and this is where we start
+getting these singularities so I got
+
+ align:start position:0%
+getting these singularities so I got
+ 
+
+ align:start position:0%
+getting these singularities so I got
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space so we have D equals zero we get
+
+ align:start position:0%
+space so we have D equals zero we get
+ 
+
+ align:start position:0%
+space so we have D equals zero we get
+singularities in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I is equal to i z over the size of
+
+ align:start position:0%
+I I is equal to i z over the size of
+ 
+
+ align:start position:0%
+I I is equal to i z over the size of
+D and this corresponds to proton
+
+ align:start position:0%
+D and this corresponds to proton
+ 
+
+ align:start position:0%
+D and this corresponds to proton
+trajectories Crossing so we have
+
+ align:start position:0%
+trajectories Crossing so we have
+ 
+
+ align:start position:0%
+trajectories Crossing so we have
+deflection within the
+
+ align:start position:0%
+deflection within the
+ 
+
+ align:start position:0%
+deflection within the
+plasma and we have two protons which
+
+ align:start position:0%
+plasma and we have two protons which
+ 
+
+ align:start position:0%
+plasma and we have two protons which
+take different paths but end up at the
+
+ align:start position:0%
+take different paths but end up at the
+ 
+
+ align:start position:0%
+take different paths but end up at the
+same place and if you can imagine if
+
+ align:start position:0%
+same place and if you can imagine if
+ 
+
+ align:start position:0%
+same place and if you can imagine if
+there's multiple of these happening you
+
+ align:start position:0%
+there's multiple of these happening you
+ 
+
+ align:start position:0%
+there's multiple of these happening you
+end up with a huge amount of fluence in
+
+ align:start position:0%
+end up with a huge amount of fluence in
+ 
+
+ align:start position:0%
+end up with a huge amount of fluence in
+one spot and so you get very very high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intensity and this is usually called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acostic so these cotic features are very
+
+ align:start position:0%
+acostic so these cotic features are very
+ 
+
+ align:start position:0%
+acostic so these cotic features are very
+very strong you can see them very very
+
+ align:start position:0%
+very strong you can see them very very
+ 
+
+ align:start position:0%
+very strong you can see them very very
+easily um but they mean that there is no
+
+ align:start position:0%
+easily um but they mean that there is no
+ 
+
+ align:start position:0%
+easily um but they mean that there is no
+longer a unique reconstruction so we can
+
+ align:start position:0%
+longer a unique reconstruction so we can
+ 
+
+ align:start position:0%
+longer a unique reconstruction so we can
+no longer uniquely take our modulation
+
+ align:start position:0%
+no longer uniquely take our modulation
+ 
+
+ align:start position:0%
+no longer uniquely take our modulation
+intensity I on our detector and work out
+
+ align:start position:0%
+intensity I on our detector and work out
+ 
+
+ align:start position:0%
+intensity I on our detector and work out
+the properties of the plasma through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D so we want to avoid being in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regime avoid being in the regime where
+
+ align:start position:0%
+regime avoid being in the regime where
+ 
+
+ align:start position:0%
+regime avoid being in the regime where
+mu is approximately one and to avoid
+
+ align:start position:0%
+mu is approximately one and to avoid
+ 
+
+ align:start position:0%
+mu is approximately one and to avoid
+being in that regime we just have to
+
+ align:start position:0%
+being in that regime we just have to
+ 
+
+ align:start position:0%
+being in that regime we just have to
+look at the definition of mu and try and
+
+ align:start position:0%
+look at the definition of mu and try and
+ 
+
+ align:start position:0%
+look at the definition of mu and try and
+make it as small as possible so we want
+
+ align:start position:0%
+make it as small as possible so we want
+ 
+
+ align:start position:0%
+make it as small as possible so we want
+l over a much much less than one so
+
+ align:start position:0%
+l over a much much less than one so
+ 
+
+ align:start position:0%
+l over a much much less than one so
+again that's the distance between the
+
+ align:start position:0%
+again that's the distance between the
+ 
+
+ align:start position:0%
+again that's the distance between the
+source I've got it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already The Source distance Le plasma is
+
+ align:start position:0%
+already The Source distance Le plasma is
+ 
+
+ align:start position:0%
+already The Source distance Le plasma is
+L and the size of the plasma is a so
+
+ align:start position:0%
+L and the size of the plasma is a so
+ 
+
+ align:start position:0%
+L and the size of the plasma is a so
+obviously in this case I haven't
+
+ align:start position:0%
+obviously in this case I haven't
+ 
+
+ align:start position:0%
+obviously in this case I haven't
+succeeded L A is roughly one but I could
+
+ align:start position:0%
+succeeded L A is roughly one but I could
+ 
+
+ align:start position:0%
+succeeded L A is roughly one but I could
+put the source much further away and
+
+ align:start position:0%
+put the source much further away and
+ 
+
+ align:start position:0%
+put the source much further away and
+then L A would be much smaller and that
+
+ align:start position:0%
+then L A would be much smaller and that
+ 
+
+ align:start position:0%
+then L A would be much smaller and that
+would help me make mu smaller and and
+
+ align:start position:0%
+would help me make mu smaller and and
+ 
+
+ align:start position:0%
+would help me make mu smaller and and
+the other thing I can do is
+
+ align:start position:0%
+the other thing I can do is
+ 
+
+ align:start position:0%
+the other thing I can do is
+have the size of alpha be much much less
+
+ align:start position:0%
+have the size of alpha be much much less
+ 
+
+ align:start position:0%
+have the size of alpha be much much less
+than one so that's effectively insisting
+
+ align:start position:0%
+than one so that's effectively insisting
+ 
+
+ align:start position:0%
+than one so that's effectively insisting
+that my deflections are small now for a
+
+ align:start position:0%
+that my deflections are small now for a
+ 
+
+ align:start position:0%
+that my deflections are small now for a
+given plasma there are some given
+
+ align:start position:0%
+given plasma there are some given
+ 
+
+ align:start position:0%
+given plasma there are some given
+electric and magnetic fields I can't
+
+ align:start position:0%
+electric and magnetic fields I can't
+ 
+
+ align:start position:0%
+electric and magnetic fields I can't
+just ask the deflections to be small
+
+ align:start position:0%
+just ask the deflections to be small
+ 
+
+ align:start position:0%
+just ask the deflections to be small
+what I can do however as we'll see in a
+
+ align:start position:0%
+what I can do however as we'll see in a
+ 
+
+ align:start position:0%
+what I can do however as we'll see in a
+moment is use very fast particles or
+
+ align:start position:0%
+moment is use very fast particles or
+ 
+
+ align:start position:0%
+moment is use very fast particles or
+fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protons because if we make the protons
+
+ align:start position:0%
+protons because if we make the protons
+ 
+
+ align:start position:0%
+protons because if we make the protons
+go very fast they def become smaller and
+
+ align:start position:0%
+go very fast they def become smaller and
+ 
+
+ align:start position:0%
+go very fast they def become smaller and
+smaller as we're about to
+
+ align:start position:0%
+smaller as we're about to
+ 
+
+ align:start position:0%
+smaller as we're about to
+show okay now none of this really has
+
+ align:start position:0%
+show okay now none of this really has
+ 
+
+ align:start position:0%
+show okay now none of this really has
+talked about protons at any point all of
+
+ align:start position:0%
+talked about protons at any point all of
+ 
+
+ align:start position:0%
+talked about protons at any point all of
+this applies just the same theography
+
+ align:start position:0%
+this applies just the same theography
+ 
+
+ align:start position:0%
+this applies just the same theography
+we're just thinking about particles or
+
+ align:start position:0%
+we're just thinking about particles or
+ 
+
+ align:start position:0%
+we're just thinking about particles or
+rays that get deflected going through a
+
+ align:start position:0%
+rays that get deflected going through a
+ 
+
+ align:start position:0%
+rays that get deflected going through a
+plasma and we've sort of put some
+
+ align:start position:0%
+plasma and we've sort of put some
+ 
+
+ align:start position:0%
+plasma and we've sort of put some
+geometric formalism on top of us or on
+
+ align:start position:0%
+geometric formalism on top of us or on
+ 
+
+ align:start position:0%
+geometric formalism on top of us or on
+top of it to tell us what we expect to
+
+ align:start position:0%
+top of it to tell us what we expect to
+ 
+
+ align:start position:0%
+top of it to tell us what we expect to
+see on our
+
+ align:start position:0%
+see on our
+ 
+
+ align:start position:0%
+see on our
+detector so bearing that in mind any
+
+ align:start position:0%
+detector so bearing that in mind any
+ 
+
+ align:start position:0%
+detector so bearing that in mind any
+questions before we go on and actually
+
+ align:start position:0%
+questions before we go on and actually
+ 
+
+ align:start position:0%
+questions before we go on and actually
+talk about protons and plasmas and
+
+ align:start position:0%
+talk about protons and plasmas and
+ 
+
+ align:start position:0%
+talk about protons and plasmas and
+electromag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I saw some folks still writing but yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question oh looks like I got it the
+
+ align:start position:0%
+question oh looks like I got it the
+ 
+
+ align:start position:0%
+question oh looks like I got it the
+wrong way around didn't I yes L needs to
+
+ align:start position:0%
+wrong way around didn't I yes L needs to
+ 
+
+ align:start position:0%
+wrong way around didn't I yes L needs to
+be much less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean like your
+
+ align:start position:0%
+mean like your
+ 
+
+ align:start position:0%
+mean like your
+plasma no I I can still do that if the
+
+ align:start position:0%
+plasma no I I can still do that if the
+ 
+
+ align:start position:0%
+plasma no I I can still do that if the
+plasma is spherical right because if I I
+
+ align:start position:0%
+plasma is spherical right because if I I
+ 
+
+ align:start position:0%
+plasma is spherical right because if I I
+have for example a source here and a
+
+ align:start position:0%
+have for example a source here and a
+ 
+
+ align:start position:0%
+have for example a source here and a
+spherical plasma over here this is a and
+
+ align:start position:0%
+spherical plasma over here this is a and
+ 
+
+ align:start position:0%
+spherical plasma over here this is a and
+this is L and it's pretty clear that L
+
+ align:start position:0%
+this is L and it's pretty clear that L
+ 
+
+ align:start position:0%
+this is L and it's pretty clear that L
+over a is much greater than
+
+ align:start position:0%
+over a is much greater than
+ 
+
+ align:start position:0%
+over a is much greater than
+one yeah so
+
+ align:start position:0%
+one yeah so
+ 
+
+ align:start position:0%
+one yeah so
+I well no no no no this is the condition
+
+ align:start position:0%
+I well no no no no this is the condition
+ 
+
+ align:start position:0%
+I well no no no no this is the condition
+that you want what I said earlier is
+
+ align:start position:0%
+that you want what I said earlier is
+ 
+
+ align:start position:0%
+that you want what I said earlier is
+incorrect you don't want this condition
+
+ align:start position:0%
+incorrect you don't want this condition
+ 
+
+ align:start position:0%
+incorrect you don't want this condition
+you want to have your plasma very close
+
+ align:start position:0%
+you want to have your plasma very close
+ 
+
+ align:start position:0%
+you want to have your plasma very close
+to your source so I my words are wrong
+
+ align:start position:0%
+to your source so I my words are wrong
+ 
+
+ align:start position:0%
+to your source so I my words are wrong
+but the algebra is right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh I see yes yes I I take your
+
+ align:start position:0%
+yeah oh I see yes yes I I take your
+ 
+
+ align:start position:0%
+yeah oh I see yes yes I I take your
+point yeah if if you're plasma is
+
+ align:start position:0%
+point yeah if if you're plasma is
+ 
+
+ align:start position:0%
+point yeah if if you're plasma is
+spherical a lot of the time people are
+
+ align:start position:0%
+spherical a lot of the time people are
+ 
+
+ align:start position:0%
+spherical a lot of the time people are
+Imaging plasmas which are quite quite
+
+ align:start position:0%
+Imaging plasmas which are quite quite
+ 
+
+ align:start position:0%
+Imaging plasmas which are quite quite
+big so but yeah you're
+
+ align:start position:0%
+big so but yeah you're
+ 
+
+ align:start position:0%
+big so but yeah you're
+right okay other question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes oh radians everything's in
+
+ align:start position:0%
+yes oh radians everything's in
+ 
+
+ align:start position:0%
+yes oh radians everything's in
+radians yes much less than one radiant
+
+ align:start position:0%
+radians yes much less than one radiant
+ 
+
+ align:start position:0%
+radians yes much less than one radiant
+it's in radians because we're using this
+
+ align:start position:0%
+it's in radians because we're using this
+ 
+
+ align:start position:0%
+it's in radians because we're using this
+approximation right so if we're using
+
+ align:start position:0%
+approximation right so if we're using
+ 
+
+ align:start position:0%
+approximation right so if we're using
+this approximation Alpha has to be in
+
+ align:start position:0%
+this approximation Alpha has to be in
+ 
+
+ align:start position:0%
+this approximation Alpha has to be in
+radiant that be
+
+ align:start position:0%
+radiant that be
+ 
+
+ align:start position:0%
+radiant that be
+true nothing special about no no no no
+
+ align:start position:0%
+true nothing special about no no no no
+ 
+
+ align:start position:0%
+true nothing special about no no no no
+I'm no there's nothing special about one
+
+ align:start position:0%
+I'm no there's nothing special about one
+ 
+
+ align:start position:0%
+I'm no there's nothing special about one
+Radia it just has to be we want it to be
+
+ align:start position:0%
+Radia it just has to be we want it to be
+ 
+
+ align:start position:0%
+Radia it just has to be we want it to be
+as small as possible one is a number
+
+ align:start position:0%
+as small as possible one is a number
+ 
+
+ align:start position:0%
+as small as possible one is a number
+that it could be smaller than that but I
+
+ align:start position:0%
+that it could be smaller than that but I
+ 
+
+ align:start position:0%
+that it could be smaller than that but I
+guess I could have rised in 10 plus six
+
+ align:start position:0%
+guess I could have rised in 10 plus six
+ 
+
+ align:start position:0%
+guess I could have rised in 10 plus six
+right but yeah yeah sure sure sure I
+
+ align:start position:0%
+right but yeah yeah sure sure sure I
+ 
+
+ align:start position:0%
+right but yeah yeah sure sure sure I
+mean in particular you know we we said
+
+ align:start position:0%
+mean in particular you know we we said
+ 
+
+ align:start position:0%
+mean in particular you know we we said
+that we can get L over a less than one
+
+ align:start position:0%
+that we can get L over a less than one
+ 
+
+ align:start position:0%
+that we can get L over a less than one
+so if we want to get mu much less than
+
+ align:start position:0%
+so if we want to get mu much less than
+ 
+
+ align:start position:0%
+so if we want to get mu much less than
+one that means that Alpha has to be much
+
+ align:start position:0%
+one that means that Alpha has to be much
+ 
+
+ align:start position:0%
+one that means that Alpha has to be much
+less than one from that point of view so
+
+ align:start position:0%
+less than one from that point of view so
+ 
+
+ align:start position:0%
+less than one from that point of view so
+if if you know yeah I think this is a
+
+ align:start position:0%
+if if you know yeah I think this is a
+ 
+
+ align:start position:0%
+if if you know yeah I think this is a
+reasonable that but yeah okay
+
+ align:start position:0%
+reasonable that but yeah okay
+ 
+
+ align:start position:0%
+reasonable that but yeah okay
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online okay let's have a look at what
+
+ align:start position:0%
+online okay let's have a look at what
+ 
+
+ align:start position:0%
+online okay let's have a look at what
+the actual deflection what this Alpha is
+
+ align:start position:0%
+the actual deflection what this Alpha is
+ 
+
+ align:start position:0%
+the actual deflection what this Alpha is
+here um because that's what you need to
+
+ align:start position:0%
+here um because that's what you need to
+ 
+
+ align:start position:0%
+here um because that's what you need to
+know in order to work out this quantity
+
+ align:start position:0%
+know in order to work out this quantity
+ 
+
+ align:start position:0%
+know in order to work out this quantity
+which is D and work out all the rest of
+
+ align:start position:0%
+which is D and work out all the rest of
+ 
+
+ align:start position:0%
+which is D and work out all the rest of
+the stuff so which Bo should I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so Alpha for electric and magnetic
+
+ align:start position:0%
+okay so Alpha for electric and magnetic
+ 
+
+ align:start position:0%
+okay so Alpha for electric and magnetic
+Fields
+
+ align:start position:0%
+Fields
+ 
+
+ align:start position:0%
+Fields
+together is simply the integral of that
+
+ align:start position:0%
+together is simply the integral of that
+ 
+
+ align:start position:0%
+together is simply the integral of that
+Force which is e plus v cross
+
+ align:start position:0%
+Force which is e plus v cross
+ 
+
+ align:start position:0%
+Force which is e plus v cross
+B along the path which remember we're
+
+ align:start position:0%
+B along the path which remember we're
+ 
+
+ align:start position:0%
+B along the path which remember we're
+approximating as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z like that and the deflection angle is
+
+ align:start position:0%
+Z like that and the deflection angle is
+ 
+
+ align:start position:0%
+Z like that and the deflection angle is
+to do is the charge of course because
+
+ align:start position:0%
+to do is the charge of course because
+ 
+
+ align:start position:0%
+to do is the charge of course because
+that's what goes into the force um but
+
+ align:start position:0%
+that's what goes into the force um but
+ 
+
+ align:start position:0%
+that's what goes into the force um but
+there's also a factor of two and W out
+
+ align:start position:0%
+there's also a factor of two and W out
+ 
+
+ align:start position:0%
+there's also a factor of two and W out
+the front here is
+
+ align:start position:0%
+the front here is
+ 
+
+ align:start position:0%
+the front here is
+W is again the kinetic energy of our
+
+ align:start position:0%
+W is again the kinetic energy of our
+ 
+
+ align:start position:0%
+W is again the kinetic energy of our
+proton M proton V proton
+
+ align:start position:0%
+proton M proton V proton
+ 
+
+ align:start position:0%
+proton M proton V proton
+squ
+
+ align:start position:0%
+squ
+ 
+
+ align:start position:0%
+squ
+there you can work this out if you want
+
+ align:start position:0%
+there you can work this out if you want
+ 
+
+ align:start position:0%
+there you can work this out if you want
+to I haven't proven this exactly so what
+
+ align:start position:0%
+to I haven't proven this exactly so what
+ 
+
+ align:start position:0%
+to I haven't proven this exactly so what
+we notice is interestingly we got a w
+
+ align:start position:0%
+we notice is interestingly we got a w
+ 
+
+ align:start position:0%
+we notice is interestingly we got a w
+that depends on V and here we've got V
+
+ align:start position:0%
+that depends on V and here we've got V
+ 
+
+ align:start position:0%
+that depends on V and here we've got V
+inside this and so we can separately
+
+ align:start position:0%
+inside this and so we can separately
+ 
+
+ align:start position:0%
+inside this and so we can separately
+write out that there's going to be a
+
+ align:start position:0%
+write out that there's going to be a
+ 
+
+ align:start position:0%
+write out that there's going to be a
+deflection due to the electric field
+
+ align:start position:0%
+deflection due to the electric field
+ 
+
+ align:start position:0%
+deflection due to the electric field
+which is e over 2 W integral electric
+
+ align:start position:0%
+which is e over 2 W integral electric
+ 
+
+ align:start position:0%
+which is e over 2 W integral electric
+field d
+
+ align:start position:0%
+field d
+ 
+
+ align:start position:0%
+field d
+z that's pretty obvious I've just taken
+
+ align:start position:0%
+z that's pretty obvious I've just taken
+ 
+
+ align:start position:0%
+z that's pretty obvious I've just taken
+the first there and we have a deflection
+
+ align:start position:0%
+the first there and we have a deflection
+ 
+
+ align:start position:0%
+the first there and we have a deflection
+due to the magnetic
+
+ align:start position:0%
+due to the magnetic
+ 
+
+ align:start position:0%
+due to the magnetic
+field Alpha b equals e over square root
+
+ align:start position:0%
+field Alpha b equals e over square root
+ 
+
+ align:start position:0%
+field Alpha b equals e over square root
+to m
+
+ align:start position:0%
+to m
+ 
+
+ align:start position:0%
+to m
+w taking this velocity and we're
+
+ align:start position:0%
+w taking this velocity and we're
+ 
+
+ align:start position:0%
+w taking this velocity and we're
+combining it with the velocity squ over
+
+ align:start position:0%
+combining it with the velocity squ over
+ 
+
+ align:start position:0%
+combining it with the velocity squ over
+there integral of DL
+
+ align:start position:0%
+there integral of DL
+ 
+
+ align:start position:0%
+there integral of DL
+Frost with B whereas of course this DL
+
+ align:start position:0%
+Frost with B whereas of course this DL
+ 
+
+ align:start position:0%
+Frost with B whereas of course this DL
+is really DZ because of our perial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation so we're going to have a
+
+ align:start position:0%
+approximation so we're going to have a
+ 
+
+ align:start position:0%
+approximation so we're going to have a
+deflection angle that depends on the
+
+ align:start position:0%
+deflection angle that depends on the
+ 
+
+ align:start position:0%
+deflection angle that depends on the
+cross product of the path and the
+
+ align:start position:0%
+cross product of the path and the
+ 
+
+ align:start position:0%
+cross product of the path and the
+magnetic
+
+ align:start position:0%
+magnetic
+ 
+
+ align:start position:0%
+magnetic
+field what's interesting about these two
+
+ align:start position:0%
+field what's interesting about these two
+ 
+
+ align:start position:0%
+field what's interesting about these two
+is they have different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scalings one has a scaling with the
+
+ align:start position:0%
+scalings one has a scaling with the
+ 
+
+ align:start position:0%
+scalings one has a scaling with the
+particle energy one has a scaling with
+
+ align:start position:0%
+particle energy one has a scaling with
+ 
+
+ align:start position:0%
+particle energy one has a scaling with
+the square root of the particle energy
+
+ align:start position:0%
+the square root of the particle energy
+ 
+
+ align:start position:0%
+the square root of the particle energy
+so this suggests to us straight away how
+
+ align:start position:0%
+so this suggests to us straight away how
+ 
+
+ align:start position:0%
+so this suggests to us straight away how
+to distinguish between e and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b or I call them Alpha
+
+ align:start position:0%
+b or I call them Alpha
+ 
+
+ align:start position:0%
+b or I call them Alpha
+e and Alpha B so the deflections due to
+
+ align:start position:0%
+e and Alpha B so the deflections due to
+ 
+
+ align:start position:0%
+e and Alpha B so the deflections due to
+electric and magnetic
+
+ align:start position:0%
+electric and magnetic
+ 
+
+ align:start position:0%
+electric and magnetic
+fields and we distinguish between them
+
+ align:start position:0%
+fields and we distinguish between them
+ 
+
+ align:start position:0%
+fields and we distinguish between them
+by using two or
+
+ align:start position:0%
+by using two or
+ 
+
+ align:start position:0%
+by using two or
+more proton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energies if we have a source that
+
+ align:start position:0%
+energies if we have a source that
+ 
+
+ align:start position:0%
+energies if we have a source that
+produces one me protons and 10 me
+
+ align:start position:0%
+produces one me protons and 10 me
+ 
+
+ align:start position:0%
+produces one me protons and 10 me
+protons they will go through the same
+
+ align:start position:0%
+protons they will go through the same
+ 
+
+ align:start position:0%
+protons they will go through the same
+plasma but the one Meb protons will be
+
+ align:start position:0%
+plasma but the one Meb protons will be
+ 
+
+ align:start position:0%
+plasma but the one Meb protons will be
+much more sensitive to oh I've got to
+
+ align:start position:0%
+much more sensitive to oh I've got to
+ 
+
+ align:start position:0%
+much more sensitive to oh I've got to
+get this right now lower energy of this
+
+ align:start position:0%
+get this right now lower energy of this
+ 
+
+ align:start position:0%
+get this right now lower energy of this
+is a bigger number to the electric field
+
+ align:start position:0%
+is a bigger number to the electric field
+ 
+
+ align:start position:0%
+is a bigger number to the electric field
+than the 10 MB protons and so we can use
+
+ align:start position:0%
+than the 10 MB protons and so we can use
+ 
+
+ align:start position:0%
+than the 10 MB protons and so we can use
+a differential measurement effectively
+
+ align:start position:0%
+a differential measurement effectively
+ 
+
+ align:start position:0%
+a differential measurement effectively
+to work out the contribution of alpha e
+
+ align:start position:0%
+to work out the contribution of alpha e
+ 
+
+ align:start position:0%
+to work out the contribution of alpha e
+and Alpha B there'll be two simultaneous
+
+ align:start position:0%
+and Alpha B there'll be two simultaneous
+ 
+
+ align:start position:0%
+and Alpha B there'll be two simultaneous
+equations and we'll have uh two things
+
+ align:start position:0%
+equations and we'll have uh two things
+ 
+
+ align:start position:0%
+equations and we'll have uh two things
+we want to solve for so we'll be able to
+
+ align:start position:0%
+we want to solve for so we'll be able to
+ 
+
+ align:start position:0%
+we want to solve for so we'll be able to
+get it out so this looks an awful lot
+
+ align:start position:0%
+get it out so this looks an awful lot
+ 
+
+ align:start position:0%
+get it out so this looks an awful lot
+like when we talked about two color
+
+ align:start position:0%
+like when we talked about two color
+ 
+
+ align:start position:0%
+like when we talked about two color
+interferometry to determine the
+
+ align:start position:0%
+interferometry to determine the
+ 
+
+ align:start position:0%
+interferometry to determine the
+difference between vibrations or
+
+ align:start position:0%
+difference between vibrations or
+ 
+
+ align:start position:0%
+difference between vibrations or
+neutrals in our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma and people do this a lot because
+
+ align:start position:0%
+plasma and people do this a lot because
+ 
+
+ align:start position:0%
+plasma and people do this a lot because
+if you're doing experiment you don't a
+
+ align:start position:0%
+if you're doing experiment you don't a
+ 
+
+ align:start position:0%
+if you're doing experiment you don't a
+priority know whether the electric
+
+ align:start position:0%
+priority know whether the electric
+ 
+
+ align:start position:0%
+priority know whether the electric
+fields are small compared to the
+
+ align:start position:0%
+fields are small compared to the
+ 
+
+ align:start position:0%
+fields are small compared to the
+magnetic fields most people want to use
+
+ align:start position:0%
+magnetic fields most people want to use
+ 
+
+ align:start position:0%
+magnetic fields most people want to use
+this technique to measure magnetic
+
+ align:start position:0%
+this technique to measure magnetic
+ 
+
+ align:start position:0%
+this technique to measure magnetic
+fields um and usually it's the case
+
+ align:start position:0%
+fields um and usually it's the case
+ 
+
+ align:start position:0%
+fields um and usually it's the case
+magnetic fields do dominate but you
+
+ align:start position:0%
+magnetic fields do dominate but you
+ 
+
+ align:start position:0%
+magnetic fields do dominate but you
+still need to check and you can do it
+
+ align:start position:0%
+still need to check and you can do it
+ 
+
+ align:start position:0%
+still need to check and you can do it
+with these two different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energies so we've been talking a lot
+
+ align:start position:0%
+energies so we've been talking a lot
+ 
+
+ align:start position:0%
+energies so we've been talking a lot
+about Alpha here but there's a rather
+
+ align:start position:0%
+about Alpha here but there's a rather
+ 
+
+ align:start position:0%
+about Alpha here but there's a rather
+neat
+
+ align:start position:0%
+neat
+ 
+
+ align:start position:0%
+neat
+formulation which says well instead of
+
+ align:start position:0%
+formulation which says well instead of
+ 
+
+ align:start position:0%
+formulation which says well instead of
+talking about this Vector Alpha and that
+
+ align:start position:0%
+talking about this Vector Alpha and that
+ 
+
+ align:start position:0%
+talking about this Vector Alpha and that
+deflection angle Alpha depends on where
+
+ align:start position:0%
+deflection angle Alpha depends on where
+ 
+
+ align:start position:0%
+deflection angle Alpha depends on where
+you are in the plasma so it depends on
+
+ align:start position:0%
+you are in the plasma so it depends on
+ 
+
+ align:start position:0%
+you are in the plasma so it depends on
+your position X not within the plasma if
+
+ align:start position:0%
+your position X not within the plasma if
+ 
+
+ align:start position:0%
+your position X not within the plasma if
+this is a vector then we can just write
+
+ align:start position:0%
+this is a vector then we can just write
+ 
+
+ align:start position:0%
+this is a vector then we can just write
+it as the gradient of some scalar that's
+
+ align:start position:0%
+it as the gradient of some scalar that's
+ 
+
+ align:start position:0%
+it as the gradient of some scalar that's
+just generally true so we can say what
+
+ align:start position:0%
+just generally true so we can say what
+ 
+
+ align:start position:0%
+just generally true so we can say what
+if there is some scalar by of X zero and
+
+ align:start position:0%
+if there is some scalar by of X zero and
+ 
+
+ align:start position:0%
+if there is some scalar by of X zero and
+Alpha is just its gradient and the
+
+ align:start position:0%
+Alpha is just its gradient and the
+ 
+
+ align:start position:0%
+Alpha is just its gradient and the
+reason you want to do this is you can
+
+ align:start position:0%
+reason you want to do this is you can
+ 
+
+ align:start position:0%
+reason you want to do this is you can
+now write dial expression for fi which
+
+ align:start position:0%
+now write dial expression for fi which
+ 
+
+ align:start position:0%
+now write dial expression for fi which
+works for shog graphy as well as proton
+
+ align:start position:0%
+works for shog graphy as well as proton
+ 
+
+ align:start position:0%
+works for shog graphy as well as proton
+Imaging and then all of the mathematics
+
+ align:start position:0%
+Imaging and then all of the mathematics
+ 
+
+ align:start position:0%
+Imaging and then all of the mathematics
+that you've done previously you just do
+
+ align:start position:0%
+that you've done previously you just do
+ 
+
+ align:start position:0%
+that you've done previously you just do
+it in terms of
+
+ align:start position:0%
+it in terms of
+ 
+
+ align:start position:0%
+it in terms of
+and it doesn't it's sort of agnostically
+
+ align:start position:0%
+and it doesn't it's sort of agnostically
+ 
+
+ align:start position:0%
+and it doesn't it's sort of agnostically
+exact technique that we use so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geography you find that your deflection
+
+ align:start position:0%
+geography you find that your deflection
+ 
+
+ align:start position:0%
+geography you find that your deflection
+potential is equal to minus the integral
+
+ align:start position:0%
+potential is equal to minus the integral
+ 
+
+ align:start position:0%
+potential is equal to minus the integral
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+logarithm of the refractive index n and
+
+ align:start position:0%
+logarithm of the refractive index n and
+ 
+
+ align:start position:0%
+logarithm of the refractive index n and
+I'll explicitly write this out in terms
+
+ align:start position:0%
+I'll explicitly write this out in terms
+ 
+
+ align:start position:0%
+I'll explicitly write this out in terms
+of the position within the plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the z0 so the integral along through the
+
+ align:start position:0%
+the z0 so the integral along through the
+ 
+
+ align:start position:0%
+the z0 so the integral along through the
+plasma in The Zed Direction and this
+
+ align:start position:0%
+plasma in The Zed Direction and this
+ 
+
+ align:start position:0%
+plasma in The Zed Direction and this
+logarithm here or this n here is of
+
+ align:start position:0%
+logarithm here or this n here is of
+ 
+
+ align:start position:0%
+logarithm here or this n here is of
+course the one where we have n^2 equal 1
+
+ align:start position:0%
+course the one where we have n^2 equal 1
+ 
+
+ align:start position:0%
+course the one where we have n^2 equal 1
+minus NE over n c that we saw in all our
+
+ align:start position:0%
+minus NE over n c that we saw in all our
+ 
+
+ align:start position:0%
+minus NE over n c that we saw in all our
+refractive index things though of course
+
+ align:start position:0%
+refractive index things though of course
+ 
+
+ align:start position:0%
+refractive index things though of course
+it could be whatever o mode X mode but
+
+ align:start position:0%
+it could be whatever o mode X mode but
+ 
+
+ align:start position:0%
+it could be whatever o mode X mode but
+people don't do proton radiography in so
+
+ align:start position:0%
+people don't do proton radiography in so
+ 
+
+ align:start position:0%
+people don't do proton radiography in so
+um the plasmas we're working with
+
+ align:start position:0%
+um the plasmas we're working with
+ 
+
+ align:start position:0%
+um the plasmas we're working with
+they're mostly unmagnified this is fine
+
+ align:start position:0%
+they're mostly unmagnified this is fine
+ 
+
+ align:start position:0%
+they're mostly unmagnified this is fine
+for the E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields this potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is just equal to Q over two w did I
+
+ align:start position:0%
+here is just equal to Q over two w did I
+ 
+
+ align:start position:0%
+here is just equal to Q over two w did I
+use Q over there no I switched to e so
+
+ align:start position:0%
+use Q over there no I switched to e so
+ 
+
+ align:start position:0%
+use Q over there no I switched to e so
+I'll put it back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e integral of the real electros datic
+
+ align:start position:0%
+e integral of the real electros datic
+ 
+
+ align:start position:0%
+e integral of the real electros datic
+potential lowercase f
+
+ align:start position:0%
+potential lowercase f
+ 
+
+ align:start position:0%
+potential lowercase f
+x0 y0 z0 D z0 so they are related they
+
+ align:start position:0%
+x0 y0 z0 D z0 so they are related they
+ 
+
+ align:start position:0%
+x0 y0 z0 D z0 so they are related they
+don't have to be but they are in this
+
+ align:start position:0%
+don't have to be but they are in this
+ 
+
+ align:start position:0%
+don't have to be but they are in this
+case the related the deflection
+
+ align:start position:0%
+case the related the deflection
+ 
+
+ align:start position:0%
+case the related the deflection
+potential is related to electrostatic
+
+ align:start position:0%
+potential is related to electrostatic
+ 
+
+ align:start position:0%
+potential is related to electrostatic
+potential and then the final one is the
+
+ align:start position:0%
+potential and then the final one is the
+ 
+
+ align:start position:0%
+potential and then the final one is the
+magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields Capital 5
+
+ align:start position:0%
+fields Capital 5
+ 
+
+ align:start position:0%
+fields Capital 5
+x0 is equal to e upon square root of 2 m
+
+ align:start position:0%
+x0 is equal to e upon square root of 2 m
+ 
+
+ align:start position:0%
+x0 is equal to e upon square root of 2 m
+w integral of
+
+ align:start position:0%
+w integral of
+ 
+
+ align:start position:0%
+w integral of
+a do
+
+ align:start position:0%
+a do
+ 
+
+ align:start position:0%
+a do
+dz0 and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is the magnetic Vector potential so B
+
+ align:start position:0%
+a is the magnetic Vector potential so B
+ 
+
+ align:start position:0%
+a is the magnetic Vector potential so B
+is equal to the curl of
+
+ align:start position:0%
+is equal to the curl of
+ 
+
+ align:start position:0%
+is equal to the curl of
+a but the idea is that we will seek
+
+ align:start position:0%
+a but the idea is that we will seek
+ 
+
+ align:start position:0%
+a but the idea is that we will seek
+techniques which will take our intensity
+
+ align:start position:0%
+techniques which will take our intensity
+ 
+
+ align:start position:0%
+techniques which will take our intensity
+Vari
+
+ align:start position:0%
+Vari
+ 
+
+ align:start position:0%
+Vari
+I on our detector and we will use them
+
+ align:start position:0%
+I on our detector and we will use them
+ 
+
+ align:start position:0%
+I on our detector and we will use them
+to infer some sort of deflection
+
+ align:start position:0%
+to infer some sort of deflection
+ 
+
+ align:start position:0%
+to infer some sort of deflection
+potential and then the neat thing is it
+
+ align:start position:0%
+potential and then the neat thing is it
+ 
+
+ align:start position:0%
+potential and then the neat thing is it
+doesn't matter whether we're looking at
+
+ align:start position:0%
+doesn't matter whether we're looking at
+ 
+
+ align:start position:0%
+doesn't matter whether we're looking at
+electric fields or magnetic fields
+
+ align:start position:0%
+electric fields or magnetic fields
+ 
+
+ align:start position:0%
+electric fields or magnetic fields
+orography that's sort of like a detail
+
+ align:start position:0%
+orography that's sort of like a detail
+ 
+
+ align:start position:0%
+orography that's sort of like a detail
+that the end user has to use but the
+
+ align:start position:0%
+that the end user has to use but the
+ 
+
+ align:start position:0%
+that the end user has to use but the
+algorithms are all the same so this is
+
+ align:start position:0%
+algorithms are all the same so this is
+ 
+
+ align:start position:0%
+algorithms are all the same so this is
+very powerful we can share techniques
+
+ align:start position:0%
+very powerful we can share techniques
+ 
+
+ align:start position:0%
+very powerful we can share techniques
+between very disperate looking
+
+ align:start position:0%
+between very disperate looking
+ 
+
+ align:start position:0%
+between very disperate looking
+Diagnostics um Professor yes does the B
+
+ align:start position:0%
+Diagnostics um Professor yes does the B
+ 
+
+ align:start position:0%
+Diagnostics um Professor yes does the B
+is a where b equals uh R uh the like the
+
+ align:start position:0%
+is a where b equals uh R uh the like the
+ 
+
+ align:start position:0%
+is a where b equals uh R uh the like the
+Cur of a is that from um the Maxwell's
+
+ align:start position:0%
+Cur of a is that from um the Maxwell's
+ 
+
+ align:start position:0%
+Cur of a is that from um the Maxwell's
+law B like the Divergence is zero is
+
+ align:start position:0%
+law B like the Divergence is zero is
+ 
+
+ align:start position:0%
+law B like the Divergence is zero is
+that where that comes
+
+ align:start position:0%
+that where that comes
+ 
+
+ align:start position:0%
+that where that comes
+from oh gosh
+
+ align:start position:0%
+from oh gosh
+ 
+
+ align:start position:0%
+from oh gosh
+yes um Can Divergence fre Fields be
+
+ align:start position:0%
+yes um Can Divergence fre Fields be
+ 
+
+ align:start position:0%
+yes um Can Divergence fre Fields be
+written as the Cur of another Vector I
+
+ align:start position:0%
+written as the Cur of another Vector I
+ 
+
+ align:start position:0%
+written as the Cur of another Vector I
+think so yeah okay then where does um
+
+ align:start position:0%
+think so yeah okay then where does um
+ 
+
+ align:start position:0%
+think so yeah okay then where does um
+the potential come is it just like a
+
+ align:start position:0%
+the potential come is it just like a
+ 
+
+ align:start position:0%
+the potential come is it just like a
+regular electric potential or yeah this
+
+ align:start position:0%
+regular electric potential or yeah this
+ 
+
+ align:start position:0%
+regular electric potential or yeah this
+is the electric potential right this is
+
+ align:start position:0%
+is the electric potential right this is
+ 
+
+ align:start position:0%
+is the electric potential right this is
+the potential that's defined by Bon's
+
+ align:start position:0%
+the potential that's defined by Bon's
+ 
+
+ align:start position:0%
+the potential that's defined by Bon's
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+I see okay yeah just wanted to check
+
+ align:start position:0%
+I see okay yeah just wanted to check
+ 
+
+ align:start position:0%
+I see okay yeah just wanted to check
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay any questions on that the next
+
+ align:start position:0%
+yeah okay any questions on that the next
+ 
+
+ align:start position:0%
+yeah okay any questions on that the next
+thing I'm going to cover is how do we
+
+ align:start position:0%
+thing I'm going to cover is how do we
+ 
+
+ align:start position:0%
+thing I'm going to cover is how do we
+make these beams of protons we're going
+
+ align:start position:0%
+make these beams of protons we're going
+ 
+
+ align:start position:0%
+make these beams of protons we're going
+to switch gears a little bit so if you
+
+ align:start position:0%
+to switch gears a little bit so if you
+ 
+
+ align:start position:0%
+to switch gears a little bit so if you
+have any questions on uh what's happened
+
+ align:start position:0%
+have any questions on uh what's happened
+ 
+
+ align:start position:0%
+have any questions on uh what's happened
+so far this is a good time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+yeah we these are these are
+
+ align:start position:0%
+yeah we these are these are
+ 
+
+ align:start position:0%
+yeah we these are these are
+contradictory yes yeah so so the prac
+
+ align:start position:0%
+contradictory yes yeah so so the prac
+ 
+
+ align:start position:0%
+contradictory yes yeah so so the prac
+approximation also makes it very hard to
+
+ align:start position:0%
+approximation also makes it very hard to
+ 
+
+ align:start position:0%
+approximation also makes it very hard to
+have your object very close that if you
+
+ align:start position:0%
+have your object very close that if you
+ 
+
+ align:start position:0%
+have your object very close that if you
+were able to do that you would reduce
+
+ align:start position:0%
+were able to do that you would reduce
+ 
+
+ align:start position:0%
+were able to do that you would reduce
+the contrast parameter but you would
+
+ align:start position:0%
+the contrast parameter but you would
+ 
+
+ align:start position:0%
+the contrast parameter but you would
+also break all of the mathematics we've
+
+ align:start position:0%
+also break all of the mathematics we've
+ 
+
+ align:start position:0%
+also break all of the mathematics we've
+done which is used the parial
+
+ align:start position:0%
+done which is used the parial
+ 
+
+ align:start position:0%
+done which is used the parial
+approximation so far so in practice your
+
+ align:start position:0%
+approximation so far so in practice your
+ 
+
+ align:start position:0%
+approximation so far so in practice your
+best bet is to reduce Alpha instead and
+
+ align:start position:0%
+best bet is to reduce Alpha instead and
+ 
+
+ align:start position:0%
+best bet is to reduce Alpha instead and
+you reduce Alpha by making your protons
+
+ align:start position:0%
+you reduce Alpha by making your protons
+ 
+
+ align:start position:0%
+you reduce Alpha by making your protons
+as fast as possible because the faster
+
+ align:start position:0%
+as fast as possible because the faster
+ 
+
+ align:start position:0%
+as fast as possible because the faster
+your protons are the higher their energy
+
+ align:start position:0%
+your protons are the higher their energy
+ 
+
+ align:start position:0%
+your protons are the higher their energy
+they lower their deflections so this is
+
+ align:start position:0%
+they lower their deflections so this is
+ 
+
+ align:start position:0%
+they lower their deflections so this is
+what motivates us using me or higher
+
+ align:start position:0%
+what motivates us using me or higher
+ 
+
+ align:start position:0%
+what motivates us using me or higher
+beams of pro
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the particle is being deflected a
+
+ align:start position:0%
+yeah the particle is being deflected a
+ 
+
+ align:start position:0%
+yeah the particle is being deflected a
+little bit approximation mostly same
+
+ align:start position:0%
+little bit approximation mostly same
+ 
+
+ align:start position:0%
+little bit approximation mostly same
+direction it's certainly not being
+
+ align:start position:0%
+direction it's certainly not being
+ 
+
+ align:start position:0%
+direction it's certainly not being
+decelerated velocity is constant right
+
+ align:start position:0%
+decelerated velocity is constant right
+ 
+
+ align:start position:0%
+decelerated velocity is constant right
+so the site the the size of its velocity
+
+ align:start position:0%
+so the site the the size of its velocity
+ 
+
+ align:start position:0%
+so the site the the size of its velocity
+its speed doesn't change as it goes
+
+ align:start position:0%
+its speed doesn't change as it goes
+ 
+
+ align:start position:0%
+its speed doesn't change as it goes
+through the plasma that's also
+
+ align:start position:0%
+through the plasma that's also
+ 
+
+ align:start position:0%
+through the plasma that's also
+consistent with our test particle
+
+ align:start position:0%
+consistent with our test particle
+ 
+
+ align:start position:0%
+consistent with our test particle
+picture where the test particle is
+
+ align:start position:0%
+picture where the test particle is
+ 
+
+ align:start position:0%
+picture where the test particle is
+experiencing the fields but it's not
+
+ align:start position:0%
+experiencing the fields but it's not
+ 
+
+ align:start position:0%
+experiencing the fields but it's not
+sort of like being slowed down yeah is
+
+ align:start position:0%
+sort of like being slowed down yeah is
+ 
+
+ align:start position:0%
+sort of like being slowed down yeah is
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like yeah the particles are really
+
+ align:start position:0%
+like yeah the particles are really
+ 
+
+ align:start position:0%
+like yeah the particles are really
+really fast they don't they don't
+
+ align:start position:0%
+really fast they don't they don't
+ 
+
+ align:start position:0%
+really fast they don't they don't
+scatter at all they're way faster than
+
+ align:start position:0%
+scatter at all they're way faster than
+ 
+
+ align:start position:0%
+scatter at all they're way faster than
+everything else yeah yeah so this is a
+
+ align:start position:0%
+everything else yeah yeah so this is a
+ 
+
+ align:start position:0%
+everything else yeah yeah so this is a
+completely reasonable approximation yeah
+
+ align:start position:0%
+completely reasonable approximation yeah
+ 
+
+ align:start position:0%
+completely reasonable approximation yeah
+yeah yeah it's basically this you can
+
+ align:start position:0%
+yeah yeah it's basically this you can
+ 
+
+ align:start position:0%
+yeah yeah it's basically this you can
+treat the plasma as this like static
+
+ align:start position:0%
+treat the plasma as this like static
+ 
+
+ align:start position:0%
+treat the plasma as this like static
+unmoving thing on the time scale of
+
+ align:start position:0%
+unmoving thing on the time scale of
+ 
+
+ align:start position:0%
+unmoving thing on the time scale of
+these protons going through and the
+
+ align:start position:0%
+these protons going through and the
+ 
+
+ align:start position:0%
+these protons going through and the
+protons barely see it apart from they
+
+ align:start position:0%
+protons barely see it apart from they
+ 
+
+ align:start position:0%
+protons barely see it apart from they
+get deflected a tiny amount and it's
+
+ align:start position:0%
+get deflected a tiny amount and it's
+ 
+
+ align:start position:0%
+get deflected a tiny amount and it's
+only because we put our detector so far
+
+ align:start position:0%
+only because we put our detector so far
+ 
+
+ align:start position:0%
+only because we put our detector so far
+way that those tiny deflections show up
+
+ align:start position:0%
+way that those tiny deflections show up
+ 
+
+ align:start position:0%
+way that those tiny deflections show up
+as significant changes
+
+ align:start position:0%
+as significant changes
+ 
+
+ align:start position:0%
+as significant changes
+fluence okay any other questions
+
+ align:start position:0%
+fluence okay any other questions
+ 
+
+ align:start position:0%
+fluence okay any other questions
+anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah it's the Su the the
+
+ align:start position:0%
+yeah yeah yeah it's the Su the the
+ 
+
+ align:start position:0%
+yeah yeah yeah it's the Su the the
+reflection potentials add linearly which
+
+ align:start position:0%
+reflection potentials add linearly which
+ 
+
+ align:start position:0%
+reflection potentials add linearly which
+is neat as well yeah and then when you
+
+ align:start position:0%
+is neat as well yeah and then when you
+ 
+
+ align:start position:0%
+is neat as well yeah and then when you
+use two different
+
+ align:start position:0%
+use two different
+ 
+
+ align:start position:0%
+use two different
+energies you can solve separately for
+
+ align:start position:0%
+energies you can solve separately for
+ 
+
+ align:start position:0%
+energies you can solve separately for
+the two deflection potentials and then
+
+ align:start position:0%
+the two deflection potentials and then
+ 
+
+ align:start position:0%
+the two deflection potentials and then
+see how big they
+
+ align:start position:0%
+see how big they
+ 
+
+ align:start position:0%
+see how big they
+are okay let's talk about how to make a
+
+ align:start position:0%
+are okay let's talk about how to make a
+ 
+
+ align:start position:0%
+are okay let's talk about how to make a
+f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prot this is actually quite frustrating
+
+ align:start position:0%
+prot this is actually quite frustrating
+ 
+
+ align:start position:0%
+prot this is actually quite frustrating
+when I taught this in 2021 there was no
+
+ align:start position:0%
+when I taught this in 2021 there was no
+ 
+
+ align:start position:0%
+when I taught this in 2021 there was no
+good reference on this and I had to
+
+ align:start position:0%
+good reference on this and I had to
+ 
+
+ align:start position:0%
+good reference on this and I had to
+spend ages looking it up and then Derek
+
+ align:start position:0%
+spend ages looking it up and then Derek
+ 
+
+ align:start position:0%
+spend ages looking it up and then Derek
+schaer put his paper on archive and
+
+ align:start position:0%
+schaer put his paper on archive and
+ 
+
+ align:start position:0%
+schaer put his paper on archive and
+explains it all really straightforwardly
+
+ align:start position:0%
+explains it all really straightforwardly
+ 
+
+ align:start position:0%
+explains it all really straightforwardly
+so if you want to understand it you can
+
+ align:start position:0%
+so if you want to understand it you can
+ 
+
+ align:start position:0%
+so if you want to understand it you can
+just paper but uh yeah this interesting
+
+ align:start position:0%
+just paper but uh yeah this interesting
+ 
+
+ align:start position:0%
+just paper but uh yeah this interesting
+stuff because this technique is
+
+ align:start position:0%
+stuff because this technique is
+ 
+
+ align:start position:0%
+stuff because this technique is
+relatively modern it's only within about
+
+ align:start position:0%
+relatively modern it's only within about
+ 
+
+ align:start position:0%
+relatively modern it's only within about
+the last 20 years that people have
+
+ align:start position:0%
+the last 20 years that people have
+ 
+
+ align:start position:0%
+the last 20 years that people have
+really been using it and a lot of the
+
+ align:start position:0%
+really been using it and a lot of the
+ 
+
+ align:start position:0%
+really been using it and a lot of the
+development of this technique was led by
+
+ align:start position:0%
+development of this technique was led by
+ 
+
+ align:start position:0%
+development of this technique was led by
+the H group here at MIT so a lot of the
+
+ align:start position:0%
+the H group here at MIT so a lot of the
+ 
+
+ align:start position:0%
+the H group here at MIT so a lot of the
+things I'm going to tell you about are
+
+ align:start position:0%
+things I'm going to tell you about are
+ 
+
+ align:start position:0%
+things I'm going to tell you about are
+MIT diagn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+development
+
+ align:start position:0%
+development
+ 
+
+ align:start position:0%
+development
+so we need to have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+source and for each Source there is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detector but the First Source that I'm
+
+ align:start position:0%
+detector but the First Source that I'm
+ 
+
+ align:start position:0%
+detector but the First Source that I'm
+going to talk about is a technique
+
+ align:start position:0%
+going to talk about is a technique
+ 
+
+ align:start position:0%
+going to talk about is a technique
+called P
+
+ align:start position:0%
+called P
+ 
+
+ align:start position:0%
+called P
+NS
+
+ align:start position:0%
+NS
+ 
+
+ align:start position:0%
+NS
+a this stands
+
+ align:start position:0%
+a this stands
+ 
+
+ align:start position:0%
+a this stands
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+Target and doesn't really matter uh
+
+ align:start position:0%
+Target and doesn't really matter uh
+ 
+
+ align:start position:0%
+Target and doesn't really matter uh
+Target
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration you can't quite sing it to
+
+ align:start position:0%
+acceleration you can't quite sing it to
+ 
+
+ align:start position:0%
+acceleration you can't quite sing it to
+the tune of teenage mutants nja Turtle
+
+ align:start position:0%
+the tune of teenage mutants nja Turtle
+ 
+
+ align:start position:0%
+the tune of teenage mutants nja Turtle
+sadly but it's getting pretty close so
+
+ align:start position:0%
+sadly but it's getting pretty close so
+ 
+
+ align:start position:0%
+sadly but it's getting pretty close so
+the idea of tnsa and I will never say
+
+ align:start position:0%
+the idea of tnsa and I will never say
+ 
+
+ align:start position:0%
+the idea of tnsa and I will never say
+Target normal sheet acceleration again
+
+ align:start position:0%
+Target normal sheet acceleration again
+ 
+
+ align:start position:0%
+Target normal sheet acceleration again
+uh is you have a metal
+
+ align:start position:0%
+uh is you have a metal
+ 
+
+ align:start position:0%
+uh is you have a metal
+fo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's thin you know tens of microns
+
+ align:start position:0%
+and it's thin you know tens of microns
+ 
+
+ align:start position:0%
+and it's thin you know tens of microns
+thin and any metal that you have is
+
+ align:start position:0%
+thin and any metal that you have is
+ 
+
+ align:start position:0%
+thin and any metal that you have is
+going to have absorbed on its
+
+ align:start position:0%
+going to have absorbed on its
+ 
+
+ align:start position:0%
+going to have absorbed on its
+surface lots of hydrocarbons which means
+
+ align:start position:0%
+surface lots of hydrocarbons which means
+ 
+
+ align:start position:0%
+surface lots of hydrocarbons which means
+lots of little
+
+ align:start position:0%
+lots of little
+ 
+
+ align:start position:0%
+lots of little
+protons so again we're not accelerating
+
+ align:start position:0%
+protons so again we're not accelerating
+ 
+
+ align:start position:0%
+protons so again we're not accelerating
+copper or something like this here we're
+
+ align:start position:0%
+copper or something like this here we're
+ 
+
+ align:start position:0%
+copper or something like this here we're
+still accelerating protons it just turns
+
+ align:start position:0%
+still accelerating protons it just turns
+ 
+
+ align:start position:0%
+still accelerating protons it just turns
+out there's lots of little protons
+
+ align:start position:0%
+out there's lots of little protons
+ 
+
+ align:start position:0%
+out there's lots of little protons
+absorbed in the structure on the front
+
+ align:start position:0%
+absorbed in the structure on the front
+ 
+
+ align:start position:0%
+absorbed in the structure on the front
+here and we take our laser
+
+ align:start position:0%
+here and we take our laser
+ 
+
+ align:start position:0%
+here and we take our laser
+beam and we focus it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down and hit the back side of this
+
+ align:start position:0%
+down and hit the back side of this
+ 
+
+ align:start position:0%
+down and hit the back side of this
+Target and our laser beam is ultra short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pulse so this tends to be something like
+
+ align:start position:0%
+pulse so this tends to be something like
+ 
+
+ align:start position:0%
+pulse so this tends to be something like
+a 50 Jewel laser in one PC 10 to minus
+
+ align:start position:0%
+a 50 Jewel laser in one PC 10 to minus
+ 
+
+ align:start position:0%
+a 50 Jewel laser in one PC 10 to minus
+12 seconds so this is over 100 ter
+
+ align:start position:0%
+12 seconds so this is over 100 ter
+ 
+
+ align:start position:0%
+12 seconds so this is over 100 ter
+terawatts of laser power or if if you
+
+ align:start position:0%
+terawatts of laser power or if if you
+ 
+
+ align:start position:0%
+terawatts of laser power or if if you
+got a really short pulse you can do one
+
+ align:start position:0%
+got a really short pulse you can do one
+ 
+
+ align:start position:0%
+got a really short pulse you can do one
+Jewel in 50 F to seconds a fc is 10 to
+
+ align:start position:0%
+Jewel in 50 F to seconds a fc is 10 to
+ 
+
+ align:start position:0%
+Jewel in 50 F to seconds a fc is 10 to
+the minus 15 seconds so these are
+
+ align:start position:0%
+the minus 15 seconds so these are
+ 
+
+ align:start position:0%
+the minus 15 seconds so these are
+seriously short laser pulses and this is
+
+ align:start position:0%
+seriously short laser pulses and this is
+ 
+
+ align:start position:0%
+seriously short laser pulses and this is
+a seriously intense focal spot here down
+
+ align:start position:0%
+a seriously intense focal spot here down
+ 
+
+ align:start position:0%
+a seriously intense focal spot here down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+about 10 microns we can focus the laser
+
+ align:start position:0%
+about 10 microns we can focus the laser
+ 
+
+ align:start position:0%
+about 10 microns we can focus the laser
+down to so that's a lot of electrical
+
+ align:start position:0%
+down to so that's a lot of electrical
+ 
+
+ align:start position:0%
+down to so that's a lot of electrical
+energy being focused into a very small
+
+ align:start position:0%
+energy being focused into a very small
+ 
+
+ align:start position:0%
+energy being focused into a very small
+spot uh on a very short time scale and
+
+ align:start position:0%
+spot uh on a very short time scale and
+ 
+
+ align:start position:0%
+spot uh on a very short time scale and
+what that does is it initially
+
+ align:start position:0%
+what that does is it initially
+ 
+
+ align:start position:0%
+what that does is it initially
+electrons off the foil so there is some
+
+ align:start position:0%
+electrons off the foil so there is some
+ 
+
+ align:start position:0%
+electrons off the foil so there is some
+heating there are some strong electric
+
+ align:start position:0%
+heating there are some strong electric
+ 
+
+ align:start position:0%
+heating there are some strong electric
+fields for reasons that we're not going
+
+ align:start position:0%
+fields for reasons that we're not going
+ 
+
+ align:start position:0%
+fields for reasons that we're not going
+to go into very much this drives
+
+ align:start position:0%
+to go into very much this drives
+ 
+
+ align:start position:0%
+to go into very much this drives
+electrons off the foil at high speed and
+
+ align:start position:0%
+electrons off the foil at high speed and
+ 
+
+ align:start position:0%
+electrons off the foil at high speed and
+they form a sort of little Cloud going
+
+ align:start position:0%
+they form a sort of little Cloud going
+ 
+
+ align:start position:0%
+they form a sort of little Cloud going
+outwards because there's been electrons
+
+ align:start position:0%
+outwards because there's been electrons
+ 
+
+ align:start position:0%
+outwards because there's been electrons
+ejected we then have an electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field and that electric field drags
+
+ align:start position:0%
+field and that electric field drags
+ 
+
+ align:start position:0%
+field and that electric field drags
+these protons off the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+like that and this is how the protons
+
+ align:start position:0%
+like that and this is how the protons
+ 
+
+ align:start position:0%
+like that and this is how the protons
+are accelerating so this technique some
+
+ align:start position:0%
+are accelerating so this technique some
+ 
+
+ align:start position:0%
+are accelerating so this technique some
+good things about it it gives us many
+
+ align:start position:0%
+good things about it it gives us many
+ 
+
+ align:start position:0%
+good things about it it gives us many
+protons it's a very efficient way of
+
+ align:start position:0%
+protons it's a very efficient way of
+ 
+
+ align:start position:0%
+protons it's a very efficient way of
+accelerating the protons here it gives
+
+ align:start position:0%
+accelerating the protons here it gives
+ 
+
+ align:start position:0%
+accelerating the protons here it gives
+us a range of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energies remember we said we'd like
+
+ align:start position:0%
+energies remember we said we'd like
+ 
+
+ align:start position:0%
+energies remember we said we'd like
+several different energies for telling
+
+ align:start position:0%
+several different energies for telling
+ 
+
+ align:start position:0%
+several different energies for telling
+difference in electric and magnetic
+
+ align:start position:0%
+difference in electric and magnetic
+ 
+
+ align:start position:0%
+difference in electric and magnetic
+fields the spot
+
+ align:start position:0%
+fields the spot
+ 
+
+ align:start position:0%
+fields the spot
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+is around about 10 microns so as we said
+
+ align:start position:0%
+is around about 10 microns so as we said
+ 
+
+ align:start position:0%
+is around about 10 microns so as we said
+that's a nice small spot that's
+
+ align:start position:0%
+that's a nice small spot that's
+ 
+
+ align:start position:0%
+that's a nice small spot that's
+something we wanted in order for all our
+
+ align:start position:0%
+something we wanted in order for all our
+ 
+
+ align:start position:0%
+something we wanted in order for all our
+praxial approximation and stuff to work
+
+ align:start position:0%
+praxial approximation and stuff to work
+ 
+
+ align:start position:0%
+praxial approximation and stuff to work
+and it's a
+
+ align:start position:0%
+and it's a
+ 
+
+ align:start position:0%
+and it's a
+beam it's in One Direction and we'll see
+
+ align:start position:0%
+beam it's in One Direction and we'll see
+ 
+
+ align:start position:0%
+beam it's in One Direction and we'll see
+why that's important when we compare the
+
+ align:start position:0%
+why that's important when we compare the
+ 
+
+ align:start position:0%
+why that's important when we compare the
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meth the big disadvantage of this
+
+ align:start position:0%
+meth the big disadvantage of this
+ 
+
+ align:start position:0%
+meth the big disadvantage of this
+technique is you
+
+ align:start position:0%
+technique is you
+ 
+
+ align:start position:0%
+technique is you
+need a petat
+
+ align:start position:0%
+need a petat
+ 
+
+ align:start position:0%
+need a petat
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+laser or higher so you need to have one
+
+ align:start position:0%
+laser or higher so you need to have one
+ 
+
+ align:start position:0%
+laser or higher so you need to have one
+of these Ultra short pulse lasers not
+
+ align:start position:0%
+of these Ultra short pulse lasers not
+ 
+
+ align:start position:0%
+of these Ultra short pulse lasers not
+every facility has that these are very
+
+ align:start position:0%
+every facility has that these are very
+ 
+
+ align:start position:0%
+every facility has that these are very
+expensive things to build so it's not
+
+ align:start position:0%
+expensive things to build so it's not
+ 
+
+ align:start position:0%
+expensive things to build so it's not
+like you can just go down to the toop
+
+ align:start position:0%
+like you can just go down to the toop
+ 
+
+ align:start position:0%
+like you can just go down to the toop
+and get this I thought about trying to
+
+ align:start position:0%
+and get this I thought about trying to
+ 
+
+ align:start position:0%
+and get this I thought about trying to
+get one of these for a puffing facility
+
+ align:start position:0%
+get one of these for a puffing facility
+ 
+
+ align:start position:0%
+get one of these for a puffing facility
+and we got a quote about $2 million for
+
+ align:start position:0%
+and we got a quote about $2 million for
+ 
+
+ align:start position:0%
+and we got a quote about $2 million for
+a laser to just do a not very good tnsa
+
+ align:start position:0%
+a laser to just do a not very good tnsa
+ 
+
+ align:start position:0%
+a laser to just do a not very good tnsa
+signal so um is a very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exp but that's your source your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detector is something which is called
+
+ align:start position:0%
+detector is something which is called
+ 
+
+ align:start position:0%
+detector is something which is called
+radio chromic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+film another acronym I'm not going to
+
+ align:start position:0%
+film another acronym I'm not going to
+ 
+
+ align:start position:0%
+film another acronym I'm not going to
+repeat we'll call it RCF from now on
+
+ align:start position:0%
+repeat we'll call it RCF from now on
+ 
+
+ align:start position:0%
+repeat we'll call it RCF from now on
+okay now RCF changes color when it's hit
+
+ align:start position:0%
+okay now RCF changes color when it's hit
+ 
+
+ align:start position:0%
+okay now RCF changes color when it's hit
+by protons that's the chromic part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and the more protons that hit it the
+
+ align:start position:0%
+it and the more protons that hit it the
+ 
+
+ align:start position:0%
+it and the more protons that hit it the
+more it changes color it sort of starts
+
+ align:start position:0%
+more it changes color it sort of starts
+ 
+
+ align:start position:0%
+more it changes color it sort of starts
+off quite clear and it turns this
+
+ align:start position:0%
+off quite clear and it turns this
+ 
+
+ align:start position:0%
+off quite clear and it turns this
+beautiful like ghostly blue and then
+
+ align:start position:0%
+beautiful like ghostly blue and then
+ 
+
+ align:start position:0%
+beautiful like ghostly blue and then
+goes into a very dark deep blue they're
+
+ align:start position:0%
+goes into a very dark deep blue they're
+ 
+
+ align:start position:0%
+goes into a very dark deep blue they're
+very beautiful the raw proton uh
+
+ align:start position:0%
+very beautiful the raw proton uh
+ 
+
+ align:start position:0%
+very beautiful the raw proton uh
+radiochromic film
+
+ align:start position:0%
+radiochromic film
+ 
+
+ align:start position:0%
+radiochromic film
+images now what you end up doing is you
+
+ align:start position:0%
+images now what you end up doing is you
+ 
+
+ align:start position:0%
+images now what you end up doing is you
+have stacks of this film you have
+
+ align:start position:0%
+have stacks of this film you have
+ 
+
+ align:start position:0%
+have stacks of this film you have
+multiple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sheets so imagine these are squares of
+
+ align:start position:0%
+sheets so imagine these are squares of
+ 
+
+ align:start position:0%
+sheets so imagine these are squares of
+film and I've just made a stack out of
+
+ align:start position:0%
+film and I've just made a stack out of
+ 
+
+ align:start position:0%
+film and I've just made a stack out of
+lots of them like this and the reason
+
+ align:start position:0%
+lots of them like this and the reason
+ 
+
+ align:start position:0%
+lots of them like this and the reason
+you make lots of stacks out of these is
+
+ align:start position:0%
+you make lots of stacks out of these is
+ 
+
+ align:start position:0%
+you make lots of stacks out of these is
+due to a peculiarity of charge particle
+
+ align:start position:0%
+due to a peculiarity of charge particle
+ 
+
+ align:start position:0%
+due to a peculiarity of charge particle
+stopping and this peculiarity is called
+
+ align:start position:0%
+stopping and this peculiarity is called
+ 
+
+ align:start position:0%
+stopping and this peculiarity is called
+the brag Peak which some of you may have
+
+ align:start position:0%
+the brag Peak which some of you may have
+ 
+
+ align:start position:0%
+the brag Peak which some of you may have
+come across
+
+ align:start position:0%
+come across
+ 
+
+ align:start position:0%
+come across
+before the idea of the brag Peak is your
+
+ align:start position:0%
+before the idea of the brag Peak is your
+ 
+
+ align:start position:0%
+before the idea of the brag Peak is your
+charged particles tend to stop in a very
+
+ align:start position:0%
+charged particles tend to stop in a very
+ 
+
+ align:start position:0%
+charged particles tend to stop in a very
+specific place for a material which is
+
+ align:start position:0%
+specific place for a material which is
+ 
+
+ align:start position:0%
+specific place for a material which is
+to do with their energy so for example
+
+ align:start position:0%
+to do with their energy so for example
+ 
+
+ align:start position:0%
+to do with their energy so for example
+uh if this is the stopping location
+
+ align:start position:0%
+uh if this is the stopping location
+ 
+
+ align:start position:0%
+uh if this is the stopping location
+X call this the x coordinate I guess
+
+ align:start position:0%
+X call this the x coordinate I guess
+ 
+
+ align:start position:0%
+X call this the x coordinate I guess
+I've called it Z everywh else but
+
+ align:start position:0%
+I've called it Z everywh else but
+ 
+
+ align:start position:0%
+I've called it Z everywh else but
+whatever um you tend to have a lot of
+
+ align:start position:0%
+whatever um you tend to have a lot of
+ 
+
+ align:start position:0%
+whatever um you tend to have a lot of
+deposition of your particles all at one
+
+ align:start position:0%
+deposition of your particles all at one
+ 
+
+ align:start position:0%
+deposition of your particles all at one
+place and this is energy dependent so
+
+ align:start position:0%
+place and this is energy dependent so
+ 
+
+ align:start position:0%
+place and this is energy dependent so
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+energy dependent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deposition the reason this is peculiar
+
+ align:start position:0%
+deposition the reason this is peculiar
+ 
+
+ align:start position:0%
+deposition the reason this is peculiar
+is you'll remember that for photons
+
+ align:start position:0%
+is you'll remember that for photons
+ 
+
+ align:start position:0%
+is you'll remember that for photons
+we just had this exponential decay
+
+ align:start position:0%
+we just had this exponential decay
+ 
+
+ align:start position:0%
+we just had this exponential decay
+here that was J with the opacity of it
+
+ align:start position:0%
+here that was J with the opacity of it
+ 
+
+ align:start position:0%
+here that was J with the opacity of it
+but that's not what we get for
+
+ align:start position:0%
+but that's not what we get for
+ 
+
+ align:start position:0%
+but that's not what we get for
+particles the fact that all the
+
+ align:start position:0%
+particles the fact that all the
+ 
+
+ align:start position:0%
+particles the fact that all the
+particles are the same energy roughly
+
+ align:start position:0%
+particles are the same energy roughly
+ 
+
+ align:start position:0%
+particles are the same energy roughly
+stop in the same bit of film means that
+
+ align:start position:0%
+stop in the same bit of film means that
+ 
+
+ align:start position:0%
+stop in the same bit of film means that
+each film corresponds to a specific
+
+ align:start position:0%
+each film corresponds to a specific
+ 
+
+ align:start position:0%
+each film corresponds to a specific
+energy maybe the first film stack here
+
+ align:start position:0%
+energy maybe the first film stack here
+ 
+
+ align:start position:0%
+energy maybe the first film stack here
+corresponds to one Meb and the next one
+
+ align:start position:0%
+corresponds to one Meb and the next one
+ 
+
+ align:start position:0%
+corresponds to one Meb and the next one
+to two three four five six and so on you
+
+ align:start position:0%
+to two three four five six and so on you
+ 
+
+ align:start position:0%
+to two three four five six and so on you
+can put different filters between these
+
+ align:start position:0%
+can put different filters between these
+ 
+
+ align:start position:0%
+can put different filters between these
+to slow to to select different proton
+
+ align:start position:0%
+to slow to to select different proton
+ 
+
+ align:start position:0%
+to slow to to select different proton
+energies but it means that each of these
+
+ align:start position:0%
+energies but it means that each of these
+ 
+
+ align:start position:0%
+energies but it means that each of these
+bits of fil now corresponds to a
+
+ align:start position:0%
+bits of fil now corresponds to a
+ 
+
+ align:start position:0%
+bits of fil now corresponds to a
+different energy which is very useful if
+
+ align:start position:0%
+different energy which is very useful if
+ 
+
+ align:start position:0%
+different energy which is very useful if
+you want to do your multi-energy trick
+
+ align:start position:0%
+you want to do your multi-energy trick
+ 
+
+ align:start position:0%
+you want to do your multi-energy trick
+of unfolding the electric and magnetic
+
+ align:start position:0%
+of unfolding the electric and magnetic
+ 
+
+ align:start position:0%
+of unfolding the electric and magnetic
+fields so this first result of this is
+
+ align:start position:0%
+fields so this first result of this is
+ 
+
+ align:start position:0%
+fields so this first result of this is
+that we have
+
+ align:start position:0%
+that we have
+ 
+
+ align:start position:0%
+that we have
+uh uh we call it one
+
+ align:start position:0%
+uh uh we call it one
+ 
+
+ align:start position:0%
+uh uh we call it one
+energy per fi
+
+ align:start position:0%
+energy per fi
+ 
+
+ align:start position:0%
+energy per fi
+it's obviously not quite true because
+
+ align:start position:0%
+it's obviously not quite true because
+ 
+
+ align:start position:0%
+it's obviously not quite true because
+you have some bleed through some some
+
+ align:start position:0%
+you have some bleed through some some
+ 
+
+ align:start position:0%
+you have some bleed through some some
+particles which stopped early so there's
+
+ align:start position:0%
+particles which stopped early so there's
+ 
+
+ align:start position:0%
+particles which stopped early so there's
+a little bit of cross talk between them
+
+ align:start position:0%
+a little bit of cross talk between them
+ 
+
+ align:start position:0%
+a little bit of cross talk between them
+the other neat thing about this if you
+
+ align:start position:0%
+the other neat thing about this if you
+ 
+
+ align:start position:0%
+the other neat thing about this if you
+don't want to use these in order to back
+
+ align:start position:0%
+don't want to use these in order to back
+ 
+
+ align:start position:0%
+don't want to use these in order to back
+out the difference between electric and
+
+ align:start position:0%
+out the difference between electric and
+ 
+
+ align:start position:0%
+out the difference between electric and
+magnetic fields you can make a different
+
+ align:start position:0%
+magnetic fields you can make a different
+ 
+
+ align:start position:0%
+magnetic fields you can make a different
+argument and you can argue in fact that
+
+ align:start position:0%
+argument and you can argue in fact that
+ 
+
+ align:start position:0%
+argument and you can argue in fact that
+my particles were born here and they
+
+ align:start position:0%
+my particles were born here and they
+ 
+
+ align:start position:0%
+my particles were born here and they
+were born at different
+
+ align:start position:0%
+were born at different
+ 
+
+ align:start position:0%
+were born at different
+energies and they stream through this
+
+ align:start position:0%
+energies and they stream through this
+ 
+
+ align:start position:0%
+energies and they stream through this
+plasma here but that means that a
+
+ align:start position:0%
+plasma here but that means that a
+ 
+
+ align:start position:0%
+plasma here but that means that a
+particle going at 10
+
+ align:start position:0%
+particle going at 10
+ 
+
+ align:start position:0%
+particle going at 10
+Meb reaches the plasma at time t0 so
+
+ align:start position:0%
+Meb reaches the plasma at time t0 so
+ 
+
+ align:start position:0%
+Meb reaches the plasma at time t0 so
+instead of 10 I'll write six because
+
+ align:start position:0%
+instead of 10 I'll write six because
+ 
+
+ align:start position:0%
+instead of 10 I'll write six because
+I've got six here so these particles all
+
+ align:start position:0%
+I've got six here so these particles all
+ 
+
+ align:start position:0%
+I've got six here so these particles all
+stream through at
+
+ align:start position:0%
+stream through at
+ 
+
+ align:start position:0%
+stream through at
+t0 but a particle at one me is going
+
+ align:start position:0%
+t0 but a particle at one me is going
+ 
+
+ align:start position:0%
+t0 but a particle at one me is going
+more slowly going six times more slowly
+
+ align:start position:0%
+more slowly going six times more slowly
+ 
+
+ align:start position:0%
+more slowly going six times more slowly
+modulos and relativistic stuff and so
+
+ align:start position:0%
+modulos and relativistic stuff and so
+ 
+
+ align:start position:0%
+modulos and relativistic stuff and so
+that means that this particle arrives at
+
+ align:start position:0%
+that means that this particle arrives at
+ 
+
+ align:start position:0%
+that means that this particle arrives at
+t0 plus delta T and so not only do the
+
+ align:start position:0%
+t0 plus delta T and so not only do the
+ 
+
+ align:start position:0%
+t0 plus delta T and so not only do the
+different energies maybe give you a way
+
+ align:start position:0%
+different energies maybe give you a way
+ 
+
+ align:start position:0%
+different energies maybe give you a way
+of unfolding the Electric magnetic
+
+ align:start position:0%
+of unfolding the Electric magnetic
+ 
+
+ align:start position:0%
+of unfolding the Electric magnetic
+fields the different energies are
+
+ align:start position:0%
+fields the different energies are
+ 
+
+ align:start position:0%
+fields the different energies are
+different slices in time so if this is
+
+ align:start position:0%
+different slices in time so if this is
+ 
+
+ align:start position:0%
+different slices in time so if this is
+energy in this direction it means that
+
+ align:start position:0%
+energy in this direction it means that
+ 
+
+ align:start position:0%
+energy in this direction it means that
+if you read the films back they
+
+ align:start position:0%
+if you read the films back they
+ 
+
+ align:start position:0%
+if you read the films back they
+correspond to time in this direction and
+
+ align:start position:0%
+correspond to time in this direction and
+ 
+
+ align:start position:0%
+correspond to time in this direction and
+so you can make a little movie of how
+
+ align:start position:0%
+so you can make a little movie of how
+ 
+
+ align:start position:0%
+so you can make a little movie of how
+your plasma revolves in time so that's
+
+ align:start position:0%
+your plasma revolves in time so that's
+ 
+
+ align:start position:0%
+your plasma revolves in time so that's
+really cool you get time resolution and
+
+ align:start position:0%
+really cool you get time resolution and
+ 
+
+ align:start position:0%
+really cool you get time resolution and
+the more different bits of film you have
+
+ align:start position:0%
+the more different bits of film you have
+ 
+
+ align:start position:0%
+the more different bits of film you have
+and The Wider range of energies you have
+
+ align:start position:0%
+and The Wider range of energies you have
+ 
+
+ align:start position:0%
+and The Wider range of energies you have
+the better time resolution you can get
+
+ align:start position:0%
+the better time resolution you can get
+ 
+
+ align:start position:0%
+the better time resolution you can get
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep yeah the radiorc film isn't
+
+ align:start position:0%
+yep yeah the radiorc film isn't
+ 
+
+ align:start position:0%
+yep yeah the radiorc film isn't
+sensitive to other particles so yeah not
+
+ align:start position:0%
+sensitive to other particles so yeah not
+ 
+
+ align:start position:0%
+sensitive to other particles so yeah not
+to neutrons and gamas and things like
+
+ align:start position:0%
+to neutrons and gamas and things like
+ 
+
+ align:start position:0%
+to neutrons and gamas and things like
+that you can also yeah yeah in in this
+
+ align:start position:0%
+that you can also yeah yeah in in this
+ 
+
+ align:start position:0%
+that you can also yeah yeah in in this
+case I think it's almost that things
+
+ align:start position:0%
+case I think it's almost that things
+ 
+
+ align:start position:0%
+case I think it's almost that things
+like uh the lower energy particles and
+
+ align:start position:0%
+like uh the lower energy particles and
+ 
+
+ align:start position:0%
+like uh the lower energy particles and
+photons you could filter out and the
+
+ align:start position:0%
+photons you could filter out and the
+ 
+
+ align:start position:0%
+photons you could filter out and the
+high energy ones like gamma rays will
+
+ align:start position:0%
+high energy ones like gamma rays will
+ 
+
+ align:start position:0%
+high energy ones like gamma rays will
+just go straight through without
+
+ align:start position:0%
+just go straight through without
+ 
+
+ align:start position:0%
+just go straight through without
+interacting so this is pretty much just
+
+ align:start position:0%
+interacting so this is pretty much just
+ 
+
+ align:start position:0%
+interacting so this is pretty much just
+sensitive to the proton yeah that's a
+
+ align:start position:0%
+sensitive to the proton yeah that's a
+ 
+
+ align:start position:0%
+sensitive to the proton yeah that's a
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it's the same thing so these the the
+
+ align:start position:0%
+yes it's the same thing so these the the
+ 
+
+ align:start position:0%
+yes it's the same thing so these the the
+protons are all emitted in a very very
+
+ align:start position:0%
+protons are all emitted in a very very
+ 
+
+ align:start position:0%
+protons are all emitted in a very very
+narrow burst okay yeah that's no that's
+
+ align:start position:0%
+narrow burst okay yeah that's no that's
+ 
+
+ align:start position:0%
+narrow burst okay yeah that's no that's
+that's a great that's a great thank you
+
+ align:start position:0%
+that's a great that's a great thank you
+ 
+
+ align:start position:0%
+that's a great that's a great thank you
+let have a little figure here of
+
+ align:start position:0%
+let have a little figure here of
+ 
+
+ align:start position:0%
+let have a little figure here of
+time and I don't know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluence so at Time Zero all of the
+
+ align:start position:0%
+fluence so at Time Zero all of the
+ 
+
+ align:start position:0%
+fluence so at Time Zero all of the
+protons are
+
+ align:start position:0%
+protons are
+ 
+
+ align:start position:0%
+protons are
+emitted very
+
+ align:start position:0%
+emitted very
+ 
+
+ align:start position:0%
+emitted very
+narrow remember this is Peak a second or
+
+ align:start position:0%
+narrow remember this is Peak a second or
+ 
+
+ align:start position:0%
+narrow remember this is Peak a second or
+f a second here so I could say this is
+
+ align:start position:0%
+f a second here so I could say this is
+ 
+
+ align:start position:0%
+f a second here so I could say this is
+Peak a second and maybe I've got two
+
+ align:start position:0%
+Peak a second and maybe I've got two
+ 
+
+ align:start position:0%
+Peak a second and maybe I've got two
+energies here the blue energy which is
+
+ align:start position:0%
+energies here the blue energy which is
+ 
+
+ align:start position:0%
+energies here the blue energy which is
+one me and the purple energy which is 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MP they have to travel some distance
+
+ align:start position:0%
+MP they have to travel some distance
+ 
+
+ align:start position:0%
+MP they have to travel some distance
+from The Source through the plasma and
+
+ align:start position:0%
+from The Source through the plasma and
+ 
+
+ align:start position:0%
+from The Source through the plasma and
+they will go through it at different
+
+ align:start position:0%
+they will go through it at different
+ 
+
+ align:start position:0%
+they will go through it at different
+times the 10 m V1 will get there first
+
+ align:start position:0%
+times the 10 m V1 will get there first
+ 
+
+ align:start position:0%
+times the 10 m V1 will get there first
+and the one mv1 will get there second
+
+ align:start position:0%
+and the one mv1 will get there second
+ 
+
+ align:start position:0%
+and the one mv1 will get there second
+and then finally they will travel
+
+ align:start position:0%
+and then finally they will travel
+ 
+
+ align:start position:0%
+and then finally they will travel
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+detector and they'll arrive there much
+
+ align:start position:0%
+detector and they'll arrive there much
+ 
+
+ align:start position:0%
+detector and they'll arrive there much
+later but we don't really care the
+
+ align:start position:0%
+later but we don't really care the
+ 
+
+ align:start position:0%
+later but we don't really care the
+detector is time integrating so it will
+
+ align:start position:0%
+detector is time integrating so it will
+ 
+
+ align:start position:0%
+detector is time integrating so it will
+see protons which sample the plasma at
+
+ align:start position:0%
+see protons which sample the plasma at
+ 
+
+ align:start position:0%
+see protons which sample the plasma at
+an earlier time uh sorry it will the the
+
+ align:start position:0%
+an earlier time uh sorry it will the the
+ 
+
+ align:start position:0%
+an earlier time uh sorry it will the the
+10 m film will see protons that sample
+
+ align:start position:0%
+10 m film will see protons that sample
+ 
+
+ align:start position:0%
+10 m film will see protons that sample
+the plasma earlier than the 1 M film
+
+ align:start position:0%
+the plasma earlier than the 1 M film
+ 
+
+ align:start position:0%
+the plasma earlier than the 1 M film
+yeah but you do actually have to have
+
+ align:start position:0%
+yeah but you do actually have to have
+ 
+
+ align:start position:0%
+yeah but you do actually have to have
+that requirement you have a very very
+
+ align:start position:0%
+that requirement you have a very very
+ 
+
+ align:start position:0%
+that requirement you have a very very
+short burst protons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so you can only do one or the
+
+ align:start position:0%
+yeah yeah so you can only do one or the
+ 
+
+ align:start position:0%
+yeah yeah so you can only do one or the
+other you can either claim that there
+
+ align:start position:0%
+other you can either claim that there
+ 
+
+ align:start position:0%
+other you can either claim that there
+are like no electric fields and you know
+
+ align:start position:0%
+are like no electric fields and you know
+ 
+
+ align:start position:0%
+are like no electric fields and you know
+it's all magnetic fields and then you
+
+ align:start position:0%
+it's all magnetic fields and then you
+ 
+
+ align:start position:0%
+it's all magnetic fields and then you
+get a Time series or you can claim that
+
+ align:start position:0%
+get a Time series or you can claim that
+ 
+
+ align:start position:0%
+get a Time series or you can claim that
+um the plasma doesn't change in time and
+
+ align:start position:0%
+um the plasma doesn't change in time and
+ 
+
+ align:start position:0%
+um the plasma doesn't change in time and
+therefore you can use a different
+
+ align:start position:0%
+therefore you can use a different
+ 
+
+ align:start position:0%
+therefore you can use a different
+energies so you've got to be a little
+
+ align:start position:0%
+energies so you've got to be a little
+ 
+
+ align:start position:0%
+energies so you've got to be a little
+bit careful when you see someone
+
+ align:start position:0%
+bit careful when you see someone
+ 
+
+ align:start position:0%
+bit careful when you see someone
+claiming with proton radiography it's
+
+ align:start position:0%
+claiming with proton radiography it's
+ 
+
+ align:start position:0%
+claiming with proton radiography it's
+like it's difficult to do both but you
+
+ align:start position:0%
+like it's difficult to do both but you
+ 
+
+ align:start position:0%
+like it's difficult to do both but you
+might have like a simulation or some
+
+ align:start position:0%
+might have like a simulation or some
+ 
+
+ align:start position:0%
+might have like a simulation or some
+other experiment that suggests the
+
+ align:start position:0%
+other experiment that suggests the
+ 
+
+ align:start position:0%
+other experiment that suggests the
+electric fields are minimal in which
+
+ align:start position:0%
+electric fields are minimal in which
+ 
+
+ align:start position:0%
+electric fields are minimal in which
+case you can just say okay everything I
+
+ align:start position:0%
+case you can just say okay everything I
+ 
+
+ align:start position:0%
+case you can just say okay everything I
+see is due to magnetic fields now I have
+
+ align:start position:0%
+see is due to magnetic fields now I have
+ 
+
+ align:start position:0%
+see is due to magnetic fields now I have
+a time people will do that and maybe
+
+ align:start position:0%
+a time people will do that and maybe
+ 
+
+ align:start position:0%
+a time people will do that and maybe
+reason was there another question that I
+
+ align:start position:0%
+reason was there another question that I
+ 
+
+ align:start position:0%
+reason was there another question that I
+see okay let's talk about this second
+
+ align:start position:0%
+see okay let's talk about this second
+ 
+
+ align:start position:0%
+see okay let's talk about this second
+method uh which is an imploding capsule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second second method would be for
+
+ align:start position:0%
+the second second method would be for
+ 
+
+ align:start position:0%
+the second second method would be for
+example a d helium 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implosion so this is literally a little
+
+ align:start position:0%
+implosion so this is literally a little
+ 
+
+ align:start position:0%
+implosion so this is literally a little
+inertial confinement Fusion Target here
+
+ align:start position:0%
+inertial confinement Fusion Target here
+ 
+
+ align:start position:0%
+inertial confinement Fusion Target here
+filled with uterum and helium 3 and you
+
+ align:start position:0%
+filled with uterum and helium 3 and you
+ 
+
+ align:start position:0%
+filled with uterum and helium 3 and you
+get a load of direct drive
+
+ align:start position:0%
+get a load of direct drive
+ 
+
+ align:start position:0%
+get a load of direct drive
+lasers pushing on
+
+ align:start position:0%
+lasers pushing on
+ 
+
+ align:start position:0%
+lasers pushing on
+it and making a nice symmetric
+
+ align:start position:0%
+it and making a nice symmetric
+ 
+
+ align:start position:0%
+it and making a nice symmetric
+is implosion of this and then when this
+
+ align:start position:0%
+is implosion of this and then when this
+ 
+
+ align:start position:0%
+is implosion of this and then when this
+implodes it's going to send out all of
+
+ align:start position:0%
+implodes it's going to send out all of
+ 
+
+ align:start position:0%
+implodes it's going to send out all of
+the particles that come from the fusion
+
+ align:start position:0%
+the particles that come from the fusion
+ 
+
+ align:start position:0%
+the particles that come from the fusion
+reaction between the duum and the helium
+
+ align:start position:0%
+reaction between the duum and the helium
+ 
+
+ align:start position:0%
+reaction between the duum and the helium
+3 so just to save for this you need to
+
+ align:start position:0%
+3 so just to save for this you need to
+ 
+
+ align:start position:0%
+3 so just to save for this you need to
+have multiple I'm going to write
+
+ align:start position:0%
+have multiple I'm going to write
+ 
+
+ align:start position:0%
+have multiple I'm going to write
+many kogle
+
+ align:start position:0%
+many kogle
+ 
+
+ align:start position:0%
+many kogle
+class beams with a one nanc pulse one
+
+ align:start position:0%
+class beams with a one nanc pulse one
+ 
+
+ align:start position:0%
+class beams with a one nanc pulse one
+nanc in the laser world is considered a
+
+ align:start position:0%
+nanc in the laser world is considered a
+ 
+
+ align:start position:0%
+nanc in the laser world is considered a
+long PSE right so these are much longer
+
+ align:start position:0%
+long PSE right so these are much longer
+ 
+
+ align:start position:0%
+long PSE right so these are much longer
+than PC andc these are long pulse
+
+ align:start position:0%
+than PC andc these are long pulse
+ 
+
+ align:start position:0%
+than PC andc these are long pulse
+lasers so the interesting thing is that
+
+ align:start position:0%
+lasers so the interesting thing is that
+ 
+
+ align:start position:0%
+lasers so the interesting thing is that
+this reaction produc prod es two
+
+ align:start position:0%
+this reaction produc prod es two
+ 
+
+ align:start position:0%
+this reaction produc prod es two
+different energies from it but only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two we have the three
+
+ align:start position:0%
+two we have the three
+ 
+
+ align:start position:0%
+two we have the three
+MV DD
+
+ align:start position:0%
+MV DD
+ 
+
+ align:start position:0%
+MV DD
+protons remember we're not interested in
+
+ align:start position:0%
+protons remember we're not interested in
+ 
+
+ align:start position:0%
+protons remember we're not interested in
+neutrons there may be neutrons coming
+
+ align:start position:0%
+neutrons there may be neutrons coming
+ 
+
+ align:start position:0%
+neutrons there may be neutrons coming
+out but they're not being used for this
+
+ align:start position:0%
+out but they're not being used for this
+ 
+
+ align:start position:0%
+out but they're not being used for this
+Diagnostic and we have the
+
+ align:start position:0%
+Diagnostic and we have the
+ 
+
+ align:start position:0%
+Diagnostic and we have the
+14.7 me the helium
+
+ align:start position:0%
+14.7 me the helium
+ 
+
+ align:start position:0%
+14.7 me the helium
+3 protons as well so this could be a
+
+ align:start position:0%
+3 protons as well so this could be a
+ 
+
+ align:start position:0%
+3 protons as well so this could be a
+positive or a negative the positive is
+
+ align:start position:0%
+positive or a negative the positive is
+ 
+
+ align:start position:0%
+positive or a negative the positive is
+you know exactly what your particle
+
+ align:start position:0%
+you know exactly what your particle
+ 
+
+ align:start position:0%
+you know exactly what your particle
+energies are they're sort of set by
+
+ align:start position:0%
+energies are they're sort of set by
+ 
+
+ align:start position:0%
+energies are they're sort of set by
+Fusion they're going to be shifted a
+
+ align:start position:0%
+Fusion they're going to be shifted a
+ 
+
+ align:start position:0%
+Fusion they're going to be shifted a
+little bit because uh there's thermal
+
+ align:start position:0%
+little bit because uh there's thermal
+ 
+
+ align:start position:0%
+little bit because uh there's thermal
+motion here but roughly you know what
+
+ align:start position:0%
+motion here but roughly you know what
+ 
+
+ align:start position:0%
+motion here but roughly you know what
+the energies are exactly but it's good
+
+ align:start position:0%
+the energies are exactly but it's good
+ 
+
+ align:start position:0%
+the energies are exactly but it's good
+so the positive is we know the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy um the negative is there's only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two people have recently add a little
+
+ align:start position:0%
+two people have recently add a little
+ 
+
+ align:start position:0%
+two people have recently add a little
+bit of spice in the form of some
+
+ align:start position:0%
+bit of spice in the form of some
+ 
+
+ align:start position:0%
+bit of spice in the form of some
+uh and then you also get the tritium
+
+ align:start position:0%
+uh and then you also get the tritium
+ 
+
+ align:start position:0%
+uh and then you also get the tritium
+helium 3 reaction which gives you a
+
+ align:start position:0%
+helium 3 reaction which gives you a
+ 
+
+ align:start position:0%
+helium 3 reaction which gives you a
+proton at 12 me so that gives you a tri
+
+ align:start position:0%
+proton at 12 me so that gives you a tri
+ 
+
+ align:start position:0%
+proton at 12 me so that gives you a tri
+particle source so that's nice now you
+
+ align:start position:0%
+particle source so that's nice now you
+ 
+
+ align:start position:0%
+particle source so that's nice now you
+have three particle so that's pretty
+
+ align:start position:0%
+have three particle so that's pretty
+ 
+
+ align:start position:0%
+have three particle so that's pretty
+good um another negative
+
+ align:start position:0%
+good um another negative
+ 
+
+ align:start position:0%
+good um another negative
+here is the spot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size these implosions tend to get down
+
+ align:start position:0%
+size these implosions tend to get down
+ 
+
+ align:start position:0%
+size these implosions tend to get down
+to slightly larger sizes than you can
+
+ align:start position:0%
+to slightly larger sizes than you can
+ 
+
+ align:start position:0%
+to slightly larger sizes than you can
+reach with the focal spot for TNS say so
+
+ align:start position:0%
+reach with the focal spot for TNS say so
+ 
+
+ align:start position:0%
+reach with the focal spot for TNS say so
+the spot size is around about 40 microns
+
+ align:start position:0%
+the spot size is around about 40 microns
+ 
+
+ align:start position:0%
+the spot size is around about 40 microns
+or so it's not too much worse but it is
+
+ align:start position:0%
+or so it's not too much worse but it is
+ 
+
+ align:start position:0%
+or so it's not too much worse but it is
+significantly larger than the tnsa
+
+ align:start position:0%
+significantly larger than the tnsa
+ 
+
+ align:start position:0%
+significantly larger than the tnsa
+size the other problem is that we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isotropic
+
+ align:start position:0%
+isotropic
+ 
+
+ align:start position:0%
+isotropic
+emission so the nice thing about tnsa is
+
+ align:start position:0%
+emission so the nice thing about tnsa is
+ 
+
+ align:start position:0%
+emission so the nice thing about tnsa is
+all the particles are going roughly in
+
+ align:start position:0%
+all the particles are going roughly in
+ 
+
+ align:start position:0%
+all the particles are going roughly in
+the direction you want to here if your
+
+ align:start position:0%
+the direction you want to here if your
+ 
+
+ align:start position:0%
+the direction you want to here if your
+plasma is over here most of your
+
+ align:start position:0%
+plasma is over here most of your
+ 
+
+ align:start position:0%
+plasma is over here most of your
+particles are just flying off in
+
+ align:start position:0%
+particles are just flying off in
+ 
+
+ align:start position:0%
+particles are just flying off in
+completely random directions and you
+
+ align:start position:0%
+completely random directions and you
+ 
+
+ align:start position:0%
+completely random directions and you
+don't get to capture them at all um and
+
+ align:start position:0%
+don't get to capture them at all um and
+ 
+
+ align:start position:0%
+don't get to capture them at all um and
+so this means that we
+
+ align:start position:0%
+so this means that we
+ 
+
+ align:start position:0%
+so this means that we
+have few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles this is in contrast to tnsa
+
+ align:start position:0%
+particles this is in contrast to tnsa
+ 
+
+ align:start position:0%
+particles this is in contrast to tnsa
+where we were able to create a very
+
+ align:start position:0%
+where we were able to create a very
+ 
+
+ align:start position:0%
+where we were able to create a very
+large number of particles but the fact
+
+ align:start position:0%
+large number of particles but the fact
+ 
+
+ align:start position:0%
+large number of particles but the fact
+that we have very few particles also
+
+ align:start position:0%
+that we have very few particles also
+ 
+
+ align:start position:0%
+that we have very few particles also
+leads to a change in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detector this is sort of the big
+
+ align:start position:0%
+detector this is sort of the big
+ 
+
+ align:start position:0%
+detector this is sort of the big
+Workhorse of the MIT group because they
+
+ align:start position:0%
+Workhorse of the MIT group because they
+ 
+
+ align:start position:0%
+Workhorse of the MIT group because they
+realized that they could use a detector
+
+ align:start position:0%
+realized that they could use a detector
+ 
+
+ align:start position:0%
+realized that they could use a detector
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+CR
+
+ align:start position:0%
+CR
+ 
+
+ align:start position:0%
+CR
+39 now cr39 is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polymer the interesting thing about it
+
+ align:start position:0%
+polymer the interesting thing about it
+ 
+
+ align:start position:0%
+polymer the interesting thing about it
+you have a sheet of cr39 you have a
+
+ align:start position:0%
+you have a sheet of cr39 you have a
+ 
+
+ align:start position:0%
+you have a sheet of cr39 you have a
+proton going through it is it causes a
+
+ align:start position:0%
+proton going through it is it causes a
+ 
+
+ align:start position:0%
+proton going through it is it causes a
+little area of damage a little track as
+
+ align:start position:0%
+little area of damage a little track as
+ 
+
+ align:start position:0%
+little area of damage a little track as
+a proton goes through and you can then
+
+ align:start position:0%
+a proton goes through and you can then
+ 
+
+ align:start position:0%
+a proton goes through and you can then
+dip your polymer after the shot in an
+
+ align:start position:0%
+dip your polymer after the shot in an
+ 
+
+ align:start position:0%
+dip your polymer after the shot in an
+etching solu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it turns each of these tracks into
+
+ align:start position:0%
+and it turns each of these tracks into
+ 
+
+ align:start position:0%
+and it turns each of these tracks into
+little holes so now if you look at your
+
+ align:start position:0%
+little holes so now if you look at your
+ 
+
+ align:start position:0%
+little holes so now if you look at your
+cr39 there's all sorts
+
+ align:start position:0%
+cr39 there's all sorts
+ 
+
+ align:start position:0%
+cr39 there's all sorts
+of little holes on
+
+ align:start position:0%
+of little holes on
+ 
+
+ align:start position:0%
+of little holes on
+it it turns out
+
+ align:start position:0%
+it it turns out
+ 
+
+ align:start position:0%
+it it turns out
+the size of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hole is in some way related to the
+
+ align:start position:0%
+hole is in some way related to the
+ 
+
+ align:start position:0%
+hole is in some way related to the
+energy so you can tell the difference
+
+ align:start position:0%
+energy so you can tell the difference
+ 
+
+ align:start position:0%
+energy so you can tell the difference
+between the 3 m and the 14 .7
+
+ align:start position:0%
+between the 3 m and the 14 .7
+ 
+
+ align:start position:0%
+between the 3 m and the 14 .7
+Meb um and theoretically though again
+
+ align:start position:0%
+Meb um and theoretically though again
+ 
+
+ align:start position:0%
+Meb um and theoretically though again
+I'm not sure that anyone has done this
+
+ align:start position:0%
+I'm not sure that anyone has done this
+ 
+
+ align:start position:0%
+I'm not sure that anyone has done this
+since it was first suggested if you have
+
+ align:start position:0%
+since it was first suggested if you have
+ 
+
+ align:start position:0%
+since it was first suggested if you have
+multiple pieces of cr39 and protons are
+
+ align:start position:0%
+multiple pieces of cr39 and protons are
+ 
+
+ align:start position:0%
+multiple pieces of cr39 and protons are
+just going through it you should be able
+
+ align:start position:0%
+just going through it you should be able
+ 
+
+ align:start position:0%
+just going through it you should be able
+to the tracks in different bits of film
+
+ align:start position:0%
+to the tracks in different bits of film
+ 
+
+ align:start position:0%
+to the tracks in different bits of film
+and go aha the track in this bit of film
+
+ align:start position:0%
+and go aha the track in this bit of film
+ 
+
+ align:start position:0%
+and go aha the track in this bit of film
+is now over
+
+ align:start position:0%
+is now over
+ 
+
+ align:start position:0%
+is now over
+here and I should be able to work out
+
+ align:start position:0%
+here and I should be able to work out
+ 
+
+ align:start position:0%
+here and I should be able to work out
+the angle of the particles so you you
+
+ align:start position:0%
+the angle of the particles so you you
+ 
+
+ align:start position:0%
+the angle of the particles so you you
+may be able to correlate
+
+ align:start position:0%
+may be able to correlate
+ 
+
+ align:start position:0%
+may be able to correlate
+tracks but I'm not sure anyone actually
+
+ align:start position:0%
+tracks but I'm not sure anyone actually
+ 
+
+ align:start position:0%
+tracks but I'm not sure anyone actually
+used that as a serious diagnostic
+
+ align:start position:0%
+used that as a serious diagnostic
+ 
+
+ align:start position:0%
+used that as a serious diagnostic
+recently it's just in one of the early
+
+ align:start position:0%
+recently it's just in one of the early
+ 
+
+ align:start position:0%
+recently it's just in one of the early
+papers um so what do you actually do
+
+ align:start position:0%
+papers um so what do you actually do
+ 
+
+ align:start position:0%
+papers um so what do you actually do
+with all these tracks here well you set
+
+ align:start position:0%
+with all these tracks here well you set
+ 
+
+ align:start position:0%
+with all these tracks here well you set
+up a very good microscope and you put
+
+ align:start position:0%
+up a very good microscope and you put
+ 
+
+ align:start position:0%
+up a very good microscope and you put
+one of these bits of cr39 in and the
+
+ align:start position:0%
+one of these bits of cr39 in and the
+ 
+
+ align:start position:0%
+one of these bits of cr39 in and the
+microscope looks at a small square here
+
+ align:start position:0%
+microscope looks at a small square here
+ 
+
+ align:start position:0%
+microscope looks at a small square here
+and it counts all of the holes in this
+
+ align:start position:0%
+and it counts all of the holes in this
+ 
+
+ align:start position:0%
+and it counts all of the holes in this
+little square and this Square represents
+
+ align:start position:0%
+little square and this Square represents
+ 
+
+ align:start position:0%
+little square and this Square represents
+a pixel and it outputs for example 100
+
+ align:start position:0%
+a pixel and it outputs for example 100
+ 
+
+ align:start position:0%
+a pixel and it outputs for example 100
+holes now it goes to the next
+
+ align:start position:0%
+holes now it goes to the next
+ 
+
+ align:start position:0%
+holes now it goes to the next
+one and it outputs 102 so it's
+
+ align:start position:0%
+one and it outputs 102 so it's
+ 
+
+ align:start position:0%
+one and it outputs 102 so it's
+effectively reading off the number of
+
+ align:start position:0%
+effectively reading off the number of
+ 
+
+ align:start position:0%
+effectively reading off the number of
+protons one by one individually
+
+ align:start position:0%
+protons one by one individually
+ 
+
+ align:start position:0%
+protons one by one individually
+automated but still individually and
+
+ align:start position:0%
+automated but still individually and
+ 
+
+ align:start position:0%
+automated but still individually and
+building up that intensity whereas the
+
+ align:start position:0%
+building up that intensity whereas the
+ 
+
+ align:start position:0%
+building up that intensity whereas the
+radiochromic film we don't know the
+
+ align:start position:0%
+radiochromic film we don't know the
+ 
+
+ align:start position:0%
+radiochromic film we don't know the
+exact number of protons we just have a
+
+ align:start position:0%
+exact number of protons we just have a
+ 
+
+ align:start position:0%
+exact number of protons we just have a
+different uh darkness of the film
+
+ align:start position:0%
+different uh darkness of the film
+ 
+
+ align:start position:0%
+different uh darkness of the film
+depending on the proton fluence here so
+
+ align:start position:0%
+depending on the proton fluence here so
+ 
+
+ align:start position:0%
+depending on the proton fluence here so
+I did a scientific poll at APS DPP 2021
+
+ align:start position:0%
+I did a scientific poll at APS DPP 2021
+ 
+
+ align:start position:0%
+I did a scientific poll at APS DPP 2021
+three out of three physicists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preferred I probably SP preferred wrong
+
+ align:start position:0%
+preferred I probably SP preferred wrong
+ 
+
+ align:start position:0%
+preferred I probably SP preferred wrong
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+pnsa plus radiochromic
+
+ align:start position:0%
+pnsa plus radiochromic
+ 
+
+ align:start position:0%
+pnsa plus radiochromic
+Bill however there are many facilities
+
+ align:start position:0%
+Bill however there are many facilities
+ 
+
+ align:start position:0%
+Bill however there are many facilities
+which do not have a sufficiently
+
+ align:start position:0%
+which do not have a sufficiently
+ 
+
+ align:start position:0%
+which do not have a sufficiently
+powerful short pulse laser but they do
+
+ align:start position:0%
+powerful short pulse laser but they do
+ 
+
+ align:start position:0%
+powerful short pulse laser but they do
+have an awful lot of ker class laser
+
+ align:start position:0%
+have an awful lot of ker class laser
+ 
+
+ align:start position:0%
+have an awful lot of ker class laser
+beams floating around that they don't
+
+ align:start position:0%
+beams floating around that they don't
+ 
+
+ align:start position:0%
+beams floating around that they don't
+have to use so for example on Omega or
+
+ align:start position:0%
+have to use so for example on Omega or
+ 
+
+ align:start position:0%
+have to use so for example on Omega or
+on nith you have lots of these beams you
+
+ align:start position:0%
+on nith you have lots of these beams you
+ 
+
+ align:start position:0%
+on nith you have lots of these beams you
+can use some of the beams to drive your
+
+ align:start position:0%
+can use some of the beams to drive your
+ 
+
+ align:start position:0%
+can use some of the beams to drive your
+target plasma and the other beams to
+
+ align:start position:0%
+target plasma and the other beams to
+ 
+
+ align:start position:0%
+target plasma and the other beams to
+drive your imploding capsule and you'll
+
+ align:start position:0%
+drive your imploding capsule and you'll
+ 
+
+ align:start position:0%
+drive your imploding capsule and you'll
+still be able to do proton radiography
+
+ align:start position:0%
+still be able to do proton radiography
+ 
+
+ align:start position:0%
+still be able to do proton radiography
+so there's definitely a place for this
+
+ align:start position:0%
+so there's definitely a place for this
+ 
+
+ align:start position:0%
+so there's definitely a place for this
+technique it's just that it seems like
+
+ align:start position:0%
+technique it's just that it seems like
+ 
+
+ align:start position:0%
+technique it's just that it seems like
+people prefer in general
+
+ align:start position:0%
+people prefer in general
+ 
+
+ align:start position:0%
+people prefer in general
+tnsa okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+uh I don't know whether people have done
+
+ align:start position:0%
+uh I don't know whether people have done
+ 
+
+ align:start position:0%
+uh I don't know whether people have done
+that yeah possibly you need to have
+
+ align:start position:0%
+that yeah possibly you need to have
+ 
+
+ align:start position:0%
+that yeah possibly you need to have
+magnetic fields right in this and so in
+
+ align:start position:0%
+magnetic fields right in this and so in
+ 
+
+ align:start position:0%
+magnetic fields right in this and so in
+general people don't think too much
+
+ align:start position:0%
+general people don't think too much
+ 
+
+ align:start position:0%
+general people don't think too much
+about the magnetic fields in ICF but
+
+ align:start position:0%
+about the magnetic fields in ICF but
+ 
+
+ align:start position:0%
+about the magnetic fields in ICF but
+might be there there are mechanisms
+
+ align:start position:0%
+might be there there are mechanisms
+ 
+
+ align:start position:0%
+might be there there are mechanisms
+which could self-generate the field like
+
+ align:start position:0%
+which could self-generate the field like
+ 
+
+ align:start position:0%
+which could self-generate the field like
+B and Battery I don't know if anyone's
+
+ align:start position:0%
+B and Battery I don't know if anyone's
+ 
+
+ align:start position:0%
+B and Battery I don't know if anyone's
+done that but it could be done I imagine
+
+ align:start position:0%
+done that but it could be done I imagine
+ 
+
+ align:start position:0%
+done that but it could be done I imagine
+it's then complicated you have to work
+
+ align:start position:0%
+it's then complicated you have to work
+ 
+
+ align:start position:0%
+it's then complicated you have to work
+out exactly what you're measuring but
+
+ align:start position:0%
+out exactly what you're measuring but
+ 
+
+ align:start position:0%
+out exactly what you're measuring but
+yeah an interesting idea sorry yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh we do alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles yeah I would have thought that
+
+ align:start position:0%
+particles yeah I would have thought that
+ 
+
+ align:start position:0%
+particles yeah I would have thought that
+the energy is the the velocity is a fair
+
+ align:start position:0%
+the energy is the the velocity is a fair
+ 
+
+ align:start position:0%
+the energy is the the velocity is a fair
+bit lower because of the higher Mass
+
+ align:start position:0%
+bit lower because of the higher Mass
+ 
+
+ align:start position:0%
+bit lower because of the higher Mass
+yeah um I don't know exactly so good
+
+ align:start position:0%
+yeah um I don't know exactly so good
+ 
+
+ align:start position:0%
+yeah um I don't know exactly so good
+question I mean in general the reason
+
+ align:start position:0%
+question I mean in general the reason
+ 
+
+ align:start position:0%
+question I mean in general the reason
+why people haven't put tritium in is you
+
+ align:start position:0%
+why people haven't put tritium in is you
+ 
+
+ align:start position:0%
+why people haven't put tritium in is you
+know you don't necessarily want to keep
+
+ align:start position:0%
+know you don't necessarily want to keep
+ 
+
+ align:start position:0%
+know you don't necessarily want to keep
+playing with tritium so this is
+
+ align:start position:0%
+playing with tritium so this is
+ 
+
+ align:start position:0%
+playing with tritium so this is
+relatively easy to fill this capsule and
+
+ align:start position:0%
+relatively easy to fill this capsule and
+ 
+
+ align:start position:0%
+relatively easy to fill this capsule and
+this is just like a pain in the ass so
+
+ align:start position:0%
+this is just like a pain in the ass so
+ 
+
+ align:start position:0%
+this is just like a pain in the ass so
+it's not like everyone has rushed out to
+
+ align:start position:0%
+it's not like everyone has rushed out to
+ 
+
+ align:start position:0%
+it's not like everyone has rushed out to
+start doing the triar thing yeah okay
+
+ align:start position:0%
+start doing the triar thing yeah okay
+ 
+
+ align:start position:0%
+start doing the triar thing yeah okay
+other questions anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online
+
+ align:start position:0%
+online
+ 
+
+ align:start position:0%
+online
+okay now we'll go through some issues
+
+ align:start position:0%
+okay now we'll go through some issues
+ 
+
+ align:start position:0%
+okay now we'll go through some issues
+with doing this diagnostic practically
+
+ align:start position:0%
+with doing this diagnostic practically
+ 
+
+ align:start position:0%
+with doing this diagnostic practically
+we've got our source we've got our
+
+ align:start position:0%
+we've got our source we've got our
+ 
+
+ align:start position:0%
+we've got our source we've got our
+detector we understand how to make a map
+
+ align:start position:0%
+detector we understand how to make a map
+ 
+
+ align:start position:0%
+detector we understand how to make a map
+of the intensity after the plasma but
+
+ align:start position:0%
+of the intensity after the plasma but
+ 
+
+ align:start position:0%
+of the intensity after the plasma but
+are there any problems with doing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+one this
+
+ align:start position:0%
+one this
+ 
+
+ align:start position:0%
+one this
+condition that our beam was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform remember we need that because
+
+ align:start position:0%
+uniform remember we need that because
+ 
+
+ align:start position:0%
+uniform remember we need that because
+we're trying to
+
+ align:start position:0%
+we're trying to
+ 
+
+ align:start position:0%
+we're trying to
+determine from I equals i z over the
+
+ align:start position:0%
+determine from I equals i z over the
+ 
+
+ align:start position:0%
+determine from I equals i z over the
+size of the Jacobian and remember the
+
+ align:start position:0%
+size of the Jacobian and remember the
+ 
+
+ align:start position:0%
+size of the Jacobian and remember the
+Jacobian is the thing that has all the
+
+ align:start position:0%
+Jacobian is the thing that has all the
+ 
+
+ align:start position:0%
+Jacobian is the thing that has all the
+physics in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we want to work out what the size of
+
+ align:start position:0%
+if we want to work out what the size of
+ 
+
+ align:start position:0%
+if we want to work out what the size of
+the Jacobian is we are measuring I but
+
+ align:start position:0%
+the Jacobian is we are measuring I but
+ 
+
+ align:start position:0%
+the Jacobian is we are measuring I but
+we need to make some asum out what I
+
+ align:start position:0%
+we need to make some asum out what I
+ 
+
+ align:start position:0%
+we need to make some asum out what I
+zero is we can't measure it because we
+
+ align:start position:0%
+zero is we can't measure it because we
+ 
+
+ align:start position:0%
+zero is we can't measure it because we
+do the target normal sheath acceleration
+
+ align:start position:0%
+do the target normal sheath acceleration
+ 
+
+ align:start position:0%
+do the target normal sheath acceleration
+through the plasma we can't put a beam
+
+ align:start position:0%
+through the plasma we can't put a beam
+ 
+
+ align:start position:0%
+through the plasma we can't put a beam
+splitter in and measure what the protons
+
+ align:start position:0%
+splitter in and measure what the protons
+ 
+
+ align:start position:0%
+splitter in and measure what the protons
+look like if we don't have beam
+
+ align:start position:0%
+look like if we don't have beam
+ 
+
+ align:start position:0%
+look like if we don't have beam
+Splitters protons so knowing I zero and
+
+ align:start position:0%
+Splitters protons so knowing I zero and
+ 
+
+ align:start position:0%
+Splitters protons so knowing I zero and
+knowing that it's uniform is very very
+
+ align:start position:0%
+knowing that it's uniform is very very
+ 
+
+ align:start position:0%
+knowing that it's uniform is very very
+difficult and so you could say well what
+
+ align:start position:0%
+difficult and so you could say well what
+ 
+
+ align:start position:0%
+difficult and so you could say well what
+if I have reproducibility what if I do
+
+ align:start position:0%
+if I have reproducibility what if I do
+ 
+
+ align:start position:0%
+if I have reproducibility what if I do
+the tnsa over and over again and I
+
+ align:start position:0%
+the tnsa over and over again and I
+ 
+
+ align:start position:0%
+the tnsa over and over again and I
+measure it without any plasma and I see
+
+ align:start position:0%
+measure it without any plasma and I see
+ 
+
+ align:start position:0%
+measure it without any plasma and I see
+that it's uniform well the trouble is we
+
+ align:start position:0%
+that it's uniform well the trouble is we
+ 
+
+ align:start position:0%
+that it's uniform well the trouble is we
+see that is not uniform right so we have
+
+ align:start position:0%
+see that is not uniform right so we have
+ 
+
+ align:start position:0%
+see that is not uniform right so we have
+poor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reproducibility so a solution to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is that you include a grid in your
+
+ align:start position:0%
+this is that you include a grid in your
+ 
+
+ align:start position:0%
+this is that you include a grid in your
+system you still have your point source
+
+ align:start position:0%
+system you still have your point source
+ 
+
+ align:start position:0%
+system you still have your point source
+and your protons
+
+ align:start position:0%
+and your protons
+ 
+
+ align:start position:0%
+and your protons
+scaming out through your plasma but on
+
+ align:start position:0%
+scaming out through your plasma but on
+ 
+
+ align:start position:0%
+scaming out through your plasma but on
+the other side of the
+
+ align:start position:0%
+the other side of the
+ 
+
+ align:start position:0%
+the other side of the
+plasma you put a grid like this so in
+
+ align:start position:0%
+plasma you put a grid like this so in
+ 
+
+ align:start position:0%
+plasma you put a grid like this so in
+the absence of the plasma this splits up
+
+ align:start position:0%
+the absence of the plasma this splits up
+ 
+
+ align:start position:0%
+the absence of the plasma this splits up
+your beam into a series of beam looks so
+
+ align:start position:0%
+your beam into a series of beam looks so
+ 
+
+ align:start position:0%
+your beam into a series of beam looks so
+for example we have regions where the
+
+ align:start position:0%
+for example we have regions where the
+ 
+
+ align:start position:0%
+for example we have regions where the
+protons can pass through the grid I'm
+
+ align:start position:0%
+protons can pass through the grid I'm
+ 
+
+ align:start position:0%
+protons can pass through the grid I'm
+just going to draw nine of them here and
+
+ align:start position:0%
+just going to draw nine of them here and
+ 
+
+ align:start position:0%
+just going to draw nine of them here and
+we effectively have little points on a
+
+ align:start position:0%
+we effectively have little points on a
+ 
+
+ align:start position:0%
+we effectively have little points on a
+grid like this this is the case without
+
+ align:start position:0%
+grid like this this is the case without
+ 
+
+ align:start position:0%
+grid like this this is the case without
+plasma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when the plasma is present these
+
+ align:start position:0%
+now when the plasma is present these
+ 
+
+ align:start position:0%
+now when the plasma is present these
+protons are going to be deflected in
+
+ align:start position:0%
+protons are going to be deflected in
+ 
+
+ align:start position:0%
+protons are going to be deflected in
+different ways and we'll see these
+
+ align:start position:0%
+different ways and we'll see these
+ 
+
+ align:start position:0%
+different ways and we'll see these
+points move so for example this point
+
+ align:start position:0%
+points move so for example this point
+ 
+
+ align:start position:0%
+points move so for example this point
+might move to here this point might move
+
+ align:start position:0%
+might move to here this point might move
+ 
+
+ align:start position:0%
+might move to here this point might move
+to here this point might move to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and actually
+
+ align:start position:0%
+here and actually
+ 
+
+ align:start position:0%
+here and actually
+we can now directly
+
+ align:start position:0%
+we can now directly
+ 
+
+ align:start position:0%
+we can now directly
+calculate the deflection angle Alpha and
+
+ align:start position:0%
+calculate the deflection angle Alpha and
+ 
+
+ align:start position:0%
+calculate the deflection angle Alpha and
+therefore back out the electric and
+
+ align:start position:0%
+therefore back out the electric and
+ 
+
+ align:start position:0%
+therefore back out the electric and
+magnetic field from this technique so
+
+ align:start position:0%
+magnetic field from this technique so
+ 
+
+ align:start position:0%
+magnetic field from this technique so
+this is very good because we uh can
+
+ align:start position:0%
+this is very good because we uh can
+ 
+
+ align:start position:0%
+this is very good because we uh can
+calculate Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directly but the downside of it is we
+
+ align:start position:0%
+directly but the downside of it is we
+ 
+
+ align:start position:0%
+directly but the downside of it is we
+have very low spatial resolution
+
+ align:start position:0%
+have very low spatial resolution
+ 
+
+ align:start position:0%
+have very low spatial resolution
+now because you've gone from having a
+
+ align:start position:0%
+now because you've gone from having a
+ 
+
+ align:start position:0%
+now because you've gone from having a
+Contin image into a discret image
+
+ align:start position:0%
+Contin image into a discret image
+ 
+
+ align:start position:0%
+Contin image into a discret image
+instead but this technique is still very
+
+ align:start position:0%
+instead but this technique is still very
+ 
+
+ align:start position:0%
+instead but this technique is still very
+powerful because it does give you a
+
+ align:start position:0%
+powerful because it does give you a
+ 
+
+ align:start position:0%
+powerful because it does give you a
+direct handle on Alpha without needing
+
+ align:start position:0%
+direct handle on Alpha without needing
+ 
+
+ align:start position:0%
+direct handle on Alpha without needing
+to know what i z was
+
+ align:start position:0%
+to know what i z was
+ 
+
+ align:start position:0%
+to know what i z was
+okay the second
+
+ align:start position:0%
+okay the second
+ 
+
+ align:start position:0%
+okay the second
+issue I want to talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about is if we had have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform magnetic
+
+ align:start position:0%
+uniform magnetic
+ 
+
+ align:start position:0%
+uniform magnetic
+field as well as some varing magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields we have a uniform magnetic field
+
+ align:start position:0%
+fields we have a uniform magnetic field
+ 
+
+ align:start position:0%
+fields we have a uniform magnetic field
+all of the particles are going to be
+
+ align:start position:0%
+all of the particles are going to be
+ 
+
+ align:start position:0%
+all of the particles are going to be
+swept in the same direction as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's actually extremely hard to
+
+ align:start position:0%
+well it's actually extremely hard to
+ 
+
+ align:start position:0%
+well it's actually extremely hard to
+align these detectors and know exactly
+
+ align:start position:0%
+align these detectors and know exactly
+ 
+
+ align:start position:0%
+align these detectors and know exactly
+where the center is because we're
+
+ align:start position:0%
+where the center is because we're
+ 
+
+ align:start position:0%
+where the center is because we're
+talking about like submillimeter
+
+ align:start position:0%
+talking about like submillimeter
+ 
+
+ align:start position:0%
+talking about like submillimeter
+Precision so if you see this
+
+ align:start position:0%
+Precision so if you see this
+ 
+
+ align:start position:0%
+Precision so if you see this
+grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+initially you see a grid like that that
+
+ align:start position:0%
+initially you see a grid like that that
+ 
+
+ align:start position:0%
+initially you see a grid like that that
+could be a grid that's been formed
+
+ align:start position:0%
+could be a grid that's been formed
+ 
+
+ align:start position:0%
+could be a grid that's been formed
+without any background magnetic field or
+
+ align:start position:0%
+without any background magnetic field or
+ 
+
+ align:start position:0%
+without any background magnetic field or
+it could be a grid that's been displaced
+
+ align:start position:0%
+it could be a grid that's been displaced
+ 
+
+ align:start position:0%
+it could be a grid that's been displaced
+some distance by background magnetic
+
+ align:start position:0%
+some distance by background magnetic
+ 
+
+ align:start position:0%
+some distance by background magnetic
+field you're not going to be able to
+
+ align:start position:0%
+field you're not going to be able to
+ 
+
+ align:start position:0%
+field you're not going to be able to
+tell the difference between those two so
+
+ align:start position:0%
+tell the difference between those two so
+ 
+
+ align:start position:0%
+tell the difference between those two so
+you cannot measure this background
+
+ align:start position:0%
+you cannot measure this background
+ 
+
+ align:start position:0%
+you cannot measure this background
+magnetic field and in many experiments
+
+ align:start position:0%
+magnetic field and in many experiments
+ 
+
+ align:start position:0%
+magnetic field and in many experiments
+where this is externally applied with
+
+ align:start position:0%
+where this is externally applied with
+ 
+
+ align:start position:0%
+where this is externally applied with
+some magnetic
+
+ align:start position:0%
+some magnetic
+ 
+
+ align:start position:0%
+some magnetic
+coils they really want to be able to
+
+ align:start position:0%
+coils they really want to be able to
+ 
+
+ align:start position:0%
+coils they really want to be able to
+measure that background magnetic field
+
+ align:start position:0%
+measure that background magnetic field
+ 
+
+ align:start position:0%
+measure that background magnetic field
+externally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applied so a very neat
+
+ align:start position:0%
+applied so a very neat
+ 
+
+ align:start position:0%
+applied so a very neat
+technique that's come up recently is to
+
+ align:start position:0%
+technique that's come up recently is to
+ 
+
+ align:start position:0%
+technique that's come up recently is to
+use a second detector which is sensitive
+
+ align:start position:0%
+use a second detector which is sensitive
+ 
+
+ align:start position:0%
+use a second detector which is sensitive
+to the x-rays here so the idea once
+
+ align:start position:0%
+to the x-rays here so the idea once
+ 
+
+ align:start position:0%
+to the x-rays here so the idea once
+again is that we have our source of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protons but alongside the protons we're
+
+ align:start position:0%
+protons but alongside the protons we're
+ 
+
+ align:start position:0%
+protons but alongside the protons we're
+also going to have a source of x-rays
+
+ align:start position:0%
+also going to have a source of x-rays
+ 
+
+ align:start position:0%
+also going to have a source of x-rays
+because this thing is
+
+ align:start position:0%
+because this thing is
+ 
+
+ align:start position:0%
+because this thing is
+hot and in this case I drew the mesh
+
+ align:start position:0%
+hot and in this case I drew the mesh
+ 
+
+ align:start position:0%
+hot and in this case I drew the mesh
+afterwards some of you may have realized
+
+ align:start position:0%
+afterwards some of you may have realized
+ 
+
+ align:start position:0%
+afterwards some of you may have realized
+I think the mesh needs to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before now we have our mesh
+
+ align:start position:0%
+before now we have our mesh
+ 
+
+ align:start position:0%
+before now we have our mesh
+again here and we have our
+
+ align:start position:0%
+again here and we have our
+ 
+
+ align:start position:0%
+again here and we have our
+plasma and the neat thing is we have our
+
+ align:start position:0%
+plasma and the neat thing is we have our
+ 
+
+ align:start position:0%
+plasma and the neat thing is we have our
+for example our RCF which is sensitive
+
+ align:start position:0%
+for example our RCF which is sensitive
+ 
+
+ align:start position:0%
+for example our RCF which is sensitive
+to the protons and we have some image
+
+ align:start position:0%
+to the protons and we have some image
+ 
+
+ align:start position:0%
+to the protons and we have some image
+plate which is sensitive to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x-rays then Although our protons will be
+
+ align:start position:0%
+x-rays then Although our protons will be
+ 
+
+ align:start position:0%
+x-rays then Although our protons will be
+swept up by magnetic fields and do all
+
+ align:start position:0%
+swept up by magnetic fields and do all
+ 
+
+ align:start position:0%
+swept up by magnetic fields and do all
+sorts of strange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things the electron the x-rays are just
+
+ align:start position:0%
+things the electron the x-rays are just
+ 
+
+ align:start position:0%
+things the electron the x-rays are just
+going to go in straight lines which are
+
+ align:start position:0%
+going to go in straight lines which are
+ 
+
+ align:start position:0%
+going to go in straight lines which are
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+unaffected by uh any magnetic fields
+
+ align:start position:0%
+unaffected by uh any magnetic fields
+ 
+
+ align:start position:0%
+unaffected by uh any magnetic fields
+here so we're going to use high energy
+
+ align:start position:0%
+here so we're going to use high energy
+ 
+
+ align:start position:0%
+here so we're going to use high energy
+x-rays here such that the refractive
+
+ align:start position:0%
+x-rays here such that the refractive
+ 
+
+ align:start position:0%
+x-rays here such that the refractive
+index at like 10 kilo electron volts is
+
+ align:start position:0%
+index at like 10 kilo electron volts is
+ 
+
+ align:start position:0%
+index at like 10 kilo electron volts is
+roughly one and so we don't see any
+
+ align:start position:0%
+roughly one and so we don't see any
+ 
+
+ align:start position:0%
+roughly one and so we don't see any
+refraction of the X-rays and so that
+
+ align:start position:0%
+refraction of the X-rays and so that
+ 
+
+ align:start position:0%
+refraction of the X-rays and so that
+means what we end up with
+
+ align:start position:0%
+means what we end up with
+ 
+
+ align:start position:0%
+means what we end up with
+is we'll have a grid the X-ray
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points in the absence of any background
+
+ align:start position:0%
+points in the absence of any background
+ 
+
+ align:start position:0%
+points in the absence of any background
+magnetic field and in the absence of any
+
+ align:start position:0%
+magnetic field and in the absence of any
+ 
+
+ align:start position:0%
+magnetic field and in the absence of any
+plasma we should see all of the protons
+
+ align:start position:0%
+plasma we should see all of the protons
+ 
+
+ align:start position:0%
+plasma we should see all of the protons
+end up in the same place as the x-rays
+
+ align:start position:0%
+end up in the same place as the x-rays
+ 
+
+ align:start position:0%
+end up in the same place as the x-rays
+if there is some uniform magnetic field
+
+ align:start position:0%
+if there is some uniform magnetic field
+ 
+
+ align:start position:0%
+if there is some uniform magnetic field
+that will shift all the
+
+ align:start position:0%
+that will shift all the
+ 
+
+ align:start position:0%
+that will shift all the
+protons like this this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform and then if there's a uniform
+
+ align:start position:0%
+uniform and then if there's a uniform
+ 
+
+ align:start position:0%
+uniform and then if there's a uniform
+magnetic field plus a a of magnetic
+
+ align:start position:0%
+magnetic field plus a a of magnetic
+ 
+
+ align:start position:0%
+magnetic field plus a a of magnetic
+field it will further shift them on top
+
+ align:start position:0%
+field it will further shift them on top
+ 
+
+ align:start position:0%
+field it will further shift them on top
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so the X-ray grid acts as a really nice
+
+ align:start position:0%
+so the X-ray grid acts as a really nice
+ 
+
+ align:start position:0%
+so the X-ray grid acts as a really nice
+fiducial uh it allows us to directly
+
+ align:start position:0%
+fiducial uh it allows us to directly
+ 
+
+ align:start position:0%
+fiducial uh it allows us to directly
+measure the deflections without having
+
+ align:start position:0%
+measure the deflections without having
+ 
+
+ align:start position:0%
+measure the deflections without having
+to worry about the uniform magnetic
+
+ align:start position:0%
+to worry about the uniform magnetic
+ 
+
+ align:start position:0%
+to worry about the uniform magnetic
+field screwing things up so this is very
+
+ align:start position:0%
+field screwing things up so this is very
+ 
+
+ align:start position:0%
+field screwing things up so this is very
+nice bit of work uh by Johnson and
+
+ align:start position:0%
+nice bit of work uh by Johnson and
+ 
+
+ align:start position:0%
+nice bit of work uh by Johnson and
+others and this is in review of
+
+ align:start position:0%
+others and this is in review of
+ 
+
+ align:start position:0%
+others and this is in review of
+scientific instruments published last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year
\ No newline at end of file
diff --git a/GrrEdi84cV4.txt b/GrrEdi84cV4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..127b19b55d7e6950dcfe3b259fbdc60b18c2d019
--- /dev/null
+++ b/GrrEdi84cV4.txt
@@ -0,0 +1,451 @@
+align:start position:0%
+ 
+as I mentioned I'm diabetic and one
+
+ align:start position:0%
+as I mentioned I'm diabetic and one
+ 
+
+ align:start position:0%
+as I mentioned I'm diabetic and one
+things that I noticed in my dad before
+
+ align:start position:0%
+things that I noticed in my dad before
+ 
+
+ align:start position:0%
+things that I noticed in my dad before
+he knew he was diabetic he had come home
+
+ align:start position:0%
+he knew he was diabetic he had come home
+ 
+
+ align:start position:0%
+he knew he was diabetic he had come home
+from the train at night and my sister
+
+ align:start position:0%
+from the train at night and my sister
+ 
+
+ align:start position:0%
+from the train at night and my sister
+and I would rub his legs because they
+
+ align:start position:0%
+and I would rub his legs because they
+ 
+
+ align:start position:0%
+and I would rub his legs because they
+hurt this is one of the problems with
+
+ align:start position:0%
+hurt this is one of the problems with
+ 
+
+ align:start position:0%
+hurt this is one of the problems with
+diabetics his feet hurt and I remember
+
+ align:start position:0%
+diabetics his feet hurt and I remember
+ 
+
+ align:start position:0%
+diabetics his feet hurt and I remember
+my sister Nancy saying once gee daddy
+
+ align:start position:0%
+my sister Nancy saying once gee daddy
+ 
+
+ align:start position:0%
+my sister Nancy saying once gee daddy
+smells like mommy's nail polish remover
+
+ align:start position:0%
+smells like mommy's nail polish remover
+ 
+
+ align:start position:0%
+smells like mommy's nail polish remover
+which was acetone okay and acetone is
+
+ align:start position:0%
+which was acetone okay and acetone is
+ 
+
+ align:start position:0%
+which was acetone okay and acetone is
+one of the three ketone bodies the other
+
+ align:start position:0%
+one of the three ketone bodies the other
+ 
+
+ align:start position:0%
+one of the three ketone bodies the other
+two being beta-hydroxybutyrate acid and
+
+ align:start position:0%
+two being beta-hydroxybutyrate acid and
+ 
+
+ align:start position:0%
+two being beta-hydroxybutyrate acid and
+acetoacetate so what happens in diabetes
+
+ align:start position:0%
+acetoacetate so what happens in diabetes
+ 
+
+ align:start position:0%
+acetoacetate so what happens in diabetes
+is you know the diabetic doesn't have
+
+ align:start position:0%
+is you know the diabetic doesn't have
+ 
+
+ align:start position:0%
+is you know the diabetic doesn't have
+ample carbohydrate reserves within their
+
+ align:start position:0%
+ample carbohydrate reserves within their
+ 
+
+ align:start position:0%
+ample carbohydrate reserves within their
+cells as glycogen so they're you doing a
+
+ align:start position:0%
+cells as glycogen so they're you doing a
+ 
+
+ align:start position:0%
+cells as glycogen so they're you doing a
+lot of fatty acid oxidation rather than
+
+ align:start position:0%
+lot of fatty acid oxidation rather than
+ 
+
+ align:start position:0%
+lot of fatty acid oxidation rather than
+carbohydrate metabolism if you take a
+
+ align:start position:0%
+carbohydrate metabolism if you take a
+ 
+
+ align:start position:0%
+carbohydrate metabolism if you take a
+fatty acid and you break it down to ask
+
+ align:start position:0%
+fatty acid and you break it down to ask
+ 
+
+ align:start position:0%
+fatty acid and you break it down to ask
+the Toa
+
+ align:start position:0%
+the Toa
+ 
+
+ align:start position:0%
+the Toa
+the last steps called beta kita thiolase
+
+ align:start position:0%
+the last steps called beta kita thiolase
+ 
+
+ align:start position:0%
+the last steps called beta kita thiolase
+backs up then your two carbons of acetic
+
+ align:start position:0%
+backs up then your two carbons of acetic
+ 
+
+ align:start position:0%
+backs up then your two carbons of acetic
+away will be four carbons of
+
+ align:start position:0%
+away will be four carbons of
+ 
+
+ align:start position:0%
+away will be four carbons of
+acetoacetate and then that acetoacetate
+
+ align:start position:0%
+acetoacetate and then that acetoacetate
+ 
+
+ align:start position:0%
+acetoacetate and then that acetoacetate
+a third acetic we can add to it to form
+
+ align:start position:0%
+a third acetic we can add to it to form
+ 
+
+ align:start position:0%
+a third acetic we can add to it to form
+what's called hydroxymethyl glute a real
+
+ align:start position:0%
+what's called hydroxymethyl glute a real
+ 
+
+ align:start position:0%
+what's called hydroxymethyl glute a real
+coenzyme a okay hmg-coa and then
+
+ align:start position:0%
+coenzyme a okay hmg-coa and then
+ 
+
+ align:start position:0%
+coenzyme a okay hmg-coa and then
+rearrangements can happen they give rise
+
+ align:start position:0%
+rearrangements can happen they give rise
+ 
+
+ align:start position:0%
+rearrangements can happen they give rise
+altum Utley to the to the three ketone
+
+ align:start position:0%
+altum Utley to the to the three ketone
+ 
+
+ align:start position:0%
+altum Utley to the to the three ketone
+bodies acetoacetate beta hydroxy
+
+ align:start position:0%
+bodies acetoacetate beta hydroxy
+ 
+
+ align:start position:0%
+bodies acetoacetate beta hydroxy
+butyrate and acetone so in situations
+
+ align:start position:0%
+butyrate and acetone so in situations
+ 
+
+ align:start position:0%
+butyrate and acetone so in situations
+where of starvation and diabetes is
+
+ align:start position:0%
+where of starvation and diabetes is
+ 
+
+ align:start position:0%
+where of starvation and diabetes is
+basically my cells we're in a technical
+
+ align:start position:0%
+basically my cells we're in a technical
+ 
+
+ align:start position:0%
+basically my cells we're in a technical
+state of starvation in a case of
+
+ align:start position:0%
+state of starvation in a case of
+ 
+
+ align:start position:0%
+state of starvation in a case of
+starvation what happens is you you're
+
+ align:start position:0%
+starvation what happens is you you're
+ 
+
+ align:start position:0%
+starvation what happens is you you're
+you get this backup of the lipid
+
+ align:start position:0%
+you get this backup of the lipid
+ 
+
+ align:start position:0%
+you get this backup of the lipid
+breakdown or catabolism pathway and then
+
+ align:start position:0%
+breakdown or catabolism pathway and then
+ 
+
+ align:start position:0%
+breakdown or catabolism pathway and then
+these ketone bodies flush out into your
+
+ align:start position:0%
+these ketone bodies flush out into your
+ 
+
+ align:start position:0%
+these ketone bodies flush out into your
+blood in starvation situations the
+
+ align:start position:0%
+blood in starvation situations the
+ 
+
+ align:start position:0%
+blood in starvation situations the
+ketone bodies will act as fuels for your
+
+ align:start position:0%
+ketone bodies will act as fuels for your
+ 
+
+ align:start position:0%
+ketone bodies will act as fuels for your
+your your brain and other organs it's a
+
+ align:start position:0%
+your your brain and other organs it's a
+ 
+
+ align:start position:0%
+your your brain and other organs it's a
+it's a difficult transition but ketone
+
+ align:start position:0%
+it's a difficult transition but ketone
+ 
+
+ align:start position:0%
+it's a difficult transition but ketone
+bodies are are in the case of diabetics
+
+ align:start position:0%
+bodies are are in the case of diabetics
+ 
+
+ align:start position:0%
+bodies are are in the case of diabetics
+they're produced to access to such a
+
+ align:start position:0%
+they're produced to access to such a
+ 
+
+ align:start position:0%
+they're produced to access to such a
+stand
+
+ align:start position:0%
+stand
+ 
+
+ align:start position:0%
+stand
+that they're they're actually quite
+
+ align:start position:0%
+that they're they're actually quite
+ 
+
+ align:start position:0%
+that they're they're actually quite
+harmful to you the reason a person
+
+ align:start position:0%
+harmful to you the reason a person
+ 
+
+ align:start position:0%
+harmful to you the reason a person
+smells of acetone is the intermediate
+
+ align:start position:0%
+smells of acetone is the intermediate
+ 
+
+ align:start position:0%
+smells of acetone is the intermediate
+ketone body the acetoacetate basically D
+
+ align:start position:0%
+ketone body the acetoacetate basically D
+ 
+
+ align:start position:0%
+ketone body the acetoacetate basically D
+carboxylates it's a beta keto acid and
+
+ align:start position:0%
+carboxylates it's a beta keto acid and
+ 
+
+ align:start position:0%
+carboxylates it's a beta keto acid and
+so it's a spontaneous decomposition to
+
+ align:start position:0%
+so it's a spontaneous decomposition to
+ 
+
+ align:start position:0%
+so it's a spontaneous decomposition to
+form acetone acetone is not to my
+
+ align:start position:0%
+form acetone acetone is not to my
+ 
+
+ align:start position:0%
+form acetone acetone is not to my
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+biochemically useful as a kind of an
+
+ align:start position:0%
+biochemically useful as a kind of an
+ 
+
+ align:start position:0%
+biochemically useful as a kind of an
+energy source but it's a sentinel or
+
+ align:start position:0%
+energy source but it's a sentinel or
+ 
+
+ align:start position:0%
+energy source but it's a sentinel or
+it's something that is smelled so that
+
+ align:start position:0%
+it's something that is smelled so that
+ 
+
+ align:start position:0%
+it's something that is smelled so that
+it can be diagnostic of the disease
\ No newline at end of file
diff --git a/GtuMlWMajtw.txt b/GtuMlWMajtw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bbabb8f7ae645a693827a219db481f8d24c0cd95
--- /dev/null
+++ b/GtuMlWMajtw.txt
@@ -0,0 +1,2283 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while working in the laboratory you will
+
+ align:start position:0%
+while working in the laboratory you will
+ 
+
+ align:start position:0%
+while working in the laboratory you will
+often be required to separate liquid
+
+ align:start position:0%
+often be required to separate liquid
+ 
+
+ align:start position:0%
+often be required to separate liquid
+mixtures or to purify liquid from
+
+ align:start position:0%
+mixtures or to purify liquid from
+ 
+
+ align:start position:0%
+mixtures or to purify liquid from
+nonvolatile substances this separation
+
+ align:start position:0%
+nonvolatile substances this separation
+ 
+
+ align:start position:0%
+nonvolatile substances this separation
+or purification can be done by utilizing
+
+ align:start position:0%
+or purification can be done by utilizing
+ 
+
+ align:start position:0%
+or purification can be done by utilizing
+the liquid's boiling point through a
+
+ align:start position:0%
+the liquid's boiling point through a
+ 
+
+ align:start position:0%
+the liquid's boiling point through a
+technique called
+
+ align:start position:0%
+technique called
+ 
+
+ align:start position:0%
+technique called
+distillation distillation Works through
+
+ align:start position:0%
+distillation distillation Works through
+ 
+
+ align:start position:0%
+distillation distillation Works through
+the processes of vapor ation and
+
+ align:start position:0%
+the processes of vapor ation and
+ 
+
+ align:start position:0%
+the processes of vapor ation and
+condensation vaporization is a
+
+ align:start position:0%
+condensation vaporization is a
+ 
+
+ align:start position:0%
+condensation vaporization is a
+transformation of a liquid to a gas and
+
+ align:start position:0%
+transformation of a liquid to a gas and
+ 
+
+ align:start position:0%
+transformation of a liquid to a gas and
+condensation is the conversion of a gous
+
+ align:start position:0%
+condensation is the conversion of a gous
+ 
+
+ align:start position:0%
+condensation is the conversion of a gous
+species into a
+
+ align:start position:0%
+species into a
+ 
+
+ align:start position:0%
+species into a
+liquid to perform a distillation a
+
+ align:start position:0%
+liquid to perform a distillation a
+ 
+
+ align:start position:0%
+liquid to perform a distillation a
+mixture of two missible liquids is
+
+ align:start position:0%
+mixture of two missible liquids is
+ 
+
+ align:start position:0%
+mixture of two missible liquids is
+heated until the liquid with the higher
+
+ align:start position:0%
+heated until the liquid with the higher
+ 
+
+ align:start position:0%
+heated until the liquid with the higher
+vapor pressure reaches its boiling point
+
+ align:start position:0%
+vapor pressure reaches its boiling point
+ 
+
+ align:start position:0%
+vapor pressure reaches its boiling point
+this Vapor travels up the inside of the
+
+ align:start position:0%
+this Vapor travels up the inside of the
+ 
+
+ align:start position:0%
+this Vapor travels up the inside of the
+flask through a distilling head and into
+
+ align:start position:0%
+flask through a distilling head and into
+ 
+
+ align:start position:0%
+flask through a distilling head and into
+a condenser the cold water jacket on the
+
+ align:start position:0%
+a condenser the cold water jacket on the
+ 
+
+ align:start position:0%
+a condenser the cold water jacket on the
+condenser transforms The Vapor back into
+
+ align:start position:0%
+condenser transforms The Vapor back into
+ 
+
+ align:start position:0%
+condenser transforms The Vapor back into
+liquid which then travels into the
+
+ align:start position:0%
+liquid which then travels into the
+ 
+
+ align:start position:0%
+liquid which then travels into the
+receiving flask in this manner
+
+ align:start position:0%
+receiving flask in this manner
+ 
+
+ align:start position:0%
+receiving flask in this manner
+distillation effectively separates lower
+
+ align:start position:0%
+distillation effectively separates lower
+ 
+
+ align:start position:0%
+distillation effectively separates lower
+boiling point compounds from higher
+
+ align:start position:0%
+boiling point compounds from higher
+ 
+
+ align:start position:0%
+boiling point compounds from higher
+boiling point
+
+ align:start position:0%
+boiling point
+ 
+
+ align:start position:0%
+boiling point
+compounds three types of distillations
+
+ align:start position:0%
+compounds three types of distillations
+ 
+
+ align:start position:0%
+compounds three types of distillations
+are commonly used in the laboratory
+
+ align:start position:0%
+are commonly used in the laboratory
+ 
+
+ align:start position:0%
+are commonly used in the laboratory
+depending on your liquid solution you
+
+ align:start position:0%
+depending on your liquid solution you
+ 
+
+ align:start position:0%
+depending on your liquid solution you
+will have to decide which type of
+
+ align:start position:0%
+will have to decide which type of
+ 
+
+ align:start position:0%
+will have to decide which type of
+distillation will be the most
+
+ align:start position:0%
+distillation will be the most
+ 
+
+ align:start position:0%
+distillation will be the most
+effective the first type of distillation
+
+ align:start position:0%
+effective the first type of distillation
+ 
+
+ align:start position:0%
+effective the first type of distillation
+is a simple distillation this technique
+
+ align:start position:0%
+is a simple distillation this technique
+ 
+
+ align:start position:0%
+is a simple distillation this technique
+is used when separating missible liquids
+
+ align:start position:0%
+is used when separating missible liquids
+ 
+
+ align:start position:0%
+is used when separating missible liquids
+that boil below 150° C at one atmosphere
+
+ align:start position:0%
+that boil below 150° C at one atmosphere
+ 
+
+ align:start position:0%
+that boil below 150° C at one atmosphere
+from either nonvolatile impurities or
+
+ align:start position:0%
+from either nonvolatile impurities or
+ 
+
+ align:start position:0%
+from either nonvolatile impurities or
+from a second liquid that boils at least
+
+ align:start position:0%
+from a second liquid that boils at least
+ 
+
+ align:start position:0%
+from a second liquid that boils at least
+25° C higher than the first the second
+
+ align:start position:0%
+25° C higher than the first the second
+ 
+
+ align:start position:0%
+25° C higher than the first the second
+type of distillation is the fractional
+
+ align:start position:0%
+type of distillation is the fractional
+ 
+
+ align:start position:0%
+type of distillation is the fractional
+distillation this technique should be
+
+ align:start position:0%
+distillation this technique should be
+ 
+
+ align:start position:0%
+distillation this technique should be
+used to separate liquid mixtures that
+
+ align:start position:0%
+used to separate liquid mixtures that
+ 
+
+ align:start position:0%
+used to separate liquid mixtures that
+have less than a 25° C difference in
+
+ align:start position:0%
+have less than a 25° C difference in
+ 
+
+ align:start position:0%
+have less than a 25° C difference in
+Boiling Point the third type of
+
+ align:start position:0%
+Boiling Point the third type of
+ 
+
+ align:start position:0%
+Boiling Point the third type of
+distillation is a vacuum distillation
+
+ align:start position:0%
+distillation is a vacuum distillation
+ 
+
+ align:start position:0%
+distillation is a vacuum distillation
+this technique should be used to
+
+ align:start position:0%
+this technique should be used to
+ 
+
+ align:start position:0%
+this technique should be used to
+separate missible liquids that boil
+
+ align:start position:0%
+separate missible liquids that boil
+ 
+
+ align:start position:0%
+separate missible liquids that boil
+above 150° cus at one
+
+ align:start position:0%
+above 150° cus at one
+ 
+
+ align:start position:0%
+above 150° cus at one
+atmosphere in this video distillation
+
+ align:start position:0%
+atmosphere in this video distillation
+ 
+
+ align:start position:0%
+atmosphere in this video distillation
+part one we will discuss simple and
+
+ align:start position:0%
+part one we will discuss simple and
+ 
+
+ align:start position:0%
+part one we will discuss simple and
+fractional
+
+ align:start position:0%
+fractional
+ 
+
+ align:start position:0%
+fractional
+distillations in distillation part two
+
+ align:start position:0%
+distillations in distillation part two
+ 
+
+ align:start position:0%
+distillations in distillation part two
+we will discuss vacuum
+
+ align:start position:0%
+we will discuss vacuum
+ 
+
+ align:start position:0%
+we will discuss vacuum
+distillations to carry out a simple
+
+ align:start position:0%
+distillations to carry out a simple
+ 
+
+ align:start position:0%
+distillations to carry out a simple
+distillation you will need a cork ring a
+
+ align:start position:0%
+distillation you will need a cork ring a
+ 
+
+ align:start position:0%
+distillation you will need a cork ring a
+round bottom distilling flask two ring
+
+ align:start position:0%
+round bottom distilling flask two ring
+ 
+
+ align:start position:0%
+round bottom distilling flask two ring
+stands a stir bar and magnetic stirer a
+
+ align:start position:0%
+stands a stir bar and magnetic stirer a
+ 
+
+ align:start position:0%
+stands a stir bar and magnetic stirer a
+distilling head a condenser a vacuum
+
+ align:start position:0%
+distilling head a condenser a vacuum
+ 
+
+ align:start position:0%
+distilling head a condenser a vacuum
+adapter grease three yellow kek clamps a
+
+ align:start position:0%
+adapter grease three yellow kek clamps a
+ 
+
+ align:start position:0%
+adapter grease three yellow kek clamps a
+thermometer and thermometer adapter
+
+ align:start position:0%
+thermometer and thermometer adapter
+ 
+
+ align:start position:0%
+thermometer and thermometer adapter
+three round bottom receiving flasks two
+
+ align:start position:0%
+three round bottom receiving flasks two
+ 
+
+ align:start position:0%
+three round bottom receiving flasks two
+extension clamps and fasteners a heating
+
+ align:start position:0%
+extension clamps and fasteners a heating
+ 
+
+ align:start position:0%
+extension clamps and fasteners a heating
+mantle an iron ring a variable voltage
+
+ align:start position:0%
+mantle an iron ring a variable voltage
+ 
+
+ align:start position:0%
+mantle an iron ring a variable voltage
+Transformer or variac three hose Clips
+
+ align:start position:0%
+Transformer or variac three hose Clips
+ 
+
+ align:start position:0%
+Transformer or variac three hose Clips
+two pieces of rubber tubing and a
+
+ align:start position:0%
+two pieces of rubber tubing and a
+ 
+
+ align:start position:0%
+two pieces of rubber tubing and a
+container for an ice water bath the
+
+ align:start position:0%
+container for an ice water bath the
+ 
+
+ align:start position:0%
+container for an ice water bath the
+first step in performing a distillation
+
+ align:start position:0%
+first step in performing a distillation
+ 
+
+ align:start position:0%
+first step in performing a distillation
+is choosing the proper size distillation
+
+ align:start position:0%
+is choosing the proper size distillation
+ 
+
+ align:start position:0%
+is choosing the proper size distillation
+flask the distilling flask should not be
+
+ align:start position:0%
+flask the distilling flask should not be
+ 
+
+ align:start position:0%
+flask the distilling flask should not be
+more than half full or less than 1/3
+
+ align:start position:0%
+more than half full or less than 1/3
+ 
+
+ align:start position:0%
+more than half full or less than 1/3
+thir full when the distillation begins
+
+ align:start position:0%
+thir full when the distillation begins
+ 
+
+ align:start position:0%
+thir full when the distillation begins
+if the flask is overfilled the solution
+
+ align:start position:0%
+if the flask is overfilled the solution
+ 
+
+ align:start position:0%
+if the flask is overfilled the solution
+will likely overheat or bump into the
+
+ align:start position:0%
+will likely overheat or bump into the
+ 
+
+ align:start position:0%
+will likely overheat or bump into the
+condenser bumping will cause impurities
+
+ align:start position:0%
+condenser bumping will cause impurities
+ 
+
+ align:start position:0%
+condenser bumping will cause impurities
+to be collected in the receiving flask
+
+ align:start position:0%
+to be collected in the receiving flask
+ 
+
+ align:start position:0%
+to be collected in the receiving flask
+rendering the distillation worthless if
+
+ align:start position:0%
+rendering the distillation worthless if
+ 
+
+ align:start position:0%
+rendering the distillation worthless if
+the flask is less than a third full then
+
+ align:start position:0%
+the flask is less than a third full then
+ 
+
+ align:start position:0%
+the flask is less than a third full then
+you'll have a greater chance of losing
+
+ align:start position:0%
+you'll have a greater chance of losing
+ 
+
+ align:start position:0%
+you'll have a greater chance of losing
+some product because a substantial
+
+ align:start position:0%
+some product because a substantial
+ 
+
+ align:start position:0%
+some product because a substantial
+amount of the material will be needed
+
+ align:start position:0%
+amount of the material will be needed
+ 
+
+ align:start position:0%
+amount of the material will be needed
+just to fill the flask and Distilling
+
+ align:start position:0%
+just to fill the flask and Distilling
+ 
+
+ align:start position:0%
+just to fill the flask and Distilling
+head with Vapor while we're on the topic
+
+ align:start position:0%
+head with Vapor while we're on the topic
+ 
+
+ align:start position:0%
+head with Vapor while we're on the topic
+of size we'd like to speak briefly about
+
+ align:start position:0%
+of size we'd like to speak briefly about
+ 
+
+ align:start position:0%
+of size we'd like to speak briefly about
+heating mantel
+
+ align:start position:0%
+heating mantel
+ 
+
+ align:start position:0%
+heating mantel
+if you do not have an appropriately
+
+ align:start position:0%
+if you do not have an appropriately
+ 
+
+ align:start position:0%
+if you do not have an appropriately
+sized heating mantle then use one that
+
+ align:start position:0%
+sized heating mantle then use one that
+ 
+
+ align:start position:0%
+sized heating mantle then use one that
+is too big never use a heating mantle
+
+ align:start position:0%
+is too big never use a heating mantle
+ 
+
+ align:start position:0%
+is too big never use a heating mantle
+that is too small because heat is not
+
+ align:start position:0%
+that is too small because heat is not
+ 
+
+ align:start position:0%
+that is too small because heat is not
+easily transferred between the mantle
+
+ align:start position:0%
+easily transferred between the mantle
+ 
+
+ align:start position:0%
+easily transferred between the mantle
+and flask due to poor contact which
+
+ align:start position:0%
+and flask due to poor contact which
+ 
+
+ align:start position:0%
+and flask due to poor contact which
+causes the mantle to burn out if the
+
+ align:start position:0%
+causes the mantle to burn out if the
+ 
+
+ align:start position:0%
+causes the mantle to burn out if the
+mantle is too big for the flask then add
+
+ align:start position:0%
+mantle is too big for the flask then add
+ 
+
+ align:start position:0%
+mantle is too big for the flask then add
+sand to fill in the empty space after
+
+ align:start position:0%
+sand to fill in the empty space after
+ 
+
+ align:start position:0%
+sand to fill in the empty space after
+you have chosen a distilling flask
+
+ align:start position:0%
+you have chosen a distilling flask
+ 
+
+ align:start position:0%
+you have chosen a distilling flask
+transfer your sample into it and add an
+
+ align:start position:0%
+transfer your sample into it and add an
+ 
+
+ align:start position:0%
+transfer your sample into it and add an
+appropriately sized stir bar bar if you
+
+ align:start position:0%
+appropriately sized stir bar bar if you
+ 
+
+ align:start position:0%
+appropriately sized stir bar bar if you
+will not have access to a magnetic
+
+ align:start position:0%
+will not have access to a magnetic
+ 
+
+ align:start position:0%
+will not have access to a magnetic
+stirer then add a few boiling stones to
+
+ align:start position:0%
+stirer then add a few boiling stones to
+ 
+
+ align:start position:0%
+stirer then add a few boiling stones to
+the distilling flask instead the next
+
+ align:start position:0%
+the distilling flask instead the next
+ 
+
+ align:start position:0%
+the distilling flask instead the next
+step is the Assembly of the distillation
+
+ align:start position:0%
+step is the Assembly of the distillation
+ 
+
+ align:start position:0%
+step is the Assembly of the distillation
+apparatus which is likely one of the
+
+ align:start position:0%
+apparatus which is likely one of the
+ 
+
+ align:start position:0%
+apparatus which is likely one of the
+most difficult glassware subl you'll
+
+ align:start position:0%
+most difficult glassware subl you'll
+ 
+
+ align:start position:0%
+most difficult glassware subl you'll
+ever encounter the neck of the
+
+ align:start position:0%
+ever encounter the neck of the
+ 
+
+ align:start position:0%
+ever encounter the neck of the
+distilling flask is clamped onto one of
+
+ align:start position:0%
+distilling flask is clamped onto one of
+ 
+
+ align:start position:0%
+distilling flask is clamped onto one of
+the Ring stands with an extension clamp
+
+ align:start position:0%
+the Ring stands with an extension clamp
+ 
+
+ align:start position:0%
+the Ring stands with an extension clamp
+and Fastener a heating mantle which is
+
+ align:start position:0%
+and Fastener a heating mantle which is
+ 
+
+ align:start position:0%
+and Fastener a heating mantle which is
+plugged into the variac rests on an iron
+
+ align:start position:0%
+plugged into the variac rests on an iron
+ 
+
+ align:start position:0%
+plugged into the variac rests on an iron
+ring below the distilling flask if
+
+ align:start position:0%
+ring below the distilling flask if
+ 
+
+ align:start position:0%
+ring below the distilling flask if
+you're using a stir bar then place a
+
+ align:start position:0%
+you're using a stir bar then place a
+ 
+
+ align:start position:0%
+you're using a stir bar then place a
+magnetic stirer underneath the heating
+
+ align:start position:0%
+magnetic stirer underneath the heating
+ 
+
+ align:start position:0%
+magnetic stirer underneath the heating
+mantle leave enough room below below the
+
+ align:start position:0%
+mantle leave enough room below below the
+ 
+
+ align:start position:0%
+mantle leave enough room below below the
+iron ring so that the heating mantle can
+
+ align:start position:0%
+iron ring so that the heating mantle can
+ 
+
+ align:start position:0%
+iron ring so that the heating mantle can
+be dropped away from the distilling
+
+ align:start position:0%
+be dropped away from the distilling
+ 
+
+ align:start position:0%
+be dropped away from the distilling
+flask if necessary the distilling head
+
+ align:start position:0%
+flask if necessary the distilling head
+ 
+
+ align:start position:0%
+flask if necessary the distilling head
+is attached to the top of the distilling
+
+ align:start position:0%
+is attached to the top of the distilling
+ 
+
+ align:start position:0%
+is attached to the top of the distilling
+flask and a condenser is attached to the
+
+ align:start position:0%
+flask and a condenser is attached to the
+ 
+
+ align:start position:0%
+flask and a condenser is attached to the
+sidearm of the distilling head the
+
+ align:start position:0%
+sidearm of the distilling head the
+ 
+
+ align:start position:0%
+sidearm of the distilling head the
+vacuum adapter is attached to the other
+
+ align:start position:0%
+vacuum adapter is attached to the other
+ 
+
+ align:start position:0%
+vacuum adapter is attached to the other
+end of the condenser and this joint is
+
+ align:start position:0%
+end of the condenser and this joint is
+ 
+
+ align:start position:0%
+end of the condenser and this joint is
+attached to the second ringstand with an
+
+ align:start position:0%
+attached to the second ringstand with an
+ 
+
+ align:start position:0%
+attached to the second ringstand with an
+extension clamp and Fastener a small
+
+ align:start position:0%
+extension clamp and Fastener a small
+ 
+
+ align:start position:0%
+extension clamp and Fastener a small
+receiving flask is clamped to the vacuum
+
+ align:start position:0%
+receiving flask is clamped to the vacuum
+ 
+
+ align:start position:0%
+receiving flask is clamped to the vacuum
+adapter with a yellow cat clamp and an
+
+ align:start position:0%
+adapter with a yellow cat clamp and an
+ 
+
+ align:start position:0%
+adapter with a yellow cat clamp and an
+ice waterer bath is placed underneath
+
+ align:start position:0%
+ice waterer bath is placed underneath
+ 
+
+ align:start position:0%
+ice waterer bath is placed underneath
+the thermometer and thermometer adapter
+
+ align:start position:0%
+the thermometer and thermometer adapter
+ 
+
+ align:start position:0%
+the thermometer and thermometer adapter
+are attached to the top of the
+
+ align:start position:0%
+are attached to the top of the
+ 
+
+ align:start position:0%
+are attached to the top of the
+distilling head and clamped in place
+
+ align:start position:0%
+distilling head and clamped in place
+ 
+
+ align:start position:0%
+distilling head and clamped in place
+with a green C clamp the top of the
+
+ align:start position:0%
+with a green C clamp the top of the
+ 
+
+ align:start position:0%
+with a green C clamp the top of the
+thermometer bulb should be aligned with
+
+ align:start position:0%
+thermometer bulb should be aligned with
+ 
+
+ align:start position:0%
+thermometer bulb should be aligned with
+the bottom of the sidearm on the
+
+ align:start position:0%
+the bottom of the sidearm on the
+ 
+
+ align:start position:0%
+the bottom of the sidearm on the
+distillation head yellow cat clamps are
+
+ align:start position:0%
+distillation head yellow cat clamps are
+ 
+
+ align:start position:0%
+distillation head yellow cat clamps are
+used to secure both ends of the
+
+ align:start position:0%
+used to secure both ends of the
+ 
+
+ align:start position:0%
+used to secure both ends of the
+condenser rubber tubing is attached to
+
+ align:start position:0%
+condenser rubber tubing is attached to
+ 
+
+ align:start position:0%
+condenser rubber tubing is attached to
+the water inlet and Outlet of the
+
+ align:start position:0%
+the water inlet and Outlet of the
+ 
+
+ align:start position:0%
+the water inlet and Outlet of the
+condenser and secured with hose Clips
+
+ align:start position:0%
+condenser and secured with hose Clips
+ 
+
+ align:start position:0%
+condenser and secured with hose Clips
+finally place two clean dry receiving
+
+ align:start position:0%
+finally place two clean dry receiving
+ 
+
+ align:start position:0%
+finally place two clean dry receiving
+flasks near the distillation apparatus
+
+ align:start position:0%
+flasks near the distillation apparatus
+ 
+
+ align:start position:0%
+flasks near the distillation apparatus
+before continuing confirm that all of
+
+ align:start position:0%
+before continuing confirm that all of
+ 
+
+ align:start position:0%
+before continuing confirm that all of
+the joints have been lightly greased and
+
+ align:start position:0%
+the joints have been lightly greased and
+ 
+
+ align:start position:0%
+the joints have been lightly greased and
+that no cut clamps are used on any joint
+
+ align:start position:0%
+that no cut clamps are used on any joint
+ 
+
+ align:start position:0%
+that no cut clamps are used on any joint
+that will become hot after assembling
+
+ align:start position:0%
+that will become hot after assembling
+ 
+
+ align:start position:0%
+that will become hot after assembling
+the distillation apparatus attach the
+
+ align:start position:0%
+the distillation apparatus attach the
+ 
+
+ align:start position:0%
+the distillation apparatus attach the
+tubing at the bottom of the condenser to
+
+ align:start position:0%
+tubing at the bottom of the condenser to
+ 
+
+ align:start position:0%
+tubing at the bottom of the condenser to
+the Water Source place the end of the
+
+ align:start position:0%
+the Water Source place the end of the
+ 
+
+ align:start position:0%
+the Water Source place the end of the
+tubing at the top of the condenser into
+
+ align:start position:0%
+tubing at the top of the condenser into
+ 
+
+ align:start position:0%
+tubing at the top of the condenser into
+a sink remember water goes in at the
+
+ align:start position:0%
+a sink remember water goes in at the
+ 
+
+ align:start position:0%
+a sink remember water goes in at the
+bottom and out at the top to discourage
+
+ align:start position:0%
+bottom and out at the top to discourage
+ 
+
+ align:start position:0%
+bottom and out at the top to discourage
+the formation of air bubbles double
+
+ align:start position:0%
+the formation of air bubbles double
+ 
+
+ align:start position:0%
+the formation of air bubbles double
+check that all of the joints are secured
+
+ align:start position:0%
+check that all of the joints are secured
+ 
+
+ align:start position:0%
+check that all of the joints are secured
+with hose clips and start the water flow
+
+ align:start position:0%
+with hose clips and start the water flow
+ 
+
+ align:start position:0%
+with hose clips and start the water flow
+the water should flow at the slowest
+
+ align:start position:0%
+the water should flow at the slowest
+ 
+
+ align:start position:0%
+the water should flow at the slowest
+rate that is necessary to keep the
+
+ align:start position:0%
+rate that is necessary to keep the
+ 
+
+ align:start position:0%
+rate that is necessary to keep the
+condenser cold if the Flor rate is too
+
+ align:start position:0%
+condenser cold if the Flor rate is too
+ 
+
+ align:start position:0%
+condenser cold if the Flor rate is too
+fast the chance of the tubing popping
+
+ align:start position:0%
+fast the chance of the tubing popping
+ 
+
+ align:start position:0%
+fast the chance of the tubing popping
+off the condenser and spraying all over
+
+ align:start position:0%
+off the condenser and spraying all over
+ 
+
+ align:start position:0%
+off the condenser and spraying all over
+your workspace greatly increases to
+
+ align:start position:0%
+your workspace greatly increases to
+ 
+
+ align:start position:0%
+your workspace greatly increases to
+perform the simple distillation turn on
+
+ align:start position:0%
+perform the simple distillation turn on
+ 
+
+ align:start position:0%
+perform the simple distillation turn on
+the variac and heat the sample to a
+
+ align:start position:0%
+the variac and heat the sample to a
+ 
+
+ align:start position:0%
+the variac and heat the sample to a
+gentle boil make sure that the vacuum
+
+ align:start position:0%
+gentle boil make sure that the vacuum
+ 
+
+ align:start position:0%
+gentle boil make sure that the vacuum
+adapter remains open to the air never
+
+ align:start position:0%
+adapter remains open to the air never
+ 
+
+ align:start position:0%
+adapter remains open to the air never
+heat to close system or it will explode
+
+ align:start position:0%
+heat to close system or it will explode
+ 
+
+ align:start position:0%
+heat to close system or it will explode
+a ring of condensate will move up the
+
+ align:start position:0%
+a ring of condensate will move up the
+ 
+
+ align:start position:0%
+a ring of condensate will move up the
+flask and into the distilling head when
+
+ align:start position:0%
+flask and into the distilling head when
+ 
+
+ align:start position:0%
+flask and into the distilling head when
+the vapor reaches the height of the
+
+ align:start position:0%
+the vapor reaches the height of the
+ 
+
+ align:start position:0%
+the vapor reaches the height of the
+thermometer bulb the temperature reading
+
+ align:start position:0%
+thermometer bulb the temperature reading
+ 
+
+ align:start position:0%
+thermometer bulb the temperature reading
+will jump dramatically indicating the
+
+ align:start position:0%
+will jump dramatically indicating the
+ 
+
+ align:start position:0%
+will jump dramatically indicating the
+formation of a droplet of liquid on the
+
+ align:start position:0%
+formation of a droplet of liquid on the
+ 
+
+ align:start position:0%
+formation of a droplet of liquid on the
+thermometer bulb if the condensate ring
+
+ align:start position:0%
+thermometer bulb if the condensate ring
+ 
+
+ align:start position:0%
+thermometer bulb if the condensate ring
+completely stops rising at any point
+
+ align:start position:0%
+completely stops rising at any point
+ 
+
+ align:start position:0%
+completely stops rising at any point
+slightly increase the setting on the
+
+ align:start position:0%
+slightly increase the setting on the
+ 
+
+ align:start position:0%
+slightly increase the setting on the
+variac after the vapor reaches the
+
+ align:start position:0%
+variac after the vapor reaches the
+ 
+
+ align:start position:0%
+variac after the vapor reaches the
+condenser it transforms back into liquid
+
+ align:start position:0%
+condenser it transforms back into liquid
+ 
+
+ align:start position:0%
+condenser it transforms back into liquid
+flows down the condenser and into a
+
+ align:start position:0%
+flows down the condenser and into a
+ 
+
+ align:start position:0%
+flows down the condenser and into a
+small receiving flask when approximately
+
+ align:start position:0%
+small receiving flask when approximately
+ 
+
+ align:start position:0%
+small receiving flask when approximately
+10 drops have been collected in the
+
+ align:start position:0%
+10 drops have been collected in the
+ 
+
+ align:start position:0%
+10 drops have been collected in the
+small receiving flask quickly replace it
+
+ align:start position:0%
+small receiving flask quickly replace it
+ 
+
+ align:start position:0%
+small receiving flask quickly replace it
+with the larger one the first couple of
+
+ align:start position:0%
+with the larger one the first couple of
+ 
+
+ align:start position:0%
+with the larger one the first couple of
+drops of a distillation are always
+
+ align:start position:0%
+drops of a distillation are always
+ 
+
+ align:start position:0%
+drops of a distillation are always
+discarded because they may contain some
+
+ align:start position:0%
+discarded because they may contain some
+ 
+
+ align:start position:0%
+discarded because they may contain some
+lower boiling impurities at this point
+
+ align:start position:0%
+lower boiling impurities at this point
+ 
+
+ align:start position:0%
+lower boiling impurities at this point
+the distillate should be dropping into
+
+ align:start position:0%
+the distillate should be dropping into
+ 
+
+ align:start position:0%
+the distillate should be dropping into
+the receiving flask at a rate of 10
+
+ align:start position:0%
+the receiving flask at a rate of 10
+ 
+
+ align:start position:0%
+the receiving flask at a rate of 10
+drops per minute if the rate is faster
+
+ align:start position:0%
+drops per minute if the rate is faster
+ 
+
+ align:start position:0%
+drops per minute if the rate is faster
+then the heat is too high and higher
+
+ align:start position:0%
+then the heat is too high and higher
+ 
+
+ align:start position:0%
+then the heat is too high and higher
+boiling point impurities may have
+
+ align:start position:0%
+boiling point impurities may have
+ 
+
+ align:start position:0%
+boiling point impurities may have
+escaped into the receiving flask if the
+
+ align:start position:0%
+escaped into the receiving flask if the
+ 
+
+ align:start position:0%
+escaped into the receiving flask if the
+rate is too slow then the distillation
+
+ align:start position:0%
+rate is too slow then the distillation
+ 
+
+ align:start position:0%
+rate is too slow then the distillation
+will occur over too long of a time
+
+ align:start position:0%
+will occur over too long of a time
+ 
+
+ align:start position:0%
+will occur over too long of a time
+period after the lower boiling liquid
+
+ align:start position:0%
+period after the lower boiling liquid
+ 
+
+ align:start position:0%
+period after the lower boiling liquid
+has been completely distilled no drop of
+
+ align:start position:0%
+has been completely distilled no drop of
+ 
+
+ align:start position:0%
+has been completely distilled no drop of
+liquid will be on the thermometer bulb
+
+ align:start position:0%
+liquid will be on the thermometer bulb
+ 
+
+ align:start position:0%
+liquid will be on the thermometer bulb
+and the temperature will plunge
+
+ align:start position:0%
+and the temperature will plunge
+ 
+
+ align:start position:0%
+and the temperature will plunge
+dramatically at this point immediately
+
+ align:start position:0%
+dramatically at this point immediately
+ 
+
+ align:start position:0%
+dramatically at this point immediately
+Ely replace the large receiving flask
+
+ align:start position:0%
+Ely replace the large receiving flask
+ 
+
+ align:start position:0%
+Ely replace the large receiving flask
+with a new small receiving flask to
+
+ align:start position:0%
+with a new small receiving flask to
+ 
+
+ align:start position:0%
+with a new small receiving flask to
+collect the last few drops of liquid
+
+ align:start position:0%
+collect the last few drops of liquid
+ 
+
+ align:start position:0%
+collect the last few drops of liquid
+these drops may contain some higher
+
+ align:start position:0%
+these drops may contain some higher
+ 
+
+ align:start position:0%
+these drops may contain some higher
+boiling impurities that should not be
+
+ align:start position:0%
+boiling impurities that should not be
+ 
+
+ align:start position:0%
+boiling impurities that should not be
+collected in the main receiving flask
+
+ align:start position:0%
+collected in the main receiving flask
+ 
+
+ align:start position:0%
+collected in the main receiving flask
+record the temperature range of when the
+
+ align:start position:0%
+record the temperature range of when the
+ 
+
+ align:start position:0%
+record the temperature range of when the
+mixture first started to boil until
+
+ align:start position:0%
+mixture first started to boil until
+ 
+
+ align:start position:0%
+mixture first started to boil until
+right before the dramatic drop in
+
+ align:start position:0%
+right before the dramatic drop in
+ 
+
+ align:start position:0%
+right before the dramatic drop in
+temperature this is the boiling point of
+
+ align:start position:0%
+temperature this is the boiling point of
+ 
+
+ align:start position:0%
+temperature this is the boiling point of
+the distillate if the range is within 2°
+
+ align:start position:0%
+the distillate if the range is within 2°
+ 
+
+ align:start position:0%
+the distillate if the range is within 2°
+C your distillate is fairly pure after
+
+ align:start position:0%
+C your distillate is fairly pure after
+ 
+
+ align:start position:0%
+C your distillate is fairly pure after
+you have collected the final few drops
+
+ align:start position:0%
+you have collected the final few drops
+ 
+
+ align:start position:0%
+you have collected the final few drops
+of liquid turn off the heat Source a
+
+ align:start position:0%
+of liquid turn off the heat Source a
+ 
+
+ align:start position:0%
+of liquid turn off the heat Source a
+simple distillation is performed more
+
+ align:start position:0%
+simple distillation is performed more
+ 
+
+ align:start position:0%
+simple distillation is performed more
+effectively if certain guidelines are
+
+ align:start position:0%
+effectively if certain guidelines are
+ 
+
+ align:start position:0%
+effectively if certain guidelines are
+followed first make sure all the joints
+
+ align:start position:0%
+followed first make sure all the joints
+ 
+
+ align:start position:0%
+followed first make sure all the joints
+on the apparatus are tight and that the
+
+ align:start position:0%
+on the apparatus are tight and that the
+ 
+
+ align:start position:0%
+on the apparatus are tight and that the
+water lines are secured second fill the
+
+ align:start position:0%
+water lines are secured second fill the
+ 
+
+ align:start position:0%
+water lines are secured second fill the
+distilling flask between 1/3 and 1/2
+
+ align:start position:0%
+distilling flask between 1/3 and 1/2
+ 
+
+ align:start position:0%
+distilling flask between 1/3 and 1/2
+full prior to distillation third allow
+
+ align:start position:0%
+full prior to distillation third allow
+ 
+
+ align:start position:0%
+full prior to distillation third allow
+the distillation to proceed at a rate of
+
+ align:start position:0%
+the distillation to proceed at a rate of
+ 
+
+ align:start position:0%
+the distillation to proceed at a rate of
+10 drops per minute fourth use separate
+
+ align:start position:0%
+10 drops per minute fourth use separate
+ 
+
+ align:start position:0%
+10 drops per minute fourth use separate
+receiving flasks for the beginning
+
+ align:start position:0%
+receiving flasks for the beginning
+ 
+
+ align:start position:0%
+receiving flasks for the beginning
+middle and end of the distillation to
+
+ align:start position:0%
+middle and end of the distillation to
+ 
+
+ align:start position:0%
+middle and end of the distillation to
+disallow low and high boiling impurities
+
+ align:start position:0%
+disallow low and high boiling impurities
+ 
+
+ align:start position:0%
+disallow low and high boiling impurities
+into the distillate fifth never let the
+
+ align:start position:0%
+into the distillate fifth never let the
+ 
+
+ align:start position:0%
+into the distillate fifth never let the
+distillation flask run dry a flask that
+
+ align:start position:0%
+distillation flask run dry a flask that
+ 
+
+ align:start position:0%
+distillation flask run dry a flask that
+is allowed to run dry May overheat and
+
+ align:start position:0%
+is allowed to run dry May overheat and
+ 
+
+ align:start position:0%
+is allowed to run dry May overheat and
+break the second type of distillation
+
+ align:start position:0%
+break the second type of distillation
+ 
+
+ align:start position:0%
+break the second type of distillation
+that we will cover is the fractional
+
+ align:start position:0%
+that we will cover is the fractional
+ 
+
+ align:start position:0%
+that we will cover is the fractional
+distillation this technique should be
+
+ align:start position:0%
+distillation this technique should be
+ 
+
+ align:start position:0%
+distillation this technique should be
+used if you need to separate two liquids
+
+ align:start position:0%
+used if you need to separate two liquids
+ 
+
+ align:start position:0%
+used if you need to separate two liquids
+that have a small difference in boiling
+
+ align:start position:0%
+that have a small difference in boiling
+ 
+
+ align:start position:0%
+that have a small difference in boiling
+point less than 25° C a fractional
+
+ align:start position:0%
+point less than 25° C a fractional
+ 
+
+ align:start position:0%
+point less than 25° C a fractional
+distillation is more effective at
+
+ align:start position:0%
+distillation is more effective at
+ 
+
+ align:start position:0%
+distillation is more effective at
+separating liquids with similar boiling
+
+ align:start position:0%
+separating liquids with similar boiling
+ 
+
+ align:start position:0%
+separating liquids with similar boiling
+points because it utilizes a fr
+
+ align:start position:0%
+points because it utilizes a fr
+ 
+
+ align:start position:0%
+points because it utilizes a fr
+fractionating column a fractionating
+
+ align:start position:0%
+fractionating column a fractionating
+ 
+
+ align:start position:0%
+fractionating column a fractionating
+column contains column packing with a
+
+ align:start position:0%
+column contains column packing with a
+ 
+
+ align:start position:0%
+column contains column packing with a
+large surface area and works by
+
+ align:start position:0%
+large surface area and works by
+ 
+
+ align:start position:0%
+large surface area and works by
+promoting a lot of tiny distillations on
+
+ align:start position:0%
+promoting a lot of tiny distillations on
+ 
+
+ align:start position:0%
+promoting a lot of tiny distillations on
+the surface of this packing specifically
+
+ align:start position:0%
+the surface of this packing specifically
+ 
+
+ align:start position:0%
+the surface of this packing specifically
+when the liquid mixture is heated to
+
+ align:start position:0%
+when the liquid mixture is heated to
+ 
+
+ align:start position:0%
+when the liquid mixture is heated to
+Boiling the resulting vapor is richer in
+
+ align:start position:0%
+Boiling the resulting vapor is richer in
+ 
+
+ align:start position:0%
+Boiling the resulting vapor is richer in
+the lower boiling component The Vapor
+
+ align:start position:0%
+the lower boiling component The Vapor
+ 
+
+ align:start position:0%
+the lower boiling component The Vapor
+moves out of the flask and condenses on
+
+ align:start position:0%
+moves out of the flask and condenses on
+ 
+
+ align:start position:0%
+moves out of the flask and condenses on
+the bottom few cenm of the fractionating
+
+ align:start position:0%
+the bottom few cenm of the fractionating
+ 
+
+ align:start position:0%
+the bottom few cenm of the fractionating
+column now the condensed droplet is
+
+ align:start position:0%
+column now the condensed droplet is
+ 
+
+ align:start position:0%
+column now the condensed droplet is
+richer in lower boiling component and
+
+ align:start position:0%
+richer in lower boiling component and
+ 
+
+ align:start position:0%
+richer in lower boiling component and
+the liquid in the distilling flask is
+
+ align:start position:0%
+the liquid in the distilling flask is
+ 
+
+ align:start position:0%
+the liquid in the distilling flask is
+richer in the higher boiling component
+
+ align:start position:0%
+richer in the higher boiling component
+ 
+
+ align:start position:0%
+richer in the higher boiling component
+if that liquid droplet is reheated it
+
+ align:start position:0%
+if that liquid droplet is reheated it
+ 
+
+ align:start position:0%
+if that liquid droplet is reheated it
+will vaporize and condense a little
+
+ align:start position:0%
+will vaporize and condense a little
+ 
+
+ align:start position:0%
+will vaporize and condense a little
+further up the fractionating column this
+
+ align:start position:0%
+further up the fractionating column this
+ 
+
+ align:start position:0%
+further up the fractionating column this
+distillate will have an even higher
+
+ align:start position:0%
+distillate will have an even higher
+ 
+
+ align:start position:0%
+distillate will have an even higher
+percentage of the lower boiling
+
+ align:start position:0%
+percentage of the lower boiling
+ 
+
+ align:start position:0%
+percentage of the lower boiling
+component this process is repeated until
+
+ align:start position:0%
+component this process is repeated until
+ 
+
+ align:start position:0%
+component this process is repeated until
+the vapor reaches the top of the
+
+ align:start position:0%
+the vapor reaches the top of the
+ 
+
+ align:start position:0%
+the vapor reaches the top of the
+fractionating column where theoretically
+
+ align:start position:0%
+fractionating column where theoretically
+ 
+
+ align:start position:0%
+fractionating column where theoretically
+it should be pure in lower boiling
+
+ align:start position:0%
+it should be pure in lower boiling
+ 
+
+ align:start position:0%
+it should be pure in lower boiling
+component to assemble the apparatus for
+
+ align:start position:0%
+component to assemble the apparatus for
+ 
+
+ align:start position:0%
+component to assemble the apparatus for
+a fractional distillation place a
+
+ align:start position:0%
+a fractional distillation place a
+ 
+
+ align:start position:0%
+a fractional distillation place a
+fractionating column between the
+
+ align:start position:0%
+fractionating column between the
+ 
+
+ align:start position:0%
+fractionating column between the
+distillation flask and the distillation
+
+ align:start position:0%
+distillation flask and the distillation
+ 
+
+ align:start position:0%
+distillation flask and the distillation
+head alternatively your lab may have
+
+ align:start position:0%
+head alternatively your lab may have
+ 
+
+ align:start position:0%
+head alternatively your lab may have
+all-in-one distillation glassware that
+
+ align:start position:0%
+all-in-one distillation glassware that
+ 
+
+ align:start position:0%
+all-in-one distillation glassware that
+contains a fractionating column perform
+
+ align:start position:0%
+contains a fractionating column perform
+ 
+
+ align:start position:0%
+contains a fractionating column perform
+the fractional distillation in the same
+
+ align:start position:0%
+the fractional distillation in the same
+ 
+
+ align:start position:0%
+the fractional distillation in the same
+manner as the simple distillation to
+
+ align:start position:0%
+manner as the simple distillation to
+ 
+
+ align:start position:0%
+manner as the simple distillation to
+ensure an effective fractional
+
+ align:start position:0%
+ensure an effective fractional
+ 
+
+ align:start position:0%
+ensure an effective fractional
+distillation heat the distilling flask
+
+ align:start position:0%
+distillation heat the distilling flask
+ 
+
+ align:start position:0%
+distillation heat the distilling flask
+very slowly too much heat causes the
+
+ align:start position:0%
+very slowly too much heat causes the
+ 
+
+ align:start position:0%
+very slowly too much heat causes the
+distillation to occur too rapidly
+
+ align:start position:0%
+distillation to occur too rapidly
+ 
+
+ align:start position:0%
+distillation to occur too rapidly
+disallowing the liquid Vapor equilibria
+
+ align:start position:0%
+disallowing the liquid Vapor equilibria
+ 
+
+ align:start position:0%
+disallowing the liquid Vapor equilibria
+on the surface of the fractionating
+
+ align:start position:0%
+on the surface of the fractionating
+ 
+
+ align:start position:0%
+on the surface of the fractionating
+column if too little heat is used then
+
+ align:start position:0%
+column if too little heat is used then
+ 
+
+ align:start position:0%
+column if too little heat is used then
+the column May lose heat faster than it
+
+ align:start position:0%
+the column May lose heat faster than it
+ 
+
+ align:start position:0%
+the column May lose heat faster than it
+can be warmed up by the vapor preventing
+
+ align:start position:0%
+can be warmed up by the vapor preventing
+ 
+
+ align:start position:0%
+can be warmed up by the vapor preventing
+the vapor from reaching the top of the
+
+ align:start position:0%
+the vapor from reaching the top of the
+ 
+
+ align:start position:0%
+the vapor from reaching the top of the
+column if the column seems to be losing
+
+ align:start position:0%
+column if the column seems to be losing
+ 
+
+ align:start position:0%
+column if the column seems to be losing
+heat faster than it can be warmed up by
+
+ align:start position:0%
+heat faster than it can be warmed up by
+ 
+
+ align:start position:0%
+heat faster than it can be warmed up by
+the vapor you may insulate the column by
+
+ align:start position:0%
+the vapor you may insulate the column by
+ 
+
+ align:start position:0%
+the vapor you may insulate the column by
+wrapping it with glass wool or cotton
+
+ align:start position:0%
+wrapping it with glass wool or cotton
+ 
+
+ align:start position:0%
+wrapping it with glass wool or cotton
+and aluminum foil as a general rule a
+
+ align:start position:0%
+and aluminum foil as a general rule a
+ 
+
+ align:start position:0%
+and aluminum foil as a general rule a
+slow steady distillation where one drop
+
+ align:start position:0%
+slow steady distillation where one drop
+ 
+
+ align:start position:0%
+slow steady distillation where one drop
+is collected every 2 to 3 seconds is
+
+ align:start position:0%
+is collected every 2 to 3 seconds is
+ 
+
+ align:start position:0%
+is collected every 2 to 3 seconds is
+reasonable distillation is an effective
+
+ align:start position:0%
+reasonable distillation is an effective
+ 
+
+ align:start position:0%
+reasonable distillation is an effective
+technique for separating and purifying
+
+ align:start position:0%
+technique for separating and purifying
+ 
+
+ align:start position:0%
+technique for separating and purifying
+liquids when used correctly pure
+
+ align:start position:0%
+liquids when used correctly pure
+ 
+
+ align:start position:0%
+liquids when used correctly pure
+compounds and good yields are readily
+
+ align:start position:0%
+compounds and good yields are readily
+ 
+
+ align:start position:0%
+compounds and good yields are readily
+attained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/GuiIyYbI0HM.txt b/GuiIyYbI0HM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b7da897541d1e6b735ae9470585ea4b7769b787d
--- /dev/null
+++ b/GuiIyYbI0HM.txt
@@ -0,0 +1,539 @@
+align:start position:0%
+ 
+when we did our analytic analysis of the
+
+ align:start position:0%
+when we did our analytic analysis of the
+ 
+
+ align:start position:0%
+when we did our analytic analysis of the
+constraint conditions between the
+
+ align:start position:0%
+constraint conditions between the
+ 
+
+ align:start position:0%
+constraint conditions between the
+accelerations of objects 1 and two we
+
+ align:start position:0%
+accelerations of objects 1 and two we
+ 
+
+ align:start position:0%
+accelerations of objects 1 and two we
+came up with the condition that A1 was
+
+ align:start position:0%
+came up with the condition that A1 was
+ 
+
+ align:start position:0%
+came up with the condition that A1 was
+equal to minus 2 A2 now let's do
+
+ align:start position:0%
+equal to minus 2 A2 now let's do
+ 
+
+ align:start position:0%
+equal to minus 2 A2 now let's do
+something which we call virtual
+
+ align:start position:0%
+something which we call virtual
+ 
+
+ align:start position:0%
+something which we call virtual
+displacement argument suppose that b and
+
+ align:start position:0%
+displacement argument suppose that b and
+ 
+
+ align:start position:0%
+displacement argument suppose that b and
+two move down a certain amount let's
+
+ align:start position:0%
+two move down a certain amount let's
+ 
+
+ align:start position:0%
+two move down a certain amount let's
+imagine and I'm going to draw it in a
+
+ align:start position:0%
+imagine and I'm going to draw it in a
+ 
+
+ align:start position:0%
+imagine and I'm going to draw it in a
+different color two so we have object
+
+ align:start position:0%
+different color two so we have object
+ 
+
+ align:start position:0%
+different color two so we have object
+two and pulley 2 has moved down
+
+ align:start position:0%
+two and pulley 2 has moved down
+ 
+
+ align:start position:0%
+two and pulley 2 has moved down
+now this object has displaced by a
+
+ align:start position:0%
+now this object has displaced by a
+ 
+
+ align:start position:0%
+now this object has displaced by a
+distance Delta Y2 which is also equal to
+
+ align:start position:0%
+distance Delta Y2 which is also equal to
+ 
+
+ align:start position:0%
+distance Delta Y2 which is also equal to
+Delta YB because they're connected now
+
+ align:start position:0%
+Delta YB because they're connected now
+ 
+
+ align:start position:0%
+Delta YB because they're connected now
+what happens when the system does that
+
+ align:start position:0%
+what happens when the system does that
+ 
+
+ align:start position:0%
+what happens when the system does that
+is our rope has to
+
+ align:start position:0%
+is our rope has to
+ 
+
+ align:start position:0%
+is our rope has to
+extend
+
+ align:start position:0%
+extend
+ 
+
+ align:start position:0%
+extend
+downwards around this pulley and come
+
+ align:start position:0%
+downwards around this pulley and come
+ 
+
+ align:start position:0%
+downwards around this pulley and come
+back up and that means that the rope
+
+ align:start position:0%
+back up and that means that the rope
+ 
+
+ align:start position:0%
+back up and that means that the rope
+that object one has been foreshortened
+
+ align:start position:0%
+that object one has been foreshortened
+ 
+
+ align:start position:0%
+that object one has been foreshortened
+by not just Delta y 2 but on both sides
+
+ align:start position:0%
+by not just Delta y 2 but on both sides
+ 
+
+ align:start position:0%
+by not just Delta y 2 but on both sides
+Delta Y2 and Delta Y2 object one has
+
+ align:start position:0%
+Delta Y2 and Delta Y2 object one has
+ 
+
+ align:start position:0%
+Delta Y2 and Delta Y2 object one has
+displaced up by that
+
+ align:start position:0%
+displaced up by that
+ 
+
+ align:start position:0%
+displaced up by that
+amount so we'll
+
+ align:start position:0%
+amount so we'll
+ 
+
+ align:start position:0%
+amount so we'll
+just make this so we can draw it in a
+
+ align:start position:0%
+just make this so we can draw it in a
+ 
+
+ align:start position:0%
+just make this so we can draw it in a
+reasonable way so what we see here is
+
+ align:start position:0%
+reasonable way so what we see here is
+ 
+
+ align:start position:0%
+reasonable way so what we see here is
+that Delta
+
+ align:start position:0%
+that Delta
+ 
+
+ align:start position:0%
+that Delta
+y1 is equal to now notice if two goes
+
+ align:start position:0%
+y1 is equal to now notice if two goes
+ 
+
+ align:start position:0%
+y1 is equal to now notice if two goes
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+y by Delta Y2 then Delta y1 which is
+
+ align:start position:0%
+y by Delta Y2 then Delta y1 which is
+ 
+
+ align:start position:0%
+y by Delta Y2 then Delta y1 which is
+this whole distance is a negative
+
+ align:start position:0%
+this whole distance is a negative
+ 
+
+ align:start position:0%
+this whole distance is a negative
+quantity and it's going upwards and so
+
+ align:start position:0%
+quantity and it's going upwards and so
+ 
+
+ align:start position:0%
+quantity and it's going upwards and so
+we see that that's min-2 Delta
+
+ align:start position:0%
+we see that that's min-2 Delta
+ 
+
+ align:start position:0%
+we see that that's min-2 Delta
+Y2 and if we took two derivatives or
+
+ align:start position:0%
+Y2 and if we took two derivatives or
+ 
+
+ align:start position:0%
+Y2 and if we took two derivatives or
+displacement and then look at the change
+
+ align:start position:0%
+displacement and then look at the change
+ 
+
+ align:start position:0%
+displacement and then look at the change
+in displacement we would see that this
+
+ align:start position:0%
+in displacement we would see that this
+ 
+
+ align:start position:0%
+in displacement we would see that this
+implies that the acceleration of one is
+
+ align:start position:0%
+implies that the acceleration of one is
+ 
+
+ align:start position:0%
+implies that the acceleration of one is
+-2 A2 but let's come back to our two
+
+ align:start position:0%
+-2 A2 but let's come back to our two
+ 
+
+ align:start position:0%
+-2 A2 but let's come back to our two
+conditions for length and see the same
+
+ align:start position:0%
+conditions for length and see the same
+ 
+
+ align:start position:0%
+conditions for length and see the same
+thing here because Delta L2 is
+
+ align:start position:0%
+thing here because Delta L2 is
+ 
+
+ align:start position:0%
+thing here because Delta L2 is
+zero this tells us that Delta Y2 is
+
+ align:start position:0%
+zero this tells us that Delta Y2 is
+ 
+
+ align:start position:0%
+zero this tells us that Delta Y2 is
+equal to Delta YB so we'll write minus
+
+ align:start position:0%
+equal to Delta YB so we'll write minus
+ 
+
+ align:start position:0%
+equal to Delta YB so we'll write minus
+equals z and that was our condition that
+
+ align:start position:0%
+equals z and that was our condition that
+ 
+
+ align:start position:0%
+equals z and that was our condition that
+two the block and two are moving
+
+ align:start position:0%
+two the block and two are moving
+ 
+
+ align:start position:0%
+two the block and two are moving
+together and up here we see that because
+
+ align:start position:0%
+together and up here we see that because
+ 
+
+ align:start position:0%
+together and up here we see that because
+Delta L1 is also
+
+ align:start position:0%
+Delta L1 is also
+ 
+
+ align:start position:0%
+Delta L1 is also
+zero this
+
+ align:start position:0%
+zero this
+ 
+
+ align:start position:0%
+zero this
+implies and now I'll make that
+
+ align:start position:0%
+implies and now I'll make that
+ 
+
+ align:start position:0%
+implies and now I'll make that
+substitution that Delta YB is equal to
+
+ align:start position:0%
+substitution that Delta YB is equal to
+ 
+
+ align:start position:0%
+substitution that Delta YB is equal to
+Delta Y2 that two deltay 2 here and
+
+ align:start position:0%
+Delta Y2 that two deltay 2 here and
+ 
+
+ align:start position:0%
+Delta Y2 that two deltay 2 here and
+here plus Delta y1 has to be zero coming
+
+ align:start position:0%
+here plus Delta y1 has to be zero coming
+ 
+
+ align:start position:0%
+here plus Delta y1 has to be zero coming
+from that piece and so we see that Delta
+
+ align:start position:0%
+from that piece and so we see that Delta
+ 
+
+ align:start position:0%
+from that piece and so we see that Delta
+y1 is minus 2 Delta Y2 which is what our
+
+ align:start position:0%
+y1 is minus 2 Delta Y2 which is what our
+ 
+
+ align:start position:0%
+y1 is minus 2 Delta Y2 which is what our
+virtual displacement argument showed us
+
+ align:start position:0%
+virtual displacement argument showed us
+ 
+
+ align:start position:0%
+virtual displacement argument showed us
+and again if you take two
+
+ align:start position:0%
+and again if you take two
+ 
+
+ align:start position:0%
+and again if you take two
+derivatives here
+
+ align:start position:0%
+derivatives here
+ 
+
+ align:start position:0%
+derivatives here
+we have that recall that in the simplest
+
+ align:start position:0%
+we have that recall that in the simplest
+ 
+
+ align:start position:0%
+we have that recall that in the simplest
+way that the velocity is D y1
+
+ align:start position:0%
+way that the velocity is D y1
+ 
+
+ align:start position:0%
+way that the velocity is D y1
+DT and the
+
+ align:start position:0%
+DT and the
+ 
+
+ align:start position:0%
+DT and the
+acceleration A1 is d^2 y1 DT ^2 then the
+
+ align:start position:0%
+acceleration A1 is d^2 y1 DT ^2 then the
+ 
+
+ align:start position:0%
+acceleration A1 is d^2 y1 DT ^2 then the
+same proportionality is maintained under
+
+ align:start position:0%
+same proportionality is maintained under
+ 
+
+ align:start position:0%
+same proportionality is maintained under
+the two derivatives and that's another
+
+ align:start position:0%
+the two derivatives and that's another
+ 
+
+ align:start position:0%
+the two derivatives and that's another
+way of thinking about how to get the
+
+ align:start position:0%
+way of thinking about how to get the
+ 
+
+ align:start position:0%
+way of thinking about how to get the
+relationship between accelerations but
+
+ align:start position:0%
+relationship between accelerations but
+ 
+
+ align:start position:0%
+relationship between accelerations but
+you have to be extremely careful about
+
+ align:start position:0%
+you have to be extremely careful about
+ 
+
+ align:start position:0%
+you have to be extremely careful about
+that sign because as two goes in the
+
+ align:start position:0%
+that sign because as two goes in the
+ 
+
+ align:start position:0%
+that sign because as two goes in the
+positive direction one will go in the
+
+ align:start position:0%
+positive direction one will go in the
+ 
+
+ align:start position:0%
+positive direction one will go in the
+negative Direction
\ No newline at end of file
diff --git a/H7xmTMQ265s.txt b/H7xmTMQ265s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..11c580d522f7aa88f6773e8218e7201642144856
--- /dev/null
+++ b/H7xmTMQ265s.txt
@@ -0,0 +1,3491 @@
+align:start position:0%
+ 
+if we know the position X of T of an
+
+ align:start position:0%
+if we know the position X of T of an
+ 
+
+ align:start position:0%
+if we know the position X of T of an
+object as a function of time we can use
+
+ align:start position:0%
+object as a function of time we can use
+ 
+
+ align:start position:0%
+object as a function of time we can use
+differentiation to calculate its
+
+ align:start position:0%
+differentiation to calculate its
+ 
+
+ align:start position:0%
+differentiation to calculate its
+velocity and its acceleration at later
+
+ align:start position:0%
+velocity and its acceleration at later
+ 
+
+ align:start position:0%
+velocity and its acceleration at later
+times essentially by taking the
+
+ align:start position:0%
+times essentially by taking the
+ 
+
+ align:start position:0%
+times essentially by taking the
+derivatives of the position we know
+
+ align:start position:0%
+derivatives of the position we know
+ 
+
+ align:start position:0%
+derivatives of the position we know
+everything there is to know about the
+
+ align:start position:0%
+everything there is to know about the
+ 
+
+ align:start position:0%
+everything there is to know about the
+motion sometimes however we'll want to
+
+ align:start position:0%
+motion sometimes however we'll want to
+ 
+
+ align:start position:0%
+motion sometimes however we'll want to
+go in the other direction we'll have the
+
+ align:start position:0%
+go in the other direction we'll have the
+ 
+
+ align:start position:0%
+go in the other direction we'll have the
+acceleration as a function of time and
+
+ align:start position:0%
+acceleration as a function of time and
+ 
+
+ align:start position:0%
+acceleration as a function of time and
+we'll want to find the velocity as a
+
+ align:start position:0%
+we'll want to find the velocity as a
+ 
+
+ align:start position:0%
+we'll want to find the velocity as a
+function of time or the position as a
+
+ align:start position:0%
+function of time or the position as a
+ 
+
+ align:start position:0%
+function of time or the position as a
+function of time we'll use a technique
+
+ align:start position:0%
+function of time we'll use a technique
+ 
+
+ align:start position:0%
+function of time we'll use a technique
+called integration and let's see how
+
+ align:start position:0%
+called integration and let's see how
+ 
+
+ align:start position:0%
+called integration and let's see how
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+works to begin with suppose we have a
+
+ align:start position:0%
+works to begin with suppose we have a
+ 
+
+ align:start position:0%
+works to begin with suppose we have a
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration so our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration a of T is some constant a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not in that case we know that this
+
+ align:start position:0%
+not in that case we know that this
+ 
+
+ align:start position:0%
+not in that case we know that this
+constant acceleration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be written as the change in velocity
+
+ align:start position:0%
+can be written as the change in velocity
+ 
+
+ align:start position:0%
+can be written as the change in velocity
+Delta V over some time interval delta
+
+ align:start position:0%
+Delta V over some time interval delta
+ 
+
+ align:start position:0%
+Delta V over some time interval delta
+T and therefore that the change in
+
+ align:start position:0%
+T and therefore that the change in
+ 
+
+ align:start position:0%
+T and therefore that the change in
+velocity Delta V over some time interval
+
+ align:start position:0%
+velocity Delta V over some time interval
+ 
+
+ align:start position:0%
+velocity Delta V over some time interval
+delta T can just be written as a KN the
+
+ align:start position:0%
+delta T can just be written as a KN the
+ 
+
+ align:start position:0%
+delta T can just be written as a KN the
+acceleration the constant acceleration
+
+ align:start position:0%
+acceleration the constant acceleration
+ 
+
+ align:start position:0%
+acceleration the constant acceleration
+times the elapsed time delta T and we
+
+ align:start position:0%
+times the elapsed time delta T and we
+ 
+
+ align:start position:0%
+times the elapsed time delta T and we
+can see this graphically if I plot
+
+ align:start position:0%
+can see this graphically if I plot
+ 
+
+ align:start position:0%
+can see this graphically if I plot
+acceleration versus time
+
+ align:start position:0%
+acceleration versus time
+ 
+
+ align:start position:0%
+acceleration versus time
+here's my constant
+
+ align:start position:0%
+here's my constant
+ 
+
+ align:start position:0%
+here's my constant
+acceleration a KN let's say this is time
+
+ align:start position:0%
+acceleration a KN let's say this is time
+ 
+
+ align:start position:0%
+acceleration a KN let's say this is time
+Z and here's the time delta T the change
+
+ align:start position:0%
+Z and here's the time delta T the change
+ 
+
+ align:start position:0%
+Z and here's the time delta T the change
+in velocity a KN time delta T is just
+
+ align:start position:0%
+in velocity a KN time delta T is just
+ 
+
+ align:start position:0%
+in velocity a KN time delta T is just
+the area of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+box that box being defined by the time
+
+ align:start position:0%
+box that box being defined by the time
+ 
+
+ align:start position:0%
+box that box being defined by the time
+interval 0 to delta T and it's the area
+
+ align:start position:0%
+interval 0 to delta T and it's the area
+ 
+
+ align:start position:0%
+interval 0 to delta T and it's the area
+under the curve a kn
+
+ align:start position:0%
+under the curve a kn
+ 
+
+ align:start position:0%
+under the curve a kn
+so if we know the velocity at time zero
+
+ align:start position:0%
+so if we know the velocity at time zero
+ 
+
+ align:start position:0%
+so if we know the velocity at time zero
+and we know the Accel the constant
+
+ align:start position:0%
+and we know the Accel the constant
+ 
+
+ align:start position:0%
+and we know the Accel the constant
+acceleration a we can calculate the
+
+ align:start position:0%
+acceleration a we can calculate the
+ 
+
+ align:start position:0%
+acceleration a we can calculate the
+velocity at any later time in this way
+
+ align:start position:0%
+velocity at any later time in this way
+ 
+
+ align:start position:0%
+velocity at any later time in this way
+because the change in velocity from that
+
+ align:start position:0%
+because the change in velocity from that
+ 
+
+ align:start position:0%
+because the change in velocity from that
+initial velocity is given by a KN time
+
+ align:start position:0%
+initial velocity is given by a KN time
+ 
+
+ align:start position:0%
+initial velocity is given by a KN time
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+T now let's consider a slightly more
+
+ align:start position:0%
+T now let's consider a slightly more
+ 
+
+ align:start position:0%
+T now let's consider a slightly more
+complicated example suppose the
+
+ align:start position:0%
+complicated example suppose the
+ 
+
+ align:start position:0%
+complicated example suppose the
+acceleration isn't constant but is
+
+ align:start position:0%
+acceleration isn't constant but is
+ 
+
+ align:start position:0%
+acceleration isn't constant but is
+changing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linearly so for a linearly changing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration I can draw this
+
+ align:start position:0%
+acceleration I can draw this
+ 
+
+ align:start position:0%
+acceleration I can draw this
+graphically as well here's acceleration
+
+ align:start position:0%
+graphically as well here's acceleration
+ 
+
+ align:start position:0%
+graphically as well here's acceleration
+this is uh time equals zero suppose the
+
+ align:start position:0%
+this is uh time equals zero suppose the
+ 
+
+ align:start position:0%
+this is uh time equals zero suppose the
+acceleration is just
+
+ align:start position:0%
+acceleration is just
+ 
+
+ align:start position:0%
+acceleration is just
+increasing linearly and I'll call this
+
+ align:start position:0%
+increasing linearly and I'll call this
+ 
+
+ align:start position:0%
+increasing linearly and I'll call this
+time delta
+
+ align:start position:0%
+time delta
+ 
+
+ align:start position:0%
+time delta
+T this is a of t
+
+ align:start position:0%
+T this is a of t
+ 
+
+ align:start position:0%
+T this is a of t
+note that we can define an average
+
+ align:start position:0%
+note that we can define an average
+ 
+
+ align:start position:0%
+note that we can define an average
+acceleration over the interval from 0 to
+
+ align:start position:0%
+acceleration over the interval from 0 to
+ 
+
+ align:start position:0%
+acceleration over the interval from 0 to
+delta T the average
+
+ align:start position:0%
+delta T the average
+ 
+
+ align:start position:0%
+delta T the average
+acceleration is the change in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity over the elapsed
+
+ align:start position:0%
+velocity over the elapsed
+ 
+
+ align:start position:0%
+velocity over the elapsed
+time that average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration will look something like
+
+ align:start position:0%
+acceleration will look something like
+ 
+
+ align:start position:0%
+acceleration will look something like
+that and so then the change in
+
+ align:start position:0%
+that and so then the change in
+ 
+
+ align:start position:0%
+that and so then the change in
+velocity Delta V is equal to the
+
+ align:start position:0%
+velocity Delta V is equal to the
+ 
+
+ align:start position:0%
+velocity Delta V is equal to the
+average acceleration times the elapsed
+
+ align:start position:0%
+average acceleration times the elapsed
+ 
+
+ align:start position:0%
+average acceleration times the elapsed
+time and this
+
+ align:start position:0%
+time and this
+ 
+
+ align:start position:0%
+time and this
+time notice from the
+
+ align:start position:0%
+time notice from the
+ 
+
+ align:start position:0%
+time notice from the
+diagram this product is actually the
+
+ align:start position:0%
+diagram this product is actually the
+ 
+
+ align:start position:0%
+diagram this product is actually the
+area of this
+
+ align:start position:0%
+area of this
+ 
+
+ align:start position:0%
+area of this
+trapezoid that's basically the area
+
+ align:start position:0%
+trapezoid that's basically the area
+ 
+
+ align:start position:0%
+trapezoid that's basically the area
+under the AF of function going from0 to
+
+ align:start position:0%
+under the AF of function going from0 to
+ 
+
+ align:start position:0%
+under the AF of function going from0 to
+delta T we've calculated it sort of as a
+
+ align:start position:0%
+delta T we've calculated it sort of as a
+ 
+
+ align:start position:0%
+delta T we've calculated it sort of as a
+rectangular area involving the average
+
+ align:start position:0%
+rectangular area involving the average
+ 
+
+ align:start position:0%
+rectangular area involving the average
+acceleration but that's also equal to
+
+ align:start position:0%
+acceleration but that's also equal to
+ 
+
+ align:start position:0%
+acceleration but that's also equal to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+area under the time
+
+ align:start position:0%
+area under the time
+ 
+
+ align:start position:0%
+area under the time
+changing acceleration
+
+ align:start position:0%
+changing acceleration
+ 
+
+ align:start position:0%
+changing acceleration
+function so this is again the
+
+ align:start position:0%
+function so this is again the
+ 
+
+ align:start position:0%
+function so this is again the
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+under a of T over the time interval
+
+ align:start position:0%
+under a of T over the time interval
+ 
+
+ align:start position:0%
+under a of T over the time interval
+delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T now let's consider a more generally
+
+ align:start position:0%
+T now let's consider a more generally
+ 
+
+ align:start position:0%
+T now let's consider a more generally
+changing acceleration as a function of
+
+ align:start position:0%
+changing acceleration as a function of
+ 
+
+ align:start position:0%
+changing acceleration as a function of
+time so let me plug B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so suppose we have just some
+
+ align:start position:0%
+this so suppose we have just some
+ 
+
+ align:start position:0%
+this so suppose we have just some
+general function I'll draw it like this
+
+ align:start position:0%
+general function I'll draw it like this
+ 
+
+ align:start position:0%
+general function I'll draw it like this
+which is our
+
+ align:start position:0%
+which is our
+ 
+
+ align:start position:0%
+which is our
+acceleration as a function of time the
+
+ align:start position:0%
+acceleration as a function of time the
+ 
+
+ align:start position:0%
+acceleration as a function of time the
+change in velocity will still be the
+
+ align:start position:0%
+change in velocity will still be the
+ 
+
+ align:start position:0%
+change in velocity will still be the
+area under the curve AF of T over the
+
+ align:start position:0%
+area under the curve AF of T over the
+ 
+
+ align:start position:0%
+area under the curve AF of T over the
+time interval we're interested in so
+
+ align:start position:0%
+time interval we're interested in so
+ 
+
+ align:start position:0%
+time interval we're interested in so
+let's suppose we want to go from this
+
+ align:start position:0%
+let's suppose we want to go from this
+ 
+
+ align:start position:0%
+let's suppose we want to go from this
+time here I'll call it t sub a and
+
+ align:start position:0%
+time here I'll call it t sub a and
+ 
+
+ align:start position:0%
+time here I'll call it t sub a and
+my ending time will be T
+
+ align:start position:0%
+my ending time will be T
+ 
+
+ align:start position:0%
+my ending time will be T
+subb so we're interested in figuring out
+
+ align:start position:0%
+subb so we're interested in figuring out
+ 
+
+ align:start position:0%
+subb so we're interested in figuring out
+what the area under this curve is over
+
+ align:start position:0%
+what the area under this curve is over
+ 
+
+ align:start position:0%
+what the area under this curve is over
+the interval from T sub a to T subb we
+
+ align:start position:0%
+the interval from T sub a to T subb we
+ 
+
+ align:start position:0%
+the interval from T sub a to T subb we
+can estimate this by breaking up the
+
+ align:start position:0%
+can estimate this by breaking up the
+ 
+
+ align:start position:0%
+can estimate this by breaking up the
+interval into a bunch of little
+
+ align:start position:0%
+interval into a bunch of little
+ 
+
+ align:start position:0%
+interval into a bunch of little
+rectangles suppose I break this up into
+
+ align:start position:0%
+rectangles suppose I break this up into
+ 
+
+ align:start position:0%
+rectangles suppose I break this up into
+n rectangles just under this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve right so this is one two 3 four
+
+ align:start position:0%
+curve right so this is one two 3 four
+ 
+
+ align:start position:0%
+curve right so this is one two 3 four
+Etc up to n and with each one because
+
+ align:start position:0%
+Etc up to n and with each one because
+ 
+
+ align:start position:0%
+Etc up to n and with each one because
+this is a curved graph I can't get the
+
+ align:start position:0%
+this is a curved graph I can't get the
+ 
+
+ align:start position:0%
+this is a curved graph I can't get the
+rectangle to fit
+
+ align:start position:0%
+rectangle to fit
+ 
+
+ align:start position:0%
+rectangle to fit
+exactly so a little bit of it will stick
+
+ align:start position:0%
+exactly so a little bit of it will stick
+ 
+
+ align:start position:0%
+exactly so a little bit of it will stick
+out at the top in each one I'm not going
+
+ align:start position:0%
+out at the top in each one I'm not going
+ 
+
+ align:start position:0%
+out at the top in each one I'm not going
+to go through that for all of these but
+
+ align:start position:0%
+to go through that for all of these but
+ 
+
+ align:start position:0%
+to go through that for all of these but
+you get the idea um I'll fit these
+
+ align:start position:0%
+you get the idea um I'll fit these
+ 
+
+ align:start position:0%
+you get the idea um I'll fit these
+rectangles as well as I can the narrower
+
+ align:start position:0%
+rectangles as well as I can the narrower
+ 
+
+ align:start position:0%
+rectangles as well as I can the narrower
+I make the rectangles the more easily I
+
+ align:start position:0%
+I make the rectangles the more easily I
+ 
+
+ align:start position:0%
+I make the rectangles the more easily I
+can fit them under the curve for each
+
+ align:start position:0%
+can fit them under the curve for each
+ 
+
+ align:start position:0%
+can fit them under the curve for each
+strip for each rectangular strip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say from he over box one from here
+
+ align:start position:0%
+let's say from he over box one from here
+ 
+
+ align:start position:0%
+let's say from he over box one from here
+to here the change in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity is equal to the average
+
+ align:start position:0%
+velocity is equal to the average
+ 
+
+ align:start position:0%
+velocity is equal to the average
+velocity over that time
+
+ align:start position:0%
+velocity over that time
+ 
+
+ align:start position:0%
+velocity over that time
+interval times the width of that
+
+ align:start position:0%
+interval times the width of that
+ 
+
+ align:start position:0%
+interval times the width of that
+rectangle delta T so that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area of the strip essentially what we're
+
+ align:start position:0%
+area of the strip essentially what we're
+ 
+
+ align:start position:0%
+area of the strip essentially what we're
+saying is that if we make the rectangles
+
+ align:start position:0%
+saying is that if we make the rectangles
+ 
+
+ align:start position:0%
+saying is that if we make the rectangles
+narrow enough we can treat the
+
+ align:start position:0%
+narrow enough we can treat the
+ 
+
+ align:start position:0%
+narrow enough we can treat the
+acceleration the curve of the
+
+ align:start position:0%
+acceleration the curve of the
+ 
+
+ align:start position:0%
+acceleration the curve of the
+acceleration as roughly constant over
+
+ align:start position:0%
+acceleration as roughly constant over
+ 
+
+ align:start position:0%
+acceleration as roughly constant over
+that interval okay and we can make n as
+
+ align:start position:0%
+that interval okay and we can make n as
+ 
+
+ align:start position:0%
+that interval okay and we can make n as
+big as we need to to make those
+
+ align:start position:0%
+big as we need to to make those
+ 
+
+ align:start position:0%
+big as we need to to make those
+rectangles very very narrow okay so in
+
+ align:start position:0%
+rectangles very very narrow okay so in
+ 
+
+ align:start position:0%
+rectangles very very narrow okay so in
+that case we can estimate the total
+
+ align:start position:0%
+that case we can estimate the total
+ 
+
+ align:start position:0%
+that case we can estimate the total
+change in velocity from time T sub a to
+
+ align:start position:0%
+change in velocity from time T sub a to
+ 
+
+ align:start position:0%
+change in velocity from time T sub a to
+time T subb by adding up the area of all
+
+ align:start position:0%
+time T subb by adding up the area of all
+ 
+
+ align:start position:0%
+time T subb by adding up the area of all
+of these rectangular strips okay so in
+
+ align:start position:0%
+of these rectangular strips okay so in
+ 
+
+ align:start position:0%
+of these rectangular strips okay so in
+that case we write that the change in
+
+ align:start position:0%
+that case we write that the change in
+ 
+
+ align:start position:0%
+that case we write that the change in
+Vel vity so I'll say V subb minus V sub
+
+ align:start position:0%
+Vel vity so I'll say V subb minus V sub
+ 
+
+ align:start position:0%
+Vel vity so I'll say V subb minus V sub
+a that's the change in velocity going
+
+ align:start position:0%
+a that's the change in velocity going
+ 
+
+ align:start position:0%
+a that's the change in velocity going
+from time a to time
+
+ align:start position:0%
+from time a to time
+ 
+
+ align:start position:0%
+from time a to time
+B is equal to the
+
+ align:start position:0%
+B is equal to the
+ 
+
+ align:start position:0%
+B is equal to the
+sum as J goes from 1 to
+
+ align:start position:0%
+sum as J goes from 1 to
+ 
+
+ align:start position:0%
+sum as J goes from 1 to
+n of the area of each of these strips
+
+ align:start position:0%
+n of the area of each of these strips
+ 
+
+ align:start position:0%
+n of the area of each of these strips
+and so we want the acceleration at the I
+
+ align:start position:0%
+and so we want the acceleration at the I
+ 
+
+ align:start position:0%
+and so we want the acceleration at the I
+rectangle so that's a of T
+
+ align:start position:0%
+rectangle so that's a of T
+ 
+
+ align:start position:0%
+rectangle so that's a of T
+subj times the width of the strip which
+
+ align:start position:0%
+subj times the width of the strip which
+ 
+
+ align:start position:0%
+subj times the width of the strip which
+each strip has the same width we'll just
+
+ align:start position:0%
+each strip has the same width we'll just
+ 
+
+ align:start position:0%
+each strip has the same width we'll just
+call that delta T and that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area of n strips now for a finite I
+
+ align:start position:0%
+area of n strips now for a finite I
+ 
+
+ align:start position:0%
+area of n strips now for a finite I
+really should write this as
+
+ align:start position:0%
+really should write this as
+ 
+
+ align:start position:0%
+really should write this as
+approximately equal to because for a
+
+ align:start position:0%
+approximately equal to because for a
+ 
+
+ align:start position:0%
+approximately equal to because for a
+finite number of rectangular strips this
+
+ align:start position:0%
+finite number of rectangular strips this
+ 
+
+ align:start position:0%
+finite number of rectangular strips this
+is just an approximation because as I
+
+ align:start position:0%
+is just an approximation because as I
+ 
+
+ align:start position:0%
+is just an approximation because as I
+mentioned the rectangles don't exactly
+
+ align:start position:0%
+mentioned the rectangles don't exactly
+ 
+
+ align:start position:0%
+mentioned the rectangles don't exactly
+fit Under The Curve they can't because
+
+ align:start position:0%
+fit Under The Curve they can't because
+ 
+
+ align:start position:0%
+fit Under The Curve they can't because
+the rectangle doesn't have a curved top
+
+ align:start position:0%
+the rectangle doesn't have a curved top
+ 
+
+ align:start position:0%
+the rectangle doesn't have a curved top
+but the function is curved but the
+
+ align:start position:0%
+but the function is curved but the
+ 
+
+ align:start position:0%
+but the function is curved but the
+narrower I make the rectangles or
+
+ align:start position:0%
+narrower I make the rectangles or
+ 
+
+ align:start position:0%
+narrower I make the rectangles or
+equivalently the larger I make
+
+ align:start position:0%
+equivalently the larger I make
+ 
+
+ align:start position:0%
+equivalently the larger I make
+n the better the approximation will be
+
+ align:start position:0%
+n the better the approximation will be
+ 
+
+ align:start position:0%
+n the better the approximation will be
+so what what I want to do is go to the
+
+ align:start position:0%
+so what what I want to do is go to the
+ 
+
+ align:start position:0%
+so what what I want to do is go to the
+limit of an infinite number of
+
+ align:start position:0%
+limit of an infinite number of
+ 
+
+ align:start position:0%
+limit of an infinite number of
+rectangles or equivalently the limit of
+
+ align:start position:0%
+rectangles or equivalently the limit of
+ 
+
+ align:start position:0%
+rectangles or equivalently the limit of
+infinitesimally narrow strips I want
+
+ align:start position:0%
+infinitesimally narrow strips I want
+ 
+
+ align:start position:0%
+infinitesimally narrow strips I want
+delta T to go to zero so to make this
+
+ align:start position:0%
+delta T to go to zero so to make this
+ 
+
+ align:start position:0%
+delta T to go to zero so to make this
+exact what I would write is
+
+ align:start position:0%
+exact what I would write is
+ 
+
+ align:start position:0%
+exact what I would write is
+that the change in velocity from time a
+
+ align:start position:0%
+that the change in velocity from time a
+ 
+
+ align:start position:0%
+that the change in velocity from time a
+to time B is equal to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit of the sum from J = 1 to n of the
+
+ align:start position:0%
+limit of the sum from J = 1 to n of the
+ 
+
+ align:start position:0%
+limit of the sum from J = 1 to n of the
+acceleration at time T subj time delta T
+
+ align:start position:0%
+acceleration at time T subj time delta T
+ 
+
+ align:start position:0%
+acceleration at time T subj time delta T
+and we want to evaluate that limit as
+
+ align:start position:0%
+and we want to evaluate that limit as
+ 
+
+ align:start position:0%
+and we want to evaluate that limit as
+delta T goes to zero or equivalently as
+
+ align:start position:0%
+delta T goes to zero or equivalently as
+ 
+
+ align:start position:0%
+delta T goes to zero or equivalently as
+n the number of rectangles goes to
+
+ align:start position:0%
+n the number of rectangles goes to
+ 
+
+ align:start position:0%
+n the number of rectangles goes to
+Infinity okay now this is a very
+
+ align:start position:0%
+Infinity okay now this is a very
+ 
+
+ align:start position:0%
+Infinity okay now this is a very
+important expression
+
+ align:start position:0%
+important expression
+ 
+
+ align:start position:0%
+important expression
+and we have a special way of writing it
+
+ align:start position:0%
+and we have a special way of writing it
+ 
+
+ align:start position:0%
+and we have a special way of writing it
+we can also write it as an integral so
+
+ align:start position:0%
+we can also write it as an integral so
+ 
+
+ align:start position:0%
+we can also write it as an integral so
+we write it as the integral of the
+
+ align:start position:0%
+we write it as the integral of the
+ 
+
+ align:start position:0%
+we write it as the integral of the
+function a of
+
+ align:start position:0%
+function a of
+ 
+
+ align:start position:0%
+function a of
+T DT evaluated
+
+ align:start position:0%
+T DT evaluated
+ 
+
+ align:start position:0%
+T DT evaluated
+from time equals T sub a to time equals
+
+ align:start position:0%
+from time equals T sub a to time equals
+ 
+
+ align:start position:0%
+from time equals T sub a to time equals
+T subb and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the area
+
+ align:start position:0%
+is the area
+ 
+
+ align:start position:0%
+is the area
+under the AF oft
+
+ align:start position:0%
+under the AF oft
+ 
+
+ align:start position:0%
+under the AF oft
+curve the exact area not the approximate
+
+ align:start position:0%
+curve the exact area not the approximate
+ 
+
+ align:start position:0%
+curve the exact area not the approximate
+area but the exact area under the AF of
+
+ align:start position:0%
+area but the exact area under the AF of
+ 
+
+ align:start position:0%
+area but the exact area under the AF of
+curve over the interval from T of a to T
+
+ align:start position:0%
+curve over the interval from T of a to T
+ 
+
+ align:start position:0%
+curve over the interval from T of a to T
+of B this limiting
+
+ align:start position:0%
+of B this limiting
+ 
+
+ align:start position:0%
+of B this limiting
+sum that we've written this way on the
+
+ align:start position:0%
+sum that we've written this way on the
+ 
+
+ align:start position:0%
+sum that we've written this way on the
+right hand side is called the definite
+
+ align:start position:0%
+right hand side is called the definite
+ 
+
+ align:start position:0%
+right hand side is called the definite
+integral of a of
+
+ align:start position:0%
+integral of a of
+ 
+
+ align:start position:0%
+integral of a of
+T and it's related
+
+ align:start position:0%
+T and it's related
+ 
+
+ align:start position:0%
+T and it's related
+to the process of integration that
+
+ align:start position:0%
+to the process of integration that
+ 
+
+ align:start position:0%
+to the process of integration that
+you've learned about in calculus which
+
+ align:start position:0%
+you've learned about in calculus which
+ 
+
+ align:start position:0%
+you've learned about in calculus which
+is the in inverse of taking the
+
+ align:start position:0%
+is the in inverse of taking the
+ 
+
+ align:start position:0%
+is the in inverse of taking the
+derivative the inverse of
+
+ align:start position:0%
+derivative the inverse of
+ 
+
+ align:start position:0%
+derivative the inverse of
+differentiation I want to take a moment
+
+ align:start position:0%
+differentiation I want to take a moment
+ 
+
+ align:start position:0%
+differentiation I want to take a moment
+to summarize the basic principles of
+
+ align:start position:0%
+to summarize the basic principles of
+ 
+
+ align:start position:0%
+to summarize the basic principles of
+integration from
+
+ align:start position:0%
+integration from
+ 
+
+ align:start position:0%
+integration from
+calculus let's begin by considering a
+
+ align:start position:0%
+calculus let's begin by considering a
+ 
+
+ align:start position:0%
+calculus let's begin by considering a
+function G ofx with some derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so consider a function G ofx and let's
+
+ align:start position:0%
+so consider a function G ofx and let's
+ 
+
+ align:start position:0%
+so consider a function G ofx and let's
+assume it's a well- behaved function by
+
+ align:start position:0%
+assume it's a well- behaved function by
+ 
+
+ align:start position:0%
+assume it's a well- behaved function by
+which I mean that it's continuous and
+
+ align:start position:0%
+which I mean that it's continuous and
+ 
+
+ align:start position:0%
+which I mean that it's continuous and
+differentiable over the interval that
+
+ align:start position:0%
+differentiable over the interval that
+ 
+
+ align:start position:0%
+differentiable over the interval that
+we're interested in so consider gfx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the derivative so
+
+ align:start position:0%
+with the derivative so
+ 
+
+ align:start position:0%
+with the derivative so
+DG DX equal to another function which
+
+ align:start position:0%
+DG DX equal to another function which
+ 
+
+ align:start position:0%
+DG DX equal to another function which
+I'll call F
+
+ align:start position:0%
+I'll call F
+ 
+
+ align:start position:0%
+I'll call F
+ofx now note that if I add a constant to
+
+ align:start position:0%
+ofx now note that if I add a constant to
+ 
+
+ align:start position:0%
+ofx now note that if I add a constant to
+G ofx I'll still get the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative so note that the derivative
+
+ align:start position:0%
+derivative so note that the derivative
+ 
+
+ align:start position:0%
+derivative so note that the derivative
+with respect to X of G of X Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a constant is still equal to the same
+
+ align:start position:0%
+a constant is still equal to the same
+ 
+
+ align:start position:0%
+a constant is still equal to the same
+function f ofx and this is because the
+
+ align:start position:0%
+function f ofx and this is because the
+ 
+
+ align:start position:0%
+function f ofx and this is because the
+derivative of a constant is equal to
+
+ align:start position:0%
+derivative of a constant is equal to
+ 
+
+ align:start position:0%
+derivative of a constant is equal to
+zero now suppose I want to invert this
+
+ align:start position:0%
+zero now suppose I want to invert this
+ 
+
+ align:start position:0%
+zero now suppose I want to invert this
+process then I can write that the
+
+ align:start position:0%
+process then I can write that the
+ 
+
+ align:start position:0%
+process then I can write that the
+anti-derivative of f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx the anti-derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of f ofx which I'll write as the
+
+ align:start position:0%
+of f ofx which I'll write as the
+ 
+
+ align:start position:0%
+of f ofx which I'll write as the
+integral of f
+
+ align:start position:0%
+integral of f
+ 
+
+ align:start position:0%
+integral of f
+ofx
+
+ align:start position:0%
+ofx
+ 
+
+ align:start position:0%
+ofx
+DX is equal
+
+ align:start position:0%
+DX is equal
+ 
+
+ align:start position:0%
+DX is equal
+to g ofx
+
+ align:start position:0%
+to g ofx
+ 
+
+ align:start position:0%
+to g ofx
+plus a constant okay the left hand side
+
+ align:start position:0%
+plus a constant okay the left hand side
+ 
+
+ align:start position:0%
+plus a constant okay the left hand side
+of this we call an indefinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral and so we see that if the
+
+ align:start position:0%
+integral and so we see that if the
+ 
+
+ align:start position:0%
+integral and so we see that if the
+derivative of G ofx is f ofx plus a
+
+ align:start position:0%
+derivative of G ofx is f ofx plus a
+ 
+
+ align:start position:0%
+derivative of G ofx is f ofx plus a
+constant the anti-derivative of f ofx is
+
+ align:start position:0%
+constant the anti-derivative of f ofx is
+ 
+
+ align:start position:0%
+constant the anti-derivative of f ofx is
+G ofx plus a
+
+ align:start position:0%
+G ofx plus a
+ 
+
+ align:start position:0%
+G ofx plus a
+constant and and that can be any
+
+ align:start position:0%
+constant and and that can be any
+ 
+
+ align:start position:0%
+constant and and that can be any
+arbitrary constant now in calculus one
+
+ align:start position:0%
+arbitrary constant now in calculus one
+ 
+
+ align:start position:0%
+arbitrary constant now in calculus one
+learns how to calculate the indefinite
+
+ align:start position:0%
+learns how to calculate the indefinite
+ 
+
+ align:start position:0%
+learns how to calculate the indefinite
+integral of various
+
+ align:start position:0%
+integral of various
+ 
+
+ align:start position:0%
+integral of various
+functions pols trigonometric functions
+
+ align:start position:0%
+functions pols trigonometric functions
+ 
+
+ align:start position:0%
+functions pols trigonometric functions
+logarithmic functions
+
+ align:start position:0%
+logarithmic functions
+ 
+
+ align:start position:0%
+logarithmic functions
+Etc calculus also shows us how to
+
+ align:start position:0%
+Etc calculus also shows us how to
+ 
+
+ align:start position:0%
+Etc calculus also shows us how to
+compute the definite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the definite
+
+ align:start position:0%
+so the definite
+ 
+
+ align:start position:0%
+so the definite
+integral the integral of
+
+ align:start position:0%
+integral the integral of
+ 
+
+ align:start position:0%
+integral the integral of
+FFX DX evaluated from xal A to xal B so
+
+ align:start position:0%
+FFX DX evaluated from xal A to xal B so
+ 
+
+ align:start position:0%
+FFX DX evaluated from xal A to xal B so
+this is the definite integral computed
+
+ align:start position:0%
+this is the definite integral computed
+ 
+
+ align:start position:0%
+this is the definite integral computed
+over some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interval is equal to
+
+ align:start position:0%
+interval is equal to
+ 
+
+ align:start position:0%
+interval is equal to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+anti-derivative at X = B minus the
+
+ align:start position:0%
+anti-derivative at X = B minus the
+ 
+
+ align:start position:0%
+anti-derivative at X = B minus the
+anti-derivative evaluated at xal a and
+
+ align:start position:0%
+anti-derivative evaluated at xal a and
+ 
+
+ align:start position:0%
+anti-derivative evaluated at xal a and
+this turns out to
+
+ align:start position:0%
+this turns out to
+ 
+
+ align:start position:0%
+this turns out to
+be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area under the
+
+ align:start position:0%
+area under the
+ 
+
+ align:start position:0%
+area under the
+curve F
+
+ align:start position:0%
+curve F
+ 
+
+ align:start position:0%
+curve F
+ofx in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interval between xal a and xal b
+
+ align:start position:0%
+interval between xal a and xal b
+ 
+
+ align:start position:0%
+interval between xal a and xal b
+okay now notice that there's no
+
+ align:start position:0%
+okay now notice that there's no
+ 
+
+ align:start position:0%
+okay now notice that there's no
+arbitrary constant in the definite
+
+ align:start position:0%
+arbitrary constant in the definite
+ 
+
+ align:start position:0%
+arbitrary constant in the definite
+integral in the indefinite integral we
+
+ align:start position:0%
+integral in the indefinite integral we
+ 
+
+ align:start position:0%
+integral in the indefinite integral we
+have an arbitrary constant but in the
+
+ align:start position:0%
+have an arbitrary constant but in the
+ 
+
+ align:start position:0%
+have an arbitrary constant but in the
+definite integral that arbitrary
+
+ align:start position:0%
+definite integral that arbitrary
+ 
+
+ align:start position:0%
+definite integral that arbitrary
+constant is determined by setting the
+
+ align:start position:0%
+constant is determined by setting the
+ 
+
+ align:start position:0%
+constant is determined by setting the
+integration limits okay so there's no
+
+ align:start position:0%
+integration limits okay so there's no
+ 
+
+ align:start position:0%
+integration limits okay so there's no
+arbitrary constant we just have this
+
+ align:start position:0%
+arbitrary constant we just have this
+ 
+
+ align:start position:0%
+arbitrary constant we just have this
+difference okay and so just to see this
+
+ align:start position:0%
+difference okay and so just to see this
+ 
+
+ align:start position:0%
+difference okay and so just to see this
+graphically if I
+
+ align:start position:0%
+graphically if I
+ 
+
+ align:start position:0%
+graphically if I
+plot my function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of X and suppose this is xal
+
+ align:start position:0%
+of X and suppose this is xal
+ 
+
+ align:start position:0%
+of X and suppose this is xal
+a and this is xal B this definite
+
+ align:start position:0%
+a and this is xal B this definite
+ 
+
+ align:start position:0%
+a and this is xal B this definite
+integral represents the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area under the curve F ofx in the
+
+ align:start position:0%
+area under the curve F ofx in the
+ 
+
+ align:start position:0%
+area under the curve F ofx in the
+interval from xal A to xals B so
+
+ align:start position:0%
+interval from xal A to xals B so
+ 
+
+ align:start position:0%
+interval from xal A to xals B so
+calculus tells us how to solve this area
+
+ align:start position:0%
+calculus tells us how to solve this area
+ 
+
+ align:start position:0%
+calculus tells us how to solve this area
+problem how to compute a definite
+
+ align:start position:0%
+problem how to compute a definite
+ 
+
+ align:start position:0%
+problem how to compute a definite
+integral from the anti-derivative that
+
+ align:start position:0%
+integral from the anti-derivative that
+ 
+
+ align:start position:0%
+integral from the anti-derivative that
+you get from indefinite
+
+ align:start position:0%
+you get from indefinite
+ 
+
+ align:start position:0%
+you get from indefinite
+integration and so this same technique
+
+ align:start position:0%
+integration and so this same technique
+ 
+
+ align:start position:0%
+integration and so this same technique
+tells us how to determine uh the
+
+ align:start position:0%
+tells us how to determine uh the
+ 
+
+ align:start position:0%
+tells us how to determine uh the
+velocity from the acceleration since we
+
+ align:start position:0%
+velocity from the acceleration since we
+ 
+
+ align:start position:0%
+velocity from the acceleration since we
+saw that that was equivalent to an area
+
+ align:start position:0%
+saw that that was equivalent to an area
+ 
+
+ align:start position:0%
+saw that that was equivalent to an area
+under the curve
+
+ align:start position:0%
+under the curve
+ 
+
+ align:start position:0%
+under the curve
+problem so to come back to the motion of
+
+ align:start position:0%
+problem so to come back to the motion of
+ 
+
+ align:start position:0%
+problem so to come back to the motion of
+objects we've shown that the change in
+
+ align:start position:0%
+objects we've shown that the change in
+ 
+
+ align:start position:0%
+objects we've shown that the change in
+velocity of an object can be written as
+
+ align:start position:0%
+velocity of an object can be written as
+ 
+
+ align:start position:0%
+velocity of an object can be written as
+the definite integral of the
+
+ align:start position:0%
+the definite integral of the
+ 
+
+ align:start position:0%
+the definite integral of the
+acceleration so uh just to write that a
+
+ align:start position:0%
+acceleration so uh just to write that a
+ 
+
+ align:start position:0%
+acceleration so uh just to write that a
+little bit more formally uh first with a
+
+ align:start position:0%
+little bit more formally uh first with a
+ 
+
+ align:start position:0%
+little bit more formally uh first with a
+plot if this is
+
+ align:start position:0%
+plot if this is
+ 
+
+ align:start position:0%
+plot if this is
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+acceleration as a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time we know that the time derivative of
+
+ align:start position:0%
+time we know that the time derivative of
+ 
+
+ align:start position:0%
+time we know that the time derivative of
+the Velocity is equal
+
+ align:start position:0%
+the Velocity is equal
+ 
+
+ align:start position:0%
+the Velocity is equal
+to the acceleration as a function of
+
+ align:start position:0%
+to the acceleration as a function of
+ 
+
+ align:start position:0%
+to the acceleration as a function of
+time I can rewrite that as the
+
+ align:start position:0%
+time I can rewrite that as the
+ 
+
+ align:start position:0%
+time I can rewrite that as the
+differential DV is equal
+
+ align:start position:0%
+differential DV is equal
+ 
+
+ align:start position:0%
+differential DV is equal
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to a of T times the differential d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T and so then I can integrate both sides
+
+ align:start position:0%
+T and so then I can integrate both sides
+ 
+
+ align:start position:0%
+T and so then I can integrate both sides
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+equation by writing the
+
+ align:start position:0%
+equation by writing the
+ 
+
+ align:start position:0%
+equation by writing the
+integral over DV is equal to the
+
+ align:start position:0%
+integral over DV is equal to the
+ 
+
+ align:start position:0%
+integral over DV is equal to the
+integral of the acceleration AF of
+
+ align:start position:0%
+integral of the acceleration AF of
+ 
+
+ align:start position:0%
+integral of the acceleration AF of
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+DT and I can go from time
+
+ align:start position:0%
+DT and I can go from time
+ 
+
+ align:start position:0%
+DT and I can go from time
+equals some initial time T KN
+
+ align:start position:0%
+equals some initial time T KN
+ 
+
+ align:start position:0%
+equals some initial time T KN
+to time equal to some later time T sub
+
+ align:start position:0%
+to time equal to some later time T sub
+ 
+
+ align:start position:0%
+to time equal to some later time T sub
+one on the right hand side to make a
+
+ align:start position:0%
+one on the right hand side to make a
+ 
+
+ align:start position:0%
+one on the right hand side to make a
+definite integral and then on the left
+
+ align:start position:0%
+definite integral and then on the left
+ 
+
+ align:start position:0%
+definite integral and then on the left
+hand side the corresponding limits are
+
+ align:start position:0%
+hand side the corresponding limits are
+ 
+
+ align:start position:0%
+hand side the corresponding limits are
+the velocity at Time Zero I'll call that
+
+ align:start position:0%
+the velocity at Time Zero I'll call that
+ 
+
+ align:start position:0%
+the velocity at Time Zero I'll call that
+V KN and the velocity at time one which
+
+ align:start position:0%
+V KN and the velocity at time one which
+ 
+
+ align:start position:0%
+V KN and the velocity at time one which
+I'll call V1 so just to be clear I'm
+
+ align:start position:0%
+I'll call V1 so just to be clear I'm
+ 
+
+ align:start position:0%
+I'll call V1 so just to be clear I'm
+assuming here that V KN is equal to the
+
+ align:start position:0%
+assuming here that V KN is equal to the
+ 
+
+ align:start position:0%
+assuming here that V KN is equal to the
+velocity at time T KN and V1 is equal to
+
+ align:start position:0%
+velocity at time T KN and V1 is equal to
+ 
+
+ align:start position:0%
+velocity at time T KN and V1 is equal to
+the velocity at time T sub
+
+ align:start position:0%
+the velocity at time T sub
+ 
+
+ align:start position:0%
+the velocity at time T sub
+1 so this is the integral of a constant
+
+ align:start position:0%
+1 so this is the integral of a constant
+ 
+
+ align:start position:0%
+1 so this is the integral of a constant
+over over an interval of V this is an
+
+ align:start position:0%
+over over an interval of V this is an
+ 
+
+ align:start position:0%
+over over an interval of V this is an
+interval of the acceleration over the
+
+ align:start position:0%
+interval of the acceleration over the
+ 
+
+ align:start position:0%
+interval of the acceleration over the
+time uh time interval in T and so the
+
+ align:start position:0%
+time uh time interval in T and so the
+ 
+
+ align:start position:0%
+time uh time interval in T and so the
+left hand side this is
+
+ align:start position:0%
+left hand side this is
+ 
+
+ align:start position:0%
+left hand side this is
+just V1 minus V KN and the right hand
+
+ align:start position:0%
+just V1 minus V KN and the right hand
+ 
+
+ align:start position:0%
+just V1 minus V KN and the right hand
+side without specifying AF of T I can't
+
+ align:start position:0%
+side without specifying AF of T I can't
+ 
+
+ align:start position:0%
+side without specifying AF of T I can't
+actually evaluate this integral I can't
+
+ align:start position:0%
+actually evaluate this integral I can't
+ 
+
+ align:start position:0%
+actually evaluate this integral I can't
+specify what the anti-derivative of AF
+
+ align:start position:0%
+specify what the anti-derivative of AF
+ 
+
+ align:start position:0%
+specify what the anti-derivative of AF
+of T is unless I tell you what the
+
+ align:start position:0%
+of T is unless I tell you what the
+ 
+
+ align:start position:0%
+of T is unless I tell you what the
+function AF of T is so we'll just have
+
+ align:start position:0%
+function AF of T is so we'll just have
+ 
+
+ align:start position:0%
+function AF of T is so we'll just have
+to leave it in terms of an integral and
+
+ align:start position:0%
+to leave it in terms of an integral and
+ 
+
+ align:start position:0%
+to leave it in terms of an integral and
+so that's just the integral of a of T
+
+ align:start position:0%
+so that's just the integral of a of T
+ 
+
+ align:start position:0%
+so that's just the integral of a of T
+DT from tal T to tal T sub1 so again
+
+ align:start position:0%
+DT from tal T to tal T sub1 so again
+ 
+
+ align:start position:0%
+DT from tal T to tal T sub1 so again
+this shows us that the change in the
+
+ align:start position:0%
+this shows us that the change in the
+ 
+
+ align:start position:0%
+this shows us that the change in the
+velocity from time t 0 to a later time
+
+ align:start position:0%
+velocity from time t 0 to a later time
+ 
+
+ align:start position:0%
+velocity from time t 0 to a later time
+T1 is equal to the definite integral of
+
+ align:start position:0%
+T1 is equal to the definite integral of
+ 
+
+ align:start position:0%
+T1 is equal to the definite integral of
+a of T over that
+
+ align:start position:0%
+a of T over that
+ 
+
+ align:start position:0%
+a of T over that
+interval I can rewrite this uh in terms
+
+ align:start position:0%
+interval I can rewrite this uh in terms
+ 
+
+ align:start position:0%
+interval I can rewrite this uh in terms
+of what the velocity at some later time
+
+ align:start position:0%
+of what the velocity at some later time
+ 
+
+ align:start position:0%
+of what the velocity at some later time
+T1 by writing the velocity
+
+ align:start position:0%
+T1 by writing the velocity
+ 
+
+ align:start position:0%
+T1 by writing the velocity
+at T1 is equal
+
+ align:start position:0%
+at T1 is equal
+ 
+
+ align:start position:0%
+at T1 is equal
+to V plus the integral of a of T DT from
+
+ align:start position:0%
+to V plus the integral of a of T DT from
+ 
+
+ align:start position:0%
+to V plus the integral of a of T DT from
+tal T to
+
+ align:start position:0%
+tal T to
+ 
+
+ align:start position:0%
+tal T to
+tal
+
+ align:start position:0%
+tal
+ 
+
+ align:start position:0%
+tal
+T1 note that T1 is just any later Time
+
+ align:start position:0%
+T1 note that T1 is just any later Time
+ 
+
+ align:start position:0%
+T1 note that T1 is just any later Time
+After Time T KN where we have the
+
+ align:start position:0%
+After Time T KN where we have the
+ 
+
+ align:start position:0%
+After Time T KN where we have the
+initial velocity so a more convenient
+
+ align:start position:0%
+initial velocity so a more convenient
+ 
+
+ align:start position:0%
+initial velocity so a more convenient
+way of writing this function might be to
+
+ align:start position:0%
+way of writing this function might be to
+ 
+
+ align:start position:0%
+way of writing this function might be to
+write the velocity as aun function of
+
+ align:start position:0%
+write the velocity as aun function of
+ 
+
+ align:start position:0%
+write the velocity as aun function of
+some later time
+
+ align:start position:0%
+some later time
+ 
+
+ align:start position:0%
+some later time
+T So suppose I were to do that I'll just
+
+ align:start position:0%
+T So suppose I were to do that I'll just
+ 
+
+ align:start position:0%
+T So suppose I were to do that I'll just
+rewrite this equation replacing T1 with
+
+ align:start position:0%
+rewrite this equation replacing T1 with
+ 
+
+ align:start position:0%
+rewrite this equation replacing T1 with
+an arbitrary time
+
+ align:start position:0%
+an arbitrary time
+ 
+
+ align:start position:0%
+an arbitrary time
+T so I have that V of T is equal to V KN
+
+ align:start position:0%
+T so I have that V of T is equal to V KN
+ 
+
+ align:start position:0%
+T so I have that V of T is equal to V KN
+plus the
+
+ align:start position:0%
+plus the
+ 
+
+ align:start position:0%
+plus the
+integral of a of T
+
+ align:start position:0%
+integral of a of T
+ 
+
+ align:start position:0%
+integral of a of T
+DT from T =
+
+ align:start position:0%
+DT from T =
+ 
+
+ align:start position:0%
+DT from T =
+t0 to t = t now there's something funny
+
+ align:start position:0%
+t0 to t = t now there's something funny
+ 
+
+ align:start position:0%
+t0 to t = t now there's something funny
+here because I have t in the integration
+
+ align:start position:0%
+here because I have t in the integration
+ 
+
+ align:start position:0%
+here because I have t in the integration
+variable here but I have t as one of my
+
+ align:start position:0%
+variable here but I have t as one of my
+ 
+
+ align:start position:0%
+variable here but I have t as one of my
+limits here as well okay whereas if I
+
+ align:start position:0%
+limits here as well okay whereas if I
+ 
+
+ align:start position:0%
+limits here as well okay whereas if I
+look at this expression here there's a
+
+ align:start position:0%
+look at this expression here there's a
+ 
+
+ align:start position:0%
+look at this expression here there's a
+difference between the T in the
+
+ align:start position:0%
+difference between the T in the
+ 
+
+ align:start position:0%
+difference between the T in the
+integration variable and the limit T1
+
+ align:start position:0%
+integration variable and the limit T1
+ 
+
+ align:start position:0%
+integration variable and the limit T1
+they actually represent different things
+
+ align:start position:0%
+they actually represent different things
+ 
+
+ align:start position:0%
+they actually represent different things
+so to keep track of that the notation
+
+ align:start position:0%
+so to keep track of that the notation
+ 
+
+ align:start position:0%
+so to keep track of that the notation
+that we generally use in physics is to
+
+ align:start position:0%
+that we generally use in physics is to
+ 
+
+ align:start position:0%
+that we generally use in physics is to
+call this integration variable T Prime
+
+ align:start position:0%
+call this integration variable T Prime
+ 
+
+ align:start position:0%
+call this integration variable T Prime
+and so we write this acceleration of T
+
+ align:start position:0%
+and so we write this acceleration of T
+ 
+
+ align:start position:0%
+and so we write this acceleration of T
+Prime DT Prime with the time T Prime
+
+ align:start position:0%
+Prime DT Prime with the time T Prime
+ 
+
+ align:start position:0%
+Prime DT Prime with the time T Prime
+going from T KN to some later time T now
+
+ align:start position:0%
+going from T KN to some later time T now
+ 
+
+ align:start position:0%
+going from T KN to some later time T now
+one has to be cautious here in some
+
+ align:start position:0%
+one has to be cautious here in some
+ 
+
+ align:start position:0%
+one has to be cautious here in some
+fields that Prime on a variable is used
+
+ align:start position:0%
+fields that Prime on a variable is used
+ 
+
+ align:start position:0%
+fields that Prime on a variable is used
+to denote a derivative differentiation
+
+ align:start position:0%
+to denote a derivative differentiation
+ 
+
+ align:start position:0%
+to denote a derivative differentiation
+that's not what it means here I'm
+
+ align:start position:0%
+that's not what it means here I'm
+ 
+
+ align:start position:0%
+that's not what it means here I'm
+writing T Prime just to distinguish it
+
+ align:start position:0%
+writing T Prime just to distinguish it
+ 
+
+ align:start position:0%
+writing T Prime just to distinguish it
+from the specific later time T that I
+
+ align:start position:0%
+from the specific later time T that I
+ 
+
+ align:start position:0%
+from the specific later time T that I
+want to calculate the velocity at and
+
+ align:start position:0%
+want to calculate the velocity at and
+ 
+
+ align:start position:0%
+want to calculate the velocity at and
+it's worth thinking about what this
+
+ align:start position:0%
+it's worth thinking about what this
+ 
+
+ align:start position:0%
+it's worth thinking about what this
+expression means this equation is
+
+ align:start position:0%
+expression means this equation is
+ 
+
+ align:start position:0%
+expression means this equation is
+identical to this earli equation that we
+
+ align:start position:0%
+identical to this earli equation that we
+ 
+
+ align:start position:0%
+identical to this earli equation that we
+derived except for a change in notation
+
+ align:start position:0%
+derived except for a change in notation
+ 
+
+ align:start position:0%
+derived except for a change in notation
+and so let's think about what that
+
+ align:start position:0%
+and so let's think about what that
+ 
+
+ align:start position:0%
+and so let's think about what that
+notation means T Prime here is the
+
+ align:start position:0%
+notation means T Prime here is the
+ 
+
+ align:start position:0%
+notation means T Prime here is the
+integration variable it's a placeholder
+
+ align:start position:0%
+integration variable it's a placeholder
+ 
+
+ align:start position:0%
+integration variable it's a placeholder
+remember the integral here the definite
+
+ align:start position:0%
+remember the integral here the definite
+ 
+
+ align:start position:0%
+remember the integral here the definite
+integral represents an infinite sum an
+
+ align:start position:0%
+integral represents an infinite sum an
+ 
+
+ align:start position:0%
+integral represents an infinite sum an
+infinite sum of rectangles
+
+ align:start position:0%
+infinite sum of rectangles
+ 
+
+ align:start position:0%
+infinite sum of rectangles
+between a Time T KN and a later time
+
+ align:start position:0%
+between a Time T KN and a later time
+ 
+
+ align:start position:0%
+between a Time T KN and a later time
+T and that variable T Prime actually
+
+ align:start position:0%
+T and that variable T Prime actually
+ 
+
+ align:start position:0%
+T and that variable T Prime actually
+what I should do now is I should call
+
+ align:start position:0%
+what I should do now is I should call
+ 
+
+ align:start position:0%
+what I should do now is I should call
+this T
+
+ align:start position:0%
+this T
+ 
+
+ align:start position:0%
+this T
+Prime this variable T Prime is taking
+
+ align:start position:0%
+Prime this variable T Prime is taking
+ 
+
+ align:start position:0%
+Prime this variable T Prime is taking
+every value from T KN to T So T Prime is
+
+ align:start position:0%
+every value from T KN to T So T Prime is
+ 
+
+ align:start position:0%
+every value from T KN to T So T Prime is
+representing the running time variable
+
+ align:start position:0%
+representing the running time variable
+ 
+
+ align:start position:0%
+representing the running time variable
+for all of our strips that we're adding
+
+ align:start position:0%
+for all of our strips that we're adding
+ 
+
+ align:start position:0%
+for all of our strips that we're adding
+up over this definite integral okay so
+
+ align:start position:0%
+up over this definite integral okay so
+ 
+
+ align:start position:0%
+up over this definite integral okay so
+it's a placeholder variable we sometimes
+
+ align:start position:0%
+it's a placeholder variable we sometimes
+ 
+
+ align:start position:0%
+it's a placeholder variable we sometimes
+call it a dummy variable it's just a
+
+ align:start position:0%
+call it a dummy variable it's just a
+ 
+
+ align:start position:0%
+call it a dummy variable it's just a
+placeholder to represent time whereas T
+
+ align:start position:0%
+placeholder to represent time whereas T
+ 
+
+ align:start position:0%
+placeholder to represent time whereas T
+the T and the limit here without the
+
+ align:start position:0%
+the T and the limit here without the
+ 
+
+ align:start position:0%
+the T and the limit here without the
+prime represents a specific choice of
+
+ align:start position:0%
+prime represents a specific choice of
+ 
+
+ align:start position:0%
+prime represents a specific choice of
+later time some later time T where we
+
+ align:start position:0%
+later time some later time T where we
+ 
+
+ align:start position:0%
+later time some later time T where we
+want to calculate the velocity so we
+
+ align:start position:0%
+want to calculate the velocity so we
+ 
+
+ align:start position:0%
+want to calculate the velocity so we
+know the velocity at some initial time
+
+ align:start position:0%
+know the velocity at some initial time
+ 
+
+ align:start position:0%
+know the velocity at some initial time
+T we' like to know the velocity at some
+
+ align:start position:0%
+T we' like to know the velocity at some
+ 
+
+ align:start position:0%
+T we' like to know the velocity at some
+specific later time T and to compute
+
+ align:start position:0%
+specific later time T and to compute
+ 
+
+ align:start position:0%
+specific later time T and to compute
+that we have to integrate over all times
+
+ align:start position:0%
+that we have to integrate over all times
+ 
+
+ align:start position:0%
+that we have to integrate over all times
+running from T KN to T and that running
+
+ align:start position:0%
+running from T KN to T and that running
+ 
+
+ align:start position:0%
+running from T KN to T and that running
+integration variable we represent as T
+
+ align:start position:0%
+integration variable we represent as T
+ 
+
+ align:start position:0%
+integration variable we represent as T
+Prime just to distinguish it from the
+
+ align:start position:0%
+Prime just to distinguish it from the
+ 
+
+ align:start position:0%
+Prime just to distinguish it from the
+specific time T that we are trying to
+
+ align:start position:0%
+specific time T that we are trying to
+ 
+
+ align:start position:0%
+specific time T that we are trying to
+compute the velocity for so now in just
+
+ align:start position:0%
+compute the velocity for so now in just
+ 
+
+ align:start position:0%
+compute the velocity for so now in just
+the same way that we've obtained the
+
+ align:start position:0%
+the same way that we've obtained the
+ 
+
+ align:start position:0%
+the same way that we've obtained the
+velocity by integrating the acceleration
+
+ align:start position:0%
+velocity by integrating the acceleration
+ 
+
+ align:start position:0%
+velocity by integrating the acceleration
+we can integrate again we can integrate
+
+ align:start position:0%
+we can integrate again we can integrate
+ 
+
+ align:start position:0%
+we can integrate again we can integrate
+the velocity to calculate the position
+
+ align:start position:0%
+the velocity to calculate the position
+ 
+
+ align:start position:0%
+the velocity to calculate the position
+so given V of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T we can show that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position at time T is equal to the
+
+ align:start position:0%
+position at time T is equal to the
+ 
+
+ align:start position:0%
+position at time T is equal to the
+position at time
+
+ align:start position:0%
+position at time
+ 
+
+ align:start position:0%
+position at time
+t plus the integral of the
+
+ align:start position:0%
+t plus the integral of the
+ 
+
+ align:start position:0%
+t plus the integral of the
+velocity as a function of time I'll
+
+ align:start position:0%
+velocity as a function of time I'll
+ 
+
+ align:start position:0%
+velocity as a function of time I'll
+write this as T Prime DT Prime going
+
+ align:start position:0%
+write this as T Prime DT Prime going
+ 
+
+ align:start position:0%
+write this as T Prime DT Prime going
+from T Prime equals T KN to T Prime
+
+ align:start position:0%
+from T Prime equals T KN to T Prime
+ 
+
+ align:start position:0%
+from T Prime equals T KN to T Prime
+equal T so this is exactly analogous to
+
+ align:start position:0%
+equal T so this is exactly analogous to
+ 
+
+ align:start position:0%
+equal T so this is exactly analogous to
+how we computed velocity from
+
+ align:start position:0%
+how we computed velocity from
+ 
+
+ align:start position:0%
+how we computed velocity from
+acceleration by integrating a second
+
+ align:start position:0%
+acceleration by integrating a second
+ 
+
+ align:start position:0%
+acceleration by integrating a second
+time we can go from uh velocity to
+
+ align:start position:0%
+time we can go from uh velocity to
+ 
+
+ align:start position:0%
+time we can go from uh velocity to
+position so once we know the
+
+ align:start position:0%
+position so once we know the
+ 
+
+ align:start position:0%
+position so once we know the
+acceleration a of T we can use
+
+ align:start position:0%
+acceleration a of T we can use
+ 
+
+ align:start position:0%
+acceleration a of T we can use
+integration to compute the velocity V of
+
+ align:start position:0%
+integration to compute the velocity V of
+ 
+
+ align:start position:0%
+integration to compute the velocity V of
+T if we know the velocity at some
+
+ align:start position:0%
+T if we know the velocity at some
+ 
+
+ align:start position:0%
+T if we know the velocity at some
+initial time T KN and we can also
+
+ align:start position:0%
+initial time T KN and we can also
+ 
+
+ align:start position:0%
+initial time T KN and we can also
+compute the position X of T if we know
+
+ align:start position:0%
+compute the position X of T if we know
+ 
+
+ align:start position:0%
+compute the position X of T if we know
+the initial position at time T KN X knot
+
+ align:start position:0%
+the initial position at time T KN X knot
+ 
+
+ align:start position:0%
+the initial position at time T KN X knot
+so we see that given the acceleration we
+
+ align:start position:0%
+so we see that given the acceleration we
+ 
+
+ align:start position:0%
+so we see that given the acceleration we
+can recover the velocity and the
+
+ align:start position:0%
+can recover the velocity and the
+ 
+
+ align:start position:0%
+can recover the velocity and the
+position and as it happens from Newton's
+
+ align:start position:0%
+position and as it happens from Newton's
+ 
+
+ align:start position:0%
+position and as it happens from Newton's
+Second Law if we know the forces acting
+
+ align:start position:0%
+Second Law if we know the forces acting
+ 
+
+ align:start position:0%
+Second Law if we know the forces acting
+on an object that gives us the ability
+
+ align:start position:0%
+on an object that gives us the ability
+ 
+
+ align:start position:0%
+on an object that gives us the ability
+to compute what the acceleration is and
+
+ align:start position:0%
+to compute what the acceleration is and
+ 
+
+ align:start position:0%
+to compute what the acceleration is and
+then given the acceleration we can use
+
+ align:start position:0%
+then given the acceleration we can use
+ 
+
+ align:start position:0%
+then given the acceleration we can use
+integration to find the velocity and the
+
+ align:start position:0%
+integration to find the velocity and the
+ 
+
+ align:start position:0%
+integration to find the velocity and the
+position
\ No newline at end of file
diff --git a/I0Psvvky-44.txt b/I0Psvvky-44.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a1554c7ce065f5b037c73c25ef0554a6e807bd3
--- /dev/null
+++ b/I0Psvvky-44.txt
@@ -0,0 +1,17307 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right let's get started
+
+ align:start position:0%
+ocw.mit.edu all right let's get started
+ 
+
+ align:start position:0%
+ocw.mit.edu all right let's get started
+so um today we're going to talk about uh
+
+ align:start position:0%
+so um today we're going to talk about uh
+ 
+
+ align:start position:0%
+so um today we're going to talk about uh
+the system called native client which um
+
+ align:start position:0%
+the system called native client which um
+ 
+
+ align:start position:0%
+the system called native client which um
+is actually a real world system used uh
+
+ align:start position:0%
+is actually a real world system used uh
+ 
+
+ align:start position:0%
+is actually a real world system used uh
+by Google uh as one example they
+
+ align:start position:0%
+by Google uh as one example they
+ 
+
+ align:start position:0%
+by Google uh as one example they
+actually use it in the Chrome browser to
+
+ align:start position:0%
+actually use it in the Chrome browser to
+ 
+
+ align:start position:0%
+actually use it in the Chrome browser to
+allow web applications to run arbitrary
+
+ align:start position:0%
+allow web applications to run arbitrary
+ 
+
+ align:start position:0%
+allow web applications to run arbitrary
+native code it's actually a pretty cool
+
+ align:start position:0%
+native code it's actually a pretty cool
+ 
+
+ align:start position:0%
+native code it's actually a pretty cool
+system and uh it's also an illustration
+
+ align:start position:0%
+system and uh it's also an illustration
+ 
+
+ align:start position:0%
+system and uh it's also an illustration
+of another isolation or sort of
+
+ align:start position:0%
+of another isolation or sort of
+ 
+
+ align:start position:0%
+of another isolation or sort of
+sandboxing or privilege separation
+
+ align:start position:0%
+sandboxing or privilege separation
+ 
+
+ align:start position:0%
+sandboxing or privilege separation
+technique that's called software fault
+
+ align:start position:0%
+technique that's called software fault
+ 
+
+ align:start position:0%
+technique that's called software fault
+isolation that doesn't rely on operating
+
+ align:start position:0%
+isolation that doesn't rely on operating
+ 
+
+ align:start position:0%
+isolation that doesn't rely on operating
+systems to sandbox a process virtual
+
+ align:start position:0%
+systems to sandbox a process virtual
+ 
+
+ align:start position:0%
+systems to sandbox a process virtual
+machines but instead has a very
+
+ align:start position:0%
+machines but instead has a very
+ 
+
+ align:start position:0%
+machines but instead has a very
+different approach to looking at the
+
+ align:start position:0%
+different approach to looking at the
+ 
+
+ align:start position:0%
+different approach to looking at the
+particular instructions in a binary to
+
+ align:start position:0%
+particular instructions in a binary to
+ 
+
+ align:start position:0%
+particular instructions in a binary to
+figure out whether it's going to be safe
+
+ align:start position:0%
+figure out whether it's going to be safe
+ 
+
+ align:start position:0%
+figure out whether it's going to be safe
+to run or not so before we I guess start
+
+ align:start position:0%
+to run or not so before we I guess start
+ 
+
+ align:start position:0%
+to run or not so before we I guess start
+looking at the technical details of this
+
+ align:start position:0%
+looking at the technical details of this
+ 
+
+ align:start position:0%
+looking at the technical details of this
+system um let's figure out why do these
+
+ align:start position:0%
+system um let's figure out why do these
+ 
+
+ align:start position:0%
+system um let's figure out why do these
+guys actually want to run native code
+
+ align:start position:0%
+guys actually want to run native code
+ 
+
+ align:start position:0%
+guys actually want to run native code
+right so the particular context they are
+
+ align:start position:0%
+right so the particular context they are
+ 
+
+ align:start position:0%
+right so the particular context they are
+interested in applying their solution to
+
+ align:start position:0%
+interested in applying their solution to
+ 
+
+ align:start position:0%
+interested in applying their solution to
+is a web browser where you could already
+
+ align:start position:0%
+is a web browser where you could already
+ 
+
+ align:start position:0%
+is a web browser where you could already
+run JavaScript code and maybe Flash and
+
+ align:start position:0%
+run JavaScript code and maybe Flash and
+ 
+
+ align:start position:0%
+run JavaScript code and maybe Flash and
+maybe a couple couple of other things
+
+ align:start position:0%
+maybe a couple couple of other things
+ 
+
+ align:start position:0%
+maybe a couple couple of other things
+why are these guys so excited about
+
+ align:start position:0%
+why are these guys so excited about
+ 
+
+ align:start position:0%
+why are these guys so excited about
+running raw x86 it seems like a step
+
+ align:start position:0%
+running raw x86 it seems like a step
+ 
+
+ align:start position:0%
+running raw x86 it seems like a step
+backwards like really fast computation
+
+ align:start position:0%
+backwards like really fast computation
+ 
+
+ align:start position:0%
+backwards like really fast computation
+yeah so one huge advantage of native
+
+ align:start position:0%
+yeah so one huge advantage of native
+ 
+
+ align:start position:0%
+yeah so one huge advantage of native
+code even though it might be unsafe from
+
+ align:start position:0%
+code even though it might be unsafe from
+ 
+
+ align:start position:0%
+code even though it might be unsafe from
+some perspectives uh it's really high
+
+ align:start position:0%
+some perspectives uh it's really high
+ 
+
+ align:start position:0%
+some perspectives uh it's really high
+performance whatever you can do in
+
+ align:start position:0%
+performance whatever you can do in
+ 
+
+ align:start position:0%
+performance whatever you can do in
+JavaScript presumably you can just write
+
+ align:start position:0%
+JavaScript presumably you can just write
+ 
+
+ align:start position:0%
+JavaScript presumably you can just write
+the same thing in assembly and it'll go
+
+ align:start position:0%
+the same thing in assembly and it'll go
+ 
+
+ align:start position:0%
+the same thing in assembly and it'll go
+at least as fast probably much faster
+
+ align:start position:0%
+at least as fast probably much faster
+ 
+
+ align:start position:0%
+at least as fast probably much faster
+any other reasons yeah code yeah so
+
+ align:start position:0%
+any other reasons yeah code yeah so
+ 
+
+ align:start position:0%
+any other reasons yeah code yeah so
+another big thing is maybe not
+
+ align:start position:0%
+another big thing is maybe not
+ 
+
+ align:start position:0%
+another big thing is maybe not
+everything is written in JavaScript so
+
+ align:start position:0%
+everything is written in JavaScript so
+ 
+
+ align:start position:0%
+everything is written in JavaScript so
+if you have an existing
+
+ align:start position:0%
+if you have an existing
+ 
+
+ align:start position:0%
+if you have an existing
+application I guess Legacy in Industry
+
+ align:start position:0%
+application I guess Legacy in Industry
+ 
+
+ align:start position:0%
+application I guess Legacy in Industry
+terminology uh if you have some existing
+
+ align:start position:0%
+terminology uh if you have some existing
+ 
+
+ align:start position:0%
+terminology uh if you have some existing
+code that you really want to run in the
+
+ align:start position:0%
+code that you really want to run in the
+ 
+
+ align:start position:0%
+code that you really want to run in the
+web uh then this seems like a great
+
+ align:start position:0%
+web uh then this seems like a great
+ 
+
+ align:start position:0%
+web uh then this seems like a great
+solution because you can just take an
+
+ align:start position:0%
+solution because you can just take an
+ 
+
+ align:start position:0%
+solution because you can just take an
+existing Library like some complicated I
+
+ align:start position:0%
+existing Library like some complicated I
+ 
+
+ align:start position:0%
+existing Library like some complicated I
+don't know Graphics processing engine
+
+ align:start position:0%
+don't know Graphics processing engine
+ 
+
+ align:start position:0%
+don't know Graphics processing engine
+that's both performance sensitive and
+
+ align:start position:0%
+that's both performance sensitive and
+ 
+
+ align:start position:0%
+that's both performance sensitive and
+like lots of complicated stuff you don't
+
+ align:start position:0%
+like lots of complicated stuff you don't
+ 
+
+ align:start position:0%
+like lots of complicated stuff you don't
+want to reimplement then this seems like
+
+ align:start position:0%
+want to reimplement then this seems like
+ 
+
+ align:start position:0%
+want to reimplement then this seems like
+a good
+
+ align:start position:0%
+a good
+ 
+
+ align:start position:0%
+a good
+solution anything else if you're just
+
+ align:start position:0%
+solution anything else if you're just
+ 
+
+ align:start position:0%
+solution anything else if you're just
+like programming a new web app should
+
+ align:start position:0%
+like programming a new web app should
+ 
+
+ align:start position:0%
+like programming a new web app should
+you use native client if you don't care
+
+ align:start position:0%
+you use native client if you don't care
+ 
+
+ align:start position:0%
+you use native client if you don't care
+about Legacy or performance so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much any other
+
+ align:start position:0%
+much any other
+ 
+
+ align:start position:0%
+much any other
+reasons I guess another yeah you don't
+
+ align:start position:0%
+reasons I guess another yeah you don't
+ 
+
+ align:start position:0%
+reasons I guess another yeah you don't
+have to use JavaScript yeah that's an
+
+ align:start position:0%
+have to use JavaScript yeah that's an
+ 
+
+ align:start position:0%
+have to use JavaScript yeah that's an
+awesome reason right like you know it
+
+ align:start position:0%
+awesome reason right like you know it
+ 
+
+ align:start position:0%
+awesome reason right like you know it
+might if you don't like JavaScript then
+
+ align:start position:0%
+might if you don't like JavaScript then
+ 
+
+ align:start position:0%
+might if you don't like JavaScript then
+you don't have to use it right you can
+
+ align:start position:0%
+you don't have to use it right you can
+ 
+
+ align:start position:0%
+you don't have to use it right you can
+actually use I don't know well see if
+
+ align:start position:0%
+actually use I don't know well see if
+ 
+
+ align:start position:0%
+actually use I don't know well see if
+you're so inclined you could run python
+
+ align:start position:0%
+you're so inclined you could run python
+ 
+
+ align:start position:0%
+you're so inclined you could run python
+code you could write hascal whatever you
+
+ align:start position:0%
+code you could write hascal whatever you
+ 
+
+ align:start position:0%
+code you could write hascal whatever you
+think is useful uh you can actually
+
+ align:start position:0%
+think is useful uh you can actually
+ 
+
+ align:start position:0%
+think is useful uh you can actually
+support other languages all of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sudden so this is a you know reasonably
+
+ align:start position:0%
+sudden so this is a you know reasonably
+ 
+
+ align:start position:0%
+sudden so this is a you know reasonably
+compelling
+
+ align:start position:0%
+compelling
+ 
+
+ align:start position:0%
+compelling
+list of sort of motivation uh for them
+
+ align:start position:0%
+list of sort of motivation uh for them
+ 
+
+ align:start position:0%
+list of sort of motivation uh for them
+to run native code in the browser and um
+
+ align:start position:0%
+to run native code in the browser and um
+ 
+
+ align:start position:0%
+to run native code in the browser and um
+turns out to be reasonably tricky to get
+
+ align:start position:0%
+turns out to be reasonably tricky to get
+ 
+
+ align:start position:0%
+turns out to be reasonably tricky to get
+right so we'll look at the technical
+
+ align:start position:0%
+right so we'll look at the technical
+ 
+
+ align:start position:0%
+right so we'll look at the technical
+details I guess of how it works in a
+
+ align:start position:0%
+details I guess of how it works in a
+ 
+
+ align:start position:0%
+details I guess of how it works in a
+second but just to show you guys what
+
+ align:start position:0%
+second but just to show you guys what
+ 
+
+ align:start position:0%
+second but just to show you guys what
+this paper is talking about I just want
+
+ align:start position:0%
+this paper is talking about I just want
+ 
+
+ align:start position:0%
+this paper is talking about I just want
+to show a very simple tutorial demo
+
+ align:start position:0%
+to show a very simple tutorial demo
+ 
+
+ align:start position:0%
+to show a very simple tutorial demo
+almost that I got out of their native
+
+ align:start position:0%
+almost that I got out of their native
+ 
+
+ align:start position:0%
+almost that I got out of their native
+client you know website it's fairly
+
+ align:start position:0%
+client you know website it's fairly
+ 
+
+ align:start position:0%
+client you know website it's fairly
+simple as it turns out to just take a
+
+ align:start position:0%
+simple as it turns out to just take a
+ 
+
+ align:start position:0%
+simple as it turns out to just take a
+C++ or a c program and run it in the
+
+ align:start position:0%
+C++ or a c program and run it in the
+ 
+
+ align:start position:0%
+C++ or a c program and run it in the
+browser so just to show you what this
+
+ align:start position:0%
+browser so just to show you what this
+ 
+
+ align:start position:0%
+browser so just to show you what this
+looks like here's the basically a demo I
+
+ align:start position:0%
+looks like here's the basically a demo I
+ 
+
+ align:start position:0%
+looks like here's the basically a demo I
+mostly sort of took from one of their
+
+ align:start position:0%
+mostly sort of took from one of their
+ 
+
+ align:start position:0%
+mostly sort of took from one of their
+examples so you can look at you know a
+
+ align:start position:0%
+examples so you can look at you know a
+ 
+
+ align:start position:0%
+examples so you can look at you know a
+web page like this index HTML file and
+
+ align:start position:0%
+web page like this index HTML file and
+ 
+
+ align:start position:0%
+web page like this index HTML file and
+inside of it you have a bunch of
+
+ align:start position:0%
+inside of it you have a bunch of
+ 
+
+ align:start position:0%
+inside of it you have a bunch of
+JavaScript code and the reason this
+
+ align:start position:0%
+JavaScript code and the reason this
+ 
+
+ align:start position:0%
+JavaScript code and the reason this
+JavaScript code exists is to sort of
+
+ align:start position:0%
+JavaScript code exists is to sort of
+ 
+
+ align:start position:0%
+JavaScript code exists is to sort of
+interact with the native client piece so
+
+ align:start position:0%
+interact with the native client piece so
+ 
+
+ align:start position:0%
+interact with the native client piece so
+the way you can sort of think of this
+
+ align:start position:0%
+the way you can sort of think of this
+ 
+
+ align:start position:0%
+the way you can sort of think of this
+running in the browser is that you have
+
+ align:start position:0%
+running in the browser is that you have
+ 
+
+ align:start position:0%
+running in the browser is that you have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+browser you have well we'll talk about
+
+ align:start position:0%
+browser you have well we'll talk about
+ 
+
+ align:start position:0%
+browser you have well we'll talk about
+much more about web security later but
+
+ align:start position:0%
+much more about web security later but
+ 
+
+ align:start position:0%
+much more about web security later but
+roughly you have some sort of a page uh
+
+ align:start position:0%
+roughly you have some sort of a page uh
+ 
+
+ align:start position:0%
+roughly you have some sort of a page uh
+web page that contains JavaScript code
+
+ align:start position:0%
+web page that contains JavaScript code
+ 
+
+ align:start position:0%
+web page that contains JavaScript code
+and this runs with the pages Privileges
+
+ align:start position:0%
+and this runs with the pages Privileges
+ 
+
+ align:start position:0%
+and this runs with the pages Privileges
+and this can do you know various things
+
+ align:start position:0%
+and this can do you know various things
+ 
+
+ align:start position:0%
+and this can do you know various things
+to the web page itself maybe talk to the
+
+ align:start position:0%
+to the web page itself maybe talk to the
+ 
+
+ align:start position:0%
+to the web page itself maybe talk to the
+network in some circumstances but what
+
+ align:start position:0%
+network in some circumstances but what
+ 
+
+ align:start position:0%
+network in some circumstances but what
+Native client allows you to do is to
+
+ align:start position:0%
+Native client allows you to do is to
+ 
+
+ align:start position:0%
+Native client allows you to do is to
+have this native client module running
+
+ align:start position:0%
+have this native client module running
+ 
+
+ align:start position:0%
+have this native client module running
+sort of to the side in the browser as
+
+ align:start position:0%
+sort of to the side in the browser as
+ 
+
+ align:start position:0%
+sort of to the side in the browser as
+well and the JavaScript code can
+
+ align:start position:0%
+well and the JavaScript code can
+ 
+
+ align:start position:0%
+well and the JavaScript code can
+actually interact with the native client
+
+ align:start position:0%
+actually interact with the native client
+ 
+
+ align:start position:0%
+actually interact with the native client
+module and get responses
+
+ align:start position:0%
+module and get responses
+ 
+
+ align:start position:0%
+module and get responses
+back and what you see here in this web
+
+ align:start position:0%
+back and what you see here in this web
+ 
+
+ align:start position:0%
+back and what you see here in this web
+page is the little bit of JavaScript
+
+ align:start position:0%
+page is the little bit of JavaScript
+ 
+
+ align:start position:0%
+page is the little bit of JavaScript
+code that's necessary a native client to
+
+ align:start position:0%
+code that's necessary a native client to
+ 
+
+ align:start position:0%
+code that's necessary a native client to
+interact with a particular nackle module
+
+ align:start position:0%
+interact with a particular nackle module
+ 
+
+ align:start position:0%
+interact with a particular nackle module
+that we're going to be running and you
+
+ align:start position:0%
+that we're going to be running and you
+ 
+
+ align:start position:0%
+that we're going to be running and you
+can send messages to this module the way
+
+ align:start position:0%
+can send messages to this module the way
+ 
+
+ align:start position:0%
+can send messages to this module the way
+you do it is you take this module object
+
+ align:start position:0%
+you do it is you take this module object
+ 
+
+ align:start position:0%
+you do it is you take this module object
+in JavaScript and you call Post message
+
+ align:start position:0%
+in JavaScript and you call Post message
+ 
+
+ align:start position:0%
+in JavaScript and you call Post message
+in it and you can actually Supply a
+
+ align:start position:0%
+in it and you can actually Supply a
+ 
+
+ align:start position:0%
+in it and you can actually Supply a
+message to send to the native client
+
+ align:start position:0%
+message to send to the native client
+ 
+
+ align:start position:0%
+message to send to the native client
+module and when the native client module
+
+ align:start position:0%
+module and when the native client module
+ 
+
+ align:start position:0%
+module and when the native client module
+responds it'll run this handle message
+
+ align:start position:0%
+responds it'll run this handle message
+ 
+
+ align:start position:0%
+responds it'll run this handle message
+function in JavaScript and in this
+
+ align:start position:0%
+function in JavaScript and in this
+ 
+
+ align:start position:0%
+function in JavaScript and in this
+particular case it just pops up an alert
+
+ align:start position:0%
+particular case it just pops up an alert
+ 
+
+ align:start position:0%
+particular case it just pops up an alert
+dialogue box in my
+
+ align:start position:0%
+dialogue box in my
+ 
+
+ align:start position:0%
+dialogue box in my
+browser so this is actually air simple
+
+ align:start position:0%
+browser so this is actually air simple
+ 
+
+ align:start position:0%
+browser so this is actually air simple
+interface from the web page side from
+
+ align:start position:0%
+interface from the web page side from
+ 
+
+ align:start position:0%
+interface from the web page side from
+the JavaScript side and the only thing
+
+ align:start position:0%
+the JavaScript side and the only thing
+ 
+
+ align:start position:0%
+the JavaScript side and the only thing
+you Additionally you have to do is you
+
+ align:start position:0%
+you Additionally you have to do is you
+ 
+
+ align:start position:0%
+you Additionally you have to do is you
+actually have to declare this native
+
+ align:start position:0%
+actually have to declare this native
+ 
+
+ align:start position:0%
+actually have to declare this native
+client module this way so you just say
+
+ align:start position:0%
+client module this way so you just say
+ 
+
+ align:start position:0%
+client module this way so you just say
+embed a module with a particular ID and
+
+ align:start position:0%
+embed a module with a particular ID and
+ 
+
+ align:start position:0%
+embed a module with a particular ID and
+the sort of most interesting part is the
+
+ align:start position:0%
+the sort of most interesting part is the
+ 
+
+ align:start position:0%
+the sort of most interesting part is the
+source equals hello. some nmf part
+
+ align:start position:0%
+source equals hello. some nmf part
+ 
+
+ align:start position:0%
+source equals hello. some nmf part
+attribute and this one just says well
+
+ align:start position:0%
+attribute and this one just says well
+ 
+
+ align:start position:0%
+attribute and this one just says well
+here's the roughly executable file that
+
+ align:start position:0%
+here's the roughly executable file that
+ 
+
+ align:start position:0%
+here's the roughly executable file that
+you need to load and start running in
+
+ align:start position:0%
+you need to load and start running in
+ 
+
+ align:start position:0%
+you need to load and start running in
+the native side of things and this
+
+ align:start position:0%
+the native side of things and this
+ 
+
+ align:start position:0%
+the native side of things and this
+native code actually looks like any
+
+ align:start position:0%
+native code actually looks like any
+ 
+
+ align:start position:0%
+native code actually looks like any
+other C++ code you might write roughly
+
+ align:start position:0%
+other C++ code you might write roughly
+ 
+
+ align:start position:0%
+other C++ code you might write roughly
+so here's the program the interesting
+
+ align:start position:0%
+so here's the program the interesting
+ 
+
+ align:start position:0%
+so here's the program the interesting
+part is roughly this handle message
+
+ align:start position:0%
+part is roughly this handle message
+ 
+
+ align:start position:0%
+part is roughly this handle message
+function so this is a C++ class and
+
+ align:start position:0%
+function so this is a C++ class and
+ 
+
+ align:start position:0%
+function so this is a C++ class and
+whenever the JavaScript code sends some
+
+ align:start position:0%
+whenever the JavaScript code sends some
+ 
+
+ align:start position:0%
+whenever the JavaScript code sends some
+message to the native code it'll
+
+ align:start position:0%
+message to the native code it'll
+ 
+
+ align:start position:0%
+message to the native code it'll
+actually run this function and it'll
+
+ align:start position:0%
+actually run this function and it'll
+ 
+
+ align:start position:0%
+actually run this function and it'll
+check if the message that's being sent
+
+ align:start position:0%
+check if the message that's being sent
+ 
+
+ align:start position:0%
+check if the message that's being sent
+is hello and if so construct a reply
+
+ align:start position:0%
+is hello and if so construct a reply
+ 
+
+ align:start position:0%
+is hello and if so construct a reply
+string of some sort and send it back
+
+ align:start position:0%
+string of some sort and send it back
+ 
+
+ align:start position:0%
+string of some sort and send it back
+it's like fairly simple stuff but just
+
+ align:start position:0%
+it's like fairly simple stuff but just
+ 
+
+ align:start position:0%
+it's like fairly simple stuff but just
+to be concrete uh let's try to run it
+
+ align:start position:0%
+to be concrete uh let's try to run it
+ 
+
+ align:start position:0%
+to be concrete uh let's try to run it
+and see what happens so we can actually
+
+ align:start position:0%
+and see what happens so we can actually
+ 
+
+ align:start position:0%
+and see what happens so we can actually
+build it
+
+ align:start position:0%
+build it
+ 
+
+ align:start position:0%
+build it
+and uh run a little web server that uh
+
+ align:start position:0%
+and uh run a little web server that uh
+ 
+
+ align:start position:0%
+and uh run a little web server that uh
+is going
+
+ align:start position:0%
+is going
+ 
+
+ align:start position:0%
+is going
+to serve up this page and Native client
+
+ align:start position:0%
+to serve up this page and Native client
+ 
+
+ align:start position:0%
+to serve up this page and Native client
+module so here I can go to this URL and
+
+ align:start position:0%
+module so here I can go to this URL and
+ 
+
+ align:start position:0%
+module so here I can go to this URL and
+here we go right it's actually loaded in
+
+ align:start position:0%
+here we go right it's actually loaded in
+ 
+
+ align:start position:0%
+here we go right it's actually loaded in
+the module the module seems to have
+
+ align:start position:0%
+the module the module seems to have
+ 
+
+ align:start position:0%
+the module the module seems to have
+gotten our Hello message from JavaScript
+
+ align:start position:0%
+gotten our Hello message from JavaScript
+ 
+
+ align:start position:0%
+gotten our Hello message from JavaScript
+replied back with the string back to
+
+ align:start position:0%
+replied back with the string back to
+ 
+
+ align:start position:0%
+replied back with the string back to
+JavaScript and the JavaScript code
+
+ align:start position:0%
+JavaScript and the JavaScript code
+ 
+
+ align:start position:0%
+JavaScript and the JavaScript code
+popped up a dialog box containing that
+
+ align:start position:0%
+popped up a dialog box containing that
+ 
+
+ align:start position:0%
+popped up a dialog box containing that
+response so it actually does kind of
+
+ align:start position:0%
+response so it actually does kind of
+ 
+
+ align:start position:0%
+response so it actually does kind of
+work um we can try to see if we can
+
+ align:start position:0%
+work um we can try to see if we can
+ 
+
+ align:start position:0%
+work um we can try to see if we can
+crash native client but hopefully not
+
+ align:start position:0%
+crash native client but hopefully not
+ 
+
+ align:start position:0%
+crash native client but hopefully not
+but uh we can you know take this code
+
+ align:start position:0%
+but uh we can you know take this code
+ 
+
+ align:start position:0%
+but uh we can you know take this code
+and we have this buffer we could you
+
+ align:start position:0%
+and we have this buffer we could you
+ 
+
+ align:start position:0%
+and we have this buffer we could you
+know write a bunch of A's to it I don't
+
+ align:start position:0%
+know write a bunch of A's to it I don't
+ 
+
+ align:start position:0%
+know write a bunch of A's to it I don't
+know quite a lot um and see what happens
+
+ align:start position:0%
+know quite a lot um and see what happens
+ 
+
+ align:start position:0%
+know quite a lot um and see what happens
+so hopefully this shouldn't crash my
+
+ align:start position:0%
+so hopefully this shouldn't crash my
+ 
+
+ align:start position:0%
+so hopefully this shouldn't crash my
+browser because native client is trying
+
+ align:start position:0%
+browser because native client is trying
+ 
+
+ align:start position:0%
+browser because native client is trying
+to provide isolation um um but let's see
+
+ align:start position:0%
+to provide isolation um um but let's see
+ 
+
+ align:start position:0%
+to provide isolation um um but let's see
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+happens so we can rebuild it rerun the
+
+ align:start position:0%
+happens so we can rebuild it rerun the
+ 
+
+ align:start position:0%
+happens so we can rebuild it rerun the
+web server and here if you run it
+
+ align:start position:0%
+web server and here if you run it
+ 
+
+ align:start position:0%
+web server and here if you run it
+nothing happens we don't get the message
+
+ align:start position:0%
+nothing happens we don't get the message
+ 
+
+ align:start position:0%
+nothing happens we don't get the message
+back anymore so clearly message didn't
+
+ align:start position:0%
+back anymore so clearly message didn't
+ 
+
+ align:start position:0%
+back anymore so clearly message didn't
+get sent back from the Native client
+
+ align:start position:0%
+get sent back from the Native client
+ 
+
+ align:start position:0%
+get sent back from the Native client
+module because I don't see any popup we
+
+ align:start position:0%
+module because I don't see any popup we
+ 
+
+ align:start position:0%
+module because I don't see any popup we
+can look at the JavaScript console here
+
+ align:start position:0%
+can look at the JavaScript console here
+ 
+
+ align:start position:0%
+can look at the JavaScript console here
+and we can see that the native client
+
+ align:start position:0%
+and we can see that the native client
+ 
+
+ align:start position:0%
+and we can see that the native client
+module tells us knle module crashed so
+
+ align:start position:0%
+module tells us knle module crashed so
+ 
+
+ align:start position:0%
+module tells us knle module crashed so
+somehow it caught this buff overflow uh
+
+ align:start position:0%
+somehow it caught this buff overflow uh
+ 
+
+ align:start position:0%
+somehow it caught this buff overflow uh
+scribbling over some memory or maybe it
+
+ align:start position:0%
+scribbling over some memory or maybe it
+ 
+
+ align:start position:0%
+scribbling over some memory or maybe it
+jump to some bad address containing all
+
+ align:start position:0%
+jump to some bad address containing all
+ 
+
+ align:start position:0%
+jump to some bad address containing all
+A's uh but in any case the native client
+
+ align:start position:0%
+A's uh but in any case the native client
+ 
+
+ align:start position:0%
+A's uh but in any case the native client
+module is actually able to contain this
+
+ align:start position:0%
+module is actually able to contain this
+ 
+
+ align:start position:0%
+module is actually able to contain this
+without this arbitary sort of memory
+
+ align:start position:0%
+without this arbitary sort of memory
+ 
+
+ align:start position:0%
+without this arbitary sort of memory
+corruption in the module affecting the
+
+ align:start position:0%
+corruption in the module affecting the
+ 
+
+ align:start position:0%
+corruption in the module affecting the
+rest of the
+
+ align:start position:0%
+rest of the
+ 
+
+ align:start position:0%
+rest of the
+browser so this is roughly just a sort
+
+ align:start position:0%
+browser so this is roughly just a sort
+ 
+
+ align:start position:0%
+browser so this is roughly just a sort
+of quick demo of what the system is and
+
+ align:start position:0%
+of quick demo of what the system is and
+ 
+
+ align:start position:0%
+of quick demo of what the system is and
+um what how how you use it as as a end
+
+ align:start position:0%
+um what how how you use it as as a end
+ 
+
+ align:start position:0%
+um what how how you use it as as a end
+user or web
+
+ align:start position:0%
+user or web
+ 
+
+ align:start position:0%
+user or web
+developer so let's look now some more so
+
+ align:start position:0%
+developer so let's look now some more so
+ 
+
+ align:start position:0%
+developer so let's look now some more so
+that's all in terms of demos I have to
+
+ align:start position:0%
+that's all in terms of demos I have to
+ 
+
+ align:start position:0%
+that's all in terms of demos I have to
+show you uh so let's look more now in at
+
+ align:start position:0%
+show you uh so let's look more now in at
+ 
+
+ align:start position:0%
+show you uh so let's look more now in at
+uh how Native client is going to work or
+
+ align:start position:0%
+uh how Native client is going to work or
+ 
+
+ align:start position:0%
+uh how Native client is going to work or
+perhaps even why we need this particular
+
+ align:start position:0%
+perhaps even why we need this particular
+ 
+
+ align:start position:0%
+perhaps even why we need this particular
+design as opposed to some of the
+
+ align:start position:0%
+design as opposed to some of the
+ 
+
+ align:start position:0%
+design as opposed to some of the
+Alternatives so so if your goal I guess
+
+ align:start position:0%
+Alternatives so so if your goal I guess
+ 
+
+ align:start position:0%
+Alternatives so so if your goal I guess
+is to sandbox native
+
+ align:start position:0%
+is to sandbox native
+ 
+
+ align:start position:0%
+is to sandbox native
+code there's a number of Alternatives
+
+ align:start position:0%
+code there's a number of Alternatives
+ 
+
+ align:start position:0%
+code there's a number of Alternatives
+you could make right people actually had
+
+ align:start position:0%
+you could make right people actually had
+ 
+
+ align:start position:0%
+you could make right people actually had
+these problems before of performance
+
+ align:start position:0%
+these problems before of performance
+ 
+
+ align:start position:0%
+these problems before of performance
+existing Legacy code and other languages
+
+ align:start position:0%
+existing Legacy code and other languages
+ 
+
+ align:start position:0%
+existing Legacy code and other languages
+before native client came around and
+
+ align:start position:0%
+before native client came around and
+ 
+
+ align:start position:0%
+before native client came around and
+people just solved them in different
+
+ align:start position:0%
+people just solved them in different
+ 
+
+ align:start position:0%
+people just solved them in different
+ways that maybe weren't as satisfying in
+
+ align:start position:0%
+ways that maybe weren't as satisfying in
+ 
+
+ align:start position:0%
+ways that maybe weren't as satisfying in
+from a security standpoint orbe a
+
+ align:start position:0%
+from a security standpoint orbe a
+ 
+
+ align:start position:0%
+from a security standpoint orbe a
+usability standpoint as native client
+
+ align:start position:0%
+usability standpoint as native client
+ 
+
+ align:start position:0%
+usability standpoint as native client
+but it is doable so let's see so what so
+
+ align:start position:0%
+but it is doable so let's see so what so
+ 
+
+ align:start position:0%
+but it is doable so let's see so what so
+what what could you do if you really
+
+ align:start position:0%
+what what could you do if you really
+ 
+
+ align:start position:0%
+what what could you do if you really
+want to run native code in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+browser so one option that people did
+
+ align:start position:0%
+browser so one option that people did
+ 
+
+ align:start position:0%
+browser so one option that people did
+was to trust the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+developer and maybe a variant of this
+
+ align:start position:0%
+developer and maybe a variant of this
+ 
+
+ align:start position:0%
+developer and maybe a variant of this
+approach is to ask the user whether they
+
+ align:start position:0%
+approach is to ask the user whether they
+ 
+
+ align:start position:0%
+approach is to ask the user whether they
+want to run some piece of code in their
+
+ align:start position:0%
+want to run some piece of code in their
+ 
+
+ align:start position:0%
+want to run some piece of code in their
+browser or
+
+ align:start position:0%
+browser or
+ 
+
+ align:start position:0%
+browser or
+not so does everyone understand roughly
+
+ align:start position:0%
+not so does everyone understand roughly
+ 
+
+ align:start position:0%
+not so does everyone understand roughly
+what the plan is right like instead of
+
+ align:start position:0%
+what the plan is right like instead of
+ 
+
+ align:start position:0%
+what the plan is right like instead of
+having that whole native client
+
+ align:start position:0%
+having that whole native client
+ 
+
+ align:start position:0%
+having that whole native client
+compilation strategy I could have just
+
+ align:start position:0%
+compilation strategy I could have just
+ 
+
+ align:start position:0%
+compilation strategy I could have just
+built a simple C program served it up on
+
+ align:start position:0%
+built a simple C program served it up on
+ 
+
+ align:start position:0%
+built a simple C program served it up on
+the browser and maybe the browser asked
+
+ align:start position:0%
+the browser and maybe the browser asked
+ 
+
+ align:start position:0%
+the browser and maybe the browser asked
+do you want to run this site or not if I
+
+ align:start position:0%
+do you want to run this site or not if I
+ 
+
+ align:start position:0%
+do you want to run this site or not if I
+click yes then it accidentally scri over
+
+ align:start position:0%
+click yes then it accidentally scri over
+ 
+
+ align:start position:0%
+click yes then it accidentally scri over
+the browser's memory and crashes the
+
+ align:start position:0%
+the browser's memory and crashes the
+ 
+
+ align:start position:0%
+the browser's memory and crashes the
+browser
+
+ align:start position:0%
+browser
+ 
+
+ align:start position:0%
+browser
+so it's possible Right it certainly
+
+ align:start position:0%
+so it's possible Right it certainly
+ 
+
+ align:start position:0%
+so it's possible Right it certainly
+solves all these goals but what's wrong
+
+ align:start position:0%
+solves all these goals but what's wrong
+ 
+
+ align:start position:0%
+solves all these goals but what's wrong
+with it well I guess there's the
+
+ align:start position:0%
+with it well I guess there's the
+ 
+
+ align:start position:0%
+with it well I guess there's the
+insecurity part uh which is unfortunate
+
+ align:start position:0%
+insecurity part uh which is unfortunate
+ 
+
+ align:start position:0%
+insecurity part uh which is unfortunate
+uh one way to potentially get around
+
+ align:start position:0%
+uh one way to potentially get around
+ 
+
+ align:start position:0%
+uh one way to potentially get around
+this and some systems did like uh
+
+ align:start position:0%
+this and some systems did like uh
+ 
+
+ align:start position:0%
+this and some systems did like uh
+Microsoft had the system called active
+
+ align:start position:0%
+Microsoft had the system called active
+ 
+
+ align:start position:0%
+Microsoft had the system called active
+X that basically implemented this plan
+
+ align:start position:0%
+X that basically implemented this plan
+ 
+
+ align:start position:0%
+X that basically implemented this plan
+you could serve binaries to IE the
+
+ align:start position:0%
+you could serve binaries to IE the
+ 
+
+ align:start position:0%
+you could serve binaries to IE the
+browser on your machine and as long as
+
+ align:start position:0%
+browser on your machine and as long as
+ 
+
+ align:start position:0%
+browser on your machine and as long as
+it came with a certificate from a
+
+ align:start position:0%
+it came with a certificate from a
+ 
+
+ align:start position:0%
+it came with a certificate from a
+particular developer signed by let's say
+
+ align:start position:0%
+particular developer signed by let's say
+ 
+
+ align:start position:0%
+particular developer signed by let's say
+Microsoft or someone else then it would
+
+ align:start position:0%
+Microsoft or someone else then it would
+ 
+
+ align:start position:0%
+Microsoft or someone else then it would
+actually run this code so what do you
+
+ align:start position:0%
+actually run this code so what do you
+ 
+
+ align:start position:0%
+actually run this code so what do you
+guys think about this plan is this
+
+ align:start position:0%
+guys think about this plan is this
+ 
+
+ align:start position:0%
+guys think about this plan is this
+useful yeah well doesn't tell you
+
+ align:start position:0%
+useful yeah well doesn't tell you
+ 
+
+ align:start position:0%
+useful yeah well doesn't tell you
+anything about does just a signature on
+
+ align:start position:0%
+anything about does just a signature on
+ 
+
+ align:start position:0%
+anything about does just a signature on
+the code the code should be contining
+
+ align:start position:0%
+the code the code should be contining
+ 
+
+ align:start position:0%
+the code the code should be contining
+malicious that's right yeah so right you
+
+ align:start position:0%
+malicious that's right yeah so right you
+ 
+
+ align:start position:0%
+malicious that's right yeah so right you
+really have to put quite a bit of trust
+
+ align:start position:0%
+really have to put quite a bit of trust
+ 
+
+ align:start position:0%
+really have to put quite a bit of trust
+into whoever it is that's signing this
+
+ align:start position:0%
+into whoever it is that's signing this
+ 
+
+ align:start position:0%
+into whoever it is that's signing this
+that they will only sign binaries that
+
+ align:start position:0%
+that they will only sign binaries that
+ 
+
+ align:start position:0%
+that they will only sign binaries that
+will not do something bad um but it's
+
+ align:start position:0%
+will not do something bad um but it's
+ 
+
+ align:start position:0%
+will not do something bad um but it's
+kind of vague what this bad thing is and
+
+ align:start position:0%
+kind of vague what this bad thing is and
+ 
+
+ align:start position:0%
+kind of vague what this bad thing is and
+presumably they're just writing C code
+
+ align:start position:0%
+presumably they're just writing C code
+ 
+
+ align:start position:0%
+presumably they're just writing C code
+and you know signing it blindly without
+
+ align:start position:0%
+and you know signing it blindly without
+ 
+
+ align:start position:0%
+and you know signing it blindly without
+doing a huge amount of work um in which
+
+ align:start position:0%
+doing a huge amount of work um in which
+ 
+
+ align:start position:0%
+doing a huge amount of work um in which
+case you might well be susceptible to
+
+ align:start position:0%
+case you might well be susceptible to
+ 
+
+ align:start position:0%
+case you might well be susceptible to
+some problems down the line what if we
+
+ align:start position:0%
+some problems down the line what if we
+ 
+
+ align:start position:0%
+some problems down the line what if we
+ask the user yeah that like we read that
+
+ align:start position:0%
+ask the user yeah that like we read that
+ 
+
+ align:start position:0%
+ask the user yeah that like we read that
+paper in 6033 where user sometimes will
+
+ align:start position:0%
+paper in 6033 where user sometimes will
+ 
+
+ align:start position:0%
+paper in 6033 where user sometimes will
+not even read the message oh yeah yeah
+
+ align:start position:0%
+not even read the message oh yeah yeah
+ 
+
+ align:start position:0%
+not even read the message oh yeah yeah
+yeah right like the user's goal is to
+
+ align:start position:0%
+yeah right like the user's goal is to
+ 
+
+ align:start position:0%
+yeah right like the user's goal is to
+run this thing and uh you know even if
+
+ align:start position:0%
+run this thing and uh you know even if
+ 
+
+ align:start position:0%
+run this thing and uh you know even if
+the user wants to be cautious it's
+
+ align:start position:0%
+the user wants to be cautious it's
+ 
+
+ align:start position:0%
+the user wants to be cautious it's
+actually not clear how should the user
+
+ align:start position:0%
+actually not clear how should the user
+ 
+
+ align:start position:0%
+actually not clear how should the user
+decide like suppose I really want to
+
+ align:start position:0%
+decide like suppose I really want to
+ 
+
+ align:start position:0%
+decide like suppose I really want to
+understand should I allow this program
+
+ align:start position:0%
+understand should I allow this program
+ 
+
+ align:start position:0%
+understand should I allow this program
+to run all it tells me is well maybe it
+
+ align:start position:0%
+to run all it tells me is well maybe it
+ 
+
+ align:start position:0%
+to run all it tells me is well maybe it
+came from google.com or microsoft.com
+
+ align:start position:0%
+came from google.com or microsoft.com
+ 
+
+ align:start position:0%
+came from google.com or microsoft.com
+and its file name is food. exe I don't
+
+ align:start position:0%
+and its file name is food. exe I don't
+ 
+
+ align:start position:0%
+and its file name is food. exe I don't
+know like what's in there right even if
+
+ align:start position:0%
+know like what's in there right even if
+ 
+
+ align:start position:0%
+know like what's in there right even if
+I disassemble the code it might be very
+
+ align:start position:0%
+I disassemble the code it might be very
+ 
+
+ align:start position:0%
+I disassemble the code it might be very
+hard to tell whether it's going to do
+
+ align:start position:0%
+hard to tell whether it's going to do
+ 
+
+ align:start position:0%
+hard to tell whether it's going to do
+something bad or not so it's actually
+
+ align:start position:0%
+something bad or not so it's actually
+ 
+
+ align:start position:0%
+something bad or not so it's actually
+really hard to decide so one way to
+
+ align:start position:0%
+really hard to decide so one way to
+ 
+
+ align:start position:0%
+really hard to decide so one way to
+think of native client is it's a
+
+ align:start position:0%
+think of native client is it's a
+ 
+
+ align:start position:0%
+think of native client is it's a
+mechanism by which users can actually
+
+ align:start position:0%
+mechanism by which users can actually
+ 
+
+ align:start position:0%
+mechanism by which users can actually
+get some confidence whether they should
+
+ align:start position:0%
+get some confidence whether they should
+ 
+
+ align:start position:0%
+get some confidence whether they should
+say yes or not to running this thing so
+
+ align:start position:0%
+say yes or not to running this thing so
+ 
+
+ align:start position:0%
+say yes or not to running this thing so
+in practice I guess like Paul Jan was
+
+ align:start position:0%
+in practice I guess like Paul Jan was
+ 
+
+ align:start position:0%
+in practice I guess like Paul Jan was
+giving this guest lecture last week and
+
+ align:start position:0%
+giving this guest lecture last week and
+ 
+
+ align:start position:0%
+giving this guest lecture last week and
+he suggested that you should enable this
+
+ align:start position:0%
+he suggested that you should enable this
+ 
+
+ align:start position:0%
+he suggested that you should enable this
+click to play extension and chrome so
+
+ align:start position:0%
+click to play extension and chrome so
+ 
+
+ align:start position:0%
+click to play extension and chrome so
+every extension including native client
+
+ align:start position:0%
+every extension including native client
+ 
+
+ align:start position:0%
+every extension including native client
+you should first click on this thing
+
+ align:start position:0%
+you should first click on this thing
+ 
+
+ align:start position:0%
+you should first click on this thing
+before it starts running so in some way
+
+ align:start position:0%
+before it starts running so in some way
+ 
+
+ align:start position:0%
+before it starts running so in some way
+let's ask the user but then the user
+
+ align:start position:0%
+let's ask the user but then the user
+ 
+
+ align:start position:0%
+let's ask the user but then the user
+actually has some sense that well if I
+
+ align:start position:0%
+actually has some sense that well if I
+ 
+
+ align:start position:0%
+actually has some sense that well if I
+click it I'm still hopefully safe in the
+
+ align:start position:0%
+click it I'm still hopefully safe in the
+ 
+
+ align:start position:0%
+click it I'm still hopefully safe in the
+sense that native client will protect me
+
+ align:start position:0%
+sense that native client will protect me
+ 
+
+ align:start position:0%
+sense that native client will protect me
+so the two aren't necessarily exclusive
+
+ align:start position:0%
+so the two aren't necessarily exclusive
+ 
+
+ align:start position:0%
+so the two aren't necessarily exclusive
+but you really want some technical
+
+ align:start position:0%
+but you really want some technical
+ 
+
+ align:start position:0%
+but you really want some technical
+guarantee from native client that
+
+ align:start position:0%
+guarantee from native client that
+ 
+
+ align:start position:0%
+guarantee from native client that
+ensures that even if you say yes there's
+
+ align:start position:0%
+ensures that even if you say yes there's
+ 
+
+ align:start position:0%
+ensures that even if you say yes there's
+something meaningful that is enforcing
+
+ align:start position:0%
+something meaningful that is enforcing
+ 
+
+ align:start position:0%
+something meaningful that is enforcing
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+security soes this make
+
+ align:start position:0%
+security soes this make
+ 
+
+ align:start position:0%
+security soes this make
+sense okay so the other I guess approach
+
+ align:start position:0%
+sense okay so the other I guess approach
+ 
+
+ align:start position:0%
+sense okay so the other I guess approach
+that uh people have taken is uh to use
+
+ align:start position:0%
+that uh people have taken is uh to use
+ 
+
+ align:start position:0%
+that uh people have taken is uh to use
+Os or Hardware sandboxing or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isolation so this is uh things we looked
+
+ align:start position:0%
+isolation so this is uh things we looked
+ 
+
+ align:start position:0%
+isolation so this is uh things we looked
+at in the last couple of lectures so uh
+
+ align:start position:0%
+at in the last couple of lectures so uh
+ 
+
+ align:start position:0%
+at in the last couple of lectures so uh
+maybe you would use Unix isolation
+
+ align:start position:0%
+maybe you would use Unix isolation
+ 
+
+ align:start position:0%
+maybe you would use Unix isolation
+mechanisms uh maybe if you had something
+
+ align:start position:0%
+mechanisms uh maybe if you had something
+ 
+
+ align:start position:0%
+mechanisms uh maybe if you had something
+more sophisticated if you're running on
+
+ align:start position:0%
+more sophisticated if you're running on
+ 
+
+ align:start position:0%
+more sophisticated if you're running on
+FreeBSD maybe You' use capsicum it seems
+
+ align:start position:0%
+FreeBSD maybe You' use capsicum it seems
+ 
+
+ align:start position:0%
+FreeBSD maybe You' use capsicum it seems
+very well suited to sandboxing some
+
+ align:start position:0%
+very well suited to sandboxing some
+ 
+
+ align:start position:0%
+very well suited to sandboxing some
+piece of code because you could give it
+
+ align:start position:0%
+piece of code because you could give it
+ 
+
+ align:start position:0%
+piece of code because you could give it
+very few two capabilities and then seems
+
+ align:start position:0%
+very few two capabilities and then seems
+ 
+
+ align:start position:0%
+very few two capabilities and then seems
+great and Linux has a similar mechanism
+
+ align:start position:0%
+great and Linux has a similar mechanism
+ 
+
+ align:start position:0%
+great and Linux has a similar mechanism
+called SEC comp that we briefly touched
+
+ align:start position:0%
+called SEC comp that we briefly touched
+ 
+
+ align:start position:0%
+called SEC comp that we briefly touched
+on in last lecture that could allow you
+
+ align:start position:0%
+on in last lecture that could allow you
+ 
+
+ align:start position:0%
+on in last lecture that could allow you
+to do similar
+
+ align:start position:0%
+to do similar
+ 
+
+ align:start position:0%
+to do similar
+things so it seems like there's already
+
+ align:start position:0%
+things so it seems like there's already
+ 
+
+ align:start position:0%
+things so it seems like there's already
+a mechanism for running code and
+
+ align:start position:0%
+a mechanism for running code and
+ 
+
+ align:start position:0%
+a mechanism for running code and
+isolation on your machine why are these
+
+ align:start position:0%
+isolation on your machine why are these
+ 
+
+ align:start position:0%
+isolation on your machine why are these
+guys opposed to using this existing
+
+ align:start position:0%
+guys opposed to using this existing
+ 
+
+ align:start position:0%
+guys opposed to using this existing
+solution and they're like Reinventing
+
+ align:start position:0%
+solution and they're like Reinventing
+ 
+
+ align:start position:0%
+solution and they're like Reinventing
+the wheel for some
+
+ align:start position:0%
+the wheel for some
+ 
+
+ align:start position:0%
+the wheel for some
+reason so what's going
+
+ align:start position:0%
+reason so what's going
+ 
+
+ align:start position:0%
+reason so what's going
+on yeah oh yeah maybe they want to
+
+ align:start position:0%
+on yeah oh yeah maybe they want to
+ 
+
+ align:start position:0%
+on yeah oh yeah maybe they want to
+minimize the PCD
+
+ align:start position:0%
+minimize the PCD
+ 
+
+ align:start position:0%
+minimize the PCD
+yeah so in some sense maybe they don't
+
+ align:start position:0%
+yeah so in some sense maybe they don't
+ 
+
+ align:start position:0%
+yeah so in some sense maybe they don't
+want to trust uh the operating system so
+
+ align:start position:0%
+want to trust uh the operating system so
+ 
+
+ align:start position:0%
+want to trust uh the operating system so
+maybe they're here they're actually
+
+ align:start position:0%
+maybe they're here they're actually
+ 
+
+ align:start position:0%
+maybe they're here they're actually
+worried about OS
+
+ align:start position:0%
+worried about OS
+ 
+
+ align:start position:0%
+worried about OS
+bugs it might be that the FreeBSD kernel
+
+ align:start position:0%
+bugs it might be that the FreeBSD kernel
+ 
+
+ align:start position:0%
+bugs it might be that the FreeBSD kernel
+or the Linux kernel has quite a lot of C
+
+ align:start position:0%
+or the Linux kernel has quite a lot of C
+ 
+
+ align:start position:0%
+or the Linux kernel has quite a lot of C
+code written that they don't want to
+
+ align:start position:0%
+code written that they don't want to
+ 
+
+ align:start position:0%
+code written that they don't want to
+audit for correctness or maybe can't
+
+ align:start position:0%
+audit for correctness or maybe can't
+ 
+
+ align:start position:0%
+audit for correctness or maybe can't
+even audit for correctness even if they
+
+ align:start position:0%
+even audit for correctness even if they
+ 
+
+ align:start position:0%
+even audit for correctness even if they
+wanted to and in one of these capsicum
+
+ align:start position:0%
+wanted to and in one of these capsicum
+ 
+
+ align:start position:0%
+wanted to and in one of these capsicum
+or seccom based isolation plans you
+
+ align:start position:0%
+or seccom based isolation plans you
+ 
+
+ align:start position:0%
+or seccom based isolation plans you
+probably do trust quite a bit of code in
+
+ align:start position:0%
+probably do trust quite a bit of code in
+ 
+
+ align:start position:0%
+probably do trust quite a bit of code in
+the kernel to be correct for the sandbox
+
+ align:start position:0%
+the kernel to be correct for the sandbox
+ 
+
+ align:start position:0%
+the kernel to be correct for the sandbox
+to actually hold and enforce
+
+ align:start position:0%
+to actually hold and enforce
+ 
+
+ align:start position:0%
+to actually hold and enforce
+isolation yeah as you get a lot more uh
+
+ align:start position:0%
+isolation yeah as you get a lot more uh
+ 
+
+ align:start position:0%
+isolation yeah as you get a lot more uh
+ways to use browsers and stuff like you
+
+ align:start position:0%
+ways to use browsers and stuff like you
+ 
+
+ align:start position:0%
+ways to use browsers and stuff like you
+have to deal with having some sort of
+
+ align:start position:0%
+have to deal with having some sort of
+ 
+
+ align:start position:0%
+have to deal with having some sort of
+thing and doing with it on like IOS and
+
+ align:start position:0%
+thing and doing with it on like IOS and
+ 
+
+ align:start position:0%
+thing and doing with it on like IOS and
+Android and all these other things
+
+ align:start position:0%
+Android and all these other things
+ 
+
+ align:start position:0%
+Android and all these other things
+access yeah so so actually another
+
+ align:start position:0%
+access yeah so so actually another
+ 
+
+ align:start position:0%
+access yeah so so actually another
+interesting consideration is that not
+
+ align:start position:0%
+interesting consideration is that not
+ 
+
+ align:start position:0%
+interesting consideration is that not
+only might the os's have bugs but
+
+ align:start position:0%
+only might the os's have bugs but
+ 
+
+ align:start position:0%
+only might the os's have bugs but
+actually the os's are incompatible with
+
+ align:start position:0%
+actually the os's are incompatible with
+ 
+
+ align:start position:0%
+actually the os's are incompatible with
+each other in some ways uh meaning that
+
+ align:start position:0%
+each other in some ways uh meaning that
+ 
+
+ align:start position:0%
+each other in some ways uh meaning that
+each OS has its own mechanis like right
+
+ align:start position:0%
+each OS has its own mechanis like right
+ 
+
+ align:start position:0%
+each OS has its own mechanis like right
+here well there's Unix there's capsicum
+
+ align:start position:0%
+here well there's Unix there's capsicum
+ 
+
+ align:start position:0%
+here well there's Unix there's capsicum
+there's setc comp and this is just the
+
+ align:start position:0%
+there's setc comp and this is just the
+ 
+
+ align:start position:0%
+there's setc comp and this is just the
+Unix variants there's Mac OS seat belt
+
+ align:start position:0%
+Unix variants there's Mac OS seat belt
+ 
+
+ align:start position:0%
+Unix variants there's Mac OS seat belt
+there's windows something else and and
+
+ align:start position:0%
+there's windows something else and and
+ 
+
+ align:start position:0%
+there's windows something else and and
+this just keeps going on and on so as a
+
+ align:start position:0%
+this just keeps going on and on so as a
+ 
+
+ align:start position:0%
+this just keeps going on and on so as a
+result every platform you will have to
+
+ align:start position:0%
+result every platform you will have to
+ 
+
+ align:start position:0%
+result every platform you will have to
+use a different isolation mechanism and
+
+ align:start position:0%
+use a different isolation mechanism and
+ 
+
+ align:start position:0%
+use a different isolation mechanism and
+the thing that actually bothers them is
+
+ align:start position:0%
+the thing that actually bothers them is
+ 
+
+ align:start position:0%
+the thing that actually bothers them is
+not so much they'll have to write
+
+ align:start position:0%
+not so much they'll have to write
+ 
+
+ align:start position:0%
+not so much they'll have to write
+different code for mac and windows and
+
+ align:start position:0%
+different code for mac and windows and
+ 
+
+ align:start position:0%
+different code for mac and windows and
+Linux but more that this impacts how you
+
+ align:start position:0%
+Linux but more that this impacts how you
+ 
+
+ align:start position:0%
+Linux but more that this impacts how you
+write the thing inside of the sandbox
+
+ align:start position:0%
+write the thing inside of the sandbox
+ 
+
+ align:start position:0%
+write the thing inside of the sandbox
+because a native client you actually
+
+ align:start position:0%
+because a native client you actually
+ 
+
+ align:start position:0%
+because a native client you actually
+write a piece of code and it runs the
+
+ align:start position:0%
+write a piece of code and it runs the
+ 
+
+ align:start position:0%
+write a piece of code and it runs the
+same way or it's the same piece of code
+
+ align:start position:0%
+same way or it's the same piece of code
+ 
+
+ align:start position:0%
+same way or it's the same piece of code
+that runs on Apple or Windows or Linux
+
+ align:start position:0%
+that runs on Apple or Windows or Linux
+ 
+
+ align:start position:0%
+that runs on Apple or Windows or Linux
+systems and if you use these isolation
+
+ align:start position:0%
+systems and if you use these isolation
+ 
+
+ align:start position:0%
+systems and if you use these isolation
+mechanisms they actually impose
+
+ align:start position:0%
+mechanisms they actually impose
+ 
+
+ align:start position:0%
+mechanisms they actually impose
+different restrictions on the program
+
+ align:start position:0%
+different restrictions on the program
+ 
+
+ align:start position:0%
+different restrictions on the program
+being sandboxed so you'll have to run
+
+ align:start position:0%
+being sandboxed so you'll have to run
+ 
+
+ align:start position:0%
+being sandboxed so you'll have to run
+right one program that's going to run
+
+ align:start position:0%
+right one program that's going to run
+ 
+
+ align:start position:0%
+right one program that's going to run
+inside of a Linux sandbox another
+
+ align:start position:0%
+inside of a Linux sandbox another
+ 
+
+ align:start position:0%
+inside of a Linux sandbox another
+program inside of a Windows sandbox and
+
+ align:start position:0%
+program inside of a Windows sandbox and
+ 
+
+ align:start position:0%
+program inside of a Windows sandbox and
+so on so this is actually not acceptable
+
+ align:start position:0%
+so on so this is actually not acceptable
+ 
+
+ align:start position:0%
+so on so this is actually not acceptable
+to them they don't want to deal with
+
+ align:start position:0%
+to them they don't want to deal with
+ 
+
+ align:start position:0%
+to them they don't want to deal with
+these kinds of
+
+ align:start position:0%
+these kinds of
+ 
+
+ align:start position:0%
+these kinds of
+problems so are there other
+
+ align:start position:0%
+problems so are there other
+ 
+
+ align:start position:0%
+problems so are there other
+considerations yeah presumably
+
+ align:start position:0%
+considerations yeah presumably
+ 
+
+ align:start position:0%
+considerations yeah presumably
+performance as well because if you if
+
+ align:start position:0%
+performance as well because if you if
+ 
+
+ align:start position:0%
+performance as well because if you if
+you use a uh capsum you need to Fork up
+
+ align:start position:0%
+you use a uh capsum you need to Fork up
+ 
+
+ align:start position:0%
+you use a uh capsum you need to Fork up
+a separate process for whatever is
+
+ align:start position:0%
+a separate process for whatever is
+ 
+
+ align:start position:0%
+a separate process for whatever is
+running inside the sandbox whereas here
+
+ align:start position:0%
+running inside the sandbox whereas here
+ 
+
+ align:start position:0%
+running inside the sandbox whereas here
+they can actually run it in the same in
+
+ align:start position:0%
+they can actually run it in the same in
+ 
+
+ align:start position:0%
+they can actually run it in the same in
+that's true yeah so potentially the
+
+ align:start position:0%
+that's true yeah so potentially the
+ 
+
+ align:start position:0%
+that's true yeah so potentially the
+approach they take the software fault
+
+ align:start position:0%
+approach they take the software fault
+ 
+
+ align:start position:0%
+approach they take the software fault
+isolation plan is actually highly
+
+ align:start position:0%
+isolation plan is actually highly
+ 
+
+ align:start position:0%
+isolation plan is actually highly
+performant and could outperform these uh
+
+ align:start position:0%
+performant and could outperform these uh
+ 
+
+ align:start position:0%
+performant and could outperform these uh
+sandboxes at the OS level it turns out
+
+ align:start position:0%
+sandboxes at the OS level it turns out
+ 
+
+ align:start position:0%
+sandboxes at the OS level it turns out
+that a native client actually use both
+
+ align:start position:0%
+that a native client actually use both
+ 
+
+ align:start position:0%
+that a native client actually use both
+their sandbox and the OS sandbox just
+
+ align:start position:0%
+their sandbox and the OS sandbox just
+ 
+
+ align:start position:0%
+their sandbox and the OS sandbox just
+for extra precaution for safety so they
+
+ align:start position:0%
+for extra precaution for safety so they
+ 
+
+ align:start position:0%
+for extra precaution for safety so they
+don't actually win on performance in
+
+ align:start position:0%
+don't actually win on performance in
+ 
+
+ align:start position:0%
+don't actually win on performance in
+their implementation but they could
+
+ align:start position:0%
+their implementation but they could
+ 
+
+ align:start position:0%
+their implementation but they could
+you're right yeah can there be some like
+
+ align:start position:0%
+you're right yeah can there be some like
+ 
+
+ align:start position:0%
+you're right yeah can there be some like
+control aspect to it they can control
+
+ align:start position:0%
+control aspect to it they can control
+ 
+
+ align:start position:0%
+control aspect to it they can control
+what happens in the browser but if they
+
+ align:start position:0%
+what happens in the browser but if they
+ 
+
+ align:start position:0%
+what happens in the browser but if they
+send C off to the client's machine into
+
+ align:start position:0%
+send C off to the client's machine into
+ 
+
+ align:start position:0%
+send C off to the client's machine into
+their OS sort of don't necessarily know
+
+ align:start position:0%
+their OS sort of don't necessarily know
+ 
+
+ align:start position:0%
+their OS sort of don't necessarily know
+what might be happening so I guess one
+
+ align:start position:0%
+what might be happening so I guess one
+ 
+
+ align:start position:0%
+what might be happening so I guess one
+maybe one way to think of that is that
+
+ align:start position:0%
+maybe one way to think of that is that
+ 
+
+ align:start position:0%
+maybe one way to think of that is that
+yeah the OS might have bugs so my OS
+
+ align:start position:0%
+yeah the OS might have bugs so my OS
+ 
+
+ align:start position:0%
+yeah the OS might have bugs so my OS
+might not do as good of a job at
+
+ align:start position:0%
+might not do as good of a job at
+ 
+
+ align:start position:0%
+might not do as good of a job at
+sandboxing it or maybe there's you know
+
+ align:start position:0%
+sandboxing it or maybe there's you know
+ 
+
+ align:start position:0%
+sandboxing it or maybe there's you know
+the interfaces are all different so you
+
+ align:start position:0%
+the interfaces are all different so you
+ 
+
+ align:start position:0%
+the interfaces are all different so you
+don't know what the O is going to expose
+
+ align:start position:0%
+don't know what the O is going to expose
+ 
+
+ align:start position:0%
+don't know what the O is going to expose
+yeah uh so doesn't like prevent the cach
+
+ align:start position:0%
+yeah uh so doesn't like prevent the cach
+ 
+
+ align:start position:0%
+yeah uh so doesn't like prevent the cach
+doing some bad things like there are a
+
+ align:start position:0%
+doing some bad things like there are a
+ 
+
+ align:start position:0%
+doing some bad things like there are a
+lot of cases of bad things that the code
+
+ align:start position:0%
+lot of cases of bad things that the code
+ 
+
+ align:start position:0%
+lot of cases of bad things that the code
+can just do like maybe you want to
+
+ align:start position:0%
+can just do like maybe you want to
+ 
+
+ align:start position:0%
+can just do like maybe you want to
+statically analyze it just as one to sit
+
+ align:start position:0%
+statically analyze it just as one to sit
+ 
+
+ align:start position:0%
+statically analyze it just as one to sit
+in a loop and then not allow that as a
+
+ align:start position:0%
+in a loop and then not allow that as a
+ 
+
+ align:start position:0%
+in a loop and then not allow that as a
+valid program so you could right so
+
+ align:start position:0%
+valid program so you could right so
+ 
+
+ align:start position:0%
+valid program so you could right so
+their approach is quite powerful in the
+
+ align:start position:0%
+their approach is quite powerful in the
+ 
+
+ align:start position:0%
+their approach is quite powerful in the
+sense that you could try to look for
+
+ align:start position:0%
+sense that you could try to look for
+ 
+
+ align:start position:0%
+sense that you could try to look for
+various kinds of problems in the code
+
+ align:start position:0%
+various kinds of problems in the code
+ 
+
+ align:start position:0%
+various kinds of problems in the code
+like maybe infinite Loops Etc it's hard
+
+ align:start position:0%
+like maybe infinite Loops Etc it's hard
+ 
+
+ align:start position:0%
+like maybe infinite Loops Etc it's hard
+to decide kind of like the halting
+
+ align:start position:0%
+to decide kind of like the halting
+ 
+
+ align:start position:0%
+to decide kind of like the halting
+problem whether it's going to have
+
+ align:start position:0%
+problem whether it's going to have
+ 
+
+ align:start position:0%
+problem whether it's going to have
+infinite Loops or not uh but in
+
+ align:start position:0%
+infinite Loops or not uh but in
+ 
+
+ align:start position:0%
+infinite Loops or not uh but in
+principle you might be able to catch
+
+ align:start position:0%
+principle you might be able to catch
+ 
+
+ align:start position:0%
+principle you might be able to catch
+some problems um I think one actually
+
+ align:start position:0%
+some problems um I think one actually
+ 
+
+ align:start position:0%
+some problems um I think one actually
+interesting example that I almost didn't
+
+ align:start position:0%
+interesting example that I almost didn't
+ 
+
+ align:start position:0%
+interesting example that I almost didn't
+realize sort of existed before reading
+
+ align:start position:0%
+realize sort of existed before reading
+ 
+
+ align:start position:0%
+realize sort of existed before reading
+this paper is these guys are worried
+
+ align:start position:0%
+this paper is these guys are worried
+ 
+
+ align:start position:0%
+this paper is these guys are worried
+about Hardware bugs as well
+
+ align:start position:0%
+about Hardware bugs as well
+ 
+
+ align:start position:0%
+about Hardware bugs as well
+that not only are they worried that the
+
+ align:start position:0%
+that not only are they worried that the
+ 
+
+ align:start position:0%
+that not only are they worried that the
+operating system might have
+
+ align:start position:0%
+operating system might have
+ 
+
+ align:start position:0%
+operating system might have
+vulnerabilities that the malicious code
+
+ align:start position:0%
+vulnerabilities that the malicious code
+ 
+
+ align:start position:0%
+vulnerabilities that the malicious code
+will exploit but also that the processor
+
+ align:start position:0%
+will exploit but also that the processor
+ 
+
+ align:start position:0%
+will exploit but also that the processor
+itself has some instructions that will
+
+ align:start position:0%
+itself has some instructions that will
+ 
+
+ align:start position:0%
+itself has some instructions that will
+hang it or it'll reboot your machine and
+
+ align:start position:0%
+hang it or it'll reboot your machine and
+ 
+
+ align:start position:0%
+hang it or it'll reboot your machine and
+in principle your Hardware shouldn't
+
+ align:start position:0%
+in principle your Hardware shouldn't
+ 
+
+ align:start position:0%
+in principle your Hardware shouldn't
+have such bugs because the operating
+
+ align:start position:0%
+have such bugs because the operating
+ 
+
+ align:start position:0%
+have such bugs because the operating
+system relies on the hardware to trap
+
+ align:start position:0%
+system relies on the hardware to trap
+ 
+
+ align:start position:0%
+system relies on the hardware to trap
+into the kernel if there's anything bad
+
+ align:start position:0%
+into the kernel if there's anything bad
+ 
+
+ align:start position:0%
+into the kernel if there's anything bad
+executing in user mode so that the
+
+ align:start position:0%
+executing in user mode so that the
+ 
+
+ align:start position:0%
+executing in user mode so that the
+operating system can take care of it but
+
+ align:start position:0%
+operating system can take care of it but
+ 
+
+ align:start position:0%
+operating system can take care of it but
+experimentally it turns out that
+
+ align:start position:0%
+experimentally it turns out that
+ 
+
+ align:start position:0%
+experimentally it turns out that
+processors are so complicated they do
+
+ align:start position:0%
+processors are so complicated they do
+ 
+
+ align:start position:0%
+processors are so complicated they do
+have bugs and these guys actually say
+
+ align:start position:0%
+have bugs and these guys actually say
+ 
+
+ align:start position:0%
+have bugs and these guys actually say
+well we actually found some evidence
+
+ align:start position:0%
+well we actually found some evidence
+ 
+
+ align:start position:0%
+well we actually found some evidence
+that this happens if you have a some
+
+ align:start position:0%
+that this happens if you have a some
+ 
+
+ align:start position:0%
+that this happens if you have a some
+complicated instruction the CPU wasn't
+
+ align:start position:0%
+complicated instruction the CPU wasn't
+ 
+
+ align:start position:0%
+complicated instruction the CPU wasn't
+expecting the CPU will actually halt
+
+ align:start position:0%
+expecting the CPU will actually halt
+ 
+
+ align:start position:0%
+expecting the CPU will actually halt
+instead of trapping to the kernel so
+
+ align:start position:0%
+instead of trapping to the kernel so
+ 
+
+ align:start position:0%
+instead of trapping to the kernel so
+that seems bad but I guess it's not as
+
+ align:start position:0%
+that seems bad but I guess it's not as
+ 
+
+ align:start position:0%
+that seems bad but I guess it's not as
+disastrous if I'm sort of only running
+
+ align:start position:0%
+disastrous if I'm sort of only running
+ 
+
+ align:start position:0%
+disastrous if I'm sort of only running
+reasonable things on my laptop but it is
+
+ align:start position:0%
+reasonable things on my laptop but it is
+ 
+
+ align:start position:0%
+reasonable things on my laptop but it is
+bad if you visit some web page and your
+
+ align:start position:0%
+bad if you visit some web page and your
+ 
+
+ align:start position:0%
+bad if you visit some web page and your
+computer hangs so they want basically a
+
+ align:start position:0%
+computer hangs so they want basically a
+ 
+
+ align:start position:0%
+computer hangs so they want basically a
+stronger level of protection for these
+
+ align:start position:0%
+stronger level of protection for these
+ 
+
+ align:start position:0%
+stronger level of protection for these
+native client modules than what you
+
+ align:start position:0%
+native client modules than what you
+ 
+
+ align:start position:0%
+native client modules than what you
+would get out of
+
+ align:start position:0%
+would get out of
+ 
+
+ align:start position:0%
+would get out of
+sort of os level isolation even from a
+
+ align:start position:0%
+sort of os level isolation even from a
+ 
+
+ align:start position:0%
+sort of os level isolation even from a
+hardware B bug standpoint so that's
+
+ align:start position:0%
+hardware B bug standpoint so that's
+ 
+
+ align:start position:0%
+hardware B bug standpoint so that's
+actually pretty cool they're like really
+
+ align:start position:0%
+actually pretty cool they're like really
+ 
+
+ align:start position:0%
+actually pretty cool they're like really
+paranoid about uh security uh including
+
+ align:start position:0%
+paranoid about uh security uh including
+ 
+
+ align:start position:0%
+paranoid about uh security uh including
+even Hardware uh
+
+ align:start position:0%
+even Hardware uh
+ 
+
+ align:start position:0%
+even Hardware uh
+problems all right so any questions
+
+ align:start position:0%
+problems all right so any questions
+ 
+
+ align:start position:0%
+problems all right so any questions
+about all these alternativ how that
+
+ align:start position:0%
+about all these alternativ how that
+ 
+
+ align:start position:0%
+about all these alternativ how that
+works or why these guys are not excited
+
+ align:start position:0%
+works or why these guys are not excited
+ 
+
+ align:start position:0%
+works or why these guys are not excited
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+them make
+
+ align:start position:0%
+them make
+ 
+
+ align:start position:0%
+them make
+sense all right so I guess let's uh try
+
+ align:start position:0%
+sense all right so I guess let's uh try
+ 
+
+ align:start position:0%
+sense all right so I guess let's uh try
+to look at now how Native client does
+
+ align:start position:0%
+to look at now how Native client does
+ 
+
+ align:start position:0%
+to look at now how Native client does
+actually uh decide to s box processes so
+
+ align:start position:0%
+actually uh decide to s box processes so
+ 
+
+ align:start position:0%
+actually uh decide to s box processes so
+let me pull up these
+
+ align:start position:0%
+let me pull up these
+ 
+
+ align:start position:0%
+let me pull up these
+boards so native client takes this
+
+ align:start position:0%
+boards so native client takes this
+ 
+
+ align:start position:0%
+boards so native client takes this
+different approach that's uh in general
+
+ align:start position:0%
+different approach that's uh in general
+ 
+
+ align:start position:0%
+different approach that's uh in general
+called software fault
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isolation and the plan is to actually
+
+ align:start position:0%
+isolation and the plan is to actually
+ 
+
+ align:start position:0%
+isolation and the plan is to actually
+not rely on the operating system or
+
+ align:start position:0%
+not rely on the operating system or
+ 
+
+ align:start position:0%
+not rely on the operating system or
+Hardware to check things at runtime but
+
+ align:start position:0%
+Hardware to check things at runtime but
+ 
+
+ align:start position:0%
+Hardware to check things at runtime but
+instead to somehow look at the
+
+ align:start position:0%
+instead to somehow look at the
+ 
+
+ align:start position:0%
+instead to somehow look at the
+instructions ahead of time and decide
+
+ align:start position:0%
+instructions ahead of time and decide
+ 
+
+ align:start position:0%
+instructions ahead of time and decide
+that they're always going to be safe to
+
+ align:start position:0%
+that they're always going to be safe to
+ 
+
+ align:start position:0%
+that they're always going to be safe to
+execute so actually you actually look at
+
+ align:start position:0%
+execute so actually you actually look at
+ 
+
+ align:start position:0%
+execute so actually you actually look at
+the binary and you check all the
+
+ align:start position:0%
+the binary and you check all the
+ 
+
+ align:start position:0%
+the binary and you check all the
+possible instructions to see whether
+
+ align:start position:0%
+possible instructions to see whether
+ 
+
+ align:start position:0%
+possible instructions to see whether
+there're going to be safe instructions
+
+ align:start position:0%
+there're going to be safe instructions
+ 
+
+ align:start position:0%
+there're going to be safe instructions
+or unsafe instructions and once you've
+
+ align:start position:0%
+or unsafe instructions and once you've
+ 
+
+ align:start position:0%
+or unsafe instructions and once you've
+decided that it's all going to be safe
+
+ align:start position:0%
+decided that it's all going to be safe
+ 
+
+ align:start position:0%
+decided that it's all going to be safe
+you can just jump in and start executing
+
+ align:start position:0%
+you can just jump in and start executing
+ 
+
+ align:start position:0%
+you can just jump in and start executing
+because you know it's all composed of
+
+ align:start position:0%
+because you know it's all composed of
+ 
+
+ align:start position:0%
+because you know it's all composed of
+safe things so it cannot go wrong so
+
+ align:start position:0%
+safe things so it cannot go wrong so
+ 
+
+ align:start position:0%
+safe things so it cannot go wrong so
+we'll talk about exactly what this means
+
+ align:start position:0%
+we'll talk about exactly what this means
+ 
+
+ align:start position:0%
+we'll talk about exactly what this means
+but roughly what they're going to do is
+
+ align:start position:0%
+but roughly what they're going to do is
+ 
+
+ align:start position:0%
+but roughly what they're going to do is
+they're going to look at pretty much
+
+ align:start position:0%
+they're going to look at pretty much
+ 
+
+ align:start position:0%
+they're going to look at pretty much
+every instruction in the binary code
+
+ align:start position:0%
+every instruction in the binary code
+ 
+
+ align:start position:0%
+every instruction in the binary code
+that is served up to the browser and
+
+ align:start position:0%
+that is served up to the browser and
+ 
+
+ align:start position:0%
+that is served up to the browser and
+they're going to decide that particular
+
+ align:start position:0%
+they're going to decide that particular
+ 
+
+ align:start position:0%
+they're going to decide that particular
+instructions are going to be safe or
+
+ align:start position:0%
+instructions are going to be safe or
+ 
+
+ align:start position:0%
+instructions are going to be safe or
+unsafe so what do they do for safe
+
+ align:start position:0%
+unsafe so what do they do for safe
+ 
+
+ align:start position:0%
+unsafe so what do they do for safe
+instructions well they're they're just
+
+ align:start position:0%
+instructions well they're they're just
+ 
+
+ align:start position:0%
+instructions well they're they're just
+going to allow them uh what's an example
+
+ align:start position:0%
+going to allow them uh what's an example
+ 
+
+ align:start position:0%
+going to allow them uh what's an example
+of a safe instruction what are they
+
+ align:start position:0%
+of a safe instruction what are they
+ 
+
+ align:start position:0%
+of a safe instruction what are they
+thinking of that doesn't need any extra
+
+ align:start position:0%
+thinking of that doesn't need any extra
+ 
+
+ align:start position:0%
+thinking of that doesn't need any extra
+checks or protection
+
+ align:start position:0%
+checks or protection
+ 
+
+ align:start position:0%
+checks or protection
+Etc yeah so like any kind of ALU
+
+ align:start position:0%
+Etc yeah so like any kind of ALU
+ 
+
+ align:start position:0%
+Etc yeah so like any kind of ALU
+operation basically yeah MTH
+
+ align:start position:0%
+operation basically yeah MTH
+ 
+
+ align:start position:0%
+operation basically yeah MTH
+presumably
+
+ align:start position:0%
+presumably
+ 
+
+ align:start position:0%
+presumably
+moves between registers uh and so on so
+
+ align:start position:0%
+moves between registers uh and so on so
+ 
+
+ align:start position:0%
+moves between registers uh and so on so
+this doesn't actually affect the
+
+ align:start position:0%
+this doesn't actually affect the
+ 
+
+ align:start position:0%
+this doesn't actually affect the
+security of the system as far as their
+
+ align:start position:0%
+security of the system as far as their
+ 
+
+ align:start position:0%
+security of the system as far as their
+concern because all they really care
+
+ align:start position:0%
+concern because all they really care
+ 
+
+ align:start position:0%
+concern because all they really care
+about is things like memory safety where
+
+ align:start position:0%
+about is things like memory safety where
+ 
+
+ align:start position:0%
+about is things like memory safety where
+what code you execute and so on um so as
+
+ align:start position:0%
+what code you execute and so on um so as
+ 
+
+ align:start position:0%
+what code you execute and so on um so as
+long as you're just Computing on some
+
+ align:start position:0%
+long as you're just Computing on some
+ 
+
+ align:start position:0%
+long as you're just Computing on some
+stuff and registers they don't really
+
+ align:start position:0%
+stuff and registers they don't really
+ 
+
+ align:start position:0%
+stuff and registers they don't really
+care it's not going to affect the rest
+
+ align:start position:0%
+care it's not going to affect the rest
+ 
+
+ align:start position:0%
+care it's not going to affect the rest
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+browser so what about unsafe operations
+
+ align:start position:0%
+browser so what about unsafe operations
+ 
+
+ align:start position:0%
+browser so what about unsafe operations
+I guess these are things that they might
+
+ align:start position:0%
+I guess these are things that they might
+ 
+
+ align:start position:0%
+I guess these are things that they might
+care much more about so this is anything
+
+ align:start position:0%
+care much more about so this is anything
+ 
+
+ align:start position:0%
+care much more about so this is anything
+that maybe does a memory access or maybe
+
+ align:start position:0%
+that maybe does a memory access or maybe
+ 
+
+ align:start position:0%
+that maybe does a memory access or maybe
+some privileged
+
+ align:start position:0%
+some privileged
+ 
+
+ align:start position:0%
+some privileged
+instruction maybe invoking a system call
+
+ align:start position:0%
+instruction maybe invoking a system call
+ 
+
+ align:start position:0%
+instruction maybe invoking a system call
+on this machine um maybe trying to jump
+
+ align:start position:0%
+on this machine um maybe trying to jump
+ 
+
+ align:start position:0%
+on this machine um maybe trying to jump
+out of the sandbox who knows what so for
+
+ align:start position:0%
+out of the sandbox who knows what so for
+ 
+
+ align:start position:0%
+out of the sandbox who knows what so for
+these kinds of instructions they're
+
+ align:start position:0%
+these kinds of instructions they're
+ 
+
+ align:start position:0%
+these kinds of instructions they're
+going to do one of two things if the
+
+ align:start position:0%
+going to do one of two things if the
+ 
+
+ align:start position:0%
+going to do one of two things if the
+instruction actually is necessary for
+
+ align:start position:0%
+instruction actually is necessary for
+ 
+
+ align:start position:0%
+instruction actually is necessary for
+the application to do its job like
+
+ align:start position:0%
+the application to do its job like
+ 
+
+ align:start position:0%
+the application to do its job like
+accessing memory seems important then
+
+ align:start position:0%
+accessing memory seems important then
+ 
+
+ align:start position:0%
+accessing memory seems important then
+they're going to somehow make sure that
+
+ align:start position:0%
+they're going to somehow make sure that
+ 
+
+ align:start position:0%
+they're going to somehow make sure that
+they can execute this unsafe instruction
+
+ align:start position:0%
+they can execute this unsafe instruction
+ 
+
+ align:start position:0%
+they can execute this unsafe instruction
+safely or if you're jumping around for
+
+ align:start position:0%
+safely or if you're jumping around for
+ 
+
+ align:start position:0%
+safely or if you're jumping around for
+example in the program's address space
+
+ align:start position:0%
+example in the program's address space
+ 
+
+ align:start position:0%
+example in the program's address space
+then what they're going to do is somehow
+
+ align:start position:0%
+then what they're going to do is somehow
+ 
+
+ align:start position:0%
+then what they're going to do is somehow
+instrument the
+
+ align:start position:0%
+instrument the
+ 
+
+ align:start position:0%
+instrument the
+instruction and what instrumenting the
+
+ align:start position:0%
+instruction and what instrumenting the
+ 
+
+ align:start position:0%
+instruction and what instrumenting the
+instruction means is that you used to
+
+ align:start position:0%
+instruction means is that you used to
+ 
+
+ align:start position:0%
+instruction means is that you used to
+have one unsafe instruction that
+
+ align:start position:0%
+have one unsafe instruction that
+ 
+
+ align:start position:0%
+have one unsafe instruction that
+sometimes does good things that the
+
+ align:start position:0%
+sometimes does good things that the
+ 
+
+ align:start position:0%
+sometimes does good things that the
+application might actually want to do
+
+ align:start position:0%
+application might actually want to do
+ 
+
+ align:start position:0%
+application might actually want to do
+legitimately and sometimes that
+
+ align:start position:0%
+legitimately and sometimes that
+ 
+
+ align:start position:0%
+legitimately and sometimes that
+instruction could do bad things so what
+
+ align:start position:0%
+instruction could do bad things so what
+ 
+
+ align:start position:0%
+instruction could do bad things so what
+instrumenting it means is that you add
+
+ align:start position:0%
+instrumenting it means is that you add
+ 
+
+ align:start position:0%
+instrumenting it means is that you add
+some extra instructions before it that
+
+ align:start position:0%
+some extra instructions before it that
+ 
+
+ align:start position:0%
+some extra instructions before it that
+will check or enforce that only good
+
+ align:start position:0%
+will check or enforce that only good
+ 
+
+ align:start position:0%
+will check or enforce that only good
+things are going to happen with that
+
+ align:start position:0%
+things are going to happen with that
+ 
+
+ align:start position:0%
+things are going to happen with that
+instruction so for example if you're
+
+ align:start position:0%
+instruction so for example if you're
+ 
+
+ align:start position:0%
+instruction so for example if you're
+accessing a memory location what you
+
+ align:start position:0%
+accessing a memory location what you
+ 
+
+ align:start position:0%
+accessing a memory location what you
+could do turns out they don't do it for
+
+ align:start position:0%
+could do turns out they don't do it for
+ 
+
+ align:start position:0%
+could do turns out they don't do it for
+performance reasons but one way to
+
+ align:start position:0%
+performance reasons but one way to
+ 
+
+ align:start position:0%
+performance reasons but one way to
+instrument A Memory access would be to
+
+ align:start position:0%
+instrument A Memory access would be to
+ 
+
+ align:start position:0%
+instrument A Memory access would be to
+put some checks like an if statement
+
+ align:start position:0%
+put some checks like an if statement
+ 
+
+ align:start position:0%
+put some checks like an if statement
+before the instruction saying well is
+
+ align:start position:0%
+before the instruction saying well is
+ 
+
+ align:start position:0%
+before the instruction saying well is
+this address you're accessing in range
+
+ align:start position:0%
+this address you're accessing in range
+ 
+
+ align:start position:0%
+this address you're accessing in range
+of what's allowed for this module and if
+
+ align:start position:0%
+of what's allowed for this module and if
+ 
+
+ align:start position:0%
+of what's allowed for this module and if
+so do they access otherwise exit so that
+
+ align:start position:0%
+so do they access otherwise exit so that
+ 
+
+ align:start position:0%
+so do they access otherwise exit so that
+would instrument an instruction and that
+
+ align:start position:0%
+would instrument an instruction and that
+ 
+
+ align:start position:0%
+would instrument an instruction and that
+would turn an unsafe instruction into
+
+ align:start position:0%
+would turn an unsafe instruction into
+ 
+
+ align:start position:0%
+would turn an unsafe instruction into
+one that's always safe to execute
+
+ align:start position:0%
+one that's always safe to execute
+ 
+
+ align:start position:0%
+one that's always safe to execute
+because there is always that check in
+
+ align:start position:0%
+because there is always that check in
+ 
+
+ align:start position:0%
+because there is always that check in
+front of it so does that make sense this
+
+ align:start position:0%
+front of it so does that make sense this
+ 
+
+ align:start position:0%
+front of it so does that make sense this
+is their sort of big idea for running
+
+ align:start position:0%
+is their sort of big idea for running
+ 
+
+ align:start position:0%
+is their sort of big idea for running
+this enforcing safety without support
+
+ align:start position:0%
+this enforcing safety without support
+ 
+
+ align:start position:0%
+this enforcing safety without support
+from the operating system at some
+
+ align:start position:0%
+from the operating system at some
+ 
+
+ align:start position:0%
+from the operating system at some
+level and I guess for other unsafe
+
+ align:start position:0%
+level and I guess for other unsafe
+ 
+
+ align:start position:0%
+level and I guess for other unsafe
+instructions they don't instrument all
+
+ align:start position:0%
+instructions they don't instrument all
+ 
+
+ align:start position:0%
+instructions they don't instrument all
+of them some of them they actually
+
+ align:start position:0%
+of them some of them they actually
+ 
+
+ align:start position:0%
+of them some of them they actually
+prohibit if they believe that this is an
+
+ align:start position:0%
+prohibit if they believe that this is an
+ 
+
+ align:start position:0%
+prohibit if they believe that this is an
+instruction that's not really necessary
+
+ align:start position:0%
+instruction that's not really necessary
+ 
+
+ align:start position:0%
+instruction that's not really necessary
+during normal operation and if an
+
+ align:start position:0%
+during normal operation and if an
+ 
+
+ align:start position:0%
+during normal operation and if an
+application tries to run it there we
+
+ align:start position:0%
+application tries to run it there we
+ 
+
+ align:start position:0%
+application tries to run it there we
+should just kill the application or not
+
+ align:start position:0%
+should just kill the application or not
+ 
+
+ align:start position:0%
+should just kill the application or not
+allow it to run in the first
+
+ align:start position:0%
+allow it to run in the first
+ 
+
+ align:start position:0%
+allow it to run in the first
+place makes sense so this is their sort
+
+ align:start position:0%
+place makes sense so this is their sort
+ 
+
+ align:start position:0%
+place makes sense so this is their sort
+of big plan for software fault isolation
+
+ align:start position:0%
+of big plan for software fault isolation
+ 
+
+ align:start position:0%
+of big plan for software fault isolation
+and once you've checked the
+
+ align:start position:0%
+and once you've checked the
+ 
+
+ align:start position:0%
+and once you've checked the
+application's binary and It All Passes
+
+ align:start position:0%
+application's binary and It All Passes
+ 
+
+ align:start position:0%
+application's binary and It All Passes
+and everything seems to be properly
+
+ align:start position:0%
+and everything seems to be properly
+ 
+
+ align:start position:0%
+and everything seems to be properly
+instrumented then you can just run the
+
+ align:start position:0%
+instrumented then you can just run the
+ 
+
+ align:start position:0%
+instrumented then you can just run the
+program and off it goes and by
+
+ align:start position:0%
+program and off it goes and by
+ 
+
+ align:start position:0%
+program and off it goes and by
+definition almost it'll not do bad
+
+ align:start position:0%
+definition almost it'll not do bad
+ 
+
+ align:start position:0%
+definition almost it'll not do bad
+things if we do all these checks and
+
+ align:start position:0%
+things if we do all these checks and
+ 
+
+ align:start position:0%
+things if we do all these checks and
+instrumentations
+
+ align:start position:0%
+instrumentations
+ 
+
+ align:start position:0%
+instrumentations
+right and I guess there's one more part
+
+ align:start position:0%
+right and I guess there's one more part
+ 
+
+ align:start position:0%
+right and I guess there's one more part
+to the software fault isolation story
+
+ align:start position:0%
+to the software fault isolation story
+ 
+
+ align:start position:0%
+to the software fault isolation story
+which is that once you've made sure that
+
+ align:start position:0%
+which is that once you've made sure that
+ 
+
+ align:start position:0%
+which is that once you've made sure that
+everything is safe then it can't
+
+ align:start position:0%
+everything is safe then it can't
+ 
+
+ align:start position:0%
+everything is safe then it can't
+actually do anything terribly
+
+ align:start position:0%
+actually do anything terribly
+ 
+
+ align:start position:0%
+actually do anything terribly
+interesting other than compute stuff in
+
+ align:start position:0%
+interesting other than compute stuff in
+ 
+
+ align:start position:0%
+interesting other than compute stuff in
+its own little memory so it can't access
+
+ align:start position:0%
+its own little memory so it can't access
+ 
+
+ align:start position:0%
+its own little memory so it can't access
+the network can't access the disc can't
+
+ align:start position:0%
+the network can't access the disc can't
+ 
+
+ align:start position:0%
+the network can't access the disc can't
+access your browser display keyboard
+
+ align:start position:0%
+access your browser display keyboard
+ 
+
+ align:start position:0%
+access your browser display keyboard
+almost anything so in pretty much every
+
+ align:start position:0%
+almost anything so in pretty much every
+ 
+
+ align:start position:0%
+almost anything so in pretty much every
+software fault isolation story there's
+
+ align:start position:0%
+software fault isolation story there's
+ 
+
+ align:start position:0%
+software fault isolation story there's
+actually also some trusted service
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+runtime and this trusted runtime is
+
+ align:start position:0%
+runtime and this trusted runtime is
+ 
+
+ align:start position:0%
+runtime and this trusted runtime is
+going to not be subject to these checks
+
+ align:start position:0%
+going to not be subject to these checks
+ 
+
+ align:start position:0%
+going to not be subject to these checks
+on its instructions so the trusted
+
+ align:start position:0%
+on its instructions so the trusted
+ 
+
+ align:start position:0%
+on its instructions so the trusted
+runtime could actually do all these
+
+ align:start position:0%
+runtime could actually do all these
+ 
+
+ align:start position:0%
+runtime could actually do all these
+potentially unsafe things but the
+
+ align:start position:0%
+potentially unsafe things but the
+ 
+
+ align:start position:0%
+potentially unsafe things but the
+trusted runtime is written by Google so
+
+ align:start position:0%
+trusted runtime is written by Google so
+ 
+
+ align:start position:0%
+trusted runtime is written by Google so
+hopefully they get it right and it's
+
+ align:start position:0%
+hopefully they get it right and it's
+ 
+
+ align:start position:0%
+hopefully they get it right and it's
+going to implement all the functions
+
+ align:start position:0%
+going to implement all the functions
+ 
+
+ align:start position:0%
+going to implement all the functions
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Google's native client team believes are
+
+ align:start position:0%
+Google's native client team believes are
+ 
+
+ align:start position:0%
+Google's native client team believes are
+okay to allow for these modules so these
+
+ align:start position:0%
+okay to allow for these modules so these
+ 
+
+ align:start position:0%
+okay to allow for these modules so these
+are going to be things like maybe
+
+ align:start position:0%
+are going to be things like maybe
+ 
+
+ align:start position:0%
+are going to be things like maybe
+allocating memory maybe creating a
+
+ align:start position:0%
+allocating memory maybe creating a
+ 
+
+ align:start position:0%
+allocating memory maybe creating a
+thread maybe communicating with the
+
+ align:start position:0%
+thread maybe communicating with the
+ 
+
+ align:start position:0%
+thread maybe communicating with the
+browser as we saw so some sort of a
+
+ align:start position:0%
+browser as we saw so some sort of a
+ 
+
+ align:start position:0%
+browser as we saw so some sort of a
+message passing
+
+ align:start position:0%
+message passing
+ 
+
+ align:start position:0%
+message passing
+system Etc and the way it's going to be
+
+ align:start position:0%
+system Etc and the way it's going to be
+ 
+
+ align:start position:0%
+system Etc and the way it's going to be
+exposed to this isolated module is
+
+ align:start position:0%
+exposed to this isolated module is
+ 
+
+ align:start position:0%
+exposed to this isolated module is
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+certain presumably um special jumps or
+
+ align:start position:0%
+certain presumably um special jumps or
+ 
+
+ align:start position:0%
+certain presumably um special jumps or
+operations that the uh module is going
+
+ align:start position:0%
+operations that the uh module is going
+ 
+
+ align:start position:0%
+operations that the uh module is going
+to perform to transition control into
+
+ align:start position:0%
+to perform to transition control into
+ 
+
+ align:start position:0%
+to perform to transition control into
+this trusted runtime but hopefully in a
+
+ align:start position:0%
+this trusted runtime but hopefully in a
+ 
+
+ align:start position:0%
+this trusted runtime but hopefully in a
+very predictable way so question I'm
+
+ align:start position:0%
+very predictable way so question I'm
+ 
+
+ align:start position:0%
+very predictable way so question I'm
+just curious um so do you have to design
+
+ align:start position:0%
+just curious um so do you have to design
+ 
+
+ align:start position:0%
+just curious um so do you have to design
+this application um knowing that it's
+
+ align:start position:0%
+this application um knowing that it's
+ 
+
+ align:start position:0%
+this application um knowing that it's
+going to be sent to the NC module or is
+
+ align:start position:0%
+going to be sent to the NC module or is
+ 
+
+ align:start position:0%
+going to be sent to the NC module or is
+it like change the code so that it'll
+
+ align:start position:0%
+it like change the code so that it'll
+ 
+
+ align:start position:0%
+it like change the code so that it'll
+make necessary call to the
+
+ align:start position:0%
+make necessary call to the
+ 
+
+ align:start position:0%
+make necessary call to the
+service so I think if you're taking an
+
+ align:start position:0%
+service so I think if you're taking an
+ 
+
+ align:start position:0%
+service so I think if you're taking an
+if you're building an application you do
+
+ align:start position:0%
+if you're building an application you do
+ 
+
+ align:start position:0%
+if you're building an application you do
+have to be sort of aware that it's going
+
+ align:start position:0%
+have to be sort of aware that it's going
+ 
+
+ align:start position:0%
+have to be sort of aware that it's going
+to be running inside of native client um
+
+ align:start position:0%
+to be running inside of native client um
+ 
+
+ align:start position:0%
+to be running inside of native client um
+so some function calls like Malo or
+
+ align:start position:0%
+so some function calls like Malo or
+ 
+
+ align:start position:0%
+so some function calls like Malo or
+pthread create I think they just
+
+ align:start position:0%
+pthread create I think they just
+ 
+
+ align:start position:0%
+pthread create I think they just
+transparently replace with calls to
+
+ align:start position:0%
+transparently replace with calls to
+ 
+
+ align:start position:0%
+transparently replace with calls to
+their trusted runtime but if you do
+
+ align:start position:0%
+their trusted runtime but if you do
+ 
+
+ align:start position:0%
+their trusted runtime but if you do
+anything like opening a file by path
+
+ align:start position:0%
+anything like opening a file by path
+ 
+
+ align:start position:0%
+anything like opening a file by path
+name or anything else that sort of you
+
+ align:start position:0%
+name or anything else that sort of you
+ 
+
+ align:start position:0%
+name or anything else that sort of you
+would expect to do on a Unix machine
+
+ align:start position:0%
+would expect to do on a Unix machine
+ 
+
+ align:start position:0%
+would expect to do on a Unix machine
+that You' probably have to replace with
+
+ align:start position:0%
+that You' probably have to replace with
+ 
+
+ align:start position:0%
+that You' probably have to replace with
+something else and you'd probably want
+
+ align:start position:0%
+something else and you'd probably want
+ 
+
+ align:start position:0%
+something else and you'd probably want
+to structure your thing to interact at
+
+ align:start position:0%
+to structure your thing to interact at
+ 
+
+ align:start position:0%
+to structure your thing to interact at
+least a little bit with your JavaScript
+
+ align:start position:0%
+least a little bit with your JavaScript
+ 
+
+ align:start position:0%
+least a little bit with your JavaScript
+or web page in some way and that you
+
+ align:start position:0%
+or web page in some way and that you
+ 
+
+ align:start position:0%
+or web page in some way and that you
+would have to do by explicitly doing
+
+ align:start position:0%
+would have to do by explicitly doing
+ 
+
+ align:start position:0%
+would have to do by explicitly doing
+some message passing or rpcs into the
+
+ align:start position:0%
+some message passing or rpcs into the
+ 
+
+ align:start position:0%
+some message passing or rpcs into the
+JavaScript part so that you would have
+
+ align:start position:0%
+JavaScript part so that you would have
+ 
+
+ align:start position:0%
+JavaScript part so that you would have
+to probably change uh so there's some so
+
+ align:start position:0%
+to probably change uh so there's some so
+ 
+
+ align:start position:0%
+to probably change uh so there's some so
+it's not like you can run an arbitrary
+
+ align:start position:0%
+it's not like you can run an arbitrary
+ 
+
+ align:start position:0%
+it's not like you can run an arbitrary
+Unix program in there and you'll just
+
+ align:start position:0%
+Unix program in there and you'll just
+ 
+
+ align:start position:0%
+Unix program in there and you'll just
+sort of get a shell and you can run
+
+ align:start position:0%
+sort of get a shell and you can run
+ 
+
+ align:start position:0%
+sort of get a shell and you can run
+commands all of a sudden probably if you
+
+ align:start position:0%
+commands all of a sudden probably if you
+ 
+
+ align:start position:0%
+commands all of a sudden probably if you
+Tred hard maybe you could create such an
+
+ align:start position:0%
+Tred hard maybe you could create such an
+ 
+
+ align:start position:0%
+Tred hard maybe you could create such an
+environment uh but by default you
+
+ align:start position:0%
+environment uh but by default you
+ 
+
+ align:start position:0%
+environment uh but by default you
+probably have to make it operate inside
+
+ align:start position:0%
+probably have to make it operate inside
+ 
+
+ align:start position:0%
+probably have to make it operate inside
+of this web page and interact with it in
+
+ align:start position:0%
+of this web page and interact with it in
+ 
+
+ align:start position:0%
+of this web page and interact with it in
+some way make
+
+ align:start position:0%
+some way make
+ 
+
+ align:start position:0%
+some way make
+sense all right
+
+ align:start position:0%
+sense all right
+ 
+
+ align:start position:0%
+sense all right
+okay so so that's the overall plan for
+
+ align:start position:0%
+okay so so that's the overall plan for
+ 
+
+ align:start position:0%
+okay so so that's the overall plan for
+software of isolation so I guess let's
+
+ align:start position:0%
+software of isolation so I guess let's
+ 
+
+ align:start position:0%
+software of isolation so I guess let's
+look at actually what safety means in
+
+ align:start position:0%
+look at actually what safety means in
+ 
+
+ align:start position:0%
+look at actually what safety means in
+their case for Native client so we
+
+ align:start position:0%
+their case for Native client so we
+ 
+
+ align:start position:0%
+their case for Native client so we
+talked Loosely about this notion of safe
+
+ align:start position:0%
+talked Loosely about this notion of safe
+ 
+
+ align:start position:0%
+talked Loosely about this notion of safe
+instructions unsafe instructions what do
+
+ align:start position:0%
+instructions unsafe instructions what do
+ 
+
+ align:start position:0%
+instructions unsafe instructions what do
+they actually care about here so as far
+
+ align:start position:0%
+they actually care about here so as far
+ 
+
+ align:start position:0%
+they actually care about here so as far
+as I can tell for a native client safety
+
+ align:start position:0%
+as I can tell for a native client safety
+ 
+
+ align:start position:0%
+as I can tell for a native client safety
+uh basically means two things one is
+
+ align:start position:0%
+uh basically means two things one is
+ 
+
+ align:start position:0%
+uh basically means two things one is
+that there's no disallowed
+
+ align:start position:0%
+that there's no disallowed
+ 
+
+ align:start position:0%
+that there's no disallowed
+instructions that can execute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh these disallowed instructions are
+
+ align:start position:0%
+and uh these disallowed instructions are
+ 
+
+ align:start position:0%
+and uh these disallowed instructions are
+things like maybe system calls or
+
+ align:start position:0%
+things like maybe system calls or
+ 
+
+ align:start position:0%
+things like maybe system calls or
+triggering an interupt which is another
+
+ align:start position:0%
+triggering an interupt which is another
+ 
+
+ align:start position:0%
+triggering an interupt which is another
+mechanism on x86 to jump into the kernel
+
+ align:start position:0%
+mechanism on x86 to jump into the kernel
+ 
+
+ align:start position:0%
+mechanism on x86 to jump into the kernel
+and invoke a system call uh and probably
+
+ align:start position:0%
+and invoke a system call uh and probably
+ 
+
+ align:start position:0%
+and invoke a system call uh and probably
+other privileged instructions that would
+
+ align:start position:0%
+other privileged instructions that would
+ 
+
+ align:start position:0%
+other privileged instructions that would
+allow you to escape out of the sandbox
+
+ align:start position:0%
+allow you to escape out of the sandbox
+ 
+
+ align:start position:0%
+allow you to escape out of the sandbox
+so we'll look a little bit more later at
+
+ align:start position:0%
+so we'll look a little bit more later at
+ 
+
+ align:start position:0%
+so we'll look a little bit more later at
+what instructions could actually let you
+
+ align:start position:0%
+what instructions could actually let you
+ 
+
+ align:start position:0%
+what instructions could actually let you
+jump out of a
+
+ align:start position:0%
+jump out of a
+ 
+
+ align:start position:0%
+jump out of a
+Sandbox and in addition to this no
+
+ align:start position:0%
+Sandbox and in addition to this no
+ 
+
+ align:start position:0%
+Sandbox and in addition to this no
+disallowed instructions rule they also
+
+ align:start position:0%
+disallowed instructions rule they also
+ 
+
+ align:start position:0%
+disallowed instructions rule they also
+um want to make make sure that all code
+
+ align:start position:0%
+um want to make make sure that all code
+ 
+
+ align:start position:0%
+um want to make make sure that all code
+and data
+
+ align:start position:0%
+and data
+ 
+
+ align:start position:0%
+and data
+accesses are in
+
+ align:start position:0%
+accesses are in
+ 
+
+ align:start position:0%
+accesses are in
+bounds for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+module so what this means is that they
+
+ align:start position:0%
+module so what this means is that they
+ 
+
+ align:start position:0%
+module so what this means is that they
+actually dedicate a particular part of
+
+ align:start position:0%
+actually dedicate a particular part of
+ 
+
+ align:start position:0%
+actually dedicate a particular part of
+the program's address space specifically
+
+ align:start position:0%
+the program's address space specifically
+ 
+
+ align:start position:0%
+the program's address space specifically
+it goes from zero up to 256 Megs in the
+
+ align:start position:0%
+it goes from zero up to 256 Megs in the
+ 
+
+ align:start position:0%
+it goes from zero up to 256 Megs in the
+process and everything that this
+
+ align:start position:0%
+process and everything that this
+ 
+
+ align:start position:0%
+process and everything that this
+untrusted module does has to refer to
+
+ align:start position:0%
+untrusted module does has to refer to
+ 
+
+ align:start position:0%
+untrusted module does has to refer to
+locations within this chunk of memory in
+
+ align:start position:0%
+locations within this chunk of memory in
+ 
+
+ align:start position:0%
+locations within this chunk of memory in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+program all right so just a double check
+
+ align:start position:0%
+program all right so just a double check
+ 
+
+ align:start position:0%
+program all right so just a double check
+so why do they want to disallow these
+
+ align:start position:0%
+so why do they want to disallow these
+ 
+
+ align:start position:0%
+so why do they want to disallow these
+instructions so what if they fail to
+
+ align:start position:0%
+instructions so what if they fail to
+ 
+
+ align:start position:0%
+instructions so what if they fail to
+disallow the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instructions yeah module can make a CIS
+
+ align:start position:0%
+instructions yeah module can make a CIS
+ 
+
+ align:start position:0%
+instructions yeah module can make a CIS
+right so that's yeah fairly
+
+ align:start position:0%
+right so that's yeah fairly
+ 
+
+ align:start position:0%
+right so that's yeah fairly
+straightforward exactly yeah so you
+
+ align:start position:0%
+straightforward exactly yeah so you
+ 
+
+ align:start position:0%
+straightforward exactly yeah so you
+could just directly reboot the machine
+
+ align:start position:0%
+could just directly reboot the machine
+ 
+
+ align:start position:0%
+could just directly reboot the machine
+or open your home directory and
+
+ align:start position:0%
+or open your home directory and
+ 
+
+ align:start position:0%
+or open your home directory and
+enumerate all the files and do all these
+
+ align:start position:0%
+enumerate all the files and do all these
+ 
+
+ align:start position:0%
+enumerate all the files and do all these
+things so that seems like a good thing
+
+ align:start position:0%
+things so that seems like a good thing
+ 
+
+ align:start position:0%
+things so that seems like a good thing
+to do why do they care about this plan
+
+ align:start position:0%
+to do why do they care about this plan
+ 
+
+ align:start position:0%
+to do why do they care about this plan
+like isolating the code on data to only
+
+ align:start position:0%
+like isolating the code on data to only
+ 
+
+ align:start position:0%
+like isolating the code on data to only
+access these low addresses so what goes
+
+ align:start position:0%
+access these low addresses so what goes
+ 
+
+ align:start position:0%
+access these low addresses so what goes
+wrong if they fail to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that does anything yeah then they can
+
+ align:start position:0%
+that does anything yeah then they can
+ 
+
+ align:start position:0%
+that does anything yeah then they can
+start accessing interrupting memory that
+
+ align:start position:0%
+start accessing interrupting memory that
+ 
+
+ align:start position:0%
+start accessing interrupting memory that
+doesn't belong that module like on your
+
+ align:start position:0%
+doesn't belong that module like on your
+ 
+
+ align:start position:0%
+doesn't belong that module like on your
+computer we don't care if they ruin
+
+ align:start position:0%
+computer we don't care if they ruin
+ 
+
+ align:start position:0%
+computer we don't care if they ruin
+their own program and it crashes that's
+
+ align:start position:0%
+their own program and it crashes that's
+ 
+
+ align:start position:0%
+their own program and it crashes that's
+fine as long as it's not going to crash
+
+ align:start position:0%
+fine as long as it's not going to crash
+ 
+
+ align:start position:0%
+fine as long as it's not going to crash
+the computer that's running yeah so in
+
+ align:start position:0%
+the computer that's running yeah so in
+ 
+
+ align:start position:0%
+the computer that's running yeah so in
+some sense uh that's true but and in
+
+ align:start position:0%
+some sense uh that's true but and in
+ 
+
+ align:start position:0%
+some sense uh that's true but and in
+their case they actually run the thing
+
+ align:start position:0%
+their case they actually run the thing
+ 
+
+ align:start position:0%
+their case they actually run the thing
+in a separate process so in in theory
+
+ align:start position:0%
+in a separate process so in in theory
+ 
+
+ align:start position:0%
+in a separate process so in in theory
+this would only crash that extra process
+
+ align:start position:0%
+this would only crash that extra process
+ 
+
+ align:start position:0%
+this would only crash that extra process
+um I think that I guess what they're
+
+ align:start position:0%
+um I think that I guess what they're
+ 
+
+ align:start position:0%
+um I think that I guess what they're
+really worried about is that this is a
+
+ align:start position:0%
+really worried about is that this is a
+ 
+
+ align:start position:0%
+really worried about is that this is a
+necessary condition to ensure there's no
+
+ align:start position:0%
+necessary condition to ensure there's no
+ 
+
+ align:start position:0%
+necessary condition to ensure there's no
+disallowed instructions in some way
+
+ align:start position:0%
+disallowed instructions in some way
+ 
+
+ align:start position:0%
+disallowed instructions in some way
+because there's other stuff like this
+
+ align:start position:0%
+because there's other stuff like this
+ 
+
+ align:start position:0%
+because there's other stuff like this
+trusted runtime in your process so if
+
+ align:start position:0%
+trusted runtime in your process so if
+ 
+
+ align:start position:0%
+trusted runtime in your process so if
+what you really care about is not
+
+ align:start position:0%
+what you really care about is not
+ 
+
+ align:start position:0%
+what you really care about is not
+corrupting the rest of your computer
+
+ align:start position:0%
+corrupting the rest of your computer
+ 
+
+ align:start position:0%
+corrupting the rest of your computer
+then if the untrusted module could
+
+ align:start position:0%
+then if the untrusted module could
+ 
+
+ align:start position:0%
+then if the untrusted module could
+arbitrarily jump into this trusted
+
+ align:start position:0%
+arbitrarily jump into this trusted
+ 
+
+ align:start position:0%
+arbitrarily jump into this trusted
+service runtime and do anything that the
+
+ align:start position:0%
+service runtime and do anything that the
+ 
+
+ align:start position:0%
+service runtime and do anything that the
+trusted service runtime can do then they
+
+ align:start position:0%
+trusted service runtime can do then they
+ 
+
+ align:start position:0%
+trusted service runtime can do then they
+could sort of violate this property so
+
+ align:start position:0%
+could sort of violate this property so
+ 
+
+ align:start position:0%
+could sort of violate this property so
+in some ways this is really like a
+
+ align:start position:0%
+in some ways this is really like a
+ 
+
+ align:start position:0%
+in some ways this is really like a
+supporting mechanism for enforcing that
+
+ align:start position:0%
+supporting mechanism for enforcing that
+ 
+
+ align:start position:0%
+supporting mechanism for enforcing that
+um in in principle this could also be
+
+ align:start position:0%
+um in in principle this could also be
+ 
+
+ align:start position:0%
+um in in principle this could also be
+used for lighter weight isolation if you
+
+ align:start position:0%
+used for lighter weight isolation if you
+ 
+
+ align:start position:0%
+used for lighter weight isolation if you
+could run this native client module
+
+ align:start position:0%
+could run this native client module
+ 
+
+ align:start position:0%
+could run this native client module
+inside of the browser process itself and
+
+ align:start position:0%
+inside of the browser process itself and
+ 
+
+ align:start position:0%
+inside of the browser process itself and
+not start an extra process but it turns
+
+ align:start position:0%
+not start an extra process but it turns
+ 
+
+ align:start position:0%
+not start an extra process but it turns
+out for performance reasons they really
+
+ align:start position:0%
+out for performance reasons they really
+ 
+
+ align:start position:0%
+out for performance reasons they really
+have to tie down the module to this
+
+ align:start position:0%
+have to tie down the module to this
+ 
+
+ align:start position:0%
+have to tie down the module to this
+particular range of memory or it has to
+
+ align:start position:0%
+particular range of memory or it has to
+ 
+
+ align:start position:0%
+particular range of memory or it has to
+start at zero anyway uh so this means
+
+ align:start position:0%
+start at zero anyway uh so this means
+ 
+
+ align:start position:0%
+start at zero anyway uh so this means
+that you can only have one really native
+
+ align:start position:0%
+that you can only have one really native
+ 
+
+ align:start position:0%
+that you can only have one really native
+client untrusted module per process so
+
+ align:start position:0%
+client untrusted module per process so
+ 
+
+ align:start position:0%
+client untrusted module per process so
+you probably are going to start a
+
+ align:start position:0%
+you probably are going to start a
+ 
+
+ align:start position:0%
+you probably are going to start a
+separate process
+
+ align:start position:0%
+separate process
+ 
+
+ align:start position:0%
+separate process
+anyway make sense other questions yeah
+
+ align:start position:0%
+anyway make sense other questions yeah
+ 
+
+ align:start position:0%
+anyway make sense other questions yeah
+is it like is there actually a reason
+
+ align:start position:0%
+is it like is there actually a reason
+ 
+
+ align:start position:0%
+is it like is there actually a reason
+why it has to start at zero yeah so it
+
+ align:start position:0%
+why it has to start at zero yeah so it
+ 
+
+ align:start position:0%
+why it has to start at zero yeah so it
+turns out it's more efficient in terms
+
+ align:start position:0%
+turns out it's more efficient in terms
+ 
+
+ align:start position:0%
+turns out it's more efficient in terms
+of performance to enforce jump targets
+
+ align:start position:0%
+of performance to enforce jump targets
+ 
+
+ align:start position:0%
+of performance to enforce jump targets
+if you know that the legitimate address
+
+ align:start position:0%
+if you know that the legitimate address
+ 
+
+ align:start position:0%
+if you know that the legitimate address
+is a contiguous set of addresses
+
+ align:start position:0%
+is a contiguous set of addresses
+ 
+
+ align:start position:0%
+is a contiguous set of addresses
+starting at zero because you can then do
+
+ align:start position:0%
+starting at zero because you can then do
+ 
+
+ align:start position:0%
+starting at zero because you can then do
+it with a single and mask where all the
+
+ align:start position:0%
+it with a single and mask where all the
+ 
+
+ align:start position:0%
+it with a single and mask where all the
+High bits are one and only a couple of
+
+ align:start position:0%
+High bits are one and only a couple of
+ 
+
+ align:start position:0%
+High bits are one and only a couple of
+low bits are zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if you're willing well
+
+ align:start position:0%
+well if you're willing well
+ 
+
+ align:start position:0%
+well if you're willing well
+I thought the an mask was to ensure
+
+ align:start position:0%
+I thought the an mask was to ensure
+ 
+
+ align:start position:0%
+I thought the an mask was to ensure
+alignment right so the N mask ensures
+
+ align:start position:0%
+alignment right so the N mask ensures
+ 
+
+ align:start position:0%
+alignment right so the N mask ensures
+alignment you're right uh so so yeah so
+
+ align:start position:0%
+alignment you're right uh so so yeah so
+ 
+
+ align:start position:0%
+alignment you're right uh so so yeah so
+why do they start at zero um I think it
+
+ align:start position:0%
+why do they start at zero um I think it
+ 
+
+ align:start position:0%
+why do they start at zero um I think it
+probably helps them to avoid well I
+
+ align:start position:0%
+probably helps them to avoid well I
+ 
+
+ align:start position:0%
+probably helps them to avoid well I
+guess they rely on these on the
+
+ align:start position:0%
+guess they rely on these on the
+ 
+
+ align:start position:0%
+guess they rely on these on the
+segmentation Hardware so in principle
+
+ align:start position:0%
+segmentation Hardware so in principle
+ 
+
+ align:start position:0%
+segmentation Hardware so in principle
+maybe they could use the segmentation
+
+ align:start position:0%
+maybe they could use the segmentation
+ 
+
+ align:start position:0%
+maybe they could use the segmentation
+Hardware to shift the region up in terms
+
+ align:start position:0%
+Hardware to shift the region up in terms
+ 
+
+ align:start position:0%
+Hardware to shift the region up in terms
+of linear space so maybe it's just that
+
+ align:start position:0%
+of linear space so maybe it's just that
+ 
+
+ align:start position:0%
+of linear space so maybe it's just that
+the application sort of sees this range
+
+ align:start position:0%
+the application sort of sees this range
+ 
+
+ align:start position:0%
+the application sort of sees this range
+and you could actually place at
+
+ align:start position:0%
+and you could actually place at
+ 
+
+ align:start position:0%
+and you could actually place at
+different offsets in your virtual
+
+ align:start position:0%
+different offsets in your virtual
+ 
+
+ align:start position:0%
+different offsets in your virtual
+address space could be um
+
+ align:start position:0%
+address space could be um
+ 
+
+ align:start position:0%
+address space could be um
+yeah so maybe you could actually play
+
+ align:start position:0%
+yeah so maybe you could actually play
+ 
+
+ align:start position:0%
+yeah so maybe you could actually play
+tricks with the segmentation Hardware to
+
+ align:start position:0%
+tricks with the segmentation Hardware to
+ 
+
+ align:start position:0%
+tricks with the segmentation Hardware to
+run multiple modules in same address
+
+ align:start position:0%
+run multiple modules in same address
+ 
+
+ align:start position:0%
+run multiple modules in same address
+space it's also because they want to
+
+ align:start position:0%
+space it's also because they want to
+ 
+
+ align:start position:0%
+space it's also because they want to
+catch no point exceptions yeah so they
+
+ align:start position:0%
+catch no point exceptions yeah so they
+ 
+
+ align:start position:0%
+catch no point exceptions yeah so they
+want to catch null pointer exceptions
+
+ align:start position:0%
+want to catch null pointer exceptions
+ 
+
+ align:start position:0%
+want to catch null pointer exceptions
+but you could sort of do that because
+
+ align:start position:0%
+but you could sort of do that because
+ 
+
+ align:start position:0%
+but you could sort of do that because
+the null pointer I guess we'll talk
+
+ align:start position:0%
+the null pointer I guess we'll talk
+ 
+
+ align:start position:0%
+the null pointer I guess we'll talk
+about segmentation in a second but the
+
+ align:start position:0%
+about segmentation in a second but the
+ 
+
+ align:start position:0%
+about segmentation in a second but the
+null pointer actually go is relative to
+
+ align:start position:0%
+null pointer actually go is relative to
+ 
+
+ align:start position:0%
+null pointer actually go is relative to
+the segment in which you're accessing so
+
+ align:start position:0%
+the segment in which you're accessing so
+ 
+
+ align:start position:0%
+the segment in which you're accessing so
+if you shift the segment around then you
+
+ align:start position:0%
+if you shift the segment around then you
+ 
+
+ align:start position:0%
+if you shift the segment around then you
+could map a unused zero page at the
+
+ align:start position:0%
+could map a unused zero page at the
+ 
+
+ align:start position:0%
+could map a unused zero page at the
+beginning of everyone's segment uh so
+
+ align:start position:0%
+beginning of everyone's segment uh so
+ 
+
+ align:start position:0%
+beginning of everyone's segment uh so
+yeah it might be that uh you could do
+
+ align:start position:0%
+yeah it might be that uh you could do
+ 
+
+ align:start position:0%
+yeah it might be that uh you could do
+multiple modules
+
+ align:start position:0%
+multiple modules
+ 
+
+ align:start position:0%
+multiple modules
+um I think for well I guess one one
+
+ align:start position:0%
+um I think for well I guess one one
+ 
+
+ align:start position:0%
+um I think for well I guess one one
+reason they probably want to do this is
+
+ align:start position:0%
+reason they probably want to do this is
+ 
+
+ align:start position:0%
+reason they probably want to do this is
+that when they Port their stuff to 64
+
+ align:start position:0%
+that when they Port their stuff to 64
+ 
+
+ align:start position:0%
+that when they Port their stuff to 64
+bits they have a slightly different
+
+ align:start position:0%
+bits they have a slightly different
+ 
+
+ align:start position:0%
+bits they have a slightly different
+design this paper doesn't really talk
+
+ align:start position:0%
+design this paper doesn't really talk
+ 
+
+ align:start position:0%
+design this paper doesn't really talk
+about it and I think in that 64-bit
+
+ align:start position:0%
+about it and I think in that 64-bit
+ 
+
+ align:start position:0%
+about it and I think in that 64-bit
+design the hardware itself got rid of
+
+ align:start position:0%
+design the hardware itself got rid of
+ 
+
+ align:start position:0%
+design the hardware itself got rid of
+some of the segmentation Hardware they
+
+ align:start position:0%
+some of the segmentation Hardware they
+ 
+
+ align:start position:0%
+some of the segmentation Hardware they
+were relying on for efficiency reasons
+
+ align:start position:0%
+were relying on for efficiency reasons
+ 
+
+ align:start position:0%
+were relying on for efficiency reasons
+uh and they have to do a much more
+
+ align:start position:0%
+uh and they have to do a much more
+ 
+
+ align:start position:0%
+uh and they have to do a much more
+software oriented approach in which case
+
+ align:start position:0%
+software oriented approach in which case
+ 
+
+ align:start position:0%
+software oriented approach in which case
+having the low bits does help them uh
+
+ align:start position:0%
+having the low bits does help them uh
+ 
+
+ align:start position:0%
+having the low bits does help them uh
+but in this 32-bit version I think yeah
+
+ align:start position:0%
+but in this 32-bit version I think yeah
+ 
+
+ align:start position:0%
+but in this 32-bit version I think yeah
+maybe that's true they there's not a
+
+ align:start position:0%
+maybe that's true they there's not a
+ 
+
+ align:start position:0%
+maybe that's true they there's not a
+deep reason why it has to start at zero
+
+ align:start position:0%
+deep reason why it has to start at zero
+ 
+
+ align:start position:0%
+deep reason why it has to start at zero
+fair enough other
+
+ align:start position:0%
+fair enough other
+ 
+
+ align:start position:0%
+fair enough other
+questions all right so so I guess we
+
+ align:start position:0%
+questions all right so so I guess we
+ 
+
+ align:start position:0%
+questions all right so so I guess we
+sort of roughly understand what uh the
+
+ align:start position:0%
+sort of roughly understand what uh the
+ 
+
+ align:start position:0%
+sort of roughly understand what uh the
+plan is or what we want to enforce in
+
+ align:start position:0%
+plan is or what we want to enforce in
+ 
+
+ align:start position:0%
+plan is or what we want to enforce in
+terms of safety so how do we do this so
+
+ align:start position:0%
+terms of safety so how do we do this so
+ 
+
+ align:start position:0%
+terms of safety so how do we do this so
+let's look at some at least naive
+
+ align:start position:0%
+let's look at some at least naive
+ 
+
+ align:start position:0%
+let's look at some at least naive
+approach and see what's how could we
+
+ align:start position:0%
+approach and see what's how could we
+ 
+
+ align:start position:0%
+approach and see what's how could we
+screw it up I guess and then we'll try
+
+ align:start position:0%
+screw it up I guess and then we'll try
+ 
+
+ align:start position:0%
+screw it up I guess and then we'll try
+to fix it afterwards so I guess the
+
+ align:start position:0%
+to fix it afterwards so I guess the
+ 
+
+ align:start position:0%
+to fix it afterwards so I guess the
+naive plan that uh you know sort of
+
+ align:start position:0%
+naive plan that uh you know sort of
+ 
+
+ align:start position:0%
+naive plan that uh you know sort of
+looks like what they do is is to just
+
+ align:start position:0%
+looks like what they do is is to just
+ 
+
+ align:start position:0%
+looks like what they do is is to just
+look for disallowed instructions by just
+
+ align:start position:0%
+look for disallowed instructions by just
+ 
+
+ align:start position:0%
+look for disallowed instructions by just
+scanning the executable from the start
+
+ align:start position:0%
+scanning the executable from the start
+ 
+
+ align:start position:0%
+scanning the executable from the start
+going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forward so how do you detect bad
+
+ align:start position:0%
+forward so how do you detect bad
+ 
+
+ align:start position:0%
+forward so how do you detect bad
+instructions well you could just take
+
+ align:start position:0%
+instructions well you could just take
+ 
+
+ align:start position:0%
+instructions well you could just take
+the sort of program code and you sort of
+
+ align:start position:0%
+the sort of program code and you sort of
+ 
+
+ align:start position:0%
+the sort of program code and you sort of
+lay it out in a giant string that goes
+
+ align:start position:0%
+lay it out in a giant string that goes
+ 
+
+ align:start position:0%
+lay it out in a giant string that goes
+from zero up to well maybe all the way
+
+ align:start position:0%
+from zero up to well maybe all the way
+ 
+
+ align:start position:0%
+from zero up to well maybe all the way
+to 256 megabytes depending on how big
+
+ align:start position:0%
+to 256 megabytes depending on how big
+ 
+
+ align:start position:0%
+to 256 megabytes depending on how big
+your code is and you start looking okay
+
+ align:start position:0%
+your code is and you start looking okay
+ 
+
+ align:start position:0%
+your code is and you start looking okay
+well maybe there's a op instruction here
+
+ align:start position:0%
+well maybe there's a op instruction here
+ 
+
+ align:start position:0%
+well maybe there's a op instruction here
+maybe there are some sort of an ad
+
+ align:start position:0%
+maybe there are some sort of an ad
+ 
+
+ align:start position:0%
+maybe there are some sort of an ad
+instruction there maybe there's a knot I
+
+ align:start position:0%
+instruction there maybe there's a knot I
+ 
+
+ align:start position:0%
+instruction there maybe there's a knot I
+don't know some sort of a jump Etc and
+
+ align:start position:0%
+don't know some sort of a jump Etc and
+ 
+
+ align:start position:0%
+don't know some sort of a jump Etc and
+you just keep looking and if you find a
+
+ align:start position:0%
+you just keep looking and if you find a
+ 
+
+ align:start position:0%
+you just keep looking and if you find a
+bad instruction you say ah it's a bad
+
+ align:start position:0%
+bad instruction you say ah it's a bad
+ 
+
+ align:start position:0%
+bad instruction you say ah it's a bad
+module and then you discard it and if
+
+ align:start position:0%
+module and then you discard it and if
+ 
+
+ align:start position:0%
+module and then you discard it and if
+you don't see any system call or in
+
+ align:start position:0%
+you don't see any system call or in
+ 
+
+ align:start position:0%
+you don't see any system call or in
+instructions then you're going to allow
+
+ align:start position:0%
+instructions then you're going to allow
+ 
+
+ align:start position:0%
+instructions then you're going to allow
+this module to run module or whatever it
+
+ align:start position:0%
+this module to run module or whatever it
+ 
+
+ align:start position:0%
+this module to run module or whatever it
+is will do for the inbounds
+
+ align:start position:0%
+is will do for the inbounds
+ 
+
+ align:start position:0%
+is will do for the inbounds
+checks so is this going to
+
+ align:start position:0%
+checks so is this going to
+ 
+
+ align:start position:0%
+checks so is this going to
+work so why not what are they worried
+
+ align:start position:0%
+work so why not what are they worried
+ 
+
+ align:start position:0%
+work so why not what are they worried
+about why is this so complicated
+
+ align:start position:0%
+about why is this so complicated
+ 
+
+ align:start position:0%
+about why is this so complicated
+overlapping instruction yeah so the
+
+ align:start position:0%
+overlapping instruction yeah so the
+ 
+
+ align:start position:0%
+overlapping instruction yeah so the
+weird thing is that x86 which is the
+
+ align:start position:0%
+weird thing is that x86 which is the
+ 
+
+ align:start position:0%
+weird thing is that x86 which is the
+sort of platform they're targeting has
+
+ align:start position:0%
+sort of platform they're targeting has
+ 
+
+ align:start position:0%
+sort of platform they're targeting has
+variable length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instructions so this means that the
+
+ align:start position:0%
+instructions so this means that the
+ 
+
+ align:start position:0%
+instructions so this means that the
+particular size of an instruction
+
+ align:start position:0%
+particular size of an instruction
+ 
+
+ align:start position:0%
+particular size of an instruction
+depends on the first few bytes of that
+
+ align:start position:0%
+depends on the first few bytes of that
+ 
+
+ align:start position:0%
+depends on the first few bytes of that
+instruction so you have to actually look
+
+ align:start position:0%
+instruction so you have to actually look
+ 
+
+ align:start position:0%
+instruction so you have to actually look
+at the first bite and say okay well the
+
+ align:start position:0%
+at the first bite and say okay well the
+ 
+
+ align:start position:0%
+at the first bite and say okay well the
+instruction is going to be this much
+
+ align:start position:0%
+instruction is going to be this much
+ 
+
+ align:start position:0%
+instruction is going to be this much
+more and then maybe you sort of have to
+
+ align:start position:0%
+more and then maybe you sort of have to
+ 
+
+ align:start position:0%
+more and then maybe you sort of have to
+look at a couple more bites and then
+
+ align:start position:0%
+look at a couple more bites and then
+ 
+
+ align:start position:0%
+look at a couple more bites and then
+decide okay well that's exactly how long
+
+ align:start position:0%
+decide okay well that's exactly how long
+ 
+
+ align:start position:0%
+decide okay well that's exactly how long
+it's going to be but you don't know
+
+ align:start position:0%
+it's going to be but you don't know
+ 
+
+ align:start position:0%
+it's going to be but you don't know
+ahead of time so some architectures like
+
+ align:start position:0%
+ahead of time so some architectures like
+ 
+
+ align:start position:0%
+ahead of time so some architectures like
+Spark arm uh myips um have more fixed
+
+ align:start position:0%
+Spark arm uh myips um have more fixed
+ 
+
+ align:start position:0%
+Spark arm uh myips um have more fixed
+length instructions well on arm for ex
+
+ align:start position:0%
+length instructions well on arm for ex
+ 
+
+ align:start position:0%
+length instructions well on arm for ex
+arm is slightly weird but it has two
+
+ align:start position:0%
+arm is slightly weird but it has two
+ 
+
+ align:start position:0%
+arm is slightly weird but it has two
+instruction lengths either everything is
+
+ align:start position:0%
+instruction lengths either everything is
+ 
+
+ align:start position:0%
+instruction lengths either everything is
+two bytes or everything is four bytes
+
+ align:start position:0%
+two bytes or everything is four bytes
+ 
+
+ align:start position:0%
+two bytes or everything is four bytes
+but in x86 the instructions could be
+
+ align:start position:0%
+but in x86 the instructions could be
+ 
+
+ align:start position:0%
+but in x86 the instructions could be
+like one b or 10 bytes or five bytes
+
+ align:start position:0%
+like one b or 10 bytes or five bytes
+ 
+
+ align:start position:0%
+like one b or 10 bytes or five bytes
+anything in between as well I forget
+
+ align:start position:0%
+anything in between as well I forget
+ 
+
+ align:start position:0%
+anything in between as well I forget
+actually how big you can get a pretty
+
+ align:start position:0%
+actually how big you can get a pretty
+ 
+
+ align:start position:0%
+actually how big you can get a pretty
+long instruction I think you can get
+
+ align:start position:0%
+long instruction I think you can get
+ 
+
+ align:start position:0%
+long instruction I think you can get
+like a 15 B instruction on x86 if you
+
+ align:start position:0%
+like a 15 B instruction on x86 if you
+ 
+
+ align:start position:0%
+like a 15 B instruction on x86 if you
+try hard um it's a complicated
+
+ align:start position:0%
+try hard um it's a complicated
+ 
+
+ align:start position:0%
+try hard um it's a complicated
+instruction set um but uh as a result
+
+ align:start position:0%
+instruction set um but uh as a result
+ 
+
+ align:start position:0%
+instruction set um but uh as a result
+the problem that could show up is that
+
+ align:start position:0%
+the problem that could show up is that
+ 
+
+ align:start position:0%
+the problem that could show up is that
+maybe you're scanning linearly and
+
+ align:start position:0%
+maybe you're scanning linearly and
+ 
+
+ align:start position:0%
+maybe you're scanning linearly and
+everything seems to be fine but maybe at
+
+ align:start position:0%
+everything seems to be fine but maybe at
+ 
+
+ align:start position:0%
+everything seems to be fine but maybe at
+runtime you'll actually jump into the
+
+ align:start position:0%
+runtime you'll actually jump into the
+ 
+
+ align:start position:0%
+runtime you'll actually jump into the
+middle of some instruction maybe it was
+
+ align:start position:0%
+middle of some instruction maybe it was
+ 
+
+ align:start position:0%
+middle of some instruction maybe it was
+a multi-te instruction if you interpret
+
+ align:start position:0%
+a multi-te instruction if you interpret
+ 
+
+ align:start position:0%
+a multi-te instruction if you interpret
+it starting from the second bite it
+
+ align:start position:0%
+it starting from the second bite it
+ 
+
+ align:start position:0%
+it starting from the second bite it
+looks like a completely different thing
+
+ align:start position:0%
+looks like a completely different thing
+ 
+
+ align:start position:0%
+looks like a completely different thing
+so just one example sort of playing
+
+ align:start position:0%
+so just one example sort of playing
+ 
+
+ align:start position:0%
+so just one example sort of playing
+around with an assembler and if you have
+
+ align:start position:0%
+around with an assembler and if you have
+ 
+
+ align:start position:0%
+around with an assembler and if you have
+an instruction like this
+
+ align:start position:0%
+an instruction like this
+ 
+
+ align:start position:0%
+an instruction like this
+25 uh CD 80 00 and if you interpret it
+
+ align:start position:0%
+25 uh CD 80 00 and if you interpret it
+ 
+
+ align:start position:0%
+25 uh CD 80 00 and if you interpret it
+as this five byte instruction meaning
+
+ align:start position:0%
+as this five byte instruction meaning
+ 
+
+ align:start position:0%
+as this five byte instruction meaning
+that you you look at this B and says oh
+
+ align:start position:0%
+that you you look at this B and says oh
+ 
+
+ align:start position:0%
+that you you look at this B and says oh
+yeah this is going to be a five byte
+
+ align:start position:0%
+yeah this is going to be a five byte
+ 
+
+ align:start position:0%
+yeah this is going to be a five byte
+instruction so you have to look five
+
+ align:start position:0%
+instruction so you have to look five
+ 
+
+ align:start position:0%
+instruction so you have to look five
+bytes forward and then this turns out to
+
+ align:start position:0%
+bytes forward and then this turns out to
+ 
+
+ align:start position:0%
+bytes forward and then this turns out to
+be a fairly benign instruction that's an
+
+ align:start position:0%
+be a fairly benign instruction that's an
+ 
+
+ align:start position:0%
+be a fairly benign instruction that's an
+end of the eax register with some
+
+ align:start position:0%
+end of the eax register with some
+ 
+
+ align:start position:0%
+end of the eax register with some
+particular constant that happens to be
+
+ align:start position:0%
+particular constant that happens to be
+ 
+
+ align:start position:0%
+particular constant that happens to be
+um I think
+
+ align:start position:0%
+um I think
+ 
+
+ align:start position:0%
+um I think
+0000 um 80 CD so this is one of these
+
+ align:start position:0%
+0000 um 80 CD so this is one of these
+ 
+
+ align:start position:0%
+0000 um 80 CD so this is one of these
+safe instructions that native client
+
+ align:start position:0%
+safe instructions that native client
+ 
+
+ align:start position:0%
+safe instructions that native client
+should just allow under the first rule
+
+ align:start position:0%
+should just allow under the first rule
+ 
+
+ align:start position:0%
+should just allow under the first rule
+in checking these binary instructions
+
+ align:start position:0%
+in checking these binary instructions
+ 
+
+ align:start position:0%
+in checking these binary instructions
+but if it turns out at runtime the CPU
+
+ align:start position:0%
+but if it turns out at runtime the CPU
+ 
+
+ align:start position:0%
+but if it turns out at runtime the CPU
+decides this is where it has to start
+
+ align:start position:0%
+decides this is where it has to start
+ 
+
+ align:start position:0%
+decides this is where it has to start
+executing the code then this instruction
+
+ align:start position:0%
+executing the code then this instruction
+ 
+
+ align:start position:0%
+executing the code then this instruction
+is actually a 4 byte instruction and
+
+ align:start position:0%
+is actually a 4 byte instruction and
+ 
+
+ align:start position:0%
+is actually a 4 byte instruction and
+it's actually an in instruction that
+
+ align:start position:0%
+it's actually an in instruction that
+ 
+
+ align:start position:0%
+it's actually an in instruction that
+makes an ox ad0 interrupt which is a way
+
+ align:start position:0%
+makes an ox ad0 interrupt which is a way
+ 
+
+ align:start position:0%
+makes an ox ad0 interrupt which is a way
+one way to make system calls in Linux so
+
+ align:start position:0%
+one way to make system calls in Linux so
+ 
+
+ align:start position:0%
+one way to make system calls in Linux so
+if you miss this fact then potentially
+
+ align:start position:0%
+if you miss this fact then potentially
+ 
+
+ align:start position:0%
+if you miss this fact then potentially
+you're going to allow this unrusted
+
+ align:start position:0%
+you're going to allow this unrusted
+ 
+
+ align:start position:0%
+you're going to allow this unrusted
+module to jump into the kernel and make
+
+ align:start position:0%
+module to jump into the kernel and make
+ 
+
+ align:start position:0%
+module to jump into the kernel and make
+system calls which is what you wanted to
+
+ align:start position:0%
+system calls which is what you wanted to
+ 
+
+ align:start position:0%
+system calls which is what you wanted to
+prevent make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how could we prevent it like one
+
+ align:start position:0%
+so how could we prevent it like one
+ 
+
+ align:start position:0%
+so how could we prevent it like one
+possibility is maybe we should like
+
+ align:start position:0%
+possibility is maybe we should like
+ 
+
+ align:start position:0%
+possibility is maybe we should like
+try looking at every bite offet because
+
+ align:start position:0%
+try looking at every bite offet because
+ 
+
+ align:start position:0%
+try looking at every bite offet because
+you know at least x86 can only start
+
+ align:start position:0%
+you know at least x86 can only start
+ 
+
+ align:start position:0%
+you know at least x86 can only start
+interpreting instruction on a bite
+
+ align:start position:0%
+interpreting instruction on a bite
+ 
+
+ align:start position:0%
+interpreting instruction on a bite
+boundary instead of a bit boundary um so
+
+ align:start position:0%
+boundary instead of a bit boundary um so
+ 
+
+ align:start position:0%
+boundary instead of a bit boundary um so
+you like look at every single possible
+
+ align:start position:0%
+you like look at every single possible
+ 
+
+ align:start position:0%
+you like look at every single possible
+bite offset and you see what instruction
+
+ align:start position:0%
+bite offset and you see what instruction
+ 
+
+ align:start position:0%
+bite offset and you see what instruction
+starts
+
+ align:start position:0%
+starts
+ 
+
+ align:start position:0%
+starts
+there is this a reasonable plan could it
+
+ align:start position:0%
+there is this a reasonable plan could it
+ 
+
+ align:start position:0%
+there is this a reasonable plan could it
+work yeah I mean what if someone
+
+ align:start position:0%
+work yeah I mean what if someone
+ 
+
+ align:start position:0%
+work yeah I mean what if someone
+actually is doing in and that they're
+
+ align:start position:0%
+actually is doing in and that they're
+ 
+
+ align:start position:0%
+actually is doing in and that they're
+never going to jump into that and now
+
+ align:start position:0%
+never going to jump into that and now
+ 
+
+ align:start position:0%
+never going to jump into that and now
+you're disallowing their program right
+
+ align:start position:0%
+you're disallowing their program right
+ 
+
+ align:start position:0%
+you're disallowing their program right
+so it's basically prone to potentially
+
+ align:start position:0%
+so it's basically prone to potentially
+ 
+
+ align:start position:0%
+so it's basically prone to potentially
+false positives um now you know if you
+
+ align:start position:0%
+false positives um now you know if you
+ 
+
+ align:start position:0%
+false positives um now you know if you
+really wanted to you could probably
+
+ align:start position:0%
+really wanted to you could probably
+ 
+
+ align:start position:0%
+really wanted to you could probably
+contort yourself and change the uh code
+
+ align:start position:0%
+contort yourself and change the uh code
+ 
+
+ align:start position:0%
+contort yourself and change the uh code
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+little and somehow avoid this if you
+
+ align:start position:0%
+little and somehow avoid this if you
+ 
+
+ align:start position:0%
+little and somehow avoid this if you
+knew exactly what the Checker was
+
+ align:start position:0%
+knew exactly what the Checker was
+ 
+
+ align:start position:0%
+knew exactly what the Checker was
+looking for you could potentially change
+
+ align:start position:0%
+looking for you could potentially change
+ 
+
+ align:start position:0%
+looking for you could potentially change
+these instructions you know maybe like
+
+ align:start position:0%
+these instructions you know maybe like
+ 
+
+ align:start position:0%
+these instructions you know maybe like
+end it with one thing first and then end
+
+ align:start position:0%
+end it with one thing first and then end
+ 
+
+ align:start position:0%
+end it with one thing first and then end
+it for with another mask later but to
+
+ align:start position:0%
+it for with another mask later but to
+ 
+
+ align:start position:0%
+it for with another mask later but to
+just avoid these suspicious bite
+
+ align:start position:0%
+just avoid these suspicious bite
+ 
+
+ align:start position:0%
+just avoid these suspicious bite
+patterns but that just seems pretty
+
+ align:start position:0%
+patterns but that just seems pretty
+ 
+
+ align:start position:0%
+patterns but that just seems pretty
+awkward to do um now it is actually
+
+ align:start position:0%
+awkward to do um now it is actually
+ 
+
+ align:start position:0%
+awkward to do um now it is actually
+possible Right their architecture does
+
+ align:start position:0%
+possible Right their architecture does
+ 
+
+ align:start position:0%
+possible Right their architecture does
+involve changing the compiler so in
+
+ align:start position:0%
+involve changing the compiler so in
+ 
+
+ align:start position:0%
+involve changing the compiler so in
+principle they do have some component
+
+ align:start position:0%
+principle they do have some component
+ 
+
+ align:start position:0%
+principle they do have some component
+that actually has to compile the code
+
+ align:start position:0%
+that actually has to compile the code
+ 
+
+ align:start position:0%
+that actually has to compile the code
+correctly it's not like you can you
+
+ align:start position:0%
+correctly it's not like you can you
+ 
+
+ align:start position:0%
+correctly it's not like you can you
+can't just take offthe shelf GCC and
+
+ align:start position:0%
+can't just take offthe shelf GCC and
+ 
+
+ align:start position:0%
+can't just take offthe shelf GCC and
+compile code for Native client so in
+
+ align:start position:0%
+compile code for Native client so in
+ 
+
+ align:start position:0%
+compile code for Native client so in
+principle it's doable but I think
+
+ align:start position:0%
+principle it's doable but I think
+ 
+
+ align:start position:0%
+principle it's doable but I think
+they're just thinking it's too much
+
+ align:start position:0%
+they're just thinking it's too much
+ 
+
+ align:start position:0%
+they're just thinking it's too much
+hassle and it's not going to be reliable
+
+ align:start position:0%
+hassle and it's not going to be reliable
+ 
+
+ align:start position:0%
+hassle and it's not going to be reliable
+or high performance
+
+ align:start position:0%
+or high performance
+ 
+
+ align:start position:0%
+or high performance
+Etc makes sense and plus there's a
+
+ align:start position:0%
+Etc makes sense and plus there's a
+ 
+
+ align:start position:0%
+Etc makes sense and plus there's a
+couple of x86 instructions that are
+
+ align:start position:0%
+couple of x86 instructions that are
+ 
+
+ align:start position:0%
+couple of x86 instructions that are
+prohibited or should be unsafe and
+
+ align:start position:0%
+prohibited or should be unsafe and
+ 
+
+ align:start position:0%
+prohibited or should be unsafe and
+prohibited but they're like one bite
+
+ align:start position:0%
+prohibited but they're like one bite
+ 
+
+ align:start position:0%
+prohibited but they're like one bite
+long so that is gonna be pretty damaging
+
+ align:start position:0%
+long so that is gonna be pretty damaging
+ 
+
+ align:start position:0%
+long so that is gonna be pretty damaging
+to to look for or to filter
+
+ align:start position:0%
+to to look for or to filter
+ 
+
+ align:start position:0%
+to to look for or to filter
+out okay so if they can't just
+
+ align:start position:0%
+out okay so if they can't just
+ 
+
+ align:start position:0%
+out okay so if they can't just
+disassemble sort of straight up and hope
+
+ align:start position:0%
+disassemble sort of straight up and hope
+ 
+
+ align:start position:0%
+disassemble sort of straight up and hope
+for the best then they need some other
+
+ align:start position:0%
+for the best then they need some other
+ 
+
+ align:start position:0%
+for the best then they need some other
+plan for doing this disassembly in a
+
+ align:start position:0%
+plan for doing this disassembly in a
+ 
+
+ align:start position:0%
+plan for doing this disassembly in a
+reliable fashion so so what is their
+
+ align:start position:0%
+reliable fashion so so what is their
+ 
+
+ align:start position:0%
+reliable fashion so so what is their
+plan a native client to ensure they
+
+ align:start position:0%
+plan a native client to ensure they
+ 
+
+ align:start position:0%
+plan a native client to ensure they
+don't get tripped up by this variable
+
+ align:start position:0%
+don't get tripped up by this variable
+ 
+
+ align:start position:0%
+don't get tripped up by this variable
+length
+
+ align:start position:0%
+length
+ 
+
+ align:start position:0%
+length
+encoding so I guess one way to think of
+
+ align:start position:0%
+encoding so I guess one way to think of
+ 
+
+ align:start position:0%
+encoding so I guess one way to think of
+it is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay so how are we're going to
+
+ align:start position:0%
+well okay so how are we're going to
+ 
+
+ align:start position:0%
+well okay so how are we're going to
+solve this reliable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disassembly so in some sense right if we
+
+ align:start position:0%
+disassembly so in some sense right if we
+ 
+
+ align:start position:0%
+disassembly so in some sense right if we
+if we really do scan forward from the
+
+ align:start position:0%
+if we really do scan forward from the
+ 
+
+ align:start position:0%
+if we really do scan forward from the
+left to the right and we look for all
+
+ align:start position:0%
+left to the right and we look for all
+ 
+
+ align:start position:0%
+left to the right and we look for all
+the possible up
+
+ align:start position:0%
+the possible up
+ 
+
+ align:start position:0%
+the possible up
+codes if that's the way the code
+
+ align:start position:0%
+codes if that's the way the code
+ 
+
+ align:start position:0%
+codes if that's the way the code
+executes then we're in good shape so
+
+ align:start position:0%
+executes then we're in good shape so
+ 
+
+ align:start position:0%
+executes then we're in good shape so
+even if there is some weird instruction
+
+ align:start position:0%
+even if there is some weird instruction
+ 
+
+ align:start position:0%
+even if there is some weird instruction
+at a some offset then the CPU isn't
+
+ align:start position:0%
+at a some offset then the CPU isn't
+ 
+
+ align:start position:0%
+at a some offset then the CPU isn't
+actually going to jump there if it
+
+ align:start position:0%
+actually going to jump there if it
+ 
+
+ align:start position:0%
+actually going to jump there if it
+actually executes the same way that
+
+ align:start position:0%
+actually executes the same way that
+ 
+
+ align:start position:0%
+actually executes the same way that
+we're scanning the instructions stream
+
+ align:start position:0%
+we're scanning the instructions stream
+ 
+
+ align:start position:0%
+we're scanning the instructions stream
+from left to right so the problem with
+
+ align:start position:0%
+from left to right so the problem with
+ 
+
+ align:start position:0%
+from left to right so the problem with
+reli with getting the disassembly to be
+
+ align:start position:0%
+reli with getting the disassembly to be
+ 
+
+ align:start position:0%
+reli with getting the disassembly to be
+reliable really comes from the fact that
+
+ align:start position:0%
+reliable really comes from the fact that
+ 
+
+ align:start position:0%
+reliable really comes from the fact that
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+jumps because if if we execute linearly
+
+ align:start position:0%
+jumps because if if we execute linearly
+ 
+
+ align:start position:0%
+jumps because if if we execute linearly
+from left to right then the CPU will
+
+ align:start position:0%
+from left to right then the CPU will
+ 
+
+ align:start position:0%
+from left to right then the CPU will
+follow the same rules that our Checker
+
+ align:start position:0%
+follow the same rules that our Checker
+ 
+
+ align:start position:0%
+follow the same rules that our Checker
+is following and see the same
+
+ align:start position:0%
+is following and see the same
+ 
+
+ align:start position:0%
+is following and see the same
+instruction Stream So the problem really
+
+ align:start position:0%
+instruction Stream So the problem really
+ 
+
+ align:start position:0%
+instruction Stream So the problem really
+comes down to what happens if there's a
+
+ align:start position:0%
+comes down to what happens if there's a
+ 
+
+ align:start position:0%
+comes down to what happens if there's a
+jump somewhere in the application could
+
+ align:start position:0%
+jump somewhere in the application could
+ 
+
+ align:start position:0%
+jump somewhere in the application could
+have jump to some position in the code
+
+ align:start position:0%
+have jump to some position in the code
+ 
+
+ align:start position:0%
+have jump to some position in the code
+that we didn't observe in our left to
+
+ align:start position:0%
+that we didn't observe in our left to
+ 
+
+ align:start position:0%
+that we didn't observe in our left to
+right scan
+
+ align:start position:0%
+right scan
+ 
+
+ align:start position:0%
+right scan
+so this is what they're sort of going
+
+ align:start position:0%
+so this is what they're sort of going
+ 
+
+ align:start position:0%
+so this is what they're sort of going
+after in the reliable disassembly and
+
+ align:start position:0%
+after in the reliable disassembly and
+ 
+
+ align:start position:0%
+after in the reliable disassembly and
+the basic plan is to just check where
+
+ align:start position:0%
+the basic plan is to just check where
+ 
+
+ align:start position:0%
+the basic plan is to just check where
+all the jumps go so it's actually fairly
+
+ align:start position:0%
+all the jumps go so it's actually fairly
+ 
+
+ align:start position:0%
+all the jumps go so it's actually fairly
+straightforward at some level um they
+
+ align:start position:0%
+straightforward at some level um they
+ 
+
+ align:start position:0%
+straightforward at some level um they
+have I guess a bunch of rules we'll look
+
+ align:start position:0%
+have I guess a bunch of rules we'll look
+ 
+
+ align:start position:0%
+have I guess a bunch of rules we'll look
+at in a second but roughly the plan is
+
+ align:start position:0%
+at in a second but roughly the plan is
+ 
+
+ align:start position:0%
+at in a second but roughly the plan is
+if you see a jump
+
+ align:start position:0%
+if you see a jump
+ 
+
+ align:start position:0%
+if you see a jump
+instruction then it actually has to be
+
+ align:start position:0%
+instruction then it actually has to be
+ 
+
+ align:start position:0%
+instruction then it actually has to be
+uh well you have to check that the
+
+ align:start position:0%
+uh well you have to check that the
+ 
+
+ align:start position:0%
+uh well you have to check that the
+target was seen before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you basically do the left to right
+
+ align:start position:0%
+so you basically do the left to right
+ 
+
+ align:start position:0%
+so you basically do the left to right
+scan that we sort of described in our
+
+ align:start position:0%
+scan that we sort of described in our
+ 
+
+ align:start position:0%
+scan that we sort of described in our
+naive approach here but then if you see
+
+ align:start position:0%
+naive approach here but then if you see
+ 
+
+ align:start position:0%
+naive approach here but then if you see
+any kind of a jump instruction then you
+
+ align:start position:0%
+any kind of a jump instruction then you
+ 
+
+ align:start position:0%
+any kind of a jump instruction then you
+see what the what is the address to
+
+ align:start position:0%
+see what the what is the address to
+ 
+
+ align:start position:0%
+see what the what is the address to
+which the jump instruction is pointing
+
+ align:start position:0%
+which the jump instruction is pointing
+ 
+
+ align:start position:0%
+which the jump instruction is pointing
+to and you make sure that it's an
+
+ align:start position:0%
+to and you make sure that it's an
+ 
+
+ align:start position:0%
+to and you make sure that it's an
+address that you saw in your left to
+
+ align:start position:0%
+address that you saw in your left to
+ 
+
+ align:start position:0%
+address that you saw in your left to
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+disassembly so if there's a jump
+
+ align:start position:0%
+disassembly so if there's a jump
+ 
+
+ align:start position:0%
+disassembly so if there's a jump
+instruction for example that goes to
+
+ align:start position:0%
+instruction for example that goes to
+ 
+
+ align:start position:0%
+instruction for example that goes to
+that CD bite then we're going to flag
+
+ align:start position:0%
+that CD bite then we're going to flag
+ 
+
+ align:start position:0%
+that CD bite then we're going to flag
+that jump as invalid because we never
+
+ align:start position:0%
+that jump as invalid because we never
+ 
+
+ align:start position:0%
+that jump as invalid because we never
+saw an instruction starting at the CD
+
+ align:start position:0%
+saw an instruction starting at the CD
+ 
+
+ align:start position:0%
+saw an instruction starting at the CD
+bite we saw a different instruction but
+
+ align:start position:0%
+bite we saw a different instruction but
+ 
+
+ align:start position:0%
+bite we saw a different instruction but
+if all the instruction if all the jumps
+
+ align:start position:0%
+if all the instruction if all the jumps
+ 
+
+ align:start position:0%
+if all the instruction if all the jumps
+go to the start of instructions we saw
+
+ align:start position:0%
+go to the start of instructions we saw
+ 
+
+ align:start position:0%
+go to the start of instructions we saw
+then we're in good
+
+ align:start position:0%
+then we're in good
+ 
+
+ align:start position:0%
+then we're in good
+shape that make
+
+ align:start position:0%
+shape that make
+ 
+
+ align:start position:0%
+shape that make
+sense so the one of course problem is
+
+ align:start position:0%
+sense so the one of course problem is
+ 
+
+ align:start position:0%
+sense so the one of course problem is
+that you can't check the targets of
+
+ align:start position:0%
+that you can't check the targets of
+ 
+
+ align:start position:0%
+that you can't check the targets of
+every jump in the program because there
+
+ align:start position:0%
+every jump in the program because there
+ 
+
+ align:start position:0%
+every jump in the program because there
+might be indirect jumps so for example
+
+ align:start position:0%
+might be indirect jumps so for example
+ 
+
+ align:start position:0%
+might be indirect jumps so for example
+in xd6 you could actually have something
+
+ align:start position:0%
+in xd6 you could actually have something
+ 
+
+ align:start position:0%
+in xd6 you could actually have something
+like jump to the value of the eax
+
+ align:start position:0%
+like jump to the value of the eax
+ 
+
+ align:start position:0%
+like jump to the value of the eax
+register so this is great for
+
+ align:start position:0%
+register so this is great for
+ 
+
+ align:start position:0%
+register so this is great for
+implementing function pointers you store
+
+ align:start position:0%
+implementing function pointers you store
+ 
+
+ align:start position:0%
+implementing function pointers you store
+the function pointer somewhere in memory
+
+ align:start position:0%
+the function pointer somewhere in memory
+ 
+
+ align:start position:0%
+the function pointer somewhere in memory
+then you load the function pointer into
+
+ align:start position:0%
+then you load the function pointer into
+ 
+
+ align:start position:0%
+then you load the function pointer into
+some register at run time and then you
+
+ align:start position:0%
+some register at run time and then you
+ 
+
+ align:start position:0%
+some register at run time and then you
+jump to whatever address was in the that
+
+ align:start position:0%
+jump to whatever address was in the that
+ 
+
+ align:start position:0%
+jump to whatever address was in the that
+memory location and
+
+ align:start position:0%
+memory location and
+ 
+
+ align:start position:0%
+memory location and
+register so how do these guys deal with
+
+ align:start position:0%
+register so how do these guys deal with
+ 
+
+ align:start position:0%
+register so how do these guys deal with
+these indirect jumps so they have no
+
+ align:start position:0%
+these indirect jumps so they have no
+ 
+
+ align:start position:0%
+these indirect jumps so they have no
+idea if it's actually going to jump to
+
+ align:start position:0%
+idea if it's actually going to jump to
+ 
+
+ align:start position:0%
+idea if it's actually going to jump to
+the CD b or the 25 byte what do they do
+
+ align:start position:0%
+the CD b or the 25 byte what do they do
+ 
+
+ align:start position:0%
+the CD b or the 25 byte what do they do
+yeah yeah so this is their basically
+
+ align:start position:0%
+yeah yeah so this is their basically
+ 
+
+ align:start position:0%
+yeah yeah so this is their basically
+main trick here is instrumentation so
+
+ align:start position:0%
+main trick here is instrumentation so
+ 
+
+ align:start position:0%
+main trick here is instrumentation so
+whenever they see a jump like this what
+
+ align:start position:0%
+whenever they see a jump like this what
+ 
+
+ align:start position:0%
+whenever they see a jump like this what
+they actually what the compiler is going
+
+ align:start position:0%
+they actually what the compiler is going
+ 
+
+ align:start position:0%
+they actually what the compiler is going
+to generate is a proof that this jump is
+
+ align:start position:0%
+to generate is a proof that this jump is
+ 
+
+ align:start position:0%
+to generate is a proof that this jump is
+actually going to do the the right thing
+
+ align:start position:0%
+actually going to do the the right thing
+ 
+
+ align:start position:0%
+actually going to do the the right thing
+and the way they actually do this is
+
+ align:start position:0%
+and the way they actually do this is
+ 
+
+ align:start position:0%
+and the way they actually do this is
+well they don't actually know it's
+
+ align:start position:0%
+well they don't actually know it's
+ 
+
+ align:start position:0%
+well they don't actually know it's
+actually kind of hard to put in a proof
+
+ align:start position:0%
+actually kind of hard to put in a proof
+ 
+
+ align:start position:0%
+actually kind of hard to put in a proof
+here that it's one of the addresses that
+
+ align:start position:0%
+here that it's one of the addresses that
+ 
+
+ align:start position:0%
+here that it's one of the addresses that
+you saw during the left to right
+
+ align:start position:0%
+you saw during the left to right
+ 
+
+ align:start position:0%
+you saw during the left to right
+disassembly so instead what they do is
+
+ align:start position:0%
+disassembly so instead what they do is
+ 
+
+ align:start position:0%
+disassembly so instead what they do is
+they want to make sure that all the
+
+ align:start position:0%
+they want to make sure that all the
+ 
+
+ align:start position:0%
+they want to make sure that all the
+jumps go to multiples of 32 bytes and
+
+ align:start position:0%
+jumps go to multiples of 32 bytes and
+ 
+
+ align:start position:0%
+jumps go to multiples of 32 bytes and
+the way they do this is they actually
+
+ align:start position:0%
+the way they do this is they actually
+ 
+
+ align:start position:0%
+the way they do this is they actually
+change all the jump instructions into
+
+ align:start position:0%
+change all the jump instructions into
+ 
+
+ align:start position:0%
+change all the jump instructions into
+something that they call a pseudo
+
+ align:start position:0%
+something that they call a pseudo
+ 
+
+ align:start position:0%
+something that they call a pseudo
+instruction so there's still that sort
+
+ align:start position:0%
+instruction so there's still that sort
+ 
+
+ align:start position:0%
+instruction so there's still that sort
+of jump to you know gu the eax register
+
+ align:start position:0%
+of jump to you know gu the eax register
+ 
+
+ align:start position:0%
+of jump to you know gu the eax register
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+end but they prefix it with an end
+
+ align:start position:0%
+end but they prefix it with an end
+ 
+
+ align:start position:0%
+end but they prefix it with an end
+instruction that uh is going to
+
+ align:start position:0%
+instruction that uh is going to
+ 
+
+ align:start position:0%
+instruction that uh is going to
+clear the low five
+
+ align:start position:0%
+clear the low five
+ 
+
+ align:start position:0%
+clear the low five
+bits
+
+ align:start position:0%
+bits
+ 
+
+ align:start position:0%
+bits
+F uh 1 2 3 4 5 6 e0 with the eax
+
+ align:start position:0%
+F uh 1 2 3 4 5 6 e0 with the eax
+ 
+
+ align:start position:0%
+F uh 1 2 3 4 5 6 e0 with the eax
+register so this and instruction clears
+
+ align:start position:0%
+register so this and instruction clears
+ 
+
+ align:start position:0%
+register so this and instruction clears
+the low five bits which means that it
+
+ align:start position:0%
+the low five bits which means that it
+ 
+
+ align:start position:0%
+the low five bits which means that it
+forces this value to be a multiple of 32
+
+ align:start position:0%
+forces this value to be a multiple of 32
+ 
+
+ align:start position:0%
+forces this value to be a multiple of 32
+2 to the
+
+ align:start position:0%
+2 to the
+ 
+
+ align:start position:0%
+2 to the
+5 and then you jump to it so if you look
+
+ align:start position:0%
+5 and then you jump to it so if you look
+ 
+
+ align:start position:0%
+5 and then you jump to it so if you look
+at it during verification time then you
+
+ align:start position:0%
+at it during verification time then you
+ 
+
+ align:start position:0%
+at it during verification time then you
+can sort of convince yourself that this
+
+ align:start position:0%
+can sort of convince yourself that this
+ 
+
+ align:start position:0%
+can sort of convince yourself that this
+instruction this in this instruction
+
+ align:start position:0%
+instruction this in this instruction
+ 
+
+ align:start position:0%
+instruction this in this instruction
+pair will only jump to a multiple of 32
+
+ align:start position:0%
+pair will only jump to a multiple of 32
+ 
+
+ align:start position:0%
+pair will only jump to a multiple of 32
+bytes and then in order to make sure
+
+ align:start position:0%
+bytes and then in order to make sure
+ 
+
+ align:start position:0%
+bytes and then in order to make sure
+that this is not going to jump to some
+
+ align:start position:0%
+that this is not going to jump to some
+ 
+
+ align:start position:0%
+that this is not going to jump to some
+weird instruction you're going to
+
+ align:start position:0%
+weird instruction you're going to
+ 
+
+ align:start position:0%
+weird instruction you're going to
+enforce an extra rule which is that
+
+ align:start position:0%
+enforce an extra rule which is that
+ 
+
+ align:start position:0%
+enforce an extra rule which is that
+during your disassembly when you're
+
+ align:start position:0%
+during your disassembly when you're
+ 
+
+ align:start position:0%
+during your disassembly when you're
+scanning the instructions from left to
+
+ align:start position:0%
+scanning the instructions from left to
+ 
+
+ align:start position:0%
+scanning the instructions from left to
+right you're going to ensure that every
+
+ align:start position:0%
+right you're going to ensure that every
+ 
+
+ align:start position:0%
+right you're going to ensure that every
+multiple of 32 bytes is a start of a
+
+ align:start position:0%
+multiple of 32 bytes is a start of a
+ 
+
+ align:start position:0%
+multiple of 32 bytes is a start of a
+valid
+
+ align:start position:0%
+valid
+ 
+
+ align:start position:0%
+valid
+instruction so in addition to this
+
+ align:start position:0%
+instruction so in addition to this
+ 
+
+ align:start position:0%
+instruction so in addition to this
+instrumentation you also are going to
+
+ align:start position:0%
+instrumentation you also are going to
+ 
+
+ align:start position:0%
+instrumentation you also are going to
+check that
+
+ align:start position:0%
+check that
+ 
+
+ align:start position:0%
+check that
+every multiple of
+
+ align:start position:0%
+every multiple of
+ 
+
+ align:start position:0%
+every multiple of
+32 is a valid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instruction and well what what I mean by
+
+ align:start position:0%
+instruction and well what what I mean by
+ 
+
+ align:start position:0%
+instruction and well what what I mean by
+valid instruction here is it's an
+
+ align:start position:0%
+valid instruction here is it's an
+ 
+
+ align:start position:0%
+valid instruction here is it's an
+instruction that you see when you
+
+ align:start position:0%
+instruction that you see when you
+ 
+
+ align:start position:0%
+instruction that you see when you
+disassemble from left to right
+
+ align:start position:0%
+disassemble from left to right
+ 
+
+ align:start position:0%
+disassemble from left to right
+yeah2 well yeah so why do they choose 32
+
+ align:start position:0%
+yeah2 well yeah so why do they choose 32
+ 
+
+ align:start position:0%
+yeah2 well yeah so why do they choose 32
+that seems like some magic number they
+
+ align:start position:0%
+that seems like some magic number they
+ 
+
+ align:start position:0%
+that seems like some magic number they
+pulled out of a hat like should you
+
+ align:start position:0%
+pulled out of a hat like should you
+ 
+
+ align:start position:0%
+pulled out of a hat like should you
+choose a thousand or
+
+ align:start position:0%
+choose a thousand or
+ 
+
+ align:start position:0%
+choose a thousand or
+five any comment okay like should we
+
+ align:start position:0%
+five any comment okay like should we
+ 
+
+ align:start position:0%
+five any comment okay like should we
+choose five is okay so why is five bad
+
+ align:start position:0%
+choose five is okay so why is five bad
+ 
+
+ align:start position:0%
+choose five is okay so why is five bad
+power of two yes okay so we want a power
+
+ align:start position:0%
+power of two yes okay so we want a power
+ 
+
+ align:start position:0%
+power of two yes okay so we want a power
+of two okay so good point because
+
+ align:start position:0%
+of two okay so good point because
+ 
+
+ align:start position:0%
+of two okay so good point because
+otherwise like ensuring something is a
+
+ align:start position:0%
+otherwise like ensuring something is a
+ 
+
+ align:start position:0%
+otherwise like ensuring something is a
+multiple of five is going to require a
+
+ align:start position:0%
+multiple of five is going to require a
+ 
+
+ align:start position:0%
+multiple of five is going to require a
+couple of instruction here which is
+
+ align:start position:0%
+couple of instruction here which is
+ 
+
+ align:start position:0%
+couple of instruction here which is
+going to lead to overhead okay how about
+
+ align:start position:0%
+going to lead to overhead okay how about
+ 
+
+ align:start position:0%
+going to lead to overhead okay how about
+eight is eight good enough yeah you can
+
+ align:start position:0%
+eight is eight good enough yeah you can
+ 
+
+ align:start position:0%
+eight is eight good enough yeah you can
+have instruction long yeah okay so it
+
+ align:start position:0%
+have instruction long yeah okay so it
+ 
+
+ align:start position:0%
+have instruction long yeah okay so it
+has to be at least as long as the
+
+ align:start position:0%
+has to be at least as long as the
+ 
+
+ align:start position:0%
+has to be at least as long as the
+longest x86 instruction you want to
+
+ align:start position:0%
+longest x86 instruction you want to
+ 
+
+ align:start position:0%
+longest x86 instruction you want to
+allow so if there's a 10 BTE instruction
+
+ align:start position:0%
+allow so if there's a 10 BTE instruction
+ 
+
+ align:start position:0%
+allow so if there's a 10 BTE instruction
+everything has to be a multiple of eight
+
+ align:start position:0%
+everything has to be a multiple of eight
+ 
+
+ align:start position:0%
+everything has to be a multiple of eight
+well you're kind of screwed with that 10
+
+ align:start position:0%
+well you're kind of screwed with that 10
+ 
+
+ align:start position:0%
+well you're kind of screwed with that 10
+B instruction there's nowhere to put it
+
+ align:start position:0%
+B instruction there's nowhere to put it
+ 
+
+ align:start position:0%
+B instruction there's nowhere to put it
+um so it has to be at least as long so
+
+ align:start position:0%
+um so it has to be at least as long so
+ 
+
+ align:start position:0%
+um so it has to be at least as long so
+32 is pretty good like the biggest I
+
+ align:start position:0%
+32 is pretty good like the biggest I
+ 
+
+ align:start position:0%
+32 is pretty good like the biggest I
+could find was 15 bytes so it's probably
+
+ align:start position:0%
+could find was 15 bytes so it's probably
+ 
+
+ align:start position:0%
+could find was 15 bytes so it's probably
+good enough yeah be longer than that I
+
+ align:start position:0%
+good enough yeah be longer than that I
+ 
+
+ align:start position:0%
+good enough yeah be longer than that I
+think it's called the trampoline code
+
+ align:start position:0%
+think it's called the trampoline code
+ 
+
+ align:start position:0%
+think it's called the trampoline code
+they have to like you know have a he
+
+ align:start position:0%
+they have to like you know have a he
+ 
+
+ align:start position:0%
+they have to like you know have a he
+instruction at the beginning second so
+
+ align:start position:0%
+instruction at the beginning second so
+ 
+
+ align:start position:0%
+instruction at the beginning second so
+you can't just jump directly into there
+
+ align:start position:0%
+you can't just jump directly into there
+ 
+
+ align:start position:0%
+you can't just jump directly into there
+like code and then they also need REM
+
+ align:start position:0%
+like code and then they also need REM
+ 
+
+ align:start position:0%
+like code and then they also need REM
+jump instruction that like jumps to you
+
+ align:start position:0%
+jump instruction that like jumps to you
+ 
+
+ align:start position:0%
+jump instruction that like jumps to you
+know another like that's right yeah so
+
+ align:start position:0%
+know another like that's right yeah so
+ 
+
+ align:start position:0%
+know another like that's right yeah so
+you have to be able to fit for their
+
+ align:start position:0%
+you have to be able to fit for their
+ 
+
+ align:start position:0%
+you have to be able to fit for their
+entry and exit from The Trusted service
+
+ align:start position:0%
+entry and exit from The Trusted service
+ 
+
+ align:start position:0%
+entry and exit from The Trusted service
+run time you need to be able to fit some
+
+ align:start position:0%
+run time you need to be able to fit some
+ 
+
+ align:start position:0%
+run time you need to be able to fit some
+non-trivial amount of code in a single
+
+ align:start position:0%
+non-trivial amount of code in a single
+ 
+
+ align:start position:0%
+non-trivial amount of code in a single
+32 byte slot we'll see how this works in
+
+ align:start position:0%
+32 byte slot we'll see how this works in
+ 
+
+ align:start position:0%
+32 byte slot we'll see how this works in
+a second or even 31 byte slot as you're
+
+ align:start position:0%
+a second or even 31 byte slot as you're
+ 
+
+ align:start position:0%
+a second or even 31 byte slot as you're
+pointing out for one hold instruction um
+
+ align:start position:0%
+pointing out for one hold instruction um
+ 
+
+ align:start position:0%
+pointing out for one hold instruction um
+should it be much larger should we make
+
+ align:start position:0%
+should it be much larger should we make
+ 
+
+ align:start position:0%
+should it be much larger should we make
+it I don't know a th by well 1024
+
+ align:start position:0%
+it I don't know a th by well 1024
+ 
+
+ align:start position:0%
+it I don't know a th by well 1024
+problem your too SP because you have
+
+ align:start position:0%
+problem your too SP because you have
+ 
+
+ align:start position:0%
+problem your too SP because you have
+jum yeah so if if you if you have a lot
+
+ align:start position:0%
+jum yeah so if if you if you have a lot
+ 
+
+ align:start position:0%
+jum yeah so if if you if you have a lot
+of function pointers or lots of sort of
+
+ align:start position:0%
+of function pointers or lots of sort of
+ 
+
+ align:start position:0%
+of function pointers or lots of sort of
+indirect jumps then every time you want
+
+ align:start position:0%
+indirect jumps then every time you want
+ 
+
+ align:start position:0%
+indirect jumps then every time you want
+to create some place where you're going
+
+ align:start position:0%
+to create some place where you're going
+ 
+
+ align:start position:0%
+to create some place where you're going
+to jump two you have to Pat it out to
+
+ align:start position:0%
+to jump two you have to Pat it out to
+ 
+
+ align:start position:0%
+to jump two you have to Pat it out to
+the next boundary of whatever this value
+
+ align:start position:0%
+the next boundary of whatever this value
+ 
+
+ align:start position:0%
+the next boundary of whatever this value
+is so with 32 maybe that's okay you're
+
+ align:start position:0%
+is so with 32 maybe that's okay you're
+ 
+
+ align:start position:0%
+is so with 32 maybe that's okay you're
+like well worst case you waste 31 bytes
+
+ align:start position:0%
+like well worst case you waste 31 bytes
+ 
+
+ align:start position:0%
+like well worst case you waste 31 bytes
+because you just need to fast forward to
+
+ align:start position:0%
+because you just need to fast forward to
+ 
+
+ align:start position:0%
+because you just need to fast forward to
+the next boundary but if it's a multiple
+
+ align:start position:0%
+the next boundary but if it's a multiple
+ 
+
+ align:start position:0%
+the next boundary but if it's a multiple
+of a 1024 then all of a sudden you're
+
+ align:start position:0%
+of a 1024 then all of a sudden you're
+ 
+
+ align:start position:0%
+of a 1024 then all of a sudden you're
+wasting a kilobyte of memory for an
+
+ align:start position:0%
+wasting a kilobyte of memory for an
+ 
+
+ align:start position:0%
+wasting a kilobyte of memory for an
+indirect
+
+ align:start position:0%
+indirect
+ 
+
+ align:start position:0%
+indirect
+jump and if you have probably you know
+
+ align:start position:0%
+jump and if you have probably you know
+ 
+
+ align:start position:0%
+jump and if you have probably you know
+short functions or you know lots of
+
+ align:start position:0%
+short functions or you know lots of
+ 
+
+ align:start position:0%
+short functions or you know lots of
+function pointers then this might
+
+ align:start position:0%
+function pointers then this might
+ 
+
+ align:start position:0%
+function pointers then this might
+actually be a memory overhead all of a
+
+ align:start position:0%
+actually be a memory overhead all of a
+ 
+
+ align:start position:0%
+actually be a memory overhead all of a
+sudden as well do that make sense
+
+ align:start position:0%
+sudden as well do that make sense
+ 
+
+ align:start position:0%
+sudden as well do that make sense
+roughly so yeah I think the 32 is not
+
+ align:start position:0%
+roughly so yeah I think the 32 is not
+ 
+
+ align:start position:0%
+roughly so yeah I think the 32 is not
+like set in stone like native client has
+
+ align:start position:0%
+like set in stone like native client has
+ 
+
+ align:start position:0%
+like set in stone like native client has
+to have 32 byte blocks but you know
+
+ align:start position:0%
+to have 32 byte blocks but you know
+ 
+
+ align:start position:0%
+to have 32 byte blocks but you know
+something on that order probably works
+
+ align:start position:0%
+something on that order probably works
+ 
+
+ align:start position:0%
+something on that order probably works
+16 is probably a little short on the
+
+ align:start position:0%
+16 is probably a little short on the
+ 
+
+ align:start position:0%
+16 is probably a little short on the
+other hand like 64 could work 128 maybe
+
+ align:start position:0%
+other hand like 64 could work 128 maybe
+ 
+
+ align:start position:0%
+other hand like 64 could work 128 maybe
+it's getting a little longish but it's I
+
+ align:start position:0%
+it's getting a little longish but it's I
+ 
+
+ align:start position:0%
+it's getting a little longish but it's I
+don't think you can derive 32 from first
+
+ align:start position:0%
+don't think you can derive 32 from first
+ 
+
+ align:start position:0%
+don't think you can derive 32 from first
+principles make sense
+
+ align:start position:0%
+principles make sense
+ 
+
+ align:start position:0%
+principles make sense
+all right so that's sort a plan for
+
+ align:start position:0%
+all right so that's sort a plan for
+ 
+
+ align:start position:0%
+all right so that's sort a plan for
+Reliable disassembly and as a result
+
+ align:start position:0%
+Reliable disassembly and as a result
+ 
+
+ align:start position:0%
+Reliable disassembly and as a result
+sort of the the compiler has to be a has
+
+ align:start position:0%
+sort of the the compiler has to be a has
+ 
+
+ align:start position:0%
+sort of the the compiler has to be a has
+to be a little bit careful when it's
+
+ align:start position:0%
+to be a little bit careful when it's
+ 
+
+ align:start position:0%
+to be a little bit careful when it's
+compiling your C or C++ code into a
+
+ align:start position:0%
+compiling your C or C++ code into a
+ 
+
+ align:start position:0%
+compiling your C or C++ code into a
+native client binary it has to basically
+
+ align:start position:0%
+native client binary it has to basically
+ 
+
+ align:start position:0%
+native client binary it has to basically
+follow these rules so whenever it has a
+
+ align:start position:0%
+follow these rules so whenever it has a
+ 
+
+ align:start position:0%
+follow these rules so whenever it has a
+jump it has to instru add this extra
+
+ align:start position:0%
+jump it has to instru add this extra
+ 
+
+ align:start position:0%
+jump it has to instru add this extra
+instruction in front and whenever it's
+
+ align:start position:0%
+instruction in front and whenever it's
+ 
+
+ align:start position:0%
+instruction in front and whenever it's
+creating a function that it's going to
+
+ align:start position:0%
+creating a function that it's going to
+ 
+
+ align:start position:0%
+creating a function that it's going to
+jump to or an instruction is going to
+
+ align:start position:0%
+jump to or an instruction is going to
+ 
+
+ align:start position:0%
+jump to or an instruction is going to
+jump to as we were talking about it has
+
+ align:start position:0%
+jump to as we were talking about it has
+ 
+
+ align:start position:0%
+jump to as we were talking about it has
+to Pat out and it can just Pat it out
+
+ align:start position:0%
+to Pat out and it can just Pat it out
+ 
+
+ align:start position:0%
+to Pat out and it can just Pat it out
+with zeros because all those have to be
+
+ align:start position:0%
+with zeros because all those have to be
+ 
+
+ align:start position:0%
+with zeros because all those have to be
+valid up code so it actually has to Pat
+
+ align:start position:0%
+valid up code so it actually has to Pat
+ 
+
+ align:start position:0%
+valid up code so it actually has to Pat
+it out with knobs just to make the
+
+ align:start position:0%
+it out with knobs just to make the
+ 
+
+ align:start position:0%
+it out with knobs just to make the
+validator happy just to make sure that
+
+ align:start position:0%
+validator happy just to make sure that
+ 
+
+ align:start position:0%
+validator happy just to make sure that
+every possible instruction is a valid
+
+ align:start position:0%
+every possible instruction is a valid
+ 
+
+ align:start position:0%
+every possible instruction is a valid
+one and luckily on x86 KN is a single
+
+ align:start position:0%
+one and luckily on x86 KN is a single
+ 
+
+ align:start position:0%
+one and luckily on x86 KN is a single
+bite so or at least there is a no that's
+
+ align:start position:0%
+bite so or at least there is a no that's
+ 
+
+ align:start position:0%
+bite so or at least there is a no that's
+a single bite there's many NOS on x86 uh
+
+ align:start position:0%
+a single bite there's many NOS on x86 uh
+ 
+
+ align:start position:0%
+a single bite there's many NOS on x86 uh
+so you can always pan things out to a
+
+ align:start position:0%
+so you can always pan things out to a
+ 
+
+ align:start position:0%
+so you can always pan things out to a
+multiple of whatever this constant
+
+ align:start position:0%
+multiple of whatever this constant
+ 
+
+ align:start position:0%
+multiple of whatever this constant
+is make
+
+ align:start position:0%
+is make
+ 
+
+ align:start position:0%
+is make
+sense all right so
+
+ align:start position:0%
+sense all right so
+ 
+
+ align:start position:0%
+sense all right so
+so what does this guarantee to us I
+
+ align:start position:0%
+so what does this guarantee to us I
+ 
+
+ align:start position:0%
+so what does this guarantee to us I
+guess what what what what this makes
+
+ align:start position:0%
+guess what what what what this makes
+ 
+
+ align:start position:0%
+guess what what what what this makes
+sure is that we always see what happens
+
+ align:start position:0%
+sure is that we always see what happens
+ 
+
+ align:start position:0%
+sure is that we always see what happens
+in terms of the instructions that will
+
+ align:start position:0%
+in terms of the instructions that will
+ 
+
+ align:start position:0%
+in terms of the instructions that will
+be executed so this finally gets us this
+
+ align:start position:0%
+be executed so this finally gets us this
+ 
+
+ align:start position:0%
+be executed so this finally gets us this
+rule so we can be sure there's never a
+
+ align:start position:0%
+rule so we can be sure there's never a
+ 
+
+ align:start position:0%
+rule so we can be sure there's never a
+system call being
+
+ align:start position:0%
+system call being
+ 
+
+ align:start position:0%
+system call being
+issued what about so this is for jumps
+
+ align:start position:0%
+issued what about so this is for jumps
+ 
+
+ align:start position:0%
+issued what about so this is for jumps
+what about returns how do they deal with
+
+ align:start position:0%
+what about returns how do they deal with
+ 
+
+ align:start position:0%
+what about returns how do they deal with
+returns can you return from a function
+
+ align:start position:0%
+returns can you return from a function
+ 
+
+ align:start position:0%
+returns can you return from a function
+in Native
+
+ align:start position:0%
+in Native
+ 
+
+ align:start position:0%
+in Native
+client gu what would happen if you ran a
+
+ align:start position:0%
+client gu what would happen if you ran a
+ 
+
+ align:start position:0%
+client gu what would happen if you ran a
+red op
+
+ align:start position:0%
+red op
+ 
+
+ align:start position:0%
+red op
+code that' be good yeah po the stack you
+
+ align:start position:0%
+code that' be good yeah po the stack you
+ 
+
+ align:start position:0%
+code that' be good yeah po the stack you
+don't want theode to be modifying your
+
+ align:start position:0%
+don't want theode to be modifying your
+ 
+
+ align:start position:0%
+don't want theode to be modifying your
+overall St well so it's true that it
+
+ align:start position:0%
+overall St well so it's true that it
+ 
+
+ align:start position:0%
+overall St well so it's true that it
+pops the stack
+
+ align:start position:0%
+pops the stack
+ 
+
+ align:start position:0%
+pops the stack
+but the stack that native client modules
+
+ align:start position:0%
+but the stack that native client modules
+ 
+
+ align:start position:0%
+but the stack that native client modules
+use is actually just some data inside of
+
+ align:start position:0%
+use is actually just some data inside of
+ 
+
+ align:start position:0%
+use is actually just some data inside of
+their section so you don't actually care
+
+ align:start position:0%
+their section so you don't actually care
+ 
+
+ align:start position:0%
+their section so you don't actually care
+well the native client runtime doesn't
+
+ align:start position:0%
+well the native client runtime doesn't
+ 
+
+ align:start position:0%
+well the native client runtime doesn't
+care whether this guy screws up their
+
+ align:start position:0%
+care whether this guy screws up their
+ 
+
+ align:start position:0%
+care whether this guy screws up their
+stack overflows their stack or what but
+
+ align:start position:0%
+stack overflows their stack or what but
+ 
+
+ align:start position:0%
+stack overflows their stack or what but
+but you can put anything on the stack
+
+ align:start position:0%
+but you can put anything on the stack
+ 
+
+ align:start position:0%
+but you can put anything on the stack
+and when you return you jump for that
+
+ align:start position:0%
+and when you return you jump for that
+ 
+
+ align:start position:0%
+and when you return you jump for that
+that's true yeah so return is almost
+
+ align:start position:0%
+that's true yeah so return is almost
+ 
+
+ align:start position:0%
+that's true yeah so return is almost
+like an indirect jump from a particular
+
+ align:start position:0%
+like an indirect jump from a particular
+ 
+
+ align:start position:0%
+like an indirect jump from a particular
+weird memory location that's the top of
+
+ align:start position:0%
+weird memory location that's the top of
+ 
+
+ align:start position:0%
+weird memory location that's the top of
+the stack so I guess one thing they
+
+ align:start position:0%
+the stack so I guess one thing they
+ 
+
+ align:start position:0%
+the stack so I guess one thing they
+could do for returns is maybe prefix it
+
+ align:start position:0%
+could do for returns is maybe prefix it
+ 
+
+ align:start position:0%
+could do for returns is maybe prefix it
+with a similar check where maybe you
+
+ align:start position:0%
+with a similar check where maybe you
+ 
+
+ align:start position:0%
+with a similar check where maybe you
+like pop the top thing of the stack you
+
+ align:start position:0%
+like pop the top thing of the stack you
+ 
+
+ align:start position:0%
+like pop the top thing of the stack you
+check whether it's valid and then you WR
+
+ align:start position:0%
+check whether it's valid and then you WR
+ 
+
+ align:start position:0%
+check whether it's valid and then you WR
+maybe you somehow do an and to a memory
+
+ align:start position:0%
+maybe you somehow do an and to a memory
+ 
+
+ align:start position:0%
+maybe you somehow do an and to a memory
+oper and that's the top of the stack um
+
+ align:start position:0%
+oper and that's the top of the stack um
+ 
+
+ align:start position:0%
+oper and that's the top of the stack um
+that seems a little fragile um partly
+
+ align:start position:0%
+that seems a little fragile um partly
+ 
+
+ align:start position:0%
+that seems a little fragile um partly
+because of race conditions because for
+
+ align:start position:0%
+because of race conditions because for
+ 
+
+ align:start position:0%
+because of race conditions because for
+example if you look at the top location
+
+ align:start position:0%
+example if you look at the top location
+ 
+
+ align:start position:0%
+example if you look at the top location
+on a stack and you check that it's okay
+
+ align:start position:0%
+on a stack and you check that it's okay
+ 
+
+ align:start position:0%
+on a stack and you check that it's okay
+and then you do a r later another thread
+
+ align:start position:0%
+and then you do a r later another thread
+ 
+
+ align:start position:0%
+and then you do a r later another thread
+in the same module could modify the
+
+ align:start position:0%
+in the same module could modify the
+ 
+
+ align:start position:0%
+in the same module could modify the
+thing at the top of the stack uh and
+
+ align:start position:0%
+thing at the top of the stack uh and
+ 
+
+ align:start position:0%
+thing at the top of the stack uh and
+then you would be returning to a bad
+
+ align:start position:0%
+then you would be returning to a bad
+ 
+
+ align:start position:0%
+then you would be returning to a bad
+address could this not be the case with
+
+ align:start position:0%
+address could this not be the case with
+ 
+
+ align:start position:0%
+address could this not be the case with
+the jumps as well yeah so what happens
+
+ align:start position:0%
+the jumps as well yeah so what happens
+ 
+
+ align:start position:0%
+the jumps as well yeah so what happens
+with a jump could a race condition
+
+ align:start position:0%
+with a jump could a race condition
+ 
+
+ align:start position:0%
+with a jump could a race condition
+somehow invalidate this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check yeah notable well so the code is
+
+ align:start position:0%
+check yeah notable well so the code is
+ 
+
+ align:start position:0%
+check yeah notable well so the code is
+not writable that's true so you can't
+
+ align:start position:0%
+not writable that's true so you can't
+ 
+
+ align:start position:0%
+not writable that's true so you can't
+modify the and but could another thread
+
+ align:start position:0%
+modify the and but could another thread
+ 
+
+ align:start position:0%
+modify the and but could another thread
+modify this jump Target in between these
+
+ align:start position:0%
+modify this jump Target in between these
+ 
+
+ align:start position:0%
+modify this jump Target in between these
+two instructions
+
+ align:start position:0%
+two instructions
+ 
+
+ align:start position:0%
+two instructions
+yeah yeah so that's the cool thing there
+
+ align:start position:0%
+yeah yeah so that's the cool thing there
+ 
+
+ align:start position:0%
+yeah yeah so that's the cool thing there
+there's basically well if if it modifies
+
+ align:start position:0%
+there's basically well if if it modifies
+ 
+
+ align:start position:0%
+there's basically well if if it modifies
+it in memory or wherever it loaded into
+
+ align:start position:0%
+it in memory or wherever it loaded into
+ 
+
+ align:start position:0%
+it in memory or wherever it loaded into
+E from sure it could do it before you
+
+ align:start position:0%
+E from sure it could do it before you
+ 
+
+ align:start position:0%
+E from sure it could do it before you
+load in which case this e will be bad
+
+ align:start position:0%
+load in which case this e will be bad
+ 
+
+ align:start position:0%
+load in which case this e will be bad
+but then will clear the bad bits or it
+
+ align:start position:0%
+but then will clear the bad bits or it
+ 
+
+ align:start position:0%
+but then will clear the bad bits or it
+could modify it after at which point
+
+ align:start position:0%
+could modify it after at which point
+ 
+
+ align:start position:0%
+could modify it after at which point
+it's already in eex so it doesn't matter
+
+ align:start position:0%
+it's already in eex so it doesn't matter
+ 
+
+ align:start position:0%
+it's already in eex so it doesn't matter
+that it's modifying the memory location
+
+ align:start position:0%
+that it's modifying the memory location
+ 
+
+ align:start position:0%
+that it's modifying the memory location
+from which the E register was
+
+ align:start position:0%
+from which the E register was
+ 
+
+ align:start position:0%
+from which the E register was
+loaded and threads don't actually share
+
+ align:start position:0%
+loaded and threads don't actually share
+ 
+
+ align:start position:0%
+loaded and threads don't actually share
+the register sets so if another thread
+
+ align:start position:0%
+the register sets so if another thread
+ 
+
+ align:start position:0%
+the register sets so if another thread
+modifies the eax register it will not
+
+ align:start position:0%
+modifies the eax register it will not
+ 
+
+ align:start position:0%
+modifies the eax register it will not
+affect this thread's eax register so
+
+ align:start position:0%
+affect this thread's eax register so
+ 
+
+ align:start position:0%
+affect this thread's eax register so
+this instruction actually is sort of
+
+ align:start position:0%
+this instruction actually is sort of
+ 
+
+ align:start position:0%
+this instruction actually is sort of
+race proof in some sense other threads
+
+ align:start position:0%
+race proof in some sense other threads
+ 
+
+ align:start position:0%
+race proof in some sense other threads
+can't invalidate this instruction
+
+ align:start position:0%
+can't invalidate this instruction
+ 
+
+ align:start position:0%
+can't invalidate this instruction
+sequence make
+
+ align:start position:0%
+sequence make
+ 
+
+ align:start position:0%
+sequence make
+sense all right so here's another
+
+ align:start position:0%
+sense all right so here's another
+ 
+
+ align:start position:0%
+sense all right so here's another
+interesting question
+
+ align:start position:0%
+interesting question
+ 
+
+ align:start position:0%
+interesting question
+um could we bypass this and like I can
+
+ align:start position:0%
+um could we bypass this and like I can
+ 
+
+ align:start position:0%
+um could we bypass this and like I can
+jump around on this address space all I
+
+ align:start position:0%
+jump around on this address space all I
+ 
+
+ align:start position:0%
+jump around on this address space all I
+want and when I'm disassembling this
+
+ align:start position:0%
+want and when I'm disassembling this
+ 
+
+ align:start position:0%
+want and when I'm disassembling this
+instruction this seems like a perfectly
+
+ align:start position:0%
+instruction this seems like a perfectly
+ 
+
+ align:start position:0%
+instruction this seems like a perfectly
+fine pair of instructions an and and a
+
+ align:start position:0%
+fine pair of instructions an and and a
+ 
+
+ align:start position:0%
+fine pair of instructions an and and a
+jump and the check for
+
+ align:start position:0%
+jump and the check for
+ 
+
+ align:start position:0%
+jump and the check for
+static jumps is that well it just has to
+
+ align:start position:0%
+static jumps is that well it just has to
+ 
+
+ align:start position:0%
+static jumps is that well it just has to
+point to some Target that was seen so
+
+ align:start position:0%
+point to some Target that was seen so
+ 
+
+ align:start position:0%
+point to some Target that was seen so
+yeah we saw an end that's one
+
+ align:start position:0%
+yeah we saw an end that's one
+ 
+
+ align:start position:0%
+yeah we saw an end that's one
+instruction that's valid we saw a jump
+
+ align:start position:0%
+instruction that's valid we saw a jump
+ 
+
+ align:start position:0%
+instruction that's valid we saw a jump
+that's another valid instruction so when
+
+ align:start position:0%
+that's another valid instruction so when
+ 
+
+ align:start position:0%
+that's another valid instruction so when
+I see a direct jump up here maybe I you
+
+ align:start position:0%
+I see a direct jump up here maybe I you
+ 
+
+ align:start position:0%
+I see a direct jump up here maybe I you
+know jump to some address I don't know 1
+
+ align:start position:0%
+know jump to some address I don't know 1
+ 
+
+ align:start position:0%
+know jump to some address I don't know 1
+2 3
+
+ align:start position:0%
+2 3
+ 
+
+ align:start position:0%
+2 3
+7 that's actually okay even though it's
+
+ align:start position:0%
+7 that's actually okay even though it's
+ 
+
+ align:start position:0%
+7 that's actually okay even though it's
+not a multiple of 32 native client
+
+ align:start position:0%
+not a multiple of 32 native client
+ 
+
+ align:start position:0%
+not a multiple of 32 native client
+doesn't General allow direct jumps to
+
+ align:start position:0%
+doesn't General allow direct jumps to
+ 
+
+ align:start position:0%
+doesn't General allow direct jumps to
+arbitrary addresses as long as that
+
+ align:start position:0%
+arbitrary addresses as long as that
+ 
+
+ align:start position:0%
+arbitrary addresses as long as that
+address is a instruction that we saw
+
+ align:start position:0%
+address is a instruction that we saw
+ 
+
+ align:start position:0%
+address is a instruction that we saw
+during this assembly as we were just
+
+ align:start position:0%
+during this assembly as we were just
+ 
+
+ align:start position:0%
+during this assembly as we were just
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about so could I put in this very nicely
+
+ align:start position:0%
+about so could I put in this very nicely
+ 
+
+ align:start position:0%
+about so could I put in this very nicely
+checked indirect jump and then later on
+
+ align:start position:0%
+checked indirect jump and then later on
+ 
+
+ align:start position:0%
+checked indirect jump and then later on
+in the code jump to the second
+
+ align:start position:0%
+in the code jump to the second
+ 
+
+ align:start position:0%
+in the code jump to the second
+instruction in that sequence so then
+
+ align:start position:0%
+instruction in that sequence so then
+ 
+
+ align:start position:0%
+instruction in that sequence so then
+I'll load something into e jump here and
+
+ align:start position:0%
+I'll load something into e jump here and
+ 
+
+ align:start position:0%
+I'll load something into e jump here and
+then directly jump into this unsandboxed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+address so that would violate the
+
+ align:start position:0%
+address so that would violate the
+ 
+
+ align:start position:0%
+address so that would violate the
+security right did everyone see that so
+
+ align:start position:0%
+security right did everyone see that so
+ 
+
+ align:start position:0%
+security right did everyone see that so
+how how is this avoided well the any
+
+ align:start position:0%
+how how is this avoided well the any
+ 
+
+ align:start position:0%
+how how is this avoided well the any
+should and jump as a single instruction
+
+ align:start position:0%
+should and jump as a single instruction
+ 
+
+ align:start position:0%
+should and jump as a single instruction
+yeah so this is why they call this thing
+
+ align:start position:0%
+yeah so this is why they call this thing
+ 
+
+ align:start position:0%
+yeah so this is why they call this thing
+a single pseudo
+
+ align:start position:0%
+a single pseudo
+ 
+
+ align:start position:0%
+a single pseudo
+instruction and even though at the x86
+
+ align:start position:0%
+instruction and even though at the x86
+ 
+
+ align:start position:0%
+instruction and even though at the x86
+level they're actually distinct
+
+ align:start position:0%
+level they're actually distinct
+ 
+
+ align:start position:0%
+level they're actually distinct
+instruction as far as the knal validator
+
+ align:start position:0%
+instruction as far as the knal validator
+ 
+
+ align:start position:0%
+instruction as far as the knal validator
+thinks of it it's actually a single
+
+ align:start position:0%
+thinks of it it's actually a single
+ 
+
+ align:start position:0%
+thinks of it it's actually a single
+Atomic unit so as far as this check for
+
+ align:start position:0%
+Atomic unit so as far as this check for
+ 
+
+ align:start position:0%
+Atomic unit so as far as this check for
+whether it's an instruction that you saw
+
+ align:start position:0%
+whether it's an instruction that you saw
+ 
+
+ align:start position:0%
+whether it's an instruction that you saw
+before they think oh this is the only
+
+ align:start position:0%
+before they think oh this is the only
+ 
+
+ align:start position:0%
+before they think oh this is the only
+instruction that I saw before jumping in
+
+ align:start position:0%
+instruction that I saw before jumping in
+ 
+
+ align:start position:0%
+instruction that I saw before jumping in
+the middle it's like jumping in the
+
+ align:start position:0%
+the middle it's like jumping in the
+ 
+
+ align:start position:0%
+the middle it's like jumping in the
+middle of this guy it's the same thing
+
+ align:start position:0%
+middle of this guy it's the same thing
+ 
+
+ align:start position:0%
+middle of this guy it's the same thing
+so they basically enfor slightly
+
+ align:start position:0%
+so they basically enfor slightly
+ 
+
+ align:start position:0%
+so they basically enfor slightly
+different semantics than what x86
+
+ align:start position:0%
+different semantics than what x86
+ 
+
+ align:start position:0%
+different semantics than what x86
+enforces in terms of what an instruction
+
+ align:start position:0%
+enforces in terms of what an instruction
+ 
+
+ align:start position:0%
+enforces in terms of what an instruction
+is and this might actually mean that you
+
+ align:start position:0%
+is and this might actually mean that you
+ 
+
+ align:start position:0%
+is and this might actually mean that you
+can't represent certain instruction
+
+ align:start position:0%
+can't represent certain instruction
+ 
+
+ align:start position:0%
+can't represent certain instruction
+sequences in knle so you know if you
+
+ align:start position:0%
+sequences in knle so you know if you
+ 
+
+ align:start position:0%
+sequences in knle so you know if you
+actually had legitimate code that looked
+
+ align:start position:0%
+actually had legitimate code that looked
+ 
+
+ align:start position:0%
+actually had legitimate code that looked
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+before this is going to be turned into a
+
+ align:start position:0%
+before this is going to be turned into a
+ 
+
+ align:start position:0%
+before this is going to be turned into a
+single op code and knle but hopefully
+
+ align:start position:0%
+single op code and knle but hopefully
+ 
+
+ align:start position:0%
+single op code and knle but hopefully
+that's not a problem yeah presumably
+
+ align:start position:0%
+that's not a problem yeah presumably
+ 
+
+ align:start position:0%
+that's not a problem yeah presumably
+they could put that in the the trusted
+
+ align:start position:0%
+they could put that in the the trusted
+ 
+
+ align:start position:0%
+they could put that in the the trusted
+codebase in the start of the the text
+
+ align:start position:0%
+codebase in the start of the the text
+ 
+
+ align:start position:0%
+codebase in the start of the the text
+segment because that way all you would
+
+ align:start position:0%
+segment because that way all you would
+ 
+
+ align:start position:0%
+segment because that way all you would
+always replace those two instead of
+
+ align:start position:0%
+always replace those two instead of
+ 
+
+ align:start position:0%
+always replace those two instead of
+putting those in the binary that you
+
+ align:start position:0%
+putting those in the binary that you
+ 
+
+ align:start position:0%
+putting those in the binary that you
+produce anyway you just jump straight to
+
+ align:start position:0%
+produce anyway you just jump straight to
+ 
+
+ align:start position:0%
+produce anyway you just jump straight to
+that jump Target that's in the
+
+ align:start position:0%
+that jump Target that's in the
+ 
+
+ align:start position:0%
+that jump Target that's in the
+privileged section in this trusted run
+
+ align:start position:0%
+privileged section in this trusted run
+ 
+
+ align:start position:0%
+privileged section in this trusted run
+time you mean or something no so in the
+
+ align:start position:0%
+time you mean or something no so in the
+ 
+
+ align:start position:0%
+time you mean or something no so in the
+the first 64k the yeah they have these
+
+ align:start position:0%
+the first 64k the yeah they have these
+ 
+
+ align:start position:0%
+the first 64k the yeah they have these
+trampolines and yeah right so they could
+
+ align:start position:0%
+trampolines and yeah right so they could
+ 
+
+ align:start position:0%
+trampolines and yeah right so they could
+make that one of the trampolines except
+
+ align:start position:0%
+make that one of the trampolines except
+ 
+
+ align:start position:0%
+make that one of the trampolines except
+that it doesn't jump out it jumps back
+
+ align:start position:0%
+that it doesn't jump out it jumps back
+ 
+
+ align:start position:0%
+that it doesn't jump out it jumps back
+in so that way the it wouldn't need to
+
+ align:start position:0%
+in so that way the it wouldn't need to
+ 
+
+ align:start position:0%
+in so that way the it wouldn't need to
+be a superu it just be a single x86 jump
+
+ align:start position:0%
+be a superu it just be a single x86 jump
+ 
+
+ align:start position:0%
+be a superu it just be a single x86 jump
+into there which would then jump out
+
+ align:start position:0%
+into there which would then jump out
+ 
+
+ align:start position:0%
+into there which would then jump out
+that's true yeah so so that's another
+
+ align:start position:0%
+that's true yeah so so that's another
+ 
+
+ align:start position:0%
+that's true yeah so so that's another
+sort of clever solution that you could
+
+ align:start position:0%
+sort of clever solution that you could
+ 
+
+ align:start position:0%
+sort of clever solution that you could
+do is instead so does everyone sort of
+
+ align:start position:0%
+do is instead so does everyone sort of
+ 
+
+ align:start position:0%
+do is instead so does everyone sort of
+see what what the plan is so suppose
+
+ align:start position:0%
+see what what the plan is so suppose
+ 
+
+ align:start position:0%
+see what what the plan is so suppose
+that you didn't want to do this pseudo
+
+ align:start position:0%
+that you didn't want to do this pseudo
+ 
+
+ align:start position:0%
+that you didn't want to do this pseudo
+instruction trick and you just wanted to
+
+ align:start position:0%
+instruction trick and you just wanted to
+ 
+
+ align:start position:0%
+instruction trick and you just wanted to
+have a single instruction replacing the
+
+ align:start position:0%
+have a single instruction replacing the
+ 
+
+ align:start position:0%
+have a single instruction replacing the
+jump eax well what you could basically
+
+ align:start position:0%
+jump eax well what you could basically
+ 
+
+ align:start position:0%
+jump eax well what you could basically
+come up with is a library of all
+
+ align:start position:0%
+come up with is a library of all
+ 
+
+ align:start position:0%
+come up with is a library of all
+possible indirect jumps you could ever
+
+ align:start position:0%
+possible indirect jumps you could ever
+ 
+
+ align:start position:0%
+possible indirect jumps you could ever
+do so like well there's jump
+
+ align:start position:0%
+do so like well there's jump
+ 
+
+ align:start position:0%
+do so like well there's jump
+eax there's jump ebx and so on and you
+
+ align:start position:0%
+eax there's jump ebx and so on and you
+ 
+
+ align:start position:0%
+eax there's jump ebx and so on and you
+would construct a library of these guys
+
+ align:start position:0%
+would construct a library of these guys
+ 
+
+ align:start position:0%
+would construct a library of these guys
+for each of them you would construct the
+
+ align:start position:0%
+for each of them you would construct the
+ 
+
+ align:start position:0%
+for each of them you would construct the
+safe check that you want to replace them
+
+ align:start position:0%
+safe check that you want to replace them
+ 
+
+ align:start position:0%
+safe check that you want to replace them
+with so for this one you would put an
+
+ align:start position:0%
+with so for this one you would put an
+ 
+
+ align:start position:0%
+with so for this one you would put an
+and in front of it and so on for this
+
+ align:start position:0%
+and in front of it and so on for this
+ 
+
+ align:start position:0%
+and in front of it and so on for this
+one You' also put an end in front of it
+
+ align:start position:0%
+one You' also put an end in front of it
+ 
+
+ align:start position:0%
+one You' also put an end in front of it
+and so on and then in the compiled
+
+ align:start position:0%
+and so on and then in the compiled
+ 
+
+ align:start position:0%
+and so on and then in the compiled
+binary every time you want to jump to
+
+ align:start position:0%
+binary every time you want to jump to
+ 
+
+ align:start position:0%
+binary every time you want to jump to
+eax what you actually do is you actually
+
+ align:start position:0%
+eax what you actually do is you actually
+ 
+
+ align:start position:0%
+eax what you actually do is you actually
+jump to a fixed address that corresponds
+
+ align:start position:0%
+jump to a fixed address that corresponds
+ 
+
+ align:start position:0%
+jump to a fixed address that corresponds
+to this helpful piece of code stored
+
+ align:start position:0%
+to this helpful piece of code stored
+ 
+
+ align:start position:0%
+to this helpful piece of code stored
+somewhere in that low 64k of the program
+
+ align:start position:0%
+somewhere in that low 64k of the program
+ 
+
+ align:start position:0%
+somewhere in that low 64k of the program
+and then this guy will do the end and
+
+ align:start position:0%
+and then this guy will do the end and
+ 
+
+ align:start position:0%
+and then this guy will do the end and
+jump again the reason that they probably
+
+ align:start position:0%
+jump again the reason that they probably
+ 
+
+ align:start position:0%
+jump again the reason that they probably
+don't do this is performance for this
+
+ align:start position:0%
+don't do this is performance for this
+ 
+
+ align:start position:0%
+don't do this is performance for this
+sort of interesting reason so the Intel
+
+ align:start position:0%
+sort of interesting reason so the Intel
+ 
+
+ align:start position:0%
+sort of interesting reason so the Intel
+processor and actually most processors
+
+ align:start position:0%
+processor and actually most processors
+ 
+
+ align:start position:0%
+processor and actually most processors
+these days um
+
+ align:start position:0%
+these days um
+ 
+
+ align:start position:0%
+these days um
+have have to predict where the Branch
+
+ align:start position:0%
+have have to predict where the Branch
+ 
+
+ align:start position:0%
+have have to predict where the Branch
+goes to keep the pipeline of the
+
+ align:start position:0%
+goes to keep the pipeline of the
+ 
+
+ align:start position:0%
+goes to keep the pipeline of the
+processor full at all times so there's a
+
+ align:start position:0%
+processor full at all times so there's a
+ 
+
+ align:start position:0%
+processor full at all times so there's a
+really complicated Branch predictor that
+
+ align:start position:0%
+really complicated Branch predictor that
+ 
+
+ align:start position:0%
+really complicated Branch predictor that
+not only decides whether you're going to
+
+ align:start position:0%
+not only decides whether you're going to
+ 
+
+ align:start position:0%
+not only decides whether you're going to
+Branch or not like if statements but it
+
+ align:start position:0%
+Branch or not like if statements but it
+ 
+
+ align:start position:0%
+Branch or not like if statements but it
+also actually guesses where you're going
+
+ align:start position:0%
+also actually guesses where you're going
+ 
+
+ align:start position:0%
+also actually guesses where you're going
+to jump so if you see an indirect jump
+
+ align:start position:0%
+to jump so if you see an indirect jump
+ 
+
+ align:start position:0%
+to jump so if you see an indirect jump
+it actually is going to guess what the
+
+ align:start position:0%
+it actually is going to guess what the
+ 
+
+ align:start position:0%
+it actually is going to guess what the
+address is going to be and this is
+
+ align:start position:0%
+address is going to be and this is
+ 
+
+ align:start position:0%
+address is going to be and this is
+actually a guess that's stored per cach
+
+ align:start position:0%
+actually a guess that's stored per cach
+ 
+
+ align:start position:0%
+actually a guess that's stored per cach
+line storing the jump instruction so if
+
+ align:start position:0%
+line storing the jump instruction so if
+ 
+
+ align:start position:0%
+line storing the jump instruction so if
+you have a single place where all the
+
+ align:start position:0%
+you have a single place where all the
+ 
+
+ align:start position:0%
+you have a single place where all the
+jump EXs come from then the CPU is
+
+ align:start position:0%
+jump EXs come from then the CPU is
+ 
+
+ align:start position:0%
+jump EXs come from then the CPU is
+always going to be very confused because
+
+ align:start position:0%
+always going to be very confused because
+ 
+
+ align:start position:0%
+always going to be very confused because
+these jump EXs seem to be going all over
+
+ align:start position:0%
+these jump EXs seem to be going all over
+ 
+
+ align:start position:0%
+these jump EXs seem to be going all over
+the place everywhere whereas if you
+
+ align:start position:0%
+the place everywhere whereas if you
+ 
+
+ align:start position:0%
+the place everywhere whereas if you
+really tie to a particular jump
+
+ align:start position:0%
+really tie to a particular jump
+ 
+
+ align:start position:0%
+really tie to a particular jump
+instruction it'll be a better prediction
+
+ align:start position:0%
+instruction it'll be a better prediction
+ 
+
+ align:start position:0%
+instruction it'll be a better prediction
+but that's just a sort of performance uh
+
+ align:start position:0%
+but that's just a sort of performance uh
+ 
+
+ align:start position:0%
+but that's just a sort of performance uh
+trick that they play make
+
+ align:start position:0%
+trick that they play make
+ 
+
+ align:start position:0%
+trick that they play make
+sense all right
+
+ align:start position:0%
+sense all right
+ 
+
+ align:start position:0%
+sense all right
+so so I guess we roughly understand how
+
+ align:start position:0%
+so so I guess we roughly understand how
+ 
+
+ align:start position:0%
+so so I guess we roughly understand how
+it's going to disassemble all the
+
+ align:start position:0%
+it's going to disassemble all the
+ 
+
+ align:start position:0%
+it's going to disassemble all the
+instructions how it's going to prevent
+
+ align:start position:0%
+instructions how it's going to prevent
+ 
+
+ align:start position:0%
+instructions how it's going to prevent
+these instructions so now let's look at
+
+ align:start position:0%
+these instructions so now let's look at
+ 
+
+ align:start position:0%
+these instructions so now let's look at
+the set of rules they are going to
+
+ align:start position:0%
+the set of rules they are going to
+ 
+
+ align:start position:0%
+the set of rules they are going to
+enforce so there's this table in the
+
+ align:start position:0%
+enforce so there's this table in the
+ 
+
+ align:start position:0%
+enforce so there's this table in the
+paper table one that has all these
+
+ align:start position:0%
+paper table one that has all these
+ 
+
+ align:start position:0%
+paper table one that has all these
+different rules for the validator to
+
+ align:start position:0%
+different rules for the validator to
+ 
+
+ align:start position:0%
+different rules for the validator to
+follow or that the binaries have to
+
+ align:start position:0%
+follow or that the binaries have to
+ 
+
+ align:start position:0%
+follow or that the binaries have to
+follow and the validator checks so let's
+
+ align:start position:0%
+follow and the validator checks so let's
+ 
+
+ align:start position:0%
+follow and the validator checks so let's
+go through these rules and just double
+
+ align:start position:0%
+go through these rules and just double
+ 
+
+ align:start position:0%
+go through these rules and just double
+check that we understand why all of
+
+ align:start position:0%
+check that we understand why all of
+ 
+
+ align:start position:0%
+check that we understand why all of
+these rules are there so so they have
+
+ align:start position:0%
+these rules are there so so they have
+ 
+
+ align:start position:0%
+these rules are there so so they have
+these things C1 all the way to
+
+ align:start position:0%
+these things C1 all the way to
+ 
+
+ align:start position:0%
+these things C1 all the way to
+C7 so C1 basically says that once you
+
+ align:start position:0%
+C7 so C1 basically says that once you
+ 
+
+ align:start position:0%
+C7 so C1 basically says that once you
+load the binary in memory then the
+
+ align:start position:0%
+load the binary in memory then the
+ 
+
+ align:start position:0%
+load the binary in memory then the
+binary is actually not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+writable at the page table level so they
+
+ align:start position:0%
+writable at the page table level so they
+ 
+
+ align:start position:0%
+writable at the page table level so they
+map they set the permission bits for the
+
+ align:start position:0%
+map they set the permission bits for the
+ 
+
+ align:start position:0%
+map they set the permission bits for the
+binary to be non-writable so
+
+ align:start position:0%
+binary to be non-writable so
+ 
+
+ align:start position:0%
+binary to be non-writable so
+why should be fairly obvious
+
+ align:start position:0%
+why should be fairly obvious
+ 
+
+ align:start position:0%
+why should be fairly obvious
+hopefully so I guess the the the reason
+
+ align:start position:0%
+hopefully so I guess the the the reason
+ 
+
+ align:start position:0%
+hopefully so I guess the the the reason
+is that their whole security plan relies
+
+ align:start position:0%
+is that their whole security plan relies
+ 
+
+ align:start position:0%
+is that their whole security plan relies
+on them checking that your binary is
+
+ align:start position:0%
+on them checking that your binary is
+ 
+
+ align:start position:0%
+on them checking that your binary is
+correct so once they've checked it they
+
+ align:start position:0%
+correct so once they've checked it they
+ 
+
+ align:start position:0%
+correct so once they've checked it they
+want to make sure you can't modify the
+
+ align:start position:0%
+want to make sure you can't modify the
+ 
+
+ align:start position:0%
+want to make sure you can't modify the
+binary and have it do something illegal
+
+ align:start position:0%
+binary and have it do something illegal
+ 
+
+ align:start position:0%
+binary and have it do something illegal
+uh that they prohibited so this is I
+
+ align:start position:0%
+uh that they prohibited so this is I
+ 
+
+ align:start position:0%
+uh that they prohibited so this is I
+think reasonably clear then so C2 is
+
+ align:start position:0%
+think reasonably clear then so C2 is
+ 
+
+ align:start position:0%
+think reasonably clear then so C2 is
+their plan that basically has to you
+
+ align:start position:0%
+their plan that basically has to you
+ 
+
+ align:start position:0%
+their plan that basically has to you
+know linked at zero and start at 64k so
+
+ align:start position:0%
+know linked at zero and start at 64k so
+ 
+
+ align:start position:0%
+know linked at zero and start at 64k so
+this requirement I think doesn't
+
+ align:start position:0%
+this requirement I think doesn't
+ 
+
+ align:start position:0%
+this requirement I think doesn't
+actually have to do with security so
+
+ align:start position:0%
+actually have to do with security so
+ 
+
+ align:start position:0%
+actually have to do with security so
+much I think it's just for convenience
+
+ align:start position:0%
+much I think it's just for convenience
+ 
+
+ align:start position:0%
+much I think it's just for convenience
+because they just want to have a
+
+ align:start position:0%
+because they just want to have a
+ 
+
+ align:start position:0%
+because they just want to have a
+standard layout for the program in some
+
+ align:start position:0%
+standard layout for the program in some
+ 
+
+ align:start position:0%
+standard layout for the program in some
+sense it's for simp licity so that they
+
+ align:start position:0%
+sense it's for simp licity so that they
+ 
+
+ align:start position:0%
+sense it's for simp licity so that they
+don't have to deal with complicated
+
+ align:start position:0%
+don't have to deal with complicated
+ 
+
+ align:start position:0%
+don't have to deal with complicated
+relocation records which means that
+
+ align:start position:0%
+relocation records which means that
+ 
+
+ align:start position:0%
+relocation records which means that
+there's fewer things that the validator
+
+ align:start position:0%
+there's fewer things that the validator
+ 
+
+ align:start position:0%
+there's fewer things that the validator
+or loader would might screw up but
+
+ align:start position:0%
+or loader would might screw up but
+ 
+
+ align:start position:0%
+or loader would might screw up but
+basically this is a sort of a
+
+ align:start position:0%
+basically this is a sort of a
+ 
+
+ align:start position:0%
+basically this is a sort of a
+standardization plan for them in terms
+
+ align:start position:0%
+standardization plan for them in terms
+ 
+
+ align:start position:0%
+standardization plan for them in terms
+of how to load their um executable make
+
+ align:start position:0%
+of how to load their um executable make
+ 
+
+ align:start position:0%
+of how to load their um executable make
+sense all right so the third requirement
+
+ align:start position:0%
+sense all right so the third requirement
+ 
+
+ align:start position:0%
+sense all right so the third requirement
+um is that I guess their
+
+ align:start position:0%
+um is that I guess their
+ 
+
+ align:start position:0%
+um is that I guess their
+indirect
+
+ align:start position:0%
+indirect
+ 
+
+ align:start position:0%
+indirect
+jumps use the Pudo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instruction so the the Pudo instruction
+
+ align:start position:0%
+instruction so the the Pudo instruction
+ 
+
+ align:start position:0%
+instruction so the the Pudo instruction
+is this thing above so that we just
+
+ align:start position:0%
+is this thing above so that we just
+ 
+
+ align:start position:0%
+is this thing above so that we just
+talked about why it needs to ensure this
+
+ align:start position:0%
+talked about why it needs to ensure this
+ 
+
+ align:start position:0%
+talked about why it needs to ensure this
+so that you don't jump to the middle of
+
+ align:start position:0%
+so that you don't jump to the middle of
+ 
+
+ align:start position:0%
+so that you don't jump to the middle of
+some instruction or sort of somehow
+
+ align:start position:0%
+some instruction or sort of somehow
+ 
+
+ align:start position:0%
+some instruction or sort of somehow
+invoke you know CIS Call Etc make
+
+ align:start position:0%
+invoke you know CIS Call Etc make
+ 
+
+ align:start position:0%
+invoke you know CIS Call Etc make
+sense all right so what's going on with
+
+ align:start position:0%
+sense all right so what's going on with
+ 
+
+ align:start position:0%
+sense all right so what's going on with
+C4 so basically you have to pad
+
+ align:start position:0%
+C4 so basically you have to pad
+ 
+
+ align:start position:0%
+C4 so basically you have to pad
+out to page
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary with a halt
+
+ align:start position:0%
+boundary with a halt
+ 
+
+ align:start position:0%
+boundary with a halt
+instruction why do they want to pad
+
+ align:start position:0%
+instruction why do they want to pad
+ 
+
+ align:start position:0%
+instruction why do they want to pad
+their binary out with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+halts any
+
+ align:start position:0%
+halts any
+ 
+
+ align:start position:0%
+halts any
+ideas yeah maybe
+
+ align:start position:0%
+ideas yeah maybe
+ 
+
+ align:start position:0%
+ideas yeah maybe
+like like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead yeah I think um so I I I don't
+
+ align:start position:0%
+instead yeah I think um so I I I don't
+ 
+
+ align:start position:0%
+instead yeah I think um so I I I don't
+actually I have to admit I don't have a
+
+ align:start position:0%
+actually I have to admit I don't have a
+ 
+
+ align:start position:0%
+actually I have to admit I don't have a
+crisp answer for why C4 exists but I
+
+ align:start position:0%
+crisp answer for why C4 exists but I
+ 
+
+ align:start position:0%
+crisp answer for why C4 exists but I
+think it's roughly what you're saying
+
+ align:start position:0%
+think it's roughly what you're saying
+ 
+
+ align:start position:0%
+think it's roughly what you're saying
+which is that if you well this code
+
+ align:start position:0%
+which is that if you well this code
+ 
+
+ align:start position:0%
+which is that if you well this code
+module stops at some point there's some
+
+ align:start position:0%
+module stops at some point there's some
+ 
+
+ align:start position:0%
+module stops at some point there's some
+end to it and the question is what
+
+ align:start position:0%
+end to it and the question is what
+ 
+
+ align:start position:0%
+end to it and the question is what
+happens when when you just keep
+
+ align:start position:0%
+happens when when you just keep
+ 
+
+ align:start position:0%
+happens when when you just keep
+executing and you get to the end then
+
+ align:start position:0%
+executing and you get to the end then
+ 
+
+ align:start position:0%
+executing and you get to the end then
+the processor might just keep executing
+
+ align:start position:0%
+the processor might just keep executing
+ 
+
+ align:start position:0%
+the processor might just keep executing
+past the end and execute some extra
+
+ align:start position:0%
+past the end and execute some extra
+ 
+
+ align:start position:0%
+past the end and execute some extra
+instructions or maybe it wraps around in
+
+ align:start position:0%
+instructions or maybe it wraps around in
+ 
+
+ align:start position:0%
+instructions or maybe it wraps around in
+some weird way so they just want to make
+
+ align:start position:0%
+some weird way so they just want to make
+ 
+
+ align:start position:0%
+some weird way so they just want to make
+sure that there's no ambiguity about
+
+ align:start position:0%
+sure that there's no ambiguity about
+ 
+
+ align:start position:0%
+sure that there's no ambiguity about
+what happens if you keep running and you
+
+ align:start position:0%
+what happens if you keep running and you
+ 
+
+ align:start position:0%
+what happens if you keep running and you
+don't jump and you just run off the end
+
+ align:start position:0%
+don't jump and you just run off the end
+ 
+
+ align:start position:0%
+don't jump and you just run off the end
+of the instruction Stream So this just
+
+ align:start position:0%
+of the instruction Stream So this just
+ 
+
+ align:start position:0%
+of the instruction Stream So this just
+make sure that the only answer there is
+
+ align:start position:0%
+make sure that the only answer there is
+ 
+
+ align:start position:0%
+make sure that the only answer there is
+if you keep executing you'll Halt and
+
+ align:start position:0%
+if you keep executing you'll Halt and
+ 
+
+ align:start position:0%
+if you keep executing you'll Halt and
+that'll trap into the runtime and you'll
+
+ align:start position:0%
+that'll trap into the runtime and you'll
+ 
+
+ align:start position:0%
+that'll trap into the runtime and you'll
+terminate the module so think it's just
+
+ align:start position:0%
+terminate the module so think it's just
+ 
+
+ align:start position:0%
+terminate the module so think it's just
+sort of a Simplicity safety guarantee
+
+ align:start position:0%
+sort of a Simplicity safety guarantee
+ 
+
+ align:start position:0%
+sort of a Simplicity safety guarantee
+there uh I don't think there's a
+
+ align:start position:0%
+there uh I don't think there's a
+ 
+
+ align:start position:0%
+there uh I don't think there's a
+concrete attack that I could at least
+
+ align:start position:0%
+concrete attack that I could at least
+ 
+
+ align:start position:0%
+concrete attack that I could at least
+construct in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+head yeah but uh here's the thing you
+
+ align:start position:0%
+head yeah but uh here's the thing you
+ 
+
+ align:start position:0%
+head yeah but uh here's the thing you
+can't jump past the end so the last
+
+ align:start position:0%
+can't jump past the end so the last
+ 
+
+ align:start position:0%
+can't jump past the end so the last
+thing that you could jump to is the last
+
+ align:start position:0%
+thing that you could jump to is the last
+ 
+
+ align:start position:0%
+thing that you could jump to is the last
+instruction and by this rule that
+
+ align:start position:0%
+instruction and by this rule that
+ 
+
+ align:start position:0%
+instruction and by this rule that
+instruction must be halt so you could
+
+ align:start position:0%
+instruction must be halt so you could
+ 
+
+ align:start position:0%
+instruction must be halt so you could
+jump to the halt but then you'll
+
+ align:start position:0%
+jump to the halt but then you'll
+ 
+
+ align:start position:0%
+jump to the halt but then you'll
+immediately Halt and you won't ran past
+
+ align:start position:0%
+immediately Halt and you won't ran past
+ 
+
+ align:start position:0%
+immediately Halt and you won't ran past
+past the end either so I think it's just
+
+ align:start position:0%
+past the end either so I think it's just
+ 
+
+ align:start position:0%
+past the end either so I think it's just
+sort of a cleanliness uh as far as I
+
+ align:start position:0%
+sort of a cleanliness uh as far as I
+ 
+
+ align:start position:0%
+sort of a cleanliness uh as far as I
+could tell again guante for them to make
+
+ align:start position:0%
+could tell again guante for them to make
+ 
+
+ align:start position:0%
+could tell again guante for them to make
+sure that there's no weirdness in terms
+
+ align:start position:0%
+sure that there's no weirdness in terms
+ 
+
+ align:start position:0%
+sure that there's no weirdness in terms
+of wrap around at the
+
+ align:start position:0%
+of wrap around at the
+ 
+
+ align:start position:0%
+of wrap around at the
+edges all right so then the the C5 is
+
+ align:start position:0%
+edges all right so then the the C5 is
+ 
+
+ align:start position:0%
+edges all right so then the the C5 is
+basically no
+
+ align:start position:0%
+basically no
+ 
+
+ align:start position:0%
+basically no
+instructions that span the 32bit bound
+
+ align:start position:0%
+instructions that span the 32bit bound
+ 
+
+ align:start position:0%
+instructions that span the 32bit bound
+the 32 byte
+
+ align:start position:0%
+the 32 byte
+ 
+
+ align:start position:0%
+the 32 byte
+boundary so this is sort of a variant of
+
+ align:start position:0%
+boundary so this is sort of a variant of
+ 
+
+ align:start position:0%
+boundary so this is sort of a variant of
+this rule that we talked about before
+
+ align:start position:0%
+this rule that we talked about before
+ 
+
+ align:start position:0%
+this rule that we talked about before
+where every uh multiple of 32 must be a
+
+ align:start position:0%
+where every uh multiple of 32 must be a
+ 
+
+ align:start position:0%
+where every uh multiple of 32 must be a
+valid instruction that we saw during
+
+ align:start position:0%
+valid instruction that we saw during
+ 
+
+ align:start position:0%
+valid instruction that we saw during
+disassembly so otherwise we'll jump to
+
+ align:start position:0%
+disassembly so otherwise we'll jump to
+ 
+
+ align:start position:0%
+disassembly so otherwise we'll jump to
+the middle of an instruction and have
+
+ align:start position:0%
+the middle of an instruction and have
+ 
+
+ align:start position:0%
+the middle of an instruction and have
+the problem with that csol that might be
+
+ align:start position:0%
+the problem with that csol that might be
+ 
+
+ align:start position:0%
+the problem with that csol that might be
+hidden
+
+ align:start position:0%
+hidden
+ 
+
+ align:start position:0%
+hidden
+there okay and then we have C6 which is
+
+ align:start position:0%
+there okay and then we have C6 which is
+ 
+
+ align:start position:0%
+there okay and then we have C6 which is
+basically all
+
+ align:start position:0%
+basically all
+ 
+
+ align:start position:0%
+basically all
+instructions
+
+ align:start position:0%
+instructions
+ 
+
+ align:start position:0%
+instructions
+reachable by
+
+ align:start position:0%
+reachable by
+ 
+
+ align:start position:0%
+reachable by
+disassembly from the start so this
+
+ align:start position:0%
+disassembly from the start so this
+ 
+
+ align:start position:0%
+disassembly from the start so this
+ensures that we see every instruction we
+
+ align:start position:0%
+ensures that we see every instruction we
+ 
+
+ align:start position:0%
+ensures that we see every instruction we
+can check every instruction that can
+
+ align:start position:0%
+can check every instruction that can
+ 
+
+ align:start position:0%
+can check every instruction that can
+possibly be run at runtime and I guess
+
+ align:start position:0%
+possibly be run at runtime and I guess
+ 
+
+ align:start position:0%
+possibly be run at runtime and I guess
+C7 is this basically all direct jumps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are okay so this is an example of that
+
+ align:start position:0%
+are okay so this is an example of that
+ 
+
+ align:start position:0%
+are okay so this is an example of that
+jump up there where you code in the
+
+ align:start position:0%
+jump up there where you code in the
+ 
+
+ align:start position:0%
+jump up there where you code in the
+Target right away so it doesn't have a
+
+ align:start position:0%
+Target right away so it doesn't have a
+ 
+
+ align:start position:0%
+Target right away so it doesn't have a
+multiple of 32 but it still has to be a
+
+ align:start position:0%
+multiple of 32 but it still has to be a
+ 
+
+ align:start position:0%
+multiple of 32 but it still has to be a
+valid instruction that we saw during the
+
+ align:start position:0%
+valid instruction that we saw during the
+ 
+
+ align:start position:0%
+valid instruction that we saw during the
+left to right disassembly question
+
+ align:start position:0%
+left to right disassembly question
+ 
+
+ align:start position:0%
+left to right disassembly question
+what's the difference between C5 and
+
+ align:start position:0%
+what's the difference between C5 and
+ 
+
+ align:start position:0%
+what's the difference between C5 and
+C3 yeah so I think C5 says that if I
+
+ align:start position:0%
+C3 yeah so I think C5 says that if I
+ 
+
+ align:start position:0%
+C3 yeah so I think C5 says that if I
+have a instruction that's multiple bytes
+
+ align:start position:0%
+have a instruction that's multiple bytes
+ 
+
+ align:start position:0%
+have a instruction that's multiple bytes
+it cannot uh span that 32 byte boundary
+
+ align:start position:0%
+it cannot uh span that 32 byte boundary
+ 
+
+ align:start position:0%
+it cannot uh span that 32 byte boundary
+so suppose that I have uh you know my
+
+ align:start position:0%
+so suppose that I have uh you know my
+ 
+
+ align:start position:0%
+so suppose that I have uh you know my
+instruction stream and here's you know
+
+ align:start position:0%
+instruction stream and here's you know
+ 
+
+ align:start position:0%
+instruction stream and here's you know
+an address 32 here's address 64 and
+
+ align:start position:0%
+an address 32 here's address 64 and
+ 
+
+ align:start position:0%
+an address 32 here's address 64 and
+maybe I have some sort of an end
+
+ align:start position:0%
+maybe I have some sort of an end
+ 
+
+ align:start position:0%
+maybe I have some sort of an end
+instruction that sort of spans this
+
+ align:start position:0%
+instruction that sort of spans this
+ 
+
+ align:start position:0%
+instruction that sort of spans this
+boundary so this is what C5 prohibits no
+
+ align:start position:0%
+boundary so this is what C5 prohibits no
+ 
+
+ align:start position:0%
+boundary so this is what C5 prohibits no
+instructions can span this boundary
+
+ align:start position:0%
+instructions can span this boundary
+ 
+
+ align:start position:0%
+instructions can span this boundary
+because otherwise we saw this s
+
+ align:start position:0%
+because otherwise we saw this s
+ 
+
+ align:start position:0%
+because otherwise we saw this s
+instruction but because you can always
+
+ align:start position:0%
+instruction but because you can always
+ 
+
+ align:start position:0%
+instruction but because you can always
+jump to 32 by multiples you could jump
+
+ align:start position:0%
+jump to 32 by multiples you could jump
+ 
+
+ align:start position:0%
+jump to 32 by multiples you could jump
+into the middle of the end and who knows
+
+ align:start position:0%
+into the middle of the end and who knows
+ 
+
+ align:start position:0%
+into the middle of the end and who knows
+what will happen there so this is what
+
+ align:start position:0%
+what will happen there so this is what
+ 
+
+ align:start position:0%
+what will happen there so this is what
+C5 prohibits for them and C3 is the sort
+
+ align:start position:0%
+C5 prohibits for them and C3 is the sort
+ 
+
+ align:start position:0%
+C5 prohibits for them and C3 is the sort
+of counterpart to it on the jump side so
+
+ align:start position:0%
+of counterpart to it on the jump side so
+ 
+
+ align:start position:0%
+of counterpart to it on the jump side so
+C3 says that whenever you jump you're
+
+ align:start position:0%
+C3 says that whenever you jump you're
+ 
+
+ align:start position:0%
+C3 says that whenever you jump you're
+going to jump to a multiple of 32 bytes
+
+ align:start position:0%
+going to jump to a multiple of 32 bytes
+ 
+
+ align:start position:0%
+going to jump to a multiple of 32 bytes
+and C5 says that everything you can find
+
+ align:start position:0%
+and C5 says that everything you can find
+ 
+
+ align:start position:0%
+and C5 says that everything you can find
+at a multiple of 32 bytes is a safe
+
+ align:start position:0%
+at a multiple of 32 bytes is a safe
+ 
+
+ align:start position:0%
+at a multiple of 32 bytes is a safe
+instruction I'm wondering if there's any
+
+ align:start position:0%
+instruction I'm wondering if there's any
+ 
+
+ align:start position:0%
+instruction I'm wondering if there's any
+redundancy between some yeah I don't
+
+ align:start position:0%
+redundancy between some yeah I don't
+ 
+
+ align:start position:0%
+redundancy between some yeah I don't
+know I I'm not sure I I had a little bit
+
+ align:start position:0%
+know I I'm not sure I I had a little bit
+ 
+
+ align:start position:0%
+know I I'm not sure I I had a little bit
+of that feeling when reading this list
+
+ align:start position:0%
+of that feeling when reading this list
+ 
+
+ align:start position:0%
+of that feeling when reading this list
+it seems like well they're all good
+
+ align:start position:0%
+it seems like well they're all good
+ 
+
+ align:start position:0%
+it seems like well they're all good
+rules but I'm not sure it's the minimal
+
+ align:start position:0%
+rules but I'm not sure it's the minimal
+ 
+
+ align:start position:0%
+rules but I'm not sure it's the minimal
+non-orthogonal set of or set of
+
+ align:start position:0%
+non-orthogonal set of or set of
+ 
+
+ align:start position:0%
+non-orthogonal set of or set of
+orthogonal rules that that uh um you
+
+ align:start position:0%
+orthogonal rules that that uh um you
+ 
+
+ align:start position:0%
+orthogonal rules that that uh um you
+need to enforce this um but any other
+
+ align:start position:0%
+need to enforce this um but any other
+ 
+
+ align:start position:0%
+need to enforce this um but any other
+questions about the set of restrictions
+
+ align:start position:0%
+questions about the set of restrictions
+ 
+
+ align:start position:0%
+questions about the set of restrictions
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+have all right so I guess let's uh think
+
+ align:start position:0%
+have all right so I guess let's uh think
+ 
+
+ align:start position:0%
+have all right so I guess let's uh think
+about uh this homework question that we
+
+ align:start position:0%
+about uh this homework question that we
+ 
+
+ align:start position:0%
+about uh this homework question that we
+sort of assigned it turns out I think
+
+ align:start position:0%
+sort of assigned it turns out I think
+ 
+
+ align:start position:0%
+sort of assigned it turns out I think
+there was actually a bug that native
+
+ align:start position:0%
+there was actually a bug that native
+ 
+
+ align:start position:0%
+there was actually a bug that native
+client had in its inner sandbox at some
+
+ align:start position:0%
+client had in its inner sandbox at some
+ 
+
+ align:start position:0%
+client had in its inner sandbox at some
+point which is that for some complicated
+
+ align:start position:0%
+point which is that for some complicated
+ 
+
+ align:start position:0%
+point which is that for some complicated
+instruction I believe they didn't have
+
+ align:start position:0%
+instruction I believe they didn't have
+ 
+
+ align:start position:0%
+instruction I believe they didn't have
+the length encoding correctly if I
+
+ align:start position:0%
+the length encoding correctly if I
+ 
+
+ align:start position:0%
+the length encoding correctly if I
+remember properly uh in which case
+
+ align:start position:0%
+remember properly uh in which case
+ 
+
+ align:start position:0%
+remember properly uh in which case
+something bad might happen I don't
+
+ align:start position:0%
+something bad might happen I don't
+ 
+
+ align:start position:0%
+something bad might happen I don't
+remember exactly what the bug was but uh
+
+ align:start position:0%
+remember exactly what the bug was but uh
+ 
+
+ align:start position:0%
+remember exactly what the bug was but uh
+suppose that the inter sandbox validator
+
+ align:start position:0%
+suppose that the inter sandbox validator
+ 
+
+ align:start position:0%
+suppose that the inter sandbox validator
+gets the length of some instruction
+
+ align:start position:0%
+gets the length of some instruction
+ 
+
+ align:start position:0%
+gets the length of some instruction
+wrong what what bad things could happen
+
+ align:start position:0%
+wrong what what bad things could happen
+ 
+
+ align:start position:0%
+wrong what what bad things could happen
+how would you exploit this we can hide
+
+ align:start position:0%
+how would you exploit this we can hide
+ 
+
+ align:start position:0%
+how would you exploit this we can hide
+this call or R and eventually yeah so
+
+ align:start position:0%
+this call or R and eventually yeah so
+ 
+
+ align:start position:0%
+this call or R and eventually yeah so
+suppose that you know there's some you
+
+ align:start position:0%
+suppose that you know there's some you
+ 
+
+ align:start position:0%
+suppose that you know there's some you
+know fancy variant of some and
+
+ align:start position:0%
+know fancy variant of some and
+ 
+
+ align:start position:0%
+know fancy variant of some and
+instruction that you could write down
+
+ align:start position:0%
+instruction that you could write down
+ 
+
+ align:start position:0%
+instruction that you could write down
+and maybe the validator gets that wrong
+
+ align:start position:0%
+and maybe the validator gets that wrong
+ 
+
+ align:start position:0%
+and maybe the validator gets that wrong
+and thinks that ah this guy is actually
+
+ align:start position:0%
+and thinks that ah this guy is actually
+ 
+
+ align:start position:0%
+and thinks that ah this guy is actually
+six bytes when in reality it's five
+
+ align:start position:0%
+six bytes when in reality it's five
+ 
+
+ align:start position:0%
+six bytes when in reality it's five
+bytes long so you could plop this down
+
+ align:start position:0%
+bytes long so you could plop this down
+ 
+
+ align:start position:0%
+bytes long so you could plop this down
+plop this and down and then the
+
+ align:start position:0%
+plop this and down and then the
+ 
+
+ align:start position:0%
+plop this and down and then the
+validator thinks oh it's six bytes so
+
+ align:start position:0%
+validator thinks oh it's six bytes so
+ 
+
+ align:start position:0%
+validator thinks oh it's six bytes so
+I'll look six bytes further and I'll
+
+ align:start position:0%
+I'll look six bytes further and I'll
+ 
+
+ align:start position:0%
+I'll look six bytes further and I'll
+check whether this is a valid
+
+ align:start position:0%
+check whether this is a valid
+ 
+
+ align:start position:0%
+check whether this is a valid
+instruction and we just have to make
+
+ align:start position:0%
+instruction and we just have to make
+ 
+
+ align:start position:0%
+instruction and we just have to make
+sure that whatever is six bytes later
+
+ align:start position:0%
+sure that whatever is six bytes later
+ 
+
+ align:start position:0%
+sure that whatever is six bytes later
+looks like a valid instruction but the
+
+ align:start position:0%
+looks like a valid instruction but the
+ 
+
+ align:start position:0%
+looks like a valid instruction but the
+CPU itself when it runs this code is
+
+ align:start position:0%
+CPU itself when it runs this code is
+ 
+
+ align:start position:0%
+CPU itself when it runs this code is
+going to maybe only look five bytes
+
+ align:start position:0%
+going to maybe only look five bytes
+ 
+
+ align:start position:0%
+going to maybe only look five bytes
+since from the end because that's the
+
+ align:start position:0%
+since from the end because that's the
+ 
+
+ align:start position:0%
+since from the end because that's the
+real length of the instruction so if we
+
+ align:start position:0%
+real length of the instruction so if we
+ 
+
+ align:start position:0%
+real length of the instruction so if we
+can use this extra bite to stick a sisol
+
+ align:start position:0%
+can use this extra bite to stick a sisol
+ 
+
+ align:start position:0%
+can use this extra bite to stick a sisol
+instruction then we could be in business
+
+ align:start position:0%
+instruction then we could be in business
+ 
+
+ align:start position:0%
+instruction then we could be in business
+so if we stick that you know remember
+
+ align:start position:0%
+so if we stick that you know remember
+ 
+
+ align:start position:0%
+so if we stick that you know remember
+from that example above on x86 Ox CD is
+
+ align:start position:0%
+from that example above on x86 Ox CD is
+ 
+
+ align:start position:0%
+from that example above on x86 Ox CD is
+how you make an in instruction so if we
+
+ align:start position:0%
+how you make an in instruction so if we
+ 
+
+ align:start position:0%
+how you make an in instruction so if we
+stick a CD bite at the end of that and
+
+ align:start position:0%
+stick a CD bite at the end of that and
+ 
+
+ align:start position:0%
+stick a CD bite at the end of that and
+then maybe we can put something here
+
+ align:start position:0%
+then maybe we can put something here
+ 
+
+ align:start position:0%
+then maybe we can put something here
+that looks like an instruction but
+
+ align:start position:0%
+that looks like an instruction but
+ 
+
+ align:start position:0%
+that looks like an instruction but
+actually is going to be part of the in
+
+ align:start position:0%
+actually is going to be part of the in
+ 
+
+ align:start position:0%
+actually is going to be part of the in
+instruction here and then we could all
+
+ align:start position:0%
+instruction here and then we could all
+ 
+
+ align:start position:0%
+instruction here and then we could all
+of a sudden make a CIS call and escape
+
+ align:start position:0%
+of a sudden make a CIS call and escape
+ 
+
+ align:start position:0%
+of a sudden make a CIS call and escape
+the inner
+
+ align:start position:0%
+the inner
+ 
+
+ align:start position:0%
+the inner
+sandbox make sense any
+
+ align:start position:0%
+sandbox make sense any
+ 
+
+ align:start position:0%
+sandbox make sense any
+questions so the validator in Native
+
+ align:start position:0%
+questions so the validator in Native
+ 
+
+ align:start position:0%
+questions so the validator in Native
+client has to be really in sync with
+
+ align:start position:0%
+client has to be really in sync with
+ 
+
+ align:start position:0%
+client has to be really in sync with
+what the CPU is doing because it's sort
+
+ align:start position:0%
+what the CPU is doing because it's sort
+ 
+
+ align:start position:0%
+what the CPU is doing because it's sort
+of guessing well here's exactly how the
+
+ align:start position:0%
+of guessing well here's exactly how the
+ 
+
+ align:start position:0%
+of guessing well here's exactly how the
+CPU is going to interpret every
+
+ align:start position:0%
+CPU is going to interpret every
+ 
+
+ align:start position:0%
+CPU is going to interpret every
+instruction it has to be right at every
+
+ align:start position:0%
+instruction it has to be right at every
+ 
+
+ align:start position:0%
+instruction it has to be right at every
+level here um so that's going to be a
+
+ align:start position:0%
+level here um so that's going to be a
+ 
+
+ align:start position:0%
+level here um so that's going to be a
+little bit tricky to do right um there's
+
+ align:start position:0%
+little bit tricky to do right um there's
+ 
+
+ align:start position:0%
+little bit tricky to do right um there's
+been actually sort of other interesting
+
+ align:start position:0%
+been actually sort of other interesting
+ 
+
+ align:start position:0%
+been actually sort of other interesting
+bugs in Native client that people have
+
+ align:start position:0%
+bugs in Native client that people have
+ 
+
+ align:start position:0%
+bugs in Native client that people have
+found one I think has to do with not
+
+ align:start position:0%
+found one I think has to do with not
+ 
+
+ align:start position:0%
+found one I think has to do with not
+properly sanitizing the environment of
+
+ align:start position:0%
+properly sanitizing the environment of
+ 
+
+ align:start position:0%
+properly sanitizing the environment of
+the CPU when you're jumping into the
+
+ align:start position:0%
+the CPU when you're jumping into the
+ 
+
+ align:start position:0%
+the CPU when you're jumping into the
+trusted service runtime so I guess we'll
+
+ align:start position:0%
+trusted service runtime so I guess we'll
+ 
+
+ align:start position:0%
+trusted service runtime so I guess we'll
+talk about this in a second but the
+
+ align:start position:0%
+talk about this in a second but the
+ 
+
+ align:start position:0%
+talk about this in a second but the
+trusted service runtime is going to
+
+ align:start position:0%
+trusted service runtime is going to
+ 
+
+ align:start position:0%
+trusted service runtime is going to
+basically run with the same sort of set
+
+ align:start position:0%
+basically run with the same sort of set
+ 
+
+ align:start position:0%
+basically run with the same sort of set
+of CPU registers initially that the
+
+ align:start position:0%
+of CPU registers initially that the
+ 
+
+ align:start position:0%
+of CPU registers initially that the
+untrusted module was running with so if
+
+ align:start position:0%
+untrusted module was running with so if
+ 
+
+ align:start position:0%
+untrusted module was running with so if
+there's something that it forgets to
+
+ align:start position:0%
+there's something that it forgets to
+ 
+
+ align:start position:0%
+there's something that it forgets to
+clear or reset or whatnot then the
+
+ align:start position:0%
+clear or reset or whatnot then the
+ 
+
+ align:start position:0%
+clear or reset or whatnot then the
+trusted service runtime might be tricked
+
+ align:start position:0%
+trusted service runtime might be tricked
+ 
+
+ align:start position:0%
+trusted service runtime might be tricked
+into doing something uh that wasn't
+
+ align:start position:0%
+into doing something uh that wasn't
+ 
+
+ align:start position:0%
+into doing something uh that wasn't
+meant to do or the developers didn't
+
+ align:start position:0%
+meant to do or the developers didn't
+ 
+
+ align:start position:0%
+meant to do or the developers didn't
+want to do it
+
+ align:start position:0%
+want to do it
+ 
+
+ align:start position:0%
+want to do it
+initially okay so let's see where are we
+
+ align:start position:0%
+initially okay so let's see where are we
+ 
+
+ align:start position:0%
+initially okay so let's see where are we
+now so what we understand now is roughly
+
+ align:start position:0%
+now so what we understand now is roughly
+ 
+
+ align:start position:0%
+now so what we understand now is roughly
+how we can disassemble all the
+
+ align:start position:0%
+how we can disassemble all the
+ 
+
+ align:start position:0%
+how we can disassemble all the
+instructions and how to prevent
+
+ align:start position:0%
+instructions and how to prevent
+ 
+
+ align:start position:0%
+instructions and how to prevent
+disallowed instructions so now let's
+
+ align:start position:0%
+disallowed instructions so now let's
+ 
+
+ align:start position:0%
+disallowed instructions so now let's
+look at how do we keep the memory
+
+ align:start position:0%
+look at how do we keep the memory
+ 
+
+ align:start position:0%
+look at how do we keep the memory
+references for both code and data within
+
+ align:start position:0%
+references for both code and data within
+ 
+
+ align:start position:0%
+references for both code and data within
+the bounds of the
+
+ align:start position:0%
+the bounds of the
+ 
+
+ align:start position:0%
+the bounds of the
+module so for performance reasons the
+
+ align:start position:0%
+module so for performance reasons the
+ 
+
+ align:start position:0%
+module so for performance reasons the
+native client guys actually start using
+
+ align:start position:0%
+native client guys actually start using
+ 
+
+ align:start position:0%
+native client guys actually start using
+some Hardware support at this point to
+
+ align:start position:0%
+some Hardware support at this point to
+ 
+
+ align:start position:0%
+some Hardware support at this point to
+make sure this actually doesn't impose
+
+ align:start position:0%
+make sure this actually doesn't impose
+ 
+
+ align:start position:0%
+make sure this actually doesn't impose
+much overhead but before we look at the
+
+ align:start position:0%
+much overhead but before we look at the
+ 
+
+ align:start position:0%
+much overhead but before we look at the
+hardware support that they use does
+
+ align:start position:0%
+hardware support that they use does
+ 
+
+ align:start position:0%
+hardware support that they use does
+anyone have any suggestions for how we
+
+ align:start position:0%
+anyone have any suggestions for how we
+ 
+
+ align:start position:0%
+anyone have any suggestions for how we
+could do it actually without any
+
+ align:start position:0%
+could do it actually without any
+ 
+
+ align:start position:0%
+could do it actually without any
+hardware support could we just enforce
+
+ align:start position:0%
+hardware support could we just enforce
+ 
+
+ align:start position:0%
+hardware support could we just enforce
+all the memory accesses going in bounds
+
+ align:start position:0%
+all the memory accesses going in bounds
+ 
+
+ align:start position:0%
+all the memory accesses going in bounds
+with the Machinery we have so
+
+ align:start position:0%
+with the Machinery we have so
+ 
+
+ align:start position:0%
+with the Machinery we have so
+far yeah we can instrument the
+
+ align:start position:0%
+far yeah we can instrument the
+ 
+
+ align:start position:0%
+far yeah we can instrument the
+instruction is to clear all the higher
+
+ align:start position:0%
+instruction is to clear all the higher
+ 
+
+ align:start position:0%
+instruction is to clear all the higher
+that's right yeah so actually we see we
+
+ align:start position:0%
+that's right yeah so actually we see we
+ 
+
+ align:start position:0%
+that's right yeah so actually we see we
+have this instruction over here which at
+
+ align:start position:0%
+have this instruction over here which at
+ 
+
+ align:start position:0%
+have this instruction over here which at
+every time we s for example jump
+
+ align:start position:0%
+every time we s for example jump
+ 
+
+ align:start position:0%
+every time we s for example jump
+somewhere right now we clear the low
+
+ align:start position:0%
+somewhere right now we clear the low
+ 
+
+ align:start position:0%
+somewhere right now we clear the low
+bits but if you want to keep all the
+
+ align:start position:0%
+bits but if you want to keep all the
+ 
+
+ align:start position:0%
+bits but if you want to keep all the
+possible code that you're executing
+
+ align:start position:0%
+possible code that you're executing
+ 
+
+ align:start position:0%
+possible code that you're executing
+within the low 256 Megs then we could
+
+ align:start position:0%
+within the low 256 Megs then we could
+ 
+
+ align:start position:0%
+within the low 256 Megs then we could
+just replace this with a zero so we end
+
+ align:start position:0%
+just replace this with a zero so we end
+ 
+
+ align:start position:0%
+just replace this with a zero so we end
+with zero FFF Fe zero so this makes
+
+ align:start position:0%
+with zero FFF Fe zero so this makes
+ 
+
+ align:start position:0%
+with zero FFF Fe zero so this makes
+clear as the low bits and also caps the
+
+ align:start position:0%
+clear as the low bits and also caps the
+ 
+
+ align:start position:0%
+clear as the low bits and also caps the
+address to at most 256 Megs so this does
+
+ align:start position:0%
+address to at most 256 Megs so this does
+ 
+
+ align:start position:0%
+address to at most 256 Megs so this does
+exactly what you're sort of suggesting
+
+ align:start position:0%
+exactly what you're sort of suggesting
+ 
+
+ align:start position:0%
+exactly what you're sort of suggesting
+and would make sure that whenever you're
+
+ align:start position:0%
+and would make sure that whenever you're
+ 
+
+ align:start position:0%
+and would make sure that whenever you're
+jumping you're staying within the low
+
+ align:start position:0%
+jumping you're staying within the low
+ 
+
+ align:start position:0%
+jumping you're staying within the low
+256 Megs and the fact that uh I guess
+
+ align:start position:0%
+256 Megs and the fact that uh I guess
+ 
+
+ align:start position:0%
+256 Megs and the fact that uh I guess
+you're we're doing disassembly you can
+
+ align:start position:0%
+you're we're doing disassembly you can
+ 
+
+ align:start position:0%
+you're we're doing disassembly you can
+also check for all the direct jumps that
+
+ align:start position:0%
+also check for all the direct jumps that
+ 
+
+ align:start position:0%
+also check for all the direct jumps that
+they're all in
+
+ align:start position:0%
+they're all in
+ 
+
+ align:start position:0%
+they're all in
+bounds and that's actually not so bad
+
+ align:start position:0%
+bounds and that's actually not so bad
+ 
+
+ align:start position:0%
+bounds and that's actually not so bad
+right the reason I think they don't do
+
+ align:start position:0%
+right the reason I think they don't do
+ 
+
+ align:start position:0%
+right the reason I think they don't do
+this for code is because in x86 you can
+
+ align:start position:0%
+this for code is because in x86 you can
+ 
+
+ align:start position:0%
+this for code is because in x86 you can
+very efficiently encode an and where all
+
+ align:start position:0%
+very efficiently encode an and where all
+ 
+
+ align:start position:0%
+very efficiently encode an and where all
+the top bits are one so this turns out
+
+ align:start position:0%
+the top bits are one so this turns out
+ 
+
+ align:start position:0%
+the top bits are one so this turns out
+to be I think uh basically a three bite
+
+ align:start position:0%
+to be I think uh basically a three bite
+ 
+
+ align:start position:0%
+to be I think uh basically a three bite
+instruction for the end and a two bite
+
+ align:start position:0%
+instruction for the end and a two bite
+ 
+
+ align:start position:0%
+instruction for the end and a two bite
+instruction for the jump so the overhead
+
+ align:start position:0%
+instruction for the jump so the overhead
+ 
+
+ align:start position:0%
+instruction for the jump so the overhead
+is like three more bytes but if you want
+
+ align:start position:0%
+is like three more bytes but if you want
+ 
+
+ align:start position:0%
+is like three more bytes but if you want
+to have non one Pi bits then this is
+
+ align:start position:0%
+to have non one Pi bits then this is
+ 
+
+ align:start position:0%
+to have non one Pi bits then this is
+actually now a five byte instruction all
+
+ align:start position:0%
+actually now a five byte instruction all
+ 
+
+ align:start position:0%
+actually now a five byte instruction all
+of a sudden so I think they're worried a
+
+ align:start position:0%
+of a sudden so I think they're worried a
+ 
+
+ align:start position:0%
+of a sudden so I think they're worried a
+little bit about the overhead here
+
+ align:start position:0%
+little bit about the overhead here
+ 
+
+ align:start position:0%
+little bit about the overhead here
+question there also the problem that you
+
+ align:start position:0%
+question there also the problem that you
+ 
+
+ align:start position:0%
+question there also the problem that you
+might as some instructions which like
+
+ align:start position:0%
+might as some instructions which like
+ 
+
+ align:start position:0%
+might as some instructions which like
+increment the like location that you're
+
+ align:start position:0%
+increment the like location that you're
+ 
+
+ align:start position:0%
+increment the like location that you're
+trying to get so you might say like your
+
+ align:start position:0%
+trying to get so you might say like your
+ 
+
+ align:start position:0%
+trying to get so you might say like your
+instruction might have like a constant
+
+ align:start position:0%
+instruction might have like a constant
+ 
+
+ align:start position:0%
+instruction might have like a constant
+offset or something like that well so I
+
+ align:start position:0%
+offset or something like that well so I
+ 
+
+ align:start position:0%
+offset or something like that well so I
+think yeah you would probably prohibit
+
+ align:start position:0%
+think yeah you would probably prohibit
+ 
+
+ align:start position:0%
+think yeah you would probably prohibit
+instructions that jump to some
+
+ align:start position:0%
+instructions that jump to some
+ 
+
+ align:start position:0%
+instructions that jump to some
+complicated formula of an address so you
+
+ align:start position:0%
+complicated formula of an address so you
+ 
+
+ align:start position:0%
+complicated formula of an address so you
+only support an instruction that jumps
+
+ align:start position:0%
+only support an instruction that jumps
+ 
+
+ align:start position:0%
+only support an instruction that jumps
+directly to this value and this value
+
+ align:start position:0%
+directly to this value and this value
+ 
+
+ align:start position:0%
+directly to this value and this value
+always gets anded and more for memory
+
+ align:start position:0%
+always gets anded and more for memory
+ 
+
+ align:start position:0%
+always gets anded and more for memory
+accesses rather yeah okay so yeah so
+
+ align:start position:0%
+accesses rather yeah okay so yeah so
+ 
+
+ align:start position:0%
+accesses rather yeah okay so yeah so
+that's a good point because this is just
+
+ align:start position:0%
+that's a good point because this is just
+ 
+
+ align:start position:0%
+that's a good point because this is just
+code and for memory access there's lots
+
+ align:start position:0%
+code and for memory access there's lots
+ 
+
+ align:start position:0%
+code and for memory access there's lots
+of weird ways on x86 to refer to a
+
+ align:start position:0%
+of weird ways on x86 to refer to a
+ 
+
+ align:start position:0%
+of weird ways on x86 to refer to a
+particular memory location and in that
+
+ align:start position:0%
+particular memory location and in that
+ 
+
+ align:start position:0%
+particular memory location and in that
+case you'd basically have to first
+
+ align:start position:0%
+case you'd basically have to first
+ 
+
+ align:start position:0%
+case you'd basically have to first
+compute the memory location then insert
+
+ align:start position:0%
+compute the memory location then insert
+ 
+
+ align:start position:0%
+compute the memory location then insert
+an extra end and then do the access and
+
+ align:start position:0%
+an extra end and then do the access and
+ 
+
+ align:start position:0%
+an extra end and then do the access and
+I think that's the real reason why
+
+ align:start position:0%
+I think that's the real reason why
+ 
+
+ align:start position:0%
+I think that's the real reason why
+they're actually very worried about the
+
+ align:start position:0%
+they're actually very worried about the
+ 
+
+ align:start position:0%
+they're actually very worried about the
+performance overheads of this
+
+ align:start position:0%
+performance overheads of this
+ 
+
+ align:start position:0%
+performance overheads of this
+instrumentation uh so on x86 at least on
+
+ align:start position:0%
+instrumentation uh so on x86 at least on
+ 
+
+ align:start position:0%
+instrumentation uh so on x86 at least on
+30 two bit which is what this paper
+
+ align:start position:0%
+30 two bit which is what this paper
+ 
+
+ align:start position:0%
+30 two bit which is what this paper
+talks about they actually use some
+
+ align:start position:0%
+talks about they actually use some
+ 
+
+ align:start position:0%
+talks about they actually use some
+Hardware support instead to limit the
+
+ align:start position:0%
+Hardware support instead to limit the
+ 
+
+ align:start position:0%
+Hardware support instead to limit the
+code and data addresses that the
+
+ align:start position:0%
+code and data addresses that the
+ 
+
+ align:start position:0%
+code and data addresses that the
+untrusted module can refer
+
+ align:start position:0%
+untrusted module can refer
+ 
+
+ align:start position:0%
+untrusted module can refer
+to so this actually leverages some
+
+ align:start position:0%
+to so this actually leverages some
+ 
+
+ align:start position:0%
+to so this actually leverages some
+somewhat esoteric Hardware in x86 so
+
+ align:start position:0%
+somewhat esoteric Hardware in x86 so
+ 
+
+ align:start position:0%
+somewhat esoteric Hardware in x86 so
+let's see what it looks like first
+
+ align:start position:0%
+let's see what it looks like first
+ 
+
+ align:start position:0%
+let's see what it looks like first
+before we start figuring out how we're
+
+ align:start position:0%
+before we start figuring out how we're
+ 
+
+ align:start position:0%
+before we start figuring out how we're
+going to use it to sandbox the Naco
+
+ align:start position:0%
+going to use it to sandbox the Naco
+ 
+
+ align:start position:0%
+going to use it to sandbox the Naco
+module so this Hardware is called
+
+ align:start position:0%
+module so this Hardware is called
+ 
+
+ align:start position:0%
+module so this Hardware is called
+segmentation and sort of left over from
+
+ align:start position:0%
+segmentation and sort of left over from
+ 
+
+ align:start position:0%
+segmentation and sort of left over from
+from the days before x86 actually even
+
+ align:start position:0%
+from the days before x86 actually even
+ 
+
+ align:start position:0%
+from the days before x86 actually even
+had paging so the way it works is
+
+ align:start position:0%
+had paging so the way it works is
+ 
+
+ align:start position:0%
+had paging so the way it works is
+actually um there's
+
+ align:start position:0%
+actually um there's
+ 
+
+ align:start position:0%
+actually um there's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+segmentation on x86 the way it works is
+
+ align:start position:0%
+segmentation on x86 the way it works is
+ 
+
+ align:start position:0%
+segmentation on x86 the way it works is
+that whenever a process is
+
+ align:start position:0%
+that whenever a process is
+ 
+
+ align:start position:0%
+that whenever a process is
+running um there's
+
+ align:start position:0%
+running um there's
+ 
+
+ align:start position:0%
+running um there's
+actually a table maintained by the
+
+ align:start position:0%
+actually a table maintained by the
+ 
+
+ align:start position:0%
+actually a table maintained by the
+hardware uh that's called a segment
+
+ align:start position:0%
+hardware uh that's called a segment
+ 
+
+ align:start position:0%
+hardware uh that's called a segment
+descriptor table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what this table has is just a bunch
+
+ align:start position:0%
+and what this table has is just a bunch
+ 
+
+ align:start position:0%
+and what this table has is just a bunch
+of segments numbered from zero up to
+
+ align:start position:0%
+of segments numbered from zero up to
+ 
+
+ align:start position:0%
+of segments numbered from zero up to
+whatever the size of the table is kind
+
+ align:start position:0%
+whatever the size of the table is kind
+ 
+
+ align:start position:0%
+whatever the size of the table is kind
+of like file descriptors in Unix except
+
+ align:start position:0%
+of like file descriptors in Unix except
+ 
+
+ align:start position:0%
+of like file descriptors in Unix except
+every entry has two values in it some
+
+ align:start position:0%
+every entry has two values in it some
+ 
+
+ align:start position:0%
+every entry has two values in it some
+sort of a
+
+ align:start position:0%
+sort of a
+ 
+
+ align:start position:0%
+sort of a
+base and a length and same for every
+
+ align:start position:0%
+base and a length and same for every
+ 
+
+ align:start position:0%
+base and a length and same for every
+entry base and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length Okay so what this table does is
+
+ align:start position:0%
+length Okay so what this table does is
+ 
+
+ align:start position:0%
+length Okay so what this table does is
+tells us uh that we have you know a
+
+ align:start position:0%
+tells us uh that we have you know a
+ 
+
+ align:start position:0%
+tells us uh that we have you know a
+couple of segments and whenever we refer
+
+ align:start position:0%
+couple of segments and whenever we refer
+ 
+
+ align:start position:0%
+couple of segments and whenever we refer
+to a particular segment uh what this in
+
+ align:start position:0%
+to a particular segment uh what this in
+ 
+
+ align:start position:0%
+to a particular segment uh what this in
+some sense means is that we're talking
+
+ align:start position:0%
+some sense means is that we're talking
+ 
+
+ align:start position:0%
+some sense means is that we're talking
+about a chunk of memory that starts at
+
+ align:start position:0%
+about a chunk of memory that starts at
+ 
+
+ align:start position:0%
+about a chunk of memory that starts at
+address base and goes for this length
+
+ align:start position:0%
+address base and goes for this length
+ 
+
+ align:start position:0%
+address base and goes for this length
+from that base
+
+ align:start position:0%
+from that base
+ 
+
+ align:start position:0%
+from that base
+upwards and the way that this actually
+
+ align:start position:0%
+upwards and the way that this actually
+ 
+
+ align:start position:0%
+upwards and the way that this actually
+helps us to enforce memory bounds is
+
+ align:start position:0%
+helps us to enforce memory bounds is
+ 
+
+ align:start position:0%
+helps us to enforce memory bounds is
+that on x86 every single instruction in
+
+ align:start position:0%
+that on x86 every single instruction in
+ 
+
+ align:start position:0%
+that on x86 every single instruction in
+one way or another um whenever it's
+
+ align:start position:0%
+one way or another um whenever it's
+ 
+
+ align:start position:0%
+one way or another um whenever it's
+talking about memory actually talks
+
+ align:start position:0%
+talking about memory actually talks
+ 
+
+ align:start position:0%
+talking about memory actually talks
+talks about memory with respect to a
+
+ align:start position:0%
+talks about memory with respect to a
+ 
+
+ align:start position:0%
+talks about memory with respect to a
+particular particular segment in this
+
+ align:start position:0%
+particular particular segment in this
+ 
+
+ align:start position:0%
+particular particular segment in this
+table so for example when you actually
+
+ align:start position:0%
+table so for example when you actually
+ 
+
+ align:start position:0%
+table so for example when you actually
+do something like move a a memory value
+
+ align:start position:0%
+do something like move a a memory value
+ 
+
+ align:start position:0%
+do something like move a a memory value
+from the value from a pointer stored in
+
+ align:start position:0%
+from the value from a pointer stored in
+ 
+
+ align:start position:0%
+from the value from a pointer stored in
+the eex register into maybe another
+
+ align:start position:0%
+the eex register into maybe another
+ 
+
+ align:start position:0%
+the eex register into maybe another
+pointer stored in the ebx register what
+
+ align:start position:0%
+pointer stored in the ebx register what
+ 
+
+ align:start position:0%
+pointer stored in the ebx register what
+you would sort of think it does is it
+
+ align:start position:0%
+you would sort of think it does is it
+ 
+
+ align:start position:0%
+you would sort of think it does is it
+figures out well what's this address
+
+ align:start position:0%
+figures out well what's this address
+ 
+
+ align:start position:0%
+figures out well what's this address
+loads memory at this address and then
+
+ align:start position:0%
+loads memory at this address and then
+ 
+
+ align:start position:0%
+loads memory at this address and then
+figures out okay what's this address and
+
+ align:start position:0%
+figures out okay what's this address and
+ 
+
+ align:start position:0%
+figures out okay what's this address and
+stores the value there but in fact on
+
+ align:start position:0%
+stores the value there but in fact on
+ 
+
+ align:start position:0%
+stores the value there but in fact on
+x86 there's whenever you're talking
+
+ align:start position:0%
+x86 there's whenever you're talking
+ 
+
+ align:start position:0%
+x86 there's whenever you're talking
+about memory there's an implicit what's
+
+ align:start position:0%
+about memory there's an implicit what's
+ 
+
+ align:start position:0%
+about memory there's an implicit what's
+called a segment descriptor which is
+
+ align:start position:0%
+called a segment descriptor which is
+ 
+
+ align:start position:0%
+called a segment descriptor which is
+kind of like a file descriptor in Unix
+
+ align:start position:0%
+kind of like a file descriptor in Unix
+ 
+
+ align:start position:0%
+kind of like a file descriptor in Unix
+it's just an index into this descriptor
+
+ align:start position:0%
+it's just an index into this descriptor
+ 
+
+ align:start position:0%
+it's just an index into this descriptor
+table and unless sort of specified
+
+ align:start position:0%
+table and unless sort of specified
+ 
+
+ align:start position:0%
+table and unless sort of specified
+otherwise every op code has a default
+
+ align:start position:0%
+otherwise every op code has a default
+ 
+
+ align:start position:0%
+otherwise every op code has a default
+segment in it so in when you're doing a
+
+ align:start position:0%
+segment in it so in when you're doing a
+ 
+
+ align:start position:0%
+segment in it so in when you're doing a
+move this is actually relative to the DS
+
+ align:start position:0%
+move this is actually relative to the DS
+ 
+
+ align:start position:0%
+move this is actually relative to the DS
+or the data segment register so it's
+
+ align:start position:0%
+or the data segment register so it's
+ 
+
+ align:start position:0%
+or the data segment register so it's
+like a special register in your CPU
+
+ align:start position:0%
+like a special register in your CPU
+ 
+
+ align:start position:0%
+like a special register in your CPU
+that's a 16bit integer if I remember
+
+ align:start position:0%
+that's a 16bit integer if I remember
+ 
+
+ align:start position:0%
+that's a 16bit integer if I remember
+correctly and that 16bit integer points
+
+ align:start position:0%
+correctly and that 16bit integer points
+ 
+
+ align:start position:0%
+correctly and that 16bit integer points
+into this descriptor table and the same
+
+ align:start position:0%
+into this descriptor table and the same
+ 
+
+ align:start position:0%
+into this descriptor table and the same
+here here this is actually relative to
+
+ align:start position:0%
+here here this is actually relative to
+ 
+
+ align:start position:0%
+here here this is actually relative to
+that DS segment selector actually a
+
+ align:start position:0%
+that DS segment selector actually a
+ 
+
+ align:start position:0%
+that DS segment selector actually a
+bunch of these guys there are six
+
+ align:start position:0%
+bunch of these guys there are six
+ 
+
+ align:start position:0%
+bunch of these guys there are six
+segment selectors on x86 there's the
+
+ align:start position:0%
+segment selectors on x86 there's the
+ 
+
+ align:start position:0%
+segment selectors on x86 there's the
+code selector CS DS es FS GS and SS
+
+ align:start position:0%
+code selector CS DS es FS GS and SS
+ 
+
+ align:start position:0%
+code selector CS DS es FS GS and SS
+and the code selector is sort of
+
+ align:start position:0%
+and the code selector is sort of
+ 
+
+ align:start position:0%
+and the code selector is sort of
+implicitly used to fetch the instruction
+
+ align:start position:0%
+implicitly used to fetch the instruction
+ 
+
+ align:start position:0%
+implicitly used to fetch the instruction
+so if your instruction pointer points
+
+ align:start position:0%
+so if your instruction pointer points
+ 
+
+ align:start position:0%
+so if your instruction pointer points
+somewhere it's actually relative to what
+
+ align:start position:0%
+somewhere it's actually relative to what
+ 
+
+ align:start position:0%
+somewhere it's actually relative to what
+the Cs segment selector says and most
+
+ align:start position:0%
+the Cs segment selector says and most
+ 
+
+ align:start position:0%
+the Cs segment selector says and most
+data references implicitly use either DS
+
+ align:start position:0%
+data references implicitly use either DS
+ 
+
+ align:start position:0%
+data references implicitly use either DS
+or ES and then fs and Gs are like some
+
+ align:start position:0%
+or ES and then fs and Gs are like some
+ 
+
+ align:start position:0%
+or ES and then fs and Gs are like some
+special things and SS is always used for
+
+ align:start position:0%
+special things and SS is always used for
+ 
+
+ align:start position:0%
+special things and SS is always used for
+the stack operations if you push and pop
+
+ align:start position:0%
+the stack operations if you push and pop
+ 
+
+ align:start position:0%
+the stack operations if you push and pop
+they implicitly come off of this segment
+
+ align:start position:0%
+they implicitly come off of this segment
+ 
+
+ align:start position:0%
+they implicitly come off of this segment
+selector it's like a fairly Baroque
+
+ align:start position:0%
+selector it's like a fairly Baroque
+ 
+
+ align:start position:0%
+selector it's like a fairly Baroque
+Machinery but it turns out to be hugely
+
+ align:start position:0%
+Machinery but it turns out to be hugely
+ 
+
+ align:start position:0%
+Machinery but it turns out to be hugely
+useful for this particular use case
+
+ align:start position:0%
+useful for this particular use case
+ 
+
+ align:start position:0%
+useful for this particular use case
+because what happens is if you access
+
+ align:start position:0%
+because what happens is if you access
+ 
+
+ align:start position:0%
+because what happens is if you access
+some address at you know maybe some
+
+ align:start position:0%
+some address at you know maybe some
+ 
+
+ align:start position:0%
+some address at you know maybe some
+selector DS you know callon some offset
+
+ align:start position:0%
+selector DS you know callon some offset
+ 
+
+ align:start position:0%
+selector DS you know callon some offset
+or some address here what the hardware
+
+ align:start position:0%
+or some address here what the hardware
+ 
+
+ align:start position:0%
+or some address here what the hardware
+will actually do is translate it into
+
+ align:start position:0%
+will actually do is translate it into
+ 
+
+ align:start position:0%
+will actually do is translate it into
+well it'll put this address and it'll
+
+ align:start position:0%
+well it'll put this address and it'll
+ 
+
+ align:start position:0%
+well it'll put this address and it'll
+add the table of
+
+ align:start position:0%
+add the table of
+ 
+
+ align:start position:0%
+add the table of
+DS base to this guy and it'll actually
+
+ align:start position:0%
+DS base to this guy and it'll actually
+ 
+
+ align:start position:0%
+DS base to this guy and it'll actually
+take the address
+
+ align:start position:0%
+take the address
+ 
+
+ align:start position:0%
+take the address
+modul the length from the same table so
+
+ align:start position:0%
+modul the length from the same table so
+ 
+
+ align:start position:0%
+modul the length from the same table so
+whenever you're doing a memory access
+
+ align:start position:0%
+whenever you're doing a memory access
+ 
+
+ align:start position:0%
+whenever you're doing a memory access
+it's actually going to add the base of
+
+ align:start position:0%
+it's actually going to add the base of
+ 
+
+ align:start position:0%
+it's actually going to add the base of
+your segment selectors sort of
+
+ align:start position:0%
+your segment selectors sort of
+ 
+
+ align:start position:0%
+your segment selectors sort of
+descriptor table entry and take your
+
+ align:start position:0%
+descriptor table entry and take your
+ 
+
+ align:start position:0%
+descriptor table entry and take your
+address that you're actually specifying
+
+ align:start position:0%
+address that you're actually specifying
+ 
+
+ align:start position:0%
+address that you're actually specifying
+and mod it with the l of the
+
+ align:start position:0%
+and mod it with the l of the
+ 
+
+ align:start position:0%
+and mod it with the l of the
+corresponding segment does this make
+
+ align:start position:0%
+corresponding segment does this make
+ 
+
+ align:start position:0%
+corresponding segment does this make
+sense it's a little Baro but that's what
+
+ align:start position:0%
+sense it's a little Baro but that's what
+ 
+
+ align:start position:0%
+sense it's a little Baro but that's what
+the hardware gives us so why isn't this
+
+ align:start position:0%
+the hardware gives us so why isn't this
+ 
+
+ align:start position:0%
+the hardware gives us so why isn't this
+use for example for like buffer
+
+ align:start position:0%
+use for example for like buffer
+ 
+
+ align:start position:0%
+use for example for like buffer
+protection yeah a good question so could
+
+ align:start position:0%
+protection yeah a good question so could
+ 
+
+ align:start position:0%
+protection yeah a good question so could
+you use this for protecting against
+
+ align:start position:0%
+you use this for protecting against
+ 
+
+ align:start position:0%
+you use this for protecting against
+buffer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+overflows so how what's the plan like
+
+ align:start position:0%
+overflows so how what's the plan like
+ 
+
+ align:start position:0%
+overflows so how what's the plan like
+you could basically set up uh a for
+
+ align:start position:0%
+you could basically set up uh a for
+ 
+
+ align:start position:0%
+you could basically set up uh a for
+every buffer that you have you could put
+
+ align:start position:0%
+every buffer that you have you could put
+ 
+
+ align:start position:0%
+every buffer that you have you could put
+the Buffer's base here you could put the
+
+ align:start position:0%
+the Buffer's base here you could put the
+ 
+
+ align:start position:0%
+the Buffer's base here you could put the
+size of the buffer
+
+ align:start position:0%
+size of the buffer
+ 
+
+ align:start position:0%
+size of the buffer
+there you don't need to there before you
+
+ align:start position:0%
+there you don't need to there before you
+ 
+
+ align:start position:0%
+there you don't need to there before you
+want to write to it you wouldn't need it
+
+ align:start position:0%
+want to write to it you wouldn't need it
+ 
+
+ align:start position:0%
+want to write to it you wouldn't need it
+there conly yeah so I think the reason
+
+ align:start position:0%
+there conly yeah so I think the reason
+ 
+
+ align:start position:0%
+there conly yeah so I think the reason
+that this isn't used so much for
+
+ align:start position:0%
+that this isn't used so much for
+ 
+
+ align:start position:0%
+that this isn't used so much for
+protecting against buffer overflows is
+
+ align:start position:0%
+protecting against buffer overflows is
+ 
+
+ align:start position:0%
+protecting against buffer overflows is
+that this table has at most two to the
+
+ align:start position:0%
+that this table has at most two to the
+ 
+
+ align:start position:0%
+that this table has at most two to the
+16 entries because these descriptors are
+
+ align:start position:0%
+16 entries because these descriptors are
+ 
+
+ align:start position:0%
+16 entries because these descriptors are
+actually 16 bits long and in fact a
+
+ align:start position:0%
+actually 16 bits long and in fact a
+ 
+
+ align:start position:0%
+actually 16 bits long and in fact a
+couple of the bits are used for other
+
+ align:start position:0%
+couple of the bits are used for other
+ 
+
+ align:start position:0%
+couple of the bits are used for other
+stuff so in fact I think you can only
+
+ align:start position:0%
+stuff so in fact I think you can only
+ 
+
+ align:start position:0%
+stuff so in fact I think you can only
+stick like two to the 13 entries here so
+
+ align:start position:0%
+stick like two to the 13 entries here so
+ 
+
+ align:start position:0%
+stick like two to the 13 entries here so
+if you have more than two to the 13
+
+ align:start position:0%
+if you have more than two to the 13
+ 
+
+ align:start position:0%
+if you have more than two to the 13
+variable size array things in your code
+
+ align:start position:0%
+variable size array things in your code
+ 
+
+ align:start position:0%
+variable size array things in your code
+then that's probably going to overflow
+
+ align:start position:0%
+then that's probably going to overflow
+ 
+
+ align:start position:0%
+then that's probably going to overflow
+this stable
+
+ align:start position:0%
+this stable
+ 
+
+ align:start position:0%
+this stable
+it actually a little bit weird for the
+
+ align:start position:0%
+it actually a little bit weird for the
+ 
+
+ align:start position:0%
+it actually a little bit weird for the
+compiler to manipulate this table
+
+ align:start position:0%
+compiler to manipulate this table
+ 
+
+ align:start position:0%
+compiler to manipulate this table
+because the way you actually manipulate
+
+ align:start position:0%
+because the way you actually manipulate
+ 
+
+ align:start position:0%
+because the way you actually manipulate
+it is through system calls so you can't
+
+ align:start position:0%
+it is through system calls so you can't
+ 
+
+ align:start position:0%
+it is through system calls so you can't
+actually directly write to this table
+
+ align:start position:0%
+actually directly write to this table
+ 
+
+ align:start position:0%
+actually directly write to this table
+you have to issue a system call to the
+
+ align:start position:0%
+you have to issue a system call to the
+ 
+
+ align:start position:0%
+you have to issue a system call to the
+operating system and the operating
+
+ align:start position:0%
+operating system and the operating
+ 
+
+ align:start position:0%
+operating system and the operating
+system will put this table into the
+
+ align:start position:0%
+system will put this table into the
+ 
+
+ align:start position:0%
+system will put this table into the
+hardware for you so I think most
+
+ align:start position:0%
+hardware for you so I think most
+ 
+
+ align:start position:0%
+hardware for you so I think most
+compilers just don't bother having this
+
+ align:start position:0%
+compilers just don't bother having this
+ 
+
+ align:start position:0%
+compilers just don't bother having this
+complicated story for managing buffers
+
+ align:start position:0%
+complicated story for managing buffers
+ 
+
+ align:start position:0%
+complicated story for managing buffers
+multic actually did this though so like
+
+ align:start position:0%
+multic actually did this though so like
+ 
+
+ align:start position:0%
+multic actually did this though so like
+on multic you actually had two to the 18
+
+ align:start position:0%
+on multic you actually had two to the 18
+ 
+
+ align:start position:0%
+on multic you actually had two to the 18
+distinct segments and two to the 18
+
+ align:start position:0%
+distinct segments and two to the 18
+ 
+
+ align:start position:0%
+distinct segments and two to the 18
+possible offsets within a segment and
+
+ align:start position:0%
+possible offsets within a segment and
+ 
+
+ align:start position:0%
+possible offsets within a segment and
+every sort of possible like shared
+
+ align:start position:0%
+every sort of possible like shared
+ 
+
+ align:start position:0%
+every sort of possible like shared
+Library chunk or chunk of memory was a
+
+ align:start position:0%
+Library chunk or chunk of memory was a
+ 
+
+ align:start position:0%
+Library chunk or chunk of memory was a
+distinct segment and then they would all
+
+ align:start position:0%
+distinct segment and then they would all
+ 
+
+ align:start position:0%
+distinct segment and then they would all
+be range checked not maybe at the
+
+ align:start position:0%
+be range checked not maybe at the
+ 
+
+ align:start position:0%
+be range checked not maybe at the
+variable level but still yeah presumably
+
+ align:start position:0%
+variable level but still yeah presumably
+ 
+
+ align:start position:0%
+variable level but still yeah presumably
+it's also a bit slower if you have to
+
+ align:start position:0%
+it's also a bit slower if you have to
+ 
+
+ align:start position:0%
+it's also a bit slower if you have to
+chop into the kernel all the time to
+
+ align:start position:0%
+chop into the kernel all the time to
+ 
+
+ align:start position:0%
+chop into the kernel all the time to
+that's right yeah so there's also the
+
+ align:start position:0%
+that's right yeah so there's also the
+ 
+
+ align:start position:0%
+that's right yeah so there's also the
+overhead uh I guess to set this up there
+
+ align:start position:0%
+overhead uh I guess to set this up there
+ 
+
+ align:start position:0%
+overhead uh I guess to set this up there
+would be some overhead or if you create
+
+ align:start position:0%
+would be some overhead or if you create
+ 
+
+ align:start position:0%
+would be some overhead or if you create
+a new buffer on the stack all of a
+
+ align:start position:0%
+a new buffer on the stack all of a
+ 
+
+ align:start position:0%
+a new buffer on the stack all of a
+sudden you have to call in to this guy
+
+ align:start position:0%
+sudden you have to call in to this guy
+ 
+
+ align:start position:0%
+sudden you have to call in to this guy
+and uh uh add an extra entry so yeah
+
+ align:start position:0%
+and uh uh add an extra entry so yeah
+ 
+
+ align:start position:0%
+and uh uh add an extra entry so yeah
+it's U it is nice machinery and but it's
+
+ align:start position:0%
+it's U it is nice machinery and but it's
+ 
+
+ align:start position:0%
+it's U it is nice machinery and but it's
+mostly used for coarser grain things
+
+ align:start position:0%
+mostly used for coarser grain things
+ 
+
+ align:start position:0%
+mostly used for coarser grain things
+because of the overheads of changing it
+
+ align:start position:0%
+because of the overheads of changing it
+ 
+
+ align:start position:0%
+because of the overheads of changing it
+a bit make
+
+ align:start position:0%
+a bit make
+ 
+
+ align:start position:0%
+a bit make
+sense all right so how do these guys
+
+ align:start position:0%
+sense all right so how do these guys
+ 
+
+ align:start position:0%
+sense all right so how do these guys
+actually use now the segmentation
+
+ align:start position:0%
+actually use now the segmentation
+ 
+
+ align:start position:0%
+actually use now the segmentation
+Machinery well you can sort of guess
+
+ align:start position:0%
+Machinery well you can sort of guess
+ 
+
+ align:start position:0%
+Machinery well you can sort of guess
+what how it works I guess by default all
+
+ align:start position:0%
+what how it works I guess by default all
+ 
+
+ align:start position:0%
+what how it works I guess by default all
+these segments in x86 have a base of
+
+ align:start position:0%
+these segments in x86 have a base of
+ 
+
+ align:start position:0%
+these segments in x86 have a base of
+zero and a length of 2 to the 32 so you
+
+ align:start position:0%
+zero and a length of 2 to the 32 so you
+ 
+
+ align:start position:0%
+zero and a length of 2 to the 32 so you
+can access the entire range of memory
+
+ align:start position:0%
+can access the entire range of memory
+ 
+
+ align:start position:0%
+can access the entire range of memory
+you could possibly want so for Native
+
+ align:start position:0%
+you could possibly want so for Native
+ 
+
+ align:start position:0%
+you could possibly want so for Native
+client what they do is code in a base of
+
+ align:start position:0%
+client what they do is code in a base of
+ 
+
+ align:start position:0%
+client what they do is code in a base of
+zero and a length of 256
+
+ align:start position:0%
+zero and a length of 256
+ 
+
+ align:start position:0%
+zero and a length of 256
+Megs and then they Point all these six
+
+ align:start position:0%
+Megs and then they Point all these six
+ 
+
+ align:start position:0%
+Megs and then they Point all these six
+segment selector registers to this entry
+
+ align:start position:0%
+segment selector registers to this entry
+ 
+
+ align:start position:0%
+segment selector registers to this entry
+for a 256 Meg region So then whenever
+
+ align:start position:0%
+for a 256 Meg region So then whenever
+ 
+
+ align:start position:0%
+for a 256 Meg region So then whenever
+the hardware does a memory access it's
+
+ align:start position:0%
+the hardware does a memory access it's
+ 
+
+ align:start position:0%
+the hardware does a memory access it's
+going to modit the the offset with 256
+
+ align:start position:0%
+going to modit the the offset with 256
+ 
+
+ align:start position:0%
+going to modit the the offset with 256
+Megs and it'll be restricted to that 256
+
+ align:start position:0%
+Megs and it'll be restricted to that 256
+ 
+
+ align:start position:0%
+Megs and it'll be restricted to that 256
+Meg range of memory that's allowed for
+
+ align:start position:0%
+Meg range of memory that's allowed for
+ 
+
+ align:start position:0%
+Meg range of memory that's allowed for
+the module to read and modify make
+
+ align:start position:0%
+the module to read and modify make
+ 
+
+ align:start position:0%
+the module to read and modify make
+sense all right so I guess we sort of
+
+ align:start position:0%
+sense all right so I guess we sort of
+ 
+
+ align:start position:0%
+sense all right so I guess we sort of
+roughly understand now this Hardware
+
+ align:start position:0%
+roughly understand now this Hardware
+ 
+
+ align:start position:0%
+roughly understand now this Hardware
+support and how this works uh and how
+
+ align:start position:0%
+support and how this works uh and how
+ 
+
+ align:start position:0%
+support and how this works uh and how
+you could potenti do it without segment
+
+ align:start position:0%
+you could potenti do it without segment
+ 
+
+ align:start position:0%
+you could potenti do it without segment
+selectors um so if we just implement
+
+ align:start position:0%
+selectors um so if we just implement
+ 
+
+ align:start position:0%
+selectors um so if we just implement
+this plan um is there anything that
+
+ align:start position:0%
+this plan um is there anything that
+ 
+
+ align:start position:0%
+this plan um is there anything that
+could go wrong like could we escape out
+
+ align:start position:0%
+could go wrong like could we escape out
+ 
+
+ align:start position:0%
+could go wrong like could we escape out
+of this segment
+
+ align:start position:0%
+of this segment
+ 
+
+ align:start position:0%
+of this segment
+selector in the untrusted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+module I guess there's one one thing you
+
+ align:start position:0%
+module I guess there's one one thing you
+ 
+
+ align:start position:0%
+module I guess there's one one thing you
+have to watch out for is that these
+
+ align:start position:0%
+have to watch out for is that these
+ 
+
+ align:start position:0%
+have to watch out for is that these
+registers are just like regular
+
+ align:start position:0%
+registers are just like regular
+ 
+
+ align:start position:0%
+registers are just like regular
+registers and you can actually move
+
+ align:start position:0%
+registers and you can actually move
+ 
+
+ align:start position:0%
+registers and you can actually move
+values in and out of them so you have to
+
+ align:start position:0%
+values in and out of them so you have to
+ 
+
+ align:start position:0%
+values in and out of them so you have to
+make sure that the untrusted module now
+
+ align:start position:0%
+make sure that the untrusted module now
+ 
+
+ align:start position:0%
+make sure that the untrusted module now
+doesn't tamper with these registers the
+
+ align:start position:0%
+doesn't tamper with these registers the
+ 
+
+ align:start position:0%
+doesn't tamper with these registers the
+segment selectors because somewhere in
+
+ align:start position:0%
+segment selectors because somewhere in
+ 
+
+ align:start position:0%
+segment selectors because somewhere in
+your descriptor table is also the
+
+ align:start position:0%
+your descriptor table is also the
+ 
+
+ align:start position:0%
+your descriptor table is also the
+original segment descriptor for your
+
+ align:start position:0%
+original segment descriptor for your
+ 
+
+ align:start position:0%
+original segment descriptor for your
+entire process which has a base of zero
+
+ align:start position:0%
+entire process which has a base of zero
+ 
+
+ align:start position:0%
+entire process which has a base of zero
+and a length of two to the 32 so if the
+
+ align:start position:0%
+and a length of two to the 32 so if the
+ 
+
+ align:start position:0%
+and a length of two to the 32 so if the
+untrusted module could somehow change
+
+ align:start position:0%
+untrusted module could somehow change
+ 
+
+ align:start position:0%
+untrusted module could somehow change
+the Cs or DS or ES or any of these guys
+
+ align:start position:0%
+the Cs or DS or ES or any of these guys
+ 
+
+ align:start position:0%
+the Cs or DS or ES or any of these guys
+to point to this original operating
+
+ align:start position:0%
+to point to this original operating
+ 
+
+ align:start position:0%
+to point to this original operating
+system segment that covers your entire
+
+ align:start position:0%
+system segment that covers your entire
+ 
+
+ align:start position:0%
+system segment that covers your entire
+address space then you could then do
+
+ align:start position:0%
+address space then you could then do
+ 
+
+ align:start position:0%
+address space then you could then do
+memory references with respect to this
+
+ align:start position:0%
+memory references with respect to this
+ 
+
+ align:start position:0%
+memory references with respect to this
+segment and get out of this
+
+ align:start position:0%
+segment and get out of this
+ 
+
+ align:start position:0%
+segment and get out of this
+sandbox so as a result native client has
+
+ align:start position:0%
+sandbox so as a result native client has
+ 
+
+ align:start position:0%
+sandbox so as a result native client has
+to add some more instructions to this
+
+ align:start position:0%
+to add some more instructions to this
+ 
+
+ align:start position:0%
+to add some more instructions to this
+prohibited list so I think they
+
+ align:start position:0%
+prohibited list so I think they
+ 
+
+ align:start position:0%
+prohibited list so I think they
+basically prohibit all instructions that
+
+ align:start position:0%
+basically prohibit all instructions that
+ 
+
+ align:start position:0%
+basically prohibit all instructions that
+you know move into a segment selector DS
+
+ align:start position:0%
+you know move into a segment selector DS
+ 
+
+ align:start position:0%
+you know move into a segment selector DS
+es Etc so that once you're in the
+
+ align:start position:0%
+es Etc so that once you're in the
+ 
+
+ align:start position:0%
+es Etc so that once you're in the
+sandbox you cannot change the segment
+
+ align:start position:0%
+sandbox you cannot change the segment
+ 
+
+ align:start position:0%
+sandbox you cannot change the segment
+that you're referencing things with
+
+ align:start position:0%
+that you're referencing things with
+ 
+
+ align:start position:0%
+that you're referencing things with
+respect to make sense yeah the
+
+ align:start position:0%
+respect to make sense yeah the
+ 
+
+ align:start position:0%
+respect to make sense yeah the
+segmentation AR privil yeah so it turns
+
+ align:start position:0%
+segmentation AR privil yeah so it turns
+ 
+
+ align:start position:0%
+segmentation AR privil yeah so it turns
+out that on x86 the instructions to
+
+ align:start position:0%
+out that on x86 the instructions to
+ 
+
+ align:start position:0%
+out that on x86 the instructions to
+change the segment descriptor table are
+
+ align:start position:0%
+change the segment descriptor table are
+ 
+
+ align:start position:0%
+change the segment descriptor table are
+privileged but changing these sort of es
+
+ align:start position:0%
+privileged but changing these sort of es
+ 
+
+ align:start position:0%
+privileged but changing these sort of es
+into the table are completely
+
+ align:start position:0%
+into the table are completely
+ 
+
+ align:start position:0%
+into the table are completely
+unprivileged
+
+ align:start position:0%
+unprivileged
+ 
+
+ align:start position:0%
+unprivileged
+yeah sense other questions yeah can you
+
+ align:start position:0%
+yeah sense other questions yeah can you
+ 
+
+ align:start position:0%
+yeah sense other questions yeah can you
+initialize the table to put all zero
+
+ align:start position:0%
+initialize the table to put all zero
+ 
+
+ align:start position:0%
+initialize the table to put all zero
+lens in the unused slots well yes so the
+
+ align:start position:0%
+lens in the unused slots well yes so the
+ 
+
+ align:start position:0%
+lens in the unused slots well yes so the
+the unused slots uh you could yeah you
+
+ align:start position:0%
+the unused slots uh you could yeah you
+ 
+
+ align:start position:0%
+the unused slots uh you could yeah you
+can set the length of the table to
+
+ align:start position:0%
+can set the length of the table to
+ 
+
+ align:start position:0%
+can set the length of the table to
+something so there are no unused slots
+
+ align:start position:0%
+something so there are no unused slots
+ 
+
+ align:start position:0%
+something so there are no unused slots
+it turns out that you actually need this
+
+ align:start position:0%
+it turns out that you actually need this
+ 
+
+ align:start position:0%
+it turns out that you actually need this
+extra slot containing zero and 2 to the
+
+ align:start position:0%
+extra slot containing zero and 2 to the
+ 
+
+ align:start position:0%
+extra slot containing zero and 2 to the
+32 because the trusted runtime is going
+
+ align:start position:0%
+32 because the trusted runtime is going
+ 
+
+ align:start position:0%
+32 because the trusted runtime is going
+to need to run in this segment and
+
+ align:start position:0%
+to need to run in this segment and
+ 
+
+ align:start position:0%
+to need to run in this segment and
+access the entire memory range so you
+
+ align:start position:0%
+access the entire memory range so you
+ 
+
+ align:start position:0%
+access the entire memory range so you
+need this entry in there for the trusted
+
+ align:start position:0%
+need this entry in there for the trusted
+ 
+
+ align:start position:0%
+need this entry in there for the trusted
+runtime to work question in order to set
+
+ align:start position:0%
+runtime to work question in order to set
+ 
+
+ align:start position:0%
+runtime to work question in order to set
+this in order to set the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out no actually it's pretty cool there's
+
+ align:start position:0%
+out no actually it's pretty cool there's
+ 
+
+ align:start position:0%
+out no actually it's pretty cool there's
+like something that you don't have to be
+
+ align:start position:0%
+like something that you don't have to be
+ 
+
+ align:start position:0%
+like something that you don't have to be
+root for on Linux there's actually a
+
+ align:start position:0%
+root for on Linux there's actually a
+ 
+
+ align:start position:0%
+root for on Linux there's actually a
+system called I think it's called modify
+
+ align:start position:0%
+system called I think it's called modify
+ 
+
+ align:start position:0%
+system called I think it's called modify
+unor ldt for local descriptor table and
+
+ align:start position:0%
+unor ldt for local descriptor table and
+ 
+
+ align:start position:0%
+unor ldt for local descriptor table and
+it lets any process modify its own table
+
+ align:start position:0%
+it lets any process modify its own table
+ 
+
+ align:start position:0%
+it lets any process modify its own table
+these tables are actually per process
+
+ align:start position:0%
+these tables are actually per process
+ 
+
+ align:start position:0%
+these tables are actually per process
+well as everything in X is actually more
+
+ align:start position:0%
+well as everything in X is actually more
+ 
+
+ align:start position:0%
+well as everything in X is actually more
+complicated there's a global table and
+
+ align:start position:0%
+complicated there's a global table and
+ 
+
+ align:start position:0%
+complicated there's a global table and
+there's a local table table but the
+
+ align:start position:0%
+there's a local table table but the
+ 
+
+ align:start position:0%
+there's a local table table but the
+local table is per process you can
+
+ align:start position:0%
+local table is per process you can
+ 
+
+ align:start position:0%
+local table is per process you can
+modify that one uh at least yeah Mak
+
+ align:start position:0%
+modify that one uh at least yeah Mak
+ 
+
+ align:start position:0%
+modify that one uh at least yeah Mak
+sense all
+
+ align:start position:0%
+sense all
+ 
+
+ align:start position:0%
+sense all
+right okay so I guess one thing we could
+
+ align:start position:0%
+right okay so I guess one thing we could
+ 
+
+ align:start position:0%
+right okay so I guess one thing we could
+uh now try to figure out is how do we
+
+ align:start position:0%
+uh now try to figure out is how do we
+ 
+
+ align:start position:0%
+uh now try to figure out is how do we
+jump in and out of the Native client
+
+ align:start position:0%
+jump in and out of the Native client
+ 
+
+ align:start position:0%
+jump in and out of the Native client
+runtime or or out of the sandbox right
+
+ align:start position:0%
+runtime or or out of the sandbox right
+ 
+
+ align:start position:0%
+runtime or or out of the sandbox right
+so what does it mean for us to jump out
+
+ align:start position:0%
+so what does it mean for us to jump out
+ 
+
+ align:start position:0%
+so what does it mean for us to jump out
+so we need to run that trusted code and
+
+ align:start position:0%
+so we need to run that trusted code and
+ 
+
+ align:start position:0%
+so we need to run that trusted code and
+the trusted code lives somewhere up
+
+ align:start position:0%
+the trusted code lives somewhere up
+ 
+
+ align:start position:0%
+the trusted code lives somewhere up
+above the 256 Meg limit and in order to
+
+ align:start position:0%
+above the 256 Meg limit and in order to
+ 
+
+ align:start position:0%
+above the 256 Meg limit and in order to
+jump there we basically have to undo all
+
+ align:start position:0%
+jump there we basically have to undo all
+ 
+
+ align:start position:0%
+jump there we basically have to undo all
+these protections that native client
+
+ align:start position:0%
+these protections that native client
+ 
+
+ align:start position:0%
+these protections that native client
+sets in place and they basically boil
+
+ align:start position:0%
+sets in place and they basically boil
+ 
+
+ align:start position:0%
+sets in place and they basically boil
+down to changing these uh selectors so
+
+ align:start position:0%
+down to changing these uh selectors so
+ 
+
+ align:start position:0%
+down to changing these uh selectors so
+we already I guess our validator isn't
+
+ align:start position:0%
+we already I guess our validator isn't
+ 
+
+ align:start position:0%
+we already I guess our validator isn't
+going to enforce the same rules for the
+
+ align:start position:0%
+going to enforce the same rules for the
+ 
+
+ align:start position:0%
+going to enforce the same rules for the
+stuff above 256 Meg so that's easy
+
+ align:start position:0%
+stuff above 256 Meg so that's easy
+ 
+
+ align:start position:0%
+stuff above 256 Meg so that's easy
+enough but then we need to somehow jump
+
+ align:start position:0%
+enough but then we need to somehow jump
+ 
+
+ align:start position:0%
+enough but then we need to somehow jump
+into the trusted runtime and reset these
+
+ align:start position:0%
+into the trusted runtime and reset these
+ 
+
+ align:start position:0%
+into the trusted runtime and reset these
+segment selectors to the right values to
+
+ align:start position:0%
+segment selectors to the right values to
+ 
+
+ align:start position:0%
+segment selectors to the right values to
+this sort of giant segment that covers
+
+ align:start position:0%
+this sort of giant segment that covers
+ 
+
+ align:start position:0%
+this sort of giant segment that covers
+the entire process address space so the
+
+ align:start position:0%
+the entire process address space so the
+ 
+
+ align:start position:0%
+the entire process address space so the
+way that works on uh Native client is
+
+ align:start position:0%
+way that works on uh Native client is
+ 
+
+ align:start position:0%
+way that works on uh Native client is
+through this mechanism they call
+
+ align:start position:0%
+through this mechanism they call
+ 
+
+ align:start position:0%
+through this mechanism they call
+trampolines and spring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+springboards so all these guys are
+
+ align:start position:0%
+springboards so all these guys are
+ 
+
+ align:start position:0%
+springboards so all these guys are
+things that uh live in the low 64k of
+
+ align:start position:0%
+things that uh live in the low 64k of
+ 
+
+ align:start position:0%
+things that uh live in the low 64k of
+the process of the module um and the
+
+ align:start position:0%
+the process of the module um and the
+ 
+
+ align:start position:0%
+the process of the module um and the
+cool thing about that is that these are
+
+ align:start position:0%
+cool thing about that is that these are
+ 
+
+ align:start position:0%
+cool thing about that is that these are
+going to be sort of chunks of code
+
+ align:start position:0%
+going to be sort of chunks of code
+ 
+
+ align:start position:0%
+going to be sort of chunks of code
+living that low 64k of the process space
+
+ align:start position:0%
+living that low 64k of the process space
+ 
+
+ align:start position:0%
+living that low 64k of the process space
+so that means that this untrusted module
+
+ align:start position:0%
+so that means that this untrusted module
+ 
+
+ align:start position:0%
+so that means that this untrusted module
+can actually jump there because it's a
+
+ align:start position:0%
+can actually jump there because it's a
+ 
+
+ align:start position:0%
+can actually jump there because it's a
+valid code address it's going to be on a
+
+ align:start position:0%
+valid code address it's going to be on a
+ 
+
+ align:start position:0%
+valid code address it's going to be on a
+32 by boundary potentially and it's
+
+ align:start position:0%
+32 by boundary potentially and it's
+ 
+
+ align:start position:0%
+32 by boundary potentially and it's
+going to be within the 256 Meg limit so
+
+ align:start position:0%
+going to be within the 256 Meg limit so
+ 
+
+ align:start position:0%
+going to be within the 256 Meg limit so
+you can jump to these
+
+ align:start position:0%
+you can jump to these
+ 
+
+ align:start position:0%
+you can jump to these
+trampolines but the native client
+
+ align:start position:0%
+trampolines but the native client
+ 
+
+ align:start position:0%
+trampolines but the native client
+runtime is going to actually copy these
+
+ align:start position:0%
+runtime is going to actually copy these
+ 
+
+ align:start position:0%
+runtime is going to actually copy these
+trampolines from somewhere outside so
+
+ align:start position:0%
+trampolines from somewhere outside so
+ 
+
+ align:start position:0%
+trampolines from somewhere outside so
+the native client module isn't allowed
+
+ align:start position:0%
+the native client module isn't allowed
+ 
+
+ align:start position:0%
+the native client module isn't allowed
+to supply its own trampoline code the
+
+ align:start position:0%
+to supply its own trampoline code the
+ 
+
+ align:start position:0%
+to supply its own trampoline code the
+trampoline code comes from The Trusted
+
+ align:start position:0%
+trampoline code comes from The Trusted
+ 
+
+ align:start position:0%
+trampoline code comes from The Trusted
+runtime so as a result it can actually
+
+ align:start position:0%
+runtime so as a result it can actually
+ 
+
+ align:start position:0%
+runtime so as a result it can actually
+contain some of these sensitive
+
+ align:start position:0%
+contain some of these sensitive
+ 
+
+ align:start position:0%
+contain some of these sensitive
+instructions like moving DS and CS
+
+ align:start position:0%
+instructions like moving DS and CS
+ 
+
+ align:start position:0%
+instructions like moving DS and CS
+Etc that the untrusted code itself is
+
+ align:start position:0%
+Etc that the untrusted code itself is
+ 
+
+ align:start position:0%
+Etc that the untrusted code itself is
+not allowed to have
+
+ align:start position:0%
+not allowed to have
+ 
+
+ align:start position:0%
+not allowed to have
+so the way you actually jump out of the
+
+ align:start position:0%
+so the way you actually jump out of the
+ 
+
+ align:start position:0%
+so the way you actually jump out of the
+sandbox and into the trusted run time to
+
+ align:start position:0%
+sandbox and into the trusted run time to
+ 
+
+ align:start position:0%
+sandbox and into the trusted run time to
+do something like malok or create a
+
+ align:start position:0%
+do something like malok or create a
+ 
+
+ align:start position:0%
+do something like malok or create a
+thread is you jump to a trampoline which
+
+ align:start position:0%
+thread is you jump to a trampoline which
+ 
+
+ align:start position:0%
+thread is you jump to a trampoline which
+uh lives at a 32 by offset so maybe it's
+
+ align:start position:0%
+uh lives at a 32 by offset so maybe it's
+ 
+
+ align:start position:0%
+uh lives at a 32 by offset so maybe it's
+an address well who knows maybe it's
+
+ align:start position:0%
+an address well who knows maybe it's
+ 
+
+ align:start position:0%
+an address well who knows maybe it's
+4096 plus 32 and it's going to have some
+
+ align:start position:0%
+4096 plus 32 and it's going to have some
+ 
+
+ align:start position:0%
+4096 plus 32 and it's going to have some
+instructions to basically undo these
+
+ align:start position:0%
+instructions to basically undo these
+ 
+
+ align:start position:0%
+instructions to basically undo these
+segment selector so what it's probably
+
+ align:start position:0%
+segment selector so what it's probably
+ 
+
+ align:start position:0%
+segment selector so what it's probably
+going to do is it's going to you know
+
+ align:start position:0%
+going to do is it's going to you know
+ 
+
+ align:start position:0%
+going to do is it's going to you know
+move some value I don't know maybe seven
+
+ align:start position:0%
+move some value I don't know maybe seven
+ 
+
+ align:start position:0%
+move some value I don't know maybe seven
+into the DS register and maybe 7 point
+
+ align:start position:0%
+into the DS register and maybe 7 point
+ 
+
+ align:start position:0%
+into the DS register and maybe 7 point
+to this entry here that's allowed for
+
+ align:start position:0%
+to this entry here that's allowed for
+ 
+
+ align:start position:0%
+to this entry here that's allowed for
+the entire 2 to 32 address space and
+
+ align:start position:0%
+the entire 2 to 32 address space and
+ 
+
+ align:start position:0%
+the entire 2 to 32 address space and
+then you're going to effectively move Cs
+
+ align:start position:0%
+then you're going to effectively move Cs
+ 
+
+ align:start position:0%
+then you're going to effectively move Cs
+and then jump somewhere up into the
+
+ align:start position:0%
+and then jump somewhere up into the
+ 
+
+ align:start position:0%
+and then jump somewhere up into the
+service
+
+ align:start position:0%
+service
+ 
+
+ align:start position:0%
+service
+runtime and this is basically going to
+
+ align:start position:0%
+runtime and this is basically going to
+ 
+
+ align:start position:0%
+runtime and this is basically going to
+be past 256
+
+ align:start position:0%
+be past 256
+ 
+
+ align:start position:0%
+be past 256
+Megs so there's going to be this jump in
+
+ align:start position:0%
+Megs so there's going to be this jump in
+ 
+
+ align:start position:0%
+Megs so there's going to be this jump in
+here that's not regularly allowed but
+
+ align:start position:0%
+here that's not regularly allowed but
+ 
+
+ align:start position:0%
+here that's not regularly allowed but
+we're going to be okay with it because
+
+ align:start position:0%
+we're going to be okay with it because
+ 
+
+ align:start position:0%
+we're going to be okay with it because
+it's going to be into a point in The
+
+ align:start position:0%
+it's going to be into a point in The
+ 
+
+ align:start position:0%
+it's going to be into a point in The
+Trusted service runtime that is
+
+ align:start position:0%
+Trusted service runtime that is
+ 
+
+ align:start position:0%
+Trusted service runtime that is
+expecting these jumps and it's going to
+
+ align:start position:0%
+expecting these jumps and it's going to
+ 
+
+ align:start position:0%
+expecting these jumps and it's going to
+perform proper checks afterwards uh on
+
+ align:start position:0%
+perform proper checks afterwards uh on
+ 
+
+ align:start position:0%
+perform proper checks afterwards uh on
+the jump on the arguments and whatever
+
+ align:start position:0%
+the jump on the arguments and whatever
+ 
+
+ align:start position:0%
+the jump on the arguments and whatever
+else that is being passed around and we
+
+ align:start position:0%
+else that is being passed around and we
+ 
+
+ align:start position:0%
+else that is being passed around and we
+can actually do this move DS here
+
+ align:start position:0%
+can actually do this move DS here
+ 
+
+ align:start position:0%
+can actually do this move DS here
+because we know that it's actually safe
+
+ align:start position:0%
+because we know that it's actually safe
+ 
+
+ align:start position:0%
+because we know that it's actually safe
+the code we're going to jump to isn't
+
+ align:start position:0%
+the code we're going to jump to isn't
+ 
+
+ align:start position:0%
+the code we're going to jump to isn't
+going to do anything arbitrary or funny
+
+ align:start position:0%
+going to do anything arbitrary or funny
+ 
+
+ align:start position:0%
+going to do anything arbitrary or funny
+with our untrusted module make sense
+
+ align:start position:0%
+with our untrusted module make sense
+ 
+
+ align:start position:0%
+with our untrusted module make sense
+roughly what's going
+
+ align:start position:0%
+roughly what's going
+ 
+
+ align:start position:0%
+roughly what's going
+on so why do these guys bother jumping
+
+ align:start position:0%
+on so why do these guys bother jumping
+ 
+
+ align:start position:0%
+on so why do these guys bother jumping
+out of this segments like why not just
+
+ align:start position:0%
+out of this segments like why not just
+ 
+
+ align:start position:0%
+out of this segments like why not just
+put the whole thing in in the trampoline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seems like more work in some level yeah
+
+ align:start position:0%
+seems like more work in some level yeah
+ 
+
+ align:start position:0%
+seems like more work in some level yeah
+only have4 yeah you don't actually have
+
+ align:start position:0%
+only have4 yeah you don't actually have
+ 
+
+ align:start position:0%
+only have4 yeah you don't actually have
+a lot of space and well I guess you have
+
+ align:start position:0%
+a lot of space and well I guess you have
+ 
+
+ align:start position:0%
+a lot of space and well I guess you have
+64k so that's potentially maybe enough
+
+ align:start position:0%
+64k so that's potentially maybe enough
+ 
+
+ align:start position:0%
+64k so that's potentially maybe enough
+for like maybe you can Implement maloc
+
+ align:start position:0%
+for like maybe you can Implement maloc
+ 
+
+ align:start position:0%
+for like maybe you can Implement maloc
+in there but the problem is not so much
+
+ align:start position:0%
+in there but the problem is not so much
+ 
+
+ align:start position:0%
+in there but the problem is not so much
+the 64k I think but this 32 by
+
+ align:start position:0%
+the 64k I think but this 32 by
+ 
+
+ align:start position:0%
+the 64k I think but this 32 by
+restriction and it's actually not a
+
+ align:start position:0%
+restriction and it's actually not a
+ 
+
+ align:start position:0%
+restriction and it's actually not a
+restriction on The Trusted code because
+
+ align:start position:0%
+restriction on The Trusted code because
+ 
+
+ align:start position:0%
+restriction on The Trusted code because
+the trusted code can do whatever it
+
+ align:start position:0%
+the trusted code can do whatever it
+ 
+
+ align:start position:0%
+the trusted code can do whatever it
+wants here it's not going to be checked
+
+ align:start position:0%
+wants here it's not going to be checked
+ 
+
+ align:start position:0%
+wants here it's not going to be checked
+the problem is that the untrusted code
+
+ align:start position:0%
+the problem is that the untrusted code
+ 
+
+ align:start position:0%
+the problem is that the untrusted code
+can jump to every 32 byte offset so
+
+ align:start position:0%
+can jump to every 32 byte offset so
+ 
+
+ align:start position:0%
+can jump to every 32 byte offset so
+every 32 white offset has to be prepared
+
+ align:start position:0%
+every 32 white offset has to be prepared
+ 
+
+ align:start position:0%
+every 32 white offset has to be prepared
+to be very suspicious of its arguments
+
+ align:start position:0%
+to be very suspicious of its arguments
+ 
+
+ align:start position:0%
+to be very suspicious of its arguments
+so you probably are going to be are
+
+ align:start position:0%
+so you probably are going to be are
+ 
+
+ align:start position:0%
+so you probably are going to be are
+going to have a hard time writing this
+
+ align:start position:0%
+going to have a hard time writing this
+ 
+
+ align:start position:0%
+going to have a hard time writing this
+code here with every 32 by rechecking
+
+ align:start position:0%
+code here with every 32 by rechecking
+ 
+
+ align:start position:0%
+code here with every 32 by rechecking
+the arguments and values and so on so
+
+ align:start position:0%
+the arguments and values and so on so
+ 
+
+ align:start position:0%
+the arguments and values and so on so
+basically you have to jump out of the
+
+ align:start position:0%
+basically you have to jump out of the
+ 
+
+ align:start position:0%
+basically you have to jump out of the
+trampoline and into the runtime up here
+
+ align:start position:0%
+trampoline and into the runtime up here
+ 
+
+ align:start position:0%
+trampoline and into the runtime up here
+within 32 bytes of
+
+ align:start position:0%
+within 32 bytes of
+ 
+
+ align:start position:0%
+within 32 bytes of
+code so then if you jump to the next
+
+ align:start position:0%
+code so then if you jump to the next
+ 
+
+ align:start position:0%
+code so then if you jump to the next
+thing then well something else is going
+
+ align:start position:0%
+thing then well something else is going
+ 
+
+ align:start position:0%
+thing then well something else is going
+to happen here but it's not part of this
+
+ align:start position:0%
+to happen here but it's not part of this
+ 
+
+ align:start position:0%
+to happen here but it's not part of this
+same trusted routine
+
+ align:start position:0%
+same trusted routine
+ 
+
+ align:start position:0%
+same trusted routine
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+sense okay so this is how you sort of
+
+ align:start position:0%
+sense okay so this is how you sort of
+ 
+
+ align:start position:0%
+sense okay so this is how you sort of
+jump out of the uh sandbox to jump back
+
+ align:start position:0%
+jump out of the uh sandbox to jump back
+ 
+
+ align:start position:0%
+jump out of the uh sandbox to jump back
+in you also need to you basically need
+
+ align:start position:0%
+in you also need to you basically need
+ 
+
+ align:start position:0%
+in you also need to you basically need
+to invert the these Transformations you
+
+ align:start position:0%
+to invert the these Transformations you
+ 
+
+ align:start position:0%
+to invert the these Transformations you
+need to sort of set the DS back and CS
+
+ align:start position:0%
+need to sort of set the DS back and CS
+ 
+
+ align:start position:0%
+need to sort of set the DS back and CS
+back and so on and the tricky thing is
+
+ align:start position:0%
+back and so on and the tricky thing is
+ 
+
+ align:start position:0%
+back and so on and the tricky thing is
+that if you're running outside of this
+
+ align:start position:0%
+that if you're running outside of this
+ 
+
+ align:start position:0%
+that if you're running outside of this
+um 256 Meg limit if you're running
+
+ align:start position:0%
+um 256 Meg limit if you're running
+ 
+
+ align:start position:0%
+um 256 Meg limit if you're running
+inside of the trusted runtime then you
+
+ align:start position:0%
+inside of the trusted runtime then you
+ 
+
+ align:start position:0%
+inside of the trusted runtime then you
+can't really reset these registers yet
+
+ align:start position:0%
+can't really reset these registers yet
+ 
+
+ align:start position:0%
+can't really reset these registers yet
+because otherwise you won't then be able
+
+ align:start position:0%
+because otherwise you won't then be able
+ 
+
+ align:start position:0%
+because otherwise you won't then be able
+to access any of the memory in your sort
+
+ align:start position:0%
+to access any of the memory in your sort
+ 
+
+ align:start position:0%
+to access any of the memory in your sort
+of space outside so what they actually
+
+ align:start position:0%
+of space outside so what they actually
+ 
+
+ align:start position:0%
+of space outside so what they actually
+do is they have this thing called a
+
+ align:start position:0%
+do is they have this thing called a
+ 
+
+ align:start position:0%
+do is they have this thing called a
+springboard which is how the trusted
+
+ align:start position:0%
+springboard which is how the trusted
+ 
+
+ align:start position:0%
+springboard which is how the trusted
+runtime from outside the 256 Meg limit
+
+ align:start position:0%
+runtime from outside the 256 Meg limit
+ 
+
+ align:start position:0%
+runtime from outside the 256 Meg limit
+is actually going to jump back into the
+
+ align:start position:0%
+is actually going to jump back into the
+ 
+
+ align:start position:0%
+is actually going to jump back into the
+native client module so here it's going
+
+ align:start position:0%
+native client module so here it's going
+ 
+
+ align:start position:0%
+native client module so here it's going
+to reload the DS register with maybe
+
+ align:start position:0%
+to reload the DS register with maybe
+ 
+
+ align:start position:0%
+to reload the DS register with maybe
+whatever that limited segment descriptor
+
+ align:start position:0%
+whatever that limited segment descriptor
+ 
+
+ align:start position:0%
+whatever that limited segment descriptor
+is maybe let's say it's one and then
+
+ align:start position:0%
+is maybe let's say it's one and then
+ 
+
+ align:start position:0%
+is maybe let's say it's one and then
+it's going to reset other things and
+
+ align:start position:0%
+it's going to reset other things and
+ 
+
+ align:start position:0%
+it's going to reset other things and
+then it'll jump to you know whatever
+
+ align:start position:0%
+then it'll jump to you know whatever
+ 
+
+ align:start position:0%
+then it'll jump to you know whatever
+address the trust runtime wants to
+
+ align:start position:0%
+address the trust runtime wants to
+ 
+
+ align:start position:0%
+address the trust runtime wants to
+return to in the untrusted module Mak
+
+ align:start position:0%
+return to in the untrusted module Mak
+ 
+
+ align:start position:0%
+return to in the untrusted module Mak
+sense so this is how you sort of jump
+
+ align:start position:0%
+sense so this is how you sort of jump
+ 
+
+ align:start position:0%
+sense so this is how you sort of jump
+back in and the only sort of tricky
+
+ align:start position:0%
+back in and the only sort of tricky
+ 
+
+ align:start position:0%
+back in and the only sort of tricky
+piece here is that you don't want the
+
+ align:start position:0%
+piece here is that you don't want the
+ 
+
+ align:start position:0%
+piece here is that you don't want the
+untrusted code to jump into the
+
+ align:start position:0%
+untrusted code to jump into the
+ 
+
+ align:start position:0%
+untrusted code to jump into the
+springboard itself maybe something weird
+
+ align:start position:0%
+springboard itself maybe something weird
+ 
+
+ align:start position:0%
+springboard itself maybe something weird
+will happen who knows so what they do is
+
+ align:start position:0%
+will happen who knows so what they do is
+ 
+
+ align:start position:0%
+will happen who knows so what they do is
+they actually put a halt instruction as
+
+ align:start position:0%
+they actually put a halt instruction as
+ 
+
+ align:start position:0%
+they actually put a halt instruction as
+the first bite of this 32 by multiple
+
+ align:start position:0%
+the first bite of this 32 by multiple
+ 
+
+ align:start position:0%
+the first bite of this 32 by multiple
+sequence so if you jump into the middle
+
+ align:start position:0%
+sequence so if you jump into the middle
+ 
+
+ align:start position:0%
+sequence so if you jump into the middle
+of to the beginning of this guy you'll
+
+ align:start position:0%
+of to the beginning of this guy you'll
+ 
+
+ align:start position:0%
+of to the beginning of this guy you'll
+immediately halt the trusted runtime is
+
+ align:start position:0%
+immediately halt the trusted runtime is
+ 
+
+ align:start position:0%
+immediately halt the trusted runtime is
+going to jump to one past this bite and
+
+ align:start position:0%
+going to jump to one past this bite and
+ 
+
+ align:start position:0%
+going to jump to one past this bite and
+be able to execute the springboard but
+
+ align:start position:0%
+be able to execute the springboard but
+ 
+
+ align:start position:0%
+be able to execute the springboard but
+this is something that only The Trusted
+
+ align:start position:0%
+this is something that only The Trusted
+ 
+
+ align:start position:0%
+this is something that only The Trusted
+runtime can do because regularly check
+
+ align:start position:0%
+runtime can do because regularly check
+ 
+
+ align:start position:0%
+runtime can do because regularly check
+this is not going to be allowed question
+
+ align:start position:0%
+this is not going to be allowed question
+ 
+
+ align:start position:0%
+this is not going to be allowed question
+is a springboard in the untrusted module
+
+ align:start position:0%
+is a springboard in the untrusted module
+ 
+
+ align:start position:0%
+is a springboard in the untrusted module
+so the springboard is within the 0 to 56
+
+ align:start position:0%
+so the springboard is within the 0 to 56
+ 
+
+ align:start position:0%
+so the springboard is within the 0 to 56
+Meg part of the untrusted module but it
+
+ align:start position:0%
+Meg part of the untrusted module but it
+ 
+
+ align:start position:0%
+Meg part of the untrusted module but it
+actually lives in that 64-bit chunk at
+
+ align:start position:0%
+actually lives in that 64-bit chunk at
+ 
+
+ align:start position:0%
+actually lives in that 64-bit chunk at
+the very beginning that doesn't actually
+
+ align:start position:0%
+the very beginning that doesn't actually
+ 
+
+ align:start position:0%
+the very beginning that doesn't actually
+come from the binary you download from
+
+ align:start position:0%
+come from the binary you download from
+ 
+
+ align:start position:0%
+come from the binary you download from
+some website but it's actually patched
+
+ align:start position:0%
+some website but it's actually patched
+ 
+
+ align:start position:0%
+some website but it's actually patched
+into it by the native client runtime
+
+ align:start position:0%
+into it by the native client runtime
+ 
+
+ align:start position:0%
+into it by the native client runtime
+when it first loads this modu memory why
+
+ align:start position:0%
+when it first loads this modu memory why
+ 
+
+ align:start position:0%
+when it first loads this modu memory why
+not just have it in the runtime yeah so
+
+ align:start position:0%
+not just have it in the runtime yeah so
+ 
+
+ align:start position:0%
+not just have it in the runtime yeah so
+why not have it in the runtime so what
+
+ align:start position:0%
+why not have it in the runtime so what
+ 
+
+ align:start position:0%
+why not have it in the runtime so what
+happens if the runtime was allowed to
+
+ align:start position:0%
+happens if the runtime was allowed to
+ 
+
+ align:start position:0%
+happens if the runtime was allowed to
+supply the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+springboard is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bad
+
+ align:start position:0%
+bad
+ 
+
+ align:start position:0%
+bad
+yeah how how would it know how would it
+
+ align:start position:0%
+yeah how how would it know how would it
+ 
+
+ align:start position:0%
+yeah how how would it know how would it
+know where to jump back to well so
+
+ align:start position:0%
+know where to jump back to well so
+ 
+
+ align:start position:0%
+know where to jump back to well so
+actually I think what this actually is
+
+ align:start position:0%
+actually I think what this actually is
+ 
+
+ align:start position:0%
+actually I think what this actually is
+is it actually jumps to something like
+
+ align:start position:0%
+is it actually jumps to something like
+ 
+
+ align:start position:0%
+is it actually jumps to something like
+eax so the trusted runtime says oh I
+
+ align:start position:0%
+eax so the trusted runtime says oh I
+ 
+
+ align:start position:0%
+eax so the trusted runtime says oh I
+want to return to this address it puts
+
+ align:start position:0%
+want to return to this address it puts
+ 
+
+ align:start position:0%
+want to return to this address it puts
+it in the eax register jumps here the
+
+ align:start position:0%
+it in the eax register jumps here the
+ 
+
+ align:start position:0%
+it in the eax register jumps here the
+springboard does this this this and then
+
+ align:start position:0%
+springboard does this this this and then
+ 
+
+ align:start position:0%
+springboard does this this this and then
+jumps to eax wherever the trusted run
+
+ align:start position:0%
+jumps to eax wherever the trusted run
+ 
+
+ align:start position:0%
+jumps to eax wherever the trusted run
+time set to
+
+ align:start position:0%
+time set to
+ 
+
+ align:start position:0%
+time set to
+jump so what if the module came with its
+
+ align:start position:0%
+jump so what if the module came with its
+ 
+
+ align:start position:0%
+jump so what if the module came with its
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+springboard um well in theory you could
+
+ align:start position:0%
+springboard um well in theory you could
+ 
+
+ align:start position:0%
+springboard um well in theory you could
+do it as like a natural jump type thing
+
+ align:start position:0%
+do it as like a natural jump type thing
+ 
+
+ align:start position:0%
+do it as like a natural jump type thing
+but it shouldn't know anything about the
+
+ align:start position:0%
+but it shouldn't know anything about the
+ 
+
+ align:start position:0%
+but it shouldn't know anything about the
+descriptor table like that's like a
+
+ align:start position:0%
+descriptor table like that's like a
+ 
+
+ align:start position:0%
+descriptor table like that's like a
+hardware yeah so actually this is like a
+
+ align:start position:0%
+hardware yeah so actually this is like a
+ 
+
+ align:start position:0%
+hardware yeah so actually this is like a
+really important instruction for
+
+ align:start position:0%
+really important instruction for
+ 
+
+ align:start position:0%
+really important instruction for
+sandboxing the fact that we reload that
+
+ align:start position:0%
+sandboxing the fact that we reload that
+ 
+
+ align:start position:0%
+sandboxing the fact that we reload that
+descriptor to point at one of those
+
+ align:start position:0%
+descriptor to point at one of those
+ 
+
+ align:start position:0%
+descriptor to point at one of those
+limited descriptors up there it's really
+
+ align:start position:0%
+limited descriptors up there it's really
+ 
+
+ align:start position:0%
+limited descriptors up there it's really
+important and if the module was allowed
+
+ align:start position:0%
+important and if the module was allowed
+ 
+
+ align:start position:0%
+important and if the module was allowed
+to supply its own springboard maybe
+
+ align:start position:0%
+to supply its own springboard maybe
+ 
+
+ align:start position:0%
+to supply its own springboard maybe
+it'll just skip this part and then not
+
+ align:start position:0%
+it'll just skip this part and then not
+ 
+
+ align:start position:0%
+it'll just skip this part and then not
+restrict itself back to 26 Megs so then
+
+ align:start position:0%
+restrict itself back to 26 Megs so then
+ 
+
+ align:start position:0%
+restrict itself back to 26 Megs so then
+once you jump through the springboard
+
+ align:start position:0%
+once you jump through the springboard
+ 
+
+ align:start position:0%
+once you jump through the springboard
+you'll be able to still access the
+
+ align:start position:0%
+you'll be able to still access the
+ 
+
+ align:start position:0%
+you'll be able to still access the
+entire process address space so it's
+
+ align:start position:0%
+entire process address space so it's
+ 
+
+ align:start position:0%
+entire process address space so it's
+actually the springboard is part of the
+
+ align:start position:0%
+actually the springboard is part of the
+ 
+
+ align:start position:0%
+actually the springboard is part of the
+enforcement mechanism it sort of sets up
+
+ align:start position:0%
+enforcement mechanism it sort of sets up
+ 
+
+ align:start position:0%
+enforcement mechanism it sort of sets up
+the boundaries so this is the reason why
+
+ align:start position:0%
+the boundaries so this is the reason why
+ 
+
+ align:start position:0%
+the boundaries so this is the reason why
+I think they don't want the springboard
+
+ align:start position:0%
+I think they don't want the springboard
+ 
+
+ align:start position:0%
+I think they don't want the springboard
+to come from the
+
+ align:start position:0%
+to come from the
+ 
+
+ align:start position:0%
+to come from the
+developer now yeah question put the
+
+ align:start position:0%
+developer now yeah question put the
+ 
+
+ align:start position:0%
+developer now yeah question put the
+spring board p the 256 me so I think uh
+
+ align:start position:0%
+spring board p the 256 me so I think uh
+ 
+
+ align:start position:0%
+spring board p the 256 me so I think uh
+they don't want to put the springboard
+
+ align:start position:0%
+they don't want to put the springboard
+ 
+
+ align:start position:0%
+they don't want to put the springboard
+past the 256 Megs because then you might
+
+ align:start position:0%
+past the 256 Megs because then you might
+ 
+
+ align:start position:0%
+past the 256 Megs because then you might
+have trouble jumping down so you want to
+
+ align:start position:0%
+have trouble jumping down so you want to
+ 
+
+ align:start position:0%
+have trouble jumping down so you want to
+jump to a particular address but you
+
+ align:start position:0%
+jump to a particular address but you
+ 
+
+ align:start position:0%
+jump to a particular address but you
+also want to set some extra registers
+
+ align:start position:0%
+also want to set some extra registers
+ 
+
+ align:start position:0%
+also want to set some extra registers
+here so if
+
+ align:start position:0%
+here so if
+ 
+
+ align:start position:0%
+here so if
+you're I think this basically has to
+
+ align:start position:0%
+you're I think this basically has to
+ 
+
+ align:start position:0%
+you're I think this basically has to
+sorry this has to do with setting that
+
+ align:start position:0%
+sorry this has to do with setting that
+ 
+
+ align:start position:0%
+sorry this has to do with setting that
+CS code descriptor segment because you
+
+ align:start position:0%
+CS code descriptor segment because you
+ 
+
+ align:start position:0%
+CS code descriptor segment because you
+want to set the code descriptor segment
+
+ align:start position:0%
+want to set the code descriptor segment
+ 
+
+ align:start position:0%
+want to set the code descriptor segment
+to this bounded segment and you want to
+
+ align:start position:0%
+to this bounded segment and you want to
+ 
+
+ align:start position:0%
+to this bounded segment and you want to
+jump to some particular address at the
+
+ align:start position:0%
+jump to some particular address at the
+ 
+
+ align:start position:0%
+jump to some particular address at the
+same time so I think it's easier for
+
+ align:start position:0%
+same time so I think it's easier for
+ 
+
+ align:start position:0%
+same time so I think it's easier for
+these guys to do it through a
+
+ align:start position:0%
+these guys to do it through a
+ 
+
+ align:start position:0%
+these guys to do it through a
+springboard because you first sort of
+
+ align:start position:0%
+springboard because you first sort of
+ 
+
+ align:start position:0%
+springboard because you first sort of
+jump to here then you can set your CS
+
+ align:start position:0%
+jump to here then you can set your CS
+ 
+
+ align:start position:0%
+jump to here then you can set your CS
+value but you can still execute the same
+
+ align:start position:0%
+value but you can still execute the same
+ 
+
+ align:start position:0%
+value but you can still execute the same
+code you're still
+
+ align:start position:0%
+code you're still
+ 
+
+ align:start position:0%
+code you're still
+running uh because you're within the 256
+
+ align:start position:0%
+running uh because you're within the 256
+ 
+
+ align:start position:0%
+running uh because you're within the 256
+bound make sense hold bit I think it
+
+ align:start position:0%
+bound make sense hold bit I think it
+ 
+
+ align:start position:0%
+bound make sense hold bit I think it
+basically has to do with what Atomic
+
+ align:start position:0%
+basically has to do with what Atomic
+ 
+
+ align:start position:0%
+basically has to do with what Atomic
+Primitives the hardware provides to you
+
+ align:start position:0%
+Primitives the hardware provides to you
+ 
+
+ align:start position:0%
+Primitives the hardware provides to you
+so you basically you want to set a whole
+
+ align:start position:0%
+so you basically you want to set a whole
+ 
+
+ align:start position:0%
+so you basically you want to set a whole
+bunch of these DS segment selector
+
+ align:start position:0%
+bunch of these DS segment selector
+ 
+
+ align:start position:0%
+bunch of these DS segment selector
+registers and the Cs register and jump
+
+ align:start position:0%
+registers and the Cs register and jump
+ 
+
+ align:start position:0%
+registers and the Cs register and jump
+to somewhere at the same time so it's
+
+ align:start position:0%
+to somewhere at the same time so it's
+ 
+
+ align:start position:0%
+to somewhere at the same time so it's
+sort of this is one way to for them to
+
+ align:start position:0%
+sort of this is one way to for them to
+ 
+
+ align:start position:0%
+sort of this is one way to for them to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+it sense I think that's maybe not as
+
+ align:start position:0%
+it sense I think that's maybe not as
+ 
+
+ align:start position:0%
+it sense I think that's maybe not as
+fundamental I you probably if you if you
+
+ align:start position:0%
+fundamental I you probably if you if you
+ 
+
+ align:start position:0%
+fundamental I you probably if you if you
+tried hard you could probably come up
+
+ align:start position:0%
+tried hard you could probably come up
+ 
+
+ align:start position:0%
+tried hard you could probably come up
+with some x86 instruction sequence that
+
+ align:start position:0%
+with some x86 instruction sequence that
+ 
+
+ align:start position:0%
+with some x86 instruction sequence that
+could do it from outside the uh bounded
+
+ align:start position:0%
+could do it from outside the uh bounded
+ 
+
+ align:start position:0%
+could do it from outside the uh bounded
+address space of the
+
+ align:start position:0%
+address space of the
+ 
+
+ align:start position:0%
+address space of the
+module make sense all right so I guess
+
+ align:start position:0%
+module make sense all right so I guess
+ 
+
+ align:start position:0%
+module make sense all right so I guess
+that's it for uh Native client uh and I
+
+ align:start position:0%
+that's it for uh Native client uh and I
+ 
+
+ align:start position:0%
+that's it for uh Native client uh and I
+see you guys next week we'll talk about
+
+ align:start position:0%
+see you guys next week we'll talk about
+ 
+
+ align:start position:0%
+see you guys next week we'll talk about
+web security starting then
\ No newline at end of file
diff --git a/I6ZSrgxiofs.txt b/I6ZSrgxiofs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4066b23ed63e1d1a776511bd4875c8deb939b46c
--- /dev/null
+++ b/I6ZSrgxiofs.txt
@@ -0,0 +1,12027 @@
+align:start position:0%
+ 
+All right. Well, we have two more
+
+ align:start position:0%
+All right. Well, we have two more
+ 
+
+ align:start position:0%
+All right. Well, we have two more
+classes and this is uh day two of trying
+
+ align:start position:0%
+classes and this is uh day two of trying
+ 
+
+ align:start position:0%
+classes and this is uh day two of trying
+to grapple with the recent big
+
+ align:start position:0%
+to grapple with the recent big
+ 
+
+ align:start position:0%
+to grapple with the recent big
+breakthrough in projection theory. So,
+
+ align:start position:0%
+breakthrough in projection theory. So,
+ 
+
+ align:start position:0%
+breakthrough in projection theory. So,
+this is sharp projection theorems part
+
+ align:start position:0%
+this is sharp projection theorems part
+ 
+
+ align:start position:0%
+this is sharp projection theorems part
+two. And in part two we're going to talk
+
+ align:start position:0%
+two. And in part two we're going to talk
+ 
+
+ align:start position:0%
+two. And in part two we're going to talk
+about the ad regular case. So let's
+
+ align:start position:0%
+about the ad regular case. So let's
+ 
+
+ align:start position:0%
+about the ad regular case. So let's
+first remember our goal and remember
+
+ align:start position:0%
+first remember our goal and remember
+ 
+
+ align:start position:0%
+first remember our goal and remember
+what is the ad regular case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So our goal is the first set conjecture
+
+ align:start position:0%
+So our goal is the first set conjecture
+ 
+
+ align:start position:0%
+So our goal is the first set conjecture
+which is a theorem of Orpin and Schmurk
+
+ align:start position:0%
+which is a theorem of Orpin and Schmurk
+ 
+
+ align:start position:0%
+which is a theorem of Orpin and Schmurk
+and Ren and W says if E contained in R2
+
+ align:start position:0%
+and Ren and W says if E contained in R2
+ 
+
+ align:start position:0%
+and Ren and W says if E contained in R2
+is a delta T C set
+
+ align:start position:0%
+is a delta T C set
+ 
+
+ align:start position:0%
+is a delta T C set
+and then for every point in E there are
+
+ align:start position:0%
+and then for every point in E there are
+ 
+
+ align:start position:0%
+and then for every point in E there are
+a bunch of delta tubes going through it.
+
+ align:start position:0%
+a bunch of delta tubes going through it.
+ 
+
+ align:start position:0%
+a bunch of delta tubes going through it.
+So t subx is a set of delta tubes
+
+ align:start position:0%
+So t subx is a set of delta tubes
+ 
+
+ align:start position:0%
+So t subx is a set of delta tubes
+through x
+
+ align:start position:0%
+through x
+ 
+
+ align:start position:0%
+through x
+and the the directions if you like of
+
+ align:start position:0%
+and the the directions if you like of
+ 
+
+ align:start position:0%
+and the the directions if you like of
+this set of delta tubes is a delta s c
+
+ align:start position:0%
+this set of delta tubes is a delta s c
+ 
+
+ align:start position:0%
+this set of delta tubes is a delta s c
+set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And parenthetically we can assume
+
+ align:start position:0%
+Okay. And parenthetically we can assume
+ 
+
+ align:start position:0%
+Okay. And parenthetically we can assume
+a couple of things. uh we can assume
+
+ align:start position:0%
+a couple of things. uh we can assume
+ 
+
+ align:start position:0%
+a couple of things. uh we can assume
+that this is uh is uniform
+
+ align:start position:0%
+that this is uh is uniform
+ 
+
+ align:start position:0%
+that this is uh is uniform
+and also that the number of them it's
+
+ align:start position:0%
+and also that the number of them it's
+ 
+
+ align:start position:0%
+and also that the number of them it's
+like delta to the minus s and s should
+
+ align:start position:0%
+like delta to the minus s and s should
+ 
+
+ align:start position:0%
+like delta to the minus s and s should
+be bigger than zero.
+
+ align:start position:0%
+be bigger than zero.
+ 
+
+ align:start position:0%
+be bigger than zero.
+Okay, so we put all of these tubes
+
+ align:start position:0%
+Okay, so we put all of these tubes
+ 
+
+ align:start position:0%
+Okay, so we put all of these tubes
+together to get one big set of tubes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the question is how many tubes are
+
+ align:start position:0%
+and the question is how many tubes are
+ 
+
+ align:start position:0%
+and the question is how many tubes are
+there?
+
+ align:start position:0%
+there?
+ 
+
+ align:start position:0%
+there?
+Um so then the conclusion is
+
+ align:start position:0%
+Um so then the conclusion is
+ 
+
+ align:start position:0%
+Um so then the conclusion is
+that the number of tubes is at least a
+
+ align:start position:0%
+that the number of tubes is at least a
+ 
+
+ align:start position:0%
+that the number of tubes is at least a
+little fudge factor.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this whole thing I'll abbreviate like
+
+ align:start position:0%
+So this whole thing I'll abbreviate like
+ 
+
+ align:start position:0%
+So this whole thing I'll abbreviate like
+that and then the minimum of a few
+
+ align:start position:0%
+that and then the minimum of a few
+ 
+
+ align:start position:0%
+that and then the minimum of a few
+options
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we'll call option A, option B and
+
+ align:start position:0%
+which we'll call option A, option B and
+ 
+
+ align:start position:0%
+which we'll call option A, option B and
+option C.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And these exponents are hard to
+
+ align:start position:0%
+Okay. And these exponents are hard to
+ 
+
+ align:start position:0%
+Okay. And these exponents are hard to
+remember, but I would prefer to remember
+
+ align:start position:0%
+remember, but I would prefer to remember
+ 
+
+ align:start position:0%
+remember, but I would prefer to remember
+for everyone to think of them in terms
+
+ align:start position:0%
+for everyone to think of them in terms
+ 
+
+ align:start position:0%
+for everyone to think of them in terms
+of three different scenarios.
+
+ align:start position:0%
+of three different scenarios.
+ 
+
+ align:start position:0%
+of three different scenarios.
+So option A that corresponds to the I
+
+ align:start position:0%
+So option A that corresponds to the I
+ 
+
+ align:start position:0%
+So option A that corresponds to the I
+call it the stars scenario. Have a bunch
+
+ align:start position:0%
+call it the stars scenario. Have a bunch
+ 
+
+ align:start position:0%
+call it the stars scenario. Have a bunch
+of points and through each you have a
+
+ align:start position:0%
+of points and through each you have a
+ 
+
+ align:start position:0%
+of points and through each you have a
+bunch of tubes and they're just
+
+ align:start position:0%
+bunch of tubes and they're just
+ 
+
+ align:start position:0%
+bunch of tubes and they're just
+unrelated to each other.
+
+ align:start position:0%
+unrelated to each other.
+ 
+
+ align:start position:0%
+unrelated to each other.
+Option B is more intricate. It's the
+
+ align:start position:0%
+Option B is more intricate. It's the
+ 
+
+ align:start position:0%
+Option B is more intricate. It's the
+integer grid scenario.
+
+ align:start position:0%
+integer grid scenario.
+ 
+
+ align:start position:0%
+integer grid scenario.
+Um and option C is a kind of random
+
+ align:start position:0%
+Um and option C is a kind of random
+ 
+
+ align:start position:0%
+Um and option C is a kind of random
+scenario. So E is arbitrary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and T is random.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+now it's it's really a good idea to
+
+ align:start position:0%
+now it's it's really a good idea to
+ 
+
+ align:start position:0%
+now it's it's really a good idea to
+think about this theorem in these three
+
+ align:start position:0%
+think about this theorem in these three
+ 
+
+ align:start position:0%
+think about this theorem in these three
+different scenarios. So it's good to
+
+ align:start position:0%
+different scenarios. So it's good to
+ 
+
+ align:start position:0%
+different scenarios. So it's good to
+separate out the case where each one of
+
+ align:start position:0%
+separate out the case where each one of
+ 
+
+ align:start position:0%
+separate out the case where each one of
+those things is the minimum. Um, so let
+
+ align:start position:0%
+those things is the minimum. Um, so let
+ 
+
+ align:start position:0%
+those things is the minimum. Um, so let
+me do that and recall for you how much
+
+ align:start position:0%
+me do that and recall for you how much
+ 
+
+ align:start position:0%
+me do that and recall for you how much
+we know about each case so far.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, and I said something about this last
+
+ align:start position:0%
+Um, and I said something about this last
+ 
+
+ align:start position:0%
+Um, and I said something about this last
+time, but what I said wasn't uh the best
+
+ align:start position:0%
+time, but what I said wasn't uh the best
+ 
+
+ align:start position:0%
+time, but what I said wasn't uh the best
+thing to say. So I wanted to do it again
+
+ align:start position:0%
+thing to say. So I wanted to do it again
+ 
+
+ align:start position:0%
+thing to say. So I wanted to do it again
+and get it right.
+
+ align:start position:0%
+and get it right.
+ 
+
+ align:start position:0%
+and get it right.
+All right. So there's the case where a
+
+ align:start position:0%
+All right. So there's the case where a
+ 
+
+ align:start position:0%
+All right. So there's the case where a
+is the minimum option. And if you do a
+
+ align:start position:0%
+is the minimum option. And if you do a
+ 
+
+ align:start position:0%
+is the minimum option. And if you do a
+little algebra that corresponds to s
+
+ align:start position:0%
+little algebra that corresponds to s
+ 
+
+ align:start position:0%
+little algebra that corresponds to s
+being at least as big as t.
+
+ align:start position:0%
+being at least as big as t.
+ 
+
+ align:start position:0%
+being at least as big as t.
+Um and in this case
+
+ align:start position:0%
+Um and in this case
+ 
+
+ align:start position:0%
+Um and in this case
+so if s is at least as big as t then the
+
+ align:start position:0%
+so if s is at least as big as t then the
+ 
+
+ align:start position:0%
+so if s is at least as big as t then the
+uh the theorem is is true the first so
+
+ align:start position:0%
+uh the theorem is is true the first so
+ 
+
+ align:start position:0%
+uh the theorem is is true the first so
+first is is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it follows just by double counting.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we did it very early in the course
+
+ align:start position:0%
+So we did it very early in the course
+ 
+
+ align:start position:0%
+So we did it very early in the course
+like on the second one.
+
+ align:start position:0%
+like on the second one.
+ 
+
+ align:start position:0%
+like on the second one.
+Okay. Then I'll come back to B which is
+
+ align:start position:0%
+Okay. Then I'll come back to B which is
+ 
+
+ align:start position:0%
+Okay. Then I'll come back to B which is
+the most interesting. C is the minimal.
+
+ align:start position:0%
+the most interesting. C is the minimal.
+ 
+
+ align:start position:0%
+the most interesting. C is the minimal.
+If you do a little algebra it's if S
+
+ align:start position:0%
+If you do a little algebra it's if S
+ 
+
+ align:start position:0%
+If you do a little algebra it's if S
+plus T is at least two.
+
+ align:start position:0%
+plus T is at least two.
+ 
+
+ align:start position:0%
+plus T is at least two.
+Um and in this whole range where S plus
+
+ align:start position:0%
+Um and in this whole range where S plus
+ 
+
+ align:start position:0%
+Um and in this whole range where S plus
+T is at least two the theorem is is also
+
+ align:start position:0%
+T is at least two the theorem is is also
+ 
+
+ align:start position:0%
+T is at least two the theorem is is also
+true true and it's true by the forier
+
+ align:start position:0%
+true true and it's true by the forier
+ 
+
+ align:start position:0%
+true true and it's true by the forier
+method. So it follows from the theorem
+
+ align:start position:0%
+method. So it follows from the theorem
+ 
+
+ align:start position:0%
+method. So it follows from the theorem
+we proved in the second or third week
+
+ align:start position:0%
+we proved in the second or third week
+ 
+
+ align:start position:0%
+we proved in the second or third week
+using for a analysis. So the whole case
+
+ align:start position:0%
+using for a analysis. So the whole case
+ 
+
+ align:start position:0%
+using for a analysis. So the whole case
+where C is minimal uh we we also already
+
+ align:start position:0%
+where C is minimal uh we we also already
+ 
+
+ align:start position:0%
+where C is minimal uh we we also already
+understand that
+
+ align:start position:0%
+understand that
+ 
+
+ align:start position:0%
+understand that
+okay and that leaves a case where B is
+
+ align:start position:0%
+okay and that leaves a case where B is
+ 
+
+ align:start position:0%
+okay and that leaves a case where B is
+minimal and that's like otherwise if
+
+ align:start position:0%
+minimal and that's like otherwise if
+ 
+
+ align:start position:0%
+minimal and that's like otherwise if
+neither of these things are true then B
+
+ align:start position:0%
+neither of these things are true then B
+ 
+
+ align:start position:0%
+neither of these things are true then B
+is minimal and um and so that's that's
+
+ align:start position:0%
+is minimal and um and so that's that's
+ 
+
+ align:start position:0%
+is minimal and um and so that's that's
+the content of this theorem. So this is
+
+ align:start position:0%
+the content of this theorem. So this is
+ 
+
+ align:start position:0%
+the content of this theorem. So this is
+the hard new thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the uh OSRW thing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+cool.
+
+ align:start position:0%
+cool.
+ 
+
+ align:start position:0%
+cool.
+Another little comment is that the the
+
+ align:start position:0%
+Another little comment is that the the
+ 
+
+ align:start position:0%
+Another little comment is that the the
+number of tubes is not my favorite
+
+ align:start position:0%
+number of tubes is not my favorite
+ 
+
+ align:start position:0%
+number of tubes is not my favorite
+parameter to keep track of. Um, my
+
+ align:start position:0%
+parameter to keep track of. Um, my
+ 
+
+ align:start position:0%
+parameter to keep track of. Um, my
+favorite parameter to keep track of is
+
+ align:start position:0%
+favorite parameter to keep track of is
+ 
+
+ align:start position:0%
+favorite parameter to keep track of is
+I'll call it R
+
+ align:start position:0%
+I'll call it R
+ 
+
+ align:start position:0%
+I'll call it R
+of of ET,
+
+ align:start position:0%
+of of ET,
+ 
+
+ align:start position:0%
+of of ET,
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+which in words is like the typical
+
+ align:start position:0%
+which in words is like the typical
+ 
+
+ align:start position:0%
+which in words is like the typical
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+of delta balls
+
+ align:start position:0%
+of delta balls
+ 
+
+ align:start position:0%
+of delta balls
+of E on a typical tube of T.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so let's make a uh
+
+ align:start position:0%
+Um so let's make a uh
+ 
+
+ align:start position:0%
+Um so let's make a uh
+let's make a picture. Um so we have some
+
+ align:start position:0%
+let's make a picture. Um so we have some
+ 
+
+ align:start position:0%
+let's make a picture. Um so we have some
+delta balls and then we have some delta
+
+ align:start position:0%
+delta balls and then we have some delta
+ 
+
+ align:start position:0%
+delta balls and then we have some delta
+tubes going through them
+
+ align:start position:0%
+tubes going through them
+ 
+
+ align:start position:0%
+tubes going through them
+and in in an interesting scenario each
+
+ align:start position:0%
+and in in an interesting scenario each
+ 
+
+ align:start position:0%
+and in in an interesting scenario each
+tube will have many balls in it and r is
+
+ align:start position:0%
+tube will have many balls in it and r is
+ 
+
+ align:start position:0%
+tube will have many balls in it and r is
+this number of balls in a tube. Okay.
+
+ align:start position:0%
+this number of balls in a tube. Okay.
+ 
+
+ align:start position:0%
+this number of balls in a tube. Okay.
+So algebraically
+
+ align:start position:0%
+So algebraically
+ 
+
+ align:start position:0%
+So algebraically
+by double counting
+
+ align:start position:0%
+by double counting
+ 
+
+ align:start position:0%
+by double counting
+number of balls in a tube would be the
+
+ align:start position:0%
+number of balls in a tube would be the
+ 
+
+ align:start position:0%
+number of balls in a tube would be the
+number of points times the number of
+
+ align:start position:0%
+number of points times the number of
+ 
+
+ align:start position:0%
+number of points times the number of
+tubes going through a point divided by
+
+ align:start position:0%
+tubes going through a point divided by
+ 
+
+ align:start position:0%
+tubes going through a point divided by
+uh the number of tubes. So that would be
+
+ align:start position:0%
+uh the number of tubes. So that would be
+ 
+
+ align:start position:0%
+uh the number of tubes. So that would be
+the algebraic definition of r. And then
+
+ align:start position:0%
+the algebraic definition of r. And then
+ 
+
+ align:start position:0%
+the algebraic definition of r. And then
+it's easy to convert bounds for t into
+
+ align:start position:0%
+it's easy to convert bounds for t into
+ 
+
+ align:start position:0%
+it's easy to convert bounds for t into
+bounds for r. So our theorem is
+
+ align:start position:0%
+bounds for r. So our theorem is
+ 
+
+ align:start position:0%
+bounds for r. So our theorem is
+equivalent to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that r is upper bounded by the
+
+ align:start position:0%
+um that r is upper bounded by the
+ 
+
+ align:start position:0%
+um that r is upper bounded by the
+maximum of three things. Scenario one is
+
+ align:start position:0%
+maximum of three things. Scenario one is
+ 
+
+ align:start position:0%
+maximum of three things. Scenario one is
+a. So scenario one the number of balls
+
+ align:start position:0%
+a. So scenario one the number of balls
+ 
+
+ align:start position:0%
+a. So scenario one the number of balls
+per tube is one which is always easy to
+
+ align:start position:0%
+per tube is one which is always easy to
+ 
+
+ align:start position:0%
+per tube is one which is always easy to
+arrange.
+
+ align:start position:0%
+arrange.
+ 
+
+ align:start position:0%
+arrange.
+Uh b you have to do a little
+
+ align:start position:0%
+Uh b you have to do a little
+ 
+
+ align:start position:0%
+Uh b you have to do a little
+computation. It works out to this.
+
+ align:start position:0%
+computation. It works out to this.
+ 
+
+ align:start position:0%
+computation. It works out to this.
+I don't really care what the exponent.
+
+ align:start position:0%
+I don't really care what the exponent.
+ 
+
+ align:start position:0%
+I don't really care what the exponent.
+It's not important what the exponents
+
+ align:start position:0%
+It's not important what the exponents
+ 
+
+ align:start position:0%
+It's not important what the exponents
+are. And C is delta to the uh t + one.
+
+ align:start position:0%
+are. And C is delta to the uh t + one.
+ 
+
+ align:start position:0%
+are. And C is delta to the uh t + one.
+Okay. And this delta to the t + one has
+
+ align:start position:0%
+Okay. And this delta to the t + one has
+ 
+
+ align:start position:0%
+Okay. And this delta to the t + one has
+a nice interpretation which might
+
+ align:start position:0%
+a nice interpretation which might
+ 
+
+ align:start position:0%
+a nice interpretation which might
+clarify a little bit what we mean by
+
+ align:start position:0%
+clarify a little bit what we mean by
+ 
+
+ align:start position:0%
+clarify a little bit what we mean by
+this random case. So if um e is a set is
+
+ align:start position:0%
+this random case. So if um e is a set is
+ 
+
+ align:start position:0%
+this random case. So if um e is a set is
+a delta tc set. So the size of e is
+
+ align:start position:0%
+a delta tc set. So the size of e is
+ 
+
+ align:start position:0%
+a delta tc set. So the size of e is
+delta to the minus t. Uh let me say it
+
+ align:start position:0%
+delta to the minus t. Uh let me say it
+ 
+
+ align:start position:0%
+delta to the minus t. Uh let me say it
+this way. Suppose that E
+
+ align:start position:0%
+this way. Suppose that E
+ 
+
+ align:start position:0%
+this way. Suppose that E
+is a set of delta to the minus T delta
+
+ align:start position:0%
+is a set of delta to the minus T delta
+ 
+
+ align:start position:0%
+is a set of delta to the minus T delta
+balls in the unit ball.
+
+ align:start position:0%
+balls in the unit ball.
+ 
+
+ align:start position:0%
+balls in the unit ball.
+And then I take the average over any
+
+ align:start position:0%
+And then I take the average over any
+ 
+
+ align:start position:0%
+And then I take the average over any
+choice of delta by one rectangles of um
+
+ align:start position:0%
+choice of delta by one rectangles of um
+ 
+
+ align:start position:0%
+choice of delta by one rectangles of um
+the number of delta balls that the
+
+ align:start position:0%
+the number of delta balls that the
+ 
+
+ align:start position:0%
+the number of delta balls that the
+rectangle covers. You would get delta to
+
+ align:start position:0%
+rectangle covers. You would get delta to
+ 
+
+ align:start position:0%
+rectangle covers. You would get delta to
+the minus t + 1.
+
+ align:start position:0%
+the minus t + 1.
+ 
+
+ align:start position:0%
+the minus t + 1.
+So it's not difficult to locate
+
+ align:start position:0%
+So it's not difficult to locate
+ 
+
+ align:start position:0%
+So it's not difficult to locate
+rectangles with that richness. Almost
+
+ align:start position:0%
+rectangles with that richness. Almost
+ 
+
+ align:start position:0%
+rectangles with that richness. Almost
+any rectangle would do the job. And
+
+ align:start position:0%
+any rectangle would do the job. And
+ 
+
+ align:start position:0%
+any rectangle would do the job. And
+scenario C is when the rectangles just
+
+ align:start position:0%
+scenario C is when the rectangles just
+ 
+
+ align:start position:0%
+scenario C is when the rectangles just
+have this average richness. There's
+
+ align:start position:0%
+have this average richness. There's
+ 
+
+ align:start position:0%
+have this average richness. There's
+really nothing special about them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So next let's remember. So their
+
+ align:start position:0%
+Okay. So next let's remember. So their
+ 
+
+ align:start position:0%
+Okay. So next let's remember. So their
+goal today is to talk about the ad
+
+ align:start position:0%
+goal today is to talk about the ad
+ 
+
+ align:start position:0%
+goal today is to talk about the ad
+regular case. So let's remember what
+
+ align:start position:0%
+regular case. So let's remember what
+ 
+
+ align:start position:0%
+regular case. So let's remember what
+what is the ad regular case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So we're going to suppose
+
+ align:start position:0%
+Okay. So we're going to suppose
+ 
+
+ align:start position:0%
+Okay. So we're going to suppose
+that E is uniform.
+
+ align:start position:0%
+that E is uniform.
+ 
+
+ align:start position:0%
+that E is uniform.
+So that means that our delta is some um
+
+ align:start position:0%
+So that means that our delta is some um
+ 
+
+ align:start position:0%
+So that means that our delta is some um
+capital delta to the m where m is a
+
+ align:start position:0%
+capital delta to the m where m is a
+ 
+
+ align:start position:0%
+capital delta to the m where m is a
+large number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the uniformity is that if I take e
+
+ align:start position:0%
+and the uniformity is that if I take e
+ 
+
+ align:start position:0%
+and the uniformity is that if I take e
+and I intersect it with a cube of side
+
+ align:start position:0%
+and I intersect it with a cube of side
+ 
+
+ align:start position:0%
+and I intersect it with a cube of side
+length delta to the j and I ask about
+
+ align:start position:0%
+length delta to the j and I ask about
+ 
+
+ align:start position:0%
+length delta to the j and I ask about
+its delta to the j + one covering number
+
+ align:start position:0%
+its delta to the j + one covering number
+ 
+
+ align:start position:0%
+its delta to the j + one covering number
+that's around some uh beta j
+
+ align:start position:0%
+that's around some uh beta j
+ 
+
+ align:start position:0%
+that's around some uh beta j
+for all the iatic
+
+ align:start position:0%
+for all the iatic
+ 
+
+ align:start position:0%
+for all the iatic
+Q delta J um that intersect E.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so these beta J are the branching
+
+ align:start position:0%
+Okay, so these beta J are the branching
+ 
+
+ align:start position:0%
+Okay, so these beta J are the branching
+numbers. We drew pictures last time to
+
+ align:start position:0%
+numbers. We drew pictures last time to
+ 
+
+ align:start position:0%
+numbers. We drew pictures last time to
+illustrate what they mean. Um and so
+
+ align:start position:0%
+illustrate what they mean. Um and so
+ 
+
+ align:start position:0%
+illustrate what they mean. Um and so
+definition would be that E is C L4 is to
+
+ align:start position:0%
+definition would be that E is C L4 is to
+ 
+
+ align:start position:0%
+definition would be that E is C L4 is to
+be regular. So actually let's say it's a
+
+ align:start position:0%
+be regular. So actually let's say it's a
+ 
+
+ align:start position:0%
+be regular. So actually let's say it's a
+delta t c a d regular set
+
+ align:start position:0%
+delta t c a d regular set
+ 
+
+ align:start position:0%
+delta t c a d regular set
+f um has a this branching structure like
+
+ align:start position:0%
+f um has a this branching structure like
+ 
+
+ align:start position:0%
+f um has a this branching structure like
+above and um if I take the product j = 1
+
+ align:start position:0%
+above and um if I take the product j = 1
+ 
+
+ align:start position:0%
+above and um if I take the product j = 1
+to capital j of beta j. So that would be
+
+ align:start position:0%
+to capital j of beta j. So that would be
+ 
+
+ align:start position:0%
+to capital j of beta j. So that would be
+the delta j covering number delta to the
+
+ align:start position:0%
+the delta j covering number delta to the
+ 
+
+ align:start position:0%
+the delta j covering number delta to the
+j covering number of our set.
+
+ align:start position:0%
+j covering number of our set.
+ 
+
+ align:start position:0%
+j covering number of our set.
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it is at most C * delta to the J to the
+
+ align:start position:0%
+it is at most C * delta to the J to the
+ 
+
+ align:start position:0%
+it is at most C * delta to the J to the
+minus T and it is at least 1 / C * delta
+
+ align:start position:0%
+minus T and it is at least 1 / C * delta
+ 
+
+ align:start position:0%
+minus T and it is at least 1 / C * delta
+to the J to the minus T.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, let's label all these hypotheses in
+
+ align:start position:0%
+So, let's label all these hypotheses in
+ 
+
+ align:start position:0%
+So, let's label all these hypotheses in
+our theorem by each our hypothesis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And what we'd like to understand is
+
+ align:start position:0%
+And what we'd like to understand is
+ 
+
+ align:start position:0%
+And what we'd like to understand is
+given these hypotheses, how big could R
+
+ align:start position:0%
+given these hypotheses, how big could R
+ 
+
+ align:start position:0%
+given these hypotheses, how big could R
+be?
+
+ align:start position:0%
+be?
+ 
+
+ align:start position:0%
+be?
+And for for today we're going to talk
+
+ align:start position:0%
+And for for today we're going to talk
+ 
+
+ align:start position:0%
+And for for today we're going to talk
+about the AD regular case. So let's give
+
+ align:start position:0%
+about the AD regular case. So let's give
+ 
+
+ align:start position:0%
+about the AD regular case. So let's give
+that a name. So R A D of S T delta C
+
+ align:start position:0%
+that a name. So R A D of S T delta C
+ 
+
+ align:start position:0%
+that a name. So R A D of S T delta C
+that is the maximum
+
+ align:start position:0%
+that is the maximum
+ 
+
+ align:start position:0%
+that is the maximum
+over E and T obey our hypothesis
+
+ align:start position:0%
+over E and T obey our hypothesis
+ 
+
+ align:start position:0%
+over E and T obey our hypothesis
+and E is a
+
+ align:start position:0%
+and E is a
+ 
+
+ align:start position:0%
+and E is a
+delta T C a d regular
+
+ align:start position:0%
+delta T C a d regular
+ 
+
+ align:start position:0%
+delta T C a d regular
+of R of E and T. How big could it be in
+
+ align:start position:0%
+of R of E and T. How big could it be in
+ 
+
+ align:start position:0%
+of R of E and T. How big could it be in
+in this case?
+
+ align:start position:0%
+in this case?
+ 
+
+ align:start position:0%
+in this case?
+Okay, there's really a mouthful of
+
+ align:start position:0%
+Okay, there's really a mouthful of
+ 
+
+ align:start position:0%
+Okay, there's really a mouthful of
+parameters. So, let me just say to uh
+
+ align:start position:0%
+parameters. So, let me just say to uh
+ 
+
+ align:start position:0%
+parameters. So, let me just say to uh
+reduce a little bit for today, we'll
+
+ align:start position:0%
+reduce a little bit for today, we'll
+ 
+
+ align:start position:0%
+reduce a little bit for today, we'll
+have C equals 1. Um so, that means it's
+
+ align:start position:0%
+have C equals 1. Um so, that means it's
+ 
+
+ align:start position:0%
+have C equals 1. Um so, that means it's
+you know really ad regular and
+
+ align:start position:0%
+you know really ad regular and
+ 
+
+ align:start position:0%
+you know really ad regular and
+everything we say actually um will work
+
+ align:start position:0%
+everything we say actually um will work
+ 
+
+ align:start position:0%
+everything we say actually um will work
+for small C that are bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that will allow us to not write the
+
+ align:start position:0%
+that will allow us to not write the
+ 
+
+ align:start position:0%
+that will allow us to not write the
+letter C. And then s and t will not be
+
+ align:start position:0%
+letter C. And then s and t will not be
+ 
+
+ align:start position:0%
+letter C. And then s and t will not be
+changing through our arguments. So I
+
+ align:start position:0%
+changing through our arguments. So I
+ 
+
+ align:start position:0%
+changing through our arguments. So I
+won't write them every time. So now I'll
+
+ align:start position:0%
+won't write them every time. So now I'll
+ 
+
+ align:start position:0%
+won't write them every time. So now I'll
+just abbreviate it
+
+ align:start position:0%
+just abbreviate it
+ 
+
+ align:start position:0%
+just abbreviate it
+as r a d of dot.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So um
+
+ align:start position:0%
+All right. So um
+ 
+
+ align:start position:0%
+All right. So um
+so the theorem that orbit and smirkin
+
+ align:start position:0%
+so the theorem that orbit and smirkin
+ 
+
+ align:start position:0%
+so the theorem that orbit and smirkin
+proved is that they they proved this
+
+ align:start position:0%
+proved is that they they proved this
+ 
+
+ align:start position:0%
+proved is that they they proved this
+thing in the ad case. So r a d s delta
+
+ align:start position:0%
+thing in the ad case. So r a d s delta
+ 
+
+ align:start position:0%
+thing in the ad case. So r a d s delta
+is indeed bounded by
+
+ align:start position:0%
+is indeed bounded by
+ 
+
+ align:start position:0%
+is indeed bounded by
+that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not sure I computed right.
+
+ align:start position:0%
+I'm not sure I computed right.
+ 
+
+ align:start position:0%
+I'm not sure I computed right.
+Got the minus signs wrong.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's our goal for today is to
+
+ align:start position:0%
+So that's our goal for today is to
+ 
+
+ align:start position:0%
+So that's our goal for today is to
+understand this theorem which is a
+
+ align:start position:0%
+understand this theorem which is a
+ 
+
+ align:start position:0%
+understand this theorem which is a
+really important special case of that
+
+ align:start position:0%
+really important special case of that
+ 
+
+ align:start position:0%
+really important special case of that
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool.
+
+ align:start position:0%
+Cool.
+ 
+
+ align:start position:0%
+Cool.
+So maybe so it's clearly a special case
+
+ align:start position:0%
+So maybe so it's clearly a special case
+ 
+
+ align:start position:0%
+So maybe so it's clearly a special case
+of that theorem. Um and at first it
+
+ align:start position:0%
+of that theorem. Um and at first it
+ 
+
+ align:start position:0%
+of that theorem. Um and at first it
+might seem like a very special case
+
+ align:start position:0%
+might seem like a very special case
+ 
+
+ align:start position:0%
+might seem like a very special case
+because these branching function
+
+ align:start position:0%
+because these branching function
+ 
+
+ align:start position:0%
+because these branching function
+basically there's a huge range of what
+
+ align:start position:0%
+basically there's a huge range of what
+ 
+
+ align:start position:0%
+basically there's a huge range of what
+the branching function could be and ad
+
+ align:start position:0%
+the branching function could be and ad
+ 
+
+ align:start position:0%
+the branching function could be and ad
+regular is just one particular choice in
+
+ align:start position:0%
+regular is just one particular choice in
+ 
+
+ align:start position:0%
+regular is just one particular choice in
+this huge range but it's a particularly
+
+ align:start position:0%
+this huge range but it's a particularly
+ 
+
+ align:start position:0%
+this huge range but it's a particularly
+important case and we'll see tomorrow or
+
+ align:start position:0%
+important case and we'll see tomorrow or
+ 
+
+ align:start position:0%
+important case and we'll see tomorrow or
+next class that that this is really a
+
+ align:start position:0%
+next class that that this is really a
+ 
+
+ align:start position:0%
+next class that that this is really a
+crucial case plays a big role in
+
+ align:start position:0%
+crucial case plays a big role in
+ 
+
+ align:start position:0%
+crucial case plays a big role in
+understanding the theorem in general.
+
+ align:start position:0%
+understanding the theorem in general.
+ 
+
+ align:start position:0%
+understanding the theorem in general.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool. Um, yeah. So, so it was a really
+
+ align:start position:0%
+cool. Um, yeah. So, so it was a really
+ 
+
+ align:start position:0%
+cool. Um, yeah. So, so it was a really
+it was a really important realization in
+
+ align:start position:0%
+it was a really important realization in
+ 
+
+ align:start position:0%
+it was a really important realization in
+thinking about this theorem that we
+
+ align:start position:0%
+thinking about this theorem that we
+ 
+
+ align:start position:0%
+thinking about this theorem that we
+should break it into cases. The
+
+ align:start position:0%
+should break it into cases. The
+ 
+
+ align:start position:0%
+should break it into cases. The
+different cases have their different
+
+ align:start position:0%
+different cases have their different
+ 
+
+ align:start position:0%
+different cases have their different
+things that are useful and their
+
+ align:start position:0%
+things that are useful and their
+ 
+
+ align:start position:0%
+things that are useful and their
+different things that are difficult um
+
+ align:start position:0%
+different things that are difficult um
+ 
+
+ align:start position:0%
+different things that are difficult um
+and um and and so that recognition is is
+
+ align:start position:0%
+and um and and so that recognition is is
+ 
+
+ align:start position:0%
+and um and and so that recognition is is
+key. So the next thing I want to try to
+
+ align:start position:0%
+key. So the next thing I want to try to
+ 
+
+ align:start position:0%
+key. So the next thing I want to try to
+talk about is like what is special about
+
+ align:start position:0%
+talk about is like what is special about
+ 
+
+ align:start position:0%
+talk about is like what is special about
+ad regular sets that we could use to to
+
+ align:start position:0%
+ad regular sets that we could use to to
+ 
+
+ align:start position:0%
+ad regular sets that we could use to to
+get a handle on them um that we couldn't
+
+ align:start position:0%
+get a handle on them um that we couldn't
+ 
+
+ align:start position:0%
+get a handle on them um that we couldn't
+use just for the for the general setup.
+
+ align:start position:0%
+use just for the for the general setup.
+ 
+
+ align:start position:0%
+use just for the for the general setup.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this proof is is quite
+
+ align:start position:0%
+Okay. So this proof is is quite
+ 
+
+ align:start position:0%
+Okay. So this proof is is quite
+difficult. We won't do all of it, but I
+
+ align:start position:0%
+difficult. We won't do all of it, but I
+ 
+
+ align:start position:0%
+difficult. We won't do all of it, but I
+would like to share some key ideas about
+
+ align:start position:0%
+would like to share some key ideas about
+ 
+
+ align:start position:0%
+would like to share some key ideas about
+it which I think are really cool and and
+
+ align:start position:0%
+it which I think are really cool and and
+ 
+
+ align:start position:0%
+it which I think are really cool and and
+are like sort of worth taking with you
+
+ align:start position:0%
+are like sort of worth taking with you
+ 
+
+ align:start position:0%
+are like sort of worth taking with you
+away from this class.
+
+ align:start position:0%
+away from this class.
+ 
+
+ align:start position:0%
+away from this class.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so in a nutshell, the important
+
+ align:start position:0%
+Okay, so in a nutshell, the important
+ 
+
+ align:start position:0%
+Okay, so in a nutshell, the important
+special thing about ad regular sets is
+
+ align:start position:0%
+special thing about ad regular sets is
+ 
+
+ align:start position:0%
+special thing about ad regular sets is
+in this lema that has a one board proof
+
+ align:start position:0%
+in this lema that has a one board proof
+ 
+
+ align:start position:0%
+in this lema that has a one board proof
+which is called the sub multiplicative
+
+ align:start position:0%
+which is called the sub multiplicative
+ 
+
+ align:start position:0%
+which is called the sub multiplicative
+lema.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so it says that RA a delta, let me
+
+ align:start position:0%
+Okay, so it says that RA a delta, let me
+ 
+
+ align:start position:0%
+Okay, so it says that RA a delta, let me
+put it this way. If delta is delta 1 *
+
+ align:start position:0%
+put it this way. If delta is delta 1 *
+ 
+
+ align:start position:0%
+put it this way. If delta is delta 1 *
+delta 2, then RA a delta is bounded by
+
+ align:start position:0%
+delta 2, then RA a delta is bounded by
+ 
+
+ align:start position:0%
+delta 2, then RA a delta is bounded by
+with a little bit of fudge RA a delta 1
+
+ align:start position:0%
+with a little bit of fudge RA a delta 1
+ 
+
+ align:start position:0%
+with a little bit of fudge RA a delta 1
+time ra
+
+ align:start position:0%
+time ra
+ 
+
+ align:start position:0%
+time ra
+delta 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It is sub multiplicative.
+
+ align:start position:0%
+It is sub multiplicative.
+ 
+
+ align:start position:0%
+It is sub multiplicative.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it follows from understanding thinking a
+
+ align:start position:0%
+it follows from understanding thinking a
+ 
+
+ align:start position:0%
+it follows from understanding thinking a
+lot about a picture of an ad regular
+
+ align:start position:0%
+lot about a picture of an ad regular
+ 
+
+ align:start position:0%
+lot about a picture of an ad regular
+set.
+
+ align:start position:0%
+set.
+ 
+
+ align:start position:0%
+set.
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+remember that E is a set of delta balls
+
+ align:start position:0%
+remember that E is a set of delta balls
+ 
+
+ align:start position:0%
+remember that E is a set of delta balls
+and T is a set of delta tubes and we're
+
+ align:start position:0%
+and T is a set of delta tubes and we're
+ 
+
+ align:start position:0%
+and T is a set of delta tubes and we're
+going to imagine thickening them.
+
+ align:start position:0%
+going to imagine thickening them.
+ 
+
+ align:start position:0%
+going to imagine thickening them.
+So, so in this setup here, um, delta is
+
+ align:start position:0%
+So, so in this setup here, um, delta is
+ 
+
+ align:start position:0%
+So, so in this setup here, um, delta is
+smaller than delta 1 and delta 2, which
+
+ align:start position:0%
+smaller than delta 1 and delta 2, which
+ 
+
+ align:start position:0%
+smaller than delta 1 and delta 2, which
+are smaller than one. So, delta 1 and
+
+ align:start position:0%
+are smaller than one. So, delta 1 and
+ 
+
+ align:start position:0%
+are smaller than one. So, delta 1 and
+delta 2 are each bigger than delta. So,
+
+ align:start position:0%
+delta 2 are each bigger than delta. So,
+ 
+
+ align:start position:0%
+delta 2 are each bigger than delta. So,
+I'm going to thicken them, and I'll get
+
+ align:start position:0%
+I'm going to thicken them, and I'll get
+ 
+
+ align:start position:0%
+I'm going to thicken them, and I'll get
+E1,
+
+ align:start position:0%
+E1,
+ 
+
+ align:start position:0%
+E1,
+I'll call it, which are the delta 1
+
+ align:start position:0%
+I'll call it, which are the delta 1
+ 
+
+ align:start position:0%
+I'll call it, which are the delta 1
+balls around E, and T1, which are delta
+
+ align:start position:0%
+balls around E, and T1, which are delta
+ 
+
+ align:start position:0%
+balls around E, and T1, which are delta
+1 tools.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, what does it look like?
+
+ align:start position:0%
+All right. So, what does it look like?
+ 
+
+ align:start position:0%
+All right. So, what does it look like?
+Let's think about E and thickening E.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here is E1 is this bunch of circles.
+
+ align:start position:0%
+So here is E1 is this bunch of circles.
+ 
+
+ align:start position:0%
+So here is E1 is this bunch of circles.
+Each circle has radius delta 1
+
+ align:start position:0%
+Each circle has radius delta 1
+ 
+
+ align:start position:0%
+Each circle has radius delta 1
+and inside of those circles there are
+
+ align:start position:0%
+and inside of those circles there are
+ 
+
+ align:start position:0%
+and inside of those circles there are
+some delta balls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those guys are my delta balls E.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now,
+
+ align:start position:0%
+Okay. Now,
+ 
+
+ align:start position:0%
+Okay. Now,
+um, T1 are some delta 1 tubes.
+
+ align:start position:0%
+um, T1 are some delta 1 tubes.
+ 
+
+ align:start position:0%
+um, T1 are some delta 1 tubes.
+So, they might look sort of like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's put one more ball up here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That looks like that. So, those are my
+
+ align:start position:0%
+That looks like that. So, those are my
+ 
+
+ align:start position:0%
+That looks like that. So, those are my
+fat tubes. T1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and then there are inside of them
+
+ align:start position:0%
+Um and then there are inside of them
+ 
+
+ align:start position:0%
+Um and then there are inside of them
+there are some delta tubes T2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+there are too many but I'll try to give
+
+ align:start position:0%
+there are too many but I'll try to give
+ 
+
+ align:start position:0%
+there are too many but I'll try to give
+some idea. So,
+
+ align:start position:0%
+some idea. So,
+ 
+
+ align:start position:0%
+some idea. So,
+so through this point here,
+
+ align:start position:0%
+so through this point here,
+ 
+
+ align:start position:0%
+so through this point here,
+there might be a couple of red tubes
+
+ align:start position:0%
+there might be a couple of red tubes
+ 
+
+ align:start position:0%
+there might be a couple of red tubes
+that are inside of that orange tube. And
+
+ align:start position:0%
+that are inside of that orange tube. And
+ 
+
+ align:start position:0%
+that are inside of that orange tube. And
+then there might be a couple of red
+
+ align:start position:0%
+then there might be a couple of red
+ 
+
+ align:start position:0%
+then there might be a couple of red
+tubes
+
+ align:start position:0%
+tubes
+ 
+
+ align:start position:0%
+tubes
+that are inside of that orange tube.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? And I just drew the ones through
+
+ align:start position:0%
+Okay? And I just drew the ones through
+ 
+
+ align:start position:0%
+Okay? And I just drew the ones through
+this point. Experience has taught me
+
+ align:start position:0%
+this point. Experience has taught me
+ 
+
+ align:start position:0%
+this point. Experience has taught me
+that if I draw more, this picture will
+
+ align:start position:0%
+that if I draw more, this picture will
+ 
+
+ align:start position:0%
+that if I draw more, this picture will
+get too messy. But you should imagine
+
+ align:start position:0%
+get too messy. But you should imagine
+ 
+
+ align:start position:0%
+get too messy. But you should imagine
+that this is happening at every point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first observation is that E1 and T1 obey
+
+ align:start position:0%
+first observation is that E1 and T1 obey
+ 
+
+ align:start position:0%
+first observation is that E1 and T1 obey
+the hypothesis of our theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because actually if so if you take a
+
+ align:start position:0%
+because actually if so if you take a
+ 
+
+ align:start position:0%
+because actually if so if you take a
+delta t set of balls and you thicken
+
+ align:start position:0%
+delta t set of balls and you thicken
+ 
+
+ align:start position:0%
+delta t set of balls and you thicken
+them up to radius delta 1, you get a
+
+ align:start position:0%
+them up to radius delta 1, you get a
+ 
+
+ align:start position:0%
+them up to radius delta 1, you get a
+delta onet set of balls
+
+ align:start position:0%
+delta onet set of balls
+ 
+
+ align:start position:0%
+delta onet set of balls
+at least if because if it's uniform
+
+ align:start position:0%
+at least if because if it's uniform
+ 
+
+ align:start position:0%
+at least if because if it's uniform
+and um if you Look at who's going
+
+ align:start position:0%
+and um if you Look at who's going
+ 
+
+ align:start position:0%
+and um if you Look at who's going
+through this point. Uh we have a delta s
+
+ align:start position:0%
+through this point. Uh we have a delta s
+ 
+
+ align:start position:0%
+through this point. Uh we have a delta s
+set of directions leaving that point.
+
+ align:start position:0%
+set of directions leaving that point.
+ 
+
+ align:start position:0%
+set of directions leaving that point.
+And if you thicken them up a little bit,
+
+ align:start position:0%
+And if you thicken them up a little bit,
+ 
+
+ align:start position:0%
+And if you thicken them up a little bit,
+you get um the directions corresponding
+
+ align:start position:0%
+you get um the directions corresponding
+ 
+
+ align:start position:0%
+you get um the directions corresponding
+to the orange tubes. And that will be a
+
+ align:start position:0%
+to the orange tubes. And that will be a
+ 
+
+ align:start position:0%
+to the orange tubes. And that will be a
+delta 1 s set of directions.
+
+ align:start position:0%
+delta 1 s set of directions.
+ 
+
+ align:start position:0%
+delta 1 s set of directions.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+great. Um then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah. Okay, so
+
+ align:start position:0%
+yeah. Okay, so
+ 
+
+ align:start position:0%
+yeah. Okay, so
+let let me put the punch line and then
+
+ align:start position:0%
+let let me put the punch line and then
+ 
+
+ align:start position:0%
+let let me put the punch line and then
+we'll think through why this works.
+
+ align:start position:0%
+we'll think through why this works.
+ 
+
+ align:start position:0%
+we'll think through why this works.
+So R A D of delta that's the number of
+
+ align:start position:0%
+So R A D of delta that's the number of
+ 
+
+ align:start position:0%
+So R A D of delta that's the number of
+white balls in a red tube, but that's
+
+ align:start position:0%
+white balls in a red tube, but that's
+ 
+
+ align:start position:0%
+white balls in a red tube, but that's
+bounded by the number of delta 1 balls
+
+ align:start position:0%
+bounded by the number of delta 1 balls
+ 
+
+ align:start position:0%
+bounded by the number of delta 1 balls
+in a delta 1 tube.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So I look in this orange tube, I
+
+ align:start position:0%
+Right? So I look in this orange tube, I
+ 
+
+ align:start position:0%
+Right? So I look in this orange tube, I
+see how many of these balls there are
+
+ align:start position:0%
+see how many of these balls there are
+ 
+
+ align:start position:0%
+see how many of these balls there are
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+the number of delta balls
+
+ align:start position:0%
+the number of delta balls
+ 
+
+ align:start position:0%
+the number of delta balls
+in a delta tube within
+
+ align:start position:0%
+in a delta tube within
+ 
+
+ align:start position:0%
+in a delta tube within
+one delta 1 bar.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I'm looking at this at this red
+
+ align:start position:0%
+So if I'm looking at this at this red
+ 
+
+ align:start position:0%
+So if I'm looking at this at this red
+tube here, I want to know how many delta
+
+ align:start position:0%
+tube here, I want to know how many delta
+ 
+
+ align:start position:0%
+tube here, I want to know how many delta
+balls are in it. It's bounded by the
+
+ align:start position:0%
+balls are in it. It's bounded by the
+ 
+
+ align:start position:0%
+balls are in it. It's bounded by the
+number of big balls that it enters
+
+ align:start position:0%
+number of big balls that it enters
+ 
+
+ align:start position:0%
+number of big balls that it enters
+times the number of little balls in each
+
+ align:start position:0%
+times the number of little balls in each
+ 
+
+ align:start position:0%
+times the number of little balls in each
+of the big balls.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, we'd like to relate these two
+
+ align:start position:0%
+Okay. So, we'd like to relate these two
+ 
+
+ align:start position:0%
+Okay. So, we'd like to relate these two
+things to our problem at a coarser
+
+ align:start position:0%
+things to our problem at a coarser
+ 
+
+ align:start position:0%
+things to our problem at a coarser
+scale.
+
+ align:start position:0%
+scale.
+ 
+
+ align:start position:0%
+scale.
+And this one here well E1 and T1 obey
+
+ align:start position:0%
+And this one here well E1 and T1 obey
+ 
+
+ align:start position:0%
+And this one here well E1 and T1 obey
+our hypothesis. So this this one here is
+
+ align:start position:0%
+our hypothesis. So this this one here is
+ 
+
+ align:start position:0%
+our hypothesis. So this this one here is
+bounded by RA a D of delta 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now here
+
+ align:start position:0%
+Now here
+ 
+
+ align:start position:0%
+Now here
+if you take E and T and you restrict
+
+ align:start position:0%
+if you take E and T and you restrict
+ 
+
+ align:start position:0%
+if you take E and T and you restrict
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+to a delta 1 ball
+
+ align:start position:0%
+to a delta 1 ball
+ 
+
+ align:start position:0%
+to a delta 1 ball
+and then you magnify it to bring it up
+
+ align:start position:0%
+and then you magnify it to bring it up
+ 
+
+ align:start position:0%
+and then you magnify it to bring it up
+to scale one. Um this also obeys our
+
+ align:start position:0%
+to scale one. Um this also obeys our
+ 
+
+ align:start position:0%
+to scale one. Um this also obeys our
+hypothesis.
+
+ align:start position:0%
+hypothesis.
+ 
+
+ align:start position:0%
+hypothesis.
+So if you look inside of here, you see a
+
+ align:start position:0%
+So if you look inside of here, you see a
+ 
+
+ align:start position:0%
+So if you look inside of here, you see a
+little delta TC sat a little a little uh
+
+ align:start position:0%
+little delta TC sat a little a little uh
+ 
+
+ align:start position:0%
+little delta TC sat a little a little uh
+you know this this this
+
+ align:start position:0%
+you know this this this
+ 
+
+ align:start position:0%
+you know this this this
+and and these red tubes. That's the same
+
+ align:start position:0%
+and and these red tubes. That's the same
+ 
+
+ align:start position:0%
+and and these red tubes. That's the same
+situation on a smaller scale or on a
+
+ align:start position:0%
+situation on a smaller scale or on a
+ 
+
+ align:start position:0%
+situation on a smaller scale or on a
+coarser scale. So when you when you blow
+
+ align:start position:0%
+coarser scale. So when you when you blow
+ 
+
+ align:start position:0%
+coarser scale. So when you when you blow
+this up um uh if you blow it up then you
+
+ align:start position:0%
+this up um uh if you blow it up then you
+ 
+
+ align:start position:0%
+this up um uh if you blow it up then you
+get delta 2 balls
+
+ align:start position:0%
+get delta 2 balls
+ 
+
+ align:start position:0%
+get delta 2 balls
+and delta 2 tubes
+
+ align:start position:0%
+and delta 2 tubes
+ 
+
+ align:start position:0%
+and delta 2 tubes
+in the unit ball.
+
+ align:start position:0%
+in the unit ball.
+ 
+
+ align:start position:0%
+in the unit ball.
+So this guy is bounded by the uh ra of
+
+ align:start position:0%
+So this guy is bounded by the uh ra of
+ 
+
+ align:start position:0%
+So this guy is bounded by the uh ra of
+delta 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I'm going call this claim one and
+
+ align:start position:0%
+Okay, I'm going call this claim one and
+ 
+
+ align:start position:0%
+Okay, I'm going call this claim one and
+claim two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right,
+
+ align:start position:0%
+All right,
+ 
+
+ align:start position:0%
+All right,
+so this picture is perhaps the most
+
+ align:start position:0%
+so this picture is perhaps the most
+ 
+
+ align:start position:0%
+so this picture is perhaps the most
+important thing uh to take away from
+
+ align:start position:0%
+important thing uh to take away from
+ 
+
+ align:start position:0%
+important thing uh to take away from
+this proof and this class. So take a
+
+ align:start position:0%
+this proof and this class. So take a
+ 
+
+ align:start position:0%
+this proof and this class. So take a
+moment and see if you have questions
+
+ align:start position:0%
+moment and see if you have questions
+ 
+
+ align:start position:0%
+moment and see if you have questions
+about this proof.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ready to verify.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. Okay. So the question is do we
+
+ align:start position:0%
+>> Yeah. Okay. So the question is do we
+ 
+
+ align:start position:0%
+>> Yeah. Okay. So the question is do we
+need to check that everything is ad
+
+ align:start position:0%
+need to check that everything is ad
+ 
+
+ align:start position:0%
+need to check that everything is ad
+regular? Yeah. Okay. So let me add to
+
+ align:start position:0%
+regular? Yeah. Okay. So let me add to
+ 
+
+ align:start position:0%
+regular? Yeah. Okay. So let me add to
+these claims and then if we want to
+
+ align:start position:0%
+these claims and then if we want to
+ 
+
+ align:start position:0%
+these claims and then if we want to
+we'll we'll prove we can add details to
+
+ align:start position:0%
+we'll we'll prove we can add details to
+ 
+
+ align:start position:0%
+we'll we'll prove we can add details to
+the proof of these claims. E E1 and T1
+
+ align:start position:0%
+the proof of these claims. E E1 and T1
+ 
+
+ align:start position:0%
+the proof of these claims. E E1 and T1
+obey the hypothesis and they're ad
+
+ align:start position:0%
+obey the hypothesis and they're ad
+ 
+
+ align:start position:0%
+obey the hypothesis and they're ad
+regular. And we need that this blow up
+
+ align:start position:0%
+regular. And we need that this blow up
+ 
+
+ align:start position:0%
+regular. And we need that this blow up
+here obeys the hypothesis and it's ad
+
+ align:start position:0%
+here obeys the hypothesis and it's ad
+ 
+
+ align:start position:0%
+here obeys the hypothesis and it's ad
+regular. And if you believe those two
+
+ align:start position:0%
+regular. And if you believe those two
+ 
+
+ align:start position:0%
+regular. And if you believe those two
+things, then you can plug you just plug
+
+ align:start position:0%
+things, then you can plug you just plug
+ 
+
+ align:start position:0%
+things, then you can plug you just plug
+in and you get that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. And we we can talk a little bit
+
+ align:start position:0%
+Yeah. And we we can talk a little bit
+ 
+
+ align:start position:0%
+Yeah. And we we can talk a little bit
+more about those two things if you want.
+
+ align:start position:0%
+more about those two things if you want.
+ 
+
+ align:start position:0%
+more about those two things if you want.
+Are there other questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, I'll probably add a little
+
+ align:start position:0%
+Okay. So, I'll probably add a little
+ 
+
+ align:start position:0%
+Okay. So, I'll probably add a little
+more, but actually I wanted to ask you
+
+ align:start position:0%
+more, but actually I wanted to ask you
+ 
+
+ align:start position:0%
+more, but actually I wanted to ask you
+all a question. Um, in this argument,
+
+ align:start position:0%
+all a question. Um, in this argument,
+ 
+
+ align:start position:0%
+all a question. Um, in this argument,
+where did we take advantage of the fact
+
+ align:start position:0%
+where did we take advantage of the fact
+ 
+
+ align:start position:0%
+where did we take advantage of the fact
+that the original E was ad regular?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Jonathan,
+
+ align:start position:0%
+Yeah. Jonathan,
+ 
+
+ align:start position:0%
+Yeah. Jonathan,
+>> is it like picking one delta one ball
+
+ align:start position:0%
+>> is it like picking one delta one ball
+ 
+
+ align:start position:0%
+>> is it like picking one delta one ball
+and magnifying it?
+
+ align:start position:0%
+and magnifying it?
+ 
+
+ align:start position:0%
+and magnifying it?
+>> Yeah. So, it's related to when we picked
+
+ align:start position:0%
+>> Yeah. So, it's related to when we picked
+ 
+
+ align:start position:0%
+>> Yeah. So, it's related to when we picked
+this one delta 1 ball and magnified it.
+
+ align:start position:0%
+this one delta 1 ball and magnified it.
+ 
+
+ align:start position:0%
+this one delta 1 ball and magnified it.
+Yeah. So, so let's talk about one and
+
+ align:start position:0%
+Yeah. So, so let's talk about one and
+ 
+
+ align:start position:0%
+Yeah. So, so let's talk about one and
+two a little more carefully. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's discuss
+
+ align:start position:0%
+So let's discuss
+ 
+
+ align:start position:0%
+So let's discuss
+one and two. Okay. So point one if e and
+
+ align:start position:0%
+one and two. Okay. So point one if e and
+ 
+
+ align:start position:0%
+one and two. Okay. So point one if e and
+tx are uniform which we can pretty much
+
+ align:start position:0%
+tx are uniform which we can pretty much
+ 
+
+ align:start position:0%
+tx are uniform which we can pretty much
+assume in the which we can assume from
+
+ align:start position:0%
+assume in the which we can assume from
+ 
+
+ align:start position:0%
+assume in the which we can assume from
+the beginning with a little pruning
+
+ align:start position:0%
+the beginning with a little pruning
+ 
+
+ align:start position:0%
+the beginning with a little pruning
+um then um
+
+ align:start position:0%
+um then um
+ 
+
+ align:start position:0%
+um then um
+e delta t implies that e1 is delta1 t
+
+ align:start position:0%
+e delta t implies that e1 is delta1 t
+ 
+
+ align:start position:0%
+e delta t implies that e1 is delta1 t
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+tx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+delta s implies that t1x
+
+ align:start position:0%
+delta s implies that t1x
+ 
+
+ align:start position:0%
+delta s implies that t1x
+is is delta 1x.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And also uh if E is ad regular
+
+ align:start position:0%
+Okay. And also uh if E is ad regular
+ 
+
+ align:start position:0%
+Okay. And also uh if E is ad regular
+it implies that E1 is AD regular
+
+ align:start position:0%
+it implies that E1 is AD regular
+ 
+
+ align:start position:0%
+it implies that E1 is AD regular
+because this is saying all the branching
+
+ align:start position:0%
+because this is saying all the branching
+ 
+
+ align:start position:0%
+because this is saying all the branching
+numbers of E are the same as each other
+
+ align:start position:0%
+numbers of E are the same as each other
+ 
+
+ align:start position:0%
+numbers of E are the same as each other
+and this is saying that all the
+
+ align:start position:0%
+and this is saying that all the
+ 
+
+ align:start position:0%
+and this is saying that all the
+branching numbers of E down to the depth
+
+ align:start position:0%
+branching numbers of E down to the depth
+ 
+
+ align:start position:0%
+branching numbers of E down to the depth
+of delta 1 are the same as each other.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+we didn't need E to be ad regular to do
+
+ align:start position:0%
+we didn't need E to be ad regular to do
+ 
+
+ align:start position:0%
+we didn't need E to be ad regular to do
+this or this,
+
+ align:start position:0%
+this or this,
+ 
+
+ align:start position:0%
+this or this,
+but it comes in in part two. So
+
+ align:start position:0%
+but it comes in in part two. So
+ 
+
+ align:start position:0%
+but it comes in in part two. So
+because E is a deregular
+
+ align:start position:0%
+because E is a deregular
+ 
+
+ align:start position:0%
+because E is a deregular
+then we get that if you take E and you
+
+ align:start position:0%
+then we get that if you take E and you
+ 
+
+ align:start position:0%
+then we get that if you take E and you
+intersect it with a small ball and
+
+ align:start position:0%
+intersect it with a small ball and
+ 
+
+ align:start position:0%
+intersect it with a small ball and
+magnify it
+
+ align:start position:0%
+magnify it
+ 
+
+ align:start position:0%
+magnify it
+then this is uh a delta I guess delta 2
+
+ align:start position:0%
+then this is uh a delta I guess delta 2
+ 
+
+ align:start position:0%
+then this is uh a delta I guess delta 2
+t and a d regular.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let me illustrate this with pictures
+
+ align:start position:0%
+So let me illustrate this with pictures
+ 
+
+ align:start position:0%
+So let me illustrate this with pictures
+instead of equations. So what does it
+
+ align:start position:0%
+instead of equations. So what does it
+ 
+
+ align:start position:0%
+instead of equations. So what does it
+look like? Let's draw an ad regular set
+
+ align:start position:0%
+look like? Let's draw an ad regular set
+ 
+
+ align:start position:0%
+look like? Let's draw an ad regular set
+and a not regular set and we'll look at
+
+ align:start position:0%
+and a not regular set and we'll look at
+ 
+
+ align:start position:0%
+and a not regular set and we'll look at
+both of them. Okay. So if E is ad
+
+ align:start position:0%
+both of them. Okay. So if E is ad
+ 
+
+ align:start position:0%
+both of them. Okay. So if E is ad
+regular
+
+ align:start position:0%
+regular
+ 
+
+ align:start position:0%
+regular
+what I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I pick say four of them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me do this in the color.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Then for each one that I picked, I
+
+ align:start position:0%
+Okay. Then for each one that I picked, I
+ 
+
+ align:start position:0%
+Okay. Then for each one that I picked, I
+subdivide it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and I pick four of them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I'll stop drawing. You get the
+
+ align:start position:0%
+Okay, I'll stop drawing. You get the
+ 
+
+ align:start position:0%
+Okay, I'll stop drawing. You get the
+idea, right? Okay, now this is a self
+
+ align:start position:0%
+idea, right? Okay, now this is a self
+ 
+
+ align:start position:0%
+idea, right? Okay, now this is a self
+similar construction. If I take this
+
+ align:start position:0%
+similar construction. If I take this
+ 
+
+ align:start position:0%
+similar construction. If I take this
+thing in here and I blow it up, it's
+
+ align:start position:0%
+thing in here and I blow it up, it's
+ 
+
+ align:start position:0%
+thing in here and I blow it up, it's
+just like what I started with. So it
+
+ align:start position:0%
+just like what I started with. So it
+ 
+
+ align:start position:0%
+just like what I started with. So it
+will be a dere regular and it will be in
+
+ align:start position:0%
+will be a dere regular and it will be in
+ 
+
+ align:start position:0%
+will be a dere regular and it will be in
+particular a delta it will be a a delta
+
+ align:start position:0%
+particular a delta it will be a a delta
+ 
+
+ align:start position:0%
+particular a delta it will be a a delta
+t set for the appropriate delta.
+
+ align:start position:0%
+t set for the appropriate delta.
+ 
+
+ align:start position:0%
+t set for the appropriate delta.
+Okay what would it look like if e was
+
+ align:start position:0%
+Okay what would it look like if e was
+ 
+
+ align:start position:0%
+Okay what would it look like if e was
+not a d regular?
+
+ align:start position:0%
+not a d regular?
+ 
+
+ align:start position:0%
+not a d regular?
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+for example,
+
+ align:start position:0%
+for example,
+ 
+
+ align:start position:0%
+for example,
+I might do the following thing. Might
+
+ align:start position:0%
+I might do the following thing. Might
+ 
+
+ align:start position:0%
+I might do the following thing. Might
+cut it into a 4x4 grid. And I might take
+
+ align:start position:0%
+cut it into a 4x4 grid. And I might take
+ 
+
+ align:start position:0%
+cut it into a 4x4 grid. And I might take
+all of the boxes. And then I could cut
+
+ align:start position:0%
+all of the boxes. And then I could cut
+ 
+
+ align:start position:0%
+all of the boxes. And then I could cut
+each of each one of them into a 4x4 grid
+
+ align:start position:0%
+each of each one of them into a 4x4 grid
+ 
+
+ align:start position:0%
+each of each one of them into a 4x4 grid
+and pick just one box.
+
+ align:start position:0%
+and pick just one box.
+ 
+
+ align:start position:0%
+and pick just one box.
+So this was the, you know, the well
+
+ align:start position:0%
+So this was the, you know, the well
+ 
+
+ align:start position:0%
+So this was the, you know, the well
+spaced example that we drew last time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this whole thing is a delta t
+
+ align:start position:0%
+Okay. So this whole thing is a delta t
+ 
+
+ align:start position:0%
+Okay. So this whole thing is a delta t
+set. But if I took just one of these
+
+ align:start position:0%
+set. But if I took just one of these
+ 
+
+ align:start position:0%
+set. But if I took just one of these
+boxes, what I would see is much more
+
+ align:start position:0%
+boxes, what I would see is much more
+ 
+
+ align:start position:0%
+boxes, what I would see is much more
+concentrated. This is not a delta t set.
+
+ align:start position:0%
+concentrated. This is not a delta t set.
+ 
+
+ align:start position:0%
+concentrated. This is not a delta t set.
+So if I were to take this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and take it out here and magnify it,
+
+ align:start position:0%
+and take it out here and magnify it,
+ 
+
+ align:start position:0%
+and take it out here and magnify it,
+then inside of here, I would just see
+
+ align:start position:0%
+then inside of here, I would just see
+ 
+
+ align:start position:0%
+then inside of here, I would just see
+this. This here is a blank T set. But
+
+ align:start position:0%
+this. This here is a blank T set. But
+ 
+
+ align:start position:0%
+this. This here is a blank T set. But
+this here is not a blank T- set.
+
+ align:start position:0%
+this here is not a blank T- set.
+ 
+
+ align:start position:0%
+this here is not a blank T- set.
+Whereas in the AD regular case, if I
+
+ align:start position:0%
+Whereas in the AD regular case, if I
+ 
+
+ align:start position:0%
+Whereas in the AD regular case, if I
+were to take one of these and bring it
+
+ align:start position:0%
+were to take one of these and bring it
+ 
+
+ align:start position:0%
+were to take one of these and bring it
+out and magnify it, then what I would
+
+ align:start position:0%
+out and magnify it, then what I would
+ 
+
+ align:start position:0%
+out and magnify it, then what I would
+see in here would be very similar to the
+
+ align:start position:0%
+see in here would be very similar to the
+ 
+
+ align:start position:0%
+see in here would be very similar to the
+original set. This is um
+
+ align:start position:0%
+original set. This is um
+ 
+
+ align:start position:0%
+original set. This is um
+similar to B. So this here is a
+
+ align:start position:0%
+similar to B. So this here is a
+ 
+
+ align:start position:0%
+similar to B. So this here is a
+blank T set and it's a dregular. And
+
+ align:start position:0%
+blank T set and it's a dregular. And
+ 
+
+ align:start position:0%
+blank T set and it's a dregular. And
+that thing in there is still a blank T
+
+ align:start position:0%
+that thing in there is still a blank T
+ 
+
+ align:start position:0%
+that thing in there is still a blank T
+set and it's still ad regular.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this is the special feature of
+
+ align:start position:0%
+Okay, so this is the special feature of
+ 
+
+ align:start position:0%
+Okay, so this is the special feature of
+ad regular. The word regular refers to
+
+ align:start position:0%
+ad regular. The word regular refers to
+ 
+
+ align:start position:0%
+ad regular. The word regular refers to
+the fact that all the different scales
+
+ align:start position:0%
+the fact that all the different scales
+ 
+
+ align:start position:0%
+the fact that all the different scales
+look the same. And so when we uh look
+
+ align:start position:0%
+look the same. And so when we uh look
+ 
+
+ align:start position:0%
+look the same. And so when we uh look
+inside this ball here, we have another
+
+ align:start position:0%
+inside this ball here, we have another
+ 
+
+ align:start position:0%
+inside this ball here, we have another
+example of our original problem at a
+
+ align:start position:0%
+example of our original problem at a
+ 
+
+ align:start position:0%
+example of our original problem at a
+coarser scale. And that feeds into an
+
+ align:start position:0%
+coarser scale. And that feeds into an
+ 
+
+ align:start position:0%
+coarser scale. And that feeds into an
+inductive argument and we can say for
+
+ align:start position:0%
+inductive argument and we can say for
+ 
+
+ align:start position:0%
+inductive argument and we can say for
+example we can say this sub
+
+ align:start position:0%
+example we can say this sub
+ 
+
+ align:start position:0%
+example we can say this sub
+multiplicative lema.
+
+ align:start position:0%
+multiplicative lema.
+ 
+
+ align:start position:0%
+multiplicative lema.
+>> Yeah first inequality over there do you
+
+ align:start position:0%
+>> Yeah first inequality over there do you
+ 
+
+ align:start position:0%
+>> Yeah first inequality over there do you
+need some sort of uniformity on the
+
+ align:start position:0%
+need some sort of uniformity on the
+ 
+
+ align:start position:0%
+need some sort of uniformity on the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+cuz like the average and you're saying
+
+ align:start position:0%
+cuz like the average and you're saying
+ 
+
+ align:start position:0%
+cuz like the average and you're saying
+something like the average.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah that's right. That's right. So so
+
+ align:start position:0%
+>> Yeah that's right. That's right. So so
+ 
+
+ align:start position:0%
+>> Yeah that's right. That's right. So so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yes that is a good point. Okay, so the
+
+ align:start position:0%
+yes that is a good point. Okay, so the
+ 
+
+ align:start position:0%
+yes that is a good point. Okay, so the
+comment is that RA was defined as an
+
+ align:start position:0%
+comment is that RA was defined as an
+ 
+
+ align:start position:0%
+comment is that RA was defined as an
+average number of delta tubes per delta
+
+ align:start position:0%
+average number of delta tubes per delta
+ 
+
+ align:start position:0%
+average number of delta tubes per delta
+ball. And here I was pretending that all
+
+ align:start position:0%
+ball. And here I was pretending that all
+ 
+
+ align:start position:0%
+ball. And here I was pretending that all
+the tubes are average. Um so
+
+ align:start position:0%
+the tubes are average. Um so
+ 
+
+ align:start position:0%
+the tubes are average. Um so
+let's call this a proof sketch.
+
+ align:start position:0%
+let's call this a proof sketch.
+ 
+
+ align:start position:0%
+let's call this a proof sketch.
+Um you do need some uniformity. If you
+
+ align:start position:0%
+Um you do need some uniformity. If you
+ 
+
+ align:start position:0%
+Um you do need some uniformity. If you
+think back to the original setting, you
+
+ align:start position:0%
+think back to the original setting, you
+ 
+
+ align:start position:0%
+think back to the original setting, you
+know, you have the set E and then you
+
+ align:start position:0%
+know, you have the set E and then you
+ 
+
+ align:start position:0%
+know, you have the set E and then you
+draw all these tubes. You can sort them
+
+ align:start position:0%
+draw all these tubes. You can sort them
+ 
+
+ align:start position:0%
+draw all these tubes. You can sort them
+by how many delta tubes are in each one
+
+ align:start position:0%
+by how many delta tubes are in each one
+ 
+
+ align:start position:0%
+by how many delta tubes are in each one
+and you take the category that has the
+
+ align:start position:0%
+and you take the category that has the
+ 
+
+ align:start position:0%
+and you take the category that has the
+most delta tubes and that will still you
+
+ align:start position:0%
+most delta tubes and that will still you
+ 
+
+ align:start position:0%
+most delta tubes and that will still you
+can work with that. So you can do it you
+
+ align:start position:0%
+can work with that. So you can do it you
+ 
+
+ align:start position:0%
+can work with that. So you can do it you
+you you're correct. You we have to
+
+ align:start position:0%
+you you're correct. You we have to
+ 
+
+ align:start position:0%
+you you're correct. You we have to
+uniformize it. Um and it is possible to
+
+ align:start position:0%
+uniformize it. Um and it is possible to
+ 
+
+ align:start position:0%
+uniformize it. Um and it is possible to
+uniformize it.
+
+ align:start position:0%
+uniformize it.
+ 
+
+ align:start position:0%
+uniformize it.
+Okay. So let me scribe that. So um
+
+ align:start position:0%
+Okay. So let me scribe that. So um
+ 
+
+ align:start position:0%
+Okay. So let me scribe that. So um
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+can do some
+
+ align:start position:0%
+can do some
+ 
+
+ align:start position:0%
+can do some
+uniformizing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all tubes
+
+ align:start position:0%
+so all tubes
+ 
+
+ align:start position:0%
+so all tubes
+have the same number of balls.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, other questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Cool.
+
+ align:start position:0%
+Okay. Cool.
+ 
+
+ align:start position:0%
+Okay. Cool.
+All right. So, this little lema is very
+
+ align:start position:0%
+All right. So, this little lema is very
+ 
+
+ align:start position:0%
+All right. So, this little lema is very
+important. Um, for people who have some
+
+ align:start position:0%
+important. Um, for people who have some
+ 
+
+ align:start position:0%
+important. Um, for people who have some
+seen some other things in harmonic
+
+ align:start position:0%
+seen some other things in harmonic
+ 
+
+ align:start position:0%
+seen some other things in harmonic
+analysis, there's a submative lema
+
+ align:start position:0%
+analysis, there's a submative lema
+ 
+
+ align:start position:0%
+analysis, there's a submative lema
+that's sort of like this in decoupling
+
+ align:start position:0%
+that's sort of like this in decoupling
+ 
+
+ align:start position:0%
+that's sort of like this in decoupling
+theory and it's the beginning of what's
+
+ align:start position:0%
+theory and it's the beginning of what's
+ 
+
+ align:start position:0%
+theory and it's the beginning of what's
+special about decoupling. If those words
+
+ align:start position:0%
+special about decoupling. If those words
+ 
+
+ align:start position:0%
+special about decoupling. If those words
+don't mean anything to you, don't worry
+
+ align:start position:0%
+don't mean anything to you, don't worry
+ 
+
+ align:start position:0%
+don't mean anything to you, don't worry
+about it. Um so let me show you some uh
+
+ align:start position:0%
+about it. Um so let me show you some uh
+ 
+
+ align:start position:0%
+about it. Um so let me show you some uh
+corlary some applications of this lema
+
+ align:start position:0%
+corlary some applications of this lema
+ 
+
+ align:start position:0%
+corlary some applications of this lema
+and then we'll um and then we'll sort of
+
+ align:start position:0%
+and then we'll um and then we'll sort of
+ 
+
+ align:start position:0%
+and then we'll um and then we'll sort of
+go in earnest into using it to prove
+
+ align:start position:0%
+go in earnest into using it to prove
+ 
+
+ align:start position:0%
+go in earnest into using it to prove
+this theorem.
+
+ align:start position:0%
+this theorem.
+ 
+
+ align:start position:0%
+this theorem.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So the first application is sort
+
+ align:start position:0%
+right. So the first application is sort
+ 
+
+ align:start position:0%
+right. So the first application is sort
+of tongue and cheek
+
+ align:start position:0%
+of tongue and cheek
+ 
+
+ align:start position:0%
+of tongue and cheek
+but uh also I I I think it's
+
+ align:start position:0%
+but uh also I I I think it's
+ 
+
+ align:start position:0%
+but uh also I I I think it's
+philosophically important. I'm going to
+
+ align:start position:0%
+philosophically important. I'm going to
+ 
+
+ align:start position:0%
+philosophically important. I'm going to
+call it so applications.
+
+ align:start position:0%
+call it so applications.
+ 
+
+ align:start position:0%
+call it so applications.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+I'm gonna call it uh brute force proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a theorem of theorem um of the the ad
+
+ align:start position:0%
+of a theorem of theorem um of the the ad
+ 
+
+ align:start position:0%
+of a theorem of theorem um of the the ad
+regular case.
+
+ align:start position:0%
+regular case.
+ 
+
+ align:start position:0%
+regular case.
+So here's how it goes.
+
+ align:start position:0%
+So here's how it goes.
+ 
+
+ align:start position:0%
+So here's how it goes.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+so for some
+
+ align:start position:0%
+so for some
+ 
+
+ align:start position:0%
+so for some
+for some specific delta knot
+
+ align:start position:0%
+for some specific delta knot
+ 
+
+ align:start position:0%
+for some specific delta knot
+we check by brute force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that r a d
+
+ align:start position:0%
+that r a d
+ 
+
+ align:start position:0%
+that r a d
+s delta kn is bounded by um the right
+
+ align:start position:0%
+s delta kn is bounded by um the right
+ 
+
+ align:start position:0%
+s delta kn is bounded by um the right
+hand side
+
+ align:start position:0%
+hand side
+ 
+
+ align:start position:0%
+hand side
+and we won't be able to get it perfectly
+
+ align:start position:0%
+and we won't be able to get it perfectly
+ 
+
+ align:start position:0%
+and we won't be able to get it perfectly
+but we could get something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, how could you do this? Once
+
+ align:start position:0%
+Okay. So, how could you do this? Once
+ 
+
+ align:start position:0%
+Okay. So, how could you do this? Once
+you fix a particular delta knot, like
+
+ align:start position:0%
+you fix a particular delta knot, like
+ 
+
+ align:start position:0%
+you fix a particular delta knot, like
+one over a million, there are really
+
+ align:start position:0%
+one over a million, there are really
+ 
+
+ align:start position:0%
+one over a million, there are really
+only finitely many different ways you
+
+ align:start position:0%
+only finitely many different ways you
+ 
+
+ align:start position:0%
+only finitely many different ways you
+could arrange the delta balls. And there
+
+ align:start position:0%
+could arrange the delta balls. And there
+ 
+
+ align:start position:0%
+could arrange the delta balls. And there
+are really only finitely many ways you
+
+ align:start position:0%
+are really only finitely many ways you
+ 
+
+ align:start position:0%
+are really only finitely many ways you
+could put the tubes. So, there's a giant
+
+ align:start position:0%
+could put the tubes. So, there's a giant
+ 
+
+ align:start position:0%
+could put the tubes. So, there's a giant
+brute force calculation that you
+
+ align:start position:0%
+brute force calculation that you
+ 
+
+ align:start position:0%
+brute force calculation that you
+couldn't really do, but we could
+
+ align:start position:0%
+couldn't really do, but we could
+ 
+
+ align:start position:0%
+couldn't really do, but we could
+imagine. And you could just check this.
+
+ align:start position:0%
+imagine. And you could just check this.
+ 
+
+ align:start position:0%
+imagine. And you could just check this.
+Once you have this then you use the
+
+ align:start position:0%
+Once you have this then you use the
+ 
+
+ align:start position:0%
+Once you have this then you use the
+submultiplicative lema
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many times.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and so you know when you used it once
+
+ align:start position:0%
+Um and so you know when you used it once
+ 
+
+ align:start position:0%
+Um and so you know when you used it once
+you would get ra s delta kn squared that
+
+ align:start position:0%
+you would get ra s delta kn squared that
+ 
+
+ align:start position:0%
+you would get ra s delta kn squared that
+would be bounded by right hand side
+
+ align:start position:0%
+would be bounded by right hand side
+ 
+
+ align:start position:0%
+would be bounded by right hand side
+times delta kn squar to the minus
+
+ align:start position:0%
+times delta kn squar to the minus
+ 
+
+ align:start position:0%
+times delta kn squar to the minus
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+because the the right hand side is just
+
+ align:start position:0%
+because the the right hand side is just
+ 
+
+ align:start position:0%
+because the the right hand side is just
+a power delta kn. So it multiplies
+
+ align:start position:0%
+a power delta kn. So it multiplies
+ 
+
+ align:start position:0%
+a power delta kn. So it multiplies
+everything fits and you you keep going.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so of course this so this brute
+
+ align:start position:0%
+Okay, so of course this so this brute
+ 
+
+ align:start position:0%
+Okay, so of course this so this brute
+force computation is so large that it's
+
+ align:start position:0%
+force computation is so large that it's
+ 
+
+ align:start position:0%
+force computation is so large that it's
+out of the question to do it even with a
+
+ align:start position:0%
+out of the question to do it even with a
+ 
+
+ align:start position:0%
+out of the question to do it even with a
+supercomputer etc. Um, nevertheless, it
+
+ align:start position:0%
+supercomputer etc. Um, nevertheless, it
+ 
+
+ align:start position:0%
+supercomputer etc. Um, nevertheless, it
+is worth noticing that this very
+
+ align:start position:0%
+is worth noticing that this very
+ 
+
+ align:start position:0%
+is worth noticing that this very
+difficult theorem has a one blackboard
+
+ align:start position:0%
+difficult theorem has a one blackboard
+ 
+
+ align:start position:0%
+difficult theorem has a one blackboard
+proof up to a brute force computation.
+
+ align:start position:0%
+proof up to a brute force computation.
+ 
+
+ align:start position:0%
+proof up to a brute force computation.
+Up to a finite computation. Most
+
+ align:start position:0%
+Up to a finite computation. Most
+ 
+
+ align:start position:0%
+Up to a finite computation. Most
+difficult theorems in math, it's not
+
+ align:start position:0%
+difficult theorems in math, it's not
+ 
+
+ align:start position:0%
+difficult theorems in math, it's not
+obvious how to reduce to a finite
+
+ align:start position:0%
+obvious how to reduce to a finite
+ 
+
+ align:start position:0%
+obvious how to reduce to a finite
+computation. I wouldn't say this is
+
+ align:start position:0%
+computation. I wouldn't say this is
+ 
+
+ align:start position:0%
+computation. I wouldn't say this is
+obvious either, but for most difficult
+
+ align:start position:0%
+obvious either, but for most difficult
+ 
+
+ align:start position:0%
+obvious either, but for most difficult
+theorems in math, there's not a
+
+ align:start position:0%
+theorems in math, there's not a
+ 
+
+ align:start position:0%
+theorems in math, there's not a
+half-page argument to reduce it to a
+
+ align:start position:0%
+half-page argument to reduce it to a
+ 
+
+ align:start position:0%
+half-page argument to reduce it to a
+finite computation. For this one, there
+
+ align:start position:0%
+finite computation. For this one, there
+ 
+
+ align:start position:0%
+finite computation. For this one, there
+is, but it shows that this is quite
+
+ align:start position:0%
+is, but it shows that this is quite
+ 
+
+ align:start position:0%
+is, but it shows that this is quite
+important.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let me give another application.
+
+ align:start position:0%
+Okay, let me give another application.
+ 
+
+ align:start position:0%
+Okay, let me give another application.
+Um, second application is the general
+
+ align:start position:0%
+Um, second application is the general
+ 
+
+ align:start position:0%
+Um, second application is the general
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+general ad versus the projective ad.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, okay. So, the course was called
+
+ align:start position:0%
+Um, okay. So, the course was called
+ 
+
+ align:start position:0%
+Um, okay. So, the course was called
+projection theory. Uh, and at the
+
+ align:start position:0%
+projection theory. Uh, and at the
+ 
+
+ align:start position:0%
+projection theory. Uh, and at the
+beginning we talked about problems about
+
+ align:start position:0%
+beginning we talked about problems about
+ 
+
+ align:start position:0%
+beginning we talked about problems about
+orthogonal projections. And this theorem
+
+ align:start position:0%
+orthogonal projections. And this theorem
+ 
+
+ align:start position:0%
+orthogonal projections. And this theorem
+is really more general. I guess I've
+
+ align:start position:0%
+is really more general. I guess I've
+ 
+
+ align:start position:0%
+is really more general. I guess I've
+erased the theorem. The theorem we're
+
+ align:start position:0%
+erased the theorem. The theorem we're
+ 
+
+ align:start position:0%
+erased the theorem. The theorem we're
+talking about today is more general than
+
+ align:start position:0%
+talking about today is more general than
+ 
+
+ align:start position:0%
+talking about today is more general than
+just orthogonal projections. Um, and if
+
+ align:start position:0%
+just orthogonal projections. Um, and if
+ 
+
+ align:start position:0%
+just orthogonal projections. Um, and if
+you had some orthogonal projections, the
+
+ align:start position:0%
+you had some orthogonal projections, the
+ 
+
+ align:start position:0%
+you had some orthogonal projections, the
+way you would get all these tubes is you
+
+ align:start position:0%
+way you would get all these tubes is you
+ 
+
+ align:start position:0%
+way you would get all these tubes is you
+would pick a direction from your
+
+ align:start position:0%
+would pick a direction from your
+ 
+
+ align:start position:0%
+would pick a direction from your
+direction set. And then you would get a
+
+ align:start position:0%
+direction set. And then you would get a
+ 
+
+ align:start position:0%
+direction set. And then you would get a
+bunch of tubes in that direction that
+
+ align:start position:0%
+bunch of tubes in that direction that
+ 
+
+ align:start position:0%
+bunch of tubes in that direction that
+cover your set.
+
+ align:start position:0%
+cover your set.
+ 
+
+ align:start position:0%
+cover your set.
+So um, so I make a definition.
+
+ align:start position:0%
+So um, so I make a definition.
+ 
+
+ align:start position:0%
+So um, so I make a definition.
+Let's say that ET is projective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+for every X and E,
+
+ align:start position:0%
+for every X and E,
+ 
+
+ align:start position:0%
+for every X and E,
+the direction set of the tubes TX, let
+
+ align:start position:0%
+the direction set of the tubes TX, let
+ 
+
+ align:start position:0%
+the direction set of the tubes TX, let
+me put it this way, for every X1 and X2
+
+ align:start position:0%
+me put it this way, for every X1 and X2
+ 
+
+ align:start position:0%
+me put it this way, for every X1 and X2
+and E, the direction of the tubes
+
+ align:start position:0%
+and E, the direction of the tubes
+ 
+
+ align:start position:0%
+and E, the direction of the tubes
+through X1 is the same as the direction
+
+ align:start position:0%
+through X1 is the same as the direction
+ 
+
+ align:start position:0%
+through X1 is the same as the direction
+of the tubes through X2.
+
+ align:start position:0%
+of the tubes through X2.
+ 
+
+ align:start position:0%
+of the tubes through X2.
+In other words, you have just one set of
+
+ align:start position:0%
+In other words, you have just one set of
+ 
+
+ align:start position:0%
+In other words, you have just one set of
+directions and TX is all the tubes
+
+ align:start position:0%
+directions and TX is all the tubes
+ 
+
+ align:start position:0%
+directions and TX is all the tubes
+through X in that set of directions.
+
+ align:start position:0%
+through X in that set of directions.
+ 
+
+ align:start position:0%
+through X in that set of directions.
+Okay, so if you think about the general
+
+ align:start position:0%
+Okay, so if you think about the general
+ 
+
+ align:start position:0%
+Okay, so if you think about the general
+the problem that we wrote down, this is
+
+ align:start position:0%
+the problem that we wrote down, this is
+ 
+
+ align:start position:0%
+the problem that we wrote down, this is
+a very special case. So it used to be at
+
+ align:start position:0%
+a very special case. So it used to be at
+ 
+
+ align:start position:0%
+a very special case. So it used to be at
+every point you picked your own
+
+ align:start position:0%
+every point you picked your own
+ 
+
+ align:start position:0%
+every point you picked your own
+independent set of tubes, but now
+
+ align:start position:0%
+independent set of tubes, but now
+ 
+
+ align:start position:0%
+independent set of tubes, but now
+there's an extra rule that that the
+
+ align:start position:0%
+there's an extra rule that that the
+ 
+
+ align:start position:0%
+there's an extra rule that that the
+directions have to be the same at each
+
+ align:start position:0%
+directions have to be the same at each
+ 
+
+ align:start position:0%
+directions have to be the same at each
+point. It's a very special case.
+
+ align:start position:0%
+point. It's a very special case.
+ 
+
+ align:start position:0%
+point. It's a very special case.
+Okay, so
+
+ align:start position:0%
+Okay, so
+ 
+
+ align:start position:0%
+Okay, so
+let's say RA a projection of delta is uh
+
+ align:start position:0%
+let's say RA a projection of delta is uh
+ 
+
+ align:start position:0%
+let's say RA a projection of delta is uh
+the maximum over the usual stuff. So ET
+
+ align:start position:0%
+the maximum over the usual stuff. So ET
+ 
+
+ align:start position:0%
+the maximum over the usual stuff. So ET
+obeys our hypothesis. Uh E is a regular
+
+ align:start position:0%
+obeys our hypothesis. Uh E is a regular
+ 
+
+ align:start position:0%
+obeys our hypothesis. Uh E is a regular
+but also ET is projective.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So um
+
+ align:start position:0%
+So um
+ 
+
+ align:start position:0%
+So um
+in general that you know that we're
+
+ align:start position:0%
+in general that you know that we're
+ 
+
+ align:start position:0%
+in general that you know that we're
+taking a maximum and this is a
+
+ align:start position:0%
+taking a maximum and this is a
+ 
+
+ align:start position:0%
+taking a maximum and this is a
+restricted maximum. So we clearly have
+
+ align:start position:0%
+restricted maximum. So we clearly have
+ 
+
+ align:start position:0%
+restricted maximum. So we clearly have
+that ra a projective
+
+ align:start position:0%
+that ra a projective
+ 
+
+ align:start position:0%
+that ra a projective
+is smaller than rather
+
+ align:start position:0%
+is smaller than rather
+ 
+
+ align:start position:0%
+is smaller than rather
+more cases
+
+ align:start position:0%
+more cases
+ 
+
+ align:start position:0%
+more cases
+but it turns out that they're basically
+
+ align:start position:0%
+but it turns out that they're basically
+ 
+
+ align:start position:0%
+but it turns out that they're basically
+equal to each other. So let's make that
+
+ align:start position:0%
+equal to each other. So let's make that
+ 
+
+ align:start position:0%
+equal to each other. So let's make that
+a lema.
+
+ align:start position:0%
+a lema.
+ 
+
+ align:start position:0%
+a lema.
+So r a d of delta is less than here
+
+ align:start position:0%
+So r a d of delta is less than here
+ 
+
+ align:start position:0%
+So r a d of delta is less than here
+there are some fudge factors so I'll
+
+ align:start position:0%
+there are some fudge factors so I'll
+ 
+
+ align:start position:0%
+there are some fudge factors so I'll
+write something like this c epsilon
+
+ align:start position:0%
+write something like this c epsilon
+ 
+
+ align:start position:0%
+write something like this c epsilon
+delta to the minus epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually let me I don't quite say that
+
+ align:start position:0%
+actually let me I don't quite say that
+ 
+
+ align:start position:0%
+actually let me I don't quite say that
+that's true but
+
+ align:start position:0%
+that's true but
+ 
+
+ align:start position:0%
+that's true but
+let me just say something uh okay so
+
+ align:start position:0%
+let me just say something uh okay so
+ 
+
+ align:start position:0%
+let me just say something uh okay so
+here so here's a cool observation based
+
+ align:start position:0%
+here so here's a cool observation based
+ 
+
+ align:start position:0%
+here so here's a cool observation based
+on that diagram and that proof
+
+ align:start position:0%
+on that diagram and that proof
+ 
+
+ align:start position:0%
+on that diagram and that proof
+so notice
+
+ align:start position:0%
+so notice
+ 
+
+ align:start position:0%
+so notice
+that in the uh sub multip applicative
+
+ align:start position:0%
+that in the uh sub multip applicative
+ 
+
+ align:start position:0%
+that in the uh sub multip applicative
+lama.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If um delta 1 equals delta 2= square
+
+ align:start position:0%
+If um delta 1 equals delta 2= square
+ 
+
+ align:start position:0%
+If um delta 1 equals delta 2= square
+root of delta,
+
+ align:start position:0%
+root of delta,
+ 
+
+ align:start position:0%
+root of delta,
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+inner uh the the small ball problems are
+
+ align:start position:0%
+inner uh the the small ball problems are
+ 
+
+ align:start position:0%
+inner uh the the small ball problems are
+all projective.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in this in this problem we sort of we
+
+ align:start position:0%
+So in this in this problem we sort of we
+ 
+
+ align:start position:0%
+So in this in this problem we sort of we
+have a a delta scale
+
+ align:start position:0%
+have a a delta scale
+ 
+
+ align:start position:0%
+have a a delta scale
+>> fenberg problem and we broke it up into
+
+ align:start position:0%
+>> fenberg problem and we broke it up into
+ 
+
+ align:start position:0%
+>> fenberg problem and we broke it up into
+two pieces a coarse piece at the large
+
+ align:start position:0%
+two pieces a coarse piece at the large
+ 
+
+ align:start position:0%
+two pieces a coarse piece at the large
+scale and a piece a small piece inside
+
+ align:start position:0%
+scale and a piece a small piece inside
+ 
+
+ align:start position:0%
+scale and a piece a small piece inside
+each small ball. Okay so I claim that
+
+ align:start position:0%
+each small ball. Okay so I claim that
+ 
+
+ align:start position:0%
+each small ball. Okay so I claim that
+this piece inside the small ball is
+
+ align:start position:0%
+this piece inside the small ball is
+ 
+
+ align:start position:0%
+this piece inside the small ball is
+projective.
+
+ align:start position:0%
+projective.
+ 
+
+ align:start position:0%
+projective.
+Why is it? Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so pick one of these points and I'm
+
+ align:start position:0%
+so pick one of these points and I'm
+ 
+
+ align:start position:0%
+so pick one of these points and I'm
+going to look at the directions of the
+
+ align:start position:0%
+going to look at the directions of the
+ 
+
+ align:start position:0%
+going to look at the directions of the
+red tubes going through this point.
+
+ align:start position:0%
+red tubes going through this point.
+ 
+
+ align:start position:0%
+red tubes going through this point.
+Um, now I'm working in this small ball,
+
+ align:start position:0%
+Um, now I'm working in this small ball,
+ 
+
+ align:start position:0%
+Um, now I'm working in this small ball,
+so I can only distinguish them up to an
+
+ align:start position:0%
+so I can only distinguish them up to an
+ 
+
+ align:start position:0%
+so I can only distinguish them up to an
+angle of square root of delta.
+
+ align:start position:0%
+angle of square root of delta.
+ 
+
+ align:start position:0%
+angle of square root of delta.
+So what directions will they be? They'll
+
+ align:start position:0%
+So what directions will they be? They'll
+ 
+
+ align:start position:0%
+So what directions will they be? They'll
+be the directions of these orange tubes
+
+ align:start position:0%
+be the directions of these orange tubes
+ 
+
+ align:start position:0%
+be the directions of these orange tubes
+going out through here.
+
+ align:start position:0%
+going out through here.
+ 
+
+ align:start position:0%
+going out through here.
+So, so there there could well be two
+
+ align:start position:0%
+So, so there there could well be two
+ 
+
+ align:start position:0%
+So, so there there could well be two
+long red tubes going through here in the
+
+ align:start position:0%
+long red tubes going through here in the
+ 
+
+ align:start position:0%
+long red tubes going through here in the
+that are in the same orange tube, but
+
+ align:start position:0%
+that are in the same orange tube, but
+ 
+
+ align:start position:0%
+that are in the same orange tube, but
+inside of this small ball, they'll just
+
+ align:start position:0%
+inside of this small ball, they'll just
+ 
+
+ align:start position:0%
+inside of this small ball, they'll just
+be on top of each other. I won't see any
+
+ align:start position:0%
+be on top of each other. I won't see any
+ 
+
+ align:start position:0%
+be on top of each other. I won't see any
+difference between them.
+
+ align:start position:0%
+difference between them.
+ 
+
+ align:start position:0%
+difference between them.
+So, the directions that I'll see within
+
+ align:start position:0%
+So, the directions that I'll see within
+ 
+
+ align:start position:0%
+So, the directions that I'll see within
+the small ball, they just correspond to
+
+ align:start position:0%
+the small ball, they just correspond to
+ 
+
+ align:start position:0%
+the small ball, they just correspond to
+these orange tubes.
+
+ align:start position:0%
+these orange tubes.
+ 
+
+ align:start position:0%
+these orange tubes.
+And if I look at different guys inside
+
+ align:start position:0%
+And if I look at different guys inside
+ 
+
+ align:start position:0%
+And if I look at different guys inside
+the small ball, I have the same set of
+
+ align:start position:0%
+the small ball, I have the same set of
+ 
+
+ align:start position:0%
+the small ball, I have the same set of
+orange tubes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that gives me an inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r a delta is bounded by
+
+ align:start position:0%
+r a delta is bounded by
+ 
+
+ align:start position:0%
+r a delta is bounded by
+R a D delta to the half times R A D
+
+ align:start position:0%
+R a D delta to the half times R A D
+ 
+
+ align:start position:0%
+R a D delta to the half times R A D
+projective
+
+ align:start position:0%
+projective
+ 
+
+ align:start position:0%
+projective
+delta to the 12.
+
+ align:start position:0%
+delta to the 12.
+ 
+
+ align:start position:0%
+delta to the 12.
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+>> I thought that you were writing
+
+ align:start position:0%
+>> I thought that you were writing
+ 
+
+ align:start position:0%
+>> I thought that you were writing
+projective,
+
+ align:start position:0%
+projective,
+ 
+
+ align:start position:0%
+projective,
+>> right? Only the inner one is projective.
+
+ align:start position:0%
+>> right? Only the inner one is projective.
+ 
+
+ align:start position:0%
+>> right? Only the inner one is projective.
+The outer one is arbitrary.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+However, we can repeat this.
+
+ align:start position:0%
+However, we can repeat this.
+ 
+
+ align:start position:0%
+However, we can repeat this.
+So now that's bounded by RA a delta to
+
+ align:start position:0%
+So now that's bounded by RA a delta to
+ 
+
+ align:start position:0%
+So now that's bounded by RA a delta to
+the quarter R A projective delta to the
+
+ align:start position:0%
+the quarter R A projective delta to the
+ 
+
+ align:start position:0%
+the quarter R A projective delta to the
+quarter
+
+ align:start position:0%
+quarter
+ 
+
+ align:start position:0%
+quarter
+R A projective
+
+ align:start position:0%
+R A projective
+ 
+
+ align:start position:0%
+R A projective
+delta to the half.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now you can keep going.
+
+ align:start position:0%
+And now you can keep going.
+ 
+
+ align:start position:0%
+And now you can keep going.
+Okay, so you do this many times.
+
+ align:start position:0%
+Okay, so you do this many times.
+ 
+
+ align:start position:0%
+Okay, so you do this many times.
+There'll be a T appendix left here that
+
+ align:start position:0%
+There'll be a T appendix left here that
+ 
+
+ align:start position:0%
+There'll be a T appendix left here that
+is still has no projective on it, but
+
+ align:start position:0%
+is still has no projective on it, but
+ 
+
+ align:start position:0%
+is still has no projective on it, but
+it'll be very minor. And the rest of
+
+ align:start position:0%
+it'll be very minor. And the rest of
+ 
+
+ align:start position:0%
+it'll be very minor. And the rest of
+them all have projective. And so the
+
+ align:start position:0%
+them all have projective. And so the
+ 
+
+ align:start position:0%
+them all have projective. And so the
+conclusion is that to prove the theorem,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it suffices to check the projective
+
+ align:start position:0%
+it suffices to check the projective
+ 
+
+ align:start position:0%
+it suffices to check the projective
+case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's a cute application of being
+
+ align:start position:0%
+So that's a cute application of being
+ 
+
+ align:start position:0%
+So that's a cute application of being
+submitted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So those are a couple of cute
+
+ align:start position:0%
+So those are a couple of cute
+ 
+
+ align:start position:0%
+So those are a couple of cute
+applications of this lama. Yeah.
+
+ align:start position:0%
+applications of this lama. Yeah.
+ 
+
+ align:start position:0%
+applications of this lama. Yeah.
+>> Is that like extra r that kind of went
+
+ align:start position:0%
+>> Is that like extra r that kind of went
+ 
+
+ align:start position:0%
+>> Is that like extra r that kind of went
+over epsilon
+
+ align:start position:0%
+over epsilon
+ 
+
+ align:start position:0%
+over epsilon
+uh kind of where the delta epsilon kind
+
+ align:start position:0%
+uh kind of where the delta epsilon kind
+ 
+
+ align:start position:0%
+uh kind of where the delta epsilon kind
+of error term final or is there as well?
+
+ align:start position:0%
+of error term final or is there as well?
+ 
+
+ align:start position:0%
+of error term final or is there as well?
+>> There are several places where we might
+
+ align:start position:0%
+>> There are several places where we might
+ 
+
+ align:start position:0%
+>> There are several places where we might
+incur a delta to the epsilon in the
+
+ align:start position:0%
+incur a delta to the epsilon in the
+ 
+
+ align:start position:0%
+incur a delta to the epsilon in the
+final thing and this is one of them.
+
+ align:start position:0%
+final thing and this is one of them.
+ 
+
+ align:start position:0%
+final thing and this is one of them.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Okay. Um,
+
+ align:start position:0%
+Okay. Um,
+ 
+
+ align:start position:0%
+Okay. Um,
+so let's say something big picture about
+
+ align:start position:0%
+so let's say something big picture about
+ 
+
+ align:start position:0%
+so let's say something big picture about
+trying to prove this theorem.
+
+ align:start position:0%
+trying to prove this theorem.
+ 
+
+ align:start position:0%
+trying to prove this theorem.
+So we were saying yesterday that for a
+
+ align:start position:0%
+So we were saying yesterday that for a
+ 
+
+ align:start position:0%
+So we were saying yesterday that for a
+while in this subject there were only
+
+ align:start position:0%
+while in this subject there were only
+ 
+
+ align:start position:0%
+while in this subject there were only
+kind of there were only epsilon
+
+ align:start position:0%
+kind of there were only epsilon
+ 
+
+ align:start position:0%
+kind of there were only epsilon
+improvements on some classical things.
+
+ align:start position:0%
+improvements on some classical things.
+ 
+
+ align:start position:0%
+improvements on some classical things.
+And what was very striking to me is to
+
+ align:start position:0%
+And what was very striking to me is to
+ 
+
+ align:start position:0%
+And what was very striking to me is to
+go from just making epsilon improvements
+
+ align:start position:0%
+go from just making epsilon improvements
+ 
+
+ align:start position:0%
+go from just making epsilon improvements
+to go to making to to proving the sharp
+
+ align:start position:0%
+to go to making to to proving the sharp
+ 
+
+ align:start position:0%
+to go to making to to proving the sharp
+theorem.
+
+ align:start position:0%
+theorem.
+ 
+
+ align:start position:0%
+theorem.
+And while Pablush Murkin was visiting, I
+
+ align:start position:0%
+And while Pablush Murkin was visiting, I
+ 
+
+ align:start position:0%
+And while Pablush Murkin was visiting, I
+talked with him a lot about all this
+
+ align:start position:0%
+talked with him a lot about all this
+ 
+
+ align:start position:0%
+talked with him a lot about all this
+stuff. And he said to me something one
+
+ align:start position:0%
+stuff. And he said to me something one
+ 
+
+ align:start position:0%
+stuff. And he said to me something one
+day that really stuck with me. He said
+
+ align:start position:0%
+day that really stuck with me. He said
+ 
+
+ align:start position:0%
+day that really stuck with me. He said
+sort of philosophically.
+
+ align:start position:0%
+sort of philosophically.
+ 
+
+ align:start position:0%
+sort of philosophically.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that here, yeah, here's how I would like
+
+ align:start position:0%
+that here, yeah, here's how I would like
+ 
+
+ align:start position:0%
+that here, yeah, here's how I would like
+to put it. Um
+
+ align:start position:0%
+to put it. Um
+ 
+
+ align:start position:0%
+to put it. Um
+that in order to prove this theorem,
+
+ align:start position:0%
+that in order to prove this theorem,
+ 
+
+ align:start position:0%
+that in order to prove this theorem,
+what we need to do is make an epsilon
+
+ align:start position:0%
+what we need to do is make an epsilon
+ 
+
+ align:start position:0%
+what we need to do is make an epsilon
+improvement on the submicative lema.
+
+ align:start position:0%
+improvement on the submicative lema.
+ 
+
+ align:start position:0%
+improvement on the submicative lema.
+So let me write that down because I
+
+ align:start position:0%
+So let me write that down because I
+ 
+
+ align:start position:0%
+So let me write that down because I
+think it's worth taking with you out of
+
+ align:start position:0%
+think it's worth taking with you out of
+ 
+
+ align:start position:0%
+think it's worth taking with you out of
+this class.
+
+ align:start position:0%
+this class.
+ 
+
+ align:start position:0%
+this class.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+philosophy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to prove the theorem
+
+ align:start position:0%
+to prove the theorem
+ 
+
+ align:start position:0%
+to prove the theorem
+what we need
+
+ align:start position:0%
+what we need
+ 
+
+ align:start position:0%
+what we need
+an epsilon improvement
+
+ align:start position:0%
+an epsilon improvement
+ 
+
+ align:start position:0%
+an epsilon improvement
+on the sub multiplicative length.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So in other words, we'd like to
+
+ align:start position:0%
+Okay. So in other words, we'd like to
+ 
+
+ align:start position:0%
+Okay. So in other words, we'd like to
+say either
+
+ align:start position:0%
+say either
+ 
+
+ align:start position:0%
+say either
+one possibility is that ra a d square
+
+ align:start position:0%
+one possibility is that ra a d square
+ 
+
+ align:start position:0%
+one possibility is that ra a d square
+root of delta is already obeys the
+
+ align:start position:0%
+root of delta is already obeys the
+ 
+
+ align:start position:0%
+root of delta is already obeys the
+bound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Well then we're happy and you know
+
+ align:start position:0%
+Okay. Well then we're happy and you know
+ 
+
+ align:start position:0%
+Okay. Well then we're happy and you know
+by by the sub multiplicative lema our
+
+ align:start position:0%
+by by the sub multiplicative lema our
+ 
+
+ align:start position:0%
+by by the sub multiplicative lema our
+ide of delta also will obey the bound.
+
+ align:start position:0%
+ide of delta also will obey the bound.
+ 
+
+ align:start position:0%
+ide of delta also will obey the bound.
+So we'll be happy
+
+ align:start position:0%
+So we'll be happy
+ 
+
+ align:start position:0%
+So we'll be happy
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+we have so I'll write down the um sub
+
+ align:start position:0%
+we have so I'll write down the um sub
+ 
+
+ align:start position:0%
+we have so I'll write down the um sub
+multiplicative lema.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's the sub multiplicative lema
+
+ align:start position:0%
+So that's the sub multiplicative lema
+ 
+
+ align:start position:0%
+So that's the sub multiplicative lema
+but or we have not not this lema but a
+
+ align:start position:0%
+but or we have not not this lema but a
+ 
+
+ align:start position:0%
+but or we have not not this lema but a
+little tiny improvement on it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so in this case of course we're
+
+ align:start position:0%
+Okay, so in this case of course we're
+ 
+
+ align:start position:0%
+Okay, so in this case of course we're
+happy and in this case we can iterate
+
+ align:start position:0%
+happy and in this case we can iterate
+ 
+
+ align:start position:0%
+happy and in this case we can iterate
+and so you can think of ra of delta as
+
+ align:start position:0%
+and so you can think of ra of delta as
+ 
+
+ align:start position:0%
+and so you can think of ra of delta as
+being some power of delta
+
+ align:start position:0%
+being some power of delta
+ 
+
+ align:start position:0%
+being some power of delta
+and then every time we do this that
+
+ align:start position:0%
+and then every time we do this that
+ 
+
+ align:start position:0%
+and then every time we do this that
+power goes down
+
+ align:start position:0%
+power goes down
+ 
+
+ align:start position:0%
+power goes down
+uh or some negative power of delta.
+
+ align:start position:0%
+uh or some negative power of delta.
+ 
+
+ align:start position:0%
+uh or some negative power of delta.
+Every time we do this, that power is
+
+ align:start position:0%
+Every time we do this, that power is
+ 
+
+ align:start position:0%
+Every time we do this, that power is
+going to go down. Um and um uh and so
+
+ align:start position:0%
+going to go down. Um and um uh and so
+ 
+
+ align:start position:0%
+going to go down. Um and um uh and so
+it'll keep going down until we get into
+
+ align:start position:0%
+it'll keep going down until we get into
+ 
+
+ align:start position:0%
+it'll keep going down until we get into
+this case and we're happy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+so let's illustrate that. So if say we
+
+ align:start position:0%
+so let's illustrate that. So if say we
+ 
+
+ align:start position:0%
+so let's illustrate that. So if say we
+have ra a delta
+
+ align:start position:0%
+have ra a delta
+ 
+
+ align:start position:0%
+have ra a delta
+um let me write it this way be easier as
+
+ align:start position:0%
+um let me write it this way be easier as
+ 
+
+ align:start position:0%
+um let me write it this way be easier as
+delta to the minus gamma then we'd have
+
+ align:start position:0%
+delta to the minus gamma then we'd have
+ 
+
+ align:start position:0%
+delta to the minus gamma then we'd have
+ra a d of delta squared
+
+ align:start position:0%
+ra a d of delta squared
+ 
+
+ align:start position:0%
+ra a d of delta squared
+would be bounded by um so this would
+
+ align:start position:0%
+would be bounded by um so this would
+ 
+
+ align:start position:0%
+would be bounded by um so this would
+give us delta to the minus 2 gamma but
+
+ align:start position:0%
+give us delta to the minus 2 gamma but
+ 
+
+ align:start position:0%
+give us delta to the minus 2 gamma but
+plus epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then we would do this again.
+
+ align:start position:0%
+Then we would do this again.
+ 
+
+ align:start position:0%
+Then we would do this again.
+RA a D delta 4th would be bounded by
+
+ align:start position:0%
+RA a D delta 4th would be bounded by
+ 
+
+ align:start position:0%
+RA a D delta 4th would be bounded by
+delta 4 to the minus gamma plus epsilon
+
+ align:start position:0%
+delta 4 to the minus gamma plus epsilon
+ 
+
+ align:start position:0%
+delta 4 to the minus gamma plus epsilon
+plus epsilon. We keep going and this
+
+ align:start position:0%
+plus epsilon. We keep going and this
+ 
+
+ align:start position:0%
+plus epsilon. We keep going and this
+exponent keeps getting better and better
+
+ align:start position:0%
+exponent keeps getting better and better
+ 
+
+ align:start position:0%
+exponent keeps getting better and better
+until we can't make an epsilon
+
+ align:start position:0%
+until we can't make an epsilon
+ 
+
+ align:start position:0%
+until we can't make an epsilon
+improvement anymore. So if we have this
+
+ align:start position:0%
+improvement anymore. So if we have this
+ 
+
+ align:start position:0%
+improvement anymore. So if we have this
+dichotomy then we can get um the
+
+ align:start position:0%
+dichotomy then we can get um the
+ 
+
+ align:start position:0%
+dichotomy then we can get um the
+theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Cool.
+
+ align:start position:0%
+Cool.
+ 
+
+ align:start position:0%
+Cool.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right. So so then you might reflect
+
+ align:start position:0%
+all right. So so then you might reflect
+ 
+
+ align:start position:0%
+all right. So so then you might reflect
+well you know why is it easier to make
+
+ align:start position:0%
+well you know why is it easier to make
+ 
+
+ align:start position:0%
+well you know why is it easier to make
+an epsilon improvement kind of theorem
+
+ align:start position:0%
+an epsilon improvement kind of theorem
+ 
+
+ align:start position:0%
+an epsilon improvement kind of theorem
+than it is to uh you know prove a really
+
+ align:start position:0%
+than it is to uh you know prove a really
+ 
+
+ align:start position:0%
+than it is to uh you know prove a really
+sharp bound straight out. Well, there's
+
+ align:start position:0%
+sharp bound straight out. Well, there's
+ 
+
+ align:start position:0%
+sharp bound straight out. Well, there's
+a thought process for that. If we have
+
+ align:start position:0%
+a thought process for that. If we have
+ 
+
+ align:start position:0%
+a thought process for that. If we have
+we already have a result and then we
+
+ align:start position:0%
+we already have a result and then we
+ 
+
+ align:start position:0%
+we already have a result and then we
+want to make an epsilon improvement,
+
+ align:start position:0%
+want to make an epsilon improvement,
+ 
+
+ align:start position:0%
+want to make an epsilon improvement,
+then we say to ourselves, you know, what
+
+ align:start position:0%
+then we say to ourselves, you know, what
+ 
+
+ align:start position:0%
+then we say to ourselves, you know, what
+would it look like if the result we have
+
+ align:start position:0%
+would it look like if the result we have
+ 
+
+ align:start position:0%
+would it look like if the result we have
+is sharp
+
+ align:start position:0%
+is sharp
+ 
+
+ align:start position:0%
+is sharp
+and maybe there's a lot of specific
+
+ align:start position:0%
+and maybe there's a lot of specific
+ 
+
+ align:start position:0%
+and maybe there's a lot of specific
+things that have to happen for the
+
+ align:start position:0%
+things that have to happen for the
+ 
+
+ align:start position:0%
+things that have to happen for the
+result we have to be sharp. So, we get a
+
+ align:start position:0%
+result we have to be sharp. So, we get a
+ 
+
+ align:start position:0%
+result we have to be sharp. So, we get a
+lot of structure and then we have then
+
+ align:start position:0%
+lot of structure and then we have then
+ 
+
+ align:start position:0%
+lot of structure and then we have then
+we have to get a contradiction and that
+
+ align:start position:0%
+we have to get a contradiction and that
+ 
+
+ align:start position:0%
+we have to get a contradiction and that
+shows you can do just a little bit
+
+ align:start position:0%
+shows you can do just a little bit
+ 
+
+ align:start position:0%
+shows you can do just a little bit
+better. That's why an epsilon
+
+ align:start position:0%
+better. That's why an epsilon
+ 
+
+ align:start position:0%
+better. That's why an epsilon
+improvement result is is easier than um
+
+ align:start position:0%
+improvement result is is easier than um
+ 
+
+ align:start position:0%
+improvement result is is easier than um
+than just getting a a great balance
+
+ align:start position:0%
+than just getting a a great balance
+ 
+
+ align:start position:0%
+than just getting a a great balance
+straight away. And you know and when we
+
+ align:start position:0%
+straight away. And you know and when we
+ 
+
+ align:start position:0%
+straight away. And you know and when we
+so you know if if we go back to Bans's
+
+ align:start position:0%
+so you know if if we go back to Bans's
+ 
+
+ align:start position:0%
+so you know if if we go back to Bans's
+projection theorem and we tried to make
+
+ align:start position:0%
+projection theorem and we tried to make
+ 
+
+ align:start position:0%
+projection theorem and we tried to make
+you know epsilon improvement in a in a
+
+ align:start position:0%
+you know epsilon improvement in a in a
+ 
+
+ align:start position:0%
+you know epsilon improvement in a in a
+projection theorem well we we didn't say
+
+ align:start position:0%
+projection theorem well we we didn't say
+ 
+
+ align:start position:0%
+projection theorem well we we didn't say
+this at the time but it might have been
+
+ align:start position:0%
+this at the time but it might have been
+ 
+
+ align:start position:0%
+this at the time but it might have been
+good to say you know what would it be
+
+ align:start position:0%
+good to say you know what would it be
+ 
+
+ align:start position:0%
+good to say you know what would it be
+like what would it mean if the bound we
+
+ align:start position:0%
+like what would it mean if the bound we
+ 
+
+ align:start position:0%
+like what would it mean if the bound we
+have so far is sharp would mean we have
+
+ align:start position:0%
+have so far is sharp would mean we have
+ 
+
+ align:start position:0%
+have so far is sharp would mean we have
+this structure and that structure and
+
+ align:start position:0%
+this structure and that structure and
+ 
+
+ align:start position:0%
+this structure and that structure and
+eventually we have this subset that is
+
+ align:start position:0%
+eventually we have this subset that is
+ 
+
+ align:start position:0%
+eventually we have this subset that is
+almost closed under addition and almost
+
+ align:start position:0%
+almost closed under addition and almost
+ 
+
+ align:start position:0%
+almost closed under addition and almost
+closed under multiplication anda d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so the idea is we are going to try
+
+ align:start position:0%
+Okay, so the idea is we are going to try
+ 
+
+ align:start position:0%
+Okay, so the idea is we are going to try
+to do the same thing. We're going to
+
+ align:start position:0%
+to do the same thing. We're going to
+ 
+
+ align:start position:0%
+to do the same thing. We're going to
+think about what would it mean if the
+
+ align:start position:0%
+think about what would it mean if the
+ 
+
+ align:start position:0%
+think about what would it mean if the
+sub multiplicative lema was sharp and
+
+ align:start position:0%
+sub multiplicative lema was sharp and
+ 
+
+ align:start position:0%
+sub multiplicative lema was sharp and
+we're going to see that it just means
+
+ align:start position:0%
+we're going to see that it just means
+ 
+
+ align:start position:0%
+we're going to see that it just means
+the set has to have a lot of structure
+
+ align:start position:0%
+the set has to have a lot of structure
+ 
+
+ align:start position:0%
+the set has to have a lot of structure
+and eventually we'll get down maybe not
+
+ align:start position:0%
+and eventually we'll get down maybe not
+ 
+
+ align:start position:0%
+and eventually we'll get down maybe not
+today but eventually
+
+ align:start position:0%
+today but eventually
+ 
+
+ align:start position:0%
+today but eventually
+orin and smirkin uh got down to to the
+
+ align:start position:0%
+orin and smirkin uh got down to to the
+ 
+
+ align:start position:0%
+orin and smirkin uh got down to to the
+structures got down to the banan
+
+ align:start position:0%
+structures got down to the banan
+ 
+
+ align:start position:0%
+structures got down to the banan
+projection theorem or um and got a
+
+ align:start position:0%
+projection theorem or um and got a
+ 
+
+ align:start position:0%
+projection theorem or um and got a
+contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's talk about what would it mean
+
+ align:start position:0%
+so let's talk about what would it mean
+ 
+
+ align:start position:0%
+so let's talk about what would it mean
+if the sub multiplic Licative llama is
+
+ align:start position:0%
+if the sub multiplic Licative llama is
+ 
+
+ align:start position:0%
+if the sub multiplic Licative llama is
+sharp.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let me draw a couple pictures
+
+ align:start position:0%
+Okay. So let me draw a couple pictures
+ 
+
+ align:start position:0%
+Okay. So let me draw a couple pictures
+for you. And one of the pictures it
+
+ align:start position:0%
+for you. And one of the pictures it
+ 
+
+ align:start position:0%
+for you. And one of the pictures it
+corresponds to the sub multiplicative
+
+ align:start position:0%
+corresponds to the sub multiplicative
+ 
+
+ align:start position:0%
+corresponds to the sub multiplicative
+lamina is sharp and in the other one it
+
+ align:start position:0%
+lamina is sharp and in the other one it
+ 
+
+ align:start position:0%
+lamina is sharp and in the other one it
+it it's not.
+
+ align:start position:0%
+it it's not.
+ 
+
+ align:start position:0%
+it it's not.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll have some fat balls in a fat
+
+ align:start position:0%
+so we'll have some fat balls in a fat
+ 
+
+ align:start position:0%
+so we'll have some fat balls in a fat
+tube.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+then in each fat tube, in each fat ball,
+
+ align:start position:0%
+then in each fat tube, in each fat ball,
+ 
+
+ align:start position:0%
+then in each fat tube, in each fat ball,
+we have some little balls.
+
+ align:start position:0%
+we have some little balls.
+ 
+
+ align:start position:0%
+we have some little balls.
+And the little balls are in little
+
+ align:start position:0%
+And the little balls are in little
+ 
+
+ align:start position:0%
+And the little balls are in little
+tubes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's your typical little tube and
+
+ align:start position:0%
+So there's your typical little tube and
+ 
+
+ align:start position:0%
+So there's your typical little tube and
+okay in each of these balls there are
+
+ align:start position:0%
+okay in each of these balls there are
+ 
+
+ align:start position:0%
+okay in each of these balls there are
+some each of these back balls there are
+
+ align:start position:0%
+some each of these back balls there are
+ 
+
+ align:start position:0%
+some each of these back balls there are
+some little balls.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in the scenario in this picture would
+
+ align:start position:0%
+So in the scenario in this picture would
+ 
+
+ align:start position:0%
+So in the scenario in this picture would
+the sub multiplicative lema be sharp or
+
+ align:start position:0%
+the sub multiplicative lema be sharp or
+ 
+
+ align:start position:0%
+the sub multiplicative lema be sharp or
+not sharp?
+
+ align:start position:0%
+not sharp?
+ 
+
+ align:start position:0%
+not sharp?
+Stand next to the picture
+
+ align:start position:0%
+Stand next to the picture
+ 
+
+ align:start position:0%
+Stand next to the picture
+in this picture. Would the sub
+
+ align:start position:0%
+in this picture. Would the sub
+ 
+
+ align:start position:0%
+in this picture. Would the sub
+multiplicative lema be sharp or not
+
+ align:start position:0%
+multiplicative lema be sharp or not
+ 
+
+ align:start position:0%
+multiplicative lema be sharp or not
+sharp?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't think it's sharp because there's
+
+ align:start position:0%
+I don't think it's sharp because there's
+ 
+
+ align:start position:0%
+I don't think it's sharp because there's
+just one tube for the like coarser
+
+ align:start position:0%
+just one tube for the like coarser
+ 
+
+ align:start position:0%
+just one tube for the like coarser
+scale. that could be consist of several
+
+ align:start position:0%
+scale. that could be consist of several
+ 
+
+ align:start position:0%
+scale. that could be consist of several
+tubes for the fine scale.
+
+ align:start position:0%
+tubes for the fine scale.
+ 
+
+ align:start position:0%
+tubes for the fine scale.
+>> Um, okay. So, let me clarify what this
+
+ align:start position:0%
+>> Um, okay. So, let me clarify what this
+ 
+
+ align:start position:0%
+>> Um, okay. So, let me clarify what this
+is a picture of.
+
+ align:start position:0%
+is a picture of.
+ 
+
+ align:start position:0%
+is a picture of.
+So, so there are many coarse scale
+
+ align:start position:0%
+So, so there are many coarse scale
+ 
+
+ align:start position:0%
+So, so there are many coarse scale
+tubes, but I just drew one of them. And
+
+ align:start position:0%
+tubes, but I just drew one of them. And
+ 
+
+ align:start position:0%
+tubes, but I just drew one of them. And
+I'm just drawing what's happening inside
+
+ align:start position:0%
+I'm just drawing what's happening inside
+ 
+
+ align:start position:0%
+I'm just drawing what's happening inside
+of one of them. So, inside of that one
+
+ align:start position:0%
+of one of them. So, inside of that one
+ 
+
+ align:start position:0%
+of one of them. So, inside of that one
+coarse tube, this is what we see based
+
+ align:start position:0%
+coarse tube, this is what we see based
+ 
+
+ align:start position:0%
+coarse tube, this is what we see based
+on this is the
+
+ align:start position:0%
+on this is the
+ 
+
+ align:start position:0%
+on this is the
+>> So, there's only one fine scale tube. Um
+
+ align:start position:0%
+>> So, there's only one fine scale tube. Um
+ 
+
+ align:start position:0%
+>> So, there's only one fine scale tube. Um
+there could be more fine scale tubes but
+
+ align:start position:0%
+there could be more fine scale tubes but
+ 
+
+ align:start position:0%
+there could be more fine scale tubes but
+this is a typical one. Yes, there are
+
+ align:start position:0%
+this is a typical one. Yes, there are
+ 
+
+ align:start position:0%
+this is a typical one. Yes, there are
+many orange tubes and many red tubes but
+
+ align:start position:0%
+many orange tubes and many red tubes but
+ 
+
+ align:start position:0%
+many orange tubes and many red tubes but
+I'm drawing uh only one of each to
+
+ align:start position:0%
+I'm drawing uh only one of each to
+ 
+
+ align:start position:0%
+I'm drawing uh only one of each to
+direct your to focus our attention.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let's review for a second the
+
+ align:start position:0%
+Okay, so let's review for a second the
+ 
+
+ align:start position:0%
+Okay, so let's review for a second the
+proof of the sub multiplicative lama uh
+
+ align:start position:0%
+proof of the sub multiplicative lama uh
+ 
+
+ align:start position:0%
+proof of the sub multiplicative lama uh
+because it's really important and maybe
+
+ align:start position:0%
+because it's really important and maybe
+ 
+
+ align:start position:0%
+because it's really important and maybe
+it'll go in a little deeper and then
+
+ align:start position:0%
+it'll go in a little deeper and then
+ 
+
+ align:start position:0%
+it'll go in a little deeper and then
+I'll try this again. Okay, so our goal
+
+ align:start position:0%
+I'll try this again. Okay, so our goal
+ 
+
+ align:start position:0%
+I'll try this again. Okay, so our goal
+is to estimate ra of delta, which is the
+
+ align:start position:0%
+is to estimate ra of delta, which is the
+ 
+
+ align:start position:0%
+is to estimate ra of delta, which is the
+number of delta balls per delta tube.
+
+ align:start position:0%
+number of delta balls per delta tube.
+ 
+
+ align:start position:0%
+number of delta balls per delta tube.
+So I picked a delta tube like this red
+
+ align:start position:0%
+So I picked a delta tube like this red
+ 
+
+ align:start position:0%
+So I picked a delta tube like this red
+one here. I I have to estimate the
+
+ align:start position:0%
+one here. I I have to estimate the
+ 
+
+ align:start position:0%
+one here. I I have to estimate the
+number of delta balls in it. First I
+
+ align:start position:0%
+number of delta balls in it. First I
+ 
+
+ align:start position:0%
+number of delta balls in it. First I
+estimate the number of fat balls that it
+
+ align:start position:0%
+estimate the number of fat balls that it
+ 
+
+ align:start position:0%
+estimate the number of fat balls that it
+intersects
+
+ align:start position:0%
+intersects
+ 
+
+ align:start position:0%
+intersects
+and then I multiply that by the number
+
+ align:start position:0%
+and then I multiply that by the number
+ 
+
+ align:start position:0%
+and then I multiply that by the number
+of delta balls that it intersects within
+
+ align:start position:0%
+of delta balls that it intersects within
+ 
+
+ align:start position:0%
+of delta balls that it intersects within
+each fat ball. And that was my bat.
+
+ align:start position:0%
+each fat ball. And that was my bat.
+ 
+
+ align:start position:0%
+each fat ball. And that was my bat.
+And that each one of those things I
+
+ align:start position:0%
+And that each one of those things I
+ 
+
+ align:start position:0%
+And that each one of those things I
+bounded sort of by induction and I got
+
+ align:start position:0%
+bounded sort of by induction and I got
+ 
+
+ align:start position:0%
+bounded sort of by induction and I got
+those two members. All right. So
+
+ align:start position:0%
+those two members. All right. So
+ 
+
+ align:start position:0%
+those two members. All right. So
+if I take a particular fat tube and
+
+ align:start position:0%
+if I take a particular fat tube and
+ 
+
+ align:start position:0%
+if I take a particular fat tube and
+inside of it a particular thin tube and
+
+ align:start position:0%
+inside of it a particular thin tube and
+ 
+
+ align:start position:0%
+inside of it a particular thin tube and
+I see this would that argument be sharp?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. Okay. So so the suggestion is
+
+ align:start position:0%
+Right. Okay. So so the suggestion is
+ 
+
+ align:start position:0%
+Right. Okay. So so the suggestion is
+that this is not sharp because uh inside
+
+ align:start position:0%
+that this is not sharp because uh inside
+ 
+
+ align:start position:0%
+that this is not sharp because uh inside
+of this red tube most of the fat balls
+
+ align:start position:0%
+of this red tube most of the fat balls
+ 
+
+ align:start position:0%
+of this red tube most of the fat balls
+are contributed nothing.
+
+ align:start position:0%
+are contributed nothing.
+ 
+
+ align:start position:0%
+are contributed nothing.
+And only this one fat ball is
+
+ align:start position:0%
+And only this one fat ball is
+ 
+
+ align:start position:0%
+And only this one fat ball is
+contributing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And it would be sharp if the number of
+
+ align:start position:0%
+And it would be sharp if the number of
+ 
+
+ align:start position:0%
+And it would be sharp if the number of
+delta balls in the fat ball was the
+
+ align:start position:0%
+delta balls in the fat ball was the
+ 
+
+ align:start position:0%
+delta balls in the fat ball was the
+number of sorry the number of delta
+
+ align:start position:0%
+number of sorry the number of delta
+ 
+
+ align:start position:0%
+number of sorry the number of delta
+balls in the delta tube was the number
+
+ align:start position:0%
+balls in the delta tube was the number
+ 
+
+ align:start position:0%
+balls in the delta tube was the number
+of fat balls times the number of delta
+
+ align:start position:0%
+of fat balls times the number of delta
+ 
+
+ align:start position:0%
+of fat balls times the number of delta
+balls in one of them. So let me show. So
+
+ align:start position:0%
+balls in one of them. So let me show. So
+ 
+
+ align:start position:0%
+balls in one of them. So let me show. So
+this is not sharp. And let me draw the
+
+ align:start position:0%
+this is not sharp. And let me draw the
+ 
+
+ align:start position:0%
+this is not sharp. And let me draw the
+one that's sharp. You'll see the
+
+ align:start position:0%
+one that's sharp. You'll see the
+ 
+
+ align:start position:0%
+one that's sharp. You'll see the
+difference. This is not sharp.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta tube
+
+ align:start position:0%
+Delta tube
+ 
+
+ align:start position:0%
+Delta tube
+should look like this,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? So the delta tube should
+
+ align:start position:0%
+right? So the delta tube should
+ 
+
+ align:start position:0%
+right? So the delta tube should
+intersect a bunch of fat balls. It
+
+ align:start position:0%
+intersect a bunch of fat balls. It
+ 
+
+ align:start position:0%
+intersect a bunch of fat balls. It
+should intersect that many fat balls as
+
+ align:start position:0%
+should intersect that many fat balls as
+ 
+
+ align:start position:0%
+should intersect that many fat balls as
+many as possible. And inside each one of
+
+ align:start position:0%
+many as possible. And inside each one of
+ 
+
+ align:start position:0%
+many as possible. And inside each one of
+them, it should intersect a lot of delta
+
+ align:start position:0%
+them, it should intersect a lot of delta
+ 
+
+ align:start position:0%
+them, it should intersect a lot of delta
+balls, as many as possible. That's what
+
+ align:start position:0%
+balls, as many as possible. That's what
+ 
+
+ align:start position:0%
+balls, as many as possible. That's what
+it takes for the sub multiplicative lema
+
+ align:start position:0%
+it takes for the sub multiplicative lema
+ 
+
+ align:start position:0%
+it takes for the sub multiplicative lema
+to be sharp.
+
+ align:start position:0%
+to be sharp.
+ 
+
+ align:start position:0%
+to be sharp.
+So it should look like this. So this is
+
+ align:start position:0%
+So it should look like this. So this is
+ 
+
+ align:start position:0%
+So it should look like this. So this is
+sharp.
+
+ align:start position:0%
+sharp.
+ 
+
+ align:start position:0%
+sharp.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a kind of striking picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So
+
+ align:start position:0%
+right. So
+ 
+
+ align:start position:0%
+right. So
+in this ball, these points are in just a
+
+ align:start position:0%
+in this ball, these points are in just a
+ 
+
+ align:start position:0%
+in this ball, these points are in just a
+few tubes in a certain direction. Could
+
+ align:start position:0%
+few tubes in a certain direction. Could
+ 
+
+ align:start position:0%
+few tubes in a certain direction. Could
+also imagine we're in the projective
+
+ align:start position:0%
+also imagine we're in the projective
+ 
+
+ align:start position:0%
+also imagine we're in the projective
+case. And in these other balls, the
+
+ align:start position:0%
+case. And in these other balls, the
+ 
+
+ align:start position:0%
+case. And in these other balls, the
+points are in those same tubes.
+
+ align:start position:0%
+points are in those same tubes.
+ 
+
+ align:start position:0%
+points are in those same tubes.
+Goes all the way across. Of course, the
+
+ align:start position:0%
+Goes all the way across. Of course, the
+ 
+
+ align:start position:0%
+Goes all the way across. Of course, the
+balls don't have to look exactly the
+
+ align:start position:0%
+balls don't have to look exactly the
+ 
+
+ align:start position:0%
+balls don't have to look exactly the
+same as each other. So maybe a better
+
+ align:start position:0%
+same as each other. So maybe a better
+ 
+
+ align:start position:0%
+same as each other. So maybe a better
+picture might be like so.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But the the tubes are exactly the same.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me pause. I'm going to erase a
+
+ align:start position:0%
+let me pause. I'm going to erase a
+ 
+
+ align:start position:0%
+let me pause. I'm going to erase a
+little bit to make some space around
+
+ align:start position:0%
+little bit to make some space around
+ 
+
+ align:start position:0%
+little bit to make some space around
+here. Is that okay with everybody? that
+
+ align:start position:0%
+here. Is that okay with everybody? that
+ 
+
+ align:start position:0%
+here. Is that okay with everybody? that
+if the sub multiplicative lema is sharp,
+
+ align:start position:0%
+if the sub multiplicative lema is sharp,
+ 
+
+ align:start position:0%
+if the sub multiplicative lema is sharp,
+it has to look like this, not like that.
+
+ align:start position:0%
+it has to look like this, not like that.
+ 
+
+ align:start position:0%
+it has to look like this, not like that.
+Okay. All right. So, let's erase around
+
+ align:start position:0%
+Okay. All right. So, let's erase around
+ 
+
+ align:start position:0%
+Okay. All right. So, let's erase around
+here a little bit.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, um we already reduced to the
+
+ align:start position:0%
+Okay. So, um we already reduced to the
+ 
+
+ align:start position:0%
+Okay. So, um we already reduced to the
+projective case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say D is the set of directions
+
+ align:start position:0%
+So let's say D is the set of directions
+ 
+
+ align:start position:0%
+So let's say D is the set of directions
+which is the same everywhere as our
+
+ align:start position:0%
+which is the same everywhere as our
+ 
+
+ align:start position:0%
+which is the same everywhere as our
+projections
+
+ align:start position:0%
+projections
+ 
+
+ align:start position:0%
+projections
+and so D is a delta S set in the circle
+
+ align:start position:0%
+and so D is a delta S set in the circle
+ 
+
+ align:start position:0%
+and so D is a delta S set in the circle
+and here I fixed a typical fat tube. So
+
+ align:start position:0%
+and here I fixed a typical fat tube. So
+ 
+
+ align:start position:0%
+and here I fixed a typical fat tube. So
+here's a typical
+
+ align:start position:0%
+here's a typical
+ 
+
+ align:start position:0%
+here's a typical
+root delta tube.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, and I'm going to look at the angles
+
+ align:start position:0%
+Um, and I'm going to look at the angles
+ 
+
+ align:start position:0%
+Um, and I'm going to look at the angles
+that are within this fat tube.
+
+ align:start position:0%
+that are within this fat tube.
+ 
+
+ align:start position:0%
+that are within this fat tube.
+So, um, so let's say,
+
+ align:start position:0%
+So, um, so let's say,
+ 
+
+ align:start position:0%
+So, um, so let's say,
+so here's our circle and, um, there's a
+
+ align:start position:0%
+so here's our circle and, um, there's a
+ 
+
+ align:start position:0%
+so here's our circle and, um, there's a
+little range of angles here. This is a
+
+ align:start position:0%
+little range of angles here. This is a
+ 
+
+ align:start position:0%
+little range of angles here. This is a
+delta to the here's theta, which is a
+
+ align:start position:0%
+delta to the here's theta, which is a
+ 
+
+ align:start position:0%
+delta to the here's theta, which is a
+delta to the 1/2 arc that corresponds to
+
+ align:start position:0%
+delta to the 1/2 arc that corresponds to
+ 
+
+ align:start position:0%
+delta to the 1/2 arc that corresponds to
+the that tube.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um okay
+
+ align:start position:0%
+Um okay
+ 
+
+ align:start position:0%
+Um okay
+and so D is some delta set delta SC set
+
+ align:start position:0%
+and so D is some delta set delta SC set
+ 
+
+ align:start position:0%
+and so D is some delta set delta SC set
+in here and let's say that C is D
+
+ align:start position:0%
+in here and let's say that C is D
+ 
+
+ align:start position:0%
+in here and let's say that C is D
+intersected with theta. So it's just
+
+ align:start position:0%
+intersected with theta. So it's just
+ 
+
+ align:start position:0%
+intersected with theta. So it's just
+these directions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um so
+
+ align:start position:0%
+Um so
+ 
+
+ align:start position:0%
+Um so
+so the red tubes correspond to one of
+
+ align:start position:0%
+so the red tubes correspond to one of
+ 
+
+ align:start position:0%
+so the red tubes correspond to one of
+the directions in theta. So this one
+
+ align:start position:0%
+the directions in theta. So this one
+ 
+
+ align:start position:0%
+the directions in theta. So this one
+there red tube.
+
+ align:start position:0%
+there red tube.
+ 
+
+ align:start position:0%
+there red tube.
+And um so when I project the set in the
+
+ align:start position:0%
+And um so when I project the set in the
+ 
+
+ align:start position:0%
+And um so when I project the set in the
+red direction, I just get a small set.
+
+ align:start position:0%
+red direction, I just get a small set.
+ 
+
+ align:start position:0%
+red direction, I just get a small set.
+But it's not just the red direction. I
+
+ align:start position:0%
+But it's not just the red direction. I
+ 
+
+ align:start position:0%
+But it's not just the red direction. I
+could draw some other directions inside
+
+ align:start position:0%
+could draw some other directions inside
+ 
+
+ align:start position:0%
+could draw some other directions inside
+of the tube also. Let me do one more.
+
+ align:start position:0%
+of the tube also. Let me do one more.
+ 
+
+ align:start position:0%
+of the tube also. Let me do one more.
+I'll take here a blue direction inside
+
+ align:start position:0%
+I'll take here a blue direction inside
+ 
+
+ align:start position:0%
+I'll take here a blue direction inside
+of here.
+
+ align:start position:0%
+of here.
+ 
+
+ align:start position:0%
+of here.
+So I draw the tubes in the blue
+
+ align:start position:0%
+So I draw the tubes in the blue
+ 
+
+ align:start position:0%
+So I draw the tubes in the blue
+direction. What would it look like? I
+
+ align:start position:0%
+direction. What would it look like? I
+ 
+
+ align:start position:0%
+direction. What would it look like? I
+think I need to make this picture come
+
+ align:start position:0%
+think I need to make this picture come
+ 
+
+ align:start position:0%
+think I need to make this picture come
+out nicely. I need to add a few more
+
+ align:start position:0%
+out nicely. I need to add a few more
+ 
+
+ align:start position:0%
+out nicely. I need to add a few more
+points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then so there'll be one more red
+
+ align:start position:0%
+And then so there'll be one more red
+ 
+
+ align:start position:0%
+And then so there'll be one more red
+tube.
+
+ align:start position:0%
+tube.
+ 
+
+ align:start position:0%
+tube.
+Oops.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now I'll draw a typical blue tube.
+
+ align:start position:0%
+And now I'll draw a typical blue tube.
+ 
+
+ align:start position:0%
+And now I'll draw a typical blue tube.
+The blue tube also manages to intersect
+
+ align:start position:0%
+The blue tube also manages to intersect
+ 
+
+ align:start position:0%
+The blue tube also manages to intersect
+our points a lot. So it should look sort
+
+ align:start position:0%
+our points a lot. So it should look sort
+ 
+
+ align:start position:0%
+our points a lot. So it should look sort
+of like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I don't think I can draw anymore
+
+ align:start position:0%
+Okay, I don't think I can draw anymore
+ 
+
+ align:start position:0%
+Okay, I don't think I can draw anymore
+without making a complete mess, but get
+
+ align:start position:0%
+without making a complete mess, but get
+ 
+
+ align:start position:0%
+without making a complete mess, but get
+the idea.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the blue tube passes through all
+
+ align:start position:0%
+So the blue tube passes through all
+ 
+
+ align:start position:0%
+So the blue tube passes through all
+these balls also. And each time the blue
+
+ align:start position:0%
+these balls also. And each time the blue
+ 
+
+ align:start position:0%
+these balls also. And each time the blue
+tube passes through a ball, it manages
+
+ align:start position:0%
+tube passes through a ball, it manages
+ 
+
+ align:start position:0%
+tube passes through a ball, it manages
+to line up with one of the red tubes.
+
+ align:start position:0%
+to line up with one of the red tubes.
+ 
+
+ align:start position:0%
+to line up with one of the red tubes.
+All right. Okay.
+
+ align:start position:0%
+All right. Okay.
+ 
+
+ align:start position:0%
+All right. Okay.
+So, we have a kind of special situation
+
+ align:start position:0%
+So, we have a kind of special situation
+ 
+
+ align:start position:0%
+So, we have a kind of special situation
+here with a product structure.
+
+ align:start position:0%
+here with a product structure.
+ 
+
+ align:start position:0%
+here with a product structure.
+So, what is our set? Um, so let's say
+
+ align:start position:0%
+So, what is our set? Um, so let's say
+ 
+
+ align:start position:0%
+So, what is our set? Um, so let's say
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+these dots this the projection in the
+
+ align:start position:0%
+these dots this the projection in the
+ 
+
+ align:start position:0%
+these dots this the projection in the
+red direction. Let's call this A.
+
+ align:start position:0%
+red direction. Let's call this A.
+ 
+
+ align:start position:0%
+red direction. Let's call this A.
+And then um down here we can make a set
+
+ align:start position:0%
+And then um down here we can make a set
+ 
+
+ align:start position:0%
+And then um down here we can make a set
+that illustrates where the fat balls are
+
+ align:start position:0%
+that illustrates where the fat balls are
+ 
+
+ align:start position:0%
+that illustrates where the fat balls are
+in the fat tube. Let's call that B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so what we see is that for every C
+
+ align:start position:0%
+And so what we see is that for every C
+ 
+
+ align:start position:0%
+And so what we see is that for every C
+in C
+
+ align:start position:0%
+in C
+ 
+
+ align:start position:0%
+in C
+the projection
+
+ align:start position:0%
+the projection
+ 
+
+ align:start position:0%
+the projection
+uh in the C direction or I'll write it
+
+ align:start position:0%
+uh in the C direction or I'll write it
+ 
+
+ align:start position:0%
+uh in the C direction or I'll write it
+this way. A + C B that's the projection
+
+ align:start position:0%
+this way. A + C B that's the projection
+ 
+
+ align:start position:0%
+this way. A + C B that's the projection
+in the C direction
+
+ align:start position:0%
+in the C direction
+ 
+
+ align:start position:0%
+in the C direction
+is not much bigger than A.
+
+ align:start position:0%
+is not much bigger than A.
+ 
+
+ align:start position:0%
+is not much bigger than A.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+the you know the projection in every one
+
+ align:start position:0%
+the you know the projection in every one
+ 
+
+ align:start position:0%
+the you know the projection in every one
+of these directions is small. They're
+
+ align:start position:0%
+of these directions is small. They're
+ 
+
+ align:start position:0%
+of these directions is small. They're
+all about the same as each other. A was
+
+ align:start position:0%
+all about the same as each other. A was
+ 
+
+ align:start position:0%
+all about the same as each other. A was
+the projection in the red direction. B
+
+ align:start position:0%
+the projection in the red direction. B
+ 
+
+ align:start position:0%
+the projection in the red direction. B
+the blue one is just as good. So A plus
+
+ align:start position:0%
+the blue one is just as good. So A plus
+ 
+
+ align:start position:0%
+the blue one is just as good. So A plus
+CB should be not much bigger than A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let me summarize what we have
+
+ align:start position:0%
+Okay. So, let me summarize what we have
+ 
+
+ align:start position:0%
+Okay. So, let me summarize what we have
+seen here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+f sub multiplicative lama
+
+ align:start position:0%
+f sub multiplicative lama
+ 
+
+ align:start position:0%
+f sub multiplicative lama
+is sharp.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we get sets A and B and C which are
+
+ align:start position:0%
+we get sets A and B and C which are
+ 
+
+ align:start position:0%
+we get sets A and B and C which are
+subsets of real numbers.
+
+ align:start position:0%
+subsets of real numbers.
+ 
+
+ align:start position:0%
+subsets of real numbers.
+And in the main case,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is a delta a a set.
+
+ align:start position:0%
+a is a delta a a set.
+ 
+
+ align:start position:0%
+a is a delta a a set.
+Well, it's a row a set. Uh size of a is
+
+ align:start position:0%
+Well, it's a row a set. Uh size of a is
+ 
+
+ align:start position:0%
+Well, it's a row a set. Uh size of a is
+like row to the minus a.
+
+ align:start position:0%
+like row to the minus a.
+ 
+
+ align:start position:0%
+like row to the minus a.
+B is a row B set. Size of B is like row
+
+ align:start position:0%
+B is a row B set. Size of B is like row
+ 
+
+ align:start position:0%
+B is a row B set. Size of B is like row
+to the minus B. C is a row C set.
+
+ align:start position:0%
+to the minus B. C is a row C set.
+ 
+
+ align:start position:0%
+to the minus B. C is a row C set.
+size of C is like row to the minus C.
+
+ align:start position:0%
+size of C is like row to the minus C.
+ 
+
+ align:start position:0%
+size of C is like row to the minus C.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+for every C in C,
+
+ align:start position:0%
+for every C in C,
+ 
+
+ align:start position:0%
+for every C in C,
+A + CB is not very much bigger than A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now, the size of A and B and C can
+
+ align:start position:0%
+Okay. Now, the size of A and B and C can
+ 
+
+ align:start position:0%
+Okay. Now, the size of A and B and C can
+all be traced back to the numbers in our
+
+ align:start position:0%
+all be traced back to the numbers in our
+ 
+
+ align:start position:0%
+all be traced back to the numbers in our
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+Um and
+
+ align:start position:0%
+Um and
+ 
+
+ align:start position:0%
+Um and
+we find that if uh
+
+ align:start position:0%
+we find that if uh
+ 
+
+ align:start position:0%
+we find that if uh
+if a is smaller than b + c that's
+
+ align:start position:0%
+if a is smaller than b + c that's
+ 
+
+ align:start position:0%
+if a is smaller than b + c that's
+equivalent to saying that ra a d square
+
+ align:start position:0%
+equivalent to saying that ra a d square
+ 
+
+ align:start position:0%
+equivalent to saying that ra a d square
+root of delta is good
+
+ align:start position:0%
+root of delta is good
+ 
+
+ align:start position:0%
+root of delta is good
+a sorry if a is larger than b plus c
+
+ align:start position:0%
+a sorry if a is larger than b plus c
+ 
+
+ align:start position:0%
+a sorry if a is larger than b plus c
+then that means you do a boring
+
+ align:start position:0%
+then that means you do a boring
+ 
+
+ align:start position:0%
+then that means you do a boring
+computation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so there's a
+
+ align:start position:0%
+Um so there's a
+ 
+
+ align:start position:0%
+Um so there's a
+intermediate result maybe I'll call it a
+
+ align:start position:0%
+intermediate result maybe I'll call it a
+ 
+
+ align:start position:0%
+intermediate result maybe I'll call it a
+key lema which is called the ABC sum
+
+ align:start position:0%
+key lema which is called the ABC sum
+ 
+
+ align:start position:0%
+key lema which is called the ABC sum
+product lema
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is goes into this paper of open
+
+ align:start position:0%
+which is goes into this paper of open
+ 
+
+ align:start position:0%
+which is goes into this paper of open
+schwarin. Uh, and it says if you have
+
+ align:start position:0%
+schwarin. Uh, and it says if you have
+ 
+
+ align:start position:0%
+schwarin. Uh, and it says if you have
+all of this stuff, um, then indeed a is
+
+ align:start position:0%
+all of this stuff, um, then indeed a is
+ 
+
+ align:start position:0%
+all of this stuff, um, then indeed a is
+bigger than b + c.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let's yeah,
+
+ align:start position:0%
+Okay, let's yeah,
+ 
+
+ align:start position:0%
+Okay, let's yeah,
+>> good means that it obeys the theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so the theorem's up there. So smaller
+
+ align:start position:0%
+Um so the theorem's up there. So smaller
+ 
+
+ align:start position:0%
+Um so the theorem's up there. So smaller
+than the maximum of one and
+
+ align:start position:0%
+than the maximum of one and
+ 
+
+ align:start position:0%
+than the maximum of one and
+root delta to the minus t / 2 + s / 2
+
+ align:start position:0%
+root delta to the minus t / 2 + s / 2
+ 
+
+ align:start position:0%
+root delta to the minus t / 2 + s / 2
+and root delta to the 1us t.
+
+ align:start position:0%
+and root delta to the 1us t.
+ 
+
+ align:start position:0%
+and root delta to the 1us t.
+So if if that's the case, we're we're
+
+ align:start position:0%
+So if if that's the case, we're we're
+ 
+
+ align:start position:0%
+So if if that's the case, we're we're
+happy. And otherwise uh yeah. Okay.
+
+ align:start position:0%
+happy. And otherwise uh yeah. Okay.
+ 
+
+ align:start position:0%
+happy. And otherwise uh yeah. Okay.
+Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's go back to our general
+
+ align:start position:0%
+Okay. So, let's go back to our general
+ 
+
+ align:start position:0%
+Okay. So, let's go back to our general
+strategy, our big our big picture
+
+ align:start position:0%
+strategy, our big our big picture
+ 
+
+ align:start position:0%
+strategy, our big our big picture
+strategy. We'd like to prove this
+
+ align:start position:0%
+strategy. We'd like to prove this
+ 
+
+ align:start position:0%
+strategy. We'd like to prove this
+theorem that RA of delta is always
+
+ align:start position:0%
+theorem that RA of delta is always
+ 
+
+ align:start position:0%
+theorem that RA of delta is always
+smaller than that.
+
+ align:start position:0%
+smaller than that.
+ 
+
+ align:start position:0%
+smaller than that.
+And we consider the sub multiplicative
+
+ align:start position:0%
+And we consider the sub multiplicative
+ 
+
+ align:start position:0%
+And we consider the sub multiplicative
+limit which doesn't give us the theorem
+
+ align:start position:0%
+limit which doesn't give us the theorem
+ 
+
+ align:start position:0%
+limit which doesn't give us the theorem
+yet, but it's an important tool.
+
+ align:start position:0%
+yet, but it's an important tool.
+ 
+
+ align:start position:0%
+yet, but it's an important tool.
+And we'd like to say
+
+ align:start position:0%
+And we'd like to say
+ 
+
+ align:start position:0%
+And we'd like to say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if if the if we can have an epsilon
+
+ align:start position:0%
+if if the if we can have an epsilon
+ 
+
+ align:start position:0%
+if if the if we can have an epsilon
+improvement in the sub multiplicative
+
+ align:start position:0%
+improvement in the sub multiplicative
+ 
+
+ align:start position:0%
+improvement in the sub multiplicative
+lema then that's great. We go to the
+
+ align:start position:0%
+lema then that's great. We go to the
+ 
+
+ align:start position:0%
+lema then that's great. We go to the
+next scale and we have a better bound.
+
+ align:start position:0%
+next scale and we have a better bound.
+ 
+
+ align:start position:0%
+next scale and we have a better bound.
+So you keep doing that until you stop
+
+ align:start position:0%
+So you keep doing that until you stop
+ 
+
+ align:start position:0%
+So you keep doing that until you stop
+and we must stop in a situation where
+
+ align:start position:0%
+and we must stop in a situation where
+ 
+
+ align:start position:0%
+and we must stop in a situation where
+there's no more where the sub
+
+ align:start position:0%
+there's no more where the sub
+ 
+
+ align:start position:0%
+there's no more where the sub
+multiplicative lema becomes sharp.
+
+ align:start position:0%
+multiplicative lema becomes sharp.
+ 
+
+ align:start position:0%
+multiplicative lema becomes sharp.
+And maybe that's a better way to say it.
+
+ align:start position:0%
+And maybe that's a better way to say it.
+ 
+
+ align:start position:0%
+And maybe that's a better way to say it.
+We have the sub multiplicative lama. we
+
+ align:start position:0%
+We have the sub multiplicative lama. we
+ 
+
+ align:start position:0%
+We have the sub multiplicative lama. we
+use it. It's either sharp or it's not.
+
+ align:start position:0%
+use it. It's either sharp or it's not.
+ 
+
+ align:start position:0%
+use it. It's either sharp or it's not.
+If it's not, we get a, you know, a nicer
+
+ align:start position:0%
+If it's not, we get a, you know, a nicer
+ 
+
+ align:start position:0%
+If it's not, we get a, you know, a nicer
+exponent at at delta squared than we did
+
+ align:start position:0%
+exponent at at delta squared than we did
+ 
+
+ align:start position:0%
+exponent at at delta squared than we did
+at delta. We keep doing that and the
+
+ align:start position:0%
+at delta. We keep doing that and the
+ 
+
+ align:start position:0%
+at delta. We keep doing that and the
+exponent is not going to keep getting
+
+ align:start position:0%
+exponent is not going to keep getting
+ 
+
+ align:start position:0%
+exponent is not going to keep getting
+better forever. So, we stop at some
+
+ align:start position:0%
+better forever. So, we stop at some
+ 
+
+ align:start position:0%
+better forever. So, we stop at some
+moment where the sub multiplicative lama
+
+ align:start position:0%
+moment where the sub multiplicative lama
+ 
+
+ align:start position:0%
+moment where the sub multiplicative lama
+is basically sharp.
+
+ align:start position:0%
+is basically sharp.
+ 
+
+ align:start position:0%
+is basically sharp.
+But the fact that the sub multiplicative
+
+ align:start position:0%
+But the fact that the sub multiplicative
+ 
+
+ align:start position:0%
+But the fact that the sub multiplicative
+lama is sharp gives us a lot of
+
+ align:start position:0%
+lama is sharp gives us a lot of
+ 
+
+ align:start position:0%
+lama is sharp gives us a lot of
+structure. It gives us uh the structure
+
+ align:start position:0%
+structure. It gives us uh the structure
+ 
+
+ align:start position:0%
+structure. It gives us uh the structure
+of being projective
+
+ align:start position:0%
+of being projective
+ 
+
+ align:start position:0%
+of being projective
+and it gives us this kind of product
+
+ align:start position:0%
+and it gives us this kind of product
+ 
+
+ align:start position:0%
+and it gives us this kind of product
+structure and it leads us to this
+
+ align:start position:0%
+structure and it leads us to this
+ 
+
+ align:start position:0%
+structure and it leads us to this
+problem which looks a lot like additive
+
+ align:start position:0%
+problem which looks a lot like additive
+ 
+
+ align:start position:0%
+problem which looks a lot like additive
+combinotaurics and which is very special
+
+ align:start position:0%
+combinotaurics and which is very special
+ 
+
+ align:start position:0%
+combinotaurics and which is very special
+problem compared to our original setup.
+
+ align:start position:0%
+problem compared to our original setup.
+ 
+
+ align:start position:0%
+problem compared to our original setup.
+Um okay and then the bound we need to
+
+ align:start position:0%
+Um okay and then the bound we need to
+ 
+
+ align:start position:0%
+Um okay and then the bound we need to
+prove for this problem if you just
+
+ align:start position:0%
+prove for this problem if you just
+ 
+
+ align:start position:0%
+prove for this problem if you just
+unwind the computation we need to prove
+
+ align:start position:0%
+unwind the computation we need to prove
+ 
+
+ align:start position:0%
+unwind the computation we need to prove
+this bound for this problem and if you
+
+ align:start position:0%
+this bound for this problem and if you
+ 
+
+ align:start position:0%
+this bound for this problem and if you
+unwind it it will tell us that um that
+
+ align:start position:0%
+unwind it it will tell us that um that
+ 
+
+ align:start position:0%
+unwind it it will tell us that um that
+ra obeys the desired bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah row I guess row is also row here is
+
+ align:start position:0%
+yeah row I guess row is also row here is
+ 
+
+ align:start position:0%
+yeah row I guess row is also row here is
+square root of delta
+
+ align:start position:0%
+square root of delta
+ 
+
+ align:start position:0%
+square root of delta
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. So this situation
+
+ align:start position:0%
+Okay. So this situation
+ 
+
+ align:start position:0%
+Okay. So this situation
+is now a lot more structured than what
+
+ align:start position:0%
+is now a lot more structured than what
+ 
+
+ align:start position:0%
+is now a lot more structured than what
+we started with and it looks reminiscent
+
+ align:start position:0%
+we started with and it looks reminiscent
+ 
+
+ align:start position:0%
+we started with and it looks reminiscent
+of uh additive cominatorics maybe of
+
+ align:start position:0%
+of uh additive cominatorics maybe of
+ 
+
+ align:start position:0%
+of uh additive cominatorics maybe of
+brian projection theorem and so on and
+
+ align:start position:0%
+brian projection theorem and so on and
+ 
+
+ align:start position:0%
+brian projection theorem and so on and
+indeed they were able to deal with it
+
+ align:start position:0%
+indeed they were able to deal with it
+ 
+
+ align:start position:0%
+indeed they were able to deal with it
+with that toolkit.
+
+ align:start position:0%
+with that toolkit.
+ 
+
+ align:start position:0%
+with that toolkit.
+I could say a little I don't I don't
+
+ align:start position:0%
+I could say a little I don't I don't
+ 
+
+ align:start position:0%
+I could say a little I don't I don't
+want to write too many equations so I
+
+ align:start position:0%
+want to write too many equations so I
+ 
+
+ align:start position:0%
+want to write too many equations so I
+won't say the whole thing. I could say a
+
+ align:start position:0%
+won't say the whole thing. I could say a
+ 
+
+ align:start position:0%
+won't say the whole thing. I could say a
+little bit about it. Um, but I I think
+
+ align:start position:0%
+little bit about it. Um, but I I think
+ 
+
+ align:start position:0%
+little bit about it. Um, but I I think
+that what we've done so far is what what
+
+ align:start position:0%
+that what we've done so far is what what
+ 
+
+ align:start position:0%
+that what we've done so far is what what
+I feel is most worth remembering about
+
+ align:start position:0%
+I feel is most worth remembering about
+ 
+
+ align:start position:0%
+I feel is most worth remembering about
+the proof of this theorem. So, let's
+
+ align:start position:0%
+the proof of this theorem. So, let's
+ 
+
+ align:start position:0%
+the proof of this theorem. So, let's
+pause here and see if people have any
+
+ align:start position:0%
+pause here and see if people have any
+ 
+
+ align:start position:0%
+pause here and see if people have any
+questions or comments about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me let me summarize it.
+
+ align:start position:0%
+Let me let me summarize it.
+ 
+
+ align:start position:0%
+Let me let me summarize it.
+So the ad regular case is special
+
+ align:start position:0%
+So the ad regular case is special
+ 
+
+ align:start position:0%
+So the ad regular case is special
+because all the scales are related to
+
+ align:start position:0%
+because all the scales are related to
+ 
+
+ align:start position:0%
+because all the scales are related to
+each other and so we can break it up
+
+ align:start position:0%
+each other and so we can break it up
+ 
+
+ align:start position:0%
+each other and so we can break it up
+into problems at different scales and
+
+ align:start position:0%
+into problems at different scales and
+ 
+
+ align:start position:0%
+into problems at different scales and
+put them together. And by doing that we
+
+ align:start position:0%
+put them together. And by doing that we
+ 
+
+ align:start position:0%
+put them together. And by doing that we
+get problems that are somewhat nicer. So
+
+ align:start position:0%
+get problems that are somewhat nicer. So
+ 
+
+ align:start position:0%
+get problems that are somewhat nicer. So
+first of all if we look at the problem
+
+ align:start position:0%
+first of all if we look at the problem
+ 
+
+ align:start position:0%
+first of all if we look at the problem
+in a small ball instead of the original
+
+ align:start position:0%
+in a small ball instead of the original
+ 
+
+ align:start position:0%
+in a small ball instead of the original
+problem it becomes nicer because the
+
+ align:start position:0%
+problem it becomes nicer because the
+ 
+
+ align:start position:0%
+problem it becomes nicer because the
+directions through any point are the
+
+ align:start position:0%
+directions through any point are the
+ 
+
+ align:start position:0%
+directions through any point are the
+same for any two points. the directions
+
+ align:start position:0%
+same for any two points. the directions
+ 
+
+ align:start position:0%
+same for any two points. the directions
+are the same because they correspond to
+
+ align:start position:0%
+are the same because they correspond to
+ 
+
+ align:start position:0%
+are the same because they correspond to
+the directions of the fat tube through
+
+ align:start position:0%
+the directions of the fat tube through
+ 
+
+ align:start position:0%
+the directions of the fat tube through
+there. So this already made it a little
+
+ align:start position:0%
+there. So this already made it a little
+ 
+
+ align:start position:0%
+there. So this already made it a little
+bit nicer.
+
+ align:start position:0%
+bit nicer.
+ 
+
+ align:start position:0%
+bit nicer.
+Then moreover in order for the sub
+
+ align:start position:0%
+Then moreover in order for the sub
+ 
+
+ align:start position:0%
+Then moreover in order for the sub
+multiplicative lema to be sharp. So if
+
+ align:start position:0%
+multiplicative lema to be sharp. So if
+ 
+
+ align:start position:0%
+multiplicative lema to be sharp. So if
+the sub multiplicative lema is not sharp
+
+ align:start position:0%
+the sub multiplicative lema is not sharp
+ 
+
+ align:start position:0%
+the sub multiplicative lema is not sharp
+then you just keep going down scales and
+
+ align:start position:0%
+then you just keep going down scales and
+ 
+
+ align:start position:0%
+then you just keep going down scales and
+you keep getting better exponents and
+
+ align:start position:0%
+you keep getting better exponents and
+ 
+
+ align:start position:0%
+you keep getting better exponents and
+eventually that has to stop when the sub
+
+ align:start position:0%
+eventually that has to stop when the sub
+ 
+
+ align:start position:0%
+eventually that has to stop when the sub
+multiplicative lema is sharp. when the
+
+ align:start position:0%
+multiplicative lema is sharp. when the
+ 
+
+ align:start position:0%
+multiplicative lema is sharp. when the
+sub multiplicative lema is sharp,
+
+ align:start position:0%
+sub multiplicative lema is sharp,
+ 
+
+ align:start position:0%
+sub multiplicative lema is sharp,
+there's even more structure because
+
+ align:start position:0%
+there's even more structure because
+ 
+
+ align:start position:0%
+there's even more structure because
+these different balls have to talk to
+
+ align:start position:0%
+these different balls have to talk to
+ 
+
+ align:start position:0%
+these different balls have to talk to
+each other. Um, and so if you know
+
+ align:start position:0%
+each other. Um, and so if you know
+ 
+
+ align:start position:0%
+each other. Um, and so if you know
+there's a if if you see in this ball,
+
+ align:start position:0%
+there's a if if you see in this ball,
+ 
+
+ align:start position:0%
+there's a if if you see in this ball,
+you see a tube here, then you have to
+
+ align:start position:0%
+you see a tube here, then you have to
+ 
+
+ align:start position:0%
+you see a tube here, then you have to
+see a tube in the same place in that
+
+ align:start position:0%
+see a tube in the same place in that
+ 
+
+ align:start position:0%
+see a tube in the same place in that
+ball.
+
+ align:start position:0%
+ball.
+ 
+
+ align:start position:0%
+ball.
+Um, and that means that this set of
+
+ align:start position:0%
+Um, and that means that this set of
+ 
+
+ align:start position:0%
+Um, and that means that this set of
+points has kind of a product structure.
+
+ align:start position:0%
+points has kind of a product structure.
+ 
+
+ align:start position:0%
+points has kind of a product structure.
+And in particular if you what what's
+
+ align:start position:0%
+And in particular if you what what's
+ 
+
+ align:start position:0%
+And in particular if you what what's
+literally true is that if you take this
+
+ align:start position:0%
+literally true is that if you take this
+ 
+
+ align:start position:0%
+literally true is that if you take this
+uh well anyway so if you if you take the
+
+ align:start position:0%
+uh well anyway so if you if you take the
+ 
+
+ align:start position:0%
+uh well anyway so if you if you take the
+set of red tubes in this ball and then
+
+ align:start position:0%
+set of red tubes in this ball and then
+ 
+
+ align:start position:0%
+set of red tubes in this ball and then
+in this ball and then in this ball that
+
+ align:start position:0%
+in this ball and then in this ball that
+ 
+
+ align:start position:0%
+in this ball and then in this ball that
+is a product which is very helpful.
+
+ align:start position:0%
+is a product which is very helpful.
+ 
+
+ align:start position:0%
+is a product which is very helpful.
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+cool. So,
+
+ align:start position:0%
+cool. So,
+ 
+
+ align:start position:0%
+cool. So,
+so the the the ad regular case allows us
+
+ align:start position:0%
+so the the the ad regular case allows us
+ 
+
+ align:start position:0%
+so the the the ad regular case allows us
+to restrict to a situation which has a
+
+ align:start position:0%
+to restrict to a situation which has a
+ 
+
+ align:start position:0%
+to restrict to a situation which has a
+lot more structure and uh it restricts
+
+ align:start position:0%
+lot more structure and uh it restricts
+ 
+
+ align:start position:0%
+lot more structure and uh it restricts
+to to to this lema about projections of
+
+ align:start position:0%
+to to to this lema about projections of
+ 
+
+ align:start position:0%
+to to to this lema about projections of
+a product set.
+
+ align:start position:0%
+a product set.
+ 
+
+ align:start position:0%
+a product set.
+>> Okay. Yeah. Um, so the argument like can
+
+ align:start position:0%
+>> Okay. Yeah. Um, so the argument like can
+ 
+
+ align:start position:0%
+>> Okay. Yeah. Um, so the argument like can
+continue sort of until the
+
+ align:start position:0%
+continue sort of until the
+ 
+
+ align:start position:0%
+continue sort of until the
+more is sharp. How do you know that kind
+
+ align:start position:0%
+more is sharp. How do you know that kind
+ 
+
+ align:start position:0%
+more is sharp. How do you know that kind
+of sharpness corresponds to kind of the
+
+ align:start position:0%
+of sharpness corresponds to kind of the
+ 
+
+ align:start position:0%
+of sharpness corresponds to kind of the
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+delta to the epsilon factor rather than
+
+ align:start position:0%
+delta to the epsilon factor rather than
+ 
+
+ align:start position:0%
+delta to the epsilon factor rather than
+just kind of something much smaller?
+
+ align:start position:0%
+just kind of something much smaller?
+ 
+
+ align:start position:0%
+just kind of something much smaller?
+It's seems like I don't I don't
+
+ align:start position:0%
+It's seems like I don't I don't
+ 
+
+ align:start position:0%
+It's seems like I don't I don't
+understand how to kind of get a
+
+ align:start position:0%
+understand how to kind of get a
+ 
+
+ align:start position:0%
+understand how to kind of get a
+quantitative bound kind of a more
+
+ align:start position:0%
+quantitative bound kind of a more
+ 
+
+ align:start position:0%
+quantitative bound kind of a more
+qualitative proof by contradiction.
+
+ align:start position:0%
+qualitative proof by contradiction.
+ 
+
+ align:start position:0%
+qualitative proof by contradiction.
+>> Yeah. Okay. Okay. So the quest this
+
+ align:start position:0%
+>> Yeah. Okay. Okay. So the quest this
+ 
+
+ align:start position:0%
+>> Yeah. Okay. Okay. So the quest this
+question is about keeping track of the
+
+ align:start position:0%
+question is about keeping track of the
+ 
+
+ align:start position:0%
+question is about keeping track of the
+small parameters. So every time I apply
+
+ align:start position:0%
+small parameters. So every time I apply
+ 
+
+ align:start position:0%
+small parameters. So every time I apply
+the sub multiplicative lema
+
+ align:start position:0%
+the sub multiplicative lema
+ 
+
+ align:start position:0%
+the sub multiplicative lema
+I was using the word sharp or not sharp
+
+ align:start position:0%
+I was using the word sharp or not sharp
+ 
+
+ align:start position:0%
+I was using the word sharp or not sharp
+but of course there's some kind of a
+
+ align:start position:0%
+but of course there's some kind of a
+ 
+
+ align:start position:0%
+but of course there's some kind of a
+gray zone and I have to decide where I'm
+
+ align:start position:0%
+gray zone and I have to decide where I'm
+ 
+
+ align:start position:0%
+gray zone and I have to decide where I'm
+going to cut how how what am I going to
+
+ align:start position:0%
+going to cut how how what am I going to
+ 
+
+ align:start position:0%
+going to cut how how what am I going to
+consider to be sharp and what is not
+
+ align:start position:0%
+consider to be sharp and what is not
+ 
+
+ align:start position:0%
+consider to be sharp and what is not
+sharp. Um and um then
+
+ align:start position:0%
+sharp. Um and um then
+ 
+
+ align:start position:0%
+sharp. Um and um then
+in this analysis um
+
+ align:start position:0%
+in this analysis um
+ 
+
+ align:start position:0%
+in this analysis um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um yeah okay so so actually so in in
+
+ align:start position:0%
+um yeah okay so so actually so in in
+ 
+
+ align:start position:0%
+um yeah okay so so actually so in in
+order for this to stop in a reasonable
+
+ align:start position:0%
+order for this to stop in a reasonable
+ 
+
+ align:start position:0%
+order for this to stop in a reasonable
+amount of time I'm going to have to have
+
+ align:start position:0%
+amount of time I'm going to have to have
+ 
+
+ align:start position:0%
+amount of time I'm going to have to have
+a cutoff that's a tiny power of delta
+
+ align:start position:0%
+a cutoff that's a tiny power of delta
+ 
+
+ align:start position:0%
+a cutoff that's a tiny power of delta
+otherwise this would go on too long
+
+ align:start position:0%
+otherwise this would go on too long
+ 
+
+ align:start position:0%
+otherwise this would go on too long
+wouldn't work. Um, so my so I would say
+
+ align:start position:0%
+wouldn't work. Um, so my so I would say
+ 
+
+ align:start position:0%
+wouldn't work. Um, so my so I would say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so what would the definition of sharp
+
+ align:start position:0%
+so what would the definition of sharp
+ 
+
+ align:start position:0%
+so what would the definition of sharp
+be?
+
+ align:start position:0%
+be?
+ 
+
+ align:start position:0%
+be?
+Keep that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+All right, let's get rid of this stuff.
+
+ align:start position:0%
+All right, let's get rid of this stuff.
+ 
+
+ align:start position:0%
+All right, let's get rid of this stuff.
+So we're going to we're going to use the
+
+ align:start position:0%
+So we're going to we're going to use the
+ 
+
+ align:start position:0%
+So we're going to we're going to use the
+sub multiplicative lama
+
+ align:start position:0%
+sub multiplicative lama
+ 
+
+ align:start position:0%
+sub multiplicative lama
+repeatedly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so if ra a d of delta is bigger than
+
+ align:start position:0%
+And so if ra a d of delta is bigger than
+ 
+
+ align:start position:0%
+And so if ra a d of delta is bigger than
+I need to put something here ra a d of
+
+ align:start position:0%
+I need to put something here ra a d of
+ 
+
+ align:start position:0%
+I need to put something here ra a d of
+root delta squared and here I'm going to
+
+ align:start position:0%
+root delta squared and here I'm going to
+ 
+
+ align:start position:0%
+root delta squared and here I'm going to
+put delta to the epsilon kn where
+
+ align:start position:0%
+put delta to the epsilon kn where
+ 
+
+ align:start position:0%
+put delta to the epsilon kn where
+epsilon kn is a tiny parameter then I'm
+
+ align:start position:0%
+epsilon kn is a tiny parameter then I'm
+ 
+
+ align:start position:0%
+epsilon kn is a tiny parameter then I'm
+going to call this sharp
+
+ align:start position:0%
+going to call this sharp
+ 
+
+ align:start position:0%
+going to call this sharp
+and I'm going to stop and analyze
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Other possibility is that RA A of
+
+ align:start position:0%
+the Other possibility is that RA A of
+ 
+
+ align:start position:0%
+the Other possibility is that RA A of
+delta is less than delta to the epsilon
+
+ align:start position:0%
+delta is less than delta to the epsilon
+ 
+
+ align:start position:0%
+delta is less than delta to the epsilon
+KN RA a
+
+ align:start position:0%
+KN RA a
+ 
+
+ align:start position:0%
+KN RA a
+root delta squared. And here I'm making
+
+ align:start position:0%
+root delta squared. And here I'm making
+ 
+
+ align:start position:0%
+root delta squared. And here I'm making
+progress. So I'll keep going. So this is
+
+ align:start position:0%
+progress. So I'll keep going. So this is
+ 
+
+ align:start position:0%
+progress. So I'll keep going. So this is
+the not sharp case.
+
+ align:start position:0%
+the not sharp case.
+ 
+
+ align:start position:0%
+the not sharp case.
+So now I'll keep going.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's that's if we're more
+
+ align:start position:0%
+Okay. So that's that's if we're more
+ 
+
+ align:start position:0%
+Okay. So that's that's if we're more
+careful about what is sharp and not
+
+ align:start position:0%
+careful about what is sharp and not
+ 
+
+ align:start position:0%
+careful about what is sharp and not
+sharpening. All right. So here um if I
+
+ align:start position:0%
+sharpening. All right. So here um if I
+ 
+
+ align:start position:0%
+sharpening. All right. So here um if I
+keep going every time I make a definite
+
+ align:start position:0%
+keep going every time I make a definite
+ 
+
+ align:start position:0%
+keep going every time I make a definite
+amount of progress and so uh this this
+
+ align:start position:0%
+amount of progress and so uh this this
+ 
+
+ align:start position:0%
+amount of progress and so uh this this
+actually cannot keep going forever
+
+ align:start position:0%
+actually cannot keep going forever
+ 
+
+ align:start position:0%
+actually cannot keep going forever
+because eventually the exponents would
+
+ align:start position:0%
+because eventually the exponents would
+ 
+
+ align:start position:0%
+because eventually the exponents would
+be negative instead of positive. So it
+
+ align:start position:0%
+be negative instead of positive. So it
+ 
+
+ align:start position:0%
+be negative instead of positive. So it
+will stop. So we will end up here. Once
+
+ align:start position:0%
+will stop. So we will end up here. Once
+ 
+
+ align:start position:0%
+will stop. So we will end up here. Once
+we end up here we have to analyze the
+
+ align:start position:0%
+we end up here we have to analyze the
+ 
+
+ align:start position:0%
+we end up here we have to analyze the
+sharp case and we do have to remember it
+
+ align:start position:0%
+sharp case and we do have to remember it
+ 
+
+ align:start position:0%
+sharp case and we do have to remember it
+wasn't perfectly sharp but we had a
+
+ align:start position:0%
+wasn't perfectly sharp but we had a
+ 
+
+ align:start position:0%
+wasn't perfectly sharp but we had a
+fudge factor of a tiny power of delta
+
+ align:start position:0%
+fudge factor of a tiny power of delta
+ 
+
+ align:start position:0%
+fudge factor of a tiny power of delta
+and that complicates all the pictures
+
+ align:start position:0%
+and that complicates all the pictures
+ 
+
+ align:start position:0%
+and that complicates all the pictures
+that we have drawn. So in this picture
+
+ align:start position:0%
+that we have drawn. So in this picture
+ 
+
+ align:start position:0%
+that we have drawn. So in this picture
+here,
+
+ align:start position:0%
+here,
+ 
+
+ align:start position:0%
+here,
+this tube goes through many fat tubes.
+
+ align:start position:0%
+this tube goes through many fat tubes.
+ 
+
+ align:start position:0%
+this tube goes through many fat tubes.
+It doesn't have to have many delta balls
+
+ align:start position:0%
+It doesn't have to have many delta balls
+ 
+
+ align:start position:0%
+It doesn't have to have many delta balls
+in all of them. It has to have many
+
+ align:start position:0%
+in all of them. It has to have many
+ 
+
+ align:start position:0%
+in all of them. It has to have many
+delta balls in a fraction like delta to
+
+ align:start position:0%
+delta balls in a fraction like delta to
+ 
+
+ align:start position:0%
+delta balls in a fraction like delta to
+the epsilon, not fraction of them. It
+
+ align:start position:0%
+the epsilon, not fraction of them. It
+ 
+
+ align:start position:0%
+the epsilon, not fraction of them. It
+makes the picture a little bit more
+
+ align:start position:0%
+makes the picture a little bit more
+ 
+
+ align:start position:0%
+makes the picture a little bit more
+complicated. Um and actually because of
+
+ align:start position:0%
+complicated. Um and actually because of
+ 
+
+ align:start position:0%
+complicated. Um and actually because of
+that in in this theorem,
+
+ align:start position:0%
+that in in this theorem,
+ 
+
+ align:start position:0%
+that in in this theorem,
+if we're honest, it's a little bit more
+
+ align:start position:0%
+if we're honest, it's a little bit more
+ 
+
+ align:start position:0%
+if we're honest, it's a little bit more
+complicated. It's not um so it's um
+
+ align:start position:0%
+complicated. It's not um so it's um
+ 
+
+ align:start position:0%
+complicated. It's not um so it's um
+this would actually be pi c of x where x
+
+ align:start position:0%
+this would actually be pi c of x where x
+ 
+
+ align:start position:0%
+this would actually be pi c of x where x
+is a subset of a cross b and it's like a
+
+ align:start position:0%
+is a subset of a cross b and it's like a
+ 
+
+ align:start position:0%
+is a subset of a cross b and it's like a
+delta to the epsilon subset.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we wouldn't have to fill the whole
+
+ align:start position:0%
+So we wouldn't have to fill the whole
+ 
+
+ align:start position:0%
+So we wouldn't have to fill the whole
+product. we'd only have.
+
+ align:start position:0%
+product. we'd only have.
+ 
+
+ align:start position:0%
+product. we'd only have.
+Okay. So for that's what how we would be
+
+ align:start position:0%
+Okay. So for that's what how we would be
+ 
+
+ align:start position:0%
+Okay. So for that's what how we would be
+careful about sharp and how we would
+
+ align:start position:0%
+careful about sharp and how we would
+ 
+
+ align:start position:0%
+careful about sharp and how we would
+have to be more careful here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um let me tell you just the first
+
+ align:start position:0%
+Okay. Um let me tell you just the first
+ 
+
+ align:start position:0%
+Okay. Um let me tell you just the first
+idea of the of the proof of um of this
+
+ align:start position:0%
+idea of the of the proof of um of this
+ 
+
+ align:start position:0%
+idea of the of the proof of um of this
+key lama.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So um so we have
+
+ align:start position:0%
+So um so we have
+ 
+
+ align:start position:0%
+So um so we have
+just a step proof
+
+ align:start position:0%
+just a step proof
+ 
+
+ align:start position:0%
+just a step proof
+um so we have a plus cb is only a little
+
+ align:start position:0%
+um so we have a plus cb is only a little
+ 
+
+ align:start position:0%
+um so we have a plus cb is only a little
+bit bigger than a
+
+ align:start position:0%
+bit bigger than a
+ 
+
+ align:start position:0%
+bit bigger than a
+um that reminds us of plunicus. So an
+
+ align:start position:0%
+um that reminds us of plunicus. So an
+ 
+
+ align:start position:0%
+um that reminds us of plunicus. So an
+appropriate version of plunicusia
+
+ align:start position:0%
+appropriate version of plunicusia
+ 
+
+ align:start position:0%
+appropriate version of plunicusia
+well okay we have this big subset x we
+
+ align:start position:0%
+well okay we have this big subset x we
+ 
+
+ align:start position:0%
+well okay we have this big subset x we
+might want to get rid of that by doing
+
+ align:start position:0%
+might want to get rid of that by doing
+ 
+
+ align:start position:0%
+might want to get rid of that by doing
+bix gowers. Um so a val 80 hours would
+
+ align:start position:0%
+bix gowers. Um so a val 80 hours would
+ 
+
+ align:start position:0%
+bix gowers. Um so a val 80 hours would
+reduce
+
+ align:start position:0%
+reduce
+ 
+
+ align:start position:0%
+reduce
+to um a prime plus c b prime smaller
+
+ align:start position:0%
+to um a prime plus c b prime smaller
+ 
+
+ align:start position:0%
+to um a prime plus c b prime smaller
+than a prime we actually have all of it
+
+ align:start position:0%
+than a prime we actually have all of it
+ 
+
+ align:start position:0%
+than a prime we actually have all of it
+instead of just a big piece of it and
+
+ align:start position:0%
+instead of just a big piece of it and
+ 
+
+ align:start position:0%
+instead of just a big piece of it and
+then uh plunicus
+
+ align:start position:0%
+then uh plunicus
+ 
+
+ align:start position:0%
+then uh plunicus
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+would give us so this would be true for
+
+ align:start position:0%
+would give us so this would be true for
+ 
+
+ align:start position:0%
+would give us so this would be true for
+man c and c
+
+ align:start position:0%
+man c and c
+ 
+
+ align:start position:0%
+man c and c
+and that would give us a prime prime
+
+ align:start position:0%
+and that would give us a prime prime
+ 
+
+ align:start position:0%
+and that would give us a prime prime
+plus C1 B prime plus C2 B prime plus C3
+
+ align:start position:0%
+plus C1 B prime plus C2 B prime plus C3
+ 
+
+ align:start position:0%
+plus C1 B prime plus C2 B prime plus C3
+B prime would still be smaller than A
+
+ align:start position:0%
+B prime would still be smaller than A
+ 
+
+ align:start position:0%
+B prime would still be smaller than A
+prime could get that from plunicus
+
+ align:start position:0%
+prime could get that from plunicus
+ 
+
+ align:start position:0%
+prime could get that from plunicus
+okay and so now you we're not done yet
+
+ align:start position:0%
+okay and so now you we're not done yet
+ 
+
+ align:start position:0%
+okay and so now you we're not done yet
+but you sort of have the feeling that
+
+ align:start position:0%
+but you sort of have the feeling that
+ 
+
+ align:start position:0%
+but you sort of have the feeling that
+we keep using these tools from additive
+
+ align:start position:0%
+we keep using these tools from additive
+ 
+
+ align:start position:0%
+we keep using these tools from additive
+commentary we keep having stronger and
+
+ align:start position:0%
+commentary we keep having stronger and
+ 
+
+ align:start position:0%
+commentary we keep having stronger and
+stronger sounding uh information about A
+
+ align:start position:0%
+stronger sounding uh information about A
+ 
+
+ align:start position:0%
+stronger sounding uh information about A
+and B more and more suspicious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay And it definitely takes some some
+
+ align:start position:0%
+okay And it definitely takes some some
+ 
+
+ align:start position:0%
+okay And it definitely takes some some
+skill and some some good ideas to to
+
+ align:start position:0%
+skill and some some good ideas to to
+ 
+
+ align:start position:0%
+skill and some some good ideas to to
+finish from here. But we're in a setting
+
+ align:start position:0%
+finish from here. But we're in a setting
+ 
+
+ align:start position:0%
+finish from here. But we're in a setting
+where the tools of additive
+
+ align:start position:0%
+where the tools of additive
+ 
+
+ align:start position:0%
+where the tools of additive
+combinatorics are quite powerful and
+
+ align:start position:0%
+combinatorics are quite powerful and
+ 
+
+ align:start position:0%
+combinatorics are quite powerful and
+they're able to analyze what happens.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Any final questions or comments?
+
+ align:start position:0%
+Any final questions or comments?
+ 
+
+ align:start position:0%
+Any final questions or comments?
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> How did we reduce the projected case? we
+
+ align:start position:0%
+>> How did we reduce the projected case? we
+ 
+
+ align:start position:0%
+>> How did we reduce the projected case? we
+reduced to the projective case at the
+
+ align:start position:0%
+reduced to the projective case at the
+ 
+
+ align:start position:0%
+reduced to the projective case at the
+beginning. Um we said uh so after we had
+
+ align:start position:0%
+beginning. Um we said uh so after we had
+ 
+
+ align:start position:0%
+beginning. Um we said uh so after we had
+the um sub multiplicative lama we
+
+ align:start position:0%
+the um sub multiplicative lama we
+ 
+
+ align:start position:0%
+the um sub multiplicative lama we
+reduced to the projective case by saying
+
+ align:start position:0%
+reduced to the projective case by saying
+ 
+
+ align:start position:0%
+reduced to the projective case by saying
+that um this ball is in the projective
+
+ align:start position:0%
+that um this ball is in the projective
+ 
+
+ align:start position:0%
+that um this ball is in the projective
+case.
+
+ align:start position:0%
+case.
+ 
+
+ align:start position:0%
+case.
+Um and so using that we were able to
+
+ align:start position:0%
+Um and so using that we were able to
+ 
+
+ align:start position:0%
+Um and so using that we were able to
+show that it suffices to prove it for
+
+ align:start position:0%
+show that it suffices to prove it for
+ 
+
+ align:start position:0%
+show that it suffices to prove it for
+the projective case.
+
+ align:start position:0%
+the projective case.
+ 
+
+ align:start position:0%
+the projective case.
+How do you put that? How do you chain
+
+ align:start position:0%
+How do you put that? How do you chain
+ 
+
+ align:start position:0%
+How do you put that? How do you chain
+that argument?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> What's that like? Like like I I don't
+
+ align:start position:0%
+>> What's that like? Like like I I don't
+ 
+
+ align:start position:0%
+>> What's that like? Like like I I don't
+understand how you use uh like that kind
+
+ align:start position:0%
+understand how you use uh like that kind
+ 
+
+ align:start position:0%
+understand how you use uh like that kind
+of argument and the and the reduction at
+
+ align:start position:0%
+of argument and the and the reduction at
+ 
+
+ align:start position:0%
+of argument and the and the reduction at
+the same time.
+
+ align:start position:0%
+the same time.
+ 
+
+ align:start position:0%
+the same time.
+>> Ah um so the question is about how we
+
+ align:start position:0%
+>> Ah um so the question is about how we
+ 
+
+ align:start position:0%
+>> Ah um so the question is about how we
+put together reducing to the projective
+
+ align:start position:0%
+put together reducing to the projective
+ 
+
+ align:start position:0%
+put together reducing to the projective
+case with all the other things that we
+
+ align:start position:0%
+case with all the other things that we
+ 
+
+ align:start position:0%
+case with all the other things that we
+did. Yeah. Um
+
+ align:start position:0%
+did. Yeah. Um
+ 
+
+ align:start position:0%
+did. Yeah. Um
+um okay. So,
+
+ align:start position:0%
+um okay. So,
+ 
+
+ align:start position:0%
+um okay. So,
+so using this lama, we had an argument
+
+ align:start position:0%
+so using this lama, we had an argument
+ 
+
+ align:start position:0%
+so using this lama, we had an argument
+that if you could prove a good bound for
+
+ align:start position:0%
+that if you could prove a good bound for
+ 
+
+ align:start position:0%
+that if you could prove a good bound for
+the projective case, then combining it
+
+ align:start position:0%
+the projective case, then combining it
+ 
+
+ align:start position:0%
+the projective case, then combining it
+with this lama and and noticing that
+
+ align:start position:0%
+with this lama and and noticing that
+ 
+
+ align:start position:0%
+with this lama and and noticing that
+this is projective that then we get a
+
+ align:start position:0%
+this is projective that then we get a
+ 
+
+ align:start position:0%
+this is projective that then we get a
+good bound for the general case. So now
+
+ align:start position:0%
+good bound for the general case. So now
+ 
+
+ align:start position:0%
+good bound for the general case. So now
+we just imagine we're trying to prove
+
+ align:start position:0%
+we just imagine we're trying to prove
+ 
+
+ align:start position:0%
+we just imagine we're trying to prove
+the theorem in the projective case.
+
+ align:start position:0%
+the theorem in the projective case.
+ 
+
+ align:start position:0%
+the theorem in the projective case.
+Um so we can assume that we're in the
+
+ align:start position:0%
+Um so we can assume that we're in the
+ 
+
+ align:start position:0%
+Um so we can assume that we're in the
+projective case
+
+ align:start position:0%
+projective case
+ 
+
+ align:start position:0%
+projective case
+and then we start applying the sub
+
+ align:start position:0%
+and then we start applying the sub
+ 
+
+ align:start position:0%
+and then we start applying the sub
+multiplicative lema.
+
+ align:start position:0%
+multiplicative lema.
+ 
+
+ align:start position:0%
+multiplicative lema.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+ah so you're wondering when we do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you can so you can think of this in
+
+ align:start position:0%
+yeah you can so you can think of this in
+ 
+
+ align:start position:0%
+yeah you can so you can think of this in
+this picture um where over here we have
+
+ align:start position:0%
+this picture um where over here we have
+ 
+
+ align:start position:0%
+this picture um where over here we have
+um not just some abstract thing but the
+
+ align:start position:0%
+um not just some abstract thing but the
+ 
+
+ align:start position:0%
+um not just some abstract thing but the
+this would be the R in the small ball
+
+ align:start position:0%
+this would be the R in the small ball
+ 
+
+ align:start position:0%
+this would be the R in the small ball
+and the R for the fat tubes. So, we look
+
+ align:start position:0%
+and the R for the fat tubes. So, we look
+ 
+
+ align:start position:0%
+and the R for the fat tubes. So, we look
+at those and if if the R if the R is
+
+ align:start position:0%
+at those and if if the R if the R is
+ 
+
+ align:start position:0%
+at those and if if the R if the R is
+better than multiplying the small balls
+
+ align:start position:0%
+better than multiplying the small balls
+ 
+
+ align:start position:0%
+better than multiplying the small balls
+times the fat tubes, then we keep
+
+ align:start position:0%
+times the fat tubes, then we keep
+ 
+
+ align:start position:0%
+times the fat tubes, then we keep
+breaking things up. Take the small balls
+
+ align:start position:0%
+breaking things up. Take the small balls
+ 
+
+ align:start position:0%
+breaking things up. Take the small balls
+and break them into smaller balls. And
+
+ align:start position:0%
+and break them into smaller balls. And
+ 
+
+ align:start position:0%
+and break them into smaller balls. And
+otherwise, if if they're comparable,
+
+ align:start position:0%
+otherwise, if if they're comparable,
+ 
+
+ align:start position:0%
+otherwise, if if they're comparable,
+then we look at at what's happening.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah, that's a good question. Yeah.
+
+ align:start position:0%
+>> Yeah, that's a good question. Yeah.
+ 
+
+ align:start position:0%
+>> Yeah, that's a good question. Yeah.
+>> So, I understand uh what's going on. Is
+
+ align:start position:0%
+>> So, I understand uh what's going on. Is
+ 
+
+ align:start position:0%
+>> So, I understand uh what's going on. Is
+this example uh supposed to be similar
+
+ align:start position:0%
+this example uh supposed to be similar
+ 
+
+ align:start position:0%
+this example uh supposed to be similar
+to the case B that we had at the
+
+ align:start position:0%
+to the case B that we had at the
+ 
+
+ align:start position:0%
+to the case B that we had at the
+beginning where like for instance if we
+
+ align:start position:0%
+beginning where like for instance if we
+ 
+
+ align:start position:0%
+beginning where like for instance if we
+started with tubes and points on a
+
+ align:start position:0%
+started with tubes and points on a
+ 
+
+ align:start position:0%
+started with tubes and points on a
+bridge would we kind of immediately fall
+
+ align:start position:0%
+bridge would we kind of immediately fall
+ 
+
+ align:start position:0%
+bridge would we kind of immediately fall
+just into the situation and what we're
+
+ align:start position:0%
+just into the situation and what we're
+ 
+
+ align:start position:0%
+just into the situation and what we're
+doing is blowing things up until we get
+
+ align:start position:0%
+doing is blowing things up until we get
+ 
+
+ align:start position:0%
+doing is blowing things up until we get
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+>> Yeah. Okay. So the question is how how
+
+ align:start position:0%
+>> Yeah. Okay. So the question is how how
+ 
+
+ align:start position:0%
+>> Yeah. Okay. So the question is how how
+these pictures and these examples relate
+
+ align:start position:0%
+these pictures and these examples relate
+ 
+
+ align:start position:0%
+these pictures and these examples relate
+to the the the three examples that we
+
+ align:start position:0%
+to the the the three examples that we
+ 
+
+ align:start position:0%
+to the the the three examples that we
+had in mind at the beginning. Um so the
+
+ align:start position:0%
+had in mind at the beginning. Um so the
+ 
+
+ align:start position:0%
+had in mind at the beginning. Um so the
+three examples we had in mind at the
+
+ align:start position:0%
+three examples we had in mind at the
+ 
+
+ align:start position:0%
+three examples we had in mind at the
+beginning were there was a simple one
+
+ align:start position:0%
+beginning were there was a simple one
+ 
+
+ align:start position:0%
+beginning were there was a simple one
+the stars example there was the grid
+
+ align:start position:0%
+the stars example there was the grid
+ 
+
+ align:start position:0%
+the stars example there was the grid
+that was interesting and there was like
+
+ align:start position:0%
+that was interesting and there was like
+ 
+
+ align:start position:0%
+that was interesting and there was like
+the random example
+
+ align:start position:0%
+the random example
+ 
+
+ align:start position:0%
+the random example
+and a funny thing is that none of those
+
+ align:start position:0%
+and a funny thing is that none of those
+ 
+
+ align:start position:0%
+and a funny thing is that none of those
+is ad regular
+
+ align:start position:0%
+is ad regular
+ 
+
+ align:start position:0%
+is ad regular
+right and now the the the
+
+ align:start position:0%
+right and now the the the
+ 
+
+ align:start position:0%
+right and now the the the
+random one we could fidget to make it ad
+
+ align:start position:0%
+random one we could fidget to make it ad
+ 
+
+ align:start position:0%
+random one we could fidget to make it ad
+regular if we wanted to um and the stars
+
+ align:start position:0%
+regular if we wanted to um and the stars
+ 
+
+ align:start position:0%
+regular if we wanted to um and the stars
+we we could make it ad regular if we
+
+ align:start position:0%
+we we could make it ad regular if we
+ 
+
+ align:start position:0%
+we we could make it ad regular if we
+wanted to but the grid is is actually is
+
+ align:start position:0%
+wanted to but the grid is is actually is
+ 
+
+ align:start position:0%
+wanted to but the grid is is actually is
+really not adular
+
+ align:start position:0%
+really not adular
+ 
+
+ align:start position:0%
+really not adular
+Um and so that is a little bit funny
+
+ align:start position:0%
+Um and so that is a little bit funny
+ 
+
+ align:start position:0%
+Um and so that is a little bit funny
+that in the most important example is
+
+ align:start position:0%
+that in the most important example is
+ 
+
+ align:start position:0%
+that in the most important example is
+not in this case. Um even though this
+
+ align:start position:0%
+not in this case. Um even though this
+ 
+
+ align:start position:0%
+not in this case. Um even though this
+case is very important in the final
+
+ align:start position:0%
+case is very important in the final
+ 
+
+ align:start position:0%
+case is very important in the final
+proof.
+
+ align:start position:0%
+proof.
+ 
+
+ align:start position:0%
+proof.
+Um so you can't really start with the
+
+ align:start position:0%
+Um so you can't really start with the
+ 
+
+ align:start position:0%
+Um so you can't really start with the
+grid
+
+ align:start position:0%
+grid
+ 
+
+ align:start position:0%
+grid
+and it is
+
+ align:start position:0%
+and it is
+ 
+
+ align:start position:0%
+and it is
+not at least until recently it was not
+
+ align:start position:0%
+not at least until recently it was not
+ 
+
+ align:start position:0%
+not at least until recently it was not
+known what is the actual worst behavior
+
+ align:start position:0%
+known what is the actual worst behavior
+ 
+
+ align:start position:0%
+known what is the actual worst behavior
+in the AD regular case. It may be so it
+
+ align:start position:0%
+in the AD regular case. It may be so it
+ 
+
+ align:start position:0%
+in the AD regular case. It may be so it
+may be that RA a is much smaller than R.
+
+ align:start position:0%
+may be that RA a is much smaller than R.
+ 
+
+ align:start position:0%
+may be that RA a is much smaller than R.
+Um uh although but the argument so far
+
+ align:start position:0%
+Um uh although but the argument so far
+ 
+
+ align:start position:0%
+Um uh although but the argument so far
+doesn't prove that and that's a little
+
+ align:start position:0%
+doesn't prove that and that's a little
+ 
+
+ align:start position:0%
+doesn't prove that and that's a little
+it's a little bit funny because it means
+
+ align:start position:0%
+it's a little bit funny because it means
+ 
+
+ align:start position:0%
+it's a little bit funny because it means
+there's not an example that you can keep
+
+ align:start position:0%
+there's not an example that you can keep
+ 
+
+ align:start position:0%
+there's not an example that you can keep
+in mind when you go through the ad
+
+ align:start position:0%
+in mind when you go through the ad
+ 
+
+ align:start position:0%
+in mind when you go through the ad
+regular case.
+
+ align:start position:0%
+regular case.
+ 
+
+ align:start position:0%
+regular case.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> What what goes wrong with trying to kind
+
+ align:start position:0%
+>> What what goes wrong with trying to kind
+ 
+
+ align:start position:0%
+>> What what goes wrong with trying to kind
+construct an ad regular grid where you
+
+ align:start position:0%
+construct an ad regular grid where you
+ 
+
+ align:start position:0%
+construct an ad regular grid where you
+just kind of have a grid wherein each
+
+ align:start position:0%
+just kind of have a grid wherein each
+ 
+
+ align:start position:0%
+just kind of have a grid wherein each
+point has a lot of sort of nested
+
+ align:start position:0%
+point has a lot of sort of nested
+ 
+
+ align:start position:0%
+point has a lot of sort of nested
+subgrids within it.
+
+ align:start position:0%
+subgrids within it.
+ 
+
+ align:start position:0%
+subgrids within it.
+>> Yeah. So the question is could you make
+
+ align:start position:0%
+>> Yeah. So the question is could you make
+ 
+
+ align:start position:0%
+>> Yeah. So the question is could you make
+an ad? Yeah, I guess that's true. You
+
+ align:start position:0%
+an ad? Yeah, I guess that's true. You
+ 
+
+ align:start position:0%
+an ad? Yeah, I guess that's true. You
+could make a roughly a somewhat ad
+
+ align:start position:0%
+could make a roughly a somewhat ad
+ 
+
+ align:start position:0%
+could make a roughly a somewhat ad
+regular grid by taking a grid of balls
+
+ align:start position:0%
+regular grid by taking a grid of balls
+ 
+
+ align:start position:0%
+regular grid by taking a grid of balls
+and then in each one of those balls you
+
+ align:start position:0%
+and then in each one of those balls you
+ 
+
+ align:start position:0%
+and then in each one of those balls you
+put a grid of balls and you repeat like
+
+ align:start position:0%
+put a grid of balls and you repeat like
+ 
+
+ align:start position:0%
+put a grid of balls and you repeat like
+this. Um uh but it's not since the grid
+
+ align:start position:0%
+this. Um uh but it's not since the grid
+ 
+
+ align:start position:0%
+this. Um uh but it's not since the grid
+itself is not a dregular. This this is
+
+ align:start position:0%
+itself is not a dregular. This this is
+ 
+
+ align:start position:0%
+itself is not a dregular. This this is
+only a it's only a dregular with a big
+
+ align:start position:0%
+only a it's only a dregular with a big
+ 
+
+ align:start position:0%
+only a it's only a dregular with a big
+c. Um could you do that? Yeah, I guess
+
+ align:start position:0%
+c. Um could you do that? Yeah, I guess
+ 
+
+ align:start position:0%
+c. Um could you do that? Yeah, I guess
+you could do that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Yeah. Okay. So you could do that.
+
+ align:start position:0%
+Yeah. Yeah. Okay. So you could do that.
+ 
+
+ align:start position:0%
+Yeah. Yeah. Okay. So you could do that.
+And then what would happen here? The A,
+
+ align:start position:0%
+And then what would happen here? The A,
+ 
+
+ align:start position:0%
+And then what would happen here? The A,
+B and C would be like sets of integers
+
+ align:start position:0%
+B and C would be like sets of integers
+ 
+
+ align:start position:0%
+B and C would be like sets of integers
+except they would have this ad regular
+
+ align:start position:0%
+except they would have this ad regular
+ 
+
+ align:start position:0%
+except they would have this ad regular
+structure. So A would be like take an
+
+ align:start position:0%
+structure. So A would be like take an
+ 
+
+ align:start position:0%
+structure. So A would be like take an
+arithmetic progression of intervals and
+
+ align:start position:0%
+arithmetic progression of intervals and
+ 
+
+ align:start position:0%
+arithmetic progression of intervals and
+in each one of them put an arithmetic
+
+ align:start position:0%
+in each one of them put an arithmetic
+ 
+
+ align:start position:0%
+in each one of them put an arithmetic
+progression of smaller intervals and so
+
+ align:start position:0%
+progression of smaller intervals and so
+ 
+
+ align:start position:0%
+progression of smaller intervals and so
+on. That's what A and B and C would look
+
+ align:start position:0%
+on. That's what A and B and C would look
+ 
+
+ align:start position:0%
+on. That's what A and B and C would look
+like.
+
+ align:start position:0%
+like.
+ 
+
+ align:start position:0%
+like.
+>> Can you cancept them?
+
+ align:start position:0%
+>> Can you cancept them?
+ 
+
+ align:start position:0%
+>> Can you cancept them?
+>> Yeah, it's kind of like a caner. It's
+
+ align:start position:0%
+>> Yeah, it's kind of like a caner. It's
+ 
+
+ align:start position:0%
+>> Yeah, it's kind of like a caner. It's
+like a counter set but the but with but
+
+ align:start position:0%
+like a counter set but the but with but
+ 
+
+ align:start position:0%
+like a counter set but the but with but
+in order to make it make the numbers
+
+ align:start position:0%
+in order to make it make the numbers
+ 
+
+ align:start position:0%
+in order to make it make the numbers
+come out well you you need to have a lot
+
+ align:start position:0%
+come out well you you need to have a lot
+ 
+
+ align:start position:0%
+come out well you you need to have a lot
+of intervals in an arithmetic
+
+ align:start position:0%
+of intervals in an arithmetic
+ 
+
+ align:start position:0%
+of intervals in an arithmetic
+progression in each step. Here I'll draw
+
+ align:start position:0%
+progression in each step. Here I'll draw
+ 
+
+ align:start position:0%
+progression in each step. Here I'll draw
+it and then I'm over so I'm going to
+
+ align:start position:0%
+it and then I'm over so I'm going to
+ 
+
+ align:start position:0%
+it and then I'm over so I'm going to
+stop.
+
+ align:start position:0%
+stop.
+ 
+
+ align:start position:0%
+stop.
+So the example is um for a big line you
+
+ align:start position:0%
+So the example is um for a big line you
+ 
+
+ align:start position:0%
+So the example is um for a big line you
+make an arithmetic progression with a
+
+ align:start position:0%
+make an arithmetic progression with a
+ 
+
+ align:start position:0%
+make an arithmetic progression with a
+lot of intervals.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? Then you look inside of each one
+
+ align:start position:0%
+Okay? Then you look inside of each one
+ 
+
+ align:start position:0%
+Okay? Then you look inside of each one
+of these intervals and you repeat what I
+
+ align:start position:0%
+of these intervals and you repeat what I
+ 
+
+ align:start position:0%
+of these intervals and you repeat what I
+just did. Um and for for this to for
+
+ align:start position:0%
+just did. Um and for for this to for
+ 
+
+ align:start position:0%
+just did. Um and for for this to for
+this to be a kind of sharp interesting
+
+ align:start position:0%
+this to be a kind of sharp interesting
+ 
+
+ align:start position:0%
+this to be a kind of sharp interesting
+example, it needs to be a lot of
+
+ align:start position:0%
+example, it needs to be a lot of
+ 
+
+ align:start position:0%
+example, it needs to be a lot of
+intervals.
+
+ align:start position:0%
+intervals.
+ 
+
+ align:start position:0%
+intervals.
+Okay. Okay. Good. Sorry for going a
+
+ align:start position:0%
+Okay. Okay. Good. Sorry for going a
+ 
+
+ align:start position:0%
+Okay. Okay. Good. Sorry for going a
+little bit over. Um, those are great
+
+ align:start position:0%
+little bit over. Um, those are great
+ 
+
+ align:start position:0%
+little bit over. Um, those are great
+questions. Let's stop there and I will
+
+ align:start position:0%
+questions. Let's stop there and I will
+ 
+
+ align:start position:0%
+questions. Let's stop there and I will
+see you next week.
\ No newline at end of file
diff --git a/IC-pnm6PEGk.txt b/IC-pnm6PEGk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..90a4ab9262441f9818ee5da673220242935cc683
--- /dev/null
+++ b/IC-pnm6PEGk.txt
@@ -0,0 +1,1531 @@
+align:start position:0%
+ 
+we will now apply our multinomial
+
+ align:start position:0%
+we will now apply our multinomial
+ 
+
+ align:start position:0%
+we will now apply our multinomial
+formula for counting the number of
+
+ align:start position:0%
+formula for counting the number of
+ 
+
+ align:start position:0%
+formula for counting the number of
+partitions to solve the following
+
+ align:start position:0%
+partitions to solve the following
+ 
+
+ align:start position:0%
+partitions to solve the following
+probability problem we have a standard
+
+ align:start position:0%
+probability problem we have a standard
+ 
+
+ align:start position:0%
+probability problem we have a standard
+52-card deck which we deal to four
+
+ align:start position:0%
+52-card deck which we deal to four
+ 
+
+ align:start position:0%
+52-card deck which we deal to four
+persons each person gets 13 cards as for
+
+ align:start position:0%
+persons each person gets 13 cards as for
+ 
+
+ align:start position:0%
+persons each person gets 13 cards as for
+example in bridge what is the
+
+ align:start position:0%
+example in bridge what is the
+ 
+
+ align:start position:0%
+example in bridge what is the
+probability that each person gets
+
+ align:start position:0%
+probability that each person gets
+ 
+
+ align:start position:0%
+probability that each person gets
+exactly one ace well before we start as
+
+ align:start position:0%
+exactly one ace well before we start as
+ 
+
+ align:start position:0%
+exactly one ace well before we start as
+always we will need a probability model
+
+ align:start position:0%
+always we will need a probability model
+ 
+
+ align:start position:0%
+always we will need a probability model
+we deal the cards
+
+ align:start position:0%
+we deal the cards
+ 
+
+ align:start position:0%
+we deal the cards
+fairly and this is going to be our model
+
+ align:start position:0%
+fairly and this is going to be our model
+ 
+
+ align:start position:0%
+fairly and this is going to be our model
+but we still need to interpret our
+
+ align:start position:0%
+but we still need to interpret our
+ 
+
+ align:start position:0%
+but we still need to interpret our
+statements to give this interpretation
+
+ align:start position:0%
+statements to give this interpretation
+ 
+
+ align:start position:0%
+statements to give this interpretation
+let us first think of the outcomes of
+
+ align:start position:0%
+let us first think of the outcomes of
+ 
+
+ align:start position:0%
+let us first think of the outcomes of
+the experiment what are the possible
+
+ align:start position:0%
+the experiment what are the possible
+ 
+
+ align:start position:0%
+the experiment what are the possible
+outcomes and outcome of this experiment
+
+ align:start position:0%
+outcomes and outcome of this experiment
+ 
+
+ align:start position:0%
+outcomes and outcome of this experiment
+is a partition of the fifty-two cards
+
+ align:start position:0%
+is a partition of the fifty-two cards
+ 
+
+ align:start position:0%
+is a partition of the fifty-two cards
+into the four persons so that each
+
+ align:start position:0%
+into the four persons so that each
+ 
+
+ align:start position:0%
+into the four persons so that each
+person gets exactly 13 cards our
+
+ align:start position:0%
+person gets exactly 13 cards our
+ 
+
+ align:start position:0%
+person gets exactly 13 cards our
+statement about dealing the cards fairly
+
+ align:start position:0%
+statement about dealing the cards fairly
+ 
+
+ align:start position:0%
+statement about dealing the cards fairly
+will be an assumption that all
+
+ align:start position:0%
+will be an assumption that all
+ 
+
+ align:start position:0%
+will be an assumption that all
+partitions are equally likely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so since all partitions all
+
+ align:start position:0%
+okay so since all partitions all
+ 
+
+ align:start position:0%
+okay so since all partitions all
+outcomes of the experiment are equally
+
+ align:start position:0%
+outcomes of the experiment are equally
+ 
+
+ align:start position:0%
+outcomes of the experiment are equally
+likely this means that we can solve a
+
+ align:start position:0%
+likely this means that we can solve a
+ 
+
+ align:start position:0%
+likely this means that we can solve a
+probability question by Counting we need
+
+ align:start position:0%
+probability question by Counting we need
+ 
+
+ align:start position:0%
+probability question by Counting we need
+to count the number of elements of our
+
+ align:start position:0%
+to count the number of elements of our
+ 
+
+ align:start position:0%
+to count the number of elements of our
+sample space the number of possible
+
+ align:start position:0%
+sample space the number of possible
+ 
+
+ align:start position:0%
+sample space the number of possible
+outcomes and then count the number of
+
+ align:start position:0%
+outcomes and then count the number of
+ 
+
+ align:start position:0%
+outcomes and then count the number of
+outcomes that make the event of interest
+
+ align:start position:0%
+outcomes that make the event of interest
+ 
+
+ align:start position:0%
+outcomes that make the event of interest
+to occur let us start with the number of
+
+ align:start position:0%
+to occur let us start with the number of
+ 
+
+ align:start position:0%
+to occur let us start with the number of
+elements of the sample space this is the
+
+ align:start position:0%
+elements of the sample space this is the
+ 
+
+ align:start position:0%
+elements of the sample space this is the
+problem that we just dealt with a little
+
+ align:start position:0%
+problem that we just dealt with a little
+ 
+
+ align:start position:0%
+problem that we just dealt with a little
+while ago the number of outcomes the
+
+ align:start position:0%
+while ago the number of outcomes the
+ 
+
+ align:start position:0%
+while ago the number of outcomes the
+number of partitions of 52 items by into
+
+ align:start position:0%
+number of partitions of 52 items by into
+ 
+
+ align:start position:0%
+number of partitions of 52 items by into
+four persons where we give thirteen
+
+ align:start position:0%
+four persons where we give thirteen
+ 
+
+ align:start position:0%
+four persons where we give thirteen
+cards to person one thirteen cards to
+
+ align:start position:0%
+cards to person one thirteen cards to
+ 
+
+ align:start position:0%
+cards to person one thirteen cards to
+person two thirteen cards to person
+
+ align:start position:0%
+person two thirteen cards to person
+ 
+
+ align:start position:0%
+person two thirteen cards to person
+three and thirteen cards to person for
+
+ align:start position:0%
+three and thirteen cards to person for
+ 
+
+ align:start position:0%
+three and thirteen cards to person for
+the number of possible ways of doing
+
+ align:start position:0%
+the number of possible ways of doing
+ 
+
+ align:start position:0%
+the number of possible ways of doing
+this is equal to this multinomial
+
+ align:start position:0%
+this is equal to this multinomial
+ 
+
+ align:start position:0%
+this is equal to this multinomial
+coefficient so now let us count the
+
+ align:start position:0%
+coefficient so now let us count the
+ 
+
+ align:start position:0%
+coefficient so now let us count the
+number of outcomes that belong to the
+
+ align:start position:0%
+number of outcomes that belong to the
+ 
+
+ align:start position:0%
+number of outcomes that belong to the
+event of interest namely the outcomes
+
+ align:start position:0%
+event of interest namely the outcomes
+ 
+
+ align:start position:0%
+event of interest namely the outcomes
+were where each person gets an ace we
+
+ align:start position:0%
+were where each person gets an ace we
+ 
+
+ align:start position:0%
+were where each person gets an ace we
+think of the process of constructing
+
+ align:start position:0%
+think of the process of constructing
+ 
+
+ align:start position:0%
+think of the process of constructing
+such an outcome as a multi-stage process
+
+ align:start position:0%
+such an outcome as a multi-stage process
+ 
+
+ align:start position:0%
+such an outcome as a multi-stage process
+and we count the number of choices that
+
+ align:start position:0%
+and we count the number of choices that
+ 
+
+ align:start position:0%
+and we count the number of choices that
+we have at each stage the process is as
+
+ align:start position:0%
+we have at each stage the process is as
+ 
+
+ align:start position:0%
+we have at each stage the process is as
+follows we first distribute the four
+
+ align:start position:0%
+follows we first distribute the four
+ 
+
+ align:start position:0%
+follows we first distribute the four
+aces we take the ace of spades and give
+
+ align:start position:0%
+aces we take the ace of spades and give
+ 
+
+ align:start position:0%
+aces we take the ace of spades and give
+it to one person in how many ways can we
+
+ align:start position:0%
+it to one person in how many ways can we
+ 
+
+ align:start position:0%
+it to one person in how many ways can we
+do it we can do it in four ways then we
+
+ align:start position:0%
+do it we can do it in four ways then we
+ 
+
+ align:start position:0%
+do it we can do it in four ways then we
+take the next ace the next ace must be
+
+ align:start position:0%
+take the next ace the next ace must be
+ 
+
+ align:start position:0%
+take the next ace the next ace must be
+given to a different person and so at
+
+ align:start position:0%
+given to a different person and so at
+ 
+
+ align:start position:0%
+given to a different person and so at
+that stage we have three different
+
+ align:start position:0%
+that stage we have three different
+ 
+
+ align:start position:0%
+that stage we have three different
+choices about whom to give that ace to
+
+ align:start position:0%
+choices about whom to give that ace to
+ 
+
+ align:start position:0%
+choices about whom to give that ace to
+then we consider the next ace at this
+
+ align:start position:0%
+then we consider the next ace at this
+ 
+
+ align:start position:0%
+then we consider the next ace at this
+point two persons already have aces so
+
+ align:start position:0%
+point two persons already have aces so
+ 
+
+ align:start position:0%
+point two persons already have aces so
+we have two available choices for who
+
+ align:start position:0%
+we have two available choices for who
+ 
+
+ align:start position:0%
+we have two available choices for who
+can get the next ace and finally for the
+
+ align:start position:0%
+can get the next ace and finally for the
+ 
+
+ align:start position:0%
+can get the next ace and finally for the
+last ace we do not have any choice we
+
+ align:start position:0%
+last ace we do not have any choice we
+ 
+
+ align:start position:0%
+last ace we do not have any choice we
+give it to the only remaining person who
+
+ align:start position:0%
+give it to the only remaining person who
+ 
+
+ align:start position:0%
+give it to the only remaining person who
+doesn't yet have an ace having
+
+ align:start position:0%
+doesn't yet have an ace having
+ 
+
+ align:start position:0%
+doesn't yet have an ace having
+distributed the four aces then we need
+
+ align:start position:0%
+distributed the four aces then we need
+ 
+
+ align:start position:0%
+distributed the four aces then we need
+to somehow distribute the remaining 48
+
+ align:start position:0%
+to somehow distribute the remaining 48
+ 
+
+ align:start position:0%
+to somehow distribute the remaining 48
+cards to the four people but we can do
+
+ align:start position:0%
+cards to the four people but we can do
+ 
+
+ align:start position:0%
+cards to the four people but we can do
+that in any way we want
+
+ align:start position:0%
+that in any way we want
+ 
+
+ align:start position:0%
+that in any way we want
+so all we need to do is to
+
+ align:start position:0%
+so all we need to do is to
+ 
+
+ align:start position:0%
+so all we need to do is to
+partition the 48 cards into four subsets
+
+ align:start position:0%
+partition the 48 cards into four subsets
+ 
+
+ align:start position:0%
+partition the 48 cards into four subsets
+of given cardinalities and this can done
+
+ align:start position:0%
+of given cardinalities and this can done
+ 
+
+ align:start position:0%
+of given cardinalities and this can done
+by a number of ways which is the number
+
+ align:start position:0%
+by a number of ways which is the number
+ 
+
+ align:start position:0%
+by a number of ways which is the number
+of such partitions we have already found
+
+ align:start position:0%
+of such partitions we have already found
+ 
+
+ align:start position:0%
+of such partitions we have already found
+what that number is and it is this
+
+ align:start position:0%
+what that number is and it is this
+ 
+
+ align:start position:0%
+what that number is and it is this
+particular multinomial coefficient so
+
+ align:start position:0%
+particular multinomial coefficient so
+ 
+
+ align:start position:0%
+particular multinomial coefficient so
+the number of ways that we can
+
+ align:start position:0%
+the number of ways that we can
+ 
+
+ align:start position:0%
+the number of ways that we can
+distribute the cards so that each person
+
+ align:start position:0%
+distribute the cards so that each person
+ 
+
+ align:start position:0%
+distribute the cards so that each person
+gets an A is according to the counting
+
+ align:start position:0%
+gets an A is according to the counting
+ 
+
+ align:start position:0%
+gets an A is according to the counting
+principle is going to be the number of
+
+ align:start position:0%
+principle is going to be the number of
+ 
+
+ align:start position:0%
+principle is going to be the number of
+ways that we can distribute the aces
+
+ align:start position:0%
+ways that we can distribute the aces
+ 
+
+ align:start position:0%
+ways that we can distribute the aces
+times the number of ways that we can
+
+ align:start position:0%
+times the number of ways that we can
+ 
+
+ align:start position:0%
+times the number of ways that we can
+distribute the remaining cards the
+
+ align:start position:0%
+distribute the remaining cards the
+ 
+
+ align:start position:0%
+distribute the remaining cards the
+product of this number gives us the
+
+ align:start position:0%
+product of this number gives us the
+ 
+
+ align:start position:0%
+product of this number gives us the
+count gives us the cardinality of the
+
+ align:start position:0%
+count gives us the cardinality of the
+ 
+
+ align:start position:0%
+count gives us the cardinality of the
+event of interest we also have the
+
+ align:start position:0%
+event of interest we also have the
+ 
+
+ align:start position:0%
+event of interest we also have the
+cardinality of the sample space so the
+
+ align:start position:0%
+cardinality of the sample space so the
+ 
+
+ align:start position:0%
+cardinality of the sample space so the
+desired probability can be found by
+
+ align:start position:0%
+desired probability can be found by
+ 
+
+ align:start position:0%
+desired probability can be found by
+dividing these two numbers and the final
+
+ align:start position:0%
+dividing these two numbers and the final
+ 
+
+ align:start position:0%
+dividing these two numbers and the final
+answer takes this form let us now look
+
+ align:start position:0%
+answer takes this form let us now look
+ 
+
+ align:start position:0%
+answer takes this form let us now look
+at the same problem but in a different
+
+ align:start position:0%
+at the same problem but in a different
+ 
+
+ align:start position:0%
+at the same problem but in a different
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+probability problems can often be solved
+
+ align:start position:0%
+probability problems can often be solved
+ 
+
+ align:start position:0%
+probability problems can often be solved
+in multiple ways and some can be faster
+
+ align:start position:0%
+in multiple ways and some can be faster
+ 
+
+ align:start position:0%
+in multiple ways and some can be faster
+than others so we want to look for a
+
+ align:start position:0%
+than others so we want to look for a
+ 
+
+ align:start position:0%
+than others so we want to look for a
+smarter solution that perhaps will get
+
+ align:start position:0%
+smarter solution that perhaps will get
+ 
+
+ align:start position:0%
+smarter solution that perhaps will get
+us in a faster way to the desired answer
+
+ align:start position:0%
+us in a faster way to the desired answer
+ 
+
+ align:start position:0%
+us in a faster way to the desired answer
+we will use the following trick we will
+
+ align:start position:0%
+we will use the following trick we will
+ 
+
+ align:start position:0%
+we will use the following trick we will
+think about a very specific way of
+
+ align:start position:0%
+think about a very specific way of
+ 
+
+ align:start position:0%
+think about a very specific way of
+dealing the currents which is the
+
+ align:start position:0%
+dealing the currents which is the
+ 
+
+ align:start position:0%
+dealing the currents which is the
+following we take the 52 cards the card
+
+ align:start position:0%
+following we take the 52 cards the card
+ 
+
+ align:start position:0%
+following we take the 52 cards the card
+deck and stack it so that the four aces
+
+ align:start position:0%
+deck and stack it so that the four aces
+ 
+
+ align:start position:0%
+deck and stack it so that the four aces
+are at the top so they are first and
+
+ align:start position:0%
+are at the top so they are first and
+ 
+
+ align:start position:0%
+are at the top so they are first and
+then we deal those cards to the players
+
+ align:start position:0%
+then we deal those cards to the players
+ 
+
+ align:start position:0%
+then we deal those cards to the players
+as follows we think of each player
+
+ align:start position:0%
+as follows we think of each player
+ 
+
+ align:start position:0%
+as follows we think of each player
+having 13 slots of his own and the cards
+
+ align:start position:0%
+having 13 slots of his own and the cards
+ 
+
+ align:start position:0%
+having 13 slots of his own and the cards
+will be placed randomly into the
+
+ align:start position:0%
+will be placed randomly into the
+ 
+
+ align:start position:0%
+will be placed randomly into the
+different slots so we can do this one
+
+ align:start position:0%
+different slots so we can do this one
+ 
+
+ align:start position:0%
+different slots so we can do this one
+card at a time starting from the top we
+
+ align:start position:0%
+card at a time starting from the top we
+ 
+
+ align:start position:0%
+card at a time starting from the top we
+take the first ace and send it to a
+
+ align:start position:0%
+take the first ace and send it to a
+ 
+
+ align:start position:0%
+take the first ace and send it to a
+random location then we will take the
+
+ align:start position:0%
+random location then we will take the
+ 
+
+ align:start position:0%
+random location then we will take the
+second ace and it to a random location
+
+ align:start position:0%
+second ace and it to a random location
+ 
+
+ align:start position:0%
+second ace and it to a random location
+and so on what we want to calculate
+
+ align:start position:0%
+and so on what we want to calculate
+ 
+
+ align:start position:0%
+and so on what we want to calculate
+is the probability that the four aces we
+
+ align:start position:0%
+is the probability that the four aces we
+ 
+
+ align:start position:0%
+is the probability that the four aces we
+end up in locations or in slots that are
+
+ align:start position:0%
+end up in locations or in slots that are
+ 
+
+ align:start position:0%
+end up in locations or in slots that are
+associated with different persons so let
+
+ align:start position:0%
+associated with different persons so let
+ 
+
+ align:start position:0%
+associated with different persons so let
+us calculate this probability the first
+
+ align:start position:0%
+us calculate this probability the first
+ 
+
+ align:start position:0%
+us calculate this probability the first
+ace can go anywhere it doesn't matter
+
+ align:start position:0%
+ace can go anywhere it doesn't matter
+ 
+
+ align:start position:0%
+ace can go anywhere it doesn't matter
+for the second ace it has 51 slots to
+
+ align:start position:0%
+for the second ace it has 51 slots to
+ 
+
+ align:start position:0%
+for the second ace it has 51 slots to
+choose from it's 51 because we started
+
+ align:start position:0%
+choose from it's 51 because we started
+ 
+
+ align:start position:0%
+choose from it's 51 because we started
+with 52 but one slot has already been
+
+ align:start position:0%
+with 52 but one slot has already been
+ 
+
+ align:start position:0%
+with 52 but one slot has already been
+taken by that particular ace so for the
+
+ align:start position:0%
+taken by that particular ace so for the
+ 
+
+ align:start position:0%
+taken by that particular ace so for the
+ace of hearts we have 51 slots that it
+
+ align:start position:0%
+ace of hearts we have 51 slots that it
+ 
+
+ align:start position:0%
+ace of hearts we have 51 slots that it
+can go to and out of those 51 we have 39
+
+ align:start position:0%
+can go to and out of those 51 we have 39
+ 
+
+ align:start position:0%
+can go to and out of those 51 we have 39
+of them that belong to people who do not
+
+ align:start position:0%
+of them that belong to people who do not
+ 
+
+ align:start position:0%
+of them that belong to people who do not
+yet have an ace so this is the
+
+ align:start position:0%
+yet have an ace so this is the
+ 
+
+ align:start position:0%
+yet have an ace so this is the
+probability that the ace of hearts gets
+
+ align:start position:0%
+probability that the ace of hearts gets
+ 
+
+ align:start position:0%
+probability that the ace of hearts gets
+placed into a slot that belongs to a
+
+ align:start position:0%
+placed into a slot that belongs to a
+ 
+
+ align:start position:0%
+placed into a slot that belongs to a
+person who is different than the person
+
+ align:start position:0%
+person who is different than the person
+ 
+
+ align:start position:0%
+person who is different than the person
+who got the second the first ace now let
+
+ align:start position:0%
+who got the second the first ace now let
+ 
+
+ align:start position:0%
+who got the second the first ace now let
+us consider this ace what is the
+
+ align:start position:0%
+us consider this ace what is the
+ 
+
+ align:start position:0%
+us consider this ace what is the
+probability that this ace will get into
+
+ align:start position:0%
+probability that this ace will get into
+ 
+
+ align:start position:0%
+probability that this ace will get into
+a slot which belongs to either this
+
+ align:start position:0%
+a slot which belongs to either this
+ 
+
+ align:start position:0%
+a slot which belongs to either this
+person or that person it has 26 slots in
+
+ align:start position:0%
+person or that person it has 26 slots in
+ 
+
+ align:start position:0%
+person or that person it has 26 slots in
+which this desired event is going to
+
+ align:start position:0%
+which this desired event is going to
+ 
+
+ align:start position:0%
+which this desired event is going to
+happen and it's 26 out of the 50
+
+ align:start position:0%
+happen and it's 26 out of the 50
+ 
+
+ align:start position:0%
+happen and it's 26 out of the 50
+available slots finally let us consider
+
+ align:start position:0%
+available slots finally let us consider
+ 
+
+ align:start position:0%
+available slots finally let us consider
+this ace so having placed that ace and
+
+ align:start position:0%
+this ace so having placed that ace and
+ 
+
+ align:start position:0%
+this ace so having placed that ace and
+assuming that it goes to a different
+
+ align:start position:0%
+assuming that it goes to a different
+ 
+
+ align:start position:0%
+assuming that it goes to a different
+person what is the probability now that
+
+ align:start position:0%
+person what is the probability now that
+ 
+
+ align:start position:0%
+person what is the probability now that
+this ace is going to go to this person
+
+ align:start position:0%
+this ace is going to go to this person
+ 
+
+ align:start position:0%
+this ace is going to go to this person
+who doesn't yet have one the probability
+
+ align:start position:0%
+who doesn't yet have one the probability
+ 
+
+ align:start position:0%
+who doesn't yet have one the probability
+of this happening is the number of slots
+
+ align:start position:0%
+of this happening is the number of slots
+ 
+
+ align:start position:0%
+of this happening is the number of slots
+associated with that person which is
+
+ align:start position:0%
+associated with that person which is
+ 
+
+ align:start position:0%
+associated with that person which is
+equal to 13 divided by the number of
+
+ align:start position:0%
+equal to 13 divided by the number of
+ 
+
+ align:start position:0%
+equal to 13 divided by the number of
+slots that this card can choose from and
+
+ align:start position:0%
+slots that this card can choose from and
+ 
+
+ align:start position:0%
+slots that this card can choose from and
+the number of slots is 52 - the three
+
+ align:start position:0%
+the number of slots is 52 - the three
+ 
+
+ align:start position:0%
+the number of slots is 52 - the three
+slots that have already been taken
+
+ align:start position:0%
+slots that have already been taken
+ 
+
+ align:start position:0%
+slots that have already been taken
+so it's 49 and so this is the answer to
+
+ align:start position:0%
+so it's 49 and so this is the answer to
+ 
+
+ align:start position:0%
+so it's 49 and so this is the answer to
+our problem this expression looks very
+
+ align:start position:0%
+our problem this expression looks very
+ 
+
+ align:start position:0%
+our problem this expression looks very
+different from the expression that we
+
+ align:start position:0%
+different from the expression that we
+ 
+
+ align:start position:0%
+different from the expression that we
+derived a little earlier but you can do
+
+ align:start position:0%
+derived a little earlier but you can do
+ 
+
+ align:start position:0%
+derived a little earlier but you can do
+the algebra the arithmetic simplify the
+
+ align:start position:0%
+the algebra the arithmetic simplify the
+ 
+
+ align:start position:0%
+the algebra the arithmetic simplify the
+answer and you will
+
+ align:start position:0%
+answer and you will
+ 
+
+ align:start position:0%
+answer and you will
+verify that indeed it's exactly the same
+
+ align:start position:0%
+verify that indeed it's exactly the same
+ 
+
+ align:start position:0%
+verify that indeed it's exactly the same
+answer and case you're curious the
+
+ align:start position:0%
+answer and case you're curious the
+ 
+
+ align:start position:0%
+answer and case you're curious the
+numerical value turns out to be point
+
+ align:start position:0%
+numerical value turns out to be point
+ 
+
+ align:start position:0%
+numerical value turns out to be point
+105 so there is about 10% that when you
+
+ align:start position:0%
+105 so there is about 10% that when you
+ 
+
+ align:start position:0%
+105 so there is about 10% that when you
+deal the cards in bridge each one of the
+
+ align:start position:0%
+deal the cards in bridge each one of the
+ 
+
+ align:start position:0%
+deal the cards in bridge each one of the
+players is going to end up by half
+
+ align:start position:0%
+players is going to end up by half
+ 
+
+ align:start position:0%
+players is going to end up by half
+having exactly one ace so this was a
+
+ align:start position:0%
+having exactly one ace so this was a
+ 
+
+ align:start position:0%
+having exactly one ace so this was a
+faster way of getting to the answer to
+
+ align:start position:0%
+faster way of getting to the answer to
+ 
+
+ align:start position:0%
+faster way of getting to the answer to
+our problem compared to the previous one
+
+ align:start position:0%
+our problem compared to the previous one
+ 
+
+ align:start position:0%
+our problem compared to the previous one
+but it raises a legitimate question is
+
+ align:start position:0%
+but it raises a legitimate question is
+ 
+
+ align:start position:0%
+but it raises a legitimate question is
+the way that we dealt the cards by
+
+ align:start position:0%
+the way that we dealt the cards by
+ 
+
+ align:start position:0%
+the way that we dealt the cards by
+putting the aces on top and then dealing
+
+ align:start position:0%
+putting the aces on top and then dealing
+ 
+
+ align:start position:0%
+putting the aces on top and then dealing
+them is that way a fair way of dealing
+
+ align:start position:0%
+them is that way a fair way of dealing
+ 
+
+ align:start position:0%
+them is that way a fair way of dealing
+the cards is it true that with this way
+
+ align:start position:0%
+the cards is it true that with this way
+ 
+
+ align:start position:0%
+the cards is it true that with this way
+of dealing the cards all partitions are
+
+ align:start position:0%
+of dealing the cards all partitions are
+ 
+
+ align:start position:0%
+of dealing the cards all partitions are
+equally likely it turns out that this is
+
+ align:start position:0%
+equally likely it turns out that this is
+ 
+
+ align:start position:0%
+equally likely it turns out that this is
+indeed the case but it does require a
+
+ align:start position:0%
+indeed the case but it does require a
+ 
+
+ align:start position:0%
+indeed the case but it does require a
+bit of thinking maybe you can see it
+
+ align:start position:0%
+bit of thinking maybe you can see it
+ 
+
+ align:start position:0%
+bit of thinking maybe you can see it
+intuitively that this is the case but if
+
+ align:start position:0%
+intuitively that this is the case but if
+ 
+
+ align:start position:0%
+intuitively that this is the case but if
+not then it is something that one can
+
+ align:start position:0%
+not then it is something that one can
+ 
+
+ align:start position:0%
+not then it is something that one can
+prove it can be proved formally as
+
+ align:start position:0%
+prove it can be proved formally as
+ 
+
+ align:start position:0%
+prove it can be proved formally as
+follows one first needs to check that
+
+ align:start position:0%
+follows one first needs to check that
+ 
+
+ align:start position:0%
+follows one first needs to check that
+all permutations that is all possible
+
+ align:start position:0%
+all permutations that is all possible
+ 
+
+ align:start position:0%
+all permutations that is all possible
+allocations of cards into slots are
+
+ align:start position:0%
+allocations of cards into slots are
+ 
+
+ align:start position:0%
+allocations of cards into slots are
+equally likely and because of this one
+
+ align:start position:0%
+equally likely and because of this one
+ 
+
+ align:start position:0%
+equally likely and because of this one
+can then argue that any possible
+
+ align:start position:0%
+can then argue that any possible
+ 
+
+ align:start position:0%
+can then argue that any possible
+partition in two subsets of 12 is also
+
+ align:start position:0%
+partition in two subsets of 12 is also
+ 
+
+ align:start position:0%
+partition in two subsets of 12 is also
+equally likely so this is an equivalent
+
+ align:start position:0%
+equally likely so this is an equivalent
+ 
+
+ align:start position:0%
+equally likely so this is an equivalent
+way of dealing the cards to the one that
+
+ align:start position:0%
+way of dealing the cards to the one that
+ 
+
+ align:start position:0%
+way of dealing the cards to the one that
+we considered earlier which was that
+
+ align:start position:0%
+we considered earlier which was that
+ 
+
+ align:start position:0%
+we considered earlier which was that
+every partition is equally likely
+
+ align:start position:0%
+every partition is equally likely
+ 
+
+ align:start position:0%
+every partition is equally likely
+therefore we did indeed solve the same
+
+ align:start position:0%
+therefore we did indeed solve the same
+ 
+
+ align:start position:0%
+therefore we did indeed solve the same
+problem and so this is a legitimate
+
+ align:start position:0%
+problem and so this is a legitimate
+ 
+
+ align:start position:0%
+problem and so this is a legitimate
+alternative way of getting to the answer
+
+ align:start position:0%
+alternative way of getting to the answer
+ 
+
+ align:start position:0%
+alternative way of getting to the answer
+and of course it's reassuring to check
+
+ align:start position:0%
+and of course it's reassuring to check
+ 
+
+ align:start position:0%
+and of course it's reassuring to check
+that this numerical expression agrees
+
+ align:start position:0%
+that this numerical expression agrees
+ 
+
+ align:start position:0%
+that this numerical expression agrees
+with a numerical expression we had
+
+ align:start position:0%
+with a numerical expression we had
+ 
+
+ align:start position:0%
+with a numerical expression we had
+derived earlier
\ No newline at end of file
diff --git a/IXwPD4R6V6M.txt b/IXwPD4R6V6M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0d64f8bbb6f82bbec8d3a8292e2d2f25b76d036c
--- /dev/null
+++ b/IXwPD4R6V6M.txt
@@ -0,0 +1,899 @@
+align:start position:0%
+ 
+okay so now we know what CP is we can go
+
+ align:start position:0%
+okay so now we know what CP is we can go
+ 
+
+ align:start position:0%
+okay so now we know what CP is we can go
+ahead and build one last tree using
+
+ align:start position:0%
+ahead and build one last tree using
+ 
+
+ align:start position:0%
+ahead and build one last tree using
+cross-validation so we need to make sure
+
+ align:start position:0%
+cross-validation so we need to make sure
+ 
+
+ align:start position:0%
+cross-validation so we need to make sure
+that we have the required libraries and
+
+ align:start position:0%
+that we have the required libraries and
+ 
+
+ align:start position:0%
+that we have the required libraries and
+install and use so those packages the
+
+ align:start position:0%
+install and use so those packages the
+ 
+
+ align:start position:0%
+install and use so those packages the
+carrot package and secondly we need this
+
+ align:start position:0%
+carrot package and secondly we need this
+ 
+
+ align:start position:0%
+carrot package and secondly we need this
+e 107 1 package okay so we need to tell
+
+ align:start position:0%
+e 107 1 package okay so we need to tell
+ 
+
+ align:start position:0%
+e 107 1 package okay so we need to tell
+the carrot package how is that clear we
+
+ align:start position:0%
+the carrot package how is that clear we
+ 
+
+ align:start position:0%
+the carrot package how is that clear we
+want to do our parameter tuning there
+
+ align:start position:0%
+want to do our parameter tuning there
+ 
+
+ align:start position:0%
+want to do our parameter tuning there
+are actually quite a few ways of doing
+
+ align:start position:0%
+are actually quite a few ways of doing
+ 
+
+ align:start position:0%
+are actually quite a few ways of doing
+it but we're gonna restrict ourselves in
+
+ align:start position:0%
+it but we're gonna restrict ourselves in
+ 
+
+ align:start position:0%
+it but we're gonna restrict ourselves in
+this course to just 10-fold
+
+ align:start position:0%
+this course to just 10-fold
+ 
+
+ align:start position:0%
+this course to just 10-fold
+cross-validation as was explained in the
+
+ align:start position:0%
+cross-validation as was explained in the
+ 
+
+ align:start position:0%
+cross-validation as was explained in the
+literature so let's say train troll is
+
+ align:start position:0%
+literature so let's say train troll is
+ 
+
+ align:start position:0%
+literature so let's say train troll is
+Sue's method cross-validation and to use
+
+ align:start position:0%
+Sue's method cross-validation and to use
+ 
+
+ align:start position:0%
+Sue's method cross-validation and to use
+in folks okay that was easy now
+
+ align:start position:0%
+in folks okay that was easy now
+ 
+
+ align:start position:0%
+in folks okay that was easy now
+now we need to tell carrot which range
+
+ align:start position:0%
+now we need to tell carrot which range
+ 
+
+ align:start position:0%
+now we need to tell carrot which range
+of CP parameters to try out now remember
+
+ align:start position:0%
+of CP parameters to try out now remember
+ 
+
+ align:start position:0%
+of CP parameters to try out now remember
+that CP varies between 0 and 1 it's
+
+ align:start position:0%
+that CP varies between 0 and 1 it's
+ 
+
+ align:start position:0%
+that CP varies between 0 and 1 it's
+likely that for any given problem we
+
+ align:start position:0%
+likely that for any given problem we
+ 
+
+ align:start position:0%
+likely that for any given problem we
+don't need to explore the full range I
+
+ align:start position:0%
+don't need to explore the full range I
+ 
+
+ align:start position:0%
+don't need to explore the full range I
+happen to know by the fact that made
+
+ align:start position:0%
+happen to know by the fact that made
+ 
+
+ align:start position:0%
+happen to know by the fact that made
+this recitation here time that the value
+
+ align:start position:0%
+this recitation here time that the value
+ 
+
+ align:start position:0%
+this recitation here time that the value
+of CP we're gonna pick who's very small
+
+ align:start position:0%
+of CP we're gonna pick who's very small
+ 
+
+ align:start position:0%
+of CP we're gonna pick who's very small
+so what I want to do is make a grid of
+
+ align:start position:0%
+so what I want to do is make a grid of
+ 
+
+ align:start position:0%
+so what I want to do is make a grid of
+CP values to try then we'll be over the
+
+ align:start position:0%
+CP values to try then we'll be over the
+ 
+
+ align:start position:0%
+CP values to try then we'll be over the
+range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of zero
+
+ align:start position:0%
+of zero
+ 
+
+ align:start position:0%
+of zero
+oops zero to 0.01 okay so how does what
+
+ align:start position:0%
+oops zero to 0.01 okay so how does what
+ 
+
+ align:start position:0%
+oops zero to 0.01 okay so how does what
+I Roach think to that well 1 times 0.01
+
+ align:start position:0%
+I Roach think to that well 1 times 0.01
+ 
+
+ align:start position:0%
+I Roach think to that well 1 times 0.01
+is obviously zero point zero zero one
+
+ align:start position:0%
+is obviously zero point zero zero one
+ 
+
+ align:start position:0%
+is obviously zero point zero zero one
+and ten times 0.001 is obviously zero
+
+ align:start position:0%
+and ten times 0.001 is obviously zero
+ 
+
+ align:start position:0%
+and ten times 0.001 is obviously zero
+point zero one zero two five zero to ten
+
+ align:start position:0%
+point zero one zero two five zero to ten
+ 
+
+ align:start position:0%
+point zero one zero two five zero to ten
+means the numbers zero one two three
+
+ align:start position:0%
+means the numbers zero one two three
+ 
+
+ align:start position:0%
+means the numbers zero one two three
+four five six seven eight nine ten
+
+ align:start position:0%
+four five six seven eight nine ten
+ 
+
+ align:start position:0%
+four five six seven eight nine ten
+so zero to ten times 0.001 is those
+
+ align:start position:0%
+so zero to ten times 0.001 is those
+ 
+
+ align:start position:0%
+so zero to ten times 0.001 is those
+numbers scale it by 0.001 suppose my
+
+ align:start position:0%
+numbers scale it by 0.001 suppose my
+ 
+
+ align:start position:0%
+numbers scale it by 0.001 suppose my
+values of CP that carrot will try so
+
+ align:start position:0%
+values of CP that carrot will try so
+ 
+
+ align:start position:0%
+values of CP that carrot will try so
+let's stole the results of the
+
+ align:start position:0%
+let's stole the results of the
+ 
+
+ align:start position:0%
+let's stole the results of the
+cross-validation fitting in a very local
+
+ align:start position:0%
+cross-validation fitting in a very local
+ 
+
+ align:start position:0%
+cross-validation fitting in a very local
+truck and we'll use a train function
+
+ align:start position:0%
+truck and we'll use a train function
+ 
+
+ align:start position:0%
+truck and we'll use a train function
+predicting with V based on lat/long
+
+ align:start position:0%
+predicting with V based on lat/long
+ 
+
+ align:start position:0%
+predicting with V based on lat/long
+crime starting industry charles river
+
+ align:start position:0%
+crime starting industry charles river
+ 
+
+ align:start position:0%
+crime starting industry charles river
+pollution rooms age distance distance
+
+ align:start position:0%
+pollution rooms age distance distance
+ 
+
+ align:start position:0%
+pollution rooms age distance distance
+from highways tax
+
+ align:start position:0%
+from highways tax
+ 
+
+ align:start position:0%
+from highways tax
+and people teacher ratio okay
+
+ align:start position:0%
+and people teacher ratio okay
+ 
+
+ align:start position:0%
+and people teacher ratio okay
+we're using the training days we're
+
+ align:start position:0%
+we're using the training days we're
+ 
+
+ align:start position:0%
+we're using the training days we're
+using trees haha how train control is
+
+ align:start position:0%
+using trees haha how train control is
+ 
+
+ align:start position:0%
+using trees haha how train control is
+what we just made before and shooting
+
+ align:start position:0%
+what we just made before and shooting
+ 
+
+ align:start position:0%
+what we just made before and shooting
+fruit is the other thing we just made
+
+ align:start position:0%
+fruit is the other thing we just made
+ 
+
+ align:start position:0%
+fruit is the other thing we just made
+which we called steeply throughs and it
+
+ align:start position:0%
+which we called steeply throughs and it
+ 
+
+ align:start position:0%
+which we called steeply throughs and it
+was a way and what it's doing there is
+
+ align:start position:0%
+was a way and what it's doing there is
+ 
+
+ align:start position:0%
+was a way and what it's doing there is
+it's trying all different values of CP
+
+ align:start position:0%
+it's trying all different values of CP
+ 
+
+ align:start position:0%
+it's trying all different values of CP
+that we asked it to so we can see what
+
+ align:start position:0%
+that we asked it to so we can see what
+ 
+
+ align:start position:0%
+that we asked it to so we can see what
+is done by typing Tia did you can see it
+
+ align:start position:0%
+is done by typing Tia did you can see it
+ 
+
+ align:start position:0%
+is done by typing Tia did you can see it
+tried Tim that 11 who values of CP and
+
+ align:start position:0%
+tried Tim that 11 who values of CP and
+ 
+
+ align:start position:0%
+tried Tim that 11 who values of CP and
+they decided that CP equals 0.001 was
+
+ align:start position:0%
+they decided that CP equals 0.001 was
+ 
+
+ align:start position:0%
+they decided that CP equals 0.001 was
+the best because I had the best rmsd
+
+ align:start position:0%
+the best because I had the best rmsd
+ 
+
+ align:start position:0%
+the best because I had the best rmsd
+root mean square error and it was 5.03
+
+ align:start position:0%
+root mean square error and it was 5.03
+ 
+
+ align:start position:0%
+root mean square error and it was 5.03
+of 0.001 you can see that it's pretty
+
+ align:start position:0%
+of 0.001 you can see that it's pretty
+ 
+
+ align:start position:0%
+of 0.001 you can see that it's pretty
+insensitive to tickle value of cv a CP
+
+ align:start position:0%
+insensitive to tickle value of cv a CP
+ 
+
+ align:start position:0%
+insensitive to tickle value of cv a CP
+so it's maybe not too important
+
+ align:start position:0%
+so it's maybe not too important
+ 
+
+ align:start position:0%
+so it's maybe not too important
+it's interesting though that the numbers
+
+ align:start position:0%
+it's interesting though that the numbers
+ 
+
+ align:start position:0%
+it's interesting though that the numbers
+are so low I tried it for a much larger
+
+ align:start position:0%
+are so low I tried it for a much larger
+ 
+
+ align:start position:0%
+are so low I tried it for a much larger
+range of CP values and it is the best
+
+ align:start position:0%
+range of CP values and it is the best
+ 
+
+ align:start position:0%
+range of CP values and it is the best
+solutions are always very close to 0 so
+
+ align:start position:0%
+solutions are always very close to 0 so
+ 
+
+ align:start position:0%
+solutions are always very close to 0 so
+it wants us to build a very detailed a
+
+ align:start position:0%
+it wants us to build a very detailed a
+ 
+
+ align:start position:0%
+it wants us to build a very detailed a
+rich tree so let's let's see what the
+
+ align:start position:0%
+rich tree so let's let's see what the
+ 
+
+ align:start position:0%
+rich tree so let's let's see what the
+tree that that value of CP corresponds
+
+ align:start position:0%
+tree that that value of CP corresponds
+ 
+
+ align:start position:0%
+tree that that value of CP corresponds
+to is so we can get that from
+
+ align:start position:0%
+to is so we can get that from
+ 
+
+ align:start position:0%
+to is so we can get that from
+during Tia we have to say base tree is T
+
+ align:start position:0%
+during Tia we have to say base tree is T
+ 
+
+ align:start position:0%
+during Tia we have to say base tree is T
+as the train functions final model and
+
+ align:start position:0%
+as the train functions final model and
+ 
+
+ align:start position:0%
+as the train functions final model and
+we can plot that tree so that's the
+
+ align:start position:0%
+we can plot that tree so that's the
+ 
+
+ align:start position:0%
+we can plot that tree so that's the
+model that corresponds to 0.01 0.001
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wow okay it's best a very detailed tree
+
+ align:start position:0%
+Wow okay it's best a very detailed tree
+ 
+
+ align:start position:0%
+Wow okay it's best a very detailed tree
+you can see that looks pretty much like
+
+ align:start position:0%
+you can see that looks pretty much like
+ 
+
+ align:start position:0%
+you can see that looks pretty much like
+the same tree we had before initially
+
+ align:start position:0%
+the same tree we had before initially
+ 
+
+ align:start position:0%
+the same tree we had before initially
+the dense us or get much more detail at
+
+ align:start position:0%
+the dense us or get much more detail at
+ 
+
+ align:start position:0%
+the dense us or get much more detail at
+the bottom and in fact if you can see
+
+ align:start position:0%
+the bottom and in fact if you can see
+ 
+
+ align:start position:0%
+the bottom and in fact if you can see
+close enough there's actually latitude
+
+ align:start position:0%
+close enough there's actually latitude
+ 
+
+ align:start position:0%
+close enough there's actually latitude
+and longitude in there right down the
+
+ align:start position:0%
+and longitude in there right down the
+ 
+
+ align:start position:0%
+and longitude in there right down the
+bottom as well so maybe you know maybe
+
+ align:start position:0%
+bottom as well so maybe you know maybe
+ 
+
+ align:start position:0%
+bottom as well so maybe you know maybe
+the tree is finally gonna be blooming a
+
+ align:start position:0%
+the tree is finally gonna be blooming a
+ 
+
+ align:start position:0%
+the tree is finally gonna be blooming a
+regression model well we can test it out
+
+ align:start position:0%
+regression model well we can test it out
+ 
+
+ align:start position:0%
+regression model well we can test it out
+same we did it before
+
+ align:start position:0%
+same we did it before
+ 
+
+ align:start position:0%
+same we did it before
+this tree predictions is a predictions
+
+ align:start position:0%
+this tree predictions is a predictions
+ 
+
+ align:start position:0%
+this tree predictions is a predictions
+or a best tree on the new data the test
+
+ align:start position:0%
+or a best tree on the new data the test
+ 
+
+ align:start position:0%
+or a best tree on the new data the test
+set the best tree SSE sum of squared
+
+ align:start position:0%
+set the best tree SSE sum of squared
+ 
+
+ align:start position:0%
+set the best tree SSE sum of squared
+errors this is some the best trees
+
+ align:start position:0%
+errors this is some the best trees
+ 
+
+ align:start position:0%
+errors this is some the best trees
+predictions less the truth values that's
+
+ align:start position:0%
+predictions less the truth values that's
+ 
+
+ align:start position:0%
+predictions less the truth values that's
+when that number is 3675
+
+ align:start position:0%
+when that number is 3675
+ 
+
+ align:start position:0%
+when that number is 3675
+so if you can remember from the last
+
+ align:start position:0%
+so if you can remember from the last
+ 
+
+ align:start position:0%
+so if you can remember from the last
+video the street from the previous video
+
+ align:start position:0%
+video the street from the previous video
+ 
+
+ align:start position:0%
+video the street from the previous video
+actually or need got something in the
+
+ align:start position:0%
+actually or need got something in the
+ 
+
+ align:start position:0%
+actually or need got something in the
+for thousands so not very good so we
+
+ align:start position:0%
+for thousands so not very good so we
+ 
+
+ align:start position:0%
+for thousands so not very good so we
+have actually improved this treat is
+
+ align:start position:0%
+have actually improved this treat is
+ 
+
+ align:start position:0%
+have actually improved this treat is
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+Alma testing set then the original tree
+
+ align:start position:0%
+Alma testing set then the original tree
+ 
+
+ align:start position:0%
+Alma testing set then the original tree
+we created but you may also remember
+
+ align:start position:0%
+we created but you may also remember
+ 
+
+ align:start position:0%
+we created but you may also remember
+that the linear regression model did
+
+ align:start position:0%
+that the linear regression model did
+ 
+
+ align:start position:0%
+that the linear regression model did
+actually better than that still the
+
+ align:start position:0%
+actually better than that still the
+ 
+
+ align:start position:0%
+actually better than that still the
+linear regression SSE was more around
+
+ align:start position:0%
+linear regression SSE was more around
+ 
+
+ align:start position:0%
+linear regression SSE was more around
+three thousands of 30 so the mystery is
+
+ align:start position:0%
+three thousands of 30 so the mystery is
+ 
+
+ align:start position:0%
+three thousands of 30 so the mystery is
+not as good as a linear regression model
+
+ align:start position:0%
+not as good as a linear regression model
+ 
+
+ align:start position:0%
+not as good as a linear regression model
+but cross-validation did improve
+
+ align:start position:0%
+but cross-validation did improve
+ 
+
+ align:start position:0%
+but cross-validation did improve
+performance so the takeaway is I guess
+
+ align:start position:0%
+performance so the takeaway is I guess
+ 
+
+ align:start position:0%
+performance so the takeaway is I guess
+that Teresa always I know is the best
+
+ align:start position:0%
+that Teresa always I know is the best
+ 
+
+ align:start position:0%
+that Teresa always I know is the best
+you get to be available to you but
+
+ align:start position:0%
+you get to be available to you but
+ 
+
+ align:start position:0%
+you get to be available to you but
+should always try cross validated
+
+ align:start position:0%
+should always try cross validated
+ 
+
+ align:start position:0%
+should always try cross validated
+possibility cost validating them feed as
+
+ align:start position:0%
+possibility cost validating them feed as
+ 
+
+ align:start position:0%
+possibility cost validating them feed as
+much performance out of
+
+ align:start position:0%
+much performance out of
+ 
+
+ align:start position:0%
+much performance out of
+as you can and as in the first station
+
+ align:start position:0%
+as you can and as in the first station
+ 
+
+ align:start position:0%
+as you can and as in the first station
+thank you
\ No newline at end of file
diff --git a/Ih01TfuEfqU.txt b/Ih01TfuEfqU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a721aea1360e123b60df84d07dabf59fa9aa1cd9
--- /dev/null
+++ b/Ih01TfuEfqU.txt
@@ -0,0 +1,4415 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK, good afternoon.
+
+So this week we talk
+about quantum gases,
+
+ultra-cold atomic gases.
+
+And sure, they're ideal Bose
+gases, ideal Fermi gases,
+
+but I will spend one
+or two minutes on each,
+
+because that's exactly solvable.
+
+It's in all the textbooks.
+
+That's simple.
+
+Quantum gases become interesting
+because of interactions.
+
+And in my lecture today
+and my last lecture
+
+I want to introduce you
+to Bose gases and Fermi
+
+gases with inter actions.
+
+And they both turn superfluid,
+and the superfluid properties
+
+are determined by the
+interactions between the atoms.
+
+So the purpose of those
+lectures is number one,
+
+to acquaint to you with
+important phenomena
+
+in cold gases-- superfluidity,
+superfluidity in lattices,
+
+superfluidity just in
+free gas, in a normal gas
+
+without lattice, and
+superfluidity of fermions.
+
+But at the same
+time, I also want
+
+to have sort of a theme for you
+how we deal with interactions.
+
+And that kind of theme
+is how theoretically we
+
+reduce unsolvable
+Hamiltonians to Hamiltonians
+
+which can be solved.
+
+And you will see that
+actually appearing
+
+in different situations
+with similarities,
+
+but important differences.
+
+So just to remind
+you, we started out
+
+with the interacting Bose
+gas in a homogeneous system.
+
+We have a very general
+way to describe
+
+scattering two particles with
+initial momentum disappear
+
+and two particles
+with momenta appear.
+
+This is a scattering event.
+
+Now this means we have products
+of four operators, which
+
+is very difficult to solve.
+
+And the Bogoliubov approximation
+which we discussed on Monday
+
+replaces the operator for
+the condensate for the zero
+
+momentum state with a Z number,
+saying that N 0, N 0 plus 1
+
+is the same-- a little
+bit waving your hands.
+
+But it's also you can say
+the macroscopic limit when
+
+we have a photon field
+with many, many photons,
+
+we can use a Z number
+in our Hamiltonian
+
+to describe the electric field.
+
+So that's the same spirit.
+
+So maybe I should emphasize it.
+
+This is for atoms.
+
+What you're used to do with
+photons for your whole life.
+
+OK.
+
+With that we have
+transformed the Hamiltonian
+
+into a bilinear expression.
+
+And so at the moment your
+bilinear expression--
+
+you do a Bogoliubov
+transformation.
+
+You simply diagonalize it by
+finding a new set operators
+
+where the cross term
+between a and b or between a
+
+of k and a of minus k disappear.
+
+And then you've solved it.
+
+And this is what we arrived at
+at the end of the last lecture.
+
+With those
+approximations, we have
+
+diagonalized the Hamiltonian.
+
+Our Hamiltonian is now, you
+can say harmonic oscillator
+
+Hamiltonian, or
+you can see it has
+
+become a gas of non-interacting
+quasi particles.
+
+Each of those operators
+creates a quasi particle,
+
+and the quasi particle
+energy is U of k.
+
+And I explained to
+you that as expected,
+
+the quasi particle
+energy is simply
+
+particles with momentum
+h-bar k for high momenta,
+
+because in high excitation
+of Bose quantums
+
+it is a free particle.
+
+But a low-lying excitation
+is affected in a major way
+
+by all of these
+interactions with
+
+the Bose-Einstein condensate.
+
+And that turns the quadratic
+dispersion relation
+
+into a linear one,
+or you can say
+
+that turns the free particle
+into a photon or something.
+
+So that's my review
+of the last class.
+
+Are there any questions
+before we go further?
+
+Colin.
+
+AUDIENCE: Does this require
+low density and [INAUDIBLE],
+
+or one or the other?
+
+PROFESSOR: We come a little bit
+later to that, but in the end,
+
+there is a small parameter.
+
+The small parameter will be N
+a cubed-- the gas parameter--
+
+N, the density, a cubed,
+the scattering length.
+
+It's usually the dimensionless
+combination of the two
+
+which decides whether we are
+in the weakly or strongly
+
+interacting limit.
+
+There is another assumption
+which we have made here,
+
+but it's related to that-- as
+you will see a few moments--
+
+that most of the are
+in the condensate.
+
+We assumed N0 is peak.
+
+The condensate depletion-- the
+number of atoms which are not
+
+in the condensate,
+t equals 0 is small.
+
+But let me just
+first show you-- I
+
+want to mix in
+theory and experiment
+
+how sound can be observed.
+
+I should actually say this
+experiment is sort of dear
+
+to my heart, because
+at some point
+
+it clicked to me how the
+new world of atomic physics
+
+connects with condensed
+matter physics.
+
+Soon after we had realized
+Bose-Einstein condensates,
+
+a famous condensed matter
+theorist said hey, Wolfgang,
+
+you should now observe sound.
+
+Sound is important.
+
+Yeah, OK, but how do
+you observe sound?
+
+You know, use a piezo
+and just kick the system
+
+and create a sound wave.
+
+And I said, oh, gosh, this
+guy doesn't know with that
+
+if you put anything in contact
+with the quantum gases--
+
+a piezo-- the gases
+will just stick to it.
+
+He has no idea
+what our system is.
+
+But then I said wait a
+moment-- we have to translate.
+
+He says use a piezo.
+
+Well, I have to translate.
+
+In atomic physics
+how do we kick atoms?
+
+With a laser beam.
+
+And in that moment,
+I had the idea
+
+that we can take a
+Bose-Einstein condensate,
+
+suddenly switch on a blue
+de-tuned repulsive laser beam.
+
+This will do exactly as a
+piezo-- create a density
+
+perturbation, and then
+the density perturbation
+
+will propagate with
+the speed of sound.
+
+And that worked.
+
+That was just when Bose-Einstein
+condensations were very fresh.
+
+One of the first
+scientific experiments
+
+done-- we switch on
+the laser and you
+
+see color-coded in red the
+density perturbation which
+
+propagates out of it.
+
+And the slope of this line
+is the speed of sound.
+
+And here we determined
+the speed of sound
+
+as a function of density.
+
+So that's how phonons--
+or at least how
+
+the speed of sound
+and wave packets which
+
+propagate with the speed
+of sound can be prepared.
+
+I come back to phonons
+and collective excitations
+
+in a few moments.
+
+But let me first say
+when we have diagonalized
+
+the Hamiltonian we know
+everything we want to know.
+
+I just focused on the
+quasi particle energies,
+
+but you also know the
+ground-state energy.
+
+And actually here Colin,
+you see that the corrections
+
+to the ground-state
+energy scale with N
+
+a cubed, so this is really the
+small parameter in this system.
+
+But we can also find out what is
+the ground state wave function.
+
+And let me use it to introduce
+an important concept to you
+
+called the quantum depletion.
+
+When you have two atoms in the
+condensator at zero momentum
+
+and you switch on
+the interactions,
+
+the delta function interaction
+couples zero momentum state
+
+to higher momentum states.
+
+So therefore, the
+effect of interactions
+
+is that the condensate is
+not just at zero momentum.
+
+It has some probability,
+or some admixture,
+
+of finite momentum states.
+
+This is the ground state.
+
+This is how the Hamiltonian
+is diagonalized.
+
+So from the Bogoliubov
+approximation,
+
+where we introduced
+this V and U parameter
+
+to transfer from one
+set of Bose operators
+
+to another set of
+Bose operators,
+
+those coefficients
+give us the population
+
+of those momentum states in the
+[INAUDIBLE] of the condensate.
+
+So if I now ask, what is
+the condensate fraction?
+
+What is the number of atoms
+in the zero momentum states?
+
+It's all atoms, but those
+who have finite momentum.
+
+And we find again the
+small parameter N a cubed.
+
+Now this quantum
+depletion allows me now
+
+to make a distinction
+between the cold atomic gas
+
+condensates and
+superfluid helium form.
+
+In cold atomic gas condensates,
+this correction is about 1%.
+
+So therefore, I can say
+with 99% probability,
+
+or with 99% weight,
+the condensate,
+
+the many-body wave
+function of the condensate
+
+is just the zero momentum
+state to the power N.
+
+And this very complicated
+admixture of correlation
+
+into the ideal gas wave function
+is only 1% for alkali gases.
+
+But for liquid helium,
+the condensate fraction--
+
+even at zero
+temperature-- is only 10%.
+
+So when people use
+neutron scattering--
+
+it would be a long story in
+itself how this is done--
+
+but when they use neutron
+scattering to analyze
+
+the liquid helium
+at low temperature,
+
+and figure out what is the
+fraction of atoms which
+
+have zero momentum,
+they found 10%.
+
+The quantum depletion is 90%.
+
+But that's just the
+difference between a quantum
+
+gas and a quantum liquid.
+
+And in the quantum liquid--
+in liquid helium-- N
+
+a cubed is on the
+order of unity.
+
+OK, I mentioned this
+dispersion relation.
+
+These are sort of
+quasi particles.
+
+And I at least
+showed you how you
+
+can measure the slope of the
+quasi particle dispersion
+
+relation by propagating
+sound waves.
+
+But let me now tell you how we
+can observe quasi particles'
+
+elementary excitations directly.
+
+And this is actually simply
+done by light scattering.
+
+If you scatter a photon,
+and the scattered photon
+
+loses energy h-bar U. And
+it is scattered at an angle.
+
+Therefore, it
+transfers momentum q.
+
+These forces can
+only happen if there
+
+is an elementary excitation
+with momentum q and energy h U.
+
+So in other words,
+on a photon basis,
+
+you can see photon
+by photon, if you
+
+scatter a photon, the photon
+transfers momentum and energy.
+
+The process can only happen if
+you can form a quasiparticle
+
+with this momentum and energy.
+
+So since this is sort of the
+direct way of mapping out
+
+whether the system
+has the possibility
+
+to absorb momentum q and energy
+h nu, this has sort of a name.
+
+The scattering probability is
+called the dynamic structure
+
+factor.
+
+And the dynamic structure
+factor is just an integral
+
+over all the possibilities
+that a many-body system can
+
+absorb momentum and energy.
+
+Now there is one
+nice feature which
+
+was introduced by
+us at MIT, and that
+
+is if you're going to measure
+the dynamic structure factor,
+
+often you do it with
+neutron scattering.
+
+You scatter neutrons or x-rays
+and they scatter spontaneously
+
+at an angle, and
+you need a detector
+
+to detect the
+scattered particles.
+
+But in our case, because
+the gas is so dilute,
+
+the distance between
+atoms is on the order
+
+of the optical wavelengths.
+
+We don't want neutrons.
+
+We don't want x-rays.
+
+We want photons, because
+the wavelengths of photons
+
+is perfectly matched
+to the properties,
+
+to momentum transfer and
+such we need for our system.
+
+But photons-- we
+have photon lasers.
+
+So instead of in a painstakingly
+way analyzing the frequency
+
+and the momentum of
+scattered photons,
+
+we don't do the spontaneous
+scattering process.
+
+We do a stimulated process.
+
+We use two laser beams,
+and we stimulate a photon
+
+to be scattered into
+the other laser beam.
+
+And by having the two laser
+beams at frequency difference
+
+delta omega, we're
+really asking the system,
+
+are you ready to absorb
+delta omega energy?
+
+If yes, then you
+have a quasiparticle.
+
+So this is how we do
+quasiparticle spectroscopy.
+
+And a few years
+later, this method
+
+was defined by the
+[INAUDIBLE] Institute.
+
+And what you see
+here is they varied
+
+the angles between the
+two laser beams, realized
+
+different momentum
+transfer, and what
+
+you see is the low dispersion,
+the linear dispersion
+
+relation for low
+momenta, and then
+
+the quadratic part
+at high momentum.
+
+So this is called
+BEC spectroscopy.
+
+It's a variant, you can see,
+of Raman spectroscopy where
+
+you go from a zero quasiparticle
+state to a one quasiparticle
+
+state through a
+simulated Raman process,
+
+and this is how the dispersion
+relation is determined.
+
+OK so I've so far
+dealt with aspects
+
+of a homogeneous Bose-Einstein
+condensate where,
+
+of course, if you're
+a homogeneous system,
+
+you formulate everything
+in momentum space.
+
+But now we want to
+deal with the situation
+
+that our condensates
+are finite in size.
+
+And in addition, they're
+usually in a harmonic oscillator
+
+potential, and therefore their
+density is inhomogeneous.
+
+Let me start the discussion with
+the inhomogeneous Bose-Einstein
+
+condensate by showing
+again a picture which
+
+brings in some
+memories of '90, '96.
+
+It was the first
+time that we could
+
+see the Bose-Einstein
+condensate in the trap.
+
+Before people have just
+seen it by time of flight
+
+when it was pretty
+much already destroyed
+
+or it was just flying out.
+
+But here we see the trapped
+Bose-Einstein condensate
+
+and we could even
+take multiple pictures
+
+of the same condensate.
+
+So you can see that
+this was the first time
+
+that a condensate
+was seen alive.
+
+What you see here is actually
+the bimodal distribution.
+
+You see the condensate and
+then due to speckled pattern,
+
+the Fermi cloud
+looks fragmented,
+
+but this is just a
+speckled pattern due
+
+to the signal to noise.
+
+But here you really see now--
+not in ballistic expansion
+
+as I showed you on Monday--
+but really insight to the size
+
+and shape of the condensate.
+
+OK, how do we describe it?
+
+Well, the message is pretty
+much exactly the same way
+
+as we did with the Bogoliubov
+approximation and such,
+
+but instead of in
+momentum space,
+
+we do it now in position space.
+
+Actually, I have
+to say this week,
+
+I go through a lot of material.
+
+But what I'm trying
+is to give you
+
+sort of a spirited
+and animated overview
+
+that you really know
+what is important.
+
+Where is the same
+concept appearing again
+
+in a different way.
+
+The details-- I've
+posted, actually,
+
+the original
+articles, references.
+
+Some of are school
+notes, some of them
+
+written by myself
+on the backside.
+
+So yes, it's a little
+bit different character
+
+than other lectures.
+
+I want to show you
+a lot of things,
+
+and put a special
+emphasis on the ideas.
+
+OK, so in second
+quantization, we
+
+are now using field operators
+which create and annihilate
+
+particles at position R.
+This is the single particle
+
+Hamiltonian-- kinetic
+energy and potential energy.
+
+And our interaction term has
+now, again, four operators--
+
+two interrelation operators,
+two creation operators,
+
+but they're now formulated
+in position space.
+
+We do exactly the same as we
+did in the homogeneous gas.
+
+We assume the potential
+is short range.
+
+That means delta function.
+
+And that means we
+can get rid of one
+
+of the integrations
+in r and r prime.
+
+But we still have product
+of four operators.
+
+We can formally solve the
+equation by writing down
+
+Heisenberg's situation for the
+equation of motion for those
+
+field operators, but of
+course this cannot be solved.
+
+Remember products are
+four operators are hard.
+
+We have to reduce
+it to two operators.
+
+And this is actually done by the
+Bogoliubov approximation again.
+
+But it's done here
+in the following way.
+
+Remember, in the momentum space
+we replaced a0 and a0 dagger
+
+by the square root of a0.
+
+What we do here is we say this
+is sort of a quantum field.
+
+And when we have a superfluid,
+this field operator
+
+has an average value.
+
+It's actually the macroscopic
+superfluid order parameter.
+
+So we replace the operator
+by an average value
+
+which we assume is large,
+because many, many particles
+
+are in the superfluid state.
+
+And then we have
+fluctuations which are small.
+
+And what we will do is-- it's
+pretty clear-- when it comes
+
+to the fluctuations, we will
+neglect higher products--
+
+products of four
+fluctuation operators.
+
+And we are down to C
+numbers and, as you
+
+will see, two operators.
+
+We can-- and this is
+even more dramatic--
+
+it wouldn't make sense
+in momentum space,
+
+but it does make sense
+in position space--
+
+we can even do a
+first approximation
+
+where we completely
+neglect those fluctuations.
+
+And then what we have
+is when we simply
+
+insert a [? Z ?] number
+into this Hamiltonian.
+
+We have then an equation
+for this number,
+
+for this function psi.
+
+And this is the nonlinear
+Schrodinger equation,
+
+or it's also called
+Gross-Pitaevskii equation,
+
+which is now the analogy
+to Schrodinger's equation,
+
+but now for the macroscopic
+wave function which
+
+is occupied by many,
+many particles.
+
+And in addition to
+the kinetic energy
+
+and the trapping potential
+in the external potential,
+
+it has a term which is
+proportional to the density.
+
+And this is just
+mean field repulsion
+
+which one atom feels
+exerted by the other atoms.
+
+I should say--
+just to connect it
+
+to what I've said earlier
+about the quantum depletion--
+
+that you can regard the
+function psi as the best
+
+approximation to an ideal
+Bose-Einstein condensate.
+
+So if you want to write
+your many-body wave
+
+function as a function
+psi to the power N,
+
+all particles are in
+the same quantum state,
+
+then a variational
+calculation would
+
+say that this function psi
+should obey this equation.
+
+If you want to read
+up what I've said,
+
+I've posted a recent paper,
+which I found very pedagogical,
+
+where they derive the
+Gross-Pitaevskii equation
+
+without even using an
+operator psi dagger,
+
+without using any
+second quantization.
+
+They just say we have an
+Hamiltonian for an interaction
+
+system, and we try to write
+the complicated, many-body wave
+
+function as a wave
+function to the power N.
+
+And then you put this
+ansatz into your Hamiltonian
+
+and do a variation optimization
+which single-particle wave
+
+function psi, if
+taken to the power N,
+
+minimizes the total
+energy of N particles,
+
+including interactions.
+
+And the answer is this equation.
+
+So there are many
+ways this equation
+
+is sort of very natural.
+
+Now you all know about
+single-particle physics--
+
+kinetic energy in an
+external potential.
+
+Let's now learn what this
+density-dependent term does.
+
+Well, it's pretty clear.
+
+There is a price to
+be paid for density.
+
+And while the total
+integrated density, of course,
+
+is given by the total
+number of particles.
+
+That means if you lower
+the density somewhere,
+
+you have to increase
+the density.
+
+But because this is
+a non-linear term,
+
+if you have an average
+density and you lower it
+
+here and increase it here, you
+have actually more repulsive
+
+energy than if the
+density is flat.
+
+So this term has only one goal.
+
+It wants to flatten
+out densities.
+
+So therefore if we
+have a box potential
+
+and you know the
+ground state in a box
+
+is just half a period
+of a sine function.
+
+This is a non-interacting
+condensate.
+
+This would be the
+macroscopic wave
+
+function in a box potential.
+
+But if you now put in
+strong interactions,
+
+the strong interaction's going
+to flatten out the potential.
+
+They flatten out the
+potential, and only at the very
+
+last moment-- all
+right, now it's
+
+time to go down because we have
+to meet our boundary condition.
+
+And the length scale where
+you eventually go down-- it
+
+has a famous name,
+the healing length--
+
+is the length scale
+where the kinetic energy
+
+due to the curvature
+of the wave function
+
+is now comparable to
+the interaction energy.
+
+If the system would
+curve down earlier,
+
+it would cause too
+much repulsive energy,
+
+because the density
+is not kept flat.
+
+If it would curve down too
+late, the enormous curvature
+
+would mean a lot
+of kinetic energy.
+
+And this is just
+the best compromise
+
+between those two criteria.
+
+So that's how you derive
+the healing length.
+
+The healing length is
+now the length scale
+
+over which the system is willing
+to meet boundary conditions,
+
+and not stay flat,
+as flat as possible.
+
+Yes.
+
+AUDIENCE: Just curious--
+in that equation,
+
+the atom has the mass
+of each individual--
+
+PROFESSOR: The mass is
+the mass of a single atom.
+
+AUDIENCE: Single atom,
+it's not-- sorry,
+
+I wasn't here last time.
+
+But the quasiparticles are
+the same mass [INAUDIBLE].
+
+PROFESSOR: In a Bose-Einstein
+condensate they are.
+
+We haven't changed the mass.
+
+But we're not talking
+actually about quasiparticle.
+
+We're actually really talking
+about here qualitative features
+
+of the solution of the
+Gross-Pitaevskii equation.
+
+And the Gross-Pitaevskii
+equation
+
+is sort of a single particle
+equation for particles of mass,
+
+of the original bare mass
+M. It's a macroscopic wave
+
+function, but I sometimes say
+it describes the wave function
+
+of a single particle where
+all the other particles are
+
+included at the
+mean field level.
+
+So therefore, it is really
+this, the atomic mass,
+
+and not any form of
+collective mass here.
+
+Well, if you would now
+ask how do interactions
+
+transform the first excited
+state in the box potential?
+
+Well, then it's again flat
+this as much as possible.
+
+But then if you want to
+maintain the parity of the wave
+
+function, then it's
+only close to the zero
+
+crossing within a healing length
+that the system says OK, now I
+
+change sign.
+
+So that's sort of what is inside
+the Gross-Pitaevskii equation.
+
+Now once we realize that, we
+can take it to the next level
+
+and say, well, if you
+neglect-- let's say
+
+we're interested
+in the ground state
+
+and we neglect this
+boundary region where
+
+the kinetic energy
+becomes important-- maybe
+
+we can simplify the
+Gross-Pitaevskii equation
+
+by neglecting the
+kinetic energy.
+
+If potential energy dominates
+by far, we can neglect that.
+
+And then we should
+get a good description
+
+which will not be valid in
+the wings of the wave function
+
+but in most of space.
+
+But now if you look
+at this equation,
+
+it's no longer a
+differential equation.
+
+It has no derivatives.
+
+It's just something
+which applies
+
+to the wave function psi itself.
+
+And we can simply solve that.
+
+The solution of that
+is that psi squared--
+
+the density-- is
+nothing else than there
+
+is a constant minus the
+inverted trapping potential.
+
+So therefore in this
+Thomas-Fermi approximation
+
+where we neglect the
+kinetic energy completely,
+
+you just take your trapping
+potential, turn it upside down,
+
+and then you fill
+it up with density
+
+until you have accommodated
+the number of atoms
+
+you want to accommodate.
+
+And this is, of
+course-- the constraint
+
+in the number of atoms is
+determined by the chemical
+
+potential.
+
+Or if you have a more
+complicated W-shaped potential,
+
+the same construction.
+
+Flip it over, fill it up,
+gives you the condensate wave
+
+function, the
+density distribution
+
+of the condensate
+in this potential.
+
+I don't want to belabor
+it, but coming back
+
+to the question of
+the small parameter,
+
+if you look at
+those equations, you
+
+can identify a parameter-- this
+is now the small parameter,
+
+or the parameter
+in the system which
+
+is the important
+dimensionless parameter.
+
+It depends on the
+number of atoms,
+
+and it depends now on the ratio
+of the scattering length--
+
+which characterizes
+the interaction--
+
+and the harmonic
+oscillator length.
+
+You can say the
+harmonic oscillator
+
+length is the ideal wave
+function harmonic oscillator.
+
+So this parametrizes the
+importance of kinetic energy,
+
+whereas the scattering
+length parametrizes
+
+the importance of interactions.
+
+And all those solutions
+can be nicely written
+
+as what you would
+have in an ideal gas,
+
+and then this parameter X. So
+in typical experiments, N a,
+
+N is a million.
+
+The scattering length is smaller
+than the oscillator length,
+
+but N is a million, and this
+parameter X is usually large.
+
+So therefore-- and I'm
+simply just talking
+
+about this solution-- we have
+the situation that the chemical
+
+potential is larger
+by a power of X
+
+than the ideal gas solution,
+which would just be the ground
+
+state with its zero point energy
+in the harmonic oscillator
+
+potential, or the width-- the
+size-- of the wave function
+
+is larger than the ground state
+of the harmonic oscillator,
+
+but only with an exponent,
+which is one-fifth.
+
+Well, we can see that.
+
+These are now, again,
+somewhat improved pictures
+
+of condensates inside the trap.
+
+For the expert, the
+previous picture
+
+was dark-ground imaging.
+
+This is now
+phase-contrast imaging.
+
+And if you take a
+profile, we clearly
+
+see the condensate wave function
+and we see the thermal wings.
+
+When we look at the size of
+the condensate wave function,
+
+you realize what I just meant--
+that the ground-state wave
+
+function, the harmonic
+oscillator length
+
+is 7 micron in the
+axial direction,
+
+but here you have 300 micron.
+
+So this condensate is completely
+dominated by interactions.
+
+And it fulfils very nice, and
+pretty much the whole shape,
+
+except maybe some
+details in the wings,
+
+are quantitatively described
+by the simple approximation
+
+I have explained to you.
+
+So just a little
+bit show and tell.
+
+We have this
+Gross-Pitaevskii equation.
+
+The Gross-Pitaevskii equation
+has, as Schrodinger's equation,
+
+a time independent form
+to get the ground state.
+
+It has also a time
+dependent form.
+
+You simply replace the
+energy by the derivative
+
+of the wave function.
+
+This is the time-dependent form.
+
+Everything is very simple, and
+you can do many-body physics,
+
+but on your computer,
+you pretty much look
+
+for single-particle
+wave function
+
+and take them to the power N.
+
+So some areas where the
+Gross-Pitaevskii equation
+
+has quantitatively
+explained experiments-- one
+
+is the expansion of a
+Bose-Einstein condensate.
+
+It's this famous
+situation when you
+
+have an elongated condensate
+and let it expand.
+
+It expands faster in
+the radial direction.
+
+One simple argument
+is the pressure
+
+of the mean field is larger and
+leads to faster acceleration.
+
+So therefore, if you have
+a cigar-shaped condensate
+
+and release it, it
+turns into a disk.
+
+It inverts the aspect ratio,
+going from a cigar shape
+
+to a disk shape.
+
+And that has been beautifully
+and quantitatively described
+
+by the Gross-Pitaevskii
+equation.
+
+Here we have measured
+the interaction energy
+
+as a number of condensed atoms.
+
+And I mentioned to you that
+this X parameter comes often
+
+with power 1/5 and 2/5.
+
+And this here is a
+fit to the power 2/5,
+
+beautifully
+confirming the theory.
+
+So the Gross-Pitaevskii
+equation was
+
+invented in 1962, about 50 years
+ago by Gross and Pitaevskii
+
+to describe vortices.
+
+Actually, Lev Pitaevskii
+is still alive,
+
+going strong, and
+publishing papers.
+
+One of his latest predictions
+was solitons in Fermi gases,
+
+and I know in Professor
+Zwierlein's group,
+
+one of his lab just looked
+at the same physics,
+
+and compared to the
+theory of Lev Pitaevskii.
+
+And this year we
+are celebrating--
+
+I forgot, the 85th or
+90th birthday of him.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: 90?
+
+AUDIENCE: There's a poster.
+
+PROFESSOR: I know there's
+a poster next to my door,
+
+but I forgot which anniversary.
+
+So I mean, he's an legend.
+
+But he's still walking.
+
+He's still doing science.
+
+So if you meet him, you go
+back to 50 years in history.
+
+Anyway, it is this
+Lev Pitaevskii,
+
+and he invented his equations
+to describe vortices.
+
+So anyway so we have this
+nonlinear Schrodinger equation.
+
+Let me just show you
+what vortices are
+
+and how they are formed.
+
+Vortices come-- if you solve
+the Gross-Pitaevskii equation--
+
+if you ever any quantum
+fluid or quantum gas,
+
+and you add angular momentum,
+the angular momentum cannot
+
+lead to rigid body rotation.
+
+This would violate the fact
+that the velocity field has
+
+to be irrotational to make
+sure that the phase of the wave
+
+function is well defined.
+
+So if you rotate the system,
+it can absorb angular momentum
+
+only by forming vortices.
+
+And vortices are singular points
+of the wave function-- singular
+
+points where the density is 0.
+
+In other words-- I don't have
+time to be exhaustive here--
+
+but when something
+rotates, there
+
+is a dynamic phase you
+can say, because there
+
+are matter waves
+going in circles.
+
+And the integral
+of the phase has
+
+to be an integer number
+of 2 pi, otherwise
+
+you would not have a
+well-defined phase of the wave
+
+function.
+
+And if you now say you make
+a circle, which is 2 pi.
+
+You make the circle
+smaller, smaller, smaller.
+
+In the middle of the
+circle, you go around.
+
+The wave function
+changes by 2 pi,
+
+but what should the wave
+function do on one point?
+
+Which number between 0 and 2 pi
+should the wave function peak?
+
+Well, the wave function
+says I can't peak.
+
+I just go to 0.
+
+And a 0 value has no
+phase and I'm fine.
+
+That's exactly what the
+wave function tells you.
+
+So therefore if you want
+to describe vortices,
+
+you want to now describe the
+Gross-Pitaevskii equation,
+
+but with the boundary condition
+that the wave function
+
+goes to 0.
+
+And if you want to
+describe one vortex,
+
+you want the wave function to
+go 0 in the center of the cloud.
+
+And so you make a
+corresponding Ansatz.
+
+You allow the phase to
+wrap around by 2 pi,
+
+when the angle phi is varied.
+
+And then when you solve
+it, you have, of course,
+
+put in that there should be a
+0 of the density at the center.
+
+And it's now nice for me to--
+there's an important review
+
+paper which describes
+all that and more--
+
+but it's nice to
+show you now the two
+
+extreme cases of the ideal
+condensate without interaction,
+
+and the strong
+interacting condensate.
+
+The ideal condensate-- well, we
+are in the first excited state
+
+of the harmonic
+oscillator potential.
+
+And this is the dashed line.
+
+And of course, the size
+of the whole, the 0,
+
+is pretty much on the order
+of the oscillator length,
+
+because there is no
+other length scale
+
+in the ideal
+harmonic oscillator.
+
+But if you have the
+interacting system,
+
+remember what
+interactions are doing.
+
+They want to keep the density
+as constant as possible.
+
+Well, we are not
+in a box potential.
+
+We're in an inverted
+parabola potential.
+
+And remember, our
+Thomas-Fermi solution,
+
+which neglects kinetic energy,
+is the inverted parabola
+
+up to here.
+
+And then the tail is
+when we can no longer
+
+neglect the kinetic energy.
+
+But if we now say, OK, fine,
+but now in addition, we
+
+want a vortex in
+the center, the wave
+
+function out there says no.
+
+We do what minimizes
+kinetic energy,
+
+and what minimizes
+repulsive energy.
+
+We follow the inverted
+parabola, and only
+
+at the very last moment-- on
+the scale of the healing length,
+
+the system meets the
+required boundary condition
+
+that the density goes to 0.
+
+Anyway, with this
+qualitative understanding,
+
+you can get a lot out of those.
+
+You can immediately
+understand the salient feature
+
+of the solution.
+
+Question?
+
+AUDIENCE: I know we're
+not talking details,
+
+but is there a simple,
+maybe clear reason why
+
+when you spin a
+Bose-Einstein condensate
+
+you get many vortices, but
+when you spin your coffee
+
+in your cup, you
+just get one big one?
+
+PROFESSOR: Yes.
+
+So the question is, if I have
+a wrap-around of 4 pi in phase,
+
+whether the system should have
+a doubly charged vortex, or two
+
+singly charged vortices?
+
+What is the
+difference in energy?
+
+Well, what happens is doubly
+charged vortices are unstable.
+
+My group, at some point,
+were the first to create
+
+doubly charged
+vortices, but we saw
+
+that they immediately decayed.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Pardon?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Initially,
+we couldn't observe.
+
+We just saw that
+it was unstable.
+
+But it's a decay
+into two vortices.
+
+But it's easy to understand.
+
+If you put two vortices
+on top of each other,
+
+what is the energy of the
+system compared to one vortex?
+
+Well, the energy of a vortex is
+the rotational field around it,
+
+and if you superimpose
+two vortices,
+
+the velocity around the
+doubly charged vortices
+
+is twice the velocity
+of one vortex.
+
+And therefore, the kinetic
+energy is four times.
+
+If you have two
+vortices which are
+
+far separated that it has
+its own velocity field.
+
+It has its own
+velocity field here.
+
+And when the two velocity
+fields come together,
+
+the velocity is
+already so low that you
+
+don't have to consider that,
+then those two vortices have
+
+an energy which is two times
+the energy of a single vortex.
+
+So therefore, when
+the two vortices,
+
+they start out with four times
+the energy of a single vortex,
+
+and when they dissociate
+and repel each other,
+
+they have shed half
+of their energy.
+
+So this argument
+tells you immediately
+
+that vortices are
+in effect repulsive.
+
+And therefore, any
+multiple-charged vortex
+
+will spontaneously decay.
+
+It's also this net
+repulsion between vortices
+
+which makes the vortices
+arrange in a regular lattice.
+
+The regular lattice
+which you saw before
+
+is Nature's answer to
+how can we minimize
+
+the energy of all
+those vortices?
+
+And the idea is let's keep the
+average distance between them
+
+as large as possible, and the
+answer is a hexagonal lattice.
+
+Yeah.
+
+AUDIENCE: So a few
+slides back, when
+
+you write the G-P equation, when
+you plotted sort of for the box
+
+potential, the ground state
+and the excited state comparing
+
+the G-P equation to the typical
+single-particle [INAUDIBLE].
+
+And so I guess I'm a
+little bit confused
+
+about how excitations manifest
+themselves in the system.
+
+Because in some sense, if you
+were to solve the G-P equation,
+
+would you arrive at a
+spectrum of solutions?
+
+Then I guess I'd be confused
+at whether excitations manifest
+
+themselves into that
+spectrum of solutions,
+
+or rather than they become
+excitations, sort of deviations
+
+from the mean field as
+including the [INAUDIBLE].
+
+PROFESSOR: You are now
+asking about something
+
+more complicated.
+
+You're asking what
+are the excited
+
+states of the many-body system?
+
+And actually, we have
+already found one answer.
+
+And this is if you want
+these small excitations,
+
+it's one particle
+becomes a phonon,
+
+or one particle becomes
+a quasiparticle.
+
+What we are talking
+about here is
+
+what happens if the
+whole macroscopic wave
+
+function is in an excited state.
+
+So we are asking here in
+the box potential what
+
+happens if you force all N atoms
+to have one node in the wave
+
+function.
+
+And this is what I'm
+talking about here.
+
+So the excitation
+energy of this state
+
+here is much, much higher
+than of single quasiparticle
+
+excitations.
+
+I'm not sure if I'm addressing
+your question here, but--
+
+AUDIENCE: So with
+single quasiparticle
+
+excitations, are
+those essentially sort
+
+of deviations from
+the mean field?
+
+PROFESSOR: No, they
+are-- you really
+
+look for many-body physics--
+main field deviations--
+
+probably.
+
+I mean, what you do
+is in that sense, yes.
+
+You're allowing in this
+Ansatz that psi operator
+
+is psi average
+plus fluctuations.
+
+You now look for
+fluctuations, and you're
+
+looking for the
+energy eigenspectrum
+
+of those fluctuations.
+
+And the answer are
+quasiparticles.
+
+So it is, actually,
+the Bogoliubov solution
+
+for the spectrum of
+the fluctuations.
+
+And the answer is the dispersion
+relation I presented to you.
+
+Whereas here we
+are asking what are
+
+excited states of the
+macroscopic wave function?
+
+It's a very, very
+different question
+
+which we've addressed here.
+
+Yes.
+
+AUDIENCE: So when you
+stir the condensate,
+
+do you view it as-- do you
+stir, sort of, at the trap
+
+frequency, so I do sort
+of N single excitations?
+
+Or do you stir at N
+times the trap frequency,
+
+so you get one sort of
+N particle excitation?
+
+PROFESSOR: Well, the
+experimental answer
+
+is you want to stir at the
+quadrupole frequency, which
+
+is square root 2 times
+the trap frequency.
+
+Then you create
+quadrupolar excitations.
+
+The quadrupolar excitation can
+be regarded as a standing sound
+
+wave, but you create
+a macroscopic number
+
+of those excitations.
+
+So you make, actually, the
+whole condensate wave function
+
+oscillate in a
+quadrupolar pattern,
+
+but it's a rotating
+quadrupole, and that
+
+eventually then rearranges
+itself and leads to vortices.
+
+So I think the correct answer
+is the most efficient way
+
+to create vortices would be to
+excite quasiparticles, but then
+
+create so many-- and this may
+relate to Matt's question--
+
+create so many quasiparticles
+that you have really
+
+a time-dependent and oscillating
+macroscopic wave function.
+
+So eventually, you have
+a coherent excitation
+
+of quasiparticles.
+
+And that eventually means
+the condensate moves
+
+in a quadrupolar pattern, but
+it's a quadrupolar pattern
+
+with rotation, and
+that eventually
+
+turns into many vortices.
+
+But that's really a very rich
+question which you're asking,
+
+which has been studied-- a lot
+of different aspects of that
+
+have been studied.
+
+OK, so we've talked about
+Bose-Einstein condensates
+
+in a homogeneous system, just
+sort of to lay the groundwork.
+
+We've talked about
+Bose-Einstein condensates
+
+in traps in
+inhomogeneous system.
+
+Now we want to talk about
+Bose-Einstein condensates
+
+in optical lattices.
+
+Well, there are two reasons
+why we want to do that.
+
+One is we want to use the
+Bose-Einstein condensate
+
+to obtain deeper insight into
+the properties of matter.
+
+And a lot of forms of matter
+appear in periodic lattices.
+
+So if you put a
+Bose-Einstein condensate
+
+into a periodic
+potential, we can at least
+
+understand some
+of the properties
+
+of crystalline
+matter, or electrons
+
+which are block waves
+in a periodic potential.
+
+So this is one reason why.
+
+The other reason why we want
+to go to optical lattices
+
+is the following-- ideal
+Bose-Einstein condensates
+
+are trivial.
+
+Weakly interacting Bose-Einstein
+condensates are entertaining,
+
+and you can write a lot of
+papers, have a lot of fun
+
+with it, develop your methods--
+also mildly intellectually
+
+interesting because how those
+weak interactions manifest
+
+itself in vortices and all.
+
+It's really rich
+and interesting.
+
+But the conceptional
+problems appear
+
+when you go to
+strong interactions.
+
+Strongly correlated matter is
+where mean field descriptions
+
+no longer work.
+
+This is really the frontier
+of our understanding
+
+of many-body systems.
+
+And when you want
+to be there, you
+
+want to create a strongly
+correlated system.
+
+And strongly correlated systems
+means that the interaction
+
+energy dominates
+over kinetic energy.
+
+In Bose-Einstein
+condensates you can only
+
+go so far with
+increasing interactions--
+
+why are Feshbach resonances?
+
+Because you get into some
+inelastic collisions.
+
+So that's one knob to turn.
+
+You go to larger and larger
+of scattering lengths,
+
+and crank up the interactions.
+
+But if atoms strongly interact,
+they start to do bad chemistry.
+
+They start to spin flip.
+
+They do other things.
+
+And in some cases you
+keep it under control.
+
+In others, you just can't
+keep it under control.
+
+But another way to get
+to strong interactions
+
+means you reduce
+the kinetic energy.
+
+It's the ratio of the
+two which matters.
+
+And when you put particles
+in a lattice, well,
+
+the lattice actually
+reduces the kinetic energy.
+
+You may know from
+condensed matter physics
+
+that in a lattice there is
+an effective mass, which
+
+is higher than the
+[INAUDIBLE] mass.
+
+Therefore you've reduced
+the kinetic energy.
+
+Or if you want another
+hand-waving approximation,
+
+the kinetic energy is
+given by the bandwidths.
+
+And if the tunneling
+becomes slower and slower,
+
+the width of your
+band becomes narrower,
+
+and your kinetic energy is less.
+
+So anyway, I can give you many
+hand-waving approximations
+
+why in a lattice,
+kinetic energy is reduced
+
+and repulsive energy
+is probably enhanced,
+
+because instead of having
+your atoms spread out,
+
+they're bunched up
+at each lattice site
+
+into a higher density cloud.
+
+So anyway, maybe you're
+interested in parity
+
+potentials, or you're
+interested in quantum systems
+
+with strong correlations.
+
+For whatever reasons, you
+want optical lattices.
+
+Now I have here a
+few slides which
+
+introduce periodic
+potentials, but it is really
+
+just the single particle
+physics in a periodic potential.
+
+It has nothing do
+with quantum gases.
+
+This could be the
+first lecture of how
+
+to describe
+electrons in a metal.
+
+So let me just quickly
+go through assuming
+
+that almost all of
+you are familiar.
+
+But I use those slides also just
+to give you a few definitions
+
+and introduce a few symbols.
+
+So this is simple, boring,
+exactly understood physics.
+
+We have a Hamiltonian
+which has kinetic energy,
+
+and a periodic potential which
+is our lattice potential.
+
+It's rather trivial to solve,
+but exactly for your wave
+
+function, you use
+Bloch's theorem
+
+and divide it by an exponential
+factor with quasi momentum
+
+times a periodic function.
+
+And if you now solve
+Schrodinger's equation,
+
+you want to use Fourier space.
+
+You Fourier analyze
+the wave function.
+
+You Fourier analyze
+the potential.
+
+And since the
+potential is periodic,
+
+sine square potential has
+only three Fourier components
+
+at 0 plus/minus 1 times the
+periodicity of the lattice.
+
+You do a Fourier expansion for
+your periodic wave function.
+
+And if you insert that into
+Schrodinger's equation,
+
+well, the Fourier transform
+has turned the differential
+
+equation into an
+algebraic equation,
+
+because the second
+derivative simply
+
+becomes now k
+squared or q squared.
+
+So in other words, you have
+a set of linear equations.
+
+There is an index
+which is the band
+
+index-- how high
+do you want to go?
+
+And usually you truncate it.
+
+But it's the same.
+
+It is that same
+trivial story which
+
+is told in all textbooks of
+condensed matter physics.
+
+If you have no band structure,
+well, you have the parabola,
+
+but to prepare for
+band structure,
+
+I've opened it down here in
+the first Brillouin zone.
+
+And if you now
+introduce a lattice,
+
+you introduce band gaps, and you
+go from the left to the middle
+
+to the right for stronger
+and stronger lattices.
+
+So the case which
+I will focus on,
+
+because it is the most extreme
+case away from free space,
+
+is this case which is called
+the tight binding limit, where
+
+the potential energy of
+the lattice is large.
+
+And large means compared
+with the kinetic energy
+
+at the Brillouin
+Zone, which is k
+
+squared-- k is the lattice
+momentum-- k squared over 2 m.
+
+And that's the recoil energy.
+
+So that our dimensionless
+parameter here
+
+is the depth of the
+lattice measured
+
+in recoil energies
+of the photon,
+
+because that is
+the kinetic energy
+
+of the free gas at
+the Brillouin zone.
+
+OK there are few things which
+immediately simplify that.
+
+Once we're in the
+tight binding limit,
+
+our lattice is really
+deep, and each side
+
+forms a harmonic oscillator.
+
+And the harmonic
+oscillator frequency
+
+is analytically given by
+the depth of the lattice.
+
+And the solution here
+for the lowest band
+
+is that the lowest
+band-- the energy
+
+in the lowest band, the
+dispersion relation is-- well,
+
+we have a harmonic oscillator
+in each site at x y z.
+
+So the average energy
+in the lowest band
+
+is the 0 point energy in x, y,
+and z-- three half h-bar omega
+
+0.
+
+And then we have a
+cosinusoidal band structure
+
+where q is the quasimomentum.
+
+And what appears here as the
+only interesting parameter
+
+is j.
+
+And j is I think this 4
+should be 4j is the bandwidth.
+
+So what appears here now
+for the first time is j.
+
+It appears here
+as the bandwidth.
+
+But let me immediately give
+it another interpretation
+
+as a tunneling matrix element in
+the following way-- right now,
+
+we have formulated the physics
+in Bloch wave functions
+
+which are infinitely extended.
+
+The Bloch wave functions
+are for the lattice
+
+what plain waves
+are for free space.
+
+But if you have
+tight binding limit,
+
+there is another limit
+which is important.
+
+Namely, a particle is localized
+and hops around in the lattice.
+
+The localized particle, of
+course, is in free space.
+
+It would be a wave packet-- a
+superposition of plain waves.
+
+So let's do the
+same in the lattice.
+
+Let's construct
+superpositions of Bloch waves.
+
+And these are our wave packets.
+
+And the wave packet is now
+called the Wannier function.
+
+And there is a
+mathematical procedure
+
+how you should pick
+the phases here
+
+to get the maximal
+normalization.
+
+But the simple picture is
+those Wannier functions are
+
+very, very close to the
+Gaussian ground state
+
+solution of the harmonic
+oscillator on each side.
+
+The wings are different, but
+I don't want to go into that.
+
+You transform from an
+orthonormal basis of Bloch wave
+
+function to another orthonormal
+basis Wannier function.
+
+And the Wannier functions are
+as well localized as possible.
+
+That's the procedure.
+
+And now we can simply
+rewrite our total Hamiltonian
+
+or everything we're interested
+in, not in Bloch wave functions
+
+but in Wannier wave functions.
+
+And what comes out now is,
+is that the bandwidth j
+
+is nothing else than our
+Hamiltonian with kinetic energy
+
+in the periodic potential.
+
+But j becomes now
+a matrix element
+
+between two Wannier functions.
+
+But the Wannier
+functions have now-- I'll
+
+put in some indices
+in a moment--
+
+connect now two different sides.
+
+So it is-- you have
+Wannier function.
+
+You have the Hamiltonian
+and connect it
+
+to another Wannier function.
+
+So it is the amplitude
+that, with the Hamiltonian,
+
+the particle can hop from
+one side to another side.
+
+So therefore j, which
+was the bandwidth,
+
+is now the tunneling
+energy divided
+
+by h bar-- the tunneling
+rate from on one side
+
+to the other side.
+
+For very deep lattice,
+everything is analytic
+
+and it can easily be solved.
+
+And I mentioned already in the
+tight binding approximation,
+
+you should think about
+your Wannier function
+
+as just localized
+Gaussian eigensolutions
+
+of the harmonic oscillator.
+
+Yes?
+
+AUDIENCE: So qualitatively, this
+question sounds sort of silly,
+
+but normally when we write
+down the solution for j,
+
+we're only considering
+nearest neighbor.
+
+But from the math,
+I don't immediately
+
+see why we wouldn't
+include i equal to j.
+
+PROFESSOR: Give
+me one more slide.
+
+So I should've
+actually-- what I should
+
+have done is that--
+j has an index here.
+
+I just didn't want to
+overload you with indices.
+
+I mean, this is sort
+of just telling you
+
+what j is in its simplest form.
+
+It is loaded with indices and
+I well show you in a moment
+
+where those indices come in.
+
+So I just wanted to
+give you the idea
+
+if we want to have
+Wannier function.
+
+We hop from one Wannier
+function to the other one,
+
+and the operator
+is the Hamiltonian.
+
+And therefore, there
+should be an index j and l.
+
+And maybe-- let me just do the
+next step first and then come
+
+back to it, but I
+wanted to tell you here
+
+what I'm aiming at--
+namely interpretation of j,
+
+of tunneling from
+one side to the next.
+
+But right now I haven't really
+told you which j I really mean.
+
+There should be-- based
+on the right-hand side,
+
+there is a j which
+has two indices.
+
+And I will make the indices
+disappear in a moment.
+
+But before I make those
+indices disappear,
+
+let me introduce the other
+relevant parameter, which
+
+will also have
+indices, and that is we
+
+have to bring in
+the interactions.
+
+We want to describe
+an interacting system.
+
+We describe an
+interacting system
+
+using the short-range
+approximation
+
+by assuming that two particles
+interact with a delta function.
+
+And if you have two particles
+on site, each of them
+
+has a density which is the
+Wannier function squared.
+
+And the product of the
+two densities integrated
+
+gives us the expectation value
+for the repulsive energy.
+
+And this is given here.
+
+So the moment we
+introduce interactions,
+
+we are now interested in
+the interaction energy
+
+between two particles which in
+this case occupy the same side.
+
+OK so I've tried to introduce
+was what sort of j is.
+
+j is a matrix element
+between two Wannier functions
+
+with a Hamiltonian in between.
+
+And u is the matrix element
+of two Wannier functions
+
+with the interaction
+operator in between.
+
+And now I want to
+use that concept
+
+to take my full
+Hamiltonian and transform
+
+from field operators localized
+at x to Wannier functions.
+
+So they B operators are
+now creation operators.
+
+They create an atom
+in a Wannier function.
+
+In other words, B
+dagger means you
+
+have a particle in a
+Wannier function at site i.
+
+And I just use that as
+a basis transformation
+
+and the exact transformation
+of this Hamiltonian
+
+is now into this form.
+
+So
+
+What I have right now is, I have
+the tunneling matrix element
+
+between particles
+at site i and j,
+
+and I have to sum
+over all of them.
+
+And in terms of interaction,
+I can calculate this matrix
+
+element by using Wannier
+function with four
+
+different indices
+and ask what happens.
+
+And this is simply an
+exact way of rewriting it.
+
+And here I've given
+you the definition.
+
+So if you want to
+forget everything
+
+I told you about j and u, I've
+done an exact transformation
+
+from field operators to Wannier
+function creation operators.
+
+And this introduces tunneling
+terms like this from site i
+
+to site j.
+
+And these here includes products
+of four Wannier functions
+
+which are responsible
+for the interaction term.
+
+Actually, if this is
+not complicated enough,
+
+I've suppressed
+band indices here.
+
+I should also now sum
+over all possible bands.
+
+But OK, I want to come now
+to the leading approximation
+
+in a tight binding model.
+
+And that is where--
+I mean those Wannier
+
+functions are overlapped.
+
+Two neighboring Wannier
+functions barely overlap.
+
+If I go further away, the
+overlap becomes even smaller.
+
+So the most dominant terms are
+nearest neighbor interactions.
+
+And the nearest
+neighbor interaction
+
+is where i and j differ by 1.
+
+And this is what I
+call j without indices.
+
+And similarly, when it comes
+to the interaction term
+
+where we have products
+of four Wannier functions
+
+and we want to get the
+overlap of all four,
+
+and then multiply it with g,
+the prefactor of our delta
+
+function to get an
+interaction term,
+
+well the best overlap is if
+all indices are the same.
+
+And this is what I call U.
+
+So in that limit, in
+that tight binding limit,
+
+my Hamiltonian is
+now very simple.
+
+It consists of a tunneling
+term parametrized with j,
+
+and an on site interaction
+term parametrized with U. Yes.
+
+AUDIENCE: So you're saying
+i, j and k are all the same,
+
+so the interaction
+is with itself?
+
+PROFESSOR: No, two
+particles per site.
+
+When the four
+particles are the same,
+
+it turns into-- this
+Hamiltonian here has
+
+all indices are the same.
+
+And if you calculate that, it
+turns into the product of 2 b.
+
+b dagger is the occupation
+number at each site.
+
+But if you're careful
+with commutators,
+
+it becomes occupation number
+times occupation number
+
+minus 1.
+
+If you have only one particle
+per site, this term is 0.
+
+So technically U is, if
+you put in 2 times 1,
+
+if you have two
+particles per site,
+
+U is the interaction energy
+between two particles.
+
+Just use this
+expression to figure out
+
+what it is for three or four.
+
+But for one particle, you get 0.
+
+The self interaction of a
+particle is absolutely 0.
+
+One particle does not
+interact with itself.
+
+AUDIENCE: That gets back to my
+question with the [INAUDIBLE].
+
+So when you have i equals j, the
+[INAUDIBLE] term, do you just--
+
+PROFESSOR: No, I assume,
+i j is nearest neighbor.
+
+I assume that the index
+i and j differ by 1.
+
+AUDIENCE: Yeah, I mean your
+argument was that the best
+
+overlap is between
+nearest neighbors.
+
+PROFESSOR: Yes.
+
+AUDIENCE: So an overlap
+with the Wannier functions
+
+at the same site is sort
+of the kinetic energy term.
+
+Is it approximately 0,
+or you just absorb that
+
+into the chemical potential?
+
+PROFESSOR: This is a 0.
+
+AUDIENCE: [INAUDIBLE]
+So we're only
+
+looking at nearest neighbor,
+so are we essentially saying
+
+the case where i equals j is
+approximately 0 [INAUDIBLE].
+
+AUDIENCE 2: Because
+it's the matrix element
+
+of a Hamiltonian.
+
+So p, the candidate, plus
+the lattice operator.
+
+So if I take my
+Wannier function,
+
+which is built out of
+eigenvalues for that equation,
+
+[INAUDIBLE] bunch
+of energy terms.
+
+On every site [INAUDIBLE]
+they're the same.
+
+Because you have a common
+[INAUDIBLE] energy that you can
+
+[INAUDIBLE].
+
+AUDIENCE: Well then just
+multiple it by [INAUDIBLE].
+
+PROFESSOR: My gut
+feeling is-- and this
+
+is why nobody considers
+it-- it's just
+
+a constant energy, which is
+probably something like the 0
+
+point energy times the number
+of particles, which is not
+
+affecting any dynamics.
+
+It's pretty much a constant
+which can be simply dropped.
+
+Let me just go
+back to that slide.
+
+I hope-- let me just
+look up the reference.
+
+I haven't looked at it recently.
+
+When we do this
+exact transformation,
+
+there should be a
+reference whether i
+
+and j, what happens
+when i equals j.
+
+I think it's just
+a constant term.
+
+AUDIENCE: Because
+if you're summing
+
+over every single
+lattice site, so
+
+you get the number of
+particles times 0 [INAUDIBLE].
+
+PROFESSOR: Yeah, but
+even mathematically
+
+it gives just a constant term,
+here, which is [INAUDIBLE].
+
+Thanks.
+
+It was good to clarify it.
+
+OK, I think within
+the next 20 minutes,
+
+I can step you through
+the superfluid to Mott
+
+insulator transition.
+
+First, references for what
+I've just said are given here.
+
+But let me now come take
+this Bose-Hubbard model
+
+and discuss its
+two limiting cases.
+
+One case is where U
+is much larger than j.
+
+The other case is where
+j is much larger than U.
+
+These are the two
+limiting cases,
+
+and it will turn out
+that one is an insulator
+
+and one is a superfluid.
+
+And that makes perfect
+sense, of course.
+
+If U is much larger than
+j, I can set j equals to 0
+
+if I can neglect it.
+
+No tunneling means no transport,
+and that means an insulator.
+
+It's also clear that when
+there is no tunneling,
+
+that the system is
+really described
+
+by a product of so and so
+many particles per site.
+
+So it could be one
+particle per site.
+
+And I have a product
+over all sites,
+
+or two particles per site.
+
+So this will be
+the ground state.
+
+And it's called the ground
+state of the Mott insulator.
+
+It's also trivial
+to discuss what
+
+happens if j is much,
+much larger than U,
+
+because then I simply neglect
+U, and I have a free gas.
+
+Well, a free gas of
+Bloch wave function,
+
+but that's the same as a free
+gas of planar wave function.
+
+It's just that quasimomentum
+replaces momentum.
+
+And if you have just
+an ideal Bose gas
+
+in a periodic lattice instead
+of Bose-Einstein condensation
+
+in the lowest
+momentum state, you
+
+have Bose-Einstein condensation
+in the lowest quasimomentum
+
+state.
+
+The lowest quasimomentum
+state is a superposition
+
+of all Wannier
+function-- I mean,
+
+the 0 momentum
+state in free space
+
+is a superposition of all
+position delta functions.
+
+The plane wave is delocalized.
+
+And the lowest
+quasimomentum state
+
+is just completely delocalized
+over all Wannier functions.
+
+But this is nothing
+else than the q
+
+equals 0 quasimomentum
+Bloch wave.
+
+The interesting
+question is-- and this
+
+has led to hundreds if not
+more papers in the literature--
+
+how do we go from one
+limit to the other limit?
+
+And now you would
+say, well, maybe we
+
+should use what
+has worked so well.
+
+We should use the
+Bogoliubov approximation.
+
+Just assume we
+have a condensate,
+
+replace all those kind of a 0
+operators for the lowest Bloch
+
+waves.
+
+However, this doesn't work,
+because the interesting thing
+
+here is to find the
+transition from the superfluid
+
+from the Bose-Einstein
+condensate
+
+to an insulating state.
+
+The nature of this
+approximation is
+
+that you need N 0 to be large.
+
+But we're interested when the
+condensate wave function turns
+
+to 0, and in the
+insulator it becomes 0.
+
+So we are actually interested
+in the opposite limit.
+
+And indeed, if you
+would ignore everything
+
+I've just said that
+doesn't make sense
+
+to make this approximation
+and make it nevertheless,
+
+you will find that you never
+get the insulating state
+
+because you've pretty much
+eliminated the possibility
+
+to describe an insulating state
+by doing this approximation.
+
+So I want to show
+you now that we
+
+have to do another mean
+field approximation, which
+
+is actually nice.
+
+It's very different from this
+Bogoliubov approximation,
+
+but it's also a mean
+field approximation
+
+which will describe our system.
+
+So the goal is now
+that I want to find
+
+an effective Hamiltonian
+which describes
+
+the transition
+from here to there.
+
+And the important
+approximation I will use
+
+was is the following-- again,
+I have to get rid of operators.
+
+Products of two many
+operators cannot be solved.
+
+And so what I will do is I
+will use products of operators,
+
+write them as average
+value plus fluctuations.
+
+And then when I
+multiply that out,
+
+I take the product of
+the average values,
+
+and I include the
+fluctuations in leading order.
+
+So I take delta A times B
+and delta B times A average,
+
+but I neglect the product
+of those fluctuations.
+
+You can say I neglect the
+correlation of fluctuations
+
+here.
+
+So this is spelled out here.
+
+But the sign is important.
+
+Just look at this equation--
+A delta B plus delta B with B
+
+plus A average times B average.
+
+If I absorb A times B by
+upgrading delta B to B,
+
+but I do the same here,
+I have to subtract
+
+1 product of the
+two average values.
+
+It's actually this minus sign
+which will play a role later,
+
+but here you see already that
+I will make this decoupling
+
+approximation-- that I
+decouple the fluctuations
+
+from each other and I
+write it in this way,
+
+there is an
+important minus sign.
+
+OK, so we want to start
+in the insulating state.
+
+And we're going to figure out
+how does the system develop
+
+superfluidity out of
+the insulation state?
+
+And the perturbation
+operator which takes me out
+
+of the insulating
+state is tunneling.
+
+So therefore, the operator which
+is responsible for breaking out
+
+of the insulating
+state is the operator
+
+which induces tunneling
+between neighboring sites.
+
+And the tunneling operator
+in this Hamiltonian--
+
+remember, the Bose-Hubbard
+model had j times B dagger B--
+
+this was our tunneling
+term-- this involves now
+
+products of operators.
+
+And I told you we want to get
+rid of products of operators
+
+to get something we
+can easily solve.
+
+So we use now this
+product of operators
+
+on two neighboring sites.
+
+And we use exactly this
+decoupling approximation.
+
+So therefore, we replace each
+operator by an average value,
+
+and we neglect the product
+of the fluctuations.
+
+And then we obtain this.
+
+And I explained to you where
+the minus sign came from.
+
+So now I call this average
+value of the operator B l,
+
+I call the superfluid
+order parameter psi.
+
+I think I could have
+chosen psi to be complex,
+
+and then B l dagger B l
+would have complex conjugate.
+
+But it's sufficient here
+to restrict the discussion
+
+on real numbers, and it
+makes the notation simpler.
+
+So anyway, I introduce that.
+
+And what happens now
+is the following--
+
+that I have my Hamiltonian.
+
+The Hamiltonian had
+the interaction energy.
+
+But the tunneling term
+is now very simplified,
+
+because instead of
+tunneling from one site
+
+to a neighboring
+site, the other side
+
+is sort of absorbed
+by the mean field,
+
+by the superfluid
+order parameter psi.
+
+And therefore, and this
+here gives me a psi
+
+squared term which appears here.
+
+Trust me, this is just
+an identical rewrite
+
+of the previous Hamiltonian
+by using this decoupling
+
+approximation.
+
+So what we have gained now
+is something really dramatic.
+
+We had many sites and
+tunneling from site to site.
+
+But if you look at
+it now, we simply sum
+
+the effective Hamiltonian
+over site index l.
+
+So our effective
+Hamiltonian is now
+
+the sum of an identical
+Hamiltonian per site.
+
+The sites no longer
+interact with each other.
+
+Each site interacts with all
+the other sites described
+
+by the mean field by the
+superfluid order parameter psi.
+
+So therefore, our
+many-body problem,
+
+which is still a
+many-body problem,
+
+but has turned into an effective
+Hamiltonian for each site,
+
+because each side has
+the same Hamiltonian.
+
+Colin.
+
+AUDIENCE: What happened
+to the j psi squared term?
+
+PROFESSOR: This here?
+
+AUDIENCE: Oh, OK.
+
+PROFESSOR: OK so I can say
+instead of solving for the sum,
+
+I can just solve for
+each site individually.
+
+And this is now my effective
+Hamiltonian for each site.
+
+Now I want to catch the
+onset of superfluidity.
+
+So I want to get the
+system when psi is small.
+
+And therefore, I can just
+ask-- I don't know what psi is.
+
+It's part of my solution.
+
+But I'm interested
+in the moment when
+
+psi begins to take off from
+0, when superfluidity emerges.
+
+So what I can therefore do is,
+I can regard psi as an epsilon
+
+parameter, as a small parameter.
+
+And the psi parameter
+comes with an operator V.
+
+And this operator V is nothing
+else than B l dagger plus B l.
+
+So in other words,
+what I'm doing is,
+
+I'm separating my Hamiltonian
+into a Hamiltonian which
+
+is diagonal in the
+quantum numbers
+
+of the isolating state--
+just one, two, three
+
+particles per site.
+
+And psi squared is the Z number.
+
+Psi squared is also
+diagonal in that.
+
+And now the possibility
+of tunneling,
+
+the possibility of
+superfluidity is now
+
+perturbative in this
+term psi times V.
+
+OK, I don't want to explain,
+actually, this expression.
+
+It just formalizes
+[INAUDIBLE] intermediate step.
+
+When we have the
+chemical potential,
+
+and we raise the
+chemical potential--
+
+we go from zero to
+one particle per site
+
+to two particles per site.
+
+And whatever the
+chemical potential is
+
+determines whether we have
+one or two particles per site.
+
+This is just telling me as a
+function of chemical potential,
+
+what is the ground
+state of the insulator?
+
+So now we take this ground
+state-- it's actually
+
+much easier described
+in words then
+
+by this formula-- we
+take this ground state
+
+and do perturbation theory in
+our term psi times V. Remember,
+
+the operator is B dagger
+B. And the epsilon is psi.
+
+So in second-order perturbation
+theory, we get psi squared.
+
+And then V, because B B
+dagger, is very simple.
+
+It only couples one occupation
+number N to N plus 1
+
+and N minus 1,
+because B and B dagger
+
+destroy or create a
+particle per site.
+
+So therefore, I can
+immediately write down
+
+what this matrix element is
+in second-order perturbation
+
+theory.
+
+I mean, these are all--
+sorry, it's all defined here.
+
+I know I'm losing you now.
+
+Nobody will tell me what is the
+difference between U bar and U,
+
+but it's trivially defined.
+
+So the idea is we have
+the isolating system.
+
+We do perturbation
+theory in tunneling.
+
+And the perturbative operator
+is psi times B plus B dagger.
+
+The B plus B dagger
+matrix elements
+
+are trivial, because
+they admix to N particles
+
+per site-- N plus
+1 and N minus 1.
+
+And this is what
+we've done here.
+
+AUDIENCE: And the j is
+just occupation number?
+
+PROFESSOR: The j is the
+occupation number of our site.
+
+AUDIENCE: I have two questions.
+
+So in the bottom equation, what
+happened to the psi squared?
+
+PROFESSOR: Sorry,
+this is the sum.
+
+The psi square is missing.
+
+AUDIENCE: I guess I
+had the same question
+
+for the equation next
+to the green thing.
+
+Is there supposed to be
+a psi squared in there?
+
+Because originally, there's
+a psi squared and an h0.
+
+PROFESSOR: No, this is the
+ground state where psi is 0.
+
+And now we do
+perturbation theory
+
+in psi V. These are the
+unperturbed energies which
+
+appear in the
+energy denominator.
+
+The wave functions
+we are using are
+
+Fock states-- number
+states-- per site.
+
+And here we couple occupation
+number j to all possible N's.
+
+But because of B and B dagger,
+N has only two values--
+
+j plus 1 and j minus 1.
+
+And this is what's given here.
+
+It's mathematically trivial.
+
+The notation is more complicated
+than the physics behind it.
+
+But now comes again-- I think I
+need five minutes and I'm done.
+
+But now comes the
+interesting physics.
+
+We have to ask what
+are we doing here?
+
+It's all the mathematical, and
+the math is really simple here.
+
+What we have done is we have
+looked at the isolating state,
+
+and we have done perturbation
+theory in psi times B plus B
+
+dagger.
+
+And now we get an
+energy correction
+
+which is psi squared.
+
+And what are we
+really doing here?
+
+Well, you can say
+the following--
+
+we started with a
+hypothesis that we
+
+have a superfluid state
+characterized by psi and psi,
+
+at the onset of
+superfluidity-- is small.
+
+But now we have
+done the calculation
+
+assuming that there is a psi.
+
+But now we are turning around
+and said have we really
+
+done the system a favor by
+introducing superfluidity?
+
+In other words, has our
+perturbation theory in psi
+
+lowered the energy of
+the state or raised
+
+the energy of the state.
+
+So in other words, we've done
+a hypothetical calculation.
+
+Hey, what would the
+system feel like if there
+
+were a little bit
+of superfluidity?
+
+If the system says great,
+I've lowered my energy,
+
+then we know we are in
+the superfluid state.
+
+When the system says no,
+I raised my energy because
+
+of the psi, then the system
+has rejected our idea
+
+to introduce superfluidity.
+
+So therefore, the question
+we are raising now
+
+is after we have done the
+calculation, for what values
+
+of U and j is it favorable
+to introduce a psi or not?
+
+Now I was expecting the
+question of some of you
+
+that in second-order
+perturbation theory,
+
+second-order perturbation
+theory always lowers the energy.
+
+But remember, this is why I
+emphasized the minus sign--
+
+we had a psi squared term
+which came from that, which
+
+came from the last term of the
+decoupling approximation, which
+
+had a minus sign.
+
+And therefore, we
+have in psi squared
+
+one term which came
+from this special psi--
+
+and I emphasized in the
+decoupling approximation.
+
+And we have a contribution
+of psi squared
+
+which comes from
+perturbation theory.
+
+And the two together can
+actually change their sign.
+
+So what we have right now is
+if you describe the ground
+
+state as a function of psi,
+we have our unperturbed energy
+
+of the Mott insulating
+states, and then we
+
+have a term in psi squared.
+
+And we should-- and we could,
+but we don't-- calculate
+
+the next order in
+psi to the four.
+
+And it turns out in fourth-order
+perturbation theory,
+
+this term is always positive.
+
+So what happens now
+to the total energy
+
+when this term A2, which we
+have exactly analytically
+
+calculated-- if this term A2
+is larger or smaller than 0.
+
+Well, if you have a parabolic
+term and a quartic term,
+
+in this case, both the
+quadratic and the quartic term
+
+are opening up
+like in a U shape,
+
+but here the total energy
+turns into W shape.
+
+And the interpretation
+is fairly simple.
+
+Under those
+conditions, the system
+
+prefers to have psi equal
+0, whereas here, it's
+
+like the system wants to
+have a psi parameter which
+
+is finite, either
+positive or negative.
+
+And whether it's
+positive or negative
+
+is sometimes called
+spontaneous symmetry breaking
+
+between two
+degenerate solutions.
+
+What I'm showing
+here is, of course,
+
+very similar to the
+Ginzburg-Landau theory
+
+of phase transitions, where
+you have an effective potential
+
+and the phase transition
+takes place when
+
+the second-order
+coefficient changes sign,
+
+and the effective potential
+turns from U-shaped
+
+into W-shaped.
+
+So that's what we have done.
+
+So anyway, I think this
+is a nice problem where
+
+the interpretation
+is, I think, much more
+
+subtle than the
+calculation itself.
+
+But we've calculated
+the phase transition.
+
+Everything is analytic.
+
+Here is the analytic
+result, which
+
+I know with very
+indigestible notation.
+
+I followed exactly the paper
+by Vanderstraeten, [? Stouff ?]
+
+and collaborators, which
+is posted on the website.
+
+You can plot this phase
+diagram in this way.
+
+But if you use what
+is more common,
+
+normalize the chemical potential
+by U and normalize j by U,
+
+you get these wonderful
+lobes of the Mott insulator
+
+where you see that,
+if you increase
+
+the chemical potential, you
+have N equals 1, N equals 2,
+
+N equals 3, Mott insulator,
+and in between you
+
+go through superfluid regions.
+
+However if your
+tunneling is larger,
+
+if your tunneling is too
+large, you're only superfluid.
+
+So this is sort
+of the way how you
+
+derive this rather
+rich phase diagram
+
+of bosonic atoms in
+an optical lattice.
+
+Green is an insulating state.
+
+And white is the
+superfluid state.
+
+Let me just conclude by
+showing a few slides how
+
+this can be observed.
+
+So in one case, we have
+an insulating state
+
+with a definite number
+of particles per site.
+
+And here we have
+superfluid state,
+
+which has the normal
+fluctuations in number.
+
+Here's another cartoon picture
+of an condensate in the lowest
+
+Bloch wave function.
+
+And here you have
+localized number states.
+
+Often, you observe the
+transition by taking the system
+
+and releasing it
+in time of flight
+
+into ballistic expansion.
+
+If the superfluidity
+is coherent,
+
+the wave function on the
+different sites is coherent.
+
+And what you get is a
+multi-slit interference pattern,
+
+which is a diffraction pattern.
+
+And you see these characteristic
+diffraction patterns.
+
+It's an in-slit
+diffraction pattern
+
+which characterizes the
+coherence in the initial state.
+
+However if you have a
+completely isolating state,
+
+you have a Gaussian wave
+packet on each side, which
+
+has nothing to do with
+the next neighbor.
+
+And then the Gaussian
+wave function simply
+
+expands in a structureless way.
+
+And so the transition
+from here to there
+
+happens exactly when
+the ratio of U over j
+
+crosses the value
+we have derived.
+
+There's another
+technique of observing
+
+that which is more recent.
+
+This is a quantum
+gas microscopes
+
+where you do the same
+physics in two dimensions,
+
+so you have only one plane
+where this physics takes place.
+
+And you can observe atoms
+now with a microscope.
+
+So each green dot
+here is an atom.
+
+If you sort of zoom in.
+
+And if you now study
+the region where
+
+you go through the superfluid
+to the Mott insulator,
+
+you see that you have
+exactly one atom per site.
+
+If you increase the atom
+number, you have an insulator
+
+with one atom per site.
+
+And in the middle,
+you have state
+
+with two atoms per site,
+which-- for reasons
+
+I don't want to discuss-- are
+color-coded here in black.
+
+And that sort of
+goes on and goes on.
+
+So you can really
+resolve site per site
+
+the occupation of the
+number of atoms per site.
+
+So I think I'll stop
+here with the Bose gases.
+
+When you think the
+Mott insulator is
+
+the end of the story, all
+motion has been frozen out
+
+and you have one
+particle per site, well,
+
+it could be the
+beginning of a new story.
+
+Because if you use two
+different hyperfine states,
+
+spin up and spin down, we
+can talk about spin ordering.
+
+But this would be a
+whole different lecture.
\ No newline at end of file
diff --git a/Iq8yyEHm_jI.txt b/Iq8yyEHm_jI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d63fb6fa4837f205f9d461794b4d37827a0ef202
--- /dev/null
+++ b/Iq8yyEHm_jI.txt
@@ -0,0 +1,4626 @@
+The following content is
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+
+Your support will help
+MIT OpenCourseWare
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+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+JEFFREY C. GROSSMAN: All right.
+
+So we are here.
+
+I'm highlighting
+two, because I really
+
+want to keep talking
+about solar thermal fuels,
+
+mostly because it really
+captures a key problem
+
+that only quantum
+mechanics can solve.
+
+OK?
+
+So I really want to
+hit that home hard.
+
+Also, because it's the
+topic of your next homework,
+
+and also because I'm biased.
+
+I'm more excited
+about this than this.
+
+But I want to tell you a little
+bit about hydrogen storage
+
+too, and why I think
+that's a perfect problem
+
+for atomic-scale
+computational modeling.
+
+OK?
+
+So we're going to do a lot
+more of solar thermal fuels,
+
+picking up where we did
+before, and then a little bit
+
+of hydrogen storage.
+
+Now, before we do that,
+I want to keep blending
+
+in some reinforcement
+of key basic concepts
+
+that we have touched on,
+and we need to make sure
+
+we feel good about them.
+
+So we're going to
+feel good today
+
+about energy levels, first
+bullet of the outline,
+
+feeling good.
+
+It's a good way
+to start, I think.
+
+I didn't need to put
+that there, because you
+
+would have felt good anyway.
+
+Right?
+
+But there it is in writing.
+
+We're going to feel good
+about energy levels,
+
+and then we're going to keep
+talking about solar fuels.
+
+And we'll do a few
+calculations, more calculations
+
+on the nanoHUB together.
+
+Right?
+
+Again, no better
+way to pass time.
+
+OK?
+
+And then we'll talk
+about hydrogen storage.
+
+That's our plan.
+
+Now, like I said, I want
+to keep reinforcing--
+
+I did this, and it
+put me off balance.
+
+It's excitement.
+
+That's a little bit
+more than my usual even.
+
+It's also, I think,
+just old age.
+
+I think sometimes, you
+get a little off balance.
+
+Anyway, now, point is
+that I think probably I
+
+like watch the NBA so
+much, because I still
+
+don't want to give up the
+idea that I could someday
+
+be in the NBA myself.
+
+So I'm not letting
+go of that dream,
+
+but anyway, I want to go back to
+one of my original excitements
+
+here about materials
+design which
+
+is one of the
+things I really want
+
+to make sure we
+capture in this class,
+
+designing materials
+and computers.
+
+Right?
+
+So I want to take
+carbon, and I just
+
+have two or three slides here.
+
+So I want to touch
+on what I think
+
+is a really exciting
+example of materials design,
+
+and you all know this.
+
+Right?
+
+You know carbon can do this
+and this, and many of you
+
+know that carbon can do--
+
+well, where are my fullerenes?
+
+Well, there's some nanotubes.
+
+There's fullerenes inside
+of nanotubes, p-pods.
+
+Right?
+
+Now, there's all kinds
+of forms of carbon
+
+that there didn't used to
+be, or there used to be,
+
+but we didn't see them, and
+we couldn't control them.
+
+OK?
+
+And I want to give
+you a really, I think,
+
+interesting analysis of one
+thing you can do with carbon.
+
+OK?
+
+And then another thing you can
+do with it, when you design it,
+
+when you can do
+materials design.
+
+So this is what we do with
+carbon now that we find in oil.
+
+Right?
+
+We burn it, and there's 1.73
+megawatt hours of energy
+
+when you burn a barrel of oil.
+
+Right?
+
+I didn't show you this example.
+
+Did I?
+
+OK.
+
+Because I think it's
+a really neat one.
+
+So that's how much energy
+is in a barrel of oil,
+
+and it's a lot of energy.
+
+That's a really nice--
+
+oil is amazing.
+
+It's like this incredible
+energy-dense, safe,
+
+transportable, storage system.
+
+Right?
+
+It's solar powered.
+
+Right?
+
+You all know that
+it's made by the sun,
+
+but it's not renewable,
+which is a problem,
+
+but it's a really
+beautiful fuel.
+
+Now, oil has a lot
+of carbon in it
+
+which is what's burning there
+and giving you that energy
+
+release.
+
+But there are other things
+you can do with that material,
+
+and one thing you can do is
+you can make these other forms
+
+of carbon from the oil.
+
+In fact, that's how we
+make a lot of our plastics.
+
+OK?
+
+We make a lot of
+plastics using oil.
+
+If I take 1%, just 1% of the
+carbon in these 159 liters
+
+of oil, just 1% of it, and
+I make that into plastic,
+
+then because I know how to
+design carbon to be something
+
+else, like fullerenes, I can
+make polymers and fullerenes
+
+out of that same element
+carbon and put them together--
+
+gesundheit, whoever that was--
+
+and make solar cells,
+new kinds of solar cells,
+
+in fact, solar cells made
+out of mostly carbon.
+
+If I take 1% of that
+carbon that was in here,
+
+and I turn it into this,
+which we now know how to do,
+
+then I can make really
+bad solar cells.
+
+5% efficient, not so
+good, die in one year,
+
+not so good. right?
+
+The efficiency goes down.
+
+Most solar cells, you
+get a 20-year warranty.
+
+This one, one-year warranty,
+then efficiency is gone.
+
+Even in that case,
+this solar cell
+
+over that one year of
+really crappy efficiency
+
+will give me 10,000
+times as much energy than
+
+by burning the carbon, 10,000.
+
+Now, these are hand-waving
+arguments that are
+
+back-of-the-envelope
+calculations,
+
+but when you've got five orders
+of magnitude to play with,
+
+things are good.
+
+Right?
+
+And this is an example
+in the energy space.
+
+This is why I get so excited
+about designing materials,
+
+and this in particular, this
+is only 100 nanometers thick.
+
+Right?
+
+The solar cell's
+thicker, because it's
+
+packaged but the active layer,
+the part of the material that's
+
+making the sun turn into
+electrons and holes,
+
+something we're going to talk
+about in our next example,
+
+in a few weeks.
+
+That part is 100
+nanometers thick.
+
+That's atomic scale.
+
+That's the atomic scale.
+
+You can't pack that many
+polymers and fullerenes
+
+into 100 nanometers.
+
+Things at the atomic scale and
+the quantum mechanical aspects
+
+of that material are
+critical, and designing
+
+that material is
+something you can
+
+do using atomistic modeling.
+
+So this is what I mean.
+
+You want to give elements
+completely new possibilities,
+
+and you can see the
+power of doing that.
+
+It changes the way we know
+how to use those elements,
+
+and I think that's just
+a very powerful concept.
+
+OK.
+
+Any questions
+about that example.
+
+So that's my little my material
+design example of the day,
+
+if you will.
+
+We should make like a
+calendar, each day a new--
+
+OK.
+
+Now, I want to pause and feel
+our oneness with energy levels
+
+and basis sets.
+
+So this is, again, going back
+to some important key elements
+
+of the computations,
+and then we're
+
+going to come back to the
+calculations and the example
+
+of the solar thermal fuels.
+
+OK?
+
+Now these are things that
+we have talked about,
+
+but they're so
+important that I want
+
+to talk about them again and
+make sure there's no questions.
+
+Make sure that we are
+all on the same page
+
+and know what these things mean.
+
+OK?
+
+So I want to give you,
+this is my attempt
+
+at summarizing our beautiful
+path to the energy level.
+
+OK?
+
+So let's make sure
+we're with it.
+
+All right?
+
+So it all started back
+in the day in lecture one
+
+with the Schrodinger equation.
+
+Does everybody recognized that?
+
+Now, that is the
+equation we're solving.
+
+When you click
+Simulate to calculate
+
+the energy versus separation
+in say, I don't know,
+
+n-2, then the equation that's
+being solved in a computer
+
+is this one, the
+Schrodinger equation.
+
+Now, what are you getting
+out of that equation?
+
+Well, what you're
+getting are what?
+
+These, what are these?
+
+AUDIENCE: Wave functions.
+
+JEFFREY C. GROSSMAN: OK.
+
+Thank you, and why
+do I want those?
+
+What do they tell me?
+
+AUDIENCE: Probability.
+
+JEFFREY C. GROSSMAN: OK.
+
+Yeah.
+
+The tell me the probability,
+and they tell me more than
+
+that which is what we need
+to make sure we understand.
+
+So you see, solving
+that equation gives me
+
+wave function, and the wave
+functions, well, they're waves.
+
+Right?
+
+They have some shape to them.
+
+They may change in time.
+
+Do we care about that?
+
+Not in this class, not in
+this class, in this class,
+
+its all time independent.
+
+So we're doing like a snapshot,
+but they may change in time.
+
+But they certainly vary
+in space, and that is psi.
+
+Right?
+
+Now, what we talked about
+is how these wave functions
+
+themselves, we don't know how
+to draw physical meaning from.
+
+That doesn't mean that
+they're meaningless,
+
+and this is a really
+important point
+
+that we have to feel good about.
+
+OK?
+
+So I'm going to
+come back to that,
+
+but we know that when you square
+them, we know what they mean,
+
+and that's this.
+
+Right?
+
+So what are These do you
+guys remember what these are?
+
+AUDIENCE: Orbitals.
+
+JEFFREY C. GROSSMAN:
+Orbitals, such a bad name,
+
+but anyway, because
+why is it a bad name?
+
+AUDIENCE: Because they
+don't really orbit.
+
+JEFFREY C. GROSSMAN:
+Yeah, totally, but anyway,
+
+these are orbitals.
+
+So these are those wave
+functions squared for what?
+
+Who knows what-- but
+what system is this?
+
+These are the atomic
+orbitals of a hydrogen
+
+atom, one electron, one proton.
+
+OK?
+
+You can solve that analytically.
+
+Now, so we said, OK,
+well, this gives us
+
+like an electron sitting in
+one of these little wiggles.
+
+OK?
+
+We said that they
+go up in energy.
+
+They have different energies.
+
+That's really important.
+
+Each wave function you solve
+for has a different energy.
+
+Right?
+
+So you get these functions, and
+they have different energies,
+
+and there it is for
+hydrogen. There's
+
+the energy for hydrogen. It just
+depends on 1 over the principle
+
+quantum number squared.
+
+Right?
+
+Remember, we talked
+about how it's quantized?
+
+But these little wiggles,
+when you square them,
+
+they give you the picture of
+where that electron is going
+
+to be, where it's likely to be.
+
+And we looked at how the
+shapes got more complicated,
+
+and what are these
+type of orbitals?
+
+AUDIENCE: P
+
+JEFFREY C. GROSSMAN: p?
+
+And then it goes to other
+things, d and then f.
+
+And then we said,
+OK, that's nice.
+
+That's great, but also there's
+this thing called spin.
+
+OK?
+
+And somebody remind
+me what spin is.
+
+AUDIENCE: Property
+of the material.
+
+JEFFREY C. GROSSMAN: Property
+of what thing in particular?
+
+Yeah?
+
+AUDIENCE: It's some
+intrinsic angular momentum
+
+that a particle has.
+
+JEFFREY C. GROSSMAN: OK.
+
+AUDIENCE: Regardless
+of its motion.
+
+JEFFREY C. GROSSMAN:
+And if that particle
+
+happens to be an electron,
+what are your options?
+
+AUDIENCE: In the first one?
+
+JEFFREY C. GROSSMAN: Yes.
+
+AUDIENCE: Plus or minus.
+
+JEFFREY C. GROSSMAN:
+Plus or minus.
+
+It can only be--
+
+or as we like to say
+up or down or as we
+
+like to draw this or that.
+
+Lots of ways of doing this,
+but I think you get the point.
+
+And then we talked
+about poly which
+
+gave us rules for how
+electrons can be together
+
+in one of these orbitals.
+
+OK?
+
+So you have wave
+functions that wiggle.
+
+We don't know how to
+interpret what they mean,
+
+but we know that their square
+gives you the probability
+
+distribution of that electron.
+
+And we know that
+these electrons also
+
+have another important quantity
+associated with them, a spin,
+
+and the spin can only be one
+of two values, up or down.
+
+OK?
+
+That is the information we
+need to go to energy levels.
+
+OK?
+
+To this point, this is a
+review, but it's about to be--
+
+well, maybe
+something some of you
+
+know, but it's about to
+be a little different.
+
+OK?
+
+So I want to make sure
+we all understand this.
+
+Once I know that you can
+have two kinds of spin,
+
+and once I know that you get
+energies out of this equation,
+
+then the answer to
+the energy levels,
+
+to what energy
+levels are, is there
+
+are these things that you fill.
+
+There are these things that
+you fill with electrons.
+
+How do you fill them?
+
+I keep blocking the screen,
+but it's fun to go in there.
+
+It makes me feel
+important maybe.
+
+I don't know.
+
+Never mind.
+
+How do you fill them?
+
+I'll use this.
+
+Oh, yeah.
+
+What do you do here?
+
+What's going on?
+
+I want to fill these orbitals.
+
+Do I fill this one
+
+AUDIENCE: You start
+at the lowest end
+
+and work to the highest.
+
+JEFFREY C. GROSSMAN:
+Yeah, and when do I stop?
+
+AUDIENCE: When you
+run out of electrons.
+
+JEFFREY C. GROSSMAN: When
+you run out of electrons.
+
+How many electrons did I have?
+
+AUDIENCE: 29.
+
+JEFFREY C. GROSSMAN: It depends
+on the atom or molecule which
+
+is where we are now or solid.
+
+Now, that is really
+in a way-- the reason
+
+I'm focusing on it is this
+is the key quantum mechanical
+
+nature thingy,
+property of materials,
+
+I want you to come away with
+being able to understand
+
+and calculate in this class.
+
+OK?
+
+It's these energy levels.
+
+This is the most important
+thing I want you to come away
+
+with from this class.
+
+Why?
+
+Well, we can calculate
+other things,
+
+and I've talked about that.
+
+We can calculate energies.
+
+We can calculate
+binding energies.
+
+We can calculate
+all kinds of things,
+
+but these energy levels are
+purely quantum mechanical.
+
+Right?
+
+There where those electrons
+want to be in energy,
+
+and they matter so much to
+the properties of materials.
+
+So I want to focus on
+these and connect them
+
+to real exciting problems.
+
+OK?
+
+And make sure that
+you understand
+
+where they come from and
+also how to calculate them
+
+and what they can mean.
+
+So that's where we are.
+
+So that's why I keep
+drawing things like this.
+
+You see me just drawing this.
+
+Right?
+
+Now, what did I draw?
+
+I don't know.
+
+I drew a bunch of levels.
+
+Right?
+
+If I'm a little more
+careful, and I do this,
+
+now what am I drawing?
+
+What is that?
+
+AUDIENCE: Energy diagram.
+
+JEFFREY C. GROSSMAN:
+Energy diagram.
+
+OK, good.
+
+What is it though?
+
+Do we know?
+
+AUDIENCE: Like there's
+no electrons in there.
+
+JEFFREY C. GROSSMAN:
+OK, and it's
+
+the solution to which problem?
+
+Actually, this is
+infinite square well.
+
+So that's not the
+hydrogen atom, but those
+
+are the energy levels
+you get for the solution
+
+of the hydrogen atom.
+
+OK?
+
+Now, if I ask you what this
+is though without putting
+
+any electrons down, we don't
+know, but what if I do this?
+
+Now, what is it?
+
+Hydrogen, what about now?
+
+AUDIENCE: Lithium.
+
+JEFFREY C. GROSSMAN:
+Lithium, what is this?
+
+Oh, I love this one.
+
+AUDIENCE: Carbon.
+
+JEFFREY C. GROSSMAN:
+Carbon, carbon,
+
+it's a beautiful material.
+
+I love carbon.
+
+OK?
+
+I almost feel like you
+need a little moment.
+
+When you draw the
+energy levels of carbon,
+
+you need a little
+moment of respect.
+
+Now, but you see,
+this is what we did.
+
+We solved for these wiggles.
+
+We got energies, and
+we put them in order
+
+from lowest to highest.
+
+And then we said how many
+electrons do we have?
+
+Six, OK, fill them,
+and then there
+
+are rules that we talked
+about about how you fill them.
+
+Now, why am I
+going through this?
+
+Well, because that is only
+good for what kind of material?
+
+That is only a correct picture
+for what kind of material?
+
+Atoms, that's an atomic picture.
+
+We solve for the atom, and
+this is true-- and remember,
+
+I said that we can solve
+for the hydrogen atom
+
+and see the whole
+periodic table.
+
+Right?
+
+Powerful stuff, but
+this is only an atom.
+
+These are how you would fill
+the energy levels of an atom,
+
+and we've talked about this.
+
+But see now, we're going
+onto other things, where
+
+you bring atoms together,
+and you form molecules.
+
+This is not a chemistry class.
+
+So I'm not going to spend
+a lot of time telling you
+
+about sigma orbitals, pi
+orbitals, bonding orbitals,
+
+antibonding orbitals.
+
+That's not what
+we're about, but I
+
+do need you to understand that,
+when you bring atoms together,
+
+the orbitals from those
+atoms come together
+
+and form new orbitals.
+
+They form molecular orbitals.
+
+OK?
+
+Now, in this case, you're
+seeing the H2 molecule,
+
+and this is from this website.
+
+There's lots of great
+websites that talk
+
+about molecular orbital theory.
+
+OK?
+
+And in this case, you
+brought two s electrons
+
+together, see, from a hydrogen
+atom over here and a hydrogen
+
+atom over there, and they
+drew those energy levels.
+
+And then they brought
+them together,
+
+and it turns out, when
+you bring to 1s levels
+
+together to form a molecule,
+you get two new levels.
+
+Right?
+
+And the chemists love names, and
+so they gave this one a sigma
+
+1s, and that's a sigma star 1s.
+
+Those are just two
+new levels that
+
+are formed, when you bring
+these atomic levels together.
+
+Now, all the same rules-- and
+one of them, ah, two points--
+
+one of them is a
+bonding orbital.
+
+See, this actually looks like
+I brought two circles together,
+
+and they overlapped.
+
+That's a bonding orbital.
+
+OK?
+
+Another one of them, though,
+is an antibonding orbital.
+
+All right?
+
+And an antibonding orbital
+is higher in energy.
+
+So it's going to come up higher.
+
+Its energy is going to be
+higher than the bonding orbital,
+
+when you bring two
+orbitals together.
+
+when you bring two
+orbitals together.
+
+And often, an
+antibonding orbital
+
+will actually have
+a node, which means
+
+there's zero chance
+of any electron being
+
+in between, exactly in between.
+
+That doesn't sound
+very binding-y.
+
+Right?
+
+Doesn't have a lot of
+appeal for bonding,
+
+if there's like a
+plane of no existing.
+
+Now, why would that be possible?
+
+Doesn't it seem
+from this picture--
+
+I took to 1s orbitals, and
+I brought them together.
+
+Right?
+
+How can I get a
+node between them?
+
+AUDIENCE: Is it [INAUDIBLE]
+
+JEFFREY C. GROSSMAN: Not quite.
+
+What is it?
+
+AUDIENCE: Coulomb repulsion.
+
+JEFFREY C. GROSSMAN: Yeah.
+
+It is actually.
+
+It does have to do
+with Coulomb repulsion,
+
+but there's something
+more basic here at play.
+
+How is it that I can
+bring two spheres,
+
+probability spheres
+like this together
+
+and have two orbitals
+that form, one of which
+
+has a node in between,
+and one of which is
+
+like really nicely happy bound.
+
+AUDIENCE: [INAUDIBLE]
+
+JEFFREY C. GROSSMAN:
+Not quite, any other?
+
+Yeah?
+
+AUDIENCE: It looks like the
+infinite square well there.
+
+You've got the ground state
+that doesn't have any nodes
+
+and then the first excited
+state does, the same deal.
+
+JEFFREY C. GROSSMAN: Exactly.
+
+Well, so that's exactly right.
+
+We're not bringing together
+probability distributions.
+
+OK?
+
+That is not the right
+way to think about it.
+
+I won't stand in front anymore.
+
+We're not bringing together
+probability distributions.
+
+We're bringing together
+wave functions,
+
+and then when those
+come together,
+
+they form a probability
+distribution or two,
+
+in the case I just showed you.
+
+And we all know that,
+when waves come together,
+
+they can do what and what?
+
+AUDIENCE: Construct
+and deconstruct.
+
+JEFFREY C. GROSSMAN: Exactly.
+
+They can construct, and they
+can deconstruct one another.
+
+Sounds like they're
+going to have
+
+like a philosophical discussion.
+
+So that's what's happening.
+
+We're bringing the
+wave function together,
+
+when we bring atoms together
+and molecules together.
+
+We're bringing
+their size together.
+
+Oh, size, you can't get away
+from size being so important,
+
+and we're solving for
+the collective psi.
+
+And when you bring waves
+together, they have phase,
+
+and they can form constructive
+and destructive interference,
+
+as we talked about in
+lectures one and two,
+
+and that's what's
+happening here.
+
+And then you square those,
+and you get new orbitals
+
+which have those properties.
+
+OK?
+
+So this is the simplest
+example which is H2 molecule,
+
+and then we fill those orbitals.
+
+And when we fill these
+orbitals, when we draw them
+
+for a molecule, very often,
+I'll lose this notation,
+
+because there isn't--
+
+and I'm not going to go
+through this notation,
+
+mostly because I can't
+remember past sigma and pi.
+
+But there's a whole
+lot of notation
+
+out there for
+molecular orbitals,
+
+and it depends on the
+symmetry and the group
+
+symmetry of the molecule
+you're working with,
+
+and there are rules
+and all that stuff.
+
+But all we're going
+to need in this class
+
+is to know that, when
+you have a molecule,
+
+and you calculate
+this wave function
+
+which gives you the wiggles.
+
+And then you square it,
+you get the distributions,
+
+and that helps set
+the energy levels.
+
+It tells you where those
+energy levels are going to be,
+
+that will just draw
+them like this.
+
+Right?
+
+Now, this is how
+I'll draw molecules,
+
+the energy levels of molecules,
+and again this is it.
+
+This is one of the most
+important properties
+
+I want to focus on,
+because this is everything.
+
+This is where those electrons
+are in energy space,
+
+and I can plot them.
+
+I can look at their energy,
+and there's all kinds
+
+of important information here.
+
+OK?
+
+And so what this
+means is usually I'll
+
+leave a space here.
+
+Does anybody know
+what this is called?
+
+AUDIENCE: Gap.
+
+JEFFREY C. GROSSMAN: Right.
+
+This is the gap,
+because that's how many
+
+electrons I had in my molecule.
+
+Not my atom, but in my molecule.
+
+So I do the same thing.
+
+I calculate energy levels,
+I fill them up, and I stop.
+
+I apply some rules,
+like you wouldn't
+
+have one level with two
+electrons up, Pauli exclusion.
+
+Right?
+
+And then I stop,
+and then there's
+
+another level beyond that.
+
+Oh, that's important.
+
+So we're going to
+talk about that today.
+
+There's another level beyond
+that that's not filled,
+
+but the distance in
+energy between these
+
+is called the gap, and
+it's really important.
+
+And the energy gap is
+what determines all kinds
+
+of properties about a material.
+
+It determines how
+it absorbs light.
+
+It determines how
+it conducts charge.
+
+It can determine things about
+its magnetic properties,
+
+certainly transport properties.
+
+And what's going to
+happen, and that's
+
+why I really want
+to make sure we all
+
+understand this for a molecule.
+
+What's going to happen
+is, when we go to solids--
+
+on Thursday, we're
+going to start talking
+
+about moving to solids--
+
+this is going to happen.
+
+These are no longer
+simple lines.
+
+These go like this,
+and that's really cool.
+
+That happens because
+you're putting them
+
+in a periodic arrangement.
+
+That's called a band structure.
+
+It doesn't happen for molecules.
+
+They're just little flat
+lines, like they are in atoms.
+
+OK?
+
+So are we all good with this?
+
+Are there questions?
+
+Energy levels,
+energy levels, need
+
+to know about energy levels.
+
+No questions?
+
+Yeah?
+
+AUDIENCE: So when you
+put up every central gas
+
+and you calculated
+all the total energy,
+
+if you like have big molecules--
+
+JEFFREY C. GROSSMAN: Yeah.
+
+AUDIENCE: --you got huge gap and
+it's harder to identify that.
+
+JEFFREY C. GROSSMAN: Which one?
+
+What's harder to identify?
+
+AUDIENCE: Ammonia.
+
+Because if you have one
+more unit, for example--
+
+JEFFREY C. GROSSMAN: One more.
+
+AUDIENCE: --some group.
+
+JEFFREY C. GROSSMAN: OK.
+
+So you put an electron here?
+
+Or what do you mean?
+
+AUDIENCE: So when you
+calculated the wave function--
+
+JEFFREY C. GROSSMAN: Yeah.
+
+AUDIENCE: --how did you know
+the electron wave function
+
+for this type of ammonia?
+
+JEFFREY C. GROSSMAN:
+Well, that's--
+
+Yeah.
+
+So that's where really
+lecture three covers that.
+
+Where basically, you need
+to use an approximation
+
+to the Schrodinger equation,
+and that approximation
+
+that we're using
+in this class is
+
+called density function theory.
+
+But then you simply what
+goes into that equation
+
+is the approximations
+you choose,
+
+and the positions of the atoms
+and the number of electrons.
+
+And once you have
+that, you basically
+
+are solving for the psi.
+
+You're solving for these.
+
+Right?
+
+And you get them and
+their energies out,
+
+and it's in the outputs
+of the nanoHUB runs.
+
+OK?
+
+Now, one last thing before
+we go back to solar fuels
+
+that I want to make sure
+we feel our oneness with
+
+are these basis functions.
+
+So this is a slide from another
+lecture, an older lecture,
+
+but I just want to
+be sure we understand
+
+what we're doing here.
+
+OK?
+
+So we said we needed to
+make size for our materials.
+
+We need the code to give us psi.
+
+Now, for a hydrogen atom,
+these are analytic functions.
+
+Right?
+
+They're like sines, cosines,
+but for more complex material,
+
+a complex atom, they
+can look like this.
+
+They can be really complicated.
+
+OK?
+
+So but a computer
+can't just draw lines.
+
+Right?
+
+A computer can't do that.
+
+It needs to have some
+mathematical representation
+
+for that function, and
+that's what a basis set is.
+
+But as I stressed
+last week, this
+
+is a new sort of not
+a problem, but it's
+
+a parameter that is not present
+in classical simulations.
+
+But it's one you have to
+be very carefully aware of,
+
+and you have to know
+when you've converted it.
+
+OK?
+
+And the question
+came up last week
+
+of when is a basis
+set converged?
+
+OK?
+
+And what do I mean?
+
+Well, I can make a
+basis out of anything--
+
+Gaussians, exponents,
+plane waves.
+
+I can make a basis
+out of wavelets
+
+which are really interesting
+hat-like functions.
+
+But I can take any function,
+and if I add enough of them
+
+in the right places, and they
+have the right width and size,
+
+I can recreate a curve.
+
+That's what we're
+doing, but I want
+
+to have as few as possible.
+
+OK?
+
+So this is a basis set
+study that somebody did
+
+and randomly put on the
+web, which I randomly
+
+found and didn't credit,
+which I should have.
+
+Anyway, this is the
+number of basis functions
+
+going this way, number
+of basis functions,
+
+and that's the energy.
+
+And you can see that the
+energy is going to change,
+
+as you increase the
+number of basis functions,
+
+and there's this thing
+called the basis set limit.
+
+Sometimes it's called the
+complete basis set limit,
+
+and that complete basis set
+limit is basically just saying,
+
+hey, I've represented
+my wave function
+
+now numerically correctly.
+
+So infinite number of basis
+functions should give you that.
+
+We don't have
+enough computer time
+
+to have that many basis
+functions, because it
+
+gets really long and slow.
+
+So we don't do that.
+
+Usually, we do calculations out
+here, and maybe we extrapolate.
+
+OK?
+
+Or we just do a few
+cases, and we say,
+
+well, my results are converged.
+
+But when is a basis
+set converged?
+
+It's a really important
+point of quantum mechanical--
+
+hey, that would be like
+a good quiz question.
+
+Right?
+
+Like it's a really
+important part of quantum
+
+mechanical simulations are
+always a quiz question.
+
+It's not a bad one.
+
+Is it converged here,
+or is it converged here?
+
+You know what answer
+I'm looking for.
+
+AUDIENCE: Depends
+on the problem.
+
+JEFFREY C. GROSSMAN: It depends.
+
+I love that answer
+for this class.
+
+It depends, because
+here, I'm plotting
+
+the total energy of
+the whole system,
+
+but is that what I want?
+
+Is that what I'm calculating?
+
+I don't know, maybe, but what if
+I'm actually calculating this?
+
+What if I'm calculating the gap
+between the highest occupied
+
+and lowest occupied level?
+
+Well then, I should plot
+that versus the basis set,
+
+and that, this line, the total
+energy may converge like this.
+
+Whereas, if I do the gap, it
+kind of goes-- maybe it's here,
+
+and then I get
+another value here,
+
+and then everything is fully
+converged all the way in.
+
+So the gap value
+converged there.
+
+You don't know.
+
+Different properties will
+converge differently,
+
+and you start to
+get a feel for it,
+
+as you do more calculations.
+
+I'm not expecting you to get
+to that point in this class,
+
+but I want you to
+understand this.
+
+It's really important.
+
+OK?
+
+So basis sets must be converged.
+
+That's one point.
+
+This can lead to big tables.
+
+Chemists love big tables.
+
+So it's actually a perfect fit.
+
+So you see papers like this.
+
+Oh, you can go to bse.pnl.gov,
+and let's see, maybe I can just
+
+go there really quickly.
+
+And you can see,
+oh, look at that.
+
+There's the nanoHUB.
+
+We're coming.
+
+We're coming, and look at this.
+
+Oh, this is beautiful.
+
+See, many basis sets have
+been made over the years.
+
+Right?
+
+And so here, they are.
+
+Look at all these basis sets
+for different-- and you see,
+
+I can scroll down here.
+
+Look at these basis sets.
+
+You have a few of these to
+choose from in the nanoHUB,
+
+but look at how many there are.
+
+These are all
+published basis sets,
+
+and you can go to
+a place like this.
+
+And you can click on one, like
+3-21G*, and you can click on--
+
+well, I don't think that--
+
+and you can say what
+code am I going to use?
+
+Right?
+
+And then, you can say get the
+basis sets, and there they are.
+
+And there are the papers,
+where basically, they're
+
+trying to say what is the
+fewest number of Gaussians
+
+that we can use to
+represent these atoms?
+
+So basis sets are fit to
+atomic orbital wave functions.
+
+OK?
+
+And this is just a
+certain form, where
+
+you have the exponent
+of the Gaussian
+
+and a coefficient
+of the Gaussian.
+
+And I'm not going
+to go into details,
+
+because we don't need them.
+
+OK?
+
+There's a lot of
+work on basis sets.
+
+There's also a
+lot of papers that
+
+were published in the 1970s
+and also '80s using basis sets,
+
+like this, that show
+really good answers using
+
+like Hartree-Fock theory or
+density functional theory
+
+even but for the
+completely wrong reason.
+
+Because they used a level of
+theory that wasn't accurate
+
+and a basis set that
+wasn't converged,
+
+because the computers couldn't
+go to larger basis sets,
+
+and so the errors canceled.
+
+So there are many papers
+with really nice agreement
+
+with experiment from theory
+that are complete nonsense,
+
+because they're using very
+inaccurate theory and really
+
+bad basis sets.
+
+And so the errors cancel, and
+you get beautiful results.
+
+It's something that
+we need to be aware of
+
+and understand in this
+class, but we're not
+
+going to go into great detail in
+all these different basis sets.
+
+But you can go there,
+and there's just a lot
+
+of information there.
+
+And you can play around, and you
+can make big tables like this.
+
+I don't recommend
+that you do this.
+
+But this was a study, this
+is like the kind of thing--
+
+I think that some people
+really like big tables.
+
+This one goes on and
+on and on, by the way.
+
+It never stops.
+
+It almost never stops.
+
+And you see, different
+levels theory here.
+
+These ones we
+haven't talked about.
+
+That's LDA, Hartree-Fock and
+then different basis sets.
+
+You see?
+
+And some property,
+the binding energy
+
+and some other properties
+that they care about.
+
+OK?
+
+Yeah.
+
+Not expecting you
+to do that, but I
+
+want you to be aware
+of how big of a concern
+
+this is in quantum
+mechanical calculations.
+
+Any questions about basis sets?
+
+Basis sets.
+
+The last theory
+point, last question
+
+I want to ask, so we
+asked, with basis sets,
+
+how do we know when
+we're converged?
+
+Well, it depends.
+
+When you add more basis
+functions or do a larger basis
+
+and things don't
+change, your converged.
+
+But there's another
+bigger question,
+
+which is how do we know when
+the calculation is right,
+
+that we talked about here.
+
+Now, this is very
+important, and it
+
+goes to the point I just made.
+
+Just because you
+agree with experiment,
+
+if you're not doing your
+calculations carefully,
+
+it can be still dangerous.
+
+OK?
+
+But let's suppose that you
+have done your calculations
+
+carefully, and you have
+converged your basis set.
+
+And you have checked everything
+else about your code,
+
+and you're asking
+the question of which
+
+of these structures of carbon--
+
+remember, I really like carbon.
+
+Which of these three
+structures-- a ring,
+
+a kind of bowl, or a cage--
+
+gives you-- is most
+stable for 20 atoms?
+
+That's a pretty simple question.
+
+Right?
+
+This is the question I asked
+as a second-year grad student,
+
+a few years ago now.
+
+Who laughed?
+
+Sam?
+
+And it was really
+cool, because see,
+
+you could try one
+level of theory
+
+and work really hard to
+converge it completely.
+
+And you'd get, for
+example with LDA--
+
+something you can
+do on the nanoHUB--
+
+you would get that the cage,
+this guy, is the lowest energy.
+
+This means the most stable.
+
+And then you would do another
+level of theory, Hartree-Fock
+
+or this other thing
+that you also have,
+
+this is called the GGA.
+
+It's another flavor of
+density function theory,
+
+and you would get
+exactly the opposite.
+
+You would get that the
+ring is the most stable,
+
+and the cage is
+the least stable.
+
+So what's going on?
+
+What's going on?
+
+Two different DFT
+functionals gave me
+
+completely different answers,
+and I've converged everything.
+
+AUDIENCE: Two more functionals.
+
+JEFFREY C. GROSSMAN:
+Two more functionals.
+
+Now, that's actually
+a really good idea,
+
+and it's actually
+what people do.
+
+OK?
+
+In fact, you see, if you go to--
+
+I think I left
+this web page open.
+
+Here's one of the
+codes that does
+
+density functional theory
+and other quantum chemistry
+
+calculations.
+
+It's called Gaussian.
+
+And if you look in
+their 2009 version,
+
+this is a code you
+have to pay for.
+
+There's lots of codes
+that are free, by the way.
+
+NWChem, if anybody wants to
+play with a code, download it,
+
+that does quantum
+chemistry, that's
+
+a pretty darn good one that's
+free which you can download,
+
+and there are others.
+
+I'm happy to provide a list.
+
+But look at the
+number of functionals
+
+you have to choose from.
+
+OK?
+
+Here's a little bit
+about density functional
+
+theory and the methods, and
+then here are the functionals.
+
+exchange functionals.
+
+You see S, XA, B, PW, G96, PBE.
+
+That's one of the
+ones on the nanoHUB.
+
+Right?
+
+And correlation functionals,
+VWN, LYP, B95, and so
+
+what you wind up getting--
+and then it goes on,
+
+standalone functionals,
+hybrid functionals.
+
+OK?
+
+Here's some more.
+
+User defined functionals, you
+can actually make up your own.
+
+Right?
+
+So here's a short list
+of some of the keywords
+
+you can enter and get
+different functionals out.
+
+So now, what do I do?
+
+AUDIENCE: All of them.
+
+JEFFREY C. GROSSMAN:
+All of them.
+
+Well, sadly, I think
+some researchers do that.
+
+So here's the broader point.
+
+OK?
+
+Density functional theory is
+an approximation in the way
+
+that we use it in our codes.
+
+The actual theory
+itself could be exact,
+
+but the way that it
+has to be implemented
+
+requires this
+approximate functional,
+
+as you learned in lecture three.
+
+OK?
+
+What functional do I use?
+
+Well, some of these
+have been well tested
+
+for broad classes
+of materials and are
+
+known to do well for certain
+properties, certain materials,
+
+and known to do not
+as well for others,
+
+but it's mostly empirical in
+terms of our understanding.
+
+It's because it's been
+tried for many systems.
+
+OK?
+
+And so in a way,
+we're a little bit
+
+back to the classical world.
+
+In the sense that
+density functional theory
+
+is a beautiful theory,
+but to make it practical,
+
+you have to make
+approximations that make it
+
+so that you have almost
+an empirical nature to it,
+
+or a semi-empirical
+nature which is what you
+
+have in classical force fields.
+
+Right?
+
+In classical force
+fields, the potential
+
+is as good as the
+complexity of the potential
+
+and what you fit it to.
+
+Right?
+
+Density function theory is,
+I think, much more powerful,
+
+in the sense that
+you can really solve
+
+for the electronic
+structure, but we
+
+have the same kind of problem
+in density functional theory.
+
+So the functionals that I've
+given you on the nanoHUB
+
+are some of the
+most popular ones,
+
+but you always
+need to be aware--
+
+[NON-ENGLISH]---- of the fact that
+we're making an approximation.
+
+And yes, one way to check
+is to try two functionals,
+
+and if they don't disagree
+too much, you may be OK.
+
+That's not the most
+gratifying way to do it.
+
+Another way would be to
+compare with experiment,
+
+and that's actually the
+most gratifying way.
+
+Once you converge
+everything else,
+
+if you're functional
+agrees with experiment
+
+for the kind of
+problem you're trying
+
+to solve, then that's a pretty
+good indication that it's
+
+an accurate solution to
+the Schrodinger equation,
+
+but you are making
+a approximations.
+
+OK?
+
+And that is something
+that we won't--
+
+as you can see, I don't
+give you much options
+
+on the nanoHUB, because I
+don't really want to go there,
+
+but I do want you
+to be aware of this.
+
+We are not solving
+quantum mechanics exactly.
+
+We cannot, and with
+density functional theory,
+
+there are some systems.
+
+So in my graduate days,
+I worked on a method
+
+that goes beyond density
+functional theory inaccuracy.
+
+So it's a very accurate method,
+very slow but very accurate.
+
+And so I was
+purposefully looking
+
+for systems where DFT fails, and
+I was very happy with this one,
+
+where you basically
+don't know the answer.
+
+You can try
+functionals, and you'll
+
+get all kinds of
+different results.
+
+So the only thing you
+can do in that case
+
+is go to a higher
+accuracy method.
+
+OK?
+
+What I found out is
+that this method here
+
+is the most accurate one, that
+actually none of the functions
+
+were right, and the bowl
+was the most stable.
+
+So it's pretty cool.
+
+It was exciting.
+
+What can I say?
+
+I was a physicist at
+the time, so you know.
+
+I won't say anything more.
+
+OK.
+
+Now, let's go back to our
+first application example.
+
+Does everybody remember
+this from last week?
+
+OK.
+
+So let me make sure we know why.
+
+OK.
+
+I want to make
+sure we understand
+
+why this is such an important
+problem for quantum mechanics.
+
+OK?
+
+So sun shines on a molecule,
+the molecule changes shape,
+
+and that changed shape
+is a higher energy.
+
+So if you draw the
+reaction, if you
+
+draw the reaction
+coordinate for this system,
+
+It looks like this.
+
+OK?
+
+So that would be the trans
+state and the cis state,
+
+and this is the higher
+energy that that forms,
+
+and it stores that much
+energy in the molecule.
+
+OK?
+
+Now, what we found
+is that there's
+
+all these molecules
+that do this,
+
+but they're not very
+good solar fuels.
+
+OK?
+
+So there's lots of
+them that do this trans
+
+to cis photoisomerization.
+
+So the sun makes it go, or light
+makes it go, from one state
+
+to another.
+
+None of them are good
+solar fuels on their own,
+
+but we found this way of making
+them in general into good ones.
+
+And this is a slide
+I skipped last week,
+
+so I want to just very
+quickly explain this again.
+
+Because it's really
+important to understand why
+
+we're so excited about this.
+
+If you put these molecules
+that switch back and forth
+
+onto a template, and the
+template can be anything,
+
+but here it's a nanotube.
+
+But if you put them onto it,
+and you covalently bind them--
+
+that means you attach
+them really strongly,
+
+so they're not
+going to come off.
+
+Then, what you've done is
+you've packed them in a way
+
+that they're not
+able to get out of.
+
+So you've packed them
+together, and they're not
+
+allowed to get out, because
+they're covalently bound.
+
+Some self-assembly
+work is weakly bound.
+
+Some is not.
+
+Here, it's really
+strongly bound.
+
+So they're really forced
+into this packing.
+
+Now, what does that mean?
+
+Well, look up here for a minute.
+
+It's a little busy,
+but look at that cyan
+
+curve, the light blue.
+
+This is the spacing that they're
+packing on on this template.
+
+This is it, 4.2 angstroms.
+
+OK?
+
+And that's also exactly the
+minimum of that molecule,
+
+when it's in the T state, here.
+
+When it's in the T state,
+it's happy at that spacing.
+
+It's happiest.
+
+Right?
+
+But when it's in
+the cis state, you
+
+see the cis state has
+a different spacing
+
+that it wants to be at.
+
+That's the red curve.
+
+Right?
+
+These are the
+kinds of curves you
+
+should be getting in your
+homework for problem two.
+
+That's the curve
+for the cis state,
+
+and you can see that it's a
+happy place is much further
+
+out, but it can't
+be much further out.
+
+It does not have that
+flexibility anymore.
+
+So you've constrained
+it to always
+
+be in the trans, happy place,
+in terms of its spacing.
+
+Now, what that means is that,
+you can see right away, what
+
+that means is that, when
+it's in the cis state,
+
+the energy of the cis state
+is going to be higher.
+
+So already, what you've done is
+you've made this state go up,
+
+because you've sterically
+inhibited it just
+
+by forcing it to be this
+close and never further apart.
+
+In the gas phase or in solution,
+when it goes back and forth
+
+between trans and cis.
+
+It's always going to
+find its happy place.
+
+They're not going to worry
+about this, but here they can't.
+
+But as I mentioned last week,
+much more importantly even,
+
+when you're in this highly
+confined geometry, this highly
+
+constrained rigid packing,
+what you can do now
+
+is you can play
+chemistry between them.
+
+So I can actually
+create functional groups
+
+on these molecules that
+bond them to each other
+
+and to themselves
+in different ways,
+
+depending on whether they're
+in the cis or the trans state.
+
+OK?
+
+And what that does
+is that allows me
+
+to lower this and lower this.
+
+That's the key.
+
+OK?
+
+So now, because the
+key is, remember,
+
+goal is to increase
+this and this barrier.
+
+Going back, we want to be
+able to tune it separately.
+
+And you can see that, if you
+just look at this reaction
+
+coordinate, if I
+increase delta H,
+
+it looks like I'm going
+to probably decrease
+
+the activation barrier
+which is not a good thing.
+
+Because that's related to the
+stability of the fuel, when
+
+it's charged, the lifetime.
+
+These molecules
+on their own last
+
+in the charged state
+for a few minutes.
+
+That's not very useful.
+
+So what we'd like to do is
+to be able to change both,
+
+and this trick
+allows us to do that.
+
+We push this up from
+steric inhibition,
+
+but we pull it back
+down from reactions.
+
+We pull this, from interactions,
+we pull this down even more,
+
+because we can customize
+the interactions that
+
+happen between these molecules
+and within the molecule.
+
+So that's the key.
+
+That's the magic sauce.
+
+Right?
+
+Now, all that is fine,
+except that, as I--
+
+OK.
+
+So we have this new
+class of materials
+
+we're very excited about.
+
+We're making them in the lab.
+
+We're designing
+them on a computer.
+
+They're going to save the
+world, or maybe they'll
+
+just de-ice windows, but
+anyway, that's very exciting.
+
+Now, all of that can be done
+using classical force fields.
+
+You can calculate
+delta H. You could
+
+try to get a good model of
+potentials for these molecules.
+
+You could maybe try
+different potentials
+
+and see when it agrees with
+experiment and all that
+
+and try to explore this phase
+space using classical force
+
+fields.
+
+That is accessible.
+
+You may not-- gesundheit--
+you may not be accurate.
+
+You may have some
+worries about validating
+
+the potentials and
+all that, but you
+
+can do this with
+classical force fields.
+
+You can get energies as a
+function of these twists
+
+in the bonds and try to
+engineer it this way,
+
+but you cannot talk about
+the optical properties.
+
+You cannot do that using
+classical potentials.
+
+You need the electrons, and this
+goes back to our energy levels.
+
+OK?
+
+So now, it will come
+in to play here.
+
+We're going to go
+back to energy levels.
+
+You see, I can make
+a really dense energy
+
+fuel, a really highly
+energy dense fuel,
+
+but if it doesn't absorb
+the sunlight efficiently,
+
+then I can never charge it.
+
+Right?
+
+So that's a critical
+part of this.
+
+If it doesn't absorb sunlight
+well, it's useless to me.
+
+OK?
+
+Now, so this is the thing
+that we've been talking about,
+
+but that part can be looked at
+with potentials, if you wanted.
+
+This part here, where you
+absorb the light, cannot.
+
+So here's the light that
+comes down to Earth.
+
+Right?
+
+We talked about this.
+
+That's the solar flux.
+
+And the key point here is that--
+
+I keep that?
+
+We don't need that anymore.
+
+The key point here is that those
+molecules have energy levels,
+
+like this and like this,
+and they have a gap.
+
+Right?
+
+These are what we call occupied,
+and these are unoccupied.
+
+Unoccupied levels,
+occupied levels,
+
+I just don't want
+to draw the arrows,
+
+and that's the energy gap.
+
+Now, why does the energy
+gap matter with respect
+
+to this picture?
+
+Yeah?
+
+At the same time--
+
+one, two, no.
+
+Go ahead.
+
+AUDIENCE: Because
+all the absorption
+
+are at certain frequencies--
+or certain light
+
+coming in at frequencies
+with great enough energy that
+
+surpass the energy gap.
+
+JEFFREY C. GROSSMAN: Why?
+
+That's really good.
+
+That's exactly right.
+
+AUDIENCE: So it's too low.
+
+It's not enough
+energy to shut it off
+
+from occupied to unoccupied.
+
+JEFFREY C. GROSSMAN: Yeah.
+
+AUDIENCE: I mean,
+too low of energy.
+
+JEFFREY C. GROSSMAN: Too
+low of an energy, right?
+
+So this is energy going--
+
+this is wavelength
+going that way.
+
+So energy goes this way.
+
+OK?
+
+Right?
+
+So there is going to be some
+minimum energy below which
+
+you can no longer absorb light.
+
+The molecule is transparent.
+
+That is the energy gap.
+
+That's this energy gap here.
+
+Any energy that that
+molecule receives
+
+that's from those photons--
+
+and this is the energy.
+
+Wavelength, as we know
+same, as the energy.
+
+Any photons it receives
+from the sun that's less
+
+than this just go right past.
+
+They cannot get absorbed.
+
+If I don't absorb a
+photon, I don't do this.
+
+I don't switch.
+
+OK?
+
+So this is important.
+
+Now, the question
+is what do I want?
+
+Well, do I want the material to
+have a very high gap or a very
+
+low gap?
+
+Out here would be a
+very low energy gap,
+
+and over here, it would
+be a very high energy gap.
+
+What do you guys
+think I want here?
+
+How would I get-- and I'm
+going to collect energy only
+
+above the gap.
+
+So if my energy
+gap is here, it's
+
+only going to be this part
+of the sun I can collect.
+
+So where do you think
+I want my gap to be?
+
+Over here?
+
+That's definitely
+what you would think.
+
+Why not just make this
+material have almost no gap?
+
+Right?
+
+If it had almost no gap, then
+if this were the gap, then
+
+any little bit of sunlight
+would excite electrons up,
+
+and you'd absorbed the photon.
+
+Why is that not a
+good solar fuel?
+
+AUDIENCE: They fall easily.
+
+JEFFREY C. GROSSMAN:
+Say that again.
+
+AUDIENCE: They fall
+back down easily.
+
+JEFFREY C. GROSSMAN: Well, they
+certainly could fall back down,
+
+and actually usually, they'd
+be absorbed say up here,
+
+and they'd usually trickle
+down to here anyway
+
+to the LUMO state.
+
+That's called thermalization.
+
+They could also fall back
+down to the homo state
+
+and re-emit a photon.
+
+That's absolutely right,
+but there's another reason.
+
+AUDIENCE: Lower energy density.
+
+JEFFREY C. GROSSMAN: Yeah.
+
+Why?
+
+AUDIENCE: There's a band
+gap in the partial delta H.
+
+JEFFREY C. GROSSMAN: Yeah.
+
+That's it.
+
+So what are we doing
+in storage materials?
+
+What are we doing with
+electrons in batteries,
+
+in solar thermal fuels?
+
+What are we doing
+with those electrons?
+
+AUDIENCE: Storing them.
+
+JEFFREY C. GROSSMAN:
+We are storing them.
+
+Yes, but what are we
+doing to make them--
+
+what are we doing
+when we convert them?
+
+Maybe I should say it that way.
+
+Same thing happens
+in a solar cell.
+
+I'm doing something
+to these electrons.
+
+AUDIENCE: Putting
+them on a shelf.
+
+JEFFREY C. GROSSMAN: Yeah.
+
+You know I love that analogy.
+
+Yeah?
+
+It's like pumping hydro.
+
+Hydro pumping is one of
+the best technologies
+
+we know of to store energy.
+
+It's even creating a little
+stir here in the third row,
+
+because he has read
+the reports, and he
+
+knows that there are
+certain areas where
+
+that's the only
+game in town, pumped
+
+hydro, a beautiful technology.
+
+It works.
+
+You pump water up a hill.
+
+When you got too much
+energy, and you let
+
+it roll back down
+when you need it.
+
+Right?
+
+Now, that's all we're
+doing with electrons.
+
+That's it.
+
+It's the same exact thing.
+
+We're pumping
+electrons up a hill.
+
+We're using light to do it here.
+
+For a battery, when you
+plug your electric car
+
+in, you're using current
+and electrons, potential,
+
+voltage to do it, but you're
+driving electrons up the hill.
+
+And then you're trying
+to keep them up there,
+
+and then let them come
+back when you need them,
+
+when you need them
+to release energy.
+
+OK?
+
+Now, if my gap is
+really low, you
+
+see, the hill, it's never
+going to get to the top.
+
+Here's my hill.
+
+OK?
+
+If my gap is only
+this much in energy,
+
+then I'm just going
+to roll around here,
+
+and I'm never going to
+get any amount of storage.
+
+Right?
+
+So you want this to be
+as large as possible,
+
+because that's how
+much energy you store.
+
+But the gap can't be
+any smaller than this,
+
+or you're not going to give
+those electrons enough energy
+
+to get up the hill to go there,
+so the material can go there.
+
+Yeah?
+
+AUDIENCE: So let's see
+you have some material
+
+with some small
+gap, and you just
+
+have it exposed to sunlight
+and then compare it
+
+with some material
+with a large gap.
+
+Wouldn't they both on average
+collect the same number
+
+of high-energy photons anyway?
+
+JEFFREY C. GROSSMAN: Yes.
+
+AUDIENCE: So with
+the low-gap material,
+
+you'd get some with height
+that collect higher--
+
+JEFFREY C. GROSSMAN:
+Great question.
+
+AUDIENCE: High energy
+photons, and then they
+
+have some excited state.
+
+And then the ones
+with the high gap
+
+will also have
+that excited state,
+
+but the ones with
+the low gap will also
+
+have these lower,
+excited states.
+
+JEFFREY C. GROSSMAN: Yes.
+
+Yes.
+
+AUDIENCE: On top of that?
+
+JEFFREY C. GROSSMAN:
+It's a great question,
+
+and what you're talking
+about is such a cool idea
+
+in solar PV called hot carrier.
+
+What you'd like to do is get
+those excited, really high
+
+energy electrons
+out in solar cells,
+
+before they come back down.
+
+In this case, they
+come back down.
+
+See in this case,
+they thermalize,
+
+and the reaction happens in
+the lowest excited state.
+
+But it also happens
+in solar cells,
+
+because there are no hot
+carrier solar cells today.
+
+It's a great theory.
+
+It's a great idea.
+
+So this is the idea, and
+there's a lot of active research
+
+in this area.
+
+And it's basically the
+idea of multijunction cells
+
+which are cells that work, and
+in fact, the highest efficiency
+
+solar cells to date
+are multijunction,
+
+triple-junction solar cells.
+
+Where basically, you have
+different band gaps together,
+
+and those different band
+gaps do exactly what you say.
+
+OK?
+
+They let you take some
+electrons out here,
+
+and then you have another
+material with a higher gap,
+
+and you can take them out here.
+
+And then you have
+another material
+
+with an even higher gap, and
+you can take those electrons out
+
+there.
+
+OK?
+
+And see because
+otherwise, what happens?
+
+Otherwise, all the electrons
+will-- in each case--
+
+all the electrons
+cascade down to here.
+
+They all wind up in that
+conduction band or that LUMO
+
+state, if it's a molecule.
+
+No matter what, that's just
+the dramatic and traumatic loss
+
+of solar materials.
+
+Right?
+
+Solar conversion, solar capture,
+those electrons thermalize,
+
+because that process
+of thermalization
+
+is so fast, that it's
+very hard to beat.
+
+The way you beat it in
+multijunction solar cells--
+
+42% maybe is the record,
+something like that.
+
+The way you beat it
+is you literally just
+
+stick a level in there.
+
+So it's sort of a
+cheat, but that's
+
+the only way to do it that we
+know technologically today.
+
+If there were other ways
+of extracting electrons out
+
+at their higher energies,
+you could do wonders
+
+in solar capture and storage.
+
+In the molecule, the
+electron thermalizes down,
+
+and the reaction goes in
+that lowest excited state.
+
+So that gap has to be
+bigger than delta H. OK?
+
+Does everybody see that?
+
+It's a very good question.
+
+So it's this
+beautiful, constrained
+
+optimization problem.
+
+I love those, because
+constrained optimization
+
+problems, I want this
+to be really big,
+
+but I want this to stay not
+less than an electron volt.
+
+But then if this
+is really big, I
+
+can't absorb any of the light.
+
+Right?
+
+If I made delta H
+huge, then I'd have
+
+to have a gap that
+was like here,
+
+and I'd get almost
+no solar efficiency.
+
+These are beautiful problems
+for materials design
+
+and for computation,
+because they're constrained,
+
+but they're not
+that constrained.
+
+And using computers,
+you can get your way out
+
+of that, those
+constraints, sometimes.
+
+OK?
+
+And that's what's, I
+think, really exciting.
+
+That's what your homework
+is going to be about, and so
+
+let's calculate one of these.
+
+OK?
+
+Because that is the key
+to the optical efficiency.
+
+Yeah?
+
+AUDIENCE: So is the gas thinner
+than the just delta H or delta
+
+H plus the base?
+
+JEFFREY C. GROSSMAN: That's
+a very good question, and--
+
+AUDIENCE: He told me to ask.
+
+JEFFREY C. GROSSMAN: Yeah.
+
+Yeah.
+
+It's a very good question.
+
+So in general,
+most of these kinds
+
+of photoactive molecules--
+
+I've already talked to a
+chemist, so I'm well armed.
+
+Most of these
+photoactive molecules
+
+need the gap plus the
+activation barrier,
+
+because in the excited state,
+you'll get a similar barrier.
+
+It's not clear that's
+always true though,
+
+and so that puts more
+constraints on this.
+
+So it's even less of the
+spectrum you can absorb,
+
+basically.
+
+Right?
+
+If you want to store
+1 1/2 electron volts,
+
+and you need an electron volt
+of an activation barrier,
+
+that's a 2 1/2 v-gap minimum.
+
+Which means you're closing
+in on the UV, which
+
+means your optical efficiency
+is probably at most 5%, 8%, 10%,
+
+at most.
+
+Right?
+
+That doesn't mean it's
+a deal breaker at all.
+
+But there are also
+cases where you
+
+do change the barrier
+in the exciting state,
+
+and so we're looking into that.
+
+Now, I want another concept
+here to come across which
+
+is really important.
+
+OK?
+
+And that is nothing more than
+these levels smoothed out,
+
+and it's called the
+density of states.
+
+OK?
+
+So if you do a calculation
+of one of these molecules--
+
+let me go back to here.
+
+Oh, yeah.
+
+You know we love this.
+
+Have you all rated this
+say a 10 out of 10?
+
+Come on.
+
+You know it's a 10 experience.
+
+AUDIENCE: Someone gave it a 9.5?
+
+JEFFREY C. GROSSMAN: No.
+
+That's an average.
+
+OK.
+
+I want to start using--
+
+we're going to use a different
+tool for our next homework.
+
+We're going to use DFT
+for solids, surfaces,
+
+and molecules.
+
+It's called SIESTA.
+
+It's another free software
+that you can download.
+
+And it's solving
+the same equations,
+
+but it uses different
+approximations, different basis
+
+sets, and so forth.
+
+OK?
+
+But here, and you
+see that basis sets
+
+are called different
+things, but I've still
+
+tried to help by saying really
+bad, mediocre, and OK, in terms
+
+of the quality.
+
+OK?
+
+Again, that's not the
+focus in this class.
+
+Let's look at it, and we're
+going to do a molecule here--
+
+Uh-oh, there we go--
+
+a molecule.
+
+And I'm going to upload one,
+and you're going to get these.
+
+We'll give these
+with the homeworks.
+
+We'll put them on Steller.
+
+So here's a trans state.
+
+Let's do the phenyl.
+
+Here's a trans state.
+
+We're going to upload
+it and simulate.
+
+OK?
+
+And this is doing just
+what the other code does.
+
+It's doing this self-consistent
+cycle, where it's
+
+solving for the wave function.
+
+OK?
+
+And it's getting
+the wave functions
+
+of all these levels for the
+molecule I just entered.
+
+So it's going to give
+me all these levels.
+
+That's what I want.
+
+Now, the way this plots
+it though is in something
+
+called the density
+of states, and all
+
+that is, as we'll see in a
+minute, is you take these,
+
+and you turn it on the side.
+
+OK?
+
+So let's take a look.
+
+Is it done?
+
+Yes.
+
+There it is.
+
+Oh, this is a
+beautiful solar fuel.
+
+It's actually got two
+photo-switchable molecules
+
+hanging off the same
+azobenzene ring.
+
+But anyway, and this--
+
+where is the-- there we go.
+
+OK.
+
+So the key outputs, so
+it tells you some things,
+
+and then you can go
+to Density of States,
+
+and this is a very
+important property.
+
+OK?
+
+This is the way that we like
+to look at energy levels,
+
+especially in solids.
+
+So we're going to be
+looking at DOS plots
+
+when we get to solids.
+
+OK?
+
+But in molecules, you
+can look at the DOS plot
+
+as well, and
+basically, what it is
+
+it's just these levels
+turned on their side.
+
+So if there's a bunch of
+levels near each other,
+
+you'll get a higher
+peak in the DOS.
+
+You want to think about
+it as averaging over
+
+the likelihood of finding
+states at these energies.
+
+Has anybody seen a DOS plot?
+
+How many of you have seen a
+DOS plot, a density of states?
+
+One or two?
+
+That's OK.
+
+They're energy levels
+turned on their side.
+
+Right?
+
+Now, when we do solids,
+it gets really fun.
+
+It gets really fun
+when we do solids,
+
+because when we do
+solids, like I said,
+
+these things go like this in
+a space yet to be determined.
+
+And then you turn
+those on their sides,
+
+and you still get the
+same kind of DOS plot.
+
+But for molecules, this is
+what it would look like.
+
+So there's a little
+smoothing going on,
+
+but you're also
+representing how many states
+
+you have near these energies.
+
+So that's why it's called
+the density of states.
+
+Right?
+
+Gesundheit.
+
+Does everybody see that
+this is that energy gap?
+
+This is it.
+
+That's the energy
+gap, but there's
+
+more in the density of states.
+
+OK?
+
+So the energy gap, now I can--
+
+watch this-- I can go
+back, and I can magically
+
+put on some functional groups
+and go to the amino benzene
+
+case, and I can do
+that simulation.
+
+How many people really want
+to hear about hydrogen storage
+
+or don't care?
+
+Be honest.
+
+Really want to hear
+about hydrogen storage?
+
+In the back.
+
+Because I really want to make
+this point, because also,
+
+this will be the basis
+of your homework.
+
+But I can also take the
+first 10 minutes of Thursday
+
+and talk about hydrogen storage.
+
+Hydrogen storage, nobody cares
+about hydrogen storage anymore,
+
+do they?
+
+In the back, we have
+one hydrogen storage.
+
+The hydrogen economy,
+it was a big myth.
+
+Well, it's not a myth,
+but it's a long way off.
+
+That we'd all be--
+
+I'm not sure I would
+use that-- that we'd all
+
+be driving hydrogen-powered
+cars in this decade
+
+was a little bit of an
+exaggeration, to say the least.
+
+So here's this guy.
+
+Now, what I did
+is I decorated it.
+
+I did some, like I
+thought-- oh, by the way,
+
+your computation is only
+as good as what's up here.
+
+Right?
+
+So you need to think about
+what you want to simulate,
+
+and here, we thought,
+well, we had this one.
+
+OK?
+
+We had this one, and it's
+not quite the same angle,
+
+but it's close.
+
+OK?
+
+So these guys are
+going to switch,
+
+when the sun shines on
+them, and store some energy
+
+and switch back.
+
+But I decided that I wanted
+to try to do something
+
+about the strain in this state.
+
+Again, you're trying
+to lower, remember--
+
+you're trying to
+lower these states,
+
+or change them, figure
+out how to tune them.
+
+Right?
+
+So what I did is we
+put a group in there.
+
+You can see, you put
+a group in here which
+
+is going to cause some bonding,
+when it's in the trans state.
+
+And you put another
+group here which
+
+causes some bonding
+between those OH
+
+groups and the nitrogen,
+and that adds to the energy.
+
+It lowers the energy.
+
+Right?
+
+Now, as I said, we do that
+with quantum mechanics,
+
+because it's actually not
+that big of a problem,
+
+but that doesn't
+tell me whether--
+
+I may have made this a great
+solar thermal fuel that
+
+can never absorb light.
+
+And so you got to go, and you've
+got to look at these things,
+
+like the density of states.
+
+OK?
+
+And so here they are together,
+and you can see that in--
+
+so that's one.
+
+OK.
+
+So one is now bold, and you can
+see that my modifications have
+
+done some interesting things.
+
+My chemical
+modifications have really
+
+changed where those
+energy levels are.
+
+Now, remember, they're
+getting filled from here.
+
+Remember the filling.
+
+Right?
+
+You draw from the bottom, the
+most energy favorable ones,
+
+all the way up, and
+then you fill them up,
+
+and you stop filling here.
+
+Right?
+
+You stop filling here,
+and that's your gap,
+
+and you can see that the gap
+has changed considerably.
+
+So the gap has
+changed considerably,
+
+and that changes
+what kind of sunlight
+
+that molecule can absorb.
+
+Now, what's nice about
+having the density of states
+
+is that, you see,
+I'm getting-- in all
+
+of the energy levels-- is I'm
+getting more than just the gap.
+
+Right?
+
+I'm getting other things.
+
+I'm getting shapes and peaks,
+and here's a double peak.
+
+There's a single peak.
+
+Here's a little narrow peak,
+but there's a really broad thing
+
+with like three
+peaks and a shoulder.
+
+Right?
+
+That matters too.
+
+That matters a whole lot.
+
+OK?
+
+And the reason is that to a
+very, very crude approximation,
+
+you can consider these peaks in
+where the states are in energy
+
+as the places where
+this molecule will
+
+be able to absorb light.
+
+OK?
+
+And so you can match this
+up with the solar spectrum.
+
+Right?
+
+Because what you want
+is for the molecules
+
+to be able to absorb light,
+where there's a lot of light.
+
+And you don't really care
+about them absorbing light.
+
+You don't necessarily need
+them to have huge peaks,
+
+where there's no sunlight.
+
+Right?
+
+So now, you have an
+interesting comparison
+
+of where these molecules
+tend to absorb light
+
+and where the light is.
+
+OK?
+
+So let's go back
+to this and make
+
+sure we know where I'm going.
+
+OK?
+
+So see, we talked about--
+
+just another five
+minutes or so I think
+
+to finish this discussion.
+
+We talked about how,
+well, you don't want--
+
+there are constraints on just
+thinking about how big of a gap
+
+you want.
+
+Because it's a
+constrained optimization
+
+problem with this thing and
+this thing and this stuff.
+
+Right?
+
+We just talked about that.
+
+Now, I'm going to tell you
+there's another problem,
+
+and that is that this
+state is also photoactive.
+
+So this state can absorb
+light which makes it go back.
+
+Well, that's a bummer.
+
+Right?
+
+That is a bummer.
+
+Now, what that
+means is that, when
+
+I shine light on
+this material, I
+
+will never get it
+all to convert.
+
+I will never charge
+all of the material
+
+and make it all go
+from here to here,
+
+because there's constantly
+a competition at play.
+
+Some of it will be going
+this way, and some of it
+
+will be going that way.
+
+And what holds the key to
+determining how much of which
+
+one is made?
+
+What holds the key?
+
+AUDIENCE: The ratio
+of delta H plus EA.
+
+JEFFREY C. GROSSMAN: Well,
+actually, but the delta H
+
+and EA are out of
+the picture for now,
+
+because I'm only talking about
+the absorption efficiency.
+
+What type of photons it
+could absorb and what else?
+
+What type of photons
+it can absorb and?
+
+Yeah?
+
+AUDIENCE: How many of
+those types of photons--
+
+JEFFREY C. GROSSMAN: Exactly.
+
+AUDIENCE: Your solar cell.
+
+JEFFREY C. GROSSMAN:
+Exactly, and this.
+
+Right?
+
+So you're given this much
+photons on planet Earth.
+
+You're give given the yellow,
+if you go up a little bit.
+
+Right?
+
+We're not going to charge
+our fuels in space.
+
+So this is what you
+got, the red, and that's
+
+where the photons are in
+energy, in wavelength energy,
+
+same thing.
+
+Now, I'm giving you the
+fact that some molecules--
+
+let's go back here.
+
+I can't just delete one, can I?
+
+I'm going to do one more
+simulation while I talk.
+
+I wish it wouldn't show
+my picture everywhere.
+
+I'm going to do the cis state.
+
+OK?
+
+You see, some molecules
+in their cis state,
+
+they're still photoactive,
+which means they go back here,
+
+when you shine light on them.
+
+What that means is that there's
+going to be a stationary state.
+
+When I hold the
+fuel out in the sun,
+
+the light is converting this
+into this, as well as this
+
+into this with some
+efficiency in both directions.
+
+And there will be
+a stationary state
+
+that gives me a
+percentage, or a yield,
+
+or as it's called
+in the literature
+
+a quantum yield, of
+charged material.
+
+How much is it?
+
+Well, in isolated azobenzene,
+when you don't do anything
+
+to it, it's 25%.
+
+I can only charge
+25% of this stuff
+
+in the photo-stationary state,
+when I hold it out in the sun.
+
+And you can see why this
+is such an important part
+
+of the problem, I
+will remind you,
+
+a purely quantum mechanical
+part of the problem.
+
+Because if I increase this, I
+work so hard to increase this
+
+by a factor of three
+or four, and then I
+
+can only charge a
+fourth of it, that's
+
+a whole factor of four hit.
+
+If you can only charge a
+fourth of it at a time,
+
+it's four times less useful.
+
+So it's effectively changing
+this by four times back.
+
+Right?
+
+So this is critical.
+
+How much of this can you charge?
+
+Right?
+
+And that comes from
+the quantum mechanics.
+
+Now, the way that you
+get it is by looking at--
+
+and I'll go through
+the equations
+
+on the next line a minute.
+
+So here it is now in
+the charged state.
+
+OK?
+
+So it's flipped.
+
+It's done its flip.
+
+You can see, it's rotated
+those nitrogen bonds.
+
+It's a beautiful thing, kind of
+an emotional moment in a way.
+
+And you go back to here,
+and you look at your DOS,
+
+and now this is
+kind of hard to see.
+
+Isn't it?
+
+One of these is the cis
+state that I just mentioned,
+
+and it's different.
+
+I can't see, because
+there's two trans
+
+states here and one cis state.
+
+I don't think there's any
+way to just do simulations
+
+two and three, but I think you
+know what I'm talking about.
+
+There's a density of
+states for the trans.
+
+These levels here
+turn on their side,
+
+and there's a density of
+states for the cis state.
+
+And matching that
+with the solar flux
+
+is what will give you the
+photo-stationary state.
+
+It will give you the quantum
+yield of the material.
+
+OK?
+
+That will be your
+second homework.
+
+So this, let's see, this is
+two ways that you could do it.
+
+OK?
+
+One way is you could just assume
+that all of the photons higher
+
+in energy than the gap are
+absorbed and lead to a switch.
+
+And if you do that, then the
+fraction of the molecules
+
+in the cis state, if
+you let them be x,
+
+you can show that
+it's just going
+
+to be a simple integral
+over the solar spectrum,
+
+that this I function,
+up to the gap times x.
+
+That's how many are
+in the cis state.
+
+Gesundheit.
+
+[NON-ENGLISH] Equals the number
+that are in the trans state,
+
+1 minus x, times the integral
+over the number of photons that
+
+convert the trans.
+
+OK?
+
+That's just
+stationary-- that's just
+
+telling you that the change
+in the concentration of cis
+
+is the same.
+
+It's like a reaction
+kinetics equation,
+
+the rate of going from
+one state to another times
+
+the number in that state equals
+the same as the other way.
+
+That's all we've done here.
+
+But it gets more interesting if
+you use the density of states,
+
+because now, you
+have the absorption--
+
+what I'm calling the absorption.
+
+Again, it's a
+crude approximation
+
+for the absorption, but
+let's just call it that--
+
+of the cis state as a
+function of the wavelength,
+
+convoluted with, or
+times, the solar spectrum.
+
+Where you have states in
+both is where it matters.
+
+Right?
+
+Where you have states in both
+is where you hit the integral,
+
+and it's when those
+are taken together
+
+that you can calculate
+more accurately than just
+
+using the gap.
+
+You can calculate the
+photo-stationary yield,
+
+and you get this all
+from those energy levels,
+
+those beautiful energy
+levels that we started
+
+this lecture talking about.
+
+OK?
+
+That yield is so important,
+because it can kill your--
+
+great idea for improving
+delta H can get
+
+killed if the yield isn't good.
+
+OK?
+
+Maybe I'll spend 10 minutes
+on hydrogen storage.
+
+Nobody raised their hands,
+but we'll do another poll.
+
+And we're going to start
+moving now-- you'll
+
+have a homework on this.
+
+It'll be lots of fun, and
+then on Thursday, we're
+
+going to move into solids.
\ No newline at end of file
diff --git a/J5Mg_tqT18g.txt b/J5Mg_tqT18g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..44e66441bfedf96b5da99cff071eefcdb0b2ab41
--- /dev/null
+++ b/J5Mg_tqT18g.txt
@@ -0,0 +1,120 @@
+Using more complicated series/parallel networks
+of switches, we can build devices that implement
+
+more complex logic functions.
+
+To design a more complex logic gate, first
+figure the series and parallel connections
+
+of PFET switches that will connect the gate's
+output to V_DD for the right combination of
+
+inputs.
+
+In this example, the output F will be 1 when
+A is 0 OR when both B is 0 AND C is 0.
+
+The "OR" translates into a parallel connection,
+and the "AND" translates into a series connection,
+
+giving the pullup circuit you see to the right.
+
+To build the complementary pulldown circuit,
+systematically walk the hierarchy of pullup
+
+connections, replacing PFETs with NFETs, series
+subcircuits with parallel subcircuits, and
+
+parallel subcircuits with series subcircuits.
+
+In the example shown, the pullup circuit had
+a switch controlled by A in parallel with
+
+a series subcircuit consisting of switches
+controlled by B and C.
+
+The complementary pulldown circuit uses NFETs,
+with the switch controlled by A in series
+
+with a parallel subcircuit consisting of switches
+controlled by B and C.
+
+Finally combine the pullup and pulldown circuits
+to form a fully-complementary CMOS implementation.
+
+This probably went by a quickly, but with
+practice you'll get comfortable with the CMOS
+
+design process.
+
+Mr. Blue is asking a good question: will this
+recipe work for any and all logic functions?
+
+The answer is "no", let's see why.
+
+Using CMOS, a single gate (a circuit with
+one pullup network and one pulldown network)
+
+can only implement the so-called inverting
+functions where rising inputs lead to falling
+
+outputs and vice versa.
+
+To see why, consider what happens with one
+of the gate's inputs goes from 0 to 1.
+
+Any NFET switches controlled by the rising
+input will go from off to on.
+
+This may enable one or more paths between
+the gate's output and GROUND.
+
+And PFET switches controlled by the rising
+input will from on to off.
+
+This may disable one or more paths between
+the gate's output and V_DD.
+
+So if the gate's output changes as the result
+of the rising input, it must be because some
+
+pulldown path was enabled and some pullup
+path was disabled.
+
+In other words, any change in the output voltage
+due to a rising input must be a falling transition
+
+from 1 to 0.
+
+Similar reasoning tells us that falling inputs
+must lead to rising outputs.
+
+In fact, for any non-constant CMOS gate, we
+know that its output must be 1 when all inputs
+
+are 0 (since all the NFETs are off and all
+the PFETs are on).
+
+And vice-versa: if all the inputs are 1, the
+gate's output must be 0.
+
+This means that so-called positive logic can't
+be implemented with a single CMOS gate.
+
+Look at this truth table for the AND function.
+
+It's value when both inputs are 0 or both
+inputs are 1 is inconsistent with our deductions
+
+about the output of a CMOS gate for these
+combinations of inputs.
+
+Furthermore, we can see that when A is 1 and
+B rises from 0 to 1, the output rises instead
+
+of falls.
+
+Moral of the story: when you're a CMOS designer,
+you'll get very good at implementing functionality
+
+with inverting logic!
\ No newline at end of file
diff --git a/J8L9kRGSvSY.txt b/J8L9kRGSvSY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2a0d1a8dd0edee5c9aa00358057cb68a29a03411
--- /dev/null
+++ b/J8L9kRGSvSY.txt
@@ -0,0 +1,499 @@
+align:start position:0%
+ 
+we now want to introduce some examples
+
+ align:start position:0%
+we now want to introduce some examples
+ 
+
+ align:start position:0%
+we now want to introduce some examples
+of random variables and we will start
+
+ align:start position:0%
+of random variables and we will start
+ 
+
+ align:start position:0%
+of random variables and we will start
+with the simplest conceivable random
+
+ align:start position:0%
+with the simplest conceivable random
+ 
+
+ align:start position:0%
+with the simplest conceivable random
+variable a random variable that takes
+
+ align:start position:0%
+variable a random variable that takes
+ 
+
+ align:start position:0%
+variable a random variable that takes
+the values of zero or one with certain
+
+ align:start position:0%
+the values of zero or one with certain
+ 
+
+ align:start position:0%
+the values of zero or one with certain
+given probabilities such a random
+
+ align:start position:0%
+given probabilities such a random
+ 
+
+ align:start position:0%
+given probabilities such a random
+variable is called a Bernoulli random
+
+ align:start position:0%
+variable is called a Bernoulli random
+ 
+
+ align:start position:0%
+variable is called a Bernoulli random
+variable and the distribution of this
+
+ align:start position:0%
+variable and the distribution of this
+ 
+
+ align:start position:0%
+variable and the distribution of this
+random variable is determined by this
+
+ align:start position:0%
+random variable is determined by this
+ 
+
+ align:start position:0%
+random variable is determined by this
+parameter P which is a given number that
+
+ align:start position:0%
+parameter P which is a given number that
+ 
+
+ align:start position:0%
+parameter P which is a given number that
+lies in the interval between 0 & 1
+
+ align:start position:0%
+lies in the interval between 0 & 1
+ 
+
+ align:start position:0%
+lies in the interval between 0 & 1
+using PMF notation we have the
+
+ align:start position:0%
+using PMF notation we have the
+ 
+
+ align:start position:0%
+using PMF notation we have the
+probability of 0 being equal to 1 minus
+
+ align:start position:0%
+probability of 0 being equal to 1 minus
+ 
+
+ align:start position:0%
+probability of 0 being equal to 1 minus
+P and the probability of taking the
+
+ align:start position:0%
+P and the probability of taking the
+ 
+
+ align:start position:0%
+P and the probability of taking the
+value of 1 equal to P if you wish to
+
+ align:start position:0%
+value of 1 equal to P if you wish to
+ 
+
+ align:start position:0%
+value of 1 equal to P if you wish to
+plot this particular PMF the plot is
+
+ align:start position:0%
+plot this particular PMF the plot is
+ 
+
+ align:start position:0%
+plot this particular PMF the plot is
+rather simple it consists of two bars
+
+ align:start position:0%
+rather simple it consists of two bars
+ 
+
+ align:start position:0%
+rather simple it consists of two bars
+one at 0 and 1 at 1 this one has a
+
+ align:start position:0%
+one at 0 and 1 at 1 this one has a
+ 
+
+ align:start position:0%
+one at 0 and 1 at 1 this one has a
+height of P and this has a height of 1
+
+ align:start position:0%
+height of P and this has a height of 1
+ 
+
+ align:start position:0%
+height of P and this has a height of 1
+minus P Bernoulli random variables show
+
+ align:start position:0%
+minus P Bernoulli random variables show
+ 
+
+ align:start position:0%
+minus P Bernoulli random variables show
+up whenever you are trying to model a
+
+ align:start position:0%
+up whenever you are trying to model a
+ 
+
+ align:start position:0%
+up whenever you are trying to model a
+situation where you run a trial and that
+
+ align:start position:0%
+situation where you run a trial and that
+ 
+
+ align:start position:0%
+situation where you run a trial and that
+trial can result in two alternative
+
+ align:start position:0%
+trial can result in two alternative
+ 
+
+ align:start position:0%
+trial can result in two alternative
+outcomes either success or failure or
+
+ align:start position:0%
+outcomes either success or failure or
+ 
+
+ align:start position:0%
+outcomes either success or failure or
+heads versus tails and so on another
+
+ align:start position:0%
+heads versus tails and so on another
+ 
+
+ align:start position:0%
+heads versus tails and so on another
+situation where Bernoulli random
+
+ align:start position:0%
+situation where Bernoulli random
+ 
+
+ align:start position:0%
+situation where Bernoulli random
+variables show up is when we're making a
+
+ align:start position:0%
+variables show up is when we're making a
+ 
+
+ align:start position:0%
+variables show up is when we're making a
+connection between events and random
+
+ align:start position:0%
+connection between events and random
+ 
+
+ align:start position:0%
+connection between events and random
+variables here's how this connection is
+
+ align:start position:0%
+variables here's how this connection is
+ 
+
+ align:start position:0%
+variables here's how this connection is
+made we have our sample space Omega and
+
+ align:start position:0%
+made we have our sample space Omega and
+ 
+
+ align:start position:0%
+made we have our sample space Omega and
+within that sample space we have a
+
+ align:start position:0%
+within that sample space we have a
+ 
+
+ align:start position:0%
+within that sample space we have a
+certain event a and outside the event a
+
+ align:start position:0%
+certain event a and outside the event a
+ 
+
+ align:start position:0%
+certain event a and outside the event a
+of course we have the complement of a
+
+ align:start position:0%
+of course we have the complement of a
+ 
+
+ align:start position:0%
+of course we have the complement of a
+our random variable is defined so that
+
+ align:start position:0%
+our random variable is defined so that
+ 
+
+ align:start position:0%
+our random variable is defined so that
+it takes a value of 1 whenever the
+
+ align:start position:0%
+it takes a value of 1 whenever the
+ 
+
+ align:start position:0%
+it takes a value of 1 whenever the
+outcome of the experiment lies in a and
+
+ align:start position:0%
+outcome of the experiment lies in a and
+ 
+
+ align:start position:0%
+outcome of the experiment lies in a and
+it takes a value of 0
+
+ align:start position:0%
+it takes a value of 0
+ 
+
+ align:start position:0%
+it takes a value of 0
+whenever the outcome of the experiment
+
+ align:start position:0%
+whenever the outcome of the experiment
+ 
+
+ align:start position:0%
+whenever the outcome of the experiment
+lies outside the event a so that it lies
+
+ align:start position:0%
+lies outside the event a so that it lies
+ 
+
+ align:start position:0%
+lies outside the event a so that it lies
+in the complement this random variable
+
+ align:start position:0%
+in the complement this random variable
+ 
+
+ align:start position:0%
+in the complement this random variable
+is called the indicator random variable
+
+ align:start position:0%
+is called the indicator random variable
+ 
+
+ align:start position:0%
+is called the indicator random variable
+of the event a it is equal to 1 if and
+
+ align:start position:0%
+of the event a it is equal to 1 if and
+ 
+
+ align:start position:0%
+of the event a it is equal to 1 if and
+only if event a occurs
+
+ align:start position:0%
+only if event a occurs
+ 
+
+ align:start position:0%
+only if event a occurs
+and the PMF of that random variable can
+
+ align:start position:0%
+and the PMF of that random variable can
+ 
+
+ align:start position:0%
+and the PMF of that random variable can
+be found as follows
+
+ align:start position:0%
+be found as follows
+ 
+
+ align:start position:0%
+be found as follows
+this is PMF notation this is the
+
+ align:start position:0%
+this is PMF notation this is the
+ 
+
+ align:start position:0%
+this is PMF notation this is the
+equivalent probabilistic notation this
+
+ align:start position:0%
+equivalent probabilistic notation this
+ 
+
+ align:start position:0%
+equivalent probabilistic notation this
+is the probability that a random
+
+ align:start position:0%
+is the probability that a random
+ 
+
+ align:start position:0%
+is the probability that a random
+variable takes a value of 1 now the
+
+ align:start position:0%
+variable takes a value of 1 now the
+ 
+
+ align:start position:0%
+variable takes a value of 1 now the
+random variable takes the value of 1 if
+
+ align:start position:0%
+random variable takes the value of 1 if
+ 
+
+ align:start position:0%
+random variable takes the value of 1 if
+and only if event a occurs and so what
+
+ align:start position:0%
+and only if event a occurs and so what
+ 
+
+ align:start position:0%
+and only if event a occurs and so what
+we have is that our random variable the
+
+ align:start position:0%
+we have is that our random variable the
+ 
+
+ align:start position:0%
+we have is that our random variable the
+indicator random variable is a Bernoulli
+
+ align:start position:0%
+indicator random variable is a Bernoulli
+ 
+
+ align:start position:0%
+indicator random variable is a Bernoulli
+random variable with a parameter P equal
+
+ align:start position:0%
+random variable with a parameter P equal
+ 
+
+ align:start position:0%
+random variable with a parameter P equal
+to the probability of the event of
+
+ align:start position:0%
+to the probability of the event of
+ 
+
+ align:start position:0%
+to the probability of the event of
+interest indicator random variables are
+
+ align:start position:0%
+interest indicator random variables are
+ 
+
+ align:start position:0%
+interest indicator random variables are
+very useful because they allow us to
+
+ align:start position:0%
+very useful because they allow us to
+ 
+
+ align:start position:0%
+very useful because they allow us to
+translate a manipulation of events to a
+
+ align:start position:0%
+translate a manipulation of events to a
+ 
+
+ align:start position:0%
+translate a manipulation of events to a
+manipulation of random variables and
+
+ align:start position:0%
+manipulation of random variables and
+ 
+
+ align:start position:0%
+manipulation of random variables and
+sometimes the algebra of working with
+
+ align:start position:0%
+sometimes the algebra of working with
+ 
+
+ align:start position:0%
+sometimes the algebra of working with
+random variables is easier than working
+
+ align:start position:0%
+random variables is easier than working
+ 
+
+ align:start position:0%
+random variables is easier than working
+with events as we will see in some later
+
+ align:start position:0%
+with events as we will see in some later
+ 
+
+ align:start position:0%
+with events as we will see in some later
+examples
\ No newline at end of file
diff --git a/JZkT3NU2mPM.txt b/JZkT3NU2mPM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..08babdc75b86af921acf4455a688324e67e77a4e
--- /dev/null
+++ b/JZkT3NU2mPM.txt
@@ -0,0 +1,127 @@
+Let us now discuss an
+interesting fact about
+
+independence that should enhance
+our understanding.
+
+Suppose that events A and
+B are independent.
+
+Intuitively, if I tell you that
+A occurred, this does not
+
+change your beliefs as to the
+likelihood that B will occur.
+
+But in that case, this should
+not change your beliefs as to
+
+the likelihood that
+B will not occur.
+
+So A should be independent
+of B complement.
+
+In other words, the occurrence
+of A tells you nothing about
+
+B, and therefore tells
+you nothing about
+
+B complement either.
+
+This was an intuitive argument
+that if A and B are
+
+independent, then A and
+B complement are also
+
+independent.
+
+But let us now verify
+this intuition
+
+through a formal proof.
+
+The formal proof goes
+as follows.
+
+We have the two events, A and
+B. And event A can be broken
+
+down into two pieces.
+
+One piece is the intersection
+of A with B. So that's the
+
+first piece.
+
+And the second piece is the part
+of A which is outside B.
+
+And that piece is A intersection
+with the
+
+complement of B. So these are
+the two pieces that together
+
+comprise event A.
+
+Now, these two pieces are
+disjoint from each other.
+
+And therefore, by the additivity
+axiom, the
+
+probability of A is equal
+to the probability of A
+
+intersection B plus the
+probability of A intersection
+
+with B complement.
+
+Using independence, the first
+term becomes probability of A
+
+times probability of B. And we
+leave the second term as is.
+
+Now let us move this term
+to the other side.
+
+And we obtain that the
+probability of A intersection
+
+with B complement is the
+probability of A minus the
+
+probability of A times the
+probability of B. We factor
+
+out the term probability of A,
+and we are left with 1 minus
+
+probability of B. And then we
+recognize that 1 minus the
+
+probability of B is the same
+as the probability of B
+
+complement.
+
+So we proved that the
+probability of A and B
+
+complement occurring together
+is the product of their
+
+individual probabilities.
+
+And that's exactly the
+definition of A being
+
+independent from B complement.
+
+And this concludes
+the formal proof.
\ No newline at end of file
diff --git a/JyIsB5D3ZCg.txt b/JyIsB5D3ZCg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..095c2c0d896f0f3b59d00fcdba0ce2463b3f88f2
--- /dev/null
+++ b/JyIsB5D3ZCg.txt
@@ -0,0 +1,1719 @@
+PROFESSOR: We had begun to
+discuss, really what is,
+
+although you would not gather
+it from last time, a fairly
+
+straightforward matter.
+
+Set up our usual Cartesian
+coordinate system.
+
+And then look at the surface of
+the solid, and applied to
+
+this solid a force per unit
+area, which we'll represent by
+
+a vector k.
+
+And then put on some
+labels here.
+
+Let this be O. Let this be A,
+let this be B, and this be
+
+point C. Then we
+proceeded to--
+
+I will say, attempt to--
+
+set up a balance of forces
+between the external force per
+
+unit area and the internal
+forces per unit area, which
+
+have to push back on the
+external force if the solid is
+
+to remain motionless.
+
+The thing that I did not carry
+through is that there are two
+
+directions involved.
+
+One is the direction to the
+normal, to the particular
+
+surface that we're looking at.
+
+We'll call that N. And there is
+the direction that k, the
+
+vector k, makes with respect to
+the three reference x axes,
+
+x1, x2, x3.
+
+Let's take k and immediately
+split it up into the three
+
+components, k1, k2, k3, because
+throughout, we're
+
+going to be dealing with the
+balance of those three forces
+
+per unit area in the directions
+of x1, x2, and x3.
+
+We want to take this surface
+area and resolve it into three
+
+separate areas that are
+normal to x1, x2, x3.
+
+And what I did at the end of
+last hour was to look at k and
+
+try to express these internal
+areas in terms of the
+
+direction cosines of k.
+
+Forget that.
+
+We've split up k into its three
+components, and I didn't
+
+draw in the direction
+of the normal to the
+
+surface N last time.
+
+So I kept saying, direction
+cosines of k, and people in
+
+the audience said,
+no, no, no, no.
+
+And I said, yeah, because you
+see, that's the ratio
+
+of these two areas.
+
+And everybody said, no, that's
+wrong, and I said, ha.
+
+And that's where we ended
+my most inglorious hour.
+
+And they've got this
+all down on tape.
+
+My reputation's going
+to be ruined.
+
+So, anyway, let's now
+do it properly.
+
+And what I will say is that in
+the x1 direction, we have to
+
+have internal forces that push
+back, and we have to balance
+
+those forces in all
+three directions.
+
+So I'll say is that in the x1
+direction, and this as you saw
+
+last time, gets very cumbersome
+because we have to
+
+deal with all these clumsy
+areas, that the force per unit
+
+area on ABC has to be balanced
+for each of the three
+
+components of k by internal
+forces acting
+
+along x1, x2, and x3.
+
+So we can say is that the first
+in the x1 direction, the
+
+component of k that acts on
+the surface ABC in the x1
+
+direction has to be balanced
+by internal forces.
+
+And let's look first at
+the x1 direction.
+
+So there are three internal
+surfaces.
+
+They are the area BOC.
+
+That is this back surface here,
+and the normal to that
+
+surface is x1.
+
+So let me define some forces
+per unit area that are
+
+internal, and I'll use the
+term sigma for that.
+
+And I will use a first subscript
+that gives the
+
+direction in which that force
+per unit area acts, and I'll
+
+use a second subscript that
+indicates the normal to the
+
+internal surface.
+
+So area BOC obviously, as we
+observed a moment ago, has x1
+
+as its normal.
+
+But there are three
+internal surfaces.
+
+There will also be an internal
+area, AOC, on which a force
+
+per unit area acts in
+the x1 direction.
+
+So I'll call this one
+by analogy to what I
+
+did a moment ago.
+
+I'll call this sigma 1, because
+it acts in the x1
+
+direction, and it acts on the
+surface AOC, which has x2 as
+
+its normal.
+
+Then finally, there will be a
+third force per unit area,
+
+sigma 1 3, acting in the x1
+direction, on a surface whose
+
+normal is perpendicular
+to-- along x3.
+
+The surface is perpendicular
+to x3.
+
+And that's area AOB.
+
+OK, so this is just a simple
+balance of forces, external
+
+and internal balancing forces,
+which act in the x1 direction.
+
+Then we'll write a similar thing
+for the x2 direction.
+
+And we'll say that the x2
+component of force per unit
+
+area external to the volume
+element acting on area ABC is
+
+going to be balanced by, again,
+forces now acting in
+
+the x2 direction.
+
+So first, there will be a
+component of 4 sigma 2 acting
+
+on the area that's normal to x1,
+and that's the same area
+
+BOC, plus another force per
+unit area acting in the x2
+
+direction on the surface, whose
+normal is a long x2.
+
+And that is, once
+more, area AOC.
+
+And that would be a force per
+unit area that I'll define,
+
+because it's my ball game
+and I own the ball.
+
+So again, that would be sigma 2
+2, and then finally a sigma
+
+2 3 times the area whose
+normal is x3.
+
+And I think I need not write
+the third term that follows
+
+automatically from what
+I've written so far.
+
+So now comes the geometry part,
+where I'm going to get
+
+rid of these messy areas, and
+I'm going to divide through by
+
+the external area on the
+surface of the solid.
+
+I will then write accordingly
+that k1 is equal to sigma 11
+
+times the ratio of area BOC
+divided by area ABC plus sigma
+
+12 times area AOC divided
+by area AOB--
+
+ABC, excuse me.
+
+Then finally sigma 1 3 times
+area AOB divided by area ABC.
+
+So now I'll introduce a little
+bit of geometry that caused
+
+such difficulties last time.
+
+If I have an area and project
+it onto another area that
+
+makes an angle C with respect
+to the first, this area A
+
+prime is equal to the area A
+times the cosine of Phi and
+
+you could define that Phi in a
+different way, namely take the
+
+normal to one of the two areas
+and let M prime be the other
+
+normal, so C then is exactly
+the same thing as the angle
+
+between the normals to
+these two surfaces.
+
+So let's now look at what the
+ratio of these two areas that
+
+we have is.
+
+What we're dealing with here is
+an angle between the normal
+
+to the surface, not k, but the
+normal to the surface, and
+
+either x1, x2, or x3.
+
+So the ratio of--
+
+let's look at one of these
+specific terms.
+
+The ratio of area BOC through
+the ratio of the area ABC
+
+should be the cosine of the
+angle between the normal to
+
+the surface and the normal
+to area BOC.
+
+Well, the normal to area BOC is
+x1, so that first ratio of
+
+areas is just going to be the
+cosine of this angle.
+
+And that cosine is just the
+direction cosine of N1 along
+
+the x1 of M along the
+x1 direction.
+
+So this is just the direction
+cosine between N, the normal
+
+to the surface, and x1.
+
+And let me say then that, by
+definition, I'll let the
+
+direction to the normal be its
+three direction cosines, L 1
+
+plus L 2, plus J plus
+L3 times k.
+
+These are the direction cosines
+of the normal to the
+
+surface, and not k.
+
+So this then simply comes down
+to sigma 11 times L1, the
+
+ratio of the area AOC to ABC
+is going to be the angle
+
+between N and x2.
+
+And that's the angle whose
+direction cosine is L2.
+
+And similarly, the ratio of
+these two areas will be cosine
+
+minus 1 of L3.
+
+So this cumbersome construction
+with ratios of
+
+areas just reduces to sigma 11
+L1 plus sigma 12 times L2 plus
+
+sigma 13 times L3.
+
+And the other two equations will
+follow a similar form.
+
+K2 will be sigma 21 times L1
+plus sigma 22 times L2 plus
+
+sigma 23 times L3.
+
+Or in general, case of I will be
+given by sigma I J times L
+
+to J. Easy.
+
+Nice and compact.
+
+Nice and simple.
+
+What can we say about this?
+
+K is a vector which has
+components k1, k2, and k3.
+
+The direction cosines can be,
+as we said a moment ago, can
+
+be regarded as the components
+of a unit vector pointing
+
+along the normal
+to the surface.
+
+So k is a vector.
+
+These three direction cosines
+are the direction cosine to a
+
+unit vector normal
+to the surface.
+
+If we were to be so foolish to
+try to change the coordinate
+
+system., having just gotten it
+right for the first time in
+
+one coordinate system, we know
+exactly how the two vectors
+
+will change because
+we have a law for
+
+transformation of a vector.
+
+If we were to change the
+coordinate system, the
+
+components of k would wink on
+end of and take new values and
+
+we know exactly how the
+components of a vector will
+
+change as we change
+coordinate system.
+
+OK, if this transforms like a
+vector and this transforms
+
+like the vector, then the 3 by
+3 array of coefficients which
+
+relate those to quantities
+must be a tensor.
+
+So we've proven rigorously that
+sigma IJ is a tensor, in
+
+particular, it's a second
+rank tensor.
+
+And were we to change coordinate
+system, we know
+
+from what we've done in the
+past, exactly how the numbers
+
+that make up this 3 by 3
+array will transform.
+
+These quantities, sigma IJ,
+are something that you've
+
+probably encountered, introduced
+to be sure,
+
+probably in a little
+different way.
+
+These are the elements of
+stress, and sigma IJ is the
+
+stress tensor.
+
+We can immediately, on physical
+grounds, established
+
+that sigma IJ must be
+a symmetric tensor.
+
+So let's set up two axes, x1,
+and x2, and x3 obviously is
+
+normal to the board.
+
+And let us look at some
+off-diagonal terms like sigma
+
+12 and sigma 21.
+
+Sigma 1 2 would be a force
+acting on the x1 direction on
+
+a surface whose normal is x2.
+
+So this is going to be a sheer
+stress and that, to prevent
+
+any translation of the volume
+element, must be balanced by a
+
+sigma 12 on the other
+face that acts in
+
+the opposite direction.
+
+We're going to need a convention
+for defining sign,
+
+S-I-G-N, of what constitutes a
+positive element of stress and
+
+a negative element of stress.
+
+And I'll define a plus sigma
+IJ as a force per unit area
+
+acting in the plus xi direction
+on a surface whose
+
+normal is plus xj.
+
+So if this is a force per unit
+area acting on this surface,
+
+and it acts in the direction
+of x1 on a surface whose
+
+normal is x2, what I've shown
+here is a positive sigma 12.
+
+A sheer force going in the
+opposite direction would be a
+
+negative sigma 12.
+
+A positive sigma 11 would be
+a stress that's tensile, a
+
+negative sigma 11 would be a
+stress that's compressive.
+
+So here's a sigma 12, a sigma
+12 on the opposite face.
+
+If we went away and turned our
+back, this volume element
+
+would start accelerating,
+getting an angular
+
+acceleration, would start
+furiously spinning about the
+
+x3 axis like a top.
+
+So something, if this volume
+element is, by definition, an
+
+equilibrium, something has
+to balance this couple.
+
+And if it's to stay put, we must
+have a sheer force like
+
+this and a sheer force
+like this.
+
+And that's the only thing
+available from the nine
+
+elements of stress that will
+give a net torque on the
+
+volume element.
+
+So what are these?
+
+This is a stress that
+acts on the surface
+
+whose normal is x2--
+
+whose normal as x1 in
+the x2 direction.
+
+So this is sigma 21.
+
+It acts in x2 direction,
+and its normal is x1.
+
+An x, and then [? plus ?]
+
+x2 direction on [? I ?]
+
+surface, which has a normal
+that is along x1.
+
+So the only way we can avoid an
+angular acceleration is to
+
+say that sigma 12 has to be
+identical to sigma 21 if
+
+there's no rotation about x3.
+
+And looking at the couple's that
+act about x2, and x3, we
+
+could say in general that sigma
+IJ is going to have to
+
+be equal to sigma JI for a
+volume element in equilibrium.
+
+So stress then is equilibrium
+is in place, has to be a
+
+symmetric tensor.
+
+It is, however, a plain old
+second-rank tensor like all of
+
+the other second-rank tensors
+that we've spent the last
+
+month talking about.
+
+And I think I tried to swindle
+you on this one before.
+
+If this is a second-rank tensor,
+the stress tensor must
+
+be symmetric and diagonal
+for a cubic crystal.
+
+In other words, the stress
+tensor sigma IJ must have the
+
+form sigma 0 0, 0 sigma 0, 0 0
+sigma because we've shown that
+
+that is what is required of a
+tensor if the crystal has
+
+cubic symmetry.
+
+So surprisingly, you cannot
+subject a single crystal with
+
+cubic material to
+sheer stress.
+
+Any quarrel with that?
+
+Should we move on?
+
+We better not, but somebody
+better raise an objection.
+
+That's not true, obviously.
+
+I can take a cubic crystal and
+shear the stuffings out of it.
+
+So what's going on here?
+
+AUDIENCE: The tensor property
+that you are applying to
+
+[INAUDIBLE]
+
+property of the [? crystal. ?]
+
+But if it is an outside force,
+it doesn't [INAUDIBLE].
+
+PROFESSOR: This is one
+of your good days.
+
+AUDIENCE: [INAUDIBLE]
+
+society [INAUDIBLE].
+
+PROFESSOR: That makes it an
+especially good day because
+
+you're paying attention to
+what I said for a change.
+
+The distinction here, and I did
+make it last time-- it was
+
+one of the things that
+I did correctly--
+
+that there are really two kinds
+of things that have to
+
+be described by second-rank
+tensors.
+
+There are the things that we
+have been spending most of our
+
+time on, and these are property
+tensors and--
+
+I mentioned last time, too, so
+I know I said this before--
+
+Nye calls them field tensors.
+
+I'm sorry.
+
+Nye calls them property
+tensors, also.
+
+And these are something that
+depends on the structure and
+
+bonding and other
+
+characteristics of the material.
+
+The stress is something that we
+we're taking and imposing
+
+on an innocent, unsuspecting
+crystal, and that is
+
+something we do.
+
+And we can, by design, twist it,
+shear it, stretch it, as
+
+hard as we like, provided
+we don't break it.
+
+And so this is something that
+is externally imposed on the
+
+crystal, and this is something
+that's called a field tensor.
+
+We mentioned last time
+the meaning of field.
+
+The field is a volume of space
+and a field tensor is a space
+
+in which a value of the tensor
+is defined as every point, x1,
+
+x2, x3, in the space.
+
+Just as an electric field is a
+vector field and you define
+
+the electric field we as a
+function of every point x1,
+
+x2, x3, in the space.
+
+So there's no reason whatsoever
+that there need be
+
+restrictions on the tensor
+that we apply.
+
+And when we can cross out that
+interesting, but incorrect,
+
+supposition.
+
+But they can be a lot of
+different forms, special
+
+forms, of stress tensors which
+have special forms simply
+
+because of the nature
+of what we do.
+
+And these have restrictions and
+equalities that have no
+
+counterpart in property
+tensors.
+
+For example, we can have the
+cancer sigma 00000000, which
+
+is something we could never
+have identically so for a
+
+property tensor.
+
+And what does this represent?
+
+This is a tensor for which sigma
+IJ is 0, unless I equals
+
+J equals 1.
+
+So this is the only thing that's
+going on, is a force
+
+per unit area along
+the x1 direction.
+
+So this is a uniaxial stress.
+
+And that is a stress field
+which we could apply on a
+
+piece of material very easily.
+
+Just screw a hook into the
+material and hang a weight on
+
+the hook and you've got
+uniaxial stress.
+
+We can also have something
+that's a little harder to
+
+visualize, a biaxial stress.
+
+And this would be a stress that
+had elements sigma 11,
+
+register 0--
+
+at least when we refer
+to principal axes--
+
+0 sigma 2 2 0 0 0 0.
+
+When it's in diagonal
+form, two of the
+
+diagonal terms are 0.
+
+That doesn't seem to make sense
+because, if this is a
+
+force per unit area along x1,
+and this is a force per unit
+
+area along x2, can't we add up
+those vectors and say that
+
+that's a uniaxial stress?
+
+Depends on your coordinate
+system.
+
+If you want an example of a
+biaxial stress, imagine some
+
+firemen underneath a burning
+building, and they're holding
+
+out a blanket for somebody
+to jump into.
+
+You have one pair of firemen
+pulling in this direction to
+
+keep the blanket taut, and
+another pair of firemen are
+
+not quite so vigorous, and
+they're pulling in an
+
+orthogonal direction.
+
+And those two forces, sigma 11
+and sigma 22, create a biaxial
+
+stress event material.
+
+You could change the form of
+the tensor by rotating the
+
+coordinate system, but
+this is one example
+
+of a biaxial stress.
+
+The final general form, a
+triaxial stress, obviously by
+
+extension, is going to be where
+of all three diagonals,
+
+sigma 11, sigma 22, and sigma
+33, are non-zero when you put
+
+the tensor in diagonal form.
+
+This would be a general
+triaxial stress.
+
+And an example of that would
+be when the jumping person
+
+lands on the blanket, there's
+going to be a force that his
+
+or her mass exerts on the
+blanket, and that would be a
+
+third sigma 3 3.
+
+So that would be a
+triaxial stress.
+
+Let me give you a couple of
+special cases of specialized
+
+stress tensors.
+
+And suppose I had a triaxial
+stress, but all the diagonal
+
+terms were equal.
+
+That's something that I tried
+a moment ago to hoodwink you
+
+into believing was required by
+a cubic crystal, but suppose
+
+that was the form of
+the stress tensor.
+
+What would that represent?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: That is something
+that's going to be--
+
+yeah, very good.
+
+That's not a pressure.
+
+It's a dilation.
+
+But if I make it into a more
+familiar form, put it here,
+
+minus P, minus P, minus P. It's
+a force prevented area.
+
+That's where the stress is.
+
+If it's a hydrostatic pressure,
+it's squeezing the
+
+volume element so it has to be,
+by our definition, acting
+
+in a negative x1 direction
+on a surface whose
+
+normal is plus x1.
+
+So minus P, minus P,
+minus P, represents
+
+a hydrostatic pressure.
+
+And now, unless you've seen it
+before, or you're reading the
+
+notes instead of listening to
+me, let me give you a really
+
+strange-looking one.
+
+What is this stress tensor?
+
+Where sigma 22 is opposite
+in sign but equal in
+
+magnitude to sigma 11.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+Good.
+
+The way to see that
+
+geometrically is the following.
+
+What we're doing is, we're
+pushing with a force per unit
+
+area in this direction.
+
+That would be sigma 11, and
+then we squeeze in the
+
+orthogonal direction.
+
+And that is a sigma 22,
+which is negative.
+
+If we rotate the solid by 90
+degrees, then we've got this,
+
+plus this, acting on this face,
+same forces per unit
+
+area as we have here.
+
+And that is a net force per
+unit area like this.
+
+On the opposite surface, we've
+got this force per unit area
+
+and this force per unit
+area, component
+
+going in this direction.
+
+And that is going to be a force
+that goes like this.
+
+That's going to be a force per
+unit area like this, and
+
+similarly, this combined with
+this is going to be a force
+
+acting in the reverse
+direction.
+
+That would be, again, this with
+this, and this would be
+
+this with that.
+
+So clearly, that is a body
+that's being subjected to pure
+
+sheer, and if we rotated the
+axes x1 and x2 by 45 degrees
+
+to an x1 prime and x2 prime
+like this, and then
+
+transformed the tensor, it
+would take the form 0
+
+sigma sigma 0 0.
+
+And then, what do we want now?
+
+This would be the only
+thing we get.
+
+Except I should be careful to
+put a sigma prime on this
+
+because, when we change axes,
+these sigmas will not be of
+
+the same magnitude as
+the original ones.
+
+There's going to be a square
+root of 2 coming from cosine
+
+of 45 degrees in there.
+
+But, anyway, just rotating the
+axes 45 degrees of as I've
+
+indicated schematically here
+with vector sums is going to
+
+give me two off diagonal terms
+equal in magnitude that would
+
+correspond to sigma
+12 and sigma 21.
+
+So those are some special forms
+of a stress tensor when
+
+you place it in a diagonalized
+form.
+
+But let's conclude this part of
+our discussion by observing
+
+that everything that we've said
+about second-rank tensors
+
+holds for the stress tensor.
+
+For example, you can always
+select new axes that put the
+
+tensor in diagonal form.
+
+So that's one general
+property.
+
+You can define a stress quadric,
+and we'll do that
+
+with the equation sigma
+ij xi xj equals 1.
+
+Why not?
+
+It's a second-ranked tensor.
+
+We can take the elements and
+construct a surface from it.
+
+This quadric will have the
+properties of any other
+
+quadric for a second-rank
+tensor.
+
+In particular, if we construct
+the quadric, it's now for sure
+
+going to be able to be either
+an ellipsoid, an hyperboloid
+
+of one or two sheets, or in this
+case, even an imaginary
+
+ellipsoid for a stress that's
+everywhere compressive.
+
+The quadric could have
+its diagonal
+
+elements all negative.
+
+The radius of the stress
+quadric in a particular
+
+direction is going to be the 1
+over the square root of the
+
+property in that direction.
+
+What does that mean, stress
+in a given direction?
+
+Well, let's again remember
+how we have
+
+defined the stress tensor.
+
+A force per unit area has three
+components, k1, k2, k3,
+
+and they're equal to
+sigma ij times lj.
+
+So the value of the property in
+this direction is going to
+
+be the value of the property
+in the direction defined by
+
+[? elsa ?] j and the values of
+[? elsa ?] j are components of
+
+the unit vector that point
+in that direction.
+
+So if this is the direction of
+k, [? off ?] like this, the
+
+value of this quadric in this
+direction is going to be the
+
+value of the part of k that's
+parallel to the radius vector
+
+over the magnitude of
+the radius vector.
+
+But the [? radius ?] vector is
+a unit vector, so it's simply
+
+going to be equal
+to k parallel.
+
+And if k parallel is the part
+of the vector that is along
+
+the surface normal, that is
+going to be the component of k
+
+which is purely tensile.
+
+This is a force per unit area,
+has parts that are, components
+
+that are normal to the
+surface normal.
+
+Those are shear components.
+
+The component that's directly
+along the normal to the
+
+surface is going to be a purely
+tensile component.
+
+And, therefore, the radius
+of the quadric in a given
+
+direction gives us the tensile
+component of the force density
+
+vector k that is transmitted
+across the face--
+
+so let's not say face,
+but interface--
+
+whose normal is in the
+direction of R.
+
+So this is the radius vector.
+
+That's the direction of the
+normal to a surface and 1 over
+
+the radius of--
+
+The radius of the quadric in
+that direction is going to be
+
+1 over the square root of the
+tensile component of stress
+
+that's transmitted across an
+interface in this direction.
+
+How are we doing on time?
+
+Any questions at this point?
+
+AUDIENCE: Can you explain how
+you know that's [INAUDIBLE]?
+
+PROFESSOR: Remember what our
+radius normal property said.
+
+If we have a tensor like good
+conductivity, where a current
+
+density is related to an
+applied electric field,
+
+[? essa ?] j and we've--
+
+unfortunately, that's
+segment 2.
+
+This is the conductivity
+tensor.
+
+What we said is that, if we
+take the components of the
+
+tensor, sigma ij, and construct
+the surface sigma ij
+
+xij equals unity, that will be
+some sort of quadratic form
+
+that has the property that the
+radius in any given direction
+
+is 1 over the square root of
+the value of the property,
+
+sigma conductivity
+in this case.
+
+Bad case.
+
+I shouldn't have picked
+things where the
+
+sigma is also involved.
+
+And the value of the property
+in the given direction is
+
+going to be the parallel
+component of what happens over
+
+the magnitude of what you do.
+
+So in the case of electrical
+conductivity, if we apply a
+
+field in this direction, the
+value of the property is going
+
+to be that part of the current
+flow, which is parallel to the
+
+electric field, divided
+by the magnitude of
+
+the electric field.
+
+So that is a relation that you
+know by heart and have come to
+
+not only know, but to love.
+
+So what are we saying here?
+
+For the stress tensor, we can
+take the elements of the
+
+stress tensor and construct
+a quadric.
+
+And the thing that's related
+here is a force per unit area
+
+that we're applying to the
+surface of the crystal, and
+
+that's transmitted through the
+volume of the crystal by the
+
+relation that we have defined
+as the stress tensor.
+
+So, unfortunately,
+again, sigma Ij.
+
+And now what is involved are the
+direction cosines of the
+
+normal to the surface.
+
+So what is the applied vector?
+
+The applied vector is a unit
+vector, and this is the normal
+
+to the surface.
+
+And the surface in question
+would be a surface like this.
+
+The thing that results is
+a force per unit area k.
+
+So what we're doing is taking
+k, the value of
+
+sigma, in that direction.
+
+A scalar quantity will be the
+part of k that's parallel to
+
+the normal vector,
+divided by the
+
+magnitude of the unit vector.
+
+And that's, a magnitude
+of n is 1, so
+
+that's just k parallel.
+
+So this is the surface.
+
+This is its normal.
+
+And what the radius of the
+quadric is going to give us is
+
+that part of the force density,
+which is the force
+
+density vector resolved onto
+the normal vector.
+
+And this is a tensile.
+
+This is the part of the
+tensile stress that's
+
+transmitted.
+
+This is the total stress
+that has a sheer part
+
+and a tensile part.
+
+The radius of the quadric is
+going to give you the part
+
+that's transmitted across the
+surface in this orientation.
+
+That is purely a
+tensile force.
+
+That make sense?
+
+I should have done it
+without sigmas being
+
+present in both tensors.
+
+So everything you want to know
+about stress that's applied to
+
+a solid is contained in a
+second-rank tensor that is
+
+symmetric and obeys all of the
+characteristics that we
+
+derived earlier for property
+tensors, even though this is a
+
+field tensor, and not
+a property tensor.
+
+Let us then turn to the next
+thing that I want to discuss,
+
+again something you've
+heard before.
+
+But we'll do it within the
+context of the tensor algebra
+
+that we've developed before.
+
+And this is the concept
+of strength.
+
+And let me introduce
+the subject by a
+
+one-dimensional analog.
+
+Suppose we have a very thin
+elastic band fastened to some
+
+immovable surface, and this
+will be the direction x.
+
+And then we pull on it.
+
+And here again, we have to be
+complete and note that there
+
+are several different
+kinds of behavior.
+
+One type of behavior is a case
+where the elastic band
+
+stretches, and if there's some
+point P on the initial state
+
+that point P will move to
+a point P prime that is
+
+displaced from the original
+location by a vector U.
+
+There's another point Q part
+way along the elastic band.
+
+If the thing that we have
+fastened to the elastic band
+
+slipped, and there's no
+deformation at all, Q would be
+
+displaced by the same amount U
+if there was just translation
+
+of the elastic because it wasn't
+fastened down solidly.
+
+But if it's stretching here
+between this point and this
+
+point, it's going to stretch
+up here, too.
+
+And, in general, it will move
+over to some point Q prime,
+
+and this displacement vector is
+going to be the original U
+
+plus delta U. And what we care
+about in defining strength is
+
+not the absolute coordinates,
+but the interval
+
+between these points.
+
+This separation is U, and this
+separation is U plus delta U.
+
+Now this is a common, but
+not a necessarily
+
+unique, sort of behavior.
+
+This is something where the
+displacement does not change
+
+along the length of
+the elastic bands.
+
+This is something that's
+called homogeneous
+
+deformation.
+
+And this is characterized by a
+displacement view that varies
+
+linearly with position along
+the elastic band.
+
+Does something like this.
+
+It's possible, in a [? grade ?]
+of material, if
+
+you'd like a real example,
+that U, as a function of
+
+distance along this
+one-dimensional object, does
+
+something like this.
+
+Why not?
+
+That's what might happen
+for example in--
+
+that's almost an oxymoron, a
+one-dimensional elastic band
+
+whose cross-sectional area
+changes with distance in that
+
+one dimension.
+
+So this is homogeneous
+deformation, as opposed to
+
+inhomogeneous deformation.
+
+There's another type of
+behavior, and this is apparent
+
+if you place a thin piece of
+metal or plastic, let's say,
+
+between the pair of grips in the
+Instron machine, and after
+
+deformation, it does something
+like this.
+
+There's an inhomogeneous
+deformation, which is to
+
+referred to colloquially
+as necking.
+
+A very good example of that is
+what happens when you grab
+
+hold of some cheap plastic
+shrink wrap that has been
+
+shrunk around a package that
+has been mailed to you.
+
+And you want to get it
+off, so you grab it.
+
+And it doesn't deform
+elastically.
+
+What happens is that it necks
+in places where there's a
+
+stress concentration.
+
+And you get something
+exactly like this.
+
+And if we were to indicate that
+sort of behavior, U as a
+
+function of position would be
+one U, and then it would
+
+increase very rapidly.
+
+The [? UDX ?]
+
+would be very much larger than
+the places which had uniform
+
+elastic deformation, so it would
+be a nonlinear behavior
+
+of this sort.
+
+And that would be necking.
+
+If you've never noticed that
+sort of behavior before, I
+
+give you an assignment tonight
+of going home and getting a
+
+piece of Saran wrap from your
+kitchen drawer and grabbing
+
+hold of it and pulling it.
+
+And it deforms non-uniformly in
+a fashion that's indicative
+
+of necking.
+
+OK, it's just about five of.
+
+Why don't I stop there.
+
+And what I would like to do next
+is to cast this relation,
+
+which is a one-dimensional
+stream, into a
+
+three-dimensional situation.
+
+And we'll look at some of the
+properties of the description
+
+of a body that's been deformed
+in three dimensions.
\ No newline at end of file
diff --git a/KSD3avale8o.txt b/KSD3avale8o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3fdfd9e7cb701725d8049204faddefd7c182bbbd
--- /dev/null
+++ b/KSD3avale8o.txt
@@ -0,0 +1,8115 @@
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+ 
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+will help MIT open courseware continue
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+resources for free to make a donation or
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+view additional materials from hundreds
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+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu in the last class we were
+
+ align:start position:0%
+ocw.mit.edu in the last class we were
+ 
+
+ align:start position:0%
+ocw.mit.edu in the last class we were
+talking about the parasitic birds that
+
+ align:start position:0%
+talking about the parasitic birds that
+ 
+
+ align:start position:0%
+talking about the parasitic birds that
+lay their eggs in the nest of another
+
+ align:start position:0%
+lay their eggs in the nest of another
+ 
+
+ align:start position:0%
+lay their eggs in the nest of another
+bird and I asked you a question you know
+
+ align:start position:0%
+bird and I asked you a question you know
+ 
+
+ align:start position:0%
+bird and I asked you a question you know
+how why wouldn't these other
+
+ align:start position:0%
+how why wouldn't these other
+ 
+
+ align:start position:0%
+how why wouldn't these other
+birds evolve means of opposing that why
+
+ align:start position:0%
+birds evolve means of opposing that why
+ 
+
+ align:start position:0%
+birds evolve means of opposing that why
+don't they just learn to th recognize
+
+ align:start position:0%
+don't they just learn to th recognize
+ 
+
+ align:start position:0%
+don't they just learn to th recognize
+the eggs of the other bird you can see
+
+ align:start position:0%
+the eggs of the other bird you can see
+ 
+
+ align:start position:0%
+the eggs of the other bird you can see
+here that in many cases the can see that
+
+ align:start position:0%
+here that in many cases the can see that
+ 
+
+ align:start position:0%
+here that in many cases the can see that
+much larger egg
+
+ align:start position:0%
+much larger egg
+ 
+
+ align:start position:0%
+much larger egg
+there uh and yet they generally will
+
+ align:start position:0%
+there uh and yet they generally will
+ 
+
+ align:start position:0%
+there uh and yet they generally will
+raise it raise the check in fact it's
+
+ align:start position:0%
+raise it raise the check in fact it's
+ 
+
+ align:start position:0%
+raise it raise the check in fact it's
+it's often at the expense of their own
+
+ align:start position:0%
+it's often at the expense of their own
+ 
+
+ align:start position:0%
+it's often at the expense of their own
+chicks because the cuu is an aggressive
+
+ align:start position:0%
+chicks because the cuu is an aggressive
+ 
+
+ align:start position:0%
+chicks because the cuu is an aggressive
+chick uh often you know pushes the other
+
+ align:start position:0%
+chick uh often you know pushes the other
+ 
+
+ align:start position:0%
+chick uh often you know pushes the other
+the smaller chicks out of the nest
+
+ align:start position:0%
+the smaller chicks out of the nest
+ 
+
+ align:start position:0%
+the smaller chicks out of the nest
+sometimes the the Foster mother in this
+
+ align:start position:0%
+sometimes the the Foster mother in this
+ 
+
+ align:start position:0%
+sometimes the the Foster mother in this
+case uh is Raising only the
+
+ align:start position:0%
+case uh is Raising only the
+ 
+
+ align:start position:0%
+case uh is Raising only the
+kuu but at least her reproduction is
+
+ align:start position:0%
+kuu but at least her reproduction is
+ 
+
+ align:start position:0%
+kuu but at least her reproduction is
+considerably diminished by
+
+ align:start position:0%
+considerably diminished by
+ 
+
+ align:start position:0%
+considerably diminished by
+this by this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of the reasons they do it has
+
+ align:start position:0%
+and one of the reasons they do it has
+ 
+
+ align:start position:0%
+and one of the reasons they do it has
+been investigated in a study of the the
+
+ align:start position:0%
+been investigated in a study of the the
+ 
+
+ align:start position:0%
+been investigated in a study of the the
+spotted Kaku and magpies um in
+
+ align:start position:0%
+spotted Kaku and magpies um in
+ 
+
+ align:start position:0%
+spotted Kaku and magpies um in
+Spain when
+
+ align:start position:0%
+Spain when
+ 
+
+ align:start position:0%
+Spain when
+the at a time when the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the cus moved into an area the
+
+ align:start position:0%
+uh the cus moved into an area the
+ 
+
+ align:start position:0%
+uh the cus moved into an area the
+magpies were living or the mag Pi moved
+
+ align:start position:0%
+magpies were living or the mag Pi moved
+ 
+
+ align:start position:0%
+magpies were living or the mag Pi moved
+in I can't remember which I think the
+
+ align:start position:0%
+in I can't remember which I think the
+ 
+
+ align:start position:0%
+in I can't remember which I think the
+cus came in later okay and so they
+
+ align:start position:0%
+cus came in later okay and so they
+ 
+
+ align:start position:0%
+cus came in later okay and so they
+started laying their eggs in other
+
+ align:start position:0%
+started laying their eggs in other
+ 
+
+ align:start position:0%
+started laying their eggs in other
+bird's
+
+ align:start position:0%
+bird's
+ 
+
+ align:start position:0%
+bird's
+nest but then they found out that the
+
+ align:start position:0%
+nest but then they found out that the
+ 
+
+ align:start position:0%
+nest but then they found out that the
+birds often
+
+ align:start position:0%
+birds often
+ 
+
+ align:start position:0%
+birds often
+do destroy the kaku's
+
+ align:start position:0%
+do destroy the kaku's
+ 
+
+ align:start position:0%
+do destroy the kaku's
+egg but when they
+
+ align:start position:0%
+egg but when they
+ 
+
+ align:start position:0%
+egg but when they
+do there's sort of a MAG a Kaku Mafia
+
+ align:start position:0%
+do there's sort of a MAG a Kaku Mafia
+ 
+
+ align:start position:0%
+do there's sort of a MAG a Kaku Mafia
+that comes around and destroys their
+
+ align:start position:0%
+that comes around and destroys their
+ 
+
+ align:start position:0%
+that comes around and destroys their
+nest so then they don't reproduce at all
+
+ align:start position:0%
+nest so then they don't reproduce at all
+ 
+
+ align:start position:0%
+nest so then they don't reproduce at all
+and it's better to
+
+ align:start position:0%
+and it's better to
+ 
+
+ align:start position:0%
+and it's better to
+reproduce even a few than
+
+ align:start position:0%
+reproduce even a few than
+ 
+
+ align:start position:0%
+reproduce even a few than
+none so that was the mafia hypothesis
+
+ align:start position:0%
+none so that was the mafia hypothesis
+ 
+
+ align:start position:0%
+none so that was the mafia hypothesis
+and it was
+
+ align:start position:0%
+and it was
+ 
+
+ align:start position:0%
+and it was
+verified uh in
+
+ align:start position:0%
+verified uh in
+ 
+
+ align:start position:0%
+verified uh in
+Spain but there have been reports and I
+
+ align:start position:0%
+Spain but there have been reports and I
+ 
+
+ align:start position:0%
+Spain but there have been reports and I
+don't know of any uh really quanitative
+
+ align:start position:0%
+don't know of any uh really quanitative
+ 
+
+ align:start position:0%
+don't know of any uh really quanitative
+description of this but were cases
+
+ align:start position:0%
+description of this but were cases
+ 
+
+ align:start position:0%
+description of this but were cases
+when the song bird would uh build a a
+
+ align:start position:0%
+when the song bird would uh build a a
+ 
+
+ align:start position:0%
+when the song bird would uh build a a
+decoy Nest above his real nest and lay
+
+ align:start position:0%
+decoy Nest above his real nest and lay
+ 
+
+ align:start position:0%
+decoy Nest above his real nest and lay
+eggs in both and uh the caku generally
+
+ align:start position:0%
+eggs in both and uh the caku generally
+ 
+
+ align:start position:0%
+eggs in both and uh the caku generally
+will lay the egg in the the conspicuous
+
+ align:start position:0%
+will lay the egg in the the conspicuous
+ 
+
+ align:start position:0%
+will lay the egg in the the conspicuous
+Nest The Nest at the
+
+ align:start position:0%
+Nest The Nest at the
+ 
+
+ align:start position:0%
+Nest The Nest at the
+top and the nest below is more hidden U
+
+ align:start position:0%
+top and the nest below is more hidden U
+ 
+
+ align:start position:0%
+top and the nest below is more hidden U
+but I don't know just how often that
+
+ align:start position:0%
+but I don't know just how often that
+ 
+
+ align:start position:0%
+but I don't know just how often that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+happen but they have to do it in a way
+
+ align:start position:0%
+happen but they have to do it in a way
+ 
+
+ align:start position:0%
+happen but they have to do it in a way
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+this uh group of tuus couldn't force
+
+ align:start position:0%
+this uh group of tuus couldn't force
+ 
+
+ align:start position:0%
+this uh group of tuus couldn't force
+them or couldn't destroy their n because
+
+ align:start position:0%
+them or couldn't destroy their n because
+ 
+
+ align:start position:0%
+them or couldn't destroy their n because
+they destroyed their
+
+ align:start position:0%
+they destroyed their
+ 
+
+ align:start position:0%
+they destroyed their
+egg but we saw this last time
+
+ align:start position:0%
+egg but we saw this last time
+ 
+
+ align:start position:0%
+egg but we saw this last time
+uh well so the Kaku is exploiting the
+
+ align:start position:0%
+uh well so the Kaku is exploiting the
+ 
+
+ align:start position:0%
+uh well so the Kaku is exploiting the
+innate releasing mechanism of the song
+
+ align:start position:0%
+innate releasing mechanism of the song
+ 
+
+ align:start position:0%
+innate releasing mechanism of the song
+birds that they use to raise their
+
+ align:start position:0%
+birds that they use to raise their
+ 
+
+ align:start position:0%
+birds that they use to raise their
+young it's because the they can't resist
+
+ align:start position:0%
+young it's because the they can't resist
+ 
+
+ align:start position:0%
+young it's because the they can't resist
+that big gape of the kuu
+
+ align:start position:0%
+that big gape of the kuu
+ 
+
+ align:start position:0%
+that big gape of the kuu
+chick it elicits feeding
+
+ align:start position:0%
+chick it elicits feeding
+ 
+
+ align:start position:0%
+chick it elicits feeding
+Behavior so they get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fed but this kind of thing happens in
+
+ align:start position:0%
+fed but this kind of thing happens in
+ 
+
+ align:start position:0%
+fed but this kind of thing happens in
+humans too we discussed earlier how the
+
+ align:start position:0%
+humans too we discussed earlier how the
+ 
+
+ align:start position:0%
+humans too we discussed earlier how the
+food industry uh and restaurants add
+
+ align:start position:0%
+food industry uh and restaurants add
+ 
+
+ align:start position:0%
+food industry uh and restaurants add
+extra fat including saturated fat to
+
+ align:start position:0%
+extra fat including saturated fat to
+ 
+
+ align:start position:0%
+extra fat including saturated fat to
+Foods
+
+ align:start position:0%
+Foods
+ 
+
+ align:start position:0%
+Foods
+especially the fast food industry
+
+ align:start position:0%
+especially the fast food industry
+ 
+
+ align:start position:0%
+especially the fast food industry
+because people prefer the taste they
+
+ align:start position:0%
+because people prefer the taste they
+ 
+
+ align:start position:0%
+because people prefer the taste they
+want it to be fat think of all the
+
+ align:start position:0%
+want it to be fat think of all the
+ 
+
+ align:start position:0%
+want it to be fat think of all the
+people that that are eating the high fat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh potato uh what do they call
+
+ align:start position:0%
+uh potato uh what do they call
+ 
+
+ align:start position:0%
+uh potato uh what do they call
+them french fries the french fries I
+
+ align:start position:0%
+them french fries the french fries I
+ 
+
+ align:start position:0%
+them french fries the french fries I
+never eat them don't even remember their
+
+ align:start position:0%
+never eat them don't even remember their
+ 
+
+ align:start position:0%
+never eat them don't even remember their
+name all right when you're diabetic you
+
+ align:start position:0%
+name all right when you're diabetic you
+ 
+
+ align:start position:0%
+name all right when you're diabetic you
+know you really pay if you eat stuff
+
+ align:start position:0%
+know you really pay if you eat stuff
+ 
+
+ align:start position:0%
+know you really pay if you eat stuff
+Lake that the high fat because fat
+
+ align:start position:0%
+Lake that the high fat because fat
+ 
+
+ align:start position:0%
+Lake that the high fat because fat
+digests very slowly and it raises blood
+
+ align:start position:0%
+digests very slowly and it raises blood
+ 
+
+ align:start position:0%
+digests very slowly and it raises blood
+sugar for many hours afterwards has more
+
+ align:start position:0%
+sugar for many hours afterwards has more
+ 
+
+ align:start position:0%
+sugar for many hours afterwards has more
+than double the number of calories of
+
+ align:start position:0%
+than double the number of calories of
+ 
+
+ align:start position:0%
+than double the number of calories of
+protein and
+
+ align:start position:0%
+protein and
+ 
+
+ align:start position:0%
+protein and
+carbohydrate but what I mention here the
+
+ align:start position:0%
+carbohydrate but what I mention here the
+ 
+
+ align:start position:0%
+carbohydrate but what I mention here the
+doll indust stre uh this these are
+
+ align:start position:0%
+doll indust stre uh this these are
+ 
+
+ align:start position:0%
+doll indust stre uh this these are
+pictures from the iel iisi one of his
+
+ align:start position:0%
+pictures from the iel iisi one of his
+ 
+
+ align:start position:0%
+pictures from the iel iisi one of his
+papers uh and some of these properties
+
+ align:start position:0%
+papers uh and some of these properties
+ 
+
+ align:start position:0%
+papers uh and some of these properties
+of infants were pointed out by Lawrence
+
+ align:start position:0%
+of infants were pointed out by Lawrence
+ 
+
+ align:start position:0%
+of infants were pointed out by Lawrence
+and how you find it in many different
+
+ align:start position:0%
+and how you find it in many different
+ 
+
+ align:start position:0%
+and how you find it in many different
+species that babies have a relatively
+
+ align:start position:0%
+species that babies have a relatively
+ 
+
+ align:start position:0%
+species that babies have a relatively
+larger head relatively larger eyes they
+
+ align:start position:0%
+larger head relatively larger eyes they
+ 
+
+ align:start position:0%
+larger head relatively larger eyes they
+have short limbs
+
+ align:start position:0%
+have short limbs
+ 
+
+ align:start position:0%
+have short limbs
+uh short usually chubby Limbs and that
+
+ align:start position:0%
+uh short usually chubby Limbs and that
+ 
+
+ align:start position:0%
+uh short usually chubby Limbs and that
+that appearance of the baby elicits
+
+ align:start position:0%
+that appearance of the baby elicits
+ 
+
+ align:start position:0%
+that appearance of the baby elicits
+caregiving you know even
+
+ align:start position:0%
+caregiving you know even
+ 
+
+ align:start position:0%
+caregiving you know even
+uh a big aggressive male will respond to
+
+ align:start position:0%
+uh a big aggressive male will respond to
+ 
+
+ align:start position:0%
+uh a big aggressive male will respond to
+babies showing these properties
+
+ align:start position:0%
+babies showing these properties
+ 
+
+ align:start position:0%
+babies showing these properties
+especially if the baby's emitting the
+
+ align:start position:0%
+especially if the baby's emitting the
+ 
+
+ align:start position:0%
+especially if the baby's emitting the
+cute little sounds they make we call
+
+ align:start position:0%
+cute little sounds they make we call
+ 
+
+ align:start position:0%
+cute little sounds they make we call
+them cute because of the stimuli they
+
+ align:start position:0%
+them cute because of the stimuli they
+ 
+
+ align:start position:0%
+them cute because of the stimuli they
+have even
+
+ align:start position:0%
+have even
+ 
+
+ align:start position:0%
+have even
+men are affected by it and the doll
+
+ align:start position:0%
+men are affected by it and the doll
+ 
+
+ align:start position:0%
+men are affected by it and the doll
+industry uses that
+
+ align:start position:0%
+industry uses that
+ 
+
+ align:start position:0%
+industry uses that
+also uh in creating dolls the Cy doll is
+
+ align:start position:0%
+also uh in creating dolls the Cy doll is
+ 
+
+ align:start position:0%
+also uh in creating dolls the Cy doll is
+normally made with again relatively
+
+ align:start position:0%
+normally made with again relatively
+ 
+
+ align:start position:0%
+normally made with again relatively
+larger head and large eyes but if you
+
+ align:start position:0%
+larger head and large eyes but if you
+ 
+
+ align:start position:0%
+larger head and large eyes but if you
+overdo that what
+
+ align:start position:0%
+overdo that what
+ 
+
+ align:start position:0%
+overdo that what
+happens there's a line between what's
+
+ align:start position:0%
+happens there's a line between what's
+ 
+
+ align:start position:0%
+happens there's a line between what's
+cute and what's
+
+ align:start position:0%
+cute and what's
+ 
+
+ align:start position:0%
+cute and what's
+grotesque okay so obviously they they
+
+ align:start position:0%
+grotesque okay so obviously they they
+ 
+
+ align:start position:0%
+grotesque okay so obviously they they
+simply use uh human reactions to uh to
+
+ align:start position:0%
+simply use uh human reactions to uh to
+ 
+
+ align:start position:0%
+simply use uh human reactions to uh to
+shape the way they design those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things okay now we we talk about key
+
+ align:start position:0%
+things okay now we we talk about key
+ 
+
+ align:start position:0%
+things okay now we we talk about key
+stimuli and we say that they can release
+
+ align:start position:0%
+stimuli and we say that they can release
+ 
+
+ align:start position:0%
+stimuli and we say that they can release
+fixed action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns but we don't call all T
+
+ align:start position:0%
+patterns but we don't call all T
+ 
+
+ align:start position:0%
+patterns but we don't call all T
+stimuli that Engage The innate releasing
+
+ align:start position:0%
+stimuli that Engage The innate releasing
+ 
+
+ align:start position:0%
+stimuli that Engage The innate releasing
+mechanisms we don't call them releasers
+
+ align:start position:0%
+mechanisms we don't call them releasers
+ 
+
+ align:start position:0%
+mechanisms we don't call them releasers
+generally because that term is used
+
+ align:start position:0%
+generally because that term is used
+ 
+
+ align:start position:0%
+generally because that term is used
+somewhat
+
+ align:start position:0%
+somewhat
+ 
+
+ align:start position:0%
+somewhat
+differently a
+
+ align:start position:0%
+differently a
+ 
+
+ align:start position:0%
+differently a
+releaser
+
+ align:start position:0%
+releaser
+ 
+
+ align:start position:0%
+releaser
+is a stimulus property that has evolved
+
+ align:start position:0%
+is a stimulus property that has evolved
+ 
+
+ align:start position:0%
+is a stimulus property that has evolved
+for the purpose of communicating for the
+
+ align:start position:0%
+for the purpose of communicating for the
+ 
+
+ align:start position:0%
+for the purpose of communicating for the
+purpose of eliciting behavior from
+
+ align:start position:0%
+purpose of eliciting behavior from
+ 
+
+ align:start position:0%
+purpose of eliciting behavior from
+members of the same species
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is the way it's defined a
+
+ align:start position:0%
+so so this is the way it's defined a
+ 
+
+ align:start position:0%
+so so this is the way it's defined a
+structure or a
+
+ align:start position:0%
+structure or a
+ 
+
+ align:start position:0%
+structure or a
+movement most often a combination that's
+
+ align:start position:0%
+movement most often a combination that's
+ 
+
+ align:start position:0%
+movement most often a combination that's
+evolved in the service of sending a
+
+ align:start position:0%
+evolved in the service of sending a
+ 
+
+ align:start position:0%
+evolved in the service of sending a
+signal so that is they emit key
+
+ align:start position:0%
+signal so that is they emit key
+ 
+
+ align:start position:0%
+signal so that is they emit key
+stimula so in nature whenever you see
+
+ align:start position:0%
+stimula so in nature whenever you see
+ 
+
+ align:start position:0%
+stimula so in nature whenever you see
+really showy color patterns or
+
+ align:start position:0%
+really showy color patterns or
+ 
+
+ align:start position:0%
+really showy color patterns or
+structures in any
+
+ align:start position:0%
+structures in any
+ 
+
+ align:start position:0%
+structures in any
+vertebrate and they don't have to be in
+
+ align:start position:0%
+vertebrate and they don't have to be in
+ 
+
+ align:start position:0%
+vertebrate and they don't have to be in
+vertebrates they can be in invertebrates
+
+ align:start position:0%
+vertebrates they can be in invertebrates
+ 
+
+ align:start position:0%
+vertebrates they can be in invertebrates
+as well and also any loud or regular
+
+ align:start position:0%
+as well and also any loud or regular
+ 
+
+ align:start position:0%
+as well and also any loud or regular
+sound utterance any regular complicated
+
+ align:start position:0%
+sound utterance any regular complicated
+ 
+
+ align:start position:0%
+sound utterance any regular complicated
+and rhythmically perform Movement Like
+
+ align:start position:0%
+and rhythmically perform Movement Like
+ 
+
+ align:start position:0%
+and rhythmically perform Movement Like
+evolves in the rituals of
+
+ align:start position:0%
+evolves in the rituals of
+ 
+
+ align:start position:0%
+evolves in the rituals of
+cording it functions as
+
+ align:start position:0%
+cording it functions as
+ 
+
+ align:start position:0%
+cording it functions as
+releaser
+
+ align:start position:0%
+releaser
+ 
+
+ align:start position:0%
+releaser
+and I'm showing you the cover of
+
+ align:start position:0%
+and I'm showing you the cover of
+ 
+
+ align:start position:0%
+and I'm showing you the cover of
+Smithsonian uh a Smithsonian publication
+
+ align:start position:0%
+Smithsonian uh a Smithsonian publication
+ 
+
+ align:start position:0%
+Smithsonian uh a Smithsonian publication
+there that shows the hamadryas ballooon
+
+ align:start position:0%
+there that shows the hamadryas ballooon
+ 
+
+ align:start position:0%
+there that shows the hamadryas ballooon
+face um but let's start with with humans
+
+ align:start position:0%
+face um but let's start with with humans
+ 
+
+ align:start position:0%
+face um but let's start with with humans
+describe two releasers in human one
+
+ align:start position:0%
+describe two releasers in human one
+ 
+
+ align:start position:0%
+describe two releasers in human one
+involving a motor pattern well that's
+
+ align:start position:0%
+involving a motor pattern well that's
+ 
+
+ align:start position:0%
+involving a motor pattern well that's
+easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smiling smiling is a movement but it's
+
+ align:start position:0%
+smiling smiling is a movement but it's
+ 
+
+ align:start position:0%
+smiling smiling is a movement but it's
+evolved because of the way it the
+
+ align:start position:0%
+evolved because of the way it the
+ 
+
+ align:start position:0%
+evolved because of the way it the
+stimuli it that cause a reaction in
+
+ align:start position:0%
+stimuli it that cause a reaction in
+ 
+
+ align:start position:0%
+stimuli it that cause a reaction in
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+okay almost all of us respond positively
+
+ align:start position:0%
+okay almost all of us respond positively
+ 
+
+ align:start position:0%
+okay almost all of us respond positively
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+smile okay and we smile whether we're
+
+ align:start position:0%
+smile okay and we smile whether we're
+ 
+
+ align:start position:0%
+smile okay and we smile whether we're
+aware of it or not in order to you know
+
+ align:start position:0%
+aware of it or not in order to you know
+ 
+
+ align:start position:0%
+aware of it or not in order to you know
+get those positive
+
+ align:start position:0%
+get those positive
+ 
+
+ align:start position:0%
+get those positive
+responses uh what other can can you
+
+ align:start position:0%
+responses uh what other can can you
+ 
+
+ align:start position:0%
+responses uh what other can can you
+think of anything else think of babies
+
+ align:start position:0%
+think of anything else think of babies
+ 
+
+ align:start position:0%
+think of anything else think of babies
+and their appearance they evolves not
+
+ align:start position:0%
+and their appearance they evolves not
+ 
+
+ align:start position:0%
+and their appearance they evolves not
+just the the larger head and the short
+
+ align:start position:0%
+just the the larger head and the short
+ 
+
+ align:start position:0%
+just the the larger head and the short
+limbs I mean there could be various
+
+ align:start position:0%
+limbs I mean there could be various
+ 
+
+ align:start position:0%
+limbs I mean there could be various
+reasons for that but they've evolved
+
+ align:start position:0%
+reasons for that but they've evolved
+ 
+
+ align:start position:0%
+reasons for that but they've evolved
+these chubby cheeks they actually have
+
+ align:start position:0%
+these chubby cheeks they actually have
+ 
+
+ align:start position:0%
+these chubby cheeks they actually have
+fat pads in their cheeks that disappear
+
+ align:start position:0%
+fat pads in their cheeks that disappear
+ 
+
+ align:start position:0%
+fat pads in their cheeks that disappear
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+on they've even Evol
+
+ align:start position:0%
+on they've even Evol
+ 
+
+ align:start position:0%
+on they've even Evol
+specifically to
+
+ align:start position:0%
+specifically to
+ 
+
+ align:start position:0%
+specifically to
+elicit a certain reaction and there's no
+
+ align:start position:0%
+elicit a certain reaction and there's no
+ 
+
+ align:start position:0%
+elicit a certain reaction and there's no
+doubt that human breasts have a similar
+
+ align:start position:0%
+doubt that human breasts have a similar
+ 
+
+ align:start position:0%
+doubt that human breasts have a similar
+function that is breasts don't have to
+
+ align:start position:0%
+function that is breasts don't have to
+ 
+
+ align:start position:0%
+function that is breasts don't have to
+be as large as they are they evolved in
+
+ align:start position:0%
+be as large as they are they evolved in
+ 
+
+ align:start position:0%
+be as large as they are they evolved in
+order to elicit
+
+ align:start position:0%
+order to elicit
+ 
+
+ align:start position:0%
+order to elicit
+response okay so these are what
+
+ align:start position:0%
+response okay so these are what
+ 
+
+ align:start position:0%
+response okay so these are what
+releasers
+
+ align:start position:0%
+releasers
+ 
+
+ align:start position:0%
+releasers
+are and there's of course many others
+
+ align:start position:0%
+are and there's of course many others
+ 
+
+ align:start position:0%
+are and there's of course many others
+you can think of very as emotionally
+
+ align:start position:0%
+you can think of very as emotionally
+ 
+
+ align:start position:0%
+you can think of very as emotionally
+expressions and things that also have
+
+ align:start position:0%
+expressions and things that also have
+ 
+
+ align:start position:0%
+expressions and things that also have
+evolved to as these signals social
+
+ align:start position:0%
+evolved to as these signals social
+ 
+
+ align:start position:0%
+evolved to as these signals social
+signals of various
+
+ align:start position:0%
+signals of various
+ 
+
+ align:start position:0%
+signals of various
+sorts now when we talk about mimicry
+
+ align:start position:0%
+sorts now when we talk about mimicry
+ 
+
+ align:start position:0%
+sorts now when we talk about mimicry
+we're usually talking about something
+
+ align:start position:0%
+we're usually talking about something
+ 
+
+ align:start position:0%
+we're usually talking about something
+that's evolved to affect the behavior of
+
+ align:start position:0%
+that's evolved to affect the behavior of
+ 
+
+ align:start position:0%
+that's evolved to affect the behavior of
+another species like the monarch
+
+ align:start position:0%
+another species like the monarch
+ 
+
+ align:start position:0%
+another species like the monarch
+butterfly has mimics because the Monarch
+
+ align:start position:0%
+butterfly has mimics because the Monarch
+ 
+
+ align:start position:0%
+butterfly has mimics because the Monarch
+is tastes terrible uh other you know
+
+ align:start position:0%
+is tastes terrible uh other you know
+ 
+
+ align:start position:0%
+is tastes terrible uh other you know
+Birds won't generally attack monarchs
+
+ align:start position:0%
+Birds won't generally attack monarchs
+ 
+
+ align:start position:0%
+Birds won't generally attack monarchs
+because they taste bad
+
+ align:start position:0%
+because they taste bad
+ 
+
+ align:start position:0%
+because they taste bad
+uh so they quickly learn you know it
+
+ align:start position:0%
+uh so they quickly learn you know it
+ 
+
+ align:start position:0%
+uh so they quickly learn you know it
+only takes one experience of a really
+
+ align:start position:0%
+only takes one experience of a really
+ 
+
+ align:start position:0%
+only takes one experience of a really
+horrible taste and animals won't do it
+
+ align:start position:0%
+horrible taste and animals won't do it
+ 
+
+ align:start position:0%
+horrible taste and animals won't do it
+again but so other butterflies and moths
+
+ align:start position:0%
+again but so other butterflies and moths
+ 
+
+ align:start position:0%
+again but so other butterflies and moths
+have evolved to mimic the bitter tasting
+
+ align:start position:0%
+have evolved to mimic the bitter tasting
+ 
+
+ align:start position:0%
+have evolved to mimic the bitter tasting
+ones and the same thing happens in some
+
+ align:start position:0%
+ones and the same thing happens in some
+ 
+
+ align:start position:0%
+ones and the same thing happens in some
+insects but in some cases a species
+
+ align:start position:0%
+insects but in some cases a species
+ 
+
+ align:start position:0%
+insects but in some cases a species
+evolves some way to mimic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aminic that it affects its own species
+
+ align:start position:0%
+aminic that it affects its own species
+ 
+
+ align:start position:0%
+aminic that it affects its own species
+and I these are the two examples I like
+
+ align:start position:0%
+and I these are the two examples I like
+ 
+
+ align:start position:0%
+and I these are the two examples I like
+the mouth breeder fish let's look at
+
+ align:start position:0%
+the mouth breeder fish let's look at
+ 
+
+ align:start position:0%
+the mouth breeder fish let's look at
+that here the mouth breeder fish here's
+
+ align:start position:0%
+that here the mouth breeder fish here's
+ 
+
+ align:start position:0%
+that here the mouth breeder fish here's
+the male and if you look here at the uh
+
+ align:start position:0%
+the male and if you look here at the uh
+ 
+
+ align:start position:0%
+the male and if you look here at the uh
+the anal fin you see the little spots
+
+ align:start position:0%
+the anal fin you see the little spots
+ 
+
+ align:start position:0%
+the anal fin you see the little spots
+what are those orange
+
+ align:start position:0%
+what are those orange
+ 
+
+ align:start position:0%
+what are those orange
+spots well they look just like the eggs
+
+ align:start position:0%
+spots well they look just like the eggs
+ 
+
+ align:start position:0%
+spots well they look just like the eggs
+of the female mouth breeder well what is
+
+ align:start position:0%
+of the female mouth breeder well what is
+ 
+
+ align:start position:0%
+of the female mouth breeder well what is
+the mouth bre her do She lays her eggs
+
+ align:start position:0%
+the mouth bre her do She lays her eggs
+ 
+
+ align:start position:0%
+the mouth bre her do She lays her eggs
+and she takes them up in her mouth she
+
+ align:start position:0%
+and she takes them up in her mouth she
+ 
+
+ align:start position:0%
+and she takes them up in her mouth she
+breeds them in her
+
+ align:start position:0%
+breeds them in her
+ 
+
+ align:start position:0%
+breeds them in her
+mouth so she tries to get these
+
+ align:start position:0%
+mouth so she tries to get these
+ 
+
+ align:start position:0%
+mouth so she tries to get these
+too perfect for the
+
+ align:start position:0%
+too perfect for the
+ 
+
+ align:start position:0%
+too perfect for the
+male he comes after she comes after the
+
+ align:start position:0%
+male he comes after she comes after the
+ 
+
+ align:start position:0%
+male he comes after she comes after the
+male her her mouth is there trying to
+
+ align:start position:0%
+male her her mouth is there trying to
+ 
+
+ align:start position:0%
+male her her mouth is there trying to
+get at those eggs and what does he do he
+
+ align:start position:0%
+get at those eggs and what does he do he
+ 
+
+ align:start position:0%
+get at those eggs and what does he do he
+injects seen right into her
+
+ align:start position:0%
+injects seen right into her
+ 
+
+ align:start position:0%
+injects seen right into her
+mouth so he fertilizes her
+
+ align:start position:0%
+mouth so he fertilizes her
+ 
+
+ align:start position:0%
+mouth so he fertilizes her
+eggs so that's why the mouth breeder
+
+ align:start position:0%
+eggs so that's why the mouth breeder
+ 
+
+ align:start position:0%
+eggs so that's why the mouth breeder
+fish has evolved that way mouth breed or
+
+ align:start position:0%
+fish has evolved that way mouth breed or
+ 
+
+ align:start position:0%
+fish has evolved that way mouth breed or
+male now let's take
+
+ align:start position:0%
+male now let's take
+ 
+
+ align:start position:0%
+male now let's take
+baboons here's a here's a female Olive
+
+ align:start position:0%
+baboons here's a here's a female Olive
+ 
+
+ align:start position:0%
+baboons here's a here's a female Olive
+baboon and notice this pink patch on a
+
+ align:start position:0%
+baboon and notice this pink patch on a
+ 
+
+ align:start position:0%
+baboon and notice this pink patch on a
+rump used as a signal it's evolved to
+
+ align:start position:0%
+rump used as a signal it's evolved to
+ 
+
+ align:start position:0%
+rump used as a signal it's evolved to
+affect the male but then look males
+
+ align:start position:0%
+affect the male but then look males
+ 
+
+ align:start position:0%
+affect the male but then look males
+evolve a patch too and some of them like
+
+ align:start position:0%
+evolve a patch too and some of them like
+ 
+
+ align:start position:0%
+evolve a patch too and some of them like
+this I couldn't find a really pink one
+
+ align:start position:0%
+this I couldn't find a really pink one
+ 
+
+ align:start position:0%
+this I couldn't find a really pink one
+but this one's pink only at the edge but
+
+ align:start position:0%
+but this one's pink only at the edge but
+ 
+
+ align:start position:0%
+but this one's pink only at the edge but
+the hamadryas baboon it's even more
+
+ align:start position:0%
+the hamadryas baboon it's even more
+ 
+
+ align:start position:0%
+the hamadryas baboon it's even more
+obvious you know here's male hamadryas
+
+ align:start position:0%
+obvious you know here's male hamadryas
+ 
+
+ align:start position:0%
+obvious you know here's male hamadryas
+baboon and look at the pink rump on that
+
+ align:start position:0%
+baboon and look at the pink rump on that
+ 
+
+ align:start position:0%
+baboon and look at the pink rump on that
+animal and here are two females actually
+
+ align:start position:0%
+animal and here are two females actually
+ 
+
+ align:start position:0%
+animal and here are two females actually
+presenting to a male and you can see you
+
+ align:start position:0%
+presenting to a male and you can see you
+ 
+
+ align:start position:0%
+presenting to a male and you can see you
+know that's what's being imitated well
+
+ align:start position:0%
+know that's what's being imitated well
+ 
+
+ align:start position:0%
+know that's what's being imitated well
+why would they do that why would a male
+
+ align:start position:0%
+why would they do that why would a male
+ 
+
+ align:start position:0%
+why would they do that why would a male
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+that because if a female appears and
+
+ align:start position:0%
+that because if a female appears and
+ 
+
+ align:start position:0%
+that because if a female appears and
+presents to him it totally inhibits his
+
+ align:start position:0%
+presents to him it totally inhibits his
+ 
+
+ align:start position:0%
+presents to him it totally inhibits his
+aggressive
+
+ align:start position:0%
+aggressive
+ 
+
+ align:start position:0%
+aggressive
+response these are pretty aggressive
+
+ align:start position:0%
+response these are pretty aggressive
+ 
+
+ align:start position:0%
+response these are pretty aggressive
+animals okay and they need ways to turn
+
+ align:start position:0%
+animals okay and they need ways to turn
+ 
+
+ align:start position:0%
+animals okay and they need ways to turn
+off the aggression
+
+ align:start position:0%
+off the aggression
+ 
+
+ align:start position:0%
+off the aggression
+so the males have taken advantage of
+
+ align:start position:0%
+so the males have taken advantage of
+ 
+
+ align:start position:0%
+so the males have taken advantage of
+that they evolve a signal where they can
+
+ align:start position:0%
+that they evolve a signal where they can
+ 
+
+ align:start position:0%
+that they evolve a signal where they can
+turn off the aggression of a more
+
+ align:start position:0%
+turn off the aggression of a more
+ 
+
+ align:start position:0%
+turn off the aggression of a more
+dominant male and it protects
+
+ align:start position:0%
+dominant male and it protects
+ 
+
+ align:start position:0%
+dominant male and it protects
+them and many rodents many of these
+
+ align:start position:0%
+them and many rodents many of these
+ 
+
+ align:start position:0%
+them and many rodents many of these
+things are a little more subtle you know
+
+ align:start position:0%
+things are a little more subtle you know
+ 
+
+ align:start position:0%
+things are a little more subtle you know
+the uh a
+
+ align:start position:0%
+the uh a
+ 
+
+ align:start position:0%
+the uh a
+hamster a normal Syrian hamster is
+
+ align:start position:0%
+hamster a normal Syrian hamster is
+ 
+
+ align:start position:0%
+hamster a normal Syrian hamster is
+evolved
+
+ align:start position:0%
+evolved
+ 
+
+ align:start position:0%
+evolved
+uh these white patches on his vest okay
+
+ align:start position:0%
+uh these white patches on his vest okay
+ 
+
+ align:start position:0%
+uh these white patches on his vest okay
+if those are exposed it reduces the
+
+ align:start position:0%
+if those are exposed it reduces the
+ 
+
+ align:start position:0%
+if those are exposed it reduces the
+aggression of a male okay if he wants to
+
+ align:start position:0%
+aggression of a male okay if he wants to
+ 
+
+ align:start position:0%
+aggression of a male okay if he wants to
+attack he actually covers them with his
+
+ align:start position:0%
+attack he actually covers them with his
+ 
+
+ align:start position:0%
+attack he actually covers them with his
+feet okay because of the signal property
+
+ align:start position:0%
+feet okay because of the signal property
+ 
+
+ align:start position:0%
+feet okay because of the signal property
+that they have and similarly their white
+
+ align:start position:0%
+that they have and similarly their white
+ 
+
+ align:start position:0%
+that they have and similarly their white
+underbelly if they expose that because
+
+ align:start position:0%
+underbelly if they expose that because
+ 
+
+ align:start position:0%
+underbelly if they expose that because
+they're defeated in a fight it generally
+
+ align:start position:0%
+they're defeated in a fight it generally
+ 
+
+ align:start position:0%
+they're defeated in a fight it generally
+works pretty well to inhibit the attack
+
+ align:start position:0%
+works pretty well to inhibit the attack
+ 
+
+ align:start position:0%
+works pretty well to inhibit the attack
+so they won't get killed the only time
+
+ align:start position:0%
+so they won't get killed the only time
+ 
+
+ align:start position:0%
+so they won't get killed the only time
+I've had hamster males kill or or
+
+ align:start position:0%
+I've had hamster males kill or or
+ 
+
+ align:start position:0%
+I've had hamster males kill or or
+females they both are pretty aggressive
+
+ align:start position:0%
+females they both are pretty aggressive
+ 
+
+ align:start position:0%
+females they both are pretty aggressive
+kill another animal is is when it's an
+
+ align:start position:0%
+kill another animal is is when it's an
+ 
+
+ align:start position:0%
+kill another animal is is when it's an
+artificial situation in a cage where the
+
+ align:start position:0%
+artificial situation in a cage where the
+ 
+
+ align:start position:0%
+artificial situation in a cage where the
+animal gets caught and he can't expose
+
+ align:start position:0%
+animal gets caught and he can't expose
+ 
+
+ align:start position:0%
+animal gets caught and he can't expose
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+stimuli like he's caught in the wire
+
+ align:start position:0%
+stimuli like he's caught in the wire
+ 
+
+ align:start position:0%
+stimuli like he's caught in the wire
+mesh or where they he's not they're in
+
+ align:start position:0%
+mesh or where they he's not they're in
+ 
+
+ align:start position:0%
+mesh or where they he's not they're in
+such Close Quarters he can't you know
+
+ align:start position:0%
+such Close Quarters he can't you know
+ 
+
+ align:start position:0%
+such Close Quarters he can't you know
+actually expose those signals all right
+
+ align:start position:0%
+actually expose those signals all right
+ 
+
+ align:start position:0%
+actually expose those signals all right
+just a couple of things we'll get on to
+
+ align:start position:0%
+just a couple of things we'll get on to
+ 
+
+ align:start position:0%
+just a couple of things we'll get on to
+the next class here the I want you to
+
+ align:start position:0%
+the next class here the I want you to
+ 
+
+ align:start position:0%
+the next class here the I want you to
+know what the dummy rule is it the rule
+
+ align:start position:0%
+know what the dummy rule is it the rule
+ 
+
+ align:start position:0%
+know what the dummy rule is it the rule
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um that if you can make a simple
+
+ align:start position:0%
+um that if you can make a simple
+ 
+
+ align:start position:0%
+um that if you can make a simple
+model like those models of the
+
+ align:start position:0%
+model like those models of the
+ 
+
+ align:start position:0%
+model like those models of the
+stickleback female that elicits a fixed
+
+ align:start position:0%
+stickleback female that elicits a fixed
+ 
+
+ align:start position:0%
+stickleback female that elicits a fixed
+action pattern like the following
+
+ align:start position:0%
+action pattern like the following
+ 
+
+ align:start position:0%
+action pattern like the following
+response the male then we're dealing
+
+ align:start position:0%
+response the male then we're dealing
+ 
+
+ align:start position:0%
+response the male then we're dealing
+with a innate releasing mechanism
+
+ align:start position:0%
+with a innate releasing mechanism
+ 
+
+ align:start position:0%
+with a innate releasing mechanism
+something that
+
+ align:start position:0%
+something that
+ 
+
+ align:start position:0%
+something that
+has on the sensory side that's evolved
+
+ align:start position:0%
+has on the sensory side that's evolved
+ 
+
+ align:start position:0%
+has on the sensory side that's evolved
+to respond to those stimula but if you
+
+ align:start position:0%
+to respond to those stimula but if you
+ 
+
+ align:start position:0%
+to respond to those stimula but if you
+can't find a dummy stimulus that works
+
+ align:start position:0%
+can't find a dummy stimulus that works
+ 
+
+ align:start position:0%
+can't find a dummy stimulus that works
+it doesn't mean there's no releasing
+
+ align:start position:0%
+it doesn't mean there's no releasing
+ 
+
+ align:start position:0%
+it doesn't mean there's no releasing
+mechanism and the reason is this
+
+ align:start position:0%
+mechanism and the reason is this
+ 
+
+ align:start position:0%
+mechanism and the reason is this
+learning the usual role of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learning in animals it does affect
+
+ align:start position:0%
+learning in animals it does affect
+ 
+
+ align:start position:0%
+learning in animals it does affect
+instinctive Behavior and the way it it
+
+ align:start position:0%
+instinctive Behavior and the way it it
+ 
+
+ align:start position:0%
+instinctive Behavior and the way it it
+usually doesn't affect the motor side
+
+ align:start position:0%
+usually doesn't affect the motor side
+ 
+
+ align:start position:0%
+usually doesn't affect the motor side
+very much different motor patterns can
+
+ align:start position:0%
+very much different motor patterns can
+ 
+
+ align:start position:0%
+very much different motor patterns can
+be linked in specific ways as we've
+
+ align:start position:0%
+be linked in specific ways as we've
+ 
+
+ align:start position:0%
+be linked in specific ways as we've
+talked about with the attack Behavior
+
+ align:start position:0%
+talked about with the attack Behavior
+ 
+
+ align:start position:0%
+talked about with the attack Behavior
+predatory attack and cats they do have
+
+ align:start position:0%
+predatory attack and cats they do have
+ 
+
+ align:start position:0%
+predatory attack and cats they do have
+to put the various individual fixed
+
+ align:start position:0%
+to put the various individual fixed
+ 
+
+ align:start position:0%
+to put the various individual fixed
+motor patterns together okay they learn
+
+ align:start position:0%
+motor patterns together okay they learn
+ 
+
+ align:start position:0%
+motor patterns together okay they learn
+that but the selectivity of the stimuli
+
+ align:start position:0%
+that but the selectivity of the stimuli
+ 
+
+ align:start position:0%
+that but the selectivity of the stimuli
+that elicit a fixed action pattern can
+
+ align:start position:0%
+that elicit a fixed action pattern can
+ 
+
+ align:start position:0%
+that elicit a fixed action pattern can
+be increased with
+
+ align:start position:0%
+be increased with
+ 
+
+ align:start position:0%
+be increased with
+learning okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in imprinting you see that happening
+
+ align:start position:0%
+so in imprinting you see that happening
+ 
+
+ align:start position:0%
+so in imprinting you see that happening
+it it can change with the experience of
+
+ align:start position:0%
+it it can change with the experience of
+ 
+
+ align:start position:0%
+it it can change with the experience of
+the animal uh but even an animal that
+
+ align:start position:0%
+the animal uh but even an animal that
+ 
+
+ align:start position:0%
+the animal uh but even an animal that
+doesn't have to imprint he responds
+
+ align:start position:0%
+doesn't have to imprint he responds
+ 
+
+ align:start position:0%
+doesn't have to imprint he responds
+innately to something like the a novel
+
+ align:start position:0%
+innately to something like the a novel
+ 
+
+ align:start position:0%
+innately to something like the a novel
+box moved overhead above turkeys can
+
+ align:start position:0%
+box moved overhead above turkeys can
+ 
+
+ align:start position:0%
+box moved overhead above turkeys can
+elicit the anti-predator response of
+
+ align:start position:0%
+elicit the anti-predator response of
+ 
+
+ align:start position:0%
+elicit the anti-predator response of
+crouching and freezing but that can
+
+ align:start position:0%
+crouching and freezing but that can
+ 
+
+ align:start position:0%
+crouching and freezing but that can
+become more specific with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experience okay now this will take us
+
+ align:start position:0%
+experience okay now this will take us
+ 
+
+ align:start position:0%
+experience okay now this will take us
+the rest of this hour and
+
+ align:start position:0%
+the rest of this hour and
+ 
+
+ align:start position:0%
+the rest of this hour and
+Monday
+
+ align:start position:0%
+Monday
+ 
+
+ align:start position:0%
+Monday
+uh I want to go through the theoretical
+
+ align:start position:0%
+uh I want to go through the theoretical
+ 
+
+ align:start position:0%
+uh I want to go through the theoretical
+models of fixed action pattern
+
+ align:start position:0%
+models of fixed action pattern
+ 
+
+ align:start position:0%
+models of fixed action pattern
+and the innate releasing
+
+ align:start position:0%
+and the innate releasing
+ 
+
+ align:start position:0%
+and the innate releasing
+mechanism of Lawrence and tenbergen
+
+ align:start position:0%
+mechanism of Lawrence and tenbergen
+ 
+
+ align:start position:0%
+mechanism of Lawrence and tenbergen
+which have been the major
+
+ align:start position:0%
+which have been the major
+ 
+
+ align:start position:0%
+which have been the major
+ones and you can easily see how their
+
+ align:start position:0%
+ones and you can easily see how their
+ 
+
+ align:start position:0%
+ones and you can easily see how their
+models can be uh put into computer
+
+ align:start position:0%
+models can be uh put into computer
+ 
+
+ align:start position:0%
+models can be uh put into computer
+models using uh information flow uh and
+
+ align:start position:0%
+models using uh information flow uh and
+ 
+
+ align:start position:0%
+models using uh information flow uh and
+that has been done uh fairly
+
+ align:start position:0%
+that has been done uh fairly
+ 
+
+ align:start position:0%
+that has been done uh fairly
+successfully the second thing is the
+
+ align:start position:0%
+successfully the second thing is the
+ 
+
+ align:start position:0%
+successfully the second thing is the
+hierarchy and chains of
+
+ align:start position:0%
+hierarchy and chains of
+ 
+
+ align:start position:0%
+hierarchy and chains of
+behavior the hierarchical organization
+
+ align:start position:0%
+behavior the hierarchical organization
+ 
+
+ align:start position:0%
+behavior the hierarchical organization
+of instinctive
+
+ align:start position:0%
+of instinctive
+ 
+
+ align:start position:0%
+of instinctive
+behavior and then
+
+ align:start position:0%
+behavior and then
+ 
+
+ align:start position:0%
+behavior and then
+uh special
+
+ align:start position:0%
+uh special
+ 
+
+ align:start position:0%
+uh special
+orientation by reflexes and an internal
+
+ align:start position:0%
+orientation by reflexes and an internal
+ 
+
+ align:start position:0%
+orientation by reflexes and an internal
+model we'll talk about that and then
+
+ align:start position:0%
+model we'll talk about that and then
+ 
+
+ align:start position:0%
+model we'll talk about that and then
+finally what happens when there are
+
+ align:start position:0%
+finally what happens when there are
+ 
+
+ align:start position:0%
+finally what happens when there are
+multiple motivations aroused
+
+ align:start position:0%
+multiple motivations aroused
+ 
+
+ align:start position:0%
+multiple motivations aroused
+simultaneously and that happens very
+
+ align:start position:0%
+simultaneously and that happens very
+ 
+
+ align:start position:0%
+simultaneously and that happens very
+commonly and
+
+ align:start position:0%
+commonly and
+ 
+
+ align:start position:0%
+commonly and
+sometimes two two motivations can be
+
+ align:start position:0%
+sometimes two two motivations can be
+ 
+
+ align:start position:0%
+sometimes two two motivations can be
+almost equally strong how does an animal
+
+ align:start position:0%
+almost equally strong how does an animal
+ 
+
+ align:start position:0%
+almost equally strong how does an animal
+handle that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so Lawrence's model we call a it's
+
+ align:start position:0%
+so Lawrence's model we call a it's
+ 
+
+ align:start position:0%
+so Lawrence's model we call a it's
+sometimes been called a psycho hydraulic
+
+ align:start position:0%
+sometimes been called a psycho hydraulic
+ 
+
+ align:start position:0%
+sometimes been called a psycho hydraulic
+model it's really a sort of hydraulic
+
+ align:start position:0%
+model it's really a sort of hydraulic
+ 
+
+ align:start position:0%
+model it's really a sort of hydraulic
+mechanical model of U of the
+
+ align:start position:0%
+mechanical model of U of the
+ 
+
+ align:start position:0%
+mechanical model of U of the
+motivational State the action specific
+
+ align:start position:0%
+motivational State the action specific
+ 
+
+ align:start position:0%
+motivational State the action specific
+potential in his terms and he had two
+
+ align:start position:0%
+potential in his terms and he had two
+ 
+
+ align:start position:0%
+potential in his terms and he had two
+models he changed it after a while on
+
+ align:start position:0%
+models he changed it after a while on
+ 
+
+ align:start position:0%
+models he changed it after a while on
+the left there you see his old model uh
+
+ align:start position:0%
+the left there you see his old model uh
+ 
+
+ align:start position:0%
+the left there you see his old model uh
+the action specific potential was
+
+ align:start position:0%
+the action specific potential was
+ 
+
+ align:start position:0%
+the action specific potential was
+represent entered as a reservoir that
+
+ align:start position:0%
+represent entered as a reservoir that
+ 
+
+ align:start position:0%
+represent entered as a reservoir that
+they the
+
+ align:start position:0%
+they the
+ 
+
+ align:start position:0%
+they the
+endogenous uh stimulus that is an
+
+ align:start position:0%
+endogenous uh stimulus that is an
+ 
+
+ align:start position:0%
+endogenous uh stimulus that is an
+internal stimulus is always there and so
+
+ align:start position:0%
+internal stimulus is always there and so
+ 
+
+ align:start position:0%
+internal stimulus is always there and so
+it's gradually building up that level
+
+ align:start position:0%
+it's gradually building up that level
+ 
+
+ align:start position:0%
+it's gradually building up that level
+until uh it's released and he he has the
+
+ align:start position:0%
+until uh it's released and he he has the
+ 
+
+ align:start position:0%
+until uh it's released and he he has the
+release there by the
+
+ align:start position:0%
+release there by the
+ 
+
+ align:start position:0%
+release there by the
+uh he throws this mechanical thing where
+
+ align:start position:0%
+uh he throws this mechanical thing where
+ 
+
+ align:start position:0%
+uh he throws this mechanical thing where
+the the spring there represents some
+
+ align:start position:0%
+the the spring there represents some
+ 
+
+ align:start position:0%
+the the spring there represents some
+kind of inertia of the system but the
+
+ align:start position:0%
+kind of inertia of the system but the
+ 
+
+ align:start position:0%
+kind of inertia of the system but the
+releasing stimulus
+
+ align:start position:0%
+releasing stimulus
+ 
+
+ align:start position:0%
+releasing stimulus
+there caused the discharge of that
+
+ align:start position:0%
+there caused the discharge of that
+ 
+
+ align:start position:0%
+there caused the discharge of that
+fluid but then his observations on
+
+ align:start position:0%
+fluid but then his observations on
+ 
+
+ align:start position:0%
+fluid but then his observations on
+animals made him realize that it's not
+
+ align:start position:0%
+animals made him realize that it's not
+ 
+
+ align:start position:0%
+animals made him realize that it's not
+accurate enough so he revised
+
+ align:start position:0%
+accurate enough so he revised
+ 
+
+ align:start position:0%
+accurate enough so he revised
+it and he he realized that there's not
+
+ align:start position:0%
+it and he he realized that there's not
+ 
+
+ align:start position:0%
+it and he he realized that there's not
+only this
+
+ align:start position:0%
+only this
+ 
+
+ align:start position:0%
+only this
+endogenous
+
+ align:start position:0%
+endogenous
+ 
+
+ align:start position:0%
+endogenous
+input that's gradually building
+
+ align:start position:0%
+input that's gradually building
+ 
+
+ align:start position:0%
+input that's gradually building
+up like our tendency to blink our eyes
+
+ align:start position:0%
+up like our tendency to blink our eyes
+ 
+
+ align:start position:0%
+up like our tendency to blink our eyes
+gradually builds up until we blink and
+
+ align:start position:0%
+gradually builds up until we blink and
+ 
+
+ align:start position:0%
+gradually builds up until we blink and
+we do it spontaneously and we don't even
+
+ align:start position:0%
+we do it spontaneously and we don't even
+ 
+
+ align:start position:0%
+we do it spontaneously and we don't even
+think about it unless right now I'm
+
+ align:start position:0%
+think about it unless right now I'm
+ 
+
+ align:start position:0%
+think about it unless right now I'm
+conscious of it and I realized i' now
+
+ align:start position:0%
+conscious of it and I realized i' now
+ 
+
+ align:start position:0%
+conscious of it and I realized i' now
+blink twice since I started talking okay
+
+ align:start position:0%
+blink twice since I started talking okay
+ 
+
+ align:start position:0%
+blink twice since I started talking okay
+but he's got other stimuli there too and
+
+ align:start position:0%
+but he's got other stimuli there too and
+ 
+
+ align:start position:0%
+but he's got other stimuli there too and
+these are he calls Readiness increasing
+
+ align:start position:0%
+these are he calls Readiness increasing
+ 
+
+ align:start position:0%
+these are he calls Readiness increasing
+stimuli they are stimuli that don't act
+
+ align:start position:0%
+stimuli they are stimuli that don't act
+ 
+
+ align:start position:0%
+stimuli they are stimuli that don't act
+quite like the releasing they're not
+
+ align:start position:0%
+quite like the releasing they're not
+ 
+
+ align:start position:0%
+quite like the releasing they're not
+adequate to actually release the
+
+ align:start position:0%
+adequate to actually release the
+ 
+
+ align:start position:0%
+adequate to actually release the
+movement but they do increase the
+
+ align:start position:0%
+movement but they do increase the
+ 
+
+ align:start position:0%
+movement but they do increase the
+motivation
+
+ align:start position:0%
+motivation
+ 
+
+ align:start position:0%
+motivation
+okay and you can think how many of those
+
+ align:start position:0%
+okay and you can think how many of those
+ 
+
+ align:start position:0%
+okay and you can think how many of those
+could be
+
+ align:start position:0%
+could be
+ 
+
+ align:start position:0%
+could be
+learned but then the releasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stimulus the key stimuli that caused
+
+ align:start position:0%
+stimulus the key stimuli that caused
+ 
+
+ align:start position:0%
+stimulus the key stimuli that caused
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+discharge of the fixed motor pattern is
+
+ align:start position:0%
+discharge of the fixed motor pattern is
+ 
+
+ align:start position:0%
+discharge of the fixed motor pattern is
+like just pouring more fluid rapidly
+
+ align:start position:0%
+like just pouring more fluid rapidly
+ 
+
+ align:start position:0%
+like just pouring more fluid rapidly
+into the cup so it he sees the releasing
+
+ align:start position:0%
+into the cup so it he sees the releasing
+ 
+
+ align:start position:0%
+into the cup so it he sees the releasing
+stimula is just something that raises
+
+ align:start position:0%
+stimula is just something that raises
+ 
+
+ align:start position:0%
+stimula is just something that raises
+the motivation to a high level and it
+
+ align:start position:0%
+the motivation to a high level and it
+ 
+
+ align:start position:0%
+the motivation to a high level and it
+does so rapidly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I've defined the various things
+
+ align:start position:0%
+and I've defined the various things
+ 
+
+ align:start position:0%
+and I've defined the various things
+there uh below
+
+ align:start position:0%
+there uh below
+ 
+
+ align:start position:0%
+there uh below
+now the major difference of course is
+
+ align:start position:0%
+now the major difference of course is
+ 
+
+ align:start position:0%
+now the major difference of course is
+the the way the releasing stimuli are
+
+ align:start position:0%
+the the way the releasing stimuli are
+ 
+
+ align:start position:0%
+the the way the releasing stimuli are
+acting as I pointed
+
+ align:start position:0%
+acting as I pointed
+ 
+
+ align:start position:0%
+acting as I pointed
+out and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh where these things are in the CNS
+
+ align:start position:0%
+uh where these things are in the CNS
+ 
+
+ align:start position:0%
+uh where these things are in the CNS
+this is very far from any kind of CNS
+
+ align:start position:0%
+this is very far from any kind of CNS
+ 
+
+ align:start position:0%
+this is very far from any kind of CNS
+model it's an analogist model okay
+
+ align:start position:0%
+model it's an analogist model okay
+ 
+
+ align:start position:0%
+model it's an analogist model okay
+uh it's
+
+ align:start position:0%
+uh it's
+ 
+
+ align:start position:0%
+uh it's
+a hydraulic mechanical model
+
+ align:start position:0%
+a hydraulic mechanical model
+ 
+
+ align:start position:0%
+a hydraulic mechanical model
+that unfortunately looks more like a
+
+ align:start position:0%
+that unfortunately looks more like a
+ 
+
+ align:start position:0%
+that unfortunately looks more like a
+flush toilet than other things you can
+
+ align:start position:0%
+flush toilet than other things you can
+ 
+
+ align:start position:0%
+flush toilet than other things you can
+think of and so sometimes Lawrence was
+
+ align:start position:0%
+think of and so sometimes Lawrence was
+ 
+
+ align:start position:0%
+think of and so sometimes Lawrence was
+made fun of for
+
+ align:start position:0%
+made fun of for
+ 
+
+ align:start position:0%
+made fun of for
+this uh but in fact the model was
+
+ align:start position:0%
+this uh but in fact the model was
+ 
+
+ align:start position:0%
+this uh but in fact the model was
+youthful in that it it pointed out
+
+ align:start position:0%
+youthful in that it it pointed out
+ 
+
+ align:start position:0%
+youthful in that it it pointed out
+properties he's basically summarizing
+
+ align:start position:0%
+properties he's basically summarizing
+ 
+
+ align:start position:0%
+properties he's basically summarizing
+properties that he observed for many
+
+ align:start position:0%
+properties that he observed for many
+ 
+
+ align:start position:0%
+properties that he observed for many
+different fixed action
+
+ align:start position:0%
+different fixed action
+ 
+
+ align:start position:0%
+different fixed action
+patterns and the one on the the right
+
+ align:start position:0%
+patterns and the one on the the right
+ 
+
+ align:start position:0%
+patterns and the one on the the right
+does a better job than the one on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left now if we talk about where these
+
+ align:start position:0%
+left now if we talk about where these
+ 
+
+ align:start position:0%
+left now if we talk about where these
+things are in the brain it's interesting
+
+ align:start position:0%
+things are in the brain it's interesting
+ 
+
+ align:start position:0%
+things are in the brain it's interesting
+because if
+
+ align:start position:0%
+because if
+ 
+
+ align:start position:0%
+because if
+we go here now let's say you were
+
+ align:start position:0%
+we go here now let's say you were
+ 
+
+ align:start position:0%
+we go here now let's say you were
+stimulating the spinal cord or the hind
+
+ align:start position:0%
+stimulating the spinal cord or the hind
+ 
+
+ align:start position:0%
+stimulating the spinal cord or the hind
+brain you can get various components of
+
+ align:start position:0%
+brain you can get various components of
+ 
+
+ align:start position:0%
+brain you can get various components of
+fixed motor patterns okay uh but
+
+ align:start position:0%
+fixed motor patterns okay uh but
+ 
+
+ align:start position:0%
+fixed motor patterns okay uh but
+generally only when the stimulus is on
+
+ align:start position:0%
+generally only when the stimulus is on
+ 
+
+ align:start position:0%
+generally only when the stimulus is on
+you get them so it's not acting at all
+
+ align:start position:0%
+you get them so it's not acting at all
+ 
+
+ align:start position:0%
+you get them so it's not acting at all
+like the action specific potential in
+
+ align:start position:0%
+like the action specific potential in
+ 
+
+ align:start position:0%
+like the action specific potential in
+the reservoir
+
+ align:start position:0%
+the reservoir
+ 
+
+ align:start position:0%
+the reservoir
+here where you get the whole
+
+ align:start position:0%
+here where you get the whole
+ 
+
+ align:start position:0%
+here where you get the whole
+sequence okay
+
+ align:start position:0%
+sequence okay
+ 
+
+ align:start position:0%
+sequence okay
+and and when you suddenly take the
+
+ align:start position:0%
+and and when you suddenly take the
+ 
+
+ align:start position:0%
+and and when you suddenly take the
+stimulus away the action doesn't just
+
+ align:start position:0%
+stimulus away the action doesn't just
+ 
+
+ align:start position:0%
+stimulus away the action doesn't just
+suddenly stop just like in the model
+
+ align:start position:0%
+suddenly stop just like in the model
+ 
+
+ align:start position:0%
+suddenly stop just like in the model
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so I just summarize that here for low
+
+ align:start position:0%
+uh so I just summarize that here for low
+ 
+
+ align:start position:0%
+uh so I just summarize that here for low
+levels the the behavioral changes occur
+
+ align:start position:0%
+levels the the behavioral changes occur
+ 
+
+ align:start position:0%
+levels the the behavioral changes occur
+only during the periods of stimulation
+
+ align:start position:0%
+only during the periods of stimulation
+ 
+
+ align:start position:0%
+only during the periods of stimulation
+then they
+
+ align:start position:0%
+then they
+ 
+
+ align:start position:0%
+then they
+stop and in fact if you have an animal
+
+ align:start position:0%
+stop and in fact if you have an animal
+ 
+
+ align:start position:0%
+stop and in fact if you have an animal
+that's had a transection of the higher
+
+ align:start position:0%
+that's had a transection of the higher
+ 
+
+ align:start position:0%
+that's had a transection of the higher
+areas of the brain they've been totally
+
+ align:start position:0%
+areas of the brain they've been totally
+ 
+
+ align:start position:0%
+areas of the brain they've been totally
+separated they're no longer influ the
+
+ align:start position:0%
+separated they're no longer influ the
+ 
+
+ align:start position:0%
+separated they're no longer influ the
+hypothalamic region the whole forbrain
+
+ align:start position:0%
+hypothalamic region the whole forbrain
+ 
+
+ align:start position:0%
+hypothalamic region the whole forbrain
+is cut off from those lower regions you
+
+ align:start position:0%
+is cut off from those lower regions you
+ 
+
+ align:start position:0%
+is cut off from those lower regions you
+can still stimulate fixed action
+
+ align:start position:0%
+can still stimulate fixed action
+ 
+
+ align:start position:0%
+can still stimulate fixed action
+patterns but only the motor component
+
+ align:start position:0%
+patterns but only the motor component
+ 
+
+ align:start position:0%
+patterns but only the motor component
+and they just stop immediately just like
+
+ align:start position:0%
+and they just stop immediately just like
+ 
+
+ align:start position:0%
+and they just stop immediately just like
+the effects of electrical stimulation of
+
+ align:start position:0%
+the effects of electrical stimulation of
+ 
+
+ align:start position:0%
+the effects of electrical stimulation of
+those lower levels
+
+ align:start position:0%
+those lower levels
+ 
+
+ align:start position:0%
+those lower levels
+but when you stimulate in the coddle
+
+ align:start position:0%
+but when you stimulate in the coddle
+ 
+
+ align:start position:0%
+but when you stimulate in the coddle
+forbrain there the hypothalamic area
+
+ align:start position:0%
+forbrain there the hypothalamic area
+ 
+
+ align:start position:0%
+forbrain there the hypothalamic area
+then you do illicit
+
+ align:start position:0%
+then you do illicit
+ 
+
+ align:start position:0%
+then you do illicit
+moods that are very very hard to
+
+ align:start position:0%
+moods that are very very hard to
+ 
+
+ align:start position:0%
+moods that are very very hard to
+distinguish
+
+ align:start position:0%
+distinguish
+ 
+
+ align:start position:0%
+distinguish
+from the mood that would occur in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normally and that's been done for both
+
+ align:start position:0%
+normally and that's been done for both
+ 
+
+ align:start position:0%
+normally and that's been done for both
+the quiet biting attack the predatory
+
+ align:start position:0%
+the quiet biting attack the predatory
+ 
+
+ align:start position:0%
+the quiet biting attack the predatory
+attack of a cat and or the the more
+
+ align:start position:0%
+attack of a cat and or the the more
+ 
+
+ align:start position:0%
+attack of a cat and or the the more
+aggressive defensive attack and you are
+
+ align:start position:0%
+aggressive defensive attack and you are
+ 
+
+ align:start position:0%
+aggressive defensive attack and you are
+all familiar with that the cat that
+
+ align:start position:0%
+all familiar with that the cat that
+ 
+
+ align:start position:0%
+all familiar with that the cat that
+arches its back you know and extends its
+
+ align:start position:0%
+arches its back you know and extends its
+ 
+
+ align:start position:0%
+arches its back you know and extends its
+claws and makes a lot of
+
+ align:start position:0%
+claws and makes a lot of
+ 
+
+ align:start position:0%
+claws and makes a lot of
+noise okay where we call the other one a
+
+ align:start position:0%
+noise okay where we call the other one a
+ 
+
+ align:start position:0%
+noise okay where we call the other one a
+quiet biting attack because he does not
+
+ align:start position:0%
+quiet biting attack because he does not
+ 
+
+ align:start position:0%
+quiet biting attack because he does not
+make noise it's designed specifically to
+
+ align:start position:0%
+make noise it's designed specifically to
+ 
+
+ align:start position:0%
+make noise it's designed specifically to
+kill
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prey so I'm just pointing out uh I want
+
+ align:start position:0%
+prey so I'm just pointing out uh I want
+ 
+
+ align:start position:0%
+prey so I'm just pointing out uh I want
+want you to give examples of the effects
+
+ align:start position:0%
+want you to give examples of the effects
+ 
+
+ align:start position:0%
+want you to give examples of the effects
+of the inertia of excitation in animal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior think of an example from human
+
+ align:start position:0%
+behavior think of an example from human
+ 
+
+ align:start position:0%
+behavior think of an example from human
+behavior but it occurs with animals too
+
+ align:start position:0%
+behavior but it occurs with animals too
+ 
+
+ align:start position:0%
+behavior but it occurs with animals too
+if you suddenly remove a stimulus you
+
+ align:start position:0%
+if you suddenly remove a stimulus you
+ 
+
+ align:start position:0%
+if you suddenly remove a stimulus you
+elicit the whole you increase the level
+
+ align:start position:0%
+elicit the whole you increase the level
+ 
+
+ align:start position:0%
+elicit the whole you increase the level
+of motivation that remember the
+
+ align:start position:0%
+of motivation that remember the
+ 
+
+ align:start position:0%
+of motivation that remember the
+Lawrence's model on the right there you
+
+ align:start position:0%
+Lawrence's model on the right there you
+ 
+
+ align:start position:0%
+Lawrence's model on the right there you
+you cause the the motivation to go way
+
+ align:start position:0%
+you cause the the motivation to go way
+ 
+
+ align:start position:0%
+you cause the the motivation to go way
+way up if you just sudden L remove that
+
+ align:start position:0%
+way up if you just sudden L remove that
+ 
+
+ align:start position:0%
+way up if you just sudden L remove that
+stimulus the behavior doesn't just go
+
+ align:start position:0%
+stimulus the behavior doesn't just go
+ 
+
+ align:start position:0%
+stimulus the behavior doesn't just go
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+okay I like the example from a Disney
+
+ align:start position:0%
+okay I like the example from a Disney
+ 
+
+ align:start position:0%
+okay I like the example from a Disney
+movie of a bear they show the bear
+
+ align:start position:0%
+movie of a bear they show the bear
+ 
+
+ align:start position:0%
+movie of a bear they show the bear
+that's high on a hill and he's trying to
+
+ align:start position:0%
+that's high on a hill and he's trying to
+ 
+
+ align:start position:0%
+that's high on a hill and he's trying to
+get something in a log a big log and he
+
+ align:start position:0%
+get something in a log a big log and he
+ 
+
+ align:start position:0%
+get something in a log a big log and he
+crawls into the log as far as he can get
+
+ align:start position:0%
+crawls into the log as far as he can get
+ 
+
+ align:start position:0%
+crawls into the log as far as he can get
+and he gets stuck there and then the log
+
+ align:start position:0%
+and he gets stuck there and then the log
+ 
+
+ align:start position:0%
+and he gets stuck there and then the log
+starts rolling down the hill bounding
+
+ align:start position:0%
+starts rolling down the hill bounding
+ 
+
+ align:start position:0%
+starts rolling down the hill bounding
+down the hill until finally it crashes
+
+ align:start position:0%
+down the hill until finally it crashes
+ 
+
+ align:start position:0%
+down the hill until finally it crashes
+against a tree and breaks open the log
+
+ align:start position:0%
+against a tree and breaks open the log
+ 
+
+ align:start position:0%
+against a tree and breaks open the log
+and the bear comes out angry as can be
+
+ align:start position:0%
+and the bear comes out angry as can be
+ 
+
+ align:start position:0%
+and the bear comes out angry as can be
+and he starts swatting he pulls little
+
+ align:start position:0%
+and he starts swatting he pulls little
+ 
+
+ align:start position:0%
+and he starts swatting he pulls little
+trees you know he just like an angry
+
+ align:start position:0%
+trees you know he just like an angry
+ 
+
+ align:start position:0%
+trees you know he just like an angry
+human that you don't get over it
+
+ align:start position:0%
+human that you don't get over it
+ 
+
+ align:start position:0%
+human that you don't get over it
+suddenly even if the stimuli are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gone if something on the TV makes you
+
+ align:start position:0%
+gone if something on the TV makes you
+ 
+
+ align:start position:0%
+gone if something on the TV makes you
+very angry some people have been known
+
+ align:start position:0%
+very angry some people have been known
+ 
+
+ align:start position:0%
+very angry some people have been known
+to break their
+
+ align:start position:0%
+to break their
+ 
+
+ align:start position:0%
+to break their
+TV you know this
+
+ align:start position:0%
+TV you know this
+ 
+
+ align:start position:0%
+TV you know this
+this is the inertia of excitation of a
+
+ align:start position:0%
+this is the inertia of excitation of a
+ 
+
+ align:start position:0%
+this is the inertia of excitation of a
+fixed action pattern okay by this change
+
+ align:start position:0%
+fixed action pattern okay by this change
+ 
+
+ align:start position:0%
+fixed action pattern okay by this change
+in the motivational
+
+ align:start position:0%
+in the motivational
+ 
+
+ align:start position:0%
+in the motivational
+level here on the right that you can
+
+ align:start position:0%
+level here on the right that you can
+ 
+
+ align:start position:0%
+level here on the right that you can
+remove that stimulus there but the
+
+ align:start position:0%
+remove that stimulus there but the
+ 
+
+ align:start position:0%
+remove that stimulus there but the
+reservoir is so full that the action
+
+ align:start position:0%
+reservoir is so full that the action
+ 
+
+ align:start position:0%
+reservoir is so full that the action
+continues for some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so you see that with fear with
+
+ align:start position:0%
+so you see that with fear with
+ 
+
+ align:start position:0%
+so you see that with fear with
+aggression with sexual excitement
+
+ align:start position:0%
+aggression with sexual excitement
+ 
+
+ align:start position:0%
+aggression with sexual excitement
+certainly these are the areas certainly
+
+ align:start position:0%
+certainly these are the areas certainly
+ 
+
+ align:start position:0%
+certainly these are the areas certainly
+in human behavior but also in many
+
+ align:start position:0%
+in human behavior but also in many
+ 
+
+ align:start position:0%
+in human behavior but also in many
+animals that you see that the
+
+ align:start position:0%
+animals that you see that the
+ 
+
+ align:start position:0%
+animals that you see that the
+most how can we explain the fact that
+
+ align:start position:0%
+most how can we explain the fact that
+ 
+
+ align:start position:0%
+most how can we explain the fact that
+the urination activities of a male dog
+
+ align:start position:0%
+the urination activities of a male dog
+ 
+
+ align:start position:0%
+the urination activities of a male dog
+often don't depend on the amount of
+
+ align:start position:0%
+often don't depend on the amount of
+ 
+
+ align:start position:0%
+often don't depend on the amount of
+urine in the ladder you say well why do
+
+ align:start position:0%
+urine in the ladder you say well why do
+ 
+
+ align:start position:0%
+urine in the ladder you say well why do
+we urinate well we have an urge to
+
+ align:start position:0%
+we urinate well we have an urge to
+ 
+
+ align:start position:0%
+we urinate well we have an urge to
+urinate because the ladder's full but in
+
+ align:start position:0%
+urinate because the ladder's full but in
+ 
+
+ align:start position:0%
+urinate because the ladder's full but in
+the case of a
+
+ align:start position:0%
+the case of a
+ 
+
+ align:start position:0%
+the case of a
+dog urination has other
+
+ align:start position:0%
+dog urination has other
+ 
+
+ align:start position:0%
+dog urination has other
+functions so there's two very different
+
+ align:start position:0%
+functions so there's two very different
+ 
+
+ align:start position:0%
+functions so there's two very different
+motivations that make at least the male
+
+ align:start position:0%
+motivations that make at least the male
+ 
+
+ align:start position:0%
+motivations that make at least the male
+dog
+
+ align:start position:0%
+dog
+ 
+
+ align:start position:0%
+dog
+urinate and in the case of female cats
+
+ align:start position:0%
+urinate and in the case of female cats
+ 
+
+ align:start position:0%
+urinate and in the case of female cats
+uh in in the case of cats I don't know
+
+ align:start position:0%
+uh in in the case of cats I don't know
+ 
+
+ align:start position:0%
+uh in in the case of cats I don't know
+about I don't think
+
+ align:start position:0%
+about I don't think
+ 
+
+ align:start position:0%
+about I don't think
+dogs uh but what are they
+
+ align:start position:0%
+dogs uh but what are they
+ 
+
+ align:start position:0%
+dogs uh but what are they
+doing why do they hold back they don't
+
+ align:start position:0%
+doing why do they hold back they don't
+ 
+
+ align:start position:0%
+doing why do they hold back they don't
+discharge all their
+
+ align:start position:0%
+discharge all their
+ 
+
+ align:start position:0%
+discharge all their
+urine they need it percent marking
+
+ align:start position:0%
+urine they need it percent marking
+ 
+
+ align:start position:0%
+urine they need it percent marking
+Behavior so that's a separate
+
+ align:start position:0%
+Behavior so that's a separate
+ 
+
+ align:start position:0%
+Behavior so that's a separate
+motivation okay and cats do it too both
+
+ align:start position:0%
+motivation okay and cats do it too both
+ 
+
+ align:start position:0%
+motivation okay and cats do it too both
+male and
+
+ align:start position:0%
+male and
+ 
+
+ align:start position:0%
+male and
+female uh because of the odor these are
+
+ align:start position:0%
+female uh because of the odor these are
+ 
+
+ align:start position:0%
+female uh because of the odor these are
+very old factory animals and
+
+ align:start position:0%
+very old factory animals and
+ 
+
+ align:start position:0%
+very old factory animals and
+they're their whole world is very
+
+ align:start position:0%
+they're their whole world is very
+ 
+
+ align:start position:0%
+they're their whole world is very
+different from ours it is Visual and
+
+ align:start position:0%
+different from ours it is Visual and
+ 
+
+ align:start position:0%
+different from ours it is Visual and
+auditory Lars but much more old factory
+
+ align:start position:0%
+auditory Lars but much more old factory
+ 
+
+ align:start position:0%
+auditory Lars but much more old factory
+they come into an area they
+
+ align:start position:0%
+they come into an area they
+ 
+
+ align:start position:0%
+they come into an area they
+know which other cats which individual
+
+ align:start position:0%
+know which other cats which individual
+ 
+
+ align:start position:0%
+know which other cats which individual
+cats have been in that region and
+
+ align:start position:0%
+cats have been in that region and
+ 
+
+ align:start position:0%
+cats have been in that region and
+whether they were male or female okay
+
+ align:start position:0%
+whether they were male or female okay
+ 
+
+ align:start position:0%
+whether they were male or female okay
+and they leave their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mark humans sometimes do that too they
+
+ align:start position:0%
+Mark humans sometimes do that too they
+ 
+
+ align:start position:0%
+Mark humans sometimes do that too they
+write on walls and things like
+
+ align:start position:0%
+write on walls and things like
+ 
+
+ align:start position:0%
+write on walls and things like
+that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's talk about chains of behavior
+
+ align:start position:0%
+uh let's talk about chains of behavior
+ 
+
+ align:start position:0%
+uh let's talk about chains of behavior
+and then the hierarchy of the system
+
+ align:start position:0%
+and then the hierarchy of the system
+ 
+
+ align:start position:0%
+and then the hierarchy of the system
+systems of fixed action
+
+ align:start position:0%
+systems of fixed action
+ 
+
+ align:start position:0%
+systems of fixed action
+patterns so as an example here I'm
+
+ align:start position:0%
+patterns so as an example here I'm
+ 
+
+ align:start position:0%
+patterns so as an example here I'm
+asking for a description of the chain of
+
+ align:start position:0%
+asking for a description of the chain of
+ 
+
+ align:start position:0%
+asking for a description of the chain of
+behavior pattern shown by newborn
+
+ align:start position:0%
+behavior pattern shown by newborn
+ 
+
+ align:start position:0%
+behavior pattern shown by newborn
+kittens in nursing Behavior it's very
+
+ align:start position:0%
+kittens in nursing Behavior it's very
+ 
+
+ align:start position:0%
+kittens in nursing Behavior it's very
+interesting it's a consistent chain of
+
+ align:start position:0%
+interesting it's a consistent chain of
+ 
+
+ align:start position:0%
+interesting it's a consistent chain of
+behavior that they
+
+ align:start position:0%
+behavior that they
+ 
+
+ align:start position:0%
+behavior that they
+show and normally one Behavior leads to
+
+ align:start position:0%
+show and normally one Behavior leads to
+ 
+
+ align:start position:0%
+show and normally one Behavior leads to
+the next because it leads to the
+
+ align:start position:0%
+the next because it leads to the
+ 
+
+ align:start position:0%
+the next because it leads to the
+stimulus that elicits the next and I've
+
+ align:start position:0%
+stimulus that elicits the next and I've
+ 
+
+ align:start position:0%
+stimulus that elicits the next and I've
+listed them here if he's awake and he's
+
+ align:start position:0%
+listed them here if he's awake and he's
+ 
+
+ align:start position:0%
+listed them here if he's awake and he's
+not suckling he shows this constant to
+
+ align:start position:0%
+not suckling he shows this constant to
+ 
+
+ align:start position:0%
+not suckling he shows this constant to
+and fro sideways sweeping movement of
+
+ align:start position:0%
+and fro sideways sweeping movement of
+ 
+
+ align:start position:0%
+and fro sideways sweeping movement of
+the head and four parts of the body
+
+ align:start position:0%
+the head and four parts of the body
+ 
+
+ align:start position:0%
+the head and four parts of the body
+while he creeps
+
+ align:start position:0%
+while he creeps
+ 
+
+ align:start position:0%
+while he creeps
+forward like no of course he's normally
+
+ align:start position:0%
+forward like no of course he's normally
+ 
+
+ align:start position:0%
+forward like no of course he's normally
+near the
+
+ align:start position:0%
+near the
+ 
+
+ align:start position:0%
+near the
+mother and if he touches a solid
+
+ align:start position:0%
+mother and if he touches a solid
+ 
+
+ align:start position:0%
+mother and if he touches a solid
+vertical surface even if it's not the
+
+ align:start position:0%
+vertical surface even if it's not the
+ 
+
+ align:start position:0%
+vertical surface even if it's not the
+mother he snuggles up to it and
+
+ align:start position:0%
+mother he snuggles up to it and
+ 
+
+ align:start position:0%
+mother he snuggles up to it and
+maintains contact while he continues
+
+ align:start position:0%
+maintains contact while he continues
+ 
+
+ align:start position:0%
+maintains contact while he continues
+that sweeping
+
+ align:start position:0%
+that sweeping
+ 
+
+ align:start position:0%
+that sweeping
+motion it's designed of course even
+
+ align:start position:0%
+motion it's designed of course even
+ 
+
+ align:start position:0%
+motion it's designed of course even
+though it's a fixed motor pattern uh
+
+ align:start position:0%
+though it's a fixed motor pattern uh
+ 
+
+ align:start position:0%
+though it's a fixed motor pattern uh
+it's designed to find the teeth of the
+
+ align:start position:0%
+it's designed to find the teeth of the
+ 
+
+ align:start position:0%
+it's designed to find the teeth of the
+mother so if he contacts fur he stops
+
+ align:start position:0%
+mother so if he contacts fur he stops
+ 
+
+ align:start position:0%
+mother so if he contacts fur he stops
+his Forward Motion okay but he continues
+
+ align:start position:0%
+his Forward Motion okay but he continues
+ 
+
+ align:start position:0%
+his Forward Motion okay but he continues
+the sweeping motions his nose pressed
+
+ align:start position:0%
+the sweeping motions his nose pressed
+ 
+
+ align:start position:0%
+the sweeping motions his nose pressed
+against the fur if he touches a bare
+
+ align:start position:0%
+against the fur if he touches a bare
+ 
+
+ align:start position:0%
+against the fur if he touches a bare
+spot then he ceases the sweeping motion
+
+ align:start position:0%
+spot then he ceases the sweeping motion
+ 
+
+ align:start position:0%
+spot then he ceases the sweeping motion
+and initiates a different Behavior it's
+
+ align:start position:0%
+and initiates a different Behavior it's
+ 
+
+ align:start position:0%
+and initiates a different Behavior it's
+kind of snapping he's trying to get the
+
+ align:start position:0%
+kind of snapping he's trying to get the
+ 
+
+ align:start position:0%
+kind of snapping he's trying to get the
+tee in his mouth so he finds it he stops
+
+ align:start position:0%
+tee in his mouth so he finds it he stops
+ 
+
+ align:start position:0%
+tee in his mouth so he finds it he stops
+his other movements and that initiates
+
+ align:start position:0%
+his other movements and that initiates
+ 
+
+ align:start position:0%
+his other movements and that initiates
+the sucking Behavior sucking behavior
+
+ align:start position:0%
+the sucking Behavior sucking behavior
+ 
+
+ align:start position:0%
+the sucking Behavior sucking behavior
+and also melt treading while he's
+
+ align:start position:0%
+and also melt treading while he's
+ 
+
+ align:start position:0%
+and also melt treading while he's
+sucking he's you see this movement of
+
+ align:start position:0%
+sucking he's you see this movement of
+ 
+
+ align:start position:0%
+sucking he's you see this movement of
+the front
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paws so each motor pattern serves as
+
+ align:start position:0%
+paws so each motor pattern serves as
+ 
+
+ align:start position:0%
+paws so each motor pattern serves as
+competitive behavior for the next fixed
+
+ align:start position:0%
+competitive behavior for the next fixed
+ 
+
+ align:start position:0%
+competitive behavior for the next fixed
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+pattern or I would say the next
+
+ align:start position:0%
+pattern or I would say the next
+ 
+
+ align:start position:0%
+pattern or I would say the next
+component of the
+
+ align:start position:0%
+component of the
+ 
+
+ align:start position:0%
+component of the
+sequence because these are always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linked but Lawrence sees them as
+
+ align:start position:0%
+linked but Lawrence sees them as
+ 
+
+ align:start position:0%
+linked but Lawrence sees them as
+a very different fixed action
+
+ align:start position:0%
+a very different fixed action
+ 
+
+ align:start position:0%
+a very different fixed action
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+uh because in fact you don't have to
+
+ align:start position:0%
+uh because in fact you don't have to
+ 
+
+ align:start position:0%
+uh because in fact you don't have to
+have the whole sequence if you put the
+
+ align:start position:0%
+have the whole sequence if you put the
+ 
+
+ align:start position:0%
+have the whole sequence if you put the
+an the animal right next to the mother
+
+ align:start position:0%
+an the animal right next to the mother
+ 
+
+ align:start position:0%
+an the animal right next to the mother
+then he won't show the earlier compounds
+
+ align:start position:0%
+then he won't show the earlier compounds
+ 
+
+ align:start position:0%
+then he won't show the earlier compounds
+he does not have to go through the
+
+ align:start position:0%
+he does not have to go through the
+ 
+
+ align:start position:0%
+he does not have to go through the
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+ones because they're
+
+ align:start position:0%
+ones because they're
+ 
+
+ align:start position:0%
+ones because they're
+all somewhat independent fixed action
+
+ align:start position:0%
+all somewhat independent fixed action
+ 
+
+ align:start position:0%
+all somewhat independent fixed action
+patterns but they're normally linked
+
+ align:start position:0%
+patterns but they're normally linked
+ 
+
+ align:start position:0%
+patterns but they're normally linked
+because of the situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Timber had described these kinds of
+
+ align:start position:0%
+and Timber had described these kinds of
+ 
+
+ align:start position:0%
+and Timber had described these kinds of
+things as examples of the hierarchical
+
+ align:start position:0%
+things as examples of the hierarchical
+ 
+
+ align:start position:0%
+things as examples of the hierarchical
+organization of
+
+ align:start position:0%
+organization of
+ 
+
+ align:start position:0%
+organization of
+instinct and he he has some very
+
+ align:start position:0%
+instinct and he he has some very
+ 
+
+ align:start position:0%
+instinct and he he has some very
+well-known diagrams that you should be
+
+ align:start position:0%
+well-known diagrams that you should be
+ 
+
+ align:start position:0%
+well-known diagrams that you should be
+familiar
+
+ align:start position:0%
+familiar
+ 
+
+ align:start position:0%
+familiar
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+uh he shows a view of innate releasing
+
+ align:start position:0%
+uh he shows a view of innate releasing
+ 
+
+ align:start position:0%
+uh he shows a view of innate releasing
+mechanisms that are quite a bit
+
+ align:start position:0%
+mechanisms that are quite a bit
+ 
+
+ align:start position:0%
+mechanisms that are quite a bit
+different from Lawrence they did work
+
+ align:start position:0%
+different from Lawrence they did work
+ 
+
+ align:start position:0%
+different from Lawrence they did work
+together some but they had a different
+
+ align:start position:0%
+together some but they had a different
+ 
+
+ align:start position:0%
+together some but they had a different
+way of picturing it
+
+ align:start position:0%
+way of picturing it
+ 
+
+ align:start position:0%
+way of picturing it
+uh and you can see that he doesn't
+
+ align:start position:0%
+uh and you can see that he doesn't
+ 
+
+ align:start position:0%
+uh and you can see that he doesn't
+explain some of the aspects that
+
+ align:start position:0%
+explain some of the aspects that
+ 
+
+ align:start position:0%
+explain some of the aspects that
+Lawrence was dealing with all that stuff
+
+ align:start position:0%
+Lawrence was dealing with all that stuff
+ 
+
+ align:start position:0%
+Lawrence was dealing with all that stuff
+about the inertia behavior and so forth
+
+ align:start position:0%
+about the inertia behavior and so forth
+ 
+
+ align:start position:0%
+about the inertia behavior and so forth
+he didn't try to deal with but he did
+
+ align:start position:0%
+he didn't try to deal with but he did
+ 
+
+ align:start position:0%
+he didn't try to deal with but he did
+deal with the hierarchy in this case we
+
+ align:start position:0%
+deal with the hierarchy in this case we
+ 
+
+ align:start position:0%
+deal with the hierarchy in this case we
+just take one component of it
+
+ align:start position:0%
+just take one component of it
+ 
+
+ align:start position:0%
+just take one component of it
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay and this is just
+
+ align:start position:0%
+okay and this is just
+ 
+
+ align:start position:0%
+okay and this is just
+uh for example um and we're dealing with
+
+ align:start position:0%
+uh for example um and we're dealing with
+ 
+
+ align:start position:0%
+uh for example um and we're dealing with
+an aspect of reproductive Behavior
+
+ align:start position:0%
+an aspect of reproductive Behavior
+ 
+
+ align:start position:0%
+an aspect of reproductive Behavior
+hormones provide a major
+
+ align:start position:0%
+hormones provide a major
+ 
+
+ align:start position:0%
+hormones provide a major
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+uh the higher level could be coming from
+
+ align:start position:0%
+uh the higher level could be coming from
+ 
+
+ align:start position:0%
+uh the higher level could be coming from
+the visual system that signals time of
+
+ align:start position:0%
+the visual system that signals time of
+ 
+
+ align:start position:0%
+the visual system that signals time of
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+uh other input that increase that
+
+ align:start position:0%
+uh other input that increase that
+ 
+
+ align:start position:0%
+uh other input that increase that
+motivation and then unlike Lawrence he
+
+ align:start position:0%
+motivation and then unlike Lawrence he
+ 
+
+ align:start position:0%
+motivation and then unlike Lawrence he
+has a
+
+ align:start position:0%
+has a
+ 
+
+ align:start position:0%
+has a
+block preventing the continuous
+
+ align:start position:0%
+block preventing the continuous
+ 
+
+ align:start position:0%
+block preventing the continuous
+discharge of the motor paddings
+
+ align:start position:0%
+discharge of the motor paddings
+ 
+
+ align:start position:0%
+discharge of the motor paddings
+and the innate releasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanism then the stimulus that
+
+ align:start position:0%
+mechanism then the stimulus that
+ 
+
+ align:start position:0%
+mechanism then the stimulus that
+activates the innate releasing mechanism
+
+ align:start position:0%
+activates the innate releasing mechanism
+ 
+
+ align:start position:0%
+activates the innate releasing mechanism
+its function is simply to remove that
+
+ align:start position:0%
+its function is simply to remove that
+ 
+
+ align:start position:0%
+its function is simply to remove that
+block and then the block once it's
+
+ align:start position:0%
+block and then the block once it's
+ 
+
+ align:start position:0%
+block and then the block once it's
+removed can elicit a whole
+
+ align:start position:0%
+removed can elicit a whole
+ 
+
+ align:start position:0%
+removed can elicit a whole
+series and which one would be first well
+
+ align:start position:0%
+series and which one would be first well
+ 
+
+ align:start position:0%
+series and which one would be first well
+the one with the lowest threshold and
+
+ align:start position:0%
+the one with the lowest threshold and
+ 
+
+ align:start position:0%
+the one with the lowest threshold and
+normally that's ative
+
+ align:start position:0%
+normally that's ative
+ 
+
+ align:start position:0%
+normally that's ative
+Behavior okay and these different
+
+ align:start position:0%
+Behavior okay and these different
+ 
+
+ align:start position:0%
+Behavior okay and these different
+components of the fixed action pattern
+
+ align:start position:0%
+components of the fixed action pattern
+ 
+
+ align:start position:0%
+components of the fixed action pattern
+are normally inhibiting each other and
+
+ align:start position:0%
+are normally inhibiting each other and
+ 
+
+ align:start position:0%
+are normally inhibiting each other and
+this shows a more complete model where
+
+ align:start position:0%
+this shows a more complete model where
+ 
+
+ align:start position:0%
+this shows a more complete model where
+he shows uh male stick stickleback
+
+ align:start position:0%
+he shows uh male stick stickleback
+ 
+
+ align:start position:0%
+he shows uh male stick stickleback
+reproductive Behavior basically the
+
+ align:start position:0%
+reproductive Behavior basically the
+ 
+
+ align:start position:0%
+reproductive Behavior basically the
+whole hierarchy starting with hormones
+
+ align:start position:0%
+whole hierarchy starting with hormones
+ 
+
+ align:start position:0%
+whole hierarchy starting with hormones
+with a spring
+
+ align:start position:0%
+with a spring
+ 
+
+ align:start position:0%
+with a spring
+migration uh the nature of the water has
+
+ align:start position:0%
+migration uh the nature of the water has
+ 
+
+ align:start position:0%
+migration uh the nature of the water has
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+influence uh the plants and the vicinity
+
+ align:start position:0%
+influence uh the plants and the vicinity
+ 
+
+ align:start position:0%
+influence uh the plants and the vicinity
+and various internal factors and then
+
+ align:start position:0%
+and various internal factors and then
+ 
+
+ align:start position:0%
+and various internal factors and then
+there's the block the innate releasing
+
+ align:start position:0%
+there's the block the innate releasing
+ 
+
+ align:start position:0%
+there's the block the innate releasing
+mechanism that can remove the block and
+
+ align:start position:0%
+mechanism that can remove the block and
+ 
+
+ align:start position:0%
+mechanism that can remove the block and
+start these various behaviors and note
+
+ align:start position:0%
+start these various behaviors and note
+ 
+
+ align:start position:0%
+start these various behaviors and note
+he has the mutual inhibition shown by
+
+ align:start position:0%
+he has the mutual inhibition shown by
+ 
+
+ align:start position:0%
+he has the mutual inhibition shown by
+the double arrows here he has fighting
+
+ align:start position:0%
+the double arrows here he has fighting
+ 
+
+ align:start position:0%
+the double arrows here he has fighting
+nesting courtship and parental Behavior
+
+ align:start position:0%
+nesting courtship and parental Behavior
+ 
+
+ align:start position:0%
+nesting courtship and parental Behavior
+each with somewhat different stimuli and
+
+ align:start position:0%
+each with somewhat different stimuli and
+ 
+
+ align:start position:0%
+each with somewhat different stimuli and
+so depending on the stimuli there uh
+
+ align:start position:0%
+so depending on the stimuli there uh
+ 
+
+ align:start position:0%
+so depending on the stimuli there uh
+these will be
+
+ align:start position:0%
+these will be
+ 
+
+ align:start position:0%
+these will be
+discharged and then he shows the lower
+
+ align:start position:0%
+discharged and then he shows the lower
+ 
+
+ align:start position:0%
+discharged and then he shows the lower
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+too the level of the actual action so
+
+ align:start position:0%
+too the level of the actual action so
+ 
+
+ align:start position:0%
+too the level of the actual action so
+here for fighting Behavior he has the
+
+ align:start position:0%
+here for fighting Behavior he has the
+ 
+
+ align:start position:0%
+here for fighting Behavior he has the
+displaying the biting and the
+
+ align:start position:0%
+displaying the biting and the
+ 
+
+ align:start position:0%
+displaying the biting and the
+chasing okay and if if you get the
+
+ align:start position:0%
+chasing okay and if if you get the
+ 
+
+ align:start position:0%
+chasing okay and if if you get the
+display hurrying uh then you get whole
+
+ align:start position:0%
+display hurrying uh then you get whole
+ 
+
+ align:start position:0%
+display hurrying uh then you get whole
+fins rays of one fin muscle fibers of
+
+ align:start position:0%
+fins rays of one fin muscle fibers of
+ 
+
+ align:start position:0%
+fins rays of one fin muscle fibers of
+one Ray and motor
+
+ align:start position:0%
+one Ray and motor
+ 
+
+ align:start position:0%
+one Ray and motor
+neurons for for one the muscle fiber so
+
+ align:start position:0%
+neurons for for one the muscle fiber so
+ 
+
+ align:start position:0%
+neurons for for one the muscle fiber so
+he shows the whole hierarchy here and
+
+ align:start position:0%
+he shows the whole hierarchy here and
+ 
+
+ align:start position:0%
+he shows the whole hierarchy here and
+this is often reproduced because
+
+ align:start position:0%
+this is often reproduced because
+ 
+
+ align:start position:0%
+this is often reproduced because
+neuroscientists like it because it sort
+
+ align:start position:0%
+neuroscientists like it because it sort
+ 
+
+ align:start position:0%
+neuroscientists like it because it sort
+of fits the hierarchical organization of
+
+ align:start position:0%
+of fits the hierarchical organization of
+ 
+
+ align:start position:0%
+of fits the hierarchical organization of
+the nervous system and this shows a
+
+ align:start position:0%
+the nervous system and this shows a
+ 
+
+ align:start position:0%
+the nervous system and this shows a
+functional picture of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I'm
+
+ align:start position:0%
+okay and I'm
+ 
+
+ align:start position:0%
+okay and I'm
+uh this is the level of ethology up here
+
+ align:start position:0%
+uh this is the level of ethology up here
+ 
+
+ align:start position:0%
+uh this is the level of ethology up here
+and here we're at the level of
+
+ align:start position:0%
+and here we're at the level of
+ 
+
+ align:start position:0%
+and here we're at the level of
+neurophysiology they study different
+
+ align:start position:0%
+neurophysiology they study different
+ 
+
+ align:start position:0%
+neurophysiology they study different
+aspects of it but in fact the
+
+ align:start position:0%
+aspects of it but in fact the
+ 
+
+ align:start position:0%
+aspects of it but in fact the
+physiologists working on hypothalamus
+
+ align:start position:0%
+physiologists working on hypothalamus
+ 
+
+ align:start position:0%
+physiologists working on hypothalamus
+have also studied many of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things so the major difference then
+
+ align:start position:0%
+things so the major difference then
+ 
+
+ align:start position:0%
+things so the major difference then
+between the Lawrence model and the
+
+ align:start position:0%
+between the Lawrence model and the
+ 
+
+ align:start position:0%
+between the Lawrence model and the
+tinbergen model I've listed for you here
+
+ align:start position:0%
+tinbergen model I've listed for you here
+ 
+
+ align:start position:0%
+tinbergen model I've listed for you here
+here obviously tinbergen's view is the
+
+ align:start position:0%
+here obviously tinbergen's view is the
+ 
+
+ align:start position:0%
+here obviously tinbergen's view is the
+broader
+
+ align:start position:0%
+broader
+ 
+
+ align:start position:0%
+broader
+one uh it looks more like an information
+
+ align:start position:0%
+one uh it looks more like an information
+ 
+
+ align:start position:0%
+one uh it looks more like an information
+flow scheme uh but Lawrence by focusing
+
+ align:start position:0%
+flow scheme uh but Lawrence by focusing
+ 
+
+ align:start position:0%
+flow scheme uh but Lawrence by focusing
+on dynamics of the of the drive State
+
+ align:start position:0%
+on dynamics of the of the drive State
+ 
+
+ align:start position:0%
+on dynamics of the of the drive State
+the action specific potential and the
+
+ align:start position:0%
+the action specific potential and the
+ 
+
+ align:start position:0%
+the action specific potential and the
+innate releasing
+
+ align:start position:0%
+innate releasing
+ 
+
+ align:start position:0%
+innate releasing
+mechanism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it showing very different aspects of
+
+ align:start position:0%
+uh it showing very different aspects of
+ 
+
+ align:start position:0%
+uh it showing very different aspects of
+these the properties of innate behavior
+
+ align:start position:0%
+these the properties of innate behavior
+ 
+
+ align:start position:0%
+these the properties of innate behavior
+and here I just point out the strengths
+
+ align:start position:0%
+and here I just point out the strengths
+ 
+
+ align:start position:0%
+and here I just point out the strengths
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weaknesses and I I also note that
+
+ align:start position:0%
+weaknesses and I I also note that
+ 
+
+ align:start position:0%
+weaknesses and I I also note that
+tinbergen's model has been more popular
+
+ align:start position:0%
+tinbergen's model has been more popular
+ 
+
+ align:start position:0%
+tinbergen's model has been more popular
+among the the neural
+
+ align:start position:0%
+among the the neural
+ 
+
+ align:start position:0%
+among the the neural
+people um but it was the Lawrence view
+
+ align:start position:0%
+people um but it was the Lawrence view
+ 
+
+ align:start position:0%
+people um but it was the Lawrence view
+that was actually used in the modeling
+
+ align:start position:0%
+that was actually used in the modeling
+ 
+
+ align:start position:0%
+that was actually used in the modeling
+of real Behavior patterns in
+
+ align:start position:0%
+of real Behavior patterns in
+ 
+
+ align:start position:0%
+of real Behavior patterns in
+animals
+
+ align:start position:0%
+animals
+ 
+
+ align:start position:0%
+animals
+uh in the work of uh Bruce plumberg here
+
+ align:start position:0%
+uh in the work of uh Bruce plumberg here
+ 
+
+ align:start position:0%
+uh in the work of uh Bruce plumberg here
+that might when he was doing that in the
+
+ align:start position:0%
+that might when he was doing that in the
+ 
+
+ align:start position:0%
+that might when he was doing that in the
+media lab
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's go
+
+ align:start position:0%
+okay so let's go
+ 
+
+ align:start position:0%
+okay so let's go
+to the discussion of Lawrence of the
+
+ align:start position:0%
+to the discussion of Lawrence of the
+ 
+
+ align:start position:0%
+to the discussion of Lawrence of the
+work of Barons and this is his work on
+
+ align:start position:0%
+work of Barons and this is his work on
+ 
+
+ align:start position:0%
+work of Barons and this is his work on
+the female Digger was because it points
+
+ align:start position:0%
+the female Digger was because it points
+ 
+
+ align:start position:0%
+the female Digger was because it points
+out another aspect of innate behavior
+
+ align:start position:0%
+out another aspect of innate behavior
+ 
+
+ align:start position:0%
+out another aspect of innate behavior
+that I think is quite important and this
+
+ align:start position:0%
+that I think is quite important and this
+ 
+
+ align:start position:0%
+that I think is quite important and this
+uh we're going to come back to the
+
+ align:start position:0%
+uh we're going to come back to the
+ 
+
+ align:start position:0%
+uh we're going to come back to the
+digger wasp next week when we read uh uh
+
+ align:start position:0%
+digger wasp next week when we read uh uh
+ 
+
+ align:start position:0%
+digger wasp next week when we read uh uh
+little bit from tinbergen and his
+
+ align:start position:0%
+little bit from tinbergen and his
+ 
+
+ align:start position:0%
+little bit from tinbergen and his
+studies of uh
+
+ align:start position:0%
+studies of uh
+ 
+
+ align:start position:0%
+studies of uh
+orienting uh behavior in that that wasp
+
+ align:start position:0%
+orienting uh behavior in that that wasp
+ 
+
+ align:start position:0%
+orienting uh behavior in that that wasp
+how does he find
+
+ align:start position:0%
+how does he find
+ 
+
+ align:start position:0%
+how does he find
+things okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he's he's doing experiments on the
+
+ align:start position:0%
+so he's he's doing experiments on the
+ 
+
+ align:start position:0%
+so he's he's doing experiments on the
+influence of inspections of the nest by
+
+ align:start position:0%
+influence of inspections of the nest by
+ 
+
+ align:start position:0%
+influence of inspections of the nest by
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+WASP it's a behavior that has a lot of
+
+ align:start position:0%
+WASP it's a behavior that has a lot of
+ 
+
+ align:start position:0%
+WASP it's a behavior that has a lot of
+plasticity okay and uh this is what this
+
+ align:start position:0%
+plasticity okay and uh this is what this
+ 
+
+ align:start position:0%
+plasticity okay and uh this is what this
+is what the digger wasp is like and note
+
+ align:start position:0%
+is what the digger wasp is like and note
+ 
+
+ align:start position:0%
+is what the digger wasp is like and note
+there's a hole in the sand and she's
+
+ align:start position:0%
+there's a hole in the sand and she's
+ 
+
+ align:start position:0%
+there's a hole in the sand and she's
+made that hole and she it's basically a
+
+ align:start position:0%
+made that hole and she it's basically a
+ 
+
+ align:start position:0%
+made that hole and she it's basically a
+nest she makes nests in the sand and
+
+ align:start position:0%
+nest she makes nests in the sand and
+ 
+
+ align:start position:0%
+nest she makes nests in the sand and
+little holes in the
+
+ align:start position:0%
+little holes in the
+ 
+
+ align:start position:0%
+little holes in the
+sand and she digs a separate hole for
+
+ align:start position:0%
+sand and she digs a separate hole for
+ 
+
+ align:start position:0%
+sand and she digs a separate hole for
+every egg She
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lays and she has
+
+ align:start position:0%
+lays and she has
+ 
+
+ align:start position:0%
+lays and she has
+to the egg will hatch lar comes out and
+
+ align:start position:0%
+to the egg will hatch lar comes out and
+ 
+
+ align:start position:0%
+to the egg will hatch lar comes out and
+when the lar comes out they have to have
+
+ align:start position:0%
+when the lar comes out they have to have
+ 
+
+ align:start position:0%
+when the lar comes out they have to have
+food right away so
+
+ align:start position:0%
+food right away so
+ 
+
+ align:start position:0%
+food right away so
+she
+
+ align:start position:0%
+she
+ 
+
+ align:start position:0%
+she
+catches insects this wasp is catching
+
+ align:start position:0%
+catches insects this wasp is catching
+ 
+
+ align:start position:0%
+catches insects this wasp is catching
+little insects and worms and bringing
+
+ align:start position:0%
+little insects and worms and bringing
+ 
+
+ align:start position:0%
+little insects and worms and bringing
+them killing them and bringing them
+
+ align:start position:0%
+them killing them and bringing them
+ 
+
+ align:start position:0%
+them killing them and bringing them
+putting them in these
+
+ align:start position:0%
+putting them in these
+ 
+
+ align:start position:0%
+putting them in these
+nests but she doesn't have just one Nest
+
+ align:start position:0%
+nests but she doesn't have just one Nest
+ 
+
+ align:start position:0%
+nests but she doesn't have just one Nest
+she has a bunch of them and so when she
+
+ align:start position:0%
+she has a bunch of them and so when she
+ 
+
+ align:start position:0%
+she has a bunch of them and so when she
+comes to a
+
+ align:start position:0%
+comes to a
+ 
+
+ align:start position:0%
+comes to a
+nest she inspect her first task is just
+
+ align:start position:0%
+nest she inspect her first task is just
+ 
+
+ align:start position:0%
+nest she inspect her first task is just
+to inspect
+
+ align:start position:0%
+to inspect
+ 
+
+ align:start position:0%
+to inspect
+it and if it's already got some food
+
+ align:start position:0%
+it and if it's already got some food
+ 
+
+ align:start position:0%
+it and if it's already got some food
+there then she goes
+
+ align:start position:0%
+there then she goes
+ 
+
+ align:start position:0%
+there then she goes
+on and if it's
+
+ align:start position:0%
+on and if it's
+ 
+
+ align:start position:0%
+on and if it's
+empty then she will fly off and she will
+
+ align:start position:0%
+empty then she will fly off and she will
+ 
+
+ align:start position:0%
+empty then she will fly off and she will
+bring food back and she has to remember
+
+ align:start position:0%
+bring food back and she has to remember
+ 
+
+ align:start position:0%
+bring food back and she has to remember
+which Nest it was and she does she does
+
+ align:start position:0%
+which Nest it was and she does she does
+ 
+
+ align:start position:0%
+which Nest it was and she does she does
+does it pretty
+
+ align:start position:0%
+does it pretty
+ 
+
+ align:start position:0%
+does it pretty
+accurately
+
+ align:start position:0%
+accurately
+ 
+
+ align:start position:0%
+accurately
+okay and she can have a a lot of
+
+ align:start position:0%
+okay and she can have a a lot of
+ 
+
+ align:start position:0%
+okay and she can have a a lot of
+different nests so when you look at the
+
+ align:start position:0%
+different nests so when you look at the
+ 
+
+ align:start position:0%
+different nests so when you look at the
+whole whole situation it seems like
+
+ align:start position:0%
+whole whole situation it seems like
+ 
+
+ align:start position:0%
+whole whole situation it seems like
+quite complex behavior that obviously
+
+ align:start position:0%
+quite complex behavior that obviously
+ 
+
+ align:start position:0%
+quite complex behavior that obviously
+involves some learning and yet the whole
+
+ align:start position:0%
+involves some learning and yet the whole
+ 
+
+ align:start position:0%
+involves some learning and yet the whole
+structure is innate behavior but with
+
+ align:start position:0%
+structure is innate behavior but with
+ 
+
+ align:start position:0%
+structure is innate behavior but with
+these specific things she has to
+
+ align:start position:0%
+these specific things she has to
+ 
+
+ align:start position:0%
+these specific things she has to
+remember in order to carry out the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence so what she detects in the nest
+
+ align:start position:0%
+sequence so what she detects in the nest
+ 
+
+ align:start position:0%
+sequence so what she detects in the nest
+determines her next Behavior looks like
+
+ align:start position:0%
+determines her next Behavior looks like
+ 
+
+ align:start position:0%
+determines her next Behavior looks like
+my words didn't all copy
+
+ align:start position:0%
+my words didn't all copy
+ 
+
+ align:start position:0%
+my words didn't all copy
+there so the behavior sequences are
+
+ align:start position:0%
+there so the behavior sequences are
+ 
+
+ align:start position:0%
+there so the behavior sequences are
+Complicated by the fact that she digs
+
+ align:start position:0%
+Complicated by the fact that she digs
+ 
+
+ align:start position:0%
+Complicated by the fact that she digs
+and uses multip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nest and that LE LED uh in general
+
+ align:start position:0%
+nest and that LE LED uh in general
+ 
+
+ align:start position:0%
+nest and that LE LED uh in general
+motivational States underlying the
+
+ align:start position:0%
+motivational States underlying the
+ 
+
+ align:start position:0%
+motivational States underlying the
+feeding Behavior chicks and geese also
+
+ align:start position:0%
+feeding Behavior chicks and geese also
+ 
+
+ align:start position:0%
+feeding Behavior chicks and geese also
+show this relative hierarchy of moods
+
+ align:start position:0%
+show this relative hierarchy of moods
+ 
+
+ align:start position:0%
+show this relative hierarchy of moods
+and a good example is the feeding of
+
+ align:start position:0%
+and a good example is the feeding of
+ 
+
+ align:start position:0%
+and a good example is the feeding of
+ducks which we we talked about that a
+
+ align:start position:0%
+ducks which we we talked about that a
+ 
+
+ align:start position:0%
+ducks which we we talked about that a
+little bit but we didn't describe this
+
+ align:start position:0%
+little bit but we didn't describe this
+ 
+
+ align:start position:0%
+little bit but we didn't describe this
+Behavior the upending behavior of ducks
+
+ align:start position:0%
+Behavior the upending behavior of ducks
+ 
+
+ align:start position:0%
+Behavior the upending behavior of ducks
+and geese what is
+
+ align:start position:0%
+and geese what is
+ 
+
+ align:start position:0%
+and geese what is
+upending have you ever watched ducks or
+
+ align:start position:0%
+upending have you ever watched ducks or
+ 
+
+ align:start position:0%
+upending have you ever watched ducks or
+geese feeding in a pond uh much of the
+
+ align:start position:0%
+geese feeding in a pond uh much of the
+ 
+
+ align:start position:0%
+geese feeding in a pond uh much of the
+time you only see their
+
+ align:start position:0%
+time you only see their
+ 
+
+ align:start position:0%
+time you only see their
+tail they're upended they're they're
+
+ align:start position:0%
+tail they're upended they're they're
+ 
+
+ align:start position:0%
+tail they're upended they're they're
+looking for something down below okay
+
+ align:start position:0%
+looking for something down below okay
+ 
+
+ align:start position:0%
+looking for something down below okay
+and that's how they
+
+ align:start position:0%
+and that's how they
+ 
+
+ align:start position:0%
+and that's how they
+feed if you feed the geese or the ducks
+
+ align:start position:0%
+feed if you feed the geese or the ducks
+ 
+
+ align:start position:0%
+feed if you feed the geese or the ducks
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+ground uh then they wouldn't have to do
+
+ align:start position:0%
+ground uh then they wouldn't have to do
+ 
+
+ align:start position:0%
+ground uh then they wouldn't have to do
+that right ah but they're highly
+
+ align:start position:0%
+that right ah but they're highly
+ 
+
+ align:start position:0%
+that right ah but they're highly
+motivated to do upending see it's a
+
+ align:start position:0%
+motivated to do upending see it's a
+ 
+
+ align:start position:0%
+motivated to do upending see it's a
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+motivation so if you deprive them of
+
+ align:start position:0%
+motivation so if you deprive them of
+ 
+
+ align:start position:0%
+motivation so if you deprive them of
+food they will go out and
+
+ align:start position:0%
+food they will go out and
+ 
+
+ align:start position:0%
+food they will go out and
+upend okay they're not they're
+
+ align:start position:0%
+upend okay they're not they're
+ 
+
+ align:start position:0%
+upend okay they're not they're
+feeding because they want to upend
+
+ align:start position:0%
+feeding because they want to upend
+ 
+
+ align:start position:0%
+feeding because they want to upend
+they're not upending in order to feed
+
+ align:start position:0%
+they're not upending in order to feed
+ 
+
+ align:start position:0%
+they're not upending in order to feed
+and that's similar to what we talked
+
+ align:start position:0%
+and that's similar to what we talked
+ 
+
+ align:start position:0%
+and that's similar to what we talked
+about before when we talked about the
+
+ align:start position:0%
+about before when we talked about the
+ 
+
+ align:start position:0%
+about before when we talked about the
+Starling poking into things he's so
+
+ align:start position:0%
+Starling poking into things he's so
+ 
+
+ align:start position:0%
+Starling poking into things he's so
+highly motivated to poke that even if
+
+ align:start position:0%
+highly motivated to poke that even if
+ 
+
+ align:start position:0%
+highly motivated to poke that even if
+he's well fed he will do it and
+
+ align:start position:0%
+he's well fed he will do it and
+ 
+
+ align:start position:0%
+he's well fed he will do it and
+similarly the cactus Finch will still
+
+ align:start position:0%
+similarly the cactus Finch will still
+ 
+
+ align:start position:0%
+similarly the cactus Finch will still
+find a cactus spine and poke in the
+
+ align:start position:0%
+find a cactus spine and poke in the
+ 
+
+ align:start position:0%
+find a cactus spine and poke in the
+things cuz he's high even if he's
+
+ align:start position:0%
+things cuz he's high even if he's
+ 
+
+ align:start position:0%
+things cuz he's high even if he's
+wellfed because he's highly motivated to
+
+ align:start position:0%
+wellfed because he's highly motivated to
+ 
+
+ align:start position:0%
+wellfed because he's highly motivated to
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so well-fed Birds deprived of
+
+ align:start position:0%
+that so well-fed Birds deprived of
+ 
+
+ align:start position:0%
+that so well-fed Birds deprived of
+upending um we'll do
+
+ align:start position:0%
+upending um we'll do
+ 
+
+ align:start position:0%
+upending um we'll do
+that here's the picture of what it looks
+
+ align:start position:0%
+that here's the picture of what it looks
+ 
+
+ align:start position:0%
+that here's the picture of what it looks
+like and two ducks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upending
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I just point out here that the
+
+ align:start position:0%
+and I just point out here that the
+ 
+
+ align:start position:0%
+and I just point out here that the
+action specific potential for that
+
+ align:start position:0%
+action specific potential for that
+ 
+
+ align:start position:0%
+action specific potential for that
+behavior is separate than for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hunger so if you deprive them of it they
+
+ align:start position:0%
+Hunger so if you deprive them of it they
+ 
+
+ align:start position:0%
+Hunger so if you deprive them of it they
+will show the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior Lawrence has this interesting
+
+ align:start position:0%
+behavior Lawrence has this interesting
+ 
+
+ align:start position:0%
+behavior Lawrence has this interesting
+little discussion of why the
+
+ align:start position:0%
+little discussion of why the
+ 
+
+ align:start position:0%
+little discussion of why the
+head which he says contains the Locust
+
+ align:start position:0%
+head which he says contains the Locust
+ 
+
+ align:start position:0%
+head which he says contains the Locust
+of superior command had to e be invented
+
+ align:start position:0%
+of superior command had to e be invented
+ 
+
+ align:start position:0%
+of superior command had to e be invented
+in evolution
+
+ align:start position:0%
+in evolution
+ 
+
+ align:start position:0%
+in evolution
+so how is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function has I'm asking has the function
+
+ align:start position:0%
+function has I'm asking has the function
+ 
+
+ align:start position:0%
+function has I'm asking has the function
+of the head ganglion changed in higher
+
+ align:start position:0%
+of the head ganglion changed in higher
+ 
+
+ align:start position:0%
+of the head ganglion changed in higher
+vertebrates with respect to fixed action
+
+ align:start position:0%
+vertebrates with respect to fixed action
+ 
+
+ align:start position:0%
+vertebrates with respect to fixed action
+patterns and that's an interesting
+
+ align:start position:0%
+patterns and that's an interesting
+ 
+
+ align:start position:0%
+patterns and that's an interesting
+question Lawrence says the head had to
+
+ align:start position:0%
+question Lawrence says the head had to
+ 
+
+ align:start position:0%
+question Lawrence says the head had to
+evolve to limit Behavior to one motor
+
+ align:start position:0%
+evolve to limit Behavior to one motor
+ 
+
+ align:start position:0%
+evolve to limit Behavior to one motor
+pattern at a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time it was to embody the innate
+
+ align:start position:0%
+time it was to embody the innate
+ 
+
+ align:start position:0%
+time it was to embody the innate
+releasing mechanisms also because most
+
+ align:start position:0%
+releasing mechanisms also because most
+ 
+
+ align:start position:0%
+releasing mechanisms also because most
+innate releasing mechanisms involve
+
+ align:start position:0%
+innate releasing mechanisms involve
+ 
+
+ align:start position:0%
+innate releasing mechanisms involve
+stimuli coming into the head and the
+
+ align:start position:0%
+stimuli coming into the head and the
+ 
+
+ align:start position:0%
+stimuli coming into the head and the
+stimuli come in through the cranial
+
+ align:start position:0%
+stimuli come in through the cranial
+ 
+
+ align:start position:0%
+stimuli come in through the cranial
+nerves most of them do not come in
+
+ align:start position:0%
+nerves most of them do not come in
+ 
+
+ align:start position:0%
+nerves most of them do not come in
+through the spinal nerves
+
+ align:start position:0%
+through the spinal nerves
+ 
+
+ align:start position:0%
+through the spinal nerves
+okay there are some components for
+
+ align:start position:0%
+okay there are some components for
+ 
+
+ align:start position:0%
+okay there are some components for
+example in
+
+ align:start position:0%
+example in
+ 
+
+ align:start position:0%
+example in
+that nursing behavior of the the kitten
+
+ align:start position:0%
+that nursing behavior of the the kitten
+ 
+
+ align:start position:0%
+that nursing behavior of the the kitten
+looking for the opportunity to nurse
+
+ align:start position:0%
+looking for the opportunity to nurse
+ 
+
+ align:start position:0%
+looking for the opportunity to nurse
+that do come in through the spinal cord
+
+ align:start position:0%
+that do come in through the spinal cord
+ 
+
+ align:start position:0%
+that do come in through the spinal cord
+but most of them are coming in through
+
+ align:start position:0%
+but most of them are coming in through
+ 
+
+ align:start position:0%
+but most of them are coming in through
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+head
+
+ align:start position:0%
+head
+ 
+
+ align:start position:0%
+head
+then I'm asking here how the function
+
+ align:start position:0%
+then I'm asking here how the function
+ 
+
+ align:start position:0%
+then I'm asking here how the function
+has changed in higher vertebrates I
+
+ align:start position:0%
+has changed in higher vertebrates I
+ 
+
+ align:start position:0%
+has changed in higher vertebrates I
+would say that the main thing that's
+
+ align:start position:0%
+would say that the main thing that's
+ 
+
+ align:start position:0%
+would say that the main thing that's
+been changing is increased linkage
+
+ align:start position:0%
+been changing is increased linkage
+ 
+
+ align:start position:0%
+been changing is increased linkage
+between innate and learned aspects of
+
+ align:start position:0%
+between innate and learned aspects of
+ 
+
+ align:start position:0%
+between innate and learned aspects of
+behavior and that reaches a peak in
+
+ align:start position:0%
+behavior and that reaches a peak in
+ 
+
+ align:start position:0%
+behavior and that reaches a peak in
+humans uh but it's very prominent in
+
+ align:start position:0%
+humans uh but it's very prominent in
+ 
+
+ align:start position:0%
+humans uh but it's very prominent in
+other other
+
+ align:start position:0%
+other other
+ 
+
+ align:start position:0%
+other other
+animals uh and the other is initiation
+
+ align:start position:0%
+animals uh and the other is initiation
+ 
+
+ align:start position:0%
+animals uh and the other is initiation
+of behavior
+
+ align:start position:0%
+of behavior
+ 
+
+ align:start position:0%
+of behavior
+patterns by learn
+
+ align:start position:0%
+patterns by learn
+ 
+
+ align:start position:0%
+patterns by learn
+motivations motivations can be learned
+
+ align:start position:0%
+motivations motivations can be learned
+ 
+
+ align:start position:0%
+motivations motivations can be learned
+okay and uh acquired motivations are
+
+ align:start position:0%
+okay and uh acquired motivations are
+ 
+
+ align:start position:0%
+okay and uh acquired motivations are
+common we all know about of course some
+
+ align:start position:0%
+common we all know about of course some
+ 
+
+ align:start position:0%
+common we all know about of course some
+of the the bad ones The Addictive
+
+ align:start position:0%
+of the the bad ones The Addictive
+ 
+
+ align:start position:0%
+of the the bad ones The Addictive
+behaviors but there are many different
+
+ align:start position:0%
+behaviors but there are many different
+ 
+
+ align:start position:0%
+behaviors but there are many different
+motivations we become highly motivated
+
+ align:start position:0%
+motivations we become highly motivated
+ 
+
+ align:start position:0%
+motivations we become highly motivated
+to do certain tasks okay well that was
+
+ align:start position:0%
+to do certain tasks okay well that was
+ 
+
+ align:start position:0%
+to do certain tasks okay well that was
+not we didn't carry that with us from
+
+ align:start position:0%
+not we didn't carry that with us from
+ 
+
+ align:start position:0%
+not we didn't carry that with us from
+the uterus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but also our cognitive level
+
+ align:start position:0%
+okay but also our cognitive level
+ 
+
+ align:start position:0%
+okay but also our cognitive level
+uh we contain a model of the world and
+
+ align:start position:0%
+uh we contain a model of the world and
+ 
+
+ align:start position:0%
+uh we contain a model of the world and
+in that we make we embod choices we make
+
+ align:start position:0%
+in that we make we embod choices we make
+ 
+
+ align:start position:0%
+in that we make we embod choices we make
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forth I just point out here that the
+
+ align:start position:0%
+forth I just point out here that the
+ 
+
+ align:start position:0%
+forth I just point out here that the
+cognitive level is at the
+
+ align:start position:0%
+cognitive level is at the
+ 
+
+ align:start position:0%
+cognitive level is at the
+top of a neural hierarchy but it doesn't
+
+ align:start position:0%
+top of a neural hierarchy but it doesn't
+ 
+
+ align:start position:0%
+top of a neural hierarchy but it doesn't
+mean just because it's at the top that
+
+ align:start position:0%
+mean just because it's at the top that
+ 
+
+ align:start position:0%
+mean just because it's at the top that
+it's always dominant and we all know
+
+ align:start position:0%
+it's always dominant and we all know
+ 
+
+ align:start position:0%
+it's always dominant and we all know
+that for sure people can be totally
+
+ align:start position:0%
+that for sure people can be totally
+ 
+
+ align:start position:0%
+that for sure people can be totally
+dominated by
+
+ align:start position:0%
+dominated by
+ 
+
+ align:start position:0%
+dominated by
+see drive to enact
+
+ align:start position:0%
+see drive to enact
+ 
+
+ align:start position:0%
+see drive to enact
+Revenge uh drive to feed drive to
+
+ align:start position:0%
+Revenge uh drive to feed drive to
+ 
+
+ align:start position:0%
+Revenge uh drive to feed drive to
+acquire things these are innate behavior
+
+ align:start position:0%
+acquire things these are innate behavior
+ 
+
+ align:start position:0%
+acquire things these are innate behavior
+patterns and
+
+ align:start position:0%
+patterns and
+ 
+
+ align:start position:0%
+patterns and
+uh that cognitive level is often not at
+
+ align:start position:0%
+uh that cognitive level is often not at
+ 
+
+ align:start position:0%
+uh that cognitive level is often not at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+top maybe in true
+
+ align:start position:0%
+top maybe in true
+ 
+
+ align:start position:0%
+top maybe in true
+intellectuals it
+
+ align:start position:0%
+intellectuals it
+ 
+
+ align:start position:0%
+intellectuals it
+is I Define a true intellectual as
+
+ align:start position:0%
+is I Define a true intellectual as
+ 
+
+ align:start position:0%
+is I Define a true intellectual as
+somebody who by what he knows and what
+
+ align:start position:0%
+somebody who by what he knows and what
+ 
+
+ align:start position:0%
+somebody who by what he knows and what
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+learns the cognitions that he acquires
+
+ align:start position:0%
+learns the cognitions that he acquires
+ 
+
+ align:start position:0%
+learns the cognitions that he acquires
+actually affect his behavior in a major
+
+ align:start position:0%
+actually affect his behavior in a major
+ 
+
+ align:start position:0%
+actually affect his behavior in a major
+way it's not true most
+
+ align:start position:0%
+way it's not true most
+ 
+
+ align:start position:0%
+way it's not true most
+people in fact when the one student uh
+
+ align:start position:0%
+people in fact when the one student uh
+ 
+
+ align:start position:0%
+people in fact when the one student uh
+working with Bruce and with me here at
+
+ align:start position:0%
+working with Bruce and with me here at
+ 
+
+ align:start position:0%
+working with Bruce and with me here at
+MIT was simulating human
+
+ align:start position:0%
+MIT was simulating human
+ 
+
+ align:start position:0%
+MIT was simulating human
+behavior everything in it except for
+
+ align:start position:0%
+behavior everything in it except for
+ 
+
+ align:start position:0%
+behavior everything in it except for
+some very simple spatial things was not
+
+ align:start position:0%
+some very simple spatial things was not
+ 
+
+ align:start position:0%
+some very simple spatial things was not
+learned it was all built into the
+
+ align:start position:0%
+learned it was all built into the
+ 
+
+ align:start position:0%
+learned it was all built into the
+software and yet you show the the
+
+ align:start position:0%
+software and yet you show the the
+ 
+
+ align:start position:0%
+software and yet you show the the
+results of simulations where you see
+
+ align:start position:0%
+results of simulations where you see
+ 
+
+ align:start position:0%
+results of simulations where you see
+people moving around making choices and
+
+ align:start position:0%
+people moving around making choices and
+ 
+
+ align:start position:0%
+people moving around making choices and
+this and that it looks like pretty
+
+ align:start position:0%
+this and that it looks like pretty
+ 
+
+ align:start position:0%
+this and that it looks like pretty
+normal human
+
+ align:start position:0%
+normal human
+ 
+
+ align:start position:0%
+normal human
+behavior so a lot of times when we're
+
+ align:start position:0%
+behavior so a lot of times when we're
+ 
+
+ align:start position:0%
+behavior so a lot of times when we're
+observing human behavior we're just
+
+ align:start position:0%
+observing human behavior we're just
+ 
+
+ align:start position:0%
+observing human behavior we're just
+looking at fixed action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns all right
+
+ align:start position:0%
+patterns all right
+ 
+
+ align:start position:0%
+patterns all right
+uh next topic here is concerns what we
+
+ align:start position:0%
+uh next topic here is concerns what we
+ 
+
+ align:start position:0%
+uh next topic here is concerns what we
+call taxes and reflexes this involves
+
+ align:start position:0%
+call taxes and reflexes this involves
+ 
+
+ align:start position:0%
+call taxes and reflexes this involves
+spatial
+
+ align:start position:0%
+spatial
+ 
+
+ align:start position:0%
+spatial
+orientation and that leads to a
+
+ align:start position:0%
+orientation and that leads to a
+ 
+
+ align:start position:0%
+orientation and that leads to a
+discussion of thinking in higher
+
+ align:start position:0%
+discussion of thinking in higher
+ 
+
+ align:start position:0%
+discussion of thinking in higher
+animals uh first of all and we won't
+
+ align:start position:0%
+animals uh first of all and we won't
+ 
+
+ align:start position:0%
+animals uh first of all and we won't
+have time for too much more than this uh
+
+ align:start position:0%
+have time for too much more than this uh
+ 
+
+ align:start position:0%
+have time for too much more than this uh
+explain how the mantle of reflexes the
+
+ align:start position:0%
+explain how the mantle of reflexes the
+ 
+
+ align:start position:0%
+explain how the mantle of reflexes the
+term I've used from from phone
+
+ align:start position:0%
+term I've used from from phone
+ 
+
+ align:start position:0%
+term I've used from from phone
+Holst uh and Lawrence uses it I
+
+ align:start position:0%
+Holst uh and Lawrence uses it I
+ 
+
+ align:start position:0%
+Holst uh and Lawrence uses it I
+believe it tends to conceal the rigidity
+
+ align:start position:0%
+believe it tends to conceal the rigidity
+ 
+
+ align:start position:0%
+believe it tends to conceal the rigidity
+of fixed motor patterns
+
+ align:start position:0%
+of fixed motor patterns
+ 
+
+ align:start position:0%
+of fixed motor patterns
+you know when we walk for example we
+
+ align:start position:0%
+you know when we walk for example we
+ 
+
+ align:start position:0%
+you know when we walk for example we
+know that's a fixed motor pattern it
+
+ align:start position:0%
+know that's a fixed motor pattern it
+ 
+
+ align:start position:0%
+know that's a fixed motor pattern it
+appears at a certain age when the neural
+
+ align:start position:0%
+appears at a certain age when the neural
+ 
+
+ align:start position:0%
+appears at a certain age when the neural
+mechanisms of the spinal cord mature and
+
+ align:start position:0%
+mechanisms of the spinal cord mature and
+ 
+
+ align:start position:0%
+mechanisms of the spinal cord mature and
+the various gates are walking and
+
+ align:start position:0%
+the various gates are walking and
+ 
+
+ align:start position:0%
+the various gates are walking and
+running the various Gates of a horse
+
+ align:start position:0%
+running the various Gates of a horse
+ 
+
+ align:start position:0%
+running the various Gates of a horse
+which are multiple they're all
+
+ align:start position:0%
+which are multiple they're all
+ 
+
+ align:start position:0%
+which are multiple they're all
+inherited and yet at least especially
+
+ align:start position:0%
+inherited and yet at least especially
+ 
+
+ align:start position:0%
+inherited and yet at least especially
+for humans when we're walking around it
+
+ align:start position:0%
+for humans when we're walking around it
+ 
+
+ align:start position:0%
+for humans when we're walking around it
+seems to vary a lot it depends on what
+
+ align:start position:0%
+seems to vary a lot it depends on what
+ 
+
+ align:start position:0%
+seems to vary a lot it depends on what
+we're walking on it depends on the
+
+ align:start position:0%
+we're walking on it depends on the
+ 
+
+ align:start position:0%
+we're walking on it depends on the
+terrain even horses change the way they
+
+ align:start position:0%
+terrain even horses change the way they
+ 
+
+ align:start position:0%
+terrain even horses change the way they
+walk even though much less than say the
+
+ align:start position:0%
+walk even though much less than say the
+ 
+
+ align:start position:0%
+walk even though much less than say the
+more sure-footed animals like goats and
+
+ align:start position:0%
+more sure-footed animals like goats and
+ 
+
+ align:start position:0%
+more sure-footed animals like goats and
+donkeys but it's being adjusted by the
+
+ align:start position:0%
+donkeys but it's being adjusted by the
+ 
+
+ align:start position:0%
+donkeys but it's being adjusted by the
+reflexes you know if I'm walking along
+
+ align:start position:0%
+reflexes you know if I'm walking along
+ 
+
+ align:start position:0%
+reflexes you know if I'm walking along
+here I'm responding visually here too
+
+ align:start position:0%
+here I'm responding visually here too
+ 
+
+ align:start position:0%
+here I'm responding visually here too
+and I don't even look here but I can see
+
+ align:start position:0%
+and I don't even look here but I can see
+ 
+
+ align:start position:0%
+and I don't even look here but I can see
+the edge of this table and I will walk
+
+ align:start position:0%
+the edge of this table and I will walk
+ 
+
+ align:start position:0%
+the edge of this table and I will walk
+around it without even thinking about it
+
+ align:start position:0%
+around it without even thinking about it
+ 
+
+ align:start position:0%
+around it without even thinking about it
+this is just an example of simple
+
+ align:start position:0%
+this is just an example of simple
+ 
+
+ align:start position:0%
+this is just an example of simple
+spatial
+
+ align:start position:0%
+spatial
+ 
+
+ align:start position:0%
+spatial
+orientation uh reflexes that alter the
+
+ align:start position:0%
+orientation uh reflexes that alter the
+ 
+
+ align:start position:0%
+orientation uh reflexes that alter the
+way The Locomotion is expressed and
+
+ align:start position:0%
+way The Locomotion is expressed and
+ 
+
+ align:start position:0%
+way The Locomotion is expressed and
+there's much simpler examples uh like
+
+ align:start position:0%
+there's much simpler examples uh like
+ 
+
+ align:start position:0%
+there's much simpler examples uh like
+the egg rolling behavior of the grey leg
+
+ align:start position:0%
+the egg rolling behavior of the grey leg
+ 
+
+ align:start position:0%
+the egg rolling behavior of the grey leg
+Goose every time you see a grey leg
+
+ align:start position:0%
+Goose every time you see a grey leg
+ 
+
+ align:start position:0%
+Goose every time you see a grey leg
+Goose rolling a leg an egg back into the
+
+ align:start position:0%
+Goose rolling a leg an egg back into the
+ 
+
+ align:start position:0%
+Goose rolling a leg an egg back into the
+nest it looks a little different than
+
+ align:start position:0%
+nest it looks a little different than
+ 
+
+ align:start position:0%
+nest it looks a little different than
+other times you see it because the egg
+
+ align:start position:0%
+other times you see it because the egg
+ 
+
+ align:start position:0%
+other times you see it because the egg
+is rolling this way and that it's
+
+ align:start position:0%
+is rolling this way and that it's
+ 
+
+ align:start position:0%
+is rolling this way and that it's
+meeting little stones and he has to keep
+
+ align:start position:0%
+meeting little stones and he has to keep
+ 
+
+ align:start position:0%
+meeting little stones and he has to keep
+adjusting how
+
+ align:start position:0%
+adjusting how
+ 
+
+ align:start position:0%
+adjusting how
+he's getting his beak over the egg and
+
+ align:start position:0%
+he's getting his beak over the egg and
+ 
+
+ align:start position:0%
+he's getting his beak over the egg and
+pulling it back towards the nest so it
+
+ align:start position:0%
+pulling it back towards the nest so it
+ 
+
+ align:start position:0%
+pulling it back towards the nest so it
+looks like it's complex and yet it's a
+
+ align:start position:0%
+looks like it's complex and yet it's a
+ 
+
+ align:start position:0%
+looks like it's complex and yet it's a
+fixed motor pattern it's basically the
+
+ align:start position:0%
+fixed motor pattern it's basically the
+ 
+
+ align:start position:0%
+fixed motor pattern it's basically the
+same motor pattern but it's working at a
+
+ align:start position:0%
+same motor pattern but it's working at a
+ 
+
+ align:start position:0%
+same motor pattern but it's working at a
+higher level than all these reflexes
+
+ align:start position:0%
+higher level than all these reflexes
+ 
+
+ align:start position:0%
+higher level than all these reflexes
+that are constantly adjusting it and the
+
+ align:start position:0%
+that are constantly adjusting it and the
+ 
+
+ align:start position:0%
+that are constantly adjusting it and the
+reflexes never stop remember they don't
+
+ align:start position:0%
+reflexes never stop remember they don't
+ 
+
+ align:start position:0%
+reflexes never stop remember they don't
+depend on the
+
+ align:start position:0%
+depend on the
+ 
+
+ align:start position:0%
+depend on the
+motivation they always
+
+ align:start position:0%
+motivation they always
+ 
+
+ align:start position:0%
+motivation they always
+act so it looks variable and complex
+
+ align:start position:0%
+act so it looks variable and complex
+ 
+
+ align:start position:0%
+act so it looks variable and complex
+because it's
+
+ align:start position:0%
+because it's
+ 
+
+ align:start position:0%
+because it's
+superimposed um superimposed on the
+
+ align:start position:0%
+superimposed um superimposed on the
+ 
+
+ align:start position:0%
+superimposed um superimposed on the
+behavior are these various reflexes
+
+ align:start position:0%
+behavior are these various reflexes
+ 
+
+ align:start position:0%
+behavior are these various reflexes
+they're vestibular they're tactile
+
+ align:start position:0%
+they're vestibular they're tactile
+ 
+
+ align:start position:0%
+they're vestibular they're tactile
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+visual uh and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forth last topic a
+
+ align:start position:0%
+forth last topic a
+ 
+
+ align:start position:0%
+forth last topic a
+goldfish behind a barrier let's say
+
+ align:start position:0%
+goldfish behind a barrier let's say
+ 
+
+ align:start position:0%
+goldfish behind a barrier let's say
+these are thick weeds he can't swim
+
+ align:start position:0%
+these are thick weeds he can't swim
+ 
+
+ align:start position:0%
+these are thick weeds he can't swim
+through but he can see through it well
+
+ align:start position:0%
+through but he can see through it well
+ 
+
+ align:start position:0%
+through but he can see through it well
+enough to see that there's food on the
+
+ align:start position:0%
+enough to see that there's food on the
+ 
+
+ align:start position:0%
+enough to see that there's food on the
+other side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how does he solve that problem and
+
+ align:start position:0%
+how does he solve that problem and
+ 
+
+ align:start position:0%
+how does he solve that problem and
+actually goldfish show pretty well
+
+ align:start position:0%
+actually goldfish show pretty well
+ 
+
+ align:start position:0%
+actually goldfish show pretty well
+better than dogs
+
+ align:start position:0%
+better than dogs
+ 
+
+ align:start position:0%
+better than dogs
+actually here's what he does he swims
+
+ align:start position:0%
+actually here's what he does he swims
+ 
+
+ align:start position:0%
+actually here's what he does he swims
+right for
+
+ align:start position:0%
+right for
+ 
+
+ align:start position:0%
+right for
+it and as soon as he touches it he's got
+
+ align:start position:0%
+it and as soon as he touches it he's got
+ 
+
+ align:start position:0%
+it and as soon as he touches it he's got
+another reflex okay we call it a
+
+ align:start position:0%
+another reflex okay we call it a
+ 
+
+ align:start position:0%
+another reflex okay we call it a
+negative figmo taxis a negative response
+
+ align:start position:0%
+negative figmo taxis a negative response
+ 
+
+ align:start position:0%
+negative figmo taxis a negative response
+to touching with his snout and that
+
+ align:start position:0%
+to touching with his snout and that
+ 
+
+ align:start position:0%
+to touching with his snout and that
+causes him to pull back now of course
+
+ align:start position:0%
+causes him to pull back now of course
+ 
+
+ align:start position:0%
+causes him to pull back now of course
+the algorithm can vary among fish and
+
+ align:start position:0%
+the algorithm can vary among fish and
+ 
+
+ align:start position:0%
+the algorithm can vary among fish and
+it's very different in dogs but normally
+
+ align:start position:0%
+it's very different in dogs but normally
+ 
+
+ align:start position:0%
+it's very different in dogs but normally
+he will keep trying to get at the food
+
+ align:start position:0%
+he will keep trying to get at the food
+ 
+
+ align:start position:0%
+he will keep trying to get at the food
+but he will keep moving like this until
+
+ align:start position:0%
+but he will keep moving like this until
+ 
+
+ align:start position:0%
+but he will keep moving like this until
+he can get it the
+
+ align:start position:0%
+he can get it the
+ 
+
+ align:start position:0%
+he can get it the
+food so just two reflexes are enough
+
+ align:start position:0%
+food so just two reflexes are enough
+ 
+
+ align:start position:0%
+food so just two reflexes are enough
+positive tilot taxis is what we call his
+
+ align:start position:0%
+positive tilot taxis is what we call his
+ 
+
+ align:start position:0%
+positive tilot taxis is what we call his
+moving towards the food there just a
+
+ align:start position:0%
+moving towards the food there just a
+ 
+
+ align:start position:0%
+moving towards the food there just a
+technical name for it positive tilo
+
+ align:start position:0%
+technical name for it positive tilo
+ 
+
+ align:start position:0%
+technical name for it positive tilo
+taxis tilo means the end taxis movement
+
+ align:start position:0%
+taxis tilo means the end taxis movement
+ 
+
+ align:start position:0%
+taxis tilo means the end taxis movement
+okay directed towards the towards the
+
+ align:start position:0%
+okay directed towards the towards the
+ 
+
+ align:start position:0%
+okay directed towards the towards the
+prey or towards other food that he was
+
+ align:start position:0%
+prey or towards other food that he was
+ 
+
+ align:start position:0%
+prey or towards other food that he was
+trying to get to and then the negative
+
+ align:start position:0%
+trying to get to and then the negative
+ 
+
+ align:start position:0%
+trying to get to and then the negative
+thigo
+
+ align:start position:0%
+thigo
+ 
+
+ align:start position:0%
+thigo
+thigmotaxis causes him to avoid the
+
+ align:start position:0%
+thigmotaxis causes him to avoid the
+ 
+
+ align:start position:0%
+thigmotaxis causes him to avoid the
+obstacles branches plants so forth so it
+
+ align:start position:0%
+obstacles branches plants so forth so it
+ 
+
+ align:start position:0%
+obstacles branches plants so forth so it
+looks like intelligent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Behavior he seems to figure out how to
+
+ align:start position:0%
+Behavior he seems to figure out how to
+ 
+
+ align:start position:0%
+Behavior he seems to figure out how to
+reach the food but in fact it's just two
+
+ align:start position:0%
+reach the food but in fact it's just two
+ 
+
+ align:start position:0%
+reach the food but in fact it's just two
+reflexes running off okay so now think
+
+ align:start position:0%
+reflexes running off okay so now think
+ 
+
+ align:start position:0%
+reflexes running off okay so now think
+about how a dog does it and we'll come
+
+ align:start position:0%
+about how a dog does it and we'll come
+ 
+
+ align:start position:0%
+about how a dog does it and we'll come
+back here next time
\ No newline at end of file
diff --git a/Ke2CpF8M0mc.txt b/Ke2CpF8M0mc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..acb3394686543a2e4c937a661a9cda6c0b9c3f84
--- /dev/null
+++ b/Ke2CpF8M0mc.txt
@@ -0,0 +1,79 @@
+Hello. This is Cheryl Siegel from MIT OpenCourseWare.
+Today I'm going to show you the Chandra Astrophysics
+
+Institute course on Highlights for High School.
+This section of OCW is for high school students,
+
+teachers, and parents who want to learn about
+math, science, engineering, and technology.
+
+You can find this course under High School
+Courses Developed by MIT. I chose Chandra
+
+Astrophysics, because it is a unique resource
+for high school teachers and their students.
+
+Astrophysics isn't usually taught at the
+high school level, but this course makes the
+
+subject easy and interesting for anyone that
+wants to learn about this branch of astronomy.
+
+This course also offers models and instructions
+to replicate many hands-on activities and
+
+includes dozens of hours of video.
+Chandra Astrophysics Institute is an MIT program
+
+for students in grades 9 through 11. Students
+tackle astrophysics projects, are mentored
+
+by MIT scientists, and use images from the
+Chandra X-Ray space telescope. The sessions
+
+weÕve published here were taught by Mark
+Hartman in the summer of 2008.
+
+As you can see, the course is divided into
+six investigations, each focusing on a specific
+
+area of astrophysics. Each investigation builds
+on the knowledge from the previous one.
+
+The investigations are organized around a
+series of activities.
+
+Activity 2 in Investigation 1 taught students
+about the size of objects in images and how
+
+to make observations about angular size.
+Here, students can see examples of trick photography...
+
+...and even a video of Kobe Bryant demonstrating
+the concept by appearing to jump over a car.
+
+There are detailed instructions for teachers,
+including notes, tips and tricks, as well
+
+as ideas for assessment.
+Also you will see several embedded videos,
+
+which correspond to the investigation and
+activity. This is a great way to get a glimpse
+
+of what it was like to be in this class.
+The image gallery shows dozens of photographs
+
+taken during the course.
+Here a student demonstrates his attempt at
+
+creating his own trick photograph.
+You can explore more high school resources
+
+at ocw.mit.edu/highschool
+You can also subscribe to our newsletter to
+
+get email updates from OCW.
+Finally, you can help support OCW by making
+
+a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/KhT9m9kFzv8.txt b/KhT9m9kFzv8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..22afb394ff36f9c0184d6333e1b394aecd185472
--- /dev/null
+++ b/KhT9m9kFzv8.txt
@@ -0,0 +1,7619 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I might actually use all 16
+
+ align:start position:0%
+I think I might actually use all 16
+ 
+
+ align:start position:0%
+I think I might actually use all 16
+colors today oh no this is the most
+
+ align:start position:0%
+colors today oh no this is the most
+ 
+
+ align:start position:0%
+colors today oh no this is the most
+satisfying day whereas Tuesday was
+
+ align:start position:0%
+satisfying day whereas Tuesday was
+ 
+
+ align:start position:0%
+satisfying day whereas Tuesday was
+probably the most mathematically intense
+
+ align:start position:0%
+probably the most mathematically intense
+ 
+
+ align:start position:0%
+probably the most mathematically intense
+because we developed this equation right
+
+ align:start position:0%
+because we developed this equation right
+ 
+
+ align:start position:0%
+because we developed this equation right
+here today is gonna be the most
+
+ align:start position:0%
+here today is gonna be the most
+ 
+
+ align:start position:0%
+here today is gonna be the most
+satisfying because we are going to
+
+ align:start position:0%
+satisfying because we are going to
+ 
+
+ align:start position:0%
+satisfying because we are going to
+cancel out just about every term leaving
+
+ align:start position:0%
+cancel out just about every term leaving
+ 
+
+ align:start position:0%
+cancel out just about every term leaving
+a homogeneous infinite reactor
+
+ align:start position:0%
+a homogeneous infinite reactor
+ 
+
+ align:start position:0%
+a homogeneous infinite reactor
+criticality condition so we will go over
+
+ align:start position:0%
+criticality condition so we will go over
+ 
+
+ align:start position:0%
+criticality condition so we will go over
+today how do you go from this to what is
+
+ align:start position:0%
+today how do you go from this to what is
+ 
+
+ align:start position:0%
+today how do you go from this to what is
+criticality in a reactor so I want to
+
+ align:start position:0%
+criticality in a reactor so I want to
+ 
+
+ align:start position:0%
+criticality in a reactor so I want to
+get a couple of variables up over here
+
+ align:start position:0%
+get a couple of variables up over here
+ 
+
+ align:start position:0%
+get a couple of variables up over here
+to remind you guys we had this variable
+
+ align:start position:0%
+to remind you guys we had this variable
+ 
+
+ align:start position:0%
+to remind you guys we had this variable
+flux of our I Omega T in the number of
+
+ align:start position:0%
+flux of our I Omega T in the number of
+ 
+
+ align:start position:0%
+flux of our I Omega T in the number of
+neutrons per centimeter squared per
+
+ align:start position:0%
+neutrons per centimeter squared per
+ 
+
+ align:start position:0%
+neutrons per centimeter squared per
+second travelling through something and
+
+ align:start position:0%
+second travelling through something and
+ 
+
+ align:start position:0%
+second travelling through something and
+we also had its corresponding non
+
+ align:start position:0%
+we also had its corresponding non
+ 
+
+ align:start position:0%
+we also had its corresponding non
+angular dependent term on just R et if
+
+ align:start position:0%
+angular dependent term on just R et if
+ 
+
+ align:start position:0%
+angular dependent term on just R et if
+we don't care what angle things go
+
+ align:start position:0%
+we don't care what angle things go
+ 
+
+ align:start position:0%
+we don't care what angle things go
+through we've got a corresponding
+
+ align:start position:0%
+through we've got a corresponding
+ 
+
+ align:start position:0%
+through we've got a corresponding
+variable called current so I'll put this
+
+ align:start position:0%
+variable called current so I'll put this
+ 
+
+ align:start position:0%
+variable called current so I'll put this
+as flux we have current J R Omega T and
+
+ align:start position:0%
+as flux we have current J R Omega T and
+ 
+
+ align:start position:0%
+as flux we have current J R Omega T and
+it's corresponding we don't care about
+
+ align:start position:0%
+it's corresponding we don't care about
+ 
+
+ align:start position:0%
+it's corresponding we don't care about
+angle form and today what we're gonna do
+
+ align:start position:0%
+angle form and today what we're gonna do
+ 
+
+ align:start position:0%
+angle form and today what we're gonna do
+is first go over this equation again so
+
+ align:start position:0%
+is first go over this equation again so
+ 
+
+ align:start position:0%
+is first go over this equation again so
+that we understand all of its parts and
+
+ align:start position:0%
+that we understand all of its parts and
+ 
+
+ align:start position:0%
+that we understand all of its parts and
+there are more parts here than are in
+
+ align:start position:0%
+there are more parts here than are in
+ 
+
+ align:start position:0%
+there are more parts here than are in
+the reading if you remember that's
+
+ align:start position:0%
+the reading if you remember that's
+ 
+
+ align:start position:0%
+the reading if you remember that's
+because I wanted to show you how all of
+
+ align:start position:0%
+because I wanted to show you how all of
+ 
+
+ align:start position:0%
+because I wanted to show you how all of
+these terms are created just about every
+
+ align:start position:0%
+these terms are created just about every
+ 
+
+ align:start position:0%
+these terms are created just about every
+one of these terms except the external
+
+ align:start position:0%
+one of these terms except the external
+ 
+
+ align:start position:0%
+one of these terms except the external
+source and the flow through some surface
+
+ align:start position:0%
+source and the flow through some surface
+ 
+
+ align:start position:0%
+source and the flow through some surface
+has the form of some multiplier times
+
+ align:start position:0%
+has the form of some multiplier times
+ 
+
+ align:start position:0%
+has the form of some multiplier times
+the integral over all possible variables
+
+ align:start position:0%
+the integral over all possible variables
+ 
+
+ align:start position:0%
+the integral over all possible variables
+that we care about times a reaction rate
+
+ align:start position:0%
+that we care about times a reaction rate
+ 
+
+ align:start position:0%
+that we care about times a reaction rate
+D stuff where this reaction rate is
+
+ align:start position:0%
+D stuff where this reaction rate is
+ 
+
+ align:start position:0%
+D stuff where this reaction rate is
+always going to be some cross-section
+
+ align:start position:0%
+always going to be some cross-section
+ 
+
+ align:start position:0%
+always going to be some cross-section
+times some flux so when you look at this
+
+ align:start position:0%
+times some flux so when you look at this
+ 
+
+ align:start position:0%
+times some flux so when you look at this
+equation using that template it's
+
+ align:start position:0%
+equation using that template it's
+ 
+
+ align:start position:0%
+equation using that template it's
+actually not so bad so let's go through
+
+ align:start position:0%
+actually not so bad so let's go through
+ 
+
+ align:start position:0%
+actually not so bad so let's go through
+each of these pieces right here and then
+
+ align:start position:0%
+each of these pieces right here and then
+ 
+
+ align:start position:0%
+each of these pieces right here and then
+we're going to start simplifying things
+
+ align:start position:0%
+we're going to start simplifying things
+ 
+
+ align:start position:0%
+we're going to start simplifying things
+and this boards going to look like
+
+ align:start position:0%
+and this boards going to look like
+ 
+
+ align:start position:0%
+and this boards going to look like
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+rainbow explosion but all that's gonna
+
+ align:start position:0%
+rainbow explosion but all that's gonna
+ 
+
+ align:start position:0%
+rainbow explosion but all that's gonna
+be left is a much simpler form of the
+
+ align:start position:0%
+be left is a much simpler form of the
+ 
+
+ align:start position:0%
+be left is a much simpler form of the
+neutron diffusion equation so we've got
+
+ align:start position:0%
+neutron diffusion equation so we've got
+ 
+
+ align:start position:0%
+neutron diffusion equation so we've got
+our time dependent term right here where
+
+ align:start position:0%
+our time dependent term right here where
+ 
+
+ align:start position:0%
+our time dependent term right here where
+I've stuck in this variable flux instead
+
+ align:start position:0%
+I've stuck in this variable flux instead
+ 
+
+ align:start position:0%
+I've stuck in this variable flux instead
+of the number of neutrons n because we
+
+ align:start position:0%
+of the number of neutrons n because we
+ 
+
+ align:start position:0%
+of the number of neutrons n because we
+know that flux is the number of neutrons
+
+ align:start position:0%
+know that flux is the number of neutrons
+ 
+
+ align:start position:0%
+know that flux is the number of neutrons
+times the speed V at which they're
+
+ align:start position:0%
+times the speed V at which they're
+ 
+
+ align:start position:0%
+times the speed V at which they're
+moving and just to check our units flux
+
+ align:start position:0%
+moving and just to check our units flux
+ 
+
+ align:start position:0%
+moving and just to check our units flux
+should be in neutrons per centimeter
+
+ align:start position:0%
+should be in neutrons per centimeter
+ 
+
+ align:start position:0%
+should be in neutrons per centimeter
+squared per second and n is in neutrons
+
+ align:start position:0%
+squared per second and n is in neutrons
+ 
+
+ align:start position:0%
+squared per second and n is in neutrons
+per cubic centimeter and velocity is in
+
+ align:start position:0%
+per cubic centimeter and velocity is in
+ 
+
+ align:start position:0%
+per cubic centimeter and velocity is in
+centimeters per second so the unit's
+
+ align:start position:0%
+centimeters per second so the unit's
+ 
+
+ align:start position:0%
+centimeters per second so the unit's
+check out that's why I made that
+
+ align:start position:0%
+check out that's why I made that
+ 
+
+ align:start position:0%
+check out that's why I made that
+substitution right there and this way
+
+ align:start position:0%
+substitution right there and this way
+ 
+
+ align:start position:0%
+substitution right there and this way
+everything is in terms of little Phi the
+
+ align:start position:0%
+everything is in terms of little Phi the
+ 
+
+ align:start position:0%
+everything is in terms of little Phi the
+flux we have our first term here I think
+
+ align:start position:0%
+flux we have our first term here I think
+ 
+
+ align:start position:0%
+flux we have our first term here I think
+I'll have a labeling color that'll make
+
+ align:start position:0%
+I'll have a labeling color that'll make
+ 
+
+ align:start position:0%
+I'll have a labeling color that'll make
+things a little easier to understand
+
+ align:start position:0%
+things a little easier to understand
+ 
+
+ align:start position:0%
+things a little easier to understand
+which is due to a regular old fission in
+
+ align:start position:0%
+which is due to a regular old fission in
+ 
+
+ align:start position:0%
+which is due to a regular old fission in
+this case we have knew the number of
+
+ align:start position:0%
+this case we have knew the number of
+ 
+
+ align:start position:0%
+this case we have knew the number of
+neutrons created per fission times Chi
+
+ align:start position:0%
+neutrons created per fission times Chi
+ 
+
+ align:start position:0%
+neutrons created per fission times Chi
+the sort of the fission births spectrum
+
+ align:start position:0%
+the sort of the fission births spectrum
+ 
+
+ align:start position:0%
+the sort of the fission births spectrum
+or at what energy the neutrons are born
+
+ align:start position:0%
+or at what energy the neutrons are born
+ 
+
+ align:start position:0%
+or at what energy the neutrons are born
+over 4pi to account for all different
+
+ align:start position:0%
+over 4pi to account for all different
+ 
+
+ align:start position:0%
+over 4pi to account for all different
+angles in which they could go out times
+
+ align:start position:0%
+angles in which they could go out times
+ 
+
+ align:start position:0%
+angles in which they could go out times
+the integral over our whole control
+
+ align:start position:0%
+the integral over our whole control
+ 
+
+ align:start position:0%
+the integral over our whole control
+volume and all other energies and angles
+
+ align:start position:0%
+volume and all other energies and angles
+ 
+
+ align:start position:0%
+volume and all other energies and angles
+if you remember now we're trying to
+
+ align:start position:0%
+if you remember now we're trying to
+ 
+
+ align:start position:0%
+if you remember now we're trying to
+track the number of neutrons in some
+
+ align:start position:0%
+track the number of neutrons in some
+ 
+
+ align:start position:0%
+track the number of neutrons in some
+small Energy Group e traveling in some
+
+ align:start position:0%
+small Energy Group e traveling in some
+ 
+
+ align:start position:0%
+small Energy Group e traveling in some
+small direction Omega and those have
+
+ align:start position:0%
+small direction Omega and those have
+ 
+
+ align:start position:0%
+small direction Omega and those have
+little vector things on it at some
+
+ align:start position:0%
+little vector things on it at some
+ 
+
+ align:start position:0%
+little vector things on it at some
+specific position as a function of time
+
+ align:start position:0%
+specific position as a function of time
+ 
+
+ align:start position:0%
+specific position as a function of time
+so in order to figure out how many
+
+ align:start position:0%
+so in order to figure out how many
+ 
+
+ align:start position:0%
+so in order to figure out how many
+neutrons are entering our group from
+
+ align:start position:0%
+neutrons are entering our group from
+ 
+
+ align:start position:0%
+neutrons are entering our group from
+fission we need to know what are all
+
+ align:start position:0%
+fission we need to know what are all
+ 
+
+ align:start position:0%
+fission we need to know what are all
+divisions happening in all the other
+
+ align:start position:0%
+divisions happening in all the other
+ 
+
+ align:start position:0%
+divisions happening in all the other
+groups
+
+ align:start position:0%
+groups
+ 
+
+ align:start position:0%
+groups
+I've also escalated this problem a
+
+ align:start position:0%
+I've also escalated this problem a
+ 
+
+ align:start position:0%
+I've also escalated this problem a
+little bit to not assume that the
+
+ align:start position:0%
+little bit to not assume that the
+ 
+
+ align:start position:0%
+little bit to not assume that the
+reactors homogeneous so I've added an R
+
+ align:start position:0%
+reactors homogeneous so I've added an R
+ 
+
+ align:start position:0%
+reactors homogeneous so I've added an R
+or a spatial dependence for every cross
+
+ align:start position:0%
+or a spatial dependence for every cross
+ 
+
+ align:start position:0%
+or a spatial dependence for every cross
+section here which means that as you
+
+ align:start position:0%
+section here which means that as you
+ 
+
+ align:start position:0%
+section here which means that as you
+move through the reactor you might
+
+ align:start position:0%
+move through the reactor you might
+ 
+
+ align:start position:0%
+move through the reactor you might
+encounter different materials you almost
+
+ align:start position:0%
+encounter different materials you almost
+ 
+
+ align:start position:0%
+encounter different materials you almost
+certainly will unless your reactors been
+
+ align:start position:0%
+certainly will unless your reactors been
+ 
+
+ align:start position:0%
+certainly will unless your reactors been
+in a blender so it except for that case
+
+ align:start position:0%
+in a blender so it except for that case
+ 
+
+ align:start position:0%
+in a blender so it except for that case
+you would actually have different cross
+
+ align:start position:0%
+you would actually have different cross
+ 
+
+ align:start position:0%
+you would actually have different cross
+sections in different parts of the
+
+ align:start position:0%
+sections in different parts of the
+ 
+
+ align:start position:0%
+sections in different parts of the
+reactor so all of a sudden this is
+
+ align:start position:0%
+reactor so all of a sudden this is
+ 
+
+ align:start position:0%
+reactor so all of a sudden this is
+starting to get awfully interesting or
+
+ align:start position:0%
+starting to get awfully interesting or
+ 
+
+ align:start position:0%
+starting to get awfully interesting or
+messy depending on what
+
+ align:start position:0%
+messy depending on what
+ 
+
+ align:start position:0%
+messy depending on what
+want to think about it there's the
+
+ align:start position:0%
+want to think about it there's the
+ 
+
+ align:start position:0%
+want to think about it there's the
+external source which is actually a real
+
+ align:start position:0%
+external source which is actually a real
+ 
+
+ align:start position:0%
+external source which is actually a real
+phenomenon because reactors do stick in
+
+ align:start position:0%
+phenomenon because reactors do stick in
+ 
+
+ align:start position:0%
+phenomenon because reactors do stick in
+those californium kickstarter sources so
+
+ align:start position:0%
+those californium kickstarter sources so
+ 
+
+ align:start position:0%
+those californium kickstarter sources so
+for some amount of time there is an
+
+ align:start position:0%
+for some amount of time there is an
+ 
+
+ align:start position:0%
+for some amount of time there is an
+external source of neutrons giving them
+
+ align:start position:0%
+external source of neutrons giving them
+ 
+
+ align:start position:0%
+external source of neutrons giving them
+out with some positional energy angle
+
+ align:start position:0%
+out with some positional energy angle
+ 
+
+ align:start position:0%
+out with some positional energy angle
+and time dependence so let's call this
+
+ align:start position:0%
+and time dependence so let's call this
+ 
+
+ align:start position:0%
+and time dependence so let's call this
+the Kickstarter source there's this term
+
+ align:start position:0%
+the Kickstarter source there's this term
+ 
+
+ align:start position:0%
+the Kickstarter source there's this term
+right here the n i n reactions so these
+
+ align:start position:0%
+right here the n i n reactions so these
+ 
+
+ align:start position:0%
+right here the n i n reactions so these
+are other reactions where it's absorb a
+
+ align:start position:0%
+are other reactions where it's absorb a
+ 
+
+ align:start position:0%
+are other reactions where it's absorb a
+neutron and give off anywhere between 2
+
+ align:start position:0%
+neutron and give off anywhere between 2
+ 
+
+ align:start position:0%
+neutron and give off anywhere between 2
+& 4 neutrons beyond that there it's just
+
+ align:start position:0%
+& 4 neutrons beyond that there it's just
+ 
+
+ align:start position:0%
+& 4 neutrons beyond that there it's just
+not energetically possible in a fission
+
+ align:start position:0%
+not energetically possible in a fission
+ 
+
+ align:start position:0%
+not energetically possible in a fission
+reactor but don't undergo fission they
+
+ align:start position:0%
+reactor but don't undergo fission they
+ 
+
+ align:start position:0%
+reactor but don't undergo fission they
+have their own cross-sections their own
+
+ align:start position:0%
+have their own cross-sections their own
+ 
+
+ align:start position:0%
+have their own cross-sections their own
+birth spectrum and I've stuck in
+
+ align:start position:0%
+birth spectrum and I've stuck in
+ 
+
+ align:start position:0%
+birth spectrum and I've stuck in
+something right here if we're summing
+
+ align:start position:0%
+something right here if we're summing
+ 
+
+ align:start position:0%
+something right here if we're summing
+over all possible I where you have this
+
+ align:start position:0%
+over all possible I where you have this
+ 
+
+ align:start position:0%
+over all possible I where you have this
+reaction D and I an reaction where one
+
+ align:start position:0%
+reaction D and I an reaction where one
+ 
+
+ align:start position:0%
+reaction D and I an reaction where one
+Neutron goes in and I neutrons come out
+
+ align:start position:0%
+Neutron goes in and I neutrons come out
+ 
+
+ align:start position:0%
+Neutron goes in and I neutrons come out
+you've got to multiply by the number of
+
+ align:start position:0%
+you've got to multiply by the number of
+ 
+
+ align:start position:0%
+you've got to multiply by the number of
+neutrons per reaction for fission that
+
+ align:start position:0%
+neutrons per reaction for fission that
+ 
+
+ align:start position:0%
+neutrons per reaction for fission that
+was new for an ni n reaction that's just
+
+ align:start position:0%
+was new for an ni n reaction that's just
+ 
+
+ align:start position:0%
+was new for an ni n reaction that's just
+AI but otherwise the term looks the same
+
+ align:start position:0%
+AI but otherwise the term looks the same
+ 
+
+ align:start position:0%
+AI but otherwise the term looks the same
+you have your multiplier your birth
+
+ align:start position:0%
+you have your multiplier your birth
+ 
+
+ align:start position:0%
+you have your multiplier your birth
+spectrum your 4pi your integral over
+
+ align:start position:0%
+spectrum your 4pi your integral over
+ 
+
+ align:start position:0%
+spectrum your 4pi your integral over
+stuff your unique cross-section and the
+
+ align:start position:0%
+stuff your unique cross-section and the
+ 
+
+ align:start position:0%
+stuff your unique cross-section and the
+flux and these two together give you a
+
+ align:start position:0%
+flux and these two together give you a
+ 
+
+ align:start position:0%
+flux and these two together give you a
+reaction rate I've just written all of
+
+ align:start position:0%
+reaction rate I've just written all of
+ 
+
+ align:start position:0%
+reaction rate I've just written all of
+the differentials as D stuff because it
+
+ align:start position:0%
+the differentials as D stuff because it
+ 
+
+ align:start position:0%
+the differentials as D stuff because it
+takes a lot of time to write those over
+
+ align:start position:0%
+takes a lot of time to write those over
+ 
+
+ align:start position:0%
+takes a lot of time to write those over
+and over again and then we have our
+
+ align:start position:0%
+and over again and then we have our
+ 
+
+ align:start position:0%
+and over again and then we have our
+photo fission term where gamma rays of
+
+ align:start position:0%
+photo fission term where gamma rays of
+ 
+
+ align:start position:0%
+photo fission term where gamma rays of
+sufficiently high energy can also induce
+
+ align:start position:0%
+sufficiently high energy can also induce
+ 
+
+ align:start position:0%
+sufficiently high energy can also induce
+fission external to the neutrons the
+
+ align:start position:0%
+fission external to the neutrons the
+ 
+
+ align:start position:0%
+fission external to the neutrons the
+term looks exactly the same there's
+
+ align:start position:0%
+term looks exactly the same there's
+ 
+
+ align:start position:0%
+term looks exactly the same there's
+going to be some new for photo fission
+
+ align:start position:0%
+going to be some new for photo fission
+ 
+
+ align:start position:0%
+going to be some new for photo fission
+some birth spectrum for photo fission
+
+ align:start position:0%
+some birth spectrum for photo fission
+ 
+
+ align:start position:0%
+some birth spectrum for photo fission
+some cross-section for photo fission and
+
+ align:start position:0%
+some cross-section for photo fission and
+ 
+
+ align:start position:0%
+some cross-section for photo fission and
+the same flux that we're using
+
+ align:start position:0%
+the same flux that we're using
+ 
+
+ align:start position:0%
+the same flux that we're using
+everywhere else then we had what's
+
+ align:start position:0%
+everywhere else then we had what's
+ 
+
+ align:start position:0%
+everywhere else then we had what's
+called the in scattering term where
+
+ align:start position:0%
+called the in scattering term where
+ 
+
+ align:start position:0%
+called the in scattering term where
+neutrons can undergo scattering lose
+
+ align:start position:0%
+neutrons can undergo scattering lose
+ 
+
+ align:start position:0%
+neutrons can undergo scattering lose
+some energy and enter our group from
+
+ align:start position:0%
+some energy and enter our group from
+ 
+
+ align:start position:0%
+some energy and enter our group from
+somewhere else
+
+ align:start position:0%
+somewhere else
+ 
+
+ align:start position:0%
+somewhere else
+that's why we have those Ian Omega
+
+ align:start position:0%
+that's why we have those Ian Omega
+ 
+
+ align:start position:0%
+that's why we have those Ian Omega
+Prime's because it's some other energy
+
+ align:start position:0%
+Prime's because it's some other energy
+ 
+
+ align:start position:0%
+Prime's because it's some other energy
+and we have to account for all of those
+
+ align:start position:0%
+and we have to account for all of those
+ 
+
+ align:start position:0%
+and we have to account for all of those
+energy groups that's why we have this
+
+ align:start position:0%
+energy groups that's why we have this
+ 
+
+ align:start position:0%
+energy groups that's why we have this
+integral there and it looks very much
+
+ align:start position:0%
+integral there and it looks very much
+ 
+
+ align:start position:0%
+integral there and it looks very much
+the same there's a scattering
+
+ align:start position:0%
+the same there's a scattering
+ 
+
+ align:start position:0%
+the same there's a scattering
+cross-section and those should actually
+
+ align:start position:0%
+cross-section and those should actually
+ 
+
+ align:start position:0%
+cross-section and those should actually
+be it should be an e Prime right there
+
+ align:start position:0%
+be it should be an e Prime right there
+ 
+
+ align:start position:0%
+be it should be an e Prime right there
+make sure I'm not missing any more of
+
+ align:start position:0%
+make sure I'm not missing any more of
+ 
+
+ align:start position:0%
+make sure I'm not missing any more of
+those inside the integral that's all
+
+ align:start position:0%
+those inside the integral that's all
+ 
+
+ align:start position:0%
+those inside the integral that's all
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+that's a prime good there's also a flux
+
+ align:start position:0%
+that's a prime good there's also a flux
+ 
+
+ align:start position:0%
+that's a prime good there's also a flux
+and then there was this probability
+
+ align:start position:0%
+and then there was this probability
+ 
+
+ align:start position:0%
+and then there was this probability
+function that a given Neutron starting
+
+ align:start position:0%
+function that a given Neutron starting
+ 
+
+ align:start position:0%
+function that a given Neutron starting
+off at energy E prime Omega prime ends
+
+ align:start position:0%
+off at energy E prime Omega prime ends
+ 
+
+ align:start position:0%
+off at energy E prime Omega prime ends
+up scattering into our energy in Omega
+
+ align:start position:0%
+up scattering into our energy in Omega
+ 
+
+ align:start position:0%
+up scattering into our energy in Omega
+so this would be the other one and this
+
+ align:start position:0%
+so this would be the other one and this
+ 
+
+ align:start position:0%
+so this would be the other one and this
+would be our group but otherwise the
+
+ align:start position:0%
+would be our group but otherwise the
+ 
+
+ align:start position:0%
+would be our group but otherwise the
+term looks very much the same and that
+
+ align:start position:0%
+term looks very much the same and that
+ 
+
+ align:start position:0%
+term looks very much the same and that
+takes care of all the possible gains of
+
+ align:start position:0%
+takes care of all the possible gains of
+ 
+
+ align:start position:0%
+takes care of all the possible gains of
+neutrons into our group the losses are a
+
+ align:start position:0%
+neutrons into our group the losses are a
+ 
+
+ align:start position:0%
+neutrons into our group the losses are a
+fair bit simpler there's reaction of
+
+ align:start position:0%
+fair bit simpler there's reaction of
+ 
+
+ align:start position:0%
+fair bit simpler there's reaction of
+absolutely any kind let's say this would
+
+ align:start position:0%
+absolutely any kind let's say this would
+ 
+
+ align:start position:0%
+absolutely any kind let's say this would
+be the total cross-section which says
+
+ align:start position:0%
+be the total cross-section which says
+ 
+
+ align:start position:0%
+be the total cross-section which says
+that if a neutron undergoes any reaction
+
+ align:start position:0%
+that if a neutron undergoes any reaction
+ 
+
+ align:start position:0%
+that if a neutron undergoes any reaction
+at all it's going to lose energy and go
+
+ align:start position:0%
+at all it's going to lose energy and go
+ 
+
+ align:start position:0%
+at all it's going to lose energy and go
+out of our energy group de notice here
+
+ align:start position:0%
+out of our energy group de notice here
+ 
+
+ align:start position:0%
+out of our energy group de notice here
+that these are all these energies and
+
+ align:start position:0%
+that these are all these energies and
+ 
+
+ align:start position:0%
+that these are all these energies and
+omegas are all our group because we only
+
+ align:start position:0%
+omegas are all our group because we only
+ 
+
+ align:start position:0%
+omegas are all our group because we only
+care about how many neutrons in our
+
+ align:start position:0%
+care about how many neutrons in our
+ 
+
+ align:start position:0%
+care about how many neutrons in our
+group undergo a reaction and leaf and
+
+ align:start position:0%
+group undergo a reaction and leaf and
+ 
+
+ align:start position:0%
+group undergo a reaction and leaf and
+the form is very simple integrate over
+
+ align:start position:0%
+the form is very simple integrate over
+ 
+
+ align:start position:0%
+the form is very simple integrate over
+volume energy in and Direction times a
+
+ align:start position:0%
+volume energy in and Direction times a
+ 
+
+ align:start position:0%
+volume energy in and Direction times a
+cross section times the flux just like
+
+ align:start position:0%
+cross section times the flux just like
+ 
+
+ align:start position:0%
+cross section times the flux just like
+all the other ones then the only
+
+ align:start position:0%
+all the other ones then the only
+ 
+
+ align:start position:0%
+all the other ones then the only
+difference and one right here is what
+
+ align:start position:0%
+difference and one right here is what
+ 
+
+ align:start position:0%
+difference and one right here is what
+we'll call leakage these are neutrons
+
+ align:start position:0%
+we'll call leakage these are neutrons
+ 
+
+ align:start position:0%
+we'll call leakage these are neutrons
+moving out of whatever control surface
+
+ align:start position:0%
+moving out of whatever control surface
+ 
+
+ align:start position:0%
+moving out of whatever control surface
+that we're looking at and this can be
+
+ align:start position:0%
+that we're looking at and this can be
+ 
+
+ align:start position:0%
+that we're looking at and this can be
+some arbitrarily complex control surface
+
+ align:start position:0%
+some arbitrarily complex control surface
+ 
+
+ align:start position:0%
+some arbitrarily complex control surface
+in 3d I don't really know how to draw a
+
+ align:start position:0%
+in 3d I don't really know how to draw a
+ 
+
+ align:start position:0%
+in 3d I don't really know how to draw a
+blob in 3d but at every point on that
+
+ align:start position:0%
+blob in 3d but at every point on that
+ 
+
+ align:start position:0%
+blob in 3d but at every point on that
+glob there's going to be a normal vector
+
+ align:start position:0%
+glob there's going to be a normal vector
+ 
+
+ align:start position:0%
+glob there's going to be a normal vector
+and you can then take the current of
+
+ align:start position:0%
+and you can then take the current of
+ 
+
+ align:start position:0%
+and you can then take the current of
+neutrons traveling out that normal
+
+ align:start position:0%
+neutrons traveling out that normal
+ 
+
+ align:start position:0%
+neutrons traveling out that normal
+vector and figure out how much of that
+
+ align:start position:0%
+vector and figure out how much of that
+ 
+
+ align:start position:0%
+vector and figure out how much of that
+is actually leaving our surface DS the
+
+ align:start position:0%
+is actually leaving our surface DS the
+ 
+
+ align:start position:0%
+is actually leaving our surface DS the
+one problem we had is that everything
+
+ align:start position:0%
+one problem we had is that everything
+ 
+
+ align:start position:0%
+one problem we had is that everything
+here is in terms of volume volume volume
+
+ align:start position:0%
+here is in terms of volume volume volume
+ 
+
+ align:start position:0%
+here is in terms of volume volume volume
+surface so we don't have all the same
+
+ align:start position:0%
+surface so we don't have all the same
+ 
+
+ align:start position:0%
+surface so we don't have all the same
+terms because once we have everything in
+
+ align:start position:0%
+terms because once we have everything in
+ 
+
+ align:start position:0%
+terms because once we have everything in
+the same variables we can start to make
+
+ align:start position:0%
+the same variables we can start to make
+ 
+
+ align:start position:0%
+the same variables we can start to make
+some pretty crazy simplifications the
+
+ align:start position:0%
+some pretty crazy simplifications the
+ 
+
+ align:start position:0%
+some pretty crazy simplifications the
+last thing we did is we invoked the
+
+ align:start position:0%
+last thing we did is we invoked the
+ 
+
+ align:start position:0%
+last thing we did is we invoked the
+divergence theorem that says that the
+
+ align:start position:0%
+divergence theorem that says that the
+ 
+
+ align:start position:0%
+divergence theorem that says that the
+surface integral of some variable f DS
+
+ align:start position:0%
+surface integral of some variable f DS
+ 
+
+ align:start position:0%
+surface integral of some variable f DS
+is the same as the volume integral of
+
+ align:start position:0%
+is the same as the volume integral of
+ 
+
+ align:start position:0%
+is the same as the volume integral of
+the divergence of that variable DV so I
+
+ align:start position:0%
+the divergence of that variable DV so I
+ 
+
+ align:start position:0%
+the divergence of that variable DV so I
+remember there was some snickering last
+
+ align:start position:0%
+remember there was some snickering last
+ 
+
+ align:start position:0%
+remember there was some snickering last
+time because you probably haven't seen
+
+ align:start position:0%
+time because you probably haven't seen
+ 
+
+ align:start position:0%
+time because you probably haven't seen
+this since was it 1801 or 1802 1802 okay
+
+ align:start position:0%
+this since was it 1801 or 1802 1802 okay
+ 
+
+ align:start position:0%
+this since was it 1801 or 1802 1802 okay
+that makes sense because divergence
+
+ align:start position:0%
+that makes sense because divergence
+ 
+
+ align:start position:0%
+that makes sense because divergence
+usually has more than one variable
+
+ align:start position:0%
+usually has more than one variable
+ 
+
+ align:start position:0%
+usually has more than one variable
+associated with it I'll include the dot
+
+ align:start position:0%
+associated with it I'll include the dot
+ 
+
+ align:start position:0%
+associated with it I'll include the dot
+because that's what makes it divergence
+
+ align:start position:0%
+because that's what makes it divergence
+ 
+
+ align:start position:0%
+because that's what makes it divergence
+so we can then rewrite this term let's
+
+ align:start position:0%
+so we can then rewrite this term let's
+ 
+
+ align:start position:0%
+so we can then rewrite this term let's
+start our simplification colors that's
+
+ align:start position:0%
+start our simplification colors that's
+ 
+
+ align:start position:0%
+start our simplification colors that's
+our divergence theorem so let's get rid
+
+ align:start position:0%
+our divergence theorem so let's get rid
+ 
+
+ align:start position:0%
+our divergence theorem so let's get rid
+of it in this form and call it minus
+
+ align:start position:0%
+of it in this form and call it minus
+ 
+
+ align:start position:0%
+of it in this form and call it minus
+integral over all that stuff then we'll
+
+ align:start position:0%
+integral over all that stuff then we'll
+ 
+
+ align:start position:0%
+integral over all that stuff then we'll
+have del dot little J to be careful R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega T so for every step I'm going to
+
+ align:start position:0%
+Omega T so for every step I'm going to
+ 
+
+ align:start position:0%
+Omega T so for every step I'm going to
+use a different color so you can see
+
+ align:start position:0%
+use a different color so you can see
+ 
+
+ align:start position:0%
+use a different color so you can see
+which simplification led to how much
+
+ align:start position:0%
+which simplification led to how much
+ 
+
+ align:start position:0%
+which simplification led to how much
+crossing stuff out and so like I said
+
+ align:start position:0%
+crossing stuff out and so like I said
+ 
+
+ align:start position:0%
+crossing stuff out and so like I said
+this board is gonna look like a rainbow
+
+ align:start position:0%
+this board is gonna look like a rainbow
+ 
+
+ align:start position:0%
+this board is gonna look like a rainbow
+explosion but then we'll rewrite it at
+
+ align:start position:0%
+explosion but then we'll rewrite it at
+ 
+
+ align:start position:0%
+explosion but then we'll rewrite it at
+the end and it's gonna look a whole lot
+
+ align:start position:0%
+the end and it's gonna look a whole lot
+ 
+
+ align:start position:0%
+the end and it's gonna look a whole lot
+simpler so now let's start making some
+
+ align:start position:0%
+simpler so now let's start making some
+ 
+
+ align:start position:0%
+simpler so now let's start making some
+simplifications let's say you're an
+
+ align:start position:0%
+simplifications let's say you're an
+ 
+
+ align:start position:0%
+simplifications let's say you're an
+actual reactor designer and all you care
+
+ align:start position:0%
+actual reactor designer and all you care
+ 
+
+ align:start position:0%
+actual reactor designer and all you care
+about is how many neutrons are here of
+
+ align:start position:0%
+about is how many neutrons are here of
+ 
+
+ align:start position:0%
+about is how many neutrons are here of
+the variables here which one do you
+
+ align:start position:0%
+the variables here which one do you
+ 
+
+ align:start position:0%
+the variables here which one do you
+think we care the least about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle I mean do we really care which
+
+ align:start position:0%
+angle I mean do we really care which
+ 
+
+ align:start position:0%
+angle I mean do we really care which
+direction the neutrons are going no we
+
+ align:start position:0%
+direction the neutrons are going no we
+ 
+
+ align:start position:0%
+direction the neutrons are going no we
+pretty much care where are they and are
+
+ align:start position:0%
+pretty much care where are they and are
+ 
+
+ align:start position:0%
+pretty much care where are they and are
+they causing fission or getting absorbed
+
+ align:start position:0%
+they causing fission or getting absorbed
+ 
+
+ align:start position:0%
+they causing fission or getting absorbed
+so let's start our simplification board
+
+ align:start position:0%
+so let's start our simplification board
+ 
+
+ align:start position:0%
+so let's start our simplification board
+and in blue neglect angle this is where
+
+ align:start position:0%
+and in blue neglect angle this is where
+ 
+
+ align:start position:0%
+and in blue neglect angle this is where
+it starts to get fun so in this case we
+
+ align:start position:0%
+it starts to get fun so in this case we
+ 
+
+ align:start position:0%
+it starts to get fun so in this case we
+will just perform the Omega integral
+
+ align:start position:0%
+will just perform the Omega integral
+ 
+
+ align:start position:0%
+will just perform the Omega integral
+over all angles we just neglect angle
+
+ align:start position:0%
+over all angles we just neglect angle
+ 
+
+ align:start position:0%
+over all angles we just neglect angle
+here we forget the Omega integral forget
+
+ align:start position:0%
+here we forget the Omega integral forget
+ 
+
+ align:start position:0%
+here we forget the Omega integral forget
+Omega there away goes the 4 pi because
+
+ align:start position:0%
+Omega there away goes the 4 pi because
+ 
+
+ align:start position:0%
+Omega there away goes the 4 pi because
+we've integrated over all 4 pi star ad
+
+ align:start position:0%
+we've integrated over all 4 pi star ad
+ 
+
+ align:start position:0%
+we've integrated over all 4 pi star ad
+ins or all solid angle and let's just
+
+ align:start position:0%
+ins or all solid angle and let's just
+ 
+
+ align:start position:0%
+ins or all solid angle and let's just
+keep going
+
+ align:start position:0%
+keep going
+ 
+
+ align:start position:0%
+keep going
+forget the 4 pi forget the Omega forget
+
+ align:start position:0%
+forget the 4 pi forget the Omega forget
+ 
+
+ align:start position:0%
+forget the 4 pi forget the Omega forget
+the Omega forget the 4 PI and the Omega
+
+ align:start position:0%
+the Omega forget the 4 PI and the Omega
+ 
+
+ align:start position:0%
+the Omega forget the 4 PI and the Omega
+and the Omega same thing here
+
+ align:start position:0%
+and the Omega same thing here
+ 
+
+ align:start position:0%
+and the Omega same thing here
+forget the Omega in the scattering
+
+ align:start position:0%
+forget the Omega in the scattering
+ 
+
+ align:start position:0%
+forget the Omega in the scattering
+kernel forget it in the flux forget it
+
+ align:start position:0%
+kernel forget it in the flux forget it
+ 
+
+ align:start position:0%
+kernel forget it in the flux forget it
+there forget it there and there as well
+
+ align:start position:0%
+there forget it there and there as well
+ 
+
+ align:start position:0%
+there forget it there and there as well
+okay we've now completely eliminated one
+
+ align:start position:0%
+okay we've now completely eliminated one
+ 
+
+ align:start position:0%
+okay we've now completely eliminated one
+variable and all we had to do is ditch
+
+ align:start position:0%
+variable and all we had to do is ditch
+ 
+
+ align:start position:0%
+variable and all we had to do is ditch
+the for PI's and one of the integrals
+
+ align:start position:0%
+the for PI's and one of the integrals
+ 
+
+ align:start position:0%
+the for PI's and one of the integrals
+what next we're tracking right now every
+
+ align:start position:0%
+what next we're tracking right now every
+ 
+
+ align:start position:0%
+what next we're tracking right now every
+possible position every possible energy
+
+ align:start position:0%
+possible position every possible energy
+ 
+
+ align:start position:0%
+possible position every possible energy
+at every possible time if you want to
+
+ align:start position:0%
+at every possible time if you want to
+ 
+
+ align:start position:0%
+at every possible time if you want to
+know what is your flux going to be in
+
+ align:start position:0%
+know what is your flux going to be in
+ 
+
+ align:start position:0%
+know what is your flux going to be in
+the reactor at steady state what
+
+ align:start position:0%
+the reactor at steady state what
+ 
+
+ align:start position:0%
+the reactor at steady state what
+variable do you attack next yep time so
+
+ align:start position:0%
+variable do you attack next yep time so
+ 
+
+ align:start position:0%
+variable do you attack next yep time so
+let's just say this reactor is at steady
+
+ align:start position:0%
+let's just say this reactor is at steady
+ 
+
+ align:start position:0%
+let's just say this reactor is at steady
+state that's going to invoke a few
+
+ align:start position:0%
+state that's going to invoke a few
+ 
+
+ align:start position:0%
+state that's going to invoke a few
+things for one it's going to ditch the
+
+ align:start position:0%
+things for one it's going to ditch the
+ 
+
+ align:start position:0%
+things for one it's going to ditch the
+entire steady state term we're gonna get
+
+ align:start position:0%
+entire steady state term we're gonna get
+ 
+
+ align:start position:0%
+entire steady state term we're gonna get
+rid of all the T's in all the fluxes
+
+ align:start position:0%
+rid of all the T's in all the fluxes
+ 
+
+ align:start position:0%
+rid of all the T's in all the fluxes
+this shouldn't take too long to do I
+
+ align:start position:0%
+this shouldn't take too long to do I
+ 
+
+ align:start position:0%
+this shouldn't take too long to do I
+think that's all of them and the third
+
+ align:start position:0%
+think that's all of them and the third
+ 
+
+ align:start position:0%
+think that's all of them and the third
+thing is if this reactor is at steady
+
+ align:start position:0%
+thing is if this reactor is at steady
+ 
+
+ align:start position:0%
+thing is if this reactor is at steady
+state chances are we've taken our
+
+ align:start position:0%
+state chances are we've taken our
+ 
+
+ align:start position:0%
+state chances are we've taken our
+Kickstarter source out because we just
+
+ align:start position:0%
+Kickstarter source out because we just
+ 
+
+ align:start position:0%
+Kickstarter source out because we just
+needed it to get it going but the
+
+ align:start position:0%
+needed it to get it going but the
+ 
+
+ align:start position:0%
+needed it to get it going but the
+reactor should be self-sustaining once
+
+ align:start position:0%
+reactor should be self-sustaining once
+ 
+
+ align:start position:0%
+reactor should be self-sustaining once
+it's at steady state so let's just get
+
+ align:start position:0%
+it's at steady state so let's just get
+ 
+
+ align:start position:0%
+it's at steady state so let's just get
+rid of our source term so you just want
+
+ align:start position:0%
+rid of our source term so you just want
+ 
+
+ align:start position:0%
+rid of our source term so you just want
+to make sure I didn't miss any here okay
+
+ align:start position:0%
+to make sure I didn't miss any here okay
+ 
+
+ align:start position:0%
+to make sure I didn't miss any here okay
+next up go with green what else do you
+
+ align:start position:0%
+next up go with green what else do you
+ 
+
+ align:start position:0%
+next up go with green what else do you
+think we can simplify about this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if you look far enough away from
+
+ align:start position:0%
+well if you look far enough away from
+ 
+
+ align:start position:0%
+well if you look far enough away from
+the reactor we can make an assumption
+
+ align:start position:0%
+the reactor we can make an assumption
+ 
+
+ align:start position:0%
+the reactor we can make an assumption
+that the reactor is roughly homogeneous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in some cases it's not so good of an
+
+ align:start position:0%
+in some cases it's not so good of an
+ 
+
+ align:start position:0%
+in some cases it's not so good of an
+assumption like very close to anything
+
+ align:start position:0%
+assumption like very close to anything
+ 
+
+ align:start position:0%
+assumption like very close to anything
+that has a huge absorption cross-section
+
+ align:start position:0%
+that has a huge absorption cross-section
+ 
+
+ align:start position:0%
+that has a huge absorption cross-section
+now I want to explain the physics behind
+
+ align:start position:0%
+now I want to explain the physics behind
+ 
+
+ align:start position:0%
+now I want to explain the physics behind
+this if the neutrons travel a very long
+
+ align:start position:0%
+this if the neutrons travel a very long
+ 
+
+ align:start position:0%
+this if the neutrons travel a very long
+distance through any group of materials
+
+ align:start position:0%
+distance through any group of materials
+ 
+
+ align:start position:0%
+distance through any group of materials
+then those materials will appear to be
+
+ align:start position:0%
+then those materials will appear to be
+ 
+
+ align:start position:0%
+then those materials will appear to be
+roughly homogeneous to the neutrons if
+
+ align:start position:0%
+roughly homogeneous to the neutrons if
+ 
+
+ align:start position:0%
+roughly homogeneous to the neutrons if
+however the neutrons travel through
+
+ align:start position:0%
+however the neutrons travel through
+ 
+
+ align:start position:0%
+however the neutrons travel through
+something that's very different from the
+
+ align:start position:0%
+something that's very different from the
+ 
+
+ align:start position:0%
+something that's very different from the
+materials around it then that
+
+ align:start position:0%
+materials around it then that
+ 
+
+ align:start position:0%
+materials around it then that
+homogeneous assumption breaks down so in
+
+ align:start position:0%
+homogeneous assumption breaks down so in
+ 
+
+ align:start position:0%
+homogeneous assumption breaks down so in
+what locations in a nuclear reactor do
+
+ align:start position:0%
+what locations in a nuclear reactor do
+ 
+
+ align:start position:0%
+what locations in a nuclear reactor do
+you think you cannot treat the system is
+
+ align:start position:0%
+you think you cannot treat the system is
+ 
+
+ align:start position:0%
+you think you cannot treat the system is
+homogeneous where do the properties of
+
+ align:start position:0%
+homogeneous where do the properties of
+ 
+
+ align:start position:0%
+homogeneous where do the properties of
+materials suddenly change by a huge
+
+ align:start position:0%
+materials suddenly change by a huge
+ 
+
+ align:start position:0%
+materials suddenly change by a huge
+amount yeah Luke control rods right so
+
+ align:start position:0%
+amount yeah Luke control rods right so
+ 
+
+ align:start position:0%
+amount yeah Luke control rods right so
+let's say it's bad for control rods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how about the fuel all of a sudden
+
+ align:start position:0%
+how about the fuel all of a sudden
+ 
+
+ align:start position:0%
+how about the fuel all of a sudden
+you're moving from a bunch of structural
+
+ align:start position:0%
+you're moving from a bunch of structural
+ 
+
+ align:start position:0%
+you're moving from a bunch of structural
+materials where Sigma fission equals
+
+ align:start position:0%
+materials where Sigma fission equals
+ 
+
+ align:start position:0%
+materials where Sigma fission equals
+zero to the fuel where Sigma fission
+
+ align:start position:0%
+zero to the fuel where Sigma fission
+ 
+
+ align:start position:0%
+zero to the fuel where Sigma fission
+like you saw in the test can be like
+
+ align:start position:0%
+like you saw in the test can be like
+ 
+
+ align:start position:0%
+like you saw in the test can be like
+five hundred barns which even though
+
+ align:start position:0%
+five hundred barns which even though
+ 
+
+ align:start position:0%
+five hundred barns which even though
+it's got a very small exponent in front
+
+ align:start position:0%
+it's got a very small exponent in front
+ 
+
+ align:start position:0%
+it's got a very small exponent in front
+of it ten to the minus 22 centimeters
+
+ align:start position:0%
+of it ten to the minus 22 centimeters
+ 
+
+ align:start position:0%
+of it ten to the minus 22 centimeters
+squared it's still pretty significant so
+
+ align:start position:0%
+squared it's still pretty significant so
+ 
+
+ align:start position:0%
+squared it's still pretty significant so
+this assumption breaks down around the
+
+ align:start position:0%
+this assumption breaks down around the
+ 
+
+ align:start position:0%
+this assumption breaks down around the
+control rods and around the fuel but we
+
+ align:start position:0%
+control rods and around the fuel but we
+ 
+
+ align:start position:0%
+control rods and around the fuel but we
+can get around this let's analyze the
+
+ align:start position:0%
+can get around this let's analyze the
+ 
+
+ align:start position:0%
+can get around this let's analyze the
+simplest crazy as possible reactor which
+
+ align:start position:0%
+simplest crazy as possible reactor which
+ 
+
+ align:start position:0%
+simplest crazy as possible reactor which
+would be a molten salt fueled reactor
+
+ align:start position:0%
+would be a molten salt fueled reactor
+ 
+
+ align:start position:0%
+would be a molten salt fueled reactor
+it's just a blob of 700 Celsius goo
+
+ align:start position:0%
+it's just a blob of 700 Celsius goo
+ 
+
+ align:start position:0%
+it's just a blob of 700 Celsius goo
+that's got its fuel coolant and control
+
+ align:start position:0%
+that's got its fuel coolant and control
+ 
+
+ align:start position:0%
+that's got its fuel coolant and control
+rods all built in so if we assume that
+
+ align:start position:0%
+rods all built in so if we assume that
+ 
+
+ align:start position:0%
+rods all built in so if we assume that
+the reactor is homogeneous which is a
+
+ align:start position:0%
+the reactor is homogeneous which is a
+ 
+
+ align:start position:0%
+the reactor is homogeneous which is a
+pretty good assumption for molten salt
+
+ align:start position:0%
+pretty good assumption for molten salt
+ 
+
+ align:start position:0%
+pretty good assumption for molten salt
+fueled reactors because the fuels
+
+ align:start position:0%
+fueled reactors because the fuels
+ 
+
+ align:start position:0%
+fueled reactors because the fuels
+dissolved in the coolant and it builds
+
+ align:start position:0%
+dissolved in the coolant and it builds
+ 
+
+ align:start position:0%
+dissolved in the coolant and it builds
+up its own fission product poisons so
+
+ align:start position:0%
+up its own fission product poisons so
+ 
+
+ align:start position:0%
+up its own fission product poisons so
+it's got some of its own control rods
+
+ align:start position:0%
+it's got some of its own control rods
+ 
+
+ align:start position:0%
+it's got some of its own control rods
+kind of built in usually will have other
+
+ align:start position:0%
+kind of built in usually will have other
+ 
+
+ align:start position:0%
+kind of built in usually will have other
+extra ones too but whatever then we can
+
+ align:start position:0%
+extra ones too but whatever then we can
+ 
+
+ align:start position:0%
+extra ones too but whatever then we can
+start to really simplify things if we
+
+ align:start position:0%
+start to really simplify things if we
+ 
+
+ align:start position:0%
+start to really simplify things if we
+get rid of any homogeneity assumptions
+
+ align:start position:0%
+get rid of any homogeneity assumptions
+ 
+
+ align:start position:0%
+get rid of any homogeneity assumptions
+we cannot necessarily get rid of the R
+
+ align:start position:0%
+we cannot necessarily get rid of the R
+ 
+
+ align:start position:0%
+we cannot necessarily get rid of the R
+in the flux because even if the reactors
+
+ align:start position:0%
+in the flux because even if the reactors
+ 
+
+ align:start position:0%
+in the flux because even if the reactors
+homogeneous it still might have
+
+ align:start position:0%
+homogeneous it still might have
+ 
+
+ align:start position:0%
+homogeneous it still might have
+boundaries so you might be able to
+
+ align:start position:0%
+boundaries so you might be able to
+ 
+
+ align:start position:0%
+boundaries so you might be able to
+approximate it as just a cylinder or a
+
+ align:start position:0%
+approximate it as just a cylinder or a
+ 
+
+ align:start position:0%
+approximate it as just a cylinder or a
+slab of uniform materials but if we were
+
+ align:start position:0%
+slab of uniform materials but if we were
+ 
+
+ align:start position:0%
+slab of uniform materials but if we were
+to get rid of the R's in the flux term
+
+ align:start position:0%
+to get rid of the R's in the flux term
+ 
+
+ align:start position:0%
+to get rid of the R's in the flux term
+that would mean that as we graph flux as
+
+ align:start position:0%
+that would mean that as we graph flux as
+ 
+
+ align:start position:0%
+that would mean that as we graph flux as
+a function of distance it would look
+
+ align:start position:0%
+a function of distance it would look
+ 
+
+ align:start position:0%
+a function of distance it would look
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+including infinitely far away from the
+
+ align:start position:0%
+including infinitely far away from the
+ 
+
+ align:start position:0%
+including infinitely far away from the
+reactor and now is that true absolutely
+
+ align:start position:0%
+reactor and now is that true absolutely
+ 
+
+ align:start position:0%
+reactor and now is that true absolutely
+not so I don't want to leave that up for
+
+ align:start position:0%
+not so I don't want to leave that up for
+ 
+
+ align:start position:0%
+not so I don't want to leave that up for
+anyone we'll fill in what these graphs
+
+ align:start position:0%
+anyone we'll fill in what these graphs
+ 
+
+ align:start position:0%
+anyone we'll fill in what these graphs
+look like a little later just leave them
+
+ align:start position:0%
+look like a little later just leave them
+ 
+
+ align:start position:0%
+look like a little later just leave them
+there for now we can get rid of some of
+
+ align:start position:0%
+there for now we can get rid of some of
+ 
+
+ align:start position:0%
+there for now we can get rid of some of
+the other ARS though like these
+
+ align:start position:0%
+the other ARS though like these
+ 
+
+ align:start position:0%
+the other ARS though like these
+cross-sections if the reactor is
+
+ align:start position:0%
+cross-sections if the reactor is
+ 
+
+ align:start position:0%
+cross-sections if the reactor is
+actually homogeneous then the
+
+ align:start position:0%
+actually homogeneous then the
+ 
+
+ align:start position:0%
+actually homogeneous then the
+cross-section is the same everywhere
+
+ align:start position:0%
+cross-section is the same everywhere
+ 
+
+ align:start position:0%
+cross-section is the same everywhere
+because the materials are the same
+
+ align:start position:0%
+because the materials are the same
+ 
+
+ align:start position:0%
+because the materials are the same
+everywhere so we can get rid of the ARS
+
+ align:start position:0%
+everywhere so we can get rid of the ARS
+ 
+
+ align:start position:0%
+everywhere so we can get rid of the ARS
+here the R's here and there and there
+
+ align:start position:0%
+here the R's here and there and there
+ 
+
+ align:start position:0%
+here the R's here and there and there
+and that's it I think don't think I
+
+ align:start position:0%
+and that's it I think don't think I
+ 
+
+ align:start position:0%
+and that's it I think don't think I
+missed any good next up if this reactors
+
+ align:start position:0%
+missed any good next up if this reactors
+ 
+
+ align:start position:0%
+missed any good next up if this reactors
+homogeneous then does it really matter
+
+ align:start position:0%
+homogeneous then does it really matter
+ 
+
+ align:start position:0%
+homogeneous then does it really matter
+at which location were taking this
+
+ align:start position:0%
+at which location were taking this
+ 
+
+ align:start position:0%
+at which location were taking this
+balance does it really matter which
+
+ align:start position:0%
+balance does it really matter which
+ 
+
+ align:start position:0%
+balance does it really matter which
+little volume element we're looking at
+
+ align:start position:0%
+little volume element we're looking at
+ 
+
+ align:start position:0%
+little volume element we're looking at
+we say these equations are will call
+
+ align:start position:0%
+we say these equations are will call
+ 
+
+ align:start position:0%
+we say these equations are will call
+them volume identical which means if
+
+ align:start position:0%
+them volume identical which means if
+ 
+
+ align:start position:0%
+them volume identical which means if
+this same equation is satisfied at any
+
+ align:start position:0%
+this same equation is satisfied at any
+ 
+
+ align:start position:0%
+this same equation is satisfied at any
+point in the reactor we don't need to do
+
+ align:start position:0%
+point in the reactor we don't need to do
+ 
+
+ align:start position:0%
+point in the reactor we don't need to do
+the volume integral over the whole
+
+ align:start position:0%
+the volume integral over the whole
+ 
+
+ align:start position:0%
+the volume integral over the whole
+reactor it's not like it's gonna change
+
+ align:start position:0%
+reactor it's not like it's gonna change
+ 
+
+ align:start position:0%
+reactor it's not like it's gonna change
+anywhere we go so forget the volume
+
+ align:start position:0%
+anywhere we go so forget the volume
+ 
+
+ align:start position:0%
+anywhere we go so forget the volume
+integrals hopefully you guys see where
+
+ align:start position:0%
+integrals hopefully you guys see where
+ 
+
+ align:start position:0%
+integrals hopefully you guys see where
+I'm going with this and I've never I've
+
+ align:start position:0%
+I'm going with this and I've never I've
+ 
+
+ align:start position:0%
+I'm going with this and I've never I've
+never tried teaching it like this
+
+ align:start position:0%
+never tried teaching it like this
+ 
+
+ align:start position:0%
+never tried teaching it like this
+rainbow explosion before but I'm kind of
+
+ align:start position:0%
+rainbow explosion before but I'm kind of
+ 
+
+ align:start position:0%
+rainbow explosion before but I'm kind of
+excited to see how it turns out
+
+ align:start position:0%
+excited to see how it turns out
+ 
+
+ align:start position:0%
+excited to see how it turns out
+so already like 2/3 of the stuff that we
+
+ align:start position:0%
+so already like 2/3 of the stuff that we
+ 
+
+ align:start position:0%
+so already like 2/3 of the stuff that we
+had written are gone what's the only
+
+ align:start position:0%
+had written are gone what's the only
+ 
+
+ align:start position:0%
+had written are gone what's the only
+variable left that we can go after and
+
+ align:start position:0%
+variable left that we can go after and
+ 
+
+ align:start position:0%
+variable left that we can go after and
+what's the only color left that I
+
+ align:start position:0%
+what's the only color left that I
+ 
+
+ align:start position:0%
+what's the only color left that I
+haven't really used energy yeah so we
+
+ align:start position:0%
+haven't really used energy yeah so we
+ 
+
+ align:start position:0%
+haven't really used energy yeah so we
+can make a couple of us different
+
+ align:start position:0%
+can make a couple of us different
+ 
+
+ align:start position:0%
+can make a couple of us different
+assumptions this equation as it is is
+
+ align:start position:0%
+assumptions this equation as it is is
+ 
+
+ align:start position:0%
+assumptions this equation as it is is
+not yet really analytically solvable
+
+ align:start position:0%
+not yet really analytically solvable
+ 
+
+ align:start position:0%
+not yet really analytically solvable
+because a lot of these energy dependent
+
+ align:start position:0%
+because a lot of these energy dependent
+ 
+
+ align:start position:0%
+because a lot of these energy dependent
+terms don't have analytical solutions or
+
+ align:start position:0%
+terms don't have analytical solutions or
+ 
+
+ align:start position:0%
+terms don't have analytical solutions or
+even forms like the cross-sections but
+
+ align:start position:0%
+even forms like the cross-sections but
+ 
+
+ align:start position:0%
+even forms like the cross-sections but
+we can start attacking energy hopefully
+
+ align:start position:0%
+we can start attacking energy hopefully
+ 
+
+ align:start position:0%
+we can start attacking energy hopefully
+this is different enough from white yeah
+
+ align:start position:0%
+this is different enough from white yeah
+ 
+
+ align:start position:0%
+this is different enough from white yeah
+is that big enough difference for you
+
+ align:start position:0%
+is that big enough difference for you
+ 
+
+ align:start position:0%
+is that big enough difference for you
+guys to see good ok we can start doing
+
+ align:start position:0%
+guys to see good ok we can start doing
+ 
+
+ align:start position:0%
+guys to see good ok we can start doing
+this in a few different ways I want to
+
+ align:start position:0%
+this in a few different ways I want to
+ 
+
+ align:start position:0%
+this in a few different ways I want to
+mention what they are and then we're
+
+ align:start position:0%
+mention what they are and then we're
+ 
+
+ align:start position:0%
+mention what they are and then we're
+gonna do the easiest one
+
+ align:start position:0%
+gonna do the easiest one
+ 
+
+ align:start position:0%
+gonna do the easiest one
+so the way it's done for real like in
+
+ align:start position:0%
+so the way it's done for real like in
+ 
+
+ align:start position:0%
+so the way it's done for real like in
+the computational reactor physics group
+
+ align:start position:0%
+the computational reactor physics group
+ 
+
+ align:start position:0%
+the computational reactor physics group
+is you can discretize the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discretize the energy into a bunch of
+
+ align:start position:0%
+discretize the energy into a bunch of
+ 
+
+ align:start position:0%
+discretize the energy into a bunch of
+little energy groups so you can write
+
+ align:start position:0%
+little energy groups so you can write
+ 
+
+ align:start position:0%
+little energy groups so you can write
+this equation for every little energy
+
+ align:start position:0%
+this equation for every little energy
+ 
+
+ align:start position:0%
+this equation for every little energy
+group and assume that along this energy
+
+ align:start position:0%
+group and assume that along this energy
+ 
+
+ align:start position:0%
+group and assume that along this energy
+scale ranging from your maximum energy
+
+ align:start position:0%
+scale ranging from your maximum energy
+ 
+
+ align:start position:0%
+scale ranging from your maximum energy
+to probably thermal energy yeah oh to
+
+ align:start position:0%
+to probably thermal energy yeah oh to
+ 
+
+ align:start position:0%
+to probably thermal energy yeah oh to
+five okay let's do this clearly with
+
+ align:start position:0%
+five okay let's do this clearly with
+ 
+
+ align:start position:0%
+five okay let's do this clearly with
+thick chalk there we go
+
+ align:start position:0%
+thick chalk there we go
+ 
+
+ align:start position:0%
+thick chalk there we go
+you can then discretize into some little
+
+ align:start position:0%
+you can then discretize into some little
+ 
+
+ align:start position:0%
+you can then discretize into some little
+energy group let's say that's eg I
+
+ align:start position:0%
+energy group let's say that's eg I
+ 
+
+ align:start position:0%
+energy group let's say that's eg I
+that's eg I plus one and so on and so on
+
+ align:start position:0%
+that's eg I plus one and so on and so on
+ 
+
+ align:start position:0%
+that's eg I plus one and so on and so on
+and depending on the type of reactor
+
+ align:start position:0%
+and depending on the type of reactor
+ 
+
+ align:start position:0%
+and depending on the type of reactor
+that you're looking at and the energy
+
+ align:start position:0%
+that you're looking at and the energy
+ 
+
+ align:start position:0%
+that you're looking at and the energy
+resolution that you need you choose the
+
+ align:start position:0%
+resolution that you need you choose the
+ 
+
+ align:start position:0%
+resolution that you need you choose the
+number of energy groups accordingly does
+
+ align:start position:0%
+number of energy groups accordingly does
+ 
+
+ align:start position:0%
+number of energy groups accordingly does
+anyone happen to know for a light water
+
+ align:start position:0%
+anyone happen to know for a light water
+ 
+
+ align:start position:0%
+anyone happen to know for a light water
+reactor how many energy groups do you
+
+ align:start position:0%
+reactor how many energy groups do you
+ 
+
+ align:start position:0%
+reactor how many energy groups do you
+think we need to model a light water
+
+ align:start position:0%
+think we need to model a light water
+ 
+
+ align:start position:0%
+think we need to model a light water
+reactor the answer might surprise you
+
+ align:start position:0%
+reactor the answer might surprise you
+ 
+
+ align:start position:0%
+reactor the answer might surprise you
+it's just two actually all we care about
+
+ align:start position:0%
+it's just two actually all we care about
+ 
+
+ align:start position:0%
+it's just two actually all we care about
+so let's say this would be for the
+
+ align:start position:0%
+so let's say this would be for the
+ 
+
+ align:start position:0%
+so let's say this would be for the
+general case all we care about for a
+
+ align:start position:0%
+general case all we care about for a
+ 
+
+ align:start position:0%
+general case all we care about for a
+light water reactor is are your neutrons
+
+ align:start position:0%
+light water reactor is are your neutrons
+ 
+
+ align:start position:0%
+light water reactor is are your neutrons
+thermal or are they not because the
+
+ align:start position:0%
+thermal or are they not because the
+ 
+
+ align:start position:0%
+thermal or are they not because the
+neutrons that are not thermal are not
+
+ align:start position:0%
+neutrons that are not thermal are not
+ 
+
+ align:start position:0%
+neutrons that are not thermal are not
+contributing to fission that much they
+
+ align:start position:0%
+contributing to fission that much they
+ 
+
+ align:start position:0%
+contributing to fission that much they
+are just a little bit and you can
+
+ align:start position:0%
+are just a little bit and you can
+ 
+
+ align:start position:0%
+are just a little bit and you can
+account for those but pretty much
+
+ align:start position:0%
+account for those but pretty much
+ 
+
+ align:start position:0%
+account for those but pretty much
+they're not once the neutrons slow down
+
+ align:start position:0%
+they're not once the neutrons slow down
+ 
+
+ align:start position:0%
+they're not once the neutrons slow down
+to get thermal in the range from like
+
+ align:start position:0%
+to get thermal in the range from like
+ 
+
+ align:start position:0%
+to get thermal in the range from like
+let's say about an e V to that
+
+ align:start position:0%
+let's say about an e V to that
+ 
+
+ align:start position:0%
+let's say about an e V to that
+temperature took a surprising amount of
+
+ align:start position:0%
+temperature took a surprising amount of
+ 
+
+ align:start position:0%
+temperature took a surprising amount of
+time to write with sidewalk chalk then
+
+ align:start position:0%
+time to write with sidewalk chalk then
+ 
+
+ align:start position:0%
+time to write with sidewalk chalk then
+you've got things that are about 500 or
+
+ align:start position:0%
+you've got things that are about 500 or
+ 
+
+ align:start position:0%
+you've got things that are about 500 or
+a thousand times more likely to undergo
+
+ align:start position:0%
+a thousand times more likely to undergo
+ 
+
+ align:start position:0%
+a thousand times more likely to undergo
+fission and so all you care about is the
+
+ align:start position:0%
+fission and so all you care about is the
+ 
+
+ align:start position:0%
+fission and so all you care about is the
+neutrons are all born they're all born
+
+ align:start position:0%
+neutrons are all born they're all born
+ 
+
+ align:start position:0%
+neutrons are all born they're all born
+right about here and they scatter
+
+ align:start position:0%
+right about here and they scatter
+ 
+
+ align:start position:0%
+right about here and they scatter
+and bounce around and you don't care
+
+ align:start position:0%
+and bounce around and you don't care
+ 
+
+ align:start position:0%
+and bounce around and you don't care
+because they're just in this not thermal
+
+ align:start position:0%
+because they're just in this not thermal
+ 
+
+ align:start position:0%
+because they're just in this not thermal
+region and when they enter the thermal
+
+ align:start position:0%
+region and when they enter the thermal
+ 
+
+ align:start position:0%
+region and when they enter the thermal
+region you start tracking them because
+
+ align:start position:0%
+region you start tracking them because
+ 
+
+ align:start position:0%
+region you start tracking them because
+those are the ones that really count for
+
+ align:start position:0%
+those are the ones that really count for
+ 
+
+ align:start position:0%
+those are the ones that really count for
+fission and if you actually look up the
+
+ align:start position:0%
+fission and if you actually look up the
+ 
+
+ align:start position:0%
+fission and if you actually look up the
+specifications for the ap1000 this is a
+
+ align:start position:0%
+specifications for the ap1000 this is a
+ 
+
+ align:start position:0%
+specifications for the ap1000 this is a
+modern reactor under construction in
+
+ align:start position:0%
+modern reactor under construction in
+ 
+
+ align:start position:0%
+modern reactor under construction in
+many different places in the world when
+
+ align:start position:0%
+many different places in the world when
+ 
+
+ align:start position:0%
+many different places in the world when
+you see how do they do the neutronic
+
+ align:start position:0%
+you see how do they do the neutronic
+ 
+
+ align:start position:0%
+you see how do they do the neutronic
+analysis two group approximation so this
+
+ align:start position:0%
+analysis two group approximation so this
+ 
+
+ align:start position:0%
+analysis two group approximation so this
+isn't just an academic exercise to make
+
+ align:start position:0%
+isn't just an academic exercise to make
+ 
+
+ align:start position:0%
+isn't just an academic exercise to make
+it easier for sophomores to understand
+
+ align:start position:0%
+it easier for sophomores to understand
+ 
+
+ align:start position:0%
+it easier for sophomores to understand
+this is actually something that's done
+
+ align:start position:0%
+this is actually something that's done
+ 
+
+ align:start position:0%
+this is actually something that's done
+for real reactors so if you ever felt
+
+ align:start position:0%
+for real reactors so if you ever felt
+ 
+
+ align:start position:0%
+for real reactors so if you ever felt
+like I'm making it too simple no no this
+
+ align:start position:0%
+like I'm making it too simple no no this
+ 
+
+ align:start position:0%
+like I'm making it too simple no no this
+is I'm simplifying it down to what's
+
+ align:start position:0%
+is I'm simplifying it down to what's
+ 
+
+ align:start position:0%
+is I'm simplifying it down to what's
+really done and I will get you that
+
+ align:start position:0%
+really done and I will get you that
+ 
+
+ align:start position:0%
+really done and I will get you that
+specification so you can see what
+
+ align:start position:0%
+specification so you can see what
+ 
+
+ align:start position:0%
+specification so you can see what
+westinghouse says like this is how we
+
+ align:start position:0%
+westinghouse says like this is how we
+ 
+
+ align:start position:0%
+westinghouse says like this is how we
+design the reactor we made a two group
+
+ align:start position:0%
+design the reactor we made a two group
+ 
+
+ align:start position:0%
+design the reactor we made a two group
+simplification in many cases so you can
+
+ align:start position:0%
+simplification in many cases so you can
+ 
+
+ align:start position:0%
+simplification in many cases so you can
+discretize you can forget it
+
+ align:start position:0%
+discretize you can forget it
+ 
+
+ align:start position:0%
+discretize you can forget it
+which we're going to call the one group
+
+ align:start position:0%
+which we're going to call the one group
+ 
+
+ align:start position:0%
+which we're going to call the one group
+approximation or you can well let's say
+
+ align:start position:0%
+approximation or you can well let's say
+ 
+
+ align:start position:0%
+approximation or you can well let's say
+two group is the other one that we're
+
+ align:start position:0%
+two group is the other one that we're
+ 
+
+ align:start position:0%
+two group is the other one that we're
+actually gonna tackle we're gonna do
+
+ align:start position:0%
+actually gonna tackle we're gonna do
+ 
+
+ align:start position:0%
+actually gonna tackle we're gonna do
+this one forget energy but we're not
+
+ align:start position:0%
+this one forget energy but we're not
+ 
+
+ align:start position:0%
+this one forget energy but we're not
+really going to forget energy because
+
+ align:start position:0%
+really going to forget energy because
+ 
+
+ align:start position:0%
+really going to forget energy because
+you can't just pick an energy and pick a
+
+ align:start position:0%
+you can't just pick an energy and pick a
+ 
+
+ align:start position:0%
+you can't just pick an energy and pick a
+cross-section and say okay that's the
+
+ align:start position:0%
+cross-section and say okay that's the
+ 
+
+ align:start position:0%
+cross-section and say okay that's the
+cross-section we're going to use if most
+
+ align:start position:0%
+cross-section we're going to use if most
+ 
+
+ align:start position:0%
+cross-section we're going to use if most
+cross-sections have the following form
+
+ align:start position:0%
+cross-sections have the following form
+ 
+
+ align:start position:0%
+cross-sections have the following form
+if this is log of energy and this is log
+
+ align:start position:0%
+if this is log of energy and this is log
+ 
+
+ align:start position:0%
+if this is log of energy and this is log
+of Sigma and it goes something like that
+
+ align:start position:0%
+of Sigma and it goes something like that
+ 
+
+ align:start position:0%
+of Sigma and it goes something like that
+what energy do you pick go ahead tell me
+
+ align:start position:0%
+what energy do you pick go ahead tell me
+ 
+
+ align:start position:0%
+what energy do you pick go ahead tell me
+which energy do you pick anyone want to
+
+ align:start position:0%
+which energy do you pick anyone want to
+ 
+
+ align:start position:0%
+which energy do you pick anyone want to
+wager a guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ones before after the big squigglies
+
+ align:start position:0%
+the ones before after the big squigglies
+ 
+
+ align:start position:0%
+the ones before after the big squigglies
+I don't think that's correct because if
+
+ align:start position:0%
+I don't think that's correct because if
+ 
+
+ align:start position:0%
+I don't think that's correct because if
+you do it this then you're gonna weigh
+
+ align:start position:0%
+you do it this then you're gonna weigh
+ 
+
+ align:start position:0%
+you do it this then you're gonna weigh
+underestimate vision if you do it here
+
+ align:start position:0%
+underestimate vision if you do it here
+ 
+
+ align:start position:0%
+underestimate vision if you do it here
+you're gonna weigh overestimate vision
+
+ align:start position:0%
+you're gonna weigh overestimate vision
+ 
+
+ align:start position:0%
+you're gonna weigh overestimate vision
+or whatever rank we have the reaction
+
+ align:start position:0%
+or whatever rank we have the reaction
+ 
+
+ align:start position:0%
+or whatever rank we have the reaction
+you have we didn't say which reaction
+
+ align:start position:0%
+you have we didn't say which reaction
+ 
+
+ align:start position:0%
+you have we didn't say which reaction
+this is the rest of you who are silent
+
+ align:start position:0%
+this is the rest of you who are silent
+ 
+
+ align:start position:0%
+this is the rest of you who are silent
+and afraid to speak up you're actually
+
+ align:start position:0%
+and afraid to speak up you're actually
+ 
+
+ align:start position:0%
+and afraid to speak up you're actually
+correct I wouldn't actually pick any
+
+ align:start position:0%
+correct I wouldn't actually pick any
+ 
+
+ align:start position:0%
+correct I wouldn't actually pick any
+single value here what you need to do is
+
+ align:start position:0%
+single value here what you need to do is
+ 
+
+ align:start position:0%
+single value here what you need to do is
+find some sort of average cross-section
+
+ align:start position:0%
+find some sort of average cross-section
+ 
+
+ align:start position:0%
+find some sort of average cross-section
+for whatever reaction that accurately
+
+ align:start position:0%
+for whatever reaction that accurately
+ 
+
+ align:start position:0%
+for whatever reaction that accurately
+represents the number of reactions
+
+ align:start position:0%
+represents the number of reactions
+ 
+
+ align:start position:0%
+represents the number of reactions
+happening in the system and in order to
+
+ align:start position:0%
+happening in the system and in order to
+ 
+
+ align:start position:0%
+happening in the system and in order to
+do that you have to come up with some
+
+ align:start position:0%
+do that you have to come up with some
+ 
+
+ align:start position:0%
+do that you have to come up with some
+average cross-section for whatever
+
+ align:start position:0%
+average cross-section for whatever
+ 
+
+ align:start position:0%
+average cross-section for whatever
+reaction you have by integrating over
+
+ align:start position:0%
+reaction you have by integrating over
+ 
+
+ align:start position:0%
+reaction you have by integrating over
+your whole energy range of the energy
+
+ align:start position:0%
+your whole energy range of the energy
+ 
+
+ align:start position:0%
+your whole energy range of the energy
+dependent cross-section as a function of
+
+ align:start position:0%
+dependent cross-section as a function of
+ 
+
+ align:start position:0%
+dependent cross-section as a function of
+energy times your flux de over this look
+
+ align:start position:0%
+energy times your flux de over this look
+ 
+
+ align:start position:0%
+energy times your flux de over this look
+familiar from 1801 or two as well what's
+
+ align:start position:0%
+familiar from 1801 or two as well what's
+ 
+
+ align:start position:0%
+familiar from 1801 or two as well what's
+the average value of some function a
+
+ align:start position:0%
+the average value of some function a
+ 
+
+ align:start position:0%
+the average value of some function a
+little bit well we'll bring it back here
+
+ align:start position:0%
+little bit well we'll bring it back here
+ 
+
+ align:start position:0%
+little bit well we'll bring it back here
+now so retrieve it from cold storage in
+
+ align:start position:0%
+now so retrieve it from cold storage in
+ 
+
+ align:start position:0%
+now so retrieve it from cold storage in
+your memories because this is how actual
+
+ align:start position:0%
+your memories because this is how actual
+ 
+
+ align:start position:0%
+your memories because this is how actual
+cross-sections are averaged for whatever
+
+ align:start position:0%
+cross-sections are averaged for whatever
+ 
+
+ align:start position:0%
+cross-sections are averaged for whatever
+energy range you're picking you know
+
+ align:start position:0%
+energy range you're picking you know
+ 
+
+ align:start position:0%
+energy range you're picking you know
+what I'm gonna make this a little more
+
+ align:start position:0%
+what I'm gonna make this a little more
+ 
+
+ align:start position:0%
+what I'm gonna make this a little more
+general I won't say zero I'll just say
+
+ align:start position:0%
+general I won't say zero I'll just say
+ 
+
+ align:start position:0%
+general I won't say zero I'll just say
+your minimum energy for your group so
+
+ align:start position:0%
+your minimum energy for your group so
+ 
+
+ align:start position:0%
+your minimum energy for your group so
+now this equation is general for the
+
+ align:start position:0%
+now this equation is general for the
+ 
+
+ align:start position:0%
+now this equation is general for the
+multi group and the one group and two
+
+ align:start position:0%
+multi group and the one group and two
+ 
+
+ align:start position:0%
+multi group and the one group and two
+group method for whatever cross-section
+
+ align:start position:0%
+group method for whatever cross-section
+ 
+
+ align:start position:0%
+group method for whatever cross-section
+you want to pick and whatever energy
+
+ align:start position:0%
+you want to pick and whatever energy
+ 
+
+ align:start position:0%
+you want to pick and whatever energy
+range you're looking at you take the
+
+ align:start position:0%
+range you're looking at you take the
+ 
+
+ align:start position:0%
+range you're looking at you take the
+actual data and perform an average for
+
+ align:start position:0%
+actual data and perform an average for
+ 
+
+ align:start position:0%
+actual data and perform an average for
+the fast and thermal delineation where
+
+ align:start position:0%
+the fast and thermal delineation where
+ 
+
+ align:start position:0%
+the fast and thermal delineation where
+let's say this is fast and this is
+
+ align:start position:0%
+let's say this is fast and this is
+ 
+
+ align:start position:0%
+let's say this is fast and this is
+thermal you would have two different
+
+ align:start position:0%
+thermal you would have two different
+ 
+
+ align:start position:0%
+thermal you would have two different
+averages maybe this average would be
+
+ align:start position:0%
+averages maybe this average would be
+ 
+
+ align:start position:0%
+averages maybe this average would be
+right there you know what let's use
+
+ align:start position:0%
+right there you know what let's use
+ 
+
+ align:start position:0%
+right there you know what let's use
+white so it actually has some contrast
+
+ align:start position:0%
+white so it actually has some contrast
+ 
+
+ align:start position:0%
+white so it actually has some contrast
+so this would be one value of the
+
+ align:start position:0%
+so this would be one value of the
+ 
+
+ align:start position:0%
+so this would be one value of the
+cross-section and maybe the next average
+
+ align:start position:0%
+cross-section and maybe the next average
+ 
+
+ align:start position:0%
+cross-section and maybe the next average
+would be right there so you simplify
+
+ align:start position:0%
+would be right there so you simplify
+ 
+
+ align:start position:0%
+would be right there so you simplify
+this absolutely non analytical
+
+ align:start position:0%
+this absolutely non analytical
+ 
+
+ align:start position:0%
+this absolutely non analytical
+form of your complicated cross-section
+
+ align:start position:0%
+form of your complicated cross-section
+ 
+
+ align:start position:0%
+form of your complicated cross-section
+to just a couple of values maybe we'll
+
+ align:start position:0%
+to just a couple of values maybe we'll
+ 
+
+ align:start position:0%
+to just a couple of values maybe we'll
+call that average Sigma fast and we'll
+
+ align:start position:0%
+call that average Sigma fast and we'll
+ 
+
+ align:start position:0%
+call that average Sigma fast and we'll
+call that average Sigma thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so using this analogy and this color we
+
+ align:start position:0%
+so using this analogy and this color we
+ 
+
+ align:start position:0%
+so using this analogy and this color we
+can then say we're gonna take an average
+
+ align:start position:0%
+can then say we're gonna take an average
+ 
+
+ align:start position:0%
+can then say we're gonna take an average
+new an average CAI get rid of the
+
+ align:start position:0%
+new an average CAI get rid of the
+ 
+
+ align:start position:0%
+new an average CAI get rid of the
+energies because we can perform the same
+
+ align:start position:0%
+energies because we can perform the same
+ 
+
+ align:start position:0%
+energies because we can perform the same
+energy average integration on every
+
+ align:start position:0%
+energy average integration on every
+ 
+
+ align:start position:0%
+energy average integration on every
+quantity with energy dependence so all
+
+ align:start position:0%
+quantity with energy dependence so all
+ 
+
+ align:start position:0%
+quantity with energy dependence so all
+we do is we put a bar there ditch the
+
+ align:start position:0%
+we do is we put a bar there ditch the
+ 
+
+ align:start position:0%
+we do is we put a bar there ditch the
+energies
+
+ align:start position:0%
+energies
+ 
+
+ align:start position:0%
+energies
+it's the energies and let's just say
+
+ align:start position:0%
+it's the energies and let's just say
+ 
+
+ align:start position:0%
+it's the energies and let's just say
+that flux is going to be what it is
+
+ align:start position:0%
+that flux is going to be what it is
+ 
+
+ align:start position:0%
+that flux is going to be what it is
+same thing here yeah same thing there
+
+ align:start position:0%
+same thing here yeah same thing there
+ 
+
+ align:start position:0%
+same thing here yeah same thing there
+and there and there they're there
+
+ align:start position:0%
+and there and there they're there
+ 
+
+ align:start position:0%
+and there and there they're there
+they're here and here and here and
+
+ align:start position:0%
+they're here and here and here and
+ 
+
+ align:start position:0%
+they're here and here and here and
+there's a cross-section there's an
+
+ align:start position:0%
+there's a cross-section there's an
+ 
+
+ align:start position:0%
+there's a cross-section there's an
+energy there's an energy there is a
+
+ align:start position:0%
+energy there's an energy there is a
+ 
+
+ align:start position:0%
+energy there's an energy there is a
+cross-section we don't care about those
+
+ align:start position:0%
+cross-section we don't care about those
+ 
+
+ align:start position:0%
+cross-section we don't care about those
+anymore and there's a couple of other
+
+ align:start position:0%
+anymore and there's a couple of other
+ 
+
+ align:start position:0%
+anymore and there's a couple of other
+implications of this energy
+
+ align:start position:0%
+implications of this energy
+ 
+
+ align:start position:0%
+implications of this energy
+simplification what is the birth
+
+ align:start position:0%
+simplification what is the birth
+ 
+
+ align:start position:0%
+simplification what is the birth
+spectrum now what's the probability that
+
+ align:start position:0%
+spectrum now what's the probability that
+ 
+
+ align:start position:0%
+spectrum now what's the probability that
+a neutron is born in our energy group
+
+ align:start position:0%
+a neutron is born in our energy group
+ 
+
+ align:start position:0%
+a neutron is born in our energy group
+which contains all energies one yeah
+
+ align:start position:0%
+which contains all energies one yeah
+ 
+
+ align:start position:0%
+which contains all energies one yeah
+okay so forget the Chi and that one and
+
+ align:start position:0%
+okay so forget the Chi and that one and
+ 
+
+ align:start position:0%
+okay so forget the Chi and that one and
+that one and what about this scattering
+
+ align:start position:0%
+that one and what about this scattering
+ 
+
+ align:start position:0%
+that one and what about this scattering
+kernel what's the probability that a
+
+ align:start position:0%
+kernel what's the probability that a
+ 
+
+ align:start position:0%
+kernel what's the probability that a
+neutron scatters from any other energy
+
+ align:start position:0%
+neutron scatters from any other energy
+ 
+
+ align:start position:0%
+neutron scatters from any other energy
+which is already in our group into our
+
+ align:start position:0%
+which is already in our group into our
+ 
+
+ align:start position:0%
+which is already in our group into our
+group which contains all energies yeah
+
+ align:start position:0%
+group which contains all energies yeah
+ 
+
+ align:start position:0%
+group which contains all energies yeah
+scattering no longer matters when you do
+
+ align:start position:0%
+scattering no longer matters when you do
+ 
+
+ align:start position:0%
+scattering no longer matters when you do
+the one group approximation because if
+
+ align:start position:0%
+the one group approximation because if
+ 
+
+ align:start position:0%
+the one group approximation because if
+the neutron loses some of its energy
+
+ align:start position:0%
+the neutron loses some of its energy
+ 
+
+ align:start position:0%
+the neutron loses some of its energy
+it's still in our energy group because
+
+ align:start position:0%
+it's still in our energy group because
+ 
+
+ align:start position:0%
+it's still in our energy group because
+our energy group contains all energies
+
+ align:start position:0%
+our energy group contains all energies
+ 
+
+ align:start position:0%
+our energy group contains all energies
+so forget the scattering kernel and
+
+ align:start position:0%
+so forget the scattering kernel and
+ 
+
+ align:start position:0%
+so forget the scattering kernel and
+forget the energy integrals what are we
+
+ align:start position:0%
+forget the energy integrals what are we
+ 
+
+ align:start position:0%
+forget the energy integrals what are we
+actually left with not much there's no
+
+ align:start position:0%
+actually left with not much there's no
+ 
+
+ align:start position:0%
+actually left with not much there's no
+green in here yet good because I need to
+
+ align:start position:0%
+green in here yet good because I need to
+ 
+
+ align:start position:0%
+green in here yet good because I need to
+do one more thing there is no more green
+
+ align:start position:0%
+do one more thing there is no more green
+ 
+
+ align:start position:0%
+do one more thing there is no more green
+oh we did green we did time okay green
+
+ align:start position:0%
+oh we did green we did time okay green
+ 
+
+ align:start position:0%
+oh we did green we did time okay green
+red
+
+ align:start position:0%
+red
+ 
+
+ align:start position:0%
+red
+orange is if the orange I used damn it
+
+ align:start position:0%
+orange is if the orange I used damn it
+ 
+
+ align:start position:0%
+orange is if the orange I used damn it
+okay we've used those purple no we've
+
+ align:start position:0%
+okay we've used those purple no we've
+ 
+
+ align:start position:0%
+okay we've used those purple no we've
+used that oh my god we've used both
+
+ align:start position:0%
+used that oh my god we've used both
+ 
+
+ align:start position:0%
+used that oh my god we've used both
+blues bright yellow yeah yes
+
+ align:start position:0%
+blues bright yellow yeah yes
+ 
+
+ align:start position:0%
+blues bright yellow yeah yes
+chi is the fission birth spectrum the
+
+ align:start position:0%
+chi is the fission birth spectrum the
+ 
+
+ align:start position:0%
+chi is the fission birth spectrum the
+probability that a neutron is born at
+
+ align:start position:0%
+probability that a neutron is born at
+ 
+
+ align:start position:0%
+probability that a neutron is born at
+any given energy but because all
+
+ align:start position:0%
+any given energy but because all
+ 
+
+ align:start position:0%
+any given energy but because all
+neutrons are born in our energy group
+
+ align:start position:0%
+neutrons are born in our energy group
+ 
+
+ align:start position:0%
+neutrons are born in our energy group
+which contains all energies then that
+
+ align:start position:0%
+which contains all energies then that
+ 
+
+ align:start position:0%
+which contains all energies then that
+just becomes one and goes away there's
+
+ align:start position:0%
+just becomes one and goes away there's
+ 
+
+ align:start position:0%
+just becomes one and goes away there's
+there's no birth spectrum because
+
+ align:start position:0%
+there's no birth spectrum because
+ 
+
+ align:start position:0%
+there's no birth spectrum because
+they're just born in our group yes that
+
+ align:start position:0%
+they're just born in our group yes that
+ 
+
+ align:start position:0%
+they're just born in our group yes that
+makes sense yeah
+
+ align:start position:0%
+makes sense yeah
+ 
+
+ align:start position:0%
+makes sense yeah
+okay I think I found the reaction we'll
+
+ align:start position:0%
+okay I think I found the reaction we'll
+ 
+
+ align:start position:0%
+okay I think I found the reaction we'll
+only color besides black on a black
+
+ align:start position:0%
+only color besides black on a black
+ 
+
+ align:start position:0%
+only color besides black on a black
+chalkboard and white which we already
+
+ align:start position:0%
+chalkboard and white which we already
+ 
+
+ align:start position:0%
+chalkboard and white which we already
+have that I have left we also have a
+
+ align:start position:0%
+have that I have left we also have a
+ 
+
+ align:start position:0%
+have that I have left we also have a
+slightly darker shade of gray but I'm
+
+ align:start position:0%
+slightly darker shade of gray but I'm
+ 
+
+ align:start position:0%
+slightly darker shade of gray but I'm
+literally out this worked out awesome
+
+ align:start position:0%
+literally out this worked out awesome
+ 
+
+ align:start position:0%
+literally out this worked out awesome
+because there's one more thing that we
+
+ align:start position:0%
+because there's one more thing that we
+ 
+
+ align:start position:0%
+because there's one more thing that we
+want to deal with what do we even have
+
+ align:start position:0%
+want to deal with what do we even have
+ 
+
+ align:start position:0%
+want to deal with what do we even have
+left all right
+
+ align:start position:0%
+left all right
+ 
+
+ align:start position:0%
+left all right
+what is the one term that is not in all
+
+ align:start position:0%
+what is the one term that is not in all
+ 
+
+ align:start position:0%
+what is the one term that is not in all
+of the same variables as the others that
+
+ align:start position:0%
+of the same variables as the others that
+ 
+
+ align:start position:0%
+of the same variables as the others that
+current that J what do we do about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going sorry yeah the F e to e
+
+ align:start position:0%
+so we're going sorry yeah the F e to e
+ 
+
+ align:start position:0%
+so we're going sorry yeah the F e to e
+so I'll actually I'll recreate some of
+
+ align:start position:0%
+so I'll actually I'll recreate some of
+ 
+
+ align:start position:0%
+so I'll actually I'll recreate some of
+our variables here because there's a lot
+
+ align:start position:0%
+our variables here because there's a lot
+ 
+
+ align:start position:0%
+our variables here because there's a lot
+of them so our F of e prime to e is
+
+ align:start position:0%
+of them so our F of e prime to e is
+ 
+
+ align:start position:0%
+of them so our F of e prime to e is
+what's called the scattering kernel and
+
+ align:start position:0%
+what's called the scattering kernel and
+ 
+
+ align:start position:0%
+what's called the scattering kernel and
+that's the probability that a neutron
+
+ align:start position:0%
+that's the probability that a neutron
+ 
+
+ align:start position:0%
+that's the probability that a neutron
+scatters from some other energy Group E
+
+ align:start position:0%
+scatters from some other energy Group E
+ 
+
+ align:start position:0%
+scatters from some other energy Group E
+Prime in two hours in a about de and Chi
+
+ align:start position:0%
+Prime in two hours in a about de and Chi
+ 
+
+ align:start position:0%
+Prime in two hours in a about de and Chi
+of e is the fission birth spectrum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just for completeness knew of e is
+
+ align:start position:0%
+and just for completeness knew of e is
+ 
+
+ align:start position:0%
+and just for completeness knew of e is
+our Neutron multiplier or neutrons per
+
+ align:start position:0%
+our Neutron multiplier or neutrons per
+ 
+
+ align:start position:0%
+our Neutron multiplier or neutrons per
+fission I think that gives a pretty
+
+ align:start position:0%
+fission I think that gives a pretty
+ 
+
+ align:start position:0%
+fission I think that gives a pretty
+complete explanation of what's up here
+
+ align:start position:0%
+complete explanation of what's up here
+ 
+
+ align:start position:0%
+complete explanation of what's up here
+so now let's figure out how to deal with
+
+ align:start position:0%
+so now let's figure out how to deal with
+ 
+
+ align:start position:0%
+so now let's figure out how to deal with
+the current term this is when we make
+
+ align:start position:0%
+the current term this is when we make
+ 
+
+ align:start position:0%
+the current term this is when we make
+one of the biggest approximations here
+
+ align:start position:0%
+one of the biggest approximations here
+ 
+
+ align:start position:0%
+one of the biggest approximations here
+and go from what's called the neutron
+
+ align:start position:0%
+and go from what's called the neutron
+ 
+
+ align:start position:0%
+and go from what's called the neutron
+transport equation which is a fully
+
+ align:start position:0%
+transport equation which is a fully
+ 
+
+ align:start position:0%
+transport equation which is a fully
+accurate physical model of what's really
+
+ align:start position:0%
+accurate physical model of what's really
+ 
+
+ align:start position:0%
+accurate physical model of what's really
+going on to the neutron diffusion
+
+ align:start position:0%
+going on to the neutron diffusion
+ 
+
+ align:start position:0%
+going on to the neutron diffusion
+equation and this is where it gets
+
+ align:start position:0%
+equation and this is where it gets
+ 
+
+ align:start position:0%
+equation and this is where it gets
+really fun you don't assume that
+
+ align:start position:0%
+really fun you don't assume that
+ 
+
+ align:start position:0%
+really fun you don't assume that
+neutrons are subatomic particles that
+
+ align:start position:0%
+neutrons are subatomic particles that
+ 
+
+ align:start position:0%
+neutrons are subatomic particles that
+are whizzing about and knocking off of
+
+ align:start position:0%
+are whizzing about and knocking off of
+ 
+
+ align:start position:0%
+are whizzing about and knocking off of
+everything else you then treat the
+
+ align:start position:0%
+everything else you then treat the
+ 
+
+ align:start position:0%
+everything else you then treat the
+neutrons kind of like a gas or like a
+
+ align:start position:0%
+neutrons kind of like a gas or like a
+ 
+
+ align:start position:0%
+neutrons kind of like a gas or like a
+chemical and you just say that it
+
+ align:start position:0%
+chemical and you just say that it
+ 
+
+ align:start position:0%
+chemical and you just say that it
+follows the laws of diffusion again this
+
+ align:start position:0%
+follows the laws of diffusion again this
+ 
+
+ align:start position:0%
+follows the laws of diffusion again this
+works out very well except for places
+
+ align:start position:0%
+works out very well except for places
+ 
+
+ align:start position:0%
+works out very well except for places
+where cross sections suddenly change
+
+ align:start position:0%
+where cross sections suddenly change
+ 
+
+ align:start position:0%
+where cross sections suddenly change
+like near control rods or near fuel but
+
+ align:start position:0%
+like near control rods or near fuel but
+ 
+
+ align:start position:0%
+like near control rods or near fuel but
+for most of the reactor especially if we
+
+ align:start position:0%
+for most of the reactor especially if we
+ 
+
+ align:start position:0%
+for most of the reactor especially if we
+have a molten salt fuel reactor we can
+
+ align:start position:0%
+have a molten salt fuel reactor we can
+ 
+
+ align:start position:0%
+have a molten salt fuel reactor we can
+invoke what's called ficks law this
+
+ align:start position:0%
+invoke what's called ficks law this
+ 
+
+ align:start position:0%
+invoke what's called ficks law this
+sound familiar to anyone ficks law of
+
+ align:start position:0%
+sound familiar to anyone ficks law of
+ 
+
+ align:start position:0%
+sound familiar to anyone ficks law of
+diffusion three or nine one or five
+
+ align:start position:0%
+diffusion three or nine one or five
+ 
+
+ align:start position:0%
+diffusion three or nine one or five
+eleven one it's it is that it's the
+
+ align:start position:0%
+eleven one it's it is that it's the
+ 
+
+ align:start position:0%
+eleven one it's it is that it's the
+change of a chemical on down a density
+
+ align:start position:0%
+change of a chemical on down a density
+ 
+
+ align:start position:0%
+change of a chemical on down a density
+or concentration gradient so yeah you've
+
+ align:start position:0%
+or concentration gradient so yeah you've
+ 
+
+ align:start position:0%
+or concentration gradient so yeah you've
+got the idea what ficks law says is that
+
+ align:start position:0%
+got the idea what ficks law says is that
+ 
+
+ align:start position:0%
+got the idea what ficks law says is that
+the current or let's say the diffusion
+
+ align:start position:0%
+the current or let's say the diffusion
+ 
+
+ align:start position:0%
+the current or let's say the diffusion
+current or the Neutron current is going
+
+ align:start position:0%
+current or the Neutron current is going
+ 
+
+ align:start position:0%
+current or the Neutron current is going
+to be equal to some diffusion
+
+ align:start position:0%
+to be equal to some diffusion
+ 
+
+ align:start position:0%
+to be equal to some diffusion
+coefficient times the gradient of
+
+ align:start position:0%
+coefficient times the gradient of
+ 
+
+ align:start position:0%
+coefficient times the gradient of
+whatever a chemical concentration you've
+
+ align:start position:0%
+whatever a chemical concentration you've
+ 
+
+ align:start position:0%
+whatever a chemical concentration you've
+got let me put the C in there so right
+
+ align:start position:0%
+got let me put the C in there so right
+ 
+
+ align:start position:0%
+got let me put the C in there so right
+here this would be the current I'll
+
+ align:start position:0%
+here this would be the current I'll
+ 
+
+ align:start position:0%
+here this would be the current I'll
+label in a different color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this would be your variable of interest
+
+ align:start position:0%
+this would be your variable of interest
+ 
+
+ align:start position:0%
+this would be your variable of interest
+maybe C is for concentration or Phi is
+
+ align:start position:0%
+maybe C is for concentration or Phi is
+ 
+
+ align:start position:0%
+maybe C is for concentration or Phi is
+for flux oh that reminds me where are
+
+ align:start position:0%
+for flux oh that reminds me where are
+ 
+
+ align:start position:0%
+for flux oh that reminds me where are
+those bars on our flux which term did we
+
+ align:start position:0%
+those bars on our flux which term did we
+ 
+
+ align:start position:0%
+those bars on our flux which term did we
+do energy whereas my slightly
+
+ align:start position:0%
+do energy whereas my slightly
+ 
+
+ align:start position:0%
+do energy whereas my slightly
+blue over here all of these Phi's become
+
+ align:start position:0%
+blue over here all of these Phi's become
+ 
+
+ align:start position:0%
+blue over here all of these Phi's become
+Capitol because we've gotten rid of all
+
+ align:start position:0%
+Capitol because we've gotten rid of all
+ 
+
+ align:start position:0%
+Capitol because we've gotten rid of all
+the angular and energy in everything
+
+ align:start position:0%
+the angular and energy in everything
+ 
+
+ align:start position:0%
+the angular and energy in everything
+dependence Oh angular dependence neglect
+
+ align:start position:0%
+dependence Oh angular dependence neglect
+ 
+
+ align:start position:0%
+dependence Oh angular dependence neglect
+Omega that should be dark blue mega goes
+
+ align:start position:0%
+Omega that should be dark blue mega goes
+ 
+
+ align:start position:0%
+Omega that should be dark blue mega goes
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+and the flux has become capital so many
+
+ align:start position:0%
+and the flux has become capital so many
+ 
+
+ align:start position:0%
+and the flux has become capital so many
+terms to keep track of luckily you will
+
+ align:start position:0%
+terms to keep track of luckily you will
+ 
+
+ align:start position:0%
+terms to keep track of luckily you will
+never have to and then the J becomes a
+
+ align:start position:0%
+never have to and then the J becomes a
+ 
+
+ align:start position:0%
+never have to and then the J becomes a
+capital J miss any Phi's here no because
+
+ align:start position:0%
+capital J miss any Phi's here no because
+ 
+
+ align:start position:0%
+capital J miss any Phi's here no because
+that one was already gone cool alright
+
+ align:start position:0%
+that one was already gone cool alright
+ 
+
+ align:start position:0%
+that one was already gone cool alright
+so we can use ficks law and transform
+
+ align:start position:0%
+so we can use ficks law and transform
+ 
+
+ align:start position:0%
+so we can use ficks law and transform
+the current into something related to
+
+ align:start position:0%
+the current into something related to
+ 
+
+ align:start position:0%
+the current into something related to
+flux and what we're saying here is that
+
+ align:start position:0%
+flux and what we're saying here is that
+ 
+
+ align:start position:0%
+flux and what we're saying here is that
+we're getting rid of the true physics
+
+ align:start position:0%
+we're getting rid of the true physics
+ 
+
+ align:start position:0%
+we're getting rid of the true physics
+which is that there's some fixed Neutron
+
+ align:start position:0%
+which is that there's some fixed Neutron
+ 
+
+ align:start position:0%
+which is that there's some fixed Neutron
+current and we're saying that neutrons
+
+ align:start position:0%
+current and we're saying that neutrons
+ 
+
+ align:start position:0%
+current and we're saying that neutrons
+behave kind of like a gas or a chemical
+
+ align:start position:0%
+behave kind of like a gas or a chemical
+ 
+
+ align:start position:0%
+behave kind of like a gas or a chemical
+in solution and so in yellow we can
+
+ align:start position:0%
+in solution and so in yellow we can
+ 
+
+ align:start position:0%
+in solution and so in yellow we can
+ditch our current related term and
+
+ align:start position:0%
+ditch our current related term and
+ 
+
+ align:start position:0%
+ditch our current related term and
+rewrite it we don't have any integrals
+
+ align:start position:0%
+rewrite it we don't have any integrals
+ 
+
+ align:start position:0%
+rewrite it we don't have any integrals
+left as negative del squared Phi I think
+
+ align:start position:0%
+left as negative del squared Phi I think
+ 
+
+ align:start position:0%
+left as negative del squared Phi I think
+the only variable left is our not too
+
+ align:start position:0%
+the only variable left is our not too
+ 
+
+ align:start position:0%
+the only variable left is our not too
+bad now we have a second order linear
+
+ align:start position:0%
+bad now we have a second order linear
+ 
+
+ align:start position:0%
+bad now we have a second order linear
+differential equation describing the
+
+ align:start position:0%
+differential equation describing the
+ 
+
+ align:start position:0%
+differential equation describing the
+flow of neutrons in this system it's we
+
+ align:start position:0%
+flow of neutrons in this system it's we
+ 
+
+ align:start position:0%
+flow of neutrons in this system it's we
+actually have something that we can
+
+ align:start position:0%
+actually have something that we can
+ 
+
+ align:start position:0%
+actually have something that we can
+solve for flux I think it's time to
+
+ align:start position:0%
+solve for flux I think it's time to
+ 
+
+ align:start position:0%
+solve for flux I think it's time to
+rewrite it wouldn't you say this has
+
+ align:start position:0%
+rewrite it wouldn't you say this has
+ 
+
+ align:start position:0%
+rewrite it wouldn't you say this has
+been fun so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's rewrite what's left actually see
+
+ align:start position:0%
+let's rewrite what's left actually see
+ 
+
+ align:start position:0%
+let's rewrite what's left actually see
+everything there will write it in boring
+
+ align:start position:0%
+everything there will write it in boring
+ 
+
+ align:start position:0%
+everything there will write it in boring
+old white so we have no transient
+
+ align:start position:0%
+old white so we have no transient
+ 
+
+ align:start position:0%
+old white so we have no transient
+dependence and we have left Sigma
+
+ align:start position:0%
+dependence and we have left Sigma
+ 
+
+ align:start position:0%
+dependence and we have left Sigma
+fission times flux as a function of our
+
+ align:start position:0%
+fission times flux as a function of our
+ 
+
+ align:start position:0%
+fission times flux as a function of our
+no source and we have our Neutron and I
+
+ align:start position:0%
+no source and we have our Neutron and I
+ 
+
+ align:start position:0%
+no source and we have our Neutron and I
+n reactions of oh we forgot our new
+
+ align:start position:0%
+n reactions of oh we forgot our new
+ 
+
+ align:start position:0%
+n reactions of oh we forgot our new
+Sigma fission then we have our I Sigma
+
+ align:start position:0%
+Sigma fission then we have our I Sigma
+ 
+
+ align:start position:0%
+Sigma fission then we have our I Sigma
+fission from n I n times flux next term
+
+ align:start position:0%
+fission from n I n times flux next term
+ 
+
+ align:start position:0%
+fission from n I n times flux next term
+we have photo fission so we have a new
+
+ align:start position:0%
+we have photo fission so we have a new
+ 
+
+ align:start position:0%
+we have photo fission so we have a new
+from gamma rays times Sigma fission from
+
+ align:start position:0%
+from gamma rays times Sigma fission from
+ 
+
+ align:start position:0%
+from gamma rays times Sigma fission from
+gamma rays times flux next up we have
+
+ align:start position:0%
+gamma rays times flux next up we have
+ 
+
+ align:start position:0%
+gamma rays times flux next up we have
+well last last simplification to make we
+
+ align:start position:0%
+well last last simplification to make we
+ 
+
+ align:start position:0%
+well last last simplification to make we
+have scattering and we have total
+
+ align:start position:0%
+have scattering and we have total
+ 
+
+ align:start position:0%
+have scattering and we have total
+cross-section when we said forget about
+
+ align:start position:0%
+cross-section when we said forget about
+ 
+
+ align:start position:0%
+cross-section when we said forget about
+energy and our scattering kernel becomes
+
+ align:start position:0%
+energy and our scattering kernel becomes
+ 
+
+ align:start position:0%
+energy and our scattering kernel becomes
+one and that's light blue gonna make one
+
+ align:start position:0%
+one and that's light blue gonna make one
+ 
+
+ align:start position:0%
+one and that's light blue gonna make one
+more modification to this board do we
+
+ align:start position:0%
+more modification to this board do we
+ 
+
+ align:start position:0%
+more modification to this board do we
+care about scattering at all anymore
+
+ align:start position:0%
+care about scattering at all anymore
+ 
+
+ align:start position:0%
+care about scattering at all anymore
+whatsoever because scattering doesn't
+
+ align:start position:0%
+whatsoever because scattering doesn't
+ 
+
+ align:start position:0%
+whatsoever because scattering doesn't
+change the number of neutrons left so we
+
+ align:start position:0%
+change the number of neutrons left so we
+ 
+
+ align:start position:0%
+change the number of neutrons left so we
+can then take these two terms and just
+
+ align:start position:0%
+can then take these two terms and just
+ 
+
+ align:start position:0%
+can then take these two terms and just
+call it Sigma absorption times flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if we take scattering minus the
+
+ align:start position:0%
+because if we take scattering minus the
+ 
+
+ align:start position:0%
+because if we take scattering minus the
+total cross-section it's like saying all
+
+ align:start position:0%
+total cross-section it's like saying all
+ 
+
+ align:start position:0%
+total cross-section it's like saying all
+that's left if you don't scatter is you
+
+ align:start position:0%
+that's left if you don't scatter is you
+ 
+
+ align:start position:0%
+that's left if you don't scatter is you
+absorb and if you remember all add to
+
+ align:start position:0%
+absorb and if you remember all add to
+ 
+
+ align:start position:0%
+absorb and if you remember all add to
+the energy pile we said that our total
+
+ align:start position:0%
+the energy pile we said that our total
+ 
+
+ align:start position:0%
+the energy pile we said that our total
+cross-section is scattering plus
+
+ align:start position:0%
+cross-section is scattering plus
+ 
+
+ align:start position:0%
+cross-section is scattering plus
+absorption and absorption could be
+
+ align:start position:0%
+absorption and absorption could be
+ 
+
+ align:start position:0%
+absorption and absorption could be
+vision and capture and capture could be
+
+ align:start position:0%
+vision and capture and capture could be
+ 
+
+ align:start position:0%
+vision and capture and capture could be
+lets say capture with nothing happens
+
+ align:start position:0%
+lets say capture with nothing happens
+ 
+
+ align:start position:0%
+lets say capture with nothing happens
+Plus these end I and reactions plus any
+
+ align:start position:0%
+Plus these end I and reactions plus any
+ 
+
+ align:start position:0%
+Plus these end I and reactions plus any
+other capture reaction that does
+
+ align:start position:0%
+other capture reaction that does
+ 
+
+ align:start position:0%
+other capture reaction that does
+something so we're going to use this
+
+ align:start position:0%
+something so we're going to use this
+ 
+
+ align:start position:0%
+something so we're going to use this
+cross section identity right here with a
+
+ align:start position:0%
+cross section identity right here with a
+ 
+
+ align:start position:0%
+cross section identity right here with a
+couple of minus signs on it and say well
+
+ align:start position:0%
+couple of minus signs on it and say well
+ 
+
+ align:start position:0%
+couple of minus signs on it and say well
+scattering minus total leaves you with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative absorption to simplify terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll leave that up there for everyone to
+
+ align:start position:0%
+I'll leave that up there for everyone to
+ 
+
+ align:start position:0%
+I'll leave that up there for everyone to
+see so then we have scattering and total
+
+ align:start position:0%
+see so then we have scattering and total
+ 
+
+ align:start position:0%
+see so then we have scattering and total
+just becomes minus Sigma absorption
+
+ align:start position:0%
+just becomes minus Sigma absorption
+ 
+
+ align:start position:0%
+just becomes minus Sigma absorption
+times Phi of R and we're left with what
+
+ align:start position:0%
+times Phi of R and we're left with what
+ 
+
+ align:start position:0%
+times Phi of R and we're left with what
+was that current that becomes plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's Adi missing in there isn't there
+
+ align:start position:0%
+there's Adi missing in there isn't there
+ 
+
+ align:start position:0%
+there's Adi missing in there isn't there
+a yellow D minus D okay and that's it
+
+ align:start position:0%
+a yellow D minus D okay and that's it
+ 
+
+ align:start position:0%
+a yellow D minus D okay and that's it
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+D is the diffusion coefficient right
+
+ align:start position:0%
+D is the diffusion coefficient right
+ 
+
+ align:start position:0%
+D is the diffusion coefficient right
+here so we're assuming that neutrons
+
+ align:start position:0%
+here so we're assuming that neutrons
+ 
+
+ align:start position:0%
+here so we're assuming that neutrons
+diffused like a gas or a chemical with
+
+ align:start position:0%
+diffused like a gas or a chemical with
+ 
+
+ align:start position:0%
+diffused like a gas or a chemical with
+some diffusion coefficient and so we'll
+
+ align:start position:0%
+some diffusion coefficient and so we'll
+ 
+
+ align:start position:0%
+some diffusion coefficient and so we'll
+define what that is Oh probably next
+
+ align:start position:0%
+define what that is Oh probably next
+ 
+
+ align:start position:0%
+define what that is Oh probably next
+class because we have seven minutes yeah
+
+ align:start position:0%
+class because we have seven minutes yeah
+ 
+
+ align:start position:0%
+class because we have seven minutes yeah
+Luke
+
+ align:start position:0%
+Luke
+ 
+
+ align:start position:0%
+Luke
+uh-huh the see right here that's
+
+ align:start position:0%
+uh-huh the see right here that's
+ 
+
+ align:start position:0%
+uh-huh the see right here that's
+whatever variable we're tracking so
+
+ align:start position:0%
+whatever variable we're tracking so
+ 
+
+ align:start position:0%
+whatever variable we're tracking so
+let's call that flux or let's call it an
+
+ align:start position:0%
+let's call that flux or let's call it an
+ 
+
+ align:start position:0%
+let's call that flux or let's call it an
+the number of neutrons because flux is
+
+ align:start position:0%
+the number of neutrons because flux is
+ 
+
+ align:start position:0%
+the number of neutrons because flux is
+just number of neutrons times velocity
+
+ align:start position:0%
+just number of neutrons times velocity
+ 
+
+ align:start position:0%
+just number of neutrons times velocity
+so let's say that the concentration was
+
+ align:start position:0%
+so let's say that the concentration was
+ 
+
+ align:start position:0%
+so let's say that the concentration was
+the concentration of neutrons and we
+
+ align:start position:0%
+the concentration of neutrons and we
+ 
+
+ align:start position:0%
+the concentration of neutrons and we
+just multiplied by their velocity to get
+
+ align:start position:0%
+just multiplied by their velocity to get
+ 
+
+ align:start position:0%
+just multiplied by their velocity to get
+flux so it's almost like we can say that
+
+ align:start position:0%
+flux so it's almost like we can say that
+ 
+
+ align:start position:0%
+flux so it's almost like we can say that
+the concentration of neutrons is
+
+ align:start position:0%
+the concentration of neutrons is
+ 
+
+ align:start position:0%
+the concentration of neutrons is
+directly related to the flux and that
+
+ align:start position:0%
+directly related to the flux and that
+ 
+
+ align:start position:0%
+directly related to the flux and that
+way we have everything in flux and
+
+ align:start position:0%
+way we have everything in flux and
+ 
+
+ align:start position:0%
+way we have everything in flux and
+that's the entire Neutron diffusion
+
+ align:start position:0%
+that's the entire Neutron diffusion
+ 
+
+ align:start position:0%
+that's the entire Neutron diffusion
+equation yep this is for one group with
+
+ align:start position:0%
+equation yep this is for one group with
+ 
+
+ align:start position:0%
+equation yep this is for one group with
+all the assumptions we made right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+homogeneous what other assumptions did
+
+ align:start position:0%
+homogeneous what other assumptions did
+ 
+
+ align:start position:0%
+homogeneous what other assumptions did
+we make steady state and we already
+
+ align:start position:0%
+we make steady state and we already
+ 
+
+ align:start position:0%
+we make steady state and we already
+neglected that and I think that's enough
+
+ align:start position:0%
+neglected that and I think that's enough
+ 
+
+ align:start position:0%
+neglected that and I think that's enough
+qualifiers for this but it's directly
+
+ align:start position:0%
+qualifiers for this but it's directly
+ 
+
+ align:start position:0%
+qualifiers for this but it's directly
+from this equation right here that we
+
+ align:start position:0%
+from this equation right here that we
+ 
+
+ align:start position:0%
+from this equation right here that we
+can develop what's called our
+
+ align:start position:0%
+can develop what's called our
+ 
+
+ align:start position:0%
+can develop what's called our
+criticality condition under what
+
+ align:start position:0%
+criticality condition under what
+ 
+
+ align:start position:0%
+criticality condition under what
+conditions is the reactor critical so
+
+ align:start position:0%
+conditions is the reactor critical so
+ 
+
+ align:start position:0%
+conditions is the reactor critical so
+then in this case by critical we're
+
+ align:start position:0%
+then in this case by critical we're
+ 
+
+ align:start position:0%
+then in this case by critical we're
+gonna have some variable called K
+
+ align:start position:0%
+gonna have some variable called K
+ 
+
+ align:start position:0%
+gonna have some variable called K
+effective which defines whether that's
+
+ align:start position:0%
+effective which defines whether that's
+ 
+
+ align:start position:0%
+effective which defines whether that's
+defines the number of neutrons produced
+
+ align:start position:0%
+defines the number of neutrons produced
+ 
+
+ align:start position:0%
+defines the number of neutrons produced
+over the number of neutrons consumed and
+
+ align:start position:0%
+over the number of neutrons consumed and
+ 
+
+ align:start position:0%
+over the number of neutrons consumed and
+if K effective equals 1 then we say that
+
+ align:start position:0%
+if K effective equals 1 then we say that
+ 
+
+ align:start position:0%
+if K effective equals 1 then we say that
+the reactor is critical that means that
+
+ align:start position:0%
+the reactor is critical that means that
+ 
+
+ align:start position:0%
+the reactor is critical that means that
+exactly the number of neutrons produced
+
+ align:start position:0%
+exactly the number of neutrons produced
+ 
+
+ align:start position:0%
+exactly the number of neutrons produced
+by regular fission ni n reactions and
+
+ align:start position:0%
+by regular fission ni n reactions and
+ 
+
+ align:start position:0%
+by regular fission ni n reactions and
+photo fission equals exactly the number
+
+ align:start position:0%
+photo fission equals exactly the number
+ 
+
+ align:start position:0%
+photo fission equals exactly the number
+of neutrons absorbed in the anything and
+
+ align:start position:0%
+of neutrons absorbed in the anything and
+ 
+
+ align:start position:0%
+of neutrons absorbed in the anything and
+that leaked out
+
+ align:start position:0%
+that leaked out
+ 
+
+ align:start position:0%
+that leaked out
+so let's relabeled our terms in the same
+
+ align:start position:0%
+so let's relabeled our terms in the same
+ 
+
+ align:start position:0%
+so let's relabeled our terms in the same
+font that we did here so this would be
+
+ align:start position:0%
+font that we did here so this would be
+ 
+
+ align:start position:0%
+font that we did here so this would be
+the fission term this would be n i n
+
+ align:start position:0%
+the fission term this would be n i n
+ 
+
+ align:start position:0%
+the fission term this would be n i n
+reactions
+
+ align:start position:0%
+reactions
+ 
+
+ align:start position:0%
+reactions
+this would be photo fission this would
+
+ align:start position:0%
+this would be photo fission this would
+ 
+
+ align:start position:0%
+this would be photo fission this would
+be absorption this would be leakage how
+
+ align:start position:0%
+be absorption this would be leakage how
+ 
+
+ align:start position:0%
+be absorption this would be leakage how
+many neutrons get out of our finite
+
+ align:start position:0%
+many neutrons get out of our finite
+ 
+
+ align:start position:0%
+many neutrons get out of our finite
+boundary and if you remember when we
+
+ align:start position:0%
+boundary and if you remember when we
+ 
+
+ align:start position:0%
+boundary and if you remember when we
+started out we said we're gonna make the
+
+ align:start position:0%
+started out we said we're gonna make the
+ 
+
+ align:start position:0%
+started out we said we're gonna make the
+neutron balance equation equal to gains
+
+ align:start position:0%
+neutron balance equation equal to gains
+ 
+
+ align:start position:0%
+neutron balance equation equal to gains
+minus losses and through our rainbow
+
+ align:start position:0%
+minus losses and through our rainbow
+ 
+
+ align:start position:0%
+minus losses and through our rainbow
+explosion simplification we've done
+
+ align:start position:0%
+explosion simplification we've done
+ 
+
+ align:start position:0%
+explosion simplification we've done
+exactly that these are your gains these
+
+ align:start position:0%
+exactly that these are your gains these
+ 
+
+ align:start position:0%
+exactly that these are your gains these
+are your losses when gains minus losses
+
+ align:start position:0%
+are your losses when gains minus losses
+ 
+
+ align:start position:0%
+are your losses when gains minus losses
+equals zero the reactors in perfect
+
+ align:start position:0%
+equals zero the reactors in perfect
+ 
+
+ align:start position:0%
+equals zero the reactors in perfect
+balance yep leakage comes out to be
+
+ align:start position:0%
+balance yep leakage comes out to be
+ 
+
+ align:start position:0%
+balance yep leakage comes out to be
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+despite the plus sign here and that's
+
+ align:start position:0%
+despite the plus sign here and that's
+ 
+
+ align:start position:0%
+despite the plus sign here and that's
+actually intentional
+
+ align:start position:0%
+actually intentional
+ 
+
+ align:start position:0%
+actually intentional
+that's because neutrons travel down the
+
+ align:start position:0%
+that's because neutrons travel down the
+ 
+
+ align:start position:0%
+that's because neutrons travel down the
+concentration gradient so let's say
+
+ align:start position:0%
+concentration gradient so let's say
+ 
+
+ align:start position:0%
+concentration gradient so let's say
+we're gonna draw an imaginary flux
+
+ align:start position:0%
+we're gonna draw an imaginary flux
+ 
+
+ align:start position:0%
+we're gonna draw an imaginary flux
+spectrum that's gonna be quite correct
+
+ align:start position:0%
+spectrum that's gonna be quite correct
+ 
+
+ align:start position:0%
+spectrum that's gonna be quite correct
+and I'm doing all of those features for
+
+ align:start position:0%
+and I'm doing all of those features for
+ 
+
+ align:start position:0%
+and I'm doing all of those features for
+a reason but let's look at the
+
+ align:start position:0%
+a reason but let's look at the
+ 
+
+ align:start position:0%
+a reason but let's look at the
+concentration gradient right here
+
+ align:start position:0%
+concentration gradient right here
+ 
+
+ align:start position:0%
+concentration gradient right here
+leakage is positive when your flux
+
+ align:start position:0%
+leakage is positive when your flux
+ 
+
+ align:start position:0%
+leakage is positive when your flux
+gradient is negative that's why the sign
+
+ align:start position:0%
+gradient is negative that's why the sign
+ 
+
+ align:start position:0%
+gradient is negative that's why the sign
+is flipped right there so a positive
+
+ align:start position:0%
+is flipped right there so a positive
+ 
+
+ align:start position:0%
+is flipped right there so a positive
+diffusion term means you have neutrons
+
+ align:start position:0%
+diffusion term means you have neutrons
+ 
+
+ align:start position:0%
+diffusion term means you have neutrons
+leaking out down a negative
+
+ align:start position:0%
+leaking out down a negative
+ 
+
+ align:start position:0%
+leaking out down a negative
+concentration gradient because if you
+
+ align:start position:0%
+concentration gradient because if you
+ 
+
+ align:start position:0%
+concentration gradient because if you
+look at the slope here the change in X
+
+ align:start position:0%
+look at the slope here the change in X
+ 
+
+ align:start position:0%
+look at the slope here the change in X
+is positive and the change in flux is
+
+ align:start position:0%
+is positive and the change in flux is
+ 
+
+ align:start position:0%
+is positive and the change in flux is
+negative so the slope is negative
+
+ align:start position:0%
+negative so the slope is negative
+ 
+
+ align:start position:0%
+negative so the slope is negative
+concentration gradients negative that's
+
+ align:start position:0%
+concentration gradients negative that's
+ 
+
+ align:start position:0%
+concentration gradients negative that's
+why the sign is the opposite of what you
+
+ align:start position:0%
+why the sign is the opposite of what you
+ 
+
+ align:start position:0%
+why the sign is the opposite of what you
+may expect and the same thing goes for
+
+ align:start position:0%
+may expect and the same thing goes for
+ 
+
+ align:start position:0%
+may expect and the same thing goes for
+chemical or gaseous or any other kind of
+
+ align:start position:0%
+chemical or gaseous or any other kind of
+ 
+
+ align:start position:0%
+chemical or gaseous or any other kind of
+diffusion that's come glad you asked
+
+ align:start position:0%
+diffusion that's come glad you asked
+ 
+
+ align:start position:0%
+diffusion that's come glad you asked
+because that's always a point of
+
+ align:start position:0%
+because that's always a point of
+ 
+
+ align:start position:0%
+because that's always a point of
+confusion is why is there that plus sign
+
+ align:start position:0%
+confusion is why is there that plus sign
+ 
+
+ align:start position:0%
+confusion is why is there that plus sign
+that's intentional and that's correct
+
+ align:start position:0%
+that's intentional and that's correct
+ 
+
+ align:start position:0%
+that's intentional and that's correct
+cool so it's in yeah Sean
+
+ align:start position:0%
+cool so it's in yeah Sean
+ 
+
+ align:start position:0%
+cool so it's in yeah Sean
+in that case if you really explicitly
+
+ align:start position:0%
+in that case if you really explicitly
+ 
+
+ align:start position:0%
+in that case if you really explicitly
+write our losses would it be -
+
+ align:start position:0%
+write our losses would it be -
+ 
+
+ align:start position:0%
+write our losses would it be -
+absorption let's put some parentheses on
+
+ align:start position:0%
+absorption let's put some parentheses on
+ 
+
+ align:start position:0%
+absorption let's put some parentheses on
+here equals zero and a minus and when we
+
+ align:start position:0%
+here equals zero and a minus and when we
+ 
+
+ align:start position:0%
+here equals zero and a minus and when we
+say plus leakage we have that plus sign
+
+ align:start position:0%
+say plus leakage we have that plus sign
+ 
+
+ align:start position:0%
+say plus leakage we have that plus sign
+in there so I'm not gonna put any
+
+ align:start position:0%
+in there so I'm not gonna put any
+ 
+
+ align:start position:0%
+in there so I'm not gonna put any
+parentheses up here because that
+
+ align:start position:0%
+parentheses up here because that
+ 
+
+ align:start position:0%
+parentheses up here because that
+wouldn't be correct but what I can say
+
+ align:start position:0%
+wouldn't be correct but what I can say
+ 
+
+ align:start position:0%
+wouldn't be correct but what I can say
+is that gains minus losses have to be in
+
+ align:start position:0%
+is that gains minus losses have to be in
+ 
+
+ align:start position:0%
+is that gains minus losses have to be in
+perfect balance to have a K effective
+
+ align:start position:0%
+perfect balance to have a K effective
+ 
+
+ align:start position:0%
+perfect balance to have a K effective
+equal to one anyone else have any
+
+ align:start position:0%
+equal to one anyone else have any
+ 
+
+ align:start position:0%
+equal to one anyone else have any
+questions before I continue the
+
+ align:start position:0%
+questions before I continue the
+ 
+
+ align:start position:0%
+questions before I continue the
+explanation cool let's say you're
+
+ align:start position:0%
+explanation cool let's say you're
+ 
+
+ align:start position:0%
+explanation cool let's say you're
+producing more neutrons than you're
+
+ align:start position:0%
+producing more neutrons than you're
+ 
+
+ align:start position:0%
+producing more neutrons than you're
+destroying that's what we call
+
+ align:start position:0%
+destroying that's what we call
+ 
+
+ align:start position:0%
+destroying that's what we call
+supercritical so I just did an interview
+
+ align:start position:0%
+supercritical so I just did an interview
+ 
+
+ align:start position:0%
+supercritical so I just did an interview
+for this K through 12 outreach program
+
+ align:start position:0%
+for this K through 12 outreach program
+ 
+
+ align:start position:0%
+for this K through 12 outreach program
+and they said should be people be afraid
+
+ align:start position:0%
+and they said should be people be afraid
+ 
+
+ align:start position:0%
+and they said should be people be afraid
+when something quote-unquote goes
+
+ align:start position:0%
+when something quote-unquote goes
+ 
+
+ align:start position:0%
+when something quote-unquote goes
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+sounds scary emotionally right and the
+
+ align:start position:0%
+sounds scary emotionally right and the
+ 
+
+ align:start position:0%
+sounds scary emotionally right and the
+answer is absolutely not if your reactor
+
+ align:start position:0%
+answer is absolutely not if your reactor
+ 
+
+ align:start position:0%
+answer is absolutely not if your reactor
+goes critical it's turned on and it's in
+
+ align:start position:0%
+goes critical it's turned on and it's in
+ 
+
+ align:start position:0%
+goes critical it's turned on and it's in
+perfect balance that's exactly what you
+
+ align:start position:0%
+perfect balance that's exactly what you
+ 
+
+ align:start position:0%
+perfect balance that's exactly what you
+want so going critical is not a scary
+
+ align:start position:0%
+want so going critical is not a scary
+ 
+
+ align:start position:0%
+want so going critical is not a scary
+thing it means we have control if
+
+ align:start position:0%
+thing it means we have control if
+ 
+
+ align:start position:0%
+thing it means we have control if
+something goes supercritical it doesn't
+
+ align:start position:0%
+something goes supercritical it doesn't
+ 
+
+ align:start position:0%
+something goes supercritical it doesn't
+necessarily mean it's out of control
+
+ align:start position:0%
+necessarily mean it's out of control
+ 
+
+ align:start position:0%
+necessarily mean it's out of control
+reactors can be very slightly
+
+ align:start position:0%
+reactors can be very slightly
+ 
+
+ align:start position:0%
+reactors can be very slightly
+supercritical and still in control
+
+ align:start position:0%
+supercritical and still in control
+ 
+
+ align:start position:0%
+supercritical and still in control
+because of what's called delayed
+
+ align:start position:0%
+because of what's called delayed
+ 
+
+ align:start position:0%
+because of what's called delayed
+neutrons which I will not introduce
+
+ align:start position:0%
+neutrons which I will not introduce
+ 
+
+ align:start position:0%
+neutrons which I will not introduce
+today because we have two minutes if a
+
+ align:start position:0%
+today because we have two minutes if a
+ 
+
+ align:start position:0%
+today because we have two minutes if a
+reactor has a K effective of less than 1
+
+ align:start position:0%
+reactor has a K effective of less than 1
+ 
+
+ align:start position:0%
+reactor has a K effective of less than 1
+we call that subcritical so it's
+
+ align:start position:0%
+we call that subcritical so it's
+ 
+
+ align:start position:0%
+we call that subcritical so it's
+important to note that the the nuclear
+
+ align:start position:0%
+important to note that the the nuclear
+ 
+
+ align:start position:0%
+important to note that the the nuclear
+terminology that's kind of leaked out
+
+ align:start position:0%
+terminology that's kind of leaked out
+ 
+
+ align:start position:0%
+terminology that's kind of leaked out
+into our vernacular is not physically
+
+ align:start position:0%
+into our vernacular is not physically
+ 
+
+ align:start position:0%
+into our vernacular is not physically
+correct in the way that it's used words
+
+ align:start position:0%
+correct in the way that it's used words
+ 
+
+ align:start position:0%
+correct in the way that it's used words
+like critical or me are used to incite
+
+ align:start position:0%
+like critical or me are used to incite
+ 
+
+ align:start position:0%
+like critical or me are used to incite
+emotions and bring about fear when to a
+
+ align:start position:0%
+emotions and bring about fear when to a
+ 
+
+ align:start position:0%
+emotions and bring about fear when to a
+nuclear engineer critical means in
+
+ align:start position:0%
+nuclear engineer critical means in
+ 
+
+ align:start position:0%
+nuclear engineer critical means in
+perfect control in balance like you
+
+ align:start position:0%
+perfect control in balance like you
+ 
+
+ align:start position:0%
+perfect control in balance like you
+would expect are in equilibrium that all
+
+ align:start position:0%
+would expect are in equilibrium that all
+ 
+
+ align:start position:0%
+would expect are in equilibrium that all
+sounds kind of nice makes you calm down
+
+ align:start position:0%
+sounds kind of nice makes you calm down
+ 
+
+ align:start position:0%
+sounds kind of nice makes you calm down
+a little bit yeah so we can put one last
+
+ align:start position:0%
+a little bit yeah so we can put one last
+ 
+
+ align:start position:0%
+a little bit yeah so we can put one last
+term in front of our criticality
+
+ align:start position:0%
+term in front of our criticality
+ 
+
+ align:start position:0%
+term in front of our criticality
+condition we can take either the gains
+
+ align:start position:0%
+condition we can take either the gains
+ 
+
+ align:start position:0%
+condition we can take either the gains
+or the losses move the equal sign and
+
+ align:start position:0%
+or the losses move the equal sign and
+ 
+
+ align:start position:0%
+or the losses move the equal sign and
+zero over a little bit
+
+ align:start position:0%
+zero over a little bit
+ 
+
+ align:start position:0%
+zero over a little bit
+and put a 1 over K effective here this
+
+ align:start position:0%
+and put a 1 over K effective here this
+ 
+
+ align:start position:0%
+and put a 1 over K effective here this
+then perfectly describes the difference
+
+ align:start position:0%
+then perfectly describes the difference
+ 
+
+ align:start position:0%
+then perfectly describes the difference
+between the gains and the losses in a
+
+ align:start position:0%
+between the gains and the losses in a
+ 
+
+ align:start position:0%
+between the gains and the losses in a
+reactor so if the gains equal the losses
+
+ align:start position:0%
+reactor so if the gains equal the losses
+ 
+
+ align:start position:0%
+reactor so if the gains equal the losses
+then k effective must equal 1 and the
+
+ align:start position:0%
+then k effective must equal 1 and the
+ 
+
+ align:start position:0%
+then k effective must equal 1 and the
+reactor has got to be in balance if
+
+ align:start position:0%
+reactor has got to be in balance if
+ 
+
+ align:start position:0%
+reactor has got to be in balance if
+there are more gains than losses which
+
+ align:start position:0%
+there are more gains than losses which
+ 
+
+ align:start position:0%
+there are more gains than losses which
+means if you are producing more neutrons
+
+ align:start position:0%
+means if you are producing more neutrons
+ 
+
+ align:start position:0%
+means if you are producing more neutrons
+than you're consuming then k effective
+
+ align:start position:0%
+than you're consuming then k effective
+ 
+
+ align:start position:0%
+than you're consuming then k effective
+must be greater than 1 for this equation
+
+ align:start position:0%
+must be greater than 1 for this equation
+ 
+
+ align:start position:0%
+must be greater than 1 for this equation
+to still equal zero because this
+
+ align:start position:0%
+to still equal zero because this
+ 
+
+ align:start position:0%
+to still equal zero because this
+equation must be satisfied so if you're
+
+ align:start position:0%
+equation must be satisfied so if you're
+ 
+
+ align:start position:0%
+equation must be satisfied so if you're
+making more neutrons your k effectives
+
+ align:start position:0%
+making more neutrons your k effectives
+ 
+
+ align:start position:0%
+making more neutrons your k effectives
+got to be greater than 1 so you have a
+
+ align:start position:0%
+got to be greater than 1 so you have a
+ 
+
+ align:start position:0%
+got to be greater than 1 so you have a
+less than 1 multiplier in front and on
+
+ align:start position:0%
+less than 1 multiplier in front and on
+ 
+
+ align:start position:0%
+less than 1 multiplier in front and on
+the opposite side if you're losing more
+
+ align:start position:0%
+the opposite side if you're losing more
+ 
+
+ align:start position:0%
+the opposite side if you're losing more
+neutrons than you're gaining your K
+
+ align:start position:0%
+neutrons than you're gaining your K
+ 
+
+ align:start position:0%
+neutrons than you're gaining your K
+effective has to be less than 1 to make
+
+ align:start position:0%
+effective has to be less than 1 to make
+ 
+
+ align:start position:0%
+effective has to be less than 1 to make
+this equation balanced going along with
+
+ align:start position:0%
+this equation balanced going along with
+ 
+
+ align:start position:0%
+this equation balanced going along with
+all these definitions right here so it's
+
+ align:start position:0%
+all these definitions right here so it's
+ 
+
+ align:start position:0%
+all these definitions right here so it's
+exactly 505 of I've given you delivered
+
+ align:start position:0%
+exactly 505 of I've given you delivered
+ 
+
+ align:start position:0%
+exactly 505 of I've given you delivered
+promised blackboard of Lucky Charms and
+
+ align:start position:0%
+promised blackboard of Lucky Charms and
+ 
+
+ align:start position:0%
+promised blackboard of Lucky Charms and
+we've hit perfect spot which is the one
+
+ align:start position:0%
+we've hit perfect spot which is the one
+ 
+
+ align:start position:0%
+we've hit perfect spot which is the one
+group homogeneous steady-state neutron
+
+ align:start position:0%
+group homogeneous steady-state neutron
+ 
+
+ align:start position:0%
+group homogeneous steady-state neutron
+diffusion equation from which we can
+
+ align:start position:0%
+diffusion equation from which we can
+ 
+
+ align:start position:0%
+diffusion equation from which we can
+develop our criticality conditions and
+
+ align:start position:0%
+develop our criticality conditions and
+ 
+
+ align:start position:0%
+develop our criticality conditions and
+solve this much simpler equation to get
+
+ align:start position:0%
+solve this much simpler equation to get
+ 
+
+ align:start position:0%
+solve this much simpler equation to get
+the flux profiles that I've started to
+
+ align:start position:0%
+the flux profiles that I've started to
+ 
+
+ align:start position:0%
+the flux profiles that I've started to
+draw here so I want to stop here and
+
+ align:start position:0%
+draw here so I want to stop here and
+ 
+
+ align:start position:0%
+draw here so I want to stop here and
+take any questions on any of the terms
+
+ align:start position:0%
+take any questions on any of the terms
+ 
+
+ align:start position:0%
+take any questions on any of the terms
+you see here yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the disparate energy groups and then
+
+ align:start position:0%
+the disparate energy groups and then
+ 
+
+ align:start position:0%
+the disparate energy groups and then
+when we're doing the one group you're
+
+ align:start position:0%
+when we're doing the one group you're
+ 
+
+ align:start position:0%
+when we're doing the one group you're
+actually just treating sperm one fast
+
+ align:start position:0%
+actually just treating sperm one fast
+ 
+
+ align:start position:0%
+actually just treating sperm one fast
+together we are that's right yep so a
+
+ align:start position:0%
+together we are that's right yep so a
+ 
+
+ align:start position:0%
+together we are that's right yep so a
+lot of reactors at least thermal
+
+ align:start position:0%
+lot of reactors at least thermal
+ 
+
+ align:start position:0%
+lot of reactors at least thermal
+reactors where you only care if neutrons
+
+ align:start position:0%
+reactors where you only care if neutrons
+ 
+
+ align:start position:0%
+reactors where you only care if neutrons
+are thermal or not two groups enough
+
+ align:start position:0%
+are thermal or not two groups enough
+ 
+
+ align:start position:0%
+are thermal or not two groups enough
+when you have a one group or a two group
+
+ align:start position:0%
+when you have a one group or a two group
+ 
+
+ align:start position:0%
+when you have a one group or a two group
+equation these are fairly analytically
+
+ align:start position:0%
+equation these are fairly analytically
+ 
+
+ align:start position:0%
+equation these are fairly analytically
+solvable things and get to any more
+
+ align:start position:0%
+solvable things and get to any more
+ 
+
+ align:start position:0%
+solvable things and get to any more
+groups than that and yes they're
+
+ align:start position:0%
+groups than that and yes they're
+ 
+
+ align:start position:0%
+groups than that and yes they're
+analytically solvable but it gets
+
+ align:start position:0%
+analytically solvable but it gets
+ 
+
+ align:start position:0%
+analytically solvable but it gets
+horrible and that's why we have
+
+ align:start position:0%
+horrible and that's why we have
+ 
+
+ align:start position:0%
+horrible and that's why we have
+computers to do the sorts of repetitive
+
+ align:start position:0%
+computers to do the sorts of repetitive
+ 
+
+ align:start position:0%
+computers to do the sorts of repetitive
+calculations over and over again once
+
+ align:start position:0%
+calculations over and over again once
+ 
+
+ align:start position:0%
+calculations over and over again once
+we've solved the one group equation I'll
+
+ align:start position:0%
+we've solved the one group equation I'll
+ 
+
+ align:start position:0%
+we've solved the one group equation I'll
+then show you intuitive ways to write
+
+ align:start position:0%
+then show you intuitive ways to write
+ 
+
+ align:start position:0%
+then show you intuitive ways to write
+but not solve the equations for multi
+
+ align:start position:0%
+but not solve the equations for multi
+ 
+
+ align:start position:0%
+but not solve the equations for multi
+group equations sure any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so like I promise we didn't stay complex
+
+ align:start position:0%
+so like I promise we didn't stay complex
+ 
+
+ align:start position:0%
+so like I promise we didn't stay complex
+for long because there's basically
+
+ align:start position:0%
+for long because there's basically
+ 
+
+ align:start position:0%
+for long because there's basically
+nothing left yeah oh that's a partial
+
+ align:start position:0%
+nothing left yeah oh that's a partial
+ 
+
+ align:start position:0%
+nothing left yeah oh that's a partial
+derivatives yep that yeah there we go
+
+ align:start position:0%
+derivatives yep that yeah there we go
+ 
+
+ align:start position:0%
+derivatives yep that yeah there we go
+yeah so this is saying a change in
+
+ align:start position:0%
+yeah so this is saying a change in
+ 
+
+ align:start position:0%
+yeah so this is saying a change in
+Neutron population or the partial
+
+ align:start position:0%
+Neutron population or the partial
+ 
+
+ align:start position:0%
+Neutron population or the partial
+derivative of n with respect to T cuz n
+
+ align:start position:0%
+derivative of n with respect to T cuz n
+ 
+
+ align:start position:0%
+derivative of n with respect to T cuz n
+varies with space energy angle time and
+
+ align:start position:0%
+varies with space energy angle time and
+ 
+
+ align:start position:0%
+varies with space energy angle time and
+anything else you could possibly think
+
+ align:start position:0%
+anything else you could possibly think
+ 
+
+ align:start position:0%
+anything else you could possibly think
+about equals the gains minus the losses
+
+ align:start position:0%
+about equals the gains minus the losses
+ 
+
+ align:start position:0%
+about equals the gains minus the losses
+I think this is worthy of a t-shirt if
+
+ align:start position:0%
+I think this is worthy of a t-shirt if
+ 
+
+ align:start position:0%
+I think this is worthy of a t-shirt if
+any of you guys would like to update the
+
+ align:start position:0%
+any of you guys would like to update the
+ 
+
+ align:start position:0%
+any of you guys would like to update the
+department shirts to properly take into
+
+ align:start position:0%
+department shirts to properly take into
+ 
+
+ align:start position:0%
+department shirts to properly take into
+account photo fission external sources
+
+ align:start position:0%
+account photo fission external sources
+ 
+
+ align:start position:0%
+account photo fission external sources
+and ni n reactions I think it would make
+
+ align:start position:0%
+and ni n reactions I think it would make
+ 
+
+ align:start position:0%
+and ni n reactions I think it would make
+for a much more impressive thing because
+
+ align:start position:0%
+for a much more impressive thing because
+ 
+
+ align:start position:0%
+for a much more impressive thing because
+we kind of printed an oversimplification
+
+ align:start position:0%
+we kind of printed an oversimplification
+ 
+
+ align:start position:0%
+we kind of printed an oversimplification
+before it's too bad and we definitely
+
+ align:start position:0%
+before it's too bad and we definitely
+ 
+
+ align:start position:0%
+before it's too bad and we definitely
+had room on the shirt there was like
+
+ align:start position:0%
+had room on the shirt there was like
+ 
+
+ align:start position:0%
+had room on the shirt there was like
+room on the sides and on the sleeves
+
+ align:start position:0%
+room on the sides and on the sleeves
+ 
+
+ align:start position:0%
+room on the sides and on the sleeves
+yeah keep going on that might have to be
+
+ align:start position:0%
+yeah keep going on that might have to be
+ 
+
+ align:start position:0%
+yeah keep going on that might have to be
+long-sleeved I think they'll be pretty
+
+ align:start position:0%
+long-sleeved I think they'll be pretty
+ 
+
+ align:start position:0%
+long-sleeved I think they'll be pretty
+soon yeah okay if no one else has any
+
+ align:start position:0%
+soon yeah okay if no one else has any
+ 
+
+ align:start position:0%
+soon yeah okay if no one else has any
+immediate questions you'll have plenty
+
+ align:start position:0%
+immediate questions you'll have plenty
+ 
+
+ align:start position:0%
+immediate questions you'll have plenty
+of time tomorrow because the whole goal
+
+ align:start position:0%
+of time tomorrow because the whole goal
+ 
+
+ align:start position:0%
+of time tomorrow because the whole goal
+tomorrow is gonna be to solve this
+
+ align:start position:0%
+tomorrow is gonna be to solve this
+ 
+
+ align:start position:0%
+tomorrow is gonna be to solve this
+equation that's only gonna take like 20
+
+ align:start position:0%
+equation that's only gonna take like 20
+ 
+
+ align:start position:0%
+equation that's only gonna take like 20
+minutes so we can do a quick review of
+
+ align:start position:0%
+minutes so we can do a quick review of
+ 
+
+ align:start position:0%
+minutes so we can do a quick review of
+the simplification of the neutron
+
+ align:start position:0%
+the simplification of the neutron
+ 
+
+ align:start position:0%
+the simplification of the neutron
+transport equation solve the neutron
+
+ align:start position:0%
+transport equation solve the neutron
+ 
+
+ align:start position:0%
+transport equation solve the neutron
+diffusion equation if you have questions
+
+ align:start position:0%
+diffusion equation if you have questions
+ 
+
+ align:start position:0%
+diffusion equation if you have questions
+we'll spend time to answer them there
+
+ align:start position:0%
+we'll spend time to answer them there
+ 
+
+ align:start position:0%
+we'll spend time to answer them there
+and if you don't we'll move on to
+
+ align:start position:0%
+and if you don't we'll move on to
+ 
+
+ align:start position:0%
+and if you don't we'll move on to
+writing multi group equations and also
+
+ align:start position:0%
+writing multi group equations and also
+ 
+
+ align:start position:0%
+writing multi group equations and also
+Friday for recitation it's electron
+
+ align:start position:0%
+Friday for recitation it's electron
+ 
+
+ align:start position:0%
+Friday for recitation it's electron
+microscope time so now that you guys
+
+ align:start position:0%
+microscope time so now that you guys
+ 
+
+ align:start position:0%
+microscope time so now that you guys
+have learned different electron
+
+ align:start position:0%
+have learned different electron
+ 
+
+ align:start position:0%
+have learned different electron
+interactions with matter you're going to
+
+ align:start position:0%
+interactions with matter you're going to
+ 
+
+ align:start position:0%
+interactions with matter you're going to
+see them so we're going to be analyzing
+
+ align:start position:0%
+see them so we're going to be analyzing
+ 
+
+ align:start position:0%
+see them so we're going to be analyzing
+a couple of different pieces of
+
+ align:start position:0%
+a couple of different pieces of
+ 
+
+ align:start position:0%
+a couple of different pieces of
+materials that a couple of you are gonna
+
+ align:start position:0%
+materials that a couple of you are gonna
+ 
+
+ align:start position:0%
+materials that a couple of you are gonna
+get to select and we're going to image
+
+ align:start position:0%
+get to select and we're going to image
+ 
+
+ align:start position:0%
+get to select and we're going to image
+them with electrons to show how you can
+
+ align:start position:0%
+them with electrons to show how you can
+ 
+
+ align:start position:0%
+them with electrons to show how you can
+beat the wavelength of light imaging
+
+ align:start position:0%
+beat the wavelength of light imaging
+ 
+
+ align:start position:0%
+beat the wavelength of light imaging
+limit like I told you before we're gonna
+
+ align:start position:0%
+limit like I told you before we're gonna
+ 
+
+ align:start position:0%
+limit like I told you before we're gonna
+produce our own x-ray spectra to analyze
+
+ align:start position:0%
+produce our own x-ray spectra to analyze
+ 
+
+ align:start position:0%
+produce our own x-ray spectra to analyze
+them elementally where you'll see the
+
+ align:start position:0%
+them elementally where you'll see the
+ 
+
+ align:start position:0%
+them elementally where you'll see the
+bremsstrahlung you'll see the
+
+ align:start position:0%
+bremsstrahlung you'll see the
+ 
+
+ align:start position:0%
+bremsstrahlung you'll see the
+characteristic Peaks and you'll see a
+
+ align:start position:0%
+characteristic Peaks and you'll see a
+ 
+
+ align:start position:0%
+characteristic Peaks and you'll see a
+couple of other features that I'll
+
+ align:start position:0%
+couple of other features that I'll
+ 
+
+ align:start position:0%
+couple of other features that I'll
+explain too so get ready for some SEM
+
+ align:start position:0%
+explain too so get ready for some SEM
+ 
+
+ align:start position:0%
+explain too so get ready for some SEM
+tomorrow
\ No newline at end of file
diff --git a/L8PXcZ2ExiU.txt b/L8PXcZ2ExiU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cb7ae02b6c124893ed810e43c3d640c1a672ef82
--- /dev/null
+++ b/L8PXcZ2ExiU.txt
@@ -0,0 +1,15307 @@
+align:start position:0%
+ 
+today we're going to uh continue we're
+
+ align:start position:0%
+today we're going to uh continue we're
+ 
+
+ align:start position:0%
+today we're going to uh continue we're
+going to talk about a new notion a
+
+ align:start position:0%
+going to talk about a new notion a
+ 
+
+ align:start position:0%
+going to talk about a new notion a
+really really interesting notion in my
+
+ align:start position:0%
+really really interesting notion in my
+ 
+
+ align:start position:0%
+really really interesting notion in my
+opinion uh called probabilistically
+
+ align:start position:0%
+opinion uh called probabilistically
+ 
+
+ align:start position:0%
+opinion uh called probabilistically
+checkable proofs I'll explain what it is
+
+ align:start position:0%
+checkable proofs I'll explain what it is
+ 
+
+ align:start position:0%
+checkable proofs I'll explain what it is
+so we'll we're going to Define this
+
+ align:start position:0%
+so we'll we're going to Define this
+ 
+
+ align:start position:0%
+so we'll we're going to Define this
+notion and we're going to construct it
+
+ align:start position:0%
+notion and we're going to construct it
+ 
+
+ align:start position:0%
+notion and we're going to construct it
+uh from the GK protocol so you'll kind
+
+ align:start position:0%
+uh from the GK protocol so you'll kind
+ 
+
+ align:start position:0%
+uh from the GK protocol so you'll kind
+of see not only the definition but
+
+ align:start position:0%
+of see not only the definition but
+ 
+
+ align:start position:0%
+of see not only the definition but
+you'll be able after this class the hope
+
+ align:start position:0%
+you'll be able after this class the hope
+ 
+
+ align:start position:0%
+you'll be able after this class the hope
+is that you'll be able to construct a
+
+ align:start position:0%
+is that you'll be able to construct a
+ 
+
+ align:start position:0%
+is that you'll be able to construct a
+PCP if you need to construct proof
+
+ align:start position:0%
+PCP if you need to construct proof
+ 
+
+ align:start position:0%
+PCP if you need to construct proof
+you'll be able to do that so that's
+
+ align:start position:0%
+you'll be able to do that so that's
+ 
+
+ align:start position:0%
+you'll be able to do that so that's
+going to be the first part of today's
+
+ align:start position:0%
+going to be the first part of today's
+ 
+
+ align:start position:0%
+going to be the first part of today's
+lecture and the second part of today's
+
+ align:start position:0%
+lecture and the second part of today's
+ 
+
+ align:start position:0%
+lecture and the second part of today's
+lecture is actually going to be the
+
+ align:start position:0%
+lecture is actually going to be the
+ 
+
+ align:start position:0%
+lecture is actually going to be the
+first time we actually use cryptography
+
+ align:start position:0%
+first time we actually use cryptography
+ 
+
+ align:start position:0%
+first time we actually use cryptography
+so so far this class has not been at all
+
+ align:start position:0%
+so so far this class has not been at all
+ 
+
+ align:start position:0%
+so so far this class has not been at all
+about cryptography it was everything was
+
+ align:start position:0%
+about cryptography it was everything was
+ 
+
+ align:start position:0%
+about cryptography it was everything was
+information it was actually complexity
+
+ align:start position:0%
+information it was actually complexity
+ 
+
+ align:start position:0%
+information it was actually complexity
+Theory uh but today is going to be the
+
+ align:start position:0%
+Theory uh but today is going to be the
+ 
+
+ align:start position:0%
+Theory uh but today is going to be the
+first time we're going to move
+
+ align:start position:0%
+first time we're going to move
+ 
+
+ align:start position:0%
+first time we're going to move
+into uh
+
+ align:start position:0%
+into uh
+ 
+
+ align:start position:0%
+into uh
+cryptography and uh as we'll talk we'll
+
+ align:start position:0%
+cryptography and uh as we'll talk we'll
+ 
+
+ align:start position:0%
+cryptography and uh as we'll talk we'll
+see that doing this information
+
+ align:start position:0%
+see that doing this information
+ 
+
+ align:start position:0%
+see that doing this information
+theoretic proofs where you say okay no
+
+ align:start position:0%
+theoretic proofs where you say okay no
+ 
+
+ align:start position:0%
+theoretic proofs where you say okay no
+Pro can create a give you a false proof
+
+ align:start position:0%
+Pro can create a give you a false proof
+ 
+
+ align:start position:0%
+Pro can create a give you a false proof
+that is limiting okay we can do
+
+ align:start position:0%
+that is limiting okay we can do
+ 
+
+ align:start position:0%
+that is limiting okay we can do
+everything we want using that uh a this
+
+ align:start position:0%
+everything we want using that uh a this
+ 
+
+ align:start position:0%
+everything we want using that uh a this
+notion and therefore we're going to go
+
+ align:start position:0%
+notion and therefore we're going to go
+ 
+
+ align:start position:0%
+notion and therefore we're going to go
+into a new notion of soundness which is
+
+ align:start position:0%
+into a new notion of soundness which is
+ 
+
+ align:start position:0%
+into a new notion of soundness which is
+what we call arguments or computational
+
+ align:start position:0%
+what we call arguments or computational
+ 
+
+ align:start position:0%
+what we call arguments or computational
+soundness and we're going to relax the
+
+ align:start position:0%
+soundness and we're going to relax the
+ 
+
+ align:start position:0%
+soundness and we're going to relax the
+prover and say an all Power Pro an all
+
+ align:start position:0%
+prover and say an all Power Pro an all
+ 
+
+ align:start position:0%
+prover and say an all Power Pro an all
+powerful approver may be able to cheat
+
+ align:start position:0%
+powerful approver may be able to cheat
+ 
+
+ align:start position:0%
+powerful approver may be able to cheat
+but the guarantee we give hey Tony is
+
+ align:start position:0%
+but the guarantee we give hey Tony is
+ 
+
+ align:start position:0%
+but the guarantee we give hey Tony is
+that a computationally bounded PR cannot
+
+ align:start position:0%
+that a computationally bounded PR cannot
+ 
+
+ align:start position:0%
+that a computationally bounded PR cannot
+cheat okay that's going to be the
+
+ align:start position:0%
+cheat okay that's going to be the
+ 
+
+ align:start position:0%
+cheat okay that's going to be the
+guarantee we get and we'll see once we
+
+ align:start position:0%
+guarantee we get and we'll see once we
+ 
+
+ align:start position:0%
+guarantee we get and we'll see once we
+relax the soundness requirement to a
+
+ align:start position:0%
+relax the soundness requirement to a
+ 
+
+ align:start position:0%
+relax the soundness requirement to a
+requirement that's only computational
+
+ align:start position:0%
+requirement that's only computational
+ 
+
+ align:start position:0%
+requirement that's only computational
+sound then we'll be able to get a lot
+
+ align:start position:0%
+sound then we'll be able to get a lot
+ 
+
+ align:start position:0%
+sound then we'll be able to get a lot
+more and kind of uh you know the life
+
+ align:start position:0%
+more and kind of uh you know the life
+ 
+
+ align:start position:0%
+more and kind of uh you know the life
+will kind of open for us and we're going
+
+ align:start position:0%
+will kind of open for us and we're going
+ 
+
+ align:start position:0%
+will kind of open for us and we're going
+to have a lot a lot of new uh kind of
+
+ align:start position:0%
+to have a lot a lot of new uh kind of
+ 
+
+ align:start position:0%
+to have a lot a lot of new uh kind of
+constructions and things that we were
+
+ align:start position:0%
+constructions and things that we were
+ 
+
+ align:start position:0%
+constructions and things that we were
+unable to do information
+
+ align:start position:0%
+unable to do information
+ 
+
+ align:start position:0%
+unable to do information
+theoretically so this is uh the plan for
+
+ align:start position:0%
+theoretically so this is uh the plan for
+ 
+
+ align:start position:0%
+theoretically so this is uh the plan for
+today questions before we start I
+
+ align:start position:0%
+today questions before we start I
+ 
+
+ align:start position:0%
+today questions before we start I
+haven't seen you guys in a
+
+ align:start position:0%
+haven't seen you guys in a
+ 
+
+ align:start position:0%
+haven't seen you guys in a
+while so it's good to see you a lot of
+
+ align:start position:0%
+while so it's good to see you a lot of
+ 
+
+ align:start position:0%
+while so it's good to see you a lot of
+things changed since the last time I've
+
+ align:start position:0%
+things changed since the last time I've
+ 
+
+ align:start position:0%
+things changed since the last time I've
+seen you I'm probably going to be a bit
+
+ align:start position:0%
+seen you I'm probably going to be a bit
+ 
+
+ align:start position:0%
+seen you I'm probably going to be a bit
+distracted today so I'm sorry
+
+ align:start position:0%
+distracted today so I'm sorry
+ 
+
+ align:start position:0%
+distracted today so I'm sorry
+okay okay let's start so what are no
+
+ align:start position:0%
+okay okay let's start so what are no
+ 
+
+ align:start position:0%
+okay okay let's start so what are no
+questions okay so let's start with pcps
+
+ align:start position:0%
+questions okay so let's start with pcps
+ 
+
+ align:start position:0%
+questions okay so let's start with pcps
+what are probity checkable proofs
+
+ align:start position:0%
+what are probity checkable proofs
+ 
+
+ align:start position:0%
+what are probity checkable proofs
+so these are the idea of probability
+
+ align:start position:0%
+so these are the idea of probability
+ 
+
+ align:start position:0%
+so these are the idea of probability
+checkable proofs is to take a proof like
+
+ align:start position:0%
+checkable proofs is to take a proof like
+ 
+
+ align:start position:0%
+checkable proofs is to take a proof like
+a classical proof think of NP in NP we
+
+ align:start position:0%
+a classical proof think of NP in NP we
+ 
+
+ align:start position:0%
+a classical proof think of NP in NP we
+have a instance X and A Witness this
+
+ align:start position:0%
+have a instance X and A Witness this
+ 
+
+ align:start position:0%
+have a instance X and A Witness this
+witness is like a proof for X being in
+
+ align:start position:0%
+witness is like a proof for X being in
+ 
+
+ align:start position:0%
+witness is like a proof for X being in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+language to verify this proof you need
+
+ align:start position:0%
+language to verify this proof you need
+ 
+
+ align:start position:0%
+language to verify this proof you need
+to read the entire thing and do some
+
+ align:start position:0%
+to read the entire thing and do some
+ 
+
+ align:start position:0%
+to read the entire thing and do some
+computation like this verification
+
+ align:start position:0%
+computation like this verification
+ 
+
+ align:start position:0%
+computation like this verification
+circuit you know a that checks that X
+
+ align:start position:0%
+circuit you know a that checks that X
+ 
+
+ align:start position:0%
+circuit you know a that checks that X
+and W is in the relation there's a
+
+ align:start position:0%
+and W is in the relation there's a
+ 
+
+ align:start position:0%
+and W is in the relation there's a
+circuit that checks this
+
+ align:start position:0%
+circuit that checks this
+ 
+
+ align:start position:0%
+circuit that checks this
+okay what is the idea of a probability
+
+ align:start position:0%
+okay what is the idea of a probability
+ 
+
+ align:start position:0%
+okay what is the idea of a probability
+checkable proof the idea here what we
+
+ align:start position:0%
+checkable proof the idea here what we
+ 
+
+ align:start position:0%
+checkable proof the idea here what we
+want is to take this proof and convert
+
+ align:start position:0%
+want is to take this proof and convert
+ 
+
+ align:start position:0%
+want is to take this proof and convert
+it into a new proof it may be larger
+
+ align:start position:0%
+it into a new proof it may be larger
+ 
+
+ align:start position:0%
+it into a new proof it may be larger
+actually than the original proof so
+
+ align:start position:0%
+actually than the original proof so
+ 
+
+ align:start position:0%
+actually than the original proof so
+maybe you know the original proof was of
+
+ align:start position:0%
+maybe you know the original proof was of
+ 
+
+ align:start position:0%
+maybe you know the original proof was of
+size M let's say the instance of size n
+
+ align:start position:0%
+size M let's say the instance of size n
+ 
+
+ align:start position:0%
+size M let's say the instance of size n
+this may be of size much bigger still we
+
+ align:start position:0%
+this may be of size much bigger still we
+ 
+
+ align:start position:0%
+this may be of size much bigger still we
+want it to be polinomial in n&
+
+ align:start position:0%
+want it to be polinomial in n&
+ 
+
+ align:start position:0%
+want it to be polinomial in n&
+M but now so we just made it bigger so
+
+ align:start position:0%
+M but now so we just made it bigger so
+ 
+
+ align:start position:0%
+M but now so we just made it bigger so
+what's what's good about it so what's
+
+ align:start position:0%
+what's what's good about it so what's
+ 
+
+ align:start position:0%
+what's what's good about it so what's
+nice about this proof is the IDE is you
+
+ align:start position:0%
+nice about this proof is the IDE is you
+ 
+
+ align:start position:0%
+nice about this proof is the IDE is you
+don't actually have to read all of it to
+
+ align:start position:0%
+don't actually have to read all of it to
+ 
+
+ align:start position:0%
+don't actually have to read all of it to
+check it and that's weird so the idea
+
+ align:start position:0%
+check it and that's weird so the idea
+ 
+
+ align:start position:0%
+check it and that's weird so the idea
+here yeah the proof may be a little
+
+ align:start position:0%
+here yeah the proof may be a little
+ 
+
+ align:start position:0%
+here yeah the proof may be a little
+longer polom longer but you only need to
+
+ align:start position:0%
+longer polom longer but you only need to
+ 
+
+ align:start position:0%
+longer polom longer but you only need to
+read a few
+
+ align:start position:0%
+read a few
+ 
+
+ align:start position:0%
+read a few
+locations to and to check that it's
+
+ align:start position:0%
+locations to and to check that it's
+ 
+
+ align:start position:0%
+locations to and to check that it's
+valid so to verify often pcps are
+
+ align:start position:0%
+valid so to verify often pcps are
+ 
+
+ align:start position:0%
+valid so to verify often pcps are
+denoted by pi uh to verify PCP proof
+
+ align:start position:0%
+denoted by pi uh to verify PCP proof
+ 
+
+ align:start position:0%
+denoted by pi uh to verify PCP proof
+given X all the verifier needs to do is
+
+ align:start position:0%
+given X all the verifier needs to do is
+ 
+
+ align:start position:0%
+given X all the verifier needs to do is
+query doesn't actually need to read
+
+ align:start position:0%
+query doesn't actually need to read
+ 
+
+ align:start position:0%
+query doesn't actually need to read
+these things he queries a few locations
+
+ align:start position:0%
+these things he queries a few locations
+ 
+
+ align:start position:0%
+these things he queries a few locations
+a few bits checks a few bits of the
+
+ align:start position:0%
+a few bits checks a few bits of the
+ 
+
+ align:start position:0%
+a few bits checks a few bits of the
+proof and then applies a verification
+
+ align:start position:0%
+proof and then applies a verification
+ 
+
+ align:start position:0%
+proof and then applies a verification
+circuit that depends only on these
+
+ align:start position:0%
+circuit that depends only on these
+ 
+
+ align:start position:0%
+circuit that depends only on these
+bits okay and importantly the bits he
+
+ align:start position:0%
+bits okay and importantly the bits he
+ 
+
+ align:start position:0%
+bits okay and importantly the bits he
+chooses are random the the prover
+
+ align:start position:0%
+chooses are random the the prover
+ 
+
+ align:start position:0%
+chooses are random the the prover
+doesn't know otherwise he will it's like
+
+ align:start position:0%
+doesn't know otherwise he will it's like
+ 
+
+ align:start position:0%
+doesn't know otherwise he will it's like
+shrinking if he knew the prover knew oh
+
+ align:start position:0%
+shrinking if he knew the prover knew oh
+ 
+
+ align:start position:0%
+shrinking if he knew the prover knew oh
+the refer is going to only check in bit
+
+ align:start position:0%
+the refer is going to only check in bit
+ 
+
+ align:start position:0%
+the refer is going to only check in bit
+17 22 and 25 then he would just give you
+
+ align:start position:0%
+17 22 and 25 then he would just give you
+ 
+
+ align:start position:0%
+17 22 and 25 then he would just give you
+it's like you'll have a succinct witness
+
+ align:start position:0%
+it's like you'll have a succinct witness
+ 
+
+ align:start position:0%
+it's like you'll have a succinct witness
+and of course we can't take arbitrary
+
+ align:start position:0%
+and of course we can't take arbitrary
+ 
+
+ align:start position:0%
+and of course we can't take arbitrary
+Witnesses and just make them 16 if you
+
+ align:start position:0%
+Witnesses and just make them 16 if you
+ 
+
+ align:start position:0%
+Witnesses and just make them 16 if you
+don't believe that's possible yeah so
+
+ align:start position:0%
+don't believe that's possible yeah so
+ 
+
+ align:start position:0%
+don't believe that's possible yeah so
+it's a PTP then only used for as m is
+
+ align:start position:0%
+it's a PTP then only used for as m is
+ 
+
+ align:start position:0%
+it's a PTP then only used for as m is
+much greater than M okay so the question
+
+ align:start position:0%
+much greater than M okay so the question
+ 
+
+ align:start position:0%
+much greater than M okay so the question
+was is a PCP used if m is much greater
+
+ align:start position:0%
+was is a PCP used if m is much greater
+ 
+
+ align:start position:0%
+was is a PCP used if m is much greater
+than n and the answer is no actually we
+
+ align:start position:0%
+than n and the answer is no actually we
+ 
+
+ align:start position:0%
+than n and the answer is no actually we
+can think of it we can even use it where
+
+ align:start position:0%
+can think of it we can even use it where
+ 
+
+ align:start position:0%
+can think of it we can even use it where
+M the length of w is n to the Epsilon
+
+ align:start position:0%
+M the length of w is n to the Epsilon
+ 
+
+ align:start position:0%
+M the length of w is n to the Epsilon
+okay even less than n to the EPS even n
+
+ align:start position:0%
+okay even less than n to the EPS even n
+ 
+
+ align:start position:0%
+okay even less than n to the EPS even n
+to the little o of n now you this will
+
+ align:start position:0%
+to the little o of n now you this will
+ 
+
+ align:start position:0%
+to the little o of n now you this will
+still be polinomial in N so actually you
+
+ align:start position:0%
+still be polinomial in N so actually you
+ 
+
+ align:start position:0%
+still be polinomial in N so actually you
+you took the proof and make it actually
+
+ align:start position:0%
+you took the proof and make it actually
+ 
+
+ align:start position:0%
+you took the proof and make it actually
+more than polom larger because it's
+
+ align:start position:0%
+more than polom larger because it's
+ 
+
+ align:start position:0%
+more than polom larger because it's
+polinomial an n and M and if the proof
+
+ align:start position:0%
+polinomial an n and M and if the proof
+ 
+
+ align:start position:0%
+polinomial an n and M and if the proof
+here is smaller is n to the little of
+
+ align:start position:0%
+here is smaller is n to the little of
+ 
+
+ align:start position:0%
+here is smaller is n to the little of
+one then this is polyn it's actually
+
+ align:start position:0%
+one then this is polyn it's actually
+ 
+
+ align:start position:0%
+one then this is polyn it's actually
+more than polinomial bigger but so
+
+ align:start position:0%
+more than polinomial bigger but so
+ 
+
+ align:start position:0%
+more than polinomial bigger but so
+you're saying what did we gain we took
+
+ align:start position:0%
+you're saying what did we gain we took
+ 
+
+ align:start position:0%
+you're saying what did we gain we took
+us a short proof made it so much bigger
+
+ align:start position:0%
+us a short proof made it so much bigger
+ 
+
+ align:start position:0%
+us a short proof made it so much bigger
+what did we gain and what we gained is
+
+ align:start position:0%
+what did we gain and what we gained is
+ 
+
+ align:start position:0%
+what did we gain and what we gained is
+the Hope is that you can query this the
+
+ align:start position:0%
+the Hope is that you can query this the
+ 
+
+ align:start position:0%
+the Hope is that you can query this the
+verif can query this in very very few
+
+ align:start position:0%
+verif can query this in very very few
+ 
+
+ align:start position:0%
+verif can query this in very very few
+locations read only very very few bits
+
+ align:start position:0%
+locations read only very very few bits
+ 
+
+ align:start position:0%
+locations read only very very few bits
+of this proof okay okay verifier also
+
+ align:start position:0%
+of this proof okay okay verifier also
+ 
+
+ align:start position:0%
+of this proof okay okay verifier also
+have to Rex that yeah the verifier all
+
+ align:start position:0%
+have to Rex that yeah the verifier all
+ 
+
+ align:start position:0%
+have to Rex that yeah the verifier all
+of so yes good so the question that's a
+
+ align:start position:0%
+of so yes good so the question that's a
+ 
+
+ align:start position:0%
+of so yes good so the question that's a
+good question so the question was does
+
+ align:start position:0%
+good question so the question was does
+ 
+
+ align:start position:0%
+good question so the question was does
+the verifier have to read all of X and
+
+ align:start position:0%
+the verifier have to read all of X and
+ 
+
+ align:start position:0%
+the verifier have to read all of X and
+because I said he only needs to read a
+
+ align:start position:0%
+because I said he only needs to read a
+ 
+
+ align:start position:0%
+because I said he only needs to read a
+few location the proof does he need to
+
+ align:start position:0%
+few location the proof does he need to
+ 
+
+ align:start position:0%
+few location the proof does he need to
+read all of X and a prior of course he
+
+ align:start position:0%
+read all of X and a prior of course he
+ 
+
+ align:start position:0%
+read all of X and a prior of course he
+needs to read all of X because even if
+
+ align:start position:0%
+needs to read all of X because even if
+ 
+
+ align:start position:0%
+needs to read all of X because even if
+there's one bit in X that he doesn't
+
+ align:start position:0%
+there's one bit in X that he doesn't
+ 
+
+ align:start position:0%
+there's one bit in X that he doesn't
+read you know what if that bit is it's
+
+ align:start position:0%
+read you know what if that bit is it's
+ 
+
+ align:start position:0%
+read you know what if that bit is it's
+actually what the state what the
+
+ align:start position:0%
+actually what the state what the
+ 
+
+ align:start position:0%
+actually what the state what the
+sentence is what the statement is you
+
+ align:start position:0%
+sentence is what the statement is you
+ 
+
+ align:start position:0%
+sentence is what the statement is you
+know the Prov need to know what am I
+
+ align:start position:0%
+know the Prov need to know what am I
+ 
+
+ align:start position:0%
+know the Prov need to know what am I
+reading what am I what are you proving
+
+ align:start position:0%
+reading what am I what are you proving
+ 
+
+ align:start position:0%
+reading what am I what are you proving
+to me but there are extensions called
+
+ align:start position:0%
+to me but there are extensions called
+ 
+
+ align:start position:0%
+to me but there are extensions called
+called PCP of proximity which I'm not
+
+ align:start position:0%
+called PCP of proximity which I'm not
+ 
+
+ align:start position:0%
+called PCP of proximity which I'm not
+going to get into in this class where
+
+ align:start position:0%
+going to get into in this class where
+ 
+
+ align:start position:0%
+going to get into in this class where
+actually the verify the verifier also
+
+ align:start position:0%
+actually the verify the verifier also
+ 
+
+ align:start position:0%
+actually the verify the verifier also
+doesn't read all of X but the guarantee
+
+ align:start position:0%
+doesn't read all of X but the guarantee
+ 
+
+ align:start position:0%
+doesn't read all of X but the guarantee
+is not that X is in the language it's
+
+ align:start position:0%
+is not that X is in the language it's
+ 
+
+ align:start position:0%
+is not that X is in the language it's
+the guarantee is that kind of it's a the
+
+ align:start position:0%
+the guarantee is that kind of it's a the
+ 
+
+ align:start position:0%
+the guarantee is that kind of it's a the
+Oracle that is given to the verifier
+
+ align:start position:0%
+Oracle that is given to the verifier
+ 
+
+ align:start position:0%
+Oracle that is given to the verifier
+there is something close to it that's in
+
+ align:start position:0%
+there is something close to it that's in
+ 
+
+ align:start position:0%
+there is something close to it that's in
+the linguage so it there is a notion of
+
+ align:start position:0%
+the linguage so it there is a notion of
+ 
+
+ align:start position:0%
+the linguage so it there is a notion of
+extension of this notion of the PCP
+
+ align:start position:0%
+extension of this notion of the PCP
+ 
+
+ align:start position:0%
+extension of this notion of the PCP
+where the verifier doesn't even need to
+
+ align:start position:0%
+where the verifier doesn't even need to
+ 
+
+ align:start position:0%
+where the verifier doesn't even need to
+read all of X the guarantees there are
+
+ align:start position:0%
+read all of X the guarantees there are
+ 
+
+ align:start position:0%
+read all of X the guarantees there are
+not very easy to state but it's a very
+
+ align:start position:0%
+not very easy to state but it's a very
+ 
+
+ align:start position:0%
+not very easy to state but it's a very
+useful notion actually it's used a lot
+
+ align:start position:0%
+useful notion actually it's used a lot
+ 
+
+ align:start position:0%
+useful notion actually it's used a lot
+it's called prob uh pcps of
+
+ align:start position:0%
+it's called prob uh pcps of
+ 
+
+ align:start position:0%
+it's called prob uh pcps of
+proximity okay
+
+ align:start position:0%
+proximity okay
+ 
+
+ align:start position:0%
+proximity okay
+so okay so that's what we're going to do
+
+ align:start position:0%
+so okay so that's what we're going to do
+ 
+
+ align:start position:0%
+so okay so that's what we're going to do
+today okay and let me just mention
+
+ align:start position:0%
+today okay and let me just mention
+ 
+
+ align:start position:0%
+today okay and let me just mention
+before even we start the formal thing
+
+ align:start position:0%
+before even we start the formal thing
+ 
+
+ align:start position:0%
+before even we start the formal thing
+let me just say this is really an
+
+ align:start position:0%
+let me just say this is really an
+ 
+
+ align:start position:0%
+let me just say this is really an
+amazing line of work today we know how
+
+ align:start position:0%
+amazing line of work today we know how
+ 
+
+ align:start position:0%
+amazing line of work today we know how
+to take any witness convert it to a
+
+ align:start position:0%
+to take any witness convert it to a
+ 
+
+ align:start position:0%
+to take any witness convert it to a
+probity checkable one that the verifier
+
+ align:start position:0%
+probity checkable one that the verifier
+ 
+
+ align:start position:0%
+probity checkable one that the verifier
+only reads three bits three three bits
+
+ align:start position:0%
+only reads three bits three three bits
+ 
+
+ align:start position:0%
+only reads three bits three three bits
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+uh proof and is convinced with cut and
+
+ align:start position:0%
+uh proof and is convinced with cut and
+ 
+
+ align:start position:0%
+uh proof and is convinced with cut and
+probability 78 is the the parameter but
+
+ align:start position:0%
+probability 78 is the the parameter but
+ 
+
+ align:start position:0%
+probability 78 is the the parameter but
+and then if you want more of course you
+
+ align:start position:0%
+and then if you want more of course you
+ 
+
+ align:start position:0%
+and then if you want more of course you
+repeat but even with just three bits you
+
+ align:start position:0%
+repeat but even with just three bits you
+ 
+
+ align:start position:0%
+repeat but even with just three bits you
+get uh some soundness that's really
+
+ align:start position:0%
+get uh some soundness that's really
+ 
+
+ align:start position:0%
+get uh some soundness that's really
+amazing so we're not going to see the
+
+ align:start position:0%
+amazing so we're not going to see the
+ 
+
+ align:start position:0%
+amazing so we're not going to see the
+three bit proof but we're going to see a
+
+ align:start position:0%
+three bit proof but we're going to see a
+ 
+
+ align:start position:0%
+three bit proof but we're going to see a
+poly Logan proof so what we're going to
+
+ align:start position:0%
+poly Logan proof so what we're going to
+ 
+
+ align:start position:0%
+poly Logan proof so what we're going to
+show what what the construction we're
+
+ align:start position:0%
+show what what the construction we're
+ 
+
+ align:start position:0%
+show what what the construction we're
+going to see today is how to go from a
+
+ align:start position:0%
+going to see today is how to go from a
+ 
+
+ align:start position:0%
+going to see today is how to go from a
+witness to a probability checkable one
+
+ align:start position:0%
+witness to a probability checkable one
+ 
+
+ align:start position:0%
+witness to a probability checkable one
+that the verifier only needs to read
+
+ align:start position:0%
+that the verifier only needs to read
+ 
+
+ align:start position:0%
+that the verifier only needs to read
+polylog
+
+ align:start position:0%
+polylog
+ 
+
+ align:start position:0%
+polylog
+n of this of these uh bits and verify
+
+ align:start position:0%
+n of this of these uh bits and verify
+ 
+
+ align:start position:0%
+n of this of these uh bits and verify
+and to go to the constant there's an
+
+ align:start position:0%
+and to go to the constant there's an
+ 
+
+ align:start position:0%
+and to go to the constant there's an
+additional tricks of recursion and so on
+
+ align:start position:0%
+additional tricks of recursion and so on
+ 
+
+ align:start position:0%
+additional tricks of recursion and so on
+that one needs to do to get there but
+
+ align:start position:0%
+that one needs to do to get there but
+ 
+
+ align:start position:0%
+that one needs to do to get there but
+we're not going to cover that
+
+ align:start position:0%
+we're not going to cover that
+ 
+
+ align:start position:0%
+we're not going to cover that
+part okay ready to roll
+
+ align:start position:0%
+part okay ready to roll
+ 
+
+ align:start position:0%
+part okay ready to roll
+sleeves okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's okay so let me just Define the
+
+ align:start position:0%
+let's okay so let me just Define the
+ 
+
+ align:start position:0%
+let's okay so let me just Define the
+complexity class people often think of
+
+ align:start position:0%
+complexity class people often think of
+ 
+
+ align:start position:0%
+complexity class people often think of
+it as a complexity class even though for
+
+ align:start position:0%
+it as a complexity class even though for
+ 
+
+ align:start position:0%
+it as a complexity class even though for
+us because this is more of a proof
+
+ align:start position:0%
+us because this is more of a proof
+ 
+
+ align:start position:0%
+us because this is more of a proof
+system cryptography I know class we
+
+ align:start position:0%
+system cryptography I know class we
+ 
+
+ align:start position:0%
+system cryptography I know class we
+always want efficiency we want we don't
+
+ align:start position:0%
+always want efficiency we want we don't
+ 
+
+ align:start position:0%
+always want efficiency we want we don't
+care just about complexity we want to
+
+ align:start position:0%
+care just about complexity we want to
+ 
+
+ align:start position:0%
+care just about complexity we want to
+say that actually you can take any
+
+ align:start position:0%
+say that actually you can take any
+ 
+
+ align:start position:0%
+say that actually you can take any
+witness and efficiently convert it it's
+
+ align:start position:0%
+witness and efficiently convert it it's
+ 
+
+ align:start position:0%
+witness and efficiently convert it it's
+not just about existence we want to
+
+ align:start position:0%
+not just about existence we want to
+ 
+
+ align:start position:0%
+not just about existence we want to
+actually use these things and let me
+
+ align:start position:0%
+actually use these things and let me
+ 
+
+ align:start position:0%
+actually use these things and let me
+just jump ahead and say that these
+
+ align:start position:0%
+just jump ahead and say that these
+ 
+
+ align:start position:0%
+just jump ahead and say that these
+things are used it's not just a
+
+ align:start position:0%
+things are used it's not just a
+ 
+
+ align:start position:0%
+things are used it's not just a
+theoretical uh you know even though
+
+ align:start position:0%
+theoretical uh you know even though
+ 
+
+ align:start position:0%
+theoretical uh you know even though
+everything we've seen so far in the
+
+ align:start position:0%
+everything we've seen so far in the
+ 
+
+ align:start position:0%
+everything we've seen so far in the
+class is like very just beautiful
+
+ align:start position:0%
+class is like very just beautiful
+ 
+
+ align:start position:0%
+class is like very just beautiful
+mathematically it seems a very um a you
+
+ align:start position:0%
+mathematically it seems a very um a you
+ 
+
+ align:start position:0%
+mathematically it seems a very um a you
+know uh a
+
+ align:start position:0%
+know uh a
+ 
+
+ align:start position:0%
+know uh a
+kind of low like a very uh away from
+
+ align:start position:0%
+kind of low like a very uh away from
+ 
+
+ align:start position:0%
+kind of low like a very uh away from
+very far from practice you know and but
+
+ align:start position:0%
+very far from practice you know and but
+ 
+
+ align:start position:0%
+very far from practice you know and but
+actually it's not all these things that
+
+ align:start position:0%
+actually it's not all these things that
+ 
+
+ align:start position:0%
+actually it's not all these things that
+I've shown you so far that you've seen
+
+ align:start position:0%
+I've shown you so far that you've seen
+ 
+
+ align:start position:0%
+I've shown you so far that you've seen
+so far are things that actually are used
+
+ align:start position:0%
+so far are things that actually are used
+ 
+
+ align:start position:0%
+so far are things that actually are used
+and uh so and and the PCP as well uh all
+
+ align:start position:0%
+and uh so and and the PCP as well uh all
+ 
+
+ align:start position:0%
+and uh so and and the PCP as well uh all
+this Machinery are things that too so we
+
+ align:start position:0%
+this Machinery are things that too so we
+ 
+
+ align:start position:0%
+this Machinery are things that too so we
+actually do care about efficiency but
+
+ align:start position:0%
+actually do care about efficiency but
+ 
+
+ align:start position:0%
+actually do care about efficiency but
+let me first kind of Define it as a
+
+ align:start position:0%
+let me first kind of Define it as a
+ 
+
+ align:start position:0%
+let me first kind of Define it as a
+complexity class so we defined the
+
+ align:start position:0%
+complexity class so we defined the
+ 
+
+ align:start position:0%
+complexity class so we defined the
+complex the complexity class PCP C for
+
+ align:start position:0%
+complex the complexity class PCP C for
+ 
+
+ align:start position:0%
+complex the complexity class PCP C for
+for completeness parameter s for
+
+ align:start position:0%
+for completeness parameter s for
+ 
+
+ align:start position:0%
+for completeness parameter s for
+soundness parameter R for Randomness
+
+ align:start position:0%
+soundness parameter R for Randomness
+ 
+
+ align:start position:0%
+soundness parameter R for Randomness
+parameter and Q for query parameter so
+
+ align:start position:0%
+parameter and Q for query parameter so
+ 
+
+ align:start position:0%
+parameter and Q for query parameter so
+this is a class this is the
+
+ align:start position:0%
+this is a class this is the
+ 
+
+ align:start position:0%
+this is a class this is the
+class of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+languages
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L A that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have a probabilistically able proof but
+
+ align:start position:0%
+have a probabilistically able proof but
+ 
+
+ align:start position:0%
+have a probabilistically able proof but
+I'll explain exactly what I mean uh okay
+
+ align:start position:0%
+I'll explain exactly what I mean uh okay
+ 
+
+ align:start position:0%
+I'll explain exactly what I mean uh okay
+so actually let me say a okay these are
+
+ align:start position:0%
+so actually let me say a okay these are
+ 
+
+ align:start position:0%
+so actually let me say a okay these are
+all the let me write it
+
+ align:start position:0%
+all the let me write it
+ 
+
+ align:start position:0%
+all the let me write it
+formally for which these are all the
+
+ align:start position:0%
+formally for which these are all the
+ 
+
+ align:start position:0%
+formally for which these are all the
+languages L such that there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists uh PPT a probabilistic polinomial
+
+ align:start position:0%
+exists uh PPT a probabilistic polinomial
+ 
+
+ align:start position:0%
+exists uh PPT a probabilistic polinomial
+Time
+
+ align:start position:0%
+Time
+ 
+
+ align:start position:0%
+Time
+verifier
+
+ align:start position:0%
+verifier
+ 
+
+ align:start position:0%
+verifier
+a actually it's a a PPT Oracle machine
+
+ align:start position:0%
+a actually it's a a PPT Oracle machine
+ 
+
+ align:start position:0%
+a actually it's a a PPT Oracle machine
+because it takes the PCP is an oracle
+
+ align:start position:0%
+because it takes the PCP is an oracle
+ 
+
+ align:start position:0%
+because it takes the PCP is an oracle
+Oracle
+
+ align:start position:0%
+Oracle
+ 
+
+ align:start position:0%
+Oracle
+machine v such
+
+ align:start position:0%
+machine v such
+ 
+
+ align:start position:0%
+machine v such
+that okay so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+completeness here's the condition the
+
+ align:start position:0%
+completeness here's the condition the
+ 
+
+ align:start position:0%
+completeness here's the condition the
+completeness says that for every X in
+
+ align:start position:0%
+completeness says that for every X in
+ 
+
+ align:start position:0%
+completeness says that for every X in
+the language there exists a PCP Pi such
+
+ align:start position:0%
+the language there exists a PCP Pi such
+ 
+
+ align:start position:0%
+the language there exists a PCP Pi such
+that the probability that V the verifier
+
+ align:start position:0%
+that the probability that V the verifier
+ 
+
+ align:start position:0%
+that the probability that V the verifier
+given Oracle access to this PCP pi and
+
+ align:start position:0%
+given Oracle access to this PCP pi and
+ 
+
+ align:start position:0%
+given Oracle access to this PCP pi and
+input the instance so for every instance
+
+ align:start position:0%
+input the instance so for every instance
+ 
+
+ align:start position:0%
+input the instance so for every instance
+there exists a PCP so that the verifier
+
+ align:start position:0%
+there exists a PCP so that the verifier
+ 
+
+ align:start position:0%
+there exists a PCP so that the verifier
+will accept it will output one with
+
+ align:start position:0%
+will accept it will output one with
+ 
+
+ align:start position:0%
+will accept it will output one with
+probability at least C that's the
+
+ align:start position:0%
+probability at least C that's the
+ 
+
+ align:start position:0%
+probability at least C that's the
+completeness parameter for us the PCP
+
+ align:start position:0%
+completeness parameter for us the PCP
+ 
+
+ align:start position:0%
+completeness parameter for us the PCP
+will see we'll have complet this
+
+ align:start position:0%
+will see we'll have complet this
+ 
+
+ align:start position:0%
+will see we'll have complet this
+parameter one okay so we'll see so we
+
+ align:start position:0%
+parameter one okay so we'll see so we
+ 
+
+ align:start position:0%
+parameter one okay so we'll see so we
+want to say that a class that a language
+
+ align:start position:0%
+want to say that a class that a language
+ 
+
+ align:start position:0%
+want to say that a class that a language
+L has such a PCP if there's a verifier V
+
+ align:start position:0%
+L has such a PCP if there's a verifier V
+ 
+
+ align:start position:0%
+L has such a PCP if there's a verifier V
+efficient verifier it takes Oracle axis
+
+ align:start position:0%
+efficient verifier it takes Oracle axis
+ 
+
+ align:start position:0%
+efficient verifier it takes Oracle axis
+so if x is in the language there exists
+
+ align:start position:0%
+so if x is in the language there exists
+ 
+
+ align:start position:0%
+so if x is in the language there exists
+in PCP so I to verify with Oracle axis
+
+ align:start position:0%
+in PCP so I to verify with Oracle axis
+ 
+
+ align:start position:0%
+in PCP so I to verify with Oracle axis
+of this PCP given this input outputs one
+
+ align:start position:0%
+of this PCP given this input outputs one
+ 
+
+ align:start position:0%
+of this PCP given this input outputs one
+with probity C yes maybe I'm jumping a
+
+ align:start position:0%
+with probity C yes maybe I'm jumping a
+ 
+
+ align:start position:0%
+with probity C yes maybe I'm jumping a
+bit but what does the Oracle look like
+
+ align:start position:0%
+bit but what does the Oracle look like
+ 
+
+ align:start position:0%
+bit but what does the Oracle look like
+like what are the inputs okay good good
+
+ align:start position:0%
+like what are the inputs okay good good
+ 
+
+ align:start position:0%
+like what are the inputs okay good good
+good so this okay oh good no you're not
+
+ align:start position:0%
+good so this okay oh good no you're not
+ 
+
+ align:start position:0%
+good so this okay oh good no you're not
+jumping so good good question so this Pi
+
+ align:start position:0%
+jumping so good good question so this Pi
+ 
+
+ align:start position:0%
+jumping so good good question so this Pi
+you should think of it as a
+
+ align:start position:0%
+you should think of it as a
+ 
+
+ align:start position:0%
+you should think of it as a
+string it has bits B1 maybe I call it Pi
+
+ align:start position:0%
+string it has bits B1 maybe I call it Pi
+ 
+
+ align:start position:0%
+string it has bits B1 maybe I call it Pi
+1 Pi 2 up to Pi I don't know
+
+ align:start position:0%
+1 Pi 2 up to Pi I don't know
+ 
+
+ align:start position:0%
+1 Pi 2 up to Pi I don't know
+n and uh the verifier can ask give me
+
+ align:start position:0%
+n and uh the verifier can ask give me
+ 
+
+ align:start position:0%
+n and uh the verifier can ask give me
+like Pi 1 give me pi 2 give me pi 3 so
+
+ align:start position:0%
+like Pi 1 give me pi 2 give me pi 3 so
+ 
+
+ align:start position:0%
+like Pi 1 give me pi 2 give me pi 3 so
+he just has Oracle queries he can query
+
+ align:start position:0%
+he just has Oracle queries he can query
+ 
+
+ align:start position:0%
+he just has Oracle queries he can query
+this string okay that's what Oracle it's
+
+ align:start position:0%
+this string okay that's what Oracle it's
+ 
+
+ align:start position:0%
+this string okay that's what Oracle it's
+not really don't think of it as a
+
+ align:start position:0%
+not really don't think of it as a
+ 
+
+ align:start position:0%
+not really don't think of it as a
+function he has Oracle access to the
+
+ align:start position:0%
+function he has Oracle access to the
+ 
+
+ align:start position:0%
+function he has Oracle access to the
+string and he can just ask for specific
+
+ align:start position:0%
+string and he can just ask for specific
+ 
+
+ align:start position:0%
+string and he can just ask for specific
+bits from the string great question
+
+ align:start position:0%
+bits from the string great question
+ 
+
+ align:start position:0%
+bits from the string great question
+thank
+
+ align:start position:0%
+thank
+ 
+
+ align:start position:0%
+thank
+you okay uh good and the sound is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guarantee says that that for every X
+
+ align:start position:0%
+guarantee says that that for every X
+ 
+
+ align:start position:0%
+guarantee says that that for every X
+that's not in the
+
+ align:start position:0%
+that's not in the
+ 
+
+ align:start position:0%
+that's not in the
+language any any guesses by the way what
+
+ align:start position:0%
+language any any guesses by the way what
+ 
+
+ align:start position:0%
+language any any guesses by the way what
+would you okay so you need to define a
+
+ align:start position:0%
+would you okay so you need to define a
+ 
+
+ align:start position:0%
+would you okay so you need to define a
+PCP here how would you define
+
+ align:start position:0%
+PCP here how would you define
+ 
+
+ align:start position:0%
+PCP here how would you define
+sonus yeah for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+wonderful exactly you want to say that
+
+ align:start position:0%
+wonderful exactly you want to say that
+ 
+
+ align:start position:0%
+wonderful exactly you want to say that
+for every Pi star this know how we do
+
+ align:start position:0%
+for every Pi star this know how we do
+ 
+
+ align:start position:0%
+for every Pi star this know how we do
+note bad things Prime will do too uh for
+
+ align:start position:0%
+note bad things Prime will do too uh for
+ 
+
+ align:start position:0%
+note bad things Prime will do too uh for
+every bad now there's a cheating Pro he
+
+ align:start position:0%
+every bad now there's a cheating Pro he
+ 
+
+ align:start position:0%
+every bad now there's a cheating Pro he
+tries to fool the verifier he cannot so
+
+ align:start position:0%
+tries to fool the verifier he cannot so
+ 
+
+ align:start position:0%
+tries to fool the verifier he cannot so
+for no matter what he tries to give him
+
+ align:start position:0%
+for no matter what he tries to give him
+ 
+
+ align:start position:0%
+for no matter what he tries to give him
+the verifier will reject him with
+
+ align:start position:0%
+the verifier will reject him with
+ 
+
+ align:start position:0%
+the verifier will reject him with
+probability or a will accept probability
+
+ align:start position:0%
+probability or a will accept probability
+ 
+
+ align:start position:0%
+probability or a will accept probability
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+S that's the soundness guarantee okay
+
+ align:start position:0%
+S that's the soundness guarantee okay
+ 
+
+ align:start position:0%
+S that's the soundness guarantee okay
+and ideally we want to push the
+
+ align:start position:0%
+and ideally we want to push the
+ 
+
+ align:start position:0%
+and ideally we want to push the
+completeness to one the soundness to
+
+ align:start position:0%
+completeness to one the soundness to
+ 
+
+ align:start position:0%
+completeness to one the soundness to
+zero great and then the a the
+
+ align:start position:0%
+zero great and then the a the
+ 
+
+ align:start position:0%
+zero great and then the a the
+complexity uh is now we want to say in
+
+ align:start position:0%
+complexity uh is now we want to say in
+ 
+
+ align:start position:0%
+complexity uh is now we want to say in
+terms of complexity now we'll go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the V
+
+ align:start position:0%
+the the V
+ 
+
+ align:start position:0%
+the the V
+uses our bits of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Randomness and Q Oracle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calls and moreover we'll see this is
+
+ align:start position:0%
+calls and moreover we'll see this is
+ 
+
+ align:start position:0%
+calls and moreover we'll see this is
+important for us this is often in the
+
+ align:start position:0%
+important for us this is often in the
+ 
+
+ align:start position:0%
+important for us this is often in the
+definition though not always but often
+
+ align:start position:0%
+definition though not always but often
+ 
+
+ align:start position:0%
+definition though not always but often
+this is part of the Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonadaptive what do I mean by
+
+ align:start position:0%
+nonadaptive what do I mean by
+ 
+
+ align:start position:0%
+nonadaptive what do I mean by
+nonadaptive what I mean is the way V
+
+ align:start position:0%
+nonadaptive what I mean is the way V
+ 
+
+ align:start position:0%
+nonadaptive what I mean is the way V
+Works he gets input X he gets input X he
+
+ align:start position:0%
+Works he gets input X he gets input X he
+ 
+
+ align:start position:0%
+Works he gets input X he gets input X he
+then chooses kind of
+
+ align:start position:0%
+then chooses kind of
+ 
+
+ align:start position:0%
+then chooses kind of
+i1 up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+IQ locations in the PCP okay so here's
+
+ align:start position:0%
+IQ locations in the PCP okay so here's
+ 
+
+ align:start position:0%
+IQ locations in the PCP okay so here's
+the v v he doesn't even look at the
+
+ align:start position:0%
+the v v he doesn't even look at the
+ 
+
+ align:start position:0%
+the v v he doesn't even look at the
+Oracle yet he has an input X
+
+ align:start position:0%
+Oracle yet he has an input X
+ 
+
+ align:start position:0%
+Oracle yet he has an input X
+he first computes Q
+
+ align:start position:0%
+he first computes Q
+ 
+
+ align:start position:0%
+he first computes Q
+locations he then goes to the Oracle
+
+ align:start position:0%
+locations he then goes to the Oracle
+ 
+
+ align:start position:0%
+locations he then goes to the Oracle
+asks these Q locations and then so V1
+
+ align:start position:0%
+asks these Q locations and then so V1
+ 
+
+ align:start position:0%
+asks these Q locations and then so V1
+just just these locations and then V2 so
+
+ align:start position:0%
+just just these locations and then V2 so
+ 
+
+ align:start position:0%
+just just these locations and then V2 so
+you can think of v as being like V1 and
+
+ align:start position:0%
+you can think of v as being like V1 and
+ 
+
+ align:start position:0%
+you can think of v as being like V1 and
+V2 V1 doesn't look at his Oracle he just
+
+ align:start position:0%
+V2 V1 doesn't look at his Oracle he just
+ 
+
+ align:start position:0%
+V2 V1 doesn't look at his Oracle he just
+looks as an
+
+ align:start position:0%
+looks as an
+ 
+
+ align:start position:0%
+looks as an
+input and using Randomness chooses Q
+
+ align:start position:0%
+input and using Randomness chooses Q
+ 
+
+ align:start position:0%
+input and using Randomness chooses Q
+locations and then
+
+ align:start position:0%
+locations and then
+ 
+
+ align:start position:0%
+locations and then
+V2 kind of uh just given
+
+ align:start position:0%
+V2 kind of uh just given
+ 
+
+ align:start position:0%
+V2 kind of uh just given
+X i1 up to IQ and Pi i1 up to Pi
+
+ align:start position:0%
+X i1 up to IQ and Pi i1 up to Pi
+ 
+
+ align:start position:0%
+X i1 up to IQ and Pi i1 up to Pi
+IQ decides if to like uh accept or
+
+ align:start position:0%
+IQ decides if to like uh accept or
+ 
+
+ align:start position:0%
+IQ decides if to like uh accept or
+reject okay so this is the how you
+
+ align:start position:0%
+reject okay so this is the how you
+ 
+
+ align:start position:0%
+reject okay so this is the how you
+should think of the of the verifier the
+
+ align:start position:0%
+should think of the of the verifier the
+ 
+
+ align:start position:0%
+should think of the of the verifier the
+verifier has access to the proof Pi but
+
+ align:start position:0%
+verifier has access to the proof Pi but
+ 
+
+ align:start position:0%
+verifier has access to the proof Pi but
+what he does he does he because a more
+
+ align:start position:0%
+what he does he does he because a more
+ 
+
+ align:start position:0%
+what he does he does he because a more
+General verifier will have X decide on
+
+ align:start position:0%
+General verifier will have X decide on
+ 
+
+ align:start position:0%
+General verifier will have X decide on
+location first location 3 i1 look at Pi
+
+ align:start position:0%
+location first location 3 i1 look at Pi
+ 
+
+ align:start position:0%
+location first location 3 i1 look at Pi
+1 then hm interesting okay in that case
+
+ align:start position:0%
+1 then hm interesting okay in that case
+ 
+
+ align:start position:0%
+1 then hm interesting okay in that case
+I want to see location I2 h i get Pi I2
+
+ align:start position:0%
+I want to see location I2 h i get Pi I2
+ 
+
+ align:start position:0%
+I want to see location I2 h i get Pi I2
+interesting given Pi I2 I want to see
+
+ align:start position:0%
+interesting given Pi I2 I want to see
+ 
+
+ align:start position:0%
+interesting given Pi I2 I want to see
+location that would be an Adaptive
+
+ align:start position:0%
+location that would be an Adaptive
+ 
+
+ align:start position:0%
+location that would be an Adaptive
+verifier okay but often in the PCP
+
+ align:start position:0%
+verifier okay but often in the PCP
+ 
+
+ align:start position:0%
+verifier okay but often in the PCP
+literature when we Define PCP we require
+
+ align:start position:0%
+literature when we Define PCP we require
+ 
+
+ align:start position:0%
+literature when we Define PCP we require
+the verifier to be
+
+ align:start position:0%
+the verifier to be
+ 
+
+ align:start position:0%
+the verifier to be
+non-adaptive and this non- adaptivity is
+
+ align:start position:0%
+non-adaptive and this non- adaptivity is
+ 
+
+ align:start position:0%
+non-adaptive and this non- adaptivity is
+kind of uh is it's a property that we
+
+ align:start position:0%
+kind of uh is it's a property that we
+ 
+
+ align:start position:0%
+kind of uh is it's a property that we
+like for applications and we'll see that
+
+ align:start position:0%
+like for applications and we'll see that
+ 
+
+ align:start position:0%
+like for applications and we'll see that
+today uh why an example for why when
+
+ align:start position:0%
+today uh why an example for why when
+ 
+
+ align:start position:0%
+today uh why an example for why when
+we'll construct succinct arguments we'll
+
+ align:start position:0%
+we'll construct succinct arguments we'll
+ 
+
+ align:start position:0%
+we'll construct succinct arguments we'll
+use the fact that it's non adaptive but
+
+ align:start position:0%
+use the fact that it's non adaptive but
+ 
+
+ align:start position:0%
+use the fact that it's non adaptive but
+let me just say most PCP all pcps I know
+
+ align:start position:0%
+let me just say most PCP all pcps I know
+ 
+
+ align:start position:0%
+let me just say most PCP all pcps I know
+are nonadaptive maybe there other was
+
+ align:start position:0%
+are nonadaptive maybe there other was
+ 
+
+ align:start position:0%
+are nonadaptive maybe there other was
+that your question yeah so I don't I
+
+ align:start position:0%
+that your question yeah so I don't I
+ 
+
+ align:start position:0%
+that your question yeah so I don't I
+there may exist I'm not you know I'm not
+
+ align:start position:0%
+there may exist I'm not you know I'm not
+ 
+
+ align:start position:0%
+there may exist I'm not you know I'm not
+uh I didn't do a full literature search
+
+ align:start position:0%
+uh I didn't do a full literature search
+ 
+
+ align:start position:0%
+uh I didn't do a full literature search
+but the pcps that are you know the most
+
+ align:start position:0%
+but the pcps that are you know the most
+ 
+
+ align:start position:0%
+but the pcps that are you know the most
+common ones that we talk about are all
+
+ align:start position:0%
+common ones that we talk about are all
+ 
+
+ align:start position:0%
+common ones that we talk about are all
+non-adaptive yeah did V get to know what
+
+ align:start position:0%
+non-adaptive yeah did V get to know what
+ 
+
+ align:start position:0%
+non-adaptive yeah did V get to know what
+capital N is yeah yeah yeah yeah so V
+
+ align:start position:0%
+capital N is yeah yeah yeah yeah so V
+ 
+
+ align:start position:0%
+capital N is yeah yeah yeah yeah so V
+yes V knows yeah so V good very good
+
+ align:start position:0%
+yes V knows yeah so V good very good
+ 
+
+ align:start position:0%
+yes V knows yeah so V good very good
+question let me repeat for the uh video
+
+ align:start position:0%
+question let me repeat for the uh video
+ 
+
+ align:start position:0%
+question let me repeat for the uh video
+uh so the question was does v know what
+
+ align:start position:0%
+uh so the question was does v know what
+ 
+
+ align:start position:0%
+uh so the question was does v know what
+n what capital N is so the answer is yes
+
+ align:start position:0%
+n what capital N is so the answer is yes
+ 
+
+ align:start position:0%
+n what capital N is so the answer is yes
+and the V knows uh V knows the language
+
+ align:start position:0%
+and the V knows uh V knows the language
+ 
+
+ align:start position:0%
+and the V knows uh V knows the language
+so he knows what small n is well he got
+
+ align:start position:0%
+so he knows what small n is well he got
+ 
+
+ align:start position:0%
+so he knows what small n is well he got
+small n he knows small n the language
+
+ align:start position:0%
+small n he knows small n the language
+ 
+
+ align:start position:0%
+small n he knows small n the language
+has like is there's M so he V get small
+
+ align:start position:0%
+has like is there's M so he V get small
+ 
+
+ align:start position:0%
+has like is there's M so he V get small
+n so he knows what an N is the language
+
+ align:start position:0%
+n so he knows what an N is the language
+ 
+
+ align:start position:0%
+n so he knows what an N is the language
+is associated with the witness size M of
+
+ align:start position:0%
+is associated with the witness size M of
+ 
+
+ align:start position:0%
+is associated with the witness size M of
+n so he knows that because he knows n so
+
+ align:start position:0%
+n so he knows that because he knows n so
+ 
+
+ align:start position:0%
+n so he knows that because he knows n so
+he knows the witness size and the PCP
+
+ align:start position:0%
+he knows the witness size and the PCP
+ 
+
+ align:start position:0%
+he knows the witness size and the PCP
+itself is associated with n which
+
+ align:start position:0%
+itself is associated with n which
+ 
+
+ align:start position:0%
+itself is associated with n which
+is you know you can think of it this way
+
+ align:start position:0%
+is you know you can think of it this way
+ 
+
+ align:start position:0%
+is you know you can think of it this way
+so so the answer is yes these are kind
+
+ align:start position:0%
+so so the answer is yes these are kind
+ 
+
+ align:start position:0%
+so so the answer is yes these are kind
+of fixed these uh M and N are fixed
+
+ align:start position:0%
+of fixed these uh M and N are fixed
+ 
+
+ align:start position:0%
+of fixed these uh M and N are fixed
+parameters that are defined by the PCP
+
+ align:start position:0%
+parameters that are defined by the PCP
+ 
+
+ align:start position:0%
+parameters that are defined by the PCP
+and the prover knows them the verifier
+
+ align:start position:0%
+and the prover knows them the verifier
+ 
+
+ align:start position:0%
+and the prover knows them the verifier
+the pro they yeah yes we gain
+
+ align:start position:0%
+the pro they yeah yes we gain
+ 
+
+ align:start position:0%
+the pro they yeah yes we gain
+orose yes good good good so the question
+
+ align:start position:0%
+orose yes good good good so the question
+ 
+
+ align:start position:0%
+orose yes good good good so the question
+is do we lose something and the answer
+
+ align:start position:0%
+is do we lose something and the answer
+ 
+
+ align:start position:0%
+is do we lose something and the answer
+is we do uh okay so what do we lose and
+
+ align:start position:0%
+is we do uh okay so what do we lose and
+ 
+
+ align:start position:0%
+is we do uh okay so what do we lose and
+what do we gain is your question what we
+
+ align:start position:0%
+what do we gain is your question what we
+ 
+
+ align:start position:0%
+what do we gain is your question what we
+lose is for application so we you when
+
+ align:start position:0%
+lose is for application so we you when
+ 
+
+ align:start position:0%
+lose is for application so we you when
+we'll go to in the second part of
+
+ align:start position:0%
+we'll go to in the second part of
+ 
+
+ align:start position:0%
+we'll go to in the second part of
+today's class we're going to construct
+
+ align:start position:0%
+today's class we're going to construct
+ 
+
+ align:start position:0%
+today's class we're going to construct
+succinct arguments and we're going to
+
+ align:start position:0%
+succinct arguments and we're going to
+ 
+
+ align:start position:0%
+succinct arguments and we're going to
+construct them from pcps and you'll see
+
+ align:start position:0%
+construct them from pcps and you'll see
+ 
+
+ align:start position:0%
+construct them from pcps and you'll see
+that if our PCP is adaptive this becomes
+
+ align:start position:0%
+that if our PCP is adaptive this becomes
+ 
+
+ align:start position:0%
+that if our PCP is adaptive this becomes
+the problem so we do gain now you're
+
+ align:start position:0%
+the problem so we do gain now you're
+ 
+
+ align:start position:0%
+the problem so we do gain now you're
+saying what do we Lo and so we do lose
+
+ align:start position:0%
+saying what do we Lo and so we do lose
+ 
+
+ align:start position:0%
+saying what do we Lo and so we do lose
+sorry we do lose if we make it adapted
+
+ align:start position:0%
+sorry we do lose if we make it adapted
+ 
+
+ align:start position:0%
+sorry we do lose if we make it adapted
+now you're saying but maybe we gain
+
+ align:start position:0%
+now you're saying but maybe we gain
+ 
+
+ align:start position:0%
+now you're saying but maybe we gain
+something maybe we construct pcps that
+
+ align:start position:0%
+something maybe we construct pcps that
+ 
+
+ align:start position:0%
+something maybe we construct pcps that
+are much better if you make them
+
+ align:start position:0%
+are much better if you make them
+ 
+
+ align:start position:0%
+are much better if you make them
+adaptive and I I don't think so but I'm
+
+ align:start position:0%
+adaptive and I I don't think so but I'm
+ 
+
+ align:start position:0%
+adaptive and I I don't think so but I'm
+not sure maybe maybe one can actually
+
+ align:start position:0%
+not sure maybe maybe one can actually
+ 
+
+ align:start position:0%
+not sure maybe maybe one can actually
+argue that you don't gain anything but I
+
+ align:start position:0%
+argue that you don't gain anything but I
+ 
+
+ align:start position:0%
+argue that you don't gain anything but I
+haven't thought about it um but it's not
+
+ align:start position:0%
+haven't thought about it um but it's not
+ 
+
+ align:start position:0%
+haven't thought about it um but it's not
+something that making it nonadaptive
+
+ align:start position:0%
+something that making it nonadaptive
+ 
+
+ align:start position:0%
+something that making it nonadaptive
+that for all we know is not a price it's
+
+ align:start position:0%
+that for all we know is not a price it's
+ 
+
+ align:start position:0%
+that for all we know is not a price it's
+just our pcps happen to be that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good good good very very good
+
+ align:start position:0%
+yeah good good good very very good
+ 
+
+ align:start position:0%
+yeah good good good very very good
+question so uh I think I I think maybe I
+
+ align:start position:0%
+question so uh I think I I think maybe I
+ 
+
+ align:start position:0%
+question so uh I think I I think maybe I
+misunderstood but maybe your question
+
+ align:start position:0%
+misunderstood but maybe your question
+ 
+
+ align:start position:0%
+misunderstood but maybe your question
+was is it clear that these have to
+
+ align:start position:0%
+was is it clear that these have to
+ 
+
+ align:start position:0%
+was is it clear that these have to
+depend on X can they even not depend on
+
+ align:start position:0%
+depend on X can they even not depend on
+ 
+
+ align:start position:0%
+depend on X can they even not depend on
+X and the answer is yes actually in the
+
+ align:start position:0%
+X and the answer is yes actually in the
+ 
+
+ align:start position:0%
+X and the answer is yes actually in the
+pcps will see they don't depend on x
+
+ align:start position:0%
+pcps will see they don't depend on x
+ 
+
+ align:start position:0%
+pcps will see they don't depend on x
+okay the pcps we know actually these
+
+ align:start position:0%
+okay the pcps we know actually these
+ 
+
+ align:start position:0%
+okay the pcps we know actually these
+they only depend on you know n and the
+
+ align:start position:0%
+they only depend on you know n and the
+ 
+
+ align:start position:0%
+they only depend on you know n and the
+instance size or or again it's but they
+
+ align:start position:0%
+instance size or or again it's but they
+ 
+
+ align:start position:0%
+instance size or or again it's but they
+don't actually depend on the instance
+
+ align:start position:0%
+don't actually depend on the instance
+ 
+
+ align:start position:0%
+don't actually depend on the instance
+and the PCP I'll construct today you'll
+
+ align:start position:0%
+and the PCP I'll construct today you'll
+ 
+
+ align:start position:0%
+and the PCP I'll construct today you'll
+see that so we'll get back to that that
+
+ align:start position:0%
+see that so we'll get back to that that
+ 
+
+ align:start position:0%
+see that so we'll get back to that that
+really really great questions
+
+ align:start position:0%
+really really great questions
+ 
+
+ align:start position:0%
+really really great questions
+yeah does that
+
+ align:start position:0%
+yeah does that
+ 
+
+ align:start position:0%
+yeah does that
+think knows what indes you're going
+
+ align:start position:0%
+think knows what indes you're going
+ 
+
+ align:start position:0%
+think knows what indes you're going
+Advance you could construct a of course
+
+ align:start position:0%
+Advance you could construct a of course
+ 
+
+ align:start position:0%
+Advance you could construct a of course
+of course great wow guys you're really
+
+ align:start position:0%
+of course great wow guys you're really
+ 
+
+ align:start position:0%
+of course great wow guys you're really
+Lifting me up this is great thank you uh
+
+ align:start position:0%
+Lifting me up this is great thank you uh
+ 
+
+ align:start position:0%
+Lifting me up this is great thank you uh
+yeah 100% so you're what you're saying
+
+ align:start position:0%
+yeah 100% so you're what you're saying
+ 
+
+ align:start position:0%
+yeah 100% so you're what you're saying
+is of course if the ver if the prover
+
+ align:start position:0%
+is of course if the ver if the prover
+ 
+
+ align:start position:0%
+is of course if the ver if the prover
+knew the locations you're quering he
+
+ align:start position:0%
+knew the locations you're quering he
+ 
+
+ align:start position:0%
+knew the locations you're quering he
+will cheat the thing is these locations
+
+ align:start position:0%
+will cheat the thing is these locations
+ 
+
+ align:start position:0%
+will cheat the thing is these locations
+are random the prover doesn't know what
+
+ align:start position:0%
+are random the prover doesn't know what
+ 
+
+ align:start position:0%
+are random the prover doesn't know what
+they are they just don't depend on X
+
+ align:start position:0%
+they are they just don't depend on X
+ 
+
+ align:start position:0%
+they are they just don't depend on X
+okay okay but they they come from a
+
+ align:start position:0%
+okay okay but they they come from a
+ 
+
+ align:start position:0%
+okay okay but they they come from a
+distribution it's very important if
+
+ align:start position:0%
+distribution it's very important if
+ 
+
+ align:start position:0%
+distribution it's very important if
+these were deterministic there's no way
+
+ align:start position:0%
+these were deterministic there's no way
+ 
+
+ align:start position:0%
+these were deterministic there's no way
+if you can do a PCP where these are
+
+ align:start position:0%
+if you can do a PCP where these are
+ 
+
+ align:start position:0%
+if you can do a PCP where these are
+deterministic it's like you took NP and
+
+ align:start position:0%
+deterministic it's like you took NP and
+ 
+
+ align:start position:0%
+deterministic it's like you took NP and
+you just made it end time much smaller
+
+ align:start position:0%
+you just made it end time much smaller
+ 
+
+ align:start position:0%
+you just made it end time much smaller
+like we don't believe that that can
+
+ align:start position:0%
+like we don't believe that that can
+ 
+
+ align:start position:0%
+like we don't believe that that can
+happen in so no it the there's no way we
+
+ align:start position:0%
+happen in so no it the there's no way we
+ 
+
+ align:start position:0%
+happen in so no it the there's no way we
+believe you can construct pcps for which
+
+ align:start position:0%
+believe you can construct pcps for which
+ 
+
+ align:start position:0%
+believe you can construct pcps for which
+the qu the query distribution is
+
+ align:start position:0%
+the qu the query distribution is
+ 
+
+ align:start position:0%
+the qu the query distribution is
+deterministic it's like just fixed this
+
+ align:start position:0%
+deterministic it's like just fixed this
+ 
+
+ align:start position:0%
+deterministic it's like just fixed this
+has to come from a distribution but the
+
+ align:start position:0%
+has to come from a distribution but the
+ 
+
+ align:start position:0%
+has to come from a distribution but the
+question is does this distribution
+
+ align:start position:0%
+question is does this distribution
+ 
+
+ align:start position:0%
+question is does this distribution
+depend on X or does it only depend on
+
+ align:start position:0%
+depend on X or does it only depend on
+ 
+
+ align:start position:0%
+depend on X or does it only depend on
+the parameter n and then and what we'll
+
+ align:start position:0%
+the parameter n and then and what we'll
+ 
+
+ align:start position:0%
+the parameter n and then and what we'll
+see it actually only depends on N it
+
+ align:start position:0%
+see it actually only depends on N it
+ 
+
+ align:start position:0%
+see it actually only depends on N it
+doesn't depend on X so that's what we'll
+
+ align:start position:0%
+doesn't depend on X so that's what we'll
+ 
+
+ align:start position:0%
+doesn't depend on X so that's what we'll
+see a in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute great question guys any any more
+
+ align:start position:0%
+minute great question guys any any more
+ 
+
+ align:start position:0%
+minute great question guys any any more
+questions before we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so okay good so actually V1 you can
+
+ align:start position:0%
+yeah so okay good so actually V1 you can
+ 
+
+ align:start position:0%
+yeah so okay good so actually V1 you can
+think of usually V1 is randomized and V2
+
+ align:start position:0%
+think of usually V1 is randomized and V2
+ 
+
+ align:start position:0%
+think of usually V1 is randomized and V2
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+deterministic uh so you can think of it
+
+ align:start position:0%
+deterministic uh so you can think of it
+ 
+
+ align:start position:0%
+deterministic uh so you can think of it
+that way that V1 is randomized V2 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deterministic okay
+
+ align:start position:0%
+deterministic okay
+ 
+
+ align:start position:0%
+deterministic okay
+uh great so now let me tell you what we
+
+ align:start position:0%
+uh great so now let me tell you what we
+ 
+
+ align:start position:0%
+uh great so now let me tell you what we
+know and what we're going to construct
+
+ align:start position:0%
+know and what we're going to construct
+ 
+
+ align:start position:0%
+know and what we're going to construct
+so here's what we're going to prove
+
+ align:start position:0%
+so here's what we're going to prove
+ 
+
+ align:start position:0%
+so here's what we're going to prove
+today um here is a theorem that we're
+
+ align:start position:0%
+today um here is a theorem that we're
+ 
+
+ align:start position:0%
+today um here is a theorem that we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+prove that
+
+ align:start position:0%
+prove that
+ 
+
+ align:start position:0%
+prove that
+PCP with a let's say completeness one
+
+ align:start position:0%
+PCP with a let's say completeness one
+ 
+
+ align:start position:0%
+PCP with a let's say completeness one
+I'll put S as half we can get smaller
+
+ align:start position:0%
+I'll put S as half we can get smaller
+ 
+
+ align:start position:0%
+I'll put S as half we can get smaller
+any con and smaller but I'll just put
+
+ align:start position:0%
+any con and smaller but I'll just put
+ 
+
+ align:start position:0%
+any con and smaller but I'll just put
+half because by repetition uh it doesn't
+
+ align:start position:0%
+half because by repetition uh it doesn't
+ 
+
+ align:start position:0%
+half because by repetition uh it doesn't
+really matter you can get a PCP where
+
+ align:start position:0%
+really matter you can get a PCP where
+ 
+
+ align:start position:0%
+really matter you can get a PCP where
+the query
+
+ align:start position:0%
+the query
+ 
+
+ align:start position:0%
+the query
+complexity is so okay we can get a PCP
+
+ align:start position:0%
+complexity is so okay we can get a PCP
+ 
+
+ align:start position:0%
+complexity is so okay we can get a PCP
+with poly log n query complexity and
+
+ align:start position:0%
+with poly log n query complexity and
+ 
+
+ align:start position:0%
+with poly log n query complexity and
+poly a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+login H sorry poly log and Randomness
+
+ align:start position:0%
+login H sorry poly log and Randomness
+ 
+
+ align:start position:0%
+login H sorry poly log and Randomness
+complexity and query complexity for all
+
+ align:start position:0%
+complexity and query complexity for all
+ 
+
+ align:start position:0%
+complexity and query complexity for all
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+NP that's what we're going to see today
+
+ align:start position:0%
+NP that's what we're going to see today
+ 
+
+ align:start position:0%
+NP that's what we're going to see today
+so we're going to see how for any NP
+
+ align:start position:0%
+so we're going to see how for any NP
+ 
+
+ align:start position:0%
+so we're going to see how for any NP
+language we can construct a PCP where
+
+ align:start position:0%
+language we can construct a PCP where
+ 
+
+ align:start position:0%
+language we can construct a PCP where
+the verifier the amount of Randomness he
+
+ align:start position:0%
+the verifier the amount of Randomness he
+ 
+
+ align:start position:0%
+the verifier the amount of Randomness he
+uses is polog and bits of Randomness and
+
+ align:start position:0%
+uses is polog and bits of Randomness and
+ 
+
+ align:start position:0%
+uses is polog and bits of Randomness and
+polog and queries and then we get
+
+ align:start position:0%
+polog and queries and then we get
+ 
+
+ align:start position:0%
+polog and queries and then we get
+completeness one and sound as half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeaha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usually right right right yeah yeah yeah
+
+ align:start position:0%
+usually right right right yeah yeah yeah
+ 
+
+ align:start position:0%
+usually right right right yeah yeah yeah
+so you're right so often uh okay you're
+
+ align:start position:0%
+so you're right so often uh okay you're
+ 
+
+ align:start position:0%
+so you're right so often uh okay you're
+right the way I wrote it here uh so okay
+
+ align:start position:0%
+right the way I wrote it here uh so okay
+ 
+
+ align:start position:0%
+right the way I wrote it here uh so okay
+why do people care about Randomness
+
+ align:start position:0%
+why do people care about Randomness
+ 
+
+ align:start position:0%
+why do people care about Randomness
+complexity one can say who cares about
+
+ align:start position:0%
+complexity one can say who cares about
+ 
+
+ align:start position:0%
+complexity one can say who cares about
+the random complexity and usually the
+
+ align:start position:0%
+the random complexity and usually the
+ 
+
+ align:start position:0%
+the random complexity and usually the
+way the way I Define PCP and this is
+
+ align:start position:0%
+way the way I Define PCP and this is
+ 
+
+ align:start position:0%
+way the way I Define PCP and this is
+that's why I said it's a complexity
+
+ align:start position:0%
+that's why I said it's a complexity
+ 
+
+ align:start position:0%
+that's why I said it's a complexity
+Theory this is how it's
+
+ align:start position:0%
+Theory this is how it's
+ 
+
+ align:start position:0%
+Theory this is how it's
+defined if if the verifier has only log
+
+ align:start position:0%
+defined if if the verifier has only log
+ 
+
+ align:start position:0%
+defined if if the verifier has only log
+and bits or order lend bits of of
+
+ align:start position:0%
+and bits or order lend bits of of
+ 
+
+ align:start position:0%
+and bits or order lend bits of of
+Randomness then it means that the PCP is
+
+ align:start position:0%
+Randomness then it means that the PCP is
+ 
+
+ align:start position:0%
+Randomness then it means that the PCP is
+only polyn size because look go over all
+
+ align:start position:0%
+only polyn size because look go over all
+ 
+
+ align:start position:0%
+only polyn size because look go over all
+the PO and all the log and bit random
+
+ align:start position:0%
+the PO and all the log and bit random
+ 
+
+ align:start position:0%
+the PO and all the log and bit random
+there's only n of them so that's as much
+
+ align:start position:0%
+there's only n of them so that's as much
+ 
+
+ align:start position:0%
+there's only n of them so that's as much
+as you can uh kind of query so uh so
+
+ align:start position:0%
+as you can uh kind of query so uh so
+ 
+
+ align:start position:0%
+as you can uh kind of query so uh so
+that means the PCV is aized and that's
+
+ align:start position:0%
+that means the PCV is aized and that's
+ 
+
+ align:start position:0%
+that means the PCV is aized and that's
+all we care about okay for me I'm going
+
+ align:start position:0%
+all we care about okay for me I'm going
+ 
+
+ align:start position:0%
+all we care about okay for me I'm going
+to care about so actually for me I'm
+
+ align:start position:0%
+to care about so actually for me I'm
+ 
+
+ align:start position:0%
+to care about so actually for me I'm
+going to add a a requirement actually I
+
+ align:start position:0%
+going to add a a requirement actually I
+ 
+
+ align:start position:0%
+going to add a a requirement actually I
+didn't write it here because it's
+
+ align:start position:0%
+didn't write it here because it's
+ 
+
+ align:start position:0%
+didn't write it here because it's
+usually not defined but I can add a
+
+ align:start position:0%
+usually not defined but I can add a
+ 
+
+ align:start position:0%
+usually not defined but I can add a
+requirement that says this a I'll okay
+
+ align:start position:0%
+requirement that says this a I'll okay
+ 
+
+ align:start position:0%
+requirement that says this a I'll okay
+I'll add it here in tiny this is a a
+
+ align:start position:0%
+I'll add it here in tiny this is a a
+ 
+
+ align:start position:0%
+I'll add it here in tiny this is a a
+requirement that we add in in
+
+ align:start position:0%
+requirement that we add in in
+ 
+
+ align:start position:0%
+requirement that we add in in
+cryptography often what I'm writing now
+
+ align:start position:0%
+cryptography often what I'm writing now
+ 
+
+ align:start position:0%
+cryptography often what I'm writing now
+is not added in the in in the
+
+ align:start position:0%
+is not added in the in in the
+ 
+
+ align:start position:0%
+is not added in the in in the
+definitions but let me write another
+
+ align:start position:0%
+definitions but let me write another
+ 
+
+ align:start position:0%
+definitions but let me write another
+cryptography another that given for
+
+ align:start position:0%
+cryptography another that given for
+ 
+
+ align:start position:0%
+cryptography another that given for
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+X in or X for for every X in l and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+witness if it has a
+
+ align:start position:0%
+witness if it has a
+ 
+
+ align:start position:0%
+witness if it has a
+witness W okay so suppose this is a
+
+ align:start position:0%
+witness W okay so suppose this is a
+ 
+
+ align:start position:0%
+witness W okay so suppose this is a
+language in N time I don't know NP or n
+
+ align:start position:0%
+language in N time I don't know NP or n
+ 
+
+ align:start position:0%
+language in N time I don't know NP or n
+time T so it has some witness I want it
+
+ align:start position:0%
+time T so it has some witness I want it
+ 
+
+ align:start position:0%
+time T so it has some witness I want it
+to be the case that given X and W you
+
+ align:start position:0%
+to be the case that given X and W you
+ 
+
+ align:start position:0%
+to be the case that given X and W you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+efficiently compute Pi so not only there
+
+ align:start position:0%
+efficiently compute Pi so not only there
+ 
+
+ align:start position:0%
+efficiently compute Pi so not only there
+exists Pi of of poly and size you can
+
+ align:start position:0%
+exists Pi of of poly and size you can
+ 
+
+ align:start position:0%
+exists Pi of of poly and size you can
+actually efficiently compute it and
+
+ align:start position:0%
+actually efficiently compute it and
+ 
+
+ align:start position:0%
+actually efficiently compute it and
+because I require efficient Computing I
+
+ align:start position:0%
+because I require efficient Computing I
+ 
+
+ align:start position:0%
+because I require efficient Computing I
+actually don't care anymore so much
+
+ align:start position:0%
+actually don't care anymore so much
+ 
+
+ align:start position:0%
+actually don't care anymore so much
+about the randomness the amount the
+
+ align:start position:0%
+about the randomness the amount the
+ 
+
+ align:start position:0%
+about the randomness the amount the
+number of Randomness uh bits but yeah
+
+ align:start position:0%
+number of Randomness uh bits but yeah
+ 
+
+ align:start position:0%
+number of Randomness uh bits but yeah
+that's a very good point Thank you guys
+
+ align:start position:0%
+that's a very good point Thank you guys
+ 
+
+ align:start position:0%
+that's a very good point Thank you guys
+thank you for the question this is
+
+ align:start position:0%
+thank you for the question this is
+ 
+
+ align:start position:0%
+thank you for the question this is
+great H okay so that's what I'm going to
+
+ align:start position:0%
+great H okay so that's what I'm going to
+ 
+
+ align:start position:0%
+great H okay so that's what I'm going to
+prove even though let me just mention
+
+ align:start position:0%
+prove even though let me just mention
+ 
+
+ align:start position:0%
+prove even though let me just mention
+what is known is you can make this order
+
+ align:start position:0%
+what is known is you can make this order
+ 
+
+ align:start position:0%
+what is known is you can make this order
+login and you can make this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three okay so it's really remarkable if
+
+ align:start position:0%
+three okay so it's really remarkable if
+ 
+
+ align:start position:0%
+three okay so it's really remarkable if
+you think about it wow you can take any
+
+ align:start position:0%
+you think about it wow you can take any
+ 
+
+ align:start position:0%
+you think about it wow you can take any
+proof so you know how I don't know take
+
+ align:start position:0%
+proof so you know how I don't know take
+ 
+
+ align:start position:0%
+proof so you know how I don't know take
+a foras last the take the hardest proof
+
+ align:start position:0%
+a foras last the take the hardest proof
+ 
+
+ align:start position:0%
+a foras last the take the hardest proof
+that we know in mathematics you know one
+
+ align:start position:0%
+that we know in mathematics you know one
+ 
+
+ align:start position:0%
+that we know in mathematics you know one
+can write them in a pro propos checkable
+
+ align:start position:0%
+can write them in a pro propos checkable
+ 
+
+ align:start position:0%
+can write them in a pro propos checkable
+way they you can just take three bits
+
+ align:start position:0%
+way they you can just take three bits
+ 
+
+ align:start position:0%
+way they you can just take three bits
+and verify and if you're not happy with
+
+ align:start position:0%
+and verify and if you're not happy with
+ 
+
+ align:start position:0%
+and verify and if you're not happy with
+probability half repeat it as many times
+
+ align:start position:0%
+probability half repeat it as many times
+ 
+
+ align:start position:0%
+probability half repeat it as many times
+as you want you want prob you want to be
+
+ align:start position:0%
+as you want you want prob you want to be
+ 
+
+ align:start position:0%
+as you want you want prob you want to be
+sure that he can cheat with probability
+
+ align:start position:0%
+sure that he can cheat with probability
+ 
+
+ align:start position:0%
+sure that he can cheat with probability
+only one over two to the 500 repeat it
+
+ align:start position:0%
+only one over two to the 500 repeat it
+ 
+
+ align:start position:0%
+only one over two to the 500 repeat it
+500 times and each one it's like a very
+
+ align:start position:0%
+500 times and each one it's like a very
+ 
+
+ align:start position:0%
+500 times and each one it's like a very
+simple check it depends on three bits so
+
+ align:start position:0%
+simple check it depends on three bits so
+ 
+
+ align:start position:0%
+simple check it depends on three bits so
+it's really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remarkable no never
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mindo I guess it doesn't matter
+
+ align:start position:0%
+mindo I guess it doesn't matter
+ 
+
+ align:start position:0%
+mindo I guess it doesn't matter
+to all oh you're saying it's too big
+
+ align:start position:0%
+to all oh you're saying it's too big
+ 
+
+ align:start position:0%
+to all oh you're saying it's too big
+because for theory for practice Yeah but
+
+ align:start position:0%
+because for theory for practice Yeah but
+ 
+
+ align:start position:0%
+because for theory for practice Yeah but
+we're still in theory land yeah in
+
+ align:start position:0%
+we're still in theory land yeah in
+ 
+
+ align:start position:0%
+we're still in theory land yeah in
+practice these pcps you want them to be
+
+ align:start position:0%
+practice these pcps you want them to be
+ 
+
+ align:start position:0%
+practice these pcps you want them to be
+like linear that's the ideal the Quasi
+
+ align:start position:0%
+like linear that's the ideal the Quasi
+ 
+
+ align:start position:0%
+like linear that's the ideal the Quasi
+linear even if they're quadratic people
+
+ align:start position:0%
+linear even if they're quadratic people
+ 
+
+ align:start position:0%
+linear even if they're quadratic people
+don't like them you really want linear
+
+ align:start position:0%
+don't like them you really want linear
+ 
+
+ align:start position:0%
+don't like them you really want linear
+quasi linear pcps for for practice but
+
+ align:start position:0%
+quasi linear pcps for for practice but
+ 
+
+ align:start position:0%
+quasi linear pcps for for practice but
+for here PA is fantastic we're you know
+
+ align:start position:0%
+for here PA is fantastic we're you know
+ 
+
+ align:start position:0%
+for here PA is fantastic we're you know
+we're not we're not the let us stand the
+
+ align:start position:0%
+we're not we're not the let us stand the
+ 
+
+ align:start position:0%
+we're not we're not the let us stand the
+cloud a little bit okay so uh so okay so
+
+ align:start position:0%
+cloud a little bit okay so uh so okay so
+ 
+
+ align:start position:0%
+cloud a little bit okay so uh so okay so
+let's uh let's construct
+
+ align:start position:0%
+let's uh let's construct
+ 
+
+ align:start position:0%
+let's uh let's construct
+this ready okay so okay so we have the
+
+ align:start position:0%
+this ready okay so okay so we have the
+ 
+
+ align:start position:0%
+this ready okay so okay so we have the
+three but we're going to construct for
+
+ align:start position:0%
+three but we're going to construct for
+ 
+
+ align:start position:0%
+three but we're going to construct for
+the polog polog and what actually here's
+
+ align:start position:0%
+the polog polog and what actually here's
+ 
+
+ align:start position:0%
+the polog polog and what actually here's
+what you what's amazing you actually
+
+ align:start position:0%
+what you what's amazing you actually
+ 
+
+ align:start position:0%
+what you what's amazing you actually
+already know how to construct the PCP
+
+ align:start position:0%
+already know how to construct the PCP
+ 
+
+ align:start position:0%
+already know how to construct the PCP
+you just don't know that you know and
+
+ align:start position:0%
+you just don't know that you know and
+ 
+
+ align:start position:0%
+you just don't know that you know and
+how do you construct the PCP it's really
+
+ align:start position:0%
+how do you construct the PCP it's really
+ 
+
+ align:start position:0%
+how do you construct the PCP it's really
+only the GK protocol that's it so you
+
+ align:start position:0%
+only the GK protocol that's it so you
+ 
+
+ align:start position:0%
+only the GK protocol that's it so you
+can unfold gkr and I'm going to show you
+
+ align:start position:0%
+can unfold gkr and I'm going to show you
+ 
+
+ align:start position:0%
+can unfold gkr and I'm going to show you
+exactly how to make it a
+
+ align:start position:0%
+exactly how to make it a
+ 
+
+ align:start position:0%
+exactly how to make it a
+PCP okay so to do that but before and
+
+ align:start position:0%
+PCP okay so to do that but before and
+ 
+
+ align:start position:0%
+PCP okay so to do that but before and
+I'll recall the GK in a second on that
+
+ align:start position:0%
+I'll recall the GK in a second on that
+ 
+
+ align:start position:0%
+I'll recall the GK in a second on that
+board but to do that let's first let's
+
+ align:start position:0%
+board but to do that let's first let's
+ 
+
+ align:start position:0%
+board but to do that let's first let's
+first so I want to say any any language
+
+ align:start position:0%
+first so I want to say any any language
+ 
+
+ align:start position:0%
+first so I want to say any any language
+has a PCP let's con let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+focus on on three set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so thre set is an NP complete
+
+ align:start position:0%
+okay so thre set is an NP complete
+ 
+
+ align:start position:0%
+okay so thre set is an NP complete
+language let's just construct a PTP for
+
+ align:start position:0%
+language let's just construct a PTP for
+ 
+
+ align:start position:0%
+language let's just construct a PTP for
+three set and what's nice about three
+
+ align:start position:0%
+three set and what's nice about three
+ 
+
+ align:start position:0%
+three set and what's nice about three
+set is that I mean any NP language you
+
+ align:start position:0%
+set is that I mean any NP language you
+ 
+
+ align:start position:0%
+set is that I mean any NP language you
+can convert to three set so it's nice
+
+ align:start position:0%
+can convert to three set so it's nice
+ 
+
+ align:start position:0%
+can convert to three set so it's nice
+any NP language is that you have a
+
+ align:start position:0%
+any NP language is that you have a
+ 
+
+ align:start position:0%
+any NP language is that you have a
+circuit a verification
+
+ align:start position:0%
+circuit a verification
+ 
+
+ align:start position:0%
+circuit a verification
+circuit so a circuit verifying so you
+
+ align:start position:0%
+circuit so a circuit verifying so you
+ 
+
+ align:start position:0%
+circuit so a circuit verifying so you
+can think of it uh given W verifying
+
+ align:start position:0%
+can think of it uh given W verifying
+ 
+
+ align:start position:0%
+can think of it uh given W verifying
+that it's a valid witness of very small
+
+ align:start position:0%
+that it's a valid witness of very small
+ 
+
+ align:start position:0%
+that it's a valid witness of very small
+depth okay poly and depth and this is
+
+ align:start position:0%
+depth okay poly and depth and this is
+ 
+
+ align:start position:0%
+depth okay poly and depth and this is
+important because if you remember the GK
+
+ align:start position:0%
+important because if you remember the GK
+ 
+
+ align:start position:0%
+important because if you remember the GK
+protocol which we're going to use to
+
+ align:start position:0%
+protocol which we're going to use to
+ 
+
+ align:start position:0%
+protocol which we're going to use to
+construct this
+
+ align:start position:0%
+construct this
+ 
+
+ align:start position:0%
+construct this
+PCP kind of the number the communication
+
+ align:start position:0%
+PCP kind of the number the communication
+ 
+
+ align:start position:0%
+PCP kind of the number the communication
+complexity grows with the depth so we
+
+ align:start position:0%
+complexity grows with the depth so we
+ 
+
+ align:start position:0%
+complexity grows with the depth so we
+want the depth of the circuit to be
+
+ align:start position:0%
+want the depth of the circuit to be
+ 
+
+ align:start position:0%
+want the depth of the circuit to be
+small but any NP language you can
+
+ align:start position:0%
+small but any NP language you can
+ 
+
+ align:start position:0%
+small but any NP language you can
+convert into a three set and thre set
+
+ align:start position:0%
+convert into a three set and thre set
+ 
+
+ align:start position:0%
+convert into a three set and thre set
+has actually it's like the depth of
+
+ align:start position:0%
+has actually it's like the depth of
+ 
+
+ align:start position:0%
+has actually it's like the depth of
+three set is like actually only two but
+
+ align:start position:0%
+three set is like actually only two but
+ 
+
+ align:start position:0%
+three set is like actually only two but
+like you need to do you know uh little
+
+ align:start position:0%
+like you need to do you know uh little
+ 
+
+ align:start position:0%
+like you need to do you know uh little
+ores and then one big end but if
+
+ align:start position:0%
+ores and then one big end but if
+ 
+
+ align:start position:0%
+ores and then one big end but if
+remember gkr we wanted fan in two
+
+ align:start position:0%
+remember gkr we wanted fan in two
+ 
+
+ align:start position:0%
+remember gkr we wanted fan in two
+so once you have F in two it's like
+
+ align:start position:0%
+so once you have F in two it's like
+ 
+
+ align:start position:0%
+so once you have F in two it's like
+order log okay so this is depth you can
+
+ align:start position:0%
+order log okay so this is depth you can
+ 
+
+ align:start position:0%
+order log okay so this is depth you can
+think of it as being uh a like log in or
+
+ align:start position:0%
+think of it as being uh a like log in or
+ 
+
+ align:start position:0%
+think of it as being uh a like log in or
+I'm okay with poogan it doesn't
+
+ align:start position:0%
+I'm okay with poogan it doesn't
+ 
+
+ align:start position:0%
+I'm okay with poogan it doesn't
+matter the point is it's
+
+ align:start position:0%
+matter the point is it's
+ 
+
+ align:start position:0%
+matter the point is it's
+small and uh the reason why I write also
+
+ align:start position:0%
+small and uh the reason why I write also
+ 
+
+ align:start position:0%
+small and uh the reason why I write also
+polog is because uh it's actually log
+
+ align:start position:0%
+polog is because uh it's actually log
+ 
+
+ align:start position:0%
+polog is because uh it's actually log
+however uh this circuit is also any kind
+
+ align:start position:0%
+however uh this circuit is also any kind
+ 
+
+ align:start position:0%
+however uh this circuit is also any kind
+of the circuit is and this I'm not going
+
+ align:start position:0%
+of the circuit is and this I'm not going
+ 
+
+ align:start position:0%
+of the circuit is and this I'm not going
+to get into but it's log space uniform
+
+ align:start position:0%
+to get into but it's log space uniform
+ 
+
+ align:start position:0%
+to get into but it's log space uniform
+and now you can consider the circuit
+
+ align:start position:0%
+and now you can consider the circuit
+ 
+
+ align:start position:0%
+and now you can consider the circuit
+change it a little bit the way Rachel
+
+ align:start position:0%
+change it a little bit the way Rachel
+ 
+
+ align:start position:0%
+change it a little bit the way Rachel
+taught you two weeks ago if you don't
+
+ align:start position:0%
+taught you two weeks ago if you don't
+ 
+
+ align:start position:0%
+taught you two weeks ago if you don't
+remember it's not it's okay you can take
+
+ align:start position:0%
+remember it's not it's okay you can take
+ 
+
+ align:start position:0%
+remember it's not it's okay you can take
+it as a black box uh you can assume that
+
+ align:start position:0%
+it as a black box uh you can assume that
+ 
+
+ align:start position:0%
+it as a black box uh you can assume that
+The Circuit by kind of looking at a
+
+ align:start position:0%
+The Circuit by kind of looking at a
+ 
+
+ align:start position:0%
+The Circuit by kind of looking at a
+universal version of it you can assume
+
+ align:start position:0%
+universal version of it you can assume
+ 
+
+ align:start position:0%
+universal version of it you can assume
+that it has like the gates add I and
+
+ align:start position:0%
+that it has like the gates add I and
+ 
+
+ align:start position:0%
+that it has like the gates add I and
+multi are efficiently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computable and that's what we'll need so
+
+ align:start position:0%
+computable and that's what we'll need so
+ 
+
+ align:start position:0%
+computable and that's what we'll need so
+we can so if if you don't remember uh
+
+ align:start position:0%
+we can so if if you don't remember uh
+ 
+
+ align:start position:0%
+we can so if if you don't remember uh
+things from weeks ago it's okay I'll
+
+ align:start position:0%
+things from weeks ago it's okay I'll
+ 
+
+ align:start position:0%
+things from weeks ago it's okay I'll
+remind you what add I in multi in a
+
+ align:start position:0%
+remind you what add I in multi in a
+ 
+
+ align:start position:0%
+remind you what add I in multi in a
+second but you take any three set you
+
+ align:start position:0%
+second but you take any three set you
+ 
+
+ align:start position:0%
+second but you take any three set you
+can convert it uh or convert to 3 CNF so
+
+ align:start position:0%
+can convert it uh or convert to 3 CNF so
+ 
+
+ align:start position:0%
+can convert it uh or convert to 3 CNF so
+now given a witness you just check that
+
+ align:start position:0%
+now given a witness you just check that
+ 
+
+ align:start position:0%
+now given a witness you just check that
+it verifies hi hello hey wow all my kids
+
+ align:start position:0%
+it verifies hi hello hey wow all my kids
+ 
+
+ align:start position:0%
+it verifies hi hello hey wow all my kids
+come coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in okay so uh
+
+ align:start position:0%
+in okay so uh
+ 
+
+ align:start position:0%
+in okay so uh
+a you just uh we talking about how to
+
+ align:start position:0%
+a you just uh we talking about how to
+ 
+
+ align:start position:0%
+a you just uh we talking about how to
+construct pcps from gkr right
+
+ align:start position:0%
+construct pcps from gkr right
+ 
+
+ align:start position:0%
+construct pcps from gkr right
+now so what we're proving is that we're
+
+ align:start position:0%
+now so what we're proving is that we're
+ 
+
+ align:start position:0%
+now so what we're proving is that we're
+going to show how you can take any NP
+
+ align:start position:0%
+going to show how you can take any NP
+ 
+
+ align:start position:0%
+going to show how you can take any NP
+language in particular we're focusing on
+
+ align:start position:0%
+language in particular we're focusing on
+ 
+
+ align:start position:0%
+language in particular we're focusing on
+three sat and we're going to show how
+
+ align:start position:0%
+three sat and we're going to show how
+ 
+
+ align:start position:0%
+three sat and we're going to show how
+you can convert three sat into a PCP
+
+ align:start position:0%
+you can convert three sat into a PCP
+ 
+
+ align:start position:0%
+you can convert three sat into a PCP
+where the query complexity is poly Logan
+
+ align:start position:0%
+where the query complexity is poly Logan
+ 
+
+ align:start position:0%
+where the query complexity is poly Logan
+so converting to PCP the verifier needs
+
+ align:start position:0%
+so converting to PCP the verifier needs
+ 
+
+ align:start position:0%
+so converting to PCP the verifier needs
+to query only poly Logan uh locations we
+
+ align:start position:0%
+to query only poly Logan uh locations we
+ 
+
+ align:start position:0%
+to query only poly Logan uh locations we
+know you can do go all the way down to
+
+ align:start position:0%
+know you can do go all the way down to
+ 
+
+ align:start position:0%
+know you can do go all the way down to
+three but we're not uh today we're going
+
+ align:start position:0%
+three but we're not uh today we're going
+ 
+
+ align:start position:0%
+three but we're not uh today we're going
+to so polog this is the randomness
+
+ align:start position:0%
+to so polog this is the randomness
+ 
+
+ align:start position:0%
+to so polog this is the randomness
+complexity this is the query complexity
+
+ align:start position:0%
+complexity this is the query complexity
+ 
+
+ align:start position:0%
+complexity this is the query complexity
+we're focusing on completeness one sound
+
+ align:start position:0%
+we're focusing on completeness one sound
+ 
+
+ align:start position:0%
+we're focusing on completeness one sound
+is half okay so we're going to now
+
+ align:start position:0%
+is half okay so we're going to now
+ 
+
+ align:start position:0%
+is half okay so we're going to now
+construct the PCP and uh before we conr
+
+ align:start position:0%
+construct the PCP and uh before we conr
+ 
+
+ align:start position:0%
+construct the PCP and uh before we conr
+the P the PCP essentially uses gkr so
+
+ align:start position:0%
+the P the PCP essentially uses gkr so
+ 
+
+ align:start position:0%
+the P the PCP essentially uses gkr so
+let me first on this board remind you
+
+ align:start position:0%
+let me first on this board remind you
+ 
+
+ align:start position:0%
+let me first on this board remind you
+quickly what gkr looks like because
+
+ align:start position:0%
+quickly what gkr looks like because
+ 
+
+ align:start position:0%
+quickly what gkr looks like because
+we're going to use it to constuct the
+
+ align:start position:0%
+we're going to use it to constuct the
+ 
+
+ align:start position:0%
+we're going to use it to constuct the
+PCP okay you're cameraman it's okay to
+
+ align:start position:0%
+PCP okay you're cameraman it's okay to
+ 
+
+ align:start position:0%
+PCP okay you're cameraman it's okay to
+move okay okay
+
+ align:start position:0%
+move okay okay
+ 
+
+ align:start position:0%
+move okay okay
+um good so let's let's just recall the
+
+ align:start position:0%
+um good so let's let's just recall the
+ 
+
+ align:start position:0%
+um good so let's let's just recall the
+gkr how does it work we have a
+
+ align:start position:0%
+gkr how does it work we have a
+ 
+
+ align:start position:0%
+gkr how does it work we have a
+circuit there's an input W we're going
+
+ align:start position:0%
+circuit there's an input W we're going
+ 
+
+ align:start position:0%
+circuit there's an input W we're going
+to think of w here as the the satisfying
+
+ align:start position:0%
+to think of w here as the the satisfying
+ 
+
+ align:start position:0%
+to think of w here as the the satisfying
+assignment okay remember in the DK we
+
+ align:start position:0%
+assignment okay remember in the DK we
+ 
+
+ align:start position:0%
+assignment okay remember in the DK we
+assume the verifier has W in his hand
+
+ align:start position:0%
+assume the verifier has W in his hand
+ 
+
+ align:start position:0%
+assume the verifier has W in his hand
+the W the input in his hand here he
+
+ align:start position:0%
+the W the input in his hand here he
+ 
+
+ align:start position:0%
+the W the input in his hand here he
+doesn't W is going to be the witness for
+
+ align:start position:0%
+doesn't W is going to be the witness for
+ 
+
+ align:start position:0%
+doesn't W is going to be the witness for
+the satisfying assignment but that's
+
+ align:start position:0%
+the satisfying assignment but that's
+ 
+
+ align:start position:0%
+the satisfying assignment but that's
+okay now here's what so I'm I'm GNA
+
+ align:start position:0%
+okay now here's what so I'm I'm GNA
+ 
+
+ align:start position:0%
+okay now here's what so I'm I'm GNA
+construct the PCP proof okay I have my
+
+ align:start position:0%
+construct the PCP proof okay I have my
+ 
+
+ align:start position:0%
+construct the PCP proof okay I have my
+witness my satisfying
+
+ align:start position:0%
+witness my satisfying
+ 
+
+ align:start position:0%
+witness my satisfying
+assignment I'm going to construct a
+
+ align:start position:0%
+assignment I'm going to construct a
+ 
+
+ align:start position:0%
+assignment I'm going to construct a
+protic I'm going to convert W into a PCP
+
+ align:start position:0%
+protic I'm going to convert W into a PCP
+ 
+
+ align:start position:0%
+protic I'm going to convert W into a PCP
+into a protic checkable proof okay
+
+ align:start position:0%
+into a protic checkable proof okay
+ 
+
+ align:start position:0%
+into a protic checkable proof okay
+here's how I do it I look at the kind
+
+ align:start position:0%
+here's how I do it I look at the kind
+ 
+
+ align:start position:0%
+here's how I do it I look at the kind
+the circuit that checks that uh W
+
+ align:start position:0%
+the circuit that checks that uh W
+ 
+
+ align:start position:0%
+the circuit that checks that uh W
+actually you can if you want to think of
+
+ align:start position:0%
+actually you can if you want to think of
+ 
+
+ align:start position:0%
+actually you can if you want to think of
+it's completely new form you can think
+
+ align:start position:0%
+it's completely new form you can think
+ 
+
+ align:start position:0%
+it's completely new form you can think
+of having X and W so X and W and it
+
+ align:start position:0%
+of having X and W so X and W and it
+ 
+
+ align:start position:0%
+of having X and W so X and W and it
+checks that uh kind of fe uh sorry that
+
+ align:start position:0%
+checks that uh kind of fe uh sorry that
+ 
+
+ align:start position:0%
+checks that uh kind of fe uh sorry that
+or okay X which is Fe and it checks that
+
+ align:start position:0%
+or okay X which is Fe and it checks that
+ 
+
+ align:start position:0%
+or okay X which is Fe and it checks that
+F of w is one okay this is a log space
+
+ align:start position:0%
+F of w is one okay this is a log space
+ 
+
+ align:start position:0%
+F of w is one okay this is a log space
+uniform uh circuit and uh okay now what
+
+ align:start position:0%
+uniform uh circuit and uh okay now what
+ 
+
+ align:start position:0%
+uniform uh circuit and uh okay now what
+do I do so here's me I know W every we
+
+ align:start position:0%
+do I do so here's me I know W every we
+ 
+
+ align:start position:0%
+do I do so here's me I know W every we
+both know the three set
+
+ align:start position:0%
+both know the three set
+ 
+
+ align:start position:0%
+both know the three set
+formula what I
+
+ align:start position:0%
+formula what I
+ 
+
+ align:start position:0%
+formula what I
+do I and and we assume that this circuit
+
+ align:start position:0%
+do I and and we assume that this circuit
+ 
+
+ align:start position:0%
+do I and and we assume that this circuit
+is kind of has addition Gates and
+
+ align:start position:0%
+is kind of has addition Gates and
+ 
+
+ align:start position:0%
+is kind of has addition Gates and
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+Gates what I do for every
+
+ align:start position:0%
+Gates what I do for every
+ 
+
+ align:start position:0%
+Gates what I do for every
+layer I compute the values of the layer
+
+ align:start position:0%
+layer I compute the values of the layer
+ 
+
+ align:start position:0%
+layer I compute the values of the layer
+okay so I compute for every layer
+
+ align:start position:0%
+okay so I compute for every layer
+ 
+
+ align:start position:0%
+okay so I compute for every layer
+remember I have VI the I assume every
+
+ align:start position:0%
+remember I have VI the I assume every
+ 
+
+ align:start position:0%
+remember I have VI the I assume every
+layer let's say has size let's say the
+
+ align:start position:0%
+layer let's say has size let's say the
+ 
+
+ align:start position:0%
+layer let's say has size let's say the
+same size without L of generality we
+
+ align:start position:0%
+same size without L of generality we
+ 
+
+ align:start position:0%
+same size without L of generality we
+said size s we called it s so each layer
+
+ align:start position:0%
+said size s we called it s so each layer
+ 
+
+ align:start position:0%
+said size s we called it s so each layer
+has s
+
+ align:start position:0%
+has s
+ 
+
+ align:start position:0%
+has s
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+wires and uh and we ass and we write we
+
+ align:start position:0%
+wires and uh and we ass and we write we
+ 
+
+ align:start position:0%
+wires and uh and we ass and we write we
+compute all these wires for every layer
+
+ align:start position:0%
+compute all these wires for every layer
+ 
+
+ align:start position:0%
+compute all these wires for every layer
+I we think of this wire as go as going
+
+ align:start position:0%
+I we think of this wire as go as going
+ 
+
+ align:start position:0%
+I we think of this wire as go as going
+from H to M to 01 so H is some set and
+
+ align:start position:0%
+from H to M to 01 so H is some set and
+ 
+
+ align:start position:0%
+from H to M to 01 so H is some set and
+we assume that H to the m is s okay so
+
+ align:start position:0%
+we assume that H to the m is s okay so
+ 
+
+ align:start position:0%
+we assume that H to the m is s okay so
+we just encode these s wires in a kind
+
+ align:start position:0%
+we just encode these s wires in a kind
+ 
+
+ align:start position:0%
+we just encode these s wires in a kind
+of cube uh uh M dimensional cube of size
+
+ align:start position:0%
+of cube uh uh M dimensional cube of size
+ 
+
+ align:start position:0%
+of cube uh uh M dimensional cube of size
+H and we just write all the values of
+
+ align:start position:0%
+H and we just write all the values of
+ 
+
+ align:start position:0%
+H and we just write all the values of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+wires okay and then what we do we look
+
+ align:start position:0%
+wires okay and then what we do we look
+ 
+
+ align:start position:0%
+wires okay and then what we do we look
+at the extension V Tilda which is
+
+ align:start position:0%
+at the extension V Tilda which is
+ 
+
+ align:start position:0%
+at the extension V Tilda which is
+extends to a field F to the m to F and
+
+ align:start position:0%
+extends to a field F to the m to F and
+ 
+
+ align:start position:0%
+extends to a field F to the m to F and
+this is kind of the low degree extension
+
+ align:start position:0%
+this is kind of the low degree extension
+ 
+
+ align:start position:0%
+this is kind of the low degree extension
+so we take any F that can contains the
+
+ align:start position:0%
+so we take any F that can contains the
+ 
+
+ align:start position:0%
+so we take any F that can contains the
+set H and we extend VI via the low
+
+ align:start position:0%
+set H and we extend VI via the low
+ 
+
+ align:start position:0%
+set H and we extend VI via the low
+degree extension so these are things we
+
+ align:start position:0%
+degree extension so these are things we
+ 
+
+ align:start position:0%
+degree extension so these are things we
+covered okay now now is the first time
+
+ align:start position:0%
+covered okay now now is the first time
+ 
+
+ align:start position:0%
+covered okay now now is the first time
+you remember when I when we taught gkr I
+
+ align:start position:0%
+you remember when I when we taught gkr I
+ 
+
+ align:start position:0%
+you remember when I when we taught gkr I
+told you okay why I do why not do 0o one
+
+ align:start position:0%
+told you okay why I do why not do 0o one
+ 
+
+ align:start position:0%
+told you okay why I do why not do 0o one
+to the m you know 0o to the log in it's
+
+ align:start position:0%
+to the m you know 0o to the log in it's
+ 
+
+ align:start position:0%
+to the m you know 0o to the log in it's
+much natural to think of binary
+
+ align:start position:0%
+much natural to think of binary
+ 
+
+ align:start position:0%
+much natural to think of binary
+representation of s as opposed to this H
+
+ align:start position:0%
+representation of s as opposed to this H
+ 
+
+ align:start position:0%
+representation of s as opposed to this H
+to the m which is what H and I told you
+
+ align:start position:0%
+to the m which is what H and I told you
+ 
+
+ align:start position:0%
+to the m which is what H and I told you
+how often we like parameters we like to
+
+ align:start position:0%
+how often we like parameters we like to
+ 
+
+ align:start position:0%
+how often we like parameters we like to
+think of H as
+
+ align:start position:0%
+think of H as
+ 
+
+ align:start position:0%
+think of H as
+login ah sorry log n and M is log n over
+
+ align:start position:0%
+login ah sorry log n and M is log n over
+ 
+
+ align:start position:0%
+login ah sorry log n and M is log n over
+log log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n uh and if you'll see H to the m is
+
+ align:start position:0%
+n uh and if you'll see H to the m is
+ 
+
+ align:start position:0%
+n uh and if you'll see H to the m is
+just becomes n because uh you can think
+
+ align:start position:0%
+just becomes n because uh you can think
+ 
+
+ align:start position:0%
+just becomes n because uh you can think
+of a so H to the
+
+ align:start position:0%
+of a so H to the
+ 
+
+ align:start position:0%
+of a so H to the
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+m is log n to the N but log n is just
+
+ align:start position:0%
+m is log n to the N but log n is just
+ 
+
+ align:start position:0%
+m is log n to the N but log n is just
+like two log log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n to the n and the log log n cancels out
+
+ align:start position:0%
+n to the n and the log log n cancels out
+ 
+
+ align:start position:0%
+n to the n and the log log n cancels out
+so you have two to the
+
+ align:start position:0%
+so you have two to the
+ 
+
+ align:start position:0%
+so you have two to the
+again so you have uh oh I did everything
+
+ align:start position:0%
+again so you have uh oh I did everything
+ 
+
+ align:start position:0%
+again so you have uh oh I did everything
+everything is s sorry
+
+ align:start position:0%
+everything is s sorry
+ 
+
+ align:start position:0%
+everything is s sorry
+s the N here is s s s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s so you have S now remember I told I
+
+ align:start position:0%
+s so you have S now remember I told I
+ 
+
+ align:start position:0%
+s so you have S now remember I told I
+told you oh we'll need the set of
+
+ align:start position:0%
+told you oh we'll need the set of
+ 
+
+ align:start position:0%
+told you oh we'll need the set of
+parameters as opposed to say 01 it's
+
+ align:start position:0%
+parameters as opposed to say 01 it's
+ 
+
+ align:start position:0%
+parameters as opposed to say 01 it's
+natural to think of H as 01 and M is log
+
+ align:start position:0%
+natural to think of H as 01 and M is log
+ 
+
+ align:start position:0%
+natural to think of H as 01 and M is log
+n that's much more natural uh we used as
+
+ align:start position:0%
+n that's much more natural uh we used as
+ 
+
+ align:start position:0%
+n that's much more natural uh we used as
+computer science to think in binary now
+
+ align:start position:0%
+computer science to think in binary now
+ 
+
+ align:start position:0%
+computer science to think in binary now
+we're thinking of like log ass it's like
+
+ align:start position:0%
+we're thinking of like log ass it's like
+ 
+
+ align:start position:0%
+we're thinking of like log ass it's like
+really how how annoying can you be and
+
+ align:start position:0%
+really how how annoying can you be and
+ 
+
+ align:start position:0%
+really how how annoying can you be and
+the reason is it's for this now now we
+
+ align:start position:0%
+the reason is it's for this now now we
+ 
+
+ align:start position:0%
+the reason is it's for this now now we
+need it why now we take F that is going
+
+ align:start position:0%
+need it why now we take F that is going
+ 
+
+ align:start position:0%
+need it why now we take F that is going
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be it's going to be extension of size
+
+ align:start position:0%
+be it's going to be extension of size
+ 
+
+ align:start position:0%
+be it's going to be extension of size
+poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logus okay we'll see the poly will need
+
+ align:start position:0%
+logus okay we'll see the poly will need
+ 
+
+ align:start position:0%
+logus okay we'll see the poly will need
+to be big enough we'll talk about in a
+
+ align:start position:0%
+to be big enough we'll talk about in a
+ 
+
+ align:start position:0%
+to be big enough we'll talk about in a
+second but the field we don't we don't
+
+ align:start position:0%
+second but the field we don't we don't
+ 
+
+ align:start position:0%
+second but the field we don't we don't
+want more than poly log s and the reason
+
+ align:start position:0%
+want more than poly log s and the reason
+ 
+
+ align:start position:0%
+want more than poly log s and the reason
+is we want
+
+ align:start position:0%
+is we want
+ 
+
+ align:start position:0%
+is we want
+F to the m to be
+
+ align:start position:0%
+F to the m to be
+ 
+
+ align:start position:0%
+F to the m to be
+polys okay so we know we know that H to
+
+ align:start position:0%
+polys okay so we know we know that H to
+ 
+
+ align:start position:0%
+polys okay so we know we know that H to
+the m is s if if uh f is only poly
+
+ align:start position:0%
+the m is s if if uh f is only poly
+ 
+
+ align:start position:0%
+the m is s if if uh f is only poly
+bigger then we have this is poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s okay and that's important for us okay
+
+ align:start position:0%
+s okay and that's important for us okay
+ 
+
+ align:start position:0%
+s okay and that's important for us okay
+note if H was just 01 so the size of H
+
+ align:start position:0%
+note if H was just 01 so the size of H
+ 
+
+ align:start position:0%
+note if H was just 01 so the size of H
+was two
+
+ align:start position:0%
+was two
+ 
+
+ align:start position:0%
+was two
+we couldn't keep F poly and to we
+
+ align:start position:0%
+we couldn't keep F poly and to we
+ 
+
+ align:start position:0%
+we couldn't keep F poly and to we
+couldn't keep F constant you'll see F
+
+ align:start position:0%
+couldn't keep F constant you'll see F
+ 
+
+ align:start position:0%
+couldn't keep F constant you'll see F
+will need to grow with m m f so for
+
+ align:start position:0%
+will need to grow with m m f so for
+ 
+
+ align:start position:0%
+will need to grow with m m f so for
+soundness m f will need to be
+
+ align:start position:0%
+soundness m f will need to be
+ 
+
+ align:start position:0%
+soundness m f will need to be
+bigger than M *
+
+ align:start position:0%
+bigger than M *
+ 
+
+ align:start position:0%
+bigger than M *
+H actually there's also D that will come
+
+ align:start position:0%
+H actually there's also D that will come
+ 
+
+ align:start position:0%
+H actually there's also D that will come
+in it's significantly bigger so if we
+
+ align:start position:0%
+in it's significantly bigger so if we
+ 
+
+ align:start position:0%
+in it's significantly bigger so if we
+take H to be two we'll need to take F to
+
+ align:start position:0%
+take H to be two we'll need to take F to
+ 
+
+ align:start position:0%
+take H to be two we'll need to take F to
+be at least log n and then we'll have F
+
+ align:start position:0%
+be at least log n and then we'll have F
+ 
+
+ align:start position:0%
+be at least log n and then we'll have F
+to them is log to the power of log n
+
+ align:start position:0%
+to them is log to the power of log n
+ 
+
+ align:start position:0%
+to them is log to the power of log n
+that's more that's super
+
+ align:start position:0%
+that's more that's super
+ 
+
+ align:start position:0%
+that's more that's super
+poly and I want after them to be
+
+ align:start position:0%
+poly and I want after them to be
+ 
+
+ align:start position:0%
+poly and I want after them to be
+poly okay so we do this so now I so what
+
+ align:start position:0%
+poly okay so we do this so now I so what
+ 
+
+ align:start position:0%
+poly okay so we do this so now I so what
+is the PCP the
+
+ align:start position:0%
+is the PCP the
+ 
+
+ align:start position:0%
+is the PCP the
+PCP so actually I'll write there the PCP
+
+ align:start position:0%
+PCP so actually I'll write there the PCP
+ 
+
+ align:start position:0%
+PCP so actually I'll write there the PCP
+but uh now let's let's just finish
+
+ align:start position:0%
+but uh now let's let's just finish
+ 
+
+ align:start position:0%
+but uh now let's let's just finish
+recalling the GK so what does the
+
+ align:start position:0%
+recalling the GK so what does the
+ 
+
+ align:start position:0%
+recalling the GK so what does the
+verifier do in the GK the pro do in the
+
+ align:start position:0%
+verifier do in the GK the pro do in the
+ 
+
+ align:start position:0%
+verifier do in the GK the pro do in the
+GK he computes all these low degree
+
+ align:start position:0%
+GK he computes all these low degree
+ 
+
+ align:start position:0%
+GK he computes all these low degree
+extensions and then the GK consists of D
+
+ align:start position:0%
+extensions and then the GK consists of D
+ 
+
+ align:start position:0%
+extensions and then the GK consists of D
+phases going from the output layer to
+
+ align:start position:0%
+phases going from the output layer to
+ 
+
+ align:start position:0%
+phases going from the output layer to
+the input layer layer where in each
+
+ align:start position:0%
+the input layer layer where in each
+ 
+
+ align:start position:0%
+the input layer layer where in each
+phase we run two Su check protocols in
+
+ align:start position:0%
+phase we run two Su check protocols in
+ 
+
+ align:start position:0%
+phase we run two Su check protocols in
+parallel where the verifier uses the
+
+ align:start position:0%
+parallel where the verifier uses the
+ 
+
+ align:start position:0%
+parallel where the verifier uses the
+same Randomness and what what the
+
+ align:start position:0%
+same Randomness and what what the
+ 
+
+ align:start position:0%
+same Randomness and what what the
+subject protocol does is it it reduces
+
+ align:start position:0%
+subject protocol does is it it reduces
+ 
+
+ align:start position:0%
+subject protocol does is it it reduces
+from checking two values here to
+
+ align:start position:0%
+from checking two values here to
+ 
+
+ align:start position:0%
+from checking two values here to
+reducing checking two values in the
+
+ align:start position:0%
+reducing checking two values in the
+ 
+
+ align:start position:0%
+reducing checking two values in the
+layer below and we kind of go kind of
+
+ align:start position:0%
+layer below and we kind of go kind of
+ 
+
+ align:start position:0%
+layer below and we kind of go kind of
+from checking uh until we get to the
+
+ align:start position:0%
+from checking uh until we get to the
+ 
+
+ align:start position:0%
+from checking uh until we get to the
+input and then input the verifier can
+
+ align:start position:0%
+input and then input the verifier can
+ 
+
+ align:start position:0%
+input and then input the verifier can
+check on his own that's the
+
+ align:start position:0%
+check on his own that's the
+ 
+
+ align:start position:0%
+check on his own that's the
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+okay okay now let's just Rec in a
+
+ align:start position:0%
+okay okay now let's just Rec in a
+ 
+
+ align:start position:0%
+okay okay now let's just Rec in a
+subject protocol here each subject
+
+ align:start position:0%
+subject protocol here each subject
+ 
+
+ align:start position:0%
+subject protocol here each subject
+protocol if you uh remember maybe you
+
+ align:start position:0%
+protocol if you uh remember maybe you
+ 
+
+ align:start position:0%
+protocol if you uh remember maybe you
+don't it's not the details are not so
+
+ align:start position:0%
+don't it's not the details are not so
+ 
+
+ align:start position:0%
+don't it's not the details are not so
+important right now but it's kind of you
+
+ align:start position:0%
+important right now but it's kind of you
+ 
+
+ align:start position:0%
+important right now but it's kind of you
+go from VI inex tension which is let's
+
+ align:start position:0%
+go from VI inex tension which is let's
+ 
+
+ align:start position:0%
+go from VI inex tension which is let's
+say VI Tilda of some
+
+ align:start position:0%
+say VI Tilda of some
+ 
+
+ align:start position:0%
+say VI Tilda of some
+Z and you write it as this is kind of
+
+ align:start position:0%
+Z and you write it as this is kind of
+ 
+
+ align:start position:0%
+Z and you write it as this is kind of
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+of uh points in the in h to the m
+
+ align:start position:0%
+of uh points in the in h to the m
+ 
+
+ align:start position:0%
+of uh points in the in h to the m
+because that's the definition of
+
+ align:start position:0%
+because that's the definition of
+ 
+
+ align:start position:0%
+because that's the definition of
+extension times some k p uh Z this is
+
+ align:start position:0%
+extension times some k p uh Z this is
+ 
+
+ align:start position:0%
+extension times some k p uh Z this is
+the function that checks equality again
+
+ align:start position:0%
+the function that checks equality again
+ 
+
+ align:start position:0%
+the function that checks equality again
+it's not important but what's important
+
+ align:start position:0%
+it's not important but what's important
+ 
+
+ align:start position:0%
+it's not important but what's important
+to me to show is that and then you do
+
+ align:start position:0%
+to me to show is that and then you do
+ 
+
+ align:start position:0%
+to me to show is that and then you do
+sum over P W1 W2 in h of
+
+ align:start position:0%
+sum over P W1 W2 in h of
+ 
+
+ align:start position:0%
+sum over P W1 W2 in h of
+M and you convert VI to either kind of
+
+ align:start position:0%
+M and you convert VI to either kind of
+ 
+
+ align:start position:0%
+M and you convert VI to either kind of
+uh a if if if this is a plus gate you
+
+ align:start position:0%
+uh a if if if this is a plus gate you
+ 
+
+ align:start position:0%
+uh a if if if this is a plus gate you
+convert it to uh like um the plus of the
+
+ align:start position:0%
+convert it to uh like um the plus of the
+ 
+
+ align:start position:0%
+convert it to uh like um the plus of the
+of the wires below with multiplication
+
+ align:start position:0%
+of the wires below with multiplication
+ 
+
+ align:start position:0%
+of the wires below with multiplication
+you check the multiplication so in other
+
+ align:start position:0%
+you check the multiplication so in other
+ 
+
+ align:start position:0%
+you check the multiplication so in other
+words what this
+
+ align:start position:0%
+words what this
+ 
+
+ align:start position:0%
+words what this
+is what this is or I should say what
+
+ align:start position:0%
+is what this is or I should say what
+ 
+
+ align:start position:0%
+is what this is or I should say what
+this is let me just open this what is VI
+
+ align:start position:0%
+this is let me just open this what is VI
+ 
+
+ align:start position:0%
+this is let me just open this what is VI
+P it's if it's an
+
+ align:start position:0%
+P it's if it's an
+ 
+
+ align:start position:0%
+P it's if it's an
+ad if it's an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ad P W1 W2 so if Point p is this just
+
+ align:start position:0%
+ad P W1 W2 so if Point p is this just
+ 
+
+ align:start position:0%
+ad P W1 W2 so if Point p is this just
+the addition of the two wires below then
+
+ align:start position:0%
+the addition of the two wires below then
+ 
+
+ align:start position:0%
+the addition of the two wires below then
+you replace p with W1 with v
+
+ align:start position:0%
+you replace p with W1 with v
+ 
+
+ align:start position:0%
+you replace p with W1 with v
+ius1
+
+ align:start position:0%
+ius1
+ 
+
+ align:start position:0%
+ius1
+W1 plus VI -1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W2 and plus if it was not an adgate if
+
+ align:start position:0%
+W2 and plus if it was not an adgate if
+ 
+
+ align:start position:0%
+W2 and plus if it was not an adgate if
+it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mgate then you replace it with the
+
+ align:start position:0%
+mgate then you replace it with the
+ 
+
+ align:start position:0%
+mgate then you replace it with the
+multiplication of vi- 1 W1 Time vi- 1 W2
+
+ align:start position:0%
+multiplication of vi- 1 W1 Time vi- 1 W2
+ 
+
+ align:start position:0%
+multiplication of vi- 1 W1 Time vi- 1 W2
+so just uh right the idea was and all
+
+ align:start position:0%
+so just uh right the idea was and all
+ 
+
+ align:start position:0%
+so just uh right the idea was and all
+this is times
+
+ align:start position:0%
+this is times
+ 
+
+ align:start position:0%
+this is times
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+Kai k
+
+ align:start position:0%
+Kai k
+ 
+
+ align:start position:0%
+Kai k
+p z but again how do we go from layer I
+
+ align:start position:0%
+p z but again how do we go from layer I
+ 
+
+ align:start position:0%
+p z but again how do we go from layer I
+toay to one layer below we take that
+
+ align:start position:0%
+toay to one layer below we take that
+ 
+
+ align:start position:0%
+toay to one layer below we take that
+element in the extension we think of it
+
+ align:start position:0%
+element in the extension we think of it
+ 
+
+ align:start position:0%
+element in the extension we think of it
+as a sum that's the definition of lree
+
+ align:start position:0%
+as a sum that's the definition of lree
+ 
+
+ align:start position:0%
+as a sum that's the definition of lree
+extension it's sum of the elements in
+
+ align:start position:0%
+extension it's sum of the elements in
+ 
+
+ align:start position:0%
+extension it's sum of the elements in
+the circuit itself with some with some
+
+ align:start position:0%
+the circuit itself with some with some
+ 
+
+ align:start position:0%
+the circuit itself with some with some
+function uh with some weight and now
+
+ align:start position:0%
+function uh with some weight and now
+ 
+
+ align:start position:0%
+function uh with some weight and now
+look at the at the value what what is
+
+ align:start position:0%
+look at the at the value what what is
+ 
+
+ align:start position:0%
+look at the at the value what what is
+the value of this gate well if it's an
+
+ align:start position:0%
+the value of this gate well if it's an
+ 
+
+ align:start position:0%
+the value of this gate well if it's an
+and if it's an add gate it's the sum of
+
+ align:start position:0%
+and if it's an add gate it's the sum of
+ 
+
+ align:start position:0%
+and if it's an add gate it's the sum of
+the two children and if it's a mgate it
+
+ align:start position:0%
+the two children and if it's a mgate it
+ 
+
+ align:start position:0%
+the two children and if it's a mgate it
+should be the multiplication of the two
+
+ align:start position:0%
+should be the multiplication of the two
+ 
+
+ align:start position:0%
+should be the multiplication of the two
+children and so add I just outputs one
+
+ align:start position:0%
+children and so add I just outputs one
+ 
+
+ align:start position:0%
+children and so add I just outputs one
+of these if you know W1 W2 are the
+
+ align:start position:0%
+of these if you know W1 W2 are the
+ 
+
+ align:start position:0%
+of these if you know W1 W2 are the
+children of P zero otherwise similarly
+
+ align:start position:0%
+children of P zero otherwise similarly
+ 
+
+ align:start position:0%
+children of P zero otherwise similarly
+malt and but we do everything in the
+
+ align:start position:0%
+malt and but we do everything in the
+ 
+
+ align:start position:0%
+malt and but we do everything in the
+extension uh we look at everything in
+
+ align:start position:0%
+extension uh we look at everything in
+ 
+
+ align:start position:0%
+extension uh we look at everything in
+the extension because we want to think
+
+ align:start position:0%
+the extension because we want to think
+ 
+
+ align:start position:0%
+the extension because we want to think
+of it as a polinomial and once we think
+
+ align:start position:0%
+of it as a polinomial and once we think
+ 
+
+ align:start position:0%
+of it as a polinomial and once we think
+once we these are all pols then this is
+
+ align:start position:0%
+once we these are all pols then this is
+ 
+
+ align:start position:0%
+once we these are all pols then this is
+just a sum
+
+ align:start position:0%
+just a sum
+ 
+
+ align:start position:0%
+just a sum
+check okay and we saw a sum check how to
+
+ align:start position:0%
+check okay and we saw a sum check how to
+ 
+
+ align:start position:0%
+check okay and we saw a sum check how to
+do it efficiently so now the point is G
+
+ align:start position:0%
+do it efficiently so now the point is G
+ 
+
+ align:start position:0%
+do it efficiently so now the point is G
+consists of only these two D Su checks
+
+ align:start position:0%
+consists of only these two D Su checks
+ 
+
+ align:start position:0%
+consists of only these two D Su checks
+so now let me go to my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PCP a is this so here's uh our PCP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially my PCP is just gkr but
+
+ align:start position:0%
+essentially my PCP is just gkr but
+ 
+
+ align:start position:0%
+essentially my PCP is just gkr but
+opened up completely completely
+
+ align:start position:0%
+opened up completely completely
+ 
+
+ align:start position:0%
+opened up completely completely
+unraveled so okay so here's my PCP I
+
+ align:start position:0%
+unraveled so okay so here's my PCP I
+ 
+
+ align:start position:0%
+unraveled so okay so here's my PCP I
+have my X in W here's what I do I'm
+
+ align:start position:0%
+have my X in W here's what I do I'm
+ 
+
+ align:start position:0%
+have my X in W here's what I do I'm
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+compute all the V1 V VI Tilda the
+
+ align:start position:0%
+compute all the V1 V VI Tilda the
+ 
+
+ align:start position:0%
+compute all the V1 V VI Tilda the
+extension of the values of each of all
+
+ align:start position:0%
+extension of the values of each of all
+ 
+
+ align:start position:0%
+extension of the values of each of all
+the gate in each wire for every
+
+ align:start position:0%
+the gate in each wire for every
+ 
+
+ align:start position:0%
+the gate in each wire for every
+Z for every Z and F to the
+
+ align:start position:0%
+Z for every Z and F to the
+ 
+
+ align:start position:0%
+Z for every Z and F to the
+m it's
+
+ align:start position:0%
+m it's
+ 
+
+ align:start position:0%
+m it's
+important this is going to be all this
+
+ align:start position:0%
+important this is going to be all this
+ 
+
+ align:start position:0%
+important this is going to be all this
+is going to be part of the PCP so if F
+
+ align:start position:0%
+is going to be part of the PCP so if F
+ 
+
+ align:start position:0%
+is going to be part of the PCP so if F
+to m is more than polinomial my PCP is
+
+ align:start position:0%
+to m is more than polinomial my PCP is
+ 
+
+ align:start position:0%
+to m is more than polinomial my PCP is
+super
+
+ align:start position:0%
+super
+ 
+
+ align:start position:0%
+super
+polinomial okay so after to them has to
+
+ align:start position:0%
+polinomial okay so after to them has to
+ 
+
+ align:start position:0%
+polinomial okay so after to them has to
+be polinomial this is a ready sized
+
+ align:start position:0%
+be polinomial this is a ready sized
+ 
+
+ align:start position:0%
+be polinomial this is a ready sized
+polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah again sorry we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the oh yeah yeah yeah yeah yeah yeah
+
+ align:start position:0%
+the oh yeah yeah yeah yeah yeah yeah
+ 
+
+ align:start position:0%
+the oh yeah yeah yeah yeah yeah yeah
+okay good good good yes so for gkr we
+
+ align:start position:0%
+okay good good good yes so for gkr we
+ 
+
+ align:start position:0%
+okay good good good yes so for gkr we
+had a restriction that the
+
+ align:start position:0%
+had a restriction that the
+ 
+
+ align:start position:0%
+had a restriction that the
+circuit to do gkr we said gkr is like is
+
+ align:start position:0%
+circuit to do gkr we said gkr is like is
+ 
+
+ align:start position:0%
+circuit to do gkr we said gkr is like is
+proving that uh bounded depth circuit
+
+ align:start position:0%
+proving that uh bounded depth circuit
+ 
+
+ align:start position:0%
+proving that uh bounded depth circuit
+and put x equals y and we had a
+
+ align:start position:0%
+and put x equals y and we had a
+ 
+
+ align:start position:0%
+and put x equals y and we had a
+restriction that the circuit has to be B
+
+ align:start position:0%
+restriction that the circuit has to be B
+ 
+
+ align:start position:0%
+restriction that the circuit has to be B
+bounded uh space uniform or in other
+
+ align:start position:0%
+bounded uh space uniform or in other
+ 
+
+ align:start position:0%
+bounded uh space uniform or in other
+words we needed to ensure that add I and
+
+ align:start position:0%
+words we needed to ensure that add I and
+ 
+
+ align:start position:0%
+words we needed to ensure that add I and
+mul this ex extended Andi and extended
+
+ align:start position:0%
+mul this ex extended Andi and extended
+ 
+
+ align:start position:0%
+mul this ex extended Andi and extended
+multi are computed computer
+
+ align:start position:0%
+multi are computed computer
+ 
+
+ align:start position:0%
+multi are computed computer
+efficiently threat has that property
+
+ align:start position:0%
+efficiently threat has that property
+ 
+
+ align:start position:0%
+efficiently threat has that property
+okay I again I did go into the details
+
+ align:start position:0%
+okay I again I did go into the details
+ 
+
+ align:start position:0%
+okay I again I did go into the details
+but uh the threet is it's a very unifor
+
+ align:start position:0%
+but uh the threet is it's a very unifor
+ 
+
+ align:start position:0%
+but uh the threet is it's a very unifor
+you know given a FNX it's very uniform
+
+ align:start position:0%
+you know given a FNX it's very uniform
+ 
+
+ align:start position:0%
+you know given a FNX it's very uniform
+to check it's a very it is a loog space
+
+ align:start position:0%
+to check it's a very it is a loog space
+ 
+
+ align:start position:0%
+to check it's a very it is a loog space
+uniform and then we can convert it as
+
+ align:start position:0%
+uniform and then we can convert it as
+ 
+
+ align:start position:0%
+uniform and then we can convert it as
+Rachel uh did two weeks ago uh to kind
+
+ align:start position:0%
+Rachel uh did two weeks ago uh to kind
+ 
+
+ align:start position:0%
+Rachel uh did two weeks ago uh to kind
+of one that has uh by increasing the the
+
+ align:start position:0%
+of one that has uh by increasing the the
+ 
+
+ align:start position:0%
+of one that has uh by increasing the the
+depth by poly factors uh so keeping it
+
+ align:start position:0%
+depth by poly factors uh so keeping it
+ 
+
+ align:start position:0%
+depth by poly factors uh so keeping it
+poly log you can make at I at till and
+
+ align:start position:0%
+poly log you can make at I at till and
+ 
+
+ align:start position:0%
+poly log you can make at I at till and
+multi be efficiently computable so yeah
+
+ align:start position:0%
+multi be efficiently computable so yeah
+ 
+
+ align:start position:0%
+multi be efficiently computable so yeah
+great that's a very good question uh so
+
+ align:start position:0%
+great that's a very good question uh so
+ 
+
+ align:start position:0%
+great that's a very good question uh so
+yes good so this is going to be part of
+
+ align:start position:0%
+yes good so this is going to be part of
+ 
+
+ align:start position:0%
+yes good so this is going to be part of
+the uh PCP but that's not all uh by the
+
+ align:start position:0%
+the uh PCP but that's not all uh by the
+ 
+
+ align:start position:0%
+the uh PCP but that's not all uh by the
+way we should also give uh this we give
+
+ align:start position:0%
+way we should also give uh this we give
+ 
+
+ align:start position:0%
+way we should also give uh this we give
+this for every I from the input layer
+
+ align:start position:0%
+this for every I from the input layer
+ 
+
+ align:start position:0%
+this for every I from the input layer
+zero one up to D this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output and this is the input layer
+
+ align:start position:0%
+output and this is the input layer
+ 
+
+ align:start position:0%
+output and this is the input layer
+we have to give him the input layer
+
+ align:start position:0%
+we have to give him the input layer
+ 
+
+ align:start position:0%
+we have to give him the input layer
+because the poor verifi verifier doesn't
+
+ align:start position:0%
+because the poor verifi verifier doesn't
+ 
+
+ align:start position:0%
+because the poor verifi verifier doesn't
+have W so he doesn't have actually the
+
+ align:start position:0%
+have W so he doesn't have actually the
+ 
+
+ align:start position:0%
+have W so he doesn't have actually the
+input before he and do you care he had
+
+ align:start position:0%
+input before he and do you care he had
+ 
+
+ align:start position:0%
+input before he and do you care he had
+the input here he doesn't have the input
+
+ align:start position:0%
+the input here he doesn't have the input
+ 
+
+ align:start position:0%
+the input here he doesn't have the input
+but we're going to give him the Lo
+
+ align:start position:0%
+but we're going to give him the Lo
+ 
+
+ align:start position:0%
+but we're going to give him the Lo
+extension of this W okay good now but
+
+ align:start position:0%
+extension of this W okay good now but
+ 
+
+ align:start position:0%
+extension of this W okay good now but
+okay so I'm the verifier what do I do I
+
+ align:start position:0%
+okay so I'm the verifier what do I do I
+ 
+
+ align:start position:0%
+okay so I'm the verifier what do I do I
+need to verify the sum checks who do I
+
+ align:start position:0%
+need to verify the sum checks who do I
+ 
+
+ align:start position:0%
+need to verify the sum checks who do I
+interact with Su checks I'll put all the
+
+ align:start position:0%
+interact with Su checks I'll put all the
+ 
+
+ align:start position:0%
+interact with Su checks I'll put all the
+possible answers in the Oracle so now we
+
+ align:start position:0%
+possible answers in the Oracle so now we
+ 
+
+ align:start position:0%
+possible answers in the Oracle so now we
+do two DM checks okay so okay so for
+
+ align:start position:0%
+do two DM checks okay so okay so for
+ 
+
+ align:start position:0%
+do two DM checks okay so okay so for
+every pass possible for okay for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ey and for every
+
+ align:start position:0%
+ey and for every
+ 
+
+ align:start position:0%
+ey and for every
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Z in the GTR protocol we may need to do
+
+ align:start position:0%
+Z in the GTR protocol we may need to do
+ 
+
+ align:start position:0%
+Z in the GTR protocol we may need to do
+a sum check because in the sum Che
+
+ align:start position:0%
+a sum check because in the sum Che
+ 
+
+ align:start position:0%
+a sum check because in the sum Che
+protocol what is in the GK what does it
+
+ align:start position:0%
+protocol what is in the GK what does it
+ 
+
+ align:start position:0%
+protocol what is in the GK what does it
+how does it look like the ver the
+
+ align:start position:0%
+how does it look like the ver the
+ 
+
+ align:start position:0%
+how does it look like the ver the
+verifier first decides okay prove the
+
+ align:start position:0%
+verifier first decides okay prove the
+ 
+
+ align:start position:0%
+verifier first decides okay prove the
+output layer is correct let's say the
+
+ align:start position:0%
+output layer is correct let's say the
+ 
+
+ align:start position:0%
+output layer is correct let's say the
+output the Z is fixed fine then he
+
+ align:start position:0%
+output the Z is fixed fine then he
+ 
+
+ align:start position:0%
+output the Z is fixed fine then he
+chooses Randomness Randomness Randomness
+
+ align:start position:0%
+chooses Randomness Randomness Randomness
+ 
+
+ align:start position:0%
+chooses Randomness Randomness Randomness
+in a some check it reduces is the
+
+ align:start position:0%
+in a some check it reduces is the
+ 
+
+ align:start position:0%
+in a some check it reduces is the
+checking Z D minus one in a random
+
+ align:start position:0%
+checking Z D minus one in a random
+ 
+
+ align:start position:0%
+checking Z D minus one in a random
+Z the the Z is determined by the random
+
+ align:start position:0%
+Z the the Z is determined by the random
+ 
+
+ align:start position:0%
+Z the the Z is determined by the random
+coins of the
+
+ align:start position:0%
+coins of the
+ 
+
+ align:start position:0%
+coins of the
+verifier so which Z do I put and I want
+
+ align:start position:0%
+verifier so which Z do I put and I want
+ 
+
+ align:start position:0%
+verifier so which Z do I put and I want
+to show something for every possible Z
+
+ align:start position:0%
+to show something for every possible Z
+ 
+
+ align:start position:0%
+to show something for every possible Z
+so for every possible I for every
+
+ align:start position:0%
+so for every possible I for every
+ 
+
+ align:start position:0%
+so for every possible I for every
+possible Z I'm going to put in the PCP a
+
+ align:start position:0%
+possible Z I'm going to put in the PCP a
+ 
+
+ align:start position:0%
+possible Z I'm going to put in the PCP a
+sum check a sum check so I'm going to
+
+ align:start position:0%
+sum check a sum check so I'm going to
+ 
+
+ align:start position:0%
+sum check a sum check so I'm going to
+give a a su check I'm going to add kind
+
+ align:start position:0%
+give a a su check I'm going to add kind
+ 
+
+ align:start position:0%
+give a a su check I'm going to add kind
+of all the possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcript for some check corresponding
+
+ align:start position:0%
+transcript for some check corresponding
+ 
+
+ align:start position:0%
+transcript for some check corresponding
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+VI which VI
+
+ align:start position:0%
+VI which VI
+ 
+
+ align:start position:0%
+VI which VI
+Z or maybe to v i equals VI till the Z
+
+ align:start position:0%
+Z or maybe to v i equals VI till the Z
+ 
+
+ align:start position:0%
+Z or maybe to v i equals VI till the Z
+so for every I and Z I'm going to give a
+
+ align:start position:0%
+so for every I and Z I'm going to give a
+ 
+
+ align:start position:0%
+so for every I and Z I'm going to give a
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+check with respect
+
+ align:start position:0%
+check with respect
+ 
+
+ align:start position:0%
+check with respect
+to Randomness R from the from the
+
+ align:start position:0%
+to Randomness R from the from the
+ 
+
+ align:start position:0%
+to Randomness R from the from the
+verifier so for every I for every Z and
+
+ align:start position:0%
+verifier so for every I for every Z and
+ 
+
+ align:start position:0%
+verifier so for every I for every Z and
+for any Randomness R of the verifier now
+
+ align:start position:0%
+for any Randomness R of the verifier now
+ 
+
+ align:start position:0%
+for any Randomness R of the verifier now
+what is how much Randomness that the
+
+ align:start position:0%
+what is how much Randomness that the
+ 
+
+ align:start position:0%
+what is how much Randomness that the
+verifier use in a sum check protocol so
+
+ align:start position:0%
+verifier use in a sum check protocol so
+ 
+
+ align:start position:0%
+verifier use in a sum check protocol so
+remember the sum check is sum over H to
+
+ align:start position:0%
+remember the sum check is sum over H to
+ 
+
+ align:start position:0%
+remember the sum check is sum over H to
+the 3M kind of variables okay sum over p
+
+ align:start position:0%
+the 3M kind of variables okay sum over p
+ 
+
+ align:start position:0%
+the 3M kind of variables okay sum over p
+p W1 W2 all of them in h to the m so the
+
+ align:start position:0%
+p W1 W2 all of them in h to the m so the
+ 
+
+ align:start position:0%
+p W1 W2 all of them in h to the m so the
+r is going to be for every R in F to the
+
+ align:start position:0%
+r is going to be for every R in F to the
+ 
+
+ align:start position:0%
+r is going to be for every R in F to the
+3M because in the subject protocol what
+
+ align:start position:0%
+3M because in the subject protocol what
+ 
+
+ align:start position:0%
+3M because in the subject protocol what
+you do is every single H you every
+
+ align:start position:0%
+you do is every single H you every
+ 
+
+ align:start position:0%
+you do is every single H you every
+single kind of uh you have three M
+
+ align:start position:0%
+single kind of uh you have three M
+ 
+
+ align:start position:0%
+single kind of uh you have three M
+variables every one you give a random
+
+ align:start position:0%
+variables every one you give a random
+ 
+
+ align:start position:0%
+variables every one you give a random
+field element to kind of reduce get rid
+
+ align:start position:0%
+field element to kind of reduce get rid
+ 
+
+ align:start position:0%
+field element to kind of reduce get rid
+of one of the sums so the verifier will
+
+ align:start position:0%
+of one of the sums so the verifier will
+ 
+
+ align:start position:0%
+of one of the sums so the verifier will
+use will choose kind of R1 up to
+
+ align:start position:0%
+use will choose kind of R1 up to
+ 
+
+ align:start position:0%
+use will choose kind of R1 up to
+r3m so 3M field
+
+ align:start position:0%
+r3m so 3M field
+ 
+
+ align:start position:0%
+r3m so 3M field
+elements so for every Poss for for every
+
+ align:start position:0%
+elements so for every Poss for for every
+ 
+
+ align:start position:0%
+elements so for every Poss for for every
+hour I'm going to actually give you the
+
+ align:start position:0%
+hour I'm going to actually give you the
+ 
+
+ align:start position:0%
+hour I'm going to actually give you the
+transcript so now I know I'm going to
+
+ align:start position:0%
+transcript so now I know I'm going to
+ 
+
+ align:start position:0%
+transcript so now I know I'm going to
+give you the entire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcript okay but here's the thing I
+
+ align:start position:0%
+transcript okay but here's the thing I
+ 
+
+ align:start position:0%
+transcript okay but here's the thing I
+so I'm gonna have a su check for for all
+
+ align:start position:0%
+so I'm gonna have a su check for for all
+ 
+
+ align:start position:0%
+so I'm gonna have a su check for for all
+of them and now the verifier okay but we
+
+ align:start position:0%
+of them and now the verifier okay but we
+ 
+
+ align:start position:0%
+of them and now the verifier okay but we
+need to be careful we don't just give
+
+ align:start position:0%
+need to be careful we don't just give
+ 
+
+ align:start position:0%
+need to be careful we don't just give
+for every R subject if I knew R I would
+
+ align:start position:0%
+for every R subject if I knew R I would
+ 
+
+ align:start position:0%
+for every R subject if I knew R I would
+cheat so what I what what I mean here is
+
+ align:start position:0%
+cheat so what I what what I mean here is
+ 
+
+ align:start position:0%
+cheat so what I what what I mean here is
+for every Su check for every Z
+
+ align:start position:0%
+for every Su check for every Z
+ 
+
+ align:start position:0%
+for every Su check for every Z
+VI for every our so so uh for every
+
+ align:start position:0%
+VI for every our so so uh for every
+ 
+
+ align:start position:0%
+VI for every our so so uh for every
+R1 I'm going to give all the outputs for
+
+ align:start position:0%
+R1 I'm going to give all the outputs for
+ 
+
+ align:start position:0%
+R1 I'm going to give all the outputs for
+R1 like all the kind of answers of the
+
+ align:start position:0%
+R1 like all the kind of answers of the
+ 
+
+ align:start position:0%
+R1 like all the kind of answers of the
+Su check for R1 then for each one of
+
+ align:start position:0%
+Su check for R1 then for each one of
+ 
+
+ align:start position:0%
+Su check for R1 then for each one of
+them for every R2 I have all the
+
+ align:start position:0%
+them for every R2 I have all the
+ 
+
+ align:start position:0%
+them for every R2 I have all the
+possible answers so no competition you
+
+ align:start position:0%
+possible answers so no competition you
+ 
+
+ align:start position:0%
+possible answers so no competition you
+can't have two different element you
+
+ align:start position:0%
+can't have two different element you
+ 
+
+ align:start position:0%
+can't have two different element you
+can't have one value if you had R1 R2
+
+ align:start position:0%
+can't have one value if you had R1 R2
+ 
+
+ align:start position:0%
+can't have one value if you had R1 R2
+but later different RS or R1 R2 it for
+
+ align:start position:0%
+but later different RS or R1 R2 it for
+ 
+
+ align:start position:0%
+but later different RS or R1 R2 it for
+every for every possible partial
+
+ align:start position:0%
+every for every possible partial
+ 
+
+ align:start position:0%
+every for every possible partial
+transcript you give a value that's what
+
+ align:start position:0%
+transcript you give a value that's what
+ 
+
+ align:start position:0%
+transcript you give a value that's what
+the PCP has in it okay so for every so
+
+ align:start position:0%
+the PCP has in it okay so for every so
+ 
+
+ align:start position:0%
+the PCP has in it okay so for every so
+yeah I should say yeah so for every eye
+
+ align:start position:0%
+yeah I should say yeah so for every eye
+ 
+
+ align:start position:0%
+yeah I should say yeah so for every eye
+for every Z and for every maybe I should
+
+ align:start position:0%
+for every Z and for every maybe I should
+ 
+
+ align:start position:0%
+for every Z and for every maybe I should
+write it
+
+ align:start position:0%
+write it
+ 
+
+ align:start position:0%
+write it
+as R1 up to
+
+ align:start position:0%
+as R1 up to
+ 
+
+ align:start position:0%
+as R1 up to
+r3m I have a
+
+ align:start position:0%
+r3m I have a
+ 
+
+ align:start position:0%
+r3m I have a
+transcript all the part I I should have
+
+ align:start position:0%
+transcript all the part I I should have
+ 
+
+ align:start position:0%
+transcript all the part I I should have
+all all
+
+ align:start position:0%
+all all
+ 
+
+ align:start position:0%
+all all
+partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcripts of sum
+
+ align:start position:0%
+transcripts of sum
+ 
+
+ align:start position:0%
+transcripts of sum
+check with with respect to VI IAL v
+
+ align:start position:0%
+check with with respect to VI IAL v
+ 
+
+ align:start position:0%
+check with with respect to VI IAL v
+z and
+
+ align:start position:0%
+z and
+ 
+
+ align:start position:0%
+z and
+Randomness no R1 up to RJ for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J okay between uh I don't know
+
+ align:start position:0%
+J okay between uh I don't know
+ 
+
+ align:start position:0%
+J okay between uh I don't know
+one and 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m okay so for every for every for every
+
+ align:start position:0%
+m okay so for every for every for every
+ 
+
+ align:start position:0%
+m okay so for every for every for every
+I for every R1 I will say what would be
+
+ align:start position:0%
+I for every R1 I will say what would be
+ 
+
+ align:start position:0%
+I for every R1 I will say what would be
+my answer so now I have F to the m
+
+ align:start position:0%
+my answer so now I have F to the m
+ 
+
+ align:start position:0%
+my answer so now I have F to the m
+answers for every one of these answers
+
+ align:start position:0%
+answers for every one of these answers
+ 
+
+ align:start position:0%
+answers for every one of these answers
+for every R2 I'm going to tell you what
+
+ align:start position:0%
+for every R2 I'm going to tell you what
+ 
+
+ align:start position:0%
+for every R2 I'm going to tell you what
+is the answer for
+
+ align:start position:0%
+is the answer for
+ 
+
+ align:start position:0%
+is the answer for
+every sorry I I said I said it wrong for
+
+ align:start position:0%
+every sorry I I said I said it wrong for
+ 
+
+ align:start position:0%
+every sorry I I said I said it wrong for
+every R1 I would give all the answer I
+
+ align:start position:0%
+every R1 I would give all the answer I
+ 
+
+ align:start position:0%
+every R1 I would give all the answer I
+have F each one each one is one field so
+
+ align:start position:0%
+have F each one each one is one field so
+ 
+
+ align:start position:0%
+have F each one each one is one field so
+for every R1 I'll tell you the answer
+
+ align:start position:0%
+for every R1 I'll tell you the answer
+ 
+
+ align:start position:0%
+for every R1 I'll tell you the answer
+that's F options because there are F
+
+ align:start position:0%
+that's F options because there are F
+ 
+
+ align:start position:0%
+that's F options because there are F
+options for R1 and then out of these f
+
+ align:start position:0%
+options for R1 and then out of these f
+ 
+
+ align:start position:0%
+options for R1 and then out of these f
+for each of these FS for every R2 I'm
+
+ align:start position:0%
+for each of these FS for every R2 I'm
+ 
+
+ align:start position:0%
+for each of these FS for every R2 I'm
+going to give you what the prover will
+
+ align:start position:0%
+going to give you what the prover will
+ 
+
+ align:start position:0%
+going to give you what the prover will
+send that F that's f squ and then for
+
+ align:start position:0%
+send that F that's f squ and then for
+ 
+
+ align:start position:0%
+send that F that's f squ and then for
+each of these I'm going to give you R3
+
+ align:start position:0%
+each of these I'm going to give you R3
+ 
+
+ align:start position:0%
+each of these I'm going to give you R3
+so really what this PCP for every VI for
+
+ align:start position:0%
+so really what this PCP for every VI for
+ 
+
+ align:start position:0%
+so really what this PCP for every VI for
+every such VI or for every kind of v i
+
+ align:start position:0%
+every such VI or for every kind of v i
+ 
+
+ align:start position:0%
+every such VI or for every kind of v i
+z for every possible R1 I'm going to
+
+ align:start position:0%
+z for every possible R1 I'm going to
+ 
+
+ align:start position:0%
+z for every possible R1 I'm going to
+give you this is over R1 I'm going to
+
+ align:start position:0%
+give you this is over R1 I'm going to
+ 
+
+ align:start position:0%
+give you this is over R1 I'm going to
+give you the possible answers in the sum
+
+ align:start position:0%
+give you the possible answers in the sum
+ 
+
+ align:start position:0%
+give you the possible answers in the sum
+check protocol like if the pro in the Su
+
+ align:start position:0%
+check protocol like if the pro in the Su
+ 
+
+ align:start position:0%
+check protocol like if the pro in the Su
+if the verer in the sum check protocol
+
+ align:start position:0%
+if the verer in the sum check protocol
+ 
+
+ align:start position:0%
+if the verer in the sum check protocol
+the first Randomness was this R1 this R1
+
+ align:start position:0%
+the first Randomness was this R1 this R1
+ 
+
+ align:start position:0%
+the first Randomness was this R1 this R1
+this R1 I'm going to write all of these
+
+ align:start position:0%
+this R1 I'm going to write all of these
+ 
+
+ align:start position:0%
+this R1 I'm going to write all of these
+in the PCP and then for each R1 and
+
+ align:start position:0%
+in the PCP and then for each R1 and
+ 
+
+ align:start position:0%
+in the PCP and then for each R1 and
+every possible R2 I'm going to write my
+
+ align:start position:0%
+every possible R2 I'm going to write my
+ 
+
+ align:start position:0%
+every possible R2 I'm going to write my
+answers and then for each R1 R2 for
+
+ align:start position:0%
+answers and then for each R1 R2 for
+ 
+
+ align:start position:0%
+answers and then for each R1 R2 for
+every possible R3 I'm going to write my
+
+ align:start position:0%
+every possible R3 I'm going to write my
+ 
+
+ align:start position:0%
+every possible R3 I'm going to write my
+answers it seems like an exponential
+
+ align:start position:0%
+answers it seems like an exponential
+ 
+
+ align:start position:0%
+answers it seems like an exponential
+tree and it is an exponential tree but
+
+ align:start position:0%
+tree and it is an exponential tree but
+ 
+
+ align:start position:0%
+tree and it is an exponential tree but
+that the depth is so small so this is a
+
+ align:start position:0%
+that the depth is so small so this is a
+ 
+
+ align:start position:0%
+that the depth is so small so this is a
+huge tree but this tree is only of size
+
+ align:start position:0%
+huge tree but this tree is only of size
+ 
+
+ align:start position:0%
+huge tree but this tree is only of size
+F to the m or to the 3M
+
+ align:start position:0%
+F to the m or to the 3M
+ 
+
+ align:start position:0%
+F to the m or to the 3M
+sorry which is polinomial it's it's uh s
+
+ align:start position:0%
+sorry which is polinomial it's it's uh s
+ 
+
+ align:start position:0%
+sorry which is polinomial it's it's uh s
+to the 3 and you're right that you know
+
+ align:start position:0%
+to the 3 and you're right that you know
+ 
+
+ align:start position:0%
+to the 3 and you're right that you know
+this is not good enough for practice but
+
+ align:start position:0%
+this is not good enough for practice but
+ 
+
+ align:start position:0%
+this is not good enough for practice but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then there's a lot of optimizations on
+
+ align:start position:0%
+then there's a lot of optimizations on
+ 
+
+ align:start position:0%
+then there's a lot of optimizations on
+the gkr that make it quasi linear and
+
+ align:start position:0%
+the gkr that make it quasi linear and
+ 
+
+ align:start position:0%
+the gkr that make it quasi linear and
+today even linear so you can actually
+
+ align:start position:0%
+today even linear so you can actually
+ 
+
+ align:start position:0%
+today even linear so you can actually
+optimize this to get uh you know uh
+
+ align:start position:0%
+optimize this to get uh you know uh
+ 
+
+ align:start position:0%
+optimize this to get uh you know uh
+linear time but uh but or uh but or
+
+ align:start position:0%
+linear time but uh but or uh but or
+ 
+
+ align:start position:0%
+linear time but uh but or uh but or
+quasi linear as a PCP but but for now we
+
+ align:start position:0%
+quasi linear as a PCP but but for now we
+ 
+
+ align:start position:0%
+quasi linear as a PCP but but for now we
+don't care about these a polinomial is
+
+ align:start position:0%
+don't care about these a polinomial is
+ 
+
+ align:start position:0%
+don't care about these a polinomial is
+good enough for
+
+ align:start position:0%
+good enough for
+ 
+
+ align:start position:0%
+good enough for
+us okay so for every I and for every Z
+
+ align:start position:0%
+us okay so for every I and for every Z
+ 
+
+ align:start position:0%
+us okay so for every I and for every Z
+we give this
+
+ align:start position:0%
+we give this
+ 
+
+ align:start position:0%
+we give this
+tree that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PTP that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good good good good good fantastic
+
+ align:start position:0%
+yeah good good good good good fantastic
+ 
+
+ align:start position:0%
+yeah good good good good good fantastic
+you're like wait that's a problem do we
+
+ align:start position:0%
+you're like wait that's a problem do we
+ 
+
+ align:start position:0%
+you're like wait that's a problem do we
+if I require F to be small do we even
+
+ align:start position:0%
+if I require F to be small do we even
+ 
+
+ align:start position:0%
+if I require F to be small do we even
+get soundness that's a great question so
+
+ align:start position:0%
+get soundness that's a great question so
+ 
+
+ align:start position:0%
+get soundness that's a great question so
+the answer is barely but yes so let's
+
+ align:start position:0%
+the answer is barely but yes so let's
+ 
+
+ align:start position:0%
+the answer is barely but yes so let's
+see what's the okay what is the
+
+ align:start position:0%
+see what's the okay what is the
+ 
+
+ align:start position:0%
+see what's the okay what is the
+soundness that we get for to be sound
+
+ align:start position:0%
+soundness that we get for to be sound
+ 
+
+ align:start position:0%
+soundness that we get for to be sound
+each Su check so the the okay so let's
+
+ align:start position:0%
+each Su check so the the okay so let's
+ 
+
+ align:start position:0%
+each Su check so the the okay so let's
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+soundness maybe I'll put it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here let's talk about soundness here for
+
+ align:start position:0%
+here let's talk about soundness here for
+ 
+
+ align:start position:0%
+here let's talk about soundness here for
+a second because you rais a very but you
+
+ align:start position:0%
+a second because you rais a very but you
+ 
+
+ align:start position:0%
+a second because you rais a very but you
+know what actually before we talk about
+
+ align:start position:0%
+know what actually before we talk about
+ 
+
+ align:start position:0%
+know what actually before we talk about
+soundness I I'll jump to soundness you
+
+ align:start position:0%
+soundness I I'll jump to soundness you
+ 
+
+ align:start position:0%
+soundness I I'll jump to soundness you
+have a very good point I'll we'll talk
+
+ align:start position:0%
+have a very good point I'll we'll talk
+ 
+
+ align:start position:0%
+have a very good point I'll we'll talk
+about soundness but just to make sure
+
+ align:start position:0%
+about soundness but just to make sure
+ 
+
+ align:start position:0%
+about soundness but just to make sure
+the construction is clear okay so let me
+
+ align:start position:0%
+the construction is clear okay so let me
+ 
+
+ align:start position:0%
+the construction is clear okay so let me
+just reiterate one last time I'm a PCP
+
+ align:start position:0%
+just reiterate one last time I'm a PCP
+ 
+
+ align:start position:0%
+just reiterate one last time I'm a PCP
+prover I want to convince you guys that
+
+ align:start position:0%
+prover I want to convince you guys that
+ 
+
+ align:start position:0%
+prover I want to convince you guys that
+I have a satisfying assignment to a
+
+ align:start position:0%
+I have a satisfying assignment to a
+ 
+
+ align:start position:0%
+I have a satisfying assignment to a
+threat formula I have my w what I do I
+
+ align:start position:0%
+threat formula I have my w what I do I
+ 
+
+ align:start position:0%
+threat formula I have my w what I do I
+construct low deegree extension of my w
+
+ align:start position:0%
+construct low deegree extension of my w
+ 
+
+ align:start position:0%
+construct low deegree extension of my w
+my witness but also I have this entire
+
+ align:start position:0%
+my witness but also I have this entire
+ 
+
+ align:start position:0%
+my witness but also I have this entire
+circuit that verifies this witness and
+
+ align:start position:0%
+circuit that verifies this witness and
+ 
+
+ align:start position:0%
+circuit that verifies this witness and
+I'm going to construct a low degree
+
+ align:start position:0%
+I'm going to construct a low degree
+ 
+
+ align:start position:0%
+I'm going to construct a low degree
+extension of each and every layer in
+
+ align:start position:0%
+extension of each and every layer in
+ 
+
+ align:start position:0%
+extension of each and every layer in
+this circuit now the way I wrote it
+
+ align:start position:0%
+this circuit now the way I wrote it
+ 
+
+ align:start position:0%
+this circuit now the way I wrote it
+actually I will construct a low degree
+
+ align:start position:0%
+actually I will construct a low degree
+ 
+
+ align:start position:0%
+actually I will construct a low degree
+extension of X and W that's kind of if I
+
+ align:start position:0%
+extension of X and W that's kind of if I
+ 
+
+ align:start position:0%
+extension of X and W that's kind of if I
+think of the input as X and W I need the
+
+ align:start position:0%
+think of the input as X and W I need the
+ 
+
+ align:start position:0%
+think of the input as X and W I need the
+constru L degree extension of both but
+
+ align:start position:0%
+constru L degree extension of both but
+ 
+
+ align:start position:0%
+constru L degree extension of both but
+you the verifying Knows X so if I
+
+ align:start position:0%
+you the verifying Knows X so if I
+ 
+
+ align:start position:0%
+you the verifying Knows X so if I
+construct a low degree extension of w he
+
+ align:start position:0%
+construct a low degree extension of w he
+ 
+
+ align:start position:0%
+construct a low degree extension of w he
+himself can construct a low extension of
+
+ align:start position:0%
+himself can construct a low extension of
+ 
+
+ align:start position:0%
+himself can construct a low extension of
+X and W together so in the PCP because I
+
+ align:start position:0%
+X and W together so in the PCP because I
+ 
+
+ align:start position:0%
+X and W together so in the PCP because I
+don't want to in the PCP I don't want to
+
+ align:start position:0%
+don't want to in the PCP I don't want to
+ 
+
+ align:start position:0%
+don't want to in the PCP I don't want to
+put X in there the verifier has X and if
+
+ align:start position:0%
+put X in there the verifier has X and if
+ 
+
+ align:start position:0%
+put X in there the verifier has X and if
+I have the freedom to put X in there and
+
+ align:start position:0%
+I have the freedom to put X in there and
+ 
+
+ align:start position:0%
+I have the freedom to put X in there and
+you don't read it then I can put the
+
+ align:start position:0%
+you don't read it then I can put the
+ 
+
+ align:start position:0%
+you don't read it then I can put the
+wrong X so I'm just going to put
+
+ align:start position:0%
+wrong X so I'm just going to put
+ 
+
+ align:start position:0%
+wrong X so I'm just going to put
+v0 is just going to
+
+ align:start position:0%
+v0 is just going to
+ 
+
+ align:start position:0%
+v0 is just going to
+be of the witness I'm going to think of
+
+ align:start position:0%
+be of the witness I'm going to think of
+ 
+
+ align:start position:0%
+be of the witness I'm going to think of
+X as fixed so I'm just going to
+
+ align:start position:0%
+X as fixed so I'm just going to
+ 
+
+ align:start position:0%
+X as fixed so I'm just going to
+construct the loading extension of W and
+
+ align:start position:0%
+construct the loading extension of W and
+ 
+
+ align:start position:0%
+construct the loading extension of W and
+then I'm going to construct the low
+
+ align:start position:0%
+then I'm going to construct the low
+ 
+
+ align:start position:0%
+then I'm going to construct the low
+degree extension of each and every layer
+
+ align:start position:0%
+degree extension of each and every layer
+ 
+
+ align:start position:0%
+degree extension of each and every layer
+of the of the
+
+ align:start position:0%
+of the of the
+ 
+
+ align:start position:0%
+of the of the
+circuit and I'm going to go for every
+
+ align:start position:0%
+circuit and I'm going to go for every
+ 
+
+ align:start position:0%
+circuit and I'm going to go for every
+layer and for every Z I'm going to
+
+ align:start position:0%
+layer and for every Z I'm going to
+ 
+
+ align:start position:0%
+layer and for every Z I'm going to
+construct all the
+
+ align:start position:0%
+construct all the
+ 
+
+ align:start position:0%
+construct all the
+possible Pro messages in the Su protocol
+
+ align:start position:0%
+possible Pro messages in the Su protocol
+ 
+
+ align:start position:0%
+possible Pro messages in the Su protocol
+now because the randomness the options
+
+ align:start position:0%
+now because the randomness the options
+ 
+
+ align:start position:0%
+now because the randomness the options
+for the for the uh the number of
+
+ align:start position:0%
+for the for the uh the number of
+ 
+
+ align:start position:0%
+for the for the uh the number of
+possible random bits for the from the
+
+ align:start position:0%
+possible random bits for the from the
+ 
+
+ align:start position:0%
+possible random bits for the from the
+verifier is only F to the 3M because
+
+ align:start position:0%
+verifier is only F to the 3M because
+ 
+
+ align:start position:0%
+verifier is only F to the 3M because
+there's 3M
+
+ align:start position:0%
+there's 3M
+ 
+
+ align:start position:0%
+there's 3M
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a variables and F is the field so it's
+
+ align:start position:0%
+a variables and F is the field so it's
+ 
+
+ align:start position:0%
+a variables and F is the field so it's
+only F to the
+
+ align:start position:0%
+only F to the
+ 
+
+ align:start position:0%
+only F to the
+3M then this tree is only going to be of
+
+ align:start position:0%
+3M then this tree is only going to be of
+ 
+
+ align:start position:0%
+3M then this tree is only going to be of
+size after the 3M so it's not too
+
+ align:start position:0%
+size after the 3M so it's not too
+ 
+
+ align:start position:0%
+size after the 3M so it's not too
+bad and I put all of them I put all the
+
+ align:start position:0%
+bad and I put all of them I put all the
+ 
+
+ align:start position:0%
+bad and I put all of them I put all the
+possible Su checks in there so sorry
+
+ align:start position:0%
+possible Su checks in there so sorry
+ 
+
+ align:start position:0%
+possible Su checks in there so sorry
+it's F to the 3M for every I have this
+
+ align:start position:0%
+it's F to the 3M for every I have this
+ 
+
+ align:start position:0%
+it's F to the 3M for every I have this
+size for every I and for every Z okay so
+
+ align:start position:0%
+size for every I and for every Z okay so
+ 
+
+ align:start position:0%
+size for every I and for every Z okay so
+for every I I is only D this is small
+
+ align:start position:0%
+for every I I is only D this is small
+ 
+
+ align:start position:0%
+for every I I is only D this is small
+and Z is another F to them I pay fine so
+
+ align:start position:0%
+and Z is another F to them I pay fine so
+ 
+
+ align:start position:0%
+and Z is another F to them I pay fine so
+after to the
+
+ align:start position:0%
+after to the
+ 
+
+ align:start position:0%
+after to the
+4M okay so for every Z and for every I I
+
+ align:start position:0%
+4M okay so for every Z and for every I I
+ 
+
+ align:start position:0%
+4M okay so for every Z and for every I I
+have the sum
+
+ align:start position:0%
+have the sum
+ 
+
+ align:start position:0%
+have the sum
+check now what the what is so that's
+
+ align:start position:0%
+check now what the what is so that's
+ 
+
+ align:start position:0%
+check now what the what is so that's
+that's the PCP but now what's what does
+
+ align:start position:0%
+that's the PCP but now what's what does
+ 
+
+ align:start position:0%
+that's the PCP but now what's what does
+the verifier do what does v I need to
+
+ align:start position:0%
+the verifier do what does v I need to
+ 
+
+ align:start position:0%
+the verifier do what does v I need to
+Define I told you how to construct this
+
+ align:start position:0%
+Define I told you how to construct this
+ 
+
+ align:start position:0%
+Define I told you how to construct this
+Pi efficiently and it's uh but what does
+
+ align:start position:0%
+Pi efficiently and it's uh but what does
+ 
+
+ align:start position:0%
+Pi efficiently and it's uh but what does
+v do so what does what V
+
+ align:start position:0%
+v do so what does what V
+ 
+
+ align:start position:0%
+v do so what does what V
+does he says I'm going to pretend that
+
+ align:start position:0%
+does he says I'm going to pretend that
+ 
+
+ align:start position:0%
+does he says I'm going to pretend that
+I'm I'm interacting with the gkr prover
+
+ align:start position:0%
+I'm I'm interacting with the gkr prover
+ 
+
+ align:start position:0%
+I'm I'm interacting with the gkr prover
+so he says look what is out he's going
+
+ align:start position:0%
+so he says look what is out he's going
+ 
+
+ align:start position:0%
+so he says look what is out he's going
+to read the output
+
+ align:start position:0%
+to read the output
+ 
+
+ align:start position:0%
+to read the output
+VD and he's going to expect a one if he
+
+ align:start position:0%
+VD and he's going to expect a one if he
+ 
+
+ align:start position:0%
+VD and he's going to expect a one if he
+sees a zero so that's one query I'm
+
+ align:start position:0%
+sees a zero so that's one query I'm
+ 
+
+ align:start position:0%
+sees a zero so that's one query I'm
+going to read the output is it's one
+
+ align:start position:0%
+going to read the output is it's one
+ 
+
+ align:start position:0%
+going to read the output is it's one
+good I'm happy okay now he's going to go
+
+ align:start position:0%
+good I'm happy okay now he's going to go
+ 
+
+ align:start position:0%
+good I'm happy okay now he's going to go
+from verifying D to verifying D minus
+
+ align:start position:0%
+from verifying D to verifying D minus
+ 
+
+ align:start position:0%
+from verifying D to verifying D minus
+one D minus 2 D minus 3 now he he wants
+
+ align:start position:0%
+one D minus 2 D minus 3 now he he wants
+ 
+
+ align:start position:0%
+one D minus 2 D minus 3 now he he wants
+to talk to aover he said okay here's my
+
+ align:start position:0%
+to talk to aover he said okay here's my
+ 
+
+ align:start position:0%
+to talk to aover he said okay here's my
+Randomness my first message in the sum
+
+ align:start position:0%
+Randomness my first message in the sum
+ 
+
+ align:start position:0%
+Randomness my first message in the sum
+check give me back something okay he
+
+ align:start position:0%
+check give me back something okay he
+ 
+
+ align:start position:0%
+check give me back something okay he
+this is the approver the Prov is fixed
+
+ align:start position:0%
+this is the approver the Prov is fixed
+ 
+
+ align:start position:0%
+this is the approver the Prov is fixed
+in the PCP okay so he gets back an
+
+ align:start position:0%
+in the PCP okay so he gets back an
+ 
+
+ align:start position:0%
+in the PCP okay so he gets back an
+answer good now here these at the end
+
+ align:start position:0%
+answer good now here these at the end
+ 
+
+ align:start position:0%
+answer good now here these at the end
+this defines V IUS one Z this this
+
+ align:start position:0%
+this defines V IUS one Z this this
+ 
+
+ align:start position:0%
+this defines V IUS one Z this this
+should be all kind of uh elements in V
+
+ align:start position:0%
+should be all kind of uh elements in V
+ 
+
+ align:start position:0%
+should be all kind of uh elements in V
+minus one Z now actually here what you
+
+ align:start position:0%
+minus one Z now actually here what you
+ 
+
+ align:start position:0%
+minus one Z now actually here what you
+have here is at the end of the gkr
+
+ align:start position:0%
+have here is at the end of the gkr
+ 
+
+ align:start position:0%
+have here is at the end of the gkr
+protocol you're left with two two two V
+
+ align:start position:0%
+protocol you're left with two two two V
+ 
+
+ align:start position:0%
+protocol you're left with two two two V
+two v's right so if you verify here
+
+ align:start position:0%
+two v's right so if you verify here
+ 
+
+ align:start position:0%
+two v's right so if you verify here
+you'll have like at the end you'll have
+
+ align:start position:0%
+you'll have like at the end you'll have
+ 
+
+ align:start position:0%
+you'll have like at the end you'll have
+like V I don't know zero and v z z0 and
+
+ align:start position:0%
+like V I don't know zero and v z z0 and
+ 
+
+ align:start position:0%
+like V I don't know zero and v z z0 and
+Z1 you know you'll verify you need to
+
+ align:start position:0%
+Z1 you know you'll verify you need to
+ 
+
+ align:start position:0%
+Z1 you know you'll verify you need to
+verify two points because we did two
+
+ align:start position:0%
+verify two points because we did two
+ 
+
+ align:start position:0%
+verify two points because we did two
+something called ways so fine he sees
+
+ align:start position:0%
+something called ways so fine he sees
+ 
+
+ align:start position:0%
+something called ways so fine he sees
+these two he checks there's these he
+
+ align:start position:0%
+these two he checks there's these he
+ 
+
+ align:start position:0%
+these two he checks there's these he
+checks that they're equal this is only
+
+ align:start position:0%
+checks that they're equal this is only
+ 
+
+ align:start position:0%
+checks that they're equal this is only
+one okay so we're giving him all the low
+
+ align:start position:0%
+one okay so we're giving him all the low
+ 
+
+ align:start position:0%
+one okay so we're giving him all the low
+degree extension of VI minus one he
+
+ align:start position:0%
+degree extension of VI minus one he
+ 
+
+ align:start position:0%
+degree extension of VI minus one he
+checks oh yeah this is corresponds this
+
+ align:start position:0%
+checks oh yeah this is corresponds this
+ 
+
+ align:start position:0%
+checks oh yeah this is corresponds this
+corresponds this is just to ensure that
+
+ align:start position:0%
+corresponds this is just to ensure that
+ 
+
+ align:start position:0%
+corresponds this is just to ensure that
+he doesn't put different ones in
+
+ align:start position:0%
+he doesn't put different ones in
+ 
+
+ align:start position:0%
+he doesn't put different ones in
+different you know here he may uh you
+
+ align:start position:0%
+different you know here he may uh you
+ 
+
+ align:start position:0%
+different you know here he may uh you
+know and in this Branch he may put the
+
+ align:start position:0%
+know and in this Branch he may put the
+ 
+
+ align:start position:0%
+know and in this Branch he may put the
+value of z0 to be something and in this
+
+ align:start position:0%
+value of z0 to be something and in this
+ 
+
+ align:start position:0%
+value of z0 to be something and in this
+Branch you may put the value of z0 to be
+
+ align:start position:0%
+Branch you may put the value of z0 to be
+ 
+
+ align:start position:0%
+Branch you may put the value of z0 to be
+something else that's
+
+ align:start position:0%
+something else that's
+ 
+
+ align:start position:0%
+something else that's
+that's not not good for us so we just
+
+ align:start position:0%
+that's not not good for us so we just
+ 
+
+ align:start position:0%
+that's not not good for us so we just
+check because he put aside all the low
+
+ align:start position:0%
+check because he put aside all the low
+ 
+
+ align:start position:0%
+check because he put aside all the low
+degree extensions so we check that it's
+
+ align:start position:0%
+degree extensions so we check that it's
+ 
+
+ align:start position:0%
+degree extensions so we check that it's
+equal to what he gave us and we continue
+
+ align:start position:0%
+equal to what he gave us and we continue
+ 
+
+ align:start position:0%
+equal to what he gave us and we continue
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um one second actually I'm not sure
+
+ align:start position:0%
+um one second actually I'm not sure
+ 
+
+ align:start position:0%
+um one second actually I'm not sure
+maybe what I said is incorrect I'm not
+
+ align:start position:0%
+maybe what I said is incorrect I'm not
+ 
+
+ align:start position:0%
+maybe what I said is incorrect I'm not
+actually sure that this is a problem
+
+ align:start position:0%
+actually sure that this is a problem
+ 
+
+ align:start position:0%
+actually sure that this is a problem
+even if he gives us different let me
+
+ align:start position:0%
+even if he gives us different let me
+ 
+
+ align:start position:0%
+even if he gives us different let me
+think about it for a
+
+ align:start position:0%
+think about it for a
+ 
+
+ align:start position:0%
+think about it for a
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a yeah actually I'm not even sure that
+
+ align:start position:0%
+a yeah actually I'm not even sure that
+ 
+
+ align:start position:0%
+a yeah actually I'm not even sure that
+we need we can just put the Su checks
+
+ align:start position:0%
+we need we can just put the Su checks
+ 
+
+ align:start position:0%
+we need we can just put the Su checks
+even if he gives us even if he gives
+
+ align:start position:0%
+even if he gives us even if he gives
+ 
+
+ align:start position:0%
+even if he gives us even if he gives
+us a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay yeah I want to say even if he
+
+ align:start position:0%
+no okay yeah I want to say even if he
+ 
+
+ align:start position:0%
+no okay yeah I want to say even if he
+gives us in this branch and this Branch
+
+ align:start position:0%
+gives us in this branch and this Branch
+ 
+
+ align:start position:0%
+gives us in this branch and this Branch
+different things uh why do we care it's
+
+ align:start position:0%
+different things uh why do we care it's
+ 
+
+ align:start position:0%
+different things uh why do we care it's
+like we run the sum check the sum check
+
+ align:start position:0%
+like we run the sum check the sum check
+ 
+
+ align:start position:0%
+like we run the sum check the sum check
+is sound but we we do care a little bit
+
+ align:start position:0%
+is sound but we we do care a little bit
+ 
+
+ align:start position:0%
+is sound but we we do care a little bit
+because then in the next
+
+ align:start position:0%
+because then in the next
+ 
+
+ align:start position:0%
+because then in the next
+round
+
+ align:start position:0%
+round
+ 
+
+ align:start position:0%
+round
+which let me think you know what I'm not
+
+ align:start position:0%
+which let me think you know what I'm not
+ 
+
+ align:start position:0%
+which let me think you know what I'm not
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+what lay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theand exactly you you let all the verif
+
+ align:start position:0%
+theand exactly you you let all the verif
+ 
+
+ align:start position:0%
+theand exactly you you let all the verif
+so yeah so I don't think actually you
+
+ align:start position:0%
+so yeah so I don't think actually you
+ 
+
+ align:start position:0%
+so yeah so I don't think actually you
+need to give these specific you can just
+
+ align:start position:0%
+need to give these specific you can just
+ 
+
+ align:start position:0%
+need to give these specific you can just
+give give for every VI Tilda you give
+
+ align:start position:0%
+give give for every VI Tilda you give
+ 
+
+ align:start position:0%
+give give for every VI Tilda you give
+but it's the same because you give for
+
+ align:start position:0%
+but it's the same because you give for
+ 
+
+ align:start position:0%
+but it's the same because you give for
+every VI Tilda so actually I think these
+
+ align:start position:0%
+every VI Tilda so actually I think these
+ 
+
+ align:start position:0%
+every VI Tilda so actually I think these
+two are the same so I okay what I I
+
+ align:start position:0%
+two are the same so I okay what I I
+ 
+
+ align:start position:0%
+two are the same so I okay what I I
+guess what I said is uh you know these
+
+ align:start position:0%
+guess what I said is uh you know these
+ 
+
+ align:start position:0%
+guess what I said is uh you know these
+can be maybe V uh VI minus one of z0
+
+ align:start position:0%
+can be maybe V uh VI minus one of z0
+ 
+
+ align:start position:0%
+can be maybe V uh VI minus one of z0
+appears here and it appears here and
+
+ align:start position:0%
+appears here and it appears here and
+ 
+
+ align:start position:0%
+appears here and it appears here and
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+different are we worried we're not
+
+ align:start position:0%
+different are we worried we're not
+ 
+
+ align:start position:0%
+different are we worried we're not
+really worried because it's like you
+
+ align:start position:0%
+really worried because it's like you
+ 
+
+ align:start position:0%
+really worried because it's like you
+think of it it interacts with the prover
+
+ align:start position:0%
+think of it it interacts with the prover
+ 
+
+ align:start position:0%
+think of it it interacts with the prover
+the prover the cheating prover may give
+
+ align:start position:0%
+the prover the cheating prover may give
+ 
+
+ align:start position:0%
+the prover the cheating prover may give
+him different Z here and different Z
+
+ align:start position:0%
+him different Z here and different Z
+ 
+
+ align:start position:0%
+him different Z here and different Z
+here but later the point is later you'll
+
+ align:start position:0%
+here but later the point is later you'll
+ 
+
+ align:start position:0%
+here but later the point is later you'll
+have in VI minus one you'll just
+
+ align:start position:0%
+have in VI minus one you'll just
+ 
+
+ align:start position:0%
+have in VI minus one you'll just
+continue so actually you just need to
+
+ align:start position:0%
+continue so actually you just need to
+ 
+
+ align:start position:0%
+continue so actually you just need to
+give but but but really I think the two
+
+ align:start position:0%
+give but but but really I think the two
+ 
+
+ align:start position:0%
+give but but but really I think the two
+are equivalent so it doesn't really
+
+ align:start position:0%
+are equivalent so it doesn't really
+ 
+
+ align:start position:0%
+are equivalent so it doesn't really
+matter a okay so this is the pp and
+
+ align:start position:0%
+matter a okay so this is the pp and
+ 
+
+ align:start position:0%
+matter a okay so this is the pp and
+that's how you verify and at the end at
+
+ align:start position:0%
+that's how you verify and at the end at
+ 
+
+ align:start position:0%
+that's how you verify and at the end at
+the end of the end of the gkr the
+
+ align:start position:0%
+the end of the end of the gkr the
+ 
+
+ align:start position:0%
+the end of the end of the gkr the
+verifier needs to read the input he
+
+ align:start position:0%
+verifier needs to read the input he
+ 
+
+ align:start position:0%
+verifier needs to read the input he
+needs to check the input and some load
+
+ align:start position:0%
+needs to check the input and some load
+ 
+
+ align:start position:0%
+needs to check the input and some load
+in some locations he doesn't have the
+
+ align:start position:0%
+in some locations he doesn't have the
+ 
+
+ align:start position:0%
+in some locations he doesn't have the
+input but he does because we gave him
+
+ align:start position:0%
+input but he does because we gave him
+ 
+
+ align:start position:0%
+input but he does because we gave him
+the low degree extension of w so once he
+
+ align:start position:0%
+the low degree extension of w so once he
+ 
+
+ align:start position:0%
+the low degree extension of w so once he
+has the low degree extension of w he can
+
+ align:start position:0%
+has the low degree extension of w he can
+ 
+
+ align:start position:0%
+has the low degree extension of w he can
+compute anything uh he so the verifier
+
+ align:start position:0%
+compute anything uh he so the verifier
+ 
+
+ align:start position:0%
+compute anything uh he so the verifier
+needs to
+
+ align:start position:0%
+needs to
+ 
+
+ align:start position:0%
+needs to
+compute a low degree extension of X in W
+
+ align:start position:0%
+compute a low degree extension of X in W
+ 
+
+ align:start position:0%
+compute a low degree extension of X in W
+but any point in the low degree
+
+ align:start position:0%
+but any point in the low degree
+ 
+
+ align:start position:0%
+but any point in the low degree
+extension of X and W is a point in the
+
+ align:start position:0%
+extension of X and W is a point in the
+ 
+
+ align:start position:0%
+extension of X and W is a point in the
+low degree EXT is a sum of points in the
+
+ align:start position:0%
+low degree EXT is a sum of points in the
+ 
+
+ align:start position:0%
+low degree EXT is a sum of points in the
+low degree extension of X and point in
+
+ align:start position:0%
+low degree extension of X and point in
+ 
+
+ align:start position:0%
+low degree extension of X and point in
+the Lo extension of w so every every
+
+ align:start position:0%
+the Lo extension of w so every every
+ 
+
+ align:start position:0%
+the Lo extension of w so every every
+point in the low degree extension of X
+
+ align:start position:0%
+point in the low degree extension of X
+ 
+
+ align:start position:0%
+point in the low degree extension of X
+and W you can write as a weighted sum of
+
+ align:start position:0%
+and W you can write as a weighted sum of
+ 
+
+ align:start position:0%
+and W you can write as a weighted sum of
+a point in the lowre low degree
+
+ align:start position:0%
+a point in the lowre low degree
+ 
+
+ align:start position:0%
+a point in the lowre low degree
+extension of X and a point in the Lo
+
+ align:start position:0%
+extension of X and a point in the Lo
+ 
+
+ align:start position:0%
+extension of X and a point in the Lo
+extension of w so you know once he needs
+
+ align:start position:0%
+extension of w so you know once he needs
+ 
+
+ align:start position:0%
+extension of w so you know once he needs
+to read the point in the Lo extension of
+
+ align:start position:0%
+to read the point in the Lo extension of
+ 
+
+ align:start position:0%
+to read the point in the Lo extension of
+w he has it here so that's all that's
+
+ align:start position:0%
+w he has it here so that's all that's
+ 
+
+ align:start position:0%
+w he has it here so that's all that's
+all the verifier does so he really he's
+
+ align:start position:0%
+all the verifier does so he really he's
+ 
+
+ align:start position:0%
+all the verifier does so he really he's
+it's interesting this PCP he as if he's
+
+ align:start position:0%
+it's interesting this PCP he as if he's
+ 
+
+ align:start position:0%
+it's interesting this PCP he as if he's
+talking to the prover but the prover is
+
+ align:start position:0%
+talking to the prover but the prover is
+ 
+
+ align:start position:0%
+talking to the prover but the prover is
+sitting in the sky in the
+
+ align:start position:0%
+sitting in the sky in the
+ 
+
+ align:start position:0%
+sitting in the sky in the
+PCP the pro strategy just kind of opened
+
+ align:start position:0%
+PCP the pro strategy just kind of opened
+ 
+
+ align:start position:0%
+PCP the pro strategy just kind of opened
+up in in the
+
+ align:start position:0%
+up in in the
+ 
+
+ align:start position:0%
+up in in the
+Oracle okay okay great so now any
+
+ align:start position:0%
+Oracle okay okay great so now any
+ 
+
+ align:start position:0%
+Oracle okay okay great so now any
+questions before we talk about
+
+ align:start position:0%
+questions before we talk about
+ 
+
+ align:start position:0%
+questions before we talk about
+soundness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so right so uh okay good good good
+
+ align:start position:0%
+yeah so right so uh okay good good good
+ 
+
+ align:start position:0%
+yeah so right so uh okay good good good
+good good question the verify great
+
+ align:start position:0%
+good good question the verify great
+ 
+
+ align:start position:0%
+good good question the verify great
+question the verifier needs to check
+
+ align:start position:0%
+question the verifier needs to check
+ 
+
+ align:start position:0%
+question the verifier needs to check
+also that all these things are actually
+
+ align:start position:0%
+also that all these things are actually
+ 
+
+ align:start position:0%
+also that all these things are actually
+low deegree extension okay so what if I
+
+ align:start position:0%
+low deegree extension okay so what if I
+ 
+
+ align:start position:0%
+low deegree extension okay so what if I
+I I said here oh put um you put VI Tilda
+
+ align:start position:0%
+I I said here oh put um you put VI Tilda
+ 
+
+ align:start position:0%
+I I said here oh put um you put VI Tilda
+Z how do I know that you actually put a
+
+ align:start position:0%
+Z how do I know that you actually put a
+ 
+
+ align:start position:0%
+Z how do I know that you actually put a
+low degree extension maybe you put a
+
+ align:start position:0%
+low degree extension maybe you put a
+ 
+
+ align:start position:0%
+low degree extension maybe you put a
+very high degree polinomial there maybe
+
+ align:start position:0%
+very high degree polinomial there maybe
+ 
+
+ align:start position:0%
+very high degree polinomial there maybe
+you just put an arbitrary truth table of
+
+ align:start position:0%
+you just put an arbitrary truth table of
+ 
+
+ align:start position:0%
+you just put an arbitrary truth table of
+size after
+
+ align:start position:0%
+size after
+ 
+
+ align:start position:0%
+size after
+them that would be
+
+ align:start position:0%
+them that would be
+ 
+
+ align:start position:0%
+them that would be
+problematic so you're totally right the
+
+ align:start position:0%
+problematic so you're totally right the
+ 
+
+ align:start position:0%
+problematic so you're totally right the
+verifier so let let me write what the
+
+ align:start position:0%
+verifier so let let me write what the
+ 
+
+ align:start position:0%
+verifier so let let me write what the
+verifier does uh maybe before the sound
+
+ align:start position:0%
+verifier does uh maybe before the sound
+ 
+
+ align:start position:0%
+verifier does uh maybe before the sound
+is yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me actually write it okay so the
+
+ align:start position:0%
+so let me actually write it okay so the
+ 
+
+ align:start position:0%
+so let me actually write it okay so the
+verifier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay he
+
+ align:start position:0%
+okay he
+ 
+
+ align:start position:0%
+okay he
+runs first thing he does he runs V of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gkr with its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oracle okay so he runs the just the gkr
+
+ align:start position:0%
+Oracle okay so he runs the just the gkr
+ 
+
+ align:start position:0%
+Oracle okay so he runs the just the gkr
+but he thinks of kind of the Oracle part
+
+ align:start position:0%
+but he thinks of kind of the Oracle part
+ 
+
+ align:start position:0%
+but he thinks of kind of the Oracle part
+as kind of the the prover he's talking
+
+ align:start position:0%
+as kind of the the prover he's talking
+ 
+
+ align:start position:0%
+as kind of the the prover he's talking
+with and the other thing he needs needs
+
+ align:start position:0%
+with and the other thing he needs needs
+ 
+
+ align:start position:0%
+with and the other thing he needs needs
+to do is he needs to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check that for every
+
+ align:start position:0%
+check that for every
+ 
+
+ align:start position:0%
+check that for every
+I VI
+
+ align:start position:0%
+I VI
+ 
+
+ align:start position:0%
+I VI
+Tilda is of low degree is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah what you're saying is that if
+
+ align:start position:0%
+um yeah what you're saying is that if
+ 
+
+ align:start position:0%
+um yeah what you're saying is that if
+you're right so what you're saying is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what you're saying is if he comp If
+
+ align:start position:0%
+okay what you're saying is if he comp If
+ 
+
+ align:start position:0%
+okay what you're saying is if he comp If
+he if he gave VI Tilda that was high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree then you're saying that GK would
+
+ align:start position:0%
+degree then you're saying that GK would
+ 
+
+ align:start position:0%
+degree then you're saying that GK would
+fail you you would be rejected by the GK
+
+ align:start position:0%
+fail you you would be rejected by the GK
+ 
+
+ align:start position:0%
+fail you you would be rejected by the GK
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+bewi it should be rejected by the GK a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think you may be right but actually
+
+ align:start position:0%
+I think you may be right but actually
+ 
+
+ align:start position:0%
+I think you may be right but actually
+I'm not 100% sure now
+
+ align:start position:0%
+I'm not 100% sure now
+ 
+
+ align:start position:0%
+I'm not 100% sure now
+uh yeah that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ISE yeah so here's here's the concern
+
+ align:start position:0%
+ISE yeah so here's here's the concern
+ 
+
+ align:start position:0%
+ISE yeah so here's here's the concern
+here's the concern the concern is we
+
+ align:start position:0%
+here's the concern the concern is we
+ 
+
+ align:start position:0%
+here's the concern the concern is we
+want to make sure that the
+
+ align:start position:0%
+want to make sure that the
+ 
+
+ align:start position:0%
+want to make sure that the
+verifier is uh
+
+ align:start position:0%
+verifier is uh
+ 
+
+ align:start position:0%
+verifier is uh
+behaving like that we want to okay we
+
+ align:start position:0%
+behaving like that we want to okay we
+ 
+
+ align:start position:0%
+behaving like that we want to okay we
+want to make sure that this VI Tilda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is of low
+
+ align:start position:0%
+is of low
+ 
+
+ align:start position:0%
+is of low
+degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why sorry one second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah actually I I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't think we need to check that via
+
+ align:start position:0%
+I don't think we need to check that via
+ 
+
+ align:start position:0%
+I don't think we need to check that via
+is a low degree because I I agree that
+
+ align:start position:0%
+is a low degree because I I agree that
+ 
+
+ align:start position:0%
+is a low degree because I I agree that
+we need to check that VI is a low degree
+
+ align:start position:0%
+we need to check that VI is a low degree
+ 
+
+ align:start position:0%
+we need to check that VI is a low degree
+but I think gkr checks that the vi till
+
+ align:start position:0%
+but I think gkr checks that the vi till
+ 
+
+ align:start position:0%
+but I think gkr checks that the vi till
+there's a low degree so I actually don't
+
+ align:start position:0%
+there's a low degree so I actually don't
+ 
+
+ align:start position:0%
+there's a low degree so I actually don't
+want to recheck it so all I want to do
+
+ align:start position:0%
+want to recheck it so all I want to do
+ 
+
+ align:start position:0%
+want to recheck it so all I want to do
+here I think GK test tests it for you so
+
+ align:start position:0%
+here I think GK test tests it for you so
+ 
+
+ align:start position:0%
+here I think GK test tests it for you so
+we're convinced that the gkr is sound
+
+ align:start position:0%
+we're convinced that the gkr is sound
+ 
+
+ align:start position:0%
+we're convinced that the gkr is sound
+let's not recall why it sound but let's
+
+ align:start position:0%
+let's not recall why it sound but let's
+ 
+
+ align:start position:0%
+let's not recall why it sound but let's
+remember we we learned that it sound so
+
+ align:start position:0%
+remember we we learned that it sound so
+ 
+
+ align:start position:0%
+remember we we learned that it sound so
+GK is good now what are we doing I
+
+ align:start position:0%
+GK is good now what are we doing I
+ 
+
+ align:start position:0%
+GK is good now what are we doing I
+essentially what we're saying is
+
+ align:start position:0%
+essentially what we're saying is
+ 
+
+ align:start position:0%
+essentially what we're saying is
+verifier I'm giving you all the possible
+
+ align:start position:0%
+verifier I'm giving you all the possible
+ 
+
+ align:start position:0%
+verifier I'm giving you all the possible
+answers of I'm what is the prover the
+
+ align:start position:0%
+answers of I'm what is the prover the
+ 
+
+ align:start position:0%
+answers of I'm what is the prover the
+prover is a tree you can think what is a
+
+ align:start position:0%
+prover is a tree you can think what is a
+ 
+
+ align:start position:0%
+prover is a tree you can think what is a
+cheating prover a cheating prover for
+
+ align:start position:0%
+cheating prover a cheating prover for
+ 
+
+ align:start position:0%
+cheating prover a cheating prover for
+every possible you know for every
+
+ align:start position:0%
+every possible you know for every
+ 
+
+ align:start position:0%
+every possible you know for every
+possible question he gives you an answer
+
+ align:start position:0%
+possible question he gives you an answer
+ 
+
+ align:start position:0%
+possible question he gives you an answer
+for every question he gives you an
+
+ align:start position:0%
+for every question he gives you an
+ 
+
+ align:start position:0%
+for every question he gives you an
+answer that's what it does so now you're
+
+ align:start position:0%
+answer that's what it does so now you're
+ 
+
+ align:start position:0%
+answer that's what it does so now you're
+saying look I'm going to give you the
+
+ align:start position:0%
+saying look I'm going to give you the
+ 
+
+ align:start position:0%
+saying look I'm going to give you the
+tree now in general this tree is really
+
+ align:start position:0%
+tree now in general this tree is really
+ 
+
+ align:start position:0%
+tree now in general this tree is really
+really big and even in gkr if you give
+
+ align:start position:0%
+really big and even in gkr if you give
+ 
+
+ align:start position:0%
+really big and even in gkr if you give
+the entire if you just open like GK has
+
+ align:start position:0%
+the entire if you just open like GK has
+ 
+
+ align:start position:0%
+the entire if you just open like GK has
+D rounds D rounds of su Che if you just
+
+ align:start position:0%
+D rounds D rounds of su Che if you just
+ 
+
+ align:start position:0%
+D rounds D rounds of su Che if you just
+open the S Che it will be terrible
+
+ align:start position:0%
+open the S Che it will be terrible
+ 
+
+ align:start position:0%
+open the S Che it will be terrible
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+a gkr has this property that it's kind
+
+ align:start position:0%
+a gkr has this property that it's kind
+ 
+
+ align:start position:0%
+a gkr has this property that it's kind
+of memory lless what do I mean by memory
+
+ align:start position:0%
+of memory lless what do I mean by memory
+ 
+
+ align:start position:0%
+of memory lless what do I mean by memory
+list you can compute the first Su check
+
+ align:start position:0%
+list you can compute the first Su check
+ 
+
+ align:start position:0%
+list you can compute the first Su check
+then you don't care what happened before
+
+ align:start position:0%
+then you don't care what happened before
+ 
+
+ align:start position:0%
+then you don't care what happened before
+all you care is what is VI minus one
+
+ align:start position:0%
+all you care is what is VI minus one
+ 
+
+ align:start position:0%
+all you care is what is VI minus one
+that you cut and you check
+
+ align:start position:0%
+that you cut and you check
+ 
+
+ align:start position:0%
+that you cut and you check
+those so now I'm saying so you know
+
+ align:start position:0%
+those so now I'm saying so you know
+ 
+
+ align:start position:0%
+those so now I'm saying so you know
+actually for let's think about this
+
+ align:start position:0%
+actually for let's think about this
+ 
+
+ align:start position:0%
+actually for let's think about this
+first of all we can say open gkr to a
+
+ align:start position:0%
+first of all we can say open gkr to a
+ 
+
+ align:start position:0%
+first of all we can say open gkr to a
+huge tree okay any pro this is true in
+
+ align:start position:0%
+huge tree okay any pro this is true in
+ 
+
+ align:start position:0%
+huge tree okay any pro this is true in
+in general if you had any interactive
+
+ align:start position:0%
+in general if you had any interactive
+ 
+
+ align:start position:0%
+in general if you had any interactive
+proof you can think of a pro write all
+
+ align:start position:0%
+proof you can think of a pro write all
+ 
+
+ align:start position:0%
+proof you can think of a pro write all
+the possible answers like think of its
+
+ align:start position:0%
+the possible answers like think of its
+ 
+
+ align:start position:0%
+the possible answers like think of its
+kind of H strategy as a huge huge tree
+
+ align:start position:0%
+kind of H strategy as a huge huge tree
+ 
+
+ align:start position:0%
+kind of H strategy as a huge huge tree
+right the tree now of course you get
+
+ align:start position:0%
+right the tree now of course you get
+ 
+
+ align:start position:0%
+right the tree now of course you get
+sound this you interact with the
+
+ align:start position:0%
+sound this you interact with the
+ 
+
+ align:start position:0%
+sound this you interact with the
+approver what's the difference okay you
+
+ align:start position:0%
+approver what's the difference okay you
+ 
+
+ align:start position:0%
+approver what's the difference okay you
+can do that with G but of course if you
+
+ align:start position:0%
+can do that with G but of course if you
+ 
+
+ align:start position:0%
+can do that with G but of course if you
+do this huge tree it's going to be
+
+ align:start position:0%
+do this huge tree it's going to be
+ 
+
+ align:start position:0%
+do this huge tree it's going to be
+gigantic because GK consists of d kind
+
+ align:start position:0%
+gigantic because GK consists of d kind
+ 
+
+ align:start position:0%
+gigantic because GK consists of d kind
+of um
+
+ align:start position:0%
+of um
+ 
+
+ align:start position:0%
+of um
+a uh subprotocols each one is a su check
+
+ align:start position:0%
+a uh subprotocols each one is a su check
+ 
+
+ align:start position:0%
+a uh subprotocols each one is a su check
+so now if you think of like a D Cab then
+
+ align:start position:0%
+so now if you think of like a D Cab then
+ 
+
+ align:start position:0%
+so now if you think of like a D Cab then
+you'll be too big but I'm saying we
+
+ align:start position:0%
+you'll be too big but I'm saying we
+ 
+
+ align:start position:0%
+you'll be too big but I'm saying we
+don't need to because gkr has a property
+
+ align:start position:0%
+don't need to because gkr has a property
+ 
+
+ align:start position:0%
+don't need to because gkr has a property
+that actually it consist of this
+
+ align:start position:0%
+that actually it consist of this
+ 
+
+ align:start position:0%
+that actually it consist of this
+subprotocol and then all you need to
+
+ align:start position:0%
+subprotocol and then all you need to
+ 
+
+ align:start position:0%
+subprotocol and then all you need to
+remember you don't need to remember
+
+ align:start position:0%
+remember you don't need to remember
+ 
+
+ align:start position:0%
+remember you don't need to remember
+which branch you're on here all you need
+
+ align:start position:0%
+which branch you're on here all you need
+ 
+
+ align:start position:0%
+which branch you're on here all you need
+to remember is what are the values here
+
+ align:start position:0%
+to remember is what are the values here
+ 
+
+ align:start position:0%
+to remember is what are the values here
+that's all you need to
+
+ align:start position:0%
+that's all you need to
+ 
+
+ align:start position:0%
+that's all you need to
+remember so there's no point in
+
+ align:start position:0%
+remember so there's no point in
+ 
+
+ align:start position:0%
+remember so there's no point in
+repeating it's like you're repeating the
+
+ align:start position:0%
+repeating it's like you're repeating the
+ 
+
+ align:start position:0%
+repeating it's like you're repeating the
+tree for no reason so all you need
+
+ align:start position:0%
+tree for no reason so all you need
+ 
+
+ align:start position:0%
+tree for no reason so all you need
+there's a way to open kind of this Pro
+
+ align:start position:0%
+there's a way to open kind of this Pro
+ 
+
+ align:start position:0%
+there's a way to open kind of this Pro
+in a more efficient
+
+ align:start position:0%
+in a more efficient
+ 
+
+ align:start position:0%
+in a more efficient
+way so by not giving the entire tree and
+
+ align:start position:0%
+way so by not giving the entire tree and
+ 
+
+ align:start position:0%
+way so by not giving the entire tree and
+giving kind of a more efficient kind of
+
+ align:start position:0%
+giving kind of a more efficient kind of
+ 
+
+ align:start position:0%
+giving kind of a more efficient kind of
+opening where all the vi Z all the vi
+
+ align:start position:0%
+opening where all the vi Z all the vi
+ 
+
+ align:start position:0%
+opening where all the vi Z all the vi
+IUS one Z I'm going to say okay forget
+
+ align:start position:0%
+IUS one Z I'm going to say okay forget
+ 
+
+ align:start position:0%
+IUS one Z I'm going to say okay forget
+about it let's just go from VI minus one
+
+ align:start position:0%
+about it let's just go from VI minus one
+ 
+
+ align:start position:0%
+about it let's just go from VI minus one
+Z and continue why do you need to repeat
+
+ align:start position:0%
+Z and continue why do you need to repeat
+ 
+
+ align:start position:0%
+Z and continue why do you need to repeat
+this kind of tree a 100 times it's it's
+
+ align:start position:0%
+this kind of tree a 100 times it's it's
+ 
+
+ align:start position:0%
+this kind of tree a 100 times it's it's
+but it's you can go go from here to kind
+
+ align:start position:0%
+but it's you can go go from here to kind
+ 
+
+ align:start position:0%
+but it's you can go go from here to kind
+of simulating an entire GK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approver yeah if I understand correctly
+
+ align:start position:0%
+approver yeah if I understand correctly
+ 
+
+ align:start position:0%
+approver yeah if I understand correctly
+you're saying like actually the tree of
+
+ align:start position:0%
+you're saying like actually the tree of
+ 
+
+ align:start position:0%
+you're saying like actually the tree of
+gkr is such that most of the parts cof
+
+ align:start position:0%
+gkr is such that most of the parts cof
+ 
+
+ align:start position:0%
+gkr is such that most of the parts cof
+right and so you don't need to repeat
+
+ align:start position:0%
+right and so you don't need to repeat
+ 
+
+ align:start position:0%
+right and so you don't need to repeat
+the copies you can just look it up
+
+ align:start position:0%
+the copies you can just look it up
+ 
+
+ align:start position:0%
+the copies you can just look it up
+exactly exactly
+
+ align:start position:0%
+exactly exactly
+ 
+
+ align:start position:0%
+exactly exactly
+exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly actually in some sense we're
+
+ align:start position:0%
+exactly actually in some sense we're
+ 
+
+ align:start position:0%
+exactly actually in some sense we're
+restricting the prover here more than
+
+ align:start position:0%
+restricting the prover here more than
+ 
+
+ align:start position:0%
+restricting the prover here more than
+he's restricted in
+
+ align:start position:0%
+he's restricted in
+ 
+
+ align:start position:0%
+he's restricted in
+gkr exactly because in gkr he can be you
+
+ align:start position:0%
+gkr exactly because in gkr he can be you
+ 
+
+ align:start position:0%
+gkr exactly because in gkr he can be you
+know what I'm going to remember the RS
+
+ align:start position:0%
+know what I'm going to remember the RS
+ 
+
+ align:start position:0%
+know what I'm going to remember the RS
+if he's cheating and based on the RS I'm
+
+ align:start position:0%
+if he's cheating and based on the RS I'm
+ 
+
+ align:start position:0%
+if he's cheating and based on the RS I'm
+going to give you a different strategy
+
+ align:start position:0%
+going to give you a different strategy
+ 
+
+ align:start position:0%
+going to give you a different strategy
+whatever here we're not even letting him
+
+ align:start position:0%
+whatever here we're not even letting him
+ 
+
+ align:start position:0%
+whatever here we're not even letting him
+do that we're telling look you tell me
+
+ align:start position:0%
+do that we're telling look you tell me
+ 
+
+ align:start position:0%
+do that we're telling look you tell me
+what you are here from here now you
+
+ align:start position:0%
+what you are here from here now you
+ 
+
+ align:start position:0%
+what you are here from here now you
+forget Ours from VI minus one what's
+
+ align:start position:0%
+forget Ours from VI minus one what's
+ 
+
+ align:start position:0%
+forget Ours from VI minus one what's
+your strategy and now you forget from
+
+ align:start position:0%
+your strategy and now you forget from
+ 
+
+ align:start position:0%
+your strategy and now you forget from
+here what is your
+
+ align:start position:0%
+here what is your
+ 
+
+ align:start position:0%
+here what is your
+strategy so we're really just doing gkr
+
+ align:start position:0%
+strategy so we're really just doing gkr
+ 
+
+ align:start position:0%
+strategy so we're really just doing gkr
+now you're right at the vi minus one do
+
+ align:start position:0%
+now you're right at the vi minus one do
+ 
+
+ align:start position:0%
+now you're right at the vi minus one do
+till they do need to be of low degree
+
+ align:start position:0%
+till they do need to be of low degree
+ 
+
+ align:start position:0%
+till they do need to be of low degree
+but do the Gare test this for you so you
+
+ align:start position:0%
+but do the Gare test this for you so you
+ 
+
+ align:start position:0%
+but do the Gare test this for you so you
+don't need to do it on your
+
+ align:start position:0%
+don't need to do it on your
+ 
+
+ align:start position:0%
+don't need to do it on your
+own but you're right it's confusing a
+
+ align:start position:0%
+own but you're right it's confusing a
+ 
+
+ align:start position:0%
+own but you're right it's confusing a
+little bit because if you if any if
+
+ align:start position:0%
+little bit because if you if any if
+ 
+
+ align:start position:0%
+little bit because if you if any if
+anyone is familiar with the PCP
+
+ align:start position:0%
+anyone is familiar with the PCP
+ 
+
+ align:start position:0%
+anyone is familiar with the PCP
+literature there's always a low deegree
+
+ align:start position:0%
+literature there's always a low deegree
+ 
+
+ align:start position:0%
+literature there's always a low deegree
+test in it so it's kind of interesting
+
+ align:start position:0%
+test in it so it's kind of interesting
+ 
+
+ align:start position:0%
+test in it so it's kind of interesting
+this this kind of is hidden with within
+
+ align:start position:0%
+this this kind of is hidden with within
+ 
+
+ align:start position:0%
+this this kind of is hidden with within
+the Gare
+
+ align:start position:0%
+the Gare
+ 
+
+ align:start position:0%
+the Gare
+protocol this kind of transformation not
+
+ align:start position:0%
+protocol this kind of transformation not
+ 
+
+ align:start position:0%
+protocol this kind of transformation not
+only as as there is efficient way to
+
+ align:start position:0%
+only as as there is efficient way to
+ 
+
+ align:start position:0%
+only as as there is efficient way to
+change the into a sequence that the know
+
+ align:start position:0%
+change the into a sequence that the know
+ 
+
+ align:start position:0%
+change the into a sequence that the know
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+to exactly exactly so yeah this this
+
+ align:start position:0%
+to exactly exactly so yeah this this
+ 
+
+ align:start position:0%
+to exactly exactly so yeah this this
+proof holds it's not specific to gkr
+
+ align:start position:0%
+proof holds it's not specific to gkr
+ 
+
+ align:start position:0%
+proof holds it's not specific to gkr
+it's kind of you can take any sixing
+
+ align:start position:0%
+it's kind of you can take any sixing
+ 
+
+ align:start position:0%
+it's kind of you can take any sixing
+protocol and and interactive protocol
+
+ align:start position:0%
+protocol and and interactive protocol
+ 
+
+ align:start position:0%
+protocol and and interactive protocol
+and lay it open however let me just
+
+ align:start position:0%
+and lay it open however let me just
+ 
+
+ align:start position:0%
+and lay it open however let me just
+mention we have very few actually kind
+
+ align:start position:0%
+mention we have very few actually kind
+ 
+
+ align:start position:0%
+mention we have very few actually kind
+of two examples of suing protocols so it
+
+ align:start position:0%
+of two examples of suing protocols so it
+ 
+
+ align:start position:0%
+of two examples of suing protocols so it
+sound like you can take any of your
+
+ align:start position:0%
+sound like you can take any of your
+ 
+
+ align:start position:0%
+sound like you can take any of your
+choice yeah any but we don't have much
+
+ align:start position:0%
+choice yeah any but we don't have much
+ 
+
+ align:start position:0%
+choice yeah any but we don't have much
+choice so uh you know a coming up with
+
+ align:start position:0%
+choice so uh you know a coming up with
+ 
+
+ align:start position:0%
+choice so uh you know a coming up with
+these succinct interactive proofs is a
+
+ align:start position:0%
+these succinct interactive proofs is a
+ 
+
+ align:start position:0%
+these succinct interactive proofs is a
+super interesting question I'll I'll
+
+ align:start position:0%
+super interesting question I'll I'll
+ 
+
+ align:start position:0%
+super interesting question I'll I'll
+talk a little bit more about this after
+
+ align:start position:0%
+talk a little bit more about this after
+ 
+
+ align:start position:0%
+talk a little bit more about this after
+we do the analysis of the
+
+ align:start position:0%
+we do the analysis of the
+ 
+
+ align:start position:0%
+we do the analysis of the
+PCB okay so great
+
+ align:start position:0%
+PCB okay so great
+ 
+
+ align:start position:0%
+PCB okay so great
+uh any questions before we move to
+
+ align:start position:0%
+uh any questions before we move to
+ 
+
+ align:start position:0%
+uh any questions before we move to
+soundness okay so let's talk about
+
+ align:start position:0%
+soundness okay so let's talk about
+ 
+
+ align:start position:0%
+soundness okay so let's talk about
+soundness and the question that was
+
+ align:start position:0%
+soundness and the question that was
+ 
+
+ align:start position:0%
+soundness and the question that was
+raised which was a great question is
+
+ align:start position:0%
+raised which was a great question is
+ 
+
+ align:start position:0%
+raised which was a great question is
+Wait f needs to be big to get soundness
+
+ align:start position:0%
+Wait f needs to be big to get soundness
+ 
+
+ align:start position:0%
+Wait f needs to be big to get soundness
+so let's really understand what the size
+
+ align:start position:0%
+so let's really understand what the size
+ 
+
+ align:start position:0%
+so let's really understand what the size
+of f needs to be so to get soundness we
+
+ align:start position:0%
+of f needs to be so to get soundness we
+ 
+
+ align:start position:0%
+of f needs to be so to get soundness we
+do 2D Su check
+
+ align:start position:0%
+do 2D Su check
+ 
+
+ align:start position:0%
+do 2D Su check
+protocols each Su check protocol needs
+
+ align:start position:0%
+protocols each Su check protocol needs
+ 
+
+ align:start position:0%
+protocols each Su check protocol needs
+to be pretty sound because it's enough
+
+ align:start position:0%
+to be pretty sound because it's enough
+ 
+
+ align:start position:0%
+to be pretty sound because it's enough
+that you cheat on one of them and we're
+
+ align:start position:0%
+that you cheat on one of them and we're
+ 
+
+ align:start position:0%
+that you cheat on one of them and we're
+dead right
+
+ align:start position:0%
+dead right
+ 
+
+ align:start position:0%
+dead right
+so now each Su Che protocol this is this
+
+ align:start position:0%
+so now each Su Che protocol this is this
+ 
+
+ align:start position:0%
+so now each Su Che protocol this is this
+is just
+
+ align:start position:0%
+is just
+ 
+
+ align:start position:0%
+is just
+recall that
+
+ align:start position:0%
+recall that
+ 
+
+ align:start position:0%
+recall that
+each Su check
+
+ align:start position:0%
+each Su check
+ 
+
+ align:start position:0%
+each Su check
+protocol has sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is which is
+
+ align:start position:0%
+is which is
+ 
+
+ align:start position:0%
+is which is
+H over F times M the number of variables
+
+ align:start position:0%
+H over F times M the number of variables
+ 
+
+ align:start position:0%
+H over F times M the number of variables
+but for us it's 3M because we have 3M
+
+ align:start position:0%
+but for us it's 3M because we have 3M
+ 
+
+ align:start position:0%
+but for us it's 3M because we have 3M
+variables okay this is just the the each
+
+ align:start position:0%
+variables okay this is just the the each
+ 
+
+ align:start position:0%
+variables okay this is just the the each
+subject protocol now for us so you can
+
+ align:start position:0%
+subject protocol now for us so you can
+ 
+
+ align:start position:0%
+subject protocol now for us so you can
+cheat but with this
+
+ align:start position:0%
+cheat but with this
+ 
+
+ align:start position:0%
+cheat but with this
+probability now for us we have 2D D is
+
+ align:start position:0%
+probability now for us we have 2D D is
+ 
+
+ align:start position:0%
+probability now for us we have 2D D is
+poly Logan like the depth of the circuit
+
+ align:start position:0%
+poly Logan like the depth of the circuit
+ 
+
+ align:start position:0%
+poly Logan like the depth of the circuit
+so for us our sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is I'm just doing a union bound so to
+
+ align:start position:0%
+is is I'm just doing a union bound so to
+ 
+
+ align:start position:0%
+is is I'm just doing a union bound so to
+cheat there exist needs to be at least
+
+ align:start position:0%
+cheat there exist needs to be at least
+ 
+
+ align:start position:0%
+cheat there exist needs to be at least
+kind of uh one subject protoc for which
+
+ align:start position:0%
+kind of uh one subject protoc for which
+ 
+
+ align:start position:0%
+kind of uh one subject protoc for which
+you cheated on so you get by Union bound
+
+ align:start position:0%
+you cheated on so you get by Union bound
+ 
+
+ align:start position:0%
+you cheated on so you get by Union bound
+so we have 2D sum checks and then
+
+ align:start position:0%
+so we have 2D sum checks and then
+ 
+
+ align:start position:0%
+so we have 2D sum checks and then
+therefore the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soundness is 2D * 3 m h divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F so now if we want sound this half
+
+ align:start position:0%
+F so now if we want sound this half
+ 
+
+ align:start position:0%
+F so now if we want sound this half
+let's say which is what we want after
+
+ align:start position:0%
+let's say which is what we want after
+ 
+
+ align:start position:0%
+let's say which is what we want after
+that you can repeat to increase the
+
+ align:start position:0%
+that you can repeat to increase the
+ 
+
+ align:start position:0%
+that you can repeat to increase the
+soundness all we need is that F so if we
+
+ align:start position:0%
+soundness all we need is that F so if we
+ 
+
+ align:start position:0%
+soundness all we need is that F so if we
+want this to be smaller than
+
+ align:start position:0%
+want this to be smaller than
+ 
+
+ align:start position:0%
+want this to be smaller than
+half then we need F to be bigger than uh
+
+ align:start position:0%
+half then we need F to be bigger than uh
+ 
+
+ align:start position:0%
+half then we need F to be bigger than uh
+12 D
+
+ align:start position:0%
+12 D
+ 
+
+ align:start position:0%
+12 D
+MH but that's good this is log N I don't
+
+ align:start position:0%
+MH but that's good this is log N I don't
+ 
+
+ align:start position:0%
+MH but that's good this is log N I don't
+know if you guys can see H log s sorry
+
+ align:start position:0%
+know if you guys can see H log s sorry
+ 
+
+ align:start position:0%
+know if you guys can see H log s sorry
+this is smaller than log
+
+ align:start position:0%
+this is smaller than log
+ 
+
+ align:start position:0%
+this is smaller than log
+s this is some poly log s okay so just
+
+ align:start position:0%
+s this is some poly log s okay so just
+ 
+
+ align:start position:0%
+s this is some poly log s okay so just
+make it bigger than all of them it's
+
+ align:start position:0%
+make it bigger than all of them it's
+ 
+
+ align:start position:0%
+make it bigger than all of them it's
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+polylog and polylog S is good enough
+
+ align:start position:0%
+polylog and polylog S is good enough
+ 
+
+ align:start position:0%
+polylog and polylog S is good enough
+because then after them is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polys okay so this was sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is oh oh good why do we need you're
+
+ align:start position:0%
+is oh oh good why do we need you're
+ 
+
+ align:start position:0%
+is oh oh good why do we need you're
+saying why can't it be bigger because
+
+ align:start position:0%
+saying why can't it be bigger because
+ 
+
+ align:start position:0%
+saying why can't it be bigger because
+good because we want our PCP to be of so
+
+ align:start position:0%
+good because we want our PCP to be of so
+ 
+
+ align:start position:0%
+good because we want our PCP to be of so
+the question is just to recap why do we
+
+ align:start position:0%
+the question is just to recap why do we
+ 
+
+ align:start position:0%
+the question is just to recap why do we
+need why do we insist that f is not
+
+ align:start position:0%
+need why do we insist that f is not
+ 
+
+ align:start position:0%
+need why do we insist that f is not
+bigger why does it have to be poom
+
+ align:start position:0%
+bigger why does it have to be poom
+ 
+
+ align:start position:0%
+bigger why does it have to be poom
+related to F and the reason is we want
+
+ align:start position:0%
+related to F and the reason is we want
+ 
+
+ align:start position:0%
+related to F and the reason is we want
+the PCP to beide polys we want the ver
+
+ align:start position:0%
+the PCP to beide polys we want the ver
+ 
+
+ align:start position:0%
+the PCP to beide polys we want the ver
+we want the PCP a to be not we want it
+
+ align:start position:0%
+we want the PCP a to be not we want it
+ 
+
+ align:start position:0%
+we want the PCP a to be not we want it
+to be efficient we want to efficiently
+
+ align:start position:0%
+to be efficient we want to efficiently
+ 
+
+ align:start position:0%
+to be efficient we want to efficiently
+convert a witness to a PCP and the PCP
+
+ align:start position:0%
+convert a witness to a PCP and the PCP
+ 
+
+ align:start position:0%
+convert a witness to a PCP and the PCP
+grows with f to the m much more it's
+
+ align:start position:0%
+grows with f to the m much more it's
+ 
+
+ align:start position:0%
+grows with f to the m much more it's
+like f to the 3M and it needs to be
+
+ align:start position:0%
+like f to the 3M and it needs to be
+ 
+
+ align:start position:0%
+like f to the 3M and it needs to be
+repeated and F to the m is poly so okay
+
+ align:start position:0%
+repeated and F to the m is poly so okay
+ 
+
+ align:start position:0%
+repeated and F to the m is poly so okay
+it's if this is bigger than poly if f is
+
+ align:start position:0%
+it's if this is bigger than poly if f is
+ 
+
+ align:start position:0%
+it's if this is bigger than poly if f is
+more than poly H then F to the m will be
+
+ align:start position:0%
+more than poly H then F to the m will be
+ 
+
+ align:start position:0%
+more than poly H then F to the m will be
+more than poly H to the m so that's why
+
+ align:start position:0%
+more than poly H to the m so that's why
+ 
+
+ align:start position:0%
+more than poly H to the m so that's why
+we want we want it to be it's for the
+
+ align:start position:0%
+we want we want it to be it's for the
+ 
+
+ align:start position:0%
+we want we want it to be it's for the
+sake of efficiency for the for the PCP
+
+ align:start position:0%
+sake of efficiency for the for the PCP
+ 
+
+ align:start position:0%
+sake of efficiency for the for the PCP
+to be small or palomi related to the
+
+ align:start position:0%
+to be small or palomi related to the
+ 
+
+ align:start position:0%
+to be small or palomi related to the
+Circuit um so here you saying that the
+
+ align:start position:0%
+Circuit um so here you saying that the
+ 
+
+ align:start position:0%
+Circuit um so here you saying that the
+randomness complexity is poly now
+
+ align:start position:0%
+randomness complexity is poly now
+ 
+
+ align:start position:0%
+randomness complexity is poly now
+normally you'd be like okay the pro size
+
+ align:start position:0%
+normally you'd be like okay the pro size
+ 
+
+ align:start position:0%
+normally you'd be like okay the pro size
+is just two to the random but You' like
+
+ align:start position:0%
+is just two to the random but You' like
+ 
+
+ align:start position:0%
+is just two to the random but You' like
+more right you found a way to make than
+
+ align:start position:0%
+more right you found a way to make than
+ 
+
+ align:start position:0%
+more right you found a way to make than
+it would be okay good good good so now
+
+ align:start position:0%
+it would be okay good good good so now
+ 
+
+ align:start position:0%
+it would be okay good good good so now
+let's go to the we didn't do the
+
+ align:start position:0%
+let's go to the we didn't do the
+ 
+
+ align:start position:0%
+let's go to the we didn't do the
+complexity yet but yeah you're a bit a
+
+ align:start position:0%
+complexity yet but yeah you're a bit a
+ 
+
+ align:start position:0%
+complexity yet but yeah you're a bit a
+bit ahead of me but you're you're
+
+ align:start position:0%
+bit ahead of me but you're you're
+ 
+
+ align:start position:0%
+bit ahead of me but you're you're
+totally right so now so so far we talked
+
+ align:start position:0%
+totally right so now so so far we talked
+ 
+
+ align:start position:0%
+totally right so now so so far we talked
+about soundness completeness is one
+
+ align:start position:0%
+about soundness completeness is one
+ 
+
+ align:start position:0%
+about soundness completeness is one
+because the G is complete has
+
+ align:start position:0%
+because the G is complete has
+ 
+
+ align:start position:0%
+because the G is complete has
+completeness one so we the Su check has
+
+ align:start position:0%
+completeness one so we the Su check has
+ 
+
+ align:start position:0%
+completeness one so we the Su check has
+completeness one so we're good we talked
+
+ align:start position:0%
+completeness one so we're good we talked
+ 
+
+ align:start position:0%
+completeness one so we're good we talked
+about Su checks any question about
+
+ align:start position:0%
+about Su checks any question about
+ 
+
+ align:start position:0%
+about Su checks any question about
+soundness any question about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soundness okay uh let's talk about the
+
+ align:start position:0%
+soundness okay uh let's talk about the
+ 
+
+ align:start position:0%
+soundness okay uh let's talk about the
+complexity the so uh the randomness
+
+ align:start position:0%
+complexity the so uh the randomness
+ 
+
+ align:start position:0%
+complexity the so uh the randomness
+complexity in the communic in the query
+
+ align:start position:0%
+complexity in the communic in the query
+ 
+
+ align:start position:0%
+complexity in the communic in the query
+complexity so how much query and
+
+ align:start position:0%
+complexity so how much query and
+ 
+
+ align:start position:0%
+complexity so how much query and
+Randomness do we need so the randomness
+
+ align:start position:0%
+Randomness do we need so the randomness
+ 
+
+ align:start position:0%
+Randomness do we need so the randomness
+complexity is well there's 2D a so let's
+
+ align:start position:0%
+complexity is well there's 2D a so let's
+ 
+
+ align:start position:0%
+complexity is well there's 2D a so let's
+put here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Randomness so there's 2D sum check so
+
+ align:start position:0%
+Randomness so there's 2D sum check so
+ 
+
+ align:start position:0%
+Randomness so there's 2D sum check so
+the verifier kind of he interacts with
+
+ align:start position:0%
+the verifier kind of he interacts with
+ 
+
+ align:start position:0%
+the verifier kind of he interacts with
+his Oracle on 2D sum checks so for each
+
+ align:start position:0%
+his Oracle on 2D sum checks so for each
+ 
+
+ align:start position:0%
+his Oracle on 2D sum checks so for each
+2D sum checks he needs to toss coins now
+
+ align:start position:0%
+2D sum checks he needs to toss coins now
+ 
+
+ align:start position:0%
+2D sum checks he needs to toss coins now
+how much coins does he toss well he
+
+ align:start position:0%
+how much coins does he toss well he
+ 
+
+ align:start position:0%
+how much coins does he toss well he
+needs to generate our random in F to the
+
+ align:start position:0%
+needs to generate our random in F to the
+ 
+
+ align:start position:0%
+needs to generate our random in F to the
+3M that's a su each Su check you need so
+
+ align:start position:0%
+3M that's a su each Su check you need so
+ 
+
+ align:start position:0%
+3M that's a su each Su check you need so
+it's F to the it's like 3M log F bits of
+
+ align:start position:0%
+it's F to the it's like 3M log F bits of
+ 
+
+ align:start position:0%
+it's F to the it's like 3M log F bits of
+Randomness now this is really poly log F
+
+ align:start position:0%
+Randomness now this is really poly log F
+ 
+
+ align:start position:0%
+Randomness now this is really poly log F
+it's it's it's uh it's like poly s it's
+
+ align:start position:0%
+it's it's it's uh it's like poly s it's
+ 
+
+ align:start position:0%
+it's it's it's uh it's like poly s it's
+not log s okay this is really poly not
+
+ align:start position:0%
+not log s okay this is really poly not
+ 
+
+ align:start position:0%
+not log s okay this is really poly not
+not poly log s not just logs so one can
+
+ align:start position:0%
+not poly log s not just logs so one can
+ 
+
+ align:start position:0%
+not poly log s not just logs so one can
+be wait we need to be careful because uh
+
+ align:start position:0%
+be wait we need to be careful because uh
+ 
+
+ align:start position:0%
+be wait we need to be careful because uh
+are we sure we're getting an efficient
+
+ align:start position:0%
+are we sure we're getting an efficient
+ 
+
+ align:start position:0%
+are we sure we're getting an efficient
+PCP here it's a lot of Randomness are we
+
+ align:start position:0%
+PCP here it's a lot of Randomness are we
+ 
+
+ align:start position:0%
+PCP here it's a lot of Randomness are we
+sure there's no blow up in PCP and the
+
+ align:start position:0%
+sure there's no blow up in PCP and the
+ 
+
+ align:start position:0%
+sure there's no blow up in PCP and the
+reason there's no blow up the reason we
+
+ align:start position:0%
+reason there's no blow up the reason we
+ 
+
+ align:start position:0%
+reason there's no blow up the reason we
+have large Randomness yet the the PCP is
+
+ align:start position:0%
+have large Randomness yet the the PCP is
+ 
+
+ align:start position:0%
+have large Randomness yet the the PCP is
+small is exactly because GK has this
+
+ align:start position:0%
+small is exactly because GK has this
+ 
+
+ align:start position:0%
+small is exactly because GK has this
+property of forgetting this uh the fact
+
+ align:start position:0%
+property of forgetting this uh the fact
+ 
+
+ align:start position:0%
+property of forgetting this uh the fact
+we actually don't need to open the
+
+ align:start position:0%
+we actually don't need to open the
+ 
+
+ align:start position:0%
+we actually don't need to open the
+entire tree because of that we use kind
+
+ align:start position:0%
+entire tree because of that we use kind
+ 
+
+ align:start position:0%
+entire tree because of that we use kind
+of an additional property if the point
+
+ align:start position:0%
+of an additional property if the point
+ 
+
+ align:start position:0%
+of an additional property if the point
+is if you know nothing about the
+
+ align:start position:0%
+is if you know nothing about the
+ 
+
+ align:start position:0%
+is if you know nothing about the
+PCP then of course as I said if it's
+
+ align:start position:0%
+PCP then of course as I said if it's
+ 
+
+ align:start position:0%
+PCP then of course as I said if it's
+order log as bits of Randomness it's
+
+ align:start position:0%
+order log as bits of Randomness it's
+ 
+
+ align:start position:0%
+order log as bits of Randomness it's
+always the size PS but the fact that
+
+ align:start position:0%
+always the size PS but the fact that
+ 
+
+ align:start position:0%
+always the size PS but the fact that
+there more bits of Randomness does not
+
+ align:start position:0%
+there more bits of Randomness does not
+ 
+
+ align:start position:0%
+there more bits of Randomness does not
+necessarily Force our PCP to be bigger
+
+ align:start position:0%
+necessarily Force our PCP to be bigger
+ 
+
+ align:start position:0%
+necessarily Force our PCP to be bigger
+we're just not going to open it like
+
+ align:start position:0%
+we're just not going to open it like
+ 
+
+ align:start position:0%
+we're just not going to open it like
+trivially like oh if if we did open it
+
+ align:start position:0%
+trivially like oh if if we did open it
+ 
+
+ align:start position:0%
+trivially like oh if if we did open it
+trivially then we would look at all the
+
+ align:start position:0%
+trivially then we would look at all the
+ 
+
+ align:start position:0%
+trivially then we would look at all the
+around it would be a huge tree like the
+
+ align:start position:0%
+around it would be a huge tree like the
+ 
+
+ align:start position:0%
+around it would be a huge tree like the
+depth but because we do it kind of we
+
+ align:start position:0%
+depth but because we do it kind of we
+ 
+
+ align:start position:0%
+depth but because we do it kind of we
+pack it efficiently we're able to get a
+
+ align:start position:0%
+pack it efficiently we're able to get a
+ 
+
+ align:start position:0%
+pack it efficiently we're able to get a
+small PCP even though we have a lot of
+
+ align:start position:0%
+small PCP even though we have a lot of
+ 
+
+ align:start position:0%
+small PCP even though we have a lot of
+Randomness is it because you're saying
+
+ align:start position:0%
+Randomness is it because you're saying
+ 
+
+ align:start position:0%
+Randomness is it because you're saying
+each tree is size poly and po exactly
+
+ align:start position:0%
+each tree is size poly and po exactly
+ 
+
+ align:start position:0%
+each tree is size poly and po exactly
+each tree is size poly and they're poly
+
+ align:start position:0%
+each tree is size poly and they're poly
+ 
+
+ align:start position:0%
+each tree is size poly and they're poly
+trees and we're not like there's a more
+
+ align:start position:0%
+trees and we're not like there's a more
+ 
+
+ align:start position:0%
+trees and we're not like there's a more
+kind of straightforward way to do it is
+
+ align:start position:0%
+kind of straightforward way to do it is
+ 
+
+ align:start position:0%
+kind of straightforward way to do it is
+for each tree a pen a p like in no we're
+
+ align:start position:0%
+for each tree a pen a p like in no we're
+ 
+
+ align:start position:0%
+for each tree a pen a p like in no we're
+we're kind of doing them in chunks uh
+
+ align:start position:0%
+we're kind of doing them in chunks uh
+ 
+
+ align:start position:0%
+we're kind of doing them in chunks uh
+and so we get the the
+
+ align:start position:0%
+and so we get the the
+ 
+
+ align:start position:0%
+and so we get the the
+efficiency okay uh let's go let's go for
+
+ align:start position:0%
+efficiency okay uh let's go let's go for
+ 
+
+ align:start position:0%
+efficiency okay uh let's go let's go for
+the uh query
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complexity okay I'll just put it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so let's see so for again what's
+
+ align:start position:0%
+here so let's see so for again what's
+ 
+
+ align:start position:0%
+here so let's see so for again what's
+the query he does gkr so he does
+
+ align:start position:0%
+the query he does gkr so he does
+ 
+
+ align:start position:0%
+the query he does gkr so he does
+2D sum checks for each sum check he
+
+ align:start position:0%
+2D sum checks for each sum check he
+ 
+
+ align:start position:0%
+2D sum checks for each sum check he
+needs to read kind of what's what what
+
+ align:start position:0%
+needs to read kind of what's what what
+ 
+
+ align:start position:0%
+needs to read kind of what's what what
+the answer is each answer so there's
+
+ align:start position:0%
+the answer is each answer so there's
+ 
+
+ align:start position:0%
+the answer is each answer so there's
+three M rounds that he needs to read in
+
+ align:start position:0%
+three M rounds that he needs to read in
+ 
+
+ align:start position:0%
+three M rounds that he needs to read in
+each answer he gets kind of a univariate
+
+ align:start position:0%
+each answer he gets kind of a univariate
+ 
+
+ align:start position:0%
+each answer he gets kind of a univariate
+polinomial of small degree so he that
+
+ align:start position:0%
+polinomial of small degree so he that
+ 
+
+ align:start position:0%
+polinomial of small degree so he that
+each answer is not just one field
+
+ align:start position:0%
+each answer is not just one field
+ 
+
+ align:start position:0%
+each answer is not just one field
+element it's actually a few field
+
+ align:start position:0%
+element it's actually a few field
+ 
+
+ align:start position:0%
+element it's actually a few field
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+um a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's so he gets log F
+
+ align:start position:0%
+so it's so he gets log F
+ 
+
+ align:start position:0%
+so it's so he gets log F
+elements times a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the degree which will be in each Su
+
+ align:start position:0%
+um the degree which will be in each Su
+ 
+
+ align:start position:0%
+um the degree which will be in each Su
+check like poly
+
+ align:start position:0%
+check like poly
+ 
+
+ align:start position:0%
+check like poly
+H and most and this again goes back to
+
+ align:start position:0%
+H and most and this again goes back to
+ 
+
+ align:start position:0%
+H and most and this again goes back to
+the gold what's exactly the degree of
+
+ align:start position:0%
+the gold what's exactly the degree of
+ 
+
+ align:start position:0%
+the gold what's exactly the degree of
+the a multi it's polinomial so I'm not
+
+ align:start position:0%
+the a multi it's polinomial so I'm not
+ 
+
+ align:start position:0%
+the a multi it's polinomial so I'm not
+it's polinomial in h it's poly log H I
+
+ align:start position:0%
+it's polinomial in h it's poly log H I
+ 
+
+ align:start position:0%
+it's polinomial in h it's poly log H I
+don't want this is kind of the
+
+ align:start position:0%
+don't want this is kind of the
+ 
+
+ align:start position:0%
+don't want this is kind of the
+degree of uh each of the Su check
+
+ align:start position:0%
+degree of uh each of the Su check
+ 
+
+ align:start position:0%
+degree of uh each of the Su check
+polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the degrees affected by the ADI and
+
+ align:start position:0%
+and the degrees affected by the ADI and
+ 
+
+ align:start position:0%
+and the degrees affected by the ADI and
+multi which we assumed are the degree is
+
+ align:start position:0%
+multi which we assumed are the degree is
+ 
+
+ align:start position:0%
+multi which we assumed are the degree is
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+poly uh but it's still again polylog so
+
+ align:start position:0%
+poly uh but it's still again polylog so
+ 
+
+ align:start position:0%
+poly uh but it's still again polylog so
+this gives so okay so before we take a
+
+ align:start position:0%
+this gives so okay so before we take a
+ 
+
+ align:start position:0%
+this gives so okay so before we take a
+break H let
+
+ align:start position:0%
+break H let
+ 
+
+ align:start position:0%
+break H let
+me where where where are we now uh so
+
+ align:start position:0%
+me where where where are we now uh so
+ 
+
+ align:start position:0%
+me where where where are we now uh so
+you know we studied the we started
+
+ align:start position:0%
+you know we studied the we started
+ 
+
+ align:start position:0%
+you know we studied the we started
+actually this this class by looking at
+
+ align:start position:0%
+actually this this class by looking at
+ 
+
+ align:start position:0%
+actually this this class by looking at
+some check so I started this class by
+
+ align:start position:0%
+some check so I started this class by
+ 
+
+ align:start position:0%
+some check so I started this class by
+telling you look some Che is a miracle
+
+ align:start position:0%
+telling you look some Che is a miracle
+ 
+
+ align:start position:0%
+telling you look some Che is a miracle
+like giving some Che it gives you
+
+ align:start position:0%
+like giving some Che it gives you
+ 
+
+ align:start position:0%
+like giving some Che it gives you
+everything everything and I hope that
+
+ align:start position:0%
+everything everything and I hope that
+ 
+
+ align:start position:0%
+everything everything and I hope that
+now you see why so we surve some Che and
+
+ align:start position:0%
+now you see why so we surve some Che and
+ 
+
+ align:start position:0%
+now you see why so we surve some Che and
+we looked at some like who cares okay
+
+ align:start position:0%
+we looked at some like who cares okay
+ 
+
+ align:start position:0%
+we looked at some like who cares okay
+this it seemed like why would we need to
+
+ align:start position:0%
+this it seemed like why would we need to
+ 
+
+ align:start position:0%
+this it seemed like why would we need to
+some over so many very multivariate
+
+ align:start position:0%
+some over so many very multivariate
+ 
+
+ align:start position:0%
+some over so many very multivariate
+polinomial where does that come up I
+
+ align:start position:0%
+polinomial where does that come up I
+ 
+
+ align:start position:0%
+polinomial where does that come up I
+don't know it was like okay why am I
+
+ align:start position:0%
+don't know it was like okay why am I
+ 
+
+ align:start position:0%
+don't know it was like okay why am I
+learning this but you know so now where
+
+ align:start position:0%
+learning this but you know so now where
+ 
+
+ align:start position:0%
+learning this but you know so now where
+what did we do with it we start with
+
+ align:start position:0%
+what did we do with it we start with
+ 
+
+ align:start position:0%
+what did we do with it we start with
+with Su we saw
+
+ align:start position:0%
+with Su we saw
+ 
+
+ align:start position:0%
+with Su we saw
+oh just by doing something
+
+ align:start position:0%
+oh just by doing something
+ 
+
+ align:start position:0%
+oh just by doing something
+repeatedly you can verify any low depth
+
+ align:start position:0%
+repeatedly you can verify any low depth
+ 
+
+ align:start position:0%
+repeatedly you can verify any low depth
+computation that's pretty amazing and
+
+ align:start position:0%
+computation that's pretty amazing and
+ 
+
+ align:start position:0%
+computation that's pretty amazing and
+then we saw that actually you can
+
+ align:start position:0%
+then we saw that actually you can
+ 
+
+ align:start position:0%
+then we saw that actually you can
+recover the IP equals P space theorem
+
+ align:start position:0%
+recover the IP equals P space theorem
+ 
+
+ align:start position:0%
+recover the IP equals P space theorem
+that GK actually gives his IP equals P
+
+ align:start position:0%
+that GK actually gives his IP equals P
+ 
+
+ align:start position:0%
+that GK actually gives his IP equals P
+space theorem and now we see gkr
+
+ align:start position:0%
+space theorem and now we see gkr
+ 
+
+ align:start position:0%
+space theorem and now we see gkr
+actually gives you
+
+ align:start position:0%
+actually gives you
+ 
+
+ align:start position:0%
+actually gives you
+PCP and what is GK is just Su
+
+ align:start position:0%
+PCP and what is GK is just Su
+ 
+
+ align:start position:0%
+PCP and what is GK is just Su
+checks okay so just these Su checks you
+
+ align:start position:0%
+checks okay so just these Su checks you
+ 
+
+ align:start position:0%
+checks okay so just these Su checks you
+kind of unroll them unravel them and you
+
+ align:start position:0%
+kind of unroll them unravel them and you
+ 
+
+ align:start position:0%
+kind of unroll them unravel them and you
+get a PCP with polog and
+
+ align:start position:0%
+get a PCP with polog and
+ 
+
+ align:start position:0%
+get a PCP with polog and
+queries and not and it's like efficient
+
+ align:start position:0%
+queries and not and it's like efficient
+ 
+
+ align:start position:0%
+queries and not and it's like efficient
+you can take your input effic your
+
+ align:start position:0%
+you can take your input effic your
+ 
+
+ align:start position:0%
+you can take your input effic your
+witness and efficiently generate this
+
+ align:start position:0%
+witness and efficiently generate this
+ 
+
+ align:start position:0%
+witness and efficiently generate this
+PCP and in a very
+
+ align:start position:0%
+PCP and in a very
+ 
+
+ align:start position:0%
+PCP and in a very
+a like a straightforward way in a sense
+
+ align:start position:0%
+a like a straightforward way in a sense
+ 
+
+ align:start position:0%
+a like a straightforward way in a sense
+you do your computation you have your
+
+ align:start position:0%
+you do your computation you have your
+ 
+
+ align:start position:0%
+you do your computation you have your
+witness you do the computation you do
+
+ align:start position:0%
+witness you do the computation you do
+ 
+
+ align:start position:0%
+witness you do the computation you do
+all the lree extensions and you convince
+
+ align:start position:0%
+all the lree extensions and you convince
+ 
+
+ align:start position:0%
+all the lree extensions and you convince
+round by round you just lay it out
+
+ align:start position:0%
+round by round you just lay it out
+ 
+
+ align:start position:0%
+round by round you just lay it out
+that's it and you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PCP okay any any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that relies on just the fact that
+
+ align:start position:0%
+yeah that relies on just the fact that
+ 
+
+ align:start position:0%
+yeah that relies on just the fact that
+it consists of these kind of like
+
+ align:start position:0%
+it consists of these kind of like
+ 
+
+ align:start position:0%
+it consists of these kind of like
+independent subs or also the fact that
+
+ align:start position:0%
+independent subs or also the fact that
+ 
+
+ align:start position:0%
+independent subs or also the fact that
+some itself that each is just random
+
+ align:start position:0%
+some itself that each is just random
+ 
+
+ align:start position:0%
+some itself that each is just random
+good good good so the question is again
+
+ align:start position:0%
+good good good so the question is again
+ 
+
+ align:start position:0%
+good good good so the question is again
+let's understand why do we get this PCP
+
+ align:start position:0%
+let's understand why do we get this PCP
+ 
+
+ align:start position:0%
+let's understand why do we get this PCP
+that's efficient okay why do we get only
+
+ align:start position:0%
+that's efficient okay why do we get only
+ 
+
+ align:start position:0%
+that's efficient okay why do we get only
+poly siiz PCP and the reason we get is
+
+ align:start position:0%
+poly siiz PCP and the reason we get is
+ 
+
+ align:start position:0%
+poly siiz PCP and the reason we get is
+to both twofolds you you said both
+
+ align:start position:0%
+to both twofolds you you said both
+ 
+
+ align:start position:0%
+to both twofolds you you said both
+reasons reason number one that when we
+
+ align:start position:0%
+reasons reason number one that when we
+ 
+
+ align:start position:0%
+reasons reason number one that when we
+do each sum check after that we can
+
+ align:start position:0%
+do each sum check after that we can
+ 
+
+ align:start position:0%
+do each sum check after that we can
+forget about this Randomness and for
+
+ align:start position:0%
+forget about this Randomness and for
+ 
+
+ align:start position:0%
+forget about this Randomness and for
+each VI consider so we really need to
+
+ align:start position:0%
+each VI consider so we really need to
+ 
+
+ align:start position:0%
+each VI consider so we really need to
+write down only kind of D times F to the
+
+ align:start position:0%
+write down only kind of D times F to the
+ 
+
+ align:start position:0%
+write down only kind of D times F to the
+m sub checks okay that's D the depth of
+
+ align:start position:0%
+m sub checks okay that's D the depth of
+ 
+
+ align:start position:0%
+m sub checks okay that's D the depth of
+the circuit time F to the M Subs that's
+
+ align:start position:0%
+the circuit time F to the M Subs that's
+ 
+
+ align:start position:0%
+the circuit time F to the M Subs that's
+number one but number two why is the sum
+
+ align:start position:0%
+number one but number two why is the sum
+ 
+
+ align:start position:0%
+number one but number two why is the sum
+check can we write out all the sum check
+
+ align:start position:0%
+check can we write out all the sum check
+ 
+
+ align:start position:0%
+check can we write out all the sum check
+I mean the sum check is also an
+
+ align:start position:0%
+I mean the sum check is also an
+ 
+
+ align:start position:0%
+I mean the sum check is also an
+interactive protocol can we actually
+
+ align:start position:0%
+interactive protocol can we actually
+ 
+
+ align:start position:0%
+interactive protocol can we actually
+open it up and write the entire thing
+
+ align:start position:0%
+open it up and write the entire thing
+ 
+
+ align:start position:0%
+open it up and write the entire thing
+and the answer is well yeah but at a
+
+ align:start position:0%
+and the answer is well yeah but at a
+ 
+
+ align:start position:0%
+and the answer is well yeah but at a
+exponential cost and but an exponential
+
+ align:start position:0%
+exponential cost and but an exponential
+ 
+
+ align:start position:0%
+exponential cost and but an exponential
+cost in M the number of variables but
+
+ align:start position:0%
+cost in M the number of variables but
+ 
+
+ align:start position:0%
+cost in M the number of variables but
+here the number of variables is
+
+ align:start position:0%
+here the number of variables is
+ 
+
+ align:start position:0%
+here the number of variables is
+log that's important we if M was polog
+
+ align:start position:0%
+log that's important we if M was polog
+ 
+
+ align:start position:0%
+log that's important we if M was polog
+we would have been
+
+ align:start position:0%
+we would have been
+ 
+
+ align:start position:0%
+we would have been
+doomed but M or I mean okay uh it's not
+
+ align:start position:0%
+doomed but M or I mean okay uh it's not
+ 
+
+ align:start position:0%
+doomed but M or I mean okay uh it's not
+just log it's it's we set the parameter
+
+ align:start position:0%
+just log it's it's we set the parameter
+ 
+
+ align:start position:0%
+just log it's it's we set the parameter
+so that it's okay that's what we needed
+
+ align:start position:0%
+so that it's okay that's what we needed
+ 
+
+ align:start position:0%
+so that it's okay that's what we needed
+that's exactly so why can we open up
+
+ align:start position:0%
+that's exactly so why can we open up
+ 
+
+ align:start position:0%
+that's exactly so why can we open up
+this entire sum check it's because we
+
+ align:start position:0%
+this entire sum check it's because we
+ 
+
+ align:start position:0%
+this entire sum check it's because we
+set F to be poly H and H to the m is s
+
+ align:start position:0%
+set F to be poly H and H to the m is s
+ 
+
+ align:start position:0%
+set F to be poly H and H to the m is s
+so we we set it up so that you know
+
+ align:start position:0%
+so we we set it up so that you know
+ 
+
+ align:start position:0%
+so we we set it up so that you know
+opening the sum check
+
+ align:start position:0%
+opening the sum check
+ 
+
+ align:start position:0%
+opening the sum check
+requires F to the m kind of answers uh F
+
+ align:start position:0%
+requires F to the m kind of answers uh F
+ 
+
+ align:start position:0%
+requires F to the m kind of answers uh F
+to the m answers each one is kind of a
+
+ align:start position:0%
+to the m answers each one is kind of a
+ 
+
+ align:start position:0%
+to the m answers each one is kind of a
+low degree polinomial but that's that's
+
+ align:start position:0%
+low degree polinomial but that's that's
+ 
+
+ align:start position:0%
+low degree polinomial but that's that's
+fine but F to the m of them or F to the
+
+ align:start position:0%
+fine but F to the m of them or F to the
+ 
+
+ align:start position:0%
+fine but F to the m of them or F to the
+3M here because we have the number of
+
+ align:start position:0%
+3M here because we have the number of
+ 
+
+ align:start position:0%
+3M here because we have the number of
+variables is 3M
+
+ align:start position:0%
+variables is 3M
+ 
+
+ align:start position:0%
+variables is 3M
+uh and we just need to make sure that
+
+ align:start position:0%
+uh and we just need to make sure that
+ 
+
+ align:start position:0%
+uh and we just need to make sure that
+after the 3M is polinomial and to ensure
+
+ align:start position:0%
+after the 3M is polinomial and to ensure
+ 
+
+ align:start position:0%
+after the 3M is polinomial and to ensure
+that we did do some parameter
+
+ align:start position:0%
+that we did do some parameter
+ 
+
+ align:start position:0%
+that we did do some parameter
+engineering that's why we didn't go the
+
+ align:start position:0%
+engineering that's why we didn't go the
+ 
+
+ align:start position:0%
+engineering that's why we didn't go the
+natural route of taking H to be two and
+
+ align:start position:0%
+natural route of taking H to be two and
+ 
+
+ align:start position:0%
+natural route of taking H to be two and
+M to be log s that would be natural but
+
+ align:start position:0%
+M to be log s that would be natural but
+ 
+
+ align:start position:0%
+M to be log s that would be natural but
+then we would not get so we actually did
+
+ align:start position:0%
+then we would not get so we actually did
+ 
+
+ align:start position:0%
+then we would not get so we actually did
+need to do some kind of Engineering in
+
+ align:start position:0%
+need to do some kind of Engineering in
+ 
+
+ align:start position:0%
+need to do some kind of Engineering in
+parameters uh like an annoying fiddling
+
+ align:start position:0%
+parameters uh like an annoying fiddling
+ 
+
+ align:start position:0%
+parameters uh like an annoying fiddling
+of parameters uh you know this uh this
+
+ align:start position:0%
+of parameters uh you know this uh this
+ 
+
+ align:start position:0%
+of parameters uh you know this uh this
+setting of parameters that you see over
+
+ align:start position:0%
+setting of parameters that you see over
+ 
+
+ align:start position:0%
+setting of parameters that you see over
+and over in any PCP construction this is
+
+ align:start position:0%
+and over in any PCP construction this is
+ 
+
+ align:start position:0%
+and over in any PCP construction this is
+you know we're not the first so we're
+
+ align:start position:0%
+you know we're not the first so we're
+ 
+
+ align:start position:0%
+you know we're not the first so we're
+actually the last if anything to come to
+
+ align:start position:0%
+actually the last if anything to come to
+ 
+
+ align:start position:0%
+actually the last if anything to come to
+use this this was used in the '90s in
+
+ align:start position:0%
+use this this was used in the '90s in
+ 
+
+ align:start position:0%
+use this this was used in the '90s in
+the early PCP constructions and um and
+
+ align:start position:0%
+the early PCP constructions and um and
+ 
+
+ align:start position:0%
+the early PCP constructions and um and
+it's when you look at it first like oh
+
+ align:start position:0%
+it's when you look at it first like oh
+ 
+
+ align:start position:0%
+it's when you look at it first like oh
+really like log n over log log n are you
+
+ align:start position:0%
+really like log n over log log n are you
+ 
+
+ align:start position:0%
+really like log n over log log n are you
+kidding me like couldn't you find
+
+ align:start position:0%
+kidding me like couldn't you find
+ 
+
+ align:start position:0%
+kidding me like couldn't you find
+something nicer but this is this is why
+
+ align:start position:0%
+something nicer but this is this is why
+ 
+
+ align:start position:0%
+something nicer but this is this is why
+because we want these parameters to be
+
+ align:start position:0%
+because we want these parameters to be
+ 
+
+ align:start position:0%
+because we want these parameters to be
+poly yeah so since you're essentially
+
+ align:start position:0%
+poly yeah so since you're essentially
+ 
+
+ align:start position:0%
+poly yeah so since you're essentially
+asking for this for this to be like a
+
+ align:start position:0%
+asking for this for this to be like a
+ 
+
+ align:start position:0%
+asking for this for this to be like a
+nonadaptive can you just like use the
+
+ align:start position:0%
+nonadaptive can you just like use the
+ 
+
+ align:start position:0%
+nonadaptive can you just like use the
+same for and get
+
+ align:start position:0%
+same for and get
+ 
+
+ align:start position:0%
+same for and get
+the so sorry so you're saying sorry your
+
+ align:start position:0%
+the so sorry so you're saying sorry your
+ 
+
+ align:start position:0%
+the so sorry so you're saying sorry your
+question is you're saying you are you
+
+ align:start position:0%
+question is you're saying you are you
+ 
+
+ align:start position:0%
+question is you're saying you are you
+talking about the non the fact that this
+
+ align:start position:0%
+talking about the non the fact that this
+ 
+
+ align:start position:0%
+talking about the non the fact that this
+verifier is nonadaptive or or that
+
+ align:start position:0%
+verifier is nonadaptive or or that
+ 
+
+ align:start position:0%
+verifier is nonadaptive or or that
+theover is nonadaptive right the prover
+
+ align:start position:0%
+theover is nonadaptive right the prover
+ 
+
+ align:start position:0%
+theover is nonadaptive right the prover
+in the yes M like it's not adaptive in
+
+ align:start position:0%
+in the yes M like it's not adaptive in
+ 
+
+ align:start position:0%
+in the yes M like it's not adaptive in
+the previous in the previous uh Su
+
+ align:start position:0%
+the previous in the previous uh Su
+ 
+
+ align:start position:0%
+the previous in the previous uh Su
+checks previous Su checks yeah so then
+
+ align:start position:0%
+checks previous Su checks yeah so then
+ 
+
+ align:start position:0%
+checks previous Su checks yeah so then
+what can you use the same Randomness for
+
+ align:start position:0%
+what can you use the same Randomness for
+ 
+
+ align:start position:0%
+what can you use the same Randomness for
+each round like what would happen if you
+
+ align:start position:0%
+each round like what would happen if you
+ 
+
+ align:start position:0%
+each round like what would happen if you
+theand no okay okay okay that's a good
+
+ align:start position:0%
+theand no okay okay okay that's a good
+ 
+
+ align:start position:0%
+theand no okay okay okay that's a good
+question so you're asking you're saying
+
+ align:start position:0%
+question so you're asking you're saying
+ 
+
+ align:start position:0%
+question so you're asking you're saying
+look we're doing the sum check D times
+
+ align:start position:0%
+look we're doing the sum check D times
+ 
+
+ align:start position:0%
+look we're doing the sum check D times
+can't we use the same Randomness and the
+
+ align:start position:0%
+can't we use the same Randomness and the
+ 
+
+ align:start position:0%
+can't we use the same Randomness and the
+answer is we cannot why because you
+
+ align:start position:0%
+answer is we cannot why because you
+ 
+
+ align:start position:0%
+answer is we cannot why because you
+should think if you use the same
+
+ align:start position:0%
+should think if you use the same
+ 
+
+ align:start position:0%
+should think if you use the same
+Randomness for different rounds then you
+
+ align:start position:0%
+Randomness for different rounds then you
+ 
+
+ align:start position:0%
+Randomness for different rounds then you
+should think of I'm aover I'm like oh I
+
+ align:start position:0%
+should think of I'm aover I'm like oh I
+ 
+
+ align:start position:0%
+should think of I'm aover I'm like oh I
+I'm you're going to use the same
+
+ align:start position:0%
+I'm you're going to use the same
+ 
+
+ align:start position:0%
+I'm you're going to use the same
+Randomness for all your rounds I know
+
+ align:start position:0%
+Randomness for all your rounds I know
+ 
+
+ align:start position:0%
+Randomness for all your rounds I know
+that because you're telling me already
+
+ align:start position:0%
+that because you're telling me already
+ 
+
+ align:start position:0%
+that because you're telling me already
+that you're going to use the same
+
+ align:start position:0%
+that you're going to use the same
+ 
+
+ align:start position:0%
+that you're going to use the same
+Randomness so now in the first round I'm
+
+ align:start position:0%
+Randomness so now in the first round I'm
+ 
+
+ align:start position:0%
+Randomness so now in the first round I'm
+I'm going to behave honestly just learn
+
+ align:start position:0%
+I'm going to behave honestly just learn
+ 
+
+ align:start position:0%
+I'm going to behave honestly just learn
+your Randomness give you so I'm sorry
+
+ align:start position:0%
+your Randomness give you so I'm sorry
+ 
+
+ align:start position:0%
+your Randomness give you so I'm sorry
+I'm not going to be I'm going to cheat
+
+ align:start position:0%
+I'm not going to be I'm going to cheat
+ 
+
+ align:start position:0%
+I'm not going to be I'm going to cheat
+in the first round okay so of course I'm
+
+ align:start position:0%
+in the first round okay so of course I'm
+ 
+
+ align:start position:0%
+in the first round okay so of course I'm
+going to I'm the output is one even
+
+ align:start position:0%
+going to I'm the output is one even
+ 
+
+ align:start position:0%
+going to I'm the output is one even
+though it's zero I'm going to manage to
+
+ align:start position:0%
+though it's zero I'm going to manage to
+ 
+
+ align:start position:0%
+though it's zero I'm going to manage to
+convince you in the first kind of in the
+
+ align:start position:0%
+convince you in the first kind of in the
+ 
+
+ align:start position:0%
+convince you in the first kind of in the
+first Su check I do yeah because I'm
+
+ align:start position:0%
+first Su check I do yeah because I'm
+ 
+
+ align:start position:0%
+first Su check I do yeah because I'm
+just going to lie consistently with
+
+ align:start position:0%
+just going to lie consistently with
+ 
+
+ align:start position:0%
+just going to lie consistently with
+myself arrive to VI to the next layer
+
+ align:start position:0%
+myself arrive to VI to the next layer
+ 
+
+ align:start position:0%
+myself arrive to VI to the next layer
+and the wrong still inconsistent but now
+
+ align:start position:0%
+and the wrong still inconsistent but now
+ 
+
+ align:start position:0%
+and the wrong still inconsistent but now
+I know the randomness that cuz you're
+
+ align:start position:0%
+I know the randomness that cuz you're
+ 
+
+ align:start position:0%
+I know the randomness that cuz you're
+going to reuse you see here the point is
+
+ align:start position:0%
+going to reuse you see here the point is
+ 
+
+ align:start position:0%
+going to reuse you see here the point is
+that the following the verifier here
+
+ align:start position:0%
+that the following the verifier here
+ 
+
+ align:start position:0%
+that the following the verifier here
+should behave like a like an honest
+
+ align:start position:0%
+should behave like a like an honest
+ 
+
+ align:start position:0%
+should behave like a like an honest
+verifier in the gkr if the verifier here
+
+ align:start position:0%
+verifier in the gkr if the verifier here
+ 
+
+ align:start position:0%
+verifier in the gkr if the verifier here
+you cannot if when you use this verifier
+
+ align:start position:0%
+you cannot if when you use this verifier
+ 
+
+ align:start position:0%
+you cannot if when you use this verifier
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+essentially behaves like a GK verifier
+
+ align:start position:0%
+essentially behaves like a GK verifier
+ 
+
+ align:start position:0%
+essentially behaves like a GK verifier
+so now you're telling you're saying look
+
+ align:start position:0%
+so now you're telling you're saying look
+ 
+
+ align:start position:0%
+so now you're telling you're saying look
+why doesn't he use the same Randomness
+
+ align:start position:0%
+why doesn't he use the same Randomness
+ 
+
+ align:start position:0%
+why doesn't he use the same Randomness
+for the different uh subprotocols
+
+ align:start position:0%
+for the different uh subprotocols
+ 
+
+ align:start position:0%
+for the different uh subprotocols
+because if he didn't gkr then he would
+
+ align:start position:0%
+because if he didn't gkr then he would
+ 
+
+ align:start position:0%
+because if he didn't gkr then he would
+fail then you the a cheating prover can
+
+ align:start position:0%
+fail then you the a cheating prover can
+ 
+
+ align:start position:0%
+fail then you the a cheating prover can
+can take advantage of him is isn't there
+
+ align:start position:0%
+can take advantage of him is isn't there
+ 
+
+ align:start position:0%
+can take advantage of him is isn't there
+the difference here that this is
+
+ align:start position:0%
+the difference here that this is
+ 
+
+ align:start position:0%
+the difference here that this is
+nonadaptive like it doesn't remember the
+
+ align:start position:0%
+nonadaptive like it doesn't remember the
+ 
+
+ align:start position:0%
+nonadaptive like it doesn't remember the
+randomness all it depends on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is right so you can't just be like oh
+
+ align:start position:0%
+is right so you can't just be like oh
+ 
+
+ align:start position:0%
+is right so you can't just be like oh
+this is the random oh I see you're
+
+ align:start position:0%
+this is the random oh I see you're
+ 
+
+ align:start position:0%
+this is the random oh I see you're
+saying I see I see okay okay now I
+
+ align:start position:0%
+saying I see I see okay okay now I
+ 
+
+ align:start position:0%
+saying I see I see okay okay now I
+understand your question you're saying
+
+ align:start position:0%
+understand your question you're saying
+ 
+
+ align:start position:0%
+understand your question you're saying
+this guy this uh prover is stuck okay
+
+ align:start position:0%
+this guy this uh prover is stuck okay
+ 
+
+ align:start position:0%
+this guy this uh prover is stuck okay
+okay sorry now I'm I understand what
+
+ align:start position:0%
+okay sorry now I'm I understand what
+ 
+
+ align:start position:0%
+okay sorry now I'm I understand what
+you're saying you're saying look you're
+
+ align:start position:0%
+you're saying you're saying look you're
+ 
+
+ align:start position:0%
+you're saying you're saying look you're
+tying the hand of the prover the prover
+
+ align:start position:0%
+tying the hand of the prover the prover
+ 
+
+ align:start position:0%
+tying the hand of the prover the prover
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+gkr he has power he sees your Randomness
+
+ align:start position:0%
+gkr he has power he sees your Randomness
+ 
+
+ align:start position:0%
+gkr he has power he sees your Randomness
+and based on that he can continue the
+
+ align:start position:0%
+and based on that he can continue the
+ 
+
+ align:start position:0%
+and based on that he can continue the
+honest Pro of course won't do that but
+
+ align:start position:0%
+honest Pro of course won't do that but
+ 
+
+ align:start position:0%
+honest Pro of course won't do that but
+the cheating prover May here you're
+
+ align:start position:0%
+the cheating prover May here you're
+ 
+
+ align:start position:0%
+the cheating prover May here you're
+saying I'm not going to let the prover
+
+ align:start position:0%
+saying I'm not going to let the prover
+ 
+
+ align:start position:0%
+saying I'm not going to let the prover
+do that to me I'm G to force him to
+
+ align:start position:0%
+do that to me I'm G to force him to
+ 
+
+ align:start position:0%
+do that to me I'm G to force him to
+forget because I force him to forget can
+
+ align:start position:0%
+forget because I force him to forget can
+ 
+
+ align:start position:0%
+forget because I force him to forget can
+I think of using the same Randomness
+
+ align:start position:0%
+I think of using the same Randomness
+ 
+
+ align:start position:0%
+I think of using the same Randomness
+that's a good question
+
+ align:start position:0%
+that's a good question
+ 
+
+ align:start position:0%
+that's a good question
+actually a great very good question I it
+
+ align:start position:0%
+actually a great very good question I it
+ 
+
+ align:start position:0%
+actually a great very good question I it
+took me time to understand what you're
+
+ align:start position:0%
+took me time to understand what you're
+ 
+
+ align:start position:0%
+took me time to understand what you're
+asking a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you use the same it's great qu great
+
+ align:start position:0%
+can you use the same it's great qu great
+ 
+
+ align:start position:0%
+can you use the same it's great qu great
+point verif just said to break that well
+
+ align:start position:0%
+point verif just said to break that well
+ 
+
+ align:start position:0%
+point verif just said to break that well
+no because what okay so I'm so okay so
+
+ align:start position:0%
+no because what okay so I'm so okay so
+ 
+
+ align:start position:0%
+no because what okay so I'm so okay so
+we are pointed the F said you know what
+
+ align:start position:0%
+we are pointed the F said you know what
+ 
+
+ align:start position:0%
+we are pointed the F said you know what
+use the same Randomness in all the
+
+ align:start position:0%
+use the same Randomness in all the
+ 
+
+ align:start position:0%
+use the same Randomness in all the
+subprotocols now in the gkr it's a big
+
+ align:start position:0%
+subprotocols now in the gkr it's a big
+ 
+
+ align:start position:0%
+subprotocols now in the gkr it's a big
+problem because the prover he knows what
+
+ align:start position:0%
+problem because the prover he knows what
+ 
+
+ align:start position:0%
+problem because the prover he knows what
+you saw and he'll use that like he know
+
+ align:start position:0%
+you saw and he'll use that like he know
+ 
+
+ align:start position:0%
+you saw and he'll use that like he know
+the but in in the PCP the
+
+ align:start position:0%
+the but in in the PCP the
+ 
+
+ align:start position:0%
+the but in in the PCP the
+PCP gkr prover his hands are tied yeah
+
+ align:start position:0%
+PCP gkr prover his hands are tied yeah
+ 
+
+ align:start position:0%
+PCP gkr prover his hands are tied yeah
+but the fact like if the Prov knows that
+
+ align:start position:0%
+but the fact like if the Prov knows that
+ 
+
+ align:start position:0%
+but the fact like if the Prov knows that
+you're going to do this then he might be
+
+ align:start position:0%
+you're going to do this then he might be
+ 
+
+ align:start position:0%
+you're going to do this then he might be
+able to engineer all of his responses in
+
+ align:start position:0%
+able to engineer all of his responses in
+ 
+
+ align:start position:0%
+able to engineer all of his responses in
+a way that like takes advantage of the
+
+ align:start position:0%
+a way that like takes advantage of the
+ 
+
+ align:start position:0%
+a way that like takes advantage of the
+correlation of right like by exactly
+
+ align:start position:0%
+correlation of right like by exactly
+ 
+
+ align:start position:0%
+correlation of right like by exactly
+using the same verifier you said like
+
+ align:start position:0%
+using the same verifier you said like
+ 
+
+ align:start position:0%
+using the same verifier you said like
+you pretend you have that verifier that
+
+ align:start position:0%
+you pretend you have that verifier that
+ 
+
+ align:start position:0%
+you pretend you have that verifier that
+cheats you use the same Randomness now
+
+ align:start position:0%
+cheats you use the same Randomness now
+ 
+
+ align:start position:0%
+cheats you use the same Randomness now
+this tree follows that verifier
+
+ align:start position:0%
+this tree follows that verifier
+ 
+
+ align:start position:0%
+this tree follows that verifier
+strategy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shouldn't yeah I mean it is it could be
+
+ align:start position:0%
+shouldn't yeah I mean it is it could be
+ 
+
+ align:start position:0%
+shouldn't yeah I mean it is it could be
+some but like there's this correlation
+
+ align:start position:0%
+some but like there's this correlation
+ 
+
+ align:start position:0%
+some but like there's this correlation
+between the randomness the would know
+
+ align:start position:0%
+between the randomness the would know
+ 
+
+ align:start position:0%
+between the randomness the would know
+about it in advance right so even though
+
+ align:start position:0%
+about it in advance right so even though
+ 
+
+ align:start position:0%
+about it in advance right so even though
+he can't remember the random he can
+
+ align:start position:0%
+he can't remember the random he can
+ 
+
+ align:start position:0%
+he can't remember the random he can
+engineer the strategy to take advantage
+
+ align:start position:0%
+engineer the strategy to take advantage
+ 
+
+ align:start position:0%
+engineer the strategy to take advantage
+of the fact the
+
+ align:start position:0%
+of the fact the
+ 
+
+ align:start position:0%
+of the fact the
+Rand okay let me say the following um to
+
+ align:start position:0%
+Rand okay let me say the following um to
+ 
+
+ align:start position:0%
+Rand okay let me say the following um to
+close this discussion a the discussion
+
+ align:start position:0%
+close this discussion a the discussion
+ 
+
+ align:start position:0%
+close this discussion a the discussion
+is super interesting the question you
+
+ align:start position:0%
+is super interesting the question you
+ 
+
+ align:start position:0%
+is super interesting the question you
+raised is super
+
+ align:start position:0%
+raised is super
+ 
+
+ align:start position:0%
+raised is super
+interesting you know we have one pet in
+
+ align:start position:0%
+interesting you know we have one pet in
+ 
+
+ align:start position:0%
+interesting you know we have one pet in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+class you gave me a great uh idea for a
+
+ align:start position:0%
+class you gave me a great uh idea for a
+ 
+
+ align:start position:0%
+class you gave me a great uh idea for a
+question a a by the way um before we
+
+ align:start position:0%
+question a a by the way um before we
+ 
+
+ align:start position:0%
+question a a by the way um before we
+break I just want to make a quick
+
+ align:start position:0%
+break I just want to make a quick
+ 
+
+ align:start position:0%
+break I just want to make a quick
+announcement so I wrote in the in the
+
+ align:start position:0%
+announcement so I wrote in the in the
+ 
+
+ align:start position:0%
+announcement so I wrote in the in the
+website that the pet will come later in
+
+ align:start position:0%
+website that the pet will come later in
+ 
+
+ align:start position:0%
+website that the pet will come later in
+during this class because I thought it
+
+ align:start position:0%
+during this class because I thought it
+ 
+
+ align:start position:0%
+during this class because I thought it
+would be good to cover more
+
+ align:start position:0%
+would be good to cover more
+ 
+
+ align:start position:0%
+would be good to cover more
+material but uh I know that I wrote it
+
+ align:start position:0%
+material but uh I know that I wrote it
+ 
+
+ align:start position:0%
+material but uh I know that I wrote it
+pretty close like to the break and maybe
+
+ align:start position:0%
+pretty close like to the break and maybe
+ 
+
+ align:start position:0%
+pretty close like to the break and maybe
+that's so okay so maybe I'll I'll put it
+
+ align:start position:0%
+that's so okay so maybe I'll I'll put it
+ 
+
+ align:start position:0%
+that's so okay so maybe I'll I'll put it
+out earlier give you two weeks and just
+
+ align:start position:0%
+out earlier give you two weeks and just
+ 
+
+ align:start position:0%
+out earlier give you two weeks and just
+because I don't want to sit with it too
+
+ align:start position:0%
+because I don't want to sit with it too
+ 
+
+ align:start position:0%
+because I don't want to sit with it too
+long it's just annoying but if you feel
+
+ align:start position:0%
+long it's just annoying but if you feel
+ 
+
+ align:start position:0%
+long it's just annoying but if you feel
+like the time is doesn't work and you
+
+ align:start position:0%
+like the time is doesn't work and you
+ 
+
+ align:start position:0%
+like the time is doesn't work and you
+want an extension just let me know
+
+ align:start position:0%
+want an extension just let me know
+ 
+
+ align:start position:0%
+want an extension just let me know
+I don't really
+
+ align:start position:0%
+I don't really
+ 
+
+ align:start position:0%
+I don't really
+care I just want you to think about it
+
+ align:start position:0%
+care I just want you to think about it
+ 
+
+ align:start position:0%
+care I just want you to think about it
+and have fun with the you know with the
+
+ align:start position:0%
+and have fun with the you know with the
+ 
+
+ align:start position:0%
+and have fun with the you know with the
+material yeah the way we all do sound is
+
+ align:start position:0%
+material yeah the way we all do sound is
+ 
+
+ align:start position:0%
+material yeah the way we all do sound is
+are we using un bound like yeah exactly
+
+ align:start position:0%
+are we using un bound like yeah exactly
+ 
+
+ align:start position:0%
+are we using un bound like yeah exactly
+we're doing a union bound yeah yes
+
+ align:start position:0%
+we're doing a union bound yeah yes
+ 
+
+ align:start position:0%
+we're doing a union bound yeah yes
+exactly because the in the soundness we
+
+ align:start position:0%
+exactly because the in the soundness we
+ 
+
+ align:start position:0%
+exactly because the in the soundness we
+say the following we say that
+
+ align:start position:0%
+say the following we say that
+ 
+
+ align:start position:0%
+say the following we say that
+uh uh in the so essentially we're we're
+
+ align:start position:0%
+uh uh in the so essentially we're we're
+ 
+
+ align:start position:0%
+uh uh in the so essentially we're we're
+talking with a prover and GK prover and
+
+ align:start position:0%
+talking with a prover and GK prover and
+ 
+
+ align:start position:0%
+talking with a prover and GK prover and
+we're saying for the GK even like a tied
+
+ align:start position:0%
+we're saying for the GK even like a tied
+ 
+
+ align:start position:0%
+we're saying for the GK even like a tied
+GK Pro as you as you mentioned even it's
+
+ align:start position:0%
+GK Pro as you as you mentioned even it's
+ 
+
+ align:start position:0%
+GK Pro as you as you mentioned even it's
+a gar prover with tied hands so for this
+
+ align:start position:0%
+a gar prover with tied hands so for this
+ 
+
+ align:start position:0%
+a gar prover with tied hands so for this
+for this prover to cheat he need so the
+
+ align:start position:0%
+for this prover to cheat he need so the
+ 
+
+ align:start position:0%
+for this prover to cheat he need so the
+output is false that's kind of he
+
+ align:start position:0%
+output is false that's kind of he
+ 
+
+ align:start position:0%
+output is false that's kind of he
+cheated so somewhere he needs to cheat
+
+ align:start position:0%
+cheated so somewhere he needs to cheat
+ 
+
+ align:start position:0%
+cheated so somewhere he needs to cheat
+in one of the gkrs one of the one of the
+
+ align:start position:0%
+in one of the gkrs one of the one of the
+ 
+
+ align:start position:0%
+in one of the gkrs one of the one of the
+sum checks he needs to go from false to
+
+ align:start position:0%
+sum checks he needs to go from false to
+ 
+
+ align:start position:0%
+sum checks he needs to go from false to
+True somewhere because at the end you're
+
+ align:start position:0%
+True somewhere because at the end you're
+ 
+
+ align:start position:0%
+True somewhere because at the end you're
+verifying you verifying that you know he
+
+ align:start position:0%
+verifying you verifying that you know he
+ 
+
+ align:start position:0%
+verifying you verifying that you know he
+put here a witness so he put in the sky
+
+ align:start position:0%
+put here a witness so he put in the sky
+ 
+
+ align:start position:0%
+put here a witness so he put in the sky
+a witness that witness is false because
+
+ align:start position:0%
+a witness that witness is false because
+ 
+
+ align:start position:0%
+a witness that witness is false because
+there's no satisfying assignment so he
+
+ align:start position:0%
+there's no satisfying assignment so he
+ 
+
+ align:start position:0%
+there's no satisfying assignment so he
+put something that's actually
+
+ align:start position:0%
+put something that's actually
+ 
+
+ align:start position:0%
+put something that's actually
+false oh one second there is something
+
+ align:start position:0%
+false oh one second there is something
+ 
+
+ align:start position:0%
+false oh one second there is something
+okay sorry now I remember there is
+
+ align:start position:0%
+okay sorry now I remember there is
+ 
+
+ align:start position:0%
+okay sorry now I remember there is
+something there is a low deegree test to
+
+ align:start position:0%
+something there is a low deegree test to
+ 
+
+ align:start position:0%
+something there is a low deegree test to
+do we'll get back to that sorry uh we'll
+
+ align:start position:0%
+do we'll get back to that sorry uh we'll
+ 
+
+ align:start position:0%
+do we'll get back to that sorry uh we'll
+get back to the low degree test but uh
+
+ align:start position:0%
+get back to the low degree test but uh
+ 
+
+ align:start position:0%
+get back to the low degree test but uh
+there so you're talking with a um a
+
+ align:start position:0%
+there so you're talking with a um a
+ 
+
+ align:start position:0%
+there so you're talking with a um a
+you're talking with a GK prover and this
+
+ align:start position:0%
+you're talking with a GK prover and this
+ 
+
+ align:start position:0%
+you're talking with a GK prover and this
+prover the only way he can convince you
+
+ align:start position:0%
+prover the only way he can convince you
+ 
+
+ align:start position:0%
+prover the only way he can convince you
+is to go from like a false statement to
+
+ align:start position:0%
+is to go from like a false statement to
+ 
+
+ align:start position:0%
+is to go from like a false statement to
+a true statement because at the end you
+
+ align:start position:0%
+a true statement because at the end you
+ 
+
+ align:start position:0%
+a true statement because at the end you
+ver you and to do that you need to break
+
+ align:start position:0%
+ver you and to do that you need to break
+ 
+
+ align:start position:0%
+ver you and to do that you need to break
+one of the sum checks so to break one of
+
+ align:start position:0%
+one of the sum checks so to break one of
+ 
+
+ align:start position:0%
+one of the sum checks so to break one of
+the Su checks you have two Su checks and
+
+ align:start position:0%
+the Su checks you have two Su checks and
+ 
+
+ align:start position:0%
+the Su checks you have two Su checks and
+now I'm using a union bound to say that
+
+ align:start position:0%
+now I'm using a union bound to say that
+ 
+
+ align:start position:0%
+now I'm using a union bound to say that
+the probability that you kind of manag
+
+ align:start position:0%
+the probability that you kind of manag
+ 
+
+ align:start position:0%
+the probability that you kind of manag
+to break one of them is two to the D
+
+ align:start position:0%
+to break one of them is two to the D
+ 
+
+ align:start position:0%
+to break one of them is two to the D
+times the probability that you manage to
+
+ align:start position:0%
+times the probability that you manage to
+ 
+
+ align:start position:0%
+times the probability that you manage to
+break one of
+
+ align:start position:0%
+break one of
+ 
+
+ align:start position:0%
+break one of
+them okay but then back to discussion
+
+ align:start position:0%
+them okay but then back to discussion
+ 
+
+ align:start position:0%
+them okay but then back to discussion
+where like like sharing Randomness so
+
+ align:start position:0%
+where like like sharing Randomness so
+ 
+
+ align:start position:0%
+where like like sharing Randomness so
+does un help
+
+ align:start position:0%
+does un help
+ 
+
+ align:start position:0%
+does un help
+here you you're saying oh you're because
+
+ align:start position:0%
+here you you're saying oh you're because
+ 
+
+ align:start position:0%
+here you you're saying oh you're because
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+theend okay so this is is this related
+
+ align:start position:0%
+theend okay so this is is this related
+ 
+
+ align:start position:0%
+theend okay so this is is this related
+to this qu okay okay actually I don't
+
+ align:start position:0%
+to this qu okay okay actually I don't
+ 
+
+ align:start position:0%
+to this qu okay okay actually I don't
+think so because Union Bound in general
+
+ align:start position:0%
+think so because Union Bound in general
+ 
+
+ align:start position:0%
+think so because Union Bound in general
+it it can be correlated a union Bound in
+
+ align:start position:0%
+it it can be correlated a union Bound in
+ 
+
+ align:start position:0%
+it it can be correlated a union Bound in
+general says that the probability that
+
+ align:start position:0%
+general says that the probability that
+ 
+
+ align:start position:0%
+general says that the probability that
+this or this I don't care how they're
+
+ align:start position:0%
+this or this I don't care how they're
+ 
+
+ align:start position:0%
+this or this I don't care how they're
+correlated it's smaller or equal the
+
+ align:start position:0%
+correlated it's smaller or equal the
+ 
+
+ align:start position:0%
+correlated it's smaller or equal the
+probability of this plus the probability
+
+ align:start position:0%
+probability of this plus the probability
+ 
+
+ align:start position:0%
+probability of this plus the probability
+of this so the correlation here the
+
+ align:start position:0%
+of this so the correlation here the
+ 
+
+ align:start position:0%
+of this so the correlation here the
+union bound is
+
+ align:start position:0%
+union bound is
+ 
+
+ align:start position:0%
+union bound is
+very uh easily used in any situation you
+
+ align:start position:0%
+very uh easily used in any situation you
+ 
+
+ align:start position:0%
+very uh easily used in any situation you
+know just at the probability that you
+
+ align:start position:0%
+know just at the probability that you
+ 
+
+ align:start position:0%
+know just at the probability that you
+have an event you CH you cheated on test
+
+ align:start position:0%
+have an event you CH you cheated on test
+ 
+
+ align:start position:0%
+have an event you CH you cheated on test
+one you cheated on test two you cheated
+
+ align:start position:0%
+one you cheated on test two you cheated
+ 
+
+ align:start position:0%
+one you cheated on test two you cheated
+on test three I don't care how they're
+
+ align:start position:0%
+on test three I don't care how they're
+ 
+
+ align:start position:0%
+on test three I don't care how they're
+correlated the probability that you Che
+
+ align:start position:0%
+correlated the probability that you Che
+ 
+
+ align:start position:0%
+correlated the probability that you Che
+on one of them is small or equal
+
+ align:start position:0%
+on one of them is small or equal
+ 
+
+ align:start position:0%
+on one of them is small or equal
+then yeah but actually before we break
+
+ align:start position:0%
+then yeah but actually before we break
+ 
+
+ align:start position:0%
+then yeah but actually before we break
+sorry there is a some there is a low
+
+ align:start position:0%
+sorry there is a some there is a low
+ 
+
+ align:start position:0%
+sorry there is a some there is a low
+degree extension
+
+ align:start position:0%
+degree extension
+ 
+
+ align:start position:0%
+degree extension
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+exactly you can just
+
+ align:start position:0%
+exactly you can just
+ 
+
+ align:start position:0%
+exactly you can just
+use good okay okay okay
+
+ align:start position:0%
+use good okay okay okay
+ 
+
+ align:start position:0%
+use good okay okay okay
+sorry good uh I love you guys uh so uh
+
+ align:start position:0%
+sorry good uh I love you guys uh so uh
+ 
+
+ align:start position:0%
+sorry good uh I love you guys uh so uh
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+V uh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check v0 Tilda is low
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree because in
+
+ align:start position:0%
+degree because in
+ 
+
+ align:start position:0%
+degree because in
+gkr the verifier has the W the the input
+
+ align:start position:0%
+gkr the verifier has the W the the input
+ 
+
+ align:start position:0%
+gkr the verifier has the W the the input
+which is the witness he computes the Lo
+
+ align:start position:0%
+which is the witness he computes the Lo
+ 
+
+ align:start position:0%
+which is the witness he computes the Lo
+extension by
+
+ align:start position:0%
+extension by
+ 
+
+ align:start position:0%
+extension by
+himself here the poer is giving it to
+
+ align:start position:0%
+himself here the poer is giving it to
+ 
+
+ align:start position:0%
+himself here the poer is giving it to
+him what if you didn't give a low degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we do need one low degree test in the
+
+ align:start position:0%
+so we do need one low degree test in the
+ 
+
+ align:start position:0%
+so we do need one low degree test in the
+input other than that it's GK black box
+
+ align:start position:0%
+input other than that it's GK black box
+ 
+
+ align:start position:0%
+input other than that it's GK black box
+but we do need this and by the way note
+
+ align:start position:0%
+but we do need this and by the way note
+ 
+
+ align:start position:0%
+but we do need this and by the way note
+that we're using the gkr the gkr has
+
+ align:start position:0%
+that we're using the gkr the gkr has
+ 
+
+ align:start position:0%
+that we're using the gkr the gkr has
+actually um properties and now I want to
+
+ align:start position:0%
+actually um properties and now I want to
+ 
+
+ align:start position:0%
+actually um properties and now I want to
+go back to the succinctness because
+
+ align:start position:0%
+go back to the succinctness because
+ 
+
+ align:start position:0%
+go back to the succinctness because
+actually you're saying can't you do it
+
+ align:start position:0%
+actually you're saying can't you do it
+ 
+
+ align:start position:0%
+actually you're saying can't you do it
+with any succinct protocol and the
+
+ align:start position:0%
+with any succinct protocol and the
+ 
+
+ align:start position:0%
+with any succinct protocol and the
+answer is maybe but there's also this
+
+ align:start position:0%
+answer is maybe but there's also this
+ 
+
+ align:start position:0%
+answer is maybe but there's also this
+point which is problematic that in gkr
+
+ align:start position:0%
+point which is problematic that in gkr
+ 
+
+ align:start position:0%
+point which is problematic that in gkr
+it's nice because you just check one
+
+ align:start position:0%
+it's nice because you just check one
+ 
+
+ align:start position:0%
+it's nice because you just check one
+point in the low degree
+
+ align:start position:0%
+point in the low degree
+ 
+
+ align:start position:0%
+point in the low degree
+extension and we can verify that you do
+
+ align:start position:0%
+extension and we can verify that you do
+ 
+
+ align:start position:0%
+extension and we can verify that you do
+the low degree
+
+ align:start position:0%
+the low degree
+ 
+
+ align:start position:0%
+the low degree
+extension there there's a low deegree
+
+ align:start position:0%
+extension there there's a low deegree
+ 
+
+ align:start position:0%
+extension there there's a low deegree
+test that I didn't talk to you about but
+
+ align:start position:0%
+test that I didn't talk to you about but
+ 
+
+ align:start position:0%
+test that I didn't talk to you about but
+we'll mention that after the break so
+
+ align:start position:0%
+we'll mention that after the break so
+ 
+
+ align:start position:0%
+we'll mention that after the break so
+there's a uh gkr you can verify the
+
+ align:start position:0%
+there's a uh gkr you can verify the
+ 
+
+ align:start position:0%
+there's a uh gkr you can verify the
+verifier to verify all he needs to do is
+
+ align:start position:0%
+verifier to verify all he needs to do is
+ 
+
+ align:start position:0%
+verifier to verify all he needs to do is
+take his input and compute only one
+
+ align:start position:0%
+take his input and compute only one
+ 
+
+ align:start position:0%
+take his input and compute only one
+point two points in the low degree
+
+ align:start position:0%
+point two points in the low degree
+ 
+
+ align:start position:0%
+point two points in the low degree
+extension of that
+
+ align:start position:0%
+extension of that
+ 
+
+ align:start position:0%
+extension of that
+input this is actually used here
+
+ align:start position:0%
+input this is actually used here
+ 
+
+ align:start position:0%
+input this is actually used here
+because now the ver the prover the
+
+ align:start position:0%
+because now the ver the prover the
+ 
+
+ align:start position:0%
+because now the ver the prover the
+verifier doesn't have the input the
+
+ align:start position:0%
+verifier doesn't have the input the
+ 
+
+ align:start position:0%
+verifier doesn't have the input the
+witness the prover has it he's going to
+
+ align:start position:0%
+witness the prover has it he's going to
+ 
+
+ align:start position:0%
+witness the prover has it he's going to
+put it in the in the sky and now you
+
+ align:start position:0%
+put it in the in the sky and now you
+ 
+
+ align:start position:0%
+put it in the in the sky and now you
+can't read the entire input that's a
+
+ align:start position:0%
+can't read the entire input that's a
+ 
+
+ align:start position:0%
+can't read the entire input that's a
+witness but you can read like you know
+
+ align:start position:0%
+witness but you can read like you know
+ 
+
+ align:start position:0%
+witness but you can read like you know
+what the what what the kind of succinct
+
+ align:start position:0%
+what the what what the kind of succinct
+ 
+
+ align:start position:0%
+what the what what the kind of succinct
+protocol tells you to read you know and
+
+ align:start position:0%
+protocol tells you to read you know and
+ 
+
+ align:start position:0%
+protocol tells you to read you know and
+so this this part is is important in the
+
+ align:start position:0%
+so this this part is is important in the
+ 
+
+ align:start position:0%
+so this this part is is important in the
+G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay a questions before we break okay so
+
+ align:start position:0%
+okay a questions before we break okay so
+ 
+
+ align:start position:0%
+okay a questions before we break okay so
+after the we'll take a five minutes
+
+ align:start position:0%
+after the we'll take a five minutes
+ 
+
+ align:start position:0%
+after the we'll take a five minutes
+break and then we'll talk quickly about
+
+ align:start position:0%
+break and then we'll talk quickly about
+ 
+
+ align:start position:0%
+break and then we'll talk quickly about
+the low degree test wrap up the
+
+ align:start position:0%
+the low degree test wrap up the
+ 
+
+ align:start position:0%
+the low degree test wrap up the
+information Theory and go to
+
+ align:start position:0%
+information Theory and go to
+ 
+
+ align:start position:0%
+information Theory and go to
+cryptography okay
\ No newline at end of file
diff --git a/L98VIorbFB0.txt b/L98VIorbFB0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f70e683762c35ad20c1ccd2514c086c9c4213858
--- /dev/null
+++ b/L98VIorbFB0.txt
@@ -0,0 +1,2719 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to
+
+lecture number 9.
+
+In this lecture, I would like
+to discuss with you the
+
+solution of equilibrium
+equations in static analysis.
+
+In the earlier lectures, we
+derived equations KU equals R.
+
+And we now have to solve
+these equations for the
+
+displacements stored
+in the vector U.
+
+This is an important phase of
+the finite element analysis,
+
+because much of the
+computational effort goes into
+
+the solution of these
+equations.
+
+In the earliest finite element
+analyses, iterative methods
+
+were used, among them the
+Gauss-Seidel method.
+
+Now, the basic disadvantage of
+using an iterative method is
+
+that we do not know how many
+iterations have to be
+
+performed for solution, and thus
+it is very difficult to
+
+estimate the total solution
+effort to solve the equations
+
+KU equals R. Now we use almost
+exclusively direct methods, or
+
+computer programs that are in
+industry, in abundance use,
+
+are basically using
+direct methods.
+
+And these direct methods are
+basically variations of Gauss
+
+elimination, a method that
+Gauss some 100 years ago
+
+proposed for the solution
+of equations.
+
+Now we are talking about
+static condensation,
+
+substructuring, frontal
+solution, LDL transpose
+
+factorization, Cholesky
+decomposition.
+
+We are also talking about the
+crude method, the column
+
+reduction skyline solver.
+
+But all of these methods are
+indeed variations of the basic
+
+Gauss elimination procedure.
+
+These are direct methods
+because the number of
+
+operations can be counted for
+the solution of the equations.
+
+In fact, the number of
+operations for a system with n
+
+equations, a half bandwidth m,
+is 1/2 nm squared, where we of
+
+course use a half bandwidth
+m that is
+
+constant for the system.
+
+If the bandwidth varied, some
+adjustments have to be made to
+
+that variable m.
+
+A mean value has to be used.
+
+However, the important point is
+that we actually can count
+
+the number of operations to
+obtain the solution, which was
+
+not the case in the iterative
+method, because we did not
+
+know how many iterations
+have to be performed.
+
+What I would like to do now
+in this lecture is to very
+
+briefly review with you how the
+basic Gauss elimination is
+
+performed, and then I would like
+to show to you how this
+
+method is indeed the basis
+of static condensation
+
+substructuring, et cetera.
+
+We will finally also consider
+the column reduction skyline
+
+solver, which is very
+effectively used, and that is
+
+in fact the equation solver that
+is used in Sab and the
+
+ADINA program.
+
+Well, I have prepared, as
+before, some view graphs here.
+
+And the first view graph here
+shows a system of equations.
+
+This is the K matrix here.
+
+This is a displacement vector.
+
+This a load vector.
+
+And I will show you later on a
+physical system which in fact
+
+gives this stiffness matrix K.
+But let's look now at the
+
+system simply as an example
+for solving equations.
+
+In the basic Gauss elimination
+procedure,
+
+we proceed as follows.
+
+We subtract a multiple of this
+equation here from the second
+
+equation and the third equation
+in order to produce
+
+here a 0, and to produce
+here a 0.
+
+Well, to obtain a 0 here, we
+have to take 1/5 of this
+
+equation, 1/5 of that equation,
+and subtract it from
+
+this equation.
+
+1/5 because then we obtain a 1
+here, and that 1 knocks that 1
+
+out to obtain a 0.
+
+We have to subtract minus 4/5
+of this equation from the
+
+second equation, and we
+obtain a 0 here, too.
+
+While this process is shown on
+the next view graph, the
+
+result of that process is
+this set of equations.
+
+We now have produced our
+0 here, our 0 here.
+
+Of course we had already
+a 0 here.
+
+We will see later on that the
+matrix in here, the 3-by-3
+
+matrix, bounded by the dash
+lines on the side, in fact
+
+represents a stiffness matrix.
+
+That's important, because a
+stiffness matrix has always
+
+positive elements
+on the diagonal.
+
+Otherwise it is not a
+stiffness matrix.
+
+It does not govern a
+stable structure.
+
+See, here we have diagonal
+elements that are all
+
+positive, and if we can show
+that in the Gauss elimination
+
+procedure, we are still always
+producing new stiffness
+
+matrices, here a 3-by-3 matrix,
+then we directly can
+
+conclude that the diagonal
+elements must remain positive.
+
+Well, in the Gauss elimination
+procedure, the same process
+
+that we use to obtain from the
+4-by-4 or 3-by-3 system is now
+
+carried on to obtain, from
+the 3-by-3 system,
+
+a new 2-by-2 system.
+
+This means that we have to
+subtract a multiple of the
+
+third equation from the fourth
+equation and the fifth
+
+equation in order to obtain
+a 0 here and a 0 here.
+
+For example, 5/14 of the second
+equation is subtracted
+
+from the fourth equation
+to obtain a 0 here.
+
+The result of that operation
+is this matrix here.
+
+Now we have a 2-by-2
+matrix here.
+
+Again, positive elements
+on the diagonal.
+
+In fact, this is a 2-by-2
+stiffness matrix, as I will be
+
+showing to you just now.
+
+Finally we proceed again, once
+more, with the same step, to
+
+produce a 0 here, which means
+that we have to subtract from
+
+this fourth equation a
+minus 20/7 divided by
+
+15/7 of this equation.
+
+And the result, then, is this
+set of equations here.
+
+Notice that we now have a single
+element here, and in
+
+fact, this is a stiffness
+matrix, in this case, a 1-by-1
+
+stiffness matrix, just one
+element, that governs the
+
+behavior of a single spring.
+
+The solution off the equations
+is now completed by solving
+
+for u4 from this relation
+down here.
+
+This is a 1 degree of
+freedom system.
+
+Knowing u4, we can go back to
+this equation here, substitute
+
+u4 in, and the only unknown
+variable is u3.
+
+We solve, therefore, u3
+from this equation.
+
+Now we know u4 and u3.
+
+We now go to this equation.
+
+Knowing u3 u4, the only
+unknown in this
+
+equation here is now u2.
+
+We can calculate u2, and
+repeating the process, we can
+
+calculate u1.
+
+A very simple, straightforward
+procedure,
+
+but extremely powerful.
+
+The result of that solution
+is shown here.
+
+Notice u1 is simply obtained
+by this operation here.
+
+Of course, here we're having
+u2 and u3 in that we
+
+calculated already.
+
+u2 is calculated here. u4
+is calculated here.
+
+It might be easier to actually
+look at it the way we
+
+discussed it just now.
+
+We call that the back
+substitution, because we are
+
+coming from below upwards, and
+in the back substitution, we
+
+have u4 first.
+
+We then calculate u3.
+
+u4 is known now, remember.
+
+We can substitute directly u4
+into here, and we get u3.
+
+Knowing now u3 and u4, we can
+get u2, as shown here.
+
+And finally, we get u2.
+
+This is the basic Gauss
+elimination procedure, an
+
+extremely powerful process.
+
+And I would like to show you
+know how this procedure
+
+relates to the static
+condensation and relates to
+
+the other techniques, and how
+we then actually use this
+
+basic Gauss elimination
+procedure in an actual finite
+
+element program.
+
+Well, static condensation is the
+first topic that I'd like
+
+to talk about.
+
+The basic process is here that
+we are partitioning the total
+
+matrix into the following
+parts.
+
+A Kaa, Kac, Kca, and Kcc part.
+
+The cc part goes with Uc, the
+displacements Uc, which we
+
+want to condense
+statically out.
+
+Notice I'm putting the degrees
+of freedom that I want to
+
+condense out at the bottom
+of the U vector.
+
+Well, by static condensation we
+mean that we express Uc in
+
+terms of Ua, which this equation
+here is obtained from
+
+the bottom equation here.
+
+We then substitute Uc in the
+top equation here, and the
+
+result is this equation here.
+
+Notice that the results can
+be remembered quite easily
+
+because we have here an aa, Kaa,
+then we have an a here, a
+
+c, a cc, ca.
+
+Notice that one might say, just
+for remembering it, that
+
+this c knocks out that c, this
+c knocks out that c, and what
+
+we are left with are aa's.
+
+And that means an aa
+here, an aa here.
+
+So the dimensions are compatible
+of the matrices,
+
+and the result is, I call
+it here, K bar aa.
+
+Of course the right-hand side
+has also changed, because the
+
+components must have an effect
+on the equation that give Ua.
+
+Well, let's look at this
+process, called the static
+
+condensation process, for
+our simple example.
+
+And in this example now,
+I deliberately
+
+put the Kcc up here.
+
+In other words, the Uc degree
+of freedom is now the U1.
+
+This is all our Uc vector only
+containing now one component.
+
+The static condensation was
+originally proposed by
+
+considering or statically
+condensing out of the last
+
+equation, and that is how it's
+usually used also in finite
+
+element analysis.
+
+As an example, if we have
+incompatible modes, we might
+
+condense out the incompatible
+degrees of freedom, just as
+
+shown here.
+
+Or if we have internal degrees
+of freedom in finite elements
+
+that only that only couple with
+the bound the degrees of
+
+freedom of a finite element,
+we could condense them out
+
+this way, and then we would have
+this as the last degree
+
+of freedom.
+
+This would be Uc degrees of
+freedom, and we would condense
+
+them out, just as shown here.
+
+However, in order to show you
+how the static condensation
+
+relates to Gauss elimination, I
+want to look at the example
+
+that we looked at earlier
+already, and this the
+
+partitioning I have used.
+
+U1 now being the UC,
+U2 U4 being the
+
+Ua degrees of freedom.
+
+So I want to now statically
+condense out Uc.
+
+The result of the K bar
+aa is shown here.
+
+Notice we are taking this part,
+this part here, this
+
+part here goes right there,
+this vector here is this
+
+vector here, 1/5 is the inverse
+of Kcc, and this
+
+vector here is that
+vector there.
+
+Well, performing these
+operations, the
+
+result is this one here.
+
+That is the result.
+
+And if we go back to our earlier
+Gauss elimination
+
+procedure, we in fact notice
+that this matrix, K bar aa, is
+
+nothing else than the matrix
+that we derived from the
+
+4-by-4 system when we eliminated
+the non-zero
+
+elements here.
+
+In other words, we subtracted in
+the Gauss elimination from
+
+the second equation and the
+third equation a multiple of
+
+the first equation, we
+got these zeros here.
+
+The result was this
+3-by-3 matrix.
+
+And that 3-by-3 matrix is
+exactly this matrix.
+
+So what have we been doing then
+in the Gauss elimination?
+
+We have really statically
+condensed out the first degree
+
+of freedom, and we have obtained
+a stiffness matrix, K
+
+bar aa, in that Gauss
+elimination procedure.
+
+We can now also look at the
+physics that we have been
+
+going through, and this is,
+in my opinion, a very
+
+important part also.
+
+We start off with this
+matrix here.
+
+Notice the following00 this now
+is the stiffness matrix of
+
+this beam for the U1 to the
+U4 degrees of freedom.
+
+This stiffness matrix actually
+has been derived by finite
+
+differences.
+
+It is a nice example to show
+demonstratively what happens
+
+in the Gauss elimination.
+
+Of course, we could've also used
+a finite element system,
+
+but I chose here a finite
+difference matrix, which is
+
+still a stiffness matrix, and
+which I can use very nicely to
+
+show to you the basic procedures
+of the Gauss
+
+elimination.
+
+So this stiffness matrix
+governed this system here.
+
+Notice the following.
+
+The first column, this column
+here, represents the forces.
+
+When I displace this node, if
+you think of this as a note,
+
+by unity, and keep all
+the other degrees
+
+of freedom to 0--
+
+in other words, if I
+put this deflected
+
+shape onto the beam--
+
+0 displacements right here, but
+a unit displacement here.
+
+That is a unit displacement.
+
+Now notice, these are the forces
+that have to act at
+
+these degrees of freedom
+in order to give
+
+this deflected shape.
+
+The force here, if I
+put them here in
+
+blue, is 5, as an example.
+
+The force here is minus 4.
+
+The force here is 1, and the
+force here turns out to be 0.
+
+That element, or that element,
+of course, we
+
+have a symmetric matrix.
+
+And of course, in the same way,
+we can interpret other
+
+elements in this matrix.
+
+1 column represents always
+forces that have to act onto
+
+the system in order to obtain
+unit displacements at 1 degree
+
+of freedom.
+
+If you look at the I's
+column, then it's the
+
+I's degree of freedom.
+
+And all the other degrees
+of freedom are set to 0.
+
+Well, if we perform our Gauss
+elimination or static
+
+condensation-- we have shown
+that it is the same--
+
+on this system, in the
+first step, we
+
+obtain a 3-by-3 matrix.
+
+Physically, what we have
+obtained is the stiffness
+
+matrix of this system now.
+
+And the following important
+point is now to be noted.
+
+If I look at this column just in
+the same way as I looked at
+
+the first column of the 4-by-4
+system, then this column
+
+represents now the forces that
+are required at these degrees
+
+of freedom to impose a unit
+displacement here at this
+
+degree of freedom, this now
+being unity, with 0
+
+displacements here.
+
+And the force required
+here is 14/5.
+
+That is the force that I have
+to apply here to get a unit
+
+displacement here.
+
+At the same time, I have to
+apply here a force of minus
+
+16/5, and I have to apply
+here a force of 1.
+
+So I'm talking again about
+forces acting onto the system
+
+in this matrix here.
+
+And these forces are stored in
+the columns or the rows off
+
+the matrix, and in the I's
+column or row, I have the
+
+forces required to impose a unit
+displacement at the I's
+
+degree of freedom with all the
+degrees of freedom being 0.
+
+And the important point is that
+having performed now the
+
+Gauss elimination, here
+I do not have
+
+anymore a degree of freedom.
+
+The system is free
+to go down here.
+
+And that's what we mean by
+static condensation, really.
+
+We have taken a degree of
+freedom out of the system.
+
+Proceeding in the same way, we
+obtain this 2 by 2 system.
+
+Now we only have 2 degrees
+of freedom.
+
+I have condensed out this degree
+of freedom and that
+
+degree of freedom,
+which were there.
+
+The beam is now free to move
+down here, so the deflected
+
+shape corresponding to U3, this
+one here, would be like
+
+that, with 0 displacement
+here, and unit
+
+displacement there.
+
+The forces required at these
+degrees of freedom are stored
+
+in this column here.
+
+Now, we immediately can observe
+that since we are
+
+talking about a physical system
+into which we have to
+
+put energy to deform it, we
+can conclude that these
+
+elements here must be
+positive elements.
+
+In other words, the diagonal
+elements in the stiffness
+
+matrices that we derive
+must be positive.
+
+They must be positive because
+if I push down the U3 degree
+
+of freedom to obtain a unit
+displacement, surely the force
+
+that I have to apply here
+must be positive.
+
+In other words, it must be a
+force into the direction of
+
+the degree of freedom U3.
+
+And that means this must
+be a positive element.
+
+So if, in a Gauss elimination
+procedure, we obtain, all of a
+
+sudden, a negative diagonal
+element, this one or that one,
+
+as an example, then we would
+know that the structure we are
+
+analyzing is unstable.
+
+In the final step of the Gauss
+elimination, we obtain a
+
+single degree of
+freedom system.
+
+And that single degree
+of freedom system
+
+behaves like that.
+
+Notice no more degree
+of freedoms here.
+
+And the equation--
+
+I have to apologize that this
+matrix has been written a
+
+little bit down.
+
+It should be a little
+bit higher.
+
+They should, of course, be
+aligned these three.
+
+But basically, we have 5/6
+times U4 equals 7/6.
+
+And this here is really
+nothing else than the
+
+stiffness of a spring.
+
+A spring K having
+us a number 5/6.
+
+In other words, a spring
+stiffness of 5/6 here.
+
+This is U4, the U4 degree
+of freedom.
+
+And the force applied to
+that spring is 7/6.
+
+We have a single degree
+of freedom system.
+
+But notice that this single
+degree of freedom system, this
+
+stiffness now, K equals 5/6,
+contains really all the
+
+physical properties
+of that beam.
+
+The effect of the other degrees
+of freedom, U1, U2,
+
+U3, have been carried over into
+this spring stiffness.
+
+Similarly, 7/6 is the force
+which is a result off the
+
+other forces that were
+applied to the
+
+other degrees of freedom.
+
+And now from the single degree
+of freedom system, of course,
+
+we can solve for U4, and then we
+go back to the 2 degree of
+
+freedom system to solve
+for U3, and so on.
+
+By that back substitution
+process, we obtain thus the
+
+displacement that the beam
+is actually undergoing.
+
+So the important point is that
+when we do perform Gauss
+
+elimination, we really operate
+always on physical systems.
+
+We operate always from one
+stiffness matrix on to another
+
+stiffness matrix, and the next
+stiffness matrix is basically
+
+obtained by static
+condensation.
+
+We are statically condensing
+out 1 degree of
+
+freedom after the next.
+
+Well, if that is very well
+understood, and I urge you to
+
+read up in the book on this
+procedure, then I think you
+
+can very well appreciate how
+the substructuring process,
+
+frontal solution method,
+directly relates, again, to
+
+Gauss elimination.
+
+And here I summarize once the
+basic procedure that we use in
+
+substructuring analysis.
+
+We really go through static
+condensation on the internal
+
+degrees of freedom of
+a substructure.
+
+Here I'm showing a substructure,
+which is an
+
+assemblage, in this case, of
+the plane stress 4-node
+
+elements, just for
+illustration.
+
+Of course, there could be beam
+elements internally here or
+
+externally here.
+
+There could be shell elements.
+
+Any kind of elements.
+
+But the important point is that
+we have an assemblage of
+
+elements, which by itself,
+of course, gives
+
+us a structure already.
+
+We use static condensation on
+the internal degrees of
+
+freedom of the substructure.
+
+Well, the result, then, is a
+new stiffness matrix of the
+
+substructure involving boundary
+
+degrees of freedom only.
+
+Let us look, then,
+at this example.
+
+Here we have 2 degrees of
+freedom at each node.
+
+At the boundary nodes, which are
+shown solid, here, and the
+
+hollow points here, the
+circles here are
+
+the internal nodes.
+
+2 degrees of freedom at each.
+
+The result is that we have a
+50-by-50 stiffness matrix,
+
+because we have 1, 2, 3, 4, 5
+nodes along this length, and 5
+
+layers this way.
+
+So 25 nodes times 2 degrees of
+freedom per node gives us a
+
+50-by-50 stiffness matrix.
+
+Now what we do in the
+substructuring analysis, we
+
+statically condense out the
+internal degrees of freedom,
+
+just in the way I have shown
+how we condense out in that
+
+beam element, in that beam
+analysis, U1 to U3, the same
+
+way we are condensing out the
+internal degrees of freedom.
+
+Notice that we do not need to
+perform Gauss elimination from
+
+U1 to U3 or U4 onwards.
+
+We could also first deal with
+U2, then with U4, then with
+
+U1, and then solve for U3.
+
+So we have really a lot of
+flexibility in the Gauss
+
+elimination procedure.
+
+The important point is that now
+we're using it to condense
+
+these internal degrees
+of freedom out.
+
+The result, then, is a stiffness
+matrix that only
+
+involves the boundary
+degrees of freedom.
+
+Now in this case, we have 1,
+2, 3, 4, 5 nodes here.
+
+Another 5 is 10.
+
+3 here and 3 here means 16,
+times 2 means it's going to be
+
+is 32 by 32 stiffness matrix.
+
+Notice that the internal degrees
+of freedom have been
+
+statically condensed out, which
+means that if I impose,
+
+for example, a unit displacement
+here, keeping all
+
+the other displacements 0 at
+the other nodes, and I keep
+
+this one also 0, then in this
+case, I would have internal
+
+displacements at these nodes.
+
+Whereas in this case, if I put
+a unit displacement only
+
+corresponding to this degree of
+freedom and keep all other
+
+displacements equal to 0, I
+would have 0 displacements at
+
+these nodes, at these points.
+
+Here these nodes are free to go
+wherever they want to go in
+
+the finite element solution.
+
+And if I put a unit displacement
+on here, they
+
+will be taking on a
+particular value.
+
+These nodal displacements will
+take on a particular value.
+
+What we really have derived,
+and this is important, is a
+
+new stiffness matrix.
+
+A new, we might call it, element
+stiffness matrix.
+
+A superelement, or substructure
+stiffness matrix.
+
+These are all equivalent words
+that, however, only involve
+
+boundary degrees of freedom.
+
+This is now a new finite element
+that can be used just
+
+as any ordinary finite element
+in the assemblage process to
+
+obtain the stiffness matrix
+of the complete structure.
+
+Let me show to you
+a simple example.
+
+Here is a very simple structure,
+a truss element
+
+that has only 3 degrees
+of freedom.
+
+U1, U2, U3.
+
+The stiffness matrix of
+that truss element is
+
+shown here as 3-by-3.
+
+Matrix here, we see U1,
+U2, U3, and the forces
+
+corresponding to these degrees
+of freedom, of course, are
+
+listed here.
+
+The objective in this example is
+to statically condense out
+
+this degree of freedom, and
+thus obtain a new element
+
+stiffness matrix that only
+involve the boundary degrees
+
+of freedom.
+
+Well, the first step that I've
+pursued here was to rearrange
+
+the equation so as to have U1
+and U3 as the top equations,
+
+and U2 as the bottom equation.
+
+So we want to do static
+condensation now from the
+
+back, or from the bottom, the
+way it's usually done.
+
+And it's usually done that way
+because it is numerically
+
+effective to proceed that way.
+
+The result, then,
+is shown here.
+
+We write down just
+to identify, to
+
+use the various parts.
+
+This matrix here is this
+2-by-2 matrix.
+
+This minus 20, minus 28
+is that one here.
+
+Here we get the Kcc inverse,
+which is this part here, and
+
+then of course here we have
+this vector, shown here.
+
+If we perform these
+multiplications here, we
+
+obtain this stiffness
+matrix here.
+
+A 1 minus 1 minus 11 with
+a constant in front.
+
+Of course, the load vector
+also has changed.
+
+There is a carry over from the
+2 degree of freedom in to the
+
+1 and 3 degrees of freedom.
+
+The U2 degree of freedom then
+can be recovered via this
+
+equation here, going back to
+the original equation.
+
+The important point is that
+we have now obtained the
+
+stiffness matrix of the truss
+element, this stiffness matrix
+
+of the trust element, involving
+U1 and U3 only.
+
+U2 is not anymore present.
+
+It has been statically
+condensed out.
+
+The U2 will adjust itself to a
+particular value, and that
+
+value, of course, is
+given right here.
+
+But the stiffness matrix that
+we have now here only
+
+corresponds to U1 and U3.
+
+Well, that process can then
+be repeated, and we can go
+
+through a process that we call
+multilevel substructuring.
+
+In other words, we don't
+just go once through a
+
+substructuring process, but
+we go repeatedly through
+
+substructuring processes.
+
+And basically, what we are doing
+is we are solving the
+
+system of equations KU equals R
+of the complete system in a
+
+very effective way.
+
+Let me show you here
+an example.
+
+Here we have a simple
+truss assemblage.
+
+We have 1, 2, 3, 4 elements.
+
+The important point
+is here that the
+
+elements are all similar.
+
+The area is varying 2A1,
+4A1, 8A1, 16A1.
+
+And what I want to do is,
+I want to deal now, via
+
+substructuring with the
+equations to obtain a very
+
+effective solution.
+
+The first step is to look at
+this element, which involves
+
+U1 and U3 and U2.
+
+And here you see, once more,
+a sketch of that element.
+
+That is the element here.
+
+Now I condense out U2, and
+that's what we just did in the
+
+previous example.
+
+The only degrees of freedom
+that we are left with,
+
+then, are U1 U3.
+
+So now we have an element
+stiffness matrix, this element
+
+stiffness matrix, but in terms
+of U1 and U3 only.
+
+The next step, then,
+is to say, let
+
+us repeat this process.
+
+Let us now say, since we have
+this element stiffness matrix
+
+here in terms of U1 and U3 only,
+and since this adamant
+
+is similar to this element here,
+there is only a scalar
+
+involved because the area is
+varying as shown, from A1 to
+
+2A1 to 4A1 and so on, we can
+use this stiffness matrix
+
+here, this element stiffness
+matrix, which, however, is
+
+already a substructure the way
+I've defined it, to assemble
+
+the stiffness matrix
+corresponding to
+
+both of these elements.
+
+And that process is
+schematically shown here.
+
+This stiffness matrix now will
+involve U1, U3, and U5.
+
+Notice U2 is gone, and the
+important point U4 is gone
+
+also, because I've dealt with
+U2, I have statically
+
+condensed out U2, and by that,
+of course, I also have
+
+statically condensed out U4
+simultaneously, because I'm
+
+using this element stiffness
+matrix here again.
+
+So U4 is also gone already.
+
+And now all I need to do is
+condense out U3, and I obtain
+
+a second level substructure,
+which I can use again now to
+
+assemble this element here
+with that element.
+
+And that is shown on the
+next view graph here.
+
+I repeat that process using this
+element here now, which
+
+is this part here, involving
+only U1 and U5, and this
+
+element here, which is similar
+to that element.
+
+Again, an area variation
+there, of course.
+
+And I obtain an element
+stiffness matrix, or a
+
+structural stiffness matrix,
+whichever way you want to look
+
+at it, that involves U1,
+U5, and U9 only.
+
+I can now statically
+condense out U5.
+
+The only unknowns I'm left with
+are U1 and U9, and of
+
+course then I can simply
+solve for U1 and U9.
+
+Of course, we would have
+to have also one of the
+
+displacement being
+prescribed to
+
+actually perform a solution.
+
+Otherwise we have a rigid
+body mode in the system.
+
+Assuming that, say, U1 is 0, we
+now would impose U1 being
+
+0, solve for U9, go back, solve
+for U5, and proceed
+
+backwards to solve for all
+the displacements.
+
+The important point is that
+via this substructuring
+
+process, a multilevel
+substructuring process, we
+
+have saved operations.
+
+We have saved operations because
+in this particular
+
+case, you see, I have condensed
+out these degrees of
+
+freedom already, and I use this
+fact in this assemblage
+
+process and solution in such a
+way as that I do not need to
+
+condense out these degrees of
+freedom, that I do not need to
+
+deal with these degrees of
+freedom again, because I've
+
+dealt with them in effect
+already by condensing out
+
+these degrees of freedom here.
+
+There are also other
+advantages using
+
+substructuring, and one
+important advantage that I
+
+should mention is that in the
+input definition phase, we
+
+only need to define the
+elements, nodal points, and so
+
+on of a typical substructure,
+and we can use that definition
+
+in a computer program, then,
+again and again, to assemble
+
+the complete structure.
+
+In other words, if I have
+defined, typically for a
+
+high-rise building, one typical
+floor, and I have
+
+assembled the floor stiffness
+matrix with columns, beams,
+
+and so on, that pertain to
+that floor, if I then
+
+statically condense out the
+degrees of freedom that we
+
+want to condense out for that
+part of the substructure, I
+
+can use that floor substructure,
+so to say, again
+
+and again, to assemble the
+complete building structure.
+
+And this means I only have to
+define really the particular
+
+substructure input, and I
+deal, then, with that
+
+substructure numerically,
+as I have
+
+shown here in the example.
+
+The next important procedure
+that I like to discuss very
+
+briefly with you is the
+frontal solution.
+
+And the frontal solution really,
+again, only represents
+
+a variation of the basic Gauss
+elimination procedure.
+
+It represents, really, a static
+condensation procedure.
+
+And that static condensation,
+however, is performed in a
+
+particular way.
+
+And this is really where the
+advantages of the frontal
+
+solution can lie.
+
+It's performed via looking
+at the elements.
+
+Let me describe to you
+the basic process.
+
+Here we have, as an example, a
+two-dimensional plane stress
+
+element mesh.
+
+We have 4-node elements, as
+shown here, element 1, element
+
+2, element 3, element 4,
+q, q plus 1, and so on.
+
+In other words, there's a whole
+lay of elements this
+
+way, and that way, and so on.
+
+This mesh could represent, for
+example, a cantilever plate
+
+that acts in plane stress.
+
+In the frontal solution, the
+solution of the KU equals R
+
+equation is performed
+by elements.
+
+So we're putting in element 1,
+which couples into node 1,
+
+node 2, node m, and
+node n plus 1.
+
+Since the degrees of freedom
+at node 1 only obtain
+
+stiffness from element 1, and
+no other element, the
+
+assemblage of this element
+into the global structure
+
+stiffness matrix gives
+the only stiffness
+
+contribution at node 1.
+
+Therefore, we have the final
+equations at node 1, and we
+
+can deal with them already.
+
+And that's how the frontal
+solution proceeds now.
+
+It statically condenses out
+these degrees of freedom.
+
+Then we move on to the
+next node of element
+
+1, this node here.
+
+However, this node gets
+stiffness from element
+
+1 and element 2.
+
+So in order to obtain the final
+equations here, we have
+
+to add the element 2 stiffness
+matrix to the element 1
+
+stiffness matrix.
+
+And that means in this way,
+then, of course, we obtain the
+
+final equation, corresponding
+to node 2.
+
+We now can statically condense
+out the degrees of
+
+freedom at node 2.
+
+We then move on to the next
+node, involving element 1 and
+
+element 2, which
+is node 3, say.
+
+And now we have to, however,
+assemble the stiffness matrix
+
+of elements 3, also into the
+equations that we have
+
+assembled already.
+
+Having done so, we can now use
+static condensation to
+
+condense out these degrees
+of freedom.
+
+We proceed, therefore, via
+elements, and we are talking
+
+about a wave front--
+
+which is this one for node 1,
+this is the wave front for
+
+node 2, this is the
+wave front--
+
+in other words, what we are
+saying is, the wave front
+
+really embodies or contains all
+the elements that we need
+
+to have assembled before
+we can condense
+
+out degrees of freedom.
+
+To condense out the degrees of
+freedom at node 2, we have to
+
+have a wave front such
+as shown here.
+
+We have to have assembled
+element 1 and 2, because
+
+element 1 and element 2 give
+stiffness to node 2.
+
+The important point is that we
+are proceeding via static
+
+condensation from node 1 to
+node 2 and so on, and this
+
+means really that we
+are performing
+
+Gauss elimination again.
+
+The process is summarized
+here once more.
+
+The frontal solution consists
+of successive static
+
+condensation of nodal
+degrees for freedom.
+
+The solution is performed
+in the order
+
+of the element numbering.
+
+That's important.
+
+Same number of operations are
+performed in the frontal
+
+solution as in the skyline
+solution, if the element
+
+numbering in the wave front
+solution corresponds to the
+
+nodal point numbering in
+the skyline solution.
+
+So if the element numbering
+in the frontal solution
+
+corresponds to the nodal point
+numbering in the skyline
+
+solution, we perform in the
+skyline solution, which I have
+
+not really talked about yet, and
+that's what I want to get
+
+on now, the same number
+of operations as
+
+in the frontal solution.
+
+By corresponding, I mean in this
+particular case here, we
+
+would condense out in the
+frontal solution the degrees
+
+of freedom at node 1, then 2,
+then 3, then 4, and so on.
+
+And of course, in the skyline
+solution, or in the Gauss
+
+elimination procedure, we also
+proceed via node 1, 2,
+
+3, 4, and so on.
+
+So in this particular example,
+the frontal solution and the
+
+skyline solution would give the
+same number of operations.
+
+Well, let me go on to the
+skyline solution, then.
+
+And the basis of that solution
+is LDL transpose
+
+factorization.
+
+Basically again, Gauss
+elimination.
+
+The basic step here
+is the following.
+
+We are having our stiffness
+matrix, K here, and now I'm
+
+going back to that example which
+I discussed earlier, the
+
+beam example.
+
+We're talking about the 4-by-4
+stiffness matrix again.
+
+We're using this stiffness
+matrix, and we premultiply it
+
+by an L1 inverse matrix,
+this matrix here.
+
+In fact we never perform
+formally this
+
+premultiplication via matrix,
+because what this does is, it
+
+subtracts a multiple of this
+first row from the rows below
+
+it to update a 0 here
+and a 0 there.
+
+That's all this
+premultiplication does.
+
+And the result is this matrix
+here, which I've shown to you
+
+earlier already.
+
+The next step is then
+to operate on this
+
+matrix in the same way.
+
+However, before doing so, let me
+show you here a view graph
+
+in which I have written out
+specifically the L1 inverse.
+
+And the important point, L1.
+
+Notice that L1, the inverse of
+this matrix, is obtained by
+
+trivial operation.
+
+Namely, simply changing the plus
+here to a minus sign, and
+
+the minus sign to a plus here.
+
+Changing the signs of the
+off-diagonal elements gives us
+
+directly the inverse
+of that matrix.
+
+Well, having obtained,
+therefore, via this operation,
+
+or having carried out via this
+operation, I should say, the
+
+first step of the basic Gauss
+elimination procedure, namely
+
+subtracting the top row from
+the rows below it to obtain
+
+zeroes in the first column below
+the diagonal element, we
+
+proceed in the same way.
+
+and via this procedure here--
+
+now, of course, we have an L2
+inverse, and so on-- we obtain
+
+what we call an upper
+triangular matrix.
+
+S, an upper triangular matrix.
+
+Zeroes all below the diagonal,
+and only non-zero elements
+
+right here.
+
+Of course, if the matrix has a
+bandwidth originally, that
+
+bandwidth would be preserved,
+and we would have no non-zero
+
+elements outside that band.
+
+In other words, all elements
+outside the band would, in
+
+fact, be also zero elements.
+
+This upper triangular matrix,
+then, obtained--
+
+this is the S matrix, here--
+
+will be used in the
+back substitution.
+
+This is here the element that
+gives us the single degree of
+
+freedom stiffness, which I
+talked about earlier, from
+
+which we can solve Un.
+
+Here I'm talking about
+a general case with
+
+n degrees of freedom.
+
+However, looking at this
+equation, let us first
+
+identify that we can put all of
+these inverse matrices onto
+
+the right-hand side, and we
+obtain this equation here.
+
+Now notice that this L1 is
+obtained by trivial operation
+
+from L1 inverse.
+
+The same holds for
+L2 and so on.
+
+So we never really had
+to invert a matrix to
+
+obtain this part here.
+
+Furthermore, this L1 was an
+identity matrix with only
+
+non-zero, off-diagonal elements
+in the first column.
+
+This one is a matrix which
+looks like the identity
+
+matrix, but has also non-zero,
+off-diagonal elements in the
+
+second column.
+
+And so on.
+
+And the product of these
+matrices here, then, is very
+
+simply obtained by writing
+the 1's into the diagonal
+
+positions, and the off-diagonal
+elements here are
+
+those of L1 in the first column,
+those of L2 in the
+
+second column, and so on.
+
+So even this multiplication is
+obtained in a very simple way.
+
+We only need to write the first
+column of L1 into here,
+
+the second column of L2
+into here, the third
+
+column of L3 into here.
+
+And the result, all of that,
+I call the L matrix.
+
+Now notice that once again, we
+do not perform any matrix
+
+multiplication.
+
+We have n minus 1 matrices here,
+but we do not perform a
+
+matrix multiplication, because
+all we do is, we take the
+
+first column of L1 and put it
+into the first column of L.
+
+The second column of L2 is the
+second column in L. The n
+
+minus second column in L is
+nothing else than the n minus
+
+second column in L n minus 2.
+
+And so on.
+
+The result, therefore, is that
+we have written k equal to Lf,
+
+L being equal to this
+product here.
+
+Now because K is symmetric, we
+can, in fact, write this F
+
+matrix here as D times L
+transposed, where d is a
+
+diagonal matrix, dii
+being equal to sii.
+
+So now we have factorized the K
+matrix into LDL transposed.
+
+The d elements, or the dii
+elements, must all be positive
+
+if our structure is stable,
+as I pointed out earlier.
+
+The Cholesky factorization,
+just by remark, uses this
+
+form, K being L curl times L
+curl transpose, where we
+
+should note that L curl is
+really nothing else than L
+
+times d to the 1/2, where d to
+the 1/2 is obtained by using
+
+the D matrix and taking
+square roots of
+
+the diagonal elements.
+
+In other words, the ith
+elemental of d to the 1/2 is
+
+nothing else than square
+root out of dii.
+
+Well, having performed the LDL
+transpose factorization, we
+
+now are ready to solve the
+equations, and they are solved
+
+in the following steps.
+
+We have LV equals R, where V
+is defined as shown here.
+
+Notice that if I were to put
+this part into there, I really
+
+obtain nothing else than LDL
+transpose times U equals R,
+
+where this is, of course,
+nothing else than K times U
+
+equals R, if I were
+to substitute
+
+from here into there.
+
+However, we separate these two
+steps out, and we call this
+
+the forward reduction of R,
+which is really obtained by
+
+subtracting specific elements
+of R from other elements.
+
+We never really perform
+a matrix product here.
+
+We write it that way, but
+really, it means nothing else
+
+than taking, say, the ith
+element off R and subtracting
+
+that element, or multiple of
+that element, from the
+
+elements below it.
+
+That is a typical operation
+performed when
+
+we form the V vector.
+
+Having obtained V, we go back to
+this equation here, and we
+
+perform this step.
+
+Notice that this step is nothing
+else than the division
+
+off the V elements by
+the D elements.
+
+In other words, here we take
+Vi and divide it by dii.
+
+The final step, then, is the
+back substitution, which gives
+
+us U. The back substitution
+is performed
+
+as I discussed earlier.
+
+Already we're going from UN,
+from the last degree of
+
+freedom, upwards to calculate
+the values of
+
+the degrees of freedom.
+
+Let us now look at the actual
+implementation.
+
+The implementation has
+to be performed very
+
+effectively, of course.
+
+All I have been giving to
+you now so far were the
+
+mathematical equations that we
+are basically operating on.
+
+The LDL transpose factorization
+is, of course, a
+
+way of writing a set of steps
+of solution that we are
+
+performing.
+
+However, we want to perform
+them as effectively as
+
+possible, and the scheme that
+we're using is related,
+
+really, to the crude scheme--
+
+we call it the column
+reduction scheme--
+
+that we are going through for
+the solution of the equation.
+
+And the procedure that we're
+using is as follows.
+
+Here we have the stiffness
+matrix.
+
+Notice that we only store
+the upper part.
+
+Since we have a asymmetric
+matrix, we can directly obtain
+
+the lower part elements from
+the upper part elements.
+
+We do not need to store them
+in the computer program.
+
+We also perform the Gauss
+elimination in a very, you
+
+might say, strange way, when
+you look at it first.
+
+And the way we're performing
+it is the following.
+
+That we are reducing
+this column first.
+
+In other words, we are
+going column-wise.
+
+We are reducing this
+column first.
+
+The result is that one.
+
+In the next step, then, we are
+going through the reduction of
+
+the next column.
+
+See here, we are now reducing
+this column, and the
+
+result is that one.
+
+The dashed line always is on
+the right-hand side of that
+
+part of the matrix, which has
+already been reduced.
+
+And now we are looking here at
+the third column, and this is
+
+the reduction off the third
+column The final step is then
+
+that we are reducing
+the fourth column,
+
+and this is the result.
+
+Now notice that having performed
+these operations
+
+column-wise--
+
+and I have not given
+you the details.
+
+We do not have time
+in this lecture
+
+to look at the details.
+
+The details are in the book, if
+you want to read them up.
+
+All I'd like to convey to you
+now are the procedures that
+
+we're using to show you
+the effectiveness.
+
+Notice that the final result
+here in this operation is the
+
+D matrix on the diagonal and
+the L transpose in the
+
+off-diagonal elements.
+
+And we have done
+it column-wise.
+
+Well, what does this mean,
+then, in practice?
+
+In practice it means
+the following.
+
+Notice that I have now a system
+which has different
+
+column heights for different
+equations.
+
+The column heights are being
+defined by the first non-zero
+
+element in a column.
+
+So this is the column height
+for this last column here,
+
+because this is the
+first non-zero
+
+element in the column.
+
+The zero elements below this
+element here, in general,
+
+become non-zero elements.
+
+In general, not always.
+
+But because they in general
+become non-zero elements, we
+
+have defined our column
+height this way.
+
+And what we are now doing in the
+actual solution is that we
+
+are reducing, column by column,
+just the way I have
+
+shown it, to obtain finally the
+elements of the D matrix
+
+on the diagonal, and the
+elements of the L transpose
+
+matrix in the off-diagonal
+elements here.
+
+And we can do so--
+
+this is important--
+
+by simply replacing elements.
+
+If you go back to an earlier
+step that we looked at, what
+
+we have done here is looked at
+this matrix here, and we, in
+
+the reduction process, simply
+replaced this element by 1/5,
+
+replaced this element by the
+minus 4 element, by minus 8/7,
+
+over and so on.
+
+So we don't need additional
+storage.
+
+We can simply replace
+elements.
+
+In the same way, we proceed
+now here, as shown, on the
+
+next view graph.
+
+Here we have filled in the
+zero element, and the
+
+reduction has been performed
+column after column.
+
+The effectiveness of this whole
+procedure is really seen
+
+on this view graph here, when
+we talk about large systems.
+
+I want to denote here this as
+a large system, because the
+
+high speed core storage is not
+sufficient to store the
+
+whole matrix in.
+
+And so what we have been doing
+is, we are storing
+
+the matrix in blocks.
+
+This is here the first block,
+shown by the dashed line.
+
+This is the second block.
+
+This is the third block, and
+that's the fourth block.
+
+What I'm saying is that we
+have divided the total
+
+stiffness matrix into blocks,
+and in fact, we divided the
+
+blocks in such a way as to be
+able to take always at least
+
+two blocks into core.
+
+In other words, in this solution
+process, we have to
+
+be able to take this
+block into core,
+
+that block into core.
+
+Two blocks.
+
+We also would have to be able to
+take this block into core,
+
+that block into core,
+and so on.
+
+Of course, the way this is
+actually automatized in a
+
+computer program, is that
+we say we have so
+
+much storage available.
+
+Say that we have 40,000 storage
+locations available.
+
+Then for the solution of the
+equations, or for the storing
+
+of the stiffness matrix,
+then 20,000 locations
+
+would be used per block.
+
+And what the solution routine
+simply does-- it counts these
+
+elements and puts this dashed
+line in such a way that 20,000
+
+elements are in here, 20,000
+elements are in here, 20,000
+
+elements are in here,
+and so on.
+
+The solution procedure, or the
+solution of the equation, is
+
+now performed in the
+following way,
+
+using the block structure.
+
+We proceed with the reduction
+off this column, of that
+
+column, of that column
+and that column.
+
+Now, I should point out the
+following important point.
+
+When we do we do reduce this
+column, this column coupled
+
+into the first equation.
+
+So we have to have these
+elements in core.
+
+Of course, since this is 1
+block, and since we can store
+
+that block in core anyway,
+there is no problem.
+
+We can reduce this
+column directly.
+
+These elements that we
+already have obtained
+
+are indeed in core.
+
+Now let's go on to
+the second block.
+
+The second block coupled into
+the first block, because these
+
+elements here couple into
+these equations.
+
+So in order to reduce the second
+block column by column,
+
+we have to have the first
+block in core.
+
+And that's what we do.
+
+We take this block into core and
+reduce the second block.
+
+Having finished the second block
+reduction, we go on to
+
+the fourth block.
+
+And the fourth block now is
+reduced by first taking the
+
+first block into core, because
+the first block also couples
+
+into the third block.
+
+Then taking the second block
+into core together with this
+
+one, and reducing this one, and
+then of course, finally,
+
+we reduce this one.
+
+So the general procedure,
+therefore, is that we take a
+
+particular block into core that
+we want to reduce, we
+
+have reduced already all the
+previous blocks, we have
+
+storage available also for one
+of the previous blocks, and we
+
+sequentially take the previous
+blocks into core to take into
+
+account all the coupling that
+these previous blocks have
+
+onto the current block that
+we want to reduce.
+
+In this example, we're taking
+this block into core.
+
+We then take first also
+this block into core.
+
+That means we have two
+blocks in core.
+
+We take the effect of
+this block into
+
+account onto that block.
+
+Then we throw this book out.
+
+We take this block into core.
+
+We take the effect of this block
+into account onto this
+
+block, and finally, we reduce
+the block by itself.
+
+In the same way, we would
+proceed with this block, just
+
+as another example.
+
+We take this block
+into a core.
+
+This one couples into all
+previous blocks, so what we
+
+have to do is take this into
+core, and first take this into
+
+core, take the effect of this
+coupling into account onto
+
+this block, throw this out, take
+this one into core, put
+
+this block coupling onto that
+block, throw this out, take
+
+this one into core, and finally
+take the effect of
+
+this block coupling onto that
+one into account, and finally
+
+then, of course, reduce
+this block by itself.
+
+This, then, completes
+the complete
+
+solution of a large system.
+
+I only was able to give you
+the basic principles, the
+
+basic ideas.
+
+Some of the details are
+described in the textbook, and
+
+you can read up there
+further on it.
+
+Thank you very much for
+your attention.
+
+This was all what I wanted
+to say in this lecture.
\ No newline at end of file
diff --git a/LCiH8faydGk.txt b/LCiH8faydGk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09653cdeee8c8c082954400cba63e93ba49a7010
--- /dev/null
+++ b/LCiH8faydGk.txt
@@ -0,0 +1,2859 @@
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+
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+we're now at story board 19 panel B in
+the last lecture I mentioned that we're
+
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+the last lecture I mentioned that we're
+ 
+
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+the last lecture I mentioned that we're
+going to be looking at several special
+
+ align:start position:0%
+going to be looking at several special
+ 
+
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+going to be looking at several special
+cases with regard to the metabolism of
+
+ align:start position:0%
+cases with regard to the metabolism of
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+
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+cases with regard to the metabolism of
+fatty acids the first special case
+
+ align:start position:0%
+fatty acids the first special case
+ 
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+ align:start position:0%
+fatty acids the first special case
+concerns and metabolism of fatty acids
+
+ align:start position:0%
+concerns and metabolism of fatty acids
+ 
+
+ align:start position:0%
+concerns and metabolism of fatty acids
+that can already contain double bond you
+
+ align:start position:0%
+that can already contain double bond you
+ 
+
+ align:start position:0%
+that can already contain double bond you
+remember from last time that a double
+
+ align:start position:0%
+remember from last time that a double
+ 
+
+ align:start position:0%
+remember from last time that a double
+bond with a trans configuration forms
+
+ align:start position:0%
+bond with a trans configuration forms
+ 
+
+ align:start position:0%
+bond with a trans configuration forms
+naturally during beta oxidation in the
+
+ align:start position:0%
+naturally during beta oxidation in the
+ 
+
+ align:start position:0%
+naturally during beta oxidation in the
+special case we're going to look at now
+
+ align:start position:0%
+special case we're going to look at now
+ 
+
+ align:start position:0%
+special case we're going to look at now
+the double bond has a sis configuration
+
+ align:start position:0%
+the double bond has a sis configuration
+ 
+
+ align:start position:0%
+the double bond has a sis configuration
+fatty acids with a syst double bond
+
+ align:start position:0%
+fatty acids with a syst double bond
+ 
+
+ align:start position:0%
+fatty acids with a syst double bond
+typically come from membranes one of the
+
+ align:start position:0%
+typically come from membranes one of the
+ 
+
+ align:start position:0%
+typically come from membranes one of the
+ways nature plasticizers our membranes
+
+ align:start position:0%
+ways nature plasticizers our membranes
+ 
+
+ align:start position:0%
+ways nature plasticizers our membranes
+is to make them more fluid by putting in
+
+ align:start position:0%
+is to make them more fluid by putting in
+ 
+
+ align:start position:0%
+is to make them more fluid by putting in
+sis double bonds that bend the fatty
+
+ align:start position:0%
+sis double bonds that bend the fatty
+ 
+
+ align:start position:0%
+sis double bonds that bend the fatty
+acid molecule and reduce stacking
+
+ align:start position:0%
+acid molecule and reduce stacking
+ 
+
+ align:start position:0%
+acid molecule and reduce stacking
+ultimately this reduction in stacking
+
+ align:start position:0%
+ultimately this reduction in stacking
+ 
+
+ align:start position:0%
+ultimately this reduction in stacking
+results in a lowering of the overall
+
+ align:start position:0%
+results in a lowering of the overall
+ 
+
+ align:start position:0%
+results in a lowering of the overall
+melting temperature of that part of the
+
+ align:start position:0%
+melting temperature of that part of the
+ 
+
+ align:start position:0%
+melting temperature of that part of the
+membrane the example I'm going to uses
+
+ align:start position:0%
+membrane the example I'm going to uses
+ 
+
+ align:start position:0%
+membrane the example I'm going to uses
+allele coenzyme a this fatty acid a CL
+
+ align:start position:0%
+allele coenzyme a this fatty acid a CL
+ 
+
+ align:start position:0%
+allele coenzyme a this fatty acid a CL
+coenzyme a comes from oleic acid which
+
+ align:start position:0%
+coenzyme a comes from oleic acid which
+ 
+
+ align:start position:0%
+coenzyme a comes from oleic acid which
+also has the short km notation 18:1
+
+ align:start position:0%
+also has the short km notation 18:1
+ 
+
+ align:start position:0%
+also has the short km notation 18:1
+Delta 9 that is there is a double bond
+
+ align:start position:0%
+Delta 9 that is there is a double bond
+ 
+
+ align:start position:0%
+Delta 9 that is there is a double bond
+nine carbons in from the carboxylate the
+
+ align:start position:0%
+nine carbons in from the carboxylate the
+ 
+
+ align:start position:0%
+nine carbons in from the carboxylate the
+reaction I've shown in panel B goes
+
+ align:start position:0%
+reaction I've shown in panel B goes
+ 
+
+ align:start position:0%
+reaction I've shown in panel B goes
+through three rounds of beta oxidation
+
+ align:start position:0%
+through three rounds of beta oxidation
+ 
+
+ align:start position:0%
+through three rounds of beta oxidation
+resulting in a sis
+
+ align:start position:0%
+resulting in a sis
+ 
+
+ align:start position:0%
+resulting in a sis
+Delta three inwe'll coenzyme a the
+
+ align:start position:0%
+Delta three inwe'll coenzyme a the
+ 
+
+ align:start position:0%
+Delta three inwe'll coenzyme a the
+enzyme Olli Weil coenzyme a isomerase
+
+ align:start position:0%
+enzyme Olli Weil coenzyme a isomerase
+ 
+
+ align:start position:0%
+enzyme Olli Weil coenzyme a isomerase
+will then remove the acidic hydrogen
+
+ align:start position:0%
+will then remove the acidic hydrogen
+ 
+
+ align:start position:0%
+will then remove the acidic hydrogen
+from the two carbon repositioning the
+
+ align:start position:0%
+from the two carbon repositioning the
+ 
+
+ align:start position:0%
+from the two carbon repositioning the
+double bond and then putting that double
+
+ align:start position:0%
+double bond and then putting that double
+ 
+
+ align:start position:0%
+double bond and then putting that double
+bond into trans configuration which is
+
+ align:start position:0%
+bond into trans configuration which is
+ 
+
+ align:start position:0%
+bond into trans configuration which is
+now amenable to further hydration and
+
+ align:start position:0%
+now amenable to further hydration and
+ 
+
+ align:start position:0%
+now amenable to further hydration and
+beta oxidation
+
+ align:start position:0%
+beta oxidation
+ 
+
+ align:start position:0%
+beta oxidation
+overall the isomerase has taken this
+
+ align:start position:0%
+overall the isomerase has taken this
+ 
+
+ align:start position:0%
+overall the isomerase has taken this
+double bond and repositioned it to make
+
+ align:start position:0%
+double bond and repositioned it to make
+ 
+
+ align:start position:0%
+double bond and repositioned it to make
+it a trans double bond that is now able
+
+ align:start position:0%
+it a trans double bond that is now able
+ 
+
+ align:start position:0%
+it a trans double bond that is now able
+to undergo further oxidation by the
+
+ align:start position:0%
+to undergo further oxidation by the
+ 
+
+ align:start position:0%
+to undergo further oxidation by the
+classical beta oxidation pathway let's
+
+ align:start position:0%
+classical beta oxidation pathway let's
+ 
+
+ align:start position:0%
+classical beta oxidation pathway let's
+turn now to panel C of story board 19
+
+ align:start position:0%
+turn now to panel C of story board 19
+ 
+
+ align:start position:0%
+turn now to panel C of story board 19
+second special case that I'd like to
+
+ align:start position:0%
+second special case that I'd like to
+ 
+
+ align:start position:0%
+second special case that I'd like to
+deal with concerns the way that we
+
+ align:start position:0%
+deal with concerns the way that we
+ 
+
+ align:start position:0%
+deal with concerns the way that we
+metabolize fatty acids that have an
+
+ align:start position:0%
+metabolize fatty acids that have an
+ 
+
+ align:start position:0%
+metabolize fatty acids that have an
+uneven that is odd number of carbons in
+
+ align:start position:0%
+uneven that is odd number of carbons in
+ 
+
+ align:start position:0%
+uneven that is odd number of carbons in
+them one example would be the C 15 fatty
+
+ align:start position:0%
+them one example would be the C 15 fatty
+ 
+
+ align:start position:0%
+them one example would be the C 15 fatty
+acid Penta decanoic acid which we get
+
+ align:start position:0%
+acid Penta decanoic acid which we get
+ 
+
+ align:start position:0%
+acid Penta decanoic acid which we get
+from milk fat in this case six rounds of
+
+ align:start position:0%
+from milk fat in this case six rounds of
+ 
+
+ align:start position:0%
+from milk fat in this case six rounds of
+beta oxidation will release six acetyl
+
+ align:start position:0%
+beta oxidation will release six acetyl
+ 
+
+ align:start position:0%
+beta oxidation will release six acetyl
+coenzyme a s but note that we're left
+
+ align:start position:0%
+coenzyme a s but note that we're left
+ 
+
+ align:start position:0%
+coenzyme a s but note that we're left
+with a three carbon residue a carboxylic
+
+ align:start position:0%
+with a three carbon residue a carboxylic
+ 
+
+ align:start position:0%
+with a three carbon residue a carboxylic
+acid called propionyl coenzyme a nature
+
+ align:start position:0%
+acid called propionyl coenzyme a nature
+ 
+
+ align:start position:0%
+acid called propionyl coenzyme a nature
+doesn't like to throw anything away
+
+ align:start position:0%
+doesn't like to throw anything away
+ 
+
+ align:start position:0%
+doesn't like to throw anything away
+it's going to take this three carbon
+
+ align:start position:0%
+it's going to take this three carbon
+ 
+
+ align:start position:0%
+it's going to take this three carbon
+molecule propene ilk away that doesn't
+
+ align:start position:0%
+molecule propene ilk away that doesn't
+ 
+
+ align:start position:0%
+molecule propene ilk away that doesn't
+easily integrate into any other
+
+ align:start position:0%
+easily integrate into any other
+ 
+
+ align:start position:0%
+easily integrate into any other
+biochemical pathways nature is going to
+
+ align:start position:0%
+biochemical pathways nature is going to
+ 
+
+ align:start position:0%
+biochemical pathways nature is going to
+add a carbon to it hence making it into
+
+ align:start position:0%
+add a carbon to it hence making it into
+ 
+
+ align:start position:0%
+add a carbon to it hence making it into
+a four carbon molecule as we'll see that
+
+ align:start position:0%
+a four carbon molecule as we'll see that
+ 
+
+ align:start position:0%
+a four carbon molecule as we'll see that
+four carbon molecule will integrate
+
+ align:start position:0%
+four carbon molecule will integrate
+ 
+
+ align:start position:0%
+four carbon molecule will integrate
+seamlessly into the TCA cycle the
+
+ align:start position:0%
+seamlessly into the TCA cycle the
+ 
+
+ align:start position:0%
+seamlessly into the TCA cycle the
+conversion of the three carbon compound
+
+ align:start position:0%
+conversion of the three carbon compound
+ 
+
+ align:start position:0%
+conversion of the three carbon compound
+into a four carbon compound begins with
+
+ align:start position:0%
+into a four carbon compound begins with
+ 
+
+ align:start position:0%
+into a four carbon compound begins with
+the enzyme propionyl coenzyme a
+
+ align:start position:0%
+the enzyme propionyl coenzyme a
+ 
+
+ align:start position:0%
+the enzyme propionyl coenzyme a
+carboxylase in a few minutes we'll look
+
+ align:start position:0%
+carboxylase in a few minutes we'll look
+ 
+
+ align:start position:0%
+carboxylase in a few minutes we'll look
+at these fine details of how this enzyme
+
+ align:start position:0%
+at these fine details of how this enzyme
+ 
+
+ align:start position:0%
+at these fine details of how this enzyme
+works for now however what it does is
+
+ align:start position:0%
+works for now however what it does is
+ 
+
+ align:start position:0%
+works for now however what it does is
+use the cofactor biotin in order to
+
+ align:start position:0%
+use the cofactor biotin in order to
+ 
+
+ align:start position:0%
+use the cofactor biotin in order to
+introduce a carbon dioxide or co2 into
+
+ align:start position:0%
+introduce a carbon dioxide or co2 into
+ 
+
+ align:start position:0%
+introduce a carbon dioxide or co2 into
+the two carbon or of the propionyl
+
+ align:start position:0%
+the two carbon or of the propionyl
+ 
+
+ align:start position:0%
+the two carbon or of the propionyl
+coenzyme a the two carbon is the middle
+
+ align:start position:0%
+coenzyme a the two carbon is the middle
+ 
+
+ align:start position:0%
+coenzyme a the two carbon is the middle
+carbon of the propia neill group this is
+
+ align:start position:0%
+carbon of the propia neill group this is
+ 
+
+ align:start position:0%
+carbon of the propia neill group this is
+now a branched molecule that's called
+
+ align:start position:0%
+now a branched molecule that's called
+ 
+
+ align:start position:0%
+now a branched molecule that's called
+methylmalonyl coenzyme a next the
+
+ align:start position:0%
+methylmalonyl coenzyme a next the
+ 
+
+ align:start position:0%
+methylmalonyl coenzyme a next the
+molecule is subjected to a carbon chain
+
+ align:start position:0%
+molecule is subjected to a carbon chain
+ 
+
+ align:start position:0%
+molecule is subjected to a carbon chain
+rearrangement that takes the branched
+
+ align:start position:0%
+rearrangement that takes the branched
+ 
+
+ align:start position:0%
+rearrangement that takes the branched
+molecule and linearizes it to form
+
+ align:start position:0%
+molecule and linearizes it to form
+ 
+
+ align:start position:0%
+molecule and linearizes it to form
+succinylcholine Sime a sectional
+
+ align:start position:0%
+succinylcholine Sime a sectional
+ 
+
+ align:start position:0%
+succinylcholine Sime a sectional
+coenzyme a will then enter it directly
+
+ align:start position:0%
+coenzyme a will then enter it directly
+ 
+
+ align:start position:0%
+coenzyme a will then enter it directly
+into the TCA cycle to allow its carbons
+
+ align:start position:0%
+into the TCA cycle to allow its carbons
+ 
+
+ align:start position:0%
+into the TCA cycle to allow its carbons
+to be metabolized fully to co2 in
+
+ align:start position:0%
+to be metabolized fully to co2 in
+ 
+
+ align:start position:0%
+to be metabolized fully to co2 in
+summary nature puts a co2 into the three
+
+ align:start position:0%
+summary nature puts a co2 into the three
+ 
+
+ align:start position:0%
+summary nature puts a co2 into the three
+carbon propia neill co a forming a four
+
+ align:start position:0%
+carbon propia neill co a forming a four
+ 
+
+ align:start position:0%
+carbon propia neill co a forming a four
+carbon branch structure then in an
+
+ align:start position:0%
+carbon branch structure then in an
+ 
+
+ align:start position:0%
+carbon branch structure then in an
+amazing rearrangement that we'll look at
+
+ align:start position:0%
+amazing rearrangement that we'll look at
+ 
+
+ align:start position:0%
+amazing rearrangement that we'll look at
+later the branch molecule is made linear
+
+ align:start position:0%
+later the branch molecule is made linear
+ 
+
+ align:start position:0%
+later the branch molecule is made linear
+forming succinylcholine tur mediate so
+
+ align:start position:0%
+forming succinylcholine tur mediate so
+ 
+
+ align:start position:0%
+forming succinylcholine tur mediate so
+the otherwise useless c3 molecule
+
+ align:start position:0%
+the otherwise useless c3 molecule
+ 
+
+ align:start position:0%
+the otherwise useless c3 molecule
+propionyl coenzyme a is converted to
+
+ align:start position:0%
+propionyl coenzyme a is converted to
+ 
+
+ align:start position:0%
+propionyl coenzyme a is converted to
+something of value lastly let's turn to
+
+ align:start position:0%
+something of value lastly let's turn to
+ 
+
+ align:start position:0%
+something of value lastly let's turn to
+panel D I'm going to deal more with the
+
+ align:start position:0%
+panel D I'm going to deal more with the
+ 
+
+ align:start position:0%
+panel D I'm going to deal more with the
+details of this reaction in a few
+
+ align:start position:0%
+details of this reaction in a few
+ 
+
+ align:start position:0%
+details of this reaction in a few
+minutes but for now what I'd like to say
+
+ align:start position:0%
+minutes but for now what I'd like to say
+ 
+
+ align:start position:0%
+minutes but for now what I'd like to say
+is that there are many sources
+
+ align:start position:0%
+is that there are many sources
+ 
+
+ align:start position:0%
+is that there are many sources
+appropriate
+
+ align:start position:0%
+appropriate
+ 
+
+ align:start position:0%
+appropriate
+not just from odd chain fatty acids in
+
+ align:start position:0%
+not just from odd chain fatty acids in
+ 
+
+ align:start position:0%
+not just from odd chain fatty acids in
+the diet secondly the introduction of
+
+ align:start position:0%
+the diet secondly the introduction of
+ 
+
+ align:start position:0%
+the diet secondly the introduction of
+succinate into the TCA cycle results in
+
+ align:start position:0%
+succinate into the TCA cycle results in
+ 
+
+ align:start position:0%
+succinate into the TCA cycle results in
+an increase in the amount of carbon
+
+ align:start position:0%
+an increase in the amount of carbon
+ 
+
+ align:start position:0%
+an increase in the amount of carbon
+going through the TCA cycle that is this
+
+ align:start position:0%
+going through the TCA cycle that is this
+ 
+
+ align:start position:0%
+going through the TCA cycle that is this
+is truly an antibiotic reaction this is
+
+ align:start position:0%
+is truly an antibiotic reaction this is
+ 
+
+ align:start position:0%
+is truly an antibiotic reaction this is
+an reaction that we can use to increase
+
+ align:start position:0%
+an reaction that we can use to increase
+ 
+
+ align:start position:0%
+an reaction that we can use to increase
+the overall rate of carbon metabolism in
+
+ align:start position:0%
+the overall rate of carbon metabolism in
+ 
+
+ align:start position:0%
+the overall rate of carbon metabolism in
+the TCA cycle we're now going to turn to
+
+ align:start position:0%
+the TCA cycle we're now going to turn to
+ 
+
+ align:start position:0%
+the TCA cycle we're now going to turn to
+storyboard 20 let's look at panel a in
+
+ align:start position:0%
+storyboard 20 let's look at panel a in
+ 
+
+ align:start position:0%
+storyboard 20 let's look at panel a in
+the last lecture on fatty acid
+
+ align:start position:0%
+the last lecture on fatty acid
+ 
+
+ align:start position:0%
+the last lecture on fatty acid
+metabolism I talked about protein Eelco
+
+ align:start position:0%
+metabolism I talked about protein Eelco
+ 
+
+ align:start position:0%
+metabolism I talked about protein Eelco
+a carboxylase which uses biotin to add a
+
+ align:start position:0%
+a carboxylase which uses biotin to add a
+ 
+
+ align:start position:0%
+a carboxylase which uses biotin to add a
+co2 moiety to the middle carbon of
+
+ align:start position:0%
+co2 moiety to the middle carbon of
+ 
+
+ align:start position:0%
+co2 moiety to the middle carbon of
+propionyl coenzyme a this lecture is a
+
+ align:start position:0%
+propionyl coenzyme a this lecture is a
+ 
+
+ align:start position:0%
+propionyl coenzyme a this lecture is a
+chemical interlude in which we're going
+
+ align:start position:0%
+chemical interlude in which we're going
+ 
+
+ align:start position:0%
+chemical interlude in which we're going
+to look at propane eel Co a carboxylase
+
+ align:start position:0%
+to look at propane eel Co a carboxylase
+ 
+
+ align:start position:0%
+to look at propane eel Co a carboxylase
+and several other car box lasers that
+
+ align:start position:0%
+and several other car box lasers that
+ 
+
+ align:start position:0%
+and several other car box lasers that
+are used in biochemistry one of these is
+
+ align:start position:0%
+are used in biochemistry one of these is
+ 
+
+ align:start position:0%
+are used in biochemistry one of these is
+acetate co8 carboxylase this carboxylase
+
+ align:start position:0%
+acetate co8 carboxylase this carboxylase
+ 
+
+ align:start position:0%
+acetate co8 carboxylase this carboxylase
+puts the co2 group onto acetyl co a to
+
+ align:start position:0%
+puts the co2 group onto acetyl co a to
+ 
+
+ align:start position:0%
+puts the co2 group onto acetyl co a to
+make malonyl-coa
+
+ align:start position:0%
+make malonyl-coa
+ 
+
+ align:start position:0%
+make malonyl-coa
+which is the precursor to fatty acids
+
+ align:start position:0%
+which is the precursor to fatty acids
+ 
+
+ align:start position:0%
+which is the precursor to fatty acids
+during the fatty acid biosynthesis
+
+ align:start position:0%
+during the fatty acid biosynthesis
+ 
+
+ align:start position:0%
+during the fatty acid biosynthesis
+reactions let's also look at panel B
+
+ align:start position:0%
+reactions let's also look at panel B
+ 
+
+ align:start position:0%
+reactions let's also look at panel B
+we're also going to be looking at
+
+ align:start position:0%
+we're also going to be looking at
+ 
+
+ align:start position:0%
+we're also going to be looking at
+pyruvate carboxylase which adds a
+
+ align:start position:0%
+pyruvate carboxylase which adds a
+ 
+
+ align:start position:0%
+pyruvate carboxylase which adds a
+carbonyl group to the pyruvic acid
+
+ align:start position:0%
+carbonyl group to the pyruvic acid
+ 
+
+ align:start position:0%
+carbonyl group to the pyruvic acid
+molecule in order to make oxaloacetate
+
+ align:start position:0%
+molecule in order to make oxaloacetate
+ 
+
+ align:start position:0%
+molecule in order to make oxaloacetate
+this is one of the anaplerotic enzymes
+
+ align:start position:0%
+this is one of the anaplerotic enzymes
+ 
+
+ align:start position:0%
+this is one of the anaplerotic enzymes
+that can increase the quantity of carbon
+
+ align:start position:0%
+that can increase the quantity of carbon
+ 
+
+ align:start position:0%
+that can increase the quantity of carbon
+going through the TCA cycle that is it
+
+ align:start position:0%
+going through the TCA cycle that is it
+ 
+
+ align:start position:0%
+going through the TCA cycle that is it
+facilitates and applause as' in the
+
+ align:start position:0%
+facilitates and applause as' in the
+ 
+
+ align:start position:0%
+facilitates and applause as' in the
+biological system let's now look at
+
+ align:start position:0%
+biological system let's now look at
+ 
+
+ align:start position:0%
+biological system let's now look at
+storyboard 21 panel a the carboxyl aces
+
+ align:start position:0%
+storyboard 21 panel a the carboxyl aces
+ 
+
+ align:start position:0%
+storyboard 21 panel a the carboxyl aces
+all use carbon dioxide as their
+
+ align:start position:0%
+all use carbon dioxide as their
+ 
+
+ align:start position:0%
+all use carbon dioxide as their
+carboxylated
+
+ align:start position:0%
+carboxylated
+ 
+
+ align:start position:0%
+carboxylated
+reagent co2 itself is not very soluble
+
+ align:start position:0%
+reagent co2 itself is not very soluble
+ 
+
+ align:start position:0%
+reagent co2 itself is not very soluble
+in water so cells use carbonic anhydrase
+
+ align:start position:0%
+in water so cells use carbonic anhydrase
+ 
+
+ align:start position:0%
+in water so cells use carbonic anhydrase
+in order to hydrate it to form carbonic
+
+ align:start position:0%
+in order to hydrate it to form carbonic
+ 
+
+ align:start position:0%
+in order to hydrate it to form carbonic
+acid the biotin carboxyl a subunit will
+
+ align:start position:0%
+acid the biotin carboxyl a subunit will
+ 
+
+ align:start position:0%
+acid the biotin carboxyl a subunit will
+then phosphorylate the carbonic acid in
+
+ align:start position:0%
+then phosphorylate the carbonic acid in
+ 
+
+ align:start position:0%
+then phosphorylate the carbonic acid in
+order to form a chemically reactive
+
+ align:start position:0%
+order to form a chemically reactive
+ 
+
+ align:start position:0%
+order to form a chemically reactive
+intermediate known as carbonyl phosphate
+
+ align:start position:0%
+intermediate known as carbonyl phosphate
+ 
+
+ align:start position:0%
+intermediate known as carbonyl phosphate
+or carboxy phosphate now carbon dioxide
+
+ align:start position:0%
+or carboxy phosphate now carbon dioxide
+ 
+
+ align:start position:0%
+or carboxy phosphate now carbon dioxide
+by virtue of its structure that is a
+
+ align:start position:0%
+by virtue of its structure that is a
+ 
+
+ align:start position:0%
+by virtue of its structure that is a
+carbon with two electronegative oxygens
+
+ align:start position:0%
+carbon with two electronegative oxygens
+ 
+
+ align:start position:0%
+carbon with two electronegative oxygens
+pulling on it is pre activated for
+
+ align:start position:0%
+pulling on it is pre activated for
+ 
+
+ align:start position:0%
+pulling on it is pre activated for
+nucleophilic attack and as I said a few
+
+ align:start position:0%
+nucleophilic attack and as I said a few
+ 
+
+ align:start position:0%
+nucleophilic attack and as I said a few
+minutes ago co2 is just not present at
+
+ align:start position:0%
+minutes ago co2 is just not present at
+ 
+
+ align:start position:0%
+minutes ago co2 is just not present at
+high enough concentration in the cell
+
+ align:start position:0%
+high enough concentration in the cell
+ 
+
+ align:start position:0%
+high enough concentration in the cell
+for it to be able to add effectively to
+
+ align:start position:0%
+for it to be able to add effectively to
+ 
+
+ align:start position:0%
+for it to be able to add effectively to
+nucleophiles a nucleophile such as the a
+
+ align:start position:0%
+nucleophiles a nucleophile such as the a
+ 
+
+ align:start position:0%
+nucleophiles a nucleophile such as the a
+midnight region of biotin
+
+ align:start position:0%
+midnight region of biotin
+ 
+
+ align:start position:0%
+midnight region of biotin
+would be an example so what the cell
+
+ align:start position:0%
+would be an example so what the cell
+ 
+
+ align:start position:0%
+would be an example so what the cell
+does is use ATP to make carbonyl
+
+ align:start position:0%
+does is use ATP to make carbonyl
+ 
+
+ align:start position:0%
+does is use ATP to make carbonyl
+phosphate which is a very water soluble
+
+ align:start position:0%
+phosphate which is a very water soluble
+ 
+
+ align:start position:0%
+phosphate which is a very water soluble
+molecule it's a very efficient delivery
+
+ align:start position:0%
+molecule it's a very efficient delivery
+ 
+
+ align:start position:0%
+molecule it's a very efficient delivery
+vehicle for carbon dioxide into the
+
+ align:start position:0%
+vehicle for carbon dioxide into the
+ 
+
+ align:start position:0%
+vehicle for carbon dioxide into the
+active site of an enzyme now let's look
+
+ align:start position:0%
+active site of an enzyme now let's look
+ 
+
+ align:start position:0%
+active site of an enzyme now let's look
+at panel B the biotin carboxylase
+
+ align:start position:0%
+at panel B the biotin carboxylase
+ 
+
+ align:start position:0%
+at panel B the biotin carboxylase
+subunit of pyruvate carboxylase has a
+
+ align:start position:0%
+subunit of pyruvate carboxylase has a
+ 
+
+ align:start position:0%
+subunit of pyruvate carboxylase has a
+biotin cofactor at the end of a 14
+
+ align:start position:0%
+biotin cofactor at the end of a 14
+ 
+
+ align:start position:0%
+biotin cofactor at the end of a 14
+angstrom long swinging arm this subunit
+
+ align:start position:0%
+angstrom long swinging arm this subunit
+ 
+
+ align:start position:0%
+angstrom long swinging arm this subunit
+of the enzyme breaks the bicarbonate
+
+ align:start position:0%
+of the enzyme breaks the bicarbonate
+ 
+
+ align:start position:0%
+of the enzyme breaks the bicarbonate
+phosphate bond and releases carbon
+
+ align:start position:0%
+phosphate bond and releases carbon
+ 
+
+ align:start position:0%
+phosphate bond and releases carbon
+dioxide in high concentration in the
+
+ align:start position:0%
+dioxide in high concentration in the
+ 
+
+ align:start position:0%
+dioxide in high concentration in the
+active site biotin on the swinging arm
+
+ align:start position:0%
+active site biotin on the swinging arm
+ 
+
+ align:start position:0%
+active site biotin on the swinging arm
+then attacks the high concentration of
+
+ align:start position:0%
+then attacks the high concentration of
+ 
+
+ align:start position:0%
+then attacks the high concentration of
+carbon dioxide in order to become n
+
+ align:start position:0%
+carbon dioxide in order to become n
+ 
+
+ align:start position:0%
+carbon dioxide in order to become n
+carboxy biotin as shown in this figure
+
+ align:start position:0%
+carboxy biotin as shown in this figure
+ 
+
+ align:start position:0%
+carboxy biotin as shown in this figure
+the n carboxy biotin takes advantage of
+
+ align:start position:0%
+the n carboxy biotin takes advantage of
+ 
+
+ align:start position:0%
+the n carboxy biotin takes advantage of
+its swinging arm to move away from the
+
+ align:start position:0%
+its swinging arm to move away from the
+ 
+
+ align:start position:0%
+its swinging arm to move away from the
+active site at which it acquired the co2
+
+ align:start position:0%
+active site at which it acquired the co2
+ 
+
+ align:start position:0%
+active site at which it acquired the co2
+and then move to a second site on the
+
+ align:start position:0%
+and then move to a second site on the
+ 
+
+ align:start position:0%
+and then move to a second site on the
+enzyme at which the arm releases carbon
+
+ align:start position:0%
+enzyme at which the arm releases carbon
+ 
+
+ align:start position:0%
+enzyme at which the arm releases carbon
+dioxide once again at high concentration
+
+ align:start position:0%
+dioxide once again at high concentration
+ 
+
+ align:start position:0%
+dioxide once again at high concentration
+but this time co2 is released at high
+
+ align:start position:0%
+but this time co2 is released at high
+ 
+
+ align:start position:0%
+but this time co2 is released at high
+concentration in the vicinity of the
+
+ align:start position:0%
+concentration in the vicinity of the
+ 
+
+ align:start position:0%
+concentration in the vicinity of the
+substrate pyruvate pyruvate in order to
+
+ align:start position:0%
+substrate pyruvate pyruvate in order to
+ 
+
+ align:start position:0%
+substrate pyruvate pyruvate in order to
+be a good nucleophile to acquire the co2
+
+ align:start position:0%
+be a good nucleophile to acquire the co2
+ 
+
+ align:start position:0%
+be a good nucleophile to acquire the co2
+probably exists as shown in the figure
+
+ align:start position:0%
+probably exists as shown in the figure
+ 
+
+ align:start position:0%
+probably exists as shown in the figure
+as the pyruvate enolate let me review
+
+ align:start position:0%
+as the pyruvate enolate let me review
+ 
+
+ align:start position:0%
+as the pyruvate enolate let me review
+panel B at this point overall this
+
+ align:start position:0%
+panel B at this point overall this
+ 
+
+ align:start position:0%
+panel B at this point overall this
+reaction has resulted in putting a
+
+ align:start position:0%
+reaction has resulted in putting a
+ 
+
+ align:start position:0%
+reaction has resulted in putting a
+carboxylic acid residue on the 3 carbon
+
+ align:start position:0%
+carboxylic acid residue on the 3 carbon
+ 
+
+ align:start position:0%
+carboxylic acid residue on the 3 carbon
+of pyruvate and this results in the
+
+ align:start position:0%
+of pyruvate and this results in the
+ 
+
+ align:start position:0%
+of pyruvate and this results in the
+formation of oxaloacetate thus
+
+ align:start position:0%
+formation of oxaloacetate thus
+ 
+
+ align:start position:0%
+formation of oxaloacetate thus
+activation of pyruvate carboxylase will
+
+ align:start position:0%
+activation of pyruvate carboxylase will
+ 
+
+ align:start position:0%
+activation of pyruvate carboxylase will
+result in taking a molecule of pyruvate
+
+ align:start position:0%
+result in taking a molecule of pyruvate
+ 
+
+ align:start position:0%
+result in taking a molecule of pyruvate
+and converting it to oxaloacetate this
+
+ align:start position:0%
+and converting it to oxaloacetate this
+ 
+
+ align:start position:0%
+and converting it to oxaloacetate this
+anaplerotic reaction gives the ability
+
+ align:start position:0%
+anaplerotic reaction gives the ability
+ 
+
+ align:start position:0%
+anaplerotic reaction gives the ability
+to increase the volume of carbon that's
+
+ align:start position:0%
+to increase the volume of carbon that's
+ 
+
+ align:start position:0%
+to increase the volume of carbon that's
+cycling in the TCA cycle thus allowing
+
+ align:start position:0%
+cycling in the TCA cycle thus allowing
+ 
+
+ align:start position:0%
+cycling in the TCA cycle thus allowing
+you to be able to increase their overall
+
+ align:start position:0%
+you to be able to increase their overall
+ 
+
+ align:start position:0%
+you to be able to increase their overall
+rate of respiration and as I've said
+
+ align:start position:0%
+rate of respiration and as I've said
+ 
+
+ align:start position:0%
+rate of respiration and as I've said
+several times in the past oxaloacetate
+
+ align:start position:0%
+several times in the past oxaloacetate
+ 
+
+ align:start position:0%
+several times in the past oxaloacetate
+is present at rather limiting
+
+ align:start position:0%
+is present at rather limiting
+ 
+
+ align:start position:0%
+is present at rather limiting
+concentrations within the mitochondrial
+
+ align:start position:0%
+concentrations within the mitochondrial
+ 
+
+ align:start position:0%
+concentrations within the mitochondrial
+matrix so this is a very useful
+
+ align:start position:0%
+matrix so this is a very useful
+ 
+
+ align:start position:0%
+matrix so this is a very useful
+biochemical reaction at this point let's
+
+ align:start position:0%
+biochemical reaction at this point let's
+ 
+
+ align:start position:0%
+biochemical reaction at this point let's
+move on to storyboard 22 and look at
+
+ align:start position:0%
+move on to storyboard 22 and look at
+ 
+
+ align:start position:0%
+move on to storyboard 22 and look at
+panel a let me loop back now and give
+
+ align:start position:0%
+panel a let me loop back now and give
+ 
+
+ align:start position:0%
+panel a let me loop back now and give
+some bigger picture points with regard
+
+ align:start position:0%
+some bigger picture points with regard
+ 
+
+ align:start position:0%
+some bigger picture points with regard
+to carboxylate chemistry pyruvate
+
+ align:start position:0%
+to carboxylate chemistry pyruvate
+ 
+
+ align:start position:0%
+to carboxylate chemistry pyruvate
+carboxylase and the other enzymes of
+
+ align:start position:0%
+carboxylase and the other enzymes of
+ 
+
+ align:start position:0%
+carboxylase and the other enzymes of
+this class have two active sites one of
+
+ align:start position:0%
+this class have two active sites one of
+ 
+
+ align:start position:0%
+this class have two active sites one of
+them is the biotin
+
+ align:start position:0%
+them is the biotin
+ 
+
+ align:start position:0%
+them is the biotin
+box'll age domain where a biotin moiety
+
+ align:start position:0%
+box'll age domain where a biotin moiety
+ 
+
+ align:start position:0%
+box'll age domain where a biotin moiety
+covalently attached to the enzyme will
+
+ align:start position:0%
+covalently attached to the enzyme will
+ 
+
+ align:start position:0%
+covalently attached to the enzyme will
+acquire co2 let's call this step one of
+
+ align:start position:0%
+acquire co2 let's call this step one of
+ 
+
+ align:start position:0%
+acquire co2 let's call this step one of
+the reaction scheme once the blatant on
+
+ align:start position:0%
+the reaction scheme once the blatant on
+ 
+
+ align:start position:0%
+the reaction scheme once the blatant on
+the swinging arm has been n carboxylated
+
+ align:start position:0%
+the swinging arm has been n carboxylated
+ 
+
+ align:start position:0%
+the swinging arm has been n carboxylated
+as in step one the N carboxy biotin
+
+ align:start position:0%
+as in step one the N carboxy biotin
+ 
+
+ align:start position:0%
+as in step one the N carboxy biotin
+moves to site 2 where the substrate is
+
+ align:start position:0%
+moves to site 2 where the substrate is
+ 
+
+ align:start position:0%
+moves to site 2 where the substrate is
+the second site is the biotin
+
+ align:start position:0%
+the second site is the biotin
+ 
+
+ align:start position:0%
+the second site is the biotin
+transferase domain in the example I just
+
+ align:start position:0%
+transferase domain in the example I just
+ 
+
+ align:start position:0%
+transferase domain in the example I just
+used the substrate was pyruvate but it
+
+ align:start position:0%
+used the substrate was pyruvate but it
+ 
+
+ align:start position:0%
+used the substrate was pyruvate but it
+just as easily could have been another
+
+ align:start position:0%
+just as easily could have been another
+ 
+
+ align:start position:0%
+just as easily could have been another
+quote-unquote carboxylation substrate
+
+ align:start position:0%
+quote-unquote carboxylation substrate
+ 
+
+ align:start position:0%
+quote-unquote carboxylation substrate
+for example propia Neel Co a in the case
+
+ align:start position:0%
+for example propia Neel Co a in the case
+ 
+
+ align:start position:0%
+for example propia Neel Co a in the case
+of pyruvate as we just saw
+
+ align:start position:0%
+of pyruvate as we just saw
+ 
+
+ align:start position:0%
+of pyruvate as we just saw
+it's the pyruvate enolate that becomes
+
+ align:start position:0%
+it's the pyruvate enolate that becomes
+ 
+
+ align:start position:0%
+it's the pyruvate enolate that becomes
+carboxylated insight 2 in order to form
+
+ align:start position:0%
+carboxylated insight 2 in order to form
+ 
+
+ align:start position:0%
+carboxylated insight 2 in order to form
+the final product oxaloacetate this
+
+ align:start position:0%
+the final product oxaloacetate this
+ 
+
+ align:start position:0%
+the final product oxaloacetate this
+carboxylation of substrate is the second
+
+ align:start position:0%
+carboxylation of substrate is the second
+ 
+
+ align:start position:0%
+carboxylation of substrate is the second
+and final step of the overall reaction
+
+ align:start position:0%
+and final step of the overall reaction
+ 
+
+ align:start position:0%
+and final step of the overall reaction
+take a look at panel B now let me give
+
+ align:start position:0%
+take a look at panel B now let me give
+ 
+
+ align:start position:0%
+take a look at panel B now let me give
+you a second example of carboxylase
+
+ align:start position:0%
+you a second example of carboxylase
+ 
+
+ align:start position:0%
+you a second example of carboxylase
+chemistry in this case our substrate
+
+ align:start position:0%
+chemistry in this case our substrate
+ 
+
+ align:start position:0%
+chemistry in this case our substrate
+will be asked to tell coenzyme a we're
+
+ align:start position:0%
+will be asked to tell coenzyme a we're
+ 
+
+ align:start position:0%
+will be asked to tell coenzyme a we're
+going to use the same chemistry we
+
+ align:start position:0%
+going to use the same chemistry we
+ 
+
+ align:start position:0%
+going to use the same chemistry we
+described a minute ago for pyruvate but
+
+ align:start position:0%
+described a minute ago for pyruvate but
+ 
+
+ align:start position:0%
+described a minute ago for pyruvate but
+in this case it is another carboxylase
+
+ align:start position:0%
+in this case it is another carboxylase
+ 
+
+ align:start position:0%
+in this case it is another carboxylase
+acetyl co a carboxylase that picks up
+
+ align:start position:0%
+acetyl co a carboxylase that picks up
+ 
+
+ align:start position:0%
+acetyl co a carboxylase that picks up
+the co 2 residue at its carboxy
+
+ align:start position:0%
+the co 2 residue at its carboxy
+ 
+
+ align:start position:0%
+the co 2 residue at its carboxy
+transferase domain in step 2 which
+
+ align:start position:0%
+transferase domain in step 2 which
+ 
+
+ align:start position:0%
+transferase domain in step 2 which
+occurs in the carboxy transferase domain
+
+ align:start position:0%
+occurs in the carboxy transferase domain
+ 
+
+ align:start position:0%
+occurs in the carboxy transferase domain
+the substrate esse teal'c away picks up
+
+ align:start position:0%
+the substrate esse teal'c away picks up
+ 
+
+ align:start position:0%
+the substrate esse teal'c away picks up
+co 2 on its 2 carbon the one distal to
+
+ align:start position:0%
+co 2 on its 2 carbon the one distal to
+ 
+
+ align:start position:0%
+co 2 on its 2 carbon the one distal to
+the coenzyme a group to form the 3
+
+ align:start position:0%
+the coenzyme a group to form the 3
+ 
+
+ align:start position:0%
+the coenzyme a group to form the 3
+carbon product malonyl coenzyme a we'll
+
+ align:start position:0%
+carbon product malonyl coenzyme a we'll
+ 
+
+ align:start position:0%
+carbon product malonyl coenzyme a we'll
+see later that the carbon dioxide that's
+
+ align:start position:0%
+see later that the carbon dioxide that's
+ 
+
+ align:start position:0%
+see later that the carbon dioxide that's
+been added to acetyl co a to form
+
+ align:start position:0%
+been added to acetyl co a to form
+ 
+
+ align:start position:0%
+been added to acetyl co a to form
+melanie Ocoee
+
+ align:start position:0%
+melanie Ocoee
+ 
+
+ align:start position:0%
+melanie Ocoee
+is an excellent leaving group millennial
+
+ align:start position:0%
+is an excellent leaving group millennial
+ 
+
+ align:start position:0%
+is an excellent leaving group millennial
+co a is the fundamental precursor to all
+
+ align:start position:0%
+co a is the fundamental precursor to all
+ 
+
+ align:start position:0%
+co a is the fundamental precursor to all
+fatty acids through the fatty acid
+
+ align:start position:0%
+fatty acids through the fatty acid
+ 
+
+ align:start position:0%
+fatty acids through the fatty acid
+biosynthesis pathway again we'll see the
+
+ align:start position:0%
+biosynthesis pathway again we'll see the
+ 
+
+ align:start position:0%
+biosynthesis pathway again we'll see the
+details of this reaction scheme later
+
+ align:start position:0%
+details of this reaction scheme later
+ 
+
+ align:start position:0%
+details of this reaction scheme later
+but keep in mind now that this is a
+
+ align:start position:0%
+but keep in mind now that this is a
+ 
+
+ align:start position:0%
+but keep in mind now that this is a
+biotin requiring reaction just as the
+
+ align:start position:0%
+biotin requiring reaction just as the
+ 
+
+ align:start position:0%
+biotin requiring reaction just as the
+one we just looked at with pyruvate
+
+ align:start position:0%
+one we just looked at with pyruvate
+ 
+
+ align:start position:0%
+one we just looked at with pyruvate
+carboxylase let's look now at panel C my
+
+ align:start position:0%
+carboxylase let's look now at panel C my
+ 
+
+ align:start position:0%
+carboxylase let's look now at panel C my
+last example of carboxylase chemistry
+
+ align:start position:0%
+last example of carboxylase chemistry
+ 
+
+ align:start position:0%
+last example of carboxylase chemistry
+will be propia Neel coenzyme a
+
+ align:start position:0%
+will be propia Neel coenzyme a
+ 
+
+ align:start position:0%
+will be propia Neel coenzyme a
+carboxylase i mentioned earlier that the
+
+ align:start position:0%
+carboxylase i mentioned earlier that the
+ 
+
+ align:start position:0%
+carboxylase i mentioned earlier that the
+breakdown of odd chain number fatty
+
+ align:start position:0%
+breakdown of odd chain number fatty
+ 
+
+ align:start position:0%
+breakdown of odd chain number fatty
+acids results in the formation of a
+
+ align:start position:0%
+acids results in the formation of a
+ 
+
+ align:start position:0%
+acids results in the formation of a
+three carbon linear fatty acid called
+
+ align:start position:0%
+three carbon linear fatty acid called
+ 
+
+ align:start position:0%
+three carbon linear fatty acid called
+propane Eelco a I also said that nature
+
+ align:start position:0%
+propane Eelco a I also said that nature
+ 
+
+ align:start position:0%
+propane Eelco a I also said that nature
+doesn't want to waste any of the
+
+ align:start position:0%
+doesn't want to waste any of the
+ 
+
+ align:start position:0%
+doesn't want to waste any of the
+carbons what she is going to do is add a
+
+ align:start position:0%
+carbons what she is going to do is add a
+ 
+
+ align:start position:0%
+carbons what she is going to do is add a
+carbon dioxide or co2 to the central
+
+ align:start position:0%
+carbon dioxide or co2 to the central
+ 
+
+ align:start position:0%
+carbon dioxide or co2 to the central
+carbon of the propia Neel group as well
+
+ align:start position:0%
+carbon of the propia Neel group as well
+ 
+
+ align:start position:0%
+carbon of the propia Neel group as well
+as fatty acids with odd numbers of
+
+ align:start position:0%
+as fatty acids with odd numbers of
+ 
+
+ align:start position:0%
+as fatty acids with odd numbers of
+carbons certain amino acids such as
+
+ align:start position:0%
+carbons certain amino acids such as
+ 
+
+ align:start position:0%
+carbons certain amino acids such as
+isoleucine methionine and baleen and
+
+ align:start position:0%
+isoleucine methionine and baleen and
+ 
+
+ align:start position:0%
+isoleucine methionine and baleen and
+threonine for example also break down to
+
+ align:start position:0%
+threonine for example also break down to
+ 
+
+ align:start position:0%
+threonine for example also break down to
+form propia neoui so what I'm going to
+
+ align:start position:0%
+form propia neoui so what I'm going to
+ 
+
+ align:start position:0%
+form propia neoui so what I'm going to
+do now is describe a fairly general
+
+ align:start position:0%
+do now is describe a fairly general
+ 
+
+ align:start position:0%
+do now is describe a fairly general
+method of metabolism that involves
+
+ align:start position:0%
+method of metabolism that involves
+ 
+
+ align:start position:0%
+method of metabolism that involves
+restructuring of the carbon chain
+
+ align:start position:0%
+restructuring of the carbon chain
+ 
+
+ align:start position:0%
+restructuring of the carbon chain
+subsequent to the carboxyl age reaction
+
+ align:start position:0%
+subsequent to the carboxyl age reaction
+ 
+
+ align:start position:0%
+subsequent to the carboxyl age reaction
+in this overall reaction a carboxylase
+
+ align:start position:0%
+in this overall reaction a carboxylase
+ 
+
+ align:start position:0%
+in this overall reaction a carboxylase
+is going to carboxylate the middle
+
+ align:start position:0%
+is going to carboxylate the middle
+ 
+
+ align:start position:0%
+is going to carboxylate the middle
+carbon of the propia neill group then
+
+ align:start position:0%
+carbon of the propia neill group then
+ 
+
+ align:start position:0%
+carbon of the propia neill group then
+following the carboxylase reaction
+
+ align:start position:0%
+following the carboxylase reaction
+ 
+
+ align:start position:0%
+following the carboxylase reaction
+there's going to be a skeletal
+
+ align:start position:0%
+there's going to be a skeletal
+ 
+
+ align:start position:0%
+there's going to be a skeletal
+rearrangement to form succinylcholine
+
+ align:start position:0%
+rearrangement to form succinylcholine
+ 
+
+ align:start position:0%
+rearrangement to form succinylcholine
+enter the TCA cycle as shown in the
+
+ align:start position:0%
+enter the TCA cycle as shown in the
+ 
+
+ align:start position:0%
+enter the TCA cycle as shown in the
+reaction scheme propionyl coenzyme a
+
+ align:start position:0%
+reaction scheme propionyl coenzyme a
+ 
+
+ align:start position:0%
+reaction scheme propionyl coenzyme a
+carboxylase carboxylates
+
+ align:start position:0%
+carboxylase carboxylates
+ 
+
+ align:start position:0%
+carboxylase carboxylates
+pro pineal co a to form a very specific
+
+ align:start position:0%
+pro pineal co a to form a very specific
+ 
+
+ align:start position:0%
+pro pineal co a to form a very specific
+stereo isomer s methyl malonyl coenzyme
+
+ align:start position:0%
+stereo isomer s methyl malonyl coenzyme
+ 
+
+ align:start position:0%
+stereo isomer s methyl malonyl coenzyme
+a please note the position of the
+
+ align:start position:0%
+a please note the position of the
+ 
+
+ align:start position:0%
+a please note the position of the
+carbonyl group that's highlighted in
+
+ align:start position:0%
+carbonyl group that's highlighted in
+ 
+
+ align:start position:0%
+carbonyl group that's highlighted in
+blue this carboxylate in blue is
+
+ align:start position:0%
+blue this carboxylate in blue is
+ 
+
+ align:start position:0%
+blue this carboxylate in blue is
+attached to a methylene carbon that has
+
+ align:start position:0%
+attached to a methylene carbon that has
+ 
+
+ align:start position:0%
+attached to a methylene carbon that has
+an inverted triangle on top of it
+
+ align:start position:0%
+an inverted triangle on top of it
+ 
+
+ align:start position:0%
+an inverted triangle on top of it
+epimer ization about the carbon with the
+
+ align:start position:0%
+epimer ization about the carbon with the
+ 
+
+ align:start position:0%
+epimer ization about the carbon with the
+triangle results in the blue carboxylate
+
+ align:start position:0%
+triangle results in the blue carboxylate
+ 
+
+ align:start position:0%
+triangle results in the blue carboxylate
+pointed down the way i've drawn it the
+
+ align:start position:0%
+pointed down the way i've drawn it the
+ 
+
+ align:start position:0%
+pointed down the way i've drawn it the
+resulting epimer is our methyl malonyl
+
+ align:start position:0%
+resulting epimer is our methyl malonyl
+ 
+
+ align:start position:0%
+resulting epimer is our methyl malonyl
+coenzyme a in the art methyl malonyl
+
+ align:start position:0%
+coenzyme a in the art methyl malonyl
+ 
+
+ align:start position:0%
+coenzyme a in the art methyl malonyl
+coenzyme a molecule I put a little lasso
+
+ align:start position:0%
+coenzyme a molecule I put a little lasso
+ 
+
+ align:start position:0%
+coenzyme a molecule I put a little lasso
+around the hydrogen atom at the
+
+ align:start position:0%
+around the hydrogen atom at the
+ 
+
+ align:start position:0%
+around the hydrogen atom at the
+methylene moiety of the molecule I've
+
+ align:start position:0%
+methylene moiety of the molecule I've
+ 
+
+ align:start position:0%
+methylene moiety of the molecule I've
+also lassoed an electron in some of the
+
+ align:start position:0%
+also lassoed an electron in some of the
+ 
+
+ align:start position:0%
+also lassoed an electron in some of the
+atoms of the coenzyme a moiety a vitamin
+
+ align:start position:0%
+atoms of the coenzyme a moiety a vitamin
+ 
+
+ align:start position:0%
+atoms of the coenzyme a moiety a vitamin
+b12 dependent enzyme called methyl
+
+ align:start position:0%
+b12 dependent enzyme called methyl
+ 
+
+ align:start position:0%
+b12 dependent enzyme called methyl
+malonyl coenzyme a mutase which contains
+
+ align:start position:0%
+malonyl coenzyme a mutase which contains
+ 
+
+ align:start position:0%
+malonyl coenzyme a mutase which contains
+an adenosylcobalamin functional group
+
+ align:start position:0%
+an adenosylcobalamin functional group
+ 
+
+ align:start position:0%
+an adenosylcobalamin functional group
+will now act on this molecule in this
+
+ align:start position:0%
+will now act on this molecule in this
+ 
+
+ align:start position:0%
+will now act on this molecule in this
+enzyme a cobalt residue is going to
+
+ align:start position:0%
+enzyme a cobalt residue is going to
+ 
+
+ align:start position:0%
+enzyme a cobalt residue is going to
+enable the formation of an adenosyl
+
+ align:start position:0%
+enable the formation of an adenosyl
+ 
+
+ align:start position:0%
+enable the formation of an adenosyl
+radical look at the book for the
+
+ align:start position:0%
+radical look at the book for the
+ 
+
+ align:start position:0%
+radical look at the book for the
+detailed mechanism but for now it's
+
+ align:start position:0%
+detailed mechanism but for now it's
+ 
+
+ align:start position:0%
+detailed mechanism but for now it's
+sufficient to say that this adenosyl
+
+ align:start position:0%
+sufficient to say that this adenosyl
+ 
+
+ align:start position:0%
+sufficient to say that this adenosyl
+radical is going to facilitate the homo
+
+ align:start position:0%
+radical is going to facilitate the homo
+ 
+
+ align:start position:0%
+radical is going to facilitate the homo
+lid excision of the bond between the
+
+ align:start position:0%
+lid excision of the bond between the
+ 
+
+ align:start position:0%
+lid excision of the bond between the
+carbon and hydrogen of the our methyl
+
+ align:start position:0%
+carbon and hydrogen of the our methyl
+ 
+
+ align:start position:0%
+carbon and hydrogen of the our methyl
+malonyl coenzyme a
+
+ align:start position:0%
+malonyl coenzyme a
+ 
+
+ align:start position:0%
+malonyl coenzyme a
+that is you're going to get a free
+
+ align:start position:0%
+that is you're going to get a free
+ 
+
+ align:start position:0%
+that is you're going to get a free
+radical formed at the carbon that has
+
+ align:start position:0%
+radical formed at the carbon that has
+ 
+
+ align:start position:0%
+radical formed at the carbon that has
+the small blue o written over it that
+
+ align:start position:0%
+the small blue o written over it that
+ 
+
+ align:start position:0%
+the small blue o written over it that
+molecule will lose its hydrogen atom
+
+ align:start position:0%
+molecule will lose its hydrogen atom
+ 
+
+ align:start position:0%
+molecule will lose its hydrogen atom
+that hydrogen atom will migrate to the
+
+ align:start position:0%
+that hydrogen atom will migrate to the
+ 
+
+ align:start position:0%
+that hydrogen atom will migrate to the
+carbon that has the small blue triangle
+
+ align:start position:0%
+carbon that has the small blue triangle
+ 
+
+ align:start position:0%
+carbon that has the small blue triangle
+coordinate Li the carbon with the small
+
+ align:start position:0%
+coordinate Li the carbon with the small
+ 
+
+ align:start position:0%
+coordinate Li the carbon with the small
+box that's part of the coenzyme a
+
+ align:start position:0%
+box that's part of the coenzyme a
+ 
+
+ align:start position:0%
+box that's part of the coenzyme a
+carbonyl group will migrate to the
+
+ align:start position:0%
+carbonyl group will migrate to the
+ 
+
+ align:start position:0%
+carbonyl group will migrate to the
+position originally occupied by the
+
+ align:start position:0%
+position originally occupied by the
+ 
+
+ align:start position:0%
+position originally occupied by the
+hydrogen atom on the carbon with the
+
+ align:start position:0%
+hydrogen atom on the carbon with the
+ 
+
+ align:start position:0%
+hydrogen atom on the carbon with the
+small o over it the skeletal
+
+ align:start position:0%
+small o over it the skeletal
+ 
+
+ align:start position:0%
+small o over it the skeletal
+rearrangement is shown here in panel C
+
+ align:start position:0%
+rearrangement is shown here in panel C
+ 
+
+ align:start position:0%
+rearrangement is shown here in panel C
+and it results in a linearization of the
+
+ align:start position:0%
+and it results in a linearization of the
+ 
+
+ align:start position:0%
+and it results in a linearization of the
+original methylmalonyl coenzyme a if we
+
+ align:start position:0%
+original methylmalonyl coenzyme a if we
+ 
+
+ align:start position:0%
+original methylmalonyl coenzyme a if we
+redraw it as in the box you'll see that
+
+ align:start position:0%
+redraw it as in the box you'll see that
+ 
+
+ align:start position:0%
+redraw it as in the box you'll see that
+you form succinylcholine xym a sectional
+
+ align:start position:0%
+you form succinylcholine xym a sectional
+ 
+
+ align:start position:0%
+you form succinylcholine xym a sectional
+coenzyme a will then feed directly into
+
+ align:start position:0%
+coenzyme a will then feed directly into
+ 
+
+ align:start position:0%
+coenzyme a will then feed directly into
+the TCA cycle this is an antibiotic
+
+ align:start position:0%
+the TCA cycle this is an antibiotic
+ 
+
+ align:start position:0%
+the TCA cycle this is an antibiotic
+reaction that is it will increase the
+
+ align:start position:0%
+reaction that is it will increase the
+ 
+
+ align:start position:0%
+reaction that is it will increase the
+volume of carbon that's rotating in the
+
+ align:start position:0%
+volume of carbon that's rotating in the
+ 
+
+ align:start position:0%
+volume of carbon that's rotating in the
+TCA cycle
+
+ align:start position:0%
+TCA cycle
+ 
+
+ align:start position:0%
+TCA cycle
+overall in the way of review the three
+
+ align:start position:0%
+overall in the way of review the three
+ 
+
+ align:start position:0%
+overall in the way of review the three
+carbon compound propia Neel coenzyme a
+
+ align:start position:0%
+carbon compound propia Neel coenzyme a
+ 
+
+ align:start position:0%
+carbon compound propia Neel coenzyme a
+by way of the carboxylase reaction is
+
+ align:start position:0%
+by way of the carboxylase reaction is
+ 
+
+ align:start position:0%
+by way of the carboxylase reaction is
+converted to a four carbon branched
+
+ align:start position:0%
+converted to a four carbon branched
+ 
+
+ align:start position:0%
+converted to a four carbon branched
+molecule called s methylmalonyl coenzyme
+
+ align:start position:0%
+molecule called s methylmalonyl coenzyme
+ 
+
+ align:start position:0%
+molecule called s methylmalonyl coenzyme
+a it's appears a ssin forms the our
+
+ align:start position:0%
+a it's appears a ssin forms the our
+ 
+
+ align:start position:0%
+a it's appears a ssin forms the our
+methyl malonyl coenzyme a which is the
+
+ align:start position:0%
+methyl malonyl coenzyme a which is the
+ 
+
+ align:start position:0%
+methyl malonyl coenzyme a which is the
+substrate for a third enzyme methyl
+
+ align:start position:0%
+substrate for a third enzyme methyl
+ 
+
+ align:start position:0%
+substrate for a third enzyme methyl
+malonyl coenzyme a mutase a vitamin b-12
+
+ align:start position:0%
+malonyl coenzyme a mutase a vitamin b-12
+ 
+
+ align:start position:0%
+malonyl coenzyme a mutase a vitamin b-12
+enzyme this enzyme catalyzes a free
+
+ align:start position:0%
+enzyme this enzyme catalyzes a free
+ 
+
+ align:start position:0%
+enzyme this enzyme catalyzes a free
+radical mediated rearrangement of the
+
+ align:start position:0%
+radical mediated rearrangement of the
+ 
+
+ align:start position:0%
+radical mediated rearrangement of the
+side chains specifically one hydrogen
+
+ align:start position:0%
+side chains specifically one hydrogen
+ 
+
+ align:start position:0%
+side chains specifically one hydrogen
+and one coenzyme a functionality
+
+ align:start position:0%
+and one coenzyme a functionality
+ 
+
+ align:start position:0%
+and one coenzyme a functionality
+switched positions this rearrangement
+
+ align:start position:0%
+switched positions this rearrangement
+ 
+
+ align:start position:0%
+switched positions this rearrangement
+linearizes the molecule forming
+
+ align:start position:0%
+linearizes the molecule forming
+ 
+
+ align:start position:0%
+linearizes the molecule forming
+ultimately succinylcholine xym a which
+
+ align:start position:0%
+ultimately succinylcholine xym a which
+ 
+
+ align:start position:0%
+ultimately succinylcholine xym a which
+then flows into the TCA cycle
\ No newline at end of file
diff --git a/LXa9j8ZN5gU.txt b/LXa9j8ZN5gU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4755e025d71ecba8d9725b5ab96a9694c362da81
--- /dev/null
+++ b/LXa9j8ZN5gU.txt
@@ -0,0 +1,8288 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so today uh I want to talk
+
+ align:start position:0%
+ocw.mit.edu so today uh I want to talk
+ 
+
+ align:start position:0%
+ocw.mit.edu so today uh I want to talk
+about uh now that we
+
+ align:start position:0%
+about uh now that we
+ 
+
+ align:start position:0%
+about uh now that we
+have the machinery for describing
+
+ align:start position:0%
+have the machinery for describing
+ 
+
+ align:start position:0%
+have the machinery for describing
+vibrations uh in polyatomic
+
+ align:start position:0%
+vibrations uh in polyatomic
+ 
+
+ align:start position:0%
+vibrations uh in polyatomic
+molecules um we go to the quantum
+
+ align:start position:0%
+molecules um we go to the quantum
+ 
+
+ align:start position:0%
+molecules um we go to the quantum
+mechanics and we start looking at the uh
+
+ align:start position:0%
+mechanics and we start looking at the uh
+ 
+
+ align:start position:0%
+mechanics and we start looking at the uh
+the actual behavior of real uh
+
+ align:start position:0%
+the actual behavior of real uh
+ 
+
+ align:start position:0%
+the actual behavior of real uh
+polyatomic molecules and so you know we
+
+ align:start position:0%
+polyatomic molecules and so you know we
+ 
+
+ align:start position:0%
+polyatomic molecules and so you know we
+start out with the harmonic
+
+ align:start position:0%
+start out with the harmonic
+ 
+
+ align:start position:0%
+start out with the harmonic
+oscillator basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set so we showed classically that we can
+
+ align:start position:0%
+set so we showed classically that we can
+ 
+
+ align:start position:0%
+set so we showed classically that we can
+take a polyatomic molecule and uh and
+
+ align:start position:0%
+take a polyatomic molecule and uh and
+ 
+
+ align:start position:0%
+take a polyatomic molecule and uh and
+solve the classical mechanics and find
+
+ align:start position:0%
+solve the classical mechanics and find
+ 
+
+ align:start position:0%
+solve the classical mechanics and find
+the normal modes we know their
+
+ align:start position:0%
+the normal modes we know their
+ 
+
+ align:start position:0%
+the normal modes we know their
+frequencies we know what they are as
+
+ align:start position:0%
+frequencies we know what they are as
+ 
+
+ align:start position:0%
+frequencies we know what they are as
+explicit combinations of internal
+
+ align:start position:0%
+explicit combinations of internal
+ 
+
+ align:start position:0%
+explicit combinations of internal
+coordinates um and the important thing
+
+ align:start position:0%
+coordinates um and the important thing
+ 
+
+ align:start position:0%
+coordinates um and the important thing
+is that there are 3 nus 6 normal modes
+
+ align:start position:0%
+is that there are 3 nus 6 normal modes
+ 
+
+ align:start position:0%
+is that there are 3 nus 6 normal modes
+and that means that the
+
+ align:start position:0%
+and that means that the
+ 
+
+ align:start position:0%
+and that means that the
+hamiltonian can be written or the zero
+
+ align:start position:0%
+hamiltonian can be written or the zero
+ 
+
+ align:start position:0%
+hamiltonian can be written or the zero
+order hamiltonian can be written as a
+
+ align:start position:0%
+order hamiltonian can be written as a
+ 
+
+ align:start position:0%
+order hamiltonian can be written as a
+sum I = 1 to 3 N - 6
+
+ align:start position:0%
+sum I = 1 to 3 N - 6
+ 
+
+ align:start position:0%
+sum I = 1 to 3 N - 6
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+order individual oscillator
+
+ align:start position:0%
+order individual oscillator
+ 
+
+ align:start position:0%
+order individual oscillator
+hamiltonians and this provides a
+
+ align:start position:0%
+hamiltonians and this provides a
+ 
+
+ align:start position:0%
+hamiltonians and this provides a
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+mode basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set we can say that we have wave
+
+ align:start position:0%
+set we can say that we have wave
+ 
+
+ align:start position:0%
+set we can say that we have wave
+function uh or state vectors
+
+ align:start position:0%
+function uh or state vectors
+ 
+
+ align:start position:0%
+function uh or state vectors
+V1 v 3n- 6 which are just the product
+
+ align:start position:0%
+V1 v 3n- 6 which are just the product
+ 
+
+ align:start position:0%
+V1 v 3n- 6 which are just the product
+I = 1 to 3 N - 6 of VI
+
+ align:start position:0%
+I = 1 to 3 N - 6 of VI
+ 
+
+ align:start position:0%
+I = 1 to 3 N - 6 of VI
+I so this is
+
+ align:start position:0%
+I so this is
+ 
+
+ align:start position:0%
+I so this is
+wonderful once
+
+ align:start position:0%
+wonderful once
+ 
+
+ align:start position:0%
+wonderful once
+we can describe the normal modes we have
+
+ align:start position:0%
+we can describe the normal modes we have
+ 
+
+ align:start position:0%
+we can describe the normal modes we have
+can immediately go to quantum mechanics
+
+ align:start position:0%
+can immediately go to quantum mechanics
+ 
+
+ align:start position:0%
+can immediately go to quantum mechanics
+and we can describe we can write a
+
+ align:start position:0%
+and we can describe we can write a
+ 
+
+ align:start position:0%
+and we can describe we can write a
+complete basis set of normal mode
+
+ align:start position:0%
+complete basis set of normal mode
+ 
+
+ align:start position:0%
+complete basis set of normal mode
+oscillators with which we will deal uh
+
+ align:start position:0%
+oscillators with which we will deal uh
+ 
+
+ align:start position:0%
+oscillators with which we will deal uh
+represent all complexity that could
+
+ align:start position:0%
+represent all complexity that could
+ 
+
+ align:start position:0%
+represent all complexity that could
+occur in a real system where it's not
+
+ align:start position:0%
+occur in a real system where it's not
+ 
+
+ align:start position:0%
+occur in a real system where it's not
+harmonic and so this leads us
+
+ align:start position:0%
+harmonic and so this leads us
+ 
+
+ align:start position:0%
+harmonic and so this leads us
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model which is the anharmonically
+
+ align:start position:0%
+model which is the anharmonically
+ 
+
+ align:start position:0%
+model which is the anharmonically
+coupled harmonic
+
+ align:start position:0%
+coupled harmonic
+ 
+
+ align:start position:0%
+coupled harmonic
+oscillators so we have harmonic
+
+ align:start position:0%
+oscillators so we have harmonic
+ 
+
+ align:start position:0%
+oscillators so we have harmonic
+oscillators and we introduce harmonic
+
+ align:start position:0%
+oscillators and we introduce harmonic
+ 
+
+ align:start position:0%
+oscillators and we introduce harmonic
+coupling terms and we use what we know
+
+ align:start position:0%
+coupling terms and we use what we know
+ 
+
+ align:start position:0%
+coupling terms and we use what we know
+about creation Annihilation operators uh
+
+ align:start position:0%
+about creation Annihilation operators uh
+ 
+
+ align:start position:0%
+about creation Annihilation operators uh
+to evaluate all conceivable Matrix
+
+ align:start position:0%
+to evaluate all conceivable Matrix
+ 
+
+ align:start position:0%
+to evaluate all conceivable Matrix
+elements among these zero order states
+
+ align:start position:0%
+elements among these zero order states
+ 
+
+ align:start position:0%
+elements among these zero order states
+to describe the real
+
+ align:start position:0%
+to describe the real
+ 
+
+ align:start position:0%
+to describe the real
+problem and so when we do this we get
+
+ align:start position:0%
+problem and so when we do this we get
+ 
+
+ align:start position:0%
+problem and so when we do this we get
+what are called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polyads we have this is an opportunity
+
+ align:start position:0%
+polyads we have this is an opportunity
+ 
+
+ align:start position:0%
+polyads we have this is an opportunity
+for unemployed perturbation theorists I
+
+ align:start position:0%
+for unemployed perturbation theorists I
+ 
+
+ align:start position:0%
+for unemployed perturbation theorists I
+mean as soon as we we do this we have
+
+ align:start position:0%
+mean as soon as we we do this we have
+ 
+
+ align:start position:0%
+mean as soon as we we do this we have
+all sorts of anharmonic terms and we can
+
+ align:start position:0%
+all sorts of anharmonic terms and we can
+ 
+
+ align:start position:0%
+all sorts of anharmonic terms and we can
+do lots of perturbation Theory and many
+
+ align:start position:0%
+do lots of perturbation Theory and many
+ 
+
+ align:start position:0%
+do lots of perturbation Theory and many
+people spend their lives doing that uh
+
+ align:start position:0%
+people spend their lives doing that uh
+ 
+
+ align:start position:0%
+people spend their lives doing that uh
+but one of the things that emerges is
+
+ align:start position:0%
+but one of the things that emerges is
+ 
+
+ align:start position:0%
+but one of the things that emerges is
+there are special cases where because of
+
+ align:start position:0%
+there are special cases where because of
+ 
+
+ align:start position:0%
+there are special cases where because of
+near integer uh ratios of the normal
+
+ align:start position:0%
+near integer uh ratios of the normal
+ 
+
+ align:start position:0%
+near integer uh ratios of the normal
+mode frequencies or combinations of the
+
+ align:start position:0%
+mode frequencies or combinations of the
+ 
+
+ align:start position:0%
+mode frequencies or combinations of the
+normal mode frequencies we get
+
+ align:start position:0%
+normal mode frequencies we get
+ 
+
+ align:start position:0%
+normal mode frequencies we get
+systematic
+
+ align:start position:0%
+systematic
+ 
+
+ align:start position:0%
+systematic
+degeneracies and so the
+
+ align:start position:0%
+degeneracies and so the
+ 
+
+ align:start position:0%
+degeneracies and so the
+antonian uh arranges itself or we
+
+ align:start position:0%
+antonian uh arranges itself or we
+ 
+
+ align:start position:0%
+antonian uh arranges itself or we
+arrange it but we recognize these near
+
+ align:start position:0%
+arrange it but we recognize these near
+ 
+
+ align:start position:0%
+arrange it but we recognize these near
+degeneracies we arrange the groups of
+
+ align:start position:0%
+degeneracies we arrange the groups of
+ 
+
+ align:start position:0%
+degeneracies we arrange the groups of
+near degenerate levels and we say okay
+
+ align:start position:0%
+near degenerate levels and we say okay
+ 
+
+ align:start position:0%
+near degenerate levels and we say okay
+now we have to diagonalize blocks of the
+
+ align:start position:0%
+now we have to diagonalize blocks of the
+ 
+
+ align:start position:0%
+now we have to diagonalize blocks of the
+hamiltonian because those states are
+
+ align:start position:0%
+hamiltonian because those states are
+ 
+
+ align:start position:0%
+hamiltonian because those states are
+coupled by off diagonal matrix elements
+
+ align:start position:0%
+coupled by off diagonal matrix elements
+ 
+
+ align:start position:0%
+coupled by off diagonal matrix elements
+that are large compared to their energy
+
+ align:start position:0%
+that are large compared to their energy
+ 
+
+ align:start position:0%
+that are large compared to their energy
+zero order energy differences and so we
+
+ align:start position:0%
+zero order energy differences and so we
+ 
+
+ align:start position:0%
+zero order energy differences and so we
+get a lot of insights into uh
+
+ align:start position:0%
+get a lot of insights into uh
+ 
+
+ align:start position:0%
+get a lot of insights into uh
+vibrational Dynamics by looking at
+
+ align:start position:0%
+vibrational Dynamics by looking at
+ 
+
+ align:start position:0%
+vibrational Dynamics by looking at
+polyads and I'm going to talk about
+
+ align:start position:0%
+polyads and I'm going to talk about
+ 
+
+ align:start position:0%
+polyads and I'm going to talk about
+polyads a lot today and
+
+ align:start position:0%
+polyads a lot today and
+ 
+
+ align:start position:0%
+polyads a lot today and
+uh there'll be scaling Matrix element
+
+ align:start position:0%
+uh there'll be scaling Matrix element
+ 
+
+ align:start position:0%
+uh there'll be scaling Matrix element
+scaling and selection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules that are amazingly simple and
+
+ align:start position:0%
+rules that are amazingly simple and
+ 
+
+ align:start position:0%
+rules that are amazingly simple and
+amazingly
+
+ align:start position:0%
+amazingly
+ 
+
+ align:start position:0%
+amazingly
+beautiful and as a result one can
+
+ align:start position:0%
+beautiful and as a result one can
+ 
+
+ align:start position:0%
+beautiful and as a result one can
+understand what's called intr molecular
+
+ align:start position:0%
+understand what's called intr molecular
+ 
+
+ align:start position:0%
+understand what's called intr molecular
+vibrational
+
+ align:start position:0%
+vibrational
+ 
+
+ align:start position:0%
+vibrational
+redistribution uh in a very simple
+
+ align:start position:0%
+redistribution uh in a very simple
+ 
+
+ align:start position:0%
+redistribution uh in a very simple
+mechanistic way simply by looking at the
+
+ align:start position:0%
+mechanistic way simply by looking at the
+ 
+
+ align:start position:0%
+mechanistic way simply by looking at the
+structure of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polyads and another thing that's
+
+ align:start position:0%
+polyads and another thing that's
+ 
+
+ align:start position:0%
+polyads and another thing that's
+surprising and wonderful is uh
+
+ align:start position:0%
+surprising and wonderful is uh
+ 
+
+ align:start position:0%
+surprising and wonderful is uh
+new uh
+
+ align:start position:0%
+new uh
+ 
+
+ align:start position:0%
+new uh
+classes of
+
+ align:start position:0%
+classes of
+ 
+
+ align:start position:0%
+classes of
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+emerge so we start out with a picture
+
+ align:start position:0%
+emerge so we start out with a picture
+ 
+
+ align:start position:0%
+emerge so we start out with a picture
+expressed in terms of normal
+
+ align:start position:0%
+expressed in terms of normal
+ 
+
+ align:start position:0%
+expressed in terms of normal
+modes and uh remember the normal modes
+
+ align:start position:0%
+modes and uh remember the normal modes
+ 
+
+ align:start position:0%
+modes and uh remember the normal modes
+were explicit combination of internal
+
+ align:start position:0%
+were explicit combination of internal
+ 
+
+ align:start position:0%
+were explicit combination of internal
+displacements and
+
+ align:start position:0%
+displacements and
+ 
+
+ align:start position:0%
+displacements and
+amazingly local modes
+
+ align:start position:0%
+amazingly local modes
+ 
+
+ align:start position:0%
+amazingly local modes
+emerge local uh igen states which are
+
+ align:start position:0%
+emerge local uh igen states which are
+ 
+
+ align:start position:0%
+emerge local uh igen states which are
+predominantly local in other words
+
+ align:start position:0%
+predominantly local in other words
+ 
+
+ align:start position:0%
+predominantly local in other words
+particular internal displacements the
+
+ align:start position:0%
+particular internal displacements the
+ 
+
+ align:start position:0%
+particular internal displacements the
+things that we had to combine to make
+
+ align:start position:0%
+things that we had to combine to make
+ 
+
+ align:start position:0%
+things that we had to combine to make
+the normal modes they reemerge in all
+
+ align:start position:0%
+the normal modes they reemerge in all
+ 
+
+ align:start position:0%
+the normal modes they reemerge in all
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+glory and uh and so and there are many
+
+ align:start position:0%
+glory and uh and so and there are many
+ 
+
+ align:start position:0%
+glory and uh and so and there are many
+classes of uh organized motion that
+
+ align:start position:0%
+classes of uh organized motion that
+ 
+
+ align:start position:0%
+classes of uh organized motion that
+emerge spontaneously from this model
+
+ align:start position:0%
+emerge spontaneously from this model
+ 
+
+ align:start position:0%
+emerge spontaneously from this model
+that doesn't know about them we build a
+
+ align:start position:0%
+that doesn't know about them we build a
+ 
+
+ align:start position:0%
+that doesn't know about them we build a
+model in which we have harmonic
+
+ align:start position:0%
+model in which we have harmonic
+ 
+
+ align:start position:0%
+model in which we have harmonic
+oscillators and we have some coupling
+
+ align:start position:0%
+oscillators and we have some coupling
+ 
+
+ align:start position:0%
+oscillators and we have some coupling
+terms and the coupling terms are mostly
+
+ align:start position:0%
+terms and the coupling terms are mostly
+ 
+
+ align:start position:0%
+terms and the coupling terms are mostly
+dictated by which modes are near
+
+ align:start position:0%
+dictated by which modes are near
+ 
+
+ align:start position:0%
+dictated by which modes are near
+degenerate and so the the molecule sort
+
+ align:start position:0%
+degenerate and so the the molecule sort
+ 
+
+ align:start position:0%
+degenerate and so the the molecule sort
+of selects which are the important
+
+ align:start position:0%
+of selects which are the important
+ 
+
+ align:start position:0%
+of selects which are the important
+dynamically important and Harmon
+
+ align:start position:0%
+dynamically important and Harmon
+ 
+
+ align:start position:0%
+dynamically important and Harmon
+ities and those dynamically important
+
+ align:start position:0%
+ities and those dynamically important
+ 
+
+ align:start position:0%
+ities and those dynamically important
+anharmonicities give birth to
+
+ align:start position:0%
+anharmonicities give birth to
+ 
+
+ align:start position:0%
+anharmonicities give birth to
+qualitatively new classes of organized
+
+ align:start position:0%
+qualitatively new classes of organized
+ 
+
+ align:start position:0%
+qualitatively new classes of organized
+motion which appear in characteristic
+
+ align:start position:0%
+motion which appear in characteristic
+ 
+
+ align:start position:0%
+motion which appear in characteristic
+ways in the spectrum that we'll talk a
+
+ align:start position:0%
+ways in the spectrum that we'll talk a
+ 
+
+ align:start position:0%
+ways in the spectrum that we'll talk a
+little bit about and so one example that
+
+ align:start position:0%
+little bit about and so one example that
+ 
+
+ align:start position:0%
+little bit about and so one example that
+I expect to talk about is the uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normal to
+
+ align:start position:0%
+normal to
+ 
+
+ align:start position:0%
+normal to
+local mode Evolution and that's why I
+
+ align:start position:0%
+local mode Evolution and that's why I
+ 
+
+ align:start position:0%
+local mode Evolution and that's why I
+handed out the pages from the paper
+
+ align:start position:0%
+handed out the pages from the paper
+ 
+
+ align:start position:0%
+handed out the pages from the paper
+which you already have in Toto so I
+
+ align:start position:0%
+which you already have in Toto so I
+ 
+
+ align:start position:0%
+which you already have in Toto so I
+think I gave everybody a copy of the VOR
+
+ align:start position:0%
+think I gave everybody a copy of the VOR
+ 
+
+ align:start position:0%
+think I gave everybody a copy of the VOR
+okay so that's what we're going to do
+
+ align:start position:0%
+okay so that's what we're going to do
+ 
+
+ align:start position:0%
+okay so that's what we're going to do
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+uh not following the notes that I wrote
+
+ align:start position:0%
+uh not following the notes that I wrote
+ 
+
+ align:start position:0%
+uh not following the notes that I wrote
+12 years ago and so I'm doing this
+
+ align:start position:0%
+12 years ago and so I'm doing this
+ 
+
+ align:start position:0%
+12 years ago and so I'm doing this
+mostly on the Fly and so let's just see
+
+ align:start position:0%
+mostly on the Fly and so let's just see
+ 
+
+ align:start position:0%
+mostly on the Fly and so let's just see
+if I can uh make this
+
+ align:start position:0%
+if I can uh make this
+ 
+
+ align:start position:0%
+if I can uh make this
+clear okay so um we start out and we
+
+ align:start position:0%
+clear okay so um we start out and we
+ 
+
+ align:start position:0%
+clear okay so um we start out and we
+Define an effect Ive hamiltonian which
+
+ align:start position:0%
+Define an effect Ive hamiltonian which
+ 
+
+ align:start position:0%
+Define an effect Ive hamiltonian which
+is a sum of individual oscillator
+
+ align:start position:0%
+is a sum of individual oscillator
+ 
+
+ align:start position:0%
+is a sum of individual oscillator
+hamiltonians and those can be
+
+ align:start position:0%
+hamiltonians and those can be
+ 
+
+ align:start position:0%
+hamiltonians and those can be
+written uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as as uh uh remember Omega because we're
+
+ align:start position:0%
+as as uh uh remember Omega because we're
+ 
+
+ align:start position:0%
+as as uh uh remember Omega because we're
+spectroscopist is always in reciprocal
+
+ align:start position:0%
+spectroscopist is always in reciprocal
+ 
+
+ align:start position:0%
+spectroscopist is always in reciprocal
+centimeter units and uh uh this is
+
+ align:start position:0%
+centimeter units and uh uh this is
+ 
+
+ align:start position:0%
+centimeter units and uh uh this is
+supposed to be an energy unit so we have
+
+ align:start position:0%
+supposed to be an energy unit so we have
+ 
+
+ align:start position:0%
+supposed to be an energy unit so we have
+this factor of HC which
+
+ align:start position:0%
+this factor of HC which
+ 
+
+ align:start position:0%
+this factor of HC which
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+forget but uh to be honest and since
+
+ align:start position:0%
+forget but uh to be honest and since
+ 
+
+ align:start position:0%
+forget but uh to be honest and since
+this is a class rather than a uh um
+
+ align:start position:0%
+this is a class rather than a uh um
+ 
+
+ align:start position:0%
+this is a class rather than a uh um
+whatever okay and so uh we also know
+
+ align:start position:0%
+whatever okay and so uh we also know
+ 
+
+ align:start position:0%
+whatever okay and so uh we also know
+that this is going to be multiplied by
+
+ align:start position:0%
+that this is going to be multiplied by
+ 
+
+ align:start position:0%
+that this is going to be multiplied by
+Vi plus a half but we write v
+
+ align:start position:0%
+Vi plus a half but we write v
+ 
+
+ align:start position:0%
+Vi plus a half but we write v
+v uh in terms of creation and
+
+ align:start position:0%
+v uh in terms of creation and
+ 
+
+ align:start position:0%
+v uh in terms of creation and
+Annihilation
+
+ align:start position:0%
+Annihilation
+ 
+
+ align:start position:0%
+Annihilation
+operators or we write this as n subi
+
+ align:start position:0%
+operators or we write this as n subi
+ 
+
+ align:start position:0%
+operators or we write this as n subi
+which so this is the number
+
+ align:start position:0%
+which so this is the number
+ 
+
+ align:start position:0%
+which so this is the number
+operator and uh because it's convenient
+
+ align:start position:0%
+operator and uh because it's convenient
+ 
+
+ align:start position:0%
+operator and uh because it's convenient
+to replace this thing by the number
+
+ align:start position:0%
+to replace this thing by the number
+ 
+
+ align:start position:0%
+to replace this thing by the number
+operator whenever it appears because it
+
+ align:start position:0%
+operator whenever it appears because it
+ 
+
+ align:start position:0%
+operator whenever it appears because it
+makes the algebra
+
+ align:start position:0%
+makes the algebra
+ 
+
+ align:start position:0%
+makes the algebra
+simpler uh uh we have two symbols to
+
+ align:start position:0%
+simpler uh uh we have two symbols to
+ 
+
+ align:start position:0%
+simpler uh uh we have two symbols to
+describe pretty much the same thing
+
+ align:start position:0%
+describe pretty much the same thing
+ 
+
+ align:start position:0%
+describe pretty much the same thing
+so uh and we talked about the creation
+
+ align:start position:0%
+so uh and we talked about the creation
+ 
+
+ align:start position:0%
+so uh and we talked about the creation
+Annihilation operators earlier so you
+
+ align:start position:0%
+Annihilation operators earlier so you
+ 
+
+ align:start position:0%
+Annihilation operators earlier so you
+you know that if I have ai operating on
+
+ align:start position:0%
+you know that if I have ai operating on
+ 
+
+ align:start position:0%
+you know that if I have ai operating on
+V we get uh uh Square < TK of V vus
+
+ align:start position:0%
+V we get uh uh Square < TK of V vus
+ 
+
+ align:start position:0%
+V we get uh uh Square < TK of V vus
+one and so an AI dagger operating on V
+
+ align:start position:0%
+one and so an AI dagger operating on V
+ 
+
+ align:start position:0%
+one and so an AI dagger operating on V
+gives me V + one square square root uh
+
+ align:start position:0%
+gives me V + one square square root uh
+ 
+
+ align:start position:0%
+gives me V + one square square root uh
+v+ one here and the number that appears
+
+ align:start position:0%
+v+ one here and the number that appears
+ 
+
+ align:start position:0%
+v+ one here and the number that appears
+here is always the higher of the
+
+ align:start position:0%
+here is always the higher of the
+ 
+
+ align:start position:0%
+here is always the higher of the
+two uh quantum
+
+ align:start position:0%
+two uh quantum
+ 
+
+ align:start position:0%
+two uh quantum
+numbers and so it's very it's easily
+
+ align:start position:0%
+numbers and so it's very it's easily
+ 
+
+ align:start position:0%
+numbers and so it's very it's easily
+memorable so we have this this way of
+
+ align:start position:0%
+memorable so we have this this way of
+ 
+
+ align:start position:0%
+memorable so we have this this way of
+representing the zero order hamiltonian
+
+ align:start position:0%
+representing the zero order hamiltonian
+ 
+
+ align:start position:0%
+representing the zero order hamiltonian
+and so then we say everything else and
+
+ align:start position:0%
+and so then we say everything else and
+ 
+
+ align:start position:0%
+and so then we say everything else and
+this is not the way it's done generally
+
+ align:start position:0%
+this is not the way it's done generally
+ 
+
+ align:start position:0%
+this is not the way it's done generally
+although uh keeping with what we did for
+
+ align:start position:0%
+although uh keeping with what we did for
+ 
+
+ align:start position:0%
+although uh keeping with what we did for
+datomic molecules we say there is this
+
+ align:start position:0%
+datomic molecules we say there is this
+ 
+
+ align:start position:0%
+datomic molecules we say there is this
+zero order world and everything else
+
+ align:start position:0%
+zero order world and everything else
+ 
+
+ align:start position:0%
+zero order world and everything else
+that accounts for reality but for the
+
+ align:start position:0%
+that accounts for reality but for the
+ 
+
+ align:start position:0%
+that accounts for reality but for the
+time being I'm just going to talk about
+
+ align:start position:0%
+time being I'm just going to talk about
+ 
+
+ align:start position:0%
+time being I'm just going to talk about
+all of the nonharmonic Beyond harmonic
+
+ align:start position:0%
+all of the nonharmonic Beyond harmonic
+ 
+
+ align:start position:0%
+all of the nonharmonic Beyond harmonic
+terms as a prime rather than as a series
+
+ align:start position:0%
+terms as a prime rather than as a series
+ 
+
+ align:start position:0%
+terms as a prime rather than as a series
+expressed in terms of
+
+ align:start position:0%
+expressed in terms of
+ 
+
+ align:start position:0%
+expressed in terms of
+orders and okay so this is then a power
+
+ align:start position:0%
+orders and okay so this is then a power
+ 
+
+ align:start position:0%
+orders and okay so this is then a power
+series of Beyond harmonic remember in
+
+ align:start position:0%
+series of Beyond harmonic remember in
+ 
+
+ align:start position:0%
+series of Beyond harmonic remember in
+the harmonic oscillator there's no first
+
+ align:start position:0%
+the harmonic oscillator there's no first
+ 
+
+ align:start position:0%
+the harmonic oscillator there's no first
+derivative terms the only second
+
+ align:start position:0%
+derivative terms the only second
+ 
+
+ align:start position:0%
+derivative terms the only second
+derivative terms are the uh are the uh
+
+ align:start position:0%
+derivative terms are the uh are the uh
+ 
+
+ align:start position:0%
+derivative terms are the uh are the uh
+uh squared terms no cross terms and so
+
+ align:start position:0%
+uh squared terms no cross terms and so
+ 
+
+ align:start position:0%
+uh squared terms no cross terms and so
+the first time we encounter cross terms
+
+ align:start position:0%
+the first time we encounter cross terms
+ 
+
+ align:start position:0%
+the first time we encounter cross terms
+is at the cubic stage and uh so we have
+
+ align:start position:0%
+is at the cubic stage and uh so we have
+ 
+
+ align:start position:0%
+is at the cubic stage and uh so we have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh a triple sum for the
+
+ align:start position:0%
+uh a triple sum for the
+ 
+
+ align:start position:0%
+uh a triple sum for the
+cubic
+
+ align:start position:0%
+cubic
+ 
+
+ align:start position:0%
+cubic
+and it's f i j k q i q j q k now it
+
+ align:start position:0%
+and it's f i j k q i q j q k now it
+ 
+
+ align:start position:0%
+and it's f i j k q i q j q k now it
+turns out to be convenient to write
+
+ align:start position:0%
+turns out to be convenient to write
+ 
+
+ align:start position:0%
+turns out to be convenient to write
+these as unrestricted
+
+ align:start position:0%
+these as unrestricted
+ 
+
+ align:start position:0%
+these as unrestricted
+sums even though it's more natural to
+
+ align:start position:0%
+sums even though it's more natural to
+ 
+
+ align:start position:0%
+sums even though it's more natural to
+think about you know the the cubic the
+
+ align:start position:0%
+think about you know the the cubic the
+ 
+
+ align:start position:0%
+think about you know the the cubic the
+the the Cub term and the the squar Plus
+
+ align:start position:0%
+the the Cub term and the the squar Plus
+ 
+
+ align:start position:0%
+the the Cub term and the the squar Plus
+lar term times linear term as separate
+
+ align:start position:0%
+lar term times linear term as separate
+ 
+
+ align:start position:0%
+lar term times linear term as separate
+and each of them would have a different
+
+ align:start position:0%
+and each of them would have a different
+ 
+
+ align:start position:0%
+and each of them would have a different
+uh uh factor out here but uh
+
+ align:start position:0%
+uh uh factor out here but uh
+ 
+
+ align:start position:0%
+uh uh factor out here but uh
+combinatorics is much easier and it's
+
+ align:start position:0%
+combinatorics is much easier and it's
+ 
+
+ align:start position:0%
+combinatorics is much easier and it's
+much easier to program using
+
+ align:start position:0%
+much easier to program using
+ 
+
+ align:start position:0%
+much easier to program using
+unrestricted sums and so you really
+
+ align:start position:0%
+unrestricted sums and so you really
+ 
+
+ align:start position:0%
+unrestricted sums and so you really
+should use unrestricted
+
+ align:start position:0%
+should use unrestricted
+ 
+
+ align:start position:0%
+should use unrestricted
+sums and uh um and so and then there's
+
+ align:start position:0%
+sums and uh um and so and then there's
+ 
+
+ align:start position:0%
+sums and uh um and so and then there's
+the the next one the Cordic term and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's what we
+
+ align:start position:0%
+okay so that's what we
+ 
+
+ align:start position:0%
+okay so that's what we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+and this is the third derivative of the
+
+ align:start position:0%
+and this is the third derivative of the
+ 
+
+ align:start position:0%
+and this is the third derivative of the
+potential with respect to
+
+ align:start position:0%
+potential with respect to
+ 
+
+ align:start position:0%
+potential with respect to
+Qi QJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qk evaluated at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium and uh
+
+ align:start position:0%
+equilibrium and uh
+ 
+
+ align:start position:0%
+equilibrium and uh
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in order to be able to make use of
+
+ align:start position:0%
+now in order to be able to make use of
+ 
+
+ align:start position:0%
+now in order to be able to make use of
+creation analiation operators and to see
+
+ align:start position:0%
+creation analiation operators and to see
+ 
+
+ align:start position:0%
+creation analiation operators and to see
+the underlying structure of the problem
+
+ align:start position:0%
+the underlying structure of the problem
+ 
+
+ align:start position:0%
+the underlying structure of the problem
+it's useful to replace the actual normal
+
+ align:start position:0%
+it's useful to replace the actual normal
+ 
+
+ align:start position:0%
+it's useful to replace the actual normal
+coordinate displacements by
+
+ align:start position:0%
+coordinate displacements by
+ 
+
+ align:start position:0%
+coordinate displacements by
+dimensionless objects and then uh
+
+ align:start position:0%
+dimensionless objects and then uh
+ 
+
+ align:start position:0%
+dimensionless objects and then uh
+replace those by the creation
+
+ align:start position:0%
+replace those by the creation
+ 
+
+ align:start position:0%
+replace those by the creation
+Annihilation operator
+
+ align:start position:0%
+Annihilation operator
+ 
+
+ align:start position:0%
+Annihilation operator
+so there is a simple prescription for
+
+ align:start position:0%
+so there is a simple prescription for
+ 
+
+ align:start position:0%
+so there is a simple prescription for
+replacing uh an
+
+ align:start position:0%
+replacing uh an
+ 
+
+ align:start position:0%
+replacing uh an
+ordinary uh coordinate with units by a
+
+ align:start position:0%
+ordinary uh coordinate with units by a
+ 
+
+ align:start position:0%
+ordinary uh coordinate with units by a
+dimensionless quantity and uh uh so we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get so this is uh this is a factor uh
+
+ align:start position:0%
+get so this is uh this is a factor uh
+ 
+
+ align:start position:0%
+get so this is uh this is a factor uh
+this is the normal mode frequency this
+
+ align:start position:0%
+this is the normal mode frequency this
+ 
+
+ align:start position:0%
+this is the normal mode frequency this
+is a mass factor and I haven't had time
+
+ align:start position:0%
+is a mass factor and I haven't had time
+ 
+
+ align:start position:0%
+is a mass factor and I haven't had time
+to figure out what's the appropriate
+
+ align:start position:0%
+to figure out what's the appropriate
+ 
+
+ align:start position:0%
+to figure out what's the appropriate
+Mass Factor uh and that's something that
+
+ align:start position:0%
+Mass Factor uh and that's something that
+ 
+
+ align:start position:0%
+Mass Factor uh and that's something that
+uh I'm sorry about but since I made this
+
+ align:start position:0%
+uh I'm sorry about but since I made this
+ 
+
+ align:start position:0%
+uh I'm sorry about but since I made this
+up on the Fly and and we didn't I didn't
+
+ align:start position:0%
+up on the Fly and and we didn't I didn't
+ 
+
+ align:start position:0%
+up on the Fly and and we didn't I didn't
+do this either in the paper uh this Mass
+
+ align:start position:0%
+do this either in the paper uh this Mass
+ 
+
+ align:start position:0%
+do this either in the paper uh this Mass
+Factor does come out of the FG Matrix uh
+
+ align:start position:0%
+Factor does come out of the FG Matrix uh
+ 
+
+ align:start position:0%
+Factor does come out of the FG Matrix uh
+treatment but I'm not sure what it
+
+ align:start position:0%
+treatment but I'm not sure what it
+ 
+
+ align:start position:0%
+treatment but I'm not sure what it
+is but the there is a factor here that
+
+ align:start position:0%
+is but the there is a factor here that
+ 
+
+ align:start position:0%
+is but the there is a factor here that
+has dimensions of mass and it's knowable
+
+ align:start position:0%
+has dimensions of mass and it's knowable
+ 
+
+ align:start position:0%
+has dimensions of mass and it's knowable
+it's just I don't know it and going from
+
+ align:start position:0%
+it's just I don't know it and going from
+ 
+
+ align:start position:0%
+it's just I don't know it and going from
+now this Dimension quantity to the
+
+ align:start position:0%
+now this Dimension quantity to the
+ 
+
+ align:start position:0%
+now this Dimension quantity to the
+non-dimension the dimensionless quantity
+
+ align:start position:0%
+non-dimension the dimensionless quantity
+ 
+
+ align:start position:0%
+non-dimension the dimensionless quantity
+and then we write that as AI plus AI
+
+ align:start position:0%
+and then we write that as AI plus AI
+ 
+
+ align:start position:0%
+and then we write that as AI plus AI
+dagger 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so that's the procedure we start out
+
+ align:start position:0%
+two so that's the procedure we start out
+ 
+
+ align:start position:0%
+two so that's the procedure we start out
+with this thing written out in standard
+
+ align:start position:0%
+with this thing written out in standard
+ 
+
+ align:start position:0%
+with this thing written out in standard
+form and we reduce it to something
+
+ align:start position:0%
+form and we reduce it to something
+ 
+
+ align:start position:0%
+form and we reduce it to something
+expressed entirely in terms of creation
+
+ align:start position:0%
+expressed entirely in terms of creation
+ 
+
+ align:start position:0%
+expressed entirely in terms of creation
+Annihilation and number operators
+
+ align:start position:0%
+Annihilation and number operators
+ 
+
+ align:start position:0%
+Annihilation and number operators
+and one reason for doing that is this is
+
+ align:start position:0%
+and one reason for doing that is this is
+ 
+
+ align:start position:0%
+and one reason for doing that is this is
+quantum mechanics and we have to be a
+
+ align:start position:0%
+quantum mechanics and we have to be a
+ 
+
+ align:start position:0%
+quantum mechanics and we have to be a
+little careful with commutation rules
+
+ align:start position:0%
+little careful with commutation rules
+ 
+
+ align:start position:0%
+little careful with commutation rules
+and the operator algebra is much more
+
+ align:start position:0%
+and the operator algebra is much more
+ 
+
+ align:start position:0%
+and the operator algebra is much more
+transparent if we go to this now there's
+
+ align:start position:0%
+transparent if we go to this now there's
+ 
+
+ align:start position:0%
+transparent if we go to this now there's
+more advantages we also uh although in
+
+ align:start position:0%
+more advantages we also uh although in
+ 
+
+ align:start position:0%
+more advantages we also uh although in
+the normal mode hamiltonian the momentum
+
+ align:start position:0%
+the normal mode hamiltonian the momentum
+ 
+
+ align:start position:0%
+the normal mode hamiltonian the momentum
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+disappeared um it's useful to keep in
+
+ align:start position:0%
+disappeared um it's useful to keep in
+ 
+
+ align:start position:0%
+disappeared um it's useful to keep in
+mind that if we go to a local mode
+
+ align:start position:0%
+mind that if we go to a local mode
+ 
+
+ align:start position:0%
+mind that if we go to a local mode
+hamiltonian there will be uh off dial
+
+ align:start position:0%
+hamiltonian there will be uh off dial
+ 
+
+ align:start position:0%
+hamiltonian there will be uh off dial
+Matrix elements of the
+
+ align:start position:0%
+Matrix elements of the
+ 
+
+ align:start position:0%
+Matrix elements of the
+momentum between inter uh uh we already
+
+ align:start position:0%
+momentum between inter uh uh we already
+ 
+
+ align:start position:0%
+momentum between inter uh uh we already
+know that uh if if we're writing in
+
+ align:start position:0%
+know that uh if if we're writing in
+ 
+
+ align:start position:0%
+know that uh if if we're writing in
+classical mechanics if we're writing
+
+ align:start position:0%
+classical mechanics if we're writing
+ 
+
+ align:start position:0%
+classical mechanics if we're writing
+things in terms of the internal
+
+ align:start position:0%
+things in terms of the internal
+ 
+
+ align:start position:0%
+things in terms of the internal
+coordinate displacements the s's there
+
+ align:start position:0%
+coordinate displacements the s's there
+ 
+
+ align:start position:0%
+coordinate displacements the s's there
+are off diagonal matrix elements between
+
+ align:start position:0%
+are off diagonal matrix elements between
+ 
+
+ align:start position:0%
+are off diagonal matrix elements between
+them or that they're coupled by the
+
+ align:start position:0%
+them or that they're coupled by the
+ 
+
+ align:start position:0%
+them or that they're coupled by the
+kinetic energy term and so we don't just
+
+ align:start position:0%
+kinetic energy term and so we don't just
+ 
+
+ align:start position:0%
+kinetic energy term and so we don't just
+forget about the the kinetic energy or
+
+ align:start position:0%
+forget about the the kinetic energy or
+ 
+
+ align:start position:0%
+forget about the the kinetic energy or
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+momentum the reason we can be lulled
+
+ align:start position:0%
+momentum the reason we can be lulled
+ 
+
+ align:start position:0%
+momentum the reason we can be lulled
+into this sense that we can forget about
+
+ align:start position:0%
+into this sense that we can forget about
+ 
+
+ align:start position:0%
+into this sense that we can forget about
+the momentum terms is that in the
+
+ align:start position:0%
+the momentum terms is that in the
+ 
+
+ align:start position:0%
+the momentum terms is that in the
+harmonic oscillator you only have q^2
+
+ align:start position:0%
+harmonic oscillator you only have q^2
+ 
+
+ align:start position:0%
+harmonic oscillator you only have q^2
+terms I'm sorry in the harmonic
+
+ align:start position:0%
+terms I'm sorry in the harmonic
+ 
+
+ align:start position:0%
+terms I'm sorry in the harmonic
+oscillator uh you only have diagonal
+
+ align:start position:0%
+oscillator uh you only have diagonal
+ 
+
+ align:start position:0%
+oscillator uh you only have diagonal
+elements we also have in the harmonic
+
+ align:start position:0%
+elements we also have in the harmonic
+ 
+
+ align:start position:0%
+elements we also have in the harmonic
+oscillator q^ s terms and we know that
+
+ align:start position:0%
+oscillator q^ s terms and we know that
+ 
+
+ align:start position:0%
+oscillator q^ s terms and we know that
+they're going to have Matrix elements
+
+ align:start position:0%
+they're going to have Matrix elements
+ 
+
+ align:start position:0%
+they're going to have Matrix elements
+off diag and V by plus orus
+
+ align:start position:0%
+off diag and V by plus orus
+ 
+
+ align:start position:0%
+off diag and V by plus orus
+2 and we don't just forget them it just
+
+ align:start position:0%
+2 and we don't just forget them it just
+ 
+
+ align:start position:0%
+2 and we don't just forget them it just
+happens they're exactly cancelled by the
+
+ align:start position:0%
+happens they're exactly cancelled by the
+ 
+
+ align:start position:0%
+happens they're exactly cancelled by the
+off diagle by two Matrix elements of p^
+
+ align:start position:0%
+off diagle by two Matrix elements of p^
+ 
+
+ align:start position:0%
+off diagle by two Matrix elements of p^
+s and as a result we get to forget about
+
+ align:start position:0%
+s and as a result we get to forget about
+ 
+
+ align:start position:0%
+s and as a result we get to forget about
+momentum but it's not gone it's just
+
+ align:start position:0%
+momentum but it's not gone it's just
+ 
+
+ align:start position:0%
+momentum but it's not gone it's just
+that in the standard uh ex the simple
+
+ align:start position:0%
+that in the standard uh ex the simple
+ 
+
+ align:start position:0%
+that in the standard uh ex the simple
+Expressions it's
+
+ align:start position:0%
+Expressions it's
+ 
+
+ align:start position:0%
+Expressions it's
+suppressed now when we go beyond the
+
+ align:start position:0%
+suppressed now when we go beyond the
+ 
+
+ align:start position:0%
+suppressed now when we go beyond the
+harmonic oscillator approximation
+
+ align:start position:0%
+harmonic oscillator approximation
+ 
+
+ align:start position:0%
+harmonic oscillator approximation
+the kinetic energy term doesn't
+
+ align:start position:0%
+the kinetic energy term doesn't
+ 
+
+ align:start position:0%
+the kinetic energy term doesn't
+change and so it's
+
+ align:start position:0%
+change and so it's
+ 
+
+ align:start position:0%
+change and so it's
+gone unless we go away from the harmonic
+
+ align:start position:0%
+gone unless we go away from the harmonic
+ 
+
+ align:start position:0%
+gone unless we go away from the harmonic
+oscillator basis set then it's not
+
+ align:start position:0%
+oscillator basis set then it's not
+ 
+
+ align:start position:0%
+oscillator basis set then it's not
+gone and so then we have to be honest
+
+ align:start position:0%
+gone and so then we have to be honest
+ 
+
+ align:start position:0%
+gone and so then we have to be honest
+about Matrix elements of p^
+
+ align:start position:0%
+about Matrix elements of p^
+ 
+
+ align:start position:0%
+about Matrix elements of p^
+s okay so there's a similar operator
+
+ align:start position:0%
+s okay so there's a similar operator
+ 
+
+ align:start position:0%
+s okay so there's a similar operator
+replacement for
+
+ align:start position:0%
+replacement for
+ 
+
+ align:start position:0%
+replacement for
+p uh and uh um might as well just write
+
+ align:start position:0%
+p uh and uh um might as well just write
+ 
+
+ align:start position:0%
+p uh and uh um might as well just write
+it HR 2 pi C mu the same unknown uh Mass
+
+ align:start position:0%
+it HR 2 pi C mu the same unknown uh Mass
+ 
+
+ align:start position:0%
+it HR 2 pi C mu the same unknown uh Mass
+Factor Omega
+
+ align:start position:0%
+Factor Omega
+ 
+
+ align:start position:0%
+Factor Omega
+I uh square
+
+ align:start position:0%
+I uh square
+ 
+
+ align:start position:0%
+I uh square
+root and now we have the dimensionless
+
+ align:start position:0%
+root and now we have the dimensionless
+ 
+
+ align:start position:0%
+root and now we have the dimensionless
+momentum and that is expressed as 1 /
+
+ align:start position:0%
+momentum and that is expressed as 1 /
+ 
+
+ align:start position:0%
+momentum and that is expressed as 1 /
+2 uh time I time a dagger a i dagger
+
+ align:start position:0%
+2 uh time I time a dagger a i dagger
+ 
+
+ align:start position:0%
+2 uh time I time a dagger a i dagger
+minus a
+
+ align:start position:0%
+minus a
+ 
+
+ align:start position:0%
+minus a
+I so there's this factor of I and that's
+
+ align:start position:0%
+I so there's this factor of I and that's
+ 
+
+ align:start position:0%
+I so there's this factor of I and that's
+why in fact the uh uh the square p squ
+
+ align:start position:0%
+why in fact the uh uh the square p squ
+ 
+
+ align:start position:0%
+why in fact the uh uh the square p squ
+and q^ squ terms exactly
+
+ align:start position:0%
+and q^ squ terms exactly
+ 
+
+ align:start position:0%
+and q^ squ terms exactly
+cancel off diagonal but diagonally they
+
+ align:start position:0%
+cancel off diagonal but diagonally they
+ 
+
+ align:start position:0%
+cancel off diagonal but diagonally they
+add okay so we have uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay we're interested in the uh uh
+
+ align:start position:0%
+that okay we're interested in the uh uh
+ 
+
+ align:start position:0%
+that okay we're interested in the uh uh
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+i uh
+
+ align:start position:0%
+i uh
+ 
+
+ align:start position:0%
+i uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+terms that are higher than
+
+ align:start position:0%
+terms that are higher than
+ 
+
+ align:start position:0%
+terms that are higher than
+harmonic and and there are several of
+
+ align:start position:0%
+harmonic and and there are several of
+ 
+
+ align:start position:0%
+harmonic and and there are several of
+these that appear
+
+ align:start position:0%
+these that appear
+ 
+
+ align:start position:0%
+these that appear
+commonly um and it's not just because
+
+ align:start position:0%
+commonly um and it's not just because
+ 
+
+ align:start position:0%
+commonly um and it's not just because
+well it is actually because they're the
+
+ align:start position:0%
+well it is actually because they're the
+ 
+
+ align:start position:0%
+well it is actually because they're the
+lowest order uh we have often uh a
+
+ align:start position:0%
+lowest order uh we have often uh a
+ 
+
+ align:start position:0%
+lowest order uh we have often uh a
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+where um we have cubic
+
+ align:start position:0%
+where um we have cubic
+ 
+
+ align:start position:0%
+where um we have cubic
+terms and they have the form uh K1
+
+ align:start position:0%
+terms and they have the form uh K1
+ 
+
+ align:start position:0%
+terms and they have the form uh K1
+22 uh
+
+ align:start position:0%
+22 uh
+ 
+
+ align:start position:0%
+22 uh
+q1 squ uh q1 Q2
+
+ align:start position:0%
+q1 squ uh q1 Q2
+ 
+
+ align:start position:0%
+q1 squ uh q1 Q2
+2 and
+
+ align:start position:0%
+2 and
+ 
+
+ align:start position:0%
+2 and
+uh because in the
+
+ align:start position:0%
+uh because in the
+ 
+
+ align:start position:0%
+uh because in the
+scaling when we replace Q by this
+
+ align:start position:0%
+scaling when we replace Q by this
+ 
+
+ align:start position:0%
+scaling when we replace Q by this
+dimensionless q and there's a Omega in
+
+ align:start position:0%
+dimensionless q and there's a Omega in
+ 
+
+ align:start position:0%
+dimensionless q and there's a Omega in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+denominator every Power of
+
+ align:start position:0%
+denominator every Power of
+ 
+
+ align:start position:0%
+denominator every Power of
+Q uh results in a term which is reduced
+
+ align:start position:0%
+Q uh results in a term which is reduced
+ 
+
+ align:start position:0%
+Q uh results in a term which is reduced
+in magnitude by this uh one over square
+
+ align:start position:0%
+in magnitude by this uh one over square
+ 
+
+ align:start position:0%
+in magnitude by this uh one over square
+of Omega term and so the higher the
+
+ align:start position:0%
+of Omega term and so the higher the
+ 
+
+ align:start position:0%
+of Omega term and so the higher the
+order the more qes you have in there the
+
+ align:start position:0%
+order the more qes you have in there the
+ 
+
+ align:start position:0%
+order the more qes you have in there the
+smaller it's going to be in absolute
+
+ align:start position:0%
+smaller it's going to be in absolute
+ 
+
+ align:start position:0%
+smaller it's going to be in absolute
+strength okay so cubic terms are the
+
+ align:start position:0%
+strength okay so cubic terms are the
+ 
+
+ align:start position:0%
+strength okay so cubic terms are the
+most important generally beyond the
+
+ align:start position:0%
+most important generally beyond the
+ 
+
+ align:start position:0%
+most important generally beyond the
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+limit and
+
+ align:start position:0%
+limit and
+ 
+
+ align:start position:0%
+limit and
+um they also are a class of term which
+
+ align:start position:0%
+um they also are a class of term which
+ 
+
+ align:start position:0%
+um they also are a class of term which
+you often encounter when Omega 1 is
+
+ align:start position:0%
+you often encounter when Omega 1 is
+ 
+
+ align:start position:0%
+you often encounter when Omega 1 is
+approximately equal to 2 Omega
+
+ align:start position:0%
+approximately equal to 2 Omega
+ 
+
+ align:start position:0%
+approximately equal to 2 Omega
+2 and and this is the case uh for Bend
+
+ align:start position:0%
+2 and and this is the case uh for Bend
+ 
+
+ align:start position:0%
+2 and and this is the case uh for Bend
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+interactions uh it doesn't have to be
+
+ align:start position:0%
+interactions uh it doesn't have to be
+ 
+
+ align:start position:0%
+interactions uh it doesn't have to be
+that way but bends are always lower
+
+ align:start position:0%
+that way but bends are always lower
+ 
+
+ align:start position:0%
+that way but bends are always lower
+frequency than stretches and it's
+
+ align:start position:0%
+frequency than stretches and it's
+ 
+
+ align:start position:0%
+frequency than stretches and it's
+amazing how common 2:1 resonances are
+
+ align:start position:0%
+amazing how common 2:1 resonances are
+ 
+
+ align:start position:0%
+amazing how common 2:1 resonances are
+and they have a name
+
+ align:start position:0%
+and they have a name
+ 
+
+ align:start position:0%
+and they have a name
+fairy uh fairy resonance is explicitly a
+
+ align:start position:0%
+fairy uh fairy resonance is explicitly a
+ 
+
+ align:start position:0%
+fairy uh fairy resonance is explicitly a
+cubic term of 2:1
+
+ align:start position:0%
+cubic term of 2:1
+ 
+
+ align:start position:0%
+cubic term of 2:1
+resonance we could have a cubic term
+
+ align:start position:0%
+resonance we could have a cubic term
+ 
+
+ align:start position:0%
+resonance we could have a cubic term
+which is a 1: one: one resonance that
+
+ align:start position:0%
+which is a 1: one: one resonance that
+ 
+
+ align:start position:0%
+which is a 1: one: one resonance that
+would not strictly be called fairy and
+
+ align:start position:0%
+would not strictly be called fairy and
+ 
+
+ align:start position:0%
+would not strictly be called fairy and
+uh but so this is an important term that
+
+ align:start position:0%
+uh but so this is an important term that
+ 
+
+ align:start position:0%
+uh but so this is an important term that
+you would include in the hamiltonian and
+
+ align:start position:0%
+you would include in the hamiltonian and
+ 
+
+ align:start position:0%
+you would include in the hamiltonian and
+there's uh there are many quartic
+
+ align:start position:0%
+there's uh there are many quartic
+ 
+
+ align:start position:0%
+there's uh there are many quartic
+terms one of them would be something
+
+ align:start position:0%
+terms one of them would be something
+ 
+
+ align:start position:0%
+terms one of them would be something
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this where Omega 1 is approximately
+
+ align:start position:0%
+this where Omega 1 is approximately
+ 
+
+ align:start position:0%
+this where Omega 1 is approximately
+equal to Omega 2 this is even more
+
+ align:start position:0%
+equal to Omega 2 this is even more
+ 
+
+ align:start position:0%
+equal to Omega 2 this is even more
+common
+
+ align:start position:0%
+common
+ 
+
+ align:start position:0%
+common
+because whenever you have two identical
+
+ align:start position:0%
+because whenever you have two identical
+ 
+
+ align:start position:0%
+because whenever you have two identical
+Moes in the
+
+ align:start position:0%
+Moes in the
+ 
+
+ align:start position:0%
+Moes in the
+molecule they're going to give rise to
+
+ align:start position:0%
+molecule they're going to give rise to
+ 
+
+ align:start position:0%
+molecule they're going to give rise to
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+frequencies uh that are equal and so
+
+ align:start position:0%
+frequencies uh that are equal and so
+ 
+
+ align:start position:0%
+frequencies uh that are equal and so
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+guaranteed uh to have uh uh degeneracy
+
+ align:start position:0%
+guaranteed uh to have uh uh degeneracy
+ 
+
+ align:start position:0%
+guaranteed uh to have uh uh degeneracy
+between local uh frequencies and if
+
+ align:start position:0%
+between local uh frequencies and if
+ 
+
+ align:start position:0%
+between local uh frequencies and if
+they're degenerate then any any tiny
+
+ align:start position:0%
+they're degenerate then any any tiny
+ 
+
+ align:start position:0%
+they're degenerate then any any tiny
+little thing will mix them and so it
+
+ align:start position:0%
+little thing will mix them and so it
+ 
+
+ align:start position:0%
+little thing will mix them and so it
+turns out to be really important and so
+
+ align:start position:0%
+turns out to be really important and so
+ 
+
+ align:start position:0%
+turns out to be really important and so
+molecules with two identical uh
+
+ align:start position:0%
+molecules with two identical uh
+ 
+
+ align:start position:0%
+molecules with two identical uh
+stretchers or two identical Benders will
+
+ align:start position:0%
+stretchers or two identical Benders will
+ 
+
+ align:start position:0%
+stretchers or two identical Benders will
+give rise to this now why is it a two to
+
+ align:start position:0%
+give rise to this now why is it a two to
+ 
+
+ align:start position:0%
+give rise to this now why is it a two to
+two as opposed to a 1: one it's 2:2
+
+ align:start position:0%
+two as opposed to a 1: one it's 2:2
+ 
+
+ align:start position:0%
+two as opposed to a 1: one it's 2:2
+because when there's symmetry generally
+
+ align:start position:0%
+because when there's symmetry generally
+ 
+
+ align:start position:0%
+because when there's symmetry generally
+uh one of the uh
+
+ align:start position:0%
+uh one of the uh
+ 
+
+ align:start position:0%
+uh one of the uh
+um the normal modes will be non-totally
+
+ align:start position:0%
+um the normal modes will be non-totally
+ 
+
+ align:start position:0%
+um the normal modes will be non-totally
+symmetric cuz you're making the
+
+ align:start position:0%
+symmetric cuz you're making the
+ 
+
+ align:start position:0%
+symmetric cuz you're making the
+symmetric and antisymmetric combinations
+
+ align:start position:0%
+symmetric and antisymmetric combinations
+ 
+
+ align:start position:0%
+symmetric and antisymmetric combinations
+of the two two identical
+
+ align:start position:0%
+of the two two identical
+ 
+
+ align:start position:0%
+of the two two identical
+objects and when that's
+
+ align:start position:0%
+objects and when that's
+ 
+
+ align:start position:0%
+objects and when that's
+true uh in order to have a term in the
+
+ align:start position:0%
+true uh in order to have a term in the
+ 
+
+ align:start position:0%
+true uh in order to have a term in the
+hamiltonian be non zero it has to be
+
+ align:start position:0%
+hamiltonian be non zero it has to be
+ 
+
+ align:start position:0%
+hamiltonian be non zero it has to be
+totally symmetric all terms in the
+
+ align:start position:0%
+totally symmetric all terms in the
+ 
+
+ align:start position:0%
+totally symmetric all terms in the
+hamiltonian have to be totally
+
+ align:start position:0%
+hamiltonian have to be totally
+ 
+
+ align:start position:0%
+hamiltonian have to be totally
+symmetric and so if you have uh a
+
+ align:start position:0%
+symmetric and so if you have uh a
+ 
+
+ align:start position:0%
+symmetric and so if you have uh a
+non-totally symmetric coordinate
+
+ align:start position:0%
+non-totally symmetric coordinate
+ 
+
+ align:start position:0%
+non-totally symmetric coordinate
+displacement it has to be appear as an
+
+ align:start position:0%
+displacement it has to be appear as an
+ 
+
+ align:start position:0%
+displacement it has to be appear as an
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+power and so it is a one to one
+
+ align:start position:0%
+power and so it is a one to one
+ 
+
+ align:start position:0%
+power and so it is a one to one
+resonance but it it appears in the
+
+ align:start position:0%
+resonance but it it appears in the
+ 
+
+ align:start position:0%
+resonance but it it appears in the
+hiloni as a 2:2 resonance and it's
+
+ align:start position:0%
+hiloni as a 2:2 resonance and it's
+ 
+
+ align:start position:0%
+hiloni as a 2:2 resonance and it's
+extremely
+
+ align:start position:0%
+extremely
+ 
+
+ align:start position:0%
+extremely
+common and uh uh it even though it's of
+
+ align:start position:0%
+common and uh uh it even though it's of
+ 
+
+ align:start position:0%
+common and uh uh it even though it's of
+a higher order than the cubic terms it's
+
+ align:start position:0%
+a higher order than the cubic terms it's
+ 
+
+ align:start position:0%
+a higher order than the cubic terms it's
+more common and it's more important
+
+ align:start position:0%
+more common and it's more important
+ 
+
+ align:start position:0%
+more common and it's more important
+because the resonances are more
+
+ align:start position:0%
+because the resonances are more
+ 
+
+ align:start position:0%
+because the resonances are more
+perfect and so these two are the thing
+
+ align:start position:0%
+perfect and so these two are the thing
+ 
+
+ align:start position:0%
+perfect and so these two are the thing
+and this one is called
+
+ align:start position:0%
+and this one is called
+ 
+
+ align:start position:0%
+and this one is called
+darling andison
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I never met fmy but I did meet Denson he
+
+ align:start position:0%
+I never met fmy but I did meet Denson he
+ 
+
+ align:start position:0%
+I never met fmy but I did meet Denson he
+used to be coming he used to go to the
+
+ align:start position:0%
+used to be coming he used to go to the
+ 
+
+ align:start position:0%
+used to be coming he used to go to the
+spectroscopy conference at Ohio State
+
+ align:start position:0%
+spectroscopy conference at Ohio State
+ 
+
+ align:start position:0%
+spectroscopy conference at Ohio State
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+uh this both of these uh were first most
+
+ align:start position:0%
+uh this both of these uh were first most
+ 
+
+ align:start position:0%
+uh this both of these uh were first most
+fundamentally understood in the 1940s
+
+ align:start position:0%
+fundamentally understood in the 1940s
+ 
+
+ align:start position:0%
+fundamentally understood in the 1940s
+about the time I was born but Dennison
+
+ align:start position:0%
+about the time I was born but Dennison
+ 
+
+ align:start position:0%
+about the time I was born but Dennison
+was only 20 years or so older than I I
+
+ align:start position:0%
+was only 20 years or so older than I I
+ 
+
+ align:start position:0%
+was only 20 years or so older than I I
+no 30 so he was a very uh Old Gentleman
+
+ align:start position:0%
+no 30 so he was a very uh Old Gentleman
+ 
+
+ align:start position:0%
+no 30 so he was a very uh Old Gentleman
+when I first met him so anyway um that's
+
+ align:start position:0%
+when I first met him so anyway um that's
+ 
+
+ align:start position:0%
+when I first met him so anyway um that's
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+um so we have these kinds of resonances
+
+ align:start position:0%
+um so we have these kinds of resonances
+ 
+
+ align:start position:0%
+um so we have these kinds of resonances
+that we want to deal
+
+ align:start position:0%
+that we want to deal
+ 
+
+ align:start position:0%
+that we want to deal
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+okay so question about the the other
+
+ align:start position:0%
+okay so question about the the other
+ 
+
+ align:start position:0%
+okay so question about the the other
+cubic terms like the one to one to one
+
+ align:start position:0%
+cubic terms like the one to one to one
+ 
+
+ align:start position:0%
+cubic terms like the one to one to one
+res yes that you mentioned
+
+ align:start position:0%
+res yes that you mentioned
+ 
+
+ align:start position:0%
+res yes that you mentioned
+um that would also happen I guess if you
+
+ align:start position:0%
+um that would also happen I guess if you
+ 
+
+ align:start position:0%
+um that would also happen I guess if you
+have any three identical Vo
+
+ align:start position:0%
+have any three identical Vo
+ 
+
+ align:start position:0%
+have any three identical Vo
+mole well but the problem then would be
+
+ align:start position:0%
+mole well but the problem then would be
+ 
+
+ align:start position:0%
+mole well but the problem then would be
+that it's likely that one of them would
+
+ align:start position:0%
+that it's likely that one of them would
+ 
+
+ align:start position:0%
+that it's likely that one of them would
+not be totally symmetric that when you
+
+ align:start position:0%
+not be totally symmetric that when you
+ 
+
+ align:start position:0%
+not be totally symmetric that when you
+have you're combining three things that
+
+ align:start position:0%
+have you're combining three things that
+ 
+
+ align:start position:0%
+have you're combining three things that
+are identical you tend to get an a
+
+ align:start position:0%
+are identical you tend to get an a
+ 
+
+ align:start position:0%
+are identical you tend to get an a
+representation and an e
+
+ align:start position:0%
+representation and an e
+ 
+
+ align:start position:0%
+representation and an e
+representation and so you would then not
+
+ align:start position:0%
+representation and so you would then not
+ 
+
+ align:start position:0%
+representation and so you would then not
+be able to have a one to a one to one to
+
+ align:start position:0%
+be able to have a one to a one to one to
+ 
+
+ align:start position:0%
+be able to have a one to a one to one to
+one so
+
+ align:start position:0%
+one so
+ 
+
+ align:start position:0%
+one so
+um but there is a possibility that you
+
+ align:start position:0%
+um but there is a possibility that you
+ 
+
+ align:start position:0%
+um but there is a possibility that you
+have one of one that's totally symmet uh
+
+ align:start position:0%
+have one of one that's totally symmet uh
+ 
+
+ align:start position:0%
+have one of one that's totally symmet uh
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there are cases when you have a
+
+ align:start position:0%
+um there are cases when you have a
+ 
+
+ align:start position:0%
+um there are cases when you have a
+certain coordinate which not totally
+
+ align:start position:0%
+certain coordinate which not totally
+ 
+
+ align:start position:0%
+certain coordinate which not totally
+symmetric and another coordinate it's
+
+ align:start position:0%
+symmetric and another coordinate it's
+ 
+
+ align:start position:0%
+symmetric and another coordinate it's
+not but the product of the two makes so
+
+ align:start position:0%
+not but the product of the two makes so
+ 
+
+ align:start position:0%
+not but the product of the two makes so
+you you can you can have one to one to
+
+ align:start position:0%
+you you can you can have one to one to
+ 
+
+ align:start position:0%
+you you can you can have one to one to
+one where not all three of them are
+
+ align:start position:0%
+one where not all three of them are
+ 
+
+ align:start position:0%
+one where not all three of them are
+totally symmetric two of them have to be
+
+ align:start position:0%
+totally symmetric two of them have to be
+ 
+
+ align:start position:0%
+totally symmetric two of them have to be
+not or all three of them have to be not
+
+ align:start position:0%
+not or all three of them have to be not
+ 
+
+ align:start position:0%
+not or all three of them have to be not
+and depends on the the group Okay so
+
+ align:start position:0%
+and depends on the the group Okay so
+ 
+
+ align:start position:0%
+and depends on the the group Okay so
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um for the cubic we would write the
+
+ align:start position:0%
+um for the cubic we would write the
+ 
+
+ align:start position:0%
+um for the cubic we would write the
+coupling term
+
+ align:start position:0%
+coupling term
+ 
+
+ align:start position:0%
+coupling term
+as 3 over
+
+ align:start position:0%
+as 3 over
+ 
+
+ align:start position:0%
+as 3 over
+6 uh K1
+
+ align:start position:0%
+6 uh K1
+ 
+
+ align:start position:0%
+6 uh K1
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+q1
+
+ align:start position:0%
+q1
+ 
+
+ align:start position:0%
+q1
+Q
+
+ align:start position:0%
+Q
+ 
+
+ align:start position:0%
+Q
+2^2 now we had the six because it was a
+
+ align:start position:0%
+2^2 now we had the six because it was a
+ 
+
+ align:start position:0%
+2^2 now we had the six because it was a
+cubic term and we have the three because
+
+ align:start position:0%
+cubic term and we have the three because
+ 
+
+ align:start position:0%
+cubic term and we have the three because
+we can put uh you know we can have uh
+
+ align:start position:0%
+we can put uh you know we can have uh
+ 
+
+ align:start position:0%
+we can put uh you know we can have uh
+modes one and two in any of three
+
+ align:start position:0%
+modes one and two in any of three
+ 
+
+ align:start position:0%
+modes one and two in any of three
+different orders we can put the unique
+
+ align:start position:0%
+different orders we can put the unique
+ 
+
+ align:start position:0%
+different orders we can put the unique
+term first second or third and so that
+
+ align:start position:0%
+term first second or third and so that
+ 
+
+ align:start position:0%
+term first second or third and so that
+was gives us the third the six 3 over 6
+
+ align:start position:0%
+was gives us the third the six 3 over 6
+ 
+
+ align:start position:0%
+was gives us the third the six 3 over 6
+and then so that's 1 12 and then uh we
+
+ align:start position:0%
+and then so that's 1 12 and then uh we
+ 
+
+ align:start position:0%
+and then so that's 1 12 and then uh we
+can replace the these dimensionless cues
+
+ align:start position:0%
+can replace the these dimensionless cues
+ 
+
+ align:start position:0%
+can replace the these dimensionless cues
+by the creation Annihilation
+
+ align:start position:0%
+by the creation Annihilation
+ 
+
+ align:start position:0%
+by the creation Annihilation
+operators and so we get an additional
+
+ align:start position:0%
+operators and so we get an additional
+ 
+
+ align:start position:0%
+operators and so we get an additional
+factor of 1/ 2 2
+
+ align:start position:0%
+factor of 1/ 2 2
+ 
+
+ align:start position:0%
+factor of 1/ 2 2
+cubed uh we have K1 22
+
+ align:start position:0%
+cubed uh we have K1 22
+ 
+
+ align:start position:0%
+cubed uh we have K1 22
+in reciprocal centimeter units here and
+
+ align:start position:0%
+in reciprocal centimeter units here and
+ 
+
+ align:start position:0%
+in reciprocal centimeter units here and
+here and uh then A1 + A1 dagger A2 + A2
+
+ align:start position:0%
+here and uh then A1 + A1 dagger A2 + A2
+ 
+
+ align:start position:0%
+here and uh then A1 + A1 dagger A2 + A2
+dagger qu^ squar so that's the the
+
+ align:start position:0%
+dagger qu^ squar so that's the the
+ 
+
+ align:start position:0%
+dagger qu^ squar so that's the the
+quantum mechanical operator that appears
+
+ align:start position:0%
+quantum mechanical operator that appears
+ 
+
+ align:start position:0%
+quantum mechanical operator that appears
+uh that gives rise to off diagonal
+
+ align:start position:0%
+uh that gives rise to off diagonal
+ 
+
+ align:start position:0%
+uh that gives rise to off diagonal
+elements in the uh 2:1
+
+ align:start position:0%
+elements in the uh 2:1
+ 
+
+ align:start position:0%
+elements in the uh 2:1
+resonance you're absorbing the extra
+
+ align:start position:0%
+resonance you're absorbing the extra
+ 
+
+ align:start position:0%
+resonance you're absorbing the extra
+constants into the case yes
+
+ align:start position:0%
+constants into the case yes
+ 
+
+ align:start position:0%
+constants into the case yes
+you usually use Big K for that right I
+
+ align:start position:0%
+you usually use Big K for that right I
+ 
+
+ align:start position:0%
+you usually use Big K for that right I
+don't remember what I did but some of
+
+ align:start position:0%
+don't remember what I did but some of
+ 
+
+ align:start position:0%
+don't remember what I did but some of
+that was idiosyncratic and so let's make
+
+ align:start position:0%
+that was idiosyncratic and so let's make
+ 
+
+ align:start position:0%
+that was idiosyncratic and so let's make
+them big
+
+ align:start position:0%
+them big
+ 
+
+ align:start position:0%
+them big
+K okay you see here I used F instead of
+
+ align:start position:0%
+K okay you see here I used F instead of
+ 
+
+ align:start position:0%
+K okay you see here I used F instead of
+so I get uh I get so this is a big K and
+
+ align:start position:0%
+so I get uh I get so this is a big K and
+ 
+
+ align:start position:0%
+so I get uh I get so this is a big K and
+in the paper it's probably Big K right
+
+ align:start position:0%
+in the paper it's probably Big K right
+ 
+
+ align:start position:0%
+in the paper it's probably Big K right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so we have an off diagonal coupling
+
+ align:start position:0%
+okay so we have an off diagonal coupling
+ 
+
+ align:start position:0%
+okay so we have an off diagonal coupling
+term and
+
+ align:start position:0%
+term and
+ 
+
+ align:start position:0%
+term and
+now when you're faced with a real
+
+ align:start position:0%
+now when you're faced with a real
+ 
+
+ align:start position:0%
+now when you're faced with a real
+molecule uh normally you've done some
+
+ align:start position:0%
+molecule uh normally you've done some
+ 
+
+ align:start position:0%
+molecule uh normally you've done some
+spectroscopy or someone else has done
+
+ align:start position:0%
+spectroscopy or someone else has done
+ 
+
+ align:start position:0%
+spectroscopy or someone else has done
+some spectroscopy and so you have a a
+
+ align:start position:0%
+some spectroscopy and so you have a a
+ 
+
+ align:start position:0%
+some spectroscopy and so you have a a
+nearly complete set of uh vibrational
+
+ align:start position:0%
+nearly complete set of uh vibrational
+ 
+
+ align:start position:0%
+nearly complete set of uh vibrational
+frequencies and so you often look at
+
+ align:start position:0%
+frequencies and so you often look at
+ 
+
+ align:start position:0%
+frequencies and so you often look at
+that thing and you say oh well it looks
+
+ align:start position:0%
+that thing and you say oh well it looks
+ 
+
+ align:start position:0%
+that thing and you say oh well it looks
+like I've got a 2 to1 resonance or it
+
+ align:start position:0%
+like I've got a 2 to1 resonance or it
+ 
+
+ align:start position:0%
+like I've got a 2 to1 resonance or it
+looks like I've got a 2 to2
+
+ align:start position:0%
+looks like I've got a 2 to2
+ 
+
+ align:start position:0%
+looks like I've got a 2 to2
+resonance and so I know that I ought to
+
+ align:start position:0%
+resonance and so I know that I ought to
+ 
+
+ align:start position:0%
+resonance and so I know that I ought to
+be careful about writing the
+
+ align:start position:0%
+be careful about writing the
+ 
+
+ align:start position:0%
+be careful about writing the
+hamiltonian uh in terms of uh couplings
+
+ align:start position:0%
+hamiltonian uh in terms of uh couplings
+ 
+
+ align:start position:0%
+hamiltonian uh in terms of uh couplings
+among states which are near
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degenerate and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if when you look at the list of the
+
+ align:start position:0%
+uh if when you look at the list of the
+ 
+
+ align:start position:0%
+uh if when you look at the list of the
+harmonic frequencies and one of the
+
+ align:start position:0%
+harmonic frequencies and one of the
+ 
+
+ align:start position:0%
+harmonic frequencies and one of the
+beautiful things about Spectra is that
+
+ align:start position:0%
+beautiful things about Spectra is that
+ 
+
+ align:start position:0%
+beautiful things about Spectra is that
+if you're looking in the fundamental
+
+ align:start position:0%
+if you're looking in the fundamental
+ 
+
+ align:start position:0%
+if you're looking in the fundamental
+region uh you in other words words only
+
+ align:start position:0%
+region uh you in other words words only
+ 
+
+ align:start position:0%
+region uh you in other words words only
+the the uh uh one Quantum in each of the
+
+ align:start position:0%
+the the uh uh one Quantum in each of the
+ 
+
+ align:start position:0%
+the the uh uh one Quantum in each of the
+modes there are very few uh anharmonic
+
+ align:start position:0%
+modes there are very few uh anharmonic
+ 
+
+ align:start position:0%
+modes there are very few uh anharmonic
+terms that are
+
+ align:start position:0%
+terms that are
+ 
+
+ align:start position:0%
+terms that are
+relevant and
+
+ align:start position:0%
+relevant and
+ 
+
+ align:start position:0%
+relevant and
+so and if you do some work you can get a
+
+ align:start position:0%
+so and if you do some work you can get a
+ 
+
+ align:start position:0%
+so and if you do some work you can get a
+pretty good estimate of all of the
+
+ align:start position:0%
+pretty good estimate of all of the
+ 
+
+ align:start position:0%
+pretty good estimate of all of the
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+frequencies uh and so you can know that
+
+ align:start position:0%
+frequencies uh and so you can know that
+ 
+
+ align:start position:0%
+frequencies uh and so you can know that
+there are or are not likely to be some
+
+ align:start position:0%
+there are or are not likely to be some
+ 
+
+ align:start position:0%
+there are or are not likely to be some
+near
+
+ align:start position:0%
+near
+ 
+
+ align:start position:0%
+near
+resonances Suppose there are
+
+ align:start position:0%
+resonances Suppose there are
+ 
+
+ align:start position:0%
+resonances Suppose there are
+uh and suppose you have something that
+
+ align:start position:0%
+uh and suppose you have something that
+ 
+
+ align:start position:0%
+uh and suppose you have something that
+looks like a 2:1 resonance well then
+
+ align:start position:0%
+looks like a 2:1 resonance well then
+ 
+
+ align:start position:0%
+looks like a 2:1 resonance well then
+what you do is you say I'm going to take
+
+ align:start position:0%
+what you do is you say I'm going to take
+ 
+
+ align:start position:0%
+what you do is you say I'm going to take
+those two modes and I'm going to
+
+ align:start position:0%
+those two modes and I'm going to
+ 
+
+ align:start position:0%
+those two modes and I'm going to
+construct I'm going to organize them
+
+ align:start position:0%
+construct I'm going to organize them
+ 
+
+ align:start position:0%
+construct I'm going to organize them
+according to a meas a a new quantum
+
+ align:start position:0%
+according to a meas a a new quantum
+ 
+
+ align:start position:0%
+according to a meas a a new quantum
+number what we call a polyad quantum
+
+ align:start position:0%
+number what we call a polyad quantum
+ 
+
+ align:start position:0%
+number what we call a polyad quantum
+number which more or less keeps track of
+
+ align:start position:0%
+number which more or less keeps track of
+ 
+
+ align:start position:0%
+number which more or less keeps track of
+the near degeneracies so we say n is
+
+ align:start position:0%
+the near degeneracies so we say n is
+ 
+
+ align:start position:0%
+the near degeneracies so we say n is
+going to be equal to 2 * V1 + V2 if
+
+ align:start position:0%
+going to be equal to 2 * V1 + V2 if
+ 
+
+ align:start position:0%
+going to be equal to 2 * V1 + V2 if
+Omega 1 is approximately equal to 2
+
+ align:start position:0%
+Omega 1 is approximately equal to 2
+ 
+
+ align:start position:0%
+Omega 1 is approximately equal to 2
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+2 one Quantum in V1 is equal to two in
+
+ align:start position:0%
+2 one Quantum in V1 is equal to two in
+ 
+
+ align:start position:0%
+2 one Quantum in V1 is equal to two in
+in mode one Quantum in mode one is equal
+
+ align:start position:0%
+in mode one Quantum in mode one is equal
+ 
+
+ align:start position:0%
+in mode one Quantum in mode one is equal
+to to two in mode two so we get we
+
+ align:start position:0%
+to to two in mode two so we get we
+ 
+
+ align:start position:0%
+to to two in mode two so we get we
+multiply the number Quantum mode one by
+
+ align:start position:0%
+multiply the number Quantum mode one by
+ 
+
+ align:start position:0%
+multiply the number Quantum mode one by
+two you get two points for each Quantum
+
+ align:start position:0%
+two you get two points for each Quantum
+ 
+
+ align:start position:0%
+two you get two points for each Quantum
+in mode one and one point for each
+
+ align:start position:0%
+in mode one and one point for each
+ 
+
+ align:start position:0%
+in mode one and one point for each
+Quantum mode two and so we have this and
+
+ align:start position:0%
+Quantum mode two and so we have this and
+ 
+
+ align:start position:0%
+Quantum mode two and so we have this and
+so uh we make a little table of
+
+ align:start position:0%
+so uh we make a little table of
+ 
+
+ align:start position:0%
+so uh we make a little table of
+uh the states that we're going to
+
+ align:start position:0%
+uh the states that we're going to
+ 
+
+ align:start position:0%
+uh the states that we're going to
+encounter and so if we have zero n then
+
+ align:start position:0%
+encounter and so if we have zero n then
+ 
+
+ align:start position:0%
+encounter and so if we have zero n then
+that's the0 0 state if we have one
+
+ align:start position:0%
+that's the0 0 state if we have one
+ 
+
+ align:start position:0%
+that's the0 0 state if we have one
+that's the 01 state if we have two
+
+ align:start position:0%
+that's the 01 state if we have two
+ 
+
+ align:start position:0%
+that's the 01 state if we have two
+that's the uh one zero state but it's
+
+ align:start position:0%
+that's the uh one zero state but it's
+ 
+
+ align:start position:0%
+that's the uh one zero state but it's
+also the 02 state so here's in a case
+
+ align:start position:0%
+also the 02 state so here's in a case
+ 
+
+ align:start position:0%
+also the 02 state so here's in a case
+where that fundamental is near
+
+ align:start position:0%
+where that fundamental is near
+ 
+
+ align:start position:0%
+where that fundamental is near
+degenerate with something else and so
+
+ align:start position:0%
+degenerate with something else and so
+ 
+
+ align:start position:0%
+degenerate with something else and so
+that if you were looking for this
+
+ align:start position:0%
+that if you were looking for this
+ 
+
+ align:start position:0%
+that if you were looking for this
+fundamental uh and you saw something
+
+ align:start position:0%
+fundamental uh and you saw something
+ 
+
+ align:start position:0%
+fundamental uh and you saw something
+that you wanted to assign as the uh this
+
+ align:start position:0%
+that you wanted to assign as the uh this
+ 
+
+ align:start position:0%
+that you wanted to assign as the uh this
+fundamental it will have some effect
+
+ align:start position:0%
+fundamental it will have some effect
+ 
+
+ align:start position:0%
+fundamental it will have some effect
+being perturbed by this and often when
+
+ align:start position:0%
+being perturbed by this and often when
+ 
+
+ align:start position:0%
+being perturbed by this and often when
+you have these anharmonic resonances
+
+ align:start position:0%
+you have these anharmonic resonances
+ 
+
+ align:start position:0%
+you have these anharmonic resonances
+that are near degenerate you get too
+
+ align:start position:0%
+that are near degenerate you get too
+ 
+
+ align:start position:0%
+that are near degenerate you get too
+many candidates for the 3 nus 6 normal
+
+ align:start position:0%
+many candidates for the 3 nus 6 normal
+ 
+
+ align:start position:0%
+many candidates for the 3 nus 6 normal
+modes and you know that something is
+
+ align:start position:0%
+modes and you know that something is
+ 
+
+ align:start position:0%
+modes and you know that something is
+wrong so it's one by one 1 by 1 2x two
+
+ align:start position:0%
+wrong so it's one by one 1 by 1 2x two
+ 
+
+ align:start position:0%
+wrong so it's one by one 1 by 1 2x two
+that's called a
+
+ align:start position:0%
+that's called a
+ 
+
+ align:start position:0%
+that's called a
+diad and with three we have one one and
+
+ align:start position:0%
+diad and with three we have one one and
+ 
+
+ align:start position:0%
+diad and with three we have one one and
+uh 03 another diad and then
+
+ align:start position:0%
+uh 03 another diad and then
+ 
+
+ align:start position:0%
+uh 03 another diad and then
+four 2
+
+ align:start position:0%
+four 2
+ 
+
+ align:start position:0%
+four 2
+0 1 2 and
+
+ align:start position:0%
+0 1 2 and
+ 
+
+ align:start position:0%
+0 1 2 and
+04 and if I just I'm picking 10 we could
+
+ align:start position:0%
+04 and if I just I'm picking 10 we could
+ 
+
+ align:start position:0%
+04 and if I just I'm picking 10 we could
+have uh 5 0 all the way down to 010
+
+ align:start position:0%
+have uh 5 0 all the way down to 010
+ 
+
+ align:start position:0%
+have uh 5 0 all the way down to 010
+and there's six of them so diad Triad
+
+ align:start position:0%
+and there's six of them so diad Triad
+ 
+
+ align:start position:0%
+and there's six of them so diad Triad
+sex
+
+ align:start position:0%
+sex
+ 
+
+ align:start position:0%
+sex
+ad uh you can and it as you go up in
+
+ align:start position:0%
+ad uh you can and it as you go up in
+ 
+
+ align:start position:0%
+ad uh you can and it as you go up in
+polyad quantum number you get more and
+
+ align:start position:0%
+polyad quantum number you get more and
+ 
+
+ align:start position:0%
+polyad quantum number you get more and
+more states that are systematically
+
+ align:start position:0%
+more states that are systematically
+ 
+
+ align:start position:0%
+more states that are systematically
+degenerate and then you say oh well we
+
+ align:start position:0%
+degenerate and then you say oh well we
+ 
+
+ align:start position:0%
+degenerate and then you say oh well we
+have cubic couplings or we have two: one
+
+ align:start position:0%
+have cubic couplings or we have two: one
+ 
+
+ align:start position:0%
+have cubic couplings or we have two: one
+couplings and so there ought to be terms
+
+ align:start position:0%
+couplings and so there ought to be terms
+ 
+
+ align:start position:0%
+couplings and so there ought to be terms
+in the hamiltonian that couple this with
+
+ align:start position:0%
+in the hamiltonian that couple this with
+ 
+
+ align:start position:0%
+in the hamiltonian that couple this with
+this and this with that because we're
+
+ align:start position:0%
+this and this with that because we're
+ 
+
+ align:start position:0%
+this and this with that because we're
+taking one Quantum away from here and
+
+ align:start position:0%
+taking one Quantum away from here and
+ 
+
+ align:start position:0%
+taking one Quantum away from here and
+putting qu in there and each of the off
+
+ align:start position:0%
+putting qu in there and each of the off
+ 
+
+ align:start position:0%
+putting qu in there and each of the off
+diagonal coupling terms will allow you
+
+ align:start position:0%
+diagonal coupling terms will allow you
+ 
+
+ align:start position:0%
+diagonal coupling terms will allow you
+to take one step you can't go from here
+
+ align:start position:0%
+to take one step you can't go from here
+ 
+
+ align:start position:0%
+to take one step you can't go from here
+to here because that would take two
+
+ align:start position:0%
+to here because that would take two
+ 
+
+ align:start position:0%
+to here because that would take two
+Quant away from here and add four to
+
+ align:start position:0%
+Quant away from here and add four to
+ 
+
+ align:start position:0%
+Quant away from here and add four to
+that so you have to do that in two steps
+
+ align:start position:0%
+that so you have to do that in two steps
+ 
+
+ align:start position:0%
+that so you have to do that in two steps
+so as soon as you think that there is
+
+ align:start position:0%
+so as soon as you think that there is
+ 
+
+ align:start position:0%
+so as soon as you think that there is
+some kind of systematic degeneracy you
+
+ align:start position:0%
+some kind of systematic degeneracy you
+ 
+
+ align:start position:0%
+some kind of systematic degeneracy you
+make a table like this and you discover
+
+ align:start position:0%
+make a table like this and you discover
+ 
+
+ align:start position:0%
+make a table like this and you discover
+that there is a uh a pattern like that
+
+ align:start position:0%
+that there is a uh a pattern like that
+ 
+
+ align:start position:0%
+that there is a uh a pattern like that
+and uh if it's a 2:1 resonance then you
+
+ align:start position:0%
+and uh if it's a 2:1 resonance then you
+ 
+
+ align:start position:0%
+and uh if it's a 2:1 resonance then you
+know you're going to be looking for
+
+ align:start position:0%
+know you're going to be looking for
+ 
+
+ align:start position:0%
+know you're going to be looking for
+terms of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form and uh but as soon as you express
+
+ align:start position:0%
+form and uh but as soon as you express
+ 
+
+ align:start position:0%
+form and uh but as soon as you express
+it in terms of creation Annihilation
+
+ align:start position:0%
+it in terms of creation Annihilation
+ 
+
+ align:start position:0%
+it in terms of creation Annihilation
+operators and you say okay we have a two
+
+ align:start position:0%
+operators and you say okay we have a two
+ 
+
+ align:start position:0%
+operators and you say okay we have a two
+Z and we're going to a one two
+
+ align:start position:0%
+Z and we're going to a one two
+ 
+
+ align:start position:0%
+Z and we're going to a one two
+then by specifying the two states that
+
+ align:start position:0%
+then by specifying the two states that
+ 
+
+ align:start position:0%
+then by specifying the two states that
+we want to couple we know exactly which
+
+ align:start position:0%
+we want to couple we know exactly which
+ 
+
+ align:start position:0%
+we want to couple we know exactly which
+operator we want we're going to have uh
+
+ align:start position:0%
+operator we want we're going to have uh
+ 
+
+ align:start position:0%
+operator we want we're going to have uh
+A1 dagger A2 squar n
+
+ align:start position:0%
+A1 dagger A2 squar n
+ 
+
+ align:start position:0%
+A1 dagger A2 squar n
+dagger so uh you make a list of all of
+
+ align:start position:0%
+dagger so uh you make a list of all of
+ 
+
+ align:start position:0%
+dagger so uh you make a list of all of
+the states that are near togenerate and
+
+ align:start position:0%
+the states that are near togenerate and
+ 
+
+ align:start position:0%
+the states that are near togenerate and
+then uh you discover what is going to be
+
+ align:start position:0%
+then uh you discover what is going to be
+ 
+
+ align:start position:0%
+then uh you discover what is going to be
+the lowest order of term that will
+
+ align:start position:0%
+the lowest order of term that will
+ 
+
+ align:start position:0%
+the lowest order of term that will
+couple all of those States and you know
+
+ align:start position:0%
+couple all of those States and you know
+ 
+
+ align:start position:0%
+couple all of those States and you know
+also how to write the Matrix elements so
+
+ align:start position:0%
+also how to write the Matrix elements so
+ 
+
+ align:start position:0%
+also how to write the Matrix elements so
+this is going to give give a term a
+
+ align:start position:0%
+this is going to give give a term a
+ 
+
+ align:start position:0%
+this is going to give give a term a
+dagger one to two is going to give a
+
+ align:start position:0%
+dagger one to two is going to give a
+ 
+
+ align:start position:0%
+dagger one to two is going to give a
+square of Two and a uh squar on two is
+
+ align:start position:0%
+square of Two and a uh squar on two is
+ 
+
+ align:start position:0%
+square of Two and a uh squar on two is
+going to give 2 *
+
+ align:start position:0%
+going to give 2 *
+ 
+
+ align:start position:0%
+going to give 2 *
+1ot so this is just equal to two so
+
+ align:start position:0%
+1ot so this is just equal to two so
+ 
+
+ align:start position:0%
+1ot so this is just equal to two so
+uh once you organize things in terms of
+
+ align:start position:0%
+uh once you organize things in terms of
+ 
+
+ align:start position:0%
+uh once you organize things in terms of
+near degenerate States it tells you what
+
+ align:start position:0%
+near degenerate States it tells you what
+ 
+
+ align:start position:0%
+near degenerate States it tells you what
+terms are going to be important and it
+
+ align:start position:0%
+terms are going to be important and it
+ 
+
+ align:start position:0%
+terms are going to be important and it
+gives you all of the Matrix elements
+
+ align:start position:0%
+gives you all of the Matrix elements
+ 
+
+ align:start position:0%
+gives you all of the Matrix elements
+among them you
+
+ align:start position:0%
+among them you
+ 
+
+ align:start position:0%
+among them you
+have both selection Rule and Matrix
+
+ align:start position:0%
+have both selection Rule and Matrix
+ 
+
+ align:start position:0%
+have both selection Rule and Matrix
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+scaling it
+
+ align:start position:0%
+scaling it
+ 
+
+ align:start position:0%
+scaling it
+becomes really trivial and this is the
+
+ align:start position:0%
+becomes really trivial and this is the
+ 
+
+ align:start position:0%
+becomes really trivial and this is the
+power of the
+
+ align:start position:0%
+power of the
+ 
+
+ align:start position:0%
+power of the
+technique you don't have to know nothing
+
+ align:start position:0%
+technique you don't have to know nothing
+ 
+
+ align:start position:0%
+technique you don't have to know nothing
+uh and one of the nice things about this
+
+ align:start position:0%
+uh and one of the nice things about this
+ 
+
+ align:start position:0%
+uh and one of the nice things about this
+also is once you've say looked at a
+
+ align:start position:0%
+also is once you've say looked at a
+ 
+
+ align:start position:0%
+also is once you've say looked at a
+diad you have determined all of the
+
+ align:start position:0%
+diad you have determined all of the
+ 
+
+ align:start position:0%
+diad you have determined all of the
+adjustable parameters that will describe
+
+ align:start position:0%
+adjustable parameters that will describe
+ 
+
+ align:start position:0%
+adjustable parameters that will describe
+the energy levels and so yes you can you
+
+ align:start position:0%
+the energy levels and so yes you can you
+ 
+
+ align:start position:0%
+the energy levels and so yes you can you
+can go up to 10 uh The Matrix is Big
+
+ align:start position:0%
+can go up to 10 uh The Matrix is Big
+ 
+
+ align:start position:0%
+can go up to 10 uh The Matrix is Big
+it's a 6x6 instead of a 2X two but you
+
+ align:start position:0%
+it's a 6x6 instead of a 2X two but you
+ 
+
+ align:start position:0%
+it's a 6x6 instead of a 2X two but you
+know all the elements in that Matrix and
+
+ align:start position:0%
+know all the elements in that Matrix and
+ 
+
+ align:start position:0%
+know all the elements in that Matrix and
+so you should be able based on what
+
+ align:start position:0%
+so you should be able based on what
+ 
+
+ align:start position:0%
+so you should be able based on what
+you've already determined up to here you
+
+ align:start position:0%
+you've already determined up to here you
+ 
+
+ align:start position:0%
+you've already determined up to here you
+should be able to extrapolate because
+
+ align:start position:0%
+should be able to extrapolate because
+ 
+
+ align:start position:0%
+should be able to extrapolate because
+you DET the value of
+
+ align:start position:0%
+you DET the value of
+ 
+
+ align:start position:0%
+you DET the value of
+K22 yes yeah and now of course nothing
+
+ align:start position:0%
+K22 yes yeah and now of course nothing
+ 
+
+ align:start position:0%
+K22 yes yeah and now of course nothing
+is perfect but uh uh usually the
+
+ align:start position:0%
+is perfect but uh uh usually the
+ 
+
+ align:start position:0%
+is perfect but uh uh usually the
+breakdown of an extrapolation tells you
+
+ align:start position:0%
+breakdown of an extrapolation tells you
+ 
+
+ align:start position:0%
+breakdown of an extrapolation tells you
+you've neglected some other coupling
+
+ align:start position:0%
+you've neglected some other coupling
+ 
+
+ align:start position:0%
+you've neglected some other coupling
+term and then you know that you have to
+
+ align:start position:0%
+term and then you know that you have to
+ 
+
+ align:start position:0%
+term and then you know that you have to
+look for some other coupling term and
+
+ align:start position:0%
+look for some other coupling term and
+ 
+
+ align:start position:0%
+look for some other coupling term and
+where it's important from the pattern of
+
+ align:start position:0%
+where it's important from the pattern of
+ 
+
+ align:start position:0%
+where it's important from the pattern of
+the breakdown and so it's it's really a
+
+ align:start position:0%
+the breakdown and so it's it's really a
+ 
+
+ align:start position:0%
+the breakdown and so it's it's really a
+an amazingly powerful tool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now of course it's totally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonsensical because the modes the normal
+
+ align:start position:0%
+nonsensical because the modes the normal
+ 
+
+ align:start position:0%
+nonsensical because the modes the normal
+coordinates or or the individual normal
+
+ align:start position:0%
+coordinates or or the individual normal
+ 
+
+ align:start position:0%
+coordinates or or the individual normal
+modes are not harmonic there are
+
+ align:start position:0%
+modes are not harmonic there are
+ 
+
+ align:start position:0%
+modes are not harmonic there are
+diagonal anharmonicities
+
+ align:start position:0%
+diagonal anharmonicities
+ 
+
+ align:start position:0%
+diagonal anharmonicities
+and so uh it is a lie or it is an
+
+ align:start position:0%
+and so uh it is a lie or it is an
+ 
+
+ align:start position:0%
+and so uh it is a lie or it is an
+inaccuracy to represent the
+
+ align:start position:0%
+inaccuracy to represent the
+ 
+
+ align:start position:0%
+inaccuracy to represent the
+problem uh by putting
+
+ align:start position:0%
+problem uh by putting
+ 
+
+ align:start position:0%
+problem uh by putting
+in uh uh on the diagonal saying the
+
+ align:start position:0%
+in uh uh on the diagonal saying the
+ 
+
+ align:start position:0%
+in uh uh on the diagonal saying the
+energy is Omega time V + a half + x * V
+
+ align:start position:0%
+energy is Omega time V + a half + x * V
+ 
+
+ align:start position:0%
+energy is Omega time V + a half + x * V
++ a half 2ar and y + V + a half cubed
+
+ align:start position:0%
++ a half 2ar and y + V + a half cubed
+ 
+
+ align:start position:0%
++ a half 2ar and y + V + a half cubed
+whatever you
+
+ align:start position:0%
+whatever you
+ 
+
+ align:start position:0%
+whatever you
+need it's a lie because you're only
+
+ align:start position:0%
+need it's a lie because you're only
+ 
+
+ align:start position:0%
+need it's a lie because you're only
+allowed in the harmonic limit to do this
+
+ align:start position:0%
+allowed in the harmonic limit to do this
+ 
+
+ align:start position:0%
+allowed in the harmonic limit to do this
+but we put these things on the
+
+ align:start position:0%
+but we put these things on the
+ 
+
+ align:start position:0%
+but we put these things on the
+diagonal and so they are not harmonic
+
+ align:start position:0%
+diagonal and so they are not harmonic
+ 
+
+ align:start position:0%
+diagonal and so they are not harmonic
+oscillators they're anharmonic
+
+ align:start position:0%
+oscillators they're anharmonic
+ 
+
+ align:start position:0%
+oscillators they're anharmonic
+oscillators and the correct application
+
+ align:start position:0%
+oscillators and the correct application
+ 
+
+ align:start position:0%
+oscillators and the correct application
+of perturbation theory is to then
+
+ align:start position:0%
+of perturbation theory is to then
+ 
+
+ align:start position:0%
+of perturbation theory is to then
+calculate Matrix elements of the
+
+ align:start position:0%
+calculate Matrix elements of the
+ 
+
+ align:start position:0%
+calculate Matrix elements of the
+anharmonic oscillators and that's never
+
+ align:start position:0%
+anharmonic oscillators and that's never
+ 
+
+ align:start position:0%
+anharmonic oscillators and that's never
+done and we can get away with that for a
+
+ align:start position:0%
+done and we can get away with that for a
+ 
+
+ align:start position:0%
+done and we can get away with that for a
+long time but that's the reason why this
+
+ align:start position:0%
+long time but that's the reason why this
+ 
+
+ align:start position:0%
+long time but that's the reason why this
+paper was written uh trying to say okay
+
+ align:start position:0%
+paper was written uh trying to say okay
+ 
+
+ align:start position:0%
+paper was written uh trying to say okay
+well this is a wonderful approximation
+
+ align:start position:0%
+well this is a wonderful approximation
+ 
+
+ align:start position:0%
+well this is a wonderful approximation
+but uh it has to
+
+ align:start position:0%
+but uh it has to
+ 
+
+ align:start position:0%
+but uh it has to
+break okay so but let's just say that we
+
+ align:start position:0%
+break okay so but let's just say that we
+ 
+
+ align:start position:0%
+break okay so but let's just say that we
+have a way of representing all the
+
+ align:start position:0%
+have a way of representing all the
+ 
+
+ align:start position:0%
+have a way of representing all the
+energy levels using models based on one
+
+ align:start position:0%
+energy levels using models based on one
+ 
+
+ align:start position:0%
+energy levels using models based on one
+or two a small number of anharmonic
+
+ align:start position:0%
+or two a small number of anharmonic
+ 
+
+ align:start position:0%
+or two a small number of anharmonic
+coupling terms and we have this
+
+ align:start position:0%
+coupling terms and we have this
+ 
+
+ align:start position:0%
+coupling terms and we have this
+incredible
+
+ align:start position:0%
+incredible
+ 
+
+ align:start position:0%
+incredible
+scaling uh then one of the things we can
+
+ align:start position:0%
+scaling uh then one of the things we can
+ 
+
+ align:start position:0%
+scaling uh then one of the things we can
+do is we can understand inmolecular
+
+ align:start position:0%
+do is we can understand inmolecular
+ 
+
+ align:start position:0%
+do is we can understand inmolecular
+vibrational
+
+ align:start position:0%
+vibrational
+ 
+
+ align:start position:0%
+vibrational
+redistribution now when I came into this
+
+ align:start position:0%
+redistribution now when I came into this
+ 
+
+ align:start position:0%
+redistribution now when I came into this
+game the words
+
+ align:start position:0%
+game the words
+ 
+
+ align:start position:0%
+game the words
+ivr nobody really knew what they stood
+
+ align:start position:0%
+ivr nobody really knew what they stood
+ 
+
+ align:start position:0%
+ivr nobody really knew what they stood
+for because nobody knew what ivr was it
+
+ align:start position:0%
+for because nobody knew what ivr was it
+ 
+
+ align:start position:0%
+for because nobody knew what ivr was it
+was basically you know at high exitation
+
+ align:start position:0%
+was basically you know at high exitation
+ 
+
+ align:start position:0%
+was basically you know at high exitation
+there's strong coupling between modes
+
+ align:start position:0%
+there's strong coupling between modes
+ 
+
+ align:start position:0%
+there's strong coupling between modes
+and you get an evolution towards
+
+ align:start position:0%
+and you get an evolution towards
+ 
+
+ align:start position:0%
+and you get an evolution towards
+chaos and and so uh is this
+
+ align:start position:0%
+chaos and and so uh is this
+ 
+
+ align:start position:0%
+chaos and and so uh is this
+redistribution or randomization
+
+ align:start position:0%
+redistribution or randomization
+ 
+
+ align:start position:0%
+redistribution or randomization
+randomization implies chaos
+
+ align:start position:0%
+randomization implies chaos
+ 
+
+ align:start position:0%
+randomization implies chaos
+redistribution implies a mechanism
+
+ align:start position:0%
+redistribution implies a mechanism
+ 
+
+ align:start position:0%
+redistribution implies a mechanism
+uh and this is inmolecular vibration so
+
+ align:start position:0%
+uh and this is inmolecular vibration so
+ 
+
+ align:start position:0%
+uh and this is inmolecular vibration so
+uh ivr was basically one of these uh
+
+ align:start position:0%
+uh ivr was basically one of these uh
+ 
+
+ align:start position:0%
+uh ivr was basically one of these uh
+non-radiative processes that occur in
+
+ align:start position:0%
+non-radiative processes that occur in
+ 
+
+ align:start position:0%
+non-radiative processes that occur in
+molecules where people had taken a
+
+ align:start position:0%
+molecules where people had taken a
+ 
+
+ align:start position:0%
+molecules where people had taken a
+phenomenological mostly
+
+ align:start position:0%
+phenomenological mostly
+ 
+
+ align:start position:0%
+phenomenological mostly
+statistical uh picture of it that there
+
+ align:start position:0%
+statistical uh picture of it that there
+ 
+
+ align:start position:0%
+statistical uh picture of it that there
+was not enough uh information to
+
+ align:start position:0%
+was not enough uh information to
+ 
+
+ align:start position:0%
+was not enough uh information to
+describe it but if we have a polyad
+
+ align:start position:0%
+describe it but if we have a polyad
+ 
+
+ align:start position:0%
+describe it but if we have a polyad
+model then we can always write the ual
+
+ align:start position:0%
+model then we can always write the ual
+ 
+
+ align:start position:0%
+model then we can always write the ual
+Ian States as some linear combination of
+
+ align:start position:0%
+Ian States as some linear combination of
+ 
+
+ align:start position:0%
+Ian States as some linear combination of
+uh zero order States and I'm sorry about
+
+ align:start position:0%
+uh zero order States and I'm sorry about
+ 
+
+ align:start position:0%
+uh zero order States and I'm sorry about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+notation and we can imagine doing some
+
+ align:start position:0%
+notation and we can imagine doing some
+ 
+
+ align:start position:0%
+notation and we can imagine doing some
+short puls exitation where we prepare a
+
+ align:start position:0%
+short puls exitation where we prepare a
+ 
+
+ align:start position:0%
+short puls exitation where we prepare a
+system at T equals z with a short pulse
+
+ align:start position:0%
+system at T equals z with a short pulse
+ 
+
+ align:start position:0%
+system at T equals z with a short pulse
+and we prepare it not in one igen state
+
+ align:start position:0%
+and we prepare it not in one igen state
+ 
+
+ align:start position:0%
+and we prepare it not in one igen state
+but in a
+
+ align:start position:0%
+but in a
+ 
+
+ align:start position:0%
+but in a
+state a zero order
+
+ align:start position:0%
+state a zero order
+ 
+
+ align:start position:0%
+state a zero order
+State because the the zero order states
+
+ align:start position:0%
+State because the the zero order states
+ 
+
+ align:start position:0%
+State because the the zero order states
+are the are the things that uh uh often
+
+ align:start position:0%
+are the are the things that uh uh often
+ 
+
+ align:start position:0%
+are the are the things that uh uh often
+get picked out by exitation by a
+
+ align:start position:0%
+get picked out by exitation by a
+ 
+
+ align:start position:0%
+get picked out by exitation by a
+photon we'll talk about that more
+
+ align:start position:0%
+photon we'll talk about that more
+ 
+
+ align:start position:0%
+photon we'll talk about that more
+probably uh although how much time do I
+
+ align:start position:0%
+probably uh although how much time do I
+ 
+
+ align:start position:0%
+probably uh although how much time do I
+have not not a lot okay so uh in order
+
+ align:start position:0%
+have not not a lot okay so uh in order
+ 
+
+ align:start position:0%
+have not not a lot okay so uh in order
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+describe s of
+
+ align:start position:0%
+describe s of
+ 
+
+ align:start position:0%
+describe s of
+T you have to reexpress this zero order
+
+ align:start position:0%
+T you have to reexpress this zero order
+ 
+
+ align:start position:0%
+T you have to reexpress this zero order
+State as a sum over ion state it's doing
+
+ align:start position:0%
+State as a sum over ion state it's doing
+ 
+
+ align:start position:0%
+State as a sum over ion state it's doing
+this transformation backwards and so we
+
+ align:start position:0%
+this transformation backwards and so we
+ 
+
+ align:start position:0%
+this transformation backwards and so we
+have b j e to Theus e i t h
+
+ align:start position:0%
+have b j e to Theus e i t h
+ 
+
+ align:start position:0%
+have b j e to Theus e i t h
+bar I so this is an expansion in terms
+
+ align:start position:0%
+bar I so this is an expansion in terms
+ 
+
+ align:start position:0%
+bar I so this is an expansion in terms
+of IG States and this is the time
+
+ align:start position:0%
+of IG States and this is the time
+ 
+
+ align:start position:0%
+of IG States and this is the time
+dependence so it's a superposition of I
+
+ align:start position:0%
+dependence so it's a superposition of I
+ 
+
+ align:start position:0%
+dependence so it's a superposition of I
+States and these two terms come from the
+
+ align:start position:0%
+States and these two terms come from the
+ 
+
+ align:start position:0%
+States and these two terms come from the
+unitary transformation that takes you
+
+ align:start position:0%
+unitary transformation that takes you
+ 
+
+ align:start position:0%
+unitary transformation that takes you
+between the order and the Ian state
+
+ align:start position:0%
+between the order and the Ian state
+ 
+
+ align:start position:0%
+between the order and the Ian state
+representation and it's just a matter of
+
+ align:start position:0%
+representation and it's just a matter of
+ 
+
+ align:start position:0%
+representation and it's just a matter of
+which way you're
+
+ align:start position:0%
+which way you're
+ 
+
+ align:start position:0%
+which way you're
+going okay so we know these things
+
+ align:start position:0%
+going okay so we know these things
+ 
+
+ align:start position:0%
+going okay so we know these things
+because we did diagonalize The Matrix
+
+ align:start position:0%
+because we did diagonalize The Matrix
+ 
+
+ align:start position:0%
+because we did diagonalize The Matrix
+and so if we know by the nature of what
+
+ align:start position:0%
+and so if we know by the nature of what
+ 
+
+ align:start position:0%
+and so if we know by the nature of what
+the molecule is and what the process is
+
+ align:start position:0%
+the molecule is and what the process is
+ 
+
+ align:start position:0%
+the molecule is and what the process is
+for getting into this energy region what
+
+ align:start position:0%
+for getting into this energy region what
+ 
+
+ align:start position:0%
+for getting into this energy region what
+is the bright State then we can always
+
+ align:start position:0%
+is the bright State then we can always
+ 
+
+ align:start position:0%
+is the bright State then we can always
+say okay the time evolving
+
+ align:start position:0%
+say okay the time evolving
+ 
+
+ align:start position:0%
+say okay the time evolving
+State uh well uh we can always write the
+
+ align:start position:0%
+State uh well uh we can always write the
+ 
+
+ align:start position:0%
+State uh well uh we can always write the
+time evolving State as a superposition
+
+ align:start position:0%
+time evolving State as a superposition
+ 
+
+ align:start position:0%
+time evolving State as a superposition
+but one of the members of the
+
+ align:start position:0%
+but one of the members of the
+ 
+
+ align:start position:0%
+but one of the members of the
+superposition is going to I'm
+
+ align:start position:0%
+superposition is going to I'm
+ 
+
+ align:start position:0%
+superposition is going to I'm
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+backup uh one of the
+
+ align:start position:0%
+backup uh one of the
+ 
+
+ align:start position:0%
+backup uh one of the
+um one of the zero order States is
+
+ align:start position:0%
+um one of the zero order States is
+ 
+
+ align:start position:0%
+um one of the zero order States is
+usually the bright State and
+
+ align:start position:0%
+usually the bright State and
+ 
+
+ align:start position:0%
+usually the bright State and
+there there are two classes of
+
+ align:start position:0%
+there there are two classes of
+ 
+
+ align:start position:0%
+there there are two classes of
+experiment that prepare highly excited
+
+ align:start position:0%
+experiment that prepare highly excited
+ 
+
+ align:start position:0%
+experiment that prepare highly excited
+molecules one is called High
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+overtone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pumping and the other is called
+
+ align:start position:0%
+pumping and the other is called
+ 
+
+ align:start position:0%
+pumping and the other is called
+stimulated emission
+
+ align:start position:0%
+stimulated emission
+ 
+
+ align:start position:0%
+stimulated emission
+pumping High overtone pumping was very
+
+ align:start position:0%
+pumping High overtone pumping was very
+ 
+
+ align:start position:0%
+pumping High overtone pumping was very
+popular uh in the
+
+ align:start position:0%
+popular uh in the
+ 
+
+ align:start position:0%
+popular uh in the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh late
+
+ align:start position:0%
+uh late
+ 
+
+ align:start position:0%
+uh late
+70s uh because people started to have
+
+ align:start position:0%
+70s uh because people started to have
+ 
+
+ align:start position:0%
+70s uh because people started to have
+tunable lasers and started to have
+
+ align:start position:0%
+tunable lasers and started to have
+ 
+
+ align:start position:0%
+tunable lasers and started to have
+sufficient ability with the lasers they
+
+ align:start position:0%
+sufficient ability with the lasers they
+ 
+
+ align:start position:0%
+sufficient ability with the lasers they
+could look at Spectra at fairly High
+
+ align:start position:0%
+could look at Spectra at fairly High
+ 
+
+ align:start position:0%
+could look at Spectra at fairly High
+sensitivity and so they were putting all
+
+ align:start position:0%
+sensitivity and so they were putting all
+ 
+
+ align:start position:0%
+sensitivity and so they were putting all
+sorts of gases into their apparatus and
+
+ align:start position:0%
+sorts of gases into their apparatus and
+ 
+
+ align:start position:0%
+sorts of gases into their apparatus and
+they observed vibrational transitions in
+
+ align:start position:0%
+they observed vibrational transitions in
+ 
+
+ align:start position:0%
+they observed vibrational transitions in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+visible and we know vibrational
+
+ align:start position:0%
+visible and we know vibrational
+ 
+
+ align:start position:0%
+visible and we know vibrational
+transitions are going to be in the
+
+ align:start position:0%
+transitions are going to be in the
+ 
+
+ align:start position:0%
+transitions are going to be in the
+infrared but they observed instead of
+
+ align:start position:0%
+infrared but they observed instead of
+ 
+
+ align:start position:0%
+infrared but they observed instead of
+something really complicated they
+
+ align:start position:0%
+something really complicated they
+ 
+
+ align:start position:0%
+something really complicated they
+observed something really simple they
+
+ align:start position:0%
+observed something really simple they
+ 
+
+ align:start position:0%
+observed something really simple they
+observed a progression of RH stretch
+
+ align:start position:0%
+observed a progression of RH stretch
+ 
+
+ align:start position:0%
+observed a progression of RH stretch
+vibrations as and it didn't matter how
+
+ align:start position:0%
+vibrations as and it didn't matter how
+ 
+
+ align:start position:0%
+vibrations as and it didn't matter how
+complicated the molecule was you had a
+
+ align:start position:0%
+complicated the molecule was you had a
+ 
+
+ align:start position:0%
+complicated the molecule was you had a
+nice slightly anharmonic progression of
+
+ align:start position:0%
+nice slightly anharmonic progression of
+ 
+
+ align:start position:0%
+nice slightly anharmonic progression of
+transitions uh and usually uh the lasers
+
+ align:start position:0%
+transitions uh and usually uh the lasers
+ 
+
+ align:start position:0%
+transitions uh and usually uh the lasers
+started around uh um say 12,000 wave
+
+ align:start position:0%
+started around uh um say 12,000 wave
+ 
+
+ align:start position:0%
+started around uh um say 12,000 wave
+numbers which is 4 *
+
+ align:start position:0%
+numbers which is 4 *
+ 
+
+ align:start position:0%
+numbers which is 4 *
+3,000 and R8 stretches are 3,000 wave
+
+ align:start position:0%
+3,000 and R8 stretches are 3,000 wave
+ 
+
+ align:start position:0%
+3,000 and R8 stretches are 3,000 wave
+numbers and so you often had four five
+
+ align:start position:0%
+numbers and so you often had four five
+ 
+
+ align:start position:0%
+numbers and so you often had four five
+six maybe seven depending if you could
+
+ align:start position:0%
+six maybe seven depending if you could
+ 
+
+ align:start position:0%
+six maybe seven depending if you could
+go the lasers were
+
+ align:start position:0%
+go the lasers were
+ 
+
+ align:start position:0%
+go the lasers were
+sufficiently uh blue uh so you might see
+
+ align:start position:0%
+sufficiently uh blue uh so you might see
+ 
+
+ align:start position:0%
+sufficiently uh blue uh so you might see
+several members of this progression and
+
+ align:start position:0%
+several members of this progression and
+ 
+
+ align:start position:0%
+several members of this progression and
+it was very well behaved and uh uh there
+
+ align:start position:0%
+it was very well behaved and uh uh there
+ 
+
+ align:start position:0%
+it was very well behaved and uh uh there
+was a lot of interest in
+
+ align:start position:0%
+was a lot of interest in
+ 
+
+ align:start position:0%
+was a lot of interest in
+ivr uh on the overtones and so what one
+
+ align:start position:0%
+ivr uh on the overtones and so what one
+ 
+
+ align:start position:0%
+ivr uh on the overtones and so what one
+measured was how broad were these things
+
+ align:start position:0%
+measured was how broad were these things
+ 
+
+ align:start position:0%
+measured was how broad were these things
+and the width was somehow related to
+
+ align:start position:0%
+and the width was somehow related to
+ 
+
+ align:start position:0%
+and the width was somehow related to
+some ivr rate and there were a lot of
+
+ align:start position:0%
+some ivr rate and there were a lot of
+ 
+
+ align:start position:0%
+some ivr rate and there were a lot of
+theories uh what determined these widths
+
+ align:start position:0%
+theories uh what determined these widths
+ 
+
+ align:start position:0%
+theories uh what determined these widths
+now these are not homogeneous widths the
+
+ align:start position:0%
+now these are not homogeneous widths the
+ 
+
+ align:start position:0%
+now these are not homogeneous widths the
+they often at higher resolution you
+
+ align:start position:0%
+they often at higher resolution you
+ 
+
+ align:start position:0%
+they often at higher resolution you
+started to see some structure under
+
+ align:start position:0%
+started to see some structure under
+ 
+
+ align:start position:0%
+started to see some structure under
+these uh they couldn't be homogeneous
+
+ align:start position:0%
+these uh they couldn't be homogeneous
+ 
+
+ align:start position:0%
+these uh they couldn't be homogeneous
+widths but in a molecule like Benzene
+
+ align:start position:0%
+widths but in a molecule like Benzene
+ 
+
+ align:start position:0%
+widths but in a molecule like Benzene
+the density of states is so high that it
+
+ align:start position:0%
+the density of states is so high that it
+ 
+
+ align:start position:0%
+the density of states is so high that it
+would be impossible to resolve but in a
+
+ align:start position:0%
+would be impossible to resolve but in a
+ 
+
+ align:start position:0%
+would be impossible to resolve but in a
+molecule uh like from Malahide or uh uh
+
+ align:start position:0%
+molecule uh like from Malahide or uh uh
+ 
+
+ align:start position:0%
+molecule uh like from Malahide or uh uh
+methyl fluoride or something like that
+
+ align:start position:0%
+methyl fluoride or something like that
+ 
+
+ align:start position:0%
+methyl fluoride or something like that
+you could resolve the lines and there
+
+ align:start position:0%
+you could resolve the lines and there
+ 
+
+ align:start position:0%
+you could resolve the lines and there
+was interesting structure so even in the
+
+ align:start position:0%
+was interesting structure so even in the
+ 
+
+ align:start position:0%
+was interesting structure so even in the
+1970s yeah even oh
+
+ align:start position:0%
+1970s yeah even oh
+ 
+
+ align:start position:0%
+1970s yeah even oh
+sure uh so there was a lot of stuff and
+
+ align:start position:0%
+sure uh so there was a lot of stuff and
+ 
+
+ align:start position:0%
+sure uh so there was a lot of stuff and
+a lot of really stupid stuff said about
+
+ align:start position:0%
+a lot of really stupid stuff said about
+ 
+
+ align:start position:0%
+a lot of really stupid stuff said about
+them and uh um but the possibility of
+
+ align:start position:0%
+them and uh um but the possibility of
+ 
+
+ align:start position:0%
+them and uh um but the possibility of
+looking at high vibrational Levels by
+
+ align:start position:0%
+looking at high vibrational Levels by
+ 
+
+ align:start position:0%
+looking at high vibrational Levels by
+overtones uh stimulated an awful lot of
+
+ align:start position:0%
+overtones uh stimulated an awful lot of
+ 
+
+ align:start position:0%
+overtones uh stimulated an awful lot of
+belief that you could put a lot of
+
+ align:start position:0%
+belief that you could put a lot of
+ 
+
+ align:start position:0%
+belief that you could put a lot of
+exitation in one
+
+ align:start position:0%
+exitation in one
+ 
+
+ align:start position:0%
+exitation in one
+Bond uh because it was clear that these
+
+ align:start position:0%
+Bond uh because it was clear that these
+ 
+
+ align:start position:0%
+Bond uh because it was clear that these
+were local excitations and so it was
+
+ align:start position:0%
+were local excitations and so it was
+ 
+
+ align:start position:0%
+were local excitations and so it was
+clear that you know you could make
+
+ align:start position:0%
+clear that you know you could make
+ 
+
+ align:start position:0%
+clear that you know you could make
+Benzene with 16 six Quant of exitation
+
+ align:start position:0%
+Benzene with 16 six Quant of exitation
+ 
+
+ align:start position:0%
+Benzene with 16 six Quant of exitation
+on in an R8 stretch and this width was
+
+ align:start position:0%
+on in an R8 stretch and this width was
+ 
+
+ align:start position:0%
+on in an R8 stretch and this width was
+somehow telling you how long it would
+
+ align:start position:0%
+somehow telling you how long it would
+ 
+
+ align:start position:0%
+somehow telling you how long it would
+stay there and there are people in fact
+
+ align:start position:0%
+stay there and there are people in fact
+ 
+
+ align:start position:0%
+stay there and there are people in fact
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um Mike Barry at Allied chemical uh
+
+ align:start position:0%
+um Mike Barry at Allied chemical uh
+ 
+
+ align:start position:0%
+um Mike Barry at Allied chemical uh
+built up a big division promising to do
+
+ align:start position:0%
+built up a big division promising to do
+ 
+
+ align:start position:0%
+built up a big division promising to do
+Bond specific
+
+ align:start position:0%
+Bond specific
+ 
+
+ align:start position:0%
+Bond specific
+chemistry based on the appearance of
+
+ align:start position:0%
+chemistry based on the appearance of
+ 
+
+ align:start position:0%
+chemistry based on the appearance of
+these local modes I mean we're chemists
+
+ align:start position:0%
+these local modes I mean we're chemists
+ 
+
+ align:start position:0%
+these local modes I mean we're chemists
+we we believe in bonds and here
+
+ align:start position:0%
+we we believe in bonds and here
+ 
+
+ align:start position:0%
+we we believe in bonds and here
+something in the spectrum that looks
+
+ align:start position:0%
+something in the spectrum that looks
+ 
+
+ align:start position:0%
+something in the spectrum that looks
+like a bond a selective exitation of a
+
+ align:start position:0%
+like a bond a selective exitation of a
+ 
+
+ align:start position:0%
+like a bond a selective exitation of a
+bond and so here was this dream that you
+
+ align:start position:0%
+bond and so here was this dream that you
+ 
+
+ align:start position:0%
+bond and so here was this dream that you
+could you could excite to a specific put
+
+ align:start position:0%
+could you could excite to a specific put
+ 
+
+ align:start position:0%
+could you could excite to a specific put
+all the energy into a specific Bond and
+
+ align:start position:0%
+all the energy into a specific Bond and
+ 
+
+ align:start position:0%
+all the energy into a specific Bond and
+and then do chemistry on that Bond and
+
+ align:start position:0%
+and then do chemistry on that Bond and
+ 
+
+ align:start position:0%
+and then do chemistry on that Bond and
+that that was sold very hard by Mike
+
+ align:start position:0%
+that that was sold very hard by Mike
+ 
+
+ align:start position:0%
+that that was sold very hard by Mike
+Barry and some several other people okay
+
+ align:start position:0%
+Barry and some several other people okay
+ 
+
+ align:start position:0%
+Barry and some several other people okay
+it turned out to be impossible
+
+ align:start position:0%
+it turned out to be impossible
+ 
+
+ align:start position:0%
+it turned out to be impossible
+uh and stimulator emission pumping was
+
+ align:start position:0%
+uh and stimulator emission pumping was
+ 
+
+ align:start position:0%
+uh and stimulator emission pumping was
+invented by me and this was was a
+
+ align:start position:0%
+invented by me and this was was a
+ 
+
+ align:start position:0%
+invented by me and this was was a
+different class this gave access to a
+
+ align:start position:0%
+different class this gave access to a
+ 
+
+ align:start position:0%
+different class this gave access to a
+different class of Highly vibrationally
+
+ align:start position:0%
+different class of Highly vibrationally
+ 
+
+ align:start position:0%
+different class of Highly vibrationally
+excited
+
+ align:start position:0%
+excited
+ 
+
+ align:start position:0%
+excited
+state the local modes were uh present in
+
+ align:start position:0%
+state the local modes were uh present in
+ 
+
+ align:start position:0%
+state the local modes were uh present in
+the spectrum
+
+ align:start position:0%
+the spectrum
+ 
+
+ align:start position:0%
+the spectrum
+because um the RH stretches were most
+
+ align:start position:0%
+because um the RH stretches were most
+ 
+
+ align:start position:0%
+because um the RH stretches were most
+anharmonic and highest frequency and so
+
+ align:start position:0%
+anharmonic and highest frequency and so
+ 
+
+ align:start position:0%
+anharmonic and highest frequency and so
+in any given energy region a state a
+
+ align:start position:0%
+in any given energy region a state a
+ 
+
+ align:start position:0%
+in any given energy region a state a
+zero order state that has the most Quant
+
+ align:start position:0%
+zero order state that has the most Quant
+ 
+
+ align:start position:0%
+zero order state that has the most Quant
+in this lowest this highest frequency
+
+ align:start position:0%
+in this lowest this highest frequency
+ 
+
+ align:start position:0%
+in this lowest this highest frequency
+mode uh well that that will have the
+
+ align:start position:0%
+mode uh well that that will have the
+ 
+
+ align:start position:0%
+mode uh well that that will have the
+strongest uh the strongest uh uh
+
+ align:start position:0%
+strongest uh the strongest uh uh
+ 
+
+ align:start position:0%
+strongest uh the strongest uh uh
+transition and so because of the
+
+ align:start position:0%
+transition and so because of the
+ 
+
+ align:start position:0%
+transition and so because of the
+anharmonicity and because the fewer
+
+ align:start position:0%
+anharmonicity and because the fewer
+ 
+
+ align:start position:0%
+anharmonicity and because the fewer
+Quant each the rule of thumb is each
+
+ align:start position:0%
+Quant each the rule of thumb is each
+ 
+
+ align:start position:0%
+Quant each the rule of thumb is each
+successive harmonic cost you about a
+
+ align:start position:0%
+successive harmonic cost you about a
+ 
+
+ align:start position:0%
+successive harmonic cost you about a
+factor of 100 in intensity so if you
+
+ align:start position:0%
+factor of 100 in intensity so if you
+ 
+
+ align:start position:0%
+factor of 100 in intensity so if you
+have some states with eight quana in one
+
+ align:start position:0%
+have some states with eight quana in one
+ 
+
+ align:start position:0%
+have some states with eight quana in one
+lower frequency mode degenerate with
+
+ align:start position:0%
+lower frequency mode degenerate with
+ 
+
+ align:start position:0%
+lower frequency mode degenerate with
+states of six quana you would expect
+
+ align:start position:0%
+states of six quana you would expect
+ 
+
+ align:start position:0%
+states of six quana you would expect
+that all things being equal they're
+
+ align:start position:0%
+that all things being equal they're
+ 
+
+ align:start position:0%
+that all things being equal they're
+going to be 10,000 times weak
+
+ align:start position:0%
+going to be 10,000 times weak
+ 
+
+ align:start position:0%
+going to be 10,000 times weak
+transitions at those levels will be
+
+ align:start position:0%
+transitions at those levels will be
+ 
+
+ align:start position:0%
+transitions at those levels will be
+10,000 times weaker and that's true and
+
+ align:start position:0%
+10,000 times weaker and that's true and
+ 
+
+ align:start position:0%
+10,000 times weaker and that's true and
+so what happened in the overtones is
+
+ align:start position:0%
+so what happened in the overtones is
+ 
+
+ align:start position:0%
+so what happened in the overtones is
+that you had one bright State one class
+
+ align:start position:0%
+that you had one bright State one class
+ 
+
+ align:start position:0%
+that you had one bright State one class
+of bright state only one it plucks the
+
+ align:start position:0%
+of bright state only one it plucks the
+ 
+
+ align:start position:0%
+of bright state only one it plucks the
+system in a way which is relatively
+
+ align:start position:0%
+system in a way which is relatively
+ 
+
+ align:start position:0%
+system in a way which is relatively
+special and relatively uh uncoupled from
+
+ align:start position:0%
+special and relatively uh uncoupled from
+ 
+
+ align:start position:0%
+special and relatively uh uncoupled from
+chaos cuz how you know by stretching a
+
+ align:start position:0%
+chaos cuz how you know by stretching a
+ 
+
+ align:start position:0%
+chaos cuz how you know by stretching a
+bond uh uh it takes a while for the
+
+ align:start position:0%
+bond uh uh it takes a while for the
+ 
+
+ align:start position:0%
+bond uh uh it takes a while for the
+energy to leave that
+
+ align:start position:0%
+energy to leave that
+ 
+
+ align:start position:0%
+energy to leave that
+Bond and so it it's uh not a democratic
+
+ align:start position:0%
+Bond and so it it's uh not a democratic
+ 
+
+ align:start position:0%
+Bond and so it it's uh not a democratic
+sample of what's going on in the uh
+
+ align:start position:0%
+sample of what's going on in the uh
+ 
+
+ align:start position:0%
+sample of what's going on in the uh
+vibrational
+
+ align:start position:0%
+vibrational
+ 
+
+ align:start position:0%
+vibrational
+manifold uh and uh and so people were
+
+ align:start position:0%
+manifold uh and uh and so people were
+ 
+
+ align:start position:0%
+manifold uh and uh and so people were
+anxious to have some other way of
+
+ align:start position:0%
+anxious to have some other way of
+ 
+
+ align:start position:0%
+anxious to have some other way of
+starting out the Dynamics some other
+
+ align:start position:0%
+starting out the Dynamics some other
+ 
+
+ align:start position:0%
+starting out the Dynamics some other
+class of zero order bright State
+
+ align:start position:0%
+class of zero order bright State
+ 
+
+ align:start position:0%
+class of zero order bright State
+stimulated emission
+
+ align:start position:0%
+stimulated emission
+ 
+
+ align:start position:0%
+stimulated emission
+pumping was we go from the ground state
+
+ align:start position:0%
+pumping was we go from the ground state
+ 
+
+ align:start position:0%
+pumping was we go from the ground state
+to an electronically excited state and
+
+ align:start position:0%
+to an electronically excited state and
+ 
+
+ align:start position:0%
+to an electronically excited state and
+then back to high vibrational levels of
+
+ align:start position:0%
+then back to high vibrational levels of
+ 
+
+ align:start position:0%
+then back to high vibrational levels of
+the ground state and that's driven not
+
+ align:start position:0%
+the ground state and that's driven not
+ 
+
+ align:start position:0%
+the ground state and that's driven not
+by infrared selection rules or VI
+
+ align:start position:0%
+by infrared selection rules or VI
+ 
+
+ align:start position:0%
+by infrared selection rules or VI
+vibrational selection rules but by Frank
+
+ align:start position:0%
+vibrational selection rules but by Frank
+ 
+
+ align:start position:0%
+vibrational selection rules but by Frank
+Condon factors and so if you used an
+
+ align:start position:0%
+Condon factors and so if you used an
+ 
+
+ align:start position:0%
+Condon factors and so if you used an
+electronically excited state with
+
+ align:start position:0%
+electronically excited state with
+ 
+
+ align:start position:0%
+electronically excited state with
+geometry very different from the ground
+
+ align:start position:0%
+geometry very different from the ground
+ 
+
+ align:start position:0%
+geometry very different from the ground
+state then one can get access to high
+
+ align:start position:0%
+state then one can get access to high
+ 
+
+ align:start position:0%
+state then one can get access to high
+vibrational levels of the ground state
+
+ align:start position:0%
+vibrational levels of the ground state
+ 
+
+ align:start position:0%
+vibrational levels of the ground state
+that uh our frankc and
+
+ align:start position:0%
+that uh our frankc and
+ 
+
+ align:start position:0%
+that uh our frankc and
+selected and so this profoundly changed
+
+ align:start position:0%
+selected and so this profoundly changed
+ 
+
+ align:start position:0%
+selected and so this profoundly changed
+the name of the game because now it's
+
+ align:start position:0%
+the name of the game because now it's
+ 
+
+ align:start position:0%
+the name of the game because now it's
+not just one other class of bright state
+
+ align:start position:0%
+not just one other class of bright state
+ 
+
+ align:start position:0%
+not just one other class of bright state
+but depending on which vibrational level
+
+ align:start position:0%
+but depending on which vibrational level
+ 
+
+ align:start position:0%
+but depending on which vibrational level
+of this state you went to you could get
+
+ align:start position:0%
+of this state you went to you could get
+ 
+
+ align:start position:0%
+of this state you went to you could get
+different bright States and so one could
+
+ align:start position:0%
+different bright States and so one could
+ 
+
+ align:start position:0%
+different bright States and so one could
+start to pick away at the Dynamics and
+
+ align:start position:0%
+start to pick away at the Dynamics and
+ 
+
+ align:start position:0%
+start to pick away at the Dynamics and
+to understand them and so this led to an
+
+ align:start position:0%
+to understand them and so this led to an
+ 
+
+ align:start position:0%
+to understand them and so this led to an
+explosion of uh knowledge and
+
+ align:start position:0%
+explosion of uh knowledge and
+ 
+
+ align:start position:0%
+explosion of uh knowledge and
+experimentation on high vibrational
+
+ align:start position:0%
+experimentation on high vibrational
+ 
+
+ align:start position:0%
+experimentation on high vibrational
+levels because now we had it a much more
+
+ align:start position:0%
+levels because now we had it a much more
+ 
+
+ align:start position:0%
+levels because now we had it a much more
+democratic or at least a much more
+
+ align:start position:0%
+democratic or at least a much more
+ 
+
+ align:start position:0%
+democratic or at least a much more
+systematic view of the uh um the
+
+ align:start position:0%
+systematic view of the uh um the
+ 
+
+ align:start position:0%
+systematic view of the uh um the
+couplings that occur at high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exitation okay I I should stop but I
+
+ align:start position:0%
+exitation okay I I should stop but I
+ 
+
+ align:start position:0%
+exitation okay I I should stop but I
+want to say a couple more things about
+
+ align:start position:0%
+want to say a couple more things about
+ 
+
+ align:start position:0%
+want to say a couple more things about
+uh local
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modes so in the early
+
+ align:start position:0%
+modes so in the early
+ 
+
+ align:start position:0%
+modes so in the early
+days uh
+
+ align:start position:0%
+days uh
+ 
+
+ align:start position:0%
+days uh
+one saw experimentally that
+
+ align:start position:0%
+one saw experimentally that
+ 
+
+ align:start position:0%
+one saw experimentally that
+something appeared in the spectrum that
+
+ align:start position:0%
+something appeared in the spectrum that
+ 
+
+ align:start position:0%
+something appeared in the spectrum that
+looked like local RH stretch
+
+ align:start position:0%
+looked like local RH stretch
+ 
+
+ align:start position:0%
+looked like local RH stretch
+overtones and then going to these polyad
+
+ align:start position:0%
+overtones and then going to these polyad
+ 
+
+ align:start position:0%
+overtones and then going to these polyad
+models we discovered that what are the
+
+ align:start position:0%
+models we discovered that what are the
+ 
+
+ align:start position:0%
+models we discovered that what are the
+symptoms of local mode well what you one
+
+ align:start position:0%
+symptoms of local mode well what you one
+ 
+
+ align:start position:0%
+symptoms of local mode well what you one
+of the symptoms is there are almost
+
+ align:start position:0%
+of the symptoms is there are almost
+ 
+
+ align:start position:0%
+of the symptoms is there are almost
+always two
+
+ align:start position:0%
+always two
+ 
+
+ align:start position:0%
+always two
+symmetries I mean if you take two
+
+ align:start position:0%
+symmetries I mean if you take two
+ 
+
+ align:start position:0%
+symmetries I mean if you take two
+identical things and combine them
+
+ align:start position:0%
+identical things and combine them
+ 
+
+ align:start position:0%
+identical things and combine them
+symmetrically and antisymmetrically you
+
+ align:start position:0%
+symmetrically and antisymmetrically you
+ 
+
+ align:start position:0%
+symmetrically and antisymmetrically you
+have two states of different
+
+ align:start position:0%
+have two states of different
+ 
+
+ align:start position:0%
+have two states of different
+Symmetry and because the local modes
+
+ align:start position:0%
+Symmetry and because the local modes
+ 
+
+ align:start position:0%
+Symmetry and because the local modes
+don't know about each
+
+ align:start position:0%
+don't know about each
+ 
+
+ align:start position:0%
+don't know about each
+other they become degenerate and so this
+
+ align:start position:0%
+other they become degenerate and so this
+ 
+
+ align:start position:0%
+other they become degenerate and so this
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degeneracy was the the prime evidence
+
+ align:start position:0%
+degeneracy was the the prime evidence
+ 
+
+ align:start position:0%
+degeneracy was the the prime evidence
+for for the appearance of local
+
+ align:start position:0%
+for for the appearance of local
+ 
+
+ align:start position:0%
+for for the appearance of local
+modes remember when you record a
+
+ align:start position:0%
+modes remember when you record a
+ 
+
+ align:start position:0%
+modes remember when you record a
+spectrum you don't observe the wave
+
+ align:start position:0%
+spectrum you don't observe the wave
+ 
+
+ align:start position:0%
+spectrum you don't observe the wave
+function but when you fit a spectrum to
+
+ align:start position:0%
+function but when you fit a spectrum to
+ 
+
+ align:start position:0%
+function but when you fit a spectrum to
+a model you have igen vectors and you
+
+ align:start position:0%
+a model you have igen vectors and you
+ 
+
+ align:start position:0%
+a model you have igen vectors and you
+can look at what the igen vectors are
+
+ align:start position:0%
+can look at what the igen vectors are
+ 
+
+ align:start position:0%
+can look at what the igen vectors are
+like and you can re write the igen
+
+ align:start position:0%
+like and you can re write the igen
+ 
+
+ align:start position:0%
+like and you can re write the igen
+vectors Express them in terms of the
+
+ align:start position:0%
+vectors Express them in terms of the
+ 
+
+ align:start position:0%
+vectors Express them in terms of the
+internal coordinate displacements and
+
+ align:start position:0%
+internal coordinate displacements and
+ 
+
+ align:start position:0%
+internal coordinate displacements and
+You by examining the igen vectors of the
+
+ align:start position:0%
+You by examining the igen vectors of the
+ 
+
+ align:start position:0%
+You by examining the igen vectors of the
+effect of Hamilton you can see that you
+
+ align:start position:0%
+effect of Hamilton you can see that you
+ 
+
+ align:start position:0%
+effect of Hamilton you can see that you
+do have uh left oscillator and right
+
+ align:start position:0%
+do have uh left oscillator and right
+ 
+
+ align:start position:0%
+do have uh left oscillator and right
+oscillator but the igen states are
+
+ align:start position:0%
+oscillator but the igen states are
+ 
+
+ align:start position:0%
+oscillator but the igen states are
+always symmetric and antisymmetric
+
+ align:start position:0%
+always symmetric and antisymmetric
+ 
+
+ align:start position:0%
+always symmetric and antisymmetric
+combinations and that they're degenerate
+
+ align:start position:0%
+combinations and that they're degenerate
+ 
+
+ align:start position:0%
+combinations and that they're degenerate
+and if you if you took s+ plus SI
+
+ align:start position:0%
+and if you if you took s+ plus SI
+ 
+
+ align:start position:0%
+and if you if you took s+ plus SI
+minus uh where this is just some
+
+ align:start position:0%
+minus uh where this is just some
+ 
+
+ align:start position:0%
+minus uh where this is just some
+symmetric and any symmetric then you get
+
+ align:start position:0%
+symmetric and any symmetric then you get
+ 
+
+ align:start position:0%
+symmetric and any symmetric then you get
+S right and uh uh if you take the minus
+
+ align:start position:0%
+S right and uh uh if you take the minus
+ 
+
+ align:start position:0%
+S right and uh uh if you take the minus
+combination you get S left so the first
+
+ align:start position:0%
+combination you get S left so the first
+ 
+
+ align:start position:0%
+combination you get S left so the first
+thing is the observation of degeneracy
+
+ align:start position:0%
+thing is the observation of degeneracy
+ 
+
+ align:start position:0%
+thing is the observation of degeneracy
+then you look at the igen vectors and
+
+ align:start position:0%
+then you look at the igen vectors and
+ 
+
+ align:start position:0%
+then you look at the igen vectors and
+you see that they really are localized
+
+ align:start position:0%
+you see that they really are localized
+ 
+
+ align:start position:0%
+you see that they really are localized
+but they're not
+
+ align:start position:0%
+but they're not
+ 
+
+ align:start position:0%
+but they're not
+localized uh uh in the sense of one
+
+ align:start position:0%
+localized uh uh in the sense of one
+ 
+
+ align:start position:0%
+localized uh uh in the sense of one
+state because you can't do that you have
+
+ align:start position:0%
+state because you can't do that you have
+ 
+
+ align:start position:0%
+state because you can't do that you have
+left oscillator and right oscillator
+
+ align:start position:0%
+left oscillator and right oscillator
+ 
+
+ align:start position:0%
+left oscillator and right oscillator
+they're equivalent but you make the some
+
+ align:start position:0%
+they're equivalent but you make the some
+ 
+
+ align:start position:0%
+they're equivalent but you make the some
+some indifference terms and then you
+
+ align:start position:0%
+some indifference terms and then you
+ 
+
+ align:start position:0%
+some indifference terms and then you
+take sums IND differences of those you
+
+ align:start position:0%
+take sums IND differences of those you
+ 
+
+ align:start position:0%
+take sums IND differences of those you
+get back to these local mode
+
+ align:start position:0%
+get back to these local mode
+ 
+
+ align:start position:0%
+get back to these local mode
+States um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the other thing is that the
+
+ align:start position:0%
+and the other thing is that the
+ 
+
+ align:start position:0%
+and the other thing is that the
+intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pattern the intensity pattern in the
+
+ align:start position:0%
+pattern the intensity pattern in the
+ 
+
+ align:start position:0%
+pattern the intensity pattern in the
+Spectrum The Disappearance of all but
+
+ align:start position:0%
+Spectrum The Disappearance of all but
+ 
+
+ align:start position:0%
+Spectrum The Disappearance of all but
+one class of state which is recognized
+
+ align:start position:0%
+one class of state which is recognized
+ 
+
+ align:start position:0%
+one class of state which is recognized
+as an overtone of something that looks
+
+ align:start position:0%
+as an overtone of something that looks
+ 
+
+ align:start position:0%
+as an overtone of something that looks
+like an RH stretch because it has a
+
+ align:start position:0%
+like an RH stretch because it has a
+ 
+
+ align:start position:0%
+like an RH stretch because it has a
+frequency on the order of 3,000 wave
+
+ align:start position:0%
+frequency on the order of 3,000 wave
+ 
+
+ align:start position:0%
+frequency on the order of 3,000 wave
+numbers and the different R8 stretches o
+
+ align:start position:0%
+numbers and the different R8 stretches o
+ 
+
+ align:start position:0%
+numbers and the different R8 stretches o
+versus CH they have slightly different
+
+ align:start position:0%
+versus CH they have slightly different
+ 
+
+ align:start position:0%
+versus CH they have slightly different
+frequencies and so uh uh
+
+ align:start position:0%
+frequencies and so uh uh
+ 
+
+ align:start position:0%
+frequencies and so uh uh
+all of this implied the existence of
+
+ align:start position:0%
+all of this implied the existence of
+ 
+
+ align:start position:0%
+all of this implied the existence of
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+modes and uh
+
+ align:start position:0%
+modes and uh
+ 
+
+ align:start position:0%
+modes and uh
+so the the thing that I had hoped to get
+
+ align:start position:0%
+so the the thing that I had hoped to get
+ 
+
+ align:start position:0%
+so the the thing that I had hoped to get
+to today and why I handed out pages from
+
+ align:start position:0%
+to today and why I handed out pages from
+ 
+
+ align:start position:0%
+to today and why I handed out pages from
+the paper was that we can write the
+
+ align:start position:0%
+the paper was that we can write the
+ 
+
+ align:start position:0%
+the paper was that we can write the
+hamiltonian in a normal mode picture or
+
+ align:start position:0%
+hamiltonian in a normal mode picture or
+ 
+
+ align:start position:0%
+hamiltonian in a normal mode picture or
+in a local mode
+
+ align:start position:0%
+in a local mode
+ 
+
+ align:start position:0%
+in a local mode
+picture and
+
+ align:start position:0%
+picture and
+ 
+
+ align:start position:0%
+picture and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh the hamiltonian is expressed in terms
+
+ align:start position:0%
+uh the hamiltonian is expressed in terms
+ 
+
+ align:start position:0%
+uh the hamiltonian is expressed in terms
+of frequencies of modes and and
+
+ align:start position:0%
+of frequencies of modes and and
+ 
+
+ align:start position:0%
+of frequencies of modes and and
+harmonici of modes and coupling terms so
+
+ align:start position:0%
+harmonici of modes and coupling terms so
+ 
+
+ align:start position:0%
+harmonici of modes and coupling terms so
+you have two different
+
+ align:start position:0%
+you have two different
+ 
+
+ align:start position:0%
+you have two different
+models they're really describing the
+
+ align:start position:0%
+models they're really describing the
+ 
+
+ align:start position:0%
+models they're really describing the
+same phenomenon and you have the energy
+
+ align:start position:0%
+same phenomenon and you have the energy
+ 
+
+ align:start position:0%
+same phenomenon and you have the energy
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+so you fit the energy levels
+
+ align:start position:0%
+so you fit the energy levels
+ 
+
+ align:start position:0%
+so you fit the energy levels
+to frequencies and anharmonicities and
+
+ align:start position:0%
+to frequencies and anharmonicities and
+ 
+
+ align:start position:0%
+to frequencies and anharmonicities and
+coupling terms so you have a model where
+
+ align:start position:0%
+coupling terms so you have a model where
+ 
+
+ align:start position:0%
+coupling terms so you have a model where
+you fit the energy levels and what you
+
+ align:start position:0%
+you fit the energy levels and what you
+ 
+
+ align:start position:0%
+you fit the energy levels and what you
+fit in the energy level should be
+
+ align:start position:0%
+fit in the energy level should be
+ 
+
+ align:start position:0%
+fit in the energy level should be
+related to the fundamental parameters in
+
+ align:start position:0%
+related to the fundamental parameters in
+ 
+
+ align:start position:0%
+related to the fundamental parameters in
+these two so all three of these things
+
+ align:start position:0%
+these two so all three of these things
+ 
+
+ align:start position:0%
+these two so all three of these things
+are related and the pages from the paper
+
+ align:start position:0%
+are related and the pages from the paper
+ 
+
+ align:start position:0%
+are related and the pages from the paper
+show how you relate the various
+
+ align:start position:0%
+show how you relate the various
+ 
+
+ align:start position:0%
+show how you relate the various
+quantities there's a lot of insight into
+
+ align:start position:0%
+quantities there's a lot of insight into
+ 
+
+ align:start position:0%
+quantities there's a lot of insight into
+uh the Rel gain from the relationships
+
+ align:start position:0%
+uh the Rel gain from the relationships
+ 
+
+ align:start position:0%
+uh the Rel gain from the relationships
+between these two the last word is as is
+
+ align:start position:0%
+between these two the last word is as is
+ 
+
+ align:start position:0%
+between these two the last word is as is
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+true uh in
+
+ align:start position:0%
+true uh in
+ 
+
+ align:start position:0%
+true uh in
+um uh problems in
+
+ align:start position:0%
+um uh problems in
+ 
+
+ align:start position:0%
+um uh problems in
+spectroscopy you have a war between a
+
+ align:start position:0%
+spectroscopy you have a war between a
+ 
+
+ align:start position:0%
+spectroscopy you have a war between a
+term that tries to make things simple
+
+ align:start position:0%
+term that tries to make things simple
+ 
+
+ align:start position:0%
+term that tries to make things simple
+and a term that tries to make things
+
+ align:start position:0%
+and a term that tries to make things
+ 
+
+ align:start position:0%
+and a term that tries to make things
+complicated and there's usually two
+
+ align:start position:0%
+complicated and there's usually two
+ 
+
+ align:start position:0%
+complicated and there's usually two
+representations and the role of the
+
+ align:start position:0%
+representations and the role of the
+ 
+
+ align:start position:0%
+representations and the role of the
+destroying term and the saving term get
+
+ align:start position:0%
+destroying term and the saving term get
+ 
+
+ align:start position:0%
+destroying term and the saving term get
+switched in the two
+
+ align:start position:0%
+switched in the two
+ 
+
+ align:start position:0%
+switched in the two
+representations and this local and
+
+ align:start position:0%
+representations and this local and
+ 
+
+ align:start position:0%
+representations and this local and
+normal picture are is a beautifully
+
+ align:start position:0%
+normal picture are is a beautifully
+ 
+
+ align:start position:0%
+normal picture are is a beautifully
+instructive situation where you see how
+
+ align:start position:0%
+instructive situation where you see how
+ 
+
+ align:start position:0%
+instructive situation where you see how
+what destroys the regularity in one
+
+ align:start position:0%
+what destroys the regularity in one
+ 
+
+ align:start position:0%
+what destroys the regularity in one
+model preserves in the other and after
+
+ align:start position:0%
+model preserves in the other and after
+ 
+
+ align:start position:0%
+model preserves in the other and after
+all you're trying to the the molecule is
+
+ align:start position:0%
+all you're trying to the the molecule is
+ 
+
+ align:start position:0%
+all you're trying to the the molecule is
+trying to go from this to this so if
+
+ align:start position:0%
+trying to go from this to this so if
+ 
+
+ align:start position:0%
+trying to go from this to this so if
+something is good here it has to be bad
+
+ align:start position:0%
+something is good here it has to be bad
+ 
+
+ align:start position:0%
+something is good here it has to be bad
+here and vice
+
+ align:start position:0%
+here and vice
+ 
+
+ align:start position:0%
+here and vice
+versa but this is so Universal in in
+
+ align:start position:0%
+versa but this is so Universal in in
+ 
+
+ align:start position:0%
+versa but this is so Universal in in
+spectroscopy that as soon as you get
+
+ align:start position:0%
+spectroscopy that as soon as you get
+ 
+
+ align:start position:0%
+spectroscopy that as soon as you get
+away from textbook Spectra you have a
+
+ align:start position:0%
+away from textbook Spectra you have a
+ 
+
+ align:start position:0%
+away from textbook Spectra you have a
+choice of two representations and the
+
+ align:start position:0%
+choice of two representations and the
+ 
+
+ align:start position:0%
+choice of two representations and the
+role played by the good and bad terms is
+
+ align:start position:0%
+role played by the good and bad terms is
+ 
+
+ align:start position:0%
+role played by the good and bad terms is
+reversed and and uh you never get
+
+ align:start position:0%
+reversed and and uh you never get
+ 
+
+ align:start position:0%
+reversed and and uh you never get
+something for nothing you never for
+
+ align:start position:0%
+something for nothing you never for
+ 
+
+ align:start position:0%
+something for nothing you never for
+example in redberg States going to case
+
+ align:start position:0%
+example in redberg States going to case
+ 
+
+ align:start position:0%
+example in redberg States going to case
+D is a wonderful thing because the
+
+ align:start position:0%
+D is a wonderful thing because the
+ 
+
+ align:start position:0%
+D is a wonderful thing because the
+rotational hamiltonian becomes diagonal
+
+ align:start position:0%
+rotational hamiltonian becomes diagonal
+ 
+
+ align:start position:0%
+rotational hamiltonian becomes diagonal
+but magically the electronic hamiltonian
+
+ align:start position:0%
+but magically the electronic hamiltonian
+ 
+
+ align:start position:0%
+but magically the electronic hamiltonian
+becomes off diagonal and most people
+
+ align:start position:0%
+becomes off diagonal and most people
+ 
+
+ align:start position:0%
+becomes off diagonal and most people
+don't know about that and so they think
+
+ align:start position:0%
+don't know about that and so they think
+ 
+
+ align:start position:0%
+don't know about that and so they think
+oh it's just great let's just do this so
+
+ align:start position:0%
+oh it's just great let's just do this so
+ 
+
+ align:start position:0%
+oh it's just great let's just do this so
+there are many many cases where you know
+
+ align:start position:0%
+there are many many cases where you know
+ 
+
+ align:start position:0%
+there are many many cases where you know
+uh you're going to be going between
+
+ align:start position:0%
+uh you're going to be going between
+ 
+
+ align:start position:0%
+uh you're going to be going between
+these two representations there's one
+
+ align:start position:0%
+these two representations there's one
+ 
+
+ align:start position:0%
+these two representations there's one
+that's always better than the other for
+
+ align:start position:0%
+that's always better than the other for
+ 
+
+ align:start position:0%
+that's always better than the other for
+the particular case
+
+ align:start position:0%
+the particular case
+ 
+
+ align:start position:0%
+the particular case
+but um you have to be careful about
+
+ align:start position:0%
+but um you have to be careful about
+ 
+
+ align:start position:0%
+but um you have to be careful about
+remembering what's good and what's bad
+
+ align:start position:0%
+remembering what's good and what's bad
+ 
+
+ align:start position:0%
+remembering what's good and what's bad
+it's all
+
+ align:start position:0%
+it's all
+ 
+
+ align:start position:0%
+it's all
+relative okay so that's that's it I'm
+
+ align:start position:0%
+relative okay so that's that's it I'm
+ 
+
+ align:start position:0%
+relative okay so that's that's it I'm
+not sure what I'm going to do next week
+
+ align:start position:0%
+not sure what I'm going to do next week
+ 
+
+ align:start position:0%
+not sure what I'm going to do next week
+but we're getting close to the end I
+
+ align:start position:0%
+but we're getting close to the end I
+ 
+
+ align:start position:0%
+but we're getting close to the end I
+think I'm not quite finished with
+
+ align:start position:0%
+think I'm not quite finished with
+ 
+
+ align:start position:0%
+think I'm not quite finished with
+vibrations but we'll see
\ No newline at end of file
diff --git a/LbKKzMag5Rc.txt b/LbKKzMag5Rc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..523870b51f19da333226dcad2cd8431c3d3ed480
--- /dev/null
+++ b/LbKKzMag5Rc.txt
@@ -0,0 +1,8163 @@
+align:start position:0%
+ 
+oh the
+
+ align:start position:0%
+oh the
+ 
+
+ align:start position:0%
+oh the
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the topic for today is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the uh today we're going to talk uh I'm
+
+ align:start position:0%
+the uh today we're going to talk uh I'm
+ 
+
+ align:start position:0%
+the uh today we're going to talk uh I'm
+postponing the linear equation to next
+
+ align:start position:0%
+postponing the linear equation to next
+ 
+
+ align:start position:0%
+postponing the linear equation to next
+time uh instead uh I think it's a good
+
+ align:start position:0%
+time uh instead uh I think it's a good
+ 
+
+ align:start position:0%
+time uh instead uh I think it's a good
+idea since in real life most of the
+
+ align:start position:0%
+idea since in real life most of the
+ 
+
+ align:start position:0%
+idea since in real life most of the
+differential equations are solved by
+
+ align:start position:0%
+differential equations are solved by
+ 
+
+ align:start position:0%
+differential equations are solved by
+numerical methods to introduce you to
+
+ align:start position:0%
+numerical methods to introduce you to
+ 
+
+ align:start position:0%
+numerical methods to introduce you to
+those right away even when you see the
+
+ align:start position:0%
+those right away even when you see the
+ 
+
+ align:start position:0%
+those right away even when you see the
+compu where you saw the computer screen
+
+ align:start position:0%
+compu where you saw the computer screen
+ 
+
+ align:start position:0%
+compu where you saw the computer screen
+uh the solutions being drawn of course
+
+ align:start position:0%
+uh the solutions being drawn of course
+ 
+
+ align:start position:0%
+uh the solutions being drawn of course
+that what really was happening is that
+
+ align:start position:0%
+that what really was happening is that
+ 
+
+ align:start position:0%
+that what really was happening is that
+the computer was calculating the
+
+ align:start position:0%
+the computer was calculating the
+ 
+
+ align:start position:0%
+the computer was calculating the
+solutions numerically and plotting the
+
+ align:start position:0%
+solutions numerically and plotting the
+ 
+
+ align:start position:0%
+solutions numerically and plotting the
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+so this is the main way numerically is
+
+ align:start position:0%
+so this is the main way numerically is
+ 
+
+ align:start position:0%
+so this is the main way numerically is
+the main way differential equations are
+
+ align:start position:0%
+the main way differential equations are
+ 
+
+ align:start position:0%
+the main way differential equations are
+actually solved there of any complexity
+
+ align:start position:0%
+actually solved there of any complexity
+ 
+
+ align:start position:0%
+actually solved there of any complexity
+at all now so the problem is an initial
+
+ align:start position:0%
+at all now so the problem is an initial
+ 
+
+ align:start position:0%
+at all now so the problem is an initial
+value problem let's write it A first
+
+ align:start position:0%
+value problem let's write it A first
+ 
+
+ align:start position:0%
+value problem let's write it A first
+order problem the way we talked about it
+
+ align:start position:0%
+order problem the way we talked about it
+ 
+
+ align:start position:0%
+order problem the way we talked about it
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+Wednesday uh and now I'll specifically
+
+ align:start position:0%
+Wednesday uh and now I'll specifically
+ 
+
+ align:start position:0%
+Wednesday uh and now I'll specifically
+add to that the starting point that you
+
+ align:start position:0%
+add to that the starting point that you
+ 
+
+ align:start position:0%
+add to that the starting point that you
+used when you did the computer
+
+ align:start position:0%
+used when you did the computer
+ 
+
+ align:start position:0%
+used when you did the computer
+experiments and I'll write the starting
+
+ align:start position:0%
+experiments and I'll write the starting
+ 
+
+ align:start position:0%
+experiments and I'll write the starting
+point this way so y of x0 should be y0
+
+ align:start position:0%
+point this way so y of x0 should be y0
+ 
+
+ align:start position:0%
+point this way so y of x0 should be y0
+so this is the initial condition and
+
+ align:start position:0%
+so this is the initial condition and
+ 
+
+ align:start position:0%
+so this is the initial condition and
+this is the first order differential
+
+ align:start position:0%
+this is the first order differential
+ 
+
+ align:start position:0%
+this is the first order differential
+equation and as you know the two of them
+
+ align:start position:0%
+equation and as you know the two of them
+ 
+
+ align:start position:0%
+equation and as you know the two of them
+together are called an ivp an initial
+
+ align:start position:0%
+together are called an ivp an initial
+ 
+
+ align:start position:0%
+together are called an ivp an initial
+value problem which means two things the
+
+ align:start position:0%
+value problem which means two things the
+ 
+
+ align:start position:0%
+value problem which means two things the
+differential equation and the initial
+
+ align:start position:0%
+differential equation and the initial
+ 
+
+ align:start position:0%
+differential equation and the initial
+value uh that you are want to start the
+
+ align:start position:0%
+value uh that you are want to start the
+ 
+
+ align:start position:0%
+value uh that you are want to start the
+solution at
+
+ align:start position:0%
+solution at
+ 
+
+ align:start position:0%
+solution at
+okay the uh now the
+
+ align:start position:0%
+okay the uh now the
+ 
+
+ align:start position:0%
+okay the uh now the
+method we're going to talk about the
+
+ align:start position:0%
+method we're going to talk about the
+ 
+
+ align:start position:0%
+method we're going to talk about the
+basic method of which many others are
+
+ align:start position:0%
+basic method of which many others are
+ 
+
+ align:start position:0%
+basic method of which many others are
+merely refinements in one way or another
+
+ align:start position:0%
+merely refinements in one way or another
+ 
+
+ align:start position:0%
+merely refinements in one way or another
+is uh called Oilers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method Oiler who did of course
+
+ align:start position:0%
+method Oiler who did of course
+ 
+
+ align:start position:0%
+method Oiler who did of course
+everything in analysis did
+
+ align:start position:0%
+everything in analysis did
+ 
+
+ align:start position:0%
+everything in analysis did
+as far as I know didn't actually use it
+
+ align:start position:0%
+as far as I know didn't actually use it
+ 
+
+ align:start position:0%
+as far as I know didn't actually use it
+to compute Solutions of differential
+
+ align:start position:0%
+to compute Solutions of differential
+ 
+
+ align:start position:0%
+to compute Solutions of differential
+equations his interest was theoretical
+
+ align:start position:0%
+equations his interest was theoretical
+ 
+
+ align:start position:0%
+equations his interest was theoretical
+uh he used it as a method of proving the
+
+ align:start position:0%
+uh he used it as a method of proving the
+ 
+
+ align:start position:0%
+uh he used it as a method of proving the
+existence theorem that proving that
+
+ align:start position:0%
+existence theorem that proving that
+ 
+
+ align:start position:0%
+existence theorem that proving that
+Solutions
+
+ align:start position:0%
+Solutions
+ 
+
+ align:start position:0%
+Solutions
+existed but uh nowadays it's used to
+
+ align:start position:0%
+existed but uh nowadays it's used to
+ 
+
+ align:start position:0%
+existed but uh nowadays it's used to
+calculate the solutions numerically and
+
+ align:start position:0%
+calculate the solutions numerically and
+ 
+
+ align:start position:0%
+calculate the solutions numerically and
+the method is very simple to describe
+
+ align:start position:0%
+the method is very simple to describe
+ 
+
+ align:start position:0%
+the method is very simple to describe
+it's so naive if you probably think that
+
+ align:start position:0%
+it's so naive if you probably think that
+ 
+
+ align:start position:0%
+it's so naive if you probably think that
+if you had been living 300 years ago you
+
+ align:start position:0%
+if you had been living 300 years ago you
+ 
+
+ align:start position:0%
+if you had been living 300 years ago you
+would have discovered a and covered
+
+ align:start position:0%
+would have discovered a and covered
+ 
+
+ align:start position:0%
+would have discovered a and covered
+yourself with glory for all
+
+ align:start position:0%
+yourself with glory for all
+ 
+
+ align:start position:0%
+yourself with glory for all
+eternity here is uh so here is our
+
+ align:start position:0%
+eternity here is uh so here is our
+ 
+
+ align:start position:0%
+eternity here is uh so here is our
+starting point uh x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y0 now what information do we have at
+
+ align:start position:0%
+y0 now what information do we have at
+ 
+
+ align:start position:0%
+y0 now what information do we have at
+that point all we have is the little
+
+ align:start position:0%
+that point all we have is the little
+ 
+
+ align:start position:0%
+that point all we have is the little
+line element whose slope is given by F
+
+ align:start position:0%
+line element whose slope is given by F
+ 
+
+ align:start position:0%
+line element whose slope is given by F
+ofx Y so if I start the solution the
+
+ align:start position:0%
+ofx Y so if I start the solution the
+ 
+
+ align:start position:0%
+ofx Y so if I start the solution the
+only way the solution could possibly go
+
+ align:start position:0%
+only way the solution could possibly go
+ 
+
+ align:start position:0%
+only way the solution could possibly go
+would be to start off in that Direction
+
+ align:start position:0%
+would be to start off in that Direction
+ 
+
+ align:start position:0%
+would be to start off in that Direction
+since I have no other
+
+ align:start position:0%
+since I have no other
+ 
+
+ align:start position:0%
+since I have no other
+information at least it's cor has the
+
+ align:start position:0%
+information at least it's cor has the
+ 
+
+ align:start position:0%
+information at least it's cor has the
+correct direction at x0 y0 but of course
+
+ align:start position:0%
+correct direction at x0 y0 but of course
+ 
+
+ align:start position:0%
+correct direction at x0 y0 but of course
+it's not likely to have the correct
+
+ align:start position:0%
+it's not likely to have the correct
+ 
+
+ align:start position:0%
+it's not likely to have the correct
+direction anywhere else now what you do
+
+ align:start position:0%
+direction anywhere else now what you do
+ 
+
+ align:start position:0%
+direction anywhere else now what you do
+then is choose a step size I'll draw
+
+ align:start position:0%
+then is choose a step size I'll draw
+ 
+
+ align:start position:0%
+then is choose a step size I'll draw
+just a few two steps of the method
+
+ align:start position:0%
+just a few two steps of the method
+ 
+
+ align:start position:0%
+just a few two steps of the method
+that's I think good enough uh you choose
+
+ align:start position:0%
+that's I think good enough uh you choose
+ 
+
+ align:start position:0%
+that's I think good enough uh you choose
+a steps a uniform step size which is
+
+ align:start position:0%
+a steps a uniform step size which is
+ 
+
+ align:start position:0%
+a steps a uniform step size which is
+usually called
+
+ align:start position:0%
+usually called
+ 
+
+ align:start position:0%
+usually called
+H and you continue that solution until
+
+ align:start position:0%
+H and you continue that solution until
+ 
+
+ align:start position:0%
+H and you continue that solution until
+you get to the next point which will be
+
+ align:start position:0%
+you get to the next point which will be
+ 
+
+ align:start position:0%
+you get to the next point which will be
+x0 plus h as I've drawn it on the
+
+ align:start position:0%
+x0 plus h as I've drawn it on the
+ 
+
+ align:start position:0%
+x0 plus h as I've drawn it on the
+picture so we get to here uh we stop at
+
+ align:start position:0%
+picture so we get to here uh we stop at
+ 
+
+ align:start position:0%
+picture so we get to here uh we stop at
+that point and now you recalculate what
+
+ align:start position:0%
+that point and now you recalculate what
+ 
+
+ align:start position:0%
+that point and now you recalculate what
+the line element is here suppose here
+
+ align:start position:0%
+the line element is here suppose here
+ 
+
+ align:start position:0%
+the line element is here suppose here
+the line element now through this point
+
+ align:start position:0%
+the line element now through this point
+ 
+
+ align:start position:0%
+the line element now through this point
+goes like that well then that's the new
+
+ align:start position:0%
+goes like that well then that's the new
+ 
+
+ align:start position:0%
+goes like that well then that's the new
+direction that you should start out with
+
+ align:start position:0%
+direction that you should start out with
+ 
+
+ align:start position:0%
+direction that you should start out with
+going from here and so the next step of
+
+ align:start position:0%
+going from here and so the next step of
+ 
+
+ align:start position:0%
+going from here and so the next step of
+the process will carry you to here
+
+ align:start position:0%
+the process will carry you to here
+ 
+
+ align:start position:0%
+the process will carry you to here
+that's two steps of Oilers method notice
+
+ align:start position:0%
+that's two steps of Oilers method notice
+ 
+
+ align:start position:0%
+that's two steps of Oilers method notice
+it produces a broken line approximation
+
+ align:start position:0%
+it produces a broken line approximation
+ 
+
+ align:start position:0%
+it produces a broken line approximation
+to the solution but in fact you only see
+
+ align:start position:0%
+to the solution but in fact you only see
+ 
+
+ align:start position:0%
+to the solution but in fact you only see
+that broken
+
+ align:start position:0%
+that broken
+ 
+
+ align:start position:0%
+that broken
+line if you're at a computer if you're
+
+ align:start position:0%
+line if you're at a computer if you're
+ 
+
+ align:start position:0%
+line if you're at a computer if you're
+uh looking at the computer visual for
+
+ align:start position:0%
+uh looking at the computer visual for
+ 
+
+ align:start position:0%
+uh looking at the computer visual for
+example which is whose purpose is to
+
+ align:start position:0%
+example which is whose purpose is to
+ 
+
+ align:start position:0%
+example which is whose purpose is to
+illustrate for you Oilers method in
+
+ align:start position:0%
+illustrate for you Oilers method in
+ 
+
+ align:start position:0%
+illustrate for you Oilers method in
+actual practice what you see is just the
+
+ align:start position:0%
+actual practice what you see is just the
+ 
+
+ align:start position:0%
+actual practice what you see is just the
+computer is simply calculating this
+
+ align:start position:0%
+computer is simply calculating this
+ 
+
+ align:start position:0%
+computer is simply calculating this
+point that point that point and the
+
+ align:start position:0%
+point that point that point and the
+ 
+
+ align:start position:0%
+point that point that point and the
+succession of points and many programs
+
+ align:start position:0%
+succession of points and many programs
+ 
+
+ align:start position:0%
+succession of points and many programs
+will just automatically connect those
+
+ align:start position:0%
+will just automatically connect those
+ 
+
+ align:start position:0%
+will just automatically connect those
+points by a smooth looking curve if uh
+
+ align:start position:0%
+points by a smooth looking curve if uh
+ 
+
+ align:start position:0%
+points by a smooth looking curve if uh
+that's what you prefer to
+
+ align:start position:0%
+that's what you prefer to
+ 
+
+ align:start position:0%
+that's what you prefer to
+see well that's that's all there is to
+
+ align:start position:0%
+see well that's that's all there is to
+ 
+
+ align:start position:0%
+see well that's that's all there is to
+the method uh what we have to do now is
+
+ align:start position:0%
+the method uh what we have to do now is
+ 
+
+ align:start position:0%
+the method uh what we have to do now is
+derive the equations for the
+
+ align:start position:0%
+derive the equations for the
+ 
+
+ align:start position:0%
+derive the equations for the
+method how are we going to do that well
+
+ align:start position:0%
+method how are we going to do that well
+ 
+
+ align:start position:0%
+method how are we going to do that well
+the essence of it is how to get from the
+
+ align:start position:0%
+the essence of it is how to get from the
+ 
+
+ align:start position:0%
+the essence of it is how to get from the
+nth step to the N plus First Step so I'm
+
+ align:start position:0%
+nth step to the N plus First Step so I'm
+ 
+
+ align:start position:0%
+nth step to the N plus First Step so I'm
+going to draw that a picture just to
+
+ align:start position:0%
+going to draw that a picture just to
+ 
+
+ align:start position:0%
+going to draw that a picture just to
+illustr
+
+ align:start position:0%
+illustr
+ 
+
+ align:start position:0%
+illustr
+that so now we're not at x0 but let's
+
+ align:start position:0%
+that so now we're not at x0 but let's
+ 
+
+ align:start position:0%
+that so now we're not at x0 but let's
+say we've already gotten to xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+YN how do I take the next step well I
+
+ align:start position:0%
+YN how do I take the next step well I
+ 
+
+ align:start position:0%
+YN how do I take the next step well I
+take the line element and it goes up
+
+ align:start position:0%
+take the line element and it goes up
+ 
+
+ align:start position:0%
+take the line element and it goes up
+like that let's say because the slope is
+
+ align:start position:0%
+like that let's say because the slope is
+ 
+
+ align:start position:0%
+like that let's say because the slope is
+uh this I'm going to call that slope a
+
+ align:start position:0%
+uh this I'm going to call that slope a
+ 
+
+ align:start position:0%
+uh this I'm going to call that slope a
+subn of course a subn is the value of
+
+ align:start position:0%
+subn of course a subn is the value of
+ 
+
+ align:start position:0%
+subn of course a subn is the value of
+the right hand side at the point xn1 YN
+
+ align:start position:0%
+the right hand side at the point xn1 YN
+ 
+
+ align:start position:0%
+the right hand side at the point xn1 YN
+and we'll need that in the equation but
+
+ align:start position:0%
+and we'll need that in the equation but
+ 
+
+ align:start position:0%
+and we'll need that in the equation but
+I think it will be a little clearer if I
+
+ align:start position:0%
+I think it will be a little clearer if I
+ 
+
+ align:start position:0%
+I think it will be a little clearer if I
+just give it a capital letter at this
+
+ align:start position:0%
+just give it a capital letter at this
+ 
+
+ align:start position:0%
+just give it a capital letter at this
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+now how this is the new point and all I
+
+ align:start position:0%
+now how this is the new point and all I
+ 
+
+ align:start position:0%
+now how this is the new point and all I
+want to know is what are its coordinates
+
+ align:start position:0%
+want to know is what are its coordinates
+ 
+
+ align:start position:0%
+want to know is what are its coordinates
+well the xn + one is there the YN + one
+
+ align:start position:0%
+well the xn + one is there the YN + one
+ 
+
+ align:start position:0%
+well the xn + one is there the YN + one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+here clearly I should draw this triangle
+
+ align:start position:0%
+here clearly I should draw this triangle
+ 
+
+ align:start position:0%
+here clearly I should draw this triangle
+complete the
+
+ align:start position:0%
+complete the
+ 
+
+ align:start position:0%
+complete the
+triangle this side of the triangle this
+
+ align:start position:0%
+triangle this side of the triangle this
+ 
+
+ align:start position:0%
+triangle this side of the triangle this
+the hypotenuse has slope a n this side
+
+ align:start position:0%
+the hypotenuse has slope a n this side
+ 
+
+ align:start position:0%
+the hypotenuse has slope a n this side
+of the triangle has length H H is the
+
+ align:start position:0%
+of the triangle has length H H is the
+ 
+
+ align:start position:0%
+of the triangle has length H H is the
+step size perhaps I better indicate that
+
+ align:start position:0%
+step size perhaps I better indicate that
+ 
+
+ align:start position:0%
+step size perhaps I better indicate that
+actually put that up so that you know
+
+ align:start position:0%
+actually put that up so that you know
+ 
+
+ align:start position:0%
+actually put that up so that you know
+the word step size it means how it's the
+
+ align:start position:0%
+the word step size it means how it's the
+ 
+
+ align:start position:0%
+the word step size it means how it's the
+step size on the x axis how far you have
+
+ align:start position:0%
+step size on the x axis how far you have
+ 
+
+ align:start position:0%
+step size on the x axis how far you have
+to go to get from each x to the next
+
+ align:start position:0%
+to go to get from each x to the next
+ 
+
+ align:start position:0%
+to go to get from each x to the next
+one what's this well if that slope has
+
+ align:start position:0%
+one what's this well if that slope has
+ 
+
+ align:start position:0%
+one what's this well if that slope has
+this the slope a n this is H then this
+
+ align:start position:0%
+this the slope a n this is H then this
+ 
+
+ align:start position:0%
+this the slope a n this is H then this
+must be H * a
+
+ align:start position:0%
+must be H * a
+ 
+
+ align:start position:0%
+must be H * a
+n the length of that side
+
+ align:start position:0%
+n the length of that side
+ 
+
+ align:start position:0%
+n the length of that side
+right in order that the ratio of the
+
+ align:start position:0%
+right in order that the ratio of the
+ 
+
+ align:start position:0%
+right in order that the ratio of the
+height to this width should be a n and
+
+ align:start position:0%
+height to this width should be a n and
+ 
+
+ align:start position:0%
+height to this width should be a n and
+that gives us the
+
+ align:start position:0%
+that gives us the
+ 
+
+ align:start position:0%
+that gives us the
+method what's
+
+ align:start position:0%
+method what's
+ 
+
+ align:start position:0%
+method what's
+the how do I get from uh clearly to get
+
+ align:start position:0%
+the how do I get from uh clearly to get
+ 
+
+ align:start position:0%
+the how do I get from uh clearly to get
+from xn to xn plus one I simply add H so
+
+ align:start position:0%
+from xn to xn plus one I simply add H so
+ 
+
+ align:start position:0%
+from xn to xn plus one I simply add H so
+that's the trivial part of it the
+
+ align:start position:0%
+that's the trivial part of it the
+ 
+
+ align:start position:0%
+that's the trivial part of it the
+interesting thing is how do I get the
+
+ align:start position:0%
+interesting thing is how do I get the
+ 
+
+ align:start position:0%
+interesting thing is how do I get the
+new YN + one and so the best way to
+
+ align:start position:0%
+new YN + one and so the best way to
+ 
+
+ align:start position:0%
+new YN + one and so the best way to
+write it as that YN + 1us
+
+ align:start position:0%
+write it as that YN + 1us
+ 
+
+ align:start position:0%
+write it as that YN + 1us
+YN divided by
+
+ align:start position:0%
+YN divided by
+ 
+
+ align:start position:0%
+YN divided by
+H well YN sorry YN + 1 minus YN is is
+
+ align:start position:0%
+H well YN sorry YN + 1 minus YN is is
+ 
+
+ align:start position:0%
+H well YN sorry YN + 1 minus YN is is
+this line the same as the line H * a n
+
+ align:start position:0%
+this line the same as the line H * a n
+ 
+
+ align:start position:0%
+this line the same as the line H * a n
+so that's the way to write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it or since the computer is interested
+
+ align:start position:0%
+it or since the computer is interested
+ 
+
+ align:start position:0%
+it or since the computer is interested
+in calculating YN + one itself put this
+
+ align:start position:0%
+in calculating YN + one itself put this
+ 
+
+ align:start position:0%
+in calculating YN + one itself put this
+on the other side it you take the old YN
+
+ align:start position:0%
+on the other side it you take the old YN
+ 
+
+ align:start position:0%
+on the other side it you take the old YN
+the previous one and to it you add H
+
+ align:start position:0%
+the previous one and to it you add H
+ 
+
+ align:start position:0%
+the previous one and to it you add H
+time a n and what prel is a n well the
+
+ align:start position:0%
+time a n and what prel is a n well the
+ 
+
+ align:start position:0%
+time a n and what prel is a n well the
+computer has to be told that a n is the
+
+ align:start position:0%
+computer has to be told that a n is the
+ 
+
+ align:start position:0%
+computer has to be told that a n is the
+value of f so now with that let's
+
+ align:start position:0%
+value of f so now with that let's
+ 
+
+ align:start position:0%
+value of f so now with that let's
+actually write the oiler program not the
+
+ align:start position:0%
+actually write the oiler program not the
+ 
+
+ align:start position:0%
+actually write the oiler program not the
+program but the oiler the oiler method
+
+ align:start position:0%
+program but the oiler the oiler method
+ 
+
+ align:start position:0%
+program but the oiler the oiler method
+equations let's just call it the oiler
+
+ align:start position:0%
+equations let's just call it the oiler
+ 
+
+ align:start position:0%
+equations let's just call it the oiler
+equations what will they be first of all
+
+ align:start position:0%
+equations what will they be first of all
+ 
+
+ align:start position:0%
+equations what will they be first of all
+the new X is the old x +
+
+ align:start position:0%
+the new X is the old x +
+ 
+
+ align:start position:0%
+the new X is the old x +
+H the new Y is is just what I've written
+
+ align:start position:0%
+H the new Y is is just what I've written
+ 
+
+ align:start position:0%
+H the new Y is is just what I've written
+there the old y plus h * a certain
+
+ align:start position:0%
+there the old y plus h * a certain
+ 
+
+ align:start position:0%
+there the old y plus h * a certain
+number a n and finally a n has the value
+
+ align:start position:0%
+number a n and finally a n has the value
+ 
+
+ align:start position:0%
+number a n and finally a n has the value
+it's the slope of the line element here
+
+ align:start position:0%
+it's the slope of the line element here
+ 
+
+ align:start position:0%
+it's the slope of the line element here
+and therefore by definition that's F of
+
+ align:start position:0%
+and therefore by definition that's F of
+ 
+
+ align:start position:0%
+and therefore by definition that's F of
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+YN so it's these three equations which
+
+ align:start position:0%
+YN so it's these three equations which
+ 
+
+ align:start position:0%
+YN so it's these three equations which
+Define Oilers method if I assume in 100
+
+ align:start position:0%
+Define Oilers method if I assume in 100
+ 
+
+ align:start position:0%
+Define Oilers method if I assume in 100
+surely you must be asked is uh to at
+
+ align:start position:0%
+surely you must be asked is uh to at
+ 
+
+ align:start position:0%
+surely you must be asked is uh to at
+some point as an exercise in the term at
+
+ align:start position:0%
+some point as an exercise in the term at
+ 
+
+ align:start position:0%
+some point as an exercise in the term at
+one point to uh to uh calculate to
+
+ align:start position:0%
+one point to uh to uh calculate to
+ 
+
+ align:start position:0%
+one point to uh to uh calculate to
+program the computer in C or whatever
+
+ align:start position:0%
+program the computer in C or whatever
+ 
+
+ align:start position:0%
+program the computer in C or whatever
+they're using Java now I guess uh to do
+
+ align:start position:0%
+they're using Java now I guess uh to do
+ 
+
+ align:start position:0%
+they're using Java now I guess uh to do
+Oiler Oilers method and these are the
+
+ align:start position:0%
+Oiler Oilers method and these are the
+ 
+
+ align:start position:0%
+Oiler Oilers method and these are the
+equations you these would be the
+
+ align:start position:0%
+equations you these would be the
+ 
+
+ align:start position:0%
+equations you these would be the
+recursive equations that you would put
+
+ align:start position:0%
+recursive equations that you would put
+ 
+
+ align:start position:0%
+recursive equations that you would put
+in to do
+
+ align:start position:0%
+in to do
+ 
+
+ align:start position:0%
+in to do
+that okay uh let's try uh an example
+
+ align:start position:0%
+that okay uh let's try uh an example
+ 
+
+ align:start position:0%
+that okay uh let's try uh an example
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what would be a good color for wher
+
+ align:start position:0%
+so what would be a good color for wher
+ 
+
+ align:start position:0%
+so what would be a good color for wher
+well a purple I assume nobody can see
+
+ align:start position:0%
+well a purple I assume nobody can see
+ 
+
+ align:start position:0%
+well a purple I assume nobody can see
+purple is that
+
+ align:start position:0%
+purple is that
+ 
+
+ align:start position:0%
+purple is that
+correct can anyone in the back of the
+
+ align:start position:0%
+correct can anyone in the back of the
+ 
+
+ align:start position:0%
+correct can anyone in the back of the
+room see that that that's
+
+ align:start position:0%
+room see that that that's
+ 
+
+ align:start position:0%
+room see that that that's
+purple
+
+ align:start position:0%
+purple
+ 
+
+ align:start position:0%
+purple
+what okay sit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closer so let's calculate uh the example
+
+ align:start position:0%
+closer so let's calculate uh the example
+ 
+
+ align:start position:0%
+closer so let's calculate uh the example
+I'll use a simple example but it's not
+
+ align:start position:0%
+I'll use a simple example but it's not
+ 
+
+ align:start position:0%
+I'll use a simple example but it's not
+entirely trivial
+
+ align:start position:0%
+entirely trivial
+ 
+
+ align:start position:0%
+entirely trivial
+my example is going to be the equation
+
+ align:start position:0%
+my example is going to be the equation
+ 
+
+ align:start position:0%
+my example is going to be the equation
+x^2 - y^2 on the right hand side and
+
+ align:start position:0%
+x^2 - y^2 on the right hand side and
+ 
+
+ align:start position:0%
+x^2 - y^2 on the right hand side and
+let's start with Y of 0 equals one let's
+
+ align:start position:0%
+let's start with Y of 0 equals one let's
+ 
+
+ align:start position:0%
+let's start with Y of 0 equals one let's
+say and so this is my initial value
+
+ align:start position:0%
+say and so this is my initial value
+ 
+
+ align:start position:0%
+say and so this is my initial value
+problem that pair of equations and uh I
+
+ align:start position:0%
+problem that pair of equations and uh I
+ 
+
+ align:start position:0%
+problem that pair of equations and uh I
+have to specify a step size so let's
+
+ align:start position:0%
+have to specify a step size so let's
+ 
+
+ align:start position:0%
+have to specify a step size so let's
+take the step size to be
+
+ align:start position:0%
+take the step size to be
+ 
+
+ align:start position:0%
+take the step size to be
+0.1 you choose the step size or the
+
+ align:start position:0%
+0.1 you choose the step size or the
+ 
+
+ align:start position:0%
+0.1 you choose the step size or the
+computer does uh we'll have to talk
+
+ align:start position:0%
+computer does uh we'll have to talk
+ 
+
+ align:start position:0%
+computer does uh we'll have to talk
+about that in a few minutes
+
+ align:start position:0%
+about that in a few minutes
+ 
+
+ align:start position:0%
+about that in a few minutes
+now what do you do
+
+ align:start position:0%
+now what do you do
+ 
+
+ align:start position:0%
+now what do you do
+well I say this is a non-trivial
+
+ align:start position:0%
+well I say this is a non-trivial
+ 
+
+ align:start position:0%
+well I say this is a non-trivial
+equation because uh this equation as far
+
+ align:start position:0%
+equation because uh this equation as far
+ 
+
+ align:start position:0%
+equation because uh this equation as far
+as I know cannot be solved in terms of
+
+ align:start position:0%
+as I know cannot be solved in terms of
+ 
+
+ align:start position:0%
+as I know cannot be solved in terms of
+Elementary functions so this equation
+
+ align:start position:0%
+Elementary functions so this equation
+ 
+
+ align:start position:0%
+Elementary functions so this equation
+would be in fact a very good candidate
+
+ align:start position:0%
+would be in fact a very good candidate
+ 
+
+ align:start position:0%
+would be in fact a very good candidate
+for numerical a numerical method like
+
+ align:start position:0%
+for numerical a numerical method like
+ 
+
+ align:start position:0%
+for numerical a numerical method like
+Oilers and you had to use it or maybe it
+
+ align:start position:0%
+Oilers and you had to use it or maybe it
+ 
+
+ align:start position:0%
+Oilers and you had to use it or maybe it
+was the other way around I forget on
+
+ align:start position:0%
+was the other way around I forget on
+ 
+
+ align:start position:0%
+was the other way around I forget on
+your problem Set uh you drew a picture
+
+ align:start position:0%
+your problem Set uh you drew a picture
+ 
+
+ align:start position:0%
+your problem Set uh you drew a picture
+of the direction field and answered some
+
+ align:start position:0%
+of the direction field and answered some
+ 
+
+ align:start position:0%
+of the direction field and answered some
+questions about the iines
+
+ align:start position:0%
+questions about the iines
+ 
+
+ align:start position:0%
+questions about the iines
+how the solutions behave all right now
+
+ align:start position:0%
+how the solutions behave all right now
+ 
+
+ align:start position:0%
+how the solutions behave all right now
+the main thing I want you to get uh this
+
+ align:start position:0%
+the main thing I want you to get uh this
+ 
+
+ align:start position:0%
+the main thing I want you to get uh this
+is not just for Oilers talking about
+
+ align:start position:0%
+is not just for Oilers talking about
+ 
+
+ align:start position:0%
+is not just for Oilers talking about
+Oilers equations but in
+
+ align:start position:0%
+Oilers equations but in
+ 
+
+ align:start position:0%
+Oilers equations but in
+general for the calculations you have to
+
+ align:start position:0%
+general for the calculations you have to
+ 
+
+ align:start position:0%
+general for the calculations you have to
+do in this course it's extremely
+
+ align:start position:0%
+do in this course it's extremely
+ 
+
+ align:start position:0%
+do in this course it's extremely
+important to be systematic because if
+
+ align:start position:0%
+important to be systematic because if
+ 
+
+ align:start position:0%
+important to be systematic because if
+you are not systematic you know if you
+
+ align:start position:0%
+you are not systematic you know if you
+ 
+
+ align:start position:0%
+you are not systematic you know if you
+just scribble scribble scribble scribble
+
+ align:start position:0%
+just scribble scribble scribble scribble
+ 
+
+ align:start position:0%
+just scribble scribble scribble scribble
+scribble you can do the work but it
+
+ align:start position:0%
+scribble you can do the work but it
+ 
+
+ align:start position:0%
+scribble you can do the work but it
+becomes impossible to find
+
+ align:start position:0%
+becomes impossible to find
+ 
+
+ align:start position:0%
+becomes impossible to find
+mistakes you must do the work in a form
+
+ align:start position:0%
+mistakes you must do the work in a form
+ 
+
+ align:start position:0%
+mistakes you must do the work in a form
+in which which you can check in which it
+
+ align:start position:0%
+in which which you can check in which it
+ 
+
+ align:start position:0%
+in which which you can check in which it
+can be checked which you can look over
+
+ align:start position:0%
+can be checked which you can look over
+ 
+
+ align:start position:0%
+can be checked which you can look over
+it find and try to see where mistakes
+
+ align:start position:0%
+it find and try to see where mistakes
+ 
+
+ align:start position:0%
+it find and try to see where mistakes
+are if in fact there are any so I I
+
+ align:start position:0%
+are if in fact there are any so I I
+ 
+
+ align:start position:0%
+are if in fact there are any so I I
+strongly
+
+ align:start position:0%
+strongly
+ 
+
+ align:start position:0%
+strongly
+suggest uh this is not a suggestion this
+
+ align:start position:0%
+suggest uh this is not a suggestion this
+ 
+
+ align:start position:0%
+suggest uh this is not a suggestion this
+is a command uh that you make a little
+
+ align:start position:0%
+is a command uh that you make a little
+ 
+
+ align:start position:0%
+is a command uh that you make a little
+tight to do a Oilers method by hand I'd
+
+ align:start position:0%
+tight to do a Oilers method by hand I'd
+ 
+
+ align:start position:0%
+tight to do a Oilers method by hand I'd
+only ask you for a step or two since I'm
+
+ align:start position:0%
+only ask you for a step or two since I'm
+ 
+
+ align:start position:0%
+only ask you for a step or two since I'm
+just trying to make sure you have some
+
+ align:start position:0%
+just trying to make sure you have some
+ 
+
+ align:start position:0%
+just trying to make sure you have some
+idea of these equations and where they
+
+ align:start position:0%
+idea of these equations and where they
+ 
+
+ align:start position:0%
+idea of these equations and where they
+come from
+
+ align:start position:0%
+come from
+ 
+
+ align:start position:0%
+come from
+so first the value of n then the value
+
+ align:start position:0%
+so first the value of n then the value
+ 
+
+ align:start position:0%
+so first the value of n then the value
+of xn then the value of the
+
+ align:start position:0%
+of xn then the value of the
+ 
+
+ align:start position:0%
+of xn then the value of the
+YN and then a couple of more columns
+
+ align:start position:0%
+YN and then a couple of more columns
+ 
+
+ align:start position:0%
+YN and then a couple of more columns
+which tell you what the calcul how to do
+
+ align:start position:0%
+which tell you what the calcul how to do
+ 
+
+ align:start position:0%
+which tell you what the calcul how to do
+the calculation you're going to need the
+
+ align:start position:0%
+the calculation you're going to need the
+ 
+
+ align:start position:0%
+the calculation you're going to need the
+value of the
+
+ align:start position:0%
+value of the
+ 
+
+ align:start position:0%
+value of the
+slope and it's probably a good idea also
+
+ align:start position:0%
+slope and it's probably a good idea also
+ 
+
+ align:start position:0%
+slope and it's probably a good idea also
+because otherwise you'll forget it to
+
+ align:start position:0%
+because otherwise you'll forget it to
+ 
+
+ align:start position:0%
+because otherwise you'll forget it to
+put in h a because that occurs in the
+
+ align:start position:0%
+put in h a because that occurs in the
+ 
+
+ align:start position:0%
+put in h a because that occurs in the
+formula all right let's start doing it
+
+ align:start position:0%
+formula all right let's start doing it
+ 
+
+ align:start position:0%
+formula all right let's start doing it
+well the first value of n is zero that's
+
+ align:start position:0%
+well the first value of n is zero that's
+ 
+
+ align:start position:0%
+well the first value of n is zero that's
+the starting point at the starting point
+
+ align:start position:0%
+the starting point at the starting point
+ 
+
+ align:start position:0%
+the starting point at the starting point
+x0 y0 x has the value zero and Y has the
+
+ align:start position:0%
+x0 y0 x has the value zero and Y has the
+ 
+
+ align:start position:0%
+x0 y0 x has the value zero and Y has the
+value one so zero and
+
+ align:start position:0%
+value one so zero and
+ 
+
+ align:start position:0%
+value one so zero and
+one in other words I'm starting I'm
+
+ align:start position:0%
+one in other words I'm starting I'm
+ 
+
+ align:start position:0%
+one in other words I'm starting I'm
+carrying out exactly what I drew
+
+ align:start position:0%
+carrying out exactly what I drew
+ 
+
+ align:start position:0%
+carrying out exactly what I drew
+pictorially only now I'm doing it
+
+ align:start position:0%
+pictorially only now I'm doing it
+ 
+
+ align:start position:0%
+pictorially only now I'm doing it
+arithmetically using a table and
+
+ align:start position:0%
+arithmetically using a table and
+ 
+
+ align:start position:0%
+arithmetically using a table and
+substituting into the formulas okay the
+
+ align:start position:0%
+substituting into the formulas okay the
+ 
+
+ align:start position:0%
+substituting into the formulas okay the
+next thing we have to calc Cal is a n
+
+ align:start position:0%
+next thing we have to calc Cal is a n
+ 
+
+ align:start position:0%
+next thing we have to calc Cal is a n
+well that's since a n is the value of
+
+ align:start position:0%
+well that's since a n is the value of
+ 
+
+ align:start position:0%
+well that's since a n is the value of
+the right hand
+
+ align:start position:0%
+the right hand
+ 
+
+ align:start position:0%
+the right hand
+side at the 01 you have to plug that in
+
+ align:start position:0%
+side at the 01 you have to plug that in
+ 
+
+ align:start position:0%
+side at the 01 you have to plug that in
+the right hand side is x0 x^2 - y^2 so
+
+ align:start position:0%
+the right hand side is x0 x^2 - y^2 so
+ 
+
+ align:start position:0%
+the right hand side is x0 x^2 - y^2 so
+it's 0^ 2us 1^ squar the value of the
+
+ align:start position:0%
+it's 0^ 2us 1^ squar the value of the
+ 
+
+ align:start position:0%
+it's 0^ 2us 1^ squar the value of the
+slope there is minus one negative 1 now
+
+ align:start position:0%
+slope there is minus one negative 1 now
+ 
+
+ align:start position:0%
+slope there is minus one negative 1 now
+I have to multiply that by H H is 0.1 so
+
+ align:start position:0%
+I have to multiply that by H H is 0.1 so
+ 
+
+ align:start position:0%
+I have to multiply that by H H is 0.1 so
+it's minus sorry negative I'll never
+
+ align:start position:0%
+it's minus sorry negative I'll never
+ 
+
+ align:start position:0%
+it's minus sorry negative I'll never
+learn that
+
+ align:start position:0%
+learn that
+ 
+
+ align:start position:0%
+learn that
+the way you learn to talk in
+
+ align:start position:0%
+the way you learn to talk in
+ 
+
+ align:start position:0%
+the way you learn to talk in
+kindergarten is the way you learn to
+
+ align:start position:0%
+kindergarten is the way you learn to
+ 
+
+ align:start position:0%
+kindergarten is the way you learn to
+talk the rest of your life
+
+ align:start position:0%
+talk the rest of your life
+ 
+
+ align:start position:0%
+talk the rest of your life
+unfortunately uh kindergarten we said
+
+ align:start position:0%
+unfortunately uh kindergarten we said
+ 
+
+ align:start position:0%
+unfortunately uh kindergarten we said
+minus uh Sor negative
+
+ align:start position:0%
+minus uh Sor negative
+ 
+
+ align:start position:0%
+minus uh Sor negative
+.1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh n is one now what's the value of xn
+
+ align:start position:0%
+uh n is one now what's the value of xn
+ 
+
+ align:start position:0%
+uh n is one now what's the value of xn
+well to the old one I add
+
+ align:start position:0%
+well to the old one I add
+ 
+
+ align:start position:0%
+well to the old one I add
+on10th what's the value of y well at
+
+ align:start position:0%
+on10th what's the value of y well at
+ 
+
+ align:start position:0%
+on10th what's the value of y well at
+this point you have to do the
+
+ align:start position:0%
+this point you have to do the
+ 
+
+ align:start position:0%
+this point you have to do the
+calculation it's the old value of y to
+
+ align:start position:0%
+calculation it's the old value of y to
+ 
+
+ align:start position:0%
+calculation it's the old value of y to
+get this new value it's the old Value
+
+ align:start position:0%
+get this new value it's the old Value
+ 
+
+ align:start position:0%
+get this new value it's the old Value
+Plus this number well that's this plus
+
+ align:start position:0%
+Plus this number well that's this plus
+ 
+
+ align:start position:0%
+Plus this number well that's this plus
+that number is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9/10 a n now I have to calculate the new
+
+ align:start position:0%
+9/10 a n now I have to calculate the new
+ 
+
+ align:start position:0%
+9/10 a n now I have to calculate the new
+slope at this point okay that is one10
+
+ align:start position:0%
+slope at this point okay that is one10
+ 
+
+ align:start position:0%
+slope at this point okay that is one10
+squared - 910 squared Gul that's
+
+ align:start position:0%
+squared - 910 squared Gul that's
+ 
+
+ align:start position:0%
+squared - 910 squared Gul that's
+0.001 minus
+
+ align:start position:0%
+0.001 minus
+ 
+
+ align:start position:0%
+0.001 minus
+81 which makes
+
+ align:start position:0%
+81 which makes
+ 
+
+ align:start position:0%
+81 which makes
+minus80 I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hope check it on your calculators uh
+
+ align:start position:0%
+hope check it on your calculators uh
+ 
+
+ align:start position:0%
+hope check it on your calculators uh
+whip them out and press the buttons uh I
+
+ align:start position:0%
+whip them out and press the buttons uh I
+ 
+
+ align:start position:0%
+whip them out and press the buttons uh I
+now multiply that by H and which means
+
+ align:start position:0%
+now multiply that by H and which means
+ 
+
+ align:start position:0%
+now multiply that by H and which means
+it's going to be minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+.08 uh perhaps with a zero after I
+
+ align:start position:0%
+.08 uh perhaps with a zero after I
+ 
+
+ align:start position:0%
+.08 uh perhaps with a zero after I
+didn't tell you how many decimal places
+
+ align:start position:0%
+didn't tell you how many decimal places
+ 
+
+ align:start position:0%
+didn't tell you how many decimal places
+let's carry it out to two decimal places
+
+ align:start position:0%
+let's carry it out to two decimal places
+ 
+
+ align:start position:0%
+let's carry it out to two decimal places
+I think uh that'll be uh good
+
+ align:start position:0%
+I think uh that'll be uh good
+ 
+
+ align:start position:0%
+I think uh that'll be uh good
+enough and finally the last step two
+
+ align:start position:0%
+enough and finally the last step two
+ 
+
+ align:start position:0%
+enough and finally the last step two
+here add one add another one10 so the
+
+ align:start position:0%
+here add one add another one10 so the
+ 
+
+ align:start position:0%
+here add one add another one10 so the
+value of x is now 210 and finally what's
+
+ align:start position:0%
+value of x is now 210 and finally what's
+ 
+
+ align:start position:0%
+value of x is now 210 and finally what's
+the value of y well I didn't tell you
+
+ align:start position:0%
+the value of y well I didn't tell you
+ 
+
+ align:start position:0%
+the value of y well I didn't tell you
+where to stop let's stop at y of Point
+
+ align:start position:0%
+where to stop let's stop at y of Point
+ 
+
+ align:start position:0%
+where to stop let's stop at y of Point
+let's stop at y of point2 because
+
+ align:start position:0%
+let's stop at y of point2 because
+ 
+
+ align:start position:0%
+let's stop at y of point2 because
+there's no more room on the Blackboard
+
+ align:start position:0%
+there's no more room on the Blackboard
+ 
+
+ align:start position:0%
+there's no more room on the Blackboard
+seems like an
+
+ align:start position:0%
+seems like an
+ 
+
+ align:start position:0%
+seems like an
+excellent about approximately how big is
+
+ align:start position:0%
+excellent about approximately how big is
+ 
+
+ align:start position:0%
+excellent about approximately how big is
+that in other words then uh this is
+
+ align:start position:0%
+that in other words then uh this is
+ 
+
+ align:start position:0%
+that in other words then uh this is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+uh this uh the old y uh plus this number
+
+ align:start position:0%
+uh this uh the old y uh plus this number
+ 
+
+ align:start position:0%
+uh this uh the old y uh plus this number
+which seems to be0 82 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me so the answer is the new value is
+
+ align:start position:0%
+me so the answer is the new value is
+ 
+
+ align:start position:0%
+me so the answer is the new value is
+82 okay well we got a number we did what
+
+ align:start position:0%
+82 okay well we got a number we did what
+ 
+
+ align:start position:0%
+82 okay well we got a number we did what
+we were supposed to do we got a number
+
+ align:start position:0%
+we were supposed to do we got a number
+ 
+
+ align:start position:0%
+we were supposed to do we got a number
+next question well now let's ask a few
+
+ align:start position:0%
+next question well now let's ask a few
+ 
+
+ align:start position:0%
+next question well now let's ask a few
+questions one of the first most basic
+
+ align:start position:0%
+questions one of the first most basic
+ 
+
+ align:start position:0%
+questions one of the first most basic
+thing is you know how right is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this how can I answer such a question if
+
+ align:start position:0%
+this how can I answer such a question if
+ 
+
+ align:start position:0%
+this how can I answer such a question if
+I can't calc if I have no explicit
+
+ align:start position:0%
+I can't calc if I have no explicit
+ 
+
+ align:start position:0%
+I can't calc if I have no explicit
+formula for that Solution that's the
+
+ align:start position:0%
+formula for that Solution that's the
+ 
+
+ align:start position:0%
+formula for that Solution that's the
+basic problem with numerical
+
+ align:start position:0%
+basic problem with numerical
+ 
+
+ align:start position:0%
+basic problem with numerical
+calculation in other words I have to
+
+ align:start position:0%
+calculation in other words I have to
+ 
+
+ align:start position:0%
+calculation in other words I have to
+wander around in the dark to some extent
+
+ align:start position:0%
+wander around in the dark to some extent
+ 
+
+ align:start position:0%
+wander around in the dark to some extent
+and yet have some idea when I've arrived
+
+ align:start position:0%
+and yet have some idea when I've arrived
+ 
+
+ align:start position:0%
+and yet have some idea when I've arrived
+at the place that I want to
+
+ align:start position:0%
+at the place that I want to
+ 
+
+ align:start position:0%
+at the place that I want to
+go well the first question I'd like to
+
+ align:start position:0%
+go well the first question I'd like to
+ 
+
+ align:start position:0%
+go well the first question I'd like to
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+question is is this too high or too low
+
+ align:start position:0%
+question is is this too high or too low
+ 
+
+ align:start position:0%
+question is is this too high or too low
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Oiler sorry he will forgive me in heaven
+
+ align:start position:0%
+Oiler sorry he will forgive me in heaven
+ 
+
+ align:start position:0%
+Oiler sorry he will forgive me in heaven
+I will use him by this I mean is the
+
+ align:start position:0%
+I will use him by this I mean is the
+ 
+
+ align:start position:0%
+I will use him by this I mean is the
+result well let me say something first
+
+ align:start position:0%
+result well let me say something first
+ 
+
+ align:start position:0%
+result well let me say something first
+and then I'll criticize it uh is Oiler
+
+ align:start position:0%
+and then I'll criticize it uh is Oiler
+ 
+
+ align:start position:0%
+and then I'll criticize it uh is Oiler
+too high or too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low in other words is the result of
+
+ align:start position:0%
+low in other words is the result of
+ 
+
+ align:start position:0%
+low in other words is the result of
+using Oilers method I.E is this number
+
+ align:start position:0%
+using Oilers method I.E is this number
+ 
+
+ align:start position:0%
+using Oilers method I.E is this number
+too high or too low is it higher than
+
+ align:start position:0%
+too high or too low is it higher than
+ 
+
+ align:start position:0%
+too high or too low is it higher than
+the right answer what it should be or is
+
+ align:start position:0%
+the right answer what it should be or is
+ 
+
+ align:start position:0%
+the right answer what it should be or is
+it lower than the right answer or God
+
+ align:start position:0%
+it lower than the right answer or God
+ 
+
+ align:start position:0%
+it lower than the right answer or God
+forbid is it exactly right uh it's
+
+ align:start position:0%
+forbid is it exactly right uh it's
+ 
+
+ align:start position:0%
+forbid is it exactly right uh it's
+almost never exactly right that's not an
+
+ align:start position:0%
+almost never exactly right that's not an
+ 
+
+ align:start position:0%
+almost never exactly right that's not an
+option
+
+ align:start position:0%
+option
+ 
+
+ align:start position:0%
+option
+um how will we answer that question well
+
+ align:start position:0%
+um how will we answer that question well
+ 
+
+ align:start position:0%
+um how will we answer that question well
+let's answer it geometrically
+
+ align:start position:0%
+let's answer it geometrically
+ 
+
+ align:start position:0%
+let's answer it geometrically
+if basically if the solution were a line
+
+ align:start position:0%
+if basically if the solution were a line
+ 
+
+ align:start position:0%
+if basically if the solution were a line
+were a straight line then the oiler
+
+ align:start position:0%
+were a straight line then the oiler
+ 
+
+ align:start position:0%
+were a straight line then the oiler
+method would be exactly right all the
+
+ align:start position:0%
+method would be exactly right all the
+ 
+
+ align:start position:0%
+method would be exactly right all the
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's not a line then it's a it's a
+
+ align:start position:0%
+but it's not a line then it's a it's a
+ 
+
+ align:start position:0%
+but it's not a line then it's a it's a
+curve well the critical question is is
+
+ align:start position:0%
+curve well the critical question is is
+ 
+
+ align:start position:0%
+curve well the critical question is is
+it curved is the solution so here's the
+
+ align:start position:0%
+it curved is the solution so here's the
+ 
+
+ align:start position:0%
+it curved is the solution so here's the
+solution let's call it y1 of X and let's
+
+ align:start position:0%
+solution let's call it y1 of X and let's
+ 
+
+ align:start position:0%
+solution let's call it y1 of X and let's
+say here was the starting point here the
+
+ align:start position:0%
+say here was the starting point here the
+ 
+
+ align:start position:0%
+say here was the starting point here the
+solution is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convex and here the solution is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concave right a concave up a concave
+
+ align:start position:0%
+concave right a concave up a concave
+ 
+
+ align:start position:0%
+concave right a concave up a concave
+down if you learn those words I think
+
+ align:start position:0%
+down if you learn those words I think
+ 
+
+ align:start position:0%
+down if you learn those words I think
+those have by now pretty I hope pretty
+
+ align:start position:0%
+those have by now pretty I hope pretty
+ 
+
+ align:start position:0%
+those have by now pretty I hope pretty
+well disappeared from the curriculum uh
+
+ align:start position:0%
+well disappeared from the curriculum uh
+ 
+
+ align:start position:0%
+well disappeared from the curriculum uh
+call it if you haven't up till now what
+
+ align:start position:0%
+call it if you haven't up till now what
+ 
+
+ align:start position:0%
+call it if you haven't up till now what
+mathematicians call it convex is that
+
+ align:start position:0%
+mathematicians call it convex is that
+ 
+
+ align:start position:0%
+mathematicians call it convex is that
+and the other one is
+
+ align:start position:0%
+and the other one is
+ 
+
+ align:start position:0%
+and the other one is
+concave uh well how do the oiler
+
+ align:start position:0%
+concave uh well how do the oiler
+ 
+
+ align:start position:0%
+concave uh well how do the oiler
+Solutions look well I'll just sketch I
+
+ align:start position:0%
+Solutions look well I'll just sketch I
+ 
+
+ align:start position:0%
+Solutions look well I'll just sketch I
+think from this you can see already when
+
+ align:start position:0%
+think from this you can see already when
+ 
+
+ align:start position:0%
+think from this you can see already when
+you start out on the oiler solution it's
+
+ align:start position:0%
+you start out on the oiler solution it's
+ 
+
+ align:start position:0%
+you start out on the oiler solution it's
+going to go like that now you're too low
+
+ align:start position:0%
+going to go like that now you're too low
+ 
+
+ align:start position:0%
+going to go like that now you're too low
+well let's suppose after that it the
+
+ align:start position:0%
+well let's suppose after that it the
+ 
+
+ align:start position:0%
+well let's suppose after that it the
+line element here is approximately the
+
+ align:start position:0%
+line element here is approximately the
+ 
+
+ align:start position:0%
+line element here is approximately the
+same as what it is there you know
+
+ align:start position:0%
+same as what it is there you know
+ 
+
+ align:start position:0%
+same as what it is there you know
+roughly parallel after all they're not
+
+ align:start position:0%
+roughly parallel after all they're not
+ 
+
+ align:start position:0%
+roughly parallel after all they're not
+too far apart and the direction field is
+
+ align:start position:0%
+too far apart and the direction field is
+ 
+
+ align:start position:0%
+too far apart and the direction field is
+continuous that is the directions don't
+
+ align:start position:0%
+continuous that is the directions don't
+ 
+
+ align:start position:0%
+continuous that is the directions don't
+change drastically from one point to
+
+ align:start position:0%
+change drastically from one point to
+ 
+
+ align:start position:0%
+change drastically from one point to
+another well then it'll sort of but now
+
+ align:start position:0%
+another well then it'll sort of but now
+ 
+
+ align:start position:0%
+another well then it'll sort of but now
+you see it's still too low it's even
+
+ align:start position:0%
+you see it's still too low it's even
+ 
+
+ align:start position:0%
+you see it's still too low it's even
+lower as it pathetically tries to follow
+
+ align:start position:0%
+lower as it pathetically tries to follow
+ 
+
+ align:start position:0%
+lower as it pathetically tries to follow
+its losing territory and that's
+
+ align:start position:0%
+its losing territory and that's
+ 
+
+ align:start position:0%
+its losing territory and that's
+basically because the curve is convex
+
+ align:start position:0%
+basically because the curve is convex
+ 
+
+ align:start position:0%
+basically because the curve is convex
+exactly the opposite would happen if the
+
+ align:start position:0%
+exactly the opposite would happen if the
+ 
+
+ align:start position:0%
+exactly the opposite would happen if the
+curve were concave if the solution curve
+
+ align:start position:0%
+curve were concave if the solution curve
+ 
+
+ align:start position:0%
+curve were concave if the solution curve
+or concave now it's too high and it's
+
+ align:start position:0%
+or concave now it's too high and it's
+ 
+
+ align:start position:0%
+or concave now it's too high and it's
+not going to be able to correct that as
+
+ align:start position:0%
+not going to be able to correct that as
+ 
+
+ align:start position:0%
+not going to be able to correct that as
+long as the solution curve stays con con
+
+ align:start position:0%
+long as the solution curve stays con con
+ 
+
+ align:start position:0%
+long as the solution curve stays con con
+concave well that's probably too
+
+ align:start position:0%
+concave well that's probably too
+ 
+
+ align:start position:0%
+concave well that's probably too
+optimistic it's probably more like
+
+ align:start position:0%
+optimistic it's probably more like
+ 
+
+ align:start position:0%
+optimistic it's probably more like
+this so in other words in this case if
+
+ align:start position:0%
+this so in other words in this case if
+ 
+
+ align:start position:0%
+this so in other words in this case if
+the curve is convex the oiler is going
+
+ align:start position:0%
+the curve is convex the oiler is going
+ 
+
+ align:start position:0%
+the curve is convex the oiler is going
+to be too high H sorry too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low let's put E for Oiler how about that
+
+ align:start position:0%
+low let's put E for Oiler how about that
+ 
+
+ align:start position:0%
+low let's put E for Oiler how about that
+Oiler is too low if it's concave then
+
+ align:start position:0%
+Oiler is too low if it's concave then
+ 
+
+ align:start position:0%
+Oiler is too low if it's concave then
+Oiler is too
+
+ align:start position:0%
+Oiler is too
+ 
+
+ align:start position:0%
+Oiler is too
+high okay that's
+
+ align:start position:0%
+high okay that's
+ 
+
+ align:start position:0%
+high okay that's
+great uh there's just one little problem
+
+ align:start position:0%
+great uh there's just one little problem
+ 
+
+ align:start position:0%
+great uh there's just one little problem
+left namely if we don't have a formula
+
+ align:start position:0%
+left namely if we don't have a formula
+ 
+
+ align:start position:0%
+left namely if we don't have a formula
+for the solution and we don't have a
+
+ align:start position:0%
+for the solution and we don't have a
+ 
+
+ align:start position:0%
+for the solution and we don't have a
+computer that's busy drawing the picture
+
+ align:start position:0%
+computer that's busy drawing the picture
+ 
+
+ align:start position:0%
+computer that's busy drawing the picture
+for us in which case we wouldn't need
+
+ align:start position:0%
+for us in which case we wouldn't need
+ 
+
+ align:start position:0%
+for us in which case we wouldn't need
+any of this anyway uh how are we
+
+ align:start position:0%
+any of this anyway uh how are we
+ 
+
+ align:start position:0%
+any of this anyway uh how are we
+supposed to tell if it's convex or
+
+ align:start position:0%
+supposed to tell if it's convex or
+ 
+
+ align:start position:0%
+supposed to tell if it's convex or
+concave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah back to calculus calculus to the
+
+ align:start position:0%
+ah back to calculus calculus to the
+ 
+
+ align:start position:0%
+ah back to calculus calculus to the
+rescue when is it a curve convex a curve
+
+ align:start position:0%
+rescue when is it a curve convex a curve
+ 
+
+ align:start position:0%
+rescue when is it a curve convex a curve
+is convex if its second derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is positive because the first to be
+
+ align:start position:0%
+is positive because the first to be
+ 
+
+ align:start position:0%
+is positive because the first to be
+convex means the first derivative is
+
+ align:start position:0%
+convex means the first derivative is
+ 
+
+ align:start position:0%
+convex means the first derivative is
+increasing all the time and therefore
+
+ align:start position:0%
+increasing all the time and therefore
+ 
+
+ align:start position:0%
+increasing all the time and therefore
+the second derivative which is the
+
+ align:start position:0%
+the second derivative which is the
+ 
+
+ align:start position:0%
+the second derivative which is the
+derivative of the first derivative
+
+ align:start position:0%
+derivative of the first derivative
+ 
+
+ align:start position:0%
+derivative of the first derivative
+should be positive just the opposite
+
+ align:start position:0%
+should be positive just the opposite
+ 
+
+ align:start position:0%
+should be positive just the opposite
+here the Curve the slope is the first
+
+ align:start position:0%
+here the Curve the slope is the first
+ 
+
+ align:start position:0%
+here the Curve the slope is the first
+derivative is decreasing all the time
+
+ align:start position:0%
+derivative is decreasing all the time
+ 
+
+ align:start position:0%
+derivative is decreasing all the time
+and therefore the second derivative is
+
+ align:start position:0%
+and therefore the second derivative is
+ 
+
+ align:start position:0%
+and therefore the second derivative is
+negative so all we have to do is decide
+
+ align:start position:0%
+negative so all we have to do is decide
+ 
+
+ align:start position:0%
+negative so all we have to do is decide
+what the first and SEC what the
+
+ align:start position:0%
+what the first and SEC what the
+ 
+
+ align:start position:0%
+what the first and SEC what the
+derivative the second derivative of this
+
+ align:start position:0%
+derivative the second derivative of this
+ 
+
+ align:start position:0%
+derivative the second derivative of this
+solution is let's we should probably
+
+ align:start position:0%
+solution is let's we should probably
+ 
+
+ align:start position:0%
+solution is let's we should probably
+call it a solution to Y of X is a little
+
+ align:start position:0%
+call it a solution to Y of X is a little
+ 
+
+ align:start position:0%
+call it a solution to Y of X is a little
+too vague y1 means the solution that's
+
+ align:start position:0%
+too vague y1 means the solution that's
+ 
+
+ align:start position:0%
+too vague y1 means the solution that's
+started at this point so in fact
+
+ align:start position:0%
+started at this point so in fact
+ 
+
+ align:start position:0%
+started at this point so in fact
+probably it would have been better from
+
+ align:start position:0%
+probably it would have been better from
+ 
+
+ align:start position:0%
+probably it would have been better from
+the beginning to call that y1 except
+
+ align:start position:0%
+the beginning to call that y1 except
+ 
+
+ align:start position:0%
+the beginning to call that y1 except
+there's no
+
+ align:start position:0%
+there's no
+ 
+
+ align:start position:0%
+there's no
+room y1 left say that means the solution
+
+ align:start position:0%
+room y1 left say that means the solution
+ 
+
+ align:start position:0%
+room y1 left say that means the solution
+which started out at the0 01 so I'm
+
+ align:start position:0%
+which started out at the0 01 so I'm
+ 
+
+ align:start position:0%
+which started out at the0 01 so I'm
+still talking about a solution like that
+
+ align:start position:0%
+still talking about a solution like that
+ 
+
+ align:start position:0%
+still talking about a solution like that
+all right so I want to know if this is
+
+ align:start position:0%
+all right so I want to know if this is
+ 
+
+ align:start position:0%
+all right so I want to know if this is
+positive the second derivative is
+
+ align:start position:0%
+positive the second derivative is
+ 
+
+ align:start position:0%
+positive the second derivative is
+positive at the starting point zero or
+
+ align:start position:0%
+positive at the starting point zero or
+ 
+
+ align:start position:0%
+positive at the starting point zero or
+it's negative now again how do you
+
+ align:start position:0%
+it's negative now again how do you
+ 
+
+ align:start position:0%
+it's negative now again how do you
+calculate the second derivative if you
+
+ align:start position:0%
+calculate the second derivative if you
+ 
+
+ align:start position:0%
+calculate the second derivative if you
+can't even if you don't know what the
+
+ align:start position:0%
+can't even if you don't know what the
+ 
+
+ align:start position:0%
+can't even if you don't know what the
+solution is explicitly and the answer is
+
+ align:start position:0%
+solution is explicitly and the answer is
+ 
+
+ align:start position:0%
+solution is explicitly and the answer is
+you can do it from the differential
+
+ align:start position:0%
+you can do it from the differential
+ 
+
+ align:start position:0%
+you can do it from the differential
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself how do I do that well easy y
+
+ align:start position:0%
+itself how do I do that well easy y
+ 
+
+ align:start position:0%
+itself how do I do that well easy y
+Prime = x^2 - y^2 okay that tells me how
+
+ align:start position:0%
+Prime = x^2 - y^2 okay that tells me how
+ 
+
+ align:start position:0%
+Prime = x^2 - y^2 okay that tells me how
+to calculate y Prime if I know the value
+
+ align:start position:0%
+to calculate y Prime if I know the value
+ 
+
+ align:start position:0%
+to calculate y Prime if I know the value
+of x and y in other words the 0 Z1 what
+
+ align:start position:0%
+of x and y in other words the 0 Z1 what
+ 
+
+ align:start position:0%
+of x and y in other words the 0 Z1 what
+would be the value of y double Prime
+
+ align:start position:0%
+would be the value of y double Prime
+ 
+
+ align:start position:0%
+would be the value of y double Prime
+well differentiate the equation it's 2x
+
+ align:start position:0%
+well differentiate the equation it's 2x
+ 
+
+ align:start position:0%
+well differentiate the equation it's 2x
+- 2 y y Prime don't forget to use the
+
+ align:start position:0%
+- 2 y y Prime don't forget to use the
+ 
+
+ align:start position:0%
+- 2 y y Prime don't forget to use the
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+rule so if I want to calculate at 01
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words at my starting point is
+
+ align:start position:0%
+in other words at my starting point is
+ 
+
+ align:start position:0%
+in other words at my starting point is
+that curve convex or concave well let's
+
+ align:start position:0%
+that curve convex or concave well let's
+ 
+
+ align:start position:0%
+that curve convex or concave well let's
+calculate y of 0 equals
+
+ align:start position:0%
+calculate y of 0 equals
+ 
+
+ align:start position:0%
+calculate y of 0 equals
+1 okay what's y Prime of 0 well I don't
+
+ align:start position:0%
+1 okay what's y Prime of 0 well I don't
+ 
+
+ align:start position:0%
+1 okay what's y Prime of 0 well I don't
+have to repeat that calculation using
+
+ align:start position:0%
+have to repeat that calculation using
+ 
+
+ align:start position:0%
+have to repeat that calculation using
+this I already calculated that it was
+
+ align:start position:0%
+this I already calculated that it was
+ 
+
+ align:start position:0%
+this I already calculated that it was
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+one and now the new thing is what's y
+
+ align:start position:0%
+one and now the new thing is what's y
+ 
+
+ align:start position:0%
+one and now the new thing is what's y
+double Prime of zero well it is this it
+
+ align:start position:0%
+double Prime of zero well it is this it
+ 
+
+ align:start position:0%
+double Prime of zero well it is this it
+is I'll write it out it's 2 * 0 0 - 2
+
+ align:start position:0%
+is I'll write it out it's 2 * 0 0 - 2
+ 
+
+ align:start position:0%
+is I'll write it out it's 2 * 0 0 - 2
+* Nega uh Y which is 1 2 * 1 * y Prime
+
+ align:start position:0%
+* Nega uh Y which is 1 2 * 1 * y Prime
+ 
+
+ align:start position:0%
+* Nega uh Y which is 1 2 * 1 * y Prime
+which is negative 1 you you want to see
+
+ align:start position:0%
+which is negative 1 you you want to see
+ 
+
+ align:start position:0%
+which is negative 1 you you want to see
+we're pulling ourselves up our own
+
+ align:start position:0%
+we're pulling ourselves up our own
+ 
+
+ align:start position:0%
+we're pulling ourselves up our own
+bootstraps which is impossible but it is
+
+ align:start position:0%
+bootstraps which is impossible but it is
+ 
+
+ align:start position:0%
+bootstraps which is impossible but it is
+not impossible because we're doing it uh
+
+ align:start position:0%
+not impossible because we're doing it uh
+ 
+
+ align:start position:0%
+not impossible because we're doing it uh
+so so what's the answer zero here two
+
+ align:start position:0%
+so so what's the answer zero here two
+ 
+
+ align:start position:0%
+so so what's the answer zero here two
+I've calculated without having the
+
+ align:start position:0%
+I've calculated without having the
+ 
+
+ align:start position:0%
+I've calculated without having the
+foggiest idea of what the solution is is
+
+ align:start position:0%
+foggiest idea of what the solution is is
+ 
+
+ align:start position:0%
+foggiest idea of what the solution is is
+how it looks I've calculated that its
+
+ align:start position:0%
+how it looks I've calculated that its
+ 
+
+ align:start position:0%
+how it looks I've calculated that its
+second derivative at the starting point
+
+ align:start position:0%
+second derivative at the starting point
+ 
+
+ align:start position:0%
+second derivative at the starting point
+is two therefore my solution is convex
+
+ align:start position:0%
+is two therefore my solution is convex
+ 
+
+ align:start position:0%
+is two therefore my solution is convex
+at the starting point and therefore this
+
+ align:start position:0%
+at the starting point and therefore this
+ 
+
+ align:start position:0%
+at the starting point and therefore this
+Oiler approximation if I don't carry it
+
+ align:start position:0%
+Oiler approximation if I don't carry it
+ 
+
+ align:start position:0%
+Oiler approximation if I don't carry it
+out too far will be too low so it's
+
+ align:start position:0%
+out too far will be too low so it's
+ 
+
+ align:start position:0%
+out too far will be too low so it's
+convex Oiler too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low now you could argue yeah well what
+
+ align:start position:0%
+low now you could argue yeah well what
+ 
+
+ align:start position:0%
+low now you could argue yeah well what
+about this uh you
+
+ align:start position:0%
+about this uh you
+ 
+
+ align:start position:0%
+about this uh you
+know suppose
+
+ align:start position:0%
+know suppose
+ 
+
+ align:start position:0%
+know suppose
+it you know
+
+ align:start position:0%
+it you know
+ 
+
+ align:start position:0%
+it you know
+yeah so you go like this and then then
+
+ align:start position:0%
+yeah so you go like this and then then
+ 
+
+ align:start position:0%
+yeah so you go like this and then then
+but then it uh see it catches up and
+
+ align:start position:0%
+but then it uh see it catches up and
+ 
+
+ align:start position:0%
+but then it uh see it catches up and
+then so well of course if the curve
+
+ align:start position:0%
+then so well of course if the curve
+ 
+
+ align:start position:0%
+then so well of course if the curve
+changes from convex to concave then then
+
+ align:start position:0%
+changes from convex to concave then then
+ 
+
+ align:start position:0%
+changes from convex to concave then then
+it's really impossible to make any
+
+ align:start position:0%
+it's really impossible to make any
+ 
+
+ align:start position:0%
+it's really impossible to make any
+prediction at all uh that's a difficulty
+
+ align:start position:0%
+prediction at all uh that's a difficulty
+ 
+
+ align:start position:0%
+prediction at all uh that's a difficulty
+uh so all this analysis is only if you
+
+ align:start position:0%
+uh so all this analysis is only if you
+ 
+
+ align:start position:0%
+uh so all this analysis is only if you
+stay stay very
+
+ align:start position:0%
+stay stay very
+ 
+
+ align:start position:0%
+stay stay very
+nearby uh however I wanted to show you
+
+ align:start position:0%
+nearby uh however I wanted to show you
+ 
+
+ align:start position:0%
+nearby uh however I wanted to show you
+uh the main purpose of it in my mind was
+
+ align:start position:0%
+uh the main purpose of it in my mind was
+ 
+
+ align:start position:0%
+uh the main purpose of it in my mind was
+to show you how to use the diff it's
+
+ align:start position:0%
+to show you how to use the diff it's
+ 
+
+ align:start position:0%
+to show you how to use the diff it's
+these equations how to use the
+
+ align:start position:0%
+these equations how to use the
+ 
+
+ align:start position:0%
+these equations how to use the
+differential equation itself to get
+
+ align:start position:0%
+differential equation itself to get
+ 
+
+ align:start position:0%
+differential equation itself to get
+information about the solutions without
+
+ align:start position:0%
+information about the solutions without
+ 
+
+ align:start position:0%
+information about the solutions without
+actually being able to calculate the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solutions now so that's the method and
+
+ align:start position:0%
+solutions now so that's the method and
+ 
+
+ align:start position:0%
+solutions now so that's the method and
+that's how to find out something about
+
+ align:start position:0%
+that's how to find out something about
+ 
+
+ align:start position:0%
+that's how to find out something about
+it and now what I'd like to talk talk
+
+ align:start position:0%
+it and now what I'd like to talk talk
+ 
+
+ align:start position:0%
+it and now what I'd like to talk talk
+about is
+
+ align:start position:0%
+about is
+ 
+
+ align:start position:0%
+about is
+errors how do I handle
+
+ align:start position:0%
+errors how do I handle
+ 
+
+ align:start position:0%
+errors how do I handle
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh right so I mean that's an anal in a
+
+ align:start position:0%
+oh right so I mean that's an anal in a
+ 
+
+ align:start position:0%
+oh right so I mean that's an anal in a
+sense I've started the error analysis in
+
+ align:start position:0%
+sense I've started the error analysis in
+ 
+
+ align:start position:0%
+sense I've started the error analysis in
+other words the error by definition the
+
+ align:start position:0%
+other words the error by definition the
+ 
+
+ align:start position:0%
+other words the error by definition the
+error is this difference e the error so
+
+ align:start position:0%
+error is this difference e the error so
+ 
+
+ align:start position:0%
+error is this difference e the error so
+in other words I'm asking here is the
+
+ align:start position:0%
+in other words I'm asking here is the
+ 
+
+ align:start position:0%
+in other words I'm asking here is the
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+positive as it would be uh it's depends
+
+ align:start position:0%
+positive as it would be uh it's depends
+ 
+
+ align:start position:0%
+positive as it would be uh it's depends
+which way you measure it usually you
+
+ align:start position:0%
+which way you measure it usually you
+ 
+
+ align:start position:0%
+which way you measure it usually you
+take this minus that so here the
+
+ align:start position:0%
+take this minus that so here the
+ 
+
+ align:start position:0%
+take this minus that so here the
+error the error would be considered
+
+ align:start position:0%
+error the error would be considered
+ 
+
+ align:start position:0%
+error the error would be considered
+positive and here it would be considered
+
+ align:start position:0%
+positive and here it would be considered
+ 
+
+ align:start position:0%
+positive and here it would be considered
+negative although I'm sure there's a
+
+ align:start position:0%
+negative although I'm sure there's a
+ 
+
+ align:start position:0%
+negative although I'm sure there's a
+book somewhere in the world which does
+
+ align:start position:0%
+book somewhere in the world which does
+ 
+
+ align:start position:0%
+book somewhere in the world which does
+the opposite uh most hedge by just using
+
+ align:start position:0%
+the opposite uh most hedge by just using
+ 
+
+ align:start position:0%
+the opposite uh most hedge by just using
+the absolute value of the
+
+ align:start position:0%
+the absolute value of the
+ 
+
+ align:start position:0%
+the absolute value of the
+error plus a statement that the method
+
+ align:start position:0%
+error plus a statement that the method
+ 
+
+ align:start position:0%
+error plus a statement that the method
+is producing answers which are too low
+
+ align:start position:0%
+is producing answers which are too low
+ 
+
+ align:start position:0%
+is producing answers which are too low
+or too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high the question then is naturally
+
+ align:start position:0%
+high the question then is naturally
+ 
+
+ align:start position:0%
+high the question then is naturally
+this is not the world's best method it's
+
+ align:start position:0%
+this is not the world's best method it's
+ 
+
+ align:start position:0%
+this is not the world's best method it's
+not as bad as it seems It's not the
+
+ align:start position:0%
+not as bad as it seems It's not the
+ 
+
+ align:start position:0%
+not as bad as it seems It's not the
+world's best method because that
+
+ align:start position:0%
+world's best method because that
+ 
+
+ align:start position:0%
+world's best method because that
+convexity and concavity means that
+
+ align:start position:0%
+convexity and concavity means that
+ 
+
+ align:start position:0%
+convexity and concavity means that
+you're automatically IND introducing a
+
+ align:start position:0%
+you're automatically IND introducing a
+ 
+
+ align:start position:0%
+you're automatically IND introducing a
+systematic
+
+ align:start position:0%
+systematic
+ 
+
+ align:start position:0%
+systematic
+error if you can predict which way the
+
+ align:start position:0%
+error if you can predict which way the
+ 
+
+ align:start position:0%
+error if you can predict which way the
+error is going to be by just knowing if
+
+ align:start position:0%
+error is going to be by just knowing if
+ 
+
+ align:start position:0%
+error is going to be by just knowing if
+the curve is convex or concave then
+
+ align:start position:0%
+the curve is convex or concave then
+ 
+
+ align:start position:0%
+the curve is convex or concave then
+that's it's just it's not what you want
+
+ align:start position:0%
+that's it's just it's not what you want
+ 
+
+ align:start position:0%
+that's it's just it's not what you want
+I mean you want to at least have a
+
+ align:start position:0%
+I mean you want to at least have a
+ 
+
+ align:start position:0%
+I mean you want to at least have a
+chance of getting the right answer
+
+ align:start position:0%
+chance of getting the right answer
+ 
+
+ align:start position:0%
+chance of getting the right answer
+whereas this is telling you you're
+
+ align:start position:0%
+whereas this is telling you you're
+ 
+
+ align:start position:0%
+whereas this is telling you you're
+definitely going to get the wrong answer
+
+ align:start position:0%
+definitely going to get the wrong answer
+ 
+
+ align:start position:0%
+definitely going to get the wrong answer
+all it tells you is and it's telling you
+
+ align:start position:0%
+all it tells you is and it's telling you
+ 
+
+ align:start position:0%
+all it tells you is and it's telling you
+your answer is going to be too high or
+
+ align:start position:0%
+your answer is going to be too high or
+ 
+
+ align:start position:0%
+your answer is going to be too high or
+too low we'd like a better chance of
+
+ align:start position:0%
+too low we'd like a better chance of
+ 
+
+ align:start position:0%
+too low we'd like a better chance of
+getting the right answer
+
+ align:start position:0%
+getting the right answer
+ 
+
+ align:start position:0%
+getting the right answer
+now so the question is how do you get a
+
+ align:start position:0%
+now so the question is how do you get a
+ 
+
+ align:start position:0%
+now so the question is how do you get a
+better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method a search is for a better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method now
+
+ align:start position:0%
+method now
+ 
+
+ align:start position:0%
+method now
+the first method which will occur I'm
+
+ align:start position:0%
+the first method which will occur I'm
+ 
+
+ align:start position:0%
+the first method which will occur I'm
+sure to anyone who looks at that picture
+
+ align:start position:0%
+sure to anyone who looks at that picture
+ 
+
+ align:start position:0%
+sure to anyone who looks at that picture
+is look if you want this yellow line to
+
+ align:start position:0%
+is look if you want this yellow line to
+ 
+
+ align:start position:0%
+is look if you want this yellow line to
+follow the white
+
+ align:start position:0%
+follow the white
+ 
+
+ align:start position:0%
+follow the white
+one the white solution more accurately
+
+ align:start position:0%
+one the white solution more accurately
+ 
+
+ align:start position:0%
+one the white solution more accurately
+For Heaven's Sake don't take such big
+
+ align:start position:0%
+For Heaven's Sake don't take such big
+ 
+
+ align:start position:0%
+For Heaven's Sake don't take such big
+steps take small steps and then it will
+
+ align:start position:0%
+steps take small steps and then it will
+ 
+
+ align:start position:0%
+steps take small steps and then it will
+follow better all right let's draw a
+
+ align:start position:0%
+follow better all right let's draw a
+ 
+
+ align:start position:0%
+follow better all right let's draw a
+picture excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my little box of treasures
+
+ align:start position:0%
+my little box of treasures
+ 
+
+ align:start position:0%
+my little box of treasures
+here take any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away so use a smaller step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size and the picture roughly which is
+
+ align:start position:0%
+size and the picture roughly which is
+ 
+
+ align:start position:0%
+size and the picture roughly which is
+going to justify that will look like
+
+ align:start position:0%
+going to justify that will look like
+ 
+
+ align:start position:0%
+going to justify that will look like
+this uh if the solution curve looks like
+
+ align:start position:0%
+this uh if the solution curve looks like
+ 
+
+ align:start position:0%
+this uh if the solution curve looks like
+this then with a big step size I'm
+
+ align:start position:0%
+this then with a big step size I'm
+ 
+
+ align:start position:0%
+this then with a big step size I'm
+liable to have something that looks like
+
+ align:start position:0%
+liable to have something that looks like
+ 
+
+ align:start position:0%
+liable to have something that looks like
+that but if I take a smaller step size
+
+ align:start position:0%
+that but if I take a smaller step size
+ 
+
+ align:start position:0%
+that but if I take a smaller step size
+suppose I have the step size how is it
+
+ align:start position:0%
+suppose I have the step size how is it
+ 
+
+ align:start position:0%
+suppose I have the step size how is it
+going to look then well I better switch
+
+ align:start position:0%
+going to look then well I better switch
+ 
+
+ align:start position:0%
+going to look then well I better switch
+to a different color if I have the step
+
+ align:start position:0%
+to a different color if I have the step
+ 
+
+ align:start position:0%
+to a different color if I have the step
+size I'll get a a uh a little it goes
+
+ align:start position:0%
+size I'll get a a uh a little it goes
+ 
+
+ align:start position:0%
+size I'll get a a uh a little it goes
+like that and now it's following closer
+
+ align:start position:0%
+like that and now it's following closer
+ 
+
+ align:start position:0%
+like that and now it's following closer
+of course I'm stacking the deck but see
+
+ align:start position:0%
+of course I'm stacking the deck but see
+ 
+
+ align:start position:0%
+of course I'm stacking the deck but see
+how close it follows uh
+
+ align:start position:0%
+how close it follows uh
+ 
+
+ align:start position:0%
+how close it follows uh
+you know I'm definitely not to be
+
+ align:start position:0%
+you know I'm definitely not to be
+ 
+
+ align:start position:0%
+you know I'm definitely not to be
+trusted on this but uh there okay let's
+
+ align:start position:0%
+trusted on this but uh there okay let's
+ 
+
+ align:start position:0%
+trusted on this but uh there okay let's
+do the opposite make a really big steps
+
+ align:start position:0%
+do the opposite make a really big steps
+ 
+
+ align:start position:0%
+do the opposite make a really big steps
+suppose instead of the yellow one I'd
+
+ align:start position:0%
+suppose instead of the yellow one I'd
+ 
+
+ align:start position:0%
+suppose instead of the yellow one I'd
+used the green one well a double step
+
+ align:start position:0%
+used the green one well a double step
+ 
+
+ align:start position:0%
+used the green one well a double step
+size well what would have happened then
+
+ align:start position:0%
+size well what would have happened then
+ 
+
+ align:start position:0%
+size well what would have happened then
+well I started out but now I've gone all
+
+ align:start position:0%
+well I started out but now I've gone all
+ 
+
+ align:start position:0%
+well I started out but now I've gone all
+the way to there and now on my way up of
+
+ align:start position:0%
+the way to there and now on my way up of
+ 
+
+ align:start position:0%
+the way to there and now on my way up of
+course it it has a little further to go
+
+ align:start position:0%
+course it it has a little further to go
+ 
+
+ align:start position:0%
+course it it has a little further to go
+but if for some reason I had stopped
+
+ align:start position:0%
+but if for some reason I had stopped
+ 
+
+ align:start position:0%
+but if for some reason I had stopped
+there you could see I would be still
+
+ align:start position:0%
+there you could see I would be still
+ 
+
+ align:start position:0%
+there you could see I would be still
+lower in other words the bigger the step
+
+ align:start position:0%
+lower in other words the bigger the step
+ 
+
+ align:start position:0%
+lower in other words the bigger the step
+size the the more the error and where
+
+ align:start position:0%
+size the the more the error and where
+ 
+
+ align:start position:0%
+size the the more the error and where
+are the errors that we're talking about
+
+ align:start position:0%
+are the errors that we're talking about
+ 
+
+ align:start position:0%
+are the errors that we're talking about
+well uh the way to think of the errors
+
+ align:start position:0%
+well uh the way to think of the errors
+ 
+
+ align:start position:0%
+well uh the way to think of the errors
+this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+error that number the error and you can
+
+ align:start position:0%
+error that number the error and you can
+ 
+
+ align:start position:0%
+error that number the error and you can
+make it a positive negative or just put
+
+ align:start position:0%
+make it a positive negative or just put
+ 
+
+ align:start position:0%
+make it a positive negative or just put
+an automatically an absolute value sign
+
+ align:start position:0%
+an automatically an absolute value sign
+ 
+
+ align:start position:0%
+an automatically an absolute value sign
+around it that's not so
+
+ align:start position:0%
+around it that's not so
+ 
+
+ align:start position:0%
+around it that's not so
+important so in other words the
+
+ align:start position:0%
+important so in other words the
+ 
+
+ align:start position:0%
+important so in other words the
+conclusion is that the error that the
+
+ align:start position:0%
+conclusion is that the error that the
+ 
+
+ align:start position:0%
+conclusion is that the error that the
+error E the difference between the True
+
+ align:start position:0%
+error E the difference between the True
+ 
+
+ align:start position:0%
+error E the difference between the True
+Value that I should have gotten the
+
+ align:start position:0%
+Value that I should have gotten the
+ 
+
+ align:start position:0%
+Value that I should have gotten the
+oiler value that the calculation
+
+ align:start position:0%
+oiler value that the calculation
+ 
+
+ align:start position:0%
+oiler value that the calculation
+produced the the error E depends on the
+
+ align:start position:0%
+produced the the error E depends on the
+ 
+
+ align:start position:0%
+produced the the error E depends on the
+step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size now how does it depend on the step
+
+ align:start position:0%
+size now how does it depend on the step
+ 
+
+ align:start position:0%
+size now how does it depend on the step
+size well it's impossible to give an
+
+ align:start position:0%
+size well it's impossible to give an
+ 
+
+ align:start position:0%
+size well it's impossible to give an
+exact formula but there's an approximate
+
+ align:start position:0%
+exact formula but there's an approximate
+ 
+
+ align:start position:0%
+exact formula but there's an approximate
+answer which is by and large true and uh
+
+ align:start position:0%
+answer which is by and large true and uh
+ 
+
+ align:start position:0%
+answer which is by and large true and uh
+the answer is so e is going to be a
+
+ align:start position:0%
+the answer is so e is going to be a
+ 
+
+ align:start position:0%
+the answer is so e is going to be a
+function of H what function well
+
+ align:start position:0%
+function of H what function well
+ 
+
+ align:start position:0%
+function of H what function well
+asymptotically which means is another
+
+ align:start position:0%
+asymptotically which means is another
+ 
+
+ align:start position:0%
+asymptotically which means is another
+way of putting quotation marks uh around
+
+ align:start position:0%
+way of putting quotation marks uh around
+ 
+
+ align:start position:0%
+way of putting quotation marks uh around
+what do I say it's going to be a
+
+ align:start position:0%
+what do I say it's going to be a
+ 
+
+ align:start position:0%
+what do I say it's going to be a
+constant some constant times
+
+ align:start position:0%
+constant some constant times
+ 
+
+ align:start position:0%
+constant some constant times
+H late you pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boy nobody right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there it looks like this and for this
+
+ align:start position:0%
+there it looks like this and for this
+ 
+
+ align:start position:0%
+there it looks like this and for this
+reason it's called a uh first
+
+ align:start position:0%
+reason it's called a uh first
+ 
+
+ align:start position:0%
+reason it's called a uh first
+order the oiler is a first order method
+
+ align:start position:0%
+order the oiler is a first order method
+ 
+
+ align:start position:0%
+order the oiler is a first order method
+and now first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order does not refer to the first order
+
+ align:start position:0%
+order does not refer to the first order
+ 
+
+ align:start position:0%
+order does not refer to the first order
+of the differential equation it's not
+
+ align:start position:0%
+of the differential equation it's not
+ 
+
+ align:start position:0%
+of the differential equation it's not
+that use of the word first it's not the
+
+ align:start position:0%
+that use of the word first it's not the
+ 
+
+ align:start position:0%
+that use of the word first it's not the
+first order because it's y Prime equals
+
+ align:start position:0%
+first order because it's y Prime equals
+ 
+
+ align:start position:0%
+first order because it's y Prime equals
+f ofx y the first order means the fact
+
+ align:start position:0%
+f ofx y the first order means the fact
+ 
+
+ align:start position:0%
+f ofx y the first order means the fact
+that H occurs to the first
+
+ align:start position:0%
+that H occurs to the first
+ 
+
+ align:start position:0%
+that H occurs to the first
+Power the way people usually say this
+
+ align:start position:0%
+Power the way people usually say this
+ 
+
+ align:start position:0%
+Power the way people usually say this
+is since the normal way of decreasing
+
+ align:start position:0%
+is since the normal way of decreasing
+ 
+
+ align:start position:0%
+is since the normal way of decreasing
+the step size as you'll see as soon as
+
+ align:start position:0%
+the step size as you'll see as soon as
+ 
+
+ align:start position:0%
+the step size as you'll see as soon as
+you try to use the computer visual that
+
+ align:start position:0%
+you try to use the computer visual that
+ 
+
+ align:start position:0%
+you try to use the computer visual that
+deals with Oiler method which I highly
+
+ align:start position:0%
+deals with Oiler method which I highly
+ 
+
+ align:start position:0%
+deals with Oiler method which I highly
+recommend by the way so highly
+
+ align:start position:0%
+recommend by the way so highly
+ 
+
+ align:start position:0%
+recommend by the way so highly
+recommended that you have to do
+
+ align:start position:0%
+recommended that you have to do
+ 
+
+ align:start position:0%
+recommended that you have to do
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+is is
+
+ align:start position:0%
+is is
+ 
+
+ align:start position:0%
+is is
+that the way to say it that since you
+
+ align:start position:0%
+that the way to say it that since you
+ 
+
+ align:start position:0%
+that the way to say it that since you
+con each new Step hases the step size
+
+ align:start position:0%
+con each new Step hases the step size
+ 
+
+ align:start position:0%
+con each new Step hases the step size
+that's the usual way to do it uh if you
+
+ align:start position:0%
+that's the usual way to do it uh if you
+ 
+
+ align:start position:0%
+that's the usual way to do it uh if you
+have the step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size since this is a constant if I have
+
+ align:start position:0%
+size since this is a constant if I have
+ 
+
+ align:start position:0%
+size since this is a constant if I have
+the step size I have the eror
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximately have the step size have
+
+ align:start position:0%
+approximately have the step size have
+ 
+
+ align:start position:0%
+approximately have the step size have
+the error that tells you how the error
+
+ align:start position:0%
+the error that tells you how the error
+ 
+
+ align:start position:0%
+the error that tells you how the error
+varies with step size for Oilers
+
+ align:start position:0%
+varies with step size for Oilers
+ 
+
+ align:start position:0%
+varies with step size for Oilers
+method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh please understand that's what
+
+ align:start position:0%
+uh uh please understand that's what
+ 
+
+ align:start position:0%
+uh uh please understand that's what
+people say and please understand the
+
+ align:start position:0%
+people say and please understand the
+ 
+
+ align:start position:0%
+people say and please understand the
+grammatical construction
+
+ align:start position:0%
+grammatical construction
+ 
+
+ align:start position:0%
+grammatical construction
+uh since everyone the math department
+
+ align:start position:0%
+uh since everyone the math department
+ 
+
+ align:start position:0%
+uh since everyone the math department
+has a cold these days except me for the
+
+ align:start position:0%
+has a cold these days except me for the
+ 
+
+ align:start position:0%
+has a cold these days except me for the
+moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh everyone goes around chanting this
+
+ align:start position:0%
+uh everyone goes around chanting this
+ 
+
+ align:start position:0%
+uh everyone goes around chanting this
+Mantra this is totally irrelevant
+
+ align:start position:0%
+Mantra this is totally irrelevant
+ 
+
+ align:start position:0%
+Mantra this is totally irrelevant
+uh total Mantra uh you know feed a cold
+
+ align:start position:0%
+uh total Mantra uh you know feed a cold
+ 
+
+ align:start position:0%
+uh total Mantra uh you know feed a cold
+starve a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fever and if you ask them what it means
+
+ align:start position:0%
+fever and if you ask them what it means
+ 
+
+ align:start position:0%
+fever and if you ask them what it means
+they say it means you know eat a lot if
+
+ align:start position:0%
+they say it means you know eat a lot if
+ 
+
+ align:start position:0%
+they say it means you know eat a lot if
+you have a cold and if you have a fever
+
+ align:start position:0%
+you have a cold and if you have a fever
+ 
+
+ align:start position:0%
+you have a cold and if you have a fever
+don't eat very much
+
+ align:start position:0%
+don't eat very much
+ 
+
+ align:start position:0%
+don't eat very much
+which is not what it means at all
+
+ align:start position:0%
+which is not what it means at all
+ 
+
+ align:start position:0%
+which is not what it means at all
+grammatically it's exactly the same
+
+ align:start position:0%
+grammatically it's exactly the same
+ 
+
+ align:start position:0%
+grammatically it's exactly the same
+construction as
+
+ align:start position:0%
+construction as
+ 
+
+ align:start position:0%
+construction as
+this have the what this means is if you
+
+ align:start position:0%
+this have the what this means is if you
+ 
+
+ align:start position:0%
+this have the what this means is if you
+have the step size you will have the
+
+ align:start position:0%
+have the step size you will have the
+ 
+
+ align:start position:0%
+have the step size you will have the
+error and that's what feed a cold starve
+
+ align:start position:0%
+error and that's what feed a cold starve
+ 
+
+ align:start position:0%
+error and that's what feed a cold starve
+a fever means and remember this for the
+
+ align:start position:0%
+a fever means and remember this for the
+ 
+
+ align:start position:0%
+a fever means and remember this for the
+rest of your life if you feed a cold if
+
+ align:start position:0%
+rest of your life if you feed a cold if
+ 
+
+ align:start position:0%
+rest of your life if you feed a cold if
+you eat too much when you have a cold
+
+ align:start position:0%
+you eat too much when you have a cold
+ 
+
+ align:start position:0%
+you eat too much when you have a cold
+you will get a fever and end up St
+
+ align:start position:0%
+you will get a fever and end up St
+ 
+
+ align:start position:0%
+you will get a fever and end up St
+having to starve starve yourself because
+
+ align:start position:0%
+having to starve starve yourself because
+ 
+
+ align:start position:0%
+having to starve starve yourself because
+of course nobody when you have a fever
+
+ align:start position:0%
+of course nobody when you have a fever
+ 
+
+ align:start position:0%
+of course nobody when you have a fever
+nobody feels like eating so they don't
+
+ align:start position:0%
+nobody feels like eating so they don't
+ 
+
+ align:start position:0%
+nobody feels like eating so they don't
+eat
+
+ align:start position:0%
+eat
+ 
+
+ align:start position:0%
+eat
+anything all right you got that you got
+
+ align:start position:0%
+anything all right you got that you got
+ 
+
+ align:start position:0%
+anything all right you got that you got
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go I want all of you to go home and tell
+
+ align:start position:0%
+go I want all of you to go home and tell
+ 
+
+ align:start position:0%
+go I want all of you to go home and tell
+that to your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mothers you know that's the way we
+
+ align:start position:0%
+mothers you know that's the way we
+ 
+
+ align:start position:0%
+mothers you know that's the way we
+always used to speak back you know a
+
+ align:start position:0%
+always used to speak back you know a
+ 
+
+ align:start position:0%
+always used to speak back you know a
+Grimmer one spare the rod and spoil the
+
+ align:start position:0%
+Grimmer one spare the rod and spoil the
+ 
+
+ align:start position:0%
+Grimmer one spare the rod and spoil the
+child does not mean that you should not
+
+ align:start position:0%
+child does not mean that you should not
+ 
+
+ align:start position:0%
+child does not mean that you should not
+hit your kid and
+
+ align:start position:0%
+hit your kid and
+ 
+
+ align:start position:0%
+hit your kid and
+uh it means it means that if you fail to
+
+ align:start position:0%
+uh it means it means that if you fail to
+ 
+
+ align:start position:0%
+uh it means it means that if you fail to
+hit your kid uh he or she will be
+
+ align:start position:0%
+hit your kid uh he or she will be
+ 
+
+ align:start position:0%
+hit your kid uh he or she will be
+spoiled whatever that means uh so uh you
+
+ align:start position:0%
+spoiled whatever that means uh so uh you
+ 
+
+ align:start position:0%
+spoiled whatever that means uh so uh you
+don't want to you want to do with that
+
+ align:start position:0%
+don't want to you want to do with that
+ 
+
+ align:start position:0%
+don't want to you want to do with that
+the I guess the mantra today would be uh
+
+ align:start position:0%
+the I guess the mantra today would be uh
+ 
+
+ align:start position:0%
+the I guess the mantra today would be uh
+What
+
+ align:start position:0%
+What
+ 
+
+ align:start position:0%
+What
+uh I don't know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the first line of defense is
+
+ align:start position:0%
+okay so the first line of defense is
+ 
+
+ align:start position:0%
+okay so the first line of defense is
+simply to uh keep having the step size
+
+ align:start position:0%
+simply to uh keep having the step size
+ 
+
+ align:start position:0%
+simply to uh keep having the step size
+in Oiler and what people do is if they
+
+ align:start position:0%
+in Oiler and what people do is if they
+ 
+
+ align:start position:0%
+in Oiler and what people do is if they
+don't want to use anything better than
+
+ align:start position:0%
+don't want to use anything better than
+ 
+
+ align:start position:0%
+don't want to use anything better than
+Oilers method is you keep having the
+
+ align:start position:0%
+Oilers method is you keep having the
+ 
+
+ align:start position:0%
+Oilers method is you keep having the
+step size until the curve doesn't seem
+
+ align:start position:0%
+step size until the curve doesn't seem
+ 
+
+ align:start position:0%
+step size until the curve doesn't seem
+to change anymore and then you say well
+
+ align:start position:0%
+to change anymore and then you say well
+ 
+
+ align:start position:0%
+to change anymore and then you say well
+that must be the
+
+ align:start position:0%
+that must be the
+ 
+
+ align:start position:0%
+that must be the
+solution and I ask you on the problem
+
+ align:start position:0%
+solution and I ask you on the problem
+ 
+
+ align:start position:0%
+solution and I ask you on the problem
+set how much would you could continue to
+
+ align:start position:0%
+set how much would you could continue to
+ 
+
+ align:start position:0%
+set how much would you could continue to
+have to have the step size in order for
+
+ align:start position:0%
+have to have the step size in order for
+ 
+
+ align:start position:0%
+have to have the step size in order for
+that good thing to
+
+ align:start position:0%
+that good thing to
+ 
+
+ align:start position:0%
+that good thing to
+happen however there are more efficient
+
+ align:start position:0%
+happen however there are more efficient
+ 
+
+ align:start position:0%
+happen however there are more efficient
+methods which gets the result
+
+ align:start position:0%
+methods which gets the result
+ 
+
+ align:start position:0%
+methods which gets the result
+faster and so if that's our good method
+
+ align:start position:0%
+faster and so if that's our good method
+ 
+
+ align:start position:0%
+faster and so if that's our good method
+let's call this our a bet a still better
+
+ align:start position:0%
+let's call this our a bet a still better
+ 
+
+ align:start position:0%
+let's call this our a bet a still better
+method the better
+
+ align:start position:0%
+method the better
+ 
+
+ align:start position:0%
+method the better
+methods aim at being better they keep
+
+ align:start position:0%
+methods aim at being better they keep
+ 
+
+ align:start position:0%
+methods aim at being better they keep
+the same idea as Oilers method but they
+
+ align:start position:0%
+the same idea as Oilers method but they
+ 
+
+ align:start position:0%
+the same idea as Oilers method but they
+say look let's try to improve that slope
+
+ align:start position:0%
+say look let's try to improve that slope
+ 
+
+ align:start position:0%
+say look let's try to improve that slope
+a end in other words since the slope a n
+
+ align:start position:0%
+a end in other words since the slope a n
+ 
+
+ align:start position:0%
+a end in other words since the slope a n
+that we start with is guaranteed to be
+
+ align:start position:0%
+that we start with is guaranteed to be
+ 
+
+ align:start position:0%
+that we start with is guaranteed to be
+wrong if the curve is convex or concave
+
+ align:start position:0%
+wrong if the curve is convex or concave
+ 
+
+ align:start position:0%
+wrong if the curve is convex or concave
+can we somehow correct it so that for
+
+ align:start position:0%
+can we somehow correct it so that for
+ 
+
+ align:start position:0%
+can we somehow correct it so that for
+example instead of a immediately aiming
+
+ align:start position:0%
+example instead of a immediately aiming
+ 
+
+ align:start position:0%
+example instead of a immediately aiming
+there can't we somehow aim it so that by
+
+ align:start position:0%
+there can't we somehow aim it so that by
+ 
+
+ align:start position:0%
+there can't we somehow aim it so that by
+luck we just the next step just lands us
+
+ align:start position:0%
+luck we just the next step just lands us
+ 
+
+ align:start position:0%
+luck we just the next step just lands us
+back on the curve again in other words
+
+ align:start position:0%
+back on the curve again in other words
+ 
+
+ align:start position:0%
+back on the curve again in other words
+we're sort of looking for the short path
+
+ align:start position:0%
+we're sort of looking for the short path
+ 
+
+ align:start position:0%
+we're sort of looking for the short path
+a shortcut path which by good luck will
+
+ align:start position:0%
+a shortcut path which by good luck will
+ 
+
+ align:start position:0%
+a shortcut path which by good luck will
+end us up back on the curve again and
+
+ align:start position:0%
+end us up back on the curve again and
+ 
+
+ align:start position:0%
+end us up back on the curve again and
+all the Improv ments the simple
+
+ align:start position:0%
+all the Improv ments the simple
+ 
+
+ align:start position:0%
+all the Improv ments the simple
+improvements on Oiler method method and
+
+ align:start position:0%
+improvements on Oiler method method and
+ 
+
+ align:start position:0%
+improvements on Oiler method method and
+they are the most stable in ways to do
+
+ align:start position:0%
+they are the most stable in ways to do
+ 
+
+ align:start position:0%
+they are the most stable in ways to do
+solve differential equations numerically
+
+ align:start position:0%
+solve differential equations numerically
+ 
+
+ align:start position:0%
+solve differential equations numerically
+aim at finding a better
+
+ align:start position:0%
+aim at finding a better
+ 
+
+ align:start position:0%
+aim at finding a better
+slope so they find a better value for a
+
+ align:start position:0%
+slope so they find a better value for a
+ 
+
+ align:start position:0%
+slope so they find a better value for a
+better a better slope find a better
+
+ align:start position:0%
+better a better slope find a better
+ 
+
+ align:start position:0%
+better a better slope find a better
+value value
+
+ align:start position:0%
+value value
+ 
+
+ align:start position:0%
+value value
+for than a
+
+ align:start position:0%
+for than a
+ 
+
+ align:start position:0%
+for than a
+n try to improve that slope that you
+
+ align:start position:0%
+n try to improve that slope that you
+ 
+
+ align:start position:0%
+n try to improve that slope that you
+found now once you have the idea that
+
+ align:start position:0%
+found now once you have the idea that
+ 
+
+ align:start position:0%
+found now once you have the idea that
+you should look for a better slope uh
+
+ align:start position:0%
+you should look for a better slope uh
+ 
+
+ align:start position:0%
+you should look for a better slope uh
+it's not very difficult to see what in
+
+ align:start position:0%
+it's not very difficult to see what in
+ 
+
+ align:start position:0%
+it's not very difficult to see what in
+fact you should try again I think most
+
+ align:start position:0%
+fact you should try again I think most
+ 
+
+ align:start position:0%
+fact you should try again I think most
+of you would say uh hey I would have
+
+ align:start position:0%
+of you would say uh hey I would have
+ 
+
+ align:start position:0%
+of you would say uh hey I would have
+thought of
+
+ align:start position:0%
+thought of
+ 
+
+ align:start position:0%
+thought of
+that uh and you'd be closer in time
+
+ align:start position:0%
+that uh and you'd be closer in time
+ 
+
+ align:start position:0%
+that uh and you'd be closer in time
+since these methods were only found
+
+ align:start position:0%
+since these methods were only found
+ 
+
+ align:start position:0%
+since these methods were only found
+about uh maybe 100 around the turn of
+
+ align:start position:0%
+about uh maybe 100 around the turn of
+ 
+
+ align:start position:0%
+about uh maybe 100 around the turn of
+the last century is when I plac
+
+ align:start position:0%
+the last century is when I plac
+ 
+
+ align:start position:0%
+the last century is when I plac
+them mostly by some German
+
+ align:start position:0%
+them mostly by some German
+ 
+
+ align:start position:0%
+them mostly by some German
+mathematicians interested in solving
+
+ align:start position:0%
+mathematicians interested in solving
+ 
+
+ align:start position:0%
+mathematicians interested in solving
+equations numerically all right so what
+
+ align:start position:0%
+equations numerically all right so what
+ 
+
+ align:start position:0%
+equations numerically all right so what
+is uh the better method
+
+ align:start position:0%
+is uh the better method
+ 
+
+ align:start position:0%
+is uh the better method
+our better slope what should we look for
+
+ align:start position:0%
+our better slope what should we look for
+ 
+
+ align:start position:0%
+our better slope what should we look for
+in our better slope well the simplest
+
+ align:start position:0%
+in our better slope well the simplest
+ 
+
+ align:start position:0%
+in our better slope well the simplest
+procedure is once again we're starting
+
+ align:start position:0%
+procedure is once again we're starting
+ 
+
+ align:start position:0%
+procedure is once again we're starting
+from there and the oiler slope would be
+
+ align:start position:0%
+from there and the oiler slope would be
+ 
+
+ align:start position:0%
+from there and the oiler slope would be
+the same as the line element so it uh
+
+ align:start position:0%
+the same as the line element so it uh
+ 
+
+ align:start position:0%
+the same as the line element so it uh
+the line element looks like this and our
+
+ align:start position:0%
+the line element looks like this and our
+ 
+
+ align:start position:0%
+the line element looks like this and our
+yellow slope a an I'll still continue to
+
+ align:start position:0%
+yellow slope a an I'll still continue to
+ 
+
+ align:start position:0%
+yellow slope a an I'll still continue to
+call it a goes like that and gets to
+
+ align:start position:0%
+call it a goes like that and gets to
+ 
+
+ align:start position:0%
+call it a goes like that and gets to
+here okay now if it were convex if the
+
+ align:start position:0%
+here okay now if it were convex if the
+ 
+
+ align:start position:0%
+here okay now if it were convex if the
+curve were convex this would be too low
+
+ align:start position:0%
+curve were convex this would be too low
+ 
+
+ align:start position:0%
+curve were convex this would be too low
+and therefore the next step would
+
+ align:start position:0%
+and therefore the next step would
+ 
+
+ align:start position:0%
+and therefore the next step would
+be I'm going to draw this next step in
+
+ align:start position:0%
+be I'm going to draw this next step in
+ 
+
+ align:start position:0%
+be I'm going to draw this next step in
+pink well uh let's let's continue in uh
+
+ align:start position:0%
+pink well uh let's let's continue in uh
+ 
+
+ align:start position:0%
+pink well uh let's let's continue in uh
+here would be uh going up like that I'll
+
+ align:start position:0%
+here would be uh going up like that I'll
+ 
+
+ align:start position:0%
+here would be uh going up like that I'll
+call this BN just because it's the next
+
+ align:start position:0%
+call this BN just because it's the next
+ 
+
+ align:start position:0%
+call this BN just because it's the next
+step of Oilers method it could be called
+
+ align:start position:0%
+step of Oilers method it could be called
+ 
+
+ align:start position:0%
+step of Oilers method it could be called
+a an prime or something like that but
+
+ align:start position:0%
+a an prime or something like that but
+ 
+
+ align:start position:0%
+a an prime or something like that but
+this will do and now what you do is let
+
+ align:start position:0%
+this will do and now what you do is let
+ 
+
+ align:start position:0%
+this will do and now what you do is let
+me put an arrow on it to indicate
+
+ align:start position:0%
+me put an arrow on it to indicate
+ 
+
+ align:start position:0%
+me put an arrow on it to indicate
+parallel this go back to the beginning
+
+ align:start position:0%
+parallel this go back to the beginning
+ 
+
+ align:start position:0%
+parallel this go back to the beginning
+draw this parallel to BN so here is BN
+
+ align:start position:0%
+draw this parallel to BN so here is BN
+ 
+
+ align:start position:0%
+draw this parallel to BN so here is BN
+again just a line of slope that same
+
+ align:start position:0%
+again just a line of slope that same
+ 
+
+ align:start position:0%
+again just a line of slope that same
+slope and now what you should use as the
+
+ align:start position:0%
+slope and now what you should use as the
+ 
+
+ align:start position:0%
+slope and now what you should use as the
+simplest Improvement on Oilers method is
+
+ align:start position:0%
+simplest Improvement on Oilers method is
+ 
+
+ align:start position:0%
+simplest Improvement on Oilers method is
+take the average of these two because
+
+ align:start position:0%
+take the average of these two because
+ 
+
+ align:start position:0%
+take the average of these two because
+that's more likely to hit the curve than
+
+ align:start position:0%
+that's more likely to hit the curve than
+ 
+
+ align:start position:0%
+that's more likely to hit the curve than
+a an will which is sure to be too low if
+
+ align:start position:0%
+a an will which is sure to be too low if
+ 
+
+ align:start position:0%
+a an will which is sure to be too low if
+the curve is convex in other words use
+
+ align:start position:0%
+the curve is convex in other words use
+ 
+
+ align:start position:0%
+the curve is convex in other words use
+this instead use
+
+ align:start position:0%
+this instead use
+ 
+
+ align:start position:0%
+this instead use
+that so this is our better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slope okay what will we call that slope
+
+ align:start position:0%
+slope okay what will we call that slope
+ 
+
+ align:start position:0%
+slope okay what will we call that slope
+we don't have to call it anything what
+
+ align:start position:0%
+we don't have to call it anything what
+ 
+
+ align:start position:0%
+we don't have to call it anything what
+would the equations for the method be
+
+ align:start position:0%
+would the equations for the method be
+ 
+
+ align:start position:0%
+would the equations for the method be
+well xn + 1 is gotten by adding the step
+
+ align:start position:0%
+well xn + 1 is gotten by adding the step
+ 
+
+ align:start position:0%
+well xn + 1 is gotten by adding the step
+size so here's my step size just as it
+
+ align:start position:0%
+size so here's my step size just as it
+ 
+
+ align:start position:0%
+size so here's my step size just as it
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+before just as it was before the new
+
+ align:start position:0%
+before just as it was before the new
+ 
+
+ align:start position:0%
+before just as it was before the new
+thing is how to get the new value of y
+
+ align:start position:0%
+thing is how to get the new value of y
+ 
+
+ align:start position:0%
+thing is how to get the new value of y
+so y n + one should be the old YN plus h
+
+ align:start position:0%
+so y n + one should be the old YN plus h
+ 
+
+ align:start position:0%
+so y n + one should be the old YN plus h
+* not this crummy slope a n but the
+
+ align:start position:0%
+* not this crummy slope a n but the
+ 
+
+ align:start position:0%
+* not this crummy slope a n but the
+better the pink slope what's the formula
+
+ align:start position:0%
+better the pink slope what's the formula
+ 
+
+ align:start position:0%
+better the pink slope what's the formula
+for the pink slope well let's do it in
+
+ align:start position:0%
+for the pink slope well let's do it in
+ 
+
+ align:start position:0%
+for the pink slope well let's do it in
+two steps it's the average of a and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+BN hey but you didn't tell me or I
+
+ align:start position:0%
+BN hey but you didn't tell me or I
+ 
+
+ align:start position:0%
+BN hey but you didn't tell me or I
+didn't tell you what BN was so you now
+
+ align:start position:0%
+didn't tell you what BN was so you now
+ 
+
+ align:start position:0%
+didn't tell you what BN was so you now
+must tell the computer oh yes by the way
+
+ align:start position:0%
+must tell the computer oh yes by the way
+ 
+
+ align:start position:0%
+must tell the computer oh yes by the way
+you remember that a an was what it
+
+ align:start position:0%
+you remember that a an was what it
+ 
+
+ align:start position:0%
+you remember that a an was what it
+always was
+
+ align:start position:0%
+always was
+ 
+
+ align:start position:0%
+always was
+the interesting thing is what is BN well
+
+ align:start position:0%
+the interesting thing is what is BN well
+ 
+
+ align:start position:0%
+the interesting thing is what is BN well
+to get BN BN is the slope of the line
+
+ align:start position:0%
+to get BN BN is the slope of the line
+ 
+
+ align:start position:0%
+to get BN BN is the slope of the line
+element at this new
+
+ align:start position:0%
+element at this new
+ 
+
+ align:start position:0%
+element at this new
+point now what am I going to call that
+
+ align:start position:0%
+point now what am I going to call that
+ 
+
+ align:start position:0%
+point now what am I going to call that
+new point I don't want to call this y
+
+ align:start position:0%
+new point I don't want to call this y
+ 
+
+ align:start position:0%
+new point I don't want to call this y
+value YN + one because that's it's this
+
+ align:start position:0%
+value YN + one because that's it's this
+ 
+
+ align:start position:0%
+value YN + one because that's it's this
+up here that's going to be the YN plus
+
+ align:start position:0%
+up here that's going to be the YN plus
+ 
+
+ align:start position:0%
+up here that's going to be the YN plus
+one all this is is a temporary value
+
+ align:start position:0%
+one all this is is a temporary value
+ 
+
+ align:start position:0%
+one all this is is a temporary value
+used to make another calculation which
+
+ align:start position:0%
+used to make another calculation which
+ 
+
+ align:start position:0%
+used to make another calculation which
+will then be combined with the previous
+
+ align:start position:0%
+will then be combined with the previous
+ 
+
+ align:start position:0%
+will then be combined with the previous
+calculations to get the right value
+
+ align:start position:0%
+calculations to get the right value
+ 
+
+ align:start position:0%
+calculations to get the right value
+therefore give it a temporary
+
+ align:start position:0%
+therefore give it a temporary
+ 
+
+ align:start position:0%
+therefore give it a temporary
+name that point we'll call it it's not
+
+ align:start position:0%
+name that point we'll call it it's not
+ 
+
+ align:start position:0%
+name that point we'll call it it's not
+going to be the final the real YN + one
+
+ align:start position:0%
+going to be the final the real YN + one
+ 
+
+ align:start position:0%
+going to be the final the real YN + one
+we'll call it yn+1 twiddles YN plus1
+
+ align:start position:0%
+we'll call it yn+1 twiddles YN plus1
+ 
+
+ align:start position:0%
+we'll call it yn+1 twiddles YN plus1
+temporary uh and what's the formula for
+
+ align:start position:0%
+temporary uh and what's the formula for
+ 
+
+ align:start position:0%
+temporary uh and what's the formula for
+it well it's just going to be what the
+
+ align:start position:0%
+it well it's just going to be what the
+ 
+
+ align:start position:0%
+it well it's just going to be what the
+oiler formula original Oiler formula
+
+ align:start position:0%
+oiler formula original Oiler formula
+ 
+
+ align:start position:0%
+oiler formula original Oiler formula
+it's going to be YN plus what you would
+
+ align:start position:0%
+it's going to be YN plus what you would
+ 
+
+ align:start position:0%
+it's going to be YN plus what you would
+have gotten if you would
+
+ align:start position:0%
+have gotten if you would
+ 
+
+ align:start position:0%
+have gotten if you would
+calculated in other words it's the point
+
+ align:start position:0%
+calculated in other words it's the point
+ 
+
+ align:start position:0%
+calculated in other words it's the point
+that the oiler method produced
+
+ align:start position:0%
+that the oiler method produced
+ 
+
+ align:start position:0%
+that the oiler method produced
+uh but it's not finally the point that
+
+ align:start position:0%
+uh but it's not finally the point that
+ 
+
+ align:start position:0%
+uh but it's not finally the point that
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+want now do I have to say anything else
+
+ align:start position:0%
+want now do I have to say anything else
+ 
+
+ align:start position:0%
+want now do I have to say anything else
+uh yeah I didn't tell the computer what
+
+ align:start position:0%
+uh yeah I didn't tell the computer what
+ 
+
+ align:start position:0%
+uh yeah I didn't tell the computer what
+BN was okay BN is the
+
+ align:start position:0%
+BN was okay BN is the
+ 
+
+ align:start position:0%
+BN was okay BN is the
+slope of the direction field at the
+
+ align:start position:0%
+slope of the direction field at the
+ 
+
+ align:start position:0%
+slope of the direction field at the
+point n + one and the computer knows
+
+ align:start position:0%
+point n + one and the computer knows
+ 
+
+ align:start position:0%
+point n + one and the computer knows
+what that is and this point y n + one
+
+ align:start position:0%
+what that is and this point y n + one
+ 
+
+ align:start position:0%
+what that is and this point y n + one
+temporary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you make a temporary choice of this
+
+ align:start position:0%
+so you make a temporary choice of this
+ 
+
+ align:start position:0%
+so you make a temporary choice of this
+calculate that number and then go back
+
+ align:start position:0%
+calculate that number and then go back
+ 
+
+ align:start position:0%
+calculate that number and then go back
+and as it were correct that value to
+
+ align:start position:0%
+and as it were correct that value to
+ 
+
+ align:start position:0%
+and as it were correct that value to
+this value by using this better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slope now that's all there is to the
+
+ align:start position:0%
+slope now that's all there is to the
+ 
+
+ align:start position:0%
+slope now that's all there is to the
+method except I didn't give you its name
+
+ align:start position:0%
+method except I didn't give you its name
+ 
+
+ align:start position:0%
+method except I didn't give you its name
+uh well it has three names four names in
+
+ align:start position:0%
+uh well it has three names four names in
+ 
+
+ align:start position:0%
+uh well it has three names four names in
+fact uh which one shall I give you uh I
+
+ align:start position:0%
+fact uh which one shall I give you uh I
+ 
+
+ align:start position:0%
+fact uh which one shall I give you uh I
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+care okay if you the short name is hoins
+
+ align:start position:0%
+care okay if you the short name is hoins
+ 
+
+ align:start position:0%
+care okay if you the short name is hoins
+Method but nobody knows pronounces that
+
+ align:start position:0%
+Method but nobody knows pronounces that
+ 
+
+ align:start position:0%
+Method but nobody knows pronounces that
+correctly uh so that's Hy's method uh
+
+ align:start position:0%
+correctly uh so that's Hy's method uh
+ 
+
+ align:start position:0%
+correctly uh so that's Hy's method uh
+it's called also the improved Oiler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method it's called modified
+
+ align:start position:0%
+method it's called modified
+ 
+
+ align:start position:0%
+method it's called modified
+Oiler very expressive
+
+ align:start position:0%
+Oiler very expressive
+ 
+
+ align:start position:0%
+Oiler very expressive
+word modified Oilers method and it's
+
+ align:start position:0%
+word modified Oilers method and it's
+ 
+
+ align:start position:0%
+word modified Oilers method and it's
+also called AR
+
+ align:start position:0%
+also called AR
+ 
+
+ align:start position:0%
+also called AR
+K2 I'm sure you'll like that name best
+
+ align:start position:0%
+K2 I'm sure you'll like that name best
+ 
+
+ align:start position:0%
+K2 I'm sure you'll like that name best
+it has a Star Wars sort of sound to it
+
+ align:start position:0%
+it has a Star Wars sort of sound to it
+ 
+
+ align:start position:0%
+it has a Star Wars sort of sound to it
+uh R Cas stands for runga cuta and the
+
+ align:start position:0%
+uh R Cas stands for runga cuta and the
+ 
+
+ align:start position:0%
+uh R Cas stands for runga cuta and the
+reason for the
+
+ align:start position:0%
+reason for the
+ 
+
+ align:start position:0%
+reason for the
+two is not that it uses two well it is
+
+ align:start position:0%
+two is not that it uses two well it is
+ 
+
+ align:start position:0%
+two is not that it uses two well it is
+that it uses two slopes but the real
+
+ align:start position:0%
+that it uses two slopes but the real
+ 
+
+ align:start position:0%
+that it uses two slopes but the real
+reason for the two is that it it is a
+
+ align:start position:0%
+reason for the two is that it it is a
+ 
+
+ align:start position:0%
+reason for the two is that it it is a
+second order method so let's that's the
+
+ align:start position:0%
+second order method so let's that's the
+ 
+
+ align:start position:0%
+second order method so let's that's the
+most important thing to put down about
+
+ align:start position:0%
+most important thing to put down about
+ 
+
+ align:start position:0%
+most important thing to put down about
+it it's a second order method whereas
+
+ align:start position:0%
+it it's a second order method whereas
+ 
+
+ align:start position:0%
+it it's a second order method whereas
+Oilers was only a first order method so
+
+ align:start position:0%
+Oilers was only a first order method so
+ 
+
+ align:start position:0%
+Oilers was only a first order method so
+this is a so Ho's
+
+ align:start position:0%
+this is a so Ho's
+ 
+
+ align:start position:0%
+this is a so Ho's
+method or rk2 let's write it that's the
+
+ align:start position:0%
+method or rk2 let's write it that's the
+ 
+
+ align:start position:0%
+method or rk2 let's write it that's the
+shortest thing to write is a second
+
+ align:start position:0%
+shortest thing to write is a second
+ 
+
+ align:start position:0%
+shortest thing to write is a second
+order method
+
+ align:start position:0%
+order method
+ 
+
+ align:start position:0%
+order method
+meaning that the error varies with the
+
+ align:start position:0%
+meaning that the error varies with the
+ 
+
+ align:start position:0%
+meaning that the error varies with the
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+size like some constant it won't be the
+
+ align:start position:0%
+size like some constant it won't be the
+ 
+
+ align:start position:0%
+size like some constant it won't be the
+same as the constant for Oilers method
+
+ align:start position:0%
+same as the constant for Oilers method
+ 
+
+ align:start position:0%
+same as the constant for Oilers method
+times H
+
+ align:start position:0%
+times H
+ 
+
+ align:start position:0%
+times H
+squared that's a big saving because it
+
+ align:start position:0%
+squared that's a big saving because it
+ 
+
+ align:start position:0%
+squared that's a big saving because it
+now means that if you have the step size
+
+ align:start position:0%
+now means that if you have the step size
+ 
+
+ align:start position:0%
+now means that if you have the step size
+you're going to decrease the error by a
+
+ align:start position:0%
+you're going to decrease the error by a
+ 
+
+ align:start position:0%
+you're going to decrease the error by a
+factor of one quarter you will quarter
+
+ align:start position:0%
+factor of one quarter you will quarter
+ 
+
+ align:start position:0%
+factor of one quarter you will quarter
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+error now you say hey great why should
+
+ align:start position:0%
+error now you say hey great why should
+ 
+
+ align:start position:0%
+error now you say hey great why should
+anyone use anything else well think a
+
+ align:start position:0%
+anyone use anything else well think a
+ 
+
+ align:start position:0%
+anyone use anything else well think a
+little second the real thing which
+
+ align:start position:0%
+little second the real thing which
+ 
+
+ align:start position:0%
+little second the real thing which
+determines how slowly one of these
+
+ align:start position:0%
+determines how slowly one of these
+ 
+
+ align:start position:0%
+determines how slowly one of these
+methods run is you look at the hardest
+
+ align:start position:0%
+methods run is you look at the hardest
+ 
+
+ align:start position:0%
+methods run is you look at the hardest
+step of the method and ask how long does
+
+ align:start position:0%
+step of the method and ask how long does
+ 
+
+ align:start position:0%
+step of the method and ask how long does
+the computer take how many of those
+
+ align:start position:0%
+the computer take how many of those
+ 
+
+ align:start position:0%
+the computer take how many of those
+hardest steps are there now the answer
+
+ align:start position:0%
+hardest steps are there now the answer
+ 
+
+ align:start position:0%
+hardest steps are there now the answer
+is the hardest step is always the
+
+ align:start position:0%
+is the hardest step is always the
+ 
+
+ align:start position:0%
+is the hardest step is always the
+evaluation of the slope the evaluation
+
+ align:start position:0%
+evaluation of the slope the evaluation
+ 
+
+ align:start position:0%
+evaluation of the slope the evaluation
+of the function because you know I the
+
+ align:start position:0%
+of the function because you know I the
+ 
+
+ align:start position:0%
+of the function because you know I the
+functions that are in common use are not
+
+ align:start position:0%
+functions that are in common use are not
+ 
+
+ align:start position:0%
+functions that are in common use are not
+x^2 minus y^2 they take half a page and
+
+ align:start position:0%
+x^2 minus y^2 they take half a page and
+ 
+
+ align:start position:0%
+x^2 minus y^2 they take half a page and
+have his coefficients you know 10
+
+ align:start position:0%
+have his coefficients you know 10
+ 
+
+ align:start position:0%
+have his coefficients you know 10
+decimal place numbers whatever the guy
+
+ align:start position:0%
+decimal place numbers whatever the guy
+ 
+
+ align:start position:0%
+decimal place numbers whatever the guy
+the engineer is doing it you know
+
+ align:start position:0%
+the engineer is doing it you know
+ 
+
+ align:start position:0%
+the engineer is doing it you know
+whatever their accuracy
+
+ align:start position:0%
+whatever their accuracy
+ 
+
+ align:start position:0%
+whatever their accuracy
+was so the thing that controls how long
+
+ align:start position:0%
+was so the thing that controls how long
+ 
+
+ align:start position:0%
+was so the thing that controls how long
+a method runs is how many times the
+
+ align:start position:0%
+a method runs is how many times the
+ 
+
+ align:start position:0%
+a method runs is how many times the
+slope the function must be
+
+ align:start position:0%
+slope the function must be
+ 
+
+ align:start position:0%
+slope the function must be
+evaluated for Oiler I only have to
+
+ align:start position:0%
+evaluated for Oiler I only have to
+ 
+
+ align:start position:0%
+evaluated for Oiler I only have to
+evaluate it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once here I have to evaluate it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+twice now roughly speaking the number of
+
+ align:start position:0%
+twice now roughly speaking the number of
+ 
+
+ align:start position:0%
+twice now roughly speaking the number of
+function evaluations will each will give
+
+ align:start position:0%
+function evaluations will each will give
+ 
+
+ align:start position:0%
+function evaluations will each will give
+you the exponent the method that's
+
+ align:start position:0%
+you the exponent the method that's
+ 
+
+ align:start position:0%
+you the exponent the method that's
+called rung a cut a fourth order will
+
+ align:start position:0%
+called rung a cut a fourth order will
+ 
+
+ align:start position:0%
+called rung a cut a fourth order will
+require four evaluations of slope but
+
+ align:start position:0%
+require four evaluations of slope but
+ 
+
+ align:start position:0%
+require four evaluations of slope but
+the accuracy will be like H to the
+
+ align:start position:0%
+the accuracy will be like H to the
+ 
+
+ align:start position:0%
+the accuracy will be like H to the
+4th very accurate you have the step size
+
+ align:start position:0%
+4th very accurate you have the step size
+ 
+
+ align:start position:0%
+4th very accurate you have the step size
+and it goes down by a factor of 16 great
+
+ align:start position:0%
+and it goes down by a factor of 16 great
+ 
+
+ align:start position:0%
+and it goes down by a factor of 16 great
+but you had to do it for you had to
+
+ align:start position:0%
+but you had to do it for you had to
+ 
+
+ align:start position:0%
+but you had to do it for you had to
+evaluate the slope four times suppose
+
+ align:start position:0%
+evaluate the slope four times suppose
+ 
+
+ align:start position:0%
+evaluate the slope four times suppose
+instead you
+
+ align:start position:0%
+instead you
+ 
+
+ align:start position:0%
+instead you
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+have four times this thing and what
+
+ align:start position:0%
+have four times this thing and what
+ 
+
+ align:start position:0%
+have four times this thing and what
+would you have done you would have
+
+ align:start position:0%
+would you have done you would have
+ 
+
+ align:start position:0%
+would you have done you would have
+decreased it to 116th of what it
+
+ align:start position:0%
+decreased it to 116th of what it
+ 
+
+ align:start position:0%
+decreased it to 116th of what it
+was you still you would increase the
+
+ align:start position:0%
+was you still you would increase the
+ 
+
+ align:start position:0%
+was you still you would increase the
+number of functions evaluations you
+
+ align:start position:0%
+number of functions evaluations you
+ 
+
+ align:start position:0%
+number of functions evaluations you
+needed
+
+ align:start position:0%
+needed
+ 
+
+ align:start position:0%
+needed
+to four and you would have decreased the
+
+ align:start position:0%
+to four and you would have decreased the
+ 
+
+ align:start position:0%
+to four and you would have decreased the
+error by a 16th so in some sense it
+
+ align:start position:0%
+error by a 16th so in some sense it
+ 
+
+ align:start position:0%
+error by a 16th so in some sense it
+really doesn't matter whether you use a
+
+ align:start position:0%
+really doesn't matter whether you use a
+ 
+
+ align:start position:0%
+really doesn't matter whether you use a
+very fancy method which requires more
+
+ align:start position:0%
+very fancy method which requires more
+ 
+
+ align:start position:0%
+very fancy method which requires more
+function evaluation it's true the eror
+
+ align:start position:0%
+function evaluation it's true the eror
+ 
+
+ align:start position:0%
+function evaluation it's true the eror
+goes down faster but you having to do
+
+ align:start position:0%
+goes down faster but you having to do
+ 
+
+ align:start position:0%
+goes down faster but you having to do
+more work to get it so anyway nothing's
+
+ align:start position:0%
+more work to get it so anyway nothing's
+ 
+
+ align:start position:0%
+more work to get it so anyway nothing's
+free now uh I was I there is an arcave
+
+ align:start position:0%
+free now uh I was I there is an arcave
+ 
+
+ align:start position:0%
+free now uh I was I there is an arcave
+for I think I'll skip that since I
+
+ align:start position:0%
+for I think I'll skip that since I
+ 
+
+ align:start position:0%
+for I think I'll skip that since I
+wouldn't dare to ask you any questions
+
+ align:start position:0%
+wouldn't dare to ask you any questions
+ 
+
+ align:start position:0%
+wouldn't dare to ask you any questions
+about it but uh let me I just mention it
+
+ align:start position:0%
+about it but uh let me I just mention it
+ 
+
+ align:start position:0%
+about it but uh let me I just mention it
+at least because it's the standard it
+
+ align:start position:0%
+at least because it's the standard it
+ 
+
+ align:start position:0%
+at least because it's the standard it
+uses for evaluation it's the standard
+
+ align:start position:0%
+uses for evaluation it's the standard
+ 
+
+ align:start position:0%
+uses for evaluation it's the standard
+method if uh you don't want to do
+
+ align:start position:0%
+method if uh you don't want to do
+ 
+
+ align:start position:0%
+method if uh you don't want to do
+anything fancier uh it's rather
+
+ align:start position:0%
+anything fancier uh it's rather
+ 
+
+ align:start position:0%
+anything fancier uh it's rather
+inefficient but it's very accurate
+
+ align:start position:0%
+inefficient but it's very accurate
+ 
+
+ align:start position:0%
+inefficient but it's very accurate
+standard method uh
+
+ align:start position:0%
+standard method uh
+ 
+
+ align:start position:0%
+standard method uh
+accurate and uh you'll see when you use
+
+ align:start position:0%
+accurate and uh you'll see when you use
+ 
+
+ align:start position:0%
+accurate and uh you'll see when you use
+the programs it's in fact the program
+
+ align:start position:0%
+the programs it's in fact the program
+ 
+
+ align:start position:0%
+the programs it's in fact the program
+which is drawing those curves the
+
+ align:start position:0%
+which is drawing those curves the
+ 
+
+ align:start position:0%
+which is drawing those curves the
+numerical method which draws all those
+
+ align:start position:0%
+numerical method which draws all those
+ 
+
+ align:start position:0%
+numerical method which draws all those
+curves that you believe
+
+ align:start position:0%
+curves that you believe
+ 
+
+ align:start position:0%
+curves that you believe
+in uh on the computer screen is the rk4
+
+ align:start position:0%
+in uh on the computer screen is the rk4
+ 
+
+ align:start position:0%
+in uh on the computer screen is the rk4
+method the runga cut up I should give
+
+ align:start position:0%
+method the runga cut up I should give
+ 
+
+ align:start position:0%
+method the runga cut up I should give
+them the names rangaka fourth order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method two mathemati two I believe both
+
+ align:start position:0%
+method two mathemati two I believe both
+ 
+
+ align:start position:0%
+method two mathemati two I believe both
+German mathematicians around the turn of
+
+ align:start position:0%
+German mathematicians around the turn of
+ 
+
+ align:start position:0%
+German mathematicians around the turn of
+last century rangaka fourth order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method requires four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slopes requires you to calculate four
+
+ align:start position:0%
+slopes requires you to calculate four
+ 
+
+ align:start position:0%
+slopes requires you to calculate four
+slopes I won't bother telling you what
+
+ align:start position:0%
+slopes I won't bother telling you what
+ 
+
+ align:start position:0%
+slopes I won't bother telling you what
+you do but it's a procedure like that
+
+ align:start position:0%
+you do but it's a procedure like that
+ 
+
+ align:start position:0%
+you do but it's a procedure like that
+it's just a little more elaborate and
+
+ align:start position:0%
+it's just a little more elaborate and
+ 
+
+ align:start position:0%
+it's just a little more elaborate and
+you take two of these you make up a
+
+ align:start position:0%
+you take two of these you make up a
+ 
+
+ align:start position:0%
+you take two of these you make up a
+weighted average for the super slope you
+
+ align:start position:0%
+weighted average for the super slope you
+ 
+
+ align:start position:0%
+weighted average for the super slope you
+use weighted average what should I
+
+ align:start position:0%
+use weighted average what should I
+ 
+
+ align:start position:0%
+use weighted average what should I
+divide that
+
+ align:start position:0%
+divide that
+ 
+
+ align:start position:0%
+divide that
+by to get the
+
+ align:start position:0%
+by to get the
+ 
+
+ align:start position:0%
+by to get the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+six why why six well because if all
+
+ align:start position:0%
+six why why six well because if all
+ 
+
+ align:start position:0%
+six why why six well because if all
+these numbers were the same I'd want it
+
+ align:start position:0%
+these numbers were the same I'd want it
+ 
+
+ align:start position:0%
+these numbers were the same I'd want it
+to come out to be whatever that common
+
+ align:start position:0%
+to come out to be whatever that common
+ 
+
+ align:start position:0%
+to come out to be whatever that common
+value was therefore you always must
+
+ align:start position:0%
+value was therefore you always must
+ 
+
+ align:start position:0%
+value was therefore you always must
+divide by in a weighted average you must
+
+ align:start position:0%
+divide by in a weighted average you must
+ 
+
+ align:start position:0%
+divide by in a weighted average you must
+always divide by the sum of the
+
+ align:start position:0%
+always divide by the sum of the
+ 
+
+ align:start position:0%
+always divide by the sum of the
+coefficients so this is the super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slope and if you plug that super slope
+
+ align:start position:0%
+slope and if you plug that super slope
+ 
+
+ align:start position:0%
+slope and if you plug that super slope
+in uh to here you will be using the
+
+ align:start position:0%
+in uh to here you will be using the
+ 
+
+ align:start position:0%
+in uh to here you will be using the
+wrong a cutter method and get the best
+
+ align:start position:0%
+wrong a cutter method and get the best
+ 
+
+ align:start position:0%
+wrong a cutter method and get the best
+possible results now I wanted to spend
+
+ align:start position:0%
+possible results now I wanted to spend
+ 
+
+ align:start position:0%
+possible results now I wanted to spend
+the last three minutes uh talking about
+
+ align:start position:0%
+the last three minutes uh talking about
+ 
+
+ align:start position:0%
+the last three minutes uh talking about
+pitfalls of numerical computation in
+
+ align:start position:0%
+pitfalls of numerical computation in
+ 
+
+ align:start position:0%
+pitfalls of numerical computation in
+general uh one Pitfall I'm leaving you
+
+ align:start position:0%
+general uh one Pitfall I'm leaving you
+ 
+
+ align:start position:0%
+general uh one Pitfall I'm leaving you
+on the homework to discover for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yourself don't worry it won't cause you
+
+ align:start position:0%
+yourself don't worry it won't cause you
+ 
+
+ align:start position:0%
+yourself don't worry it won't cause you
+any grief
+
+ align:start position:0%
+any grief
+ 
+
+ align:start position:0%
+any grief
+just it'll just destroy your faith in
+
+ align:start position:0%
+just it'll just destroy your faith in
+ 
+
+ align:start position:0%
+just it'll just destroy your faith in
+these things for the rest of your life
+
+ align:start position:0%
+these things for the rest of your life
+ 
+
+ align:start position:0%
+these things for the rest of your life
+which is probably a good thing so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pitfalls number one you find you'll
+
+ align:start position:0%
+pitfalls number one you find you'll
+ 
+
+ align:start position:0%
+pitfalls number one you find you'll
+find let me talk instead briefly about
+
+ align:start position:0%
+find let me talk instead briefly about
+ 
+
+ align:start position:0%
+find let me talk instead briefly about
+number two which I'm not giving you an
+
+ align:start position:0%
+number two which I'm not giving you an
+ 
+
+ align:start position:0%
+number two which I'm not giving you an
+exercise in number two is illustrated by
+
+ align:start position:0%
+exercise in number two is illustrated by
+ 
+
+ align:start position:0%
+exercise in number two is illustrated by
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+equation what could be
+
+ align:start position:0%
+equation what could be
+ 
+
+ align:start position:0%
+equation what could be
+simpler this is a very bad equation to
+
+ align:start position:0%
+simpler this is a very bad equation to
+ 
+
+ align:start position:0%
+simpler this is a very bad equation to
+try to solve numerically now why well
+
+ align:start position:0%
+try to solve numerically now why well
+ 
+
+ align:start position:0%
+try to solve numerically now why well
+because if I separate
+
+ align:start position:0%
+because if I separate
+ 
+
+ align:start position:0%
+because if I separate
+variables uh why don't I save a little
+
+ align:start position:0%
+variables uh why don't I save a little
+ 
+
+ align:start position:0%
+variables uh why don't I save a little
+time I'll just tell you what the
+
+ align:start position:0%
+time I'll just tell you what the
+ 
+
+ align:start position:0%
+time I'll just tell you what the
+solution is okay okay you obviously you
+
+ align:start position:0%
+solution is okay okay you obviously you
+ 
+
+ align:start position:0%
+solution is okay okay you obviously you
+separate variables maybe you can do it
+
+ align:start position:0%
+separate variables maybe you can do it
+ 
+
+ align:start position:0%
+separate variables maybe you can do it
+in your head the solution will be the
+
+ align:start position:0%
+in your head the solution will be the
+ 
+
+ align:start position:0%
+in your head the solution will be the
+solutions will have an arbitrary
+
+ align:start position:0%
+solutions will have an arbitrary
+ 
+
+ align:start position:0%
+solutions will have an arbitrary
+constant in them and they won't be very
+
+ align:start position:0%
+constant in them and they won't be very
+ 
+
+ align:start position:0%
+constant in them and they won't be very
+complicated they will be one over C
+
+ align:start position:0%
+complicated they will be one over C
+ 
+
+ align:start position:0%
+complicated they will be one over C
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+x c is an arbitrary constant and as you
+
+ align:start position:0%
+x c is an arbitrary constant and as you
+ 
+
+ align:start position:0%
+x c is an arbitrary constant and as you
+give different values you get now what
+
+ align:start position:0%
+give different values you get now what
+ 
+
+ align:start position:0%
+give different values you get now what
+do those guys look like okay so here I
+
+ align:start position:0%
+do those guys look like okay so here I
+ 
+
+ align:start position:0%
+do those guys look like okay so here I
+am I I'm start out at The Point one and
+
+ align:start position:0%
+am I I'm start out at The Point one and
+ 
+
+ align:start position:0%
+am I I'm start out at The Point one and
+I start out I tell the computer compute
+
+ align:start position:0%
+I start out I tell the computer compute
+ 
+
+ align:start position:0%
+I start out I tell the computer compute
+for me the value of the solution at one
+
+ align:start position:0%
+for me the value of the solution at one
+ 
+
+ align:start position:0%
+for me the value of the solution at one
+starting out at one and it computes and
+
+ align:start position:0%
+starting out at one and it computes and
+ 
+
+ align:start position:0%
+starting out at one and it computes and
+computes a little while but the solution
+
+ align:start position:0%
+computes a little while but the solution
+ 
+
+ align:start position:0%
+computes a little while but the solution
+how does this curve actually look so in
+
+ align:start position:0%
+how does this curve actually look so in
+ 
+
+ align:start position:0%
+how does this curve actually look so in
+other words suppose I say that y of 0
+
+ align:start position:0%
+other words suppose I say that y of 0
+ 
+
+ align:start position:0%
+other words suppose I say that y of 0
+equals 1 find me y of two in other words
+
+ align:start position:0%
+equals 1 find me y of two in other words
+ 
+
+ align:start position:0%
+equals 1 find me y of two in other words
+take a a nice small step size use the
+
+ align:start position:0%
+take a a nice small step size use the
+ 
+
+ align:start position:0%
+take a a nice small step size use the
+rung of cut of fourth order method
+
+ align:start position:0%
+rung of cut of fourth order method
+ 
+
+ align:start position:0%
+rung of cut of fourth order method
+calculate a little bit and tell me I
+
+ align:start position:0%
+calculate a little bit and tell me I
+ 
+
+ align:start position:0%
+calculate a little bit and tell me I
+just want to know what y of two
+
+ align:start position:0%
+just want to know what y of two
+ 
+
+ align:start position:0%
+just want to know what y of two
+is well what is y of2 oh well
+
+ align:start position:0%
+is well what is y of2 oh well
+ 
+
+ align:start position:0%
+is well what is y of2 oh well
+unfortunately how does that curve look
+
+ align:start position:0%
+unfortunately how does that curve look
+ 
+
+ align:start position:0%
+unfortunately how does that curve look
+the curve looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at that point it drops to
+
+ align:start position:0%
+at that point it drops to
+ 
+
+ align:start position:0%
+at that point it drops to
+Infinity in a manner of speaking and
+
+ align:start position:0%
+Infinity in a manner of speaking and
+ 
+
+ align:start position:0%
+Infinity in a manner of speaking and
+then sort of comes back up again like
+
+ align:start position:0%
+then sort of comes back up again like
+ 
+
+ align:start position:0%
+then sort of comes back up again like
+that what is the value of y this is the
+
+ align:start position:0%
+that what is the value of y this is the
+ 
+
+ align:start position:0%
+that what is the value of y this is the
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+one what is the value of y of two is it
+
+ align:start position:0%
+one what is the value of y of two is it
+ 
+
+ align:start position:0%
+one what is the value of y of two is it
+here is it this well I don't know but I
+
+ align:start position:0%
+here is it this well I don't know but I
+ 
+
+ align:start position:0%
+here is it this well I don't know but I
+do know that the computer will not find
+
+ align:start position:0%
+do know that the computer will not find
+ 
+
+ align:start position:0%
+do know that the computer will not find
+it the computer will follow this along
+
+ align:start position:0%
+it the computer will follow this along
+ 
+
+ align:start position:0%
+it the computer will follow this along
+and get lost in eternity in infinity and
+
+ align:start position:0%
+and get lost in eternity in infinity and
+ 
+
+ align:start position:0%
+and get lost in eternity in infinity and
+see no reason whatever just why it
+
+ align:start position:0%
+see no reason whatever just why it
+ 
+
+ align:start position:0%
+see no reason whatever just why it
+should start again on this branch of the
+
+ align:start position:0%
+should start again on this branch of the
+ 
+
+ align:start position:0%
+should start again on this branch of the
+curve okay well we should can't we
+
+ align:start position:0%
+curve okay well we should can't we
+ 
+
+ align:start position:0%
+curve okay well we should can't we
+predict that that's going to happen
+
+ align:start position:0%
+predict that that's going to happen
+ 
+
+ align:start position:0%
+predict that that's going to happen
+somehow and you know avoided what I
+
+ align:start position:0%
+somehow and you know avoided what I
+ 
+
+ align:start position:0%
+somehow and you know avoided what I
+should have you know the whole
+
+ align:start position:0%
+should have you know the whole
+ 
+
+ align:start position:0%
+should have you know the whole
+difficulty is this is called a singular
+
+ align:start position:0%
+difficulty is this is called a singular
+ 
+
+ align:start position:0%
+difficulty is this is called a singular
+point this this solution has a
+
+ align:start position:0%
+point this this solution has a
+ 
+
+ align:start position:0%
+point this this solution has a
+singularity in other words a place where
+
+ align:start position:0%
+singularity in other words a place where
+ 
+
+ align:start position:0%
+singularity in other words a place where
+it goes to infinity or becomes
+
+ align:start position:0%
+it goes to infinity or becomes
+ 
+
+ align:start position:0%
+it goes to infinity or becomes
+discontinuous maybe has a jump
+
+ align:start position:0%
+discontinuous maybe has a jump
+ 
+
+ align:start position:0%
+discontinuous maybe has a jump
+discontinu
+
+ align:start position:0%
+discontinu
+ 
+
+ align:start position:0%
+discontinu
+it has a singularity at xal
+
+ align:start position:0%
+it has a singularity at xal
+ 
+
+ align:start position:0%
+it has a singularity at xal
+C this in particular at x equal 1 here
+
+ align:start position:0%
+C this in particular at x equal 1 here
+ 
+
+ align:start position:0%
+C this in particular at x equal 1 here
+but from the differential equation there
+
+ align:start position:0%
+but from the differential equation there
+ 
+
+ align:start position:0%
+but from the differential equation there
+is where is that c there is no way of
+
+ align:start position:0%
+is where is that c there is no way of
+ 
+
+ align:start position:0%
+is where is that c there is no way of
+predicting it each solution in other
+
+ align:start position:0%
+predicting it each solution in other
+ 
+
+ align:start position:0%
+predicting it each solution in other
+words to this differential equation has
+
+ align:start position:0%
+words to this differential equation has
+ 
+
+ align:start position:0%
+words to this differential equation has
+its own private Singularity which only
+
+ align:start position:0%
+its own private Singularity which only
+ 
+
+ align:start position:0%
+its own private Singularity which only
+it knows about and where it's going to
+
+ align:start position:0%
+it knows about and where it's going to
+ 
+
+ align:start position:0%
+it knows about and where it's going to
+blow up and there's no way of telling
+
+ align:start position:0%
+blow up and there's no way of telling
+ 
+
+ align:start position:0%
+blow up and there's no way of telling
+from the differential equation where
+
+ align:start position:0%
+from the differential equation where
+ 
+
+ align:start position:0%
+from the differential equation where
+that's going to be that's what makes
+
+ align:start position:0%
+that's going to be that's what makes
+ 
+
+ align:start position:0%
+that's going to be that's what makes
+numerical c one of the things that makes
+
+ align:start position:0%
+numerical c one of the things that makes
+ 
+
+ align:start position:0%
+numerical c one of the things that makes
+numerical calculation difficult when you
+
+ align:start position:0%
+numerical calculation difficult when you
+ 
+
+ align:start position:0%
+numerical calculation difficult when you
+cannot predict where things are going to
+
+ align:start position:0%
+cannot predict where things are going to
+ 
+
+ align:start position:0%
+cannot predict where things are going to
+go bad in advance
\ No newline at end of file
diff --git a/LgWFurXHX8U.txt b/LgWFurXHX8U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3ef420ee3091d9926a718c6c0479a7f97f1f4266
--- /dev/null
+++ b/LgWFurXHX8U.txt
@@ -0,0 +1,1573 @@
+PROFESSOR: Hi.
+
+Well, this is sort of a summary
+lecture for the big
+
+group about differential
+calculus.
+
+And it's got a fancy title, Six
+Functions, that we know.
+
+Well, five of them
+that we know.
+
+And a new one-- of course,
+there has to
+
+be something new--
+
+Six Rules, and Six Theorems.
+So I haven't emphasized
+
+theorems, but it seemed like
+this was an occasion where we
+
+could see the main points of the
+math behind the functions
+
+and the rules.
+
+OK.
+
+So, here are my first five
+functions, all familiar.
+
+And, what I'm happy about is
+that, if we understand those
+
+five and the rules to create
+more out of them, we get
+
+practically everything,
+everything we frequently use.
+
+OK.
+
+So, I wrote down function
+one, power of x, and its
+
+derivative, function
+two and its
+
+derivative, function three.
+
+Function four has,
+a little bit,
+
+something that is important.
+
+If it's e to the x,
+then we know the
+
+derivative is e to the x.
+
+But, if it's e to the c, x
+of factor c, comes down.
+
+Important case, you could
+say the chain rule.
+
+The derivative is that times
+the derivative of what's
+
+inside, which is the c.
+
+And, finally, the natural
+logarithm with the great
+
+derivative of 1/x.
+
+And now, oh, I left space
+to go from function one
+
+backwards, to remember the
+function that came before it.
+
+So, what function has
+this derivative?
+
+I'm looking here at the other
+generation, the older
+
+generation.
+
+Well, the function with that
+derivative is we need the
+
+power to be one higher, right?
+
+And then, the derivative of
+that, we need to divide by n
+
+plus 1 so that, when we take the
+derivative, the n plus 1
+
+comes down, cancels this, and
+gives us x to the n-th.
+
+The function that comes before
+sine x will be--
+
+oh, there was cos x
+in that direction.
+
+In this direction, we need
+minus cos x because the
+
+derivative of minus cos
+x is plus sine x.
+
+But, for this guy, cosine x,
+that came from sine x.
+
+And, what about this one?
+
+What function has
+this derivative?
+
+Well, with exponentials, we
+expect to see that exponential
+
+always, e to the c, x again,
+but, since this would bring
+
+down a c and here we don't
+want it, we'd better
+
+divide by that c.
+
+So then, if I take that, that's
+e to the c, x divided
+
+by c, so the c will come
+down, cancel the c,
+
+just the way here.
+
+And, oh, we've never
+figured out log x.
+
+That'll be something novel to
+do for integral calculus.
+
+But, I think, if I write down
+the answer, I think it's x
+
+times log x minus x.
+
+I believe that works.
+
+I would use the product
+rule on that.
+
+x times the derivative of that
+would be a 1 minus that.
+
+And the derivative of that
+would be a 1, so two ones
+
+would cancel, and the product
+rule would leave me with log x
+
+times the derivative of that.
+
+It works.
+
+It works.
+
+And notice the one beautiful
+thing in this list, that the
+
+case here is great unless
+I'm dividing by 0.
+
+If n is minus 1,
+I'm in trouble.
+
+If n is minus 1, I don't have
+here something whose--
+
+if n is minus 1, I can't
+divide by 0.
+
+I don't get x to the minus
+1 out of x to the 0.
+
+That rule fails at
+n equal minus 1.
+
+But look, here, is exactly
+fills in that whole.
+
+Wonderful.
+
+Here is the minus 1 power, and
+here is where it comes from.
+
+So that log just filled in the
+one hole that was left there.
+
+OK.
+
+Otherwise, you know
+these guys.
+
+But here's a new one:
+a step function.
+
+A step function, it's 0 and it
+jumps up to 1 at x equals 0.
+
+So, here's x.
+
+The function is 0 until
+it gets to that point.
+
+So it's level, then it takes
+a step up, a jump up, to 1.
+
+And let's say it's 1 at that
+point, so it takes that jump.
+
+All right.
+
+OK.
+
+That's a function that's
+actually quite important.
+
+And it's sort of like a two-part
+function, it's got a
+
+part to the left and a
+part to the right.
+
+And they don't meet, it's a
+non-continuous function.
+
+Can I figure out what is it
+that-- so here will be the old
+
+generation, what graph do
+I put there so that the
+
+derivative is 0 and then 1?
+
+Well, that's not too hard.
+
+If I put 0's here, the
+derivative will be 0.
+
+And now, over here, I want the
+derivative to be a constant 1.
+
+And we know that the derivative
+of x is what I
+
+need, so this is 0 and then
+x, two parts again.
+
+And the derivatives of those
+parts are 0 and then 1.
+
+And I often call that a ramp
+function because it looks a
+
+little like a ramp.
+
+OK.
+
+What about going this way?
+
+Ah, that's a little more
+interesting because what's the
+
+derivative of a step function?
+
+What's the slope of
+a step function?
+
+Well, the slope here is
+certainly 0, and the slope
+
+along here is certainly 0,
+so, is the answer 0?
+
+Well, of course not.
+
+All the action is
+at this jump.
+
+And what's the derivative
+there?
+
+Now, a careful person
+would say there is
+
+no derivative there.
+
+The limit of delta f/delta x,
+you don't get a correct answer
+
+there because delta f jumps
+by one, and delta x
+
+could be very small.
+
+And, as delta x goes to 0, we
+have 1/0, we have infinite.
+
+Well, I say, what?
+
+Let's go for infinite.
+
+So my derivative is
+0 and 0, and, at
+
+this point, it's infinite.
+
+It's a spike, or sometimes
+called a delta function.
+
+It's 0, and then infinite at
+one point, and then 0.
+
+And the oddball thing is that
+the area under that one-point
+
+tower, spike, is supposed
+to be 1.
+
+Because, do you remember--
+
+and we'll do more areas if we
+get to integral calculus--
+
+but, the area under
+this function is
+
+supposed to be this one.
+
+The area under the cosine
+function is sine x.
+
+The area under this function
+should be this one, so the
+
+area is 0 here.
+
+Run along here.
+
+No area under it.
+
+Then, I have a one-point
+spike, and the area is
+
+supposed to jump to 1
+under that spike,
+
+at that single point.
+
+That spike is infinitely tall,
+and it actually has a little
+
+area under it.
+
+Ah, well, your teacher may say
+get that function out of here.
+
+That's not a function.
+
+And I'm afraid that's
+a true fact that
+
+it's not a real function.
+
+So you could say I don't
+want to see this
+
+thing, clear it out.
+
+But, actually, that's
+very useful.
+
+It's a model for something that
+happens very quickly: an
+
+instant, an impulse, so
+I'll leave it there.
+
+I'll leave it there,
+but I'll go on.
+
+So, if you don't like it, you
+don't have to look at it.
+
+OK.
+
+So those were the
+six functions,
+
+now for the six rules.
+
+Nothing too fancy here.
+
+I don't think I really
+emphasized the most important
+
+and simplest rule that, if you
+have as a combination, like
+
+you add two functions, then
+the derivatives add.
+
+Or, if you multiply that
+function by 2 and that
+
+function by 3 before you add,
+then you multiply the
+
+derivatives by 2 and
+3 before you add.
+
+It's that fact that
+allowed us--
+
+I mean, you've used
+it all the time.
+
+If you integrated x plus x
+squared, you used the sum rule
+
+to integrate--
+
+ah, sorry--
+
+took the derivative.
+
+If you want the slope of x plus
+x squared, you would say
+
+oh, no problem: 1 plus 2x.
+
+1 coming from the first
+function, 2x from the x
+
+squared function.
+
+So the slope of a sum is just
+the sum of the slopes.
+
+You constantly use that to build
+many more functions out
+
+of the simple, anything, x
+squared plus x cubed plus x 4,
+
+if you know its derivative and
+you're using this rule.
+
+Now, the product rule,
+we worked through.
+
+You've practiced that.
+
+The quotient rule is a little
+messier with this minus sign
+
+and the division by g squared.
+
+It's a fraction.
+
+And then, a little more
+complicated, was
+
+this inverse function.
+
+Do you remember that if you
+start from y equals f of x--
+
+which is what we always
+have been doing--
+
+and then you say all right,
+switch it so that x isn't the
+
+input anymore, it's now
+the output, and the
+
+input is the y.
+
+So you're reversing
+the function.
+
+You're flipping the graph.
+
+We did this to get between
+e to the x and log x.
+
+That was the most important
+case of doing this flip
+
+between y equals e to the
+x and x equals log of y.
+
+And the chain rule tells us that
+the derivative of this
+
+inverse function is 1 over the
+derivative of the original.
+
+Nice rule.
+
+And here's the full-scale
+chain rule.
+
+Oh, that deserves to be put
+inside a box or something
+
+because this is a really
+great way to create new
+
+functions as a chain.
+
+You start with x.
+
+You do g of x, and then
+that's the input to f.
+
+You will know that chain rule.
+
+And you remember that that
+produces a product, the
+
+derivative of f times the
+derivative of g, but there was
+
+this little trick, right?
+
+This g of x was the y.
+
+I'll just remind you that this
+g of x is the y, and you have
+
+to get y out of the answer.
+
+Use this to get an answer
+in terms of x.
+
+Wherever you see y, you
+have to put in g of x.
+
+So, that's the chain rule.
+
+And then the final rule that
+I want to mention is this
+
+L'hopital rule about--
+
+well, a lot of calculus is about
+a ratio of f of x to g
+
+of x when it's going to 0/0.
+
+What do you do about 0/0?
+
+Well, as we're going to some
+point, like x equals a, if
+
+this is going to 0/0, then
+you're allowed to look.
+
+The slopes will tell you how
+quickly each one is going to
+
+0, and the ratio becomes a
+ratio of the two slopes.
+
+So, normally then, this answer
+would be the derivative at a
+
+divided by the derivative
+at a.
+
+If we're lucky, this 0/0 thing,
+when we look at the
+
+slopes, isn't 0/0 any more.
+
+It's good numbers,
+and L'hopital
+
+gets the answer right.
+
+OK.
+
+That's a review of L'hopital's
+rule, just really remembering
+
+that that's an important rule
+that came directly from the
+
+idea of the derivative.
+
+We're using the important part
+of the function because the
+
+constant term in that
+function is 0.
+
+Good.
+
+OK, are you ready for
+six theorems?
+
+That is a handful, but
+let's just tackle it.
+
+Why not?
+
+Why not?
+
+OK.
+
+So, six functions were easy.
+
+Well, we start with the big
+theorem, the big theorem, the
+
+fundamental theorem
+of calculus.
+
+The fundamental theorem
+of calculus, OK,
+
+that ought to be important.
+
+And what does it say?
+
+It says that the two operations
+of going from
+
+function one to two by taking
+the derivative, the slope, the
+
+speed, is the reverse of
+going the other way,
+
+from two back to one.
+
+It's really saying that, if
+I start with a function--
+
+Here, this would be one way.
+
+If I start with a function, f,
+I take the derivative to get
+
+function two, the speed,
+the slope.
+
+Then, if I go backwards--
+
+which is this integrating that
+integration symbol that's the
+
+core in integral calculus--
+
+if I take the derivative
+and then take the
+
+integral, I'm back to f.
+
+And what you actually get
+in this number is f at--
+
+it depends.
+
+It's like a delta f, really.
+
+It's the f at the end minus
+the f at the start.
+
+Maybe you'll remember that.
+
+When we talked about it, there
+was one lecture on big picture
+
+of the integral, and there may
+be more coming, but that was
+
+the one where we had
+this kind of thing.
+
+And, in the other direction, if
+I start with function two,
+
+do its integral to get function
+one, take the
+
+derivative of that, then I'm
+back to function two.
+
+Actually, you're going to say
+I knew that: function one to
+
+two, back to one.
+
+Or start with two, go to one,
+then back to two, that's the
+
+fundamental theorem.
+
+That those two operations,
+of taking the
+
+derivative, that limit--
+
+You remember what's tricky about
+all that is that this
+
+d,f, d,x, involves a limit
+as delta x goes to 0.
+
+And this integral will also
+involve a limit as
+
+delta x goes to 0.
+
+So that's the point at which it
+became calculus instead of
+
+just algebra.
+
+Well, important.
+
+I should say, let's assume here,
+that these functions are
+
+all continuous functions.
+
+And I'm going to assume that
+these theorems will apply to
+
+continuous functions.
+
+And do you remember
+what that meant?
+
+Basically, it meant that that
+jump function is not
+
+continuous.
+
+And that delta function is--
+
+well, that's not even
+a function.
+
+The ramp function is continuous
+but, of course, the
+
+derivative isn't.
+
+OK.
+
+All right.
+
+So, we've got functions that
+we can draw without raising
+
+our pen, without lifting
+the chalk.
+
+And here's the fact about
+them, that if I have a
+
+continuous function on an
+interval-- so, here is some
+
+point, a, and here is some
+point, b, and my
+
+function goes like that.
+
+Oh, it doesn't do that.
+
+It goes like that.
+
+Then this thing says that this
+maximum is actually reached,
+
+and this minimum is
+actually reached.
+
+And any value in-between,
+anywhere between this height
+
+and this height, there are
+points where the function
+
+equals that.
+
+The continuous function hits its
+maximum, hits its minimum,
+
+hits every point in-between.
+
+Where, if it wasn't continuous,
+you see it could
+
+go up, and then, suddenly,
+never reach that point,
+
+suddenly drop to there.
+
+There's a function not
+continuous, of course, because
+
+it fell down there.
+
+And it never reached m because
+it was this close, as close as
+
+it could be.
+
+But it never got there because,
+at the last minute,
+
+it jumped down.
+
+OK.
+
+So, that's sort of a good
+theoretical bit about
+
+continuous functions.
+
+OK.
+
+So, that's new.
+
+That was not mentioned before.
+
+But you can see it by just
+drawing a picture where it
+
+hits the max, hits the min, hits
+all values in-between.
+
+And then, you see the point,
+y, continuous was needed
+
+because, if you let it jump,
+the result doesn't work.
+
+OK.
+
+Here's another thing.
+
+This is now called the
+mean value theorem.
+
+That's a neat theorem.
+
+OK.
+
+Oh.
+
+Now, here, our function is going
+to have a derivative
+
+over some region.
+
+That function probably
+had a derivative.
+
+OK.
+
+OK.
+
+So, that function, or this
+function, f of x, here's the
+
+idea of the mean
+value theorem.
+
+This is like delta f/delta
+x for the whole
+
+interval from a to b.
+
+Delta x is b minus a,
+the whole jump.
+
+Delta f is f at the end
+minus f at this end.
+
+So that delta f/delta x is like
+your average speed over
+
+the whole trip.
+
+Like you went on the
+MassPike, right?
+
+And you entered at 1:00 o'clock
+and came out at 4:00
+
+o'clock, so you were on the
+pike for three hours.
+
+And your trip meter
+shows 200 miles.
+
+So your average speed, average
+speed, was 200 divided by 3,
+
+that number of miles per hour.
+
+Yeah, about 66 miles-- well,
+probably illegal.
+
+OK.
+
+A little over 66 miles an
+hour: 200/3, so you're
+
+slightly over the speed limit.
+
+Well, the mean value theorem
+catches you because you could
+
+say well, but when did
+I pass the limit?
+
+When was I going more than 65?
+
+And the mean value theorem says
+there was a time, there
+
+was a moment when your speed,
+when the speedometer, itself,
+
+was exactly.
+
+This instant speed equaled
+the average speed.
+
+Shall I say that again?
+
+If you travel with a smooth
+changes of speed, no jumps in
+
+speed, then, if I look at the
+average speed over a delta t,
+
+there is some point inside that
+one where the average
+
+speed agrees with the
+instant speed.
+
+Or you could say, if
+you prefer slope--
+
+Suppose the average slope, the
+up over a cross, is 10, So in
+
+the time at cross, you
+eventually got up 10.
+
+Then there will be some
+point when your
+
+climbing rate was 10.
+
+There'd be some point when that
+instant slope is also 10.
+
+OK.
+
+That's the mean value theorem.
+
+This is called the mean value.
+
+Mean value is another
+word for average.
+
+So the mean value equals the
+instant value at some point.
+
+But we don't know, that point
+could be anywhere.
+
+OK.
+
+Now, I'm ready for the last two
+theorems. And the first
+
+one is called Taylor Series,
+the Taylor's theorem.
+
+And we have touched on that.
+
+And what is Taylor
+Series about?
+
+Taylor Series is when you know
+what's going on at some point
+
+x equal a, and you want to know
+what the function is at
+
+some point x near a.
+
+So x is near a.
+
+And, to a very low
+approximation, f of x is
+
+pretty close to f of a.
+
+This is the constant term.
+
+That's where the trip started.
+
+So this is like a trip meter
+for a very short trip.
+
+The first thing would be to know
+what was the trip meter
+
+reading at the start.
+
+But then the correction term, so
+this is the calculus term,
+
+it's the speed at the start
+times the time of the trip.
+
+If you only keep this, the
+trip meter isn't moving.
+
+When you add on this, you're
+like following a tangent line.
+
+If I try to describe it, you're
+pretending the speed
+
+didn't change.
+
+Here, you're pretending the
+trip meter didn't change.
+
+Nothing happened.
+
+Here is the next term.
+
+But now, of course, this speed
+normally changes too.
+
+So calculus says there is
+a term from the second
+
+derivative, there's
+a bending term.
+
+This, we would be correct to
+stop right there on a straight
+
+line: constant speed.
+
+But now, if the speed is
+increasing, your trip meter
+
+graph is bending upwards, you'd
+better have a correction
+
+from the second derivative.
+
+That's the slope of the slope,
+the rate of change
+
+of the rate of change.
+
+It's the acceleration.
+
+So, if I had constant
+acceleration, like I drop this
+
+chalk, it accelerates.
+
+So, from where I drop it, that
+gives me its original height.
+
+Its original speed might be
+0, if I hold onto it.
+
+But then, this term would
+account for the second
+
+derivative, the acceleration.
+
+And that would give me the right
+answer, the right answer
+
+to the next term, but now I've
+drawn the famous three dots.
+
+So three dots is the way to
+say there are more terms
+
+because the acceleration
+might not be constant.
+
+What's the next term?
+
+If you know the next
+term, then you
+
+and Taylor are square.
+
+The next term will be
+1/3 factorial, 1/6.
+
+It'll be a third derivative of
+f at the known point times
+
+this x minus a cubed.
+
+You see that these terms
+are getting,
+
+typically, for a nice function--
+
+and we saw this for
+e to the x.
+
+We saw the Taylor Series
+for e to the x.
+
+Can I remind you of the Taylor
+Series for e to the x around
+
+the point 0 because e to the x
+is the greatest function I've
+
+spoken about, at all?
+
+So, if this was e to the x, it
+would start out at e to the 0,
+
+which is 1.
+
+Its slope is 1, so this
+is 1 times x.
+
+Its second derivative
+is, again, 1.
+
+And a is 0 here, so
+this would be 1/2,
+
+1/2 factorial x squared.
+
+And then that next three-dot
+term would be
+
+1/3 factorial x cube.
+
+And you remember what
+it looks like.
+
+So the Taylor Series just
+looks messy because I'm
+
+writing any old f.
+
+I'm allowing it to be the start
+point, to be a, and not
+
+necessarily 0.
+
+But, typically, it's 0.
+
+And the e to the x series
+is the best example.
+
+But I want to show you
+one more example.
+
+That'll be my last theorem.
+
+I just mention it here because
+it's just like
+
+the mean value theorem.
+
+If I do stop, suppose I stop
+here and I don't include the x
+
+cube term, the third derivative
+term, then I've
+
+made an error.
+
+And, of course, that error
+depends on what the third
+
+derivative is, the one I
+skipped, the x minus a cube,
+
+the thing I skipped, and
+the 1/3 factorial.
+
+And this third derivative
+is, at some point,
+
+between a and x.
+
+That's a lot to put in, but the
+mean value theorem said
+
+you could take the derivative at
+some point in-between, some
+
+point along the MassPike.
+
+And this is just the same thing,
+but I'm keeping more
+
+terms. I'm quitting at any
+point, and then I would take
+
+the next derivative at somewhere
+along the MassPike.
+
+What should you learn
+out of that?
+
+I think the idea is
+Taylor Series.
+
+And, of course, we have
+two possibilities.
+
+Either we cut the series off and
+we make some error, but we
+
+get a pretty good answer, or we
+let the series go forever.
+
+And then comes the question.
+
+Then we have an infinite number
+of terms, and then the
+
+question is does that series add
+up to a finite thing like
+
+e to the x?
+
+Or does it add up to a delta
+function or something
+
+impossible?
+
+So that leads to the question
+of learning
+
+about infinite series.
+
+In calculus, Taylor
+Series is where
+
+infinite series come from.
+
+And, if we want to go all the
+way with them, then we have to
+
+begin to think about what does
+it mean for that infinite
+
+series to add up to a
+number, or maybe it
+
+just goes off to infinity.
+
+Does it converge, or
+does it diverge?
+
+Ah, that would be another
+lecture or two.
+
+Let me complete today with one
+more theorem, a famous one,
+
+the binomial theorem.
+
+So, what's the binomial
+theorem about?
+
+The binomial theorem is about
+powers of 1 plus x.
+
+1 plus x is a typical binomial:
+two things, 1 and x.
+
+And we have various powers.
+
+Well, if the powers are the
+first power, the second power,
+
+the third power, we can write
+out, we can square 1 plus x,
+
+and we can get 1 plus x cubed.
+
+And, out of it, we get this.
+
+And there would be 1 plus
+x to the 0-th power.
+
+And do you see that there's a
+whole lot of ones in the neat
+
+pattern there?
+
+And then there's a
+2, and a 3, 3.
+
+And if you'd like to know this
+one, it would be 1, 4, 6, 4, 1
+
+would be the next
+row of Pascal.
+
+Pascal really had a sense of
+beauty or art in this triangle
+
+of numbers.
+
+And that's the triangle you
+get, Pascal's triangle, if
+
+you're taking--
+
+A whole number, a power is 1
+plus x to the third power,
+
+fourth power, fifth power,
+sixth power, but what if
+
+you're taking to some other
+power, any power, p?
+
+So now I'm interested in this
+guy to a power of p that,
+
+maybe, is not two, three,
+four, five.
+
+It could be 1/2, 1 plus x square
+root to the 1/2 power,
+
+or 1 plus x to the
+minus 1 power.
+
+All other powers are possible
+and, for those,
+
+the Taylor's theorem.
+
+And here's my function.
+
+And I could apply Taylor's
+theorem to find the--
+
+and I'll do it at x equals 0,
+that's the place Taylor liked
+
+the best. So the
+constant term--
+
+think of this Taylor expansion
+that we just did--
+
+at x equals 0, this
+thing is 1.
+
+So, the big theory starts
+out with a 1 for
+
+the constant term.
+
+Then what I do for the next
+term of the Taylor Series?
+
+I take the derivative and
+I put x equals 0.
+
+And what do I get then?
+
+I get p times x.
+
+So this is the constant
+term: f of 0.
+
+This is the derivative:
+times x minus a
+
+divided by 1 factorial.
+
+Well, you didn't see all those
+things because one factorial I
+
+didn't write.
+
+And then the next term would be
+the next derivative, of p
+
+minus 1 will come down, so
+you'll have p, p minus 1.
+
+You're supposed to divide
+by 2 factorial.
+
+That multiplies x squared.
+
+Well, my point is just that
+this binomial formula is
+
+Taylor's formula.
+
+The binomial theorem, with
+these, this is called a
+
+binomial coefficient.
+
+Gamblers know all about
+that, you know?
+
+If you've got p things and you
+want to take two, how many
+
+ways to do it?
+
+You know, how many ways to get
+two aces out of a deck, all
+
+these things are hidden in those
+numbers, which gamblers
+
+learn or lose.
+
+OK.
+
+So, I'll make one last point
+about the binomial theorem.
+
+Those were Taylor Series.
+
+This is a Taylor series.
+
+What's the difference?
+
+The difference is these
+series stop.
+
+This is a series: 1
+plus x squared.
+
+That's the Taylor Series,
+but the third
+
+derivative is 0, right?
+
+The third derivative of that
+function, because that
+
+function's only going up to x
+squared, the third derivative
+
+is 0, so the rest of Taylor
+Series has died.
+
+It's not there.
+
+So that's all there is.
+
+The derivative of any of those
+powers, one, two, three, four,
+
+five powers, after I take enough
+derivatives, gone.
+
+But, if I take a power like
+minus 1, or 1/2, or pi, or
+
+anything, then I can take
+derivatives forever
+
+without hitting 0.
+
+In other words, this series
+goes on, and on, and on.
+
+Those three dots--
+
+let me move that eraser so you
+see those three dots--
+
+that signals an infinite series
+and the question of
+
+does it add up to a finite
+number, what's going on with
+
+infinite series?
+
+But, for the moment, my point
+is just this is what
+
+calculus can do.
+
+If you not only take that slope,
+but the slope of the
+
+slope, and the third derivative,
+and all higher
+
+derivatives, that's what Taylor
+Series tells you.
+
+OK.
+
+So that's the, in some way, high
+point of the highlights
+
+of calculus, and I sure hope
+they're helpful to you.
+
+Thank you.
+
+FEMALE VOICE: This has been
+a production of MIT
+
+OpenCourseWare and
+Gilbert Strang.
+
+Funding for this video was
+provided by the Lord
+
+Foundation.
+
+To help OCW continue to provide
+free and open access
+
+to MIT courses, please
+make a donation at
+
+ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/Lm4p4YPC_q0.txt b/Lm4p4YPC_q0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d1ba1fa510a287c18fdb36da0c9483de6f2704c2
--- /dev/null
+++ b/Lm4p4YPC_q0.txt
@@ -0,0 +1,5051 @@
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+this motor uh was that the original
+
+ align:start position:0%
+this motor uh was that the original
+ 
+
+ align:start position:0%
+this motor uh was that the original
+a assisted human power vehicle uh the
+
+ align:start position:0%
+a assisted human power vehicle uh the
+ 
+
+ align:start position:0%
+a assisted human power vehicle uh the
+motor was prohibitively expensive they
+
+ align:start position:0%
+motor was prohibitively expensive they
+ 
+
+ align:start position:0%
+motor was prohibitively expensive they
+use a new generation motor vehicle a
+
+ align:start position:0%
+use a new generation motor vehicle a
+ 
+
+ align:start position:0%
+use a new generation motor vehicle a
+motor and it cost $8,000 it's pictured
+
+ align:start position:0%
+motor and it cost $8,000 it's pictured
+ 
+
+ align:start position:0%
+motor and it cost $8,000 it's pictured
+right here our main goal was to create a
+
+ align:start position:0%
+right here our main goal was to create a
+ 
+
+ align:start position:0%
+right here our main goal was to create a
+motor that would fit in the same area
+
+ align:start position:0%
+motor that would fit in the same area
+ 
+
+ align:start position:0%
+motor that would fit in the same area
+and also as a stepping stone to move on
+
+ align:start position:0%
+and also as a stepping stone to move on
+ 
+
+ align:start position:0%
+and also as a stepping stone to move on
+to the bds2 the new
+
+ align:start position:0%
+to the bds2 the new
+ 
+
+ align:start position:0%
+to the bds2 the new
+design and these requirements were
+
+ align:start position:0%
+design and these requirements were
+ 
+
+ align:start position:0%
+design and these requirements were
+handed down to us by VDS we wanted 10 KW
+
+ align:start position:0%
+handed down to us by VDS we wanted 10 KW
+ 
+
+ align:start position:0%
+handed down to us by VDS we wanted 10 KW
+continuous power uh the original motor
+
+ align:start position:0%
+continuous power uh the original motor
+ 
+
+ align:start position:0%
+continuous power uh the original motor
+that was pictured before had
+
+ align:start position:0%
+that was pictured before had
+ 
+
+ align:start position:0%
+that was pictured before had
+3.4 uh we want 90% or above efficiently
+
+ align:start position:0%
+3.4 uh we want 90% or above efficiently
+ 
+
+ align:start position:0%
+3.4 uh we want 90% or above efficiently
+optimally at 45 mph which we considered
+
+ align:start position:0%
+optimally at 45 mph which we considered
+ 
+
+ align:start position:0%
+optimally at 45 mph which we considered
+you know reasonable speed the old motor
+
+ align:start position:0%
+you know reasonable speed the old motor
+ 
+
+ align:start position:0%
+you know reasonable speed the old motor
+had about 94% efficiency and Medi
+
+ align:start position:0%
+had about 94% efficiency and Medi
+ 
+
+ align:start position:0%
+had about 94% efficiency and Medi
+decided that it was acceptable to lose a
+
+ align:start position:0%
+decided that it was acceptable to lose a
+ 
+
+ align:start position:0%
+decided that it was acceptable to lose a
+few percentage to gain the extra power
+
+ align:start position:0%
+few percentage to gain the extra power
+ 
+
+ align:start position:0%
+few percentage to gain the extra power
+um they also wanted a motor that weighed
+
+ align:start position:0%
+um they also wanted a motor that weighed
+ 
+
+ align:start position:0%
+um they also wanted a motor that weighed
+less than 30 kg and you also had to
+
+ align:start position:0%
+less than 30 kg and you also had to
+ 
+
+ align:start position:0%
+less than 30 kg and you also had to
+interface an evc2 200 controller this
+
+ align:start position:0%
+interface an evc2 200 controller this
+ 
+
+ align:start position:0%
+interface an evc2 200 controller this
+controller is actually the NGM
+
+ align:start position:0%
+controller is actually the NGM
+ 
+
+ align:start position:0%
+controller is actually the NGM
+controller uh we learned later that
+
+ align:start position:0%
+controller uh we learned later that
+ 
+
+ align:start position:0%
+controller uh we learned later that
+there were some limitations to that uh
+
+ align:start position:0%
+there were some limitations to that uh
+ 
+
+ align:start position:0%
+there were some limitations to that uh
+we also wanted an acceleration from 0 to
+
+ align:start position:0%
+we also wanted an acceleration from 0 to
+ 
+
+ align:start position:0%
+we also wanted an acceleration from 0 to
+60 M hour in 15 seconds to give you a
+
+ align:start position:0%
+60 M hour in 15 seconds to give you a
+ 
+
+ align:start position:0%
+60 M hour in 15 seconds to give you a
+rough idea the too previous can do in
+
+ align:start position:0%
+rough idea the too previous can do in
+ 
+
+ align:start position:0%
+rough idea the too previous can do in
+about 12 seconds so we're on par with
+
+ align:start position:0%
+about 12 seconds so we're on par with
+ 
+
+ align:start position:0%
+about 12 seconds so we're on par with
+them um also Tor with speed variation
+
+ align:start position:0%
+them um also Tor with speed variation
+ 
+
+ align:start position:0%
+them um also Tor with speed variation
+and we're powered by electricity uh we
+
+ align:start position:0%
+and we're powered by electricity uh we
+ 
+
+ align:start position:0%
+and we're powered by electricity uh we
+have batteries we can be supplied by
+
+ align:start position:0%
+have batteries we can be supplied by
+ 
+
+ align:start position:0%
+have batteries we can be supplied by
+solar or plug into
+
+ align:start position:0%
+solar or plug into
+ 
+
+ align:start position:0%
+solar or plug into
+the and our constraints start with the
+
+ align:start position:0%
+the and our constraints start with the
+ 
+
+ align:start position:0%
+the and our constraints start with the
+physical constraints where basically we
+
+ align:start position:0%
+physical constraints where basically we
+ 
+
+ align:start position:0%
+physical constraints where basically we
+had to fit into this eyebolt and we also
+
+ align:start position:0%
+had to fit into this eyebolt and we also
+ 
+
+ align:start position:0%
+had to fit into this eyebolt and we also
+had a volume constraint because we
+
+ align:start position:0%
+had a volume constraint because we
+ 
+
+ align:start position:0%
+had a volume constraint because we
+couldn't make the motor uh prohibitively
+
+ align:start position:0%
+couldn't make the motor uh prohibitively
+ 
+
+ align:start position:0%
+couldn't make the motor uh prohibitively
+large because the wheel feature here had
+
+ align:start position:0%
+large because the wheel feature here had
+ 
+
+ align:start position:0%
+large because the wheel feature here had
+a certain diameter um also the torque
+
+ align:start position:0%
+a certain diameter um also the torque
+ 
+
+ align:start position:0%
+a certain diameter um also the torque
+couldn't surpass how much this could
+
+ align:start position:0%
+couldn't surpass how much this could
+ 
+
+ align:start position:0%
+couldn't surpass how much this could
+hold
+
+ align:start position:0%
+hold
+ 
+
+ align:start position:0%
+hold
+and also the EVC 200 which is one uh one
+
+ align:start position:0%
+and also the EVC 200 which is one uh one
+ 
+
+ align:start position:0%
+and also the EVC 200 which is one uh one
+era we did not realize at first but it
+
+ align:start position:0%
+era we did not realize at first but it
+ 
+
+ align:start position:0%
+era we did not realize at first but it
+could only Supply approximately 3.4 Kow
+
+ align:start position:0%
+could only Supply approximately 3.4 Kow
+ 
+
+ align:start position:0%
+could only Supply approximately 3.4 Kow
+continuous unfortunately we learned this
+
+ align:start position:0%
+continuous unfortunately we learned this
+ 
+
+ align:start position:0%
+continuous unfortunately we learned this
+a little bit too
+
+ align:start position:0%
+a little bit too
+ 
+
+ align:start position:0%
+a little bit too
+late can you say that again just that
+
+ align:start position:0%
+late can you say that again just that
+ 
+
+ align:start position:0%
+late can you say that again just that
+last s well we we learned it a little
+
+ align:start position:0%
+last s well we we learned it a little
+ 
+
+ align:start position:0%
+last s well we we learned it a little
+bit too late after we we accepted the
+
+ align:start position:0%
+bit too late after we we accepted the
+ 
+
+ align:start position:0%
+bit too late after we we accepted the
+VDS they handed down their requirements
+
+ align:start position:0%
+VDS they handed down their requirements
+ 
+
+ align:start position:0%
+VDS they handed down their requirements
+when they said to use the NGM controller
+
+ align:start position:0%
+when they said to use the NGM controller
+ 
+
+ align:start position:0%
+when they said to use the NGM controller
+but through our research we found out
+
+ align:start position:0%
+but through our research we found out
+ 
+
+ align:start position:0%
+but through our research we found out
+that it could Supply 8 KW Peak but not
+
+ align:start position:0%
+that it could Supply 8 KW Peak but not
+ 
+
+ align:start position:0%
+that it could Supply 8 KW Peak but not
+continuous only approximately 4 Kow
+
+ align:start position:0%
+continuous only approximately 4 Kow
+ 
+
+ align:start position:0%
+continuous only approximately 4 Kow
+continuous basically to meet the
+
+ align:start position:0%
+continuous basically to meet the
+ 
+
+ align:start position:0%
+continuous basically to meet the
+requirements that were given to us we
+
+ align:start position:0%
+requirements that were given to us we
+ 
+
+ align:start position:0%
+requirements that were given to us we
+would have to have designed a completely
+
+ align:start position:0%
+would have to have designed a completely
+ 
+
+ align:start position:0%
+would have to have designed a completely
+new uh digital brushless motor
+
+ align:start position:0%
+new uh digital brushless motor
+ 
+
+ align:start position:0%
+new uh digital brushless motor
+controller which is like from what we
+
+ align:start position:0%
+controller which is like from what we
+ 
+
+ align:start position:0%
+controller which is like from what we
+learned like a 2-year process if you
+
+ align:start position:0%
+learned like a 2-year process if you
+ 
+
+ align:start position:0%
+learned like a 2-year process if you
+want to get a really good one um in the
+
+ align:start position:0%
+want to get a really good one um in the
+ 
+
+ align:start position:0%
+want to get a really good one um in the
+lecture so that was uh we would had to
+
+ align:start position:0%
+lecture so that was uh we would had to
+ 
+
+ align:start position:0%
+lecture so that was uh we would had to
+make a decision uh whether to go for
+
+ align:start position:0%
+make a decision uh whether to go for
+ 
+
+ align:start position:0%
+make a decision uh whether to go for
+long term or a motor that wouldn't meet
+
+ align:start position:0%
+long term or a motor that wouldn't meet
+ 
+
+ align:start position:0%
+long term or a motor that wouldn't meet
+the requirements they gave us because it
+
+ align:start position:0%
+the requirements they gave us because it
+ 
+
+ align:start position:0%
+the requirements they gave us because it
+wasn't
+
+ align:start position:0%
+wasn't
+ 
+
+ align:start position:0%
+wasn't
+feasible okay
+
+ align:start position:0%
+feasible okay
+ 
+
+ align:start position:0%
+feasible okay
+preliminary design choices in the world
+
+ align:start position:0%
+preliminary design choices in the world
+ 
+
+ align:start position:0%
+preliminary design choices in the world
+of electric motors there's uh a lot of
+
+ align:start position:0%
+of electric motors there's uh a lot of
+ 
+
+ align:start position:0%
+of electric motors there's uh a lot of
+different uh selections you have to make
+
+ align:start position:0%
+different uh selections you have to make
+ 
+
+ align:start position:0%
+different uh selections you have to make
+right away lots of different uh motor
+
+ align:start position:0%
+right away lots of different uh motor
+ 
+
+ align:start position:0%
+right away lots of different uh motor
+types General Motors and we needed to
+
+ align:start position:0%
+types General Motors and we needed to
+ 
+
+ align:start position:0%
+types General Motors and we needed to
+decide just based on Research not
+
+ align:start position:0%
+decide just based on Research not
+ 
+
+ align:start position:0%
+decide just based on Research not
+talking about any design variables like
+
+ align:start position:0%
+talking about any design variables like
+ 
+
+ align:start position:0%
+talking about any design variables like
+pool numbers and such but just the vague
+
+ align:start position:0%
+pool numbers and such but just the vague
+ 
+
+ align:start position:0%
+pool numbers and such but just the vague
+idea of what kind of engine or motor we
+
+ align:start position:0%
+idea of what kind of engine or motor we
+ 
+
+ align:start position:0%
+idea of what kind of engine or motor we
+wanted to design so we started out just
+
+ align:start position:0%
+wanted to design so we started out just
+ 
+
+ align:start position:0%
+wanted to design so we started out just
+tacking this with research and looking
+
+ align:start position:0%
+tacking this with research and looking
+ 
+
+ align:start position:0%
+tacking this with research and looking
+at the field and looking at our
+
+ align:start position:0%
+at the field and looking at our
+ 
+
+ align:start position:0%
+at the field and looking at our
+requirements and deciding okay what fits
+
+ align:start position:0%
+requirements and deciding okay what fits
+ 
+
+ align:start position:0%
+requirements and deciding okay what fits
+what is going to make sense to design
+
+ align:start position:0%
+what is going to make sense to design
+ 
+
+ align:start position:0%
+what is going to make sense to design
+here so basically why did we decide
+
+ align:start position:0%
+here so basically why did we decide
+ 
+
+ align:start position:0%
+here so basically why did we decide
+designed a three-phase axial Gap
+
+ align:start position:0%
+designed a three-phase axial Gap
+ 
+
+ align:start position:0%
+designed a three-phase axial Gap
+double-sided slotted surface mounted
+
+ align:start position:0%
+double-sided slotted surface mounted
+ 
+
+ align:start position:0%
+double-sided slotted surface mounted
+brushless DC motor now it's basically
+
+ align:start position:0%
+brushless DC motor now it's basically
+ 
+
+ align:start position:0%
+brushless DC motor now it's basically
+all decided with no optimization these
+
+ align:start position:0%
+all decided with no optimization these
+ 
+
+ align:start position:0%
+all decided with no optimization these
+are just general ideas testing um first
+
+ align:start position:0%
+are just general ideas testing um first
+ 
+
+ align:start position:0%
+are just general ideas testing um first
+off the brushless home motor compared to
+
+ align:start position:0%
+off the brushless home motor compared to
+ 
+
+ align:start position:0%
+off the brushless home motor compared to
+the brush home motor which is just the
+
+ align:start position:0%
+the brush home motor which is just the
+ 
+
+ align:start position:0%
+the brush home motor which is just the
+brushes on the motor uh brush sub Motors
+
+ align:start position:0%
+brushes on the motor uh brush sub Motors
+ 
+
+ align:start position:0%
+brushes on the motor uh brush sub Motors
+are more uh standard more typical you
+
+ align:start position:0%
+are more uh standard more typical you
+ 
+
+ align:start position:0%
+are more uh standard more typical you
+see them more often brushless is
+
+ align:start position:0%
+see them more often brushless is
+ 
+
+ align:start position:0%
+see them more often brushless is
+something that's come up more in the
+
+ align:start position:0%
+something that's come up more in the
+ 
+
+ align:start position:0%
+something that's come up more in the
+last like 15 years or so um there is a
+
+ align:start position:0%
+last like 15 years or so um there is a
+ 
+
+ align:start position:0%
+last like 15 years or so um there is a
+lot of advantages to brushless motors uh
+
+ align:start position:0%
+lot of advantages to brushless motors uh
+ 
+
+ align:start position:0%
+lot of advantages to brushless motors uh
+one being higher efficiency and
+
+ align:start position:0%
+one being higher efficiency and
+ 
+
+ align:start position:0%
+one being higher efficiency and
+reliability because you reduce the
+
+ align:start position:0%
+reliability because you reduce the
+ 
+
+ align:start position:0%
+reliability because you reduce the
+electromatic interference that's the
+
+ align:start position:0%
+electromatic interference that's the
+ 
+
+ align:start position:0%
+electromatic interference that's the
+main reason why people use them and why
+
+ align:start position:0%
+main reason why people use them and why
+ 
+
+ align:start position:0%
+main reason why people use them and why
+they become more prevalent in the last
+
+ align:start position:0%
+they become more prevalent in the last
+ 
+
+ align:start position:0%
+they become more prevalent in the last
+15 or so years you also reduce the noise
+
+ align:start position:0%
+15 or so years you also reduce the noise
+ 
+
+ align:start position:0%
+15 or so years you also reduce the noise
+because you don't have the brushes
+
+ align:start position:0%
+because you don't have the brushes
+ 
+
+ align:start position:0%
+because you don't have the brushes
+obviously uh and you have a longer life
+
+ align:start position:0%
+obviously uh and you have a longer life
+ 
+
+ align:start position:0%
+obviously uh and you have a longer life
+power because you don't have brushes
+
+ align:start position:0%
+power because you don't have brushes
+ 
+
+ align:start position:0%
+power because you don't have brushes
+you're not going to have that erosion
+
+ align:start position:0%
+you're not going to have that erosion
+ 
+
+ align:start position:0%
+you're not going to have that erosion
+Factor after 5 or 10 years it's going to
+
+ align:start position:0%
+Factor after 5 or 10 years it's going to
+ 
+
+ align:start position:0%
+Factor after 5 or 10 years it's going to
+limit your engine so you have a much
+
+ align:start position:0%
+limit your engine so you have a much
+ 
+
+ align:start position:0%
+limit your engine so you have a much
+longer lifetime which is another one of
+
+ align:start position:0%
+longer lifetime which is another one of
+ 
+
+ align:start position:0%
+longer lifetime which is another one of
+the downstream goals that we have in the
+
+ align:start position:0%
+the downstream goals that we have in the
+ 
+
+ align:start position:0%
+the downstream goals that we have in the
+general electrical vehicle concept going
+
+ align:start position:0%
+general electrical vehicle concept going
+ 
+
+ align:start position:0%
+general electrical vehicle concept going
+be cheaper lastly um it is much more
+
+ align:start position:0%
+be cheaper lastly um it is much more
+ 
+
+ align:start position:0%
+be cheaper lastly um it is much more
+difficult to control like we just talked
+
+ align:start position:0%
+difficult to control like we just talked
+ 
+
+ align:start position:0%
+difficult to control like we just talked
+about the controller uh with digital
+
+ align:start position:0%
+about the controller uh with digital
+ 
+
+ align:start position:0%
+about the controller uh with digital
+control it's become a little bit easier
+
+ align:start position:0%
+control it's become a little bit easier
+ 
+
+ align:start position:0%
+control it's become a little bit easier
+but because of the way interfaces work
+
+ align:start position:0%
+but because of the way interfaces work
+ 
+
+ align:start position:0%
+but because of the way interfaces work
+with the uh the pulse currents and the
+
+ align:start position:0%
+with the uh the pulse currents and the
+ 
+
+ align:start position:0%
+with the uh the pulse currents and the
+phases it becomes much more difficult to
+
+ align:start position:0%
+phases it becomes much more difficult to
+ 
+
+ align:start position:0%
+phases it becomes much more difficult to
+control and that's a much more uh larg
+
+ align:start position:0%
+control and that's a much more uh larg
+ 
+
+ align:start position:0%
+control and that's a much more uh larg
+investment should you need to design
+
+ align:start position:0%
+investment should you need to design
+ 
+
+ align:start position:0%
+investment should you need to design
+your controller that you have to
+
+ align:start position:0%
+your controller that you have to
+ 
+
+ align:start position:0%
+your controller that you have to
+consider uh for three phase basically
+
+ align:start position:0%
+consider uh for three phase basically
+ 
+
+ align:start position:0%
+consider uh for three phase basically
+that is talking about when you're going
+
+ align:start position:0%
+that is talking about when you're going
+ 
+
+ align:start position:0%
+that is talking about when you're going
+to pulse your currents and how many
+
+ align:start position:0%
+to pulse your currents and how many
+ 
+
+ align:start position:0%
+to pulse your currents and how many
+pulse currents you're going to have at a
+
+ align:start position:0%
+pulse currents you're going to have at a
+ 
+
+ align:start position:0%
+pulse currents you're going to have at a
+minimum you can have two phase because
+
+ align:start position:0%
+minimum you can have two phase because
+ 
+
+ align:start position:0%
+minimum you can have two phase because
+if you only have one phase you're going
+
+ align:start position:0%
+if you only have one phase you're going
+ 
+
+ align:start position:0%
+if you only have one phase you're going
+to turn your you're going to turn your
+
+ align:start position:0%
+to turn your you're going to turn your
+ 
+
+ align:start position:0%
+to turn your you're going to turn your
+magnets and it's going to stop you're
+
+ align:start position:0%
+magnets and it's going to stop you're
+ 
+
+ align:start position:0%
+magnets and it's going to stop you're
+going to have nothing you can do uh two
+
+ align:start position:0%
+going to have nothing you can do uh two
+ 
+
+ align:start position:0%
+going to have nothing you can do uh two
+phase though the problem you into is if
+
+ align:start position:0%
+phase though the problem you into is if
+ 
+
+ align:start position:0%
+phase though the problem you into is if
+you pulse one of the currents and it
+
+ align:start position:0%
+you pulse one of the currents and it
+ 
+
+ align:start position:0%
+you pulse one of the currents and it
+happens to stop in a position where it's
+
+ align:start position:0%
+happens to stop in a position where it's
+ 
+
+ align:start position:0%
+happens to stop in a position where it's
+lined up perfectly with the magnet at 0°
+
+ align:start position:0%
+lined up perfectly with the magnet at 0°
+ 
+
+ align:start position:0%
+lined up perfectly with the magnet at 0°
+when you try to start your engine you're
+
+ align:start position:0%
+when you try to start your engine you're
+ 
+
+ align:start position:0%
+when you try to start your engine you're
+going to have no net uh magnet flux and
+
+ align:start position:0%
+going to have no net uh magnet flux and
+ 
+
+ align:start position:0%
+going to have no net uh magnet flux and
+you're going to have no ability to start
+
+ align:start position:0%
+you're going to have no ability to start
+ 
+
+ align:start position:0%
+you're going to have no ability to start
+your engine so there's very poor
+
+ align:start position:0%
+your engine so there's very poor
+ 
+
+ align:start position:0%
+your engine so there's very poor
+starting condition so three-phase
+
+ align:start position:0%
+starting condition so three-phase
+ 
+
+ align:start position:0%
+starting condition so three-phase
+typically is represented as a minimum
+
+ align:start position:0%
+typically is represented as a minimum
+ 
+
+ align:start position:0%
+typically is represented as a minimum
+for a uh smooth torque uh car having
+
+ align:start position:0%
+for a uh smooth torque uh car having
+ 
+
+ align:start position:0%
+for a uh smooth torque uh car having
+three phases separates the phases by
+
+ align:start position:0%
+three phases separates the phases by
+ 
+
+ align:start position:0%
+three phases separates the phases by
+120° so when you start your engine and
+
+ align:start position:0%
+120° so when you start your engine and
+ 
+
+ align:start position:0%
+120° so when you start your engine and
+the way it puls you're pulsing two at a
+
+ align:start position:0%
+the way it puls you're pulsing two at a
+ 
+
+ align:start position:0%
+the way it puls you're pulsing two at a
+time and one's off and you get a really
+
+ align:start position:0%
+time and one's off and you get a really
+ 
+
+ align:start position:0%
+time and one's off and you get a really
+really smooth torque uh that's really
+
+ align:start position:0%
+really smooth torque uh that's really
+ 
+
+ align:start position:0%
+really smooth torque uh that's really
+good for motor application because you
+
+ align:start position:0%
+good for motor application because you
+ 
+
+ align:start position:0%
+good for motor application because you
+have no torque Ripple which decreases
+
+ align:start position:0%
+have no torque Ripple which decreases
+ 
+
+ align:start position:0%
+have no torque Ripple which decreases
+your structal resonance considerably and
+
+ align:start position:0%
+your structal resonance considerably and
+ 
+
+ align:start position:0%
+your structal resonance considerably and
+you're going to have a lot less
+
+ align:start position:0%
+you're going to have a lot less
+ 
+
+ align:start position:0%
+you're going to have a lot less
+mechanical stress once again increasing
+
+ align:start position:0%
+mechanical stress once again increasing
+ 
+
+ align:start position:0%
+mechanical stress once again increasing
+the reliability and lifetime of the
+
+ align:start position:0%
+the reliability and lifetime of the
+ 
+
+ align:start position:0%
+the reliability and lifetime of the
+engine which is a big deal for us
+
+ align:start position:0%
+engine which is a big deal for us
+ 
+
+ align:start position:0%
+engine which is a big deal for us
+generally when you increase your phases
+
+ align:start position:0%
+generally when you increase your phases
+ 
+
+ align:start position:0%
+generally when you increase your phases
+you're going to increase the utilization
+
+ align:start position:0%
+you're going to increase the utilization
+ 
+
+ align:start position:0%
+you're going to increase the utilization
+of materials you're using in the motor
+
+ align:start position:0%
+of materials you're using in the motor
+ 
+
+ align:start position:0%
+of materials you're using in the motor
+that's a good thing but should you keep
+
+ align:start position:0%
+that's a good thing but should you keep
+ 
+
+ align:start position:0%
+that's a good thing but should you keep
+going for five six phases yeah you're
+
+ align:start position:0%
+going for five six phases yeah you're
+ 
+
+ align:start position:0%
+going for five six phases yeah you're
+going to get better utilization and
+
+ align:start position:0%
+going to get better utilization and
+ 
+
+ align:start position:0%
+going to get better utilization and
+lower percent losses but you're going to
+
+ align:start position:0%
+lower percent losses but you're going to
+ 
+
+ align:start position:0%
+lower percent losses but you're going to
+have a lot more leads a lot more
+
+ align:start position:0%
+have a lot more leads a lot more
+ 
+
+ align:start position:0%
+have a lot more leads a lot more
+transistors it's going to become vastly
+
+ align:start position:0%
+transistors it's going to become vastly
+ 
+
+ align:start position:0%
+transistors it's going to become vastly
+complex the control is going to be a
+
+ align:start position:0%
+complex the control is going to be a
+ 
+
+ align:start position:0%
+complex the control is going to be a
+nightmare and it's going to be much more
+
+ align:start position:0%
+nightmare and it's going to be much more
+ 
+
+ align:start position:0%
+nightmare and it's going to be much more
+expensive so that's why 3phase was
+
+ align:start position:0%
+expensive so that's why 3phase was
+ 
+
+ align:start position:0%
+expensive so that's why 3phase was
+chosen so couple more uh couple more
+
+ align:start position:0%
+chosen so couple more uh couple more
+ 
+
+ align:start position:0%
+chosen so couple more uh couple more
+decisions we need to make about the
+
+ align:start position:0%
+decisions we need to make about the
+ 
+
+ align:start position:0%
+decisions we need to make about the
+motor uh for brushless motors the
+
+ align:start position:0%
+motor uh for brushless motors the
+ 
+
+ align:start position:0%
+motor uh for brushless motors the
+difference between a brushless motor and
+
+ align:start position:0%
+difference between a brushless motor and
+ 
+
+ align:start position:0%
+difference between a brushless motor and
+a brush motor is uh you reverse where
+
+ align:start position:0%
+a brush motor is uh you reverse where
+ 
+
+ align:start position:0%
+a brush motor is uh you reverse where
+the coils and magnets are on a brush
+
+ align:start position:0%
+the coils and magnets are on a brush
+ 
+
+ align:start position:0%
+the coils and magnets are on a brush
+motor the coils are on the the rotor and
+
+ align:start position:0%
+motor the coils are on the the rotor and
+ 
+
+ align:start position:0%
+motor the coils are on the the rotor and
+the as the rotor turns it switches its
+
+ align:start position:0%
+the as the rotor turns it switches its
+ 
+
+ align:start position:0%
+the as the rotor turns it switches its
+own current with the brushes uh
+
+ align:start position:0%
+own current with the brushes uh
+ 
+
+ align:start position:0%
+own current with the brushes uh
+brushless motor is usually so the
+
+ align:start position:0%
+brushless motor is usually so the
+ 
+
+ align:start position:0%
+brushless motor is usually so the
+permanent magnets are on the rotor and
+
+ align:start position:0%
+permanent magnets are on the rotor and
+ 
+
+ align:start position:0%
+permanent magnets are on the rotor and
+the stator has the coils and you just
+
+ align:start position:0%
+the stator has the coils and you just
+ 
+
+ align:start position:0%
+the stator has the coils and you just
+pulse current through transistors and
+
+ align:start position:0%
+pulse current through transistors and
+ 
+
+ align:start position:0%
+pulse current through transistors and
+stuff so um you get basically two
+
+ align:start position:0%
+stuff so um you get basically two
+ 
+
+ align:start position:0%
+stuff so um you get basically two
+configurations that are commonly
+
+ align:start position:0%
+configurations that are commonly
+ 
+
+ align:start position:0%
+configurations that are commonly
+produced you can make a radial gas motor
+
+ align:start position:0%
+produced you can make a radial gas motor
+ 
+
+ align:start position:0%
+produced you can make a radial gas motor
+uh radial flux modities where you have
+
+ align:start position:0%
+uh radial flux modities where you have
+ 
+
+ align:start position:0%
+uh radial flux modities where you have
+the rotor in the middle magnets facing
+
+ align:start position:0%
+the rotor in the middle magnets facing
+ 
+
+ align:start position:0%
+the rotor in the middle magnets facing
+outward and stator coils ranged around
+
+ align:start position:0%
+outward and stator coils ranged around
+ 
+
+ align:start position:0%
+outward and stator coils ranged around
+uh the other the design we chose is an
+
+ align:start position:0%
+uh the other the design we chose is an
+ 
+
+ align:start position:0%
+uh the other the design we chose is an
+actual fluxus motor which is uh
+
+ align:start position:0%
+actual fluxus motor which is uh
+ 
+
+ align:start position:0%
+actual fluxus motor which is uh
+basically two discs next to
+
+ align:start position:0%
+basically two discs next to
+ 
+
+ align:start position:0%
+basically two discs next to
+one with the Perman magnets rotates one
+
+ align:start position:0%
+one with the Perman magnets rotates one
+ 
+
+ align:start position:0%
+one with the Perman magnets rotates one
+the St stay still uh we went with actual
+
+ align:start position:0%
+the St stay still uh we went with actual
+ 
+
+ align:start position:0%
+the St stay still uh we went with actual
+Gap mostly because of spatial problems
+
+ align:start position:0%
+Gap mostly because of spatial problems
+ 
+
+ align:start position:0%
+Gap mostly because of spatial problems
+um if you want to make a radial flux
+
+ align:start position:0%
+um if you want to make a radial flux
+ 
+
+ align:start position:0%
+um if you want to make a radial flux
+Motors uh more powerful you need to
+
+ align:start position:0%
+Motors uh more powerful you need to
+ 
+
+ align:start position:0%
+Motors uh more powerful you need to
+basically extend it lengthwise on the
+
+ align:start position:0%
+basically extend it lengthwise on the
+ 
+
+ align:start position:0%
+basically extend it lengthwise on the
+cylinder to get more surface area
+
+ align:start position:0%
+cylinder to get more surface area
+ 
+
+ align:start position:0%
+cylinder to get more surface area
+between the St and the motor but uh we
+
+ align:start position:0%
+between the St and the motor but uh we
+ 
+
+ align:start position:0%
+between the St and the motor but uh we
+you know we can't go too wide and we
+
+ align:start position:0%
+you know we can't go too wide and we
+ 
+
+ align:start position:0%
+you know we can't go too wide and we
+keep the wheel still in the car so we
+
+ align:start position:0%
+keep the wheel still in the car so we
+ 
+
+ align:start position:0%
+keep the wheel still in the car so we
+went with an actual Gap motor we can
+
+ align:start position:0%
+went with an actual Gap motor we can
+ 
+
+ align:start position:0%
+went with an actual Gap motor we can
+just increase the uh diameter if we want
+
+ align:start position:0%
+just increase the uh diameter if we want
+ 
+
+ align:start position:0%
+just increase the uh diameter if we want
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it'll we increase the surface area that
+
+ align:start position:0%
+it'll we increase the surface area that
+ 
+
+ align:start position:0%
+it'll we increase the surface area that
+way um we're basically going for power
+
+ align:start position:0%
+way um we're basically going for power
+ 
+
+ align:start position:0%
+way um we're basically going for power
+density here so we went with two sters
+
+ align:start position:0%
+density here so we went with two sters
+ 
+
+ align:start position:0%
+density here so we went with two sters
+one the either side of the rotor again
+
+ align:start position:0%
+one the either side of the rotor again
+ 
+
+ align:start position:0%
+one the either side of the rotor again
+we're just we get more surface area
+
+ align:start position:0%
+we're just we get more surface area
+ 
+
+ align:start position:0%
+we're just we get more surface area
+right between the mags and the St um
+
+ align:start position:0%
+right between the mags and the St um
+ 
+
+ align:start position:0%
+right between the mags and the St um
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is setting it up like this is a lot more
+
+ align:start position:0%
+is setting it up like this is a lot more
+ 
+
+ align:start position:0%
+is setting it up like this is a lot more
+efficient lot of Radix Motors that are
+
+ align:start position:0%
+efficient lot of Radix Motors that are
+ 
+
+ align:start position:0%
+efficient lot of Radix Motors that are
+often used for like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+St uh sled Armature so you can build uh
+
+ align:start position:0%
+St uh sled Armature so you can build uh
+ 
+
+ align:start position:0%
+St uh sled Armature so you can build uh
+you can build your stator it basically
+
+ align:start position:0%
+you can build your stator it basically
+ 
+
+ align:start position:0%
+you can build your stator it basically
+just has to be a coil so you can pulse
+
+ align:start position:0%
+just has to be a coil so you can pulse
+ 
+
+ align:start position:0%
+just has to be a coil so you can pulse
+it like an electromagnet but what you
+
+ align:start position:0%
+it like an electromagnet but what you
+ 
+
+ align:start position:0%
+it like an electromagnet but what you
+often do with electr magets is put
+
+ align:start position:0%
+often do with electr magets is put
+ 
+
+ align:start position:0%
+often do with electr magets is put
+something Paris in the middle to get a
+
+ align:start position:0%
+something Paris in the middle to get a
+ 
+
+ align:start position:0%
+something Paris in the middle to get a
+much stronger field right there in the
+
+ align:start position:0%
+much stronger field right there in the
+ 
+
+ align:start position:0%
+much stronger field right there in the
+middle um so rather than just embed
+
+ align:start position:0%
+middle um so rather than just embed
+ 
+
+ align:start position:0%
+middle um so rather than just embed
+coils in epoxy or something uh we we put
+
+ align:start position:0%
+coils in epoxy or something uh we we put
+ 
+
+ align:start position:0%
+coils in epoxy or something uh we we put
+slots uh basically paramagnetic
+
+ align:start position:0%
+slots uh basically paramagnetic
+ 
+
+ align:start position:0%
+slots uh basically paramagnetic
+extensions to the structure through the
+
+ align:start position:0%
+extensions to the structure through the
+ 
+
+ align:start position:0%
+extensions to the structure through the
+through the St cles so what these let
+
+ align:start position:0%
+through the St cles so what these let
+ 
+
+ align:start position:0%
+through the St cles so what these let
+you do is um you can have them go right
+
+ align:start position:0%
+you do is um you can have them go right
+ 
+
+ align:start position:0%
+you do is um you can have them go right
+up to the surface of the per so you have
+
+ align:start position:0%
+up to the surface of the per so you have
+ 
+
+ align:start position:0%
+up to the surface of the per so you have
+a really small air gap for the field you
+
+ align:start position:0%
+a really small air gap for the field you
+ 
+
+ align:start position:0%
+a really small air gap for the field you
+get a lot more power that way and it's
+
+ align:start position:0%
+get a lot more power that way and it's
+ 
+
+ align:start position:0%
+get a lot more power that way and it's
+also much more mechanically
+
+ align:start position:0%
+also much more mechanically
+ 
+
+ align:start position:0%
+also much more mechanically
+uh structurally sound I guess to have uh
+
+ align:start position:0%
+uh structurally sound I guess to have uh
+ 
+
+ align:start position:0%
+uh structurally sound I guess to have uh
+steel basically reinforcing your whole
+
+ align:start position:0%
+steel basically reinforcing your whole
+ 
+
+ align:start position:0%
+steel basically reinforcing your whole
+state structure so uh setting it up with
+
+ align:start position:0%
+state structure so uh setting it up with
+ 
+
+ align:start position:0%
+state structure so uh setting it up with
+a bunch of a bunch of slots uh is
+
+ align:start position:0%
+a bunch of a bunch of slots uh is
+ 
+
+ align:start position:0%
+a bunch of a bunch of slots uh is
+probably going to get us a lot more
+
+ align:start position:0%
+probably going to get us a lot more
+ 
+
+ align:start position:0%
+probably going to get us a lot more
+power it'll uh be a lot stronger the it
+
+ align:start position:0%
+power it'll uh be a lot stronger the it
+ 
+
+ align:start position:0%
+power it'll uh be a lot stronger the it
+does have a couple of disadvantages with
+
+ align:start position:0%
+does have a couple of disadvantages with
+ 
+
+ align:start position:0%
+does have a couple of disadvantages with
+regard to efficiency especially starting
+
+ align:start position:0%
+regard to efficiency especially starting
+ 
+
+ align:start position:0%
+regard to efficiency especially starting
+up you can get a lot of
+
+ align:start position:0%
+up you can get a lot of
+ 
+
+ align:start position:0%
+up you can get a lot of
+which is uh it's not moving fast enough
+
+ align:start position:0%
+which is uh it's not moving fast enough
+ 
+
+ align:start position:0%
+which is uh it's not moving fast enough
+for it to act continuous so it P
+
+ align:start position:0%
+for it to act continuous so it P
+ 
+
+ align:start position:0%
+for it to act continuous so it P
+specific slots and can holds can sort of
+
+ align:start position:0%
+specific slots and can holds can sort of
+ 
+
+ align:start position:0%
+specific slots and can holds can sort of
+stick to one another if not switching
+
+ align:start position:0%
+stick to one another if not switching
+ 
+
+ align:start position:0%
+stick to one another if not switching
+fast enough but besides that uh it's not
+
+ align:start position:0%
+fast enough but besides that uh it's not
+ 
+
+ align:start position:0%
+fast enough but besides that uh it's not
+much of a loss of efficiency and it
+
+ align:start position:0%
+much of a loss of efficiency and it
+ 
+
+ align:start position:0%
+much of a loss of efficiency and it
+gives us a lot more power density which
+
+ align:start position:0%
+gives us a lot more power density which
+ 
+
+ align:start position:0%
+gives us a lot more power density which
+is what we going for and surface amount
+
+ align:start position:0%
+is what we going for and surface amount
+ 
+
+ align:start position:0%
+is what we going for and surface amount
+of permanent BS so just way we machine
+
+ align:start position:0%
+of permanent BS so just way we machine
+ 
+
+ align:start position:0%
+of permanent BS so just way we machine
+try B inside
+
+ align:start position:0%
+try B inside
+ 
+
+ align:start position:0%
+try B inside
+structure given the complexity of the
+
+ align:start position:0%
+structure given the complexity of the
+ 
+
+ align:start position:0%
+structure given the complexity of the
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+uh we decided it was prudent to limit
+
+ align:start position:0%
+uh we decided it was prudent to limit
+ 
+
+ align:start position:0%
+uh we decided it was prudent to limit
+the number of design variables and we
+
+ align:start position:0%
+the number of design variables and we
+ 
+
+ align:start position:0%
+the number of design variables and we
+decided that the number of poles theator
+
+ align:start position:0%
+decided that the number of poles theator
+ 
+
+ align:start position:0%
+decided that the number of poles theator
+slots the magnet span magnet grade
+
+ align:start position:0%
+slots the magnet span magnet grade
+ 
+
+ align:start position:0%
+slots the magnet span magnet grade
+magnet skew the number of coil turns and
+
+ align:start position:0%
+magnet skew the number of coil turns and
+ 
+
+ align:start position:0%
+magnet skew the number of coil turns and
+the air gap the primary focus and with
+
+ align:start position:0%
+the air gap the primary focus and with
+ 
+
+ align:start position:0%
+the air gap the primary focus and with
+those variables it gave us this
+
+ align:start position:0%
+those variables it gave us this
+ 
+
+ align:start position:0%
+those variables it gave us this
+handdrawn preliminary sketch and we
+
+ align:start position:0%
+handdrawn preliminary sketch and we
+ 
+
+ align:start position:0%
+handdrawn preliminary sketch and we
+could obtain a fair idea of what we were
+
+ align:start position:0%
+could obtain a fair idea of what we were
+ 
+
+ align:start position:0%
+could obtain a fair idea of what we were
+a going for um to improve on it we have
+
+ align:start position:0%
+a going for um to improve on it we have
+ 
+
+ align:start position:0%
+a going for um to improve on it we have
+to find we could not use solid
+
+ align:start position:0%
+to find we could not use solid
+ 
+
+ align:start position:0%
+to find we could not use solid
+unfortunately because they only did
+
+ align:start position:0%
+unfortunately because they only did
+ 
+
+ align:start position:0%
+unfortunately because they only did
+mechanic
+
+ align:start position:0%
+mechanic
+ 
+
+ align:start position:0%
+mechanic
+finite element analysis we found that we
+
+ align:start position:0%
+finite element analysis we found that we
+ 
+
+ align:start position:0%
+finite element analysis we found that we
+could use Maxwell 3D um unfortunately
+
+ align:start position:0%
+could use Maxwell 3D um unfortunately
+ 
+
+ align:start position:0%
+could use Maxwell 3D um unfortunately
+Maxwell 3D was a program that's not
+
+ align:start position:0%
+Maxwell 3D was a program that's not
+ 
+
+ align:start position:0%
+Maxwell 3D was a program that's not
+supported directly by MIT Isn and we had
+
+ align:start position:0%
+supported directly by MIT Isn and we had
+ 
+
+ align:start position:0%
+supported directly by MIT Isn and we had
+to contact several of Engineers at Ansa
+
+ align:start position:0%
+to contact several of Engineers at Ansa
+ 
+
+ align:start position:0%
+to contact several of Engineers at Ansa
+and also uh one person here my Tran who
+
+ align:start position:0%
+and also uh one person here my Tran who
+ 
+
+ align:start position:0%
+and also uh one person here my Tran who
+would help us but even then we had many
+
+ align:start position:0%
+would help us but even then we had many
+ 
+
+ align:start position:0%
+would help us but even then we had many
+problems and we could not use it to
+
+ align:start position:0%
+problems and we could not use it to
+ 
+
+ align:start position:0%
+problems and we could not use it to
+fullest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capabilities and here uh when we did use
+
+ align:start position:0%
+capabilities and here uh when we did use
+ 
+
+ align:start position:0%
+capabilities and here uh when we did use
+maxo 3D um we couldn't use its
+
+ align:start position:0%
+maxo 3D um we couldn't use its
+ 
+
+ align:start position:0%
+maxo 3D um we couldn't use its
+optimization software but we could plug
+
+ align:start position:0%
+optimization software but we could plug
+ 
+
+ align:start position:0%
+optimization software but we could plug
+in specific values and given that it
+
+ align:start position:0%
+in specific values and given that it
+ 
+
+ align:start position:0%
+in specific values and given that it
+took about I would say half an hour to
+
+ align:start position:0%
+took about I would say half an hour to
+ 
+
+ align:start position:0%
+took about I would say half an hour to
+run one simulation and that simulation
+
+ align:start position:0%
+run one simulation and that simulation
+ 
+
+ align:start position:0%
+run one simulation and that simulation
+was quite limited to about3 seconds or 6
+
+ align:start position:0%
+was quite limited to about3 seconds or 6
+ 
+
+ align:start position:0%
+was quite limited to about3 seconds or 6
+seconds if we ran into the full this
+
+ align:start position:0%
+seconds if we ran into the full this
+ 
+
+ align:start position:0%
+seconds if we ran into the full this
+limit we can only find that these values
+
+ align:start position:0%
+limit we can only find that these values
+ 
+
+ align:start position:0%
+limit we can only find that these values
+were the optimized values where we have
+
+ align:start position:0%
+were the optimized values where we have
+ 
+
+ align:start position:0%
+were the optimized values where we have
+eight poles 18 slots um the mag grade
+
+ align:start position:0%
+eight poles 18 slots um the mag grade
+ 
+
+ align:start position:0%
+eight poles 18 slots um the mag grade
+here is neodium ironon close span of two
+
+ align:start position:0%
+here is neodium ironon close span of two
+ 
+
+ align:start position:0%
+here is neodium ironon close span of two
+air gap of 1 mm stay offset of 15°
+
+ align:start position:0%
+air gap of 1 mm stay offset of 15°
+ 
+
+ align:start position:0%
+air gap of 1 mm stay offset of 15°
+magnet span of 150° magnet skew of one
+
+ align:start position:0%
+magnet span of 150° magnet skew of one
+ 
+
+ align:start position:0%
+magnet span of 150° magnet skew of one
+pitch one slot pitch and a wi D on 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mm so we're going to talk about the
+
+ align:start position:0%
+mm so we're going to talk about the
+ 
+
+ align:start position:0%
+mm so we're going to talk about the
+design variables just uh briefly and
+
+ align:start position:0%
+design variables just uh briefly and
+ 
+
+ align:start position:0%
+design variables just uh briefly and
+tell you what they mean and what the
+
+ align:start position:0%
+tell you what they mean and what the
+ 
+
+ align:start position:0%
+tell you what they mean and what the
+optimiz values are going to do for our
+
+ align:start position:0%
+optimiz values are going to do for our
+ 
+
+ align:start position:0%
+optimiz values are going to do for our
+engine in the long term for the full
+
+ align:start position:0%
+engine in the long term for the full
+ 
+
+ align:start position:0%
+engine in the long term for the full
+number um typically you increase the
+
+ align:start position:0%
+number um typically you increase the
+ 
+
+ align:start position:0%
+number um typically you increase the
+pole number to get a smooth torque which
+
+ align:start position:0%
+pole number to get a smooth torque which
+ 
+
+ align:start position:0%
+pole number to get a smooth torque which
+we talked about several times one of the
+
+ align:start position:0%
+we talked about several times one of the
+ 
+
+ align:start position:0%
+we talked about several times one of the
+big the big things we're trying to get
+
+ align:start position:0%
+big the big things we're trying to get
+ 
+
+ align:start position:0%
+big the big things we're trying to get
+for an engine you need a smooth torque
+
+ align:start position:0%
+for an engine you need a smooth torque
+ 
+
+ align:start position:0%
+for an engine you need a smooth torque
+to reduce the stresses on the engine and
+
+ align:start position:0%
+to reduce the stresses on the engine and
+ 
+
+ align:start position:0%
+to reduce the stresses on the engine and
+uh that usually implies a large pull
+
+ align:start position:0%
+uh that usually implies a large pull
+ 
+
+ align:start position:0%
+uh that usually implies a large pull
+count by large a typical engines have
+
+ align:start position:0%
+count by large a typical engines have
+ 
+
+ align:start position:0%
+count by large a typical engines have
+two or four folds so eight actually is
+
+ align:start position:0%
+two or four folds so eight actually is
+ 
+
+ align:start position:0%
+two or four folds so eight actually is
+considered somewhat large it's more
+
+ align:start position:0%
+considered somewhat large it's more
+ 
+
+ align:start position:0%
+considered somewhat large it's more
+standard nowadays than it was about 10
+
+ align:start position:0%
+standard nowadays than it was about 10
+ 
+
+ align:start position:0%
+standard nowadays than it was about 10
+years ago but uh if you increase it past
+
+ align:start position:0%
+years ago but uh if you increase it past
+ 
+
+ align:start position:0%
+years ago but uh if you increase it past
+eight it becomes very complex and once
+
+ align:start position:0%
+eight it becomes very complex and once
+ 
+
+ align:start position:0%
+eight it becomes very complex and once
+again the control becomes a nightmare
+
+ align:start position:0%
+again the control becomes a nightmare
+ 
+
+ align:start position:0%
+again the control becomes a nightmare
+what eight FS to do is it decrease the
+
+ align:start position:0%
+what eight FS to do is it decrease the
+ 
+
+ align:start position:0%
+what eight FS to do is it decrease the
+thickness of the root yolk and the ster
+
+ align:start position:0%
+thickness of the root yolk and the ster
+ 
+
+ align:start position:0%
+thickness of the root yolk and the ster
+yolk so it decreases our overall
+
+ align:start position:0%
+yolk so it decreases our overall
+ 
+
+ align:start position:0%
+yolk so it decreases our overall
+diameter which is good for us that's
+
+ align:start position:0%
+diameter which is good for us that's
+ 
+
+ align:start position:0%
+diameter which is good for us that's
+what we're looking for it minimizes the
+
+ align:start position:0%
+what we're looking for it minimizes the
+ 
+
+ align:start position:0%
+what we're looking for it minimizes the
+flux leakage which uh will decrease the
+
+ align:start position:0%
+flux leakage which uh will decrease the
+ 
+
+ align:start position:0%
+flux leakage which uh will decrease the
+overall I mean increase the overall
+
+ align:start position:0%
+overall I mean increase the overall
+ 
+
+ align:start position:0%
+overall I mean increase the overall
+efficiency once again because you have
+
+ align:start position:0%
+efficiency once again because you have
+ 
+
+ align:start position:0%
+efficiency once again because you have
+less uh increase your power than2
+
+ align:start position:0%
+less uh increase your power than2
+ 
+
+ align:start position:0%
+less uh increase your power than2
+because you're not losing as much of the
+
+ align:start position:0%
+because you're not losing as much of the
+ 
+
+ align:start position:0%
+because you're not losing as much of the
+flux and uh thirdly it increases the
+
+ align:start position:0%
+flux and uh thirdly it increases the
+ 
+
+ align:start position:0%
+flux and uh thirdly it increases the
+actual length of the stator and in
+
+ align:start position:0%
+actual length of the stator and in
+ 
+
+ align:start position:0%
+actual length of the stator and in
+windings which once again is related to
+
+ align:start position:0%
+windings which once again is related to
+ 
+
+ align:start position:0%
+windings which once again is related to
+the efficiency of the engine uh we can
+
+ align:start position:0%
+the efficiency of the engine uh we can
+ 
+
+ align:start position:0%
+the efficiency of the engine uh we can
+increase the efficiency by reducing the
+
+ align:start position:0%
+increase the efficiency by reducing the
+ 
+
+ align:start position:0%
+increase the efficiency by reducing the
+veloc for the Stater slots uh there's
+
+ align:start position:0%
+veloc for the Stater slots uh there's
+ 
+
+ align:start position:0%
+veloc for the Stater slots uh there's
+actually a relationship between Stater
+
+ align:start position:0%
+actually a relationship between Stater
+ 
+
+ align:start position:0%
+actually a relationship between Stater
+slots full number and phase um there's
+
+ align:start position:0%
+slots full number and phase um there's
+ 
+
+ align:start position:0%
+slots full number and phase um there's
+certain fractions that you can and
+
+ align:start position:0%
+certain fractions that you can and
+ 
+
+ align:start position:0%
+certain fractions that you can and
+cannot have and what you want be
+
+ align:start position:0%
+cannot have and what you want be
+ 
+
+ align:start position:0%
+cannot have and what you want be
+fractions of the St pull it needs to
+
+ align:start position:0%
+fractions of the St pull it needs to
+ 
+
+ align:start position:0%
+fractions of the St pull it needs to
+round down it has to do with the coil
+
+ align:start position:0%
+round down it has to do with the coil
+ 
+
+ align:start position:0%
+round down it has to do with the coil
+windings um so basically we chose 18 as
+
+ align:start position:0%
+windings um so basically we chose 18 as
+ 
+
+ align:start position:0%
+windings um so basically we chose 18 as
+a maximum that's pull round down to two
+
+ align:start position:0%
+a maximum that's pull round down to two
+ 
+
+ align:start position:0%
+a maximum that's pull round down to two
+and makes it much much more uh easy to
+
+ align:start position:0%
+and makes it much much more uh easy to
+ 
+
+ align:start position:0%
+and makes it much much more uh easy to
+manufacture you can actually manufacture
+
+ align:start position:0%
+manufacture you can actually manufacture
+ 
+
+ align:start position:0%
+manufacture you can actually manufacture
+this on uh on machines that are actually
+
+ align:start position:0%
+this on uh on machines that are actually
+ 
+
+ align:start position:0%
+this on uh on machines that are actually
+offered M for the the winding turns um
+
+ align:start position:0%
+offered M for the the winding turns um
+ 
+
+ align:start position:0%
+offered M for the the winding turns um
+if you have it higher than two the three
+
+ align:start position:0%
+if you have it higher than two the three
+ 
+
+ align:start position:0%
+if you have it higher than two the three
+or four you're going to need some very
+
+ align:start position:0%
+or four you're going to need some very
+ 
+
+ align:start position:0%
+or four you're going to need some very
+expensive uh machines from what I
+
+ align:start position:0%
+expensive uh machines from what I
+ 
+
+ align:start position:0%
+expensive uh machines from what I
+understand let me ask you why didn't you
+
+ align:start position:0%
+understand let me ask you why didn't you
+ 
+
+ align:start position:0%
+understand let me ask you why didn't you
+go to 16 slots which was sort of around
+
+ align:start position:0%
+go to 16 slots which was sort of around
+ 
+
+ align:start position:0%
+go to 16 slots which was sort of around
+you know there's actually a table um
+
+ align:start position:0%
+you know there's actually a table um
+ 
+
+ align:start position:0%
+you know there's actually a table um
+that allows you and 16 / 8 gives you two
+
+ align:start position:0%
+that allows you and 16 / 8 gives you two
+ 
+
+ align:start position:0%
+that allows you and 16 / 8 gives you two
+but you don't want it to be integer
+
+ align:start position:0%
+but you don't want it to be integer
+ 
+
+ align:start position:0%
+but you don't want it to be integer
+because if it's an integer or the way it
+
+ align:start position:0%
+because if it's an integer or the way it
+ 
+
+ align:start position:0%
+because if it's an integer or the way it
+lines up with the phases you can have
+
+ align:start position:0%
+lines up with the phases you can have
+ 
+
+ align:start position:0%
+lines up with the phases you can have
+Cog problems it needs to be a fraction
+
+ align:start position:0%
+Cog problems it needs to be a fraction
+ 
+
+ align:start position:0%
+Cog problems it needs to be a fraction
+you want it to be slightly offset
+
+ align:start position:0%
+you want it to be slightly offset
+ 
+
+ align:start position:0%
+you want it to be slightly offset
+because if it's perfectly round
+
+ align:start position:0%
+because if it's perfectly round
+ 
+
+ align:start position:0%
+because if it's perfectly round
+especially if it's an even number then
+
+ align:start position:0%
+especially if it's an even number then
+ 
+
+ align:start position:0%
+especially if it's an even number then
+you're going to have it line up
+
+ align:start position:0%
+you're going to have it line up
+ 
+
+ align:start position:0%
+you're going to have it line up
+perfectly and then the poles and Staters
+
+ align:start position:0%
+perfectly and then the poles and Staters
+ 
+
+ align:start position:0%
+perfectly and then the poles and Staters
+are going to want to just sit there
+
+ align:start position:0%
+are going to want to just sit there
+ 
+
+ align:start position:0%
+are going to want to just sit there
+because they're going to start like in
+
+ align:start position:0%
+because they're going to start like in
+ 
+
+ align:start position:0%
+because they're going to start like in
+line with each other so to speak you
+
+ align:start position:0%
+line with each other so to speak you
+ 
+
+ align:start position:0%
+line with each other so to speak you
+want to fraction so it be slightly
+
+ align:start position:0%
+want to fraction so it be slightly
+ 
+
+ align:start position:0%
+want to fraction so it be slightly
+opposite that that especially during the
+
+ align:start position:0%
+opposite that that especially during the
+ 
+
+ align:start position:0%
+opposite that that especially during the
+start the thing where you have like if
+
+ align:start position:0%
+start the thing where you have like if
+ 
+
+ align:start position:0%
+start the thing where you have like if
+you have two phases it can get stuck
+
+ align:start position:0%
+you have two phases it can get stuck
+ 
+
+ align:start position:0%
+you have two phases it can get stuck
+right there same thing you don't want
+
+ align:start position:0%
+right there same thing you don't want
+ 
+
+ align:start position:0%
+right there same thing you don't want
+everything to fit just it was actually a
+
+ align:start position:0%
+everything to fit just it was actually a
+ 
+
+ align:start position:0%
+everything to fit just it was actually a
+table so we were you know we were
+
+ align:start position:0%
+table so we were you know we were
+ 
+
+ align:start position:0%
+table so we were you know we were
+limited it was actually good for this
+
+ align:start position:0%
+limited it was actually good for this
+ 
+
+ align:start position:0%
+limited it was actually good for this
+cuz we were limited to so many things we
+
+ align:start position:0%
+cuz we were limited to so many things we
+ 
+
+ align:start position:0%
+cuz we were limited to so many things we
+can pick so we actually run a simulation
+
+ align:start position:0%
+can pick so we actually run a simulation
+ 
+
+ align:start position:0%
+can pick so we actually run a simulation
+it wasn't too much of a nightmare as
+
+ align:start position:0%
+it wasn't too much of a nightmare as
+ 
+
+ align:start position:0%
+it wasn't too much of a nightmare as
+opposed to a design variable where
+
+ align:start position:0%
+opposed to a design variable where
+ 
+
+ align:start position:0%
+opposed to a design variable where
+you're looking over a range you can pick
+
+ align:start position:0%
+you're looking over a range you can pick
+ 
+
+ align:start position:0%
+you're looking over a range you can pick
+a a step size where that was much more
+
+ align:start position:0%
+a a step size where that was much more
+ 
+
+ align:start position:0%
+a a step size where that was much more
+difficult for us op ready to do them by
+
+ align:start position:0%
+difficult for us op ready to do them by
+ 
+
+ align:start position:0%
+difficult for us op ready to do them by
+manual inputs so uh for stair slots once
+
+ align:start position:0%
+manual inputs so uh for stair slots once
+ 
+
+ align:start position:0%
+manual inputs so uh for stair slots once
+again it's related to pH number and the
+
+ align:start position:0%
+again it's related to pH number and the
+ 
+
+ align:start position:0%
+again it's related to pH number and the
+and the cogn uh 18 slots gave the qu 2
+
+ align:start position:0%
+and the cogn uh 18 slots gave the qu 2
+ 
+
+ align:start position:0%
+and the cogn uh 18 slots gave the qu 2
+which is EAS manufacturer it reduced the
+
+ align:start position:0%
+which is EAS manufacturer it reduced the
+ 
+
+ align:start position:0%
+which is EAS manufacturer it reduced the
+cogn which is good because it was a
+
+ align:start position:0%
+cogn which is good because it was a
+ 
+
+ align:start position:0%
+cogn which is good because it was a
+fraction and I reduced the length of
+
+ align:start position:0%
+fraction and I reduced the length of
+ 
+
+ align:start position:0%
+fraction and I reduced the length of
+ning once again so once again it uh
+
+ align:start position:0%
+ning once again so once again it uh
+ 
+
+ align:start position:0%
+ning once again so once again it uh
+lowered the copper losses the third
+
+ align:start position:0%
+lowered the copper losses the third
+ 
+
+ align:start position:0%
+lowered the copper losses the third
+design was air graph length um it was a
+
+ align:start position:0%
+design was air graph length um it was a
+ 
+
+ align:start position:0%
+design was air graph length um it was a
+range so we picked I think three
+
+ align:start position:0%
+range so we picked I think three
+ 
+
+ align:start position:0%
+range so we picked I think three
+different ones uh and we ended up siding
+
+ align:start position:0%
+different ones uh and we ended up siding
+ 
+
+ align:start position:0%
+different ones uh and we ended up siding
+on 1 mm generally speaking increasing
+
+ align:start position:0%
+on 1 mm generally speaking increasing
+ 
+
+ align:start position:0%
+on 1 mm generally speaking increasing
+the air graph uh you're going to have
+
+ align:start position:0%
+the air graph uh you're going to have
+ 
+
+ align:start position:0%
+the air graph uh you're going to have
+more flux losses once again Lower power
+
+ align:start position:0%
+more flux losses once again Lower power
+ 
+
+ align:start position:0%
+more flux losses once again Lower power
+density and less efficiency just because
+
+ align:start position:0%
+density and less efficiency just because
+ 
+
+ align:start position:0%
+density and less efficiency just because
+there's more space for things to you
+
+ align:start position:0%
+there's more space for things to you
+ 
+
+ align:start position:0%
+there's more space for things to you
+lost and to make it too small though
+
+ align:start position:0%
+lost and to make it too small though
+ 
+
+ align:start position:0%
+lost and to make it too small though
+you're not going to have enough room for
+
+ align:start position:0%
+you're not going to have enough room for
+ 
+
+ align:start position:0%
+you're not going to have enough room for
+the torque to develop and you're going
+
+ align:start position:0%
+the torque to develop and you're going
+ 
+
+ align:start position:0%
+the torque to develop and you're going
+to have L
+
+ align:start position:0%
+to have L
+ 
+
+ align:start position:0%
+to have L
+power minute
+
+ align:start position:0%
+power minute
+ 
+
+ align:start position:0%
+power minute
+warning okay so just quickly
+
+ align:start position:0%
+warning okay so just quickly
+ 
+
+ align:start position:0%
+warning okay so just quickly
+other mag grade St offset mag skew the
+
+ align:start position:0%
+other mag grade St offset mag skew the
+ 
+
+ align:start position:0%
+other mag grade St offset mag skew the
+two magnet skew and span are just the
+
+ align:start position:0%
+two magnet skew and span are just the
+ 
+
+ align:start position:0%
+two magnet skew and span are just the
+orientation of the magnet inside the
+
+ align:start position:0%
+orientation of the magnet inside the
+ 
+
+ align:start position:0%
+orientation of the magnet inside the
+rotor and we already mentioned wire
+
+ align:start position:0%
+rotor and we already mentioned wire
+ 
+
+ align:start position:0%
+rotor and we already mentioned wire
+diameter and coil span these all have
+
+ align:start position:0%
+diameter and coil span these all have
+ 
+
+ align:start position:0%
+diameter and coil span these all have
+slight things that they do basically we
+
+ align:start position:0%
+slight things that they do basically we
+ 
+
+ align:start position:0%
+slight things that they do basically we
+just pick three values based on Research
+
+ align:start position:0%
+just pick three values based on Research
+ 
+
+ align:start position:0%
+just pick three values based on Research
+that we did and then inut
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh for the stor slot design you can you
+
+ align:start position:0%
+uh for the stor slot design you can you
+ 
+
+ align:start position:0%
+uh for the stor slot design you can you
+can include these design variables uh
+
+ align:start position:0%
+can include these design variables uh
+ 
+
+ align:start position:0%
+can include these design variables uh
+for us it would have been a nightmare
+
+ align:start position:0%
+for us it would have been a nightmare
+ 
+
+ align:start position:0%
+for us it would have been a nightmare
+because these things have so many
+
+ align:start position:0%
+because these things have so many
+ 
+
+ align:start position:0%
+because these things have so many
+variables just for each St slot we chose
+
+ align:start position:0%
+variables just for each St slot we chose
+ 
+
+ align:start position:0%
+variables just for each St slot we chose
+like we have 18 of these going around
+
+ align:start position:0%
+like we have 18 of these going around
+ 
+
+ align:start position:0%
+like we have 18 of these going around
+because we have slotted Staters uh we
+
+ align:start position:0%
+because we have slotted Staters uh we
+ 
+
+ align:start position:0%
+because we have slotted Staters uh we
+decided to use a predefined Maxell one
+
+ align:start position:0%
+decided to use a predefined Maxell one
+ 
+
+ align:start position:0%
+decided to use a predefined Maxell one
+that matched roughly what we were
+
+ align:start position:0%
+that matched roughly what we were
+ 
+
+ align:start position:0%
+that matched roughly what we were
+looking for in terms of performance and
+
+ align:start position:0%
+looking for in terms of performance and
+ 
+
+ align:start position:0%
+looking for in terms of performance and
+those are the values given the right and
+
+ align:start position:0%
+those are the values given the right and
+ 
+
+ align:start position:0%
+those are the values given the right and
+that's the actual diagram of the stat so
+
+ align:start position:0%
+that's the actual diagram of the stat so
+ 
+
+ align:start position:0%
+that's the actual diagram of the stat so
+that was very convenient the motor
+
+ align:start position:0%
+that was very convenient the motor
+ 
+
+ align:start position:0%
+that was very convenient the motor
+geometry uh typically these are very
+
+ align:start position:0%
+geometry uh typically these are very
+ 
+
+ align:start position:0%
+geometry uh typically these are very
+important design variables uh the outer
+
+ align:start position:0%
+important design variables uh the outer
+ 
+
+ align:start position:0%
+important design variables uh the outer
+we chose based on some measurements we
+
+ align:start position:0%
+we chose based on some measurements we
+ 
+
+ align:start position:0%
+we chose based on some measurements we
+did down at The Hanger uh so then we
+
+ align:start position:0%
+did down at The Hanger uh so then we
+ 
+
+ align:start position:0%
+did down at The Hanger uh so then we
+ended up optimizing what was the ratio
+
+ align:start position:0%
+ended up optimizing what was the ratio
+ 
+
+ align:start position:0%
+ended up optimizing what was the ratio
+between these uh based on different
+
+ align:start position:0%
+between these uh based on different
+ 
+
+ align:start position:0%
+between these uh based on different
+values uh we decided on 252 as the inner
+
+ align:start position:0%
+values uh we decided on 252 as the inner
+ 
+
+ align:start position:0%
+values uh we decided on 252 as the inner
+diameter of the not like the engine
+
+ align:start position:0%
+diameter of the not like the engine
+ 
+
+ align:start position:0%
+diameter of the not like the engine
+where the axle is but the inner diameter
+
+ align:start position:0%
+where the axle is but the inner diameter
+ 
+
+ align:start position:0%
+where the axle is but the inner diameter
+of the rotor and
+
+ align:start position:0%
+of the rotor and
+ 
+
+ align:start position:0%
+of the rotor and
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these okay those are all the other
+
+ align:start position:0%
+so these okay those are all the other
+ 
+
+ align:start position:0%
+so these okay those are all the other
+dimensions so we got an overall
+
+ align:start position:0%
+dimensions so we got an overall
+ 
+
+ align:start position:0%
+dimensions so we got an overall
+thickness of 86 mm
+
+ align:start position:0%
+thickness of 86 mm
+ 
+
+ align:start position:0%
+thickness of 86 mm
+uh performance analysis this is one of
+
+ align:start position:0%
+uh performance analysis this is one of
+ 
+
+ align:start position:0%
+uh performance analysis this is one of
+the images of our motor spinning on maxo
+
+ align:start position:0%
+the images of our motor spinning on maxo
+ 
+
+ align:start position:0%
+the images of our motor spinning on maxo
+which took us a while to figure out how
+
+ align:start position:0%
+which took us a while to figure out how
+ 
+
+ align:start position:0%
+which took us a while to figure out how
+to do that but finally got it to work
+
+ align:start position:0%
+to do that but finally got it to work
+ 
+
+ align:start position:0%
+to do that but finally got it to work
+kept crashing install the wrong
+
+ align:start position:0%
+kept crashing install the wrong
+ 
+
+ align:start position:0%
+kept crashing install the wrong
+operating system and then we just use
+
+ align:start position:0%
+operating system and then we just use
+ 
+
+ align:start position:0%
+operating system and then we just use
+graphs based on each one and pick the
+
+ align:start position:0%
+graphs based on each one and pick the
+ 
+
+ align:start position:0%
+graphs based on each one and pick the
+highest values um with each one as we as
+
+ align:start position:0%
+highest values um with each one as we as
+ 
+
+ align:start position:0%
+highest values um with each one as we as
+we went along can you just U just spend
+
+ align:start position:0%
+we went along can you just U just spend
+ 
+
+ align:start position:0%
+we went along can you just U just spend
+u a little bit of time explaining those
+
+ align:start position:0%
+u a little bit of time explaining those
+ 
+
+ align:start position:0%
+u a little bit of time explaining those
+graphs okay yeah uh so on this graph I
+
+ align:start position:0%
+graphs okay yeah uh so on this graph I
+ 
+
+ align:start position:0%
+graphs okay yeah uh so on this graph I
+think this is the torque graph um as one
+
+ align:start position:0%
+think this is the torque graph um as one
+ 
+
+ align:start position:0%
+think this is the torque graph um as one
+thing to notice is that on both graphs
+
+ align:start position:0%
+thing to notice is that on both graphs
+ 
+
+ align:start position:0%
+thing to notice is that on both graphs
+the time is 600 that's milliseconds so 6
+
+ align:start position:0%
+the time is 600 that's milliseconds so 6
+ 
+
+ align:start position:0%
+the time is 600 that's milliseconds so 6
+seconds is the maximum we can simulate
+
+ align:start position:0%
+seconds is the maximum we can simulate
+ 
+
+ align:start position:0%
+seconds is the maximum we can simulate
+before I ran out of memory uh
+
+ align:start position:0%
+before I ran out of memory uh
+ 
+
+ align:start position:0%
+before I ran out of memory uh
+unfortunately here this part goes back
+
+ align:start position:0%
+unfortunately here this part goes back
+ 
+
+ align:start position:0%
+unfortunately here this part goes back
+to the design of the controller we
+
+ align:start position:0%
+to the design of the controller we
+ 
+
+ align:start position:0%
+to the design of the controller we
+didn't have our team wasn't mandated to
+
+ align:start position:0%
+didn't have our team wasn't mandated to
+ 
+
+ align:start position:0%
+didn't have our team wasn't mandated to
+design the controller that's why our
+
+ align:start position:0%
+design the controller that's why our
+ 
+
+ align:start position:0%
+design the controller that's why our
+torque only went up to think about this
+
+ align:start position:0%
+torque only went up to think about this
+ 
+
+ align:start position:0%
+torque only went up to think about this
+is the8 uh 8 uh newon M and it kind of
+
+ align:start position:0%
+is the8 uh 8 uh newon M and it kind of
+ 
+
+ align:start position:0%
+is the8 uh 8 uh newon M and it kind of
+it levels off because we don't have a
+
+ align:start position:0%
+it levels off because we don't have a
+ 
+
+ align:start position:0%
+it levels off because we don't have a
+proper controller and here the speed is
+
+ align:start position:0%
+proper controller and here the speed is
+ 
+
+ align:start position:0%
+proper controller and here the speed is
+just beginning to accelerate so I mean
+
+ align:start position:0%
+just beginning to accelerate so I mean
+ 
+
+ align:start position:0%
+just beginning to accelerate so I mean
+we only have 6 seconds so we can't
+
+ align:start position:0%
+we only have 6 seconds so we can't
+ 
+
+ align:start position:0%
+we only have 6 seconds so we can't
+really say anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more um okay so as far as actually
+
+ align:start position:0%
+more um okay so as far as actually
+ 
+
+ align:start position:0%
+more um okay so as far as actually
+manufacturing it we didn't actually
+
+ align:start position:0%
+manufacturing it we didn't actually
+ 
+
+ align:start position:0%
+manufacturing it we didn't actually
+manufacture it um mostly because it's
+
+ align:start position:0%
+manufacture it um mostly because it's
+ 
+
+ align:start position:0%
+manufacture it um mostly because it's
+rather expensive and a lot of the stuff
+
+ align:start position:0%
+rather expensive and a lot of the stuff
+ 
+
+ align:start position:0%
+rather expensive and a lot of the stuff
+such as mounting magnets and winding
+
+ align:start position:0%
+such as mounting magnets and winding
+ 
+
+ align:start position:0%
+such as mounting magnets and winding
+coils we emailed some people about coil
+
+ align:start position:0%
+coils we emailed some people about coil
+ 
+
+ align:start position:0%
+coils we emailed some people about coil
+winding they didn't really get back to
+
+ align:start position:0%
+winding they didn't really get back to
+ 
+
+ align:start position:0%
+winding they didn't really get back to
+us one person that said there's very
+
+ align:start position:0%
+us one person that said there's very
+ 
+
+ align:start position:0%
+us one person that said there's very
+little chance we'd be able to actually
+
+ align:start position:0%
+little chance we'd be able to actually
+ 
+
+ align:start position:0%
+little chance we'd be able to actually
+wind something on the road but like of
+
+ align:start position:0%
+wind something on the road but like of
+ 
+
+ align:start position:0%
+wind something on the road but like of
+our own project like this um it's also
+
+ align:start position:0%
+our own project like this um it's also
+ 
+
+ align:start position:0%
+our own project like this um it's also
+pretty expensive to buy all this stuff
+
+ align:start position:0%
+pretty expensive to buy all this stuff
+ 
+
+ align:start position:0%
+pretty expensive to buy all this stuff
+which we go over in a minute but you can
+
+ align:start position:0%
+which we go over in a minute but you can
+ 
+
+ align:start position:0%
+which we go over in a minute but you can
+see see here material choices pretty
+
+ align:start position:0%
+see see here material choices pretty
+ 
+
+ align:start position:0%
+see see here material choices pretty
+simple uh copper for electrical
+
+ align:start position:0%
+simple uh copper for electrical
+ 
+
+ align:start position:0%
+simple uh copper for electrical
+components uh steel for structure poly
+
+ align:start position:0%
+components uh steel for structure poly
+ 
+
+ align:start position:0%
+components uh steel for structure poly
+carb for sort of the safety shell and
+
+ align:start position:0%
+carb for sort of the safety shell and
+ 
+
+ align:start position:0%
+carb for sort of the safety shell and
+doubles as a structure for the St coils
+
+ align:start position:0%
+doubles as a structure for the St coils
+ 
+
+ align:start position:0%
+doubles as a structure for the St coils
+on and uh we use we just bought or would
+
+ align:start position:0%
+on and uh we use we just bought or would
+ 
+
+ align:start position:0%
+on and uh we use we just bought or would
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bought um as far as the simply goes uh
+
+ align:start position:0%
+bought um as far as the simply goes uh
+ 
+
+ align:start position:0%
+bought um as far as the simply goes uh
+we're trying to get a simple design
+
+ align:start position:0%
+we're trying to get a simple design
+ 
+
+ align:start position:0%
+we're trying to get a simple design
+keep it light because it's an electric
+
+ align:start position:0%
+keep it light because it's an electric
+ 
+
+ align:start position:0%
+keep it light because it's an electric
+car um so we basically just have the
+
+ align:start position:0%
+car um so we basically just have the
+ 
+
+ align:start position:0%
+car um so we basically just have the
+rotor disc with the permanent magnets
+
+ align:start position:0%
+rotor disc with the permanent magnets
+ 
+
+ align:start position:0%
+rotor disc with the permanent magnets
+attached to the axle uh the Stater the
+
+ align:start position:0%
+attached to the axle uh the Stater the
+ 
+
+ align:start position:0%
+attached to the axle uh the Stater the
+Stater coils running two rings around
+
+ align:start position:0%
+Stater coils running two rings around
+ 
+
+ align:start position:0%
+Stater coils running two rings around
+the polycarbon safety shell those two
+
+ align:start position:0%
+the polycarbon safety shell those two
+ 
+
+ align:start position:0%
+the polycarbon safety shell those two
+ABS clamp together around the rotor and
+
+ align:start position:0%
+ABS clamp together around the rotor and
+ 
+
+ align:start position:0%
+ABS clamp together around the rotor and
+hold the axle in place and then there's
+
+ align:start position:0%
+hold the axle in place and then there's
+ 
+
+ align:start position:0%
+hold the axle in place and then there's
+sort of Steel arm to go around the
+
+ align:start position:0%
+sort of Steel arm to go around the
+ 
+
+ align:start position:0%
+sort of Steel arm to go around the
+outside and thing together we didn't
+
+ align:start position:0%
+outside and thing together we didn't
+ 
+
+ align:start position:0%
+outside and thing together we didn't
+want to use too much Shel because of
+
+ align:start position:0%
+want to use too much Shel because of
+ 
+
+ align:start position:0%
+want to use too much Shel because of
+magnetic effects you want to use it
+
+ align:start position:0%
+magnetic effects you want to use it
+ 
+
+ align:start position:0%
+magnetic effects you want to use it
+where you need it for structure and get
+
+ align:start position:0%
+where you need it for structure and get
+ 
+
+ align:start position:0%
+where you need it for structure and get
+rid of it everyone else uh so you can't
+
+ align:start position:0%
+rid of it everyone else uh so you can't
+ 
+
+ align:start position:0%
+rid of it everyone else uh so you can't
+read this really all but it's it's
+
+ align:start position:0%
+read this really all but it's it's
+ 
+
+ align:start position:0%
+read this really all but it's it's
+pretty expensive if you count like one
+
+ align:start position:0%
+pretty expensive if you count like one
+ 
+
+ align:start position:0%
+pretty expensive if you count like one
+time design cost and uh paid labor it
+
+ align:start position:0%
+time design cost and uh paid labor it
+ 
+
+ align:start position:0%
+time design cost and uh paid labor it
+comes out to 9300 bucks um which is more
+
+ align:start position:0%
+comes out to 9300 bucks um which is more
+ 
+
+ align:start position:0%
+comes out to 9300 bucks um which is more
+than the NGM one but it also uh we're
+
+ align:start position:0%
+than the NGM one but it also uh we're
+ 
+
+ align:start position:0%
+than the NGM one but it also uh we're
+going eventually for mess production and
+
+ align:start position:0%
+going eventually for mess production and
+ 
+
+ align:start position:0%
+going eventually for mess production and
+uh you know this includes design work
+
+ align:start position:0%
+uh you know this includes design work
+ 
+
+ align:start position:0%
+uh you know this includes design work
+and I just took these from the example
+
+ align:start position:0%
+and I just took these from the example
+ 
+
+ align:start position:0%
+and I just took these from the example
+sheet for like 75 bucks an hour and we
+
+ align:start position:0%
+sheet for like 75 bucks an hour and we
+ 
+
+ align:start position:0%
+sheet for like 75 bucks an hour and we
+spent a lot of time on it so you know uh
+
+ align:start position:0%
+spent a lot of time on it so you know uh
+ 
+
+ align:start position:0%
+spent a lot of time on it so you know uh
+without that and if you were to look at
+
+ align:start position:0%
+without that and if you were to look at
+ 
+
+ align:start position:0%
+without that and if you were to look at
+the economies of scale all a whole lot
+
+ align:start position:0%
+the economies of scale all a whole lot
+ 
+
+ align:start position:0%
+the economies of scale all a whole lot
+of these I think it be far cheaper
+
+ align:start position:0%
+of these I think it be far cheaper
+ 
+
+ align:start position:0%
+of these I think it be far cheaper
+than as
+
+ align:start position:0%
+than as
+ 
+
+ align:start position:0%
+than as
+as finally for uh for future work uh we
+
+ align:start position:0%
+as finally for uh for future work uh we
+ 
+
+ align:start position:0%
+as finally for uh for future work uh we
+definitely need to continue analyze this
+
+ align:start position:0%
+definitely need to continue analyze this
+ 
+
+ align:start position:0%
+definitely need to continue analyze this
+motor uh we need to do better more
+
+ align:start position:0%
+motor uh we need to do better more
+ 
+
+ align:start position:0%
+motor uh we need to do better more
+extensive more than6 uh seconds of
+
+ align:start position:0%
+extensive more than6 uh seconds of
+ 
+
+ align:start position:0%
+extensive more than6 uh seconds of
+analysis on the FDA or else we can't
+
+ align:start position:0%
+analysis on the FDA or else we can't
+ 
+
+ align:start position:0%
+analysis on the FDA or else we can't
+know how the motor will respond at a
+
+ align:start position:0%
+know how the motor will respond at a
+ 
+
+ align:start position:0%
+know how the motor will respond at a
+full speed or at any speed I me 6
+
+ align:start position:0%
+full speed or at any speed I me 6
+ 
+
+ align:start position:0%
+full speed or at any speed I me 6
+seconds just for a startup that's not
+
+ align:start position:0%
+seconds just for a startup that's not
+ 
+
+ align:start position:0%
+seconds just for a startup that's not
+enough um and then another big point is
+
+ align:start position:0%
+enough um and then another big point is
+ 
+
+ align:start position:0%
+enough um and then another big point is
+motor controller uh the our original
+
+ align:start position:0%
+motor controller uh the our original
+ 
+
+ align:start position:0%
+motor controller uh the our original
+requirement to use the EVC 200 that's
+
+ align:start position:0%
+requirement to use the EVC 200 that's
+ 
+
+ align:start position:0%
+requirement to use the EVC 200 that's
+the NGM one that was not that's not
+
+ align:start position:0%
+the NGM one that was not that's not
+ 
+
+ align:start position:0%
+the NGM one that was not that's not
+sufficient we need to design our own and
+
+ align:start position:0%
+sufficient we need to design our own and
+ 
+
+ align:start position:0%
+sufficient we need to design our own and
+that is a completely new project finally
+
+ align:start position:0%
+that is a completely new project finally
+ 
+
+ align:start position:0%
+that is a completely new project finally
+uh we we're looking for continuing
+
+ align:start position:0%
+uh we we're looking for continuing
+ 
+
+ align:start position:0%
+uh we we're looking for continuing
+reduction cost um although there are
+
+ align:start position:0%
+reduction cost um although there are
+ 
+
+ align:start position:0%
+reduction cost um although there are
+economies of scale I'm sure there are
+
+ align:start position:0%
+economies of scale I'm sure there are
+ 
+
+ align:start position:0%
+economies of scale I'm sure there are
+other suppliers and manufacturers that
+
+ align:start position:0%
+other suppliers and manufacturers that
+ 
+
+ align:start position:0%
+other suppliers and manufacturers that
+we look
+
+ align:start position:0%
+we look
+ 
+
+ align:start position:0%
+we look
+toward finally Lessons Learned uh get
+
+ align:start position:0%
+toward finally Lessons Learned uh get
+ 
+
+ align:start position:0%
+toward finally Lessons Learned uh get
+expert advice from the start we're smart
+
+ align:start position:0%
+expert advice from the start we're smart
+ 
+
+ align:start position:0%
+expert advice from the start we're smart
+MIT students but even us looking through
+
+ align:start position:0%
+MIT students but even us looking through
+ 
+
+ align:start position:0%
+MIT students but even us looking through
+the internet looking through books we
+
+ align:start position:0%
+the internet looking through books we
+ 
+
+ align:start position:0%
+the internet looking through books we
+should have known to ask experts from
+
+ align:start position:0%
+should have known to ask experts from
+ 
+
+ align:start position:0%
+should have known to ask experts from
+the start to obtain the rules of thumb
+
+ align:start position:0%
+the start to obtain the rules of thumb
+ 
+
+ align:start position:0%
+the start to obtain the rules of thumb
+to guide us um get proper simulation
+
+ align:start position:0%
+to guide us um get proper simulation
+ 
+
+ align:start position:0%
+to guide us um get proper simulation
+software Maxwell 3D we did not find that
+
+ align:start position:0%
+software Maxwell 3D we did not find that
+ 
+
+ align:start position:0%
+software Maxwell 3D we did not find that
+until the second at least the second
+
+ align:start position:0%
+until the second at least the second
+ 
+
+ align:start position:0%
+until the second at least the second
+week and even then we had many many
+
+ align:start position:0%
+week and even then we had many many
+ 
+
+ align:start position:0%
+week and even then we had many many
+problems um constrain we we constrained
+
+ align:start position:0%
+problems um constrain we we constrained
+ 
+
+ align:start position:0%
+problems um constrain we we constrained
+our variables but we had to constrain
+
+ align:start position:0%
+our variables but we had to constrain
+ 
+
+ align:start position:0%
+our variables but we had to constrain
+even further for this class um and
+
+ align:start position:0%
+even further for this class um and
+ 
+
+ align:start position:0%
+even further for this class um and
+finally we simply needed some more time
+
+ align:start position:0%
+finally we simply needed some more time
+ 
+
+ align:start position:0%
+finally we simply needed some more time
+to further flush out our design and make
+
+ align:start position:0%
+to further flush out our design and make
+ 
+
+ align:start position:0%
+to further flush out our design and make
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+viable thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody I I had a quick one I mean you
+
+ align:start position:0%
+anybody I I had a quick one I mean you
+ 
+
+ align:start position:0%
+anybody I I had a quick one I mean you
+guys this was kind of an impossible
+
+ align:start position:0%
+guys this was kind of an impossible
+ 
+
+ align:start position:0%
+guys this was kind of an impossible
+project for for a 4-we i class and I I
+
+ align:start position:0%
+project for for a 4-we i class and I I
+ 
+
+ align:start position:0%
+project for for a 4-we i class and I I
+think I think you've admire your courage
+
+ align:start position:0%
+think I think you've admire your courage
+ 
+
+ align:start position:0%
+think I think you've admire your courage
+and how far you pushed it I'm pleased
+
+ align:start position:0%
+and how far you pushed it I'm pleased
+ 
+
+ align:start position:0%
+and how far you pushed it I'm pleased
+with that the one question I have
+
+ align:start position:0%
+with that the one question I have
+ 
+
+ align:start position:0%
+with that the one question I have
+kind of surpr interesting that your cost
+
+ align:start position:0%
+kind of surpr interesting that your cost
+ 
+
+ align:start position:0%
+kind of surpr interesting that your cost
+estimate comes out almost the same as
+
+ align:start position:0%
+estimate comes out almost the same as
+ 
+
+ align:start position:0%
+estimate comes out almost the same as
+the NM motor uh the question I had was
+
+ align:start position:0%
+the NM motor uh the question I had was
+ 
+
+ align:start position:0%
+the NM motor uh the question I had was
+the NGM motor motor is a radial flux
+
+ align:start position:0%
+the NGM motor motor is a radial flux
+ 
+
+ align:start position:0%
+the NGM motor motor is a radial flux
+motor so so you said that you have to
+
+ align:start position:0%
+motor so so you said that you have to
+ 
+
+ align:start position:0%
+motor so so you said that you have to
+put these constraints in pretty quickly
+
+ align:start position:0%
+put these constraints in pretty quickly
+ 
+
+ align:start position:0%
+put these constraints in pretty quickly
+so that you could you know start getting
+
+ align:start position:0%
+so that you could you know start getting
+ 
+
+ align:start position:0%
+so that you could you know start getting
+a design uh but but it seems to me that
+
+ align:start position:0%
+a design uh but but it seems to me that
+ 
+
+ align:start position:0%
+a design uh but but it seems to me that
+the there's two things um that would
+
+ align:start position:0%
+the there's two things um that would
+ 
+
+ align:start position:0%
+the there's two things um that would
+have to be
+
+ align:start position:0%
+have to be
+ 
+
+ align:start position:0%
+have to be
+before you sort of go and fles this out
+
+ align:start position:0%
+before you sort of go and fles this out
+ 
+
+ align:start position:0%
+before you sort of go and fles this out
+in more detail one of them is the
+
+ align:start position:0%
+in more detail one of them is the
+ 
+
+ align:start position:0%
+in more detail one of them is the
+question of is actually a hub motor the
+
+ align:start position:0%
+question of is actually a hub motor the
+ 
+
+ align:start position:0%
+question of is actually a hub motor the
+right way to go for this vehicle or
+
+ align:start position:0%
+right way to go for this vehicle or
+ 
+
+ align:start position:0%
+right way to go for this vehicle or
+couldn't you have a motor sitting in the
+
+ align:start position:0%
+couldn't you have a motor sitting in the
+ 
+
+ align:start position:0%
+couldn't you have a motor sitting in the
+back of a seat with a little drive you
+
+ align:start position:0%
+back of a seat with a little drive you
+ 
+
+ align:start position:0%
+back of a seat with a little drive you
+know a simplified
+
+ align:start position:0%
+know a simplified
+ 
+
+ align:start position:0%
+know a simplified
+drive so that's that's one I just wanted
+
+ align:start position:0%
+drive so that's that's one I just wanted
+ 
+
+ align:start position:0%
+drive so that's that's one I just wanted
+you to respond to that and the second
+
+ align:start position:0%
+you to respond to that and the second
+ 
+
+ align:start position:0%
+you to respond to that and the second
+one was even if you did go with a hub
+
+ align:start position:0%
+one was even if you did go with a hub
+ 
+
+ align:start position:0%
+one was even if you did go with a hub
+motor uh if you allowed for a wider
+
+ align:start position:0%
+motor uh if you allowed for a wider
+ 
+
+ align:start position:0%
+motor uh if you allowed for a wider
+wheel you know the wheel the wheel trade
+
+ align:start position:0%
+wheel you know the wheel the wheel trade
+ 
+
+ align:start position:0%
+wheel you know the wheel the wheel trade
+off I mean um narrow Wheels give you
+
+ align:start position:0%
+off I mean um narrow Wheels give you
+ 
+
+ align:start position:0%
+off I mean um narrow Wheels give you
+good uh low rolling resistance and good
+
+ align:start position:0%
+good uh low rolling resistance and good
+ 
+
+ align:start position:0%
+good uh low rolling resistance and good
+efficiency of the vehicle uh but if you
+
+ align:start position:0%
+efficiency of the vehicle uh but if you
+ 
+
+ align:start position:0%
+efficiency of the vehicle uh but if you
+say well instead of the 86 mm how about
+
+ align:start position:0%
+say well instead of the 86 mm how about
+ 
+
+ align:start position:0%
+say well instead of the 86 mm how about
+120 mm wheel uh would that make the
+
+ align:start position:0%
+120 mm wheel uh would that make the
+ 
+
+ align:start position:0%
+120 mm wheel uh would that make the
+motor design much easier to
+
+ align:start position:0%
+motor design much easier to
+ 
+
+ align:start position:0%
+motor design much easier to
+do so the first one is on up motor yes
+
+ align:start position:0%
+do so the first one is on up motor yes
+ 
+
+ align:start position:0%
+do so the first one is on up motor yes
+or no and the second one is on wheel for
+
+ align:start position:0%
+or no and the second one is on wheel for
+ 
+
+ align:start position:0%
+or no and the second one is on wheel for
+the 1.0 see it's kind of strange cuz our
+
+ align:start position:0%
+the 1.0 see it's kind of strange cuz our
+ 
+
+ align:start position:0%
+the 1.0 see it's kind of strange cuz our
+our our we start out we have the same
+
+ align:start position:0%
+our our we start out we have the same
+ 
+
+ align:start position:0%
+our our we start out we have the same
+we're posted on motor for the 1.0 but
+
+ align:start position:0%
+we're posted on motor for the 1.0 but
+ 
+
+ align:start position:0%
+we're posted on motor for the 1.0 but
+it's supposed to be a stepping stone the
+
+ align:start position:0%
+it's supposed to be a stepping stone the
+ 
+
+ align:start position:0%
+it's supposed to be a stepping stone the
+2.0 the problem is a 1.0 and a 2.0 are
+
+ align:start position:0%
+2.0 the problem is a 1.0 and a 2.0 are
+ 
+
+ align:start position:0%
+2.0 the problem is a 1.0 and a 2.0 are
+completely different machines you know a
+
+ align:start position:0%
+completely different machines you know a
+ 
+
+ align:start position:0%
+completely different machines you know a
+1.0 machine is thr one press into a
+
+ align:start position:0%
+1.0 machine is thr one press into a
+ 
+
+ align:start position:0%
+1.0 machine is thr one press into a
+three wheel car where the Hub meter I
+
+ align:start position:0%
+three wheel car where the Hub meter I
+ 
+
+ align:start position:0%
+three wheel car where the Hub meter I
+don't know maybe it was more viable
+
+ align:start position:0%
+don't know maybe it was more viable
+ 
+
+ align:start position:0%
+don't know maybe it was more viable
+because of the spatial Dimensions but
+
+ align:start position:0%
+because of the spatial Dimensions but
+ 
+
+ align:start position:0%
+because of the spatial Dimensions but
+from the 2.0 that they're talking about
+
+ align:start position:0%
+from the 2.0 that they're talking about
+ 
+
+ align:start position:0%
+from the 2.0 that they're talking about
+a five person car with four wheels so
+
+ align:start position:0%
+a five person car with four wheels so
+ 
+
+ align:start position:0%
+a five person car with four wheels so
+then in that case for sure you might
+
+ align:start position:0%
+then in that case for sure you might
+ 
+
+ align:start position:0%
+then in that case for sure you might
+want to shy away from using the H motor
+
+ align:start position:0%
+want to shy away from using the H motor
+ 
+
+ align:start position:0%
+want to shy away from using the H motor
+because you get lost
+
+ align:start position:0%
+because you get lost
+ 
+
+ align:start position:0%
+because you get lost
+draw uh actually that's exactly say
+
+ align:start position:0%
+draw uh actually that's exactly say
+ 
+
+ align:start position:0%
+draw uh actually that's exactly say
+we're sort of done a weird match between
+
+ align:start position:0%
+we're sort of done a weird match between
+ 
+
+ align:start position:0%
+we're sort of done a weird match between
+like they want it to be able to fit in
+
+ align:start position:0%
+like they want it to be able to fit in
+ 
+
+ align:start position:0%
+like they want it to be able to fit in
+the one but a lot of design requirements
+
+ align:start position:0%
+the one but a lot of design requirements
+ 
+
+ align:start position:0%
+the one but a lot of design requirements
+are coming from the 2.0 what the 2.0
+
+ align:start position:0%
+are coming from the 2.0 what the 2.0
+ 
+
+ align:start position:0%
+are coming from the 2.0 what the 2.0
+design looks like right now so it was
+
+ align:start position:0%
+design looks like right now so it was
+ 
+
+ align:start position:0%
+design looks like right now so it was
+sort of like well yes we're going to use
+
+ align:start position:0%
+sort of like well yes we're going to use
+ 
+
+ align:start position:0%
+sort of like well yes we're going to use
+Hubers that's fixed I don't know whether
+
+ align:start position:0%
+Hubers that's fixed I don't know whether
+ 
+
+ align:start position:0%
+Hubers that's fixed I don't know whether
+or not they're they'd be better off not
+
+ align:start position:0%
+or not they're they'd be better off not
+ 
+
+ align:start position:0%
+or not they're they'd be better off not
+doing hubs Central dve TR I think a lot
+
+ align:start position:0%
+doing hubs Central dve TR I think a lot
+ 
+
+ align:start position:0%
+doing hubs Central dve TR I think a lot
+of modern electric vehicles uh are are
+
+ align:start position:0%
+of modern electric vehicles uh are are
+ 
+
+ align:start position:0%
+of modern electric vehicles uh are are
+switching to H MERS like the Tesla
+
+ align:start position:0%
+switching to H MERS like the Tesla
+ 
+
+ align:start position:0%
+switching to H MERS like the Tesla
+rooster there's a there's a little BM or
+
+ align:start position:0%
+rooster there's a there's a little BM or
+ 
+
+ align:start position:0%
+rooster there's a there's a little BM or
+not a Mini Cooper like 640 horsepower
+
+ align:start position:0%
+not a Mini Cooper like 640 horsepower
+ 
+
+ align:start position:0%
+not a Mini Cooper like 640 horsepower
+just upad
+
+ align:start position:0%
+just upad
+ 
+
+ align:start position:0%
+just upad
+main advantage of a hub motor is that
+
+ align:start position:0%
+main advantage of a hub motor is that
+ 
+
+ align:start position:0%
+main advantage of a hub motor is that
+there's no losses to gear I mean you're
+
+ align:start position:0%
+there's no losses to gear I mean you're
+ 
+
+ align:start position:0%
+there's no losses to gear I mean you're
+the motor is direct the motor is
+
+ align:start position:0%
+the motor is direct the motor is
+ 
+
+ align:start position:0%
+the motor is direct the motor is
+directly on the wheel it's actuating the
+
+ align:start position:0%
+directly on the wheel it's actuating the
+ 
+
+ align:start position:0%
+directly on the wheel it's actuating the
+wheel itself so you don't have gears to
+
+ align:start position:0%
+wheel itself so you don't have gears to
+ 
+
+ align:start position:0%
+wheel itself so you don't have gears to
+transmit U through a
+
+ align:start position:0%
+transmit U through a
+ 
+
+ align:start position:0%
+transmit U through a
+little B of the shaft where you can have
+
+ align:start position:0%
+little B of the shaft where you can have
+ 
+
+ align:start position:0%
+little B of the shaft where you can have
+glosses in you can you can actually
+
+ align:start position:0%
+glosses in you can you can actually
+ 
+
+ align:start position:0%
+glosses in you can you can actually
+entirely you can move your control
+
+ align:start position:0%
+entirely you can move your control
+ 
+
+ align:start position:0%
+entirely you can move your control
+system from half like you know moving
+
+ align:start position:0%
+system from half like you know moving
+ 
+
+ align:start position:0%
+system from half like you know moving
+levers around and have digital to being
+
+ align:start position:0%
+levers around and have digital to being
+ 
+
+ align:start position:0%
+levers around and have digital to being
+entirely digital just driving just
+
+ align:start position:0%
+entirely digital just driving just
+ 
+
+ align:start position:0%
+entirely digital just driving just
+driving the motors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we trying the VS1 wheel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay thank you very much
\ No newline at end of file
diff --git a/LoIXB2GJHkg.txt b/LoIXB2GJHkg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f357fa4acd076336401610989b5c2f992f1a648d
--- /dev/null
+++ b/LoIXB2GJHkg.txt
@@ -0,0 +1,12872 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu good so let us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start so so let me first quickly remind
+
+ align:start position:0%
+start so so let me first quickly remind
+ 
+
+ align:start position:0%
+start so so let me first quickly remind
+you what we did in the last
+
+ align:start position:0%
+you what we did in the last
+ 
+
+ align:start position:0%
+you what we did in the last
+lecture so we first talk about
+
+ align:start position:0%
+lecture so we first talk about
+ 
+
+ align:start position:0%
+lecture so we first talk about
+the say talk about General
+
+ align:start position:0%
+the say talk about General
+ 
+
+ align:start position:0%
+the say talk about General
+observables in Gage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Series so we are interested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in say correlation functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of gauging wiring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators in particular we will be uh uh
+
+ align:start position:0%
+operators in particular we will be uh uh
+ 
+
+ align:start position:0%
+operators in particular we will be uh uh
+focus on local
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+Lo so we um say for
+
+ align:start position:0%
+Lo so we um say for
+ 
+
+ align:start position:0%
+Lo so we um say for
+example so the local operator can be
+
+ align:start position:0%
+example so the local operator can be
+ 
+
+ align:start position:0%
+example so the local operator can be
+also be separated into say the single
+
+ align:start position:0%
+also be separated into say the single
+ 
+
+ align:start position:0%
+also be separated into say the single
+Chace operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh or the yeah single Choice operator so
+
+ align:start position:0%
+uh or the yeah single Choice operator so
+ 
+
+ align:start position:0%
+uh or the yeah single Choice operator so
+n just label different operators or say
+
+ align:start position:0%
+n just label different operators or say
+ 
+
+ align:start position:0%
+n just label different operators or say
+the the double Trace operator sometimes
+
+ align:start position:0%
+the the double Trace operator sometimes
+ 
+
+ align:start position:0%
+the the double Trace operator sometimes
+in order to avoid
+
+ align:start position:0%
+in order to avoid
+ 
+
+ align:start position:0%
+in order to avoid
+confusion we put some dots that means
+
+ align:start position:0%
+confusion we put some dots that means
+ 
+
+ align:start position:0%
+confusion we put some dots that means
+these two operator should be considered
+
+ align:start position:0%
+these two operator should be considered
+ 
+
+ align:start position:0%
+these two operator should be considered
+group together and then you Val then
+
+ align:start position:0%
+group together and then you Val then
+ 
+
+ align:start position:0%
+group together and then you Val then
+evaluate some SpaceTime Point say this
+
+ align:start position:0%
+evaluate some SpaceTime Point say this
+ 
+
+ align:start position:0%
+evaluate some SpaceTime Point say this
+would be a double Choice operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh or maybe the higher ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh also we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found that typical correlation function
+
+ align:start position:0%
+found that typical correlation function
+ 
+
+ align:start position:0%
+found that typical correlation function
+say if I look at endpoint
+
+ align:start position:0%
+say if I look at endpoint
+ 
+
+ align:start position:0%
+say if I look at endpoint
+function endpoint connective green
+
+ align:start position:0%
+function endpoint connective green
+ 
+
+ align:start position:0%
+function endpoint connective green
+function of single Chace
+
+ align:start position:0%
+function of single Chace
+ 
+
+ align:start position:0%
+function of single Chace
+operators then
+
+ align:start position:0%
+operators then
+ 
+
+ align:start position:0%
+operators then
+the scale with n as the
+
+ align:start position:0%
+the scale with n as the
+ 
+
+ align:start position:0%
+the scale with n as the
+following again you sum over order H
+
+ align:start position:0%
+following again you sum over order H
+ 
+
+ align:start position:0%
+following again you sum over order H
+which is a topology of your
+
+ align:start position:0%
+which is a topology of your
+ 
+
+ align:start position:0%
+which is a topology of your
+diagrams and then to the power n to the
+
+ align:start position:0%
+diagrams and then to the power n to the
+ 
+
+ align:start position:0%
+diagrams and then to the power n to the
+minus n n is the number of the the
+
+ align:start position:0%
+minus n n is the number of the the
+ 
+
+ align:start position:0%
+minus n n is the number of the the
+endpoint functions the minus 2 H then
+
+ align:start position:0%
+endpoint functions the minus 2 H then
+ 
+
+ align:start position:0%
+endpoint functions the minus 2 H then
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+some some function FN which can depend
+
+ align:start position:0%
+some some function FN which can depend
+ 
+
+ align:start position:0%
+some some function FN which can depend
+on the coing constant and also will
+
+ align:start position:0%
+on the coing constant and also will
+ 
+
+ align:start position:0%
+on the coing constant and also will
+depend on X1 X2 xn Etc okay so so this
+
+ align:start position:0%
+depend on X1 X2 xn Etc okay so so this
+ 
+
+ align:start position:0%
+depend on X1 X2 xn Etc okay so so this
+will start as leading
+
+ align:start position:0%
+will start as leading
+ 
+
+ align:start position:0%
+will start as leading
+order which n 2us n which come from the
+
+ align:start position:0%
+order which n 2us n which come from the
+ 
+
+ align:start position:0%
+order which n 2us n which come from the
+planer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram and then the next order just n
+
+ align:start position:0%
+diagram and then the next order just n
+ 
+
+ align:start position:0%
+diagram and then the next order just n
+to the minus n so this will be the
+
+ align:start position:0%
+to the minus n so this will be the
+ 
+
+ align:start position:0%
+to the minus n so this will be the
+Taurus
+
+ align:start position:0%
+Taurus
+ 
+
+ align:start position:0%
+Taurus
+diagram the diagram you can put on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Taurus or genus two diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ex so we also discuss
+
+ align:start position:0%
+ex so we also discuss
+ 
+
+ align:start position:0%
+ex so we also discuss
+that this Behavior has important
+
+ align:start position:0%
+that this Behavior has important
+ 
+
+ align:start position:0%
+that this Behavior has important
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+implications we talked about two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implications we talk about two
+
+ align:start position:0%
+implications we talk about two
+ 
+
+ align:start position:0%
+implications we talk about two
+implications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you say that kind of
+
+ align:start position:0%
+you say that kind of
+ 
+
+ align:start position:0%
+you say that kind of
+Independence means that in the L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit say in the angle to Infinity
+
+ align:start position:0%
+limit say in the angle to Infinity
+ 
+
+ align:start position:0%
+limit say in the angle to Infinity
+limit we can essentially
+
+ align:start position:0%
+limit we can essentially
+ 
+
+ align:start position:0%
+limit we can essentially
+treat the action of the single particle
+
+ align:start position:0%
+treat the action of the single particle
+ 
+
+ align:start position:0%
+treat the action of the single particle
+a single Choice operator say on the
+
+ align:start position:0%
+a single Choice operator say on the
+ 
+
+ align:start position:0%
+a single Choice operator say on the
+vacuum as a sing as generating a single
+
+ align:start position:0%
+vacuum as a sing as generating a single
+ 
+
+ align:start position:0%
+vacuum as a sing as generating a single
+particle state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say uh we often call this as Global
+
+ align:start position:0%
+say uh we often call this as Global
+ 
+
+ align:start position:0%
+say uh we often call this as Global
+State glose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this single particle
+
+ align:start position:0%
+okay so this single particle
+ 
+
+ align:start position:0%
+okay so this single particle
+State they don't have to appear really
+
+ align:start position:0%
+State they don't have to appear really
+ 
+
+ align:start position:0%
+State they don't have to appear really
+as say asymptotic
+
+ align:start position:0%
+as say asymptotic
+ 
+
+ align:start position:0%
+as say asymptotic
+States uh in your scattering ex I just
+
+ align:start position:0%
+States uh in your scattering ex I just
+ 
+
+ align:start position:0%
+States uh in your scattering ex I just
+say the behavior of such States behave
+
+ align:start position:0%
+say the behavior of such States behave
+ 
+
+ align:start position:0%
+say the behavior of such States behave
+like single particles and then if you
+
+ align:start position:0%
+like single particles and then if you
+ 
+
+ align:start position:0%
+like single particles and then if you
+act on the double Chace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator on the
+
+ align:start position:0%
+operator on the
+ 
+
+ align:start position:0%
+operator on the
+Zero then that give you the the two
+
+ align:start position:0%
+Zero then that give you the the two
+ 
+
+ align:start position:0%
+Zero then that give you the the two
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States and ex and the three and the
+
+ align:start position:0%
+States and ex and the three and the
+ 
+
+ align:start position:0%
+States and ex and the three and the
+triple chice or give you the three
+
+ align:start position:0%
+triple chice or give you the three
+ 
+
+ align:start position:0%
+triple chice or give you the three
+particle State
+
+ align:start position:0%
+particle State
+ 
+
+ align:start position:0%
+particle State
+ex
+
+ align:start position:0%
+ex
+ 
+
+ align:start position:0%
+ex
+okay so so this is one
+
+ align:start position:0%
+okay so so this is one
+ 
+
+ align:start position:0%
+okay so so this is one
+aspect and the and the second aspect
+
+ align:start position:0%
+aspect and the and the second aspect
+ 
+
+ align:start position:0%
+aspect and the and the second aspect
+is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if say if there's some single Choice
+
+ align:start position:0%
+if say if there's some single Choice
+ 
+
+ align:start position:0%
+if say if there's some single Choice
+operator whose expectation value is non
+
+ align:start position:0%
+operator whose expectation value is non
+ 
+
+ align:start position:0%
+operator whose expectation value is non
+zero then the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluctuation are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppressed okay so for example if you
+
+ align:start position:0%
+suppressed okay so for example if you
+ 
+
+ align:start position:0%
+suppressed okay so for example if you
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ratio if you look at the ratio of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance so o Square the connected part
+
+ align:start position:0%
+variance so o Square the connected part
+ 
+
+ align:start position:0%
+variance so o Square the connected part
+of the O square is essentially the
+
+ align:start position:0%
+of the O square is essentially the
+ 
+
+ align:start position:0%
+of the O square is essentially the
+variance of the of this guy and divided
+
+ align:start position:0%
+variance of the of this guy and divided
+ 
+
+ align:start position:0%
+variance of the of this guy and divided
+by expectation value itself then scale
+
+ align:start position:0%
+by expectation value itself then scale
+ 
+
+ align:start position:0%
+by expectation value itself then scale
+is one one/ M because of that behavior
+
+ align:start position:0%
+is one one/ M because of that behavior
+ 
+
+ align:start position:0%
+is one one/ M because of that behavior
+and this goes zero okay in the Lin as n
+
+ align:start position:0%
+and this goes zero okay in the Lin as n
+ 
+
+ align:start position:0%
+and this goes zero okay in the Lin as n
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+Infinity so that means the fluctuations
+
+ align:start position:0%
+Infinity so that means the fluctuations
+ 
+
+ align:start position:0%
+Infinity so that means the fluctuations
+are suppressed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so any questions regarding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this good okay so now let's talk about
+
+ align:start position:0%
+this good okay so now let's talk about
+ 
+
+ align:start position:0%
+this good okay so now let's talk about
+the third aspect of it the third
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implication so now suppose we interpret
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interpret this endpoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function so disconnected import
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function say uh we which I can
+
+ align:start position:0%
+function say uh we which I can
+ 
+
+ align:start position:0%
+function say uh we which I can
+symbolically write as say some kind of
+
+ align:start position:0%
+symbolically write as say some kind of
+ 
+
+ align:start position:0%
+symbolically write as say some kind of
+blob then you have any external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XS say one two
+
+ align:start position:0%
+XS say one two
+ 
+
+ align:start position:0%
+XS say one two
+3us one n
+
+ align:start position:0%
+3us one n
+ 
+
+ align:start position:0%
+3us one n
+okay so so each nine each N means the
+
+ align:start position:0%
+okay so so each nine each N means the
+ 
+
+ align:start position:0%
+okay so so each nine each N means the
+external operator
+
+ align:start position:0%
+external operator
+ 
+
+ align:start position:0%
+external operator
+insertions so if we interpret this as
+
+ align:start position:0%
+insertions so if we interpret this as
+ 
+
+ align:start position:0%
+insertions so if we interpret this as
+some kind of scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amplitude as some kind of scattering
+
+ align:start position:0%
+amplitude as some kind of scattering
+ 
+
+ align:start position:0%
+amplitude as some kind of scattering
+amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as generates some kind of scattering
+
+ align:start position:0%
+so as generates some kind of scattering
+ 
+
+ align:start position:0%
+so as generates some kind of scattering
+amplitude of the Ang
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glose of Ang
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+globos then you can show because of this
+
+ align:start position:0%
+globos then you can show because of this
+ 
+
+ align:start position:0%
+globos then you can show because of this
+Behavior you can show because of this n
+
+ align:start position:0%
+Behavior you can show because of this n
+ 
+
+ align:start position:0%
+Behavior you can show because of this n
+scaling
+
+ align:start position:0%
+scaling
+ 
+
+ align:start position:0%
+scaling
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then again to reading
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order in the angle to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scatterings are classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by classical
+
+ align:start position:0%
+by classical
+ 
+
+ align:start position:0%
+by classical
+means you said it only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involves only involve two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level Sky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RS okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I'm going to show this uh uh this
+
+ align:start position:0%
+so now I'm going to show this uh uh this
+ 
+
+ align:start position:0%
+so now I'm going to show this uh uh this
+is the uh conclusion so I'm going to uh
+
+ align:start position:0%
+is the uh conclusion so I'm going to uh
+ 
+
+ align:start position:0%
+is the uh conclusion so I'm going to uh
+uh justify this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement so before I start justifying
+
+ align:start position:0%
+statement so before I start justifying
+ 
+
+ align:start position:0%
+statement so before I start justifying
+this statement do you have any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions good so so let me just make a
+
+ align:start position:0%
+questions good so so let me just make a
+ 
+
+ align:start position:0%
+questions good so so let me just make a
+few uh um
+
+ align:start position:0%
+few uh um
+ 
+
+ align:start position:0%
+few uh um
+remark so first so let's look at the
+
+ align:start position:0%
+remark so first so let's look at the
+ 
+
+ align:start position:0%
+remark so first so let's look at the
+simplest case which is the
+
+ align:start position:0%
+simplest case which is the
+ 
+
+ align:start position:0%
+simplest case which is the
+three point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function so threo function can be
+
+ align:start position:0%
+function so threo function can be
+ 
+
+ align:start position:0%
+function so threo function can be
+considered just as effective vertex so
+
+ align:start position:0%
+considered just as effective vertex so
+ 
+
+ align:start position:0%
+considered just as effective vertex so
+it can be consider as effective vertex
+
+ align:start position:0%
+it can be consider as effective vertex
+ 
+
+ align:start position:0%
+it can be consider as effective vertex
+of three particle intact with each other
+
+ align:start position:0%
+of three particle intact with each other
+ 
+
+ align:start position:0%
+of three particle intact with each other
+say one say one Global split into two
+
+ align:start position:0%
+say one say one Global split into two
+ 
+
+ align:start position:0%
+say one say one Global split into two
+Global ex okay so this from that
+
+ align:start position:0%
+Global ex okay so this from that
+ 
+
+ align:start position:0%
+Global ex okay so this from that
+definition is scales as one/
+
+ align:start position:0%
+definition is scales as one/
+ 
+
+ align:start position:0%
+definition is scales as one/
+n okay this scale is one/
+
+ align:start position:0%
+n okay this scale is one/
+ 
+
+ align:start position:0%
+n okay this scale is one/
+n so if we treat it as a basic
+
+ align:start position:0%
+n so if we treat it as a basic
+ 
+
+ align:start position:0%
+n so if we treat it as a basic
+vertex so so if we treat it as a basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex so if we suppose we treat it
+
+ align:start position:0%
+vertex so if we suppose we treat it
+ 
+
+ align:start position:0%
+vertex so if we suppose we treat it
+suppose we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+treat we treat it as the basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex with cing G so G is one /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple then easy to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then then two level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amplitudes for EMP particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scattering and particle
+
+ align:start position:0%
+scattering and particle
+ 
+
+ align:start position:0%
+scattering and particle
+scatterings are precisely scales as G to
+
+ align:start position:0%
+scatterings are precisely scales as G to
+ 
+
+ align:start position:0%
+scatterings are precisely scales as G to
+the nus 2 which is n to the power minus
+
+ align:start position:0%
+the nus 2 which is n to the power minus
+ 
+
+ align:start position:0%
+the nus 2 which is n to the power minus
+2us n and this is precisely we see uh
+
+ align:start position:0%
+2us n and this is precisely we see uh
+ 
+
+ align:start position:0%
+2us n and this is precisely we see uh
+for the leading scaling
+
+ align:start position:0%
+for the leading scaling
+ 
+
+ align:start position:0%
+for the leading scaling
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so is this fact obvious to you that
+
+ align:start position:0%
+okay so is this fact obvious to you that
+ 
+
+ align:start position:0%
+okay so is this fact obvious to you that
+the tree level scattering for M
+
+ align:start position:0%
+the tree level scattering for M
+ 
+
+ align:start position:0%
+the tree level scattering for M
+particles with the with with basic
+
+ align:start position:0%
+particles with the with with basic
+ 
+
+ align:start position:0%
+particles with the with with basic
+vertex given by G with scale like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this oh sorry why is a proportional to G
+
+ align:start position:0%
+this oh sorry why is a proportional to G
+ 
+
+ align:start position:0%
+this oh sorry why is a proportional to G
+because each uh each this in the double
+
+ align:start position:0%
+because each uh each this in the double
+ 
+
+ align:start position:0%
+because each uh each this in the double
+line notation each line contributes to
+
+ align:start position:0%
+line notation each line contributes to
+ 
+
+ align:start position:0%
+line notation each line contributes to
+like a g Square so uh how letter G comes
+
+ align:start position:0%
+like a g Square so uh how letter G comes
+ 
+
+ align:start position:0%
+like a g Square so uh how letter G comes
+from no which G you are talking about oh
+
+ align:start position:0%
+from no which G you are talking about oh
+ 
+
+ align:start position:0%
+from no which G you are talking about oh
+no no no no no oh uh uh maybe let me
+
+ align:start position:0%
+no no no no no oh uh uh maybe let me
+ 
+
+ align:start position:0%
+no no no no no oh uh uh maybe let me
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+Lambda it's a different G is a different
+
+ align:start position:0%
+Lambda it's a different G is a different
+ 
+
+ align:start position:0%
+Lambda it's a different G is a different
+yeah let me call it um Kaa or let me
+
+ align:start position:0%
+yeah let me call it um Kaa or let me
+ 
+
+ align:start position:0%
+yeah let me call it um Kaa or let me
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+the GT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's not the same it's not the same
+
+ align:start position:0%
+yeah it's not the same it's not the same
+ 
+
+ align:start position:0%
+yeah it's not the same it's not the same
+G as before this is just something I I
+
+ align:start position:0%
+G as before this is just something I I
+ 
+
+ align:start position:0%
+G as before this is just something I I
+de lo I just call it some kind of
+
+ align:start position:0%
+de lo I just call it some kind of
+ 
+
+ align:start position:0%
+de lo I just call it some kind of
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+company
+
+ align:start position:0%
+company
+ 
+
+ align:start position:0%
+company
+yeah yeah just imagine you have a
+
+ align:start position:0%
+yeah yeah just imagine you have a
+ 
+
+ align:start position:0%
+yeah yeah just imagine you have a
+process whose basic interacting vertex
+
+ align:start position:0%
+process whose basic interacting vertex
+ 
+
+ align:start position:0%
+process whose basic interacting vertex
+is G
+
+ align:start position:0%
+is G
+ 
+
+ align:start position:0%
+is G
+TAA and G is order one over
+
+ align:start position:0%
+TAA and G is order one over
+ 
+
+ align:start position:0%
+TAA and G is order one over
+n and then the then the tree level
+
+ align:start position:0%
+n and then the then the tree level
+ 
+
+ align:start position:0%
+n and then the then the tree level
+scattering for imp particle will depend
+
+ align:start position:0%
+scattering for imp particle will depend
+ 
+
+ align:start position:0%
+scattering for imp particle will depend
+on this component to be G to the m minus
+
+ align:start position:0%
+on this component to be G to the m minus
+ 
+
+ align:start position:0%
+on this component to be G to the m minus
+2 okay is this clear to you yeah I can
+
+ align:start position:0%
+2 okay is this clear to you yeah I can
+ 
+
+ align:start position:0%
+2 okay is this clear to you yeah I can
+just draw a tree diagram you can see it
+
+ align:start position:0%
+just draw a tree diagram you can see it
+ 
+
+ align:start position:0%
+just draw a tree diagram you can see it
+immediately
+
+ align:start position:0%
+immediately
+ 
+
+ align:start position:0%
+immediately
+okay so uh so this is
+
+ align:start position:0%
+okay so uh so this is
+ 
+
+ align:start position:0%
+okay so uh so this is
+consistent so this behavior is
+
+ align:start position:0%
+consistent so this behavior is
+ 
+
+ align:start position:0%
+consistent so this behavior is
+consistent to to interpret that as a
+
+ align:start position:0%
+consistent to to interpret that as a
+ 
+
+ align:start position:0%
+consistent to to interpret that as a
+tree but you don't actually have to
+
+ align:start position:0%
+tree but you don't actually have to
+ 
+
+ align:start position:0%
+tree but you don't actually have to
+assume the the basic the threep point
+
+ align:start position:0%
+assume the the basic the threep point
+ 
+
+ align:start position:0%
+assume the the basic the threep point
+vertex so you can also say
+
+ align:start position:0%
+vertex so you can also say
+ 
+
+ align:start position:0%
+vertex so you can also say
+you can also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+include so how all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices but your vertices which you
+
+ align:start position:0%
+vertices but your vertices which you
+ 
+
+ align:start position:0%
+vertices but your vertices which you
+include should be consistent with this
+
+ align:start position:0%
+include should be consistent with this
+ 
+
+ align:start position:0%
+include should be consistent with this
+scaling okay say suppose if you want to
+
+ align:start position:0%
+scaling okay say suppose if you want to
+ 
+
+ align:start position:0%
+scaling okay say suppose if you want to
+include a four particle vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this should scales as G Thea
+
+ align:start position:0%
+and then this should scales as G Thea
+ 
+
+ align:start position:0%
+and then this should scales as G Thea
+Square which is n to the minus
+
+ align:start position:0%
+Square which is n to the minus
+ 
+
+ align:start position:0%
+Square which is n to the minus
+2 because the four point connective
+
+ align:start position:0%
+2 because the four point connective
+ 
+
+ align:start position:0%
+2 because the four point connective
+function should scale as a minus two and
+
+ align:start position:0%
+function should scale as a minus two and
+ 
+
+ align:start position:0%
+function should scale as a minus two and
+similarly if you have a five point
+
+ align:start position:0%
+similarly if you have a five point
+ 
+
+ align:start position:0%
+similarly if you have a five point
+vertex then you should scale s g Thea to
+
+ align:start position:0%
+vertex then you should scale s g Thea to
+ 
+
+ align:start position:0%
+vertex then you should scale s g Thea to
+the cube which is n to Theus 3 because
+
+ align:start position:0%
+the cube which is n to Theus 3 because
+ 
+
+ align:start position:0%
+the cube which is n to Theus 3 because
+the Five Point function should scale as
+
+ align:start position:0%
+the Five Point function should scale as
+ 
+
+ align:start position:0%
+the Five Point function should scale as
+m 3 okay so you can also add such higher
+
+ align:start position:0%
+m 3 okay so you can also add such higher
+ 
+
+ align:start position:0%
+m 3 okay so you can also add such higher
+all the vertices as far as you are
+
+ align:start position:0%
+all the vertices as far as you are
+ 
+
+ align:start position:0%
+all the vertices as far as you are
+consistent with this Nigerian
+
+ align:start position:0%
+consistent with this Nigerian
+ 
+
+ align:start position:0%
+consistent with this Nigerian
+scaling so you then you can easily
+
+ align:start position:0%
+scaling so you then you can easily
+ 
+
+ align:start position:0%
+scaling so you then you can easily
+convince
+
+ align:start position:0%
+convince
+ 
+
+ align:start position:0%
+convince
+yourself that even including such high
+
+ align:start position:0%
+yourself that even including such high
+ 
+
+ align:start position:0%
+yourself that even including such high
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+vertices uh that's do not change this
+
+ align:start position:0%
+vertices uh that's do not change this
+ 
+
+ align:start position:0%
+vertices uh that's do not change this
+conclusion does not change this
+
+ align:start position:0%
+conclusion does not change this
+ 
+
+ align:start position:0%
+conclusion does not change this
+conclusion that the any level
+
+ align:start position:0%
+conclusion that the any level
+ 
+
+ align:start position:0%
+conclusion that the any level
+amplitude again for for n particles with
+
+ align:start position:0%
+amplitude again for for n particles with
+ 
+
+ align:start position:0%
+amplitude again for for n particles with
+scales like this okay
+
+ align:start position:0%
+scales like this okay
+ 
+
+ align:start position:0%
+scales like this okay
+uh we not change that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conclusion so this is second
+
+ align:start position:0%
+conclusion so this is second
+ 
+
+ align:start position:0%
+conclusion so this is second
+statement and this two statement just to
+
+ align:start position:0%
+statement and this two statement just to
+ 
+
+ align:start position:0%
+statement and this two statement just to
+give you a humanistic way to see that
+
+ align:start position:0%
+give you a humanistic way to see that
+ 
+
+ align:start position:0%
+give you a humanistic way to see that
+the that that this kind of scaling can
+
+ align:start position:0%
+the that that this kind of scaling can
+ 
+
+ align:start position:0%
+the that that this kind of scaling can
+be generated indeed generated by three
+
+ align:start position:0%
+be generated indeed generated by three
+ 
+
+ align:start position:0%
+be generated indeed generated by three
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+scatterings so now I'm going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove so now I'm going to
+
+ align:start position:0%
+prove so now I'm going to
+ 
+
+ align:start position:0%
+prove so now I'm going to
+prove that in the lar limit to Le in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order in
+
+ align:start position:0%
+order in
+ 
+
+ align:start position:0%
+order in
+n in any such kind of correlation
+
+ align:start position:0%
+n in any such kind of correlation
+ 
+
+ align:start position:0%
+n in any such kind of correlation
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more than
+
+ align:start position:0%
+more than
+ 
+
+ align:start position:0%
+more than
+one there's no
+
+ align:start position:0%
+one there's no
+ 
+
+ align:start position:0%
+one there's no
+more there's there are only maybe let me
+
+ align:start position:0%
+more there's there are only maybe let me
+ 
+
+ align:start position:0%
+more there's there are only maybe let me
+just say it easier there are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only one particle in the media States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm going to show
+
+ align:start position:0%
+okay so I'm going to show
+ 
+
+ align:start position:0%
+okay so I'm going to show
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let's consider say a three part so
+
+ align:start position:0%
+um so let's consider say a three part so
+ 
+
+ align:start position:0%
+um so let's consider say a three part so
+by one particle I always mean one
+
+ align:start position:0%
+by one particle I always mean one
+ 
+
+ align:start position:0%
+by one particle I always mean one
+particle in this sense okay so one
+
+ align:start position:0%
+particle in this sense okay so one
+ 
+
+ align:start position:0%
+particle in this sense okay so one
+particle in this sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I will do it a little bit
+
+ align:start position:0%
+so I will do it a little bit
+ 
+
+ align:start position:0%
+so I will do it a little bit
+theistically not very precise but I
+
+ align:start position:0%
+theistically not very precise but I
+ 
+
+ align:start position:0%
+theistically not very precise but I
+think it's it's it's rigorous but it's
+
+ align:start position:0%
+think it's it's it's rigorous but it's
+ 
+
+ align:start position:0%
+think it's it's it's rigorous but it's
+not but I will not write the precise uh
+
+ align:start position:0%
+not but I will not write the precise uh
+ 
+
+ align:start position:0%
+not but I will not write the precise uh
+um uh yeah we not write rigorous
+
+ align:start position:0%
+um uh yeah we not write rigorous
+ 
+
+ align:start position:0%
+um uh yeah we not write rigorous
+formulas so so let's consider just as
+
+ align:start position:0%
+formulas so so let's consider just as
+ 
+
+ align:start position:0%
+formulas so so let's consider just as
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+consider uh the threep point
+
+ align:start position:0%
+consider uh the threep point
+ 
+
+ align:start position:0%
+consider uh the threep point
+scattering threo functions say I have
+
+ align:start position:0%
+scattering threo functions say I have
+ 
+
+ align:start position:0%
+scattering threo functions say I have
+three operators uh uh I look at this
+
+ align:start position:0%
+three operators uh uh I look at this
+ 
+
+ align:start position:0%
+three operators uh uh I look at this
+connected uh uh uh uh a green function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in those
+
+ align:start position:0%
+now in those
+ 
+
+ align:start position:0%
+now in those
+places we can in principle insert
+
+ align:start position:0%
+places we can in principle insert
+ 
+
+ align:start position:0%
+places we can in principle insert
+complete set of States okay uh and those
+
+ align:start position:0%
+complete set of States okay uh and those
+ 
+
+ align:start position:0%
+complete set of States okay uh and those
+can be considered as intermediate uh
+
+ align:start position:0%
+can be considered as intermediate uh
+ 
+
+ align:start position:0%
+can be considered as intermediate uh
+intermediate State contribute to this
+
+ align:start position:0%
+intermediate State contribute to this
+ 
+
+ align:start position:0%
+intermediate State contribute to this
+process say if I consider scattering
+
+ align:start position:0%
+process say if I consider scattering
+ 
+
+ align:start position:0%
+process say if I consider scattering
+process and then and then I can insert
+
+ align:start position:0%
+process and then and then I can insert
+ 
+
+ align:start position:0%
+process and then and then I can insert
+the a complete set of States here and
+
+ align:start position:0%
+the a complete set of States here and
+ 
+
+ align:start position:0%
+the a complete set of States here and
+those state which gives a non-trivial
+
+ align:start position:0%
+those state which gives a non-trivial
+ 
+
+ align:start position:0%
+those state which gives a non-trivial
+contribution can be considered as the a
+
+ align:start position:0%
+contribution can be considered as the a
+ 
+
+ align:start position:0%
+contribution can be considered as the a
+contribution from some intermediate
+
+ align:start position:0%
+contribution from some intermediate
+ 
+
+ align:start position:0%
+contribution from some intermediate
+States
+
+ align:start position:0%
+States
+ 
+
+ align:start position:0%
+States
+okay and uh
+
+ align:start position:0%
+okay and uh
+ 
+
+ align:start position:0%
+okay and uh
+so so for example let
+
+ align:start position:0%
+so so for example let
+ 
+
+ align:start position:0%
+so so for example let
+me introduce a single particle States
+
+ align:start position:0%
+me introduce a single particle States
+ 
+
+ align:start position:0%
+me introduce a single particle States
+here say say this o1 O2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O3 so suppose I insert a complete set of
+
+ align:start position:0%
+O3 so suppose I insert a complete set of
+ 
+
+ align:start position:0%
+O3 so suppose I insert a complete set of
+I insert the one
+
+ align:start position:0%
+I insert the one
+ 
+
+ align:start position:0%
+I insert the one
+here this one will cons include the sum
+
+ align:start position:0%
+here this one will cons include the sum
+ 
+
+ align:start position:0%
+here this one will cons include the sum
+of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible single particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State and uh also
+
+ align:start position:0%
+State and uh also
+ 
+
+ align:start position:0%
+State and uh also
+include
+
+ align:start position:0%
+include
+ 
+
+ align:start position:0%
+include
+also two particle state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+okay and look at Connected green
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah just realistically when I
+
+ align:start position:0%
+okay yeah just realistically when I
+ 
+
+ align:start position:0%
+okay yeah just realistically when I
+insert the complete set of State I can
+
+ align:start position:0%
+insert the complete set of State I can
+ 
+
+ align:start position:0%
+insert the complete set of State I can
+insert off like that
+
+ align:start position:0%
+insert off like that
+ 
+
+ align:start position:0%
+insert off like that
+so now now let's look at the scaling so
+
+ align:start position:0%
+so now now let's look at the scaling so
+ 
+
+ align:start position:0%
+so now now let's look at the scaling so
+this guy according to
+
+ align:start position:0%
+this guy according to
+ 
+
+ align:start position:0%
+this guy according to
+our general Behavior should scale as
+
+ align:start position:0%
+our general Behavior should scale as
+ 
+
+ align:start position:0%
+our general Behavior should scale as
+one/
+
+ align:start position:0%
+one/
+ 
+
+ align:start position:0%
+one/
+n okay so this guy is indeed scale as
+
+ align:start position:0%
+n okay so this guy is indeed scale as
+ 
+
+ align:start position:0%
+n okay so this guy is indeed scale as
+one so two point function scales as one
+
+ align:start position:0%
+one so two point function scales as one
+ 
+
+ align:start position:0%
+one so two point function scales as one
+and to the power zero and this guy and
+
+ align:start position:0%
+and to the power zero and this guy and
+ 
+
+ align:start position:0%
+and to the power zero and this guy and
+this guy scales as to the^ minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so so this term is okay so insertion
+
+ align:start position:0%
+one so so this term is okay so insertion
+ 
+
+ align:start position:0%
+one so so this term is okay so insertion
+of the single particle state is
+
+ align:start position:0%
+of the single particle state is
+ 
+
+ align:start position:0%
+of the single particle state is
+okay but now this will give you a higher
+
+ align:start position:0%
+okay but now this will give you a higher
+ 
+
+ align:start position:0%
+okay but now this will give you a higher
+order contribution because this
+
+ align:start position:0%
+order contribution because this
+ 
+
+ align:start position:0%
+order contribution because this
+scales as equal to minus one and this
+
+ align:start position:0%
+scales as equal to minus one and this
+ 
+
+ align:start position:0%
+scales as equal to minus one and this
+scale as equal to minus 2 so all
+
+ align:start position:0%
+scale as equal to minus 2 so all
+ 
+
+ align:start position:0%
+scale as equal to minus 2 so all
+together this contribute to n to the
+
+ align:start position:0%
+together this contribute to n to the
+ 
+
+ align:start position:0%
+together this contribute to n to the
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+3 okay so so the contribution of the two
+
+ align:start position:0%
+3 okay so so the contribution of the two
+ 
+
+ align:start position:0%
+3 okay so so the contribution of the two
+particle State then will be suppressed
+
+ align:start position:0%
+particle State then will be suppressed
+ 
+
+ align:start position:0%
+particle State then will be suppressed
+compared to the contribution of the
+
+ align:start position:0%
+compared to the contribution of the
+ 
+
+ align:start position:0%
+compared to the contribution of the
+single particle State and similarly with
+
+ align:start position:0%
+single particle State and similarly with
+ 
+
+ align:start position:0%
+single particle State and similarly with
+higher even higher even more particle
+
+ align:start position:0%
+higher even higher even more particle
+ 
+
+ align:start position:0%
+higher even higher even more particle
+States
+
+ align:start position:0%
+States
+ 
+
+ align:start position:0%
+States
+okay so so if I draw a
+
+ align:start position:0%
+okay so so if I draw a
+ 
+
+ align:start position:0%
+okay so so if I draw a
+diagram this process is like the
+
+ align:start position:0%
+diagram this process is like the
+ 
+
+ align:start position:0%
+diagram this process is like the
+following you said I can start with
+
+ align:start position:0%
+following you said I can start with
+ 
+
+ align:start position:0%
+following you said I can start with
+one and this one can can say turn into I
+
+ align:start position:0%
+one and this one can can say turn into I
+ 
+
+ align:start position:0%
+one and this one can can say turn into I
+through a two-point
+
+ align:start position:0%
+through a two-point
+ 
+
+ align:start position:0%
+through a two-point
+function and then this I can go to two
+
+ align:start position:0%
+function and then this I can go to two
+ 
+
+ align:start position:0%
+function and then this I can go to two
+and three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a true level
+
+ align:start position:0%
+okay so this is a true level
+ 
+
+ align:start position:0%
+okay so this is a true level
+process and this is like the following
+
+ align:start position:0%
+process and this is like the following
+ 
+
+ align:start position:0%
+process and this is like the following
+so this is a two particle state so so
+
+ align:start position:0%
+so this is a two particle state so so
+ 
+
+ align:start position:0%
+so this is a two particle state so so
+this if I draw a diagram will be like if
+
+ align:start position:0%
+this if I draw a diagram will be like if
+ 
+
+ align:start position:0%
+this if I draw a diagram will be like if
+I start with one and then this one can
+
+ align:start position:0%
+I start with one and then this one can
+ 
+
+ align:start position:0%
+I start with one and then this one can
+split into
+
+ align:start position:0%
+split into
+ 
+
+ align:start position:0%
+split into
+IJ and then then this a combine into two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three okay so this is like one Loop
+
+ align:start position:0%
+three okay so this is like one Loop
+ 
+
+ align:start position:0%
+three okay so this is like one Loop
+process okay and this we see is n to
+
+ align:start position:0%
+process okay and this we see is n to
+ 
+
+ align:start position:0%
+process okay and this we see is n to
+Theus 3 and this is indeed just n to
+
+ align:start position:0%
+Theus 3 and this is indeed just n to
+ 
+
+ align:start position:0%
+Theus 3 and this is indeed just n to
+Theus one so this is surprise compared
+
+ align:start position:0%
+Theus one so this is surprise compared
+ 
+
+ align:start position:0%
+Theus one so this is surprise compared
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+that so so this is a direct way to
+
+ align:start position:0%
+that so so this is a direct way to
+ 
+
+ align:start position:0%
+that so so this is a direct way to
+say that in this kind of in this kind to
+
+ align:start position:0%
+say that in this kind of in this kind to
+ 
+
+ align:start position:0%
+say that in this kind of in this kind to
+lead in order indeed there can only
+
+ align:start position:0%
+lead in order indeed there can only
+ 
+
+ align:start position:0%
+lead in order indeed there can only
+three level processes you can never have
+
+ align:start position:0%
+three level processes you can never have
+ 
+
+ align:start position:0%
+three level processes you can never have
+this kind of Loops because whenever you
+
+ align:start position:0%
+this kind of Loops because whenever you
+ 
+
+ align:start position:0%
+this kind of Loops because whenever you
+have a loop then corresponding you must
+
+ align:start position:0%
+have a loop then corresponding you must
+ 
+
+ align:start position:0%
+have a loop then corresponding you must
+have a multi particle you must have
+
+ align:start position:0%
+have a multi particle you must have
+ 
+
+ align:start position:0%
+have a multi particle you must have
+multi particle intermediate States and
+
+ align:start position:0%
+multi particle intermediate States and
+ 
+
+ align:start position:0%
+multi particle intermediate States and
+then they surprised by
+
+ align:start position:0%
+then they surprised by
+ 
+
+ align:start position:0%
+then they surprised by
+login is it
+
+ align:start position:0%
+login is it
+ 
+
+ align:start position:0%
+login is it
+clear so so this tells
+
+ align:start position:0%
+clear so so this tells
+ 
+
+ align:start position:0%
+clear so so this tells
+you that all
+
+ align:start position:0%
+you that all
+ 
+
+ align:start position:0%
+you that all
+Loops are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppressed and so so a BC
+
+ align:start position:0%
+suppressed and so so a BC
+ 
+
+ align:start position:0%
+suppressed and so so a BC
+together so this a BC together then
+
+ align:start position:0%
+together so this a BC together then
+ 
+
+ align:start position:0%
+together so this a BC together then
+justify the
+
+ align:start position:0%
+justify the
+ 
+
+ align:start position:0%
+justify the
+statement that to Leading order this SC
+
+ align:start position:0%
+statement that to Leading order this SC
+ 
+
+ align:start position:0%
+statement that to Leading order this SC
+this scattering
+
+ align:start position:0%
+this scattering
+ 
+
+ align:start position:0%
+this scattering
+amplitude involving only two level when
+
+ align:start position:0%
+amplitude involving only two level when
+ 
+
+ align:start position:0%
+amplitude involving only two level when
+you have only a Tre level scattering
+
+ align:start position:0%
+you have only a Tre level scattering
+ 
+
+ align:start position:0%
+you have only a Tre level scattering
+then this is like a classical uh story
+
+ align:start position:0%
+then this is like a classical uh story
+ 
+
+ align:start position:0%
+then this is like a classical uh story
+only as you Lear in Quantum fil the
+
+ align:start position:0%
+only as you Lear in Quantum fil the
+ 
+
+ align:start position:0%
+only as you Lear in Quantum fil the
+loops is the can be consider as Quantum
+
+ align:start position:0%
+loops is the can be consider as Quantum
+ 
+
+ align:start position:0%
+loops is the can be consider as Quantum
+fluctuations and if you only have trees
+
+ align:start position:0%
+fluctuations and if you only have trees
+ 
+
+ align:start position:0%
+fluctuations and if you only have trees
+it's essentially just a classical
+
+ align:start position:0%
+it's essentially just a classical
+ 
+
+ align:start position:0%
+it's essentially just a classical
+process so when you solve the classical
+
+ align:start position:0%
+process so when you solve the classical
+ 
+
+ align:start position:0%
+process so when you solve the classical
+equation motion and what you get is the
+
+ align:start position:0%
+equation motion and what you get is the
+ 
+
+ align:start position:0%
+equation motion and what you get is the
+three level processes
+
+ align:start position:0%
+three level processes
+ 
+
+ align:start position:0%
+three level processes
+okay yes what is the number of
+
+ align:start position:0%
+okay yes what is the number of
+ 
+
+ align:start position:0%
+okay yes what is the number of
+operators H what is the number of
+
+ align:start position:0%
+operators H what is the number of
+ 
+
+ align:start position:0%
+operators H what is the number of
+operator in the right SC
+
+ align:start position:0%
+operator in the right SC
+ 
+
+ align:start position:0%
+operator in the right SC
+oh that's a very good question and
+
+ align:start position:0%
+oh that's a very good question and
+ 
+
+ align:start position:0%
+oh that's a very good question and
+essentially the by definition such
+
+ align:start position:0%
+essentially the by definition such
+ 
+
+ align:start position:0%
+essentially the by definition such
+operate only
+
+ align:start position:0%
+operate only
+ 
+
+ align:start position:0%
+operate only
+scales essentially by definition those
+
+ align:start position:0%
+scales essentially by definition those
+ 
+
+ align:start position:0%
+scales essentially by definition those
+operate such kind of So-Cal single
+
+ align:start position:0%
+operate such kind of So-Cal single
+ 
+
+ align:start position:0%
+operate such kind of So-Cal single
+Choice operators and they the scales at
+
+ align:start position:0%
+Choice operators and they the scales at
+ 
+
+ align:start position:0%
+Choice operators and they the scales at
+all the one yeah there's no um
+
+ align:start position:0%
+all the one yeah there's no um
+ 
+
+ align:start position:0%
+all the one yeah there's no um
+yeah just the way you can make such
+
+ align:start position:0%
+yeah just the way you can make such
+ 
+
+ align:start position:0%
+yeah just the way you can make such
+single trace operator is not
+
+ align:start position:0%
+single trace operator is not
+ 
+
+ align:start position:0%
+single trace operator is not
+proportional to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+questions what is each of these terms
+
+ align:start position:0%
+questions what is each of these terms
+ 
+
+ align:start position:0%
+questions what is each of these terms
+individually small but when you take
+
+ align:start position:0%
+individually small but when you take
+ 
+
+ align:start position:0%
+individually small but when you take
+make summation over them yeah yeah
+
+ align:start position:0%
+make summation over them yeah yeah
+ 
+
+ align:start position:0%
+make summation over them yeah yeah
+that's a question was just asked um so
+
+ align:start position:0%
+that's a question was just asked um so
+ 
+
+ align:start position:0%
+that's a question was just asked um so
+so those operators if you count
+
+ align:start position:0%
+so those operators if you count
+ 
+
+ align:start position:0%
+so those operators if you count
+them at the number of single TR operator
+
+ align:start position:0%
+them at the number of single TR operator
+ 
+
+ align:start position:0%
+them at the number of single TR operator
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+construct is the is independent of
+
+ align:start position:0%
+construct is the is independent of
+ 
+
+ align:start position:0%
+construct is the is independent of
+n uh and so so when you suppress them by
+
+ align:start position:0%
+n uh and so so when you suppress them by
+ 
+
+ align:start position:0%
+n uh and so so when you suppress them by
+n and there's nothing you can compensate
+
+ align:start position:0%
+n and there's nothing you can compensate
+ 
+
+ align:start position:0%
+n and there's nothing you can compensate
+them uh in principle yeah uh uh there's
+
+ align:start position:0%
+them uh in principle yeah uh uh there's
+ 
+
+ align:start position:0%
+them uh in principle yeah uh uh there's
+nothing can compensate them so yeah so
+
+ align:start position:0%
+nothing can compensate them so yeah so
+ 
+
+ align:start position:0%
+nothing can compensate them so yeah so
+like how many you know how many
+
+ align:start position:0%
+like how many you know how many
+ 
+
+ align:start position:0%
+like how many you know how many
+operators that are like um
+
+ align:start position:0%
+operators that are like um
+ 
+
+ align:start position:0%
+operators that are like um
+OJ can you construct like what is the
+
+ align:start position:0%
+OJ can you construct like what is the
+ 
+
+ align:start position:0%
+OJ can you construct like what is the
+magnitude oh it's infinite number of
+
+ align:start position:0%
+magnitude oh it's infinite number of
+ 
+
+ align:start position:0%
+magnitude oh it's infinite number of
+them right it's infinite number of them
+
+ align:start position:0%
+them right it's infinite number of them
+ 
+
+ align:start position:0%
+them right it's infinite number of them
+but the key
+
+ align:start position:0%
+but the key
+ 
+
+ align:start position:0%
+but the key
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+infinite
+
+ align:start position:0%
+infinite
+ 
+
+ align:start position:0%
+infinite
+compare it's a factor we yeah it's a
+
+ align:start position:0%
+compare it's a factor we yeah it's a
+ 
+
+ align:start position:0%
+compare it's a factor we yeah it's a
+infinite is it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite but compared to the lar limit
+
+ align:start position:0%
+infinite but compared to the lar limit
+ 
+
+ align:start position:0%
+infinite but compared to the lar limit
+is still all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one it's
+
+ align:start position:0%
+one it's
+ 
+
+ align:start position:0%
+one it's
+infinite it's
+
+ align:start position:0%
+infinite it's
+ 
+
+ align:start position:0%
+infinite it's
+infinite but it's all the N to the power
+
+ align:start position:0%
+infinite but it's all the N to the power
+ 
+
+ align:start position:0%
+infinite but it's all the N to the power
+zero oh my God all right it's add m to
+
+ align:start position:0%
+zero oh my God all right it's add m to
+ 
+
+ align:start position:0%
+zero oh my God all right it's add m to
+the power zero okay and uh
+
+ align:start position:0%
+the power zero okay and uh
+ 
+
+ align:start position:0%
+the power zero okay and uh
+so but they will be
+
+ align:start position:0%
+so but they will be
+ 
+
+ align:start position:0%
+so but they will be
+suppressed by
+
+ align:start position:0%
+suppressed by
+ 
+
+ align:start position:0%
+suppressed by
+physical they will be surprised by
+
+ align:start position:0%
+physical they will be surprised by
+ 
+
+ align:start position:0%
+physical they will be surprised by
+physical process say for example say
+
+ align:start position:0%
+physical process say for example say
+ 
+
+ align:start position:0%
+physical process say for example say
+this operator it's a box or something
+
+ align:start position:0%
+this operator it's a box or something
+ 
+
+ align:start position:0%
+this operator it's a box or something
+say have some Dimension say say this
+
+ align:start position:0%
+say have some Dimension say say this
+ 
+
+ align:start position:0%
+say have some Dimension say say this
+operator say suppose this particle one
+
+ align:start position:0%
+operator say suppose this particle one
+ 
+
+ align:start position:0%
+operator say suppose this particle one
+have some
+
+ align:start position:0%
+have some
+ 
+
+ align:start position:0%
+have some
+energy and uh and particle has some
+
+ align:start position:0%
+energy and uh and particle has some
+ 
+
+ align:start position:0%
+energy and uh and particle has some
+energy and then the process of this
+
+ align:start position:0%
+energy and then the process of this
+ 
+
+ align:start position:0%
+energy and then the process of this
+generate this two and when they are then
+
+ align:start position:0%
+generate this two and when they are then
+ 
+
+ align:start position:0%
+generate this two and when they are then
+when their energy become very large then
+
+ align:start position:0%
+when their energy become very large then
+ 
+
+ align:start position:0%
+when their energy become very large then
+it's suppressed and uh and and you have
+
+ align:start position:0%
+it's suppressed and uh and and you have
+ 
+
+ align:start position:0%
+it's suppressed and uh and and you have
+this kind of physical suppression of
+
+ align:start position:0%
+this kind of physical suppression of
+ 
+
+ align:start position:0%
+this kind of physical suppression of
+course if you include all all energies
+
+ align:start position:0%
+course if you include all all energies
+ 
+
+ align:start position:0%
+course if you include all all energies
+the infinite number of them but in
+
+ align:start position:0%
+the infinite number of them but in
+ 
+
+ align:start position:0%
+the infinite number of them but in
+effective you
+
+ align:start position:0%
+effective you
+ 
+
+ align:start position:0%
+effective you
+can if you can uh yeah energy
+
+ align:start position:0%
+can if you can uh yeah energy
+ 
+
+ align:start position:0%
+can if you can uh yeah energy
+conservation this kind of thing then
+
+ align:start position:0%
+conservation this kind of thing then
+ 
+
+ align:start position:0%
+conservation this kind of thing then
+essentially there's a fight number of
+
+ align:start position:0%
+essentially there's a fight number of
+ 
+
+ align:start position:0%
+essentially there's a fight number of
+contributes okay yeah but the key is
+
+ align:start position:0%
+contributes okay yeah but the key is
+ 
+
+ align:start position:0%
+contributes okay yeah but the key is
+that this is all n to the power zero
+
+ align:start position:0%
+that this is all n to the power zero
+ 
+
+ align:start position:0%
+that this is all n to the power zero
+just uh maybe one more thing what if it
+
+ align:start position:0%
+just uh maybe one more thing what if it
+ 
+
+ align:start position:0%
+just uh maybe one more thing what if it
+includes the loop
+
+ align:start position:0%
+includes the loop
+ 
+
+ align:start position:0%
+includes the loop
+Clos by itself yeah like a like a close
+
+ align:start position:0%
+Clos by itself yeah like a like a close
+ 
+
+ align:start position:0%
+Clos by itself yeah like a like a close
+firing Loop in QED I mean it doesn't
+
+ align:start position:0%
+firing Loop in QED I mean it doesn't
+ 
+
+ align:start position:0%
+firing Loop in QED I mean it doesn't
+need to involve multiple state it can
+
+ align:start position:0%
+need to involve multiple state it can
+ 
+
+ align:start position:0%
+need to involve multiple state it can
+just bend and then no no no Loop always
+
+ align:start position:0%
+just bend and then no no no Loop always
+ 
+
+ align:start position:0%
+just bend and then no no no Loop always
+involve partic partic States say any
+
+ align:start position:0%
+involve partic partic States say any
+ 
+
+ align:start position:0%
+involve partic partic States say any
+Loop when you cross it there's always
+
+ align:start position:0%
+Loop when you cross it there's always
+ 
+
+ align:start position:0%
+Loop when you cross it there's always
+two states we don't need to cross it at
+
+ align:start position:0%
+two states we don't need to cross it at
+ 
+
+ align:start position:0%
+two states we don't need to cross it at
+the end I mean
+
+ align:start position:0%
+the end I mean
+ 
+
+ align:start position:0%
+the end I mean
+like so sorry I don't quite understand
+
+ align:start position:0%
+like so sorry I don't quite understand
+ 
+
+ align:start position:0%
+like so sorry I don't quite understand
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+Loop any Loop move by definition when
+
+ align:start position:0%
+Loop any Loop move by definition when
+ 
+
+ align:start position:0%
+Loop any Loop move by definition when
+you cross it there's always two points
+
+ align:start position:0%
+you cross it there's always two points
+ 
+
+ align:start position:0%
+you cross it there's always two points
+then that means this is more than one
+
+ align:start position:0%
+then that means this is more than one
+ 
+
+ align:start position:0%
+then that means this is more than one
+particle uh just something like this
+
+ align:start position:0%
+particle uh just something like this
+ 
+
+ align:start position:0%
+particle uh just something like this
+don't cross any no no no no no you cross
+
+ align:start position:0%
+don't cross any no no no no no you cross
+ 
+
+ align:start position:0%
+don't cross any no no no no no you cross
+here you still have two particle right
+
+ align:start position:0%
+here you still have two particle right
+ 
+
+ align:start position:0%
+here you still have two particle right
+cut okay yeah you cut at any time there
+
+ align:start position:0%
+cut okay yeah you cut at any time there
+ 
+
+ align:start position:0%
+cut okay yeah you cut at any time there
+still two particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh okay let's
+
+ align:start position:0%
+yeah uh okay let's
+ 
+
+ align:start position:0%
+yeah uh okay let's
+summarize so now let's combine 1 2 three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can combine 1 2
+
+ align:start position:0%
+so we can combine 1 2
+ 
+
+ align:start position:0%
+so we can combine 1 2
+3 so this tells
+
+ align:start position:0%
+3 so this tells
+ 
+
+ align:start position:0%
+3 so this tells
+us so this 1 2 3 tells us at leading
+
+ align:start position:0%
+us so this 1 2 3 tells us at leading
+ 
+
+ align:start position:0%
+us so this 1 2 3 tells us at leading
+order in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory a classical Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we essentially just have a
+
+ align:start position:0%
+we essentially just have a
+ 
+
+ align:start position:0%
+we essentially just have a
+CL we have a classic C of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gloos you just have a bunch of particles
+
+ align:start position:0%
+gloos you just have a bunch of particles
+ 
+
+ align:start position:0%
+gloos you just have a bunch of particles
+and they interact classically uh there's
+
+ align:start position:0%
+and they interact classically uh there's
+ 
+
+ align:start position:0%
+and they interact classically uh there's
+no Quantum
+
+ align:start position:0%
+no Quantum
+ 
+
+ align:start position:0%
+no Quantum
+fluctuations and with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions among
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+globos among them
+
+ align:start position:0%
+globos among them
+ 
+
+ align:start position:0%
+globos among them
+given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by some effective component which I
+
+ align:start position:0%
+by some effective component which I
+ 
+
+ align:start position:0%
+by some effective component which I
+called G Thea which scales at 1 /
+
+ align:start position:0%
+called G Thea which scales at 1 /
+ 
+
+ align:start position:0%
+called G Thea which scales at 1 /
+n okay scales at 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n so so let me just elaborate this
+
+ align:start position:0%
+n so so let me just elaborate this
+ 
+
+ align:start position:0%
+n so so let me just elaborate this
+statement a little bit more so this can
+
+ align:start position:0%
+statement a little bit more so this can
+ 
+
+ align:start position:0%
+statement a little bit more so this can
+be considered as say when we take a gaug
+
+ align:start position:0%
+be considered as say when we take a gaug
+ 
+
+ align:start position:0%
+be considered as say when we take a gaug
+theory say for example yam
+
+ align:start position:0%
+theory say for example yam
+ 
+
+ align:start position:0%
+theory say for example yam
+Theory say QC
+
+ align:start position:0%
+Theory say QC
+ 
+
+ align:start position:0%
+Theory say QC
+B you take angle to Infinity
+
+ align:start position:0%
+B you take angle to Infinity
+ 
+
+ align:start position:0%
+B you take angle to Infinity
+limit and you take H bar
+
+ align:start position:0%
+limit and you take H bar
+ 
+
+ align:start position:0%
+limit and you take H bar
+finite so by definition when we talk
+
+ align:start position:0%
+finite so by definition when we talk
+ 
+
+ align:start position:0%
+finite so by definition when we talk
+about this Ser H bar is always
+
+ align:start position:0%
+about this Ser H bar is always
+ 
+
+ align:start position:0%
+about this Ser H bar is always
+finite but in any equal to Infinity
+
+ align:start position:0%
+finite but in any equal to Infinity
+ 
+
+ align:start position:0%
+finite but in any equal to Infinity
+limit this is
+
+ align:start position:0%
+limit this is
+ 
+
+ align:start position:0%
+limit this is
+equivalent to a global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory with h by Thea goes to
+
+ align:start position:0%
+Theory with h by Thea goes to
+ 
+
+ align:start position:0%
+Theory with h by Thea goes to
+zero okay so you get the classical the
+
+ align:start position:0%
+zero okay so you get the classical the
+ 
+
+ align:start position:0%
+zero okay so you get the classical the
+and with effective
+
+ align:start position:0%
+and with effective
+ 
+
+ align:start position:0%
+and with effective
+H H by Thea which is contr essentially
+
+ align:start position:0%
+H H by Thea which is contr essentially
+ 
+
+ align:start position:0%
+H H by Thea which is contr essentially
+by one of n goes to
+
+ align:start position:0%
+by one of n goes to
+ 
+
+ align:start position:0%
+by one of n goes to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay so so here you can do pive
+
+ align:start position:0%
+okay so so here you can do pive
+ 
+
+ align:start position:0%
+okay so so here you can do pive
+expansion One
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n so this is just a leading order here
+
+ align:start position:0%
+n so this is just a leading order here
+ 
+
+ align:start position:0%
+n so this is just a leading order here
+you can do poity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion in one / n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this site it's like some kind of
+
+ align:start position:0%
+so in this site it's like some kind of
+ 
+
+ align:start position:0%
+so in this site it's like some kind of
+semil classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion in this H
+
+ align:start position:0%
+expansion in this H
+ 
+
+ align:start position:0%
+expansion in this H
+theoda which is of course should be
+
+ align:start position:0%
+theoda which is of course should be
+ 
+
+ align:start position:0%
+theoda which is of course should be
+scale as 1 /
+
+ align:start position:0%
+scale as 1 /
+ 
+
+ align:start position:0%
+scale as 1 /
+n okay so so on this side when H bar
+
+ align:start position:0%
+n okay so so on this side when H bar
+ 
+
+ align:start position:0%
+n okay so so on this side when H bar
+goes H bar TAA goes zero because you
+
+ align:start position:0%
+goes H bar TAA goes zero because you
+ 
+
+ align:start position:0%
+goes H bar TAA goes zero because you
+have a classical Theory but then you can
+
+ align:start position:0%
+have a classical Theory but then you can
+ 
+
+ align:start position:0%
+have a classical Theory but then you can
+do uh do expansion H TAA so this what we
+
+ align:start position:0%
+do uh do expansion H TAA so this what we
+ 
+
+ align:start position:0%
+do uh do expansion H TAA so this what we
+normally call semiclassical
+
+ align:start position:0%
+normally call semiclassical
+ 
+
+ align:start position:0%
+normally call semiclassical
+expansion okay so so the so the Lan
+
+ align:start position:0%
+expansion okay so so the so the Lan
+ 
+
+ align:start position:0%
+expansion okay so so the so the Lan
+expansion then translate into some semi
+
+ align:start position:0%
+expansion then translate into some semi
+ 
+
+ align:start position:0%
+expansion then translate into some semi
+classical uh expansion when you
+
+ align:start position:0%
+classical uh expansion when you
+ 
+
+ align:start position:0%
+classical uh expansion when you
+translate into this Global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language and we will
+
+ align:start position:0%
+language and we will
+ 
+
+ align:start position:0%
+language and we will
+now so is this clear yeah this is a
+
+ align:start position:0%
+now so is this clear yeah this is a
+ 
+
+ align:start position:0%
+now so is this clear yeah this is a
+little bit small corner is it is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+readable yeah uh this is a very
+
+ align:start position:0%
+readable yeah uh this is a very
+ 
+
+ align:start position:0%
+readable yeah uh this is a very
+important statement maybe I should
+
+ align:start position:0%
+important statement maybe I should
+ 
+
+ align:start position:0%
+important statement maybe I should
+rewrite it um yeah let me just re
+
+ align:start position:0%
+rewrite it um yeah let me just re
+ 
+
+ align:start position:0%
+rewrite it um yeah let me just re
+rewrite
+
+ align:start position:0%
+rewrite
+ 
+
+ align:start position:0%
+rewrite
+it so fortive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion fortive pation in n in one / n
+
+ align:start position:0%
+expansion fortive pation in n in one / n
+ 
+
+ align:start position:0%
+expansion fortive pation in n in one / n
+so this is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to semi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classical classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion in h by TAA H
+
+ align:start position:0%
+expansion in h by TAA H
+ 
+
+ align:start position:0%
+expansion in h by TAA H
+scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we will now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show that this guys this Global Theory
+
+ align:start position:0%
+show that this guys this Global Theory
+ 
+
+ align:start position:0%
+show that this guys this Global Theory
+and this semi classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion is actually a string
+
+ align:start position:0%
+expansion is actually a string
+ 
+
+ align:start position:0%
+expansion is actually a string
+theory okay now I will not show that I
+
+ align:start position:0%
+theory okay now I will not show that I
+ 
+
+ align:start position:0%
+theory okay now I will not show that I
+say I will motivate that uh I say that's
+
+ align:start position:0%
+say I will motivate that uh I say that's
+ 
+
+ align:start position:0%
+say I will motivate that uh I say that's
+a stren
+
+ align:start position:0%
+a stren
+ 
+
+ align:start position:0%
+a stren
+theory so so before I go that uh do you
+
+ align:start position:0%
+theory so so before I go that uh do you
+ 
+
+ align:start position:0%
+theory so so before I go that uh do you
+have any
+
+ align:start position:0%
+have any
+ 
+
+ align:start position:0%
+have any
+questions yes just to clarify I mean you
+
+ align:start position:0%
+questions yes just to clarify I mean you
+ 
+
+ align:start position:0%
+questions yes just to clarify I mean you
+I doesn't the sort of second statement
+
+ align:start position:0%
+I doesn't the sort of second statement
+ 
+
+ align:start position:0%
+I doesn't the sort of second statement
+like the fact that perturbation one of R
+
+ align:start position:0%
+like the fact that perturbation one of R
+ 
+
+ align:start position:0%
+like the fact that perturbation one of R
+corresponds to semic classical expansion
+
+ align:start position:0%
+corresponds to semic classical expansion
+ 
+
+ align:start position:0%
+corresponds to semic classical expansion
+in H part it like isn't that just more a
+
+ align:start position:0%
+in H part it like isn't that just more a
+ 
+
+ align:start position:0%
+in H part it like isn't that just more a
+generalization of the thing you just
+
+ align:start position:0%
+generalization of the thing you just
+ 
+
+ align:start position:0%
+generalization of the thing you just
+wrote like you really it's the same
+
+ align:start position:0%
+wrote like you really it's the same
+ 
+
+ align:start position:0%
+wrote like you really it's the same
+statement yeah it's the same statement
+
+ align:start position:0%
+statement yeah it's the same statement
+ 
+
+ align:start position:0%
+statement yeah it's the same statement
+no no no these two statement they are
+
+ align:start position:0%
+no no no these two statement they are
+ 
+
+ align:start position:0%
+no no no these two statement they are
+basically the
+
+ align:start position:0%
+basically the
+ 
+
+ align:start position:0%
+basically the
+same they're not equivalent this is
+
+ align:start position:0%
+same they're not equivalent this is
+ 
+
+ align:start position:0%
+same they're not equivalent this is
+talking about this particular limit okay
+
+ align:start position:0%
+talking about this particular limit okay
+ 
+
+ align:start position:0%
+talking about this particular limit okay
+this is talking about this particular
+
+ align:start position:0%
+this is talking about this particular
+ 
+
+ align:start position:0%
+this is talking about this particular
+limit and this tells you what happens we
+
+ align:start position:0%
+limit and this tells you what happens we
+ 
+
+ align:start position:0%
+limit and this tells you what happens we
+will relax this limit by including the
+
+ align:start position:0%
+will relax this limit by including the
+ 
+
+ align:start position:0%
+will relax this limit by including the
+including F any fact by one n expansion
+
+ align:start position:0%
+including F any fact by one n expansion
+ 
+
+ align:start position:0%
+including F any fact by one n expansion
+and and to make this
+
+ align:start position:0%
+and and to make this
+ 
+
+ align:start position:0%
+and and to make this
+identification so this by itself does
+
+ align:start position:0%
+identification so this by itself does
+ 
+
+ align:start position:0%
+identification so this by itself does
+not imply that because the other way
+
+ align:start position:0%
+not imply that because the other way
+ 
+
+ align:start position:0%
+not imply that because the other way
+does right yeah goes the other way does
+
+ align:start position:0%
+does right yeah goes the other way does
+ 
+
+ align:start position:0%
+does right yeah goes the other way does
+so this is a stronger statement right
+
+ align:start position:0%
+so this is a stronger statement right
+ 
+
+ align:start position:0%
+so this is a stronger statement right
+okay yeah and this
+
+ align:start position:0%
+okay yeah and this
+ 
+
+ align:start position:0%
+okay yeah and this
+statement is supported by just looking
+
+ align:start position:0%
+statement is supported by just looking
+ 
+
+ align:start position:0%
+statement is supported by just looking
+at the leading order Behavior but if you
+
+ align:start position:0%
+at the leading order Behavior but if you
+ 
+
+ align:start position:0%
+at the leading order Behavior but if you
+want to look at but if you want to look
+
+ align:start position:0%
+want to look at but if you want to look
+ 
+
+ align:start position:0%
+want to look at but if you want to look
+at this behavior and then you look at
+
+ align:start position:0%
+at this behavior and then you look at
+ 
+
+ align:start position:0%
+at this behavior and then you look at
+then then you need to look at the sub
+
+ align:start position:0%
+then then you need to look at the sub
+ 
+
+ align:start position:0%
+then then you need to look at the sub
+leing term in one / n say for example
+
+ align:start position:0%
+leing term in one / n say for example
+ 
+
+ align:start position:0%
+leing term in one / n say for example
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+then you see the
+
+ align:start position:0%
+then you see the
+ 
+
+ align:start position:0%
+then you see the
+fluctuation is controlled by one n this
+
+ align:start position:0%
+fluctuation is controlled by one n this
+ 
+
+ align:start position:0%
+fluctuation is controlled by one n this
+negative fluctuation is controlled by H
+
+ align:start position:0%
+negative fluctuation is controlled by H
+ 
+
+ align:start position:0%
+negative fluctuation is controlled by H
+bar and and the similarly here then then
+
+ align:start position:0%
+bar and and the similarly here then then
+ 
+
+ align:start position:0%
+bar and and the similarly here then then
+when you include one of any fact then
+
+ align:start position:0%
+when you include one of any fact then
+ 
+
+ align:start position:0%
+when you include one of any fact then
+you will see single particle now and the
+
+ align:start position:0%
+you will see single particle now and the
+ 
+
+ align:start position:0%
+you will see single particle now and the
+m and the two particle multi particle
+
+ align:start position:0%
+m and the two particle multi particle
+ 
+
+ align:start position:0%
+m and the two particle multi particle
+they can mix together due to
+
+ align:start position:0%
+they can mix together due to
+ 
+
+ align:start position:0%
+they can mix together due to
+fluctuations and again that amplitude is
+
+ align:start position:0%
+fluctuations and again that amplitude is
+ 
+
+ align:start position:0%
+fluctuations and again that amplitude is
+controlled by one n exact yeah just say
+
+ align:start position:0%
+controlled by one n exact yeah just say
+ 
+
+ align:start position:0%
+controlled by one n exact yeah just say
+this statement is is stronger you need
+
+ align:start position:0%
+this statement is is stronger you need
+ 
+
+ align:start position:0%
+this statement is is stronger you need
+to look at the subing fractions
+
+ align:start position:0%
+to look at the subing fractions
+ 
+
+ align:start position:0%
+to look at the subing fractions
+carefully and you see that fits into a h
+
+ align:start position:0%
+carefully and you see that fits into a h
+ 
+
+ align:start position:0%
+carefully and you see that fits into a h
+bar pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes so instead of this operators we
+
+ align:start position:0%
+yeah yes so instead of this operators we
+ 
+
+ align:start position:0%
+yeah yes so instead of this operators we
+consider regular creation destruction
+
+ align:start position:0%
+consider regular creation destruction
+ 
+
+ align:start position:0%
+consider regular creation destruction
+operators we still come to the
+
+ align:start position:0%
+operators we still come to the
+ 
+
+ align:start position:0%
+operators we still come to the
+conclusion that all the gr diagrams are
+
+ align:start position:0%
+conclusion that all the gr diagrams are
+ 
+
+ align:start position:0%
+conclusion that all the gr diagrams are
+stressed yeah that's a good point so in
+
+ align:start position:0%
+stressed yeah that's a good point so in
+ 
+
+ align:start position:0%
+stressed yeah that's a good point so in
+essence you can imagine this o oi each
+
+ align:start position:0%
+essence you can imagine this o oi each
+ 
+
+ align:start position:0%
+essence you can imagine this o oi each
+oi def
+
+ align:start position:0%
+oi def
+ 
+
+ align:start position:0%
+oi def
+defines this point one is precisely this
+
+ align:start position:0%
+defines this point one is precisely this
+ 
+
+ align:start position:0%
+defines this point one is precisely this
+statement is that you can imagine each
+
+ align:start position:0%
+statement is that you can imagine each
+ 
+
+ align:start position:0%
+statement is that you can imagine each
+oi defines a creation defines
+
+ align:start position:0%
+oi defines a creation defines
+ 
+
+ align:start position:0%
+oi defines a creation defines
+independent creation and relation
+
+ align:start position:0%
+independent creation and relation
+ 
+
+ align:start position:0%
+independent creation and relation
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+yeah the still
+
+ align:start position:0%
+yeah the still
+ 
+
+ align:start position:0%
+yeah the still
+have sorry no in the original Theory
+
+ align:start position:0%
+have sorry no in the original Theory
+ 
+
+ align:start position:0%
+have sorry no in the original Theory
+we're not only in N
+
+ align:start position:0%
+we're not only in N
+ 
+
+ align:start position:0%
+we're not only in N
+limit in the original theory in large we
+
+ align:start position:0%
+limit in the original theory in large we
+ 
+
+ align:start position:0%
+limit in the original theory in large we
+do have suppression no you don't have a
+
+ align:start position:0%
+do have suppression no you don't have a
+ 
+
+ align:start position:0%
+do have suppression no you don't have a
+suppression of loop diagram in terms of
+
+ align:start position:0%
+suppression of loop diagram in terms of
+ 
+
+ align:start position:0%
+suppression of loop diagram in terms of
+the standard Loops you only have the
+
+ align:start position:0%
+the standard Loops you only have the
+ 
+
+ align:start position:0%
+the standard Loops you only have the
+suppression of the loop diagram in terms
+
+ align:start position:0%
+suppression of the loop diagram in terms
+ 
+
+ align:start position:0%
+suppression of the loop diagram in terms
+of those Loops in terms of Loops of
+
+ align:start position:0%
+of those Loops in terms of Loops of
+ 
+
+ align:start position:0%
+of those Loops in terms of Loops of
+globos but here we don't specify like
+
+ align:start position:0%
+globos but here we don't specify like
+ 
+
+ align:start position:0%
+globos but here we don't specify like
+don't put any restrictions on what are
+
+ align:start position:0%
+don't put any restrictions on what are
+ 
+
+ align:start position:0%
+don't put any restrictions on what are
+the operators o so why can't we say just
+
+ align:start position:0%
+the operators o so why can't we say just
+ 
+
+ align:start position:0%
+the operators o so why can't we say just
+o i is just side side I no no no o is
+
+ align:start position:0%
+o i is just side side I no no no o is
+ 
+
+ align:start position:0%
+o i is just side side I no no no o is
+gaging varant operator o is composite
+
+ align:start position:0%
+gaging varant operator o is composite
+ 
+
+ align:start position:0%
+gaging varant operator o is composite
+operator or is some composite operator
+
+ align:start position:0%
+operator or is some composite operator
+ 
+
+ align:start position:0%
+operator or is some composite operator
+so so for example in the in the yam the
+
+ align:start position:0%
+so so for example in the in the yam the
+ 
+
+ align:start position:0%
+so so for example in the in the yam the
+so one example is O can be Chace F
+
+ align:start position:0%
+so one example is O can be Chace F
+ 
+
+ align:start position:0%
+so one example is O can be Chace F
+squ so if you look at the twoo function
+
+ align:start position:0%
+squ so if you look at the twoo function
+ 
+
+ align:start position:0%
+squ so if you look at the twoo function
+of O then that corresponding to two Glon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propagators two Glon propagators and so
+
+ align:start position:0%
+propagators two Glon propagators and so
+ 
+
+ align:start position:0%
+propagators two Glon propagators and so
+you have loops
+
+ align:start position:0%
+you have loops
+ 
+
+ align:start position:0%
+you have loops
+here but but this is not the loop in
+
+ align:start position:0%
+here but but this is not the loop in
+ 
+
+ align:start position:0%
+here but but this is not the loop in
+terms of the globall here when we talk
+
+ align:start position:0%
+terms of the globall here when we talk
+ 
+
+ align:start position:0%
+terms of the globall here when we talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+loops yeah so let me emphasize all Loops
+
+ align:start position:0%
+loops yeah so let me emphasize all Loops
+ 
+
+ align:start position:0%
+loops yeah so let me emphasize all Loops
+of global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because here so the key of this
+
+ align:start position:0%
+because here so the key of this
+ 
+
+ align:start position:0%
+because here so the key of this
+statement is that in the Lan limit and
+
+ align:start position:0%
+statement is that in the Lan limit and
+ 
+
+ align:start position:0%
+statement is that in the Lan limit and
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+consider if our thing is caging
+
+ align:start position:0%
+consider if our thing is caging
+ 
+
+ align:start position:0%
+consider if our thing is caging
+operators then that's the AIC you should
+
+ align:start position:0%
+operators then that's the AIC you should
+ 
+
+ align:start position:0%
+operators then that's the AIC you should
+consider and and you should not worry
+
+ align:start position:0%
+consider and and you should not worry
+ 
+
+ align:start position:0%
+consider and and you should not worry
+about the original stuff and those they
+
+ align:start position:0%
+about the original stuff and those they
+ 
+
+ align:start position:0%
+about the original stuff and those they
+have loops Etc have fin H bar Etc but in
+
+ align:start position:0%
+have loops Etc have fin H bar Etc but in
+ 
+
+ align:start position:0%
+have loops Etc have fin H bar Etc but in
+terms of the in terms of those gloal
+
+ align:start position:0%
+terms of the in terms of those gloal
+ 
+
+ align:start position:0%
+terms of the in terms of those gloal
+then you have a classical Theory there's
+
+ align:start position:0%
+then you have a classical Theory there's
+ 
+
+ align:start position:0%
+then you have a classical Theory there's
+no Loops you only have two level
+
+ align:start position:0%
+no Loops you only have two level
+ 
+
+ align:start position:0%
+no Loops you only have two level
+scattering in the lar limit
+
+ align:start position:0%
+scattering in the lar limit
+ 
+
+ align:start position:0%
+scattering in the lar limit
+yes uh so are we talking about a general
+
+ align:start position:0%
+yes uh so are we talking about a general
+ 
+
+ align:start position:0%
+yes uh so are we talking about a general
+like gaug and variant operators or
+
+ align:start position:0%
+like gaug and variant operators or
+ 
+
+ align:start position:0%
+like gaug and variant operators or
+explicitly single
+
+ align:start position:0%
+explicitly single
+ 
+
+ align:start position:0%
+explicitly single
+operators no no no I have to talk about
+
+ align:start position:0%
+operators no no no I have to talk about
+ 
+
+ align:start position:0%
+operators no no no I have to talk about
+everything okay so I mean like the the
+
+ align:start position:0%
+everything okay so I mean like the the
+ 
+
+ align:start position:0%
+everything okay so I mean like the the
+single a single o operator is can be
+
+ align:start position:0%
+single a single o operator is can be
+ 
+
+ align:start position:0%
+single a single o operator is can be
+several traces no no no single O is a
+
+ align:start position:0%
+several traces no no no single O is a
+ 
+
+ align:start position:0%
+several traces no no no single O is a
+single trace no single O is a single
+
+ align:start position:0%
+single trace no single O is a single
+ 
+
+ align:start position:0%
+single trace no single O is a single
+trace that defined there what about like
+
+ align:start position:0%
+trace that defined there what about like
+ 
+
+ align:start position:0%
+trace that defined there what about like
+non-ra gaug variance operators we don't
+
+ align:start position:0%
+non-ra gaug variance operators we don't
+ 
+
+ align:start position:0%
+non-ra gaug variance operators we don't
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+them you mean non gaug ining operator
+
+ align:start position:0%
+them you mean non gaug ining operator
+ 
+
+ align:start position:0%
+them you mean non gaug ining operator
+now every gaug in operator always
+
+ align:start position:0%
+now every gaug in operator always
+ 
+
+ align:start position:0%
+now every gaug in operator always
+involve Chace yeah
+
+ align:start position:0%
+involve Chace yeah
+ 
+
+ align:start position:0%
+involve Chace yeah
+sure you will be a famous mathematician
+
+ align:start position:0%
+sure you will be a famous mathematician
+ 
+
+ align:start position:0%
+sure you will be a famous mathematician
+if you can construct something in warant
+
+ align:start position:0%
+if you can construct something in warant
+ 
+
+ align:start position:0%
+if you can construct something in warant
+which does not involve
+
+ align:start position:0%
+which does not involve
+ 
+
+ align:start position:0%
+which does not involve
+Choice yeah construct something about
+
+ align:start position:0%
+Choice yeah construct something about
+ 
+
+ align:start position:0%
+Choice yeah construct something about
+the Matrix yeah use
+
+ align:start position:0%
+the Matrix yeah use
+ 
+
+ align:start position:0%
+the Matrix yeah use
+something construct something using
+
+ align:start position:0%
+something construct something using
+ 
+
+ align:start position:0%
+something construct something using
+matrices which does not involve in
+
+ align:start position:0%
+matrices which does not involve in
+ 
+
+ align:start position:0%
+matrices which does not involve in
+traces yeah even if you do determinant
+
+ align:start position:0%
+traces yeah even if you do determinant
+ 
+
+ align:start position:0%
+traces yeah even if you do determinant
+and determinant can still be written as
+
+ align:start position:0%
+and determinant can still be written as
+ 
+
+ align:start position:0%
+and determinant can still be written as
+traces and yeah yeah just everything can
+
+ align:start position:0%
+traces and yeah yeah just everything can
+ 
+
+ align:start position:0%
+traces and yeah yeah just everything can
+be written as
+
+ align:start position:0%
+be written as
+ 
+
+ align:start position:0%
+be written as
+CH so determinant would just have if you
+
+ align:start position:0%
+CH so determinant would just have if you
+ 
+
+ align:start position:0%
+CH so determinant would just have if you
+have a determinant operator that can
+
+ align:start position:0%
+have a determinant operator that can
+ 
+
+ align:start position:0%
+have a determinant operator that can
+just be written as like a product of
+
+ align:start position:0%
+just be written as like a product of
+ 
+
+ align:start position:0%
+just be written as like a product of
+many that's right that's right that's
+
+ align:start position:0%
+many that's right that's right that's
+ 
+
+ align:start position:0%
+many that's right that's right that's
+right that's right good any other
+
+ align:start position:0%
+right that's right good any other
+ 
+
+ align:start position:0%
+right that's right good any other
+questions yes clarify we' been talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about yeah here we are talking about
+
+ align:start position:0%
+about yeah here we are talking about
+ 
+
+ align:start position:0%
+about yeah here we are talking about
+only every field is Matrix valued Fields
+
+ align:start position:0%
+only every field is Matrix valued Fields
+ 
+
+ align:start position:0%
+only every field is Matrix valued Fields
+yeah just every field is Matrix valued
+
+ align:start position:0%
+yeah just every field is Matrix valued
+ 
+
+ align:start position:0%
+yeah just every field is Matrix valued
+Fields yeah yes
+
+ align:start position:0%
+Fields yeah yes
+ 
+
+ align:start position:0%
+Fields yeah yes
+uh I don't know I just uh I thought
+
+ align:start position:0%
+uh I don't know I just uh I thought
+ 
+
+ align:start position:0%
+uh I don't know I just uh I thought
+there was more um invari invariance even
+
+ align:start position:0%
+there was more um invari invariance even
+ 
+
+ align:start position:0%
+there was more um invari invariance even
+construct out of a matrix um like I was
+
+ align:start position:0%
+construct out of a matrix um like I was
+ 
+
+ align:start position:0%
+construct out of a matrix um like I was
+asking you the other day um basically
+
+ align:start position:0%
+asking you the other day um basically
+ 
+
+ align:start position:0%
+asking you the other day um basically
+it's all the each one of the
+
+ align:start position:0%
+it's all the each one of the
+ 
+
+ align:start position:0%
+it's all the each one of the
+coefficients of the characteristic polom
+
+ align:start position:0%
+coefficients of the characteristic polom
+ 
+
+ align:start position:0%
+coefficients of the characteristic polom
+of a mat yeah they can written they can
+
+ align:start position:0%
+of a mat yeah they can written they can
+ 
+
+ align:start position:0%
+of a mat yeah they can written they can
+be written as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traces yeah they can be Reas
+
+ align:start position:0%
+traces yeah they can be Reas
+ 
+
+ align:start position:0%
+traces yeah they can be Reas
+ches
+
+ align:start position:0%
+ches
+ 
+
+ align:start position:0%
+ches
+yeah case of discuss qus here yeah yeah
+
+ align:start position:0%
+yeah case of discuss qus here yeah yeah
+ 
+
+ align:start position:0%
+yeah case of discuss qus here yeah yeah
+here we have the not this quarks and
+
+ align:start position:0%
+here we have the not this quarks and
+ 
+
+ align:start position:0%
+here we have the not this quarks and
+we're going to mention quarks very
+
+ align:start position:0%
+we're going to mention quarks very
+ 
+
+ align:start position:0%
+we're going to mention quarks very
+briefly at the end
+
+ align:start position:0%
+briefly at the end
+ 
+
+ align:start position:0%
+briefly at the end
+yeah any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions good good okay so now let's
+
+ align:start position:0%
+questions good good okay so now let's
+ 
+
+ align:start position:0%
+questions good good okay so now let's
+talk about a little bit about String
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory maybe I will leave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+that let me see where the leave that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me leave that oh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first I we talk a little bit about
+
+ align:start position:0%
+so first I we talk a little bit about
+ 
+
+ align:start position:0%
+so first I we talk a little bit about
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings so first let me remind you Q
+
+ align:start position:0%
+strings so first let me remind you Q
+ 
+
+ align:start position:0%
+strings so first let me remind you Q
+qft normally when we say a qft we say
+
+ align:start position:0%
+qft normally when we say a qft we say
+ 
+
+ align:start position:0%
+qft normally when we say a qft we say
+qft is a theory of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles or particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the standard approach to the qft
+
+ align:start position:0%
+okay so the standard approach to the qft
+ 
+
+ align:start position:0%
+okay so the standard approach to the qft
+is that you write down a field
+
+ align:start position:0%
+is that you write down a field
+ 
+
+ align:start position:0%
+is that you write down a field
+Lin and then you quantize ex so this is
+
+ align:start position:0%
+Lin and then you quantize ex so this is
+ 
+
+ align:start position:0%
+Lin and then you quantize ex so this is
+normally called the second quanti so the
+
+ align:start position:0%
+normally called the second quanti so the
+ 
+
+ align:start position:0%
+normally called the second quanti so the
+standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach is called second Quan approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second quantise approach
+
+ align:start position:0%
+second quantise approach
+ 
+
+ align:start position:0%
+second quantise approach
+okay but there also exists a first
+
+ align:start position:0%
+okay but there also exists a first
+ 
+
+ align:start position:0%
+okay but there also exists a first
+quantise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach there also exist a first quanti
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach there also exist a first Quant
+
+ align:start position:0%
+approach there also exist a first Quant
+ 
+
+ align:start position:0%
+approach there also exist a first Quant
+approach is that you directly Quant
+
+ align:start position:0%
+approach is that you directly Quant
+ 
+
+ align:start position:0%
+approach is that you directly Quant
+you just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantize Quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion say or for a particle or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles say oh say say let's consider
+
+ align:start position:0%
+particles say oh say say let's consider
+ 
+
+ align:start position:0%
+particles say oh say say let's consider
+one particle say a particle in space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so for example if you can see the
+
+ align:start position:0%
+okay so for example if you can see the
+ 
+
+ align:start position:0%
+okay so for example if you can see the
+particle propagate in space time along
+
+ align:start position:0%
+particle propagate in space time along
+ 
+
+ align:start position:0%
+particle propagate in space time along
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+trajectory so this parameterize this
+
+ align:start position:0%
+trajectory so this parameterize this
+ 
+
+ align:start position:0%
+trajectory so this parameterize this
+trajectory say using a parameter by tow
+
+ align:start position:0%
+trajectory say using a parameter by tow
+ 
+
+ align:start position:0%
+trajectory say using a parameter by tow
+which label the point along the
+
+ align:start position:0%
+which label the point along the
+ 
+
+ align:start position:0%
+which label the point along the
+trajectory and then so this will give
+
+ align:start position:0%
+trajectory and then so this will give
+ 
+
+ align:start position:0%
+trajectory and then so this will give
+you a
+
+ align:start position:0%
+you a
+ 
+
+ align:start position:0%
+you a
+mapping say say the trajectory will map
+
+ align:start position:0%
+mapping say say the trajectory will map
+ 
+
+ align:start position:0%
+mapping say say the trajectory will map
+out the trajectory yeah so this will map
+
+ align:start position:0%
+out the trajectory yeah so this will map
+ 
+
+ align:start position:0%
+out the trajectory yeah so this will map
+out the trajectory space time which can
+
+ align:start position:0%
+out the trajectory space time which can
+ 
+
+ align:start position:0%
+out the trajectory space time which can
+be written as a space time coordinate as
+
+ align:start position:0%
+be written as a space time coordinate as
+ 
+
+ align:start position:0%
+be written as a space time coordinate as
+a function of t
+
+ align:start position:0%
+a function of t
+ 
+
+ align:start position:0%
+a function of t
+okay so this par so this parameterize
+
+ align:start position:0%
+okay so this par so this parameterize
+ 
+
+ align:start position:0%
+okay so this par so this parameterize
+the w nine of the
+
+ align:start position:0%
+the w nine of the
+ 
+
+ align:start position:0%
+the w nine of the
+particle so this parameter is the w nine
+
+ align:start position:0%
+particle so this parameter is the w nine
+ 
+
+ align:start position:0%
+particle so this parameter is the w nine
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+particle and
+
+ align:start position:0%
+particle and
+ 
+
+ align:start position:0%
+particle and
+uh to quantize the
+
+ align:start position:0%
+uh to quantize the
+ 
+
+ align:start position:0%
+uh to quantize the
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+particle the the Quant the particle the
+
+ align:start position:0%
+particle the the Quant the particle the
+ 
+
+ align:start position:0%
+particle the the Quant the particle the
+simplest way is you imagine
+
+ align:start position:0%
+simplest way is you imagine
+ 
+
+ align:start position:0%
+simplest way is you imagine
+just sum over all possible Paths of the
+
+ align:start position:0%
+just sum over all possible Paths of the
+ 
+
+ align:start position:0%
+just sum over all possible Paths of the
+particle so essentially we're doing a
+
+ align:start position:0%
+particle so essentially we're doing a
+ 
+
+ align:start position:0%
+particle so essentially we're doing a
+path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral essentially you're doing a path
+
+ align:start position:0%
+integral essentially you're doing a path
+ 
+
+ align:start position:0%
+integral essentially you're doing a path
+integral so you you you just integrate
+
+ align:start position:0%
+integral so you you you just integrate
+ 
+
+ align:start position:0%
+integral so you you you just integrate
+of all possible path of a particle and
+
+ align:start position:0%
+of all possible path of a particle and
+ 
+
+ align:start position:0%
+of all possible path of a particle and
+then this essentially a Quantum motion
+
+ align:start position:0%
+then this essentially a Quantum motion
+ 
+
+ align:start position:0%
+then this essentially a Quantum motion
+just Quantum mechanically you can
+
+ align:start position:0%
+just Quantum mechanically you can
+ 
+
+ align:start position:0%
+just Quantum mechanically you can
+fluctuate any way and then this particle
+
+ align:start position:0%
+fluctuate any way and then this particle
+ 
+
+ align:start position:0%
+fluctuate any way and then this particle
+then this
+
+ align:start position:0%
+then this
+ 
+
+ align:start position:0%
+then this
+action for the particle essentially it
+
+ align:start position:0%
+action for the particle essentially it
+ 
+
+ align:start position:0%
+action for the particle essentially it
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+it's the the
+
+ align:start position:0%
+it's the the
+ 
+
+ align:start position:0%
+it's the the
+length so suppose the particle have mass
+
+ align:start position:0%
+length so suppose the particle have mass
+ 
+
+ align:start position:0%
+length so suppose the particle have mass
+m it's just the length of the particle
+
+ align:start position:0%
+m it's just the length of the particle
+ 
+
+ align:start position:0%
+m it's just the length of the particle
+DL along the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+okay and if you include
+
+ align:start position:0%
+okay and if you include
+ 
+
+ align:start position:0%
+okay and if you include
+interactions then you you have to
+
+ align:start position:0%
+interactions then you you have to
+ 
+
+ align:start position:0%
+interactions then you you have to
+include the trajectory with the particle
+
+ align:start position:0%
+include the trajectory with the particle
+ 
+
+ align:start position:0%
+include the trajectory with the particle
+can split say uh say say line can split
+
+ align:start position:0%
+can split say uh say say line can split
+ 
+
+ align:start position:0%
+can split say uh say say line can split
+in two lines Etc so this give you
+
+ align:start position:0%
+in two lines Etc so this give you
+ 
+
+ align:start position:0%
+in two lines Etc so this give you
+interactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this and this you need to add
+
+ align:start position:0%
+okay and this and this you need to add
+ 
+
+ align:start position:0%
+okay and this and this you need to add
+by hand because the particle in
+
+ align:start position:0%
+by hand because the particle in
+ 
+
+ align:start position:0%
+by hand because the particle in
+principle can because you can draw
+
+ align:start position:0%
+principle can because you can draw
+ 
+
+ align:start position:0%
+principle can because you can draw
+infinite ways of particle split into
+
+ align:start position:0%
+infinite ways of particle split into
+ 
+
+ align:start position:0%
+infinite ways of particle split into
+more particles Etc so depend on your
+
+ align:start position:0%
+more particles Etc so depend on your
+ 
+
+ align:start position:0%
+more particles Etc so depend on your
+specific series you need specify say the
+
+ align:start position:0%
+specific series you need specify say the
+ 
+
+ align:start position:0%
+specific series you need specify say the
+interactions so this you need add by
+
+ align:start position:0%
+interactions so this you need add by
+ 
+
+ align:start position:0%
+interactions so this you need add by
+hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so in principle you can forget
+
+ align:start position:0%
+okay so so in principle you can forget
+ 
+
+ align:start position:0%
+okay so so in principle you can forget
+about the standard formulation of
+
+ align:start position:0%
+about the standard formulation of
+ 
+
+ align:start position:0%
+about the standard formulation of
+quantum field Theory just to to work
+
+ align:start position:0%
+quantum field Theory just to to work
+ 
+
+ align:start position:0%
+quantum field Theory just to to work
+with this particle theory just work with
+
+ align:start position:0%
+with this particle theory just work with
+ 
+
+ align:start position:0%
+with this particle theory just work with
+this particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory so the string theory is a
+
+ align:start position:0%
+theory so the string theory is a
+ 
+
+ align:start position:0%
+theory so the string theory is a
+generalization of this uh first quanti
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach so the string the that is
+
+ align:start position:0%
+approach so the string the that is
+ 
+
+ align:start position:0%
+approach so the string the that is
+currently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formulated is formulated in this first
+
+ align:start position:0%
+formulated is formulated in this first
+ 
+
+ align:start position:0%
+formulated is formulated in this first
+quantize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach so you just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantize motion of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string in space time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for simp for
+
+ align:start position:0%
+okay so for simp for
+ 
+
+ align:start position:0%
+okay so for simp for
+example so particle case you have a
+
+ align:start position:0%
+example so particle case you have a
+ 
+
+ align:start position:0%
+example so particle case you have a
+point particle string case you have
+
+ align:start position:0%
+point particle string case you have
+ 
+
+ align:start position:0%
+point particle string case you have
+a you have a close noops so imagine we
+
+ align:start position:0%
+a you have a close noops so imagine we
+ 
+
+ align:start position:0%
+a you have a close noops so imagine we
+have a close string okay you have a
+
+ align:start position:0%
+have a close string okay you have a
+ 
+
+ align:start position:0%
+have a close string okay you have a
+close string a string is a one
+
+ align:start position:0%
+close string a string is a one
+ 
+
+ align:start position:0%
+close string a string is a one
+dimensional object so let's consider
+
+ align:start position:0%
+dimensional object so let's consider
+ 
+
+ align:start position:0%
+dimensional object so let's consider
+close string then then the string can be
+
+ align:start position:0%
+close string then then the string can be
+ 
+
+ align:start position:0%
+close string then then the string can be
+parameterized so string itself can be
+
+ align:start position:0%
+parameterized so string itself can be
+ 
+
+ align:start position:0%
+parameterized so string itself can be
+parameterized by parameter Sigma along
+
+ align:start position:0%
+parameterized by parameter Sigma along
+ 
+
+ align:start position:0%
+parameterized by parameter Sigma along
+the along the
+
+ align:start position:0%
+the along the
+ 
+
+ align:start position:0%
+the along the
+string but then then this string can
+
+ align:start position:0%
+string but then then this string can
+ 
+
+ align:start position:0%
+string but then then this string can
+move in the space
+
+ align:start position:0%
+move in the space
+ 
+
+ align:start position:0%
+move in the space
+time then it will Trace out some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trajectory Trace out some
+
+ align:start position:0%
+trajectory Trace out some
+ 
+
+ align:start position:0%
+trajectory Trace out some
+trajectory uh TR some
+
+ align:start position:0%
+trajectory uh TR some
+ 
+
+ align:start position:0%
+trajectory uh TR some
+trajectory um so this give rise to W
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sheet so in the particle case you have a
+
+ align:start position:0%
+sheet so in the particle case you have a
+ 
+
+ align:start position:0%
+sheet so in the particle case you have a
+w nine so so in the string case you have
+
+ align:start position:0%
+w nine so so in the string case you have
+ 
+
+ align:start position:0%
+w nine so so in the string case you have
+have a w sheet which we normally called
+
+ align:start position:0%
+have a w sheet which we normally called
+ 
+
+ align:start position:0%
+have a w sheet which we normally called
+Sigma and then the sigma can be again
+
+ align:start position:0%
+Sigma and then the sigma can be again
+ 
+
+ align:start position:0%
+Sigma and then the sigma can be again
+written in terms of the space time
+
+ align:start position:0%
+written in terms of the space time
+ 
+
+ align:start position:0%
+written in terms of the space time
+coordinates as a function of this T and
+
+ align:start position:0%
+coordinates as a function of this T and
+ 
+
+ align:start position:0%
+coordinates as a function of this T and
+sigma okay so now you have two
+
+ align:start position:0%
+sigma okay so now you have two
+ 
+
+ align:start position:0%
+sigma okay so now you have two
+coordinate to parameterize this W
+
+ align:start position:0%
+coordinate to parameterize this W
+ 
+
+ align:start position:0%
+coordinate to parameterize this W
+sheet so this is essentially a two
+
+ align:start position:0%
+sheet so this is essentially a two
+ 
+
+ align:start position:0%
+sheet so this is essentially a two
+dimensional essentially you have two
+
+ align:start position:0%
+dimensional essentially you have two
+ 
+
+ align:start position:0%
+dimensional essentially you have two
+dimensional surface in the space time
+
+ align:start position:0%
+dimensional surface in the space time
+ 
+
+ align:start position:0%
+dimensional surface in the space time
+embedded in space time and and the
+
+ align:start position:0%
+embedded in space time and and the
+ 
+
+ align:start position:0%
+embedded in space time and and the
+string theory just
+
+ align:start position:0%
+string theory just
+ 
+
+ align:start position:0%
+string theory just
+quantize uh it
+
+ align:start position:0%
+quantize uh it
+ 
+
+ align:start position:0%
+quantize uh it
+you just consider the uh the motion of
+
+ align:start position:0%
+you just consider the uh the motion of
+ 
+
+ align:start position:0%
+you just consider the uh the motion of
+all such kind of surfaces yes so in the
+
+ align:start position:0%
+all such kind of surfaces yes so in the
+ 
+
+ align:start position:0%
+all such kind of surfaces yes so in the
+case of a single particle we have a
+
+ align:start position:0%
+case of a single particle we have a
+ 
+
+ align:start position:0%
+case of a single particle we have a
+point does this action actually repr
+
+ align:start position:0%
+point does this action actually repr
+ 
+
+ align:start position:0%
+point does this action actually repr
+like what does it reproduce exactly like
+
+ align:start position:0%
+like what does it reproduce exactly like
+ 
+
+ align:start position:0%
+like what does it reproduce exactly like
+does it is it capable of reproducing all
+
+ align:start position:0%
+does it is it capable of reproducing all
+ 
+
+ align:start position:0%
+does it is it capable of reproducing all
+of quantum field Theory using this pH
+
+ align:start position:0%
+of quantum field Theory using this pH
+ 
+
+ align:start position:0%
+of quantum field Theory using this pH
+yeah in principle but it's not
+
+ align:start position:0%
+yeah in principle but it's not
+ 
+
+ align:start position:0%
+yeah in principle but it's not
+convenient depend on yeah for example if
+
+ align:start position:0%
+convenient depend on yeah for example if
+ 
+
+ align:start position:0%
+convenient depend on yeah for example if
+you have a scaler particle this can
+
+ align:start position:0%
+you have a scaler particle this can
+ 
+
+ align:start position:0%
+you have a scaler particle this can
+certainly uh uh easily reproduce your
+
+ align:start position:0%
+certainly uh uh easily reproduce your
+ 
+
+ align:start position:0%
+certainly uh uh easily reproduce your
+free scaler field the yeah and if you
+
+ align:start position:0%
+free scaler field the yeah and if you
+ 
+
+ align:start position:0%
+free scaler field the yeah and if you
+want to reproduce five cube Theory then
+
+ align:start position:0%
+want to reproduce five cube Theory then
+ 
+
+ align:start position:0%
+want to reproduce five cube Theory then
+you need to add this kind of splitting
+
+ align:start position:0%
+you need to add this kind of splitting
+ 
+
+ align:start position:0%
+you need to add this kind of splitting
+in your when you uh when you do your P
+
+ align:start position:0%
+in your when you uh when you do your P
+ 
+
+ align:start position:0%
+in your when you uh when you do your P
+inte including the trajectories you need
+
+ align:start position:0%
+inte including the trajectories you need
+ 
+
+ align:start position:0%
+inte including the trajectories you need
+to include this kind of trajectories ET
+
+ align:start position:0%
+to include this kind of trajectories ET
+ 
+
+ align:start position:0%
+to include this kind of trajectories ET
+yeah in principle you can do it it's not
+
+ align:start position:0%
+yeah in principle you can do it it's not
+ 
+
+ align:start position:0%
+yeah in principle you can do it it's not
+very convenient I see okay probably
+
+ align:start position:0%
+very convenient I see okay probably
+ 
+
+ align:start position:0%
+very convenient I see okay probably
+interesting yes how do you add
+
+ align:start position:0%
+interesting yes how do you add
+ 
+
+ align:start position:0%
+interesting yes how do you add
+interactions by hand in that par oh well
+
+ align:start position:0%
+interactions by hand in that par oh well
+ 
+
+ align:start position:0%
+interactions by hand in that par oh well
+you just
+
+ align:start position:0%
+you just
+ 
+
+ align:start position:0%
+you just
+require you just in the past integral
+
+ align:start position:0%
+require you just in the past integral
+ 
+
+ align:start position:0%
+require you just in the past integral
+you in the in the yeah here you
+
+ align:start position:0%
+you in the in the yeah here you
+ 
+
+ align:start position:0%
+you in the in the yeah here you
+integrate of all such kind of paths
+
+ align:start position:0%
+integrate of all such kind of paths
+ 
+
+ align:start position:0%
+integrate of all such kind of paths
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and then you have prescription you say
+
+ align:start position:0%
+and then you have prescription you say
+ 
+
+ align:start position:0%
+and then you have prescription you say
+what kind of pass to
+
+ align:start position:0%
+what kind of pass to
+ 
+
+ align:start position:0%
+what kind of pass to
+include and uh and and and for example
+
+ align:start position:0%
+include and uh and and and for example
+ 
+
+ align:start position:0%
+include and uh and and and for example
+if I have five cube kind of interaction
+
+ align:start position:0%
+if I have five cube kind of interaction
+ 
+
+ align:start position:0%
+if I have five cube kind of interaction
+then you say we should include this kind
+
+ align:start position:0%
+then you say we should include this kind
+ 
+
+ align:start position:0%
+then you say we should include this kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+pass by the case it cannot be paramed as
+
+ align:start position:0%
+pass by the case it cannot be paramed as
+ 
+
+ align:start position:0%
+pass by the case it cannot be paramed as
+top because it has the branch yeah yeah
+
+ align:start position:0%
+top because it has the branch yeah yeah
+ 
+
+ align:start position:0%
+top because it has the branch yeah yeah
+then you have to uh uh uh uh uh yeah
+
+ align:start position:0%
+then you have to uh uh uh uh uh yeah
+ 
+
+ align:start position:0%
+then you have to uh uh uh uh uh yeah
+then you yeah then there technical
+
+ align:start position:0%
+then you yeah then there technical
+ 
+
+ align:start position:0%
+then you yeah then there technical
+complications in doing this
+
+ align:start position:0%
+complications in doing this
+ 
+
+ align:start position:0%
+complications in doing this
+Etc so one more question is string
+
+ align:start position:0%
+Etc so one more question is string
+ 
+
+ align:start position:0%
+Etc so one more question is string
+theory formulated in terms of second is
+
+ align:start position:0%
+theory formulated in terms of second is
+ 
+
+ align:start position:0%
+theory formulated in terms of second is
+it possible to formulate in terms of
+
+ align:start position:0%
+it possible to formulate in terms of
+ 
+
+ align:start position:0%
+it possible to formulate in terms of
+second qu
+
+ align:start position:0%
+second qu
+ 
+
+ align:start position:0%
+second qu
+not um not right
+
+ align:start position:0%
+not um not right
+ 
+
+ align:start position:0%
+not um not right
+now so people have people have written
+
+ align:start position:0%
+now so people have people have written
+ 
+
+ align:start position:0%
+now so people have people have written
+down classical stream field Theory and
+
+ align:start position:0%
+down classical stream field Theory and
+ 
+
+ align:start position:0%
+down classical stream field Theory and
+in principle you can quantize it but
+
+ align:start position:0%
+in principle you can quantize it but
+ 
+
+ align:start position:0%
+in principle you can quantize it but
+that's a very complicated thing I think
+
+ align:start position:0%
+that's a very complicated thing I think
+ 
+
+ align:start position:0%
+that's a very complicated thing I think
+nobody have successfully quantized even
+
+ align:start position:0%
+nobody have successfully quantized even
+ 
+
+ align:start position:0%
+nobody have successfully quantized even
+to write down the Ser is very long
+
+ align:start position:0%
+to write down the Ser is very long
+ 
+
+ align:start position:0%
+to write down the Ser is very long
+trivial
+
+ align:start position:0%
+trivial
+ 
+
+ align:start position:0%
+trivial
+okay so so the similar to do conation
+
+ align:start position:0%
+okay so so the similar to do conation
+ 
+
+ align:start position:0%
+okay so so the similar to do conation
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+string you just look at the be you just
+
+ align:start position:0%
+string you just look at the be you just
+ 
+
+ align:start position:0%
+string you just look at the be you just
+consider the pass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so in principle to do the
+
+ align:start position:0%
+integral so in principle to do the
+ 
+
+ align:start position:0%
+integral so in principle to do the
+quanti the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string you can again just imagine you
+
+ align:start position:0%
+string you can again just imagine you
+ 
+
+ align:start position:0%
+string you can again just imagine you
+sum over all
+
+ align:start position:0%
+sum over all
+ 
+
+ align:start position:0%
+sum over all
+possible worksheet
+
+ align:start position:0%
+possible worksheet
+ 
+
+ align:start position:0%
+possible worksheet
+configurations or possible this kind of
+
+ align:start position:0%
+configurations or possible this kind of
+ 
+
+ align:start position:0%
+configurations or possible this kind of
+two diens iding of this two dimensional
+
+ align:start position:0%
+two diens iding of this two dimensional
+ 
+
+ align:start position:0%
+two diens iding of this two dimensional
+surface in space time then that
+
+ align:start position:0%
+surface in space time then that
+ 
+
+ align:start position:0%
+surface in space time then that
+essentially uh give rise to all kind of
+
+ align:start position:0%
+essentially uh give rise to all kind of
+ 
+
+ align:start position:0%
+essentially uh give rise to all kind of
+stream motions okay so weighted by some
+
+ align:start position:0%
+stream motions okay so weighted by some
+ 
+
+ align:start position:0%
+stream motions okay so weighted by some
+string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action so the simplest way to write down
+
+ align:start position:0%
+action so the simplest way to write down
+ 
+
+ align:start position:0%
+action so the simplest way to write down
+the string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action it's a straightforward generation
+
+ align:start position:0%
+action it's a straightforward generation
+ 
+
+ align:start position:0%
+action it's a straightforward generation
+of this particle
+
+ align:start position:0%
+of this particle
+ 
+
+ align:start position:0%
+of this particle
+case you say you just integrate over its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area so here is just the length of the
+
+ align:start position:0%
+area so here is just the length of the
+ 
+
+ align:start position:0%
+area so here is just the length of the
+string here is the area but here we also
+
+ align:start position:0%
+string here is the area but here we also
+ 
+
+ align:start position:0%
+string here is the area but here we also
+need to
+
+ align:start position:0%
+need to
+ 
+
+ align:start position:0%
+need to
+include uh so here is the particle Mass
+
+ align:start position:0%
+include uh so here is the particle Mass
+ 
+
+ align:start position:0%
+include uh so here is the particle Mass
+so generation of the particle
+
+ align:start position:0%
+so generation of the particle
+ 
+
+ align:start position:0%
+so generation of the particle
+mass is the say So-Cal string
+
+ align:start position:0%
+mass is the say So-Cal string
+ 
+
+ align:start position:0%
+mass is the say So-Cal string
+tension so T which is normally written
+
+ align:start position:0%
+tension so T which is normally written
+ 
+
+ align:start position:0%
+tension so T which is normally written
+as two alpha Prime so you introduce a
+
+ align:start position:0%
+as two alpha Prime so you introduce a
+ 
+
+ align:start position:0%
+as two alpha Prime so you introduce a
+parameter you introduce a dimensional
+
+ align:start position:0%
+parameter you introduce a dimensional
+ 
+
+ align:start position:0%
+parameter you introduce a dimensional
+parameter Alpha Prime to parameterize
+
+ align:start position:0%
+parameter Alpha Prime to parameterize
+ 
+
+ align:start position:0%
+parameter Alpha Prime to parameterize
+this T and so this is a string tension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is mass per
+
+ align:start position:0%
+so this is mass per
+ 
+
+ align:start position:0%
+so this is mass per
+unit Str tension just ma mass per unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay and and this is normally called the
+
+ align:start position:0%
+okay and and this is normally called the
+ 
+
+ align:start position:0%
+okay and and this is normally called the
+lambug go
+
+ align:start position:0%
+lambug go
+ 
+
+ align:start position:0%
+lambug go
+action so NG so this is lambug goo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action who first wrote it down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this so This the a is
+
+ align:start position:0%
+okay so this so This the a is
+ 
+
+ align:start position:0%
+okay so this so This the a is
+essentially just the area of the surface
+
+ align:start position:0%
+essentially just the area of the surface
+ 
+
+ align:start position:0%
+essentially just the area of the surface
+in the space time okay it just St
+
+ align:start position:0%
+in the space time okay it just St
+ 
+
+ align:start position:0%
+in the space time okay it just St
+generalization of the lens of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traj and
+
+ align:start position:0%
+traj and
+ 
+
+ align:start position:0%
+traj and
+uh yeah depend on the warries depend on
+
+ align:start position:0%
+uh yeah depend on the warries depend on
+ 
+
+ align:start position:0%
+uh yeah depend on the warries depend on
+what kind of questions you are
+
+ align:start position:0%
+what kind of questions you are
+ 
+
+ align:start position:0%
+what kind of questions you are
+interested then you try to extract those
+
+ align:start position:0%
+interested then you try to extract those
+ 
+
+ align:start position:0%
+interested then you try to extract those
+kind of physical answers from this this
+
+ align:start position:0%
+kind of physical answers from this this
+ 
+
+ align:start position:0%
+kind of physical answers from this this
+path integral okay any questions so far
+
+ align:start position:0%
+path integral okay any questions so far
+ 
+
+ align:start position:0%
+path integral okay any questions so far
+yes do we allow paths that contract a
+
+ align:start position:0%
+yes do we allow paths that contract a
+ 
+
+ align:start position:0%
+yes do we allow paths that contract a
+string to a point yeah yeah I will show
+
+ align:start position:0%
+string to a point yeah yeah I will show
+ 
+
+ align:start position:0%
+string to a point yeah yeah I will show
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah two time
+
+ align:start position:0%
+yeah two time
+ 
+
+ align:start position:0%
+yeah two time
+variable no single no Sigma
+
+ align:start position:0%
+variable no single no Sigma
+ 
+
+ align:start position:0%
+variable no single no Sigma
+parameterize the string itself and the
+
+ align:start position:0%
+parameterize the string itself and the
+ 
+
+ align:start position:0%
+parameterize the string itself and the
+tow is parameterize the motion of the
+
+ align:start position:0%
+tow is parameterize the motion of the
+ 
+
+ align:start position:0%
+tow is parameterize the motion of the
+string along the uh the motion of the
+
+ align:start position:0%
+string along the uh the motion of the
+ 
+
+ align:start position:0%
+string along the uh the motion of the
+string but this the there is a Time
+
+ align:start position:0%
+string but this the there is a Time
+ 
+
+ align:start position:0%
+string but this the there is a Time
+variable in Sigma and or it's just a no
+
+ align:start position:0%
+variable in Sigma and or it's just a no
+ 
+
+ align:start position:0%
+variable in Sigma and or it's just a no
+no T is the time yeah t is the internal
+
+ align:start position:0%
+no T is the time yeah t is the internal
+ 
+
+ align:start position:0%
+no T is the time yeah t is the internal
+time for the string okay and then
+
+ align:start position:0%
+time for the string okay and then
+ 
+
+ align:start position:0%
+time for the string okay and then
+there's a time in the in here in the X
+
+ align:start position:0%
+there's a time in the in here in the X
+ 
+
+ align:start position:0%
+there's a time in the in here in the X
+zero in the space time okay so this can
+
+ align:start position:0%
+zero in the space time okay so this can
+ 
+
+ align:start position:0%
+zero in the space time okay so this can
+be considered some kind of a proper time
+
+ align:start position:0%
+be considered some kind of a proper time
+ 
+
+ align:start position:0%
+be considered some kind of a proper time
+for the string internal time for the
+
+ align:start position:0%
+for the string internal time for the
+ 
+
+ align:start position:0%
+for the string internal time for the
+string yeah just like the you
+
+ align:start position:0%
+string yeah just like the you
+ 
+
+ align:start position:0%
+string yeah just like the you
+parameterize the trajectory of the
+
+ align:start position:0%
+parameterize the trajectory of the
+ 
+
+ align:start position:0%
+parameterize the trajectory of the
+particle uh uh you have some to to
+
+ align:start position:0%
+particle uh uh you have some to to
+ 
+
+ align:start position:0%
+particle uh uh you have some to to
+parameterize the trajectory particle
+
+ align:start position:0%
+parameterize the trajectory particle
+ 
+
+ align:start position:0%
+parameterize the trajectory particle
+this the same thing but I mean for any
+
+ align:start position:0%
+this the same thing but I mean for any
+ 
+
+ align:start position:0%
+this the same thing but I mean for any
+proper time it isn't there is or itself
+
+ align:start position:0%
+proper time it isn't there is or itself
+ 
+
+ align:start position:0%
+proper time it isn't there is or itself
+is a four dimensional space time why
+
+ align:start position:0%
+is a four dimensional space time why
+ 
+
+ align:start position:0%
+is a four dimensional space time why
+there's only like one parameter of to
+
+ align:start position:0%
+there's only like one parameter of to
+ 
+
+ align:start position:0%
+there's only like one parameter of to
+which does not have this uh four
+
+ align:start position:0%
+which does not have this uh four
+ 
+
+ align:start position:0%
+which does not have this uh four
+component no I don't understand what you
+
+ align:start position:0%
+component no I don't understand what you
+ 
+
+ align:start position:0%
+component no I don't understand what you
+no this only a single time you have a
+
+ align:start position:0%
+no this only a single time you have a
+ 
+
+ align:start position:0%
+no this only a single time you have a
+particle you have only single time right
+
+ align:start position:0%
+particle you have only single time right
+ 
+
+ align:start position:0%
+particle you have only single time right
+no do you agree here there's only tow
+
+ align:start position:0%
+no do you agree here there's only tow
+ 
+
+ align:start position:0%
+no do you agree here there's only tow
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+no here I have just have a line I
+
+ align:start position:0%
+no here I have just have a line I
+ 
+
+ align:start position:0%
+no here I have just have a line I
+parameterize this nine I call it tow oh
+
+ align:start position:0%
+parameterize this nine I call it tow oh
+ 
+
+ align:start position:0%
+parameterize this nine I call it tow oh
+okay yes here I have a two dimensional
+
+ align:start position:0%
+okay yes here I have a two dimensional
+ 
+
+ align:start position:0%
+okay yes here I have a two dimensional
+here I have a string and then each point
+
+ align:start position:0%
+here I have a string and then each point
+ 
+
+ align:start position:0%
+here I have a string and then each point
+on the string moves like a particle and
+
+ align:start position:0%
+on the string moves like a particle and
+ 
+
+ align:start position:0%
+on the string moves like a particle and
+then I parametrize by a tow okay it it's
+
+ align:start position:0%
+then I parametrize by a tow okay it it's
+ 
+
+ align:start position:0%
+then I parametrize by a tow okay it it's
+the same thing that's much Clear
+
+ align:start position:0%
+the same thing that's much Clear
+ 
+
+ align:start position:0%
+the same thing that's much Clear
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+you what's the metric on the world cheap
+
+ align:start position:0%
+you what's the metric on the world cheap
+ 
+
+ align:start position:0%
+you what's the metric on the world cheap
+does that make sense to us is it like
+
+ align:start position:0%
+does that make sense to us is it like
+ 
+
+ align:start position:0%
+does that make sense to us is it like
+minus plus or of course it makes sense
+
+ align:start position:0%
+minus plus or of course it makes sense
+ 
+
+ align:start position:0%
+minus plus or of course it makes sense
+uh uh uh uh of course on the war sheet
+
+ align:start position:0%
+uh uh uh uh of course on the war sheet
+ 
+
+ align:start position:0%
+uh uh uh uh of course on the war sheet
+should be low ranging oh uh uh whatever
+
+ align:start position:0%
+should be low ranging oh uh uh whatever
+ 
+
+ align:start position:0%
+should be low ranging oh uh uh whatever
+is the uh metric on the uh War sheet is
+
+ align:start position:0%
+is the uh metric on the uh War sheet is
+ 
+
+ align:start position:0%
+is the uh metric on the uh War sheet is
+the uh will be induced from the space
+
+ align:start position:0%
+the uh will be induced from the space
+ 
+
+ align:start position:0%
+the uh will be induced from the space
+time okay so so it would be a minus plus
+
+ align:start position:0%
+time okay so so it would be a minus plus
+ 
+
+ align:start position:0%
+time okay so so it would be a minus plus
+yeah for example yeah yeah it's low
+
+ align:start position:0%
+yeah for example yeah yeah it's low
+ 
+
+ align:start position:0%
+yeah for example yeah yeah it's low
+ranging yeah yeah you can also yeah we
+
+ align:start position:0%
+ranging yeah yeah you can also yeah we
+ 
+
+ align:start position:0%
+ranging yeah yeah you can also yeah we
+can talk yes so one other question so if
+
+ align:start position:0%
+can talk yes so one other question so if
+ 
+
+ align:start position:0%
+can talk yes so one other question so if
+that should be interpreted as proper
+
+ align:start position:0%
+that should be interpreted as proper
+ 
+
+ align:start position:0%
+that should be interpreted as proper
+time if I have a string which is moving
+
+ align:start position:0%
+time if I have a string which is moving
+ 
+
+ align:start position:0%
+time if I have a string which is moving
+in some weird non-uniform way how does
+
+ align:start position:0%
+in some weird non-uniform way how does
+ 
+
+ align:start position:0%
+in some weird non-uniform way how does
+it make sense to talk about the proper
+
+ align:start position:0%
+it make sense to talk about the proper
+ 
+
+ align:start position:0%
+it make sense to talk about the proper
+time of the string when like you can
+
+ align:start position:0%
+time of the string when like you can
+ 
+
+ align:start position:0%
+time of the string when like you can
+imagine the different points on the
+
+ align:start position:0%
+imagine the different points on the
+ 
+
+ align:start position:0%
+imagine the different points on the
+string yeah yeah yeah good point so so
+
+ align:start position:0%
+string yeah yeah yeah good point so so
+ 
+
+ align:start position:0%
+string yeah yeah yeah good point so so
+often you cannot talk about that uh uh
+
+ align:start position:0%
+often you cannot talk about that uh uh
+ 
+
+ align:start position:0%
+often you cannot talk about that uh uh
+and and and this just give you aoristic
+
+ align:start position:0%
+and and and this just give you aoristic
+ 
+
+ align:start position:0%
+and and and this just give you aoristic
+picture because the in principle string
+
+ align:start position:0%
+picture because the in principle string
+ 
+
+ align:start position:0%
+picture because the in principle string
+can can do highly long classical motion
+
+ align:start position:0%
+can can do highly long classical motion
+ 
+
+ align:start position:0%
+can can do highly long classical motion
+and then that is encoded say in
+
+ align:start position:0%
+and then that is encoded say in
+ 
+
+ align:start position:0%
+and then that is encoded say in
+integrating over all such kind of
+
+ align:start position:0%
+integrating over all such kind of
+ 
+
+ align:start position:0%
+integrating over all such kind of
+surfaces okay and and some of them you
+
+ align:start position:0%
+surfaces okay and and some of them you
+ 
+
+ align:start position:0%
+surfaces okay and and some of them you
+cannot interpret it classically or semi
+
+ align:start position:0%
+cannot interpret it classically or semi
+ 
+
+ align:start position:0%
+cannot interpret it classically or semi
+classically into this kind of picture
+
+ align:start position:0%
+classically into this kind of picture
+ 
+
+ align:start position:0%
+classically into this kind of picture
+you visualize it so so I will draw some
+
+ align:start position:0%
+you visualize it so so I will draw some
+ 
+
+ align:start position:0%
+you visualize it so so I will draw some
+pictures later you will see yeah yes um
+
+ align:start position:0%
+pictures later you will see yeah yes um
+ 
+
+ align:start position:0%
+pictures later you will see yeah yes um
+might question like without a good
+
+ align:start position:0%
+might question like without a good
+ 
+
+ align:start position:0%
+might question like without a good
+answer but uh what is the I guess why
+
+ align:start position:0%
+answer but uh what is the I guess why
+ 
+
+ align:start position:0%
+answer but uh what is the I guess why
+does the action take that form what is
+
+ align:start position:0%
+does the action take that form what is
+ 
+
+ align:start position:0%
+does the action take that form what is
+that accomplishing physically or like I
+
+ align:start position:0%
+that accomplishing physically or like I
+ 
+
+ align:start position:0%
+that accomplishing physically or like I
+guess maybe an easier example would be
+
+ align:start position:0%
+guess maybe an easier example would be
+ 
+
+ align:start position:0%
+guess maybe an easier example would be
+um up there on the first bation approach
+
+ align:start position:0%
+um up there on the first bation approach
+ 
+
+ align:start position:0%
+um up there on the first bation approach
+how does that reproduce Q up um you say
+
+ align:start position:0%
+how does that reproduce Q up um you say
+ 
+
+ align:start position:0%
+how does that reproduce Q up um you say
+why that reproduce QT yeah how how that
+
+ align:start position:0%
+why that reproduce QT yeah how how that
+ 
+
+ align:start position:0%
+why that reproduce QT yeah how how that
+reproduce QT of course it's a technical
+
+ align:start position:0%
+reproduce QT of course it's a technical
+ 
+
+ align:start position:0%
+reproduce QT of course it's a technical
+question uh um which you have to
+
+ align:start position:0%
+question uh um which you have to
+ 
+
+ align:start position:0%
+question uh um which you have to
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+explicitly and uh but the question is
+
+ align:start position:0%
+explicitly and uh but the question is
+ 
+
+ align:start position:0%
+explicitly and uh but the question is
+that why do we choose that uh the reason
+
+ align:start position:0%
+that why do we choose that uh the reason
+ 
+
+ align:start position:0%
+that why do we choose that uh the reason
+we choose that is the it's based on war
+
+ align:start position:0%
+we choose that is the it's based on war
+ 
+
+ align:start position:0%
+we choose that is the it's based on war
+is principles so first uh uh uh uh uh
+
+ align:start position:0%
+is principles so first uh uh uh uh uh
+ 
+
+ align:start position:0%
+is principles so first uh uh uh uh uh
+first that thing whatever it is should
+
+ align:start position:0%
+first that thing whatever it is should
+ 
+
+ align:start position:0%
+first that thing whatever it is should
+not deter should not depend on how you
+
+ align:start position:0%
+not deter should not depend on how you
+ 
+
+ align:start position:0%
+not deter should not depend on how you
+choose this
+
+ align:start position:0%
+choose this
+ 
+
+ align:start position:0%
+choose this
+to because you can parameterize your
+
+ align:start position:0%
+to because you can parameterize your
+ 
+
+ align:start position:0%
+to because you can parameterize your
+trajectory anywhere you want so that the
+
+ align:start position:0%
+trajectory anywhere you want so that the
+ 
+
+ align:start position:0%
+trajectory anywhere you want so that the
+L so whatever this action should not
+
+ align:start position:0%
+L so whatever this action should not
+ 
+
+ align:start position:0%
+L so whatever this action should not
+depend on the parametrization and also
+
+ align:start position:0%
+depend on the parametrization and also
+ 
+
+ align:start position:0%
+depend on the parametrization and also
+uh this action should be
+
+ align:start position:0%
+uh this action should be
+ 
+
+ align:start position:0%
+uh this action should be
+Len in warant on the space and the lence
+
+ align:start position:0%
+Len in warant on the space and the lence
+ 
+
+ align:start position:0%
+Len in warant on the space and the lence
+Boost should be translation warant ETA
+
+ align:start position:0%
+Boost should be translation warant ETA
+ 
+
+ align:start position:0%
+Boost should be translation warant ETA
+and with those conditions then
+
+ align:start position:0%
+and with those conditions then
+ 
+
+ align:start position:0%
+and with those conditions then
+essentially uh uh uh essentially
+
+ align:start position:0%
+essentially uh uh uh essentially
+ 
+
+ align:start position:0%
+essentially uh uh uh essentially
+uniquely determined to be this form yeah
+
+ align:start position:0%
+uniquely determined to be this form yeah
+ 
+
+ align:start position:0%
+uniquely determined to be this form yeah
+essentially unique determined to this
+
+ align:start position:0%
+essentially unique determined to this
+ 
+
+ align:start position:0%
+essentially unique determined to this
+form yes so I guess if you were doing a
+
+ align:start position:0%
+form yes so I guess if you were doing a
+ 
+
+ align:start position:0%
+form yes so I guess if you were doing a
+quantization of the bosonic string like
+
+ align:start position:0%
+quantization of the bosonic string like
+ 
+
+ align:start position:0%
+quantization of the bosonic string like
+if you were deriving the field equations
+
+ align:start position:0%
+if you were deriving the field equations
+ 
+
+ align:start position:0%
+if you were deriving the field equations
+would you use nambo or would you use po
+
+ align:start position:0%
+would you use nambo or would you use po
+ 
+
+ align:start position:0%
+would you use nambo or would you use po
+yeah yeah that's right if you really
+
+ align:start position:0%
+yeah yeah that's right if you really
+ 
+
+ align:start position:0%
+yeah yeah that's right if you really
+quantize you actually don't use
+
+ align:start position:0%
+quantize you actually don't use
+ 
+
+ align:start position:0%
+quantize you actually don't use
+lambot lambot use it for the
+
+ align:start position:0%
+lambot lambot use it for the
+ 
+
+ align:start position:0%
+lambot lambot use it for the
+classical description yeah I did not
+
+ align:start position:0%
+classical description yeah I did not
+ 
+
+ align:start position:0%
+classical description yeah I did not
+mention the other other forms it's just
+
+ align:start position:0%
+mention the other other forms it's just
+ 
+
+ align:start position:0%
+mention the other other forms it's just
+for our prop current discussion is not
+
+ align:start position:0%
+for our prop current discussion is not
+ 
+
+ align:start position:0%
+for our prop current discussion is not
+essential yeah yeah indeed when you
+
+ align:start position:0%
+essential yeah yeah indeed when you
+ 
+
+ align:start position:0%
+essential yeah yeah indeed when you
+quantize you actually use a different
+
+ align:start position:0%
+quantize you actually use a different
+ 
+
+ align:start position:0%
+quantize you actually use a different
+form of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action any other
+
+ align:start position:0%
+action any other
+ 
+
+ align:start position:0%
+action any other
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+good so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for
+
+ align:start position:0%
+now for
+ 
+
+ align:start position:0%
+now for
+example yeah
+
+ align:start position:0%
+example yeah
+ 
+
+ align:start position:0%
+example yeah
+so say how you uh
+
+ align:start position:0%
+so say how you uh
+ 
+
+ align:start position:0%
+so say how you uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um so depend on what kind of questions
+
+ align:start position:0%
+um so depend on what kind of questions
+ 
+
+ align:start position:0%
+um so depend on what kind of questions
+you are interested and uh and you you
+
+ align:start position:0%
+you are interested and uh and you you
+ 
+
+ align:start position:0%
+you are interested and uh and you you
+try to extract try to extract them say
+
+ align:start position:0%
+try to extract try to extract them say
+ 
+
+ align:start position:0%
+try to extract try to extract them say
+from this kind of path integral and of
+
+ align:start position:0%
+from this kind of path integral and of
+ 
+
+ align:start position:0%
+from this kind of path integral and of
+course this is a highly non-trivial
+
+ align:start position:0%
+course this is a highly non-trivial
+ 
+
+ align:start position:0%
+course this is a highly non-trivial
+questions and require say some kind of
+
+ align:start position:0%
+questions and require say some kind of
+ 
+
+ align:start position:0%
+questions and require say some kind of
+TR and arrrow Etc so let me just uh tell
+
+ align:start position:0%
+TR and arrrow Etc so let me just uh tell
+ 
+
+ align:start position:0%
+TR and arrrow Etc so let me just uh tell
+you um say if I have a say say if I want
+
+ align:start position:0%
+you um say if I have a say say if I want
+ 
+
+ align:start position:0%
+you um say if I have a say say if I want
+to calculate the vacuum process so if I
+
+ align:start position:0%
+to calculate the vacuum process so if I
+ 
+
+ align:start position:0%
+to calculate the vacuum process so if I
+want to calc the vacuum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy okay so so let me call this this
+
+ align:start position:0%
+energy okay so so let me call this this
+ 
+
+ align:start position:0%
+energy okay so so let me call this this
+string so if I uh so remember when we
+
+ align:start position:0%
+string so if I uh so remember when we
+ 
+
+ align:start position:0%
+string so if I uh so remember when we
+talk about lar engage series and if you
+
+ align:start position:0%
+talk about lar engage series and if you
+ 
+
+ align:start position:0%
+talk about lar engage series and if you
+want to calculate the vacuum energy then
+
+ align:start position:0%
+want to calculate the vacuum energy then
+ 
+
+ align:start position:0%
+want to calculate the vacuum energy then
+you calculate the you sum of all POS
+
+ align:start position:0%
+you calculate the you sum of all POS
+ 
+
+ align:start position:0%
+you calculate the you sum of all POS
+vacuum diagrams Etc okay you sum of all
+
+ align:start position:0%
+vacuum diagrams Etc okay you sum of all
+ 
+
+ align:start position:0%
+vacuum diagrams Etc okay you sum of all
+possible vacuum diagrams and but suppose
+
+ align:start position:0%
+possible vacuum diagrams and but suppose
+ 
+
+ align:start position:0%
+possible vacuum diagrams and but suppose
+we we want to calculate the vacuum
+
+ align:start position:0%
+we we want to calculate the vacuum
+ 
+
+ align:start position:0%
+we we want to calculate the vacuum
+energy in the stren series
+
+ align:start position:0%
+energy in the stren series
+ 
+
+ align:start position:0%
+energy in the stren series
+and then you do the similar thing you
+
+ align:start position:0%
+and then you do the similar thing you
+ 
+
+ align:start position:0%
+and then you do the similar thing you
+you just do the what do you want to do
+
+ align:start position:0%
+you just do the what do you want to do
+ 
+
+ align:start position:0%
+you just do the what do you want to do
+for the string you say you sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Clos 2D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surfaces okay so the closed here is
+
+ align:start position:0%
+surfaces okay so the closed here is
+ 
+
+ align:start position:0%
+surfaces okay so the closed here is
+essential so this is based on the
+
+ align:start position:0%
+essential so this is based on the
+ 
+
+ align:start position:0%
+essential so this is based on the
+intuition that when we in the quantum
+
+ align:start position:0%
+intuition that when we in the quantum
+ 
+
+ align:start position:0%
+intuition that when we in the quantum
+vity when you sum over F diagrams and
+
+ align:start position:0%
+vity when you sum over F diagrams and
+ 
+
+ align:start position:0%
+vity when you sum over F diagrams and
+the F diagrams H recity can be
+
+ align:start position:0%
+the F diagrams H recity can be
+ 
+
+ align:start position:0%
+the F diagrams H recity can be
+considered as a particle trajectories
+
+ align:start position:0%
+considered as a particle trajectories
+ 
+
+ align:start position:0%
+considered as a particle trajectories
+Etc and for the vacuum
+
+ align:start position:0%
+Etc and for the vacuum
+ 
+
+ align:start position:0%
+Etc and for the vacuum
+process the none
+
+ align:start position:0%
+process the none
+ 
+
+ align:start position:0%
+process the none
+of there's no exteral LS so so
+
+ align:start position:0%
+of there's no exteral LS so so
+ 
+
+ align:start position:0%
+of there's no exteral LS so so
+everything coming out of the vacuum then
+
+ align:start position:0%
+everything coming out of the vacuum then
+ 
+
+ align:start position:0%
+everything coming out of the vacuum then
+come back to the vacuum so that's why so
+
+ align:start position:0%
+come back to the vacuum so that's why so
+ 
+
+ align:start position:0%
+come back to the vacuum so that's why so
+if we want to calculate the vacuum
+
+ align:start position:0%
+if we want to calculate the vacuum
+ 
+
+ align:start position:0%
+if we want to calculate the vacuum
+energy the string the and again should
+
+ align:start position:0%
+energy the string the and again should
+ 
+
+ align:start position:0%
+energy the string the and again should
+corresponding to the virtual stream
+
+ align:start position:0%
+corresponding to the virtual stream
+ 
+
+ align:start position:0%
+corresponding to the virtual stream
+motion and again the virtual stream
+
+ align:start position:0%
+motion and again the virtual stream
+ 
+
+ align:start position:0%
+motion and again the virtual stream
+motion should correspond to sum of all
+
+ align:start position:0%
+motion should correspond to sum of all
+ 
+
+ align:start position:0%
+motion should correspond to sum of all
+such kind of surfaces without any
+
+ align:start position:0%
+such kind of surfaces without any
+ 
+
+ align:start position:0%
+such kind of surfaces without any
+external lags uh so so should be closed
+
+ align:start position:0%
+external lags uh so so should be closed
+ 
+
+ align:start position:0%
+external lags uh so so should be closed
+surfaces okay to be close surface so as
+
+ align:start position:0%
+surfaces okay to be close surface so as
+ 
+
+ align:start position:0%
+surfaces okay to be close surface so as
+analog of the particle case and uh so as
+
+ align:start position:0%
+analog of the particle case and uh so as
+ 
+
+ align:start position:0%
+analog of the particle case and uh so as
+exactly as in the quantum fi case it's
+
+ align:start position:0%
+exactly as in the quantum fi case it's
+ 
+
+ align:start position:0%
+exactly as in the quantum fi case it's
+easier to do this using the uking by
+
+ align:start position:0%
+easier to do this using the uking by
+ 
+
+ align:start position:0%
+easier to do this using the uking by
+going to the uking
+
+ align:start position:0%
+going to the uking
+ 
+
+ align:start position:0%
+going to the uking
+signature and say say go to the uking
+
+ align:start position:0%
+signature and say say go to the uking
+ 
+
+ align:start position:0%
+signature and say say go to the uking
+signature they're going to in
+
+ align:start position:0%
+signature they're going to in
+ 
+
+ align:start position:0%
+signature they're going to in
+signature so essentially analytic so
+
+ align:start position:0%
+signature so essentially analytic so
+ 
+
+ align:start position:0%
+signature so essentially analytic so
+instead of considering a surface in the
+
+ align:start position:0%
+instead of considering a surface in the
+ 
+
+ align:start position:0%
+instead of considering a surface in the
+low range space time you consider you
+
+ align:start position:0%
+low range space time you consider you
+ 
+
+ align:start position:0%
+low range space time you consider you
+need continue your space time the full
+
+ align:start position:0%
+need continue your space time the full
+ 
+
+ align:start position:0%
+need continue your space time the full
+space time to the to theing signature
+
+ align:start position:0%
+space time to the to theing signature
+ 
+
+ align:start position:0%
+space time to the to theing signature
+and then and then and then this just
+
+ align:start position:0%
+and then and then and then this just
+ 
+
+ align:start position:0%
+and then and then and then this just
+become some surface in some ukian space
+
+ align:start position:0%
+become some surface in some ukian space
+ 
+
+ align:start position:0%
+become some surface in some ukian space
+and then this is just much easier
+
+ align:start position:0%
+and then this is just much easier
+ 
+
+ align:start position:0%
+and then this is just much easier
+mathematical object to deal with okay so
+
+ align:start position:0%
+mathematical object to deal with okay so
+ 
+
+ align:start position:0%
+mathematical object to deal with okay so
+that's what you get and if you have a
+
+ align:start position:0%
+that's what you get and if you have a
+ 
+
+ align:start position:0%
+that's what you get and if you have a
+string and then you have this
+
+ align:start position:0%
+string and then you have this
+ 
+
+ align:start position:0%
+string and then you have this
+okay okay so now when you sum over all
+
+ align:start position:0%
+okay okay so now when you sum over all
+ 
+
+ align:start position:0%
+okay okay so now when you sum over all
+surfaces now you have a choice first you
+
+ align:start position:0%
+surfaces now you have a choice first you
+ 
+
+ align:start position:0%
+surfaces now you have a choice first you
+can sum over the
+
+ align:start position:0%
+can sum over the
+ 
+
+ align:start position:0%
+can sum over the
+topology so we talked about before all
+
+ align:start position:0%
+topology so we talked about before all
+ 
+
+ align:start position:0%
+topology so we talked about before all
+two dimensional surfaces topology is
+
+ align:start position:0%
+two dimensional surfaces topology is
+ 
+
+ align:start position:0%
+two dimensional surfaces topology is
+classified by this
+
+ align:start position:0%
+classified by this
+ 
+
+ align:start position:0%
+classified by this
+genus and then you can sum
+
+ align:start position:0%
+genus and then you can sum
+ 
+
+ align:start position:0%
+genus and then you can sum
+over surfaces with a given uh so you can
+
+ align:start position:0%
+over surfaces with a given uh so you can
+ 
+
+ align:start position:0%
+over surfaces with a given uh so you can
+separate the sum into sum over
+
+ align:start position:0%
+separate the sum into sum over
+ 
+
+ align:start position:0%
+separate the sum into sum over
+topology and uh and then some Services
+
+ align:start position:0%
+topology and uh and then some Services
+ 
+
+ align:start position:0%
+topology and uh and then some Services
+of each of uh a given
+
+ align:start position:0%
+of each of uh a given
+ 
+
+ align:start position:0%
+of each of uh a given
+topology given H okay so this H is the
+
+ align:start position:0%
+topology given H okay so this H is the
+ 
+
+ align:start position:0%
+topology given H okay so this H is the
+genus so essentially we just summing of
+
+ align:start position:0%
+genus so essentially we just summing of
+ 
+
+ align:start position:0%
+genus so essentially we just summing of
+all possible two dimensional closed
+
+ align:start position:0%
+all possible two dimensional closed
+ 
+
+ align:start position:0%
+all possible two dimensional closed
+surfaces
+
+ align:start position:0%
+surfaces
+ 
+
+ align:start position:0%
+surfaces
+okay is this point clear this is Absolut
+
+ align:start position:0%
+okay is this point clear this is Absolut
+ 
+
+ align:start position:0%
+okay is this point clear this is Absolut
+key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point and uh and with this minus S and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now there's a very important
+
+ align:start position:0%
+so now there's a very important
+ 
+
+ align:start position:0%
+so now there's a very important
+mathematical
+
+ align:start position:0%
+mathematical
+ 
+
+ align:start position:0%
+mathematical
+trick and uh and this mathematical trick
+
+ align:start position:0%
+trick and uh and this mathematical trick
+ 
+
+ align:start position:0%
+trick and uh and this mathematical trick
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+um it can be justified rigorously but I
+
+ align:start position:0%
+um it can be justified rigorously but I
+ 
+
+ align:start position:0%
+um it can be justified rigorously but I
+will not just put it
+
+ align:start position:0%
+will not just put it
+ 
+
+ align:start position:0%
+will not just put it
+here I will just add it here it said now
+
+ align:start position:0%
+here I will just add it here it said now
+ 
+
+ align:start position:0%
+here I will just add it here it said now
+just in physics whenever you see a
+
+ align:start position:0%
+just in physics whenever you see a
+ 
+
+ align:start position:0%
+just in physics whenever you see a
+discrete sum like this what do you
+
+ align:start position:0%
+discrete sum like this what do you
+ 
+
+ align:start position:0%
+discrete sum like this what do you
+do or in mathematics whenever you see a
+
+ align:start position:0%
+do or in mathematics whenever you see a
+ 
+
+ align:start position:0%
+do or in mathematics whenever you see a
+discrete sum like this what do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry lar
+
+ align:start position:0%
+sorry lar
+ 
+
+ align:start position:0%
+sorry lar
+terms exactly you add the
+
+ align:start position:0%
+terms exactly you add the
+ 
+
+ align:start position:0%
+terms exactly you add the
+weight so here I will add a weight here
+
+ align:start position:0%
+weight so here I will add a weight here
+ 
+
+ align:start position:0%
+weight so here I will add a weight here
+so so here I'm summing over a
+
+ align:start position:0%
+so so here I'm summing over a
+ 
+
+ align:start position:0%
+so so here I'm summing over a
+topology but I have but in but then I
+
+ align:start position:0%
+topology but I have but in but then I
+ 
+
+ align:start position:0%
+topology but I have but in but then I
+but now I will add by hand a weight to
+
+ align:start position:0%
+but now I will add by hand a weight to
+ 
+
+ align:start position:0%
+but now I will add by hand a weight to
+weight different topology so Lambda just
+
+ align:start position:0%
+weight different topology so Lambda just
+ 
+
+ align:start position:0%
+weight different topology so Lambda just
+some parameter
+
+ align:start position:0%
+some parameter
+ 
+
+ align:start position:0%
+some parameter
+so Lambda this parameter I introduced by
+
+ align:start position:0%
+so Lambda this parameter I introduced by
+ 
+
+ align:start position:0%
+so Lambda this parameter I introduced by
+now uh by hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+myself okay so this is just the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weight for different topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Kai is the oil Lumber so Lambda just
+
+ align:start position:0%
+so Kai is the oil Lumber so Lambda just
+ 
+
+ align:start position:0%
+so Kai is the oil Lumber so Lambda just
+some uh so Kai is the oil number 2us 2
+
+ align:start position:0%
+some uh so Kai is the oil number 2us 2
+ 
+
+ align:start position:0%
+some uh so Kai is the oil number 2us 2
+H and the
+
+ align:start position:0%
+H and the
+ 
+
+ align:start position:0%
+H and the
+Lambda just can be consider as some kind
+
+ align:start position:0%
+Lambda just can be consider as some kind
+ 
+
+ align:start position:0%
+Lambda just can be consider as some kind
+of chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential some kind of chemical
+
+ align:start position:0%
+potential some kind of chemical
+ 
+
+ align:start position:0%
+potential some kind of chemical
+potential say for for topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah yeah just like uh in the
+
+ align:start position:0%
+okay yeah yeah just like uh in the
+ 
+
+ align:start position:0%
+okay yeah yeah just like uh in the
+system say you have a conserved charge
+
+ align:start position:0%
+system say you have a conserved charge
+ 
+
+ align:start position:0%
+system say you have a conserved charge
+then you then it's when you add
+
+ align:start position:0%
+then you then it's when you add
+ 
+
+ align:start position:0%
+then you then it's when you add
+particles different particle number it's
+
+ align:start position:0%
+particles different particle number it's
+ 
+
+ align:start position:0%
+particles different particle number it's
+convenient to add chemical potential so
+
+ align:start position:0%
+convenient to add chemical potential so
+ 
+
+ align:start position:0%
+convenient to add chemical potential so
+Lambda is like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so so even though I added by hand
+
+ align:start position:0%
+that so so even though I added by hand
+ 
+
+ align:start position:0%
+that so so even though I added by hand
+now even though I added by hand here but
+
+ align:start position:0%
+now even though I added by hand here but
+ 
+
+ align:start position:0%
+now even though I added by hand here but
+in stren actually this
+
+ align:start position:0%
+in stren actually this
+ 
+
+ align:start position:0%
+in stren actually this
+is arise completely natural from the
+
+ align:start position:0%
+is arise completely natural from the
+ 
+
+ align:start position:0%
+is arise completely natural from the
+stren the uh uh there's a rigorous way
+
+ align:start position:0%
+stren the uh uh there's a rigorous way
+ 
+
+ align:start position:0%
+stren the uh uh there's a rigorous way
+one can show how that arises but I will
+
+ align:start position:0%
+one can show how that arises but I will
+ 
+
+ align:start position:0%
+one can show how that arises but I will
+not do it here it's not important for
+
+ align:start position:0%
+not do it here it's not important for
+ 
+
+ align:start position:0%
+not do it here it's not important for
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+purpose and I will also introduce a
+
+ align:start position:0%
+purpose and I will also introduce a
+ 
+
+ align:start position:0%
+purpose and I will also introduce a
+rotation say GS is equal to exponential
+
+ align:start position:0%
+rotation say GS is equal to exponential
+ 
+
+ align:start position:0%
+rotation say GS is equal to exponential
+Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's look at this Pro uh uh
+
+ align:start position:0%
+okay so now let's look at this Pro uh uh
+ 
+
+ align:start position:0%
+okay so now let's look at this Pro uh uh
+now let's look at this
+
+ align:start position:0%
+now let's look at this
+ 
+
+ align:start position:0%
+now let's look at this
+summation so here you sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+so at H equal to zero you Sum of All
+
+ align:start position:0%
+so at H equal to zero you Sum of All
+ 
+
+ align:start position:0%
+so at H equal to zero you Sum of All
+Surface with the topology of a
+
+ align:start position:0%
+Surface with the topology of a
+ 
+
+ align:start position:0%
+Surface with the topology of a
+sphere and the weight is given by GS
+
+ align:start position:0%
+sphere and the weight is given by GS
+ 
+
+ align:start position:0%
+sphere and the weight is given by GS
+minus 2 which is exponential minus 2
+
+ align:start position:0%
+minus 2 which is exponential minus 2
+ 
+
+ align:start position:0%
+minus 2 which is exponential minus 2
+Lambda okay yeah because the kai when H
+
+ align:start position:0%
+Lambda okay yeah because the kai when H
+ 
+
+ align:start position:0%
+Lambda okay yeah because the kai when H
+equal to Zer Kai = to 2 so this is
+
+ align:start position:0%
+equal to Zer Kai = to 2 so this is
+ 
+
+ align:start position:0%
+equal to Zer Kai = to 2 so this is
+Justus 2 Lambda
+
+ align:start position:0%
+Justus 2 Lambda
+ 
+
+ align:start position:0%
+Justus 2 Lambda
+and uh and so this is one / GS squ okay
+
+ align:start position:0%
+and uh and so this is one / GS squ okay
+ 
+
+ align:start position:0%
+and uh and so this is one / GS squ okay
+and then the then the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Taurus this H equal to 1 so this is just
+
+ align:start position:0%
+Taurus this H equal to 1 so this is just
+ 
+
+ align:start position:0%
+Taurus this H equal to 1 so this is just
+the GS to the power
+
+ align:start position:0%
+the GS to the power
+ 
+
+ align:start position:0%
+the GS to the power
+zero it's order
+
+ align:start position:0%
+zero it's order
+ 
+
+ align:start position:0%
+zero it's order
+one if you have Genus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so this would be g h = to 2 then will
+
+ align:start position:0%
+2 so this would be g h = to 2 then will
+ 
+
+ align:start position:0%
+2 so this would be g h = to 2 then will
+be GS s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here is remarkable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact so here is a remarkable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact here's a remarkable fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you said some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+automatically
+
+ align:start position:0%
+automatically
+ 
+
+ align:start position:0%
+automatically
+automatically includes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interaction of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings
+
+ align:start position:0%
+strings
+ 
+
+ align:start position:0%
+strings
+okay in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact this fo is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specifies string interactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let me just uh elaborate on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement so so we can see this
+
+ align:start position:0%
+statement so so we can see this
+ 
+
+ align:start position:0%
+statement so so we can see this
+statement from these pmms here okay so
+
+ align:start position:0%
+statement from these pmms here okay so
+ 
+
+ align:start position:0%
+statement from these pmms here okay so
+now let's look at the physical meaning
+
+ align:start position:0%
+now let's look at the physical meaning
+ 
+
+ align:start position:0%
+now let's look at the physical meaning
+of those
+
+ align:start position:0%
+of those
+ 
+
+ align:start position:0%
+of those
+diagrams so let's first look at the
+
+ align:start position:0%
+diagrams so let's first look at the
+ 
+
+ align:start position:0%
+diagrams so let's first look at the
+sphere diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this supposed to be draw a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+okay so what I'm describing to is
+
+ align:start position:0%
+okay so what I'm describing to is
+ 
+
+ align:start position:0%
+okay so what I'm describing to is
+puristic from physical perspective from
+
+ align:start position:0%
+puristic from physical perspective from
+ 
+
+ align:start position:0%
+puristic from physical perspective from
+from physical perspective so if you
+
+ align:start position:0%
+from physical perspective so if you
+ 
+
+ align:start position:0%
+from physical perspective so if you
+think about sphere embedded in the
+
+ align:start position:0%
+think about sphere embedded in the
+ 
+
+ align:start position:0%
+think about sphere embedded in the
+space so this is
+
+ align:start position:0%
+space so this is
+ 
+
+ align:start position:0%
+space so this is
+like so if you think from say imagine
+
+ align:start position:0%
+like so if you think from say imagine
+ 
+
+ align:start position:0%
+like so if you think from say imagine
+your time going up okay imagine your
+
+ align:start position:0%
+your time going up okay imagine your
+ 
+
+ align:start position:0%
+your time going up okay imagine your
+time going up so this next you nucleate
+
+ align:start position:0%
+time going up so this next you nucleate
+ 
+
+ align:start position:0%
+time going up so this next you nucleate
+a infini tmal string at the tip of the
+
+ align:start position:0%
+a infini tmal string at the tip of the
+ 
+
+ align:start position:0%
+a infini tmal string at the tip of the
+sphere and then then this stram
+
+ align:start position:0%
+sphere and then then this stram
+ 
+
+ align:start position:0%
+sphere and then then this stram
+propagate at each time you have a string
+
+ align:start position:0%
+propagate at each time you have a string
+ 
+
+ align:start position:0%
+propagate at each time you have a string
+and then at some future time then uh
+
+ align:start position:0%
+and then at some future time then uh
+ 
+
+ align:start position:0%
+and then at some future time then uh
+then then go back to the vacuum okay and
+
+ align:start position:0%
+then then go back to the vacuum okay and
+ 
+
+ align:start position:0%
+then then go back to the vacuum okay and
+so you just have a string come in and
+
+ align:start position:0%
+so you just have a string come in and
+ 
+
+ align:start position:0%
+so you just have a string come in and
+come out a string come out from the
+
+ align:start position:0%
+come out a string come out from the
+ 
+
+ align:start position:0%
+come out a string come out from the
+vacuum and then go back and the sphere
+
+ align:start position:0%
+vacuum and then go back and the sphere
+ 
+
+ align:start position:0%
+vacuum and then go back and the sphere
+just describe this kind of virtual
+
+ align:start position:0%
+just describe this kind of virtual
+ 
+
+ align:start position:0%
+just describe this kind of virtual
+process say so you you nucleate string
+
+ align:start position:0%
+process say so you you nucleate string
+ 
+
+ align:start position:0%
+process say so you you nucleate string
+and then uh uh then light then disappear
+
+ align:start position:0%
+and then uh uh then light then disappear
+ 
+
+ align:start position:0%
+and then uh uh then light then disappear
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+okay say nucleate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string string
+
+ align:start position:0%
+string string
+ 
+
+ align:start position:0%
+string string
+nucleation and then then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disappear into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+okay yes why do we only about CL
+
+ align:start position:0%
+okay yes why do we only about CL
+ 
+
+ align:start position:0%
+okay yes why do we only about CL
+strs because it's enough for my purpose
+
+ align:start position:0%
+strs because it's enough for my purpose
+ 
+
+ align:start position:0%
+strs because it's enough for my purpose
+now yeah
+
+ align:start position:0%
+now yeah
+ 
+
+ align:start position:0%
+now yeah
+uh I'm not trying to give you the full
+
+ align:start position:0%
+uh I'm not trying to give you the full
+ 
+
+ align:start position:0%
+uh I'm not trying to give you the full
+string at Ser at moment I'm just trying
+
+ align:start position:0%
+string at Ser at moment I'm just trying
+ 
+
+ align:start position:0%
+string at Ser at moment I'm just trying
+to give
+
+ align:start position:0%
+to give
+ 
+
+ align:start position:0%
+to give
+you the bit of string series is enough
+
+ align:start position:0%
+you the bit of string series is enough
+ 
+
+ align:start position:0%
+you the bit of string series is enough
+to make that point say the say l
+
+ align:start position:0%
+to make that point say the say l
+ 
+
+ align:start position:0%
+to make that point say the say l
+expansion is like a stre the yeah yeah
+
+ align:start position:0%
+expansion is like a stre the yeah yeah
+ 
+
+ align:start position:0%
+expansion is like a stre the yeah yeah
+because uh otherwise take the whole
+
+ align:start position:0%
+because uh otherwise take the whole
+ 
+
+ align:start position:0%
+because uh otherwise take the whole
+semester to reach the point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now let's look at this Taurus diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you want to sum over all
+
+ align:start position:0%
+because if you want to sum over all
+ 
+
+ align:start position:0%
+because if you want to sum over all
+surfaces then you have to sum over
+
+ align:start position:0%
+surfaces then you have to sum over
+ 
+
+ align:start position:0%
+surfaces then you have to sum over
+different topology then you have to sum
+
+ align:start position:0%
+different topology then you have to sum
+ 
+
+ align:start position:0%
+different topology then you have to sum
+over the Taurus then let's look at what
+
+ align:start position:0%
+over the Taurus then let's look at what
+ 
+
+ align:start position:0%
+over the Taurus then let's look at what
+Taurus diagram
+
+ align:start position:0%
+Taurus diagram
+ 
+
+ align:start position:0%
+Taurus diagram
+means so let me dra the Taurus in the
+
+ align:start position:0%
+means so let me dra the Taurus in the
+ 
+
+ align:start position:0%
+means so let me dra the Taurus in the
+slightly different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way okay okay so the
+
+ align:start position:0%
+way okay okay so the
+ 
+
+ align:start position:0%
+way okay okay so the
+Taurus again if you try to view the time
+
+ align:start position:0%
+Taurus again if you try to view the time
+ 
+
+ align:start position:0%
+Taurus again if you try to view the time
+going up then from here again you loate
+
+ align:start position:0%
+going up then from here again you loate
+ 
+
+ align:start position:0%
+going up then from here again you loate
+a single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string but now at this time then you
+
+ align:start position:0%
+string but now at this time then you
+ 
+
+ align:start position:0%
+string but now at this time then you
+actually have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings and then here you have one
+
+ align:start position:0%
+strings and then here you have one
+ 
+
+ align:start position:0%
+strings and then here you have one
+string back
+
+ align:start position:0%
+string back
+ 
+
+ align:start position:0%
+string back
+again okay then the Taurus actually
+
+ align:start position:0%
+again okay then the Taurus actually
+ 
+
+ align:start position:0%
+again okay then the Taurus actually
+describe such a virtual process is that
+
+ align:start position:0%
+describe such a virtual process is that
+ 
+
+ align:start position:0%
+describe such a virtual process is that
+you do create a string from the
+
+ align:start position:0%
+you do create a string from the
+ 
+
+ align:start position:0%
+you do create a string from the
+vacuum and then this string split into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two split into two string and then this
+
+ align:start position:0%
+two split into two string and then this
+ 
+
+ align:start position:0%
+two split into two string and then this
+two string come back to join again to a
+
+ align:start position:0%
+two string come back to join again to a
+ 
+
+ align:start position:0%
+two string come back to join again to a
+single string and then go to the vacuum
+
+ align:start position:0%
+single string and then go to the vacuum
+ 
+
+ align:start position:0%
+single string and then go to the vacuum
+okay so so this is the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleation out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vacuum and then here it
+
+ align:start position:0%
+vacuum and then here it
+ 
+
+ align:start position:0%
+vacuum and then here it
+splits so here single string splits into
+
+ align:start position:0%
+splits so here single string splits into
+ 
+
+ align:start position:0%
+splits so here single string splits into
+two string
+
+ align:start position:0%
+two string
+ 
+
+ align:start position:0%
+two string
+and then here they join together join
+
+ align:start position:0%
+and then here they join together join
+ 
+
+ align:start position:0%
+and then here they join together join
+back into single string and then here
+
+ align:start position:0%
+back into single string and then here
+ 
+
+ align:start position:0%
+back into single string and then here
+disappear into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vacuum okay so so we find by including
+
+ align:start position:0%
+vacuum okay so so we find by including
+ 
+
+ align:start position:0%
+vacuum okay so so we find by including
+the toal diagram you automatically
+
+ align:start position:0%
+the toal diagram you automatically
+ 
+
+ align:start position:0%
+the toal diagram you automatically
+include this kind of
+
+ align:start position:0%
+include this kind of
+ 
+
+ align:start position:0%
+include this kind of
+interaction that the string can split
+
+ align:start position:0%
+interaction that the string can split
+ 
+
+ align:start position:0%
+interaction that the string can split
+into two strings and and two strings can
+
+ align:start position:0%
+into two strings and and two strings can
+ 
+
+ align:start position:0%
+into two strings and and two strings can
+join into single string and
+
+ align:start position:0%
+join into single string and
+ 
+
+ align:start position:0%
+join into single string and
+essentially you don't have choice this
+
+ align:start position:0%
+essentially you don't have choice this
+ 
+
+ align:start position:0%
+essentially you don't have choice this
+is just determined by the
+
+ align:start position:0%
+is just determined by the
+ 
+
+ align:start position:0%
+is just determined by the
+topology okay you don't have Choice it
+
+ align:start position:0%
+topology okay you don't have Choice it
+ 
+
+ align:start position:0%
+topology okay you don't have Choice it
+just once you write down this path
+
+ align:start position:0%
+just once you write down this path
+ 
+
+ align:start position:0%
+just once you write down this path
+integral then then this is fully
+
+ align:start position:0%
+integral then then this is fully
+ 
+
+ align:start position:0%
+integral then then this is fully
+determined okay it's fully
+
+ align:start position:0%
+determined okay it's fully
+ 
+
+ align:start position:0%
+determined okay it's fully
+determined and
+
+ align:start position:0%
+determined and
+ 
+
+ align:start position:0%
+determined and
+similarly if you look at the two Loop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process so you look at the string split
+
+ align:start position:0%
+process so you look at the string split
+ 
+
+ align:start position:0%
+process so you look at the string split
+join splits and join again so the two
+
+ align:start position:0%
+join splits and join again so the two
+ 
+
+ align:start position:0%
+join splits and join again so the two
+string again can be considered
+
+ align:start position:0%
+string again can be considered
+ 
+
+ align:start position:0%
+string again can be considered
+as such
+
+ align:start position:0%
+as such
+ 
+
+ align:start position:0%
+as such
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um such in acting process so now the
+
+ align:start position:0%
+um such in acting process so now the
+ 
+
+ align:start position:0%
+um such in acting process so now the
+key so now if we compare the GS
+
+ align:start position:0%
+key so now if we compare the GS
+ 
+
+ align:start position:0%
+key so now if we compare the GS
+dependence of of these
+
+ align:start position:0%
+dependence of of these
+ 
+
+ align:start position:0%
+dependence of of these
+diagrams so so this one so each diagram
+
+ align:start position:0%
+diagrams so so this one so each diagram
+ 
+
+ align:start position:0%
+diagrams so so this one so each diagram
+compared to the earlier one
+
+ align:start position:0%
+compared to the earlier one
+ 
+
+ align:start position:0%
+compared to the earlier one
+you increase by GS to the power
+
+ align:start position:0%
+you increase by GS to the power
+ 
+
+ align:start position:0%
+you increase by GS to the power
+square but for each whenever you include
+
+ align:start position:0%
+square but for each whenever you include
+ 
+
+ align:start position:0%
+square but for each whenever you include
+the genus essentially fact include such
+
+ align:start position:0%
+the genus essentially fact include such
+ 
+
+ align:start position:0%
+the genus essentially fact include such
+a splitting and the joining so that
+
+ align:start position:0%
+a splitting and the joining so that
+ 
+
+ align:start position:0%
+a splitting and the joining so that
+means you can actually associate with
+
+ align:start position:0%
+means you can actually associate with
+ 
+
+ align:start position:0%
+means you can actually associate with
+each process to be effect of g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string okay so for the
+
+ align:start position:0%
+string okay so for the
+ 
+
+ align:start position:0%
+string okay so for the
+sphere you have say from here say say if
+
+ align:start position:0%
+sphere you have say from here say say if
+ 
+
+ align:start position:0%
+sphere you have say from here say say if
+raliz string sphere to be gsus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 then now if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+include so essentially this
+
+ align:start position:0%
+include so essentially this
+ 
+
+ align:start position:0%
+include so essentially this
+weight this weight which we added here
+
+ align:start position:0%
+weight this weight which we added here
+ 
+
+ align:start position:0%
+weight this weight which we added here
+is to await for such a splitting and
+
+ align:start position:0%
+is to await for such a splitting and
+ 
+
+ align:start position:0%
+is to await for such a splitting and
+joining process so each splitting and
+
+ align:start position:0%
+joining process so each splitting and
+ 
+
+ align:start position:0%
+joining process so each splitting and
+joining give you weight of g string okay
+
+ align:start position:0%
+joining give you weight of g string okay
+ 
+
+ align:start position:0%
+joining give you weight of g string okay
+weight g string so in some sense we
+
+ align:start position:0%
+weight g string so in some sense we
+ 
+
+ align:start position:0%
+weight g string so in some sense we
+concluded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so we concluded that so the
+
+ align:start position:0%
+that so we concluded that so the
+ 
+
+ align:start position:0%
+that so we concluded that so the
+basic
+
+ align:start position:0%
+basic
+ 
+
+ align:start position:0%
+basic
+string interaction
+
+ align:start position:0%
+string interaction
+ 
+
+ align:start position:0%
+string interaction
+vertex it just a single
+
+ align:start position:0%
+vertex it just a single
+ 
+
+ align:start position:0%
+vertex it just a single
+string can join into two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string or or two string or or single
+
+ align:start position:0%
+string or or two string or or single
+ 
+
+ align:start position:0%
+string or or two string or or single
+string can split into two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string or two string can join into a
+
+ align:start position:0%
+string or two string can join into a
+ 
+
+ align:start position:0%
+string or two string can join into a
+single string and the weight for each
+
+ align:start position:0%
+single string and the weight for each
+ 
+
+ align:start position:0%
+single string and the weight for each
+process is given by G
+
+ align:start position:0%
+process is given by G
+ 
+
+ align:start position:0%
+process is given by G
+string okay so so that's effectively
+
+ align:start position:0%
+string okay so so that's effectively
+ 
+
+ align:start position:0%
+string okay so so that's effectively
+what this mathematical trick
+
+ align:start position:0%
+what this mathematical trick
+ 
+
+ align:start position:0%
+what this mathematical trick
+does so effective what this mathematical
+
+ align:start position:0%
+does so effective what this mathematical
+ 
+
+ align:start position:0%
+does so effective what this mathematical
+trick does is to assign a weight for
+
+ align:start position:0%
+trick does is to assign a weight for
+ 
+
+ align:start position:0%
+trick does is to assign a weight for
+each such a splitting process yes so if
+
+ align:start position:0%
+each such a splitting process yes so if
+ 
+
+ align:start position:0%
+each such a splitting process yes so if
+you start the nucle so you drew it like
+
+ align:start position:0%
+you start the nucle so you drew it like
+ 
+
+ align:start position:0%
+you start the nucle so you drew it like
+this for the two thing but if you start
+
+ align:start position:0%
+this for the two thing but if you start
+ 
+
+ align:start position:0%
+this for the two thing but if you start
+the nucleation from the side rather than
+
+ align:start position:0%
+the nucleation from the side rather than
+ 
+
+ align:start position:0%
+the nucleation from the side rather than
+the bottom then wouldn't it like split
+
+ align:start position:0%
+the bottom then wouldn't it like split
+ 
+
+ align:start position:0%
+the bottom then wouldn't it like split
+into three and then back into one that's
+
+ align:start position:0%
+into three and then back into one that's
+ 
+
+ align:start position:0%
+into three and then back into one that's
+right that's uh you uh yeah it's
+
+ align:start position:0%
+right that's uh you uh yeah it's
+ 
+
+ align:start position:0%
+right that's uh you uh yeah it's
+uh because of the topology you you can
+
+ align:start position:0%
+uh because of the topology you you can
+ 
+
+ align:start position:0%
+uh because of the topology you you can
+split in in arbitary way and this
+
+ align:start position:0%
+split in in arbitary way and this
+ 
+
+ align:start position:0%
+split in in arbitary way and this
+get this just tells you using this basic
+
+ align:start position:0%
+get this just tells you using this basic
+ 
+
+ align:start position:0%
+get this just tells you using this basic
+vertex then then for fixed
+
+ align:start position:0%
+vertex then then for fixed
+ 
+
+ align:start position:0%
+vertex then then for fixed
+paret uh yeah just this vertex already
+
+ align:start position:0%
+paret uh yeah just this vertex already
+ 
+
+ align:start position:0%
+paret uh yeah just this vertex already
+enough and you can indeed it's a very
+
+ align:start position:0%
+enough and you can indeed it's a very
+ 
+
+ align:start position:0%
+enough and you can indeed it's a very
+good question you can try to uh snce the
+
+ align:start position:0%
+good question you can try to uh snce the
+ 
+
+ align:start position:0%
+good question you can try to uh snce the
+dag in arbitary way then that may give
+
+ align:start position:0%
+dag in arbitary way then that may give
+ 
+
+ align:start position:0%
+dag in arbitary way then that may give
+you some arbitary other things then
+
+ align:start position:0%
+you some arbitary other things then
+ 
+
+ align:start position:0%
+you some arbitary other things then
+that's fine and then you can assign
+
+ align:start position:0%
+that's fine and then you can assign
+ 
+
+ align:start position:0%
+that's fine and then you can assign
+weight for some some other vertices but
+
+ align:start position:0%
+weight for some some other vertices but
+ 
+
+ align:start position:0%
+weight for some some other vertices but
+but they will be all consistent with
+
+ align:start position:0%
+but they will be all consistent with
+ 
+
+ align:start position:0%
+but they will be all consistent with
+this fundamental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices so so essentially this
+
+ align:start position:0%
+vertices so so essentially this
+ 
+
+ align:start position:0%
+vertices so so essentially this
+GS which I called to be
+
+ align:start position:0%
+GS which I called to be
+ 
+
+ align:start position:0%
+GS which I called to be
+Lambda is essentially the cing for the
+
+ align:start position:0%
+Lambda is essentially the cing for the
+ 
+
+ align:start position:0%
+Lambda is essentially the cing for the
+string
+
+ align:start position:0%
+string
+ 
+
+ align:start position:0%
+string
+okay essentially determines the strength
+
+ align:start position:0%
+okay essentially determines the strength
+ 
+
+ align:start position:0%
+okay essentially determines the strength
+of the string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions yeah our choice of weight
+
+ align:start position:0%
+interactions yeah our choice of weight
+ 
+
+ align:start position:0%
+interactions yeah our choice of weight
+is not unique do something ugly like
+
+ align:start position:0%
+is not unique do something ugly like
+ 
+
+ align:start position:0%
+is not unique do something ugly like
+sare and
+
+ align:start position:0%
+sare and
+ 
+
+ align:start position:0%
+sare and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um yeah that's a good point indeed
+
+ align:start position:0%
+um yeah that's a good point indeed
+ 
+
+ align:start position:0%
+um yeah that's a good point indeed
+indeed yeah uh uh uh so here so here is
+
+ align:start position:0%
+indeed yeah uh uh uh so here so here is
+ 
+
+ align:start position:0%
+indeed yeah uh uh uh so here so here is
+the simplest choice and it's a choice
+
+ align:start position:0%
+the simplest choice and it's a choice
+ 
+
+ align:start position:0%
+the simplest choice and it's a choice
+which you can uh um um yeah yeah so so
+
+ align:start position:0%
+which you can uh um um yeah yeah so so
+ 
+
+ align:start position:0%
+which you can uh um um yeah yeah so so
+this is the simplest choice you can put
+
+ align:start position:0%
+this is the simplest choice you can put
+ 
+
+ align:start position:0%
+this is the simplest choice you can put
+and this is a choice which will also
+
+ align:start position:0%
+and this is a choice which will also
+ 
+
+ align:start position:0%
+and this is a choice which will also
+arise if you properly quanti string
+
+ align:start position:0%
+arise if you properly quanti string
+ 
+
+ align:start position:0%
+arise if you properly quanti string
+series and indeed you can write down
+
+ align:start position:0%
+series and indeed you can write down
+ 
+
+ align:start position:0%
+series and indeed you can write down
+some other string series with a
+
+ align:start position:0%
+some other string series with a
+ 
+
+ align:start position:0%
+some other string series with a
+different Power it might be
+
+ align:start position:0%
+different Power it might be
+ 
+
+ align:start position:0%
+different Power it might be
+possible yeah I mean just as a maical
+
+ align:start position:0%
+possible yeah I mean just as a maical
+ 
+
+ align:start position:0%
+possible yeah I mean just as a maical
+say at a mathematical level L prevent
+
+ align:start position:0%
+say at a mathematical level L prevent
+ 
+
+ align:start position:0%
+say at a mathematical level L prevent
+you to add some arbitrary function of
+
+ align:start position:0%
+you to add some arbitrary function of
+ 
+
+ align:start position:0%
+you to add some arbitrary function of
+Kai and uh and this is just a simplest
+
+ align:start position:0%
+Kai and uh and this is just a simplest
+ 
+
+ align:start position:0%
+Kai and uh and this is just a simplest
+way to do it and this is the way we rise
+
+ align:start position:0%
+way to do it and this is the way we rise
+ 
+
+ align:start position:0%
+way to do it and this is the way we rise
+out of screen Series yeah uh this is so
+
+ align:start position:0%
+out of screen Series yeah uh this is so
+ 
+
+ align:start position:0%
+out of screen Series yeah uh this is so
+this process is not arbitrary it's
+
+ align:start position:0%
+this process is not arbitrary it's
+ 
+
+ align:start position:0%
+this process is not arbitrary it's
+something which you can derive from scen
+
+ align:start position:0%
+something which you can derive from scen
+ 
+
+ align:start position:0%
+something which you can derive from scen
+Ser
+
+ align:start position:0%
+Ser
+ 
+
+ align:start position:0%
+Ser
+yeah just here I will not go through the
+
+ align:start position:0%
+yeah just here I will not go through the
+ 
+
+ align:start position:0%
+yeah just here I will not go through the
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+thing any other questions um do we have
+
+ align:start position:0%
+thing any other questions um do we have
+ 
+
+ align:start position:0%
+thing any other questions um do we have
+an extra minus sign in the EXP no
+
+ align:start position:0%
+an extra minus sign in the EXP no
+ 
+
+ align:start position:0%
+an extra minus sign in the EXP no
+because more negative as H
+
+ align:start position:0%
+because more negative as H
+ 
+
+ align:start position:0%
+because more negative as H
+increases the exponent becomes larger
+
+ align:start position:0%
+increases the exponent becomes larger
+ 
+
+ align:start position:0%
+increases the exponent becomes larger
+and larger yeah yeah yeah because the
+
+ align:start position:0%
+and larger yeah yeah yeah because the
+ 
+
+ align:start position:0%
+and larger yeah yeah yeah because the
+yeah I can take G to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small yeah yeah the only thing is I'm I
+
+ align:start position:0%
+small yeah yeah the only thing is I'm I
+ 
+
+ align:start position:0%
+small yeah yeah the only thing is I'm I
+want to be consistent with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power so now here is the key so now
+
+ align:start position:0%
+power so now here is the key so now
+ 
+
+ align:start position:0%
+power so now here is the key so now
+let's look at the external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings so here at the beginning I was
+
+ align:start position:0%
+strings so here at the beginning I was
+ 
+
+ align:start position:0%
+strings so here at the beginning I was
+looking at the uh um
+
+ align:start position:0%
+looking at the uh um
+ 
+
+ align:start position:0%
+looking at the uh um
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+I being I was looking at the vacuum
+
+ align:start position:0%
+I being I was looking at the vacuum
+ 
+
+ align:start position:0%
+I being I was looking at the vacuum
+process there was nothing just
+
+ align:start position:0%
+process there was nothing just
+ 
+
+ align:start position:0%
+process there was nothing just
+everything come out of the vacuum but
+
+ align:start position:0%
+everything come out of the vacuum but
+ 
+
+ align:start position:0%
+everything come out of the vacuum but
+you can also consider say some process
+
+ align:start position:0%
+you can also consider say some process
+ 
+
+ align:start position:0%
+you can also consider say some process
+say you start with two
+
+ align:start position:0%
+say you start with two
+ 
+
+ align:start position:0%
+say you start with two
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+strings then you scatter them together
+
+ align:start position:0%
+strings then you scatter them together
+ 
+
+ align:start position:0%
+strings then you scatter them together
+you get two string
+
+ align:start position:0%
+you get two string
+ 
+
+ align:start position:0%
+you get two string
+back so you can also consider such kind
+
+ align:start position:0%
+back so you can also consider such kind
+ 
+
+ align:start position:0%
+back so you can also consider such kind
+of string so you started with actually
+
+ align:start position:0%
+of string so you started with actually
+ 
+
+ align:start position:0%
+of string so you started with actually
+two initial
+
+ align:start position:0%
+two initial
+ 
+
+ align:start position:0%
+two initial
+strings and then through some
+
+ align:start position:0%
+strings and then through some
+ 
+
+ align:start position:0%
+strings and then through some
+complicated interaction you have some
+
+ align:start position:0%
+complicated interaction you have some
+ 
+
+ align:start position:0%
+complicated interaction you have some
+two string back okay so for example this
+
+ align:start position:0%
+two string back okay so for example this
+ 
+
+ align:start position:0%
+two string back okay so for example this
+would be such kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process again anything can happen
+
+ align:start position:0%
+process again anything can happen
+ 
+
+ align:start position:0%
+process again anything can happen
+between I have two initial
+
+ align:start position:0%
+between I have two initial
+ 
+
+ align:start position:0%
+between I have two initial
+strings two initial
+
+ align:start position:0%
+strings two initial
+ 
+
+ align:start position:0%
+strings two initial
+strings but I have two final string come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay so this would be some kind of
+
+ align:start position:0%
+out okay so this would be some kind of
+ 
+
+ align:start position:0%
+out okay so this would be some kind of
+surfaces so this will correspondent you
+
+ align:start position:0%
+surfaces so this will correspondent you
+ 
+
+ align:start position:0%
+surfaces so this will correspondent you
+have the sum of all possible surfaces
+
+ align:start position:0%
+have the sum of all possible surfaces
+ 
+
+ align:start position:0%
+have the sum of all possible surfaces
+with four external string uh uh uh uh
+
+ align:start position:0%
+with four external string uh uh uh uh
+ 
+
+ align:start position:0%
+with four external string uh uh uh uh
+say two come in from minus infinity and
+
+ align:start position:0%
+say two come in from minus infinity and
+ 
+
+ align:start position:0%
+say two come in from minus infinity and
+two come from tal to plus two come out
+
+ align:start position:0%
+two come from tal to plus two come out
+ 
+
+ align:start position:0%
+two come from tal to plus two come out
+at t plus infinity
+
+ align:start position:0%
+at t plus infinity
+ 
+
+ align:start position:0%
+at t plus infinity
+okay and again you need to sum of oppos
+
+ align:start position:0%
+okay and again you need to sum of oppos
+ 
+
+ align:start position:0%
+okay and again you need to sum of oppos
+topology in
+
+ align:start position:0%
+topology in
+ 
+
+ align:start position:0%
+topology in
+between say you you you you sum of a
+
+ align:start position:0%
+between say you you you you sum of a
+ 
+
+ align:start position:0%
+between say you you you you sum of a
+sphere in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between yeah let me just uh uh uh save
+
+ align:start position:0%
+between yeah let me just uh uh uh save
+ 
+
+ align:start position:0%
+between yeah let me just uh uh uh save
+time draw it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quickly so so you can sum over all
+
+ align:start position:0%
+quickly so so you can sum over all
+ 
+
+ align:start position:0%
+quickly so so you can sum over all
+spheres in between some spheres or you
+
+ align:start position:0%
+spheres in between some spheres or you
+ 
+
+ align:start position:0%
+spheres in between some spheres or you
+sum over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Taurus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but now if if you do this weight
+
+ align:start position:0%
+okay but now if if you do this weight
+ 
+
+ align:start position:0%
+okay but now if if you do this weight
+according to this
+
+ align:start position:0%
+according to this
+ 
+
+ align:start position:0%
+according to this
+rule okay now if you do the weight
+
+ align:start position:0%
+rule okay now if you do the weight
+ 
+
+ align:start position:0%
+rule okay now if you do the weight
+according to this rule something
+
+ align:start position:0%
+according to this rule something
+ 
+
+ align:start position:0%
+according to this rule something
+changed because the again again we want
+
+ align:start position:0%
+changed because the again again we want
+ 
+
+ align:start position:0%
+changed because the again again we want
+to sum of all possible surfaces with the
+
+ align:start position:0%
+to sum of all possible surfaces with the
+ 
+
+ align:start position:0%
+to sum of all possible surfaces with the
+same rule as you do for the
+
+ align:start position:0%
+same rule as you do for the
+ 
+
+ align:start position:0%
+same rule as you do for the
+vacuum but now there's something
+
+ align:start position:0%
+vacuum but now there's something
+ 
+
+ align:start position:0%
+vacuum but now there's something
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+changes he said this kind of
+
+ align:start position:0%
+changes he said this kind of
+ 
+
+ align:start position:0%
+changes he said this kind of
+surfaces so these are the curves with
+
+ align:start position:0%
+surfaces so these are the curves with
+ 
+
+ align:start position:0%
+surfaces so these are the curves with
+the boundaries so you want to start with
+
+ align:start position:0%
+the boundaries so you want to start with
+ 
+
+ align:start position:0%
+the boundaries so you want to start with
+two two initial external two initial
+
+ align:start position:0%
+two two initial external two initial
+ 
+
+ align:start position:0%
+two two initial external two initial
+strings and two final strings so each
+
+ align:start position:0%
+strings and two final strings so each
+ 
+
+ align:start position:0%
+strings and two final strings so each
+initial string introduce a boundary so
+
+ align:start position:0%
+initial string introduce a boundary so
+ 
+
+ align:start position:0%
+initial string introduce a boundary so
+now you have two four different
+
+ align:start position:0%
+now you have two four different
+ 
+
+ align:start position:0%
+now you have two four different
+boundaries so you have four
+
+ align:start position:0%
+boundaries so you have four
+ 
+
+ align:start position:0%
+boundaries so you have four
+boundaries and so so when you introduce
+
+ align:start position:0%
+boundaries and so so when you introduce
+ 
+
+ align:start position:0%
+boundaries and so so when you introduce
+boundaries into a two dimensional
+
+ align:start position:0%
+boundaries into a two dimensional
+ 
+
+ align:start position:0%
+boundaries into a two dimensional
+surfaces then the oil number
+
+ align:start position:0%
+surfaces then the oil number
+ 
+
+ align:start position:0%
+surfaces then the oil number
+changes so some of you already may know
+
+ align:start position:0%
+changes so some of you already may know
+ 
+
+ align:start position:0%
+changes so some of you already may know
+this from high
+
+ align:start position:0%
+this from high
+ 
+
+ align:start position:0%
+this from high
+school 2 minus H and minus
+
+ align:start position:0%
+school 2 minus H and minus
+ 
+
+ align:start position:0%
+school 2 minus H and minus
+n and n is the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundaries okay number of boundaries and
+
+ align:start position:0%
+boundaries okay number of boundaries and
+ 
+
+ align:start position:0%
+boundaries okay number of boundaries and
+which is the same as the number of
+
+ align:start position:0%
+which is the same as the number of
+ 
+
+ align:start position:0%
+which is the same as the number of
+number of external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings number of external
+
+ align:start position:0%
+strings number of external
+ 
+
+ align:start position:0%
+strings number of external
+strings okay so now if you use this
+
+ align:start position:0%
+strings okay so now if you use this
+ 
+
+ align:start position:0%
+strings okay so now if you use this
+rule so now for the end string
+
+ align:start position:0%
+rule so now for the end string
+ 
+
+ align:start position:0%
+rule so now for the end string
+scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for ning scattering so let me call this
+
+ align:start position:0%
+for ning scattering so let me call this
+ 
+
+ align:start position:0%
+for ning scattering so let me call this
+n a n then you will again Su of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Genesis so now this
+
+ align:start position:0%
+Genesis so now this
+ 
+
+ align:start position:0%
+Genesis so now this
+weight when I translate into
+
+ align:start position:0%
+weight when I translate into
+ 
+
+ align:start position:0%
+weight when I translate into
+GS become nus 2 - 2 H or plus 2
+
+ align:start position:0%
+GS become nus 2 - 2 H or plus 2
+ 
+
+ align:start position:0%
+GS become nus 2 - 2 H or plus 2
+H Okay so now because of this
+
+ align:start position:0%
+H Okay so now because of this
+ 
+
+ align:start position:0%
+H Okay so now because of this
+n so I have additional power of GS to
+
+ align:start position:0%
+n so I have additional power of GS to
+ 
+
+ align:start position:0%
+n so I have additional power of GS to
+the power
+
+ align:start position:0%
+the power
+ 
+
+ align:start position:0%
+the power
+n say say I can write as FN H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so if you look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+sum so if you look at the
+
+ align:start position:0%
+sum so if you look at the
+ 
+
+ align:start position:0%
+sum so if you look at the
+sum so if you look at the sum so so this
+
+ align:start position:0%
+sum so if you look at the sum so so this
+ 
+
+ align:start position:0%
+sum so if you look at the sum so so this
+is GS to the^ nus 2 come from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sphere sphere surface spherical surfaces
+
+ align:start position:0%
+sphere sphere surface spherical surfaces
+ 
+
+ align:start position:0%
+sphere sphere surface spherical surfaces
+which can also be considered as a tree
+
+ align:start position:0%
+which can also be considered as a tree
+ 
+
+ align:start position:0%
+which can also be considered as a tree
+level from the string point of view
+
+ align:start position:0%
+level from the string point of view
+ 
+
+ align:start position:0%
+level from the string point of view
+because the string just come out and
+
+ align:start position:0%
+because the string just come out and
+ 
+
+ align:start position:0%
+because the string just come out and
+nucleate and then the next order is GS
+
+ align:start position:0%
+nucleate and then the next order is GS
+ 
+
+ align:start position:0%
+nucleate and then the next order is GS
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+GSN then this is
+
+ align:start position:0%
+GSN then this is
+ 
+
+ align:start position:0%
+GSN then this is
+Taurus topology so this may be consider
+
+ align:start position:0%
+Taurus topology so this may be consider
+ 
+
+ align:start position:0%
+Taurus topology so this may be consider
+is some kind of one Loop process and GS
+
+ align:start position:0%
+is some kind of one Loop process and GS
+ 
+
+ align:start position:0%
+is some kind of one Loop process and GS
+m+ 2 so this is Genus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now let's compare with this so so so
+
+ align:start position:0%
+now let's compare with this so so so
+ 
+
+ align:start position:0%
+now let's compare with this so so so
+this also include in the vacuum for the
+
+ align:start position:0%
+this also include in the vacuum for the
+ 
+
+ align:start position:0%
+this also include in the vacuum for the
+vacuum you just set n equal to
+
+ align:start position:0%
+vacuum you just set n equal to
+ 
+
+ align:start position:0%
+vacuum you just set n equal to
+Zer okay just send in to zero so now we
+
+ align:start position:0%
+Zer okay just send in to zero so now we
+ 
+
+ align:start position:0%
+Zer okay just send in to zero so now we
+see exactly
+
+ align:start position:0%
+see exactly
+ 
+
+ align:start position:0%
+see exactly
+parallel with what we
+
+ align:start position:0%
+parallel with what we
+ 
+
+ align:start position:0%
+parallel with what we
+see in the larage
+
+ align:start position:0%
+see in the larage
+ 
+
+ align:start position:0%
+see in the larage
+series in both cases you have summing
+
+ align:start position:0%
+series in both cases you have summing
+ 
+
+ align:start position:0%
+series in both cases you have summing
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+topology and in both cases we have
+
+ align:start position:0%
+topology and in both cases we have
+ 
+
+ align:start position:0%
+topology and in both cases we have
+summing you have this
+
+ align:start position:0%
+summing you have this
+ 
+
+ align:start position:0%
+summing you have this
+expansion and
+
+ align:start position:0%
+expansion and
+ 
+
+ align:start position:0%
+expansion and
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so identical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mathematical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+nen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion in
+
+ align:start position:0%
+expansion in
+ 
+
+ align:start position:0%
+expansion in
+particular g string now corresponding to
+
+ align:start position:0%
+particular g string now corresponding to
+ 
+
+ align:start position:0%
+particular g string now corresponding to
+just one/
+
+ align:start position:0%
+just one/
+ 
+
+ align:start position:0%
+just one/
+n and this external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings say if you have
+
+ align:start position:0%
+strings say if you have
+ 
+
+ align:start position:0%
+strings say if you have
+some just corresponding to the
+
+ align:start position:0%
+some just corresponding to the
+ 
+
+ align:start position:0%
+some just corresponding to the
+globos what we call the
+
+ align:start position:0%
+globos what we call the
+ 
+
+ align:start position:0%
+globos what we call the
+gloos so this kind of single Chace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators and the sum of
+
+ align:start position:0%
+operators and the sum of
+ 
+
+ align:start position:0%
+operators and the sum of
+string over string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worksheet of say
+
+ align:start position:0%
+worksheet of say
+ 
+
+ align:start position:0%
+worksheet of say
+topology of genus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H it's then a map to say some overment
+
+ align:start position:0%
+H it's then a map to say some overment
+ 
+
+ align:start position:0%
+H it's then a map to say some overment
+diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of genus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H yeah so you see so exactly parallel
+
+ align:start position:0%
+H yeah so you see so exactly parallel
+ 
+
+ align:start position:0%
+H yeah so you see so exactly parallel
+mathematical
+
+ align:start position:0%
+mathematical
+ 
+
+ align:start position:0%
+mathematical
+structure between the
+
+ align:start position:0%
+structure between the
+ 
+
+ align:start position:0%
+structure between the
+two so the question is whe is this a
+
+ align:start position:0%
+two so the question is whe is this a
+ 
+
+ align:start position:0%
+two so the question is whe is this a
+accident or this is something deep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I think I'm running out of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay maybe I will stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you don't want to
+
+ align:start position:0%
+here you don't want to
+ 
+
+ align:start position:0%
+here you don't want to
+stop only one and a half pages left um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah let me just say a few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words let me say a few words if you look
+
+ align:start position:0%
+words let me say a few words if you look
+ 
+
+ align:start position:0%
+words let me say a few words if you look
+at these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sums this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum and this sum oh yeah let me call
+
+ align:start position:0%
+sum and this sum oh yeah let me call
+ 
+
+ align:start position:0%
+sum and this sum oh yeah let me call
+this FN so that the distinction let me
+
+ align:start position:0%
+this FN so that the distinction let me
+ 
+
+ align:start position:0%
+this FN so that the distinction let me
+call this F so that
+
+ align:start position:0%
+call this F so that
+ 
+
+ align:start position:0%
+call this F so that
+F so if you look at these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sums so the question is can you really
+
+ align:start position:0%
+sums so the question is can you really
+ 
+
+ align:start position:0%
+sums so the question is can you really
+physically identify this two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah just say let me just say a
+
+ align:start position:0%
+okay yeah just say let me just say a
+ 
+
+ align:start position:0%
+okay yeah just say let me just say a
+couple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words say fnh
+
+ align:start position:0%
+words say fnh
+ 
+
+ align:start position:0%
+words say fnh
+h which appear in the correlation
+
+ align:start position:0%
+h which appear in the correlation
+ 
+
+ align:start position:0%
+h which appear in the correlation
+functions essentially just some over
+
+ align:start position:0%
+functions essentially just some over
+ 
+
+ align:start position:0%
+functions essentially just some over
+five some over five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams of genus age
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the just the F diagrams the
+
+ align:start position:0%
+and this is the just the F diagrams the
+ 
+
+ align:start position:0%
+and this is the just the F diagrams the
+expression for the F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams and this one this
+
+ align:start position:0%
+diagrams and this one this
+ 
+
+ align:start position:0%
+diagrams and this one this
+FH
+
+ align:start position:0%
+FH
+ 
+
+ align:start position:0%
+FH
+fnh so this is sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over this is path integral say minus S
+
+ align:start position:0%
+over this is path integral say minus S
+ 
+
+ align:start position:0%
+over this is path integral say minus S
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+G of genus h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surfaces so now
+
+ align:start position:0%
+surfaces so now
+ 
+
+ align:start position:0%
+surfaces so now
+remember so now remember one thing we
+
+ align:start position:0%
+remember so now remember one thing we
+ 
+
+ align:start position:0%
+remember so now remember one thing we
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+before is that each fman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram each fman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram can be considered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition of a 2d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface okay so now if you sum of all
+
+ align:start position:0%
+surface okay so now if you sum of all
+ 
+
+ align:start position:0%
+surface okay so now if you sum of all
+possible fan
+
+ align:start position:0%
+possible fan
+ 
+
+ align:start position:0%
+possible fan
+diagrams so you can also think of it
+
+ align:start position:0%
+diagrams so you can also think of it
+ 
+
+ align:start position:0%
+diagrams so you can also think of it
+geometrically as some over all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible triangulations of a surface
+
+ align:start position:0%
+possible triangulations of a surface
+ 
+
+ align:start position:0%
+possible triangulations of a surface
+conations of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface so this are this kind of
+
+ align:start position:0%
+surface so this are this kind of
+ 
+
+ align:start position:0%
+surface so this are this kind of
+partition essentially just a
+
+ align:start position:0%
+partition essentially just a
+ 
+
+ align:start position:0%
+partition essentially just a
+triangularization of the surfaces
+
+ align:start position:0%
+triangularization of the surfaces
+ 
+
+ align:start position:0%
+triangularization of the surfaces
+divided into different parts and with
+
+ align:start position:0%
+divided into different parts and with
+ 
+
+ align:start position:0%
+divided into different parts and with
+some altitude with some weight so Su of
+
+ align:start position:0%
+some altitude with some weight so Su of
+ 
+
+ align:start position:0%
+some altitude with some weight so Su of
+allos triangulation of the surface of
+
+ align:start position:0%
+allos triangulation of the surface of
+ 
+
+ align:start position:0%
+allos triangulation of the surface of
+course this is
+
+ align:start position:0%
+course this is
+ 
+
+ align:start position:0%
+course this is
+precisely just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discrete
+
+ align:start position:0%
+discrete
+ 
+
+ align:start position:0%
+discrete
+form of summing over all summing over
+
+ align:start position:0%
+form of summing over all summing over
+ 
+
+ align:start position:0%
+form of summing over all summing over
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surfaces so this is a disc for discrete
+
+ align:start position:0%
+surfaces so this is a disc for discrete
+ 
+
+ align:start position:0%
+surfaces so this is a disc for discrete
+sum of sum of all
+
+ align:start position:0%
+sum of sum of all
+ 
+
+ align:start position:0%
+sum of sum of all
+surfaces and so so this really identify
+
+ align:start position:0%
+surfaces and so so this really identify
+ 
+
+ align:start position:0%
+surfaces and so so this really identify
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+two are essentially the same object so
+
+ align:start position:0%
+two are essentially the same object so
+ 
+
+ align:start position:0%
+two are essentially the same object so
+when you summing over diagrams you are
+
+ align:start position:0%
+when you summing over diagrams you are
+ 
+
+ align:start position:0%
+when you summing over diagrams you are
+actually summing inly actually summing
+
+ align:start position:0%
+actually summing inly actually summing
+ 
+
+ align:start position:0%
+actually summing inly actually summing
+over all possible edance of some
+
+ align:start position:0%
+over all possible edance of some
+ 
+
+ align:start position:0%
+over all possible edance of some
+surfaces in space time and the precise L
+
+ align:start position:0%
+surfaces in space time and the precise L
+ 
+
+ align:start position:0%
+surfaces in space time and the precise L
+of that surface of course depends
+
+ align:start position:0%
+of that surface of course depends
+ 
+
+ align:start position:0%
+of that surface of course depends
+on uh the diagram
+
+ align:start position:0%
+on uh the diagram
+ 
+
+ align:start position:0%
+on uh the diagram
+itself diagam itself so this really
+
+ align:start position:0%
+itself diagam itself so this really
+ 
+
+ align:start position:0%
+itself diagam itself so this really
+tells you that the
+
+ align:start position:0%
+tells you that the
+ 
+
+ align:start position:0%
+tells you that the
+Len expansion is
+
+ align:start position:0%
+Len expansion is
+ 
+
+ align:start position:0%
+Len expansion is
+really just a string
+
+ align:start position:0%
+really just a string
+ 
+
+ align:start position:0%
+really just a string
+theory okay it's really just a string
+
+ align:start position:0%
+theory okay it's really just a string
+ 
+
+ align:start position:0%
+theory okay it's really just a string
+the and but from here you cannot
+
+ align:start position:0%
+the and but from here you cannot
+ 
+
+ align:start position:0%
+the and but from here you cannot
+immediately tell what kind of string
+
+ align:start position:0%
+immediately tell what kind of string
+ 
+
+ align:start position:0%
+immediately tell what kind of string
+theory is this because from F diagram
+
+ align:start position:0%
+theory is this because from F diagram
+ 
+
+ align:start position:0%
+theory is this because from F diagram
+itself so this L goal action which I I
+
+ align:start position:0%
+itself so this L goal action which I I
+ 
+
+ align:start position:0%
+itself so this L goal action which I I
+wrote earlier corresponding to you map
+
+ align:start position:0%
+wrote earlier corresponding to you map
+ 
+
+ align:start position:0%
+wrote earlier corresponding to you map
+from some surface embedding of some
+
+ align:start position:0%
+from some surface embedding of some
+ 
+
+ align:start position:0%
+from some surface embedding of some
+surface in some space time and that
+
+ align:start position:0%
+surface in some space time and that
+ 
+
+ align:start position:0%
+surface in some space time and that
+space time can be some arbitrary space
+
+ align:start position:0%
+space time can be some arbitrary space
+ 
+
+ align:start position:0%
+space time can be some arbitrary space
+time EX for different space time of
+
+ align:start position:0%
+time EX for different space time of
+ 
+
+ align:start position:0%
+time EX for different space time of
+course you get a different action so the
+
+ align:start position:0%
+course you get a different action so the
+ 
+
+ align:start position:0%
+course you get a different action so the
+question is what does this correspond to
+
+ align:start position:0%
+question is what does this correspond to
+ 
+
+ align:start position:0%
+question is what does this correspond to
+so I give you a set of I give you a fi
+
+ align:start position:0%
+so I give you a set of I give you a fi
+ 
+
+ align:start position:0%
+so I give you a set of I give you a fi
+series and you have those fan diagrams
+
+ align:start position:0%
+series and you have those fan diagrams
+ 
+
+ align:start position:0%
+series and you have those fan diagrams
+and what F what and for each fan diagram
+
+ align:start position:0%
+and what F what and for each fan diagram
+ 
+
+ align:start position:0%
+and what F what and for each fan diagram
+you can write expression for them just
+
+ align:start position:0%
+you can write expression for them just
+ 
+
+ align:start position:0%
+you can write expression for them just
+whether this really corresponding to say
+
+ align:start position:0%
+whether this really corresponding to say
+ 
+
+ align:start position:0%
+whether this really corresponding to say
+some geometric action the F diag whether
+
+ align:start position:0%
+some geometric action the F diag whether
+ 
+
+ align:start position:0%
+some geometric action the F diag whether
+really corresponding some geometrical
+
+ align:start position:0%
+really corresponding some geometrical
+ 
+
+ align:start position:0%
+really corresponding some geometrical
+action describing the motion of some
+
+ align:start position:0%
+action describing the motion of some
+ 
+
+ align:start position:0%
+action describing the motion of some
+surface in some space time yeah yeah so
+
+ align:start position:0%
+surface in some space time yeah yeah so
+ 
+
+ align:start position:0%
+surface in some space time yeah yeah so
+so let me just stop here
\ No newline at end of file
diff --git a/MAyraVVYB64.txt b/MAyraVVYB64.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a0dd2592cddc19039f3e386b3de277c06e35f77
--- /dev/null
+++ b/MAyraVVYB64.txt
@@ -0,0 +1,18696 @@
+align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+welcome to our fourth problem session
+
+ align:start position:0%
+welcome to our fourth problem session
+ 
+
+ align:start position:0%
+welcome to our fourth problem session
+uh we're going to be talking about
+
+ align:start position:0%
+uh we're going to be talking about
+ 
+
+ align:start position:0%
+uh we're going to be talking about
+binary trees mostly today we'll talk a
+
+ align:start position:0%
+binary trees mostly today we'll talk a
+ 
+
+ align:start position:0%
+binary trees mostly today we'll talk a
+little bit about
+
+ align:start position:0%
+little bit about
+ 
+
+ align:start position:0%
+little bit about
+binary heaps which is a topic we won't
+
+ align:start position:0%
+binary heaps which is a topic we won't
+ 
+
+ align:start position:0%
+binary heaps which is a topic we won't
+cover until
+
+ align:start position:0%
+cover until
+ 
+
+ align:start position:0%
+cover until
+next tuesday but it will appear
+
+ align:start position:0%
+next tuesday but it will appear
+ 
+
+ align:start position:0%
+next tuesday but it will appear
+in a very small ways on your problem set
+
+ align:start position:0%
+in a very small ways on your problem set
+ 
+
+ align:start position:0%
+in a very small ways on your problem set
+four which will be due next friday
+
+ align:start position:0%
+four which will be due next friday
+ 
+
+ align:start position:0%
+four which will be due next friday
+so i'm going to go over a little bit of
+
+ align:start position:0%
+so i'm going to go over a little bit of
+ 
+
+ align:start position:0%
+so i'm going to go over a little bit of
+that material today
+
+ align:start position:0%
+that material today
+ 
+
+ align:start position:0%
+that material today
+but it's mostly concern the the subject
+
+ align:start position:0%
+but it's mostly concern the the subject
+ 
+
+ align:start position:0%
+but it's mostly concern the the subject
+material for today is mostly
+
+ align:start position:0%
+material for today is mostly
+ 
+
+ align:start position:0%
+material for today is mostly
+uh binary trees specifically
+
+ align:start position:0%
+uh binary trees specifically
+ 
+
+ align:start position:0%
+uh binary trees specifically
+being applied to set data structures and
+
+ align:start position:0%
+being applied to set data structures and
+ 
+
+ align:start position:0%
+being applied to set data structures and
+sequence data structures
+
+ align:start position:0%
+sequence data structures
+ 
+
+ align:start position:0%
+sequence data structures
+as uh professor domain talked to you
+
+ align:start position:0%
+as uh professor domain talked to you
+ 
+
+ align:start position:0%
+as uh professor domain talked to you
+earlier this week um but
+
+ align:start position:0%
+earlier this week um but
+ 
+
+ align:start position:0%
+earlier this week um but
+for now uh actually as of yesterday
+
+ align:start position:0%
+for now uh actually as of yesterday
+ 
+
+ align:start position:0%
+for now uh actually as of yesterday
+you've seen all of the data structures
+
+ align:start position:0%
+you've seen all of the data structures
+ 
+
+ align:start position:0%
+you've seen all of the data structures
+that we're going to cover
+
+ align:start position:0%
+that we're going to cover
+ 
+
+ align:start position:0%
+that we're going to cover
+to imp that that will implement the set
+
+ align:start position:0%
+to imp that that will implement the set
+ 
+
+ align:start position:0%
+to imp that that will implement the set
+interface and the sequence interface
+
+ align:start position:0%
+interface and the sequence interface
+ 
+
+ align:start position:0%
+interface and the sequence interface
+right those uh those nice tables that
+
+ align:start position:0%
+right those uh those nice tables that
+ 
+
+ align:start position:0%
+right those uh those nice tables that
+uh professor domain has been showing you
+
+ align:start position:0%
+uh professor domain has been showing you
+ 
+
+ align:start position:0%
+uh professor domain has been showing you
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+uh those are now complete right we have
+
+ align:start position:0%
+uh those are now complete right we have
+ 
+
+ align:start position:0%
+uh those are now complete right we have
+uh some data structures that are really
+
+ align:start position:0%
+uh some data structures that are really
+ 
+
+ align:start position:0%
+uh some data structures that are really
+good constant time
+
+ align:start position:0%
+good constant time
+ 
+
+ align:start position:0%
+good constant time
+operations for some operations so we
+
+ align:start position:0%
+operations for some operations so we
+ 
+
+ align:start position:0%
+operations for some operations so we
+might choose them for some
+
+ align:start position:0%
+might choose them for some
+ 
+
+ align:start position:0%
+might choose them for some
+uh applications and this week
+
+ align:start position:0%
+uh applications and this week
+ 
+
+ align:start position:0%
+uh applications and this week
+we've been describing to you trees which
+
+ align:start position:0%
+we've been describing to you trees which
+ 
+
+ align:start position:0%
+we've been describing to you trees which
+achieve like really pretty good for any
+
+ align:start position:0%
+achieve like really pretty good for any
+ 
+
+ align:start position:0%
+achieve like really pretty good for any
+type of query operation on my
+
+ align:start position:0%
+type of query operation on my
+ 
+
+ align:start position:0%
+type of query operation on my
+sets or sequences pretty good meaning
+
+ align:start position:0%
+sets or sequences pretty good meaning
+ 
+
+ align:start position:0%
+sets or sequences pretty good meaning
+logarithmic time not quite constant
+
+ align:start position:0%
+logarithmic time not quite constant
+ 
+
+ align:start position:0%
+logarithmic time not quite constant
+but for our purposes log n is
+
+ align:start position:0%
+but for our purposes log n is
+ 
+
+ align:start position:0%
+but for our purposes log n is
+i mean on your computer practically
+
+ align:start position:0%
+i mean on your computer practically
+ 
+
+ align:start position:0%
+i mean on your computer practically
+right not asymptotically but practically
+
+ align:start position:0%
+right not asymptotically but practically
+ 
+
+ align:start position:0%
+right not asymptotically but practically
+log n is going to be at most what
+
+ align:start position:0%
+log n is going to be at most what
+ 
+
+ align:start position:0%
+log n is going to be at most what
+on your computer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like 64 right
+
+ align:start position:0%
+something like 64 right
+ 
+
+ align:start position:0%
+something like 64 right
+any input that you're operating on with
+
+ align:start position:0%
+any input that you're operating on with
+ 
+
+ align:start position:0%
+any input that you're operating on with
+uh and machine words as your input right
+
+ align:start position:0%
+uh and machine words as your input right
+ 
+
+ align:start position:0%
+uh and machine words as your input right
+uh you need to be able to address all
+
+ align:start position:0%
+uh you need to be able to address all
+ 
+
+ align:start position:0%
+uh you need to be able to address all
+those machine words right
+
+ align:start position:0%
+those machine words right
+ 
+
+ align:start position:0%
+those machine words right
+in in your input and on your computer
+
+ align:start position:0%
+in in your input and on your computer
+ 
+
+ align:start position:0%
+in in your input and on your computer
+the size of your machine word addresses
+
+ align:start position:0%
+the size of your machine word addresses
+ 
+
+ align:start position:0%
+the size of your machine word addresses
+is 64 bits
+
+ align:start position:0%
+is 64 bits
+ 
+
+ align:start position:0%
+is 64 bits
+right and we assume that the word size
+
+ align:start position:0%
+right and we assume that the word size
+ 
+
+ align:start position:0%
+right and we assume that the word size
+is at least log
+
+ align:start position:0%
+is at least log
+ 
+
+ align:start position:0%
+is at least log
+in the num the size of your input so
+
+ align:start position:0%
+in the num the size of your input so
+ 
+
+ align:start position:0%
+in the num the size of your input so
+that you can address the input
+
+ align:start position:0%
+that you can address the input
+ 
+
+ align:start position:0%
+that you can address the input
+right right so for your purposes on your
+
+ align:start position:0%
+right right so for your purposes on your
+ 
+
+ align:start position:0%
+right right so for your purposes on your
+computer
+
+ align:start position:0%
+computer
+ 
+
+ align:start position:0%
+computer
+log n is going to be no more than 64
+
+ align:start position:0%
+log n is going to be no more than 64
+ 
+
+ align:start position:0%
+log n is going to be no more than 64
+which means you get a maybe a 50 times
+
+ align:start position:0%
+which means you get a maybe a 50 times
+ 
+
+ align:start position:0%
+which means you get a maybe a 50 times
+overhead or you know for smaller
+
+ align:start position:0%
+overhead or you know for smaller
+ 
+
+ align:start position:0%
+overhead or you know for smaller
+instances it could be more like 10 right
+
+ align:start position:0%
+instances it could be more like 10 right
+ 
+
+ align:start position:0%
+instances it could be more like 10 right
+if you've got like
+
+ align:start position:0%
+if you've got like
+ 
+
+ align:start position:0%
+if you've got like
+a thousand things that you're working on
+
+ align:start position:0%
+a thousand things that you're working on
+ 
+
+ align:start position:0%
+a thousand things that you're working on
+right it's not that bad
+
+ align:start position:0%
+right it's not that bad
+ 
+
+ align:start position:0%
+right it's not that bad
+right it's a constant it's not a
+
+ align:start position:0%
+right it's a constant it's not a
+ 
+
+ align:start position:0%
+right it's a constant it's not a
+constant factor for theory purposes
+
+ align:start position:0%
+constant factor for theory purposes
+ 
+
+ align:start position:0%
+constant factor for theory purposes
+but for your purposes log n is much
+
+ align:start position:0%
+but for your purposes log n is much
+ 
+
+ align:start position:0%
+but for your purposes log n is much
+better than a than a polynomial factor
+
+ align:start position:0%
+better than a than a polynomial factor
+ 
+
+ align:start position:0%
+better than a than a polynomial factor
+right another factor of n okay so
+
+ align:start position:0%
+right another factor of n okay so
+ 
+
+ align:start position:0%
+right another factor of n okay so
+uh you've seen all the code
+
+ align:start position:0%
+uh you've seen all the code
+ 
+
+ align:start position:0%
+uh you've seen all the code
+you've seen implementations of all of
+
+ align:start position:0%
+you've seen implementations of all of
+ 
+
+ align:start position:0%
+you've seen implementations of all of
+these set and sequence interfaces right
+
+ align:start position:0%
+these set and sequence interfaces right
+ 
+
+ align:start position:0%
+these set and sequence interfaces right
+so i went ahead and wrote a little i
+
+ align:start position:0%
+so i went ahead and wrote a little i
+ 
+
+ align:start position:0%
+so i went ahead and wrote a little i
+compiled all of that code from your
+
+ align:start position:0%
+compiled all of that code from your
+ 
+
+ align:start position:0%
+compiled all of that code from your
+recitation notes of all of the different
+
+ align:start position:0%
+recitation notes of all of the different
+ 
+
+ align:start position:0%
+recitation notes of all of the different
+interface implementations and what i did
+
+ align:start position:0%
+interface implementations and what i did
+ 
+
+ align:start position:0%
+interface implementations and what i did
+was i
+
+ align:start position:0%
+was i
+ 
+
+ align:start position:0%
+was i
+wrote a little test program to see how
+
+ align:start position:0%
+wrote a little test program to see how
+ 
+
+ align:start position:0%
+wrote a little test program to see how
+they ran
+
+ align:start position:0%
+they ran
+ 
+
+ align:start position:0%
+they ran
+on a real machine right so i have a
+
+ align:start position:0%
+on a real machine right so i have a
+ 
+
+ align:start position:0%
+on a real machine right so i have a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+test code here um right so i have a
+
+ align:start position:0%
+test code here um right so i have a
+ 
+
+ align:start position:0%
+test code here um right so i have a
+little folder
+
+ align:start position:0%
+little folder
+ 
+
+ align:start position:0%
+little folder
+that lists you know an array
+
+ align:start position:0%
+that lists you know an array
+ 
+
+ align:start position:0%
+that lists you know an array
+implementing a sequence a binary tree
+
+ align:start position:0%
+implementing a sequence a binary tree
+ 
+
+ align:start position:0%
+implementing a sequence a binary tree
+implementing a sequence a dynamic array
+
+ align:start position:0%
+implementing a sequence a dynamic array
+ 
+
+ align:start position:0%
+implementing a sequence a dynamic array
+implementing
+
+ align:start position:0%
+implementing
+ 
+
+ align:start position:0%
+implementing
+all these kinds of things right then set
+
+ align:start position:0%
+all these kinds of things right then set
+ 
+
+ align:start position:0%
+all these kinds of things right then set
+things a sorted array being a set
+
+ align:start position:0%
+things a sorted array being a set
+ 
+
+ align:start position:0%
+things a sorted array being a set
+and a binary tree and a hash table right
+
+ align:start position:0%
+and a binary tree and a hash table right
+ 
+
+ align:start position:0%
+and a binary tree and a hash table right
+these are our implementations i'm not
+
+ align:start position:0%
+these are our implementations i'm not
+ 
+
+ align:start position:0%
+these are our implementations i'm not
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+python dictionaries for hash tables i'm
+
+ align:start position:0%
+python dictionaries for hash tables i'm
+ 
+
+ align:start position:0%
+python dictionaries for hash tables i'm
+using the implementations that are in
+
+ align:start position:0%
+using the implementations that are in
+ 
+
+ align:start position:0%
+using the implementations that are in
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+restation and i'm going to run this
+
+ align:start position:0%
+restation and i'm going to run this
+ 
+
+ align:start position:0%
+restation and i'm going to run this
+little test efficiency
+
+ align:start position:0%
+little test efficiency
+ 
+
+ align:start position:0%
+little test efficiency
+python code that basically is just gonna
+
+ align:start position:0%
+python code that basically is just gonna
+ 
+
+ align:start position:0%
+python code that basically is just gonna
+for each one it's gonna do a bunch of
+
+ align:start position:0%
+for each one it's gonna do a bunch of
+ 
+
+ align:start position:0%
+for each one it's gonna do a bunch of
+these different operations
+
+ align:start position:0%
+these different operations
+ 
+
+ align:start position:0%
+these different operations
+and measure to see how much time it took
+
+ align:start position:0%
+and measure to see how much time it took
+ 
+
+ align:start position:0%
+and measure to see how much time it took
+right i'm just logging how much time it
+
+ align:start position:0%
+right i'm just logging how much time it
+ 
+
+ align:start position:0%
+right i'm just logging how much time it
+took it's not an asymptotic analysis but
+
+ align:start position:0%
+took it's not an asymptotic analysis but
+ 
+
+ align:start position:0%
+took it's not an asymptotic analysis but
+you know hopefully we see some
+
+ align:start position:0%
+you know hopefully we see some
+ 
+
+ align:start position:0%
+you know hopefully we see some
+separation yeah
+
+ align:start position:0%
+separation yeah
+ 
+
+ align:start position:0%
+separation yeah
+so i'm going to press that it runs a
+
+ align:start position:0%
+so i'm going to press that it runs a
+ 
+
+ align:start position:0%
+so i'm going to press that it runs a
+bunch of tests so let's take a look
+
+ align:start position:0%
+bunch of tests so let's take a look
+ 
+
+ align:start position:0%
+bunch of tests so let's take a look
+uh okay so i got a bunch of sequence
+
+ align:start position:0%
+uh okay so i got a bunch of sequence
+ 
+
+ align:start position:0%
+uh okay so i got a bunch of sequence
+operations right we got build set at get
+
+ align:start position:0%
+operations right we got build set at get
+ 
+
+ align:start position:0%
+operations right we got build set at get
+at insert delete
+
+ align:start position:0%
+at insert delete
+ 
+
+ align:start position:0%
+at insert delete
+at the various places right and i'm
+
+ align:start position:0%
+at the various places right and i'm
+ 
+
+ align:start position:0%
+at the various places right and i'm
+giving these are the actual timings to
+
+ align:start position:0%
+giving these are the actual timings to
+ 
+
+ align:start position:0%
+giving these are the actual timings to
+some scale
+
+ align:start position:0%
+some scale
+ 
+
+ align:start position:0%
+some scale
+right to some resolution that i had for
+
+ align:start position:0%
+right to some resolution that i had for
+ 
+
+ align:start position:0%
+right to some resolution that i had for
+these data structures
+
+ align:start position:0%
+these data structures
+ 
+
+ align:start position:0%
+these data structures
+and you can see build actually build
+
+ align:start position:0%
+and you can see build actually build
+ 
+
+ align:start position:0%
+and you can see build actually build
+on this machine just allocating some
+
+ align:start position:0%
+on this machine just allocating some
+ 
+
+ align:start position:0%
+on this machine just allocating some
+array and clearing it is a really
+
+ align:start position:0%
+array and clearing it is a really
+ 
+
+ align:start position:0%
+array and clearing it is a really
+efficient thing that's python's going to
+
+ align:start position:0%
+efficient thing that's python's going to
+ 
+
+ align:start position:0%
+efficient thing that's python's going to
+do for me
+
+ align:start position:0%
+do for me
+ 
+
+ align:start position:0%
+do for me
+and so that's actually it's miss
+
+ align:start position:0%
+and so that's actually it's miss
+ 
+
+ align:start position:0%
+and so that's actually it's miss
+labeling that as log n right
+
+ align:start position:0%
+labeling that as log n right
+ 
+
+ align:start position:0%
+labeling that as log n right
+uh but uh you know these other things
+
+ align:start position:0%
+uh but uh you know these other things
+ 
+
+ align:start position:0%
+uh but uh you know these other things
+get out and set act
+
+ align:start position:0%
+get out and set act
+ 
+
+ align:start position:0%
+get out and set act
+really really fast right that's constant
+
+ align:start position:0%
+really really fast right that's constant
+ 
+
+ align:start position:0%
+really really fast right that's constant
+time and then these other things i
+
+ align:start position:0%
+time and then these other things i
+ 
+
+ align:start position:0%
+time and then these other things i
+essentially have
+
+ align:start position:0%
+essentially have
+ 
+
+ align:start position:0%
+essentially have
+can't do better than loop through the
+
+ align:start position:0%
+can't do better than loop through the
+ 
+
+ align:start position:0%
+can't do better than loop through the
+thing and so it takes linear time
+
+ align:start position:0%
+thing and so it takes linear time
+ 
+
+ align:start position:0%
+thing and so it takes linear time
+and again sequence uh stuff
+
+ align:start position:0%
+and again sequence uh stuff
+ 
+
+ align:start position:0%
+and again sequence uh stuff
+setting at and getting at is slow but
+
+ align:start position:0%
+setting at and getting at is slow but
+ 
+
+ align:start position:0%
+setting at and getting at is slow but
+deleting
+
+ align:start position:0%
+deleting
+ 
+
+ align:start position:0%
+deleting
+and removing from the first thing i'm
+
+ align:start position:0%
+and removing from the first thing i'm
+ 
+
+ align:start position:0%
+and removing from the first thing i'm
+just re-linking the pointer right
+
+ align:start position:0%
+just re-linking the pointer right
+ 
+
+ align:start position:0%
+just re-linking the pointer right
+dynamic arrays again set at get ad is
+
+ align:start position:0%
+dynamic arrays again set at get ad is
+ 
+
+ align:start position:0%
+dynamic arrays again set at get ad is
+fast because it's just
+
+ align:start position:0%
+fast because it's just
+ 
+
+ align:start position:0%
+fast because it's just
+dynamic it's just regular arrays and
+
+ align:start position:0%
+dynamic it's just regular arrays and
+ 
+
+ align:start position:0%
+dynamic it's just regular arrays and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+inserting and deleting last that's
+
+ align:start position:0%
+inserting and deleting last that's
+ 
+
+ align:start position:0%
+inserting and deleting last that's
+getting the essentially constant time
+
+ align:start position:0%
+getting the essentially constant time
+ 
+
+ align:start position:0%
+getting the essentially constant time
+now i'm actually when i'm running these
+
+ align:start position:0%
+now i'm actually when i'm running these
+ 
+
+ align:start position:0%
+now i'm actually when i'm running these
+tests to deal with averages
+
+ align:start position:0%
+tests to deal with averages
+ 
+
+ align:start position:0%
+tests to deal with averages
+i'm actually running these things a lot
+
+ align:start position:0%
+i'm actually running these things a lot
+ 
+
+ align:start position:0%
+i'm actually running these things a lot
+of times and testing their performance
+
+ align:start position:0%
+of times and testing their performance
+ 
+
+ align:start position:0%
+of times and testing their performance
+and so i'm not seeing the worst case
+
+ align:start position:0%
+and so i'm not seeing the worst case
+ 
+
+ align:start position:0%
+and so i'm not seeing the worst case
+happen here
+
+ align:start position:0%
+happen here
+ 
+
+ align:start position:0%
+happen here
+right i'm averaging over all of the
+
+ align:start position:0%
+right i'm averaging over all of the
+ 
+
+ align:start position:0%
+right i'm averaging over all of the
+things which is exactly what
+
+ align:start position:0%
+things which is exactly what
+ 
+
+ align:start position:0%
+things which is exactly what
+amortization
+
+ align:start position:0%
+amortization
+ 
+
+ align:start position:0%
+amortization
+means and so that's why i'm getting good
+
+ align:start position:0%
+means and so that's why i'm getting good
+ 
+
+ align:start position:0%
+means and so that's why i'm getting good
+performance here
+
+ align:start position:0%
+performance here
+ 
+
+ align:start position:0%
+performance here
+uh a hash table again
+
+ align:start position:0%
+uh a hash table again
+ 
+
+ align:start position:0%
+uh a hash table again
+really uh oh so this is what we talked
+
+ align:start position:0%
+really uh oh so this is what we talked
+ 
+
+ align:start position:0%
+really uh oh so this is what we talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+in problem session last week right
+
+ align:start position:0%
+in problem session last week right
+ 
+
+ align:start position:0%
+in problem session last week right
+implementing a uh kind of a double-ended
+
+ align:start position:0%
+implementing a uh kind of a double-ended
+ 
+
+ align:start position:0%
+implementing a uh kind of a double-ended
+queue with a hash table
+
+ align:start position:0%
+queue with a hash table
+ 
+
+ align:start position:0%
+queue with a hash table
+uh this is that implementation i just
+
+ align:start position:0%
+uh this is that implementation i just
+ 
+
+ align:start position:0%
+uh this is that implementation i just
+want to show it to you but it's actually
+
+ align:start position:0%
+want to show it to you but it's actually
+ 
+
+ align:start position:0%
+want to show it to you but it's actually
+pretty good this is what javascript uses
+
+ align:start position:0%
+pretty good this is what javascript uses
+ 
+
+ align:start position:0%
+pretty good this is what javascript uses
+for arrays
+
+ align:start position:0%
+for arrays
+ 
+
+ align:start position:0%
+for arrays
+and then a binary sequence represents a
+
+ align:start position:0%
+and then a binary sequence represents a
+ 
+
+ align:start position:0%
+and then a binary sequence represents a
+binary tree
+
+ align:start position:0%
+binary tree
+ 
+
+ align:start position:0%
+binary tree
+right a balanced binary tree this is our
+
+ align:start position:0%
+right a balanced binary tree this is our
+ 
+
+ align:start position:0%
+right a balanced binary tree this is our
+avl code that i had
+
+ align:start position:0%
+avl code that i had
+ 
+
+ align:start position:0%
+avl code that i had
+and you know all the other things have
+
+ align:start position:0%
+and you know all the other things have
+ 
+
+ align:start position:0%
+and you know all the other things have
+been really pretty bad at insert at and
+
+ align:start position:0%
+been really pretty bad at insert at and
+ 
+
+ align:start position:0%
+been really pretty bad at insert at and
+delete at
+
+ align:start position:0%
+delete at
+ 
+
+ align:start position:0%
+delete at
+but this one does comparable to all the
+
+ align:start position:0%
+but this one does comparable to all the
+ 
+
+ align:start position:0%
+but this one does comparable to all the
+other things now you see these are a
+
+ align:start position:0%
+other things now you see these are a
+ 
+
+ align:start position:0%
+other things now you see these are a
+little bit more
+
+ align:start position:0%
+little bit more
+ 
+
+ align:start position:0%
+little bit more
+you know machine cycles than the other
+
+ align:start position:0%
+you know machine cycles than the other
+ 
+
+ align:start position:0%
+you know machine cycles than the other
+things but
+
+ align:start position:0%
+things but
+ 
+
+ align:start position:0%
+things but
+you know not so bad actually uh and then
+
+ align:start position:0%
+you know not so bad actually uh and then
+ 
+
+ align:start position:0%
+you know not so bad actually uh and then
+on the set side of things
+
+ align:start position:0%
+on the set side of things
+ 
+
+ align:start position:0%
+on the set side of things
+again we had a sorted array uh sorry
+
+ align:start position:0%
+again we had a sorted array uh sorry
+ 
+
+ align:start position:0%
+again we had a sorted array uh sorry
+this is a set from
+
+ align:start position:0%
+this is a set from
+ 
+
+ align:start position:0%
+this is a set from
+an array basically it's an unsorted
+
+ align:start position:0%
+an array basically it's an unsorted
+ 
+
+ align:start position:0%
+an array basically it's an unsorted
+array i'm just looking for all the
+
+ align:start position:0%
+array i'm just looking for all the
+ 
+
+ align:start position:0%
+array i'm just looking for all the
+things that's very bad times
+
+ align:start position:0%
+things that's very bad times
+ 
+
+ align:start position:0%
+things that's very bad times
+sorted array does these fine operations
+
+ align:start position:0%
+sorted array does these fine operations
+ 
+
+ align:start position:0%
+sorted array does these fine operations
+great but inserting deleting is
+
+ align:start position:0%
+great but inserting deleting is
+ 
+
+ align:start position:0%
+great but inserting deleting is
+poor right that's why we need binary
+
+ align:start position:0%
+poor right that's why we need binary
+ 
+
+ align:start position:0%
+poor right that's why we need binary
+trees
+
+ align:start position:0%
+trees
+ 
+
+ align:start position:0%
+trees
+hash tables you know get good kind of
+
+ align:start position:0%
+hash tables you know get good kind of
+ 
+
+ align:start position:0%
+hash tables you know get good kind of
+dictionary operations but really bad
+
+ align:start position:0%
+dictionary operations but really bad
+ 
+
+ align:start position:0%
+dictionary operations but really bad
+order operations right
+
+ align:start position:0%
+order operations right
+ 
+
+ align:start position:0%
+order operations right
+and then the binary search tree right a
+
+ align:start position:0%
+and then the binary search tree right a
+ 
+
+ align:start position:0%
+and then the binary search tree right a
+set binary tree
+
+ align:start position:0%
+set binary tree
+ 
+
+ align:start position:0%
+set binary tree
+uh again does quite good on all of these
+
+ align:start position:0%
+uh again does quite good on all of these
+ 
+
+ align:start position:0%
+uh again does quite good on all of these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+in fact it's getting really quite good
+
+ align:start position:0%
+in fact it's getting really quite good
+ 
+
+ align:start position:0%
+in fact it's getting really quite good
+it's getting better for some reason than
+
+ align:start position:0%
+it's getting better for some reason than
+ 
+
+ align:start position:0%
+it's getting better for some reason than
+these the sorted array even did
+
+ align:start position:0%
+these the sorted array even did
+ 
+
+ align:start position:0%
+these the sorted array even did
+so uh i don't know why
+
+ align:start position:0%
+so uh i don't know why
+ 
+
+ align:start position:0%
+so uh i don't know why
+our implementations are not optimized at
+
+ align:start position:0%
+our implementations are not optimized at
+ 
+
+ align:start position:0%
+our implementations are not optimized at
+all but it does pretty well
+
+ align:start position:0%
+all but it does pretty well
+ 
+
+ align:start position:0%
+all but it does pretty well
+asymptotically yep um could you explain
+
+ align:start position:0%
+asymptotically yep um could you explain
+ 
+
+ align:start position:0%
+asymptotically yep um could you explain
+again why the
+
+ align:start position:0%
+again why the
+ 
+
+ align:start position:0%
+again why the
+in the first day of surgery was blog
+
+ align:start position:0%
+in the first day of surgery was blog
+ 
+
+ align:start position:0%
+in the first day of surgery was blog
+this is just labeled based off the
+
+ align:start position:0%
+this is just labeled based off the
+ 
+
+ align:start position:0%
+this is just labeled based off the
+timings right
+
+ align:start position:0%
+timings right
+ 
+
+ align:start position:0%
+timings right
+it happens to be that probably there's a
+
+ align:start position:0%
+it happens to be that probably there's a
+ 
+
+ align:start position:0%
+it happens to be that probably there's a
+c intrinsic underneath python
+
+ align:start position:0%
+c intrinsic underneath python
+ 
+
+ align:start position:0%
+c intrinsic underneath python
+that allocates this thing and so it does
+
+ align:start position:0%
+that allocates this thing and so it does
+ 
+
+ align:start position:0%
+that allocates this thing and so it does
+it really fast and so my
+
+ align:start position:0%
+it really fast and so my
+ 
+
+ align:start position:0%
+it really fast and so my
+program that's looking at these numbers
+
+ align:start position:0%
+program that's looking at these numbers
+ 
+
+ align:start position:0%
+program that's looking at these numbers
+and trying to guess what the asymptotic
+
+ align:start position:0%
+and trying to guess what the asymptotic
+ 
+
+ align:start position:0%
+and trying to guess what the asymptotic
+running time is
+
+ align:start position:0%
+running time is
+ 
+
+ align:start position:0%
+running time is
+these are just labels based on these
+
+ align:start position:0%
+these are just labels based on these
+ 
+
+ align:start position:0%
+these are just labels based on these
+things ranges
+
+ align:start position:0%
+things ranges
+ 
+
+ align:start position:0%
+things ranges
+i just it's it's mis characterizing
+
+ align:start position:0%
+i just it's it's mis characterizing
+ 
+
+ align:start position:0%
+i just it's it's mis characterizing
+actually building it at any time
+
+ align:start position:0%
+actually building it at any time
+ 
+
+ align:start position:0%
+actually building it at any time
+yeah well i mean in in actuality if it
+
+ align:start position:0%
+yeah well i mean in in actuality if it
+ 
+
+ align:start position:0%
+yeah well i mean in in actuality if it
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+c code right if all of this stuff was in
+
+ align:start position:0%
+c code right if all of this stuff was in
+ 
+
+ align:start position:0%
+c code right if all of this stuff was in
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+probably we'd see that that bar be
+
+ align:start position:0%
+probably we'd see that that bar be
+ 
+
+ align:start position:0%
+probably we'd see that that bar be
+longer because it's actually having to
+
+ align:start position:0%
+longer because it's actually having to
+ 
+
+ align:start position:0%
+longer because it's actually having to
+go through and touch all that memory
+
+ align:start position:0%
+go through and touch all that memory
+ 
+
+ align:start position:0%
+go through and touch all that memory
+it's still doing that here but all the
+
+ align:start position:0%
+it's still doing that here but all the
+ 
+
+ align:start position:0%
+it's still doing that here but all the
+python stuff is super crafty right it's
+
+ align:start position:0%
+python stuff is super crafty right it's
+ 
+
+ align:start position:0%
+python stuff is super crafty right it's
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+100 times slower than anything that c
+
+ align:start position:0%
+100 times slower than anything that c
+ 
+
+ align:start position:0%
+100 times slower than anything that c
+does and so
+
+ align:start position:0%
+does and so
+ 
+
+ align:start position:0%
+does and so
+you're seeing that that disparity here
+
+ align:start position:0%
+you're seeing that that disparity here
+ 
+
+ align:start position:0%
+you're seeing that that disparity here
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+okay so i just wanted to show you that
+
+ align:start position:0%
+okay so i just wanted to show you that
+ 
+
+ align:start position:0%
+okay so i just wanted to show you that
+uh we might release this
+
+ align:start position:0%
+uh we might release this
+ 
+
+ align:start position:0%
+uh we might release this
+for you to play around with but i just
+
+ align:start position:0%
+for you to play around with but i just
+ 
+
+ align:start position:0%
+for you to play around with but i just
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+give you a taste of that okay any
+
+ align:start position:0%
+give you a taste of that okay any
+ 
+
+ align:start position:0%
+give you a taste of that okay any
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+you move on how do i turn this off
+
+ align:start position:0%
+you move on how do i turn this off
+ 
+
+ align:start position:0%
+you move on how do i turn this off
+up and off
+
+ align:start position:0%
+up and off
+ 
+
+ align:start position:0%
+up and off
+shut down
+
+ align:start position:0%
+shut down
+ 
+
+ align:start position:0%
+shut down
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so moving on to problems
+
+ align:start position:0%
+all right so moving on to problems
+ 
+
+ align:start position:0%
+all right so moving on to problems
+working some problems uh so you have
+
+ align:start position:0%
+working some problems uh so you have
+ 
+
+ align:start position:0%
+working some problems uh so you have
+your set of problems here uh the first
+
+ align:start position:0%
+your set of problems here uh the first
+ 
+
+ align:start position:0%
+your set of problems here uh the first
+one is we're going to look at a sequence
+
+ align:start position:0%
+one is we're going to look at a sequence
+ 
+
+ align:start position:0%
+one is we're going to look at a sequence
+avl tree right this is a sequence abl
+
+ align:start position:0%
+avl tree right this is a sequence abl
+ 
+
+ align:start position:0%
+avl tree right this is a sequence abl
+tree how do i know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't necessarily but these things
+
+ align:start position:0%
+you don't necessarily but these things
+ 
+
+ align:start position:0%
+you don't necessarily but these things
+are certainly not
+
+ align:start position:0%
+are certainly not
+ 
+
+ align:start position:0%
+are certainly not
+in sorted order of the things i'm
+
+ align:start position:0%
+in sorted order of the things i'm
+ 
+
+ align:start position:0%
+in sorted order of the things i'm
+storied in them
+
+ align:start position:0%
+storied in them
+ 
+
+ align:start position:0%
+storied in them
+right so it better not be a set avl tree
+
+ align:start position:0%
+right so it better not be a set avl tree
+ 
+
+ align:start position:0%
+right so it better not be a set avl tree
+right is it an avl tree is it balanced
+
+ align:start position:0%
+right is it an avl tree is it balanced
+ 
+
+ align:start position:0%
+right is it an avl tree is it balanced
+height balanced
+
+ align:start position:0%
+height balanced
+ 
+
+ align:start position:0%
+height balanced
+yeah yeah basically actually if you take
+
+ align:start position:0%
+yeah yeah basically actually if you take
+ 
+
+ align:start position:0%
+yeah yeah basically actually if you take
+compute the size of each subtree
+
+ align:start position:0%
+compute the size of each subtree
+ 
+
+ align:start position:0%
+compute the size of each subtree
+right the left and right sub-trees on
+
+ align:start position:0%
+right the left and right sub-trees on
+ 
+
+ align:start position:0%
+right the left and right sub-trees on
+all these you can confirm for yourself
+
+ align:start position:0%
+all these you can confirm for yourself
+ 
+
+ align:start position:0%
+all these you can confirm for yourself
+are balanced right there they're
+
+ align:start position:0%
+are balanced right there they're
+ 
+
+ align:start position:0%
+are balanced right there they're
+within plus or minus one of each other
+
+ align:start position:0%
+within plus or minus one of each other
+ 
+
+ align:start position:0%
+within plus or minus one of each other
+actually this is about as far away from
+
+ align:start position:0%
+actually this is about as far away from
+ 
+
+ align:start position:0%
+actually this is about as far away from
+balance as you could get
+
+ align:start position:0%
+balance as you could get
+ 
+
+ align:start position:0%
+balance as you could get
+for this many nodes uh while still
+
+ align:start position:0%
+for this many nodes uh while still
+ 
+
+ align:start position:0%
+for this many nodes uh while still
+maintaining hype balance maintaining avl
+
+ align:start position:0%
+maintaining hype balance maintaining avl
+ 
+
+ align:start position:0%
+maintaining hype balance maintaining avl
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+which is why this is an instructive
+
+ align:start position:0%
+which is why this is an instructive
+ 
+
+ align:start position:0%
+which is why this is an instructive
+example it's kind of at the limit
+
+ align:start position:0%
+example it's kind of at the limit
+ 
+
+ align:start position:0%
+example it's kind of at the limit
+okay and uh
+
+ align:start position:0%
+okay and uh
+ 
+
+ align:start position:0%
+okay and uh
+what am i going to do this is a see
+
+ align:start position:0%
+what am i going to do this is a see
+ 
+
+ align:start position:0%
+what am i going to do this is a see
+what's missing in this picture
+
+ align:start position:0%
+what's missing in this picture
+ 
+
+ align:start position:0%
+what's missing in this picture
+if i'm claiming this is a sequence avl
+
+ align:start position:0%
+if i'm claiming this is a sequence avl
+ 
+
+ align:start position:0%
+if i'm claiming this is a sequence avl
+tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any ideas what's missing
+
+ align:start position:0%
+any ideas what's missing
+ 
+
+ align:start position:0%
+any ideas what's missing
+what is the sequence avl tree store that
+
+ align:start position:0%
+what is the sequence avl tree store that
+ 
+
+ align:start position:0%
+what is the sequence avl tree store that
+i'm not showing in this picture
+
+ align:start position:0%
+i'm not showing in this picture
+ 
+
+ align:start position:0%
+i'm not showing in this picture
+what counts and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a sequence avl tree heights
+
+ align:start position:0%
+it's a sequence avl tree heights
+ 
+
+ align:start position:0%
+it's a sequence avl tree heights
+right so it's a sequence avl trees
+
+ align:start position:0%
+right so it's a sequence avl trees
+ 
+
+ align:start position:0%
+right so it's a sequence avl trees
+different than set available trees are
+
+ align:start position:0%
+different than set available trees are
+ 
+
+ align:start position:0%
+different than set available trees are
+augmented by two things right because
+
+ align:start position:0%
+augmented by two things right because
+ 
+
+ align:start position:0%
+augmented by two things right because
+i need to be maintaining balance during
+
+ align:start position:0%
+i need to be maintaining balance during
+ 
+
+ align:start position:0%
+i need to be maintaining balance during
+rotations and so i need to store heights
+
+ align:start position:0%
+rotations and so i need to store heights
+ 
+
+ align:start position:0%
+rotations and so i need to store heights
+i need to be able to tell what the
+
+ align:start position:0%
+i need to be able to tell what the
+ 
+
+ align:start position:0%
+i need to be able to tell what the
+heights of these sub trees are in
+
+ align:start position:0%
+heights of these sub trees are in
+ 
+
+ align:start position:0%
+heights of these sub trees are in
+constant time when i'm
+
+ align:start position:0%
+constant time when i'm
+ 
+
+ align:start position:0%
+constant time when i'm
+walking up the tree fixing things and
+
+ align:start position:0%
+walking up the tree fixing things and
+ 
+
+ align:start position:0%
+walking up the tree fixing things and
+the sequence
+
+ align:start position:0%
+the sequence
+ 
+
+ align:start position:0%
+the sequence
+requires me to store their subtree the
+
+ align:start position:0%
+requires me to store their subtree the
+ 
+
+ align:start position:0%
+requires me to store their subtree the
+numbers there
+
+ align:start position:0%
+numbers there
+ 
+
+ align:start position:0%
+numbers there
+right so i don't know i'm not going to
+
+ align:start position:0%
+right so i don't know i'm not going to
+ 
+
+ align:start position:0%
+right so i don't know i'm not going to
+draw it for all of these things but how
+
+ align:start position:0%
+draw it for all of these things but how
+ 
+
+ align:start position:0%
+draw it for all of these things but how
+about for number 4
+
+ align:start position:0%
+about for number 4
+ 
+
+ align:start position:0%
+about for number 4
+what's its height
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one two three that's the longest path
+
+ align:start position:0%
+one two three that's the longest path
+ 
+
+ align:start position:0%
+one two three that's the longest path
+from the sub the root subtree of that so
+
+ align:start position:0%
+from the sub the root subtree of that so
+ 
+
+ align:start position:0%
+from the sub the root subtree of that so
+this is you know
+
+ align:start position:0%
+this is you know
+ 
+
+ align:start position:0%
+this is you know
+height equals uh three that came from
+
+ align:start position:0%
+height equals uh three that came from
+ 
+
+ align:start position:0%
+height equals uh three that came from
+height equals two and height is one let
+
+ align:start position:0%
+height equals two and height is one let
+ 
+
+ align:start position:0%
+height equals two and height is one let
+everyone see that
+
+ align:start position:0%
+everyone see that
+ 
+
+ align:start position:0%
+everyone see that
+yeah and then the size here how big is
+
+ align:start position:0%
+yeah and then the size here how big is
+ 
+
+ align:start position:0%
+yeah and then the size here how big is
+that that's
+
+ align:start position:0%
+that that's
+ 
+
+ align:start position:0%
+that that's
+one two three four five six seven right
+
+ align:start position:0%
+one two three four five six seven right
+ 
+
+ align:start position:0%
+one two three four five six seven right
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+i'm gonna put size equals seven
+
+ align:start position:0%
+i'm gonna put size equals seven
+ 
+
+ align:start position:0%
+i'm gonna put size equals seven
+here right and that's coming from this
+
+ align:start position:0%
+here right and that's coming from this
+ 
+
+ align:start position:0%
+here right and that's coming from this
+guy one two three
+
+ align:start position:0%
+guy one two three
+ 
+
+ align:start position:0%
+guy one two three
+four and this guy
+
+ align:start position:0%
+four and this guy
+ 
+
+ align:start position:0%
+four and this guy
+is two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so how do i compute the subtree
+
+ align:start position:0%
+right so how do i compute the subtree
+ 
+
+ align:start position:0%
+right so how do i compute the subtree
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+it's my left subtree size plus my right
+
+ align:start position:0%
+it's my left subtree size plus my right
+ 
+
+ align:start position:0%
+it's my left subtree size plus my right
+subtree size plus 1
+
+ align:start position:0%
+subtree size plus 1
+ 
+
+ align:start position:0%
+subtree size plus 1
+right and my height is taking the max of
+
+ align:start position:0%
+right and my height is taking the max of
+ 
+
+ align:start position:0%
+right and my height is taking the max of
+the 2 plus 1 right
+
+ align:start position:0%
+the 2 plus 1 right
+ 
+
+ align:start position:0%
+the 2 plus 1 right
+all right so we did all that yesterday
+
+ align:start position:0%
+all right so we did all that yesterday
+ 
+
+ align:start position:0%
+all right so we did all that yesterday
+so i'm
+
+ align:start position:0%
+so i'm
+ 
+
+ align:start position:0%
+so i'm
+just labeling these things and what i'm
+
+ align:start position:0%
+just labeling these things and what i'm
+ 
+
+ align:start position:0%
+just labeling these things and what i'm
+asking of you
+
+ align:start position:0%
+asking of you
+ 
+
+ align:start position:0%
+asking of you
+is to perform a delete operation
+
+ align:start position:0%
+is to perform a delete operation
+ 
+
+ align:start position:0%
+is to perform a delete operation
+is a sequence uh tree so i'm
+
+ align:start position:0%
+is a sequence uh tree so i'm
+ 
+
+ align:start position:0%
+is a sequence uh tree so i'm
+i'm finding things by their index in the
+
+ align:start position:0%
+i'm finding things by their index in the
+ 
+
+ align:start position:0%
+i'm finding things by their index in the
+tree right so i'm going to ask you to
+
+ align:start position:0%
+tree right so i'm going to ask you to
+ 
+
+ align:start position:0%
+tree right so i'm going to ask you to
+delete the eighth thing
+
+ align:start position:0%
+delete the eighth thing
+ 
+
+ align:start position:0%
+delete the eighth thing
+in my sequence okay so what is the
+
+ align:start position:0%
+in my sequence okay so what is the
+ 
+
+ align:start position:0%
+in my sequence okay so what is the
+eighth thing in my sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah all right just to clarify is not
+
+ align:start position:0%
+yeah all right just to clarify is not
+ 
+
+ align:start position:0%
+yeah all right just to clarify is not
+delete
+
+ align:start position:0%
+delete
+ 
+
+ align:start position:0%
+delete
+a number correct well delete at
+
+ align:start position:0%
+a number correct well delete at
+ 
+
+ align:start position:0%
+a number correct well delete at
+eight do you see that it's a sequence
+
+ align:start position:0%
+eight do you see that it's a sequence
+ 
+
+ align:start position:0%
+eight do you see that it's a sequence
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+yeah so this is very important that you
+
+ align:start position:0%
+yeah so this is very important that you
+ 
+
+ align:start position:0%
+yeah so this is very important that you
+differentiate between
+
+ align:start position:0%
+differentiate between
+ 
+
+ align:start position:0%
+differentiate between
+sequence and set semantics right if i'm
+
+ align:start position:0%
+sequence and set semantics right if i'm
+ 
+
+ align:start position:0%
+sequence and set semantics right if i'm
+dealing with the sequence
+
+ align:start position:0%
+dealing with the sequence
+ 
+
+ align:start position:0%
+dealing with the sequence
+i better not be looking up intrinsic
+
+ align:start position:0%
+i better not be looking up intrinsic
+ 
+
+ align:start position:0%
+i better not be looking up intrinsic
+things on this data structure right
+
+ align:start position:0%
+things on this data structure right
+ 
+
+ align:start position:0%
+things on this data structure right
+because it's not an intrinsic data
+
+ align:start position:0%
+because it's not an intrinsic data
+ 
+
+ align:start position:0%
+because it's not an intrinsic data
+structure it doesn't support that so if
+
+ align:start position:0%
+structure it doesn't support that so if
+ 
+
+ align:start position:0%
+structure it doesn't support that so if
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+wanted to support find
+
+ align:start position:0%
+wanted to support find
+ 
+
+ align:start position:0%
+wanted to support find
+the say the index of key 8
+
+ align:start position:0%
+the say the index of key 8
+ 
+
+ align:start position:0%
+the say the index of key 8
+or something like that right then all i
+
+ align:start position:0%
+or something like that right then all i
+ 
+
+ align:start position:0%
+or something like that right then all i
+could do is it's similar to like an
+
+ align:start position:0%
+could do is it's similar to like an
+ 
+
+ align:start position:0%
+could do is it's similar to like an
+array i would just have to loop through
+
+ align:start position:0%
+array i would just have to loop through
+ 
+
+ align:start position:0%
+array i would just have to loop through
+the whole sequence and tell me if the
+
+ align:start position:0%
+the whole sequence and tell me if the
+ 
+
+ align:start position:0%
+the whole sequence and tell me if the
+thing's in there
+
+ align:start position:0%
+thing's in there
+ 
+
+ align:start position:0%
+thing's in there
+right can't really do better than linear
+
+ align:start position:0%
+right can't really do better than linear
+ 
+
+ align:start position:0%
+right can't really do better than linear
+time this data structure is not designed
+
+ align:start position:0%
+time this data structure is not designed
+ 
+
+ align:start position:0%
+time this data structure is not designed
+for that what is it designed for it's
+
+ align:start position:0%
+for that what is it designed for it's
+ 
+
+ align:start position:0%
+for that what is it designed for it's
+designed to find things by their index
+
+ align:start position:0%
+designed to find things by their index
+ 
+
+ align:start position:0%
+designed to find things by their index
+in the sequence right so uh
+
+ align:start position:0%
+in the sequence right so uh
+ 
+
+ align:start position:0%
+in the sequence right so uh
+how do i find the eighth index
+
+ align:start position:0%
+how do i find the eighth index
+ 
+
+ align:start position:0%
+how do i find the eighth index
+well i mean i'm looking at the tree and
+
+ align:start position:0%
+well i mean i'm looking at the tree and
+ 
+
+ align:start position:0%
+well i mean i'm looking at the tree and
+i can just
+
+ align:start position:0%
+i can just
+ 
+
+ align:start position:0%
+i can just
+you know count along the in order
+
+ align:start position:0%
+you know count along the in order
+ 
+
+ align:start position:0%
+you know count along the in order
+traversal what's the inorder traversal
+
+ align:start position:0%
+traversal what's the inorder traversal
+ 
+
+ align:start position:0%
+traversal what's the inorder traversal
+right zero one two
+
+ align:start position:0%
+right zero one two
+ 
+
+ align:start position:0%
+right zero one two
+three four five six seven eight okay
+
+ align:start position:0%
+three four five six seven eight okay
+ 
+
+ align:start position:0%
+three four five six seven eight okay
+found eight but what does a sequence avl
+
+ align:start position:0%
+found eight but what does a sequence avl
+ 
+
+ align:start position:0%
+found eight but what does a sequence avl
+tree do
+
+ align:start position:0%
+tree do
+ 
+
+ align:start position:0%
+tree do
+right it i'm storing subtree sizes
+
+ align:start position:0%
+right it i'm storing subtree sizes
+ 
+
+ align:start position:0%
+right it i'm storing subtree sizes
+and when i'm here i don't know what
+
+ align:start position:0%
+and when i'm here i don't know what
+ 
+
+ align:start position:0%
+and when i'm here i don't know what
+index i'm at right
+
+ align:start position:0%
+index i'm at right
+ 
+
+ align:start position:0%
+index i'm at right
+how can i find out what index i'm at
+
+ align:start position:0%
+how can i find out what index i'm at
+ 
+
+ align:start position:0%
+how can i find out what index i'm at
+from the root i look at my left sub tree
+
+ align:start position:0%
+from the root i look at my left sub tree
+ 
+
+ align:start position:0%
+from the root i look at my left sub tree
+see how many it is
+
+ align:start position:0%
+see how many it is
+ 
+
+ align:start position:0%
+see how many it is
+right there are seven things here
+
+ align:start position:0%
+right there are seven things here
+ 
+
+ align:start position:0%
+right there are seven things here
+uh one two three four five seven
+
+ align:start position:0%
+uh one two three four five seven
+ 
+
+ align:start position:0%
+uh one two three four five seven
+eight right yeah because i'm looking for
+
+ align:start position:0%
+eight right yeah because i'm looking for
+ 
+
+ align:start position:0%
+eight right yeah because i'm looking for
+the ninth item
+
+ align:start position:0%
+the ninth item
+ 
+
+ align:start position:0%
+the ninth item
+by index eight right so this is saying
+
+ align:start position:0%
+by index eight right so this is saying
+ 
+
+ align:start position:0%
+by index eight right so this is saying
+that i'm the eighth item
+
+ align:start position:0%
+that i'm the eighth item
+ 
+
+ align:start position:0%
+that i'm the eighth item
+right and the guy at index seven
+
+ align:start position:0%
+right and the guy at index seven
+ 
+
+ align:start position:0%
+right and the guy at index seven
+does that make sense because i'm looking
+
+ align:start position:0%
+does that make sense because i'm looking
+ 
+
+ align:start position:0%
+does that make sense because i'm looking
+at the subtree size here
+
+ align:start position:0%
+at the subtree size here
+ 
+
+ align:start position:0%
+at the subtree size here
+so what do i know i know that the index
+
+ align:start position:0%
+so what do i know i know that the index
+ 
+
+ align:start position:0%
+so what do i know i know that the index
+that i'm looking for is to my right
+
+ align:start position:0%
+that i'm looking for is to my right
+ 
+
+ align:start position:0%
+that i'm looking for is to my right
+right so i go down over here
+
+ align:start position:0%
+right so i go down over here
+ 
+
+ align:start position:0%
+right so i go down over here
+and i happen to know what am i what
+
+ align:start position:0%
+and i happen to know what am i what
+ 
+
+ align:start position:0%
+and i happen to know what am i what
+index of
+
+ align:start position:0%
+index of
+ 
+
+ align:start position:0%
+index of
+of am i looking for in this subtree
+
+ align:start position:0%
+of am i looking for in this subtree
+ 
+
+ align:start position:0%
+of am i looking for in this subtree
+zero right i want the first thing in
+
+ align:start position:0%
+zero right i want the first thing in
+ 
+
+ align:start position:0%
+zero right i want the first thing in
+this sub tree
+
+ align:start position:0%
+this sub tree
+ 
+
+ align:start position:0%
+this sub tree
+my search index has changed now right
+
+ align:start position:0%
+my search index has changed now right
+ 
+
+ align:start position:0%
+my search index has changed now right
+because i
+
+ align:start position:0%
+because i
+ 
+
+ align:start position:0%
+because i
+essentially dealt with all of those
+
+ align:start position:0%
+essentially dealt with all of those
+ 
+
+ align:start position:0%
+essentially dealt with all of those
+eight items
+
+ align:start position:0%
+eight items
+ 
+
+ align:start position:0%
+eight items
+right so here i'm looking for the zero
+
+ align:start position:0%
+right so here i'm looking for the zero
+ 
+
+ align:start position:0%
+right so here i'm looking for the zero
+thing in my index
+
+ align:start position:0%
+thing in my index
+ 
+
+ align:start position:0%
+thing in my index
+i look to my left if i didn't have a
+
+ align:start position:0%
+i look to my left if i didn't have a
+ 
+
+ align:start position:0%
+i look to my left if i didn't have a
+left sub tree i would be the zero thing
+
+ align:start position:0%
+left sub tree i would be the zero thing
+ 
+
+ align:start position:0%
+left sub tree i would be the zero thing
+right and i would return me but there is
+
+ align:start position:0%
+right and i would return me but there is
+ 
+
+ align:start position:0%
+right and i would return me but there is
+stuff in here so i'm looking for the
+
+ align:start position:0%
+stuff in here so i'm looking for the
+ 
+
+ align:start position:0%
+stuff in here so i'm looking for the
+zero thing in here right
+
+ align:start position:0%
+zero thing in here right
+ 
+
+ align:start position:0%
+zero thing in here right
+which is just him and i return it okay
+
+ align:start position:0%
+which is just him and i return it okay
+ 
+
+ align:start position:0%
+which is just him and i return it okay
+and actually what i'm doing is i'm
+
+ align:start position:0%
+and actually what i'm doing is i'm
+ 
+
+ align:start position:0%
+and actually what i'm doing is i'm
+deleting it
+
+ align:start position:0%
+deleting it
+ 
+
+ align:start position:0%
+deleting it
+right so i delete it
+
+ align:start position:0%
+right so i delete it
+ 
+
+ align:start position:0%
+right so i delete it
+yuck what's the problem here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm not high balance weird what's not
+
+ align:start position:0%
+i'm not high balance weird what's not
+ 
+
+ align:start position:0%
+i'm not high balance weird what's not
+height balanced here
+
+ align:start position:0%
+height balanced here
+ 
+
+ align:start position:0%
+height balanced here
+um the lug subtree is earth
+
+ align:start position:0%
+um the lug subtree is earth
+ 
+
+ align:start position:0%
+um the lug subtree is earth
+so this guy's not height balance right
+
+ align:start position:0%
+so this guy's not height balance right
+ 
+
+ align:start position:0%
+so this guy's not height balance right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this guy's subtree is not height balance
+
+ align:start position:0%
+this guy's subtree is not height balance
+ 
+
+ align:start position:0%
+this guy's subtree is not height balance
+right this guy's two this guy's one
+
+ align:start position:0%
+right this guy's two this guy's one
+ 
+
+ align:start position:0%
+right this guy's two this guy's one
+okay so how do we fix it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we do some rotations right this is
+
+ align:start position:0%
+we do some rotations right this is
+ 
+
+ align:start position:0%
+we do some rotations right this is
+actually the
+
+ align:start position:0%
+actually the
+ 
+
+ align:start position:0%
+actually the
+bad case that with the third bad case
+
+ align:start position:0%
+bad case that with the third bad case
+ 
+
+ align:start position:0%
+bad case that with the third bad case
+that we talked about yesterday
+
+ align:start position:0%
+that we talked about yesterday
+ 
+
+ align:start position:0%
+that we talked about yesterday
+right if i tried to just left rotate
+
+ align:start position:0%
+right if i tried to just left rotate
+ 
+
+ align:start position:0%
+right if i tried to just left rotate
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+guy what would it look like it would put
+
+ align:start position:0%
+guy what would it look like it would put
+ 
+
+ align:start position:0%
+guy what would it look like it would put
+12 here it would put 10 here and 8 would
+
+ align:start position:0%
+12 here it would put 10 here and 8 would
+ 
+
+ align:start position:0%
+12 here it would put 10 here and 8 would
+be attached to that
+
+ align:start position:0%
+be attached to that
+ 
+
+ align:start position:0%
+be attached to that
+now it's height balance wrong in the
+
+ align:start position:0%
+now it's height balance wrong in the
+ 
+
+ align:start position:0%
+now it's height balance wrong in the
+other direction right that's no good
+
+ align:start position:0%
+other direction right that's no good
+ 
+
+ align:start position:0%
+other direction right that's no good
+right so the way to handle this case
+
+ align:start position:0%
+right so the way to handle this case
+ 
+
+ align:start position:0%
+right so the way to handle this case
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+i'm badly skewed to the right
+
+ align:start position:0%
+i'm badly skewed to the right
+ 
+
+ align:start position:0%
+i'm badly skewed to the right
+but my right subtree is badly skew is
+
+ align:start position:0%
+but my right subtree is badly skew is
+ 
+
+ align:start position:0%
+but my right subtree is badly skew is
+skewed to the left
+
+ align:start position:0%
+skewed to the left
+ 
+
+ align:start position:0%
+skewed to the left
+i have to do a rotation here right
+
+ align:start position:0%
+i have to do a rotation here right
+ 
+
+ align:start position:0%
+i have to do a rotation here right
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+and then do a rotation so that's that's
+
+ align:start position:0%
+and then do a rotation so that's that's
+ 
+
+ align:start position:0%
+and then do a rotation so that's that's
+the formula okay
+
+ align:start position:0%
+the formula okay
+ 
+
+ align:start position:0%
+the formula okay
+so here we first do a right rotation at
+
+ align:start position:0%
+so here we first do a right rotation at
+ 
+
+ align:start position:0%
+so here we first do a right rotation at
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay which gives me something that looks
+
+ align:start position:0%
+okay which gives me something that looks
+ 
+
+ align:start position:0%
+okay which gives me something that looks
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8 10 okay
+
+ align:start position:0%
+8 10 okay
+ 
+
+ align:start position:0%
+8 10 okay
+well obviously this is uh not better
+
+ align:start position:0%
+well obviously this is uh not better
+ 
+
+ align:start position:0%
+well obviously this is uh not better
+than what was before but it's an
+
+ align:start position:0%
+than what was before but it's an
+ 
+
+ align:start position:0%
+than what was before but it's an
+intermediate step so that we can fix it
+
+ align:start position:0%
+intermediate step so that we can fix it
+ 
+
+ align:start position:0%
+intermediate step so that we can fix it
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+we right rotate here and then we left
+
+ align:start position:0%
+we right rotate here and then we left
+ 
+
+ align:start position:0%
+we right rotate here and then we left
+rotate here right
+
+ align:start position:0%
+rotate here right
+ 
+
+ align:start position:0%
+rotate here right
+the default is that we would left rotate
+
+ align:start position:0%
+the default is that we would left rotate
+ 
+
+ align:start position:0%
+the default is that we would left rotate
+here but because this had
+
+ align:start position:0%
+here but because this had
+ 
+
+ align:start position:0%
+here but because this had
+the skew in the wrong direction i need
+
+ align:start position:0%
+the skew in the wrong direction i need
+ 
+
+ align:start position:0%
+the skew in the wrong direction i need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+right rotate this one first and then we
+
+ align:start position:0%
+right rotate this one first and then we
+ 
+
+ align:start position:0%
+right rotate this one first and then we
+can do it so now i
+
+ align:start position:0%
+can do it so now i
+ 
+
+ align:start position:0%
+can do it so now i
+rotate all of these guys over right
+
+ align:start position:0%
+rotate all of these guys over right
+ 
+
+ align:start position:0%
+rotate all of these guys over right
+and put 12 down here 8 here
+
+ align:start position:0%
+and put 12 down here 8 here
+ 
+
+ align:start position:0%
+and put 12 down here 8 here
+10 here done
+
+ align:start position:0%
+10 here done
+ 
+
+ align:start position:0%
+10 here done
+everyone see that that's what a rotation
+
+ align:start position:0%
+everyone see that that's what a rotation
+ 
+
+ align:start position:0%
+everyone see that that's what a rotation
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+okay it takes a little while to get your
+
+ align:start position:0%
+okay it takes a little while to get your
+ 
+
+ align:start position:0%
+okay it takes a little while to get your
+mind wrapped around
+
+ align:start position:0%
+mind wrapped around
+ 
+
+ align:start position:0%
+mind wrapped around
+what the transformation is but hopefully
+
+ align:start position:0%
+what the transformation is but hopefully
+ 
+
+ align:start position:0%
+what the transformation is but hopefully
+you guys all followed
+
+ align:start position:0%
+you guys all followed
+ 
+
+ align:start position:0%
+you guys all followed
+that transformation there was a little
+
+ align:start position:0%
+that transformation there was a little
+ 
+
+ align:start position:0%
+that transformation there was a little
+magic while i was trying to draw yeah
+
+ align:start position:0%
+magic while i was trying to draw yeah
+ 
+
+ align:start position:0%
+magic while i was trying to draw yeah
+i still don't feel like this tree is
+
+ align:start position:0%
+i still don't feel like this tree is
+ 
+
+ align:start position:0%
+i still don't feel like this tree is
+high balance it's not
+
+ align:start position:0%
+high balance it's not
+ 
+
+ align:start position:0%
+high balance it's not
+good observation why is that this thing
+
+ align:start position:0%
+good observation why is that this thing
+ 
+
+ align:start position:0%
+good observation why is that this thing
+still has height three
+
+ align:start position:0%
+still has height three
+ 
+
+ align:start position:0%
+still has height three
+what is the height of this thing one
+
+ align:start position:0%
+what is the height of this thing one
+ 
+
+ align:start position:0%
+what is the height of this thing one
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this is height one and actually when i
+
+ align:start position:0%
+this is height one and actually when i
+ 
+
+ align:start position:0%
+this is height one and actually when i
+was doing that rotation
+
+ align:start position:0%
+was doing that rotation
+ 
+
+ align:start position:0%
+was doing that rotation
+i needed to update all these
+
+ align:start position:0%
+i needed to update all these
+ 
+
+ align:start position:0%
+i needed to update all these
+augmentations right
+
+ align:start position:0%
+augmentations right
+ 
+
+ align:start position:0%
+augmentations right
+how which augmentations did i really
+
+ align:start position:0%
+how which augmentations did i really
+ 
+
+ align:start position:0%
+how which augmentations did i really
+need to which subtrees have changed
+
+ align:start position:0%
+need to which subtrees have changed
+ 
+
+ align:start position:0%
+need to which subtrees have changed
+during those things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't remember what the thing looked
+
+ align:start position:0%
+i don't remember what the thing looked
+ 
+
+ align:start position:0%
+i don't remember what the thing looked
+like what did the thing look like
+
+ align:start position:0%
+like what did the thing look like
+ 
+
+ align:start position:0%
+like what did the thing look like
+10 10 had eight in its subtree
+
+ align:start position:0%
+10 10 had eight in its subtree
+ 
+
+ align:start position:0%
+10 10 had eight in its subtree
+so its subtree definitely changed right
+
+ align:start position:0%
+so its subtree definitely changed right
+ 
+
+ align:start position:0%
+so its subtree definitely changed right
+eight sub tree changed
+
+ align:start position:0%
+eight sub tree changed
+ 
+
+ align:start position:0%
+eight sub tree changed
+twelve didn't change eventually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's the case analysis that's
+
+ align:start position:0%
+okay so there's the case analysis that's
+ 
+
+ align:start position:0%
+okay so there's the case analysis that's
+in your lecture notes and was done in
+
+ align:start position:0%
+in your lecture notes and was done in
+ 
+
+ align:start position:0%
+in your lecture notes and was done in
+recitation
+
+ align:start position:0%
+recitation
+ 
+
+ align:start position:0%
+recitation
+right it tells you that these a b
+
+ align:start position:0%
+right it tells you that these a b
+ 
+
+ align:start position:0%
+right it tells you that these a b
+c d kind of sub trees right
+
+ align:start position:0%
+c d kind of sub trees right
+ 
+
+ align:start position:0%
+c d kind of sub trees right
+the ones that could change in these
+
+ align:start position:0%
+the ones that could change in these
+ 
+
+ align:start position:0%
+the ones that could change in these
+things those sub trees don't change
+
+ align:start position:0%
+things those sub trees don't change
+ 
+
+ align:start position:0%
+things those sub trees don't change
+the only sub trees that change during
+
+ align:start position:0%
+the only sub trees that change during
+ 
+
+ align:start position:0%
+the only sub trees that change during
+one of these fixed operations when you
+
+ align:start position:0%
+one of these fixed operations when you
+ 
+
+ align:start position:0%
+one of these fixed operations when you
+do one or two rotations
+
+ align:start position:0%
+do one or two rotations
+ 
+
+ align:start position:0%
+do one or two rotations
+is either two nodes or three nodes that
+
+ align:start position:0%
+is either two nodes or three nodes that
+ 
+
+ align:start position:0%
+is either two nodes or three nodes that
+whose subtree has changed here uh it
+
+ align:start position:0%
+whose subtree has changed here uh it
+ 
+
+ align:start position:0%
+whose subtree has changed here uh it
+could have been the case that three
+
+ align:start position:0%
+could have been the case that three
+ 
+
+ align:start position:0%
+could have been the case that three
+sub trees have changed right but in the
+
+ align:start position:0%
+sub trees have changed right but in the
+ 
+
+ align:start position:0%
+sub trees have changed right but in the
+easy case
+
+ align:start position:0%
+easy case
+ 
+
+ align:start position:0%
+easy case
+only two nodes x and y i think in the
+
+ align:start position:0%
+only two nodes x and y i think in the
+ 
+
+ align:start position:0%
+only two nodes x and y i think in the
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+could have changed and so when i do that
+
+ align:start position:0%
+could have changed and so when i do that
+ 
+
+ align:start position:0%
+could have changed and so when i do that
+i have to recompute
+
+ align:start position:0%
+i have to recompute
+ 
+
+ align:start position:0%
+i have to recompute
+their augmentations from their
+
+ align:start position:0%
+their augmentations from their
+ 
+
+ align:start position:0%
+their augmentations from their
+augmentations of their children
+
+ align:start position:0%
+augmentations of their children
+ 
+
+ align:start position:0%
+augmentations of their children
+but uh it's only a constant number of
+
+ align:start position:0%
+but uh it's only a constant number of
+ 
+
+ align:start position:0%
+but uh it's only a constant number of
+those so i just
+
+ align:start position:0%
+those so i just
+ 
+
+ align:start position:0%
+those so i just
+recompute them because i the sub trees
+
+ align:start position:0%
+recompute them because i the sub trees
+ 
+
+ align:start position:0%
+recompute them because i the sub trees
+below me haven't changed
+
+ align:start position:0%
+below me haven't changed
+ 
+
+ align:start position:0%
+below me haven't changed
+right okay so we have a height mismatch
+
+ align:start position:0%
+right okay so we have a height mismatch
+ 
+
+ align:start position:0%
+right okay so we have a height mismatch
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+yeah should be where
+
+ align:start position:0%
+yeah should be where
+ 
+
+ align:start position:0%
+yeah should be where
+eight is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so uh originally in the picture
+
+ align:start position:0%
+right so uh originally in the picture
+ 
+
+ align:start position:0%
+right so uh originally in the picture
+12 has a bunch of things in its subtree
+
+ align:start position:0%
+12 has a bunch of things in its subtree
+ 
+
+ align:start position:0%
+12 has a bunch of things in its subtree
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+10 and 8 and we just deleted seven right
+
+ align:start position:0%
+10 and 8 and we just deleted seven right
+ 
+
+ align:start position:0%
+10 and 8 and we just deleted seven right
+so its subtree definitely changed there
+
+ align:start position:0%
+so its subtree definitely changed there
+ 
+
+ align:start position:0%
+so its subtree definitely changed there
+used to be three
+
+ align:start position:0%
+used to be three
+ 
+
+ align:start position:0%
+used to be three
+oh no sorry it did right yeah so here
+
+ align:start position:0%
+oh no sorry it did right yeah so here
+ 
+
+ align:start position:0%
+oh no sorry it did right yeah so here
+three node sub trees have changed but
+
+ align:start position:0%
+three node sub trees have changed but
+ 
+
+ align:start position:0%
+three node sub trees have changed but
+uh that's the actually the most i'm
+
+ align:start position:0%
+uh that's the actually the most i'm
+ 
+
+ align:start position:0%
+uh that's the actually the most i'm
+showing you the worst
+
+ align:start position:0%
+showing you the worst
+ 
+
+ align:start position:0%
+showing you the worst
+case right only three nodes possible in
+
+ align:start position:0%
+case right only three nodes possible in
+ 
+
+ align:start position:0%
+case right only three nodes possible in
+doing one of these
+
+ align:start position:0%
+doing one of these
+ 
+
+ align:start position:0%
+doing one of these
+double rotation things could have
+
+ align:start position:0%
+double rotation things could have
+ 
+
+ align:start position:0%
+double rotation things could have
+changed their sub trees and so we just
+
+ align:start position:0%
+changed their sub trees and so we just
+ 
+
+ align:start position:0%
+changed their sub trees and so we just
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+fix the augmentation of those three
+
+ align:start position:0%
+fix the augmentation of those three
+ 
+
+ align:start position:0%
+fix the augmentation of those three
+things in the easy case it's just two
+
+ align:start position:0%
+things in the easy case it's just two
+ 
+
+ align:start position:0%
+things in the easy case it's just two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+okay all right we have a uh on balance
+
+ align:start position:0%
+okay all right we have a uh on balance
+ 
+
+ align:start position:0%
+okay all right we have a uh on balance
+how can we fix this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i could have been mean right i wanna be
+
+ align:start position:0%
+i could have been mean right i wanna be
+ 
+
+ align:start position:0%
+i could have been mean right i wanna be
+able to
+
+ align:start position:0%
+able to
+ 
+
+ align:start position:0%
+able to
+right rotate here right to rebalance i
+
+ align:start position:0%
+right rotate here right to rebalance i
+ 
+
+ align:start position:0%
+right rotate here right to rebalance i
+could have been mean and switch these
+
+ align:start position:0%
+could have been mean and switch these
+ 
+
+ align:start position:0%
+could have been mean and switch these
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+right if i switch those two then i'd
+
+ align:start position:0%
+right if i switch those two then i'd
+ 
+
+ align:start position:0%
+right if i switch those two then i'd
+have to do two rotations to fix this
+
+ align:start position:0%
+have to do two rotations to fix this
+ 
+
+ align:start position:0%
+have to do two rotations to fix this
+thing because the middle one is heavier
+
+ align:start position:0%
+thing because the middle one is heavier
+ 
+
+ align:start position:0%
+thing because the middle one is heavier
+than the
+
+ align:start position:0%
+than the
+ 
+
+ align:start position:0%
+than the
+left one against what i'm doing right
+
+ align:start position:0%
+left one against what i'm doing right
+ 
+
+ align:start position:0%
+left one against what i'm doing right
+but i'm not that mean so i'm going to
+
+ align:start position:0%
+but i'm not that mean so i'm going to
+ 
+
+ align:start position:0%
+but i'm not that mean so i'm going to
+right rotate how do i do that well right
+
+ align:start position:0%
+right rotate how do i do that well right
+ 
+
+ align:start position:0%
+right rotate how do i do that well right
+rotate
+
+ align:start position:0%
+rotate
+ 
+
+ align:start position:0%
+rotate
+at 6 is going to bring all of this
+
+ align:start position:0%
+at 6 is going to bring all of this
+ 
+
+ align:start position:0%
+at 6 is going to bring all of this
+down below 4 right and stick this
+
+ align:start position:0%
+down below 4 right and stick this
+ 
+
+ align:start position:0%
+down below 4 right and stick this
+subtree
+
+ align:start position:0%
+subtree
+ 
+
+ align:start position:0%
+subtree
+as the left child of 6. does that make
+
+ align:start position:0%
+as the left child of 6. does that make
+ 
+
+ align:start position:0%
+as the left child of 6. does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+yuck that's going to be fun to draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm just going to redraw it that makes
+
+ align:start position:0%
+i'm just going to redraw it that makes
+ 
+
+ align:start position:0%
+i'm just going to redraw it that makes
+more sense right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh eleven three two
+
+ align:start position:0%
+uh eleven three two
+ 
+
+ align:start position:0%
+uh eleven three two
+one and then six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five nine
+
+ align:start position:0%
+five nine
+ 
+
+ align:start position:0%
+five nine
+eight twelve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ten that's the right rotation
+
+ align:start position:0%
+ten that's the right rotation
+ 
+
+ align:start position:0%
+ten that's the right rotation
+at six is everyone cool with this
+
+ align:start position:0%
+at six is everyone cool with this
+ 
+
+ align:start position:0%
+at six is everyone cool with this
+the rotation my x is 6 my y is 4
+
+ align:start position:0%
+the rotation my x is 6 my y is 4
+ 
+
+ align:start position:0%
+the rotation my x is 6 my y is 4
+right i have a b c sub trees
+
+ align:start position:0%
+right i have a b c sub trees
+ 
+
+ align:start position:0%
+right i have a b c sub trees
+right what i'm doing is kind of
+
+ align:start position:0%
+right what i'm doing is kind of
+ 
+
+ align:start position:0%
+right what i'm doing is kind of
+switching
+
+ align:start position:0%
+switching
+ 
+
+ align:start position:0%
+switching
+which of x and y is the root here right
+
+ align:start position:0%
+which of x and y is the root here right
+ 
+
+ align:start position:0%
+which of x and y is the root here right
+so now y is the root
+
+ align:start position:0%
+so now y is the root
+ 
+
+ align:start position:0%
+so now y is the root
+and b and c sub trees here now become
+
+ align:start position:0%
+and b and c sub trees here now become
+ 
+
+ align:start position:0%
+and b and c sub trees here now become
+the children of x
+
+ align:start position:0%
+the children of x
+ 
+
+ align:start position:0%
+the children of x
+underneath y and notice that hopefully
+
+ align:start position:0%
+underneath y and notice that hopefully
+ 
+
+ align:start position:0%
+underneath y and notice that hopefully
+through all that process
+
+ align:start position:0%
+through all that process
+ 
+
+ align:start position:0%
+through all that process
+my inorder traversal has not changed
+
+ align:start position:0%
+my inorder traversal has not changed
+ 
+
+ align:start position:0%
+my inorder traversal has not changed
+we had to update our augmentations along
+
+ align:start position:0%
+we had to update our augmentations along
+ 
+
+ align:start position:0%
+we had to update our augmentations along
+the way but you know it's a constant
+
+ align:start position:0%
+the way but you know it's a constant
+ 
+
+ align:start position:0%
+the way but you know it's a constant
+every time we walk up the tree
+
+ align:start position:0%
+every time we walk up the tree
+ 
+
+ align:start position:0%
+every time we walk up the tree
+and we walk up the tree only a
+
+ align:start position:0%
+and we walk up the tree only a
+ 
+
+ align:start position:0%
+and we walk up the tree only a
+logarithmic number of times yeah
+
+ align:start position:0%
+logarithmic number of times yeah
+ 
+
+ align:start position:0%
+logarithmic number of times yeah
+yes so every time we do a rotation we
+
+ align:start position:0%
+yes so every time we do a rotation we
+ 
+
+ align:start position:0%
+yes so every time we do a rotation we
+just like
+
+ align:start position:0%
+just like
+ 
+
+ align:start position:0%
+just like
+update the augmentation immediately
+
+ align:start position:0%
+update the augmentation immediately
+ 
+
+ align:start position:0%
+update the augmentation immediately
+afterwards before we do any other
+
+ align:start position:0%
+afterwards before we do any other
+ 
+
+ align:start position:0%
+afterwards before we do any other
+routine exactly
+
+ align:start position:0%
+routine exactly
+ 
+
+ align:start position:0%
+routine exactly
+second part updating documentation just
+
+ align:start position:0%
+second part updating documentation just
+ 
+
+ align:start position:0%
+second part updating documentation just
+means like
+
+ align:start position:0%
+means like
+ 
+
+ align:start position:0%
+means like
+updating like the count and the height
+
+ align:start position:0%
+updating like the count and the height
+ 
+
+ align:start position:0%
+updating like the count and the height
+just the properties and stuff yeah
+
+ align:start position:0%
+just the properties and stuff yeah
+ 
+
+ align:start position:0%
+just the properties and stuff yeah
+basically what we did we
+
+ align:start position:0%
+basically what we did we
+ 
+
+ align:start position:0%
+basically what we did we
+define when we augmented uh professor
+
+ align:start position:0%
+define when we augmented uh professor
+ 
+
+ align:start position:0%
+define when we augmented uh professor
+domain yesterday
+
+ align:start position:0%
+domain yesterday
+ 
+
+ align:start position:0%
+domain yesterday
+defined for you what a subtree property
+
+ align:start position:0%
+defined for you what a subtree property
+ 
+
+ align:start position:0%
+defined for you what a subtree property
+is right
+
+ align:start position:0%
+is right
+ 
+
+ align:start position:0%
+is right
+it meant a property that i can compute
+
+ align:start position:0%
+it meant a property that i can compute
+ 
+
+ align:start position:0%
+it meant a property that i can compute
+only by looking at my children
+
+ align:start position:0%
+only by looking at my children
+ 
+
+ align:start position:0%
+only by looking at my children
+the augmentations of my children
+
+ align:start position:0%
+the augmentations of my children
+ 
+
+ align:start position:0%
+the augmentations of my children
+recursively right
+
+ align:start position:0%
+recursively right
+ 
+
+ align:start position:0%
+recursively right
+so here uh instead of trying to
+
+ align:start position:0%
+so here uh instead of trying to
+ 
+
+ align:start position:0%
+so here uh instead of trying to
+increment or try to think about locally
+
+ align:start position:0%
+increment or try to think about locally
+ 
+
+ align:start position:0%
+increment or try to think about locally
+what this augmentation should be
+
+ align:start position:0%
+what this augmentation should be
+ 
+
+ align:start position:0%
+what this augmentation should be
+i'm going to throw away my old
+
+ align:start position:0%
+i'm going to throw away my old
+ 
+
+ align:start position:0%
+i'm going to throw away my old
+augmentation and just recompute it from
+
+ align:start position:0%
+augmentation and just recompute it from
+ 
+
+ align:start position:0%
+augmentation and just recompute it from
+my children because
+
+ align:start position:0%
+my children because
+ 
+
+ align:start position:0%
+my children because
+those recursively better be correct does
+
+ align:start position:0%
+those recursively better be correct does
+ 
+
+ align:start position:0%
+those recursively better be correct does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+yeah so just looking at how the rotation
+
+ align:start position:0%
+yeah so just looking at how the rotation
+ 
+
+ align:start position:0%
+yeah so just looking at how the rotation
+works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically you're swapping four and
+
+ align:start position:0%
+so basically you're swapping four and
+ 
+
+ align:start position:0%
+so basically you're swapping four and
+six so that way four becomes the parent
+
+ align:start position:0%
+six so that way four becomes the parent
+ 
+
+ align:start position:0%
+six so that way four becomes the parent
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+and six becomes the right note
+
+ align:start position:0%
+and six becomes the right note
+ 
+
+ align:start position:0%
+and six becomes the right note
+i'm gonna draw this picture just
+
+ align:start position:0%
+i'm gonna draw this picture just
+ 
+
+ align:start position:0%
+i'm gonna draw this picture just
+it's just something you gotta memorize
+
+ align:start position:0%
+it's just something you gotta memorize
+ 
+
+ align:start position:0%
+it's just something you gotta memorize
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+this is x b
+
+ align:start position:0%
+this is x b
+ 
+
+ align:start position:0%
+this is x b
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+c and a
+
+ align:start position:0%
+c and a
+ 
+
+ align:start position:0%
+c and a
+can you see that picture okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's in your notes it's not a big
+
+ align:start position:0%
+yeah it's in your notes it's not a big
+ 
+
+ align:start position:0%
+yeah it's in your notes it's not a big
+deal right
+
+ align:start position:0%
+deal right
+ 
+
+ align:start position:0%
+deal right
+but if you've got this structure where
+
+ align:start position:0%
+but if you've got this structure where
+ 
+
+ align:start position:0%
+but if you've got this structure where
+x has a left child right
+
+ align:start position:0%
+x has a left child right
+ 
+
+ align:start position:0%
+x has a left child right
+and these sub trees may be empty or not
+
+ align:start position:0%
+and these sub trees may be empty or not
+ 
+
+ align:start position:0%
+and these sub trees may be empty or not
+doesn't really matter what i can do is i
+
+ align:start position:0%
+doesn't really matter what i can do is i
+ 
+
+ align:start position:0%
+doesn't really matter what i can do is i
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+move from here to there has the same
+
+ align:start position:0%
+move from here to there has the same
+ 
+
+ align:start position:0%
+move from here to there has the same
+in-order traversal order
+
+ align:start position:0%
+in-order traversal order
+ 
+
+ align:start position:0%
+in-order traversal order
+right but it's got a different shape and
+
+ align:start position:0%
+right but it's got a different shape and
+ 
+
+ align:start position:0%
+right but it's got a different shape and
+in particular subtree
+
+ align:start position:0%
+in particular subtree
+ 
+
+ align:start position:0%
+in particular subtree
+heights have changed which means it can
+
+ align:start position:0%
+heights have changed which means it can
+ 
+
+ align:start position:0%
+heights have changed which means it can
+help us rebalance the tree
+
+ align:start position:0%
+help us rebalance the tree
+ 
+
+ align:start position:0%
+help us rebalance the tree
+and that's that's the whole point of avl
+
+ align:start position:0%
+and that's that's the whole point of avl
+ 
+
+ align:start position:0%
+and that's that's the whole point of avl
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+and that's the right rotation this one
+
+ align:start position:0%
+and that's the right rotation this one
+ 
+
+ align:start position:0%
+and that's the right rotation this one
+is this is a right rotation this is a
+
+ align:start position:0%
+is this is a right rotation this is a
+ 
+
+ align:start position:0%
+is this is a right rotation this is a
+left rotation
+
+ align:start position:0%
+left rotation
+ 
+
+ align:start position:0%
+left rotation
+any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as i'm walking up the tree every node
+
+ align:start position:0%
+so as i'm walking up the tree every node
+ 
+
+ align:start position:0%
+so as i'm walking up the tree every node
+i might have to fix with the rebalance
+
+ align:start position:0%
+i might have to fix with the rebalance
+ 
+
+ align:start position:0%
+i might have to fix with the rebalance
+but that rebalance does at most two
+
+ align:start position:0%
+but that rebalance does at most two
+ 
+
+ align:start position:0%
+but that rebalance does at most two
+rotations
+
+ align:start position:0%
+rotations
+ 
+
+ align:start position:0%
+rotations
+and there's at most log n ancestors that
+
+ align:start position:0%
+and there's at most log n ancestors that
+ 
+
+ align:start position:0%
+and there's at most log n ancestors that
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+because my tree is height balance right
+
+ align:start position:0%
+because my tree is height balance right
+ 
+
+ align:start position:0%
+because my tree is height balance right
+at 2 2 log n or something like that
+
+ align:start position:0%
+at 2 2 log n or something like that
+ 
+
+ align:start position:0%
+at 2 2 log n or something like that
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+which means that at max i might have to
+
+ align:start position:0%
+which means that at max i might have to
+ 
+
+ align:start position:0%
+which means that at max i might have to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+four log n rotations right because each
+
+ align:start position:0%
+four log n rotations right because each
+ 
+
+ align:start position:0%
+four log n rotations right because each
+one could
+
+ align:start position:0%
+one could
+ 
+
+ align:start position:0%
+one could
+do two rotations so that makes sense now
+
+ align:start position:0%
+do two rotations so that makes sense now
+ 
+
+ align:start position:0%
+do two rotations so that makes sense now
+in actuality you can prove that in a
+
+ align:start position:0%
+in actuality you can prove that in a
+ 
+
+ align:start position:0%
+in actuality you can prove that in a
+delete operation
+
+ align:start position:0%
+delete operation
+ 
+
+ align:start position:0%
+delete operation
+it's possible that you have to do a
+
+ align:start position:0%
+it's possible that you have to do a
+ 
+
+ align:start position:0%
+it's possible that you have to do a
+logarithmic number of these rotations up
+
+ align:start position:0%
+logarithmic number of these rotations up
+ 
+
+ align:start position:0%
+logarithmic number of these rotations up
+the tree
+
+ align:start position:0%
+the tree
+ 
+
+ align:start position:0%
+the tree
+this was a that bad case this is called
+
+ align:start position:0%
+this was a that bad case this is called
+ 
+
+ align:start position:0%
+this was a that bad case this is called
+the original tree i gave you is called a
+
+ align:start position:0%
+the original tree i gave you is called a
+ 
+
+ align:start position:0%
+the original tree i gave you is called a
+fibonacci tree
+
+ align:start position:0%
+fibonacci tree
+ 
+
+ align:start position:0%
+fibonacci tree
+it's the fewest it's the highest uh
+
+ align:start position:0%
+it's the fewest it's the highest uh
+ 
+
+ align:start position:0%
+it's the fewest it's the highest uh
+height balanced tree you can have on a
+
+ align:start position:0%
+height balanced tree you can have on a
+ 
+
+ align:start position:0%
+height balanced tree you can have on a
+on a given number of nodes
+
+ align:start position:0%
+on a given number of nodes
+ 
+
+ align:start position:0%
+on a given number of nodes
+um uh that's it's
+
+ align:start position:0%
+um uh that's it's
+ 
+
+ align:start position:0%
+um uh that's it's
+yeah the fewest nodes for a certain
+
+ align:start position:0%
+yeah the fewest nodes for a certain
+ 
+
+ align:start position:0%
+yeah the fewest nodes for a certain
+height i i you can think of it either
+
+ align:start position:0%
+height i i you can think of it either
+ 
+
+ align:start position:0%
+height i i you can think of it either
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+and if you generalize that to a large
+
+ align:start position:0%
+and if you generalize that to a large
+ 
+
+ align:start position:0%
+and if you generalize that to a large
+enough thing then that thing will take a
+
+ align:start position:0%
+enough thing then that thing will take a
+ 
+
+ align:start position:0%
+enough thing then that thing will take a
+logarithmic number of rotations going up
+
+ align:start position:0%
+logarithmic number of rotations going up
+ 
+
+ align:start position:0%
+logarithmic number of rotations going up
+now actually with an insertion you can
+
+ align:start position:0%
+now actually with an insertion you can
+ 
+
+ align:start position:0%
+now actually with an insertion you can
+actually prove you can go through the
+
+ align:start position:0%
+actually prove you can go through the
+ 
+
+ align:start position:0%
+actually prove you can go through the
+case analysis
+
+ align:start position:0%
+case analysis
+ 
+
+ align:start position:0%
+case analysis
+uh an insertion operation will always
+
+ align:start position:0%
+uh an insertion operation will always
+ 
+
+ align:start position:0%
+uh an insertion operation will always
+rebalance the tree after one
+
+ align:start position:0%
+rebalance the tree after one
+ 
+
+ align:start position:0%
+rebalance the tree after one
+after one rebalance operation which
+
+ align:start position:0%
+after one rebalance operation which
+ 
+
+ align:start position:0%
+after one rebalance operation which
+could include two rotations does that
+
+ align:start position:0%
+could include two rotations does that
+ 
+
+ align:start position:0%
+could include two rotations does that
+make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so in right rotation this guy
+
+ align:start position:0%
+yeah so in right rotation this guy
+ 
+
+ align:start position:0%
+yeah so in right rotation this guy
+becomes a right child
+
+ align:start position:0%
+becomes a right child
+ 
+
+ align:start position:0%
+becomes a right child
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depending on whether you have a child
+
+ align:start position:0%
+depending on whether you have a child
+ 
+
+ align:start position:0%
+depending on whether you have a child
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+if i didn't have a left subtree
+
+ align:start position:0%
+if i didn't have a left subtree
+ 
+
+ align:start position:0%
+if i didn't have a left subtree
+can't perform rotation a right rotation
+
+ align:start position:0%
+can't perform rotation a right rotation
+ 
+
+ align:start position:0%
+can't perform rotation a right rotation
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+yeah so a right rotation necessitates
+
+ align:start position:0%
+yeah so a right rotation necessitates
+ 
+
+ align:start position:0%
+yeah so a right rotation necessitates
+that i have a left child so if you're
+
+ align:start position:0%
+that i have a left child so if you're
+ 
+
+ align:start position:0%
+that i have a left child so if you're
+doing it
+
+ align:start position:0%
+doing it
+ 
+
+ align:start position:0%
+doing it
+and you'll see our code actually checks
+
+ align:start position:0%
+and you'll see our code actually checks
+ 
+
+ align:start position:0%
+and you'll see our code actually checks
+to make sure you have a left child
+
+ align:start position:0%
+to make sure you have a left child
+ 
+
+ align:start position:0%
+to make sure you have a left child
+right uh
+
+ align:start position:0%
+right uh
+ 
+
+ align:start position:0%
+right uh
+that's that's a an assertion that you
+
+ align:start position:0%
+that's that's a an assertion that you
+ 
+
+ align:start position:0%
+that's that's a an assertion that you
+might want to fire before you ever do
+
+ align:start position:0%
+might want to fire before you ever do
+ 
+
+ align:start position:0%
+might want to fire before you ever do
+one of these rotations
+
+ align:start position:0%
+one of these rotations
+ 
+
+ align:start position:0%
+one of these rotations
+anything else yeah so an insertion may
+
+ align:start position:0%
+anything else yeah so an insertion may
+ 
+
+ align:start position:0%
+anything else yeah so an insertion may
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+two rotations at most to fix a constant
+
+ align:start position:0%
+two rotations at most to fix a constant
+ 
+
+ align:start position:0%
+two rotations at most to fix a constant
+number of rotations and the deletion
+
+ align:start position:0%
+number of rotations and the deletion
+ 
+
+ align:start position:0%
+number of rotations and the deletion
+could take a logarithmic number of
+
+ align:start position:0%
+could take a logarithmic number of
+ 
+
+ align:start position:0%
+could take a logarithmic number of
+partitions
+
+ align:start position:0%
+partitions
+ 
+
+ align:start position:0%
+partitions
+now that's not something you need to
+
+ align:start position:0%
+now that's not something you need to
+ 
+
+ align:start position:0%
+now that's not something you need to
+know it's not something i'm proving here
+
+ align:start position:0%
+know it's not something i'm proving here
+ 
+
+ align:start position:0%
+know it's not something i'm proving here
+to you
+
+ align:start position:0%
+to you
+ 
+
+ align:start position:0%
+to you
+uh just just something that's
+
+ align:start position:0%
+uh just just something that's
+ 
+
+ align:start position:0%
+uh just just something that's
+interesting there are rebalancing
+
+ align:start position:0%
+interesting there are rebalancing
+ 
+
+ align:start position:0%
+interesting there are rebalancing
+schemes like
+
+ align:start position:0%
+schemes like
+ 
+
+ align:start position:0%
+schemes like
+in in clrs right they they introduce
+
+ align:start position:0%
+in in clrs right they they introduce
+ 
+
+ align:start position:0%
+in in clrs right they they introduce
+a a red black tree to to introduce
+
+ align:start position:0%
+a a red black tree to to introduce
+ 
+
+ align:start position:0%
+a a red black tree to to introduce
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+and that those trees actually have a
+
+ align:start position:0%
+and that those trees actually have a
+ 
+
+ align:start position:0%
+and that those trees actually have a
+weaker bound on
+
+ align:start position:0%
+weaker bound on
+ 
+
+ align:start position:0%
+weaker bound on
+it's not as is tightly height balanced
+
+ align:start position:0%
+it's not as is tightly height balanced
+ 
+
+ align:start position:0%
+it's not as is tightly height balanced
+as as an
+
+ align:start position:0%
+as as an
+ 
+
+ align:start position:0%
+as as an
+avl tree is it allows higher than skew
+
+ align:start position:0%
+avl tree is it allows higher than skew
+ 
+
+ align:start position:0%
+avl tree is it allows higher than skew
+to right uh and because it's
+
+ align:start position:0%
+to right uh and because it's
+ 
+
+ align:start position:0%
+to right uh and because it's
+kind of a weaker restriction they get
+
+ align:start position:0%
+kind of a weaker restriction they get
+ 
+
+ align:start position:0%
+kind of a weaker restriction they get
+away with only doing a constant number
+
+ align:start position:0%
+away with only doing a constant number
+ 
+
+ align:start position:0%
+away with only doing a constant number
+of rotations that
+
+ align:start position:0%
+of rotations that
+ 
+
+ align:start position:0%
+of rotations that
+they can afford that before they fix the
+
+ align:start position:0%
+they can afford that before they fix the
+ 
+
+ align:start position:0%
+they can afford that before they fix the
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+uh but you know a little more
+
+ align:start position:0%
+uh but you know a little more
+ 
+
+ align:start position:0%
+uh but you know a little more
+complicated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very nice okay any questions on this
+
+ align:start position:0%
+very nice okay any questions on this
+ 
+
+ align:start position:0%
+very nice okay any questions on this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh now so this is more of a
+
+ align:start position:0%
+so uh now so this is more of a
+ 
+
+ align:start position:0%
+so uh now so this is more of a
+mechanical question
+
+ align:start position:0%
+mechanical question
+ 
+
+ align:start position:0%
+mechanical question
+you'll get on your problem sets and now
+
+ align:start position:0%
+you'll get on your problem sets and now
+ 
+
+ align:start position:0%
+you'll get on your problem sets and now
+we get more onto the uh
+
+ align:start position:0%
+we get more onto the uh
+ 
+
+ align:start position:0%
+we get more onto the uh
+the theory type questions these are
+
+ align:start position:0%
+the theory type questions these are
+ 
+
+ align:start position:0%
+the theory type questions these are
+going to be reduction type questions
+
+ align:start position:0%
+going to be reduction type questions
+ 
+
+ align:start position:0%
+going to be reduction type questions
+uh okay so this first problem uh
+
+ align:start position:0%
+uh okay so this first problem uh
+ 
+
+ align:start position:0%
+uh okay so this first problem uh
+thick nuri uh this is
+
+ align:start position:0%
+thick nuri uh this is
+ 
+
+ align:start position:0%
+thick nuri uh this is
+anyone nick fury right so it's a
+
+ align:start position:0%
+anyone nick fury right so it's a
+ 
+
+ align:start position:0%
+anyone nick fury right so it's a
+an avengers reference uh so basically
+
+ align:start position:0%
+an avengers reference uh so basically
+ 
+
+ align:start position:0%
+an avengers reference uh so basically
+what happens in this thing he's got a
+
+ align:start position:0%
+what happens in this thing he's got a
+ 
+
+ align:start position:0%
+what happens in this thing he's got a
+list of
+
+ align:start position:0%
+list of
+ 
+
+ align:start position:0%
+list of
+superheroes uh that each have an opinion
+
+ align:start position:0%
+superheroes uh that each have an opinion
+ 
+
+ align:start position:0%
+superheroes uh that each have an opinion
+on whether they should go fight santa's
+
+ align:start position:0%
+on whether they should go fight santa's
+ 
+
+ align:start position:0%
+on whether they should go fight santa's
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh their opinion
+
+ align:start position:0%
+and uh their opinion
+ 
+
+ align:start position:0%
+and uh their opinion
+can be strongly positive or strongly
+
+ align:start position:0%
+can be strongly positive or strongly
+ 
+
+ align:start position:0%
+can be strongly positive or strongly
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+and so what uh fick is trying to do is
+
+ align:start position:0%
+and so what uh fick is trying to do is
+ 
+
+ align:start position:0%
+and so what uh fick is trying to do is
+find from among his
+
+ align:start position:0%
+find from among his
+ 
+
+ align:start position:0%
+find from among his
+revengers uh what their
+
+ align:start position:0%
+revengers uh what their
+ 
+
+ align:start position:0%
+revengers uh what their
+what the log n most extreme
+
+ align:start position:0%
+what the log n most extreme
+ 
+
+ align:start position:0%
+what the log n most extreme
+opinion revengers are so that you can
+
+ align:start position:0%
+opinion revengers are so that you can
+ 
+
+ align:start position:0%
+opinion revengers are so that you can
+talk to them right he doesn't want to
+
+ align:start position:0%
+talk to them right he doesn't want to
+ 
+
+ align:start position:0%
+talk to them right he doesn't want to
+talk to everybody he wants to talk to a
+
+ align:start position:0%
+talk to everybody he wants to talk to a
+ 
+
+ align:start position:0%
+talk to everybody he wants to talk to a
+you know logarithmic number of them okay
+
+ align:start position:0%
+you know logarithmic number of them okay
+ 
+
+ align:start position:0%
+you know logarithmic number of them okay
+it's kind of
+
+ align:start position:0%
+it's kind of
+ 
+
+ align:start position:0%
+it's kind of
+whatever all right so uh basically
+
+ align:start position:0%
+whatever all right so uh basically
+ 
+
+ align:start position:0%
+whatever all right so uh basically
+we have a uh a classified situation
+
+ align:start position:0%
+we have a uh a classified situation
+ 
+
+ align:start position:0%
+we have a uh a classified situation
+where you're given as a read-only input
+
+ align:start position:0%
+where you're given as a read-only input
+ 
+
+ align:start position:0%
+where you're given as a read-only input
+data store
+
+ align:start position:0%
+data store
+ 
+
+ align:start position:0%
+data store
+of these things in an array okay
+
+ align:start position:0%
+of these things in an array okay
+ 
+
+ align:start position:0%
+of these things in an array okay
+and i want to find the log n
+
+ align:start position:0%
+and i want to find the log n
+ 
+
+ align:start position:0%
+and i want to find the log n
+ones with the strongest opinions does
+
+ align:start position:0%
+ones with the strongest opinions does
+ 
+
+ align:start position:0%
+ones with the strongest opinions does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+and i want to do it and the first
+
+ align:start position:0%
+and i want to do it and the first
+ 
+
+ align:start position:0%
+and i want to do it and the first
+problem is in linear time
+
+ align:start position:0%
+problem is in linear time
+ 
+
+ align:start position:0%
+problem is in linear time
+okay so you actually don't know how to
+
+ align:start position:0%
+okay so you actually don't know how to
+ 
+
+ align:start position:0%
+okay so you actually don't know how to
+do this yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll know how to do it with material
+
+ align:start position:0%
+you'll know how to do it with material
+ 
+
+ align:start position:0%
+you'll know how to do it with material
+that you cover
+
+ align:start position:0%
+that you cover
+ 
+
+ align:start position:0%
+that you cover
+in uh well they teach you one way to do
+
+ align:start position:0%
+in uh well they teach you one way to do
+ 
+
+ align:start position:0%
+in uh well they teach you one way to do
+it in o46 but we're not going to get you
+
+ align:start position:0%
+it in o46 but we're not going to get you
+ 
+
+ align:start position:0%
+it in o46 but we're not going to get you
+there right now uh we'll teach you
+
+ align:start position:0%
+there right now uh we'll teach you
+ 
+
+ align:start position:0%
+there right now uh we'll teach you
+another way to do it
+
+ align:start position:0%
+another way to do it
+ 
+
+ align:start position:0%
+another way to do it
+uh in uh on tuesday
+
+ align:start position:0%
+uh in uh on tuesday
+ 
+
+ align:start position:0%
+uh in uh on tuesday
+right which is via binary heaps okay
+
+ align:start position:0%
+right which is via binary heaps okay
+ 
+
+ align:start position:0%
+right which is via binary heaps okay
+binary heaps are an interesting thing
+
+ align:start position:0%
+binary heaps are an interesting thing
+ 
+
+ align:start position:0%
+binary heaps are an interesting thing
+that implements a subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the set interface okay
+
+ align:start position:0%
+of the set interface okay
+ 
+
+ align:start position:0%
+of the set interface okay
+really it just you can build
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on some iterable x okay i
+
+ align:start position:0%
+on some iterable x okay i
+ 
+
+ align:start position:0%
+on some iterable x okay i
+collect a bunch of things these items
+
+ align:start position:0%
+collect a bunch of things these items
+ 
+
+ align:start position:0%
+collect a bunch of things these items
+have keys right it's a key
+
+ align:start position:0%
+have keys right it's a key
+ 
+
+ align:start position:0%
+have keys right it's a key
+data structure in the same way it's
+
+ align:start position:0%
+data structure in the same way it's
+ 
+
+ align:start position:0%
+data structure in the same way it's
+implementing what we call a priority
+
+ align:start position:0%
+implementing what we call a priority
+ 
+
+ align:start position:0%
+implementing what we call a priority
+queue interface i can build these things
+
+ align:start position:0%
+queue interface i can build these things
+ 
+
+ align:start position:0%
+queue interface i can build these things
+i can insert things
+
+ align:start position:0%
+i can insert things
+ 
+
+ align:start position:0%
+i can insert things
+but i'm not going to do that here all i
+
+ align:start position:0%
+but i'm not going to do that here all i
+ 
+
+ align:start position:0%
+but i'm not going to do that here all i
+really need here for this
+
+ align:start position:0%
+really need here for this
+ 
+
+ align:start position:0%
+really need here for this
+situation is a delete superlative kind
+
+ align:start position:0%
+situation is a delete superlative kind
+ 
+
+ align:start position:0%
+situation is a delete superlative kind
+of operation in this case
+
+ align:start position:0%
+of operation in this case
+ 
+
+ align:start position:0%
+of operation in this case
+probably max delete
+
+ align:start position:0%
+probably max delete
+ 
+
+ align:start position:0%
+probably max delete
+max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is like a i got a data
+
+ align:start position:0%
+okay so this is like a i got a data
+ 
+
+ align:start position:0%
+okay so this is like a i got a data
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+right i'm calling these things does that
+
+ align:start position:0%
+right i'm calling these things does that
+ 
+
+ align:start position:0%
+right i'm calling these things does that
+make sense yeah that's a priority
+
+ align:start position:0%
+make sense yeah that's a priority
+ 
+
+ align:start position:0%
+make sense yeah that's a priority
+yes a priority queue is essentially
+
+ align:start position:0%
+yes a priority queue is essentially
+ 
+
+ align:start position:0%
+yes a priority queue is essentially
+something that implements these two
+
+ align:start position:0%
+something that implements these two
+ 
+
+ align:start position:0%
+something that implements these two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+actually there's a third one where i can
+
+ align:start position:0%
+actually there's a third one where i can
+ 
+
+ align:start position:0%
+actually there's a third one where i can
+insert a new thing right but i'm not
+
+ align:start position:0%
+insert a new thing right but i'm not
+ 
+
+ align:start position:0%
+insert a new thing right but i'm not
+going to need that right now
+
+ align:start position:0%
+going to need that right now
+ 
+
+ align:start position:0%
+going to need that right now
+so that's what a priority queue is and
+
+ align:start position:0%
+so that's what a priority queue is and
+ 
+
+ align:start position:0%
+so that's what a priority queue is and
+actually a set this is a subset of the
+
+ align:start position:0%
+actually a set this is a subset of the
+ 
+
+ align:start position:0%
+actually a set this is a subset of the
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+interface right right the nice thing
+
+ align:start position:0%
+interface right right the nice thing
+ 
+
+ align:start position:0%
+interface right right the nice thing
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+a heap which i won't show you how it's
+
+ align:start position:0%
+a heap which i won't show you how it's
+ 
+
+ align:start position:0%
+a heap which i won't show you how it's
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+right but what a heap can do so
+
+ align:start position:0%
+right but what a heap can do so
+ 
+
+ align:start position:0%
+right but what a heap can do so
+if i had both of these operations
+
+ align:start position:0%
+if i had both of these operations
+ 
+
+ align:start position:0%
+if i had both of these operations
+implemented using a
+
+ align:start position:0%
+implemented using a
+ 
+
+ align:start position:0%
+implemented using a
+set avl tree how long would these things
+
+ align:start position:0%
+set avl tree how long would these things
+ 
+
+ align:start position:0%
+set avl tree how long would these things
+take me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how long does it take to build a set avl
+
+ align:start position:0%
+how long does it take to build a set avl
+ 
+
+ align:start position:0%
+how long does it take to build a set avl
+tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and log in right because essentially i'm
+
+ align:start position:0%
+and log in right because essentially i'm
+ 
+
+ align:start position:0%
+and log in right because essentially i'm
+getting a sorted order out of this thing
+
+ align:start position:0%
+getting a sorted order out of this thing
+ 
+
+ align:start position:0%
+getting a sorted order out of this thing
+right if i'm inserting these things one
+
+ align:start position:0%
+right if i'm inserting these things one
+ 
+
+ align:start position:0%
+right if i'm inserting these things one
+at a time right
+
+ align:start position:0%
+at a time right
+ 
+
+ align:start position:0%
+at a time right
+or i could sort them and then put them
+
+ align:start position:0%
+or i could sort them and then put them
+ 
+
+ align:start position:0%
+or i could sort them and then put them
+in a tree in linear time like you saw
+
+ align:start position:0%
+in a tree in linear time like you saw
+ 
+
+ align:start position:0%
+in a tree in linear time like you saw
+a couple days ago right in recitation
+
+ align:start position:0%
+a couple days ago right in recitation
+ 
+
+ align:start position:0%
+a couple days ago right in recitation
+but i have to sort them at some point
+
+ align:start position:0%
+but i have to sort them at some point
+ 
+
+ align:start position:0%
+but i have to sort them at some point
+right i'm kind of
+
+ align:start position:0%
+right i'm kind of
+ 
+
+ align:start position:0%
+right i'm kind of
+i need to take at least n log n time
+
+ align:start position:0%
+i need to take at least n log n time
+ 
+
+ align:start position:0%
+i need to take at least n log n time
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+if i'm going to be able to return their
+
+ align:start position:0%
+if i'm going to be able to return their
+ 
+
+ align:start position:0%
+if i'm going to be able to return their
+order their traversal order in linear
+
+ align:start position:0%
+order their traversal order in linear
+ 
+
+ align:start position:0%
+order their traversal order in linear
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and i have this lower bound of m log n
+
+ align:start position:0%
+and i have this lower bound of m log n
+ 
+
+ align:start position:0%
+and i have this lower bound of m log n
+on sorting i kind of needed to spend and
+
+ align:start position:0%
+on sorting i kind of needed to spend and
+ 
+
+ align:start position:0%
+on sorting i kind of needed to spend and
+log in
+
+ align:start position:0%
+log in
+ 
+
+ align:start position:0%
+log in
+time here right and how long would this
+
+ align:start position:0%
+time here right and how long would this
+ 
+
+ align:start position:0%
+time here right and how long would this
+delete max take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i started so long log in right so it's a
+
+ align:start position:0%
+i started so long log in right so it's a
+ 
+
+ align:start position:0%
+i started so long log in right so it's a
+set avl tree
+
+ align:start position:0%
+set avl tree
+ 
+
+ align:start position:0%
+set avl tree
+where is my max it's the rightmost thing
+
+ align:start position:0%
+where is my max it's the rightmost thing
+ 
+
+ align:start position:0%
+where is my max it's the rightmost thing
+i can just walk down the thing
+
+ align:start position:0%
+i can just walk down the thing
+ 
+
+ align:start position:0%
+i can just walk down the thing
+take it off maybe i have to rebalance
+
+ align:start position:0%
+take it off maybe i have to rebalance
+ 
+
+ align:start position:0%
+take it off maybe i have to rebalance
+but you know that's a login
+
+ align:start position:0%
+but you know that's a login
+ 
+
+ align:start position:0%
+but you know that's a login
+operation right it's the same as like
+
+ align:start position:0%
+operation right it's the same as like
+ 
+
+ align:start position:0%
+operation right it's the same as like
+insert last in my substrate
+
+ align:start position:0%
+insert last in my substrate
+ 
+
+ align:start position:0%
+insert last in my substrate
+right so for a set avl tree
+
+ align:start position:0%
+right so for a set avl tree
+ 
+
+ align:start position:0%
+right so for a set avl tree
+this is n log n this is uh log n
+
+ align:start position:0%
+this is n log n this is uh log n
+ 
+
+ align:start position:0%
+this is n log n this is uh log n
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+there's another data structure that does
+
+ align:start position:0%
+there's another data structure that does
+ 
+
+ align:start position:0%
+there's another data structure that does
+better for one of these operations and
+
+ align:start position:0%
+better for one of these operations and
+ 
+
+ align:start position:0%
+better for one of these operations and
+the same for the other one
+
+ align:start position:0%
+the same for the other one
+ 
+
+ align:start position:0%
+the same for the other one
+that we've learned earlier
+
+ align:start position:0%
+that we've learned earlier
+ 
+
+ align:start position:0%
+that we've learned earlier
+anyone remember said avl tree didn't
+
+ align:start position:0%
+anyone remember said avl tree didn't
+ 
+
+ align:start position:0%
+anyone remember said avl tree didn't
+actually give us anything over
+
+ align:start position:0%
+actually give us anything over
+ 
+
+ align:start position:0%
+actually give us anything over
+a sorted array in a dynamic
+
+ align:start position:0%
+a sorted array in a dynamic
+ 
+
+ align:start position:0%
+a sorted array in a dynamic
+array okay so what that did right
+
+ align:start position:0%
+array okay so what that did right
+ 
+
+ align:start position:0%
+array okay so what that did right
+was we have a we could sort it in n log
+
+ align:start position:0%
+was we have a we could sort it in n log
+ 
+
+ align:start position:0%
+was we have a we could sort it in n log
+n time using merge sort or something
+
+ align:start position:0%
+n time using merge sort or something
+ 
+
+ align:start position:0%
+n time using merge sort or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+and then we could just pop off the last
+
+ align:start position:0%
+and then we could just pop off the last
+ 
+
+ align:start position:0%
+and then we could just pop off the last
+one end times right
+
+ align:start position:0%
+one end times right
+ 
+
+ align:start position:0%
+one end times right
+that would be an amortize i mean if i
+
+ align:start position:0%
+that would be an amortize i mean if i
+ 
+
+ align:start position:0%
+that would be an amortize i mean if i
+didn't care about
+
+ align:start position:0%
+didn't care about
+ 
+
+ align:start position:0%
+didn't care about
+taking up that size i could do it in
+
+ align:start position:0%
+taking up that size i could do it in
+ 
+
+ align:start position:0%
+taking up that size i could do it in
+worse case constant time i just read off
+
+ align:start position:0%
+worse case constant time i just read off
+ 
+
+ align:start position:0%
+worse case constant time i just read off
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+the last one i don't need to resize the
+
+ align:start position:0%
+the last one i don't need to resize the
+ 
+
+ align:start position:0%
+the last one i don't need to resize the
+array ever right i can just
+
+ align:start position:0%
+array ever right i can just
+ 
+
+ align:start position:0%
+array ever right i can just
+ignore that does that make sense okay
+
+ align:start position:0%
+ignore that does that make sense okay
+ 
+
+ align:start position:0%
+ignore that does that make sense okay
+but that's okay if i had a data
+
+ align:start position:0%
+but that's okay if i had a data
+ 
+
+ align:start position:0%
+but that's okay if i had a data
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+that implemented these two operations
+
+ align:start position:0%
+that implemented these two operations
+ 
+
+ align:start position:0%
+that implemented these two operations
+can someone tell me a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh an algorithm to generate
+
+ align:start position:0%
+uh an algorithm to generate
+ 
+
+ align:start position:0%
+uh an algorithm to generate
+fixed list don't worry about running
+
+ align:start position:0%
+fixed list don't worry about running
+ 
+
+ align:start position:0%
+fixed list don't worry about running
+time right now but that just uses these
+
+ align:start position:0%
+time right now but that just uses these
+ 
+
+ align:start position:0%
+time right now but that just uses these
+two operations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um so we built the data structure
+
+ align:start position:0%
+yeah um so we built the data structure
+ 
+
+ align:start position:0%
+yeah um so we built the data structure
+it's ordered from least to greatest for
+
+ align:start position:0%
+it's ordered from least to greatest for
+ 
+
+ align:start position:0%
+it's ordered from least to greatest for
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+so don't don't don't worry about uh
+
+ align:start position:0%
+so don't don't don't worry about uh
+ 
+
+ align:start position:0%
+so don't don't don't worry about uh
+where things are ordered or anything
+
+ align:start position:0%
+where things are ordered or anything
+ 
+
+ align:start position:0%
+where things are ordered or anything
+like that i don't tell you how these
+
+ align:start position:0%
+like that i don't tell you how these
+ 
+
+ align:start position:0%
+like that i don't tell you how these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+are implemented right all i'm saying is
+
+ align:start position:0%
+are implemented right all i'm saying is
+ 
+
+ align:start position:0%
+are implemented right all i'm saying is
+i can
+
+ align:start position:0%
+i can
+ 
+
+ align:start position:0%
+i can
+i can accept a bunch of these things and
+
+ align:start position:0%
+i can accept a bunch of these things and
+ 
+
+ align:start position:0%
+i can accept a bunch of these things and
+i can
+
+ align:start position:0%
+i can
+ 
+
+ align:start position:0%
+i can
+remove the maximum and return it
+
+ align:start position:0%
+remove the maximum and return it
+ 
+
+ align:start position:0%
+remove the maximum and return it
+okay yeah anyways just build it but make
+
+ align:start position:0%
+okay yeah anyways just build it but make
+ 
+
+ align:start position:0%
+okay yeah anyways just build it but make
+sure that you build it such that the
+
+ align:start position:0%
+sure that you build it such that the
+ 
+
+ align:start position:0%
+sure that you build it such that the
+opinion levels are the absolute value of
+
+ align:start position:0%
+opinion levels are the absolute value of
+ 
+
+ align:start position:0%
+opinion levels are the absolute value of
+the opinion levels sure okay
+
+ align:start position:0%
+the opinion levels sure okay
+ 
+
+ align:start position:0%
+the opinion levels sure okay
+so that's that's a nice thing what i'm
+
+ align:start position:0%
+so that's that's a nice thing what i'm
+ 
+
+ align:start position:0%
+so that's that's a nice thing what i'm
+going to do as your colleague is saying
+
+ align:start position:0%
+going to do as your colleague is saying
+ 
+
+ align:start position:0%
+going to do as your colleague is saying
+is i'm going to look through all of the
+
+ align:start position:0%
+is i'm going to look through all of the
+ 
+
+ align:start position:0%
+is i'm going to look through all of the
+things in my input i'm going to
+
+ align:start position:0%
+things in my input i'm going to
+ 
+
+ align:start position:0%
+things in my input i'm going to
+copy it over to some writable memory
+
+ align:start position:0%
+copy it over to some writable memory
+ 
+
+ align:start position:0%
+copy it over to some writable memory
+store
+
+ align:start position:0%
+store
+ 
+
+ align:start position:0%
+store
+okay right that read-only thing is not
+
+ align:start position:0%
+okay right that read-only thing is not
+ 
+
+ align:start position:0%
+okay right that read-only thing is not
+relevant to this part of the problem
+
+ align:start position:0%
+relevant to this part of the problem
+ 
+
+ align:start position:0%
+relevant to this part of the problem
+right what i'm going to do is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right sorry i'm thinking about your
+
+ align:start position:0%
+right sorry i'm thinking about your
+ 
+
+ align:start position:0%
+right sorry i'm thinking about your
+problem set that we're writing
+
+ align:start position:0%
+problem set that we're writing
+ 
+
+ align:start position:0%
+problem set that we're writing
+and mixing it up okay so uh we copy it
+
+ align:start position:0%
+and mixing it up okay so uh we copy it
+ 
+
+ align:start position:0%
+and mixing it up okay so uh we copy it
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+to uh our new uh like linear size
+
+ align:start position:0%
+to uh our new uh like linear size
+ 
+
+ align:start position:0%
+to uh our new uh like linear size
+array right and but instead of putting
+
+ align:start position:0%
+array right and but instead of putting
+ 
+
+ align:start position:0%
+array right and but instead of putting
+their values there i'm going to put the
+
+ align:start position:0%
+their values there i'm going to put the
+ 
+
+ align:start position:0%
+their values there i'm going to put the
+absolute values of their values that
+
+ align:start position:0%
+absolute values of their values that
+ 
+
+ align:start position:0%
+absolute values of their values that
+make sense i just check if it's negative
+
+ align:start position:0%
+make sense i just check if it's negative
+ 
+
+ align:start position:0%
+make sense i just check if it's negative
+it is i put the positive thing there
+
+ align:start position:0%
+it is i put the positive thing there
+ 
+
+ align:start position:0%
+it is i put the positive thing there
+right okay and then and then i
+
+ align:start position:0%
+right okay and then and then i
+ 
+
+ align:start position:0%
+right okay and then and then i
+stick that array in this build right i
+
+ align:start position:0%
+stick that array in this build right i
+ 
+
+ align:start position:0%
+stick that array in this build right i
+put that
+
+ align:start position:0%
+put that
+ 
+
+ align:start position:0%
+put that
+there right so that'll take some
+
+ align:start position:0%
+there right so that'll take some
+ 
+
+ align:start position:0%
+there right so that'll take some
+whatever this build time is and then i
+
+ align:start position:0%
+whatever this build time is and then i
+ 
+
+ align:start position:0%
+whatever this build time is and then i
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+delete max k times or i can delete max
+
+ align:start position:0%
+delete max k times or i can delete max
+ 
+
+ align:start position:0%
+delete max k times or i can delete max
+some number of times however many things
+
+ align:start position:0%
+some number of times however many things
+ 
+
+ align:start position:0%
+some number of times however many things
+that i need
+
+ align:start position:0%
+that i need
+ 
+
+ align:start position:0%
+that i need
+right that the if i if i want log n
+
+ align:start position:0%
+right that the if i if i want log n
+ 
+
+ align:start position:0%
+right that the if i if i want log n
+highest things i can just
+
+ align:start position:0%
+highest things i can just
+ 
+
+ align:start position:0%
+highest things i can just
+do that log n times right so for this
+
+ align:start position:0%
+do that log n times right so for this
+ 
+
+ align:start position:0%
+do that log n times right so for this
+if i had such a data structure i could
+
+ align:start position:0%
+if i had such a data structure i could
+ 
+
+ align:start position:0%
+if i had such a data structure i could
+do this in one run of this operation
+
+ align:start position:0%
+do this in one run of this operation
+ 
+
+ align:start position:0%
+do this in one run of this operation
+and log in runs of this operation does
+
+ align:start position:0%
+and log in runs of this operation does
+ 
+
+ align:start position:0%
+and log in runs of this operation does
+that make sense i can solve this problem
+
+ align:start position:0%
+that make sense i can solve this problem
+ 
+
+ align:start position:0%
+that make sense i can solve this problem
+reducing to this data structure right
+
+ align:start position:0%
+reducing to this data structure right
+ 
+
+ align:start position:0%
+reducing to this data structure right
+now for a sorted array or a
+
+ align:start position:0%
+now for a sorted array or a
+ 
+
+ align:start position:0%
+now for a sorted array or a
+sat avl tree right this operation kind
+
+ align:start position:0%
+sat avl tree right this operation kind
+ 
+
+ align:start position:0%
+sat avl tree right this operation kind
+of kills me already
+
+ align:start position:0%
+of kills me already
+ 
+
+ align:start position:0%
+of kills me already
+takes m log in time right the nice thing
+
+ align:start position:0%
+takes m log in time right the nice thing
+ 
+
+ align:start position:0%
+takes m log in time right the nice thing
+about a binary heap
+
+ align:start position:0%
+about a binary heap
+ 
+
+ align:start position:0%
+about a binary heap
+is it does this operation in linear time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you will see that on tuesday and it does
+
+ align:start position:0%
+you will see that on tuesday and it does
+ 
+
+ align:start position:0%
+you will see that on tuesday and it does
+this operation
+
+ align:start position:0%
+this operation
+ 
+
+ align:start position:0%
+this operation
+in login time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so how what's the running time
+
+ align:start position:0%
+okay so how what's the running time
+ 
+
+ align:start position:0%
+okay so how what's the running time
+if i use a heap to binary heap to
+
+ align:start position:0%
+if i use a heap to binary heap to
+ 
+
+ align:start position:0%
+if i use a heap to binary heap to
+implement this data structure
+
+ align:start position:0%
+implement this data structure
+ 
+
+ align:start position:0%
+implement this data structure
+order of n times order log n
+
+ align:start position:0%
+order of n times order log n
+ 
+
+ align:start position:0%
+order of n times order log n
+times log n how big is log n squared
+
+ align:start position:0%
+times log n how big is log n squared
+ 
+
+ align:start position:0%
+times log n how big is log n squared
+log squared n compared to n
+
+ align:start position:0%
+log squared n compared to n
+ 
+
+ align:start position:0%
+log squared n compared to n
+is smaller right so if i add those two
+
+ align:start position:0%
+is smaller right so if i add those two
+ 
+
+ align:start position:0%
+is smaller right so if i add those two
+running times together it's still linear
+
+ align:start position:0%
+running times together it's still linear
+ 
+
+ align:start position:0%
+running times together it's still linear
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so that's how you solve the first
+
+ align:start position:0%
+okay so that's how you solve the first
+ 
+
+ align:start position:0%
+okay so that's how you solve the first
+problem okay
+
+ align:start position:0%
+problem okay
+ 
+
+ align:start position:0%
+problem okay
+i didn't have to tell you what a binary
+
+ align:start position:0%
+i didn't have to tell you what a binary
+ 
+
+ align:start position:0%
+i didn't have to tell you what a binary
+heap was or how it did what it did all i
+
+ align:start position:0%
+heap was or how it did what it did all i
+ 
+
+ align:start position:0%
+heap was or how it did what it did all i
+needed to tell you was that it did this
+
+ align:start position:0%
+needed to tell you was that it did this
+ 
+
+ align:start position:0%
+needed to tell you was that it did this
+operation in linear time
+
+ align:start position:0%
+operation in linear time
+ 
+
+ align:start position:0%
+operation in linear time
+and it did this operation login type
+
+ align:start position:0%
+and it did this operation login type
+ 
+
+ align:start position:0%
+and it did this operation login type
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah all right the magic will be shown
+
+ align:start position:0%
+yeah all right the magic will be shown
+ 
+
+ align:start position:0%
+yeah all right the magic will be shown
+to you on tuesday
+
+ align:start position:0%
+to you on tuesday
+ 
+
+ align:start position:0%
+to you on tuesday
+part b says now suppose fixed computer
+
+ align:start position:0%
+part b says now suppose fixed computer
+ 
+
+ align:start position:0%
+part b says now suppose fixed computer
+is only allowed to write to at most log
+
+ align:start position:0%
+is only allowed to write to at most log
+ 
+
+ align:start position:0%
+is only allowed to write to at most log
+and space
+
+ align:start position:0%
+and space
+ 
+
+ align:start position:0%
+and space
+well okay that's a problem here right
+
+ align:start position:0%
+well okay that's a problem here right
+ 
+
+ align:start position:0%
+well okay that's a problem here right
+because we before we copied over
+
+ align:start position:0%
+because we before we copied over
+ 
+
+ align:start position:0%
+because we before we copied over
+the entire array filtered it out right
+
+ align:start position:0%
+the entire array filtered it out right
+ 
+
+ align:start position:0%
+the entire array filtered it out right
+and then did some operations but we
+
+ align:start position:0%
+and then did some operations but we
+ 
+
+ align:start position:0%
+and then did some operations but we
+couldn't even afford this if we couldn't
+
+ align:start position:0%
+couldn't even afford this if we couldn't
+ 
+
+ align:start position:0%
+couldn't even afford this if we couldn't
+store the whole thing
+
+ align:start position:0%
+store the whole thing
+ 
+
+ align:start position:0%
+store the whole thing
+externally in writable memory right
+
+ align:start position:0%
+externally in writable memory right
+ 
+
+ align:start position:0%
+externally in writable memory right
+okay so we can't do that so in some
+
+ align:start position:0%
+okay so we can't do that so in some
+ 
+
+ align:start position:0%
+okay so we can't do that so in some
+sense this is a more restrictive
+
+ align:start position:0%
+sense this is a more restrictive
+ 
+
+ align:start position:0%
+sense this is a more restrictive
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+right i can do less things
+
+ align:start position:0%
+right i can do less things
+ 
+
+ align:start position:0%
+right i can do less things
+than i could it's a uh it's less
+
+ align:start position:0%
+than i could it's a uh it's less
+ 
+
+ align:start position:0%
+than i could it's a uh it's less
+powerful than my previous situation
+
+ align:start position:0%
+powerful than my previous situation
+ 
+
+ align:start position:0%
+powerful than my previous situation
+where i had as much space as i wanted to
+
+ align:start position:0%
+where i had as much space as i wanted to
+ 
+
+ align:start position:0%
+where i had as much space as i wanted to
+use right
+
+ align:start position:0%
+use right
+ 
+
+ align:start position:0%
+use right
+so it kind of makes sense that
+
+ align:start position:0%
+so it kind of makes sense that
+ 
+
+ align:start position:0%
+so it kind of makes sense that
+i maybe couldn't get
+
+ align:start position:0%
+i maybe couldn't get
+ 
+
+ align:start position:0%
+i maybe couldn't get
+the running time bad that bound that we
+
+ align:start position:0%
+the running time bad that bound that we
+ 
+
+ align:start position:0%
+the running time bad that bound that we
+had before right
+
+ align:start position:0%
+had before right
+ 
+
+ align:start position:0%
+had before right
+maybe i have to sacrifice something
+
+ align:start position:0%
+maybe i have to sacrifice something
+ 
+
+ align:start position:0%
+maybe i have to sacrifice something
+because i'm in a more restrictive
+
+ align:start position:0%
+because i'm in a more restrictive
+ 
+
+ align:start position:0%
+because i'm in a more restrictive
+computational setting right okay
+
+ align:start position:0%
+computational setting right okay
+ 
+
+ align:start position:0%
+computational setting right okay
+now this is something you could solve
+
+ align:start position:0%
+now this is something you could solve
+ 
+
+ align:start position:0%
+now this is something you could solve
+with binary heaps but you don't have to
+
+ align:start position:0%
+with binary heaps but you don't have to
+ 
+
+ align:start position:0%
+with binary heaps but you don't have to
+you could solve it
+
+ align:start position:0%
+you could solve it
+ 
+
+ align:start position:0%
+you could solve it
+with uh scent adl trees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as anyone have an idea of how you could
+
+ align:start position:0%
+as anyone have an idea of how you could
+ 
+
+ align:start position:0%
+as anyone have an idea of how you could
+solve this using a set avl tree
+
+ align:start position:0%
+solve this using a set avl tree
+ 
+
+ align:start position:0%
+solve this using a set avl tree
+i'm limited by my number of mice my
+
+ align:start position:0%
+i'm limited by my number of mice my
+ 
+
+ align:start position:0%
+i'm limited by my number of mice my
+my space is at most log n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah all right so how much space does
+
+ align:start position:0%
+yeah all right so how much space does
+ 
+
+ align:start position:0%
+yeah all right so how much space does
+this indial tree take
+
+ align:start position:0%
+this indial tree take
+ 
+
+ align:start position:0%
+this indial tree take
+right space right there's constant
+
+ align:start position:0%
+right space right there's constant
+ 
+
+ align:start position:0%
+right space right there's constant
+number of pointers for each one of these
+
+ align:start position:0%
+number of pointers for each one of these
+ 
+
+ align:start position:0%
+number of pointers for each one of these
+nodes
+
+ align:start position:0%
+nodes
+ 
+
+ align:start position:0%
+nodes
+right and i'm storing in nodes and space
+
+ align:start position:0%
+right and i'm storing in nodes and space
+ 
+
+ align:start position:0%
+right and i'm storing in nodes and space
+right basically every data structure
+
+ align:start position:0%
+right basically every data structure
+ 
+
+ align:start position:0%
+right basically every data structure
+we've shown you
+
+ align:start position:0%
+we've shown you
+ 
+
+ align:start position:0%
+we've shown you
+takes space the order of the things that
+
+ align:start position:0%
+takes space the order of the things that
+ 
+
+ align:start position:0%
+takes space the order of the things that
+we're storing
+
+ align:start position:0%
+we're storing
+ 
+
+ align:start position:0%
+we're storing
+right it's not using additional space it
+
+ align:start position:0%
+right it's not using additional space it
+ 
+
+ align:start position:0%
+right it's not using additional space it
+might take
+
+ align:start position:0%
+might take
+ 
+
+ align:start position:0%
+might take
+more time to do certain things but the
+
+ align:start position:0%
+more time to do certain things but the
+ 
+
+ align:start position:0%
+more time to do certain things but the
+space is
+
+ align:start position:0%
+space is
+ 
+
+ align:start position:0%
+space is
+you know takes the number of items we're
+
+ align:start position:0%
+you know takes the number of items we're
+ 
+
+ align:start position:0%
+you know takes the number of items we're
+storing plus
+
+ align:start position:0%
+storing plus
+ 
+
+ align:start position:0%
+storing plus
+maybe a constant factor right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so i'm going to draw my input here
+
+ align:start position:0%
+right so i'm going to draw my input here
+ 
+
+ align:start position:0%
+right so i'm going to draw my input here
+which i can only read i can't write
+
+ align:start position:0%
+which i can only read i can't write
+ 
+
+ align:start position:0%
+which i can only read i can't write
+do i give it i'm just going to call it a
+
+ align:start position:0%
+do i give it i'm just going to call it a
+ 
+
+ align:start position:0%
+do i give it i'm just going to call it a
+okay so this is my list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of all the revenger opinions okay i can
+
+ align:start position:0%
+of all the revenger opinions okay i can
+ 
+
+ align:start position:0%
+of all the revenger opinions okay i can
+only read it
+
+ align:start position:0%
+only read it
+ 
+
+ align:start position:0%
+only read it
+but my computer can only write to this
+
+ align:start position:0%
+but my computer can only write to this
+ 
+
+ align:start position:0%
+but my computer can only write to this
+logarithmic amount of space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what can i put in that space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i can i can certainly put log n
+
+ align:start position:0%
+well i can i can certainly put log n
+ 
+
+ align:start position:0%
+well i can i can certainly put log n
+things in there okay
+
+ align:start position:0%
+things in there okay
+ 
+
+ align:start position:0%
+things in there okay
+so if i'm given that restriction i
+
+ align:start position:0%
+so if i'm given that restriction i
+ 
+
+ align:start position:0%
+so if i'm given that restriction i
+probably want to build a data structure
+
+ align:start position:0%
+probably want to build a data structure
+ 
+
+ align:start position:0%
+probably want to build a data structure
+of that size
+
+ align:start position:0%
+of that size
+ 
+
+ align:start position:0%
+of that size
+right you know containing that number of
+
+ align:start position:0%
+right you know containing that number of
+ 
+
+ align:start position:0%
+right you know containing that number of
+things that make sense
+
+ align:start position:0%
+things that make sense
+ 
+
+ align:start position:0%
+things that make sense
+because what else are you gonna do right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i i gave you an idea maybe we
+
+ align:start position:0%
+okay so i i gave you an idea maybe we
+ 
+
+ align:start position:0%
+okay so i i gave you an idea maybe we
+could use a set avl here
+
+ align:start position:0%
+could use a set avl here
+ 
+
+ align:start position:0%
+could use a set avl here
+right i see a logarithm in my answer
+
+ align:start position:0%
+right i see a logarithm in my answer
+ 
+
+ align:start position:0%
+right i see a logarithm in my answer
+right it's very possible that we might
+
+ align:start position:0%
+right it's very possible that we might
+ 
+
+ align:start position:0%
+right it's very possible that we might
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+you know sorted arrays right or set avl
+
+ align:start position:0%
+you know sorted arrays right or set avl
+ 
+
+ align:start position:0%
+you know sorted arrays right or set avl
+things those
+
+ align:start position:0%
+things those
+ 
+
+ align:start position:0%
+things those
+those things give me a log somewhere in
+
+ align:start position:0%
+those things give me a log somewhere in
+ 
+
+ align:start position:0%
+those things give me a log somewhere in
+my running times right
+
+ align:start position:0%
+my running times right
+ 
+
+ align:start position:0%
+my running times right
+so kind of makes sense that i might have
+
+ align:start position:0%
+so kind of makes sense that i might have
+ 
+
+ align:start position:0%
+so kind of makes sense that i might have
+maybe a set avl tree here why why why
+
+ align:start position:0%
+maybe a set avl tree here why why why
+ 
+
+ align:start position:0%
+maybe a set avl tree here why why why
+would a set avl tree be helpful for me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah because it started and you know you
+
+ align:start position:0%
+yeah because it started and you know you
+ 
+
+ align:start position:0%
+yeah because it started and you know you
+have the direct russell order you can
+
+ align:start position:0%
+have the direct russell order you can
+ 
+
+ align:start position:0%
+have the direct russell order you can
+calculate the traversal order
+
+ align:start position:0%
+calculate the traversal order
+ 
+
+ align:start position:0%
+calculate the traversal order
+and insert like anxiety sure i can do
+
+ align:start position:0%
+and insert like anxiety sure i can do
+ 
+
+ align:start position:0%
+and insert like anxiety sure i can do
+all those things but in particular
+
+ align:start position:0%
+all those things but in particular
+ 
+
+ align:start position:0%
+all those things but in particular
+it's going to help me be able to find
+
+ align:start position:0%
+it's going to help me be able to find
+ 
+
+ align:start position:0%
+it's going to help me be able to find
+a large one quickly right if i if i
+
+ align:start position:0%
+a large one quickly right if i if i
+ 
+
+ align:start position:0%
+a large one quickly right if i if i
+kind of uh have a set of things it's
+
+ align:start position:0%
+kind of uh have a set of things it's
+ 
+
+ align:start position:0%
+kind of uh have a set of things it's
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+and i and i'm maintaining this data
+
+ align:start position:0%
+and i and i'm maintaining this data
+ 
+
+ align:start position:0%
+and i and i'm maintaining this data
+structure by adding things incrementally
+
+ align:start position:0%
+structure by adding things incrementally
+ 
+
+ align:start position:0%
+structure by adding things incrementally
+to it
+
+ align:start position:0%
+to it
+ 
+
+ align:start position:0%
+to it
+right i can find out what the biggest
+
+ align:start position:0%
+right i can find out what the biggest
+ 
+
+ align:start position:0%
+right i can find out what the biggest
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+or the smallest one pretty fast right
+
+ align:start position:0%
+or the smallest one pretty fast right
+ 
+
+ align:start position:0%
+or the smallest one pretty fast right
+and log in time
+
+ align:start position:0%
+and log in time
+ 
+
+ align:start position:0%
+and log in time
+right so if i have log n things in a
+
+ align:start position:0%
+right so if i have log n things in a
+ 
+
+ align:start position:0%
+right so if i have log n things in a
+in a tree here right what's the height
+
+ align:start position:0%
+in a tree here right what's the height
+ 
+
+ align:start position:0%
+in a tree here right what's the height
+of that thing
+
+ align:start position:0%
+of that thing
+ 
+
+ align:start position:0%
+of that thing
+log log n that looks familiar so what
+
+ align:start position:0%
+log log n that looks familiar so what
+ 
+
+ align:start position:0%
+log log n that looks familiar so what
+can i afford i can afford
+
+ align:start position:0%
+can i afford i can afford
+ 
+
+ align:start position:0%
+can i afford i can afford
+a linear number of op set avl tree
+
+ align:start position:0%
+a linear number of op set avl tree
+ 
+
+ align:start position:0%
+a linear number of op set avl tree
+operations on this data structure right
+
+ align:start position:0%
+operations on this data structure right
+ 
+
+ align:start position:0%
+operations on this data structure right
+okay you had a question okay i'm sorry
+
+ align:start position:0%
+okay you had a question okay i'm sorry
+ 
+
+ align:start position:0%
+okay you had a question okay i'm sorry
+yeah um for there'll be an
+
+ align:start position:0%
+yeah um for there'll be an
+ 
+
+ align:start position:0%
+yeah um for there'll be an
+avl tree does it have to be a bts tree
+
+ align:start position:0%
+avl tree does it have to be a bts tree
+ 
+
+ align:start position:0%
+avl tree does it have to be a bts tree
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+uh bts bst
+
+ align:start position:0%
+uh bts bst
+ 
+
+ align:start position:0%
+uh bts bst
+right so when i talk about uh someone
+
+ align:start position:0%
+right so when i talk about uh someone
+ 
+
+ align:start position:0%
+right so when i talk about uh someone
+likes korean k-pop
+
+ align:start position:0%
+likes korean k-pop
+ 
+
+ align:start position:0%
+likes korean k-pop
+okay uh so uh
+
+ align:start position:0%
+okay uh so uh
+ 
+
+ align:start position:0%
+okay uh so uh
+bst but in natural kind of in
+
+ align:start position:0%
+bst but in natural kind of in
+ 
+
+ align:start position:0%
+bst but in natural kind of in
+the lingo that you're probably used to
+
+ align:start position:0%
+the lingo that you're probably used to
+ 
+
+ align:start position:0%
+the lingo that you're probably used to
+hearing in other contexts
+
+ align:start position:0%
+hearing in other contexts
+ 
+
+ align:start position:0%
+hearing in other contexts
+what we mean in this class is a set adl
+
+ align:start position:0%
+what we mean in this class is a set adl
+ 
+
+ align:start position:0%
+what we mean in this class is a set adl
+tree right
+
+ align:start position:0%
+tree right
+ 
+
+ align:start position:0%
+tree right
+now sometimes what people
+
+ align:start position:0%
+now sometimes what people
+ 
+
+ align:start position:0%
+now sometimes what people
+refer to as a binary search tree doesn't
+
+ align:start position:0%
+refer to as a binary search tree doesn't
+ 
+
+ align:start position:0%
+refer to as a binary search tree doesn't
+have balance
+
+ align:start position:0%
+have balance
+ 
+
+ align:start position:0%
+have balance
+semantics right so we might call in this
+
+ align:start position:0%
+semantics right so we might call in this
+ 
+
+ align:start position:0%
+semantics right so we might call in this
+class a set binary tree
+
+ align:start position:0%
+class a set binary tree
+ 
+
+ align:start position:0%
+class a set binary tree
+right but really
+
+ align:start position:0%
+right but really
+ 
+
+ align:start position:0%
+right but really
+they're useful because they're balanced
+
+ align:start position:0%
+they're useful because they're balanced
+ 
+
+ align:start position:0%
+they're useful because they're balanced
+so we're going to usually just assume
+
+ align:start position:0%
+so we're going to usually just assume
+ 
+
+ align:start position:0%
+so we're going to usually just assume
+that we're
+
+ align:start position:0%
+that we're
+ 
+
+ align:start position:0%
+that we're
+talking about balance things here now a
+
+ align:start position:0%
+talking about balance things here now a
+ 
+
+ align:start position:0%
+talking about balance things here now a
+set avl tree has these binary search
+
+ align:start position:0%
+set avl tree has these binary search
+ 
+
+ align:start position:0%
+set avl tree has these binary search
+tree semantics
+
+ align:start position:0%
+tree semantics
+ 
+
+ align:start position:0%
+tree semantics
+where the keys are ordered these items
+
+ align:start position:0%
+where the keys are ordered these items
+ 
+
+ align:start position:0%
+where the keys are ordered these items
+have keys and they're ordered it's a set
+
+ align:start position:0%
+have keys and they're ordered it's a set
+ 
+
+ align:start position:0%
+have keys and they're ordered it's a set
+interface right
+
+ align:start position:0%
+interface right
+ 
+
+ align:start position:0%
+interface right
+whereas we also presented to a sequence
+
+ align:start position:0%
+whereas we also presented to a sequence
+ 
+
+ align:start position:0%
+whereas we also presented to a sequence
+interface
+
+ align:start position:0%
+interface
+ 
+
+ align:start position:0%
+interface
+right for which these these things don't
+
+ align:start position:0%
+right for which these these things don't
+ 
+
+ align:start position:0%
+right for which these these things don't
+even have keys how could i
+
+ align:start position:0%
+even have keys how could i
+ 
+
+ align:start position:0%
+even have keys how could i
+store set semantics there right so but
+
+ align:start position:0%
+store set semantics there right so but
+ 
+
+ align:start position:0%
+store set semantics there right so but
+that's the distinction that we mean when
+
+ align:start position:0%
+that's the distinction that we mean when
+ 
+
+ align:start position:0%
+that's the distinction that we mean when
+we say
+
+ align:start position:0%
+we say
+ 
+
+ align:start position:0%
+we say
+uh binary search tree versus
+
+ align:start position:0%
+uh binary search tree versus
+ 
+
+ align:start position:0%
+uh binary search tree versus
+really a set avl tree versus yeah so if
+
+ align:start position:0%
+really a set avl tree versus yeah so if
+ 
+
+ align:start position:0%
+really a set avl tree versus yeah so if
+we're going to make an avl tree out of
+
+ align:start position:0%
+we're going to make an avl tree out of
+ 
+
+ align:start position:0%
+we're going to make an avl tree out of
+this would that mean that like
+
+ align:start position:0%
+this would that mean that like
+ 
+
+ align:start position:0%
+this would that mean that like
+we when we make a node we tell it like
+
+ align:start position:0%
+we when we make a node we tell it like
+ 
+
+ align:start position:0%
+we when we make a node we tell it like
+we are keying on the absolute value
+
+ align:start position:0%
+we are keying on the absolute value
+ 
+
+ align:start position:0%
+we are keying on the absolute value
+okay so when you're uh
+
+ align:start position:0%
+okay so when you're uh
+ 
+
+ align:start position:0%
+okay so when you're uh
+making a set to avl tree you got to tell
+
+ align:start position:0%
+making a set to avl tree you got to tell
+ 
+
+ align:start position:0%
+making a set to avl tree you got to tell
+us what
+
+ align:start position:0%
+us what
+ 
+
+ align:start position:0%
+us what
+if you're storing objects you got to
+
+ align:start position:0%
+if you're storing objects you got to
+ 
+
+ align:start position:0%
+if you're storing objects you got to
+tell me what their key is right if
+
+ align:start position:0%
+tell me what their key is right if
+ 
+
+ align:start position:0%
+tell me what their key is right if
+you're just storing some numbers
+
+ align:start position:0%
+you're just storing some numbers
+ 
+
+ align:start position:0%
+you're just storing some numbers
+like what i'm doing here right now this
+
+ align:start position:0%
+like what i'm doing here right now this
+ 
+
+ align:start position:0%
+like what i'm doing here right now this
+isn't a set avl tree right but if i'm
+
+ align:start position:0%
+isn't a set avl tree right but if i'm
+ 
+
+ align:start position:0%
+isn't a set avl tree right but if i'm
+just storing numbers
+
+ align:start position:0%
+just storing numbers
+ 
+
+ align:start position:0%
+just storing numbers
+i have to tell you the items that i'm
+
+ align:start position:0%
+i have to tell you the items that i'm
+ 
+
+ align:start position:0%
+i have to tell you the items that i'm
+storing are the keys
+
+ align:start position:0%
+storing are the keys
+ 
+
+ align:start position:0%
+storing are the keys
+okay and then everything follows right
+
+ align:start position:0%
+okay and then everything follows right
+ 
+
+ align:start position:0%
+okay and then everything follows right
+but if you've got an object that you're
+
+ align:start position:0%
+but if you've got an object that you're
+ 
+
+ align:start position:0%
+but if you've got an object that you're
+trying to sort like
+
+ align:start position:0%
+trying to sort like
+ 
+
+ align:start position:0%
+trying to sort like
+the students in this room you got a lot
+
+ align:start position:0%
+the students in this room you got a lot
+ 
+
+ align:start position:0%
+the students in this room you got a lot
+of properties
+
+ align:start position:0%
+of properties
+ 
+
+ align:start position:0%
+of properties
+right i want to all the uh
+
+ align:start position:0%
+right i want to all the uh
+ 
+
+ align:start position:0%
+right i want to all the uh
+the people with phone number right
+
+ align:start position:0%
+the people with phone number right
+ 
+
+ align:start position:0%
+the people with phone number right
+maybe i want to key you on phone number
+
+ align:start position:0%
+maybe i want to key you on phone number
+ 
+
+ align:start position:0%
+maybe i want to key you on phone number
+for some reason that's going to help me
+
+ align:start position:0%
+for some reason that's going to help me
+ 
+
+ align:start position:0%
+for some reason that's going to help me
+find out where you live i don't know
+
+ align:start position:0%
+find out where you live i don't know
+ 
+
+ align:start position:0%
+find out where you live i don't know
+this is getting i don't want to go there
+
+ align:start position:0%
+this is getting i don't want to go there
+ 
+
+ align:start position:0%
+this is getting i don't want to go there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so but if i if i give you a set to avl
+
+ align:start position:0%
+so but if i if i give you a set to avl
+ 
+
+ align:start position:0%
+so but if i if i give you a set to avl
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+i got to tell you what it's keyed on if
+
+ align:start position:0%
+i got to tell you what it's keyed on if
+ 
+
+ align:start position:0%
+i got to tell you what it's keyed on if
+i give you a sequence avl tree
+
+ align:start position:0%
+i give you a sequence avl tree
+ 
+
+ align:start position:0%
+i give you a sequence avl tree
+right it's obvious what my traversal
+
+ align:start position:0%
+right it's obvious what my traversal
+ 
+
+ align:start position:0%
+right it's obvious what my traversal
+order is going to be because i'm giving
+
+ align:start position:0%
+order is going to be because i'm giving
+ 
+
+ align:start position:0%
+order is going to be because i'm giving
+you a sequence
+
+ align:start position:0%
+you a sequence
+ 
+
+ align:start position:0%
+you a sequence
+right that's what the input gate was
+
+ align:start position:0%
+right that's what the input gate was
+ 
+
+ align:start position:0%
+right that's what the input gate was
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+does that make sense all right so i've
+
+ align:start position:0%
+does that make sense all right so i've
+ 
+
+ align:start position:0%
+does that make sense all right so i've
+got this
+
+ align:start position:0%
+got this
+ 
+
+ align:start position:0%
+got this
+set avl tree of size log n
+
+ align:start position:0%
+set avl tree of size log n
+ 
+
+ align:start position:0%
+set avl tree of size log n
+what should it be keyed by
+
+ align:start position:0%
+what should it be keyed by
+ 
+
+ align:start position:0%
+what should it be keyed by
+absolute value of their preference right
+
+ align:start position:0%
+absolute value of their preference right
+ 
+
+ align:start position:0%
+absolute value of their preference right
+or of their
+
+ align:start position:0%
+or of their
+ 
+
+ align:start position:0%
+or of their
+opinion i don't remember what this is
+
+ align:start position:0%
+opinion i don't remember what this is
+ 
+
+ align:start position:0%
+opinion i don't remember what this is
+called so
+
+ align:start position:0%
+called so
+ 
+
+ align:start position:0%
+called so
+but i what log n things do i put in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know i i don't know anything
+
+ align:start position:0%
+i don't know i i don't know anything
+ 
+
+ align:start position:0%
+i don't know i i don't know anything
+about these things
+
+ align:start position:0%
+about these things
+ 
+
+ align:start position:0%
+about these things
+what makes one better than another right
+
+ align:start position:0%
+what makes one better than another right
+ 
+
+ align:start position:0%
+what makes one better than another right
+let's just put the first log in things
+
+ align:start position:0%
+let's just put the first log in things
+ 
+
+ align:start position:0%
+let's just put the first log in things
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+all right what could that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tell me now i've put this thing in it
+
+ align:start position:0%
+tell me now i've put this thing in it
+ 
+
+ align:start position:0%
+tell me now i've put this thing in it
+how long did that take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log n times log log n
+
+ align:start position:0%
+log n times log log n
+ 
+
+ align:start position:0%
+log n times log log n
+time right but that's much less than our
+
+ align:start position:0%
+time right but that's much less than our
+ 
+
+ align:start position:0%
+time right but that's much less than our
+running time right so
+
+ align:start position:0%
+running time right so
+ 
+
+ align:start position:0%
+running time right so
+that we're looking for so i don't really
+
+ align:start position:0%
+that we're looking for so i don't really
+ 
+
+ align:start position:0%
+that we're looking for so i don't really
+care right
+
+ align:start position:0%
+care right
+ 
+
+ align:start position:0%
+care right
+i mean i want you to say how long it
+
+ align:start position:0%
+i mean i want you to say how long it
+ 
+
+ align:start position:0%
+i mean i want you to say how long it
+took
+
+ align:start position:0%
+took
+ 
+
+ align:start position:0%
+took
+but for my purposes i know that it's
+
+ align:start position:0%
+but for my purposes i know that it's
+ 
+
+ align:start position:0%
+but for my purposes i know that it's
+lower than the running time i'm looking
+
+ align:start position:0%
+lower than the running time i'm looking
+ 
+
+ align:start position:0%
+lower than the running time i'm looking
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+so and i did that operation once i don't
+
+ align:start position:0%
+so and i did that operation once i don't
+ 
+
+ align:start position:0%
+so and i did that operation once i don't
+really care about it anymore
+
+ align:start position:0%
+really care about it anymore
+ 
+
+ align:start position:0%
+really care about it anymore
+okay yep how did you get log n because
+
+ align:start position:0%
+okay yep how did you get log n because
+ 
+
+ align:start position:0%
+okay yep how did you get log n because
+the number of things i'm storing in this
+
+ align:start position:0%
+the number of things i'm storing in this
+ 
+
+ align:start position:0%
+the number of things i'm storing in this
+thing is log n
+
+ align:start position:0%
+thing is log n
+ 
+
+ align:start position:0%
+thing is log n
+and so if i pattern match
+
+ align:start position:0%
+and so if i pattern match
+ 
+
+ align:start position:0%
+and so if i pattern match
+the build time of an avl tree and i
+
+ align:start position:0%
+the build time of an avl tree and i
+ 
+
+ align:start position:0%
+the build time of an avl tree and i
+stick log n in there
+
+ align:start position:0%
+stick log n in there
+ 
+
+ align:start position:0%
+stick log n in there
+right then it's log n times log log n
+
+ align:start position:0%
+right then it's log n times log log n
+ 
+
+ align:start position:0%
+right then it's log n times log log n
+gotcha okay so is that for one iteration
+
+ align:start position:0%
+gotcha okay so is that for one iteration
+ 
+
+ align:start position:0%
+gotcha okay so is that for one iteration
+well right now i've just built this
+
+ align:start position:0%
+well right now i've just built this
+ 
+
+ align:start position:0%
+well right now i've just built this
+thing right
+
+ align:start position:0%
+thing right
+ 
+
+ align:start position:0%
+thing right
+maybe i uh well i just built it once
+
+ align:start position:0%
+maybe i uh well i just built it once
+ 
+
+ align:start position:0%
+maybe i uh well i just built it once
+uh i'm asserting too that maybe i don't
+
+ align:start position:0%
+uh i'm asserting too that maybe i don't
+ 
+
+ align:start position:0%
+uh i'm asserting too that maybe i don't
+need to build it again
+
+ align:start position:0%
+need to build it again
+ 
+
+ align:start position:0%
+need to build it again
+right what could i do instead so right
+
+ align:start position:0%
+right what could i do instead so right
+ 
+
+ align:start position:0%
+right what could i do instead so right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+i know i haven't filtered my data at all
+
+ align:start position:0%
+i know i haven't filtered my data at all
+ 
+
+ align:start position:0%
+i know i haven't filtered my data at all
+right i'm just storing these things in
+
+ align:start position:0%
+right i'm just storing these things in
+ 
+
+ align:start position:0%
+right i'm just storing these things in
+sorted order in some way
+
+ align:start position:0%
+sorted order in some way
+ 
+
+ align:start position:0%
+sorted order in some way
+right what can i do
+
+ align:start position:0%
+right what can i do
+ 
+
+ align:start position:0%
+right what can i do
+to maybe start processing the rest of
+
+ align:start position:0%
+to maybe start processing the rest of
+ 
+
+ align:start position:0%
+to maybe start processing the rest of
+the data
+
+ align:start position:0%
+the data
+ 
+
+ align:start position:0%
+the data
+yeah well i didn't like try to scroll
+
+ align:start position:0%
+yeah well i didn't like try to scroll
+ 
+
+ align:start position:0%
+yeah well i didn't like try to scroll
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+the list a and try to like remind
+
+ align:start position:0%
+the list a and try to like remind
+ 
+
+ align:start position:0%
+the list a and try to like remind
+someone that's bigger than
+
+ align:start position:0%
+someone that's bigger than
+ 
+
+ align:start position:0%
+someone that's bigger than
+like try to keep the maximum ah
+
+ align:start position:0%
+like try to keep the maximum ah
+ 
+
+ align:start position:0%
+like try to keep the maximum ah
+kind of sweep this guy over inserting
+
+ align:start position:0%
+kind of sweep this guy over inserting
+ 
+
+ align:start position:0%
+kind of sweep this guy over inserting
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+and always maintaining you know if i do
+
+ align:start position:0%
+and always maintaining you know if i do
+ 
+
+ align:start position:0%
+and always maintaining you know if i do
+that and i keep sticking things in
+
+ align:start position:0%
+that and i keep sticking things in
+ 
+
+ align:start position:0%
+that and i keep sticking things in
+i'll have this sorted thing at the end
+
+ align:start position:0%
+i'll have this sorted thing at the end
+ 
+
+ align:start position:0%
+i'll have this sorted thing at the end
+and now i can just read off the
+
+ align:start position:0%
+and now i can just read off the
+ 
+
+ align:start position:0%
+and now i can just read off the
+biggest k things right however
+
+ align:start position:0%
+biggest k things right however
+ 
+
+ align:start position:0%
+biggest k things right however
+as i'm inserting things across here
+
+ align:start position:0%
+as i'm inserting things across here
+ 
+
+ align:start position:0%
+as i'm inserting things across here
+my thing's growing i'll just delete this
+
+ align:start position:0%
+my thing's growing i'll just delete this
+ 
+
+ align:start position:0%
+my thing's growing i'll just delete this
+oh delete small is fun
+
+ align:start position:0%
+oh delete small is fun
+ 
+
+ align:start position:0%
+oh delete small is fun
+i like that idea right basically yeah
+
+ align:start position:0%
+i like that idea right basically yeah
+ 
+
+ align:start position:0%
+i like that idea right basically yeah
+basically replace it right so
+
+ align:start position:0%
+basically replace it right so
+ 
+
+ align:start position:0%
+basically replace it right so
+what i'm going to do here's a proposal
+
+ align:start position:0%
+what i'm going to do here's a proposal
+ 
+
+ align:start position:0%
+what i'm going to do here's a proposal
+we're going to take the next guy stick
+
+ align:start position:0%
+we're going to take the next guy stick
+ 
+
+ align:start position:0%
+we're going to take the next guy stick
+it in
+
+ align:start position:0%
+it in
+ 
+
+ align:start position:0%
+it in
+awesome which one don't i care about now
+
+ align:start position:0%
+awesome which one don't i care about now
+ 
+
+ align:start position:0%
+awesome which one don't i care about now
+the smallest one there so kick the
+
+ align:start position:0%
+the smallest one there so kick the
+ 
+
+ align:start position:0%
+the smallest one there so kick the
+smallest one out
+
+ align:start position:0%
+smallest one out
+ 
+
+ align:start position:0%
+smallest one out
+now this one that i stuck in may be the
+
+ align:start position:0%
+now this one that i stuck in may be the
+ 
+
+ align:start position:0%
+now this one that i stuck in may be the
+smallest
+
+ align:start position:0%
+smallest
+ 
+
+ align:start position:0%
+smallest
+right so i just kind of passed it
+
+ align:start position:0%
+right so i just kind of passed it
+ 
+
+ align:start position:0%
+right so i just kind of passed it
+through this thing but how long did that
+
+ align:start position:0%
+through this thing but how long did that
+ 
+
+ align:start position:0%
+through this thing but how long did that
+take me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it took me the height of this tree
+
+ align:start position:0%
+it took me the height of this tree
+ 
+
+ align:start position:0%
+it took me the height of this tree
+what's the height of the tree log log n
+
+ align:start position:0%
+what's the height of the tree log log n
+ 
+
+ align:start position:0%
+what's the height of the tree log log n
+right so i put one in
+
+ align:start position:0%
+right so i put one in
+ 
+
+ align:start position:0%
+right so i put one in
+i pop one out that's the smallest right
+
+ align:start position:0%
+i pop one out that's the smallest right
+ 
+
+ align:start position:0%
+i pop one out that's the smallest right
+and i keep doing that all the way down
+
+ align:start position:0%
+and i keep doing that all the way down
+ 
+
+ align:start position:0%
+and i keep doing that all the way down
+the thing how long did that take
+
+ align:start position:0%
+the thing how long did that take
+ 
+
+ align:start position:0%
+the thing how long did that take
+yeah i'm processing n minus log n
+
+ align:start position:0%
+yeah i'm processing n minus log n
+ 
+
+ align:start position:0%
+yeah i'm processing n minus log n
+things which is basically n right
+
+ align:start position:0%
+things which is basically n right
+ 
+
+ align:start position:0%
+things which is basically n right
+and each one of those operations took me
+
+ align:start position:0%
+and each one of those operations took me
+ 
+
+ align:start position:0%
+and each one of those operations took me
+height of the tree time
+
+ align:start position:0%
+height of the tree time
+ 
+
+ align:start position:0%
+height of the tree time
+so that gives me the running time that
+
+ align:start position:0%
+so that gives me the running time that
+ 
+
+ align:start position:0%
+so that gives me the running time that
+we're looking for
+
+ align:start position:0%
+we're looking for
+ 
+
+ align:start position:0%
+we're looking for
+and log log
+
+ align:start position:0%
+and log log
+ 
+
+ align:start position:0%
+and log log
+yeah it's like recognition of like a
+
+ align:start position:0%
+yeah it's like recognition of like a
+ 
+
+ align:start position:0%
+yeah it's like recognition of like a
+slide yeah it's a kind of a sliding
+
+ align:start position:0%
+slide yeah it's a kind of a sliding
+ 
+
+ align:start position:0%
+slide yeah it's a kind of a sliding
+window technique you may have
+
+ align:start position:0%
+window technique you may have
+ 
+
+ align:start position:0%
+window technique you may have
+been using one recently
+
+ align:start position:0%
+been using one recently
+ 
+
+ align:start position:0%
+been using one recently
+okay everyone okay with this yeah let me
+
+ align:start position:0%
+okay everyone okay with this yeah let me
+ 
+
+ align:start position:0%
+okay everyone okay with this yeah let me
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+remember the context that we're talking
+
+ align:start position:0%
+remember the context that we're talking
+ 
+
+ align:start position:0%
+remember the context that we're talking
+about is log
+
+ align:start position:0%
+about is log
+ 
+
+ align:start position:0%
+about is log
+log n like tree and like what where so
+
+ align:start position:0%
+log n like tree and like what where so
+ 
+
+ align:start position:0%
+log n like tree and like what where so
+this thing
+
+ align:start position:0%
+this thing
+ 
+
+ align:start position:0%
+this thing
+the size of this thing is log log n yeah
+
+ align:start position:0%
+the size of this thing is log log n yeah
+ 
+
+ align:start position:0%
+the size of this thing is log log n yeah
+i mean sorry
+
+ align:start position:0%
+i mean sorry
+ 
+
+ align:start position:0%
+i mean sorry
+log n and the height of this thing is
+
+ align:start position:0%
+log n and the height of this thing is
+ 
+
+ align:start position:0%
+log n and the height of this thing is
+log of
+
+ align:start position:0%
+log of
+ 
+
+ align:start position:0%
+log of
+the size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in relation to like our little like
+
+ align:start position:0%
+in relation to like our little like
+ 
+
+ align:start position:0%
+in relation to like our little like
+login size
+
+ align:start position:0%
+login size
+ 
+
+ align:start position:0%
+login size
+like right there sticking this full of
+
+ align:start position:0%
+like right there sticking this full of
+ 
+
+ align:start position:0%
+like right there sticking this full of
+small log log entries or like like no so
+
+ align:start position:0%
+small log log entries or like like no so
+ 
+
+ align:start position:0%
+small log log entries or like like no so
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+i'm taking this stuff there's no
+
+ align:start position:0%
+i'm taking this stuff there's no
+ 
+
+ align:start position:0%
+i'm taking this stuff there's no
+intermediate data structure here
+
+ align:start position:0%
+intermediate data structure here
+ 
+
+ align:start position:0%
+intermediate data structure here
+i'm just sticking all these things into
+
+ align:start position:0%
+i'm just sticking all these things into
+ 
+
+ align:start position:0%
+i'm just sticking all these things into
+a via
+
+ align:start position:0%
+a via
+ 
+
+ align:start position:0%
+a via
+bsta i mean a set abl yep
+
+ align:start position:0%
+bsta i mean a set abl yep
+ 
+
+ align:start position:0%
+bsta i mean a set abl yep
+into one set avl right of size log n
+
+ align:start position:0%
+into one set avl right of size log n
+ 
+
+ align:start position:0%
+into one set avl right of size log n
+i'm sticking a guy in popping the
+
+ align:start position:0%
+i'm sticking a guy in popping the
+ 
+
+ align:start position:0%
+i'm sticking a guy in popping the
+worst guy out right going through all
+
+ align:start position:0%
+worst guy out right going through all
+ 
+
+ align:start position:0%
+worst guy out right going through all
+the things
+
+ align:start position:0%
+the things
+ 
+
+ align:start position:0%
+the things
+i need to make sure when i'm sticking it
+
+ align:start position:0%
+i need to make sure when i'm sticking it
+ 
+
+ align:start position:0%
+i need to make sure when i'm sticking it
+in i'm
+
+ align:start position:0%
+in i'm
+ 
+
+ align:start position:0%
+in i'm
+you know keeping track of which revenger
+
+ align:start position:0%
+you know keeping track of which revenger
+ 
+
+ align:start position:0%
+you know keeping track of which revenger
+it is and that i'm taking the absolute
+
+ align:start position:0%
+it is and that i'm taking the absolute
+ 
+
+ align:start position:0%
+it is and that i'm taking the absolute
+value and all those
+
+ align:start position:0%
+value and all those
+ 
+
+ align:start position:0%
+value and all those
+you know nitty-gritty kind of things but
+
+ align:start position:0%
+you know nitty-gritty kind of things but
+ 
+
+ align:start position:0%
+you know nitty-gritty kind of things but
+that's the basic idea right
+
+ align:start position:0%
+that's the basic idea right
+ 
+
+ align:start position:0%
+that's the basic idea right
+i'm just taking this i'm sliding the
+
+ align:start position:0%
+i'm just taking this i'm sliding the
+ 
+
+ align:start position:0%
+i'm just taking this i'm sliding the
+window in
+
+ align:start position:0%
+window in
+ 
+
+ align:start position:0%
+window in
+putting something in taking something
+
+ align:start position:0%
+putting something in taking something
+ 
+
+ align:start position:0%
+putting something in taking something
+out that may or may not probably is not
+
+ align:start position:0%
+out that may or may not probably is not
+ 
+
+ align:start position:0%
+out that may or may not probably is not
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+same thing and at the end of this
+
+ align:start position:0%
+same thing and at the end of this
+ 
+
+ align:start position:0%
+same thing and at the end of this
+procedure
+
+ align:start position:0%
+procedure
+ 
+
+ align:start position:0%
+procedure
+right the invariant i'm i'm maintaining
+
+ align:start position:0%
+right the invariant i'm i'm maintaining
+ 
+
+ align:start position:0%
+right the invariant i'm i'm maintaining
+here is that my thing
+
+ align:start position:0%
+here is that my thing
+ 
+
+ align:start position:0%
+here is that my thing
+always has the k largest opinions
+
+ align:start position:0%
+always has the k largest opinions
+ 
+
+ align:start position:0%
+always has the k largest opinions
+of the ones that i've processed so far
+
+ align:start position:0%
+of the ones that i've processed so far
+ 
+
+ align:start position:0%
+of the ones that i've processed so far
+right that's obviously true at the
+
+ align:start position:0%
+right that's obviously true at the
+ 
+
+ align:start position:0%
+right that's obviously true at the
+beginning when i build this thing
+
+ align:start position:0%
+beginning when i build this thing
+ 
+
+ align:start position:0%
+beginning when i build this thing
+and when i get to the end i've processed
+
+ align:start position:0%
+and when i get to the end i've processed
+ 
+
+ align:start position:0%
+and when i get to the end i've processed
+all the things
+
+ align:start position:0%
+all the things
+ 
+
+ align:start position:0%
+all the things
+so and this has size log n and so
+
+ align:start position:0%
+so and this has size log n and so
+ 
+
+ align:start position:0%
+so and this has size log n and so
+i have the log n largest
+
+ align:start position:0%
+i have the log n largest
+ 
+
+ align:start position:0%
+i have the log n largest
+like highest extremist opinions
+
+ align:start position:0%
+like highest extremist opinions
+ 
+
+ align:start position:0%
+like highest extremist opinions
+and then i can just do an inorder
+
+ align:start position:0%
+and then i can just do an inorder
+ 
+
+ align:start position:0%
+and then i can just do an inorder
+traversal of this thing and read
+
+ align:start position:0%
+traversal of this thing and read
+ 
+
+ align:start position:0%
+traversal of this thing and read
+and return does that make sense and i've
+
+ align:start position:0%
+and return does that make sense and i've
+ 
+
+ align:start position:0%
+and return does that make sense and i've
+only used
+
+ align:start position:0%
+only used
+ 
+
+ align:start position:0%
+only used
+logarithmic space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah so i don't get it are all the
+
+ align:start position:0%
+okay yeah so i don't get it are all the
+ 
+
+ align:start position:0%
+okay yeah so i don't get it are all the
+opinions in that uh
+
+ align:start position:0%
+opinions in that uh
+ 
+
+ align:start position:0%
+opinions in that uh
+are all the opinions in that avl tree
+
+ align:start position:0%
+are all the opinions in that avl tree
+ 
+
+ align:start position:0%
+are all the opinions in that avl tree
+all of these opinions are in the abl
+
+ align:start position:0%
+all of these opinions are in the abl
+ 
+
+ align:start position:0%
+all of these opinions are in the abl
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+and at ever at some point
+
+ align:start position:0%
+and at ever at some point
+ 
+
+ align:start position:0%
+and at ever at some point
+i will insert every
+
+ align:start position:0%
+i will insert every
+ 
+
+ align:start position:0%
+i will insert every
+opinion into this abl tree but i'll
+
+ align:start position:0%
+opinion into this abl tree but i'll
+ 
+
+ align:start position:0%
+opinion into this abl tree but i'll
+be removing the ones that i don't care
+
+ align:start position:0%
+be removing the ones that i don't care
+ 
+
+ align:start position:0%
+be removing the ones that i don't care
+about as i go
+
+ align:start position:0%
+about as i go
+ 
+
+ align:start position:0%
+about as i go
+does that make sense i'm always
+
+ align:start position:0%
+does that make sense i'm always
+ 
+
+ align:start position:0%
+does that make sense i'm always
+maintaining the
+
+ align:start position:0%
+maintaining the
+ 
+
+ align:start position:0%
+maintaining the
+the invariant that this thing before i
+
+ align:start position:0%
+the invariant that this thing before i
+ 
+
+ align:start position:0%
+the invariant that this thing before i
+insert something
+
+ align:start position:0%
+insert something
+ 
+
+ align:start position:0%
+insert something
+has exactly log n items in it and then
+
+ align:start position:0%
+has exactly log n items in it and then
+ 
+
+ align:start position:0%
+has exactly log n items in it and then
+i'm maintaining that invariant
+
+ align:start position:0%
+i'm maintaining that invariant
+ 
+
+ align:start position:0%
+i'm maintaining that invariant
+by sticking one in taking one out oh
+
+ align:start position:0%
+by sticking one in taking one out oh
+ 
+
+ align:start position:0%
+by sticking one in taking one out oh
+okay so then which one are you
+
+ align:start position:0%
+okay so then which one are you
+ 
+
+ align:start position:0%
+okay so then which one are you
+always the min right because i'm wanting
+
+ align:start position:0%
+always the min right because i'm wanting
+ 
+
+ align:start position:0%
+always the min right because i'm wanting
+the the largest ones
+
+ align:start position:0%
+the the largest ones
+ 
+
+ align:start position:0%
+the the largest ones
+and the mid by absolute value but yeah
+
+ align:start position:0%
+and the mid by absolute value but yeah
+ 
+
+ align:start position:0%
+and the mid by absolute value but yeah
+so i'm keying by the absolute value of
+
+ align:start position:0%
+so i'm keying by the absolute value of
+ 
+
+ align:start position:0%
+so i'm keying by the absolute value of
+these opinions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total run time here right it's
+
+ align:start position:0%
+total run time here right it's
+ 
+
+ align:start position:0%
+total run time here right it's
+bookkeeping right
+
+ align:start position:0%
+bookkeeping right
+ 
+
+ align:start position:0%
+bookkeeping right
+so it took me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a log n times log
+
+ align:start position:0%
+a log n times log
+ 
+
+ align:start position:0%
+a log n times log
+log and time to build this data
+
+ align:start position:0%
+log and time to build this data
+ 
+
+ align:start position:0%
+log and time to build this data
+structure at the beginning
+
+ align:start position:0%
+structure at the beginning
+ 
+
+ align:start position:0%
+structure at the beginning
+right plus n times
+
+ align:start position:0%
+right plus n times
+ 
+
+ align:start position:0%
+right plus n times
+log log n
+
+ align:start position:0%
+log log n
+ 
+
+ align:start position:0%
+log log n
+i did you know basically n operation
+
+ align:start position:0%
+i did you know basically n operation
+ 
+
+ align:start position:0%
+i did you know basically n operation
+asymptotically and
+
+ align:start position:0%
+asymptotically and
+ 
+
+ align:start position:0%
+asymptotically and
+operations this way it's actually n
+
+ align:start position:0%
+operations this way it's actually n
+ 
+
+ align:start position:0%
+operations this way it's actually n
+minus log n
+
+ align:start position:0%
+minus log n
+ 
+
+ align:start position:0%
+minus log n
+operations right and each one of those
+
+ align:start position:0%
+operations right and each one of those
+ 
+
+ align:start position:0%
+operations right and each one of those
+operations tree operations
+
+ align:start position:0%
+operations tree operations
+ 
+
+ align:start position:0%
+operations tree operations
+you know doing one insert one delete
+
+ align:start position:0%
+you know doing one insert one delete
+ 
+
+ align:start position:0%
+you know doing one insert one delete
+each one of those
+
+ align:start position:0%
+each one of those
+ 
+
+ align:start position:0%
+each one of those
+took the height of the tree time and so
+
+ align:start position:0%
+took the height of the tree time and so
+ 
+
+ align:start position:0%
+took the height of the tree time and so
+this is that good
+
+ align:start position:0%
+this is that good
+ 
+
+ align:start position:0%
+this is that good
+yeah if instead of blind we just insert
+
+ align:start position:0%
+yeah if instead of blind we just insert
+ 
+
+ align:start position:0%
+yeah if instead of blind we just insert
+and do we
+
+ align:start position:0%
+and do we
+ 
+
+ align:start position:0%
+and do we
+do a comparison and then so the in
+
+ align:start position:0%
+do a comparison and then so the in
+ 
+
+ align:start position:0%
+do a comparison and then so the in
+inserting and deleting
+
+ align:start position:0%
+inserting and deleting
+ 
+
+ align:start position:0%
+inserting and deleting
+uh a set avl tree is actually doing
+
+ align:start position:0%
+uh a set avl tree is actually doing
+ 
+
+ align:start position:0%
+uh a set avl tree is actually doing
+comparisons within its data structure
+
+ align:start position:0%
+comparisons within its data structure
+ 
+
+ align:start position:0%
+comparisons within its data structure
+just compare with the name sure you
+
+ align:start position:0%
+just compare with the name sure you
+ 
+
+ align:start position:0%
+just compare with the name sure you
+could do that
+
+ align:start position:0%
+could do that
+ 
+
+ align:start position:0%
+could do that
+right right so you could i could do it
+
+ align:start position:0%
+right right so you could i could do it
+ 
+
+ align:start position:0%
+right right so you could i could do it
+the other way right
+
+ align:start position:0%
+the other way right
+ 
+
+ align:start position:0%
+the other way right
+i could remove the smallest element here
+
+ align:start position:0%
+i could remove the smallest element here
+ 
+
+ align:start position:0%
+i could remove the smallest element here
+to start with
+
+ align:start position:0%
+to start with
+ 
+
+ align:start position:0%
+to start with
+right and then i compare it with this
+
+ align:start position:0%
+right and then i compare it with this
+ 
+
+ align:start position:0%
+right and then i compare it with this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+and then whichever is bigger i stick it
+
+ align:start position:0%
+and then whichever is bigger i stick it
+ 
+
+ align:start position:0%
+and then whichever is bigger i stick it
+back in
+
+ align:start position:0%
+back in
+ 
+
+ align:start position:0%
+back in
+same thing right it's just am i doing
+
+ align:start position:0%
+same thing right it's just am i doing
+ 
+
+ align:start position:0%
+same thing right it's just am i doing
+the delete first and then
+
+ align:start position:0%
+the delete first and then
+ 
+
+ align:start position:0%
+the delete first and then
+then the insertion or i'm doing the
+
+ align:start position:0%
+then the insertion or i'm doing the
+ 
+
+ align:start position:0%
+then the insertion or i'm doing the
+insertion first and then the deletion
+
+ align:start position:0%
+insertion first and then the deletion
+ 
+
+ align:start position:0%
+insertion first and then the deletion
+any other questions lots of questions
+
+ align:start position:0%
+any other questions lots of questions
+ 
+
+ align:start position:0%
+any other questions lots of questions
+all right well i'm probably gonna have
+
+ align:start position:0%
+all right well i'm probably gonna have
+ 
+
+ align:start position:0%
+all right well i'm probably gonna have
+to skip the problem
+
+ align:start position:0%
+to skip the problem
+ 
+
+ align:start position:0%
+to skip the problem
+uh we're gonna move on to uh c
+
+ align:start position:0%
+uh we're gonna move on to uh c
+ 
+
+ align:start position:0%
+uh we're gonna move on to uh c
+s so now s c l r
+
+ align:start position:0%
+s so now s c l r
+ 
+
+ align:start position:0%
+s so now s c l r
+all right what's the reference here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah clrs right so these are four
+
+ align:start position:0%
+yeah clrs right so these are four
+ 
+
+ align:start position:0%
+yeah clrs right so these are four
+academics who wrote a popular textbook
+
+ align:start position:0%
+academics who wrote a popular textbook
+ 
+
+ align:start position:0%
+academics who wrote a popular textbook
+in computer science
+
+ align:start position:0%
+in computer science
+ 
+
+ align:start position:0%
+in computer science
+uh okay this is the same kind of k kind
+
+ align:start position:0%
+uh okay this is the same kind of k kind
+ 
+
+ align:start position:0%
+uh okay this is the same kind of k kind
+of thing okay
+
+ align:start position:0%
+of thing okay
+ 
+
+ align:start position:0%
+of thing okay
+they found k first editions and they
+
+ align:start position:0%
+they found k first editions and they
+ 
+
+ align:start position:0%
+they found k first editions and they
+want to auction them off
+
+ align:start position:0%
+want to auction them off
+ 
+
+ align:start position:0%
+want to auction them off
+uh people can go on to their website
+
+ align:start position:0%
+uh people can go on to their website
+ 
+
+ align:start position:0%
+uh people can go on to their website
+they have a bitter id
+
+ align:start position:0%
+they have a bitter id
+ 
+
+ align:start position:0%
+they have a bitter id
+it's a unique identifier right and they
+
+ align:start position:0%
+it's a unique identifier right and they
+ 
+
+ align:start position:0%
+it's a unique identifier right and they
+can place a bid
+
+ align:start position:0%
+can place a bid
+ 
+
+ align:start position:0%
+can place a bid
+for one of these books right and
+
+ align:start position:0%
+for one of these books right and
+ 
+
+ align:start position:0%
+for one of these books right and
+they can change it during the bidding
+
+ align:start position:0%
+they can change it during the bidding
+ 
+
+ align:start position:0%
+they can change it during the bidding
+period but
+
+ align:start position:0%
+period but
+ 
+
+ align:start position:0%
+period but
+you know at the end of the bidding
+
+ align:start position:0%
+you know at the end of the bidding
+ 
+
+ align:start position:0%
+you know at the end of the bidding
+period the
+
+ align:start position:0%
+period the
+ 
+
+ align:start position:0%
+period the
+academics want to know who the uh
+
+ align:start position:0%
+academics want to know who the uh
+ 
+
+ align:start position:0%
+academics want to know who the uh
+you know what is the expected revenue
+
+ align:start position:0%
+you know what is the expected revenue
+ 
+
+ align:start position:0%
+you know what is the expected revenue
+i'll get by selling to the k highest
+
+ align:start position:0%
+i'll get by selling to the k highest
+ 
+
+ align:start position:0%
+i'll get by selling to the k highest
+bidders does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so
+
+ align:start position:0%
+yeah okay so
+ 
+
+ align:start position:0%
+yeah okay so
+note that before i
+
+ align:start position:0%
+note that before i
+ 
+
+ align:start position:0%
+note that before i
+build this data structure i know what k
+
+ align:start position:0%
+build this data structure i know what k
+ 
+
+ align:start position:0%
+build this data structure i know what k
+is k is a fixed thing
+
+ align:start position:0%
+is k is a fixed thing
+ 
+
+ align:start position:0%
+is k is a fixed thing
+right right because my my running time
+
+ align:start position:0%
+right right because my my running time
+ 
+
+ align:start position:0%
+right right because my my running time
+of this get revenue
+
+ align:start position:0%
+of this get revenue
+ 
+
+ align:start position:0%
+of this get revenue
+depends on this k it's not an input to
+
+ align:start position:0%
+depends on this k it's not an input to
+ 
+
+ align:start position:0%
+depends on this k it's not an input to
+that operation
+
+ align:start position:0%
+that operation
+ 
+
+ align:start position:0%
+that operation
+right so k is kind of i don't know what
+
+ align:start position:0%
+right so k is kind of i don't know what
+ 
+
+ align:start position:0%
+right so k is kind of i don't know what
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+a priori it could be n over 2 it could
+
+ align:start position:0%
+a priori it could be n over 2 it could
+ 
+
+ align:start position:0%
+a priori it could be n over 2 it could
+be log n
+
+ align:start position:0%
+be log n
+ 
+
+ align:start position:0%
+be log n
+right it could be 1
+
+ align:start position:0%
+right it could be 1
+ 
+
+ align:start position:0%
+right it could be 1
+right but the data structure i build
+
+ align:start position:0%
+right but the data structure i build
+ 
+
+ align:start position:0%
+right but the data structure i build
+needs to satisfy these running time
+
+ align:start position:0%
+needs to satisfy these running time
+ 
+
+ align:start position:0%
+needs to satisfy these running time
+properties no matter what choice okay
+
+ align:start position:0%
+properties no matter what choice okay
+ 
+
+ align:start position:0%
+properties no matter what choice okay
+that the academics told me does that
+
+ align:start position:0%
+that the academics told me does that
+ 
+
+ align:start position:0%
+that the academics told me does that
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+okay so what i need to do is
+
+ align:start position:0%
+okay so what i need to do is
+ 
+
+ align:start position:0%
+okay so what i need to do is
+as as time is going on people are
+
+ align:start position:0%
+as as time is going on people are
+ 
+
+ align:start position:0%
+as as time is going on people are
+placing new bids and updating their bids
+
+ align:start position:0%
+placing new bids and updating their bids
+ 
+
+ align:start position:0%
+placing new bids and updating their bids
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and you know those updates can take
+
+ align:start position:0%
+and you know those updates can take
+ 
+
+ align:start position:0%
+and you know those updates can take
+longer time
+
+ align:start position:0%
+longer time
+ 
+
+ align:start position:0%
+longer time
+but as soon as i close the window i want
+
+ align:start position:0%
+but as soon as i close the window i want
+ 
+
+ align:start position:0%
+but as soon as i close the window i want
+to be able to tell in constant time
+
+ align:start position:0%
+to be able to tell in constant time
+ 
+
+ align:start position:0%
+to be able to tell in constant time
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what the k highest bidders are
+
+ align:start position:0%
+what the k highest bidders are
+ 
+
+ align:start position:0%
+what the k highest bidders are
+any ideas on how to do this what are the
+
+ align:start position:0%
+any ideas on how to do this what are the
+ 
+
+ align:start position:0%
+any ideas on how to do this what are the
+operations that i have to do i have to
+
+ align:start position:0%
+operations that i have to do i have to
+ 
+
+ align:start position:0%
+operations that i have to do i have to
+be able to place a new bid right i
+
+ align:start position:0%
+be able to place a new bid right i
+ 
+
+ align:start position:0%
+be able to place a new bid right i
+associated with a bidder is an id
+
+ align:start position:0%
+associated with a bidder is an id
+ 
+
+ align:start position:0%
+associated with a bidder is an id
+and a bid which is also an integer right
+
+ align:start position:0%
+and a bid which is also an integer right
+ 
+
+ align:start position:0%
+and a bid which is also an integer right
+how many dollars i'm going to pay for
+
+ align:start position:0%
+how many dollars i'm going to pay for
+ 
+
+ align:start position:0%
+how many dollars i'm going to pay for
+this book
+
+ align:start position:0%
+this book
+ 
+
+ align:start position:0%
+this book
+uh update the bid in some sense i need
+
+ align:start position:0%
+uh update the bid in some sense i need
+ 
+
+ align:start position:0%
+uh update the bid in some sense i need
+to find
+
+ align:start position:0%
+to find
+ 
+
+ align:start position:0%
+to find
+whether that person placed the bid
+
+ align:start position:0%
+whether that person placed the bid
+ 
+
+ align:start position:0%
+whether that person placed the bid
+before right
+
+ align:start position:0%
+before right
+ 
+
+ align:start position:0%
+before right
+in my data structure so at some point
+
+ align:start position:0%
+in my data structure so at some point
+ 
+
+ align:start position:0%
+in my data structure so at some point
+i'm going to need a find on bidder id
+
+ align:start position:0%
+i'm going to need a find on bidder id
+ 
+
+ align:start position:0%
+i'm going to need a find on bidder id
+does that seem possible right so i might
+
+ align:start position:0%
+does that seem possible right so i might
+ 
+
+ align:start position:0%
+does that seem possible right so i might
+want to have some kind of dictionary
+
+ align:start position:0%
+want to have some kind of dictionary
+ 
+
+ align:start position:0%
+want to have some kind of dictionary
+on bitter ids right when i say that i
+
+ align:start position:0%
+on bitter ids right when i say that i
+ 
+
+ align:start position:0%
+on bitter ids right when i say that i
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+have a dictionary on something right i'm
+
+ align:start position:0%
+have a dictionary on something right i'm
+ 
+
+ align:start position:0%
+have a dictionary on something right i'm
+not specifying to you yet
+
+ align:start position:0%
+not specifying to you yet
+ 
+
+ align:start position:0%
+not specifying to you yet
+how i'm going to implement that
+
+ align:start position:0%
+how i'm going to implement that
+ 
+
+ align:start position:0%
+how i'm going to implement that
+dictionary right what are my usual
+
+ align:start position:0%
+dictionary right what are my usual
+ 
+
+ align:start position:0%
+dictionary right what are my usual
+options
+
+ align:start position:0%
+options
+ 
+
+ align:start position:0%
+options
+a hash table but what if i need worst
+
+ align:start position:0%
+a hash table but what if i need worst
+ 
+
+ align:start position:0%
+a hash table but what if i need worst
+case time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a set avl tree right that's going to be
+
+ align:start position:0%
+a set avl tree right that's going to be
+ 
+
+ align:start position:0%
+a set avl tree right that's going to be
+your go to for a dictionary
+
+ align:start position:0%
+your go to for a dictionary
+ 
+
+ align:start position:0%
+your go to for a dictionary
+right because that's going to give me
+
+ align:start position:0%
+right because that's going to give me
+ 
+
+ align:start position:0%
+right because that's going to give me
+log n time to find things by a key
+
+ align:start position:0%
+log n time to find things by a key
+ 
+
+ align:start position:0%
+log n time to find things by a key
+right it's the only thing except for
+
+ align:start position:0%
+right it's the only thing except for
+ 
+
+ align:start position:0%
+right it's the only thing except for
+assorted or
+
+ align:start position:0%
+assorted or
+ 
+
+ align:start position:0%
+assorted or
+sorted you could also use a sorted array
+
+ align:start position:0%
+sorted you could also use a sorted array
+ 
+
+ align:start position:0%
+sorted you could also use a sorted array
+right but that's going to
+
+ align:start position:0%
+right but that's going to
+ 
+
+ align:start position:0%
+right but that's going to
+not be dynamic and here we're updating
+
+ align:start position:0%
+not be dynamic and here we're updating
+ 
+
+ align:start position:0%
+not be dynamic and here we're updating
+who's in my data structure all the time
+
+ align:start position:0%
+who's in my data structure all the time
+ 
+
+ align:start position:0%
+who's in my data structure all the time
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+people are going in and placing bids
+
+ align:start position:0%
+people are going in and placing bids
+ 
+
+ align:start position:0%
+people are going in and placing bids
+right new
+
+ align:start position:0%
+right new
+ 
+
+ align:start position:0%
+right new
+new people placing bids so my set of
+
+ align:start position:0%
+new people placing bids so my set of
+ 
+
+ align:start position:0%
+new people placing bids so my set of
+things that i care about is changing all
+
+ align:start position:0%
+things that i care about is changing all
+ 
+
+ align:start position:0%
+things that i care about is changing all
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+so that's probably going to steer me
+
+ align:start position:0%
+so that's probably going to steer me
+ 
+
+ align:start position:0%
+so that's probably going to steer me
+away from sorted arrays because
+
+ align:start position:0%
+away from sorted arrays because
+ 
+
+ align:start position:0%
+away from sorted arrays because
+they're not good with dynamic operations
+
+ align:start position:0%
+they're not good with dynamic operations
+ 
+
+ align:start position:0%
+they're not good with dynamic operations
+okay so i'm going to need some kind of
+
+ align:start position:0%
+okay so i'm going to need some kind of
+ 
+
+ align:start position:0%
+okay so i'm going to need some kind of
+dictionary on
+
+ align:start position:0%
+dictionary on
+ 
+
+ align:start position:0%
+dictionary on
+bitter ids but i'm also going to need to
+
+ align:start position:0%
+bitter ids but i'm also going to need to
+ 
+
+ align:start position:0%
+bitter ids but i'm also going to need to
+maintain the the sum
+
+ align:start position:0%
+maintain the the sum
+ 
+
+ align:start position:0%
+maintain the the sum
+right of the k highest bidders does that
+
+ align:start position:0%
+right of the k highest bidders does that
+ 
+
+ align:start position:0%
+right of the k highest bidders does that
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+right and so in some sense i need to
+
+ align:start position:0%
+right and so in some sense i need to
+ 
+
+ align:start position:0%
+right and so in some sense i need to
+keep track of
+
+ align:start position:0%
+keep track of
+ 
+
+ align:start position:0%
+keep track of
+an ordered notion of
+
+ align:start position:0%
+an ordered notion of
+ 
+
+ align:start position:0%
+an ordered notion of
+the bidders right the bids that are in
+
+ align:start position:0%
+the bidders right the bids that are in
+ 
+
+ align:start position:0%
+the bidders right the bids that are in
+my data structure does that make sense
+
+ align:start position:0%
+my data structure does that make sense
+ 
+
+ align:start position:0%
+my data structure does that make sense
+right so order is going to be important
+
+ align:start position:0%
+right so order is going to be important
+ 
+
+ align:start position:0%
+right so order is going to be important
+on the bids i'm going to need to look up
+
+ align:start position:0%
+on the bids i'm going to need to look up
+ 
+
+ align:start position:0%
+on the bids i'm going to need to look up
+on bitter id
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's about it right
+
+ align:start position:0%
+and that's about it right
+ 
+
+ align:start position:0%
+and that's about it right
+okay yeah just checking so something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes correct yeah so uh
+
+ align:start position:0%
+yes correct yeah so uh
+ 
+
+ align:start position:0%
+yes correct yeah so uh
+that's a very good observation right if
+
+ align:start position:0%
+that's a very good observation right if
+ 
+
+ align:start position:0%
+that's a very good observation right if
+it runs in worst case
+
+ align:start position:0%
+it runs in worst case
+ 
+
+ align:start position:0%
+it runs in worst case
+time it also runs unexpected that time
+
+ align:start position:0%
+time it also runs unexpected that time
+ 
+
+ align:start position:0%
+time it also runs unexpected that time
+right because there's essentially no
+
+ align:start position:0%
+right because there's essentially no
+ 
+
+ align:start position:0%
+right because there's essentially no
+randomization that i'm talking about
+
+ align:start position:0%
+randomization that i'm talking about
+ 
+
+ align:start position:0%
+randomization that i'm talking about
+here right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's so there's a stronger notion
+
+ align:start position:0%
+yeah it's so there's a stronger notion
+ 
+
+ align:start position:0%
+yeah it's so there's a stronger notion
+which we want you to specify
+
+ align:start position:0%
+which we want you to specify
+ 
+
+ align:start position:0%
+which we want you to specify
+which that actually there is no
+
+ align:start position:0%
+which that actually there is no
+ 
+
+ align:start position:0%
+which that actually there is no
+randomization here we're not using a
+
+ align:start position:0%
+randomization here we're not using a
+ 
+
+ align:start position:0%
+randomization here we're not using a
+hash table
+
+ align:start position:0%
+hash table
+ 
+
+ align:start position:0%
+hash table
+right in this class that really that's
+
+ align:start position:0%
+right in this class that really that's
+ 
+
+ align:start position:0%
+right in this class that really that's
+the only situation where
+
+ align:start position:0%
+the only situation where
+ 
+
+ align:start position:0%
+the only situation where
+uh that's going to be an issue right uh
+
+ align:start position:0%
+uh that's going to be an issue right uh
+ 
+
+ align:start position:0%
+uh that's going to be an issue right uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh but if it is uh what this problem is
+
+ align:start position:0%
+uh but if it is uh what this problem is
+ 
+
+ align:start position:0%
+uh but if it is uh what this problem is
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+uh for each other state whether your
+
+ align:start position:0%
+uh for each other state whether your
+ 
+
+ align:start position:0%
+uh for each other state whether your
+running time is worst case expected
+
+ align:start position:0%
+running time is worst case expected
+ 
+
+ align:start position:0%
+running time is worst case expected
+and or amortized what we're really
+
+ align:start position:0%
+and or amortized what we're really
+ 
+
+ align:start position:0%
+and or amortized what we're really
+trying to get you to say is
+
+ align:start position:0%
+trying to get you to say is
+ 
+
+ align:start position:0%
+trying to get you to say is
+what's the uh
+
+ align:start position:0%
+what's the uh
+ 
+
+ align:start position:0%
+what's the uh
+evaluate the running time of your
+
+ align:start position:0%
+evaluate the running time of your
+ 
+
+ align:start position:0%
+evaluate the running time of your
+algorithm with the proper qualifications
+
+ align:start position:0%
+algorithm with the proper qualifications
+ 
+
+ align:start position:0%
+algorithm with the proper qualifications
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+if it took worst case i want you to say
+
+ align:start position:0%
+if it took worst case i want you to say
+ 
+
+ align:start position:0%
+if it took worst case i want you to say
+that it took worst case
+
+ align:start position:0%
+that it took worst case
+ 
+
+ align:start position:0%
+that it took worst case
+if it took if you use the hash table i
+
+ align:start position:0%
+if it took if you use the hash table i
+ 
+
+ align:start position:0%
+if it took if you use the hash table i
+want you to say expected
+
+ align:start position:0%
+want you to say expected
+ 
+
+ align:start position:0%
+want you to say expected
+and if these operations i were sometimes
+
+ align:start position:0%
+and if these operations i were sometimes
+ 
+
+ align:start position:0%
+and if these operations i were sometimes
+really bad
+
+ align:start position:0%
+really bad
+ 
+
+ align:start position:0%
+really bad
+but on average they're really good if i
+
+ align:start position:0%
+but on average they're really good if i
+ 
+
+ align:start position:0%
+but on average they're really good if i
+did a lot of them that's that's
+
+ align:start position:0%
+did a lot of them that's that's
+ 
+
+ align:start position:0%
+did a lot of them that's that's
+amortized right
+
+ align:start position:0%
+amortized right
+ 
+
+ align:start position:0%
+amortized right
+right or if i reduce to using a dynamic
+
+ align:start position:0%
+right or if i reduce to using a dynamic
+ 
+
+ align:start position:0%
+right or if i reduce to using a dynamic
+array
+
+ align:start position:0%
+array
+ 
+
+ align:start position:0%
+array
+right or if i reduce to using a hash
+
+ align:start position:0%
+right or if i reduce to using a hash
+ 
+
+ align:start position:0%
+right or if i reduce to using a hash
+table those dynamic operations would
+
+ align:start position:0%
+table those dynamic operations would
+ 
+
+ align:start position:0%
+table those dynamic operations would
+still be amortized right
+
+ align:start position:0%
+still be amortized right
+ 
+
+ align:start position:0%
+still be amortized right
+okay so the dynamic ones uh nice thing
+
+ align:start position:0%
+okay so the dynamic ones uh nice thing
+ 
+
+ align:start position:0%
+okay so the dynamic ones uh nice thing
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+linked data structures is that dynamic
+
+ align:start position:0%
+linked data structures is that dynamic
+ 
+
+ align:start position:0%
+linked data structures is that dynamic
+operations aren't amortized right
+
+ align:start position:0%
+operations aren't amortized right
+ 
+
+ align:start position:0%
+operations aren't amortized right
+so we're gonna get be able to get now
+
+ align:start position:0%
+so we're gonna get be able to get now
+ 
+
+ align:start position:0%
+so we're gonna get be able to get now
+for this problem we can actually get
+
+ align:start position:0%
+for this problem we can actually get
+ 
+
+ align:start position:0%
+for this problem we can actually get
+worst case bounds so we're going to try
+
+ align:start position:0%
+worst case bounds so we're going to try
+ 
+
+ align:start position:0%
+worst case bounds so we're going to try
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+you can also do it in expected using
+
+ align:start position:0%
+you can also do it in expected using
+ 
+
+ align:start position:0%
+you can also do it in expected using
+some hash tables for that
+
+ align:start position:0%
+some hash tables for that
+ 
+
+ align:start position:0%
+some hash tables for that
+that dictionary right okay so
+
+ align:start position:0%
+that dictionary right okay so
+ 
+
+ align:start position:0%
+that dictionary right okay so
+when you approach a data structures
+
+ align:start position:0%
+when you approach a data structures
+ 
+
+ align:start position:0%
+when you approach a data structures
+problem in this class
+
+ align:start position:0%
+problem in this class
+ 
+
+ align:start position:0%
+problem in this class
+you want to tell me what it is you're
+
+ align:start position:0%
+you want to tell me what it is you're
+ 
+
+ align:start position:0%
+you want to tell me what it is you're
+storing
+
+ align:start position:0%
+storing
+ 
+
+ align:start position:0%
+storing
+first off right tell me
+
+ align:start position:0%
+first off right tell me
+ 
+
+ align:start position:0%
+first off right tell me
+what's supposed to be in those things
+
+ align:start position:0%
+what's supposed to be in those things
+ 
+
+ align:start position:0%
+what's supposed to be in those things
+right some invariants on this data
+
+ align:start position:0%
+right some invariants on this data
+ 
+
+ align:start position:0%
+right some invariants on this data
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+to you know make sure that when i do
+
+ align:start position:0%
+to you know make sure that when i do
+ 
+
+ align:start position:0%
+to you know make sure that when i do
+queries later
+
+ align:start position:0%
+queries later
+ 
+
+ align:start position:0%
+queries later
+right that these things are being
+
+ align:start position:0%
+right that these things are being
+ 
+
+ align:start position:0%
+right that these things are being
+maintained right so that
+
+ align:start position:0%
+maintained right so that
+ 
+
+ align:start position:0%
+maintained right so that
+uh you know if i have you know if i'm
+
+ align:start position:0%
+uh you know if i have you know if i'm
+ 
+
+ align:start position:0%
+uh you know if i have you know if i'm
+maintaining a sorted array
+
+ align:start position:0%
+maintaining a sorted array
+ 
+
+ align:start position:0%
+maintaining a sorted array
+right and i'm supporting an operation to
+
+ align:start position:0%
+right and i'm supporting an operation to
+ 
+
+ align:start position:0%
+right and i'm supporting an operation to
+find the maximum
+
+ align:start position:0%
+find the maximum
+ 
+
+ align:start position:0%
+find the maximum
+i better anything i do to this data
+
+ align:start position:0%
+i better anything i do to this data
+ 
+
+ align:start position:0%
+i better anything i do to this data
+structure better be maintaining the
+
+ align:start position:0%
+structure better be maintaining the
+ 
+
+ align:start position:0%
+structure better be maintaining the
+invariance that these things are in
+
+ align:start position:0%
+invariance that these things are in
+ 
+
+ align:start position:0%
+invariance that these things are in
+sorted order and the last thing
+
+ align:start position:0%
+sorted order and the last thing
+ 
+
+ align:start position:0%
+sorted order and the last thing
+has the maximum item because my max
+
+ align:start position:0%
+has the maximum item because my max
+ 
+
+ align:start position:0%
+has the maximum item because my max
+return thing is going to look there and
+
+ align:start position:0%
+return thing is going to look there and
+ 
+
+ align:start position:0%
+return thing is going to look there and
+return that
+
+ align:start position:0%
+return that
+ 
+
+ align:start position:0%
+return that
+does that make sense so i want to tell
+
+ align:start position:0%
+does that make sense so i want to tell
+ 
+
+ align:start position:0%
+does that make sense so i want to tell
+you you want to tell me what is being
+
+ align:start position:0%
+you you want to tell me what is being
+ 
+
+ align:start position:0%
+you you want to tell me what is being
+stored
+
+ align:start position:0%
+stored
+ 
+
+ align:start position:0%
+stored
+at you know a generic point in time
+
+ align:start position:0%
+at you know a generic point in time
+ 
+
+ align:start position:0%
+at you know a generic point in time
+during your data structure
+
+ align:start position:0%
+during your data structure
+ 
+
+ align:start position:0%
+during your data structure
+right what is being maintained so that
+
+ align:start position:0%
+right what is being maintained so that
+ 
+
+ align:start position:0%
+right what is being maintained so that
+when i support a dynamic operation or a
+
+ align:start position:0%
+when i support a dynamic operation or a
+ 
+
+ align:start position:0%
+when i support a dynamic operation or a
+query
+
+ align:start position:0%
+query
+ 
+
+ align:start position:0%
+query
+right in a dynamic operation where i'm
+
+ align:start position:0%
+right in a dynamic operation where i'm
+ 
+
+ align:start position:0%
+right in a dynamic operation where i'm
+inserting and deleting things from this
+
+ align:start position:0%
+inserting and deleting things from this
+ 
+
+ align:start position:0%
+inserting and deleting things from this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+i need to make sure that i'm maintaining
+
+ align:start position:0%
+i need to make sure that i'm maintaining
+ 
+
+ align:start position:0%
+i need to make sure that i'm maintaining
+those invariants
+
+ align:start position:0%
+those invariants
+ 
+
+ align:start position:0%
+those invariants
+and when i'm querying i can actually
+
+ align:start position:0%
+and when i'm querying i can actually
+ 
+
+ align:start position:0%
+and when i'm querying i can actually
+rely on those invariants
+
+ align:start position:0%
+rely on those invariants
+ 
+
+ align:start position:0%
+rely on those invariants
+to to answer my query does that make
+
+ align:start position:0%
+to to answer my query does that make
+ 
+
+ align:start position:0%
+to to answer my query does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay so for this problem this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh any ideas
+
+ align:start position:0%
+okay uh any ideas
+ 
+
+ align:start position:0%
+okay uh any ideas
+i have two two kind of keys that i might
+
+ align:start position:0%
+i have two two kind of keys that i might
+ 
+
+ align:start position:0%
+i have two two kind of keys that i might
+have to deal with one's a bid id and
+
+ align:start position:0%
+have to deal with one's a bid id and
+ 
+
+ align:start position:0%
+have to deal with one's a bid id and
+one's a
+
+ align:start position:0%
+one's a
+ 
+
+ align:start position:0%
+one's a
+a bid right so how could i
+
+ align:start position:0%
+a bid right so how could i
+ 
+
+ align:start position:0%
+a bid right so how could i
+if i have two keys right that i might
+
+ align:start position:0%
+if i have two keys right that i might
+ 
+
+ align:start position:0%
+if i have two keys right that i might
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+maybe order on one and look up on
+
+ align:start position:0%
+maybe order on one and look up on
+ 
+
+ align:start position:0%
+maybe order on one and look up on
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+how many data structures do you think
+
+ align:start position:0%
+how many data structures do you think
+ 
+
+ align:start position:0%
+how many data structures do you think
+i'm going to use
+
+ align:start position:0%
+i'm going to use
+ 
+
+ align:start position:0%
+i'm going to use
+two that's a pretty good guess okay
+
+ align:start position:0%
+two that's a pretty good guess okay
+ 
+
+ align:start position:0%
+two that's a pretty good guess okay
+so one of them let's just guess right
+
+ align:start position:0%
+so one of them let's just guess right
+ 
+
+ align:start position:0%
+so one of them let's just guess right
+like i need to be able to look up on
+
+ align:start position:0%
+like i need to be able to look up on
+ 
+
+ align:start position:0%
+like i need to be able to look up on
+bid right so let's
+
+ align:start position:0%
+bid right so let's
+ 
+
+ align:start position:0%
+bid right so let's
+store these bitters
+
+ align:start position:0%
+store these bitters
+ 
+
+ align:start position:0%
+store these bitters
+right in some kind of dictionary that's
+
+ align:start position:0%
+right in some kind of dictionary that's
+ 
+
+ align:start position:0%
+right in some kind of dictionary that's
+going to be able to look up those things
+
+ align:start position:0%
+going to be able to look up those things
+ 
+
+ align:start position:0%
+going to be able to look up those things
+fast right so
+
+ align:start position:0%
+fast right so
+ 
+
+ align:start position:0%
+fast right so
+you know two data structures right one
+
+ align:start position:0%
+you know two data structures right one
+ 
+
+ align:start position:0%
+you know two data structures right one
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+a dictionary on
+
+ align:start position:0%
+a dictionary on
+ 
+
+ align:start position:0%
+a dictionary on
+a keyed
+
+ align:start position:0%
+a keyed
+ 
+
+ align:start position:0%
+a keyed
+on bitter
+
+ align:start position:0%
+on bitter
+ 
+
+ align:start position:0%
+on bitter
+id okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else am i going to want
+
+ align:start position:0%
+what else am i going to want
+ 
+
+ align:start position:0%
+what else am i going to want
+what's up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other way around a dictionary stored
+
+ align:start position:0%
+the other way around a dictionary stored
+ 
+
+ align:start position:0%
+the other way around a dictionary stored
+on the bids
+
+ align:start position:0%
+on the bids
+ 
+
+ align:start position:0%
+on the bids
+is a dictionary what i want here
+
+ align:start position:0%
+is a dictionary what i want here
+ 
+
+ align:start position:0%
+is a dictionary what i want here
+i want to maintain order somehow right
+
+ align:start position:0%
+i want to maintain order somehow right
+ 
+
+ align:start position:0%
+i want to maintain order somehow right
+because i want to maintain the k
+
+ align:start position:0%
+because i want to maintain the k
+ 
+
+ align:start position:0%
+because i want to maintain the k
+biggest things that i've seen so far
+
+ align:start position:0%
+biggest things that i've seen so far
+ 
+
+ align:start position:0%
+biggest things that i've seen so far
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+if if i had at some point in time right
+
+ align:start position:0%
+if if i had at some point in time right
+ 
+
+ align:start position:0%
+if if i had at some point in time right
+what's going to happen right if i'm
+
+ align:start position:0%
+what's going to happen right if i'm
+ 
+
+ align:start position:0%
+what's going to happen right if i'm
+maintaining the k largest at any point
+
+ align:start position:0%
+maintaining the k largest at any point
+ 
+
+ align:start position:0%
+maintaining the k largest at any point
+in time
+
+ align:start position:0%
+in time
+ 
+
+ align:start position:0%
+in time
+it's possible that one of those bidders
+
+ align:start position:0%
+it's possible that one of those bidders
+ 
+
+ align:start position:0%
+it's possible that one of those bidders
+maybe decreases his bid
+
+ align:start position:0%
+maybe decreases his bid
+ 
+
+ align:start position:0%
+maybe decreases his bid
+right so it's no longer in the highest
+
+ align:start position:0%
+right so it's no longer in the highest
+ 
+
+ align:start position:0%
+right so it's no longer in the highest
+i'm going to also need to keep track of
+
+ align:start position:0%
+i'm going to also need to keep track of
+ 
+
+ align:start position:0%
+i'm going to also need to keep track of
+the other guys to see who i should add
+
+ align:start position:0%
+the other guys to see who i should add
+ 
+
+ align:start position:0%
+the other guys to see who i should add
+back into that set
+
+ align:start position:0%
+back into that set
+ 
+
+ align:start position:0%
+back into that set
+for example right so here's an idea
+
+ align:start position:0%
+for example right so here's an idea
+ 
+
+ align:start position:0%
+for example right so here's an idea
+i'm going to keep not just one other
+
+ align:start position:0%
+i'm going to keep not just one other
+ 
+
+ align:start position:0%
+i'm going to keep not just one other
+data structure but
+
+ align:start position:0%
+data structure but
+ 
+
+ align:start position:0%
+data structure but
+two other data structures maybe this is
+
+ align:start position:0%
+two other data structures maybe this is
+ 
+
+ align:start position:0%
+two other data structures maybe this is
+a leap
+
+ align:start position:0%
+a leap
+ 
+
+ align:start position:0%
+a leap
+you don't have to do this there's a way
+
+ align:start position:0%
+you don't have to do this there's a way
+ 
+
+ align:start position:0%
+you don't have to do this there's a way
+to do it with just one another
+
+ align:start position:0%
+to do it with just one another
+ 
+
+ align:start position:0%
+to do it with just one another
+but i'm going to store two more one is a
+
+ align:start position:0%
+but i'm going to store two more one is a
+ 
+
+ align:start position:0%
+but i'm going to store two more one is a
+kind of a data structure
+
+ align:start position:0%
+kind of a data structure
+ 
+
+ align:start position:0%
+kind of a data structure
+to store
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with uh store
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the k highest
+
+ align:start position:0%
+the k highest
+ 
+
+ align:start position:0%
+the k highest
+bidders
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a data structure to store the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n minus k highest bidders
+
+ align:start position:0%
+n minus k highest bidders
+ 
+
+ align:start position:0%
+n minus k highest bidders
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+so this separates my problem quite
+
+ align:start position:0%
+so this separates my problem quite
+ 
+
+ align:start position:0%
+so this separates my problem quite
+nicely right
+
+ align:start position:0%
+nicely right
+ 
+
+ align:start position:0%
+nicely right
+if every time someone does an
+
+ align:start position:0%
+if every time someone does an
+ 
+
+ align:start position:0%
+if every time someone does an
+interaction with this data structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+i can check to see whether it's bigger
+
+ align:start position:0%
+i can check to see whether it's bigger
+ 
+
+ align:start position:0%
+i can check to see whether it's bigger
+than the smallest thing in here
+
+ align:start position:0%
+than the smallest thing in here
+ 
+
+ align:start position:0%
+than the smallest thing in here
+right if it is i can do the same kind of
+
+ align:start position:0%
+right if it is i can do the same kind of
+ 
+
+ align:start position:0%
+right if it is i can do the same kind of
+trick i did before right
+
+ align:start position:0%
+trick i did before right
+ 
+
+ align:start position:0%
+trick i did before right
+i can remove it and stick my new one in
+
+ align:start position:0%
+i can remove it and stick my new one in
+ 
+
+ align:start position:0%
+i can remove it and stick my new one in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+right and where do i but i removed it i
+
+ align:start position:0%
+right and where do i but i removed it i
+ 
+
+ align:start position:0%
+right and where do i but i removed it i
+have to maintain this
+
+ align:start position:0%
+have to maintain this
+ 
+
+ align:start position:0%
+have to maintain this
+property right so i stick it in here
+
+ align:start position:0%
+property right so i stick it in here
+ 
+
+ align:start position:0%
+property right so i stick it in here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+there's another case what's the other
+
+ align:start position:0%
+there's another case what's the other
+ 
+
+ align:start position:0%
+there's another case what's the other
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's smaller right in which case
+
+ align:start position:0%
+it's smaller right in which case
+ 
+
+ align:start position:0%
+it's smaller right in which case
+i don't do anything to this data
+
+ align:start position:0%
+i don't do anything to this data
+ 
+
+ align:start position:0%
+i don't do anything to this data
+structure and i just stick it into here
+
+ align:start position:0%
+structure and i just stick it into here
+ 
+
+ align:start position:0%
+structure and i just stick it into here
+that makes sense right so what are the
+
+ align:start position:0%
+that makes sense right so what are the
+ 
+
+ align:start position:0%
+that makes sense right so what are the
+operations these data structures need to
+
+ align:start position:0%
+operations these data structures need to
+ 
+
+ align:start position:0%
+operations these data structures need to
+maintain finding the minimum or the
+
+ align:start position:0%
+maintain finding the minimum or the
+ 
+
+ align:start position:0%
+maintain finding the minimum or the
+maximum
+
+ align:start position:0%
+maximum
+ 
+
+ align:start position:0%
+maximum
+of these two sets does that make sense
+
+ align:start position:0%
+of these two sets does that make sense
+ 
+
+ align:start position:0%
+of these two sets does that make sense
+and actually not
+
+ align:start position:0%
+and actually not
+ 
+
+ align:start position:0%
+and actually not
+really the where are those operations i
+
+ align:start position:0%
+really the where are those operations i
+ 
+
+ align:start position:0%
+really the where are those operations i
+don't have them anymore
+
+ align:start position:0%
+don't have them anymore
+ 
+
+ align:start position:0%
+don't have them anymore
+but they were the priority queue
+
+ align:start position:0%
+but they were the priority queue
+ 
+
+ align:start position:0%
+but they were the priority queue
+operations they had
+
+ align:start position:0%
+operations they had
+ 
+
+ align:start position:0%
+operations they had
+uh delete max right and also insert
+
+ align:start position:0%
+uh delete max right and also insert
+ 
+
+ align:start position:0%
+uh delete max right and also insert
+where things that it did well on right
+
+ align:start position:0%
+where things that it did well on right
+ 
+
+ align:start position:0%
+where things that it did well on right
+so any priority queue right anything
+
+ align:start position:0%
+so any priority queue right anything
+ 
+
+ align:start position:0%
+so any priority queue right anything
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+can deal with maxes and mins right
+
+ align:start position:0%
+can deal with maxes and mins right
+ 
+
+ align:start position:0%
+can deal with maxes and mins right
+is good right and and what what's a data
+
+ align:start position:0%
+is good right and and what what's a data
+ 
+
+ align:start position:0%
+is good right and and what what's a data
+structure you know that can deal with
+
+ align:start position:0%
+structure you know that can deal with
+ 
+
+ align:start position:0%
+structure you know that can deal with
+maxes and mins pretty efficiently
+
+ align:start position:0%
+maxes and mins pretty efficiently
+ 
+
+ align:start position:0%
+maxes and mins pretty efficiently
+the set avl right so
+
+ align:start position:0%
+the set avl right so
+ 
+
+ align:start position:0%
+the set avl right so
+instead of data structure here i'm going
+
+ align:start position:0%
+instead of data structure here i'm going
+ 
+
+ align:start position:0%
+instead of data structure here i'm going
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+set avm
+
+ align:start position:0%
+set avm
+ 
+
+ align:start position:0%
+set avm
+and obviously it's going to
+
+ align:start position:0%
+and obviously it's going to
+ 
+
+ align:start position:0%
+and obviously it's going to
+be keyed by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bid right because that's the thing that
+
+ align:start position:0%
+bid right because that's the thing that
+ 
+
+ align:start position:0%
+bid right because that's the thing that
+i'm going to want to find max's and mins
+
+ align:start position:0%
+i'm going to want to find max's and mins
+ 
+
+ align:start position:0%
+i'm going to want to find max's and mins
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+okay everyone following the logic here
+
+ align:start position:0%
+okay everyone following the logic here
+ 
+
+ align:start position:0%
+okay everyone following the logic here
+of why i mean
+
+ align:start position:0%
+of why i mean
+ 
+
+ align:start position:0%
+of why i mean
+i'm maintaining these things so this is
+
+ align:start position:0%
+i'm maintaining these things so this is
+ 
+
+ align:start position:0%
+i'm maintaining these things so this is
+this is the level of an invariance that
+
+ align:start position:0%
+this is the level of an invariance that
+ 
+
+ align:start position:0%
+this is the level of an invariance that
+i want to maintain because
+
+ align:start position:0%
+i want to maintain because
+ 
+
+ align:start position:0%
+i want to maintain because
+when i go to for example do this query
+
+ align:start position:0%
+when i go to for example do this query
+ 
+
+ align:start position:0%
+when i go to for example do this query
+get revenue right i can just run through
+
+ align:start position:0%
+get revenue right i can just run through
+ 
+
+ align:start position:0%
+get revenue right i can just run through
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+sum all of these things oh wait how much
+
+ align:start position:0%
+sum all of these things oh wait how much
+ 
+
+ align:start position:0%
+sum all of these things oh wait how much
+time do i have
+
+ align:start position:0%
+time do i have
+ 
+
+ align:start position:0%
+time do i have
+do i have k time no i don't have k time
+
+ align:start position:0%
+do i have k time no i don't have k time
+ 
+
+ align:start position:0%
+do i have k time no i don't have k time
+so i don't
+
+ align:start position:0%
+so i don't
+ 
+
+ align:start position:0%
+so i don't
+i can't afford to sum up all of these
+
+ align:start position:0%
+i can't afford to sum up all of these
+ 
+
+ align:start position:0%
+i can't afford to sum up all of these
+things at the end of my
+
+ align:start position:0%
+things at the end of my
+ 
+
+ align:start position:0%
+things at the end of my
+right i have to i have to return it to
+
+ align:start position:0%
+right i have to i have to return it to
+ 
+
+ align:start position:0%
+right i have to i have to return it to
+you in constant time
+
+ align:start position:0%
+you in constant time
+ 
+
+ align:start position:0%
+you in constant time
+any ideas yeah just
+
+ align:start position:0%
+any ideas yeah just
+ 
+
+ align:start position:0%
+any ideas yeah just
+compute you know update a song right
+
+ align:start position:0%
+compute you know update a song right
+ 
+
+ align:start position:0%
+compute you know update a song right
+along with this
+
+ align:start position:0%
+along with this
+ 
+
+ align:start position:0%
+along with this
+data structure i'm going to keep a
+
+ align:start position:0%
+data structure i'm going to keep a
+ 
+
+ align:start position:0%
+data structure i'm going to keep a
+fourth thing
+
+ align:start position:0%
+fourth thing
+ 
+
+ align:start position:0%
+fourth thing
+which is just total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of their bits right i'm going to call it
+
+ align:start position:0%
+of their bits right i'm going to call it
+ 
+
+ align:start position:0%
+of their bits right i'm going to call it
+like a
+
+ align:start position:0%
+like a
+ 
+
+ align:start position:0%
+like a
+t okay
+
+ align:start position:0%
+t okay
+ 
+
+ align:start position:0%
+t okay
+and that's something i'm maintaining
+
+ align:start position:0%
+and that's something i'm maintaining
+ 
+
+ align:start position:0%
+and that's something i'm maintaining
+it's part of my data structure
+
+ align:start position:0%
+it's part of my data structure
+ 
+
+ align:start position:0%
+it's part of my data structure
+right it's you could think of it as i'm
+
+ align:start position:0%
+right it's you could think of it as i'm
+ 
+
+ align:start position:0%
+right it's you could think of it as i'm
+augmenting this thing with a number
+
+ align:start position:0%
+augmenting this thing with a number
+ 
+
+ align:start position:0%
+augmenting this thing with a number
+right and the point of augmenting this
+
+ align:start position:0%
+right and the point of augmenting this
+ 
+
+ align:start position:0%
+right and the point of augmenting this
+thing with the number
+
+ align:start position:0%
+thing with the number
+ 
+
+ align:start position:0%
+thing with the number
+right is that i can just if i need to
+
+ align:start position:0%
+right is that i can just if i need to
+ 
+
+ align:start position:0%
+right is that i can just if i need to
+know what the total of this stuff is i
+
+ align:start position:0%
+know what the total of this stuff is i
+ 
+
+ align:start position:0%
+know what the total of this stuff is i
+can just look at that number
+
+ align:start position:0%
+can just look at that number
+ 
+
+ align:start position:0%
+can just look at that number
+does that make sense all right
+
+ align:start position:0%
+does that make sense all right
+ 
+
+ align:start position:0%
+does that make sense all right
+so now i think you know we're almost
+
+ align:start position:0%
+so now i think you know we're almost
+ 
+
+ align:start position:0%
+so now i think you know we're almost
+done we're basically done
+
+ align:start position:0%
+done we're basically done
+ 
+
+ align:start position:0%
+done we're basically done
+right how do we do this uh
+
+ align:start position:0%
+right how do we do this uh
+ 
+
+ align:start position:0%
+right how do we do this uh
+someone walk through to me how i would
+
+ align:start position:0%
+someone walk through to me how i would
+ 
+
+ align:start position:0%
+someone walk through to me how i would
+get revenue with this data structure
+
+ align:start position:0%
+get revenue with this data structure
+ 
+
+ align:start position:0%
+get revenue with this data structure
+i just i basically kind of told you look
+
+ align:start position:0%
+i just i basically kind of told you look
+ 
+
+ align:start position:0%
+i just i basically kind of told you look
+at this number
+
+ align:start position:0%
+at this number
+ 
+
+ align:start position:0%
+at this number
+return it right because that's the
+
+ align:start position:0%
+return it right because that's the
+ 
+
+ align:start position:0%
+return it right because that's the
+invariance that i've maintained
+
+ align:start position:0%
+invariance that i've maintained
+ 
+
+ align:start position:0%
+invariance that i've maintained
+on my data structure i'm relying on this
+
+ align:start position:0%
+on my data structure i'm relying on this
+ 
+
+ align:start position:0%
+on my data structure i'm relying on this
+invariant now
+
+ align:start position:0%
+invariant now
+ 
+
+ align:start position:0%
+invariant now
+i better make sure this is good when i
+
+ align:start position:0%
+i better make sure this is good when i
+ 
+
+ align:start position:0%
+i better make sure this is good when i
+do dynamic operations
+
+ align:start position:0%
+do dynamic operations
+ 
+
+ align:start position:0%
+do dynamic operations
+right i make sure i maintain it but if i
+
+ align:start position:0%
+right i make sure i maintain it but if i
+ 
+
+ align:start position:0%
+right i make sure i maintain it but if i
+by induction
+
+ align:start position:0%
+by induction
+ 
+
+ align:start position:0%
+by induction
+are ensured that all of this stuff is
+
+ align:start position:0%
+are ensured that all of this stuff is
+ 
+
+ align:start position:0%
+are ensured that all of this stuff is
+good and when i do a dynamic operation
+
+ align:start position:0%
+good and when i do a dynamic operation
+ 
+
+ align:start position:0%
+good and when i do a dynamic operation
+all that stuff is maintained
+
+ align:start position:0%
+all that stuff is maintained
+ 
+
+ align:start position:0%
+all that stuff is maintained
+then i'm all good right so get revenue
+
+ align:start position:0%
+then i'm all good right so get revenue
+ 
+
+ align:start position:0%
+then i'm all good right so get revenue
+after i kind of did all this extra work
+
+ align:start position:0%
+after i kind of did all this extra work
+ 
+
+ align:start position:0%
+after i kind of did all this extra work
+right it's very easy i just look at this
+
+ align:start position:0%
+right it's very easy i just look at this
+ 
+
+ align:start position:0%
+right it's very easy i just look at this
+number and return it
+
+ align:start position:0%
+number and return it
+ 
+
+ align:start position:0%
+number and return it
+okay so when we're grading a data
+
+ align:start position:0%
+okay so when we're grading a data
+ 
+
+ align:start position:0%
+okay so when we're grading a data
+structures problem usually we give you
+
+ align:start position:0%
+structures problem usually we give you
+ 
+
+ align:start position:0%
+structures problem usually we give you
+some points first for
+
+ align:start position:0%
+some points first for
+ 
+
+ align:start position:0%
+some points first for
+setting up your data structure
+
+ align:start position:0%
+setting up your data structure
+ 
+
+ align:start position:0%
+setting up your data structure
+separately from the operations and then
+
+ align:start position:0%
+separately from the operations and then
+ 
+
+ align:start position:0%
+separately from the operations and then
+we give you
+
+ align:start position:0%
+we give you
+ 
+
+ align:start position:0%
+we give you
+points per operation that you
+
+ align:start position:0%
+points per operation that you
+ 
+
+ align:start position:0%
+points per operation that you
+successfully deal with
+
+ align:start position:0%
+successfully deal with
+ 
+
+ align:start position:0%
+successfully deal with
+and then some points for correctness and
+
+ align:start position:0%
+and then some points for correctness and
+ 
+
+ align:start position:0%
+and then some points for correctness and
+running time
+
+ align:start position:0%
+running time
+ 
+
+ align:start position:0%
+running time
+yeah you have a question so
+
+ align:start position:0%
+yeah you have a question so
+ 
+
+ align:start position:0%
+yeah you have a question so
+would total be like a thing that we
+
+ align:start position:0%
+would total be like a thing that we
+ 
+
+ align:start position:0%
+would total be like a thing that we
+update whenever we
+
+ align:start position:0%
+update whenever we
+ 
+
+ align:start position:0%
+update whenever we
+um like mess around with the highest
+
+ align:start position:0%
+um like mess around with the highest
+ 
+
+ align:start position:0%
+um like mess around with the highest
+bitter tree and then
+
+ align:start position:0%
+bitter tree and then
+ 
+
+ align:start position:0%
+bitter tree and then
+and minus k highest bigger tree sorry
+
+ align:start position:0%
+and minus k highest bigger tree sorry
+ 
+
+ align:start position:0%
+and minus k highest bigger tree sorry
+say that again
+
+ align:start position:0%
+say that again
+ 
+
+ align:start position:0%
+say that again
+so like are we treating like the total
+
+ align:start position:0%
+so like are we treating like the total
+ 
+
+ align:start position:0%
+so like are we treating like the total
+like of like an augmentation that we
+
+ align:start position:0%
+like of like an augmentation that we
+ 
+
+ align:start position:0%
+like of like an augmentation that we
+update every time we do something yeah
+
+ align:start position:0%
+update every time we do something yeah
+ 
+
+ align:start position:0%
+update every time we do something yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so it's just a one number it's not
+
+ align:start position:0%
+so it's just a one number it's not
+ 
+
+ align:start position:0%
+so it's just a one number it's not
+really a data structure it's just one
+
+ align:start position:0%
+really a data structure it's just one
+ 
+
+ align:start position:0%
+really a data structure it's just one
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+that i'm storing with my my database
+
+ align:start position:0%
+that i'm storing with my my database
+ 
+
+ align:start position:0%
+that i'm storing with my my database
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay all right so how do i implement
+
+ align:start position:0%
+okay all right so how do i implement
+ 
+
+ align:start position:0%
+okay all right so how do i implement
+a uh new bid operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah can we assume that the bids will
+
+ align:start position:0%
+yeah can we assume that the bids will
+ 
+
+ align:start position:0%
+yeah can we assume that the bids will
+also be unique
+
+ align:start position:0%
+also be unique
+ 
+
+ align:start position:0%
+also be unique
+can you assume that the bids may be
+
+ align:start position:0%
+can you assume that the bids may be
+ 
+
+ align:start position:0%
+can you assume that the bids may be
+unique no
+
+ align:start position:0%
+unique no
+ 
+
+ align:start position:0%
+unique no
+right so that's actually something that
+
+ align:start position:0%
+right so that's actually something that
+ 
+
+ align:start position:0%
+right so that's actually something that
+is a really useful observation
+
+ align:start position:0%
+is a really useful observation
+ 
+
+ align:start position:0%
+is a really useful observation
+we've been talking about set data
+
+ align:start position:0%
+we've been talking about set data
+ 
+
+ align:start position:0%
+we've been talking about set data
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+as requiring unique keys right
+
+ align:start position:0%
+as requiring unique keys right
+ 
+
+ align:start position:0%
+as requiring unique keys right
+how can i deal with non-unique keys it
+
+ align:start position:0%
+how can i deal with non-unique keys it
+ 
+
+ align:start position:0%
+how can i deal with non-unique keys it
+actually turns out that you know hash
+
+ align:start position:0%
+actually turns out that you know hash
+ 
+
+ align:start position:0%
+actually turns out that you know hash
+table it's really important that these
+
+ align:start position:0%
+table it's really important that these
+ 
+
+ align:start position:0%
+table it's really important that these
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+unique keys right because i i need to
+
+ align:start position:0%
+unique keys right because i i need to
+ 
+
+ align:start position:0%
+unique keys right because i i need to
+check whether it's in there i'm looking
+
+ align:start position:0%
+check whether it's in there i'm looking
+ 
+
+ align:start position:0%
+check whether it's in there i'm looking
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+single key and when i find it i have to
+
+ align:start position:0%
+single key and when i find it i have to
+ 
+
+ align:start position:0%
+single key and when i find it i have to
+return right if i had multiple things
+
+ align:start position:0%
+return right if i had multiple things
+ 
+
+ align:start position:0%
+return right if i had multiple things
+with that key
+
+ align:start position:0%
+with that key
+ 
+
+ align:start position:0%
+with that key
+i might not return the one that i'm
+
+ align:start position:0%
+i might not return the one that i'm
+ 
+
+ align:start position:0%
+i might not return the one that i'm
+looking for right it doesn't even make
+
+ align:start position:0%
+looking for right it doesn't even make
+ 
+
+ align:start position:0%
+looking for right it doesn't even make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+right but you can generalize the
+
+ align:start position:0%
+right but you can generalize the
+ 
+
+ align:start position:0%
+right but you can generalize the
+set uh
+
+ align:start position:0%
+set uh
+ 
+
+ align:start position:0%
+set uh
+uh kind of infrastructure right
+
+ align:start position:0%
+uh kind of infrastructure right
+ 
+
+ align:start position:0%
+uh kind of infrastructure right
+to deal with multi-sets how can i how
+
+ align:start position:0%
+to deal with multi-sets how can i how
+ 
+
+ align:start position:0%
+to deal with multi-sets how can i how
+can i do that
+
+ align:start position:0%
+can i do that
+ 
+
+ align:start position:0%
+can i do that
+well with each key right
+
+ align:start position:0%
+well with each key right
+ 
+
+ align:start position:0%
+well with each key right
+again i'm storing unique keys with each
+
+ align:start position:0%
+again i'm storing unique keys with each
+ 
+
+ align:start position:0%
+again i'm storing unique keys with each
+key i can link it to a sequence data
+
+ align:start position:0%
+key i can link it to a sequence data
+ 
+
+ align:start position:0%
+key i can link it to a sequence data
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+or any other data structure right and
+
+ align:start position:0%
+or any other data structure right and
+ 
+
+ align:start position:0%
+or any other data structure right and
+what i'm do is i'm going to
+
+ align:start position:0%
+what i'm do is i'm going to
+ 
+
+ align:start position:0%
+what i'm do is i'm going to
+anything that has that key i'm going to
+
+ align:start position:0%
+anything that has that key i'm going to
+ 
+
+ align:start position:0%
+anything that has that key i'm going to
+stick it in that data structure
+
+ align:start position:0%
+stick it in that data structure
+ 
+
+ align:start position:0%
+stick it in that data structure
+right so instead of storing one item
+
+ align:start position:0%
+right so instead of storing one item
+ 
+
+ align:start position:0%
+right so instead of storing one item
+there i have the possibility of storing
+
+ align:start position:0%
+there i have the possibility of storing
+ 
+
+ align:start position:0%
+there i have the possibility of storing
+many things there
+
+ align:start position:0%
+many things there
+ 
+
+ align:start position:0%
+many things there
+now i have to change the semantics here
+
+ align:start position:0%
+now i have to change the semantics here
+ 
+
+ align:start position:0%
+now i have to change the semantics here
+right if i'm saying find on this key
+
+ align:start position:0%
+right if i'm saying find on this key
+ 
+
+ align:start position:0%
+right if i'm saying find on this key
+well now i could say i'm going to return
+
+ align:start position:0%
+well now i could say i'm going to return
+ 
+
+ align:start position:0%
+well now i could say i'm going to return
+all of the things with that key
+
+ align:start position:0%
+all of the things with that key
+ 
+
+ align:start position:0%
+all of the things with that key
+or i'm going to show our some thing with
+
+ align:start position:0%
+or i'm going to show our some thing with
+ 
+
+ align:start position:0%
+or i'm going to show our some thing with
+that key
+
+ align:start position:0%
+that key
+ 
+
+ align:start position:0%
+that key
+right but you get the idea all i have to
+
+ align:start position:0%
+right but you get the idea all i have to
+ 
+
+ align:start position:0%
+right but you get the idea all i have to
+do is map it to
+
+ align:start position:0%
+do is map it to
+ 
+
+ align:start position:0%
+do is map it to
+some other data structure to maintain
+
+ align:start position:0%
+some other data structure to maintain
+ 
+
+ align:start position:0%
+some other data structure to maintain
+those things like maybe
+
+ align:start position:0%
+those things like maybe
+ 
+
+ align:start position:0%
+those things like maybe
+i want all the things with that key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want to find the one with this other
+
+ align:start position:0%
+i want to find the one with this other
+ 
+
+ align:start position:0%
+i want to find the one with this other
+key right
+
+ align:start position:0%
+key right
+ 
+
+ align:start position:0%
+key right
+so maybe i link to a set data structure
+
+ align:start position:0%
+so maybe i link to a set data structure
+ 
+
+ align:start position:0%
+so maybe i link to a set data structure
+that can search on other things right
+
+ align:start position:0%
+that can search on other things right
+ 
+
+ align:start position:0%
+that can search on other things right
+but the idea here is we maintain this
+
+ align:start position:0%
+but the idea here is we maintain this
+ 
+
+ align:start position:0%
+but the idea here is we maintain this
+uniqueness key property
+
+ align:start position:0%
+uniqueness key property
+ 
+
+ align:start position:0%
+uniqueness key property
+right i have to relax my semantics so
+
+ align:start position:0%
+right i have to relax my semantics so
+ 
+
+ align:start position:0%
+right i have to relax my semantics so
+that i'm storing
+
+ align:start position:0%
+that i'm storing
+ 
+
+ align:start position:0%
+that i'm storing
+multiple things at that key location
+
+ align:start position:0%
+multiple things at that key location
+ 
+
+ align:start position:0%
+multiple things at that key location
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+yeah why does it matter whether you've
+
+ align:start position:0%
+yeah why does it matter whether you've
+ 
+
+ align:start position:0%
+yeah why does it matter whether you've
+said the entree
+
+ align:start position:0%
+said the entree
+ 
+
+ align:start position:0%
+said the entree
+or not uh it does uh so
+
+ align:start position:0%
+or not uh it does uh so
+ 
+
+ align:start position:0%
+or not uh it does uh so
+it's going to matter here right because
+
+ align:start position:0%
+it's going to matter here right because
+ 
+
+ align:start position:0%
+it's going to matter here right because
+i have bids
+
+ align:start position:0%
+i have bids
+ 
+
+ align:start position:0%
+i have bids
+right and the bids could be non-unique
+
+ align:start position:0%
+right and the bids could be non-unique
+ 
+
+ align:start position:0%
+right and the bids could be non-unique
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+two people could have the same you know
+
+ align:start position:0%
+two people could have the same you know
+ 
+
+ align:start position:0%
+two people could have the same you know
+uh bid and by our definition of a set
+
+ align:start position:0%
+uh bid and by our definition of a set
+ 
+
+ align:start position:0%
+uh bid and by our definition of a set
+data structure it had to have unique
+
+ align:start position:0%
+data structure it had to have unique
+ 
+
+ align:start position:0%
+data structure it had to have unique
+keys so if i stuck in all these things
+
+ align:start position:0%
+keys so if i stuck in all these things
+ 
+
+ align:start position:0%
+keys so if i stuck in all these things
+keyed by bidder you got a problem right
+
+ align:start position:0%
+keyed by bidder you got a problem right
+ 
+
+ align:start position:0%
+keyed by bidder you got a problem right
+now in actuality we can get away with
+
+ align:start position:0%
+now in actuality we can get away with
+ 
+
+ align:start position:0%
+now in actuality we can get away with
+that by storing basically a
+
+ align:start position:0%
+that by storing basically a
+ 
+
+ align:start position:0%
+that by storing basically a
+linked list of all the things with that
+
+ align:start position:0%
+linked list of all the things with that
+ 
+
+ align:start position:0%
+linked list of all the things with that
+key and we'd be fine
+
+ align:start position:0%
+key and we'd be fine
+ 
+
+ align:start position:0%
+key and we'd be fine
+right and then whenever i want to
+
+ align:start position:0%
+right and then whenever i want to
+ 
+
+ align:start position:0%
+right and then whenever i want to
+return one i could just do but actually
+
+ align:start position:0%
+return one i could just do but actually
+ 
+
+ align:start position:0%
+return one i could just do but actually
+a binary tree
+
+ align:start position:0%
+a binary tree
+ 
+
+ align:start position:0%
+a binary tree
+right actually is flexible enough that
+
+ align:start position:0%
+right actually is flexible enough that
+ 
+
+ align:start position:0%
+right actually is flexible enough that
+in most implementations you can just
+
+ align:start position:0%
+in most implementations you can just
+ 
+
+ align:start position:0%
+in most implementations you can just
+store a bunch of those things but
+
+ align:start position:0%
+store a bunch of those things but
+ 
+
+ align:start position:0%
+store a bunch of those things but
+actually our run times
+
+ align:start position:0%
+actually our run times
+ 
+
+ align:start position:0%
+actually our run times
+do worse then right what does it mean to
+
+ align:start position:0%
+do worse then right what does it mean to
+ 
+
+ align:start position:0%
+do worse then right what does it mean to
+find next in my sequence
+
+ align:start position:0%
+find next in my sequence
+ 
+
+ align:start position:0%
+find next in my sequence
+right what does it mean to find the
+
+ align:start position:0%
+right what does it mean to find the
+ 
+
+ align:start position:0%
+right what does it mean to find the
+to return the next larger thing above
+
+ align:start position:0%
+to return the next larger thing above
+ 
+
+ align:start position:0%
+to return the next larger thing above
+this key
+
+ align:start position:0%
+this key
+ 
+
+ align:start position:0%
+this key
+doesn't really make sense because there
+
+ align:start position:0%
+doesn't really make sense because there
+ 
+
+ align:start position:0%
+doesn't really make sense because there
+could be multiple ones which one do i
+
+ align:start position:0%
+could be multiple ones which one do i
+ 
+
+ align:start position:0%
+could be multiple ones which one do i
+return
+
+ align:start position:0%
+return
+ 
+
+ align:start position:0%
+return
+and if i repeatedly do find next on this
+
+ align:start position:0%
+and if i repeatedly do find next on this
+ 
+
+ align:start position:0%
+and if i repeatedly do find next on this
+data structure
+
+ align:start position:0%
+data structure
+ 
+
+ align:start position:0%
+data structure
+right i might not loop through all the
+
+ align:start position:0%
+right i might not loop through all the
+ 
+
+ align:start position:0%
+right i might not loop through all the
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+right so some stuff breaks down
+
+ align:start position:0%
+right so some stuff breaks down
+ 
+
+ align:start position:0%
+right so some stuff breaks down
+in our interface right so i would
+
+ align:start position:0%
+in our interface right so i would
+ 
+
+ align:start position:0%
+in our interface right so i would
+prefer you use unique keys in this this
+
+ align:start position:0%
+prefer you use unique keys in this this
+ 
+
+ align:start position:0%
+prefer you use unique keys in this this
+kind of situation
+
+ align:start position:0%
+kind of situation
+ 
+
+ align:start position:0%
+kind of situation
+next tuesday i think with binary heaps
+
+ align:start position:0%
+next tuesday i think with binary heaps
+ 
+
+ align:start position:0%
+next tuesday i think with binary heaps
+uh we'll deal with
+
+ align:start position:0%
+uh we'll deal with
+ 
+
+ align:start position:0%
+uh we'll deal with
+non-unique keys that's fine but
+
+ align:start position:0%
+non-unique keys that's fine but
+ 
+
+ align:start position:0%
+non-unique keys that's fine but
+if you're gonna use non-unique keys in
+
+ align:start position:0%
+if you're gonna use non-unique keys in
+ 
+
+ align:start position:0%
+if you're gonna use non-unique keys in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+you just gotta be a little bit careful
+
+ align:start position:0%
+you just gotta be a little bit careful
+ 
+
+ align:start position:0%
+you just gotta be a little bit careful
+about the semantics
+
+ align:start position:0%
+about the semantics
+ 
+
+ align:start position:0%
+about the semantics
+okay yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so you get the same uh
+
+ align:start position:0%
+uh so you get the same uh
+ 
+
+ align:start position:0%
+uh so you get the same uh
+running time you the you have to change
+
+ align:start position:0%
+running time you the you have to change
+ 
+
+ align:start position:0%
+running time you the you have to change
+the semantics on what you mean by find
+
+ align:start position:0%
+the semantics on what you mean by find
+ 
+
+ align:start position:0%
+the semantics on what you mean by find
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+right i just want to return anything
+
+ align:start position:0%
+right i just want to return anything
+ 
+
+ align:start position:0%
+right i just want to return anything
+with this key
+
+ align:start position:0%
+with this key
+ 
+
+ align:start position:0%
+with this key
+right what if everything has the same
+
+ align:start position:0%
+right what if everything has the same
+ 
+
+ align:start position:0%
+right what if everything has the same
+key then it takes constant time
+
+ align:start position:0%
+key then it takes constant time
+ 
+
+ align:start position:0%
+key then it takes constant time
+i just returned the first thing
+
+ align:start position:0%
+i just returned the first thing
+ 
+
+ align:start position:0%
+i just returned the first thing
+it's i mean these are special cases that
+
+ align:start position:0%
+it's i mean these are special cases that
+ 
+
+ align:start position:0%
+it's i mean these are special cases that
+you know you have to think about right
+
+ align:start position:0%
+you know you have to think about right
+ 
+
+ align:start position:0%
+you know you have to think about right
+uh i don't like thinking about them
+
+ align:start position:0%
+uh i don't like thinking about them
+ 
+
+ align:start position:0%
+uh i don't like thinking about them
+right so i just like
+
+ align:start position:0%
+right so i just like
+ 
+
+ align:start position:0%
+right so i just like
+having unique keys and if i want a
+
+ align:start position:0%
+having unique keys and if i want a
+ 
+
+ align:start position:0%
+having unique keys and if i want a
+situation where i have non-unique keys
+
+ align:start position:0%
+situation where i have non-unique keys
+ 
+
+ align:start position:0%
+situation where i have non-unique keys
+i'm going to basically put collisions at
+
+ align:start position:0%
+i'm going to basically put collisions at
+ 
+
+ align:start position:0%
+i'm going to basically put collisions at
+that key
+
+ align:start position:0%
+that key
+ 
+
+ align:start position:0%
+that key
+into a new data structure right it's
+
+ align:start position:0%
+into a new data structure right it's
+ 
+
+ align:start position:0%
+into a new data structure right it's
+just easier for me to separate out my
+
+ align:start position:0%
+just easier for me to separate out my
+ 
+
+ align:start position:0%
+just easier for me to separate out my
+head
+
+ align:start position:0%
+head
+ 
+
+ align:start position:0%
+head
+on what's happening because all of the
+
+ align:start position:0%
+on what's happening because all of the
+ 
+
+ align:start position:0%
+on what's happening because all of the
+running times that we proposed
+
+ align:start position:0%
+running times that we proposed
+ 
+
+ align:start position:0%
+running times that we proposed
+you know very strong definitions for
+
+ align:start position:0%
+you know very strong definitions for
+ 
+
+ align:start position:0%
+you know very strong definitions for
+unique key
+
+ align:start position:0%
+unique key
+ 
+
+ align:start position:0%
+unique key
+you know when you're dealing with a
+
+ align:start position:0%
+you know when you're dealing with a
+ 
+
+ align:start position:0%
+you know when you're dealing with a
+multi-set it's a little bit more
+
+ align:start position:0%
+multi-set it's a little bit more
+ 
+
+ align:start position:0%
+multi-set it's a little bit more
+problematic
+
+ align:start position:0%
+problematic
+ 
+
+ align:start position:0%
+problematic
+any other questions i we really need to
+
+ align:start position:0%
+any other questions i we really need to
+ 
+
+ align:start position:0%
+any other questions i we really need to
+kind of move on here
+
+ align:start position:0%
+kind of move on here
+ 
+
+ align:start position:0%
+kind of move on here
+right uh dictionary ketone bitter
+
+ align:start position:0%
+right uh dictionary ketone bitter
+ 
+
+ align:start position:0%
+right uh dictionary ketone bitter
+we still haven't implemented any dynamic
+
+ align:start position:0%
+we still haven't implemented any dynamic
+ 
+
+ align:start position:0%
+we still haven't implemented any dynamic
+operations
+
+ align:start position:0%
+operations
+ 
+
+ align:start position:0%
+operations
+new bid what do i do uh
+
+ align:start position:0%
+new bid what do i do uh
+ 
+
+ align:start position:0%
+new bid what do i do uh
+what am i going to need for my update
+
+ align:start position:0%
+what am i going to need for my update
+ 
+
+ align:start position:0%
+what am i going to need for my update
+i'm going to be able to
+
+ align:start position:0%
+i'm going to be able to
+ 
+
+ align:start position:0%
+i'm going to be able to
+need to essentially find in each of
+
+ align:start position:0%
+need to essentially find in each of
+ 
+
+ align:start position:0%
+need to essentially find in each of
+these data structures
+
+ align:start position:0%
+these data structures
+ 
+
+ align:start position:0%
+these data structures
+where that bidder is right
+
+ align:start position:0%
+where that bidder is right
+ 
+
+ align:start position:0%
+where that bidder is right
+and if i just have a thing keyed on
+
+ align:start position:0%
+and if i just have a thing keyed on
+ 
+
+ align:start position:0%
+and if i just have a thing keyed on
+their bid
+
+ align:start position:0%
+their bid
+ 
+
+ align:start position:0%
+their bid
+right the interface doesn't tell me what
+
+ align:start position:0%
+right the interface doesn't tell me what
+ 
+
+ align:start position:0%
+right the interface doesn't tell me what
+their old bid was
+
+ align:start position:0%
+their old bid was
+ 
+
+ align:start position:0%
+their old bid was
+it just tells me what their bidder id is
+
+ align:start position:0%
+it just tells me what their bidder id is
+ 
+
+ align:start position:0%
+it just tells me what their bidder id is
+right so if i just had their bidder id
+
+ align:start position:0%
+right so if i just had their bidder id
+ 
+
+ align:start position:0%
+right so if i just had their bidder id
+and their new bid how the heck am i
+
+ align:start position:0%
+and their new bid how the heck am i
+ 
+
+ align:start position:0%
+and their new bid how the heck am i
+going to find out
+
+ align:start position:0%
+going to find out
+ 
+
+ align:start position:0%
+going to find out
+which of these dash or where in these
+
+ align:start position:0%
+which of these dash or where in these
+ 
+
+ align:start position:0%
+which of these dash or where in these
+data structures they are
+
+ align:start position:0%
+data structures they are
+ 
+
+ align:start position:0%
+data structures they are
+right what i can do is i can store
+
+ align:start position:0%
+right what i can do is i can store
+ 
+
+ align:start position:0%
+right what i can do is i can store
+in this dictionary which i can look up
+
+ align:start position:0%
+in this dictionary which i can look up
+ 
+
+ align:start position:0%
+in this dictionary which i can look up
+in some amount of time right a pointer
+
+ align:start position:0%
+in some amount of time right a pointer
+ 
+
+ align:start position:0%
+in some amount of time right a pointer
+to where it exists in these things
+
+ align:start position:0%
+to where it exists in these things
+ 
+
+ align:start position:0%
+to where it exists in these things
+does that make sense this is called
+
+ align:start position:0%
+does that make sense this is called
+ 
+
+ align:start position:0%
+does that make sense this is called
+cross linking you may have
+
+ align:start position:0%
+cross linking you may have
+ 
+
+ align:start position:0%
+cross linking you may have
+done that a little bit in problem set
+
+ align:start position:0%
+done that a little bit in problem set
+ 
+
+ align:start position:0%
+done that a little bit in problem set
+two or something like that
+
+ align:start position:0%
+two or something like that
+ 
+
+ align:start position:0%
+two or something like that
+yeah are we storing a pointer to a
+
+ align:start position:0%
+yeah are we storing a pointer to a
+ 
+
+ align:start position:0%
+yeah are we storing a pointer to a
+specific figure
+
+ align:start position:0%
+specific figure
+ 
+
+ align:start position:0%
+specific figure
+yeah exactly right so the the invariant
+
+ align:start position:0%
+yeah exactly right so the the invariant
+ 
+
+ align:start position:0%
+yeah exactly right so the the invariant
+we have is that all of the bidders we've
+
+ align:start position:0%
+we have is that all of the bidders we've
+ 
+
+ align:start position:0%
+we have is that all of the bidders we've
+processed so far exist in these data
+
+ align:start position:0%
+processed so far exist in these data
+ 
+
+ align:start position:0%
+processed so far exist in these data
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+right in one of these data structures
+
+ align:start position:0%
+right in one of these data structures
+ 
+
+ align:start position:0%
+right in one of these data structures
+and because we've used a set avl tree
+
+ align:start position:0%
+and because we've used a set avl tree
+ 
+
+ align:start position:0%
+and because we've used a set avl tree
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+in particular exists in a node of one of
+
+ align:start position:0%
+in particular exists in a node of one of
+ 
+
+ align:start position:0%
+in particular exists in a node of one of
+these data structures
+
+ align:start position:0%
+these data structures
+ 
+
+ align:start position:0%
+these data structures
+right what we can do is in this thing
+
+ align:start position:0%
+right what we can do is in this thing
+ 
+
+ align:start position:0%
+right what we can do is in this thing
+maintain pointers right
+
+ align:start position:0%
+maintain pointers right
+ 
+
+ align:start position:0%
+maintain pointers right
+mapping each of the bitter ids to their
+
+ align:start position:0%
+mapping each of the bitter ids to their
+ 
+
+ align:start position:0%
+mapping each of the bitter ids to their
+location in these data structures
+
+ align:start position:0%
+location in these data structures
+ 
+
+ align:start position:0%
+location in these data structures
+and why is that going to be a useful
+
+ align:start position:0%
+and why is that going to be a useful
+ 
+
+ align:start position:0%
+and why is that going to be a useful
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+right uh say i mapped this dictionary
+
+ align:start position:0%
+right uh say i mapped this dictionary
+ 
+
+ align:start position:0%
+right uh say i mapped this dictionary
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+what could i use for this dictionary to
+
+ align:start position:0%
+what could i use for this dictionary to
+ 
+
+ align:start position:0%
+what could i use for this dictionary to
+get the running time we're looking for
+
+ align:start position:0%
+get the running time we're looking for
+ 
+
+ align:start position:0%
+get the running time we're looking for
+i could use a hash table or a set avl
+
+ align:start position:0%
+i could use a hash table or a set avl
+ 
+
+ align:start position:0%
+i could use a hash table or a set avl
+right if it's set avl
+
+ align:start position:0%
+right if it's set avl
+ 
+
+ align:start position:0%
+right if it's set avl
+i'm going to get logarithmic time worst
+
+ align:start position:0%
+i'm going to get logarithmic time worst
+ 
+
+ align:start position:0%
+i'm going to get logarithmic time worst
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+with a hash table i'm going to get
+
+ align:start position:0%
+with a hash table i'm going to get
+ 
+
+ align:start position:0%
+with a hash table i'm going to get
+constant time but it's expected right so
+
+ align:start position:0%
+constant time but it's expected right so
+ 
+
+ align:start position:0%
+constant time but it's expected right so
+it could be linear time in the worst
+
+ align:start position:0%
+it could be linear time in the worst
+ 
+
+ align:start position:0%
+it could be linear time in the worst
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+right so we're going to use a set avl
+
+ align:start position:0%
+right so we're going to use a set avl
+ 
+
+ align:start position:0%
+right so we're going to use a set avl
+tree right because that's what we do
+
+ align:start position:0%
+tree right because that's what we do
+ 
+
+ align:start position:0%
+tree right because that's what we do
+right now and that's going to give us
+
+ align:start position:0%
+right now and that's going to give us
+ 
+
+ align:start position:0%
+right now and that's going to give us
+worst case
+
+ align:start position:0%
+worst case
+ 
+
+ align:start position:0%
+worst case
+okay so what i'm going to do is for each
+
+ align:start position:0%
+okay so what i'm going to do is for each
+ 
+
+ align:start position:0%
+okay so what i'm going to do is for each
+one of these things i'm going to store
+
+ align:start position:0%
+one of these things i'm going to store
+ 
+
+ align:start position:0%
+one of these things i'm going to store
+that pointer so what i'm going to do
+
+ align:start position:0%
+that pointer so what i'm going to do
+ 
+
+ align:start position:0%
+that pointer so what i'm going to do
+is first i'm going to do that operation
+
+ align:start position:0%
+is first i'm going to do that operation
+ 
+
+ align:start position:0%
+is first i'm going to do that operation
+we had
+
+ align:start position:0%
+we had
+ 
+
+ align:start position:0%
+we had
+if i'm adding a new bitter right i'm
+
+ align:start position:0%
+if i'm adding a new bitter right i'm
+ 
+
+ align:start position:0%
+if i'm adding a new bitter right i'm
+going to take
+
+ align:start position:0%
+going to take
+ 
+
+ align:start position:0%
+going to take
+the you know the d and b right
+
+ align:start position:0%
+the you know the d and b right
+ 
+
+ align:start position:0%
+the you know the d and b right
+these two values that object that's
+
+ align:start position:0%
+these two values that object that's
+ 
+
+ align:start position:0%
+these two values that object that's
+that that bitter object or whatever i'm
+
+ align:start position:0%
+that that bitter object or whatever i'm
+ 
+
+ align:start position:0%
+that that bitter object or whatever i'm
+going to look at the smallest thing in
+
+ align:start position:0%
+going to look at the smallest thing in
+ 
+
+ align:start position:0%
+going to look at the smallest thing in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+data structure right see if it's bid
+
+ align:start position:0%
+data structure right see if it's bid
+ 
+
+ align:start position:0%
+data structure right see if it's bid
+is bigger than my
+
+ align:start position:0%
+is bigger than my
+ 
+
+ align:start position:0%
+is bigger than my
+my the the thing i'm inserting right if
+
+ align:start position:0%
+my the the thing i'm inserting right if
+ 
+
+ align:start position:0%
+my the the thing i'm inserting right if
+it is then i'm not going to touch this
+
+ align:start position:0%
+it is then i'm not going to touch this
+ 
+
+ align:start position:0%
+it is then i'm not going to touch this
+data structure i'm just going to insert
+
+ align:start position:0%
+data structure i'm just going to insert
+ 
+
+ align:start position:0%
+data structure i'm just going to insert
+it in here
+
+ align:start position:0%
+it in here
+ 
+
+ align:start position:0%
+it in here
+and now after i insert it in here i know
+
+ align:start position:0%
+and now after i insert it in here i know
+ 
+
+ align:start position:0%
+and now after i insert it in here i know
+exactly where it is in the data
+
+ align:start position:0%
+exactly where it is in the data
+ 
+
+ align:start position:0%
+exactly where it is in the data
+structure i just inserted it
+
+ align:start position:0%
+structure i just inserted it
+ 
+
+ align:start position:0%
+structure i just inserted it
+right right so now
+
+ align:start position:0%
+right right so now
+ 
+
+ align:start position:0%
+right right so now
+holding that in my hand the node right
+
+ align:start position:0%
+holding that in my hand the node right
+ 
+
+ align:start position:0%
+holding that in my hand the node right
+i can go and insert that bitter into
+
+ align:start position:0%
+i can go and insert that bitter into
+ 
+
+ align:start position:0%
+i can go and insert that bitter into
+here right
+
+ align:start position:0%
+here right
+ 
+
+ align:start position:0%
+here right
+by bit id right so it's going to take
+
+ align:start position:0%
+by bit id right so it's going to take
+ 
+
+ align:start position:0%
+by bit id right so it's going to take
+logarithmic time
+
+ align:start position:0%
+logarithmic time
+ 
+
+ align:start position:0%
+logarithmic time
+and now i can store with that node
+
+ align:start position:0%
+and now i can store with that node
+ 
+
+ align:start position:0%
+and now i can store with that node
+my pointer to this data structure does
+
+ align:start position:0%
+my pointer to this data structure does
+ 
+
+ align:start position:0%
+my pointer to this data structure does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+and in the other case i kind of do the
+
+ align:start position:0%
+and in the other case i kind of do the
+ 
+
+ align:start position:0%
+and in the other case i kind of do the
+same thing right
+
+ align:start position:0%
+same thing right
+ 
+
+ align:start position:0%
+same thing right
+if it's bigger than the smallest thing
+
+ align:start position:0%
+if it's bigger than the smallest thing
+ 
+
+ align:start position:0%
+if it's bigger than the smallest thing
+here i pop that smaller thing out stick
+
+ align:start position:0%
+here i pop that smaller thing out stick
+ 
+
+ align:start position:0%
+here i pop that smaller thing out stick
+it in there
+
+ align:start position:0%
+it in there
+ 
+
+ align:start position:0%
+it in there
+and i stick my new guy in here
+
+ align:start position:0%
+and i stick my new guy in here
+ 
+
+ align:start position:0%
+and i stick my new guy in here
+cross-linking
+
+ align:start position:0%
+cross-linking
+ 
+
+ align:start position:0%
+cross-linking
+each of those pointers along the way
+
+ align:start position:0%
+each of those pointers along the way
+ 
+
+ align:start position:0%
+each of those pointers along the way
+does that make sense hopefully
+
+ align:start position:0%
+does that make sense hopefully
+ 
+
+ align:start position:0%
+does that make sense hopefully
+kind of kind of okay yeah
+
+ align:start position:0%
+kind of kind of okay yeah
+ 
+
+ align:start position:0%
+kind of kind of okay yeah
+and for update very similar right if i
+
+ align:start position:0%
+and for update very similar right if i
+ 
+
+ align:start position:0%
+and for update very similar right if i
+want to update
+
+ align:start position:0%
+want to update
+ 
+
+ align:start position:0%
+want to update
+a certain bidder i look in this data
+
+ align:start position:0%
+a certain bidder i look in this data
+ 
+
+ align:start position:0%
+a certain bidder i look in this data
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+finds the bidder
+
+ align:start position:0%
+finds the bidder
+ 
+
+ align:start position:0%
+finds the bidder
+traverse that pointer to wherever it is
+
+ align:start position:0%
+traverse that pointer to wherever it is
+ 
+
+ align:start position:0%
+traverse that pointer to wherever it is
+in one of these avl trees
+
+ align:start position:0%
+in one of these avl trees
+ 
+
+ align:start position:0%
+in one of these avl trees
+right if it's in this if it's in this
+
+ align:start position:0%
+right if it's in this if it's in this
+ 
+
+ align:start position:0%
+right if it's in this if it's in this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+i just remove it from the tree right or
+
+ align:start position:0%
+i just remove it from the tree right or
+ 
+
+ align:start position:0%
+i just remove it from the tree right or
+i remove it from the tree and then i
+
+ align:start position:0%
+i remove it from the tree and then i
+ 
+
+ align:start position:0%
+i remove it from the tree and then i
+reinsert
+
+ align:start position:0%
+reinsert
+ 
+
+ align:start position:0%
+reinsert
+right with whatever the new bit is right
+
+ align:start position:0%
+right with whatever the new bit is right
+ 
+
+ align:start position:0%
+right with whatever the new bit is right
+and if it's in this one again i remove
+
+ align:start position:0%
+and if it's in this one again i remove
+ 
+
+ align:start position:0%
+and if it's in this one again i remove
+it from the tree
+
+ align:start position:0%
+it from the tree
+ 
+
+ align:start position:0%
+it from the tree
+reinsert and whichever these things is
+
+ align:start position:0%
+reinsert and whichever these things is
+ 
+
+ align:start position:0%
+reinsert and whichever these things is
+and then i might have to you know swap a
+
+ align:start position:0%
+and then i might have to you know swap a
+ 
+
+ align:start position:0%
+and then i might have to you know swap a
+constant number of things back and forth
+
+ align:start position:0%
+constant number of things back and forth
+ 
+
+ align:start position:0%
+constant number of things back and forth
+here to maintain that this has the
+
+ align:start position:0%
+here to maintain that this has the
+ 
+
+ align:start position:0%
+here to maintain that this has the
+k highest right and when i do those
+
+ align:start position:0%
+k highest right and when i do those
+ 
+
+ align:start position:0%
+k highest right and when i do those
+dynamic operations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm always removing some constant number
+
+ align:start position:0%
+i'm always removing some constant number
+ 
+
+ align:start position:0%
+i'm always removing some constant number
+of nodes in each of these trees and and
+
+ align:start position:0%
+of nodes in each of these trees and and
+ 
+
+ align:start position:0%
+of nodes in each of these trees and and
+adding back in a constant number of
+
+ align:start position:0%
+adding back in a constant number of
+ 
+
+ align:start position:0%
+adding back in a constant number of
+things and while i do that i just make
+
+ align:start position:0%
+things and while i do that i just make
+ 
+
+ align:start position:0%
+things and while i do that i just make
+sure to update this total as i go
+
+ align:start position:0%
+sure to update this total as i go
+ 
+
+ align:start position:0%
+sure to update this total as i go
+right his total was the sum of all of
+
+ align:start position:0%
+right his total was the sum of all of
+ 
+
+ align:start position:0%
+right his total was the sum of all of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bids in here and if i insert a new bid
+
+ align:start position:0%
+bids in here and if i insert a new bid
+ 
+
+ align:start position:0%
+bids in here and if i insert a new bid
+in here
+
+ align:start position:0%
+in here
+ 
+
+ align:start position:0%
+in here
+i have to add to that total and if i
+
+ align:start position:0%
+i have to add to that total and if i
+ 
+
+ align:start position:0%
+i have to add to that total and if i
+remove one i have to remove from that
+
+ align:start position:0%
+remove one i have to remove from that
+ 
+
+ align:start position:0%
+remove one i have to remove from that
+total but
+
+ align:start position:0%
+total but
+ 
+
+ align:start position:0%
+total but
+again it's a constant number of things
+
+ align:start position:0%
+again it's a constant number of things
+ 
+
+ align:start position:0%
+again it's a constant number of things
+i'm moving in and out of these data
+
+ align:start position:0%
+i'm moving in and out of these data
+ 
+
+ align:start position:0%
+i'm moving in and out of these data
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+and so it can update this in constant
+
+ align:start position:0%
+and so it can update this in constant
+ 
+
+ align:start position:0%
+and so it can update this in constant
+time that makes sense
+
+ align:start position:0%
+time that makes sense
+ 
+
+ align:start position:0%
+time that makes sense
+now the look up here and the insertion
+
+ align:start position:0%
+now the look up here and the insertion
+ 
+
+ align:start position:0%
+now the look up here and the insertion
+and deletion into here
+
+ align:start position:0%
+and deletion into here
+ 
+
+ align:start position:0%
+and deletion into here
+those each took logarithmic time
+
+ align:start position:0%
+those each took logarithmic time
+ 
+
+ align:start position:0%
+those each took logarithmic time
+worst case but i did a constant number
+
+ align:start position:0%
+worst case but i did a constant number
+ 
+
+ align:start position:0%
+worst case but i did a constant number
+of them so
+
+ align:start position:0%
+of them so
+ 
+
+ align:start position:0%
+of them so
+again longer than time does that make
+
+ align:start position:0%
+again longer than time does that make
+ 
+
+ align:start position:0%
+again longer than time does that make
+sense that's
+
+ align:start position:0%
+sense that's
+ 
+
+ align:start position:0%
+sense that's
+that's essentially this problem it's a
+
+ align:start position:0%
+that's essentially this problem it's a
+ 
+
+ align:start position:0%
+that's essentially this problem it's a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+it's difficult right there's a lot of
+
+ align:start position:0%
+it's difficult right there's a lot of
+ 
+
+ align:start position:0%
+it's difficult right there's a lot of
+moving parts here
+
+ align:start position:0%
+moving parts here
+ 
+
+ align:start position:0%
+moving parts here
+right but if you just break it up into
+
+ align:start position:0%
+right but if you just break it up into
+ 
+
+ align:start position:0%
+right but if you just break it up into
+describe to me and
+
+ align:start position:0%
+describe to me and
+ 
+
+ align:start position:0%
+describe to me and
+like you really do a good job on this
+
+ align:start position:0%
+like you really do a good job on this
+ 
+
+ align:start position:0%
+like you really do a good job on this
+part describe well
+
+ align:start position:0%
+part describe well
+ 
+
+ align:start position:0%
+part describe well
+to me what your data structure has then
+
+ align:start position:0%
+to me what your data structure has then
+ 
+
+ align:start position:0%
+to me what your data structure has then
+those descriptions of those algorithms
+
+ align:start position:0%
+those descriptions of those algorithms
+ 
+
+ align:start position:0%
+those descriptions of those algorithms
+can be
+
+ align:start position:0%
+can be
+ 
+
+ align:start position:0%
+can be
+pretty brief actually right so
+
+ align:start position:0%
+pretty brief actually right so
+ 
+
+ align:start position:0%
+pretty brief actually right so
+you know in this one you tell me these
+
+ align:start position:0%
+you know in this one you tell me these
+ 
+
+ align:start position:0%
+you know in this one you tell me these
+three data structures you tell me this
+
+ align:start position:0%
+three data structures you tell me this
+ 
+
+ align:start position:0%
+three data structures you tell me this
+guy's mapping to its location and these
+
+ align:start position:0%
+guy's mapping to its location and these
+ 
+
+ align:start position:0%
+guy's mapping to its location and these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+i'm maintaining this guy right and then
+
+ align:start position:0%
+i'm maintaining this guy right and then
+ 
+
+ align:start position:0%
+i'm maintaining this guy right and then
+you just maintain those things with
+
+ align:start position:0%
+you just maintain those things with
+ 
+
+ align:start position:0%
+you just maintain those things with
+dynamic operations and then use
+
+ align:start position:0%
+dynamic operations and then use
+ 
+
+ align:start position:0%
+dynamic operations and then use
+those things for query operations that
+
+ align:start position:0%
+those things for query operations that
+ 
+
+ align:start position:0%
+those things for query operations that
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wow we have 10 more minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm going to briefly do four or four
+
+ align:start position:0%
+i'm going to briefly do four or four
+ 
+
+ align:start position:0%
+i'm going to briefly do four or four
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+for you okay receiver roster we've got a
+
+ align:start position:0%
+for you okay receiver roster we've got a
+ 
+
+ align:start position:0%
+for you okay receiver roster we've got a
+coach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she's got a bunch of football players
+
+ align:start position:0%
+she's got a bunch of football players
+ 
+
+ align:start position:0%
+she's got a bunch of football players
+receivers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and wanting to start on our team
+
+ align:start position:0%
+and wanting to start on our team
+ 
+
+ align:start position:0%
+and wanting to start on our team
+the uh some number of of players that
+
+ align:start position:0%
+the uh some number of of players that
+ 
+
+ align:start position:0%
+the uh some number of of players that
+have the best
+
+ align:start position:0%
+have the best
+ 
+
+ align:start position:0%
+have the best
+the highest performance okay and by
+
+ align:start position:0%
+the highest performance okay and by
+ 
+
+ align:start position:0%
+the highest performance okay and by
+performance we mean
+
+ align:start position:0%
+performance we mean
+ 
+
+ align:start position:0%
+performance we mean
+the average number of points they've
+
+ align:start position:0%
+the average number of points they've
+ 
+
+ align:start position:0%
+the average number of points they've
+played in games that they have logged in
+
+ align:start position:0%
+played in games that they have logged in
+ 
+
+ align:start position:0%
+played in games that they have logged in
+their system
+
+ align:start position:0%
+their system
+ 
+
+ align:start position:0%
+their system
+right but actually their data is
+
+ align:start position:0%
+right but actually their data is
+ 
+
+ align:start position:0%
+right but actually their data is
+incomplete
+
+ align:start position:0%
+incomplete
+ 
+
+ align:start position:0%
+incomplete
+right they don't know which games and
+
+ align:start position:0%
+right they don't know which games and
+ 
+
+ align:start position:0%
+right they don't know which games and
+how much they scored in all these things
+
+ align:start position:0%
+how much they scored in all these things
+ 
+
+ align:start position:0%
+how much they scored in all these things
+there could be errors
+
+ align:start position:0%
+there could be errors
+ 
+
+ align:start position:0%
+there could be errors
+right and so these interns they're up
+
+ align:start position:0%
+right and so these interns they're up
+ 
+
+ align:start position:0%
+right and so these interns they're up
+they're constantly updating this
+
+ align:start position:0%
+they're constantly updating this
+ 
+
+ align:start position:0%
+they're constantly updating this
+database with queries like
+
+ align:start position:0%
+database with queries like
+ 
+
+ align:start position:0%
+database with queries like
+uh oh uh
+
+ align:start position:0%
+uh oh uh
+ 
+
+ align:start position:0%
+uh oh uh
+you know never mind this person didn't
+
+ align:start position:0%
+you know never mind this person didn't
+ 
+
+ align:start position:0%
+you know never mind this person didn't
+play in this game
+
+ align:start position:0%
+play in this game
+ 
+
+ align:start position:0%
+play in this game
+or actually they did and they scored
+
+ align:start position:0%
+or actually they did and they scored
+ 
+
+ align:start position:0%
+or actually they did and they scored
+this number of points
+
+ align:start position:0%
+this number of points
+ 
+
+ align:start position:0%
+this number of points
+right that's the clear and record things
+
+ align:start position:0%
+right that's the clear and record things
+ 
+
+ align:start position:0%
+right that's the clear and record things
+right and then at some point in time
+
+ align:start position:0%
+right and then at some point in time
+ 
+
+ align:start position:0%
+right and then at some point in time
+right like when we start
+
+ align:start position:0%
+right like when we start
+ 
+
+ align:start position:0%
+right like when we start
+when we want to play a game right i want
+
+ align:start position:0%
+when we want to play a game right i want
+ 
+
+ align:start position:0%
+when we want to play a game right i want
+to be able to return
+
+ align:start position:0%
+to be able to return
+ 
+
+ align:start position:0%
+to be able to return
+the the jersey with the k-th highest
+
+ align:start position:0%
+the the jersey with the k-th highest
+ 
+
+ align:start position:0%
+the the jersey with the k-th highest
+performance and log in time
+
+ align:start position:0%
+performance and log in time
+ 
+
+ align:start position:0%
+performance and log in time
+okay this is kind of a
+
+ align:start position:0%
+okay this is kind of a
+ 
+
+ align:start position:0%
+okay this is kind of a
+kind of a rank query right right the kth
+
+ align:start position:0%
+kind of a rank query right right the kth
+ 
+
+ align:start position:0%
+kind of a rank query right right the kth
+highest
+
+ align:start position:0%
+highest
+ 
+
+ align:start position:0%
+highest
+okay uh now in actuality i might want to
+
+ align:start position:0%
+okay uh now in actuality i might want to
+ 
+
+ align:start position:0%
+okay uh now in actuality i might want to
+return
+
+ align:start position:0%
+return
+ 
+
+ align:start position:0%
+return
+all k highest players so that that might
+
+ align:start position:0%
+all k highest players so that that might
+ 
+
+ align:start position:0%
+all k highest players so that that might
+be my
+
+ align:start position:0%
+be my
+ 
+
+ align:start position:0%
+be my
+my roster right but this is you know a
+
+ align:start position:0%
+my roster right but this is you know a
+ 
+
+ align:start position:0%
+my roster right but this is you know a
+more generalized query
+
+ align:start position:0%
+more generalized query
+ 
+
+ align:start position:0%
+more generalized query
+it's more specific more it's it's
+
+ align:start position:0%
+it's more specific more it's it's
+ 
+
+ align:start position:0%
+it's more specific more it's it's
+not really comparable but you get an
+
+ align:start position:0%
+not really comparable but you get an
+ 
+
+ align:start position:0%
+not really comparable but you get an
+idea for why that might be useful to the
+
+ align:start position:0%
+idea for why that might be useful to the
+ 
+
+ align:start position:0%
+idea for why that might be useful to the
+coach
+
+ align:start position:0%
+coach
+ 
+
+ align:start position:0%
+coach
+i don't know maybe not okay so what's
+
+ align:start position:0%
+i don't know maybe not okay so what's
+ 
+
+ align:start position:0%
+i don't know maybe not okay so what's
+the idea here
+
+ align:start position:0%
+the idea here
+ 
+
+ align:start position:0%
+the idea here
+we have a lot of different things
+
+ align:start position:0%
+we have a lot of different things
+ 
+
+ align:start position:0%
+we have a lot of different things
+floating around we got games
+
+ align:start position:0%
+floating around we got games
+ 
+
+ align:start position:0%
+floating around we got games
+they have ids unique ids we got
+
+ align:start position:0%
+they have ids unique ids we got
+ 
+
+ align:start position:0%
+they have ids unique ids we got
+receivers they have unique ids
+
+ align:start position:0%
+receivers they have unique ids
+ 
+
+ align:start position:0%
+receivers they have unique ids
+and each receiver could play in many
+
+ align:start position:0%
+and each receiver could play in many
+ 
+
+ align:start position:0%
+and each receiver could play in many
+games
+
+ align:start position:0%
+games
+ 
+
+ align:start position:0%
+games
+right oh that's kind of worrisome
+
+ align:start position:0%
+right oh that's kind of worrisome
+ 
+
+ align:start position:0%
+right oh that's kind of worrisome
+and many receivers could play in the
+
+ align:start position:0%
+and many receivers could play in the
+ 
+
+ align:start position:0%
+and many receivers could play in the
+same game
+
+ align:start position:0%
+same game
+ 
+
+ align:start position:0%
+same game
+these kind of many-to-one mappings are a
+
+ align:start position:0%
+these kind of many-to-one mappings are a
+ 
+
+ align:start position:0%
+these kind of many-to-one mappings are a
+little confusing
+
+ align:start position:0%
+little confusing
+ 
+
+ align:start position:0%
+little confusing
+and then we've got each player
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+receiver having a certain number of
+
+ align:start position:0%
+receiver having a certain number of
+ 
+
+ align:start position:0%
+receiver having a certain number of
+points per game
+
+ align:start position:0%
+points per game
+ 
+
+ align:start position:0%
+points per game
+and we're trying to sort them kind of by
+
+ align:start position:0%
+and we're trying to sort them kind of by
+ 
+
+ align:start position:0%
+and we're trying to sort them kind of by
+their performance which is a rational
+
+ align:start position:0%
+their performance which is a rational
+ 
+
+ align:start position:0%
+their performance which is a rational
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+right which has to do with the number of
+
+ align:start position:0%
+right which has to do with the number of
+ 
+
+ align:start position:0%
+right which has to do with the number of
+games they've played
+
+ align:start position:0%
+games they've played
+ 
+
+ align:start position:0%
+games they've played
+and the total number of points right
+
+ align:start position:0%
+and the total number of points right
+ 
+
+ align:start position:0%
+and the total number of points right
+now i see rational number i can't
+
+ align:start position:0%
+now i see rational number i can't
+ 
+
+ align:start position:0%
+now i see rational number i can't
+compute that
+
+ align:start position:0%
+compute that
+ 
+
+ align:start position:0%
+compute that
+right that's what we were talking about
+
+ align:start position:0%
+right that's what we were talking about
+ 
+
+ align:start position:0%
+right that's what we were talking about
+last problem session right
+
+ align:start position:0%
+last problem session right
+ 
+
+ align:start position:0%
+last problem session right
+but what i can do is i could store the
+
+ align:start position:0%
+but what i can do is i could store the
+ 
+
+ align:start position:0%
+but what i can do is i could store the
+total number of games they played and
+
+ align:start position:0%
+total number of games they played and
+ 
+
+ align:start position:0%
+total number of games they played and
+the total number of points they had
+
+ align:start position:0%
+the total number of points they had
+ 
+
+ align:start position:0%
+the total number of points they had
+right and you could imagine by
+
+ align:start position:0%
+right and you could imagine by
+ 
+
+ align:start position:0%
+right and you could imagine by
+augmentation similar to this
+
+ align:start position:0%
+augmentation similar to this
+ 
+
+ align:start position:0%
+augmentation similar to this
+right every time i add a game
+
+ align:start position:0%
+right every time i add a game
+ 
+
+ align:start position:0%
+right every time i add a game
+right one of these small operations i
+
+ align:start position:0%
+right one of these small operations i
+ 
+
+ align:start position:0%
+right one of these small operations i
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+update that information for each player
+
+ align:start position:0%
+update that information for each player
+ 
+
+ align:start position:0%
+update that information for each player
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right if i'm just if one of these these
+
+ align:start position:0%
+right if i'm just if one of these these
+ 
+
+ align:start position:0%
+right if i'm just if one of these these
+dynamic operations is affecting only one
+
+ align:start position:0%
+dynamic operations is affecting only one
+ 
+
+ align:start position:0%
+dynamic operations is affecting only one
+receiver
+
+ align:start position:0%
+receiver
+ 
+
+ align:start position:0%
+receiver
+i can you know update whatever it is in
+
+ align:start position:0%
+i can you know update whatever it is in
+ 
+
+ align:start position:0%
+i can you know update whatever it is in
+in constant time probably right if i
+
+ align:start position:0%
+in constant time probably right if i
+ 
+
+ align:start position:0%
+in constant time probably right if i
+just store with the player
+
+ align:start position:0%
+just store with the player
+ 
+
+ align:start position:0%
+just store with the player
+what their total number of games is as
+
+ align:start position:0%
+what their total number of games is as
+ 
+
+ align:start position:0%
+what their total number of games is as
+recorded by the database
+
+ align:start position:0%
+recorded by the database
+ 
+
+ align:start position:0%
+recorded by the database
+and how many points they've scored then
+
+ align:start position:0%
+and how many points they've scored then
+ 
+
+ align:start position:0%
+and how many points they've scored then
+if i have a data structure
+
+ align:start position:0%
+if i have a data structure
+ 
+
+ align:start position:0%
+if i have a data structure
+that needs to sort
+
+ align:start position:0%
+that needs to sort
+ 
+
+ align:start position:0%
+that needs to sort
+the receivers by their performance so i
+
+ align:start position:0%
+the receivers by their performance so i
+ 
+
+ align:start position:0%
+the receivers by their performance so i
+might be able to find the kth one
+
+ align:start position:0%
+might be able to find the kth one
+ 
+
+ align:start position:0%
+might be able to find the kth one
+right the k largest then
+
+ align:start position:0%
+right the k largest then
+ 
+
+ align:start position:0%
+right the k largest then
+i can't compute that performance but
+
+ align:start position:0%
+i can't compute that performance but
+ 
+
+ align:start position:0%
+i can't compute that performance but
+what can i do
+
+ align:start position:0%
+what can i do
+ 
+
+ align:start position:0%
+what can i do
+i can compare two players based on their
+
+ align:start position:0%
+i can compare two players based on their
+ 
+
+ align:start position:0%
+i can compare two players based on their
+performance using cross multiplication
+
+ align:start position:0%
+performance using cross multiplication
+ 
+
+ align:start position:0%
+performance using cross multiplication
+right right because i have the numerator
+
+ align:start position:0%
+right right because i have the numerator
+ 
+
+ align:start position:0%
+right right because i have the numerator
+and denominator of each of these
+
+ align:start position:0%
+and denominator of each of these
+ 
+
+ align:start position:0%
+and denominator of each of these
+rationals and i can cross multiply
+
+ align:start position:0%
+rationals and i can cross multiply
+ 
+
+ align:start position:0%
+rationals and i can cross multiply
+and figure out whether one's bigger or
+
+ align:start position:0%
+and figure out whether one's bigger or
+ 
+
+ align:start position:0%
+and figure out whether one's bigger or
+smaller and as long as i have a
+
+ align:start position:0%
+smaller and as long as i have a
+ 
+
+ align:start position:0%
+smaller and as long as i have a
+comparator
+
+ align:start position:0%
+comparator
+ 
+
+ align:start position:0%
+comparator
+i can do set jbl stuff does that make
+
+ align:start position:0%
+i can do set jbl stuff does that make
+ 
+
+ align:start position:0%
+i can do set jbl stuff does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay so that's the i'm just going to
+
+ align:start position:0%
+okay so that's the i'm just going to
+ 
+
+ align:start position:0%
+okay so that's the i'm just going to
+outline kind of the
+
+ align:start position:0%
+outline kind of the
+ 
+
+ align:start position:0%
+outline kind of the
+the components of this data structure
+
+ align:start position:0%
+the components of this data structure
+ 
+
+ align:start position:0%
+the components of this data structure
+okay well first off uh i'm gonna need to
+
+ align:start position:0%
+okay well first off uh i'm gonna need to
+ 
+
+ align:start position:0%
+okay well first off uh i'm gonna need to
+record a receiver and a receiver could
+
+ align:start position:0%
+record a receiver and a receiver could
+ 
+
+ align:start position:0%
+record a receiver and a receiver could
+have a lot of games
+
+ align:start position:0%
+have a lot of games
+ 
+
+ align:start position:0%
+have a lot of games
+but the important this is kind of a
+
+ align:start position:0%
+but the important this is kind of a
+ 
+
+ align:start position:0%
+but the important this is kind of a
+receiver centric kind of problem does
+
+ align:start position:0%
+receiver centric kind of problem does
+ 
+
+ align:start position:0%
+receiver centric kind of problem does
+that make sense to you guys
+
+ align:start position:0%
+that make sense to you guys
+ 
+
+ align:start position:0%
+that make sense to you guys
+right i'm not ever wanting to filter on
+
+ align:start position:0%
+right i'm not ever wanting to filter on
+ 
+
+ align:start position:0%
+right i'm not ever wanting to filter on
+all the receivers playing a game
+
+ align:start position:0%
+all the receivers playing a game
+ 
+
+ align:start position:0%
+all the receivers playing a game
+right i'm never like removing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm never removing a game from the
+
+ align:start position:0%
+i'm never removing a game from the
+ 
+
+ align:start position:0%
+i'm never removing a game from the
+system i'm removing a
+
+ align:start position:0%
+system i'm removing a
+ 
+
+ align:start position:0%
+system i'm removing a
+receiver from ever playing in a specific
+
+ align:start position:0%
+receiver from ever playing in a specific
+ 
+
+ align:start position:0%
+receiver from ever playing in a specific
+game does that make sense
+
+ align:start position:0%
+game does that make sense
+ 
+
+ align:start position:0%
+game does that make sense
+so if i'm storing a receiver and each
+
+ align:start position:0%
+so if i'm storing a receiver and each
+ 
+
+ align:start position:0%
+so if i'm storing a receiver and each
+receiver has
+
+ align:start position:0%
+receiver has
+ 
+
+ align:start position:0%
+receiver has
+some games associated with them kind of
+
+ align:start position:0%
+some games associated with them kind of
+ 
+
+ align:start position:0%
+some games associated with them kind of
+makes sense i might want to have
+
+ align:start position:0%
+makes sense i might want to have
+ 
+
+ align:start position:0%
+makes sense i might want to have
+a nested data structure right where
+
+ align:start position:0%
+a nested data structure right where
+ 
+
+ align:start position:0%
+a nested data structure right where
+with maybe i have a a dictionary on
+
+ align:start position:0%
+with maybe i have a a dictionary on
+ 
+
+ align:start position:0%
+with maybe i have a a dictionary on
+receivers
+
+ align:start position:0%
+receivers
+ 
+
+ align:start position:0%
+receivers
+and for each one i store all the games
+
+ align:start position:0%
+and for each one i store all the games
+ 
+
+ align:start position:0%
+and for each one i store all the games
+that they've played it
+
+ align:start position:0%
+that they've played it
+ 
+
+ align:start position:0%
+that they've played it
+in some other data structure right with
+
+ align:start position:0%
+in some other data structure right with
+ 
+
+ align:start position:0%
+in some other data structure right with
+each receiver
+
+ align:start position:0%
+each receiver
+ 
+
+ align:start position:0%
+each receiver
+i store another its own data structure
+
+ align:start position:0%
+i store another its own data structure
+ 
+
+ align:start position:0%
+i store another its own data structure
+containing all its games so that makes
+
+ align:start position:0%
+containing all its games so that makes
+ 
+
+ align:start position:0%
+containing all its games so that makes
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay so that's the idea right we have
+
+ align:start position:0%
+okay so that's the idea right we have
+ 
+
+ align:start position:0%
+okay so that's the idea right we have
+some kind of
+
+ align:start position:0%
+some kind of
+ 
+
+ align:start position:0%
+some kind of
+i need to be able to look up receivers
+
+ align:start position:0%
+i need to be able to look up receivers
+ 
+
+ align:start position:0%
+i need to be able to look up receivers
+right because uh you know i'm i'm
+
+ align:start position:0%
+right because uh you know i'm i'm
+ 
+
+ align:start position:0%
+right because uh you know i'm i'm
+clearing them or i'm
+
+ align:start position:0%
+clearing them or i'm
+ 
+
+ align:start position:0%
+clearing them or i'm
+recording them right so i'm gonna have a
+
+ align:start position:0%
+recording them right so i'm gonna have a
+ 
+
+ align:start position:0%
+recording them right so i'm gonna have a
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+a dictionary or you know here i'm
+
+ align:start position:0%
+a dictionary or you know here i'm
+ 
+
+ align:start position:0%
+a dictionary or you know here i'm
+looking for worst case login time
+
+ align:start position:0%
+looking for worst case login time
+ 
+
+ align:start position:0%
+looking for worst case login time
+so i'm going to you know skip the
+
+ align:start position:0%
+so i'm going to you know skip the
+ 
+
+ align:start position:0%
+so i'm going to you know skip the
+dictionary abstraction and go straight
+
+ align:start position:0%
+dictionary abstraction and go straight
+ 
+
+ align:start position:0%
+dictionary abstraction and go straight
+for the set avl
+
+ align:start position:0%
+for the set avl
+ 
+
+ align:start position:0%
+for the set avl
+avl uh
+
+ align:start position:0%
+avl uh
+ 
+
+ align:start position:0%
+avl uh
+uh keyed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on receivers
+
+ align:start position:0%
+on receivers
+ 
+
+ align:start position:0%
+on receivers
+i before c e except after c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is i e i
+
+ align:start position:0%
+it is i e i
+ 
+
+ align:start position:0%
+it is i e i
+okay that rule never works
+
+ align:start position:0%
+okay that rule never works
+ 
+
+ align:start position:0%
+okay that rule never works
+okay uh set avl tree on receivers
+
+ align:start position:0%
+okay uh set avl tree on receivers
+ 
+
+ align:start position:0%
+okay uh set avl tree on receivers
+and each one of those nodes right with
+
+ align:start position:0%
+and each one of those nodes right with
+ 
+
+ align:start position:0%
+and each one of those nodes right with
+each one of those receivers
+
+ align:start position:0%
+each one of those receivers
+ 
+
+ align:start position:0%
+each one of those receivers
+i'm going to store for each
+
+ align:start position:0%
+i'm going to store for each
+ 
+
+ align:start position:0%
+i'm going to store for each
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+store a set
+
+ align:start position:0%
+store a set
+ 
+
+ align:start position:0%
+store a set
+avl on games
+
+ align:start position:0%
+avl on games
+ 
+
+ align:start position:0%
+avl on games
+okay why do i store a set avl on games
+
+ align:start position:0%
+okay why do i store a set avl on games
+ 
+
+ align:start position:0%
+okay why do i store a set avl on games
+why don't i just store a list of all the
+
+ align:start position:0%
+why don't i just store a list of all the
+ 
+
+ align:start position:0%
+why don't i just store a list of all the
+games
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if i want to remove this game
+
+ align:start position:0%
+because if i want to remove this game
+ 
+
+ align:start position:0%
+because if i want to remove this game
+from a receiver i need to do that in
+
+ align:start position:0%
+from a receiver i need to do that in
+ 
+
+ align:start position:0%
+from a receiver i need to do that in
+login time and
+
+ align:start position:0%
+login time and
+ 
+
+ align:start position:0%
+login time and
+here what we're saying is that n is the
+
+ align:start position:0%
+here what we're saying is that n is the
+ 
+
+ align:start position:0%
+here what we're saying is that n is the
+number of games
+
+ align:start position:0%
+number of games
+ 
+
+ align:start position:0%
+number of games
+but the the number of receivers on the
+
+ align:start position:0%
+but the the number of receivers on the
+ 
+
+ align:start position:0%
+but the the number of receivers on the
+team is always less than the number of
+
+ align:start position:0%
+team is always less than the number of
+ 
+
+ align:start position:0%
+team is always less than the number of
+games so
+
+ align:start position:0%
+games so
+ 
+
+ align:start position:0%
+games so
+right if i search in this avl tree
+
+ align:start position:0%
+right if i search in this avl tree
+ 
+
+ align:start position:0%
+right if i search in this avl tree
+and i search in its avl tree i can
+
+ align:start position:0%
+and i search in its avl tree i can
+ 
+
+ align:start position:0%
+and i search in its avl tree i can
+be assured that those two searches was
+
+ align:start position:0%
+be assured that those two searches was
+ 
+
+ align:start position:0%
+be assured that those two searches was
+only login
+
+ align:start position:0%
+only login
+ 
+
+ align:start position:0%
+only login
+yeah because i might i need to remove a
+
+ align:start position:0%
+yeah because i might i need to remove a
+ 
+
+ align:start position:0%
+yeah because i might i need to remove a
+game right so
+
+ align:start position:0%
+game right so
+ 
+
+ align:start position:0%
+game right so
+there you go then
+
+ align:start position:0%
+there you go then
+ 
+
+ align:start position:0%
+there you go then
+what am i doing i'm returning the k
+
+ align:start position:0%
+what am i doing i'm returning the k
+ 
+
+ align:start position:0%
+what am i doing i'm returning the k
+highest performance well i need for with
+
+ align:start position:0%
+highest performance well i need for with
+ 
+
+ align:start position:0%
+highest performance well i need for with
+each one of these guys
+
+ align:start position:0%
+each one of these guys
+ 
+
+ align:start position:0%
+each one of these guys
+i also store what was this augmentation
+
+ align:start position:0%
+i also store what was this augmentation
+ 
+
+ align:start position:0%
+i also store what was this augmentation
+the sum of the points stored in these
+
+ align:start position:0%
+the sum of the points stored in these
+ 
+
+ align:start position:0%
+the sum of the points stored in these
+games right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum of points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh what was it
+
+ align:start position:0%
+and uh what was it
+ 
+
+ align:start position:0%
+and uh what was it
+number games
+
+ align:start position:0%
+number games
+ 
+
+ align:start position:0%
+number games
+because if i store both of those things
+
+ align:start position:0%
+because if i store both of those things
+ 
+
+ align:start position:0%
+because if i store both of those things
+in constant time i'm going to be able to
+
+ align:start position:0%
+in constant time i'm going to be able to
+ 
+
+ align:start position:0%
+in constant time i'm going to be able to
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+their performance right where i'm going
+
+ align:start position:0%
+their performance right where i'm going
+ 
+
+ align:start position:0%
+their performance right where i'm going
+to be able to
+
+ align:start position:0%
+to be able to
+ 
+
+ align:start position:0%
+to be able to
+you have the data i need to compare
+
+ align:start position:0%
+you have the data i need to compare
+ 
+
+ align:start position:0%
+you have the data i need to compare
+performances yeah so you just don't
+
+ align:start position:0%
+performances yeah so you just don't
+ 
+
+ align:start position:0%
+performances yeah so you just don't
+have variables yeah yeah it's just
+
+ align:start position:0%
+have variables yeah yeah it's just
+ 
+
+ align:start position:0%
+have variables yeah yeah it's just
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+right these aren't data structures this
+
+ align:start position:0%
+right these aren't data structures this
+ 
+
+ align:start position:0%
+right these aren't data structures this
+is data structure these are just numbers
+
+ align:start position:0%
+is data structure these are just numbers
+ 
+
+ align:start position:0%
+is data structure these are just numbers
+okay i'm storing that with each receiver
+
+ align:start position:0%
+okay i'm storing that with each receiver
+ 
+
+ align:start position:0%
+okay i'm storing that with each receiver
+right but that's not going to help me
+
+ align:start position:0%
+right but that's not going to help me
+ 
+
+ align:start position:0%
+right but that's not going to help me
+find the kth
+
+ align:start position:0%
+find the kth
+ 
+
+ align:start position:0%
+find the kth
+highest player right none of these
+
+ align:start position:0%
+highest player right none of these
+ 
+
+ align:start position:0%
+highest player right none of these
+things are sorted by performance right
+
+ align:start position:0%
+things are sorted by performance right
+ 
+
+ align:start position:0%
+things are sorted by performance right
+so i need the last data structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i need to store something dynamically
+
+ align:start position:0%
+i need to store something dynamically
+ 
+
+ align:start position:0%
+i need to store something dynamically
+sorted by
+
+ align:start position:0%
+sorted by
+ 
+
+ align:start position:0%
+sorted by
+performance so yeah
+
+ align:start position:0%
+performance so yeah
+ 
+
+ align:start position:0%
+performance so yeah
+set avl storing
+
+ align:start position:0%
+set avl storing
+ 
+
+ align:start position:0%
+set avl storing
+receivers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keyed on
+
+ align:start position:0%
+keyed on
+ 
+
+ align:start position:0%
+keyed on
+performance now when i say keyed ketone
+
+ align:start position:0%
+performance now when i say keyed ketone
+ 
+
+ align:start position:0%
+performance now when i say keyed ketone
+performance
+
+ align:start position:0%
+performance
+ 
+
+ align:start position:0%
+performance
+you want to mention something about the
+
+ align:start position:0%
+you want to mention something about the
+ 
+
+ align:start position:0%
+you want to mention something about the
+cross multiplication
+
+ align:start position:0%
+cross multiplication
+ 
+
+ align:start position:0%
+cross multiplication
+right like i'm storing with each one of
+
+ align:start position:0%
+right like i'm storing with each one of
+ 
+
+ align:start position:0%
+right like i'm storing with each one of
+these things this augmentation
+
+ align:start position:0%
+these things this augmentation
+ 
+
+ align:start position:0%
+these things this augmentation
+and when i'm comparing two things i'm
+
+ align:start position:0%
+and when i'm comparing two things i'm
+ 
+
+ align:start position:0%
+and when i'm comparing two things i'm
+using cross multiplication
+
+ align:start position:0%
+using cross multiplication
+ 
+
+ align:start position:0%
+using cross multiplication
+but other than that then we can abstract
+
+ align:start position:0%
+but other than that then we can abstract
+ 
+
+ align:start position:0%
+but other than that then we can abstract
+it away right you've
+
+ align:start position:0%
+it away right you've
+ 
+
+ align:start position:0%
+it away right you've
+abstracted that function call and i can
+
+ align:start position:0%
+abstracted that function call and i can
+ 
+
+ align:start position:0%
+abstracted that function call and i can
+imagine comparing two keys i can do this
+
+ align:start position:0%
+imagine comparing two keys i can do this
+ 
+
+ align:start position:0%
+imagine comparing two keys i can do this
+right this is a theory thing i'm not
+
+ align:start position:0%
+right this is a theory thing i'm not
+ 
+
+ align:start position:0%
+right this is a theory thing i'm not
+asking you to implement that
+
+ align:start position:0%
+asking you to implement that
+ 
+
+ align:start position:0%
+asking you to implement that
+right but that's sufficient for me as a
+
+ align:start position:0%
+right but that's sufficient for me as a
+ 
+
+ align:start position:0%
+right but that's sufficient for me as a
+reader of your solution
+
+ align:start position:0%
+reader of your solution
+ 
+
+ align:start position:0%
+reader of your solution
+to be able to say yeah you know what
+
+ align:start position:0%
+to be able to say yeah you know what
+ 
+
+ align:start position:0%
+to be able to say yeah you know what
+you're talking about
+
+ align:start position:0%
+you're talking about
+ 
+
+ align:start position:0%
+you're talking about
+okay all right so how do i connect these
+
+ align:start position:0%
+okay all right so how do i connect these
+ 
+
+ align:start position:0%
+okay all right so how do i connect these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+right the thing is i'm going to need to
+
+ align:start position:0%
+right the thing is i'm going to need to
+ 
+
+ align:start position:0%
+right the thing is i'm going to need to
+be uh i need to update this
+
+ align:start position:0%
+be uh i need to update this
+ 
+
+ align:start position:0%
+be uh i need to update this
+these things right when i
+
+ align:start position:0%
+these things right when i
+ 
+
+ align:start position:0%
+these things right when i
+insert or remove a game right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do i know where these receivers
+
+ align:start position:0%
+so how do i know where these receivers
+ 
+
+ align:start position:0%
+so how do i know where these receivers
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+in this thing i store a pointer into
+
+ align:start position:0%
+in this thing i store a pointer into
+ 
+
+ align:start position:0%
+in this thing i store a pointer into
+this data structure right
+
+ align:start position:0%
+this data structure right
+ 
+
+ align:start position:0%
+this data structure right
+so up here i store a pointer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right to where it is in the data
+
+ align:start position:0%
+right to where it is in the data
+ 
+
+ align:start position:0%
+right to where it is in the data
+structure right again i'm storing all
+
+ align:start position:0%
+structure right again i'm storing all
+ 
+
+ align:start position:0%
+structure right again i'm storing all
+the receivers
+
+ align:start position:0%
+the receivers
+ 
+
+ align:start position:0%
+the receivers
+this has the same size as the number one
+
+ align:start position:0%
+this has the same size as the number one
+ 
+
+ align:start position:0%
+this has the same size as the number one
+data structure up there
+
+ align:start position:0%
+data structure up there
+ 
+
+ align:start position:0%
+data structure up there
+has the same number of receivers right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we're not quite done yet because i'm
+
+ align:start position:0%
+but we're not quite done yet because i'm
+ 
+
+ align:start position:0%
+but we're not quite done yet because i'm
+not wanting to know
+
+ align:start position:0%
+not wanting to know
+ 
+
+ align:start position:0%
+not wanting to know
+like who has the the best
+
+ align:start position:0%
+like who has the the best
+ 
+
+ align:start position:0%
+like who has the the best
+performance right i want to know who has
+
+ align:start position:0%
+performance right i want to know who has
+ 
+
+ align:start position:0%
+performance right i want to know who has
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+kaith best performance ugh
+
+ align:start position:0%
+kaith best performance ugh
+ 
+
+ align:start position:0%
+kaith best performance ugh
+how do i find the kate best thing in
+
+ align:start position:0%
+how do i find the kate best thing in
+ 
+
+ align:start position:0%
+how do i find the kate best thing in
+this treat right i've got a tree
+
+ align:start position:0%
+this treat right i've got a tree
+ 
+
+ align:start position:0%
+this treat right i've got a tree
+right set avl tree it's
+
+ align:start position:0%
+right set avl tree it's
+ 
+
+ align:start position:0%
+right set avl tree it's
+mapped on performance right i know where
+
+ align:start position:0%
+mapped on performance right i know where
+ 
+
+ align:start position:0%
+mapped on performance right i know where
+the last one is
+
+ align:start position:0%
+the last one is
+ 
+
+ align:start position:0%
+the last one is
+but if i want to find the kate one from
+
+ align:start position:0%
+but if i want to find the kate one from
+ 
+
+ align:start position:0%
+but if i want to find the kate one from
+the end how do i do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's an avl tree a set avl tree
+
+ align:start position:0%
+it's an avl tree a set avl tree
+ 
+
+ align:start position:0%
+it's an avl tree a set avl tree
+all i'm storing is heights is there an
+
+ align:start position:0%
+all i'm storing is heights is there an
+ 
+
+ align:start position:0%
+all i'm storing is heights is there an
+operation that you've
+
+ align:start position:0%
+operation that you've
+ 
+
+ align:start position:0%
+operation that you've
+thought about you're not storing the
+
+ align:start position:0%
+thought about you're not storing the
+ 
+
+ align:start position:0%
+thought about you're not storing the
+size of each
+
+ align:start position:0%
+size of each
+ 
+
+ align:start position:0%
+size of each
+ah a set avl tree by default does not
+
+ align:start position:0%
+ah a set avl tree by default does not
+ 
+
+ align:start position:0%
+ah a set avl tree by default does not
+store sizes right that's what a sequence
+
+ align:start position:0%
+store sizes right that's what a sequence
+ 
+
+ align:start position:0%
+store sizes right that's what a sequence
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+but you think maybe that would be
+
+ align:start position:0%
+but you think maybe that would be
+ 
+
+ align:start position:0%
+but you think maybe that would be
+helpful in this situation
+
+ align:start position:0%
+helpful in this situation
+ 
+
+ align:start position:0%
+helpful in this situation
+right yeah so actually if i decided to
+
+ align:start position:0%
+right yeah so actually if i decided to
+ 
+
+ align:start position:0%
+right yeah so actually if i decided to
+augment by sizes also i could do the
+
+ align:start position:0%
+augment by sizes also i could do the
+ 
+
+ align:start position:0%
+augment by sizes also i could do the
+exact same kind of sequence
+
+ align:start position:0%
+exact same kind of sequence
+ 
+
+ align:start position:0%
+exact same kind of sequence
+find at operation right and i could be
+
+ align:start position:0%
+find at operation right and i could be
+ 
+
+ align:start position:0%
+find at operation right and i could be
+able to look up
+
+ align:start position:0%
+able to look up
+ 
+
+ align:start position:0%
+able to look up
+the n minus k item right
+
+ align:start position:0%
+the n minus k item right
+ 
+
+ align:start position:0%
+the n minus k item right
+in here using the exact same function
+
+ align:start position:0%
+in here using the exact same function
+ 
+
+ align:start position:0%
+in here using the exact same function
+for subtree at that i had
+
+ align:start position:0%
+for subtree at that i had
+ 
+
+ align:start position:0%
+for subtree at that i had
+in the sequence avl tree stuff right so
+
+ align:start position:0%
+in the sequence avl tree stuff right so
+ 
+
+ align:start position:0%
+in the sequence avl tree stuff right so
+actually in clrs they don't even bother
+
+ align:start position:0%
+actually in clrs they don't even bother
+ 
+
+ align:start position:0%
+actually in clrs they don't even bother
+with sequence avl trees
+
+ align:start position:0%
+with sequence avl trees
+ 
+
+ align:start position:0%
+with sequence avl trees
+right they go straight to if i wanted
+
+ align:start position:0%
+right they go straight to if i wanted
+ 
+
+ align:start position:0%
+right they go straight to if i wanted
+this rank find functionality
+
+ align:start position:0%
+this rank find functionality
+ 
+
+ align:start position:0%
+this rank find functionality
+on a sorted order of things right
+
+ align:start position:0%
+on a sorted order of things right
+ 
+
+ align:start position:0%
+on a sorted order of things right
+then i could augment with subtree sizes
+
+ align:start position:0%
+then i could augment with subtree sizes
+ 
+
+ align:start position:0%
+then i could augment with subtree sizes
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but it's actually a much more useful
+
+ align:start position:0%
+but it's actually a much more useful
+ 
+
+ align:start position:0%
+but it's actually a much more useful
+general property
+
+ align:start position:0%
+general property
+ 
+
+ align:start position:0%
+general property
+so we decided to present it to you in
+
+ align:start position:0%
+so we decided to present it to you in
+ 
+
+ align:start position:0%
+so we decided to present it to you in
+the in the context of sequence abs juice
+
+ align:start position:0%
+the in the context of sequence abs juice
+ 
+
+ align:start position:0%
+the in the context of sequence abs juice
+because then i can just
+
+ align:start position:0%
+because then i can just
+ 
+
+ align:start position:0%
+because then i can just
+basically reduce to it when i get to
+
+ align:start position:0%
+basically reduce to it when i get to
+ 
+
+ align:start position:0%
+basically reduce to it when i get to
+here okay so
+
+ align:start position:0%
+here okay so
+ 
+
+ align:start position:0%
+here okay so
+that's kind of a structure of the data
+
+ align:start position:0%
+that's kind of a structure of the data
+ 
+
+ align:start position:0%
+that's kind of a structure of the data
+structure that'll work on this problem
+
+ align:start position:0%
+structure that'll work on this problem
+ 
+
+ align:start position:0%
+structure that'll work on this problem
+i leave it to you as an exercise to
+
+ align:start position:0%
+i leave it to you as an exercise to
+ 
+
+ align:start position:0%
+i leave it to you as an exercise to
+implement all of these operations
+
+ align:start position:0%
+implement all of these operations
+ 
+
+ align:start position:0%
+implement all of these operations
+for yourself or take a look at the
+
+ align:start position:0%
+for yourself or take a look at the
+ 
+
+ align:start position:0%
+for yourself or take a look at the
+solutions the last one um
+
+ align:start position:0%
+solutions the last one um
+ 
+
+ align:start position:0%
+solutions the last one um
+is going to be put online the solution
+
+ align:start position:0%
+is going to be put online the solution
+ 
+
+ align:start position:0%
+is going to be put online the solution
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's pretty complicated it's what's
+
+ align:start position:0%
+it's pretty complicated it's what's
+ 
+
+ align:start position:0%
+it's pretty complicated it's what's
+called you can think of the size
+
+ align:start position:0%
+called you can think of the size
+ 
+
+ align:start position:0%
+called you can think of the size
+augmentation finding rank as a one-sided
+
+ align:start position:0%
+augmentation finding rank as a one-sided
+ 
+
+ align:start position:0%
+augmentation finding rank as a one-sided
+range query
+
+ align:start position:0%
+range query
+ 
+
+ align:start position:0%
+range query
+it's basically how many things are to
+
+ align:start position:0%
+it's basically how many things are to
+ 
+
+ align:start position:0%
+it's basically how many things are to
+the right of this value
+
+ align:start position:0%
+the right of this value
+ 
+
+ align:start position:0%
+the right of this value
+right what the last problem does is
+
+ align:start position:0%
+right what the last problem does is
+ 
+
+ align:start position:0%
+right what the last problem does is
+walks you through a two-sided range
+
+ align:start position:0%
+walks you through a two-sided range
+ 
+
+ align:start position:0%
+walks you through a two-sided range
+query
+
+ align:start position:0%
+query
+ 
+
+ align:start position:0%
+query
+right where i want to know how many
+
+ align:start position:0%
+right where i want to know how many
+ 
+
+ align:start position:0%
+right where i want to know how many
+nodes are between these two values
+
+ align:start position:0%
+nodes are between these two values
+ 
+
+ align:start position:0%
+nodes are between these two values
+okay so it's a walk-through
+
+ align:start position:0%
+okay so it's a walk-through
+ 
+
+ align:start position:0%
+okay so it's a walk-through
+all right thanks guys
\ No newline at end of file
diff --git a/MxWZwTA_PHc.txt b/MxWZwTA_PHc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c7cc16dae1c908eb95935d455bf4a2e7a7792cfd
--- /dev/null
+++ b/MxWZwTA_PHc.txt
@@ -0,0 +1,365 @@
+LORNA GIBSON: So
+really the way I
+
+set up the lectures
+is I write out
+
+notes for myself of
+what I want to cover,
+
+and the notes are
+pretty detailed.
+
+And in the past I always
+just had the notes for me.
+
+And even though they
+were reasonably neat
+
+and I could read them, I didn't
+hand them out to the students.
+
+But because I've turned my
+fall course into an MITx course
+
+and I want to make the lecture
+notes available for that,
+
+when I was doing that course for
+MITx I made really nice notes.
+
+And a friend of
+mine who lectures,
+
+I was asking her how she did it,
+and she said she actually goes
+
+and measures the chalkboard,
+and she measures the aspect
+
+ratio, how tall to
+wide the chalkboard is.
+
+And then she sets up her notes
+so that they're the same aspect
+
+ratio, and she plans
+out exactly where
+
+she's going to put everything
+on the board on her notes.
+
+And so I started doing that.
+
+And when I'm doing the lecture
+I put it all on the board,
+
+and I find a lot
+of students-- even
+
+though I hand the
+notes out now-- they
+
+like to write their own notes.
+
+And I think it helps them
+pay attention in class
+
+and helps them kind of
+focus on the material.
+
+So another thing I do in
+the lectures, when I first
+
+started lecturing and
+for a long time I just
+
+focused on the engineering,
+you know, on the equations,
+
+this is the derivation,
+this is an example,
+
+this is how you use this.
+
+And it was all just about
+kind of the engineering
+
+of whatever I was working on.
+
+And I found over
+the last few years,
+
+actually in both courses, in the
+fall one on mechanical behavior
+
+and in the spring course
+on cellular solids,
+
+I look for more interesting
+examples and stories, kind
+
+of stories about the
+people who discovered
+
+some of the principles
+that we talk about.
+
+I tell them stories about
+engineering situations that
+
+came up and there was some
+interesting thing happened.
+
+And the students love it.
+
+I mean, they really like having
+the kind of hard core mechanics
+
+broken up with some
+sort of stories.
+
+So I do that a lot more
+now than I used to do.
+
+So probably most
+lecturers have some kind
+
+of interesting example
+or historical thing
+
+that I talk about.
+
+So for instance, when I
+teach the fall course,
+
+the mechanical
+behavior materials,
+
+one of the first things
+we talk about is stress.
+
+So stress is a
+force per unit area.
+
+If I take this piece a wood
+and I pull on it like this
+
+I'm pulling on it with a
+force that goes out like this.
+
+Stress is just that force
+divided by that area.
+
+And the unit of stress in the
+SI system is called the Pascal.
+
+And it's named
+after Blaise Pascal
+
+who's a French mathematician.
+
+And a couple of years ago I
+was in France for a conference
+
+and I was in a little town
+called Clermont-Ferrand,
+
+which is in the
+middle of France.
+
+It's a pretty little town.
+
+And I'm just walking
+around one day
+
+kind of seeing the square
+and the cathedral and all
+
+this stuff, and I
+see there is sign,
+
+there's like Pascal
+something or another.
+
+And this was apparently the
+site of Blaise Pascal's house.
+
+And right next door
+to it is Cafe Pascal.
+
+So of course, I have to take
+a photograph of Cafe Pascal.
+
+And in this other course, when
+we get to the bit about stress
+
+and I tell them
+about the Pascal I
+
+show them the picture
+of the Cafe Pascal.
+
+And the other amusing thing
+that they kind of get a kick
+
+out of because of Boston, you
+know how in Boston there's
+
+the Freedom Trail and
+there's a red line
+
+goes around all these
+historical sites
+
+all this colonial and
+revolutionary stuff
+
+around Boston.
+
+It's kind of cool, all
+the tourists to it.
+
+Well in Clermont-Ferrand
+there's a Pascal Trail.
+
+And there's little
+metal medallions
+
+of the portrait of Blaise
+Pascal put in the sidewalk
+
+and you can walk
+around Clermont-Ferrand
+
+doing the Pascal Trail.
+
+So I kind of keep an eye
+out for stuff like that
+
+and I put that into
+the course now,
+
+and I never used to
+do that kind of stuff.
+
+I have a picture from
+the Library of Congress,
+
+which I went to just
+for fun a while ago.
+
+And one of the main buildings is
+this old, beautiful historical
+
+building for the
+Library of Congress.
+
+And they have a marble staircase
+that goes up the middle.
+
+And the staircase has
+all these little cherubs.
+
+And there's an
+agriculture cherub
+
+and he's holding
+a sheaf of wheat.
+
+And there's a wine
+cherub and he's holding
+
+a little thing of grapes.
+
+Well, it turns out
+there's a mechanics cherub
+
+and he's holding a gear.
+
+So at the end of
+the first lecture
+
+I show them the mechanic's
+cherub with the gear.
+
+So there's these
+cute little things.
+
+So I just keep an eye out
+for these cute little things.
+
+And last fall, this past
+fall, one of the students
+
+came up at the end of the
+first lecture and he said,
+
+I really like art.
+
+And he says, is there going
+to be more art in the class?
+
+And I'm like, not usually.
+
+This has kind of exhausted
+my art in mechanics.
+
+And I said, but I'll
+keep an eye out.
+
+And through the term there
+actually were different things
+
+that I saw that had to
+do with mechanics and art
+
+I showed the class.
+
+So one of them was at the
+Peabody Essex Museum this fall
+
+there's been and display of the
+mobile sculptures of Alexander
+
+Calder.
+
+And they also made
+these very large,
+
+I think they're called
+stabile sculptures, as well.
+
+The big sail at MIT is
+one of his sculptures.
+
+And these mobiles are
+actually a really nice example
+
+of free body diagrams in
+mechanics and balancing
+
+the forces.
+
+So anyway, I got a picture
+of one of his mobiles
+
+and I went up to the exhibit.
+
+And when I was at
+the exhibit I found
+
+that he did a degree in
+mechanical engineering.
+
+He actually was a
+mechanical engineer.
+
+And so the students
+were very, very tickled
+
+by the sculpture, the fact
+that he studied engineering.
+
+So anyway, I look out
+for stuff like that.
\ No newline at end of file
diff --git a/O5Vh5nCMMmA.txt b/O5Vh5nCMMmA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0068f13379c6ae7b9339734bee07532d2a75b351
--- /dev/null
+++ b/O5Vh5nCMMmA.txt
@@ -0,0 +1,75 @@
+JOEL SCHINDALL: Our grading
+in the class is important,
+
+but it's done a
+little bit differently
+
+from the way an ordinary
+course is graded.
+
+In an ordinary course, there's
+a specific body of material,
+
+and so you can grade
+on proficiency.
+
+Can the student solve second
+order differential equations?
+
+So you give them some second
+order differential equations
+
+on a problem set,
+and if they solve it,
+
+they get a good grade.
+
+And if they don't solve it, they
+wouldn't get as good a grade.
+
+We're trying to teach a
+way of thinking and being
+
+innovative so we give them
+exercises and presentations,
+
+and then we grade them on the
+passion of their engagement.
+
+Some of them have better
+presentation skills
+
+than others.
+
+We're not looking at an
+absolute mark, but we're saying,
+
+did you go outside the box?
+
+Did you try something new?
+
+Given where you were when
+you came into this course,
+
+did you increase your skill set
+effectively and energetically?
+
+And if you do, that's a
+good grade in the course.
+
+And we actually give many--
+many students get good grades
+
+in a course like
+this, because they've
+
+elected to take a course to
+enhance their capabilities.
+
+And that deserves a good grade.
+
+The ones who don't
+get as good a grade
+
+are the ones who simply
+haven't participated as fully.
\ No newline at end of file
diff --git a/OOmZkNa72t4.txt b/OOmZkNa72t4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4384514fd5d07768ca11add4a90c5f7dc995e318
--- /dev/null
+++ b/OOmZkNa72t4.txt
@@ -0,0 +1,10963 @@
+align:start position:0%
+ 
+all right so welcome back well had a
+
+ align:start position:0%
+all right so welcome back well had a
+ 
+
+ align:start position:0%
+all right so welcome back well had a
+little bit of a break before I get into
+
+ align:start position:0%
+little bit of a break before I get into
+ 
+
+ align:start position:0%
+little bit of a break before I get into
+I go over my quick recap you've
+
+ align:start position:0%
+I go over my quick recap you've
+ 
+
+ align:start position:0%
+I go over my quick recap you've
+hopefully all seen the announcements
+
+ align:start position:0%
+hopefully all seen the announcements
+ 
+
+ align:start position:0%
+hopefully all seen the announcements
+that we're going to delay the due date
+
+ align:start position:0%
+that we're going to delay the due date
+ 
+
+ align:start position:0%
+that we're going to delay the due date
+of the next problem set until Tuesday
+
+ align:start position:0%
+of the next problem set until Tuesday
+ 
+
+ align:start position:0%
+of the next problem set until Tuesday
+that's in part because some of the
+
+ align:start position:0%
+that's in part because some of the
+ 
+
+ align:start position:0%
+that's in part because some of the
+material that appears on it is what
+
+ align:start position:0%
+material that appears on it is what
+ 
+
+ align:start position:0%
+material that appears on it is what
+we're going to talk about in today's
+
+ align:start position:0%
+we're going to talk about in today's
+ 
+
+ align:start position:0%
+we're going to talk about in today's
+lecture I want to make sure you've at
+
+ align:start position:0%
+lecture I want to make sure you've at
+ 
+
+ align:start position:0%
+lecture I want to make sure you've at
+least seen a lecture on all the topics
+
+ align:start position:0%
+least seen a lecture on all the topics
+ 
+
+ align:start position:0%
+least seen a lecture on all the topics
+before you try to do some of the
+
+ align:start position:0%
+before you try to do some of the
+ 
+
+ align:start position:0%
+before you try to do some of the
+problems on it in truth you could
+
+ align:start position:0%
+problems on it in truth you could
+ 
+
+ align:start position:0%
+problems on it in truth you could
+probably based on things I talked about
+
+ align:start position:0%
+probably based on things I talked about
+ 
+
+ align:start position:0%
+probably based on things I talked about
+in the previous lecture you could
+
+ align:start position:0%
+in the previous lecture you could
+ 
+
+ align:start position:0%
+in the previous lecture you could
+probably deduce a lot of what you need
+
+ align:start position:0%
+probably deduce a lot of what you need
+ 
+
+ align:start position:0%
+probably deduce a lot of what you need
+to do but still it's good to go over it
+
+ align:start position:0%
+to do but still it's good to go over it
+ 
+
+ align:start position:0%
+to do but still it's good to go over it
+a little bit more methodically and then
+
+ align:start position:0%
+a little bit more methodically and then
+ 
+
+ align:start position:0%
+a little bit more methodically and then
+the next problem set will be posted a
+
+ align:start position:0%
+the next problem set will be posted a
+ 
+
+ align:start position:0%
+the next problem set will be posted a
+week from right yeah I think we posted a
+
+ align:start position:0%
+week from right yeah I think we posted a
+ 
+
+ align:start position:0%
+week from right yeah I think we posted a
+week from today all right so let me just
+
+ align:start position:0%
+week from today all right so let me just
+ 
+
+ align:start position:0%
+week from today all right so let me just
+get back to what we're talking about
+
+ align:start position:0%
+get back to what we're talking about
+ 
+
+ align:start position:0%
+get back to what we're talking about
+last time so I began introducing some
+
+ align:start position:0%
+last time so I began introducing some
+ 
+
+ align:start position:0%
+last time so I began introducing some
+geometric concepts and some quantities
+
+ align:start position:0%
+geometric concepts and some quantities
+ 
+
+ align:start position:0%
+geometric concepts and some quantities
+that we use to describe matter we've
+
+ align:start position:0%
+that we use to describe matter we've
+ 
+
+ align:start position:0%
+that we use to describe matter we've
+done a lot of things so far that's
+
+ align:start position:0%
+done a lot of things so far that's
+ 
+
+ align:start position:0%
+done a lot of things so far that's
+appropriate for describing kind of the
+
+ align:start position:0%
+appropriate for describing kind of the
+ 
+
+ align:start position:0%
+appropriate for describing kind of the
+kinematics of particles but that's
+
+ align:start position:0%
+kinematics of particles but that's
+ 
+
+ align:start position:0%
+kinematics of particles but that's
+rather restrictive okay we want to talk
+
+ align:start position:0%
+rather restrictive okay we want to talk
+ 
+
+ align:start position:0%
+rather restrictive okay we want to talk
+about a broader class of things than
+
+ align:start position:0%
+about a broader class of things than
+ 
+
+ align:start position:0%
+about a broader class of things than
+that and I began by introducing
+
+ align:start position:0%
+that and I began by introducing
+ 
+
+ align:start position:0%
+that and I began by introducing
+something which is again fairly simple
+
+ align:start position:0%
+something which is again fairly simple
+ 
+
+ align:start position:0%
+something which is again fairly simple
+but it's a useful tool for getting to
+
+ align:start position:0%
+but it's a useful tool for getting to
+ 
+
+ align:start position:0%
+but it's a useful tool for getting to
+think about how we are going to
+
+ align:start position:0%
+think about how we are going to
+ 
+
+ align:start position:0%
+think about how we are going to
+mathematically categorize certain
+
+ align:start position:0%
+mathematically categorize certain
+ 
+
+ align:start position:0%
+mathematically categorize certain
+important types of matter per me well
+
+ align:start position:0%
+important types of matter per me well
+ 
+
+ align:start position:0%
+important types of matter per me well
+that puts in my notes away also pardon
+
+ align:start position:0%
+that puts in my notes away also pardon
+ 
+
+ align:start position:0%
+that puts in my notes away also pardon
+me I'm recovering from I caught a
+
+ align:start position:0%
+me I'm recovering from I caught a
+ 
+
+ align:start position:0%
+me I'm recovering from I caught a
+terrible cold or the long weekend and
+
+ align:start position:0%
+terrible cold or the long weekend and
+ 
+
+ align:start position:0%
+terrible cold or the long weekend and
+I'm coughing incessantly so I will be
+
+ align:start position:0%
+I'm coughing incessantly so I will be
+ 
+
+ align:start position:0%
+I'm coughing incessantly so I will be
+occasionally alright so I introduced
+
+ align:start position:0%
+occasionally alright so I introduced
+ 
+
+ align:start position:0%
+occasionally alright so I introduced
+this quantity called the number floor
+
+ align:start position:0%
+this quantity called the number floor
+ 
+
+ align:start position:0%
+this quantity called the number floor
+vector and that is given by imagine you
+
+ align:start position:0%
+vector and that is given by imagine you
+ 
+
+ align:start position:0%
+vector and that is given by imagine you
+have sort of it's its best thinking
+
+ align:start position:0%
+have sort of it's its best thinking
+ 
+
+ align:start position:0%
+have sort of it's its best thinking
+about this in the context of something
+
+ align:start position:0%
+about this in the context of something
+ 
+
+ align:start position:0%
+about this in the context of something
+like dust so you have some kind of
+
+ align:start position:0%
+like dust so you have some kind of
+ 
+
+ align:start position:0%
+like dust so you have some kind of
+non-interacting a little agglomeration
+
+ align:start position:0%
+non-interacting a little agglomeration
+ 
+
+ align:start position:0%
+non-interacting a little agglomeration
+of tiny particles and in the rest frame
+
+ align:start position:0%
+of tiny particles and in the rest frame
+ 
+
+ align:start position:0%
+of tiny particles and in the rest frame
+of an element of this dust so imagine
+
+ align:start position:0%
+of an element of this dust so imagine
+ 
+
+ align:start position:0%
+of an element of this dust so imagine
+you go into the I'm gonna define the
+
+ align:start position:0%
+you go into the I'm gonna define the
+ 
+
+ align:start position:0%
+you go into the I'm gonna define the
+restaurant of that ailment by saying
+
+ align:start position:0%
+restaurant of that ailment by saying
+ 
+
+ align:start position:0%
+restaurant of that ailment by saying
+you'll imagine you've got a cubic
+
+ align:start position:0%
+you'll imagine you've got a cubic
+ 
+
+ align:start position:0%
+you'll imagine you've got a cubic
+nanometer of it or something like that
+
+ align:start position:0%
+nanometer of it or something like that
+ 
+
+ align:start position:0%
+nanometer of it or something like that
+and you go into the frame where
+
+ align:start position:0%
+and you go into the frame where
+ 
+
+ align:start position:0%
+and you go into the frame where
+everything in that cubic nanometer is on
+
+ align:start position:0%
+everything in that cubic nanometer is on
+ 
+
+ align:start position:0%
+everything in that cubic nanometer is on
+average at rest
+
+ align:start position:0%
+average at rest
+ 
+
+ align:start position:0%
+average at rest
+we'll call n sub zero the rest density
+
+ align:start position:0%
+we'll call n sub zero the rest density
+ 
+
+ align:start position:0%
+we'll call n sub zero the rest density
+okay forgot to write that down
+
+ align:start position:0%
+okay forgot to write that down
+ 
+
+ align:start position:0%
+okay forgot to write that down
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the rest density the rest
+
+ align:start position:0%
+so that's the rest density the rest
+ 
+
+ align:start position:0%
+so that's the rest density the rest
+pardon me
+
+ align:start position:0%
+pardon me
+ 
+
+ align:start position:0%
+pardon me
+number density so I go into that rest
+
+ align:start position:0%
+number density so I go into that rest
+ 
+
+ align:start position:0%
+number density so I go into that rest
+frame that tells me how many little dust
+
+ align:start position:0%
+frame that tells me how many little dust
+ 
+
+ align:start position:0%
+frame that tells me how many little dust
+particles there are per cubic volume per
+
+ align:start position:0%
+particles there are per cubic volume per
+ 
+
+ align:start position:0%
+particles there are per cubic volume per
+element of volume multiplied that by the
+
+ align:start position:0%
+element of volume multiplied that by the
+ 
+
+ align:start position:0%
+element of volume multiplied that by the
+four vector that sumi the floor velocity
+
+ align:start position:0%
+four vector that sumi the floor velocity
+ 
+
+ align:start position:0%
+four vector that sumi the floor velocity
+describing that element we're gonna call
+
+ align:start position:0%
+describing that element we're gonna call
+ 
+
+ align:start position:0%
+describing that element we're gonna call
+that capital n so that's a vector that
+
+ align:start position:0%
+that capital n so that's a vector that
+ 
+
+ align:start position:0%
+that capital n so that's a vector that
+describes its it's its components
+
+ align:start position:0%
+describes its it's its components
+ 
+
+ align:start position:0%
+describes its it's its components
+describe the number density in some
+
+ align:start position:0%
+describe the number density in some
+ 
+
+ align:start position:0%
+describe the number density in some
+other frame of reference in any frame of
+
+ align:start position:0%
+other frame of reference in any frame of
+ 
+
+ align:start position:0%
+other frame of reference in any frame of
+reference and the flux tell me about how
+
+ align:start position:0%
+reference and the flux tell me about how
+ 
+
+ align:start position:0%
+reference and the flux tell me about how
+those dust particles flow from one
+
+ align:start position:0%
+those dust particles flow from one
+ 
+
+ align:start position:0%
+those dust particles flow from one
+element to another so we spent a little
+
+ align:start position:0%
+element to another so we spent a little
+ 
+
+ align:start position:0%
+element to another so we spent a little
+bit of time talking about how to define
+
+ align:start position:0%
+bit of time talking about how to define
+ 
+
+ align:start position:0%
+bit of time talking about how to define
+volume elements in a covariant fashion
+
+ align:start position:0%
+volume elements in a covariant fashion
+ 
+
+ align:start position:0%
+volume elements in a covariant fashion
+I'm not going to go through that but
+
+ align:start position:0%
+I'm not going to go through that but
+ 
+
+ align:start position:0%
+I'm not going to go through that but
+part of the punch line of doing that is
+
+ align:start position:0%
+part of the punch line of doing that is
+ 
+
+ align:start position:0%
+part of the punch line of doing that is
+that we're going to define a sort of
+
+ align:start position:0%
+that we're going to define a sort of
+ 
+
+ align:start position:0%
+that we're going to define a sort of
+eight what I call a covariant
+
+ align:start position:0%
+eight what I call a covariant
+ 
+
+ align:start position:0%
+eight what I call a covariant
+formulation of conservation of number is
+
+ align:start position:0%
+formulation of conservation of number is
+ 
+
+ align:start position:0%
+formulation of conservation of number is
+it's going to be the space-time
+
+ align:start position:0%
+it's going to be the space-time
+ 
+
+ align:start position:0%
+it's going to be the space-time
+divergence of that vector is equal to
+
+ align:start position:0%
+divergence of that vector is equal to
+ 
+
+ align:start position:0%
+divergence of that vector is equal to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay that holds this equation holds in
+
+ align:start position:0%
+okay that holds this equation holds in
+ 
+
+ align:start position:0%
+okay that holds this equation holds in
+all frames of reference if I choose a
+
+ align:start position:0%
+all frames of reference if I choose a
+ 
+
+ align:start position:0%
+all frames of reference if I choose a
+particular frame of reference in other
+
+ align:start position:0%
+particular frame of reference in other
+ 
+
+ align:start position:0%
+particular frame of reference in other
+words I define a particular time i
+
+ align:start position:0%
+words I define a particular time i
+ 
+
+ align:start position:0%
+words I define a particular time i
+define a particular set of spatial
+
+ align:start position:0%
+define a particular set of spatial
+ 
+
+ align:start position:0%
+define a particular set of spatial
+coordinates I can then break this up and
+
+ align:start position:0%
+coordinates I can then break this up and
+ 
+
+ align:start position:0%
+coordinates I can then break this up and
+say that this is equivalent to saying
+
+ align:start position:0%
+say that this is equivalent to saying
+ 
+
+ align:start position:0%
+say that this is equivalent to saying
+that the time derivative of the T
+
+ align:start position:0%
+that the time derivative of the T
+ 
+
+ align:start position:0%
+that the time derivative of the T
+component of that plus the spatial
+
+ align:start position:0%
+component of that plus the spatial
+ 
+
+ align:start position:0%
+component of that plus the spatial
+divergence of the spatial comment so
+
+ align:start position:0%
+divergence of the spatial comment so
+ 
+
+ align:start position:0%
+divergence of the spatial comment so
+that they sum to zero I can also take
+
+ align:start position:0%
+that they sum to zero I can also take
+ 
+
+ align:start position:0%
+that they sum to zero I can also take
+this thing and integrate over eight
+
+ align:start position:0%
+this thing and integrate over eight
+ 
+
+ align:start position:0%
+this thing and integrate over eight
+loops would help to have one element to
+
+ align:start position:0%
+loops would help to have one element to
+ 
+
+ align:start position:0%
+loops would help to have one element to
+find here I integrate this over a four
+
+ align:start position:0%
+find here I integrate this over a four
+ 
+
+ align:start position:0%
+find here I integrate this over a four
+dimensional volume and by my
+
+ align:start position:0%
+dimensional volume and by my
+ 
+
+ align:start position:0%
+dimensional volume and by my
+conservation law I must get zero when I
+
+ align:start position:0%
+conservation law I must get zero when I
+ 
+
+ align:start position:0%
+conservation law I must get zero when I
+do that again having chosen a particular
+
+ align:start position:0%
+do that again having chosen a particular
+ 
+
+ align:start position:0%
+do that again having chosen a particular
+frame to find what time means to find
+
+ align:start position:0%
+frame to find what time means to find
+ 
+
+ align:start position:0%
+frame to find what time means to find
+what space means I can then split this
+
+ align:start position:0%
+what space means I can then split this
+ 
+
+ align:start position:0%
+what space means I can then split this
+out into a statement that the time
+
+ align:start position:0%
+out into a statement that the time
+ 
+
+ align:start position:0%
+out into a statement that the time
+derivative of the volume integral of
+
+ align:start position:0%
+derivative of the volume integral of
+ 
+
+ align:start position:0%
+derivative of the volume integral of
+that time component of this thing is
+
+ align:start position:0%
+that time component of this thing is
+ 
+
+ align:start position:0%
+that time component of this thing is
+balanced by the flux of the number
+
+ align:start position:0%
+balanced by the flux of the number
+ 
+
+ align:start position:0%
+balanced by the flux of the number
+across the boundaries of a particular
+
+ align:start position:0%
+across the boundaries of a particular
+ 
+
+ align:start position:0%
+across the boundaries of a particular
+three volume okay
+
+ align:start position:0%
+three volume okay
+ 
+
+ align:start position:0%
+three volume okay
+and I remind you this notation the sort
+
+ align:start position:0%
+and I remind you this notation the sort
+ 
+
+ align:start position:0%
+and I remind you this notation the sort
+of Delta V 3 means the boundaries of the
+
+ align:start position:0%
+of Delta V 3 means the boundaries of the
+ 
+
+ align:start position:0%
+of Delta V 3 means the boundaries of the
+v3 that's used under this integral ok so
+
+ align:start position:0%
+v3 that's used under this integral ok so
+ 
+
+ align:start position:0%
+v3 that's used under this integral ok so
+we talked a little bit about a few other
+
+ align:start position:0%
+we talked a little bit about a few other
+ 
+
+ align:start position:0%
+we talked a little bit about a few other
+four vectors that are used particular I
+
+ align:start position:0%
+four vectors that are used particular I
+ 
+
+ align:start position:0%
+four vectors that are used particular I
+introduced some stuff that we use in
+
+ align:start position:0%
+introduced some stuff that we use in
+ 
+
+ align:start position:0%
+introduced some stuff that we use in
+electricity and magnetism but I want to
+
+ align:start position:0%
+electricity and magnetism but I want to
+ 
+
+ align:start position:0%
+electricity and magnetism but I want to
+switch gears okay in particular I want
+
+ align:start position:0%
+switch gears okay in particular I want
+ 
+
+ align:start position:0%
+switch gears okay in particular I want
+to introduce and discuss in some detail
+
+ align:start position:0%
+to introduce and discuss in some detail
+ 
+
+ align:start position:0%
+to introduce and discuss in some detail
+one of the most important tensors we are
+
+ align:start position:0%
+one of the most important tensors we are
+ 
+
+ align:start position:0%
+one of the most important tensors we are
+going to use all term so I motivated
+
+ align:start position:0%
+going to use all term so I motivated
+ 
+
+ align:start position:0%
+going to use all term so I motivated
+this by saying imagine you know I have a
+
+ align:start position:0%
+this by saying imagine you know I have a
+ 
+
+ align:start position:0%
+this by saying imagine you know I have a
+cloud of dust and I won't recreate one
+
+ align:start position:0%
+cloud of dust and I won't recreate one
+ 
+
+ align:start position:0%
+cloud of dust and I won't recreate one
+because I'm getting home for a cold and
+
+ align:start position:0%
+because I'm getting home for a cold and
+ 
+
+ align:start position:0%
+because I'm getting home for a cold and
+I want to I don't want to breathe chalk
+
+ align:start position:0%
+I want to I don't want to breathe chalk
+ 
+
+ align:start position:0%
+I want to I don't want to breathe chalk
+dust so imagine I make a little cloud of
+
+ align:start position:0%
+dust so imagine I make a little cloud of
+ 
+
+ align:start position:0%
+dust so imagine I make a little cloud of
+these things here so far we've
+
+ align:start position:0%
+these things here so far we've
+ 
+
+ align:start position:0%
+these things here so far we've
+characterized this thing by just
+
+ align:start position:0%
+characterized this thing by just
+ 
+
+ align:start position:0%
+characterized this thing by just
+counting the number of dust particles
+
+ align:start position:0%
+counting the number of dust particles
+ 
+
+ align:start position:0%
+counting the number of dust particles
+that are in there but that's not they're
+
+ align:start position:0%
+that are in there but that's not they're
+ 
+
+ align:start position:0%
+that are in there but that's not they're
+all there is to it right that dust has
+
+ align:start position:0%
+all there is to it right that dust has
+ 
+
+ align:start position:0%
+all there is to it right that dust has
+other properties and so the next thing
+
+ align:start position:0%
+other properties and so the next thing
+ 
+
+ align:start position:0%
+other properties and so the next thing
+which I would like to do is let's
+
+ align:start position:0%
+which I would like to do is let's
+ 
+
+ align:start position:0%
+which I would like to do is let's
+consider the energy and the momentum of
+
+ align:start position:0%
+consider the energy and the momentum of
+ 
+
+ align:start position:0%
+consider the energy and the momentum of
+every particle of dust in that cloud ok
+
+ align:start position:0%
+every particle of dust in that cloud ok
+ 
+
+ align:start position:0%
+every particle of dust in that cloud ok
+so let's just imagine let's again we're
+
+ align:start position:0%
+so let's just imagine let's again we're
+ 
+
+ align:start position:0%
+so let's just imagine let's again we're
+going to start with something simple and
+
+ align:start position:0%
+going to start with something simple and
+ 
+
+ align:start position:0%
+going to start with something simple and
+then we'll kind of walk up from there to
+
+ align:start position:0%
+then we'll kind of walk up from there to
+ 
+
+ align:start position:0%
+then we'll kind of walk up from there to
+a more generic situation let's imagine
+
+ align:start position:0%
+a more generic situation let's imagine
+ 
+
+ align:start position:0%
+a more generic situation let's imagine
+that my cloud consists of particles that
+
+ align:start position:0%
+that my cloud consists of particles that
+ 
+
+ align:start position:0%
+that my cloud consists of particles that
+are all identical and each dust particle
+
+ align:start position:0%
+are all identical and each dust particle
+ 
+
+ align:start position:0%
+are all identical and each dust particle
+has the same rest mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose this guy has a rest mass so
+
+ align:start position:0%
+so suppose this guy has a rest mass so
+ 
+
+ align:start position:0%
+so suppose this guy has a rest mass so
+one of the things which I might want to
+
+ align:start position:0%
+one of the things which I might want to
+ 
+
+ align:start position:0%
+one of the things which I might want to
+do is in addition to characterizing this
+
+ align:start position:0%
+do is in addition to characterizing this
+ 
+
+ align:start position:0%
+do is in addition to characterizing this
+dust by saying that the number density
+
+ align:start position:0%
+dust by saying that the number density
+ 
+
+ align:start position:0%
+dust by saying that the number density
+mean isn't the same that the number
+
+ align:start position:0%
+mean isn't the same that the number
+ 
+
+ align:start position:0%
+mean isn't the same that the number
+density in a particular frame is N or n
+
+ align:start position:0%
+density in a particular frame is N or n
+ 
+
+ align:start position:0%
+density in a particular frame is N or n
+0 let's go into the rest frame of this
+
+ align:start position:0%
+0 let's go into the rest frame of this
+ 
+
+ align:start position:0%
+0 let's go into the rest frame of this
+thing I might be interested in knowing
+
+ align:start position:0%
+thing I might be interested in knowing
+ 
+
+ align:start position:0%
+thing I might be interested in knowing
+about the rest energy density so I'm
+
+ align:start position:0%
+about the rest energy density so I'm
+ 
+
+ align:start position:0%
+about the rest energy density so I'm
+gonna denote the rest energy density by
+
+ align:start position:0%
+gonna denote the rest energy density by
+ 
+
+ align:start position:0%
+gonna denote the rest energy density by
+Rho sub 0 each particle has a rest
+
+ align:start position:0%
+Rho sub 0 each particle has a rest
+ 
+
+ align:start position:0%
+Rho sub 0 each particle has a rest
+energy of M remember C is equal to 1 so
+
+ align:start position:0%
+energy of M remember C is equal to 1 so
+ 
+
+ align:start position:0%
+energy of M remember C is equal to 1 so
+MC squared if you want to if you want to
+
+ align:start position:0%
+MC squared if you want to if you want to
+ 
+
+ align:start position:0%
+MC squared if you want to if you want to
+hold to the formula that we've all known
+
+ align:start position:0%
+hold to the formula that we've all known
+ 
+
+ align:start position:0%
+hold to the formula that we've all known
+and loved since we were babies so that's
+
+ align:start position:0%
+and loved since we were babies so that's
+ 
+
+ align:start position:0%
+and loved since we were babies so that's
+the rest energy and then how many if I
+
+ align:start position:0%
+the rest energy and then how many if I
+ 
+
+ align:start position:0%
+the rest energy and then how many if I
+want to get the rest energy density I
+
+ align:start position:0%
+want to get the rest energy density I
+ 
+
+ align:start position:0%
+want to get the rest energy density I
+count up the number in each volume are
+
+ align:start position:0%
+count up the number in each volume are
+ 
+
+ align:start position:0%
+count up the number in each volume are
+the number per unit volume so it's M
+
+ align:start position:0%
+the number per unit volume so it's M
+ 
+
+ align:start position:0%
+the number per unit volume so it's M
+times n 0 so that's the rest energy
+
+ align:start position:0%
+times n 0 so that's the rest energy
+ 
+
+ align:start position:0%
+times n 0 so that's the rest energy
+density of this thing
+
+ align:start position:0%
+density of this thing
+ 
+
+ align:start position:0%
+density of this thing
+great let's now ask okay so that's what
+
+ align:start position:0%
+great let's now ask okay so that's what
+ 
+
+ align:start position:0%
+great let's now ask okay so that's what
+it looks like in the rest frame of this
+
+ align:start position:0%
+it looks like in the rest frame of this
+ 
+
+ align:start position:0%
+it looks like in the rest frame of this
+of this dust element let's imagine that
+
+ align:start position:0%
+of this dust element let's imagine that
+ 
+
+ align:start position:0%
+of this dust element let's imagine that
+I now bop into a frame that is moving
+
+ align:start position:0%
+I now bop into a frame that is moving
+ 
+
+ align:start position:0%
+I now bop into a frame that is moving
+with some speed relative to this
+
+ align:start position:0%
+with some speed relative to this
+ 
+
+ align:start position:0%
+with some speed relative to this
+restaurant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this frame the energy density I'm not
+
+ align:start position:0%
+in this frame the energy density I'm not
+ 
+
+ align:start position:0%
+in this frame the energy density I'm not
+gonna say rest energy down so you cuz
+
+ align:start position:0%
+gonna say rest energy down so you cuz
+ 
+
+ align:start position:0%
+gonna say rest energy down so you cuz
+I'm no longer in the rest frame but the
+
+ align:start position:0%
+I'm no longer in the rest frame but the
+ 
+
+ align:start position:0%
+I'm no longer in the rest frame but the
+energy density in this frame which I
+
+ align:start position:0%
+energy density in this frame which I
+ 
+
+ align:start position:0%
+energy density in this frame which I
+will denote by row without the
+
+ align:start position:0%
+will denote by row without the
+ 
+
+ align:start position:0%
+will denote by row without the
+subscripts zero it's gonna be the energy
+
+ align:start position:0%
+subscripts zero it's gonna be the energy
+ 
+
+ align:start position:0%
+subscripts zero it's gonna be the energy
+of each particle
+
+ align:start position:0%
+of each particle
+ 
+
+ align:start position:0%
+of each particle
+so that's gamma times M and the volume
+
+ align:start position:0%
+so that's gamma times M and the volume
+ 
+
+ align:start position:0%
+so that's gamma times M and the volume
+is going to be length cancer it's going
+
+ align:start position:0%
+is going to be length cancer it's going
+ 
+
+ align:start position:0%
+is going to be length cancer it's going
+to be a little bit larger sorry the
+
+ align:start position:0%
+to be a little bit larger sorry the
+ 
+
+ align:start position:0%
+to be a little bit larger sorry the
+volume is smaller right so because of a
+
+ align:start position:0%
+volume is smaller right so because of a
+ 
+
+ align:start position:0%
+volume is smaller right so because of a
+length contraction and so this guy
+
+ align:start position:0%
+length contraction and so this guy
+ 
+
+ align:start position:0%
+length contraction and so this guy
+actually gets boosted up to gamma and
+
+ align:start position:0%
+actually gets boosted up to gamma and
+ 
+
+ align:start position:0%
+actually gets boosted up to gamma and
+zero so in this frame the energy density
+
+ align:start position:0%
+zero so in this frame the energy density
+ 
+
+ align:start position:0%
+zero so in this frame the energy density
+is larger than the rest energy the rest
+
+ align:start position:0%
+is larger than the rest energy the rest
+ 
+
+ align:start position:0%
+is larger than the rest energy the rest
+energy density with a gamma squared
+
+ align:start position:0%
+energy density with a gamma squared
+ 
+
+ align:start position:0%
+energy density with a gamma squared
+factor okay straightforward algebra but
+
+ align:start position:0%
+factor okay straightforward algebra but
+ 
+
+ align:start position:0%
+factor okay straightforward algebra but
+I want you to stop and think about what
+
+ align:start position:0%
+I want you to stop and think about what
+ 
+
+ align:start position:0%
+I want you to stop and think about what
+that's telling us if this row were a
+
+ align:start position:0%
+that's telling us if this row were a
+ 
+
+ align:start position:0%
+that's telling us if this row were a
+component of a four vector is there any
+
+ align:start position:0%
+component of a four vector is there any
+ 
+
+ align:start position:0%
+component of a four vector is there any
+way I could get a gamma squared out of
+
+ align:start position:0%
+way I could get a gamma squared out of
+ 
+
+ align:start position:0%
+way I could get a gamma squared out of
+this thing by bopping between reference
+
+ align:start position:0%
+this thing by bopping between reference
+ 
+
+ align:start position:0%
+this thing by bopping between reference
+frames no right when I do that it's
+
+ align:start position:0%
+frames no right when I do that it's
+ 
+
+ align:start position:0%
+frames no right when I do that it's
+linear in Lorentz transformation matrix
+
+ align:start position:0%
+linear in Lorentz transformation matrix
+ 
+
+ align:start position:0%
+linear in Lorentz transformation matrix
+there's no way with a linear
+
+ align:start position:0%
+there's no way with a linear
+ 
+
+ align:start position:0%
+there's no way with a linear
+transformation that I would pick up two
+
+ align:start position:0%
+transformation that I would pick up two
+ 
+
+ align:start position:0%
+transformation that I would pick up two
+powers of gamma this is not how a you
+
+ align:start position:0%
+powers of gamma this is not how a you
+ 
+
+ align:start position:0%
+powers of gamma this is not how a you
+guys are probably all used to from
+
+ align:start position:0%
+guys are probably all used to from
+ 
+
+ align:start position:0%
+guys are probably all used to from
+Newtonian physics of thinking of energy
+
+ align:start position:0%
+Newtonian physics of thinking of energy
+ 
+
+ align:start position:0%
+Newtonian physics of thinking of energy
+density as a scalar this is not a
+
+ align:start position:0%
+density as a scalar this is not a
+ 
+
+ align:start position:0%
+density as a scalar this is not a
+Lorentz scalar okay a scalar is the same
+
+ align:start position:0%
+Lorentz scalar okay a scalar is the same
+ 
+
+ align:start position:0%
+Lorentz scalar okay a scalar is the same
+in all frames reference so this is a
+
+ align:start position:0%
+in all frames reference so this is a
+ 
+
+ align:start position:0%
+in all frames reference so this is a
+different quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's neither a for vector component
+
+ align:start position:0%
+so it's neither a for vector component
+ 
+
+ align:start position:0%
+so it's neither a for vector component
+nor scaler okay it's got two of those
+
+ align:start position:0%
+nor scaler okay it's got two of those
+ 
+
+ align:start position:0%
+nor scaler okay it's got two of those
+things so it's not going to surprise you
+
+ align:start position:0%
+things so it's not going to surprise you
+ 
+
+ align:start position:0%
+things so it's not going to surprise you
+that what's actually going on here is we
+
+ align:start position:0%
+that what's actually going on here is we
+ 
+
+ align:start position:0%
+that what's actually going on here is we
+are picking out what we've done here is
+
+ align:start position:0%
+are picking out what we've done here is
+ 
+
+ align:start position:0%
+are picking out what we've done here is
+we've picked out a particular component
+
+ align:start position:0%
+we've picked out a particular component
+ 
+
+ align:start position:0%
+we've picked out a particular component
+of a tensor let's think a little bit
+
+ align:start position:0%
+of a tensor let's think a little bit
+ 
+
+ align:start position:0%
+of a tensor let's think a little bit
+more methodically about what tensor that
+
+ align:start position:0%
+more methodically about what tensor that
+ 
+
+ align:start position:0%
+more methodically about what tensor that
+must be so when I originally wrote down
+
+ align:start position:0%
+must be so when I originally wrote down
+ 
+
+ align:start position:0%
+must be so when I originally wrote down
+my row zero here I sort of just argued
+
+ align:start position:0%
+my row zero here I sort of just argued
+ 
+
+ align:start position:0%
+my row zero here I sort of just argued
+on physical grounds that it is it's the
+
+ align:start position:0%
+on physical grounds that it is it's the
+ 
+
+ align:start position:0%
+on physical grounds that it is it's the
+energy of every particle times the
+
+ align:start position:0%
+energy of every particle times the
+ 
+
+ align:start position:0%
+energy of every particle times the
+number of particles per unit volume of
+
+ align:start position:0%
+number of particles per unit volume of
+ 
+
+ align:start position:0%
+number of particles per unit volume of
+that thing
+
+ align:start position:0%
+that thing
+ 
+
+ align:start position:0%
+that thing
+well the energy that I use in this thing
+
+ align:start position:0%
+well the energy that I use in this thing
+ 
+
+ align:start position:0%
+well the energy that I use in this thing
+doing it in both the rest frame and in
+
+ align:start position:0%
+doing it in both the rest frame and in
+ 
+
+ align:start position:0%
+doing it in both the rest frame and in
+the other frame those are the time like
+
+ align:start position:0%
+the other frame those are the time like
+ 
+
+ align:start position:0%
+the other frame those are the time like
+components a particular floor vector
+
+ align:start position:0%
+components a particular floor vector
+ 
+
+ align:start position:0%
+components a particular floor vector
+okay so we assembled row by combining
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy which is the time like component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the for momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with number density which is the time
+
+ align:start position:0%
+with number density which is the time
+ 
+
+ align:start position:0%
+with number density which is the time
+like component of the number vector that
+
+ align:start position:0%
+like component of the number vector that
+ 
+
+ align:start position:0%
+like component of the number vector that
+I just recap a few minutes ago so
+
+ align:start position:0%
+I just recap a few minutes ago so
+ 
+
+ align:start position:0%
+I just recap a few minutes ago so
+there's a two time light components of
+
+ align:start position:0%
+there's a two time light components of
+ 
+
+ align:start position:0%
+there's a two time light components of
+four vectors here so that Rho is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like well let's put it this
+
+ align:start position:0%
+something like well let's put it this
+ 
+
+ align:start position:0%
+something like well let's put it this
+way I can write this as PT NT which
+
+ align:start position:0%
+way I can write this as PT NT which
+ 
+
+ align:start position:0%
+way I can write this as PT NT which
+tells me that it belongs to a tensor so
+
+ align:start position:0%
+tells me that it belongs to a tensor so
+ 
+
+ align:start position:0%
+tells me that it belongs to a tensor so
+let's define this as sum TT of a tensor
+
+ align:start position:0%
+let's define this as sum TT of a tensor
+ 
+
+ align:start position:0%
+let's define this as sum TT of a tensor
+that I've not carefully introduced yet
+
+ align:start position:0%
+that I've not carefully introduced yet
+ 
+
+ align:start position:0%
+that I've not carefully introduced yet
+there is some underlying tensor that we
+
+ align:start position:0%
+there is some underlying tensor that we
+ 
+
+ align:start position:0%
+there is some underlying tensor that we
+have built by looking at the either just
+
+ align:start position:0%
+have built by looking at the either just
+ 
+
+ align:start position:0%
+have built by looking at the either just
+the berries names this we'll call it the
+
+ align:start position:0%
+the berries names this we'll call it the
+ 
+
+ align:start position:0%
+the berries names this we'll call it the
+tensor product of two different four
+
+ align:start position:0%
+tensor product of two different four
+ 
+
+ align:start position:0%
+tensor product of two different four
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I write this in the kind of
+
+ align:start position:0%
+so if I write this in the kind of
+ 
+
+ align:start position:0%
+so if I write this in the kind of
+abstract tensor notation that I've used
+
+ align:start position:0%
+abstract tensor notation that I've used
+ 
+
+ align:start position:0%
+abstract tensor notation that I've used
+occasionally in some of your textbooks
+
+ align:start position:0%
+occasionally in some of your textbooks
+ 
+
+ align:start position:0%
+occasionally in some of your textbooks
+this will be written with a bold-faced
+
+ align:start position:0%
+this will be written with a bold-faced
+ 
+
+ align:start position:0%
+this will be written with a bold-faced
+capital T I will use a double over line
+
+ align:start position:0%
+capital T I will use a double over line
+ 
+
+ align:start position:0%
+capital T I will use a double over line
+for this we might say that this T is the
+
+ align:start position:0%
+for this we might say that this T is the
+ 
+
+ align:start position:0%
+for this we might say that this T is the
+tensor product of the number vector with
+
+ align:start position:0%
+tensor product of the number vector with
+ 
+
+ align:start position:0%
+tensor product of the number vector with
+the 4-momentum okay now the number
+
+ align:start position:0%
+the 4-momentum okay now the number
+ 
+
+ align:start position:0%
+the 4-momentum okay now the number
+vector is itself just and zero times the
+
+ align:start position:0%
+vector is itself just and zero times the
+ 
+
+ align:start position:0%
+vector is itself just and zero times the
+floor velocity and my momentum since all
+
+ align:start position:0%
+floor velocity and my momentum since all
+ 
+
+ align:start position:0%
+floor velocity and my momentum since all
+the particles I'm assuming are the same
+
+ align:start position:0%
+the particles I'm assuming are the same
+ 
+
+ align:start position:0%
+the particles I'm assuming are the same
+is just the rest mass times a four
+
+ align:start position:0%
+is just the rest mass times a four
+ 
+
+ align:start position:0%
+is just the rest mass times a four
+momentum this thing actually looks kind
+
+ align:start position:0%
+momentum this thing actually looks kind
+ 
+
+ align:start position:0%
+momentum this thing actually looks kind
+of like for velocity times a four
+
+ align:start position:0%
+of like for velocity times a four
+ 
+
+ align:start position:0%
+of like for velocity times a four
+velocity with a pre factor and that pre
+
+ align:start position:0%
+velocity with a pre factor and that pre
+ 
+
+ align:start position:0%
+velocity with a pre factor and that pre
+factor is nothing more than the rest
+
+ align:start position:0%
+factor is nothing more than the rest
+ 
+
+ align:start position:0%
+factor is nothing more than the rest
+density okay so another way to say this
+
+ align:start position:0%
+density okay so another way to say this
+ 
+
+ align:start position:0%
+density okay so another way to say this
+is that if I make my cloud of dust and I
+
+ align:start position:0%
+is that if I make my cloud of dust and I
+ 
+
+ align:start position:0%
+is that if I make my cloud of dust and I
+go in and I look at its every little
+
+ align:start position:0%
+go in and I look at its every little
+ 
+
+ align:start position:0%
+go in and I look at its every little
+element in it I take the rest energy
+
+ align:start position:0%
+element in it I take the rest energy
+ 
+
+ align:start position:0%
+element in it I take the rest energy
+density of every dense every element in
+
+ align:start position:0%
+density of every dense every element in
+ 
+
+ align:start position:0%
+density of every dense every element in
+that dust I construct the tensor that
+
+ align:start position:0%
+that dust I construct the tensor that
+ 
+
+ align:start position:0%
+that dust I construct the tensor that
+comes from making the tensor products of
+
+ align:start position:0%
+comes from making the tensor products of
+ 
+
+ align:start position:0%
+comes from making the tensor products of
+the four velocity that dust with itself
+
+ align:start position:0%
+the four velocity that dust with itself
+ 
+
+ align:start position:0%
+the four velocity that dust with itself
+that is what this geometric object is
+
+ align:start position:0%
+that is what this geometric object is
+ 
+
+ align:start position:0%
+that is what this geometric object is
+equal to if you want to write this in
+
+ align:start position:0%
+equal to if you want to write this in
+ 
+
+ align:start position:0%
+equal to if you want to write this in
+index notation which is how we will
+
+ align:start position:0%
+index notation which is how we will
+ 
+
+ align:start position:0%
+index notation which is how we will
+write it ninety-nine point eight percent
+
+ align:start position:0%
+write it ninety-nine point eight percent
+ 
+
+ align:start position:0%
+write it ninety-nine point eight percent
+of time we would say that component
+
+ align:start position:0%
+of time we would say that component
+ 
+
+ align:start position:0%
+of time we would say that component
+alpha beta of this quantity T is that
+
+ align:start position:0%
+alpha beta of this quantity T is that
+ 
+
+ align:start position:0%
+alpha beta of this quantity T is that
+rest density times you offer you better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is in terms of the physics we're
+
+ align:start position:0%
+so this is in terms of the physics we're
+ 
+
+ align:start position:0%
+so this is in terms of the physics we're
+gonna do this term this is perhaps the
+
+ align:start position:0%
+gonna do this term this is perhaps the
+ 
+
+ align:start position:0%
+gonna do this term this is perhaps the
+most important quantity that we're going
+
+ align:start position:0%
+most important quantity that we're going
+ 
+
+ align:start position:0%
+most important quantity that we're going
+to talk about so it's worth
+
+ align:start position:0%
+to talk about so it's worth
+ 
+
+ align:start position:0%
+to talk about so it's worth
+understanding what this thing is really
+
+ align:start position:0%
+understanding what this thing is really
+ 
+
+ align:start position:0%
+understanding what this thing is really
+telling us so if I want to get these
+
+ align:start position:0%
+telling us so if I want to get these
+ 
+
+ align:start position:0%
+telling us so if I want to get these
+components the alpha-beta
+
+ align:start position:0%
+components the alpha-beta
+ 
+
+ align:start position:0%
+components the alpha-beta
+out of this thing from this sort of
+
+ align:start position:0%
+out of this thing from this sort of
+ 
+
+ align:start position:0%
+out of this thing from this sort of
+abstract notation of the tensor so I'll
+
+ align:start position:0%
+abstract notation of the tensor so I'll
+ 
+
+ align:start position:0%
+abstract notation of the tensor so I'll
+remind you that we can do this by taking
+
+ align:start position:0%
+remind you that we can do this by taking
+ 
+
+ align:start position:0%
+remind you that we can do this by taking
+the tensor and plugging into its slots
+
+ align:start position:0%
+the tensor and plugging into its slots
+ 
+
+ align:start position:0%
+the tensor and plugging into its slots
+the basis one forms which tell me
+
+ align:start position:0%
+the basis one forms which tell me
+ 
+
+ align:start position:0%
+the basis one forms which tell me
+something about basis one forms are
+
+ align:start position:0%
+something about basis one forms are
+ 
+
+ align:start position:0%
+something about basis one forms are
+really useful for sort of measuring
+
+ align:start position:0%
+really useful for sort of measuring
+ 
+
+ align:start position:0%
+really useful for sort of measuring
+fluxes across a but in a particular
+
+ align:start position:0%
+fluxes across a but in a particular
+ 
+
+ align:start position:0%
+fluxes across a but in a particular
+direction and in fact this quantity has
+
+ align:start position:0%
+direction and in fact this quantity has
+ 
+
+ align:start position:0%
+direction and in fact this quantity has
+the geometric interpretation think of
+
+ align:start position:0%
+the geometric interpretation think of
+ 
+
+ align:start position:0%
+the geometric interpretation think of
+this as the flux of momentum component
+
+ align:start position:0%
+this as the flux of momentum component
+ 
+
+ align:start position:0%
+this as the flux of momentum component
+alpha in the beta direction okay so if
+
+ align:start position:0%
+alpha in the beta direction okay so if
+ 
+
+ align:start position:0%
+alpha in the beta direction okay so if
+we look at this component by component
+
+ align:start position:0%
+we look at this component by component
+ 
+
+ align:start position:0%
+we look at this component by component
+it's worth doing that so let's do the TT
+
+ align:start position:0%
+it's worth doing that so let's do the TT
+ 
+
+ align:start position:0%
+it's worth doing that so let's do the TT
+or zero zero component okay this is the
+
+ align:start position:0%
+or zero zero component okay this is the
+ 
+
+ align:start position:0%
+or zero zero component okay this is the
+one we've already done this is just Rho
+
+ align:start position:0%
+one we've already done this is just Rho
+ 
+
+ align:start position:0%
+one we've already done this is just Rho
+0 UT UT just Rho in that thing according
+
+ align:start position:0%
+0 UT UT just Rho in that thing according
+ 
+
+ align:start position:0%
+0 UT UT just Rho in that thing according
+to the words I've written down here this
+
+ align:start position:0%
+to the words I've written down here this
+ 
+
+ align:start position:0%
+to the words I've written down here this
+is the flux of PT in the T direction ok
+
+ align:start position:0%
+is the flux of PT in the T direction ok
+ 
+
+ align:start position:0%
+is the flux of PT in the T direction ok
+so PT tells me about energy the flux of
+
+ align:start position:0%
+so PT tells me about energy the flux of
+ 
+
+ align:start position:0%
+so PT tells me about energy the flux of
+energy in the energy Direction refers to
+
+ align:start position:0%
+energy in the energy Direction refers to
+ 
+
+ align:start position:0%
+energy in the energy Direction refers to
+you know so here's my water flowing in
+
+ align:start position:0%
+you know so here's my water flowing in
+ 
+
+ align:start position:0%
+you know so here's my water flowing in
+the time like direction just sitting
+
+ align:start position:0%
+the time like direction just sitting
+ 
+
+ align:start position:0%
+the time like direction just sitting
+there apparently doing nothing but know
+
+ align:start position:0%
+there apparently doing nothing but know
+ 
+
+ align:start position:0%
+there apparently doing nothing but know
+it's moving through time this is energy
+
+ align:start position:0%
+it's moving through time this is energy
+ 
+
+ align:start position:0%
+it's moving through time this is energy
+flowing through time it's energy density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all sort of locked up in stable
+
+ align:start position:0%
+all sort of locked up in stable
+ 
+
+ align:start position:0%
+all sort of locked up in stable
+equilibrium here but if somebody comes
+
+ align:start position:0%
+equilibrium here but if somebody comes
+ 
+
+ align:start position:0%
+equilibrium here but if somebody comes
+in someday with a nice cup of anti water
+
+ align:start position:0%
+in someday with a nice cup of anti water
+ 
+
+ align:start position:0%
+in someday with a nice cup of anti water
+and combines that we get to have all
+
+ align:start position:0%
+and combines that we get to have all
+ 
+
+ align:start position:0%
+and combines that we get to have all
+that energy released and we can enjoy
+
+ align:start position:0%
+that energy released and we can enjoy
+ 
+
+ align:start position:0%
+that energy released and we can enjoy
+that for a few femtoseconds before we
+
+ align:start position:0%
+that for a few femtoseconds before we
+ 
+
+ align:start position:0%
+that for a few femtoseconds before we
+evaporate let's look at the other
+
+ align:start position:0%
+evaporate let's look at the other
+ 
+
+ align:start position:0%
+evaporate let's look at the other
+components so t0 I okay you can take the
+
+ align:start position:0%
+components so t0 I okay you can take the
+ 
+
+ align:start position:0%
+components so t0 I okay you can take the
+definition and plug it in in terms of
+
+ align:start position:0%
+definition and plug it in in terms of
+ 
+
+ align:start position:0%
+definition and plug it in in terms of
+the confluence it's obviously u T times
+
+ align:start position:0%
+the confluence it's obviously u T times
+ 
+
+ align:start position:0%
+the confluence it's obviously u T times
+UI but still use the definition by words
+
+ align:start position:0%
+UI but still use the definition by words
+ 
+
+ align:start position:0%
+UI but still use the definition by words
+so this is the flux of P sub T in the X
+
+ align:start position:0%
+so this is the flux of P sub T in the X
+ 
+
+ align:start position:0%
+so this is the flux of P sub T in the X
+I Direction okay so this is talking
+
+ align:start position:0%
+I Direction okay so this is talking
+ 
+
+ align:start position:0%
+I Direction okay so this is talking
+about energy moving in a particular
+
+ align:start position:0%
+about energy moving in a particular
+ 
+
+ align:start position:0%
+about energy moving in a particular
+direction this is nothing more than
+
+ align:start position:0%
+direction this is nothing more than
+ 
+
+ align:start position:0%
+direction this is nothing more than
+energy flux okay energy sort of flux
+
+ align:start position:0%
+energy flux okay energy sort of flux
+ 
+
+ align:start position:0%
+energy flux okay energy sort of flux
+that we're used to think about not
+
+ align:start position:0%
+that we're used to think about not
+ 
+
+ align:start position:0%
+that we're used to think about not
+flowing through time but throwing
+
+ align:start position:0%
+flowing through time but throwing
+ 
+
+ align:start position:0%
+flowing through time but throwing
+through space now T 0 I this is the flux
+
+ align:start position:0%
+through space now T 0 I this is the flux
+ 
+
+ align:start position:0%
+through space now T 0 I this is the flux
+of momentum component I in the T
+
+ align:start position:0%
+of momentum component I in the T
+ 
+
+ align:start position:0%
+of momentum component I in the T
+direction so this tells me about
+
+ align:start position:0%
+direction so this tells me about
+ 
+
+ align:start position:0%
+direction so this tells me about
+momentum density okay so if I had this
+
+ align:start position:0%
+momentum density okay so if I had this
+ 
+
+ align:start position:0%
+momentum density okay so if I had this
+stuff flowing okay there's some momentum
+
+ align:start position:0%
+stuff flowing okay there's some momentum
+ 
+
+ align:start position:0%
+stuff flowing okay there's some momentum
+associate with that flow you can count
+
+ align:start position:0%
+associate with that flow you can count
+ 
+
+ align:start position:0%
+associate with that flow you can count
+up the amount of mass and every little
+
+ align:start position:0%
+up the amount of mass and every little
+ 
+
+ align:start position:0%
+up the amount of mass and every little
+volume divided by that volume take some
+
+ align:start position:0%
+volume divided by that volume take some
+ 
+
+ align:start position:0%
+volume divided by that volume take some
+ratios that is the density of momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally this last one flux of P I in
+
+ align:start position:0%
+and finally this last one flux of P I in
+ 
+
+ align:start position:0%
+and finally this last one flux of P I in
+the X J direction she's really no great
+
+ align:start position:0%
+the X J direction she's really no great
+ 
+
+ align:start position:0%
+the X J direction she's really no great
+wisdom for that this is nothing more
+
+ align:start position:0%
+wisdom for that this is nothing more
+ 
+
+ align:start position:0%
+wisdom for that this is nothing more
+than momentum flux if I have a bucket of
+
+ align:start position:0%
+than momentum flux if I have a bucket of
+ 
+
+ align:start position:0%
+than momentum flux if I have a bucket of
+water and things are sort of sloshing
+
+ align:start position:0%
+water and things are sort of sloshing
+ 
+
+ align:start position:0%
+water and things are sort of sloshing
+around there's some momentum moving and
+
+ align:start position:0%
+around there's some momentum moving and
+ 
+
+ align:start position:0%
+around there's some momentum moving and
+the whole assembly is moving in some
+
+ align:start position:0%
+the whole assembly is moving in some
+ 
+
+ align:start position:0%
+the whole assembly is moving in some
+direction we can get a flow of momentum
+
+ align:start position:0%
+direction we can get a flow of momentum
+ 
+
+ align:start position:0%
+direction we can get a flow of momentum
+going in kind of a non normal direction
+
+ align:start position:0%
+going in kind of a non normal direction
+ 
+
+ align:start position:0%
+going in kind of a non normal direction
+sometimes it goes in a normal direction
+
+ align:start position:0%
+sometimes it goes in a normal direction
+ 
+
+ align:start position:0%
+sometimes it goes in a normal direction
+it might be moving along so it's flow
+
+ align:start position:0%
+it might be moving along so it's flow
+ 
+
+ align:start position:0%
+it might be moving along so it's flow
+I'm gonna talk about that in a few
+
+ align:start position:0%
+I'm gonna talk about that in a few
+ 
+
+ align:start position:0%
+I'm gonna talk about that in a few
+moments when I talk about a few
+
+ align:start position:0%
+moments when I talk about a few
+ 
+
+ align:start position:0%
+moments when I talk about a few
+different kinds of stress energy tensor
+
+ align:start position:0%
+different kinds of stress energy tensor
+ 
+
+ align:start position:0%
+different kinds of stress energy tensor
+x' the key thing which I want you to be
+
+ align:start position:0%
+x' the key thing which I want you to be
+ 
+
+ align:start position:0%
+x' the key thing which I want you to be
+aware of is that under the hood of this
+
+ align:start position:0%
+aware of is that under the hood of this
+ 
+
+ align:start position:0%
+aware of is that under the hood of this
+thing we're going to talk about
+
+ align:start position:0%
+thing we're going to talk about
+ 
+
+ align:start position:0%
+thing we're going to talk about
+different kinds of stress energy tensor
+
+ align:start position:0%
+different kinds of stress energy tensor
+ 
+
+ align:start position:0%
+different kinds of stress energy tensor
+x' for a little later in this class but
+
+ align:start position:0%
+x' for a little later in this class but
+ 
+
+ align:start position:0%
+x' for a little later in this class but
+this basic interpretation of the way to
+
+ align:start position:0%
+this basic interpretation of the way to
+ 
+
+ align:start position:0%
+this basic interpretation of the way to
+think about the different components it
+
+ align:start position:0%
+think about the different components it
+ 
+
+ align:start position:0%
+think about the different components it
+holds for all of them ok so this is good
+
+ align:start position:0%
+holds for all of them ok so this is good
+ 
+
+ align:start position:0%
+holds for all of them ok so this is good
+intuition to have one thing which is
+
+ align:start position:0%
+intuition to have one thing which is
+ 
+
+ align:start position:0%
+intuition to have one thing which is
+worth noting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is you know if you look at if you
+
+ align:start position:0%
+is you know if you look at if you
+ 
+
+ align:start position:0%
+is you know if you look at if you
+actually let's take the form of the
+
+ align:start position:0%
+actually let's take the form of the
+ 
+
+ align:start position:0%
+actually let's take the form of the
+stress-energy tensor the corresponds to
+
+ align:start position:0%
+stress-energy tensor the corresponds to
+ 
+
+ align:start position:0%
+stress-energy tensor the corresponds to
+the dust okay so I'm gonna write out all
+
+ align:start position:0%
+the dust okay so I'm gonna write out all
+ 
+
+ align:start position:0%
+the dust okay so I'm gonna write out all
+four of my complex I've already given
+
+ align:start position:0%
+four of my complex I've already given
+ 
+
+ align:start position:0%
+four of my complex I've already given
+you t 0 0 t 0 I I can write that as
+
+ align:start position:0%
+you t 0 0 t 0 I I can write that as
+ 
+
+ align:start position:0%
+you t 0 0 t 0 I I can write that as
+gamma squared Rho 0 VI t 0 I equals
+
+ align:start position:0%
+gamma squared Rho 0 VI t 0 I equals
+ 
+
+ align:start position:0%
+gamma squared Rho 0 VI t 0 I equals
+gamma squared Rho 0 V I this guy is
+
+ align:start position:0%
+gamma squared Rho 0 V I this guy is
+ 
+
+ align:start position:0%
+gamma squared Rho 0 V I this guy is
+gamma squared Rho 0 VI VJ there's two
+
+ align:start position:0%
+gamma squared Rho 0 VI VJ there's two
+ 
+
+ align:start position:0%
+gamma squared Rho 0 VI VJ there's two
+elements of symmetry here which I want
+
+ align:start position:0%
+elements of symmetry here which I want
+ 
+
+ align:start position:0%
+elements of symmetry here which I want
+to emphasize notice energy density and
+
+ align:start position:0%
+to emphasize notice energy density and
+ 
+
+ align:start position:0%
+to emphasize notice energy density and
+momentum flux sorry energy flux and
+
+ align:start position:0%
+momentum flux sorry energy flux and
+ 
+
+ align:start position:0%
+momentum flux sorry energy flux and
+momentum density those words are
+
+ align:start position:0%
+momentum density those words are
+ 
+
+ align:start position:0%
+momentum density those words are
+important energy flux and momentum
+
+ align:start position:0%
+important energy flux and momentum
+ 
+
+ align:start position:0%
+important energy flux and momentum
+density they're exactly the same okay
+
+ align:start position:0%
+density they're exactly the same okay
+ 
+
+ align:start position:0%
+density they're exactly the same okay
+that is actually true in all physics
+
+ align:start position:0%
+that is actually true in all physics
+ 
+
+ align:start position:0%
+that is actually true in all physics
+okay it's clouded by the fact though
+
+ align:start position:0%
+okay it's clouded by the fact though
+ 
+
+ align:start position:0%
+okay it's clouded by the fact though
+that in most units that we measure
+
+ align:start position:0%
+that in most units that we measure
+ 
+
+ align:start position:0%
+that in most units that we measure
+things in we don't typically use speed
+
+ align:start position:0%
+things in we don't typically use speed
+ 
+
+ align:start position:0%
+things in we don't typically use speed
+of light equal to 1 so when you look at
+
+ align:start position:0%
+of light equal to 1 so when you look at
+ 
+
+ align:start position:0%
+of light equal to 1 so when you look at
+these kind of quantities in the physics
+
+ align:start position:0%
+these kind of quantities in the physics
+ 
+
+ align:start position:0%
+these kind of quantities in the physics
+that you are more used to you would find
+
+ align:start position:0%
+that you are more used to you would find
+ 
+
+ align:start position:0%
+that you are more used to you would find
+you know your energy your energy flux
+
+ align:start position:0%
+you know your energy your energy flux
+ 
+
+ align:start position:0%
+you know your energy your energy flux
+your momentum density will have
+
+ align:start position:0%
+your momentum density will have
+ 
+
+ align:start position:0%
+your momentum density will have
+different units okay cuz you'll have
+
+ align:start position:0%
+different units okay cuz you'll have
+ 
+
+ align:start position:0%
+different units okay cuz you'll have
+factors of C that come into there that
+
+ align:start position:0%
+factors of C that come into there that
+ 
+
+ align:start position:0%
+factors of C that come into there that
+convert from one momentum and energy and
+
+ align:start position:0%
+convert from one momentum and energy and
+ 
+
+ align:start position:0%
+convert from one momentum and energy and
+time flow and space flow also you don't
+
+ align:start position:0%
+time flow and space flow also you don't
+ 
+
+ align:start position:0%
+time flow and space flow also you don't
+usually include rest mass and rest
+
+ align:start position:0%
+usually include rest mass and rest
+ 
+
+ align:start position:0%
+usually include rest mass and rest
+energy and the energy flows and momentum
+
+ align:start position:0%
+energy and the energy flows and momentum
+ 
+
+ align:start position:0%
+energy and the energy flows and momentum
+densities that you've probably been
+
+ align:start position:0%
+densities that you've probably been
+ 
+
+ align:start position:0%
+densities that you've probably been
+familiar with in the past okay so it's
+
+ align:start position:0%
+familiar with in the past okay so it's
+ 
+
+ align:start position:0%
+familiar with in the past okay so it's
+when we do relativity and we set the
+
+ align:start position:0%
+when we do relativity and we set the
+ 
+
+ align:start position:0%
+when we do relativity and we set the
+speed of light equal to 1 that this
+
+ align:start position:0%
+speed of light equal to 1 that this
+ 
+
+ align:start position:0%
+speed of light equal to 1 that this
+symmetry between energy flux and
+
+ align:start position:0%
+symmetry between energy flux and
+ 
+
+ align:start position:0%
+symmetry between energy flux and
+momentum density becomes apparent
+
+ align:start position:0%
+momentum density becomes apparent
+ 
+
+ align:start position:0%
+momentum density becomes apparent
+question sorry this one yeah on the
+
+ align:start position:0%
+question sorry this one yeah on the
+ 
+
+ align:start position:0%
+question sorry this one yeah on the
+right hand side this is now this is this
+
+ align:start position:0%
+right hand side this is now this is this
+ 
+
+ align:start position:0%
+right hand side this is now this is this
+is definitely what I mean to write down
+
+ align:start position:0%
+is definitely what I mean to write down
+ 
+
+ align:start position:0%
+is definitely what I mean to write down
+here so this is what I've done I've
+
+ align:start position:0%
+here so this is what I've done I've
+ 
+
+ align:start position:0%
+here so this is what I've done I've
+taken advantage of the fact that I can
+
+ align:start position:0%
+taken advantage of the fact that I can
+ 
+
+ align:start position:0%
+taken advantage of the fact that I can
+write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have it down somewhere yeah yeah so what
+
+ align:start position:0%
+have it down somewhere yeah yeah so what
+ 
+
+ align:start position:0%
+have it down somewhere yeah yeah so what
+I've done over here is I have written
+
+ align:start position:0%
+I've done over here is I have written
+ 
+
+ align:start position:0%
+I've done over here is I have written
+the fact so u sub T u T is it's just the
+
+ align:start position:0%
+the fact so u sub T u T is it's just the
+ 
+
+ align:start position:0%
+the fact so u sub T u T is it's just the
+gamma factor okay and I didn't
+
+ align:start position:0%
+gamma factor okay and I didn't
+ 
+
+ align:start position:0%
+gamma factor okay and I didn't
+explicitly write out what T the you know
+
+ align:start position:0%
+explicitly write out what T the you know
+ 
+
+ align:start position:0%
+explicitly write out what T the you know
+the the I complex but you get a similar
+
+ align:start position:0%
+the the I complex but you get a similar
+ 
+
+ align:start position:0%
+the the I complex but you get a similar
+factor that once that so know that that
+
+ align:start position:0%
+factor that once that so know that that
+ 
+
+ align:start position:0%
+factor that once that so know that that
+is correct that way yeah yeah
+
+ align:start position:0%
+is correct that way yeah yeah
+ 
+
+ align:start position:0%
+is correct that way yeah yeah
+a nice one emphasize I mean the key
+
+ align:start position:0%
+a nice one emphasize I mean the key
+ 
+
+ align:start position:0%
+a nice one emphasize I mean the key
+thing which I want to emphasize is when
+
+ align:start position:0%
+thing which I want to emphasize is when
+ 
+
+ align:start position:0%
+thing which I want to emphasize is when
+you do it in the physics that you guys
+
+ align:start position:0%
+you do it in the physics that you guys
+ 
+
+ align:start position:0%
+you do it in the physics that you guys
+have generally all seen up till now it
+
+ align:start position:0%
+have generally all seen up till now it
+ 
+
+ align:start position:0%
+have generally all seen up till now it
+won't look that way and that's to cause
+
+ align:start position:0%
+won't look that way and that's to cause
+ 
+
+ align:start position:0%
+won't look that way and that's to cause
+of that one is you're not used to
+
+ align:start position:0%
+of that one is you're not used to
+ 
+
+ align:start position:0%
+of that one is you're not used to
+necessarily working in units where the
+
+ align:start position:0%
+necessarily working in units where the
+ 
+
+ align:start position:0%
+necessarily working in units where the
+speed of light is one and two rest
+
+ align:start position:0%
+speed of light is one and two rest
+ 
+
+ align:start position:0%
+speed of light is one and two rest
+energy is built into these definitions
+
+ align:start position:0%
+energy is built into these definitions
+ 
+
+ align:start position:0%
+energy is built into these definitions
+that shift things a little bit the other
+
+ align:start position:0%
+that shift things a little bit the other
+ 
+
+ align:start position:0%
+that shift things a little bit the other
+thing which I want to emphasize is
+
+ align:start position:0%
+thing which I want to emphasize is
+ 
+
+ align:start position:0%
+thing which I want to emphasize is
+notice this is symmetric under exchange
+
+ align:start position:0%
+notice this is symmetric under exchange
+ 
+
+ align:start position:0%
+notice this is symmetric under exchange
+of indices okay you know it's obvious
+
+ align:start position:0%
+of indices okay you know it's obvious
+ 
+
+ align:start position:0%
+of indices okay you know it's obvious
+for dust it comes right back to the fact
+
+ align:start position:0%
+for dust it comes right back to the fact
+ 
+
+ align:start position:0%
+for dust it comes right back to the fact
+that these guys that those indices enter
+
+ align:start position:0%
+that these guys that those indices enter
+ 
+
+ align:start position:0%
+that these guys that those indices enter
+like so it's a exterior product the
+
+ align:start position:0%
+like so it's a exterior product the
+ 
+
+ align:start position:0%
+like so it's a exterior product the
+floor velocity with itself I'm not going
+
+ align:start position:0%
+floor velocity with itself I'm not going
+ 
+
+ align:start position:0%
+floor velocity with itself I'm not going
+to go through in detail but there is a
+
+ align:start position:0%
+to go through in detail but there is a
+ 
+
+ align:start position:0%
+to go through in detail but there is a
+physical motivation that I will sketch
+
+ align:start position:0%
+physical motivation that I will sketch
+ 
+
+ align:start position:0%
+physical motivation that I will sketch
+in a few moments that argues that it
+
+ align:start position:0%
+in a few moments that argues that it
+ 
+
+ align:start position:0%
+in a few moments that argues that it
+must be symmetric like this in all
+
+ align:start position:0%
+must be symmetric like this in all
+ 
+
+ align:start position:0%
+must be symmetric like this in all
+physical cases okay I have detailed a
+
+ align:start position:0%
+physical cases okay I have detailed a
+ 
+
+ align:start position:0%
+physical cases okay I have detailed a
+detailed sketch of this it's I keep
+
+ align:start position:0%
+detailed sketch of this it's I keep
+ 
+
+ align:start position:0%
+detailed sketch of this it's I keep
+using the word sketch because my mind
+
+ align:start position:0%
+using the word sketch because my mind
+ 
+
+ align:start position:0%
+using the word sketch because my mind
+wants to say proof but in a proof sort
+
+ align:start position:0%
+wants to say proof but in a proof sort
+ 
+
+ align:start position:0%
+wants to say proof but in a proof sort
+of a motivation and so I will post it
+
+ align:start position:0%
+of a motivation and so I will post it
+ 
+
+ align:start position:0%
+of a motivation and so I will post it
+for everyone to go through but I will
+
+ align:start position:0%
+for everyone to go through but I will
+ 
+
+ align:start position:0%
+for everyone to go through but I will
+sort of illuminate it in a couple
+
+ align:start position:0%
+sort of illuminate it in a couple
+ 
+
+ align:start position:0%
+sort of illuminate it in a couple
+moments basically if this is not true if
+
+ align:start position:0%
+moments basically if this is not true if
+ 
+
+ align:start position:0%
+moments basically if this is not true if
+it's not the case that's a symmetric a
+
+ align:start position:0%
+it's not the case that's a symmetric a
+ 
+
+ align:start position:0%
+it's not the case that's a symmetric a
+physical absurdity can be set up I'll
+
+ align:start position:0%
+physical absurdity can be set up I'll
+ 
+
+ align:start position:0%
+physical absurdity can be set up I'll
+describe that in a few moments so most
+
+ align:start position:0%
+describe that in a few moments so most
+ 
+
+ align:start position:0%
+describe that in a few moments so most
+of the world is not dust so this is a
+
+ align:start position:0%
+of the world is not dust so this is a
+ 
+
+ align:start position:0%
+of the world is not dust so this is a
+decent example for helping to understand
+
+ align:start position:0%
+decent example for helping to understand
+ 
+
+ align:start position:0%
+decent example for helping to understand
+things but we are going to want to do
+
+ align:start position:0%
+things but we are going to want to do
+ 
+
+ align:start position:0%
+things but we are going to want to do
+more complicated and interesting
+
+ align:start position:0%
+more complicated and interesting
+ 
+
+ align:start position:0%
+more complicated and interesting
+examples so for us the way that we are
+
+ align:start position:0%
+examples so for us the way that we are
+ 
+
+ align:start position:0%
+examples so for us the way that we are
+going to do this there is a fairly
+
+ align:start position:0%
+going to do this there is a fairly
+ 
+
+ align:start position:0%
+going to do this there is a fairly
+general recipe that one can imagine
+
+ align:start position:0%
+general recipe that one can imagine
+ 
+
+ align:start position:0%
+general recipe that one can imagine
+applying this I'm going to save it for a
+
+ align:start position:0%
+applying this I'm going to save it for a
+ 
+
+ align:start position:0%
+applying this I'm going to save it for a
+little later in the class it so it
+
+ align:start position:0%
+little later in the class it so it
+ 
+
+ align:start position:0%
+little later in the class it so it
+borrows some techniques from field
+
+ align:start position:0%
+borrows some techniques from field
+ 
+
+ align:start position:0%
+borrows some techniques from field
+theory basically if you can write down a
+
+ align:start position:0%
+theory basically if you can write down a
+ 
+
+ align:start position:0%
+theory basically if you can write down a
+Lagrangian density that describes the
+
+ align:start position:0%
+Lagrangian density that describes the
+ 
+
+ align:start position:0%
+Lagrangian density that describes the
+fifth system that you're under under
+
+ align:start position:0%
+fifth system that you're under under
+ 
+
+ align:start position:0%
+fifth system that you're under under
+study there's a particular particular
+
+ align:start position:0%
+study there's a particular particular
+ 
+
+ align:start position:0%
+study there's a particular particular
+variation you can do that stress energy
+
+ align:start position:0%
+variation you can do that stress energy
+ 
+
+ align:start position:0%
+variation you can do that stress energy
+tensor emerges from but for now the key
+
+ align:start position:0%
+tensor emerges from but for now the key
+ 
+
+ align:start position:0%
+tensor emerges from but for now the key
+thing which I want to sort of say is
+
+ align:start position:0%
+thing which I want to sort of say is
+ 
+
+ align:start position:0%
+thing which I want to sort of say is
+that we basically are going to deduce
+
+ align:start position:0%
+that we basically are going to deduce
+ 
+
+ align:start position:0%
+that we basically are going to deduce
+what the stress energy tensor looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by essentially going into a particular
+
+ align:start position:0%
+by essentially going into a particular
+ 
+
+ align:start position:0%
+by essentially going into a particular
+frame we'll call it the rest frame is
+
+ align:start position:0%
+frame we'll call it the rest frame is
+ 
+
+ align:start position:0%
+frame we'll call it the rest frame is
+usually the rest frame of some element
+
+ align:start position:0%
+usually the rest frame of some element
+ 
+
+ align:start position:0%
+usually the rest frame of some element
+of the material being studied and
+
+ align:start position:0%
+of the material being studied and
+ 
+
+ align:start position:0%
+of the material being studied and
+thinking carefully about this physical
+
+ align:start position:0%
+thinking carefully about this physical
+ 
+
+ align:start position:0%
+thinking carefully about this physical
+definition of what the different
+
+ align:start position:0%
+definition of what the different
+ 
+
+ align:start position:0%
+definition of what the different
+components mean okay this is not the
+
+ align:start position:0%
+components mean okay this is not the
+ 
+
+ align:start position:0%
+components mean okay this is not the
+most rigorous way to do it but it's a
+
+ align:start position:0%
+most rigorous way to do it but it's a
+ 
+
+ align:start position:0%
+most rigorous way to do it but it's a
+good way to get started and to develop
+
+ align:start position:0%
+good way to get started and to develop
+ 
+
+ align:start position:0%
+good way to get started and to develop
+some intuition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let me give one example that for
+
+ align:start position:0%
+okay so let me give one example that for
+ 
+
+ align:start position:0%
+okay so let me give one example that for
+many of us in astrophysics this is
+
+ align:start position:0%
+many of us in astrophysics this is
+ 
+
+ align:start position:0%
+many of us in astrophysics this is
+probably the one stress energy tensor
+
+ align:start position:0%
+probably the one stress energy tensor
+ 
+
+ align:start position:0%
+probably the one stress energy tensor
+that we write down and use over and over
+
+ align:start position:0%
+that we write down and use over and over
+ 
+
+ align:start position:0%
+that we write down and use over and over
+and over again in our career and it's
+
+ align:start position:0%
+and over again in our career and it's
+ 
+
+ align:start position:0%
+and over again in our career and it's
+rarely to anything more than this in
+
+ align:start position:0%
+rarely to anything more than this in
+ 
+
+ align:start position:0%
+rarely to anything more than this in
+many many cases this is called a perfect
+
+ align:start position:0%
+many many cases this is called a perfect
+ 
+
+ align:start position:0%
+many many cases this is called a perfect
+fluid so what is perfect about a perfect
+
+ align:start position:0%
+fluid so what is perfect about a perfect
+ 
+
+ align:start position:0%
+fluid so what is perfect about a perfect
+fluid let's beg the question here what
+
+ align:start position:0%
+fluid let's beg the question here what
+ 
+
+ align:start position:0%
+fluid let's beg the question here what
+is what is perfect referring to here so
+
+ align:start position:0%
+is what is perfect referring to here so
+ 
+
+ align:start position:0%
+is what is perfect referring to here so
+a perfect fluid is a fluid in which
+
+ align:start position:0%
+a perfect fluid is a fluid in which
+ 
+
+ align:start position:0%
+a perfect fluid is a fluid in which
+there is no energy flow in what I will
+
+ align:start position:0%
+there is no energy flow in what I will
+ 
+
+ align:start position:0%
+there is no energy flow in what I will
+call the rest frame
+
+ align:start position:0%
+call the rest frame
+ 
+
+ align:start position:0%
+call the rest frame
+I put rest in quotes because you have to
+
+ align:start position:0%
+I put rest in quotes because you have to
+ 
+
+ align:start position:0%
+I put rest in quotes because you have to
+sort of define it from the context of of
+
+ align:start position:0%
+sort of define it from the context of of
+ 
+
+ align:start position:0%
+sort of define it from the context of of
+what your fluid is there basically what
+
+ align:start position:0%
+what your fluid is there basically what
+ 
+
+ align:start position:0%
+what your fluid is there basically what
+it means I can find a frame in which
+
+ align:start position:0%
+it means I can find a frame in which
+ 
+
+ align:start position:0%
+it means I can find a frame in which
+each fluid element there is no energy
+
+ align:start position:0%
+each fluid element there is no energy
+ 
+
+ align:start position:0%
+each fluid element there is no energy
+flow there if a frame exists where that
+
+ align:start position:0%
+flow there if a frame exists where that
+ 
+
+ align:start position:0%
+flow there if a frame exists where that
+happens this is a candidate to be a
+
+ align:start position:0%
+happens this is a candidate to be a
+ 
+
+ align:start position:0%
+happens this is a candidate to be a
+perfect fluid and I also require there
+
+ align:start position:0%
+perfect fluid and I also require there
+ 
+
+ align:start position:0%
+perfect fluid and I also require there
+to be no lateral stresses lateral
+
+ align:start position:0%
+to be no lateral stresses lateral
+ 
+
+ align:start position:0%
+to be no lateral stresses lateral
+stresses refer to this tij when I and J
+
+ align:start position:0%
+stresses refer to this tij when I and J
+ 
+
+ align:start position:0%
+stresses refer to this tij when I and J
+are not equal to one an hour okay so
+
+ align:start position:0%
+are not equal to one an hour okay so
+ 
+
+ align:start position:0%
+are not equal to one an hour okay so
+this sort of refers to imagine that I
+
+ align:start position:0%
+this sort of refers to imagine that I
+ 
+
+ align:start position:0%
+this sort of refers to imagine that I
+have some let's say the going into the
+
+ align:start position:0%
+have some let's say the going into the
+ 
+
+ align:start position:0%
+have some let's say the going into the
+board is the Y direction so if there's
+
+ align:start position:0%
+board is the Y direction so if there's
+ 
+
+ align:start position:0%
+board is the Y direction so if there's
+like some Y stress that is somehow being
+
+ align:start position:0%
+like some Y stress that is somehow being
+ 
+
+ align:start position:0%
+like some Y stress that is somehow being
+transported in the X direction that
+
+ align:start position:0%
+transported in the X direction that
+ 
+
+ align:start position:0%
+transported in the X direction that
+would be a lateral stress physically
+
+ align:start position:0%
+would be a lateral stress physically
+ 
+
+ align:start position:0%
+would be a lateral stress physically
+this is actually that kind of a stress
+
+ align:start position:0%
+this is actually that kind of a stress
+ 
+
+ align:start position:0%
+this is actually that kind of a stress
+is hugely important when one of studying
+
+ align:start position:0%
+is hugely important when one of studying
+ 
+
+ align:start position:0%
+is hugely important when one of studying
+fluids okay and one characterizes it by
+
+ align:start position:0%
+fluids okay and one characterizes it by
+ 
+
+ align:start position:0%
+fluids okay and one characterizes it by
+a quantity known as the viscosity okay
+
+ align:start position:0%
+a quantity known as the viscosity okay
+ 
+
+ align:start position:0%
+a quantity known as the viscosity okay
+this cost he tells me about how stress
+
+ align:start position:0%
+this cost he tells me about how stress
+ 
+
+ align:start position:0%
+this cost he tells me about how stress
+gets transported how momentum rather
+
+ align:start position:0%
+gets transported how momentum rather
+ 
+
+ align:start position:0%
+gets transported how momentum rather
+gets transported in a non
+
+ align:start position:0%
+gets transported in a non
+ 
+
+ align:start position:0%
+gets transported in a non
+normal direction against the direction
+
+ align:start position:0%
+normal direction against the direction
+ 
+
+ align:start position:0%
+normal direction against the direction
+in which the fluid is moving so my
+
+ align:start position:0%
+in which the fluid is moving so my
+ 
+
+ align:start position:0%
+in which the fluid is moving so my
+perfect fluid has no viscosity and I'll
+
+ align:start position:0%
+perfect fluid has no viscosity and I'll
+ 
+
+ align:start position:0%
+perfect fluid has no viscosity and I'll
+just conclude you want to make a there's
+
+ align:start position:0%
+just conclude you want to make a there's
+ 
+
+ align:start position:0%
+just conclude you want to make a there's
+a very important point here a fluid that
+
+ align:start position:0%
+a very important point here a fluid that
+ 
+
+ align:start position:0%
+a very important point here a fluid that
+has no viscosity there's a fluid that
+
+ align:start position:0%
+has no viscosity there's a fluid that
+ 
+
+ align:start position:0%
+has no viscosity there's a fluid that
+doesn't get anything wet okay so this
+
+ align:start position:0%
+doesn't get anything wet okay so this
+ 
+
+ align:start position:0%
+doesn't get anything wet okay so this
+refers to when you pour water on
+
+ align:start position:0%
+refers to when you pour water on
+ 
+
+ align:start position:0%
+refers to when you pour water on
+yourself the reason your hand gets wet
+
+ align:start position:0%
+yourself the reason your hand gets wet
+ 
+
+ align:start position:0%
+yourself the reason your hand gets wet
+is that there's some viscosity that
+
+ align:start position:0%
+is that there's some viscosity that
+ 
+
+ align:start position:0%
+is that there's some viscosity that
+actually prevents it causes there to be
+
+ align:start position:0%
+actually prevents it causes there to be
+ 
+
+ align:start position:0%
+actually prevents it causes there to be
+sort of a shearing force which causes
+
+ align:start position:0%
+sort of a shearing force which causes
+ 
+
+ align:start position:0%
+sort of a shearing force which causes
+the water to stick to your skin so a
+
+ align:start position:0%
+the water to stick to your skin so a
+ 
+
+ align:start position:0%
+the water to stick to your skin so a
+perfect fluid this has been described as
+
+ align:start position:0%
+perfect fluid this has been described as
+ 
+
+ align:start position:0%
+perfect fluid this has been described as
+the physics of dry water okay so it is
+
+ align:start position:0%
+the physics of dry water okay so it is
+ 
+
+ align:start position:0%
+the physics of dry water okay so it is
+anyone who's in an applied math will
+
+ align:start position:0%
+anyone who's in an applied math will
+ 
+
+ align:start position:0%
+anyone who's in an applied math will
+know they'll sort of roll their eyes and
+
+ align:start position:0%
+know they'll sort of roll their eyes and
+ 
+
+ align:start position:0%
+know they'll sort of roll their eyes and
+say okay fine we'll do this sort of
+
+ align:start position:0%
+say okay fine we'll do this sort of
+ 
+
+ align:start position:0%
+say okay fine we'll do this sort of
+infant version of fluid first and then a
+
+ align:start position:0%
+infant version of fluid first and then a
+ 
+
+ align:start position:0%
+infant version of fluid first and then a
+lot of the action and a lot of the fun
+
+ align:start position:0%
+lot of the action and a lot of the fun
+ 
+
+ align:start position:0%
+lot of the action and a lot of the fun
+comes from putting in viscosity and
+
+ align:start position:0%
+comes from putting in viscosity and
+ 
+
+ align:start position:0%
+comes from putting in viscosity and
+doing the real fluids for the purposes
+
+ align:start position:0%
+doing the real fluids for the purposes
+ 
+
+ align:start position:0%
+doing the real fluids for the purposes
+of our class what this boils down to is
+
+ align:start position:0%
+of our class what this boils down to is
+ 
+
+ align:start position:0%
+of our class what this boils down to is
+this tells me that the physics of this
+
+ align:start position:0%
+this tells me that the physics of this
+ 
+
+ align:start position:0%
+this tells me that the physics of this
+quantity is totally dominated by the
+
+ align:start position:0%
+quantity is totally dominated by the
+ 
+
+ align:start position:0%
+quantity is totally dominated by the
+fluids energy density and it's pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the pressure is an isotropic spatial
+
+ align:start position:0%
+the pressure is an isotropic spatial
+ 
+
+ align:start position:0%
+the pressure is an isotropic spatial
+stress so in this particular frame where
+
+ align:start position:0%
+stress so in this particular frame where
+ 
+
+ align:start position:0%
+stress so in this particular frame where
+I have no energy being transported
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the stress-energy tensor can be
+
+ align:start position:0%
+then the stress-energy tensor can be
+ 
+
+ align:start position:0%
+then the stress-energy tensor can be
+represented as energy density as usual
+
+ align:start position:0%
+represented as energy density as usual
+ 
+
+ align:start position:0%
+represented as energy density as usual
+up in the over there now up in the titi
+
+ align:start position:0%
+up in the over there now up in the titi
+ 
+
+ align:start position:0%
+up in the over there now up in the titi
+component there is no energy flux by
+
+ align:start position:0%
+component there is no energy flux by
+ 
+
+ align:start position:0%
+component there is no energy flux by
+symmetry if there's no energy flux there
+
+ align:start position:0%
+symmetry if there's no energy flux there
+ 
+
+ align:start position:0%
+symmetry if there's no energy flux there
+is no momentum density and my spatial
+
+ align:start position:0%
+is no momentum density and my spatial
+ 
+
+ align:start position:0%
+is no momentum density and my spatial
+stresses are totally isotropic and none
+
+ align:start position:0%
+stresses are totally isotropic and none
+ 
+
+ align:start position:0%
+stresses are totally isotropic and none
+of them are lateral so it just looks
+
+ align:start position:0%
+of them are lateral so it just looks
+ 
+
+ align:start position:0%
+of them are lateral so it just looks
+like this at the diagonal of Rho okay as
+
+ align:start position:0%
+like this at the diagonal of Rho okay as
+ 
+
+ align:start position:0%
+like this at the diagonal of Rho okay as
+I said this is actually something that
+
+ align:start position:0%
+I said this is actually something that
+ 
+
+ align:start position:0%
+I said this is actually something that
+we're gonna use over and over and over
+
+ align:start position:0%
+we're gonna use over and over and over
+ 
+
+ align:start position:0%
+we're gonna use over and over and over
+again this is actually eight and so you
+
+ align:start position:0%
+again this is actually eight and so you
+ 
+
+ align:start position:0%
+again this is actually eight and so you
+can actually consider my Duff stress
+
+ align:start position:0%
+can actually consider my Duff stress
+ 
+
+ align:start position:0%
+can actually consider my Duff stress
+energy tensor to be a perfect fluid with
+
+ align:start position:0%
+energy tensor to be a perfect fluid with
+ 
+
+ align:start position:0%
+energy tensor to be a perfect fluid with
+no pressure okay so this actually
+
+ align:start position:0%
+no pressure okay so this actually
+ 
+
+ align:start position:0%
+no pressure okay so this actually
+subsumes this this other one I will just
+
+ align:start position:0%
+subsumes this this other one I will just
+ 
+
+ align:start position:0%
+subsumes this this other one I will just
+for the lust rate of purposes I'll show
+
+ align:start position:0%
+for the lust rate of purposes I'll show
+ 
+
+ align:start position:0%
+for the lust rate of purposes I'll show
+an example of a case that cannot be
+
+ align:start position:0%
+an example of a case that cannot be
+ 
+
+ align:start position:0%
+an example of a case that cannot be
+thought of as a as a perfect fluid but
+
+ align:start position:0%
+thought of as a as a perfect fluid but
+ 
+
+ align:start position:0%
+thought of as a as a perfect fluid but
+we will tend to use this a lot in our
+
+ align:start position:0%
+we will tend to use this a lot in our
+ 
+
+ align:start position:0%
+we will tend to use this a lot in our
+class and as I will demonstrate in just
+
+ align:start position:0%
+class and as I will demonstrate in just
+ 
+
+ align:start position:0%
+class and as I will demonstrate in just
+a moment we're going to find that this
+
+ align:start position:0%
+a moment we're going to find that this
+ 
+
+ align:start position:0%
+a moment we're going to find that this
+ends up playing an important role in
+
+ align:start position:0%
+ends up playing an important role in
+ 
+
+ align:start position:0%
+ends up playing an important role in
+generating gravitational fields and
+
+ align:start position:0%
+generating gravitational fields and
+ 
+
+ align:start position:0%
+generating gravitational fields and
+what's interesting about this is you
+
+ align:start position:0%
+what's interesting about this is you
+ 
+
+ align:start position:0%
+what's interesting about this is you
+guys would probably use the idea that
+
+ align:start position:0%
+guys would probably use the idea that
+ 
+
+ align:start position:0%
+guys would probably use the idea that
+mass generates gravity and then throw in
+
+ align:start position:0%
+mass generates gravity and then throw in
+ 
+
+ align:start position:0%
+mass generates gravity and then throw in
+a c square that tells you energy is
+
+ align:start position:0%
+a c square that tells you energy is
+ 
+
+ align:start position:0%
+a c square that tells you energy is
+generating gravity that's also we're
+
+ align:start position:0%
+generating gravity that's also we're
+ 
+
+ align:start position:0%
+generating gravity that's also we're
+gonna see pressure generates gravity
+
+ align:start position:0%
+gonna see pressure generates gravity
+ 
+
+ align:start position:0%
+gonna see pressure generates gravity
+okay and it's connected to the
+
+ align:start position:0%
+okay and it's connected to the
+ 
+
+ align:start position:0%
+okay and it's connected to the
+mathematical structure of this guy here
+
+ align:start position:0%
+mathematical structure of this guy here
+ 
+
+ align:start position:0%
+mathematical structure of this guy here
+so notice I've written an equal dot here
+
+ align:start position:0%
+so notice I've written an equal dot here
+ 
+
+ align:start position:0%
+so notice I've written an equal dot here
+okay so this is just the way this is
+
+ align:start position:0%
+okay so this is just the way this is
+ 
+
+ align:start position:0%
+okay so this is just the way this is
+represented in this particular frame I
+
+ align:start position:0%
+represented in this particular frame I
+ 
+
+ align:start position:0%
+represented in this particular frame I
+would like to write this in a more
+
+ align:start position:0%
+would like to write this in a more
+ 
+
+ align:start position:0%
+would like to write this in a more
+covariant form something that does not
+
+ align:start position:0%
+covariant form something that does not
+ 
+
+ align:start position:0%
+covariant form something that does not
+rely on me going into a particular frame
+
+ align:start position:0%
+rely on me going into a particular frame
+ 
+
+ align:start position:0%
+rely on me going into a particular frame
+of reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the trick which I'm going to use for
+
+ align:start position:0%
+so the trick which I'm going to use for
+ 
+
+ align:start position:0%
+so the trick which I'm going to use for
+this is that I think about that form
+
+ align:start position:0%
+this is that I think about that form
+ 
+
+ align:start position:0%
+this is that I think about that form
+there so the row piece of it clearly
+
+ align:start position:0%
+there so the row piece of it clearly
+ 
+
+ align:start position:0%
+there so the row piece of it clearly
+what I'm doing there is I'm picking out
+
+ align:start position:0%
+what I'm doing there is I'm picking out
+ 
+
+ align:start position:0%
+what I'm doing there is I'm picking out
+you know that is can be thought of as
+
+ align:start position:0%
+you know that is can be thought of as
+ 
+
+ align:start position:0%
+you know that is can be thought of as
+the energy density multiplied by the
+
+ align:start position:0%
+the energy density multiplied by the
+ 
+
+ align:start position:0%
+the energy density multiplied by the
+tensor product of the four velocity it
+
+ align:start position:0%
+tensor product of the four velocity it
+ 
+
+ align:start position:0%
+tensor product of the four velocity it
+describes a particular element of this
+
+ align:start position:0%
+describes a particular element of this
+ 
+
+ align:start position:0%
+describes a particular element of this
+fluid so I can write again using this
+
+ align:start position:0%
+fluid so I can write again using this
+ 
+
+ align:start position:0%
+fluid so I can write again using this
+sort of abstract notation this piece of
+
+ align:start position:0%
+sort of abstract notation this piece of
+ 
+
+ align:start position:0%
+sort of abstract notation this piece of
+it looks like this okay and so if I go
+
+ align:start position:0%
+it looks like this okay and so if I go
+ 
+
+ align:start position:0%
+it looks like this okay and so if I go
+into the frame if I go into the rest
+
+ align:start position:0%
+into the frame if I go into the rest
+ 
+
+ align:start position:0%
+into the frame if I go into the rest
+frame of the fluid that's just you know
+
+ align:start position:0%
+frame of the fluid that's just you know
+ 
+
+ align:start position:0%
+frame of the fluid that's just you know
+my U is one and zeros and the spatial
+
+ align:start position:0%
+my U is one and zeros and the spatial
+ 
+
+ align:start position:0%
+my U is one and zeros and the spatial
+components that builds my upper
+
+ align:start position:0%
+components that builds my upper
+ 
+
+ align:start position:0%
+components that builds my upper
+left-hand corner of this tensor how do I
+
+ align:start position:0%
+left-hand corner of this tensor how do I
+ 
+
+ align:start position:0%
+left-hand corner of this tensor how do I
+get the rest of this well to get the
+
+ align:start position:0%
+get the rest of this well to get the
+ 
+
+ align:start position:0%
+get the rest of this well to get the
+rest of it these are all sort of picked
+
+ align:start position:0%
+rest of it these are all sort of picked
+ 
+
+ align:start position:0%
+rest of it these are all sort of picked
+out of compliant to the tensors that are
+
+ align:start position:0%
+out of compliant to the tensors that are
+ 
+
+ align:start position:0%
+out of compliant to the tensors that are
+orthogonal to you and I put an Easter
+
+ align:start position:0%
+orthogonal to you and I put an Easter
+ 
+
+ align:start position:0%
+orthogonal to you and I put an Easter
+egg and pset1
+
+ align:start position:0%
+egg and pset1
+ 
+
+ align:start position:0%
+egg and pset1
+okay you guys developed a tensor that
+
+ align:start position:0%
+okay you guys developed a tensor that
+ 
+
+ align:start position:0%
+okay you guys developed a tensor that
+allows me to build it's a geometric
+
+ align:start position:0%
+allows me to build it's a geometric
+ 
+
+ align:start position:0%
+allows me to build it's a geometric
+object that allows me to describe things
+
+ align:start position:0%
+object that allows me to describe things
+ 
+
+ align:start position:0%
+object that allows me to describe things
+that are orthogonal to a given floor
+
+ align:start position:0%
+that are orthogonal to a given floor
+ 
+
+ align:start position:0%
+that are orthogonal to a given floor
+vector so if I take the projection
+
+ align:start position:0%
+vector so if I take the projection
+ 
+
+ align:start position:0%
+vector so if I take the projection
+tensor that you guys built on pset 1
+
+ align:start position:0%
+tensor that you guys built on pset 1
+ 
+
+ align:start position:0%
+tensor that you guys built on pset 1
+which looks like the metric plus the
+
+ align:start position:0%
+which looks like the metric plus the
+ 
+
+ align:start position:0%
+which looks like the metric plus the
+extra the out the tensor product of a
+
+ align:start position:0%
+extra the out the tensor product of a
+ 
+
+ align:start position:0%
+extra the out the tensor product of a
+four vector with itself that gives me
+
+ align:start position:0%
+four vector with itself that gives me
+ 
+
+ align:start position:0%
+four vector with itself that gives me
+the peas that go into that component
+
+ align:start position:0%
+the peas that go into that component
+ 
+
+ align:start position:0%
+the peas that go into that component
+okay or if I write this in index
+
+ align:start position:0%
+okay or if I write this in index
+ 
+
+ align:start position:0%
+okay or if I write this in index
+notation I can do it in two ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will also emphasize that there are a
+
+ align:start position:0%
+I will also emphasize that there are a
+ 
+
+ align:start position:0%
+I will also emphasize that there are a
+few moments in this class where I sort
+
+ align:start position:0%
+few moments in this class where I sort
+ 
+
+ align:start position:0%
+few moments in this class where I sort
+of urge you to take the sort of long
+
+ align:start position:0%
+of urge you to take the sort of long
+ 
+
+ align:start position:0%
+of urge you to take the sort of long
+term memory synapses and switch them on
+
+ align:start position:0%
+term memory synapses and switch them on
+ 
+
+ align:start position:0%
+term memory synapses and switch them on
+this is one of those moments in a couple
+
+ align:start position:0%
+this is one of those moments in a couple
+ 
+
+ align:start position:0%
+this is one of those moments in a couple
+of lectures we're gonna introduce the
+
+ align:start position:0%
+of lectures we're gonna introduce the
+ 
+
+ align:start position:0%
+of lectures we're gonna introduce the
+principle of equivalence which is the
+
+ align:start position:0%
+principle of equivalence which is the
+ 
+
+ align:start position:0%
+principle of equivalence which is the
+physical principle by which we're going
+
+ align:start position:0%
+physical principle by which we're going
+ 
+
+ align:start position:0%
+physical principle by which we're going
+to argue how we go from formulas that
+
+ align:start position:0%
+to argue how we go from formulas that
+ 
+
+ align:start position:0%
+to argue how we go from formulas that
+work in special relativity to formulas
+
+ align:start position:0%
+work in special relativity to formulas
+ 
+
+ align:start position:0%
+work in special relativity to formulas
+that work in general relativity and by
+
+ align:start position:0%
+that work in general relativity and by
+ 
+
+ align:start position:0%
+that work in general relativity and by
+invoking the principle of equivalence
+
+ align:start position:0%
+invoking the principle of equivalence
+ 
+
+ align:start position:0%
+invoking the principle of equivalence
+we're going to see that when we want to
+
+ align:start position:0%
+we're going to see that when we want to
+ 
+
+ align:start position:0%
+we're going to see that when we want to
+describe perfect fluids in a general
+
+ align:start position:0%
+describe perfect fluids in a general
+ 
+
+ align:start position:0%
+describe perfect fluids in a general
+space-time not just in special
+
+ align:start position:0%
+space-time not just in special
+ 
+
+ align:start position:0%
+space-time not just in special
+relativity of in general and general
+
+ align:start position:0%
+relativity of in general and general
+ 
+
+ align:start position:0%
+relativity of in general and general
+relativity it's exactly this formula I
+
+ align:start position:0%
+relativity it's exactly this formula I
+ 
+
+ align:start position:0%
+relativity it's exactly this formula I
+just need to modify what the metric
+
+ align:start position:0%
+just need to modify what the metric
+ 
+
+ align:start position:0%
+just need to modify what the metric
+means okay but that will allow me to
+
+ align:start position:0%
+means okay but that will allow me to
+ 
+
+ align:start position:0%
+means okay but that will allow me to
+carry that over ah let me see
+
+ align:start position:0%
+carry that over ah let me see
+ 
+
+ align:start position:0%
+carry that over ah let me see
+so my notes are a little bit
+
+ align:start position:0%
+so my notes are a little bit
+ 
+
+ align:start position:0%
+so my notes are a little bit
+disorganized here this is a piece that I
+
+ align:start position:0%
+disorganized here this is a piece that I
+ 
+
+ align:start position:0%
+disorganized here this is a piece that I
+every year I want to clean this bit up
+
+ align:start position:0%
+every year I want to clean this bit up
+ 
+
+ align:start position:0%
+every year I want to clean this bit up
+and every year at this time of year I
+
+ align:start position:0%
+and every year at this time of year I
+ 
+
+ align:start position:0%
+and every year at this time of year I
+have 70 gazillion administrative tasks
+
+ align:start position:0%
+have 70 gazillion administrative tasks
+ 
+
+ align:start position:0%
+have 70 gazillion administrative tasks
+and getting behind schedule so I will
+
+ align:start position:0%
+and getting behind schedule so I will
+ 
+
+ align:start position:0%
+and getting behind schedule so I will
+clean this up on the fly so there's a
+
+ align:start position:0%
+clean this up on the fly so there's a
+ 
+
+ align:start position:0%
+clean this up on the fly so there's a
+couple points which I want to make about
+
+ align:start position:0%
+couple points which I want to make about
+ 
+
+ align:start position:0%
+couple points which I want to make about
+this let me do this point first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by virtue of taking a graduate
+
+ align:start position:0%
+so by virtue of taking a graduate
+ 
+
+ align:start position:0%
+so by virtue of taking a graduate
+physics class I'm confident you guys
+
+ align:start position:0%
+physics class I'm confident you guys
+ 
+
+ align:start position:0%
+physics class I'm confident you guys
+know about Newtonian gravity one can
+
+ align:start position:0%
+know about Newtonian gravity one can
+ 
+
+ align:start position:0%
+know about Newtonian gravity one can
+write the field equation for Newtonian
+
+ align:start position:0%
+write the field equation for Newtonian
+ 
+
+ align:start position:0%
+write the field equation for Newtonian
+gravity as essentially a differential
+
+ align:start position:0%
+gravity as essentially a differential
+ 
+
+ align:start position:0%
+gravity as essentially a differential
+equation for the potential that governs
+
+ align:start position:0%
+equation for the potential that governs
+ 
+
+ align:start position:0%
+equation for the potential that governs
+Newtonian gravitational interaction so
+
+ align:start position:0%
+Newtonian gravitational interaction so
+ 
+
+ align:start position:0%
+Newtonian gravitational interaction so
+it's called Phi sub G the Newtonian
+
+ align:start position:0%
+it's called Phi sub G the Newtonian
+ 
+
+ align:start position:0%
+it's called Phi sub G the Newtonian
+gravitational interaction oops and I can
+
+ align:start position:0%
+gravitational interaction oops and I can
+ 
+
+ align:start position:0%
+gravitational interaction oops and I can
+write a field equation that's governing
+
+ align:start position:0%
+write a field equation that's governing
+ 
+
+ align:start position:0%
+write a field equation that's governing
+it as essentially it's poissons equation
+
+ align:start position:0%
+it as essentially it's poissons equation
+ 
+
+ align:start position:0%
+it as essentially it's poissons equation
+okay so the Laplace operator acting on
+
+ align:start position:0%
+okay so the Laplace operator acting on
+ 
+
+ align:start position:0%
+okay so the Laplace operator acting on
+that potential is up to a constant equal
+
+ align:start position:0%
+that potential is up to a constant equal
+ 
+
+ align:start position:0%
+that potential is up to a constant equal
+to Z we usually learn it in terms of
+
+ align:start position:0%
+to Z we usually learn it in terms of
+ 
+
+ align:start position:0%
+to Z we usually learn it in terms of
+mass density we're working in units
+
+ align:start position:0%
+mass density we're working in units
+ 
+
+ align:start position:0%
+mass density we're working in units
+where the speed of light is equal to 1
+
+ align:start position:0%
+where the speed of light is equal to 1
+ 
+
+ align:start position:0%
+where the speed of light is equal to 1
+so it could just as well be the energy
+
+ align:start position:0%
+so it could just as well be the energy
+ 
+
+ align:start position:0%
+so it could just as well be the energy
+density so you've all kind of seen that
+
+ align:start position:0%
+density so you've all kind of seen that
+ 
+
+ align:start position:0%
+density so you've all kind of seen that
+now if we think about how we're going to
+
+ align:start position:0%
+now if we think about how we're going to
+ 
+
+ align:start position:0%
+now if we think about how we're going to
+carry this forward and make gravity a
+
+ align:start position:0%
+carry this forward and make gravity a
+ 
+
+ align:start position:0%
+carry this forward and make gravity a
+relativistic interaction this equation
+
+ align:start position:0%
+relativistic interaction this equation
+ 
+
+ align:start position:0%
+relativistic interaction this equation
+should right away make us suspicious
+
+ align:start position:0%
+should right away make us suspicious
+ 
+
+ align:start position:0%
+should right away make us suspicious
+because we spent several minutes earlier
+
+ align:start position:0%
+because we spent several minutes earlier
+ 
+
+ align:start position:0%
+because we spent several minutes earlier
+today talking about the fact that this
+
+ align:start position:0%
+today talking about the fact that this
+ 
+
+ align:start position:0%
+today talking about the fact that this
+is not a scalar okay this is a component
+
+ align:start position:0%
+is not a scalar okay this is a component
+ 
+
+ align:start position:0%
+is not a scalar okay this is a component
+of a tensor okay a physical theory which
+
+ align:start position:0%
+of a tensor okay a physical theory which
+ 
+
+ align:start position:0%
+of a tensor okay a physical theory which
+tries to pick out just one component of
+
+ align:start position:0%
+tries to pick out just one component of
+ 
+
+ align:start position:0%
+tries to pick out just one component of
+a geometric tensor is not a healthy
+
+ align:start position:0%
+a geometric tensor is not a healthy
+ 
+
+ align:start position:0%
+a geometric tensor is not a healthy
+theory ok it would be like if you had
+
+ align:start position:0%
+theory ok it would be like if you had
+ 
+
+ align:start position:0%
+theory ok it would be like if you had
+sort of learned in enm that you know
+
+ align:start position:0%
+sort of learned in enm that you know
+ 
+
+ align:start position:0%
+sort of learned in enm that you know
+there was a preferred direction the
+
+ align:start position:0%
+there was a preferred direction the
+ 
+
+ align:start position:0%
+there was a preferred direction the
+electric field you know if there's a
+
+ align:start position:0%
+electric field you know if there's a
+ 
+
+ align:start position:0%
+electric field you know if there's a
+particular set of Maxwell's equations
+
+ align:start position:0%
+particular set of Maxwell's equations
+ 
+
+ align:start position:0%
+particular set of Maxwell's equations
+for e^x and the difference then of
+
+ align:start position:0%
+for e^x and the difference then of
+ 
+
+ align:start position:0%
+for e^x and the difference then of
+Maxwell's equations for y Y that would
+
+ align:start position:0%
+Maxwell's equations for y Y that would
+ 
+
+ align:start position:0%
+Maxwell's equations for y Y that would
+just be nonsense
+
+ align:start position:0%
+just be nonsense
+ 
+
+ align:start position:0%
+just be nonsense
+ok nature doesn't pick out spatial
+
+ align:start position:0%
+ok nature doesn't pick out spatial
+ 
+
+ align:start position:0%
+ok nature doesn't pick out spatial
+components of anyone's being
+
+ align:start position:0%
+components of anyone's being
+ 
+
+ align:start position:0%
+components of anyone's being
+particularly uh having some weight over
+
+ align:start position:0%
+particularly uh having some weight over
+ 
+
+ align:start position:0%
+particularly uh having some weight over
+the others and the same thing holds in
+
+ align:start position:0%
+the others and the same thing holds in
+ 
+
+ align:start position:0%
+the others and the same thing holds in
+relativity for space-time so when we
+
+ align:start position:0%
+relativity for space-time so when we
+ 
+
+ align:start position:0%
+relativity for space-time so when we
+make this into a relativistic theory
+
+ align:start position:0%
+make this into a relativistic theory
+ 
+
+ align:start position:0%
+make this into a relativistic theory
+we're gonna say ah
+
+ align:start position:0%
+we're gonna say ah
+ 
+
+ align:start position:0%
+we're gonna say ah
+if this component of a tensor plays a
+
+ align:start position:0%
+if this component of a tensor plays a
+ 
+
+ align:start position:0%
+if this component of a tensor plays a
+large role in gravity to make this into
+
+ align:start position:0%
+large role in gravity to make this into
+ 
+
+ align:start position:0%
+large role in gravity to make this into
+a geometric object that makes a large
+
+ align:start position:0%
+a geometric object that makes a large
+ 
+
+ align:start position:0%
+a geometric object that makes a large
+role in gravity I'm going to have to so
+
+ align:start position:0%
+role in gravity I'm going to have to so
+ 
+
+ align:start position:0%
+role in gravity I'm going to have to so
+let's call this my Newtonian equation my
+
+ align:start position:0%
+let's call this my Newtonian equation my
+ 
+
+ align:start position:0%
+let's call this my Newtonian equation my
+Einstein in equation I'm going to put an
+
+ align:start position:0%
+Einstein in equation I'm going to put an
+ 
+
+ align:start position:0%
+Einstein in equation I'm going to put an
+equal sign in quotes here because
+
+ align:start position:0%
+equal sign in quotes here because
+ 
+
+ align:start position:0%
+equal sign in quotes here because
+there's a lot of details to fill in but
+
+ align:start position:0%
+there's a lot of details to fill in but
+ 
+
+ align:start position:0%
+there's a lot of details to fill in but
+what's going to go on the right-hand
+
+ align:start position:0%
+what's going to go on the right-hand
+ 
+
+ align:start position:0%
+what's going to go on the right-hand
+side of this has to be something that
+
+ align:start position:0%
+side of this has to be something that
+ 
+
+ align:start position:0%
+side of this has to be something that
+involves the stress energy tensor okay
+
+ align:start position:0%
+involves the stress energy tensor okay
+ 
+
+ align:start position:0%
+involves the stress energy tensor okay
+Newton picks out one component of stress
+
+ align:start position:0%
+Newton picks out one component of stress
+ 
+
+ align:start position:0%
+Newton picks out one component of stress
+energy tensor relativity doesn't let me
+
+ align:start position:0%
+energy tensor relativity doesn't let me
+ 
+
+ align:start position:0%
+energy tensor relativity doesn't let me
+pick out particular components so
+
+ align:start position:0%
+pick out particular components so
+ 
+
+ align:start position:0%
+pick out particular components so
+whatever I get when I do Einstein's
+
+ align:start position:0%
+whatever I get when I do Einstein's
+ 
+
+ align:start position:0%
+whatever I get when I do Einstein's
+gravity if the whole stress energy
+
+ align:start position:0%
+gravity if the whole stress energy
+ 
+
+ align:start position:0%
+gravity if the whole stress energy
+tensor is gonna be important in setting
+
+ align:start position:0%
+tensor is gonna be important in setting
+ 
+
+ align:start position:0%
+tensor is gonna be important in setting
+the source of my gravity that then sort
+
+ align:start position:0%
+the source of my gravity that then sort
+ 
+
+ align:start position:0%
+the source of my gravity that then sort
+of says well then what the heck do you
+
+ align:start position:0%
+of says well then what the heck do you
+ 
+
+ align:start position:0%
+of says well then what the heck do you
+do with this left hand side that is in
+
+ align:start position:0%
+do with this left hand side that is in
+ 
+
+ align:start position:0%
+do with this left hand side that is in
+fact going to be starting probably on
+
+ align:start position:0%
+fact going to be starting probably on
+ 
+
+ align:start position:0%
+fact going to be starting probably on
+Tuesday the subject of the next couple
+
+ align:start position:0%
+Tuesday the subject of the next couple
+ 
+
+ align:start position:0%
+Tuesday the subject of the next couple
+of lectures basically going all the way
+
+ align:start position:0%
+of lectures basically going all the way
+ 
+
+ align:start position:0%
+of lectures basically going all the way
+up to spring break okay the week before
+
+ align:start position:0%
+up to spring break okay the week before
+ 
+
+ align:start position:0%
+up to spring break okay the week before
+spring break is when we complete the
+
+ align:start position:0%
+spring break is when we complete the
+ 
+
+ align:start position:0%
+spring break is when we complete the
+story of what goes on the right-hand
+
+ align:start position:0%
+story of what goes on the right-hand
+ 
+
+ align:start position:0%
+story of what goes on the right-hand
+side see me the left-hand side of this
+
+ align:start position:0%
+side see me the left-hand side of this
+ 
+
+ align:start position:0%
+side see me the left-hand side of this
+equation but what I will tell you is
+
+ align:start position:0%
+equation but what I will tell you is
+ 
+
+ align:start position:0%
+equation but what I will tell you is
+that it is indeed going to involve two
+
+ align:start position:0%
+that it is indeed going to involve two
+ 
+
+ align:start position:0%
+that it is indeed going to involve two
+derivatives of a potential like object
+
+ align:start position:0%
+derivatives of a potential like object
+ 
+
+ align:start position:0%
+derivatives of a potential like object
+in the potential like object is that
+
+ align:start position:0%
+in the potential like object is that
+ 
+
+ align:start position:0%
+in the potential like object is that
+you're gonna turn out to be the metric
+
+ align:start position:0%
+you're gonna turn out to be the metric
+ 
+
+ align:start position:0%
+you're gonna turn out to be the metric
+of space-time okay so that's kind of
+
+ align:start position:0%
+of space-time okay so that's kind of
+ 
+
+ align:start position:0%
+of space-time okay so that's kind of
+where we're going with this all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do a little bit more physics with
+
+ align:start position:0%
+let's do a little bit more physics with
+ 
+
+ align:start position:0%
+let's do a little bit more physics with
+the stress energy tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm I have somewhat more detailed
+
+ align:start position:0%
+so I'm I have somewhat more detailed
+ 
+
+ align:start position:0%
+so I'm I have somewhat more detailed
+notes which I will post online which I
+
+ align:start position:0%
+notes which I will post online which I
+ 
+
+ align:start position:0%
+notes which I will post online which I
+am NOT going to go through in great
+
+ align:start position:0%
+am NOT going to go through in great
+ 
+
+ align:start position:0%
+am NOT going to go through in great
+detail here but I'm gonna kind of sketch
+
+ align:start position:0%
+detail here but I'm gonna kind of sketch
+ 
+
+ align:start position:0%
+detail here but I'm gonna kind of sketch
+this so one is that I would like to
+
+ align:start position:0%
+this so one is that I would like to
+ 
+
+ align:start position:0%
+this so one is that I would like to
+prove again that word is a little bit of
+
+ align:start position:0%
+prove again that word is a little bit of
+ 
+
+ align:start position:0%
+prove again that word is a little bit of
+an overstatement but at least motivate
+
+ align:start position:0%
+an overstatement but at least motivate
+ 
+
+ align:start position:0%
+an overstatement but at least motivate
+the symmetry of this tensor okay I'm
+
+ align:start position:0%
+the symmetry of this tensor okay I'm
+ 
+
+ align:start position:0%
+the symmetry of this tensor okay I'm
+just gonna focus on the spatial bits of
+
+ align:start position:0%
+just gonna focus on the spatial bits of
+ 
+
+ align:start position:0%
+just gonna focus on the spatial bits of
+this that'll be enough okay like I said
+
+ align:start position:0%
+this that'll be enough okay like I said
+ 
+
+ align:start position:0%
+this that'll be enough okay like I said
+you can kind of see that T 0 I and ti0
+
+ align:start position:0%
+you can kind of see that T 0 I and ti0
+ 
+
+ align:start position:0%
+you can kind of see that T 0 I and ti0
+are the same thing by thinking about the
+
+ align:start position:0%
+are the same thing by thinking about the
+ 
+
+ align:start position:0%
+are the same thing by thinking about the
+physical meaning of for momentum and
+
+ align:start position:0%
+physical meaning of for momentum and
+ 
+
+ align:start position:0%
+physical meaning of for momentum and
+what a flux of for momentum is this one
+
+ align:start position:0%
+what a flux of for momentum is this one
+ 
+
+ align:start position:0%
+what a flux of for momentum is this one
+there's kind of a cute calculation you
+
+ align:start position:0%
+there's kind of a cute calculation you
+ 
+
+ align:start position:0%
+there's kind of a cute calculation you
+can do so imagine you have some little
+
+ align:start position:0%
+can do so imagine you have some little
+ 
+
+ align:start position:0%
+can do so imagine you have some little
+cube of stuff could be immersed in some
+
+ align:start position:0%
+cube of stuff could be immersed in some
+ 
+
+ align:start position:0%
+cube of stuff could be immersed in some
+field or fluid something that is
+
+ align:start position:0%
+field or fluid something that is
+ 
+
+ align:start position:0%
+field or fluid something that is
+described by a field of stress energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so to start out with let's look at
+
+ align:start position:0%
+and so to start out with let's look at
+ 
+
+ align:start position:0%
+and so to start out with let's look at
+how the flux of member with T alpha beta
+
+ align:start position:0%
+how the flux of member with T alpha beta
+ 
+
+ align:start position:0%
+how the flux of member with T alpha beta
+are really T IJ tells me about is the
+
+ align:start position:0%
+are really T IJ tells me about is the
+ 
+
+ align:start position:0%
+are really T IJ tells me about is the
+flux of momentum in a particular
+
+ align:start position:0%
+flux of momentum in a particular
+ 
+
+ align:start position:0%
+flux of momentum in a particular
+direction it's tell me about the amount
+
+ align:start position:0%
+direction it's tell me about the amount
+ 
+
+ align:start position:0%
+direction it's tell me about the amount
+of momentum going into this box on one
+
+ align:start position:0%
+of momentum going into this box on one
+ 
+
+ align:start position:0%
+of momentum going into this box on one
+side and coming out on the other okay so
+
+ align:start position:0%
+side and coming out on the other okay so
+ 
+
+ align:start position:0%
+side and coming out on the other okay so
+I'm going to look at the momentum flux
+
+ align:start position:0%
+I'm going to look at the momentum flux
+ 
+
+ align:start position:0%
+I'm going to look at the momentum flux
+into and out of this box
+
+ align:start position:0%
+into and out of this box
+ 
+
+ align:start position:0%
+into and out of this box
+and so what I'm going to do is let's
+
+ align:start position:0%
+and so what I'm going to do is let's
+ 
+
+ align:start position:0%
+and so what I'm going to do is let's
+look at the momentum going into the
+
+ align:start position:0%
+look at the momentum going into the
+ 
+
+ align:start position:0%
+look at the momentum going into the
+sides that are so let's call this the
+
+ align:start position:0%
+sides that are so let's call this the
+ 
+
+ align:start position:0%
+sides that are so let's call this the
+top and the bottom here what I'm going
+
+ align:start position:0%
+top and the bottom here what I'm going
+ 
+
+ align:start position:0%
+top and the bottom here what I'm going
+to do then is number the four sides the
+
+ align:start position:0%
+to do then is number the four sides the
+ 
+
+ align:start position:0%
+to do then is number the four sides the
+other four side of the box not the top
+
+ align:start position:0%
+other four side of the box not the top
+ 
+
+ align:start position:0%
+other four side of the box not the top
+and the bottom so let's call this side
+
+ align:start position:0%
+and the bottom so let's call this side
+ 
+
+ align:start position:0%
+and the bottom so let's call this side
+which is sort of facing away from us
+
+ align:start position:0%
+which is sort of facing away from us
+ 
+
+ align:start position:0%
+which is sort of facing away from us
+here that side one the one that is
+
+ align:start position:0%
+here that side one the one that is
+ 
+
+ align:start position:0%
+here that side one the one that is
+facing us that sort of points out in the
+
+ align:start position:0%
+facing us that sort of points out in the
+ 
+
+ align:start position:0%
+facing us that sort of points out in the
+X direction I'll call that two this side
+
+ align:start position:0%
+X direction I'll call that two this side
+ 
+
+ align:start position:0%
+X direction I'll call that two this side
+here I will call three and the one that
+
+ align:start position:0%
+here I will call three and the one that
+ 
+
+ align:start position:0%
+here I will call three and the one that
+is on the back I will call for apologies
+
+ align:start position:0%
+is on the back I will call for apologies
+ 
+
+ align:start position:0%
+is on the back I will call for apologies
+for the little bit of a a busy picture
+
+ align:start position:0%
+for the little bit of a a busy picture
+ 
+
+ align:start position:0%
+for the little bit of a a busy picture
+here but just what you want to do is
+
+ align:start position:0%
+here but just what you want to do is
+ 
+
+ align:start position:0%
+here but just what you want to do is
+there the matting of this cube in front
+
+ align:start position:0%
+there the matting of this cube in front
+ 
+
+ align:start position:0%
+there the matting of this cube in front
+of you and you go around and label the
+
+ align:start position:0%
+of you and you go around and label the
+ 
+
+ align:start position:0%
+of you and you go around and label the
+four sides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we'd like to do is calculate what
+
+ align:start position:0%
+what we'd like to do is calculate what
+ 
+
+ align:start position:0%
+what we'd like to do is calculate what
+is the force that is flowing through
+
+ align:start position:0%
+is the force that is flowing through
+ 
+
+ align:start position:0%
+is the force that is flowing through
+each of these four sides okay one two
+
+ align:start position:0%
+each of these four sides okay one two
+ 
+
+ align:start position:0%
+each of these four sides okay one two
+three and four let's ignore the top and
+
+ align:start position:0%
+three and four let's ignore the top and
+ 
+
+ align:start position:0%
+three and four let's ignore the top and
+the bottom for just a second
+
+ align:start position:0%
+the bottom for just a second
+ 
+
+ align:start position:0%
+the bottom for just a second
+I'll describe why that is in just a
+
+ align:start position:0%
+I'll describe why that is in just a
+ 
+
+ align:start position:0%
+I'll describe why that is in just a
+moment so if I look at the force on face
+
+ align:start position:0%
+moment so if I look at the force on face
+ 
+
+ align:start position:0%
+moment so if I look at the force on face
+one okay
+
+ align:start position:0%
+one okay
+ 
+
+ align:start position:0%
+one okay
+well face one is pardon me I mislabeled
+
+ align:start position:0%
+well face one is pardon me I mislabeled
+ 
+
+ align:start position:0%
+well face one is pardon me I mislabeled
+my sides I want to be synced up with my
+
+ align:start position:0%
+my sides I want to be synced up with my
+ 
+
+ align:start position:0%
+my sides I want to be synced up with my
+notes and so I realized it's annoying
+
+ align:start position:0%
+notes and so I realized it's annoying
+ 
+
+ align:start position:0%
+notes and so I realized it's annoying
+and I'm very sorry about that but if I
+
+ align:start position:0%
+and I'm very sorry about that but if I
+ 
+
+ align:start position:0%
+and I'm very sorry about that but if I
+mess this up I will get out of sync with
+
+ align:start position:0%
+mess this up I will get out of sync with
+ 
+
+ align:start position:0%
+mess this up I will get out of sync with
+what I have written down so the one that
+
+ align:start position:0%
+what I have written down so the one that
+ 
+
+ align:start position:0%
+what I have written down so the one that
+is facing us is side one two is on the
+
+ align:start position:0%
+is facing us is side one two is on the
+ 
+
+ align:start position:0%
+is facing us is side one two is on the
+right-hand side three is the back four
+
+ align:start position:0%
+right-hand side three is the back four
+ 
+
+ align:start position:0%
+right-hand side three is the back four
+is on the left-hand side my apologies
+
+ align:start position:0%
+is on the left-hand side my apologies
+ 
+
+ align:start position:0%
+is on the left-hand side my apologies
+for that but I think it's important we
+
+ align:start position:0%
+for that but I think it's important we
+ 
+
+ align:start position:0%
+for that but I think it's important we
+get that right so I don't get out of
+
+ align:start position:0%
+get that right so I don't get out of
+ 
+
+ align:start position:0%
+get that right so I don't get out of
+synch with myself so the total force on
+
+ align:start position:0%
+synch with myself so the total force on
+ 
+
+ align:start position:0%
+synch with myself so the total force on
+face one is what I get by basically
+
+ align:start position:0%
+face one is what I get by basically
+ 
+
+ align:start position:0%
+face one is what I get by basically
+adding up all the flux of momentum
+
+ align:start position:0%
+adding up all the flux of momentum
+ 
+
+ align:start position:0%
+adding up all the flux of momentum
+flowing through face one so force on
+
+ align:start position:0%
+flowing through face one so force on
+ 
+
+ align:start position:0%
+flowing through face one so force on
+face one that is the ithe component of
+
+ align:start position:0%
+face one that is the ithe component of
+ 
+
+ align:start position:0%
+face one that is the ithe component of
+that is what I get when I integrate that
+
+ align:start position:0%
+that is what I get when I integrate that
+ 
+
+ align:start position:0%
+that is what I get when I integrate that
+over face one which is normal to the
+
+ align:start position:0%
+over face one which is normal to the
+ 
+
+ align:start position:0%
+over face one which is normal to the
+x-axis each side of the cube is little L
+
+ align:start position:0%
+x-axis each side of the cube is little L
+ 
+
+ align:start position:0%
+x-axis each side of the cube is little L
+so it's t IX l squared okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force on face - okay now this is the one
+
+ align:start position:0%
+force on face - okay now this is the one
+ 
+
+ align:start position:0%
+force on face - okay now this is the one
+that is normal to the y-axis and so this
+
+ align:start position:0%
+that is normal to the y-axis and so this
+ 
+
+ align:start position:0%
+that is normal to the y-axis and so this
+guy looks like t iy l l squared okay and
+
+ align:start position:0%
+guy looks like t iy l l squared okay and
+ 
+
+ align:start position:0%
+guy looks like t iy l l squared okay and
+if you continue this f3 you look at that
+
+ align:start position:0%
+if you continue this f3 you look at that
+ 
+
+ align:start position:0%
+if you continue this f3 you look at that
+and you know if you assume that this
+
+ align:start position:0%
+and you know if you assume that this
+ 
+
+ align:start position:0%
+and you know if you assume that this
+thing is small it's approximately the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same as the force on f1 it'll become
+
+ align:start position:0%
+same as the force on f1 it'll become
+ 
+
+ align:start position:0%
+same as the force on f1 it'll become
+equal in the limit of the cube becoming
+
+ align:start position:0%
+equal in the limit of the cube becoming
+ 
+
+ align:start position:0%
+equal in the limit of the cube becoming
+infinitesimally small and this is
+
+ align:start position:0%
+infinitesimally small and this is
+ 
+
+ align:start position:0%
+infinitesimally small and this is
+approximately the same as the force on
+
+ align:start position:0%
+approximately the same as the force on
+ 
+
+ align:start position:0%
+approximately the same as the force on
+Phase two
+
+ align:start position:0%
+Phase two
+ 
+
+ align:start position:0%
+Phase two
+so that tells us that there's no
+
+ align:start position:0%
+so that tells us that there's no
+ 
+
+ align:start position:0%
+so that tells us that there's no
+unbalanced force on this thing which is
+
+ align:start position:0%
+unbalanced force on this thing which is
+ 
+
+ align:start position:0%
+unbalanced force on this thing which is
+great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically it means that you know there's
+
+ align:start position:0%
+basically it means that you know there's
+ 
+
+ align:start position:0%
+basically it means that you know there's
+no unbalanced force causing this little
+
+ align:start position:0%
+no unbalanced force causing this little
+ 
+
+ align:start position:0%
+no unbalanced force causing this little
+element to accelerate away one of the
+
+ align:start position:0%
+element to accelerate away one of the
+ 
+
+ align:start position:0%
+element to accelerate away one of the
+reasons why I am focusing on these four
+
+ align:start position:0%
+reasons why I am focusing on these four
+ 
+
+ align:start position:0%
+reasons why I am focusing on these four
+sides though is I would also like to
+
+ align:start position:0%
+sides though is I would also like to
+ 
+
+ align:start position:0%
+sides though is I would also like to
+consider torques that are acting on this
+
+ align:start position:0%
+consider torques that are acting on this
+ 
+
+ align:start position:0%
+consider torques that are acting on this
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's where I'm gonna skip over a
+
+ align:start position:0%
+and here's where I'm gonna skip over a
+ 
+
+ align:start position:0%
+and here's where I'm gonna skip over a
+couple of details and just leave a few
+
+ align:start position:0%
+couple of details and just leave a few
+ 
+
+ align:start position:0%
+couple of details and just leave a few
+notes for you guys to look X we're a
+
+ align:start position:0%
+notes for you guys to look X we're a
+ 
+
+ align:start position:0%
+notes for you guys to look X we're a
+little short on time if there are things
+
+ align:start position:0%
+little short on time if there are things
+ 
+
+ align:start position:0%
+little short on time if there are things
+this calculation is straightforward but
+
+ align:start position:0%
+this calculation is straightforward but
+ 
+
+ align:start position:0%
+this calculation is straightforward but
+it gets I already screwed up a detail
+
+ align:start position:0%
+it gets I already screwed up a detail
+ 
+
+ align:start position:0%
+it gets I already screwed up a detail
+here I don't want to sort of risk
+
+ align:start position:0%
+here I don't want to sort of risk
+ 
+
+ align:start position:0%
+here I don't want to sort of risk
+messing up a few other things what I
+
+ align:start position:0%
+messing up a few other things what I
+ 
+
+ align:start position:0%
+messing up a few other things what I
+want to do is consider the torques about
+
+ align:start position:0%
+want to do is consider the torques about
+ 
+
+ align:start position:0%
+want to do is consider the torques about
+an axis that sort of runs through the
+
+ align:start position:0%
+an axis that sort of runs through the
+ 
+
+ align:start position:0%
+an axis that sort of runs through the
+middle of this thing because it's from
+
+ align:start position:0%
+middle of this thing because it's from
+ 
+
+ align:start position:0%
+middle of this thing because it's from
+the top and the bottom of this okay so
+
+ align:start position:0%
+the top and the bottom of this okay so
+ 
+
+ align:start position:0%
+the top and the bottom of this okay so
+go through and just add up all the
+
+ align:start position:0%
+go through and just add up all the
+ 
+
+ align:start position:0%
+go through and just add up all the
+torques associated these little forces
+
+ align:start position:0%
+torques associated these little forces
+ 
+
+ align:start position:0%
+torques associated these little forces
+about an axis in the center of that goes
+
+ align:start position:0%
+about an axis in the center of that goes
+ 
+
+ align:start position:0%
+about an axis in the center of that goes
+through the center of this cube okay so
+
+ align:start position:0%
+through the center of this cube okay so
+ 
+
+ align:start position:0%
+through the center of this cube okay so
+I'm going out like I said I'm gonna
+
+ align:start position:0%
+I'm going out like I said I'm gonna
+ 
+
+ align:start position:0%
+I'm going out like I said I'm gonna
+leave out the details but basically you
+
+ align:start position:0%
+leave out the details but basically you
+ 
+
+ align:start position:0%
+leave out the details but basically you
+go through and you do the usual R cross
+
+ align:start position:0%
+go through and you do the usual R cross
+ 
+
+ align:start position:0%
+go through and you do the usual R cross
+F to get the forces the torques
+
+ align:start position:0%
+F to get the forces the torques
+ 
+
+ align:start position:0%
+F to get the forces the torques
+associate with each of these different
+
+ align:start position:0%
+associate with each of these different
+ 
+
+ align:start position:0%
+associate with each of these different
+faces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you'll find when you do this is
+
+ align:start position:0%
+and what you'll find when you do this is
+ 
+
+ align:start position:0%
+and what you'll find when you do this is
+that there is a net torque that looks
+
+ align:start position:0%
+that there is a net torque that looks
+ 
+
+ align:start position:0%
+that there is a net torque that looks
+like L cubed times T XY minus T YX
+
+ align:start position:0%
+like L cubed times T XY minus T YX
+ 
+
+ align:start position:0%
+like L cubed times T XY minus T YX
+again though this scales with the size
+
+ align:start position:0%
+again though this scales with the size
+ 
+
+ align:start position:0%
+again though this scales with the size
+of the cube right so you look at this
+
+ align:start position:0%
+of the cube right so you look at this
+ 
+
+ align:start position:0%
+of the cube right so you look at this
+and kind of go well who cares you know
+
+ align:start position:0%
+and kind of go well who cares you know
+ 
+
+ align:start position:0%
+and kind of go well who cares you know
+it's a little bit there maybe it spins
+
+ align:start position:0%
+it's a little bit there maybe it spins
+ 
+
+ align:start position:0%
+it's a little bit there maybe it spins
+up a little bit but in the limit this
+
+ align:start position:0%
+up a little bit but in the limit this
+ 
+
+ align:start position:0%
+up a little bit but in the limit this
+thing going to zero there's no net
+
+ align:start position:0%
+thing going to zero there's no net
+ 
+
+ align:start position:0%
+thing going to zero there's no net
+effect well let's be a little bit
+
+ align:start position:0%
+effect well let's be a little bit
+ 
+
+ align:start position:0%
+effect well let's be a little bit
+careful about this what is the moment of
+
+ align:start position:0%
+careful about this what is the moment of
+ 
+
+ align:start position:0%
+careful about this what is the moment of
+inertia of this cube I don't know
+
+ align:start position:0%
+inertia of this cube I don't know
+ 
+
+ align:start position:0%
+inertia of this cube I don't know
+exactly but I know that it's going to be
+
+ align:start position:0%
+exactly but I know that it's going to be
+ 
+
+ align:start position:0%
+exactly but I know that it's going to be
+something like the mass of this cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll call that L cubed times its mass
+
+ align:start position:0%
+we'll call that L cubed times its mass
+ 
+
+ align:start position:0%
+we'll call that L cubed times its mass
+density or its energy density and it's
+
+ align:start position:0%
+density or its energy density and it's
+ 
+
+ align:start position:0%
+density or its energy density and it's
+going to involve two powers of the only
+
+ align:start position:0%
+going to involve two powers of the only
+ 
+
+ align:start position:0%
+going to involve two powers of the only
+length scale characterizing this thing
+
+ align:start position:0%
+length scale characterizing this thing
+ 
+
+ align:start position:0%
+length scale characterizing this thing
+and there'll be some pre factor alpha
+
+ align:start position:0%
+and there'll be some pre factor alpha
+ 
+
+ align:start position:0%
+and there'll be some pre factor alpha
+there'll be some number that's related
+
+ align:start position:0%
+there'll be some number that's related
+ 
+
+ align:start position:0%
+there'll be some number that's related
+to the geometry of this okay an integral
+
+ align:start position:0%
+to the geometry of this okay an integral
+ 
+
+ align:start position:0%
+to the geometry of this okay an integral
+or two will easily work out what the
+
+ align:start position:0%
+or two will easily work out what the
+ 
+
+ align:start position:0%
+or two will easily work out what the
+Alpha is and make this more precise but
+
+ align:start position:0%
+Alpha is and make this more precise but
+ 
+
+ align:start position:0%
+Alpha is and make this more precise but
+the key bit which I want to emphasize is
+
+ align:start position:0%
+the key bit which I want to emphasize is
+ 
+
+ align:start position:0%
+the key bit which I want to emphasize is
+that this is something that scales as
+
+ align:start position:0%
+that this is something that scales as
+ 
+
+ align:start position:0%
+that this is something that scales as
+the size of the fifth power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah the torque vanishes as L goes to
+
+ align:start position:0%
+so yeah the torque vanishes as L goes to
+ 
+
+ align:start position:0%
+so yeah the torque vanishes as L goes to
+zero but it does so with the cubed power
+
+ align:start position:0%
+zero but it does so with the cubed power
+ 
+
+ align:start position:0%
+zero but it does so with the cubed power
+it doesn't vanish as quickly as the
+
+ align:start position:0%
+it doesn't vanish as quickly as the
+ 
+
+ align:start position:0%
+it doesn't vanish as quickly as the
+moment of inertia vanishes and I'll
+
+ align:start position:0%
+moment of inertia vanishes and I'll
+ 
+
+ align:start position:0%
+moment of inertia vanishes and I'll
+remind you the angular acceleration of
+
+ align:start position:0%
+remind you the angular acceleration of
+ 
+
+ align:start position:0%
+remind you the angular acceleration of
+the cube theta double dot is the torque
+
+ align:start position:0%
+the cube theta double dot is the torque
+ 
+
+ align:start position:0%
+the cube theta double dot is the torque
+divided by the moan of inertia so this
+
+ align:start position:0%
+divided by the moan of inertia so this
+ 
+
+ align:start position:0%
+divided by the moan of inertia so this
+is something that is proportional to t
+
+ align:start position:0%
+is something that is proportional to t
+ 
+
+ align:start position:0%
+is something that is proportional to t
+XY minus T Y
+
+ align:start position:0%
+XY minus T Y
+ 
+
+ align:start position:0%
+XY minus T Y
+/ l squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah the torque does vanish as L goes
+
+ align:start position:0%
+so yeah the torque does vanish as L goes
+ 
+
+ align:start position:0%
+so yeah the torque does vanish as L goes
+to zero but the moment of inertia
+
+ align:start position:0%
+to zero but the moment of inertia
+ 
+
+ align:start position:0%
+to zero but the moment of inertia
+vanishes more rapidly as L goes to zero
+
+ align:start position:0%
+vanishes more rapidly as L goes to zero
+ 
+
+ align:start position:0%
+vanishes more rapidly as L goes to zero
+that sort of suggests that if we're in a
+
+ align:start position:0%
+that sort of suggests that if we're in a
+ 
+
+ align:start position:0%
+that sort of suggests that if we're in a
+screwy universe little microscopic
+
+ align:start position:0%
+screwy universe little microscopic
+ 
+
+ align:start position:0%
+screwy universe little microscopic
+vortices are just gonna start randomly
+
+ align:start position:0%
+vortices are just gonna start randomly
+ 
+
+ align:start position:0%
+vortices are just gonna start randomly
+oscillating in any cup of water that you
+
+ align:start position:0%
+oscillating in any cup of water that you
+ 
+
+ align:start position:0%
+oscillating in any cup of water that you
+pour it in front of you now I don't have
+
+ align:start position:0%
+pour it in front of you now I don't have
+ 
+
+ align:start position:0%
+pour it in front of you now I don't have
+a proof that nature abhors that but it
+
+ align:start position:0%
+a proof that nature abhors that but it
+ 
+
+ align:start position:0%
+a proof that nature abhors that but it
+seems pretty screwy and so the case that
+
+ align:start position:0%
+seems pretty screwy and so the case that
+ 
+
+ align:start position:0%
+seems pretty screwy and so the case that
+most textbooks make at this point is to
+
+ align:start position:0%
+most textbooks make at this point is to
+ 
+
+ align:start position:0%
+most textbooks make at this point is to
+say physics indicates we must have txy
+
+ align:start position:0%
+say physics indicates we must have txy
+ 
+
+ align:start position:0%
+say physics indicates we must have txy
+strikingly equal to G YX in all cases
+
+ align:start position:0%
+strikingly equal to G YX in all cases
+ 
+
+ align:start position:0%
+strikingly equal to G YX in all cases
+independent of what the size of this
+
+ align:start position:0%
+independent of what the size of this
+ 
+
+ align:start position:0%
+independent of what the size of this
+thing is okay that had better just be a
+
+ align:start position:0%
+thing is okay that had better just be a
+ 
+
+ align:start position:0%
+thing is okay that had better just be a
+bloody zero in the numerator in order to
+
+ align:start position:0%
+bloody zero in the numerator in order to
+ 
+
+ align:start position:0%
+bloody zero in the numerator in order to
+prevent this physical absurdity from
+
+ align:start position:0%
+prevent this physical absurdity from
+ 
+
+ align:start position:0%
+prevent this physical absurdity from
+being set up repeat the exercise by
+
+ align:start position:0%
+being set up repeat the exercise by
+ 
+
+ align:start position:0%
+being set up repeat the exercise by
+looking at torques around the other axes
+
+ align:start position:0%
+looking at torques around the other axes
+ 
+
+ align:start position:0%
+looking at torques around the other axes
+and that drives you to the statement
+
+ align:start position:0%
+and that drives you to the statement
+ 
+
+ align:start position:0%
+and that drives you to the statement
+that this thing must in general be
+
+ align:start position:0%
+that this thing must in general be
+ 
+
+ align:start position:0%
+that this thing must in general be
+spatially symmetric and again physics of
+
+ align:start position:0%
+spatially symmetric and again physics of
+ 
+
+ align:start position:0%
+spatially symmetric and again physics of
+the way that energy momentum behaved in
+
+ align:start position:0%
+the way that energy momentum behaved in
+ 
+
+ align:start position:0%
+the way that energy momentum behaved in
+relativity makes our sort of time-space
+
+ align:start position:0%
+relativity makes our sort of time-space
+ 
+
+ align:start position:0%
+relativity makes our sort of time-space
+component symmetric as well I emphasize
+
+ align:start position:0%
+component symmetric as well I emphasize
+ 
+
+ align:start position:0%
+component symmetric as well I emphasize
+this is not a proof this is really just
+
+ align:start position:0%
+this is not a proof this is really just
+ 
+
+ align:start position:0%
+this is not a proof this is really just
+a physical motivation this is the kind
+
+ align:start position:0%
+a physical motivation this is the kind
+ 
+
+ align:start position:0%
+a physical motivation this is the kind
+of thing that I'm a bloody
+
+ align:start position:0%
+of thing that I'm a bloody
+ 
+
+ align:start position:0%
+of thing that I'm a bloody
+astrophysicist I like this kind of stuff
+
+ align:start position:0%
+astrophysicist I like this kind of stuff
+ 
+
+ align:start position:0%
+astrophysicist I like this kind of stuff
+there is a different way of developing
+
+ align:start position:0%
+there is a different way of developing
+ 
+
+ align:start position:0%
+there is a different way of developing
+the stress energy tensor as I said that
+
+ align:start position:0%
+the stress energy tensor as I said that
+ 
+
+ align:start position:0%
+the stress energy tensor as I said that
+comes from a variational principle sort
+
+ align:start position:0%
+comes from a variational principle sort
+ 
+
+ align:start position:0%
+comes from a variational principle sort
+of based on a sort of quantum field
+
+ align:start position:0%
+of based on a sort of quantum field
+ 
+
+ align:start position:0%
+of based on a sort of quantum field
+field theoretic type of methods and the
+
+ align:start position:0%
+field theoretic type of methods and the
+ 
+
+ align:start position:0%
+field theoretic type of methods and the
+symmetry in that case is manifest okay
+
+ align:start position:0%
+symmetry in that case is manifest okay
+ 
+
+ align:start position:0%
+symmetry in that case is manifest okay
+it really does would have come up but
+
+ align:start position:0%
+it really does would have come up but
+ 
+
+ align:start position:0%
+it really does would have come up but
+this is a good way of just motivating
+
+ align:start position:0%
+this is a good way of just motivating
+ 
+
+ align:start position:0%
+this is a good way of just motivating
+the fact that you're not gonna have any
+
+ align:start position:0%
+the fact that you're not gonna have any
+ 
+
+ align:start position:0%
+the fact that you're not gonna have any
+non diagonal or something non symmetric
+
+ align:start position:0%
+non diagonal or something non symmetric
+ 
+
+ align:start position:0%
+non diagonal or something non symmetric
+stretch energy time sirs if you did you
+
+ align:start position:0%
+stretch energy time sirs if you did you
+ 
+
+ align:start position:0%
+stretch energy time sirs if you did you
+would have really bizarre matter
+
+ align:start position:0%
+would have really bizarre matter
+ 
+
+ align:start position:0%
+ 
+all right now the stress-energy tensor
+
+ align:start position:0%
+all right now the stress-energy tensor
+ 
+
+ align:start position:0%
+all right now the stress-energy tensor
+has this physical interpretation that it
+
+ align:start position:0%
+has this physical interpretation that it
+ 
+
+ align:start position:0%
+has this physical interpretation that it
+tells me about the flow of energy and
+
+ align:start position:0%
+tells me about the flow of energy and
+ 
+
+ align:start position:0%
+tells me about the flow of energy and
+the flow of momentum in space-time as
+
+ align:start position:0%
+the flow of momentum in space-time as
+ 
+
+ align:start position:0%
+the flow of momentum in space-time as
+such it is the tool by which we are
+
+ align:start position:0%
+such it is the tool by which we are
+ 
+
+ align:start position:0%
+such it is the tool by which we are
+going to put conservation of energy and
+
+ align:start position:0%
+going to put conservation of energy and
+ 
+
+ align:start position:0%
+going to put conservation of energy and
+conservation of momentum into our theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the way we're going to do this is
+
+ align:start position:0%
+in the way we're going to do this is
+ 
+
+ align:start position:0%
+in the way we're going to do this is
+with a remarkably simple equation the
+
+ align:start position:0%
+with a remarkably simple equation the
+ 
+
+ align:start position:0%
+with a remarkably simple equation the
+space-time divergence of T alpha beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+must equal zero this is a covariant
+
+ align:start position:0%
+must equal zero this is a covariant
+ 
+
+ align:start position:0%
+must equal zero this is a covariant
+formulation of both conservation of
+
+ align:start position:0%
+formulation of both conservation of
+ 
+
+ align:start position:0%
+formulation of both conservation of
+energy and conservation of momentum and
+
+ align:start position:0%
+energy and conservation of momentum and
+ 
+
+ align:start position:0%
+energy and conservation of momentum and
+if you want to say well which one is
+
+ align:start position:0%
+if you want to say well which one is
+ 
+
+ align:start position:0%
+if you want to say well which one is
+that energy or is it momentum you can't
+
+ align:start position:0%
+that energy or is it momentum you can't
+ 
+
+ align:start position:0%
+that energy or is it momentum you can't
+say that in general okay I can only say
+
+ align:start position:0%
+say that in general okay I can only say
+ 
+
+ align:start position:0%
+say that in general okay I can only say
+that after I have picked a particular
+
+ align:start position:0%
+that after I have picked a particular
+ 
+
+ align:start position:0%
+that after I have picked a particular
+reference frame because it's only once I
+
+ align:start position:0%
+reference frame because it's only once I
+ 
+
+ align:start position:0%
+reference frame because it's only once I
+have defined time and I've defined space
+
+ align:start position:0%
+have defined time and I've defined space
+ 
+
+ align:start position:0%
+have defined time and I've defined space
+that I've actually defined energy and
+
+ align:start position:0%
+that I've actually defined energy and
+ 
+
+ align:start position:0%
+that I've actually defined energy and
+momentum okay prior to choosing a
+
+ align:start position:0%
+momentum okay prior to choosing a
+ 
+
+ align:start position:0%
+momentum okay prior to choosing a
+particular reference frame all I have is
+
+ align:start position:0%
+particular reference frame all I have is
+ 
+
+ align:start position:0%
+particular reference frame all I have is
+for momentum one observers energy is
+
+ align:start position:0%
+for momentum one observers energy is
+ 
+
+ align:start position:0%
+for momentum one observers energy is
+another observer superposition of energy
+
+ align:start position:0%
+another observer superposition of energy
+ 
+
+ align:start position:0%
+another observer superposition of energy
+and momentum once I have picked a
+
+ align:start position:0%
+and momentum once I have picked a
+ 
+
+ align:start position:0%
+and momentum once I have picked a
+particular frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so once I have picked a particular frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if I evaluate D alpha T alpha
+
+ align:start position:0%
+then if I evaluate D alpha T alpha
+ 
+
+ align:start position:0%
+then if I evaluate D alpha T alpha
+either 0 or T this is what conservation
+
+ align:start position:0%
+either 0 or T this is what conservation
+ 
+
+ align:start position:0%
+either 0 or T this is what conservation
+of energy looks like in that frame so in
+
+ align:start position:0%
+of energy looks like in that frame so in
+ 
+
+ align:start position:0%
+of energy looks like in that frame so in
+that frame here is conservation of
+
+ align:start position:0%
+that frame here is conservation of
+ 
+
+ align:start position:0%
+that frame here is conservation of
+energy and
+
+ align:start position:0%
+energy and
+ 
+
+ align:start position:0%
+energy and
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right the first one yeah sorry just try
+
+ align:start position:0%
+right the first one yeah sorry just try
+ 
+
+ align:start position:0%
+right the first one yeah sorry just try
+to make sure I got my indices lined up
+
+ align:start position:0%
+to make sure I got my indices lined up
+ 
+
+ align:start position:0%
+to make sure I got my indices lined up
+properly so you can't quite read the
+
+ align:start position:0%
+properly so you can't quite read the
+ 
+
+ align:start position:0%
+properly so you can't quite read the
+bottom one so well top one is
+
+ align:start position:0%
+bottom one so well top one is
+ 
+
+ align:start position:0%
+bottom one so well top one is
+conservation of energy in that
+
+ align:start position:0%
+conservation of energy in that
+ 
+
+ align:start position:0%
+conservation of energy in that
+particular frame second one is
+
+ align:start position:0%
+particular frame second one is
+ 
+
+ align:start position:0%
+particular frame second one is
+conservation of momentum in that
+
+ align:start position:0%
+conservation of momentum in that
+ 
+
+ align:start position:0%
+conservation of momentum in that
+particular frame okay and again the key
+
+ align:start position:0%
+particular frame okay and again the key
+ 
+
+ align:start position:0%
+particular frame okay and again the key
+thing which I wanted to emphasize is the
+
+ align:start position:0%
+thing which I wanted to emphasize is the
+ 
+
+ align:start position:0%
+thing which I wanted to emphasize is the
+covariant statement basically puts both
+
+ align:start position:0%
+covariant statement basically puts both
+ 
+
+ align:start position:0%
+covariant statement basically puts both
+of them together into a single equation
+
+ align:start position:0%
+of them together into a single equation
+ 
+
+ align:start position:0%
+of them together into a single equation
+I can only sensibly state conservation
+
+ align:start position:0%
+I can only sensibly state conservation
+ 
+
+ align:start position:0%
+I can only sensibly state conservation
+of energy and conservation of momentum
+
+ align:start position:0%
+of energy and conservation of momentum
+ 
+
+ align:start position:0%
+of energy and conservation of momentum
+according to some particular observer
+
+ align:start position:0%
+according to some particular observer
+ 
+
+ align:start position:0%
+according to some particular observer
+now I can repeat the game that I had
+
+ align:start position:0%
+now I can repeat the game that I had
+ 
+
+ align:start position:0%
+now I can repeat the game that I had
+done before with the number vector and
+
+ align:start position:0%
+done before with the number vector and
+ 
+
+ align:start position:0%
+done before with the number vector and
+turn these conservation laws into
+
+ align:start position:0%
+turn these conservation laws into
+ 
+
+ align:start position:0%
+turn these conservation laws into
+integral equations as well let me do it
+
+ align:start position:0%
+integral equations as well let me do it
+ 
+
+ align:start position:0%
+integral equations as well let me do it
+for energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I take that integral equation and
+
+ align:start position:0%
+so if I take that integral equation and
+ 
+
+ align:start position:0%
+so if I take that integral equation and
+integrate over a three-volume
+
+ align:start position:0%
+integrate over a three-volume
+ 
+
+ align:start position:0%
+integrate over a three-volume
+or if you prefer I can take the the
+
+ align:start position:0%
+or if you prefer I can take the the
+ 
+
+ align:start position:0%
+or if you prefer I can take the the
+original covariant formulation integrate
+
+ align:start position:0%
+original covariant formulation integrate
+ 
+
+ align:start position:0%
+original covariant formulation integrate
+that over a four-volume
+
+ align:start position:0%
+that over a four-volume
+ 
+
+ align:start position:0%
+that over a four-volume
+with a little bit of manipulation akin
+
+ align:start position:0%
+with a little bit of manipulation akin
+ 
+
+ align:start position:0%
+with a little bit of manipulation akin
+to the way I manipulated the
+
+ align:start position:0%
+to the way I manipulated the
+ 
+
+ align:start position:0%
+to the way I manipulated the
+conservation Tugrul associate the number
+
+ align:start position:0%
+conservation Tugrul associate the number
+ 
+
+ align:start position:0%
+conservation Tugrul associate the number
+vector in the previous lecture you can
+
+ align:start position:0%
+vector in the previous lecture you can
+ 
+
+ align:start position:0%
+vector in the previous lecture you can
+write down a law that looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so this again what I've done
+
+ align:start position:0%
+okay and so this again what I've done
+ 
+
+ align:start position:0%
+okay and so this again what I've done
+here is I've chosen a particular set of
+
+ align:start position:0%
+here is I've chosen a particular set of
+ 
+
+ align:start position:0%
+here is I've chosen a particular set of
+time like coordinates and the language
+
+ align:start position:0%
+time like coordinates and the language
+ 
+
+ align:start position:0%
+time like coordinates and the language
+that we often use in relativity is we
+
+ align:start position:0%
+that we often use in relativity is we
+ 
+
+ align:start position:0%
+that we often use in relativity is we
+basically say I'm going to take a single
+
+ align:start position:0%
+basically say I'm going to take a single
+ 
+
+ align:start position:0%
+basically say I'm going to take a single
+slice of time and I would say that the
+
+ align:start position:0%
+slice of time and I would say that the
+ 
+
+ align:start position:0%
+slice of time and I would say that the
+rate of change of energy so integrate
+
+ align:start position:0%
+rate of change of energy so integrate
+ 
+
+ align:start position:0%
+rate of change of energy so integrate
+energy over a volume it's the total
+
+ align:start position:0%
+energy over a volume it's the total
+ 
+
+ align:start position:0%
+energy over a volume it's the total
+energy in that v3 the rate of change of
+
+ align:start position:0%
+energy in that v3 the rate of change of
+ 
+
+ align:start position:0%
+energy in that v3 the rate of change of
+that thing is balanced by the amount of
+
+ align:start position:0%
+that thing is balanced by the amount of
+ 
+
+ align:start position:0%
+that thing is balanced by the amount of
+energy flowing into or out of through
+
+ align:start position:0%
+energy flowing into or out of through
+ 
+
+ align:start position:0%
+energy flowing into or out of through
+the boundaries of that volume okay add
+
+ align:start position:0%
+the boundaries of that volume okay add
+ 
+
+ align:start position:0%
+the boundaries of that volume okay add
+an extra index here so make this this
+
+ align:start position:0%
+an extra index here so make this this
+ 
+
+ align:start position:0%
+an extra index here so make this this
+make one of these be a J make this guy
+
+ align:start position:0%
+make one of these be a J make this guy
+ 
+
+ align:start position:0%
+make one of these be a J make this guy
+be a J and you've got a similar
+
+ align:start position:0%
+be a J and you've got a similar
+ 
+
+ align:start position:0%
+be a J and you've got a similar
+statement for the conservation of
+
+ align:start position:0%
+statement for the conservation of
+ 
+
+ align:start position:0%
+statement for the conservation of
+momentum okay this is a particular trick
+
+ align:start position:0%
+momentum okay this is a particular trick
+ 
+
+ align:start position:0%
+momentum okay this is a particular trick
+I have a set of typed up notes that just
+
+ align:start position:0%
+I have a set of typed up notes that just
+ 
+
+ align:start position:0%
+I have a set of typed up notes that just
+sort of cleaned this up a little bit
+
+ align:start position:0%
+sort of cleaned this up a little bit
+ 
+
+ align:start position:0%
+sort of cleaned this up a little bit
+they're basically exactly this point but
+
+ align:start position:0%
+they're basically exactly this point but
+ 
+
+ align:start position:0%
+they're basically exactly this point but
+I'll put them online after today's
+
+ align:start position:0%
+I'll put them online after today's
+ 
+
+ align:start position:0%
+I'll put them online after today's
+lecture you're going to want to use this
+
+ align:start position:0%
+lecture you're going to want to use this
+ 
+
+ align:start position:0%
+lecture you're going to want to use this
+on one of the pset problems this week
+
+ align:start position:0%
+on one of the pset problems this week
+ 
+
+ align:start position:0%
+on one of the pset problems this week
+okay so you guys are going to do a
+
+ align:start position:0%
+okay so you guys are going to do a
+ 
+
+ align:start position:0%
+okay so you guys are going to do a
+couple exercise that involves
+
+ align:start position:0%
+couple exercise that involves
+ 
+
+ align:start position:0%
+couple exercise that involves
+integrating and actually finding
+
+ align:start position:0%
+integrating and actually finding
+ 
+
+ align:start position:0%
+integrating and actually finding
+essentially moments of the left-hand
+
+ align:start position:0%
+essentially moments of the left-hand
+ 
+
+ align:start position:0%
+essentially moments of the left-hand
+side of this thing okay we're going to
+
+ align:start position:0%
+side of this thing okay we're going to
+ 
+
+ align:start position:0%
+side of this thing okay we're going to
+do a few exercises where you take
+
+ align:start position:0%
+do a few exercises where you take
+ 
+
+ align:start position:0%
+do a few exercises where you take
+advantage of this constant this
+
+ align:start position:0%
+advantage of this constant this
+ 
+
+ align:start position:0%
+advantage of this constant this
+formulation of conservation of energy
+
+ align:start position:0%
+formulation of conservation of energy
+ 
+
+ align:start position:0%
+formulation of conservation of energy
+and momentum to derive a few identities
+
+ align:start position:0%
+and momentum to derive a few identities
+ 
+
+ align:start position:0%
+and momentum to derive a few identities
+involving the stress energy tensor
+
+ align:start position:0%
+involving the stress energy tensor
+ 
+
+ align:start position:0%
+involving the stress energy tensor
+one of which is another Easter Egg that
+
+ align:start position:0%
+one of which is another Easter Egg that
+ 
+
+ align:start position:0%
+one of which is another Easter Egg that
+we're going to use quite a bit in a
+
+ align:start position:0%
+we're going to use quite a bit in a
+ 
+
+ align:start position:0%
+we're going to use quite a bit in a
+future lecture all right so we just wrap
+
+ align:start position:0%
+future lecture all right so we just wrap
+ 
+
+ align:start position:0%
+future lecture all right so we just wrap
+up our discussion of the stress energy
+
+ align:start position:0%
+up our discussion of the stress energy
+ 
+
+ align:start position:0%
+up our discussion of the stress energy
+tensor by just doing two more examples
+
+ align:start position:0%
+tensor by just doing two more examples
+ 
+
+ align:start position:0%
+tensor by just doing two more examples
+and then I'm gonna sort of begin
+
+ align:start position:0%
+and then I'm gonna sort of begin
+ 
+
+ align:start position:0%
+and then I'm gonna sort of begin
+switching gears a little bit so so far I
+
+ align:start position:0%
+switching gears a little bit so so far I
+ 
+
+ align:start position:0%
+switching gears a little bit so so far I
+have only described essentially I've
+
+ align:start position:0%
+have only described essentially I've
+ 
+
+ align:start position:0%
+have only described essentially I've
+really only described perfect fluids
+
+ align:start position:0%
+really only described perfect fluids
+ 
+
+ align:start position:0%
+really only described perfect fluids
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+dust is a perfect fluid with no pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are a lot of other kinds of
+
+ align:start position:0%
+there are a lot of other kinds of
+ 
+
+ align:start position:0%
+there are a lot of other kinds of
+materials that we want to work with in
+
+ align:start position:0%
+materials that we want to work with in
+ 
+
+ align:start position:0%
+materials that we want to work with in
+the universe one of them which it's
+
+ align:start position:0%
+the universe one of them which it's
+ 
+
+ align:start position:0%
+the universe one of them which it's
+unlikely many of you were going to use
+
+ align:start position:0%
+unlikely many of you were going to use
+ 
+
+ align:start position:0%
+unlikely many of you were going to use
+this but it's actually the stress energy
+
+ align:start position:0%
+this but it's actually the stress energy
+ 
+
+ align:start position:0%
+this but it's actually the stress energy
+tensor on which I have built I have
+
+ align:start position:0%
+tensor on which I have built I have
+ 
+
+ align:start position:0%
+tensor on which I have built I have
+built a big chunk of my career is
+
+ align:start position:0%
+built a big chunk of my career is
+ 
+
+ align:start position:0%
+built a big chunk of my career is
+suppose you have you know we kind of
+
+ align:start position:0%
+suppose you have you know we kind of
+ 
+
+ align:start position:0%
+suppose you have you know we kind of
+talked a little bit about how the four
+
+ align:start position:0%
+talked a little bit about how the four
+ 
+
+ align:start position:0%
+talked a little bit about how the four
+velocity in the four momentum but really
+
+ align:start position:0%
+velocity in the four momentum but really
+ 
+
+ align:start position:0%
+velocity in the four momentum but really
+only good we're talking about like the
+
+ align:start position:0%
+only good we're talking about like the
+ 
+
+ align:start position:0%
+only good we're talking about like the
+kinematics of particles well actually
+
+ align:start position:0%
+kinematics of particles well actually
+ 
+
+ align:start position:0%
+kinematics of particles well actually
+particles aren't a bad thing to focus on
+
+ align:start position:0%
+particles aren't a bad thing to focus on
+ 
+
+ align:start position:0%
+particles aren't a bad thing to focus on
+in some of your studies okay and much of
+
+ align:start position:0%
+in some of your studies okay and much of
+ 
+
+ align:start position:0%
+in some of your studies okay and much of
+my research is actually based on the
+
+ align:start position:0%
+my research is actually based on the
+ 
+
+ align:start position:0%
+my research is actually based on the
+idea of thinking about a binary system
+
+ align:start position:0%
+idea of thinking about a binary system
+ 
+
+ align:start position:0%
+idea of thinking about a binary system
+as being one member of being a black
+
+ align:start position:0%
+as being one member of being a black
+ 
+
+ align:start position:0%
+as being one member of being a black
+hole and its companion being a particle
+
+ align:start position:0%
+hole and its companion being a particle
+ 
+
+ align:start position:0%
+hole and its companion being a particle
+like object it's it's a particularly
+
+ align:start position:0%
+like object it's it's a particularly
+ 
+
+ align:start position:0%
+like object it's it's a particularly
+limit of at a part of like object that
+
+ align:start position:0%
+limit of at a part of like object that
+ 
+
+ align:start position:0%
+limit of at a part of like object that
+orbits it so a really simple stress
+
+ align:start position:0%
+orbits it so a really simple stress
+ 
+
+ align:start position:0%
+orbits it so a really simple stress
+energy tensor and I'm just throwing it
+
+ align:start position:0%
+energy tensor and I'm just throwing it
+ 
+
+ align:start position:0%
+energy tensor and I'm just throwing it
+out here because I think it nicely
+
+ align:start position:0%
+out here because I think it nicely
+ 
+
+ align:start position:0%
+out here because I think it nicely
+illustrates the principle a point
+
+ align:start position:0%
+illustrates the principle a point
+ 
+
+ align:start position:0%
+illustrates the principle a point
+particle with rest mass we'll call it m0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm gonna say it's moving on a
+
+ align:start position:0%
+and I'm gonna say it's moving on a
+ 
+
+ align:start position:0%
+and I'm gonna say it's moving on a
+particular world line through space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the way we define a world line is we
+
+ align:start position:0%
+so the way we define a world line is we
+ 
+
+ align:start position:0%
+so the way we define a world line is we
+just say it's some four-vector that
+
+ align:start position:0%
+just say it's some four-vector that
+ 
+
+ align:start position:0%
+just say it's some four-vector that
+describes there's a place in this thing
+
+ align:start position:0%
+describes there's a place in this thing
+ 
+
+ align:start position:0%
+describes there's a place in this thing
+from some chosen origin and it's
+
+ align:start position:0%
+from some chosen origin and it's
+ 
+
+ align:start position:0%
+from some chosen origin and it's
+generally most convenient to
+
+ align:start position:0%
+generally most convenient to
+ 
+
+ align:start position:0%
+generally most convenient to
+parameterize it by the proper time of
+
+ align:start position:0%
+parameterize it by the proper time of
+ 
+
+ align:start position:0%
+parameterize it by the proper time of
+whatever object or creature is moving on
+
+ align:start position:0%
+whatever object or creature is moving on
+ 
+
+ align:start position:0%
+whatever object or creature is moving on
+that world line and so it's a lot like
+
+ align:start position:0%
+that world line and so it's a lot like
+ 
+
+ align:start position:0%
+that world line and so it's a lot like
+dust only there's no volume right it's
+
+ align:start position:0%
+dust only there's no volume right it's
+ 
+
+ align:start position:0%
+dust only there's no volume right it's
+sort of like one particle of dust and so
+
+ align:start position:0%
+sort of like one particle of dust and so
+ 
+
+ align:start position:0%
+sort of like one particle of dust and so
+the stress energy tensor we use for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we back up for just a second here when
+
+ align:start position:0%
+we back up for just a second here when
+ 
+
+ align:start position:0%
+we back up for just a second here when
+you guys learned about electricity and
+
+ align:start position:0%
+you guys learned about electricity and
+ 
+
+ align:start position:0%
+you guys learned about electricity and
+magnetism okay for the first thing you
+
+ align:start position:0%
+magnetism okay for the first thing you
+ 
+
+ align:start position:0%
+magnetism okay for the first thing you
+learn about our point charges and then a
+
+ align:start position:0%
+learn about our point charges and then a
+ 
+
+ align:start position:0%
+learn about our point charges and then a
+little bit later you learn about charge
+
+ align:start position:0%
+little bit later you learn about charge
+ 
+
+ align:start position:0%
+little bit later you learn about charge
+distributions and you have charge
+
+ align:start position:0%
+distributions and you have charge
+ 
+
+ align:start position:0%
+distributions and you have charge
+densities okay and then usually at some
+
+ align:start position:0%
+densities okay and then usually at some
+ 
+
+ align:start position:0%
+densities okay and then usually at some
+point in a class it's often like junior
+
+ align:start position:0%
+point in a class it's often like junior
+ 
+
+ align:start position:0%
+point in a class it's often like junior
+level enm we say how do you describe the
+
+ align:start position:0%
+level enm we say how do you describe the
+ 
+
+ align:start position:0%
+level enm we say how do you describe the
+density of a point charge that's where
+
+ align:start position:0%
+density of a point charge that's where
+ 
+
+ align:start position:0%
+density of a point charge that's where
+you learn about the Dirac Delta function
+
+ align:start position:0%
+you learn about the Dirac Delta function
+ 
+
+ align:start position:0%
+you learn about the Dirac Delta function
+well if I have a point particle I'm
+
+ align:start position:0%
+well if I have a point particle I'm
+ 
+
+ align:start position:0%
+well if I have a point particle I'm
+going to need to describe this thing's
+
+ align:start position:0%
+going to need to describe this thing's
+ 
+
+ align:start position:0%
+going to need to describe this thing's
+energy density as essentially a Dirac
+
+ align:start position:0%
+energy density as essentially a Dirac
+ 
+
+ align:start position:0%
+energy density as essentially a Dirac
+Delta function and so what we do is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imagining that these things so this is
+
+ align:start position:0%
+imagining that these things so this is
+ 
+
+ align:start position:0%
+imagining that these things so this is
+the four velocity of that body they
+
+ align:start position:0%
+the four velocity of that body they
+ 
+
+ align:start position:0%
+the four velocity of that body they
+might be functions of time as this guy
+
+ align:start position:0%
+might be functions of time as this guy
+ 
+
+ align:start position:0%
+might be functions of time as this guy
+is moving along here what we do is we
+
+ align:start position:0%
+is moving along here what we do is we
+ 
+
+ align:start position:0%
+is moving along here what we do is we
+introduce a Dirac Delta function as this
+
+ align:start position:0%
+introduce a Dirac Delta function as this
+ 
+
+ align:start position:0%
+introduce a Dirac Delta function as this
+thing moves along through space time
+
+ align:start position:0%
+thing moves along through space time
+ 
+
+ align:start position:0%
+thing moves along through space time
+what this does you can check the
+
+ align:start position:0%
+what this does you can check the
+ 
+
+ align:start position:0%
+what this does you can check the
+dimensions this gives me exactly what we
+
+ align:start position:0%
+dimensions this gives me exactly what we
+ 
+
+ align:start position:0%
+dimensions this gives me exactly what we
+need in order to have something that's
+
+ align:start position:0%
+need in order to have something that's
+ 
+
+ align:start position:0%
+need in order to have something that's
+dimensionally correct and has all the
+
+ align:start position:0%
+dimensionally correct and has all the
+ 
+
+ align:start position:0%
+dimensionally correct and has all the
+symmetries and all the properties that
+
+ align:start position:0%
+symmetries and all the properties that
+ 
+
+ align:start position:0%
+symmetries and all the properties that
+describe a particle moving at the
+
+ align:start position:0%
+describe a particle moving at the
+ 
+
+ align:start position:0%
+describe a particle moving at the
+particular floor velocity through
+
+ align:start position:0%
+particular floor velocity through
+ 
+
+ align:start position:0%
+particular floor velocity through
+space-time now you might want to just
+
+ align:start position:0%
+space-time now you might want to just
+ 
+
+ align:start position:0%
+space-time now you might want to just
+it's the thing which I kind of want to
+
+ align:start position:0%
+it's the thing which I kind of want to
+ 
+
+ align:start position:0%
+it's the thing which I kind of want to
+pause on for a second you go the hell
+
+ align:start position:0%
+pause on for a second you go the hell
+ 
+
+ align:start position:0%
+pause on for a second you go the hell
+you do with this right well the trick we
+
+ align:start position:0%
+you do with this right well the trick we
+ 
+
+ align:start position:0%
+you do with this right well the trick we
+use to sort of clean up that Dirac Delta
+
+ align:start position:0%
+use to sort of clean up that Dirac Delta
+ 
+
+ align:start position:0%
+use to sort of clean up that Dirac Delta
+function is it's very much like what you
+
+ align:start position:0%
+function is it's very much like what you
+ 
+
+ align:start position:0%
+function is it's very much like what you
+do when you encounter a
+
+ align:start position:0%
+do when you encounter a
+ 
+
+ align:start position:0%
+do when you encounter a
+multi-dimensional Delta functions in
+
+ align:start position:0%
+multi-dimensional Delta functions in
+ 
+
+ align:start position:0%
+multi-dimensional Delta functions in
+basic physics you just build it out of a
+
+ align:start position:0%
+basic physics you just build it out of a
+ 
+
+ align:start position:0%
+basic physics you just build it out of a
+bunch of one-dimensional Delta functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+likewise you let a turn with the Y
+
+ align:start position:0%
+likewise you let a turn with the Y
+ 
+
+ align:start position:0%
+likewise you let a turn with the Y
+component and the Z component then you
+
+ align:start position:0%
+component and the Z component then you
+ 
+
+ align:start position:0%
+component and the Z component then you
+use the rule then if I integrate a
+
+ align:start position:0%
+use the rule then if I integrate a
+ 
+
+ align:start position:0%
+use the rule then if I integrate a
+function of X against a delta function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whose argument is itself a function of X
+
+ align:start position:0%
+whose argument is itself a function of X
+ 
+
+ align:start position:0%
+whose argument is itself a function of X
+I evaluate that function at the zeros of
+
+ align:start position:0%
+I evaluate that function at the zeros of
+ 
+
+ align:start position:0%
+I evaluate that function at the zeros of
+G so let's say x0 is where G has a zero
+
+ align:start position:0%
+G so let's say x0 is where G has a zero
+ 
+
+ align:start position:0%
+G so let's say x0 is where G has a zero
+normalizing to the first derivative of G
+
+ align:start position:0%
+normalizing to the first derivative of G
+ 
+
+ align:start position:0%
+normalizing to the first derivative of G
+evaluated at that zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you put all of that together
+
+ align:start position:0%
+when you put all of that together
+ 
+
+ align:start position:0%
+when you put all of that together
+it basically means you can do this
+
+ align:start position:0%
+it basically means you can do this
+ 
+
+ align:start position:0%
+it basically means you can do this
+somewhat abstract integral formally I
+
+ align:start position:0%
+somewhat abstract integral formally I
+ 
+
+ align:start position:0%
+somewhat abstract integral formally I
+mean exactly you can just do it
+
+ align:start position:0%
+mean exactly you can just do it
+ 
+
+ align:start position:0%
+mean exactly you can just do it
+analytically and what you do just you
+
+ align:start position:0%
+analytically and what you do just you
+ 
+
+ align:start position:0%
+analytically and what you do just you
+choose one of the Delta functions to
+
+ align:start position:0%
+choose one of the Delta functions to
+ 
+
+ align:start position:0%
+choose one of the Delta functions to
+apply it to traditionally people apply
+
+ align:start position:0%
+apply it to traditionally people apply
+ 
+
+ align:start position:0%
+apply it to traditionally people apply
+it to the time light component and what
+
+ align:start position:0%
+it to the time light component and what
+ 
+
+ align:start position:0%
+it to the time light component and what
+is the derivative of the world line Z
+
+ align:start position:0%
+is the derivative of the world line Z
+ 
+
+ align:start position:0%
+is the derivative of the world line Z
+component with respect to proper time
+
+ align:start position:0%
+component with respect to proper time
+ 
+
+ align:start position:0%
+component with respect to proper time
+it's the zero complement of the for
+
+ align:start position:0%
+it's the zero complement of the for
+ 
+
+ align:start position:0%
+it's the zero complement of the for
+velocity so you just divide by zero
+
+ align:start position:0%
+velocity so you just divide by zero
+ 
+
+ align:start position:0%
+velocity so you just divide by zero
+content of the floor velocity and then
+
+ align:start position:0%
+content of the floor velocity and then
+ 
+
+ align:start position:0%
+content of the floor velocity and then
+you're left with a three dimensional
+
+ align:start position:0%
+you're left with a three dimensional
+ 
+
+ align:start position:0%
+you're left with a three dimensional
+Delta function for the spatial
+
+ align:start position:0%
+Delta function for the spatial
+ 
+
+ align:start position:0%
+Delta function for the spatial
+trajectory of this thing through all
+
+ align:start position:0%
+trajectory of this thing through all
+ 
+
+ align:start position:0%
+trajectory of this thing through all
+space so it's an example of one that
+
+ align:start position:0%
+space so it's an example of one that
+ 
+
+ align:start position:0%
+space so it's an example of one that
+just again kind of the intuition is one
+
+ align:start position:0%
+just again kind of the intuition is one
+ 
+
+ align:start position:0%
+just again kind of the intuition is one
+things I want to emphasize notice we had
+
+ align:start position:0%
+things I want to emphasize notice we had
+ 
+
+ align:start position:0%
+things I want to emphasize notice we had
+this hat it's the symmetries that we
+
+ align:start position:0%
+this hat it's the symmetries that we
+ 
+
+ align:start position:0%
+this hat it's the symmetries that we
+want it to have it's not hard to show
+
+ align:start position:0%
+want it to have it's not hard to show
+ 
+
+ align:start position:0%
+want it to have it's not hard to show
+that this you can think of this as
+
+ align:start position:0%
+that this you can think of this as
+ 
+
+ align:start position:0%
+that this you can think of this as
+essentially being kinda like a gamma
+
+ align:start position:0%
+essentially being kinda like a gamma
+ 
+
+ align:start position:0%
+essentially being kinda like a gamma
+factor this all ends up giving me just
+
+ align:start position:0%
+factor this all ends up giving me just
+ 
+
+ align:start position:0%
+factor this all ends up giving me just
+what we need for this thing to have the
+
+ align:start position:0%
+what we need for this thing to have the
+ 
+
+ align:start position:0%
+what we need for this thing to have the
+right transformation properties and so
+
+ align:start position:0%
+right transformation properties and so
+ 
+
+ align:start position:0%
+right transformation properties and so
+and it does in fact play a role in some
+
+ align:start position:0%
+and it does in fact play a role in some
+ 
+
+ align:start position:0%
+and it does in fact play a role in some
+I'll just say in some research that's
+
+ align:start position:0%
+I'll just say in some research that's
+ 
+
+ align:start position:0%
+I'll just say in some research that's
+near and dear to my heart let me do
+
+ align:start position:0%
+near and dear to my heart let me do
+ 
+
+ align:start position:0%
+near and dear to my heart let me do
+another example suppose you want to know
+
+ align:start position:0%
+another example suppose you want to know
+ 
+
+ align:start position:0%
+another example suppose you want to know
+the stress energy tensor associated with
+
+ align:start position:0%
+the stress energy tensor associated with
+ 
+
+ align:start position:0%
+the stress energy tensor associated with
+a given electric and magnetic field well
+
+ align:start position:0%
+a given electric and magnetic field well
+ 
+
+ align:start position:0%
+a given electric and magnetic field well
+first let me just quote for you the
+
+ align:start position:0%
+first let me just quote for you the
+ 
+
+ align:start position:0%
+first let me just quote for you the
+exact answer which is most compactly
+
+ align:start position:0%
+exact answer which is most compactly
+ 
+
+ align:start position:0%
+exact answer which is most compactly
+written if we use that Faraday tensor F
+
+ align:start position:0%
+written if we use that Faraday tensor F
+ 
+
+ align:start position:0%
+written if we use that Faraday tensor F
+which describes Electric magnetic fields
+
+ align:start position:0%
+which describes Electric magnetic fields
+ 
+
+ align:start position:0%
+which describes Electric magnetic fields
+in a frame independent fashion the way
+
+ align:start position:0%
+in a frame independent fashion the way
+ 
+
+ align:start position:0%
+in a frame independent fashion the way
+that I introduced it in the last lecture
+
+ align:start position:0%
+that I introduced it in the last lecture
+ 
+
+ align:start position:0%
+that I introduced it in the last lecture
+so in units where basically everything
+
+ align:start position:0%
+so in units where basically everything
+ 
+
+ align:start position:0%
+so in units where basically everything
+but pi is set equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it ends up turning into this okay so
+
+ align:start position:0%
+it ends up turning into this okay so
+ 
+
+ align:start position:0%
+it ends up turning into this okay so
+that's a bit of a mouthful let's go in
+
+ align:start position:0%
+that's a bit of a mouthful let's go in
+ 
+
+ align:start position:0%
+that's a bit of a mouthful let's go in
+and look at particular components of it
+
+ align:start position:0%
+and look at particular components of it
+ 
+
+ align:start position:0%
+and look at particular components of it
+though okay so let's say I go into a
+
+ align:start position:0%
+though okay so let's say I go into a
+ 
+
+ align:start position:0%
+though okay so let's say I go into a
+particular frame I fill in my Faraday
+
+ align:start position:0%
+particular frame I fill in my Faraday
+ 
+
+ align:start position:0%
+particular frame I fill in my Faraday
+tensor with the form of the electric
+
+ align:start position:0%
+tensor with the form of the electric
+ 
+
+ align:start position:0%
+tensor with the form of the electric
+magnetic field that I introduced last
+
+ align:start position:0%
+magnetic field that I introduced last
+ 
+
+ align:start position:0%
+magnetic field that I introduced last
+time and I'll just go through and I'll
+
+ align:start position:0%
+time and I'll just go through and I'll
+ 
+
+ align:start position:0%
+time and I'll just go through and I'll
+evaluate all the different components of
+
+ align:start position:0%
+evaluate all the different components of
+ 
+
+ align:start position:0%
+evaluate all the different components of
+this thing so what you find when you
+
+ align:start position:0%
+this thing so what you find when you
+ 
+
+ align:start position:0%
+this thing so what you find when you
+fill this in is your T zero zero
+
+ align:start position:0%
+fill this in is your T zero zero
+ 
+
+ align:start position:0%
+fill this in is your T zero zero
+component 1 over 8 pi e squared plus B
+
+ align:start position:0%
+component 1 over 8 pi e squared plus B
+ 
+
+ align:start position:0%
+component 1 over 8 pi e squared plus B
+squared okay that's good okay hopefully
+
+ align:start position:0%
+squared okay that's good okay hopefully
+ 
+
+ align:start position:0%
+squared okay that's good okay hopefully
+you all remember from basic E&M the
+
+ align:start position:0%
+you all remember from basic E&M the
+ 
+
+ align:start position:0%
+you all remember from basic E&M the
+energy density of an e field is e
+
+ align:start position:0%
+energy density of an e field is e
+ 
+
+ align:start position:0%
+energy density of an e field is e
+squared over 8 pi from the right system
+
+ align:start position:0%
+squared over 8 pi from the right system
+ 
+
+ align:start position:0%
+squared over 8 pi from the right system
+of units energy dance with a B field is
+
+ align:start position:0%
+of units energy dance with a B field is
+ 
+
+ align:start position:0%
+of units energy dance with a B field is
+B squared over 8 pi if you work in
+
+ align:start position:0%
+B squared over 8 pi if you work in
+ 
+
+ align:start position:0%
+B squared over 8 pi if you work in
+gaad's units let's do the time-space
+
+ align:start position:0%
+gaad's units let's do the time-space
+ 
+
+ align:start position:0%
+gaad's units let's do the time-space
+component so again hack through that
+
+ align:start position:0%
+component so again hack through that
+ 
+
+ align:start position:0%
+component so again hack through that
+mess there this is going to be something
+
+ align:start position:0%
+mess there this is going to be something
+ 
+
+ align:start position:0%
+mess there this is going to be something
+that is a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact it's the pointing vector okay
+
+ align:start position:0%
+in fact it's the pointing vector okay
+ 
+
+ align:start position:0%
+in fact it's the pointing vector okay
+could it be anything else if you use the
+
+ align:start position:0%
+could it be anything else if you use the
+ 
+
+ align:start position:0%
+could it be anything else if you use the
+recipe that I sort of suggested is the
+
+ align:start position:0%
+recipe that I sort of suggested is the
+ 
+
+ align:start position:0%
+recipe that I sort of suggested is the
+you know the easiest way to approach
+
+ align:start position:0%
+you know the easiest way to approach
+ 
+
+ align:start position:0%
+you know the easiest way to approach
+this this is kind of what you would have
+
+ align:start position:0%
+this this is kind of what you would have
+ 
+
+ align:start position:0%
+this this is kind of what you would have
+guessed for something like that the bit
+
+ align:start position:0%
+guessed for something like that the bit
+ 
+
+ align:start position:0%
+guessed for something like that the bit
+that's actually kind of hard is then
+
+ align:start position:0%
+that's actually kind of hard is then
+ 
+
+ align:start position:0%
+that's actually kind of hard is then
+trying to get the spatial stresses of
+
+ align:start position:0%
+trying to get the spatial stresses of
+ 
+
+ align:start position:0%
+trying to get the spatial stresses of
+this thing and here I don't have any
+
+ align:start position:0%
+this thing and here I don't have any
+ 
+
+ align:start position:0%
+this thing and here I don't have any
+great intuition for this one to convey
+
+ align:start position:0%
+great intuition for this one to convey
+ 
+
+ align:start position:0%
+great intuition for this one to convey
+to you it's derived in textbooks like
+
+ align:start position:0%
+to you it's derived in textbooks like
+ 
+
+ align:start position:0%
+to you it's derived in textbooks like
+Griffiths and Jackson so I'll just quote
+
+ align:start position:0%
+Griffiths and Jackson so I'll just quote
+ 
+
+ align:start position:0%
+Griffiths and Jackson so I'll just quote
+for you the result so you get one term
+
+ align:start position:0%
+for you the result so you get one term
+ 
+
+ align:start position:0%
+for you the result so you get one term
+it looks like a squared plus B squared
+
+ align:start position:0%
+it looks like a squared plus B squared
+ 
+
+ align:start position:0%
+it looks like a squared plus B squared
+on the diagonals then there's a
+
+ align:start position:0%
+on the diagonals then there's a
+ 
+
+ align:start position:0%
+on the diagonals then there's a
+correction which looks like this I want
+
+ align:start position:0%
+correction which looks like this I want
+ 
+
+ align:start position:0%
+correction which looks like this I want
+to just quickly call out one example so
+
+ align:start position:0%
+to just quickly call out one example so
+ 
+
+ align:start position:0%
+to just quickly call out one example so
+you can see what the significance of
+
+ align:start position:0%
+you can see what the significance of
+ 
+
+ align:start position:0%
+you can see what the significance of
+this example is so suppose you have
+
+ align:start position:0%
+this example is so suppose you have
+ 
+
+ align:start position:0%
+this example is so suppose you have
+something like a pair of capacitors
+
+ align:start position:0%
+something like a pair of capacitors
+ 
+
+ align:start position:0%
+something like a pair of capacitors
+right and there's just a uniform
+
+ align:start position:0%
+right and there's just a uniform
+ 
+
+ align:start position:0%
+right and there's just a uniform
+electric field between them you want to
+
+ align:start position:0%
+electric field between them you want to
+ 
+
+ align:start position:0%
+electric field between them you want to
+evaluate the stress energy tensor
+
+ align:start position:0%
+evaluate the stress energy tensor
+ 
+
+ align:start position:0%
+evaluate the stress energy tensor
+between those pairs of capacitors so my
+
+ align:start position:0%
+between those pairs of capacitors so my
+ 
+
+ align:start position:0%
+between those pairs of capacitors so my
+spatial electric field let's say it just
+
+ align:start position:0%
+spatial electric field let's say it just
+ 
+
+ align:start position:0%
+spatial electric field let's say it just
+points in the x-direction and it's
+
+ align:start position:0%
+points in the x-direction and it's
+ 
+
+ align:start position:0%
+points in the x-direction and it's
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you actually evaluate this guy
+
+ align:start position:0%
+so when you actually evaluate this guy
+ 
+
+ align:start position:0%
+so when you actually evaluate this guy
+there's no energy flow there's no
+
+ align:start position:0%
+there's no energy flow there's no
+ 
+
+ align:start position:0%
+there's no energy flow there's no
+magnetic field so there's no pointing
+
+ align:start position:0%
+magnetic field so there's no pointing
+ 
+
+ align:start position:0%
+magnetic field so there's no pointing
+factor you of course have a squared over
+
+ align:start position:0%
+factor you of course have a squared over
+ 
+
+ align:start position:0%
+factor you of course have a squared over
+8 pi for your energy density okay
+
+ align:start position:0%
+8 pi for your energy density okay
+ 
+
+ align:start position:0%
+8 pi for your energy density okay
+very different from a perfect fluid okay
+
+ align:start position:0%
+very different from a perfect fluid okay
+ 
+
+ align:start position:0%
+very different from a perfect fluid okay
+and this kind of makes sense that's sort
+
+ align:start position:0%
+and this kind of makes sense that's sort
+ 
+
+ align:start position:0%
+and this kind of makes sense that's sort
+of telling you that there is a stress
+
+ align:start position:0%
+of telling you that there is a stress
+ 
+
+ align:start position:0%
+of telling you that there is a stress
+that you know if you have a pair of
+
+ align:start position:0%
+that you know if you have a pair of
+ 
+
+ align:start position:0%
+that you know if you have a pair of
+plain parallel capacitors you tend to
+
+ align:start position:0%
+plain parallel capacitors you tend to
+ 
+
+ align:start position:0%
+plain parallel capacitors you tend to
+attract the plates to each other right
+
+ align:start position:0%
+attract the plates to each other right
+ 
+
+ align:start position:0%
+attract the plates to each other right
+but there's a pressure associate that
+
+ align:start position:0%
+but there's a pressure associate that
+ 
+
+ align:start position:0%
+but there's a pressure associate that
+electric field it actually goes in the
+
+ align:start position:0%
+electric field it actually goes in the
+ 
+
+ align:start position:0%
+electric field it actually goes in the
+other directions okay this is your X
+
+ align:start position:0%
+other directions okay this is your X
+ 
+
+ align:start position:0%
+other directions okay this is your X
+Direction this is y and z and as a
+
+ align:start position:0%
+Direction this is y and z and as a
+ 
+
+ align:start position:0%
+Direction this is y and z and as a
+consequence of this so there's some
+
+ align:start position:0%
+consequence of this so there's some
+ 
+
+ align:start position:0%
+consequence of this so there's some
+stuff which we're not going to do too
+
+ align:start position:0%
+stuff which we're not going to do too
+ 
+
+ align:start position:0%
+stuff which we're not going to do too
+much with in this class but I may give
+
+ align:start position:0%
+much with in this class but I may give
+ 
+
+ align:start position:0%
+much with in this class but I may give
+you some pointers on this electric and
+
+ align:start position:0%
+you some pointers on this electric and
+ 
+
+ align:start position:0%
+you some pointers on this electric and
+magnetic fields generates they generate
+
+ align:start position:0%
+magnetic fields generates they generate
+ 
+
+ align:start position:0%
+magnetic fields generates they generate
+pressures at least in certain directions
+
+ align:start position:0%
+pressures at least in certain directions
+ 
+
+ align:start position:0%
+pressures at least in certain directions
+they kind of generate like an
+
+ align:start position:0%
+they kind of generate like an
+ 
+
+ align:start position:0%
+they kind of generate like an
+anisotropic pressure ah and when we
+
+ align:start position:0%
+anisotropic pressure ah and when we
+ 
+
+ align:start position:0%
+anisotropic pressure ah and when we
+start coupling this to gravity you can
+
+ align:start position:0%
+start coupling this to gravity you can
+ 
+
+ align:start position:0%
+start coupling this to gravity you can
+get electric fields and magnetic fields
+
+ align:start position:0%
+get electric fields and magnetic fields
+ 
+
+ align:start position:0%
+get electric fields and magnetic fields
+that contribute non negligibly to the
+
+ align:start position:0%
+that contribute non negligibly to the
+ 
+
+ align:start position:0%
+that contribute non negligibly to the
+gravity of their object that is it for
+
+ align:start position:0%
+gravity of their object that is it for
+ 
+
+ align:start position:0%
+gravity of their object that is it for
+the stress energy tensor as I said we
+
+ align:start position:0%
+the stress energy tensor as I said we
+ 
+
+ align:start position:0%
+the stress energy tensor as I said we
+are going to use this guy over and over
+
+ align:start position:0%
+are going to use this guy over and over
+ 
+
+ align:start position:0%
+are going to use this guy over and over
+and over again and the reason for this
+
+ align:start position:0%
+and over again and the reason for this
+ 
+
+ align:start position:0%
+and over again and the reason for this
+does come back to that little motivation
+
+ align:start position:0%
+does come back to that little motivation
+ 
+
+ align:start position:0%
+does come back to that little motivation
+that I gave probably about 45 minutes
+
+ align:start position:0%
+that I gave probably about 45 minutes
+ 
+
+ align:start position:0%
+that I gave probably about 45 minutes
+ago where we sort of looked at the
+
+ align:start position:0%
+ago where we sort of looked at the
+ 
+
+ align:start position:0%
+ago where we sort of looked at the
+Newtonian field equation and instead
+
+ align:start position:0%
+Newtonian field equation and instead
+ 
+
+ align:start position:0%
+Newtonian field equation and instead
+picking out a particular scalar as the
+
+ align:start position:0%
+picking out a particular scalar as the
+ 
+
+ align:start position:0%
+picking out a particular scalar as the
+source of gravity makes no sense in a
+
+ align:start position:0%
+source of gravity makes no sense in a
+ 
+
+ align:start position:0%
+source of gravity makes no sense in a
+relativistic covariant Theory it's got
+
+ align:start position:0%
+relativistic covariant Theory it's got
+ 
+
+ align:start position:0%
+relativistic covariant Theory it's got
+to be the whole tensor and indeed this
+
+ align:start position:0%
+to be the whole tensor and indeed this
+ 
+
+ align:start position:0%
+to be the whole tensor and indeed this
+is the one well not actually the enm one
+
+ align:start position:0%
+is the one well not actually the enm one
+ 
+
+ align:start position:0%
+is the one well not actually the enm one
+but the general notion of a stress
+
+ align:start position:0%
+but the general notion of a stress
+ 
+
+ align:start position:0%
+but the general notion of a stress
+energy tensor is the one that we are
+
+ align:start position:0%
+energy tensor is the one that we are
+ 
+
+ align:start position:0%
+energy tensor is the one that we are
+going to use for that so we have about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 minutes left and so I would like to
+
+ align:start position:0%
+10 minutes left and so I would like to
+ 
+
+ align:start position:0%
+10 minutes left and so I would like to
+start the process of switching gears
+
+ align:start position:0%
+start the process of switching gears
+ 
+
+ align:start position:0%
+start the process of switching gears
+before I do that are there any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right I will clean the board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the reason we are switching gears is
+
+ align:start position:0%
+so the reason we are switching gears is
+ 
+
+ align:start position:0%
+so the reason we are switching gears is
+we now have probably the most important
+
+ align:start position:0%
+we now have probably the most important
+ 
+
+ align:start position:0%
+we now have probably the most important
+physical tools that we need in order to
+
+ align:start position:0%
+physical tools that we need in order to
+ 
+
+ align:start position:0%
+physical tools that we need in order to
+start thinking about making a
+
+ align:start position:0%
+start thinking about making a
+ 
+
+ align:start position:0%
+start thinking about making a
+relativistic theory of gravity but we
+
+ align:start position:0%
+relativistic theory of gravity but we
+ 
+
+ align:start position:0%
+relativistic theory of gravity but we
+need a few more mathematical tools in
+
+ align:start position:0%
+need a few more mathematical tools in
+ 
+
+ align:start position:0%
+need a few more mathematical tools in
+particular I'm going to argue in a
+
+ align:start position:0%
+particular I'm going to argue in a
+ 
+
+ align:start position:0%
+particular I'm going to argue in a
+couple of lectures that flat space-time
+
+ align:start position:0%
+couple of lectures that flat space-time
+ 
+
+ align:start position:0%
+couple of lectures that flat space-time
+is not sufficient for us to build a
+
+ align:start position:0%
+is not sufficient for us to build a
+ 
+
+ align:start position:0%
+is not sufficient for us to build a
+theory of gravity we're going to need to
+
+ align:start position:0%
+theory of gravity we're going to need to
+ 
+
+ align:start position:0%
+theory of gravity we're going to need to
+firstly you have to understand what that
+
+ align:start position:0%
+firstly you have to understand what that
+ 
+
+ align:start position:0%
+firstly you have to understand what that
+means and we're not quite ready to go
+
+ align:start position:0%
+means and we're not quite ready to go
+ 
+
+ align:start position:0%
+means and we're not quite ready to go
+there so for now it's just fancy words
+
+ align:start position:0%
+there so for now it's just fancy words
+ 
+
+ align:start position:0%
+there so for now it's just fancy words
+but I'm gonna have to introduce some
+
+ align:start position:0%
+but I'm gonna have to introduce some
+ 
+
+ align:start position:0%
+but I'm gonna have to introduce some
+kind of a notion of curvature into
+
+ align:start position:0%
+kind of a notion of curvature into
+ 
+
+ align:start position:0%
+kind of a notion of curvature into
+things okay what does that even mean
+
+ align:start position:0%
+things okay what does that even mean
+ 
+
+ align:start position:0%
+things okay what does that even mean
+really we need to have the tools to do
+
+ align:start position:0%
+really we need to have the tools to do
+ 
+
+ align:start position:0%
+really we need to have the tools to do
+that and so as a prelude to going in
+
+ align:start position:0%
+that and so as a prelude to going in
+ 
+
+ align:start position:0%
+that and so as a prelude to going in
+that direction I will call this my frail
+
+ align:start position:0%
+that direction I will call this my frail
+ 
+
+ align:start position:0%
+that direction I will call this my frail
+OODA curvature what we're going to start
+
+ align:start position:0%
+OODA curvature what we're going to start
+ 
+
+ align:start position:0%
+OODA curvature what we're going to start
+doing is flat space-time in curvilinear
+
+ align:start position:0%
+doing is flat space-time in curvilinear
+ 
+
+ align:start position:0%
+doing is flat space-time in curvilinear
+coordinates and the importance of doing
+
+ align:start position:0%
+coordinates and the importance of doing
+ 
+
+ align:start position:0%
+coordinates and the importance of doing
+this why this is going to be useful to
+
+ align:start position:0%
+this why this is going to be useful to
+ 
+
+ align:start position:0%
+this why this is going to be useful to
+us is that it will introduce a so it'll
+
+ align:start position:0%
+us is that it will introduce a so it'll
+ 
+
+ align:start position:0%
+us is that it will introduce a so it'll
+keep the physics simple it's still gonna
+
+ align:start position:0%
+keep the physics simple it's still gonna
+ 
+
+ align:start position:0%
+keep the physics simple it's still gonna
+be special relativity but it's now going
+
+ align:start position:0%
+be special relativity but it's now going
+ 
+
+ align:start position:0%
+be special relativity but it's now going
+to be special relativity using a
+
+ align:start position:0%
+to be special relativity using a
+ 
+
+ align:start position:0%
+to be special relativity using a
+mathematical structure in which the
+
+ align:start position:0%
+mathematical structure in which the
+ 
+
+ align:start position:0%
+mathematical structure in which the
+basis vectors are no longer constant
+
+ align:start position:0%
+basis vectors are no longer constant
+ 
+
+ align:start position:0%
+basis vectors are no longer constant
+okay so that's going to allow us to
+
+ align:start position:0%
+okay so that's going to allow us to
+ 
+
+ align:start position:0%
+okay so that's going to allow us to
+begin making a couple of mathematical
+
+ align:start position:0%
+begin making a couple of mathematical
+ 
+
+ align:start position:0%
+begin making a couple of mathematical
+tools that are necessary to build
+
+ align:start position:0%
+tools that are necessary to build
+ 
+
+ align:start position:0%
+tools that are necessary to build
+gravity into this theory so we'll start
+
+ align:start position:0%
+gravity into this theory so we'll start
+ 
+
+ align:start position:0%
+gravity into this theory so we'll start
+by replacing this with just simple plain
+
+ align:start position:0%
+by replacing this with just simple plain
+ 
+
+ align:start position:0%
+by replacing this with just simple plain
+polar coordinates okay
+
+ align:start position:0%
+polar coordinates okay
+ 
+
+ align:start position:0%
+polar coordinates okay
+mapped in the usual way so if you want
+
+ align:start position:0%
+mapped in the usual way so if you want
+ 
+
+ align:start position:0%
+mapped in the usual way so if you want
+to go back and forth well at least one
+
+ align:start position:0%
+to go back and forth well at least one
+ 
+
+ align:start position:0%
+to go back and forth well at least one
+way transformation
+
+ align:start position:0%
+way transformation
+ 
+
+ align:start position:0%
+way transformation
+I build X&Y from R and Phi in that usual
+
+ align:start position:0%
+I build X&Y from R and Phi in that usual
+ 
+
+ align:start position:0%
+I build X&Y from R and Phi in that usual
+way there's an inverse mapping as well
+
+ align:start position:0%
+way there's an inverse mapping as well
+ 
+
+ align:start position:0%
+way there's an inverse mapping as well
+which involves trig functions so I'm not
+
+ align:start position:0%
+which involves trig functions so I'm not
+ 
+
+ align:start position:0%
+which involves trig functions so I'm not
+going to write it down one point which I
+
+ align:start position:0%
+going to write it down one point which I
+ 
+
+ align:start position:0%
+going to write it down one point which I
+really want to emphasize here is we are
+
+ align:start position:0%
+really want to emphasize here is we are
+ 
+
+ align:start position:0%
+really want to emphasize here is we are
+going to continue to use a coordinate
+
+ align:start position:0%
+going to continue to use a coordinate
+ 
+
+ align:start position:0%
+going to continue to use a coordinate
+basis and we remind you what that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a coordinate basis means that the
+
+ align:start position:0%
+so a coordinate basis means that the
+ 
+
+ align:start position:0%
+so a coordinate basis means that the
+differential displacement vector from an
+
+ align:start position:0%
+differential displacement vector from an
+ 
+
+ align:start position:0%
+differential displacement vector from an
+event a to a nearby event B is simply
+
+ align:start position:0%
+event a to a nearby event B is simply
+ 
+
+ align:start position:0%
+event a to a nearby event B is simply
+related by differentials of my
+
+ align:start position:0%
+related by differentials of my
+ 
+
+ align:start position:0%
+related by differentials of my
+coordinate contracted on to my basis
+
+ align:start position:0%
+coordinate contracted on to my basis
+ 
+
+ align:start position:0%
+coordinate contracted on to my basis
+factors but when I'm working in a
+
+ align:start position:0%
+factors but when I'm working in a
+ 
+
+ align:start position:0%
+factors but when I'm working in a
+curvilinear coordinate system like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means one of them has a somewhat
+
+ align:start position:0%
+that means one of them has a somewhat
+ 
+
+ align:start position:0%
+that means one of them has a somewhat
+different form from what you were used
+
+ align:start position:0%
+different form from what you were used
+ 
+
+ align:start position:0%
+different form from what you were used
+to okay when you guys talk about the
+
+ align:start position:0%
+to okay when you guys talk about the
+ 
+
+ align:start position:0%
+to okay when you guys talk about the
+differential of a displacement and just
+
+ align:start position:0%
+differential of a displacement and just
+ 
+
+ align:start position:0%
+differential of a displacement and just
+about every physics class up till now if
+
+ align:start position:0%
+about every physics class up till now if
+ 
+
+ align:start position:0%
+about every physics class up till now if
+you have a differential angle you'd want
+
+ align:start position:0%
+you have a differential angle you'd want
+ 
+
+ align:start position:0%
+you have a differential angle you'd want
+to throw an R and E here so it just says
+
+ align:start position:0%
+to throw an R and E here so it just says
+ 
+
+ align:start position:0%
+to throw an R and E here so it just says
+the dimensions of length we ain't gonna
+
+ align:start position:0%
+the dimensions of length we ain't gonna
+ 
+
+ align:start position:0%
+the dimensions of length we ain't gonna
+do that okay and so what this means
+
+ align:start position:0%
+do that okay and so what this means
+ 
+
+ align:start position:0%
+do that okay and so what this means
+since this is an angle every component
+
+ align:start position:0%
+since this is an angle every component
+ 
+
+ align:start position:0%
+since this is an angle every component
+of this has the dimensions of length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means that my basis vector is going
+
+ align:start position:0%
+that means that my basis vector is going
+ 
+
+ align:start position:0%
+that means that my basis vector is going
+to be something that has the dimensions
+
+ align:start position:0%
+to be something that has the dimensions
+ 
+
+ align:start position:0%
+to be something that has the dimensions
+of length associated with it okay
+
+ align:start position:0%
+of length associated with it okay
+ 
+
+ align:start position:0%
+of length associated with it okay
+this in turn means that this is not
+
+ align:start position:0%
+this in turn means that this is not
+ 
+
+ align:start position:0%
+this in turn means that this is not
+going to be a normal basis okay that's
+
+ align:start position:0%
+going to be a normal basis okay that's
+ 
+
+ align:start position:0%
+going to be a normal basis okay that's
+unfortunately a somewhat loaded word
+
+ align:start position:0%
+unfortunately a somewhat loaded word
+ 
+
+ align:start position:0%
+unfortunately a somewhat loaded word
+what I mean by that is that it has not
+
+ align:start position:0%
+what I mean by that is that it has not
+ 
+
+ align:start position:0%
+what I mean by that is that it has not
+been normalized but given that you guys
+
+ align:start position:0%
+been normalized but given that you guys
+ 
+
+ align:start position:0%
+been normalized but given that you guys
+have spent all of your career thinking
+
+ align:start position:0%
+have spent all of your career thinking
+ 
+
+ align:start position:0%
+have spent all of your career thinking
+about the dot product of a unit vector
+
+ align:start position:0%
+about the dot product of a unit vector
+ 
+
+ align:start position:0%
+about the dot product of a unit vector
+with itself of a basis backed with
+
+ align:start position:0%
+with itself of a basis backed with
+ 
+
+ align:start position:0%
+with itself of a basis backed with
+itself equal to one the other meaning of
+
+ align:start position:0%
+itself equal to one the other meaning of
+ 
+
+ align:start position:0%
+itself equal to one the other meaning of
+normal might be good for you to the keep
+
+ align:start position:0%
+normal might be good for you to the keep
+ 
+
+ align:start position:0%
+normal might be good for you to the keep
+thing which I want to emphasize here is
+
+ align:start position:0%
+thing which I want to emphasize here is
+ 
+
+ align:start position:0%
+thing which I want to emphasize here is
+'if i dot e phi does not equal one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one other little bit of notation which I
+
+ align:start position:0%
+one other little bit of notation which I
+ 
+
+ align:start position:0%
+one other little bit of notation which I
+would like to introduce so we are going
+
+ align:start position:0%
+would like to introduce so we are going
+ 
+
+ align:start position:0%
+would like to introduce so we are going
+to want to talk about transformations
+
+ align:start position:0%
+to want to talk about transformations
+ 
+
+ align:start position:0%
+to want to talk about transformations
+between different representations okay
+
+ align:start position:0%
+between different representations okay
+ 
+
+ align:start position:0%
+between different representations okay
+we've done this so far we have generally
+
+ align:start position:0%
+we've done this so far we have generally
+ 
+
+ align:start position:0%
+we've done this so far we have generally
+focused on moving between different
+
+ align:start position:0%
+focused on moving between different
+ 
+
+ align:start position:0%
+focused on moving between different
+reference frames
+
+ align:start position:0%
+reference frames
+ 
+
+ align:start position:0%
+reference frames
+I want to generalize this notion and I'm
+
+ align:start position:0%
+I want to generalize this notion and I'm
+ 
+
+ align:start position:0%
+I want to generalize this notion and I'm
+going to tweak my notation a little bit
+
+ align:start position:0%
+going to tweak my notation a little bit
+ 
+
+ align:start position:0%
+going to tweak my notation a little bit
+to indicate the difference okay so I'm
+
+ align:start position:0%
+to indicate the difference okay so I'm
+ 
+
+ align:start position:0%
+to indicate the difference okay so I'm
+going to call capital L alpha mu bar see
+
+ align:start position:0%
+going to call capital L alpha mu bar see
+ 
+
+ align:start position:0%
+going to call capital L alpha mu bar see
+what I get when I just look at the
+
+ align:start position:0%
+what I get when I just look at the
+ 
+
+ align:start position:0%
+what I get when I just look at the
+variation of coordinate the Alpha
+
+ align:start position:0%
+variation of coordinate the Alpha
+ 
+
+ align:start position:0%
+variation of coordinate the Alpha
+coordinate system sorry the unbarred
+
+ align:start position:0%
+coordinate system sorry the unbarred
+ 
+
+ align:start position:0%
+coordinate system sorry the unbarred
+chord system with the barred one okay so
+
+ align:start position:0%
+chord system with the barred one okay so
+ 
+
+ align:start position:0%
+chord system with the barred one okay so
+this is just it's there's there's no
+
+ align:start position:0%
+this is just it's there's there's no
+ 
+
+ align:start position:0%
+this is just it's there's there's no
+deep things here I just want you to be
+
+ align:start position:0%
+deep things here I just want you to be
+ 
+
+ align:start position:0%
+deep things here I just want you to be
+familiar to notation which I'm going to
+
+ align:start position:0%
+familiar to notation which I'm going to
+ 
+
+ align:start position:0%
+familiar to notation which I'm going to
+use I will always reserve lambda for the
+
+ align:start position:0%
+use I will always reserve lambda for the
+ 
+
+ align:start position:0%
+use I will always reserve lambda for the
+Lorentz transformation okay so in the
+
+ align:start position:0%
+Lorentz transformation okay so in the
+ 
+
+ align:start position:0%
+Lorentz transformation okay so in the
+interest of time you know I'll just I'll
+
+ align:start position:0%
+interest of time you know I'll just I'll
+ 
+
+ align:start position:0%
+interest of time you know I'll just I'll
+write down one of these so this sort of
+
+ align:start position:0%
+write down one of these so this sort of
+ 
+
+ align:start position:0%
+write down one of these so this sort of
+means like for instance suppose that I'm
+
+ align:start position:0%
+means like for instance suppose that I'm
+ 
+
+ align:start position:0%
+means like for instance suppose that I'm
+transforming let's let bard indicate my
+
+ align:start position:0%
+transforming let's let bard indicate my
+ 
+
+ align:start position:0%
+transforming let's let bard indicate my
+polar coordinates unbarred the Cartesian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if I want to transform in one
+
+ align:start position:0%
+okay so if I want to transform in one
+ 
+
+ align:start position:0%
+okay so if I want to transform in one
+direction between my bar to my unbarred
+
+ align:start position:0%
+direction between my bar to my unbarred
+ 
+
+ align:start position:0%
+direction between my bar to my unbarred
+ones this matrix will go through it and
+
+ align:start position:0%
+ones this matrix will go through it and
+ 
+
+ align:start position:0%
+ones this matrix will go through it and
+it looks like this so this is the thing
+
+ align:start position:0%
+it looks like this so this is the thing
+ 
+
+ align:start position:0%
+it looks like this so this is the thing
+which I will call L alpha mu bar okay in
+
+ align:start position:0%
+which I will call L alpha mu bar okay in
+ 
+
+ align:start position:0%
+which I will call L alpha mu bar okay in
+my notes I also give the inverse
+
+ align:start position:0%
+my notes I also give the inverse
+ 
+
+ align:start position:0%
+my notes I also give the inverse
+transmission and I will actually write I
+
+ align:start position:0%
+transmission and I will actually write I
+ 
+
+ align:start position:0%
+transmission and I will actually write I
+have a minute I will write that one down
+
+ align:start position:0%
+have a minute I will write that one down
+ 
+
+ align:start position:0%
+have a minute I will write that one down
+as well the other direction it's just
+
+ align:start position:0%
+as well the other direction it's just
+ 
+
+ align:start position:0%
+as well the other direction it's just
+the matrix that inverts this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason I started to take the
+
+ align:start position:0%
+and the reason I started to take the
+ 
+
+ align:start position:0%
+and the reason I started to take the
+extra 30 seconds or so to write this
+
+ align:start position:0%
+extra 30 seconds or so to write this
+ 
+
+ align:start position:0%
+extra 30 seconds or so to write this
+down is I'm going to call out the fact
+
+ align:start position:0%
+down is I'm going to call out the fact
+ 
+
+ align:start position:0%
+down is I'm going to call out the fact
+that in this kind of a transformation
+
+ align:start position:0%
+that in this kind of a transformation
+ 
+
+ align:start position:0%
+that in this kind of a transformation
+because of the fact that this is a
+
+ align:start position:0%
+because of the fact that this is a
+ 
+
+ align:start position:0%
+because of the fact that this is a
+coordinate basis that has this somewhat
+
+ align:start position:0%
+coordinate basis that has this somewhat
+ 
+
+ align:start position:0%
+coordinate basis that has this somewhat
+unusual property different elements of
+
+ align:start position:0%
+unusual property different elements of
+ 
+
+ align:start position:0%
+unusual property different elements of
+the matrix have different dimensions
+
+ align:start position:0%
+the matrix have different dimensions
+ 
+
+ align:start position:0%
+the matrix have different dimensions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the feature not a bug okay so this is
+
+ align:start position:0%
+the feature not a bug okay so this is
+ 
+
+ align:start position:0%
+the feature not a bug okay so this is
+going to show up I'm gonna do a couple
+
+ align:start position:0%
+going to show up I'm gonna do a couple
+ 
+
+ align:start position:0%
+going to show up I'm gonna do a couple
+more calculations with this a little bit
+
+ align:start position:0%
+more calculations with this a little bit
+ 
+
+ align:start position:0%
+more calculations with this a little bit
+tomorrow
+
+ align:start position:0%
+tomorrow
+ 
+
+ align:start position:0%
+tomorrow
+sorry not tomorrow on Tuesday this is
+
+ align:start position:0%
+sorry not tomorrow on Tuesday this is
+ 
+
+ align:start position:0%
+sorry not tomorrow on Tuesday this is
+gonna show up in the way the metric
+
+ align:start position:0%
+gonna show up in the way the metric
+ 
+
+ align:start position:0%
+gonna show up in the way the metric
+looks okay the metric is gonna have a
+
+ align:start position:0%
+looks okay the metric is gonna have a
+ 
+
+ align:start position:0%
+looks okay the metric is gonna have a
+very different character in this
+
+ align:start position:0%
+very different character in this
+ 
+
+ align:start position:0%
+very different character in this
+coordinate system and we're going to see
+
+ align:start position:0%
+coordinate system and we're going to see
+ 
+
+ align:start position:0%
+coordinate system and we're going to see
+the way in which it basically boils down
+
+ align:start position:0%
+the way in which it basically boils down
+ 
+
+ align:start position:0%
+the way in which it basically boils down
+to is it's gonna pick up a non-trivial
+
+ align:start position:0%
+to is it's gonna pick up a non-trivial
+ 
+
+ align:start position:0%
+to is it's gonna pick up a non-trivial
+functional form it's not going to just
+
+ align:start position:0%
+functional form it's not going to just
+ 
+
+ align:start position:0%
+functional form it's not going to just
+be a constant and that fundamentally
+
+ align:start position:0%
+be a constant and that fundamentally
+ 
+
+ align:start position:0%
+be a constant and that fundamentally
+reflects the fact that the basis vectors
+
+ align:start position:0%
+reflects the fact that the basis vectors
+ 
+
+ align:start position:0%
+reflects the fact that the basis vectors
+are not constant anymore
+
+ align:start position:0%
+are not constant anymore
+ 
+
+ align:start position:0%
+are not constant anymore
+okay we'll end it there
\ No newline at end of file
diff --git a/OZxzHcW663g.txt b/OZxzHcW663g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..525cdb037e379492fcbbe41d72d18f1a1f1b2e73
--- /dev/null
+++ b/OZxzHcW663g.txt
@@ -0,0 +1,883 @@
+align:start position:0%
+ 
+welcome today's problem was actually
+
+ align:start position:0%
+welcome today's problem was actually
+ 
+
+ align:start position:0%
+welcome today's problem was actually
+appeared at in a quiz it appeared in
+
+ align:start position:0%
+appeared at in a quiz it appeared in
+ 
+
+ align:start position:0%
+appeared at in a quiz it appeared in
+quiz 1
+
+ align:start position:0%
+quiz 1
+ 
+
+ align:start position:0%
+quiz 1
+in fall of 1999 as question for the
+
+ align:start position:0%
+in fall of 1999 as question for the
+ 
+
+ align:start position:0%
+in fall of 1999 as question for the
+problem it puts the usual solve the
+
+ align:start position:0%
+problem it puts the usual solve the
+ 
+
+ align:start position:0%
+problem it puts the usual solve the
+following system upside down by saying
+
+ align:start position:0%
+following system upside down by saying
+ 
+
+ align:start position:0%
+following system upside down by saying
+we have some matrix and we know that all
+
+ align:start position:0%
+we have some matrix and we know that all
+ 
+
+ align:start position:0%
+we have some matrix and we know that all
+the solutions to ax equals this vector
+
+ align:start position:0%
+the solutions to ax equals this vector
+ 
+
+ align:start position:0%
+the solutions to ax equals this vector
+here 1 4 1 1 all the solutions to this
+
+ align:start position:0%
+here 1 4 1 1 all the solutions to this
+ 
+
+ align:start position:0%
+here 1 4 1 1 all the solutions to this
+problem are given by x equals 0 1 1 plus
+
+ align:start position:0%
+problem are given by x equals 0 1 1 plus
+ 
+
+ align:start position:0%
+problem are given by x equals 0 1 1 plus
+any number C times 0 to 1 and we're
+
+ align:start position:0%
+any number C times 0 to 1 and we're
+ 
+
+ align:start position:0%
+any number C times 0 to 1 and we're
+asked to say everything that we can
+
+ align:start position:0%
+asked to say everything that we can
+ 
+
+ align:start position:0%
+asked to say everything that we can
+about the columns of the matrix a so I'm
+
+ align:start position:0%
+about the columns of the matrix a so I'm
+ 
+
+ align:start position:0%
+about the columns of the matrix a so I'm
+going to let you pretend that you're on
+
+ align:start position:0%
+going to let you pretend that you're on
+ 
+
+ align:start position:0%
+going to let you pretend that you're on
+an exam try to solve it yourself and
+
+ align:start position:0%
+an exam try to solve it yourself and
+ 
+
+ align:start position:0%
+an exam try to solve it yourself and
+then come back and compare your solution
+
+ align:start position:0%
+then come back and compare your solution
+ 
+
+ align:start position:0%
+then come back and compare your solution
+with mine ok welcome back so the first
+
+ align:start position:0%
+with mine ok welcome back so the first
+ 
+
+ align:start position:0%
+with mine ok welcome back so the first
+thing that you should think about in
+
+ align:start position:0%
+thing that you should think about in
+ 
+
+ align:start position:0%
+thing that you should think about in
+this sort of situation is what is the
+
+ align:start position:0%
+this sort of situation is what is the
+ 
+
+ align:start position:0%
+this sort of situation is what is the
+size of a well we want to multiply a
+
+ align:start position:0%
+size of a well we want to multiply a
+ 
+
+ align:start position:0%
+size of a well we want to multiply a
+with an X that has three entries so a
+
+ align:start position:0%
+with an X that has three entries so a
+ 
+
+ align:start position:0%
+with an X that has three entries so a
+should have three columns
+
+ align:start position:0%
+should have three columns
+ 
+
+ align:start position:0%
+should have three columns
+let me call those columns c1 c2 and c3
+
+ align:start position:0%
+let me call those columns c1 c2 and c3
+ 
+
+ align:start position:0%
+let me call those columns c1 c2 and c3
+and when I take some linear combinations
+
+ align:start position:0%
+and when I take some linear combinations
+ 
+
+ align:start position:0%
+and when I take some linear combinations
+of c1 c2 and c3 I'm going to get this
+
+ align:start position:0%
+of c1 c2 and c3 I'm going to get this
+ 
+
+ align:start position:0%
+of c1 c2 and c3 I'm going to get this
+vector here 1 4 1 1 so all the sea-ice
+
+ align:start position:0%
+vector here 1 4 1 1 so all the sea-ice
+ 
+
+ align:start position:0%
+vector here 1 4 1 1 so all the sea-ice
+c1 c2 and c3 are vectors in R 4 now if
+
+ align:start position:0%
+c1 c2 and c3 are vectors in R 4 now if
+ 
+
+ align:start position:0%
+c1 c2 and c3 are vectors in R 4 now if
+you know about if you learned about
+
+ align:start position:0%
+you know about if you learned about
+ 
+
+ align:start position:0%
+you know about if you learned about
+particular solutions and special
+
+ align:start position:0%
+particular solutions and special
+ 
+
+ align:start position:0%
+particular solutions and special
+solutions then my notation here
+
+ align:start position:0%
+solutions then my notation here
+ 
+
+ align:start position:0%
+solutions then my notation here
+shouldn't surprise you I'm going to call
+
+ align:start position:0%
+shouldn't surprise you I'm going to call
+ 
+
+ align:start position:0%
+shouldn't surprise you I'm going to call
+this vector here X P and this vector
+
+ align:start position:0%
+this vector here X P and this vector
+ 
+
+ align:start position:0%
+this vector here X P and this vector
+here XS and I'm going to use the fact
+
+ align:start position:0%
+here XS and I'm going to use the fact
+ 
+
+ align:start position:0%
+here XS and I'm going to use the fact
+that X P plus C times X s satisfies
+
+ align:start position:0%
+that X P plus C times X s satisfies
+ 
+
+ align:start position:0%
+that X P plus C times X s satisfies
+eighty times this equals B I will call
+
+ align:start position:0%
+eighty times this equals B I will call
+ 
+
+ align:start position:0%
+eighty times this equals B I will call
+this vector B for any number C in
+
+ align:start position:0%
+this vector B for any number C in
+ 
+
+ align:start position:0%
+this vector B for any number C in
+particular what I'm going to conclude is
+
+ align:start position:0%
+particular what I'm going to conclude is
+ 
+
+ align:start position:0%
+particular what I'm going to conclude is
+that when C equals zero we get a times X
+
+ align:start position:0%
+that when C equals zero we get a times X
+ 
+
+ align:start position:0%
+that when C equals zero we get a times X
+P equals B but also that when C equals
+
+ align:start position:0%
+P equals B but also that when C equals
+ 
+
+ align:start position:0%
+P equals B but also that when C equals
+one we get a times X P plus a times X s
+
+ align:start position:0%
+one we get a times X P plus a times X s
+ 
+
+ align:start position:0%
+one we get a times X P plus a times X s
+equals B replacing this by B we get the
+
+ align:start position:0%
+equals B replacing this by B we get the
+ 
+
+ align:start position:0%
+equals B replacing this by B we get the
+dis implies that a times X s equals zero
+
+ align:start position:0%
+dis implies that a times X s equals zero
+ 
+
+ align:start position:0%
+dis implies that a times X s equals zero
+so in trying to find what are the
+
+ align:start position:0%
+so in trying to find what are the
+ 
+
+ align:start position:0%
+so in trying to find what are the
+columns C 1 C 2 and C 3 of the matrix a
+
+ align:start position:0%
+columns C 1 C 2 and C 3 of the matrix a
+ 
+
+ align:start position:0%
+columns C 1 C 2 and C 3 of the matrix a
+let's look at these two equations X P
+
+ align:start position:0%
+let's look at these two equations X P
+ 
+
+ align:start position:0%
+let's look at these two equations X P
+satisfies a times X P equals B and X s
+
+ align:start position:0%
+satisfies a times X P equals B and X s
+ 
+
+ align:start position:0%
+satisfies a times X P equals B and X s
+satisfies a times X s equals 0 again if
+
+ align:start position:0%
+satisfies a times X s equals 0 again if
+ 
+
+ align:start position:0%
+satisfies a times X s equals 0 again if
+you know what particular and special
+
+ align:start position:0%
+you know what particular and special
+ 
+
+ align:start position:0%
+you know what particular and special
+solutions are this shouldn't surprise
+
+ align:start position:0%
+solutions are this shouldn't surprise
+ 
+
+ align:start position:0%
+solutions are this shouldn't surprise
+you but we also know what X P and X s
+
+ align:start position:0%
+you but we also know what X P and X s
+ 
+
+ align:start position:0%
+you but we also know what X P and X s
+are so let's use them to try to
+
+ align:start position:0%
+are so let's use them to try to
+ 
+
+ align:start position:0%
+are so let's use them to try to
+calculate C 1 C 2 and C 3 a times X P
+
+ align:start position:0%
+calculate C 1 C 2 and C 3 a times X P
+ 
+
+ align:start position:0%
+calculate C 1 C 2 and C 3 a times X P
+equals B means that the linear
+
+ align:start position:0%
+equals B means that the linear
+ 
+
+ align:start position:0%
+equals B means that the linear
+combination of C 1 C 2 and C 3 encoded
+
+ align:start position:0%
+combination of C 1 C 2 and C 3 encoded
+ 
+
+ align:start position:0%
+combination of C 1 C 2 and C 3 encoded
+in the vector X P which is 0 1 1 gives
+
+ align:start position:0%
+in the vector X P which is 0 1 1 gives
+ 
+
+ align:start position:0%
+in the vector X P which is 0 1 1 gives
+the vector B so C 1 C 2 C 3 times 0 1 1
+
+ align:start position:0%
+the vector B so C 1 C 2 C 3 times 0 1 1
+ 
+
+ align:start position:0%
+the vector B so C 1 C 2 C 3 times 0 1 1
+gives us 1 4 1 1 in other words C 2 plus
+
+ align:start position:0%
+gives us 1 4 1 1 in other words C 2 plus
+ 
+
+ align:start position:0%
+gives us 1 4 1 1 in other words C 2 plus
+C 3 equal B let's turn our attention to
+
+ align:start position:0%
+C 3 equal B let's turn our attention to
+ 
+
+ align:start position:0%
+C 3 equal B let's turn our attention to
+a times X s equals 0
+
+ align:start position:0%
+a times X s equals 0
+ 
+
+ align:start position:0%
+a times X s equals 0
+this says that C 1 C 2
+
+ align:start position:0%
+this says that C 1 C 2
+ 
+
+ align:start position:0%
+this says that C 1 C 2
+see three times excess was defined to be
+
+ align:start position:0%
+see three times excess was defined to be
+ 
+
+ align:start position:0%
+see three times excess was defined to be
+0 to 1 equals 0 in other words two times
+
+ align:start position:0%
+0 to 1 equals 0 in other words two times
+ 
+
+ align:start position:0%
+0 to 1 equals 0 in other words two times
+C 2 plus C 3 equals 0 now solving this
+
+ align:start position:0%
+C 2 plus C 3 equals 0 now solving this
+ 
+
+ align:start position:0%
+C 2 plus C 3 equals 0 now solving this
+system we were the unknowns are vectors
+
+ align:start position:0%
+system we were the unknowns are vectors
+ 
+
+ align:start position:0%
+system we were the unknowns are vectors
+but it still still just a linear system
+
+ align:start position:0%
+but it still still just a linear system
+ 
+
+ align:start position:0%
+but it still still just a linear system
+we can see for example from the second
+
+ align:start position:0%
+we can see for example from the second
+ 
+
+ align:start position:0%
+we can see for example from the second
+equation that C 3 equals -2 C 2 and
+
+ align:start position:0%
+equation that C 3 equals -2 C 2 and
+ 
+
+ align:start position:0%
+equation that C 3 equals -2 C 2 and
+plugging it back into the original
+
+ align:start position:0%
+plugging it back into the original
+ 
+
+ align:start position:0%
+plugging it back into the original
+equation getting C 2 minus 2 C 2 equals
+
+ align:start position:0%
+equation getting C 2 minus 2 C 2 equals
+ 
+
+ align:start position:0%
+equation getting C 2 minus 2 C 2 equals
+B from which it follows that C 2 is
+
+ align:start position:0%
+B from which it follows that C 2 is
+ 
+
+ align:start position:0%
+B from which it follows that C 2 is
+equal to minus B and that C 3 is equal
+
+ align:start position:0%
+equal to minus B and that C 3 is equal
+ 
+
+ align:start position:0%
+equal to minus B and that C 3 is equal
+to 2 times B so from this tiny amount of
+
+ align:start position:0%
+to 2 times B so from this tiny amount of
+ 
+
+ align:start position:0%
+to 2 times B so from this tiny amount of
+information we just knew the the
+
+ align:start position:0%
+information we just knew the the
+ 
+
+ align:start position:0%
+information we just knew the the
+solutions to this one particular
+
+ align:start position:0%
+solutions to this one particular
+ 
+
+ align:start position:0%
+solutions to this one particular
+equation involving a we got the second
+
+ align:start position:0%
+equation involving a we got the second
+ 
+
+ align:start position:0%
+equation involving a we got the second
+column of a and the third column of a
+
+ align:start position:0%
+column of a and the third column of a
+ 
+
+ align:start position:0%
+column of a and the third column of a
+completely explicitly calculated now
+
+ align:start position:0%
+completely explicitly calculated now
+ 
+
+ align:start position:0%
+completely explicitly calculated now
+what can we say about the first call I
+
+ align:start position:0%
+what can we say about the first call I
+ 
+
+ align:start position:0%
+what can we say about the first call I
+said before that um all the solutions of
+
+ align:start position:0%
+said before that um all the solutions of
+ 
+
+ align:start position:0%
+said before that um all the solutions of
+AX equals B are of the form a particular
+
+ align:start position:0%
+AX equals B are of the form a particular
+ 
+
+ align:start position:0%
+AX equals B are of the form a particular
+solution plus some number times a
+
+ align:start position:0%
+solution plus some number times a
+ 
+
+ align:start position:0%
+solution plus some number times a
+special solution and the information
+
+ align:start position:0%
+special solution and the information
+ 
+
+ align:start position:0%
+special solution and the information
+that we have is that there's just one
+
+ align:start position:0%
+that we have is that there's just one
+ 
+
+ align:start position:0%
+that we have is that there's just one
+number here so we said everything once
+
+ align:start position:0%
+number here so we said everything once
+ 
+
+ align:start position:0%
+number here so we said everything once
+we remove this vector here everything
+
+ align:start position:0%
+we remove this vector here everything
+ 
+
+ align:start position:0%
+we remove this vector here everything
+that we get here will satisfy a times x
+
+ align:start position:0%
+that we get here will satisfy a times x
+ 
+
+ align:start position:0%
+that we get here will satisfy a times x
+equals 0 and the fact that there is only
+
+ align:start position:0%
+equals 0 and the fact that there is only
+ 
+
+ align:start position:0%
+equals 0 and the fact that there is only
+that everything that satisfies a times x
+
+ align:start position:0%
+that everything that satisfies a times x
+ 
+
+ align:start position:0%
+that everything that satisfies a times x
+equals 0 is a multiple of this one
+
+ align:start position:0%
+equals 0 is a multiple of this one
+ 
+
+ align:start position:0%
+equals 0 is a multiple of this one
+vector that was given to us means that
+
+ align:start position:0%
+vector that was given to us means that
+ 
+
+ align:start position:0%
+vector that was given to us means that
+the null space of a has dimension 1
+
+ align:start position:0%
+the null space of a has dimension 1
+ 
+
+ align:start position:0%
+the null space of a has dimension 1
+there is just one special solution so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimension of the null space of a is 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so rank of a is the number of combs
+
+ align:start position:0%
+so rank of a is the number of combs
+ 
+
+ align:start position:0%
+so rank of a is the number of combs
+- this dimension of null space and it's
+
+ align:start position:0%
+- this dimension of null space and it's
+ 
+
+ align:start position:0%
+- this dimension of null space and it's
+equal to 2's rank of a is equal to 2 the
+
+ align:start position:0%
+equal to 2's rank of a is equal to 2 the
+ 
+
+ align:start position:0%
+equal to 2's rank of a is equal to 2 the
+number of linearly independent columns
+
+ align:start position:0%
+number of linearly independent columns
+ 
+
+ align:start position:0%
+number of linearly independent columns
+needs to be 2 as well so the only thing
+
+ align:start position:0%
+needs to be 2 as well so the only thing
+ 
+
+ align:start position:0%
+needs to be 2 as well so the only thing
+that we can say at this point is if the
+
+ align:start position:0%
+that we can say at this point is if the
+ 
+
+ align:start position:0%
+that we can say at this point is if the
+first column was also a multiple of B as
+
+ align:start position:0%
+first column was also a multiple of B as
+ 
+
+ align:start position:0%
+first column was also a multiple of B as
+the second and the third are then the
+
+ align:start position:0%
+the second and the third are then the
+ 
+
+ align:start position:0%
+the second and the third are then the
+ring would be smaller than 2 so that is
+
+ align:start position:0%
+ring would be smaller than 2 so that is
+ 
+
+ align:start position:0%
+ring would be smaller than 2 so that is
+the only thing that cannot happen so c1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not a multiple of B not any multiple
+
+ align:start position:0%
+is not a multiple of B not any multiple
+ 
+
+ align:start position:0%
+is not a multiple of B not any multiple
+cluding not a zero multiple and that's
+
+ align:start position:0%
+cluding not a zero multiple and that's
+ 
+
+ align:start position:0%
+cluding not a zero multiple and that's
+pretty much everything we can say umm
+
+ align:start position:0%
+pretty much everything we can say umm
+ 
+
+ align:start position:0%
+pretty much everything we can say umm
+yes if it was some other multiple of it
+
+ align:start position:0%
+yes if it was some other multiple of it
+ 
+
+ align:start position:0%
+yes if it was some other multiple of it
+then we would be able to find some other
+
+ align:start position:0%
+then we would be able to find some other
+ 
+
+ align:start position:0%
+then we would be able to find some other
+vector here and we would have two
+
+ align:start position:0%
+vector here and we would have two
+ 
+
+ align:start position:0%
+vector here and we would have two
+parameters but it's not and this is
+
+ align:start position:0%
+parameters but it's not and this is
+ 
+
+ align:start position:0%
+parameters but it's not and this is
+everything that we can say about
\ No newline at end of file
diff --git a/Oo4iCE48xCc.txt b/Oo4iCE48xCc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..012b585af202b180ead88b56fdc8784e41e25558
--- /dev/null
+++ b/Oo4iCE48xCc.txt
@@ -0,0 +1,10459 @@
+align:start position:0%
+ 
+fault tolerant Computing and today's
+
+ align:start position:0%
+fault tolerant Computing and today's
+ 
+
+ align:start position:0%
+fault tolerant Computing and today's
+topic is um one of the most important
+
+ align:start position:0%
+topic is um one of the most important
+ 
+
+ align:start position:0%
+topic is um one of the most important
+Concepts in this uh in this area and
+
+ align:start position:0%
+Concepts in this uh in this area and
+ 
+
+ align:start position:0%
+Concepts in this uh in this area and
+it's called atomicity and what we're
+
+ align:start position:0%
+it's called atomicity and what we're
+ 
+
+ align:start position:0%
+it's called atomicity and what we're
+going to do is spend time um
+
+ align:start position:0%
+going to do is spend time um
+ 
+
+ align:start position:0%
+going to do is spend time um
+understanding what this is as a concept
+
+ align:start position:0%
+understanding what this is as a concept
+ 
+
+ align:start position:0%
+understanding what this is as a concept
+and then understanding how to achieve um
+
+ align:start position:0%
+and then understanding how to achieve um
+ 
+
+ align:start position:0%
+and then understanding how to achieve um
+atomicity in in U
+
+ align:start position:0%
+atomicity in in U
+ 
+
+ align:start position:0%
+atomicity in in U
+systems and recall that the main
+
+ align:start position:0%
+systems and recall that the main
+ 
+
+ align:start position:0%
+systems and recall that the main
+goal is to handle failures and that's
+
+ align:start position:0%
+goal is to handle failures and that's
+ 
+
+ align:start position:0%
+goal is to handle failures and that's
+what we talked about um the last time um
+
+ align:start position:0%
+what we talked about um the last time um
+ 
+
+ align:start position:0%
+what we talked about um the last time um
+and we came up with a bunch of different
+
+ align:start position:0%
+and we came up with a bunch of different
+ 
+
+ align:start position:0%
+and we came up with a bunch of different
+ways of thinking about failures and how
+
+ align:start position:0%
+ways of thinking about failures and how
+ 
+
+ align:start position:0%
+ways of thinking about failures and how
+to cope with it and one idea that we saw
+
+ align:start position:0%
+to cope with it and one idea that we saw
+ 
+
+ align:start position:0%
+to cope with it and one idea that we saw
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+time was an idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involving replicating a component um
+
+ align:start position:0%
+involving replicating a component um
+ 
+
+ align:start position:0%
+involving replicating a component um
+let's say you know a dis or um any um
+
+ align:start position:0%
+let's say you know a dis or um any um
+ 
+
+ align:start position:0%
+let's say you know a dis or um any um
+component that you wish to U whose
+
+ align:start position:0%
+component that you wish to U whose
+ 
+
+ align:start position:0%
+component that you wish to U whose
+failure you wish to cope with and vote
+
+ align:start position:0%
+failure you wish to cope with and vote
+ 
+
+ align:start position:0%
+failure you wish to cope with and vote
+on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+results and so the idea is that um if
+
+ align:start position:0%
+results and so the idea is that um if
+ 
+
+ align:start position:0%
+results and so the idea is that um if
+you're not exactly sure what the right
+
+ align:start position:0%
+you're not exactly sure what the right
+ 
+
+ align:start position:0%
+you're not exactly sure what the right
+answer should be if you're not sure
+
+ align:start position:0%
+answer should be if you're not sure
+ 
+
+ align:start position:0%
+answer should be if you're not sure
+whether any given component is working
+
+ align:start position:0%
+whether any given component is working
+ 
+
+ align:start position:0%
+whether any given component is working
+correctly or not replicate that
+
+ align:start position:0%
+correctly or not replicate that
+ 
+
+ align:start position:0%
+correctly or not replicate that
+component and then give them all the
+
+ align:start position:0%
+component and then give them all the
+ 
+
+ align:start position:0%
+component and then give them all the
+same input see what output they produce
+
+ align:start position:0%
+same input see what output they produce
+ 
+
+ align:start position:0%
+same input see what output they produce
+and then vote on the results and it turn
+
+ align:start position:0%
+and then vote on the results and it turn
+ 
+
+ align:start position:0%
+and then vote on the results and it turn
+and and we did see that these things are
+
+ align:start position:0%
+and and we did see that these things are
+ 
+
+ align:start position:0%
+and and we did see that these things are
+pretty sophisticated but the main
+
+ align:start position:0%
+pretty sophisticated but the main
+ 
+
+ align:start position:0%
+pretty sophisticated but the main
+problem with replicate plus vote is that
+
+ align:start position:0%
+problem with replicate plus vote is that
+ 
+
+ align:start position:0%
+problem with replicate plus vote is that
+often it's extremely expensive to build
+
+ align:start position:0%
+often it's extremely expensive to build
+ 
+
+ align:start position:0%
+often it's extremely expensive to build
+or very very hard to get right um and
+
+ align:start position:0%
+or very very hard to get right um and
+ 
+
+ align:start position:0%
+or very very hard to get right um and
+second um it often doesn't actually work
+
+ align:start position:0%
+second um it often doesn't actually work
+ 
+
+ align:start position:0%
+second um it often doesn't actually work
+for example uh if you just take um a
+
+ align:start position:0%
+for example uh if you just take um a
+ 
+
+ align:start position:0%
+for example uh if you just take um a
+software program a software module and
+
+ align:start position:0%
+software program a software module and
+ 
+
+ align:start position:0%
+software program a software module and
+you know you make 100 copies or 95
+
+ align:start position:0%
+you know you make 100 copies or 95
+ 
+
+ align:start position:0%
+you know you make 100 copies or 95
+copies of that software module and give
+
+ align:start position:0%
+copies of that software module and give
+ 
+
+ align:start position:0%
+copies of that software module and give
+them all the same input and then vote on
+
+ align:start position:0%
+them all the same input and then vote on
+ 
+
+ align:start position:0%
+them all the same input and then vote on
+the outputs if you have a bug in one of
+
+ align:start position:0%
+the outputs if you have a bug in one of
+ 
+
+ align:start position:0%
+the outputs if you have a bug in one of
+the modules and it's a bug that's
+
+ align:start position:0%
+the modules and it's a bug that's
+ 
+
+ align:start position:0%
+the modules and it's a bug that's
+actually replicated in all of the
+
+ align:start position:0%
+actually replicated in all of the
+ 
+
+ align:start position:0%
+actually replicated in all of the
+modules then all of the replicas are
+
+ align:start position:0%
+modules then all of the replicas are
+ 
+
+ align:start position:0%
+modules then all of the replicas are
+going to give you the same wrong answer
+
+ align:start position:0%
+going to give you the same wrong answer
+ 
+
+ align:start position:0%
+going to give you the same wrong answer
+so the key assumption behind replicating
+
+ align:start position:0%
+so the key assumption behind replicating
+ 
+
+ align:start position:0%
+so the key assumption behind replicating
+and voting is that the replicas are
+
+ align:start position:0%
+and voting is that the replicas are
+ 
+
+ align:start position:0%
+and voting is that the replicas are
+independent of each other and have
+
+ align:start position:0%
+independent of each other and have
+ 
+
+ align:start position:0%
+independent of each other and have
+independent um modes of failure and that
+
+ align:start position:0%
+independent um modes of failure and that
+ 
+
+ align:start position:0%
+independent um modes of failure and that
+may not be true um in all of your
+
+ align:start position:0%
+may not be true um in all of your
+ 
+
+ align:start position:0%
+may not be true um in all of your
+modules and so the way we're going to
+
+ align:start position:0%
+modules and so the way we're going to
+ 
+
+ align:start position:0%
+modules and so the way we're going to
+deal with this problem and even though
+
+ align:start position:0%
+deal with this problem and even though
+ 
+
+ align:start position:0%
+deal with this problem and even though
+it's possible to design software systems
+
+ align:start position:0%
+it's possible to design software systems
+ 
+
+ align:start position:0%
+it's possible to design software systems
+where the replicas are in fact
+
+ align:start position:0%
+where the replicas are in fact
+ 
+
+ align:start position:0%
+where the replicas are in fact
+independent of each other uh it'll turn
+
+ align:start position:0%
+independent of each other uh it'll turn
+ 
+
+ align:start position:0%
+independent of each other uh it'll turn
+out that it's quite expensive to do uh
+
+ align:start position:0%
+out that it's quite expensive to do uh
+ 
+
+ align:start position:0%
+out that it's quite expensive to do uh
+in many cases so what we're going to do
+
+ align:start position:0%
+in many cases so what we're going to do
+ 
+
+ align:start position:0%
+in many cases so what we're going to do
+is to relax this Assumption of having a
+
+ align:start position:0%
+is to relax this Assumption of having a
+ 
+
+ align:start position:0%
+is to relax this Assumption of having a
+system which uh U handles failures by
+
+ align:start position:0%
+system which uh U handles failures by
+ 
+
+ align:start position:0%
+system which uh U handles failures by
+giving the same input to multiple
+
+ align:start position:0%
+giving the same input to multiple
+ 
+
+ align:start position:0%
+giving the same input to multiple
+outputs and then voting on it we're
+
+ align:start position:0%
+outputs and then voting on it we're
+ 
+
+ align:start position:0%
+outputs and then voting on it we're
+going to relax that and instead look at
+
+ align:start position:0%
+going to relax that and instead look at
+ 
+
+ align:start position:0%
+going to relax that and instead look at
+a different
+
+ align:start position:0%
+a different
+ 
+
+ align:start position:0%
+a different
+concept called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recoverability and the idea here is
+
+ align:start position:0%
+recoverability and the idea here is
+ 
+
+ align:start position:0%
+recoverability and the idea here is
+rather than to try to build a system to
+
+ align:start position:0%
+rather than to try to build a system to
+ 
+
+ align:start position:0%
+rather than to try to build a system to
+replicate modules so that to the higher
+
+ align:start position:0%
+replicate modules so that to the higher
+ 
+
+ align:start position:0%
+replicate modules so that to the higher
+layers it looks as if the underlying
+
+ align:start position:0%
+layers it looks as if the underlying
+ 
+
+ align:start position:0%
+layers it looks as if the underlying
+module has never failed because you've
+
+ align:start position:0%
+module has never failed because you've
+ 
+
+ align:start position:0%
+module has never failed because you've
+replicated it um the idea here is to
+
+ align:start position:0%
+replicated it um the idea here is to
+ 
+
+ align:start position:0%
+replicated it um the idea here is to
+allow the underlying module to fail but
+
+ align:start position:0%
+allow the underlying module to fail but
+ 
+
+ align:start position:0%
+allow the underlying module to fail but
+have it failed typically in a fail fast
+
+ align:start position:0%
+have it failed typically in a fail fast
+ 
+
+ align:start position:0%
+have it failed typically in a fail fast
+manner so that you can detect the
+
+ align:start position:0%
+manner so that you can detect the
+ 
+
+ align:start position:0%
+manner so that you can detect the
+failure and then arrange for that module
+
+ align:start position:0%
+failure and then arrange for that module
+ 
+
+ align:start position:0%
+failure and then arrange for that module
+to be restarted and when it restarts the
+
+ align:start position:0%
+to be restarted and when it restarts the
+ 
+
+ align:start position:0%
+to be restarted and when it restarts the
+idea is to make it so that module does
+
+ align:start position:0%
+idea is to make it so that module does
+ 
+
+ align:start position:0%
+idea is to make it so that module does
+something such that in the end you know
+
+ align:start position:0%
+something such that in the end you know
+ 
+
+ align:start position:0%
+something such that in the end you know
+know the state of the system after it
+
+ align:start position:0%
+know the state of the system after it
+ 
+
+ align:start position:0%
+know the state of the system after it
+does that thing usually some kind of a
+
+ align:start position:0%
+does that thing usually some kind of a
+ 
+
+ align:start position:0%
+does that thing usually some kind of a
+recovery procedure is that um you can
+
+ align:start position:0%
+recovery procedure is that um you can
+ 
+
+ align:start position:0%
+recovery procedure is that um you can
+get back to using that module so it's a
+
+ align:start position:0%
+get back to using that module so it's a
+ 
+
+ align:start position:0%
+get back to using that module so it's a
+little bit like rather than try to you
+
+ align:start position:0%
+little bit like rather than try to you
+ 
+
+ align:start position:0%
+little bit like rather than try to you
+know build you know the analogy might be
+
+ align:start position:0%
+know build you know the analogy might be
+ 
+
+ align:start position:0%
+know build you know the analogy might be
+something like this uh you might imagine
+
+ align:start position:0%
+something like this uh you might imagine
+ 
+
+ align:start position:0%
+something like this uh you might imagine
+let's say there's a little child who's
+
+ align:start position:0%
+let's say there's a little child who's
+ 
+
+ align:start position:0%
+let's say there's a little child who's
+learning to walk one approach for nature
+
+ align:start position:0%
+learning to walk one approach for nature
+ 
+
+ align:start position:0%
+learning to walk one approach for nature
+to have adopted would have been to try
+
+ align:start position:0%
+to have adopted would have been to try
+ 
+
+ align:start position:0%
+to have adopted would have been to try
+to make it so the child never Falls and
+
+ align:start position:0%
+to make it so the child never Falls and
+ 
+
+ align:start position:0%
+to make it so the child never Falls and
+there's a lot of complexity associated
+
+ align:start position:0%
+there's a lot of complexity associated
+ 
+
+ align:start position:0%
+there's a lot of complexity associated
+with always keeping that child walking
+
+ align:start position:0%
+with always keeping that child walking
+ 
+
+ align:start position:0%
+with always keeping that child walking
+or alternatively you could have a story
+
+ align:start position:0%
+or alternatively you could have a story
+ 
+
+ align:start position:0%
+or alternatively you could have a story
+where or a method by which every once in
+
+ align:start position:0%
+where or a method by which every once in
+ 
+
+ align:start position:0%
+where or a method by which every once in
+a while the Falls but then has a plan to
+
+ align:start position:0%
+a while the Falls but then has a plan to
+ 
+
+ align:start position:0%
+a while the Falls but then has a plan to
+wake up to get up from that fall and
+
+ align:start position:0%
+wake up to get up from that fall and
+ 
+
+ align:start position:0%
+wake up to get up from that fall and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+restart so that's the plan that we're
+
+ align:start position:0%
+restart so that's the plan that we're
+ 
+
+ align:start position:0%
+restart so that's the plan that we're
+going to adopt and this notion here um
+
+ align:start position:0%
+going to adopt and this notion here um
+ 
+
+ align:start position:0%
+going to adopt and this notion here um
+is called recoverability and the general
+
+ align:start position:0%
+is called recoverability and the general
+ 
+
+ align:start position:0%
+is called recoverability and the general
+plan is going to be that if you have a
+
+ align:start position:0%
+plan is going to be that if you have a
+ 
+
+ align:start position:0%
+plan is going to be that if you have a
+module
+
+ align:start position:0%
+module
+ 
+
+ align:start position:0%
+module
+M1 which invokes another module
+
+ align:start position:0%
+M1 which invokes another module
+ 
+
+ align:start position:0%
+M1 which invokes another module
+M2
+
+ align:start position:0%
+M2
+ 
+
+ align:start position:0%
+M2
+and M2 were to
+
+ align:start position:0%
+and M2 were to
+ 
+
+ align:start position:0%
+and M2 were to
+fail then the idea is that M2 fails and
+
+ align:start position:0%
+fail then the idea is that M2 fails and
+ 
+
+ align:start position:0%
+fail then the idea is that M2 fails and
+then it recovers and you restart the
+
+ align:start position:0%
+then it recovers and you restart the
+ 
+
+ align:start position:0%
+then it recovers and you restart the
+module and and you want to make sure
+
+ align:start position:0%
+module and and you want to make sure
+ 
+
+ align:start position:0%
+module and and you want to make sure
+that M2 is left in in a situation once
+
+ align:start position:0%
+that M2 is left in in a situation once
+ 
+
+ align:start position:0%
+that M2 is left in in a situation once
+it recovers where there's no partial
+
+ align:start position:0%
+it recovers where there's no partial
+ 
+
+ align:start position:0%
+it recovers where there's no partial
+State and I'll Define that more
+
+ align:start position:0%
+State and I'll Define that more
+ 
+
+ align:start position:0%
+State and I'll Define that more
+precisely when we as we go along today
+
+ align:start position:0%
+precisely when we as we go along today
+ 
+
+ align:start position:0%
+precisely when we as we go along today
+but the main idea is going to be to
+
+ align:start position:0%
+but the main idea is going to be to
+ 
+
+ align:start position:0%
+but the main idea is going to be to
+ensure that there is no vestage of
+
+ align:start position:0%
+ensure that there is no vestage of
+ 
+
+ align:start position:0%
+ensure that there is no vestage of
+previous computations that are in the
+
+ align:start position:0%
+previous computations that are in the
+ 
+
+ align:start position:0%
+previous computations that are in the
+middle of being wrong so the state of
+
+ align:start position:0%
+middle of being wrong so the state of
+ 
+
+ align:start position:0%
+middle of being wrong so the state of
+the system when it recovers is at a well
+
+ align:start position:0%
+the system when it recovers is at a well
+ 
+
+ align:start position:0%
+the system when it recovers is at a well
+understood point so that M1 can continue
+
+ align:start position:0%
+understood point so that M1 can continue
+ 
+
+ align:start position:0%
+understood point so that M1 can continue
+to use that so there's no partial state
+
+ align:start position:0%
+to use that so there's no partial state
+ 
+
+ align:start position:0%
+to use that so there's no partial state
+where partial uh is in quotes here and
+
+ align:start position:0%
+where partial uh is in quotes here and
+ 
+
+ align:start position:0%
+where partial uh is in quotes here and
+we'll we'll talk about what it means for
+
+ align:start position:0%
+we'll we'll talk about what it means for
+ 
+
+ align:start position:0%
+we'll we'll talk about what it means for
+some something to be in a partial State
+
+ align:start position:0%
+some something to be in a partial State
+ 
+
+ align:start position:0%
+some something to be in a partial State
+the idea is to prevent that from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happening so we're going to do this by
+
+ align:start position:0%
+happening so we're going to do this by
+ 
+
+ align:start position:0%
+happening so we're going to do this by
+um starting with an example and the same
+
+ align:start position:0%
+um starting with an example and the same
+ 
+
+ align:start position:0%
+um starting with an example and the same
+example that I mentioned the last time
+
+ align:start position:0%
+example that I mentioned the last time
+ 
+
+ align:start position:0%
+example that I mentioned the last time
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+was a transfer of money from One bank
+
+ align:start position:0%
+was a transfer of money from One bank
+ 
+
+ align:start position:0%
+was a transfer of money from One bank
+account to another so there's a from
+
+ align:start position:0%
+account to another so there's a from
+ 
+
+ align:start position:0%
+account to another so there's a from
+account there's a two account and some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dollar amount and you want to transfer
+
+ align:start position:0%
+dollar amount and you want to transfer
+ 
+
+ align:start position:0%
+dollar amount and you want to transfer
+money from from to two and it's whatever
+
+ align:start position:0%
+money from from to two and it's whatever
+ 
+
+ align:start position:0%
+money from from to two and it's whatever
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+is and the problem here is of course
+
+ align:start position:0%
+is and the problem here is of course
+ 
+
+ align:start position:0%
+is and the problem here is of course
+that um in the middle of transfer this
+
+ align:start position:0%
+that um in the middle of transfer this
+ 
+
+ align:start position:0%
+that um in the middle of transfer this
+procedure might fail or might crash the
+
+ align:start position:0%
+procedure might fail or might crash the
+ 
+
+ align:start position:0%
+procedure might fail or might crash the
+system might crash and you might be left
+
+ align:start position:0%
+system might crash and you might be left
+ 
+
+ align:start position:0%
+system might crash and you might be left
+in a situation where um a part of this
+
+ align:start position:0%
+in a situation where um a part of this
+ 
+
+ align:start position:0%
+in a situation where um a part of this
+transfer has already run so to take a
+
+ align:start position:0%
+transfer has already run so to take a
+ 
+
+ align:start position:0%
+transfer has already run so to take a
+specific example here's an example of
+
+ align:start position:0%
+specific example here's an example of
+ 
+
+ align:start position:0%
+specific example here's an example of
+what the transfer procedure might look
+
+ align:start position:0%
+what the transfer procedure might look
+ 
+
+ align:start position:0%
+what the transfer procedure might look
+like um so it takes a from and a two and
+
+ align:start position:0%
+like um so it takes a from and a two and
+ 
+
+ align:start position:0%
+like um so it takes a from and a two and
+an amount uh and the first thing it does
+
+ align:start position:0%
+an amount uh and the first thing it does
+ 
+
+ align:start position:0%
+an amount uh and the first thing it does
+is to read from this so assume that all
+
+ align:start position:0%
+is to read from this so assume that all
+ 
+
+ align:start position:0%
+is to read from this so assume that all
+of this data is stored on disk um it
+
+ align:start position:0%
+of this data is stored on disk um it
+ 
+
+ align:start position:0%
+of this data is stored on disk um it
+reads you know from the from account and
+
+ align:start position:0%
+reads you know from the from account and
+ 
+
+ align:start position:0%
+reads you know from the from account and
+then it reduces that debits that amount
+
+ align:start position:0%
+then it reduces that debits that amount
+ 
+
+ align:start position:0%
+then it reduces that debits that amount
+uh debits the amount from that account
+
+ align:start position:0%
+uh debits the amount from that account
+ 
+
+ align:start position:0%
+uh debits the amount from that account
+and then writes back and it does the
+
+ align:start position:0%
+and then writes back and it does the
+ 
+
+ align:start position:0%
+and then writes back and it does the
+same same thing to the two accounts so
+
+ align:start position:0%
+same same thing to the two accounts so
+ 
+
+ align:start position:0%
+same same thing to the two accounts so
+in the end if this procedure completely
+
+ align:start position:0%
+in the end if this procedure completely
+ 
+
+ align:start position:0%
+in the end if this procedure completely
+ran then uh from account would be
+
+ align:start position:0%
+ran then uh from account would be
+ 
+
+ align:start position:0%
+ran then uh from account would be
+reduced by amount and to account would
+
+ align:start position:0%
+reduced by amount and to account would
+ 
+
+ align:start position:0%
+reduced by amount and to account would
+be um enhanced by amount of course the
+
+ align:start position:0%
+be um enhanced by amount of course the
+ 
+
+ align:start position:0%
+be um enhanced by amount of course the
+problem is you might have a failure
+
+ align:start position:0%
+problem is you might have a failure
+ 
+
+ align:start position:0%
+problem is you might have a failure
+anywhere in the middle and as a concrete
+
+ align:start position:0%
+anywhere in the middle and as a concrete
+ 
+
+ align:start position:0%
+anywhere in the middle and as a concrete
+example if the failure were to happen if
+
+ align:start position:0%
+example if the failure were to happen if
+ 
+
+ align:start position:0%
+example if the failure were to happen if
+a crash were to happen after the first
+
+ align:start position:0%
+a crash were to happen after the first
+ 
+
+ align:start position:0%
+a crash were to happen after the first
+three lines shown above um if you owned
+
+ align:start position:0%
+three lines shown above um if you owned
+ 
+
+ align:start position:0%
+three lines shown above um if you owned
+this account you wouldn't be very happy
+
+ align:start position:0%
+this account you wouldn't be very happy
+ 
+
+ align:start position:0%
+this account you wouldn't be very happy
+because you just lost some money from an
+
+ align:start position:0%
+because you just lost some money from an
+ 
+
+ align:start position:0%
+because you just lost some money from an
+account and nothing happened right no no
+
+ align:start position:0%
+account and nothing happened right no no
+ 
+
+ align:start position:0%
+account and nothing happened right no no
+other no no other account got money
+
+ align:start position:0%
+other no no other account got money
+ 
+
+ align:start position:0%
+other no no other account got money
+added to
+
+ align:start position:0%
+added to
+ 
+
+ align:start position:0%
+added to
+it and this is the problem that we want
+
+ align:start position:0%
+it and this is the problem that we want
+ 
+
+ align:start position:0%
+it and this is the problem that we want
+to avoid so if you think about this for
+
+ align:start position:0%
+to avoid so if you think about this for
+ 
+
+ align:start position:0%
+to avoid so if you think about this for
+a moment what you would like intuitively
+
+ align:start position:0%
+a moment what you would like intuitively
+ 
+
+ align:start position:0%
+a moment what you would like intuitively
+is that if a crash like this were to
+
+ align:start position:0%
+is that if a crash like this were to
+ 
+
+ align:start position:0%
+is that if a crash like this were to
+happen and the system were to recover
+
+ align:start position:0%
+happen and the system were to recover
+ 
+
+ align:start position:0%
+happen and the system were to recover
+and come back up there's really only two
+
+ align:start position:0%
+and come back up there's really only two
+ 
+
+ align:start position:0%
+and come back up there's really only two
+states that the system should be in for
+
+ align:start position:0%
+states that the system should be in for
+ 
+
+ align:start position:0%
+states that the system should be in for
+the system to really be correct and to
+
+ align:start position:0%
+the system to really be correct and to
+ 
+
+ align:start position:0%
+the system to really be correct and to
+meet what your intuition might expect
+
+ align:start position:0%
+meet what your intuition might expect
+ 
+
+ align:start position:0%
+meet what your intuition might expect
+either this procedure must completely be
+
+ align:start position:0%
+either this procedure must completely be
+ 
+
+ align:start position:0%
+either this procedure must completely be
+finished that is the state of the system
+
+ align:start position:0%
+finished that is the state of the system
+ 
+
+ align:start position:0%
+finished that is the state of the system
+must be the same as if this procedure
+
+ align:start position:0%
+must be the same as if this procedure
+ 
+
+ align:start position:0%
+must be the same as if this procedure
+completely ran and
+
+ align:start position:0%
+completely ran and
+ 
+
+ align:start position:0%
+completely ran and
+finished or the state of the system must
+
+ align:start position:0%
+finished or the state of the system must
+ 
+
+ align:start position:0%
+finished or the state of the system must
+be such that the procedure never ran at
+
+ align:start position:0%
+be such that the procedure never ran at
+ 
+
+ align:start position:0%
+be such that the procedure never ran at
+all it is not at all okay it's not okay
+
+ align:start position:0%
+all it is not at all okay it's not okay
+ 
+
+ align:start position:0%
+all it is not at all okay it's not okay
+to let the state of the system be um
+
+ align:start position:0%
+to let the state of the system be um
+ 
+
+ align:start position:0%
+to let the state of the system be um
+equal to whatever the state was at the
+
+ align:start position:0%
+equal to whatever the state was at the
+ 
+
+ align:start position:0%
+equal to whatever the state was at the
+time in this example at the time the
+
+ align:start position:0%
+time in this example at the time the
+ 
+
+ align:start position:0%
+time in this example at the time the
+crash
+
+ align:start position:0%
+crash
+ 
+
+ align:start position:0%
+crash
+happened so
+
+ align:start position:0%
+happened so
+ 
+
+ align:start position:0%
+happened so
+what you want is a kind of All or
+
+ align:start position:0%
+what you want is a kind of All or
+ 
+
+ align:start position:0%
+what you want is a kind of All or
+Nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior of course if the crash happened
+
+ align:start position:0%
+behavior of course if the crash happened
+ 
+
+ align:start position:0%
+behavior of course if the crash happened
+as I've shown it here there's no way for
+
+ align:start position:0%
+as I've shown it here there's no way for
+ 
+
+ align:start position:0%
+as I've shown it here there's no way for
+you to have prevented those lines of
+
+ align:start position:0%
+you to have prevented those lines of
+ 
+
+ align:start position:0%
+you to have prevented those lines of
+code from being wrong right those lines
+
+ align:start position:0%
+code from being wrong right those lines
+ 
+
+ align:start position:0%
+code from being wrong right those lines
+of code ran and then the crash happened
+
+ align:start position:0%
+of code ran and then the crash happened
+ 
+
+ align:start position:0%
+of code ran and then the crash happened
+so what you really need is a way by
+
+ align:start position:0%
+so what you really need is a way by
+ 
+
+ align:start position:0%
+so what you really need is a way by
+which you can back out these changes the
+
+ align:start position:0%
+which you can back out these changes the
+ 
+
+ align:start position:0%
+which you can back out these changes the
+what the system needs is a way by which
+
+ align:start position:0%
+what the system needs is a way by which
+ 
+
+ align:start position:0%
+what the system needs is a way by which
+when the system crashes and then the
+
+ align:start position:0%
+when the system crashes and then the
+ 
+
+ align:start position:0%
+when the system crashes and then the
+recovers from the fault from the crash
+
+ align:start position:0%
+recovers from the fault from the crash
+ 
+
+ align:start position:0%
+recovers from the fault from the crash
+um during failure recovery the system
+
+ align:start position:0%
+um during failure recovery the system
+ 
+
+ align:start position:0%
+um during failure recovery the system
+has to have a way to back out of what
+
+ align:start position:0%
+has to have a way to back out of what
+ 
+
+ align:start position:0%
+has to have a way to back out of what
+whatever changes it's
+
+ align:start position:0%
+whatever changes it's
+ 
+
+ align:start position:0%
+whatever changes it's
+made in other words what we want is a
+
+ align:start position:0%
+made in other words what we want is a
+ 
+
+ align:start position:0%
+made in other words what we want is a
+concept called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recoverability so more precise
+
+ align:start position:0%
+recoverability so more precise
+ 
+
+ align:start position:0%
+recoverability so more precise
+definition of recoverability is shown on
+
+ align:start position:0%
+definition of recoverability is shown on
+ 
+
+ align:start position:0%
+definition of recoverability is shown on
+the slide and let me just read it out um
+
+ align:start position:0%
+the slide and let me just read it out um
+ 
+
+ align:start position:0%
+the slide and let me just read it out um
+a composite sequence of steps which
+
+ align:start position:0%
+a composite sequence of steps which
+ 
+
+ align:start position:0%
+a composite sequence of steps which
+we're also going to use the word action
+
+ align:start position:0%
+we're also going to use the word action
+ 
+
+ align:start position:0%
+we're also going to use the word action
+for an action is recoverable if from the
+
+ align:start position:0%
+for an action is recoverable if from the
+ 
+
+ align:start position:0%
+for an action is recoverable if from the
+point of view of the module that invokes
+
+ align:start position:0%
+point of view of the module that invokes
+ 
+
+ align:start position:0%
+point of view of the module that invokes
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+action this sequence either always
+
+ align:start position:0%
+action this sequence either always
+ 
+
+ align:start position:0%
+action this sequence either always
+completes
+
+ align:start position:0%
+completes
+ 
+
+ align:start position:0%
+completes
+or aborts that is if it fails and then
+
+ align:start position:0%
+or aborts that is if it fails and then
+ 
+
+ align:start position:0%
+or aborts that is if it fails and then
+it you know backs out aborts in a way
+
+ align:start position:0%
+it you know backs out aborts in a way
+ 
+
+ align:start position:0%
+it you know backs out aborts in a way
+such that it appears that the sequence
+
+ align:start position:0%
+such that it appears that the sequence
+ 
+
+ align:start position:0%
+such that it appears that the sequence
+sequence had never started to begin with
+
+ align:start position:0%
+sequence had never started to begin with
+ 
+
+ align:start position:0%
+sequence had never started to begin with
+and in particular what this means is
+
+ align:start position:0%
+and in particular what this means is
+ 
+
+ align:start position:0%
+and in particular what this means is
+that if a failure were to happen in the
+
+ align:start position:0%
+that if a failure were to happen in the
+ 
+
+ align:start position:0%
+that if a failure were to happen in the
+middle when the system recovers um it
+
+ align:start position:0%
+middle when the system recovers um it
+ 
+
+ align:start position:0%
+middle when the system recovers um it
+better have a plan of backing out the
+
+ align:start position:0%
+better have a plan of backing out the
+ 
+
+ align:start position:0%
+better have a plan of backing out the
+changes in other words of aborting this
+
+ align:start position:0%
+changes in other words of aborting this
+ 
+
+ align:start position:0%
+changes in other words of aborting this
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+so the way you think about
+
+ align:start position:0%
+so the way you think about
+ 
+
+ align:start position:0%
+so the way you think about
+recoverability the che the the simple
+
+ align:start position:0%
+recoverability the che the the simple
+ 
+
+ align:start position:0%
+recoverability the che the the simple
+way to think about it is is do it all or
+
+ align:start position:0%
+way to think about it is is do it all or
+ 
+
+ align:start position:0%
+way to think about it is is do it all or
+not at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all and our goal is to try to somehow
+
+ align:start position:0%
+all and our goal is to try to somehow
+ 
+
+ align:start position:0%
+all and our goal is to try to somehow
+come up with a way to achieve this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal before we get into a solution to
+
+ align:start position:0%
+goal before we get into a solution to
+ 
+
+ align:start position:0%
+goal before we get into a solution to
+this problem there's a few other
+
+ align:start position:0%
+this problem there's a few other
+ 
+
+ align:start position:0%
+this problem there's a few other
+Concepts um to discuss and they'll turn
+
+ align:start position:0%
+Concepts um to discuss and they'll turn
+ 
+
+ align:start position:0%
+Concepts um to discuss and they'll turn
+out to be very related to each other and
+
+ align:start position:0%
+out to be very related to each other and
+ 
+
+ align:start position:0%
+out to be very related to each other and
+the second concept after recoverability
+
+ align:start position:0%
+the second concept after recoverability
+ 
+
+ align:start position:0%
+the second concept after recoverability
+that's very closely related to this idea
+
+ align:start position:0%
+that's very closely related to this idea
+ 
+
+ align:start position:0%
+that's very closely related to this idea
+idea has to do with concurrent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actions so imagine for a moment that you
+
+ align:start position:0%
+actions so imagine for a moment that you
+ 
+
+ align:start position:0%
+actions so imagine for a moment that you
+had the same transfer procedure as on um
+
+ align:start position:0%
+had the same transfer procedure as on um
+ 
+
+ align:start position:0%
+had the same transfer procedure as on um
+as in this example but you had two
+
+ align:start position:0%
+as in this example but you had two
+ 
+
+ align:start position:0%
+as in this example but you had two
+transfers running at the same
+
+ align:start position:0%
+transfers running at the same
+ 
+
+ align:start position:0%
+transfers running at the same
+time and they happen to act on the same
+
+ align:start position:0%
+time and they happen to act on the same
+ 
+
+ align:start position:0%
+time and they happen to act on the same
+um data
+
+ align:start position:0%
+um data
+ 
+
+ align:start position:0%
+um data
+items like
+
+ align:start position:0%
+items like
+ 
+
+ align:start position:0%
+items like
+that so let's say that the first
+
+ align:start position:0%
+that so let's say that the first
+ 
+
+ align:start position:0%
+that so let's say that the first
+transfer um moved from a saving account
+
+ align:start position:0%
+transfer um moved from a saving account
+ 
+
+ align:start position:0%
+transfer um moved from a saving account
+to checking account it moved
+
+ align:start position:0%
+to checking account it moved
+ 
+
+ align:start position:0%
+to checking account it moved
+$100 and the second one moved from
+
+ align:start position:0%
+$100 and the second one moved from
+ 
+
+ align:start position:0%
+$100 and the second one moved from
+saving to checkings it checking it moved
+
+ align:start position:0%
+saving to checkings it checking it moved
+ 
+
+ align:start position:0%
+saving to checkings it checking it moved
+$200 and let's say at the beginning s
+
+ align:start position:0%
+$200 and let's say at the beginning s
+ 
+
+ align:start position:0%
+$200 and let's say at the beginning s
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th of course as you recall from um
+
+ align:start position:0%
+th of course as you recall from um
+ 
+
+ align:start position:0%
+th of course as you recall from um
+several lectures ago when you have these
+
+ align:start position:0%
+several lectures ago when you have these
+ 
+
+ align:start position:0%
+several lectures ago when you have these
+interl sequences um these two threads
+
+ align:start position:0%
+interl sequences um these two threads
+ 
+
+ align:start position:0%
+interl sequences um these two threads
+are running these the steps um that
+
+ align:start position:0%
+are running these the steps um that
+ 
+
+ align:start position:0%
+are running these the steps um that
+these threads are made of might be
+
+ align:start position:0%
+these threads are made of might be
+ 
+
+ align:start position:0%
+these threads are made of might be
+interleaved in arbitrary order if you
+
+ align:start position:0%
+interleaved in arbitrary order if you
+ 
+
+ align:start position:0%
+interleaved in arbitrary order if you
+don't have a plan to isolate
+
+ align:start position:0%
+don't have a plan to isolate
+ 
+
+ align:start position:0%
+don't have a plan to isolate
+them and in particular you might have
+
+ align:start position:0%
+them and in particular you might have
+ 
+
+ align:start position:0%
+them and in particular you might have
+you know many results that show up and
+
+ align:start position:0%
+you know many results that show up and
+ 
+
+ align:start position:0%
+you know many results that show up and
+one result that might show up is both of
+
+ align:start position:0%
+one result that might show up is both of
+ 
+
+ align:start position:0%
+one result that might show up is both of
+these transfers running concurrently
+
+ align:start position:0%
+these transfers running concurrently
+ 
+
+ align:start position:0%
+these transfers running concurrently
+read the same you know read thousand out
+
+ align:start position:0%
+read the same you know read thousand out
+ 
+
+ align:start position:0%
+read the same you know read thousand out
+from from account and then both of them
+
+ align:start position:0%
+from from account and then both of them
+ 
+
+ align:start position:0%
+from from account and then both of them
+debit by the right by 100 and 200
+
+ align:start position:0%
+debit by the right by 100 and 200
+ 
+
+ align:start position:0%
+debit by the right by 100 and 200
+respectively so at the end of it you
+
+ align:start position:0%
+respectively so at the end of it you
+ 
+
+ align:start position:0%
+respectively so at the end of it you
+might be left with either $800 or $900
+
+ align:start position:0%
+might be left with either $800 or $900
+ 
+
+ align:start position:0%
+might be left with either $800 or $900
+left in the account when the right
+
+ align:start position:0%
+left in the account when the right
+ 
+
+ align:start position:0%
+left in the account when the right
+answer is have been left uh intuitively
+
+ align:start position:0%
+answer is have been left uh intuitively
+ 
+
+ align:start position:0%
+answer is have been left uh intuitively
+if you ran both these transfers you
+
+ align:start position:0%
+if you ran both these transfers you
+ 
+
+ align:start position:0%
+if you ran both these transfers you
+would like to see $700 left uh in that
+
+ align:start position:0%
+would like to see $700 left uh in that
+ 
+
+ align:start position:0%
+would like to see $700 left uh in that
+account right so what you intuitively
+
+ align:start position:0%
+account right so what you intuitively
+ 
+
+ align:start position:0%
+account right so what you intuitively
+want here is if this this is the first
+
+ align:start position:0%
+want here is if this this is the first
+ 
+
+ align:start position:0%
+want here is if this this is the first
+action A1 and this is the second action
+
+ align:start position:0%
+action A1 and this is the second action
+ 
+
+ align:start position:0%
+action A1 and this is the second action
+A2 what you would like to see is a
+
+ align:start position:0%
+A2 what you would like to see is a
+ 
+
+ align:start position:0%
+A2 what you would like to see is a
+sequence you don't actually care what
+
+ align:start position:0%
+sequence you don't actually care what
+ 
+
+ align:start position:0%
+sequence you don't actually care what
+the order is between these two transfers
+
+ align:start position:0%
+the order is between these two transfers
+ 
+
+ align:start position:0%
+the order is between these two transfers
+right I mean you're transferring money
+
+ align:start position:0%
+right I mean you're transferring money
+ 
+
+ align:start position:0%
+right I mean you're transferring money
+from one account to another and you're
+
+ align:start position:0%
+from one account to another and you're
+ 
+
+ align:start position:0%
+from one account to another and you're
+doing two of these you don't actually
+
+ align:start position:0%
+doing two of these you don't actually
+ 
+
+ align:start position:0%
+doing two of these you don't actually
+care in this example and it'll turn out
+
+ align:start position:0%
+care in this example and it'll turn out
+ 
+
+ align:start position:0%
+care in this example and it'll turn out
+in most examples on all examples that
+
+ align:start position:0%
+in most examples on all examples that
+ 
+
+ align:start position:0%
+in most examples on all examples that
+we're going to be talking about um um in
+
+ align:start position:0%
+we're going to be talking about um um in
+ 
+
+ align:start position:0%
+we're going to be talking about um um in
+with this notion that you're not really
+
+ align:start position:0%
+with this notion that you're not really
+ 
+
+ align:start position:0%
+with this notion that you're not really
+going to care what the order is either
+
+ align:start position:0%
+going to care what the order is either
+ 
+
+ align:start position:0%
+going to care what the order is either
+order is perfectly fine but the order
+
+ align:start position:0%
+order is perfectly fine but the order
+ 
+
+ align:start position:0%
+order is perfectly fine but the order
+should be as if it's equivalent to
+
+ align:start position:0%
+should be as if it's equivalent to
+ 
+
+ align:start position:0%
+should be as if it's equivalent to
+either A1 before
+
+ align:start position:0%
+either A1 before
+ 
+
+ align:start position:0%
+either A1 before
+A2
+
+ align:start position:0%
+A2
+ 
+
+ align:start position:0%
+A2
+or A2 before E1 before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A1 and that's what we would
+
+ align:start position:0%
+A1 and that's what we would
+ 
+
+ align:start position:0%
+A1 and that's what we would
+like of course the you know sort of
+
+ align:start position:0%
+like of course the you know sort of
+ 
+
+ align:start position:0%
+like of course the you know sort of
+naive way to achieve this is to ensure
+
+ align:start position:0%
+naive way to achieve this is to ensure
+ 
+
+ align:start position:0%
+naive way to achieve this is to ensure
+that exactly one action runs at a time
+
+ align:start position:0%
+that exactly one action runs at a time
+ 
+
+ align:start position:0%
+that exactly one action runs at a time
+it finishes and then the second one runs
+
+ align:start position:0%
+it finishes and then the second one runs
+ 
+
+ align:start position:0%
+it finishes and then the second one runs
+but that's kind of going to be no fun
+
+ align:start position:0%
+but that's kind of going to be no fun
+ 
+
+ align:start position:0%
+but that's kind of going to be no fun
+for us to do it's the right Simple
+
+ align:start position:0%
+for us to do it's the right Simple
+ 
+
+ align:start position:0%
+for us to do it's the right Simple
+Solution but we're going to want to
+
+ align:start position:0%
+Solution but we're going to want to
+ 
+
+ align:start position:0%
+Solution but we're going to want to
+improve concurrency as we wanted to um
+
+ align:start position:0%
+improve concurrency as we wanted to um
+ 
+
+ align:start position:0%
+improve concurrency as we wanted to um
+you know several lectures ago so we're
+
+ align:start position:0%
+you know several lectures ago so we're
+ 
+
+ align:start position:0%
+you know several lectures ago so we're
+going to come up with ways of getting
+
+ align:start position:0%
+going to come up with ways of getting
+ 
+
+ align:start position:0%
+going to come up with ways of getting
+higher performance than running one
+
+ align:start position:0%
+higher performance than running one
+ 
+
+ align:start position:0%
+higher performance than running one
+after the other but the net effect is as
+
+ align:start position:0%
+after the other but the net effect is as
+ 
+
+ align:start position:0%
+after the other but the net effect is as
+if you run it in some serial order in
+
+ align:start position:0%
+if you run it in some serial order in
+ 
+
+ align:start position:0%
+if you run it in some serial order in
+some sequential order of the actions um
+
+ align:start position:0%
+some sequential order of the actions um
+ 
+
+ align:start position:0%
+some sequential order of the actions um
+that is the result of running concurrent
+
+ align:start position:0%
+that is the result of running concurrent
+ 
+
+ align:start position:0%
+that is the result of running concurrent
+actions has to be the same as some
+
+ align:start position:0%
+actions has to be the same as some
+ 
+
+ align:start position:0%
+actions has to be the same as some
+serial ordering of the of the individual
+
+ align:start position:0%
+serial ordering of the of the individual
+ 
+
+ align:start position:0%
+serial ordering of the of the individual
+actions and this idea of A1 before A2 or
+
+ align:start position:0%
+actions and this idea of A1 before A2 or
+ 
+
+ align:start position:0%
+actions and this idea of A1 before A2 or
+A2 before A1 has a name it's called
+
+ align:start position:0%
+A2 before A1 has a name it's called
+ 
+
+ align:start position:0%
+A2 before A1 has a name it's called
+isolation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you should distinguish that in your
+
+ align:start position:0%
+and you should distinguish that in your
+ 
+
+ align:start position:0%
+and you should distinguish that in your
+mind clearly from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recoverability so more precise
+
+ align:start position:0%
+recoverability so more precise
+ 
+
+ align:start position:0%
+recoverability so more precise
+definition of isolation is essentially
+
+ align:start position:0%
+definition of isolation is essentially
+ 
+
+ align:start position:0%
+definition of isolation is essentially
+what I said before
+
+ align:start position:0%
+what I said before
+ 
+
+ align:start position:0%
+what I said before
+the equivalent the a composite sequence
+
+ align:start position:0%
+the equivalent the a composite sequence
+ 
+
+ align:start position:0%
+the equivalent the a composite sequence
+of steps is isolated if its effect from
+
+ align:start position:0%
+of steps is isolated if its effect from
+ 
+
+ align:start position:0%
+of steps is isolated if its effect from
+the point of view of its invoker is the
+
+ align:start position:0%
+the point of view of its invoker is the
+ 
+
+ align:start position:0%
+the point of view of its invoker is the
+same as if the action occurred either
+
+ align:start position:0%
+same as if the action occurred either
+ 
+
+ align:start position:0%
+same as if the action occurred either
+completely before or completely after
+
+ align:start position:0%
+completely before or completely after
+ 
+
+ align:start position:0%
+completely before or completely after
+every other isolated
+
+ align:start position:0%
+every other isolated
+ 
+
+ align:start position:0%
+every other isolated
+action and the simple way to understand
+
+ align:start position:0%
+action and the simple way to understand
+ 
+
+ align:start position:0%
+action and the simple way to understand
+this is you either do it all before or
+
+ align:start position:0%
+this is you either do it all before or
+ 
+
+ align:start position:0%
+this is you either do it all before or
+do it all after there is the net effect
+
+ align:start position:0%
+do it all after there is the net effect
+ 
+
+ align:start position:0%
+do it all after there is the net effect
+has to be the same as doing it all
+
+ align:start position:0%
+has to be the same as doing it all
+ 
+
+ align:start position:0%
+has to be the same as doing it all
+before or doing it all after and it's
+
+ align:start position:0%
+before or doing it all after and it's
+ 
+
+ align:start position:0%
+before or doing it all after and it's
+different from recoverability which is
+
+ align:start position:0%
+different from recoverability which is
+ 
+
+ align:start position:0%
+different from recoverability which is
+really do it all or not at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all now when you have a A system
+
+ align:start position:0%
+all now when you have a A system
+ 
+
+ align:start position:0%
+all now when you have a A system
+that satisfies both recoverability and
+
+ align:start position:0%
+that satisfies both recoverability and
+ 
+
+ align:start position:0%
+that satisfies both recoverability and
+isolation so the way to understand this
+
+ align:start position:0%
+isolation so the way to understand this
+ 
+
+ align:start position:0%
+isolation so the way to understand this
+is both of these really although they're
+
+ align:start position:0%
+is both of these really although they're
+ 
+
+ align:start position:0%
+is both of these really although they're
+talking about different concepts this is
+
+ align:start position:0%
+talking about different concepts this is
+ 
+
+ align:start position:0%
+talking about different concepts this is
+saying all or nothing and this is saying
+
+ align:start position:0%
+saying all or nothing and this is saying
+ 
+
+ align:start position:0%
+saying all or nothing and this is saying
+all before or all after both of these
+
+ align:start position:0%
+all before or all after both of these
+ 
+
+ align:start position:0%
+all before or all after both of these
+are getting at the same intuitive idea
+
+ align:start position:0%
+are getting at the same intuitive idea
+ 
+
+ align:start position:0%
+are getting at the same intuitive idea
+which is that somehow there's the
+
+ align:start position:0%
+which is that somehow there's the
+ 
+
+ align:start position:0%
+which is that somehow there's the
+sequence of steps in um for example in
+
+ align:start position:0%
+sequence of steps in um for example in
+ 
+
+ align:start position:0%
+sequence of steps in um for example in
+this transfer procedure there are the
+
+ align:start position:0%
+this transfer procedure there are the
+ 
+
+ align:start position:0%
+this transfer procedure there are the
+sequences of steps and somehow you want
+
+ align:start position:0%
+sequences of steps and somehow you want
+ 
+
+ align:start position:0%
+sequences of steps and somehow you want
+to make it look as if for each action um
+
+ align:start position:0%
+to make it look as if for each action um
+ 
+
+ align:start position:0%
+to make it look as if for each action um
+the sequence of steps is not visible to
+
+ align:start position:0%
+the sequence of steps is not visible to
+ 
+
+ align:start position:0%
+the sequence of steps is not visible to
+somebody invoking the action right
+
+ align:start position:0%
+somebody invoking the action right
+ 
+
+ align:start position:0%
+somebody invoking the action right
+because you don't want the person
+
+ align:start position:0%
+because you don't want the person
+ 
+
+ align:start position:0%
+because you don't want the person
+invoking this action for recoverability
+
+ align:start position:0%
+invoking this action for recoverability
+ 
+
+ align:start position:0%
+invoking this action for recoverability
+you don't want him to know that it's
+
+ align:start position:0%
+you don't want him to know that it's
+ 
+
+ align:start position:0%
+you don't want him to know that it's
+built out of sequence of steps and if a
+
+ align:start position:0%
+built out of sequence of steps and if a
+ 
+
+ align:start position:0%
+built out of sequence of steps and if a
+failure happens in the middle you don't
+
+ align:start position:0%
+failure happens in the middle you don't
+ 
+
+ align:start position:0%
+failure happens in the middle you don't
+want the invoker of that action to see
+
+ align:start position:0%
+want the invoker of that action to see
+ 
+
+ align:start position:0%
+want the invoker of that action to see
+some partial State likewise when you
+
+ align:start position:0%
+some partial State likewise when you
+ 
+
+ align:start position:0%
+some partial State likewise when you
+have concurrent actions running together
+
+ align:start position:0%
+have concurrent actions running together
+ 
+
+ align:start position:0%
+have concurrent actions running together
+you don't want the different invokers of
+
+ align:start position:0%
+you don't want the different invokers of
+ 
+
+ align:start position:0%
+you don't want the different invokers of
+that action to somehow see this modeled
+
+ align:start position:0%
+that action to somehow see this modeled
+ 
+
+ align:start position:0%
+that action to somehow see this modeled
+result of the interleaving you want them
+
+ align:start position:0%
+result of the interleaving you want them
+ 
+
+ align:start position:0%
+result of the interleaving you want them
+to only see the results of running these
+
+ align:start position:0%
+to only see the results of running these
+ 
+
+ align:start position:0%
+to only see the results of running these
+actions one after the
+
+ align:start position:0%
+actions one after the
+ 
+
+ align:start position:0%
+actions one after the
+other so what you're really trying to
+
+ align:start position:0%
+other so what you're really trying to
+ 
+
+ align:start position:0%
+other so what you're really trying to
+achieve for both of these Concepts
+
+ align:start position:0%
+achieve for both of these Concepts
+ 
+
+ align:start position:0%
+achieve for both of these Concepts
+although they're distinct Concepts what
+
+ align:start position:0%
+although they're distinct Concepts what
+ 
+
+ align:start position:0%
+although they're distinct Concepts what
+you're really trying to achieve is to
+
+ align:start position:0%
+you're really trying to achieve is to
+ 
+
+ align:start position:0%
+you're really trying to achieve is to
+hide the fact that this action is a
+
+ align:start position:0%
+hide the fact that this action is a
+ 
+
+ align:start position:0%
+hide the fact that this action is a
+composite sequence of steps you want to
+
+ align:start position:0%
+composite sequence of steps you want to
+ 
+
+ align:start position:0%
+composite sequence of steps you want to
+make it look as if it's quite monolithic
+
+ align:start position:0%
+make it look as if it's quite monolithic
+ 
+
+ align:start position:0%
+make it look as if it's quite monolithic
+and this idea of wanting something to
+
+ align:start position:0%
+and this idea of wanting something to
+ 
+
+ align:start position:0%
+and this idea of wanting something to
+look monolithic is called atom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atomicity and we're going to basically
+
+ align:start position:0%
+atomicity and we're going to basically
+ 
+
+ align:start position:0%
+atomicity and we're going to basically
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hiding the fact that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composite so more
+
+ align:start position:0%
+composite so more
+ 
+
+ align:start position:0%
+composite so more
+precisely for this course we're going to
+
+ align:start position:0%
+precisely for this course we're going to
+ 
+
+ align:start position:0%
+precisely for this course we're going to
+use the word Atomic to mean recoverable
+
+ align:start position:0%
+use the word Atomic to mean recoverable
+ 
+
+ align:start position:0%
+use the word Atomic to mean recoverable
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+isolated okay I'm going to say for this
+
+ align:start position:0%
+isolated okay I'm going to say for this
+ 
+
+ align:start position:0%
+isolated okay I'm going to say for this
+course because these terms have been um
+
+ align:start position:0%
+course because these terms have been um
+ 
+
+ align:start position:0%
+course because these terms have been um
+in use in various different ways uh for
+
+ align:start position:0%
+in use in various different ways uh for
+ 
+
+ align:start position:0%
+in use in various different ways uh for
+at least you know probably more than 30
+
+ align:start position:0%
+at least you know probably more than 30
+ 
+
+ align:start position:0%
+at least you know probably more than 30
+years and I think it's about time we
+
+ align:start position:0%
+years and I think it's about time we
+ 
+
+ align:start position:0%
+years and I think it's about time we
+made these
+
+ align:start position:0%
+made these
+ 
+
+ align:start position:0%
+made these
+precise so in the literature you'll see
+
+ align:start position:0%
+precise so in the literature you'll see
+ 
+
+ align:start position:0%
+precise so in the literature you'll see
+the word Atomic to often mean
+
+ align:start position:0%
+the word Atomic to often mean
+ 
+
+ align:start position:0%
+the word Atomic to often mean
+recoverable and sometimes and this is
+
+ align:start position:0%
+recoverable and sometimes and this is
+ 
+
+ align:start position:0%
+recoverable and sometimes and this is
+unfortunate sometimes you'll see the
+
+ align:start position:0%
+unfortunate sometimes you'll see the
+ 
+
+ align:start position:0%
+unfortunate sometimes you'll see the
+word consistent to mean isolated and in
+
+ align:start position:0%
+word consistent to mean isolated and in
+ 
+
+ align:start position:0%
+word consistent to mean isolated and in
+particular you'll run into this
+
+ align:start position:0%
+particular you'll run into this
+ 
+
+ align:start position:0%
+particular you'll run into this
+confusion when you read the recitation
+
+ align:start position:0%
+confusion when you read the recitation
+ 
+
+ align:start position:0%
+confusion when you read the recitation
+paper for recitation on Thursday the
+
+ align:start position:0%
+paper for recitation on Thursday the
+ 
+
+ align:start position:0%
+paper for recitation on Thursday the
+system R
+
+ align:start position:0%
+system R
+ 
+
+ align:start position:0%
+system R
+paper um but we'll use the word uh the
+
+ align:start position:0%
+paper um but we'll use the word uh the
+ 
+
+ align:start position:0%
+paper um but we'll use the word uh the
+problem is those terms are used you know
+
+ align:start position:0%
+problem is those terms are used you know
+ 
+
+ align:start position:0%
+problem is those terms are used you know
+historically haven't been used in a very
+
+ align:start position:0%
+historically haven't been used in a very
+ 
+
+ align:start position:0%
+historically haven't been used in a very
+precise way so we'll Define it precisely
+
+ align:start position:0%
+precise way so we'll Define it precisely
+ 
+
+ align:start position:0%
+precise way so we'll Define it precisely
+when we say something is atomic we mean
+
+ align:start position:0%
+when we say something is atomic we mean
+ 
+
+ align:start position:0%
+when we say something is atomic we mean
+in general we mean both recoverable and
+
+ align:start position:0%
+in general we mean both recoverable and
+ 
+
+ align:start position:0%
+in general we mean both recoverable and
+isolated when we mean only one of them
+
+ align:start position:0%
+isolated when we mean only one of them
+ 
+
+ align:start position:0%
+isolated when we mean only one of them
+we will say Atomic with respect to
+
+ align:start position:0%
+we will say Atomic with respect to
+ 
+
+ align:start position:0%
+we will say Atomic with respect to
+recoverability or recoverable um Atomic
+
+ align:start position:0%
+recoverability or recoverable um Atomic
+ 
+
+ align:start position:0%
+recoverability or recoverable um Atomic
+with respect to isolation or
+
+ align:start position:0%
+with respect to isolation or
+ 
+
+ align:start position:0%
+with respect to isolation or
+isolated and like I said Atomic means
+
+ align:start position:0%
+isolated and like I said Atomic means
+ 
+
+ align:start position:0%
+isolated and like I said Atomic means
+recoverable and isolated
+
+ align:start position:0%
+recoverable and isolated
+ 
+
+ align:start position:0%
+recoverable and isolated
+and the general plan is to hide the fact
+
+ align:start position:0%
+and the general plan is to hide the fact
+ 
+
+ align:start position:0%
+and the general plan is to hide the fact
+that an action is built out of composite
+
+ align:start position:0%
+that an action is built out of composite
+ 
+
+ align:start position:0%
+that an action is built out of composite
+sequence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps now to add to this confusion of
+
+ align:start position:0%
+steps now to add to this confusion of
+ 
+
+ align:start position:0%
+steps now to add to this confusion of
+terminology there are actually two other
+
+ align:start position:0%
+terminology there are actually two other
+ 
+
+ align:start position:0%
+terminology there are actually two other
+terms that um or two other properties
+
+ align:start position:0%
+terms that um or two other properties
+ 
+
+ align:start position:0%
+terms that um or two other properties
+that you often want from
+
+ align:start position:0%
+that you often want from
+ 
+
+ align:start position:0%
+that you often want from
+actions in addition to recoverability
+
+ align:start position:0%
+actions in addition to recoverability
+ 
+
+ align:start position:0%
+actions in addition to recoverability
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isolation and these two other properties
+
+ align:start position:0%
+isolation and these two other properties
+ 
+
+ align:start position:0%
+isolation and these two other properties
+are provided by many database systems
+
+ align:start position:0%
+are provided by many database systems
+ 
+
+ align:start position:0%
+are provided by many database systems
+which are you know one of the most
+
+ align:start position:0%
+which are you know one of the most
+ 
+
+ align:start position:0%
+which are you know one of the most
+common users of these Concepts most
+
+ align:start position:0%
+common users of these Concepts most
+ 
+
+ align:start position:0%
+common users of these Concepts most
+common system that provides atomicity uh
+
+ align:start position:0%
+common system that provides atomicity uh
+ 
+
+ align:start position:0%
+common system that provides atomicity uh
+one example is a database system now
+
+ align:start position:0%
+one example is a database system now
+ 
+
+ align:start position:0%
+one example is a database system now
+many many systems provide um atomicity
+
+ align:start position:0%
+many many systems provide um atomicity
+ 
+
+ align:start position:0%
+many many systems provide um atomicity
+for example your every computer does it
+
+ align:start position:0%
+for example your every computer does it
+ 
+
+ align:start position:0%
+for example your every computer does it
+in its instruction set you often want
+
+ align:start position:0%
+in its instruction set you often want
+ 
+
+ align:start position:0%
+in its instruction set you often want
+your instructions to from the point of
+
+ align:start position:0%
+your instructions to from the point of
+ 
+
+ align:start position:0%
+your instructions to from the point of
+view of the invoker of the instruction
+
+ align:start position:0%
+view of the invoker of the instruction
+ 
+
+ align:start position:0%
+view of the invoker of the instruction
+be Atomic um so we're going to be
+
+ align:start position:0%
+be Atomic um so we're going to be
+ 
+
+ align:start position:0%
+be Atomic um so we're going to be
+designing techniques that in general
+
+ align:start position:0%
+designing techniques that in general
+ 
+
+ align:start position:0%
+designing techniques that in general
+operate across the whole range of
+
+ align:start position:0%
+operate across the whole range of
+ 
+
+ align:start position:0%
+operate across the whole range of
+systems but database systems are of
+
+ align:start position:0%
+systems but database systems are of
+ 
+
+ align:start position:0%
+systems but database systems are of
+particular interest because they're very
+
+ align:start position:0%
+particular interest because they're very
+ 
+
+ align:start position:0%
+particular interest because they're very
+common and they exercise these Concepts
+
+ align:start position:0%
+common and they exercise these Concepts
+ 
+
+ align:start position:0%
+common and they exercise these Concepts
+um to to a high degree and two other
+
+ align:start position:0%
+um to to a high degree and two other
+ 
+
+ align:start position:0%
+um to to a high degree and two other
+Concepts that many systems provide the
+
+ align:start position:0%
+Concepts that many systems provide the
+ 
+
+ align:start position:0%
+Concepts that many systems provide the
+first one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consistency and it's unfortunate that
+
+ align:start position:0%
+consistency and it's unfortunate that
+ 
+
+ align:start position:0%
+consistency and it's unfortunate that
+the word consistency was previously used
+
+ align:start position:0%
+the word consistency was previously used
+ 
+
+ align:start position:0%
+the word consistency was previously used
+to some extent to mean isolated so it's
+
+ align:start position:0%
+to some extent to mean isolated so it's
+ 
+
+ align:start position:0%
+to some extent to mean isolated so it's
+important not to get into that confusion
+
+ align:start position:0%
+important not to get into that confusion
+ 
+
+ align:start position:0%
+important not to get into that confusion
+so in some old papers when you see
+
+ align:start position:0%
+so in some old papers when you see
+ 
+
+ align:start position:0%
+so in some old papers when you see
+consistent they you should really um
+
+ align:start position:0%
+consistent they you should really um
+ 
+
+ align:start position:0%
+consistent they you should really um
+realize you should realize that what
+
+ align:start position:0%
+realize you should realize that what
+ 
+
+ align:start position:0%
+realize you should realize that what
+they really are talking about is um
+
+ align:start position:0%
+they really are talking about is um
+ 
+
+ align:start position:0%
+they really are talking about is um
+isolated A1 before A2 or A2 before A1
+
+ align:start position:0%
+isolated A1 before A2 or A2 before A1
+ 
+
+ align:start position:0%
+isolated A1 before A2 or A2 before A1
+but what we'll mean by consistency and
+
+ align:start position:0%
+but what we'll mean by consistency and
+ 
+
+ align:start position:0%
+but what we'll mean by consistency and
+we'll get into this next week is that
+
+ align:start position:0%
+we'll get into this next week is that
+ 
+
+ align:start position:0%
+we'll get into this next week is that
+there's some invariant for the
+
+ align:start position:0%
+there's some invariant for the
+ 
+
+ align:start position:0%
+there's some invariant for the
+application that's using um often using
+
+ align:start position:0%
+application that's using um often using
+ 
+
+ align:start position:0%
+application that's using um often using
+atomac City that's
+
+ align:start position:0%
+atomac City that's
+ 
+
+ align:start position:0%
+atomac City that's
+maintained for example in a in a banking
+
+ align:start position:0%
+maintained for example in a in a banking
+ 
+
+ align:start position:0%
+maintained for example in a in a banking
+application if you take the transfer
+
+ align:start position:0%
+application if you take the transfer
+ 
+
+ align:start position:0%
+application if you take the transfer
+examples isolated means that you want
+
+ align:start position:0%
+examples isolated means that you want
+ 
+
+ align:start position:0%
+examples isolated means that you want
+the result to be as if the transfer is
+
+ align:start position:0%
+the result to be as if the transfer is
+ 
+
+ align:start position:0%
+the result to be as if the transfer is
+ran in some serial order consistent
+
+ align:start position:0%
+ran in some serial order consistent
+ 
+
+ align:start position:0%
+ran in some serial order consistent
+means that there might be a higher level
+
+ align:start position:0%
+means that there might be a higher level
+ 
+
+ align:start position:0%
+means that there might be a higher level
+notion that the U designer of this
+
+ align:start position:0%
+notion that the U designer of this
+ 
+
+ align:start position:0%
+notion that the U designer of this
+banking application um might have wanted
+
+ align:start position:0%
+banking application um might have wanted
+ 
+
+ align:start position:0%
+banking application um might have wanted
+such as a bank might have a rule that
+
+ align:start position:0%
+such as a bank might have a rule that
+ 
+
+ align:start position:0%
+such as a bank might have a rule that
+says that at the end of each day um the
+
+ align:start position:0%
+says that at the end of each day um the
+ 
+
+ align:start position:0%
+says that at the end of each day um the
+checking account every checking account
+
+ align:start position:0%
+checking account every checking account
+ 
+
+ align:start position:0%
+checking account every checking account
+should be uh should have an amount
+
+ align:start position:0%
+should be uh should have an amount
+ 
+
+ align:start position:0%
+should be uh should have an amount
+that's at least 10% of every of the
+
+ align:start position:0%
+that's at least 10% of every of the
+ 
+
+ align:start position:0%
+that's at least 10% of every of the
+corresponding savings account now during
+
+ align:start position:0%
+corresponding savings account now during
+ 
+
+ align:start position:0%
+corresponding savings account now during
+the middle of the day there might be
+
+ align:start position:0%
+the middle of the day there might be
+ 
+
+ align:start position:0%
+the middle of the day there might be
+individual um you know there might be
+
+ align:start position:0%
+individual um you know there might be
+ 
+
+ align:start position:0%
+individual um you know there might be
+individual actions
+
+ align:start position:0%
+individual actions
+ 
+
+ align:start position:0%
+individual actions
+that transiently violate that that rule
+
+ align:start position:0%
+that transiently violate that that rule
+ 
+
+ align:start position:0%
+that transiently violate that that rule
+but at various points the designer might
+
+ align:start position:0%
+but at various points the designer might
+ 
+
+ align:start position:0%
+but at various points the designer might
+wish to ensure that the um you know a
+
+ align:start position:0%
+wish to ensure that the um you know a
+ 
+
+ align:start position:0%
+wish to ensure that the um you know a
+rule like the cons that that the
+
+ align:start position:0%
+rule like the cons that that the
+ 
+
+ align:start position:0%
+rule like the cons that that the
+checking account must have at least a
+
+ align:start position:0%
+checking account must have at least a
+ 
+
+ align:start position:0%
+checking account must have at least a
+certain amount of money some fra of the
+
+ align:start position:0%
+certain amount of money some fra of the
+ 
+
+ align:start position:0%
+certain amount of money some fra of the
+savings account or in some you know
+
+ align:start position:0%
+savings account or in some you know
+ 
+
+ align:start position:0%
+savings account or in some you know
+payroll application for a company um you
+
+ align:start position:0%
+payroll application for a company um you
+ 
+
+ align:start position:0%
+payroll application for a company um you
+know they're modifying the payroll and
+
+ align:start position:0%
+know they're modifying the payroll and
+ 
+
+ align:start position:0%
+know they're modifying the payroll and
+adding you know giving raises to various
+
+ align:start position:0%
+adding you know giving raises to various
+ 
+
+ align:start position:0%
+adding you know giving raises to various
+people but they might have a rule that
+
+ align:start position:0%
+people but they might have a rule that
+ 
+
+ align:start position:0%
+people but they might have a rule that
+says that you can give whatever raise
+
+ align:start position:0%
+says that you can give whatever raise
+ 
+
+ align:start position:0%
+says that you can give whatever raise
+you want but every manager must make at
+
+ align:start position:0%
+you want but every manager must make at
+ 
+
+ align:start position:0%
+you want but every manager must make at
+least 5% more than all of his or her
+
+ align:start position:0%
+least 5% more than all of his or her
+ 
+
+ align:start position:0%
+least 5% more than all of his or her
+direct reports so you might have a rule
+
+ align:start position:0%
+direct reports so you might have a rule
+ 
+
+ align:start position:0%
+direct reports so you might have a rule
+like that all of these are application
+
+ align:start position:0%
+like that all of these are application
+ 
+
+ align:start position:0%
+like that all of these are application
+Level invariants that correspond to the
+
+ align:start position:0%
+Level invariants that correspond to the
+ 
+
+ align:start position:0%
+Level invariants that correspond to the
+consistency of the data that's being
+
+ align:start position:0%
+consistency of the data that's being
+ 
+
+ align:start position:0%
+consistency of the data that's being
+maintained in this example in a database
+
+ align:start position:0%
+maintained in this example in a database
+ 
+
+ align:start position:0%
+maintained in this example in a database
+and uh you can use database systems to
+
+ align:start position:0%
+and uh you can use database systems to
+ 
+
+ align:start position:0%
+and uh you can use database systems to
+provide these rules these consistency
+
+ align:start position:0%
+provide these rules these consistency
+ 
+
+ align:start position:0%
+provide these rules these consistency
+rules but that's different from
+
+ align:start position:0%
+rules but that's different from
+ 
+
+ align:start position:0%
+rules but that's different from
+isolation isolation just describes the
+
+ align:start position:0%
+isolation isolation just describes the
+ 
+
+ align:start position:0%
+isolation isolation just describes the
+serial ordering in which oh sorry it
+
+ align:start position:0%
+serial ordering in which oh sorry it
+ 
+
+ align:start position:0%
+serial ordering in which oh sorry it
+just says that there has to be some
+
+ align:start position:0%
+just says that there has to be some
+ 
+
+ align:start position:0%
+just says that there has to be some
+serial equivalent serial ordering in
+
+ align:start position:0%
+serial equivalent serial ordering in
+ 
+
+ align:start position:0%
+serial equivalent serial ordering in
+which things things
+
+ align:start position:0%
+which things things
+ 
+
+ align:start position:0%
+which things things
+run and the fourth um property in
+
+ align:start position:0%
+run and the fourth um property in
+ 
+
+ align:start position:0%
+run and the fourth um property in
+addition to after recoverability
+
+ align:start position:0%
+addition to after recoverability
+ 
+
+ align:start position:0%
+addition to after recoverability
+isolation and consistency is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+durability durability basically says
+
+ align:start position:0%
+durability durability basically says
+ 
+
+ align:start position:0%
+durability durability basically says
+that the data should last for as long as
+
+ align:start position:0%
+that the data should last for as long as
+ 
+
+ align:start position:0%
+that the data should last for as long as
+um you know it depends on the it's an
+
+ align:start position:0%
+um you know it depends on the it's an
+ 
+
+ align:start position:0%
+um you know it depends on the it's an
+application specific con concept but
+
+ align:start position:0%
+application specific con concept but
+ 
+
+ align:start position:0%
+application specific con concept but
+what it says is the data must last uh
+
+ align:start position:0%
+what it says is the data must last uh
+ 
+
+ align:start position:0%
+what it says is the data must last uh
+for as long as some predefined um
+
+ align:start position:0%
+for as long as some predefined um
+ 
+
+ align:start position:0%
+for as long as some predefined um
+duration so for example you might store
+
+ align:start position:0%
+duration so for example you might store
+ 
+
+ align:start position:0%
+duration so for example you might store
+data in a database and you know in many
+
+ align:start position:0%
+data in a database and you know in many
+ 
+
+ align:start position:0%
+data in a database and you know in many
+databases you really want it to last
+
+ align:start position:0%
+databases you really want it to last
+ 
+
+ align:start position:0%
+databases you really want it to last
+quote forever but in reality nothing
+
+ align:start position:0%
+quote forever but in reality nothing
+ 
+
+ align:start position:0%
+quote forever but in reality nothing
+ever it's very hard to make things last
+
+ align:start position:0%
+ever it's very hard to make things last
+ 
+
+ align:start position:0%
+ever it's very hard to make things last
+forever uh so you might descri Define
+
+ align:start position:0%
+forever uh so you might descri Define
+ 
+
+ align:start position:0%
+forever uh so you might descri Define
+that the uh data in this database must
+
+ align:start position:0%
+that the uh data in this database must
+ 
+
+ align:start position:0%
+that the uh data in this database must
+last for three years and you work hard
+
+ align:start position:0%
+last for three years and you work hard
+ 
+
+ align:start position:0%
+last for three years and you work hard
+to preserve that or you might have an
+
+ align:start position:0%
+to preserve that or you might have an
+ 
+
+ align:start position:0%
+to preserve that or you might have an
+application that as long as the thread
+
+ align:start position:0%
+application that as long as the thread
+ 
+
+ align:start position:0%
+application that as long as the thread
+is running you want the data to last but
+
+ align:start position:0%
+is running you want the data to last but
+ 
+
+ align:start position:0%
+is running you want the data to last but
+after the thread um is terminated you
+
+ align:start position:0%
+after the thread um is terminated you
+ 
+
+ align:start position:0%
+after the thread um is terminated you
+don't actually care about the data and
+
+ align:start position:0%
+don't actually care about the data and
+ 
+
+ align:start position:0%
+don't actually care about the data and
+that's a different notion of durability
+
+ align:start position:0%
+that's a different notion of durability
+ 
+
+ align:start position:0%
+that's a different notion of durability
+but both of these have talk about the
+
+ align:start position:0%
+but both of these have talk about the
+ 
+
+ align:start position:0%
+but both of these have talk about the
+the lifetime with which you want to
+
+ align:start position:0%
+the lifetime with which you want to
+ 
+
+ align:start position:0%
+the lifetime with which you want to
+preserve
+
+ align:start position:0%
+preserve
+ 
+
+ align:start position:0%
+preserve
+data okay so now when you have a system
+
+ align:start position:0%
+data okay so now when you have a system
+ 
+
+ align:start position:0%
+data okay so now when you have a system
+that provides recoverability and
+
+ align:start position:0%
+that provides recoverability and
+ 
+
+ align:start position:0%
+that provides recoverability and
+isolation that is atomicity consistency
+
+ align:start position:0%
+isolation that is atomicity consistency
+ 
+
+ align:start position:0%
+isolation that is atomicity consistency
+and durability then we're going to call
+
+ align:start position:0%
+and durability then we're going to call
+ 
+
+ align:start position:0%
+and durability then we're going to call
+that a
+
+ align:start position:0%
+that a
+ 
+
+ align:start position:0%
+that a
+transaction so a set of actions that has
+
+ align:start position:0%
+transaction so a set of actions that has
+ 
+
+ align:start position:0%
+transaction so a set of actions that has
+an action that uh sorry a set of actions
+
+ align:start position:0%
+an action that uh sorry a set of actions
+ 
+
+ align:start position:0%
+an action that uh sorry a set of actions
+that Each of which is recoverable that
+
+ align:start position:0%
+that Each of which is recoverable that
+ 
+
+ align:start position:0%
+that Each of which is recoverable that
+are isolated from each other that has
+
+ align:start position:0%
+are isolated from each other that has
+ 
+
+ align:start position:0%
+are isolated from each other that has
+notion of consistency and can achieve it
+
+ align:start position:0%
+notion of consistency and can achieve it
+ 
+
+ align:start position:0%
+notion of consistency and can achieve it
+and where the data has durability um
+
+ align:start position:0%
+and where the data has durability um
+ 
+
+ align:start position:0%
+and where the data has durability um
+those actions are called
+
+ align:start position:0%
+those actions are called
+ 
+
+ align:start position:0%
+those actions are called
+transactions and many database systems
+
+ align:start position:0%
+transactions and many database systems
+ 
+
+ align:start position:0%
+transactions and many database systems
+work hard to provide transactions which
+
+ align:start position:0%
+work hard to provide transactions which
+ 
+
+ align:start position:0%
+work hard to provide transactions which
+means they provide all of these
+
+ align:start position:0%
+means they provide all of these
+ 
+
+ align:start position:0%
+means they provide all of these
+features but it's certainly possible and
+
+ align:start position:0%
+features but it's certainly possible and
+ 
+
+ align:start position:0%
+features but it's certainly possible and
+we'll look at many examples where you
+
+ align:start position:0%
+we'll look at many examples where you
+ 
+
+ align:start position:0%
+we'll look at many examples where you
+can just Design Systems that have just
+
+ align:start position:0%
+can just Design Systems that have just
+ 
+
+ align:start position:0%
+can just Design Systems that have just
+recoverability and
+
+ align:start position:0%
+recoverability and
+ 
+
+ align:start position:0%
+recoverability and
+isolation and we may not even worry
+
+ align:start position:0%
+isolation and we may not even worry
+ 
+
+ align:start position:0%
+isolation and we may not even worry
+about these other Notions and that's
+
+ align:start position:0%
+about these other Notions and that's
+ 
+
+ align:start position:0%
+about these other Notions and that's
+what we'll start with we don't want to
+
+ align:start position:0%
+what we'll start with we don't want to
+ 
+
+ align:start position:0%
+what we'll start with we don't want to
+solve all of the problems at once we
+
+ align:start position:0%
+solve all of the problems at once we
+ 
+
+ align:start position:0%
+solve all of the problems at once we
+start with the easier set of problems
+
+ align:start position:0%
+start with the easier set of problems
+ 
+
+ align:start position:0%
+start with the easier set of problems
+and then build from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there I don't know what happened
+
+ align:start position:0%
+there I don't know what happened
+ 
+
+ align:start position:0%
+there I don't know what happened
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so today and on Wednesday our
+
+ align:start position:0%
+okay okay so today and on Wednesday our
+ 
+
+ align:start position:0%
+okay okay so today and on Wednesday our
+plan is to come up with ways of
+
+ align:start position:0%
+plan is to come up with ways of
+ 
+
+ align:start position:0%
+plan is to come up with ways of
+achieving recoverability so that's what
+
+ align:start position:0%
+achieving recoverability so that's what
+ 
+
+ align:start position:0%
+achieving recoverability so that's what
+we're going to start doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the general approach for how we're
+
+ align:start position:0%
+so the general approach for how we're
+ 
+
+ align:start position:0%
+so the general approach for how we're
+going to achieve recoverability of
+
+ align:start position:0%
+going to achieve recoverability of
+ 
+
+ align:start position:0%
+going to achieve recoverability of
+modules is and recall that the problem
+
+ align:start position:0%
+modules is and recall that the problem
+ 
+
+ align:start position:0%
+modules is and recall that the problem
+here is M2 fails and then M1 um somehow
+
+ align:start position:0%
+here is M2 fails and then M1 um somehow
+ 
+
+ align:start position:0%
+here is M2 fails and then M1 um somehow
+discovers its failure and then when it
+
+ align:start position:0%
+discovers its failure and then when it
+ 
+
+ align:start position:0%
+discovers its failure and then when it
+restarts you don't want any partial
+
+ align:start position:0%
+restarts you don't want any partial
+ 
+
+ align:start position:0%
+restarts you don't want any partial
+state to be kept so the general plan is
+
+ align:start position:0%
+state to be kept so the general plan is
+ 
+
+ align:start position:0%
+state to be kept so the general plan is
+to design modules to be fail
+
+ align:start position:0%
+to design modules to be fail
+ 
+
+ align:start position:0%
+to design modules to be fail
+fast so you need a way to discover that
+
+ align:start position:0%
+fast so you need a way to discover that
+ 
+
+ align:start position:0%
+fast so you need a way to discover that
+things are not working and that's the
+
+ align:start position:0%
+things are not working and that's the
+ 
+
+ align:start position:0%
+things are not working and that's the
+scope of the kinds of systems we're
+
+ align:start position:0%
+scope of the kinds of systems we're
+ 
+
+ align:start position:0%
+scope of the kinds of systems we're
+going to be dealing
+
+ align:start position:0%
+going to be dealing
+ 
+
+ align:start position:0%
+going to be dealing
+with and then once um the system failure
+
+ align:start position:0%
+with and then once um the system failure
+ 
+
+ align:start position:0%
+with and then once um the system failure
+is detected and then you restart the
+
+ align:start position:0%
+is detected and then you restart the
+ 
+
+ align:start position:0%
+is detected and then you restart the
+system or recovers um you're onun some
+
+ align:start position:0%
+system or recovers um you're onun some
+ 
+
+ align:start position:0%
+system or recovers um you're onun some
+kind of a repair
+
+ align:start position:0%
+kind of a repair
+ 
+
+ align:start position:0%
+kind of a repair
+procedure this is in general you're onun
+
+ align:start position:0%
+procedure this is in general you're onun
+ 
+
+ align:start position:0%
+procedure this is in general you're onun
+some kind of repair procedure um that
+
+ align:start position:0%
+some kind of repair procedure um that
+ 
+
+ align:start position:0%
+some kind of repair procedure um that
+allows you to recover allows the failed
+
+ align:start position:0%
+allows you to recover allows the failed
+ 
+
+ align:start position:0%
+allows you to recover allows the failed
+module to
+
+ align:start position:0%
+module to
+ 
+
+ align:start position:0%
+module to
+recover and then it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+restarts where restarts means it allows
+
+ align:start position:0%
+restarts where restarts means it allows
+ 
+
+ align:start position:0%
+restarts where restarts means it allows
+um M1 in this case allows invokers to
+
+ align:start position:0%
+um M1 in this case allows invokers to
+ 
+
+ align:start position:0%
+um M1 in this case allows invokers to
+start running on that system on that
+
+ align:start position:0%
+start running on that system on that
+ 
+
+ align:start position:0%
+start running on that system on that
+module
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to do this in three steps
+
+ align:start position:0%
+so we're going to do this in three steps
+ 
+
+ align:start position:0%
+so we're going to do this in three steps
+the first thing we're going to do is to
+
+ align:start position:0%
+the first thing we're going to do is to
+ 
+
+ align:start position:0%
+the first thing we're going to do is to
+look at a very specific special case of
+
+ align:start position:0%
+look at a very specific special case of
+ 
+
+ align:start position:0%
+look at a very specific special case of
+this problem which is um realize that
+
+ align:start position:0%
+this problem which is um realize that
+ 
+
+ align:start position:0%
+this problem which is um realize that
+all of these things having to do with
+
+ align:start position:0%
+all of these things having to do with
+ 
+
+ align:start position:0%
+all of these things having to do with
+partial State occur because there's some
+
+ align:start position:0%
+partial State occur because there's some
+ 
+
+ align:start position:0%
+partial State occur because there's some
+State once once a module has crashed
+
+ align:start position:0%
+State once once a module has crashed
+ 
+
+ align:start position:0%
+State once once a module has crashed
+there's some state that it has remaining
+
+ align:start position:0%
+there's some state that it has remaining
+ 
+
+ align:start position:0%
+there's some state that it has remaining
+so if it just recovered and started
+
+ align:start position:0%
+so if it just recovered and started
+ 
+
+ align:start position:0%
+so if it just recovered and started
+running again without doing something
+
+ align:start position:0%
+running again without doing something
+ 
+
+ align:start position:0%
+running again without doing something
+then that partial state is visible to uh
+
+ align:start position:0%
+then that partial state is visible to uh
+ 
+
+ align:start position:0%
+then that partial state is visible to uh
+the invoker of that
+
+ align:start position:0%
+the invoker of that
+ 
+
+ align:start position:0%
+the invoker of that
+module now if this state were all
+
+ align:start position:0%
+module now if this state were all
+ 
+
+ align:start position:0%
+module now if this state were all
+volatile State like in just you know RAM
+
+ align:start position:0%
+volatile State like in just you know RAM
+ 
+
+ align:start position:0%
+volatile State like in just you know RAM
+for example and a thread crashed and if
+
+ align:start position:0%
+for example and a thread crashed and if
+ 
+
+ align:start position:0%
+for example and a thread crashed and if
+it was in its virtual memory and the
+
+ align:start position:0%
+it was in its virtual memory and the
+ 
+
+ align:start position:0%
+it was in its virtual memory and the
+thread crashed and it recovered then you
+
+ align:start position:0%
+thread crashed and it recovered then you
+ 
+
+ align:start position:0%
+thread crashed and it recovered then you
+don't really have to worry about this
+
+ align:start position:0%
+don't really have to worry about this
+ 
+
+ align:start position:0%
+don't really have to worry about this
+because all of the state um anyway has
+
+ align:start position:0%
+because all of the state um anyway has
+ 
+
+ align:start position:0%
+because all of the state um anyway has
+gone
+
+ align:start position:0%
+gone
+ 
+
+ align:start position:0%
+gone
+away so primarily we're worried about
+
+ align:start position:0%
+away so primarily we're worried about
+ 
+
+ align:start position:0%
+away so primarily we're worried about
+state that lasts uh across
+
+ align:start position:0%
+state that lasts uh across
+ 
+
+ align:start position:0%
+state that lasts uh across
+failures and concretely um an example of
+
+ align:start position:0%
+failures and concretely um an example of
+ 
+
+ align:start position:0%
+failures and concretely um an example of
+that concretely is state that that's
+
+ align:start position:0%
+that concretely is state that that's
+ 
+
+ align:start position:0%
+that concretely is state that that's
+maintained um on dis just as a concrete
+
+ align:start position:0%
+maintained um on dis just as a concrete
+ 
+
+ align:start position:0%
+maintained um on dis just as a concrete
+example so we're going to start first by
+
+ align:start position:0%
+example so we're going to start first by
+ 
+
+ align:start position:0%
+example so we're going to start first by
+um obtaining a coverable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector but basically coming up with a
+
+ align:start position:0%
+sector but basically coming up with a
+ 
+
+ align:start position:0%
+sector but basically coming up with a
+scheme that allows us to do reads and
+
+ align:start position:0%
+scheme that allows us to do reads and
+ 
+
+ align:start position:0%
+scheme that allows us to do reads and
+writes of a single sector of a dis in a
+
+ align:start position:0%
+writes of a single sector of a dis in a
+ 
+
+ align:start position:0%
+writes of a single sector of a dis in a
+recoverable way so we're going to Define
+
+ align:start position:0%
+recoverable way so we're going to Define
+ 
+
+ align:start position:0%
+recoverable way so we're going to Define
+two procedures a recoverable put that
+
+ align:start position:0%
+two procedures a recoverable put that
+ 
+
+ align:start position:0%
+two procedures a recoverable put that
+allows you to put stuff write stuff onto
+
+ align:start position:0%
+allows you to put stuff write stuff onto
+ 
+
+ align:start position:0%
+allows you to put stuff write stuff onto
+a single sector of a disk and a
+
+ align:start position:0%
+a single sector of a disk and a
+ 
+
+ align:start position:0%
+a single sector of a disk and a
+recoverable get that allows you to read
+
+ align:start position:0%
+recoverable get that allows you to read
+ 
+
+ align:start position:0%
+recoverable get that allows you to read
+stuff off of off of a single sector of a
+
+ align:start position:0%
+stuff off of off of a single sector of a
+ 
+
+ align:start position:0%
+stuff off of off of a single sector of a
+disk in a way that um is is recoverable
+
+ align:start position:0%
+disk in a way that um is is recoverable
+ 
+
+ align:start position:0%
+disk in a way that um is is recoverable
+and the general and the hard problem
+
+ align:start position:0%
+and the general and the hard problem
+ 
+
+ align:start position:0%
+and the general and the hard problem
+here is going to be that as the system
+
+ align:start position:0%
+here is going to be that as the system
+ 
+
+ align:start position:0%
+here is going to be that as the system
+sys crashing um for a variety of reasons
+
+ align:start position:0%
+sys crashing um for a variety of reasons
+ 
+
+ align:start position:0%
+sys crashing um for a variety of reasons
+bad data might get written on to a Bas
+
+ align:start position:0%
+bad data might get written on to a Bas
+ 
+
+ align:start position:0%
+bad data might get written on to a Bas
+to a sector so if you just took a
+
+ align:start position:0%
+to a sector so if you just took a
+ 
+
+ align:start position:0%
+to a sector so if you just took a
+regular sector of your disc um you know
+
+ align:start position:0%
+regular sector of your disc um you know
+ 
+
+ align:start position:0%
+regular sector of your disc um you know
+as you know let's say that someone you
+
+ align:start position:0%
+as you know let's say that someone you
+ 
+
+ align:start position:0%
+as you know let's say that someone you
+know this the operating system is trying
+
+ align:start position:0%
+know this the operating system is trying
+ 
+
+ align:start position:0%
+know this the operating system is trying
+to write something into a dis sector
+
+ align:start position:0%
+to write something into a dis sector
+ 
+
+ align:start position:0%
+to write something into a dis sector
+somebody turns off the power and random
+
+ align:start position:0%
+somebody turns off the power and random
+ 
+
+ align:start position:0%
+somebody turns off the power and random
+stuff might get just written out onto
+
+ align:start position:0%
+stuff might get just written out onto
+ 
+
+ align:start position:0%
+stuff might get just written out onto
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dis and so when the system comes back up
+
+ align:start position:0%
+dis and so when the system comes back up
+ 
+
+ align:start position:0%
+dis and so when the system comes back up
+the reader of that sector might get some
+
+ align:start position:0%
+the reader of that sector might get some
+ 
+
+ align:start position:0%
+the reader of that sector might get some
+garbage value some result of some
+
+ align:start position:0%
+garbage value some result of some
+ 
+
+ align:start position:0%
+garbage value some result of some
+partial right so that's what we're going
+
+ align:start position:0%
+partial right so that's what we're going
+ 
+
+ align:start position:0%
+partial right so that's what we're going
+to try to avoid so we'll do that first
+
+ align:start position:0%
+to try to avoid so we'll do that first
+ 
+
+ align:start position:0%
+to try to avoid so we'll do that first
+and then what we'll do and and and
+
+ align:start position:0%
+and then what we'll do and and and
+ 
+
+ align:start position:0%
+and then what we'll do and and and
+that's for next time to complete the
+
+ align:start position:0%
+that's for next time to complete the
+ 
+
+ align:start position:0%
+that's for next time to complete the
+story recoverability story we're going
+
+ align:start position:0%
+story recoverability story we're going
+ 
+
+ align:start position:0%
+story recoverability story we're going
+to use this solution as a bootstrap to
+
+ align:start position:0%
+to use this solution as a bootstrap to
+ 
+
+ align:start position:0%
+to use this solution as a bootstrap to
+as as a building block for a more
+
+ align:start position:0%
+as as a building block for a more
+ 
+
+ align:start position:0%
+as as a building block for a more
+General solution because it's not going
+
+ align:start position:0%
+General solution because it's not going
+ 
+
+ align:start position:0%
+General solution because it's not going
+to be enough for us to just be able to
+
+ align:start position:0%
+to be enough for us to just be able to
+ 
+
+ align:start position:0%
+to be enough for us to just be able to
+read and write single sectors in a
+
+ align:start position:0%
+read and write single sectors in a
+ 
+
+ align:start position:0%
+read and write single sectors in a
+recoverable way because you know how
+
+ align:start position:0%
+recoverable way because you know how
+ 
+
+ align:start position:0%
+recoverable way because you know how
+many applications use only one sector of
+
+ align:start position:0%
+many applications use only one sector of
+ 
+
+ align:start position:0%
+many applications use only one sector of
+a dis what you'd like to do is to make
+
+ align:start position:0%
+a dis what you'd like to do is to make
+ 
+
+ align:start position:0%
+a dis what you'd like to do is to make
+sure that you have a general solution
+
+ align:start position:0%
+sure that you have a general solution
+ 
+
+ align:start position:0%
+sure that you have a general solution
+that works across all of the data that's
+
+ align:start position:0%
+that works across all of the data that's
+ 
+
+ align:start position:0%
+that works across all of the data that's
+being written and read so we're going to
+
+ align:start position:0%
+being written and read so we're going to
+ 
+
+ align:start position:0%
+being written and read so we're going to
+use that to come up with two schemes the
+
+ align:start position:0%
+use that to come up with two schemes the
+ 
+
+ align:start position:0%
+use that to come up with two schemes the
+first scheme
+
+ align:start position:0%
+first scheme
+ 
+
+ align:start position:0%
+first scheme
+uh is uses an idea called a version
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+history and the second
+
+ align:start position:0%
+history and the second
+ 
+
+ align:start position:0%
+history and the second
+scheme um uses an idea called log
+
+ align:start position:0%
+scheme um uses an idea called log
+ 
+
+ align:start position:0%
+scheme um uses an idea called log
+logging using logs and both of these
+
+ align:start position:0%
+logging using logs and both of these
+ 
+
+ align:start position:0%
+logging using logs and both of these
+schemes have uh will turn out to be very
+
+ align:start position:0%
+schemes have uh will turn out to be very
+ 
+
+ align:start position:0%
+schemes have uh will turn out to be very
+general and useful and work but both of
+
+ align:start position:0%
+general and useful and work but both of
+ 
+
+ align:start position:0%
+general and useful and work but both of
+these scheme basically will use um this
+
+ align:start position:0%
+these scheme basically will use um this
+ 
+
+ align:start position:0%
+these scheme basically will use um this
+technique as a bootstrapping
+
+ align:start position:0%
+technique as a bootstrapping
+ 
+
+ align:start position:0%
+technique as a bootstrapping
+technique okay and so we need a solution
+
+ align:start position:0%
+technique okay and so we need a solution
+ 
+
+ align:start position:0%
+technique okay and so we need a solution
+here anyway because we're going to build
+
+ align:start position:0%
+here anyway because we're going to build
+ 
+
+ align:start position:0%
+here anyway because we're going to build
+on that to develop a more sophisticated
+
+ align:start position:0%
+on that to develop a more sophisticated
+ 
+
+ align:start position:0%
+on that to develop a more sophisticated
+solution for the general case
+
+ align:start position:0%
+solution for the general case
+ 
+
+ align:start position:0%
+solution for the general case
+and so today we're going to start with
+
+ align:start position:0%
+and so today we're going to start with
+ 
+
+ align:start position:0%
+and so today we're going to start with
+the special case um a because it's a
+
+ align:start position:0%
+the special case um a because it's a
+ 
+
+ align:start position:0%
+the special case um a because it's a
+building block and B because it'll turn
+
+ align:start position:0%
+building block and B because it'll turn
+ 
+
+ align:start position:0%
+building block and B because it'll turn
+out to show us a rule that we're going
+
+ align:start position:0%
+out to show us a rule that we're going
+ 
+
+ align:start position:0%
+out to show us a rule that we're going
+to religiously follow in coming up with
+
+ align:start position:0%
+to religiously follow in coming up with
+ 
+
+ align:start position:0%
+to religiously follow in coming up with
+Solutions systematic solutions for these
+
+ align:start position:0%
+Solutions systematic solutions for these
+ 
+
+ align:start position:0%
+Solutions systematic solutions for these
+more General uh to to work in the most
+
+ align:start position:0%
+more General uh to to work in the most
+ 
+
+ align:start position:0%
+more General uh to to work in the most
+more General case when you have more
+
+ align:start position:0%
+more General case when you have more
+ 
+
+ align:start position:0%
+more General case when you have more
+than one sector being read or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+written so let's write out um the
+
+ align:start position:0%
+written so let's write out um the
+ 
+
+ align:start position:0%
+written so let's write out um the
+assumptions and the model here for the
+
+ align:start position:0%
+assumptions and the model here for the
+ 
+
+ align:start position:0%
+assumptions and the model here for the
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+the first assumption we're going to make
+
+ align:start position:0%
+the first assumption we're going to make
+ 
+
+ align:start position:0%
+the first assumption we're going to make
+since we're dealing with recoverability
+
+ align:start position:0%
+since we're dealing with recoverability
+ 
+
+ align:start position:0%
+since we're dealing with recoverability
+and not with isolation we're going to
+
+ align:start position:0%
+and not with isolation we're going to
+ 
+
+ align:start position:0%
+and not with isolation we're going to
+deal with isolation next week the first
+
+ align:start position:0%
+deal with isolation next week the first
+ 
+
+ align:start position:0%
+deal with isolation next week the first
+assumption we'll make is that there's no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concurrency and we come up with
+
+ align:start position:0%
+concurrency and we come up with
+ 
+
+ align:start position:0%
+concurrency and we come up with
+different solutions for dealing with
+
+ align:start position:0%
+different solutions for dealing with
+ 
+
+ align:start position:0%
+different solutions for dealing with
+people concurrently trying to write uh
+
+ align:start position:0%
+people concurrently trying to write uh
+ 
+
+ align:start position:0%
+people concurrently trying to write uh
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector we'll also assume um and this is
+
+ align:start position:0%
+sector we'll also assume um and this is
+ 
+
+ align:start position:0%
+sector we'll also assume um and this is
+an assumption we'll revisit in a couple
+
+ align:start position:0%
+an assumption we'll revisit in a couple
+ 
+
+ align:start position:0%
+an assumption we'll revisit in a couple
+of weeks to show you how to actually um
+
+ align:start position:0%
+of weeks to show you how to actually um
+ 
+
+ align:start position:0%
+of weeks to show you how to actually um
+achieve this goal but we'll assume that
+
+ align:start position:0%
+achieve this goal but we'll assume that
+ 
+
+ align:start position:0%
+achieve this goal but we'll assume that
+there's no Hardware
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+failures there's no Hardware
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+errors so for example and the appendix
+
+ align:start position:0%
+errors so for example and the appendix
+ 
+
+ align:start position:0%
+errors so for example and the appendix
+to chapter 8 which we'll actually we
+
+ align:start position:0%
+to chapter 8 which we'll actually we
+ 
+
+ align:start position:0%
+to chapter 8 which we'll actually we
+we'll assign uh for reading later on uh
+
+ align:start position:0%
+we'll assign uh for reading later on uh
+ 
+
+ align:start position:0%
+we'll assign uh for reading later on uh
+in the semester um actually shows two
+
+ align:start position:0%
+in the semester um actually shows two
+ 
+
+ align:start position:0%
+in the semester um actually shows two
+methods careful put and careful get um
+
+ align:start position:0%
+methods careful put and careful get um
+ 
+
+ align:start position:0%
+methods careful put and careful get um
+that actually deal with a variety of
+
+ align:start position:0%
+that actually deal with a variety of
+ 
+
+ align:start position:0%
+that actually deal with a variety of
+Hardware problems so for example every
+
+ align:start position:0%
+Hardware problems so for example every
+ 
+
+ align:start position:0%
+Hardware problems so for example every
+sector has a dis checks them a sector
+
+ align:start position:0%
+sector has a dis checks them a sector
+ 
+
+ align:start position:0%
+sector has a dis checks them a sector
+checks them on it so if you wrote bad
+
+ align:start position:0%
+checks them on it so if you wrote bad
+ 
+
+ align:start position:0%
+checks them on it so if you wrote bad
+data um and something happened in the
+
+ align:start position:0%
+data um and something happened in the
+ 
+
+ align:start position:0%
+data um and something happened in the
+middle of that right um and then someone
+
+ align:start position:0%
+middle of that right um and then someone
+ 
+
+ align:start position:0%
+middle of that right um and then someone
+went back and read that sector they
+
+ align:start position:0%
+went back and read that sector they
+ 
+
+ align:start position:0%
+went back and read that sector they
+would discover that it's bad because the
+
+ align:start position:0%
+would discover that it's bad because the
+ 
+
+ align:start position:0%
+would discover that it's bad because the
+check sum wouldn't
+
+ align:start position:0%
+check sum wouldn't
+ 
+
+ align:start position:0%
+check sum wouldn't
+match now the appendix to this chapter
+
+ align:start position:0%
+match now the appendix to this chapter
+ 
+
+ align:start position:0%
+match now the appendix to this chapter
+9B has a more careful description of how
+
+ align:start position:0%
+9B has a more careful description of how
+ 
+
+ align:start position:0%
+9B has a more careful description of how
+you deal with a variety of Errors so
+
+ align:start position:0%
+you deal with a variety of Errors so
+ 
+
+ align:start position:0%
+you deal with a variety of Errors so
+that you can achieve this careful put
+
+ align:start position:0%
+that you can achieve this careful put
+ 
+
+ align:start position:0%
+that you can achieve this careful put
+and careful get of a dis
+
+ align:start position:0%
+and careful get of a dis
+ 
+
+ align:start position:0%
+and careful get of a dis
+sector so assume for now that there are
+
+ align:start position:0%
+sector so assume for now that there are
+ 
+
+ align:start position:0%
+sector so assume for now that there are
+no Hardware errors there's no decay of
+
+ align:start position:0%
+no Hardware errors there's no decay of
+ 
+
+ align:start position:0%
+no Hardware errors there's no decay of
+data on the disk and so on it'll turn
+
+ align:start position:0%
+data on the disk and so on it'll turn
+ 
+
+ align:start position:0%
+data on the disk and so on it'll turn
+out the problem is still interesting
+
+ align:start position:0%
+out the problem is still interesting
+ 
+
+ align:start position:0%
+out the problem is still interesting
+that it's not easy to achieve um a
+
+ align:start position:0%
+that it's not easy to achieve um a
+ 
+
+ align:start position:0%
+that it's not easy to achieve um a
+recoverable put and get even though the
+
+ align:start position:0%
+recoverable put and get even though the
+ 
+
+ align:start position:0%
+recoverable put and get even though the
+hardware is fine and that's because
+
+ align:start position:0%
+hardware is fine and that's because
+ 
+
+ align:start position:0%
+hardware is fine and that's because
+there are software
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+errors and in particular um the model
+
+ align:start position:0%
+errors and in particular um the model
+ 
+
+ align:start position:0%
+errors and in particular um the model
+here is that you have some application
+
+ align:start position:0%
+here is that you have some application
+ 
+
+ align:start position:0%
+here is that you have some application
+then you have the operating system and
+
+ align:start position:0%
+then you have the operating system and
+ 
+
+ align:start position:0%
+then you have the operating system and
+the operating system has a buffer
+
+ align:start position:0%
+the operating system has a buffer
+ 
+
+ align:start position:0%
+the operating system has a buffer
+here of data that it's waiting to write
+
+ align:start position:0%
+here of data that it's waiting to write
+ 
+
+ align:start position:0%
+here of data that it's waiting to write
+onto disk
+
+ align:start position:0%
+onto disk
+ 
+
+ align:start position:0%
+onto disk
+then you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dis and that's a dis sector the problem
+
+ align:start position:0%
+dis and that's a dis sector the problem
+ 
+
+ align:start position:0%
+dis and that's a dis sector the problem
+might be that if when as a failure
+
+ align:start position:0%
+might be that if when as a failure
+ 
+
+ align:start position:0%
+might be that if when as a failure
+occurs there's something that happens an
+
+ align:start position:0%
+occurs there's something that happens an
+ 
+
+ align:start position:0%
+occurs there's something that happens an
+error something that gets triggered in
+
+ align:start position:0%
+error something that gets triggered in
+ 
+
+ align:start position:0%
+error something that gets triggered in
+the operating system so the buffer gets
+
+ align:start position:0%
+the operating system so the buffer gets
+ 
+
+ align:start position:0%
+the operating system so the buffer gets
+corrupted and then there's some bad data
+
+ align:start position:0%
+corrupted and then there's some bad data
+ 
+
+ align:start position:0%
+corrupted and then there's some bad data
+that gets written out onto this sector
+
+ align:start position:0%
+that gets written out onto this sector
+ 
+
+ align:start position:0%
+that gets written out onto this sector
+and that's the kind of problem that we
+
+ align:start position:0%
+and that's the kind of problem that we
+ 
+
+ align:start position:0%
+and that's the kind of problem that we
+want to protect against it's not I mean
+
+ align:start position:0%
+want to protect against it's not I mean
+ 
+
+ align:start position:0%
+want to protect against it's not I mean
+so the fact that your Hardware is
+
+ align:start position:0%
+so the fact that your Hardware is
+ 
+
+ align:start position:0%
+so the fact that your Hardware is
+perfect doesn't actually solve this
+
+ align:start position:0%
+perfect doesn't actually solve this
+ 
+
+ align:start position:0%
+perfect doesn't actually solve this
+problem because this buffer itself has
+
+ align:start position:0%
+problem because this buffer itself has
+ 
+
+ align:start position:0%
+problem because this buffer itself has
+been corrupted or something happens
+
+ align:start position:0%
+been corrupted or something happens
+ 
+
+ align:start position:0%
+been corrupted or something happens
+during the process of this buffer to the
+
+ align:start position:0%
+during the process of this buffer to the
+ 
+
+ align:start position:0%
+during the process of this buffer to the
+sector so the data itself is bad and
+
+ align:start position:0%
+sector so the data itself is bad and
+ 
+
+ align:start position:0%
+sector so the data itself is bad and
+that's what we want to protect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+against so we're going to build on
+
+ align:start position:0%
+against so we're going to build on
+ 
+
+ align:start position:0%
+against so we're going to build on
+something that I've already talked about
+
+ align:start position:0%
+something that I've already talked about
+ 
+
+ align:start position:0%
+something that I've already talked about
+we're going to build on two
+
+ align:start position:0%
+we're going to build on two
+ 
+
+ align:start position:0%
+we're going to build on two
+procedures careful
+
+ align:start position:0%
+procedures careful
+ 
+
+ align:start position:0%
+procedures careful
+put um that puts to a sector it puts
+
+ align:start position:0%
+put um that puts to a sector it puts
+ 
+
+ align:start position:0%
+put um that puts to a sector it puts
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+data and the corresponding careful
+
+ align:start position:0%
+data and the corresponding careful
+ 
+
+ align:start position:0%
+data and the corresponding careful
+get which reads from a sector and
+
+ align:start position:0%
+get which reads from a sector and
+ 
+
+ align:start position:0%
+get which reads from a sector and
+Returns the data that's on that sector
+
+ align:start position:0%
+Returns the data that's on that sector
+ 
+
+ align:start position:0%
+Returns the data that's on that sector
+and the assumption is that careful put
+
+ align:start position:0%
+and the assumption is that careful put
+ 
+
+ align:start position:0%
+and the assumption is that careful put
+in get once you give it some data there
+
+ align:start position:0%
+in get once you give it some data there
+ 
+
+ align:start position:0%
+in get once you give it some data there
+are no Hardware failures for you to
+
+ align:start position:0%
+are no Hardware failures for you to
+ 
+
+ align:start position:0%
+are no Hardware failures for you to
+worry about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anymore so the solution we're going to
+
+ align:start position:0%
+anymore so the solution we're going to
+ 
+
+ align:start position:0%
+anymore so the solution we're going to
+take to this problem is to realize that
+
+ align:start position:0%
+take to this problem is to realize that
+ 
+
+ align:start position:0%
+take to this problem is to realize that
+when a failure happens for example
+
+ align:start position:0%
+when a failure happens for example
+ 
+
+ align:start position:0%
+when a failure happens for example
+somebody you know turns off power switch
+
+ align:start position:0%
+somebody you know turns off power switch
+ 
+
+ align:start position:0%
+somebody you know turns off power switch
+and this buffer gets
+
+ align:start position:0%
+and this buffer gets
+ 
+
+ align:start position:0%
+and this buffer gets
+corrupted when the operating system does
+
+ align:start position:0%
+corrupted when the operating system does
+ 
+
+ align:start position:0%
+corrupted when the operating system does
+a right to that sector the sector might
+
+ align:start position:0%
+a right to that sector the sector might
+ 
+
+ align:start position:0%
+a right to that sector the sector might
+be left in a state which doesn't
+
+ align:start position:0%
+be left in a state which doesn't
+ 
+
+ align:start position:0%
+be left in a state which doesn't
+actually correspond to the data that was
+
+ align:start position:0%
+actually correspond to the data that was
+ 
+
+ align:start position:0%
+actually correspond to the data that was
+intended to be put onto that sector and
+
+ align:start position:0%
+intended to be put onto that sector and
+ 
+
+ align:start position:0%
+intended to be put onto that sector and
+so when the system recovers you're sort
+
+ align:start position:0%
+so when the system recovers you're sort
+ 
+
+ align:start position:0%
+so when the system recovers you're sort
+of stuck because this data in the sector
+
+ align:start position:0%
+of stuck because this data in the sector
+ 
+
+ align:start position:0%
+of stuck because this data in the sector
+contains some values in it that don't
+
+ align:start position:0%
+contains some values in it that don't
+ 
+
+ align:start position:0%
+contains some values in it that don't
+actually correspond to any actual um
+
+ align:start position:0%
+actually correspond to any actual um
+ 
+
+ align:start position:0%
+actually correspond to any actual um
+intended uh put of the data any intended
+
+ align:start position:0%
+intended uh put of the data any intended
+ 
+
+ align:start position:0%
+intended uh put of the data any intended
+right of the data
+
+ align:start position:0%
+right of the data
+ 
+
+ align:start position:0%
+right of the data
+so what this suggests is that a solution
+
+ align:start position:0%
+so what this suggests is that a solution
+ 
+
+ align:start position:0%
+so what this suggests is that a solution
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+problem must involve a copy of some kind
+
+ align:start position:0%
+problem must involve a copy of some kind
+ 
+
+ align:start position:0%
+problem must involve a copy of some kind
+you you must make sure that if you have
+
+ align:start position:0%
+you you must make sure that if you have
+ 
+
+ align:start position:0%
+you you must make sure that if you have
+just one copy of the data and you write
+
+ align:start position:0%
+just one copy of the data and you write
+ 
+
+ align:start position:0%
+just one copy of the data and you write
+to it and something fails in the middle
+
+ align:start position:0%
+to it and something fails in the middle
+ 
+
+ align:start position:0%
+to it and something fails in the middle
+and you don't have a plan to back out to
+
+ align:start position:0%
+and you don't have a plan to back out to
+ 
+
+ align:start position:0%
+and you don't have a plan to back out to
+a an earlier working version that was
+
+ align:start position:0%
+a an earlier working version that was
+ 
+
+ align:start position:0%
+a an earlier working version that was
+correct you're stuck so that suggests
+
+ align:start position:0%
+correct you're stuck so that suggests
+ 
+
+ align:start position:0%
+correct you're stuck so that suggests
+that we better have a solution that
+
+ align:start position:0%
+that we better have a solution that
+ 
+
+ align:start position:0%
+that we better have a solution that
+involves a copy of
+
+ align:start position:0%
+involves a copy of
+ 
+
+ align:start position:0%
+involves a copy of
+data and later on we'll see how to
+
+ align:start position:0%
+data and later on we'll see how to
+ 
+
+ align:start position:0%
+data and later on we'll see how to
+system systematically develop a rule
+
+ align:start position:0%
+system systematically develop a rule
+ 
+
+ align:start position:0%
+system systematically develop a rule
+based on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so the inter the idea here is is
+
+ align:start position:0%
+this so the inter the idea here is is
+ 
+
+ align:start position:0%
+this so the inter the idea here is is
+very simple the way we're going to
+
+ align:start position:0%
+very simple the way we're going to
+ 
+
+ align:start position:0%
+very simple the way we're going to
+achieve recoverable put and recoverable
+
+ align:start position:0%
+achieve recoverable put and recoverable
+ 
+
+ align:start position:0%
+achieve recoverable put and recoverable
+get of a sector is actually
+
+ align:start position:0%
+get of a sector is actually
+ 
+
+ align:start position:0%
+get of a sector is actually
+to build a sector a single sector
+
+ align:start position:0%
+to build a sector a single sector
+ 
+
+ align:start position:0%
+to build a sector a single sector
+recoverable sector out of three sectors
+
+ align:start position:0%
+recoverable sector out of three sectors
+ 
+
+ align:start position:0%
+recoverable sector out of three sectors
+the first sector here is going to have
+
+ align:start position:0%
+the first sector here is going to have
+ 
+
+ align:start position:0%
+the first sector here is going to have
+one copy of the data the second sector
+
+ align:start position:0%
+one copy of the data the second sector
+ 
+
+ align:start position:0%
+one copy of the data the second sector
+is going to have another copy of the
+
+ align:start position:0%
+is going to have another copy of the
+ 
+
+ align:start position:0%
+is going to have another copy of the
+data and we're going to have a third
+
+ align:start position:0%
+data and we're going to have a third
+ 
+
+ align:start position:0%
+data and we're going to have a third
+sector here which is going to act as a
+
+ align:start position:0%
+sector here which is going to act as a
+ 
+
+ align:start position:0%
+sector here which is going to act as a
+flag um that allows us to choose one ver
+
+ align:start position:0%
+flag um that allows us to choose one ver
+ 
+
+ align:start position:0%
+flag um that allows us to choose one ver
+one version or the other version so let
+
+ align:start position:0%
+one version or the other version so let
+ 
+
+ align:start position:0%
+one version or the other version so let
+me call this d0 let me call this D1 and
+
+ align:start position:0%
+me call this d0 let me call this D1 and
+ 
+
+ align:start position:0%
+me call this d0 let me call this D1 and
+let me call
+
+ align:start position:0%
+let me call
+ 
+
+ align:start position:0%
+let me call
+this the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chooser so assume that at some point in
+
+ align:start position:0%
+Chooser so assume that at some point in
+ 
+
+ align:start position:0%
+Chooser so assume that at some point in
+time d0 has proper data on it okay so
+
+ align:start position:0%
+time d0 has proper data on it okay so
+ 
+
+ align:start position:0%
+time d0 has proper data on it okay so
+the idea now is going to be that anybody
+
+ align:start position:0%
+the idea now is going to be that anybody
+ 
+
+ align:start position:0%
+the idea now is going to be that anybody
+reading it the Chooser is going to
+
+ align:start position:0%
+reading it the Chooser is going to
+ 
+
+ align:start position:0%
+reading it the Chooser is going to
+contain the value zero in it okay now
+
+ align:start position:0%
+contain the value zero in it okay now
+ 
+
+ align:start position:0%
+contain the value zero in it okay now
+anybody reading is going to read from d0
+
+ align:start position:0%
+anybody reading is going to read from d0
+ 
+
+ align:start position:0%
+anybody reading is going to read from d0
+anybody writing um in recoverable put is
+
+ align:start position:0%
+anybody writing um in recoverable put is
+ 
+
+ align:start position:0%
+anybody writing um in recoverable put is
+not allowed to write to d0 because
+
+ align:start position:0%
+not allowed to write to d0 because
+ 
+
+ align:start position:0%
+not allowed to write to d0 because
+that's what people are reading from
+
+ align:start position:0%
+that's what people are reading from
+ 
+
+ align:start position:0%
+that's what people are reading from
+instead they will write to D1 when the
+
+ align:start position:0%
+instead they will write to D1 when the
+ 
+
+ align:start position:0%
+instead they will write to D1 when the
+Chooser value is zero they will start
+
+ align:start position:0%
+Chooser value is zero they will start
+ 
+
+ align:start position:0%
+Chooser value is zero they will start
+writing in to
+
+ align:start position:0%
+writing in to
+ 
+
+ align:start position:0%
+writing in to
+D1 the plan is going to be that if that
+
+ align:start position:0%
+D1 the plan is going to be that if that
+ 
+
+ align:start position:0%
+D1 the plan is going to be that if that
+right succeeds properly then what we'll
+
+ align:start position:0%
+right succeeds properly then what we'll
+ 
+
+ align:start position:0%
+right succeeds properly then what we'll
+do is go ahead and change the Chooser
+
+ align:start position:0%
+do is go ahead and change the Chooser
+ 
+
+ align:start position:0%
+do is go ahead and change the Chooser
+from zero to a
+
+ align:start position:0%
+from zero to a
+ 
+
+ align:start position:0%
+from zero to a
+one okay and then people will start
+
+ align:start position:0%
+one okay and then people will start
+ 
+
+ align:start position:0%
+one okay and then people will start
+reading from one but if that right were
+
+ align:start position:0%
+reading from one but if that right were
+ 
+
+ align:start position:0%
+reading from one but if that right were
+to fail in the middle the power fails or
+
+ align:start position:0%
+to fail in the middle the power fails or
+ 
+
+ align:start position:0%
+to fail in the middle the power fails or
+something like that that D1 will be left
+
+ align:start position:0%
+something like that that D1 will be left
+ 
+
+ align:start position:0%
+something like that that D1 will be left
+in a in sort of a weird intermediate
+
+ align:start position:0%
+in a in sort of a weird intermediate
+ 
+
+ align:start position:0%
+in a in sort of a weird intermediate
+state but that's okay because nobody's
+
+ align:start position:0%
+state but that's okay because nobody's
+ 
+
+ align:start position:0%
+state but that's okay because nobody's
+really going to be reading from D1
+
+ align:start position:0%
+really going to be reading from D1
+ 
+
+ align:start position:0%
+really going to be reading from D1
+they're all going to be reading from d0
+
+ align:start position:0%
+they're all going to be reading from d0
+ 
+
+ align:start position:0%
+they're all going to be reading from d0
+because the Chooser hasn't yet been
+
+ align:start position:0%
+because the Chooser hasn't yet been
+ 
+
+ align:start position:0%
+because the Chooser hasn't yet been
+changed so the only other thing we have
+
+ align:start position:0%
+changed so the only other thing we have
+ 
+
+ align:start position:0%
+changed so the only other thing we have
+to worry about is now we're okay as long
+
+ align:start position:0%
+to worry about is now we're okay as long
+ 
+
+ align:start position:0%
+to worry about is now we're okay as long
+as the failure happens you know if the
+
+ align:start position:0%
+as the failure happens you know if the
+ 
+
+ align:start position:0%
+as the failure happens you know if the
+failure happens in the middle here
+
+ align:start position:0%
+failure happens in the middle here
+ 
+
+ align:start position:0%
+failure happens in the middle here
+somewhere where we're writing D1 we're
+
+ align:start position:0%
+somewhere where we're writing D1 we're
+ 
+
+ align:start position:0%
+somewhere where we're writing D1 we're
+okay because we haven't touched the
+
+ align:start position:0%
+okay because we haven't touched the
+ 
+
+ align:start position:0%
+okay because we haven't touched the
+Chooser if the failure happens at the
+
+ align:start position:0%
+Chooser if the failure happens at the
+ 
+
+ align:start position:0%
+Chooser if the failure happens at the
+end of writing D1 so we've written D1
+
+ align:start position:0%
+end of writing D1 so we've written D1
+ 
+
+ align:start position:0%
+end of writing D1 so we've written D1
+and then we haven't yet started writing
+
+ align:start position:0%
+and then we haven't yet started writing
+ 
+
+ align:start position:0%
+and then we haven't yet started writing
+the Chooser and a failure happens here
+
+ align:start position:0%
+the Chooser and a failure happens here
+ 
+
+ align:start position:0%
+the Chooser and a failure happens here
+we're still okay because everybody will
+
+ align:start position:0%
+we're still okay because everybody will
+ 
+
+ align:start position:0%
+we're still okay because everybody will
+be reading from zero and that isn't
+
+ align:start position:0%
+be reading from zero and that isn't
+ 
+
+ align:start position:0%
+be reading from zero and that isn't
+going to have garbage in it it's it's
+
+ align:start position:0%
+going to have garbage in it it's it's
+ 
+
+ align:start position:0%
+going to have garbage in it it's it's
+not going to have the latest value in it
+
+ align:start position:0%
+not going to have the latest value in it
+ 
+
+ align:start position:0%
+not going to have the latest value in it
+but that's okay we never said that we
+
+ align:start position:0%
+but that's okay we never said that we
+ 
+
+ align:start position:0%
+but that's okay we never said that we
+should see the latest value um for a
+
+ align:start position:0%
+should see the latest value um for a
+ 
+
+ align:start position:0%
+should see the latest value um for a
+coverability to hold it's going to be
+
+ align:start position:0%
+coverability to hold it's going to be
+ 
+
+ align:start position:0%
+coverability to hold it's going to be
+okay for us to be reading from d0 and
+
+ align:start position:0%
+okay for us to be reading from d0 and
+ 
+
+ align:start position:0%
+okay for us to be reading from d0 and
+we'll continue to read from
+
+ align:start position:0%
+we'll continue to read from
+ 
+
+ align:start position:0%
+we'll continue to read from
+d0 and really the correctness of this
+
+ align:start position:0%
+d0 and really the correctness of this
+ 
+
+ align:start position:0%
+d0 and really the correctness of this
+boils down to understanding what will
+
+ align:start position:0%
+boils down to understanding what will
+ 
+
+ align:start position:0%
+boils down to understanding what will
+happen when a failure happens during the
+
+ align:start position:0%
+happen when a failure happens during the
+ 
+
+ align:start position:0%
+happen when a failure happens during the
+middle of writing this sector you're
+
+ align:start position:0%
+middle of writing this sector you're
+ 
+
+ align:start position:0%
+middle of writing this sector you're
+starting to write the Chooser sector and
+
+ align:start position:0%
+starting to write the Chooser sector and
+ 
+
+ align:start position:0%
+starting to write the Chooser sector and
+the system fails and we're don't have to
+
+ align:start position:0%
+the system fails and we're don't have to
+ 
+
+ align:start position:0%
+the system fails and we're don't have to
+worry about that because now we've
+
+ align:start position:0%
+worry about that because now we've
+ 
+
+ align:start position:0%
+worry about that because now we've
+written D1 completely and a failure
+
+ align:start position:0%
+written D1 completely and a failure
+ 
+
+ align:start position:0%
+written D1 completely and a failure
+happens in the middle of
+
+ align:start position:0%
+happens in the middle of
+ 
+
+ align:start position:0%
+happens in the middle of
+that so to understand that uh we'll get
+
+ align:start position:0%
+that so to understand that uh we'll get
+ 
+
+ align:start position:0%
+that so to understand that uh we'll get
+back to understanding the correctness of
+
+ align:start position:0%
+back to understanding the correctness of
+ 
+
+ align:start position:0%
+back to understanding the correctness of
+it but it helps to see what the pseudo
+
+ align:start position:0%
+it but it helps to see what the pseudo
+ 
+
+ align:start position:0%
+it but it helps to see what the pseudo
+code looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so that's what put looks
+
+ align:start position:0%
+like so that's what put looks
+ 
+
+ align:start position:0%
+like so that's what put looks
+like um to do a put you first read the
+
+ align:start position:0%
+like um to do a put you first read the
+ 
+
+ align:start position:0%
+like um to do a put you first read the
+Chooser sector and then you put into the
+
+ align:start position:0%
+Chooser sector and then you put into the
+ 
+
+ align:start position:0%
+Chooser sector and then you put into the
+other place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this which here is the thing that
+
+ align:start position:0%
+so this which here is the thing that
+ 
+
+ align:start position:0%
+so this which here is the thing that
+tells you what the value of the Chooser
+
+ align:start position:0%
+tells you what the value of the Chooser
+ 
+
+ align:start position:0%
+tells you what the value of the Chooser
+sector is so it tells you which of the
+
+ align:start position:0%
+sector is so it tells you which of the
+ 
+
+ align:start position:0%
+sector is so it tells you which of the
+two um copies to write into and then
+
+ align:start position:0%
+two um copies to write into and then
+ 
+
+ align:start position:0%
+two um copies to write into and then
+after you do the um careful put if which
+
+ align:start position:0%
+after you do the um careful put if which
+ 
+
+ align:start position:0%
+after you do the um careful put if which
+is zero you put it to one if uh which is
+
+ align:start position:0%
+is zero you put it to one if uh which is
+ 
+
+ align:start position:0%
+is zero you put it to one if uh which is
+one you put it into zero and after that
+
+ align:start position:0%
+one you put it into zero and after that
+ 
+
+ align:start position:0%
+one you put it into zero and after that
+you twiddle the bit and then you do a
+
+ align:start position:0%
+you twiddle the bit and then you do a
+ 
+
+ align:start position:0%
+you twiddle the bit and then you do a
+put onto onto the Chooser sector the get
+
+ align:start position:0%
+put onto onto the Chooser sector the get
+ 
+
+ align:start position:0%
+put onto onto the Chooser sector the get
+is actually easier you just look at what
+
+ align:start position:0%
+is actually easier you just look at what
+ 
+
+ align:start position:0%
+is actually easier you just look at what
+the value is of the Chooser sector and
+
+ align:start position:0%
+the value is of the Chooser sector and
+ 
+
+ align:start position:0%
+the value is of the Chooser sector and
+then um get it from the corresponding
+
+ align:start position:0%
+then um get it from the corresponding
+ 
+
+ align:start position:0%
+then um get it from the corresponding
+place now there's a line here the second
+
+ align:start position:0%
+place now there's a line here the second
+ 
+
+ align:start position:0%
+place now there's a line here the second
+line of the pseudo code which says if
+
+ align:start position:0%
+line of the pseudo code which says if
+ 
+
+ align:start position:0%
+line of the pseudo code which says if
+state is not okay so if stateus not okay
+
+ align:start position:0%
+state is not okay so if stateus not okay
+ 
+
+ align:start position:0%
+state is not okay so if stateus not okay
+is the key thing if stateus not okay is
+
+ align:start position:0%
+is the key thing if stateus not okay is
+ 
+
+ align:start position:0%
+is the key thing if stateus not okay is
+what happens when a failure happens in
+
+ align:start position:0%
+what happens when a failure happens in
+ 
+
+ align:start position:0%
+what happens when a failure happens in
+the middle of writing the Chooser sector
+
+ align:start position:0%
+the middle of writing the Chooser sector
+ 
+
+ align:start position:0%
+the middle of writing the Chooser sector
+so let's say a failure happens on this
+
+ align:start position:0%
+so let's say a failure happens on this
+ 
+
+ align:start position:0%
+so let's say a failure happens on this
+pseudo code um I already explained why
+
+ align:start position:0%
+pseudo code um I already explained why
+ 
+
+ align:start position:0%
+pseudo code um I already explained why
+there's no problem if a failure happens
+
+ align:start position:0%
+there's no problem if a failure happens
+ 
+
+ align:start position:0%
+there's no problem if a failure happens
+until you get to the last line until you
+
+ align:start position:0%
+until you get to the last line until you
+ 
+
+ align:start position:0%
+until you get to the last line until you
+get to the careful put of the Chooser
+
+ align:start position:0%
+get to the careful put of the Chooser
+ 
+
+ align:start position:0%
+get to the careful put of the Chooser
+sector until that line is executed
+
+ align:start position:0%
+sector until that line is executed
+ 
+
+ align:start position:0%
+sector until that line is executed
+nobody sees the new dat
+
+ align:start position:0%
+nobody sees the new dat
+ 
+
+ align:start position:0%
+nobody sees the new dat
+everybody doing a get is continuing to
+
+ align:start position:0%
+everybody doing a get is continuing to
+ 
+
+ align:start position:0%
+everybody doing a get is continuing to
+see the old data not the new data that
+
+ align:start position:0%
+see the old data not the new data that
+ 
+
+ align:start position:0%
+see the old data not the new data that
+just got written with careful put after
+
+ align:start position:0%
+just got written with careful put after
+ 
+
+ align:start position:0%
+just got written with careful put after
+this careful put executes and returns
+
+ align:start position:0%
+this careful put executes and returns
+ 
+
+ align:start position:0%
+this careful put executes and returns
+then everybody's going to see the new
+
+ align:start position:0%
+then everybody's going to see the new
+ 
+
+ align:start position:0%
+then everybody's going to see the new
+data because the Chooser sector has been
+
+ align:start position:0%
+data because the Chooser sector has been
+ 
+
+ align:start position:0%
+data because the Chooser sector has been
+correctly changed so the only tricky
+
+ align:start position:0%
+correctly changed so the only tricky
+ 
+
+ align:start position:0%
+correctly changed so the only tricky
+part to worry about we've reduced this
+
+ align:start position:0%
+part to worry about we've reduced this
+ 
+
+ align:start position:0%
+part to worry about we've reduced this
+problem of the more General slightly
+
+ align:start position:0%
+problem of the more General slightly
+ 
+
+ align:start position:0%
+problem of the more General slightly
+more General case of writing these
+
+ align:start position:0%
+more General case of writing these
+ 
+
+ align:start position:0%
+more General case of writing these
+sectors and switching between them to
+
+ align:start position:0%
+sectors and switching between them to
+ 
+
+ align:start position:0%
+sectors and switching between them to
+the specific problem of figuring out
+
+ align:start position:0%
+the specific problem of figuring out
+ 
+
+ align:start position:0%
+the specific problem of figuring out
+what happens if a failure occurs in the
+
+ align:start position:0%
+what happens if a failure occurs in the
+ 
+
+ align:start position:0%
+what happens if a failure occurs in the
+middle of the Chooser sector right if a
+
+ align:start position:0%
+middle of the Chooser sector right if a
+ 
+
+ align:start position:0%
+middle of the Chooser sector right if a
+failure happens here one one of the
+
+ align:start position:0%
+failure happens here one one of the
+ 
+
+ align:start position:0%
+failure happens here one one of the
+things the common thing that could
+
+ align:start position:0%
+things the common thing that could
+ 
+
+ align:start position:0%
+things the common thing that could
+happen is that the this sectors this
+
+ align:start position:0%
+happen is that the this sectors this
+ 
+
+ align:start position:0%
+happen is that the this sectors this
+particular sector's check sum doesn't
+
+ align:start position:0%
+particular sector's check sum doesn't
+ 
+
+ align:start position:0%
+particular sector's check sum doesn't
+match the data that's written here so
+
+ align:start position:0%
+match the data that's written here so
+ 
+
+ align:start position:0%
+match the data that's written here so
+when you do a get of that sector here
+
+ align:start position:0%
+when you do a get of that sector here
+ 
+
+ align:start position:0%
+when you do a get of that sector here
+when you do a get of this sector um in
+
+ align:start position:0%
+when you do a get of this sector um in
+ 
+
+ align:start position:0%
+when you do a get of this sector um in
+the first line up there uh when you do a
+
+ align:start position:0%
+the first line up there uh when you do a
+ 
+
+ align:start position:0%
+the first line up there uh when you do a
+careful get of that you'll find that um
+
+ align:start position:0%
+careful get of that you'll find that um
+ 
+
+ align:start position:0%
+careful get of that you'll find that um
+the check doesn't match so it returns a
+
+ align:start position:0%
+the check doesn't match so it returns a
+ 
+
+ align:start position:0%
+the check doesn't match so it returns a
+status of not okay so if the status is
+
+ align:start position:0%
+status of not okay so if the status is
+ 
+
+ align:start position:0%
+status of not okay so if the status is
+not okay you have to figure out which of
+
+ align:start position:0%
+not okay you have to figure out which of
+ 
+
+ align:start position:0%
+not okay you have to figure out which of
+the two copies to
+
+ align:start position:0%
+the two copies to
+ 
+
+ align:start position:0%
+the two copies to
+put now the reason you can pick either
+
+ align:start position:0%
+put now the reason you can pick either
+ 
+
+ align:start position:0%
+put now the reason you can pick either
+and you can arbitrarily pick here I've
+
+ align:start position:0%
+and you can arbitrarily pick here I've
+ 
+
+ align:start position:0%
+and you can arbitrarily pick here I've
+arbitrarily picked
+
+ align:start position:0%
+arbitrarily picked
+ 
+
+ align:start position:0%
+arbitrarily picked
+to uh read the data from sector zero but
+
+ align:start position:0%
+to uh read the data from sector zero but
+ 
+
+ align:start position:0%
+to uh read the data from sector zero but
+you could pick either of these okay and
+
+ align:start position:0%
+you could pick either of these okay and
+ 
+
+ align:start position:0%
+you could pick either of these okay and
+the reason it's okay to pick either is
+
+ align:start position:0%
+the reason it's okay to pick either is
+ 
+
+ align:start position:0%
+the reason it's okay to pick either is
+you know for sure that the failure must
+
+ align:start position:0%
+you know for sure that the failure must
+ 
+
+ align:start position:0%
+you know for sure that the failure must
+have happened here while writing this
+
+ align:start position:0%
+have happened here while writing this
+ 
+
+ align:start position:0%
+have happened here while writing this
+Chooser
+
+ align:start position:0%
+Chooser
+ 
+
+ align:start position:0%
+Chooser
+sector and because there are no
+
+ align:start position:0%
+sector and because there are no
+ 
+
+ align:start position:0%
+sector and because there are no
+concurrent threads going on you're
+
+ align:start position:0%
+concurrent threads going on you're
+ 
+
+ align:start position:0%
+concurrent threads going on you're
+assured that there is no failure that
+
+ align:start position:0%
+assured that there is no failure that
+ 
+
+ align:start position:0%
+assured that there is no failure that
+happens here while writing that happened
+
+ align:start position:0%
+happens here while writing that happened
+ 
+
+ align:start position:0%
+happens here while writing that happened
+here while writing d0 nor was there any
+
+ align:start position:0%
+here while writing d0 nor was there any
+ 
+
+ align:start position:0%
+here while writing d0 nor was there any
+failure that occurred here while writing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D1 because the Assumption we made was
+
+ align:start position:0%
+D1 because the Assumption we made was
+ 
+
+ align:start position:0%
+D1 because the Assumption we made was
+that there is no concurrency
+
+ align:start position:0%
+that there is no concurrency
+ 
+
+ align:start position:0%
+that there is no concurrency
+so system crashes and recovers and
+
+ align:start position:0%
+so system crashes and recovers and
+ 
+
+ align:start position:0%
+so system crashes and recovers and
+discovers that there's a failure or the
+
+ align:start position:0%
+discovers that there's a failure or the
+ 
+
+ align:start position:0%
+discovers that there's a failure or the
+the get of the Chooser sector the
+
+ align:start position:0%
+the get of the Chooser sector the
+ 
+
+ align:start position:0%
+the get of the Chooser sector the
+careful get of the Chooser sector didn't
+
+ align:start position:0%
+careful get of the Chooser sector didn't
+ 
+
+ align:start position:0%
+careful get of the Chooser sector didn't
+quite work out uh didn't give you the a
+
+ align:start position:0%
+quite work out uh didn't give you the a
+ 
+
+ align:start position:0%
+quite work out uh didn't give you the a
+status of okay that it was not okay then
+
+ align:start position:0%
+status of okay that it was not okay then
+ 
+
+ align:start position:0%
+status of okay that it was not okay then
+you know that the failure happened while
+
+ align:start position:0%
+you know that the failure happened while
+ 
+
+ align:start position:0%
+you know that the failure happened while
+writing here and what that means is it's
+
+ align:start position:0%
+writing here and what that means is it's
+ 
+
+ align:start position:0%
+writing here and what that means is it's
+perfectly okay for you to read from
+
+ align:start position:0%
+perfectly okay for you to read from
+ 
+
+ align:start position:0%
+perfectly okay for you to read from
+either version both of those correspond
+
+ align:start position:0%
+either version both of those correspond
+ 
+
+ align:start position:0%
+either version both of those correspond
+to a right to that individual sector
+
+ align:start position:0%
+to a right to that individual sector
+ 
+
+ align:start position:0%
+to a right to that individual sector
+that did not fail in the
+
+ align:start position:0%
+that did not fail in the
+ 
+
+ align:start position:0%
+that did not fail in the
+middle and it doesn't matter which of
+
+ align:start position:0%
+middle and it doesn't matter which of
+ 
+
+ align:start position:0%
+middle and it doesn't matter which of
+the two you
+
+ align:start position:0%
+the two you
+ 
+
+ align:start position:0%
+the two you
+pick and that's the reason why um this
+
+ align:start position:0%
+pick and that's the reason why um this
+ 
+
+ align:start position:0%
+pick and that's the reason why um this
+approach basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works and if you look at the solution
+
+ align:start position:0%
+works and if you look at the solution
+ 
+
+ align:start position:0%
+works and if you look at the solution
+this copy idea is actually a pretty
+
+ align:start position:0%
+this copy idea is actually a pretty
+ 
+
+ align:start position:0%
+this copy idea is actually a pretty
+critical idea for all of our solutions
+
+ align:start position:0%
+critical idea for all of our solutions
+ 
+
+ align:start position:0%
+critical idea for all of our solutions
+to achieving uh recoverability and it's
+
+ align:start position:0%
+to achieving uh recoverability and it's
+ 
+
+ align:start position:0%
+to achieving uh recoverability and it's
+going to lead to a rule that we're going
+
+ align:start position:0%
+going to lead to a rule that we're going
+ 
+
+ align:start position:0%
+going to lead to a rule that we're going
+to call um the golden rule of
+
+ align:start position:0%
+to call um the golden rule of
+ 
+
+ align:start position:0%
+to call um the golden rule of
+recoverability the rule says never
+
+ align:start position:0%
+recoverability the rule says never
+ 
+
+ align:start position:0%
+recoverability the rule says never
+modify the only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+copy so if you are asked to invent to
+
+ align:start position:0%
+copy so if you are asked to invent to
+ 
+
+ align:start position:0%
+copy so if you are asked to invent to
+come up with a recover way to achieve
+
+ align:start position:0%
+come up with a recover way to achieve
+ 
+
+ align:start position:0%
+come up with a recover way to achieve
+something that's recoverable
+
+ align:start position:0%
+something that's recoverable
+ 
+
+ align:start position:0%
+something that's recoverable
+um you know one guideline this is
+
+ align:start position:0%
+um you know one guideline this is
+ 
+
+ align:start position:0%
+um you know one guideline this is
+unfortunately not a sufficient condition
+
+ align:start position:0%
+unfortunately not a sufficient condition
+ 
+
+ align:start position:0%
+unfortunately not a sufficient condition
+but a necessary condition is that if you
+
+ align:start position:0%
+but a necessary condition is that if you
+ 
+
+ align:start position:0%
+but a necessary condition is that if you
+have something and you only have one
+
+ align:start position:0%
+have something and you only have one
+ 
+
+ align:start position:0%
+have something and you only have one
+copy of that that you end up writing
+
+ align:start position:0%
+copy of that that you end up writing
+ 
+
+ align:start position:0%
+copy of that that you end up writing
+then chances are that if a failure
+
+ align:start position:0%
+then chances are that if a failure
+ 
+
+ align:start position:0%
+then chances are that if a failure
+happens in the middle of writing that
+
+ align:start position:0%
+happens in the middle of writing that
+ 
+
+ align:start position:0%
+happens in the middle of writing that
+journal that one copy you can't back out
+
+ align:start position:0%
+journal that one copy you can't back out
+ 
+
+ align:start position:0%
+journal that one copy you can't back out
+of it so your scheme wouldn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work so never modify the only copy of
+
+ align:start position:0%
+work so never modify the only copy of
+ 
+
+ align:start position:0%
+work so never modify the only copy of
+anything that's the general rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there's another point to uh observe
+
+ align:start position:0%
+now there's another point to uh observe
+ 
+
+ align:start position:0%
+now there's another point to uh observe
+about this recoverable um dis Rite and
+
+ align:start position:0%
+about this recoverable um dis Rite and
+ 
+
+ align:start position:0%
+about this recoverable um dis Rite and
+that has to do with that careful put
+
+ align:start position:0%
+that has to do with that careful put
+ 
+
+ align:start position:0%
+that has to do with that careful put
+line right before that line everybody
+
+ align:start position:0%
+line right before that line everybody
+ 
+
+ align:start position:0%
+line right before that line everybody
+else reading this recoverable sector
+
+ align:start position:0%
+else reading this recoverable sector
+ 
+
+ align:start position:0%
+else reading this recoverable sector
+using recoverable get sees the old
+
+ align:start position:0%
+using recoverable get sees the old
+ 
+
+ align:start position:0%
+using recoverable get sees the old
+version of data right after that line
+
+ align:start position:0%
+version of data right after that line
+ 
+
+ align:start position:0%
+version of data right after that line
+has finished everybody reading it sees
+
+ align:start position:0%
+has finished everybody reading it sees
+ 
+
+ align:start position:0%
+has finished everybody reading it sees
+the new
+
+ align:start position:0%
+the new
+ 
+
+ align:start position:0%
+the new
+data that line is an example of
+
+ align:start position:0%
+data that line is an example of
+ 
+
+ align:start position:0%
+data that line is an example of
+something that we'll uh repeatedly visit
+
+ align:start position:0%
+something that we'll uh repeatedly visit
+ 
+
+ align:start position:0%
+something that we'll uh repeatedly visit
+uh and use called a commit point
+
+ align:start position:0%
+uh and use called a commit point
+ 
+
+ align:start position:0%
+uh and use called a commit point
+point the successful completion of that
+
+ align:start position:0%
+point the successful completion of that
+ 
+
+ align:start position:0%
+point the successful completion of that
+line ensures that everybody else
+
+ align:start position:0%
+line ensures that everybody else
+ 
+
+ align:start position:0%
+line ensures that everybody else
+following doing gets will see the data
+
+ align:start position:0%
+following doing gets will see the data
+ 
+
+ align:start position:0%
+following doing gets will see the data
+that was written by this
+
+ align:start position:0%
+that was written by this
+ 
+
+ align:start position:0%
+that was written by this
+put and before that line is run
+
+ align:start position:0%
+put and before that line is run
+ 
+
+ align:start position:0%
+put and before that line is run
+everybody else following will see the
+
+ align:start position:0%
+everybody else following will see the
+ 
+
+ align:start position:0%
+everybody else following will see the
+the older version of the
+
+ align:start position:0%
+the older version of the
+ 
+
+ align:start position:0%
+the older version of the
+data now if a failure occurs in the
+
+ align:start position:0%
+data now if a failure occurs in the
+ 
+
+ align:start position:0%
+data now if a failure occurs in the
+middle of that line then the answer
+
+ align:start position:0%
+middle of that line then the answer
+ 
+
+ align:start position:0%
+middle of that line then the answer
+depends on what the recovery procedure
+
+ align:start position:0%
+depends on what the recovery procedure
+ 
+
+ align:start position:0%
+depends on what the recovery procedure
+does and one approach might be that the
+
+ align:start position:0%
+does and one approach might be that the
+ 
+
+ align:start position:0%
+does and one approach might be that the
+invoker of this module the person who
+
+ align:start position:0%
+invoker of this module the person who
+ 
+
+ align:start position:0%
+invoker of this module the person who
+originally did the dis right if if a
+
+ align:start position:0%
+originally did the dis right if if a
+ 
+
+ align:start position:0%
+originally did the dis right if if a
+failure happens in the middle of the
+
+ align:start position:0%
+failure happens in the middle of the
+ 
+
+ align:start position:0%
+failure happens in the middle of the
+right one plan might be that the invoker
+
+ align:start position:0%
+right one plan might be that the invoker
+ 
+
+ align:start position:0%
+right one plan might be that the invoker
+of that dis right upon recovery tries
+
+ align:start position:0%
+of that dis right upon recovery tries
+ 
+
+ align:start position:0%
+of that dis right upon recovery tries
+the right again tries the tries the put
+
+ align:start position:0%
+the right again tries the tries the put
+ 
+
+ align:start position:0%
+the right again tries the tries the put
+again and the way he tries the put is he
+
+ align:start position:0%
+again and the way he tries the put is he
+ 
+
+ align:start position:0%
+again and the way he tries the put is he
+first does a get and sees what answer is
+
+ align:start position:0%
+first does a get and sees what answer is
+ 
+
+ align:start position:0%
+first does a get and sees what answer is
+returned if the answer is the new answer
+
+ align:start position:0%
+returned if the answer is the new answer
+ 
+
+ align:start position:0%
+returned if the answer is the new answer
+then he says okay everything is fine if
+
+ align:start position:0%
+then he says okay everything is fine if
+ 
+
+ align:start position:0%
+then he says okay everything is fine if
+the answer is the old answer then he
+
+ align:start position:0%
+the answer is the old answer then he
+ 
+
+ align:start position:0%
+the answer is the old answer then he
+says I'm going to retry the put and this
+
+ align:start position:0%
+says I'm going to retry the put and this
+ 
+
+ align:start position:0%
+says I'm going to retry the put and this
+is an example of something we saw the
+
+ align:start position:0%
+is an example of something we saw the
+ 
+
+ align:start position:0%
+is an example of something we saw the
+last time which is temporal redundancy
+
+ align:start position:0%
+last time which is temporal redundancy
+ 
+
+ align:start position:0%
+last time which is temporal redundancy
+you can retry things you not only can
+
+ align:start position:0%
+you can retry things you not only can
+ 
+
+ align:start position:0%
+you can retry things you not only can
+replicate in space but you can rety
+
+ align:start position:0%
+replicate in space but you can rety
+ 
+
+ align:start position:0%
+replicate in space but you can rety
+things in time which is the idea here
+
+ align:start position:0%
+things in time which is the idea here
+ 
+
+ align:start position:0%
+things in time which is the idea here
+for achieving uh fa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tolerance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so an example of this idea called a
+
+ align:start position:0%
+so so an example of this idea called a
+ 
+
+ align:start position:0%
+so so an example of this idea called a
+commit point is that line that careful
+
+ align:start position:0%
+commit point is that line that careful
+ 
+
+ align:start position:0%
+commit point is that line that careful
+put line and in general a commit point
+
+ align:start position:0%
+put line and in general a commit point
+ 
+
+ align:start position:0%
+put line and in general a commit point
+is a point in a recoverable action in
+
+ align:start position:0%
+is a point in a recoverable action in
+ 
+
+ align:start position:0%
+is a point in a recoverable action in
+this case and it'll turn out to be an
+
+ align:start position:0%
+this case and it'll turn out to be an
+ 
+
+ align:start position:0%
+this case and it'll turn out to be an
+idea that's useful for um isolated
+
+ align:start position:0%
+idea that's useful for um isolated
+ 
+
+ align:start position:0%
+idea that's useful for um isolated
+actions and for transactions more
+
+ align:start position:0%
+actions and for transactions more
+ 
+
+ align:start position:0%
+actions and for transactions more
+generally but a commit point is there's
+
+ align:start position:0%
+generally but a commit point is there's
+ 
+
+ align:start position:0%
+generally but a commit point is there's
+a point where before the commit Point
+
+ align:start position:0%
+a point where before the commit Point
+ 
+
+ align:start position:0%
+a point where before the commit Point
+other people don't see the results of
+
+ align:start position:0%
+other people don't see the results of
+ 
+
+ align:start position:0%
+other people don't see the results of
+your action and after the commit Point
+
+ align:start position:0%
+your action and after the commit Point
+ 
+
+ align:start position:0%
+your action and after the commit Point
+successfully finishes everybody sees the
+
+ align:start position:0%
+successfully finishes everybody sees the
+ 
+
+ align:start position:0%
+successfully finishes everybody sees the
+results of your action and that's the
+
+ align:start position:0%
+results of your action and that's the
+ 
+
+ align:start position:0%
+results of your action and that's the
+definition of a commit point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have to generalize this idea
+
+ align:start position:0%
+so now we have to generalize this idea
+ 
+
+ align:start position:0%
+so now we have to generalize this idea
+because what we've seen is a scheme by
+
+ align:start position:0%
+because what we've seen is a scheme by
+ 
+
+ align:start position:0%
+because what we've seen is a scheme by
+the way is this clear to everybody a
+
+ align:start position:0%
+the way is this clear to everybody a
+ 
+
+ align:start position:0%
+the way is this clear to everybody a
+scheme are any questions about
+
+ align:start position:0%
+scheme are any questions about
+ 
+
+ align:start position:0%
+scheme are any questions about
+recoverable put and
+
+ align:start position:0%
+recoverable put and
+ 
+
+ align:start position:0%
+recoverable put and
+get what does that
+
+ align:start position:0%
+get what does that
+ 
+
+ align:start position:0%
+get what does that
+mean no questions are not
+
+ align:start position:0%
+mean no questions are not
+ 
+
+ align:start position:0%
+mean no questions are not
+clear questions
+
+ align:start position:0%
+clear questions
+ 
+
+ align:start position:0%
+clear questions
+okay all right good so now we have to
+
+ align:start position:0%
+okay all right good so now we have to
+ 
+
+ align:start position:0%
+okay all right good so now we have to
+generalize this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea because you know we the the class
+
+ align:start position:0%
+idea because you know we the the class
+ 
+
+ align:start position:0%
+idea because you know we the the class
+of program s where you could just sort
+
+ align:start position:0%
+of program s where you could just sort
+ 
+
+ align:start position:0%
+of program s where you could just sort
+of read and write from one sector is
+
+ align:start position:0%
+of read and write from one sector is
+ 
+
+ align:start position:0%
+of read and write from one sector is
+quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limited and so to generalize this
+
+ align:start position:0%
+limited and so to generalize this
+ 
+
+ align:start position:0%
+limited and so to generalize this
+generalize this idea what we're going to
+
+ align:start position:0%
+generalize this idea what we're going to
+ 
+
+ align:start position:0%
+generalize this idea what we're going to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+is to change the programming model for
+
+ align:start position:0%
+is to change the programming model for
+ 
+
+ align:start position:0%
+is to change the programming model for
+writing recoverable actions a little bit
+
+ align:start position:0%
+writing recoverable actions a little bit
+ 
+
+ align:start position:0%
+writing recoverable actions a little bit
+so ideally what you would like to be
+
+ align:start position:0%
+so ideally what you would like to be
+ 
+
+ align:start position:0%
+so ideally what you would like to be
+able to do the model we're going to try
+
+ align:start position:0%
+able to do the model we're going to try
+ 
+
+ align:start position:0%
+able to do the model we're going to try
+to get at is to be able to take a
+
+ align:start position:0%
+to get at is to be able to take a
+ 
+
+ align:start position:0%
+to get at is to be able to take a
+procedure and say begin recoverable
+
+ align:start position:0%
+procedure and say begin recoverable
+ 
+
+ align:start position:0%
+procedure and say begin recoverable
+action in front of that procedure write
+
+ align:start position:0%
+action in front of that procedure write
+ 
+
+ align:start position:0%
+action in front of that procedure write
+the code for that procedure and just say
+
+ align:start position:0%
+the code for that procedure and just say
+ 
+
+ align:start position:0%
+the code for that procedure and just say
+end recoverable action and and sort of
+
+ align:start position:0%
+end recoverable action and and sort of
+ 
+
+ align:start position:0%
+end recoverable action and and sort of
+magically end up with a model where um
+
+ align:start position:0%
+magically end up with a model where um
+ 
+
+ align:start position:0%
+magically end up with a model where um
+that action the set of steps in that
+
+ align:start position:0%
+that action the set of steps in that
+ 
+
+ align:start position:0%
+that action the set of steps in that
+action becomes recoverable and it'll
+
+ align:start position:0%
+action becomes recoverable and it'll
+ 
+
+ align:start position:0%
+action becomes recoverable and it'll
+turn out we come very very close to
+
+ align:start position:0%
+turn out we come very very close to
+ 
+
+ align:start position:0%
+turn out we come very very close to
+achieving this very general model um by
+
+ align:start position:0%
+achieving this very general model um by
+ 
+
+ align:start position:0%
+achieving this very general model um by
+making some slight assumptions in the
+
+ align:start position:0%
+making some slight assumptions in the
+ 
+
+ align:start position:0%
+making some slight assumptions in the
+way people or requiring the programmer
+
+ align:start position:0%
+way people or requiring the programmer
+ 
+
+ align:start position:0%
+way people or requiring the programmer
+to make some small assumptions in the
+
+ align:start position:0%
+to make some small assumptions in the
+ 
+
+ align:start position:0%
+to make some small assumptions in the
+way they write uh their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+programs and this generalization to more
+
+ align:start position:0%
+programs and this generalization to more
+ 
+
+ align:start position:0%
+programs and this generalization to more
+General actions um that are recoverable
+
+ align:start position:0%
+General actions um that are recoverable
+ 
+
+ align:start position:0%
+General actions um that are recoverable
+and you know generalizing from a single
+
+ align:start position:0%
+and you know generalizing from a single
+ 
+
+ align:start position:0%
+and you know generalizing from a single
+sector uses the idea of a commit
+
+ align:start position:0%
+sector uses the idea of a commit
+ 
+
+ align:start position:0%
+sector uses the idea of a commit
+point so the way this is going to work
+
+ align:start position:0%
+point so the way this is going to work
+ 
+
+ align:start position:0%
+point so the way this is going to work
+out is the programmer is going to end up
+
+ align:start position:0%
+out is the programmer is going to end up
+ 
+
+ align:start position:0%
+out is the programmer is going to end up
+writing for any recoverable action's
+
+ align:start position:0%
+writing for any recoverable action's
+ 
+
+ align:start position:0%
+writing for any recoverable action's
+she's going she or he is going to end up
+
+ align:start position:0%
+she's going she or he is going to end up
+ 
+
+ align:start position:0%
+she's going she or he is going to end up
+writing this special function call um
+
+ align:start position:0%
+writing this special function call um
+ 
+
+ align:start position:0%
+writing this special function call um
+called begin recoverable action and then
+
+ align:start position:0%
+called begin recoverable action and then
+ 
+
+ align:start position:0%
+called begin recoverable action and then
+writing the code for that recoverable
+
+ align:start position:0%
+writing the code for that recoverable
+ 
+
+ align:start position:0%
+writing the code for that recoverable
+action and then at some point in the
+
+ align:start position:0%
+action and then at some point in the
+ 
+
+ align:start position:0%
+action and then at some point in the
+middle of this code
+
+ align:start position:0%
+middle of this code
+ 
+
+ align:start position:0%
+middle of this code
+calling a function called
+
+ align:start position:0%
+calling a function called
+ 
+
+ align:start position:0%
+calling a function called
+commit and the idea is that until this
+
+ align:start position:0%
+commit and the idea is that until this
+ 
+
+ align:start position:0%
+commit and the idea is that until this
+commit is called nobody else sees the
+
+ align:start position:0%
+commit is called nobody else sees the
+ 
+
+ align:start position:0%
+commit is called nobody else sees the
+results of this action which means that
+
+ align:start position:0%
+results of this action which means that
+ 
+
+ align:start position:0%
+results of this action which means that
+if a failure happened the result would
+
+ align:start position:0%
+if a failure happened the result would
+ 
+
+ align:start position:0%
+if a failure happened the result would
+be as if the upon crash recovery or um
+
+ align:start position:0%
+be as if the upon crash recovery or um
+ 
+
+ align:start position:0%
+be as if the upon crash recovery or um
+you know once the system restarts the
+
+ align:start position:0%
+you know once the system restarts the
+ 
+
+ align:start position:0%
+you know once the system restarts the
+result would be as if none of the steps
+
+ align:start position:0%
+result would be as if none of the steps
+ 
+
+ align:start position:0%
+result would be as if none of the steps
+of this action ever happened so they
+
+ align:start position:0%
+of this action ever happened so they
+ 
+
+ align:start position:0%
+of this action ever happened so they
+call commit and then once commit
+
+ align:start position:0%
+call commit and then once commit
+ 
+
+ align:start position:0%
+call commit and then once commit
+finishes then no matter what happens a
+
+ align:start position:0%
+finishes then no matter what happens a
+ 
+
+ align:start position:0%
+finishes then no matter what happens a
+failure could happen and re the system
+
+ align:start position:0%
+failure could happen and re the system
+ 
+
+ align:start position:0%
+failure could happen and re the system
+restarts but once commit is called and
+
+ align:start position:0%
+restarts but once commit is called and
+ 
+
+ align:start position:0%
+restarts but once commit is called and
+it returns then you're guaranteed that
+
+ align:start position:0%
+it returns then you're guaranteed that
+ 
+
+ align:start position:0%
+it returns then you're guaranteed that
+all other actions see the state changes
+
+ align:start position:0%
+all other actions see the state changes
+ 
+
+ align:start position:0%
+all other actions see the state changes
+made by this action and that's the you
+
+ align:start position:0%
+made by this action and that's the you
+ 
+
+ align:start position:0%
+made by this action and that's the you
+know so this is a special call and then
+
+ align:start position:0%
+know so this is a special call and then
+ 
+
+ align:start position:0%
+know so this is a special call and then
+you know after commit they might have
+
+ align:start position:0%
+you know after commit they might have
+ 
+
+ align:start position:0%
+you know after commit they might have
+some other lines that they write and
+
+ align:start position:0%
+some other lines that they write and
+ 
+
+ align:start position:0%
+some other lines that they write and
+then they end the recoverable
+
+ align:start position:0%
+then they end the recoverable
+ 
+
+ align:start position:0%
+then they end the recoverable
+action now in many many cases the very
+
+ align:start position:0%
+action now in many many cases the very
+ 
+
+ align:start position:0%
+action now in many many cases the very
+last thing that's done before before the
+
+ align:start position:0%
+last thing that's done before before the
+ 
+
+ align:start position:0%
+last thing that's done before before the
+end recoverable action is a
+
+ align:start position:0%
+end recoverable action is a
+ 
+
+ align:start position:0%
+end recoverable action is a
+commit um but in general you might have
+
+ align:start position:0%
+commit um but in general you might have
+ 
+
+ align:start position:0%
+commit um but in general you might have
+other things here uh and it turn out
+
+ align:start position:0%
+other things here uh and it turn out
+ 
+
+ align:start position:0%
+other things here uh and it turn out
+that there you can't do arbitary things
+
+ align:start position:0%
+that there you can't do arbitary things
+ 
+
+ align:start position:0%
+that there you can't do arbitary things
+here for example you can't do uh dis
+
+ align:start position:0%
+here for example you can't do uh dis
+ 
+
+ align:start position:0%
+here for example you can't do uh dis
+writes that you want to make recoverable
+
+ align:start position:0%
+writes that you want to make recoverable
+ 
+
+ align:start position:0%
+writes that you want to make recoverable
+over here because the moment you do that
+
+ align:start position:0%
+over here because the moment you do that
+ 
+
+ align:start position:0%
+over here because the moment you do that
+by definition if a crash happens after a
+
+ align:start position:0%
+by definition if a crash happens after a
+ 
+
+ align:start position:0%
+by definition if a crash happens after a
+commit we don't have a plan to back out
+
+ align:start position:0%
+commit we don't have a plan to back out
+ 
+
+ align:start position:0%
+commit we don't have a plan to back out
+of it because the semantics were that
+
+ align:start position:0%
+of it because the semantics were that
+ 
+
+ align:start position:0%
+of it because the semantics were that
+once a commit is done then no matter
+
+ align:start position:0%
+once a commit is done then no matter
+ 
+
+ align:start position:0%
+once a commit is done then no matter
+what happens the state of the system is
+
+ align:start position:0%
+what happens the state of the system is
+ 
+
+ align:start position:0%
+what happens the state of the system is
+as if all of the um things in this
+
+ align:start position:0%
+as if all of the um things in this
+ 
+
+ align:start position:0%
+as if all of the um things in this
+action finished so the discipline is
+
+ align:start position:0%
+action finished so the discipline is
+ 
+
+ align:start position:0%
+action finished so the discipline is
+going to be this thing is called the
+
+ align:start position:0%
+going to be this thing is called the
+ 
+
+ align:start position:0%
+going to be this thing is called the
+post commit the pre-commit
+
+ align:start position:0%
+post commit the pre-commit
+ 
+
+ align:start position:0%
+post commit the pre-commit
+phase and this thing here is called the
+
+ align:start position:0%
+phase and this thing here is called the
+ 
+
+ align:start position:0%
+phase and this thing here is called the
+postc commit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase and so the the idea is that in the
+
+ align:start position:0%
+phase and so the the idea is that in the
+ 
+
+ align:start position:0%
+phase and so the the idea is that in the
+pre-commit phase um you should always be
+
+ align:start position:0%
+pre-commit phase um you should always be
+ 
+
+ align:start position:0%
+pre-commit phase um you should always be
+prep prepared to back out because by
+
+ align:start position:0%
+prep prepared to back out because by
+ 
+
+ align:start position:0%
+prep prepared to back out because by
+definition if a failure occurs before
+
+ align:start position:0%
+definition if a failure occurs before
+ 
+
+ align:start position:0%
+definition if a failure occurs before
+commit is called um the results going to
+
+ align:start position:0%
+commit is called um the results going to
+ 
+
+ align:start position:0%
+commit is called um the results going to
+be as if nothing ever happened which
+
+ align:start position:0%
+be as if nothing ever happened which
+ 
+
+ align:start position:0%
+be as if nothing ever happened which
+means that any change you make here you
+
+ align:start position:0%
+means that any change you make here you
+ 
+
+ align:start position:0%
+means that any change you make here you
+better religiously Follow That Never
+
+ align:start position:0%
+better religiously Follow That Never
+ 
+
+ align:start position:0%
+better religiously Follow That Never
+modify the only copy Rule and be
+
+ align:start position:0%
+modify the only copy Rule and be
+ 
+
+ align:start position:0%
+modify the only copy Rule and be
+prepared to back out in the post commit
+
+ align:start position:0%
+prepared to back out in the post commit
+ 
+
+ align:start position:0%
+prepared to back out in the post commit
+phase conversely you better make sure
+
+ align:start position:0%
+phase conversely you better make sure
+ 
+
+ align:start position:0%
+phase conversely you better make sure
+that you can never back you you don't
+
+ align:start position:0%
+that you can never back you you don't
+ 
+
+ align:start position:0%
+that you can never back you you don't
+you know you don't have the option to
+
+ align:start position:0%
+you know you don't have the option to
+ 
+
+ align:start position:0%
+you know you don't have the option to
+back out so you better make sure that
+
+ align:start position:0%
+back out so you better make sure that
+ 
+
+ align:start position:0%
+back out so you better make sure that
+once you get here you just run to
+
+ align:start position:0%
+once you get here you just run to
+ 
+
+ align:start position:0%
+once you get here you just run to
+completion so if a failure occurs
+
+ align:start position:0%
+completion so if a failure occurs
+ 
+
+ align:start position:0%
+completion so if a failure occurs
+and in out here and you restart you
+
+ align:start position:0%
+and in out here and you restart you
+ 
+
+ align:start position:0%
+and in out here and you restart you
+better make sure that you can run to
+
+ align:start position:0%
+better make sure that you can run to
+ 
+
+ align:start position:0%
+better make sure that you can run to
+completion it in fact there are a few
+
+ align:start position:0%
+completion it in fact there are a few
+ 
+
+ align:start position:0%
+completion it in fact there are a few
+other restrictions out in the post
+
+ align:start position:0%
+other restrictions out in the post
+ 
+
+ align:start position:0%
+other restrictions out in the post
+commit phase um so let me do this by an
+
+ align:start position:0%
+commit phase um so let me do this by an
+ 
+
+ align:start position:0%
+commit phase um so let me do this by an
+example so in the pre-commit phase
+
+ align:start position:0%
+example so in the pre-commit phase
+ 
+
+ align:start position:0%
+example so in the pre-commit phase
+because you have to be prepared to back
+
+ align:start position:0%
+because you have to be prepared to back
+ 
+
+ align:start position:0%
+because you have to be prepared to back
+out it often means in practice that you
+
+ align:start position:0%
+out it often means in practice that you
+ 
+
+ align:start position:0%
+out it often means in practice that you
+can't be sending messages out onto the
+
+ align:start position:0%
+can't be sending messages out onto the
+ 
+
+ align:start position:0%
+can't be sending messages out onto the
+network you can you know maintain your
+
+ align:start position:0%
+network you can you know maintain your
+ 
+
+ align:start position:0%
+network you can you know maintain your
+local state but you know you have a way
+
+ align:start position:0%
+local state but you know you have a way
+ 
+
+ align:start position:0%
+local state but you know you have a way
+to back out of that uh but if you're
+
+ align:start position:0%
+to back out of that uh but if you're
+ 
+
+ align:start position:0%
+to back out of that uh but if you're
+sending messages out onto the network
+
+ align:start position:0%
+sending messages out onto the network
+ 
+
+ align:start position:0%
+sending messages out onto the network
+and you don't have a you know a bigger
+
+ align:start position:0%
+and you don't have a you know a bigger
+ 
+
+ align:start position:0%
+and you don't have a you know a bigger
+story to deal with it you know we'll
+
+ align:start position:0%
+story to deal with it you know we'll
+ 
+
+ align:start position:0%
+story to deal with it you know we'll
+talk later about um nesting Atomic
+
+ align:start position:0%
+talk later about um nesting Atomic
+ 
+
+ align:start position:0%
+talk later about um nesting Atomic
+actions within one another or nesting
+
+ align:start position:0%
+actions within one another or nesting
+ 
+
+ align:start position:0%
+actions within one another or nesting
+recoverable actions within one another
+
+ align:start position:0%
+recoverable actions within one another
+ 
+
+ align:start position:0%
+recoverable actions within one another
+in a few lectures from now but in the
+
+ align:start position:0%
+in a few lectures from now but in the
+ 
+
+ align:start position:0%
+in a few lectures from now but in the
+simple model if you do anything that you
+
+ align:start position:0%
+simple model if you do anything that you
+ 
+
+ align:start position:0%
+simple model if you do anything that you
+can't back out off such as sending a
+
+ align:start position:0%
+can't back out off such as sending a
+ 
+
+ align:start position:0%
+can't back out off such as sending a
+network packet then you're stuck so all
+
+ align:start position:0%
+network packet then you're stuck so all
+ 
+
+ align:start position:0%
+network packet then you're stuck so all
+of that stuff like you know printing out
+
+ align:start position:0%
+of that stuff like you know printing out
+ 
+
+ align:start position:0%
+of that stuff like you know printing out
+checks or you know sending a firing a
+
+ align:start position:0%
+checks or you know sending a firing a
+ 
+
+ align:start position:0%
+checks or you know sending a firing a
+bullet or something things like that
+
+ align:start position:0%
+bullet or something things like that
+ 
+
+ align:start position:0%
+bullet or something things like that
+that you can't back out of you better
+
+ align:start position:0%
+that you can't back out of you better
+ 
+
+ align:start position:0%
+that you can't back out of you better
+put out here all the things that you can
+
+ align:start position:0%
+put out here all the things that you can
+ 
+
+ align:start position:0%
+put out here all the things that you can
+back out off go here likewise nothing
+
+ align:start position:0%
+back out off go here likewise nothing
+ 
+
+ align:start position:0%
+back out off go here likewise nothing
+you can back out of has to go can go
+
+ align:start position:0%
+you can back out of has to go can go
+ 
+
+ align:start position:0%
+you can back out of has to go can go
+here because once you reach here and a
+
+ align:start position:0%
+here because once you reach here and a
+ 
+
+ align:start position:0%
+here because once you reach here and a
+failure happen you have to continue to
+
+ align:start position:0%
+failure happen you have to continue to
+ 
+
+ align:start position:0%
+failure happen you have to continue to
+completion what that means is in the
+
+ align:start position:0%
+completion what that means is in the
+ 
+
+ align:start position:0%
+completion what that means is in the
+post commit phase really you can't do
+
+ align:start position:0%
+post commit phase really you can't do
+ 
+
+ align:start position:0%
+post commit phase really you can't do
+very many things I mean you can do
+
+ align:start position:0%
+very many things I mean you can do
+ 
+
+ align:start position:0%
+very many things I mean you can do
+things that don't really have um um you
+
+ align:start position:0%
+things that don't really have um um you
+ 
+
+ align:start position:0%
+things that don't really have um um you
+know for example you can do things that
+
+ align:start position:0%
+know for example you can do things that
+ 
+
+ align:start position:0%
+know for example you can do things that
+are okay to keep doing for example you
+
+ align:start position:0%
+are okay to keep doing for example you
+ 
+
+ align:start position:0%
+are okay to keep doing for example you
+can do item potent operations so that if
+
+ align:start position:0%
+can do item potent operations so that if
+ 
+
+ align:start position:0%
+can do item potent operations so that if
+a failure happens here and you recover
+
+ align:start position:0%
+a failure happens here and you recover
+ 
+
+ align:start position:0%
+a failure happens here and you recover
+then you know that you're out at this
+
+ align:start position:0%
+then you know that you're out at this
+ 
+
+ align:start position:0%
+then you know that you're out at this
+point so you could keep retrying those
+
+ align:start position:0%
+point so you could keep retrying those
+ 
+
+ align:start position:0%
+point so you could keep retrying those
+actions over and over again until you
+
+ align:start position:0%
+actions over and over again until you
+ 
+
+ align:start position:0%
+actions over and over again until you
+ensure that it
+
+ align:start position:0%
+ensure that it
+ 
+
+ align:start position:0%
+ensure that it
+completes but that's the only those are
+
+ align:start position:0%
+completes but that's the only those are
+ 
+
+ align:start position:0%
+completes but that's the only those are
+the only rules there's a pre-commit
+
+ align:start position:0%
+the only rules there's a pre-commit
+ 
+
+ align:start position:0%
+the only rules there's a pre-commit
+phase and a postc commit phase there's a
+
+ align:start position:0%
+phase and a postc commit phase there's a
+ 
+
+ align:start position:0%
+phase and a postc commit phase there's a
+commit that's explicitly called
+
+ align:start position:0%
+commit that's explicitly called
+ 
+
+ align:start position:0%
+commit that's explicitly called
+now in addition there's another call
+
+ align:start position:0%
+now in addition there's another call
+ 
+
+ align:start position:0%
+now in addition there's another call
+that that a programmer can make or that
+
+ align:start position:0%
+that that a programmer can make or that
+ 
+
+ align:start position:0%
+that that a programmer can make or that
+the system can invoke automatically and
+
+ align:start position:0%
+the system can invoke automatically and
+ 
+
+ align:start position:0%
+the system can invoke automatically and
+that's called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aart for example when you're moving
+
+ align:start position:0%
+aart for example when you're moving
+ 
+
+ align:start position:0%
+aart for example when you're moving
+money from savings account to checking
+
+ align:start position:0%
+money from savings account to checking
+ 
+
+ align:start position:0%
+money from savings account to checking
+account in that transfer example um if
+
+ align:start position:0%
+account in that transfer example um if
+ 
+
+ align:start position:0%
+account in that transfer example um if
+you discover in the middle here that you
+
+ align:start position:0%
+you discover in the middle here that you
+ 
+
+ align:start position:0%
+you discover in the middle here that you
+don't have enough funds to cover that
+
+ align:start position:0%
+don't have enough funds to cover that
+ 
+
+ align:start position:0%
+don't have enough funds to cover that
+transfer you could just decide to abart
+
+ align:start position:0%
+transfer you could just decide to abart
+ 
+
+ align:start position:0%
+transfer you could just decide to abart
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+transaction excuse me about the
+
+ align:start position:0%
+transaction excuse me about the
+ 
+
+ align:start position:0%
+transaction excuse me about the
+recoverable
+
+ align:start position:0%
+recoverable
+ 
+
+ align:start position:0%
+recoverable
+action and what that means is that abort
+
+ align:start position:0%
+action and what that means is that abort
+ 
+
+ align:start position:0%
+action and what that means is that abort
+automatically will ensure that the state
+
+ align:start position:0%
+automatically will ensure that the state
+ 
+
+ align:start position:0%
+automatically will ensure that the state
+of the system is at the point right
+
+ align:start position:0%
+of the system is at the point right
+ 
+
+ align:start position:0%
+of the system is at the point right
+before the start of the recoverable
+
+ align:start position:0%
+before the start of the recoverable
+ 
+
+ align:start position:0%
+before the start of the recoverable
+action so whatever changes were made in
+
+ align:start position:0%
+action so whatever changes were made in
+ 
+
+ align:start position:0%
+action so whatever changes were made in
+the middle until abort was called um end
+
+ align:start position:0%
+the middle until abort was called um end
+ 
+
+ align:start position:0%
+the middle until abort was called um end
+up backing out now abort might also be
+
+ align:start position:0%
+up backing out now abort might also be
+ 
+
+ align:start position:0%
+up backing out now abort might also be
+invoked by the system if you know in a
+
+ align:start position:0%
+invoked by the system if you know in a
+ 
+
+ align:start position:0%
+invoked by the system if you know in a
+database system there's somebody you're
+
+ align:start position:0%
+database system there's somebody you're
+ 
+
+ align:start position:0%
+database system there's somebody you're
+booking airline tickets and car
+
+ align:start position:0%
+booking airline tickets and car
+ 
+
+ align:start position:0%
+booking airline tickets and car
+reservations and all of that and you
+
+ align:start position:0%
+reservations and all of that and you
+ 
+
+ align:start position:0%
+reservations and all of that and you
+discover in the middle that you're not
+
+ align:start position:0%
+discover in the middle that you're not
+ 
+
+ align:start position:0%
+discover in the middle that you're not
+actually able to find you know um hotel
+
+ align:start position:0%
+actually able to find you know um hotel
+ 
+
+ align:start position:0%
+actually able to find you know um hotel
+for the same dates so you might just
+
+ align:start position:0%
+for the same dates so you might just
+ 
+
+ align:start position:0%
+for the same dates so you might just
+abort the whole process you know so
+
+ align:start position:0%
+abort the whole process you know so
+ 
+
+ align:start position:0%
+abort the whole process you know so
+control C the thre you're running uh
+
+ align:start position:0%
+control C the thre you're running uh
+ 
+
+ align:start position:0%
+control C the thre you're running uh
+which means that all of the work that's
+
+ align:start position:0%
+which means that all of the work that's
+ 
+
+ align:start position:0%
+which means that all of the work that's
+been done has to be backed out and so
+
+ align:start position:0%
+been done has to be backed out and so
+ 
+
+ align:start position:0%
+been done has to be backed out and so
+the system would normally Implement that
+
+ align:start position:0%
+the system would normally Implement that
+ 
+
+ align:start position:0%
+the system would normally Implement that
+by aborting all of the changes that
+
+ align:start position:0%
+by aborting all of the changes that
+ 
+
+ align:start position:0%
+by aborting all of the changes that
+you've made um so far you know it'll
+
+ align:start position:0%
+you've made um so far you know it'll
+ 
+
+ align:start position:0%
+you've made um so far you know it'll
+back out of your hotel reservation it'll
+
+ align:start position:0%
+back out of your hotel reservation it'll
+ 
+
+ align:start position:0%
+back out of your hotel reservation it'll
+I'm sorry your car reservation back out
+
+ align:start position:0%
+I'm sorry your car reservation back out
+ 
+
+ align:start position:0%
+I'm sorry your car reservation back out
+of your Airline reservation and so on so
+
+ align:start position:0%
+of your Airline reservation and so on so
+ 
+
+ align:start position:0%
+of your Airline reservation and so on so
+bot is called in a few different
+
+ align:start position:0%
+bot is called in a few different
+ 
+
+ align:start position:0%
+bot is called in a few different
+contexts sometimes by the program itself
+
+ align:start position:0%
+contexts sometimes by the program itself
+ 
+
+ align:start position:0%
+contexts sometimes by the program itself
+sometimes by the system to free up
+
+ align:start position:0%
+sometimes by the system to free up
+ 
+
+ align:start position:0%
+sometimes by the system to free up
+resources sometimes by the user of your
+
+ align:start position:0%
+resources sometimes by the user of your
+ 
+
+ align:start position:0%
+resources sometimes by the user of your
+uh for say a transaction system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before I U I'm not going to get into
+
+ align:start position:0%
+so before I U I'm not going to get into
+ 
+
+ align:start position:0%
+so before I U I'm not going to get into
+how we Implement um you know how we
+
+ align:start position:0%
+how we Implement um you know how we
+ 
+
+ align:start position:0%
+how we Implement um you know how we
+Implement recoverable action today but
+
+ align:start position:0%
+Implement recoverable action today but
+ 
+
+ align:start position:0%
+Implement recoverable action today but
+but this programming model is important
+
+ align:start position:0%
+but this programming model is important
+ 
+
+ align:start position:0%
+but this programming model is important
+to understand I do want to mention one
+
+ align:start position:0%
+to understand I do want to mention one
+ 
+
+ align:start position:0%
+to understand I do want to mention one
+thing going back to this idea of
+
+ align:start position:0%
+thing going back to this idea of
+ 
+
+ align:start position:0%
+thing going back to this idea of
+isolation that we talked about so if you
+
+ align:start position:0%
+isolation that we talked about so if you
+ 
+
+ align:start position:0%
+isolation that we talked about so if you
+recall isolation is this idea that you
+
+ align:start position:0%
+recall isolation is this idea that you
+ 
+
+ align:start position:0%
+recall isolation is this idea that you
+have two actions or multiple actions
+
+ align:start position:0%
+have two actions or multiple actions
+ 
+
+ align:start position:0%
+have two actions or multiple actions
+whose net effect is as if they ran in
+
+ align:start position:0%
+whose net effect is as if they ran in
+ 
+
+ align:start position:0%
+whose net effect is as if they ran in
+some sequential order some serial order
+
+ align:start position:0%
+some sequential order some serial order
+ 
+
+ align:start position:0%
+some sequential order some serial order
+A1 before A2 or A2 before A1 for all you
+
+ align:start position:0%
+A1 before A2 or A2 before A1 for all you
+ 
+
+ align:start position:0%
+A1 before A2 or A2 before A1 for all you
+know permutations of A1 A2 A3 Etc now
+
+ align:start position:0%
+know permutations of A1 A2 A3 Etc now
+ 
+
+ align:start position:0%
+know permutations of A1 A2 A3 Etc now
+this idea is actually very closely
+
+ align:start position:0%
+this idea is actually very closely
+ 
+
+ align:start position:0%
+this idea is actually very closely
+related but not the same as stuff we've
+
+ align:start position:0%
+related but not the same as stuff we've
+ 
+
+ align:start position:0%
+related but not the same as stuff we've
+seen before you know earlier in the
+
+ align:start position:0%
+seen before you know earlier in the
+ 
+
+ align:start position:0%
+seen before you know earlier in the
+semester we looked at ways in which um
+
+ align:start position:0%
+semester we looked at ways in which um
+ 
+
+ align:start position:0%
+semester we looked at ways in which um
+you you have multiple threads that need
+
+ align:start position:0%
+you you have multiple threads that need
+ 
+
+ align:start position:0%
+you you have multiple threads that need
+to be synchronized with each other and
+
+ align:start position:0%
+to be synchronized with each other and
+ 
+
+ align:start position:0%
+to be synchronized with each other and
+you know we actually did look at
+
+ align:start position:0%
+you know we actually did look at
+ 
+
+ align:start position:0%
+you know we actually did look at
+isolation as a concept then but we spe
+
+ align:start position:0%
+isolation as a concept then but we spe
+ 
+
+ align:start position:0%
+isolation as a concept then but we spe
+specifically focused on things like
+
+ align:start position:0%
+specifically focused on things like
+ 
+
+ align:start position:0%
+specifically focused on things like
+sequence coordination where you want to
+
+ align:start position:0%
+sequence coordination where you want to
+ 
+
+ align:start position:0%
+sequence coordination where you want to
+have one thread run before the other
+
+ align:start position:0%
+have one thread run before the other
+ 
+
+ align:start position:0%
+have one thread run before the other
+thread or one thread um you know run
+
+ align:start position:0%
+thread or one thread um you know run
+ 
+
+ align:start position:0%
+thread or one thread um you know run
+after the other thread for example in a
+
+ align:start position:0%
+after the other thread for example in a
+ 
+
+ align:start position:0%
+after the other thread for example in a
+producer consumer uh
+
+ align:start position:0%
+producer consumer uh
+ 
+
+ align:start position:0%
+producer consumer uh
+relationship the point is that in one
+
+ align:start position:0%
+relationship the point is that in one
+ 
+
+ align:start position:0%
+relationship the point is that in one
+significant respect achieving this idea
+
+ align:start position:0%
+significant respect achieving this idea
+ 
+
+ align:start position:0%
+significant respect achieving this idea
+of isolation for actions is harder than
+
+ align:start position:0%
+of isolation for actions is harder than
+ 
+
+ align:start position:0%
+of isolation for actions is harder than
+achieving sequence
+
+ align:start position:0%
+achieving sequence
+ 
+
+ align:start position:0%
+achieving sequence
+coordination and the reason it's harder
+
+ align:start position:0%
+coordination and the reason it's harder
+ 
+
+ align:start position:0%
+coordination and the reason it's harder
+is that everybody who writes an isolated
+
+ align:start position:0%
+is that everybody who writes an isolated
+ 
+
+ align:start position:0%
+is that everybody who writes an isolated
+action in general doesn't know each any
+
+ align:start position:0%
+action in general doesn't know each any
+ 
+
+ align:start position:0%
+action in general doesn't know each any
+given isolated action doesn't know what
+
+ align:start position:0%
+given isolated action doesn't know what
+ 
+
+ align:start position:0%
+given isolated action doesn't know what
+other actions there are in the system so
+
+ align:start position:0%
+other actions there are in the system so
+ 
+
+ align:start position:0%
+other actions there are in the system so
+you might have you know 25 different
+
+ align:start position:0%
+you might have you know 25 different
+ 
+
+ align:start position:0%
+you might have you know 25 different
+actions all of which are touching the
+
+ align:start position:0%
+actions all of which are touching the
+ 
+
+ align:start position:0%
+actions all of which are touching the
+same data but no single action is aware
+
+ align:start position:0%
+same data but no single action is aware
+ 
+
+ align:start position:0%
+same data but no single action is aware
+of all of these other actions and that's
+
+ align:start position:0%
+of all of these other actions and that's
+ 
+
+ align:start position:0%
+of all of these other actions and that's
+very different from sequence
+
+ align:start position:0%
+very different from sequence
+ 
+
+ align:start position:0%
+very different from sequence
+coordination in sequence coordination
+
+ align:start position:0%
+coordination in sequence coordination
+ 
+
+ align:start position:0%
+coordination in sequence coordination
+you know there's one or two or a small
+
+ align:start position:0%
+you know there's one or two or a small
+ 
+
+ align:start position:0%
+you know there's one or two or a small
+number of threads that are actually
+
+ align:start position:0%
+number of threads that are actually
+ 
+
+ align:start position:0%
+number of threads that are actually
+aware of each other and there's a single
+
+ align:start position:0%
+aware of each other and there's a single
+ 
+
+ align:start position:0%
+aware of each other and there's a single
+programmer that's actually designing
+
+ align:start position:0%
+programmer that's actually designing
+ 
+
+ align:start position:0%
+programmer that's actually designing
+these things to specifically interact
+
+ align:start position:0%
+these things to specifically interact
+ 
+
+ align:start position:0%
+these things to specifically interact
+with each other in some fashion So This
+
+ align:start position:0%
+with each other in some fashion So This
+ 
+
+ align:start position:0%
+with each other in some fashion So This
+Thread runs then this other one runs
+
+ align:start position:0%
+Thread runs then this other one runs
+ 
+
+ align:start position:0%
+Thread runs then this other one runs
+after the data has been produced and so
+
+ align:start position:0%
+after the data has been produced and so
+ 
+
+ align:start position:0%
+after the data has been produced and so
+on so in that sense this kind of
+
+ align:start position:0%
+on so in that sense this kind of
+ 
+
+ align:start position:0%
+on so in that sense this kind of
+isolation is a little harder is is
+
+ align:start position:0%
+isolation is a little harder is is
+ 
+
+ align:start position:0%
+isolation is a little harder is is
+harder to achieve because you want to do
+
+ align:start position:0%
+harder to achieve because you want to do
+ 
+
+ align:start position:0%
+harder to achieve because you want to do
+this you know each individual action
+
+ align:start position:0%
+this you know each individual action
+ 
+
+ align:start position:0%
+this you know each individual action
+doesn't know which other actions there
+
+ align:start position:0%
+doesn't know which other actions there
+ 
+
+ align:start position:0%
+doesn't know which other actions there
+are but yet you want achieve um this
+
+ align:start position:0%
+are but yet you want achieve um this
+ 
+
+ align:start position:0%
+are but yet you want achieve um this
+sequential goal now in one other respect
+
+ align:start position:0%
+sequential goal now in one other respect
+ 
+
+ align:start position:0%
+sequential goal now in one other respect
+actually isolated actions are easier
+
+ align:start position:0%
+actually isolated actions are easier
+ 
+
+ align:start position:0%
+actually isolated actions are easier
+than sequence coordination and the way
+
+ align:start position:0%
+than sequence coordination and the way
+ 
+
+ align:start position:0%
+than sequence coordination and the way
+in which the significant way in which
+
+ align:start position:0%
+in which the significant way in which
+ 
+
+ align:start position:0%
+in which the significant way in which
+they're easier is they're easier for
+
+ align:start position:0%
+they're easier is they're easier for
+ 
+
+ align:start position:0%
+they're easier is they're easier for
+programmers because we're not worried
+
+ align:start position:0%
+programmers because we're not worried
+ 
+
+ align:start position:0%
+programmers because we're not worried
+about coordinating different actions
+
+ align:start position:0%
+about coordinating different actions
+ 
+
+ align:start position:0%
+about coordinating different actions
+with each other the programmers once you
+
+ align:start position:0%
+with each other the programmers once you
+ 
+
+ align:start position:0%
+with each other the programmers once you
+design a system that does underneath
+
+ align:start position:0%
+design a system that does underneath
+ 
+
+ align:start position:0%
+design a system that does underneath
+inside the system that deals with you
+
+ align:start position:0%
+inside the system that deals with you
+ 
+
+ align:start position:0%
+inside the system that deals with you
+know uh ways of achieving isolation the
+
+ align:start position:0%
+know uh ways of achieving isolation the
+ 
+
+ align:start position:0%
+know uh ways of achieving isolation the
+programmers don't have to think about
+
+ align:start position:0%
+programmers don't have to think about
+ 
+
+ align:start position:0%
+programmers don't have to think about
+locks and unlocks and acquiring and
+
+ align:start position:0%
+locks and unlocks and acquiring and
+ 
+
+ align:start position:0%
+locks and unlocks and acquiring and
+releasing locks or other ways in which
+
+ align:start position:0%
+releasing locks or other ways in which
+ 
+
+ align:start position:0%
+releasing locks or other ways in which
+they um um they control access to
+
+ align:start position:0%
+they um um they control access to
+ 
+
+ align:start position:0%
+they um um they control access to
+variables that might be shared so what
+
+ align:start position:0%
+variables that might be shared so what
+ 
+
+ align:start position:0%
+variables that might be shared so what
+this means is that if we can design
+
+ align:start position:0%
+this means is that if we can design
+ 
+
+ align:start position:0%
+this means is that if we can design
+isolated actions right um and we don't
+
+ align:start position:0%
+isolated actions right um and we don't
+ 
+
+ align:start position:0%
+isolated actions right um and we don't
+worry about any serial order you know A1
+
+ align:start position:0%
+worry about any serial order you know A1
+ 
+
+ align:start position:0%
+worry about any serial order you know A1
+can run before A2 or A2 before A1 then
+
+ align:start position:0%
+can run before A2 or A2 before A1 then
+ 
+
+ align:start position:0%
+can run before A2 or A2 before A1 then
+it makes life a lot easier for a
+
+ align:start position:0%
+it makes life a lot easier for a
+ 
+
+ align:start position:0%
+it makes life a lot easier for a
+programmer and our goal is to come up
+
+ align:start position:0%
+programmer and our goal is to come up
+ 
+
+ align:start position:0%
+programmer and our goal is to come up
+with ways of achieving recoverability
+
+ align:start position:0%
+with ways of achieving recoverability
+ 
+
+ align:start position:0%
+with ways of achieving recoverability
+and isolation that require very little
+
+ align:start position:0%
+and isolation that require very little
+ 
+
+ align:start position:0%
+and isolation that require very little
+from a programmer that wants these
+
+ align:start position:0%
+from a programmer that wants these
+ 
+
+ align:start position:0%
+from a programmer that wants these
+properties so in a little it's a little
+
+ align:start position:0%
+properties so in a little it's a little
+ 
+
+ align:start position:0%
+properties so in a little it's a little
+bit like pixie DK you might you might
+
+ align:start position:0%
+bit like pixie DK you might you might
+ 
+
+ align:start position:0%
+bit like pixie DK you might you might
+write a general program and come in and
+
+ align:start position:0%
+write a general program and come in and
+ 
+
+ align:start position:0%
+write a general program and come in and
+just put a begin recoverable action end
+
+ align:start position:0%
+just put a begin recoverable action end
+ 
+
+ align:start position:0%
+just put a begin recoverable action end
+recoverable action and make a few
+
+ align:start position:0%
+recoverable action and make a few
+ 
+
+ align:start position:0%
+recoverable action and make a few
+changes to your program or you might
+
+ align:start position:0%
+changes to your program or you might
+ 
+
+ align:start position:0%
+changes to your program or you might
+just say begin isolated action end
+
+ align:start position:0%
+just say begin isolated action end
+ 
+
+ align:start position:0%
+just say begin isolated action end
+isolated action and magically the system
+
+ align:start position:0%
+isolated action and magically the system
+ 
+
+ align:start position:0%
+isolated action and magically the system
+achieves isolation and recoverability
+
+ align:start position:0%
+achieves isolation and recoverability
+ 
+
+ align:start position:0%
+achieves isolation and recoverability
+for you so it's it's uh it can make life
+
+ align:start position:0%
+for you so it's it's uh it can make life
+ 
+
+ align:start position:0%
+for you so it's it's uh it can make life
+much easier for a programmer but it is a
+
+ align:start position:0%
+much easier for a programmer but it is a
+ 
+
+ align:start position:0%
+much easier for a programmer but it is a
+harder problem for us because no single
+
+ align:start position:0%
+harder problem for us because no single
+ 
+
+ align:start position:0%
+harder problem for us because no single
+action is aware of all of the other
+
+ align:start position:0%
+action is aware of all of the other
+ 
+
+ align:start position:0%
+action is aware of all of the other
+actions in the system so next time we'll
+
+ align:start position:0%
+actions in the system so next time we'll
+ 
+
+ align:start position:0%
+actions in the system so next time we'll
+see how to achieve recoverability and
+
+ align:start position:0%
+see how to achieve recoverability and
+ 
+
+ align:start position:0%
+see how to achieve recoverability and
+then isolation and transactions
+
+ align:start position:0%
+then isolation and transactions
+ 
+
+ align:start position:0%
+then isolation and transactions
+if uh if I gave you a survey might just
+
+ align:start position:0%
+if uh if I gave you a survey might just
+ 
+
+ align:start position:0%
+if uh if I gave you a survey might just
+Cy on your way out as Cy didn't get one
+
+ align:start position:0%
+Cy on your way out as Cy didn't get one
+ 
+
+ align:start position:0%
+Cy on your way out as Cy didn't get one
+and you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like design project 2 is out on the
+
+ align:start position:0%
+like design project 2 is out on the
+ 
+
+ align:start position:0%
+like design project 2 is out on the
+website now and the main thing for you
+
+ align:start position:0%
+website now and the main thing for you
+ 
+
+ align:start position:0%
+website now and the main thing for you
+to make sure you do this week is get
+
+ align:start position:0%
+to make sure you do this week is get
+ 
+
+ align:start position:0%
+to make sure you do this week is get
+project Partners uh and send a list of
+
+ align:start position:0%
+project Partners uh and send a list of
+ 
+
+ align:start position:0%
+project Partners uh and send a list of
+team members to your teaching assistant
+
+ align:start position:0%
+team members to your teaching assistant
+ 
+
+ align:start position:0%
+team members to your teaching assistant
+by Thursday's
+
+ align:start position:0%
+by Thursday's
+ 
+
+ align:start position:0%
+by Thursday's
+recitation thanks
\ No newline at end of file
diff --git a/OwNr82QgkP8.txt b/OwNr82QgkP8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..970bd8fd7e26bae635065738e290eab19884456b
--- /dev/null
+++ b/OwNr82QgkP8.txt
@@ -0,0 +1,275 @@
+align:start position:0%
+ 
+so we saw that a conservative force is
+
+ align:start position:0%
+so we saw that a conservative force is
+ 
+
+ align:start position:0%
+so we saw that a conservative force is
+path independent and we also had
+
+ align:start position:0%
+path independent and we also had
+ 
+
+ align:start position:0%
+path independent and we also had
+examples of forces which are path
+
+ align:start position:0%
+examples of forces which are path
+ 
+
+ align:start position:0%
+examples of forces which are path
+dependent if you have path two and path
+
+ align:start position:0%
+dependent if you have path two and path
+ 
+
+ align:start position:0%
+dependent if you have path two and path
+one and the work
+
+ align:start position:0%
+one and the work
+ 
+
+ align:start position:0%
+one and the work
+done is path
+
+ align:start position:0%
+done is path
+ 
+
+ align:start position:0%
+done is path
+dependent so that means for each path we
+
+ align:start position:0%
+dependent so that means for each path we
+ 
+
+ align:start position:0%
+dependent so that means for each path we
+would get a different answer then we
+
+ align:start position:0%
+would get a different answer then we
+ 
+
+ align:start position:0%
+would get a different answer then we
+call this Force F we denote it by NC is
+
+ align:start position:0%
+call this Force F we denote it by NC is
+ 
+
+ align:start position:0%
+call this Force F we denote it by NC is
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+nonconservative
+
+ align:start position:0%
+nonconservative
+ 
+
+ align:start position:0%
+nonconservative
+and again we see that friction is the
+
+ align:start position:0%
+and again we see that friction is the
+ 
+
+ align:start position:0%
+and again we see that friction is the
+best example of a non-conservative force
+
+ align:start position:0%
+best example of a non-conservative force
+ 
+
+ align:start position:0%
+best example of a non-conservative force
+and if we go again for non-conservative
+
+ align:start position:0%
+and if we go again for non-conservative
+ 
+
+ align:start position:0%
+and if we go again for non-conservative
+work if we integrate from the initial
+
+ align:start position:0%
+work if we integrate from the initial
+ 
+
+ align:start position:0%
+work if we integrate from the initial
+point to the final
+
+ align:start position:0%
+point to the final
+ 
+
+ align:start position:0%
+point to the final
+point for instance on our path
+
+ align:start position:0%
+point for instance on our path
+ 
+
+ align:start position:0%
+point for instance on our path
+one of this non-conservative Force so if
+
+ align:start position:0%
+one of this non-conservative Force so if
+ 
+
+ align:start position:0%
+one of this non-conservative Force so if
+we integrate this way and if we
+
+ align:start position:0%
+we integrate this way and if we
+ 
+
+ align:start position:0%
+we integrate this way and if we
+reverse the
+
+ align:start position:0%
+reverse the
+ 
+
+ align:start position:0%
+reverse the
+interval and so we go back from the
+
+ align:start position:0%
+interval and so we go back from the
+ 
+
+ align:start position:0%
+interval and so we go back from the
+final point to the initial point on path
+
+ align:start position:0%
+final point to the initial point on path
+ 
+
+ align:start position:0%
+final point to the initial point on path
+two that these integrals will not be
+
+ align:start position:0%
+two that these integrals will not be
+ 
+
+ align:start position:0%
+two that these integrals will not be
+equal to the negative of each other
+
+ align:start position:0%
+equal to the negative of each other
+ 
+
+ align:start position:0%
+equal to the negative of each other
+because the quantities are different for
+
+ align:start position:0%
+because the quantities are different for
+ 
+
+ align:start position:0%
+because the quantities are different for
+the different paths in general and so
+
+ align:start position:0%
+the different paths in general and so
+ 
+
+ align:start position:0%
+the different paths in general and so
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+nonzero and in fact um that's the
+
+ align:start position:0%
+nonzero and in fact um that's the
+ 
+
+ align:start position:0%
+nonzero and in fact um that's the
+property of non-conservative forces that
+
+ align:start position:0%
+property of non-conservative forces that
+ 
+
+ align:start position:0%
+property of non-conservative forces that
+the work done around the closed
+
+ align:start position:0%
+the work done around the closed
+ 
+
+ align:start position:0%
+the work done around the closed
+path for a non-conservative force is is
+
+ align:start position:0%
+path for a non-conservative force is is
+ 
+
+ align:start position:0%
+path for a non-conservative force is is
+not equal to zero in general there may
+
+ align:start position:0%
+not equal to zero in general there may
+ 
+
+ align:start position:0%
+not equal to zero in general there may
+be one specific closed path in which
+
+ align:start position:0%
+be one specific closed path in which
+ 
+
+ align:start position:0%
+be one specific closed path in which
+that answer is zero but in general it's
+
+ align:start position:0%
+that answer is zero but in general it's
+ 
+
+ align:start position:0%
+that answer is zero but in general it's
+non zero
\ No newline at end of file
diff --git a/OxcCPTc_bXw.txt b/OxcCPTc_bXw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7bd8829f9ed1e7e31a886c2a1c5e73720b6055af
--- /dev/null
+++ b/OxcCPTc_bXw.txt
@@ -0,0 +1,12070 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right I'm a little slow
+
+ align:start position:0%
+ocw.mit.edu all right I'm a little slow
+ 
+
+ align:start position:0%
+ocw.mit.edu all right I'm a little slow
+getting started today better get going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we're going to talk about today is
+
+ align:start position:0%
+what we're going to talk about today is
+ 
+
+ align:start position:0%
+what we're going to talk about today is
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technique you guys done okay thanks
+
+ align:start position:0%
+technique you guys done okay thanks
+ 
+
+ align:start position:0%
+technique you guys done okay thanks
+we're going to talk about it today is a
+
+ align:start position:0%
+we're going to talk about it today is a
+ 
+
+ align:start position:0%
+we're going to talk about it today is a
+technique known as modal analysis and
+
+ align:start position:0%
+technique known as modal analysis and
+ 
+
+ align:start position:0%
+technique known as modal analysis and
+it's a way of
+
+ align:start position:0%
+it's a way of
+ 
+
+ align:start position:0%
+it's a way of
+analyzing things that vibrate
+
+ align:start position:0%
+analyzing things that vibrate
+ 
+
+ align:start position:0%
+analyzing things that vibrate
+essentially thinking about the one mode
+
+ align:start position:0%
+essentially thinking about the one mode
+ 
+
+ align:start position:0%
+essentially thinking about the one mode
+at a time though you might not make a
+
+ align:start position:0%
+at a time though you might not make a
+ 
+
+ align:start position:0%
+at a time though you might not make a
+lot of use of the actual calculation
+
+ align:start position:0%
+lot of use of the actual calculation
+ 
+
+ align:start position:0%
+lot of use of the actual calculation
+doing the math throughout your careers I
+
+ align:start position:0%
+doing the math throughout your careers I
+ 
+
+ align:start position:0%
+doing the math throughout your careers I
+think if you understand it conceptually
+
+ align:start position:0%
+think if you understand it conceptually
+ 
+
+ align:start position:0%
+think if you understand it conceptually
+it'll help you just have a better
+
+ align:start position:0%
+it'll help you just have a better
+ 
+
+ align:start position:0%
+it'll help you just have a better
+understanding of what vibration is all
+
+ align:start position:0%
+understanding of what vibration is all
+ 
+
+ align:start position:0%
+understanding of what vibration is all
+about just give you some insight to it
+
+ align:start position:0%
+about just give you some insight to it
+ 
+
+ align:start position:0%
+about just give you some insight to it
+that you otherwise wouldn't have so the
+
+ align:start position:0%
+that you otherwise wouldn't have so the
+ 
+
+ align:start position:0%
+that you otherwise wouldn't have so the
+basic concept is that you can model just
+
+ align:start position:0%
+basic concept is that you can model just
+ 
+
+ align:start position:0%
+basic concept is that you can model just
+about any structural vibration as the
+
+ align:start position:0%
+about any structural vibration as the
+ 
+
+ align:start position:0%
+about any structural vibration as the
+summation of the individual
+
+ align:start position:0%
+summation of the individual
+ 
+
+ align:start position:0%
+summation of the individual
+contributions of each what we call
+
+ align:start position:0%
+contributions of each what we call
+ 
+
+ align:start position:0%
+contributions of each what we call
+Natural mode so what we mean by that
+
+ align:start position:0%
+Natural mode so what we mean by that
+ 
+
+ align:start position:0%
+Natural mode so what we mean by that
+let's start by thinking let me say that
+
+ align:start position:0%
+let's start by thinking let me say that
+ 
+
+ align:start position:0%
+let's start by thinking let me say that
+this applies to both continuous systems
+
+ align:start position:0%
+this applies to both continuous systems
+ 
+
+ align:start position:0%
+this applies to both continuous systems
+like vibrating strings or beams or
+
+ align:start position:0%
+like vibrating strings or beams or
+ 
+
+ align:start position:0%
+like vibrating strings or beams or
+buildings as it does to finite degree of
+
+ align:start position:0%
+buildings as it does to finite degree of
+ 
+
+ align:start position:0%
+buildings as it does to finite degree of
+Freedom rigid body systems we've been we
+
+ align:start position:0%
+Freedom rigid body systems we've been we
+ 
+
+ align:start position:0%
+Freedom rigid body systems we've been we
+haven't talked about continuous systems
+
+ align:start position:0%
+haven't talked about continuous systems
+ 
+
+ align:start position:0%
+haven't talked about continuous systems
+I'll do a lecture on
+
+ align:start position:0%
+I'll do a lecture on
+ 
+
+ align:start position:0%
+I'll do a lecture on
+it as the last lecture of the term it's
+
+ align:start position:0%
+it as the last lecture of the term it's
+ 
+
+ align:start position:0%
+it as the last lecture of the term it's
+kind of an enrichment sort of lecture
+
+ align:start position:0%
+kind of an enrichment sort of lecture
+ 
+
+ align:start position:0%
+kind of an enrichment sort of lecture
+but everything I say about finite degree
+
+ align:start position:0%
+but everything I say about finite degree
+ 
+
+ align:start position:0%
+but everything I say about finite degree
+of Freedom systems can be extended to
+
+ align:start position:0%
+of Freedom systems can be extended to
+ 
+
+ align:start position:0%
+of Freedom systems can be extended to
+continuous systems but we'll since we've
+
+ align:start position:0%
+continuous systems but we'll since we've
+ 
+
+ align:start position:0%
+continuous systems but we'll since we've
+been studying rigid bodies and systems
+
+ align:start position:0%
+been studying rigid bodies and systems
+ 
+
+ align:start position:0%
+been studying rigid bodies and systems
+with finite numbers of degrees of
+
+ align:start position:0%
+with finite numbers of degrees of
+ 
+
+ align:start position:0%
+with finite numbers of degrees of
+freedom I'll explain I'll go through
+
+ align:start position:0%
+freedom I'll explain I'll go through
+ 
+
+ align:start position:0%
+freedom I'll explain I'll go through
+this analysis in the context of rigid
+
+ align:start position:0%
+this analysis in the context of rigid
+ 
+
+ align:start position:0%
+this analysis in the context of rigid
+body finite degree of Freedom
+
+ align:start position:0%
+body finite degree of Freedom
+ 
+
+ align:start position:0%
+body finite degree of Freedom
+systems so in general we can write the
+
+ align:start position:0%
+systems so in general we can write the
+ 
+
+ align:start position:0%
+systems so in general we can write the
+equations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion for finite degree Freedom systems
+
+ align:start position:0%
+motion for finite degree Freedom systems
+ 
+
+ align:start position:0%
+motion for finite degree Freedom systems
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+a mass Matrix and to keep the kind of
+
+ align:start position:0%
+a mass Matrix and to keep the kind of
+ 
+
+ align:start position:0%
+a mass Matrix and to keep the kind of
+writing down I'm just going to
+
+ align:start position:0%
+writing down I'm just going to
+ 
+
+ align:start position:0%
+writing down I'm just going to
+underline matrices and a squiggle under
+
+ align:start position:0%
+underline matrices and a squiggle under
+ 
+
+ align:start position:0%
+underline matrices and a squiggle under
+Vector so we have a in general we can
+
+ align:start position:0%
+Vector so we have a in general we can
+ 
+
+ align:start position:0%
+Vector so we have a in general we can
+write the equations of motion it's a
+
+ align:start position:0%
+write the equations of motion it's a
+ 
+
+ align:start position:0%
+write the equations of motion it's a
+mass Matrix times a an acceleration
+
+ align:start position:0%
+mass Matrix times a an acceleration
+ 
+
+ align:start position:0%
+mass Matrix times a an acceleration
+vector plus a damping Matrix times the
+
+ align:start position:0%
+vector plus a damping Matrix times the
+ 
+
+ align:start position:0%
+vector plus a damping Matrix times the
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+Vector stiffness Matrix times a
+
+ align:start position:0%
+Vector stiffness Matrix times a
+ 
+
+ align:start position:0%
+Vector stiffness Matrix times a
+displacement Vector all equal to some
+
+ align:start position:0%
+displacement Vector all equal to some
+ 
+
+ align:start position:0%
+displacement Vector all equal to some
+external Vector of x itations now I'm
+
+ align:start position:0%
+external Vector of x itations now I'm
+ 
+
+ align:start position:0%
+external Vector of x itations now I'm
+writing these as if these are
+
+ align:start position:0%
+writing these as if these are
+ 
+
+ align:start position:0%
+writing these as if these are
+translations but you know like from
+
+ align:start position:0%
+translations but you know like from
+ 
+
+ align:start position:0%
+translations but you know like from
+doing the cart the pendulum on the cart
+
+ align:start position:0%
+doing the cart the pendulum on the cart
+ 
+
+ align:start position:0%
+doing the cart the pendulum on the cart
+problem that the equations of motion
+
+ align:start position:0%
+problem that the equations of motion
+ 
+
+ align:start position:0%
+problem that the equations of motion
+might involve rotations and
+
+ align:start position:0%
+might involve rotations and
+ 
+
+ align:start position:0%
+might involve rotations and
+displacements and we let them you know
+
+ align:start position:0%
+displacements and we let them you know
+ 
+
+ align:start position:0%
+displacements and we let them you know
+they mix together here however they fall
+
+ align:start position:0%
+they mix together here however they fall
+ 
+
+ align:start position:0%
+they mix together here however they fall
+out but just to write them symbolically
+
+ align:start position:0%
+out but just to write them symbolically
+ 
+
+ align:start position:0%
+out but just to write them symbolically
+I'm just going to call them all refer to
+
+ align:start position:0%
+I'm just going to call them all refer to
+ 
+
+ align:start position:0%
+I'm just going to call them all refer to
+all of those coordinates with an X
+
+ align:start position:0%
+all of those coordinates with an X
+ 
+
+ align:start position:0%
+all of those coordinates with an X
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+okay now the basic
+
+ align:start position:0%
+okay now the basic
+ 
+
+ align:start position:0%
+okay now the basic
+premise of modal analysis is a thing
+
+ align:start position:0%
+premise of modal analysis is a thing
+ 
+
+ align:start position:0%
+premise of modal analysis is a thing
+called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modal expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem it's basically the assertion
+
+ align:start position:0%
+theorem it's basically the assertion
+ 
+
+ align:start position:0%
+theorem it's basically the assertion
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+represent any motion set of vectors I'll
+
+ align:start position:0%
+represent any motion set of vectors I'll
+ 
+
+ align:start position:0%
+represent any motion set of vectors I'll
+write them kind of as a vector here for
+
+ align:start position:0%
+write them kind of as a vector here for
+ 
+
+ align:start position:0%
+write them kind of as a vector here for
+a moment
+
+ align:start position:0%
+a moment
+ 
+
+ align:start position:0%
+a moment
+any set of of motions X as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superposition
+
+ align:start position:0%
+superposition
+ 
+
+ align:start position:0%
+superposition
+of each contributing mode now each mode
+
+ align:start position:0%
+of each contributing mode now each mode
+ 
+
+ align:start position:0%
+of each contributing mode now each mode
+has a mode shape to it which I'm going
+
+ align:start position:0%
+has a mode shape to it which I'm going
+ 
+
+ align:start position:0%
+has a mode shape to it which I'm going
+to call
+
+ align:start position:0%
+to call
+ 
+
+ align:start position:0%
+to call
+U and up here I put a superscript For
+
+ align:start position:0%
+U and up here I put a superscript For
+ 
+
+ align:start position:0%
+U and up here I put a superscript For
+What mode it is the first mode times its
+
+ align:start position:0%
+What mode it is the first mode times its
+ 
+
+ align:start position:0%
+What mode it is the first mode times its
+time dependent behavior and this is
+
+ align:start position:0%
+time dependent behavior and this is
+ 
+
+ align:start position:0%
+time dependent behavior and this is
+called what they call in textbooks these
+
+ align:start position:0%
+called what they call in textbooks these
+ 
+
+ align:start position:0%
+called what they call in textbooks these
+are called the natural
+
+ align:start position:0%
+are called the natural
+ 
+
+ align:start position:0%
+are called the natural
+coordinates and we'll see what those are
+
+ align:start position:0%
+coordinates and we'll see what those are
+ 
+
+ align:start position:0%
+coordinates and we'll see what those are
+in a second so mode shape one this is
+
+ align:start position:0%
+in a second so mode shape one this is
+ 
+
+ align:start position:0%
+in a second so mode shape one this is
+the time dependent and amplitude part
+
+ align:start position:0%
+the time dependent and amplitude part
+ 
+
+ align:start position:0%
+the time dependent and amplitude part
+that says how much the contribution of
+
+ align:start position:0%
+that says how much the contribution of
+ 
+
+ align:start position:0%
+that says how much the contribution of
+mode one is to this motion and what its
+
+ align:start position:0%
+mode one is to this motion and what its
+ 
+
+ align:start position:0%
+mode one is to this motion and what its
+time dependence is this is and then
+
+ align:start position:0%
+time dependence is this is and then
+ 
+
+ align:start position:0%
+time dependence is this is and then
+you'd have mode 2's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contribution Q2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this goes out to the nth
+
+ align:start position:0%
+and this goes out to the nth
+ 
+
+ align:start position:0%
+and this goes out to the nth
+modes
+
+ align:start position:0%
+modes
+ 
+
+ align:start position:0%
+modes
+contribution
+
+ align:start position:0%
+contribution
+ 
+
+ align:start position:0%
+contribution
+qn of T and that's the proposition that
+
+ align:start position:0%
+qn of T and that's the proposition that
+ 
+
+ align:start position:0%
+qn of T and that's the proposition that
+you can represent the total response of
+
+ align:start position:0%
+you can represent the total response of
+ 
+
+ align:start position:0%
+you can represent the total response of
+the system as a superposition of the
+
+ align:start position:0%
+the system as a superposition of the
+ 
+
+ align:start position:0%
+the system as a superposition of the
+response of each of the natural modes of
+
+ align:start position:0%
+response of each of the natural modes of
+ 
+
+ align:start position:0%
+response of each of the natural modes of
+the system and if it's an in degree of
+
+ align:start position:0%
+the system and if it's an in degree of
+ 
+
+ align:start position:0%
+the system and if it's an in degree of
+Freedom system there'll be in natural
+
+ align:start position:0%
+Freedom system there'll be in natural
+ 
+
+ align:start position:0%
+Freedom system there'll be in natural
+mode so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now something I didn't say here is this
+
+ align:start position:0%
+now something I didn't say here is this
+ 
+
+ align:start position:0%
+now something I didn't say here is this
+is all this all assumes that the system
+
+ align:start position:0%
+is all this all assumes that the system
+ 
+
+ align:start position:0%
+is all this all assumes that the system
+vibrates so this is this is all in the
+
+ align:start position:0%
+vibrates so this is this is all in the
+ 
+
+ align:start position:0%
+vibrates so this is this is all in the
+discussion of things that exhibit
+
+ align:start position:0%
+discussion of things that exhibit
+ 
+
+ align:start position:0%
+discussion of things that exhibit
+vibratory motion so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all should see here of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is kind of a long and
+
+ align:start position:0%
+okay so this is kind of a long and
+ 
+
+ align:start position:0%
+okay so this is kind of a long and
+cumbersome way of writing this out so if
+
+ align:start position:0%
+cumbersome way of writing this out so if
+ 
+
+ align:start position:0%
+cumbersome way of writing this out so if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+notice each one of these is the mode
+
+ align:start position:0%
+notice each one of these is the mode
+ 
+
+ align:start position:0%
+notice each one of these is the mode
+shaped vector and if I put them together
+
+ align:start position:0%
+shaped vector and if I put them together
+ 
+
+ align:start position:0%
+shaped vector and if I put them together
+in a matrix it would look just side by
+
+ align:start position:0%
+in a matrix it would look just side by
+ 
+
+ align:start position:0%
+in a matrix it would look just side by
+side here's a
+
+ align:start position:0%
+side here's a
+ 
+
+ align:start position:0%
+side here's a
+U1 over two u
+
+ align:start position:0%
+U1 over two u
+ 
+
+ align:start position:0%
+U1 over two u
+n and multiply it by this Vector q1 of
+
+ align:start position:0%
+n and multiply it by this Vector q1 of
+ 
+
+ align:start position:0%
+n and multiply it by this Vector q1 of
+T down to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qn that's the same statement but said in
+
+ align:start position:0%
+qn that's the same statement but said in
+ 
+
+ align:start position:0%
+qn that's the same statement but said in
+a much more compact
+
+ align:start position:0%
+a much more compact
+ 
+
+ align:start position:0%
+a much more compact
+way so the statement this modal
+
+ align:start position:0%
+way so the statement this modal
+ 
+
+ align:start position:0%
+way so the statement this modal
+expansion theorem basically says the
+
+ align:start position:0%
+expansion theorem basically says the
+ 
+
+ align:start position:0%
+expansion theorem basically says the
+vector of
+
+ align:start position:0%
+vector of
+ 
+
+ align:start position:0%
+vector of
+these are
+
+ align:start position:0%
+these are
+ 
+
+ align:start position:0%
+these are
+your generalized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates which we've been using all
+
+ align:start position:0%
+coordinates which we've been using all
+ 
+
+ align:start position:0%
+coordinates which we've been using all
+term long these are the generalized
+
+ align:start position:0%
+term long these are the generalized
+ 
+
+ align:start position:0%
+term long these are the generalized
+coordinates that you choose to derive
+
+ align:start position:0%
+coordinates that you choose to derive
+ 
+
+ align:start position:0%
+coordinates that you choose to derive
+the equations of motion around the
+
+ align:start position:0%
+the equations of motion around the
+ 
+
+ align:start position:0%
+the equations of motion around the
+vector of generalized coordinates can be
+
+ align:start position:0%
+vector of generalized coordinates can be
+ 
+
+ align:start position:0%
+vector of generalized coordinates can be
+written as u
+
+ align:start position:0%
+written as u
+ 
+
+ align:start position:0%
+written as u
+q and these are often called the
+
+ align:start position:0%
+q and these are often called the
+ 
+
+ align:start position:0%
+q and these are often called the
+modal coordin
+
+ align:start position:0%
+modal coordin
+ 
+
+ align:start position:0%
+modal coordin
+coordinates or sometimes called the
+
+ align:start position:0%
+coordinates or sometimes called the
+ 
+
+ align:start position:0%
+coordinates or sometimes called the
+natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we can say that
+
+ align:start position:0%
+okay so if we can say that
+ 
+
+ align:start position:0%
+okay so if we can say that
+X is u q then x dot you take the Der
+
+ align:start position:0%
+X is u q then x dot you take the Der
+ 
+
+ align:start position:0%
+X is u q then x dot you take the Der
+ative of each one of those expressions
+
+ align:start position:0%
+ative of each one of those expressions
+ 
+
+ align:start position:0%
+ative of each one of those expressions
+you'll find that going to be u q
+
+ align:start position:0%
+you'll find that going to be u q
+ 
+
+ align:start position:0%
+you'll find that going to be u q
+Dot and X double dot = u q double dot
+
+ align:start position:0%
+Dot and X double dot = u q double dot
+ 
+
+ align:start position:0%
+Dot and X double dot = u q double dot
+because these are just constants the
+
+ align:start position:0%
+because these are just constants the
+ 
+
+ align:start position:0%
+because these are just constants the
+mode shape vectors are just a fixed set
+
+ align:start position:0%
+mode shape vectors are just a fixed set
+ 
+
+ align:start position:0%
+mode shape vectors are just a fixed set
+of numbers that represent the mode
+
+ align:start position:0%
+of numbers that represent the mode
+ 
+
+ align:start position:0%
+of numbers that represent the mode
+shapes of the system now just to uh I
+
+ align:start position:0%
+shapes of the system now just to uh I
+ 
+
+ align:start position:0%
+shapes of the system now just to uh I
+think maybe this a good time to do this
+
+ align:start position:0%
+think maybe this a good time to do this
+ 
+
+ align:start position:0%
+think maybe this a good time to do this
+you grabb one end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a and it's hard to see black
+
+ align:start position:0%
+so this is a and it's hard to see black
+ 
+
+ align:start position:0%
+so this is a and it's hard to see black
+against black my apologies for that but
+
+ align:start position:0%
+against black my apologies for that but
+ 
+
+ align:start position:0%
+against black my apologies for that but
+so this is a guitar
+
+ align:start position:0%
+so this is a guitar
+ 
+
+ align:start position:0%
+so this is a guitar
+string or um you know any stringed
+
+ align:start position:0%
+string or um you know any stringed
+ 
+
+ align:start position:0%
+string or um you know any stringed
+instrument or in fact any long slender
+
+ align:start position:0%
+instrument or in fact any long slender
+ 
+
+ align:start position:0%
+instrument or in fact any long slender
+thing under tension will vibrate and it
+
+ align:start position:0%
+thing under tension will vibrate and it
+ 
+
+ align:start position:0%
+thing under tension will vibrate and it
+has if I do this carefully that's called
+
+ align:start position:0%
+has if I do this carefully that's called
+ 
+
+ align:start position:0%
+has if I do this carefully that's called
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+first mode of
+
+ align:start position:0%
+first mode of
+ 
+
+ align:start position:0%
+first mode of
+vibration and that's when you pluck your
+
+ align:start position:0%
+vibration and that's when you pluck your
+ 
+
+ align:start position:0%
+vibration and that's when you pluck your
+guitar string or violin in the middle
+
+ align:start position:0%
+guitar string or violin in the middle
+ 
+
+ align:start position:0%
+guitar string or violin in the middle
+you mostly hear that
+
+ align:start position:0%
+you mostly hear that
+ 
+
+ align:start position:0%
+you mostly hear that
+and but at twice the frequency if I can
+
+ align:start position:0%
+and but at twice the frequency if I can
+ 
+
+ align:start position:0%
+and but at twice the frequency if I can
+get it going
+
+ align:start position:0%
+get it going
+ 
+
+ align:start position:0%
+get it going
+here there's the second mode of
+
+ align:start position:0%
+here there's the second mode of
+ 
+
+ align:start position:0%
+here there's the second mode of
+vibration and for a taut string it's it
+
+ align:start position:0%
+vibration and for a taut string it's it
+ 
+
+ align:start position:0%
+vibration and for a taut string it's it
+happens to be at twice the frequency of
+
+ align:start position:0%
+happens to be at twice the frequency of
+ 
+
+ align:start position:0%
+happens to be at twice the frequency of
+the first and if I my hand is well
+
+ align:start position:0%
+the first and if I my hand is well
+ 
+
+ align:start position:0%
+the first and if I my hand is well
+calibrated today may be easier it's a
+
+ align:start position:0%
+calibrated today may be easier it's a
+ 
+
+ align:start position:0%
+calibrated today may be easier it's a
+little longer I get this going
+
+ align:start position:0%
+little longer I get this going
+ 
+
+ align:start position:0%
+little longer I get this going
+right ah there's a third mode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so each that's what
+
+ align:start position:0%
+okay so each that's what
+ 
+
+ align:start position:0%
+okay so each that's what
+we that's what we're calling oh what I
+
+ align:start position:0%
+we that's what we're calling oh what I
+ 
+
+ align:start position:0%
+we that's what we're calling oh what I
+meant to say when I was doing this is
+
+ align:start position:0%
+meant to say when I was doing this is
+ 
+
+ align:start position:0%
+meant to say when I was doing this is
+these shapes for the vibrating string
+
+ align:start position:0%
+these shapes for the vibrating string
+ 
+
+ align:start position:0%
+these shapes for the vibrating string
+that second mode shape happens to be one
+
+ align:start position:0%
+that second mode shape happens to be one
+ 
+
+ align:start position:0%
+that second mode shape happens to be one
+full sine wave and the mode shape has
+
+ align:start position:0%
+full sine wave and the mode shape has
+ 
+
+ align:start position:0%
+full sine wave and the mode shape has
+the form sin n pi x over L where L's the
+
+ align:start position:0%
+the form sin n pi x over L where L's the
+ 
+
+ align:start position:0%
+the form sin n pi x over L where L's the
+length of the string 's the mode number
+
+ align:start position:0%
+length of the string 's the mode number
+ 
+
+ align:start position:0%
+length of the string 's the mode number
+so first mode second mode is this when n
+
+ align:start position:0%
+so first mode second mode is this when n
+ 
+
+ align:start position:0%
+so first mode second mode is this when n
+is two first mode n is one nth mode or
+
+ align:start position:0%
+is two first mode n is one nth mode or
+ 
+
+ align:start position:0%
+is two first mode n is one nth mode or
+something High you know you get higher
+
+ align:start position:0%
+something High you know you get higher
+ 
+
+ align:start position:0%
+something High you know you get higher
+modes like that so these are the mode
+
+ align:start position:0%
+modes like that so these are the mode
+ 
+
+ align:start position:0%
+modes like that so these are the mode
+shapes for a vibrating
+
+ align:start position:0%
+shapes for a vibrating
+ 
+
+ align:start position:0%
+shapes for a vibrating
+string so that's and this that's good
+
+ align:start position:0%
+string so that's and this that's good
+ 
+
+ align:start position:0%
+string so that's and this that's good
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+now this this uh two degree of Freedom
+
+ align:start position:0%
+now this this uh two degree of Freedom
+ 
+
+ align:start position:0%
+now this this uh two degree of Freedom
+system with the two lump masses and it's
+
+ align:start position:0%
+system with the two lump masses and it's
+ 
+
+ align:start position:0%
+system with the two lump masses and it's
+going to show up there y okay this is
+
+ align:start position:0%
+going to show up there y okay this is
+ 
+
+ align:start position:0%
+going to show up there y okay this is
+basically two Lum masses and we idealize
+
+ align:start position:0%
+basically two Lum masses and we idealize
+ 
+
+ align:start position:0%
+basically two Lum masses and we idealize
+the Springs as being massless but it's a
+
+ align:start position:0%
+the Springs as being massless but it's a
+ 
+
+ align:start position:0%
+the Springs as being massless but it's a
+pretty good approximation this has two
+
+ align:start position:0%
+pretty good approximation this has two
+ 
+
+ align:start position:0%
+pretty good approximation this has two
+modes of vibration and Professor goser
+
+ align:start position:0%
+modes of vibration and Professor goser
+ 
+
+ align:start position:0%
+modes of vibration and Professor goser
+made these neat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little things that can make it so and I
+
+ align:start position:0%
+little things that can make it so and I
+ 
+
+ align:start position:0%
+little things that can make it so and I
+I'm going to come back to this but
+
+ align:start position:0%
+I'm going to come back to this but
+ 
+
+ align:start position:0%
+I'm going to come back to this but
+there's mode
+
+ align:start position:0%
+there's mode
+ 
+
+ align:start position:0%
+there's mode
+one and the mode shape is as this goes
+
+ align:start position:0%
+one and the mode shape is as this goes
+ 
+
+ align:start position:0%
+one and the mode shape is as this goes
+down one unit that goes down about two
+
+ align:start position:0%
+down one unit that goes down about two
+ 
+
+ align:start position:0%
+down one unit that goes down about two
+two times as much I give you the exact
+
+ align:start position:0%
+two times as much I give you the exact
+ 
+
+ align:start position:0%
+two times as much I give you the exact
+numberers in a minute and the other mode
+
+ align:start position:0%
+numberers in a minute and the other mode
+ 
+
+ align:start position:0%
+numberers in a minute and the other mode
+shape of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system I do the right in if I give it
+
+ align:start position:0%
+system I do the right in if I give it
+ 
+
+ align:start position:0%
+system I do the right in if I give it
+the right initial we're going to talk
+
+ align:start position:0%
+the right initial we're going to talk
+ 
+
+ align:start position:0%
+the right initial we're going to talk
+about this today and why this happens
+
+ align:start position:0%
+about this today and why this happens
+ 
+
+ align:start position:0%
+about this today and why this happens
+but if I give it the right initial
+
+ align:start position:0%
+but if I give it the right initial
+ 
+
+ align:start position:0%
+but if I give it the right initial
+conditions I can make it vibrate only in
+
+ align:start position:0%
+conditions I can make it vibrate only in
+ 
+
+ align:start position:0%
+conditions I can make it vibrate only in
+the second mode shape and so it's now
+
+ align:start position:0%
+the second mode shape and so it's now
+ 
+
+ align:start position:0%
+the second mode shape and so it's now
+deflected with the right condition so
+
+ align:start position:0%
+deflected with the right condition so
+ 
+
+ align:start position:0%
+deflected with the right condition so
+that it'll respond only in second
+
+ align:start position:0%
+that it'll respond only in second
+ 
+
+ align:start position:0%
+that it'll respond only in second
+mode this Mass goes up and down a lot
+
+ align:start position:0%
+mode this Mass goes up and down a lot
+ 
+
+ align:start position:0%
+mode this Mass goes up and down a lot
+that mass goes up and down a little
+
+ align:start position:0%
+that mass goes up and down a little
+ 
+
+ align:start position:0%
+that mass goes up and down a little
+opposite to it actually the frequency is
+
+ align:start position:0%
+opposite to it actually the frequency is
+ 
+
+ align:start position:0%
+opposite to it actually the frequency is
+different from the first but if this is
+
+ align:start position:0%
+different from the first but if this is
+ 
+
+ align:start position:0%
+different from the first but if this is
+moving one unit then this down here is
+
+ align:start position:0%
+moving one unit then this down here is
+ 
+
+ align:start position:0%
+moving one unit then this down here is
+moving minus. 3 or something like that
+
+ align:start position:0%
+moving minus. 3 or something like that
+ 
+
+ align:start position:0%
+moving minus. 3 or something like that
+and that ratio is constant and that's
+
+ align:start position:0%
+and that ratio is constant and that's
+ 
+
+ align:start position:0%
+and that ratio is constant and that's
+called the mode shape so if you just
+
+ align:start position:0%
+called the mode shape so if you just
+ 
+
+ align:start position:0%
+called the mode shape so if you just
+pick one of them and say Let its motion
+
+ align:start position:0%
+pick one of them and say Let its motion
+ 
+
+ align:start position:0%
+pick one of them and say Let its motion
+be one then all of the other masses in
+
+ align:start position:0%
+be one then all of the other masses in
+ 
+
+ align:start position:0%
+be one then all of the other masses in
+the system will move in a particular
+
+ align:start position:0%
+the system will move in a particular
+ 
+
+ align:start position:0%
+the system will move in a particular
+ratio to the motion of that one that you
+
+ align:start position:0%
+ratio to the motion of that one that you
+ 
+
+ align:start position:0%
+ratio to the motion of that one that you
+arbitrarily set to one so this will mean
+
+ align:start position:0%
+arbitrarily set to one so this will mean
+ 
+
+ align:start position:0%
+arbitrarily set to one so this will mean
+by mode shapes and their natural
+
+ align:start position:0%
+by mode shapes and their natural
+ 
+
+ align:start position:0%
+by mode shapes and their natural
+frequencies there's the natural
+
+ align:start position:0%
+frequencies there's the natural
+ 
+
+ align:start position:0%
+frequencies there's the natural
+frequency associated with that first
+
+ align:start position:0%
+frequency associated with that first
+ 
+
+ align:start position:0%
+frequency associated with that first
+mode and we can solve these things
+
+ align:start position:0%
+mode and we can solve these things
+ 
+
+ align:start position:0%
+mode and we can solve these things
+mathematically and we've been doing that
+
+ align:start position:0%
+mathematically and we've been doing that
+ 
+
+ align:start position:0%
+mathematically and we've been doing that
+a little uh a little bit in the last
+
+ align:start position:0%
+a little uh a little bit in the last
+ 
+
+ align:start position:0%
+a little uh a little bit in the last
+couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lectures all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is the relationship
+
+ align:start position:0%
+right so this is the relationship
+ 
+
+ align:start position:0%
+right so this is the relationship
+between these thing the generalized
+
+ align:start position:0%
+between these thing the generalized
+ 
+
+ align:start position:0%
+between these thing the generalized
+coordinates and the modal
+
+ align:start position:0%
+coordinates and the modal
+ 
+
+ align:start position:0%
+coordinates and the modal
+coordinates and we now need to um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see how we are going to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these so in general we have our
+
+ align:start position:0%
+these so in general we have our
+ 
+
+ align:start position:0%
+these so in general we have our
+equations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion and I'm going to substitute
+
+ align:start position:0%
+motion and I'm going to substitute
+ 
+
+ align:start position:0%
+motion and I'm going to substitute
+for XX Dot and xou Dot
+
+ align:start position:0%
+for XX Dot and xou Dot
+ 
+
+ align:start position:0%
+for XX Dot and xou Dot
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+pre
+
+ align:start position:0%
+pre
+ 
+
+ align:start position:0%
+pre
+multiply by U transpose remember the
+
+ align:start position:0%
+multiply by U transpose remember the
+ 
+
+ align:start position:0%
+multiply by U transpose remember the
+transpose of a matrix you just take the
+
+ align:start position:0%
+transpose of a matrix you just take the
+ 
+
+ align:start position:0%
+transpose of a matrix you just take the
+column First Column make it the first
+
+ align:start position:0%
+column First Column make it the first
+ 
+
+ align:start position:0%
+column First Column make it the first
+row second column make it the second row
+
+ align:start position:0%
+row second column make it the second row
+ 
+
+ align:start position:0%
+row second column make it the second row
+so if I plug in these up here I get
+
+ align:start position:0%
+so if I plug in these up here I get
+ 
+
+ align:start position:0%
+so if I plug in these up here I get
+m u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+q going leave some space here because
+
+ align:start position:0%
+q going leave some space here because
+ 
+
+ align:start position:0%
+q going leave some space here because
+I'm going to pre-multiply in a second
+
+ align:start position:0%
+I'm going to pre-multiply in a second
+ 
+
+ align:start position:0%
+I'm going to pre-multiply in a second
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+u q dot plus k a
+
+ align:start position:0%
+u q dot plus k a
+ 
+
+ align:start position:0%
+u q dot plus k a
+u q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals the external exciting forces now
+
+ align:start position:0%
+equals the external exciting forces now
+ 
+
+ align:start position:0%
+equals the external exciting forces now
+I'm going to pre-multiply by U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+okay now a remarkable thing happens
+
+ align:start position:0%
+okay now a remarkable thing happens
+ 
+
+ align:start position:0%
+okay now a remarkable thing happens
+it happens that if you take when you
+
+ align:start position:0%
+it happens that if you take when you
+ 
+
+ align:start position:0%
+it happens that if you take when you
+when you do this calculation when you
+
+ align:start position:0%
+when you do this calculation when you
+ 
+
+ align:start position:0%
+when you do this calculation when you
+multiply this Matrix times that one row
+
+ align:start position:0%
+multiply this Matrix times that one row
+ 
+
+ align:start position:0%
+multiply this Matrix times that one row
+at a time so this has this has vectors
+
+ align:start position:0%
+at a time so this has this has vectors
+ 
+
+ align:start position:0%
+at a time so this has this has vectors
+in it one through n I'm going to pick
+
+ align:start position:0%
+in it one through n I'm going to pick
+ 
+
+ align:start position:0%
+in it one through n I'm going to pick
+Vector R the rth one if I take that arth
+
+ align:start position:0%
+Vector R the rth one if I take that arth
+ 
+
+ align:start position:0%
+Vector R the rth one if I take that arth
+vector and multiply it one at a time by
+
+ align:start position:0%
+vector and multiply it one at a time by
+ 
+
+ align:start position:0%
+vector and multiply it one at a time by
+row by row by
+
+ align:start position:0%
+row by row by
+ 
+
+ align:start position:0%
+row by row by
+row then I get
+
+ align:start position:0%
+row then I get
+ 
+
+ align:start position:0%
+row then I get
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+new vector that results which I'm going
+
+ align:start position:0%
+new vector that results which I'm going
+ 
+
+ align:start position:0%
+new vector that results which I'm going
+to multiply by this so if I'm going to
+
+ align:start position:0%
+to multiply by this so if I'm going to
+ 
+
+ align:start position:0%
+to multiply by this so if I'm going to
+but I'm I'm going to pick out one of the
+
+ align:start position:0%
+but I'm I'm going to pick out one of the
+ 
+
+ align:start position:0%
+but I'm I'm going to pick out one of the
+vectors multiplied through times one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the uh rows here which is all when you
+
+ align:start position:0%
+the uh rows here which is all when you
+ 
+
+ align:start position:0%
+the uh rows here which is all when you
+transpose them the rows are now the
+
+ align:start position:0%
+transpose them the rows are now the
+ 
+
+ align:start position:0%
+transpose them the rows are now the
+vectors so I'm going to pick if I do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation lost my right piece of paper
+
+ align:start position:0%
+calculation lost my right piece of paper
+ 
+
+ align:start position:0%
+calculation lost my right piece of paper
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I just pull this pull out one of
+
+ align:start position:0%
+so I just pull this pull out one of
+ 
+
+ align:start position:0%
+so I just pull this pull out one of
+these com one of the calculations that
+
+ align:start position:0%
+these com one of the calculations that
+ 
+
+ align:start position:0%
+these com one of the calculations that
+you end up doing is you do this whole
+
+ align:start position:0%
+you end up doing is you do this whole
+ 
+
+ align:start position:0%
+you end up doing is you do this whole
+triple Matrix M
+
+ align:start position:0%
+triple Matrix M
+ 
+
+ align:start position:0%
+triple Matrix M
+multiplication um there will you need to
+
+ align:start position:0%
+multiplication um there will you need to
+ 
+
+ align:start position:0%
+multiplication um there will you need to
+know the following fact
+
+ align:start position:0%
+know the following fact
+ 
+
+ align:start position:0%
+know the following fact
+so for mode the mode s transpose that's
+
+ align:start position:0%
+so for mode the mode s transpose that's
+ 
+
+ align:start position:0%
+so for mode the mode s transpose that's
+one of the rows out of
+
+ align:start position:0%
+one of the rows out of
+ 
+
+ align:start position:0%
+one of the rows out of
+here time
+
+ align:start position:0%
+here time
+ 
+
+ align:start position:0%
+here time
+M times one of the columns the arth
+
+ align:start position:0%
+M times one of the columns the arth
+ 
+
+ align:start position:0%
+M times one of the columns the arth
+one from
+
+ align:start position:0%
+one from
+ 
+
+ align:start position:0%
+one from
+here and I do this calculation this is
+
+ align:start position:0%
+here and I do this calculation this is
+ 
+
+ align:start position:0%
+here and I do this calculation this is
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+for R not equal to
+
+ align:start position:0%
+for R not equal to
+ 
+
+ align:start position:0%
+for R not equal to
+S what that statement says is the only
+
+ align:start position:0%
+S what that statement says is the only
+ 
+
+ align:start position:0%
+S what that statement says is the only
+nonzero result from this is the is when
+
+ align:start position:0%
+nonzero result from this is the is when
+ 
+
+ align:start position:0%
+nonzero result from this is the is when
+you multiply when you take the arth
+
+ align:start position:0%
+you multiply when you take the arth
+ 
+
+ align:start position:0%
+you multiply when you take the arth
+column from here and you use the AR Row
+
+ align:start position:0%
+column from here and you use the AR Row
+ 
+
+ align:start position:0%
+column from here and you use the AR Row
+from here all the other combinations of
+
+ align:start position:0%
+from here all the other combinations of
+ 
+
+ align:start position:0%
+from here all the other combinations of
+this thing go to zero and the net result
+
+ align:start position:0%
+this thing go to zero and the net result
+ 
+
+ align:start position:0%
+this thing go to zero and the net result
+of that is that this implies that U
+
+ align:start position:0%
+of that is that this implies that U
+ 
+
+ align:start position:0%
+of that is that this implies that U
+transpose mu
+
+ align:start position:0%
+transpose mu
+ 
+
+ align:start position:0%
+transpose mu
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+always equals to a
+
+ align:start position:0%
+always equals to a
+ 
+
+ align:start position:0%
+always equals to a
+diagonal Vector which I would call this
+
+ align:start position:0%
+diagonal Vector which I would call this
+ 
+
+ align:start position:0%
+diagonal Vector which I would call this
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that sometimes a mass Matrix is diagonal
+
+ align:start position:0%
+that sometimes a mass Matrix is diagonal
+ 
+
+ align:start position:0%
+that sometimes a mass Matrix is diagonal
+to start with but even if it isn't you
+
+ align:start position:0%
+to start with but even if it isn't you
+ 
+
+ align:start position:0%
+to start with but even if it isn't you
+do this calculation it will produce a
+
+ align:start position:0%
+do this calculation it will produce a
+ 
+
+ align:start position:0%
+do this calculation it will produce a
+diagonal matrix and that's because this
+
+ align:start position:0%
+diagonal matrix and that's because this
+ 
+
+ align:start position:0%
+diagonal matrix and that's because this
+is this these multiplications are always
+
+ align:start position:0%
+is this these multiplications are always
+ 
+
+ align:start position:0%
+is this these multiplications are always
+zero unless R is the same as
+
+ align:start position:0%
+zero unless R is the same as
+ 
+
+ align:start position:0%
+zero unless R is the same as
+s and the same is true for U transpose k
+
+ align:start position:0%
+s and the same is true for U transpose k
+ 
+
+ align:start position:0%
+s and the same is true for U transpose k
+u will give you
+
+ align:start position:0%
+u will give you
+ 
+
+ align:start position:0%
+u will give you
+a a k Matrix
+
+ align:start position:0%
+a a k Matrix
+ 
+
+ align:start position:0%
+a a k Matrix
+that is diagonal and you know normal for
+
+ align:start position:0%
+that is diagonal and you know normal for
+ 
+
+ align:start position:0%
+that is diagonal and you know normal for
+when the stiffest Matrix we've come up
+
+ align:start position:0%
+when the stiffest Matrix we've come up
+ 
+
+ align:start position:0%
+when the stiffest Matrix we've come up
+with they've generally not been they've
+
+ align:start position:0%
+with they've generally not been they've
+ 
+
+ align:start position:0%
+with they've generally not been they've
+generally been full matrices often times
+
+ align:start position:0%
+generally been full matrices often times
+ 
+
+ align:start position:0%
+generally been full matrices often times
+but you do u k u KU U you will get a
+
+ align:start position:0%
+but you do u k u KU U you will get a
+ 
+
+ align:start position:0%
+but you do u k u KU U you will get a
+diagonal stiffness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and the problem there the little
+
+ align:start position:0%
+Matrix and the problem there the little
+ 
+
+ align:start position:0%
+Matrix and the problem there the little
+problem comes because youu transpose c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u well sometimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one is diagonal only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideal conditions of damping so we're
+
+ align:start position:0%
+ideal conditions of damping so we're
+ 
+
+ align:start position:0%
+ideal conditions of damping so we're
+going to have that's something you just
+
+ align:start position:0%
+going to have that's something you just
+ 
+
+ align:start position:0%
+going to have that's something you just
+have to address
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so only for ideal conditions and that's
+
+ align:start position:0%
+so only for ideal conditions and that's
+ 
+
+ align:start position:0%
+so only for ideal conditions and that's
+just something you have to deal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with so this why is this why is this got
+
+ align:start position:0%
+with so this why is this why is this got
+ 
+
+ align:start position:0%
+with so this why is this why is this got
+you know why is there this special
+
+ align:start position:0%
+you know why is there this special
+ 
+
+ align:start position:0%
+you know why is there this special
+wonderful thing the the natural
+
+ align:start position:0%
+wonderful thing the the natural
+ 
+
+ align:start position:0%
+wonderful thing the the natural
+modes of a system this one is a two
+
+ align:start position:0%
+modes of a system this one is a two
+ 
+
+ align:start position:0%
+modes of a system this one is a two
+degree Freedom system form a complete
+
+ align:start position:0%
+degree Freedom system form a complete
+ 
+
+ align:start position:0%
+degree Freedom system form a complete
+and independent set of
+
+ align:start position:0%
+and independent set of
+ 
+
+ align:start position:0%
+and independent set of
+vectors and in this case of this two
+
+ align:start position:0%
+vectors and in this case of this two
+ 
+
+ align:start position:0%
+vectors and in this case of this two
+degree Freedom system I can pick any any
+
+ align:start position:0%
+degree Freedom system I can pick any any
+ 
+
+ align:start position:0%
+degree Freedom system I can pick any any
+allow any kinematically allowable
+
+ align:start position:0%
+allow any kinematically allowable
+ 
+
+ align:start position:0%
+allow any kinematically allowable
+position like
+
+ align:start position:0%
+position like
+ 
+
+ align:start position:0%
+position like
+this stationary static is static is one
+
+ align:start position:0%
+this stationary static is static is one
+ 
+
+ align:start position:0%
+this stationary static is static is one
+of the solutions right to this two
+
+ align:start position:0%
+of the solutions right to this two
+ 
+
+ align:start position:0%
+of the solutions right to this two
+degree freom systems so any any possible
+
+ align:start position:0%
+degree freom systems so any any possible
+ 
+
+ align:start position:0%
+degree freom systems so any any possible
+allowable position of these two things
+
+ align:start position:0%
+allowable position of these two things
+ 
+
+ align:start position:0%
+allowable position of these two things
+static or moving can be
+
+ align:start position:0%
+static or moving can be
+ 
+
+ align:start position:0%
+static or moving can be
+described by a linear combination of the
+
+ align:start position:0%
+described by a linear combination of the
+ 
+
+ align:start position:0%
+described by a linear combination of the
+mode shapes of the system a weighted sum
+
+ align:start position:0%
+mode shapes of the system a weighted sum
+ 
+
+ align:start position:0%
+mode shapes of the system a weighted sum
+of the mode shapes of the system and
+
+ align:start position:0%
+of the mode shapes of the system and
+ 
+
+ align:start position:0%
+of the mode shapes of the system and
+that's all it takes so this one has two
+
+ align:start position:0%
+that's all it takes so this one has two
+ 
+
+ align:start position:0%
+that's all it takes so this one has two
+mode shapes you know one that looks kind
+
+ align:start position:0%
+mode shapes you know one that looks kind
+ 
+
+ align:start position:0%
+mode shapes you know one that looks kind
+of like that one that looks like this
+
+ align:start position:0%
+of like that one that looks like this
+ 
+
+ align:start position:0%
+of like that one that looks like this
+one's going down this one's going up
+
+ align:start position:0%
+one's going down this one's going up
+ 
+
+ align:start position:0%
+one's going down this one's going up
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+ratios and I can take a weighted amount
+
+ align:start position:0%
+ratios and I can take a weighted amount
+ 
+
+ align:start position:0%
+ratios and I can take a weighted amount
+of that first mode so much of it and a
+
+ align:start position:0%
+of that first mode so much of it and a
+ 
+
+ align:start position:0%
+of that first mode so much of it and a
+weighted amount of the second mode and
+
+ align:start position:0%
+weighted amount of the second mode and
+ 
+
+ align:start position:0%
+weighted amount of the second mode and
+add them together and describe any
+
+ align:start position:0%
+add them together and describe any
+ 
+
+ align:start position:0%
+add them together and describe any
+possible position of the system the same
+
+ align:start position:0%
+possible position of the system the same
+ 
+
+ align:start position:0%
+possible position of the system the same
+thing is true of that strength
+
+ align:start position:0%
+thing is true of that strength
+ 
+
+ align:start position:0%
+thing is true of that strength
+it has mode shapes that are sine wise
+
+ align:start position:0%
+it has mode shapes that are sine wise
+ 
+
+ align:start position:0%
+it has mode shapes that are sine wise
+but they you know sin 1 pix sin 2 pix
+
+ align:start position:0%
+but they you know sin 1 pix sin 2 pix
+ 
+
+ align:start position:0%
+but they you know sin 1 pix sin 2 pix
+over L and so forth any possible linear
+
+ align:start position:0%
+over L and so forth any possible linear
+ 
+
+ align:start position:0%
+over L and so forth any possible linear
+any possible allowable shape of that
+
+ align:start position:0%
+any possible allowable shape of that
+ 
+
+ align:start position:0%
+any possible allowable shape of that
+guitar string can be made up of a
+
+ align:start position:0%
+guitar string can be made up of a
+ 
+
+ align:start position:0%
+guitar string can be made up of a
+weighted sum of the mode shapes of the
+
+ align:start position:0%
+weighted sum of the mode shapes of the
+ 
+
+ align:start position:0%
+weighted sum of the mode shapes of the
+system and moreover the mode
+
+ align:start position:0%
+system and moreover the mode
+ 
+
+ align:start position:0%
+system and moreover the mode
+shapes the reason this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works be is because the mode shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are orthogonal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another now you know that if you take uh
+
+ align:start position:0%
+another now you know that if you take uh
+ 
+
+ align:start position:0%
+another now you know that if you take uh
+two sine waves like that string and you
+
+ align:start position:0%
+two sine waves like that string and you
+ 
+
+ align:start position:0%
+two sine waves like that string and you
+and you take s first mode sign pix over
+
+ align:start position:0%
+and you take s first mode sign pix over
+ 
+
+ align:start position:0%
+and you take s first mode sign pix over
+L and second mode say sign 2 pix over L
+
+ align:start position:0%
+L and second mode say sign 2 pix over L
+ 
+
+ align:start position:0%
+L and second mode say sign 2 pix over L
+and you multiply them together and
+
+ align:start position:0%
+and you multiply them together and
+ 
+
+ align:start position:0%
+and you multiply them together and
+integrate from 0 to L what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get you always get zero if there if the
+
+ align:start position:0%
+get you always get zero if there if the
+ 
+
+ align:start position:0%
+get you always get zero if there if the
+two signs are if they're full
+
+ align:start position:0%
+two signs are if they're full
+ 
+
+ align:start position:0%
+two signs are if they're full
+wavelengths they go to nodes at the end
+
+ align:start position:0%
+wavelengths they go to nodes at the end
+ 
+
+ align:start position:0%
+wavelengths they go to nodes at the end
+you will always get zero if the
+
+ align:start position:0%
+you will always get zero if the
+ 
+
+ align:start position:0%
+you will always get zero if the
+wavelengths are
+
+ align:start position:0%
+wavelengths are
+ 
+
+ align:start position:0%
+wavelengths are
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+always right that's a statement of
+
+ align:start position:0%
+always right that's a statement of
+ 
+
+ align:start position:0%
+always right that's a statement of
+orthogonality of S
+
+ align:start position:0%
+orthogonality of S
+ 
+
+ align:start position:0%
+orthogonality of S
+functions right same thing is true of
+
+ align:start position:0%
+functions right same thing is true of
+ 
+
+ align:start position:0%
+functions right same thing is true of
+these simple vectors they're orthogonal
+
+ align:start position:0%
+these simple vectors they're orthogonal
+ 
+
+ align:start position:0%
+these simple vectors they're orthogonal
+to one another such that if you do this
+
+ align:start position:0%
+to one another such that if you do this
+ 
+
+ align:start position:0%
+to one another such that if you do this
+multiplication you transpose mu you only
+
+ align:start position:0%
+multiplication you transpose mu you only
+ 
+
+ align:start position:0%
+multiplication you transpose mu you only
+get contributions when you are using
+
+ align:start position:0%
+get contributions when you are using
+ 
+
+ align:start position:0%
+get contributions when you are using
+mode R transpose M mode R you only get a
+
+ align:start position:0%
+mode R transpose M mode R you only get a
+ 
+
+ align:start position:0%
+mode R transpose M mode R you only get a
+contribution from each of those that
+
+ align:start position:0%
+contribution from each of those that
+ 
+
+ align:start position:0%
+contribution from each of those that
+gives you the diagonals same is true
+
+ align:start position:0%
+gives you the diagonals same is true
+ 
+
+ align:start position:0%
+gives you the diagonals same is true
+when you do U transpose KU because of
+
+ align:start position:0%
+when you do U transpose KU because of
+ 
+
+ align:start position:0%
+when you do U transpose KU because of
+orthogonality you only get a diagonal
+
+ align:start position:0%
+orthogonality you only get a diagonal
+ 
+
+ align:start position:0%
+orthogonality you only get a diagonal
+matrix at the end and under the right
+
+ align:start position:0%
+matrix at the end and under the right
+ 
+
+ align:start position:0%
+matrix at the end and under the right
+conditions you transpose CU gives you a
+
+ align:start position:0%
+conditions you transpose CU gives you a
+ 
+
+ align:start position:0%
+conditions you transpose CU gives you a
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+matrix so what's that good for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well here was the set of equations that
+
+ align:start position:0%
+well here was the set of equations that
+ 
+
+ align:start position:0%
+well here was the set of equations that
+we get when we make that substitution
+
+ align:start position:0%
+we get when we make that substitution
+ 
+
+ align:start position:0%
+we get when we make that substitution
+this is going to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us a
+
+ align:start position:0%
+us a
+ 
+
+ align:start position:0%
+us a
+diagonal Mass Matrix time Q dot plus
+
+ align:start position:0%
+diagonal Mass Matrix time Q dot plus
+ 
+
+ align:start position:0%
+diagonal Mass Matrix time Q dot plus
+when conditions are right a diagonal
+
+ align:start position:0%
+when conditions are right a diagonal
+ 
+
+ align:start position:0%
+when conditions are right a diagonal
+damping Matrix time Q dot plus a
+
+ align:start position:0%
+damping Matrix time Q dot plus a
+ 
+
+ align:start position:0%
+damping Matrix time Q dot plus a
+diagonal stiffness Matrix time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q
+
+ align:start position:0%
+Q
+ 
+
+ align:start position:0%
+Q
+equals U transpose
+
+ align:start position:0%
+equals U transpose
+ 
+
+ align:start position:0%
+equals U transpose
+F which it's a vector times a matrix
+
+ align:start position:0%
+F which it's a vector times a matrix
+ 
+
+ align:start position:0%
+F which it's a vector times a matrix
+gives you back a vector which we call
+
+ align:start position:0%
+gives you back a vector which we call
+ 
+
+ align:start position:0%
+gives you back a vector which we call
+capital Q it's a function of time and
+
+ align:start position:0%
+capital Q it's a function of time and
+ 
+
+ align:start position:0%
+capital Q it's a function of time and
+this is called the modal Force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if you look carefully at these if I
+
+ align:start position:0%
+but if you look carefully at these if I
+ 
+
+ align:start position:0%
+but if you look carefully at these if I
+pick the arth one mode mode R out of
+
+ align:start position:0%
+pick the arth one mode mode R out of
+ 
+
+ align:start position:0%
+pick the arth one mode mode R out of
+this whole
+
+ align:start position:0%
+this whole
+ 
+
+ align:start position:0%
+this whole
+thing so
+
+ align:start position:0%
+thing so
+ 
+
+ align:start position:0%
+thing so
+the or I if I just pick any mode out of
+
+ align:start position:0%
+the or I if I just pick any mode out of
+ 
+
+ align:start position:0%
+the or I if I just pick any mode out of
+this any part of this vector and
+
+ align:start position:0%
+this any part of this vector and
+ 
+
+ align:start position:0%
+this any part of this vector and
+complete this multiplication I will find
+
+ align:start position:0%
+complete this multiplication I will find
+ 
+
+ align:start position:0%
+complete this multiplication I will find
+that I get an m r which is the rth entry
+
+ align:start position:0%
+that I get an m r which is the rth entry
+ 
+
+ align:start position:0%
+that I get an m r which is the rth entry
+here and now to to I'm going to refer to
+
+ align:start position:0%
+here and now to to I'm going to refer to
+ 
+
+ align:start position:0%
+here and now to to I'm going to refer to
+these as the modal masses and I'll write
+
+ align:start position:0%
+these as the modal masses and I'll write
+ 
+
+ align:start position:0%
+these as the modal masses and I'll write
+them with capitals and I'll give it
+
+ align:start position:0%
+them with capitals and I'll give it
+ 
+
+ align:start position:0%
+them with capitals and I'll give it
+subscript to tell you what the mode is
+
+ align:start position:0%
+subscript to tell you what the mode is
+ 
+
+ align:start position:0%
+subscript to tell you what the mode is
+this is a number this is the modal mass
+
+ align:start position:0%
+this is a number this is the modal mass
+ 
+
+ align:start position:0%
+this is a number this is the modal mass
+for mode R this gives me an equation
+
+ align:start position:0%
+for mode R this gives me an equation
+ 
+
+ align:start position:0%
+for mode R this gives me an equation
+that looks like m r QR dble dot plus CR
+
+ align:start position:0%
+that looks like m r QR dble dot plus CR
+ 
+
+ align:start position:0%
+that looks like m r QR dble dot plus CR
+QR dot plus KR QR equals QR of T and
+
+ align:start position:0%
+QR dot plus KR QR equals QR of T and
+ 
+
+ align:start position:0%
+QR dot plus KR QR equals QR of T and
+what does that remind you
+
+ align:start position:0%
+what does that remind you
+ 
+
+ align:start position:0%
+what does that remind you
+of that we've done a lot of work
+
+ align:start position:0%
+of that we've done a lot of work
+ 
+
+ align:start position:0%
+of that we've done a lot of work
+with what how many degree of Freedom
+
+ align:start position:0%
+with what how many degree of Freedom
+ 
+
+ align:start position:0%
+with what how many degree of Freedom
+system it looks that's the equation of
+
+ align:start position:0%
+system it looks that's the equation of
+ 
+
+ align:start position:0%
+system it looks that's the equation of
+motion the generic equation of motion of
+
+ align:start position:0%
+motion the generic equation of motion of
+ 
+
+ align:start position:0%
+motion the generic equation of motion of
+a single degree Freedom oscillator and
+
+ align:start position:0%
+a single degree Freedom oscillator and
+ 
+
+ align:start position:0%
+a single degree Freedom oscillator and
+you know how to calculate the response
+
+ align:start position:0%
+you know how to calculate the response
+ 
+
+ align:start position:0%
+you know how to calculate the response
+to initial conditions for that you know
+
+ align:start position:0%
+to initial conditions for that you know
+ 
+
+ align:start position:0%
+to initial conditions for that you know
+how to calculate the steady state
+
+ align:start position:0%
+how to calculate the steady state
+ 
+
+ align:start position:0%
+how to calculate the steady state
+response for that when you have harmonic
+
+ align:start position:0%
+response for that when you have harmonic
+ 
+
+ align:start position:0%
+response for that when you have harmonic
+input right when I said at the beginning
+
+ align:start position:0%
+input right when I said at the beginning
+ 
+
+ align:start position:0%
+input right when I said at the beginning
+of the beginning of the discussion about
+
+ align:start position:0%
+of the beginning of the discussion about
+ 
+
+ align:start position:0%
+of the beginning of the discussion about
+vibration is it's really important to
+
+ align:start position:0%
+vibration is it's really important to
+ 
+
+ align:start position:0%
+vibration is it's really important to
+understand the single degree of Freedom
+
+ align:start position:0%
+understand the single degree of Freedom
+ 
+
+ align:start position:0%
+understand the single degree of Freedom
+oscillator because it gives you it'll
+
+ align:start position:0%
+oscillator because it gives you it'll
+ 
+
+ align:start position:0%
+oscillator because it gives you it'll
+give you insight as to the behavior of
+
+ align:start position:0%
+give you insight as to the behavior of
+ 
+
+ align:start position:0%
+give you insight as to the behavior of
+complicated multiple degree Freedom
+
+ align:start position:0%
+complicated multiple degree Freedom
+ 
+
+ align:start position:0%
+complicated multiple degree Freedom
+systems and here's here's the the proof
+
+ align:start position:0%
+systems and here's here's the the proof
+ 
+
+ align:start position:0%
+systems and here's here's the the proof
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+any this is now n uncoupled single
+
+ align:start position:0%
+any this is now n uncoupled single
+ 
+
+ align:start position:0%
+any this is now n uncoupled single
+degree of Freedom
+
+ align:start position:0%
+degree of Freedom
+ 
+
+ align:start position:0%
+degree of Freedom
+systems this is n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent single one degree of
+
+ align:start position:0%
+independent single one degree of
+ 
+
+ align:start position:0%
+independent single one degree of
+Freedom systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which you can solve one at a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time now lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times a vibrating system a complicated
+
+ align:start position:0%
+times a vibrating system a complicated
+ 
+
+ align:start position:0%
+times a vibrating system a complicated
+one might be this
+
+ align:start position:0%
+one might be this
+ 
+
+ align:start position:0%
+one might be this
+thing if I hit this it's vibrating and
+
+ align:start position:0%
+thing if I hit this it's vibrating and
+ 
+
+ align:start position:0%
+thing if I hit this it's vibrating and
+actually it's pretty much vibrating at a
+
+ align:start position:0%
+actually it's pretty much vibrating at a
+ 
+
+ align:start position:0%
+actually it's pretty much vibrating at a
+single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency and are there any once I've
+
+ align:start position:0%
+frequency and are there any once I've
+ 
+
+ align:start position:0%
+frequency and are there any once I've
+hit it are there any external forces
+
+ align:start position:0%
+hit it are there any external forces
+ 
+
+ align:start position:0%
+hit it are there any external forces
+driving it so what kind of response are
+
+ align:start position:0%
+driving it so what kind of response are
+ 
+
+ align:start position:0%
+driving it so what kind of response are
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seeing response
+
+ align:start position:0%
+seeing response
+ 
+
+ align:start position:0%
+seeing response
+to initial conditions right now in
+
+ align:start position:0%
+to initial conditions right now in
+ 
+
+ align:start position:0%
+to initial conditions right now in
+general each one of the natural modes of
+
+ align:start position:0%
+general each one of the natural modes of
+ 
+
+ align:start position:0%
+general each one of the natural modes of
+a system has a different natural
+
+ align:start position:0%
+a system has a different natural
+ 
+
+ align:start position:0%
+a system has a different natural
+frequency right
+
+ align:start position:0%
+frequency right
+ 
+
+ align:start position:0%
+frequency right
+so if I hit this thing and I look at it
+
+ align:start position:0%
+so if I hit this thing and I look at it
+ 
+
+ align:start position:0%
+so if I hit this thing and I look at it
+you know it really I can just see it
+
+ align:start position:0%
+you know it really I can just see it
+ 
+
+ align:start position:0%
+you know it really I can just see it
+wiggling back and forth and basically at
+
+ align:start position:0%
+wiggling back and forth and basically at
+ 
+
+ align:start position:0%
+wiggling back and forth and basically at
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+frequency so if you wanted to come up
+
+ align:start position:0%
+frequency so if you wanted to come up
+ 
+
+ align:start position:0%
+frequency so if you wanted to come up
+with a simple model of this system how
+
+ align:start position:0%
+with a simple model of this system how
+ 
+
+ align:start position:0%
+with a simple model of this system how
+many natural modes do you think you'd
+
+ align:start position:0%
+many natural modes do you think you'd
+ 
+
+ align:start position:0%
+many natural modes do you think you'd
+have to include to describe the motion
+
+ align:start position:0%
+have to include to describe the motion
+ 
+
+ align:start position:0%
+have to include to describe the motion
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+system one now is that a lot easier than
+
+ align:start position:0%
+system one now is that a lot easier than
+ 
+
+ align:start position:0%
+system one now is that a lot easier than
+having to do the full General equation
+
+ align:start position:0%
+having to do the full General equation
+ 
+
+ align:start position:0%
+having to do the full General equation
+of motion for all the possible modes
+
+ align:start position:0%
+of motion for all the possible modes
+ 
+
+ align:start position:0%
+of motion for all the possible modes
+that this thing has and D out a lot
+
+ align:start position:0%
+that this thing has and D out a lot
+ 
+
+ align:start position:0%
+that this thing has and D out a lot
+right you have to deal with with
+
+ align:start position:0%
+right you have to deal with with
+ 
+
+ align:start position:0%
+right you have to deal with with
+equation of motion of a single degree
+
+ align:start position:0%
+equation of motion of a single degree
+ 
+
+ align:start position:0%
+equation of motion of a single degree
+Freedom system to describe this and
+
+ align:start position:0%
+Freedom system to describe this and
+ 
+
+ align:start position:0%
+Freedom system to describe this and
+that's the real point you know they
+
+ align:start position:0%
+that's the real point you know they
+ 
+
+ align:start position:0%
+that's the real point you know they
+built the Hancock building across the
+
+ align:start position:0%
+built the Hancock building across the
+ 
+
+ align:start position:0%
+built the Hancock building across the
+river 35 years ago was losing Windows
+
+ align:start position:0%
+river 35 years ago was losing Windows
+ 
+
+ align:start position:0%
+river 35 years ago was losing Windows
+like crazy it was brand new building and
+
+ align:start position:0%
+like crazy it was brand new building and
+ 
+
+ align:start position:0%
+like crazy it was brand new building and
+the windows when the wind would get
+
+ align:start position:0%
+the windows when the wind would get
+ 
+
+ align:start position:0%
+the windows when the wind would get
+about 40 mes hour the window started
+
+ align:start position:0%
+about 40 mes hour the window started
+ 
+
+ align:start position:0%
+about 40 mes hour the window started
+falling out 60 stories high 60 61
+
+ align:start position:0%
+falling out 60 stories high 60 61
+ 
+
+ align:start position:0%
+falling out 60 stories high 60 61
+stories high and the wind was blowing
+
+ align:start position:0%
+stories high and the wind was blowing
+ 
+
+ align:start position:0%
+stories high and the wind was blowing
+where do you suppos the window do fall
+
+ align:start position:0%
+where do you suppos the window do fall
+ 
+
+ align:start position:0%
+where do you suppos the window do fall
+out what part of the building
+
+ align:start position:0%
+out what part of the building
+ 
+
+ align:start position:0%
+out what part of the building
+huh I mean you'd think the wind wind is
+
+ align:start position:0%
+huh I mean you'd think the wind wind is
+ 
+
+ align:start position:0%
+huh I mean you'd think the wind wind is
+blown it gets stronger as it goes up
+
+ align:start position:0%
+blown it gets stronger as it goes up
+ 
+
+ align:start position:0%
+blown it gets stronger as it goes up
+it's probably blown out the wind is at
+
+ align:start position:0%
+it's probably blown out the wind is at
+ 
+
+ align:start position:0%
+it's probably blown out the wind is at
+the top right but the windows were
+
+ align:start position:0%
+the top right but the windows were
+ 
+
+ align:start position:0%
+the top right but the windows were
+breaking as you you as time went by
+
+ align:start position:0%
+breaking as you you as time went by
+ 
+
+ align:start position:0%
+breaking as you you as time went by
+every time the window would break they
+
+ align:start position:0%
+every time the window would break they
+ 
+
+ align:start position:0%
+every time the window would break they
+would they replace this 5 foot by 9t
+
+ align:start position:0%
+would they replace this 5 foot by 9t
+ 
+
+ align:start position:0%
+would they replace this 5 foot by 9t
+sheet of glass with a piece of plywood
+
+ align:start position:0%
+sheet of glass with a piece of plywood
+ 
+
+ align:start position:0%
+sheet of glass with a piece of plywood
+and so you got this statistical sampling
+
+ align:start position:0%
+and so you got this statistical sampling
+ 
+
+ align:start position:0%
+and so you got this statistical sampling
+after a while of where the breakage was
+
+ align:start position:0%
+after a while of where the breakage was
+ 
+
+ align:start position:0%
+after a while of where the breakage was
+so you had no windows broken at the
+
+ align:start position:0%
+so you had no windows broken at the
+ 
+
+ align:start position:0%
+so you had no windows broken at the
+top and a few as you got further down
+
+ align:start position:0%
+top and a few as you got further down
+ 
+
+ align:start position:0%
+top and a few as you got further down
+and more and lots of them broken out at
+
+ align:start position:0%
+and more and lots of them broken out at
+ 
+
+ align:start position:0%
+and more and lots of them broken out at
+the bottom
+
+ align:start position:0%
+the bottom
+ 
+
+ align:start position:0%
+the bottom
+it turns out that that building was
+
+ align:start position:0%
+it turns out that that building was
+ 
+
+ align:start position:0%
+it turns out that that building was
+vibrating in its both mostly in its
+
+ align:start position:0%
+vibrating in its both mostly in its
+ 
+
+ align:start position:0%
+vibrating in its both mostly in its
+first bending mode it was going back and
+
+ align:start position:0%
+first bending mode it was going back and
+ 
+
+ align:start position:0%
+first bending mode it was going back and
+forth like
+
+ align:start position:0%
+forth like
+ 
+
+ align:start position:0%
+forth like
+this also happened to have a torsional
+
+ align:start position:0%
+this also happened to have a torsional
+ 
+
+ align:start position:0%
+this also happened to have a torsional
+mode this first torsional mode was kind
+
+ align:start position:0%
+mode this first torsional mode was kind
+ 
+
+ align:start position:0%
+mode this first torsional mode was kind
+of twisting around the base like that so
+
+ align:start position:0%
+of twisting around the base like that so
+ 
+
+ align:start position:0%
+of twisting around the base like that so
+in fact this motion the mo when when to
+
+ align:start position:0%
+in fact this motion the mo when when to
+ 
+
+ align:start position:0%
+in fact this motion the mo when when to
+get about 40 miles hour this building
+
+ align:start position:0%
+get about 40 miles hour this building
+ 
+
+ align:start position:0%
+get about 40 miles hour this building
+start rocking and rolling mostly like
+
+ align:start position:0%
+start rocking and rolling mostly like
+ 
+
+ align:start position:0%
+start rocking and rolling mostly like
+this with a little of this thrown in
+
+ align:start position:0%
+this with a little of this thrown in
+ 
+
+ align:start position:0%
+this with a little of this thrown in
+okay and but you can basically model
+
+ align:start position:0%
+okay and but you can basically model
+ 
+
+ align:start position:0%
+okay and but you can basically model
+that complicated building that has
+
+ align:start position:0%
+that complicated building that has
+ 
+
+ align:start position:0%
+that complicated building that has
+millions of possible natural modes in it
+
+ align:start position:0%
+millions of possible natural modes in it
+ 
+
+ align:start position:0%
+millions of possible natural modes in it
+by one or possibly two single degree
+
+ align:start position:0%
+by one or possibly two single degree
+ 
+
+ align:start position:0%
+by one or possibly two single degree
+Freedom
+
+ align:start position:0%
+Freedom
+ 
+
+ align:start position:0%
+Freedom
+oscillators so that's the power modal
+
+ align:start position:0%
+oscillators so that's the power modal
+ 
+
+ align:start position:0%
+oscillators so that's the power modal
+analysis but I think the real power of
+
+ align:start position:0%
+analysis but I think the real power of
+ 
+
+ align:start position:0%
+analysis but I think the real power of
+understanding that you can do this is
+
+ align:start position:0%
+understanding that you can do this is
+ 
+
+ align:start position:0%
+understanding that you can do this is
+that it gives you this immediate insight
+
+ align:start position:0%
+that it gives you this immediate insight
+ 
+
+ align:start position:0%
+that it gives you this immediate insight
+as to what might be going on in
+
+ align:start position:0%
+as to what might be going on in
+ 
+
+ align:start position:0%
+as to what might be going on in
+something so I look at this I don't I
+
+ align:start position:0%
+something so I look at this I don't I
+ 
+
+ align:start position:0%
+something so I look at this I don't I
+don't see a complicated thing that I
+
+ align:start position:0%
+don't see a complicated thing that I
+ 
+
+ align:start position:0%
+don't see a complicated thing that I
+have to model with a big finite element
+
+ align:start position:0%
+have to model with a big finite element
+ 
+
+ align:start position:0%
+have to model with a big finite element
+model I see something that's vibrating
+
+ align:start position:0%
+model I see something that's vibrating
+ 
+
+ align:start position:0%
+model I see something that's vibrating
+at one frequency and I can I know it has
+
+ align:start position:0%
+at one frequency and I can I know it has
+ 
+
+ align:start position:0%
+at one frequency and I can I know it has
+a it'll Decay it'll have damping it'll
+
+ align:start position:0%
+a it'll Decay it'll have damping it'll
+ 
+
+ align:start position:0%
+a it'll Decay it'll have damping it'll
+have a natural natural frequency and I
+
+ align:start position:0%
+have a natural natural frequency and I
+ 
+
+ align:start position:0%
+have a natural natural frequency and I
+to get immediate insight as to Its
+
+ align:start position:0%
+to get immediate insight as to Its
+ 
+
+ align:start position:0%
+to get immediate insight as to Its
+Behavior by knowing this okay and that's
+
+ align:start position:0%
+Behavior by knowing this okay and that's
+ 
+
+ align:start position:0%
+Behavior by knowing this okay and that's
+the real reason why I wanted to show
+
+ align:start position:0%
+the real reason why I wanted to show
+ 
+
+ align:start position:0%
+the real reason why I wanted to show
+this to
+
+ align:start position:0%
+this to
+ 
+
+ align:start position:0%
+this to
+you so today
+
+ align:start position:0%
+you so today
+ 
+
+ align:start position:0%
+you so today
+we I want we'll do um there sort of two
+
+ align:start position:0%
+we I want we'll do um there sort of two
+ 
+
+ align:start position:0%
+we I want we'll do um there sort of two
+things two two directions we can go with
+
+ align:start position:0%
+things two two directions we can go with
+ 
+
+ align:start position:0%
+things two two directions we can go with
+this one is to talk about response to
+
+ align:start position:0%
+this one is to talk about response to
+ 
+
+ align:start position:0%
+this one is to talk about response to
+initial conditions and the other is to
+
+ align:start position:0%
+initial conditions and the other is to
+ 
+
+ align:start position:0%
+initial conditions and the other is to
+talk about the response to force
+
+ align:start position:0%
+talk about the response to force
+ 
+
+ align:start position:0%
+talk about the response to force
+excitation so let's we're going to begin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by doing response to
+
+ align:start position:0%
+by doing response to
+ 
+
+ align:start position:0%
+by doing response to
+I's okay and then we'll move on probably
+
+ align:start position:0%
+I's okay and then we'll move on probably
+ 
+
+ align:start position:0%
+I's okay and then we'll move on probably
+next time and talk about response to
+
+ align:start position:0%
+next time and talk about response to
+ 
+
+ align:start position:0%
+next time and talk about response to
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+excitations and uh be so be and we're
+
+ align:start position:0%
+excitations and uh be so be and we're
+ 
+
+ align:start position:0%
+excitations and uh be so be and we're
+going to use that as the
+
+ align:start position:0%
+going to use that as the
+ 
+
+ align:start position:0%
+going to use that as the
+example before I go there how uh once we
+
+ align:start position:0%
+example before I go there how uh once we
+ 
+
+ align:start position:0%
+example before I go there how uh once we
+have broken the system down and analyzed
+
+ align:start position:0%
+have broken the system down and analyzed
+ 
+
+ align:start position:0%
+have broken the system down and analyzed
+it this way how do we get back
+
+ align:start position:0%
+it this way how do we get back
+ 
+
+ align:start position:0%
+it this way how do we get back
+to the motion of the system in our
+
+ align:start position:0%
+to the motion of the system in our
+ 
+
+ align:start position:0%
+to the motion of the system in our
+generalized coordinates which are the
+
+ align:start position:0%
+generalized coordinates which are the
+ 
+
+ align:start position:0%
+generalized coordinates which are the
+ones we're comfortable with because I
+
+ align:start position:0%
+ones we're comfortable with because I
+ 
+
+ align:start position:0%
+ones we're comfortable with because I
+don't know how to take where to take a
+
+ align:start position:0%
+don't know how to take where to take a
+ 
+
+ align:start position:0%
+don't know how to take where to take a
+ruler and go
+
+ align:start position:0%
+ruler and go
+ 
+
+ align:start position:0%
+ruler and go
+measure measure this natural
+
+ align:start position:0%
+measure measure this natural
+ 
+
+ align:start position:0%
+measure measure this natural
+coordinate so somehow I have to get back
+
+ align:start position:0%
+coordinate so somehow I have to get back
+ 
+
+ align:start position:0%
+coordinate so somehow I have to get back
+to putting into real physical
+
+ align:start position:0%
+to putting into real physical
+ 
+
+ align:start position:0%
+to putting into real physical
+measurements that I know how that I can
+
+ align:start position:0%
+measurements that I know how that I can
+ 
+
+ align:start position:0%
+measurements that I know how that I can
+relate to well that's easy because it's
+
+ align:start position:0%
+relate to well that's easy because it's
+ 
+
+ align:start position:0%
+relate to well that's easy because it's
+where where did we start with this we
+
+ align:start position:0%
+where where did we start with this we
+ 
+
+ align:start position:0%
+where where did we start with this we
+started by saying this whole thing began
+
+ align:start position:0%
+started by saying this whole thing began
+ 
+
+ align:start position:0%
+started by saying this whole thing began
+right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so at the end you we we just come
+
+ align:start position:0%
+and so at the end you we we just come
+ 
+
+ align:start position:0%
+and so at the end you we we just come
+back and say oh well X here our
+
+ align:start position:0%
+back and say oh well X here our
+ 
+
+ align:start position:0%
+back and say oh well X here our
+generalized coordinates is this
+
+ align:start position:0%
+generalized coordinates is this
+ 
+
+ align:start position:0%
+generalized coordinates is this
+summation of the mode
+
+ align:start position:0%
+summation of the mode
+ 
+
+ align:start position:0%
+summation of the mode
+shapes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u i here summed summed over I of q i
+
+ align:start position:0%
+u i here summed summed over I of q i
+ 
+
+ align:start position:0%
+u i here summed summed over I of q i
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+T now the reason I wrote it here is a
+
+ align:start position:0%
+T now the reason I wrote it here is a
+ 
+
+ align:start position:0%
+T now the reason I wrote it here is a
+summation is to to you is to remind you
+
+ align:start position:0%
+summation is to to you is to remind you
+ 
+
+ align:start position:0%
+summation is to to you is to remind you
+that you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this that's the beauty of this thing is
+
+ align:start position:0%
+this that's the beauty of this thing is
+ 
+
+ align:start position:0%
+this that's the beauty of this thing is
+you only have to do it over the modes
+
+ align:start position:0%
+you only have to do it over the modes
+ 
+
+ align:start position:0%
+you only have to do it over the modes
+that matter or so if you've decided to
+
+ align:start position:0%
+that matter or so if you've decided to
+ 
+
+ align:start position:0%
+that matter or so if you've decided to
+approximate the motion of this complic
+
+ align:start position:0%
+approximate the motion of this complic
+ 
+
+ align:start position:0%
+approximate the motion of this complic
+comp at system by just a couple of modal
+
+ align:start position:0%
+comp at system by just a couple of modal
+ 
+
+ align:start position:0%
+comp at system by just a couple of modal
+contributions because you know they're
+
+ align:start position:0%
+contributions because you know they're
+ 
+
+ align:start position:0%
+contributions because you know they're
+the important ones this this is a pretty
+
+ align:start position:0%
+the important ones this this is a pretty
+ 
+
+ align:start position:0%
+the important ones this this is a pretty
+short summation this is how you get back
+
+ align:start position:0%
+short summation this is how you get back
+ 
+
+ align:start position:0%
+short summation this is how you get back
+to your original modal coordinates is
+
+ align:start position:0%
+to your original modal coordinates is
+ 
+
+ align:start position:0%
+to your original modal coordinates is
+take the modal
+
+ align:start position:0%
+take the modal
+ 
+
+ align:start position:0%
+take the modal
+amplitude multiply it by the mode
+
+ align:start position:0%
+amplitude multiply it by the mode
+ 
+
+ align:start position:0%
+amplitude multiply it by the mode
+shape and when you do that it says you
+
+ align:start position:0%
+shape and when you do that it says you
+ 
+
+ align:start position:0%
+shape and when you do that it says you
+know this turns out to be say some a sin
+
+ align:start position:0%
+know this turns out to be say some a sin
+ 
+
+ align:start position:0%
+know this turns out to be say some a sin
+Omega T when you multiply it by the mode
+
+ align:start position:0%
+Omega T when you multiply it by the mode
+ 
+
+ align:start position:0%
+Omega T when you multiply it by the mode
+shape it basically tells you how much
+
+ align:start position:0%
+shape it basically tells you how much
+ 
+
+ align:start position:0%
+shape it basically tells you how much
+each generalized coordinate gets of the
+
+ align:start position:0%
+each generalized coordinate gets of the
+ 
+
+ align:start position:0%
+each generalized coordinate gets of the
+motion the mode shape distributes the
+
+ align:start position:0%
+motion the mode shape distributes the
+ 
+
+ align:start position:0%
+motion the mode shape distributes the
+answer out proportionally in the correct
+
+ align:start position:0%
+answer out proportionally in the correct
+ 
+
+ align:start position:0%
+answer out proportionally in the correct
+amount so this is how you get back to
+
+ align:start position:0%
+amount so this is how you get back to
+ 
+
+ align:start position:0%
+amount so this is how you get back to
+the iginal so let's think about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and we'll do an initial
+
+ align:start position:0%
+system and we'll do an initial
+ 
+
+ align:start position:0%
+system and we'll do an initial
+conditions kind of problem so I think
+
+ align:start position:0%
+conditions kind of problem so I think
+ 
+
+ align:start position:0%
+conditions kind of problem so I think
+Professor goser you I think in class you
+
+ align:start position:0%
+Professor goser you I think in class you
+ 
+
+ align:start position:0%
+Professor goser you I think in class you
+sort of figured out what the approximate
+
+ align:start position:0%
+sort of figured out what the approximate
+ 
+
+ align:start position:0%
+sort of figured out what the approximate
+K's and M's and things were for that
+
+ align:start position:0%
+K's and M's and things were for that
+ 
+
+ align:start position:0%
+K's and M's and things were for that
+system so I actually took it apart
+
+ align:start position:0%
+system so I actually took it apart
+ 
+
+ align:start position:0%
+system so I actually took it apart
+weighed it measured some natural free
+
+ align:start position:0%
+weighed it measured some natural free
+ 
+
+ align:start position:0%
+weighed it measured some natural free
+frequencies and have come up
+
+ align:start position:0%
+frequencies and have come up
+ 
+
+ align:start position:0%
+frequencies and have come up
+with a pretty
+
+ align:start position:0%
+with a pretty
+ 
+
+ align:start position:0%
+with a pretty
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+model I release pretty good set of
+
+ align:start position:0%
+model I release pretty good set of
+ 
+
+ align:start position:0%
+model I release pretty good set of
+numbers characterizing this two degree
+
+ align:start position:0%
+numbers characterizing this two degree
+ 
+
+ align:start position:0%
+numbers characterizing this two degree
+Freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system so
+
+ align:start position:0%
+system so
+ 
+
+ align:start position:0%
+system so
+C1 K1 M1 K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C2
+
+ align:start position:0%
+C2
+ 
+
+ align:start position:0%
+C2
+X1 X2 so these are my generalized
+
+ align:start position:0%
+X1 X2 so these are my generalized
+ 
+
+ align:start position:0%
+X1 X2 so these are my generalized
+coordinates measured probably from what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position static equilibrium right so I
+
+ align:start position:0%
+position static equilibrium right so I
+ 
+
+ align:start position:0%
+position static equilibrium right so I
+don't have to mess with gravity in
+
+ align:start position:0%
+don't have to mess with gravity in
+ 
+
+ align:start position:0%
+don't have to mess with gravity in
+this measured from static equilibrium
+
+ align:start position:0%
+this measured from static equilibrium
+ 
+
+ align:start position:0%
+this measured from static equilibrium
+and to try to help keep
+
+ align:start position:0%
+and to try to help keep
+ 
+
+ align:start position:0%
+and to try to help keep
+things understandable track I've write I
+
+ align:start position:0%
+things understandable track I've write I
+ 
+
+ align:start position:0%
+things understandable track I've write I
+tried to write the parameters of the
+
+ align:start position:0%
+tried to write the parameters of the
+ 
+
+ align:start position:0%
+tried to write the parameters of the
+system as lowercase k1s k2s k3s because
+
+ align:start position:0%
+system as lowercase k1s k2s k3s because
+ 
+
+ align:start position:0%
+system as lowercase k1s k2s k3s because
+I want to write modal stiffness for mode
+
+ align:start position:0%
+I want to write modal stiffness for mode
+ 
+
+ align:start position:0%
+I want to write modal stiffness for mode
+one is a capital K1 so I'll try to be
+
+ align:start position:0%
+one is a capital K1 so I'll try to be
+ 
+
+ align:start position:0%
+one is a capital K1 so I'll try to be
+consistent about that and notice where I
+
+ align:start position:0%
+consistent about that and notice where I
+ 
+
+ align:start position:0%
+consistent about that and notice where I
+put the dampers in the
+
+ align:start position:0%
+put the dampers in the
+ 
+
+ align:start position:0%
+put the dampers in the
+system that's because most of the
+
+ align:start position:0%
+system that's because most of the
+ 
+
+ align:start position:0%
+system that's because most of the
+damping in this thing comes from the
+
+ align:start position:0%
+damping in this thing comes from the
+ 
+
+ align:start position:0%
+damping in this thing comes from the
+upper Mass rubs against the stationary
+
+ align:start position:0%
+upper Mass rubs against the stationary
+ 
+
+ align:start position:0%
+upper Mass rubs against the stationary
+object and the lower which is the the
+
+ align:start position:0%
+object and the lower which is the the
+ 
+
+ align:start position:0%
+object and the lower which is the the
+bar here the lower Mass rubs against the
+
+ align:start position:0%
+bar here the lower Mass rubs against the
+ 
+
+ align:start position:0%
+bar here the lower Mass rubs against the
+station area object so it's as if I'm
+
+ align:start position:0%
+station area object so it's as if I'm
+ 
+
+ align:start position:0%
+station area object so it's as if I'm
+going to model that as a dash putt
+
+ align:start position:0%
+going to model that as a dash putt
+ 
+
+ align:start position:0%
+going to model that as a dash putt
+between each mass and the fixed
+
+ align:start position:0%
+between each mass and the fixed
+ 
+
+ align:start position:0%
+between each mass and the fixed
+reference frame because the the bar
+
+ align:start position:0%
+reference frame because the the bar
+ 
+
+ align:start position:0%
+reference frame because the the bar
+doesn't move so it's an approximate
+
+ align:start position:0%
+doesn't move so it's an approximate
+ 
+
+ align:start position:0%
+doesn't move so it's an approximate
+model of the damping and so if we do our
+
+ align:start position:0%
+model of the damping and so if we do our
+ 
+
+ align:start position:0%
+model of the damping and so if we do our
+sum of
+
+ align:start position:0%
+sum of
+ 
+
+ align:start position:0%
+sum of
+forces on each of these masses just do
+
+ align:start position:0%
+forces on each of these masses just do
+ 
+
+ align:start position:0%
+forces on each of these masses just do
+Newton's on the mass uh we can come up
+
+ align:start position:0%
+Newton's on the mass uh we can come up
+ 
+
+ align:start position:0%
+Newton's on the mass uh we can come up
+with our two equations of motion we get
+
+ align:start position:0%
+with our two equations of motion we get
+ 
+
+ align:start position:0%
+with our two equations of motion we get
+two equations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion and let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think I give you some information here
+
+ align:start position:0%
+think I give you some information here
+ 
+
+ align:start position:0%
+think I give you some information here
+first M1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those and I really don't know the
+
+ align:start position:0%
+so those and I really don't know the
+ 
+
+ align:start position:0%
+so those and I really don't know the
+damping but we can get that by counting
+
+ align:start position:0%
+damping but we can get that by counting
+ 
+
+ align:start position:0%
+damping but we can get that by counting
+how many cycles it takes to Decay and so
+
+ align:start position:0%
+how many cycles it takes to Decay and so
+ 
+
+ align:start position:0%
+how many cycles it takes to Decay and so
+forth so that's basically what I go come
+
+ align:start position:0%
+forth so that's basically what I go come
+ 
+
+ align:start position:0%
+forth so that's basically what I go come
+into this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowing and I'm going to write my
+
+ align:start position:0%
+knowing and I'm going to write my
+ 
+
+ align:start position:0%
+knowing and I'm going to write my
+equations of motion as in Matrix form so
+
+ align:start position:0%
+equations of motion as in Matrix form so
+ 
+
+ align:start position:0%
+equations of motion as in Matrix form so
+it's going to end up looking like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M1 now notice the damping in this one
+
+ align:start position:0%
+M1 now notice the damping in this one
+ 
+
+ align:start position:0%
+M1 now notice the damping in this one
+the damping force is only proportion
+
+ align:start position:0%
+the damping force is only proportion
+ 
+
+ align:start position:0%
+the damping force is only proportion
+it'll be C1 X1 dot had nothing doesn't
+
+ align:start position:0%
+it'll be C1 X1 dot had nothing doesn't
+ 
+
+ align:start position:0%
+it'll be C1 X1 dot had nothing doesn't
+involve the motion of the other object
+
+ align:start position:0%
+involve the motion of the other object
+ 
+
+ align:start position:0%
+involve the motion of the other object
+and this one the damping Force only
+
+ align:start position:0%
+and this one the damping Force only
+ 
+
+ align:start position:0%
+and this one the damping Force only
+involves the second motion so this H
+
+ align:start position:0%
+involves the second motion so this H
+ 
+
+ align:start position:0%
+involves the second motion so this H
+this one happens to look like a
+
+ align:start position:0%
+this one happens to look like a
+ 
+
+ align:start position:0%
+this one happens to look like a
+C1 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C2 and the stiffness
+
+ align:start position:0%
+C2 and the stiffness
+ 
+
+ align:start position:0%
+C2 and the stiffness
+Matrix well it's K1 +
+
+ align:start position:0%
+Matrix well it's K1 +
+ 
+
+ align:start position:0%
+Matrix well it's K1 +
+K2 -
+
+ align:start position:0%
+K2 -
+ 
+
+ align:start position:0%
+K2 -
+K2 Min -
+
+ align:start position:0%
+K2 Min -
+ 
+
+ align:start position:0%
+K2 Min -
+K2 and K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2 X1
+
+ align:start position:0%
+K2 X1
+ 
+
+ align:start position:0%
+K2 X1
+X2 and
+
+ align:start position:0%
+X2 and
+ 
+
+ align:start position:0%
+X2 and
+for no external forces this starts off
+
+ align:start position:0%
+for no external forces this starts off
+ 
+
+ align:start position:0%
+for no external forces this starts off
+this one is a has no exter and nothing
+
+ align:start position:0%
+this one is a has no exter and nothing
+ 
+
+ align:start position:0%
+this one is a has no exter and nothing
+on the right hand side equal to zero so
+
+ align:start position:0%
+on the right hand side equal to zero so
+ 
+
+ align:start position:0%
+on the right hand side equal to zero so
+those are my equations of motion and you
+
+ align:start position:0%
+those are my equations of motion and you
+ 
+
+ align:start position:0%
+those are my equations of motion and you
+know if you multiply these out you get
+
+ align:start position:0%
+know if you multiply these out you get
+ 
+
+ align:start position:0%
+know if you multiply these out you get
+two equations and each one would be is a
+
+ align:start position:0%
+two equations and each one would be is a
+ 
+
+ align:start position:0%
+two equations and each one would be is a
+result that you get by applying Newton's
+
+ align:start position:0%
+result that you get by applying Newton's
+ 
+
+ align:start position:0%
+result that you get by applying Newton's
+law to mass one and Newton's law to mass
+
+ align:start position:0%
+law to mass one and Newton's law to mass
+ 
+
+ align:start position:0%
+law to mass one and Newton's law to mass
+two but you we've done that enough times
+
+ align:start position:0%
+two but you we've done that enough times
+ 
+
+ align:start position:0%
+two but you we've done that enough times
+I'm not going to go through that that
+
+ align:start position:0%
+I'm not going to go through that that
+ 
+
+ align:start position:0%
+I'm not going to go through that that
+part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and putting in real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers that's our Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix I don't know
+
+ align:start position:0%
+Matrix I don't know
+ 
+
+ align:start position:0%
+Matrix I don't know
+this my stiffness Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is my K Matrix
+
+ align:start position:0%
+so this is my K Matrix
+ 
+
+ align:start position:0%
+so this is my K Matrix
+here and stiffness matrices they're
+
+ align:start position:0%
+here and stiffness matrices they're
+ 
+
+ align:start position:0%
+here and stiffness matrices they're
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+symmetric damping that although this one
+
+ align:start position:0%
+symmetric damping that although this one
+ 
+
+ align:start position:0%
+symmetric damping that although this one
+happen to be diagonal you'll find the
+
+ align:start position:0%
+happen to be diagonal you'll find the
+ 
+
+ align:start position:0%
+happen to be diagonal you'll find the
+mass matrices and even the damping
+
+ align:start position:0%
+mass matrices and even the damping
+ 
+
+ align:start position:0%
+mass matrices and even the damping
+matrices for our linear systems are
+
+ align:start position:0%
+matrices for our linear systems are
+ 
+
+ align:start position:0%
+matrices for our linear systems are
+symmetric so here's my stiffest Matrix
+
+ align:start position:0%
+symmetric so here's my stiffest Matrix
+ 
+
+ align:start position:0%
+symmetric so here's my stiffest Matrix
+here's my mass
+
+ align:start position:0%
+here's my mass
+ 
+
+ align:start position:0%
+here's my mass
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+okay so now I want to do and also in
+
+ align:start position:0%
+okay so now I want to do and also in
+ 
+
+ align:start position:0%
+okay so now I want to do and also in
+this case here's my damping Matrix but I
+
+ align:start position:0%
+this case here's my damping Matrix but I
+ 
+
+ align:start position:0%
+this case here's my damping Matrix but I
+leave that because it's the one that's a
+
+ align:start position:0%
+leave that because it's the one that's a
+ 
+
+ align:start position:0%
+leave that because it's the one that's a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+Troublesome so what do I need to do to
+
+ align:start position:0%
+Troublesome so what do I need to do to
+ 
+
+ align:start position:0%
+Troublesome so what do I need to do to
+this to uh carry out my modal analysis
+
+ align:start position:0%
+this to uh carry out my modal analysis
+ 
+
+ align:start position:0%
+this to uh carry out my modal analysis
+so I need
+
+ align:start position:0%
+so I need
+ 
+
+ align:start position:0%
+so I need
+to go find the results of computing U
+
+ align:start position:0%
+to go find the results of computing U
+ 
+
+ align:start position:0%
+to go find the results of computing U
+transpose M and u u and U transpose
+
+ align:start position:0%
+transpose M and u u and U transpose
+ 
+
+ align:start position:0%
+transpose M and u u and U transpose
+KU and let's see what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get so we need to know a couple of
+
+ align:start position:0%
+get so we need to know a couple of
+ 
+
+ align:start position:0%
+get so we need to know a couple of
+things about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system we need to know natural
+
+ align:start position:0%
+system we need to know natural
+ 
+
+ align:start position:0%
+system we need to know natural
+frequencies and mode shapes so if we
+
+ align:start position:0%
+frequencies and mode shapes so if we
+ 
+
+ align:start position:0%
+frequencies and mode shapes so if we
+have this Mass Matrix and we have the
+
+ align:start position:0%
+have this Mass Matrix and we have the
+ 
+
+ align:start position:0%
+have this Mass Matrix and we have the
+stiffness Matrix then we know we can
+
+ align:start position:0%
+stiffness Matrix then we know we can
+ 
+
+ align:start position:0%
+stiffness Matrix then we know we can
+cast this we want the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+undamped natural
+
+ align:start position:0%
+undamped natural
+ 
+
+ align:start position:0%
+undamped natural
+frequencies and our mode shapes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know that we can
+
+ align:start position:0%
+and we know that we can
+ 
+
+ align:start position:0%
+and we know that we can
+transform the equation we the equations
+
+ align:start position:0%
+transform the equation we the equations
+ 
+
+ align:start position:0%
+transform the equation we the equations
+of motion into an algebraic problem or
+
+ align:start position:0%
+of motion into an algebraic problem or
+ 
+
+ align:start position:0%
+of motion into an algebraic problem or
+we solve for the natural frequencies and
+
+ align:start position:0%
+we solve for the natural frequencies and
+ 
+
+ align:start position:0%
+we solve for the natural frequencies and
+mode shapes so we have uh just to kind
+
+ align:start position:0%
+mode shapes so we have uh just to kind
+ 
+
+ align:start position:0%
+mode shapes so we have uh just to kind
+of remind you really quickly of that
+
+ align:start position:0%
+of remind you really quickly of that
+ 
+
+ align:start position:0%
+of remind you really quickly of that
+remember our equations look like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+undamped and you assume that X is some
+
+ align:start position:0%
+undamped and you assume that X is some
+ 
+
+ align:start position:0%
+undamped and you assume that X is some
+form u in fact e to the the I Omega
+
+ align:start position:0%
+form u in fact e to the the I Omega
+ 
+
+ align:start position:0%
+form u in fact e to the the I Omega
+T you plug it in you get minus Omega 2 m
+
+ align:start position:0%
+T you plug it in you get minus Omega 2 m
+ 
+
+ align:start position:0%
+T you plug it in you get minus Omega 2 m
++
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k u e to the I Omega T equals
+
+ align:start position:0%
+k u e to the I Omega T equals
+ 
+
+ align:start position:0%
+k u e to the I Omega T equals
+z and this now is your algebraic problem
+
+ align:start position:0%
+z and this now is your algebraic problem
+ 
+
+ align:start position:0%
+z and this now is your algebraic problem
+either this unknown set of amplitudes is
+
+ align:start position:0%
+either this unknown set of amplitudes is
+ 
+
+ align:start position:0%
+either this unknown set of amplitudes is
+zero what these going to turn out to be
+
+ align:start position:0%
+zero what these going to turn out to be
+ 
+
+ align:start position:0%
+zero what these going to turn out to be
+the mod shapes and they're not generally
+
+ align:start position:0%
+the mod shapes and they're not generally
+ 
+
+ align:start position:0%
+the mod shapes and they're not generally
+zero so that means this has to be zero
+
+ align:start position:0%
+zero so that means this has to be zero
+ 
+
+ align:start position:0%
+zero so that means this has to be zero
+that means we know the determinant of
+
+ align:start position:0%
+that means we know the determinant of
+ 
+
+ align:start position:0%
+that means we know the determinant of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and that'll give you the n in
+
+ align:start position:0%
+Matrix and that'll give you the n in
+ 
+
+ align:start position:0%
+Matrix and that'll give you the n in
+this case the two natural frequencies
+
+ align:start position:0%
+this case the two natural frequencies
+ 
+
+ align:start position:0%
+this case the two natural frequencies
+this gives you the Omega n's of the
+
+ align:start position:0%
+this gives you the Omega n's of the
+ 
+
+ align:start position:0%
+this gives you the Omega n's of the
+system Omega n squares is what you solve
+
+ align:start position:0%
+system Omega n squares is what you solve
+ 
+
+ align:start position:0%
+system Omega n squares is what you solve
+for okay and then you go back and you
+
+ align:start position:0%
+for okay and then you go back and you
+ 
+
+ align:start position:0%
+for okay and then you go back and you
+get the
+
+ align:start position:0%
+get the
+ 
+
+ align:start position:0%
+get the
+um the mode shapes out of it and but
+
+ align:start position:0%
+um the mode shapes out of it and but
+ 
+
+ align:start position:0%
+um the mode shapes out of it and but
+this you can do on the computer too you
+
+ align:start position:0%
+this you can do on the computer too you
+ 
+
+ align:start position:0%
+this you can do on the computer too you
+can either crank out the qu this gives
+
+ align:start position:0%
+can either crank out the qu this gives
+ 
+
+ align:start position:0%
+can either crank out the qu this gives
+you for a two degree Freedom system this
+
+ align:start position:0%
+you for a two degree Freedom system this
+ 
+
+ align:start position:0%
+you for a two degree Freedom system this
+gives you a quadratic you know Mega
+
+ align:start position:0%
+gives you a quadratic you know Mega
+ 
+
+ align:start position:0%
+gives you a quadratic you know Mega
+squar you solve it you plug it back in
+
+ align:start position:0%
+squar you solve it you plug it back in
+ 
+
+ align:start position:0%
+squar you solve it you plug it back in
+and get the mode shapes I'm not going to
+
+ align:start position:0%
+and get the mode shapes I'm not going to
+ 
+
+ align:start position:0%
+and get the mode shapes I'm not going to
+take the time to do that today because I
+
+ align:start position:0%
+take the time to do that today because I
+ 
+
+ align:start position:0%
+take the time to do that today because I
+want to do emphasize the modal analysis
+
+ align:start position:0%
+want to do emphasize the modal analysis
+ 
+
+ align:start position:0%
+want to do emphasize the modal analysis
+part so I'll give you the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answers where are we here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you get Omega 1 it's
+
+ align:start position:0%
+so you get Omega 1 it's
+ 
+
+ align:start position:0%
+so you get Omega 1 it's
+5 65 4 6 and I seem to be keeping a lot
+
+ align:start position:0%
+5 65 4 6 and I seem to be keeping a lot
+ 
+
+ align:start position:0%
+5 65 4 6 and I seem to be keeping a lot
+of lot of significant digits and there's
+
+ align:start position:0%
+of lot of significant digits and there's
+ 
+
+ align:start position:0%
+of lot of significant digits and there's
+a reason for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one of the reason you need in both
+
+ align:start position:0%
+that one of the reason you need in both
+ 
+
+ align:start position:0%
+that one of the reason you need in both
+mode shapes and natural frequencies you
+
+ align:start position:0%
+mode shapes and natural frequencies you
+ 
+
+ align:start position:0%
+mode shapes and natural frequencies you
+need to carry a lot of signal
+
+ align:start position:0%
+need to carry a lot of signal
+ 
+
+ align:start position:0%
+need to carry a lot of signal
+significant digits or modal analysis
+
+ align:start position:0%
+significant digits or modal analysis
+ 
+
+ align:start position:0%
+significant digits or modal analysis
+doesn't work or at least you don't get
+
+ align:start position:0%
+doesn't work or at least you don't get
+ 
+
+ align:start position:0%
+doesn't work or at least you don't get
+the clean results you expect if you're
+
+ align:start position:0%
+the clean results you expect if you're
+ 
+
+ align:start position:0%
+the clean results you expect if you're
+sloppy about the number of significant
+
+ align:start position:0%
+sloppy about the number of significant
+ 
+
+ align:start position:0%
+sloppy about the number of significant
+digits and you compute youu transpose mu
+
+ align:start position:0%
+digits and you compute youu transpose mu
+ 
+
+ align:start position:0%
+digits and you compute youu transpose mu
+the off diagonal terms won't quite go to
+
+ align:start position:0%
+the off diagonal terms won't quite go to
+ 
+
+ align:start position:0%
+the off diagonal terms won't quite go to
+zero and it's just because you're not
+
+ align:start position:0%
+zero and it's just because you're not
+ 
+
+ align:start position:0%
+zero and it's just because you're not
+carrying enough
+
+ align:start position:0%
+carrying enough
+ 
+
+ align:start position:0%
+carrying enough
+Precision okay now that's the two uh
+
+ align:start position:0%
+Precision okay now that's the two uh
+ 
+
+ align:start position:0%
+Precision okay now that's the two uh
+natural frequencies and now the U Matrix
+
+ align:start position:0%
+natural frequencies and now the U Matrix
+ 
+
+ align:start position:0%
+natural frequencies and now the U Matrix
+the mode shapes for this system that
+
+ align:start position:0%
+the mode shapes for this system that
+ 
+
+ align:start position:0%
+the mode shapes for this system that
+goes with that U comes out to be
+
+ align:start position:0%
+goes with that U comes out to be
+ 
+
+ align:start position:0%
+goes with that U comes out to be
+1.0
+
+ align:start position:0%
+1.0
+ 
+
+ align:start position:0%
+1.0
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2667 that's mode I'll do this to help
+
+ align:start position:0%
+2667 that's mode I'll do this to help
+ 
+
+ align:start position:0%
+2667 that's mode I'll do this to help
+you the columns are the mode shapes
+
+ align:start position:0%
+you the columns are the mode shapes
+ 
+
+ align:start position:0%
+you the columns are the mode shapes
+that's the first mode shape and the
+
+ align:start position:0%
+that's the first mode shape and the
+ 
+
+ align:start position:0%
+that's the first mode shape and the
+second mode
+
+ align:start position:0%
+second mode
+ 
+
+ align:start position:0%
+second mode
+shape is
+
+ align:start position:0%
+shape is
+ 
+
+ align:start position:0%
+shape is
+one and minus
+
+ align:start position:0%
+one and minus
+ 
+
+ align:start position:0%
+one and minus
+0 22 3
+
+ align:start position:0%
+0 22 3
+ 
+
+ align:start position:0%
+0 22 3
+six so that's your mode so those are the
+
+ align:start position:0%
+six so that's your mode so those are the
+ 
+
+ align:start position:0%
+six so that's your mode so those are the
+mode shapes for the first and second
+
+ align:start position:0%
+mode shapes for the first and second
+ 
+
+ align:start position:0%
+mode shapes for the first and second
+mode that go with these two natural
+
+ align:start position:0%
+mode that go with these two natural
+ 
+
+ align:start position:0%
+mode that go with these two natural
+frequencies so that's for this system
+
+ align:start position:0%
+frequencies so that's for this system
+ 
+
+ align:start position:0%
+frequencies so that's for this system
+the top one moves one unit the bottom
+
+ align:start position:0%
+the top one moves one unit the bottom
+ 
+
+ align:start position:0%
+the top one moves one unit the bottom
+one moves
+
+ align:start position:0%
+one moves
+ 
+
+ align:start position:0%
+one moves
+2.27 times that same direction positive
+
+ align:start position:0%
+2.27 times that same direction positive
+ 
+
+ align:start position:0%
+2.27 times that same direction positive
+positive the upper one moves one unit
+
+ align:start position:0%
+positive the upper one moves one unit
+ 
+
+ align:start position:0%
+positive the upper one moves one unit
+the bottom one moves the opposite
+
+ align:start position:0%
+the bottom one moves the opposite
+ 
+
+ align:start position:0%
+the bottom one moves the opposite
+direction that's the minus signs
+
+ align:start position:0%
+direction that's the minus signs
+ 
+
+ align:start position:0%
+direction that's the minus signs
+equivalent to a phase angle of
+
+ align:start position:0%
+equivalent to a phase angle of
+ 
+
+ align:start position:0%
+equivalent to a phase angle of
+180° minus 22% of the amount that the
+
+ align:start position:0%
+180° minus 22% of the amount that the
+ 
+
+ align:start position:0%
+180° minus 22% of the amount that the
+upper one moves so first one
+
+ align:start position:0%
+upper one moves so first one
+ 
+
+ align:start position:0%
+upper one moves so first one
+moves one unit the bottom one moves 2.2
+
+ align:start position:0%
+moves one unit the bottom one moves 2.2
+ 
+
+ align:start position:0%
+moves one unit the bottom one moves 2.2
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+that and in the second mode which is
+
+ align:start position:0%
+that and in the second mode which is
+ 
+
+ align:start position:0%
+that and in the second mode which is
+much harder to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going gu the only way I can do it is to
+
+ align:start position:0%
+going gu the only way I can do it is to
+ 
+
+ align:start position:0%
+going gu the only way I can do it is to
+do it the way Professor goser intended
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here one unit up and down
+
+ align:start position:0%
+here one unit up and down
+ 
+
+ align:start position:0%
+here one unit up and down
+minus 2236
+
+ align:start position:0%
+minus 2236
+ 
+
+ align:start position:0%
+minus 2236
+going the opposite way so those are our
+
+ align:start position:0%
+going the opposite way so those are our
+ 
+
+ align:start position:0%
+going the opposite way so those are our
+mode shapes these are the natural
+
+ align:start position:0%
+mode shapes these are the natural
+ 
+
+ align:start position:0%
+mode shapes these are the natural
+frequencies I calculated this one and
+
+ align:start position:0%
+frequencies I calculated this one and
+ 
+
+ align:start position:0%
+frequencies I calculated this one and
+measured it with stopwatch this one I
+
+ align:start position:0%
+measured it with stopwatch this one I
+ 
+
+ align:start position:0%
+measured it with stopwatch this one I
+can do watching it with a stopwatch and
+
+ align:start position:0%
+can do watching it with a stopwatch and
+ 
+
+ align:start position:0%
+can do watching it with a stopwatch and
+I came within less better than 1%
+
+ align:start position:0%
+I came within less better than 1%
+ 
+
+ align:start position:0%
+I came within less better than 1%
+getting the same
+
+ align:start position:0%
+getting the same
+ 
+
+ align:start position:0%
+getting the same
+number okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I carry I want my modal Mass Matrix I
+
+ align:start position:0%
+so I carry I want my modal Mass Matrix I
+ 
+
+ align:start position:0%
+so I carry I want my modal Mass Matrix I
+carry out this calculation and for this
+
+ align:start position:0%
+carry out this calculation and for this
+ 
+
+ align:start position:0%
+carry out this calculation and for this
+system remember it's going to give me
+
+ align:start position:0%
+system remember it's going to give me
+ 
+
+ align:start position:0%
+system remember it's going to give me
+back a diagonal matrix looking like
+
+ align:start position:0%
+back a diagonal matrix looking like
+ 
+
+ align:start position:0%
+back a diagonal matrix looking like
+this and in fact the numbers are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+35562 z0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+358 and when I can calculate U transpose
+
+ align:start position:0%
+358 and when I can calculate U transpose
+ 
+
+ align:start position:0%
+358 and when I can calculate U transpose
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+u gives me a diagonal stiffness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and I get the numbers 1 1
+
+ align:start position:0%
+Matrix and I get the numbers 1 1
+ 
+
+ align:start position:0%
+Matrix and I get the numbers 1 1
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1 and
+
+ align:start position:0%
+1 and
+ 
+
+ align:start position:0%
+1 and
+and 0
+
+ align:start position:0%
+and 0
+ 
+
+ align:start position:0%
+and 0
+0 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9839 and that's my diagonal diagonalized
+
+ align:start position:0%
+9839 and that's my diagonal diagonalized
+ 
+
+ align:start position:0%
+9839 and that's my diagonal diagonalized
+stiffness
+
+ align:start position:0%
+stiffness
+ 
+
+ align:start position:0%
+stiffness
+Matrix now something had better be true
+
+ align:start position:0%
+Matrix now something had better be true
+ 
+
+ align:start position:0%
+Matrix now something had better be true
+I'm saying that this is this is now
+
+ align:start position:0%
+I'm saying that this is this is now
+ 
+
+ align:start position:0%
+I'm saying that this is this is now
+going to give me my two independent
+
+ align:start position:0%
+going to give me my two independent
+ 
+
+ align:start position:0%
+going to give me my two independent
+single degree of Frum equations of
+
+ align:start position:0%
+single degree of Frum equations of
+ 
+
+ align:start position:0%
+single degree of Frum equations of
+motion right so I'm looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm seeking here I want to get
+
+ align:start position:0%
+so what I'm seeking here I want to get
+ 
+
+ align:start position:0%
+so what I'm seeking here I want to get
+two equations one that looks like
+
+ align:start position:0%
+two equations one that looks like
+ 
+
+ align:start position:0%
+two equations one that looks like
+M1 q1 dot plus
+
+ align:start position:0%
+M1 q1 dot plus
+ 
+
+ align:start position:0%
+M1 q1 dot plus
+C1 q1 dot plus K1 q1 equals zero for no
+
+ align:start position:0%
+C1 q1 dot plus K1 q1 equals zero for no
+ 
+
+ align:start position:0%
+C1 q1 dot plus K1 q1 equals zero for no
+external Force that's one of the
+
+ align:start position:0%
+external Force that's one of the
+ 
+
+ align:start position:0%
+external Force that's one of the
+equations I'm after and the other one it
+
+ align:start position:0%
+equations I'm after and the other one it
+ 
+
+ align:start position:0%
+equations I'm after and the other one it
+look like
+
+ align:start position:0%
+look like
+ 
+
+ align:start position:0%
+look like
+M2 Q2 dot plus c 2 Q2
+
+ align:start position:0%
+M2 Q2 dot plus c 2 Q2
+ 
+
+ align:start position:0%
+M2 Q2 dot plus c 2 Q2
+do K2
+
+ align:start position:0%
+do K2
+ 
+
+ align:start position:0%
+do K2
+Q2 now one way to check that you've
+
+ align:start position:0%
+Q2 now one way to check that you've
+ 
+
+ align:start position:0%
+Q2 now one way to check that you've
+gotten the right thing is now these are
+
+ align:start position:0%
+gotten the right thing is now these are
+ 
+
+ align:start position:0%
+gotten the right thing is now these are
+independent two independent single
+
+ align:start position:0%
+independent two independent single
+ 
+
+ align:start position:0%
+independent two independent single
+degree Freedom systems what's the
+
+ align:start position:0%
+degree Freedom systems what's the
+ 
+
+ align:start position:0%
+degree Freedom systems what's the
+natural frequency of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system yeah actually I heard somebody
+
+ align:start position:0%
+system yeah actually I heard somebody
+ 
+
+ align:start position:0%
+system yeah actually I heard somebody
+say square root of K1 over M1 that it
+
+ align:start position:0%
+say square root of K1 over M1 that it
+ 
+
+ align:start position:0%
+say square root of K1 over M1 that it
+better be true but what numerically
+
+ align:start position:0%
+better be true but what numerically
+ 
+
+ align:start position:0%
+better be true but what numerically
+what's the number what did it better
+
+ align:start position:0%
+what's the number what did it better
+ 
+
+ align:start position:0%
+what's the number what did it better
+be it better be the Omega 1 of the
+
+ align:start position:0%
+be it better be the Omega 1 of the
+ 
+
+ align:start position:0%
+be it better be the Omega 1 of the
+system right and so a check that you can
+
+ align:start position:0%
+system right and so a check that you can
+ 
+
+ align:start position:0%
+system right and so a check that you can
+perform is is to
+
+ align:start position:0%
+perform is is to
+ 
+
+ align:start position:0%
+perform is is to
+check to see if the Omega 1 squared
+
+ align:start position:0%
+check to see if the Omega 1 squared
+ 
+
+ align:start position:0%
+check to see if the Omega 1 squared
+equal K1 over M1 just you found two
+
+ align:start position:0%
+equal K1 over M1 just you found two
+ 
+
+ align:start position:0%
+equal K1 over M1 just you found two
+numbers you've got uh up here K1 is
+
+ align:start position:0%
+numbers you've got uh up here K1 is
+ 
+
+ align:start position:0%
+numbers you've got uh up here K1 is
+113.9
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M1 is 3.55 take K1 over
+
+ align:start position:0%
+M1 is 3.55 take K1 over
+ 
+
+ align:start position:0%
+M1 is 3.55 take K1 over
+M1 and take its square root so K1 over
+
+ align:start position:0%
+M1 and take its square root so K1 over
+ 
+
+ align:start position:0%
+M1 and take its square root so K1 over
+M1 that's about
+
+ align:start position:0%
+M1 that's about
+ 
+
+ align:start position:0%
+M1 that's about
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+something square root of 30 something is
+
+ align:start position:0%
+something square root of 30 something is
+ 
+
+ align:start position:0%
+something square root of 30 something is
+a little less than
+
+ align:start position:0%
+a little less than
+ 
+
+ align:start position:0%
+a little less than
+six Omega 1 is
+
+ align:start position:0%
+six Omega 1 is
+ 
+
+ align:start position:0%
+six Omega 1 is
+5.65 and the same thing Omega 2 had
+
+ align:start position:0%
+5.65 and the same thing Omega 2 had
+ 
+
+ align:start position:0%
+5.65 and the same thing Omega 2 had
+better be equal to the square < TK of
+
+ align:start position:0%
+better be equal to the square < TK of
+ 
+
+ align:start position:0%
+better be equal to the square < TK of
+K2 over M2 so one one of the things you
+
+ align:start position:0%
+K2 over M2 so one one of the things you
+ 
+
+ align:start position:0%
+K2 over M2 so one one of the things you
+can always do when you do your modal
+
+ align:start position:0%
+can always do when you do your modal
+ 
+
+ align:start position:0%
+can always do when you do your modal
+analysis you do your calculations youut
+
+ align:start position:0%
+analysis you do your calculations youut
+ 
+
+ align:start position:0%
+analysis you do your calculations youut
+transpose mu you transpose KU if you
+
+ align:start position:0%
+transpose mu you transpose KU if you
+ 
+
+ align:start position:0%
+transpose mu you transpose KU if you
+calculate the ratios of each one of
+
+ align:start position:0%
+calculate the ratios of each one of
+ 
+
+ align:start position:0%
+calculate the ratios of each one of
+these things you can go back and check
+
+ align:start position:0%
+these things you can go back and check
+ 
+
+ align:start position:0%
+these things you can go back and check
+and see the natural frequencies are the
+
+ align:start position:0%
+and see the natural frequencies are the
+ 
+
+ align:start position:0%
+and see the natural frequencies are the
+ones that you started with if you have
+
+ align:start position:0%
+ones that you started with if you have
+ 
+
+ align:start position:0%
+ones that you started with if you have
+if they are not then you've messed up in
+
+ align:start position:0%
+if they are not then you've messed up in
+ 
+
+ align:start position:0%
+if they are not then you've messed up in
+your arithmetic so now we've got our two
+
+ align:start position:0%
+your arithmetic so now we've got our two
+ 
+
+ align:start position:0%
+your arithmetic so now we've got our two
+impendent equations and the natural
+
+ align:start position:0%
+impendent equations and the natural
+ 
+
+ align:start position:0%
+impendent equations and the natural
+frequencies check
+
+ align:start position:0%
+frequencies check
+ 
+
+ align:start position:0%
+frequencies check
+out but we haven't uh we we still have a
+
+ align:start position:0%
+out but we haven't uh we we still have a
+ 
+
+ align:start position:0%
+out but we haven't uh we we still have a
+couple of things to deal with we have to
+
+ align:start position:0%
+couple of things to deal with we have to
+ 
+
+ align:start position:0%
+couple of things to deal with we have to
+figure out how to can calculate the
+
+ align:start position:0%
+figure out how to can calculate the
+ 
+
+ align:start position:0%
+figure out how to can calculate the
+initial conditions and we have to figure
+
+ align:start position:0%
+initial conditions and we have to figure
+ 
+
+ align:start position:0%
+initial conditions and we have to figure
+out how to deal with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+damping let's do
+
+ align:start position:0%
+damping let's do
+ 
+
+ align:start position:0%
+damping let's do
+initial I's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first so those of you who were here last
+
+ align:start position:0%
+first so those of you who were here last
+ 
+
+ align:start position:0%
+first so those of you who were here last
+time I ended kind right at the
+
+ align:start position:0%
+time I ended kind right at the
+ 
+
+ align:start position:0%
+time I ended kind right at the
+end we kind of worked our way through
+
+ align:start position:0%
+end we kind of worked our way through
+ 
+
+ align:start position:0%
+end we kind of worked our way through
+figuring out the initial conditions for
+
+ align:start position:0%
+figuring out the initial conditions for
+ 
+
+ align:start position:0%
+figuring out the initial conditions for
+a two degree Freedom system doing it the
+
+ align:start position:0%
+a two degree Freedom system doing it the
+ 
+
+ align:start position:0%
+a two degree Freedom system doing it the
+hard way end up with four equations and
+
+ align:start position:0%
+hard way end up with four equations and
+ 
+
+ align:start position:0%
+hard way end up with four equations and
+four unknowns for the A1 A2 F1 F2
+
+ align:start position:0%
+four unknowns for the A1 A2 F1 F2
+ 
+
+ align:start position:0%
+four unknowns for the A1 A2 F1 F2
+remember that I mean it's really
+
+ align:start position:0%
+remember that I mean it's really
+ 
+
+ align:start position:0%
+remember that I mean it's really
+painful there's a this this is
+
+ align:start position:0%
+painful there's a this this is
+ 
+
+ align:start position:0%
+painful there's a this this is
+incredibly easier we're going to do the
+
+ align:start position:0%
+incredibly easier we're going to do the
+ 
+
+ align:start position:0%
+incredibly easier we're going to do the
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+but extremely easily so I I would never
+
+ align:start position:0%
+but extremely easily so I I would never
+ 
+
+ align:start position:0%
+but extremely easily so I I would never
+go myself given the choice of grinding
+
+ align:start position:0%
+go myself given the choice of grinding
+ 
+
+ align:start position:0%
+go myself given the choice of grinding
+not all those phas angles and amplitudes
+
+ align:start position:0%
+not all those phas angles and amplitudes
+ 
+
+ align:start position:0%
+not all those phas angles and amplitudes
+I by in simultaneous equations I'd do
+
+ align:start position:0%
+I by in simultaneous equations I'd do
+ 
+
+ align:start position:0%
+I by in simultaneous equations I'd do
+the following how if I generally now I
+
+ align:start position:0%
+the following how if I generally now I
+ 
+
+ align:start position:0%
+the following how if I generally now I
+know the initial conditions are going to
+
+ align:start position:0%
+know the initial conditions are going to
+ 
+
+ align:start position:0%
+know the initial conditions are going to
+be specified not in Q coordinates but in
+
+ align:start position:0%
+be specified not in Q coordinates but in
+ 
+
+ align:start position:0%
+be specified not in Q coordinates but in
+what coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system your original generalized
+
+ align:start position:0%
+system your original generalized
+ 
+
+ align:start position:0%
+system your original generalized
+coordinates right you going to know
+
+ align:start position:0%
+coordinates right you going to know
+ 
+
+ align:start position:0%
+coordinates right you going to know
+you're X on this one the general if I'm
+
+ align:start position:0%
+you're X on this one the general if I'm
+ 
+
+ align:start position:0%
+you're X on this one the general if I'm
+going to set initial conditions here I'm
+
+ align:start position:0%
+going to set initial conditions here I'm
+ 
+
+ align:start position:0%
+going to set initial conditions here I'm
+not going to say q1 is equal to
+
+ align:start position:0%
+not going to say q1 is equal to
+ 
+
+ align:start position:0%
+not going to say q1 is equal to
+something I'm going to say I'm going to
+
+ align:start position:0%
+something I'm going to say I'm going to
+ 
+
+ align:start position:0%
+something I'm going to say I'm going to
+put this one down one unit and this one
+
+ align:start position:0%
+put this one down one unit and this one
+ 
+
+ align:start position:0%
+put this one down one unit and this one
+down two units and like go this is in X1
+
+ align:start position:0%
+down two units and like go this is in X1
+ 
+
+ align:start position:0%
+down two units and like go this is in X1
+and X2 coordinates but the beautiful
+
+ align:start position:0%
+and X2 coordinates but the beautiful
+ 
+
+ align:start position:0%
+and X2 coordinates but the beautiful
+thing here is that we know that
+
+ align:start position:0%
+thing here is that we know that
+ 
+
+ align:start position:0%
+thing here is that we know that
+x equals u
+
+ align:start position:0%
+x equals u
+ 
+
+ align:start position:0%
+x equals u
+q so if I know the initial conditions on
+
+ align:start position:0%
+q so if I know the initial conditions on
+ 
+
+ align:start position:0%
+q so if I know the initial conditions on
+I'll call it X knot
+
+ align:start position:0%
+I'll call it X knot
+ 
+
+ align:start position:0%
+I'll call it X knot
+here if I know the initial deflections
+
+ align:start position:0%
+here if I know the initial deflections
+ 
+
+ align:start position:0%
+here if I know the initial deflections
+of the system they're going to be U
+
+ align:start position:0%
+of the system they're going to be U
+ 
+
+ align:start position:0%
+of the system they're going to be U
+times the initial value the initial
+
+ align:start position:0%
+times the initial value the initial
+ 
+
+ align:start position:0%
+times the initial value the initial
+values of Q
+
+ align:start position:0%
+values of Q
+ 
+
+ align:start position:0%
+values of Q
+and if I know a vector of initial
+
+ align:start position:0%
+and if I know a vector of initial
+ 
+
+ align:start position:0%
+and if I know a vector of initial
+velocities at Time Zero they're going to
+
+ align:start position:0%
+velocities at Time Zero they're going to
+ 
+
+ align:start position:0%
+velocities at Time Zero they're going to
+be U q0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot so if I told you values of X knot
+
+ align:start position:0%
+dot so if I told you values of X knot
+ 
+
+ align:start position:0%
+dot so if I told you values of X knot
+and I and you know that this equation is
+
+ align:start position:0%
+and I and you know that this equation is
+ 
+
+ align:start position:0%
+and I and you know that this equation is
+true what we need is Q the Q knots we
+
+ align:start position:0%
+true what we need is Q the Q knots we
+ 
+
+ align:start position:0%
+true what we need is Q the Q knots we
+need the initial conditions in that in a
+
+ align:start position:0%
+need the initial conditions in that in a
+ 
+
+ align:start position:0%
+need the initial conditions in that in a
+modal coordinates in order to finish
+
+ align:start position:0%
+modal coordinates in order to finish
+ 
+
+ align:start position:0%
+modal coordinates in order to finish
+this problem how would you get if I told
+
+ align:start position:0%
+this problem how would you get if I told
+ 
+
+ align:start position:0%
+this problem how would you get if I told
+you this how would you solve for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just a little linear algebra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here inverse Matrix of you yeah do what
+
+ align:start position:0%
+here inverse Matrix of you yeah do what
+ 
+
+ align:start position:0%
+here inverse Matrix of you yeah do what
+with it and you multiply multipli
+
+ align:start position:0%
+with it and you multiply multipli
+ 
+
+ align:start position:0%
+with it and you multiply multipli
+by U inverse right okay so this
+
+ align:start position:0%
+by U inverse right okay so this
+ 
+
+ align:start position:0%
+by U inverse right okay so this
+implies
+
+ align:start position:0%
+implies
+ 
+
+ align:start position:0%
+implies
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not well better I'll write it out a
+
+ align:start position:0%
+not well better I'll write it out a
+ 
+
+ align:start position:0%
+not well better I'll write it out a
+little more fully here so if I
+
+ align:start position:0%
+little more fully here so if I
+ 
+
+ align:start position:0%
+little more fully here so if I
+do U
+
+ align:start position:0%
+do U
+ 
+
+ align:start position:0%
+do U
+inverse X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knot that's going to be equal to U
+
+ align:start position:0%
+knot that's going to be equal to U
+ 
+
+ align:start position:0%
+knot that's going to be equal to U
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+u q
+
+ align:start position:0%
+u q
+ 
+
+ align:start position:0%
+u q
+knot U inverse time U gives you one
+
+ align:start position:0%
+knot U inverse time U gives you one
+ 
+
+ align:start position:0%
+knot U inverse time U gives you one
+basically right and so I have just if I
+
+ align:start position:0%
+basically right and so I have just if I
+ 
+
+ align:start position:0%
+basically right and so I have just if I
+do U inverse X
+
+ align:start position:0%
+do U inverse X
+ 
+
+ align:start position:0%
+do U inverse X
+knot I get Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's all there is to it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I C is a problem okay I'm leaving
+
+ align:start position:0%
+yeah I C is a problem okay I'm leaving
+ 
+
+ align:start position:0%
+yeah I C is a problem okay I'm leaving
+it I'm leaving it to the end we're going
+
+ align:start position:0%
+it I'm leaving it to the end we're going
+ 
+
+ align:start position:0%
+it I'm leaving it to the end we're going
+to deal with it as the last step and if
+
+ align:start position:0%
+to deal with it as the last step and if
+ 
+
+ align:start position:0%
+to deal with it as the last step and if
+I have initial velocities U inverse
+
+ align:start position:0%
+I have initial velocities U inverse
+ 
+
+ align:start position:0%
+I have initial velocities U inverse
+times x initial velocities Vector I get
+
+ align:start position:0%
+times x initial velocities Vector I get
+ 
+
+ align:start position:0%
+times x initial velocities Vector I get
+the initial velocities Vector in the
+
+ align:start position:0%
+the initial velocities Vector in the
+ 
+
+ align:start position:0%
+the initial velocities Vector in the
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+coordinates so that's how simple it is
+
+ align:start position:0%
+coordinates so that's how simple it is
+ 
+
+ align:start position:0%
+coordinates so that's how simple it is
+to get the initial conditions in modal
+
+ align:start position:0%
+to get the initial conditions in modal
+ 
+
+ align:start position:0%
+to get the initial conditions in modal
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+boom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we're going to we'll do a
+
+ align:start position:0%
+okay and we're going to we'll do a
+ 
+
+ align:start position:0%
+okay and we're going to we'll do a
+numerical example in a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we're looking for we're seeking a
+
+ align:start position:0%
+here we're looking for we're seeking a
+ 
+
+ align:start position:0%
+here we're looking for we're seeking a
+solution of the
+
+ align:start position:0%
+solution of the
+ 
+
+ align:start position:0%
+solution of the
+form to do initial to do uh response to
+
+ align:start position:0%
+form to do initial to do uh response to
+ 
+
+ align:start position:0%
+form to do initial to do uh response to
+initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions we seek
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations that we know a right for a
+
+ align:start position:0%
+equations that we know a right for a
+ 
+
+ align:start position:0%
+equations that we know a right for a
+single degree of Freedom system response
+
+ align:start position:0%
+single degree of Freedom system response
+ 
+
+ align:start position:0%
+single degree of Freedom system response
+to initial conditions so we know that
+
+ align:start position:0%
+to initial conditions so we know that
+ 
+
+ align:start position:0%
+to initial conditions so we know that
+for a single degree of Freedom system X
+
+ align:start position:0%
+for a single degree of Freedom system X
+ 
+
+ align:start position:0%
+for a single degree of Freedom system X
+of T this is for SDF for
+
+ align:start position:0%
+of T this is for SDF for
+ 
+
+ align:start position:0%
+of T this is for SDF for
+SDF system
+
+ align:start position:0%
+SDF system
+ 
+
+ align:start position:0%
+SDF system
+here x of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've worked out before is equal to some
+
+ align:start position:0%
+we've worked out before is equal to some
+ 
+
+ align:start position:0%
+we've worked out before is equal to some
+e to the minus Zeta Omega n t this is
+
+ align:start position:0%
+e to the minus Zeta Omega n t this is
+ 
+
+ align:start position:0%
+e to the minus Zeta Omega n t this is
+just a transient Decay problem of
+
+ align:start position:0%
+just a transient Decay problem of
+ 
+
+ align:start position:0%
+just a transient Decay problem of
+xnot cosine Omega
+
+ align:start position:0%
+xnot cosine Omega
+ 
+
+ align:start position:0%
+xnot cosine Omega
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+V plus Zeta Omega n x
+
+ align:start position:0%
+V plus Zeta Omega n x
+ 
+
+ align:start position:0%
+V plus Zeta Omega n x
+knot all over Omega
+
+ align:start position:0%
+knot all over Omega
+ 
+
+ align:start position:0%
+knot all over Omega
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+sin Omega DT we know that that's what
+
+ align:start position:0%
+sin Omega DT we know that that's what
+ 
+
+ align:start position:0%
+sin Omega DT we know that that's what
+the response of a single degree Freedom
+
+ align:start position:0%
+the response of a single degree Freedom
+ 
+
+ align:start position:0%
+the response of a single degree Freedom
+system looks like to initial conditions
+
+ align:start position:0%
+system looks like to initial conditions
+ 
+
+ align:start position:0%
+system looks like to initial conditions
+X knot and V
+
+ align:start position:0%
+X knot and V
+ 
+
+ align:start position:0%
+X knot and V
+KN and for light damping for small
+
+ align:start position:0%
+KN and for light damping for small
+ 
+
+ align:start position:0%
+KN and for light damping for small
+damping you can off usually even ignore
+
+ align:start position:0%
+damping you can off usually even ignore
+ 
+
+ align:start position:0%
+damping you can off usually even ignore
+this term so it's just it's even
+
+ align:start position:0%
+this term so it's just it's even
+ 
+
+ align:start position:0%
+this term so it's just it's even
+simpler this term is usually small
+
+ align:start position:0%
+simpler this term is usually small
+ 
+
+ align:start position:0%
+simpler this term is usually small
+compared to the
+
+ align:start position:0%
+compared to the
+ 
+
+ align:start position:0%
+compared to the
+all right small this term contribution
+
+ align:start position:0%
+all right small this term contribution
+ 
+
+ align:start position:0%
+all right small this term contribution
+from X notot is small compared to this
+
+ align:start position:0%
+from X notot is small compared to this
+ 
+
+ align:start position:0%
+from X notot is small compared to this
+term so it's basically dominated by an x
+
+ align:start position:0%
+term so it's basically dominated by an x
+ 
+
+ align:start position:0%
+term so it's basically dominated by an x
+cosine and a v over Omega D sin but
+
+ align:start position:0%
+cosine and a v over Omega D sin but
+ 
+
+ align:start position:0%
+cosine and a v over Omega D sin but
+that's the we know that's the exact
+
+ align:start position:0%
+that's the we know that's the exact
+ 
+
+ align:start position:0%
+that's the we know that's the exact
+response to a a single degree Freedom
+
+ align:start position:0%
+response to a a single degree Freedom
+ 
+
+ align:start position:0%
+response to a a single degree Freedom
+system to initial conditions so just by
+
+ align:start position:0%
+system to initial conditions so just by
+ 
+
+ align:start position:0%
+system to initial conditions so just by
+analogy to that we're looking for for
+
+ align:start position:0%
+analogy to that we're looking for for
+ 
+
+ align:start position:0%
+analogy to that we're looking for for
+mode one in modal coordinates it's going
+
+ align:start position:0%
+mode one in modal coordinates it's going
+ 
+
+ align:start position:0%
+mode one in modal coordinates it's going
+to look exactly the same way e the minus
+
+ align:start position:0%
+to look exactly the same way e the minus
+ 
+
+ align:start position:0%
+to look exactly the same way e the minus
+Theta Omega n t
+
+ align:start position:0%
+Theta Omega n t
+ 
+
+ align:start position:0%
+Theta Omega n t
+Q
+
+ align:start position:0%
+Q
+ 
+
+ align:start position:0%
+Q
+not cosine Omega
+
+ align:start position:0%
+not cosine Omega
+ 
+
+ align:start position:0%
+not cosine Omega
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+D this is Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT plus Q KN dot plus Zeta 1 Omega
+
+ align:start position:0%
+DT plus Q KN dot plus Zeta 1 Omega
+ 
+
+ align:start position:0%
+DT plus Q KN dot plus Zeta 1 Omega
+1 Q KN I guess I need to do q1
+
+ align:start position:0%
+1 Q KN I guess I need to do q1
+ 
+
+ align:start position:0%
+1 Q KN I guess I need to do q1
+KN like
+
+ align:start position:0%
+KN like
+ 
+
+ align:start position:0%
+KN like
+that this is the mo first modes equation
+
+ align:start position:0%
+that this is the mo first modes equation
+ 
+
+ align:start position:0%
+that this is the mo first modes equation
+Zeta 1 and I'll call this Omega one but
+
+ align:start position:0%
+Zeta 1 and I'll call this Omega one but
+ 
+
+ align:start position:0%
+Zeta 1 and I'll call this Omega one but
+now that you get multiple degree Freedom
+
+ align:start position:0%
+now that you get multiple degree Freedom
+ 
+
+ align:start position:0%
+now that you get multiple degree Freedom
+systems you got to keep track of what
+
+ align:start position:0%
+systems you got to keep track of what
+ 
+
+ align:start position:0%
+systems you got to keep track of what
+mode you're talking about mode one
+
+ align:start position:0%
+mode you're talking about mode one
+ 
+
+ align:start position:0%
+mode you're talking about mode one
+damping ratio mode one natural frequency
+
+ align:start position:0%
+damping ratio mode one natural frequency
+ 
+
+ align:start position:0%
+damping ratio mode one natural frequency
+mode One initial displacement mode One
+
+ align:start position:0%
+mode One initial displacement mode One
+ 
+
+ align:start position:0%
+mode One initial displacement mode One
+initial velocity mode
+
+ align:start position:0%
+initial velocity mode
+ 
+
+ align:start position:0%
+initial velocity mode
+one Omega 1 D like that and mode two is
+
+ align:start position:0%
+one Omega 1 D like that and mode two is
+ 
+
+ align:start position:0%
+one Omega 1 D like that and mode two is
+going to be exactly analogous
+
+ align:start position:0%
+going to be exactly analogous
+ 
+
+ align:start position:0%
+going to be exactly analogous
+Q2 equals and
+
+ align:start position:0%
+Q2 equals and
+ 
+
+ align:start position:0%
+Q2 equals and
+it's exactly similar except you put it
+
+ align:start position:0%
+it's exactly similar except you put it
+ 
+
+ align:start position:0%
+it's exactly similar except you put it
+update it with a two instead of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and if you plug in the initial you
+
+ align:start position:0%
+one and if you plug in the initial you
+ 
+
+ align:start position:0%
+one and if you plug in the initial you
+over here have found the initial values
+
+ align:start position:0%
+over here have found the initial values
+ 
+
+ align:start position:0%
+over here have found the initial values
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+Q one and one KN and Q2 KN and q1 do not
+
+ align:start position:0%
+Q one and one KN and Q2 KN and q1 do not
+ 
+
+ align:start position:0%
+Q one and one KN and Q2 KN and q1 do not
+and so forth you found the initial
+
+ align:start position:0%
+and so forth you found the initial
+ 
+
+ align:start position:0%
+and so forth you found the initial
+values that go plug into that equation
+
+ align:start position:0%
+values that go plug into that equation
+ 
+
+ align:start position:0%
+values that go plug into that equation
+by just doing
+
+ align:start position:0%
+by just doing
+ 
+
+ align:start position:0%
+by just doing
+this and once we have this then we can
+
+ align:start position:0%
+this and once we have this then we can
+ 
+
+ align:start position:0%
+this and once we have this then we can
+go back to saying how do you get to the
+
+ align:start position:0%
+go back to saying how do you get to the
+ 
+
+ align:start position:0%
+go back to saying how do you get to the
+get back to the final answer well you
+
+ align:start position:0%
+get back to the final answer well you
+ 
+
+ align:start position:0%
+get back to the final answer well you
+just multiply the result for Q times the
+
+ align:start position:0%
+just multiply the result for Q times the
+ 
+
+ align:start position:0%
+just multiply the result for Q times the
+mode shape and add them up and you have
+
+ align:start position:0%
+mode shape and add them up and you have
+ 
+
+ align:start position:0%
+mode shape and add them up and you have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+answer but we still have to deal with
+
+ align:start position:0%
+answer but we still have to deal with
+ 
+
+ align:start position:0%
+answer but we still have to deal with
+the damping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem I'm going to do that one next
+
+ align:start position:0%
+problem I'm going to do that one next
+ 
+
+ align:start position:0%
+problem I'm going to do that one next
+but I see a bunch of hands and some
+
+ align:start position:0%
+but I see a bunch of hands and some
+ 
+
+ align:start position:0%
+but I see a bunch of hands and some
+puzzled look so it means it's a good
+
+ align:start position:0%
+puzzled look so it means it's a good
+ 
+
+ align:start position:0%
+puzzled look so it means it's a good
+time to stop and talk for a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah pardon do I can't quite hear it S I
+
+ align:start position:0%
+yeah pardon do I can't quite hear it S I
+ 
+
+ align:start position:0%
+yeah pardon do I can't quite hear it S I
+mean s Omega DT yeah what about why do
+
+ align:start position:0%
+mean s Omega DT yeah what about why do
+ 
+
+ align:start position:0%
+mean s Omega DT yeah what about why do
+we lose it why do we use it lose it oh
+
+ align:start position:0%
+we lose it why do we use it lose it oh
+ 
+
+ align:start position:0%
+we lose it why do we use it lose it oh
+you don't lose it I was saying see this
+
+ align:start position:0%
+you don't lose it I was saying see this
+ 
+
+ align:start position:0%
+you don't lose it I was saying see this
+is this bit it's like that these are two
+
+ align:start position:0%
+is this bit it's like that these are two
+ 
+
+ align:start position:0%
+is this bit it's like that these are two
+pieces that behave like
+
+ align:start position:0%
+pieces that behave like
+ 
+
+ align:start position:0%
+pieces that behave like
+sign and this see this one depends on
+
+ align:start position:0%
+sign and this see this one depends on
+ 
+
+ align:start position:0%
+sign and this see this one depends on
+initial displacement but it's multiplied
+
+ align:start position:0%
+initial displacement but it's multiplied
+ 
+
+ align:start position:0%
+initial displacement but it's multiplied
+by the damping ratio the damping ratio
+
+ align:start position:0%
+by the damping ratio the damping ratio
+ 
+
+ align:start position:0%
+by the damping ratio the damping ratio
+for things that are interesting is
+
+ align:start position:0%
+for things that are interesting is
+ 
+
+ align:start position:0%
+for things that are interesting is
+usually pretty small so here you have a
+
+ align:start position:0%
+usually pretty small so here you have a
+ 
+
+ align:start position:0%
+usually pretty small so here you have a
+term that's xot cosine Omega 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+damped and here you have a contribution
+
+ align:start position:0%
+damped and here you have a contribution
+ 
+
+ align:start position:0%
+damped and here you have a contribution
+that's X notot small time x not sine
+
+ align:start position:0%
+that's X notot small time x not sine
+ 
+
+ align:start position:0%
+that's X notot small time x not sine
+Omega one Mega one damped so you
+
+ align:start position:0%
+Omega one Mega one damped so you
+ 
+
+ align:start position:0%
+Omega one Mega one damped so you
+multiply the same they're operating the
+
+ align:start position:0%
+multiply the same they're operating the
+ 
+
+ align:start position:0%
+multiply the same they're operating the
+same frequency two terms at the same
+
+ align:start position:0%
+same frequency two terms at the same
+ 
+
+ align:start position:0%
+same frequency two terms at the same
+frequency add them together it's like a
+
+ align:start position:0%
+frequency add them together it's like a
+ 
+
+ align:start position:0%
+frequency add them together it's like a
+cosine Omega T minus some phase angle if
+
+ align:start position:0%
+cosine Omega T minus some phase angle if
+ 
+
+ align:start position:0%
+cosine Omega T minus some phase angle if
+this little term is small that phase
+
+ align:start position:0%
+this little term is small that phase
+ 
+
+ align:start position:0%
+this little term is small that phase
+angle is almost zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cosine x cosine plus something x s it
+
+ align:start position:0%
+cosine x cosine plus something x s it
+ 
+
+ align:start position:0%
+cosine x cosine plus something x s it
+gives you a cosine term that has shifted
+
+ align:start position:0%
+gives you a cosine term that has shifted
+ 
+
+ align:start position:0%
+gives you a cosine term that has shifted
+a little bit and it's at magnitude is
+
+ align:start position:0%
+a little bit and it's at magnitude is
+ 
+
+ align:start position:0%
+a little bit and it's at magnitude is
+different by this little amount I'm just
+
+ align:start position:0%
+different by this little amount I'm just
+ 
+
+ align:start position:0%
+different by this little amount I'm just
+saying often times this is small but if
+
+ align:start position:0%
+saying often times this is small but if
+ 
+
+ align:start position:0%
+saying often times this is small but if
+you don't want to make that
+
+ align:start position:0%
+you don't want to make that
+ 
+
+ align:start position:0%
+you don't want to make that
+approximation just carry it along just
+
+ align:start position:0%
+approximation just carry it along just
+ 
+
+ align:start position:0%
+approximation just carry it along just
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it oh no and I'm not throw I'm just
+
+ align:start position:0%
+it oh no and I'm not throw I'm just
+ 
+
+ align:start position:0%
+it oh no and I'm not throw I'm just
+saying you can take you can throw out
+
+ align:start position:0%
+saying you can take you can throw out
+ 
+
+ align:start position:0%
+saying you can take you can throw out
+this piece usually and it's simply it
+
+ align:start position:0%
+this piece usually and it's simply it
+ 
+
+ align:start position:0%
+this piece usually and it's simply it
+makes I keep in my
+
+ align:start position:0%
+makes I keep in my
+ 
+
+ align:start position:0%
+makes I keep in my
+mind vibr let me let me say kind of
+
+ align:start position:0%
+mind vibr let me let me say kind of
+ 
+
+ align:start position:0%
+mind vibr let me let me say kind of
+vibration engineering is full of lots of
+
+ align:start position:0%
+vibration engineering is full of lots of
+ 
+
+ align:start position:0%
+vibration engineering is full of lots of
+approximations because it's very hard to
+
+ align:start position:0%
+approximations because it's very hard to
+ 
+
+ align:start position:0%
+approximations because it's very hard to
+get oftentimes to get detailed
+
+ align:start position:0%
+get oftentimes to get detailed
+ 
+
+ align:start position:0%
+get oftentimes to get detailed
+quantitative numbers on exactly
+
+ align:start position:0%
+quantitative numbers on exactly
+ 
+
+ align:start position:0%
+quantitative numbers on exactly
+everything you need to know so I carry
+
+ align:start position:0%
+everything you need to know so I carry
+ 
+
+ align:start position:0%
+everything you need to know so I carry
+around little approximations that I know
+
+ align:start position:0%
+around little approximations that I know
+ 
+
+ align:start position:0%
+around little approximations that I know
+is the way the world mostly behaves and
+
+ align:start position:0%
+is the way the world mostly behaves and
+ 
+
+ align:start position:0%
+is the way the world mostly behaves and
+the way the world mostly behaves for a
+
+ align:start position:0%
+the way the world mostly behaves for a
+ 
+
+ align:start position:0%
+the way the world mostly behaves for a
+single degree Freedom system is the
+
+ align:start position:0%
+single degree Freedom system is the
+ 
+
+ align:start position:0%
+single degree Freedom system is the
+response to initial conditions looks
+
+ align:start position:0%
+response to initial conditions looks
+ 
+
+ align:start position:0%
+response to initial conditions looks
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this initial value here is always
+
+ align:start position:0%
+and this initial value here is always
+ 
+
+ align:start position:0%
+and this initial value here is always
+approximately X
+
+ align:start position:0%
+approximately X
+ 
+
+ align:start position:0%
+approximately X
+knot and this initial slope here is
+
+ align:start position:0%
+knot and this initial slope here is
+ 
+
+ align:start position:0%
+knot and this initial slope here is
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+approximately uh tell the slope is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vot that's the
+
+ align:start position:0%
+vot that's the
+ 
+
+ align:start position:0%
+vot that's the
+slope now it turns out that this thing
+
+ align:start position:0%
+slope now it turns out that this thing
+ 
+
+ align:start position:0%
+slope now it turns out that this thing
+has shifted just it's shifted just
+
+ align:start position:0%
+has shifted just it's shifted just
+ 
+
+ align:start position:0%
+has shifted just it's shifted just
+slightly why because of this
+
+ align:start position:0%
+slightly why because of this
+ 
+
+ align:start position:0%
+slightly why because of this
+term okay but I honest tell you the
+
+ align:start position:0%
+term okay but I honest tell you the
+ 
+
+ align:start position:0%
+term okay but I honest tell you the
+truth it almost really rarely matters so
+
+ align:start position:0%
+truth it almost really rarely matters so
+ 
+
+ align:start position:0%
+truth it almost really rarely matters so
+as a vibration engineer I often times
+
+ align:start position:0%
+as a vibration engineer I often times
+ 
+
+ align:start position:0%
+as a vibration engineer I often times
+just I just remember I have an xot
+
+ align:start position:0%
+just I just remember I have an xot
+ 
+
+ align:start position:0%
+just I just remember I have an xot
+cosine I have a vot over Mega D sign and
+
+ align:start position:0%
+cosine I have a vot over Mega D sign and
+ 
+
+ align:start position:0%
+cosine I have a vot over Mega D sign and
+the whole thing decays like that but if
+
+ align:start position:0%
+the whole thing decays like that but if
+ 
+
+ align:start position:0%
+the whole thing decays like that but if
+you like to be mathematically precise
+
+ align:start position:0%
+you like to be mathematically precise
+ 
+
+ align:start position:0%
+you like to be mathematically precise
+you carry along that little bit
+
+ align:start position:0%
+you carry along that little bit
+ 
+
+ align:start position:0%
+you carry along that little bit
+yeah you're not going to lose a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign oh oh wait a minute I just left it
+
+ align:start position:0%
+sign oh oh wait a minute I just left it
+ 
+
+ align:start position:0%
+sign oh oh wait a minute I just left it
+out ah you guys well I'm glad you're
+
+ align:start position:0%
+out ah you guys well I'm glad you're
+ 
+
+ align:start position:0%
+out ah you guys well I'm glad you're
+awake this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good now how's that ah good now I know
+
+ align:start position:0%
+good now how's that ah good now I know
+ 
+
+ align:start position:0%
+good now how's that ah good now I know
+how I had so many puzzled puzzle looks
+
+ align:start position:0%
+how I had so many puzzled puzzle looks
+ 
+
+ align:start position:0%
+how I had so many puzzled puzzle looks
+anybody have a different question just
+
+ align:start position:0%
+anybody have a different question just
+ 
+
+ align:start position:0%
+anybody have a different question just
+anything now about this whole modal
+
+ align:start position:0%
+anything now about this whole modal
+ 
+
+ align:start position:0%
+anything now about this whole modal
+analysis thing because then we have to
+
+ align:start position:0%
+analysis thing because then we have to
+ 
+
+ align:start position:0%
+analysis thing because then we have to
+deal with this awkward part that has to
+
+ align:start position:0%
+deal with this awkward part that has to
+ 
+
+ align:start position:0%
+deal with this awkward part that has to
+do with the
+
+ align:start position:0%
+do with the
+ 
+
+ align:start position:0%
+do with the
+damping and I got to finish on time
+
+ align:start position:0%
+damping and I got to finish on time
+ 
+
+ align:start position:0%
+damping and I got to finish on time
+okay the
+
+ align:start position:0%
+okay the
+ 
+
+ align:start position:0%
+okay the
+um all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so damping I've gotten this far I have
+
+ align:start position:0%
+so damping I've gotten this far I have
+ 
+
+ align:start position:0%
+so damping I've gotten this far I have
+what I need is I need estimates for the
+
+ align:start position:0%
+what I need is I need estimates for the
+ 
+
+ align:start position:0%
+what I need is I need estimates for the
+for the damping for uh mode one and
+
+ align:start position:0%
+for the damping for uh mode one and
+ 
+
+ align:start position:0%
+for the damping for uh mode one and
+damping for mode two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+u c u does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+equal some nice
+
+ align:start position:0%
+equal some nice
+ 
+
+ align:start position:0%
+equal some nice
+diagonalized Matrix you sometimes get
+
+ align:start position:0%
+diagonalized Matrix you sometimes get
+ 
+
+ align:start position:0%
+diagonalized Matrix you sometimes get
+these are not always zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it just the orthogonality principle
+
+ align:start position:0%
+okay it just the orthogonality principle
+ 
+
+ align:start position:0%
+okay it just the orthogonality principle
+just doesn't apply to the damping
+
+ align:start position:0%
+just doesn't apply to the damping
+ 
+
+ align:start position:0%
+just doesn't apply to the damping
+terms just
+
+ align:start position:0%
+terms just
+ 
+
+ align:start position:0%
+terms just
+doesn't and but hasn't but this actually
+
+ align:start position:0%
+doesn't and but hasn't but this actually
+ 
+
+ align:start position:0%
+doesn't and but hasn't but this actually
+doesn't hurt you a lot you just got to
+
+ align:start position:0%
+doesn't hurt you a lot you just got to
+ 
+
+ align:start position:0%
+doesn't hurt you a lot you just got to
+know that this is going to be a problem
+
+ align:start position:0%
+know that this is going to be a problem
+ 
+
+ align:start position:0%
+know that this is going to be a problem
+and when the systems are lightly damped
+
+ align:start position:0%
+and when the systems are lightly damped
+ 
+
+ align:start position:0%
+and when the systems are lightly damped
+the approximation even if you're the
+
+ align:start position:0%
+the approximation even if you're the
+ 
+
+ align:start position:0%
+the approximation even if you're the
+true damping in the system gives you
+
+ align:start position:0%
+true damping in the system gives you
+ 
+
+ align:start position:0%
+true damping in the system gives you
+some nonzero elements here the the first
+
+ align:start position:0%
+some nonzero elements here the the first
+ 
+
+ align:start position:0%
+some nonzero elements here the the first
+order behavior of the system is
+
+ align:start position:0%
+order behavior of the system is
+ 
+
+ align:start position:0%
+order behavior of the system is
+basically going to be you can just
+
+ align:start position:0%
+basically going to be you can just
+ 
+
+ align:start position:0%
+basically going to be you can just
+ignore the off diagonal elements what
+
+ align:start position:0%
+ignore the off diagonal elements what
+ 
+
+ align:start position:0%
+ignore the off diagonal elements what
+practical consequence do you think it
+
+ align:start position:0%
+practical consequence do you think it
+ 
+
+ align:start position:0%
+practical consequence do you think it
+has if these if you have some actual
+
+ align:start position:0%
+has if these if you have some actual
+ 
+
+ align:start position:0%
+has if these if you have some actual
+nonzero numbers
+
+ align:start position:0%
+nonzero numbers
+ 
+
+ align:start position:0%
+nonzero numbers
+here go back and look at the equations
+
+ align:start position:0%
+here go back and look at the equations
+ 
+
+ align:start position:0%
+here go back and look at the equations
+that you were trying to
+
+ align:start position:0%
+that you were trying to
+ 
+
+ align:start position:0%
+that you were trying to
+derive it's these were the equations
+
+ align:start position:0%
+derive it's these were the equations
+ 
+
+ align:start position:0%
+derive it's these were the equations
+that we were trying to come up with and
+
+ align:start position:0%
+that we were trying to come up with and
+ 
+
+ align:start position:0%
+that we were trying to come up with and
+we wanted them to be in
+
+ align:start position:0%
+we wanted them to be in
+ 
+
+ align:start position:0%
+we wanted them to be in
+individual single degree Freedom systems
+
+ align:start position:0%
+individual single degree Freedom systems
+ 
+
+ align:start position:0%
+individual single degree Freedom systems
+but if this has off non-zero off
+
+ align:start position:0%
+but if this has off non-zero off
+ 
+
+ align:start position:0%
+but if this has off non-zero off
+diagonal terms you're going to find
+
+ align:start position:0%
+diagonal terms you're going to find
+ 
+
+ align:start position:0%
+diagonal terms you're going to find
+popping up in this single degree Freedom
+
+ align:start position:0%
+popping up in this single degree Freedom
+ 
+
+ align:start position:0%
+popping up in this single degree Freedom
+equation another term that couples it
+
+ align:start position:0%
+equation another term that couples it
+ 
+
+ align:start position:0%
+equation another term that couples it
+through damping to the other modes it
+
+ align:start position:0%
+through damping to the other modes it
+ 
+
+ align:start position:0%
+through damping to the other modes it
+provides a little bit of coupling to the
+
+ align:start position:0%
+provides a little bit of coupling to the
+ 
+
+ align:start position:0%
+provides a little bit of coupling to the
+other to other modes they can talk to
+
+ align:start position:0%
+other to other modes they can talk to
+ 
+
+ align:start position:0%
+other to other modes they can talk to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+another all right and what that means is
+
+ align:start position:0%
+another all right and what that means is
+ 
+
+ align:start position:0%
+another all right and what that means is
+if I this may be a good time to do the
+
+ align:start position:0%
+if I this may be a good time to do the
+ 
+
+ align:start position:0%
+if I this may be a good time to do the
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+demonstration um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do I want to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if the initial displacement of the
+
+ align:start position:0%
+this if the initial displacement of the
+ 
+
+ align:start position:0%
+this if the initial displacement of the
+system is in the
+
+ align:start position:0%
+system is in the
+ 
+
+ align:start position:0%
+system is in the
+shape of one of the natural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modes so if this is some U this is
+
+ align:start position:0%
+modes so if this is some U this is
+ 
+
+ align:start position:0%
+modes so if this is some U this is
+exactly shaped like mode R so this looks
+
+ align:start position:0%
+exactly shaped like mode R so this looks
+ 
+
+ align:start position:0%
+exactly shaped like mode R so this looks
+like the UR Vector when I multiply it by
+
+ align:start position:0%
+like the UR Vector when I multiply it by
+ 
+
+ align:start position:0%
+like the UR Vector when I multiply it by
+this in when I when I multiply when I
+
+ align:start position:0%
+this in when I when I multiply when I
+ 
+
+ align:start position:0%
+this in when I when I multiply when I
+carry out this
+
+ align:start position:0%
+carry out this
+ 
+
+ align:start position:0%
+carry out this
+multiplication what do you think will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen if this shape if this is shaped
+
+ align:start position:0%
+happen if this shape if this is shaped
+ 
+
+ align:start position:0%
+happen if this shape if this is shaped
+like modar because of
+
+ align:start position:0%
+like modar because of
+ 
+
+ align:start position:0%
+like modar because of
+orthogonality when I do U inverse which
+
+ align:start position:0%
+orthogonality when I do U inverse which
+ 
+
+ align:start position:0%
+orthogonality when I do U inverse which
+is all about the mode shapes information
+
+ align:start position:0%
+is all about the mode shapes information
+ 
+
+ align:start position:0%
+is all about the mode shapes information
+and the mode shapes are or these
+
+ align:start position:0%
+and the mode shapes are or these
+ 
+
+ align:start position:0%
+and the mode shapes are or these
+orthogonal set of independent orthogonal
+
+ align:start position:0%
+orthogonal set of independent orthogonal
+ 
+
+ align:start position:0%
+orthogonal set of independent orthogonal
+vectors if this is exactly one mode and
+
+ align:start position:0%
+vectors if this is exactly one mode and
+ 
+
+ align:start position:0%
+vectors if this is exactly one mode and
+I do U inverse times that I will get
+
+ align:start position:0%
+I do U inverse times that I will get
+ 
+
+ align:start position:0%
+I do U inverse times that I will get
+zero over here on the right hand side
+
+ align:start position:0%
+zero over here on the right hand side
+ 
+
+ align:start position:0%
+zero over here on the right hand side
+for every mode except the mode that
+
+ align:start position:0%
+for every mode except the mode that
+ 
+
+ align:start position:0%
+for every mode except the mode that
+that's shaped
+
+ align:start position:0%
+that's shaped
+ 
+
+ align:start position:0%
+that's shaped
+like so if this is shaped like a that
+
+ align:start position:0%
+like so if this is shaped like a that
+ 
+
+ align:start position:0%
+like so if this is shaped like a that
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+mode then over here all of the modal
+
+ align:start position:0%
+mode then over here all of the modal
+ 
+
+ align:start position:0%
+mode then over here all of the modal
+initial conditions are zero except that
+
+ align:start position:0%
+initial conditions are zero except that
+ 
+
+ align:start position:0%
+initial conditions are zero except that
+mode that means if I set this give its
+
+ align:start position:0%
+mode that means if I set this give its
+ 
+
+ align:start position:0%
+mode that means if I set this give its
+initial conditions are equal to the
+
+ align:start position:0%
+initial conditions are equal to the
+ 
+
+ align:start position:0%
+initial conditions are equal to the
+shape exactly of mode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one it only responds in mode
+
+ align:start position:0%
+one it only responds in mode
+ 
+
+ align:start position:0%
+one it only responds in mode
+one and if I give it put it give it
+
+ align:start position:0%
+one and if I give it put it give it
+ 
+
+ align:start position:0%
+one and if I give it put it give it
+initial conditions that are exactly
+
+ align:start position:0%
+initial conditions that are exactly
+ 
+
+ align:start position:0%
+initial conditions that are exactly
+equal to shape like that of mode
+
+ align:start position:0%
+equal to shape like that of mode
+ 
+
+ align:start position:0%
+equal to shape like that of mode
+two then it only responds in mode
+
+ align:start position:0%
+two then it only responds in mode
+ 
+
+ align:start position:0%
+two then it only responds in mode
+two and if I give it anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else like I move just the top one but
+
+ align:start position:0%
+else like I move just the top one but
+ 
+
+ align:start position:0%
+else like I move just the top one but
+not the bottom and let it go then
+
+ align:start position:0%
+not the bottom and let it go then
+ 
+
+ align:start position:0%
+not the bottom and let it go then
+there's that one's maybe I better do the
+
+ align:start position:0%
+there's that one's maybe I better do the
+ 
+
+ align:start position:0%
+there's that one's maybe I better do the
+other one that one at too much of one
+
+ align:start position:0%
+other one that one at too much of one
+ 
+
+ align:start position:0%
+other one that one at too much of one
+not the other if I hold this one here's
+
+ align:start position:0%
+not the other if I hold this one here's
+ 
+
+ align:start position:0%
+not the other if I hold this one here's
+its reference I'm going to hold it right
+
+ align:start position:0%
+its reference I'm going to hold it right
+ 
+
+ align:start position:0%
+its reference I'm going to hold it right
+there and I'm going to give this one a
+
+ align:start position:0%
+there and I'm going to give this one a
+ 
+
+ align:start position:0%
+there and I'm going to give this one a
+unit deflection and let go
+
+ align:start position:0%
+unit deflection and let go
+ 
+
+ align:start position:0%
+unit deflection and let go
+now you see you got some of both all
+
+ align:start position:0%
+now you see you got some of both all
+ 
+
+ align:start position:0%
+now you see you got some of both all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if when I
+
+ align:start position:0%
+so if when I
+ 
+
+ align:start position:0%
+so if when I
+do this first one say first
+
+ align:start position:0%
+do this first one say first
+ 
+
+ align:start position:0%
+do this first one say first
+mode I could sit here and measure how
+
+ align:start position:0%
+mode I could sit here and measure how
+ 
+
+ align:start position:0%
+mode I could sit here and measure how
+many cycles it takes to Decay halfway
+
+ align:start position:0%
+many cycles it takes to Decay halfway
+ 
+
+ align:start position:0%
+many cycles it takes to Decay halfway
+and estimate the damping ratio for that
+
+ align:start position:0%
+and estimate the damping ratio for that
+ 
+
+ align:start position:0%
+and estimate the damping ratio for that
+mode if it's only moving in this mode I
+
+ align:start position:0%
+mode if it's only moving in this mode I
+ 
+
+ align:start position:0%
+mode if it's only moving in this mode I
+can estimate it I could estimate it
+
+ align:start position:0%
+can estimate it I could estimate it
+ 
+
+ align:start position:0%
+can estimate it I could estimate it
+damping directly for that mode and get
+
+ align:start position:0%
+damping directly for that mode and get
+ 
+
+ align:start position:0%
+damping directly for that mode and get
+Zeta one you agree okay and if I did the
+
+ align:start position:0%
+Zeta one you agree okay and if I did the
+ 
+
+ align:start position:0%
+Zeta one you agree okay and if I did the
+same thing with mode two it's too fast
+
+ align:start position:0%
+same thing with mode two it's too fast
+ 
+
+ align:start position:0%
+same thing with mode two it's too fast
+for me to make my to catch it with a
+
+ align:start position:0%
+for me to make my to catch it with a
+ 
+
+ align:start position:0%
+for me to make my to catch it with a
+stopwatch but I could measure its
+
+ align:start position:0%
+stopwatch but I could measure its
+ 
+
+ align:start position:0%
+stopwatch but I could measure its
+damping and as it decays I could get an
+
+ align:start position:0%
+damping and as it decays I could get an
+ 
+
+ align:start position:0%
+damping and as it decays I could get an
+estimate for Zeta 2 for the damping
+
+ align:start position:0%
+estimate for Zeta 2 for the damping
+ 
+
+ align:start position:0%
+estimate for Zeta 2 for the damping
+ratio for mode two right all right and
+
+ align:start position:0%
+ratio for mode two right all right and
+ 
+
+ align:start position:0%
+ratio for mode two right all right and
+somehow I have to get damping ratio for
+
+ align:start position:0%
+somehow I have to get damping ratio for
+ 
+
+ align:start position:0%
+somehow I have to get damping ratio for
+mode one zeta 1 and damping ratio for
+
+ align:start position:0%
+mode one zeta 1 and damping ratio for
+ 
+
+ align:start position:0%
+mode one zeta 1 and damping ratio for
+mode two Zeta 2 I have to somehow get it
+
+ align:start position:0%
+mode two Zeta 2 I have to somehow get it
+ 
+
+ align:start position:0%
+mode two Zeta 2 I have to somehow get it
+out of this uh
+
+ align:start position:0%
+out of this uh
+ 
+
+ align:start position:0%
+out of this uh
+I have to model it somehow with these
+
+ align:start position:0%
+I have to model it somehow with these
+ 
+
+ align:start position:0%
+I have to model it somehow with these
+stamping coefficients that come from
+
+ align:start position:0%
+stamping coefficients that come from
+ 
+
+ align:start position:0%
+stamping coefficients that come from
+Computing this UT transposed
+
+ align:start position:0%
+Computing this UT transposed
+ 
+
+ align:start position:0%
+Computing this UT transposed
+CU
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm going to this is I'm going
+
+ align:start position:0%
+okay so I'm going to this is I'm going
+ 
+
+ align:start position:0%
+okay so I'm going to this is I'm going
+to show you a kind of damping called ra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+damping okay Lord rley who did lots of
+
+ align:start position:0%
+damping okay Lord rley who did lots of
+ 
+
+ align:start position:0%
+damping okay Lord rley who did lots of
+things in science that you've probably
+
+ align:start position:0%
+things in science that you've probably
+ 
+
+ align:start position:0%
+things in science that you've probably
+run
+
+ align:start position:0%
+run
+ 
+
+ align:start position:0%
+run
+into um propose that if you let the
+
+ align:start position:0%
+into um propose that if you let the
+ 
+
+ align:start position:0%
+into um propose that if you let the
+damping if you model your damping the C
+
+ align:start position:0%
+damping if you model your damping the C
+ 
+
+ align:start position:0%
+damping if you model your damping the C
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+as this is just now the system damping
+
+ align:start position:0%
+as this is just now the system damping
+ 
+
+ align:start position:0%
+as this is just now the system damping
+Matrix that you start with as
+
+ align:start position:0%
+Matrix that you start with as
+ 
+
+ align:start position:0%
+Matrix that you start with as
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+Alpha times the mass Matrix plus beta
+
+ align:start position:0%
+Alpha times the mass Matrix plus beta
+ 
+
+ align:start position:0%
+Alpha times the mass Matrix plus beta
+time the stiffness Matrix these are now
+
+ align:start position:0%
+time the stiffness Matrix these are now
+ 
+
+ align:start position:0%
+time the stiffness Matrix these are now
+the original ones of your in your
+
+ align:start position:0%
+the original ones of your in your
+ 
+
+ align:start position:0%
+the original ones of your in your
+generalized coordinates it's your mass
+
+ align:start position:0%
+generalized coordinates it's your mass
+ 
+
+ align:start position:0%
+generalized coordinates it's your mass
+and stiffness matrices if you model if
+
+ align:start position:0%
+and stiffness matrices if you model if
+ 
+
+ align:start position:0%
+and stiffness matrices if you model if
+you say I'm going to approximate my
+
+ align:start position:0%
+you say I'm going to approximate my
+ 
+
+ align:start position:0%
+you say I'm going to approximate my
+damping model like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+then I want to compute U transpose
+
+ align:start position:0%
+then I want to compute U transpose
+ 
+
+ align:start position:0%
+then I want to compute U transpose
+CU I'm going to get Alpha you transpose
+
+ align:start position:0%
+CU I'm going to get Alpha you transpose
+ 
+
+ align:start position:0%
+CU I'm going to get Alpha you transpose
+m u plus beta you transpose k
+
+ align:start position:0%
+m u plus beta you transpose k
+ 
+
+ align:start position:0%
+m u plus beta you transpose k
+u but we know that this gives you the
+
+ align:start position:0%
+u but we know that this gives you the
+ 
+
+ align:start position:0%
+u but we know that this gives you the
+diagonalized mass Matrix and this known
+
+ align:start position:0%
+diagonalized mass Matrix and this known
+ 
+
+ align:start position:0%
+diagonalized mass Matrix and this known
+as a modal Mass Matrix this gives you
+
+ align:start position:0%
+as a modal Mass Matrix this gives you
+ 
+
+ align:start position:0%
+as a modal Mass Matrix this gives you
+the diagonalized stiffness Matrix and so
+
+ align:start position:0%
+the diagonalized stiffness Matrix and so
+ 
+
+ align:start position:0%
+the diagonalized stiffness Matrix and so
+this damping model this says this is
+
+ align:start position:0%
+this damping model this says this is
+ 
+
+ align:start position:0%
+this damping model this says this is
+guaranteed to give you a diagonalized
+
+ align:start position:0%
+guaranteed to give you a diagonalized
+ 
+
+ align:start position:0%
+guaranteed to give you a diagonalized
+damping
+
+ align:start position:0%
+damping
+ 
+
+ align:start position:0%
+damping
+Matrix which we'll call you know some
+
+ align:start position:0%
+Matrix which we'll call you know some
+ 
+
+ align:start position:0%
+Matrix which we'll call you know some
+have some Capital C1 0 0
+
+ align:start position:0%
+have some Capital C1 0 0
+ 
+
+ align:start position:0%
+have some Capital C1 0 0
+C2 right and it's going to be Alpha
+
+ align:start position:0%
+C2 right and it's going to be Alpha
+ 
+
+ align:start position:0%
+C2 right and it's going to be Alpha
+times the modal Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix plus a beta times the modal
+
+ align:start position:0%
+Matrix plus a beta times the modal
+ 
+
+ align:start position:0%
+Matrix plus a beta times the modal
+stiffness
+
+ align:start position:0%
+stiffness
+ 
+
+ align:start position:0%
+stiffness
+Matrix and these alphas and betas you
+
+ align:start position:0%
+Matrix and these alphas and betas you
+ 
+
+ align:start position:0%
+Matrix and these alphas and betas you
+adjust they're just parameters you
+
+ align:start position:0%
+adjust they're just parameters you
+ 
+
+ align:start position:0%
+adjust they're just parameters you
+adjust to get the amount of damping you
+
+ align:start position:0%
+adjust to get the amount of damping you
+ 
+
+ align:start position:0%
+adjust to get the amount of damping you
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+okay so for a two degree Freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+C1 here is Alpha M1 plus beta M beta
+
+ align:start position:0%
+C1 here is Alpha M1 plus beta M beta
+ 
+
+ align:start position:0%
+C1 here is Alpha M1 plus beta M beta
+K2 K K1 excuse me modal Mass Alpha time
+
+ align:start position:0%
+K2 K K1 excuse me modal Mass Alpha time
+ 
+
+ align:start position:0%
+K2 K K1 excuse me modal Mass Alpha time
+the modal Mass plus beta time the modal
+
+ align:start position:0%
+the modal Mass plus beta time the modal
+ 
+
+ align:start position:0%
+the modal Mass plus beta time the modal
+stiffness that's what you get for the
+
+ align:start position:0%
+stiffness that's what you get for the
+ 
+
+ align:start position:0%
+stiffness that's what you get for the
+first one and
+
+ align:start position:0%
+first one and
+ 
+
+ align:start position:0%
+first one and
+C2 is Alpha
+
+ align:start position:0%
+C2 is Alpha
+ 
+
+ align:start position:0%
+C2 is Alpha
+M2 plus beta
+
+ align:start position:0%
+M2 plus beta
+ 
+
+ align:start position:0%
+M2 plus beta
+K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the alphas and betas give you
+
+ align:start position:0%
+okay and the alphas and betas give you
+ 
+
+ align:start position:0%
+okay and the alphas and betas give you
+two free parameters you can play with
+
+ align:start position:0%
+two free parameters you can play with
+ 
+
+ align:start position:0%
+two free parameters you can play with
+and for a two degree Freedom system I
+
+ align:start position:0%
+and for a two degree Freedom system I
+ 
+
+ align:start position:0%
+and for a two degree Freedom system I
+can manipulate Alpha and beta to get the
+
+ align:start position:0%
+can manipulate Alpha and beta to get the
+ 
+
+ align:start position:0%
+can manipulate Alpha and beta to get the
+D in that I
+
+ align:start position:0%
+D in that I
+ 
+
+ align:start position:0%
+D in that I
+measure and I and I've forced my
+
+ align:start position:0%
+measure and I and I've forced my
+ 
+
+ align:start position:0%
+measure and I and I've forced my
+equations of motion to uncouple now
+
+ align:start position:0%
+equations of motion to uncouple now
+ 
+
+ align:start position:0%
+equations of motion to uncouple now
+Mother Nature may say that you know you
+
+ align:start position:0%
+Mother Nature may say that you know you
+ 
+
+ align:start position:0%
+Mother Nature may say that you know you
+know vand they don't
+
+ align:start position:0%
+know vand they don't
+ 
+
+ align:start position:0%
+know vand they don't
+uncouple and there's going to be a
+
+ align:start position:0%
+uncouple and there's going to be a
+ 
+
+ align:start position:0%
+uncouple and there's going to be a
+little cross talk between them but I say
+
+ align:start position:0%
+little cross talk between them but I say
+ 
+
+ align:start position:0%
+little cross talk between them but I say
+yeah but to first order I it's I'm going
+
+ align:start position:0%
+yeah but to first order I it's I'm going
+ 
+
+ align:start position:0%
+yeah but to first order I it's I'm going
+to get a pretty good model of the system
+
+ align:start position:0%
+to get a pretty good model of the system
+ 
+
+ align:start position:0%
+to get a pretty good model of the system
+so let's do that in this case let's uh
+
+ align:start position:0%
+so let's do that in this case let's uh
+ 
+
+ align:start position:0%
+so let's do that in this case let's uh
+maybe just to keep it I've got numbers
+
+ align:start position:0%
+maybe just to keep it I've got numbers
+ 
+
+ align:start position:0%
+maybe just to keep it I've got numbers
+here so let me find my notes so I don't
+
+ align:start position:0%
+here so let me find my notes so I don't
+ 
+
+ align:start position:0%
+here so let me find my notes so I don't
+get completely lost
+
+ align:start position:0%
+get completely lost
+ 
+
+ align:start position:0%
+get completely lost
+here so uh I don't want I'm going to
+
+ align:start position:0%
+here so uh I don't want I'm going to
+ 
+
+ align:start position:0%
+here so uh I don't want I'm going to
+just pick one for now I'm going to model
+
+ align:start position:0%
+just pick one for now I'm going to model
+ 
+
+ align:start position:0%
+just pick one for now I'm going to model
+my damping with just beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K beta time my diagonal stiffness Matrix
+
+ align:start position:0%
+K beta time my diagonal stiffness Matrix
+ 
+
+ align:start position:0%
+K beta time my diagonal stiffness Matrix
+and let's see
+
+ align:start position:0%
+and let's see
+ 
+
+ align:start position:0%
+and let's see
+let's see what happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so that says my modal stamping is
+
+ align:start position:0%
+here so that says my modal stamping is
+ 
+
+ align:start position:0%
+here so that says my modal stamping is
+going to be some for mode one which be
+
+ align:start position:0%
+going to be some for mode one which be
+ 
+
+ align:start position:0%
+going to be some for mode one which be
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+K1 now what's stamping ratio Zeta
+
+ align:start position:0%
+K1 now what's stamping ratio Zeta
+ 
+
+ align:start position:0%
+K1 now what's stamping ratio Zeta
+1 equals for a single degree Freedom
+
+ align:start position:0%
+1 equals for a single degree Freedom
+ 
+
+ align:start position:0%
+1 equals for a single degree Freedom
+system is the damping constant for the
+
+ align:start position:0%
+system is the damping constant for the
+ 
+
+ align:start position:0%
+system is the damping constant for the
+system over 2 Omega 1 m
+
+ align:start position:0%
+system over 2 Omega 1 m
+ 
+
+ align:start position:0%
+system over 2 Omega 1 m
+1 but that's going to be beta
+
+ align:start position:0%
+1 but that's going to be beta
+ 
+
+ align:start position:0%
+1 but that's going to be beta
+K1 over 2 Omega 1
+
+ align:start position:0%
+K1 over 2 Omega 1
+ 
+
+ align:start position:0%
+K1 over 2 Omega 1
+M1 but M1 over K1 is Omega 1
+
+ align:start position:0%
+M1 but M1 over K1 is Omega 1
+ 
+
+ align:start position:0%
+M1 but M1 over K1 is Omega 1
+s so I get an Omega 1 s in the
+
+ align:start position:0%
+s so I get an Omega 1 s in the
+ 
+
+ align:start position:0%
+s so I get an Omega 1 s in the
+numerator beta Omega 1^ 2ar over 2
+
+ align:start position:0%
+numerator beta Omega 1^ 2ar over 2
+ 
+
+ align:start position:0%
+numerator beta Omega 1^ 2ar over 2
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+1 remember the K over the M gave me the
+
+ align:start position:0%
+1 remember the K over the M gave me the
+ 
+
+ align:start position:0%
+1 remember the K over the M gave me the
+Omega 1 squ so the M's gone can cancel
+
+ align:start position:0%
+Omega 1 squ so the M's gone can cancel
+ 
+
+ align:start position:0%
+Omega 1 squ so the M's gone can cancel
+one of these this gives me beta Omega 1
+
+ align:start position:0%
+one of these this gives me beta Omega 1
+ 
+
+ align:start position:0%
+one of these this gives me beta Omega 1
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so this now gives me a way of I can
+
+ align:start position:0%
+two so this now gives me a way of I can
+ 
+
+ align:start position:0%
+two so this now gives me a way of I can
+fit one of the
+
+ align:start position:0%
+fit one of the
+ 
+
+ align:start position:0%
+fit one of the
+dampings I can get exactly what I want
+
+ align:start position:0%
+dampings I can get exactly what I want
+ 
+
+ align:start position:0%
+dampings I can get exactly what I want
+say for mode one if I pick beta to be
+
+ align:start position:0%
+say for mode one if I pick beta to be
+ 
+
+ align:start position:0%
+say for mode one if I pick beta to be
+the right number okay so in this case
+
+ align:start position:0%
+the right number okay so in this case
+ 
+
+ align:start position:0%
+the right number okay so in this case
+I actually did did some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+pardon can't hear
+
+ align:start position:0%
+pardon can't hear
+ 
+
+ align:start position:0%
+pardon can't hear
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+no K1 over M1 is Omega 1 squ Omega 1 squ
+
+ align:start position:0%
+no K1 over M1 is Omega 1 squ Omega 1 squ
+ 
+
+ align:start position:0%
+no K1 over M1 is Omega 1 squ Omega 1 squ
+takes care of the M1 I get rid of one of
+
+ align:start position:0%
+takes care of the M1 I get rid of one of
+ 
+
+ align:start position:0%
+takes care of the M1 I get rid of one of
+the Omega 1es I'm left with
+
+ align:start position:0%
+the Omega 1es I'm left with
+ 
+
+ align:start position:0%
+the Omega 1es I'm left with
+this okay um
+
+ align:start position:0%
+this okay um
+ 
+
+ align:start position:0%
+this okay um
+okay so what if so let's just
+
+ align:start position:0%
+okay so what if so let's just
+ 
+
+ align:start position:0%
+okay so what if so let's just
+let beta equals
+
+ align:start position:0%
+let beta equals
+ 
+
+ align:start position:0%
+let beta equals
+01 and if you let beta equal to 01 then
+
+ align:start position:0%
+01 and if you let beta equal to 01 then
+ 
+
+ align:start position:0%
+01 and if you let beta equal to 01 then
+Zeta 1 = .01 Omega 1/ 2 we know Omega 1
+
+ align:start position:0%
+Zeta 1 = .01 Omega 1/ 2 we know Omega 1
+ 
+
+ align:start position:0%
+Zeta 1 = .01 Omega 1/ 2 we know Omega 1
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+5.65 uh this when you work it out then
+
+ align:start position:0%
+5.65 uh this when you work it out then
+ 
+
+ align:start position:0%
+5.65 uh this when you work it out then
+gives you a number
+
+ align:start position:0%
+gives you a number
+ 
+
+ align:start position:0%
+gives you a number
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0283 about
+
+ align:start position:0%
+0283 about
+ 
+
+ align:start position:0%
+0283 about
+3% and that would model
+
+ align:start position:0%
+3% and that would model
+ 
+
+ align:start position:0%
+3% and that would model
+uh that would say that this system when
+
+ align:start position:0%
+uh that would say that this system when
+ 
+
+ align:start position:0%
+uh that would say that this system when
+it vibrates in mode one it's going to
+
+ align:start position:0%
+it vibrates in mode one it's going to
+ 
+
+ align:start position:0%
+it vibrates in mode one it's going to
+damp out up to 50% in about three
+
+ align:start position:0%
+damp out up to 50% in about three
+ 
+
+ align:start position:0%
+damp out up to 50% in about three
+Cycles not bad approximations I'm just
+
+ align:start position:0%
+Cycles not bad approximations I'm just
+ 
+
+ align:start position:0%
+Cycles not bad approximations I'm just
+guessing about what it is that's a
+
+ align:start position:0%
+guessing about what it is that's a
+ 
+
+ align:start position:0%
+guessing about what it is that's a
+reasonable amount of damping for mode
+
+ align:start position:0%
+reasonable amount of damping for mode
+ 
+
+ align:start position:0%
+reasonable amount of damping for mode
+one now the problem is when I only use
+
+ align:start position:0%
+one now the problem is when I only use
+ 
+
+ align:start position:0%
+one now the problem is when I only use
+just beta K as my
+
+ align:start position:0%
+just beta K as my
+ 
+
+ align:start position:0%
+just beta K as my
+model now I'm stuck with whatever
+
+ align:start position:0%
+model now I'm stuck with whatever
+ 
+
+ align:start position:0%
+model now I'm stuck with whatever
+happens for mode two once I pick beta
+
+ align:start position:0%
+happens for mode two once I pick beta
+ 
+
+ align:start position:0%
+happens for mode two once I pick beta
+because Zeta
+
+ align:start position:0%
+because Zeta
+ 
+
+ align:start position:0%
+because Zeta
+2 is going to be beta Omega 2 over two
+
+ align:start position:0%
+2 is going to be beta Omega 2 over two
+ 
+
+ align:start position:0%
+2 is going to be beta Omega 2 over two
+and Omega 2 is quite a bit larger so
+
+ align:start position:0%
+and Omega 2 is quite a bit larger so
+ 
+
+ align:start position:0%
+and Omega 2 is quite a bit larger so
+that makes I'm stuck with a greater
+
+ align:start position:0%
+that makes I'm stuck with a greater
+ 
+
+ align:start position:0%
+that makes I'm stuck with a greater
+value for the second mode in this case
+
+ align:start position:0%
+value for the second mode in this case
+ 
+
+ align:start position:0%
+value for the second mode in this case
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0885 so if I just pick a one parameter
+
+ align:start position:0%
+0885 so if I just pick a one parameter
+ 
+
+ align:start position:0%
+0885 so if I just pick a one parameter
+model for my damping I'm I can make one
+
+ align:start position:0%
+model for my damping I'm I can make one
+ 
+
+ align:start position:0%
+model for my damping I'm I can make one
+perfect I can match it perfectly but
+
+ align:start position:0%
+perfect I can match it perfectly but
+ 
+
+ align:start position:0%
+perfect I can match it perfectly but
+then I'm stuck with whatever the other
+
+ align:start position:0%
+then I'm stuck with whatever the other
+ 
+
+ align:start position:0%
+then I'm stuck with whatever the other
+one is so I I did this because I could
+
+ align:start position:0%
+one is so I I did this because I could
+ 
+
+ align:start position:0%
+one is so I I did this because I could
+do it simply with one but if IID kept
+
+ align:start position:0%
+do it simply with one but if IID kept
+ 
+
+ align:start position:0%
+do it simply with one but if IID kept
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+full Model A two parameter model I could
+
+ align:start position:0%
+full Model A two parameter model I could
+ 
+
+ align:start position:0%
+full Model A two parameter model I could
+actually with manipulating both Alpha
+
+ align:start position:0%
+actually with manipulating both Alpha
+ 
+
+ align:start position:0%
+actually with manipulating both Alpha
+and beta I could actually model get both
+
+ align:start position:0%
+and beta I could actually model get both
+ 
+
+ align:start position:0%
+and beta I could actually model get both
+of the two measured dampings exactly
+
+ align:start position:0%
+of the two measured dampings exactly
+ 
+
+ align:start position:0%
+of the two measured dampings exactly
+right but if I have an N degree if I
+
+ align:start position:0%
+right but if I have an N degree if I
+ 
+
+ align:start position:0%
+right but if I have an N degree if I
+have three deegree Freedom system I only
+
+ align:start position:0%
+have three deegree Freedom system I only
+ 
+
+ align:start position:0%
+have three deegree Freedom system I only
+have two parameters I can fit two of the
+
+ align:start position:0%
+have two parameters I can fit two of the
+ 
+
+ align:start position:0%
+have two parameters I can fit two of the
+damping ratios but then I'm going to be
+
+ align:start position:0%
+damping ratios but then I'm going to be
+ 
+
+ align:start position:0%
+damping ratios but then I'm going to be
+stuck with whatever it gives me for the
+
+ align:start position:0%
+stuck with whatever it gives me for the
+ 
+
+ align:start position:0%
+stuck with whatever it gives me for the
+third but often times it's just one mode
+
+ align:start position:0%
+third but often times it's just one mode
+ 
+
+ align:start position:0%
+third but often times it's just one mode
+you really care about it's the problem
+
+ align:start position:0%
+you really care about it's the problem
+ 
+
+ align:start position:0%
+you really care about it's the problem
+mode you're at its natural frequency
+
+ align:start position:0%
+mode you're at its natural frequency
+ 
+
+ align:start position:0%
+mode you're at its natural frequency
+it's right going like crazy initi
+
+ align:start position:0%
+it's right going like crazy initi
+ 
+
+ align:start position:0%
+it's right going like crazy initi
+conditions make it vibrate a lot in that
+
+ align:start position:0%
+conditions make it vibrate a lot in that
+ 
+
+ align:start position:0%
+conditions make it vibrate a lot in that
+mode but this is what Ray damping allows
+
+ align:start position:0%
+mode but this is what Ray damping allows
+ 
+
+ align:start position:0%
+mode but this is what Ray damping allows
+you to do it all guarantees you that you
+
+ align:start position:0%
+you to do it all guarantees you that you
+ 
+
+ align:start position:0%
+you to do it all guarantees you that you
+will have a diagonal diagonalized set of
+
+ align:start position:0%
+will have a diagonal diagonalized set of
+ 
+
+ align:start position:0%
+will have a diagonal diagonalized set of
+equations of motion and it gives you two
+
+ align:start position:0%
+equations of motion and it gives you two
+ 
+
+ align:start position:0%
+equations of motion and it gives you two
+parameters that you can play with to fit
+
+ align:start position:0%
+parameters that you can play with to fit
+ 
+
+ align:start position:0%
+parameters that you can play with to fit
+the damping model however you
+
+ align:start position:0%
+the damping model however you
+ 
+
+ align:start position:0%
+the damping model however you
+want once you have
+
+ align:start position:0%
+want once you have
+ 
+
+ align:start position:0%
+want once you have
+damping now you have the complete
+
+ align:start position:0%
+damping now you have the complete
+ 
+
+ align:start position:0%
+damping now you have the complete
+solution for Decay from initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions and there's your two model
+
+ align:start position:0%
+conditions and there's your two model
+ 
+
+ align:start position:0%
+conditions and there's your two model
+you can solve for q1 transient Decay
+
+ align:start position:0%
+you can solve for q1 transient Decay
+ 
+
+ align:start position:0%
+you can solve for q1 transient Decay
+given initial conditions you can solve
+
+ align:start position:0%
+given initial conditions you can solve
+ 
+
+ align:start position:0%
+given initial conditions you can solve
+for Q2 transient decay of the second
+
+ align:start position:0%
+for Q2 transient decay of the second
+ 
+
+ align:start position:0%
+for Q2 transient decay of the second
+mode and then to to get back to the
+
+ align:start position:0%
+mode and then to to get back to the
+ 
+
+ align:start position:0%
+mode and then to to get back to the
+initial to the response in terms of your
+
+ align:start position:0%
+initial to the response in terms of your
+ 
+
+ align:start position:0%
+initial to the response in terms of your
+modal coordinates you just add the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay got some numbers here would are
+
+ align:start position:0%
+okay got some numbers here would are
+ 
+
+ align:start position:0%
+okay got some numbers here would are
+just instructive let's uh U inverse in
+
+ align:start position:0%
+just instructive let's uh U inverse in
+ 
+
+ align:start position:0%
+just instructive let's uh U inverse in
+order to get these initial conditions
+
+ align:start position:0%
+order to get these initial conditions
+ 
+
+ align:start position:0%
+order to get these initial conditions
+you got to know you inverse do we know
+
+ align:start position:0%
+you got to know you inverse do we know
+ 
+
+ align:start position:0%
+you got to know you inverse do we know
+you I gave us you here's our mode shape
+
+ align:start position:0%
+you I gave us you here's our mode shape
+ 
+
+ align:start position:0%
+you I gave us you here's our mode shape
+set of mod shape
+
+ align:start position:0%
+set of mod shape
+ 
+
+ align:start position:0%
+set of mod shape
+vectors and I'm run out of boards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have the U Matrix we need U
+
+ align:start position:0%
+so we have the U Matrix we need U
+ 
+
+ align:start position:0%
+so we have the U Matrix we need U
+inverse so U inverse for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and we're going to quickly do
+
+ align:start position:0%
+problem and we're going to quickly do
+ 
+
+ align:start position:0%
+problem and we're going to quickly do
+some examples let's let
+
+ align:start position:0%
+some examples let's let
+ 
+
+ align:start position:0%
+some examples let's let
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+V the V kns be zero no initial
+
+ align:start position:0%
+V the V kns be zero no initial
+ 
+
+ align:start position:0%
+V the V kns be zero no initial
+conditions on
+
+ align:start position:0%
+conditions on
+ 
+
+ align:start position:0%
+conditions on
+velocities and let's do
+
+ align:start position:0%
+velocities and let's do
+ 
+
+ align:start position:0%
+velocities and let's do
+X not the initial
+
+ align:start position:0%
+X not the initial
+ 
+
+ align:start position:0%
+X not the initial
+displacements
+
+ align:start position:0%
+displacements
+ 
+
+ align:start position:0%
+displacements
+be 1 and zero so the one and zero what
+
+ align:start position:0%
+be 1 and zero so the one and zero what
+ 
+
+ align:start position:0%
+be 1 and zero so the one and zero what
+we're saying is the bottom one doesn't
+
+ align:start position:0%
+we're saying is the bottom one doesn't
+ 
+
+ align:start position:0%
+we're saying is the bottom one doesn't
+move unit deflection here let go what
+
+ align:start position:0%
+move unit deflection here let go what
+ 
+
+ align:start position:0%
+move unit deflection here let go what
+you what are you going to get for the
+
+ align:start position:0%
+you what are you going to get for the
+ 
+
+ align:start position:0%
+you what are you going to get for the
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+conditions X not equal 1 and z
+
+ align:start position:0%
+conditions X not equal 1 and z
+ 
+
+ align:start position:0%
+conditions X not equal 1 and z
+well that implies
+
+ align:start position:0%
+well that implies
+ 
+
+ align:start position:0%
+well that implies
+that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+q's are going to be U inverse X
+
+ align:start position:0%
+q's are going to be U inverse X
+ 
+
+ align:start position:0%
+q's are going to be U inverse X
+knot so by the way this if this is true
+
+ align:start position:0%
+knot so by the way this if this is true
+ 
+
+ align:start position:0%
+knot so by the way this if this is true
+this implies that all Q do initial
+
+ align:start position:0%
+this implies that all Q do initial
+ 
+
+ align:start position:0%
+this implies that all Q do initial
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+equal zero right no initial velocities
+
+ align:start position:0%
+equal zero right no initial velocities
+ 
+
+ align:start position:0%
+equal zero right no initial velocities
+in generalized coordinates no initial
+
+ align:start position:0%
+in generalized coordinates no initial
+ 
+
+ align:start position:0%
+in generalized coordinates no initial
+velocities in modal coordinates but here
+
+ align:start position:0%
+velocities in modal coordinates but here
+ 
+
+ align:start position:0%
+velocities in modal coordinates but here
+we have but we are going to have an
+
+ align:start position:0%
+we have but we are going to have an
+ 
+
+ align:start position:0%
+we have but we are going to have an
+initial deflection and if I want to
+
+ align:start position:0%
+initial deflection and if I want to
+ 
+
+ align:start position:0%
+initial deflection and if I want to
+multip I want to then compute U
+
+ align:start position:0%
+multip I want to then compute U
+ 
+
+ align:start position:0%
+multip I want to then compute U
+inverse X knot and see what I
+
+ align:start position:0%
+inverse X knot and see what I
+ 
+
+ align:start position:0%
+inverse X knot and see what I
+get and what I get back when I do this
+
+ align:start position:0%
+get and what I get back when I do this
+ 
+
+ align:start position:0%
+get and what I get back when I do this
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+9102 remember this is q1 not Q2
+
+ align:start position:0%
+9102 remember this is q1 not Q2
+ 
+
+ align:start position:0%
+9102 remember this is q1 not Q2
+not so for that case it says I'm going
+
+ align:start position:0%
+not so for that case it says I'm going
+ 
+
+ align:start position:0%
+not so for that case it says I'm going
+to get 0.08 or 09 q1 equal to q1 and 0.9
+
+ align:start position:0%
+to get 0.08 or 09 q1 equal to q1 and 0.9
+ 
+
+ align:start position:0%
+to get 0.08 or 09 q1 equal to q1 and 0.9
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Q2 and my I go back over here to my
+
+ align:start position:0%
+Q2 and my I go back over here to my
+ 
+
+ align:start position:0%
+Q2 and my I go back over here to my
+transient DK there's no velocity so this
+
+ align:start position:0%
+transient DK there's no velocity so this
+ 
+
+ align:start position:0%
+transient DK there's no velocity so this
+basically going to look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+q1 q1 KN cosine Omega DT eus th Omega t
+
+ align:start position:0%
+q1 q1 KN cosine Omega DT eus th Omega t
+ 
+
+ align:start position:0%
+q1 q1 KN cosine Omega DT eus th Omega t
+decaying
+
+ align:start position:0%
+decaying
+ 
+
+ align:start position:0%
+decaying
+cosine but for mode one its initial
+
+ align:start position:0%
+cosine but for mode one its initial
+ 
+
+ align:start position:0%
+cosine but for mode one its initial
+amplitudes you know less than 0.1 and
+
+ align:start position:0%
+amplitudes you know less than 0.1 and
+ 
+
+ align:start position:0%
+amplitudes you know less than 0.1 and
+mode two it's got a lot of mode two so
+
+ align:start position:0%
+mode two it's got a lot of mode two so
+ 
+
+ align:start position:0%
+mode two it's got a lot of mode two so
+it is what
+
+ align:start position:0%
+it is what
+ 
+
+ align:start position:0%
+it is what
+happens so unit deflection
+
+ align:start position:0%
+happens so unit deflection
+ 
+
+ align:start position:0%
+happens so unit deflection
+here in fact it's mostly mode two and if
+
+ align:start position:0%
+here in fact it's mostly mode two and if
+ 
+
+ align:start position:0%
+here in fact it's mostly mode two and if
+I just quickly I'll do one other X knot
+
+ align:start position:0%
+I just quickly I'll do one other X knot
+ 
+
+ align:start position:0%
+I just quickly I'll do one other X knot
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+01 that implies that Q
+
+ align:start position:0%
+01 that implies that Q
+ 
+
+ align:start position:0%
+01 that implies that Q
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+q that you get from that
+
+ align:start position:0%
+q that you get from that
+ 
+
+ align:start position:0%
+q that you get from that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+416 and
+
+ align:start position:0%
+416 and
+ 
+
+ align:start position:0%
+416 and
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+4016 says you get about equal
+
+ align:start position:0%
+4016 says you get about equal
+ 
+
+ align:start position:0%
+4016 says you get about equal
+amounts so that's this one I don't move
+
+ align:start position:0%
+amounts so that's this one I don't move
+ 
+
+ align:start position:0%
+amounts so that's this one I don't move
+this one but I give this one a unit
+
+ align:start position:0%
+this one but I give this one a unit
+ 
+
+ align:start position:0%
+this one but I give this one a unit
+deflection let go I get about equal
+
+ align:start position:0%
+deflection let go I get about equal
+ 
+
+ align:start position:0%
+deflection let go I get about equal
+amounts of each one
+
+ align:start position:0%
+amounts of each one
+ 
+
+ align:start position:0%
+amounts of each one
+and of course I've told you the answer
+
+ align:start position:0%
+and of course I've told you the answer
+ 
+
+ align:start position:0%
+and of course I've told you the answer
+to this one is if I let x equal mode
+
+ align:start position:0%
+to this one is if I let x equal mode
+ 
+
+ align:start position:0%
+to this one is if I let x equal mode
+one's mode shape 1 and
+
+ align:start position:0%
+one's mode shape 1 and
+ 
+
+ align:start position:0%
+one's mode shape 1 and
+2.2
+
+ align:start position:0%
+2.2
+ 
+
+ align:start position:0%
+2.2
+66 that implies that
+
+ align:start position:0%
+66 that implies that
+ 
+
+ align:start position:0%
+66 that implies that
+q1 equals 1 and Q2 when you multiply it
+
+ align:start position:0%
+q1 equals 1 and Q2 when you multiply it
+ 
+
+ align:start position:0%
+q1 equals 1 and Q2 when you multiply it
+out is zero so if I def it in the shape
+
+ align:start position:0%
+out is zero so if I def it in the shape
+ 
+
+ align:start position:0%
+out is zero so if I def it in the shape
+of mode one and I do U inverse X knot I
+
+ align:start position:0%
+of mode one and I do U inverse X knot I
+ 
+
+ align:start position:0%
+of mode one and I do U inverse X knot I
+will get back zero one and if I make
+
+ align:start position:0%
+will get back zero one and if I make
+ 
+
+ align:start position:0%
+will get back zero one and if I make
+this the shape of mode two I will get
+
+ align:start position:0%
+this the shape of mode two I will get
+ 
+
+ align:start position:0%
+this the shape of mode two I will get
+back zero for mode one and one for mode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so that will that's the run out of
+
+ align:start position:0%
+two so that will that's the run out of
+ 
+
+ align:start position:0%
+two so that will that's the run out of
+time but that's your intro to modal
+
+ align:start position:0%
+time but that's your intro to modal
+ 
+
+ align:start position:0%
+time but that's your intro to modal
+analysis so I think it's conceptually
+
+ align:start position:0%
+analysis so I think it's conceptually
+ 
+
+ align:start position:0%
+analysis so I think it's conceptually
+powerful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh is this one
+
+ align:start position:0%
+oh is this one
+ 
+
+ align:start position:0%
+oh is this one
+8 okay I may have written that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down yeah I'll I'll double check that
+
+ align:start position:0%
+down yeah I'll I'll double check that
+ 
+
+ align:start position:0%
+down yeah I'll I'll double check that
+but yeah question why is
+
+ align:start position:0%
+but yeah question why is
+ 
+
+ align:start position:0%
+but yeah question why is
+it C to be only a function of beta
+
+ align:start position:0%
+it C to be only a function of beta
+ 
+
+ align:start position:0%
+it C to be only a function of beta
+because I wanted to get done by the end
+
+ align:start position:0%
+because I wanted to get done by the end
+ 
+
+ align:start position:0%
+because I wanted to get done by the end
+of the okay 60 you know 80 minutes I
+
+ align:start position:0%
+of the okay 60 you know 80 minutes I
+ 
+
+ align:start position:0%
+of the okay 60 you know 80 minutes I
+could have put both of them in
+
+ align:start position:0%
+could have put both of them in
+ 
+
+ align:start position:0%
+could have put both of them in
+manipulated both parameters these two
+
+ align:start position:0%
+manipulated both parameters these two
+ 
+
+ align:start position:0%
+manipulated both parameters these two
+equations and two unknowns two target
+
+ align:start position:0%
+equations and two unknowns two target
+ 
+
+ align:start position:0%
+equations and two unknowns two target
+values of damping I'd find an alpha and
+
+ align:start position:0%
+values of damping I'd find an alpha and
+ 
+
+ align:start position:0%
+values of damping I'd find an alpha and
+a beta that would make both work exactly
+
+ align:start position:0%
+a beta that would make both work exactly
+ 
+
+ align:start position:0%
+a beta that would make both work exactly
+right it actually just this one model is
+
+ align:start position:0%
+right it actually just this one model is
+ 
+
+ align:start position:0%
+right it actually just this one model is
+pretty good for this case the damping
+
+ align:start position:0%
+pretty good for this case the damping
+ 
+
+ align:start position:0%
+pretty good for this case the damping
+for second mode is greater than the
+
+ align:start position:0%
+for second mode is greater than the
+ 
+
+ align:start position:0%
+for second mode is greater than the
+first mode just happens to be this model
+
+ align:start position:0%
+first mode just happens to be this model
+ 
+
+ align:start position:0%
+first mode just happens to be this model
+is not bad right so you try see what
+
+ align:start position:0%
+is not bad right so you try see what
+ 
+
+ align:start position:0%
+is not bad right so you try see what
+gets best results yeah
\ No newline at end of file
diff --git a/PC3qooaF5Xs.txt b/PC3qooaF5Xs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1a09b01c1a6fb1954f87c164e41ac0a060cb5194
--- /dev/null
+++ b/PC3qooaF5Xs.txt
@@ -0,0 +1,9195 @@
+align:start position:0%
+ 
+okay so let's continue our
+
+ align:start position:0%
+okay so let's continue our
+ 
+
+ align:start position:0%
+okay so let's continue our
+of welfare economics just to review
+
+ align:start position:0%
+of welfare economics just to review
+ 
+
+ align:start position:0%
+of welfare economics just to review
+where we are the first set of lectures
+
+ align:start position:0%
+where we are the first set of lectures
+ 
+
+ align:start position:0%
+where we are the first set of lectures
+in the course were about positive
+
+ align:start position:0%
+in the course were about positive
+ 
+
+ align:start position:0%
+in the course were about positive
+economics about understanding where
+
+ align:start position:0%
+economics about understanding where
+ 
+
+ align:start position:0%
+economics about understanding where
+supply and demand curves come from and
+
+ align:start position:0%
+supply and demand curves come from and
+ 
+
+ align:start position:0%
+supply and demand curves come from and
+what they mean now last lecture we
+
+ align:start position:0%
+what they mean now last lecture we
+ 
+
+ align:start position:0%
+what they mean now last lecture we
+turned from positive to normative
+
+ align:start position:0%
+turned from positive to normative
+ 
+
+ align:start position:0%
+turned from positive to normative
+economics and actually making judgments
+
+ align:start position:0%
+economics and actually making judgments
+ 
+
+ align:start position:0%
+economics and actually making judgments
+about whether things are good or bad and
+
+ align:start position:0%
+about whether things are good or bad and
+ 
+
+ align:start position:0%
+about whether things are good or bad and
+when choose the concept of welfare
+
+ align:start position:0%
+when choose the concept of welfare
+ 
+
+ align:start position:0%
+when choose the concept of welfare
+economic welfare or well-being and we
+
+ align:start position:0%
+economic welfare or well-being and we
+ 
+
+ align:start position:0%
+economic welfare or well-being and we
+talked about consumer surplus which is a
+
+ align:start position:0%
+talked about consumer surplus which is a
+ 
+
+ align:start position:0%
+talked about consumer surplus which is a
+measure of how well-off consumers are
+
+ align:start position:0%
+measure of how well-off consumers are
+ 
+
+ align:start position:0%
+measure of how well-off consumers are
+made by given exchange of goods and
+
+ align:start position:0%
+made by given exchange of goods and
+ 
+
+ align:start position:0%
+made by given exchange of goods and
+services and producer surplus how
+
+ align:start position:0%
+services and producer surplus how
+ 
+
+ align:start position:0%
+services and producer surplus how
+well-off police's are made we're going
+
+ align:start position:0%
+well-off police's are made we're going
+ 
+
+ align:start position:0%
+well-off police's are made we're going
+to start our lecture by proving what's
+
+ align:start position:0%
+to start our lecture by proving what's
+ 
+
+ align:start position:0%
+to start our lecture by proving what's
+modestly called the first fundamental
+
+ align:start position:0%
+modestly called the first fundamental
+ 
+
+ align:start position:0%
+modestly called the first fundamental
+theorem of welfare economics which is
+
+ align:start position:0%
+theorem of welfare economics which is
+ 
+
+ align:start position:0%
+theorem of welfare economics which is
+that competition maximizes welfare so
+
+ align:start position:0%
+that competition maximizes welfare so
+ 
+
+ align:start position:0%
+that competition maximizes welfare so
+this is basically taking our positive
+
+ align:start position:0%
+this is basically taking our positive
+ 
+
+ align:start position:0%
+this is basically taking our positive
+economics at a meeting our normative
+
+ align:start position:0%
+economics at a meeting our normative
+ 
+
+ align:start position:0%
+economics at a meeting our normative
+economics that is we are going to talk
+
+ align:start position:0%
+economics that is we are going to talk
+ 
+
+ align:start position:0%
+economics that is we are going to talk
+about how the model we've derived so far
+
+ align:start position:0%
+about how the model we've derived so far
+ 
+
+ align:start position:0%
+about how the model we've derived so far
+which is the equilibrium and a perfect
+
+ align:start position:0%
+which is the equilibrium and a perfect
+ 
+
+ align:start position:0%
+which is the equilibrium and a perfect
+competition happens to also be the
+
+ align:start position:0%
+competition happens to also be the
+ 
+
+ align:start position:0%
+competition happens to also be the
+outcome that delivers the maximum
+
+ align:start position:0%
+outcome that delivers the maximum
+ 
+
+ align:start position:0%
+outcome that delivers the maximum
+well-being to society let's step back
+
+ align:start position:0%
+well-being to society let's step back
+ 
+
+ align:start position:0%
+well-being to society let's step back
+well-being we called welfare how do we
+
+ align:start position:0%
+well-being we called welfare how do we
+ 
+
+ align:start position:0%
+well-being we called welfare how do we
+define the well-being of society well
+
+ align:start position:0%
+define the well-being of society well
+ 
+
+ align:start position:0%
+define the well-being of society well
+we're going to start with a simple
+
+ align:start position:0%
+we're going to start with a simple
+ 
+
+ align:start position:0%
+we're going to start with a simple
+definition which is we're gonna sadly
+
+ align:start position:0%
+definition which is we're gonna sadly
+ 
+
+ align:start position:0%
+definition which is we're gonna sadly
+say that social welfare social welfare
+
+ align:start position:0%
+say that social welfare social welfare
+ 
+
+ align:start position:0%
+say that social welfare social welfare
+is the total welfare of society is
+
+ align:start position:0%
+is the total welfare of society is
+ 
+
+ align:start position:0%
+is the total welfare of society is
+simply consumer surplus plus producer
+
+ align:start position:0%
+simply consumer surplus plus producer
+ 
+
+ align:start position:0%
+simply consumer surplus plus producer
+surplus that is we're not going to put
+
+ align:start position:0%
+surplus that is we're not going to put
+ 
+
+ align:start position:0%
+surplus that is we're not going to put
+any different weights we're not going to
+
+ align:start position:0%
+any different weights we're not going to
+ 
+
+ align:start position:0%
+any different weights we're not going to
+say we like somebody better than another
+
+ align:start position:0%
+say we like somebody better than another
+ 
+
+ align:start position:0%
+say we like somebody better than another
+which is because they look surplus is
+
+ align:start position:0%
+which is because they look surplus is
+ 
+
+ align:start position:0%
+which is because they look surplus is
+produced by a transaction and we just
+
+ align:start position:0%
+produced by a transaction and we just
+ 
+
+ align:start position:0%
+produced by a transaction and we just
+care about the total surplus that's
+
+ align:start position:0%
+care about the total surplus that's
+ 
+
+ align:start position:0%
+care about the total surplus that's
+produced and later we can come down via
+
+ align:start position:0%
+produced and later we can come down via
+ 
+
+ align:start position:0%
+produced and later we can come down via
+about consumers versus producers and we
+
+ align:start position:0%
+about consumers versus producers and we
+ 
+
+ align:start position:0%
+about consumers versus producers and we
+will but right now let's just say we
+
+ align:start position:0%
+will but right now let's just say we
+ 
+
+ align:start position:0%
+will but right now let's just say we
+care about the total surplus that's
+
+ align:start position:0%
+care about the total surplus that's
+ 
+
+ align:start position:0%
+care about the total surplus that's
+produced for society how much benefit is
+
+ align:start position:0%
+produced for society how much benefit is
+ 
+
+ align:start position:0%
+produced for society how much benefit is
+produced by this transaction ok well the
+
+ align:start position:0%
+produced by this transaction ok well the
+ 
+
+ align:start position:0%
+produced by this transaction ok well the
+benefits produced by this transaction is
+
+ align:start position:0%
+benefits produced by this transaction is
+ 
+
+ align:start position:0%
+benefits produced by this transaction is
+going to be the surplus derive surplus
+
+ align:start position:0%
+going to be the surplus derive surplus
+ 
+
+ align:start position:0%
+going to be the surplus derive surplus
+generated for consumers by that
+
+ align:start position:0%
+generated for consumers by that
+ 
+
+ align:start position:0%
+generated for consumers by that
+transaction and the surplus generated
+
+ align:start position:0%
+transaction and the surplus generated
+ 
+
+ align:start position:0%
+transaction and the surplus generated
+for producers by that transaction so our
+
+ align:start position:0%
+for producers by that transaction so our
+ 
+
+ align:start position:0%
+for producers by that transaction so our
+total measure of social well-being is
+
+ align:start position:0%
+total measure of social well-being is
+ 
+
+ align:start position:0%
+total measure of social well-being is
+going to be the sum of consumer and
+
+ align:start position:0%
+going to be the sum of consumer and
+ 
+
+ align:start position:0%
+going to be the sum of consumer and
+producer surplus and we are going to
+
+ align:start position:0%
+producer surplus and we are going to
+ 
+
+ align:start position:0%
+producer surplus and we are going to
+prove as I said we you don't need to
+
+ align:start position:0%
+prove as I said we you don't need to
+ 
+
+ align:start position:0%
+prove as I said we you don't need to
+know this but it's in graduating I was
+
+ align:start position:0%
+know this but it's in graduating I was
+ 
+
+ align:start position:0%
+know this but it's in graduating I was
+called the first fundamental theorem of
+
+ align:start position:0%
+called the first fundamental theorem of
+ 
+
+ align:start position:0%
+called the first fundamental theorem of
+welfare economics
+
+ align:start position:0%
+welfare economics
+ 
+
+ align:start position:0%
+welfare economics
+which is that under the assumptions
+
+ align:start position:0%
+which is that under the assumptions
+ 
+
+ align:start position:0%
+which is that under the assumptions
+we've made which are many okay under the
+
+ align:start position:0%
+we've made which are many okay under the
+ 
+
+ align:start position:0%
+we've made which are many okay under the
+assumptions we've made the competitive
+
+ align:start position:0%
+assumptions we've made the competitive
+ 
+
+ align:start position:0%
+assumptions we've made the competitive
+equilibrium where supply equals demand
+
+ align:start position:0%
+equilibrium where supply equals demand
+ 
+
+ align:start position:0%
+equilibrium where supply equals demand
+is the point that maximizes social
+
+ align:start position:0%
+is the point that maximizes social
+ 
+
+ align:start position:0%
+is the point that maximizes social
+welfare that is the key insight is the
+
+ align:start position:0%
+welfare that is the key insight is the
+ 
+
+ align:start position:0%
+welfare that is the key insight is the
+point that the market naturally delivers
+
+ align:start position:0%
+point that the market naturally delivers
+ 
+
+ align:start position:0%
+point that the market naturally delivers
+the equilibrium that's gained by the
+
+ align:start position:0%
+the equilibrium that's gained by the
+ 
+
+ align:start position:0%
+the equilibrium that's gained by the
+market naturally happens to be the point
+
+ align:start position:0%
+market naturally happens to be the point
+ 
+
+ align:start position:0%
+market naturally happens to be the point
+that also makes society as well off as
+
+ align:start position:0%
+that also makes society as well off as
+ 
+
+ align:start position:0%
+that also makes society as well off as
+possible a very profound result okay
+
+ align:start position:0%
+possible a very profound result okay
+ 
+
+ align:start position:0%
+possible a very profound result okay
+that is a positive conclusion which is
+
+ align:start position:0%
+that is a positive conclusion which is
+ 
+
+ align:start position:0%
+that is a positive conclusion which is
+that supplying a man will meet at a
+
+ align:start position:0%
+that supplying a man will meet at a
+ 
+
+ align:start position:0%
+that supplying a man will meet at a
+certain equilibrium delivers a normative
+
+ align:start position:0%
+certain equilibrium delivers a normative
+ 
+
+ align:start position:0%
+certain equilibrium delivers a normative
+conclusion which is that equilibrium is
+
+ align:start position:0%
+conclusion which is that equilibrium is
+ 
+
+ align:start position:0%
+conclusion which is that equilibrium is
+the point which maximizes social welfare
+
+ align:start position:0%
+the point which maximizes social welfare
+ 
+
+ align:start position:0%
+the point which maximizes social welfare
+okay now the best way to see this is
+
+ align:start position:0%
+okay now the best way to see this is
+ 
+
+ align:start position:0%
+okay now the best way to see this is
+just graphically so let's go to figure
+
+ align:start position:0%
+just graphically so let's go to figure
+ 
+
+ align:start position:0%
+just graphically so let's go to figure
+10:1 okay figure ten one has supply and
+
+ align:start position:0%
+10:1 okay figure ten one has supply and
+ 
+
+ align:start position:0%
+10:1 okay figure ten one has supply and
+demand curve okay once again whether
+
+ align:start position:0%
+demand curve okay once again whether
+ 
+
+ align:start position:0%
+demand curve okay once again whether
+these are curved or linear these are
+
+ align:start position:0%
+these are curved or linear these are
+ 
+
+ align:start position:0%
+these are curved or linear these are
+just you know it's still the basic idea
+
+ align:start position:0%
+just you know it's still the basic idea
+ 
+
+ align:start position:0%
+just you know it's still the basic idea
+of supply and demand curve so a curve
+
+ align:start position:0%
+of supply and demand curve so a curve
+ 
+
+ align:start position:0%
+of supply and demand curve so a curve
+supplying a main curve are things which
+
+ align:start position:0%
+supplying a main curve are things which
+ 
+
+ align:start position:0%
+supplying a main curve are things which
+more are more sort of constant
+
+ align:start position:0%
+more are more sort of constant
+ 
+
+ align:start position:0%
+more are more sort of constant
+elasticity type curves but that doesn't
+
+ align:start position:0%
+elasticity type curves but that doesn't
+ 
+
+ align:start position:0%
+elasticity type curves but that doesn't
+really affect the intuition okay we have
+
+ align:start position:0%
+really affect the intuition okay we have
+ 
+
+ align:start position:0%
+really affect the intuition okay we have
+here the triangles of consumer surplus
+
+ align:start position:0%
+here the triangles of consumer surplus
+ 
+
+ align:start position:0%
+here the triangles of consumer surplus
+and producer surplus so consumer surplus
+
+ align:start position:0%
+and producer surplus so consumer surplus
+ 
+
+ align:start position:0%
+and producer surplus so consumer surplus
+give me the letter somebody raise their
+
+ align:start position:0%
+give me the letter somebody raise their
+ 
+
+ align:start position:0%
+give me the letter somebody raise their
+hand and tell me which letters on this
+
+ align:start position:0%
+hand and tell me which letters on this
+ 
+
+ align:start position:0%
+hand and tell me which letters on this
+diagram correspond to consumer surplus
+
+ align:start position:0%
+diagram correspond to consumer surplus
+ 
+
+ align:start position:0%
+diagram correspond to consumer surplus
+and Y which which areas denoted by which
+
+ align:start position:0%
+and Y which which areas denoted by which
+ 
+
+ align:start position:0%
+and Y which which areas denoted by which
+letters correspond to consumer surplus
+
+ align:start position:0%
+letters correspond to consumer surplus
+ 
+
+ align:start position:0%
+letters correspond to consumer surplus
+and why yeah why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly everything above below the
+
+ align:start position:0%
+exactly everything above below the
+ 
+
+ align:start position:0%
+exactly everything above below the
+demand curve above the price consumer
+
+ align:start position:0%
+demand curve above the price consumer
+ 
+
+ align:start position:0%
+demand curve above the price consumer
+surplus so R plus V so therefore what's
+
+ align:start position:0%
+surplus so R plus V so therefore what's
+ 
+
+ align:start position:0%
+surplus so R plus V so therefore what's
+producer surplus same person s plus T
+
+ align:start position:0%
+producer surplus same person s plus T
+ 
+
+ align:start position:0%
+producer surplus same person s plus T
+plus U is producer surplus so consumer
+
+ align:start position:0%
+plus U is producer surplus so consumer
+ 
+
+ align:start position:0%
+plus U is producer surplus so consumer
+surplus R plus V producer surplus is s
+
+ align:start position:0%
+surplus R plus V producer surplus is s
+ 
+
+ align:start position:0%
+surplus R plus V producer surplus is s
+plus t plus u okay you can see those of
+
+ align:start position:0%
+plus t plus u okay you can see those of
+ 
+
+ align:start position:0%
+plus t plus u okay you can see those of
+you are sort of graphically oriented can
+
+ align:start position:0%
+you are sort of graphically oriented can
+ 
+
+ align:start position:0%
+you are sort of graphically oriented can
+immediately see the sum of those two
+
+ align:start position:0%
+immediately see the sum of those two
+ 
+
+ align:start position:0%
+immediately see the sum of those two
+triangles will be maximized at the
+
+ align:start position:0%
+triangles will be maximized at the
+ 
+
+ align:start position:0%
+triangles will be maximized at the
+intersection of the curves and nowhere
+
+ align:start position:0%
+intersection of the curves and nowhere
+ 
+
+ align:start position:0%
+intersection of the curves and nowhere
+else okay so for example let's think
+
+ align:start position:0%
+else okay so for example let's think
+ 
+
+ align:start position:0%
+else okay so for example let's think
+about the case where I say well look
+
+ align:start position:0%
+about the case where I say well look
+ 
+
+ align:start position:0%
+about the case where I say well look
+it's a shame the prices that high we
+
+ align:start position:0%
+it's a shame the prices that high we
+ 
+
+ align:start position:0%
+it's a shame the prices that high we
+ought to make the price lower let's set
+
+ align:start position:0%
+ought to make the price lower let's set
+ 
+
+ align:start position:0%
+ought to make the price lower let's set
+a new price let's have the government
+
+ align:start position:0%
+a new price let's have the government
+ 
+
+ align:start position:0%
+a new price let's have the government
+mandate a new price at p2 suppose the
+
+ align:start position:0%
+mandate a new price at p2 suppose the
+ 
+
+ align:start position:0%
+mandate a new price at p2 suppose the
+government intervenes and since we're
+
+ align:start position:0%
+government intervenes and since we're
+ 
+
+ align:start position:0%
+government intervenes and since we're
+gonna set a price ceiling we're gonna
+
+ align:start position:0%
+gonna set a price ceiling we're gonna
+ 
+
+ align:start position:0%
+gonna set a price ceiling we're gonna
+say no one can charge more than p2 for
+
+ align:start position:0%
+say no one can charge more than p2 for
+ 
+
+ align:start position:0%
+say no one can charge more than p2 for
+their product and won't that be a good
+
+ align:start position:0%
+their product and won't that be a good
+ 
+
+ align:start position:0%
+their product and won't that be a good
+thing because consumers ould be better
+
+ align:start position:0%
+thing because consumers ould be better
+ 
+
+ align:start position:0%
+thing because consumers ould be better
+off they'll pay lower prices well what
+
+ align:start position:0%
+off they'll pay lower prices well what
+ 
+
+ align:start position:0%
+off they'll pay lower prices well what
+does that do that does what does that do
+
+ align:start position:0%
+does that do that does what does that do
+ 
+
+ align:start position:0%
+does that do that does what does that do
+to consumer surplus
+
+ align:start position:0%
+to consumer surplus
+ 
+
+ align:start position:0%
+to consumer surplus
+well consumer surplus used to be R plus
+
+ align:start position:0%
+well consumer surplus used to be R plus
+ 
+
+ align:start position:0%
+well consumer surplus used to be R plus
+V it instead becomes R plus s which is
+
+ align:start position:0%
+V it instead becomes R plus s which is
+ 
+
+ align:start position:0%
+V it instead becomes R plus s which is
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+okay consumer surplus Rises you lose the
+
+ align:start position:0%
+okay consumer surplus Rises you lose the
+ 
+
+ align:start position:0%
+okay consumer surplus Rises you lose the
+triangle V and you gain the and you gain
+
+ align:start position:0%
+triangle V and you gain the and you gain
+ 
+
+ align:start position:0%
+triangle V and you gain the and you gain
+the rectangle S but the key point is at
+
+ align:start position:0%
+the rectangle S but the key point is at
+ 
+
+ align:start position:0%
+the rectangle S but the key point is at
+the price e to okay at the price P to
+
+ align:start position:0%
+the price e to okay at the price P to
+ 
+
+ align:start position:0%
+the price e to okay at the price P to
+yet that becomes the new consumer
+
+ align:start position:0%
+yet that becomes the new consumer
+ 
+
+ align:start position:0%
+yet that becomes the new consumer
+surplus the new producer surplus is what
+
+ align:start position:0%
+surplus the new producer surplus is what
+ 
+
+ align:start position:0%
+surplus the new producer surplus is what
+at that price p2 what's the new producer
+
+ align:start position:0%
+at that price p2 what's the new producer
+ 
+
+ align:start position:0%
+at that price p2 what's the new producer
+surplus so raise their hand and tell me
+
+ align:start position:0%
+surplus so raise their hand and tell me
+ 
+
+ align:start position:0%
+surplus so raise their hand and tell me
+yeah it's T it drops to t producers just
+
+ align:start position:0%
+yeah it's T it drops to t producers just
+ 
+
+ align:start position:0%
+yeah it's T it drops to t producers just
+get below the price above the supply
+
+ align:start position:0%
+get below the price above the supply
+ 
+
+ align:start position:0%
+get below the price above the supply
+curve so what has happened to total
+
+ align:start position:0%
+curve so what has happened to total
+ 
+
+ align:start position:0%
+curve so what has happened to total
+social welfare it has fallen by the
+
+ align:start position:0%
+social welfare it has fallen by the
+ 
+
+ align:start position:0%
+social welfare it has fallen by the
+amount V Plus u total social welfare has
+
+ align:start position:0%
+amount V Plus u total social welfare has
+ 
+
+ align:start position:0%
+amount V Plus u total social welfare has
+fallen play deepest V Plus u so in some
+
+ align:start position:0%
+fallen play deepest V Plus u so in some
+ 
+
+ align:start position:0%
+fallen play deepest V Plus u so in some
+sense two things have happened here
+
+ align:start position:0%
+sense two things have happened here
+ 
+
+ align:start position:0%
+sense two things have happened here
+we've set this price the first is a
+
+ align:start position:0%
+we've set this price the first is a
+ 
+
+ align:start position:0%
+we've set this price the first is a
+transfer we have transferred the
+
+ align:start position:0%
+transfer we have transferred the
+ 
+
+ align:start position:0%
+transfer we have transferred the
+rectangle s from producers to consumers
+
+ align:start position:0%
+rectangle s from producers to consumers
+ 
+
+ align:start position:0%
+rectangle s from producers to consumers
+s used to be part of producer surplus
+
+ align:start position:0%
+s used to be part of producer surplus
+ 
+
+ align:start position:0%
+s used to be part of producer surplus
+we're not giving it to consumers first
+
+ align:start position:0%
+we're not giving it to consumers first
+ 
+
+ align:start position:0%
+we're not giving it to consumers first
+thing that happens is a transfer that
+
+ align:start position:0%
+thing that happens is a transfer that
+ 
+
+ align:start position:0%
+thing that happens is a transfer that
+was probably the idea of this policy
+
+ align:start position:0%
+was probably the idea of this policy
+ 
+
+ align:start position:0%
+was probably the idea of this policy
+make consumers better off so who
+
+ align:start position:0%
+make consumers better off so who
+ 
+
+ align:start position:0%
+make consumers better off so who
+transferred what you see pretty surplus
+
+ align:start position:0%
+transferred what you see pretty surplus
+ 
+
+ align:start position:0%
+transferred what you see pretty surplus
+to consumers that's the rectangle s
+
+ align:start position:0%
+to consumers that's the rectangle s
+ 
+
+ align:start position:0%
+to consumers that's the rectangle s
+that's the first thing this happened so
+
+ align:start position:0%
+that's the first thing this happened so
+ 
+
+ align:start position:0%
+that's the first thing this happened so
+thing one this happened is a transfer of
+
+ align:start position:0%
+thing one this happened is a transfer of
+ 
+
+ align:start position:0%
+thing one this happened is a transfer of
+s but the second thing that's happened
+
+ align:start position:0%
+s but the second thing that's happened
+ 
+
+ align:start position:0%
+s but the second thing that's happened
+is we have created what we call a
+
+ align:start position:0%
+is we have created what we call a
+ 
+
+ align:start position:0%
+is we have created what we call a
+deadweight loss of U plus V a deadweight
+
+ align:start position:0%
+deadweight loss of U plus V a deadweight
+ 
+
+ align:start position:0%
+deadweight loss of U plus V a deadweight
+loss of U plus V dwl deadweight loss
+
+ align:start position:0%
+loss of U plus V dwl deadweight loss
+ 
+
+ align:start position:0%
+loss of U plus V dwl deadweight loss
+what does the deadweight loss that is
+
+ align:start position:0%
+what does the deadweight loss that is
+ 
+
+ align:start position:0%
+what does the deadweight loss that is
+the net reduction in welfare from trades
+
+ align:start position:0%
+the net reduction in welfare from trades
+ 
+
+ align:start position:0%
+the net reduction in welfare from trades
+that are not made the deadweight loss is
+
+ align:start position:0%
+that are not made the deadweight loss is
+ 
+
+ align:start position:0%
+that are not made the deadweight loss is
+a key concept we'll come back to I'll
+
+ align:start position:0%
+a key concept we'll come back to I'll
+ 
+
+ align:start position:0%
+a key concept we'll come back to I'll
+expect you to know it in your sleep okay
+
+ align:start position:0%
+expect you to know it in your sleep okay
+ 
+
+ align:start position:0%
+expect you to know it in your sleep okay
+is that deadweight loss is the net
+
+ align:start position:0%
+is that deadweight loss is the net
+ 
+
+ align:start position:0%
+is that deadweight loss is the net
+reduction in Social Welfare from trades
+
+ align:start position:0%
+reduction in Social Welfare from trades
+ 
+
+ align:start position:0%
+reduction in Social Welfare from trades
+that are not made the intuition here is
+
+ align:start position:0%
+that are not made the intuition here is
+ 
+
+ align:start position:0%
+that are not made the intuition here is
+that every trade that makes at least one
+
+ align:start position:0%
+that every trade that makes at least one
+ 
+
+ align:start position:0%
+that every trade that makes at least one
+party better off without making the
+
+ align:start position:0%
+party better off without making the
+ 
+
+ align:start position:0%
+party better off without making the
+other party worse off is a good trade to
+
+ align:start position:0%
+other party worse off is a good trade to
+ 
+
+ align:start position:0%
+other party worse off is a good trade to
+do under the assumption we made so far
+
+ align:start position:0%
+do under the assumption we made so far
+ 
+
+ align:start position:0%
+do under the assumption we made so far
+if you ever trade that increased
+
+ align:start position:0%
+if you ever trade that increased
+ 
+
+ align:start position:0%
+if you ever trade that increased
+consumer surplus or produce surplus or
+
+ align:start position:0%
+consumer surplus or produce surplus or
+ 
+
+ align:start position:0%
+consumer surplus or produce surplus or
+both that's a good thing to have right
+
+ align:start position:0%
+both that's a good thing to have right
+ 
+
+ align:start position:0%
+both that's a good thing to have right
+if my daughter has any song she wants to
+
+ align:start position:0%
+if my daughter has any song she wants to
+ 
+
+ align:start position:0%
+if my daughter has any song she wants to
+buy by Kendrick Lamar that you guys have
+
+ align:start position:0%
+buy by Kendrick Lamar that you guys have
+ 
+
+ align:start position:0%
+buy by Kendrick Lamar that you guys have
+more than a dollar she gets him for a
+
+ align:start position:0%
+more than a dollar she gets him for a
+ 
+
+ align:start position:0%
+more than a dollar she gets him for a
+dollar anything which stops her from
+
+ align:start position:0%
+dollar anything which stops her from
+ 
+
+ align:start position:0%
+dollar anything which stops her from
+buying those songs is bad she's losing
+
+ align:start position:0%
+buying those songs is bad she's losing
+ 
+
+ align:start position:0%
+buying those songs is bad she's losing
+surplus okay so basically the key point
+
+ align:start position:0%
+surplus okay so basically the key point
+ 
+
+ align:start position:0%
+surplus okay so basically the key point
+is that deadweight loss is an
+
+ align:start position:0%
+is that deadweight loss is an
+ 
+
+ align:start position:0%
+is that deadweight loss is an
+inefficiency okay we talked about how
+
+ align:start position:0%
+inefficiency okay we talked about how
+ 
+
+ align:start position:0%
+inefficiency okay we talked about how
+competition leads to maximally efficient
+
+ align:start position:0%
+competition leads to maximally efficient
+ 
+
+ align:start position:0%
+competition leads to maximally efficient
+production through cost minimization
+
+ align:start position:0%
+production through cost minimization
+ 
+
+ align:start position:0%
+production through cost minimization
+competition also leads to the maximum
+
+ align:start position:0%
+competition also leads to the maximum
+ 
+
+ align:start position:0%
+competition also leads to the maximum
+welfare outcome because that point is
+
+ align:start position:0%
+welfare outcome because that point is
+ 
+
+ align:start position:0%
+welfare outcome because that point is
+the point which makes society best off
+
+ align:start position:0%
+the point which makes society best off
+ 
+
+ align:start position:0%
+the point which makes society best off
+defined as the sum of consumer surplus
+
+ align:start position:0%
+defined as the sum of consumer surplus
+ 
+
+ align:start position:0%
+defined as the sum of consumer surplus
+plus producer surplus
+
+ align:start position:0%
+plus producer surplus
+ 
+
+ align:start position:0%
+plus producer surplus
+okay but once again I cannot highlight
+
+ align:start position:0%
+okay but once again I cannot highlight
+ 
+
+ align:start position:0%
+okay but once again I cannot highlight
+enough the depth of this insight at this
+
+ align:start position:0%
+enough the depth of this insight at this
+ 
+
+ align:start position:0%
+enough the depth of this insight at this
+point which before today you knew as the
+
+ align:start position:0%
+point which before today you knew as the
+ 
+
+ align:start position:0%
+point which before today you knew as the
+outcome I showed him the first lecture
+
+ align:start position:0%
+outcome I showed him the first lecture
+ 
+
+ align:start position:0%
+outcome I showed him the first lecture
+this what happens we have supply and
+
+ align:start position:0%
+this what happens we have supply and
+ 
+
+ align:start position:0%
+this what happens we have supply and
+demand you get to this equilibrium that
+
+ align:start position:0%
+demand you get to this equilibrium that
+ 
+
+ align:start position:0%
+demand you get to this equilibrium that
+happens to be the very best place to be
+
+ align:start position:0%
+happens to be the very best place to be
+ 
+
+ align:start position:0%
+happens to be the very best place to be
+and that's why we call it the first
+
+ align:start position:0%
+and that's why we call it the first
+ 
+
+ align:start position:0%
+and that's why we call it the first
+fundamental theorem it's very important
+
+ align:start position:0%
+fundamental theorem it's very important
+ 
+
+ align:start position:0%
+fundamental theorem it's very important
+okay yeah so so so let's I want to come
+
+ align:start position:0%
+okay yeah so so so let's I want to come
+ 
+
+ align:start position:0%
+okay yeah so so so let's I want to come
+to that let's talk about that let's go
+
+ align:start position:0%
+to that let's talk about that let's go
+ 
+
+ align:start position:0%
+to that let's talk about that let's go
+to another example to talk about that
+
+ align:start position:0%
+to another example to talk about that
+ 
+
+ align:start position:0%
+to another example to talk about that
+let's talk about interventions let's do
+
+ align:start position:0%
+let's talk about interventions let's do
+ 
+
+ align:start position:0%
+let's talk about interventions let's do
+it let's do it let's do an example let
+
+ align:start position:0%
+it let's do it let's do an example let
+ 
+
+ align:start position:0%
+it let's do it let's do an example let
+that was just sort of to teach you the
+
+ align:start position:0%
+that was just sort of to teach you the
+ 
+
+ align:start position:0%
+that was just sort of to teach you the
+basic idea but let's go on to more
+
+ align:start position:0%
+basic idea but let's go on to more
+ 
+
+ align:start position:0%
+basic idea but let's go on to more
+explicit example of a government
+
+ align:start position:0%
+explicit example of a government
+ 
+
+ align:start position:0%
+explicit example of a government
+intervention actually do it here let me
+
+ align:start position:0%
+intervention actually do it here let me
+ 
+
+ align:start position:0%
+intervention actually do it here let me
+do explicit example of a government
+
+ align:start position:0%
+do explicit example of a government
+ 
+
+ align:start position:0%
+do explicit example of a government
+intervention that will and that will
+
+ align:start position:0%
+intervention that will and that will
+ 
+
+ align:start position:0%
+intervention that will and that will
+address the question was just asked
+
+ align:start position:0%
+address the question was just asked
+ 
+
+ align:start position:0%
+address the question was just asked
+because I skipped over sort of a key
+
+ align:start position:0%
+because I skipped over sort of a key
+ 
+
+ align:start position:0%
+because I skipped over sort of a key
+point here that that I'm always I'm
+
+ align:start position:0%
+point here that that I'm always I'm
+ 
+
+ align:start position:0%
+point here that that I'm always I'm
+always not sure whether way order to
+
+ align:start position:0%
+always not sure whether way order to
+ 
+
+ align:start position:0%
+always not sure whether way order to
+teach you things so so let's ask let's
+
+ align:start position:0%
+teach you things so so let's ask let's
+ 
+
+ align:start position:0%
+teach you things so so let's ask let's
+take an example of a market let's
+
+ align:start position:0%
+take an example of a market let's
+ 
+
+ align:start position:0%
+take an example of a market let's
+consider the market for gas so go to
+
+ align:start position:0%
+consider the market for gas so go to
+ 
+
+ align:start position:0%
+consider the market for gas so go to
+figure 10 to this heart we talked about
+
+ align:start position:0%
+figure 10 to this heart we talked about
+ 
+
+ align:start position:0%
+figure 10 to this heart we talked about
+before the market for gas
+
+ align:start position:0%
+before the market for gas
+ 
+
+ align:start position:0%
+before the market for gas
+imagine the market for gas is initially
+
+ align:start position:0%
+imagine the market for gas is initially
+ 
+
+ align:start position:0%
+imagine the market for gas is initially
+in equilibrium with supply curve s1 and
+
+ align:start position:0%
+in equilibrium with supply curve s1 and
+ 
+
+ align:start position:0%
+in equilibrium with supply curve s1 and
+a demand curve D it's initially in
+
+ align:start position:0%
+a demand curve D it's initially in
+ 
+
+ align:start position:0%
+a demand curve D it's initially in
+equilibrium at Point little E one with
+
+ align:start position:0%
+equilibrium at Point little E one with
+ 
+
+ align:start position:0%
+equilibrium at Point little E one with
+q1 gallons of gas being sold at a price
+
+ align:start position:0%
+q1 gallons of gas being sold at a price
+ 
+
+ align:start position:0%
+q1 gallons of gas being sold at a price
+p1 that's the initial equilibrium now
+
+ align:start position:0%
+p1 that's the initial equilibrium now
+ 
+
+ align:start position:0%
+p1 that's the initial equilibrium now
+imagine that there is an oil crisis
+
+ align:start position:0%
+imagine that there is an oil crisis
+ 
+
+ align:start position:0%
+imagine that there is an oil crisis
+because for example low company cited be
+
+ align:start position:0%
+because for example low company cited be
+ 
+
+ align:start position:0%
+because for example low company cited be
+good idea to drill 8 miles underground
+
+ align:start position:0%
+good idea to drill 8 miles underground
+ 
+
+ align:start position:0%
+good idea to drill 8 miles underground
+horizontally and the busts and their
+
+ align:start position:0%
+horizontally and the busts and their
+ 
+
+ align:start position:0%
+horizontally and the busts and their
+spills everywhere something like that
+
+ align:start position:0%
+spills everywhere something like that
+ 
+
+ align:start position:0%
+spills everywhere something like that
+some random example like that ok and
+
+ align:start position:0%
+some random example like that ok and
+ 
+
+ align:start position:0%
+some random example like that ok and
+this was a supply crisis what happens
+
+ align:start position:0%
+this was a supply crisis what happens
+ 
+
+ align:start position:0%
+this was a supply crisis what happens
+now is suddenly it gets more expensive
+
+ align:start position:0%
+now is suddenly it gets more expensive
+ 
+
+ align:start position:0%
+now is suddenly it gets more expensive
+to produce gas so the supply curve
+
+ align:start position:0%
+to produce gas so the supply curve
+ 
+
+ align:start position:0%
+to produce gas so the supply curve
+shifts upwards we talked about this last
+
+ align:start position:0%
+shifts upwards we talked about this last
+ 
+
+ align:start position:0%
+shifts upwards we talked about this last
+time leading us to new equilibrium at
+
+ align:start position:0%
+time leading us to new equilibrium at
+ 
+
+ align:start position:0%
+time leading us to new equilibrium at
+Point E - and your we talked about the
+
+ align:start position:0%
+Point E - and your we talked about the
+ 
+
+ align:start position:0%
+Point E - and your we talked about the
+echolert mork's firt initially there if
+
+ align:start position:0%
+echolert mork's firt initially there if
+ 
+
+ align:start position:0%
+echolert mork's firt initially there if
+we think about in steps initially you've
+
+ align:start position:0%
+we think about in steps initially you've
+ 
+
+ align:start position:0%
+we think about in steps initially you've
+created an excess demand because gas
+
+ align:start position:0%
+created an excess demand because gas
+ 
+
+ align:start position:0%
+created an excess demand because gas
+companies no longer want to supply
+
+ align:start position:0%
+companies no longer want to supply
+ 
+
+ align:start position:0%
+companies no longer want to supply
+q1 Gallants at a price p1 from their new
+
+ align:start position:0%
+q1 Gallants at a price p1 from their new
+ 
+
+ align:start position:0%
+q1 Gallants at a price p1 from their new
+supply curve so you move you shift along
+
+ align:start position:0%
+supply curve so you move you shift along
+ 
+
+ align:start position:0%
+supply curve so you move you shift along
+the demand curve to the new point e 2
+
+ align:start position:0%
+the demand curve to the new point e 2
+ 
+
+ align:start position:0%
+the demand curve to the new point e 2
+which is new equilibrium and all's well
+
+ align:start position:0%
+which is new equilibrium and all's well
+ 
+
+ align:start position:0%
+which is new equilibrium and all's well
+and good
+
+ align:start position:0%
+and good
+ 
+
+ align:start position:0%
+and good
+okay prices go up that's what happened
+
+ align:start position:0%
+okay prices go up that's what happened
+ 
+
+ align:start position:0%
+okay prices go up that's what happened
+after deepwater and things like that
+
+ align:start position:0%
+after deepwater and things like that
+ 
+
+ align:start position:0%
+after deepwater and things like that
+okay now imagine the government doesn't
+
+ align:start position:0%
+okay now imagine the government doesn't
+ 
+
+ align:start position:0%
+okay now imagine the government doesn't
+like that magic government says well we
+
+ align:start position:0%
+like that magic government says well we
+ 
+
+ align:start position:0%
+like that magic government says well we
+don't like that we don't like the fact
+
+ align:start position:0%
+don't like that we don't like the fact
+ 
+
+ align:start position:0%
+don't like that we don't like the fact
+consumer is a table for gas consumers
+
+ align:start position:0%
+consumer is a table for gas consumers
+ 
+
+ align:start position:0%
+consumer is a table for gas consumers
+vote us out of office we'll have to pay
+
+ align:start position:0%
+vote us out of office we'll have to pay
+ 
+
+ align:start position:0%
+vote us out of office we'll have to pay
+more for gas so we are gonna solve this
+
+ align:start position:0%
+more for gas so we are gonna solve this
+ 
+
+ align:start position:0%
+more for gas so we are gonna solve this
+by imposing a price ceiling we're gonna
+
+ align:start position:0%
+by imposing a price ceiling we're gonna
+ 
+
+ align:start position:0%
+by imposing a price ceiling we're gonna
+announce the price of gas must remain at
+
+ align:start position:0%
+announce the price of gas must remain at
+ 
+
+ align:start position:0%
+announce the price of gas must remain at
+its old level p1 okay
+
+ align:start position:0%
+its old level p1 okay
+ 
+
+ align:start position:0%
+its old level p1 okay
+so let's go to figure 10 three figure 10
+
+ align:start position:0%
+so let's go to figure 10 three figure 10
+ 
+
+ align:start position:0%
+so let's go to figure 10 three figure 10
+three shows what happens when the
+
+ align:start position:0%
+three shows what happens when the
+ 
+
+ align:start position:0%
+three shows what happens when the
+government imposed that price ceiling
+
+ align:start position:0%
+government imposed that price ceiling
+ 
+
+ align:start position:0%
+government imposed that price ceiling
+okay well the first question is if the
+
+ align:start position:0%
+okay well the first question is if the
+ 
+
+ align:start position:0%
+okay well the first question is if the
+government imposed a price ceiling of p1
+
+ align:start position:0%
+government imposed a price ceiling of p1
+ 
+
+ align:start position:0%
+government imposed a price ceiling of p1
+how much actually gets sold in the
+
+ align:start position:0%
+how much actually gets sold in the
+ 
+
+ align:start position:0%
+how much actually gets sold in the
+market this comes the question was just
+
+ align:start position:0%
+market this comes the question was just
+ 
+
+ align:start position:0%
+market this comes the question was just
+asked well this is sort of a new thing
+
+ align:start position:0%
+asked well this is sort of a new thing
+ 
+
+ align:start position:0%
+asked well this is sort of a new thing
+this sort of a new thing we've looked at
+
+ align:start position:0%
+this sort of a new thing we've looked at
+ 
+
+ align:start position:0%
+this sort of a new thing we've looked at
+which is we have the situation was
+
+ align:start position:0%
+which is we have the situation was
+ 
+
+ align:start position:0%
+which is we have the situation was
+excess demand at the price p1 could
+
+ align:start position:0%
+excess demand at the price p1 could
+ 
+
+ align:start position:0%
+excess demand at the price p1 could
+sumers still want Q little deep but
+
+ align:start position:0%
+sumers still want Q little deep but
+ 
+
+ align:start position:0%
+sumers still want Q little deep but
+suppliers are only willing to supply Q s
+
+ align:start position:0%
+suppliers are only willing to supply Q s
+ 
+
+ align:start position:0%
+suppliers are only willing to supply Q s
+cute little s see consumers still are
+
+ align:start position:0%
+cute little s see consumers still are
+ 
+
+ align:start position:0%
+cute little s see consumers still are
+working off the same demand curve if
+
+ align:start position:0%
+working off the same demand curve if
+ 
+
+ align:start position:0%
+working off the same demand curve if
+used the government says we still want
+
+ align:start position:0%
+used the government says we still want
+ 
+
+ align:start position:0%
+used the government says we still want
+the price to be p1 they're like great we
+
+ align:start position:0%
+the price to be p1 they're like great we
+ 
+
+ align:start position:0%
+the price to be p1 they're like great we
+someone as much gas we had before
+
+ align:start position:0%
+someone as much gas we had before
+ 
+
+ align:start position:0%
+someone as much gas we had before
+suppliers are like no way we're not
+
+ align:start position:0%
+suppliers are like no way we're not
+ 
+
+ align:start position:0%
+suppliers are like no way we're not
+going to supply it if you're gonna keep
+
+ align:start position:0%
+going to supply it if you're gonna keep
+ 
+
+ align:start position:0%
+going to supply it if you're gonna keep
+the price at that level we're gonna
+
+ align:start position:0%
+the price at that level we're gonna
+ 
+
+ align:start position:0%
+the price at that level we're gonna
+produce less gas because we haven't
+
+ align:start position:0%
+produce less gas because we haven't
+ 
+
+ align:start position:0%
+produce less gas because we haven't
+rising marginal cost so if you're gonna
+
+ align:start position:0%
+rising marginal cost so if you're gonna
+ 
+
+ align:start position:0%
+rising marginal cost so if you're gonna
+force have that same price we're gonna
+
+ align:start position:0%
+force have that same price we're gonna
+ 
+
+ align:start position:0%
+force have that same price we're gonna
+work our way back down the supply curve
+
+ align:start position:0%
+work our way back down the supply curve
+ 
+
+ align:start position:0%
+work our way back down the supply curve
+and produce less gas so suddenly you
+
+ align:start position:0%
+and produce less gas so suddenly you
+ 
+
+ align:start position:0%
+and produce less gas so suddenly you
+have a situation of excess demand that
+
+ align:start position:0%
+have a situation of excess demand that
+ 
+
+ align:start position:0%
+have a situation of excess demand that
+doesn't get resolved remember the last
+
+ align:start position:0%
+doesn't get resolved remember the last
+ 
+
+ align:start position:0%
+doesn't get resolved remember the last
+time I said excess demand I resolved by
+
+ align:start position:0%
+time I said excess demand I resolved by
+ 
+
+ align:start position:0%
+time I said excess demand I resolved by
+moving up the demand curve well you
+
+ align:start position:0%
+moving up the demand curve well you
+ 
+
+ align:start position:0%
+moving up the demand curve well you
+can't hear you can't resolve that
+
+ align:start position:0%
+can't hear you can't resolve that
+ 
+
+ align:start position:0%
+can't hear you can't resolve that
+because the price is forced to be a p1
+
+ align:start position:0%
+because the price is forced to be a p1
+ 
+
+ align:start position:0%
+because the price is forced to be a p1
+ok now what determines what actually
+
+ align:start position:0%
+ok now what determines what actually
+ 
+
+ align:start position:0%
+ok now what determines what actually
+gets sold ones a price restriction
+
+ align:start position:0%
+gets sold ones a price restriction
+ 
+
+ align:start position:0%
+gets sold ones a price restriction
+here's the way I like to think of it I
+
+ align:start position:0%
+here's the way I like to think of it I
+ 
+
+ align:start position:0%
+here's the way I like to think of it I
+like to think of the actual quantity
+
+ align:start position:0%
+like to think of the actual quantity
+ 
+
+ align:start position:0%
+like to think of the actual quantity
+gets set by the constrained party so in
+
+ align:start position:0%
+gets set by the constrained party so in
+ 
+
+ align:start position:0%
+gets set by the constrained party so in
+this case a price ceiling means that
+
+ align:start position:0%
+this case a price ceiling means that
+ 
+
+ align:start position:0%
+this case a price ceiling means that
+suppliers want our ask supply more than
+
+ align:start position:0%
+suppliers want our ask supply more than
+ 
+
+ align:start position:0%
+suppliers want our ask supply more than
+they're willing to so they just say no
+
+ align:start position:0%
+they're willing to so they just say no
+ 
+
+ align:start position:0%
+they're willing to so they just say no
+so you actually get the ultimate quality
+
+ align:start position:0%
+so you actually get the ultimate quality
+ 
+
+ align:start position:0%
+so you actually get the ultimate quality
+in the market is qsr it doesn't matter
+
+ align:start position:0%
+in the market is qsr it doesn't matter
+ 
+
+ align:start position:0%
+in the market is qsr it doesn't matter
+that demand is yqd they can't buy stuff
+
+ align:start position:0%
+that demand is yqd they can't buy stuff
+ 
+
+ align:start position:0%
+that demand is yqd they can't buy stuff
+that's not produced likewise we'll do
+
+ align:start position:0%
+that's not produced likewise we'll do
+ 
+
+ align:start position:0%
+that's not produced likewise we'll do
+examples later with a price floor where
+
+ align:start position:0%
+examples later with a price floor where
+ 
+
+ align:start position:0%
+examples later with a price floor where
+suppliers where could worship where
+
+ align:start position:0%
+suppliers where could worship where
+ 
+
+ align:start position:0%
+suppliers where could worship where
+consumers want less the suppliers want
+
+ align:start position:0%
+consumers want less the suppliers want
+ 
+
+ align:start position:0%
+consumers want less the suppliers want
+it but will provide then its consumers
+
+ align:start position:0%
+it but will provide then its consumers
+ 
+
+ align:start position:0%
+it but will provide then its consumers
+that decide what gets sold so mace
+
+ align:start position:0%
+that decide what gets sold so mace
+ 
+
+ align:start position:0%
+that decide what gets sold so mace
+whoever wants less gets to decide
+
+ align:start position:0%
+whoever wants less gets to decide
+ 
+
+ align:start position:0%
+whoever wants less gets to decide
+because you can't force the producers to
+
+ align:start position:0%
+because you can't force the producers to
+ 
+
+ align:start position:0%
+because you can't force the producers to
+produce more we don't know we have a
+
+ align:start position:0%
+produce more we don't know we have a
+ 
+
+ align:start position:0%
+produce more we don't know we have a
+private oil industry gas industry so you
+
+ align:start position:0%
+private oil industry gas industry so you
+ 
+
+ align:start position:0%
+private oil industry gas industry so you
+end up with qsr units of gas sold at a
+
+ align:start position:0%
+end up with qsr units of gas sold at a
+ 
+
+ align:start position:0%
+end up with qsr units of gas sold at a
+price p1 so what the price ceiling does
+
+ align:start position:0%
+price p1 so what the price ceiling does
+ 
+
+ align:start position:0%
+price p1 so what the price ceiling does
+is move you from e1 to e3 you would have
+
+ align:start position:0%
+is move you from e1 to e3 you would have
+ 
+
+ align:start position:0%
+is move you from e1 to e3 you would have
+moved to e2 without the government
+
+ align:start position:0%
+moved to e2 without the government
+ 
+
+ align:start position:0%
+moved to e2 without the government
+intervention instead it moves you to e3
+
+ align:start position:0%
+intervention instead it moves you to e3
+ 
+
+ align:start position:0%
+intervention instead it moves you to e3
+ok and as a result you end up with
+
+ align:start position:0%
+ok and as a result you end up with
+ 
+
+ align:start position:0%
+ok and as a result you end up with
+consumers consumer surplus being a plus
+
+ align:start position:0%
+consumers consumer surplus being a plus
+ 
+
+ align:start position:0%
+consumers consumer surplus being a plus
+C producer surplus being e and relative
+
+ align:start position:0%
+C producer surplus being e and relative
+ 
+
+ align:start position:0%
+C producer surplus being e and relative
+to an unconstrained world I wrote over
+
+ align:start position:0%
+to an unconstrained world I wrote over
+ 
+
+ align:start position:0%
+to an unconstrained world I wrote over
+before but relative without government
+
+ align:start position:0%
+before but relative without government
+ 
+
+ align:start position:0%
+before but relative without government
+intervention you have a deadweight loss
+
+ align:start position:0%
+intervention you have a deadweight loss
+ 
+
+ align:start position:0%
+intervention you have a deadweight loss
+of B plus D yeah well that's a very deep
+
+ align:start position:0%
+of B plus D yeah well that's a very deep
+ 
+
+ align:start position:0%
+of B plus D yeah well that's a very deep
+question the guy says that we don't have
+
+ align:start position:0%
+question the guy says that we don't have
+ 
+
+ align:start position:0%
+question the guy says that we don't have
+a nationalized gas industry we just have
+
+ align:start position:0%
+a nationalized gas industry we just have
+ 
+
+ align:start position:0%
+a nationalized gas industry we just have
+private gas industries there's a
+
+ align:start position:0%
+private gas industries there's a
+ 
+
+ align:start position:0%
+private gas industries there's a
+separate issue you know a larger issue
+
+ align:start position:0%
+separate issue you know a larger issue
+ 
+
+ align:start position:0%
+separate issue you know a larger issue
+about whether private or public sector
+
+ align:start position:0%
+about whether private or public sector
+ 
+
+ align:start position:0%
+about whether private or public sector
+should be producing things and that's
+
+ align:start position:0%
+should be producing things and that's
+ 
+
+ align:start position:0%
+should be producing things and that's
+sort of beyond the scope of what we're
+
+ align:start position:0%
+sort of beyond the scope of what we're
+ 
+
+ align:start position:0%
+sort of beyond the scope of what we're
+discussing here but for now assume the
+
+ align:start position:0%
+discussing here but for now assume the
+ 
+
+ align:start position:0%
+discussing here but for now assume the
+government just has a regulatory role
+
+ align:start position:0%
+government just has a regulatory role
+ 
+
+ align:start position:0%
+government just has a regulatory role
+not a gas production role the government
+
+ align:start position:0%
+not a gas production role the government
+ 
+
+ align:start position:0%
+not a gas production role the government
+by the way does have a little gas
+
+ align:start position:0%
+by the way does have a little gas
+ 
+
+ align:start position:0%
+by the way does have a little gas
+production role because the government
+
+ align:start position:0%
+production role because the government
+ 
+
+ align:start position:0%
+production role because the government
+actually something called the strategic
+
+ align:start position:0%
+actually something called the strategic
+ 
+
+ align:start position:0%
+actually something called the strategic
+oil reserve where they have millions of
+
+ align:start position:0%
+oil reserve where they have millions of
+ 
+
+ align:start position:0%
+oil reserve where they have millions of
+barrels they can actually release and
+
+ align:start position:0%
+barrels they can actually release and
+ 
+
+ align:start position:0%
+barrels they can actually release and
+release out in the market at certain
+
+ align:start position:0%
+release out in the market at certain
+ 
+
+ align:start position:0%
+release out in the market at certain
+times the government does have a way try
+
+ align:start position:0%
+times the government does have a way try
+ 
+
+ align:start position:0%
+times the government does have a way try
+to deal with this but for now let's
+
+ align:start position:0%
+to deal with this but for now let's
+ 
+
+ align:start position:0%
+to deal with this but for now let's
+assume that I could use the strategic
+
+ align:start position:0%
+assume that I could use the strategic
+ 
+
+ align:start position:0%
+assume that I could use the strategic
+reserve just regulate price ok so they
+
+ align:start position:0%
+reserve just regulate price ok so they
+ 
+
+ align:start position:0%
+reserve just regulate price ok so they
+regulate price and what they've done is
+
+ align:start position:0%
+regulate price and what they've done is
+ 
+
+ align:start position:0%
+regulate price and what they've done is
+they've created a deadweight loss ok so
+
+ align:start position:0%
+they've created a deadweight loss ok so
+ 
+
+ align:start position:0%
+they've created a deadweight loss ok so
+basically if we think about it what are
+
+ align:start position:0%
+basically if we think about it what are
+ 
+
+ align:start position:0%
+basically if we think about it what are
+the costs and benefits of government
+
+ align:start position:0%
+the costs and benefits of government
+ 
+
+ align:start position:0%
+the costs and benefits of government
+intervention the costs of government
+
+ align:start position:0%
+intervention the costs of government
+ 
+
+ align:start position:0%
+intervention the costs of government
+intervention are twofold
+
+ align:start position:0%
+intervention are twofold
+ 
+
+ align:start position:0%
+intervention are twofold
+what are the costs of this price ceiling
+
+ align:start position:0%
+what are the costs of this price ceiling
+ 
+
+ align:start position:0%
+what are the costs of this price ceiling
+there's two costs cost one is you've
+
+ align:start position:0%
+there's two costs cost one is you've
+ 
+
+ align:start position:0%
+there's two costs cost one is you've
+created an inefficiency you've created
+
+ align:start position:0%
+created an inefficiency you've created
+ 
+
+ align:start position:0%
+created an inefficiency you've created
+you straighten this deadweight loss
+
+ align:start position:0%
+you straighten this deadweight loss
+ 
+
+ align:start position:0%
+you straighten this deadweight loss
+because basically if you didn't restrict
+
+ align:start position:0%
+because basically if you didn't restrict
+ 
+
+ align:start position:0%
+because basically if you didn't restrict
+things there are people who would have
+
+ align:start position:0%
+things there are people who would have
+ 
+
+ align:start position:0%
+things there are people who would have
+bought gas to the right of Q sub s and
+
+ align:start position:0%
+bought gas to the right of Q sub s and
+ 
+
+ align:start position:0%
+bought gas to the right of Q sub s and
+to the left of e to those units between
+
+ align:start position:0%
+to the left of e to those units between
+ 
+
+ align:start position:0%
+to the left of e to those units between
+Q sub s and E to worry to intersects the
+
+ align:start position:0%
+Q sub s and E to worry to intersects the
+ 
+
+ align:start position:0%
+Q sub s and E to worry to intersects the
+x axis those are units where the
+
+ align:start position:0%
+x axis those are units where the
+ 
+
+ align:start position:0%
+x axis those are units where the
+consumer surplus plus the Bruce surplus
+
+ align:start position:0%
+consumer surplus plus the Bruce surplus
+ 
+
+ align:start position:0%
+consumer surplus plus the Bruce surplus
+is positive right you look at the unit
+
+ align:start position:0%
+is positive right you look at the unit
+ 
+
+ align:start position:0%
+is positive right you look at the unit
+right to the right of Q sub s that's a
+
+ align:start position:0%
+right to the right of Q sub s that's a
+ 
+
+ align:start position:0%
+right to the right of Q sub s that's a
+unit that would have that consumers
+
+ align:start position:0%
+unit that would have that consumers
+ 
+
+ align:start position:0%
+unit that would have that consumers
+would have happily bought at the new
+
+ align:start position:0%
+would have happily bought at the new
+ 
+
+ align:start position:0%
+would have happily bought at the new
+higher price and producer would have
+
+ align:start position:0%
+higher price and producer would have
+ 
+
+ align:start position:0%
+higher price and producer would have
+happily sold the new higher price but
+
+ align:start position:0%
+happily sold the new higher price but
+ 
+
+ align:start position:0%
+happily sold the new higher price but
+the government isn't letting it happen
+
+ align:start position:0%
+the government isn't letting it happen
+ 
+
+ align:start position:0%
+the government isn't letting it happen
+so that's a deadweight loss so that's an
+
+ align:start position:0%
+so that's a deadweight loss so that's an
+ 
+
+ align:start position:0%
+so that's a deadweight loss so that's an
+inefficiency okay so that's the first
+
+ align:start position:0%
+inefficiency okay so that's the first
+ 
+
+ align:start position:0%
+inefficiency okay so that's the first
+cost the cost of society of trades that
+
+ align:start position:0%
+cost the cost of society of trades that
+ 
+
+ align:start position:0%
+cost the cost of society of trades that
+don't get made and we call this an
+
+ align:start position:0%
+don't get made and we call this an
+ 
+
+ align:start position:0%
+don't get made and we call this an
+efficiency loss because there are
+
+ align:start position:0%
+efficiency loss because there are
+ 
+
+ align:start position:0%
+efficiency loss because there are
+efficient trays trake things are
+
+ align:start position:0%
+efficient trays trake things are
+ 
+
+ align:start position:0%
+efficient trays trake things are
+efficient if they make the whole the
+
+ align:start position:0%
+efficient if they make the whole the
+ 
+
+ align:start position:0%
+efficient if they make the whole the
+joint surplus is positive if I net
+
+ align:start position:0%
+joint surplus is positive if I net
+ 
+
+ align:start position:0%
+joint surplus is positive if I net
+people are better off there are fishing
+
+ align:start position:0%
+people are better off there are fishing
+ 
+
+ align:start position:0%
+people are better off there are fishing
+trades
+
+ align:start position:0%
+trades
+ 
+
+ align:start position:0%
+trades
+which both sides were happy to make and
+
+ align:start position:0%
+which both sides were happy to make and
+ 
+
+ align:start position:0%
+which both sides were happy to make and
+they can't mate and they can't make so
+
+ align:start position:0%
+they can't mate and they can't make so
+ 
+
+ align:start position:0%
+they can't mate and they can't make so
+we call us an efficiency loss okay but
+
+ align:start position:0%
+we call us an efficiency loss okay but
+ 
+
+ align:start position:0%
+we call us an efficiency loss okay but
+that's not the only cost to this policy
+
+ align:start position:0%
+that's not the only cost to this policy
+ 
+
+ align:start position:0%
+that's not the only cost to this policy
+what's the other cost it's a hard
+
+ align:start position:0%
+what's the other cost it's a hard
+ 
+
+ align:start position:0%
+what's the other cost it's a hard
+question yeah so this enforcement you
+
+ align:start position:0%
+question yeah so this enforcement you
+ 
+
+ align:start position:0%
+question yeah so this enforcement you
+have to like go around send regulars
+
+ align:start position:0%
+have to like go around send regulars
+ 
+
+ align:start position:0%
+have to like go around send regulars
+around the gas stations make sure
+
+ align:start position:0%
+around the gas stations make sure
+ 
+
+ align:start position:0%
+around the gas stations make sure
+they're not charging the wrong price
+
+ align:start position:0%
+they're not charging the wrong price
+ 
+
+ align:start position:0%
+they're not charging the wrong price
+that's true I sort of make that small
+
+ align:start position:0%
+that's true I sort of make that small
+ 
+
+ align:start position:0%
+that's true I sort of make that small
+let's take more sort of a theoretical
+
+ align:start position:0%
+let's take more sort of a theoretical
+ 
+
+ align:start position:0%
+let's take more sort of a theoretical
+not theoretical but what's the other big
+
+ align:start position:0%
+not theoretical but what's the other big
+ 
+
+ align:start position:0%
+not theoretical but what's the other big
+source of what yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's sort of a dynamic but once again
+
+ align:start position:0%
+there's sort of a dynamic but once again
+ 
+
+ align:start position:0%
+there's sort of a dynamic but once again
+the producers think this may be a
+
+ align:start position:0%
+the producers think this may be a
+ 
+
+ align:start position:0%
+the producers think this may be a
+short-run thing and what's the pro you
+
+ align:start position:0%
+short-run thing and what's the pro you
+ 
+
+ align:start position:0%
+short-run thing and what's the pro you
+know once the deepwater horizon gets
+
+ align:start position:0%
+know once the deepwater horizon gets
+ 
+
+ align:start position:0%
+know once the deepwater horizon gets
+fixed they'll prices will be back down
+
+ align:start position:0%
+fixed they'll prices will be back down
+ 
+
+ align:start position:0%
+fixed they'll prices will be back down
+or whatever but what's the other miracle
+
+ align:start position:0%
+or whatever but what's the other miracle
+ 
+
+ align:start position:0%
+or whatever but what's the other miracle
+of the market that we lose here what
+
+ align:start position:0%
+of the market that we lose here what
+ 
+
+ align:start position:0%
+of the market that we lose here what
+time is the very first lecture yeah but
+
+ align:start position:0%
+time is the very first lecture yeah but
+ 
+
+ align:start position:0%
+time is the very first lecture yeah but
+that's one lets rule out of choice
+
+ align:start position:0%
+that's one lets rule out of choice
+ 
+
+ align:start position:0%
+that's one lets rule out of choice
+because just a short-run deal yeah yes
+
+ align:start position:0%
+because just a short-run deal yeah yes
+ 
+
+ align:start position:0%
+because just a short-run deal yeah yes
+there's allocated inefficiency remember
+
+ align:start position:0%
+there's allocated inefficiency remember
+ 
+
+ align:start position:0%
+there's allocated inefficiency remember
+one of the things we talked about in the
+
+ align:start position:0%
+one of the things we talked about in the
+ 
+
+ align:start position:0%
+one of the things we talked about in the
+very first lecture I think we did maybe
+
+ align:start position:0%
+very first lecture I think we did maybe
+ 
+
+ align:start position:0%
+very first lecture I think we did maybe
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+anyway one of the most important
+
+ align:start position:0%
+anyway one of the most important
+ 
+
+ align:start position:0%
+anyway one of the most important
+benefits of the competitive equilibrium
+
+ align:start position:0%
+benefits of the competitive equilibrium
+ 
+
+ align:start position:0%
+benefits of the competitive equilibrium
+it doesn't just deliver the right
+
+ align:start position:0%
+it doesn't just deliver the right
+ 
+
+ align:start position:0%
+it doesn't just deliver the right
+quantity it delivers it to the people
+
+ align:start position:0%
+quantity it delivers it to the people
+ 
+
+ align:start position:0%
+quantity it delivers it to the people
+who want it the most so if you think
+
+ align:start position:0%
+who want it the most so if you think
+ 
+
+ align:start position:0%
+who want it the most so if you think
+about let's go back to figure 10 - it's
+
+ align:start position:0%
+about let's go back to figure 10 - it's
+ 
+
+ align:start position:0%
+about let's go back to figure 10 - it's
+easy to see there if you think about who
+
+ align:start position:0%
+easy to see there if you think about who
+ 
+
+ align:start position:0%
+easy to see there if you think about who
+gets gas at the initial equity one and
+
+ align:start position:0%
+gets gas at the initial equity one and
+ 
+
+ align:start position:0%
+gets gas at the initial equity one and
+actually no but let's go ten three
+
+ align:start position:0%
+actually no but let's go ten three
+ 
+
+ align:start position:0%
+actually no but let's go ten three
+that's fine so let's say we hadn't
+
+ align:start position:0%
+that's fine so let's say we hadn't
+ 
+
+ align:start position:0%
+that's fine so let's say we hadn't
+interfered and we'd allowed the price to
+
+ align:start position:0%
+interfered and we'd allowed the price to
+ 
+
+ align:start position:0%
+interfered and we'd allowed the price to
+go to e - well fewer people would've
+
+ align:start position:0%
+go to e - well fewer people would've
+ 
+
+ align:start position:0%
+go to e - well fewer people would've
+bought gas right supply the quantity
+
+ align:start position:0%
+bought gas right supply the quantity
+ 
+
+ align:start position:0%
+bought gas right supply the quantity
+would have fallen from QD would have
+
+ align:start position:0%
+would have fallen from QD would have
+ 
+
+ align:start position:0%
+would have fallen from QD would have
+fallen all the way from e1 to e2 but the
+
+ align:start position:0%
+fallen all the way from e1 to e2 but the
+ 
+
+ align:start position:0%
+fallen all the way from e1 to e2 but the
+people who dropped out would have been
+
+ align:start position:0%
+people who dropped out would have been
+ 
+
+ align:start position:0%
+people who dropped out would have been
+who the people who value gas - the least
+
+ align:start position:0%
+who the people who value gas - the least
+ 
+
+ align:start position:0%
+who the people who value gas - the least
+the people who got the lowest surplus
+
+ align:start position:0%
+the people who got the lowest surplus
+ 
+
+ align:start position:0%
+the people who got the lowest surplus
+from it okay however now suddenly you
+
+ align:start position:0%
+from it okay however now suddenly you
+ 
+
+ align:start position:0%
+from it okay however now suddenly you
+only have qsr units of gas and you have
+
+ align:start position:0%
+only have qsr units of gas and you have
+ 
+
+ align:start position:0%
+only have qsr units of gas and you have
+QD people who want them well now who
+
+ align:start position:0%
+QD people who want them well now who
+ 
+
+ align:start position:0%
+QD people who want them well now who
+decides who gets them before the market
+
+ align:start position:0%
+decides who gets them before the market
+ 
+
+ align:start position:0%
+decides who gets them before the market
+did the magic the market made sure the
+
+ align:start position:0%
+did the magic the market made sure the
+ 
+
+ align:start position:0%
+did the magic the market made sure the
+people who wanted the unit's got them
+
+ align:start position:0%
+people who wanted the unit's got them
+ 
+
+ align:start position:0%
+people who wanted the unit's got them
+now of a sudden something else has to
+
+ align:start position:0%
+now of a sudden something else has to
+ 
+
+ align:start position:0%
+now of a sudden something else has to
+decide so how do you resolve this well
+
+ align:start position:0%
+decide so how do you resolve this well
+ 
+
+ align:start position:0%
+decide so how do you resolve this well
+we actually had an answer to this we had
+
+ align:start position:0%
+we actually had an answer to this we had
+ 
+
+ align:start position:0%
+we actually had an answer to this we had
+a gas crisis in the 1970s and the
+
+ align:start position:0%
+a gas crisis in the 1970s and the
+ 
+
+ align:start position:0%
+a gas crisis in the 1970s and the
+government imposed the price ceiling and
+
+ align:start position:0%
+government imposed the price ceiling and
+ 
+
+ align:start position:0%
+government imposed the price ceiling and
+have it get resolved how do we decide
+
+ align:start position:0%
+have it get resolved how do we decide
+ 
+
+ align:start position:0%
+have it get resolved how do we decide
+then who got the gas does anyone know
+
+ align:start position:0%
+then who got the gas does anyone know
+ 
+
+ align:start position:0%
+then who got the gas does anyone know
+raise your hand tell me if you know yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people wait in line people basically sat
+
+ align:start position:0%
+people wait in line people basically sat
+ 
+
+ align:start position:0%
+people wait in line people basically sat
+in their cars and waited in line okay
+
+ align:start position:0%
+in their cars and waited in line okay
+ 
+
+ align:start position:0%
+in their cars and waited in line okay
+now so essentially if you think about it
+
+ align:start position:0%
+now so essentially if you think about it
+ 
+
+ align:start position:0%
+now so essentially if you think about it
+we goods are going to get allocated
+
+ align:start position:0%
+we goods are going to get allocated
+ 
+
+ align:start position:0%
+we goods are going to get allocated
+somehow if the market isn't allocate
+
+ align:start position:0%
+somehow if the market isn't allocate
+ 
+
+ align:start position:0%
+somehow if the market isn't allocate
+them there'll be another less efficient
+
+ align:start position:0%
+them there'll be another less efficient
+ 
+
+ align:start position:0%
+them there'll be another less efficient
+allocation mechanism okay and basically
+
+ align:start position:0%
+allocation mechanism okay and basically
+ 
+
+ align:start position:0%
+allocation mechanism okay and basically
+why is it inefficient that people waited
+
+ align:start position:0%
+why is it inefficient that people waited
+ 
+
+ align:start position:0%
+why is it inefficient that people waited
+in line for gas there's actually two
+
+ align:start position:0%
+in line for gas there's actually two
+ 
+
+ align:start position:0%
+in line for gas there's actually two
+reasons one sort of cute but what's the
+
+ align:start position:0%
+reasons one sort of cute but what's the
+ 
+
+ align:start position:0%
+reasons one sort of cute but what's the
+main reason officially waiting in line
+
+ align:start position:0%
+main reason officially waiting in line
+ 
+
+ align:start position:0%
+main reason officially waiting in line
+for gas yeah yes the opportunity cost
+
+ align:start position:0%
+for gas yeah yes the opportunity cost
+ 
+
+ align:start position:0%
+for gas yeah yes the opportunity cost
+little point little one you have the
+
+ align:start position:0%
+little point little one you have the
+ 
+
+ align:start position:0%
+little point little one you have the
+opportunity cost okay you have the fact
+
+ align:start position:0%
+opportunity cost okay you have the fact
+ 
+
+ align:start position:0%
+opportunity cost okay you have the fact
+that that time I spent waiting in line I
+
+ align:start position:0%
+that that time I spent waiting in line I
+ 
+
+ align:start position:0%
+that that time I spent waiting in line I
+could have been working or having fun
+
+ align:start position:0%
+could have been working or having fun
+ 
+
+ align:start position:0%
+could have been working or having fun
+but certainly something I would've
+
+ align:start position:0%
+but certainly something I would've
+ 
+
+ align:start position:0%
+but certainly something I would've
+enjoyed more than waiting line for gas I
+
+ align:start position:0%
+enjoyed more than waiting line for gas I
+ 
+
+ align:start position:0%
+enjoyed more than waiting line for gas I
+think we'd all agree that there's
+
+ align:start position:0%
+think we'd all agree that there's
+ 
+
+ align:start position:0%
+think we'd all agree that there's
+something we'd rather be doing with our
+
+ align:start position:0%
+something we'd rather be doing with our
+ 
+
+ align:start position:0%
+something we'd rather be doing with our
+time than waiting in line for gas okay
+
+ align:start position:0%
+time than waiting in line for gas okay
+ 
+
+ align:start position:0%
+time than waiting in line for gas okay
+unless you really like the music getting
+
+ align:start position:0%
+unless you really like the music getting
+ 
+
+ align:start position:0%
+unless you really like the music getting
+your car stereo you can't listen
+
+ align:start position:0%
+your car stereo you can't listen
+ 
+
+ align:start position:0%
+your car stereo you can't listen
+anywhere else I don't know what the
+
+ align:start position:0%
+anywhere else I don't know what the
+ 
+
+ align:start position:0%
+anywhere else I don't know what the
+story would be but I can't imagine that
+
+ align:start position:0%
+story would be but I can't imagine that
+ 
+
+ align:start position:0%
+story would be but I can't imagine that
+many of us would prefer to wait in line
+
+ align:start position:0%
+many of us would prefer to wait in line
+ 
+
+ align:start position:0%
+many of us would prefer to wait in line
+for gas do something else does the
+
+ align:start position:0%
+for gas do something else does the
+ 
+
+ align:start position:0%
+for gas do something else does the
+opportunity cost that's it inefficiency
+
+ align:start position:0%
+opportunity cost that's it inefficiency
+ 
+
+ align:start position:0%
+opportunity cost that's it inefficiency
+society is losing out because you are
+
+ align:start position:0%
+society is losing out because you are
+ 
+
+ align:start position:0%
+society is losing out because you are
+not using your time in the most
+
+ align:start position:0%
+not using your time in the most
+ 
+
+ align:start position:0%
+not using your time in the most
+productive way and the way that maximize
+
+ align:start position:0%
+productive way and the way that maximize
+ 
+
+ align:start position:0%
+productive way and the way that maximize
+your welfare okay so there's that what
+
+ align:start position:0%
+your welfare okay so there's that what
+ 
+
+ align:start position:0%
+your welfare okay so there's that what
+else what's the other small other cost
+
+ align:start position:0%
+else what's the other small other cost
+ 
+
+ align:start position:0%
+else what's the other small other cost
+yeah yeah people use gas waiting in line
+
+ align:start position:0%
+yeah yeah people use gas waiting in line
+ 
+
+ align:start position:0%
+yeah yeah people use gas waiting in line
+so there's literally the technical and
+
+ align:start position:0%
+so there's literally the technical and
+ 
+
+ align:start position:0%
+so there's literally the technical and
+efficiency and remember this is like
+
+ align:start position:0%
+efficiency and remember this is like
+ 
+
+ align:start position:0%
+efficiency and remember this is like
+back when cars got like eight miles to
+
+ align:start position:0%
+back when cars got like eight miles to
+ 
+
+ align:start position:0%
+back when cars got like eight miles to
+the gallon so you'd like get to the
+
+ align:start position:0%
+the gallon so you'd like get to the
+ 
+
+ align:start position:0%
+the gallon so you'd like get to the
+front line get gas let's go back to the
+
+ align:start position:0%
+front line get gas let's go back to the
+ 
+
+ align:start position:0%
+front line get gas let's go back to the
+back of the line again because use so
+
+ align:start position:0%
+back of the line again because use so
+ 
+
+ align:start position:0%
+back of the line again because use so
+much gas plus not to mention the
+
+ align:start position:0%
+much gas plus not to mention the
+ 
+
+ align:start position:0%
+much gas plus not to mention the
+pollution all that other stuff so
+
+ align:start position:0%
+pollution all that other stuff so
+ 
+
+ align:start position:0%
+pollution all that other stuff so
+basically this is the inefficiency from
+
+ align:start position:0%
+basically this is the inefficiency from
+ 
+
+ align:start position:0%
+basically this is the inefficiency from
+an on market allocation mechanism okay
+
+ align:start position:0%
+an on market allocation mechanism okay
+ 
+
+ align:start position:0%
+an on market allocation mechanism okay
+which is that people could be doing more
+
+ align:start position:0%
+which is that people could be doing more
+ 
+
+ align:start position:0%
+which is that people could be doing more
+productive things and not wasting gas
+
+ align:start position:0%
+productive things and not wasting gas
+ 
+
+ align:start position:0%
+productive things and not wasting gas
+waiting in line yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ya know QD month because we fixed the
+
+ align:start position:0%
+ya know QD month because we fixed the
+ 
+
+ align:start position:0%
+ya know QD month because we fixed the
+price of p1 so it's QD months cute since
+
+ align:start position:0%
+price of p1 so it's QD months cute since
+ 
+
+ align:start position:0%
+price of p1 so it's QD months cute since
+we Prix the fysop re1 people want what's
+
+ align:start position:0%
+we Prix the fysop re1 people want what's
+ 
+
+ align:start position:0%
+we Prix the fysop re1 people want what's
+the demand at that price QD let's apply
+
+ align:start position:0%
+the demand at that price QD let's apply
+ 
+
+ align:start position:0%
+the demand at that price QD let's apply
+the price Q s so that's the excess
+
+ align:start position:0%
+the price Q s so that's the excess
+ 
+
+ align:start position:0%
+the price Q s so that's the excess
+demand okay so now no it doesn't but it
+
+ align:start position:0%
+demand okay so now no it doesn't but it
+ 
+
+ align:start position:0%
+demand okay so now no it doesn't but it
+does assume that B basically the market
+
+ align:start position:0%
+does assume that B basically the market
+ 
+
+ align:start position:0%
+does assume that B basically the market
+and this comes to the trade off what's
+
+ align:start position:0%
+and this comes to the trade off what's
+ 
+
+ align:start position:0%
+and this comes to the trade off what's
+the benefit of this policy which you've
+
+ align:start position:0%
+the benefit of this policy which you've
+ 
+
+ align:start position:0%
+the benefit of this policy which you've
+raised with your question which is
+
+ align:start position:0%
+raised with your question which is
+ 
+
+ align:start position:0%
+raised with your question which is
+equity which is I've defined consumer
+
+ align:start position:0%
+equity which is I've defined consumer
+ 
+
+ align:start position:0%
+equity which is I've defined consumer
+surplus as simply being with the market
+
+ align:start position:0%
+surplus as simply being with the market
+ 
+
+ align:start position:0%
+surplus as simply being with the market
+delivers so basically rich guys have
+
+ align:start position:0%
+delivers so basically rich guys have
+ 
+
+ align:start position:0%
+delivers so basically rich guys have
+more consumer surplus than poor guys
+
+ align:start position:0%
+more consumer surplus than poor guys
+ 
+
+ align:start position:0%
+more consumer surplus than poor guys
+okay that might not seem fair to people
+
+ align:start position:0%
+okay that might not seem fair to people
+ 
+
+ align:start position:0%
+okay that might not seem fair to people
+okay as a result the benefit is equity
+
+ align:start position:0%
+okay as a result the benefit is equity
+ 
+
+ align:start position:0%
+okay as a result the benefit is equity
+which is that if you that everyone gets
+
+ align:start position:0%
+which is that if you that everyone gets
+ 
+
+ align:start position:0%
+which is that if you that everyone gets
+gas at a lower price rather the price
+
+ align:start position:0%
+gas at a lower price rather the price
+ 
+
+ align:start position:0%
+gas at a lower price rather the price
+rise and the people who drop out may
+
+ align:start position:0%
+rise and the people who drop out may
+ 
+
+ align:start position:0%
+rise and the people who drop out may
+actually not be the people who don't
+
+ align:start position:0%
+actually not be the people who don't
+ 
+
+ align:start position:0%
+actually not be the people who don't
+need to drive the people can't afford to
+
+ align:start position:0%
+need to drive the people can't afford to
+ 
+
+ align:start position:0%
+need to drive the people can't afford to
+drive so they drop out remember where
+
+ align:start position:0%
+drive so they drop out remember where
+ 
+
+ align:start position:0%
+drive so they drop out remember where
+does the demand curve come from scums
+
+ align:start position:0%
+does the demand curve come from scums
+ 
+
+ align:start position:0%
+does the demand curve come from scums
+utility maximization that's a
+
+ align:start position:0%
+utility maximization that's a
+ 
+
+ align:start position:0%
+utility maximization that's a
+constrained maximization so the people
+
+ align:start position:0%
+constrained maximization so the people
+ 
+
+ align:start position:0%
+constrained maximization so the people
+who drop out mate maybe people we want
+
+ align:start position:0%
+who drop out mate maybe people we want
+ 
+
+ align:start position:0%
+who drop out mate maybe people we want
+maybe their people have to lose their
+
+ align:start position:0%
+maybe their people have to lose their
+ 
+
+ align:start position:0%
+maybe their people have to lose their
+jobs as they can't drive to their jobs
+
+ align:start position:0%
+jobs as they can't drive to their jobs
+ 
+
+ align:start position:0%
+jobs as they can't drive to their jobs
+anymore
+
+ align:start position:0%
+anymore
+ 
+
+ align:start position:0%
+anymore
+that's unfortunate so basically the the
+
+ align:start position:0%
+that's unfortunate so basically the the
+ 
+
+ align:start position:0%
+that's unfortunate so basically the the
+benefit of this is equity and that
+
+ align:start position:0%
+benefit of this is equity and that
+ 
+
+ align:start position:0%
+benefit of this is equity and that
+raises something were to come back to
+
+ align:start position:0%
+raises something were to come back to
+ 
+
+ align:start position:0%
+raises something were to come back to
+over and over again in this class which
+
+ align:start position:0%
+over and over again in this class which
+ 
+
+ align:start position:0%
+over and over again in this class which
+is what we call the equity efficiency
+
+ align:start position:0%
+is what we call the equity efficiency
+ 
+
+ align:start position:0%
+is what we call the equity efficiency
+trade-off okay the equity efficiency
+
+ align:start position:0%
+trade-off okay the equity efficiency
+ 
+
+ align:start position:0%
+trade-off okay the equity efficiency
+trade-off which is there are many
+
+ align:start position:0%
+trade-off which is there are many
+ 
+
+ align:start position:0%
+trade-off which is there are many
+government policies which make society
+
+ align:start position:0%
+government policies which make society
+ 
+
+ align:start position:0%
+government policies which make society
+more equal but along the way deliver
+
+ align:start position:0%
+more equal but along the way deliver
+ 
+
+ align:start position:0%
+more equal but along the way deliver
+deadweight loss and I'll actually tell
+
+ align:start position:0%
+deadweight loss and I'll actually tell
+ 
+
+ align:start position:0%
+deadweight loss and I'll actually tell
+you later in the class how to optimize
+
+ align:start position:0%
+you later in the class how to optimize
+ 
+
+ align:start position:0%
+you later in the class how to optimize
+across that problem how to optimize
+
+ align:start position:0%
+across that problem how to optimize
+ 
+
+ align:start position:0%
+across that problem how to optimize
+across - trade-off between equity and
+
+ align:start position:0%
+across - trade-off between equity and
+ 
+
+ align:start position:0%
+across - trade-off between equity and
+efficiency but for right now I just need
+
+ align:start position:0%
+efficiency but for right now I just need
+ 
+
+ align:start position:0%
+efficiency but for right now I just need
+to understand that there's that there's
+
+ align:start position:0%
+to understand that there's that there's
+ 
+
+ align:start position:0%
+to understand that there's that there's
+a trade-off okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this milk ice feeling that the people
+
+ align:start position:0%
+in this milk ice feeling that the people
+ 
+
+ align:start position:0%
+in this milk ice feeling that the people
+who are able to pay the most money will
+
+ align:start position:0%
+who are able to pay the most money will
+ 
+
+ align:start position:0%
+who are able to pay the most money will
+yeah exactly so the point is right the
+
+ align:start position:0%
+yeah exactly so the point is right the
+ 
+
+ align:start position:0%
+yeah exactly so the point is right the
+people who would do more dear it's a
+
+ align:start position:0%
+people who would do more dear it's a
+ 
+
+ align:start position:0%
+people who would do more dear it's a
+different kind of inequity so if you're
+
+ align:start position:0%
+different kind of inequity so if you're
+ 
+
+ align:start position:0%
+different kind of inequity so if you're
+worried about so in some sense the rich
+
+ align:start position:0%
+worried about so in some sense the rich
+ 
+
+ align:start position:0%
+worried about so in some sense the rich
+guy would say well that's not fair to me
+
+ align:start position:0%
+guy would say well that's not fair to me
+ 
+
+ align:start position:0%
+guy would say well that's not fair to me
+just because I've got a productive job I
+
+ align:start position:0%
+just because I've got a productive job I
+ 
+
+ align:start position:0%
+just because I've got a productive job I
+could be doing and someone else has
+
+ align:start position:0%
+could be doing and someone else has
+ 
+
+ align:start position:0%
+could be doing and someone else has
+extra time why should they get the gas
+
+ align:start position:0%
+extra time why should they get the gas
+ 
+
+ align:start position:0%
+extra time why should they get the gas
+instead of me so you're right there's
+
+ align:start position:0%
+instead of me so you're right there's
+ 
+
+ align:start position:0%
+instead of me so you're right there's
+always sort of an inequity I guess when
+
+ align:start position:0%
+always sort of an inequity I guess when
+ 
+
+ align:start position:0%
+always sort of an inequity I guess when
+I say equity that's a great point when I
+
+ align:start position:0%
+I say equity that's a great point when I
+ 
+
+ align:start position:0%
+I say equity that's a great point when I
+say could I implicitly mean what we call
+
+ align:start position:0%
+say could I implicitly mean what we call
+ 
+
+ align:start position:0%
+say could I implicitly mean what we call
+that's actually a very important point
+
+ align:start position:0%
+that's actually a very important point
+ 
+
+ align:start position:0%
+that's actually a very important point
+whatever say equity in this course I
+
+ align:start position:0%
+whatever say equity in this course I
+ 
+
+ align:start position:0%
+whatever say equity in this course I
+implicitly mean what we call vertical
+
+ align:start position:0%
+implicitly mean what we call vertical
+ 
+
+ align:start position:0%
+implicitly mean what we call vertical
+equity vertical equity is rich versus
+
+ align:start position:0%
+equity vertical equity is rich versus
+ 
+
+ align:start position:0%
+equity vertical equity is rich versus
+poor okay there are other kinds of
+
+ align:start position:0%
+poor okay there are other kinds of
+ 
+
+ align:start position:0%
+poor okay there are other kinds of
+equity you might care about like who has
+
+ align:start position:0%
+equity you might care about like who has
+ 
+
+ align:start position:0%
+equity you might care about like who has
+extra time versus who doesn't have extra
+
+ align:start position:0%
+extra time versus who doesn't have extra
+ 
+
+ align:start position:0%
+extra time versus who doesn't have extra
+time okay but and and that's a good
+
+ align:start position:0%
+time okay but and and that's a good
+ 
+
+ align:start position:0%
+time okay but and and that's a good
+point but for now and I think I could
+
+ align:start position:0%
+point but for now and I think I could
+ 
+
+ align:start position:0%
+point but for now and I think I could
+ever think about rich versus poor we
+
+ align:start position:0%
+ever think about rich versus poor we
+ 
+
+ align:start position:0%
+ever think about rich versus poor we
+think about government policy equity
+
+ align:start position:0%
+think about government policy equity
+ 
+
+ align:start position:0%
+think about government policy equity
+efficiency trade-off we really think
+
+ align:start position:0%
+efficiency trade-off we really think
+ 
+
+ align:start position:0%
+efficiency trade-off we really think
+about vertical equity okay other
+
+ align:start position:0%
+about vertical equity okay other
+ 
+
+ align:start position:0%
+about vertical equity okay other
+questions about that okay
+
+ align:start position:0%
+questions about that okay
+ 
+
+ align:start position:0%
+questions about that okay
+so let's do a couple more examples to
+
+ align:start position:0%
+so let's do a couple more examples to
+ 
+
+ align:start position:0%
+so let's do a couple more examples to
+drill this intuition home okay let's do
+
+ align:start position:0%
+drill this intuition home okay let's do
+ 
+
+ align:start position:0%
+drill this intuition home okay let's do
+a couple more examples because this is a
+
+ align:start position:0%
+a couple more examples because this is a
+ 
+
+ align:start position:0%
+a couple more examples because this is a
+very important point okay example a
+
+ align:start position:0%
+very important point okay example a
+ 
+
+ align:start position:0%
+very important point okay example a
+let's talk about ticket scalping okay I
+
+ align:start position:0%
+let's talk about ticket scalping okay I
+ 
+
+ align:start position:0%
+let's talk about ticket scalping okay I
+love going to I go I love going to music
+
+ align:start position:0%
+love going to I go I love going to music
+ 
+
+ align:start position:0%
+love going to I go I love going to music
+concerts one of my 51st concert of the
+
+ align:start position:0%
+concerts one of my 51st concert of the
+ 
+
+ align:start position:0%
+concerts one of my 51st concert of the
+year last year last night sorry went to
+
+ align:start position:0%
+year last year last night sorry went to
+ 
+
+ align:start position:0%
+year last year last night sorry went to
+my 51st cars to here I love going a
+
+ align:start position:0%
+my 51st cars to here I love going a
+ 
+
+ align:start position:0%
+my 51st cars to here I love going a
+music concert so I know a lot about the
+
+ align:start position:0%
+music concert so I know a lot about the
+ 
+
+ align:start position:0%
+music concert so I know a lot about the
+music business and ticket scalping at
+
+ align:start position:0%
+music business and ticket scalping at
+ 
+
+ align:start position:0%
+music business and ticket scalping at
+concerts a big deal for those who know
+
+ align:start position:0%
+concerts a big deal for those who know
+ 
+
+ align:start position:0%
+concerts a big deal for those who know
+the term this is the idea of buying
+
+ align:start position:0%
+the term this is the idea of buying
+ 
+
+ align:start position:0%
+the term this is the idea of buying
+tickets essentially on a secondary
+
+ align:start position:0%
+tickets essentially on a secondary
+ 
+
+ align:start position:0%
+tickets essentially on a secondary
+market so let's use the example of Adele
+
+ align:start position:0%
+market so let's use the example of Adele
+ 
+
+ align:start position:0%
+market so let's use the example of Adele
+so Adele about two years ago went on
+
+ align:start position:0%
+so Adele about two years ago went on
+ 
+
+ align:start position:0%
+so Adele about two years ago went on
+tour for the first time in four years to
+
+ align:start position:0%
+tour for the first time in four years to
+ 
+
+ align:start position:0%
+tour for the first time in four years to
+back up an incredibly successful album
+
+ align:start position:0%
+back up an incredibly successful album
+ 
+
+ align:start position:0%
+back up an incredibly successful album
+and folks really want to see your life
+
+ align:start position:0%
+and folks really want to see your life
+ 
+
+ align:start position:0%
+and folks really want to see your life
+because she had a big fan base she was
+
+ align:start position:0%
+because she had a big fan base she was
+ 
+
+ align:start position:0%
+because she had a big fan base she was
+quiet for a while she made now whom
+
+ align:start position:0%
+quiet for a while she made now whom
+ 
+
+ align:start position:0%
+quiet for a while she made now whom
+people really want to see her life she
+
+ align:start position:0%
+people really want to see her life she
+ 
+
+ align:start position:0%
+people really want to see her life she
+wanted to make sure her fans could
+
+ align:start position:0%
+wanted to make sure her fans could
+ 
+
+ align:start position:0%
+wanted to make sure her fans could
+afford to see her so what she did is she
+
+ align:start position:0%
+afford to see her so what she did is she
+ 
+
+ align:start position:0%
+afford to see her so what she did is she
+said I'm gonna price tickets that many
+
+ align:start position:0%
+said I'm gonna price tickets that many
+ 
+
+ align:start position:0%
+said I'm gonna price tickets that many
+tickets for $40 and the highest tickets
+
+ align:start position:0%
+tickets for $40 and the highest tickets
+ 
+
+ align:start position:0%
+tickets for $40 and the highest tickets
+at 150 which is really really cheap so
+
+ align:start position:0%
+at 150 which is really really cheap so
+ 
+
+ align:start position:0%
+at 150 which is really really cheap so
+my daughter's going to see Jay Cole
+
+ align:start position:0%
+my daughter's going to see Jay Cole
+ 
+
+ align:start position:0%
+my daughter's going to see Jay Cole
+tonight and she's paying
+
+ align:start position:0%
+tonight and she's paying
+ 
+
+ align:start position:0%
+tonight and she's paying
+like 150 for a mediocre ticket okay so
+
+ align:start position:0%
+like 150 for a mediocre ticket okay so
+ 
+
+ align:start position:0%
+like 150 for a mediocre ticket okay so
+40 to 150 s really cheap okay
+
+ align:start position:0%
+40 to 150 s really cheap okay
+ 
+
+ align:start position:0%
+40 to 150 s really cheap okay
+but she's saying I want to live our
+
+ align:start position:0%
+but she's saying I want to live our
+ 
+
+ align:start position:0%
+but she's saying I want to live our
+consumer surplus to my fans I wanna make
+
+ align:start position:0%
+consumer surplus to my fans I wanna make
+ 
+
+ align:start position:0%
+consumer surplus to my fans I wanna make
+sure my fans can really enjoy this enjoy
+
+ align:start position:0%
+sure my fans can really enjoy this enjoy
+ 
+
+ align:start position:0%
+sure my fans can really enjoy this enjoy
+this I get surplus but what happened
+
+ align:start position:0%
+this I get surplus but what happened
+ 
+
+ align:start position:0%
+this I get surplus but what happened
+well what happened is that the tickets
+
+ align:start position:0%
+well what happened is that the tickets
+ 
+
+ align:start position:0%
+well what happened is that the tickets
+sold out instantly
+
+ align:start position:0%
+sold out instantly
+ 
+
+ align:start position:0%
+sold out instantly
+like literally instantaneously and the
+
+ align:start position:0%
+like literally instantaneously and the
+ 
+
+ align:start position:0%
+like literally instantaneously and the
+major purchasers were what we call
+
+ align:start position:0%
+major purchasers were what we call
+ 
+
+ align:start position:0%
+major purchasers were what we call
+scalpers who are essentially
+
+ align:start position:0%
+scalpers who are essentially
+ 
+
+ align:start position:0%
+scalpers who are essentially
+professionals who buy tickets and then
+
+ align:start position:0%
+professionals who buy tickets and then
+ 
+
+ align:start position:0%
+professionals who buy tickets and then
+resell them on what we call the
+
+ align:start position:0%
+resell them on what we call the
+ 
+
+ align:start position:0%
+resell them on what we call the
+secondary market you might have heard of
+
+ align:start position:0%
+secondary market you might have heard of
+ 
+
+ align:start position:0%
+secondary market you might have heard of
+StubHub or other sites like that we're
+
+ align:start position:0%
+StubHub or other sites like that we're
+ 
+
+ align:start position:0%
+StubHub or other sites like that we're
+essentially go on and buy tickets to
+
+ align:start position:0%
+essentially go on and buy tickets to
+ 
+
+ align:start position:0%
+essentially go on and buy tickets to
+sold-out events and the prices on
+
+ align:start position:0%
+sold-out events and the prices on
+ 
+
+ align:start position:0%
+sold-out events and the prices on
+StubHub were much higher there's about
+
+ align:start position:0%
+StubHub were much higher there's about
+ 
+
+ align:start position:0%
+StubHub were much higher there's about
+$1,500 for a good ticket about ten times
+
+ align:start position:0%
+$1,500 for a good ticket about ten times
+ 
+
+ align:start position:0%
+$1,500 for a good ticket about ten times
+what she'd set the price at so basically
+
+ align:start position:0%
+what she'd set the price at so basically
+ 
+
+ align:start position:0%
+what she'd set the price at so basically
+who's getting a surplus not the fans the
+
+ align:start position:0%
+who's getting a surplus not the fans the
+ 
+
+ align:start position:0%
+who's getting a surplus not the fans the
+scalpers the people who are quick enough
+
+ align:start position:0%
+scalpers the people who are quick enough
+ 
+
+ align:start position:0%
+scalpers the people who are quick enough
+to get online who said box set up so the
+
+ align:start position:0%
+to get online who said box set up so the
+ 
+
+ align:start position:0%
+to get online who said box set up so the
+second it went online they went online
+
+ align:start position:0%
+second it went online they went online
+ 
+
+ align:start position:0%
+second it went online they went online
+and got the tickets they have thousands
+
+ align:start position:0%
+and got the tickets they have thousands
+ 
+
+ align:start position:0%
+and got the tickets they have thousands
+of BOTS set up essentially somehow they
+
+ align:start position:0%
+of BOTS set up essentially somehow they
+ 
+
+ align:start position:0%
+of BOTS set up essentially somehow they
+got around the click this if you're
+
+ align:start position:0%
+got around the click this if you're
+ 
+
+ align:start position:0%
+got around the click this if you're
+human box I don't how they do that
+
+ align:start position:0%
+human box I don't how they do that
+ 
+
+ align:start position:0%
+human box I don't how they do that
+but essentially I'm sure it's smart
+
+ align:start position:0%
+but essentially I'm sure it's smart
+ 
+
+ align:start position:0%
+but essentially I'm sure it's smart
+programmers you guys can probably do
+
+ align:start position:0%
+programmers you guys can probably do
+ 
+
+ align:start position:0%
+programmers you guys can probably do
+that in an hour as an extra credit
+
+ align:start position:0%
+that in an hour as an extra credit
+ 
+
+ align:start position:0%
+that in an hour as an extra credit
+project okay they got around it and they
+
+ align:start position:0%
+project okay they got around it and they
+ 
+
+ align:start position:0%
+project okay they got around it and they
+bought and so essentially Adele actually
+
+ align:start position:0%
+bought and so essentially Adele actually
+ 
+
+ align:start position:0%
+bought and so essentially Adele actually
+didn't create surplus for her fans she
+
+ align:start position:0%
+didn't create surplus for her fans she
+ 
+
+ align:start position:0%
+didn't create surplus for her fans she
+created surplus for scalpers okay now it
+
+ align:start position:0%
+created surplus for scalpers okay now it
+ 
+
+ align:start position:0%
+created surplus for scalpers okay now it
+didn't used to be this way when I was a
+
+ align:start position:0%
+didn't used to be this way when I was a
+ 
+
+ align:start position:0%
+didn't used to be this way when I was a
+kid we didn't have a secondary market
+
+ align:start position:0%
+kid we didn't have a secondary market
+ 
+
+ align:start position:0%
+kid we didn't have a secondary market
+we waited online so when I saw my first
+
+ align:start position:0%
+we waited online so when I saw my first
+ 
+
+ align:start position:0%
+we waited online so when I saw my first
+concert in 1981 you guys believe that
+
+ align:start position:0%
+concert in 1981 you guys believe that
+ 
+
+ align:start position:0%
+concert in 1981 you guys believe that
+1981 I saw the cars
+
+ align:start position:0%
+1981 I saw the cars
+ 
+
+ align:start position:0%
+1981 I saw the cars
+how many guys heard of the cars Oh God
+
+ align:start position:0%
+how many guys heard of the cars Oh God
+ 
+
+ align:start position:0%
+how many guys heard of the cars Oh God
+anyway so the cars I had to wait on line
+
+ align:start position:0%
+anyway so the cars I had to wait on line
+ 
+
+ align:start position:0%
+anyway so the cars I had to wait on line
+for hours to get tickets because that
+
+ align:start position:0%
+for hours to get tickets because that
+ 
+
+ align:start position:0%
+for hours to get tickets because that
+was that was the allocation mechanism so
+
+ align:start position:0%
+was that was the allocation mechanism so
+ 
+
+ align:start position:0%
+was that was the allocation mechanism so
+let's think about whether life is better
+
+ align:start position:0%
+let's think about whether life is better
+ 
+
+ align:start position:0%
+let's think about whether life is better
+or worse because on the one hand
+
+ align:start position:0%
+or worse because on the one hand
+ 
+
+ align:start position:0%
+or worse because on the one hand
+scalpers get money on the other hand
+
+ align:start position:0%
+scalpers get money on the other hand
+ 
+
+ align:start position:0%
+scalpers get money on the other hand
+people don't waste time waiting online
+
+ align:start position:0%
+people don't waste time waiting online
+ 
+
+ align:start position:0%
+people don't waste time waiting online
+so it really comes down to the same
+
+ align:start position:0%
+so it really comes down to the same
+ 
+
+ align:start position:0%
+so it really comes down to the same
+equity trade-off we talked about before
+
+ align:start position:0%
+equity trade-off we talked about before
+ 
+
+ align:start position:0%
+equity trade-off we talked about before
+now as a as a 16 year old 1981 I cannot
+
+ align:start position:0%
+now as a as a 16 year old 1981 I cannot
+ 
+
+ align:start position:0%
+now as a as a 16 year old 1981 I cannot
+have afforded to pay probably the
+
+ align:start position:0%
+have afforded to pay probably the
+ 
+
+ align:start position:0%
+have afforded to pay probably the
+secondary market price so I love but I
+
+ align:start position:0%
+secondary market price so I love but I
+ 
+
+ align:start position:0%
+secondary market price so I love but I
+was just 16 I'd nothing do with my time
+
+ align:start position:0%
+was just 16 I'd nothing do with my time
+ 
+
+ align:start position:0%
+was just 16 I'd nothing do with my time
+so I was happy to spend
+
+ align:start position:0%
+so I was happy to spend
+ 
+
+ align:start position:0%
+so I was happy to spend
+I was waiting online okay but on the
+
+ align:start position:0%
+I was waiting online okay but on the
+ 
+
+ align:start position:0%
+I was waiting online okay but on the
+other hand you could say someone is very
+
+ align:start position:0%
+other hand you could say someone is very
+ 
+
+ align:start position:0%
+other hand you could say someone is very
+productive who was a big fan who was
+
+ align:start position:0%
+productive who was a big fan who was
+ 
+
+ align:start position:0%
+productive who was a big fan who was
+very productive and could be out
+
+ align:start position:0%
+very productive and could be out
+ 
+
+ align:start position:0%
+very productive and could be out
+inventing new products if they weren't
+
+ align:start position:0%
+inventing new products if they weren't
+ 
+
+ align:start position:0%
+inventing new products if they weren't
+standing on line they might say that's
+
+ align:start position:0%
+standing on line they might say that's
+ 
+
+ align:start position:0%
+standing on line they might say that's
+really inefficient I'm happy to pay
+
+ align:start position:0%
+really inefficient I'm happy to pay
+ 
+
+ align:start position:0%
+really inefficient I'm happy to pay
+1,500 bucks to spend my time inventing
+
+ align:start position:0%
+1,500 bucks to spend my time inventing
+ 
+
+ align:start position:0%
+1,500 bucks to spend my time inventing
+new things rather than have to sit
+
+ align:start position:0%
+new things rather than have to sit
+ 
+
+ align:start position:0%
+new things rather than have to sit
+around waiting online so it's not clear
+
+ align:start position:0%
+around waiting online so it's not clear
+ 
+
+ align:start position:0%
+around waiting online so it's not clear
+which is the better or the worse system
+
+ align:start position:0%
+which is the better or the worse system
+ 
+
+ align:start position:0%
+which is the better or the worse system
+it's hard to say yeah well no but no
+
+ align:start position:0%
+it's hard to say yeah well no but no
+ 
+
+ align:start position:0%
+it's hard to say yeah well no but no
+here's the point this that's a great
+
+ align:start position:0%
+here's the point this that's a great
+ 
+
+ align:start position:0%
+here's the point this that's a great
+point which is that in some sense what
+
+ align:start position:0%
+point which is that in some sense what
+ 
+
+ align:start position:0%
+point which is that in some sense what
+the scalpers do is undo Adele's action
+
+ align:start position:0%
+the scalpers do is undo Adele's action
+ 
+
+ align:start position:0%
+the scalpers do is undo Adele's action
+and create a truly efficient market so
+
+ align:start position:0%
+and create a truly efficient market so
+ 
+
+ align:start position:0%
+and create a truly efficient market so
+think of the scalper says essentially
+
+ align:start position:0%
+think of the scalper says essentially
+ 
+
+ align:start position:0%
+think of the scalper says essentially
+undoing Adele's action which distorted
+
+ align:start position:0%
+undoing Adele's action which distorted
+ 
+
+ align:start position:0%
+undoing Adele's action which distorted
+the market so you have it you have a
+
+ align:start position:0%
+the market so you have it you have a
+ 
+
+ align:start position:0%
+the market so you have it you have a
+market for adele tickets which is an
+
+ align:start position:0%
+market for adele tickets which is an
+ 
+
+ align:start position:0%
+market for adele tickets which is an
+echo or $1500 adele tried to set a price
+
+ align:start position:0%
+echo or $1500 adele tried to set a price
+ 
+
+ align:start position:0%
+echo or $1500 adele tried to set a price
+ceiling at 150 seemingly selfishly
+
+ align:start position:0%
+ceiling at 150 seemingly selfishly
+ 
+
+ align:start position:0%
+ceiling at 150 seemingly selfishly
+saying look I'm willing to give up my
+
+ align:start position:0%
+saying look I'm willing to give up my
+ 
+
+ align:start position:0%
+saying look I'm willing to give up my
+surplus okay
+
+ align:start position:0%
+surplus okay
+ 
+
+ align:start position:0%
+surplus okay
+I'm for my for my fans but a force
+
+ align:start position:0%
+I'm for my for my fans but a force
+ 
+
+ align:start position:0%
+I'm for my for my fans but a force
+shouldn't work out that way what
+
+ align:start position:0%
+shouldn't work out that way what
+ 
+
+ align:start position:0%
+shouldn't work out that way what
+happened was the market recall but at
+
+ align:start position:0%
+happened was the market recall but at
+ 
+
+ align:start position:0%
+happened was the market recall but at
+1500 but that extra surplus didn't go to
+
+ align:start position:0%
+1500 but that extra surplus didn't go to
+ 
+
+ align:start position:0%
+1500 but that extra surplus didn't go to
+Adele the consumer surplus still
+
+ align:start position:0%
+Adele the consumer surplus still
+ 
+
+ align:start position:0%
+Adele the consumer surplus still
+remained above 1500 the difference was
+
+ align:start position:0%
+remained above 1500 the difference was
+ 
+
+ align:start position:0%
+remained above 1500 the difference was
+that extra gaped 150 and 1500 didn't go
+
+ align:start position:0%
+that extra gaped 150 and 1500 didn't go
+ 
+
+ align:start position:0%
+that extra gaped 150 and 1500 didn't go
+to dela went to the scalpers so it's
+
+ align:start position:0%
+to dela went to the scalpers so it's
+ 
+
+ align:start position:0%
+to dela went to the scalpers so it's
+probably more efficient than waiting on
+
+ align:start position:0%
+probably more efficient than waiting on
+ 
+
+ align:start position:0%
+probably more efficient than waiting on
+line because waiting in line has an
+
+ align:start position:0%
+line because waiting in line has an
+ 
+
+ align:start position:0%
+line because waiting in line has an
+efficiency where's this instantaneous
+
+ align:start position:0%
+efficiency where's this instantaneous
+ 
+
+ align:start position:0%
+efficiency where's this instantaneous
+bidding is more efficient but it in
+
+ align:start position:0%
+bidding is more efficient but it in
+ 
+
+ align:start position:0%
+bidding is more efficient but it in
+substance is delivering that if the
+
+ align:start position:0%
+substance is delivering that if the
+ 
+
+ align:start position:0%
+substance is delivering that if the
+efficiency gain is being delivered not
+
+ align:start position:0%
+efficiency gain is being delivered not
+ 
+
+ align:start position:0%
+efficiency gain is being delivered not
+to consumers as Adele wanted it's being
+
+ align:start position:0%
+to consumers as Adele wanted it's being
+ 
+
+ align:start position:0%
+to consumers as Adele wanted it's being
+delivered to scalpers okay so basically
+
+ align:start position:0%
+delivered to scalpers okay so basically
+ 
+
+ align:start position:0%
+delivered to scalpers okay so basically
+now there's another alternative
+
+ align:start position:0%
+now there's another alternative
+ 
+
+ align:start position:0%
+now there's another alternative
+what could the dell have done instead
+
+ align:start position:0%
+what could the dell have done instead
+ 
+
+ align:start position:0%
+what could the dell have done instead
+what what's what's another way adele
+
+ align:start position:0%
+what what's what's another way adele
+ 
+
+ align:start position:0%
+what what's what's another way adele
+could have approached this well she
+
+ align:start position:0%
+could have approached this well she
+ 
+
+ align:start position:0%
+could have approached this well she
+could have auctioned her tickets online
+
+ align:start position:0%
+could have auctioned her tickets online
+ 
+
+ align:start position:0%
+could have auctioned her tickets online
+she could have said look I know that I
+
+ align:start position:0%
+she could have said look I know that I
+ 
+
+ align:start position:0%
+she could have said look I know that I
+can't manage deliver $40 tickets to my
+
+ align:start position:0%
+can't manage deliver $40 tickets to my
+ 
+
+ align:start position:0%
+can't manage deliver $40 tickets to my
+fans
+
+ align:start position:0%
+fans
+ 
+
+ align:start position:0%
+fans
+it just can't defeat the scalping system
+
+ align:start position:0%
+it just can't defeat the scalping system
+ 
+
+ align:start position:0%
+it just can't defeat the scalping system
+but why so the scalpers have the money
+
+ align:start position:0%
+but why so the scalpers have the money
+ 
+
+ align:start position:0%
+but why so the scalpers have the money
+I'm gonna auction my tickets and
+
+ align:start position:0%
+I'm gonna auction my tickets and
+ 
+
+ align:start position:0%
+I'm gonna auction my tickets and
+essentially she could have set up an
+
+ align:start position:0%
+essentially she could have set up an
+ 
+
+ align:start position:0%
+essentially she could have set up an
+efficient market online we will bid and
+
+ align:start position:0%
+efficient market online we will bid and
+ 
+
+ align:start position:0%
+efficient market online we will bid and
+then you would have gotten the efficient
+
+ align:start position:0%
+then you would have gotten the efficient
+ 
+
+ align:start position:0%
+then you would have gotten the efficient
+outcome and you wouldn't wait online you
+
+ align:start position:0%
+outcome and you wouldn't wait online you
+ 
+
+ align:start position:0%
+outcome and you wouldn't wait online you
+would have bid now would have been
+
+ align:start position:0%
+would have bid now would have been
+ 
+
+ align:start position:0%
+would have bid now would have been
+inequitable outcome
+
+ align:start position:0%
+inequitable outcome
+ 
+
+ align:start position:0%
+inequitable outcome
+but basically the same fans would have
+
+ align:start position:0%
+but basically the same fans would have
+ 
+
+ align:start position:0%
+but basically the same fans would have
+gotten the tickets as in the end got
+
+ align:start position:0%
+gotten the tickets as in the end got
+ 
+
+ align:start position:0%
+gotten the tickets as in the end got
+them from the scalpers but instead it's
+
+ align:start position:0%
+them from the scalpers but instead it's
+ 
+
+ align:start position:0%
+them from the scalpers but instead it's
+paying 1500 to the scalpers unpaid 1500
+
+ align:start position:0%
+paying 1500 to the scalpers unpaid 1500
+ 
+
+ align:start position:0%
+paying 1500 to the scalpers unpaid 1500
+to Adele and probably that's a better
+
+ align:start position:0%
+to Adele and probably that's a better
+ 
+
+ align:start position:0%
+to Adele and probably that's a better
+outcome I mean you know Adele doesn't
+
+ align:start position:0%
+outcome I mean you know Adele doesn't
+ 
+
+ align:start position:0%
+outcome I mean you know Adele doesn't
+need the money but at the end of the day
+
+ align:start position:0%
+need the money but at the end of the day
+ 
+
+ align:start position:0%
+need the money but at the end of the day
+if Adele's generating that amount of
+
+ align:start position:0%
+if Adele's generating that amount of
+ 
+
+ align:start position:0%
+if Adele's generating that amount of
+goodwill from her fans it seems like she
+
+ align:start position:0%
+goodwill from her fans it seems like she
+ 
+
+ align:start position:0%
+goodwill from her fans it seems like she
+should get the money not a bunch of
+
+ align:start position:0%
+should get the money not a bunch of
+ 
+
+ align:start position:0%
+should get the money not a bunch of
+scalpers okay so I guess probably rather
+
+ align:start position:0%
+scalpers okay so I guess probably rather
+ 
+
+ align:start position:0%
+scalpers okay so I guess probably rather
+have her have it than the scalpers now
+
+ align:start position:0%
+have her have it than the scalpers now
+ 
+
+ align:start position:0%
+have her have it than the scalpers now
+ticketmasters tried to set up auction
+
+ align:start position:0%
+ticketmasters tried to set up auction
+ 
+
+ align:start position:0%
+ticketmasters tried to set up auction
+systems recognizing this problem and
+
+ align:start position:0%
+systems recognizing this problem and
+ 
+
+ align:start position:0%
+systems recognizing this problem and
+they're not really taking off and it
+
+ align:start position:0%
+they're not really taking off and it
+ 
+
+ align:start position:0%
+they're not really taking off and it
+just it sort of speaks to the fact that
+
+ align:start position:0%
+just it sort of speaks to the fact that
+ 
+
+ align:start position:0%
+just it sort of speaks to the fact that
+people don't really like to think about
+
+ align:start position:0%
+people don't really like to think about
+ 
+
+ align:start position:0%
+people don't really like to think about
+economics okay so there was that
+
+ align:start position:0%
+economics okay so there was that
+ 
+
+ align:start position:0%
+economics okay so there was that
+basically people are like yeah but if
+
+ align:start position:0%
+basically people are like yeah but if
+ 
+
+ align:start position:0%
+basically people are like yeah but if
+you auction that's ripping off the fans
+
+ align:start position:0%
+you auction that's ripping off the fans
+ 
+
+ align:start position:0%
+you auction that's ripping off the fans
+that's no fair and say why should I say
+
+ align:start position:0%
+that's no fair and say why should I say
+ 
+
+ align:start position:0%
+that's no fair and say why should I say
+well you getting ripped off anyway just
+
+ align:start position:0%
+well you getting ripped off anyway just
+ 
+
+ align:start position:0%
+well you getting ripped off anyway just
+by scalpers and they said no I can still
+
+ align:start position:0%
+by scalpers and they said no I can still
+ 
+
+ align:start position:0%
+by scalpers and they said no I can still
+get online first and get my ticket and
+
+ align:start position:0%
+get online first and get my ticket and
+ 
+
+ align:start position:0%
+get online first and get my ticket and
+people just didn't like it thought it
+
+ align:start position:0%
+people just didn't like it thought it
+ 
+
+ align:start position:0%
+people just didn't like it thought it
+was unfair even though it's almost
+
+ align:start position:0%
+was unfair even though it's almost
+ 
+
+ align:start position:0%
+was unfair even though it's almost
+certainly a better outcome for society
+
+ align:start position:0%
+certainly a better outcome for society
+ 
+
+ align:start position:0%
+certainly a better outcome for society
+if they Goodell shut the money rabbin
+
+ align:start position:0%
+if they Goodell shut the money rabbin
+ 
+
+ align:start position:0%
+if they Goodell shut the money rabbin
+the scalpers which speaks the fact that
+
+ align:start position:0%
+the scalpers which speaks the fact that
+ 
+
+ align:start position:0%
+the scalpers which speaks the fact that
+you no morals matter in markets okay we
+
+ align:start position:0%
+you no morals matter in markets okay we
+ 
+
+ align:start position:0%
+you no morals matter in markets okay we
+like think of these markets abstract a
+
+ align:start position:0%
+like think of these markets abstract a
+ 
+
+ align:start position:0%
+like think of these markets abstract a
+moral concepts but morals do matter
+
+ align:start position:0%
+moral concepts but morals do matter
+ 
+
+ align:start position:0%
+moral concepts but morals do matter
+okay and that basically it's sort of
+
+ align:start position:0%
+okay and that basically it's sort of
+ 
+
+ align:start position:0%
+okay and that basically it's sort of
+matters you know you sometimes can't do
+
+ align:start position:0%
+matters you know you sometimes can't do
+ 
+
+ align:start position:0%
+matters you know you sometimes can't do
+the right thing because it might not be
+
+ align:start position:0%
+the right thing because it might not be
+ 
+
+ align:start position:0%
+the right thing because it might not be
+huh the thing that makes consumers
+
+ align:start position:0%
+huh the thing that makes consumers
+ 
+
+ align:start position:0%
+huh the thing that makes consumers
+willing to participate okay so that's
+
+ align:start position:0%
+willing to participate okay so that's
+ 
+
+ align:start position:0%
+willing to participate okay so that's
+one example scalping another example
+
+ align:start position:0%
+one example scalping another example
+ 
+
+ align:start position:0%
+one example scalping another example
+food banks okay food banks our
+
+ align:start position:0%
+food banks okay food banks our
+ 
+
+ align:start position:0%
+food banks okay food banks our
+organizations which are right oh yeah go
+
+ align:start position:0%
+organizations which are right oh yeah go
+ 
+
+ align:start position:0%
+organizations which are right oh yeah go
+ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah I thought about that so in my if I
+
+ align:start position:0%
+yeah I thought about that so in my if I
+ 
+
+ align:start position:0%
+yeah I thought about that so in my if I
+could do anything I wanted in life I'd
+
+ align:start position:0%
+could do anything I wanted in life I'd
+ 
+
+ align:start position:0%
+could do anything I wanted in life I'd
+be a rock star and I thought if I was a
+
+ align:start position:0%
+be a rock star and I thought if I was a
+ 
+
+ align:start position:0%
+be a rock star and I thought if I was a
+rock star be cool I'd like have a
+
+ align:start position:0%
+rock star be cool I'd like have a
+ 
+
+ align:start position:0%
+rock star be cool I'd like have a
+concert for like my mega fans or like
+
+ align:start position:0%
+concert for like my mega fans or like
+ 
+
+ align:start position:0%
+concert for like my mega fans or like
+they'd have to prove who they were and I
+
+ align:start position:0%
+they'd have to prove who they were and I
+ 
+
+ align:start position:0%
+they'd have to prove who they were and I
+have a bracelet and stuff it just seems
+
+ align:start position:0%
+have a bracelet and stuff it just seems
+ 
+
+ align:start position:0%
+have a bracelet and stuff it just seems
+like it's too hard
+
+ align:start position:0%
+like it's too hard
+ 
+
+ align:start position:0%
+like it's too hard
+it seems the technology is just too hard
+
+ align:start position:0%
+it seems the technology is just too hard
+ 
+
+ align:start position:0%
+it seems the technology is just too hard
+so actually there's a really cool
+
+ align:start position:0%
+so actually there's a really cool
+ 
+
+ align:start position:0%
+so actually there's a really cool
+example that's on the phone this morning
+
+ align:start position:0%
+example that's on the phone this morning
+ 
+
+ align:start position:0%
+example that's on the phone this morning
+with a with a with a rock and roll
+
+ align:start position:0%
+with a with a with a rock and roll
+ 
+
+ align:start position:0%
+with a with a with a rock and roll
+promoter who's doing a super cool thing
+
+ align:start position:0%
+promoter who's doing a super cool thing
+ 
+
+ align:start position:0%
+promoter who's doing a super cool thing
+so as the election approaches I will nag
+
+ align:start position:0%
+so as the election approaches I will nag
+ 
+
+ align:start position:0%
+so as the election approaches I will nag
+you guys to vote voter turnout among the
+
+ align:start position:0%
+you guys to vote voter turnout among the
+ 
+
+ align:start position:0%
+you guys to vote voter turnout among the
+young is an enormous problem in the u.s.
+
+ align:start position:0%
+young is an enormous problem in the u.s.
+ 
+
+ align:start position:0%
+young is an enormous problem in the u.s.
+so she is running a series of concerts
+
+ align:start position:0%
+so she is running a series of concerts
+ 
+
+ align:start position:0%
+so she is running a series of concerts
+around the country where if you show a
+
+ align:start position:0%
+around the country where if you show a
+ 
+
+ align:start position:0%
+around the country where if you show a
+picture of yourself outside a polling
+
+ align:start position:0%
+picture of yourself outside a polling
+ 
+
+ align:start position:0%
+picture of yourself outside a polling
+place you get into the concert for free
+
+ align:start position:0%
+place you get into the concert for free
+ 
+
+ align:start position:0%
+place you get into the concert for free
+to try to promote voting among young
+
+ align:start position:0%
+to try to promote voting among young
+ 
+
+ align:start position:0%
+to try to promote voting among young
+people it's super cool it's called I
+
+ align:start position:0%
+people it's super cool it's called I
+ 
+
+ align:start position:0%
+people it's super cool it's called I
+voted you can look it up on the web it's
+
+ align:start position:0%
+voted you can look it up on the web it's
+ 
+
+ align:start position:0%
+voted you can look it up on the web it's
+kind of a cool thing there's a couple
+
+ align:start position:0%
+kind of a cool thing there's a couple
+ 
+
+ align:start position:0%
+kind of a cool thing there's a couple
+concerts here in Boston they're all over
+
+ align:start position:0%
+concerts here in Boston they're all over
+ 
+
+ align:start position:0%
+concerts here in Boston they're all over
+the country so you could think about
+
+ align:start position:0%
+the country so you could think about
+ 
+
+ align:start position:0%
+the country so you could think about
+things like that the question is
+
+ align:start position:0%
+things like that the question is
+ 
+
+ align:start position:0%
+things like that the question is
+ultimately you know two people
+
+ align:start position:0%
+ultimately you know two people
+ 
+
+ align:start position:0%
+ultimately you know two people
+photoshopped a picture from the polling
+
+ align:start position:0%
+photoshopped a picture from the polling
+ 
+
+ align:start position:0%
+photoshopped a picture from the polling
+place you know it's all it's it's just a
+
+ align:start position:0%
+place you know it's all it's it's just a
+ 
+
+ align:start position:0%
+place you know it's all it's it's just a
+question of enforcement okay so it's
+
+ align:start position:0%
+question of enforcement okay so it's
+ 
+
+ align:start position:0%
+question of enforcement okay so it's
+about food banks so basically um these
+
+ align:start position:0%
+about food banks so basically um these
+ 
+
+ align:start position:0%
+about food banks so basically um these
+are organizations provide free food to
+
+ align:start position:0%
+are organizations provide free food to
+ 
+
+ align:start position:0%
+are organizations provide free food to
+the poor and with the biggest one is
+
+ align:start position:0%
+the poor and with the biggest one is
+ 
+
+ align:start position:0%
+the poor and with the biggest one is
+called feeding America feeding America
+
+ align:start position:0%
+called feeding America feeding America
+ 
+
+ align:start position:0%
+called feeding America feeding America
+has food banks all over the nation and
+
+ align:start position:0%
+has food banks all over the nation and
+ 
+
+ align:start position:0%
+has food banks all over the nation and
+they provide free food free food to the
+
+ align:start position:0%
+they provide free food free food to the
+ 
+
+ align:start position:0%
+they provide free food free food to the
+poor okay
+
+ align:start position:0%
+poor okay
+ 
+
+ align:start position:0%
+poor okay
+now their goal then is they have to
+
+ align:start position:0%
+now their goal then is they have to
+ 
+
+ align:start position:0%
+now their goal then is they have to
+figure out where to send the food to get
+
+ align:start position:0%
+figure out where to send the food to get
+ 
+
+ align:start position:0%
+figure out where to send the food to get
+the people who need it the most
+
+ align:start position:0%
+the people who need it the most
+ 
+
+ align:start position:0%
+the people who need it the most
+now a market does this naturally
+
+ align:start position:0%
+now a market does this naturally
+ 
+
+ align:start position:0%
+now a market does this naturally
+basically if people want more Turkey in
+
+ align:start position:0%
+basically if people want more Turkey in
+ 
+
+ align:start position:0%
+basically if people want more Turkey in
+location a then also in the price for
+
+ align:start position:0%
+location a then also in the price for
+ 
+
+ align:start position:0%
+location a then also in the price for
+turkey goes up all of a sudden the store
+
+ align:start position:0%
+turkey goes up all of a sudden the store
+ 
+
+ align:start position:0%
+turkey goes up all of a sudden the store
+runs out of Turkey it says wow I can
+
+ align:start position:0%
+runs out of Turkey it says wow I can
+ 
+
+ align:start position:0%
+runs out of Turkey it says wow I can
+charge more for Turkey it raises the
+
+ align:start position:0%
+charge more for Turkey it raises the
+ 
+
+ align:start position:0%
+charge more for Turkey it raises the
+price and it a club relates the market
+
+ align:start position:0%
+price and it a club relates the market
+ 
+
+ align:start position:0%
+price and it a club relates the market
+so a market solves for sending the right
+
+ align:start position:0%
+so a market solves for sending the right
+ 
+
+ align:start position:0%
+so a market solves for sending the right
+food to where people want it but the
+
+ align:start position:0%
+food to where people want it but the
+ 
+
+ align:start position:0%
+food to where people want it but the
+problem with feeding America is that
+
+ align:start position:0%
+problem with feeding America is that
+ 
+
+ align:start position:0%
+problem with feeding America is that
+they didn't have that market so this had
+
+ align:start position:0%
+they didn't have that market so this had
+ 
+
+ align:start position:0%
+they didn't have that market so this had
+decide where to send stuff and they'd
+
+ align:start position:0%
+decide where to send stuff and they'd
+ 
+
+ align:start position:0%
+decide where to send stuff and they'd
+screw up they'd like to send potatoes to
+
+ align:start position:0%
+screw up they'd like to send potatoes to
+ 
+
+ align:start position:0%
+screw up they'd like to send potatoes to
+Idaho we're like they're drowning the
+
+ align:start position:0%
+Idaho we're like they're drowning the
+ 
+
+ align:start position:0%
+Idaho we're like they're drowning the
+potatoes stuff like that so it was very
+
+ align:start position:0%
+potatoes stuff like that so it was very
+ 
+
+ align:start position:0%
+potatoes stuff like that so it was very
+hard from the figure out where to send
+
+ align:start position:0%
+hard from the figure out where to send
+ 
+
+ align:start position:0%
+hard from the figure out where to send
+the food exactly what people wanted the
+
+ align:start position:0%
+the food exactly what people wanted the
+ 
+
+ align:start position:0%
+the food exactly what people wanted the
+most because they didn't have the market
+
+ align:start position:0%
+most because they didn't have the market
+ 
+
+ align:start position:0%
+most because they didn't have the market
+mechanism they want to give it away for
+
+ align:start position:0%
+mechanism they want to give it away for
+ 
+
+ align:start position:0%
+mechanism they want to give it away for
+free that sort of defeat the purse they
+
+ align:start position:0%
+free that sort of defeat the purse they
+ 
+
+ align:start position:0%
+free that sort of defeat the purse they
+charge for it but they didn't really
+
+ align:start position:0%
+charge for it but they didn't really
+ 
+
+ align:start position:0%
+charge for it but they didn't really
+know they didn't have the market to tell
+
+ align:start position:0%
+know they didn't have the market to tell
+ 
+
+ align:start position:0%
+know they didn't have the market to tell
+them where folks wanted which foods in
+
+ align:start position:0%
+them where folks wanted which foods in
+ 
+
+ align:start position:0%
+them where folks wanted which foods in
+the real market if you want real foods
+
+ align:start position:0%
+the real market if you want real foods
+ 
+
+ align:start position:0%
+the real market if you want real foods
+you bid the price up
+
+ align:start position:0%
+you bid the price up
+ 
+
+ align:start position:0%
+you bid the price up
+in their market you couldn't so feeding
+
+ align:start position:0%
+in their market you couldn't so feeding
+ 
+
+ align:start position:0%
+in their market you couldn't so feeding
+America came up with a really clever
+
+ align:start position:0%
+America came up with a really clever
+ 
+
+ align:start position:0%
+America came up with a really clever
+solution they made a virtual market they
+
+ align:start position:0%
+solution they made a virtual market they
+ 
+
+ align:start position:0%
+solution they made a virtual market they
+said to each food bank we are gonna give
+
+ align:start position:0%
+said to each food bank we are gonna give
+ 
+
+ align:start position:0%
+said to each food bank we are gonna give
+you a fake budget of X hundred thousands
+
+ align:start position:0%
+you a fake budget of X hundred thousands
+ 
+
+ align:start position:0%
+you a fake budget of X hundred thousands
+of dollars and you bid for which foods
+
+ align:start position:0%
+of dollars and you bid for which foods
+ 
+
+ align:start position:0%
+of dollars and you bid for which foods
+you want based on what the people in
+
+ align:start position:0%
+you want based on what the people in
+ 
+
+ align:start position:0%
+you want based on what the people in
+your area want and will then allocate it
+
+ align:start position:0%
+your area want and will then allocate it
+ 
+
+ align:start position:0%
+your area want and will then allocate it
+according to those bids so they got the
+
+ align:start position:0%
+according to those bids so they got the
+ 
+
+ align:start position:0%
+according to those bids so they got the
+market mechanism working without the
+
+ align:start position:0%
+market mechanism working without the
+ 
+
+ align:start position:0%
+market mechanism working without the
+food banks haven't actually give any
+
+ align:start position:0%
+food banks haven't actually give any
+ 
+
+ align:start position:0%
+food banks haven't actually give any
+money okay
+
+ align:start position:0%
+money okay
+ 
+
+ align:start position:0%
+money okay
+so in that way they massively
+
+ align:start position:0%
+so in that way they massively
+ 
+
+ align:start position:0%
+so in that way they massively
+reallocated food they suddenly said hey
+
+ align:start position:0%
+reallocated food they suddenly said hey
+ 
+
+ align:start position:0%
+reallocated food they suddenly said hey
+the one from Idaho is bidding really
+
+ align:start position:0%
+the one from Idaho is bidding really
+ 
+
+ align:start position:0%
+the one from Idaho is bidding really
+high for Turkey and not all for potatoes
+
+ align:start position:0%
+high for Turkey and not all for potatoes
+ 
+
+ align:start position:0%
+high for Turkey and not all for potatoes
+maybe we should send them more turkey
+
+ align:start position:0%
+maybe we should send them more turkey
+ 
+
+ align:start position:0%
+maybe we should send them more turkey
+and seven potatoes elsewhere so they
+
+ align:start position:0%
+and seven potatoes elsewhere so they
+ 
+
+ align:start position:0%
+and seven potatoes elsewhere so they
+essentially got market signals from a
+
+ align:start position:0%
+essentially got market signals from a
+ 
+
+ align:start position:0%
+essentially got market signals from a
+non financial transaction it was super
+
+ align:start position:0%
+non financial transaction it was super
+ 
+
+ align:start position:0%
+non financial transaction it was super
+cool idea and the amount of and there
+
+ align:start position:0%
+cool idea and the amount of and there
+ 
+
+ align:start position:0%
+cool idea and the amount of and there
+was a huge benefit they were able to
+
+ align:start position:0%
+was a huge benefit they were able to
+ 
+
+ align:start position:0%
+was a huge benefit they were able to
+effectively allocate about 50 million
+
+ align:start position:0%
+effectively allocate about 50 million
+ 
+
+ align:start position:0%
+effectively allocate about 50 million
+pounds of food through this mechanism
+
+ align:start position:0%
+pounds of food through this mechanism
+ 
+
+ align:start position:0%
+pounds of food through this mechanism
+making sure that food got to the folks
+
+ align:start position:0%
+making sure that food got to the folks
+ 
+
+ align:start position:0%
+making sure that food got to the folks
+that needed it so there's an example you
+
+ align:start position:0%
+that needed it so there's an example you
+ 
+
+ align:start position:0%
+that needed it so there's an example you
+can use a market mechanism without
+
+ align:start position:0%
+can use a market mechanism without
+ 
+
+ align:start position:0%
+can use a market mechanism without
+actually while while not violating
+
+ align:start position:0%
+actually while while not violating
+ 
+
+ align:start position:0%
+actually while while not violating
+equity the food was always free but if I
+
+ align:start position:0%
+equity the food was always free but if I
+ 
+
+ align:start position:0%
+equity the food was always free but if I
+set up these virtual prices they managed
+
+ align:start position:0%
+set up these virtual prices they managed
+ 
+
+ align:start position:0%
+set up these virtual prices they managed
+to get the food delivered to where
+
+ align:start position:0%
+to get the food delivered to where
+ 
+
+ align:start position:0%
+to get the food delivered to where
+people who want the most they let the
+
+ align:start position:0%
+people who want the most they let the
+ 
+
+ align:start position:0%
+people who want the most they let the
+market send its allocated signals they
+
+ align:start position:0%
+market send its allocated signals they
+ 
+
+ align:start position:0%
+market send its allocated signals they
+let the market be allocated li efficient
+
+ align:start position:0%
+let the market be allocated li efficient
+ 
+
+ align:start position:0%
+let the market be allocated li efficient
+sent signals of where people wanted the
+
+ align:start position:0%
+sent signals of where people wanted the
+ 
+
+ align:start position:0%
+sent signals of where people wanted the
+food without actually violating equity
+
+ align:start position:0%
+food without actually violating equity
+ 
+
+ align:start position:0%
+food without actually violating equity
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+questions about that okay now let's go
+
+ align:start position:0%
+questions about that okay now let's go
+ 
+
+ align:start position:0%
+questions about that okay now let's go
+to the hardest but my favorite example
+
+ align:start position:0%
+to the hardest but my favorite example
+ 
+
+ align:start position:0%
+to the hardest but my favorite example
+which is taxi medallions this is a hard
+
+ align:start position:0%
+which is taxi medallions this is a hard
+ 
+
+ align:start position:0%
+which is taxi medallions this is a hard
+example but it's a really cool one and
+
+ align:start position:0%
+example but it's a really cool one and
+ 
+
+ align:start position:0%
+example but it's a really cool one and
+it ends with a great story okay taxi
+
+ align:start position:0%
+it ends with a great story okay taxi
+ 
+
+ align:start position:0%
+it ends with a great story okay taxi
+cabs now cast your mind back pre ubirr
+
+ align:start position:0%
+cabs now cast your mind back pre ubirr
+ 
+
+ align:start position:0%
+cabs now cast your mind back pre ubirr
+okay go back ten years about ten years
+
+ align:start position:0%
+okay go back ten years about ten years
+ 
+
+ align:start position:0%
+okay go back ten years about ten years
+taxi cabs were the only way you could
+
+ align:start position:0%
+taxi cabs were the only way you could
+ 
+
+ align:start position:0%
+taxi cabs were the only way you could
+get around town if you didn't have you
+
+ align:start position:0%
+get around town if you didn't have you
+ 
+
+ align:start position:0%
+get around town if you didn't have you
+know if you want to get from one eighty
+
+ align:start position:0%
+know if you want to get from one eighty
+ 
+
+ align:start position:0%
+know if you want to get from one eighty
+point be in a car you known one you took
+
+ align:start position:0%
+point be in a car you known one you took
+ 
+
+ align:start position:0%
+point be in a car you known one you took
+a taxi okay and this was a great example
+
+ align:start position:0%
+a taxi okay and this was a great example
+ 
+
+ align:start position:0%
+a taxi okay and this was a great example
+of an economist perfectly competitive
+
+ align:start position:0%
+of an economist perfectly competitive
+ 
+
+ align:start position:0%
+of an economist perfectly competitive
+market in theory it's the identical
+
+ align:start position:0%
+market in theory it's the identical
+ 
+
+ align:start position:0%
+market in theory it's the identical
+product you want to go from point A to
+
+ align:start position:0%
+product you want to go from point A to
+ 
+
+ align:start position:0%
+product you want to go from point A to
+point B okay
+
+ align:start position:0%
+point B okay
+ 
+
+ align:start position:0%
+point B okay
+it's very there's could be lots of them
+
+ align:start position:0%
+it's very there's could be lots of them
+ 
+
+ align:start position:0%
+it's very there's could be lots of them
+are riding around the streets you can
+
+ align:start position:0%
+are riding around the streets you can
+ 
+
+ align:start position:0%
+are riding around the streets you can
+price compare because cabs are coming by
+
+ align:start position:0%
+price compare because cabs are coming by
+ 
+
+ align:start position:0%
+price compare because cabs are coming by
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+I'm okay it should have been a very
+
+ align:start position:0%
+I'm okay it should have been a very
+ 
+
+ align:start position:0%
+I'm okay it should have been a very
+effective perfectly efficient perfectly
+
+ align:start position:0%
+effective perfectly efficient perfectly
+ 
+
+ align:start position:0%
+effective perfectly efficient perfectly
+competitive market okay but it wasn't
+
+ align:start position:0%
+competitive market okay but it wasn't
+ 
+
+ align:start position:0%
+competitive market okay but it wasn't
+because every city limited the amount of
+
+ align:start position:0%
+because every city limited the amount of
+ 
+
+ align:start position:0%
+because every city limited the amount of
+taxicabs that were allowed in their city
+
+ align:start position:0%
+taxicabs that were allowed in their city
+ 
+
+ align:start position:0%
+taxicabs that were allowed in their city
+every city had a system where to be a
+
+ align:start position:0%
+every city had a system where to be a
+ 
+
+ align:start position:0%
+every city had a system where to be a
+taxicab you had to have what was called
+
+ align:start position:0%
+taxicab you had to have what was called
+ 
+
+ align:start position:0%
+taxicab you had to have what was called
+the medallion rather than really
+
+ align:start position:0%
+the medallion rather than really
+ 
+
+ align:start position:0%
+the medallion rather than really
+Manhattan's if its original Medina is
+
+ align:start position:0%
+Manhattan's if its original Medina is
+ 
+
+ align:start position:0%
+Manhattan's if its original Medina is
+there's a piece of paper actually and
+
+ align:start position:0%
+there's a piece of paper actually and
+ 
+
+ align:start position:0%
+there's a piece of paper actually and
+they regulated the number of taxicabs
+
+ align:start position:0%
+they regulated the number of taxicabs
+ 
+
+ align:start position:0%
+they regulated the number of taxicabs
+allowed in the city they said we're only
+
+ align:start position:0%
+allowed in the city they said we're only
+ 
+
+ align:start position:0%
+allowed in the city they said we're only
+going to allow X many taxicab drivers in
+
+ align:start position:0%
+going to allow X many taxicab drivers in
+ 
+
+ align:start position:0%
+going to allow X many taxicab drivers in
+the city in every city did this now
+
+ align:start position:0%
+the city in every city did this now
+ 
+
+ align:start position:0%
+the city in every city did this now
+we're gonna do both a positive and
+
+ align:start position:0%
+we're gonna do both a positive and
+ 
+
+ align:start position:0%
+we're gonna do both a positive and
+normative analysis of this policy let's
+
+ align:start position:0%
+normative analysis of this policy let's
+ 
+
+ align:start position:0%
+normative analysis of this policy let's
+start with a positive analysis what did
+
+ align:start position:0%
+start with a positive analysis what did
+ 
+
+ align:start position:0%
+start with a positive analysis what did
+this polity jit policy do okay now I'm
+
+ align:start position:0%
+this polity jit policy do okay now I'm
+ 
+
+ align:start position:0%
+this polity jit policy do okay now I'm
+gonna go figure 10 for figure 10 four
+
+ align:start position:0%
+gonna go figure 10 for figure 10 four
+ 
+
+ align:start position:0%
+gonna go figure 10 for figure 10 four
+will be one of the most complicated
+
+ align:start position:0%
+will be one of the most complicated
+ 
+
+ align:start position:0%
+will be one of the most complicated
+figures doing this class so I'm gonna go
+
+ align:start position:0%
+figures doing this class so I'm gonna go
+ 
+
+ align:start position:0%
+figures doing this class so I'm gonna go
+through two slowly as I can but please
+
+ align:start position:0%
+through two slowly as I can but please
+ 
+
+ align:start position:0%
+through two slowly as I can but please
+stop me if it's not clear okay this one
+
+ align:start position:0%
+stop me if it's not clear okay this one
+ 
+
+ align:start position:0%
+stop me if it's not clear okay this one
+of these figures will go back and forth
+
+ align:start position:0%
+of these figures will go back and forth
+ 
+
+ align:start position:0%
+of these figures will go back and forth
+between the two sides so on the right
+
+ align:start position:0%
+between the two sides so on the right
+ 
+
+ align:start position:0%
+between the two sides so on the right
+hand side is the market on the left hand
+
+ align:start position:0%
+hand side is the market on the left hand
+ 
+
+ align:start position:0%
+hand side is the market on the left hand
+side as a cab firm we're gonna start by
+
+ align:start position:0%
+side as a cab firm we're gonna start by
+ 
+
+ align:start position:0%
+side as a cab firm we're gonna start by
+assuming all cabs are identical we
+
+ align:start position:0%
+assuming all cabs are identical we
+ 
+
+ align:start position:0%
+assuming all cabs are identical we
+assume all cabs are identical so one
+
+ align:start position:0%
+assume all cabs are identical so one
+ 
+
+ align:start position:0%
+assume all cabs are identical so one
+representative firm tells us about every
+
+ align:start position:0%
+representative firm tells us about every
+ 
+
+ align:start position:0%
+representative firm tells us about every
+cat firm okay now we start with the
+
+ align:start position:0%
+cat firm okay now we start with the
+ 
+
+ align:start position:0%
+cat firm okay now we start with the
+market we have an initial demand which
+
+ align:start position:0%
+market we have an initial demand which
+ 
+
+ align:start position:0%
+market we have an initial demand which
+is d the line d the blue line is the
+
+ align:start position:0%
+is d the line d the blue line is the
+ 
+
+ align:start position:0%
+is d the line d the blue line is the
+demand for taxi cabs okay an initial
+
+ align:start position:0%
+demand for taxi cabs okay an initial
+ 
+
+ align:start position:0%
+demand for taxi cabs okay an initial
+supply curve s1 we're gonna assume that
+
+ align:start position:0%
+supply curve s1 we're gonna assume that
+ 
+
+ align:start position:0%
+supply curve s1 we're gonna assume that
+essentially in a perfectly competitive
+
+ align:start position:0%
+essentially in a perfectly competitive
+ 
+
+ align:start position:0%
+essentially in a perfectly competitive
+market you have a flat long run supply
+
+ align:start position:0%
+market you have a flat long run supply
+ 
+
+ align:start position:0%
+market you have a flat long run supply
+curve your perfectly elastic supply okay
+
+ align:start position:0%
+curve your perfectly elastic supply okay
+ 
+
+ align:start position:0%
+curve your perfectly elastic supply okay
+anybody can just grab a cab and starts
+
+ align:start position:0%
+anybody can just grab a cab and starts
+ 
+
+ align:start position:0%
+anybody can just grab a cab and starts
+right what's getting in a cab burger
+
+ align:start position:0%
+right what's getting in a cab burger
+ 
+
+ align:start position:0%
+right what's getting in a cab burger
+without medallions anyone could throw
+
+ align:start position:0%
+without medallions anyone could throw
+ 
+
+ align:start position:0%
+without medallions anyone could throw
+can throw a taxi sign in the car so
+
+ align:start position:0%
+can throw a taxi sign in the car so
+ 
+
+ align:start position:0%
+can throw a taxi sign in the car so
+drive we're not picking people up okay
+
+ align:start position:0%
+drive we're not picking people up okay
+ 
+
+ align:start position:0%
+drive we're not picking people up okay
+so it's effectively perfectly
+
+ align:start position:0%
+so it's effectively perfectly
+ 
+
+ align:start position:0%
+so it's effectively perfectly
+entry-and-exit so it's a perfectly
+
+ align:start position:0%
+entry-and-exit so it's a perfectly
+ 
+
+ align:start position:0%
+entry-and-exit so it's a perfectly
+competitive long run market therefore
+
+ align:start position:0%
+competitive long run market therefore
+ 
+
+ align:start position:0%
+competitive long run market therefore
+flat supply that's one so our initial
+
+ align:start position:0%
+flat supply that's one so our initial
+ 
+
+ align:start position:0%
+flat supply that's one so our initial
+equilibrium is that point big e one okay
+
+ align:start position:0%
+equilibrium is that point big e one okay
+ 
+
+ align:start position:0%
+equilibrium is that point big e one okay
+when you have q1 rides big q1 rides per
+
+ align:start position:0%
+when you have q1 rides big q1 rides per
+ 
+
+ align:start position:0%
+when you have q1 rides big q1 rides per
+month and that amounts to so so you have
+
+ align:start position:0%
+month and that amounts to so so you have
+ 
+
+ align:start position:0%
+month and that amounts to so so you have
+Q that's the equilibrium now how many
+
+ align:start position:0%
+Q that's the equilibrium now how many
+ 
+
+ align:start position:0%
+Q that's the equilibrium now how many
+firms are there well we know any firms
+
+ align:start position:0%
+firms are there well we know any firms
+ 
+
+ align:start position:0%
+firms are there well we know any firms
+there are because we say okay at that
+
+ align:start position:0%
+there are because we say okay at that
+ 
+
+ align:start position:0%
+there are because we say okay at that
+price p1 we go to the left
+
+ align:start position:0%
+price p1 we go to the left
+ 
+
+ align:start position:0%
+price p1 we go to the left
+we know that firms will produce where
+
+ align:start position:0%
+we know that firms will produce where
+ 
+
+ align:start position:0%
+we know that firms will produce where
+marginal cost equals average
+
+ align:start position:0%
+marginal cost equals average
+ 
+
+ align:start position:0%
+marginal cost equals average
+that the minimum of long-run average
+
+ align:start position:0%
+that the minimum of long-run average
+ 
+
+ align:start position:0%
+that the minimum of long-run average
+cost we proved that a couple lectures
+
+ align:start position:0%
+cost we proved that a couple lectures
+ 
+
+ align:start position:0%
+cost we proved that a couple lectures
+ago
+
+ align:start position:0%
+ago
+ 
+
+ align:start position:0%
+ago
+therefore if the price is a 1 we know
+
+ align:start position:0%
+therefore if the price is a 1 we know
+ 
+
+ align:start position:0%
+therefore if the price is a 1 we know
+each efficient firm will produce little
+
+ align:start position:0%
+each efficient firm will produce little
+ 
+
+ align:start position:0%
+each efficient firm will produce little
+q1 if there's if each firms could reduce
+
+ align:start position:0%
+q1 if there's if each firms could reduce
+ 
+
+ align:start position:0%
+q1 if there's if each firms could reduce
+a little q1 and the total amount of
+
+ align:start position:0%
+a little q1 and the total amount of
+ 
+
+ align:start position:0%
+a little q1 and the total amount of
+rides is gonna be big q1 then that
+
+ align:start position:0%
+rides is gonna be big q1 then that
+ 
+
+ align:start position:0%
+rides is gonna be big q1 then that
+implies little n1 firms so let me go
+
+ align:start position:0%
+implies little n1 firms so let me go
+ 
+
+ align:start position:0%
+implies little n1 firms so let me go
+through it again supply equals demand a
+
+ align:start position:0%
+through it again supply equals demand a
+ 
+
+ align:start position:0%
+through it again supply equals demand a
+big Q one that gives you a price P one
+
+ align:start position:0%
+big Q one that gives you a price P one
+ 
+
+ align:start position:0%
+big Q one that gives you a price P one
+now we shift to the left at that price P
+
+ align:start position:0%
+now we shift to the left at that price P
+ 
+
+ align:start position:0%
+now we shift to the left at that price P
+1 we know that each firm will choose to
+
+ align:start position:0%
+1 we know that each firm will choose to
+ 
+
+ align:start position:0%
+1 we know that each firm will choose to
+produce little q1 rides because that's
+
+ align:start position:0%
+produce little q1 rides because that's
+ 
+
+ align:start position:0%
+produce little q1 rides because that's
+where price equals marginal cost equals
+
+ align:start position:0%
+where price equals marginal cost equals
+ 
+
+ align:start position:0%
+where price equals marginal cost equals
+average cost now we go back to the right
+
+ align:start position:0%
+average cost now we go back to the right
+ 
+
+ align:start position:0%
+average cost now we go back to the right
+we know if this little each firms racing
+
+ align:start position:0%
+we know if this little each firms racing
+ 
+
+ align:start position:0%
+we know if this little each firms racing
+little q1 rides and you need big q1 then
+
+ align:start position:0%
+little q1 rides and you need big q1 then
+ 
+
+ align:start position:0%
+little q1 rides and you need big q1 then
+there must be n1 firms ok questions
+
+ align:start position:0%
+there must be n1 firms ok questions
+ 
+
+ align:start position:0%
+there must be n1 firms ok questions
+about that that's the initial
+
+ align:start position:0%
+about that that's the initial
+ 
+
+ align:start position:0%
+about that that's the initial
+equilibrium okay and at that point there
+
+ align:start position:0%
+equilibrium okay and at that point there
+ 
+
+ align:start position:0%
+equilibrium okay and at that point there
+are long-run zero profits consumer
+
+ align:start position:0%
+are long-run zero profits consumer
+ 
+
+ align:start position:0%
+are long-run zero profits consumer
+surplus is a plus B plus both seat bus C
+
+ align:start position:0%
+surplus is a plus B plus both seat bus C
+ 
+
+ align:start position:0%
+surplus is a plus B plus both seat bus C
+C by the way is the gray area on either
+
+ align:start position:0%
+C by the way is the gray area on either
+ 
+
+ align:start position:0%
+C by the way is the gray area on either
+side of the dash line a plus B plus C
+
+ align:start position:0%
+side of the dash line a plus B plus C
+ 
+
+ align:start position:0%
+side of the dash line a plus B plus C
+we'd mark it twice because it's
+
+ align:start position:0%
+we'd mark it twice because it's
+ 
+
+ align:start position:0%
+we'd mark it twice because it's
+confusing the dashed line there so the
+
+ align:start position:0%
+confusing the dashed line there so the
+ 
+
+ align:start position:0%
+confusing the dashed line there so the
+blue area of the green area in the gray
+
+ align:start position:0%
+blue area of the green area in the gray
+ 
+
+ align:start position:0%
+blue area of the green area in the gray
+area are the consumer surplus and what's
+
+ align:start position:0%
+area are the consumer surplus and what's
+ 
+
+ align:start position:0%
+area are the consumer surplus and what's
+the producer surplus
+
+ align:start position:0%
+the producer surplus
+ 
+
+ align:start position:0%
+the producer surplus
+what's the Bri surplus raise your hand
+
+ align:start position:0%
+what's the Bri surplus raise your hand
+ 
+
+ align:start position:0%
+what's the Bri surplus raise your hand
+and tell me yeah zero because yeah
+
+ align:start position:0%
+and tell me yeah zero because yeah
+ 
+
+ align:start position:0%
+and tell me yeah zero because yeah
+there's no it's in long run equilibrium
+
+ align:start position:0%
+there's no it's in long run equilibrium
+ 
+
+ align:start position:0%
+there's no it's in long run equilibrium
+there's no profits in long run person
+
+ align:start position:0%
+there's no profits in long run person
+ 
+
+ align:start position:0%
+there's no profits in long run person
+kinetic the Librium price remember
+
+ align:start position:0%
+kinetic the Librium price remember
+ 
+
+ align:start position:0%
+kinetic the Librium price remember
+profits are price minus average cost but
+
+ align:start position:0%
+profits are price minus average cost but
+ 
+
+ align:start position:0%
+profits are price minus average cost but
+price equals average cost okay so
+
+ align:start position:0%
+price equals average cost okay so
+ 
+
+ align:start position:0%
+price equals average cost okay so
+there's no profit so it's all consumer
+
+ align:start position:0%
+there's no profit so it's all consumer
+ 
+
+ align:start position:0%
+there's no profit so it's all consumer
+surplus all well and good now let's say
+
+ align:start position:0%
+surplus all well and good now let's say
+ 
+
+ align:start position:0%
+surplus all well and good now let's say
+the government comes in and says we're
+
+ align:start position:0%
+the government comes in and says we're
+ 
+
+ align:start position:0%
+the government comes in and says we're
+gonna have a medallion system
+
+ align:start position:0%
+gonna have a medallion system
+ 
+
+ align:start position:0%
+gonna have a medallion system
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's so let's say um we're gonna
+
+ align:start position:0%
+so let's so let's say um we're gonna
+ 
+
+ align:start position:0%
+so let's so let's say um we're gonna
+wait a minute system we're gonna have a
+
+ align:start position:0%
+wait a minute system we're gonna have a
+ 
+
+ align:start position:0%
+wait a minute system we're gonna have a
+system where only the little N two cabs
+
+ align:start position:0%
+system where only the little N two cabs
+ 
+
+ align:start position:0%
+system where only the little N two cabs
+are allowed in the market little n 2 are
+
+ align:start position:0%
+are allowed in the market little n 2 are
+ 
+
+ align:start position:0%
+are allowed in the market little n 2 are
+the only number of cabs allowed in the
+
+ align:start position:0%
+the only number of cabs allowed in the
+ 
+
+ align:start position:0%
+the only number of cabs allowed in the
+market okay so what is the new market
+
+ align:start position:0%
+market okay so what is the new market
+ 
+
+ align:start position:0%
+market okay so what is the new market
+supply curve start on the right what's
+
+ align:start position:0%
+supply curve start on the right what's
+ 
+
+ align:start position:0%
+supply curve start on the right what's
+do the market supply curve well up to
+
+ align:start position:0%
+do the market supply curve well up to
+ 
+
+ align:start position:0%
+do the market supply curve well up to
+little n 2 times Q 1 nothing's changed
+
+ align:start position:0%
+little n 2 times Q 1 nothing's changed
+ 
+
+ align:start position:0%
+little n 2 times Q 1 nothing's changed
+each cab company used to provide Q what
+
+ align:start position:0%
+each cab company used to provide Q what
+ 
+
+ align:start position:0%
+each cab company used to provide Q what
+little Q 1 rides at a price P 1 so up to
+
+ align:start position:0%
+little Q 1 rides at a price P 1 so up to
+ 
+
+ align:start position:0%
+little Q 1 rides at a price P 1 so up to
+the point little and too little Q 1
+
+ align:start position:0%
+the point little and too little Q 1
+ 
+
+ align:start position:0%
+the point little and too little Q 1
+we're on the same supply curve we used
+
+ align:start position:0%
+we're on the same supply curve we used
+ 
+
+ align:start position:0%
+we're on the same supply curve we used
+to be on but then things change why do
+
+ align:start position:0%
+to be on but then things change why do
+ 
+
+ align:start position:0%
+to be on but then things change why do
+they change because now let's say riders
+
+ align:start position:0%
+they change because now let's say riders
+ 
+
+ align:start position:0%
+they change because now let's say riders
+want more than little n 2 Q 1
+
+ align:start position:0%
+want more than little n 2 Q 1
+ 
+
+ align:start position:0%
+want more than little n 2 Q 1
+well you can't deal with that by entry
+
+ align:start position:0%
+well you can't deal with that by entry
+ 
+
+ align:start position:0%
+well you can't deal with that by entry
+you have to deal with that by the
+
+ align:start position:0%
+you have to deal with that by the
+ 
+
+ align:start position:0%
+you have to deal with that by the
+existing cab drivers working more but if
+
+ align:start position:0%
+existing cab drivers working more but if
+ 
+
+ align:start position:0%
+existing cab drivers working more but if
+they work more supply curve is upward
+
+ align:start position:0%
+they work more supply curve is upward
+ 
+
+ align:start position:0%
+they work more supply curve is upward
+sloping because now marginal costs can
+
+ align:start position:0%
+sloping because now marginal costs can
+ 
+
+ align:start position:0%
+sloping because now marginal costs can
+be rising before the resupply curve was
+
+ align:start position:0%
+be rising before the resupply curve was
+ 
+
+ align:start position:0%
+be rising before the resupply curve was
+flat is when you went to the right of
+
+ align:start position:0%
+flat is when you went to the right of
+ 
+
+ align:start position:0%
+flat is when you went to the right of
+little and to little Q 1 as you move to
+
+ align:start position:0%
+little and to little Q 1 as you move to
+ 
+
+ align:start position:0%
+little and to little Q 1 as you move to
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+you just got more entering and everyone
+
+ align:start position:0%
+you just got more entering and everyone
+ 
+
+ align:start position:0%
+you just got more entering and everyone
+still produces their efficient level of
+
+ align:start position:0%
+still produces their efficient level of
+ 
+
+ align:start position:0%
+still produces their efficient level of
+little Q 1 now when you can't allow more
+
+ align:start position:0%
+little Q 1 now when you can't allow more
+ 
+
+ align:start position:0%
+little Q 1 now when you can't allow more
+entry firms have to produce more and
+
+ align:start position:0%
+entry firms have to produce more and
+ 
+
+ align:start position:0%
+entry firms have to produce more and
+suddenly they're not at the cost
+
+ align:start position:0%
+suddenly they're not at the cost
+ 
+
+ align:start position:0%
+suddenly they're not at the cost
+minimizing point they're riding up their
+
+ align:start position:0%
+minimizing point they're riding up their
+ 
+
+ align:start position:0%
+minimizing point they're riding up their
+marginal cost curve so the supply curve
+
+ align:start position:0%
+marginal cost curve so the supply curve
+ 
+
+ align:start position:0%
+marginal cost curve so the supply curve
+becomes flat to that point and then
+
+ align:start position:0%
+becomes flat to that point and then
+ 
+
+ align:start position:0%
+becomes flat to that point and then
+becomes upward sloping and that's s2 s2
+
+ align:start position:0%
+becomes upward sloping and that's s2 s2
+ 
+
+ align:start position:0%
+becomes upward sloping and that's s2 s2
+is the red line that is flat to the left
+
+ align:start position:0%
+is the red line that is flat to the left
+ 
+
+ align:start position:0%
+is the red line that is flat to the left
+of n little n to little Q 1 and then
+
+ align:start position:0%
+of n little n to little Q 1 and then
+ 
+
+ align:start position:0%
+of n little n to little Q 1 and then
+becomes Verbeek um ZUP words sloping and
+
+ align:start position:0%
+becomes Verbeek um ZUP words sloping and
+ 
+
+ align:start position:0%
+becomes Verbeek um ZUP words sloping and
+the new equilibrium is that point e 2
+
+ align:start position:0%
+the new equilibrium is that point e 2
+ 
+
+ align:start position:0%
+the new equilibrium is that point e 2
+with n 2 firms by law you can only then
+
+ align:start position:0%
+with n 2 firms by law you can only then
+ 
+
+ align:start position:0%
+with n 2 firms by law you can only then
+two firms pricing little Q two rides
+
+ align:start position:0%
+two firms pricing little Q two rides
+ 
+
+ align:start position:0%
+two firms pricing little Q two rides
+each okay and your new equilibrium is
+
+ align:start position:0%
+each okay and your new equilibrium is
+ 
+
+ align:start position:0%
+each okay and your new equilibrium is
+big Q 2 and that new equilibrium price
+
+ align:start position:0%
+big Q 2 and that new equilibrium price
+ 
+
+ align:start position:0%
+big Q 2 and that new equilibrium price
+is the new equilibrium price is P 2 the
+
+ align:start position:0%
+is the new equilibrium price is P 2 the
+ 
+
+ align:start position:0%
+is the new equilibrium price is P 2 the
+director over in price is P 2 okay now P
+
+ align:start position:0%
+director over in price is P 2 okay now P
+ 
+
+ align:start position:0%
+director over in price is P 2 okay now P
+2 if you go to the old um P 2 is the
+
+ align:start position:0%
+2 if you go to the old um P 2 is the
+ 
+
+ align:start position:0%
+2 if you go to the old um P 2 is the
+point if you look at the prices P 2 but
+
+ align:start position:0%
+point if you look at the prices P 2 but
+ 
+
+ align:start position:0%
+point if you look at the prices P 2 but
+I forget the AC 2 curve focus on the AC
+
+ align:start position:0%
+I forget the AC 2 curve focus on the AC
+ 
+
+ align:start position:0%
+I forget the AC 2 curve focus on the AC
+1 curve
+
+ align:start position:0%
+1 curve
+ 
+
+ align:start position:0%
+1 curve
+okay average the average cost function
+
+ align:start position:0%
+okay average the average cost function
+ 
+
+ align:start position:0%
+okay average the average cost function
+hasn't changed it's still a c1 so if
+
+ align:start position:0%
+hasn't changed it's still a c1 so if
+ 
+
+ align:start position:0%
+hasn't changed it's still a c1 so if
+their price is p2 and their average cost
+
+ align:start position:0%
+their price is p2 and their average cost
+ 
+
+ align:start position:0%
+their price is p2 and their average cost
+curve is a c1 there could produce where
+
+ align:start position:0%
+curve is a c1 there could produce where
+ 
+
+ align:start position:0%
+curve is a c1 there could produce where
+price equals marginal cost at little e2
+
+ align:start position:0%
+price equals marginal cost at little e2
+ 
+
+ align:start position:0%
+price equals marginal cost at little e2
+okay so let me back up you have let's go
+
+ align:start position:0%
+okay so let me back up you have let's go
+ 
+
+ align:start position:0%
+okay so let me back up you have let's go
+back to the front curve on the right the
+
+ align:start position:0%
+back to the front curve on the right the
+ 
+
+ align:start position:0%
+back to the front curve on the right the
+equilibrium is not Big E - that's sort
+
+ align:start position:0%
+equilibrium is not Big E - that's sort
+ 
+
+ align:start position:0%
+equilibrium is not Big E - that's sort
+of priced a little P - now shift to the
+
+ align:start position:0%
+of priced a little P - now shift to the
+ 
+
+ align:start position:0%
+of priced a little P - now shift to the
+left at a price of little P - firms
+
+ align:start position:0%
+left at a price of little P - firms
+ 
+
+ align:start position:0%
+left at a price of little P - firms
+produce where price equals marginal cost
+
+ align:start position:0%
+produce where price equals marginal cost
+ 
+
+ align:start position:0%
+produce where price equals marginal cost
+right price equals marginal cost at a
+
+ align:start position:0%
+right price equals marginal cost at a
+ 
+
+ align:start position:0%
+right price equals marginal cost at a
+quantity little Q - so firms produce a
+
+ align:start position:0%
+quantity little Q - so firms produce a
+ 
+
+ align:start position:0%
+quantity little Q - so firms produce a
+little Q - because that's the point at
+
+ align:start position:0%
+little Q - because that's the point at
+ 
+
+ align:start position:0%
+little Q - because that's the point at
+which price equals marginal cost
+
+ align:start position:0%
+which price equals marginal cost
+ 
+
+ align:start position:0%
+which price equals marginal cost
+they produce it a little Q - well if
+
+ align:start position:0%
+they produce it a little Q - well if
+ 
+
+ align:start position:0%
+they produce it a little Q - well if
+they're making little Q two units at a
+
+ align:start position:0%
+they're making little Q two units at a
+ 
+
+ align:start position:0%
+they're making little Q two units at a
+price P - they're earning profits of Pi
+
+ align:start position:0%
+price P - they're earning profits of Pi
+ 
+
+ align:start position:0%
+price P - they're earning profits of Pi
+the shaded area because they are
+
+ align:start position:0%
+the shaded area because they are
+ 
+
+ align:start position:0%
+the shaded area because they are
+producing units at price above marginal
+
+ align:start position:0%
+producing units at price above marginal
+ 
+
+ align:start position:0%
+producing units at price above marginal
+cost and they're producing little Q two
+
+ align:start position:0%
+cost and they're producing little Q two
+ 
+
+ align:start position:0%
+cost and they're producing little Q two
+units so every unit they produce turning
+
+ align:start position:0%
+units so every unit they produce turning
+ 
+
+ align:start position:0%
+units so every unit they produce turning
+profits on so the taxi medallion workers
+
+ align:start position:0%
+profits on so the taxi medallion workers
+ 
+
+ align:start position:0%
+profits on so the taxi medallion workers
+are the taxi companies are now making
+
+ align:start position:0%
+are the taxi companies are now making
+ 
+
+ align:start position:0%
+are the taxi companies are now making
+money they're making profits okay
+
+ align:start position:0%
+money they're making profits okay
+ 
+
+ align:start position:0%
+money they're making profits okay
+questions about that yeah they're making
+
+ align:start position:0%
+questions about that yeah they're making
+ 
+
+ align:start position:0%
+questions about that yeah they're making
+profits so imagine where we started at E
+
+ align:start position:0%
+profits so imagine where we started at E
+ 
+
+ align:start position:0%
+profits so imagine where we started at E
+- in allowed free entry then you'd see
+
+ align:start position:0%
+- in allowed free entry then you'd see
+ 
+
+ align:start position:0%
+- in allowed free entry then you'd see
+basically more firms whenever you drive
+
+ align:start position:0%
+basically more firms whenever you drive
+ 
+
+ align:start position:0%
+basically more firms whenever you drive
+the price down to p1 but we don't allow
+
+ align:start position:0%
+the price down to p1 but we don't allow
+ 
+
+ align:start position:0%
+the price down to p1 but we don't allow
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so there's profits it's a barrier to
+
+ align:start position:0%
+so there's profits it's a barrier to
+ 
+
+ align:start position:0%
+so there's profits it's a barrier to
+entry which creates profits which breaks
+
+ align:start position:0%
+entry which creates profits which breaks
+ 
+
+ align:start position:0%
+entry which creates profits which breaks
+us from our long-run flat supply curve
+
+ align:start position:0%
+us from our long-run flat supply curve
+ 
+
+ align:start position:0%
+us from our long-run flat supply curve
+we talked about one of the reasons why
+
+ align:start position:0%
+we talked about one of the reasons why
+ 
+
+ align:start position:0%
+we talked about one of the reasons why
+that loop will be flat so now let's move
+
+ align:start position:0%
+that loop will be flat so now let's move
+ 
+
+ align:start position:0%
+that loop will be flat so now let's move
+to the normative is this a good idea or
+
+ align:start position:0%
+to the normative is this a good idea or
+ 
+
+ align:start position:0%
+to the normative is this a good idea or
+not well let's look at the welfare
+
+ align:start position:0%
+not well let's look at the welfare
+ 
+
+ align:start position:0%
+not well let's look at the welfare
+implications what's happened what's
+
+ align:start position:0%
+implications what's happened what's
+ 
+
+ align:start position:0%
+implications what's happened what's
+happened is consumers used to have a
+
+ align:start position:0%
+happened is consumers used to have a
+ 
+
+ align:start position:0%
+happened is consumers used to have a
+surplus a plus B plus C now their
+
+ align:start position:0%
+surplus a plus B plus C now their
+ 
+
+ align:start position:0%
+surplus a plus B plus C now their
+surplus is what what's to do consumer
+
+ align:start position:0%
+surplus is what what's to do consumer
+ 
+
+ align:start position:0%
+surplus is what what's to do consumer
+surplus raise their hand and tell me
+
+ align:start position:0%
+surplus raise their hand and tell me
+ 
+
+ align:start position:0%
+surplus raise their hand and tell me
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+just a because the line below the demand
+
+ align:start position:0%
+just a because the line below the demand
+ 
+
+ align:start position:0%
+just a because the line below the demand
+above price is just a producer's used to
+
+ align:start position:0%
+above price is just a producer's used to
+ 
+
+ align:start position:0%
+above price is just a producer's used to
+have zero surplus what's their new
+
+ align:start position:0%
+have zero surplus what's their new
+ 
+
+ align:start position:0%
+have zero surplus what's their new
+surplus behind you yeah B because it's
+
+ align:start position:0%
+surplus behind you yeah B because it's
+ 
+
+ align:start position:0%
+surplus behind you yeah B because it's
+the area above the supply curve below
+
+ align:start position:0%
+the area above the supply curve below
+ 
+
+ align:start position:0%
+the area above the supply curve below
+the price line and C is what the
+
+ align:start position:0%
+the price line and C is what the
+ 
+
+ align:start position:0%
+the price line and C is what the
+deadweight loss
+
+ align:start position:0%
+deadweight loss
+ 
+
+ align:start position:0%
+deadweight loss
+those the transactions no longer
+
+ align:start position:0%
+those the transactions no longer
+ 
+
+ align:start position:0%
+those the transactions no longer
+happening okay
+
+ align:start position:0%
+happening okay
+ 
+
+ align:start position:0%
+happening okay
+the deadweight loss okay so basically
+
+ align:start position:0%
+the deadweight loss okay so basically
+ 
+
+ align:start position:0%
+the deadweight loss okay so basically
+normatively you can pose the problem as
+
+ align:start position:0%
+normatively you can pose the problem as
+ 
+
+ align:start position:0%
+normatively you can pose the problem as
+the following is it worth society losing
+
+ align:start position:0%
+the following is it worth society losing
+ 
+
+ align:start position:0%
+the following is it worth society losing
+the area see in order to transfer the
+
+ align:start position:0%
+the area see in order to transfer the
+ 
+
+ align:start position:0%
+the area see in order to transfer the
+area be from consumers to taxicab
+
+ align:start position:0%
+area be from consumers to taxicab
+ 
+
+ align:start position:0%
+area be from consumers to taxicab
+drivers that's the way to think about
+
+ align:start position:0%
+drivers that's the way to think about
+ 
+
+ align:start position:0%
+drivers that's the way to think about
+this problem we say it again it's very
+
+ align:start position:0%
+this problem we say it again it's very
+ 
+
+ align:start position:0%
+this problem we say it again it's very
+important central the government policy
+
+ align:start position:0%
+important central the government policy
+ 
+
+ align:start position:0%
+important central the government policy
+doing is saying I'm going to transfer be
+
+ align:start position:0%
+doing is saying I'm going to transfer be
+ 
+
+ align:start position:0%
+doing is saying I'm going to transfer be
+from consumers to producers even though
+
+ align:start position:0%
+from consumers to producers even though
+ 
+
+ align:start position:0%
+from consumers to producers even though
+it's gonna cost me see and deadweight
+
+ align:start position:0%
+it's gonna cost me see and deadweight
+ 
+
+ align:start position:0%
+it's gonna cost me see and deadweight
+loss that's what the government's saying
+
+ align:start position:0%
+loss that's what the government's saying
+ 
+
+ align:start position:0%
+loss that's what the government's saying
+that's the government's position okay
+
+ align:start position:0%
+that's the government's position okay
+ 
+
+ align:start position:0%
+that's the government's position okay
+now why is the government wrong why in
+
+ align:start position:0%
+now why is the government wrong why in
+ 
+
+ align:start position:0%
+now why is the government wrong why in
+fact is that not the proper statement of
+
+ align:start position:0%
+fact is that not the proper statement of
+ 
+
+ align:start position:0%
+fact is that not the proper statement of
+what happens it's very complicated what
+
+ align:start position:0%
+what happens it's very complicated what
+ 
+
+ align:start position:0%
+what happens it's very complicated what
+is the government miss when it says hey
+
+ align:start position:0%
+is the government miss when it says hey
+ 
+
+ align:start position:0%
+is the government miss when it says hey
+look I've made the drivers better off
+
+ align:start position:0%
+look I've made the drivers better off
+ 
+
+ align:start position:0%
+look I've made the drivers better off
+sure I've created deadweight lost
+
+ align:start position:0%
+sure I've created deadweight lost
+ 
+
+ align:start position:0%
+sure I've created deadweight lost
+beliefs and I made consumers will help
+
+ align:start position:0%
+beliefs and I made consumers will help
+ 
+
+ align:start position:0%
+beliefs and I made consumers will help
+at least I mean these drivers better off
+
+ align:start position:0%
+at least I mean these drivers better off
+ 
+
+ align:start position:0%
+at least I mean these drivers better off
+they leave terrible lives as article in
+
+ align:start position:0%
+they leave terrible lives as article in
+ 
+
+ align:start position:0%
+they leave terrible lives as article in
+the paper all the time about suicides
+
+ align:start position:0%
+the paper all the time about suicides
+ 
+
+ align:start position:0%
+the paper all the time about suicides
+the taxicab drivers it's terrible what
+
+ align:start position:0%
+the taxicab drivers it's terrible what
+ 
+
+ align:start position:0%
+the taxicab drivers it's terrible what
+do they miss yeah they've missed the
+
+ align:start position:0%
+do they miss yeah they've missed the
+ 
+
+ align:start position:0%
+do they miss yeah they've missed the
+fact that the taxicab drivers have to
+
+ align:start position:0%
+fact that the taxicab drivers have to
+ 
+
+ align:start position:0%
+fact that the taxicab drivers have to
+buy the medallions that the limited
+
+ align:start position:0%
+buy the medallions that the limited
+ 
+
+ align:start position:0%
+buy the medallions that the limited
+numbered aliens aren't just given the
+
+ align:start position:0%
+numbered aliens aren't just given the
+ 
+
+ align:start position:0%
+numbered aliens aren't just given the
+taxicab drivers they're bought and the
+
+ align:start position:0%
+taxicab drivers they're bought and the
+ 
+
+ align:start position:0%
+taxicab drivers they're bought and the
+taxicab drivers what is a taxicab driver
+
+ align:start position:0%
+taxicab drivers what is a taxicab driver
+ 
+
+ align:start position:0%
+taxicab drivers what is a taxicab driver
+willing to pay for a medallion they are
+
+ align:start position:0%
+willing to pay for a medallion they are
+ 
+
+ align:start position:0%
+willing to pay for a medallion they are
+willing to pay in the limit the total
+
+ align:start position:0%
+willing to pay in the limit the total
+ 
+
+ align:start position:0%
+willing to pay in the limit the total
+surplus they get from driving the cab -
+
+ align:start position:0%
+surplus they get from driving the cab -
+ 
+
+ align:start position:0%
+surplus they get from driving the cab -
+a dollar or - some amount you know that
+
+ align:start position:0%
+a dollar or - some amount you know that
+ 
+
+ align:start position:0%
+a dollar or - some amount you know that
+they need to eat so if suddenly in a
+
+ align:start position:0%
+they need to eat so if suddenly in a
+ 
+
+ align:start position:0%
+they need to eat so if suddenly in a
+world with no restrictions with no tax
+
+ align:start position:0%
+world with no restrictions with no tax
+ 
+
+ align:start position:0%
+world with no restrictions with no tax
+cab medallions if you said we're gonna
+
+ align:start position:0%
+cab medallions if you said we're gonna
+ 
+
+ align:start position:0%
+cab medallions if you said we're gonna
+be a piece of paper should you drive a
+
+ align:start position:0%
+be a piece of paper should you drive a
+ 
+
+ align:start position:0%
+be a piece of paper should you drive a
+taxi but anyone could have it for free
+
+ align:start position:0%
+taxi but anyone could have it for free
+ 
+
+ align:start position:0%
+taxi but anyone could have it for free
+whoa would it be worth zero but in the
+
+ align:start position:0%
+whoa would it be worth zero but in the
+ 
+
+ align:start position:0%
+whoa would it be worth zero but in the
+world will you say you can if you have
+
+ align:start position:0%
+world will you say you can if you have
+ 
+
+ align:start position:0%
+world will you say you can if you have
+the speed paper you can drive and
+
+ align:start position:0%
+the speed paper you can drive and
+ 
+
+ align:start position:0%
+the speed paper you can drive and
+drivers earn profits pie what will the
+
+ align:start position:0%
+drivers earn profits pie what will the
+ 
+
+ align:start position:0%
+drivers earn profits pie what will the
+taxed have medallions sell for pie -
+
+ align:start position:0%
+taxed have medallions sell for pie -
+ 
+
+ align:start position:0%
+taxed have medallions sell for pie -
+some small amount so actually who wins
+
+ align:start position:0%
+some small amount so actually who wins
+ 
+
+ align:start position:0%
+some small amount so actually who wins
+the taxicab medallion owners and who are
+
+ align:start position:0%
+the taxicab medallion owners and who are
+ 
+
+ align:start position:0%
+the taxicab medallion owners and who are
+they they are random folks who happen to
+
+ align:start position:0%
+they they are random folks who happen to
+ 
+
+ align:start position:0%
+they they are random folks who happen to
+get these things in 1920 when they were
+
+ align:start position:0%
+get these things in 1920 when they were
+ 
+
+ align:start position:0%
+get these things in 1920 when they were
+issued and there
+
+ align:start position:0%
+issued and there
+ 
+
+ align:start position:0%
+issued and there
+descendants and people who bought them
+
+ align:start position:0%
+descendants and people who bought them
+ 
+
+ align:start position:0%
+descendants and people who bought them
+okay so this leads to my great story the
+
+ align:start position:0%
+okay so this leads to my great story the
+ 
+
+ align:start position:0%
+okay so this leads to my great story the
+taxicab medallion king of Long Island
+
+ align:start position:0%
+taxicab medallion king of Long Island
+ 
+
+ align:start position:0%
+taxicab medallion king of Long Island
+was the guy who happened to have a bun
+
+ align:start position:0%
+was the guy who happened to have a bun
+ 
+
+ align:start position:0%
+was the guy who happened to have a bun
+Chee's tax cabinets and as they went
+
+ align:start position:0%
+Chee's tax cabinets and as they went
+ 
+
+ align:start position:0%
+Chee's tax cabinets and as they went
+through the roof they are worth a lot in
+
+ align:start position:0%
+through the roof they are worth a lot in
+ 
+
+ align:start position:0%
+through the roof they are worth a lot in
+New York a tax New York um had 12,000
+
+ align:start position:0%
+New York a tax New York um had 12,000
+ 
+
+ align:start position:0%
+New York a tax New York um had 12,000
+permits and that number did not change
+
+ align:start position:0%
+permits and that number did not change
+ 
+
+ align:start position:0%
+permits and that number did not change
+since they originally sold for $10 each
+
+ align:start position:0%
+since they originally sold for $10 each
+ 
+
+ align:start position:0%
+since they originally sold for $10 each
+in 1937 937 you could have bought her
+
+ align:start position:0%
+in 1937 937 you could have bought her
+ 
+
+ align:start position:0%
+in 1937 937 you could have bought her
+for $10 they issued 12 12,000
+
+ align:start position:0%
+for $10 they issued 12 12,000
+ 
+
+ align:start position:0%
+for $10 they issued 12 12,000
+they've never increased it right now a
+
+ align:start position:0%
+they've never increased it right now a
+ 
+
+ align:start position:0%
+they've never increased it right now a
+tax Hammond I New York is worth $400,000
+
+ align:start position:0%
+tax Hammond I New York is worth $400,000
+ 
+
+ align:start position:0%
+tax Hammond I New York is worth $400,000
+okay well the tax cap king of New York
+
+ align:start position:0%
+okay well the tax cap king of New York
+ 
+
+ align:start position:0%
+okay well the tax cap king of New York
+is a guy lives Long Island who made so
+
+ align:start position:0%
+is a guy lives Long Island who made so
+ 
+
+ align:start position:0%
+is a guy lives Long Island who made so
+much money that he actually uh he
+
+ align:start position:0%
+much money that he actually uh he
+ 
+
+ align:start position:0%
+much money that he actually uh he
+actually first kids Bar Mitzvah
+
+ align:start position:0%
+actually first kids Bar Mitzvah
+ 
+
+ align:start position:0%
+actually first kids Bar Mitzvah
+not only had rented at a hotel ho
+
+ align:start position:0%
+not only had rented at a hotel ho
+ 
+
+ align:start position:0%
+not only had rented at a hotel ho
+basketball theme Bar Mitzvah but hired
+
+ align:start position:0%
+basketball theme Bar Mitzvah but hired
+ 
+
+ align:start position:0%
+basketball theme Bar Mitzvah but hired
+Nicki Minaj okay
+
+ align:start position:0%
+Nicki Minaj okay
+ 
+
+ align:start position:0%
+Nicki Minaj okay
+this was paid for by area B okay this
+
+ align:start position:0%
+this was paid for by area B okay this
+ 
+
+ align:start position:0%
+this was paid for by area B okay this
+was paid for so in fact it's not the
+
+ align:start position:0%
+was paid for so in fact it's not the
+ 
+
+ align:start position:0%
+was paid for so in fact it's not the
+taxi cab drivers that make at under this
+
+ align:start position:0%
+taxi cab drivers that make at under this
+ 
+
+ align:start position:0%
+taxi cab drivers that make at under this
+policy it's a taxi cab medallion king of
+
+ align:start position:0%
+policy it's a taxi cab medallion king of
+ 
+
+ align:start position:0%
+policy it's a taxi cab medallion king of
+La Llorona in who's the big loser not
+
+ align:start position:0%
+La Llorona in who's the big loser not
+ 
+
+ align:start position:0%
+La Llorona in who's the big loser not
+the taxicab drivers the taxi cab
+
+ align:start position:0%
+the taxicab drivers the taxi cab
+ 
+
+ align:start position:0%
+the taxicab drivers the taxi cab
+medallion owners so everyone tells you
+
+ align:start position:0%
+medallion owners so everyone tells you
+ 
+
+ align:start position:0%
+medallion owners so everyone tells you
+burrs a bad thing because these poor
+
+ align:start position:0%
+burrs a bad thing because these poor
+ 
+
+ align:start position:0%
+burrs a bad thing because these poor
+taxi cab drivers are starving taxi cab
+
+ align:start position:0%
+taxi cab drivers are starving taxi cab
+ 
+
+ align:start position:0%
+taxi cab drivers are starving taxi cab
+drivers were always starving it was
+
+ align:start position:0%
+drivers were always starving it was
+ 
+
+ align:start position:0%
+drivers were always starving it was
+always a terrible life the difference
+
+ align:start position:0%
+always a terrible life the difference
+ 
+
+ align:start position:0%
+always a terrible life the difference
+the difference is price and medallions
+
+ align:start position:0%
+the difference is price and medallions
+ 
+
+ align:start position:0%
+the difference is price and medallions
+is down like 50% and I cry no tears for
+
+ align:start position:0%
+is down like 50% and I cry no tears for
+ 
+
+ align:start position:0%
+is down like 50% and I cry no tears for
+the for the Nicki Minaj higher in class
+
+ align:start position:0%
+the for the Nicki Minaj higher in class
+ 
+
+ align:start position:0%
+the for the Nicki Minaj higher in class
+of America okay so basically when you
+
+ align:start position:0%
+of America okay so basically when you
+ 
+
+ align:start position:0%
+of America okay so basically when you
+think about P per se
+
+ align:start position:0%
+think about P per se
+ 
+
+ align:start position:0%
+think about P per se
+Uber's bad it steals jobs tax time
+
+ align:start position:0%
+Uber's bad it steals jobs tax time
+ 
+
+ align:start position:0%
+Uber's bad it steals jobs tax time
+drivers no it doesn't okay it steals
+
+ align:start position:0%
+drivers no it doesn't okay it steals
+ 
+
+ align:start position:0%
+drivers no it doesn't okay it steals
+money from tax cab medallion owners and
+
+ align:start position:0%
+money from tax cab medallion owners and
+ 
+
+ align:start position:0%
+money from tax cab medallion owners and
+that is something we might be okay with
+
+ align:start position:0%
+that is something we might be okay with
+ 
+
+ align:start position:0%
+that is something we might be okay with
+so feel fine taking your uber it's a
+
+ align:start position:0%
+so feel fine taking your uber it's a
+ 
+
+ align:start position:0%
+so feel fine taking your uber it's a
+great it's a great thing so let me stop
+
+ align:start position:0%
+great it's a great thing so let me stop
+ 
+
+ align:start position:0%
+great it's a great thing so let me stop
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+um I'm going to come back come back next
+
+ align:start position:0%
+um I'm going to come back come back next
+ 
+
+ align:start position:0%
+um I'm going to come back come back next
+lecture and we will start talking about
+
+ align:start position:0%
+lecture and we will start talking about
+ 
+
+ align:start position:0%
+lecture and we will start talking about
+monopoly the market structure not the
+
+ align:start position:0%
+monopoly the market structure not the
+ 
+
+ align:start position:0%
+monopoly the market structure not the
+game
\ No newline at end of file
diff --git a/Penh4mv5gAg.txt b/Penh4mv5gAg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..41b7adddafb7c491a57b6e4856c7d5f7a2216d45
--- /dev/null
+++ b/Penh4mv5gAg.txt
@@ -0,0 +1,2995 @@
+align:start position:0%
+ 
+graph coloring is the abstract version
+
+ align:start position:0%
+graph coloring is the abstract version
+ 
+
+ align:start position:0%
+graph coloring is the abstract version
+of a problem that arises from a bunch of
+
+ align:start position:0%
+of a problem that arises from a bunch of
+ 
+
+ align:start position:0%
+of a problem that arises from a bunch of
+conflict scheduling situations so let's
+
+ align:start position:0%
+conflict scheduling situations so let's
+ 
+
+ align:start position:0%
+conflict scheduling situations so let's
+look at an example first and then define
+
+ align:start position:0%
+look at an example first and then define
+ 
+
+ align:start position:0%
+look at an example first and then define
+the problem so let's think about a bunch
+
+ align:start position:0%
+the problem so let's think about a bunch
+ 
+
+ align:start position:0%
+the problem so let's think about a bunch
+of aircraft that have to be scheduled on
+
+ align:start position:0%
+of aircraft that have to be scheduled on
+ 
+
+ align:start position:0%
+of aircraft that have to be scheduled on
+the ground a Czech ports or gates now if
+
+ align:start position:0%
+the ground a Czech ports or gates now if
+ 
+
+ align:start position:0%
+the ground a Czech ports or gates now if
+two flights are on the ground at the
+
+ align:start position:0%
+two flights are on the ground at the
+ 
+
+ align:start position:0%
+two flights are on the ground at the
+same time they need to be assigned to
+
+ align:start position:0%
+same time they need to be assigned to
+ 
+
+ align:start position:0%
+same time they need to be assigned to
+different gates since again serves one
+
+ align:start position:0%
+different gates since again serves one
+ 
+
+ align:start position:0%
+different gates since again serves one
+airplane and what we'd like to do is try
+
+ align:start position:0%
+airplane and what we'd like to do is try
+ 
+
+ align:start position:0%
+airplane and what we'd like to do is try
+to figure out how many different gates
+
+ align:start position:0%
+to figure out how many different gates
+ 
+
+ align:start position:0%
+to figure out how many different gates
+do we need to be able to service all the
+
+ align:start position:0%
+do we need to be able to service all the
+ 
+
+ align:start position:0%
+do we need to be able to service all the
+planes that might be on the ground how
+
+ align:start position:0%
+planes that might be on the ground how
+ 
+
+ align:start position:0%
+planes that might be on the ground how
+many gates are needed so let's look at a
+
+ align:start position:0%
+many gates are needed so let's look at a
+ 
+
+ align:start position:0%
+many gates are needed so let's look at a
+sample schedule there are six flights
+
+ align:start position:0%
+sample schedule there are six flights
+ 
+
+ align:start position:0%
+sample schedule there are six flights
+here numbering 120 to 145 through 99 and
+
+ align:start position:0%
+here numbering 120 to 145 through 99 and
+ 
+
+ align:start position:0%
+here numbering 120 to 145 through 99 and
+these the horizontal bar is say times
+
+ align:start position:0%
+these the horizontal bar is say times
+ 
+
+ align:start position:0%
+these the horizontal bar is say times
+during the day and this blue block
+
+ align:start position:0%
+during the day and this blue block
+ 
+
+ align:start position:0%
+during the day and this blue block
+indicates that flight 122 is on the
+
+ align:start position:0%
+indicates that flight 122 is on the
+ 
+
+ align:start position:0%
+indicates that flight 122 is on the
+ground from let's say 3 a.m. to 7 a.m.
+
+ align:start position:0%
+ground from let's say 3 a.m. to 7 a.m.
+ 
+
+ align:start position:0%
+ground from let's say 3 a.m. to 7 a.m.
+and fight 145 is on the ground and a
+
+ align:start position:0%
+and fight 145 is on the ground and a
+ 
+
+ align:start position:0%
+and fight 145 is on the ground and a
+completely different disjoint time
+
+ align:start position:0%
+completely different disjoint time
+ 
+
+ align:start position:0%
+completely different disjoint time
+interval so 67 to 57 is on the ground
+
+ align:start position:0%
+interval so 67 to 57 is on the ground
+ 
+
+ align:start position:0%
+interval so 67 to 57 is on the ground
+from midnight until about 6 a.m. it does
+
+ align:start position:0%
+from midnight until about 6 a.m. it does
+ 
+
+ align:start position:0%
+from midnight until about 6 a.m. it does
+overlap with 122 and so on so this is
+
+ align:start position:0%
+overlap with 122 and so on so this is
+ 
+
+ align:start position:0%
+overlap with 122 and so on so this is
+the information we have and what we're
+
+ align:start position:0%
+the information we have and what we're
+ 
+
+ align:start position:0%
+the information we have and what we're
+trying to figure out is how many gates
+
+ align:start position:0%
+trying to figure out is how many gates
+ 
+
+ align:start position:0%
+trying to figure out is how many gates
+do we need well it's easy to see here
+
+ align:start position:0%
+do we need well it's easy to see here
+ 
+
+ align:start position:0%
+do we need well it's easy to see here
+that the worst case if you just think of
+
+ align:start position:0%
+that the worst case if you just think of
+ 
+
+ align:start position:0%
+that the worst case if you just think of
+this a vertical Green Line sliding
+
+ align:start position:0%
+this a vertical Green Line sliding
+ 
+
+ align:start position:0%
+this a vertical Green Line sliding
+across the bar and you look at the
+
+ align:start position:0%
+across the bar and you look at the
+ 
+
+ align:start position:0%
+across the bar and you look at the
+maximum number of blue intervals that
+
+ align:start position:0%
+maximum number of blue intervals that
+ 
+
+ align:start position:0%
+maximum number of blue intervals that
+the Green Line ever crosses it's 3 the
+
+ align:start position:0%
+the Green Line ever crosses it's 3 the
+ 
+
+ align:start position:0%
+the Green Line ever crosses it's 3 the
+largest number of planes that are on the
+
+ align:start position:0%
+largest number of planes that are on the
+ 
+
+ align:start position:0%
+largest number of planes that are on the
+gate at any given moment is 3 which
+
+ align:start position:0%
+gate at any given moment is 3 which
+ 
+
+ align:start position:0%
+gate at any given moment is 3 which
+means we can get by with 3 gates so we
+
+ align:start position:0%
+means we can get by with 3 gates so we
+ 
+
+ align:start position:0%
+means we can get by with 3 gates so we
+have to cope with that conflict now so
+
+ align:start position:0%
+have to cope with that conflict now so
+ 
+
+ align:start position:0%
+have to cope with that conflict now so
+abstractly what we're going to do is
+
+ align:start position:0%
+abstractly what we're going to do is
+ 
+
+ align:start position:0%
+abstractly what we're going to do is
+assign each aircraft to be a vertex of a
+
+ align:start position:0%
+assign each aircraft to be a vertex of a
+ 
+
+ align:start position:0%
+assign each aircraft to be a vertex of a
+graph and we're going to put an edge in
+
+ align:start position:0%
+graph and we're going to put an edge in
+ 
+
+ align:start position:0%
+graph and we're going to put an edge in
+to indicate not compatibility but
+
+ align:start position:0%
+to indicate not compatibility but
+ 
+
+ align:start position:0%
+to indicate not compatibility but
+conflict compatibility was what we were
+
+ align:start position:0%
+conflict compatibility was what we were
+ 
+
+ align:start position:0%
+conflict compatibility was what we were
+looking at previously with our examples
+
+ align:start position:0%
+looking at previously with our examples
+ 
+
+ align:start position:0%
+looking at previously with our examples
+of matching now this line means that 306
+
+ align:start position:0%
+of matching now this line means that 306
+ 
+
+ align:start position:0%
+of matching now this line means that 306
+and 145 are on the ground at the same
+
+ align:start position:0%
+and 145 are on the ground at the same
+ 
+
+ align:start position:0%
+and 145 are on the ground at the same
+time they conflict they need the same
+
+ align:start position:0%
+time they conflict they need the same
+ 
+
+ align:start position:0%
+time they conflict they need the same
+gate and we have to serve them with
+
+ align:start position:0%
+gate and we have to serve them with
+ 
+
+ align:start position:0%
+gate and we have to serve them with
+different gates and likewise 99 and 145
+
+ align:start position:0%
+different gates and likewise 99 and 145
+ 
+
+ align:start position:0%
+different gates and likewise 99 and 145
+are on the ground
+
+ align:start position:0%
+are on the ground
+ 
+
+ align:start position:0%
+are on the ground
+$6.99 this was that that the three
+
+ align:start position:0%
+$6.99 this was that that the three
+ 
+
+ align:start position:0%
+$6.99 this was that that the three
+flights that were on the ground at the
+
+ align:start position:0%
+flights that were on the ground at the
+ 
+
+ align:start position:0%
+flights that were on the ground at the
+same time and then if I fill in the
+
+ align:start position:0%
+same time and then if I fill in the
+ 
+
+ align:start position:0%
+same time and then if I fill in the
+computer graph with all the other
+
+ align:start position:0%
+computer graph with all the other
+ 
+
+ align:start position:0%
+computer graph with all the other
+vertices and draw an edge when two
+
+ align:start position:0%
+vertices and draw an edge when two
+ 
+
+ align:start position:0%
+vertices and draw an edge when two
+flights are on the ground at the same
+
+ align:start position:0%
+flights are on the ground at the same
+ 
+
+ align:start position:0%
+flights are on the ground at the same
+time I wind up with this little graph
+
+ align:start position:0%
+time I wind up with this little graph
+ 
+
+ align:start position:0%
+time I wind up with this little graph
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we can talk abstractly about the
+
+ align:start position:0%
+now we can talk abstractly about the
+ 
+
+ align:start position:0%
+now we can talk abstractly about the
+coloring problem which is let's assign
+
+ align:start position:0%
+coloring problem which is let's assign
+ 
+
+ align:start position:0%
+coloring problem which is let's assign
+colors to the vertices in such a way
+
+ align:start position:0%
+colors to the vertices in such a way
+ 
+
+ align:start position:0%
+colors to the vertices in such a way
+that no two adjacent vertices have the
+
+ align:start position:0%
+that no two adjacent vertices have the
+ 
+
+ align:start position:0%
+that no two adjacent vertices have the
+same color okay adjacent vertices should
+
+ align:start position:0%
+same color okay adjacent vertices should
+ 
+
+ align:start position:0%
+same color okay adjacent vertices should
+have different colors and it should be
+
+ align:start position:0%
+have different colors and it should be
+ 
+
+ align:start position:0%
+have different colors and it should be
+clear from the description of how we
+
+ align:start position:0%
+clear from the description of how we
+ 
+
+ align:start position:0%
+clear from the description of how we
+derive this graph from the airline
+
+ align:start position:0%
+derive this graph from the airline
+ 
+
+ align:start position:0%
+derive this graph from the airline
+aircraft schedules that the minimum
+
+ align:start position:0%
+aircraft schedules that the minimum
+ 
+
+ align:start position:0%
+aircraft schedules that the minimum
+number of distinct colors needed to
+
+ align:start position:0%
+number of distinct colors needed to
+ 
+
+ align:start position:0%
+number of distinct colors needed to
+color the graph corresponds to the
+
+ align:start position:0%
+color the graph corresponds to the
+ 
+
+ align:start position:0%
+color the graph corresponds to the
+minimum number of gates needed to serve
+
+ align:start position:0%
+minimum number of gates needed to serve
+ 
+
+ align:start position:0%
+minimum number of gates needed to serve
+the aircraft so let's try coloring this
+
+ align:start position:0%
+the aircraft so let's try coloring this
+ 
+
+ align:start position:0%
+the aircraft so let's try coloring this
+graph I'll start with coloring for 257
+
+ align:start position:0%
+graph I'll start with coloring for 257
+ 
+
+ align:start position:0%
+graph I'll start with coloring for 257
+red and 122 yellow and 99 green there's
+
+ align:start position:0%
+red and 122 yellow and 99 green there's
+ 
+
+ align:start position:0%
+red and 122 yellow and 99 green there's
+no loss of generality here because these
+
+ align:start position:0%
+no loss of generality here because these
+ 
+
+ align:start position:0%
+no loss of generality here because these
+are the three that are on the ground at
+
+ align:start position:0%
+are the three that are on the ground at
+ 
+
+ align:start position:0%
+are the three that are on the ground at
+the same time reflected by the fact that
+
+ align:start position:0%
+the same time reflected by the fact that
+ 
+
+ align:start position:0%
+the same time reflected by the fact that
+they're in a triangle and I'm gonna have
+
+ align:start position:0%
+they're in a triangle and I'm gonna have
+ 
+
+ align:start position:0%
+they're in a triangle and I'm gonna have
+to use three different colors since each
+
+ align:start position:0%
+to use three different colors since each
+ 
+
+ align:start position:0%
+to use three different colors since each
+one is adjacent to the other two okay
+
+ align:start position:0%
+one is adjacent to the other two okay
+ 
+
+ align:start position:0%
+one is adjacent to the other two okay
+what next well let's color 145 yellow I
+
+ align:start position:0%
+what next well let's color 145 yellow I
+ 
+
+ align:start position:0%
+what next well let's color 145 yellow I
+might as well reuse it since it's not
+
+ align:start position:0%
+might as well reuse it since it's not
+ 
+
+ align:start position:0%
+might as well reuse it since it's not
+adjacent to a yellow vertex and then um
+
+ align:start position:0%
+adjacent to a yellow vertex and then um
+ 
+
+ align:start position:0%
+adjacent to a yellow vertex and then um
+here I've got a another triangle so if
+
+ align:start position:0%
+here I've got a another triangle so if
+ 
+
+ align:start position:0%
+here I've got a another triangle so if
+I'm not going to use an extra color the
+
+ align:start position:0%
+I'm not going to use an extra color the
+ 
+
+ align:start position:0%
+I'm not going to use an extra color the
+sensible thing to do would be to color
+
+ align:start position:0%
+sensible thing to do would be to color
+ 
+
+ align:start position:0%
+sensible thing to do would be to color
+that red but opus I didn't do that I use
+
+ align:start position:0%
+that red but opus I didn't do that I use
+ 
+
+ align:start position:0%
+that red but opus I didn't do that I use
+the red here there's another triangle I
+
+ align:start position:0%
+the red here there's another triangle I
+ 
+
+ align:start position:0%
+the red here there's another triangle I
+guess that's that allows me to color and
+
+ align:start position:0%
+guess that's that allows me to color and
+ 
+
+ align:start position:0%
+guess that's that allows me to color and
+then I color this black because here I'm
+
+ align:start position:0%
+then I color this black because here I'm
+ 
+
+ align:start position:0%
+then I color this black because here I'm
+stuck I'm adjacent to both a yellow a
+
+ align:start position:0%
+stuck I'm adjacent to both a yellow a
+ 
+
+ align:start position:0%
+stuck I'm adjacent to both a yellow a
+black and a green vertex so I have to
+
+ align:start position:0%
+black and a green vertex so I have to
+ 
+
+ align:start position:0%
+black and a green vertex so I have to
+come up with a fourth color all right we
+
+ align:start position:0%
+come up with a fourth color all right we
+ 
+
+ align:start position:0%
+come up with a fourth color all right we
+did with four colors it means that we
+
+ align:start position:0%
+did with four colors it means that we
+ 
+
+ align:start position:0%
+did with four colors it means that we
+could could have gotten away with four
+
+ align:start position:0%
+could could have gotten away with four
+ 
+
+ align:start position:0%
+could could have gotten away with four
+gates and the colors tell us which
+
+ align:start position:0%
+gates and the colors tell us which
+ 
+
+ align:start position:0%
+gates and the colors tell us which
+aircraft to assign to which gate so 257
+
+ align:start position:0%
+aircraft to assign to which gate so 257
+ 
+
+ align:start position:0%
+aircraft to assign to which gate so 257
+and 67 can both be assigned to the red
+
+ align:start position:0%
+and 67 can both be assigned to the red
+ 
+
+ align:start position:0%
+and 67 can both be assigned to the red
+gate because they are not on the ground
+
+ align:start position:0%
+gate because they are not on the ground
+ 
+
+ align:start position:0%
+gate because they are not on the ground
+at the same time there's no edge between
+
+ align:start position:0%
+at the same time there's no edge between
+ 
+
+ align:start position:0%
+at the same time there's no edge between
+them 122 and 145 can be assigned a
+
+ align:start position:0%
+them 122 and 145 can be assigned a
+ 
+
+ align:start position:0%
+them 122 and 145 can be assigned a
+yellow gate and so on now this was not
+
+ align:start position:0%
+yellow gate and so on now this was not
+ 
+
+ align:start position:0%
+yellow gate and so on now this was not
+the smartest way to color a better
+
+ align:start position:0%
+the smartest way to color a better
+ 
+
+ align:start position:0%
+the smartest way to color a better
+coloring you're shown here you can check
+
+ align:start position:0%
+coloring you're shown here you can check
+ 
+
+ align:start position:0%
+coloring you're shown here you can check
+that every two adjacent vertices have
+
+ align:start position:0%
+that every two adjacent vertices have
+ 
+
+ align:start position:0%
+that every two adjacent vertices have
+different colors and now I've done it
+
+ align:start position:0%
+different colors and now I've done it
+ 
+
+ align:start position:0%
+different colors and now I've done it
+with only three colors red
+
+ align:start position:0%
+with only three colors red
+ 
+
+ align:start position:0%
+with only three colors red
+yellow and green so now there are three
+
+ align:start position:0%
+yellow and green so now there are three
+ 
+
+ align:start position:0%
+yellow and green so now there are three
+gates and I get a better schedule
+
+ align:start position:0%
+gates and I get a better schedule
+ 
+
+ align:start position:0%
+gates and I get a better schedule
+another example of this kind of conflict
+
+ align:start position:0%
+another example of this kind of conflict
+ 
+
+ align:start position:0%
+another example of this kind of conflict
+problem comes up with scheduling final
+
+ align:start position:0%
+problem comes up with scheduling final
+ 
+
+ align:start position:0%
+problem comes up with scheduling final
+exams two subjects conflict if a student
+
+ align:start position:0%
+exams two subjects conflict if a student
+ 
+
+ align:start position:0%
+exams two subjects conflict if a student
+is taking both because if a student is
+
+ align:start position:0%
+is taking both because if a student is
+ 
+
+ align:start position:0%
+is taking both because if a student is
+taking both I can't have the final exams
+
+ align:start position:0%
+taking both I can't have the final exams
+ 
+
+ align:start position:0%
+taking both I can't have the final exams
+at the same time and so I need to assign
+
+ align:start position:0%
+at the same time and so I need to assign
+ 
+
+ align:start position:0%
+at the same time and so I need to assign
+different timeslots during exam period
+
+ align:start position:0%
+different timeslots during exam period
+ 
+
+ align:start position:0%
+different timeslots during exam period
+two subjects that overlap that have a
+
+ align:start position:0%
+two subjects that overlap that have a
+ 
+
+ align:start position:0%
+two subjects that overlap that have a
+student in common and then the question
+
+ align:start position:0%
+student in common and then the question
+ 
+
+ align:start position:0%
+student in common and then the question
+is given this data about which pairs of
+
+ align:start position:0%
+is given this data about which pairs of
+ 
+
+ align:start position:0%
+is given this data about which pairs of
+subjects have a student in common we
+
+ align:start position:0%
+subjects have a student in common we
+ 
+
+ align:start position:0%
+subjects have a student in common we
+want to know how short an exam period
+
+ align:start position:0%
+want to know how short an exam period
+ 
+
+ align:start position:0%
+want to know how short an exam period
+can we get away with again it becomes a
+
+ align:start position:0%
+can we get away with again it becomes a
+ 
+
+ align:start position:0%
+can we get away with again it becomes a
+simple graph model and a coloring
+
+ align:start position:0%
+simple graph model and a coloring
+ 
+
+ align:start position:0%
+simple graph model and a coloring
+problem so here we've drawn a graph with
+
+ align:start position:0%
+problem so here we've drawn a graph with
+ 
+
+ align:start position:0%
+problem so here we've drawn a graph with
+some sample subjects 604 2 and 1802 have
+
+ align:start position:0%
+some sample subjects 604 2 and 1802 have
+ 
+
+ align:start position:0%
+some sample subjects 604 2 and 1802 have
+a student in common that's what that
+
+ align:start position:0%
+a student in common that's what that
+ 
+
+ align:start position:0%
+a student in common that's what that
+edge means they need to be have final
+
+ align:start position:0%
+edge means they need to be have final
+ 
+
+ align:start position:0%
+edge means they need to be have final
+exam scheduled at different times
+
+ align:start position:0%
+exam scheduled at different times
+ 
+
+ align:start position:0%
+exam scheduled at different times
+likewise 802 and 604 to have a student
+
+ align:start position:0%
+likewise 802 and 604 to have a student
+ 
+
+ align:start position:0%
+likewise 802 and 604 to have a student
+in common so they need to be scheduled
+
+ align:start position:0%
+in common so they need to be scheduled
+ 
+
+ align:start position:0%
+in common so they need to be scheduled
+at different times on the other hand 604
+
+ align:start position:0%
+at different times on the other hand 604
+ 
+
+ align:start position:0%
+at different times on the other hand 604
+2 and 1802 sorry what are some two that
+
+ align:start position:0%
+2 and 1802 sorry what are some two that
+ 
+
+ align:start position:0%
+2 and 1802 sorry what are some two that
+are not adjacent
+
+ align:start position:0%
+are not adjacent
+ 
+
+ align:start position:0%
+are not adjacent
+309 1 and 1802 have no edge between them
+
+ align:start position:0%
+309 1 and 1802 have no edge between them
+ 
+
+ align:start position:0%
+309 1 and 1802 have no edge between them
+which means that they can be scheduled
+
+ align:start position:0%
+which means that they can be scheduled
+ 
+
+ align:start position:0%
+which means that they can be scheduled
+at the same time there's no student
+
+ align:start position:0%
+at the same time there's no student
+ 
+
+ align:start position:0%
+at the same time there's no student
+who's taking both 309 1 and 1802 at
+
+ align:start position:0%
+who's taking both 309 1 and 1802 at
+ 
+
+ align:start position:0%
+who's taking both 309 1 and 1802 at
+least according to the data in this
+
+ align:start position:0%
+least according to the data in this
+ 
+
+ align:start position:0%
+least according to the data in this
+graph so let's try covering it and again
+
+ align:start position:0%
+graph so let's try covering it and again
+ 
+
+ align:start position:0%
+graph so let's try covering it and again
+it is a triangle I'm gonna have to use
+
+ align:start position:0%
+it is a triangle I'm gonna have to use
+ 
+
+ align:start position:0%
+it is a triangle I'm gonna have to use
+three different colors for a triangle
+
+ align:start position:0%
+three different colors for a triangle
+ 
+
+ align:start position:0%
+three different colors for a triangle
+and here's another triangle and to be
+
+ align:start position:0%
+and here's another triangle and to be
+ 
+
+ align:start position:0%
+and here's another triangle and to be
+economical let's just reuse green now
+
+ align:start position:0%
+economical let's just reuse green now
+ 
+
+ align:start position:0%
+economical let's just reuse green now
+here I've got another vertex that's
+
+ align:start position:0%
+here I've got another vertex that's
+ 
+
+ align:start position:0%
+here I've got another vertex that's
+adjacent to three different color
+
+ align:start position:0%
+adjacent to three different color
+ 
+
+ align:start position:0%
+adjacent to three different color
+vertices and so it's gonna have to be
+
+ align:start position:0%
+vertices and so it's gonna have to be
+ 
+
+ align:start position:0%
+vertices and so it's gonna have to be
+colored with a fourth color this time it
+
+ align:start position:0%
+colored with a fourth color this time it
+ 
+
+ align:start position:0%
+colored with a fourth color this time it
+turns out that the four colors are best
+
+ align:start position:0%
+turns out that the four colors are best
+ 
+
+ align:start position:0%
+turns out that the four colors are best
+possible you can check that and it
+
+ align:start position:0%
+possible you can check that and it
+ 
+
+ align:start position:0%
+possible you can check that and it
+corresponds to a schedule in which the
+
+ align:start position:0%
+corresponds to a schedule in which the
+ 
+
+ align:start position:0%
+corresponds to a schedule in which the
+604 2 is scheduled on Monday morning at
+
+ align:start position:0%
+604 2 is scheduled on Monday morning at
+ 
+
+ align:start position:0%
+604 2 is scheduled on Monday morning at
+nine and six double-o one is scheduled
+
+ align:start position:0%
+nine and six double-o one is scheduled
+ 
+
+ align:start position:0%
+nine and six double-o one is scheduled
+on Monday at 1:00
+
+ align:start position:0%
+on Monday at 1:00
+ 
+
+ align:start position:0%
+on Monday at 1:00
+but 802 and 309 one can both be
+
+ align:start position:0%
+but 802 and 309 one can both be
+ 
+
+ align:start position:0%
+but 802 and 309 one can both be
+scheduled for Tuesday 9:00 a.m. and
+
+ align:start position:0%
+scheduled for Tuesday 9:00 a.m. and
+ 
+
+ align:start position:0%
+scheduled for Tuesday 9:00 a.m. and
+finally 1802 is scheduled on Tuesday at
+
+ align:start position:0%
+finally 1802 is scheduled on Tuesday at
+ 
+
+ align:start position:0%
+finally 1802 is scheduled on Tuesday at
+1:00 p.m.
+
+ align:start position:0%
+1:00 p.m.
+ 
+
+ align:start position:0%
+1:00 p.m.
+okay so this kind of a conflict modeling
+
+ align:start position:0%
+okay so this kind of a conflict modeling
+ 
+
+ align:start position:0%
+okay so this kind of a conflict modeling
+situation comes up all the time
+
+ align:start position:0%
+situation comes up all the time
+ 
+
+ align:start position:0%
+situation comes up all the time
+another place where you get these kind
+
+ align:start position:0%
+another place where you get these kind
+ 
+
+ align:start position:0%
+another place where you get these kind
+of compatibility graphs or
+
+ align:start position:0%
+of compatibility graphs or
+ 
+
+ align:start position:0%
+of compatibility graphs or
+incompatibility graphs that you want to
+
+ align:start position:0%
+incompatibility graphs that you want to
+ 
+
+ align:start position:0%
+incompatibility graphs that you want to
+color would be if you were running a zoo
+
+ align:start position:0%
+color would be if you were running a zoo
+ 
+
+ align:start position:0%
+color would be if you were running a zoo
+and you had to have separate habit
+
+ align:start position:0%
+and you had to have separate habit
+ 
+
+ align:start position:0%
+and you had to have separate habit
+habitats for certain kinds of species of
+
+ align:start position:0%
+habitats for certain kinds of species of
+ 
+
+ align:start position:0%
+habitats for certain kinds of species of
+animals that you don't want to mix
+
+ align:start position:0%
+animals that you don't want to mix
+ 
+
+ align:start position:0%
+animals that you don't want to mix
+together big fish eat little fish it's a
+
+ align:start position:0%
+together big fish eat little fish it's a
+ 
+
+ align:start position:0%
+together big fish eat little fish it's a
+truism in the aquarium world and so you
+
+ align:start position:0%
+truism in the aquarium world and so you
+ 
+
+ align:start position:0%
+truism in the aquarium world and so you
+need to keep big fish separate from
+
+ align:start position:0%
+need to keep big fish separate from
+ 
+
+ align:start position:0%
+need to keep big fish separate from
+little fish and you don't want the
+
+ align:start position:0%
+little fish and you don't want the
+ 
+
+ align:start position:0%
+little fish and you don't want the
+Tigers living together with the
+
+ align:start position:0%
+Tigers living together with the
+ 
+
+ align:start position:0%
+Tigers living together with the
+chimpanzees so we could again model this
+
+ align:start position:0%
+chimpanzees so we could again model this
+ 
+
+ align:start position:0%
+chimpanzees so we could again model this
+problem as how many cages do we need we
+
+ align:start position:0%
+problem as how many cages do we need we
+ 
+
+ align:start position:0%
+problem as how many cages do we need we
+create a vertex for each species and put
+
+ align:start position:0%
+create a vertex for each species and put
+ 
+
+ align:start position:0%
+create a vertex for each species and put
+an arrow between an edge between two
+
+ align:start position:0%
+an arrow between an edge between two
+ 
+
+ align:start position:0%
+an arrow between an edge between two
+species that mustn't share a habitat or
+
+ align:start position:0%
+species that mustn't share a habitat or
+ 
+
+ align:start position:0%
+species that mustn't share a habitat or
+spheric or share a cage another one
+
+ align:start position:0%
+spheric or share a cage another one
+ 
+
+ align:start position:0%
+spheric or share a cage another one
+would be assigning different frequencies
+
+ align:start position:0%
+would be assigning different frequencies
+ 
+
+ align:start position:0%
+would be assigning different frequencies
+to radio stations and again if two radio
+
+ align:start position:0%
+to radio stations and again if two radio
+ 
+
+ align:start position:0%
+to radio stations and again if two radio
+stations are close to each other they
+
+ align:start position:0%
+stations are close to each other they
+ 
+
+ align:start position:0%
+stations are close to each other they
+they will interfere and so they have to
+
+ align:start position:0%
+they will interfere and so they have to
+ 
+
+ align:start position:0%
+they will interfere and so they have to
+be assigned to different colors or
+
+ align:start position:0%
+be assigned to different colors or
+ 
+
+ align:start position:0%
+be assigned to different colors or
+different frequencies so now we would be
+
+ align:start position:0%
+different frequencies so now we would be
+ 
+
+ align:start position:0%
+different frequencies so now we would be
+using radio stations as vertices and
+
+ align:start position:0%
+using radio stations as vertices and
+ 
+
+ align:start position:0%
+using radio stations as vertices and
+radio stations that were near enough to
+
+ align:start position:0%
+radio stations that were near enough to
+ 
+
+ align:start position:0%
+radio stations that were near enough to
+interfere with each other would get
+
+ align:start position:0%
+interfere with each other would get
+ 
+
+ align:start position:0%
+interfere with each other would get
+connected by an edge indicating that
+
+ align:start position:0%
+connected by an edge indicating that
+ 
+
+ align:start position:0%
+connected by an edge indicating that
+they needed to be assigned different
+
+ align:start position:0%
+they needed to be assigned different
+ 
+
+ align:start position:0%
+they needed to be assigned different
+color frequencies and one of the classic
+
+ align:start position:0%
+color frequencies and one of the classic
+ 
+
+ align:start position:0%
+color frequencies and one of the classic
+ones is literally to color a map if you
+
+ align:start position:0%
+ones is literally to color a map if you
+ 
+
+ align:start position:0%
+ones is literally to color a map if you
+were trying to take say a map of the US
+
+ align:start position:0%
+were trying to take say a map of the US
+ 
+
+ align:start position:0%
+were trying to take say a map of the US
+and assign colors to it in such a way
+
+ align:start position:0%
+and assign colors to it in such a way
+ 
+
+ align:start position:0%
+and assign colors to it in such a way
+that you never had two states that
+
+ align:start position:0%
+that you never had two states that
+ 
+
+ align:start position:0%
+that you never had two states that
+shared a border with the same color and
+
+ align:start position:0%
+shared a border with the same color and
+ 
+
+ align:start position:0%
+shared a border with the same color and
+this is an illustration of doing it with
+
+ align:start position:0%
+this is an illustration of doing it with
+ 
+
+ align:start position:0%
+this is an illustration of doing it with
+four colors the question is if I give
+
+ align:start position:0%
+four colors the question is if I give
+ 
+
+ align:start position:0%
+four colors the question is if I give
+you some kind of a planar map like this
+
+ align:start position:0%
+you some kind of a planar map like this
+ 
+
+ align:start position:0%
+you some kind of a planar map like this
+what's the minimum number of colors that
+
+ align:start position:0%
+what's the minimum number of colors that
+ 
+
+ align:start position:0%
+what's the minimum number of colors that
+will work now you're allowed to have two
+
+ align:start position:0%
+will work now you're allowed to have two
+ 
+
+ align:start position:0%
+will work now you're allowed to have two
+vertices with the two countries rather
+
+ align:start position:0%
+vertices with the two countries rather
+ 
+
+ align:start position:0%
+vertices with the two countries rather
+share the color if they only share a
+
+ align:start position:0%
+share the color if they only share a
+ 
+
+ align:start position:0%
+share the color if they only share a
+meet at one point but if they have a
+
+ align:start position:0%
+meet at one point but if they have a
+ 
+
+ align:start position:0%
+meet at one point but if they have a
+positive length boundary they have to be
+
+ align:start position:0%
+positive length boundary they have to be
+ 
+
+ align:start position:0%
+positive length boundary they have to be
+different colors okay the way that this
+
+ align:start position:0%
+different colors okay the way that this
+ 
+
+ align:start position:0%
+different colors okay the way that this
+turns into a vertex coloring problem is
+
+ align:start position:0%
+turns into a vertex coloring problem is
+ 
+
+ align:start position:0%
+turns into a vertex coloring problem is
+if you take a planar graph like this
+
+ align:start position:0%
+if you take a planar graph like this
+ 
+
+ align:start position:0%
+if you take a planar graph like this
+here's just an arbitrary one what I can
+
+ align:start position:0%
+here's just an arbitrary one what I can
+ 
+
+ align:start position:0%
+here's just an arbitrary one what I can
+do is I'm interested in coloring the
+
+ align:start position:0%
+do is I'm interested in coloring the
+ 
+
+ align:start position:0%
+do is I'm interested in coloring the
+regions the
+
+ align:start position:0%
+regions the
+ 
+
+ align:start position:0%
+regions the
+tres with different colors but I'll just
+
+ align:start position:0%
+tres with different colors but I'll just
+ 
+
+ align:start position:0%
+tres with different colors but I'll just
+replace each region by a vertex so I'm
+
+ align:start position:0%
+replace each region by a vertex so I'm
+ 
+
+ align:start position:0%
+replace each region by a vertex so I'm
+going to stick a vertex in the middle of
+
+ align:start position:0%
+going to stick a vertex in the middle of
+ 
+
+ align:start position:0%
+going to stick a vertex in the middle of
+each of the regions notice there's an
+
+ align:start position:0%
+each of the regions notice there's an
+ 
+
+ align:start position:0%
+each of the regions notice there's an
+outer region here - that gets a vertex
+
+ align:start position:0%
+outer region here - that gets a vertex
+ 
+
+ align:start position:0%
+outer region here - that gets a vertex
+so one two three four five six regions
+
+ align:start position:0%
+so one two three four five six regions
+ 
+
+ align:start position:0%
+so one two three four five six regions
+four six vertices and then I'll simply
+
+ align:start position:0%
+four six vertices and then I'll simply
+ 
+
+ align:start position:0%
+four six vertices and then I'll simply
+connect two vertices when there is a
+
+ align:start position:0%
+connect two vertices when there is a
+ 
+
+ align:start position:0%
+connect two vertices when there is a
+positive length edge that their regions
+
+ align:start position:0%
+positive length edge that their regions
+ 
+
+ align:start position:0%
+positive length edge that their regions
+share so there's that vertex that edge
+
+ align:start position:0%
+share so there's that vertex that edge
+ 
+
+ align:start position:0%
+share so there's that vertex that edge
+corresponds to the fact that there's
+
+ align:start position:0%
+corresponds to the fact that there's
+ 
+
+ align:start position:0%
+corresponds to the fact that there's
+this boundary that's shared between this
+
+ align:start position:0%
+this boundary that's shared between this
+ 
+
+ align:start position:0%
+this boundary that's shared between this
+region in this region if you look at
+
+ align:start position:0%
+region in this region if you look at
+ 
+
+ align:start position:0%
+region in this region if you look at
+this same triangular shaped region it
+
+ align:start position:0%
+this same triangular shaped region it
+ 
+
+ align:start position:0%
+this same triangular shaped region it
+has a boundary with the outside region
+
+ align:start position:0%
+has a boundary with the outside region
+ 
+
+ align:start position:0%
+has a boundary with the outside region
+so there's going to be an edge from here
+
+ align:start position:0%
+so there's going to be an edge from here
+ 
+
+ align:start position:0%
+so there's going to be an edge from here
+to the vertex that represents the
+
+ align:start position:0%
+to the vertex that represents the
+ 
+
+ align:start position:0%
+to the vertex that represents the
+outside and there's the rest of the
+
+ align:start position:0%
+outside and there's the rest of the
+ 
+
+ align:start position:0%
+outside and there's the rest of the
+edges and edge appears when between two
+
+ align:start position:0%
+edges and edge appears when between two
+ 
+
+ align:start position:0%
+edges and edge appears when between two
+regions that share a boundary and now
+
+ align:start position:0%
+regions that share a boundary and now
+ 
+
+ align:start position:0%
+regions that share a boundary and now
+the question is coloring the countries
+
+ align:start position:0%
+the question is coloring the countries
+ 
+
+ align:start position:0%
+the question is coloring the countries
+corresponds to coloring the vertices and
+
+ align:start position:0%
+corresponds to coloring the vertices and
+ 
+
+ align:start position:0%
+corresponds to coloring the vertices and
+we'd like to color the graph with as few
+
+ align:start position:0%
+we'd like to color the graph with as few
+ 
+
+ align:start position:0%
+we'd like to color the graph with as few
+colors as possible well a famous result
+
+ align:start position:0%
+colors as possible well a famous result
+ 
+
+ align:start position:0%
+colors as possible well a famous result
+that was proved in the seventies is that
+
+ align:start position:0%
+that was proved in the seventies is that
+ 
+
+ align:start position:0%
+that was proved in the seventies is that
+every planar graph is in fact four
+
+ align:start position:0%
+every planar graph is in fact four
+ 
+
+ align:start position:0%
+every planar graph is in fact four
+colorable now this was first proved to
+
+ align:start position:0%
+colorable now this was first proved to
+ 
+
+ align:start position:0%
+colorable now this was first proved to
+claim to be proved in the 1850s but in
+
+ align:start position:0%
+claim to be proved in the 1850s but in
+ 
+
+ align:start position:0%
+claim to be proved in the 1850s but in
+fact the published proof was wrong its
+
+ align:start position:0%
+fact the published proof was wrong its
+ 
+
+ align:start position:0%
+fact the published proof was wrong its
+sat around in the journal literature for
+
+ align:start position:0%
+sat around in the journal literature for
+ 
+
+ align:start position:0%
+sat around in the journal literature for
+a decade before somebody found a bug or
+
+ align:start position:0%
+a decade before somebody found a bug or
+ 
+
+ align:start position:0%
+a decade before somebody found a bug or
+that is to say that the proof was wrong
+
+ align:start position:0%
+that is to say that the proof was wrong
+ 
+
+ align:start position:0%
+that is to say that the proof was wrong
+not the result there was a big hole in
+
+ align:start position:0%
+not the result there was a big hole in
+ 
+
+ align:start position:0%
+not the result there was a big hole in
+the proof that that had not been
+
+ align:start position:0%
+the proof that that had not been
+ 
+
+ align:start position:0%
+the proof that that had not been
+adequately justified the proof did give
+
+ align:start position:0%
+adequately justified the proof did give
+ 
+
+ align:start position:0%
+adequately justified the proof did give
+a correct argument for five coloring and
+
+ align:start position:0%
+a correct argument for five coloring and
+ 
+
+ align:start position:0%
+a correct argument for five coloring and
+the four color problem was opened for
+
+ align:start position:0%
+the four color problem was opened for
+ 
+
+ align:start position:0%
+the four color problem was opened for
+over a hundred years then in the 1970s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two mathematicians came up with a proof
+
+ align:start position:0%
+two mathematicians came up with a proof
+ 
+
+ align:start position:0%
+two mathematicians came up with a proof
+of the four color theorem that was very
+
+ align:start position:0%
+of the four color theorem that was very
+ 
+
+ align:start position:0%
+of the four color theorem that was very
+controversial because a lot of it of
+
+ align:start position:0%
+controversial because a lot of it of
+ 
+
+ align:start position:0%
+controversial because a lot of it of
+their proof required a computer program
+
+ align:start position:0%
+their proof required a computer program
+ 
+
+ align:start position:0%
+their proof required a computer program
+to crank through several thousand sample
+
+ align:start position:0%
+to crank through several thousand sample
+ 
+
+ align:start position:0%
+to crank through several thousand sample
+graphs that needed to be verified for 4
+
+ align:start position:0%
+graphs that needed to be verified for 4
+ 
+
+ align:start position:0%
+graphs that needed to be verified for 4
+colorability they had an argument that
+
+ align:start position:0%
+colorability they had an argument that
+ 
+
+ align:start position:0%
+colorability they had an argument that
+showed that that there could only be a
+
+ align:start position:0%
+showed that that there could only be a
+ 
+
+ align:start position:0%
+showed that that there could only be a
+few thousand counter examples if there
+
+ align:start position:0%
+few thousand counter examples if there
+ 
+
+ align:start position:0%
+few thousand counter examples if there
+was or rather if there was any graph
+
+ align:start position:0%
+was or rather if there was any graph
+ 
+
+ align:start position:0%
+was or rather if there was any graph
+that couldn't be for colored it would be
+
+ align:start position:0%
+that couldn't be for colored it would be
+ 
+
+ align:start position:0%
+that couldn't be for colored it would be
+one of these several thousand graphs and
+
+ align:start position:0%
+one of these several thousand graphs and
+ 
+
+ align:start position:0%
+one of these several thousand graphs and
+then they went to work on coloring these
+
+ align:start position:0%
+then they went to work on coloring these
+ 
+
+ align:start position:0%
+then they went to work on coloring these
+several thousand graphs which were
+
+ align:start position:0%
+several thousand graphs which were
+ 
+
+ align:start position:0%
+several thousand graphs which were
+generated with the age eight of a
+
+ align:start position:0%
+generated with the age eight of a
+ 
+
+ align:start position:0%
+generated with the age eight of a
+computer and then colored with the aid
+
+ align:start position:0%
+computer and then colored with the aid
+ 
+
+ align:start position:0%
+computer and then colored with the aid
+of a computer and also by hand
+
+ align:start position:0%
+of a computer and also by hand
+ 
+
+ align:start position:0%
+of a computer and also by hand
+this did not make the mathematical
+
+ align:start position:0%
+this did not make the mathematical
+ 
+
+ align:start position:0%
+this did not make the mathematical
+community happy because a proof like
+
+ align:start position:0%
+community happy because a proof like
+ 
+
+ align:start position:0%
+community happy because a proof like
+that is essentially uncheck Abel a much
+
+ align:start position:0%
+that is essentially uncheck Abel a much
+ 
+
+ align:start position:0%
+that is essentially uncheck Abel a much
+improved version was developed in the
+
+ align:start position:0%
+improved version was developed in the
+ 
+
+ align:start position:0%
+improved version was developed in the
+1990s but it still requires in the end a
+
+ align:start position:0%
+1990s but it still requires in the end a
+ 
+
+ align:start position:0%
+1990s but it still requires in the end a
+computer program to generate about 600
+
+ align:start position:0%
+computer program to generate about 600
+ 
+
+ align:start position:0%
+computer program to generate about 600
+maps and verify their caller ability so
+
+ align:start position:0%
+maps and verify their caller ability so
+ 
+
+ align:start position:0%
+maps and verify their caller ability so
+it remains to find a proof of the
+
+ align:start position:0%
+it remains to find a proof of the
+ 
+
+ align:start position:0%
+it remains to find a proof of the
+four-color theorem that you could say is
+
+ align:start position:0%
+four-color theorem that you could say is
+ 
+
+ align:start position:0%
+four-color theorem that you could say is
+humanly comprehensible without the aid
+
+ align:start position:0%
+humanly comprehensible without the aid
+ 
+
+ align:start position:0%
+humanly comprehensible without the aid
+of a computer but there's no longer any
+
+ align:start position:0%
+of a computer but there's no longer any
+ 
+
+ align:start position:0%
+of a computer but there's no longer any
+doubt really about this theorem in the
+
+ align:start position:0%
+doubt really about this theorem in the
+ 
+
+ align:start position:0%
+doubt really about this theorem in the
+mathematical community in general if I
+
+ align:start position:0%
+mathematical community in general if I
+ 
+
+ align:start position:0%
+mathematical community in general if I
+take an arbitrary graph and I ask what's
+
+ align:start position:0%
+take an arbitrary graph and I ask what's
+ 
+
+ align:start position:0%
+take an arbitrary graph and I ask what's
+the minimum number of colors to color it
+
+ align:start position:0%
+the minimum number of colors to color it
+ 
+
+ align:start position:0%
+the minimum number of colors to color it
+that's called the chromatic number of
+
+ align:start position:0%
+that's called the chromatic number of
+ 
+
+ align:start position:0%
+that's called the chromatic number of
+the graph so Chi of G is the minimum
+
+ align:start position:0%
+the graph so Chi of G is the minimum
+ 
+
+ align:start position:0%
+the graph so Chi of G is the minimum
+number of colors to color G and let's
+
+ align:start position:0%
+number of colors to color G and let's
+ 
+
+ align:start position:0%
+number of colors to color G and let's
+look at some guys for different kinds of
+
+ align:start position:0%
+look at some guys for different kinds of
+ 
+
+ align:start position:0%
+look at some guys for different kinds of
+graphs so here we have a simple cycle of
+
+ align:start position:0%
+graphs so here we have a simple cycle of
+ 
+
+ align:start position:0%
+graphs so here we have a simple cycle of
+length four and it's obvious that that
+
+ align:start position:0%
+length four and it's obvious that that
+ 
+
+ align:start position:0%
+length four and it's obvious that that
+can be colored with two colors just
+
+ align:start position:0%
+can be colored with two colors just
+ 
+
+ align:start position:0%
+can be colored with two colors just
+alternate the colors on the other hand
+
+ align:start position:0%
+alternate the colors on the other hand
+ 
+
+ align:start position:0%
+alternate the colors on the other hand
+so what and if that generalizes I by the
+
+ align:start position:0%
+so what and if that generalizes I by the
+ 
+
+ align:start position:0%
+so what and if that generalizes I by the
+way to any even length cycle the the
+
+ align:start position:0%
+way to any even length cycle the the
+ 
+
+ align:start position:0%
+way to any even length cycle the the
+chromatic number of an even length cycle
+
+ align:start position:0%
+chromatic number of an even length cycle
+ 
+
+ align:start position:0%
+chromatic number of an even length cycle
+is simply two you will color the
+
+ align:start position:0%
+is simply two you will color the
+ 
+
+ align:start position:0%
+is simply two you will color the
+vertices alternately on the other hand
+
+ align:start position:0%
+vertices alternately on the other hand
+ 
+
+ align:start position:0%
+vertices alternately on the other hand
+if the cycle is of odd lengths you're
+
+ align:start position:0%
+if the cycle is of odd lengths you're
+ 
+
+ align:start position:0%
+if the cycle is of odd lengths you're
+gonna need a third color there's no way
+
+ align:start position:0%
+gonna need a third color there's no way
+ 
+
+ align:start position:0%
+gonna need a third color there's no way
+around it because even if you try to get
+
+ align:start position:0%
+around it because even if you try to get
+ 
+
+ align:start position:0%
+around it because even if you try to get
+by with two colors then your color
+
+ align:start position:0%
+by with two colors then your color
+ 
+
+ align:start position:0%
+by with two colors then your color
+things alternately and then when you
+
+ align:start position:0%
+things alternately and then when you
+ 
+
+ align:start position:0%
+things alternately and then when you
+wrap around you discover that um you
+
+ align:start position:0%
+wrap around you discover that um you
+ 
+
+ align:start position:0%
+wrap around you discover that um you
+can't alternately color you're going to
+
+ align:start position:0%
+can't alternately color you're going to
+ 
+
+ align:start position:0%
+can't alternately color you're going to
+need a third color in order to avoid a
+
+ align:start position:0%
+need a third color in order to avoid a
+ 
+
+ align:start position:0%
+need a third color in order to avoid a
+clash so in general the chromatic number
+
+ align:start position:0%
+clash so in general the chromatic number
+ 
+
+ align:start position:0%
+clash so in general the chromatic number
+of an odd length cycle is three the
+
+ align:start position:0%
+of an odd length cycle is three the
+ 
+
+ align:start position:0%
+of an odd length cycle is three the
+complete graph on five vertices is shown
+
+ align:start position:0%
+complete graph on five vertices is shown
+ 
+
+ align:start position:0%
+complete graph on five vertices is shown
+here this is a five vertex graph in
+
+ align:start position:0%
+here this is a five vertex graph in
+ 
+
+ align:start position:0%
+here this is a five vertex graph in
+which every vertex is adjacent to the
+
+ align:start position:0%
+which every vertex is adjacent to the
+ 
+
+ align:start position:0%
+which every vertex is adjacent to the
+other four and since every vertex is
+
+ align:start position:0%
+other four and since every vertex is
+ 
+
+ align:start position:0%
+other four and since every vertex is
+adjacent to the other four you're going
+
+ align:start position:0%
+adjacent to the other four you're going
+ 
+
+ align:start position:0%
+adjacent to the other four you're going
+to need five colors you can't do any
+
+ align:start position:0%
+to need five colors you can't do any
+ 
+
+ align:start position:0%
+to need five colors you can't do any
+better they have to all have different
+
+ align:start position:0%
+better they have to all have different
+ 
+
+ align:start position:0%
+better they have to all have different
+colors and so the chromatic number of
+
+ align:start position:0%
+colors and so the chromatic number of
+ 
+
+ align:start position:0%
+colors and so the chromatic number of
+the complete graph on n vertices where
+
+ align:start position:0%
+the complete graph on n vertices where
+ 
+
+ align:start position:0%
+the complete graph on n vertices where
+every vertex is adjacent to the other n
+
+ align:start position:0%
+every vertex is adjacent to the other n
+ 
+
+ align:start position:0%
+every vertex is adjacent to the other n
+minus one is n another simple example
+
+ align:start position:0%
+minus one is n another simple example
+ 
+
+ align:start position:0%
+minus one is n another simple example
+that comes up is if I take the cycle and
+
+ align:start position:0%
+that comes up is if I take the cycle and
+ 
+
+ align:start position:0%
+that comes up is if I take the cycle and
+I put a an axe
+
+ align:start position:0%
+I put a an axe
+ 
+
+ align:start position:0%
+I put a an axe
+and Axel in the middle call it a wheel
+
+ align:start position:0%
+and Axel in the middle call it a wheel
+ 
+
+ align:start position:0%
+and Axel in the middle call it a wheel
+then a wheel with a a ring of light a
+
+ align:start position:0%
+then a wheel with a a ring of light a
+ 
+
+ align:start position:0%
+then a wheel with a a ring of light a
+cycle of length five around the outside
+
+ align:start position:0%
+cycle of length five around the outside
+ 
+
+ align:start position:0%
+cycle of length five around the outside
+a perimeter of length five is called W
+
+ align:start position:0%
+a perimeter of length five is called W
+ 
+
+ align:start position:0%
+a perimeter of length five is called W
+five and we can color it with four
+
+ align:start position:0%
+five and we can color it with four
+ 
+
+ align:start position:0%
+five and we can color it with four
+colors and in general the argument for
+
+ align:start position:0%
+colors and in general the argument for
+ 
+
+ align:start position:0%
+colors and in general the argument for
+that the chromatic number for an odd
+
+ align:start position:0%
+that the chromatic number for an odd
+ 
+
+ align:start position:0%
+that the chromatic number for an odd
+length wheel is four is that I know I'm
+
+ align:start position:0%
+length wheel is four is that I know I'm
+ 
+
+ align:start position:0%
+length wheel is four is that I know I'm
+going to need three colors to color the
+
+ align:start position:0%
+going to need three colors to color the
+ 
+
+ align:start position:0%
+going to need three colors to color the
+rim and since the axle is adjacent to
+
+ align:start position:0%
+rim and since the axle is adjacent to
+ 
+
+ align:start position:0%
+rim and since the axle is adjacent to
+everything on the rim I'm going to need
+
+ align:start position:0%
+everything on the rim I'm going to need
+ 
+
+ align:start position:0%
+everything on the rim I'm going to need
+a fourth color for it on the other hand
+
+ align:start position:0%
+a fourth color for it on the other hand
+ 
+
+ align:start position:0%
+a fourth color for it on the other hand
+again if the if the perimeter is even
+
+ align:start position:0%
+again if the if the perimeter is even
+ 
+
+ align:start position:0%
+again if the if the perimeter is even
+though I can get by with three colors
+
+ align:start position:0%
+though I can get by with three colors
+ 
+
+ align:start position:0%
+though I can get by with three colors
+one more remark about chromatic numbers
+
+ align:start position:0%
+one more remark about chromatic numbers
+ 
+
+ align:start position:0%
+one more remark about chromatic numbers
+is there's an easy argument that shows
+
+ align:start position:0%
+is there's an easy argument that shows
+ 
+
+ align:start position:0%
+is there's an easy argument that shows
+that if you have a graph every one of
+
+ align:start position:0%
+that if you have a graph every one of
+ 
+
+ align:start position:0%
+that if you have a graph every one of
+whose vertices is at most degree K there
+
+ align:start position:0%
+whose vertices is at most degree K there
+ 
+
+ align:start position:0%
+whose vertices is at most degree K there
+are at most K other vertices adjacent to
+
+ align:start position:0%
+are at most K other vertices adjacent to
+ 
+
+ align:start position:0%
+are at most K other vertices adjacent to
+any given vertex then that implies that
+
+ align:start position:0%
+any given vertex then that implies that
+ 
+
+ align:start position:0%
+any given vertex then that implies that
+the graph is K plus one colorable and
+
+ align:start position:0%
+the graph is K plus one colorable and
+ 
+
+ align:start position:0%
+the graph is K plus one colorable and
+the proof is really constructive and
+
+ align:start position:0%
+the proof is really constructive and
+ 
+
+ align:start position:0%
+the proof is really constructive and
+trivial basically you just start
+
+ align:start position:0%
+trivial basically you just start
+ 
+
+ align:start position:0%
+trivial basically you just start
+coloring the vertices any way you like a
+
+ align:start position:0%
+coloring the vertices any way you like a
+ 
+
+ align:start position:0%
+coloring the vertices any way you like a
+subject to the constraint that when you
+
+ align:start position:0%
+subject to the constraint that when you
+ 
+
+ align:start position:0%
+subject to the constraint that when you
+color a vertex it's supposed to not be
+
+ align:start position:0%
+color a vertex it's supposed to not be
+ 
+
+ align:start position:0%
+color a vertex it's supposed to not be
+the same color as any of the vertices
+
+ align:start position:0%
+the same color as any of the vertices
+ 
+
+ align:start position:0%
+the same color as any of the vertices
+around it but that's easy to do because
+
+ align:start position:0%
+around it but that's easy to do because
+ 
+
+ align:start position:0%
+around it but that's easy to do because
+when it's time to color some vertex even
+
+ align:start position:0%
+when it's time to color some vertex even
+ 
+
+ align:start position:0%
+when it's time to color some vertex even
+if all the vertices around it are
+
+ align:start position:0%
+if all the vertices around it are
+ 
+
+ align:start position:0%
+if all the vertices around it are
+coloured there's only K of them and so I
+
+ align:start position:0%
+coloured there's only K of them and so I
+ 
+
+ align:start position:0%
+coloured there's only K of them and so I
+will always be able to find a k plus
+
+ align:start position:0%
+will always be able to find a k plus
+ 
+
+ align:start position:0%
+will always be able to find a k plus
+first color to assign it without and get
+
+ align:start position:0%
+first color to assign it without and get
+ 
+
+ align:start position:0%
+first color to assign it without and get
+a satisfactory coloring so I can get by
+
+ align:start position:0%
+a satisfactory coloring so I can get by
+ 
+
+ align:start position:0%
+a satisfactory coloring so I can get by
+with K plus 1 colors now the general
+
+ align:start position:0%
+with K plus 1 colors now the general
+ 
+
+ align:start position:0%
+with K plus 1 colors now the general
+setup with color ability is that to
+
+ align:start position:0%
+setup with color ability is that to
+ 
+
+ align:start position:0%
+setup with color ability is that to
+check whether a graph is 2 colorable is
+
+ align:start position:0%
+check whether a graph is 2 colorable is
+ 
+
+ align:start position:0%
+check whether a graph is 2 colorable is
+actually very easy and we may talk about
+
+ align:start position:0%
+actually very easy and we may talk about
+ 
+
+ align:start position:0%
+actually very easy and we may talk about
+that in some class problems but 3
+
+ align:start position:0%
+that in some class problems but 3
+ 
+
+ align:start position:0%
+that in some class problems but 3
+colorability dramatically changes we're
+
+ align:start position:0%
+colorability dramatically changes we're
+ 
+
+ align:start position:0%
+colorability dramatically changes we're
+back in the realm of np-complete
+
+ align:start position:0%
+back in the realm of np-complete
+ 
+
+ align:start position:0%
+back in the realm of np-complete
+problems in fact a result of a student
+
+ align:start position:0%
+problems in fact a result of a student
+ 
+
+ align:start position:0%
+problems in fact a result of a student
+of mine almost 40 years ago was that
+
+ align:start position:0%
+of mine almost 40 years ago was that
+ 
+
+ align:start position:0%
+of mine almost 40 years ago was that
+even if a graph is planar where you know
+
+ align:start position:0%
+even if a graph is planar where you know
+ 
+
+ align:start position:0%
+even if a graph is planar where you know
+it can definitely be colored with four
+
+ align:start position:0%
+it can definitely be colored with four
+ 
+
+ align:start position:0%
+it can definitely be colored with four
+colors determining whether or not it can
+
+ align:start position:0%
+colors determining whether or not it can
+ 
+
+ align:start position:0%
+colors determining whether or not it can
+be colored with three colors is as hard
+
+ align:start position:0%
+be colored with three colors is as hard
+ 
+
+ align:start position:0%
+be colored with three colors is as hard
+as satisfiability
+
+ align:start position:0%
+as satisfiability
+ 
+
+ align:start position:0%
+as satisfiability
+and it is in fact an np-complete problem
+
+ align:start position:0%
+and it is in fact an np-complete problem
+ 
+
+ align:start position:0%
+and it is in fact an np-complete problem
+in fact the proof of how you reduce
+
+ align:start position:0%
+in fact the proof of how you reduce
+ 
+
+ align:start position:0%
+in fact the proof of how you reduce
+satisfiability the color ability appears
+
+ align:start position:0%
+satisfiability the color ability appears
+ 
+
+ align:start position:0%
+satisfiability the color ability appears
+in a problem in the text which we may
+
+ align:start position:0%
+in a problem in the text which we may
+ 
+
+ align:start position:0%
+in a problem in the text which we may
+assign as a problem set problem
+
+ align:start position:0%
+assign as a problem set problem
+ 
+
+ align:start position:0%
+assign as a problem set problem
+so in general finding Chi of G is hard
+
+ align:start position:0%
+so in general finding Chi of G is hard
+ 
+
+ align:start position:0%
+so in general finding Chi of G is hard
+even for three colors now it's not any
+
+ align:start position:0%
+even for three colors now it's not any
+ 
+
+ align:start position:0%
+even for three colors now it's not any
+worse again from a theoretical point of
+
+ align:start position:0%
+worse again from a theoretical point of
+ 
+
+ align:start position:0%
+worse again from a theoretical point of
+view for for checking what Khayyam G is
+
+ align:start position:0%
+view for for checking what Khayyam G is
+ 
+
+ align:start position:0%
+view for for checking what Khayyam G is
+even if it's a very large number or the
+
+ align:start position:0%
+even if it's a very large number or the
+ 
+
+ align:start position:0%
+even if it's a very large number or the
+pragmatically three color will be easier
+
+ align:start position:0%
+pragmatically three color will be easier
+ 
+
+ align:start position:0%
+pragmatically three color will be easier
+to check than end color ability and that
+
+ align:start position:0%
+to check than end color ability and that
+ 
+
+ align:start position:0%
+to check than end color ability and that
+is our story about color ability
\ No newline at end of file
diff --git a/PsUPRyatjxw.txt b/PsUPRyatjxw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..643471067a3214ad8295a01bf1ff92e5a013e205
--- /dev/null
+++ b/PsUPRyatjxw.txt
@@ -0,0 +1,7803 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+hi today I'd like to discuss a specific
+
+ align:start position:0%
+hi today I'd like to discuss a specific
+ 
+
+ align:start position:0%
+hi today I'd like to discuss a specific
+kind of an electronic feedback system
+
+ align:start position:0%
+kind of an electronic feedback system
+ 
+
+ align:start position:0%
+kind of an electronic feedback system
+called a phase locked Loop the general
+
+ align:start position:0%
+called a phase locked Loop the general
+ 
+
+ align:start position:0%
+called a phase locked Loop the general
+topology for a phase locked Loop is
+
+ align:start position:0%
+topology for a phase locked Loop is
+ 
+
+ align:start position:0%
+topology for a phase locked Loop is
+shown on the board the input to this
+
+ align:start position:0%
+shown on the board the input to this
+ 
+
+ align:start position:0%
+shown on the board the input to this
+type of a system is a command frequency
+
+ align:start position:0%
+type of a system is a command frequency
+ 
+
+ align:start position:0%
+type of a system is a command frequency
+and the information that we're
+
+ align:start position:0%
+and the information that we're
+ 
+
+ align:start position:0%
+and the information that we're
+interested in in that input signal is
+
+ align:start position:0%
+interested in in that input signal is
+ 
+
+ align:start position:0%
+interested in in that input signal is
+specifically its
+
+ align:start position:0%
+specifically its
+ 
+
+ align:start position:0%
+specifically its
+frequency in certain kinds of phase lock
+
+ align:start position:0%
+frequency in certain kinds of phase lock
+ 
+
+ align:start position:0%
+frequency in certain kinds of phase lock
+Loops we have a sidal input and others
+
+ align:start position:0%
+Loops we have a sidal input and others
+ 
+
+ align:start position:0%
+Loops we have a sidal input and others
+we may have a digital logic kind of
+
+ align:start position:0%
+we may have a digital logic kind of
+ 
+
+ align:start position:0%
+we may have a digital logic kind of
+signal but Say in any of these the
+
+ align:start position:0%
+signal but Say in any of these the
+ 
+
+ align:start position:0%
+signal but Say in any of these the
+common feature is that the information
+
+ align:start position:0%
+common feature is that the information
+ 
+
+ align:start position:0%
+common feature is that the information
+of interest is the frequency of the
+
+ align:start position:0%
+of interest is the frequency of the
+ 
+
+ align:start position:0%
+of interest is the frequency of the
+signal that input signal or command
+
+ align:start position:0%
+signal that input signal or command
+ 
+
+ align:start position:0%
+signal that input signal or command
+signal is applied to a phase
+
+ align:start position:0%
+signal is applied to a phase
+ 
+
+ align:start position:0%
+signal is applied to a phase
+detector and the output of the phase
+
+ align:start position:0%
+detector and the output of the phase
+ 
+
+ align:start position:0%
+detector and the output of the phase
+detector goes to an element indicated as
+
+ align:start position:0%
+detector goes to an element indicated as
+ 
+
+ align:start position:0%
+detector goes to an element indicated as
+a Loop filter the loop filter is sort of
+
+ align:start position:0%
+a Loop filter the loop filter is sort of
+ 
+
+ align:start position:0%
+a Loop filter the loop filter is sort of
+jargon in phas lock loop technology for
+
+ align:start position:0%
+jargon in phas lock loop technology for
+ 
+
+ align:start position:0%
+jargon in phas lock loop technology for
+what we've been calling compensation all
+
+ align:start position:0%
+what we've been calling compensation all
+ 
+
+ align:start position:0%
+what we've been calling compensation all
+along for some reason it seems
+
+ align:start position:0%
+along for some reason it seems
+ 
+
+ align:start position:0%
+along for some reason it seems
+traditional in this technology to call
+
+ align:start position:0%
+traditional in this technology to call
+ 
+
+ align:start position:0%
+traditional in this technology to call
+the compensating element the one that
+
+ align:start position:0%
+the compensating element the one that
+ 
+
+ align:start position:0%
+the compensating element the one that
+provides Loop stability the loop filter
+
+ align:start position:0%
+provides Loop stability the loop filter
+ 
+
+ align:start position:0%
+provides Loop stability the loop filter
+the output signal from the loop filter
+
+ align:start position:0%
+the output signal from the loop filter
+ 
+
+ align:start position:0%
+the output signal from the loop filter
+is applied to a voltage controlled
+
+ align:start position:0%
+is applied to a voltage controlled
+ 
+
+ align:start position:0%
+is applied to a voltage controlled
+oscillator and of course the frequency
+
+ align:start position:0%
+oscillator and of course the frequency
+ 
+
+ align:start position:0%
+oscillator and of course the frequency
+out of this voltage controlled
+
+ align:start position:0%
+out of this voltage controlled
+ 
+
+ align:start position:0%
+out of this voltage controlled
+oscillator depends on the signal applied
+
+ align:start position:0%
+oscillator depends on the signal applied
+ 
+
+ align:start position:0%
+oscillator depends on the signal applied
+at its input that that frequency is the
+
+ align:start position:0%
+at its input that that frequency is the
+ 
+
+ align:start position:0%
+at its input that that frequency is the
+response of the system and again the
+
+ align:start position:0%
+response of the system and again the
+ 
+
+ align:start position:0%
+response of the system and again the
+thing we're interested in of course is
+
+ align:start position:0%
+thing we're interested in of course is
+ 
+
+ align:start position:0%
+thing we're interested in of course is
+the frequency of the output
+
+ align:start position:0%
+the frequency of the output
+ 
+
+ align:start position:0%
+the frequency of the output
+signal the output signal is then fed
+
+ align:start position:0%
+signal the output signal is then fed
+ 
+
+ align:start position:0%
+signal the output signal is then fed
+back to form the second input to the
+
+ align:start position:0%
+back to form the second input to the
+ 
+
+ align:start position:0%
+back to form the second input to the
+phase detector the signal out of the
+
+ align:start position:0%
+phase detector the signal out of the
+ 
+
+ align:start position:0%
+phase detector the signal out of the
+phase detector in a way that we'll see
+
+ align:start position:0%
+phase detector in a way that we'll see
+ 
+
+ align:start position:0%
+phase detector in a way that we'll see
+in a in a bit is proportional in some
+
+ align:start position:0%
+in a in a bit is proportional in some
+ 
+
+ align:start position:0%
+in a in a bit is proportional in some
+sense to the difference in Phase between
+
+ align:start position:0%
+sense to the difference in Phase between
+ 
+
+ align:start position:0%
+sense to the difference in Phase between
+its two
+
+ align:start position:0%
+its two
+ 
+
+ align:start position:0%
+its two
+inputs there are numerous applications
+
+ align:start position:0%
+inputs there are numerous applications
+ 
+
+ align:start position:0%
+inputs there are numerous applications
+for this sort of of circuit uh for
+
+ align:start position:0%
+for this sort of of circuit uh for
+ 
+
+ align:start position:0%
+for this sort of of circuit uh for
+example one way to use a phase lock loop
+
+ align:start position:0%
+example one way to use a phase lock loop
+ 
+
+ align:start position:0%
+example one way to use a phase lock loop
+is to is as a uh detector for frequency
+
+ align:start position:0%
+is to is as a uh detector for frequency
+ 
+
+ align:start position:0%
+is to is as a uh detector for frequency
+modulated
+
+ align:start position:0%
+modulated
+ 
+
+ align:start position:0%
+modulated
+signals the signal at this point the
+
+ align:start position:0%
+signals the signal at this point the
+ 
+
+ align:start position:0%
+signals the signal at this point the
+phase error between the command
+
+ align:start position:0%
+phase error between the command
+ 
+
+ align:start position:0%
+phase error between the command
+frequency and the response frequency is
+
+ align:start position:0%
+frequency and the response frequency is
+ 
+
+ align:start position:0%
+frequency and the response frequency is
+of course effectively the error signal
+
+ align:start position:0%
+of course effectively the error signal
+ 
+
+ align:start position:0%
+of course effectively the error signal
+in the loop and if we have a loop with
+
+ align:start position:0%
+in the loop and if we have a loop with
+ 
+
+ align:start position:0%
+in the loop and if we have a loop with
+highd sensitivity with large loop
+
+ align:start position:0%
+highd sensitivity with large loop
+ 
+
+ align:start position:0%
+highd sensitivity with large loop
+transmission magnitude the response
+
+ align:start position:0%
+transmission magnitude the response
+ 
+
+ align:start position:0%
+transmission magnitude the response
+frequency should be very nearly
+
+ align:start position:0%
+frequency should be very nearly
+ 
+
+ align:start position:0%
+frequency should be very nearly
+identical to the command frequency in
+
+ align:start position:0%
+identical to the command frequency in
+ 
+
+ align:start position:0%
+identical to the command frequency in
+fact the phase difference between those
+
+ align:start position:0%
+fact the phase difference between those
+ 
+
+ align:start position:0%
+fact the phase difference between those
+two signals should be very very small
+
+ align:start position:0%
+two signals should be very very small
+ 
+
+ align:start position:0%
+two signals should be very very small
+hence the name phase lock blop if in
+
+ align:start position:0%
+hence the name phase lock blop if in
+ 
+
+ align:start position:0%
+hence the name phase lock blop if in
+addition to that we have a voltage
+
+ align:start position:0%
+addition to that we have a voltage
+ 
+
+ align:start position:0%
+addition to that we have a voltage
+controlled oscillator that's linear that
+
+ align:start position:0%
+controlled oscillator that's linear that
+ 
+
+ align:start position:0%
+controlled oscillator that's linear that
+is whose output frequency is directly
+
+ align:start position:0%
+is whose output frequency is directly
+ 
+
+ align:start position:0%
+is whose output frequency is directly
+proportional to its input voltage we're
+
+ align:start position:0%
+proportional to its input voltage we're
+ 
+
+ align:start position:0%
+proportional to its input voltage we're
+able to use the voltage at this point as
+
+ align:start position:0%
+able to use the voltage at this point as
+ 
+
+ align:start position:0%
+able to use the voltage at this point as
+a measure of the frequency of operation
+
+ align:start position:0%
+a measure of the frequency of operation
+ 
+
+ align:start position:0%
+a measure of the frequency of operation
+of the voltage controlled oscillator and
+
+ align:start position:0%
+of the voltage controlled oscillator and
+ 
+
+ align:start position:0%
+of the voltage controlled oscillator and
+when the loop is locked as a measure of
+
+ align:start position:0%
+when the loop is locked as a measure of
+ 
+
+ align:start position:0%
+when the loop is locked as a measure of
+the input frequency or the command
+
+ align:start position:0%
+the input frequency or the command
+ 
+
+ align:start position:0%
+the input frequency or the command
+frequency and so in that way we're able
+
+ align:start position:0%
+frequency and so in that way we're able
+ 
+
+ align:start position:0%
+frequency and so in that way we're able
+to use a phase locked loop as an FM Dem
+
+ align:start position:0%
+to use a phase locked loop as an FM Dem
+ 
+
+ align:start position:0%
+to use a phase locked loop as an FM Dem
+modulator the signal at this point will
+
+ align:start position:0%
+modulator the signal at this point will
+ 
+
+ align:start position:0%
+modulator the signal at this point will
+be proportional to the frequency applied
+
+ align:start position:0%
+be proportional to the frequency applied
+ 
+
+ align:start position:0%
+be proportional to the frequency applied
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+input in other applications we use phase
+
+ align:start position:0%
+input in other applications we use phase
+ 
+
+ align:start position:0%
+input in other applications we use phase
+locked Loops to recover carriers in
+
+ align:start position:0%
+locked Loops to recover carriers in
+ 
+
+ align:start position:0%
+locked Loops to recover carriers in
+again communication systems where we're
+
+ align:start position:0%
+again communication systems where we're
+ 
+
+ align:start position:0%
+again communication systems where we're
+interested for example in generating a
+
+ align:start position:0%
+interested for example in generating a
+ 
+
+ align:start position:0%
+interested for example in generating a
+carrier or a center frequency locally
+
+ align:start position:0%
+carrier or a center frequency locally
+ 
+
+ align:start position:0%
+carrier or a center frequency locally
+for use in some sort of Dem modulation
+
+ align:start position:0%
+for use in some sort of Dem modulation
+ 
+
+ align:start position:0%
+for use in some sort of Dem modulation
+scheme typically in those sorts of
+
+ align:start position:0%
+scheme typically in those sorts of
+ 
+
+ align:start position:0%
+scheme typically in those sorts of
+applications because the input signal
+
+ align:start position:0%
+applications because the input signal
+ 
+
+ align:start position:0%
+applications because the input signal
+may be quite noisy we get filtering out
+
+ align:start position:0%
+may be quite noisy we get filtering out
+ 
+
+ align:start position:0%
+may be quite noisy we get filtering out
+of the phase locked Loop by really
+
+ align:start position:0%
+of the phase locked Loop by really
+ 
+
+ align:start position:0%
+of the phase locked Loop by really
+making it a narrow band filter by
+
+ align:start position:0%
+making it a narrow band filter by
+ 
+
+ align:start position:0%
+making it a narrow band filter by
+effectively greatly reducing the
+
+ align:start position:0%
+effectively greatly reducing the
+ 
+
+ align:start position:0%
+effectively greatly reducing the
+crossover frequency of the feedback
+
+ align:start position:0%
+crossover frequency of the feedback
+ 
+
+ align:start position:0%
+crossover frequency of the feedback
+system that mechanized the phase locked
+
+ align:start position:0%
+system that mechanized the phase locked
+ 
+
+ align:start position:0%
+system that mechanized the phase locked
+Loop that crossover frequency becomes
+
+ align:start position:0%
+Loop that crossover frequency becomes
+ 
+
+ align:start position:0%
+Loop that crossover frequency becomes
+approximately the filter bandwidth and
+
+ align:start position:0%
+approximately the filter bandwidth and
+ 
+
+ align:start position:0%
+approximately the filter bandwidth and
+we're able to then recover a fairly
+
+ align:start position:0%
+we're able to then recover a fairly
+ 
+
+ align:start position:0%
+we're able to then recover a fairly
+noisy carrier signal and somehow use
+
+ align:start position:0%
+noisy carrier signal and somehow use
+ 
+
+ align:start position:0%
+noisy carrier signal and somehow use
+that in a further demodulating process
+
+ align:start position:0%
+that in a further demodulating process
+ 
+
+ align:start position:0%
+that in a further demodulating process
+in a communication
+
+ align:start position:0%
+in a communication
+ 
+
+ align:start position:0%
+in a communication
+system another application of phase lock
+
+ align:start position:0%
+system another application of phase lock
+ 
+
+ align:start position:0%
+system another application of phase lock
+Loops is in frequency
+
+ align:start position:0%
+Loops is in frequency
+ 
+
+ align:start position:0%
+Loops is in frequency
+synthesizers suppose we have the basic
+
+ align:start position:0%
+synthesizers suppose we have the basic
+ 
+
+ align:start position:0%
+synthesizers suppose we have the basic
+phase lock loop as shown but in in
+
+ align:start position:0%
+phase lock loop as shown but in in
+ 
+
+ align:start position:0%
+phase lock loop as shown but in in
+addition we put in a counter in the
+
+ align:start position:0%
+addition we put in a counter in the
+ 
+
+ align:start position:0%
+addition we put in a counter in the
+feedback path uh a divide byn sort of a
+
+ align:start position:0%
+feedback path uh a divide byn sort of a
+ 
+
+ align:start position:0%
+feedback path uh a divide byn sort of a
+circuit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so in the feedback path and now
+
+ align:start position:0%
+like so in the feedback path and now
+ 
+
+ align:start position:0%
+like so in the feedback path and now
+let's see what the relationships are
+
+ align:start position:0%
+let's see what the relationships are
+ 
+
+ align:start position:0%
+let's see what the relationships are
+well the to the extent that the loop
+
+ align:start position:0%
+well the to the extent that the loop
+ 
+
+ align:start position:0%
+well the to the extent that the loop
+captures we argue that the signal at
+
+ align:start position:0%
+captures we argue that the signal at
+ 
+
+ align:start position:0%
+captures we argue that the signal at
+this point must be equal to the command
+
+ align:start position:0%
+this point must be equal to the command
+ 
+
+ align:start position:0%
+this point must be equal to the command
+frequency and consequently the response
+
+ align:start position:0%
+frequency and consequently the response
+ 
+
+ align:start position:0%
+frequency and consequently the response
+uh of the system will have to be
+
+ align:start position:0%
+uh of the system will have to be
+ 
+
+ align:start position:0%
+uh of the system will have to be
+equal I'm sorry I have have this in
+
+ align:start position:0%
+equal I'm sorry I have have this in
+ 
+
+ align:start position:0%
+equal I'm sorry I have have this in
+correct the command frequency will will
+
+ align:start position:0%
+correct the command frequency will will
+ 
+
+ align:start position:0%
+correct the command frequency will will
+be equal to the response frequency
+
+ align:start position:0%
+be equal to the response frequency
+ 
+
+ align:start position:0%
+be equal to the response frequency
+divided by n consequently the frequency
+
+ align:start position:0%
+divided by n consequently the frequency
+ 
+
+ align:start position:0%
+divided by n consequently the frequency
+of respon supplied by the system the
+
+ align:start position:0%
+of respon supplied by the system the
+ 
+
+ align:start position:0%
+of respon supplied by the system the
+output frequency of the system will
+
+ align:start position:0%
+output frequency of the system will
+ 
+
+ align:start position:0%
+output frequency of the system will
+simply be equal to n times the command
+
+ align:start position:0%
+simply be equal to n times the command
+ 
+
+ align:start position:0%
+simply be equal to n times the command
+frequency when we use this technique for
+
+ align:start position:0%
+frequency when we use this technique for
+ 
+
+ align:start position:0%
+frequency when we use this technique for
+frequency synthesis we make the command
+
+ align:start position:0%
+frequency synthesis we make the command
+ 
+
+ align:start position:0%
+frequency synthesis we make the command
+frequency a very precisely known
+
+ align:start position:0%
+frequency a very precisely known
+ 
+
+ align:start position:0%
+frequency a very precisely known
+frequency this is derived from a very
+
+ align:start position:0%
+frequency this is derived from a very
+ 
+
+ align:start position:0%
+frequency this is derived from a very
+high stability oscillator an atomicon
+
+ align:start position:0%
+high stability oscillator an atomicon
+ 
+
+ align:start position:0%
+high stability oscillator an atomicon
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+we're then able to by changing the
+
+ align:start position:0%
+we're then able to by changing the
+ 
+
+ align:start position:0%
+we're then able to by changing the
+division ratio in a digital divider and
+
+ align:start position:0%
+division ratio in a digital divider and
+ 
+
+ align:start position:0%
+division ratio in a digital divider and
+is of course an in an integral number we
+
+ align:start position:0%
+is of course an in an integral number we
+ 
+
+ align:start position:0%
+is of course an in an integral number we
+can build a divide byn sort of digital
+
+ align:start position:0%
+can build a divide byn sort of digital
+ 
+
+ align:start position:0%
+can build a divide byn sort of digital
+circuit uh we are then able to in
+
+ align:start position:0%
+circuit uh we are then able to in
+ 
+
+ align:start position:0%
+circuit uh we are then able to in
+discrete steps get a response frequency
+
+ align:start position:0%
+discrete steps get a response frequency
+ 
+
+ align:start position:0%
+discrete steps get a response frequency
+that's a direct multiple of the command
+
+ align:start position:0%
+that's a direct multiple of the command
+ 
+
+ align:start position:0%
+that's a direct multiple of the command
+frequency consequently we can generate
+
+ align:start position:0%
+frequency consequently we can generate
+ 
+
+ align:start position:0%
+frequency consequently we can generate
+uh with uh a resolution dependent on
+
+ align:start position:0%
+uh with uh a resolution dependent on
+ 
+
+ align:start position:0%
+uh with uh a resolution dependent on
+actually the frequency of the command
+
+ align:start position:0%
+actually the frequency of the command
+ 
+
+ align:start position:0%
+actually the frequency of the command
+signal with that sort of resolution
+
+ align:start position:0%
+signal with that sort of resolution
+ 
+
+ align:start position:0%
+signal with that sort of resolution
+since we get inte multiples of that
+
+ align:start position:0%
+since we get inte multiples of that
+ 
+
+ align:start position:0%
+since we get inte multiples of that
+frequency at the output we're able to
+
+ align:start position:0%
+frequency at the output we're able to
+ 
+
+ align:start position:0%
+frequency at the output we're able to
+generate multiple frequencies Each of
+
+ align:start position:0%
+generate multiple frequencies Each of
+ 
+
+ align:start position:0%
+generate multiple frequencies Each of
+which has the same stability as the
+
+ align:start position:0%
+which has the same stability as the
+ 
+
+ align:start position:0%
+which has the same stability as the
+command frequency and so this technique
+
+ align:start position:0%
+command frequency and so this technique
+ 
+
+ align:start position:0%
+command frequency and so this technique
+is is used in frequency
+
+ align:start position:0%
+is is used in frequency
+ 
+
+ align:start position:0%
+is is used in frequency
+synthesizers in order to investigate the
+
+ align:start position:0%
+synthesizers in order to investigate the
+ 
+
+ align:start position:0%
+synthesizers in order to investigate the
+feedback aspects of a phase lock loop we
+
+ align:start position:0%
+feedback aspects of a phase lock loop we
+ 
+
+ align:start position:0%
+feedback aspects of a phase lock loop we
+have to look at a a model for that sort
+
+ align:start position:0%
+have to look at a a model for that sort
+ 
+
+ align:start position:0%
+have to look at a a model for that sort
+of a system and in particular we have to
+
+ align:start position:0%
+of a system and in particular we have to
+ 
+
+ align:start position:0%
+of a system and in particular we have to
+consider how we model the phase detector
+
+ align:start position:0%
+consider how we model the phase detector
+ 
+
+ align:start position:0%
+consider how we model the phase detector
+as we'll see there these systems are
+
+ align:start position:0%
+as we'll see there these systems are
+ 
+
+ align:start position:0%
+as we'll see there these systems are
+typically non linear uh in in quite
+
+ align:start position:0%
+typically non linear uh in in quite
+ 
+
+ align:start position:0%
+typically non linear uh in in quite
+important ways and in ways that that
+
+ align:start position:0%
+important ways and in ways that that
+ 
+
+ align:start position:0%
+important ways and in ways that that
+have very profound implications for the
+
+ align:start position:0%
+have very profound implications for the
+ 
+
+ align:start position:0%
+have very profound implications for the
+operation of a system but generally we
+
+ align:start position:0%
+operation of a system but generally we
+ 
+
+ align:start position:0%
+operation of a system but generally we
+can model them for some limited range of
+
+ align:start position:0%
+can model them for some limited range of
+ 
+
+ align:start position:0%
+can model them for some limited range of
+difference between the input frequency
+
+ align:start position:0%
+difference between the input frequency
+ 
+
+ align:start position:0%
+difference between the input frequency
+and the response frequency as a linear
+
+ align:start position:0%
+and the response frequency as a linear
+ 
+
+ align:start position:0%
+and the response frequency as a linear
+system and when we do that we end up
+
+ align:start position:0%
+system and when we do that we end up
+ 
+
+ align:start position:0%
+system and when we do that we end up
+with a linearized block diagram that's
+
+ align:start position:0%
+with a linearized block diagram that's
+ 
+
+ align:start position:0%
+with a linearized block diagram that's
+something like this we have our
+
+ align:start position:0%
+something like this we have our
+ 
+
+ align:start position:0%
+something like this we have our
+commanded frequency at the input again
+
+ align:start position:0%
+commanded frequency at the input again
+ 
+
+ align:start position:0%
+commanded frequency at the input again
+I'm using linear notation or or
+
+ align:start position:0%
+I'm using linear notation or or
+ 
+
+ align:start position:0%
+I'm using linear notation or or
+frequency domain not ation here the
+
+ align:start position:0%
+frequency domain not ation here the
+ 
+
+ align:start position:0%
+frequency domain not ation here the
+capital F sub lower case C as the input
+
+ align:start position:0%
+capital F sub lower case C as the input
+ 
+
+ align:start position:0%
+capital F sub lower case C as the input
+to our system and the system responds uh
+
+ align:start position:0%
+to our system and the system responds uh
+ 
+
+ align:start position:0%
+to our system and the system responds uh
+the L the linearized or the transform of
+
+ align:start position:0%
+the L the linearized or the transform of
+ 
+
+ align:start position:0%
+the L the linearized or the transform of
+the linearized output is capital F sub
+
+ align:start position:0%
+the linearized output is capital F sub
+ 
+
+ align:start position:0%
+the linearized output is capital F sub
+lowercase R and we subtract that those
+
+ align:start position:0%
+lowercase R and we subtract that those
+ 
+
+ align:start position:0%
+lowercase R and we subtract that those
+two quantities the resultant difference
+
+ align:start position:0%
+two quantities the resultant difference
+ 
+
+ align:start position:0%
+two quantities the resultant difference
+is the error in frequency between the
+
+ align:start position:0%
+is the error in frequency between the
+ 
+
+ align:start position:0%
+is the error in frequency between the
+command signal and the signal being
+
+ align:start position:0%
+command signal and the signal being
+ 
+
+ align:start position:0%
+command signal and the signal being
+provided by the phase locked Loop but
+
+ align:start position:0%
+provided by the phase locked Loop but
+ 
+
+ align:start position:0%
+provided by the phase locked Loop but
+this is a frequency
+
+ align:start position:0%
+this is a frequency
+ 
+
+ align:start position:0%
+this is a frequency
+quantity this is a number that tells us
+
+ align:start position:0%
+quantity this is a number that tells us
+ 
+
+ align:start position:0%
+quantity this is a number that tells us
+the number of cycles per second
+
+ align:start position:0%
+the number of cycles per second
+ 
+
+ align:start position:0%
+the number of cycles per second
+difference for example between this
+
+ align:start position:0%
+difference for example between this
+ 
+
+ align:start position:0%
+difference for example between this
+signal and the
+
+ align:start position:0%
+signal and the
+ 
+
+ align:start position:0%
+signal and the
+signal but our phase detector doesn't
+
+ align:start position:0%
+signal but our phase detector doesn't
+ 
+
+ align:start position:0%
+signal but our phase detector doesn't
+measure frequency it measures phase and
+
+ align:start position:0%
+measure frequency it measures phase and
+ 
+
+ align:start position:0%
+measure frequency it measures phase and
+of course phase is simply the integral
+
+ align:start position:0%
+of course phase is simply the integral
+ 
+
+ align:start position:0%
+of course phase is simply the integral
+of frequency if we have two signals that
+
+ align:start position:0%
+of frequency if we have two signals that
+ 
+
+ align:start position:0%
+of frequency if we have two signals that
+differ in frequency by some amount their
+
+ align:start position:0%
+differ in frequency by some amount their
+ 
+
+ align:start position:0%
+differ in frequency by some amount their
+relative phase changes linearly with
+
+ align:start position:0%
+relative phase changes linearly with
+ 
+
+ align:start position:0%
+relative phase changes linearly with
+time providing the two frequencies are
+
+ align:start position:0%
+time providing the two frequencies are
+ 
+
+ align:start position:0%
+time providing the two frequencies are
+different but each constant the pH angle
+
+ align:start position:0%
+different but each constant the pH angle
+ 
+
+ align:start position:0%
+different but each constant the pH angle
+between the two of them is a progressive
+
+ align:start position:0%
+between the two of them is a progressive
+ 
+
+ align:start position:0%
+between the two of them is a progressive
+function of time and in fact linearly
+
+ align:start position:0%
+function of time and in fact linearly
+ 
+
+ align:start position:0%
+function of time and in fact linearly
+proportional to time uh consequently
+
+ align:start position:0%
+proportional to time uh consequently
+ 
+
+ align:start position:0%
+proportional to time uh consequently
+when we're interested in the error in
+
+ align:start position:0%
+when we're interested in the error in
+ 
+
+ align:start position:0%
+when we're interested in the error in
+Phase rather than the error in frequency
+
+ align:start position:0%
+Phase rather than the error in frequency
+ 
+
+ align:start position:0%
+Phase rather than the error in frequency
+and the error in phase is what our phase
+
+ align:start position:0%
+and the error in phase is what our phase
+ 
+
+ align:start position:0%
+and the error in phase is what our phase
+detector really gives us there's a
+
+ align:start position:0%
+detector really gives us there's a
+ 
+
+ align:start position:0%
+detector really gives us there's a
+single integration between frequency and
+
+ align:start position:0%
+single integration between frequency and
+ 
+
+ align:start position:0%
+single integration between frequency and
+phase and we represent that as simply a
+
+ align:start position:0%
+phase and we represent that as simply a
+ 
+
+ align:start position:0%
+phase and we represent that as simply a
+1 /s in our block
+
+ align:start position:0%
+1 /s in our block
+ 
+
+ align:start position:0%
+1 /s in our block
+diagram there's then some gain Factor
+
+ align:start position:0%
+diagram there's then some gain Factor
+ 
+
+ align:start position:0%
+diagram there's then some gain Factor
+some scale factor associated with
+
+ align:start position:0%
+some scale factor associated with
+ 
+
+ align:start position:0%
+some scale factor associated with
+whatever way we we mechanize the phase
+
+ align:start position:0%
+whatever way we we mechanize the phase
+ 
+
+ align:start position:0%
+whatever way we we mechanize the phase
+detector and again we'll see examples of
+
+ align:start position:0%
+detector and again we'll see examples of
+ 
+
+ align:start position:0%
+detector and again we'll see examples of
+that in a moment so we get some gain
+
+ align:start position:0%
+that in a moment so we get some gain
+ 
+
+ align:start position:0%
+that in a moment so we get some gain
+scale factor associated with the phase
+
+ align:start position:0%
+scale factor associated with the phase
+ 
+
+ align:start position:0%
+scale factor associated with the phase
+detector itself we then go through our
+
+ align:start position:0%
+detector itself we then go through our
+ 
+
+ align:start position:0%
+detector itself we then go through our
+Loop filter AF ofs uh there's presumably
+
+ align:start position:0%
+Loop filter AF ofs uh there's presumably
+ 
+
+ align:start position:0%
+Loop filter AF ofs uh there's presumably
+some scale factor associated with the
+
+ align:start position:0%
+some scale factor associated with the
+ 
+
+ align:start position:0%
+some scale factor associated with the
+voltage controlled oscillator in other
+
+ align:start position:0%
+voltage controlled oscillator in other
+ 
+
+ align:start position:0%
+voltage controlled oscillator in other
+words some number of volts at the input
+
+ align:start position:0%
+words some number of volts at the input
+ 
+
+ align:start position:0%
+words some number of volts at the input
+of the of the voltage controlled
+
+ align:start position:0%
+of the of the voltage controlled
+ 
+
+ align:start position:0%
+of the of the voltage controlled
+oscillator gives us a given change in
+
+ align:start position:0%
+oscillator gives us a given change in
+ 
+
+ align:start position:0%
+oscillator gives us a given change in
+its output frequency we'll call that
+
+ align:start position:0%
+its output frequency we'll call that
+ 
+
+ align:start position:0%
+its output frequency we'll call that
+scale factor a subv and then finally we
+
+ align:start position:0%
+scale factor a subv and then finally we
+ 
+
+ align:start position:0%
+scale factor a subv and then finally we
+get the output frequency from the phase
+
+ align:start position:0%
+get the output frequency from the phase
+ 
+
+ align:start position:0%
+get the output frequency from the phase
+lock loop the interesting or the
+
+ align:start position:0%
+lock loop the interesting or the
+ 
+
+ align:start position:0%
+lock loop the interesting or the
+important thing here is that there's an
+
+ align:start position:0%
+important thing here is that there's an
+ 
+
+ align:start position:0%
+important thing here is that there's an
+intrinsic integration in this system
+
+ align:start position:0%
+intrinsic integration in this system
+ 
+
+ align:start position:0%
+intrinsic integration in this system
+that simply has to do with the
+
+ align:start position:0%
+that simply has to do with the
+ 
+
+ align:start position:0%
+that simply has to do with the
+conversion from frequency to phase we've
+
+ align:start position:0%
+conversion from frequency to phase we've
+ 
+
+ align:start position:0%
+conversion from frequency to phase we've
+seen that sort of a a thing before in
+
+ align:start position:0%
+seen that sort of a a thing before in
+ 
+
+ align:start position:0%
+seen that sort of a a thing before in
+other systems when we looked at
+
+ align:start position:0%
+other systems when we looked at
+ 
+
+ align:start position:0%
+other systems when we looked at
+mechanical systems that included a motor
+
+ align:start position:0%
+mechanical systems that included a motor
+ 
+
+ align:start position:0%
+mechanical systems that included a motor
+we remember that when we put a fixed
+
+ align:start position:0%
+we remember that when we put a fixed
+ 
+
+ align:start position:0%
+we remember that when we put a fixed
+voltage onto a motor we get a uh an
+
+ align:start position:0%
+voltage onto a motor we get a uh an
+ 
+
+ align:start position:0%
+voltage onto a motor we get a uh an
+output angle that's a progressive
+
+ align:start position:0%
+output angle that's a progressive
+ 
+
+ align:start position:0%
+output angle that's a progressive
+function of time if we have a fixed
+
+ align:start position:0%
+function of time if we have a fixed
+ 
+
+ align:start position:0%
+function of time if we have a fixed
+voltage in a motor we get a a ramp for
+
+ align:start position:0%
+voltage in a motor we get a a ramp for
+ 
+
+ align:start position:0%
+voltage in a motor we get a a ramp for
+the total output angle and so if we
+
+ align:start position:0%
+the total output angle and so if we
+ 
+
+ align:start position:0%
+the total output angle and so if we
+write the transfer function that relates
+
+ align:start position:0%
+write the transfer function that relates
+ 
+
+ align:start position:0%
+write the transfer function that relates
+input voltage to Output position or
+
+ align:start position:0%
+input voltage to Output position or
+ 
+
+ align:start position:0%
+input voltage to Output position or
+Theta we get a an integration in that
+
+ align:start position:0%
+Theta we get a an integration in that
+ 
+
+ align:start position:0%
+Theta we get a an integration in that
+transfer function here we have the same
+
+ align:start position:0%
+transfer function here we have the same
+ 
+
+ align:start position:0%
+transfer function here we have the same
+sort of a thing a physical process that
+
+ align:start position:0%
+sort of a thing a physical process that
+ 
+
+ align:start position:0%
+sort of a thing a physical process that
+gives us an
+
+ align:start position:0%
+gives us an
+ 
+
+ align:start position:0%
+gives us an
+integration there are several ways of
+
+ align:start position:0%
+integration there are several ways of
+ 
+
+ align:start position:0%
+integration there are several ways of
+modeling these incidentally you may have
+
+ align:start position:0%
+modeling these incidentally you may have
+ 
+
+ align:start position:0%
+modeling these incidentally you may have
+seen them done in a different way uh in
+
+ align:start position:0%
+seen them done in a different way uh in
+ 
+
+ align:start position:0%
+seen them done in a different way uh in
+some cases the block diagram itself is
+
+ align:start position:0%
+some cases the block diagram itself is
+ 
+
+ align:start position:0%
+some cases the block diagram itself is
+written in terms of phase rather than
+
+ align:start position:0%
+written in terms of phase rather than
+ 
+
+ align:start position:0%
+written in terms of phase rather than
+frequency the input being a phase
+
+ align:start position:0%
+frequency the input being a phase
+ 
+
+ align:start position:0%
+frequency the input being a phase
+command and then keep track of the
+
+ align:start position:0%
+command and then keep track of the
+ 
+
+ align:start position:0%
+command and then keep track of the
+output phase in that case the
+
+ align:start position:0%
+output phase in that case the
+ 
+
+ align:start position:0%
+output phase in that case the
+integration appears in conjunction with
+
+ align:start position:0%
+integration appears in conjunction with
+ 
+
+ align:start position:0%
+integration appears in conjunction with
+the voltage controlled oscillator since
+
+ align:start position:0%
+the voltage controlled oscillator since
+ 
+
+ align:start position:0%
+the voltage controlled oscillator since
+the input to the voltage controlled
+
+ align:start position:0%
+the input to the voltage controlled
+ 
+
+ align:start position:0%
+the input to the voltage controlled
+oscillator is a voltage the output is
+
+ align:start position:0%
+oscillator is a voltage the output is
+ 
+
+ align:start position:0%
+oscillator is a voltage the output is
+the total phase angle that the
+
+ align:start position:0%
+the total phase angle that the
+ 
+
+ align:start position:0%
+the total phase angle that the
+oscillator has has traversed or has gone
+
+ align:start position:0%
+oscillator has has traversed or has gone
+ 
+
+ align:start position:0%
+oscillator has has traversed or has gone
+through in that case we rearrange the
+
+ align:start position:0%
+through in that case we rearrange the
+ 
+
+ align:start position:0%
+through in that case we rearrange the
+block diagram a little bit we get the
+
+ align:start position:0%
+block diagram a little bit we get the
+ 
+
+ align:start position:0%
+block diagram a little bit we get the
+integration appearing in a different
+
+ align:start position:0%
+integration appearing in a different
+ 
+
+ align:start position:0%
+integration appearing in a different
+place in the block diagram but of course
+
+ align:start position:0%
+place in the block diagram but of course
+ 
+
+ align:start position:0%
+place in the block diagram but of course
+there's still the single
+
+ align:start position:0%
+there's still the single
+ 
+
+ align:start position:0%
+there's still the single
+integration well how do we mechanize the
+
+ align:start position:0%
+integration well how do we mechanize the
+ 
+
+ align:start position:0%
+integration well how do we mechanize the
+phase detector that's an important
+
+ align:start position:0%
+phase detector that's an important
+ 
+
+ align:start position:0%
+phase detector that's an important
+consideration in this type of
+
+ align:start position:0%
+consideration in this type of
+ 
+
+ align:start position:0%
+consideration in this type of
+system there are a number of ways and
+
+ align:start position:0%
+system there are a number of ways and
+ 
+
+ align:start position:0%
+system there are a number of ways and
+and they differ particularly in their
+
+ align:start position:0%
+and they differ particularly in their
+ 
+
+ align:start position:0%
+and they differ particularly in their
+large signal Behavior one very simple
+
+ align:start position:0%
+large signal Behavior one very simple
+ 
+
+ align:start position:0%
+large signal Behavior one very simple
+way is to use an exclusive orgate if the
+
+ align:start position:0%
+way is to use an exclusive orgate if the
+ 
+
+ align:start position:0%
+way is to use an exclusive orgate if the
+input signal and the output signal of
+
+ align:start position:0%
+input signal and the output signal of
+ 
+
+ align:start position:0%
+input signal and the output signal of
+our phase locked Loop are both digital
+
+ align:start position:0%
+our phase locked Loop are both digital
+ 
+
+ align:start position:0%
+our phase locked Loop are both digital
+signals let's look at how that might
+
+ align:start position:0%
+signals let's look at how that might
+ 
+
+ align:start position:0%
+signals let's look at how that might
+work suppose our commanded frequency is
+
+ align:start position:0%
+work suppose our commanded frequency is
+ 
+
+ align:start position:0%
+work suppose our commanded frequency is
+the digital signal with a phase as
+
+ align:start position:0%
+the digital signal with a phase as
+ 
+
+ align:start position:0%
+the digital signal with a phase as
+shown and assume that the response of
+
+ align:start position:0%
+shown and assume that the response of
+ 
+
+ align:start position:0%
+shown and assume that the response of
+the system is again a digital signal
+
+ align:start position:0%
+the system is again a digital signal
+ 
+
+ align:start position:0%
+the system is again a digital signal
+phase shifted by 90° In Time by a
+
+ align:start position:0%
+phase shifted by 90° In Time by a
+ 
+
+ align:start position:0%
+phase shifted by 90° In Time by a
+quarter of a cycle uh if we applied
+
+ align:start position:0%
+quarter of a cycle uh if we applied
+ 
+
+ align:start position:0%
+quarter of a cycle uh if we applied
+those two digital signals to an
+
+ align:start position:0%
+those two digital signals to an
+ 
+
+ align:start position:0%
+those two digital signals to an
+exclusive orgate we'd get the following
+
+ align:start position:0%
+exclusive orgate we'd get the following
+ 
+
+ align:start position:0%
+exclusive orgate we'd get the following
+output from the phase detector itself if
+
+ align:start position:0%
+output from the phase detector itself if
+ 
+
+ align:start position:0%
+output from the phase detector itself if
+we used simply an exclusive orgate as
+
+ align:start position:0%
+we used simply an exclusive orgate as
+ 
+
+ align:start position:0%
+we used simply an exclusive orgate as
+the phase detector we'd get the
+
+ align:start position:0%
+the phase detector we'd get the
+ 
+
+ align:start position:0%
+the phase detector we'd get the
+following kind of an output uh here in
+
+ align:start position:0%
+following kind of an output uh here in
+ 
+
+ align:start position:0%
+following kind of an output uh here in
+this time interval one of the signals is
+
+ align:start position:0%
+this time interval one of the signals is
+ 
+
+ align:start position:0%
+this time interval one of the signals is
+high consequently the output of the
+
+ align:start position:0%
+high consequently the output of the
+ 
+
+ align:start position:0%
+high consequently the output of the
+exclusive orgate is high uh in this
+
+ align:start position:0%
+exclusive orgate is high uh in this
+ 
+
+ align:start position:0%
+exclusive orgate is high uh in this
+period both both inputs to the XR gate
+
+ align:start position:0%
+period both both inputs to the XR gate
+ 
+
+ align:start position:0%
+period both both inputs to the XR gate
+are are high the output of the XR gate
+
+ align:start position:0%
+are are high the output of the XR gate
+ 
+
+ align:start position:0%
+are are high the output of the XR gate
+is low here again one signal is high
+
+ align:start position:0%
+is low here again one signal is high
+ 
+
+ align:start position:0%
+is low here again one signal is high
+only one is high the output of the xor
+
+ align:start position:0%
+only one is high the output of the xor
+ 
+
+ align:start position:0%
+only one is high the output of the xor
+is high here uh they're both low the
+
+ align:start position:0%
+is high here uh they're both low the
+ 
+
+ align:start position:0%
+is high here uh they're both low the
+output of the xor is low the information
+
+ align:start position:0%
+output of the xor is low the information
+ 
+
+ align:start position:0%
+output of the xor is low the information
+we're interested in is really the
+
+ align:start position:0%
+we're interested in is really the
+ 
+
+ align:start position:0%
+we're interested in is really the
+average value of this signal and so to
+
+ align:start position:0%
+average value of this signal and so to
+ 
+
+ align:start position:0%
+average value of this signal and so to
+complete the phase detection process uh
+
+ align:start position:0%
+complete the phase detection process uh
+ 
+
+ align:start position:0%
+complete the phase detection process uh
+we might standardize levels not allow
+
+ align:start position:0%
+we might standardize levels not allow
+ 
+
+ align:start position:0%
+we might standardize levels not allow
+them the ambiguity associated with
+
+ align:start position:0%
+them the ambiguity associated with
+ 
+
+ align:start position:0%
+them the ambiguity associated with
+normal digital levels we go through some
+
+ align:start position:0%
+normal digital levels we go through some
+ 
+
+ align:start position:0%
+normal digital levels we go through some
+sort of an analog switch so that we got
+
+ align:start position:0%
+sort of an analog switch so that we got
+ 
+
+ align:start position:0%
+sort of an analog switch so that we got
+standard levels coming out of our
+
+ align:start position:0%
+standard levels coming out of our
+ 
+
+ align:start position:0%
+standard levels coming out of our
+exclusive orgate and then go through a
+
+ align:start position:0%
+exclusive orgate and then go through a
+ 
+
+ align:start position:0%
+exclusive orgate and then go through a
+low pass filter that extracted the
+
+ align:start position:0%
+low pass filter that extracted the
+ 
+
+ align:start position:0%
+low pass filter that extracted the
+average value of the uh output from the
+
+ align:start position:0%
+average value of the uh output from the
+ 
+
+ align:start position:0%
+average value of the uh output from the
+exclusive orgate in this particular case
+
+ align:start position:0%
+exclusive orgate in this particular case
+ 
+
+ align:start position:0%
+exclusive orgate in this particular case
+where we have a 90° relative phase shift
+
+ align:start position:0%
+where we have a 90° relative phase shift
+ 
+
+ align:start position:0%
+where we have a 90° relative phase shift
+between the command signal and the
+
+ align:start position:0%
+between the command signal and the
+ 
+
+ align:start position:0%
+between the command signal and the
+response of the system the average value
+
+ align:start position:0%
+response of the system the average value
+ 
+
+ align:start position:0%
+response of the system the average value
+of the signal out of the exclusive
+
+ align:start position:0%
+of the signal out of the exclusive
+ 
+
+ align:start position:0%
+of the signal out of the exclusive
+orgate would be simply 1/2 of its
+
+ align:start position:0%
+orgate would be simply 1/2 of its
+ 
+
+ align:start position:0%
+orgate would be simply 1/2 of its
+maximum value since it spends half its
+
+ align:start position:0%
+maximum value since it spends half its
+ 
+
+ align:start position:0%
+maximum value since it spends half its
+time in the high and half its time in
+
+ align:start position:0%
+time in the high and half its time in
+ 
+
+ align:start position:0%
+time in the high and half its time in
+the low State again I think you notice
+
+ align:start position:0%
+the low State again I think you notice
+ 
+
+ align:start position:0%
+the low State again I think you notice
+the same sort of a thing as we had in
+
+ align:start position:0%
+the same sort of a thing as we had in
+ 
+
+ align:start position:0%
+the same sort of a thing as we had in
+one of the oscillator examples before
+
+ align:start position:0%
+one of the oscillator examples before
+ 
+
+ align:start position:0%
+one of the oscillator examples before
+where we have a high frequency process
+
+ align:start position:0%
+where we have a high frequency process
+ 
+
+ align:start position:0%
+where we have a high frequency process
+going on the exclusive orgate in this
+
+ align:start position:0%
+going on the exclusive orgate in this
+ 
+
+ align:start position:0%
+going on the exclusive orgate in this
+case is running at twice the operating
+
+ align:start position:0%
+case is running at twice the operating
+ 
+
+ align:start position:0%
+case is running at twice the operating
+frequency of the loop for this
+
+ align:start position:0%
+frequency of the loop for this
+ 
+
+ align:start position:0%
+frequency of the loop for this
+particular combination of inputs the
+
+ align:start position:0%
+particular combination of inputs the
+ 
+
+ align:start position:0%
+particular combination of inputs the
+output is a double frequency component
+
+ align:start position:0%
+output is a double frequency component
+ 
+
+ align:start position:0%
+output is a double frequency component
+plus a low frequency in this case a DC
+
+ align:start position:0%
+plus a low frequency in this case a DC
+ 
+
+ align:start position:0%
+plus a low frequency in this case a DC
+component if there's no change in the
+
+ align:start position:0%
+component if there's no change in the
+ 
+
+ align:start position:0%
+component if there's no change in the
+relative phase between the two signals
+
+ align:start position:0%
+relative phase between the two signals
+ 
+
+ align:start position:0%
+relative phase between the two signals
+uh what we're interested in and the
+
+ align:start position:0%
+uh what we're interested in and the
+ 
+
+ align:start position:0%
+uh what we're interested in and the
+information is contained in the average
+
+ align:start position:0%
+information is contained in the average
+ 
+
+ align:start position:0%
+information is contained in the average
+value of the signal so we have to apply
+
+ align:start position:0%
+value of the signal so we have to apply
+ 
+
+ align:start position:0%
+value of the signal so we have to apply
+some filtering there's some sampling
+
+ align:start position:0%
+some filtering there's some sampling
+ 
+
+ align:start position:0%
+some filtering there's some sampling
+going on we we have sampling kinds of
+
+ align:start position:0%
+going on we we have sampling kinds of
+ 
+
+ align:start position:0%
+going on we we have sampling kinds of
+problems here and that puts a very real
+
+ align:start position:0%
+problems here and that puts a very real
+ 
+
+ align:start position:0%
+problems here and that puts a very real
+limit on the crossover frequency of the
+
+ align:start position:0%
+limit on the crossover frequency of the
+ 
+
+ align:start position:0%
+limit on the crossover frequency of the
+loop and as we did in the case of the
+
+ align:start position:0%
+loop and as we did in the case of the
+ 
+
+ align:start position:0%
+loop and as we did in the case of the
+oscillator whose amplitude was
+
+ align:start position:0%
+oscillator whose amplitude was
+ 
+
+ align:start position:0%
+oscillator whose amplitude was
+controlled we argued that to eliminate
+
+ align:start position:0%
+controlled we argued that to eliminate
+ 
+
+ align:start position:0%
+controlled we argued that to eliminate
+those sorts of problems we cross over in
+
+ align:start position:0%
+those sorts of problems we cross over in
+ 
+
+ align:start position:0%
+those sorts of problems we cross over in
+this kind of a loop at a very small
+
+ align:start position:0%
+this kind of a loop at a very small
+ 
+
+ align:start position:0%
+this kind of a loop at a very small
+fraction of the operating frequency here
+
+ align:start position:0%
+fraction of the operating frequency here
+ 
+
+ align:start position:0%
+fraction of the operating frequency here
+we intend to cross over at a small
+
+ align:start position:0%
+we intend to cross over at a small
+ 
+
+ align:start position:0%
+we intend to cross over at a small
+fraction of f subc or F
+
+ align:start position:0%
+fraction of f subc or F
+ 
+
+ align:start position:0%
+fraction of f subc or F
+subr and by doing that we're able to
+
+ align:start position:0%
+subr and by doing that we're able to
+ 
+
+ align:start position:0%
+subr and by doing that we're able to
+easily extract the average value of this
+
+ align:start position:0%
+easily extract the average value of this
+ 
+
+ align:start position:0%
+easily extract the average value of this
+signal to use as a a phase indication
+
+ align:start position:0%
+signal to use as a a phase indication
+ 
+
+ align:start position:0%
+signal to use as a a phase indication
+let's consider what happens if the
+
+ align:start position:0%
+let's consider what happens if the
+ 
+
+ align:start position:0%
+let's consider what happens if the
+relative phase between the input and the
+
+ align:start position:0%
+relative phase between the input and the
+ 
+
+ align:start position:0%
+relative phase between the input and the
+output signals change such that now the
+
+ align:start position:0%
+output signals change such that now the
+ 
+
+ align:start position:0%
+output signals change such that now the
+response of the system the second
+
+ align:start position:0%
+response of the system the second
+ 
+
+ align:start position:0%
+response of the system the second
+response of the system is in fact in
+
+ align:start position:0%
+response of the system is in fact in
+ 
+
+ align:start position:0%
+response of the system is in fact in
+Phase with the command signal so we have
+
+ align:start position:0%
+Phase with the command signal so we have
+ 
+
+ align:start position:0%
+Phase with the command signal so we have
+one that that's directly in Phase with
+
+ align:start position:0%
+one that that's directly in Phase with
+ 
+
+ align:start position:0%
+one that that's directly in Phase with
+the command signal in that case the
+
+ align:start position:0%
+the command signal in that case the
+ 
+
+ align:start position:0%
+the command signal in that case the
+output of our exclusive orgate is always
+
+ align:start position:0%
+output of our exclusive orgate is always
+ 
+
+ align:start position:0%
+output of our exclusive orgate is always
+low so this would be the output from the
+
+ align:start position:0%
+low so this would be the output from the
+ 
+
+ align:start position:0%
+low so this would be the output from the
+exclusive orgate that corresponds to
+
+ align:start position:0%
+exclusive orgate that corresponds to
+ 
+
+ align:start position:0%
+exclusive orgate that corresponds to
+this second response from the
+
+ align:start position:0%
+this second response from the
+ 
+
+ align:start position:0%
+this second response from the
+system uh if we average that of course
+
+ align:start position:0%
+system uh if we average that of course
+ 
+
+ align:start position:0%
+system uh if we average that of course
+we'd get zero if we average the output
+
+ align:start position:0%
+we'd get zero if we average the output
+ 
+
+ align:start position:0%
+we'd get zero if we average the output
+of the exclusive orgate when the two
+
+ align:start position:0%
+of the exclusive orgate when the two
+ 
+
+ align:start position:0%
+of the exclusive orgate when the two
+signals are 90 degrees out of phase we
+
+ align:start position:0%
+signals are 90 degrees out of phase we
+ 
+
+ align:start position:0%
+signals are 90 degrees out of phase we
+get half of full scale uh if we
+
+ align:start position:0%
+get half of full scale uh if we
+ 
+
+ align:start position:0%
+get half of full scale uh if we
+continued this and looked at what
+
+ align:start position:0%
+continued this and looked at what
+ 
+
+ align:start position:0%
+continued this and looked at what
+happened when the response of the system
+
+ align:start position:0%
+happened when the response of the system
+ 
+
+ align:start position:0%
+happened when the response of the system
+was 180° out of phase with the command
+
+ align:start position:0%
+was 180° out of phase with the command
+ 
+
+ align:start position:0%
+was 180° out of phase with the command
+frequency we'd find out that the output
+
+ align:start position:0%
+frequency we'd find out that the output
+ 
+
+ align:start position:0%
+frequency we'd find out that the output
+of the exclusive orgate was always in
+
+ align:start position:0%
+of the exclusive orgate was always in
+ 
+
+ align:start position:0%
+of the exclusive orgate was always in
+its high state if we averaged that we'd
+
+ align:start position:0%
+its high state if we averaged that we'd
+ 
+
+ align:start position:0%
+its high state if we averaged that we'd
+get the high level and so if we look at
+
+ align:start position:0%
+get the high level and so if we look at
+ 
+
+ align:start position:0%
+get the high level and so if we look at
+the average value of the output from the
+
+ align:start position:0%
+the average value of the output from the
+ 
+
+ align:start position:0%
+the average value of the output from the
+exclusive orgate as a function of the
+
+ align:start position:0%
+exclusive orgate as a function of the
+ 
+
+ align:start position:0%
+exclusive orgate as a function of the
+relative phase shift between the two
+
+ align:start position:0%
+relative phase shift between the two
+ 
+
+ align:start position:0%
+relative phase shift between the two
+signals which I've called Alpha we get a
+
+ align:start position:0%
+signals which I've called Alpha we get a
+ 
+
+ align:start position:0%
+signals which I've called Alpha we get a
+a signal that is uh 0 for 0 deg of
+
+ align:start position:0%
+a signal that is uh 0 for 0 deg of
+ 
+
+ align:start position:0%
+a signal that is uh 0 for 0 deg of
+relative phase
+
+ align:start position:0%
+relative phase
+ 
+
+ align:start position:0%
+relative phase
+uh is half of Maximum value for 90° of
+
+ align:start position:0%
+uh is half of Maximum value for 90° of
+ 
+
+ align:start position:0%
+uh is half of Maximum value for 90° of
+relative phase reaches the maximum value
+
+ align:start position:0%
+relative phase reaches the maximum value
+ 
+
+ align:start position:0%
+relative phase reaches the maximum value
+for 180 degrees of relative phase if we
+
+ align:start position:0%
+for 180 degrees of relative phase if we
+ 
+
+ align:start position:0%
+for 180 degrees of relative phase if we
+continued this we'd find out that we'd
+
+ align:start position:0%
+continued this we'd find out that we'd
+ 
+
+ align:start position:0%
+continued this we'd find out that we'd
+have a triangular function that comes
+
+ align:start position:0%
+have a triangular function that comes
+ 
+
+ align:start position:0%
+have a triangular function that comes
+back down uh once again reaching 0 degre
+
+ align:start position:0%
+back down uh once again reaching 0 degre
+ 
+
+ align:start position:0%
+back down uh once again reaching 0 degre
+when we've accumulated a total phase
+
+ align:start position:0%
+when we've accumulated a total phase
+ 
+
+ align:start position:0%
+when we've accumulated a total phase
+difference of
+
+ align:start position:0%
+difference of
+ 
+
+ align:start position:0%
+difference of
+360° between the uh two signals uh the
+
+ align:start position:0%
+360° between the uh two signals uh the
+ 
+
+ align:start position:0%
+360° between the uh two signals uh the
+error pattern the average value of the
+
+ align:start position:0%
+error pattern the average value of the
+ 
+
+ align:start position:0%
+error pattern the average value of the
+exclusive ore output signal has a
+
+ align:start position:0%
+exclusive ore output signal has a
+ 
+
+ align:start position:0%
+exclusive ore output signal has a
+function of relative phase angle between
+
+ align:start position:0%
+function of relative phase angle between
+ 
+
+ align:start position:0%
+function of relative phase angle between
+the two input signals is cyclical uh
+
+ align:start position:0%
+the two input signals is cyclical uh
+ 
+
+ align:start position:0%
+the two input signals is cyclical uh
+repeats every
+
+ align:start position:0%
+repeats every
+ 
+
+ align:start position:0%
+repeats every
+360° it exhibits both positive and
+
+ align:start position:0%
+360° it exhibits both positive and
+ 
+
+ align:start position:0%
+360° it exhibits both positive and
+negative slopes if we look at the full 0
+
+ align:start position:0%
+negative slopes if we look at the full 0
+ 
+
+ align:start position:0%
+negative slopes if we look at the full 0
+to three 360 Dee range uh one of those
+
+ align:start position:0%
+to three 360 Dee range uh one of those
+ 
+
+ align:start position:0%
+to three 360 Dee range uh one of those
+when we build a loop will represent a
+
+ align:start position:0%
+when we build a loop will represent a
+ 
+
+ align:start position:0%
+when we build a loop will represent a
+point where we have positive feedback
+
+ align:start position:0%
+point where we have positive feedback
+ 
+
+ align:start position:0%
+point where we have positive feedback
+one will represent a point where we have
+
+ align:start position:0%
+one will represent a point where we have
+ 
+
+ align:start position:0%
+one will represent a point where we have
+negative feedback in the loop uh let's
+
+ align:start position:0%
+negative feedback in the loop uh let's
+ 
+
+ align:start position:0%
+negative feedback in the loop uh let's
+assume that this slope gives us negative
+
+ align:start position:0%
+assume that this slope gives us negative
+ 
+
+ align:start position:0%
+assume that this slope gives us negative
+feedback and our our overall Loop we'd
+
+ align:start position:0%
+feedback and our our overall Loop we'd
+ 
+
+ align:start position:0%
+feedback and our our overall Loop we'd
+then presumably try to arrange the loop
+
+ align:start position:0%
+then presumably try to arrange the loop
+ 
+
+ align:start position:0%
+then presumably try to arrange the loop
+so that its operating point was
+
+ align:start position:0%
+so that its operating point was
+ 
+
+ align:start position:0%
+so that its operating point was
+somewhere in here that would allow us a
+
+ align:start position:0%
+somewhere in here that would allow us a
+ 
+
+ align:start position:0%
+somewhere in here that would allow us a
+maximum of plus or minus 90° of phase
+
+ align:start position:0%
+maximum of plus or minus 90° of phase
+ 
+
+ align:start position:0%
+maximum of plus or minus 90° of phase
+deviation between the two signals before
+
+ align:start position:0%
+deviation between the two signals before
+ 
+
+ align:start position:0%
+deviation between the two signals before
+we had a phase reversal a polarity
+
+ align:start position:0%
+we had a phase reversal a polarity
+ 
+
+ align:start position:0%
+we had a phase reversal a polarity
+reversal in the loop so we'd have a
+
+ align:start position:0%
+reversal in the loop so we'd have a
+ 
+
+ align:start position:0%
+reversal in the loop so we'd have a
+total range over which the loop would
+
+ align:start position:0%
+total range over which the loop would
+ 
+
+ align:start position:0%
+total range over which the loop would
+hopefully work normally of plus or minus
+
+ align:start position:0%
+hopefully work normally of plus or minus
+ 
+
+ align:start position:0%
+hopefully work normally of plus or minus
+90 degrees of relative phase between the
+
+ align:start position:0%
+90 degrees of relative phase between the
+ 
+
+ align:start position:0%
+90 degrees of relative phase between the
+two signals there are a lot of other
+
+ align:start position:0%
+two signals there are a lot of other
+ 
+
+ align:start position:0%
+two signals there are a lot of other
+ways to do a phase detection uh for
+
+ align:start position:0%
+ways to do a phase detection uh for
+ 
+
+ align:start position:0%
+ways to do a phase detection uh for
+example we can get much the same kind of
+
+ align:start position:0%
+example we can get much the same kind of
+ 
+
+ align:start position:0%
+example we can get much the same kind of
+thing as we do in the exclusive orgate a
+
+ align:start position:0%
+thing as we do in the exclusive orgate a
+ 
+
+ align:start position:0%
+thing as we do in the exclusive orgate a
+little bit of different detail about the
+
+ align:start position:0%
+little bit of different detail about the
+ 
+
+ align:start position:0%
+little bit of different detail about the
+way the pattern repeats if we simply use
+
+ align:start position:0%
+way the pattern repeats if we simply use
+ 
+
+ align:start position:0%
+way the pattern repeats if we simply use
+a set reset flipflop as the phase
+
+ align:start position:0%
+a set reset flipflop as the phase
+ 
+
+ align:start position:0%
+a set reset flipflop as the phase
+detector set it on one of our signals
+
+ align:start position:0%
+detector set it on one of our signals
+ 
+
+ align:start position:0%
+detector set it on one of our signals
+reset it on the second signal again if
+
+ align:start position:0%
+reset it on the second signal again if
+ 
+
+ align:start position:0%
+reset it on the second signal again if
+the two signals in that case are are 180
+
+ align:start position:0%
+the two signals in that case are are 180
+ 
+
+ align:start position:0%
+the two signals in that case are are 180
+de out of phase we'd find out that the
+
+ align:start position:0%
+de out of phase we'd find out that the
+ 
+
+ align:start position:0%
+de out of phase we'd find out that the
+duty cycle of the flip-flop would be 50%
+
+ align:start position:0%
+duty cycle of the flip-flop would be 50%
+ 
+
+ align:start position:0%
+duty cycle of the flip-flop would be 50%
+it would spend half its time in each
+
+ align:start position:0%
+it would spend half its time in each
+ 
+
+ align:start position:0%
+it would spend half its time in each
+state we'd once again average that out
+
+ align:start position:0%
+state we'd once again average that out
+ 
+
+ align:start position:0%
+state we'd once again average that out
+put and we if we Chase through the
+
+ align:start position:0%
+put and we if we Chase through the
+ 
+
+ align:start position:0%
+put and we if we Chase through the
+relationships uh assuming we're setting
+
+ align:start position:0%
+relationships uh assuming we're setting
+ 
+
+ align:start position:0%
+relationships uh assuming we're setting
+on on one of our signals and resetting
+
+ align:start position:0%
+on on one of our signals and resetting
+ 
+
+ align:start position:0%
+on on one of our signals and resetting
+on the other we'd find out that we get a
+
+ align:start position:0%
+on the other we'd find out that we get a
+ 
+
+ align:start position:0%
+on the other we'd find out that we get a
+signal proportional to the the average
+
+ align:start position:0%
+signal proportional to the the average
+ 
+
+ align:start position:0%
+signal proportional to the the average
+value of the flip-flop output would be
+
+ align:start position:0%
+value of the flip-flop output would be
+ 
+
+ align:start position:0%
+value of the flip-flop output would be
+proportional to the relative phase
+
+ align:start position:0%
+proportional to the relative phase
+ 
+
+ align:start position:0%
+proportional to the relative phase
+difference between the two digital
+
+ align:start position:0%
+difference between the two digital
+ 
+
+ align:start position:0%
+difference between the two digital
+signals for an example of this sort of
+
+ align:start position:0%
+signals for an example of this sort of
+ 
+
+ align:start position:0%
+signals for an example of this sort of
+of system we're going to look at a
+
+ align:start position:0%
+of system we're going to look at a
+ 
+
+ align:start position:0%
+of system we're going to look at a
+commercially available integrated
+
+ align:start position:0%
+commercially available integrated
+ 
+
+ align:start position:0%
+commercially available integrated
+circuit phase lock loop a type 565 which
+
+ align:start position:0%
+circuit phase lock loop a type 565 which
+ 
+
+ align:start position:0%
+circuit phase lock loop a type 565 which
+has been around a while
+
+ align:start position:0%
+has been around a while
+ 
+
+ align:start position:0%
+has been around a while
+it uh uh uses a different kind of a
+
+ align:start position:0%
+it uh uh uses a different kind of a
+ 
+
+ align:start position:0%
+it uh uh uses a different kind of a
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+detector in the
+
+ align:start position:0%
+detector in the
+ 
+
+ align:start position:0%
+detector in the
+565 the reference signal the input uh
+
+ align:start position:0%
+565 the reference signal the input uh
+ 
+
+ align:start position:0%
+565 the reference signal the input uh
+the command signal uh actually in in
+
+ align:start position:0%
+the command signal uh actually in in
+ 
+
+ align:start position:0%
+the command signal uh actually in in
+the phase locked
+
+ align:start position:0%
+the phase locked
+ 
+
+ align:start position:0%
+the phase locked
+Loop is a Soso we get a a sidal input
+
+ align:start position:0%
+Loop is a Soso we get a a sidal input
+ 
+
+ align:start position:0%
+Loop is a Soso we get a a sidal input
+the signal that's fed back is actually a
+
+ align:start position:0%
+the signal that's fed back is actually a
+ 
+
+ align:start position:0%
+the signal that's fed back is actually a
+two-level signal a digital kind of a
+
+ align:start position:0%
+two-level signal a digital kind of a
+ 
+
+ align:start position:0%
+two-level signal a digital kind of a
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+Square wave sort of a thing and the
+
+ align:start position:0%
+Square wave sort of a thing and the
+ 
+
+ align:start position:0%
+Square wave sort of a thing and the
+phase detector used in the 565 basically
+
+ align:start position:0%
+phase detector used in the 565 basically
+ 
+
+ align:start position:0%
+phase detector used in the 565 basically
+performs a multiplication of these two
+
+ align:start position:0%
+performs a multiplication of these two
+ 
+
+ align:start position:0%
+performs a multiplication of these two
+signals and then once again averages the
+
+ align:start position:0%
+signals and then once again averages the
+ 
+
+ align:start position:0%
+signals and then once again averages the
+output uh and we can look at the
+
+ align:start position:0%
+output uh and we can look at the
+ 
+
+ align:start position:0%
+output uh and we can look at the
+operation of that again we assume a
+
+ align:start position:0%
+operation of that again we assume a
+ 
+
+ align:start position:0%
+operation of that again we assume a
+relative phase angle Alpha between the
+
+ align:start position:0%
+relative phase angle Alpha between the
+ 
+
+ align:start position:0%
+relative phase angle Alpha between the
+two signals uh here if Alpha were zero
+
+ align:start position:0%
+two signals uh here if Alpha were zero
+ 
+
+ align:start position:0%
+two signals uh here if Alpha were zero
+we would get as the output of the phase
+
+ align:start position:0%
+we would get as the output of the phase
+ 
+
+ align:start position:0%
+we would get as the output of the phase
+detector uh the product these two
+
+ align:start position:0%
+detector uh the product these two
+ 
+
+ align:start position:0%
+detector uh the product these two
+signals we'd effectively get a full wave
+
+ align:start position:0%
+signals we'd effectively get a full wave
+ 
+
+ align:start position:0%
+signals we'd effectively get a full wave
+rectified sine wave if Alpha were zero
+
+ align:start position:0%
+rectified sine wave if Alpha were zero
+ 
+
+ align:start position:0%
+rectified sine wave if Alpha were zero
+we'd multiply this part of the sine wave
+
+ align:start position:0%
+we'd multiply this part of the sine wave
+ 
+
+ align:start position:0%
+we'd multiply this part of the sine wave
+by+ one this part by minus one which
+
+ align:start position:0%
+by+ one this part by minus one which
+ 
+
+ align:start position:0%
+by+ one this part by minus one which
+would flip it over so the output from
+
+ align:start position:0%
+would flip it over so the output from
+ 
+
+ align:start position:0%
+would flip it over so the output from
+the phase detector prior to filtering
+
+ align:start position:0%
+the phase detector prior to filtering
+ 
+
+ align:start position:0%
+the phase detector prior to filtering
+would be a full wave rectified sine wave
+
+ align:start position:0%
+would be a full wave rectified sine wave
+ 
+
+ align:start position:0%
+would be a full wave rectified sine wave
+uh if we have 90 degrees of relative
+
+ align:start position:0%
+uh if we have 90 degrees of relative
+ 
+
+ align:start position:0%
+uh if we have 90 degrees of relative
+phase shift we find out that the average
+
+ align:start position:0%
+phase shift we find out that the average
+ 
+
+ align:start position:0%
+phase shift we find out that the average
+value of the output is zero uh we get
+
+ align:start position:0%
+value of the output is zero uh we get
+ 
+
+ align:start position:0%
+value of the output is zero uh we get
+little segments that are this segment
+
+ align:start position:0%
+little segments that are this segment
+ 
+
+ align:start position:0%
+little segments that are this segment
+and that kind of AOS soidal segment when
+
+ align:start position:0%
+and that kind of AOS soidal segment when
+ 
+
+ align:start position:0%
+and that kind of AOS soidal segment when
+we average those we get zero for an
+
+ align:start position:0%
+we average those we get zero for an
+ 
+
+ align:start position:0%
+we average those we get zero for an
+output when there's 180 degrees of
+
+ align:start position:0%
+output when there's 180 degrees of
+ 
+
+ align:start position:0%
+output when there's 180 degrees of
+relative phase shift uh we get a
+
+ align:start position:0%
+relative phase shift uh we get a
+ 
+
+ align:start position:0%
+relative phase shift uh we get a
+negative full wave rectified sine wave
+
+ align:start position:0%
+negative full wave rectified sine wave
+ 
+
+ align:start position:0%
+negative full wave rectified sine wave
+when Alpha is such that we multiply this
+
+ align:start position:0%
+when Alpha is such that we multiply this
+ 
+
+ align:start position:0%
+when Alpha is such that we multiply this
+part by minus one this part by plus one
+
+ align:start position:0%
+part by minus one this part by plus one
+ 
+
+ align:start position:0%
+part by minus one this part by plus one
+when we have 180 degrees of relative
+
+ align:start position:0%
+when we have 180 degrees of relative
+ 
+
+ align:start position:0%
+when we have 180 degrees of relative
+phase shift we get a negative full wave
+
+ align:start position:0%
+phase shift we get a negative full wave
+ 
+
+ align:start position:0%
+phase shift we get a negative full wave
+rectified sine wave and so we get a
+
+ align:start position:0%
+rectified sine wave and so we get a
+ 
+
+ align:start position:0%
+rectified sine wave and so we get a
+maximum negative average value if we
+
+ align:start position:0%
+maximum negative average value if we
+ 
+
+ align:start position:0%
+maximum negative average value if we
+keep track of those relation ships this
+
+ align:start position:0%
+keep track of those relation ships this
+ 
+
+ align:start position:0%
+keep track of those relation ships this
+sort of a phase detector or the average
+
+ align:start position:0%
+sort of a phase detector or the average
+ 
+
+ align:start position:0%
+sort of a phase detector or the average
+value out of this sort of a phase
+
+ align:start position:0%
+value out of this sort of a phase
+ 
+
+ align:start position:0%
+value out of this sort of a phase
+detector gives us a transfer function or
+
+ align:start position:0%
+detector gives us a transfer function or
+ 
+
+ align:start position:0%
+detector gives us a transfer function or
+a transfer relationship like so a
+
+ align:start position:0%
+a transfer relationship like so a
+ 
+
+ align:start position:0%
+a transfer relationship like so a
+sinusoidal picture uh if we normalize
+
+ align:start position:0%
+sinusoidal picture uh if we normalize
+ 
+
+ align:start position:0%
+sinusoidal picture uh if we normalize
+things so that the slope is one in here
+
+ align:start position:0%
+things so that the slope is one in here
+ 
+
+ align:start position:0%
+things so that the slope is one in here
+uh we hit a maximum value of 2 over Pi
+
+ align:start position:0%
+uh we hit a maximum value of 2 over Pi
+ 
+
+ align:start position:0%
+uh we hit a maximum value of 2 over Pi
+at the extremes uh or minus 2 over Pi at
+
+ align:start position:0%
+at the extremes uh or minus 2 over Pi at
+ 
+
+ align:start position:0%
+at the extremes uh or minus 2 over Pi at
+The Other Extreme again this is cyclical
+
+ align:start position:0%
+The Other Extreme again this is cyclical
+ 
+
+ align:start position:0%
+The Other Extreme again this is cyclical
+it repeats uh we get uh points of
+
+ align:start position:0%
+it repeats uh we get uh points of
+ 
+
+ align:start position:0%
+it repeats uh we get uh points of
+positive feedback or points of negative
+
+ align:start position:0%
+positive feedback or points of negative
+ 
+
+ align:start position:0%
+positive feedback or points of negative
+feedback displaced from each other by
+
+ align:start position:0%
+feedback displaced from each other by
+ 
+
+ align:start position:0%
+feedback displaced from each other by
+180° of relative phase shift uh only one
+
+ align:start position:0%
+180° of relative phase shift uh only one
+ 
+
+ align:start position:0%
+180° of relative phase shift uh only one
+of these sets of points will be a stable
+
+ align:start position:0%
+of these sets of points will be a stable
+ 
+
+ align:start position:0%
+of these sets of points will be a stable
+equilibrium for the loop the other one
+
+ align:start position:0%
+equilibrium for the loop the other one
+ 
+
+ align:start position:0%
+equilibrium for the loop the other one
+of course will be a positive Fe feedback
+
+ align:start position:0%
+of course will be a positive Fe feedback
+ 
+
+ align:start position:0%
+of course will be a positive Fe feedback
+Point uh in many phase lock Loops we
+
+ align:start position:0%
+Point uh in many phase lock Loops we
+ 
+
+ align:start position:0%
+Point uh in many phase lock Loops we
+intentionally include an additional
+
+ align:start position:0%
+intentionally include an additional
+ 
+
+ align:start position:0%
+intentionally include an additional
+integration in the loop we indicated
+
+ align:start position:0%
+integration in the loop we indicated
+ 
+
+ align:start position:0%
+integration in the loop we indicated
+there was one inherent integration that
+
+ align:start position:0%
+there was one inherent integration that
+ 
+
+ align:start position:0%
+there was one inherent integration that
+has to do with the conversion from
+
+ align:start position:0%
+has to do with the conversion from
+ 
+
+ align:start position:0%
+has to do with the conversion from
+frequency to phase but in many other in
+
+ align:start position:0%
+frequency to phase but in many other in
+ 
+
+ align:start position:0%
+frequency to phase but in many other in
+many Loops we include an additional
+
+ align:start position:0%
+many Loops we include an additional
+ 
+
+ align:start position:0%
+many Loops we include an additional
+integration and the reason for that is
+
+ align:start position:0%
+integration and the reason for that is
+ 
+
+ align:start position:0%
+integration and the reason for that is
+so that under steady state conditions we
+
+ align:start position:0%
+so that under steady state conditions we
+ 
+
+ align:start position:0%
+so that under steady state conditions we
+get zero phase error in the system if we
+
+ align:start position:0%
+get zero phase error in the system if we
+ 
+
+ align:start position:0%
+get zero phase error in the system if we
+have one more integration following the
+
+ align:start position:0%
+have one more integration following the
+ 
+
+ align:start position:0%
+have one more integration following the
+phase detector and if we can stabilize
+
+ align:start position:0%
+phase detector and if we can stabilize
+ 
+
+ align:start position:0%
+phase detector and if we can stabilize
+the loop why the additional integration
+
+ align:start position:0%
+the loop why the additional integration
+ 
+
+ align:start position:0%
+the loop why the additional integration
+would tell us that under static
+
+ align:start position:0%
+would tell us that under static
+ 
+
+ align:start position:0%
+would tell us that under static
+conditions when the signals are time
+
+ align:start position:0%
+conditions when the signals are time
+ 
+
+ align:start position:0%
+conditions when the signals are time
+invariant the loop will work to drive
+
+ align:start position:0%
+invariant the loop will work to drive
+ 
+
+ align:start position:0%
+invariant the loop will work to drive
+the signal out of the phase detector to
+
+ align:start position:0%
+the signal out of the phase detector to
+ 
+
+ align:start position:0%
+the signal out of the phase detector to
+zero and or to its operating point
+
+ align:start position:0%
+zero and or to its operating point
+ 
+
+ align:start position:0%
+zero and or to its operating point
+exactly to its operating point so we'll
+
+ align:start position:0%
+exactly to its operating point so we'll
+ 
+
+ align:start position:0%
+exactly to its operating point so we'll
+end up with a system that has zero
+
+ align:start position:0%
+end up with a system that has zero
+ 
+
+ align:start position:0%
+end up with a system that has zero
+relative phase error whatever the
+
+ align:start position:0%
+relative phase error whatever the
+ 
+
+ align:start position:0%
+relative phase error whatever the
+operating point is in some of these
+
+ align:start position:0%
+operating point is in some of these
+ 
+
+ align:start position:0%
+operating point is in some of these
+detectors for example the operating
+
+ align:start position:0%
+detectors for example the operating
+ 
+
+ align:start position:0%
+detectors for example the operating
+Point's 90° apart in some it's 180°
+
+ align:start position:0%
+Point's 90° apart in some it's 180°
+ 
+
+ align:start position:0%
+Point's 90° apart in some it's 180°
+apart but if we included an an
+
+ align:start position:0%
+apart but if we included an an
+ 
+
+ align:start position:0%
+apart but if we included an an
+additional integration when the input
+
+ align:start position:0%
+additional integration when the input
+ 
+
+ align:start position:0%
+additional integration when the input
+frequency were constant we drive to that
+
+ align:start position:0%
+frequency were constant we drive to that
+ 
+
+ align:start position:0%
+frequency were constant we drive to that
+equilibrium point exactly the 565
+
+ align:start position:0%
+equilibrium point exactly the 565
+ 
+
+ align:start position:0%
+equilibrium point exactly the 565
+doesn't include that the output of the
+
+ align:start position:0%
+doesn't include that the output of the
+ 
+
+ align:start position:0%
+doesn't include that the output of the
+phase detector can be modeled in the 565
+
+ align:start position:0%
+phase detector can be modeled in the 565
+ 
+
+ align:start position:0%
+phase detector can be modeled in the 565
+as some sort of a thant equivalent with
+
+ align:start position:0%
+as some sort of a thant equivalent with
+ 
+
+ align:start position:0%
+as some sort of a thant equivalent with
+a voltage generator proportional to the
+
+ align:start position:0%
+a voltage generator proportional to the
+ 
+
+ align:start position:0%
+a voltage generator proportional to the
+phase error and some output resistance
+
+ align:start position:0%
+phase error and some output resistance
+ 
+
+ align:start position:0%
+phase error and some output resistance
+you mechanize the loop filter in the
+
+ align:start position:0%
+you mechanize the loop filter in the
+ 
+
+ align:start position:0%
+you mechanize the loop filter in the
+565 by adding some components external
+
+ align:start position:0%
+565 by adding some components external
+ 
+
+ align:start position:0%
+565 by adding some components external
+to this thonon equivalent bya an a
+
+ align:start position:0%
+to this thonon equivalent bya an a
+ 
+
+ align:start position:0%
+to this thonon equivalent bya an a
+terminal on the integrated circuit and
+
+ align:start position:0%
+terminal on the integrated circuit and
+ 
+
+ align:start position:0%
+terminal on the integrated circuit and
+then this signal continues on uh inside
+
+ align:start position:0%
+then this signal continues on uh inside
+ 
+
+ align:start position:0%
+then this signal continues on uh inside
+the integrated circuit to change the
+
+ align:start position:0%
+the integrated circuit to change the
+ 
+
+ align:start position:0%
+the integrated circuit to change the
+frequency of operation of the voltage
+
+ align:start position:0%
+frequency of operation of the voltage
+ 
+
+ align:start position:0%
+frequency of operation of the voltage
+controlled oscillator this signal is the
+
+ align:start position:0%
+controlled oscillator this signal is the
+ 
+
+ align:start position:0%
+controlled oscillator this signal is the
+one applied to the
+
+ align:start position:0%
+one applied to the
+ 
+
+ align:start position:0%
+one applied to the
+vco well one thing we might do is simply
+
+ align:start position:0%
+vco well one thing we might do is simply
+ 
+
+ align:start position:0%
+vco well one thing we might do is simply
+add a capacitor which I've chosen to
+
+ align:start position:0%
+add a capacitor which I've chosen to
+ 
+
+ align:start position:0%
+add a capacitor which I've chosen to
+call C big uh across this pair of
+
+ align:start position:0%
+call C big uh across this pair of
+ 
+
+ align:start position:0%
+call C big uh across this pair of
+Terminals and that provides the
+
+ align:start position:0%
+Terminals and that provides the
+ 
+
+ align:start position:0%
+Terminals and that provides the
+filtering function the signal here is
+
+ align:start position:0%
+filtering function the signal here is
+ 
+
+ align:start position:0%
+filtering function the signal here is
+really the raw signal from the phase
+
+ align:start position:0%
+really the raw signal from the phase
+ 
+
+ align:start position:0%
+really the raw signal from the phase
+detector before filtering and we
+
+ align:start position:0%
+detector before filtering and we
+ 
+
+ align:start position:0%
+detector before filtering and we
+indicated we have to do some filtering
+
+ align:start position:0%
+indicated we have to do some filtering
+ 
+
+ align:start position:0%
+indicated we have to do some filtering
+we don't want to apply a Time varying
+
+ align:start position:0%
+we don't want to apply a Time varying
+ 
+
+ align:start position:0%
+we don't want to apply a Time varying
+signal to the phase detector so we might
+
+ align:start position:0%
+signal to the phase detector so we might
+ 
+
+ align:start position:0%
+signal to the phase detector so we might
+do that by simply putting a capacitor
+
+ align:start position:0%
+do that by simply putting a capacitor
+ 
+
+ align:start position:0%
+do that by simply putting a capacitor
+onto that
+
+ align:start position:0%
+onto that
+ 
+
+ align:start position:0%
+onto that
+terminal when we do that we might find
+
+ align:start position:0%
+terminal when we do that we might find
+ 
+
+ align:start position:0%
+terminal when we do that we might find
+uh the following kind of a plot of loop
+
+ align:start position:0%
+uh the following kind of a plot of loop
+ 
+
+ align:start position:0%
+uh the following kind of a plot of loop
+transmission magnitude versus frequency
+
+ align:start position:0%
+transmission magnitude versus frequency
+ 
+
+ align:start position:0%
+transmission magnitude versus frequency
+if the capacitor were large enough we'd
+
+ align:start position:0%
+if the capacitor were large enough we'd
+ 
+
+ align:start position:0%
+if the capacitor were large enough we'd
+get this sort of behavior we have a
+
+ align:start position:0%
+get this sort of behavior we have a
+ 
+
+ align:start position:0%
+get this sort of behavior we have a
+single integration at low frequencies
+
+ align:start position:0%
+single integration at low frequencies
+ 
+
+ align:start position:0%
+single integration at low frequencies
+some constant associated with that and
+
+ align:start position:0%
+some constant associated with that and
+ 
+
+ align:start position:0%
+some constant associated with that and
+then we get a pole that's equal to or
+
+ align:start position:0%
+then we get a pole that's equal to or
+ 
+
+ align:start position:0%
+then we get a pole that's equal to or
+located a frequency that's one over this
+
+ align:start position:0%
+located a frequency that's one over this
+ 
+
+ align:start position:0%
+located a frequency that's one over this
+RC product and beyond that poll we get a
+
+ align:start position:0%
+RC product and beyond that poll we get a
+ 
+
+ align:start position:0%
+RC product and beyond that poll we get a
+second order roll off we cross over with
+
+ align:start position:0%
+second order roll off we cross over with
+ 
+
+ align:start position:0%
+second order roll off we cross over with
+a slope of 1 over S
+
+ align:start position:0%
+a slope of 1 over S
+ 
+
+ align:start position:0%
+a slope of 1 over S
+squ as shown or at least if we had a
+
+ align:start position:0%
+squ as shown or at least if we had a
+ 
+
+ align:start position:0%
+squ as shown or at least if we had a
+sufficiently large capacitor that would
+
+ align:start position:0%
+sufficiently large capacitor that would
+ 
+
+ align:start position:0%
+sufficiently large capacitor that would
+happen and if we did this if we pushed
+
+ align:start position:0%
+happen and if we did this if we pushed
+ 
+
+ align:start position:0%
+happen and if we did this if we pushed
+the pole back to very low frequencies uh
+
+ align:start position:0%
+the pole back to very low frequencies uh
+ 
+
+ align:start position:0%
+the pole back to very low frequencies uh
+we'd have
+
+ align:start position:0%
+we'd have
+ 
+
+ align:start position:0%
+we'd have
+poorly stable performance we'd have low
+
+ align:start position:0%
+poorly stable performance we'd have low
+ 
+
+ align:start position:0%
+poorly stable performance we'd have low
+phase margin in the system uh we could
+
+ align:start position:0%
+phase margin in the system uh we could
+ 
+
+ align:start position:0%
+phase margin in the system uh we could
+of course uh use a smaller value
+
+ align:start position:0%
+of course uh use a smaller value
+ 
+
+ align:start position:0%
+of course uh use a smaller value
+capacitor uh one that was adequate for
+
+ align:start position:0%
+capacitor uh one that was adequate for
+ 
+
+ align:start position:0%
+capacitor uh one that was adequate for
+filtering the Ripple out of the phase
+
+ align:start position:0%
+filtering the Ripple out of the phase
+ 
+
+ align:start position:0%
+filtering the Ripple out of the phase
+detector but didn't create this problem
+
+ align:start position:0%
+detector but didn't create this problem
+ 
+
+ align:start position:0%
+detector but didn't create this problem
+however there's an alternative that can
+
+ align:start position:0%
+however there's an alternative that can
+ 
+
+ align:start position:0%
+however there's an alternative that can
+be used to give us somewhat higher
+
+ align:start position:0%
+be used to give us somewhat higher
+ 
+
+ align:start position:0%
+be used to give us somewhat higher
+desensitivity uh given that the
+
+ align:start position:0%
+desensitivity uh given that the
+ 
+
+ align:start position:0%
+desensitivity uh given that the
+crossover frequency is is more or less a
+
+ align:start position:0%
+crossover frequency is is more or less a
+ 
+
+ align:start position:0%
+crossover frequency is is more or less a
+fixed quantity because we have to cross
+
+ align:start position:0%
+fixed quantity because we have to cross
+ 
+
+ align:start position:0%
+fixed quantity because we have to cross
+over at a small fraction of the
+
+ align:start position:0%
+over at a small fraction of the
+ 
+
+ align:start position:0%
+over at a small fraction of the
+operating
+
+ align:start position:0%
+operating
+ 
+
+ align:start position:0%
+operating
+frequency um we can use a slightly more
+
+ align:start position:0%
+frequency um we can use a slightly more
+ 
+
+ align:start position:0%
+frequency um we can use a slightly more
+complicated Network at the outside of
+
+ align:start position:0%
+complicated Network at the outside of
+ 
+
+ align:start position:0%
+complicated Network at the outside of
+the package that looks something like
+
+ align:start position:0%
+the package that looks something like
+ 
+
+ align:start position:0%
+the package that looks something like
+this we have our C sub big which might
+
+ align:start position:0%
+this we have our C sub big which might
+ 
+
+ align:start position:0%
+this we have our C sub big which might
+be the same value as the C sub big
+
+ align:start position:0%
+be the same value as the C sub big
+ 
+
+ align:start position:0%
+be the same value as the C sub big
+before but then we can put a series
+
+ align:start position:0%
+before but then we can put a series
+ 
+
+ align:start position:0%
+before but then we can put a series
+resistance associated with that uh at
+
+ align:start position:0%
+resistance associated with that uh at
+ 
+
+ align:start position:0%
+resistance associated with that uh at
+high frequencies we get simply an
+
+ align:start position:0%
+high frequencies we get simply an
+ 
+
+ align:start position:0%
+high frequencies we get simply an
+attenuation between this point and this
+
+ align:start position:0%
+attenuation between this point and this
+ 
+
+ align:start position:0%
+attenuation between this point and this
+point then we get lag kinds of transfer
+
+ align:start position:0%
+point then we get lag kinds of transfer
+ 
+
+ align:start position:0%
+point then we get lag kinds of transfer
+functions out of that combination we
+
+ align:start position:0%
+functions out of that combination we
+ 
+
+ align:start position:0%
+functions out of that combination we
+might then put a smaller capacitor
+
+ align:start position:0%
+might then put a smaller capacitor
+ 
+
+ align:start position:0%
+might then put a smaller capacitor
+across this network that would provide
+
+ align:start position:0%
+across this network that would provide
+ 
+
+ align:start position:0%
+across this network that would provide
+additional Ripple filter ing at high
+
+ align:start position:0%
+additional Ripple filter ing at high
+ 
+
+ align:start position:0%
+additional Ripple filter ing at high
+frequency so the purpose of this is
+
+ align:start position:0%
+frequency so the purpose of this is
+ 
+
+ align:start position:0%
+frequency so the purpose of this is
+simply to provide Ripple filtering if we
+
+ align:start position:0%
+simply to provide Ripple filtering if we
+ 
+
+ align:start position:0%
+simply to provide Ripple filtering if we
+do that we can get a loop transmission
+
+ align:start position:0%
+do that we can get a loop transmission
+ 
+
+ align:start position:0%
+do that we can get a loop transmission
+magnitude that's generally of of this
+
+ align:start position:0%
+magnitude that's generally of of this
+ 
+
+ align:start position:0%
+magnitude that's generally of of this
+form we have a 1 overs kind of roll off
+
+ align:start position:0%
+form we have a 1 overs kind of roll off
+ 
+
+ align:start position:0%
+form we have a 1 overs kind of roll off
+at low
+
+ align:start position:0%
+at low
+ 
+
+ align:start position:0%
+at low
+frequencies at somewhat higher
+
+ align:start position:0%
+frequencies at somewhat higher
+ 
+
+ align:start position:0%
+frequencies at somewhat higher
+frequencies we get into the pole of the
+
+ align:start position:0%
+frequencies we get into the pole of the
+ 
+
+ align:start position:0%
+frequencies we get into the pole of the
+lag type transfer function and that pole
+
+ align:start position:0%
+lag type transfer function and that pole
+ 
+
+ align:start position:0%
+lag type transfer function and that pole
+location is of course uh given by the C
+
+ align:start position:0%
+location is of course uh given by the C
+ 
+
+ align:start position:0%
+location is of course uh given by the C
+subb and the uh sum of of these two
+
+ align:start position:0%
+subb and the uh sum of of these two
+ 
+
+ align:start position:0%
+subb and the uh sum of of these two
+resistors that RC product determines the
+
+ align:start position:0%
+resistors that RC product determines the
+ 
+
+ align:start position:0%
+resistors that RC product determines the
+pole location in the lag type transfer
+
+ align:start position:0%
+pole location in the lag type transfer
+ 
+
+ align:start position:0%
+pole location in the lag type transfer
+function we later get the zero
+
+ align:start position:0%
+function we later get the zero
+ 
+
+ align:start position:0%
+function we later get the zero
+associated with the lag type transfer
+
+ align:start position:0%
+associated with the lag type transfer
+ 
+
+ align:start position:0%
+associated with the lag type transfer
+function and we'd probably we'd
+
+ align:start position:0%
+function and we'd probably we'd
+ 
+
+ align:start position:0%
+function and we'd probably we'd
+presumably arrange things so that that
+
+ align:start position:0%
+presumably arrange things so that that
+ 
+
+ align:start position:0%
+presumably arrange things so that that
+zero occurred at a a frequency below
+
+ align:start position:0%
+zero occurred at a a frequency below
+ 
+
+ align:start position:0%
+zero occurred at a a frequency below
+crossover we can then cross over with
+
+ align:start position:0%
+crossover we can then cross over with
+ 
+
+ align:start position:0%
+crossover we can then cross over with
+acceptable phase margin in our system
+
+ align:start position:0%
+acceptable phase margin in our system
+ 
+
+ align:start position:0%
+acceptable phase margin in our system
+and then finally at a frequency well
+
+ align:start position:0%
+and then finally at a frequency well
+ 
+
+ align:start position:0%
+and then finally at a frequency well
+beyond crossover we get the filtering
+
+ align:start position:0%
+beyond crossover we get the filtering
+ 
+
+ align:start position:0%
+beyond crossover we get the filtering
+action of the small capacitor and
+
+ align:start position:0%
+action of the small capacitor and
+ 
+
+ align:start position:0%
+action of the small capacitor and
+presumably we choose the value of that
+
+ align:start position:0%
+presumably we choose the value of that
+ 
+
+ align:start position:0%
+presumably we choose the value of that
+capacitor so that it provides adequate
+
+ align:start position:0%
+capacitor so that it provides adequate
+ 
+
+ align:start position:0%
+capacitor so that it provides adequate
+filtering to the residual Ripple out of
+
+ align:start position:0%
+filtering to the residual Ripple out of
+ 
+
+ align:start position:0%
+filtering to the residual Ripple out of
+the phase
+
+ align:start position:0%
+the phase
+ 
+
+ align:start position:0%
+the phase
+detector uh this is the way we've
+
+ align:start position:0%
+detector uh this is the way we've
+ 
+
+ align:start position:0%
+detector uh this is the way we've
+arranged a demonstration system using
+
+ align:start position:0%
+arranged a demonstration system using
+ 
+
+ align:start position:0%
+arranged a demonstration system using
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+565 and in fact what we're able to do in
+
+ align:start position:0%
+565 and in fact what we're able to do in
+ 
+
+ align:start position:0%
+565 and in fact what we're able to do in
+the demonstration system is change this
+
+ align:start position:0%
+the demonstration system is change this
+ 
+
+ align:start position:0%
+the demonstration system is change this
+resistor uh the net effect of doing that
+
+ align:start position:0%
+resistor uh the net effect of doing that
+ 
+
+ align:start position:0%
+resistor uh the net effect of doing that
+uh is principally to change the location
+
+ align:start position:0%
+uh is principally to change the location
+ 
+
+ align:start position:0%
+uh is principally to change the location
+of this zero so we can get a family of
+
+ align:start position:0%
+of this zero so we can get a family of
+ 
+
+ align:start position:0%
+of this zero so we can get a family of
+responses from our phase lock loop or a
+
+ align:start position:0%
+responses from our phase lock loop or a
+ 
+
+ align:start position:0%
+responses from our phase lock loop or a
+family of loop Transmissions
+
+ align:start position:0%
+family of loop Transmissions
+ 
+
+ align:start position:0%
+family of loop Transmissions
+that correspond to either crossing over
+
+ align:start position:0%
+that correspond to either crossing over
+ 
+
+ align:start position:0%
+that correspond to either crossing over
+with a 1 over s s kind of a rollof where
+
+ align:start position:0%
+with a 1 over s s kind of a rollof where
+ 
+
+ align:start position:0%
+with a 1 over s s kind of a rollof where
+we pushed out the zero to two to higher
+
+ align:start position:0%
+we pushed out the zero to two to higher
+ 
+
+ align:start position:0%
+we pushed out the zero to two to higher
+frequencies or we can cross over with a
+
+ align:start position:0%
+frequencies or we can cross over with a
+ 
+
+ align:start position:0%
+frequencies or we can cross over with a
+1 overs kind of of roll off that
+
+ align:start position:0%
+1 overs kind of of roll off that
+ 
+
+ align:start position:0%
+1 overs kind of of roll off that
+presumably should give us considerably
+
+ align:start position:0%
+presumably should give us considerably
+ 
+
+ align:start position:0%
+presumably should give us considerably
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+stability uh here we have the system
+
+ align:start position:0%
+stability uh here we have the system
+ 
+
+ align:start position:0%
+stability uh here we have the system
+we're talking about buried in here is
+
+ align:start position:0%
+we're talking about buried in here is
+ 
+
+ align:start position:0%
+we're talking about buried in here is
+the 565 type uh phase lock loop chip and
+
+ align:start position:0%
+the 565 type uh phase lock loop chip and
+ 
+
+ align:start position:0%
+the 565 type uh phase lock loop chip and
+some of the peripheral components that
+
+ align:start position:0%
+some of the peripheral components that
+ 
+
+ align:start position:0%
+some of the peripheral components that
+we need this is the potentiometer that's
+
+ align:start position:0%
+we need this is the potentiometer that's
+ 
+
+ align:start position:0%
+we need this is the potentiometer that's
+mechanizing the resistor function that I
+
+ align:start position:0%
+mechanizing the resistor function that I
+ 
+
+ align:start position:0%
+mechanizing the resistor function that I
+had mentioned we're driving the whole
+
+ align:start position:0%
+had mentioned we're driving the whole
+ 
+
+ align:start position:0%
+had mentioned we're driving the whole
+thing with an external voltage
+
+ align:start position:0%
+thing with an external voltage
+ 
+
+ align:start position:0%
+thing with an external voltage
+controlled oscillator so this box is a a
+
+ align:start position:0%
+controlled oscillator so this box is a a
+ 
+
+ align:start position:0%
+controlled oscillator so this box is a a
+function generator which can in fact be
+
+ align:start position:0%
+function generator which can in fact be
+ 
+
+ align:start position:0%
+function generator which can in fact be
+voltage controlled and we can use that
+
+ align:start position:0%
+voltage controlled and we can use that
+ 
+
+ align:start position:0%
+voltage controlled and we can use that
+function to put in a changes in in input
+
+ align:start position:0%
+function to put in a changes in in input
+ 
+
+ align:start position:0%
+function to put in a changes in in input
+frequency and here we have a a signal
+
+ align:start position:0%
+frequency and here we have a a signal
+ 
+
+ align:start position:0%
+frequency and here we have a a signal
+generated again in our little test
+
+ align:start position:0%
+generated again in our little test
+ 
+
+ align:start position:0%
+generated again in our little test
+circuit that we can use to modulate the
+
+ align:start position:0%
+circuit that we can use to modulate the
+ 
+
+ align:start position:0%
+circuit that we can use to modulate the
+frequency modulate the generator that's
+
+ align:start position:0%
+frequency modulate the generator that's
+ 
+
+ align:start position:0%
+frequency modulate the generator that's
+providing our Command
+
+ align:start position:0%
+providing our Command
+ 
+
+ align:start position:0%
+providing our Command
+signal uh the amplitude of that command
+
+ align:start position:0%
+signal uh the amplitude of that command
+ 
+
+ align:start position:0%
+signal uh the amplitude of that command
+the amplitude of the signal driving our
+
+ align:start position:0%
+the amplitude of the signal driving our
+ 
+
+ align:start position:0%
+the amplitude of the signal driving our
+our the frequency modulation input on
+
+ align:start position:0%
+our the frequency modulation input on
+ 
+
+ align:start position:0%
+our the frequency modulation input on
+our input generator uh can be controlled
+
+ align:start position:0%
+our input generator uh can be controlled
+ 
+
+ align:start position:0%
+our input generator uh can be controlled
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+potentiometer and what we see now is the
+
+ align:start position:0%
+potentiometer and what we see now is the
+ 
+
+ align:start position:0%
+potentiometer and what we see now is the
+commanded signal applied actually to the
+
+ align:start position:0%
+commanded signal applied actually to the
+ 
+
+ align:start position:0%
+commanded signal applied actually to the
+voltage controlled oscillator the bottom
+
+ align:start position:0%
+voltage controlled oscillator the bottom
+ 
+
+ align:start position:0%
+voltage controlled oscillator the bottom
+trace on the oscilloscope the square
+
+ align:start position:0%
+trace on the oscilloscope the square
+ 
+
+ align:start position:0%
+trace on the oscilloscope the square
+wave is is the signal that we're
+
+ align:start position:0%
+wave is is the signal that we're
+ 
+
+ align:start position:0%
+wave is is the signal that we're
+applying to the FM input on our signal
+
+ align:start position:0%
+applying to the FM input on our signal
+ 
+
+ align:start position:0%
+applying to the FM input on our signal
+generator so when we apply a positive
+
+ align:start position:0%
+generator so when we apply a positive
+ 
+
+ align:start position:0%
+generator so when we apply a positive
+signal the frequency speeds up a bit
+
+ align:start position:0%
+signal the frequency speeds up a bit
+ 
+
+ align:start position:0%
+signal the frequency speeds up a bit
+when we apply a negative signal the
+
+ align:start position:0%
+when we apply a negative signal the
+ 
+
+ align:start position:0%
+when we apply a negative signal the
+lower level it slows down a bit the top
+
+ align:start position:0%
+lower level it slows down a bit the top
+ 
+
+ align:start position:0%
+lower level it slows down a bit the top
+Trace uh is the really indicating the
+
+ align:start position:0%
+Trace uh is the really indicating the
+ 
+
+ align:start position:0%
+Trace uh is the really indicating the
+response of our Loop and it's there's a
+
+ align:start position:0%
+response of our Loop and it's there's a
+ 
+
+ align:start position:0%
+response of our Loop and it's there's a
+particularly convenient place to look in
+
+ align:start position:0%
+particularly convenient place to look in
+ 
+
+ align:start position:0%
+particularly convenient place to look in
+in one of these sorts of Loops that's
+
+ align:start position:0%
+in one of these sorts of Loops that's
+ 
+
+ align:start position:0%
+in one of these sorts of Loops that's
+the input to the voltage controlled
+
+ align:start position:0%
+the input to the voltage controlled
+ 
+
+ align:start position:0%
+the input to the voltage controlled
+oscillator so the the signal on the top
+
+ align:start position:0%
+oscillator so the the signal on the top
+ 
+
+ align:start position:0%
+oscillator so the the signal on the top
+trace of the oscilloscope is the signal
+
+ align:start position:0%
+trace of the oscilloscope is the signal
+ 
+
+ align:start position:0%
+trace of the oscilloscope is the signal
+into the voltage controlled oscillator
+
+ align:start position:0%
+into the voltage controlled oscillator
+ 
+
+ align:start position:0%
+into the voltage controlled oscillator
+to the extent that the vco is dynamic
+
+ align:start position:0%
+to the extent that the vco is dynamic
+ 
+
+ align:start position:0%
+to the extent that the vco is dynamic
+less that's a direct measure of the
+
+ align:start position:0%
+less that's a direct measure of the
+ 
+
+ align:start position:0%
+less that's a direct measure of the
+output frequency of the system and so
+
+ align:start position:0%
+output frequency of the system and so
+ 
+
+ align:start position:0%
+output frequency of the system and so
+rather than trying to do something some
+
+ align:start position:0%
+rather than trying to do something some
+ 
+
+ align:start position:0%
+rather than trying to do something some
+sort of discriminator that operates on
+
+ align:start position:0%
+sort of discriminator that operates on
+ 
+
+ align:start position:0%
+sort of discriminator that operates on
+the output frequency we're able to use
+
+ align:start position:0%
+the output frequency we're able to use
+ 
+
+ align:start position:0%
+the output frequency we're able to use
+the input signal to the voltage
+
+ align:start position:0%
+the input signal to the voltage
+ 
+
+ align:start position:0%
+the input signal to the voltage
+controlled oscillator as that as that
+
+ align:start position:0%
+controlled oscillator as that as that
+ 
+
+ align:start position:0%
+controlled oscillator as that as that
+frequency as that signal um now we I'll
+
+ align:start position:0%
+frequency as that signal um now we I'll
+ 
+
+ align:start position:0%
+frequency as that signal um now we I'll
+change the resistor that I indicated in
+
+ align:start position:0%
+change the resistor that I indicated in
+ 
+
+ align:start position:0%
+change the resistor that I indicated in
+the next Network and as we go to smaller
+
+ align:start position:0%
+the next Network and as we go to smaller
+ 
+
+ align:start position:0%
+the next Network and as we go to smaller
+values of resistor why we should have
+
+ align:start position:0%
+values of resistor why we should have
+ 
+
+ align:start position:0%
+values of resistor why we should have
+relatively less stability in the system
+
+ align:start position:0%
+relatively less stability in the system
+ 
+
+ align:start position:0%
+relatively less stability in the system
+so let me work on this now that's this
+
+ align:start position:0%
+so let me work on this now that's this
+ 
+
+ align:start position:0%
+so let me work on this now that's this
+is going toward uh larger values of that
+
+ align:start position:0%
+is going toward uh larger values of that
+ 
+
+ align:start position:0%
+is going toward uh larger values of that
+resistor and we get very close to first
+
+ align:start position:0%
+resistor and we get very close to first
+ 
+
+ align:start position:0%
+resistor and we get very close to first
+order kinds of
+
+ align:start position:0%
+order kinds of
+ 
+
+ align:start position:0%
+order kinds of
+responses uh as we as we make uh this
+
+ align:start position:0%
+responses uh as we as we make uh this
+ 
+
+ align:start position:0%
+responses uh as we as we make uh this
+resistor larger we get as I say very
+
+ align:start position:0%
+resistor larger we get as I say very
+ 
+
+ align:start position:0%
+resistor larger we get as I say very
+close to first order kinds of response
+
+ align:start position:0%
+close to first order kinds of response
+ 
+
+ align:start position:0%
+close to first order kinds of response
+we cross over with very nearly a 1/s
+
+ align:start position:0%
+we cross over with very nearly a 1/s
+ 
+
+ align:start position:0%
+we cross over with very nearly a 1/s
+kind of of slope we've moved
+
+ align:start position:0%
+kind of of slope we've moved
+ 
+
+ align:start position:0%
+kind of of slope we've moved
+this zero back toward lower
+
+ align:start position:0%
+this zero back toward lower
+ 
+
+ align:start position:0%
+this zero back toward lower
+frequencies uh if I now make the
+
+ align:start position:0%
+frequencies uh if I now make the
+ 
+
+ align:start position:0%
+frequencies uh if I now make the
+resistor smaller we cross over or we can
+
+ align:start position:0%
+resistor smaller we cross over or we can
+ 
+
+ align:start position:0%
+resistor smaller we cross over or we can
+force cross over in a one over
+
+ align:start position:0%
+force cross over in a one over
+ 
+
+ align:start position:0%
+force cross over in a one over
+uh s
+
+ align:start position:0%
+uh s
+ 
+
+ align:start position:0%
+uh s
+squ kind of a region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as we do that we get progressively
+
+ align:start position:0%
+and as we do that we get progressively
+ 
+
+ align:start position:0%
+and as we do that we get progressively
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+stable responses so here's the case
+
+ align:start position:0%
+stable responses so here's the case
+ 
+
+ align:start position:0%
+stable responses so here's the case
+where we have the a very small value for
+
+ align:start position:0%
+where we have the a very small value for
+ 
+
+ align:start position:0%
+where we have the a very small value for
+the resistor we notice a very highly
+
+ align:start position:0%
+the resistor we notice a very highly
+ 
+
+ align:start position:0%
+the resistor we notice a very highly
+oscillatory response probably
+
+ align:start position:0%
+oscillatory response probably
+ 
+
+ align:start position:0%
+oscillatory response probably
+corresponding to several degrees of
+
+ align:start position:0%
+corresponding to several degrees of
+ 
+
+ align:start position:0%
+corresponding to several degrees of
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+margin we can again improve the behavior
+
+ align:start position:0%
+margin we can again improve the behavior
+ 
+
+ align:start position:0%
+margin we can again improve the behavior
+of the system improve the
+
+ align:start position:0%
+of the system improve the
+ 
+
+ align:start position:0%
+of the system improve the
+damping by going to a larger value of
+
+ align:start position:0%
+damping by going to a larger value of
+ 
+
+ align:start position:0%
+damping by going to a larger value of
+resistor but the speed of the system
+
+ align:start position:0%
+resistor but the speed of the system
+ 
+
+ align:start position:0%
+resistor but the speed of the system
+slows down a little little
+
+ align:start position:0%
+slows down a little little
+ 
+
+ align:start position:0%
+slows down a little little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+uh so we can get that we can observe
+
+ align:start position:0%
+uh so we can get that we can observe
+ 
+
+ align:start position:0%
+uh so we can get that we can observe
+that sort of Behavior Uh in the output
+
+ align:start position:0%
+that sort of Behavior Uh in the output
+ 
+
+ align:start position:0%
+that sort of Behavior Uh in the output
+frequency the output frequency is of
+
+ align:start position:0%
+frequency the output frequency is of
+ 
+
+ align:start position:0%
+frequency the output frequency is of
+course being modulated being frequency
+
+ align:start position:0%
+course being modulated being frequency
+ 
+
+ align:start position:0%
+course being modulated being frequency
+modulated proportional to the signal
+
+ align:start position:0%
+modulated proportional to the signal
+ 
+
+ align:start position:0%
+modulated proportional to the signal
+shown we notice on on the signal
+
+ align:start position:0%
+shown we notice on on the signal
+ 
+
+ align:start position:0%
+shown we notice on on the signal
+relatively small we don't really see
+
+ align:start position:0%
+relatively small we don't really see
+ 
+
+ align:start position:0%
+relatively small we don't really see
+much ripple at all from the phase
+
+ align:start position:0%
+much ripple at all from the phase
+ 
+
+ align:start position:0%
+much ripple at all from the phase
+detector this particular system uh is
+
+ align:start position:0%
+detector this particular system uh is
+ 
+
+ align:start position:0%
+detector this particular system uh is
+working at a carrier frequency of about
+
+ align:start position:0%
+working at a carrier frequency of about
+ 
+
+ align:start position:0%
+working at a carrier frequency of about
+30 khz and we cross over at a fraction
+
+ align:start position:0%
+30 khz and we cross over at a fraction
+ 
+
+ align:start position:0%
+30 khz and we cross over at a fraction
+of a kilohertz somewhere on the order of
+
+ align:start position:0%
+of a kilohertz somewhere on the order of
+ 
+
+ align:start position:0%
+of a kilohertz somewhere on the order of
+700 Herz so we're crossing over at a
+
+ align:start position:0%
+700 Herz so we're crossing over at a
+ 
+
+ align:start position:0%
+700 Herz so we're crossing over at a
+small fraction of the carrier frequency
+
+ align:start position:0%
+small fraction of the carrier frequency
+ 
+
+ align:start position:0%
+small fraction of the carrier frequency
+we're able to a very good job of
+
+ align:start position:0%
+we're able to a very good job of
+ 
+
+ align:start position:0%
+we're able to a very good job of
+filtering the signal out of the phase
+
+ align:start position:0%
+filtering the signal out of the phase
+ 
+
+ align:start position:0%
+filtering the signal out of the phase
+detector with that sort of spread
+
+ align:start position:0%
+detector with that sort of spread
+ 
+
+ align:start position:0%
+detector with that sort of spread
+between crossover frequency and the
+
+ align:start position:0%
+between crossover frequency and the
+ 
+
+ align:start position:0%
+between crossover frequency and the
+frequency of
+
+ align:start position:0%
+frequency of
+ 
+
+ align:start position:0%
+frequency of
+operation I had mentioned earlier that
+
+ align:start position:0%
+operation I had mentioned earlier that
+ 
+
+ align:start position:0%
+operation I had mentioned earlier that
+there are linearity problems associated
+
+ align:start position:0%
+there are linearity problems associated
+ 
+
+ align:start position:0%
+there are linearity problems associated
+with phase lock
+
+ align:start position:0%
+with phase lock
+ 
+
+ align:start position:0%
+with phase lock
+loops and uh we can see a little bit of
+
+ align:start position:0%
+loops and uh we can see a little bit of
+ 
+
+ align:start position:0%
+loops and uh we can see a little bit of
+that let's let's look at at the response
+
+ align:start position:0%
+that let's let's look at at the response
+ 
+
+ align:start position:0%
+that let's let's look at at the response
+of our system and and let's see if we
+
+ align:start position:0%
+of our system and and let's see if we
+ 
+
+ align:start position:0%
+of our system and and let's see if we
+can observe some of those
+
+ align:start position:0%
+can observe some of those
+ 
+
+ align:start position:0%
+can observe some of those
+difficulties one of them uh we can get
+
+ align:start position:0%
+difficulties one of them uh we can get
+ 
+
+ align:start position:0%
+difficulties one of them uh we can get
+uh let's go in there for
+
+ align:start position:0%
+uh let's go in there for
+ 
+
+ align:start position:0%
+uh let's go in there for
+example we notice that that looks almost
+
+ align:start position:0%
+example we notice that that looks almost
+ 
+
+ align:start position:0%
+example we notice that that looks almost
+like a second order response but if we
+
+ align:start position:0%
+like a second order response but if we
+ 
+
+ align:start position:0%
+like a second order response but if we
+look at it very very carefully we find
+
+ align:start position:0%
+look at it very very carefully we find
+ 
+
+ align:start position:0%
+look at it very very carefully we find
+out that that really isn't the response
+
+ align:start position:0%
+out that that really isn't the response
+ 
+
+ align:start position:0%
+out that that really isn't the response
+of a linear second order system the uh
+
+ align:start position:0%
+of a linear second order system the uh
+ 
+
+ align:start position:0%
+of a linear second order system the uh
+for example the second positive
+
+ align:start position:0%
+for example the second positive
+ 
+
+ align:start position:0%
+for example the second positive
+overshoot is Big relative to the first
+
+ align:start position:0%
+overshoot is Big relative to the first
+ 
+
+ align:start position:0%
+overshoot is Big relative to the first
+negative uh undershoot if you will it's
+
+ align:start position:0%
+negative uh undershoot if you will it's
+ 
+
+ align:start position:0%
+negative uh undershoot if you will it's
+not the kind of a of a transient
+
+ align:start position:0%
+not the kind of a of a transient
+ 
+
+ align:start position:0%
+not the kind of a of a transient
+response that corresponds to a true
+
+ align:start position:0%
+response that corresponds to a true
+ 
+
+ align:start position:0%
+response that corresponds to a true
+linear system uh the response also sort
+
+ align:start position:0%
+linear system uh the response also sort
+ 
+
+ align:start position:0%
+linear system uh the response also sort
+of damps out a little bit too quickly
+
+ align:start position:0%
+of damps out a little bit too quickly
+ 
+
+ align:start position:0%
+of damps out a little bit too quickly
+compared to the size of the first
+
+ align:start position:0%
+compared to the size of the first
+ 
+
+ align:start position:0%
+compared to the size of the first
+overshoot uh so there's something just a
+
+ align:start position:0%
+overshoot uh so there's something just a
+ 
+
+ align:start position:0%
+overshoot uh so there's something just a
+little bit funny about the response of
+
+ align:start position:0%
+little bit funny about the response of
+ 
+
+ align:start position:0%
+little bit funny about the response of
+the system and that reflects the
+
+ align:start position:0%
+the system and that reflects the
+ 
+
+ align:start position:0%
+the system and that reflects the
+nonlinearities associated with the phase
+
+ align:start position:0%
+nonlinearities associated with the phase
+ 
+
+ align:start position:0%
+nonlinearities associated with the phase
+detection process and and uh the uh uh
+
+ align:start position:0%
+detection process and and uh the uh uh
+ 
+
+ align:start position:0%
+detection process and and uh the uh uh
+difficulties of of maintaining lock for
+
+ align:start position:0%
+difficulties of of maintaining lock for
+ 
+
+ align:start position:0%
+difficulties of of maintaining lock for
+large ranges of signal we can make that
+
+ align:start position:0%
+large ranges of signal we can make that
+ 
+
+ align:start position:0%
+large ranges of signal we can make that
+problem worse by increasing the amount
+
+ align:start position:0%
+problem worse by increasing the amount
+ 
+
+ align:start position:0%
+problem worse by increasing the amount
+by which we change the command input and
+
+ align:start position:0%
+by which we change the command input and
+ 
+
+ align:start position:0%
+by which we change the command input and
+if I do that with this potentiometer
+
+ align:start position:0%
+if I do that with this potentiometer
+ 
+
+ align:start position:0%
+if I do that with this potentiometer
+which simply adjusts the amplitude of
+
+ align:start position:0%
+which simply adjusts the amplitude of
+ 
+
+ align:start position:0%
+which simply adjusts the amplitude of
+the signal applied to our external
+
+ align:start position:0%
+the signal applied to our external
+ 
+
+ align:start position:0%
+the signal applied to our external
+generator well we notice we can get
+
+ align:start position:0%
+generator well we notice we can get
+ 
+
+ align:start position:0%
+generator well we notice we can get
+quite bizarre modes of behavior in the
+
+ align:start position:0%
+quite bizarre modes of behavior in the
+ 
+
+ align:start position:0%
+quite bizarre modes of behavior in the
+phase lock blue uh uh really very poor
+
+ align:start position:0%
+phase lock blue uh uh really very poor
+ 
+
+ align:start position:0%
+phase lock blue uh uh really very poor
+performance and what we're really what's
+
+ align:start position:0%
+performance and what we're really what's
+ 
+
+ align:start position:0%
+performance and what we're really what's
+really happening here is commanding such
+
+ align:start position:0%
+really happening here is commanding such
+ 
+
+ align:start position:0%
+really happening here is commanding such
+a large frequency Excursion at the input
+
+ align:start position:0%
+a large frequency Excursion at the input
+ 
+
+ align:start position:0%
+a large frequency Excursion at the input
+that the loop can't really keep up we
+
+ align:start position:0%
+that the loop can't really keep up we
+ 
+
+ align:start position:0%
+that the loop can't really keep up we
+skip a couple of Cycles the phase
+
+ align:start position:0%
+skip a couple of Cycles the phase
+ 
+
+ align:start position:0%
+skip a couple of Cycles the phase
+detector is cyclical as I mentioned we
+
+ align:start position:0%
+detector is cyclical as I mentioned we
+ 
+
+ align:start position:0%
+detector is cyclical as I mentioned we
+jump a few Cycles uh the recovery from
+
+ align:start position:0%
+jump a few Cycles uh the recovery from
+ 
+
+ align:start position:0%
+jump a few Cycles uh the recovery from
+that is quite tortured uh if we go back
+
+ align:start position:0%
+that is quite tortured uh if we go back
+ 
+
+ align:start position:0%
+that is quite tortured uh if we go back
+to a more modest input uh we get
+
+ align:start position:0%
+to a more modest input uh we get
+ 
+
+ align:start position:0%
+to a more modest input uh we get
+considerably better looking kinds of
+
+ align:start position:0%
+considerably better looking kinds of
+ 
+
+ align:start position:0%
+considerably better looking kinds of
+responses although we can see a gradual
+
+ align:start position:0%
+responses although we can see a gradual
+ 
+
+ align:start position:0%
+responses although we can see a gradual
+change in the nature uh there's a
+
+ align:start position:0%
+change in the nature uh there's a
+ 
+
+ align:start position:0%
+change in the nature uh there's a
+response that looks somewhat nonlinear
+
+ align:start position:0%
+response that looks somewhat nonlinear
+ 
+
+ align:start position:0%
+response that looks somewhat nonlinear
+again the sort of third positive
+
+ align:start position:0%
+again the sort of third positive
+ 
+
+ align:start position:0%
+again the sort of third positive
+overshoot is really too small relative
+
+ align:start position:0%
+overshoot is really too small relative
+ 
+
+ align:start position:0%
+overshoot is really too small relative
+to the others um and there again is the
+
+ align:start position:0%
+to the others um and there again is the
+ 
+
+ align:start position:0%
+to the others um and there again is the
+very bad response when we completely
+
+ align:start position:0%
+very bad response when we completely
+ 
+
+ align:start position:0%
+very bad response when we completely
+overdrive the system there's a rather
+
+ align:start position:0%
+overdrive the system there's a rather
+ 
+
+ align:start position:0%
+overdrive the system there's a rather
+complex relationship between uh uh that
+
+ align:start position:0%
+complex relationship between uh uh that
+ 
+
+ align:start position:0%
+complex relationship between uh uh that
+control and and the amount of damping in
+
+ align:start position:0%
+control and and the amount of damping in
+ 
+
+ align:start position:0%
+control and and the amount of damping in
+the system and so forth uh that all of
+
+ align:start position:0%
+the system and so forth uh that all of
+ 
+
+ align:start position:0%
+the system and so forth uh that all of
+which interact in the large signal
+
+ align:start position:0%
+which interact in the large signal
+ 
+
+ align:start position:0%
+which interact in the large signal
+performance of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system much of the difficulty in the the
+
+ align:start position:0%
+system much of the difficulty in the the
+ 
+
+ align:start position:0%
+system much of the difficulty in the the
+large signal behavior of a phase locked
+
+ align:start position:0%
+large signal behavior of a phase locked
+ 
+
+ align:start position:0%
+large signal behavior of a phase locked
+Loop deals with or has to do really with
+
+ align:start position:0%
+Loop deals with or has to do really with
+ 
+
+ align:start position:0%
+Loop deals with or has to do really with
+the cyclical nature of the phase
+
+ align:start position:0%
+the cyclical nature of the phase
+ 
+
+ align:start position:0%
+the cyclical nature of the phase
+detector the kinds of phase detectors
+
+ align:start position:0%
+detector the kinds of phase detectors
+ 
+
+ align:start position:0%
+detector the kinds of phase detectors
+that I've discussed are ones that repeat
+
+ align:start position:0%
+that I've discussed are ones that repeat
+ 
+
+ align:start position:0%
+that I've discussed are ones that repeat
+every 180 or 360 degrees or whatever
+
+ align:start position:0%
+every 180 or 360 degrees or whatever
+ 
+
+ align:start position:0%
+every 180 or 360 degrees or whatever
+and in some sense one of the one of the
+
+ align:start position:0%
+and in some sense one of the one of the
+ 
+
+ align:start position:0%
+and in some sense one of the one of the
+problems with that sort of a thing is is
+
+ align:start position:0%
+problems with that sort of a thing is is
+ 
+
+ align:start position:0%
+problems with that sort of a thing is is
+consider the behavior when we have a
+
+ align:start position:0%
+consider the behavior when we have a
+ 
+
+ align:start position:0%
+consider the behavior when we have a
+significant difference between the
+
+ align:start position:0%
+significant difference between the
+ 
+
+ align:start position:0%
+significant difference between the
+frequencies that we're applying to the
+
+ align:start position:0%
+frequencies that we're applying to the
+ 
+
+ align:start position:0%
+frequencies that we're applying to the
+phase locked Loop and the frequency that
+
+ align:start position:0%
+phase locked Loop and the frequency that
+ 
+
+ align:start position:0%
+phase locked Loop and the frequency that
+the circuit is responding at if there's
+
+ align:start position:0%
+the circuit is responding at if there's
+ 
+
+ align:start position:0%
+the circuit is responding at if there's
+a major frequency difference the output
+
+ align:start position:0%
+a major frequency difference the output
+ 
+
+ align:start position:0%
+a major frequency difference the output
+of the phase detector will be a a signal
+
+ align:start position:0%
+of the phase detector will be a a signal
+ 
+
+ align:start position:0%
+of the phase detector will be a a signal
+at basically the difference frequency
+
+ align:start position:0%
+at basically the difference frequency
+ 
+
+ align:start position:0%
+at basically the difference frequency
+between the two uh it effectively has
+
+ align:start position:0%
+between the two uh it effectively has
+ 
+
+ align:start position:0%
+between the two uh it effectively has
+zero average value uh from that kind of
+
+ align:start position:0%
+zero average value uh from that kind of
+ 
+
+ align:start position:0%
+zero average value uh from that kind of
+a phase detector and so when we're in
+
+ align:start position:0%
+a phase detector and so when we're in
+ 
+
+ align:start position:0%
+a phase detector and so when we're in
+that situation the phase lock loop has a
+
+ align:start position:0%
+that situation the phase lock loop has a
+ 
+
+ align:start position:0%
+that situation the phase lock loop has a
+very difficult time reacquiring lock
+
+ align:start position:0%
+very difficult time reacquiring lock
+ 
+
+ align:start position:0%
+very difficult time reacquiring lock
+because it doesn't get a clear
+
+ align:start position:0%
+because it doesn't get a clear
+ 
+
+ align:start position:0%
+because it doesn't get a clear
+indication of the error it doesn't get a
+
+ align:start position:0%
+indication of the error it doesn't get a
+ 
+
+ align:start position:0%
+indication of the error it doesn't get a
+clear indication of of which frequency
+
+ align:start position:0%
+clear indication of of which frequency
+ 
+
+ align:start position:0%
+clear indication of of which frequency
+applied to the phase detector is the
+
+ align:start position:0%
+applied to the phase detector is the
+ 
+
+ align:start position:0%
+applied to the phase detector is the
+higher of the two and so it has a great
+
+ align:start position:0%
+higher of the two and so it has a great
+ 
+
+ align:start position:0%
+higher of the two and so it has a great
+deal of difficulty recovering the
+
+ align:start position:0%
+deal of difficulty recovering the
+ 
+
+ align:start position:0%
+deal of difficulty recovering the
+Dynamics of those sorts of large signal
+
+ align:start position:0%
+Dynamics of those sorts of large signal
+ 
+
+ align:start position:0%
+Dynamics of those sorts of large signal
+uh behavior in in phase lock Loops uh
+
+ align:start position:0%
+uh behavior in in phase lock Loops uh
+ 
+
+ align:start position:0%
+uh behavior in in phase lock Loops uh
+are are very complicated and and the a
+
+ align:start position:0%
+are are very complicated and and the a
+ 
+
+ align:start position:0%
+are are very complicated and and the a
+lot of the difficulty of design in a
+
+ align:start position:0%
+lot of the difficulty of design in a
+ 
+
+ align:start position:0%
+lot of the difficulty of design in a
+phase lock loop comes from trying to
+
+ align:start position:0%
+phase lock loop comes from trying to
+ 
+
+ align:start position:0%
+phase lock loop comes from trying to
+build a loop that will have good
+
+ align:start position:0%
+build a loop that will have good
+ 
+
+ align:start position:0%
+build a loop that will have good
+acquisition time when it it's fairly
+
+ align:start position:0%
+acquisition time when it it's fairly
+ 
+
+ align:start position:0%
+acquisition time when it it's fairly
+easy to get to get a loop that's well
+
+ align:start position:0%
+easy to get to get a loop that's well
+ 
+
+ align:start position:0%
+easy to get to get a loop that's well
+behaved for small signals for
+
+ align:start position:0%
+behaved for small signals for
+ 
+
+ align:start position:0%
+behaved for small signals for
+sufficiently small signals but if you'd
+
+ align:start position:0%
+sufficiently small signals but if you'd
+ 
+
+ align:start position:0%
+sufficiently small signals but if you'd
+like to have a large or a very fast
+
+ align:start position:0%
+like to have a large or a very fast
+ 
+
+ align:start position:0%
+like to have a large or a very fast
+settling time for a large frequency
+
+ align:start position:0%
+settling time for a large frequency
+ 
+
+ align:start position:0%
+settling time for a large frequency
+error well we find that's a much more
+
+ align:start position:0%
+error well we find that's a much more
+ 
+
+ align:start position:0%
+error well we find that's a much more
+difficult thing to do that problem
+
+ align:start position:0%
+difficult thing to do that problem
+ 
+
+ align:start position:0%
+difficult thing to do that problem
+exists for example often times in the
+
+ align:start position:0%
+exists for example often times in the
+ 
+
+ align:start position:0%
+exists for example often times in the
+frequency synthesizer you make a change
+
+ align:start position:0%
+frequency synthesizer you make a change
+ 
+
+ align:start position:0%
+frequency synthesizer you make a change
+actually a step change in N change the
+
+ align:start position:0%
+actually a step change in N change the
+ 
+
+ align:start position:0%
+actually a step change in N change the
+value of n that disturbs the loop uh but
+
+ align:start position:0%
+value of n that disturbs the loop uh but
+ 
+
+ align:start position:0%
+value of n that disturbs the loop uh but
+in many cases you'd like to have very
+
+ align:start position:0%
+in many cases you'd like to have very
+ 
+
+ align:start position:0%
+in many cases you'd like to have very
+rapid settling to a new frequency and to
+
+ align:start position:0%
+rapid settling to a new frequency and to
+ 
+
+ align:start position:0%
+rapid settling to a new frequency and to
+the new frequency at the output that
+
+ align:start position:0%
+the new frequency at the output that
+ 
+
+ align:start position:0%
+the new frequency at the output that
+kind of of settling rapid settling is is
+
+ align:start position:0%
+kind of of settling rapid settling is is
+ 
+
+ align:start position:0%
+kind of of settling rapid settling is is
+a very challenging sort of design
+
+ align:start position:0%
+a very challenging sort of design
+ 
+
+ align:start position:0%
+a very challenging sort of design
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+part of of the secret is to use a better
+
+ align:start position:0%
+part of of the secret is to use a better
+ 
+
+ align:start position:0%
+part of of the secret is to use a better
+phase detector than the ones we've
+
+ align:start position:0%
+phase detector than the ones we've
+ 
+
+ align:start position:0%
+phase detector than the ones we've
+talked about
+
+ align:start position:0%
+talked about
+ 
+
+ align:start position:0%
+talked about
+here the uh uh for example there are
+
+ align:start position:0%
+here the uh uh for example there are
+ 
+
+ align:start position:0%
+here the uh uh for example there are
+more complicated more sophisticated uh
+
+ align:start position:0%
+more complicated more sophisticated uh
+ 
+
+ align:start position:0%
+more complicated more sophisticated uh
+phase detectors most of them digital in
+
+ align:start position:0%
+phase detectors most of them digital in
+ 
+
+ align:start position:0%
+phase detectors most of them digital in
+nature uh there are several that are
+
+ align:start position:0%
+nature uh there are several that are
+ 
+
+ align:start position:0%
+nature uh there are several that are
+available in integrated circuit form
+
+ align:start position:0%
+available in integrated circuit form
+ 
+
+ align:start position:0%
+available in integrated circuit form
+although we chose not to use them in
+
+ align:start position:0%
+although we chose not to use them in
+ 
+
+ align:start position:0%
+although we chose not to use them in
+this particular system there are several
+
+ align:start position:0%
+this particular system there are several
+ 
+
+ align:start position:0%
+this particular system there are several
+uh which keep track of which frequency
+
+ align:start position:0%
+uh which keep track of which frequency
+ 
+
+ align:start position:0%
+uh which keep track of which frequency
+is higher they are ones that work in in
+
+ align:start position:0%
+is higher they are ones that work in in
+ 
+
+ align:start position:0%
+is higher they are ones that work in in
+basically the mode we've described when
+
+ align:start position:0%
+basically the mode we've described when
+ 
+
+ align:start position:0%
+basically the mode we've described when
+the two frequencies applied to them are
+
+ align:start position:0%
+the two frequencies applied to them are
+ 
+
+ align:start position:0%
+the two frequencies applied to them are
+identical but when the frequencies are
+
+ align:start position:0%
+identical but when the frequencies are
+ 
+
+ align:start position:0%
+identical but when the frequencies are
+different such that you've slipped by a
+
+ align:start position:0%
+different such that you've slipped by a
+ 
+
+ align:start position:0%
+different such that you've slipped by a
+cycle between the one between the two
+
+ align:start position:0%
+cycle between the one between the two
+ 
+
+ align:start position:0%
+cycle between the one between the two
+inputs so that they've slipped relative
+
+ align:start position:0%
+inputs so that they've slipped relative
+ 
+
+ align:start position:0%
+inputs so that they've slipped relative
+to to each other by a cycle why then the
+
+ align:start position:0%
+to to each other by a cycle why then the
+ 
+
+ align:start position:0%
+to to each other by a cycle why then the
+phase detector hangs up and consistently
+
+ align:start position:0%
+phase detector hangs up and consistently
+ 
+
+ align:start position:0%
+phase detector hangs up and consistently
+gives you either a high output or a low
+
+ align:start position:0%
+gives you either a high output or a low
+ 
+
+ align:start position:0%
+gives you either a high output or a low
+output and that difference indicates
+
+ align:start position:0%
+output and that difference indicates
+ 
+
+ align:start position:0%
+output and that difference indicates
+which direction you should change the
+
+ align:start position:0%
+which direction you should change the
+ 
+
+ align:start position:0%
+which direction you should change the
+output frequency to get into
+
+ align:start position:0%
+output frequency to get into
+ 
+
+ align:start position:0%
+output frequency to get into
+correspondence with the command
+
+ align:start position:0%
+correspondence with the command
+ 
+
+ align:start position:0%
+correspondence with the command
+frequency the uh another possibility for
+
+ align:start position:0%
+frequency the uh another possibility for
+ 
+
+ align:start position:0%
+frequency the uh another possibility for
+a phase detector that has again a wide
+
+ align:start position:0%
+a phase detector that has again a wide
+ 
+
+ align:start position:0%
+a phase detector that has again a wide
+dynamic range uh if our signals are
+
+ align:start position:0%
+dynamic range uh if our signals are
+ 
+
+ align:start position:0%
+dynamic range uh if our signals are
+digital in nature is to Simply use a an
+
+ align:start position:0%
+digital in nature is to Simply use a an
+ 
+
+ align:start position:0%
+digital in nature is to Simply use a an
+up down counter as the the phase
+
+ align:start position:0%
+up down counter as the the phase
+ 
+
+ align:start position:0%
+up down counter as the the phase
+detecting element we'll see an example
+
+ align:start position:0%
+detecting element we'll see an example
+ 
+
+ align:start position:0%
+detecting element we'll see an example
+of that actually in the in the next
+
+ align:start position:0%
+of that actually in the in the next
+ 
+
+ align:start position:0%
+of that actually in the in the next
+lecture where I build a particular kind
+
+ align:start position:0%
+lecture where I build a particular kind
+ 
+
+ align:start position:0%
+lecture where I build a particular kind
+of a phase locked Loop and I use an up
+
+ align:start position:0%
+of a phase locked Loop and I use an up
+ 
+
+ align:start position:0%
+of a phase locked Loop and I use an up
+down counter as the phase detector
+
+ align:start position:0%
+down counter as the phase detector
+ 
+
+ align:start position:0%
+down counter as the phase detector
+uh again one might Envision such a loop
+
+ align:start position:0%
+uh again one might Envision such a loop
+ 
+
+ align:start position:0%
+uh again one might Envision such a loop
+operating when the two frequencies
+
+ align:start position:0%
+operating when the two frequencies
+ 
+
+ align:start position:0%
+operating when the two frequencies
+applied to it are identical it works as
+
+ align:start position:0%
+applied to it are identical it works as
+ 
+
+ align:start position:0%
+applied to it are identical it works as
+we've described we get a a signal uh
+
+ align:start position:0%
+we've described we get a a signal uh
+ 
+
+ align:start position:0%
+we've described we get a a signal uh
+from it which basically is averaged in
+
+ align:start position:0%
+from it which basically is averaged in
+ 
+
+ align:start position:0%
+from it which basically is averaged in
+order to get uh a phase relative phase
+
+ align:start position:0%
+order to get uh a phase relative phase
+ 
+
+ align:start position:0%
+order to get uh a phase relative phase
+error when the two signals are are
+
+ align:start position:0%
+error when the two signals are are
+ 
+
+ align:start position:0%
+error when the two signals are are
+nearly identical the U or when the two
+
+ align:start position:0%
+nearly identical the U or when the two
+ 
+
+ align:start position:0%
+nearly identical the U or when the two
+frequencies are identical but there's a
+
+ align:start position:0%
+frequencies are identical but there's a
+ 
+
+ align:start position:0%
+frequencies are identical but there's a
+relative phase difference between them
+
+ align:start position:0%
+relative phase difference between them
+ 
+
+ align:start position:0%
+relative phase difference between them
+we have some sort of a digital signal
+
+ align:start position:0%
+we have some sort of a digital signal
+ 
+
+ align:start position:0%
+we have some sort of a digital signal
+that's averaged
+
+ align:start position:0%
+that's averaged
+ 
+
+ align:start position:0%
+that's averaged
+the when the uh uh frequencies now
+
+ align:start position:0%
+the when the uh uh frequencies now
+ 
+
+ align:start position:0%
+the when the uh uh frequencies now
+differ why the up down counter
+
+ align:start position:0%
+differ why the up down counter
+ 
+
+ align:start position:0%
+differ why the up down counter
+accumulates counts either up counts or
+
+ align:start position:0%
+accumulates counts either up counts or
+ 
+
+ align:start position:0%
+accumulates counts either up counts or
+down counts depending on whether the
+
+ align:start position:0%
+down counts depending on whether the
+ 
+
+ align:start position:0%
+down counts depending on whether the
+command frequency or the response of the
+
+ align:start position:0%
+command frequency or the response of the
+ 
+
+ align:start position:0%
+command frequency or the response of the
+circuit uh is greater uh the state of
+
+ align:start position:0%
+circuit uh is greater uh the state of
+ 
+
+ align:start position:0%
+circuit uh is greater uh the state of
+that counter then is a direct measure of
+
+ align:start position:0%
+that counter then is a direct measure of
+ 
+
+ align:start position:0%
+that counter then is a direct measure of
+the total number of cycles that we've
+
+ align:start position:0%
+the total number of cycles that we've
+ 
+
+ align:start position:0%
+the total number of cycles that we've
+slipped between the two we can then
+
+ align:start position:0%
+slipped between the two we can then
+ 
+
+ align:start position:0%
+slipped between the two we can then
+conceptually D to a convert the output
+
+ align:start position:0%
+conceptually D to a convert the output
+ 
+
+ align:start position:0%
+conceptually D to a convert the output
+of the counter get an analog signal
+
+ align:start position:0%
+of the counter get an analog signal
+ 
+
+ align:start position:0%
+of the counter get an analog signal
+that's a measure of the total number of
+
+ align:start position:0%
+that's a measure of the total number of
+ 
+
+ align:start position:0%
+that's a measure of the total number of
+Cycles the total phase error we now
+
+ align:start position:0%
+Cycles the total phase error we now
+ 
+
+ align:start position:0%
+Cycles the total phase error we now
+don't have this cyclical nature where
+
+ align:start position:0%
+don't have this cyclical nature where
+ 
+
+ align:start position:0%
+don't have this cyclical nature where
+things cycle every 180 degrees of
+
+ align:start position:0%
+things cycle every 180 degrees of
+ 
+
+ align:start position:0%
+things cycle every 180 degrees of
+relative phase error every 360 Dees and
+
+ align:start position:0%
+relative phase error every 360 Dees and
+ 
+
+ align:start position:0%
+relative phase error every 360 Dees and
+we're able to keep a complete measure of
+
+ align:start position:0%
+we're able to keep a complete measure of
+ 
+
+ align:start position:0%
+we're able to keep a complete measure of
+the total phase error of the system the
+
+ align:start position:0%
+the total phase error of the system the
+ 
+
+ align:start position:0%
+the total phase error of the system the
+total accumulated phase error and uh in
+
+ align:start position:0%
+total accumulated phase error and uh in
+ 
+
+ align:start position:0%
+total accumulated phase error and uh in
+that way we're able to build a system
+
+ align:start position:0%
+that way we're able to build a system
+ 
+
+ align:start position:0%
+that way we're able to build a system
+that's linear for very large phase
+
+ align:start position:0%
+that's linear for very large phase
+ 
+
+ align:start position:0%
+that's linear for very large phase
+differences many cycles of phase error
+
+ align:start position:0%
+differences many cycles of phase error
+ 
+
+ align:start position:0%
+differences many cycles of phase error
+depending on the length of the up down
+
+ align:start position:0%
+depending on the length of the up down
+ 
+
+ align:start position:0%
+depending on the length of the up down
+counter and that will enable us to build
+
+ align:start position:0%
+counter and that will enable us to build
+ 
+
+ align:start position:0%
+counter and that will enable us to build
+a a system that that remain that that
+
+ align:start position:0%
+a a system that that remain that that
+ 
+
+ align:start position:0%
+a a system that that remain that that
+exhibits linear responses for very large
+
+ align:start position:0%
+exhibits linear responses for very large
+ 
+
+ align:start position:0%
+exhibits linear responses for very large
+changes in the commanded frequency and
+
+ align:start position:0%
+changes in the commanded frequency and
+ 
+
+ align:start position:0%
+changes in the commanded frequency and
+in that way people are able to build
+
+ align:start position:0%
+in that way people are able to build
+ 
+
+ align:start position:0%
+in that way people are able to build
+phase locked Loops that's one technique
+
+ align:start position:0%
+phase locked Loops that's one technique
+ 
+
+ align:start position:0%
+phase locked Loops that's one technique
+at least used to build phase locked
+
+ align:start position:0%
+at least used to build phase locked
+ 
+
+ align:start position:0%
+at least used to build phase locked
+Loops that have wide dynamic range we
+
+ align:start position:0%
+Loops that have wide dynamic range we
+ 
+
+ align:start position:0%
+Loops that have wide dynamic range we
+have one more demo uh we can use this
+
+ align:start position:0%
+have one more demo uh we can use this
+ 
+
+ align:start position:0%
+have one more demo uh we can use this
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+for uh here what we're looking at is uh
+
+ align:start position:0%
+for uh here what we're looking at is uh
+ 
+
+ align:start position:0%
+for uh here what we're looking at is uh
+again using effectively the same setup
+
+ align:start position:0%
+again using effectively the same setup
+ 
+
+ align:start position:0%
+again using effectively the same setup
+but where we've made a a couple of
+
+ align:start position:0%
+but where we've made a a couple of
+ 
+
+ align:start position:0%
+but where we've made a a couple of
+modific ations to component values so
+
+ align:start position:0%
+modific ations to component values so
+ 
+
+ align:start position:0%
+modific ations to component values so
+that we've increased the dynamic range
+
+ align:start position:0%
+that we've increased the dynamic range
+ 
+
+ align:start position:0%
+that we've increased the dynamic range
+of the circuit the circuit with
+
+ align:start position:0%
+of the circuit the circuit with
+ 
+
+ align:start position:0%
+of the circuit the circuit with
+parameters as we demonstrated it before
+
+ align:start position:0%
+parameters as we demonstrated it before
+ 
+
+ align:start position:0%
+parameters as we demonstrated it before
+had a very small dynamic range a very
+
+ align:start position:0%
+had a very small dynamic range a very
+ 
+
+ align:start position:0%
+had a very small dynamic range a very
+small range of frequencies over which
+
+ align:start position:0%
+small range of frequencies over which
+ 
+
+ align:start position:0%
+small range of frequencies over which
+the loop would work properly here we've
+
+ align:start position:0%
+the loop would work properly here we've
+ 
+
+ align:start position:0%
+the loop would work properly here we've
+modified that a little bit so there's
+
+ align:start position:0%
+modified that a little bit so there's
+ 
+
+ align:start position:0%
+modified that a little bit so there's
+now a few percent possibility for change
+
+ align:start position:0%
+now a few percent possibility for change
+ 
+
+ align:start position:0%
+now a few percent possibility for change
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+frequency and what we're looking at is
+
+ align:start position:0%
+frequency and what we're looking at is
+ 
+
+ align:start position:0%
+frequency and what we're looking at is
+the uh on one hand again the signal uh
+
+ align:start position:0%
+the uh on one hand again the signal uh
+ 
+
+ align:start position:0%
+the uh on one hand again the signal uh
+that's that's applied to the VC o which
+
+ align:start position:0%
+that's that's applied to the VC o which
+ 
+
+ align:start position:0%
+that's that's applied to the VC o which
+is proportional to the command signal
+
+ align:start position:0%
+is proportional to the command signal
+ 
+
+ align:start position:0%
+is proportional to the command signal
+and then the bottom Trace is a signal
+
+ align:start position:0%
+and then the bottom Trace is a signal
+ 
+
+ align:start position:0%
+and then the bottom Trace is a signal
+not the actual operating frequency of
+
+ align:start position:0%
+not the actual operating frequency of
+ 
+
+ align:start position:0%
+not the actual operating frequency of
+the loop but a divided multiple of the
+
+ align:start position:0%
+the loop but a divided multiple of the
+ 
+
+ align:start position:0%
+the loop but a divided multiple of the
+output frequency at which the phase lock
+
+ align:start position:0%
+output frequency at which the phase lock
+ 
+
+ align:start position:0%
+output frequency at which the phase lock
+loop is operating uh so we can see it
+
+ align:start position:0%
+loop is operating uh so we can see it
+ 
+
+ align:start position:0%
+loop is operating uh so we can see it
+conveniently on the same sort of a time
+
+ align:start position:0%
+conveniently on the same sort of a time
+ 
+
+ align:start position:0%
+conveniently on the same sort of a time
+scale as the vco signal and what we can
+
+ align:start position:0%
+scale as the vco signal and what we can
+ 
+
+ align:start position:0%
+scale as the vco signal and what we can
+observe here is the behavior if we
+
+ align:start position:0%
+observe here is the behavior if we
+ 
+
+ align:start position:0%
+observe here is the behavior if we
+increase the amplitude of the drive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal we again can get into nonlinear
+
+ align:start position:0%
+signal we again can get into nonlinear
+ 
+
+ align:start position:0%
+signal we again can get into nonlinear
+Behavior quite easily but if we don't go
+
+ align:start position:0%
+Behavior quite easily but if we don't go
+ 
+
+ align:start position:0%
+Behavior quite easily but if we don't go
+to that
+
+ align:start position:0%
+to that
+ 
+
+ align:start position:0%
+to that
+point we can see the fing Behavior Uh
+
+ align:start position:0%
+point we can see the fing Behavior Uh
+ 
+
+ align:start position:0%
+point we can see the fing Behavior Uh
+here on
+
+ align:start position:0%
+here on
+ 
+
+ align:start position:0%
+here on
+the first part of the signal if we were
+
+ align:start position:0%
+the first part of the signal if we were
+ 
+
+ align:start position:0%
+the first part of the signal if we were
+direct coupled on the uh signal into the
+
+ align:start position:0%
+direct coupled on the uh signal into the
+ 
+
+ align:start position:0%
+direct coupled on the uh signal into the
+vco we'd see that the first half
+
+ align:start position:0%
+vco we'd see that the first half
+ 
+
+ align:start position:0%
+vco we'd see that the first half
+maintains its DC level and the frequency
+
+ align:start position:0%
+maintains its DC level and the frequency
+ 
+
+ align:start position:0%
+maintains its DC level and the frequency
+on the first part of the cycle does not
+
+ align:start position:0%
+on the first part of the cycle does not
+ 
+
+ align:start position:0%
+on the first part of the cycle does not
+change as we change the amplitude uh
+
+ align:start position:0%
+change as we change the amplitude uh
+ 
+
+ align:start position:0%
+change as we change the amplitude uh
+however the frequency in the second
+
+ align:start position:0%
+however the frequency in the second
+ 
+
+ align:start position:0%
+however the frequency in the second
+portion the uh Following part of the
+
+ align:start position:0%
+portion the uh Following part of the
+ 
+
+ align:start position:0%
+portion the uh Following part of the
+trace we notice changing actually going
+
+ align:start position:0%
+trace we notice changing actually going
+ 
+
+ align:start position:0%
+trace we notice changing actually going
+toward higher frequencies as we increase
+
+ align:start position:0%
+toward higher frequencies as we increase
+ 
+
+ align:start position:0%
+toward higher frequencies as we increase
+the amplitude of the signal applied we
+
+ align:start position:0%
+the amplitude of the signal applied we
+ 
+
+ align:start position:0%
+the amplitude of the signal applied we
+also notice as I say some nonlinear
+
+ align:start position:0%
+also notice as I say some nonlinear
+ 
+
+ align:start position:0%
+also notice as I say some nonlinear
+Behavior there's a little bit of Pop
+
+ align:start position:0%
+Behavior there's a little bit of Pop
+ 
+
+ align:start position:0%
+Behavior there's a little bit of Pop
+there change in mode of behavior in
+
+ align:start position:0%
+there change in mode of behavior in
+ 
+
+ align:start position:0%
+there change in mode of behavior in
+there but as long as we stay down and in
+
+ align:start position:0%
+there but as long as we stay down and in
+ 
+
+ align:start position:0%
+there but as long as we stay down and in
+this range avoid slipping Cycles
+
+ align:start position:0%
+this range avoid slipping Cycles
+ 
+
+ align:start position:0%
+this range avoid slipping Cycles
+basically in the phase detector we get a
+
+ align:start position:0%
+basically in the phase detector we get a
+ 
+
+ align:start position:0%
+basically in the phase detector we get a
+fairly nice indication of the change in
+
+ align:start position:0%
+fairly nice indication of the change in
+ 
+
+ align:start position:0%
+fairly nice indication of the change in
+frequency that occurs from the voltage
+
+ align:start position:0%
+frequency that occurs from the voltage
+ 
+
+ align:start position:0%
+frequency that occurs from the voltage
+controlled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillator this concludes our
+
+ align:start position:0%
+oscillator this concludes our
+ 
+
+ align:start position:0%
+oscillator this concludes our
+introduction to phase lock Loops in the
+
+ align:start position:0%
+introduction to phase lock Loops in the
+ 
+
+ align:start position:0%
+introduction to phase lock Loops in the
+next lecture I'd like to show another
+
+ align:start position:0%
+next lecture I'd like to show another
+ 
+
+ align:start position:0%
+next lecture I'd like to show another
+example of a rather interesting
+
+ align:start position:0%
+example of a rather interesting
+ 
+
+ align:start position:0%
+example of a rather interesting
+application of a phase locked Loop and
+
+ align:start position:0%
+application of a phase locked Loop and
+ 
+
+ align:start position:0%
+application of a phase locked Loop and
+we'll see uh how we can use this to
+
+ align:start position:0%
+we'll see uh how we can use this to
+ 
+
+ align:start position:0%
+we'll see uh how we can use this to
+control a mechan mecal system uh here of
+
+ align:start position:0%
+control a mechan mecal system uh here of
+ 
+
+ align:start position:0%
+control a mechan mecal system uh here of
+course we've been looking at a at a
+
+ align:start position:0%
+course we've been looking at a at a
+ 
+
+ align:start position:0%
+course we've been looking at a at a
+purely electronic system but we'll use
+
+ align:start position:0%
+purely electronic system but we'll use
+ 
+
+ align:start position:0%
+purely electronic system but we'll use
+look at a phase lock technique for motor
+
+ align:start position:0%
+look at a phase lock technique for motor
+ 
+
+ align:start position:0%
+look at a phase lock technique for motor
+speed control in the next lecture thank
+
+ align:start position:0%
+speed control in the next lecture thank
+ 
+
+ align:start position:0%
+speed control in the next lecture thank
+you
\ No newline at end of file
diff --git a/Q47hTa1KvN0.txt b/Q47hTa1KvN0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f588576e41adc3552d4e0c0f254dcebe7ebda4c3
--- /dev/null
+++ b/Q47hTa1KvN0.txt
@@ -0,0 +1,2491 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+recrystallization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a large percentage of a chemist time in
+
+ align:start position:0%
+a large percentage of a chemist time in
+ 
+
+ align:start position:0%
+a large percentage of a chemist time in
+the laboratory is spent purifying
+
+ align:start position:0%
+the laboratory is spent purifying
+ 
+
+ align:start position:0%
+the laboratory is spent purifying
+chemicals learning to use a variety of
+
+ align:start position:0%
+chemicals learning to use a variety of
+ 
+
+ align:start position:0%
+chemicals learning to use a variety of
+different purification techniques
+
+ align:start position:0%
+different purification techniques
+ 
+
+ align:start position:0%
+different purification techniques
+efficiently and effectively is key to
+
+ align:start position:0%
+efficiently and effectively is key to
+ 
+
+ align:start position:0%
+efficiently and effectively is key to
+becoming a successful
+
+ align:start position:0%
+becoming a successful
+ 
+
+ align:start position:0%
+becoming a successful
+experimentalist recrystallization is one
+
+ align:start position:0%
+experimentalist recrystallization is one
+ 
+
+ align:start position:0%
+experimentalist recrystallization is one
+powerful method for the purification of
+
+ align:start position:0%
+powerful method for the purification of
+ 
+
+ align:start position:0%
+powerful method for the purification of
+crystall and solids this video will
+
+ align:start position:0%
+crystall and solids this video will
+ 
+
+ align:start position:0%
+crystall and solids this video will
+outline the purification of napoline by
+
+ align:start position:0%
+outline the purification of napoline by
+ 
+
+ align:start position:0%
+outline the purification of napoline by
+recrystallization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the technique of recrystallization
+
+ align:start position:0%
+the technique of recrystallization
+ 
+
+ align:start position:0%
+the technique of recrystallization
+involves five main steps first an
+
+ align:start position:0%
+involves five main steps first an
+ 
+
+ align:start position:0%
+involves five main steps first an
+appropriate solvent is determined
+
+ align:start position:0%
+appropriate solvent is determined
+ 
+
+ align:start position:0%
+appropriate solvent is determined
+recrystallizations can be carried out
+
+ align:start position:0%
+recrystallizations can be carried out
+ 
+
+ align:start position:0%
+recrystallizations can be carried out
+using either one or a mixture of two
+
+ align:start position:0%
+using either one or a mixture of two
+ 
+
+ align:start position:0%
+using either one or a mixture of two
+solvents depending on the solubility of
+
+ align:start position:0%
+solvents depending on the solubility of
+ 
+
+ align:start position:0%
+solvents depending on the solubility of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sample next the sample is dissolved in a
+
+ align:start position:0%
+sample next the sample is dissolved in a
+ 
+
+ align:start position:0%
+sample next the sample is dissolved in a
+minimal amount of the proper hot
+
+ align:start position:0%
+minimal amount of the proper hot
+ 
+
+ align:start position:0%
+minimal amount of the proper hot
+solvent at this point the solution can
+
+ align:start position:0%
+solvent at this point the solution can
+ 
+
+ align:start position:0%
+solvent at this point the solution can
+be decolorized and insoluble
+
+ align:start position:0%
+be decolorized and insoluble
+ 
+
+ align:start position:0%
+be decolorized and insoluble
+contaminants can be removed by
+
+ align:start position:0%
+contaminants can be removed by
+ 
+
+ align:start position:0%
+contaminants can be removed by
+performing a hot filtration
+
+ align:start position:0%
+performing a hot filtration
+ 
+
+ align:start position:0%
+performing a hot filtration
+the resulting solution is then cooled to
+
+ align:start position:0%
+the resulting solution is then cooled to
+ 
+
+ align:start position:0%
+the resulting solution is then cooled to
+induce
+
+ align:start position:0%
+induce
+ 
+
+ align:start position:0%
+induce
+crystallization and finally the purified
+
+ align:start position:0%
+crystallization and finally the purified
+ 
+
+ align:start position:0%
+crystallization and finally the purified
+crystals are collected by filtration
+
+ align:start position:0%
+crystals are collected by filtration
+ 
+
+ align:start position:0%
+crystals are collected by filtration
+washed and
+
+ align:start position:0%
+washed and
+ 
+
+ align:start position:0%
+washed and
+dried this video will first outline the
+
+ align:start position:0%
+dried this video will first outline the
+ 
+
+ align:start position:0%
+dried this video will first outline the
+general procedure for carrying out a one
+
+ align:start position:0%
+general procedure for carrying out a one
+ 
+
+ align:start position:0%
+general procedure for carrying out a one
+solvent recrystallization of napthalene
+
+ align:start position:0%
+solvent recrystallization of napthalene
+ 
+
+ align:start position:0%
+solvent recrystallization of napthalene
+followed by instructions for adapting
+
+ align:start position:0%
+followed by instructions for adapting
+ 
+
+ align:start position:0%
+followed by instructions for adapting
+the procedure to a two solvent
+
+ align:start position:0%
+the procedure to a two solvent
+ 
+
+ align:start position:0%
+the procedure to a two solvent
+recrystallization choosing an
+
+ align:start position:0%
+recrystallization choosing an
+ 
+
+ align:start position:0%
+recrystallization choosing an
+appropriate solvent for a
+
+ align:start position:0%
+appropriate solvent for a
+ 
+
+ align:start position:0%
+appropriate solvent for a
+recrystallization is a very important
+
+ align:start position:0%
+recrystallization is a very important
+ 
+
+ align:start position:0%
+recrystallization is a very important
+step you won't get acceptable results if
+
+ align:start position:0%
+step you won't get acceptable results if
+ 
+
+ align:start position:0%
+step you won't get acceptable results if
+you don't pick carefully it is helpful
+
+ align:start position:0%
+you don't pick carefully it is helpful
+ 
+
+ align:start position:0%
+you don't pick carefully it is helpful
+to have a variety of solvents at your
+
+ align:start position:0%
+to have a variety of solvents at your
+ 
+
+ align:start position:0%
+to have a variety of solvents at your
+disposal if solubility data for your
+
+ align:start position:0%
+disposal if solubility data for your
+ 
+
+ align:start position:0%
+disposal if solubility data for your
+compounds has been published this will
+
+ align:start position:0%
+compounds has been published this will
+ 
+
+ align:start position:0%
+compounds has been published this will
+help you to narrow the range of
+
+ align:start position:0%
+help you to narrow the range of
+ 
+
+ align:start position:0%
+help you to narrow the range of
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+candidates once you have decided on a
+
+ align:start position:0%
+candidates once you have decided on a
+ 
+
+ align:start position:0%
+candidates once you have decided on a
+few Prime contenders you will perform
+
+ align:start position:0%
+few Prime contenders you will perform
+ 
+
+ align:start position:0%
+few Prime contenders you will perform
+solubility tests to find the ideal
+
+ align:start position:0%
+solubility tests to find the ideal
+ 
+
+ align:start position:0%
+solubility tests to find the ideal
+choice you will need a hot water bath
+
+ align:start position:0%
+choice you will need a hot water bath
+ 
+
+ align:start position:0%
+choice you will need a hot water bath
+for the solubility test as well as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recrystallization caution organic
+
+ align:start position:0%
+recrystallization caution organic
+ 
+
+ align:start position:0%
+recrystallization caution organic
+solvents are
+
+ align:start position:0%
+solvents are
+ 
+
+ align:start position:0%
+solvents are
+flammable never heat over an open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flame to set up a water bath place a
+
+ align:start position:0%
+flame to set up a water bath place a
+ 
+
+ align:start position:0%
+flame to set up a water bath place a
+large crystallizing dish about half full
+
+ align:start position:0%
+large crystallizing dish about half full
+ 
+
+ align:start position:0%
+large crystallizing dish about half full
+with water on a hot plate add some
+
+ align:start position:0%
+with water on a hot plate add some
+ 
+
+ align:start position:0%
+with water on a hot plate add some
+boiling stones and turn on the heat
+
+ align:start position:0%
+boiling stones and turn on the heat
+ 
+
+ align:start position:0%
+boiling stones and turn on the heat
+don't turn it up all the way start
+
+ align:start position:0%
+don't turn it up all the way start
+ 
+
+ align:start position:0%
+don't turn it up all the way start
+halfway and adjust from there
+
+ align:start position:0%
+halfway and adjust from there
+ 
+
+ align:start position:0%
+halfway and adjust from there
+to perform a solubility test place
+
+ align:start position:0%
+to perform a solubility test place
+ 
+
+ align:start position:0%
+to perform a solubility test place
+approximately 20 mg of your compound in
+
+ align:start position:0%
+approximately 20 mg of your compound in
+ 
+
+ align:start position:0%
+approximately 20 mg of your compound in
+a test
+
+ align:start position:0%
+a test
+ 
+
+ align:start position:0%
+a test
+tube add a half of a milliliter of the
+
+ align:start position:0%
+tube add a half of a milliliter of the
+ 
+
+ align:start position:0%
+tube add a half of a milliliter of the
+appropriate solvent and swirl wait a
+
+ align:start position:0%
+appropriate solvent and swirl wait a
+ 
+
+ align:start position:0%
+appropriate solvent and swirl wait a
+couple of minutes and then make note of
+
+ align:start position:0%
+couple of minutes and then make note of
+ 
+
+ align:start position:0%
+couple of minutes and then make note of
+whether or not the compound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dissolves for example at room
+
+ align:start position:0%
+dissolves for example at room
+ 
+
+ align:start position:0%
+dissolves for example at room
+temperature napthalene is insoluble in
+
+ align:start position:0%
+temperature napthalene is insoluble in
+ 
+
+ align:start position:0%
+temperature napthalene is insoluble in
+ethanol and water but soluble in uine
+
+ align:start position:0%
+ethanol and water but soluble in uine
+ 
+
+ align:start position:0%
+ethanol and water but soluble in uine
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acetone if there is still solid
+
+ align:start position:0%
+acetone if there is still solid
+ 
+
+ align:start position:0%
+acetone if there is still solid
+remaining clamp the tube and heat it in
+
+ align:start position:0%
+remaining clamp the tube and heat it in
+ 
+
+ align:start position:0%
+remaining clamp the tube and heat it in
+the water bath until the solvent boils
+
+ align:start position:0%
+the water bath until the solvent boils
+ 
+
+ align:start position:0%
+the water bath until the solvent boils
+swirl the tube and make note of whether
+
+ align:start position:0%
+swirl the tube and make note of whether
+ 
+
+ align:start position:0%
+swirl the tube and make note of whether
+or not the compound
+
+ align:start position:0%
+or not the compound
+ 
+
+ align:start position:0%
+or not the compound
+dissolves after heating napthalene is
+
+ align:start position:0%
+dissolves after heating napthalene is
+ 
+
+ align:start position:0%
+dissolves after heating napthalene is
+still insoluble in water but it is now
+
+ align:start position:0%
+still insoluble in water but it is now
+ 
+
+ align:start position:0%
+still insoluble in water but it is now
+soluble in hot
+
+ align:start position:0%
+soluble in hot
+ 
+
+ align:start position:0%
+soluble in hot
+ethanol now that you have finished the
+
+ align:start position:0%
+ethanol now that you have finished the
+ 
+
+ align:start position:0%
+ethanol now that you have finished the
+solubility test how do you decide which
+
+ align:start position:0%
+solubility test how do you decide which
+ 
+
+ align:start position:0%
+solubility test how do you decide which
+solvent to use for your
+
+ align:start position:0%
+solvent to use for your
+ 
+
+ align:start position:0%
+solvent to use for your
+recrystallization the ideal solvent is
+
+ align:start position:0%
+recrystallization the ideal solvent is
+ 
+
+ align:start position:0%
+recrystallization the ideal solvent is
+one in which your compound is insoluble
+
+ align:start position:0%
+one in which your compound is insoluble
+ 
+
+ align:start position:0%
+one in which your compound is insoluble
+at room
+
+ align:start position:0%
+at room
+ 
+
+ align:start position:0%
+at room
+temperature but soluble at the boiling
+
+ align:start position:0%
+temperature but soluble at the boiling
+ 
+
+ align:start position:0%
+temperature but soluble at the boiling
+point remember at room temperature
+
+ align:start position:0%
+point remember at room temperature
+ 
+
+ align:start position:0%
+point remember at room temperature
+napthalene was soluble in both polline
+
+ align:start position:0%
+napthalene was soluble in both polline
+ 
+
+ align:start position:0%
+napthalene was soluble in both polline
+and acetone so neither of these will
+
+ align:start position:0%
+and acetone so neither of these will
+ 
+
+ align:start position:0%
+and acetone so neither of these will
+work after heating napthalene remained
+
+ align:start position:0%
+work after heating napthalene remained
+ 
+
+ align:start position:0%
+work after heating napthalene remained
+insoluble in water even at the boiling
+
+ align:start position:0%
+insoluble in water even at the boiling
+ 
+
+ align:start position:0%
+insoluble in water even at the boiling
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this means that ethanol is the solvent
+
+ align:start position:0%
+this means that ethanol is the solvent
+ 
+
+ align:start position:0%
+this means that ethanol is the solvent
+of choice it dissolves the sample at its
+
+ align:start position:0%
+of choice it dissolves the sample at its
+ 
+
+ align:start position:0%
+of choice it dissolves the sample at its
+boiling point but not at room
+
+ align:start position:0%
+boiling point but not at room
+ 
+
+ align:start position:0%
+boiling point but not at room
+temperature now that we have decided on
+
+ align:start position:0%
+temperature now that we have decided on
+ 
+
+ align:start position:0%
+temperature now that we have decided on
+a solvent it is time to dissolve the
+
+ align:start position:0%
+a solvent it is time to dissolve the
+ 
+
+ align:start position:0%
+a solvent it is time to dissolve the
+sample in some hot
+
+ align:start position:0%
+sample in some hot
+ 
+
+ align:start position:0%
+sample in some hot
+ethanol get ready by heating some
+
+ align:start position:0%
+ethanol get ready by heating some
+ 
+
+ align:start position:0%
+ethanol get ready by heating some
+ethanol in the water bath remember to
+
+ align:start position:0%
+ethanol in the water bath remember to
+ 
+
+ align:start position:0%
+ethanol in the water bath remember to
+add some boiling stones and clamp the
+
+ align:start position:0%
+add some boiling stones and clamp the
+ 
+
+ align:start position:0%
+add some boiling stones and clamp the
+flask securely so that it doesn't tip
+
+ align:start position:0%
+flask securely so that it doesn't tip
+ 
+
+ align:start position:0%
+flask securely so that it doesn't tip
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place the sample in an Erland Meer flask
+
+ align:start position:0%
+place the sample in an Erland Meer flask
+ 
+
+ align:start position:0%
+place the sample in an Erland Meer flask
+but before adding solvent it is a good
+
+ align:start position:0%
+but before adding solvent it is a good
+ 
+
+ align:start position:0%
+but before adding solvent it is a good
+idea to set aside a small Crystal it may
+
+ align:start position:0%
+idea to set aside a small Crystal it may
+ 
+
+ align:start position:0%
+idea to set aside a small Crystal it may
+come in handy later if you have trouble
+
+ align:start position:0%
+come in handy later if you have trouble
+ 
+
+ align:start position:0%
+come in handy later if you have trouble
+getting crystals to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form when dissolving your sample use a
+
+ align:start position:0%
+form when dissolving your sample use a
+ 
+
+ align:start position:0%
+form when dissolving your sample use a
+minimal amount of hot solvent this will
+
+ align:start position:0%
+minimal amount of hot solvent this will
+ 
+
+ align:start position:0%
+minimal amount of hot solvent this will
+ensure good recovery of crystals in the
+
+ align:start position:0%
+ensure good recovery of crystals in the
+ 
+
+ align:start position:0%
+ensure good recovery of crystals in the
+end add hot solvent in small amounts
+
+ align:start position:0%
+end add hot solvent in small amounts
+ 
+
+ align:start position:0%
+end add hot solvent in small amounts
+swirling and heating in between each
+
+ align:start position:0%
+swirling and heating in between each
+ 
+
+ align:start position:0%
+swirling and heating in between each
+addition until the sample just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dissolves caution if it won't dissolve
+
+ align:start position:0%
+dissolves caution if it won't dissolve
+ 
+
+ align:start position:0%
+dissolves caution if it won't dissolve
+it's probably an impurity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that the sample is in solution
+
+ align:start position:0%
+now that the sample is in solution
+ 
+
+ align:start position:0%
+now that the sample is in solution
+impurities can be removed through
+
+ align:start position:0%
+impurities can be removed through
+ 
+
+ align:start position:0%
+impurities can be removed through
+decoloration and hot
+
+ align:start position:0%
+decoloration and hot
+ 
+
+ align:start position:0%
+decoloration and hot
+filtration take a close look at the
+
+ align:start position:0%
+filtration take a close look at the
+ 
+
+ align:start position:0%
+filtration take a close look at the
+solution is it the right color for
+
+ align:start position:0%
+solution is it the right color for
+ 
+
+ align:start position:0%
+solution is it the right color for
+example if you're expecting white
+
+ align:start position:0%
+example if you're expecting white
+ 
+
+ align:start position:0%
+example if you're expecting white
+crystals and your solution is yellow
+
+ align:start position:0%
+crystals and your solution is yellow
+ 
+
+ align:start position:0%
+crystals and your solution is yellow
+then there is a soluble
+
+ align:start position:0%
+then there is a soluble
+ 
+
+ align:start position:0%
+then there is a soluble
+impurity one easy way to remove small
+
+ align:start position:0%
+impurity one easy way to remove small
+ 
+
+ align:start position:0%
+impurity one easy way to remove small
+amounts of colored impurities is with
+
+ align:start position:0%
+amounts of colored impurities is with
+ 
+
+ align:start position:0%
+amounts of colored impurities is with
+activated charcoal before adding any
+
+ align:start position:0%
+activated charcoal before adding any
+ 
+
+ align:start position:0%
+activated charcoal before adding any
+charcoal cool Your solution to slightly
+
+ align:start position:0%
+charcoal cool Your solution to slightly
+ 
+
+ align:start position:0%
+charcoal cool Your solution to slightly
+below the boiling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point caution adding charcoal to a
+
+ align:start position:0%
+point caution adding charcoal to a
+ 
+
+ align:start position:0%
+point caution adding charcoal to a
+boiling solution will cause it to boil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over add a small amount of charcoal to
+
+ align:start position:0%
+over add a small amount of charcoal to
+ 
+
+ align:start position:0%
+over add a small amount of charcoal to
+absorb the impurity do not add too much
+
+ align:start position:0%
+absorb the impurity do not add too much
+ 
+
+ align:start position:0%
+absorb the impurity do not add too much
+or the charcoal will also absorb your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compound swirl the flask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boil it in the water bath for 2 to 3
+
+ align:start position:0%
+boil it in the water bath for 2 to 3
+ 
+
+ align:start position:0%
+boil it in the water bath for 2 to 3
+minutes charcoal is very fine and can be
+
+ align:start position:0%
+minutes charcoal is very fine and can be
+ 
+
+ align:start position:0%
+minutes charcoal is very fine and can be
+hard to remove by
+
+ align:start position:0%
+hard to remove by
+ 
+
+ align:start position:0%
+hard to remove by
+filtration it is easiest to add a small
+
+ align:start position:0%
+filtration it is easiest to add a small
+ 
+
+ align:start position:0%
+filtration it is easiest to add a small
+amount of a filtering agent such as sea
+
+ align:start position:0%
+amount of a filtering agent such as sea
+ 
+
+ align:start position:0%
+amount of a filtering agent such as sea
+light to absorb the charcoal and
+
+ align:start position:0%
+light to absorb the charcoal and
+ 
+
+ align:start position:0%
+light to absorb the charcoal and
+facilitate the
+
+ align:start position:0%
+facilitate the
+ 
+
+ align:start position:0%
+facilitate the
+filtration add only a small amount swirl
+
+ align:start position:0%
+filtration add only a small amount swirl
+ 
+
+ align:start position:0%
+filtration add only a small amount swirl
+the flask and heat it once again for 2
+
+ align:start position:0%
+the flask and heat it once again for 2
+ 
+
+ align:start position:0%
+the flask and heat it once again for 2
+to 3 minutes before performing a hot
+
+ align:start position:0%
+to 3 minutes before performing a hot
+ 
+
+ align:start position:0%
+to 3 minutes before performing a hot
+filtration if the solution is is
+
+ align:start position:0%
+filtration if the solution is is
+ 
+
+ align:start position:0%
+filtration if the solution is is
+colorless the decoloration step is
+
+ align:start position:0%
+colorless the decoloration step is
+ 
+
+ align:start position:0%
+colorless the decoloration step is
+unnecessary but you still need to look
+
+ align:start position:0%
+unnecessary but you still need to look
+ 
+
+ align:start position:0%
+unnecessary but you still need to look
+carefully for any undissolved solid in
+
+ align:start position:0%
+carefully for any undissolved solid in
+ 
+
+ align:start position:0%
+carefully for any undissolved solid in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+flask if you find any it can be removed
+
+ align:start position:0%
+flask if you find any it can be removed
+ 
+
+ align:start position:0%
+flask if you find any it can be removed
+by performing a hot gravity filtration
+
+ align:start position:0%
+by performing a hot gravity filtration
+ 
+
+ align:start position:0%
+by performing a hot gravity filtration
+with fluted filter paper vacuum
+
+ align:start position:0%
+with fluted filter paper vacuum
+ 
+
+ align:start position:0%
+with fluted filter paper vacuum
+filtrations cool the solution too much
+
+ align:start position:0%
+filtrations cool the solution too much
+ 
+
+ align:start position:0%
+filtrations cool the solution too much
+and crystals are lost on the filter
+
+ align:start position:0%
+and crystals are lost on the filter
+ 
+
+ align:start position:0%
+and crystals are lost on the filter
+paper and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+funnel before filtering Your solution
+
+ align:start position:0%
+funnel before filtering Your solution
+ 
+
+ align:start position:0%
+funnel before filtering Your solution
+add some excess solvent and heat it to
+
+ align:start position:0%
+add some excess solvent and heat it to
+ 
+
+ align:start position:0%
+add some excess solvent and heat it to
+the boiling point to ensure that the
+
+ align:start position:0%
+the boiling point to ensure that the
+ 
+
+ align:start position:0%
+the boiling point to ensure that the
+compound stays dissolved during the
+
+ align:start position:0%
+compound stays dissolved during the
+ 
+
+ align:start position:0%
+compound stays dissolved during the
+filtration wet the filter paper with
+
+ align:start position:0%
+filtration wet the filter paper with
+ 
+
+ align:start position:0%
+filtration wet the filter paper with
+some hot solvent and filter the solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rinse the flask two or three times with
+
+ align:start position:0%
+rinse the flask two or three times with
+ 
+
+ align:start position:0%
+rinse the flask two or three times with
+hot solvent filtering each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rinse finally rinse the filter paper
+
+ align:start position:0%
+rinse finally rinse the filter paper
+ 
+
+ align:start position:0%
+rinse finally rinse the filter paper
+with hot solvent to minimize product
+
+ align:start position:0%
+with hot solvent to minimize product
+ 
+
+ align:start position:0%
+with hot solvent to minimize product
+loss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystals frequently form in the filtrate
+
+ align:start position:0%
+crystals frequently form in the filtrate
+ 
+
+ align:start position:0%
+crystals frequently form in the filtrate
+during the filtration but they easily
+
+ align:start position:0%
+during the filtration but they easily
+ 
+
+ align:start position:0%
+during the filtration but they easily
+redissolve with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heating caution your compound is no
+
+ align:start position:0%
+heating caution your compound is no
+ 
+
+ align:start position:0%
+heating caution your compound is no
+longer dissolved in a minimum amount of
+
+ align:start position:0%
+longer dissolved in a minimum amount of
+ 
+
+ align:start position:0%
+longer dissolved in a minimum amount of
+solvent before proceeding to The Next
+
+ align:start position:0%
+solvent before proceeding to The Next
+ 
+
+ align:start position:0%
+solvent before proceeding to The Next
+Step you need to boil away the excess
+
+ align:start position:0%
+Step you need to boil away the excess
+ 
+
+ align:start position:0%
+Step you need to boil away the excess
+solvent remember to add a few boiling
+
+ align:start position:0%
+solvent remember to add a few boiling
+ 
+
+ align:start position:0%
+solvent remember to add a few boiling
+stones to the solution and boil until
+
+ align:start position:0%
+stones to the solution and boil until
+ 
+
+ align:start position:0%
+stones to the solution and boil until
+solid begins to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form at this point add a small amount of
+
+ align:start position:0%
+form at this point add a small amount of
+ 
+
+ align:start position:0%
+form at this point add a small amount of
+hot solvent to redissolve the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solid when your sample is once again
+
+ align:start position:0%
+solid when your sample is once again
+ 
+
+ align:start position:0%
+solid when your sample is once again
+dissolved in the minimum amount of
+
+ align:start position:0%
+dissolved in the minimum amount of
+ 
+
+ align:start position:0%
+dissolved in the minimum amount of
+solvent set it side to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool cover the flask to prevent
+
+ align:start position:0%
+cool cover the flask to prevent
+ 
+
+ align:start position:0%
+cool cover the flask to prevent
+contamination with Airborne particles
+
+ align:start position:0%
+contamination with Airborne particles
+ 
+
+ align:start position:0%
+contamination with Airborne particles
+and allow it to cool to room temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+undisturbed the flask can also be placed
+
+ align:start position:0%
+undisturbed the flask can also be placed
+ 
+
+ align:start position:0%
+undisturbed the flask can also be placed
+in a beaker stuffed with a paper towel
+
+ align:start position:0%
+in a beaker stuffed with a paper towel
+ 
+
+ align:start position:0%
+in a beaker stuffed with a paper towel
+to slow down the Cooling and promote
+
+ align:start position:0%
+to slow down the Cooling and promote
+ 
+
+ align:start position:0%
+to slow down the Cooling and promote
+slow crystal growth this is especially
+
+ align:start position:0%
+slow crystal growth this is especially
+ 
+
+ align:start position:0%
+slow crystal growth this is especially
+helpful in a cold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laboratory ideally crystals will begin
+
+ align:start position:0%
+laboratory ideally crystals will begin
+ 
+
+ align:start position:0%
+laboratory ideally crystals will begin
+to form as the solution cools you may
+
+ align:start position:0%
+to form as the solution cools you may
+ 
+
+ align:start position:0%
+to form as the solution cools you may
+want to watch it can be very beautiful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+if the solution reaches room temperature
+
+ align:start position:0%
+if the solution reaches room temperature
+ 
+
+ align:start position:0%
+if the solution reaches room temperature
+without crystal growth you may want to
+
+ align:start position:0%
+without crystal growth you may want to
+ 
+
+ align:start position:0%
+without crystal growth you may want to
+try a trick or two to jump start the
+
+ align:start position:0%
+try a trick or two to jump start the
+ 
+
+ align:start position:0%
+try a trick or two to jump start the
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first try scratching the side or bottom
+
+ align:start position:0%
+first try scratching the side or bottom
+ 
+
+ align:start position:0%
+first try scratching the side or bottom
+of the flask with a glass rod don't
+
+ align:start position:0%
+of the flask with a glass rod don't
+ 
+
+ align:start position:0%
+of the flask with a glass rod don't
+press too hard or you'll break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it if that doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work try adding the seed Crystal that
+
+ align:start position:0%
+work try adding the seed Crystal that
+ 
+
+ align:start position:0%
+work try adding the seed Crystal that
+you set aside at the beginning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you forgot to set aside a seed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Crystal you can also try dipping a glass
+
+ align:start position:0%
+Crystal you can also try dipping a glass
+ 
+
+ align:start position:0%
+Crystal you can also try dipping a glass
+rod in the solution letting it dry so
+
+ align:start position:0%
+rod in the solution letting it dry so
+ 
+
+ align:start position:0%
+rod in the solution letting it dry so
+that the minute crystals form on the
+
+ align:start position:0%
+that the minute crystals form on the
+ 
+
+ align:start position:0%
+that the minute crystals form on the
+surface and then dipping it back in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when crystallization has begun and your
+
+ align:start position:0%
+when crystallization has begun and your
+ 
+
+ align:start position:0%
+when crystallization has begun and your
+flask is at room temperature place it in
+
+ align:start position:0%
+flask is at room temperature place it in
+ 
+
+ align:start position:0%
+flask is at room temperature place it in
+an ice bath to drive the crystallization
+
+ align:start position:0%
+an ice bath to drive the crystallization
+ 
+
+ align:start position:0%
+an ice bath to drive the crystallization
+to completion leave it in the ice bath
+
+ align:start position:0%
+to completion leave it in the ice bath
+ 
+
+ align:start position:0%
+to completion leave it in the ice bath
+for at least 15 minutes before
+
+ align:start position:0%
+for at least 15 minutes before
+ 
+
+ align:start position:0%
+for at least 15 minutes before
+collecting the
+
+ align:start position:0%
+collecting the
+ 
+
+ align:start position:0%
+collecting the
+crystals the final step in a
+
+ align:start position:0%
+crystals the final step in a
+ 
+
+ align:start position:0%
+crystals the final step in a
+recrystallization is collecting and
+
+ align:start position:0%
+recrystallization is collecting and
+ 
+
+ align:start position:0%
+recrystallization is collecting and
+washing the purified crystals to do this
+
+ align:start position:0%
+washing the purified crystals to do this
+ 
+
+ align:start position:0%
+washing the purified crystals to do this
+you will need a flask of ice cold
+
+ align:start position:0%
+you will need a flask of ice cold
+ 
+
+ align:start position:0%
+you will need a flask of ice cold
+solvent ethanol in this case and a
+
+ align:start position:0%
+solvent ethanol in this case and a
+ 
+
+ align:start position:0%
+solvent ethanol in this case and a
+vacuum filtration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+setup always use a clean dry flask to
+
+ align:start position:0%
+setup always use a clean dry flask to
+ 
+
+ align:start position:0%
+setup always use a clean dry flask to
+collect the filate in many cases a
+
+ align:start position:0%
+collect the filate in many cases a
+ 
+
+ align:start position:0%
+collect the filate in many cases a
+second batch of crystals can be obtained
+
+ align:start position:0%
+second batch of crystals can be obtained
+ 
+
+ align:start position:0%
+second batch of crystals can be obtained
+by concentrating the mother liquor and
+
+ align:start position:0%
+by concentrating the mother liquor and
+ 
+
+ align:start position:0%
+by concentrating the mother liquor and
+crystallizing a second time turn the
+
+ align:start position:0%
+crystallizing a second time turn the
+ 
+
+ align:start position:0%
+crystallizing a second time turn the
+vacuum on and wet the filter paper with
+
+ align:start position:0%
+vacuum on and wet the filter paper with
+ 
+
+ align:start position:0%
+vacuum on and wet the filter paper with
+a small amount of cold
+
+ align:start position:0%
+a small amount of cold
+ 
+
+ align:start position:0%
+a small amount of cold
+solvent pour the crystals and the mother
+
+ align:start position:0%
+solvent pour the crystals and the mother
+ 
+
+ align:start position:0%
+solvent pour the crystals and the mother
+liquor onto the funnel using cold
+
+ align:start position:0%
+liquor onto the funnel using cold
+ 
+
+ align:start position:0%
+liquor onto the funnel using cold
+solvent to transfer all of the crystals
+
+ align:start position:0%
+solvent to transfer all of the crystals
+ 
+
+ align:start position:0%
+solvent to transfer all of the crystals
+from the FL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flask use cold solvent to wash the
+
+ align:start position:0%
+flask use cold solvent to wash the
+ 
+
+ align:start position:0%
+flask use cold solvent to wash the
+crystals and pull air through them to
+
+ align:start position:0%
+crystals and pull air through them to
+ 
+
+ align:start position:0%
+crystals and pull air through them to
+begin the drying process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+after pulling air through the crystals
+
+ align:start position:0%
+after pulling air through the crystals
+ 
+
+ align:start position:0%
+after pulling air through the crystals
+for a few minutes scrape the crystals
+
+ align:start position:0%
+for a few minutes scrape the crystals
+ 
+
+ align:start position:0%
+for a few minutes scrape the crystals
+onto a weighing dish and spread them out
+
+ align:start position:0%
+onto a weighing dish and spread them out
+ 
+
+ align:start position:0%
+onto a weighing dish and spread them out
+to facilitate drying depending on the
+
+ align:start position:0%
+to facilitate drying depending on the
+ 
+
+ align:start position:0%
+to facilitate drying depending on the
+compound the crystals can be dried in a
+
+ align:start position:0%
+compound the crystals can be dried in a
+ 
+
+ align:start position:0%
+compound the crystals can be dried in a
+desiccator an oven or on a vacuum line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when one ideal solvent cannot be found
+
+ align:start position:0%
+when one ideal solvent cannot be found
+ 
+
+ align:start position:0%
+when one ideal solvent cannot be found
+for a crystallization it is possible to
+
+ align:start position:0%
+for a crystallization it is possible to
+ 
+
+ align:start position:0%
+for a crystallization it is possible to
+use a mixture of two
+
+ align:start position:0%
+use a mixture of two
+ 
+
+ align:start position:0%
+use a mixture of two
+solvents once again you must choose the
+
+ align:start position:0%
+solvents once again you must choose the
+ 
+
+ align:start position:0%
+solvents once again you must choose the
+solvents very
+
+ align:start position:0%
+solvents very
+ 
+
+ align:start position:0%
+solvents very
+carefully in the first solvent solvent
+
+ align:start position:0%
+carefully in the first solvent solvent
+ 
+
+ align:start position:0%
+carefully in the first solvent solvent
+one your sample should be soluble even
+
+ align:start position:0%
+one your sample should be soluble even
+ 
+
+ align:start position:0%
+one your sample should be soluble even
+at room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature and in the second solvent
+
+ align:start position:0%
+temperature and in the second solvent
+ 
+
+ align:start position:0%
+temperature and in the second solvent
+solvent 2 your sample must remain
+
+ align:start position:0%
+solvent 2 your sample must remain
+ 
+
+ align:start position:0%
+solvent 2 your sample must remain
+insoluble even at the boiling point
+
+ align:start position:0%
+insoluble even at the boiling point
+ 
+
+ align:start position:0%
+insoluble even at the boiling point
+the two solvents must also be missable
+
+ align:start position:0%
+the two solvents must also be missable
+ 
+
+ align:start position:0%
+the two solvents must also be missable
+at all ratios so that they don't
+
+ align:start position:0%
+at all ratios so that they don't
+ 
+
+ align:start position:0%
+at all ratios so that they don't
+separate out into different layers
+
+ align:start position:0%
+separate out into different layers
+ 
+
+ align:start position:0%
+separate out into different layers
+during the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recrystallization we know from our
+
+ align:start position:0%
+recrystallization we know from our
+ 
+
+ align:start position:0%
+recrystallization we know from our
+solubility tests that napthalene is
+
+ align:start position:0%
+solubility tests that napthalene is
+ 
+
+ align:start position:0%
+solubility tests that napthalene is
+soluble in both toine and acetone even
+
+ align:start position:0%
+soluble in both toine and acetone even
+ 
+
+ align:start position:0%
+soluble in both toine and acetone even
+at room temperature so which one should
+
+ align:start position:0%
+at room temperature so which one should
+ 
+
+ align:start position:0%
+at room temperature so which one should
+we choose to be our solvent
+
+ align:start position:0%
+we choose to be our solvent
+ 
+
+ align:start position:0%
+we choose to be our solvent
+one that depends entirely on our choice
+
+ align:start position:0%
+one that depends entirely on our choice
+ 
+
+ align:start position:0%
+one that depends entirely on our choice
+for solvent
+
+ align:start position:0%
+for solvent
+ 
+
+ align:start position:0%
+for solvent
+2 we know from our Sol ubility tests
+
+ align:start position:0%
+2 we know from our Sol ubility tests
+ 
+
+ align:start position:0%
+2 we know from our Sol ubility tests
+that napthalene is insoluble in water
+
+ align:start position:0%
+that napthalene is insoluble in water
+ 
+
+ align:start position:0%
+that napthalene is insoluble in water
+even at the boiling point that makes
+
+ align:start position:0%
+even at the boiling point that makes
+ 
+
+ align:start position:0%
+even at the boiling point that makes
+water a very good candidate for solvent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to while acetone and water are missible
+
+ align:start position:0%
+to while acetone and water are missible
+ 
+
+ align:start position:0%
+to while acetone and water are missible
+toine and water are
+
+ align:start position:0%
+toine and water are
+ 
+
+ align:start position:0%
+toine and water are
+not the recrystallization of napthalene
+
+ align:start position:0%
+not the recrystallization of napthalene
+ 
+
+ align:start position:0%
+not the recrystallization of napthalene
+will be carried out using acetone as
+
+ align:start position:0%
+will be carried out using acetone as
+ 
+
+ align:start position:0%
+will be carried out using acetone as
+solvent 1 and water as solvent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two as before dissolve your sample in
+
+ align:start position:0%
+two as before dissolve your sample in
+ 
+
+ align:start position:0%
+two as before dissolve your sample in
+the minimal amount of hot solvent in
+
+ align:start position:0%
+the minimal amount of hot solvent in
+ 
+
+ align:start position:0%
+the minimal amount of hot solvent in
+this case solvent one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acetone add just enough hot solvent to
+
+ align:start position:0%
+acetone add just enough hot solvent to
+ 
+
+ align:start position:0%
+acetone add just enough hot solvent to
+obtain a clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution then add solvent two in this
+
+ align:start position:0%
+solution then add solvent two in this
+ 
+
+ align:start position:0%
+solution then add solvent two in this
+case water dropwise until the solution
+
+ align:start position:0%
+case water dropwise until the solution
+ 
+
+ align:start position:0%
+case water dropwise until the solution
+turns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cloudy swirl and heat the solution to
+
+ align:start position:0%
+cloudy swirl and heat the solution to
+ 
+
+ align:start position:0%
+cloudy swirl and heat the solution to
+make sure that the cloudiness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+persists and do not confuse cloudiness
+
+ align:start position:0%
+persists and do not confuse cloudiness
+ 
+
+ align:start position:0%
+persists and do not confuse cloudiness
+with the turbidity that is observed upon
+
+ align:start position:0%
+with the turbidity that is observed upon
+ 
+
+ align:start position:0%
+with the turbidity that is observed upon
+mixing two solvents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together once you have obtained a
+
+ align:start position:0%
+together once you have obtained a
+ 
+
+ align:start position:0%
+together once you have obtained a
+consistently cloudy solution add hot
+
+ align:start position:0%
+consistently cloudy solution add hot
+ 
+
+ align:start position:0%
+consistently cloudy solution add hot
+solvent one dropwise until the solution
+
+ align:start position:0%
+solvent one dropwise until the solution
+ 
+
+ align:start position:0%
+solvent one dropwise until the solution
+just turns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+clear now you're ready to set the
+
+ align:start position:0%
+clear now you're ready to set the
+ 
+
+ align:start position:0%
+clear now you're ready to set the
+solution aside to
+
+ align:start position:0%
+solution aside to
+ 
+
+ align:start position:0%
+solution aside to
+cool once the crystallization is
+
+ align:start position:0%
+cool once the crystallization is
+ 
+
+ align:start position:0%
+cool once the crystallization is
+complete cool down a mixture of solvents
+
+ align:start position:0%
+complete cool down a mixture of solvents
+ 
+
+ align:start position:0%
+complete cool down a mixture of solvents
+in a ratio similar to that which you
+
+ align:start position:0%
+in a ratio similar to that which you
+ 
+
+ align:start position:0%
+in a ratio similar to that which you
+recrystallized
+
+ align:start position:0%
+recrystallized
+ 
+
+ align:start position:0%
+recrystallized
+from the this cold mixture will be used
+
+ align:start position:0%
+from the this cold mixture will be used
+ 
+
+ align:start position:0%
+from the this cold mixture will be used
+to collect and wash your crystals
+
+ align:start position:0%
+to collect and wash your crystals
+ 
+
+ align:start position:0%
+to collect and wash your crystals
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember this video is intended to help
+
+ align:start position:0%
+remember this video is intended to help
+ 
+
+ align:start position:0%
+remember this video is intended to help
+you prepare for lab by providing a
+
+ align:start position:0%
+you prepare for lab by providing a
+ 
+
+ align:start position:0%
+you prepare for lab by providing a
+demonstration of the proper experimental
+
+ align:start position:0%
+demonstration of the proper experimental
+ 
+
+ align:start position:0%
+demonstration of the proper experimental
+technique it is not intended as a
+
+ align:start position:0%
+technique it is not intended as a
+ 
+
+ align:start position:0%
+technique it is not intended as a
+replacement for reading your lab manual
+
+ align:start position:0%
+replacement for reading your lab manual
+ 
+
+ align:start position:0%
+replacement for reading your lab manual
+or the supplementary material in order
+
+ align:start position:0%
+or the supplementary material in order
+ 
+
+ align:start position:0%
+or the supplementary material in order
+to become a great experimentalist it is
+
+ align:start position:0%
+to become a great experimentalist it is
+ 
+
+ align:start position:0%
+to become a great experimentalist it is
+important that you understand both
+
+ align:start position:0%
+important that you understand both
+ 
+
+ align:start position:0%
+important that you understand both
+Theory and technique now it's your turn
+
+ align:start position:0%
+Theory and technique now it's your turn
+ 
+
+ align:start position:0%
+Theory and technique now it's your turn
+good luck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/Q9XXlbNaOXI.txt b/Q9XXlbNaOXI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26fe5f5723c0eaf2c566522467c44306c91ef593
--- /dev/null
+++ b/Q9XXlbNaOXI.txt
@@ -0,0 +1,5523 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the urban Energy Systems and policy
+
+ align:start position:0%
+in the urban Energy Systems and policy
+ 
+
+ align:start position:0%
+in the urban Energy Systems and policy
+plots at MIT my name is David Sue I'm a
+
+ align:start position:0%
+plots at MIT my name is David Sue I'm a
+ 
+
+ align:start position:0%
+plots at MIT my name is David Sue I'm a
+professor of urban studies and planning
+
+ align:start position:0%
+professor of urban studies and planning
+ 
+
+ align:start position:0%
+professor of urban studies and planning
+and today we're going to talk about
+
+ align:start position:0%
+and today we're going to talk about
+ 
+
+ align:start position:0%
+and today we're going to talk about
+cities and adjust energy transition
+
+ align:start position:0%
+cities and adjust energy transition
+ 
+
+ align:start position:0%
+cities and adjust energy transition
+what is a Just Energy transition going
+
+ align:start position:0%
+what is a Just Energy transition going
+ 
+
+ align:start position:0%
+what is a Just Energy transition going
+to look like what does it mean for us to
+
+ align:start position:0%
+to look like what does it mean for us to
+ 
+
+ align:start position:0%
+to look like what does it mean for us to
+try to achieve a just or Equitable
+
+ align:start position:0%
+try to achieve a just or Equitable
+ 
+
+ align:start position:0%
+try to achieve a just or Equitable
+Equitable energy transition
+
+ align:start position:0%
+Equitable energy transition
+ 
+
+ align:start position:0%
+Equitable energy transition
+the readings for today are listed on
+
+ align:start position:0%
+the readings for today are listed on
+ 
+
+ align:start position:0%
+the readings for today are listed on
+this slide a lot of this lecture will be
+
+ align:start position:0%
+this slide a lot of this lecture will be
+ 
+
+ align:start position:0%
+this slide a lot of this lecture will be
+setting up our discussion in class of
+
+ align:start position:0%
+setting up our discussion in class of
+ 
+
+ align:start position:0%
+setting up our discussion in class of
+these readings it'll be a fairly short
+
+ align:start position:0%
+these readings it'll be a fairly short
+ 
+
+ align:start position:0%
+these readings it'll be a fairly short
+lecture today I think that's going to be
+
+ align:start position:0%
+lecture today I think that's going to be
+ 
+
+ align:start position:0%
+lecture today I think that's going to be
+the best way to set up discussion and
+
+ align:start position:0%
+the best way to set up discussion and
+ 
+
+ align:start position:0%
+the best way to set up discussion and
+hopefully we have a lively discussion in
+
+ align:start position:0%
+hopefully we have a lively discussion in
+ 
+
+ align:start position:0%
+hopefully we have a lively discussion in
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+let me just start with a few stories to
+
+ align:start position:0%
+let me just start with a few stories to
+ 
+
+ align:start position:0%
+let me just start with a few stories to
+kind of supplement the reading I'm going
+
+ align:start position:0%
+kind of supplement the reading I'm going
+ 
+
+ align:start position:0%
+kind of supplement the reading I'm going
+to start with this rather hail looking
+
+ align:start position:0%
+to start with this rather hail looking
+ 
+
+ align:start position:0%
+to start with this rather hail looking
+fellow president Theodore Roosevelt he's
+
+ align:start position:0%
+fellow president Theodore Roosevelt he's
+ 
+
+ align:start position:0%
+fellow president Theodore Roosevelt he's
+the 26th president of the United States
+
+ align:start position:0%
+the 26th president of the United States
+ 
+
+ align:start position:0%
+the 26th president of the United States
+He is known in his lifetime as a soldier
+
+ align:start position:0%
+He is known in his lifetime as a soldier
+ 
+
+ align:start position:0%
+He is known in his lifetime as a soldier
+a naturalist a writer a politician
+
+ align:start position:0%
+a naturalist a writer a politician
+ 
+
+ align:start position:0%
+a naturalist a writer a politician
+reformer and imperialist uh he does all
+
+ align:start position:0%
+reformer and imperialist uh he does all
+ 
+
+ align:start position:0%
+reformer and imperialist uh he does all
+this despite being a Harvard graduate
+
+ align:start position:0%
+this despite being a Harvard graduate
+ 
+
+ align:start position:0%
+this despite being a Harvard graduate
+but I would think what's most relevant
+
+ align:start position:0%
+but I would think what's most relevant
+ 
+
+ align:start position:0%
+but I would think what's most relevant
+about his political career is that also
+
+ align:start position:0%
+about his political career is that also
+ 
+
+ align:start position:0%
+about his political career is that also
+he's known as a progressive a term of
+
+ align:start position:0%
+he's known as a progressive a term of
+ 
+
+ align:start position:0%
+he's known as a progressive a term of
+essential Progressive suspicious of big
+
+ align:start position:0%
+essential Progressive suspicious of big
+ 
+
+ align:start position:0%
+essential Progressive suspicious of big
+corporations a trust Buster
+
+ align:start position:0%
+corporations a trust Buster
+ 
+
+ align:start position:0%
+corporations a trust Buster
+reform-minded in favor of clean and
+
+ align:start position:0%
+reform-minded in favor of clean and
+ 
+
+ align:start position:0%
+reform-minded in favor of clean and
+strong government action and
+
+ align:start position:0%
+strong government action and
+ 
+
+ align:start position:0%
+strong government action and
+intervention into the economy
+
+ align:start position:0%
+intervention into the economy
+ 
+
+ align:start position:0%
+intervention into the economy
+that's why it's become quite relevant
+
+ align:start position:0%
+that's why it's become quite relevant
+ 
+
+ align:start position:0%
+that's why it's become quite relevant
+the Roosevelt Institute is one of our
+
+ align:start position:0%
+the Roosevelt Institute is one of our
+ 
+
+ align:start position:0%
+the Roosevelt Institute is one of our
+most Progressive economic think tanks
+
+ align:start position:0%
+most Progressive economic think tanks
+ 
+
+ align:start position:0%
+most Progressive economic think tanks
+he's also for the purposes of our class
+
+ align:start position:0%
+he's also for the purposes of our class
+ 
+
+ align:start position:0%
+he's also for the purposes of our class
+known as a conservationist he's strongly
+
+ align:start position:0%
+known as a conservationist he's strongly
+ 
+
+ align:start position:0%
+known as a conservationist he's strongly
+associated with the U.S national Park
+
+ align:start position:0%
+associated with the U.S national Park
+ 
+
+ align:start position:0%
+associated with the U.S national Park
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+uh there's a quote from Wallace stegner
+
+ align:start position:0%
+uh there's a quote from Wallace stegner
+ 
+
+ align:start position:0%
+uh there's a quote from Wallace stegner
+a noted and honorable writer he called
+
+ align:start position:0%
+a noted and honorable writer he called
+ 
+
+ align:start position:0%
+a noted and honorable writer he called
+the national parks one of the best ideas
+
+ align:start position:0%
+the national parks one of the best ideas
+ 
+
+ align:start position:0%
+the national parks one of the best ideas
+we ever had absolutely American
+
+ align:start position:0%
+we ever had absolutely American
+ 
+
+ align:start position:0%
+we ever had absolutely American
+absolutely Democratic they reflect us at
+
+ align:start position:0%
+absolutely Democratic they reflect us at
+ 
+
+ align:start position:0%
+absolutely Democratic they reflect us at
+our best rather than our worst of course
+
+ align:start position:0%
+our best rather than our worst of course
+ 
+
+ align:start position:0%
+our best rather than our worst of course
+I put the asterisks on the national park
+
+ align:start position:0%
+I put the asterisks on the national park
+ 
+
+ align:start position:0%
+I put the asterisks on the national park
+system because as many people have noted
+
+ align:start position:0%
+system because as many people have noted
+ 
+
+ align:start position:0%
+system because as many people have noted
+throughout history and more recently a
+
+ align:start position:0%
+throughout history and more recently a
+ 
+
+ align:start position:0%
+throughout history and more recently a
+lot of the national park system is also
+
+ align:start position:0%
+lot of the national park system is also
+ 
+
+ align:start position:0%
+lot of the national park system is also
+land appropriated from indigenous
+
+ align:start position:0%
+land appropriated from indigenous
+ 
+
+ align:start position:0%
+land appropriated from indigenous
+peoples of the United States
+
+ align:start position:0%
+peoples of the United States
+ 
+
+ align:start position:0%
+peoples of the United States
+but also relevant for our discussion
+
+ align:start position:0%
+but also relevant for our discussion
+ 
+
+ align:start position:0%
+but also relevant for our discussion
+today Theodore Roosevelt has fairly
+
+ align:start position:0%
+today Theodore Roosevelt has fairly
+ 
+
+ align:start position:0%
+today Theodore Roosevelt has fairly
+troubling racial beliefs even for his
+
+ align:start position:0%
+troubling racial beliefs even for his
+ 
+
+ align:start position:0%
+troubling racial beliefs even for his
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+one could argue that he was in favor of
+
+ align:start position:0%
+one could argue that he was in favor of
+ 
+
+ align:start position:0%
+one could argue that he was in favor of
+immigration but also assimilation of
+
+ align:start position:0%
+immigration but also assimilation of
+ 
+
+ align:start position:0%
+immigration but also assimilation of
+immigrants into a strong American
+
+ align:start position:0%
+immigrants into a strong American
+ 
+
+ align:start position:0%
+immigrants into a strong American
+culture one could argue that he had
+
+ align:start position:0%
+culture one could argue that he had
+ 
+
+ align:start position:0%
+culture one could argue that he had
+Booker T Washington as a dinner guest at
+
+ align:start position:0%
+Booker T Washington as a dinner guest at
+ 
+
+ align:start position:0%
+Booker T Washington as a dinner guest at
+the White House which was considered
+
+ align:start position:0%
+the White House which was considered
+ 
+
+ align:start position:0%
+the White House which was considered
+quite controversial at the time one of
+
+ align:start position:0%
+quite controversial at the time one of
+ 
+
+ align:start position:0%
+quite controversial at the time one of
+the first presidents to entertain a
+
+ align:start position:0%
+the first presidents to entertain a
+ 
+
+ align:start position:0%
+the first presidents to entertain a
+black dinner guest at the White House
+
+ align:start position:0%
+black dinner guest at the White House
+ 
+
+ align:start position:0%
+black dinner guest at the White House
+halbora Keith also known for essentially
+
+ align:start position:0%
+halbora Keith also known for essentially
+ 
+
+ align:start position:0%
+halbora Keith also known for essentially
+advocating race war against Native
+
+ align:start position:0%
+advocating race war against Native
+ 
+
+ align:start position:0%
+advocating race war against Native
+Americans early in his career in his
+
+ align:start position:0%
+Americans early in his career in his
+ 
+
+ align:start position:0%
+Americans early in his career in his
+writings and also prosecuted a black
+
+ align:start position:0%
+writings and also prosecuted a black
+ 
+
+ align:start position:0%
+writings and also prosecuted a black
+regiment in Brownsville Texas for Mutiny
+
+ align:start position:0%
+regiment in Brownsville Texas for Mutiny
+ 
+
+ align:start position:0%
+regiment in Brownsville Texas for Mutiny
+quite unjustly according to the
+
+ align:start position:0%
+quite unjustly according to the
+ 
+
+ align:start position:0%
+quite unjustly according to the
+historical evidence so we have this kind
+
+ align:start position:0%
+historical evidence so we have this kind
+ 
+
+ align:start position:0%
+historical evidence so we have this kind
+of troubling history on one hand he's
+
+ align:start position:0%
+of troubling history on one hand he's
+ 
+
+ align:start position:0%
+of troubling history on one hand he's
+known as a conservationist he's one of
+
+ align:start position:0%
+known as a conservationist he's one of
+ 
+
+ align:start position:0%
+known as a conservationist he's one of
+our more scholarly presidents he writes
+
+ align:start position:0%
+our more scholarly presidents he writes
+ 
+
+ align:start position:0%
+our more scholarly presidents he writes
+about the environment writes about the
+
+ align:start position:0%
+about the environment writes about the
+ 
+
+ align:start position:0%
+about the environment writes about the
+need to conserve nature at the same time
+
+ align:start position:0%
+need to conserve nature at the same time
+ 
+
+ align:start position:0%
+need to conserve nature at the same time
+he also has these problem racial beliefs
+
+ align:start position:0%
+he also has these problem racial beliefs
+ 
+
+ align:start position:0%
+he also has these problem racial beliefs
+let me tell you another story about John
+
+ align:start position:0%
+let me tell you another story about John
+ 
+
+ align:start position:0%
+let me tell you another story about John
+Muir John Muir was born in Scotland in
+
+ align:start position:0%
+Muir John Muir was born in Scotland in
+ 
+
+ align:start position:0%
+Muir John Muir was born in Scotland in
+1838 he is an early naturalist writer
+
+ align:start position:0%
+1838 he is an early naturalist writer
+ 
+
+ align:start position:0%
+1838 he is an early naturalist writer
+early environmentalist he's considered
+
+ align:start position:0%
+early environmentalist he's considered
+ 
+
+ align:start position:0%
+early environmentalist he's considered
+one of the founding fathers of
+
+ align:start position:0%
+one of the founding fathers of
+ 
+
+ align:start position:0%
+one of the founding fathers of
+environmentalism because of a strong
+
+ align:start position:0%
+environmentalism because of a strong
+ 
+
+ align:start position:0%
+environmentalism because of a strong
+idea about human relationships in nature
+
+ align:start position:0%
+idea about human relationships in nature
+ 
+
+ align:start position:0%
+idea about human relationships in nature
+our impact on the earth and the
+
+ align:start position:0%
+our impact on the earth and the
+ 
+
+ align:start position:0%
+our impact on the earth and the
+preservation of the idea of wilderness
+
+ align:start position:0%
+preservation of the idea of wilderness
+ 
+
+ align:start position:0%
+preservation of the idea of wilderness
+he's also closely associated with the
+
+ align:start position:0%
+he's also closely associated with the
+ 
+
+ align:start position:0%
+he's also closely associated with the
+American West the founding of Yosemite
+
+ align:start position:0%
+American West the founding of Yosemite
+ 
+
+ align:start position:0%
+American West the founding of Yosemite
+Park and the founding of the Sierra Club
+
+ align:start position:0%
+Park and the founding of the Sierra Club
+ 
+
+ align:start position:0%
+Park and the founding of the Sierra Club
+many of his writings have the Sierra
+
+ align:start position:0%
+many of his writings have the Sierra
+ 
+
+ align:start position:0%
+many of his writings have the Sierra
+Nevados leading to the founding of the
+
+ align:start position:0%
+Nevados leading to the founding of the
+ 
+
+ align:start position:0%
+Nevados leading to the founding of the
+Sierra Club
+
+ align:start position:0%
+Sierra Club
+ 
+
+ align:start position:0%
+Sierra Club
+he also has recently noted we've also
+
+ align:start position:0%
+he also has recently noted we've also
+ 
+
+ align:start position:0%
+he also has recently noted we've also
+recently noted his troubling racial
+
+ align:start position:0%
+recently noted his troubling racial
+ 
+
+ align:start position:0%
+recently noted his troubling racial
+beliefs most notably in 2020 when the
+
+ align:start position:0%
+beliefs most notably in 2020 when the
+ 
+
+ align:start position:0%
+beliefs most notably in 2020 when the
+executive director of the Sierra Club
+
+ align:start position:0%
+executive director of the Sierra Club
+ 
+
+ align:start position:0%
+executive director of the Sierra Club
+Michael brune apologized for his racial
+
+ align:start position:0%
+Michael brune apologized for his racial
+ 
+
+ align:start position:0%
+Michael brune apologized for his racial
+beliefs and racial writings he writes
+
+ align:start position:0%
+beliefs and racial writings he writes
+ 
+
+ align:start position:0%
+beliefs and racial writings he writes
+early on his career about Native
+
+ align:start position:0%
+early on his career about Native
+ 
+
+ align:start position:0%
+early on his career about Native
+Americans and blacks as lady
+
+ align:start position:0%
+Americans and blacks as lady
+ 
+
+ align:start position:0%
+Americans and blacks as lady
+at the same time later on this other
+
+ align:start position:0%
+at the same time later on this other
+ 
+
+ align:start position:0%
+at the same time later on this other
+Scholars note that he writes about
+
+ align:start position:0%
+Scholars note that he writes about
+ 
+
+ align:start position:0%
+Scholars note that he writes about
+approvingly of Native American culture
+
+ align:start position:0%
+approvingly of Native American culture
+ 
+
+ align:start position:0%
+approvingly of Native American culture
+as having much less impact on the earth
+
+ align:start position:0%
+as having much less impact on the earth
+ 
+
+ align:start position:0%
+as having much less impact on the earth
+other Scholars have noted that his idea
+
+ align:start position:0%
+other Scholars have noted that his idea
+ 
+
+ align:start position:0%
+other Scholars have noted that his idea
+of wilderness essentially assumes a
+
+ align:start position:0%
+of wilderness essentially assumes a
+ 
+
+ align:start position:0%
+of wilderness essentially assumes a
+pristine Wilderness in the absence of
+
+ align:start position:0%
+pristine Wilderness in the absence of
+ 
+
+ align:start position:0%
+pristine Wilderness in the absence of
+people ignoring the presence of
+
+ align:start position:0%
+people ignoring the presence of
+ 
+
+ align:start position:0%
+people ignoring the presence of
+indigenous peoples and cultures and so
+
+ align:start position:0%
+indigenous peoples and cultures and so
+ 
+
+ align:start position:0%
+indigenous peoples and cultures and so
+what I want to do by kind of just
+
+ align:start position:0%
+what I want to do by kind of just
+ 
+
+ align:start position:0%
+what I want to do by kind of just
+talking about his biographies a little
+
+ align:start position:0%
+talking about his biographies a little
+ 
+
+ align:start position:0%
+talking about his biographies a little
+bit is explore the idea of what is
+
+ align:start position:0%
+bit is explore the idea of what is
+ 
+
+ align:start position:0%
+bit is explore the idea of what is
+Justice going to be in a climate context
+
+ align:start position:0%
+Justice going to be in a climate context
+ 
+
+ align:start position:0%
+Justice going to be in a climate context
+do his racial writings matter or does
+
+ align:start position:0%
+do his racial writings matter or does
+ 
+
+ align:start position:0%
+do his racial writings matter or does
+his idea of wilderness and preservation
+
+ align:start position:0%
+his idea of wilderness and preservation
+ 
+
+ align:start position:0%
+his idea of wilderness and preservation
+of wilderness also matter how do they
+
+ align:start position:0%
+of wilderness also matter how do they
+ 
+
+ align:start position:0%
+of wilderness also matter how do they
+matter that's something we're going to
+
+ align:start position:0%
+matter that's something we're going to
+ 
+
+ align:start position:0%
+matter that's something we're going to
+discuss in class
+
+ align:start position:0%
+discuss in class
+ 
+
+ align:start position:0%
+discuss in class
+just to take one more example Frederick
+
+ align:start position:0%
+just to take one more example Frederick
+ 
+
+ align:start position:0%
+just to take one more example Frederick
+Law Olmsted Jr is a noted journalist
+
+ align:start position:0%
+Law Olmsted Jr is a noted journalist
+ 
+
+ align:start position:0%
+Law Olmsted Jr is a noted journalist
+writer farmer and abolitionist a
+
+ align:start position:0%
+writer farmer and abolitionist a
+ 
+
+ align:start position:0%
+writer farmer and abolitionist a
+well-known first writings before he
+
+ align:start position:0%
+well-known first writings before he
+ 
+
+ align:start position:0%
+well-known first writings before he
+becomes a landscape architect but as a
+
+ align:start position:0%
+becomes a landscape architect but as a
+ 
+
+ align:start position:0%
+becomes a landscape architect but as a
+landscape architect he's fairly prolific
+
+ align:start position:0%
+landscape architect he's fairly prolific
+ 
+
+ align:start position:0%
+landscape architect he's fairly prolific
+here in Boston he built the Boston
+
+ align:start position:0%
+here in Boston he built the Boston
+ 
+
+ align:start position:0%
+here in Boston he built the Boston
+Common the public garden the emerald
+
+ align:start position:0%
+Common the public garden the emerald
+ 
+
+ align:start position:0%
+Common the public garden the emerald
+necklace and the fence
+
+ align:start position:0%
+necklace and the fence
+ 
+
+ align:start position:0%
+necklace and the fence
+in New York he builds a prospects park
+
+ align:start position:0%
+in New York he builds a prospects park
+ 
+
+ align:start position:0%
+in New York he builds a prospects park
+in Brooklyn Belle Isle Park in the
+
+ align:start position:0%
+in Brooklyn Belle Isle Park in the
+ 
+
+ align:start position:0%
+in Brooklyn Belle Isle Park in the
+Detroit River the Biltmore Estate in
+
+ align:start position:0%
+Detroit River the Biltmore Estate in
+ 
+
+ align:start position:0%
+Detroit River the Biltmore Estate in
+North Carolina and also designs the U.S
+
+ align:start position:0%
+North Carolina and also designs the U.S
+ 
+
+ align:start position:0%
+North Carolina and also designs the U.S
+Capitol grounds more recently however
+
+ align:start position:0%
+Capitol grounds more recently however
+ 
+
+ align:start position:0%
+Capitol grounds more recently however
+there's been controversy not so much
+
+ align:start position:0%
+there's been controversy not so much
+ 
+
+ align:start position:0%
+there's been controversy not so much
+about his role but about his most noted
+
+ align:start position:0%
+about his role but about his most noted
+ 
+
+ align:start position:0%
+about his role but about his most noted
+perhaps work Central Park Central Park
+
+ align:start position:0%
+perhaps work Central Park Central Park
+ 
+
+ align:start position:0%
+perhaps work Central Park Central Park
+at the time was well north of the city
+
+ align:start position:0%
+at the time was well north of the city
+ 
+
+ align:start position:0%
+at the time was well north of the city
+so actually almost outside of New York
+
+ align:start position:0%
+so actually almost outside of New York
+ 
+
+ align:start position:0%
+so actually almost outside of New York
+City which is I think largely below 34th
+
+ align:start position:0%
+City which is I think largely below 34th
+ 
+
+ align:start position:0%
+City which is I think largely below 34th
+Street
+
+ align:start position:0%
+Street
+ 
+
+ align:start position:0%
+Street
+and at the time New York state
+
+ align:start position:0%
+and at the time New York state
+ 
+
+ align:start position:0%
+and at the time New York state
+legislators basically looked at it as
+
+ align:start position:0%
+legislators basically looked at it as
+ 
+
+ align:start position:0%
+legislators basically looked at it as
+700 Acres of not particularly desirable
+
+ align:start position:0%
+700 Acres of not particularly desirable
+ 
+
+ align:start position:0%
+700 Acres of not particularly desirable
+landscape
+
+ align:start position:0%
+landscape
+ 
+
+ align:start position:0%
+landscape
+Frederick Law Olmstead and his partner
+
+ align:start position:0%
+Frederick Law Olmstead and his partner
+ 
+
+ align:start position:0%
+Frederick Law Olmstead and his partner
+Calvert Beau are well known for our
+
+ align:start position:0%
+Calvert Beau are well known for our
+ 
+
+ align:start position:0%
+Calvert Beau are well known for our
+transforming Central Park into what we
+
+ align:start position:0%
+transforming Central Park into what we
+ 
+
+ align:start position:0%
+transforming Central Park into what we
+know it as today the design has largely
+
+ align:start position:0%
+know it as today the design has largely
+ 
+
+ align:start position:0%
+know it as today the design has largely
+preserved and they build Central Park
+
+ align:start position:0%
+preserved and they build Central Park
+ 
+
+ align:start position:0%
+preserved and they build Central Park
+and they write about Prospect Park as a
+
+ align:start position:0%
+and they write about Prospect Park as a
+ 
+
+ align:start position:0%
+and they write about Prospect Park as a
+open-air area for immigrants and people
+
+ align:start position:0%
+open-air area for immigrants and people
+ 
+
+ align:start position:0%
+open-air area for immigrants and people
+from all backgrounds to mix so they have
+
+ align:start position:0%
+from all backgrounds to mix so they have
+ 
+
+ align:start position:0%
+from all backgrounds to mix so they have
+essentially they have an essentially
+
+ align:start position:0%
+essentially they have an essentially
+ 
+
+ align:start position:0%
+essentially they have an essentially
+Democratic vision of what these parks
+
+ align:start position:0%
+Democratic vision of what these parks
+ 
+
+ align:start position:0%
+Democratic vision of what these parks
+are meant to do in a bustling turn of
+
+ align:start position:0%
+are meant to do in a bustling turn of
+ 
+
+ align:start position:0%
+are meant to do in a bustling turn of
+the century rapidly changing New York
+
+ align:start position:0%
+the century rapidly changing New York
+ 
+
+ align:start position:0%
+the century rapidly changing New York
+City of course more recently Landscape
+
+ align:start position:0%
+City of course more recently Landscape
+ 
+
+ align:start position:0%
+City of course more recently Landscape
+Architects and historians have Unearthed
+
+ align:start position:0%
+Architects and historians have Unearthed
+ 
+
+ align:start position:0%
+Architects and historians have Unearthed
+or noted these presence that it was not
+
+ align:start position:0%
+or noted these presence that it was not
+ 
+
+ align:start position:0%
+or noted these presence that it was not
+actually a Barren landscape as the New
+
+ align:start position:0%
+actually a Barren landscape as the New
+ 
+
+ align:start position:0%
+actually a Barren landscape as the New
+York state legislator wrote about it
+
+ align:start position:0%
+York state legislator wrote about it
+ 
+
+ align:start position:0%
+York state legislator wrote about it
+there were actually several small
+
+ align:start position:0%
+there were actually several small
+ 
+
+ align:start position:0%
+there were actually several small
+villages notably Seneca Village one of
+
+ align:start position:0%
+villages notably Seneca Village one of
+ 
+
+ align:start position:0%
+villages notably Seneca Village one of
+the few middle class black communities
+
+ align:start position:0%
+the few middle class black communities
+ 
+
+ align:start position:0%
+the few middle class black communities
+in New York City apparently it also had
+
+ align:start position:0%
+in New York City apparently it also had
+ 
+
+ align:start position:0%
+in New York City apparently it also had
+German and Irish immigrants but by
+
+ align:start position:0%
+German and Irish immigrants but by
+ 
+
+ align:start position:0%
+German and Irish immigrants but by
+eminent domain the city or the state
+
+ align:start position:0%
+eminent domain the city or the state
+ 
+
+ align:start position:0%
+eminent domain the city or the state
+claims the landscape of Central Park and
+
+ align:start position:0%
+claims the landscape of Central Park and
+ 
+
+ align:start position:0%
+claims the landscape of Central Park and
+essentially raises Seneca Village so
+
+ align:start position:0%
+essentially raises Seneca Village so
+ 
+
+ align:start position:0%
+essentially raises Seneca Village so
+there's a lot more historical writing
+
+ align:start position:0%
+there's a lot more historical writing
+ 
+
+ align:start position:0%
+there's a lot more historical writing
+about Seneca Village recently and the
+
+ align:start position:0%
+about Seneca Village recently and the
+ 
+
+ align:start position:0%
+about Seneca Village recently and the
+question is does this change the legacy
+
+ align:start position:0%
+question is does this change the legacy
+ 
+
+ align:start position:0%
+question is does this change the legacy
+of Frederick Law Olmstead or should we
+
+ align:start position:0%
+of Frederick Law Olmstead or should we
+ 
+
+ align:start position:0%
+of Frederick Law Olmstead or should we
+talk about his Works in a different way
+
+ align:start position:0%
+talk about his Works in a different way
+ 
+
+ align:start position:0%
+talk about his Works in a different way
+and this brings me to uh The Last Story
+
+ align:start position:0%
+and this brings me to uh The Last Story
+ 
+
+ align:start position:0%
+and this brings me to uh The Last Story
+I want to tell you it's about Professor
+
+ align:start position:0%
+I want to tell you it's about Professor
+ 
+
+ align:start position:0%
+I want to tell you it's about Professor
+Robert Bullard considered one of the
+
+ align:start position:0%
+Robert Bullard considered one of the
+ 
+
+ align:start position:0%
+Robert Bullard considered one of the
+leading Scholars on environmental racism
+
+ align:start position:0%
+leading Scholars on environmental racism
+ 
+
+ align:start position:0%
+leading Scholars on environmental racism
+and viral Justice and I think it's just
+
+ align:start position:0%
+and viral Justice and I think it's just
+ 
+
+ align:start position:0%
+and viral Justice and I think it's just
+a good story of how peace gets involved
+
+ align:start position:0%
+a good story of how peace gets involved
+ 
+
+ align:start position:0%
+a good story of how peace gets involved
+in this topic and how he
+
+ align:start position:0%
+in this topic and how he
+ 
+
+ align:start position:0%
+in this topic and how he
+continues to write about these issues
+
+ align:start position:0%
+continues to write about these issues
+ 
+
+ align:start position:0%
+continues to write about these issues
+today there's a 2012 portrait on the
+
+ align:start position:0%
+today there's a 2012 portrait on the
+ 
+
+ align:start position:0%
+today there's a 2012 portrait on the
+left this is a small excerpt on the
+
+ align:start position:0%
+left this is a small excerpt on the
+ 
+
+ align:start position:0%
+left this is a small excerpt on the
+right it's a list of a summary of
+
+ align:start position:0%
+right it's a list of a summary of
+ 
+
+ align:start position:0%
+right it's a list of a summary of
+community disputes for one of his
+
+ align:start position:0%
+community disputes for one of his
+ 
+
+ align:start position:0%
+community disputes for one of his
+earliest writings on environmental
+
+ align:start position:0%
+earliest writings on environmental
+ 
+
+ align:start position:0%
+earliest writings on environmental
+racism
+
+ align:start position:0%
+racism
+ 
+
+ align:start position:0%
+racism
+and essentially lists Grassroots
+
+ align:start position:0%
+and essentially lists Grassroots
+ 
+
+ align:start position:0%
+and essentially lists Grassroots
+movements and throughout the South but
+
+ align:start position:0%
+movements and throughout the South but
+ 
+
+ align:start position:0%
+movements and throughout the South but
+also the American West where communities
+
+ align:start position:0%
+also the American West where communities
+ 
+
+ align:start position:0%
+also the American West where communities
+and neighborhoods are trying to fight
+
+ align:start position:0%
+and neighborhoods are trying to fight
+ 
+
+ align:start position:0%
+and neighborhoods are trying to fight
+back against environmental
+
+ align:start position:0%
+back against environmental
+ 
+
+ align:start position:0%
+back against environmental
+infrastructure that'll be located in
+
+ align:start position:0%
+infrastructure that'll be located in
+ 
+
+ align:start position:0%
+infrastructure that'll be located in
+neighborhoods environmental
+
+ align:start position:0%
+neighborhoods environmental
+ 
+
+ align:start position:0%
+neighborhoods environmental
+infrastructure like landfills smelters
+
+ align:start position:0%
+infrastructure like landfills smelters
+ 
+
+ align:start position:0%
+infrastructure like landfills smelters
+houses waste incinerators petrochemical
+
+ align:start position:0%
+houses waste incinerators petrochemical
+ 
+
+ align:start position:0%
+houses waste incinerators petrochemical
+or binaries that we know will probably
+
+ align:start position:0%
+or binaries that we know will probably
+ 
+
+ align:start position:0%
+or binaries that we know will probably
+have negative environmental or health
+
+ align:start position:0%
+have negative environmental or health
+ 
+
+ align:start position:0%
+have negative environmental or health
+effects on the residents
+
+ align:start position:0%
+effects on the residents
+ 
+
+ align:start position:0%
+effects on the residents
+his wife at the time is a lawyer or his
+
+ align:start position:0%
+his wife at the time is a lawyer or his
+ 
+
+ align:start position:0%
+his wife at the time is a lawyer or his
+wife is a lawyer and at the time she's
+
+ align:start position:0%
+wife is a lawyer and at the time she's
+ 
+
+ align:start position:0%
+wife is a lawyer and at the time she's
+involved in litigation against this
+
+ align:start position:0%
+involved in litigation against this
+ 
+
+ align:start position:0%
+involved in litigation against this
+landfill she asked him to get involved
+
+ align:start position:0%
+landfill she asked him to get involved
+ 
+
+ align:start position:0%
+landfill she asked him to get involved
+in the lawsuit as an expert witness and
+
+ align:start position:0%
+in the lawsuit as an expert witness and
+ 
+
+ align:start position:0%
+in the lawsuit as an expert witness and
+to do research on where landfills are
+
+ align:start position:0%
+to do research on where landfills are
+ 
+
+ align:start position:0%
+to do research on where landfills are
+located he finds that 100 of landfills
+
+ align:start position:0%
+located he finds that 100 of landfills
+ 
+
+ align:start position:0%
+located he finds that 100 of landfills
+in Houston are actually located in black
+
+ align:start position:0%
+in Houston are actually located in black
+ 
+
+ align:start position:0%
+in Houston are actually located in black
+neighborhoods even though only 25
+
+ align:start position:0%
+neighborhoods even though only 25
+ 
+
+ align:start position:0%
+neighborhoods even though only 25
+percent of the population of Houston is
+
+ align:start position:0%
+percent of the population of Houston is
+ 
+
+ align:start position:0%
+percent of the population of Houston is
+black and so he essentially identifies
+
+ align:start position:0%
+black and so he essentially identifies
+ 
+
+ align:start position:0%
+black and so he essentially identifies
+this as a racial phenomenon that these
+
+ align:start position:0%
+this as a racial phenomenon that these
+ 
+
+ align:start position:0%
+this as a racial phenomenon that these
+infrastructures are being located in
+
+ align:start position:0%
+infrastructures are being located in
+ 
+
+ align:start position:0%
+infrastructures are being located in
+Black communities and he starts writing
+
+ align:start position:0%
+Black communities and he starts writing
+ 
+
+ align:start position:0%
+Black communities and he starts writing
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+and so this is a good example or I think
+
+ align:start position:0%
+and so this is a good example or I think
+ 
+
+ align:start position:0%
+and so this is a good example or I think
+all of these stories are good examples
+
+ align:start position:0%
+all of these stories are good examples
+ 
+
+ align:start position:0%
+all of these stories are good examples
+of how we have have to discuss race and
+
+ align:start position:0%
+of how we have have to discuss race and
+ 
+
+ align:start position:0%
+of how we have have to discuss race and
+Justice in environmental context the
+
+ align:start position:0%
+Justice in environmental context the
+ 
+
+ align:start position:0%
+Justice in environmental context the
+1960s and 70s are noted for the
+
+ align:start position:0%
+1960s and 70s are noted for the
+ 
+
+ align:start position:0%
+1960s and 70s are noted for the
+environmental and civil rights movements
+
+ align:start position:0%
+environmental and civil rights movements
+ 
+
+ align:start position:0%
+environmental and civil rights movements
+these civil rights movements obviously
+
+ align:start position:0%
+these civil rights movements obviously
+ 
+
+ align:start position:0%
+these civil rights movements obviously
+typified by the civil rights leaders
+
+ align:start position:0%
+typified by the civil rights leaders
+ 
+
+ align:start position:0%
+typified by the civil rights leaders
+like Martin Luther King Jr or Malcolm X
+
+ align:start position:0%
+like Martin Luther King Jr or Malcolm X
+ 
+
+ align:start position:0%
+like Martin Luther King Jr or Malcolm X
+or Sophie Carmichael and at the same
+
+ align:start position:0%
+or Sophie Carmichael and at the same
+ 
+
+ align:start position:0%
+or Sophie Carmichael and at the same
+time we have the environmental movement
+
+ align:start position:0%
+time we have the environmental movement
+ 
+
+ align:start position:0%
+time we have the environmental movement
+culminating in the Clean Air and clean
+
+ align:start position:0%
+culminating in the Clean Air and clean
+ 
+
+ align:start position:0%
+culminating in the Clean Air and clean
+water acts in the 1970s
+
+ align:start position:0%
+water acts in the 1970s
+ 
+
+ align:start position:0%
+water acts in the 1970s
+these two movements are largely separate
+
+ align:start position:0%
+these two movements are largely separate
+ 
+
+ align:start position:0%
+these two movements are largely separate
+typified by different people and
+
+ align:start position:0%
+typified by different people and
+ 
+
+ align:start position:0%
+typified by different people and
+different leaders
+
+ align:start position:0%
+different leaders
+ 
+
+ align:start position:0%
+different leaders
+and different groups
+
+ align:start position:0%
+and different groups
+ 
+
+ align:start position:0%
+and different groups
+of course there are kind of nascent
+
+ align:start position:0%
+of course there are kind of nascent
+ 
+
+ align:start position:0%
+of course there are kind of nascent
+linkages between some of these issues
+
+ align:start position:0%
+linkages between some of these issues
+ 
+
+ align:start position:0%
+linkages between some of these issues
+the United Church of Christ Commission
+
+ align:start position:0%
+the United Church of Christ Commission
+ 
+
+ align:start position:0%
+the United Church of Christ Commission
+on racial justice issues are reported
+
+ align:start position:0%
+on racial justice issues are reported
+ 
+
+ align:start position:0%
+on racial justice issues are reported
+1987 called toxic waste and race in the
+
+ align:start position:0%
+1987 called toxic waste and race in the
+ 
+
+ align:start position:0%
+1987 called toxic waste and race in the
+United States
+
+ align:start position:0%
+United States
+ 
+
+ align:start position:0%
+United States
+Robert Bullard starts writing about it
+
+ align:start position:0%
+Robert Bullard starts writing about it
+ 
+
+ align:start position:0%
+Robert Bullard starts writing about it
+or after this expert witness testimony
+
+ align:start position:0%
+or after this expert witness testimony
+ 
+
+ align:start position:0%
+or after this expert witness testimony
+in his wife's lawsuit he writes dumping
+
+ align:start position:0%
+in his wife's lawsuit he writes dumping
+ 
+
+ align:start position:0%
+in his wife's lawsuit he writes dumping
+in Dixie in 1990 arguing for convergence
+
+ align:start position:0%
+in Dixie in 1990 arguing for convergence
+ 
+
+ align:start position:0%
+in Dixie in 1990 arguing for convergence
+between the Civil Rights and
+
+ align:start position:0%
+between the Civil Rights and
+ 
+
+ align:start position:0%
+between the Civil Rights and
+environmental movements and he writes
+
+ align:start position:0%
+environmental movements and he writes
+ 
+
+ align:start position:0%
+environmental movements and he writes
+about environmental justice and racism
+
+ align:start position:0%
+about environmental justice and racism
+ 
+
+ align:start position:0%
+about environmental justice and racism
+using very similar terms that we now
+
+ align:start position:0%
+using very similar terms that we now
+ 
+
+ align:start position:0%
+using very similar terms that we now
+think about those things today it's also
+
+ align:start position:0%
+think about those things today it's also
+ 
+
+ align:start position:0%
+think about those things today it's also
+really interesting in these writings how
+
+ align:start position:0%
+really interesting in these writings how
+ 
+
+ align:start position:0%
+really interesting in these writings how
+he writes very clearly that racism plays
+
+ align:start position:0%
+he writes very clearly that racism plays
+ 
+
+ align:start position:0%
+he writes very clearly that racism plays
+a key factor in environmental planning
+
+ align:start position:0%
+a key factor in environmental planning
+ 
+
+ align:start position:0%
+a key factor in environmental planning
+and decision making
+
+ align:start position:0%
+and decision making
+ 
+
+ align:start position:0%
+and decision making
+and what's really striking about his
+
+ align:start position:0%
+and what's really striking about his
+ 
+
+ align:start position:0%
+and what's really striking about his
+writing is that it's a very clear
+
+ align:start position:0%
+writing is that it's a very clear
+ 
+
+ align:start position:0%
+writing is that it's a very clear
+critique of the mainstream environmental
+
+ align:start position:0%
+critique of the mainstream environmental
+ 
+
+ align:start position:0%
+critique of the mainstream environmental
+movement which is separate than the
+
+ align:start position:0%
+movement which is separate than the
+ 
+
+ align:start position:0%
+movement which is separate than the
+Civil Rights Movement he writes it is a
+
+ align:start position:0%
+Civil Rights Movement he writes it is a
+ 
+
+ align:start position:0%
+Civil Rights Movement he writes it is a
+fact of life in the United States that
+
+ align:start position:0%
+fact of life in the United States that
+ 
+
+ align:start position:0%
+fact of life in the United States that
+the mainstream environmental movement is
+
+ align:start position:0%
+the mainstream environmental movement is
+ 
+
+ align:start position:0%
+the mainstream environmental movement is
+only beginning to wake up to the fact of
+
+ align:start position:0%
+only beginning to wake up to the fact of
+ 
+
+ align:start position:0%
+only beginning to wake up to the fact of
+life being racism
+
+ align:start position:0%
+life being racism
+ 
+
+ align:start position:0%
+life being racism
+but just the same year the EPA issues a
+
+ align:start position:0%
+but just the same year the EPA issues a
+ 
+
+ align:start position:0%
+but just the same year the EPA issues a
+report called environmental Equity
+
+ align:start position:0%
+report called environmental Equity
+ 
+
+ align:start position:0%
+report called environmental Equity
+reducing risk for all communities
+
+ align:start position:0%
+reducing risk for all communities
+ 
+
+ align:start position:0%
+reducing risk for all communities
+they very self-consciously choose the
+
+ align:start position:0%
+they very self-consciously choose the
+ 
+
+ align:start position:0%
+they very self-consciously choose the
+phrase environmental equity and they put
+
+ align:start position:0%
+phrase environmental equity and they put
+ 
+
+ align:start position:0%
+phrase environmental equity and they put
+in terms of reducing risk for all
+
+ align:start position:0%
+in terms of reducing risk for all
+ 
+
+ align:start position:0%
+in terms of reducing risk for all
+communities they say in the introduction
+
+ align:start position:0%
+communities they say in the introduction
+ 
+
+ align:start position:0%
+communities they say in the introduction
+that environmental Equity is to study or
+
+ align:start position:0%
+that environmental Equity is to study or
+ 
+
+ align:start position:0%
+that environmental Equity is to study or
+to identify the distribution and effects
+
+ align:start position:0%
+to identify the distribution and effects
+ 
+
+ align:start position:0%
+to identify the distribution and effects
+of environmental problems and the
+
+ align:start position:0%
+of environmental problems and the
+ 
+
+ align:start position:0%
+of environmental problems and the
+policies and processes to reduce
+
+ align:start position:0%
+policies and processes to reduce
+ 
+
+ align:start position:0%
+policies and processes to reduce
+differences in who Bears environmental
+
+ align:start position:0%
+differences in who Bears environmental
+ 
+
+ align:start position:0%
+differences in who Bears environmental
+risks
+
+ align:start position:0%
+risks
+ 
+
+ align:start position:0%
+risks
+and in just the next year the U.S
+
+ align:start position:0%
+and in just the next year the U.S
+ 
+
+ align:start position:0%
+and in just the next year the U.S
+President Bill Clinton issued an
+
+ align:start position:0%
+President Bill Clinton issued an
+ 
+
+ align:start position:0%
+President Bill Clinton issued an
+executive order in 1994 titled Federal
+
+ align:start position:0%
+executive order in 1994 titled Federal
+ 
+
+ align:start position:0%
+executive order in 1994 titled Federal
+actions to address environmental justice
+
+ align:start position:0%
+actions to address environmental justice
+ 
+
+ align:start position:0%
+actions to address environmental justice
+and minority populations and low-income
+
+ align:start position:0%
+and minority populations and low-income
+ 
+
+ align:start position:0%
+and minority populations and low-income
+populations so even in this seven year
+
+ align:start position:0%
+populations so even in this seven year
+ 
+
+ align:start position:0%
+populations so even in this seven year
+period or so in these writings you see
+
+ align:start position:0%
+period or so in these writings you see
+ 
+
+ align:start position:0%
+period or so in these writings you see
+the idea of environmental justice
+
+ align:start position:0%
+the idea of environmental justice
+ 
+
+ align:start position:0%
+the idea of environmental justice
+essentially becoming fully normalized of
+
+ align:start position:0%
+essentially becoming fully normalized of
+ 
+
+ align:start position:0%
+essentially becoming fully normalized of
+course we still have to understand what
+
+ align:start position:0%
+course we still have to understand what
+ 
+
+ align:start position:0%
+course we still have to understand what
+it means
+
+ align:start position:0%
+it means
+ 
+
+ align:start position:0%
+it means
+of course it's also worth pointing out
+
+ align:start position:0%
+of course it's also worth pointing out
+ 
+
+ align:start position:0%
+of course it's also worth pointing out
+that environmentalists are the
+
+ align:start position:0%
+that environmentalists are the
+ 
+
+ align:start position:0%
+that environmentalists are the
+mainstream environmental movement as
+
+ align:start position:0%
+mainstream environmental movement as
+ 
+
+ align:start position:0%
+mainstream environmental movement as
+Robert Bullard calls it is still quite
+
+ align:start position:0%
+Robert Bullard calls it is still quite
+ 
+
+ align:start position:0%
+Robert Bullard calls it is still quite
+separate from the environmental justice
+
+ align:start position:0%
+separate from the environmental justice
+ 
+
+ align:start position:0%
+separate from the environmental justice
+movement here's a headline a very
+
+ align:start position:0%
+movement here's a headline a very
+ 
+
+ align:start position:0%
+movement here's a headline a very
+typical in 2020 about green groups that
+
+ align:start position:0%
+typical in 2020 about green groups that
+ 
+
+ align:start position:0%
+typical in 2020 about green groups that
+are grappling with a history of racism
+
+ align:start position:0%
+are grappling with a history of racism
+ 
+
+ align:start position:0%
+are grappling with a history of racism
+and exclusion
+
+ align:start position:0%
+and exclusion
+ 
+
+ align:start position:0%
+and exclusion
+the environmental movement in America
+
+ align:start position:0%
+the environmental movement in America
+ 
+
+ align:start position:0%
+the environmental movement in America
+has deep ties to the nation's history of
+
+ align:start position:0%
+has deep ties to the nation's history of
+ 
+
+ align:start position:0%
+has deep ties to the nation's history of
+systemic racism and white supremacy this
+
+ align:start position:0%
+systemic racism and white supremacy this
+ 
+
+ align:start position:0%
+systemic racism and white supremacy this
+article writes now as Americans confront
+
+ align:start position:0%
+article writes now as Americans confront
+ 
+
+ align:start position:0%
+article writes now as Americans confront
+racial Injustice Anew powerful Green
+
+ align:start position:0%
+racial Injustice Anew powerful Green
+ 
+
+ align:start position:0%
+racial Injustice Anew powerful Green
+groups like the Sierra Club are
+
+ align:start position:0%
+groups like the Sierra Club are
+ 
+
+ align:start position:0%
+groups like the Sierra Club are
+beginning to reckon with their own
+
+ align:start position:0%
+beginning to reckon with their own
+ 
+
+ align:start position:0%
+beginning to reckon with their own
+histories of hate and exclusion and so
+
+ align:start position:0%
+histories of hate and exclusion and so
+ 
+
+ align:start position:0%
+histories of hate and exclusion and so
+there's significant controversy within
+
+ align:start position:0%
+there's significant controversy within
+ 
+
+ align:start position:0%
+there's significant controversy within
+the Sierra Club itself Sierra Club also
+
+ align:start position:0%
+the Sierra Club itself Sierra Club also
+ 
+
+ align:start position:0%
+the Sierra Club itself Sierra Club also
+closely associated with the idea of
+
+ align:start position:0%
+closely associated with the idea of
+ 
+
+ align:start position:0%
+closely associated with the idea of
+conservation the executive director
+
+ align:start position:0%
+conservation the executive director
+ 
+
+ align:start position:0%
+conservation the executive director
+apologized for John Muir's writings
+
+ align:start position:0%
+apologized for John Muir's writings
+ 
+
+ align:start position:0%
+apologized for John Muir's writings
+about black people and Native Americans
+
+ align:start position:0%
+about black people and Native Americans
+ 
+
+ align:start position:0%
+about black people and Native Americans
+other board members disagreed and argued
+
+ align:start position:0%
+other board members disagreed and argued
+ 
+
+ align:start position:0%
+other board members disagreed and argued
+that the Sierra Club has a strong Legacy
+
+ align:start position:0%
+that the Sierra Club has a strong Legacy
+ 
+
+ align:start position:0%
+that the Sierra Club has a strong Legacy
+of conservation of course the question
+
+ align:start position:0%
+of conservation of course the question
+ 
+
+ align:start position:0%
+of conservation of course the question
+is conservation for who and what's more
+
+ align:start position:0%
+is conservation for who and what's more
+ 
+
+ align:start position:0%
+is conservation for who and what's more
+interesting about the article I
+
+ align:start position:0%
+interesting about the article I
+ 
+
+ align:start position:0%
+interesting about the article I
+encourage you to either listen to it at
+
+ align:start position:0%
+encourage you to either listen to it at
+ 
+
+ align:start position:0%
+encourage you to either listen to it at
+the radio segment or read it is that
+
+ align:start position:0%
+the radio segment or read it is that
+ 
+
+ align:start position:0%
+the radio segment or read it is that
+a reporter from Milwaukee Washington
+
+ align:start position:0%
+a reporter from Milwaukee Washington
+ 
+
+ align:start position:0%
+a reporter from Milwaukee Washington
+Post Daryl fears I started writing about
+
+ align:start position:0%
+Post Daryl fears I started writing about
+ 
+
+ align:start position:0%
+Post Daryl fears I started writing about
+green groups and their lack of diversity
+
+ align:start position:0%
+green groups and their lack of diversity
+ 
+
+ align:start position:0%
+green groups and their lack of diversity
+many years before he said that if you go
+
+ align:start position:0%
+many years before he said that if you go
+ 
+
+ align:start position:0%
+many years before he said that if you go
+to many environmental meetings and
+
+ align:start position:0%
+to many environmental meetings and
+ 
+
+ align:start position:0%
+to many environmental meetings and
+basically essentially see no other black
+
+ align:start position:0%
+basically essentially see no other black
+ 
+
+ align:start position:0%
+basically essentially see no other black
+people there and so he started writing
+
+ align:start position:0%
+people there and so he started writing
+ 
+
+ align:start position:0%
+people there and so he started writing
+about the homogeneity of the
+
+ align:start position:0%
+about the homogeneity of the
+ 
+
+ align:start position:0%
+about the homogeneity of the
+environmental movement then and so
+
+ align:start position:0%
+environmental movement then and so
+ 
+
+ align:start position:0%
+environmental movement then and so
+environmental justice movements are much
+
+ align:start position:0%
+environmental justice movements are much
+ 
+
+ align:start position:0%
+environmental justice movements are much
+more closely associated with Grassroots
+
+ align:start position:0%
+more closely associated with Grassroots
+ 
+
+ align:start position:0%
+more closely associated with Grassroots
+movements and Community groups and the
+
+ align:start position:0%
+movements and Community groups and the
+ 
+
+ align:start position:0%
+movements and Community groups and the
+question is how do we perhaps hopefully
+
+ align:start position:0%
+question is how do we perhaps hopefully
+ 
+
+ align:start position:0%
+question is how do we perhaps hopefully
+bring these two movements together into
+
+ align:start position:0%
+bring these two movements together into
+ 
+
+ align:start position:0%
+bring these two movements together into
+a coalition
+
+ align:start position:0%
+a coalition
+ 
+
+ align:start position:0%
+a coalition
+and so this has spawned many different
+
+ align:start position:0%
+and so this has spawned many different
+ 
+
+ align:start position:0%
+and so this has spawned many different
+kind of conceptions and I would argue to
+
+ align:start position:0%
+kind of conceptions and I would argue to
+ 
+
+ align:start position:0%
+kind of conceptions and I would argue to
+you that our ideas about Justice
+
+ align:start position:0%
+you that our ideas about Justice
+ 
+
+ align:start position:0%
+you that our ideas about Justice
+fairness and equity which are not
+
+ align:start position:0%
+fairness and equity which are not
+ 
+
+ align:start position:0%
+fairness and equity which are not
+necessarily the same but often used
+
+ align:start position:0%
+necessarily the same but often used
+ 
+
+ align:start position:0%
+necessarily the same but often used
+quite interchangeably have become
+
+ align:start position:0%
+quite interchangeably have become
+ 
+
+ align:start position:0%
+quite interchangeably have become
+crossed with energy and climate and this
+
+ align:start position:0%
+crossed with energy and climate and this
+ 
+
+ align:start position:0%
+crossed with energy and climate and this
+is the key thing we want to discuss in
+
+ align:start position:0%
+is the key thing we want to discuss in
+ 
+
+ align:start position:0%
+is the key thing we want to discuss in
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+uh for example climate justice has roots
+
+ align:start position:0%
+uh for example climate justice has roots
+ 
+
+ align:start position:0%
+uh for example climate justice has roots
+in ideas about historical responsibility
+
+ align:start position:0%
+in ideas about historical responsibility
+ 
+
+ align:start position:0%
+in ideas about historical responsibility
+and intergenerational Equity we would
+
+ align:start position:0%
+and intergenerational Equity we would
+ 
+
+ align:start position:0%
+and intergenerational Equity we would
+talk about historical responsibility and
+
+ align:start position:0%
+talk about historical responsibility and
+ 
+
+ align:start position:0%
+talk about historical responsibility and
+generational Equity as uh in terms of
+
+ align:start position:0%
+generational Equity as uh in terms of
+ 
+
+ align:start position:0%
+generational Equity as uh in terms of
+climate change as a problem that older
+
+ align:start position:0%
+climate change as a problem that older
+ 
+
+ align:start position:0%
+climate change as a problem that older
+Generations may be leaving for later or
+
+ align:start position:0%
+Generations may be leaving for later or
+ 
+
+ align:start position:0%
+Generations may be leaving for later or
+following Generations it is interesting
+
+ align:start position:0%
+following Generations it is interesting
+ 
+
+ align:start position:0%
+following Generations it is interesting
+to see how that rhetoric has perhaps
+
+ align:start position:0%
+to see how that rhetoric has perhaps
+ 
+
+ align:start position:0%
+to see how that rhetoric has perhaps
+diminished because climate change is
+
+ align:start position:0%
+diminished because climate change is
+ 
+
+ align:start position:0%
+diminished because climate change is
+here now we all know that climate change
+
+ align:start position:0%
+here now we all know that climate change
+ 
+
+ align:start position:0%
+here now we all know that climate change
+is happening it may not no longer be
+
+ align:start position:0%
+is happening it may not no longer be
+ 
+
+ align:start position:0%
+is happening it may not no longer be
+intergenerational problem it is a
+
+ align:start position:0%
+intergenerational problem it is a
+ 
+
+ align:start position:0%
+intergenerational problem it is a
+problem here and now and so I think a
+
+ align:start position:0%
+problem here and now and so I think a
+ 
+
+ align:start position:0%
+problem here and now and so I think a
+more modern I guess way to talk about
+
+ align:start position:0%
+more modern I guess way to talk about
+ 
+
+ align:start position:0%
+more modern I guess way to talk about
+climate justice has been about as
+
+ align:start position:0%
+climate justice has been about as
+ 
+
+ align:start position:0%
+climate justice has been about as
+disproportionate causes and burdens not
+
+ align:start position:0%
+disproportionate causes and burdens not
+ 
+
+ align:start position:0%
+disproportionate causes and burdens not
+only are older Generations causing
+
+ align:start position:0%
+only are older Generations causing
+ 
+
+ align:start position:0%
+only are older Generations causing
+greenhouse gas emissions that will
+
+ align:start position:0%
+greenhouse gas emissions that will
+ 
+
+ align:start position:0%
+greenhouse gas emissions that will
+affect future Generations in terms of
+
+ align:start position:0%
+affect future Generations in terms of
+ 
+
+ align:start position:0%
+affect future Generations in terms of
+climate change we also know that rich
+
+ align:start position:0%
+climate change we also know that rich
+ 
+
+ align:start position:0%
+climate change we also know that rich
+western or developed countries have
+
+ align:start position:0%
+western or developed countries have
+ 
+
+ align:start position:0%
+western or developed countries have
+disproportionately caused the problem
+
+ align:start position:0%
+disproportionately caused the problem
+ 
+
+ align:start position:0%
+disproportionately caused the problem
+this is an argument I've made to you
+
+ align:start position:0%
+this is an argument I've made to you
+ 
+
+ align:start position:0%
+this is an argument I've made to you
+before and that those burdens have been
+
+ align:start position:0%
+before and that those burdens have been
+ 
+
+ align:start position:0%
+before and that those burdens have been
+modeled or forecast to disruportionately
+
+ align:start position:0%
+modeled or forecast to disruportionately
+ 
+
+ align:start position:0%
+modeled or forecast to disruportionately
+affect the countries that are least
+
+ align:start position:0%
+affect the countries that are least
+ 
+
+ align:start position:0%
+affect the countries that are least
+responsible for causing climate change
+
+ align:start position:0%
+responsible for causing climate change
+ 
+
+ align:start position:0%
+responsible for causing climate change
+like the flooding happening in Pakistan
+
+ align:start position:0%
+like the flooding happening in Pakistan
+ 
+
+ align:start position:0%
+like the flooding happening in Pakistan
+like hurricanes and typhoons hitting
+
+ align:start position:0%
+like hurricanes and typhoons hitting
+ 
+
+ align:start position:0%
+like hurricanes and typhoons hitting
+Mozambique
+
+ align:start position:0%
+Mozambique
+ 
+
+ align:start position:0%
+Mozambique
+at the same time climate justice has
+
+ align:start position:0%
+at the same time climate justice has
+ 
+
+ align:start position:0%
+at the same time climate justice has
+become a more important phrase or idea
+
+ align:start position:0%
+become a more important phrase or idea
+ 
+
+ align:start position:0%
+become a more important phrase or idea
+because of the rise of Grassroots
+
+ align:start position:0%
+because of the rise of Grassroots
+ 
+
+ align:start position:0%
+because of the rise of Grassroots
+movements like Friday after the future
+
+ align:start position:0%
+movements like Friday after the future
+ 
+
+ align:start position:0%
+movements like Friday after the future
+or Extinction Rebellion when you have a
+
+ align:start position:0%
+or Extinction Rebellion when you have a
+ 
+
+ align:start position:0%
+or Extinction Rebellion when you have a
+social movement you need to have a set
+
+ align:start position:0%
+social movement you need to have a set
+ 
+
+ align:start position:0%
+social movement you need to have a set
+of organizing principles or ideas
+
+ align:start position:0%
+of organizing principles or ideas
+ 
+
+ align:start position:0%
+of organizing principles or ideas
+climate justice has become one of those
+
+ align:start position:0%
+climate justice has become one of those
+ 
+
+ align:start position:0%
+climate justice has become one of those
+important ideas
+
+ align:start position:0%
+important ideas
+ 
+
+ align:start position:0%
+important ideas
+and of course climate justice has become
+
+ align:start position:0%
+and of course climate justice has become
+ 
+
+ align:start position:0%
+and of course climate justice has become
+a more important idea because of legal
+
+ align:start position:0%
+a more important idea because of legal
+ 
+
+ align:start position:0%
+a more important idea because of legal
+actions on climate change I think the
+
+ align:start position:0%
+actions on climate change I think the
+ 
+
+ align:start position:0%
+actions on climate change I think the
+United Nations counted recently almost
+
+ align:start position:0%
+United Nations counted recently almost
+ 
+
+ align:start position:0%
+United Nations counted recently almost
+900 legal actions on climate change a
+
+ align:start position:0%
+900 legal actions on climate change a
+ 
+
+ align:start position:0%
+900 legal actions on climate change a
+lot of those adjudication of litigation
+
+ align:start position:0%
+lot of those adjudication of litigation
+ 
+
+ align:start position:0%
+lot of those adjudication of litigation
+around the effects of climate change are
+
+ align:start position:0%
+around the effects of climate change are
+ 
+
+ align:start position:0%
+around the effects of climate change are
+trying to get to an idea of who is
+
+ align:start position:0%
+trying to get to an idea of who is
+ 
+
+ align:start position:0%
+trying to get to an idea of who is
+responsible for climate change how can
+
+ align:start position:0%
+responsible for climate change how can
+ 
+
+ align:start position:0%
+responsible for climate change how can
+let's say different countries or groups
+
+ align:start position:0%
+let's say different countries or groups
+ 
+
+ align:start position:0%
+let's say different countries or groups
+or corporations be held responsible for
+
+ align:start position:0%
+or corporations be held responsible for
+ 
+
+ align:start position:0%
+or corporations be held responsible for
+the impacts of climate change do they
+
+ align:start position:0%
+the impacts of climate change do they
+ 
+
+ align:start position:0%
+the impacts of climate change do they
+owe reparations or remedies to affected
+
+ align:start position:0%
+owe reparations or remedies to affected
+ 
+
+ align:start position:0%
+owe reparations or remedies to affected
+groups
+
+ align:start position:0%
+groups
+ 
+
+ align:start position:0%
+groups
+climate Justice is also closely
+
+ align:start position:0%
+climate Justice is also closely
+ 
+
+ align:start position:0%
+climate Justice is also closely
+associated with the idea of
+
+ align:start position:0%
+associated with the idea of
+ 
+
+ align:start position:0%
+associated with the idea of
+transformative Justice these are
+
+ align:start position:0%
+transformative Justice these are
+ 
+
+ align:start position:0%
+transformative Justice these are
+practices and philosophies designed to
+
+ align:start position:0%
+practices and philosophies designed to
+ 
+
+ align:start position:0%
+practices and philosophies designed to
+create change in Social systems I would
+
+ align:start position:0%
+create change in Social systems I would
+ 
+
+ align:start position:0%
+create change in Social systems I would
+encourage you to take note of the idea
+
+ align:start position:0%
+encourage you to take note of the idea
+ 
+
+ align:start position:0%
+encourage you to take note of the idea
+of transformational Justice in shalanda
+
+ align:start position:0%
+of transformational Justice in shalanda
+ 
+
+ align:start position:0%
+of transformational Justice in shalanda
+baker's article that I assigned for this
+
+ align:start position:0%
+baker's article that I assigned for this
+ 
+
+ align:start position:0%
+baker's article that I assigned for this
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+and also the idea of energy Justice a
+
+ align:start position:0%
+and also the idea of energy Justice a
+ 
+
+ align:start position:0%
+and also the idea of energy Justice a
+number of these different articles
+
+ align:start position:0%
+number of these different articles
+ 
+
+ align:start position:0%
+number of these different articles
+mentioned in the idea of energy Justice
+
+ align:start position:0%
+mentioned in the idea of energy Justice
+ 
+
+ align:start position:0%
+mentioned in the idea of energy Justice
+as a fairly innocent idea in the
+
+ align:start position:0%
+as a fairly innocent idea in the
+ 
+
+ align:start position:0%
+as a fairly innocent idea in the
+literature and the idea of energy
+
+ align:start position:0%
+literature and the idea of energy
+ 
+
+ align:start position:0%
+literature and the idea of energy
+Justice gets at the idea that there are
+
+ align:start position:0%
+Justice gets at the idea that there are
+ 
+
+ align:start position:0%
+Justice gets at the idea that there are
+disproportionate access or
+
+ align:start position:0%
+disproportionate access or
+ 
+
+ align:start position:0%
+disproportionate access or
+disproportionate people who have access
+
+ align:start position:0%
+disproportionate people who have access
+ 
+
+ align:start position:0%
+disproportionate people who have access
+to the Energy System including its
+
+ align:start position:0%
+to the Energy System including its
+ 
+
+ align:start position:0%
+to the Energy System including its
+benefits but also the Energy System we
+
+ align:start position:0%
+benefits but also the Energy System we
+ 
+
+ align:start position:0%
+benefits but also the Energy System we
+know has clear harms and burdens that
+
+ align:start position:0%
+know has clear harms and burdens that
+ 
+
+ align:start position:0%
+know has clear harms and burdens that
+fall disreportationally on certain
+
+ align:start position:0%
+fall disreportationally on certain
+ 
+
+ align:start position:0%
+fall disreportationally on certain
+groups like black Americans and minority
+
+ align:start position:0%
+groups like black Americans and minority
+ 
+
+ align:start position:0%
+groups like black Americans and minority
+groups who live much more closely to the
+
+ align:start position:0%
+groups who live much more closely to the
+ 
+
+ align:start position:0%
+groups who live much more closely to the
+polluting infrastructure that Robert
+
+ align:start position:0%
+polluting infrastructure that Robert
+ 
+
+ align:start position:0%
+polluting infrastructure that Robert
+Bullard Bullard first identified in the
+
+ align:start position:0%
+Bullard Bullard first identified in the
+ 
+
+ align:start position:0%
+Bullard Bullard first identified in the
+70s and 80s
+
+ align:start position:0%
+70s and 80s
+ 
+
+ align:start position:0%
+70s and 80s
+and of course our discussion of kind of
+
+ align:start position:0%
+and of course our discussion of kind of
+ 
+
+ align:start position:0%
+and of course our discussion of kind of
+justice has to get at the idea of
+
+ align:start position:0%
+justice has to get at the idea of
+ 
+
+ align:start position:0%
+justice has to get at the idea of
+disproportionate to who there are plenty
+
+ align:start position:0%
+disproportionate to who there are plenty
+ 
+
+ align:start position:0%
+disproportionate to who there are plenty
+of disappointment harms of the fossil
+
+ align:start position:0%
+of disappointment harms of the fossil
+ 
+
+ align:start position:0%
+of disappointment harms of the fossil
+fuel system to go around but as we start
+
+ align:start position:0%
+fuel system to go around but as we start
+ 
+
+ align:start position:0%
+fuel system to go around but as we start
+to seek an energy transition one group
+
+ align:start position:0%
+to seek an energy transition one group
+ 
+
+ align:start position:0%
+to seek an energy transition one group
+that has been notably skeptical until
+
+ align:start position:0%
+that has been notably skeptical until
+ 
+
+ align:start position:0%
+that has been notably skeptical until
+recently of an energy transition mostly
+
+ align:start position:0%
+recently of an energy transition mostly
+ 
+
+ align:start position:0%
+recently of an energy transition mostly
+pushed by environmentalists unions and
+
+ align:start position:0%
+pushed by environmentalists unions and
+ 
+
+ align:start position:0%
+pushed by environmentalists unions and
+workers have been notably skeptical
+
+ align:start position:0%
+workers have been notably skeptical
+ 
+
+ align:start position:0%
+workers have been notably skeptical
+sometimes of the idea of an energy
+
+ align:start position:0%
+sometimes of the idea of an energy
+ 
+
+ align:start position:0%
+sometimes of the idea of an energy
+transition and the energy transition
+
+ align:start position:0%
+transition and the energy transition
+ 
+
+ align:start position:0%
+transition and the energy transition
+that we are seeking because of probably
+
+ align:start position:0%
+that we are seeking because of probably
+ 
+
+ align:start position:0%
+that we are seeking because of probably
+well-founded skepticism that they will
+
+ align:start position:0%
+well-founded skepticism that they will
+ 
+
+ align:start position:0%
+well-founded skepticism that they will
+may not have the same jobs or standard
+
+ align:start position:0%
+may not have the same jobs or standard
+ 
+
+ align:start position:0%
+may not have the same jobs or standard
+of living in an energy transition and I
+
+ align:start position:0%
+of living in an energy transition and I
+ 
+
+ align:start position:0%
+of living in an energy transition and I
+think for good reason fossil fuel
+
+ align:start position:0%
+think for good reason fossil fuel
+ 
+
+ align:start position:0%
+think for good reason fossil fuel
+dominated communities fossil fuel jobs
+
+ align:start position:0%
+dominated communities fossil fuel jobs
+ 
+
+ align:start position:0%
+dominated communities fossil fuel jobs
+typically are higher paying than average
+
+ align:start position:0%
+typically are higher paying than average
+ 
+
+ align:start position:0%
+typically are higher paying than average
+than other jobs with the same education
+
+ align:start position:0%
+than other jobs with the same education
+ 
+
+ align:start position:0%
+than other jobs with the same education
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+and fossil fuel job in our fossil fuel
+
+ align:start position:0%
+and fossil fuel job in our fossil fuel
+ 
+
+ align:start position:0%
+and fossil fuel job in our fossil fuel
+dominant Community according to this
+
+ align:start position:0%
+dominant Community according to this
+ 
+
+ align:start position:0%
+dominant Community according to this
+marchan Weber study typically creates or
+
+ align:start position:0%
+marchan Weber study typically creates or
+ 
+
+ align:start position:0%
+marchan Weber study typically creates or
+supports two to five other jobs so if we
+
+ align:start position:0%
+supports two to five other jobs so if we
+ 
+
+ align:start position:0%
+supports two to five other jobs so if we
+seek an energy transition how are we
+
+ align:start position:0%
+seek an energy transition how are we
+ 
+
+ align:start position:0%
+seek an energy transition how are we
+going to make sure that workers and
+
+ align:start position:0%
+going to make sure that workers and
+ 
+
+ align:start position:0%
+going to make sure that workers and
+unions and fossil fuel dominated
+
+ align:start position:0%
+unions and fossil fuel dominated
+ 
+
+ align:start position:0%
+unions and fossil fuel dominated
+communities maintain or even improve
+
+ align:start position:0%
+communities maintain or even improve
+ 
+
+ align:start position:0%
+communities maintain or even improve
+their standard of living
+
+ align:start position:0%
+their standard of living
+ 
+
+ align:start position:0%
+their standard of living
+and of course we know that they're just
+
+ align:start position:0%
+and of course we know that they're just
+ 
+
+ align:start position:0%
+and of course we know that they're just
+disproportionate harms on the front line
+
+ align:start position:0%
+disproportionate harms on the front line
+ 
+
+ align:start position:0%
+disproportionate harms on the front line
+our local Justice communities like
+
+ align:start position:0%
+our local Justice communities like
+ 
+
+ align:start position:0%
+our local Justice communities like
+minority groups like African Americans
+
+ align:start position:0%
+minority groups like African Americans
+ 
+
+ align:start position:0%
+minority groups like African Americans
+we know that there are particular places
+
+ align:start position:0%
+we know that there are particular places
+ 
+
+ align:start position:0%
+we know that there are particular places
+that are affected by the harms of fossil
+
+ align:start position:0%
+that are affected by the harms of fossil
+ 
+
+ align:start position:0%
+that are affected by the harms of fossil
+fuels including spills including
+
+ align:start position:0%
+fuels including spills including
+ 
+
+ align:start position:0%
+fuels including spills including
+refining including air pollution and of
+
+ align:start position:0%
+refining including air pollution and of
+ 
+
+ align:start position:0%
+refining including air pollution and of
+course it's also worth noting that these
+
+ align:start position:0%
+course it's also worth noting that these
+ 
+
+ align:start position:0%
+course it's also worth noting that these
+two groups
+
+ align:start position:0%
+two groups
+ 
+
+ align:start position:0%
+two groups
+will have disappointing effects of the
+
+ align:start position:0%
+will have disappointing effects of the
+ 
+
+ align:start position:0%
+will have disappointing effects of the
+energy system are often the same group
+
+ align:start position:0%
+energy system are often the same group
+ 
+
+ align:start position:0%
+energy system are often the same group
+you could be a member of a Frontline
+
+ align:start position:0%
+you could be a member of a Frontline
+ 
+
+ align:start position:0%
+you could be a member of a Frontline
+environmental justice Community whether
+
+ align:start position:0%
+environmental justice Community whether
+ 
+
+ align:start position:0%
+environmental justice Community whether
+you're white or black you may be a
+
+ align:start position:0%
+you're white or black you may be a
+ 
+
+ align:start position:0%
+you're white or black you may be a
+fossil fuel worker also and you may
+
+ align:start position:0%
+fossil fuel worker also and you may
+ 
+
+ align:start position:0%
+fossil fuel worker also and you may
+actually oppose change the fossil fuel
+
+ align:start position:0%
+actually oppose change the fossil fuel
+ 
+
+ align:start position:0%
+actually oppose change the fossil fuel
+system because you're worried about
+
+ align:start position:0%
+system because you're worried about
+ 
+
+ align:start position:0%
+system because you're worried about
+maintaining your standard of living or
+
+ align:start position:0%
+maintaining your standard of living or
+ 
+
+ align:start position:0%
+maintaining your standard of living or
+job
+
+ align:start position:0%
+job
+ 
+
+ align:start position:0%
+job
+and so it's interesting actually if you
+
+ align:start position:0%
+and so it's interesting actually if you
+ 
+
+ align:start position:0%
+and so it's interesting actually if you
+look at the shlanda baker article she
+
+ align:start position:0%
+look at the shlanda baker article she
+ 
+
+ align:start position:0%
+look at the shlanda baker article she
+talks about her black relatives who are
+
+ align:start position:0%
+talks about her black relatives who are
+ 
+
+ align:start position:0%
+talks about her black relatives who are
+fossil fuel workers in Port Arthur and
+
+ align:start position:0%
+fossil fuel workers in Port Arthur and
+ 
+
+ align:start position:0%
+fossil fuel workers in Port Arthur and
+of course this recent headline for the
+
+ align:start position:0%
+of course this recent headline for the
+ 
+
+ align:start position:0%
+of course this recent headline for the
+Washington Post
+
+ align:start position:0%
+Washington Post
+ 
+
+ align:start position:0%
+Washington Post
+a few weeks ago actually kind of
+
+ align:start position:0%
+a few weeks ago actually kind of
+ 
+
+ align:start position:0%
+a few weeks ago actually kind of
+describes now how the conversation has
+
+ align:start position:0%
+describes now how the conversation has
+ 
+
+ align:start position:0%
+describes now how the conversation has
+changed this headline is about people in
+
+ align:start position:0%
+changed this headline is about people in
+ 
+
+ align:start position:0%
+changed this headline is about people in
+Port Arthur Texas who are surrounded by
+
+ align:start position:0%
+Port Arthur Texas who are surrounded by
+ 
+
+ align:start position:0%
+Port Arthur Texas who are surrounded by
+fossil fuels but they fear that the
+
+ align:start position:0%
+fossil fuels but they fear that the
+ 
+
+ align:start position:0%
+fossil fuels but they fear that the
+climate Bill leaves them behind and this
+
+ align:start position:0%
+climate Bill leaves them behind and this
+ 
+
+ align:start position:0%
+climate Bill leaves them behind and this
+includes not only fossil fuel workers
+
+ align:start position:0%
+includes not only fossil fuel workers
+ 
+
+ align:start position:0%
+includes not only fossil fuel workers
+who work in Port Arthur but climate and
+
+ align:start position:0%
+who work in Port Arthur but climate and
+ 
+
+ align:start position:0%
+who work in Port Arthur but climate and
+iranical activists who've been fighting
+
+ align:start position:0%
+iranical activists who've been fighting
+ 
+
+ align:start position:0%
+iranical activists who've been fighting
+this environmental infrastructure for a
+
+ align:start position:0%
+this environmental infrastructure for a
+ 
+
+ align:start position:0%
+this environmental infrastructure for a
+long time the climate bill which I've
+
+ align:start position:0%
+long time the climate bill which I've
+ 
+
+ align:start position:0%
+long time the climate bill which I've
+been celebrating a discussion we know
+
+ align:start position:0%
+been celebrating a discussion we know
+ 
+
+ align:start position:0%
+been celebrating a discussion we know
+has significant gaps and one of the
+
+ align:start position:0%
+has significant gaps and one of the
+ 
+
+ align:start position:0%
+has significant gaps and one of the
+significant gaps of the Barnacle Justice
+
+ align:start position:0%
+significant gaps of the Barnacle Justice
+ 
+
+ align:start position:0%
+significant gaps of the Barnacle Justice
+in fact one of the compromises made in
+
+ align:start position:0%
+in fact one of the compromises made in
+ 
+
+ align:start position:0%
+in fact one of the compromises made in
+the climate legislation was to allow
+
+ align:start position:0%
+the climate legislation was to allow
+ 
+
+ align:start position:0%
+the climate legislation was to allow
+additional oil and gas leasing in the
+
+ align:start position:0%
+additional oil and gas leasing in the
+ 
+
+ align:start position:0%
+additional oil and gas leasing in the
+Gulf of Mexico and additional permitting
+
+ align:start position:0%
+Gulf of Mexico and additional permitting
+ 
+
+ align:start position:0%
+Gulf of Mexico and additional permitting
+of pipelines may be coming this fall but
+
+ align:start position:0%
+of pipelines may be coming this fall but
+ 
+
+ align:start position:0%
+of pipelines may be coming this fall but
+environable Justice activists in places
+
+ align:start position:0%
+environable Justice activists in places
+ 
+
+ align:start position:0%
+environable Justice activists in places
+like Port Arthur are quite disappointed
+
+ align:start position:0%
+like Port Arthur are quite disappointed
+ 
+
+ align:start position:0%
+like Port Arthur are quite disappointed
+by the climate Bill even as much of the
+
+ align:start position:0%
+by the climate Bill even as much of the
+ 
+
+ align:start position:0%
+by the climate Bill even as much of the
+climate movement celebrates this bill
+
+ align:start position:0%
+climate movement celebrates this bill
+ 
+
+ align:start position:0%
+climate movement celebrates this bill
+and so this brings me to kind of the
+
+ align:start position:0%
+and so this brings me to kind of the
+ 
+
+ align:start position:0%
+and so this brings me to kind of the
+basis for our discussion our class
+
+ align:start position:0%
+basis for our discussion our class
+ 
+
+ align:start position:0%
+basis for our discussion our class
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+um that we're going to have this is a
+
+ align:start position:0%
+um that we're going to have this is a
+ 
+
+ align:start position:0%
+um that we're going to have this is a
+geography article by Heffron and
+
+ align:start position:0%
+geography article by Heffron and
+ 
+
+ align:start position:0%
+geography article by Heffron and
+Macaulay asking what is the just
+
+ align:start position:0%
+Macaulay asking what is the just
+ 
+
+ align:start position:0%
+Macaulay asking what is the just
+transition they identify four components
+
+ align:start position:0%
+transition they identify four components
+ 
+
+ align:start position:0%
+transition they identify four components
+of the just transition uh the Justice
+
+ align:start position:0%
+of the just transition uh the Justice
+ 
+
+ align:start position:0%
+of the just transition uh the Justice
+universality it's a geography article
+
+ align:start position:0%
+universality it's a geography article
+ 
+
+ align:start position:0%
+universality it's a geography article
+stay focus on space and also the time I
+
+ align:start position:0%
+stay focus on space and also the time I
+ 
+
+ align:start position:0%
+stay focus on space and also the time I
+want to focus on the different forms of
+
+ align:start position:0%
+want to focus on the different forms of
+ 
+
+ align:start position:0%
+want to focus on the different forms of
+Justice because I would argue that
+
+ align:start position:0%
+Justice because I would argue that
+ 
+
+ align:start position:0%
+Justice because I would argue that
+they're rhetorical forms or rhetorical
+
+ align:start position:0%
+they're rhetorical forms or rhetorical
+ 
+
+ align:start position:0%
+they're rhetorical forms or rhetorical
+framings of the idea of justice and
+
+ align:start position:0%
+framings of the idea of justice and
+ 
+
+ align:start position:0%
+framings of the idea of justice and
+they're all quite different they're the
+
+ align:start position:0%
+they're all quite different they're the
+ 
+
+ align:start position:0%
+they're all quite different they're the
+idea of distributional Justice there's
+
+ align:start position:0%
+idea of distributional Justice there's
+ 
+
+ align:start position:0%
+idea of distributional Justice there's
+procedural Justice there's restorative
+
+ align:start position:0%
+procedural Justice there's restorative
+ 
+
+ align:start position:0%
+procedural Justice there's restorative
+justice they say there's a different
+
+ align:start position:0%
+justice they say there's a different
+ 
+
+ align:start position:0%
+justice they say there's a different
+kind of dimension of universality that
+
+ align:start position:0%
+kind of dimension of universality that
+ 
+
+ align:start position:0%
+kind of dimension of universality that
+Universal forms of Justice may include
+
+ align:start position:0%
+Universal forms of Justice may include
+ 
+
+ align:start position:0%
+Universal forms of Justice may include
+recognition Justice and cosmopolitanism
+
+ align:start position:0%
+recognition Justice and cosmopolitanism
+ 
+
+ align:start position:0%
+recognition Justice and cosmopolitanism
+let's examine that a little more closely
+
+ align:start position:0%
+let's examine that a little more closely
+ 
+
+ align:start position:0%
+let's examine that a little more closely
+how Pi uses it in their article
+
+ align:start position:0%
+how Pi uses it in their article
+ 
+
+ align:start position:0%
+how Pi uses it in their article
+distributional Justice concerns the
+
+ align:start position:0%
+distributional Justice concerns the
+ 
+
+ align:start position:0%
+distributional Justice concerns the
+equitable distribution of burdens and
+
+ align:start position:0%
+equitable distribution of burdens and
+ 
+
+ align:start position:0%
+equitable distribution of burdens and
+benefits of energy and environmental
+
+ align:start position:0%
+benefits of energy and environmental
+ 
+
+ align:start position:0%
+benefits of energy and environmental
+decisions
+
+ align:start position:0%
+decisions
+ 
+
+ align:start position:0%
+decisions
+procedural Justice highlights the right
+
+ align:start position:0%
+procedural Justice highlights the right
+ 
+
+ align:start position:0%
+procedural Justice highlights the right
+to a fair process for different
+
+ align:start position:0%
+to a fair process for different
+ 
+
+ align:start position:0%
+to a fair process for different
+stakeholders to take part equitably in
+
+ align:start position:0%
+stakeholders to take part equitably in
+ 
+
+ align:start position:0%
+stakeholders to take part equitably in
+the decision-making process
+
+ align:start position:0%
+the decision-making process
+ 
+
+ align:start position:0%
+the decision-making process
+restorative justice primarily aims to
+
+ align:start position:0%
+restorative justice primarily aims to
+ 
+
+ align:start position:0%
+restorative justice primarily aims to
+repair the harm done to individuals
+
+ align:start position:0%
+repair the harm done to individuals
+ 
+
+ align:start position:0%
+repair the harm done to individuals
+instead of focusing upon punishing the
+
+ align:start position:0%
+instead of focusing upon punishing the
+ 
+
+ align:start position:0%
+instead of focusing upon punishing the
+offender
+
+ align:start position:0%
+offender
+ 
+
+ align:start position:0%
+offender
+whereas Universal conceptions of Justice
+
+ align:start position:0%
+whereas Universal conceptions of Justice
+ 
+
+ align:start position:0%
+whereas Universal conceptions of Justice
+do draw on these other forms of justice
+
+ align:start position:0%
+do draw on these other forms of justice
+ 
+
+ align:start position:0%
+do draw on these other forms of justice
+but high at all distinguished
+
+ align:start position:0%
+but high at all distinguished
+ 
+
+ align:start position:0%
+but high at all distinguished
+recognition justice has entailing
+
+ align:start position:0%
+recognition justice has entailing
+ 
+
+ align:start position:0%
+recognition justice has entailing
+recognition of parts of society that
+
+ align:start position:0%
+recognition of parts of society that
+ 
+
+ align:start position:0%
+recognition of parts of society that
+might suffer as the result of energy in
+
+ align:start position:0%
+might suffer as the result of energy in
+ 
+
+ align:start position:0%
+might suffer as the result of energy in
+our decisions and identify individuals
+
+ align:start position:0%
+our decisions and identify individuals
+ 
+
+ align:start position:0%
+our decisions and identify individuals
+and groups who might be impacted by such
+
+ align:start position:0%
+and groups who might be impacted by such
+ 
+
+ align:start position:0%
+and groups who might be impacted by such
+decisions the jump to kind of
+
+ align:start position:0%
+decisions the jump to kind of
+ 
+
+ align:start position:0%
+decisions the jump to kind of
+universality is to start to think about
+
+ align:start position:0%
+universality is to start to think about
+ 
+
+ align:start position:0%
+universality is to start to think about
+groups of individuals rather than
+
+ align:start position:0%
+groups of individuals rather than
+ 
+
+ align:start position:0%
+groups of individuals rather than
+specific harm or specific individuals
+
+ align:start position:0%
+specific harm or specific individuals
+ 
+
+ align:start position:0%
+specific harm or specific individuals
+and of course how can Paul Injustice is
+
+ align:start position:0%
+and of course how can Paul Injustice is
+ 
+
+ align:start position:0%
+and of course how can Paul Injustice is
+an idea that reinforces all of the above
+
+ align:start position:0%
+an idea that reinforces all of the above
+ 
+
+ align:start position:0%
+an idea that reinforces all of the above
+Justice forms but states that the above
+
+ align:start position:0%
+Justice forms but states that the above
+ 
+
+ align:start position:0%
+Justice forms but states that the above
+forms of Justice must apply universally
+
+ align:start position:0%
+forms of Justice must apply universally
+ 
+
+ align:start position:0%
+forms of Justice must apply universally
+to all human beings I think it's
+
+ align:start position:0%
+to all human beings I think it's
+ 
+
+ align:start position:0%
+to all human beings I think it's
+important for us to think about how our
+
+ align:start position:0%
+important for us to think about how our
+ 
+
+ align:start position:0%
+important for us to think about how our
+conceptions of justice and how our
+
+ align:start position:0%
+conceptions of justice and how our
+ 
+
+ align:start position:0%
+conceptions of justice and how our
+rhetorical framing of Justice May apply
+
+ align:start position:0%
+rhetorical framing of Justice May apply
+ 
+
+ align:start position:0%
+rhetorical framing of Justice May apply
+to different groups does it apply
+
+ align:start position:0%
+to different groups does it apply
+ 
+
+ align:start position:0%
+to different groups does it apply
+differently to people in cities or rural
+
+ align:start position:0%
+differently to people in cities or rural
+ 
+
+ align:start position:0%
+differently to people in cities or rural
+areas does it apply differently to
+
+ align:start position:0%
+areas does it apply differently to
+ 
+
+ align:start position:0%
+areas does it apply differently to
+people involved in the fossil fuel
+
+ align:start position:0%
+people involved in the fossil fuel
+ 
+
+ align:start position:0%
+people involved in the fossil fuel
+industry but they're not their white or
+
+ align:start position:0%
+industry but they're not their white or
+ 
+
+ align:start position:0%
+industry but they're not their white or
+they're black in the United States do we
+
+ align:start position:0%
+they're black in the United States do we
+ 
+
+ align:start position:0%
+they're black in the United States do we
+expect that energy work workers the
+
+ align:start position:0%
+expect that energy work workers the
+ 
+
+ align:start position:0%
+expect that energy work workers the
+United States should have the same
+
+ align:start position:0%
+United States should have the same
+ 
+
+ align:start position:0%
+United States should have the same
+standard living as energy workers in
+
+ align:start position:0%
+standard living as energy workers in
+ 
+
+ align:start position:0%
+standard living as energy workers in
+other countries say India say in
+
+ align:start position:0%
+other countries say India say in
+ 
+
+ align:start position:0%
+other countries say India say in
+Pakistan what does this mean for us for
+
+ align:start position:0%
+Pakistan what does this mean for us for
+ 
+
+ align:start position:0%
+Pakistan what does this mean for us for
+our conception of climate Justice
+
+ align:start position:0%
+our conception of climate Justice
+ 
+
+ align:start position:0%
+our conception of climate Justice
+depending on the scale that we apply it
+
+ align:start position:0%
+depending on the scale that we apply it
+ 
+
+ align:start position:0%
+depending on the scale that we apply it
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+and of course I would argue that our
+
+ align:start position:0%
+and of course I would argue that our
+ 
+
+ align:start position:0%
+and of course I would argue that our
+idea of climate Justice is fairly
+
+ align:start position:0%
+idea of climate Justice is fairly
+ 
+
+ align:start position:0%
+idea of climate Justice is fairly
+Inseparable from our idea of politics
+
+ align:start position:0%
+Inseparable from our idea of politics
+ 
+
+ align:start position:0%
+Inseparable from our idea of politics
+just to take the climate part this is a
+
+ align:start position:0%
+just to take the climate part this is a
+ 
+
+ align:start position:0%
+just to take the climate part this is a
+figure from the Yale project on climate
+
+ align:start position:0%
+figure from the Yale project on climate
+ 
+
+ align:start position:0%
+figure from the Yale project on climate
+Communication in 2018 they look at
+
+ align:start position:0%
+Communication in 2018 they look at
+ 
+
+ align:start position:0%
+Communication in 2018 they look at
+Democratic and Republican views of
+
+ align:start position:0%
+Democratic and Republican views of
+ 
+
+ align:start position:0%
+Democratic and Republican views of
+global warming and when they asked
+
+ align:start position:0%
+global warming and when they asked
+ 
+
+ align:start position:0%
+global warming and when they asked
+estimated registered voters what percent
+
+ align:start position:0%
+estimated registered voters what percent
+ 
+
+ align:start position:0%
+estimated registered voters what percent
+if they're worried about global warming
+
+ align:start position:0%
+if they're worried about global warming
+ 
+
+ align:start position:0%
+if they're worried about global warming
+the percentages are quite striking you
+
+ align:start position:0%
+the percentages are quite striking you
+ 
+
+ align:start position:0%
+the percentages are quite striking you
+look here in the left-hand side
+
+ align:start position:0%
+look here in the left-hand side
+ 
+
+ align:start position:0%
+look here in the left-hand side
+regardless of Geography about 80 to 90
+
+ align:start position:0%
+regardless of Geography about 80 to 90
+ 
+
+ align:start position:0%
+regardless of Geography about 80 to 90
+percent of Democrats are fairly
+
+ align:start position:0%
+percent of Democrats are fairly
+ 
+
+ align:start position:0%
+percent of Democrats are fairly
+concerned about global warming if you
+
+ align:start position:0%
+concerned about global warming if you
+ 
+
+ align:start position:0%
+concerned about global warming if you
+look on the right hand side about maybe
+
+ align:start position:0%
+look on the right hand side about maybe
+ 
+
+ align:start position:0%
+look on the right hand side about maybe
+30 to 40 percent of Republicans are
+
+ align:start position:0%
+30 to 40 percent of Republicans are
+ 
+
+ align:start position:0%
+30 to 40 percent of Republicans are
+quite concerned about global warming
+
+ align:start position:0%
+quite concerned about global warming
+ 
+
+ align:start position:0%
+quite concerned about global warming
+this is not to say that there are equal
+
+ align:start position:0%
+this is not to say that there are equal
+ 
+
+ align:start position:0%
+this is not to say that there are equal
+distributions of Democrats and
+
+ align:start position:0%
+distributions of Democrats and
+ 
+
+ align:start position:0%
+distributions of Democrats and
+Republicans across the United States but
+
+ align:start position:0%
+Republicans across the United States but
+ 
+
+ align:start position:0%
+Republicans across the United States but
+I would argue for the purposes of our
+
+ align:start position:0%
+I would argue for the purposes of our
+ 
+
+ align:start position:0%
+I would argue for the purposes of our
+class talking about cities and what
+
+ align:start position:0%
+class talking about cities and what
+ 
+
+ align:start position:0%
+class talking about cities and what
+cities can do there may not be similar
+
+ align:start position:0%
+cities can do there may not be similar
+ 
+
+ align:start position:0%
+cities can do there may not be similar
+numbers of Democrats Republicans and
+
+ align:start position:0%
+numbers of Democrats Republicans and
+ 
+
+ align:start position:0%
+numbers of Democrats Republicans and
+City and rural areas that's for sure but
+
+ align:start position:0%
+City and rural areas that's for sure but
+ 
+
+ align:start position:0%
+City and rural areas that's for sure but
+at the same time it's also quite
+
+ align:start position:0%
+at the same time it's also quite
+ 
+
+ align:start position:0%
+at the same time it's also quite
+possible that our partisanship or our
+
+ align:start position:0%
+possible that our partisanship or our
+ 
+
+ align:start position:0%
+possible that our partisanship or our
+political beliefs made Trump necessarily
+
+ align:start position:0%
+political beliefs made Trump necessarily
+ 
+
+ align:start position:0%
+political beliefs made Trump necessarily
+where we live
+
+ align:start position:0%
+where we live
+ 
+
+ align:start position:0%
+where we live
+I guess unintended and this may affect
+
+ align:start position:0%
+I guess unintended and this may affect
+ 
+
+ align:start position:0%
+I guess unintended and this may affect
+how we talk about climate not only
+
+ align:start position:0%
+how we talk about climate not only
+ 
+
+ align:start position:0%
+how we talk about climate not only
+climate but even the word justice May
+
+ align:start position:0%
+climate but even the word justice May
+ 
+
+ align:start position:0%
+climate but even the word justice May
+resonate quite differently we talk about
+
+ align:start position:0%
+resonate quite differently we talk about
+ 
+
+ align:start position:0%
+resonate quite differently we talk about
+racial and social justice quite often in
+
+ align:start position:0%
+racial and social justice quite often in
+ 
+
+ align:start position:0%
+racial and social justice quite often in
+universities I would argue that Justice
+
+ align:start position:0%
+universities I would argue that Justice
+ 
+
+ align:start position:0%
+universities I would argue that Justice
+may not be a frame or a phrase that even
+
+ align:start position:0%
+may not be a frame or a phrase that even
+ 
+
+ align:start position:0%
+may not be a frame or a phrase that even
+carries very far outside of universities
+
+ align:start position:0%
+carries very far outside of universities
+ 
+
+ align:start position:0%
+carries very far outside of universities
+for example ideas about fairness May
+
+ align:start position:0%
+for example ideas about fairness May
+ 
+
+ align:start position:0%
+for example ideas about fairness May
+resonate more deeply with different
+
+ align:start position:0%
+resonate more deeply with different
+ 
+
+ align:start position:0%
+resonate more deeply with different
+audiences
+
+ align:start position:0%
+audiences
+ 
+
+ align:start position:0%
+audiences
+just to kind of reinforce this point
+
+ align:start position:0%
+just to kind of reinforce this point
+ 
+
+ align:start position:0%
+just to kind of reinforce this point
+again another figure from the Yale
+
+ align:start position:0%
+again another figure from the Yale
+ 
+
+ align:start position:0%
+again another figure from the Yale
+project in climate communication this is
+
+ align:start position:0%
+project in climate communication this is
+ 
+
+ align:start position:0%
+project in climate communication this is
+from their sixth American study they
+
+ align:start position:0%
+from their sixth American study they
+ 
+
+ align:start position:0%
+from their sixth American study they
+have run I think 20 or so surveys since
+
+ align:start position:0%
+have run I think 20 or so surveys since
+ 
+
+ align:start position:0%
+have run I think 20 or so surveys since
+2008 looking at the U.S adults
+
+ align:start position:0%
+2008 looking at the U.S adults
+ 
+
+ align:start position:0%
+2008 looking at the U.S adults
+populations attitudes about climate
+
+ align:start position:0%
+populations attitudes about climate
+ 
+
+ align:start position:0%
+populations attitudes about climate
+change they ask questions about race
+
+ align:start position:0%
+change they ask questions about race
+ 
+
+ align:start position:0%
+change they ask questions about race
+ethnicity harder than affiliation or
+
+ align:start position:0%
+ethnicity harder than affiliation or
+ 
+
+ align:start position:0%
+ethnicity harder than affiliation or
+political affiliation and they find that
+
+ align:start position:0%
+political affiliation and they find that
+ 
+
+ align:start position:0%
+political affiliation and they find that
+they can segment the US population
+
+ align:start position:0%
+they can segment the US population
+ 
+
+ align:start position:0%
+they can segment the US population
+overwhelmingly into six groups on the
+
+ align:start position:0%
+overwhelmingly into six groups on the
+ 
+
+ align:start position:0%
+overwhelmingly into six groups on the
+left hand side there's the alarmed and
+
+ align:start position:0%
+left hand side there's the alarmed and
+ 
+
+ align:start position:0%
+left hand side there's the alarmed and
+concert concerned groups these are the
+
+ align:start position:0%
+concert concerned groups these are the
+ 
+
+ align:start position:0%
+concert concerned groups these are the
+groups that had the highest belief in
+
+ align:start position:0%
+groups that had the highest belief in
+ 
+
+ align:start position:0%
+groups that had the highest belief in
+global warming they're most concerned
+
+ align:start position:0%
+global warming they're most concerned
+ 
+
+ align:start position:0%
+global warming they're most concerned
+about climate change they're most
+
+ align:start position:0%
+about climate change they're most
+ 
+
+ align:start position:0%
+about climate change they're most
+motivated to do something about it and
+
+ align:start position:0%
+motivated to do something about it and
+ 
+
+ align:start position:0%
+motivated to do something about it and
+on the right hand side these four groups
+
+ align:start position:0%
+on the right hand side these four groups
+ 
+
+ align:start position:0%
+on the right hand side these four groups
+the cautious the disengaged the doubtful
+
+ align:start position:0%
+the cautious the disengaged the doubtful
+ 
+
+ align:start position:0%
+the cautious the disengaged the doubtful
+and the dismissive happy lowest belief
+
+ align:start position:0%
+and the dismissive happy lowest belief
+ 
+
+ align:start position:0%
+and the dismissive happy lowest belief
+in global warming they're at least
+
+ align:start position:0%
+in global warming they're at least
+ 
+
+ align:start position:0%
+in global warming they're at least
+concerned they're least motivated of
+
+ align:start position:0%
+concerned they're least motivated of
+ 
+
+ align:start position:0%
+concerned they're least motivated of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+on the left hand side of these two
+
+ align:start position:0%
+on the left hand side of these two
+ 
+
+ align:start position:0%
+on the left hand side of these two
+groups alarm to concern are dominated by
+
+ align:start position:0%
+groups alarm to concern are dominated by
+ 
+
+ align:start position:0%
+groups alarm to concern are dominated by
+democrats the other four groups are
+
+ align:start position:0%
+democrats the other four groups are
+ 
+
+ align:start position:0%
+democrats the other four groups are
+dominated by Republicans the groups on
+
+ align:start position:0%
+dominated by Republicans the groups on
+ 
+
+ align:start position:0%
+dominated by Republicans the groups on
+the left tend to skew younger and more
+
+ align:start position:0%
+the left tend to skew younger and more
+ 
+
+ align:start position:0%
+the left tend to skew younger and more
+female big groups on the right tend to
+
+ align:start position:0%
+female big groups on the right tend to
+ 
+
+ align:start position:0%
+female big groups on the right tend to
+skew older and more male and so this is
+
+ align:start position:0%
+skew older and more male and so this is
+ 
+
+ align:start position:0%
+skew older and more male and so this is
+just a question about how are we going
+
+ align:start position:0%
+just a question about how are we going
+ 
+
+ align:start position:0%
+just a question about how are we going
+to present the idea of climate Justice
+
+ align:start position:0%
+to present the idea of climate Justice
+ 
+
+ align:start position:0%
+to present the idea of climate Justice
+is this an idea that is going to have
+
+ align:start position:0%
+is this an idea that is going to have
+ 
+
+ align:start position:0%
+is this an idea that is going to have
+attraction with all six of Youth groups
+
+ align:start position:0%
+attraction with all six of Youth groups
+ 
+
+ align:start position:0%
+attraction with all six of Youth groups
+we're going to discuss this in class
+
+ align:start position:0%
+we're going to discuss this in class
+ 
+
+ align:start position:0%
+we're going to discuss this in class
+finally there's this interesting quiz I
+
+ align:start position:0%
+finally there's this interesting quiz I
+ 
+
+ align:start position:0%
+finally there's this interesting quiz I
+kind of enjoy taking at the New York
+
+ align:start position:0%
+kind of enjoy taking at the New York
+ 
+
+ align:start position:0%
+kind of enjoy taking at the New York
+Times quiz if America had six parties
+
+ align:start position:0%
+Times quiz if America had six parties
+ 
+
+ align:start position:0%
+Times quiz if America had six parties
+rather than two which would you belong
+
+ align:start position:0%
+rather than two which would you belong
+ 
+
+ align:start position:0%
+rather than two which would you belong
+to this is a political scientist simply
+
+ align:start position:0%
+to this is a political scientist simply
+ 
+
+ align:start position:0%
+to this is a political scientist simply
+commenting on how our major political
+
+ align:start position:0%
+commenting on how our major political
+ 
+
+ align:start position:0%
+commenting on how our major political
+parties are distributed or comprised of
+
+ align:start position:0%
+parties are distributed or comprised of
+ 
+
+ align:start position:0%
+parties are distributed or comprised of
+different coalitions and different
+
+ align:start position:0%
+different coalitions and different
+ 
+
+ align:start position:0%
+different coalitions and different
+groups those groups have different
+
+ align:start position:0%
+groups those groups have different
+ 
+
+ align:start position:0%
+groups those groups have different
+social certain levels of social
+
+ align:start position:0%
+social certain levels of social
+ 
+
+ align:start position:0%
+social certain levels of social
+conservatism and economic conservatism
+
+ align:start position:0%
+conservatism and economic conservatism
+ 
+
+ align:start position:0%
+conservatism and economic conservatism
+for example you could take the American
+
+ align:start position:0%
+for example you could take the American
+ 
+
+ align:start position:0%
+for example you could take the American
+labor party Progressive Party a new
+
+ align:start position:0%
+labor party Progressive Party a new
+ 
+
+ align:start position:0%
+labor party Progressive Party a new
+Liberal Party as relatively Democratic
+
+ align:start position:0%
+Liberal Party as relatively Democratic
+ 
+
+ align:start position:0%
+Liberal Party as relatively Democratic
+groups but it turns out that the
+
+ align:start position:0%
+groups but it turns out that the
+ 
+
+ align:start position:0%
+groups but it turns out that the
+American labor party and the growth and
+
+ align:start position:0%
+American labor party and the growth and
+ 
+
+ align:start position:0%
+American labor party and the growth and
+opportunity party uh probably more
+
+ align:start position:0%
+opportunity party uh probably more
+ 
+
+ align:start position:0%
+opportunity party uh probably more
+Associated Republicans have similar
+
+ align:start position:0%
+Associated Republicans have similar
+ 
+
+ align:start position:0%
+Associated Republicans have similar
+attitudes about social conservatism
+
+ align:start position:0%
+attitudes about social conservatism
+ 
+
+ align:start position:0%
+attitudes about social conservatism
+at the same time if you look at the
+
+ align:start position:0%
+at the same time if you look at the
+ 
+
+ align:start position:0%
+at the same time if you look at the
+Patriot party the Christian conservative
+
+ align:start position:0%
+Patriot party the Christian conservative
+ 
+
+ align:start position:0%
+Patriot party the Christian conservative
+party and the growth opportunity party
+
+ align:start position:0%
+party and the growth opportunity party
+ 
+
+ align:start position:0%
+party and the growth opportunity party
+it turns out that part of the royal
+
+ align:start position:0%
+it turns out that part of the royal
+ 
+
+ align:start position:0%
+it turns out that part of the royal
+Republican Coalition or Republican party
+
+ align:start position:0%
+Republican Coalition or Republican party
+ 
+
+ align:start position:0%
+Republican Coalition or Republican party
+is relatively close to the economically
+
+ align:start position:0%
+is relatively close to the economically
+ 
+
+ align:start position:0%
+is relatively close to the economically
+conservative group in the Democratic
+
+ align:start position:0%
+conservative group in the Democratic
+ 
+
+ align:start position:0%
+conservative group in the Democratic
+Coalition all the new Liberal Party and
+
+ align:start position:0%
+Coalition all the new Liberal Party and
+ 
+
+ align:start position:0%
+Coalition all the new Liberal Party and
+so this is to say that all of our
+
+ align:start position:0%
+so this is to say that all of our
+ 
+
+ align:start position:0%
+so this is to say that all of our
+different rhetorical framings of Justice
+
+ align:start position:0%
+different rhetorical framings of Justice
+ 
+
+ align:start position:0%
+different rhetorical framings of Justice
+how we talk about history some of these
+
+ align:start position:0%
+how we talk about history some of these
+ 
+
+ align:start position:0%
+how we talk about history some of these
+ideas how we talk about the imperative
+
+ align:start position:0%
+ideas how we talk about the imperative
+ 
+
+ align:start position:0%
+ideas how we talk about the imperative
+to achieve climate Justice May resonate
+
+ align:start position:0%
+to achieve climate Justice May resonate
+ 
+
+ align:start position:0%
+to achieve climate Justice May resonate
+differently with all six of these groups
+
+ align:start position:0%
+differently with all six of these groups
+ 
+
+ align:start position:0%
+differently with all six of these groups
+so what we're going to do in our class
+
+ align:start position:0%
+so what we're going to do in our class
+ 
+
+ align:start position:0%
+so what we're going to do in our class
+discussion is we're going to do a
+
+ align:start position:0%
+discussion is we're going to do a
+ 
+
+ align:start position:0%
+discussion is we're going to do a
+discussion exercise that requires you to
+
+ align:start position:0%
+discussion exercise that requires you to
+ 
+
+ align:start position:0%
+discussion exercise that requires you to
+argue for a different energy policy
+
+ align:start position:0%
+argue for a different energy policy
+ 
+
+ align:start position:0%
+argue for a different energy policy
+based on different conceptions of
+
+ align:start position:0%
+based on different conceptions of
+ 
+
+ align:start position:0%
+based on different conceptions of
+Justice
+
+ align:start position:0%
+Justice
+ 
+
+ align:start position:0%
+Justice
+and we're going to do this as discussion
+
+ align:start position:0%
+and we're going to do this as discussion
+ 
+
+ align:start position:0%
+and we're going to do this as discussion
+together and it's good for you to
+
+ align:start position:0%
+together and it's good for you to
+ 
+
+ align:start position:0%
+together and it's good for you to
+prepare by looking at the Remy edel
+
+ align:start position:0%
+prepare by looking at the Remy edel
+ 
+
+ align:start position:0%
+prepare by looking at the Remy edel
+article looking at a specific energy
+
+ align:start position:0%
+article looking at a specific energy
+ 
+
+ align:start position:0%
+article looking at a specific energy
+policy and thinking about how different
+
+ align:start position:0%
+policy and thinking about how different
+ 
+
+ align:start position:0%
+policy and thinking about how different
+groups might talk about this energy
+
+ align:start position:0%
+groups might talk about this energy
+ 
+
+ align:start position:0%
+groups might talk about this energy
+policy
\ No newline at end of file
diff --git a/QC8q4oYKwBI.txt b/QC8q4oYKwBI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a547479bd9aff79660e06054611c18b096010dae
--- /dev/null
+++ b/QC8q4oYKwBI.txt
@@ -0,0 +1,16659 @@
+align:start position:0%
+ 
+Today we're going to talk about
+
+ align:start position:0%
+Today we're going to talk about
+ 
+
+ align:start position:0%
+Today we're going to talk about
+peerguided learning at scale. Um the
+
+ align:start position:0%
+peerguided learning at scale. Um the
+ 
+
+ align:start position:0%
+peerguided learning at scale. Um the
+thing I asked you to do for today was to
+
+ align:start position:0%
+thing I asked you to do for today was to
+ 
+
+ align:start position:0%
+thing I asked you to do for today was to
+write a little bit in your learning
+
+ align:start position:0%
+write a little bit in your learning
+ 
+
+ align:start position:0%
+write a little bit in your learning
+journal about um one of your hobbies
+
+ align:start position:0%
+journal about um one of your hobbies
+ 
+
+ align:start position:0%
+journal about um one of your hobbies
+that you use online resources to learn
+
+ align:start position:0%
+that you use online resources to learn
+ 
+
+ align:start position:0%
+that you use online resources to learn
+from. Um, so just get in groups of
+
+ align:start position:0%
+from. Um, so just get in groups of
+ 
+
+ align:start position:0%
+from. Um, so just get in groups of
+three, um, and spend the first few
+
+ align:start position:0%
+three, um, and spend the first few
+ 
+
+ align:start position:0%
+three, um, and spend the first few
+minutes talking to each other about what
+
+ align:start position:0%
+minutes talking to each other about what
+ 
+
+ align:start position:0%
+minutes talking to each other about what
+kinds of, uh, hobbies you have and what
+
+ align:start position:0%
+kinds of, uh, hobbies you have and what
+ 
+
+ align:start position:0%
+kinds of, uh, hobbies you have and what
+kind of online learning you do in those
+
+ align:start position:0%
+kind of online learning you do in those
+ 
+
+ align:start position:0%
+kind of online learning you do in those
+hobbies. Does that make sense? Ready?
+
+ align:start position:0%
+hobbies. Does that make sense? Ready?
+ 
+
+ align:start position:0%
+hobbies. Does that make sense? Ready?
+Go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, come on back. Great
+
+ align:start position:0%
+All right, come on back. Great
+ 
+
+ align:start position:0%
+All right, come on back. Great
+condition. So, first of all, Omar should
+
+ align:start position:0%
+condition. So, first of all, Omar should
+ 
+
+ align:start position:0%
+condition. So, first of all, Omar should
+show us his camera. Do you want to talk
+
+ align:start position:0%
+show us his camera. Do you want to talk
+ 
+
+ align:start position:0%
+show us his camera. Do you want to talk
+about um, so I I I talked about
+
+ align:start position:0%
+about um, so I I I talked about
+ 
+
+ align:start position:0%
+about um, so I I I talked about
+photography? Like I spend an unhealthy
+
+ align:start position:0%
+photography? Like I spend an unhealthy
+ 
+
+ align:start position:0%
+photography? Like I spend an unhealthy
+amount of time on YouTube like with
+
+ align:start position:0%
+amount of time on YouTube like with
+ 
+
+ align:start position:0%
+amount of time on YouTube like with
+photography tutorials. And so this
+
+ align:start position:0%
+photography tutorials. And so this
+ 
+
+ align:start position:0%
+photography tutorials. And so this
+camera is a 50-y old camera and I had no
+
+ align:start position:0%
+camera is a 50-y old camera and I had no
+ 
+
+ align:start position:0%
+camera is a 50-y old camera and I had no
+idea um how to even begin looking for
+
+ align:start position:0%
+idea um how to even begin looking for
+ 
+
+ align:start position:0%
+idea um how to even begin looking for
+one. And like these last three weeks
+
+ align:start position:0%
+one. And like these last three weeks
+ 
+
+ align:start position:0%
+one. And like these last three weeks
+I've been looking because I want to run
+
+ align:start position:0%
+I've been looking because I want to run
+ 
+
+ align:start position:0%
+I've been looking because I want to run
+a CPW event um for uh admits on how to
+
+ align:start position:0%
+a CPW event um for uh admits on how to
+ 
+
+ align:start position:0%
+a CPW event um for uh admits on how to
+use an SLR camera. Isn't that cool? So I
+
+ align:start position:0%
+use an SLR camera. Isn't that cool? So I
+ 
+
+ align:start position:0%
+use an SLR camera. Isn't that cool? So I
+don't know like this is in really great
+
+ align:start position:0%
+don't know like this is in really great
+ 
+
+ align:start position:0%
+don't know like this is in really great
+condition and I was like on eBay for
+
+ align:start position:0%
+condition and I was like on eBay for
+ 
+
+ align:start position:0%
+condition and I was like on eBay for
+hours but I you know watched YouTube
+
+ align:start position:0%
+hours but I you know watched YouTube
+ 
+
+ align:start position:0%
+hours but I you know watched YouTube
+tutorials was reading on like Reddit
+
+ align:start position:0%
+tutorials was reading on like Reddit
+ 
+
+ align:start position:0%
+tutorials was reading on like Reddit
+forums, photography forums, DP review,
+
+ align:start position:0%
+forums, photography forums, DP review,
+ 
+
+ align:start position:0%
+forums, photography forums, DP review,
+pedopixel like on what to look out for
+
+ align:start position:0%
+pedopixel like on what to look out for
+ 
+
+ align:start position:0%
+pedopixel like on what to look out for
+and before that like learning how to
+
+ align:start position:0%
+and before that like learning how to
+ 
+
+ align:start position:0%
+and before that like learning how to
+actually take photos. Um was all done
+
+ align:start position:0%
+actually take photos. Um was all done
+ 
+
+ align:start position:0%
+actually take photos. Um was all done
+through YouTube. It was selftaught. I
+
+ align:start position:0%
+through YouTube. It was selftaught. I
+ 
+
+ align:start position:0%
+through YouTube. It was selftaught. I
+started off with a phone and then I
+
+ align:start position:0%
+started off with a phone and then I
+ 
+
+ align:start position:0%
+started off with a phone and then I
+slowly built up um my toolbox once I had
+
+ align:start position:0%
+slowly built up um my toolbox once I had
+ 
+
+ align:start position:0%
+slowly built up um my toolbox once I had
+the knowledge and yeah now I'm like the
+
+ align:start position:0%
+the knowledge and yeah now I'm like the
+ 
+
+ align:start position:0%
+the knowledge and yeah now I'm like the
+photo editor for the tech. I stuff for
+
+ align:start position:0%
+photo editor for the tech. I stuff for
+ 
+
+ align:start position:0%
+photo editor for the tech. I stuff for
+yearbook and now I do a lot of stuff for
+
+ align:start position:0%
+yearbook and now I do a lot of stuff for
+ 
+
+ align:start position:0%
+yearbook and now I do a lot of stuff for
+photography and now I'm actually
+
+ align:start position:0%
+photography and now I'm actually
+ 
+
+ align:start position:0%
+photography and now I'm actually
+teaching others. Um I recently actually
+
+ align:start position:0%
+teaching others. Um I recently actually
+ 
+
+ align:start position:0%
+teaching others. Um I recently actually
+just interviewed up here this I
+
+ align:start position:0%
+just interviewed up here this I
+ 
+
+ align:start position:0%
+just interviewed up here this I
+interviewed for to teach a digital
+
+ align:start position:0%
+interviewed for to teach a digital
+ 
+
+ align:start position:0%
+interviewed for to teach a digital
+photography course although due to time
+
+ align:start position:0%
+photography course although due to time
+ 
+
+ align:start position:0%
+photography course although due to time
+conflicts I won't be able to do that. Um
+
+ align:start position:0%
+conflicts I won't be able to do that. Um
+ 
+
+ align:start position:0%
+conflicts I won't be able to do that. Um
+but I did interview and I um was about
+
+ align:start position:0%
+but I did interview and I um was about
+ 
+
+ align:start position:0%
+but I did interview and I um was about
+to go on the other side of that um
+
+ align:start position:0%
+to go on the other side of that um
+ 
+
+ align:start position:0%
+to go on the other side of that um
+learning experience.
+
+ align:start position:0%
+learning experience.
+ 
+
+ align:start position:0%
+learning experience.
+Camera's rad. I just got it um before my
+
+ align:start position:0%
+Camera's rad. I just got it um before my
+ 
+
+ align:start position:0%
+Camera's rad. I just got it um before my
+last class. So like I need to go to a
+
+ align:start position:0%
+last class. So like I need to go to a
+ 
+
+ align:start position:0%
+last class. So like I need to go to a
+camera shop just to make sure it works.
+
+ align:start position:0%
+camera shop just to make sure it works.
+ 
+
+ align:start position:0%
+camera shop just to make sure it works.
+um which I'll be doing after this class.
+
+ align:start position:0%
+um which I'll be doing after this class.
+ 
+
+ align:start position:0%
+um which I'll be doing after this class.
+A photo of that. I want a photo a photo
+
+ align:start position:0%
+A photo of that. I want a photo a photo
+ 
+
+ align:start position:0%
+A photo of that. I want a photo a photo
+of Omar with his new camera taken with a
+
+ align:start position:0%
+of Omar with his new camera taken with a
+ 
+
+ align:start position:0%
+of Omar with his new camera taken with a
+contemporary.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. I I I mean those Polaroid cameras
+
+ align:start position:0%
+Yeah. I I I mean those Polaroid cameras
+ 
+
+ align:start position:0%
+Yeah. I I I mean those Polaroid cameras
+became much more widely accessible
+
+ align:start position:0%
+became much more widely accessible
+ 
+
+ align:start position:0%
+became much more widely accessible
+probably when I was in grade school.
+
+ align:start position:0%
+probably when I was in grade school.
+ 
+
+ align:start position:0%
+probably when I was in grade school.
+Like they were pretty common and then
+
+ align:start position:0%
+Like they were pretty common and then
+ 
+
+ align:start position:0%
+Like they were pretty common and then
+and then there was sort of a revival in
+
+ align:start position:0%
+and then there was sort of a revival in
+ 
+
+ align:start position:0%
+and then there was sort of a revival in
+the last few years. So like my daughter
+
+ align:start position:0%
+the last few years. So like my daughter
+ 
+
+ align:start position:0%
+the last few years. So like my daughter
+has a Polaroid camera. I don't think
+
+ align:start position:0%
+has a Polaroid camera. I don't think
+ 
+
+ align:start position:0%
+has a Polaroid camera. I don't think
+it's called. We call them Polaroid
+
+ align:start position:0%
+it's called. We call them Polaroid
+ 
+
+ align:start position:0%
+it's called. We call them Polaroid
+cameras because they probably have some
+
+ align:start position:0%
+cameras because they probably have some
+ 
+
+ align:start position:0%
+cameras because they probably have some
+different term now of instant camera or
+
+ align:start position:0%
+different term now of instant camera or
+ 
+
+ align:start position:0%
+different term now of instant camera or
+something like that. Um, anybody have a
+
+ align:start position:0%
+something like that. Um, anybody have a
+ 
+
+ align:start position:0%
+something like that. Um, anybody have a
+completely different hobby from Omar
+
+ align:start position:0%
+completely different hobby from Omar
+ 
+
+ align:start position:0%
+completely different hobby from Omar
+where you could tell a very similar kind
+
+ align:start position:0%
+where you could tell a very similar kind
+ 
+
+ align:start position:0%
+where you could tell a very similar kind
+of story about learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or I guess like you know similar sort of
+
+ align:start position:0%
+or I guess like you know similar sort of
+ 
+
+ align:start position:0%
+or I guess like you know similar sort of
+story of learning is like you know
+
+ align:start position:0%
+story of learning is like you know
+ 
+
+ align:start position:0%
+story of learning is like you know
+through YouTube right like I want to or
+
+ align:start position:0%
+through YouTube right like I want to or
+ 
+
+ align:start position:0%
+through YouTube right like I want to or
+I'm like starting to learn how to like
+
+ align:start position:0%
+I'm like starting to learn how to like
+ 
+
+ align:start position:0%
+I'm like starting to learn how to like
+play guitar and bass and stuff. Um, but
+
+ align:start position:0%
+play guitar and bass and stuff. Um, but
+ 
+
+ align:start position:0%
+play guitar and bass and stuff. Um, but
+the thing with YouTube is it's like we
+
+ align:start position:0%
+the thing with YouTube is it's like we
+ 
+
+ align:start position:0%
+the thing with YouTube is it's like we
+talk about like algorithm guided
+
+ align:start position:0%
+talk about like algorithm guided
+ 
+
+ align:start position:0%
+talk about like algorithm guided
+learning or whatever, but like it kind
+
+ align:start position:0%
+learning or whatever, but like it kind
+ 
+
+ align:start position:0%
+learning or whatever, but like it kind
+of almost feels like YouTube's sort of
+
+ align:start position:0%
+of almost feels like YouTube's sort of
+ 
+
+ align:start position:0%
+of almost feels like YouTube's sort of
+an algorithm kind of guided learning in
+
+ align:start position:0%
+an algorithm kind of guided learning in
+ 
+
+ align:start position:0%
+an algorithm kind of guided learning in
+a way or like I feel like the YouTube
+
+ align:start position:0%
+a way or like I feel like the YouTube
+ 
+
+ align:start position:0%
+a way or like I feel like the YouTube
+algorithm really sort of drives my
+
+ align:start position:0%
+algorithm really sort of drives my
+ 
+
+ align:start position:0%
+algorithm really sort of drives my
+interests or like diverts my interests
+
+ align:start position:0%
+interests or like diverts my interests
+ 
+
+ align:start position:0%
+interests or like diverts my interests
+into different things at different
+
+ align:start position:0%
+into different things at different
+ 
+
+ align:start position:0%
+into different things at different
+periods of time. Like on a weekby- week
+
+ align:start position:0%
+periods of time. Like on a weekby- week
+ 
+
+ align:start position:0%
+periods of time. Like on a weekby- week
+beek basis, I can be interested in
+
+ align:start position:0%
+beek basis, I can be interested in
+ 
+
+ align:start position:0%
+beek basis, I can be interested in
+something completely different than what
+
+ align:start position:0%
+something completely different than what
+ 
+
+ align:start position:0%
+something completely different than what
+I was interested in last week. So, it
+
+ align:start position:0%
+I was interested in last week. So, it
+ 
+
+ align:start position:0%
+I was interested in last week. So, it
+feels like I like I'm just sort of
+
+ align:start position:0%
+feels like I like I'm just sort of
+ 
+
+ align:start position:0%
+feels like I like I'm just sort of
+moving through a bunch of like different
+
+ align:start position:0%
+moving through a bunch of like different
+ 
+
+ align:start position:0%
+moving through a bunch of like different
+hobbies and because I feel like I'm at
+
+ align:start position:0%
+hobbies and because I feel like I'm at
+ 
+
+ align:start position:0%
+hobbies and because I feel like I'm at
+the whim of the YouTube algorithm
+
+ align:start position:0%
+the whim of the YouTube algorithm
+ 
+
+ align:start position:0%
+the whim of the YouTube algorithm
+sometimes. Oh, yeah. Yeah. Yeah. Yeah.
+
+ align:start position:0%
+sometimes. Oh, yeah. Yeah. Yeah. Yeah.
+ 
+
+ align:start position:0%
+sometimes. Oh, yeah. Yeah. Yeah. Yeah.
+People Yeah. Yeah. No, I think people
+
+ align:start position:0%
+People Yeah. Yeah. No, I think people
+ 
+
+ align:start position:0%
+People Yeah. Yeah. No, I think people
+feel that way with lots of uh kind of
+
+ align:start position:0%
+feel that way with lots of uh kind of
+ 
+
+ align:start position:0%
+feel that way with lots of uh kind of
+technologies that do some kind of
+
+ align:start position:0%
+technologies that do some kind of
+ 
+
+ align:start position:0%
+technologies that do some kind of
+aggregation. Pinterest for people who do
+
+ align:start position:0%
+aggregation. Pinterest for people who do
+ 
+
+ align:start position:0%
+aggregation. Pinterest for people who do
+crafty kinds of things. Tik Tok for
+
+ align:start position:0%
+crafty kinds of things. Tik Tok for
+ 
+
+ align:start position:0%
+crafty kinds of things. Tik Tok for
+people who follow media and stuff like
+
+ align:start position:0%
+people who follow media and stuff like
+ 
+
+ align:start position:0%
+people who follow media and stuff like
+that. Yeah. Good. What other what other
+
+ align:start position:0%
+that. Yeah. Good. What other what other
+ 
+
+ align:start position:0%
+that. Yeah. Good. What other what other
+hobbies do you talk about or what other
+
+ align:start position:0%
+hobbies do you talk about or what other
+ 
+
+ align:start position:0%
+hobbies do you talk about or what other
+sort of learn like informal learning
+
+ align:start position:0%
+sort of learn like informal learning
+ 
+
+ align:start position:0%
+sort of learn like informal learning
+strategies seem important and
+
+ align:start position:0%
+strategies seem important and
+ 
+
+ align:start position:0%
+strategies seem important and
+interesting or things that you were
+
+ align:start position:0%
+interesting or things that you were
+ 
+
+ align:start position:0%
+interesting or things that you were
+talking about in your groups?
+
+ align:start position:0%
+talking about in your groups?
+ 
+
+ align:start position:0%
+talking about in your groups?
+Yeah. Awesome. I'll say like on a less I
+
+ align:start position:0%
+Yeah. Awesome. I'll say like on a less I
+ 
+
+ align:start position:0%
+Yeah. Awesome. I'll say like on a less I
+guess handson like level. Um, I like use
+
+ align:start position:0%
+guess handson like level. Um, I like use
+ 
+
+ align:start position:0%
+guess handson like level. Um, I like use
+like similar resources like YouTube and
+
+ align:start position:0%
+like similar resources like YouTube and
+ 
+
+ align:start position:0%
+like similar resources like YouTube and
+stuff like that for like a lot of like
+
+ align:start position:0%
+stuff like that for like a lot of like
+ 
+
+ align:start position:0%
+stuff like that for like a lot of like
+collecting knowledge for like things
+
+ align:start position:0%
+collecting knowledge for like things
+ 
+
+ align:start position:0%
+collecting knowledge for like things
+that I'm interested in like fashion for
+
+ align:start position:0%
+that I'm interested in like fashion for
+ 
+
+ align:start position:0%
+that I'm interested in like fashion for
+example because a lot of a lot of it is
+
+ align:start position:0%
+example because a lot of a lot of it is
+ 
+
+ align:start position:0%
+example because a lot of a lot of it is
+like you know like like in New York
+
+ align:start position:0%
+like you know like like in New York
+ 
+
+ align:start position:0%
+like you know like like in New York
+fashion week for example it's like these
+
+ align:start position:0%
+fashion week for example it's like these
+ 
+
+ align:start position:0%
+fashion week for example it's like these
+very condensed times right where like
+
+ align:start position:0%
+very condensed times right where like
+ 
+
+ align:start position:0%
+very condensed times right where like
+it's all happening and a lot of people
+
+ align:start position:0%
+it's all happening and a lot of people
+ 
+
+ align:start position:0%
+it's all happening and a lot of people
+follow very closely but if you're an MIT
+
+ align:start position:0%
+follow very closely but if you're an MIT
+ 
+
+ align:start position:0%
+follow very closely but if you're an MIT
+student you're probably like I can't
+
+ align:start position:0%
+student you're probably like I can't
+ 
+
+ align:start position:0%
+student you're probably like I can't
+feeling
+
+ align:start position:0%
+feeling
+ 
+
+ align:start position:0%
+feeling
+But like then you can like watch
+
+ align:start position:0%
+But like then you can like watch
+ 
+
+ align:start position:0%
+But like then you can like watch
+highlights from it and like actual like
+
+ align:start position:0%
+highlights from it and like actual like
+ 
+
+ align:start position:0%
+highlights from it and like actual like
+critics commentary on them and like kind
+
+ align:start position:0%
+critics commentary on them and like kind
+ 
+
+ align:start position:0%
+critics commentary on them and like kind
+of see like what that's doing both
+
+ align:start position:0%
+of see like what that's doing both
+ 
+
+ align:start position:0%
+of see like what that's doing both
+socially and also like from an artistic
+
+ align:start position:0%
+socially and also like from an artistic
+ 
+
+ align:start position:0%
+socially and also like from an artistic
+sense. Yeah. Do you use Pinterest or
+
+ align:start position:0%
+sense. Yeah. Do you use Pinterest or
+ 
+
+ align:start position:0%
+sense. Yeah. Do you use Pinterest or
+anything for sort of collecting your um
+
+ align:start position:0%
+anything for sort of collecting your um
+ 
+
+ align:start position:0%
+anything for sort of collecting your um
+I'm I've I had a social media
+
+ align:start position:0%
+I'm I've I had a social media
+ 
+
+ align:start position:0%
+I'm I've I had a social media
+problem YouTube so now I've kind of just
+
+ align:start position:0%
+problem YouTube so now I've kind of just
+ 
+
+ align:start position:0%
+problem YouTube so now I've kind of just
+continued into YouTube and stuff but I I
+
+ align:start position:0%
+continued into YouTube and stuff but I I
+ 
+
+ align:start position:0%
+continued into YouTube and stuff but I I
+do get to I guess reflect on it because
+
+ align:start position:0%
+do get to I guess reflect on it because
+ 
+
+ align:start position:0%
+do get to I guess reflect on it because
+I'm doing costume designs and stuff. Oh,
+
+ align:start position:0%
+I'm doing costume designs and stuff. Oh,
+ 
+
+ align:start position:0%
+I'm doing costume designs and stuff. Oh,
+cool. Yeah. My my my daughter is big
+
+ align:start position:0%
+cool. Yeah. My my my daughter is big
+ 
+
+ align:start position:0%
+cool. Yeah. My my my daughter is big
+into aesthetics of various kinds, craft
+
+ align:start position:0%
+into aesthetics of various kinds, craft
+ 
+
+ align:start position:0%
+into aesthetics of various kinds, craft
+things or design things. And Pinterest
+
+ align:start position:0%
+things or design things. And Pinterest
+ 
+
+ align:start position:0%
+things or design things. And Pinterest
+is like a big part of how she like she
+
+ align:start position:0%
+is like a big part of how she like she
+ 
+
+ align:start position:0%
+is like a big part of how she like she
+does the same kind of combing that you
+
+ align:start position:0%
+does the same kind of combing that you
+ 
+
+ align:start position:0%
+does the same kind of combing that you
+does, but she's deliberate about taking
+
+ align:start position:0%
+does, but she's deliberate about taking
+ 
+
+ align:start position:0%
+does, but she's deliberate about taking
+things that she likes and storing them
+
+ align:start position:0%
+things that she likes and storing them
+ 
+
+ align:start position:0%
+things that she likes and storing them
+and categorizing them and trying to make
+
+ align:start position:0%
+and categorizing them and trying to make
+ 
+
+ align:start position:0%
+and categorizing them and trying to make
+sense of them and things like
+
+ align:start position:0%
+sense of them and things like
+ 
+
+ align:start position:0%
+sense of them and things like
+that. Yeah. Dana. And then I was just
+
+ align:start position:0%
+that. Yeah. Dana. And then I was just
+ 
+
+ align:start position:0%
+that. Yeah. Dana. And then I was just
+going to say like just like another
+
+ align:start position:0%
+going to say like just like another
+ 
+
+ align:start position:0%
+going to say like just like another
+medium outside of like watching videos
+
+ align:start position:0%
+medium outside of like watching videos
+ 
+
+ align:start position:0%
+medium outside of like watching videos
+is just like online like so mine is like
+
+ align:start position:0%
+is just like online like so mine is like
+ 
+
+ align:start position:0%
+is just like online like so mine is like
+cooking. So like recipes and just like
+
+ align:start position:0%
+cooking. So like recipes and just like
+ 
+
+ align:start position:0%
+cooking. So like recipes and just like
+articles. Um, and then also like mine
+
+ align:start position:0%
+articles. Um, and then also like mine
+ 
+
+ align:start position:0%
+articles. Um, and then also like mine
+was like a little bit of TikTok just in
+
+ align:start position:0%
+was like a little bit of TikTok just in
+ 
+
+ align:start position:0%
+was like a little bit of TikTok just in
+like the one minute video of like you
+
+ align:start position:0%
+like the one minute video of like you
+ 
+
+ align:start position:0%
+like the one minute video of like you
+can cook this and it like isn't a
+
+ align:start position:0%
+can cook this and it like isn't a
+ 
+
+ align:start position:0%
+can cook this and it like isn't a
+professional chef showing you how to do
+
+ align:start position:0%
+professional chef showing you how to do
+ 
+
+ align:start position:0%
+professional chef showing you how to do
+it was cool to see that like oh like I
+
+ align:start position:0%
+it was cool to see that like oh like I
+ 
+
+ align:start position:0%
+it was cool to see that like oh like I
+can relate to that person so I can do
+
+ align:start position:0%
+can relate to that person so I can do
+ 
+
+ align:start position:0%
+can relate to that person so I can do
+it. Um, what what what are your favorite
+
+ align:start position:0%
+it. Um, what what what are your favorite
+ 
+
+ align:start position:0%
+it. Um, what what what are your favorite
+sort of recipe media or cooking media?
+
+ align:start position:0%
+sort of recipe media or cooking media?
+ 
+
+ align:start position:0%
+sort of recipe media or cooking media?
+Like how do you So I've only perfected
+
+ align:start position:0%
+Like how do you So I've only perfected
+ 
+
+ align:start position:0%
+Like how do you So I've only perfected
+one singular dish. Um, and it's
+
+ align:start position:0%
+one singular dish. Um, and it's
+ 
+
+ align:start position:0%
+one singular dish. Um, and it's
+scallops. Um, which is like a relatively
+
+ align:start position:0%
+scallops. Um, which is like a relatively
+ 
+
+ align:start position:0%
+scallops. Um, which is like a relatively
+hard thing, but like I'm scared to cook
+
+ align:start position:0%
+hard thing, but like I'm scared to cook
+ 
+
+ align:start position:0%
+hard thing, but like I'm scared to cook
+a chicken because I'm gonna give myself
+
+ align:start position:0%
+a chicken because I'm gonna give myself
+ 
+
+ align:start position:0%
+a chicken because I'm gonna give myself
+salmonilla a scallop.
+
+ align:start position:0%
+salmonilla a scallop.
+ 
+
+ align:start position:0%
+salmonilla a scallop.
+Yeah. So, my family joke is you only
+
+ align:start position:0%
+Yeah. So, my family joke is you only
+ 
+
+ align:start position:0%
+Yeah. So, my family joke is you only
+going to eat scallops for this. You're
+
+ align:start position:0%
+going to eat scallops for this. You're
+ 
+
+ align:start position:0%
+going to eat scallops for this. You're
+like, "Yeah, they're pretty good.
+
+ align:start position:0%
+like, "Yeah, they're pretty good.
+ 
+
+ align:start position:0%
+like, "Yeah, they're pretty good.
+They're healthy. Might be too many heavy
+
+ align:start position:0%
+They're healthy. Might be too many heavy
+ 
+
+ align:start position:0%
+They're healthy. Might be too many heavy
+metals if you do that your whole life or
+
+ align:start position:0%
+metals if you do that your whole life or
+ 
+
+ align:start position:0%
+metals if you do that your whole life or
+something like that." But yeah. Yeah. I
+
+ align:start position:0%
+something like that." But yeah. Yeah. I
+ 
+
+ align:start position:0%
+something like that." But yeah. Yeah. I
+don't know if bottom feeders are what
+
+ align:start position:0%
+don't know if bottom feeders are what
+ 
+
+ align:start position:0%
+don't know if bottom feeders are what
+you should do for your whole life, but
+
+ align:start position:0%
+you should do for your whole life, but
+ 
+
+ align:start position:0%
+you should do for your whole life, but
+that seems like seems like a good start.
+
+ align:start position:0%
+that seems like seems like a good start.
+ 
+
+ align:start position:0%
+that seems like seems like a good start.
+How about you, Armon? Uh I do mention
+
+ align:start position:0%
+How about you, Armon? Uh I do mention
+ 
+
+ align:start position:0%
+How about you, Armon? Uh I do mention
+this in our group but what came out from
+
+ align:start position:0%
+this in our group but what came out from
+ 
+
+ align:start position:0%
+this in our group but what came out from
+people talking like a lot of people
+
+ align:start position:0%
+people talking like a lot of people
+ 
+
+ align:start position:0%
+people talking like a lot of people
+relate is number file uh stream blue one
+
+ align:start position:0%
+relate is number file uh stream blue one
+ 
+
+ align:start position:0%
+relate is number file uh stream blue one
+brown this video I just put them in what
+
+ align:start position:0%
+brown this video I just put them in what
+ 
+
+ align:start position:0%
+brown this video I just put them in what
+is this it's a maths video they just
+
+ align:start position:0%
+is this it's a maths video they just
+ 
+
+ align:start position:0%
+is this it's a maths video they just
+tell you cool math stuff
+
+ align:start position:0%
+tell you cool math stuff
+ 
+
+ align:start position:0%
+tell you cool math stuff
+it's called number file number file
+
+ align:start position:0%
+it's called number file number file
+ 
+
+ align:start position:0%
+it's called number file number file
+street blue on brown those kind of
+
+ align:start position:0%
+street blue on brown those kind of
+ 
+
+ align:start position:0%
+street blue on brown those kind of
+videos so sometimes you learn that there
+
+ align:start position:0%
+videos so sometimes you learn that there
+ 
+
+ align:start position:0%
+videos so sometimes you learn that there
+is fractional dimension and you just be
+
+ align:start position:0%
+is fractional dimension and you just be
+ 
+
+ align:start position:0%
+is fractional dimension and you just be
+watching what that means And I watch
+
+ align:start position:0%
+watching what that means And I watch
+ 
+
+ align:start position:0%
+watching what that means And I watch
+those, too. So, they're really
+
+ align:start position:0%
+those, too. So, they're really
+ 
+
+ align:start position:0%
+those, too. So, they're really
+interested. Um, yeah. Who's who's the
+
+ align:start position:0%
+interested. Um, yeah. Who's who's the
+ 
+
+ align:start position:0%
+interested. Um, yeah. Who's who's the
+guy who came here a couple years ago for
+
+ align:start position:0%
+guy who came here a couple years ago for
+ 
+
+ align:start position:0%
+guy who came here a couple years ago for
+a graduation or convocation or
+
+ align:start position:0%
+a graduation or convocation or
+ 
+
+ align:start position:0%
+a graduation or convocation or
+something? Mark. Hm. Mark Robber. Mark
+
+ align:start position:0%
+something? Mark. Hm. Mark Robber. Mark
+ 
+
+ align:start position:0%
+something? Mark. Hm. Mark Robber. Mark
+Robber. Yep. Yeah. Yeah. He's sort of
+
+ align:start position:0%
+Robber. Yep. Yeah. Yeah. He's sort of
+ 
+
+ align:start position:0%
+Robber. Yep. Yeah. Yeah. He's sort of
+science YouTuber. Guy named Veritasium
+
+ align:start position:0%
+science YouTuber. Guy named Veritasium
+ 
+
+ align:start position:0%
+science YouTuber. Guy named Veritasium
+does uh does things like that too. Yeah.
+
+ align:start position:0%
+does uh does things like that too. Yeah.
+ 
+
+ align:start position:0%
+does uh does things like that too. Yeah.
+Yeah. Enormously uh popular and
+
+ align:start position:0%
+Yeah. Enormously uh popular and
+ 
+
+ align:start position:0%
+Yeah. Enormously uh popular and
+successful and things like that. Um I
+
+ align:start position:0%
+successful and things like that. Um I
+ 
+
+ align:start position:0%
+successful and things like that. Um I
+play a lot of computer games and I my
+
+ align:start position:0%
+play a lot of computer games and I my
+ 
+
+ align:start position:0%
+play a lot of computer games and I my
+life sort of overlaps. I don't know.
+
+ align:start position:0%
+life sort of overlaps. I don't know.
+ 
+
+ align:start position:0%
+life sort of overlaps. I don't know.
+computer games are like a couple of
+
+ align:start position:0%
+computer games are like a couple of
+ 
+
+ align:start position:0%
+computer games are like a couple of
+years older than me, but not by much. I
+
+ align:start position:0%
+years older than me, but not by much. I
+ 
+
+ align:start position:0%
+years older than me, but not by much. I
+mean, definitely some of my earliest
+
+ align:start position:0%
+mean, definitely some of my earliest
+ 
+
+ align:start position:0%
+mean, definitely some of my earliest
+memories are um games that would have
+
+ align:start position:0%
+memories are um games that would have
+ 
+
+ align:start position:0%
+memories are um games that would have
+been played off of like a cassette reel
+
+ align:start position:0%
+been played off of like a cassette reel
+ 
+
+ align:start position:0%
+been played off of like a cassette reel
+rather than any kind of rotary disc or
+
+ align:start position:0%
+rather than any kind of rotary disc or
+ 
+
+ align:start position:0%
+rather than any kind of rotary disc or
+or something like that. Um but another
+
+ align:start position:0%
+or something like that. Um but another
+ 
+
+ align:start position:0%
+or something like that. Um but another
+distinctive memory is that uh one of the
+
+ align:start position:0%
+distinctive memory is that uh one of the
+ 
+
+ align:start position:0%
+distinctive memory is that uh one of the
+first categories of games were these
+
+ align:start position:0%
+first categories of games were these
+ 
+
+ align:start position:0%
+first categories of games were these
+textbased games where you had to sort of
+
+ align:start position:0%
+textbased games where you had to sort of
+ 
+
+ align:start position:0%
+textbased games where you had to sort of
+enter prompts into a parser like open
+
+ align:start position:0%
+enter prompts into a parser like open
+ 
+
+ align:start position:0%
+enter prompts into a parser like open
+mailbox, go left, go right, walk in, you
+
+ align:start position:0%
+mailbox, go left, go right, walk in, you
+ 
+
+ align:start position:0%
+mailbox, go left, go right, walk in, you
+know, pick up key, put key and lock,
+
+ align:start position:0%
+know, pick up key, put key and lock,
+ 
+
+ align:start position:0%
+know, pick up key, put key and lock,
+those kinds of things. So, a lot of what
+
+ align:start position:0%
+those kinds of things. So, a lot of what
+ 
+
+ align:start position:0%
+those kinds of things. So, a lot of what
+you're doing Yeah. Come on in. um was
+
+ align:start position:0%
+you're doing Yeah. Come on in. um was
+ 
+
+ align:start position:0%
+you're doing Yeah. Come on in. um was
+kind of guessing like uh you know what
+
+ align:start position:0%
+kind of guessing like uh you know what
+ 
+
+ align:start position:0%
+kind of guessing like uh you know what
+what was the what was the right key term
+
+ align:start position:0%
+what was the what was the right key term
+ 
+
+ align:start position:0%
+what was the what was the right key term
+to put in to um to engage things and so
+
+ align:start position:0%
+to put in to um to engage things and so
+ 
+
+ align:start position:0%
+to put in to um to engage things and so
+actually a lot of these games Infocom
+
+ align:start position:0%
+actually a lot of these games Infocom
+ 
+
+ align:start position:0%
+actually a lot of these games Infocom
+was a company that sold a lot of them.
+
+ align:start position:0%
+was a company that sold a lot of them.
+ 
+
+ align:start position:0%
+was a company that sold a lot of them.
+Um the game companies would also publish
+
+ align:start position:0%
+Um the game companies would also publish
+ 
+
+ align:start position:0%
+Um the game companies would also publish
+a book and the book would have uh the
+
+ align:start position:0%
+a book and the book would have uh the
+ 
+
+ align:start position:0%
+a book and the book would have uh the
+answers to a whole bunch of things or
+
+ align:start position:0%
+answers to a whole bunch of things or
+ 
+
+ align:start position:0%
+answers to a whole bunch of things or
+like solution sets in invisible ink and
+
+ align:start position:0%
+like solution sets in invisible ink and
+ 
+
+ align:start position:0%
+like solution sets in invisible ink and
+so you had like a little uh um pen that
+
+ align:start position:0%
+so you had like a little uh um pen that
+ 
+
+ align:start position:0%
+so you had like a little uh um pen that
+came with it. And so when you decided
+
+ align:start position:0%
+came with it. And so when you decided
+ 
+
+ align:start position:0%
+came with it. And so when you decided
+that you had given up trying for
+
+ align:start position:0%
+that you had given up trying for
+ 
+
+ align:start position:0%
+that you had given up trying for
+yourself, you would uh you would cover
+
+ align:start position:0%
+yourself, you would uh you would cover
+ 
+
+ align:start position:0%
+yourself, you would uh you would cover
+the invisible ink with this pen that
+
+ align:start position:0%
+the invisible ink with this pen that
+ 
+
+ align:start position:0%
+the invisible ink with this pen that
+would reveal the sort of next clue and
+
+ align:start position:0%
+would reveal the sort of next clue and
+ 
+
+ align:start position:0%
+would reveal the sort of next clue and
+help you go on and so forth. Um and uh
+
+ align:start position:0%
+help you go on and so forth. Um and uh
+ 
+
+ align:start position:0%
+help you go on and so forth. Um and uh
+but now you know essentially every video
+
+ align:start position:0%
+but now you know essentially every video
+ 
+
+ align:start position:0%
+but now you know essentially every video
+game it like they almost instantly are
+
+ align:start position:0%
+game it like they almost instantly are
+ 
+
+ align:start position:0%
+game it like they almost instantly are
+created with a wiki that has you know
+
+ align:start position:0%
+created with a wiki that has you know
+ 
+
+ align:start position:0%
+created with a wiki that has you know
+every item in the game and what they do
+
+ align:start position:0%
+every item in the game and what they do
+ 
+
+ align:start position:0%
+every item in the game and what they do
+and where they go. Um a Reddit forum for
+
+ align:start position:0%
+and where they go. Um a Reddit forum for
+ 
+
+ align:start position:0%
+and where they go. Um a Reddit forum for
+conversation. um more recently Discord
+
+ align:start position:0%
+conversation. um more recently Discord
+ 
+
+ align:start position:0%
+conversation. um more recently Discord
+um pages, you know, that actually, you
+
+ align:start position:0%
+um pages, you know, that actually, you
+ 
+
+ align:start position:0%
+um pages, you know, that actually, you
+know, for smaller games can be kind of
+
+ align:start position:0%
+know, for smaller games can be kind of
+ 
+
+ align:start position:0%
+know, for smaller games can be kind of
+surprisingly intimate where you, you
+
+ align:start position:0%
+surprisingly intimate where you, you
+ 
+
+ align:start position:0%
+surprisingly intimate where you, you
+know, you really do feel like you're
+
+ align:start position:0%
+know, you really do feel like you're
+ 
+
+ align:start position:0%
+know, you really do feel like you're
+just like chatting with the guy who made
+
+ align:start position:0%
+just like chatting with the guy who made
+ 
+
+ align:start position:0%
+just like chatting with the guy who made
+the game. Um even if you know, there may
+
+ align:start position:0%
+the game. Um even if you know, there may
+ 
+
+ align:start position:0%
+the game. Um even if you know, there may
+not be responding to you directly, but
+
+ align:start position:0%
+not be responding to you directly, but
+ 
+
+ align:start position:0%
+not be responding to you directly, but
+they're certainly like responding to
+
+ align:start position:0%
+they're certainly like responding to
+ 
+
+ align:start position:0%
+they're certainly like responding to
+people that are there around with you
+
+ align:start position:0%
+people that are there around with you
+ 
+
+ align:start position:0%
+people that are there around with you
+and things like that, YouTube channels
+
+ align:start position:0%
+and things like that, YouTube channels
+ 
+
+ align:start position:0%
+and things like that, YouTube channels
+or all these kinds of things. Um yeah, I
+
+ align:start position:0%
+or all these kinds of things. Um yeah, I
+ 
+
+ align:start position:0%
+or all these kinds of things. Um yeah, I
+think there I think there's all kinds of
+
+ align:start position:0%
+think there I think there's all kinds of
+ 
+
+ align:start position:0%
+think there I think there's all kinds of
+ways. There ve there are very few
+
+ align:start position:0%
+ways. There ve there are very few
+ 
+
+ align:start position:0%
+ways. There ve there are very few
+people I think left in theorked world
+
+ align:start position:0%
+people I think left in theorked world
+ 
+
+ align:start position:0%
+people I think left in theorked world
+who don't have some kind of encounter
+
+ align:start position:0%
+who don't have some kind of encounter
+ 
+
+ align:start position:0%
+who don't have some kind of encounter
+with this sort of informal learning. Um
+
+ align:start position:0%
+with this sort of informal learning. Um
+ 
+
+ align:start position:0%
+with this sort of informal learning. Um
+I I I think you know just an enormous
+
+ align:start position:0%
+I I I think you know just an enormous
+ 
+
+ align:start position:0%
+I I I think you know just an enormous
+number of people in a very short period
+
+ align:start position:0%
+number of people in a very short period
+ 
+
+ align:start position:0%
+number of people in a very short period
+of time. I mean obviously there have
+
+ align:start position:0%
+of time. I mean obviously there have
+ 
+
+ align:start position:0%
+of time. I mean obviously there have
+always been people who do DIY kinds of
+
+ align:start position:0%
+always been people who do DIY kinds of
+ 
+
+ align:start position:0%
+always been people who do DIY kinds of
+things and stuff like that but the
+
+ align:start position:0%
+things and stuff like that but the
+ 
+
+ align:start position:0%
+things and stuff like that but the
+degree to which online resources has
+
+ align:start position:0%
+degree to which online resources has
+ 
+
+ align:start position:0%
+degree to which online resources has
+shaped those learning interactions um is
+
+ align:start position:0%
+shaped those learning interactions um is
+ 
+
+ align:start position:0%
+shaped those learning interactions um is
+a profound change over the last uh
+
+ align:start position:0%
+a profound change over the last uh
+ 
+
+ align:start position:0%
+a profound change over the last uh
+decade or two. The uh um and I think it
+
+ align:start position:0%
+decade or two. The uh um and I think it
+ 
+
+ align:start position:0%
+decade or two. The uh um and I think it
+I think it reminds us to do a few things
+
+ align:start position:0%
+I think it reminds us to do a few things
+ 
+
+ align:start position:0%
+I think it reminds us to do a few things
+that are useful. One is to um is to
+
+ align:start position:0%
+that are useful. One is to um is to
+ 
+
+ align:start position:0%
+that are useful. One is to um is to
+conceptualize learning really broadly.
+
+ align:start position:0%
+conceptualize learning really broadly.
+ 
+
+ align:start position:0%
+conceptualize learning really broadly.
+Um, you know, a lot of times that we
+
+ align:start position:0%
+Um, you know, a lot of times that we
+ 
+
+ align:start position:0%
+Um, you know, a lot of times that we
+think of learning, we sort of we pin it
+
+ align:start position:0%
+think of learning, we sort of we pin it
+ 
+
+ align:start position:0%
+think of learning, we sort of we pin it
+down in education, K12 education,
+
+ align:start position:0%
+down in education, K12 education,
+ 
+
+ align:start position:0%
+down in education, K12 education,
+college, things like that, but that's
+
+ align:start position:0%
+college, things like that, but that's
+ 
+
+ align:start position:0%
+college, things like that, but that's
+that's a relatively small part of
+
+ align:start position:0%
+that's a relatively small part of
+ 
+
+ align:start position:0%
+that's a relatively small part of
+people's lives. Um, people are learning
+
+ align:start position:0%
+people's lives. Um, people are learning
+ 
+
+ align:start position:0%
+people's lives. Um, people are learning
+all throughout their lives all the time.
+
+ align:start position:0%
+all throughout their lives all the time.
+ 
+
+ align:start position:0%
+all throughout their lives all the time.
+Um, people are developing new skills for
+
+ align:start position:0%
+Um, people are developing new skills for
+ 
+
+ align:start position:0%
+Um, people are developing new skills for
+work. They're developing new skills
+
+ align:start position:0%
+work. They're developing new skills
+ 
+
+ align:start position:0%
+work. They're developing new skills
+around their interests. They're they're
+
+ align:start position:0%
+around their interests. They're they're
+ 
+
+ align:start position:0%
+around their interests. They're they're
+they're pursuing passions. They're doing
+
+ align:start position:0%
+they're pursuing passions. They're doing
+ 
+
+ align:start position:0%
+they're pursuing passions. They're doing
+whatever else. And so think I think it's
+
+ align:start position:0%
+whatever else. And so think I think it's
+ 
+
+ align:start position:0%
+whatever else. And so think I think it's
+very helpful when thinking about online
+
+ align:start position:0%
+very helpful when thinking about online
+ 
+
+ align:start position:0%
+very helpful when thinking about online
+learning to be really open um to all
+
+ align:start position:0%
+learning to be really open um to all
+ 
+
+ align:start position:0%
+learning to be really open um to all
+these kinds of things. And then you know
+
+ align:start position:0%
+these kinds of things. And then you know
+ 
+
+ align:start position:0%
+these kinds of things. And then you know
+I I would say if there's a core argument
+
+ align:start position:0%
+I I would say if there's a core argument
+ 
+
+ align:start position:0%
+I I would say if there's a core argument
+in peerg guided learning at scale it's
+
+ align:start position:0%
+in peerg guided learning at scale it's
+ 
+
+ align:start position:0%
+in peerg guided learning at scale it's
+that these technologies have been so
+
+ align:start position:0%
+that these technologies have been so
+ 
+
+ align:start position:0%
+that these technologies have been so
+profound in changing the ways that we
+
+ align:start position:0%
+profound in changing the ways that we
+ 
+
+ align:start position:0%
+profound in changing the ways that we
+pursue learning outside of school and
+
+ align:start position:0%
+pursue learning outside of school and
+ 
+
+ align:start position:0%
+pursue learning outside of school and
+schools have proven to be institutions
+
+ align:start position:0%
+schools have proven to be institutions
+ 
+
+ align:start position:0%
+schools have proven to be institutions
+that are just remarkably resistant um to
+
+ align:start position:0%
+that are just remarkably resistant um to
+ 
+
+ align:start position:0%
+that are just remarkably resistant um to
+these forms of learning as well. Well,
+
+ align:start position:0%
+these forms of learning as well. Well,
+ 
+
+ align:start position:0%
+these forms of learning as well. Well,
+my hunch is most of you don't have an
+
+ align:start position:0%
+my hunch is most of you don't have an
+ 
+
+ align:start position:0%
+my hunch is most of you don't have an
+experience where you feel like, yeah,
+
+ align:start position:0%
+experience where you feel like, yeah,
+ 
+
+ align:start position:0%
+experience where you feel like, yeah,
+the kind of learning that I did in my
+
+ align:start position:0%
+the kind of learning that I did in my
+ 
+
+ align:start position:0%
+the kind of learning that I did in my
+eighth grade physics class was really
+
+ align:start position:0%
+eighth grade physics class was really
+ 
+
+ align:start position:0%
+eighth grade physics class was really
+just like the kind of learning that I
+
+ align:start position:0%
+just like the kind of learning that I
+ 
+
+ align:start position:0%
+just like the kind of learning that I
+did to learn photography or something
+
+ align:start position:0%
+did to learn photography or something
+ 
+
+ align:start position:0%
+did to learn photography or something
+like that. Um, there's something about
+
+ align:start position:0%
+like that. Um, there's something about
+ 
+
+ align:start position:0%
+like that. Um, there's something about
+schools um and the design and
+
+ align:start position:0%
+schools um and the design and
+ 
+
+ align:start position:0%
+schools um and the design and
+organization of schools that makes it
+
+ align:start position:0%
+organization of schools that makes it
+ 
+
+ align:start position:0%
+organization of schools that makes it
+really hard for these kinds of learning
+
+ align:start position:0%
+really hard for these kinds of learning
+ 
+
+ align:start position:0%
+really hard for these kinds of learning
+environments to make their way in. Um, I
+
+ align:start position:0%
+environments to make their way in. Um, I
+ 
+
+ align:start position:0%
+environments to make their way in. Um, I
+think a lot of what I want to share with
+
+ align:start position:0%
+think a lot of what I want to share with
+ 
+
+ align:start position:0%
+think a lot of what I want to share with
+you today are some of the most
+
+ align:start position:0%
+you today are some of the most
+ 
+
+ align:start position:0%
+you today are some of the most
+substantial efforts particularly in
+
+ align:start position:0%
+substantial efforts particularly in
+ 
+
+ align:start position:0%
+substantial efforts particularly in
+higher education to figure out how some
+
+ align:start position:0%
+higher education to figure out how some
+ 
+
+ align:start position:0%
+higher education to figure out how some
+of these approaches to um peer-guided
+
+ align:start position:0%
+of these approaches to um peer-guided
+ 
+
+ align:start position:0%
+of these approaches to um peer-guided
+learning at scale could make their way
+
+ align:start position:0%
+learning at scale could make their way
+ 
+
+ align:start position:0%
+learning at scale could make their way
+into formal institutions. Um I the ideas
+
+ align:start position:0%
+into formal institutions. Um I the ideas
+ 
+
+ align:start position:0%
+into formal institutions. Um I the ideas
+that I am presenting to you when I you
+
+ align:start position:0%
+that I am presenting to you when I you
+ 
+
+ align:start position:0%
+that I am presenting to you when I you
+know if I was talking about them 10
+
+ align:start position:0%
+know if I was talking about them 10
+ 
+
+ align:start position:0%
+know if I was talking about them 10
+years ago I would have positioned them
+
+ align:start position:0%
+years ago I would have positioned them
+ 
+
+ align:start position:0%
+years ago I would have positioned them
+more as these are very viable ways in
+
+ align:start position:0%
+more as these are very viable ways in
+ 
+
+ align:start position:0%
+more as these are very viable ways in
+which at least higher education maybe a
+
+ align:start position:0%
+which at least higher education maybe a
+ 
+
+ align:start position:0%
+which at least higher education maybe a
+number of forms of education might
+
+ align:start position:0%
+number of forms of education might
+ 
+
+ align:start position:0%
+number of forms of education might
+substantially change in the next five or
+
+ align:start position:0%
+substantially change in the next five or
+ 
+
+ align:start position:0%
+substantially change in the next five or
+10 years. Um and I think I will I'm more
+
+ align:start position:0%
+10 years. Um and I think I will I'm more
+ 
+
+ align:start position:0%
+10 years. Um and I think I will I'm more
+likely to present you them today as an
+
+ align:start position:0%
+likely to present you them today as an
+ 
+
+ align:start position:0%
+likely to present you them today as an
+interesting dead end. um as a set of
+
+ align:start position:0%
+interesting dead end. um as a set of
+ 
+
+ align:start position:0%
+interesting dead end. um as a set of
+things that people were trying putting a
+
+ align:start position:0%
+things that people were trying putting a
+ 
+
+ align:start position:0%
+things that people were trying putting a
+lot of effort behind putting a lot of
+
+ align:start position:0%
+lot of effort behind putting a lot of
+ 
+
+ align:start position:0%
+lot of effort behind putting a lot of
+design behind and and really didn't have
+
+ align:start position:0%
+design behind and and really didn't have
+ 
+
+ align:start position:0%
+design behind and and really didn't have
+um much impact in how especially higher
+
+ align:start position:0%
+um much impact in how especially higher
+ 
+
+ align:start position:0%
+um much impact in how especially higher
+education Kate in how in how formal
+
+ align:start position:0%
+education Kate in how in how formal
+ 
+
+ align:start position:0%
+education Kate in how in how formal
+education of all kinds are organized um
+
+ align:start position:0%
+education of all kinds are organized um
+ 
+
+ align:start position:0%
+education of all kinds are organized um
+you know studying things that flop is is
+
+ align:start position:0%
+you know studying things that flop is is
+ 
+
+ align:start position:0%
+you know studying things that flop is is
+good we're going to come back to this a
+
+ align:start position:0%
+good we're going to come back to this a
+ 
+
+ align:start position:0%
+good we're going to come back to this a
+few different times studying things that
+
+ align:start position:0%
+few different times studying things that
+ 
+
+ align:start position:0%
+few different times studying things that
+flop is really important to figure out
+
+ align:start position:0%
+flop is really important to figure out
+ 
+
+ align:start position:0%
+flop is really important to figure out
+um why things work if you just study uh
+
+ align:start position:0%
+um why things work if you just study uh
+ 
+
+ align:start position:0%
+um why things work if you just study uh
+things that work um you actually don't
+
+ align:start position:0%
+things that work um you actually don't
+ 
+
+ align:start position:0%
+things that work um you actually don't
+know why they work you know the
+
+ align:start position:0%
+know why they work you know the
+ 
+
+ align:start position:0%
+know why they work you know the
+characteristics I have, but but there's
+
+ align:start position:0%
+characteristics I have, but but there's
+ 
+
+ align:start position:0%
+characteristics I have, but but there's
+lots of things that are in common
+
+ align:start position:0%
+lots of things that are in common
+ 
+
+ align:start position:0%
+lots of things that are in common
+between things that work and things that
+
+ align:start position:0%
+between things that work and things that
+ 
+
+ align:start position:0%
+between things that work and things that
+don't work. Um, and so that's what we'll
+
+ align:start position:0%
+don't work. Um, and so that's what we'll
+ 
+
+ align:start position:0%
+don't work. Um, and so that's what we'll
+uh we'll delve into some today. Um,
+
+ align:start position:0%
+uh we'll delve into some today. Um,
+ 
+
+ align:start position:0%
+uh we'll delve into some today. Um,
+maybe I'll talk for a little bit and
+
+ align:start position:0%
+maybe I'll talk for a little bit and
+ 
+
+ align:start position:0%
+maybe I'll talk for a little bit and
+then see what kind of thoughts you have.
+
+ align:start position:0%
+then see what kind of thoughts you have.
+ 
+
+ align:start position:0%
+then see what kind of thoughts you have.
+All right, so we are I think we did the
+
+ align:start position:0%
+All right, so we are I think we did the
+ 
+
+ align:start position:0%
+All right, so we are I think we did the
+Rainbow Loom story. We talked about this
+
+ align:start position:0%
+Rainbow Loom story. We talked about this
+ 
+
+ align:start position:0%
+Rainbow Loom story. We talked about this
+the other the other day. This is, you
+
+ align:start position:0%
+the other the other day. This is, you
+ 
+
+ align:start position:0%
+the other the other day. This is, you
+know, one I think iconic moment of, you
+
+ align:start position:0%
+know, one I think iconic moment of, you
+ 
+
+ align:start position:0%
+know, one I think iconic moment of, you
+know, the creation of a new craft
+
+ align:start position:0%
+know, the creation of a new craft
+ 
+
+ align:start position:0%
+know, the creation of a new craft
+generates um these these new kinds of
+
+ align:start position:0%
+generates um these these new kinds of
+ 
+
+ align:start position:0%
+generates um these these new kinds of
+communities. Um, this was from 2013. You
+
+ align:start position:0%
+communities. Um, this was from 2013. You
+ 
+
+ align:start position:0%
+communities. Um, this was from 2013. You
+know, low tech but high in creativity.
+
+ align:start position:0%
+know, low tech but high in creativity.
+ 
+
+ align:start position:0%
+know, low tech but high in creativity.
+The Rainbow Loom has kids hooked,
+
+ align:start position:0%
+The Rainbow Loom has kids hooked,
+ 
+
+ align:start position:0%
+The Rainbow Loom has kids hooked,
+spending hours after school and on
+
+ align:start position:0%
+spending hours after school and on
+ 
+
+ align:start position:0%
+spending hours after school and on
+weekends making bracelets, weaving
+
+ align:start position:0%
+weekends making bracelets, weaving
+ 
+
+ align:start position:0%
+weekends making bracelets, weaving
+together small, colorful rubber bands on
+
+ align:start position:0%
+together small, colorful rubber bands on
+ 
+
+ align:start position:0%
+together small, colorful rubber bands on
+a simple plastic loom. Um, and all of
+
+ align:start position:0%
+a simple plastic loom. Um, and all of
+ 
+
+ align:start position:0%
+a simple plastic loom. Um, and all of
+the um the narrative around Rainbow Loom
+
+ align:start position:0%
+the um the narrative around Rainbow Loom
+ 
+
+ align:start position:0%
+the um the narrative around Rainbow Loom
+was, man, look, we finally got kids off
+
+ align:start position:0%
+was, man, look, we finally got kids off
+ 
+
+ align:start position:0%
+was, man, look, we finally got kids off
+their phones. Like, we finally got kids
+
+ align:start position:0%
+their phones. Like, we finally got kids
+ 
+
+ align:start position:0%
+their phones. Like, we finally got kids
+in the real world connecting to one
+
+ align:start position:0%
+in the real world connecting to one
+ 
+
+ align:start position:0%
+in the real world connecting to one
+another. You know, this is I think 2013
+
+ align:start position:0%
+another. You know, this is I think 2013
+ 
+
+ align:start position:0%
+another. You know, this is I think 2013
+that this is published right before
+
+ align:start position:0%
+that this is published right before
+ 
+
+ align:start position:0%
+that this is published right before
+Christmas. Um, but of course the kids
+
+ align:start position:0%
+Christmas. Um, but of course the kids
+ 
+
+ align:start position:0%
+Christmas. Um, but of course the kids
+were were on their phones the whole time
+
+ align:start position:0%
+were were on their phones the whole time
+ 
+
+ align:start position:0%
+were were on their phones the whole time
+that they were playing with Rainbow
+
+ align:start position:0%
+that they were playing with Rainbow
+ 
+
+ align:start position:0%
+that they were playing with Rainbow
+Loom. And so this is Ashley and Steph um
+
+ align:start position:0%
+Loom. And so this is Ashley and Steph um
+ 
+
+ align:start position:0%
+Loom. And so this is Ashley and Steph um
+who are these two girls, you know, who
+
+ align:start position:0%
+who are these two girls, you know, who
+ 
+
+ align:start position:0%
+who are these two girls, you know, who
+have 200, you know, a quarter of a
+
+ align:start position:0%
+have 200, you know, a quarter of a
+ 
+
+ align:start position:0%
+have 200, you know, a quarter of a
+million people subscribed to. Oh, this
+
+ align:start position:0%
+million people subscribed to. Oh, this
+ 
+
+ align:start position:0%
+million people subscribed to. Oh, this
+is Yeah. How to make a Rainbow Loom
+
+ align:start position:0%
+is Yeah. How to make a Rainbow Loom
+ 
+
+ align:start position:0%
+is Yeah. How to make a Rainbow Loom
+Starburst bracelet. When whenever I
+
+ align:start position:0%
+Starburst bracelet. When whenever I
+ 
+
+ align:start position:0%
+Starburst bracelet. When whenever I
+recorded this um 30 million views, um
+
+ align:start position:0%
+recorded this um 30 million views, um
+ 
+
+ align:start position:0%
+recorded this um 30 million views, um
+probably 10 times as many that were on
+
+ align:start position:0%
+probably 10 times as many that were on
+ 
+
+ align:start position:0%
+probably 10 times as many that were on
+the official Rainbow Loom um Starburst
+
+ align:start position:0%
+the official Rainbow Loom um Starburst
+ 
+
+ align:start position:0%
+the official Rainbow Loom um Starburst
+page that somehow these uh these two
+
+ align:start position:0%
+page that somehow these uh these two
+ 
+
+ align:start position:0%
+page that somehow these uh these two
+kids had um captivated. I I don't know.
+
+ align:start position:0%
+kids had um captivated. I I don't know.
+ 
+
+ align:start position:0%
+kids had um captivated. I I don't know.
+It's hard to say that it was millions of
+
+ align:start position:0%
+It's hard to say that it was millions of
+ 
+
+ align:start position:0%
+It's hard to say that it was millions of
+people because it actually could have
+
+ align:start position:0%
+people because it actually could have
+ 
+
+ align:start position:0%
+people because it actually could have
+been like a couple hundred thousand
+
+ align:start position:0%
+been like a couple hundred thousand
+ 
+
+ align:start position:0%
+been like a couple hundred thousand
+people each watch this like 10 or 20
+
+ align:start position:0%
+people each watch this like 10 or 20
+ 
+
+ align:start position:0%
+people each watch this like 10 or 20
+times because it's super hard to make
+
+ align:start position:0%
+times because it's super hard to make
+ 
+
+ align:start position:0%
+times because it's super hard to make
+one of these bracelets. Um but uh um you
+
+ align:start position:0%
+one of these bracelets. Um but uh um you
+ 
+
+ align:start position:0%
+one of these bracelets. Um but uh um you
+know I think a a compelling example of
+
+ align:start position:0%
+know I think a a compelling example of
+ 
+
+ align:start position:0%
+know I think a a compelling example of
+how network learning was you know and
+
+ align:start position:0%
+how network learning was you know and
+ 
+
+ align:start position:0%
+how network learning was you know and
+and and something like this if you're my
+
+ align:start position:0%
+and and something like this if you're my
+ 
+
+ align:start position:0%
+and and something like this if you're my
+age you know looking at this in 2013
+
+ align:start position:0%
+age you know looking at this in 2013
+ 
+
+ align:start position:0%
+age you know looking at this in 2013
+it's it's really hard to imagine
+
+ align:start position:0%
+it's it's really hard to imagine
+ 
+
+ align:start position:0%
+it's it's really hard to imagine
+something similar happening in 1990 or
+
+ align:start position:0%
+something similar happening in 1990 or
+ 
+
+ align:start position:0%
+something similar happening in 1990 or
+something like that. Like if someone had
+
+ align:start position:0%
+something like that. Like if someone had
+ 
+
+ align:start position:0%
+something like that. Like if someone had
+invented a new kind of craft you would
+
+ align:start position:0%
+invented a new kind of craft you would
+ 
+
+ align:start position:0%
+invented a new kind of craft you would
+have like had to go to a craft store.
+
+ align:start position:0%
+have like had to go to a craft store.
+ 
+
+ align:start position:0%
+have like had to go to a craft store.
+You would have had to join a club. be
+
+ align:start position:0%
+You would have had to join a club. be
+ 
+
+ align:start position:0%
+You would have had to join a club. be
+able to go to classes. There have to be
+
+ align:start position:0%
+able to go to classes. There have to be
+ 
+
+ align:start position:0%
+able to go to classes. There have to be
+a college club or something like that.
+
+ align:start position:0%
+a college club or something like that.
+ 
+
+ align:start position:0%
+a college club or something like that.
+Um there wouldn't, you know, I I mean,
+
+ align:start position:0%
+Um there wouldn't, you know, I I mean,
+ 
+
+ align:start position:0%
+Um there wouldn't, you know, I I mean,
+you know, maybe PBS would put on a
+
+ align:start position:0%
+you know, maybe PBS would put on a
+ 
+
+ align:start position:0%
+you know, maybe PBS would put on a
+television show about it. You'd have,
+
+ align:start position:0%
+television show about it. You'd have,
+ 
+
+ align:start position:0%
+television show about it. You'd have,
+you know, you could imagine like the Bob
+
+ align:start position:0%
+you know, you could imagine like the Bob
+ 
+
+ align:start position:0%
+you know, you could imagine like the Bob
+Ross of Rainbow Loom or something like
+
+ align:start position:0%
+Ross of Rainbow Loom or something like
+ 
+
+ align:start position:0%
+Ross of Rainbow Loom or something like
+that. Um but uh you know, um very hard
+
+ align:start position:0%
+that. Um but uh you know, um very hard
+ 
+
+ align:start position:0%
+that. Um but uh you know, um very hard
+to imagine the same kind of highly
+
+ align:start position:0%
+to imagine the same kind of highly
+ 
+
+ align:start position:0%
+to imagine the same kind of highly
+decentralized
+
+ align:start position:0%
+decentralized
+ 
+
+ align:start position:0%
+decentralized
+um uh mechanism by which learners
+
+ align:start position:0%
+um uh mechanism by which learners
+ 
+
+ align:start position:0%
+um uh mechanism by which learners
+connect themselves to each other. I
+
+ align:start position:0%
+connect themselves to each other. I
+ 
+
+ align:start position:0%
+connect themselves to each other. I
+think one of the things I'm going to ask
+
+ align:start position:0%
+think one of the things I'm going to ask
+ 
+
+ align:start position:0%
+think one of the things I'm going to ask
+you to um read for an upcoming week, I
+
+ align:start position:0%
+you to um read for an upcoming week, I
+ 
+
+ align:start position:0%
+you to um read for an upcoming week, I
+can't remember, it's next week. Um uh
+
+ align:start position:0%
+can't remember, it's next week. Um uh
+ 
+
+ align:start position:0%
+can't remember, it's next week. Um uh
+but this uh piece by Ivon Illich called
+
+ align:start position:0%
+but this uh piece by Ivon Illich called
+ 
+
+ align:start position:0%
+but this uh piece by Ivon Illich called
+Deschooling Society um I think it's
+
+ align:start position:0%
+Deschooling Society um I think it's
+ 
+
+ align:start position:0%
+Deschooling Society um I think it's
+written in the 1960s. Um and he he
+
+ align:start position:0%
+written in the 1960s. Um and he he
+ 
+
+ align:start position:0%
+written in the 1960s. Um and he he
+almost exactly with like the very dawn
+
+ align:start position:0%
+almost exactly with like the very dawn
+ 
+
+ align:start position:0%
+almost exactly with like the very dawn
+of computing and he predicts learning
+
+ align:start position:0%
+of computing and he predicts learning
+ 
+
+ align:start position:0%
+of computing and he predicts learning
+networks that that emerge like this. Um
+
+ align:start position:0%
+networks that that emerge like this. Um
+ 
+
+ align:start position:0%
+networks that that emerge like this. Um
+he says you know one day I mean he has a
+
+ align:start position:0%
+he says you know one day I mean he has a
+ 
+
+ align:start position:0%
+he says you know one day I mean he has a
+funny way of describing he says well you
+
+ align:start position:0%
+funny way of describing he says well you
+ 
+
+ align:start position:0%
+funny way of describing he says well you
+know one day there's going to be a bunch
+
+ align:start position:0%
+know one day there's going to be a bunch
+ 
+
+ align:start position:0%
+know one day there's going to be a bunch
+of learners um who write down the things
+
+ align:start position:0%
+of learners um who write down the things
+ 
+
+ align:start position:0%
+of learners um who write down the things
+they're interested in learning on punch
+
+ align:start position:0%
+they're interested in learning on punch
+ 
+
+ align:start position:0%
+they're interested in learning on punch
+cards because that's what computers at
+
+ align:start position:0%
+cards because that's what computers at
+ 
+
+ align:start position:0%
+cards because that's what computers at
+the time and there's going to be a bunch
+
+ align:start position:0%
+the time and there's going to be a bunch
+ 
+
+ align:start position:0%
+the time and there's going to be a bunch
+of experts who share their interests on
+
+ align:start position:0%
+of experts who share their interests on
+ 
+
+ align:start position:0%
+of experts who share their interests on
+punch cards and the computers are going
+
+ align:start position:0%
+punch cards and the computers are going
+ 
+
+ align:start position:0%
+punch cards and the computers are going
+to connect these punch cards together um
+
+ align:start position:0%
+to connect these punch cards together um
+ 
+
+ align:start position:0%
+to connect these punch cards together um
+and get people teaching and learning
+
+ align:start position:0%
+and get people teaching and learning
+ 
+
+ align:start position:0%
+and get people teaching and learning
+from one another and like we it turned
+
+ align:start position:0%
+from one another and like we it turned
+ 
+
+ align:start position:0%
+from one another and like we it turned
+out we had YouTube rather than punch
+
+ align:start position:0%
+out we had YouTube rather than punch
+ 
+
+ align:start position:0%
+out we had YouTube rather than punch
+cards but um it was a pretty similar
+
+ align:start position:0%
+cards but um it was a pretty similar
+ 
+
+ align:start position:0%
+cards but um it was a pretty similar
+kind of phenomenon um there are you know
+
+ align:start position:0%
+kind of phenomenon um there are you know
+ 
+
+ align:start position:0%
+kind of phenomenon um there are you know
+in in the in the 20 in the early 2010s,
+
+ align:start position:0%
+in in the in the 20 in the early 2010s,
+ 
+
+ align:start position:0%
+in in the in the 20 in the early 2010s,
+there were some people who were
+
+ align:start position:0%
+there were some people who were
+ 
+
+ align:start position:0%
+there were some people who were
+particularly enthusiastic about the
+
+ align:start position:0%
+particularly enthusiastic about the
+ 
+
+ align:start position:0%
+particularly enthusiastic about the
+fact, you know, so one thing about
+
+ align:start position:0%
+fact, you know, so one thing about
+ 
+
+ align:start position:0%
+fact, you know, so one thing about
+Rainbow Loom you could say is something
+
+ align:start position:0%
+Rainbow Loom you could say is something
+ 
+
+ align:start position:0%
+Rainbow Loom you could say is something
+like, well, all right, so some kids
+
+ align:start position:0%
+like, well, all right, so some kids
+ 
+
+ align:start position:0%
+like, well, all right, so some kids
+figured out how to make plastic
+
+ align:start position:0%
+figured out how to make plastic
+ 
+
+ align:start position:0%
+figured out how to make plastic
+bracelets. That's okay. Um, but there
+
+ align:start position:0%
+bracelets. That's okay. Um, but there
+ 
+
+ align:start position:0%
+bracelets. That's okay. Um, but there
+are people who achieve like elite levels
+
+ align:start position:0%
+are people who achieve like elite levels
+ 
+
+ align:start position:0%
+are people who achieve like elite levels
+of performance in a variety of different
+
+ align:start position:0%
+of performance in a variety of different
+ 
+
+ align:start position:0%
+of performance in a variety of different
+disciplines and domains by following the
+
+ align:start position:0%
+disciplines and domains by following the
+ 
+
+ align:start position:0%
+disciplines and domains by following the
+same kinds of practices that the Rainbow
+
+ align:start position:0%
+same kinds of practices that the Rainbow
+ 
+
+ align:start position:0%
+same kinds of practices that the Rainbow
+Kids, Rainbow Kids were using. So, this
+
+ align:start position:0%
+Kids, Rainbow Kids were using. So, this
+ 
+
+ align:start position:0%
+Kids, Rainbow Kids were using. So, this
+is a guy named Julius Jgo who, as I
+
+ align:start position:0%
+is a guy named Julius Jgo who, as I
+ 
+
+ align:start position:0%
+is a guy named Julius Jgo who, as I
+recall, won a silver medal in the
+
+ align:start position:0%
+recall, won a silver medal in the
+ 
+
+ align:start position:0%
+recall, won a silver medal in the
+Olympics. Um, he was from Kenya and he
+
+ align:start position:0%
+Olympics. Um, he was from Kenya and he
+ 
+
+ align:start position:0%
+Olympics. Um, he was from Kenya and he
+was a javelin thrower. There are no
+
+ align:start position:0%
+was a javelin thrower. There are no
+ 
+
+ align:start position:0%
+was a javelin thrower. There are no
+field athletes in Kenya. They're all
+
+ align:start position:0%
+field athletes in Kenya. They're all
+ 
+
+ align:start position:0%
+field athletes in Kenya. They're all
+track runners. Um, and for whatever
+
+ align:start position:0%
+track runners. Um, and for whatever
+ 
+
+ align:start position:0%
+track runners. Um, and for whatever
+reason, Julius Diego got it in his head
+
+ align:start position:0%
+reason, Julius Diego got it in his head
+ 
+
+ align:start position:0%
+reason, Julius Diego got it in his head
+like, I'm going to be a javelin thrower.
+
+ align:start position:0%
+like, I'm going to be a javelin thrower.
+ 
+
+ align:start position:0%
+like, I'm going to be a javelin thrower.
+Um, and uh, you know, I mean, here, you
+
+ align:start position:0%
+Um, and uh, you know, I mean, here, you
+ 
+
+ align:start position:0%
+Um, and uh, you know, I mean, here, you
+know, my coach is me and the YouTube
+
+ align:start position:0%
+know, my coach is me and the YouTube
+ 
+
+ align:start position:0%
+know, my coach is me and the YouTube
+videos. Um, and he became an elite, you
+
+ align:start position:0%
+videos. Um, and he became an elite, you
+ 
+
+ align:start position:0%
+videos. Um, and he became an elite, you
+know, globally recognized ath. I mean,
+
+ align:start position:0%
+know, globally recognized ath. I mean,
+ 
+
+ align:start position:0%
+know, globally recognized ath. I mean,
+there's a there's a there's a moment
+
+ align:start position:0%
+there's a there's a there's a moment
+ 
+
+ align:start position:0%
+there's a there's a there's a moment
+where this tips. there's a moment where
+
+ align:start position:0%
+where this tips. there's a moment where
+ 
+
+ align:start position:0%
+where this tips. there's a moment where
+he goes to um a track and field
+
+ align:start position:0%
+he goes to um a track and field
+ 
+
+ align:start position:0%
+he goes to um a track and field
+competition um you know he doesn't
+
+ align:start position:0%
+competition um you know he doesn't
+ 
+
+ align:start position:0%
+competition um you know he doesn't
+really have a coach and he throws a
+
+ align:start position:0%
+really have a coach and he throws a
+ 
+
+ align:start position:0%
+really have a coach and he throws a
+javelin pretty far and some people
+
+ align:start position:0%
+javelin pretty far and some people
+ 
+
+ align:start position:0%
+javelin pretty far and some people
+notice him and kind of take him under
+
+ align:start position:0%
+notice him and kind of take him under
+ 
+
+ align:start position:0%
+notice him and kind of take him under
+his wing and stuff like that. So it's
+
+ align:start position:0%
+his wing and stuff like that. So it's
+ 
+
+ align:start position:0%
+his wing and stuff like that. So it's
+not you know it's it's not just YouTube
+
+ align:start position:0%
+not you know it's it's not just YouTube
+ 
+
+ align:start position:0%
+not you know it's it's not just YouTube
+videos that get you entirely to um being
+
+ align:start position:0%
+videos that get you entirely to um being
+ 
+
+ align:start position:0%
+videos that get you entirely to um being
+the second best javelin thrower in the
+
+ align:start position:0%
+the second best javelin thrower in the
+ 
+
+ align:start position:0%
+the second best javelin thrower in the
+world. Um but uh but going quite a long
+
+ align:start position:0%
+world. Um but uh but going quite a long
+ 
+
+ align:start position:0%
+world. Um but uh but going quite a long
+way you know there's there's echoes of
+
+ align:start position:0%
+way you know there's there's echoes of
+ 
+
+ align:start position:0%
+way you know there's there's echoes of
+this of the story that I told you before
+
+ align:start position:0%
+this of the story that I told you before
+ 
+
+ align:start position:0%
+this of the story that I told you before
+of uh um Batush the boy genius of Ulan
+
+ align:start position:0%
+of uh um Batush the boy genius of Ulan
+ 
+
+ align:start position:0%
+of uh um Batush the boy genius of Ulan
+Batar the the kid who sort of discovered
+
+ align:start position:0%
+Batar the the kid who sort of discovered
+ 
+
+ align:start position:0%
+Batar the the kid who sort of discovered
+in Mongolia um through MITx and things
+
+ align:start position:0%
+in Mongolia um through MITx and things
+ 
+
+ align:start position:0%
+in Mongolia um through MITx and things
+like this the idea that these could have
+
+ align:start position:0%
+like this the idea that these could have
+ 
+
+ align:start position:0%
+like this the idea that these could have
+these profound democratizing effects
+
+ align:start position:0%
+these profound democratizing effects
+ 
+
+ align:start position:0%
+these profound democratizing effects
+like you don't you know you don't have
+
+ align:start position:0%
+like you don't you know you don't have
+ 
+
+ align:start position:0%
+like you don't you know you don't have
+to be um in in a country that has a
+
+ align:start position:0%
+to be um in in a country that has a
+ 
+
+ align:start position:0%
+to be um in in a country that has a
+really big track and field
+
+ align:start position:0%
+really big track and field
+ 
+
+ align:start position:0%
+really big track and field
+infrastructure um to be able to become a
+
+ align:start position:0%
+infrastructure um to be able to become a
+ 
+
+ align:start position:0%
+infrastructure um to be able to become a
+great athlete. You can do it anywhere
+
+ align:start position:0%
+great athlete. You can do it anywhere
+ 
+
+ align:start position:0%
+great athlete. You can do it anywhere
+because we have YouTube now.
+
+ align:start position:0%
+because we have YouTube now.
+ 
+
+ align:start position:0%
+because we have YouTube now.
+Um, so in I I was working for Harvard X
+
+ align:start position:0%
+Um, so in I I was working for Harvard X
+ 
+
+ align:start position:0%
+Um, so in I I was working for Harvard X
+in 2013. Um,
+
+ align:start position:0%
+in 2013. Um,
+ 
+
+ align:start position:0%
+in 2013. Um,
+uh, maybe I, you know, maybe I'll pause
+
+ align:start position:0%
+uh, maybe I, you know, maybe I'll pause
+ 
+
+ align:start position:0%
+uh, maybe I, you know, maybe I'll pause
+to tell this story, too. Well, I don't
+
+ align:start position:0%
+to tell this story, too. Well, I don't
+ 
+
+ align:start position:0%
+to tell this story, too. Well, I don't
+know what the right order is now that
+
+ align:start position:0%
+know what the right order is now that
+ 
+
+ align:start position:0%
+know what the right order is now that
+I'm inspired by it, but um there was
+
+ align:start position:0%
+I'm inspired by it, but um there was
+ 
+
+ align:start position:0%
+I'm inspired by it, but um there was
+this term massive open online courses
+
+ align:start position:0%
+this term massive open online courses
+ 
+
+ align:start position:0%
+this term massive open online courses
+and it actually was not originally
+
+ align:start position:0%
+and it actually was not originally
+ 
+
+ align:start position:0%
+and it actually was not originally
+applied to the courses that came out of
+
+ align:start position:0%
+applied to the courses that came out of
+ 
+
+ align:start position:0%
+applied to the courses that came out of
+Corsera um and edex and MITx and Udacity
+
+ align:start position:0%
+Corsera um and edex and MITx and Udacity
+ 
+
+ align:start position:0%
+Corsera um and edex and MITx and Udacity
+and things like that. There were a group
+
+ align:start position:0%
+and things like that. There were a group
+ 
+
+ align:start position:0%
+and things like that. There were a group
+of Canadian educators who 2008, 2009,
+
+ align:start position:0%
+of Canadian educators who 2008, 2009,
+ 
+
+ align:start position:0%
+of Canadian educators who 2008, 2009,
+2010, 2011 started building theseworked
+
+ align:start position:0%
+2010, 2011 started building theseworked
+ 
+
+ align:start position:0%
+2010, 2011 started building theseworked
+courses. Um, some of the I'll go more
+
+ align:start position:0%
+courses. Um, some of the I'll go more
+ 
+
+ align:start position:0%
+courses. Um, some of the I'll go more
+into the details of the network courses,
+
+ align:start position:0%
+into the details of the network courses,
+ 
+
+ align:start position:0%
+into the details of the network courses,
+but you would basically kind of create
+
+ align:start position:0%
+but you would basically kind of create
+ 
+
+ align:start position:0%
+but you would basically kind of create
+an online learning environment, have
+
+ align:start position:0%
+an online learning environment, have
+ 
+
+ align:start position:0%
+an online learning environment, have
+people create blogs, connect on Twitter,
+
+ align:start position:0%
+people create blogs, connect on Twitter,
+ 
+
+ align:start position:0%
+people create blogs, connect on Twitter,
+form social network connections with one
+
+ align:start position:0%
+form social network connections with one
+ 
+
+ align:start position:0%
+form social network connections with one
+another and sort of all be studying the
+
+ align:start position:0%
+another and sort of all be studying the
+ 
+
+ align:start position:0%
+another and sort of all be studying the
+same thing at the same time. Sometimes
+
+ align:start position:0%
+same thing at the same time. Sometimes
+ 
+
+ align:start position:0%
+same thing at the same time. Sometimes
+some of the people would be getting
+
+ align:start position:0%
+some of the people would be getting
+ 
+
+ align:start position:0%
+some of the people would be getting
+credit from some institution and other
+
+ align:start position:0%
+credit from some institution and other
+ 
+
+ align:start position:0%
+credit from some institution and other
+people would not be getting credit. They
+
+ align:start position:0%
+people would not be getting credit. They
+ 
+
+ align:start position:0%
+people would not be getting credit. They
+were all kind of openly being involved.
+
+ align:start position:0%
+were all kind of openly being involved.
+ 
+
+ align:start position:0%
+were all kind of openly being involved.
+You know, a few thousand people,
+
+ align:start position:0%
+You know, a few thousand people,
+ 
+
+ align:start position:0%
+You know, a few thousand people,
+probably the largest of these, um,
+
+ align:start position:0%
+probably the largest of these, um,
+ 
+
+ align:start position:0%
+probably the largest of these, um,
+signing up. And so there was actually a
+
+ align:start position:0%
+signing up. And so there was actually a
+ 
+
+ align:start position:0%
+signing up. And so there was actually a
+reporter who when um Edex and Corsera
+
+ align:start position:0%
+reporter who when um Edex and Corsera
+ 
+
+ align:start position:0%
+reporter who when um Edex and Corsera
+got started was trying to figure out
+
+ align:start position:0%
+got started was trying to figure out
+ 
+
+ align:start position:0%
+got started was trying to figure out
+what these things should be called. Um
+
+ align:start position:0%
+what these things should be called. Um
+ 
+
+ align:start position:0%
+what these things should be called. Um
+and somebody said like well these
+
+ align:start position:0%
+and somebody said like well these
+ 
+
+ align:start position:0%
+and somebody said like well these
+Canadian guys have these things called
+
+ align:start position:0%
+Canadian guys have these things called
+ 
+
+ align:start position:0%
+Canadian guys have these things called
+massive open online courses. Um and the
+
+ align:start position:0%
+massive open online courses. Um and the
+ 
+
+ align:start position:0%
+massive open online courses. Um and the
+name stuck but it stuck to describe
+
+ align:start position:0%
+name stuck but it stuck to describe
+ 
+
+ align:start position:0%
+name stuck but it stuck to describe
+something very very different. Um, one
+
+ align:start position:0%
+something very very different. Um, one
+ 
+
+ align:start position:0%
+something very very different. Um, one
+of the things that we recognized early
+
+ align:start position:0%
+of the things that we recognized early
+ 
+
+ align:start position:0%
+of the things that we recognized early
+on is that is that in the early days of
+
+ align:start position:0%
+on is that is that in the early days of
+ 
+
+ align:start position:0%
+on is that is that in the early days of
+people doing the massive open online
+
+ align:start position:0%
+people doing the massive open online
+ 
+
+ align:start position:0%
+people doing the massive open online
+courses that came out of Harvard and MIT
+
+ align:start position:0%
+courses that came out of Harvard and MIT
+ 
+
+ align:start position:0%
+courses that came out of Harvard and MIT
+is many of them were not just using the
+
+ align:start position:0%
+is many of them were not just using the
+ 
+
+ align:start position:0%
+is many of them were not just using the
+course materials that were being
+
+ align:start position:0%
+course materials that were being
+ 
+
+ align:start position:0%
+course materials that were being
+provided on these platforms, but they
+
+ align:start position:0%
+provided on these platforms, but they
+ 
+
+ align:start position:0%
+provided on these platforms, but they
+were using all kinds of other things.
+
+ align:start position:0%
+were using all kinds of other things.
+ 
+
+ align:start position:0%
+were using all kinds of other things.
+So, you'd ask people and they're like,
+
+ align:start position:0%
+So, you'd ask people and they're like,
+ 
+
+ align:start position:0%
+So, you'd ask people and they're like,
+you know, um, yeah, well, we're
+
+ align:start position:0%
+you know, um, yeah, well, we're
+ 
+
+ align:start position:0%
+you know, um, yeah, well, we're
+searching for all kinds of things that
+
+ align:start position:0%
+searching for all kinds of things that
+ 
+
+ align:start position:0%
+searching for all kinds of things that
+show up. We're reading like the
+
+ align:start position:0%
+show up. We're reading like the
+ 
+
+ align:start position:0%
+show up. We're reading like the
+Wikipedia entries about the things that
+
+ align:start position:0%
+Wikipedia entries about the things that
+ 
+
+ align:start position:0%
+Wikipedia entries about the things that
+show up in these classes. We're buying
+
+ align:start position:0%
+show up in these classes. We're buying
+ 
+
+ align:start position:0%
+show up in these classes. We're buying
+additional books that are around them.
+
+ align:start position:0%
+additional books that are around them.
+ 
+
+ align:start position:0%
+additional books that are around them.
+Um, we're looking for those books on
+
+ align:start position:0%
+Um, we're looking for those books on
+ 
+
+ align:start position:0%
+Um, we're looking for those books on
+Google books. We're joining Facebook
+
+ align:start position:0%
+Google books. We're joining Facebook
+ 
+
+ align:start position:0%
+Google books. We're joining Facebook
+groups of people who are studying these
+
+ align:start position:0%
+groups of people who are studying these
+ 
+
+ align:start position:0%
+groups of people who are studying these
+courses together and things like that.
+
+ align:start position:0%
+courses together and things like that.
+ 
+
+ align:start position:0%
+courses together and things like that.
+Um, and so the the the the barriers
+
+ align:start position:0%
+Um, and so the the the the barriers
+ 
+
+ align:start position:0%
+Um, and so the the the the barriers
+between these sort of instructorg guided
+
+ align:start position:0%
+between these sort of instructorg guided
+ 
+
+ align:start position:0%
+between these sort of instructorg guided
+learning at scale, these like highly
+
+ align:start position:0%
+learning at scale, these like highly
+ 
+
+ align:start position:0%
+learning at scale, these like highly
+structured learning management system
+
+ align:start position:0%
+structured learning management system
+ 
+
+ align:start position:0%
+structured learning management system
+kinds of things and the sort of informal
+
+ align:start position:0%
+kinds of things and the sort of informal
+ 
+
+ align:start position:0%
+kinds of things and the sort of informal
+world of people messing around on
+
+ align:start position:0%
+world of people messing around on
+ 
+
+ align:start position:0%
+world of people messing around on
+YouTube learning about stuff um sort of
+
+ align:start position:0%
+YouTube learning about stuff um sort of
+ 
+
+ align:start position:0%
+YouTube learning about stuff um sort of
+uh smooshed together. probably a bunch
+
+ align:start position:0%
+uh smooshed together. probably a bunch
+ 
+
+ align:start position:0%
+uh smooshed together. probably a bunch
+of you have some kind of experience of
+
+ align:start position:0%
+of you have some kind of experience of
+ 
+
+ align:start position:0%
+of you have some kind of experience of
+that in your classes too. I mean
+
+ align:start position:0%
+that in your classes too. I mean
+ 
+
+ align:start position:0%
+that in your classes too. I mean
+presumably all of you like are like when
+
+ align:start position:0%
+presumably all of you like are like when
+ 
+
+ align:start position:0%
+presumably all of you like are like when
+you don't understand something in class
+
+ align:start position:0%
+you don't understand something in class
+ 
+
+ align:start position:0%
+you don't understand something in class
+you're looking up online videos about it
+
+ align:start position:0%
+you're looking up online videos about it
+ 
+
+ align:start position:0%
+you're looking up online videos about it
+or you don't like the lecture and you
+
+ align:start position:0%
+or you don't like the lecture and you
+ 
+
+ align:start position:0%
+or you don't like the lecture and you
+know probably mostly in your technical
+
+ align:start position:0%
+know probably mostly in your technical
+ 
+
+ align:start position:0%
+know probably mostly in your technical
+classes you watch it from some other
+
+ align:start position:0%
+classes you watch it from some other
+ 
+
+ align:start position:0%
+classes you watch it from some other
+place. I don't know do any of you join
+
+ align:start position:0%
+place. I don't know do any of you join
+ 
+
+ align:start position:0%
+place. I don't know do any of you join
+groups or like find communities of
+
+ align:start position:0%
+groups or like find communities of
+ 
+
+ align:start position:0%
+groups or like find communities of
+people who are good at at solving
+
+ align:start position:0%
+people who are good at at solving
+ 
+
+ align:start position:0%
+people who are good at at solving
+problems and the things that you're
+
+ align:start position:0%
+problems and the things that you're
+ 
+
+ align:start position:0%
+problems and the things that you're
+interested in.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One thing about being an MIT student is
+
+ align:start position:0%
+One thing about being an MIT student is
+ 
+
+ align:start position:0%
+One thing about being an MIT student is
+you can go on OCW if you miss a lecture
+
+ align:start position:0%
+you can go on OCW if you miss a lecture
+ 
+
+ align:start position:0%
+you can go on OCW if you miss a lecture
+or you don't understand the lecture you
+
+ align:start position:0%
+or you don't understand the lecture you
+ 
+
+ align:start position:0%
+or you don't understand the lecture you
+want to explain in a different way from
+
+ align:start position:0%
+want to explain in a different way from
+ 
+
+ align:start position:0%
+want to explain in a different way from
+a different professor just watch that
+
+ align:start position:0%
+a different professor just watch that
+ 
+
+ align:start position:0%
+a different professor just watch that
+same lecture which I've done before for
+
+ align:start position:0%
+same lecture which I've done before for
+ 
+
+ align:start position:0%
+same lecture which I've done before for
+some of my more technical classes. Yep.
+
+ align:start position:0%
+some of my more technical classes. Yep.
+ 
+
+ align:start position:0%
+some of my more technical classes. Yep.
+So yeah, so you can rewatch sort of past
+
+ align:start position:0%
+So yeah, so you can rewatch sort of past
+ 
+
+ align:start position:0%
+So yeah, so you can rewatch sort of past
+things. Some professors are sort of
+
+ align:start position:0%
+things. Some professors are sort of
+ 
+
+ align:start position:0%
+things. Some professors are sort of
+pretty explicit about that. You know,
+
+ align:start position:0%
+pretty explicit about that. You know,
+ 
+
+ align:start position:0%
+pretty explicit about that. You know,
+they'll be like, "Well, this is my
+
+ align:start position:0%
+they'll be like, "Well, this is my
+ 
+
+ align:start position:0%
+they'll be like, "Well, this is my
+lecture, but like somebody else filmed,
+
+ align:start position:0%
+lecture, but like somebody else filmed,
+ 
+
+ align:start position:0%
+lecture, but like somebody else filmed,
+you know, roughly the same course four
+
+ align:start position:0%
+you know, roughly the same course four
+ 
+
+ align:start position:0%
+you know, roughly the same course four
+years ago, and so you can watch all
+
+ align:start position:0%
+years ago, and so you can watch all
+ 
+
+ align:start position:0%
+years ago, and so you can watch all
+those things." Um, how many of your
+
+ align:start position:0%
+those things." Um, how many of your
+ 
+
+ align:start position:0%
+those things." Um, how many of your
+classes still use Piaza or some kind of
+
+ align:start position:0%
+classes still use Piaza or some kind of
+ 
+
+ align:start position:0%
+classes still use Piaza or some kind of
+discussion forum sort of things? Um, are
+
+ align:start position:0%
+discussion forum sort of things? Um, are
+ 
+
+ align:start position:0%
+discussion forum sort of things? Um, are
+the are the Piaza forms ever
+
+ align:start position:0%
+the are the Piaza forms ever
+ 
+
+ align:start position:0%
+the are the Piaza forms ever
+insufficient and then you go to Stack
+
+ align:start position:0%
+insufficient and then you go to Stack
+ 
+
+ align:start position:0%
+insufficient and then you go to Stack
+Overflow or to some other kind of maybe
+
+ align:start position:0%
+Overflow or to some other kind of maybe
+ 
+
+ align:start position:0%
+Overflow or to some other kind of maybe
+for your coding classes and things like
+
+ align:start position:0%
+for your coding classes and things like
+ 
+
+ align:start position:0%
+for your coding classes and things like
+that? I would say Piaza has like a weird
+
+ align:start position:0%
+that? I would say Piaza has like a weird
+ 
+
+ align:start position:0%
+that? I would say Piaza has like a weird
+social dynamic in itself. No, I want
+
+ align:start position:0%
+social dynamic in itself. No, I want
+ 
+
+ align:start position:0%
+social dynamic in itself. No, I want
+that now. Tell me more.
+
+ align:start position:0%
+that now. Tell me more.
+ 
+
+ align:start position:0%
+that now. Tell me more.
+I think it's like um I mean like
+
+ align:start position:0%
+I think it's like um I mean like
+ 
+
+ align:start position:0%
+I think it's like um I mean like
+obviously you can both do like anonymous
+
+ align:start position:0%
+obviously you can both do like anonymous
+ 
+
+ align:start position:0%
+obviously you can both do like anonymous
+questions and non-anmous question but
+
+ align:start position:0%
+questions and non-anmous question but
+ 
+
+ align:start position:0%
+questions and non-anmous question but
+usually it seems like you know it it
+
+ align:start position:0%
+usually it seems like you know it it
+ 
+
+ align:start position:0%
+usually it seems like you know it it
+really depends
+
+ align:start position:0%
+really depends
+ 
+
+ align:start position:0%
+really depends
+on a little bit on like who's really
+
+ align:start position:0%
+on a little bit on like who's really
+ 
+
+ align:start position:0%
+on a little bit on like who's really
+using it and also how responsive the
+
+ align:start position:0%
+using it and also how responsive the
+ 
+
+ align:start position:0%
+using it and also how responsive the
+faculty and stuff are and how they
+
+ align:start position:0%
+faculty and stuff are and how they
+ 
+
+ align:start position:0%
+faculty and stuff are and how they
+choose to respond because that I have
+
+ align:start position:0%
+choose to respond because that I have
+ 
+
+ align:start position:0%
+choose to respond because that I have
+been in a in quite a few classes where
+
+ align:start position:0%
+been in a in quite a few classes where
+ 
+
+ align:start position:0%
+been in a in quite a few classes where
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+log on and then it's like yes I had that
+
+ align:start position:0%
+log on and then it's like yes I had that
+ 
+
+ align:start position:0%
+log on and then it's like yes I had that
+question and they're like oh sorry we
+
+ align:start position:0%
+question and they're like oh sorry we
+ 
+
+ align:start position:0%
+question and they're like oh sorry we
+boarded the question weird but then I've
+
+ align:start position:0%
+boarded the question weird but then I've
+ 
+
+ align:start position:0%
+boarded the question weird but then I've
+also been quite a few classes where it's
+
+ align:start position:0%
+also been quite a few classes where it's
+ 
+
+ align:start position:0%
+also been quite a few classes where it's
+like they're asking this like super
+
+ align:start position:0%
+like they're asking this like super
+ 
+
+ align:start position:0%
+like they're asking this like super
+highlevel question about the lecture and
+
+ align:start position:0%
+highlevel question about the lecture and
+ 
+
+ align:start position:0%
+highlevel question about the lecture and
+then it kind of sets that expectation
+
+ align:start position:0%
+then it kind of sets that expectation
+ 
+
+ align:start position:0%
+then it kind of sets that expectation
+for the class especially if it's a
+
+ align:start position:0%
+for the class especially if it's a
+ 
+
+ align:start position:0%
+for the class especially if it's a
+larger class of like oh like my like
+
+ align:start position:0%
+larger class of like oh like my like
+ 
+
+ align:start position:0%
+larger class of like oh like my like
+quotequote dumb questions not going to
+
+ align:start position:0%
+quotequote dumb questions not going to
+ 
+
+ align:start position:0%
+quotequote dumb questions not going to
+be answered yeah it's not going to be
+
+ align:start position:0%
+be answered yeah it's not going to be
+ 
+
+ align:start position:0%
+be answered yeah it's not going to be
+kind of respected or things like that
+
+ align:start position:0%
+kind of respected or things like that
+ 
+
+ align:start position:0%
+kind of respected or things like that
+yeah you know And um I mean because
+
+ align:start position:0%
+yeah you know And um I mean because
+ 
+
+ align:start position:0%
+yeah you know And um I mean because
+these things are social in nature, I bet
+
+ align:start position:0%
+these things are social in nature, I bet
+ 
+
+ align:start position:0%
+these things are social in nature, I bet
+a lot of those things can be determined
+
+ align:start position:0%
+a lot of those things can be determined
+ 
+
+ align:start position:0%
+a lot of those things can be determined
+pretty early on by the actions of a
+
+ align:start position:0%
+pretty early on by the actions of a
+ 
+
+ align:start position:0%
+pretty early on by the actions of a
+couple of people. Um when we were
+
+ align:start position:0%
+couple of people. Um when we were
+ 
+
+ align:start position:0%
+couple of people. Um when we were
+studying Massive Women online courses,
+
+ align:start position:0%
+studying Massive Women online courses,
+ 
+
+ align:start position:0%
+studying Massive Women online courses,
+one of the things we found in the
+
+ align:start position:0%
+one of the things we found in the
+ 
+
+ align:start position:0%
+one of the things we found in the
+discussion forums, the largest threads,
+
+ align:start position:0%
+discussion forums, the largest threads,
+ 
+
+ align:start position:0%
+discussion forums, the largest threads,
+the most upvoted kinds of things were
+
+ align:start position:0%
+the most upvoted kinds of things were
+ 
+
+ align:start position:0%
+the most upvoted kinds of things were
+almost always amongst the very first
+
+ align:start position:0%
+almost always amongst the very first
+ 
+
+ align:start position:0%
+almost always amongst the very first
+topics cho like posted. So, so it wasn't
+
+ align:start position:0%
+topics cho like posted. So, so it wasn't
+ 
+
+ align:start position:0%
+topics cho like posted. So, so it wasn't
+like the forums were surfacing um like
+
+ align:start position:0%
+like the forums were surfacing um like
+ 
+
+ align:start position:0%
+like the forums were surfacing um like
+it wasn't like there was lots of ideas
+
+ align:start position:0%
+it wasn't like there was lots of ideas
+ 
+
+ align:start position:0%
+it wasn't like there was lots of ideas
+and the most interesting or important of
+
+ align:start position:0%
+and the most interesting or important of
+ 
+
+ align:start position:0%
+and the most interesting or important of
+those ideas were surfacing at the top.
+
+ align:start position:0%
+those ideas were surfacing at the top.
+ 
+
+ align:start position:0%
+those ideas were surfacing at the top.
+It was like somebody jumped in there
+
+ align:start position:0%
+It was like somebody jumped in there
+ 
+
+ align:start position:0%
+It was like somebody jumped in there
+first and then people started talking
+
+ align:start position:0%
+first and then people started talking
+ 
+
+ align:start position:0%
+first and then people started talking
+about those things, you know. Um and you
+
+ align:start position:0%
+about those things, you know. Um and you
+ 
+
+ align:start position:0%
+about those things, you know. Um and you
+could imagine you could imagine an
+
+ align:start position:0%
+could imagine you could imagine an
+ 
+
+ align:start position:0%
+could imagine you could imagine an
+alternate timeline of the exact same
+
+ align:start position:0%
+alternate timeline of the exact same
+ 
+
+ align:start position:0%
+alternate timeline of the exact same
+course you're in where the first two
+
+ align:start position:0%
+course you're in where the first two
+ 
+
+ align:start position:0%
+course you're in where the first two
+people to co post happen to just be
+
+ align:start position:0%
+people to co post happen to just be
+ 
+
+ align:start position:0%
+people to co post happen to just be
+people who are like I don't understand
+
+ align:start position:0%
+people who are like I don't understand
+ 
+
+ align:start position:0%
+people who are like I don't understand
+this really basic thing. Will someone
+
+ align:start position:0%
+this really basic thing. Will someone
+ 
+
+ align:start position:0%
+this really basic thing. Will someone
+explain it again? And the forums have
+
+ align:start position:0%
+explain it again? And the forums have
+ 
+
+ align:start position:0%
+explain it again? And the forums have
+sort of a whole different uh character
+
+ align:start position:0%
+sort of a whole different uh character
+ 
+
+ align:start position:0%
+sort of a whole different uh character
+to them. I mean to some extent I think
+
+ align:start position:0%
+to them. I mean to some extent I think
+ 
+
+ align:start position:0%
+to them. I mean to some extent I think
+of computer programming in particular as
+
+ align:start position:0%
+of computer programming in particular as
+ 
+
+ align:start position:0%
+of computer programming in particular as
+a field that depends upon this kind of
+
+ align:start position:0%
+a field that depends upon this kind of
+ 
+
+ align:start position:0%
+a field that depends upon this kind of
+informal learning that b like that
+
+ align:start position:0%
+informal learning that b like that
+ 
+
+ align:start position:0%
+informal learning that b like that
+basically no one knows enough about
+
+ align:start position:0%
+basically no one knows enough about
+ 
+
+ align:start position:0%
+basically no one knows enough about
+programming languages and how they
+
+ align:start position:0%
+programming languages and how they
+ 
+
+ align:start position:0%
+programming languages and how they
+operate and how they solve problems and
+
+ align:start position:0%
+operate and how they solve problems and
+ 
+
+ align:start position:0%
+operate and how they solve problems and
+so you you essentially can't do that
+
+ align:start position:0%
+so you you essentially can't do that
+ 
+
+ align:start position:0%
+so you you essentially can't do that
+profession if you can't figure out how
+
+ align:start position:0%
+profession if you can't figure out how
+ 
+
+ align:start position:0%
+profession if you can't figure out how
+to navigate all the online resources all
+
+ align:start position:0%
+to navigate all the online resources all
+ 
+
+ align:start position:0%
+to navigate all the online resources all
+online communities and things like that.
+
+ align:start position:0%
+online communities and things like that.
+ 
+
+ align:start position:0%
+online communities and things like that.
+And unusually um you can you can be pro
+
+ align:start position:0%
+And unusually um you can you can be pro
+ 
+
+ align:start position:0%
+And unusually um you can you can be pro
+be promoted and thrive in those
+
+ align:start position:0%
+be promoted and thrive in those
+ 
+
+ align:start position:0%
+be promoted and thrive in those
+communities through your participation
+
+ align:start position:0%
+communities through your participation
+ 
+
+ align:start position:0%
+communities through your participation
+in some of these kind of informal
+
+ align:start position:0%
+in some of these kind of informal
+ 
+
+ align:start position:0%
+in some of these kind of informal
+learning networks. You know you can be
+
+ align:start position:0%
+learning networks. You know you can be
+ 
+
+ align:start position:0%
+learning networks. You know you can be
+really active I mean in creating open
+
+ align:start position:0%
+really active I mean in creating open
+ 
+
+ align:start position:0%
+really active I mean in creating open
+source projects or just be a really
+
+ align:start position:0%
+source projects or just be a really
+ 
+
+ align:start position:0%
+source projects or just be a really
+active contributor to Stack Overflow or
+
+ align:start position:0%
+active contributor to Stack Overflow or
+ 
+
+ align:start position:0%
+active contributor to Stack Overflow or
+other kinds of communities like that get
+
+ align:start position:0%
+other kinds of communities like that get
+ 
+
+ align:start position:0%
+other kinds of communities like that get
+recognized for your contributions and
+
+ align:start position:0%
+recognized for your contributions and
+ 
+
+ align:start position:0%
+recognized for your contributions and
+have that translate into other kinds of
+
+ align:start position:0%
+have that translate into other kinds of
+ 
+
+ align:start position:0%
+have that translate into other kinds of
+opportunities. So um the boundaries
+
+ align:start position:0%
+opportunities. So um the boundaries
+ 
+
+ align:start position:0%
+opportunities. So um the boundaries
+between um there there are ways that I
+
+ align:start position:0%
+between um there there are ways that I
+ 
+
+ align:start position:0%
+between um there there are ways that I
+think these informal learning
+
+ align:start position:0%
+think these informal learning
+ 
+
+ align:start position:0%
+think these informal learning
+environments and formal learning
+
+ align:start position:0%
+environments and formal learning
+ 
+
+ align:start position:0%
+environments and formal learning
+environments the boundaries can permeate
+
+ align:start position:0%
+environments the boundaries can permeate
+ 
+
+ align:start position:0%
+environments the boundaries can permeate
+even if as we'll keep talking about like
+
+ align:start position:0%
+even if as we'll keep talking about like
+ 
+
+ align:start position:0%
+even if as we'll keep talking about like
+just trying to take the whole informal
+
+ align:start position:0%
+just trying to take the whole informal
+ 
+
+ align:start position:0%
+just trying to take the whole informal
+peer guided learning infrastructure and
+
+ align:start position:0%
+peer guided learning infrastructure and
+ 
+
+ align:start position:0%
+peer guided learning infrastructure and
+bring it into schools seems not to to
+
+ align:start position:0%
+bring it into schools seems not to to
+ 
+
+ align:start position:0%
+bring it into schools seems not to to
+work pretty well.
+
+ align:start position:0%
+work pretty well.
+ 
+
+ align:start position:0%
+work pretty well.
+Um uh you know I think one of the
+
+ align:start position:0%
+Um uh you know I think one of the
+ 
+
+ align:start position:0%
+Um uh you know I think one of the
+actually one of the most compelling
+
+ align:start position:0%
+actually one of the most compelling
+ 
+
+ align:start position:0%
+actually one of the most compelling
+reasons for integrating technology into
+
+ align:start position:0%
+reasons for integrating technology into
+ 
+
+ align:start position:0%
+reasons for integrating technology into
+people's school learning at all is the
+
+ align:start position:0%
+people's school learning at all is the
+ 
+
+ align:start position:0%
+people's school learning at all is the
+idea that actually for most of your
+
+ align:start position:0%
+idea that actually for most of your
+ 
+
+ align:start position:0%
+idea that actually for most of your
+lives the kind of learning that you do
+
+ align:start position:0%
+lives the kind of learning that you do
+ 
+
+ align:start position:0%
+lives the kind of learning that you do
+will look more like the learning around
+
+ align:start position:0%
+will look more like the learning around
+ 
+
+ align:start position:0%
+will look more like the learning around
+your hobbies than it does look like the
+
+ align:start position:0%
+your hobbies than it does look like the
+ 
+
+ align:start position:0%
+your hobbies than it does look like the
+learning in your classes. You know in in
+
+ align:start position:0%
+learning in your classes. You know in in
+ 
+
+ align:start position:0%
+learning in your classes. You know in in
+the next couple of years some of you
+
+ align:start position:0%
+the next couple of years some of you
+ 
+
+ align:start position:0%
+the next couple of years some of you
+will keep taking classes for a long long
+
+ align:start position:0%
+will keep taking classes for a long long
+ 
+
+ align:start position:0%
+will keep taking classes for a long long
+time but most of you will probably stop
+
+ align:start position:0%
+time but most of you will probably stop
+ 
+
+ align:start position:0%
+time but most of you will probably stop
+um or take them only infrequently. You
+
+ align:start position:0%
+um or take them only infrequently. You
+ 
+
+ align:start position:0%
+um or take them only infrequently. You
+will probably however continue um to
+
+ align:start position:0%
+will probably however continue um to
+ 
+
+ align:start position:0%
+will probably however continue um to
+participate in these online learning
+
+ align:start position:0%
+participate in these online learning
+ 
+
+ align:start position:0%
+participate in these online learning
+communities. To me it raises really
+
+ align:start position:0%
+communities. To me it raises really
+ 
+
+ align:start position:0%
+communities. To me it raises really
+interesting questions like you know what
+
+ align:start position:0%
+interesting questions like you know what
+ 
+
+ align:start position:0%
+interesting questions like you know what
+responsibility does a school have for
+
+ align:start position:0%
+responsibility does a school have for
+ 
+
+ align:start position:0%
+responsibility does a school have for
+helping people become really good um you
+
+ align:start position:0%
+helping people become really good um you
+ 
+
+ align:start position:0%
+helping people become really good um you
+know at learning cooking through playing
+
+ align:start position:0%
+know at learning cooking through playing
+ 
+
+ align:start position:0%
+know at learning cooking through playing
+with recipes the way Dana described or
+
+ align:start position:0%
+with recipes the way Dana described or
+ 
+
+ align:start position:0%
+with recipes the way Dana described or
+or learning photography um through
+
+ align:start position:0%
+or learning photography um through
+ 
+
+ align:start position:0%
+or learning photography um through
+online forums or music through uh online
+
+ align:start position:0%
+online forums or music through uh online
+ 
+
+ align:start position:0%
+online forums or music through uh online
+videos in the way that that Jiren and
+
+ align:start position:0%
+videos in the way that that Jiren and
+ 
+
+ align:start position:0%
+videos in the way that that Jiren and
+Omar described. like what what would
+
+ align:start position:0%
+Omar described. like what what would
+ 
+
+ align:start position:0%
+Omar described. like what what would
+what would a K12 education look like if
+
+ align:start position:0%
+what would a K12 education look like if
+ 
+
+ align:start position:0%
+what would a K12 education look like if
+someone left school and they were like,
+
+ align:start position:0%
+someone left school and they were like,
+ 
+
+ align:start position:0%
+someone left school and they were like,
+I'm totally prepared to teach myself
+
+ align:start position:0%
+I'm totally prepared to teach myself
+ 
+
+ align:start position:0%
+I'm totally prepared to teach myself
+stuff by engaging these online
+
+ align:start position:0%
+stuff by engaging these online
+ 
+
+ align:start position:0%
+stuff by engaging these online
+communities because I've had a bunch of
+
+ align:start position:0%
+communities because I've had a bunch of
+ 
+
+ align:start position:0%
+communities because I've had a bunch of
+practice in those sorts of things. What
+
+ align:start position:0%
+practice in those sorts of things. What
+ 
+
+ align:start position:0%
+practice in those sorts of things. What
+would a what would a college education
+
+ align:start position:0%
+would a what would a college education
+ 
+
+ align:start position:0%
+would a what would a college education
+look like if it was good at that? I feel
+
+ align:start position:0%
+look like if it was good at that? I feel
+ 
+
+ align:start position:0%
+look like if it was good at that? I feel
+like that's like such an interesting
+
+ align:start position:0%
+like that's like such an interesting
+ 
+
+ align:start position:0%
+like that's like such an interesting
+point because I like think back to a
+
+ align:start position:0%
+point because I like think back to a
+ 
+
+ align:start position:0%
+point because I like think back to a
+conversation I had with my mom where she
+
+ align:start position:0%
+conversation I had with my mom where she
+ 
+
+ align:start position:0%
+conversation I had with my mom where she
+like grew up and was out of college or
+
+ align:start position:0%
+like grew up and was out of college or
+ 
+
+ align:start position:0%
+like grew up and was out of college or
+out of high school like right before the
+
+ align:start position:0%
+out of high school like right before the
+ 
+
+ align:start position:0%
+out of high school like right before the
+like really dawn of like computer
+
+ align:start position:0%
+like really dawn of like computer
+ 
+
+ align:start position:0%
+like really dawn of like computer
+classes in high school and middle school
+
+ align:start position:0%
+classes in high school and middle school
+ 
+
+ align:start position:0%
+classes in high school and middle school
+and like in middle school so like
+
+ align:start position:0%
+and like in middle school so like
+ 
+
+ align:start position:0%
+and like in middle school so like
+rudimentary to us we like learn how to
+
+ align:start position:0%
+rudimentary to us we like learn how to
+ 
+
+ align:start position:0%
+rudimentary to us we like learn how to
+use an Excel sheet and like just learn
+
+ align:start position:0%
+use an Excel sheet and like just learn
+ 
+
+ align:start position:0%
+use an Excel sheet and like just learn
+how to like Google things um and like a
+
+ align:start position:0%
+how to like Google things um and like a
+ 
+
+ align:start position:0%
+how to like Google things um and like a
+lot of just like the super basic skills
+
+ align:start position:0%
+lot of just like the super basic skills
+ 
+
+ align:start position:0%
+lot of just like the super basic skills
+like how to type on a computer a
+
+ align:start position:0%
+like how to type on a computer a
+ 
+
+ align:start position:0%
+like how to type on a computer a
+computer like keyboard that she doesn't
+
+ align:start position:0%
+computer like keyboard that she doesn't
+ 
+
+ align:start position:0%
+computer like keyboard that she doesn't
+know how to do and it almost seems like
+
+ align:start position:0%
+know how to do and it almost seems like
+ 
+
+ align:start position:0%
+know how to do and it almost seems like
+the next generation will like leave
+
+ align:start position:0%
+the next generation will like leave
+ 
+
+ align:start position:0%
+the next generation will like leave
+computer classes like knowing how to
+
+ align:start position:0%
+computer classes like knowing how to
+ 
+
+ align:start position:0%
+computer classes like knowing how to
+navigate these sites and like then all
+
+ align:start position:0%
+navigate these sites and like then all
+ 
+
+ align:start position:0%
+navigate these sites and like then all
+the stuff that I had to learn on my own
+
+ align:start position:0%
+the stuff that I had to learn on my own
+ 
+
+ align:start position:0%
+the stuff that I had to learn on my own
+like maybe I'm asking my kids like where
+
+ align:start position:0%
+like maybe I'm asking my kids like where
+ 
+
+ align:start position:0%
+like maybe I'm asking my kids like where
+did you learn that and they're just like
+
+ align:start position:0%
+did you learn that and they're just like
+ 
+
+ align:start position:0%
+did you learn that and they're just like
+in school. Um there was a phrase that
+
+ align:start position:0%
+in school. Um there was a phrase that
+ 
+
+ align:start position:0%
+in school. Um there was a phrase that
+was used for a number of years that was
+
+ align:start position:0%
+was used for a number of years that was
+ 
+
+ align:start position:0%
+was used for a number of years that was
+called digital native. Um the idea maybe
+
+ align:start position:0%
+called digital native. Um the idea maybe
+ 
+
+ align:start position:0%
+called digital native. Um the idea maybe
+maybe a more common you know phrase that
+
+ align:start position:0%
+maybe a more common you know phrase that
+ 
+
+ align:start position:0%
+maybe a more common you know phrase that
+you'll hear probably in the next few
+
+ align:start position:0%
+you'll hear probably in the next few
+ 
+
+ align:start position:0%
+you'll hear probably in the next few
+years will be something like AI native.
+
+ align:start position:0%
+years will be something like AI native.
+ 
+
+ align:start position:0%
+years will be something like AI native.
+um the idea that like what's the
+
+ align:start position:0%
+um the idea that like what's the
+ 
+
+ align:start position:0%
+um the idea that like what's the
+difference between having to learn
+
+ align:start position:0%
+difference between having to learn
+ 
+
+ align:start position:0%
+difference between having to learn
+something by by having it come into you
+
+ align:start position:0%
+something by by having it come into you
+ 
+
+ align:start position:0%
+something by by having it come into you
+into your into your life versus like
+
+ align:start position:0%
+into your into your life versus like
+ 
+
+ align:start position:0%
+into your into your life versus like
+having it be something that you kind of
+
+ align:start position:0%
+having it be something that you kind of
+ 
+
+ align:start position:0%
+having it be something that you kind of
+grow up with all the time. There's
+
+ align:start position:0%
+grow up with all the time. There's
+ 
+
+ align:start position:0%
+grow up with all the time. There's
+actually a bunch of good evidence that
+
+ align:start position:0%
+actually a bunch of good evidence that
+ 
+
+ align:start position:0%
+actually a bunch of good evidence that
+in fact that digital natives that young
+
+ align:start position:0%
+in fact that digital natives that young
+ 
+
+ align:start position:0%
+in fact that digital natives that young
+people are actually not that much better
+
+ align:start position:0%
+people are actually not that much better
+ 
+
+ align:start position:0%
+people are actually not that much better
+at using technology especially learning
+
+ align:start position:0%
+at using technology especially learning
+ 
+
+ align:start position:0%
+at using technology especially learning
+things than older folks. Um you know
+
+ align:start position:0%
+things than older folks. Um you know
+ 
+
+ align:start position:0%
+things than older folks. Um you know
+young people in schools are usually
+
+ align:start position:0%
+young people in schools are usually
+ 
+
+ align:start position:0%
+young people in schools are usually
+pretty good at doing certain kinds of
+
+ align:start position:0%
+pretty good at doing certain kinds of
+ 
+
+ align:start position:0%
+pretty good at doing certain kinds of
+technology mediated things but the
+
+ align:start position:0%
+technology mediated things but the
+ 
+
+ align:start position:0%
+technology mediated things but the
+things that are most helpful for
+
+ align:start position:0%
+things that are most helpful for
+ 
+
+ align:start position:0%
+things that are most helpful for
+learning they're often no better at than
+
+ align:start position:0%
+learning they're often no better at than
+ 
+
+ align:start position:0%
+learning they're often no better at than
+sort of anybody else. Um although I'
+
+ align:start position:0%
+sort of anybody else. Um although I'
+ 
+
+ align:start position:0%
+sort of anybody else. Um although I'
+I've always liked the idea you know one
+
+ align:start position:0%
+I've always liked the idea you know one
+ 
+
+ align:start position:0%
+I've always liked the idea you know one
+of the things that comes along with the
+
+ align:start position:0%
+of the things that comes along with the
+ 
+
+ align:start position:0%
+of the things that comes along with the
+idea of immigration of digital natives
+
+ align:start position:0%
+idea of immigration of digital natives
+ 
+
+ align:start position:0%
+idea of immigration of digital natives
+and so digital immigrants and digital
+
+ align:start position:0%
+and so digital immigrants and digital
+ 
+
+ align:start position:0%
+and so digital immigrants and digital
+natives is that uh um you know second
+
+ align:start position:0%
+natives is that uh um you know second
+ 
+
+ align:start position:0%
+natives is that uh um you know second
+generation immigrants are always taking
+
+ align:start position:0%
+generation immigrants are always taking
+ 
+
+ align:start position:0%
+generation immigrants are always taking
+on new responsibilities for teaching
+
+ align:start position:0%
+on new responsibilities for teaching
+ 
+
+ align:start position:0%
+on new responsibilities for teaching
+their first generation parents about
+
+ align:start position:0%
+their first generation parents about
+ 
+
+ align:start position:0%
+their first generation parents about
+things you know you like you you grow up
+
+ align:start position:0%
+things you know you like you you grow up
+ 
+
+ align:start position:0%
+things you know you like you you grow up
+in a country and you learn the language
+
+ align:start position:0%
+in a country and you learn the language
+ 
+
+ align:start position:0%
+in a country and you learn the language
+you learn the culture you know other
+
+ align:start position:0%
+you learn the culture you know other
+ 
+
+ align:start position:0%
+you learn the culture you know other
+kinds of things that you sort of have to
+
+ align:start position:0%
+kinds of things that you sort of have to
+ 
+
+ align:start position:0%
+kinds of things that you sort of have to
+explain to your parents so there's
+
+ align:start position:0%
+explain to your parents so there's
+ 
+
+ align:start position:0%
+explain to your parents so there's
+something kind of nice about um that
+
+ align:start position:0%
+something kind of nice about um that
+ 
+
+ align:start position:0%
+something kind of nice about um that
+metaphor carrying over
+
+ align:start position:0%
+metaphor carrying over
+ 
+
+ align:start position:0%
+metaphor carrying over
+um something that I know state of
+
+ align:start position:0%
+um something that I know state of
+ 
+
+ align:start position:0%
+um something that I know state of
+Massachusetts is doing is um I don't
+
+ align:start position:0%
+Massachusetts is doing is um I don't
+ 
+
+ align:start position:0%
+Massachusetts is doing is um I don't
+know if I completely agree with it um
+
+ align:start position:0%
+know if I completely agree with it um
+ 
+
+ align:start position:0%
+know if I completely agree with it um
+blending computer science and computer
+
+ align:start position:0%
+blending computer science and computer
+ 
+
+ align:start position:0%
+blending computer science and computer
+literacy together. I do think that
+
+ align:start position:0%
+literacy together. I do think that
+ 
+
+ align:start position:0%
+literacy together. I do think that
+teaching computer literacy is of utmost
+
+ align:start position:0%
+teaching computer literacy is of utmost
+ 
+
+ align:start position:0%
+teaching computer literacy is of utmost
+importance. Um I credit a lot of my um
+
+ align:start position:0%
+importance. Um I credit a lot of my um
+ 
+
+ align:start position:0%
+importance. Um I credit a lot of my um
+computer literacy to my seventh grade
+
+ align:start position:0%
+computer literacy to my seventh grade
+ 
+
+ align:start position:0%
+computer literacy to my seventh grade
+seventh and eighth grade technology
+
+ align:start position:0%
+seventh and eighth grade technology
+ 
+
+ align:start position:0%
+seventh and eighth grade technology
+teacher. Um you know the link that I use
+
+ align:start position:0%
+teacher. Um you know the link that I use
+ 
+
+ align:start position:0%
+teacher. Um you know the link that I use
+now was created back in seventh grade.
+
+ align:start position:0%
+now was created back in seventh grade.
+ 
+
+ align:start position:0%
+now was created back in seventh grade.
+use is the very same account and he was
+
+ align:start position:0%
+use is the very same account and he was
+ 
+
+ align:start position:0%
+use is the very same account and he was
+the one who got me um I think I
+
+ align:start position:0%
+the one who got me um I think I
+ 
+
+ align:start position:0%
+the one who got me um I think I
+mentioned the typing lessons like the
+
+ align:start position:0%
+mentioned the typing lessons like the
+ 
+
+ align:start position:0%
+mentioned the typing lessons like the
+beginning of the class that's where I
+
+ align:start position:0%
+beginning of the class that's where I
+ 
+
+ align:start position:0%
+beginning of the class that's where I
+learned how to type um that's where I
+
+ align:start position:0%
+learned how to type um that's where I
+ 
+
+ align:start position:0%
+learned how to type um that's where I
+learned how to um create a portfolio
+
+ align:start position:0%
+learned how to um create a portfolio
+ 
+
+ align:start position:0%
+learned how to um create a portfolio
+create an online website um do like
+
+ align:start position:0%
+create an online website um do like
+ 
+
+ align:start position:0%
+create an online website um do like
+individual kind of research and like
+
+ align:start position:0%
+individual kind of research and like
+ 
+
+ align:start position:0%
+individual kind of research and like
+create a project on something that I'm
+
+ align:start position:0%
+create a project on something that I'm
+ 
+
+ align:start position:0%
+create a project on something that I'm
+interested about um and I think creating
+
+ align:start position:0%
+interested about um and I think creating
+ 
+
+ align:start position:0%
+interested about um and I think creating
+projects on something that's is like
+
+ align:start position:0%
+projects on something that's is like
+ 
+
+ align:start position:0%
+projects on something that's is like
+personal to someone within a K through
+
+ align:start position:0%
+personal to someone within a K through
+ 
+
+ align:start position:0%
+personal to someone within a K through
+12 um lesson is really important for
+
+ align:start position:0%
+12 um lesson is really important for
+ 
+
+ align:start position:0%
+12 um lesson is really important for
+teaching them how to like conduct
+
+ align:start position:0%
+teaching them how to like conduct
+ 
+
+ align:start position:0%
+teaching them how to like conduct
+research
+
+ align:start position:0%
+research
+ 
+
+ align:start position:0%
+research
+take notes and uh come up with
+
+ align:start position:0%
+take notes and uh come up with
+ 
+
+ align:start position:0%
+take notes and uh come up with
+conclusions on what they've um gone up
+
+ align:start position:0%
+conclusions on what they've um gone up
+ 
+
+ align:start position:0%
+conclusions on what they've um gone up
+and looked for online. And a constant
+
+ align:start position:0%
+and looked for online. And a constant
+ 
+
+ align:start position:0%
+and looked for online. And a constant
+challenge educators have is what new
+
+ align:start position:0%
+challenge educators have is what new
+ 
+
+ align:start position:0%
+challenge educators have is what new
+things are actually worth investing
+
+ align:start position:0%
+things are actually worth investing
+ 
+
+ align:start position:0%
+things are actually worth investing
+additional discretionary time in. I
+
+ align:start position:0%
+additional discretionary time in. I
+ 
+
+ align:start position:0%
+additional discretionary time in. I
+mean, there were, you know, plenty of
+
+ align:start position:0%
+mean, there were, you know, plenty of
+ 
+
+ align:start position:0%
+mean, there were, you know, plenty of
+folks 10 years ago who said, man, it's
+
+ align:start position:0%
+folks 10 years ago who said, man, it's
+ 
+
+ align:start position:0%
+folks 10 years ago who said, man, it's
+incredibly important. Every high
+
+ align:start position:0%
+incredibly important. Every high
+ 
+
+ align:start position:0%
+incredibly important. Every high
+schooler should complete a MOO. MOUKs
+
+ align:start position:0%
+schooler should complete a MOO. MOUKs
+ 
+
+ align:start position:0%
+schooler should complete a MOO. MOUKs
+are going to be absolutely essential to
+
+ align:start position:0%
+are going to be absolutely essential to
+ 
+
+ align:start position:0%
+are going to be absolutely essential to
+how people learn and finish higher
+
+ align:start position:0%
+how people learn and finish higher
+ 
+
+ align:start position:0%
+how people learn and finish higher
+education in the future. If you can't do
+
+ align:start position:0%
+education in the future. If you can't do
+ 
+
+ align:start position:0%
+education in the future. If you can't do
+a MOO, you're really going to be left
+
+ align:start position:0%
+a MOO, you're really going to be left
+ 
+
+ align:start position:0%
+a MOO, you're really going to be left
+out. It's like, well, maybe not so much.
+
+ align:start position:0%
+out. It's like, well, maybe not so much.
+ 
+
+ align:start position:0%
+out. It's like, well, maybe not so much.
+turned like a LinkedIn profile however
+
+ align:start position:0%
+turned like a LinkedIn profile however
+ 
+
+ align:start position:0%
+turned like a LinkedIn profile however
+many years later still seems like a
+
+ align:start position:0%
+many years later still seems like a
+ 
+
+ align:start position:0%
+many years later still seems like a
+pretty handy thing to have. There is no
+
+ align:start position:0%
+pretty handy thing to have. There is no
+ 
+
+ align:start position:0%
+pretty handy thing to have. There is no
+reason 10 years ago that you could it's
+
+ align:start position:0%
+reason 10 years ago that you could it's
+ 
+
+ align:start position:0%
+reason 10 years ago that you could it's
+very easy to imagine a world where
+
+ align:start position:0%
+very easy to imagine a world where
+ 
+
+ align:start position:0%
+very easy to imagine a world where
+LinkedIn got replaced by something else
+
+ align:start position:0%
+LinkedIn got replaced by something else
+ 
+
+ align:start position:0%
+LinkedIn got replaced by something else
+entirely and mukes were super important
+
+ align:start position:0%
+entirely and mukes were super important
+ 
+
+ align:start position:0%
+entirely and mukes were super important
+like in 2013 the success paths of those
+
+ align:start position:0%
+like in 2013 the success paths of those
+ 
+
+ align:start position:0%
+like in 2013 the success paths of those
+things were not at all predictable. Um
+
+ align:start position:0%
+things were not at all predictable. Um
+ 
+
+ align:start position:0%
+things were not at all predictable. Um
+uh educators are super anxious about I I
+
+ align:start position:0%
+uh educators are super anxious about I I
+ 
+
+ align:start position:0%
+uh educators are super anxious about I I
+just gave it Aaron came to this
+
+ align:start position:0%
+just gave it Aaron came to this
+ 
+
+ align:start position:0%
+just gave it Aaron came to this
+conference with me. I gave a talk to a
+
+ align:start position:0%
+conference with me. I gave a talk to a
+ 
+
+ align:start position:0%
+conference with me. I gave a talk to a
+bunch of educators about AI and
+
+ align:start position:0%
+bunch of educators about AI and
+ 
+
+ align:start position:0%
+bunch of educators about AI and
+education on Monday. Um and there's a
+
+ align:start position:0%
+education on Monday. Um and there's a
+ 
+
+ align:start position:0%
+education on Monday. Um and there's a
+ton of anxiety about like how important
+
+ align:start position:0%
+ton of anxiety about like how important
+ 
+
+ align:start position:0%
+ton of anxiety about like how important
+are these things? What what do we not
+
+ align:start position:0%
+are these things? What what do we not
+ 
+
+ align:start position:0%
+are these things? What what do we not
+need? Does it make sense to teach kids
+
+ align:start position:0%
+need? Does it make sense to teach kids
+ 
+
+ align:start position:0%
+need? Does it make sense to teach kids
+the same way to search anymore? If you
+
+ align:start position:0%
+the same way to search anymore? If you
+ 
+
+ align:start position:0%
+the same way to search anymore? If you
+know, AI agents are just going to answer
+
+ align:start position:0%
+know, AI agents are just going to answer
+ 
+
+ align:start position:0%
+know, AI agents are just going to answer
+our questions for us or do we is it more
+
+ align:start position:0%
+our questions for us or do we is it more
+ 
+
+ align:start position:0%
+our questions for us or do we is it more
+important to be able to do that because
+
+ align:start position:0%
+important to be able to do that because
+ 
+
+ align:start position:0%
+important to be able to do that because
+the AI agents are going to say nonsense
+
+ align:start position:0%
+the AI agents are going to say nonsense
+ 
+
+ align:start position:0%
+the AI agents are going to say nonsense
+to us? Um all these all these kinds of
+
+ align:start position:0%
+to us? Um all these all these kinds of
+ 
+
+ align:start position:0%
+to us? Um all these all these kinds of
+things. Yeah. Ty, in that Oh, sorry. In
+
+ align:start position:0%
+things. Yeah. Ty, in that Oh, sorry. In
+ 
+
+ align:start position:0%
+things. Yeah. Ty, in that Oh, sorry. In
+that regard, like do you consider AI a
+
+ align:start position:0%
+that regard, like do you consider AI a
+ 
+
+ align:start position:0%
+that regard, like do you consider AI a
+form of like peer learning because it's
+
+ align:start position:0%
+form of like peer learning because it's
+ 
+
+ align:start position:0%
+form of like peer learning because it's
+been trained on pure community like
+
+ align:start position:0%
+been trained on pure community like
+ 
+
+ align:start position:0%
+been trained on pure community like
+stack overflow, all these other things.
+
+ align:start position:0%
+stack overflow, all these other things.
+ 
+
+ align:start position:0%
+stack overflow, all these other things.
+Question. Oh, so my first thing about AI
+
+ align:start position:0%
+Question. Oh, so my first thing about AI
+ 
+
+ align:start position:0%
+Question. Oh, so my first thing about AI
+um uh I was giving a talk with Jim Waldo
+
+ align:start position:0%
+um uh I was giving a talk with Jim Waldo
+ 
+
+ align:start position:0%
+um uh I was giving a talk with Jim Waldo
+um who's the who was the chief technical
+
+ align:start position:0%
+um who's the who was the chief technical
+ 
+
+ align:start position:0%
+um who's the who was the chief technical
+officer at Harvard. He's a neat guy um
+
+ align:start position:0%
+officer at Harvard. He's a neat guy um
+ 
+
+ align:start position:0%
+officer at Harvard. He's a neat guy um
+because he got he got a PhD in
+
+ align:start position:0%
+because he got he got a PhD in
+ 
+
+ align:start position:0%
+because he got he got a PhD in
+philosophy about 40 years ago then went
+
+ align:start position:0%
+philosophy about 40 years ago then went
+ 
+
+ align:start position:0%
+philosophy about 40 years ago then went
+and worked at Oracle, helped write Java.
+
+ align:start position:0%
+and worked at Oracle, helped write Java.
+ 
+
+ align:start position:0%
+and worked at Oracle, helped write Java.
+If you have an Android phone, you're
+
+ align:start position:0%
+If you have an Android phone, you're
+ 
+
+ align:start position:0%
+If you have an Android phone, you're
+probably running his code on it. Um and
+
+ align:start position:0%
+probably running his code on it. Um and
+ 
+
+ align:start position:0%
+probably running his code on it. Um and
+then he came back um and now he does
+
+ align:start position:0%
+then he came back um and now he does
+ 
+
+ align:start position:0%
+then he came back um and now he does
+policy stuff and he's sort of a
+
+ align:start position:0%
+policy stuff and he's sort of a
+ 
+
+ align:start position:0%
+policy stuff and he's sort of a
+philosopher again, but he's like AI what
+
+ align:start position:0%
+philosopher again, but he's like AI what
+ 
+
+ align:start position:0%
+philosopher again, but he's like AI what
+do you AI is what we call computing
+
+ align:start position:0%
+do you AI is what we call computing
+ 
+
+ align:start position:0%
+do you AI is what we call computing
+technologies that are new and we don't
+
+ align:start position:0%
+technologies that are new and we don't
+ 
+
+ align:start position:0%
+technologies that are new and we don't
+understand very well. Um, and 10 years
+
+ align:start position:0%
+understand very well. Um, and 10 years
+ 
+
+ align:start position:0%
+understand very well. Um, and 10 years
+from now, they won't be called AI
+
+ align:start position:0%
+from now, they won't be called AI
+ 
+
+ align:start position:0%
+from now, they won't be called AI
+anymore. Um, and so, uh, you know, like
+
+ align:start position:0%
+anymore. Um, and so, uh, you know, like
+ 
+
+ align:start position:0%
+anymore. Um, and so, uh, you know, like
+are generative pre-trained transformers
+
+ align:start position:0%
+are generative pre-trained transformers
+ 
+
+ align:start position:0%
+are generative pre-trained transformers
+peer communication? Well, you know,
+
+ align:start position:0%
+peer communication? Well, you know,
+ 
+
+ align:start position:0%
+peer communication? Well, you know,
+maybe, um, you know, if like what do I,
+
+ align:start position:0%
+maybe, um, you know, if like what do I,
+ 
+
+ align:start position:0%
+maybe, um, you know, if like what do I,
+what do I think? What do I think a
+
+ align:start position:0%
+what do I think? What do I think a
+ 
+
+ align:start position:0%
+what do I think? What do I think a
+peer-guided network is? Um, a learner
+
+ align:start position:0%
+peer-guided network is? Um, a learner
+ 
+
+ align:start position:0%
+peer-guided network is? Um, a learner
+enters a network with a wide range of
+
+ align:start position:0%
+enters a network with a wide range of
+ 
+
+ align:start position:0%
+enters a network with a wide range of
+learning resources that are generated by
+
+ align:start position:0%
+learning resources that are generated by
+ 
+
+ align:start position:0%
+learning resources that are generated by
+previously all human agents. Um, could
+
+ align:start position:0%
+previously all human agents. Um, could
+ 
+
+ align:start position:0%
+previously all human agents. Um, could
+an a, you know, could a generative
+
+ align:start position:0%
+an a, you know, could a generative
+ 
+
+ align:start position:0%
+an a, you know, could a generative
+pre-trained transformer generate a
+
+ align:start position:0%
+pre-trained transformer generate a
+ 
+
+ align:start position:0%
+pre-trained transformer generate a
+useful learning sequence? Seems
+
+ align:start position:0%
+useful learning sequence? Seems
+ 
+
+ align:start position:0%
+useful learning sequence? Seems
+plausible. Um, you know, I I I remain
+
+ align:start position:0%
+plausible. Um, you know, I I I remain
+ 
+
+ align:start position:0%
+plausible. Um, you know, I I I remain
+not entirely convinced. I I actually
+
+ align:start position:0%
+not entirely convinced. I I actually
+ 
+
+ align:start position:0%
+not entirely convinced. I I actually
+what somebody came up to me and was like
+
+ align:start position:0%
+what somebody came up to me and was like
+ 
+
+ align:start position:0%
+what somebody came up to me and was like
+like we're like we have a startup where
+
+ align:start position:0%
+like we're like we have a startup where
+ 
+
+ align:start position:0%
+like we're like we have a startup where
+we're creating online classes by having
+
+ align:start position:0%
+we're creating online classes by having
+ 
+
+ align:start position:0%
+we're creating online classes by having
+AI create the classes. And I was like,
+
+ align:start position:0%
+AI create the classes. And I was like,
+ 
+
+ align:start position:0%
+AI create the classes. And I was like,
+that just sounds like a terrible idea.
+
+ align:start position:0%
+that just sounds like a terrible idea.
+ 
+
+ align:start position:0%
+that just sounds like a terrible idea.
+In part because there's just such a huge
+
+ align:start position:0%
+In part because there's just such a huge
+ 
+
+ align:start position:0%
+In part because there's just such a huge
+surfet of classes. Like there's so many
+
+ align:start position:0%
+surfet of classes. Like there's so many
+ 
+
+ align:start position:0%
+surfet of classes. Like there's so many
+things out there and they're really not
+
+ align:start position:0%
+things out there and they're really not
+ 
+
+ align:start position:0%
+things out there and they're really not
+unfortunately that expensive to develop.
+
+ align:start position:0%
+unfortunately that expensive to develop.
+ 
+
+ align:start position:0%
+unfortunately that expensive to develop.
+Um like why do you mean machines to do
+
+ align:start position:0%
+Um like why do you mean machines to do
+ 
+
+ align:start position:0%
+Um like why do you mean machines to do
+them? Um
+
+ align:start position:0%
+them? Um
+ 
+
+ align:start position:0%
+them? Um
+uh I have a I have a colleague uh
+
+ align:start position:0%
+uh I have a I have a colleague uh
+ 
+
+ align:start position:0%
+uh I have a I have a colleague uh
+um Carolyn Ros who worked with chat bots
+
+ align:start position:0%
+um Carolyn Ros who worked with chat bots
+ 
+
+ align:start position:0%
+um Carolyn Ros who worked with chat bots
+for decades. Um
+
+ align:start position:0%
+for decades. Um
+ 
+
+ align:start position:0%
+for decades. Um
+uh and and she actually she's has
+
+ align:start position:0%
+uh and and she actually she's has
+ 
+
+ align:start position:0%
+uh and and she actually she's has
+convinced me to be very skeptical of
+
+ align:start position:0%
+convinced me to be very skeptical of
+ 
+
+ align:start position:0%
+convinced me to be very skeptical of
+interactions of individuals with chat
+
+ align:start position:0%
+interactions of individuals with chat
+ 
+
+ align:start position:0%
+interactions of individuals with chat
+bots. Um like I don't know how many of
+
+ align:start position:0%
+bots. Um like I don't know how many of
+ 
+
+ align:start position:0%
+bots. Um like I don't know how many of
+you in the last week spent more than an
+
+ align:start position:0%
+you in the last week spent more than an
+ 
+
+ align:start position:0%
+you in the last week spent more than an
+hour talking to a
+
+ align:start position:0%
+hour talking to a
+ 
+
+ align:start position:0%
+hour talking to a
+chatbot. Zero, maybe one. Um I just
+
+ align:start position:0%
+chatbot. Zero, maybe one. Um I just
+ 
+
+ align:start position:0%
+chatbot. Zero, maybe one. Um I just
+don't think people like it that much. Um
+
+ align:start position:0%
+don't think people like it that much. Um
+ 
+
+ align:start position:0%
+don't think people like it that much. Um
+she really thought that where they could
+
+ align:start position:0%
+she really thought that where they could
+ 
+
+ align:start position:0%
+she really thought that where they could
+be powerful is jumping in in the
+
+ align:start position:0%
+be powerful is jumping in in the
+ 
+
+ align:start position:0%
+be powerful is jumping in in the
+conversations between two people. Um
+
+ align:start position:0%
+conversations between two people. Um
+ 
+
+ align:start position:0%
+conversations between two people. Um
+that you just have peers talking to each
+
+ align:start position:0%
+that you just have peers talking to each
+ 
+
+ align:start position:0%
+that you just have peers talking to each
+other. So you're on this discussion
+
+ align:start position:0%
+other. So you're on this discussion
+ 
+
+ align:start position:0%
+other. So you're on this discussion
+forum and you're going back and forth or
+
+ align:start position:0%
+forum and you're going back and forth or
+ 
+
+ align:start position:0%
+forum and you're going back and forth or
+other things like that and then a bot
+
+ align:start position:0%
+other things like that and then a bot
+ 
+
+ align:start position:0%
+other things like that and then a bot
+comes in and sort of helps you um ask an
+
+ align:start position:0%
+comes in and sort of helps you um ask an
+ 
+
+ align:start position:0%
+comes in and sort of helps you um ask an
+interesting question. Get like oh look
+
+ align:start position:0%
+interesting question. Get like oh look
+ 
+
+ align:start position:0%
+interesting question. Get like oh look
+somebody over here has a different
+
+ align:start position:0%
+somebody over here has a different
+ 
+
+ align:start position:0%
+somebody over here has a different
+perspective on that. Let me connect you
+
+ align:start position:0%
+perspective on that. Let me connect you
+ 
+
+ align:start position:0%
+perspective on that. Let me connect you
+to that. and so you can talk and things
+
+ align:start position:0%
+to that. and so you can talk and things
+ 
+
+ align:start position:0%
+to that. and so you can talk and things
+like that. Um, but yeah, it totally I I
+
+ align:start position:0%
+like that. Um, but yeah, it totally I I
+ 
+
+ align:start position:0%
+like that. Um, but yeah, it totally I I
+think I think it totally seems plausible
+
+ align:start position:0%
+think I think it totally seems plausible
+ 
+
+ align:start position:0%
+think I think it totally seems plausible
+that a peer guided learning environment
+
+ align:start position:0%
+that a peer guided learning environment
+ 
+
+ align:start position:0%
+that a peer guided learning environment
+could include, you know, artificial
+
+ align:start position:0%
+could include, you know, artificial
+ 
+
+ align:start position:0%
+could include, you know, artificial
+agents that are doing things that humans
+
+ align:start position:0%
+agents that are doing things that humans
+ 
+
+ align:start position:0%
+agents that are doing things that humans
+had previously been doing.
+
+ align:start position:0%
+had previously been doing.
+ 
+
+ align:start position:0%
+had previously been doing.
+Yeah, I guess to like both your points
+
+ align:start position:0%
+Yeah, I guess to like both your points
+ 
+
+ align:start position:0%
+Yeah, I guess to like both your points
+of like a interaction, I I would say um
+
+ align:start position:0%
+of like a interaction, I I would say um
+ 
+
+ align:start position:0%
+of like a interaction, I I would say um
+um an interesting aspect of that
+
+ align:start position:0%
+um an interesting aspect of that
+ 
+
+ align:start position:0%
+um an interesting aspect of that
+especially in terms of like what can be
+
+ align:start position:0%
+especially in terms of like what can be
+ 
+
+ align:start position:0%
+especially in terms of like what can be
+a credible source for learning and stuff
+
+ align:start position:0%
+a credible source for learning and stuff
+ 
+
+ align:start position:0%
+a credible source for learning and stuff
+like that. So, I think in California, or
+
+ align:start position:0%
+like that. So, I think in California, or
+ 
+
+ align:start position:0%
+like that. So, I think in California, or
+at least the the the part of California
+
+ align:start position:0%
+at least the the the part of California
+ 
+
+ align:start position:0%
+at least the the the part of California
+I was in for a while, we did have like a
+
+ align:start position:0%
+I was in for a while, we did have like a
+ 
+
+ align:start position:0%
+I was in for a while, we did have like a
+middle school little like a week-l long
+
+ align:start position:0%
+middle school little like a week-l long
+ 
+
+ align:start position:0%
+middle school little like a week-l long
+program that every kid had to do that
+
+ align:start position:0%
+program that every kid had to do that
+ 
+
+ align:start position:0%
+program that every kid had to do that
+was like, "Oh, you're 13. Here, make an
+
+ align:start position:0%
+was like, "Oh, you're 13. Here, make an
+ 
+
+ align:start position:0%
+was like, "Oh, you're 13. Here, make an
+email and here's how you Google stuff."
+
+ align:start position:0%
+email and here's how you Google stuff."
+ 
+
+ align:start position:0%
+email and here's how you Google stuff."
+Um, and like recently with um the new
+
+ align:start position:0%
+Um, and like recently with um the new
+ 
+
+ align:start position:0%
+Um, and like recently with um the new
+Google AI feature that kind of
+
+ align:start position:0%
+Google AI feature that kind of
+ 
+
+ align:start position:0%
+Google AI feature that kind of
+summarizes answers for you. Now, I was
+
+ align:start position:0%
+summarizes answers for you. Now, I was
+ 
+
+ align:start position:0%
+summarizes answers for you. Now, I was
+like thinking about like um how does
+
+ align:start position:0%
+like thinking about like um how does
+ 
+
+ align:start position:0%
+like thinking about like um how does
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+change kind of those levels of
+
+ align:start position:0%
+change kind of those levels of
+ 
+
+ align:start position:0%
+change kind of those levels of
+instructions? Because sometimes I look
+
+ align:start position:0%
+instructions? Because sometimes I look
+ 
+
+ align:start position:0%
+instructions? Because sometimes I look
+up things and I see the summary and I'm
+
+ align:start position:0%
+up things and I see the summary and I'm
+ 
+
+ align:start position:0%
+up things and I see the summary and I'm
+like I don't know what the answer is but
+
+ align:start position:0%
+like I don't know what the answer is but
+ 
+
+ align:start position:0%
+like I don't know what the answer is but
+I know it's not
+
+ align:start position:0%
+I know it's not
+ 
+
+ align:start position:0%
+I know it's not
+that and I and I go deeper. But like
+
+ align:start position:0%
+that and I and I go deeper. But like
+ 
+
+ align:start position:0%
+that and I and I go deeper. But like
+let's say if I'm a middle schooler and
+
+ align:start position:0%
+let's say if I'm a middle schooler and
+ 
+
+ align:start position:0%
+let's say if I'm a middle schooler and
+it's like well I don't learn this or I'm
+
+ align:start position:0%
+it's like well I don't learn this or I'm
+ 
+
+ align:start position:0%
+it's like well I don't learn this or I'm
+a high schooler that took that class in
+
+ align:start position:0%
+a high schooler that took that class in
+ 
+
+ align:start position:0%
+a high schooler that took that class in
+middle school and it's like well now I'm
+
+ align:start position:0%
+middle school and it's like well now I'm
+ 
+
+ align:start position:0%
+middle school and it's like well now I'm
+not sure or I take Bard's word for good.
+
+ align:start position:0%
+not sure or I take Bard's word for good.
+ 
+
+ align:start position:0%
+not sure or I take Bard's word for good.
+Yeah. Yeah. No, a hu a huge problem with
+
+ align:start position:0%
+Yeah. Yeah. No, a hu a huge problem with
+ 
+
+ align:start position:0%
+Yeah. Yeah. No, a hu a huge problem with
+GPT generated text is that it's probably
+
+ align:start position:0%
+GPT generated text is that it's probably
+ 
+
+ align:start position:0%
+GPT generated text is that it's probably
+much more useful for experts than for
+
+ align:start position:0%
+much more useful for experts than for
+ 
+
+ align:start position:0%
+much more useful for experts than for
+noviceses. Um, so if you're an if you
+
+ align:start position:0%
+noviceses. Um, so if you're an if you
+ 
+
+ align:start position:0%
+noviceses. Um, so if you're an if you
+know you ask a GPT to make eight things
+
+ align:start position:0%
+know you ask a GPT to make eight things
+ 
+
+ align:start position:0%
+know you ask a GPT to make eight things
+and and two of them are cool and six of
+
+ align:start position:0%
+and and two of them are cool and six of
+ 
+
+ align:start position:0%
+and and two of them are cool and six of
+them are nonsense or the opposite, an
+
+ align:start position:0%
+them are nonsense or the opposite, an
+ 
+
+ align:start position:0%
+them are nonsense or the opposite, an
+expert can tell the difference and be
+
+ align:start position:0%
+expert can tell the difference and be
+ 
+
+ align:start position:0%
+expert can tell the difference and be
+like, "Oh, that was an idea I didn't
+
+ align:start position:0%
+like, "Oh, that was an idea I didn't
+ 
+
+ align:start position:0%
+like, "Oh, that was an idea I didn't
+have before." But a novice can't. A
+
+ align:start position:0%
+have before." But a novice can't. A
+ 
+
+ align:start position:0%
+have before." But a novice can't. A
+novice just looks and be like, "Okay,
+
+ align:start position:0%
+novice just looks and be like, "Okay,
+ 
+
+ align:start position:0%
+novice just looks and be like, "Okay,
+these are eight ideas. They all seem
+
+ align:start position:0%
+these are eight ideas. They all seem
+ 
+
+ align:start position:0%
+these are eight ideas. They all seem
+plausible and they're confidently stated
+
+ align:start position:0%
+plausible and they're confidently stated
+ 
+
+ align:start position:0%
+plausible and they're confidently stated
+and things like that." It's a huge
+
+ align:start position:0%
+and things like that." It's a huge
+ 
+
+ align:start position:0%
+and things like that." It's a huge
+problem that educators are going to have
+
+ align:start position:0%
+problem that educators are going to have
+ 
+
+ align:start position:0%
+problem that educators are going to have
+to wrestle with um in the in the years
+
+ align:start position:0%
+to wrestle with um in the in the years
+ 
+
+ align:start position:0%
+to wrestle with um in the in the years
+ahead.
+
+ align:start position:0%
+ahead.
+ 
+
+ align:start position:0%
+ahead.
+Um it's, you know, the kind of class
+
+ align:start position:0%
+Um it's, you know, the kind of class
+ 
+
+ align:start position:0%
+Um it's, you know, the kind of class
+that you're describing, um if if it were
+
+ align:start position:0%
+that you're describing, um if if it were
+ 
+
+ align:start position:0%
+that you're describing, um if if it were
+to be taught 10 years ago, a big thing
+
+ align:start position:0%
+to be taught 10 years ago, a big thing
+ 
+
+ align:start position:0%
+to be taught 10 years ago, a big thing
+that educators were thinking about at
+
+ align:start position:0%
+that educators were thinking about at
+ 
+
+ align:start position:0%
+that educators were thinking about at
+the time was how are people going to
+
+ align:start position:0%
+the time was how are people going to
+ 
+
+ align:start position:0%
+the time was how are people going to
+navigate a social web? Um so, um when
+
+ align:start position:0%
+navigate a social web? Um so, um when
+ 
+
+ align:start position:0%
+navigate a social web? Um so, um when
+when the web was first developed, we'll
+
+ align:start position:0%
+when the web was first developed, we'll
+ 
+
+ align:start position:0%
+when the web was first developed, we'll
+get into this a little bit more, it was
+
+ align:start position:0%
+get into this a little bit more, it was
+ 
+
+ align:start position:0%
+get into this a little bit more, it was
+pretty hard for people to contribute to
+
+ align:start position:0%
+pretty hard for people to contribute to
+ 
+
+ align:start position:0%
+pretty hard for people to contribute to
+it. Um you had to know a little bit
+
+ align:start position:0%
+it. Um you had to know a little bit
+ 
+
+ align:start position:0%
+it. Um you had to know a little bit
+about FTP, you had to know a little bit
+
+ align:start position:0%
+about FTP, you had to know a little bit
+ 
+
+ align:start position:0%
+about FTP, you had to know a little bit
+about HTML, a couple other things like
+
+ align:start position:0%
+about HTML, a couple other things like
+ 
+
+ align:start position:0%
+about HTML, a couple other things like
+that. They weren't like super hard, but
+
+ align:start position:0%
+that. They weren't like super hard, but
+ 
+
+ align:start position:0%
+that. They weren't like super hard, but
+there was a relatively small portion of
+
+ align:start position:0%
+there was a relatively small portion of
+ 
+
+ align:start position:0%
+there was a relatively small portion of
+the population that added content to the
+
+ align:start position:0%
+the population that added content to the
+ 
+
+ align:start position:0%
+the population that added content to the
+internet. Um, and there were suite of
+
+ align:start position:0%
+internet. Um, and there were suite of
+ 
+
+ align:start position:0%
+internet. Um, and there were suite of
+technologies that got bundled and called
+
+ align:start position:0%
+technologies that got bundled and called
+ 
+
+ align:start position:0%
+technologies that got bundled and called
+web 2.0. Um, which said, okay, we're
+
+ align:start position:0%
+web 2.0. Um, which said, okay, we're
+ 
+
+ align:start position:0%
+web 2.0. Um, which said, okay, we're
+going to make it much easier for anybody
+
+ align:start position:0%
+going to make it much easier for anybody
+ 
+
+ align:start position:0%
+going to make it much easier for anybody
+to type things online. You can all start
+
+ align:start position:0%
+to type things online. You can all start
+ 
+
+ align:start position:0%
+to type things online. You can all start
+a blog. You can all start a micro blog.
+
+ align:start position:0%
+a blog. You can all start a micro blog.
+ 
+
+ align:start position:0%
+a blog. You can all start a micro blog.
+You can all make a simple website. You
+
+ align:start position:0%
+You can all make a simple website. You
+ 
+
+ align:start position:0%
+You can all make a simple website. You
+don't have to know how to code to do any
+
+ align:start position:0%
+don't have to know how to code to do any
+ 
+
+ align:start position:0%
+don't have to know how to code to do any
+of these things. Um, we're gonna we're
+
+ align:start position:0%
+of these things. Um, we're gonna we're
+ 
+
+ align:start position:0%
+of these things. Um, we're gonna we're
+going to use user interfaces to take
+
+ align:start position:0%
+going to use user interfaces to take
+ 
+
+ align:start position:0%
+going to use user interfaces to take
+away all that sort of programming
+
+ align:start position:0%
+away all that sort of programming
+ 
+
+ align:start position:0%
+away all that sort of programming
+expertise that's necessary. And so
+
+ align:start position:0%
+expertise that's necessary. And so
+ 
+
+ align:start position:0%
+expertise that's necessary. And so
+people thought, "Wow, you know, I bet
+
+ align:start position:0%
+people thought, "Wow, you know, I bet
+ 
+
+ align:start position:0%
+people thought, "Wow, you know, I bet
+our lives are going to and you know,
+
+ align:start position:0%
+our lives are going to and you know,
+ 
+
+ align:start position:0%
+our lives are going to and you know,
+young people's lives." If you, you know,
+
+ align:start position:0%
+young people's lives." If you, you know,
+ 
+
+ align:start position:0%
+young people's lives." If you, you know,
+if you were teaching 11 year olds, 12
+
+ align:start position:0%
+if you were teaching 11 year olds, 12
+ 
+
+ align:start position:0%
+if you were teaching 11 year olds, 12
+year olds in 2013, you thought, man, a
+
+ align:start position:0%
+year olds in 2013, you thought, man, a
+ 
+
+ align:start position:0%
+year olds in 2013, you thought, man, a
+major thing they're going to have to do
+
+ align:start position:0%
+major thing they're going to have to do
+ 
+
+ align:start position:0%
+major thing they're going to have to do
+is how to connect and network with each
+
+ align:start position:0%
+is how to connect and network with each
+ 
+
+ align:start position:0%
+is how to connect and network with each
+other. We have to have them create their
+
+ align:start position:0%
+other. We have to have them create their
+ 
+
+ align:start position:0%
+other. We have to have them create their
+LinkedIn page um so that they know how
+
+ align:start position:0%
+LinkedIn page um so that they know how
+ 
+
+ align:start position:0%
+LinkedIn page um so that they know how
+to social network with each other. We
+
+ align:start position:0%
+to social network with each other. We
+ 
+
+ align:start position:0%
+to social network with each other. We
+have to have them um, you know,
+
+ align:start position:0%
+have to have them um, you know,
+ 
+
+ align:start position:0%
+have to have them um, you know,
+participate in online dialogues. We have
+
+ align:start position:0%
+participate in online dialogues. We have
+ 
+
+ align:start position:0%
+participate in online dialogues. We have
+to have them think about what are
+
+ align:start position:0%
+to have them think about what are
+ 
+
+ align:start position:0%
+to have them think about what are
+responsible ways of representing
+
+ align:start position:0%
+responsible ways of representing
+ 
+
+ align:start position:0%
+responsible ways of representing
+themselves. Um people talk a lot about
+
+ align:start position:0%
+themselves. Um people talk a lot about
+ 
+
+ align:start position:0%
+themselves. Um people talk a lot about
+their digital footprint um and other
+
+ align:start position:0%
+their digital footprint um and other
+ 
+
+ align:start position:0%
+their digital footprint um and other
+kinds of things like that. Um you know
+
+ align:start position:0%
+kinds of things like that. Um you know
+ 
+
+ align:start position:0%
+kinds of things like that. Um you know
+today a 13-year-old is entering a web
+
+ align:start position:0%
+today a 13-year-old is entering a web
+ 
+
+ align:start position:0%
+today a 13-year-old is entering a web
+environment in which there are lots of
+
+ align:start position:0%
+environment in which there are lots of
+ 
+
+ align:start position:0%
+environment in which there are lots of
+parts of social media which are
+
+ align:start position:0%
+parts of social media which are
+ 
+
+ align:start position:0%
+parts of social media which are
+collapsing. Um that uh um you know just
+
+ align:start position:0%
+collapsing. Um that uh um you know just
+ 
+
+ align:start position:0%
+collapsing. Um that uh um you know just
+as an example actually I was I went to
+
+ align:start position:0%
+as an example actually I was I went to
+ 
+
+ align:start position:0%
+as an example actually I was I went to
+the guy who ran this conference on
+
+ align:start position:0%
+the guy who ran this conference on
+ 
+
+ align:start position:0%
+the guy who ran this conference on
+Monday and well it was kind of so there
+
+ align:start position:0%
+Monday and well it was kind of so there
+ 
+
+ align:start position:0%
+Monday and well it was kind of so there
+were usually this conference get 100 or
+
+ align:start position:0%
+were usually this conference get 100 or
+ 
+
+ align:start position:0%
+were usually this conference get 100 or
+150 people show up. It was about AI.
+
+ align:start position:0%
+150 people show up. It was about AI.
+ 
+
+ align:start position:0%
+150 people show up. It was about AI.
+They had 240 people show up and 70 folks
+
+ align:start position:0%
+They had 240 people show up and 70 folks
+ 
+
+ align:start position:0%
+They had 240 people show up and 70 folks
+were on the wait list. Um, tons and tons
+
+ align:start position:0%
+were on the wait list. Um, tons and tons
+ 
+
+ align:start position:0%
+were on the wait list. Um, tons and tons
+of interest from educators. And I and I
+
+ align:start position:0%
+of interest from educators. And I and I
+ 
+
+ align:start position:0%
+of interest from educators. And I and I
+went to the guy who runs it, Tom
+
+ align:start position:0%
+went to the guy who runs it, Tom
+ 
+
+ align:start position:0%
+went to the guy who runs it, Tom
+Driscoll, and says, "What do you think
+
+ align:start position:0%
+Driscoll, and says, "What do you think
+ 
+
+ align:start position:0%
+Driscoll, and says, "What do you think
+these teachers are interested in? Like
+
+ align:start position:0%
+these teachers are interested in? Like
+ 
+
+ align:start position:0%
+these teachers are interested in? Like
+what are you like, what do they want to
+
+ align:start position:0%
+what are you like, what do they want to
+ 
+
+ align:start position:0%
+what are you like, what do they want to
+know? Why are they here?" Um, and he's
+
+ align:start position:0%
+know? Why are they here?" Um, and he's
+ 
+
+ align:start position:0%
+know? Why are they here?" Um, and he's
+like, "You know what? I don't know." Um,
+
+ align:start position:0%
+like, "You know what? I don't know." Um,
+ 
+
+ align:start position:0%
+like, "You know what? I don't know." Um,
+10 years ago, they would have had blogs.
+
+ align:start position:0%
+10 years ago, they would have had blogs.
+ 
+
+ align:start position:0%
+10 years ago, they would have had blogs.
+They would have, you know, participated
+
+ align:start position:0%
+They would have, you know, participated
+ 
+
+ align:start position:0%
+They would have, you know, participated
+in forums. They would have joined
+
+ align:start position:0%
+in forums. They would have joined
+ 
+
+ align:start position:0%
+in forums. They would have joined
+Facebook groups. they would have sort of
+
+ align:start position:0%
+Facebook groups. they would have sort of
+ 
+
+ align:start position:0%
+Facebook groups. they would have sort of
+like um uh they had there were many many
+
+ align:start position:0%
+like um uh they had there were many many
+ 
+
+ align:start position:0%
+like um uh they had there were many many
+more ways that educators were
+
+ align:start position:0%
+more ways that educators were
+ 
+
+ align:start position:0%
+more ways that educators were
+proactively um contributing their ideas
+
+ align:start position:0%
+proactively um contributing their ideas
+ 
+
+ align:start position:0%
+proactively um contributing their ideas
+to the web. Maybe not all of them. Maybe
+
+ align:start position:0%
+to the web. Maybe not all of them. Maybe
+ 
+
+ align:start position:0%
+to the web. Maybe not all of them. Maybe
+it was you know 10% of them or 20% of
+
+ align:start position:0%
+it was you know 10% of them or 20% of
+ 
+
+ align:start position:0%
+it was you know 10% of them or 20% of
+the time but enough of them that you
+
+ align:start position:0%
+the time but enough of them that you
+ 
+
+ align:start position:0%
+the time but enough of them that you
+could kind of get the pulse of a whole
+
+ align:start position:0%
+could kind of get the pulse of a whole
+ 
+
+ align:start position:0%
+could kind of get the pulse of a whole
+community. Um which he felt like and I
+
+ align:start position:0%
+community. Um which he felt like and I
+ 
+
+ align:start position:0%
+community. Um which he felt like and I
+agree you really can't do anymore. Um
+
+ align:start position:0%
+agree you really can't do anymore. Um
+ 
+
+ align:start position:0%
+agree you really can't do anymore. Um
+some of that is that there was there was
+
+ align:start position:0%
+some of that is that there was there was
+ 
+
+ align:start position:0%
+some of that is that there was there was
+a moment in web 2.0 know in which people
+
+ align:start position:0%
+a moment in web 2.0 know in which people
+ 
+
+ align:start position:0%
+a moment in web 2.0 know in which people
+believed that the infrastructure of the
+
+ align:start position:0%
+believed that the infrastructure of the
+ 
+
+ align:start position:0%
+believed that the infrastructure of the
+web might be really quite open and quite
+
+ align:start position:0%
+web might be really quite open and quite
+ 
+
+ align:start position:0%
+web might be really quite open and quite
+owned um or controlled by individual
+
+ align:start position:0%
+owned um or controlled by individual
+ 
+
+ align:start position:0%
+owned um or controlled by individual
+people um that there could be a world
+
+ align:start position:0%
+people um that there could be a world
+ 
+
+ align:start position:0%
+people um that there could be a world
+where people create their own websites,
+
+ align:start position:0%
+where people create their own websites,
+ 
+
+ align:start position:0%
+where people create their own websites,
+they create their own blogs, they host
+
+ align:start position:0%
+they create their own blogs, they host
+ 
+
+ align:start position:0%
+they create their own blogs, they host
+their own accounts and things like that.
+
+ align:start position:0%
+their own accounts and things like that.
+ 
+
+ align:start position:0%
+their own accounts and things like that.
+Um and uh you know I don't know when
+
+ align:start position:0%
+Um and uh you know I don't know when
+ 
+
+ align:start position:0%
+Um and uh you know I don't know when
+some of these things starting around
+
+ align:start position:0%
+some of these things starting around
+ 
+
+ align:start position:0%
+some of these things starting around
+2015 2016 people started describing um
+
+ align:start position:0%
+2015 2016 people started describing um
+ 
+
+ align:start position:0%
+2015 2016 people started describing um
+the web we lost a kind of a kind of
+
+ align:start position:0%
+the web we lost a kind of a kind of
+ 
+
+ align:start position:0%
+the web we lost a kind of a kind of
+moment in which social media took a turn
+
+ align:start position:0%
+moment in which social media took a turn
+ 
+
+ align:start position:0%
+moment in which social media took a turn
+um uh you know so these are the kinds of
+
+ align:start position:0%
+um uh you know so these are the kinds of
+ 
+
+ align:start position:0%
+um uh you know so these are the kinds of
+things that like I don't know I was
+
+ align:start position:0%
+things that like I don't know I was
+ 
+
+ align:start position:0%
+things that like I don't know I was
+playing around with in 2004 2007 any of
+
+ align:start position:0%
+playing around with in 2004 2007 any of
+ 
+
+ align:start position:0%
+playing around with in 2004 2007 any of
+you have a live journal blog as one of
+
+ align:start position:0%
+you have a live journal blog as one of
+ 
+
+ align:start position:0%
+you have a live journal blog as one of
+the early sort of blogging sites people
+
+ align:start position:0%
+the early sort of blogging sites people
+ 
+
+ align:start position:0%
+the early sort of blogging sites people
+like create their own space and hosting
+
+ align:start position:0%
+like create their own space and hosting
+ 
+
+ align:start position:0%
+like create their own space and hosting
+it this was a wordpress.com blog of my
+
+ align:start position:0%
+it this was a wordpress.com blog of my
+ 
+
+ align:start position:0%
+it this was a wordpress.com blog of my
+wife and I you know, writing little
+
+ align:start position:0%
+wife and I you know, writing little
+ 
+
+ align:start position:0%
+wife and I you know, writing little
+stories about us, going on adventures
+
+ align:start position:0%
+stories about us, going on adventures
+ 
+
+ align:start position:0%
+stories about us, going on adventures
+and things like that. Um, posting
+
+ align:start position:0%
+and things like that. Um, posting
+ 
+
+ align:start position:0%
+and things like that. Um, posting
+pictures, hosting it ourselves. Um, and
+
+ align:start position:0%
+pictures, hosting it ourselves. Um, and
+ 
+
+ align:start position:0%
+pictures, hosting it ourselves. Um, and
+essentially Facebook came and sort of
+
+ align:start position:0%
+essentially Facebook came and sort of
+ 
+
+ align:start position:0%
+essentially Facebook came and sort of
+demolished all this. Um, and said, you
+
+ align:start position:0%
+demolished all this. Um, and said, you
+ 
+
+ align:start position:0%
+demolished all this. Um, and said, you
+know what, like you don't need to host
+
+ align:start position:0%
+know what, like you don't need to host
+ 
+
+ align:start position:0%
+know what, like you don't need to host
+your own blog. You don't need to um, you
+
+ align:start position:0%
+your own blog. You don't need to um, you
+ 
+
+ align:start position:0%
+your own blog. You don't need to um, you
+know, you don't need to like figure out
+
+ align:start position:0%
+know, you don't need to like figure out
+ 
+
+ align:start position:0%
+know, you don't need to like figure out
+an FTP server to upload your own
+
+ align:start position:0%
+an FTP server to upload your own
+ 
+
+ align:start position:0%
+an FTP server to upload your own
+pictures or use a picture interface.
+
+ align:start position:0%
+pictures or use a picture interface.
+ 
+
+ align:start position:0%
+pictures or use a picture interface.
+Like we're going to create an interface
+
+ align:start position:0%
+Like we're going to create an interface
+ 
+
+ align:start position:0%
+Like we're going to create an interface
+there. people participate in a lot of
+
+ align:start position:0%
+there. people participate in a lot of
+ 
+
+ align:start position:0%
+there. people participate in a lot of
+the same kind of practices on Facebook
+
+ align:start position:0%
+the same kind of practices on Facebook
+ 
+
+ align:start position:0%
+the same kind of practices on Facebook
+of writing little stories on the trips
+
+ align:start position:0%
+of writing little stories on the trips
+ 
+
+ align:start position:0%
+of writing little stories on the trips
+they do and posting pictures and stuff
+
+ align:start position:0%
+they do and posting pictures and stuff
+ 
+
+ align:start position:0%
+they do and posting pictures and stuff
+like that. But all of a sudden it was
+
+ align:start position:0%
+like that. But all of a sudden it was
+ 
+
+ align:start position:0%
+like that. But all of a sudden it was
+all controlled by Mark Zuckerberg. Um
+
+ align:start position:0%
+all controlled by Mark Zuckerberg. Um
+ 
+
+ align:start position:0%
+all controlled by Mark Zuckerberg. Um
+this was a quote from David Weinberger.
+
+ align:start position:0%
+this was a quote from David Weinberger.
+ 
+
+ align:start position:0%
+this was a quote from David Weinberger.
+In many ways Facebook fulfilled the
+
+ align:start position:0%
+In many ways Facebook fulfilled the
+ 
+
+ align:start position:0%
+In many ways Facebook fulfilled the
+dream of blogging but like not exactly
+
+ align:start position:0%
+dream of blogging but like not exactly
+ 
+
+ align:start position:0%
+dream of blogging but like not exactly
+like like everybody was online but they
+
+ align:start position:0%
+like like everybody was online but they
+ 
+
+ align:start position:0%
+like like everybody was online but they
+weren't in spaces that they owned, had
+
+ align:start position:0%
+weren't in spaces that they owned, had
+ 
+
+ align:start position:0%
+weren't in spaces that they owned, had
+control over, had some familiarity with.
+
+ align:start position:0%
+control over, had some familiarity with.
+ 
+
+ align:start position:0%
+control over, had some familiarity with.
+Um and then um we'll talk about some of
+
+ align:start position:0%
+Um and then um we'll talk about some of
+ 
+
+ align:start position:0%
+Um and then um we'll talk about some of
+this as it goes along. Um, I think there
+
+ align:start position:0%
+this as it goes along. Um, I think there
+ 
+
+ align:start position:0%
+this as it goes along. Um, I think there
+was a there was a moment in which
+
+ align:start position:0%
+was a there was a moment in which
+ 
+
+ align:start position:0%
+was a there was a moment in which
+participation in a broad online life
+
+ align:start position:0%
+participation in a broad online life
+ 
+
+ align:start position:0%
+participation in a broad online life
+felt much less toxic and draining and
+
+ align:start position:0%
+felt much less toxic and draining and
+ 
+
+ align:start position:0%
+felt much less toxic and draining and
+vulnerability inspiring as it does right
+
+ align:start position:0%
+vulnerability inspiring as it does right
+ 
+
+ align:start position:0%
+vulnerability inspiring as it does right
+now. Um uh you know I mean if if there
+
+ align:start position:0%
+now. Um uh you know I mean if if there
+ 
+
+ align:start position:0%
+now. Um uh you know I mean if if there
+are there if you're a teacher who's
+
+ align:start position:0%
+are there if you're a teacher who's
+ 
+
+ align:start position:0%
+are there if you're a teacher who's
+working in a state which has recently
+
+ align:start position:0%
+working in a state which has recently
+ 
+
+ align:start position:0%
+working in a state which has recently
+passed a divisive concepts law um or
+
+ align:start position:0%
+passed a divisive concepts law um or
+ 
+
+ align:start position:0%
+passed a divisive concepts law um or
+other things like that regulating the
+
+ align:start position:0%
+other things like that regulating the
+ 
+
+ align:start position:0%
+other things like that regulating the
+kinds of topics you can talk about and
+
+ align:start position:0%
+kinds of topics you can talk about and
+ 
+
+ align:start position:0%
+kinds of topics you can talk about and
+things like that like all of that has a
+
+ align:start position:0%
+things like that like all of that has a
+ 
+
+ align:start position:0%
+things like that like all of that has a
+sort of chilling effect um you know not
+
+ align:start position:0%
+sort of chilling effect um you know not
+ 
+
+ align:start position:0%
+sort of chilling effect um you know not
+I mean not to mention just the the ways
+
+ align:start position:0%
+I mean not to mention just the the ways
+ 
+
+ align:start position:0%
+I mean not to mention just the the ways
+in which you know the social media
+
+ align:start position:0%
+in which you know the social media
+ 
+
+ align:start position:0%
+in which you know the social media
+services Facebook Twitter other kinds of
+
+ align:start position:0%
+services Facebook Twitter other kinds of
+ 
+
+ align:start position:0%
+services Facebook Twitter other kinds of
+things we use have sort of degraded um
+
+ align:start position:0%
+things we use have sort of degraded um
+ 
+
+ align:start position:0%
+things we use have sort of degraded um
+in their conversations over time um uh
+
+ align:start position:0%
+in their conversations over time um uh
+ 
+
+ align:start position:0%
+in their conversations over time um uh
+you This is what David Weinberger said.
+
+ align:start position:0%
+you This is what David Weinberger said.
+ 
+
+ align:start position:0%
+you This is what David Weinberger said.
+The bloggers field did not scale. Um
+
+ align:start position:0%
+The bloggers field did not scale. Um
+ 
+
+ align:start position:0%
+The bloggers field did not scale. Um
+like like there you know some people
+
+ align:start position:0%
+like like there you know some people
+ 
+
+ align:start position:0%
+like like there you know some people
+created their own blogs but not
+
+ align:start position:0%
+created their own blogs but not
+ 
+
+ align:start position:0%
+created their own blogs but not
+everyone. Um and then Facebook came in
+
+ align:start position:0%
+everyone. Um and then Facebook came in
+ 
+
+ align:start position:0%
+everyone. Um and then Facebook came in
+and many people who created blogs like
+
+ align:start position:0%
+and many people who created blogs like
+ 
+
+ align:start position:0%
+and many people who created blogs like
+I'll just post to Facebook. A lot of
+
+ align:start position:0%
+I'll just post to Facebook. A lot of
+ 
+
+ align:start position:0%
+I'll just post to Facebook. A lot of
+those people have like moved over to
+
+ align:start position:0%
+those people have like moved over to
+ 
+
+ align:start position:0%
+those people have like moved over to
+Substack now or other kinds of things
+
+ align:start position:0%
+Substack now or other kinds of things
+ 
+
+ align:start position:0%
+Substack now or other kinds of things
+like that but but systems that they
+
+ align:start position:0%
+like that but but systems that they
+ 
+
+ align:start position:0%
+like that but but systems that they
+don't control. Um there is I think a
+
+ align:start position:0%
+don't control. Um there is I think a
+ 
+
+ align:start position:0%
+don't control. Um there is I think a
+parallel to that story that happened in
+
+ align:start position:0%
+parallel to that story that happened in
+ 
+
+ align:start position:0%
+parallel to that story that happened in
+higher education. Um so in the early
+
+ align:start position:0%
+higher education. Um so in the early
+ 
+
+ align:start position:0%
+higher education. Um so in the early
+days um when the web was first made
+
+ align:start position:0%
+days um when the web was first made
+ 
+
+ align:start position:0%
+days um when the web was first made
+available broadly to schools which also
+
+ align:start position:0%
+available broadly to schools which also
+ 
+
+ align:start position:0%
+available broadly to schools which also
+h you know happens to overlap with my
+
+ align:start position:0%
+h you know happens to overlap with my
+ 
+
+ align:start position:0%
+h you know happens to overlap with my
+life. So I I think in 1993 Dartmouth
+
+ align:start position:0%
+life. So I I think in 1993 Dartmouth
+ 
+
+ align:start position:0%
+life. So I I think in 1993 Dartmouth
+College is the first college to give um
+
+ align:start position:0%
+College is the first college to give um
+ 
+
+ align:start position:0%
+College is the first college to give um
+every incoming student an email address.
+
+ align:start position:0%
+every incoming student an email address.
+ 
+
+ align:start position:0%
+every incoming student an email address.
+I think in
+
+ align:start position:0%
+I think in
+ 
+
+ align:start position:0%
+I think in
+1994 very quickly many many other
+
+ align:start position:0%
+1994 very quickly many many other
+ 
+
+ align:start position:0%
+1994 very quickly many many other
+colleges had done that. By the time I
+
+ align:start position:0%
+colleges had done that. By the time I
+ 
+
+ align:start position:0%
+colleges had done that. By the time I
+graduated high school but certainly by
+
+ align:start position:0%
+graduated high school but certainly by
+ 
+
+ align:start position:0%
+graduated high school but certainly by
+the time I was into college in 1996 um I
+
+ align:start position:0%
+the time I was into college in 1996 um I
+ 
+
+ align:start position:0%
+the time I was into college in 1996 um I
+had an email address. everybody else
+
+ align:start position:0%
+had an email address. everybody else
+ 
+
+ align:start position:0%
+had an email address. everybody else
+would have had an email address. That
+
+ align:start position:0%
+would have had an email address. That
+ 
+
+ align:start position:0%
+would have had an email address. That
+would have been, you know, um pretty
+
+ align:start position:0%
+would have been, you know, um pretty
+ 
+
+ align:start position:0%
+would have been, you know, um pretty
+pretty universal and standard. Um but
+
+ align:start position:0%
+pretty universal and standard. Um but
+ 
+
+ align:start position:0%
+pretty universal and standard. Um but
+this is what university web pages looked
+
+ align:start position:0%
+this is what university web pages looked
+ 
+
+ align:start position:0%
+this is what university web pages looked
+like at the time. Um MIT still has some
+
+ align:start position:0%
+like at the time. Um MIT still has some
+ 
+
+ align:start position:0%
+like at the time. Um MIT still has some
+of these kinds of things. Has anybody
+
+ align:start position:0%
+of these kinds of things. Has anybody
+ 
+
+ align:start position:0%
+of these kinds of things. Has anybody
+ever been to somebody's tilda space? You
+
+ align:start position:0%
+ever been to somebody's tilda space? You
+ 
+
+ align:start position:0%
+ever been to somebody's tilda space? You
+know,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+www.mmit.eduilda jri or something like
+
+ align:start position:0%
+www.mmit.eduilda jri or something like
+ 
+
+ align:start position:0%
+www.mmit.eduilda jri or something like
+that. Who do you um Oh man, the 1806
+
+ align:start position:0%
+that. Who do you um Oh man, the 1806
+ 
+
+ align:start position:0%
+that. Who do you um Oh man, the 1806
+professor. What's what's his
+
+ align:start position:0%
+professor. What's what's his
+ 
+
+ align:start position:0%
+professor. What's what's his
+forgetting? Um the one who just retired
+
+ align:start position:0%
+forgetting? Um the one who just retired
+ 
+
+ align:start position:0%
+forgetting? Um the one who just retired
+Gil String. Good. Perfect. Great. Others
+
+ align:start position:0%
+Gil String. Good. Perfect. Great. Others
+ 
+
+ align:start position:0%
+Gil String. Good. Perfect. Great. Others
+that people can think of who have these
+
+ align:start position:0%
+that people can think of who have these
+ 
+
+ align:start position:0%
+that people can think of who have these
+things? So, um um so some things that
+
+ align:start position:0%
+things? So, um um so some things that
+ 
+
+ align:start position:0%
+things? So, um um so some things that
+you'll notice about the Well, I don't
+
+ align:start position:0%
+you'll notice about the Well, I don't
+ 
+
+ align:start position:0%
+you'll notice about the Well, I don't
+know. What do you just looking at these
+
+ align:start position:0%
+know. What do you just looking at these
+ 
+
+ align:start position:0%
+know. What do you just looking at these
+pictures? What do you notice about these
+
+ align:start position:0%
+pictures? What do you notice about these
+ 
+
+ align:start position:0%
+pictures? What do you notice about these
+things? What strikes you about them?
+
+ align:start position:0%
+things? What strikes you about them?
+ 
+
+ align:start position:0%
+things? What strikes you about them?
+There were some giggles before, which I
+
+ align:start position:0%
+There were some giggles before, which I
+ 
+
+ align:start position:0%
+There were some giggles before, which I
+think is appropriate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Like everything is
+
+ align:start position:0%
+Like everything is
+ 
+
+ align:start position:0%
+Like everything is
+okay. So, you know, not a lot of font
+
+ align:start position:0%
+okay. So, you know, not a lot of font
+ 
+
+ align:start position:0%
+okay. So, you know, not a lot of font
+diversity. What else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There's no advertisements. Yeah. Good.
+
+ align:start position:0%
+There's no advertisements. Yeah. Good.
+ 
+
+ align:start position:0%
+There's no advertisements. Yeah. Good.
+No, these are so so these were not
+
+ align:start position:0%
+No, these are so so these were not
+ 
+
+ align:start position:0%
+No, these are so so these were not
+created like with Wix or something like
+
+ align:start position:0%
+created like with Wix or something like
+ 
+
+ align:start position:0%
+created like with Wix or something like
+that where in exchange for making a
+
+ align:start position:0%
+that where in exchange for making a
+ 
+
+ align:start position:0%
+that where in exchange for making a
+website you have to put a bar of
+
+ align:start position:0%
+website you have to put a bar of
+ 
+
+ align:start position:0%
+website you have to put a bar of
+advertisements at the bottom or
+
+ align:start position:0%
+advertisements at the bottom or
+ 
+
+ align:start position:0%
+advertisements at the bottom or
+something like that. So somebody
+
+ align:start position:0%
+something like that. So somebody
+ 
+
+ align:start position:0%
+something like that. So somebody
+actually made these pages. They're all
+
+ align:start position:0%
+actually made these pages. They're all
+ 
+
+ align:start position:0%
+actually made these pages. They're all
+personal homepages. Other things that
+
+ align:start position:0%
+personal homepages. Other things that
+ 
+
+ align:start position:0%
+personal homepages. Other things that
+strike you?
+
+ align:start position:0%
+strike you?
+ 
+
+ align:start position:0%
+strike you?
+The backgrounds. What about the
+
+ align:start position:0%
+The backgrounds. What about the
+ 
+
+ align:start position:0%
+The backgrounds. What about the
+backgrounds?
+
+ align:start position:0%
+backgrounds?
+ 
+
+ align:start position:0%
+backgrounds?
+Um it's certainly of like I don't know.
+
+ align:start position:0%
+Um it's certainly of like I don't know.
+ 
+
+ align:start position:0%
+Um it's certainly of like I don't know.
+I I feel like I I personally associate
+
+ align:start position:0%
+I I feel like I I personally associate
+ 
+
+ align:start position:0%
+I I feel like I I personally associate
+them with a very specific time period.
+
+ align:start position:0%
+them with a very specific time period.
+ 
+
+ align:start position:0%
+them with a very specific time period.
+Okay, good. It's like this is natural.
+
+ align:start position:0%
+Okay, good. It's like this is natural.
+ 
+
+ align:start position:0%
+Okay, good. It's like this is natural.
+They they have they have a '9s aesthetic
+
+ align:start position:0%
+They they have they have a '9s aesthetic
+ 
+
+ align:start position:0%
+They they have they have a '9s aesthetic
+to them. Yeah. I would say maybe it is
+
+ align:start position:0%
+to them. Yeah. I would say maybe it is
+ 
+
+ align:start position:0%
+to them. Yeah. I would say maybe it is
+like partially just like the quality of
+
+ align:start position:0%
+like partially just like the quality of
+ 
+
+ align:start position:0%
+like partially just like the quality of
+like like let's say a pattern or
+
+ align:start position:0%
+like like let's say a pattern or
+ 
+
+ align:start position:0%
+like like let's say a pattern or
+something you can put on or like now we
+
+ align:start position:0%
+something you can put on or like now we
+ 
+
+ align:start position:0%
+something you can put on or like now we
+have a lot of templates that make sure
+
+ align:start position:0%
+have a lot of templates that make sure
+ 
+
+ align:start position:0%
+have a lot of templates that make sure
+it's like aesthetically consistent. This
+
+ align:start position:0%
+it's like aesthetically consistent. This
+ 
+
+ align:start position:0%
+it's like aesthetically consistent. This
+is pre-CAva. We're not we're not uh Ken,
+
+ align:start position:0%
+is pre-CAva. We're not we're not uh Ken,
+ 
+
+ align:start position:0%
+is pre-CAva. We're not we're not uh Ken,
+what were you going to observe? Oh, I
+
+ align:start position:0%
+what were you going to observe? Oh, I
+ 
+
+ align:start position:0%
+what were you going to observe? Oh, I
+was about to say about the templates
+
+ align:start position:0%
+was about to say about the templates
+ 
+
+ align:start position:0%
+was about to say about the templates
+like they're not all using the exact
+
+ align:start position:0%
+like they're not all using the exact
+ 
+
+ align:start position:0%
+like they're not all using the exact
+same uh template and similar formatting.
+
+ align:start position:0%
+same uh template and similar formatting.
+ 
+
+ align:start position:0%
+same uh template and similar formatting.
+They're not all using the exact same
+
+ align:start position:0%
+They're not all using the exact same
+ 
+
+ align:start position:0%
+They're not all using the exact same
+template in similar formatting. I think
+
+ align:start position:0%
+template in similar formatting. I think
+ 
+
+ align:start position:0%
+template in similar formatting. I think
+that that is actually quite important.
+
+ align:start position:0%
+that that is actually quite important.
+ 
+
+ align:start position:0%
+that that is actually quite important.
+Um there are some good things that
+
+ align:start position:0%
+Um there are some good things that
+ 
+
+ align:start position:0%
+Um there are some good things that
+templates do of make things looking um
+
+ align:start position:0%
+templates do of make things looking um
+ 
+
+ align:start position:0%
+templates do of make things looking um
+uh aesthetic. Um but they standardize in
+
+ align:start position:0%
+uh aesthetic. Um but they standardize in
+ 
+
+ align:start position:0%
+uh aesthetic. Um but they standardize in
+a way. They they put things in the same
+
+ align:start position:0%
+a way. They they put things in the same
+ 
+
+ align:start position:0%
+a way. They they put things in the same
+way. People at universities do really
+
+ align:start position:0%
+way. People at universities do really
+ 
+
+ align:start position:0%
+way. People at universities do really
+really different kinds of things. That
+
+ align:start position:0%
+really different kinds of things. That
+ 
+
+ align:start position:0%
+really different kinds of things. That
+might be important. Other observations
+
+ align:start position:0%
+might be important. Other observations
+ 
+
+ align:start position:0%
+might be important. Other observations
+about these? It's very speromorphic. Um,
+
+ align:start position:0%
+about these? It's very speromorphic. Um,
+ 
+
+ align:start position:0%
+about these? It's very speromorphic. Um,
+like there's buttons on the the bottom
+
+ align:start position:0%
+like there's buttons on the the bottom
+ 
+
+ align:start position:0%
+like there's buttons on the the bottom
+left one with like icons that you don't
+
+ align:start position:0%
+left one with like icons that you don't
+ 
+
+ align:start position:0%
+left one with like icons that you don't
+see as often. And I want to say the
+
+ align:start position:0%
+see as often. And I want to say the
+ 
+
+ align:start position:0%
+see as often. And I want to say the
+background, especially the bottom left,
+
+ align:start position:0%
+background, especially the bottom left,
+ 
+
+ align:start position:0%
+background, especially the bottom left,
+reminds me of a a physical wallpaper.
+
+ align:start position:0%
+reminds me of a a physical wallpaper.
+ 
+
+ align:start position:0%
+reminds me of a a physical wallpaper.
+Uhhuh. Um, which is like a principle. Do
+
+ align:start position:0%
+Uhhuh. Um, which is like a principle. Do
+ 
+
+ align:start position:0%
+Uhhuh. Um, which is like a principle. Do
+you want to define skuorphism for us?
+
+ align:start position:0%
+you want to define skuorphism for us?
+ 
+
+ align:start position:0%
+you want to define skuorphism for us?
+Skeorphism is
+
+ align:start position:0%
+Skeorphism is
+ 
+
+ align:start position:0%
+Skeorphism is
+like the most famous example. It's
+
+ align:start position:0%
+like the most famous example. It's
+ 
+
+ align:start position:0%
+like the most famous example. It's
+probably like iOS 6 where you have all
+
+ align:start position:0%
+probably like iOS 6 where you have all
+ 
+
+ align:start position:0%
+probably like iOS 6 where you have all
+these buttons and like reflections that
+
+ align:start position:0%
+these buttons and like reflections that
+ 
+
+ align:start position:0%
+these buttons and like reflections that
+sort of try to mimic real life. And
+
+ align:start position:0%
+sort of try to mimic real life. And
+ 
+
+ align:start position:0%
+sort of try to mimic real life. And
+that's like what skuomorphism is trying
+
+ align:start position:0%
+that's like what skuomorphism is trying
+ 
+
+ align:start position:0%
+that's like what skuomorphism is trying
+to mimic real life. And then when we
+
+ align:start position:0%
+to mimic real life. And then when we
+ 
+
+ align:start position:0%
+to mimic real life. And then when we
+transition to iOS 7, you removed a lot
+
+ align:start position:0%
+transition to iOS 7, you removed a lot
+ 
+
+ align:start position:0%
+transition to iOS 7, you removed a lot
+of that dimension and it became a lot
+
+ align:start position:0%
+of that dimension and it became a lot
+ 
+
+ align:start position:0%
+of that dimension and it became a lot
+more simplistic and and symbolic. A lot
+
+ align:start position:0%
+more simplistic and and symbolic. A lot
+ 
+
+ align:start position:0%
+more simplistic and and symbolic. A lot
+of the early note-taking apps would have
+
+ align:start position:0%
+of the early note-taking apps would have
+ 
+
+ align:start position:0%
+of the early note-taking apps would have
+a background like a yellow legal pad or
+
+ align:start position:0%
+a background like a yellow legal pad or
+ 
+
+ align:start position:0%
+a background like a yellow legal pad or
+or like a spiral binding on the side or
+
+ align:start position:0%
+or like a spiral binding on the side or
+ 
+
+ align:start position:0%
+or like a spiral binding on the side or
+something like that and you're like,
+
+ align:start position:0%
+something like that and you're like,
+ 
+
+ align:start position:0%
+something like that and you're like,
+"Brother, we could put the we don't need
+
+ align:start position:0%
+"Brother, we could put the we don't need
+ 
+
+ align:start position:0%
+"Brother, we could put the we don't need
+the lines. Like the cursor will do that
+
+ align:start position:0%
+the lines. Like the cursor will do that
+ 
+
+ align:start position:0%
+the lines. Like the cursor will do that
+for you." Um but um people wanted to
+
+ align:start position:0%
+for you." Um but um people wanted to
+ 
+
+ align:start position:0%
+for you." Um but um people wanted to
+make some kind of connection between
+
+ align:start position:0%
+make some kind of connection between
+ 
+
+ align:start position:0%
+make some kind of connection between
+what they saw be you know what they saw
+
+ align:start position:0%
+what they saw be you know what they saw
+ 
+
+ align:start position:0%
+what they saw be you know what they saw
+in the physical world and what this new
+
+ align:start position:0%
+in the physical world and what this new
+ 
+
+ align:start position:0%
+in the physical world and what this new
+digital thing was trying to do.
+
+ align:start position:0%
+digital thing was trying to do.
+ 
+
+ align:start position:0%
+digital thing was trying to do.
+Skeumorphism shows up in that book
+
+ align:start position:0%
+Skeumorphism shows up in that book
+ 
+
+ align:start position:0%
+Skeumorphism shows up in that book
+somewhere. I can't remember now where I
+
+ align:start position:0%
+somewhere. I can't remember now where I
+ 
+
+ align:start position:0%
+somewhere. I can't remember now where I
+wrote about it but um um yeah I mean
+
+ align:start position:0%
+wrote about it but um um yeah I mean
+ 
+
+ align:start position:0%
+wrote about it but um um yeah I mean
+obviously these pictures are just
+
+ align:start position:0%
+obviously these pictures are just
+ 
+
+ align:start position:0%
+obviously these pictures are just
+outstanding. Um
+
+ align:start position:0%
+outstanding. Um
+ 
+
+ align:start position:0%
+outstanding. Um
+uh just like people had kind of like a
+
+ align:start position:0%
+uh just like people had kind of like a
+ 
+
+ align:start position:0%
+uh just like people had kind of like a
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+idiosyncratic
+
+ align:start position:0%
+idiosyncratic
+ 
+
+ align:start position:0%
+idiosyncratic
+um personalized kind of a bane in the
+
+ align:start position:0%
+um personalized kind of a bane in the
+ 
+
+ align:start position:0%
+um personalized kind of a bane in the
+butt to organize sort of blogosphere
+
+ align:start position:0%
+butt to organize sort of blogosphere
+ 
+
+ align:start position:0%
+butt to organize sort of blogosphere
+that existed that Facebook just came and
+
+ align:start position:0%
+that existed that Facebook just came and
+ 
+
+ align:start position:0%
+that existed that Facebook just came and
+sort of demolished and homogenized and
+
+ align:start position:0%
+sort of demolished and homogenized and
+ 
+
+ align:start position:0%
+sort of demolished and homogenized and
+standardized and pulled out of the
+
+ align:start position:0%
+standardized and pulled out of the
+ 
+
+ align:start position:0%
+standardized and pulled out of the
+control of individual people's spaces
+
+ align:start position:0%
+control of individual people's spaces
+ 
+
+ align:start position:0%
+control of individual people's spaces
+and into this sort of corporate space.
+
+ align:start position:0%
+and into this sort of corporate space.
+ 
+
+ align:start position:0%
+and into this sort of corporate space.
+Um, you could say that Blackboard did
+
+ align:start position:0%
+Um, you could say that Blackboard did
+ 
+
+ align:start position:0%
+Um, you could say that Blackboard did
+something very very similar to campus
+
+ align:start position:0%
+something very very similar to campus
+ 
+
+ align:start position:0%
+something very very similar to campus
+web pages. Um, that learning management
+
+ align:start position:0%
+web pages. Um, that learning management
+ 
+
+ align:start position:0%
+web pages. Um, that learning management
+systems came along um and they said,
+
+ align:start position:0%
+systems came along um and they said,
+ 
+
+ align:start position:0%
+systems came along um and they said,
+"We're gonna standardize it all." Um,
+
+ align:start position:0%
+"We're gonna standardize it all." Um,
+ 
+
+ align:start position:0%
+"We're gonna standardize it all." Um,
+you you don't have you don't have to
+
+ align:start position:0%
+you you don't have you don't have to
+ 
+
+ align:start position:0%
+you you don't have you don't have to
+create your own page anymore. Like
+
+ align:start position:0%
+create your own page anymore. Like
+ 
+
+ align:start position:0%
+create your own page anymore. Like
+Blackboard will create your own faculty
+
+ align:start position:0%
+Blackboard will create your own faculty
+ 
+
+ align:start position:0%
+Blackboard will create your own faculty
+page, create your own course page. Um,
+
+ align:start position:0%
+page, create your own course page. Um,
+ 
+
+ align:start position:0%
+page, create your own course page. Um,
+and that's going to come with some kind
+
+ align:start position:0%
+and that's going to come with some kind
+ 
+
+ align:start position:0%
+and that's going to come with some kind
+of benefits of standardization. It's
+
+ align:start position:0%
+of benefits of standardization. It's
+ 
+
+ align:start position:0%
+of benefits of standardization. It's
+going to make it a lot easier for
+
+ align:start position:0%
+going to make it a lot easier for
+ 
+
+ align:start position:0%
+going to make it a lot easier for
+people, but it's but it's also going to
+
+ align:start position:0%
+people, but it's but it's also going to
+ 
+
+ align:start position:0%
+people, but it's but it's also going to
+get rid of um some of the kind of
+
+ align:start position:0%
+get rid of um some of the kind of
+ 
+
+ align:start position:0%
+get rid of um some of the kind of
+wonderful
+
+ align:start position:0%
+wonderful
+ 
+
+ align:start position:0%
+wonderful
+idiosyncrasies um of these things. And
+
+ align:start position:0%
+idiosyncrasies um of these things. And
+ 
+
+ align:start position:0%
+idiosyncrasies um of these things. And
+it's going to mean that there's a
+
+ align:start position:0%
+it's going to mean that there's a
+ 
+
+ align:start position:0%
+it's going to mean that there's a
+corporate entity who is who is not
+
+ align:start position:0%
+corporate entity who is who is not
+ 
+
+ align:start position:0%
+corporate entity who is who is not
+accountable who's accountable to their
+
+ align:start position:0%
+accountable who's accountable to their
+ 
+
+ align:start position:0%
+accountable who's accountable to their
+shareholders and not accountable to the
+
+ align:start position:0%
+shareholders and not accountable to the
+ 
+
+ align:start position:0%
+shareholders and not accountable to the
+same values that we might have as a
+
+ align:start position:0%
+same values that we might have as a
+ 
+
+ align:start position:0%
+same values that we might have as a
+university, which is deciding what those
+
+ align:start position:0%
+university, which is deciding what those
+ 
+
+ align:start position:0%
+university, which is deciding what those
+things look like. Much like when we move
+
+ align:start position:0%
+things look like. Much like when we move
+ 
+
+ align:start position:0%
+things look like. Much like when we move
+all of our blogs onto Facebook, um you
+
+ align:start position:0%
+all of our blogs onto Facebook, um you
+ 
+
+ align:start position:0%
+all of our blogs onto Facebook, um you
+don't even you're not even accountable
+
+ align:start position:0%
+don't even you're not even accountable
+ 
+
+ align:start position:0%
+don't even you're not even accountable
+to shareholders. are just accountable to
+
+ align:start position:0%
+to shareholders. are just accountable to
+ 
+
+ align:start position:0%
+to shareholders. are just accountable to
+whatever Mark thinks you know people
+
+ align:start position:0%
+whatever Mark thinks you know people
+ 
+
+ align:start position:0%
+whatever Mark thinks you know people
+should be doing in Facebook. Um yeah, in
+
+ align:start position:0%
+should be doing in Facebook. Um yeah, in
+ 
+
+ align:start position:0%
+should be doing in Facebook. Um yeah, in
+many ways Blackboard fulfilled the dream
+
+ align:start position:0%
+many ways Blackboard fulfilled the dream
+ 
+
+ align:start position:0%
+many ways Blackboard fulfilled the dream
+of the university till the spaces did
+
+ align:start position:0%
+of the university till the spaces did
+ 
+
+ align:start position:0%
+of the university till the spaces did
+not scale. I believe the problem could
+
+ align:start position:0%
+not scale. I believe the problem could
+ 
+
+ align:start position:0%
+not scale. I believe the problem could
+have been solved but then Blackboard
+
+ align:start position:0%
+have been solved but then Blackboard
+ 
+
+ align:start position:0%
+have been solved but then Blackboard
+happened. Um why would Blackboard
+
+ align:start position:0%
+happened. Um why would Blackboard
+ 
+
+ align:start position:0%
+happened. Um why would Blackboard
+happen? Um these are the instructions
+
+ align:start position:0%
+happen? Um these are the instructions
+ 
+
+ align:start position:0%
+happen? Um these are the instructions
+for Sunni onion about how you would go
+
+ align:start position:0%
+for Sunni onion about how you would go
+ 
+
+ align:start position:0%
+for Sunni onion about how you would go
+about creating one of your tilda space
+
+ align:start position:0%
+about creating one of your tilda space
+ 
+
+ align:start position:0%
+about creating one of your tilda space
+pages. you know, log into AAD, create a
+
+ align:start position:0%
+pages. you know, log into AAD, create a
+ 
+
+ align:start position:0%
+pages. you know, log into AAD, create a
+directory, change to this directory,
+
+ align:start position:0%
+directory, change to this directory,
+ 
+
+ align:start position:0%
+directory, change to this directory,
+create HTML documents, um, HTML
+
+ align:start position:0%
+create HTML documents, um, HTML
+ 
+
+ align:start position:0%
+create HTML documents, um, HTML
+developers jumpstation, you know, set
+
+ align:start position:0%
+developers jumpstation, you know, set
+ 
+
+ align:start position:0%
+developers jumpstation, you know, set
+pro equals w file namex. You can like
+
+ align:start position:0%
+pro equals w file namex. You can like
+ 
+
+ align:start position:0%
+pro equals w file namex. You can like
+you read about a page of this stuff and
+
+ align:start position:0%
+you read about a page of this stuff and
+ 
+
+ align:start position:0%
+you read about a page of this stuff and
+you're like, "Yeah, I can see why a lot
+
+ align:start position:0%
+you're like, "Yeah, I can see why a lot
+ 
+
+ align:start position:0%
+you're like, "Yeah, I can see why a lot
+of people, you know, like why launching
+
+ align:start position:0%
+of people, you know, like why launching
+ 
+
+ align:start position:0%
+of people, you know, like why launching
+a Blackboard page might be uh might be
+
+ align:start position:0%
+a Blackboard page might be uh might be
+ 
+
+ align:start position:0%
+a Blackboard page might be uh might be
+fine." Um,
+
+ align:start position:0%
+fine." Um,
+ 
+
+ align:start position:0%
+fine." Um,
+uh, uh, this is what the um, what is
+
+ align:start position:0%
+uh, uh, this is what the um, what is
+ 
+
+ align:start position:0%
+uh, uh, this is what the um, what is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+blackboard? I don't I don't remember
+
+ align:start position:0%
+blackboard? I don't I don't remember
+ 
+
+ align:start position:0%
+blackboard? I don't I don't remember
+what uh learning management system this
+
+ align:start position:0%
+what uh learning management system this
+ 
+
+ align:start position:0%
+what uh learning management system this
+was. Maybe it's Canvas. It's not Canvas.
+
+ align:start position:0%
+was. Maybe it's Canvas. It's not Canvas.
+ 
+
+ align:start position:0%
+was. Maybe it's Canvas. It's not Canvas.
+I don't I can't remember what it is now.
+
+ align:start position:0%
+I don't I can't remember what it is now.
+ 
+
+ align:start position:0%
+I don't I can't remember what it is now.
+This is the this is the very first
+
+ align:start position:0%
+This is the this is the very first
+ 
+
+ align:start position:0%
+This is the this is the very first
+version of a sort of a version of this
+
+ align:start position:0%
+version of a sort of a version of this
+ 
+
+ align:start position:0%
+version of a sort of a version of this
+course um that I taught 10 years ago. Um
+
+ align:start position:0%
+course um that I taught 10 years ago. Um
+ 
+
+ align:start position:0%
+course um that I taught 10 years ago. Um
+and this is the this is the page that
+
+ align:start position:0%
+and this is the this is the page that
+ 
+
+ align:start position:0%
+and this is the this is the page that
+the that the system generated for me um
+
+ align:start position:0%
+the that the system generated for me um
+ 
+
+ align:start position:0%
+the that the system generated for me um
+when I first created the class. So it
+
+ align:start position:0%
+when I first created the class. So it
+ 
+
+ align:start position:0%
+when I first created the class. So it
+comes with a bunch of these sort of st
+
+ align:start position:0%
+comes with a bunch of these sort of st
+ 
+
+ align:start position:0%
+comes with a bunch of these sort of st
+not not this stuff that I added but
+
+ align:start position:0%
+not not this stuff that I added but
+ 
+
+ align:start position:0%
+not not this stuff that I added but
+syllabus class sessions other resources
+
+ align:start position:0%
+syllabus class sessions other resources
+ 
+
+ align:start position:0%
+syllabus class sessions other resources
+assignments collaborate information
+
+ align:start position:0%
+assignments collaborate information
+ 
+
+ align:start position:0%
+assignments collaborate information
+reserves list search this site lecture
+
+ align:start position:0%
+reserves list search this site lecture
+ 
+
+ align:start position:0%
+reserves list search this site lecture
+video um it makes a set of assumptions
+
+ align:start position:0%
+video um it makes a set of assumptions
+ 
+
+ align:start position:0%
+video um it makes a set of assumptions
+about what my course is um it says you
+
+ align:start position:0%
+about what my course is um it says you
+ 
+
+ align:start position:0%
+about what my course is um it says you
+know this is what the standard format of
+
+ align:start position:0%
+know this is what the standard format of
+ 
+
+ align:start position:0%
+know this is what the standard format of
+this learning experience should be um
+
+ align:start position:0%
+this learning experience should be um
+ 
+
+ align:start position:0%
+this learning experience should be um
+but maybe that's not at all what I want
+
+ align:start position:0%
+but maybe that's not at all what I want
+ 
+
+ align:start position:0%
+but maybe that's not at all what I want
+it certainly doesn't make a lot you know
+
+ align:start position:0%
+it certainly doesn't make a lot you know
+ 
+
+ align:start position:0%
+it certainly doesn't make a lot you know
+if I had if I had taught this class
+
+ align:start position:0%
+if I had if I had taught this class
+ 
+
+ align:start position:0%
+if I had if I had taught this class
+about this was in an education school if
+
+ align:start position:0%
+about this was in an education school if
+ 
+
+ align:start position:0%
+about this was in an education school if
+I had made this class about education
+
+ align:start position:0%
+I had made this class about education
+ 
+
+ align:start position:0%
+I had made this class about education
+technology ology about um the experience
+
+ align:start position:0%
+technology ology about um the experience
+ 
+
+ align:start position:0%
+technology ology about um the experience
+of indigenous kids learning on
+
+ align:start position:0%
+of indigenous kids learning on
+ 
+
+ align:start position:0%
+of indigenous kids learning on
+reservations about um I don't know the
+
+ align:start position:0%
+reservations about um I don't know the
+ 
+
+ align:start position:0%
+reservations about um I don't know the
+uh um global education policy um
+
+ align:start position:0%
+uh um global education policy um
+ 
+
+ align:start position:0%
+uh um global education policy um
+intermediate statistics it all would
+
+ align:start position:0%
+intermediate statistics it all would
+ 
+
+ align:start position:0%
+intermediate statistics it all would
+have been the exact same format um they
+
+ align:start position:0%
+have been the exact same format um they
+ 
+
+ align:start position:0%
+have been the exact same format um they
+would have given the same sort of
+
+ align:start position:0%
+would have given the same sort of
+ 
+
+ align:start position:0%
+would have given the same sort of
+standardized creation for this which
+
+ align:start position:0%
+standardized creation for this which
+ 
+
+ align:start position:0%
+standardized creation for this which
+just in lots of you know it makes sense
+
+ align:start position:0%
+just in lots of you know it makes sense
+ 
+
+ align:start position:0%
+just in lots of you know it makes sense
+in some kind of ways and it's bonkers in
+
+ align:start position:0%
+in some kind of ways and it's bonkers in
+ 
+
+ align:start position:0%
+in some kind of ways and it's bonkers in
+other kinds of ways our courses are
+
+ align:start position:0%
+other kinds of ways our courses are
+ 
+
+ align:start position:0%
+other kinds of ways our courses are
+super different why should all of our
+
+ align:start position:0%
+super different why should all of our
+ 
+
+ align:start position:0%
+super different why should all of our
+courses have the same template why
+
+ align:start position:0%
+courses have the same template why
+ 
+
+ align:start position:0%
+courses have the same template why
+should we all be sort of subtly
+
+ align:start position:0%
+should we all be sort of subtly
+ 
+
+ align:start position:0%
+should we all be sort of subtly
+invisibly squished into teaching our
+
+ align:start position:0%
+invisibly squished into teaching our
+ 
+
+ align:start position:0%
+invisibly squished into teaching our
+courses the same way um by by these
+
+ align:start position:0%
+courses the same way um by by these
+ 
+
+ align:start position:0%
+courses the same way um by by these
+kinds of structures. Um and of course
+
+ align:start position:0%
+kinds of structures. Um and of course
+ 
+
+ align:start position:0%
+kinds of structures. Um and of course
+there's all kinds of physical analoges
+
+ align:start position:0%
+there's all kinds of physical analoges
+ 
+
+ align:start position:0%
+there's all kinds of physical analoges
+to this too. Um the the way we design
+
+ align:start position:0%
+to this too. Um the the way we design
+ 
+
+ align:start position:0%
+to this too. Um the the way we design
+environments shapes the learning
+
+ align:start position:0%
+environments shapes the learning
+ 
+
+ align:start position:0%
+environments shapes the learning
+experiences um that happen in the I just
+
+ align:start position:0%
+experiences um that happen in the I just
+ 
+
+ align:start position:0%
+experiences um that happen in the I just
+read a beautiful sentence of this which
+
+ align:start position:0%
+read a beautiful sentence of this which
+ 
+
+ align:start position:0%
+read a beautiful sentence of this which
+is you know something like um it was
+
+ align:start position:0%
+is you know something like um it was
+ 
+
+ align:start position:0%
+is you know something like um it was
+something like buildings have agenda for
+
+ align:start position:0%
+something like buildings have agenda for
+ 
+
+ align:start position:0%
+something like buildings have agenda for
+their occupants. um the way that spaces
+
+ align:start position:0%
+their occupants. um the way that spaces
+ 
+
+ align:start position:0%
+their occupants. um the way that spaces
+are created, like it doesn't tell you
+
+ align:start position:0%
+are created, like it doesn't tell you
+ 
+
+ align:start position:0%
+are created, like it doesn't tell you
+what to do, but it certainly guides you.
+
+ align:start position:0%
+what to do, but it certainly guides you.
+ 
+
+ align:start position:0%
+what to do, but it certainly guides you.
+You know, you walk into a room like this
+
+ align:start position:0%
+You know, you walk into a room like this
+ 
+
+ align:start position:0%
+You know, you walk into a room like this
+um and you have some thoughts about the
+
+ align:start position:0%
+um and you have some thoughts about the
+ 
+
+ align:start position:0%
+um and you have some thoughts about the
+kind of learning that's going to happen
+
+ align:start position:0%
+kind of learning that's going to happen
+ 
+
+ align:start position:0%
+kind of learning that's going to happen
+in that space. Like, well, you're all
+
+ align:start position:0%
+in that space. Like, well, you're all
+ 
+
+ align:start position:0%
+in that space. Like, well, you're all
+going to be facing in the same
+
+ align:start position:0%
+going to be facing in the same
+ 
+
+ align:start position:0%
+going to be facing in the same
+direction. Probably not going to be
+
+ align:start position:0%
+direction. Probably not going to be
+ 
+
+ align:start position:0%
+direction. Probably not going to be
+talking to a whole each other a whole
+
+ align:start position:0%
+talking to a whole each other a whole
+ 
+
+ align:start position:0%
+talking to a whole each other a whole
+lot um in that space. There's some, you
+
+ align:start position:0%
+lot um in that space. There's some, you
+ 
+
+ align:start position:0%
+lot um in that space. There's some, you
+know, you're going to be writing with
+
+ align:start position:0%
+know, you're going to be writing with
+ 
+
+ align:start position:0%
+know, you're going to be writing with
+certain kinds of physical materials. If
+
+ align:start position:0%
+certain kinds of physical materials. If
+ 
+
+ align:start position:0%
+certain kinds of physical materials. If
+you try to use a laptop on those, uh,
+
+ align:start position:0%
+you try to use a laptop on those, uh,
+ 
+
+ align:start position:0%
+you try to use a laptop on those, uh,
+you know, square square tables, you'll
+
+ align:start position:0%
+you know, square square tables, you'll
+ 
+
+ align:start position:0%
+you know, square square tables, you'll
+have a hard time, you know, there's no
+
+ align:start position:0%
+have a hard time, you know, there's no
+ 
+
+ align:start position:0%
+have a hard time, you know, there's no
+room for power cords or other kinds of
+
+ align:start position:0%
+room for power cords or other kinds of
+ 
+
+ align:start position:0%
+room for power cords or other kinds of
+things like this. Um this is actually
+
+ align:start position:0%
+things like this. Um this is actually
+ 
+
+ align:start position:0%
+things like this. Um this is actually
+one of the most famous examples in elite
+
+ align:start position:0%
+one of the most famous examples in elite
+ 
+
+ align:start position:0%
+one of the most famous examples in elite
+private education in the United States.
+
+ align:start position:0%
+private education in the United States.
+ 
+
+ align:start position:0%
+private education in the United States.
+Um which is uh um there were um uh
+
+ align:start position:0%
+Um which is uh um there were um uh
+ 
+
+ align:start position:0%
+Um which is uh um there were um uh
+donors to the the Philips exit school
+
+ align:start position:0%
+donors to the the Philips exit school
+ 
+
+ align:start position:0%
+donors to the the Philips exit school
+who were really concerned um that that
+
+ align:start position:0%
+who were really concerned um that that
+ 
+
+ align:start position:0%
+who were really concerned um that that
+essentially there's too much
+
+ align:start position:0%
+essentially there's too much
+ 
+
+ align:start position:0%
+essentially there's too much
+instructionism and not enough
+
+ align:start position:0%
+instructionism and not enough
+ 
+
+ align:start position:0%
+instructionism and not enough
+constructionism. They wouldn't have said
+
+ align:start position:0%
+constructionism. They wouldn't have said
+ 
+
+ align:start position:0%
+constructionism. They wouldn't have said
+it the exact same way, but they would
+
+ align:start position:0%
+it the exact same way, but they would
+ 
+
+ align:start position:0%
+it the exact same way, but they would
+have said something along those lines.
+
+ align:start position:0%
+have said something along those lines.
+ 
+
+ align:start position:0%
+have said something along those lines.
+Too much sitting passive listening, not
+
+ align:start position:0%
+Too much sitting passive listening, not
+ 
+
+ align:start position:0%
+Too much sitting passive listening, not
+enough sort of engaged conversation. Um
+
+ align:start position:0%
+enough sort of engaged conversation. Um
+ 
+
+ align:start position:0%
+enough sort of engaged conversation. Um
+and so a a bunch of donors uh got
+
+ align:start position:0%
+and so a a bunch of donors uh got
+ 
+
+ align:start position:0%
+and so a a bunch of donors uh got
+together um and they said in every
+
+ align:start position:0%
+together um and they said in every
+ 
+
+ align:start position:0%
+together um and they said in every
+classroom we're going to pull out all of
+
+ align:start position:0%
+classroom we're going to pull out all of
+ 
+
+ align:start position:0%
+classroom we're going to pull out all of
+the chairs that look like this and we're
+
+ align:start position:0%
+the chairs that look like this and we're
+ 
+
+ align:start position:0%
+the chairs that look like this and we're
+going to put in these tables called
+
+ align:start position:0%
+going to put in these tables called
+ 
+
+ align:start position:0%
+going to put in these tables called
+Harkness tables. Um some of the features
+
+ align:start position:0%
+Harkness tables. Um some of the features
+ 
+
+ align:start position:0%
+Harkness tables. Um some of the features
+of Harkness tables are that you need to
+
+ align:start position:0%
+of Harkness tables are that you need to
+ 
+
+ align:start position:0%
+of Harkness tables are that you need to
+be able to fit everybody in the class
+
+ align:start position:0%
+be able to fit everybody in the class
+ 
+
+ align:start position:0%
+be able to fit everybody in the class
+sort of in an oval around the table. Um
+
+ align:start position:0%
+sort of in an oval around the table. Um
+ 
+
+ align:start position:0%
+sort of in an oval around the table. Um
+the tables are so large that they
+
+ align:start position:0%
+the tables are so large that they
+ 
+
+ align:start position:0%
+the tables are so large that they
+usually have to be like built in
+
+ align:start position:0%
+usually have to be like built in
+ 
+
+ align:start position:0%
+usually have to be like built in
+different pieces and then shipped into
+
+ align:start position:0%
+different pieces and then shipped into
+ 
+
+ align:start position:0%
+different pieces and then shipped into
+the room and then assembled inside the
+
+ align:start position:0%
+the room and then assembled inside the
+ 
+
+ align:start position:0%
+the room and then assembled inside the
+room. um they're incredibly heavy, but
+
+ align:start position:0%
+room. um they're incredibly heavy, but
+ 
+
+ align:start position:0%
+room. um they're incredibly heavy, but
+they um they they make it so there is no
+
+ align:start position:0%
+they um they they make it so there is no
+ 
+
+ align:start position:0%
+they um they they make it so there is no
+front of the room. Um they they and and
+
+ align:start position:0%
+front of the room. Um they they and and
+ 
+
+ align:start position:0%
+front of the room. Um they they and and
+they, you know, at Philips exit at other
+
+ align:start position:0%
+they, you know, at Philips exit at other
+ 
+
+ align:start position:0%
+they, you know, at Philips exit at other
+kinds of independent schools, they put
+
+ align:start position:0%
+kinds of independent schools, they put
+ 
+
+ align:start position:0%
+kinds of independent schools, they put
+these tables in every classroom. Um they
+
+ align:start position:0%
+these tables in every classroom. Um they
+ 
+
+ align:start position:0%
+these tables in every classroom. Um they
+put them in the English classrooms, they
+
+ align:start position:0%
+put them in the English classrooms, they
+ 
+
+ align:start position:0%
+put them in the English classrooms, they
+put them in the history classrooms, but
+
+ align:start position:0%
+put them in the history classrooms, but
+ 
+
+ align:start position:0%
+put them in the history classrooms, but
+they put them in the math classrooms,
+
+ align:start position:0%
+they put them in the math classrooms,
+ 
+
+ align:start position:0%
+they put them in the math classrooms,
+they put them in the science classrooms.
+
+ align:start position:0%
+they put them in the science classrooms.
+ 
+
+ align:start position:0%
+they put them in the science classrooms.
+Um and the intention was to to change
+
+ align:start position:0%
+Um and the intention was to to change
+ 
+
+ align:start position:0%
+Um and the intention was to to change
+the physical space in order to create
+
+ align:start position:0%
+the physical space in order to create
+ 
+
+ align:start position:0%
+the physical space in order to create
+certain kinds of learning environments
+
+ align:start position:0%
+certain kinds of learning environments
+ 
+
+ align:start position:0%
+certain kinds of learning environments
+and certain kinds of interactions there
+
+ align:start position:0%
+and certain kinds of interactions there
+ 
+
+ align:start position:0%
+and certain kinds of interactions there
+and there. Now, of course, um you can
+
+ align:start position:0%
+and there. Now, of course, um you can
+ 
+
+ align:start position:0%
+and there. Now, of course, um you can
+give a math lecture in a room like this,
+
+ align:start position:0%
+give a math lecture in a room like this,
+ 
+
+ align:start position:0%
+give a math lecture in a room like this,
+but it's but it's hard to lecture for 52
+
+ align:start position:0%
+but it's but it's hard to lecture for 52
+ 
+
+ align:start position:0%
+but it's but it's hard to lecture for 52
+minutes, you know, if you're standing
+
+ align:start position:0%
+minutes, you know, if you're standing
+ 
+
+ align:start position:0%
+minutes, you know, if you're standing
+here and half the kids either have their
+
+ align:start position:0%
+here and half the kids either have their
+ 
+
+ align:start position:0%
+here and half the kids either have their
+backs to you or have to, you know,
+
+ align:start position:0%
+backs to you or have to, you know,
+ 
+
+ align:start position:0%
+backs to you or have to, you know,
+rotate around or other kinds of things
+
+ align:start position:0%
+rotate around or other kinds of things
+ 
+
+ align:start position:0%
+rotate around or other kinds of things
+like that. Um it's it's designed to make
+
+ align:start position:0%
+like that. Um it's it's designed to make
+ 
+
+ align:start position:0%
+like that. Um it's it's designed to make
+people do that. So you can sort of think
+
+ align:start position:0%
+people do that. So you can sort of think
+ 
+
+ align:start position:0%
+people do that. So you can sort of think
+about like what are the you know h what
+
+ align:start position:0%
+about like what are the you know h what
+ 
+
+ align:start position:0%
+about like what are the you know h what
+are what you know what uh what agenda
+
+ align:start position:0%
+are what you know what uh what agenda
+ 
+
+ align:start position:0%
+are what you know what uh what agenda
+does this online space have for its
+
+ align:start position:0%
+does this online space have for its
+ 
+
+ align:start position:0%
+does this online space have for its
+occupants? Um what is it that a can that
+
+ align:start position:0%
+occupants? Um what is it that a can that
+ 
+
+ align:start position:0%
+occupants? Um what is it that a can that
+a sort of generic canvas classroom tells
+
+ align:start position:0%
+a sort of generic canvas classroom tells
+ 
+
+ align:start position:0%
+a sort of generic canvas classroom tells
+instructors and students that they're
+
+ align:start position:0%
+instructors and students that they're
+ 
+
+ align:start position:0%
+instructors and students that they're
+supposed to do?
+
+ align:start position:0%
+supposed to do?
+ 
+
+ align:start position:0%
+supposed to do?
+Um the you can look at these links
+
+ align:start position:0%
+Um the you can look at these links
+ 
+
+ align:start position:0%
+Um the you can look at these links
+later, but these are two of the folks
+
+ align:start position:0%
+later, but these are two of the folks
+ 
+
+ align:start position:0%
+later, but these are two of the folks
+who um as as as Blackboard was sort of
+
+ align:start position:0%
+who um as as as Blackboard was sort of
+ 
+
+ align:start position:0%
+who um as as as Blackboard was sort of
+sweeping higher education were uh um uh
+
+ align:start position:0%
+sweeping higher education were uh um uh
+ 
+
+ align:start position:0%
+sweeping higher education were uh um uh
+amongst the most active in trying to
+
+ align:start position:0%
+amongst the most active in trying to
+ 
+
+ align:start position:0%
+amongst the most active in trying to
+have these conversations. There was a
+
+ align:start position:0%
+have these conversations. There was a
+ 
+
+ align:start position:0%
+have these conversations. There was a
+book um that was written about them uh
+
+ align:start position:0%
+book um that was written about them uh
+ 
+
+ align:start position:0%
+book um that was written about them uh
+and some other people called Edupunks um
+
+ align:start position:0%
+and some other people called Edupunks um
+ 
+
+ align:start position:0%
+and some other people called Edupunks um
+and uh trying to make connection between
+
+ align:start position:0%
+and uh trying to make connection between
+ 
+
+ align:start position:0%
+and uh trying to make connection between
+the the punk movement and music um you
+
+ align:start position:0%
+the the punk movement and music um you
+ 
+
+ align:start position:0%
+the the punk movement and music um you
+know very sort of like countercultural
+
+ align:start position:0%
+know very sort of like countercultural
+ 
+
+ align:start position:0%
+know very sort of like countercultural
+do-it-yourself
+
+ align:start position:0%
+do-it-yourself
+ 
+
+ align:start position:0%
+do-it-yourself
+um you know uh kind of stand up to the
+
+ align:start position:0%
+um you know uh kind of stand up to the
+ 
+
+ align:start position:0%
+um you know uh kind of stand up to the
+man sort of thing um and folks like the
+
+ align:start position:0%
+man sort of thing um and folks like the
+ 
+
+ align:start position:0%
+man sort of thing um and folks like the
+Reverend Jim Groom um and Alan Cogdon
+
+ align:start position:0%
+Reverend Jim Groom um and Alan Cogdon
+ 
+
+ align:start position:0%
+Reverend Jim Groom um and Alan Cogdon
+living you know they have they have
+
+ align:start position:0%
+living you know they have they have
+ 
+
+ align:start position:0%
+living you know they have they have
+these monikers because if you were
+
+ align:start position:0%
+these monikers because if you were
+ 
+
+ align:start position:0%
+these monikers because if you were
+participating in social networks you
+
+ align:start position:0%
+participating in social networks you
+ 
+
+ align:start position:0%
+participating in social networks you
+create handles for those kinds of things
+
+ align:start position:0%
+create handles for those kinds of things
+ 
+
+ align:start position:0%
+create handles for those kinds of things
+but also Reverend Jim Groom was a bit a
+
+ align:start position:0%
+but also Reverend Jim Groom was a bit a
+ 
+
+ align:start position:0%
+but also Reverend Jim Groom was a bit a
+profit of such things.
+
+ align:start position:0%
+profit of such things.
+ 
+
+ align:start position:0%
+profit of such things.
+Um so what what these systems really
+
+ align:start position:0%
+Um so what what these systems really
+ 
+
+ align:start position:0%
+Um so what what these systems really
+allow um is a certain kind of
+
+ align:start position:0%
+allow um is a certain kind of
+ 
+
+ align:start position:0%
+allow um is a certain kind of
+coordination. Um it becomes very very
+
+ align:start position:0%
+coordination. Um it becomes very very
+ 
+
+ align:start position:0%
+coordination. Um it becomes very very
+easy to say all the faculty are going to
+
+ align:start position:0%
+easy to say all the faculty are going to
+ 
+
+ align:start position:0%
+easy to say all the faculty are going to
+have a page. Um you're all going to
+
+ align:start position:0%
+have a page. Um you're all going to
+ 
+
+ align:start position:0%
+have a page. Um you're all going to
+create at the same time. It's going to
+
+ align:start position:0%
+create at the same time. It's going to
+ 
+
+ align:start position:0%
+create at the same time. It's going to
+be automatically generated for you at
+
+ align:start position:0%
+be automatically generated for you at
+ 
+
+ align:start position:0%
+be automatically generated for you at
+the beginning of the semester. Even if
+
+ align:start position:0%
+the beginning of the semester. Even if
+ 
+
+ align:start position:0%
+the beginning of the semester. Even if
+you don't like computers, we're still
+
+ align:start position:0%
+you don't like computers, we're still
+ 
+
+ align:start position:0%
+you don't like computers, we're still
+going to be able to make you do it
+
+ align:start position:0%
+going to be able to make you do it
+ 
+
+ align:start position:0%
+going to be able to make you do it
+because it's not that hard. Um but there
+
+ align:start position:0%
+because it's not that hard. Um but there
+ 
+
+ align:start position:0%
+because it's not that hard. Um but there
+are a couple of characteristics of it
+
+ align:start position:0%
+are a couple of characteristics of it
+ 
+
+ align:start position:0%
+are a couple of characteristics of it
+that I think are not so good. I've
+
+ align:start position:0%
+that I think are not so good. I've
+ 
+
+ align:start position:0%
+that I think are not so good. I've
+talked mostly about the sort of stamped
+
+ align:start position:0%
+talked mostly about the sort of stamped
+ 
+
+ align:start position:0%
+talked mostly about the sort of stamped
+piece of it. Um
+
+ align:start position:0%
+piece of it. Um
+ 
+
+ align:start position:0%
+piece of it. Um
+uh there's there's a way in which um the
+
+ align:start position:0%
+uh there's there's a way in which um the
+ 
+
+ align:start position:0%
+uh there's there's a way in which um the
+control of all of the learning artifacts
+
+ align:start position:0%
+control of all of the learning artifacts
+ 
+
+ align:start position:0%
+control of all of the learning artifacts
+is with the institution and not the
+
+ align:start position:0%
+is with the institution and not the
+ 
+
+ align:start position:0%
+is with the institution and not the
+people. Um, so imagine imagine an
+
+ align:start position:0%
+people. Um, so imagine imagine an
+ 
+
+ align:start position:0%
+people. Um, so imagine imagine an
+infrastructure for um online learning
+
+ align:start position:0%
+infrastructure for um online learning
+ 
+
+ align:start position:0%
+infrastructure for um online learning
+and higher education where you didn't
+
+ align:start position:0%
+and higher education where you didn't
+ 
+
+ align:start position:0%
+and higher education where you didn't
+put all the stuff on someone else's web
+
+ align:start position:0%
+put all the stuff on someone else's web
+ 
+
+ align:start position:0%
+put all the stuff on someone else's web
+page, you put it on your own web page.
+
+ align:start position:0%
+page, you put it on your own web page.
+ 
+
+ align:start position:0%
+page, you put it on your own web page.
+Like what if when you went to do
+
+ align:start position:0%
+Like what if when you went to do
+ 
+
+ align:start position:0%
+Like what if when you went to do
+homework, you went to do writing, you
+
+ align:start position:0%
+homework, you went to do writing, you
+ 
+
+ align:start position:0%
+homework, you went to do writing, you
+went to ask questions, it didn't show up
+
+ align:start position:0%
+went to ask questions, it didn't show up
+ 
+
+ align:start position:0%
+went to ask questions, it didn't show up
+on the school's Canvas site, which you
+
+ align:start position:0%
+on the school's Canvas site, which you
+ 
+
+ align:start position:0%
+on the school's Canvas site, which you
+don't care about, but it was on your
+
+ align:start position:0%
+don't care about, but it was on your
+ 
+
+ align:start position:0%
+don't care about, but it was on your
+site in some kind of way. It was in some
+
+ align:start position:0%
+site in some kind of way. It was in some
+ 
+
+ align:start position:0%
+site in some kind of way. It was in some
+sort of space that you controlled. And
+
+ align:start position:0%
+sort of space that you controlled. And
+ 
+
+ align:start position:0%
+sort of space that you controlled. And
+then the thing that was always craziest
+
+ align:start position:0%
+then the thing that was always craziest
+ 
+
+ align:start position:0%
+then the thing that was always craziest
+to me about these sites is that we
+
+ align:start position:0%
+to me about these sites is that we
+ 
+
+ align:start position:0%
+to me about these sites is that we
+delete them every 18 months. Um, you
+
+ align:start position:0%
+delete them every 18 months. Um, you
+ 
+
+ align:start position:0%
+delete them every 18 months. Um, you
+know, it's a it's a strange thing to go
+
+ align:start position:0%
+know, it's a it's a strange thing to go
+ 
+
+ align:start position:0%
+know, it's a it's a strange thing to go
+to students and be like, "Please pour in
+
+ align:start position:0%
+to students and be like, "Please pour in
+ 
+
+ align:start position:0%
+to students and be like, "Please pour in
+um your best, most thoughtful, most
+
+ align:start position:0%
+um your best, most thoughtful, most
+ 
+
+ align:start position:0%
+um your best, most thoughtful, most
+interesting words, ideas." Um, oh, and
+
+ align:start position:0%
+interesting words, ideas." Um, oh, and
+ 
+
+ align:start position:0%
+interesting words, ideas." Um, oh, and
+by the way, nine months from now,
+
+ align:start position:0%
+by the way, nine months from now,
+ 
+
+ align:start position:0%
+by the way, nine months from now,
+they're going to be automatically
+
+ align:start position:0%
+they're going to be automatically
+ 
+
+ align:start position:0%
+they're going to be automatically
+deleted. Um, that's a that's a sort of
+
+ align:start position:0%
+deleted. Um, that's a that's a sort of
+ 
+
+ align:start position:0%
+deleted. Um, that's a that's a sort of
+strange feature to me of a of an online
+
+ align:start position:0%
+strange feature to me of a of an online
+ 
+
+ align:start position:0%
+strange feature to me of a of an online
+learning environment. Um,
+
+ align:start position:0%
+learning environment. Um,
+ 
+
+ align:start position:0%
+learning environment. Um,
+uh, so so me and other folks for a while
+
+ align:start position:0%
+uh, so so me and other folks for a while
+ 
+
+ align:start position:0%
+uh, so so me and other folks for a while
+were really interested in like, well,
+
+ align:start position:0%
+were really interested in like, well,
+ 
+
+ align:start position:0%
+were really interested in like, well,
+what would an alternative to this look
+
+ align:start position:0%
+what would an alternative to this look
+ 
+
+ align:start position:0%
+what would an alternative to this look
+like? um what would be what would be
+
+ align:start position:0%
+like? um what would be what would be
+ 
+
+ align:start position:0%
+like? um what would be what would be
+something um that was not Blackboard
+
+ align:start position:0%
+something um that was not Blackboard
+ 
+
+ align:start position:0%
+something um that was not Blackboard
+that was not Canvas um that still could
+
+ align:start position:0%
+that was not Canvas um that still could
+ 
+
+ align:start position:0%
+that was not Canvas um that still could
+have coordination um but it would let it
+
+ align:start position:0%
+have coordination um but it would let it
+ 
+
+ align:start position:0%
+have coordination um but it would let it
+would have some of these characteristics
+
+ align:start position:0%
+would have some of these characteristics
+ 
+
+ align:start position:0%
+would have some of these characteristics
+that the sort of web 2.0 open web
+
+ align:start position:0%
+that the sort of web 2.0 open web
+ 
+
+ align:start position:0%
+that the sort of web 2.0 open web
+movement had like it let students own
+
+ align:start position:0%
+movement had like it let students own
+ 
+
+ align:start position:0%
+movement had like it let students own
+their own stuff um it helped them
+
+ align:start position:0%
+their own stuff um it helped them
+ 
+
+ align:start position:0%
+their own stuff um it helped them
+develop some technology proficiency. It
+
+ align:start position:0%
+develop some technology proficiency. It
+ 
+
+ align:start position:0%
+develop some technology proficiency. It
+connected people um to each other and to
+
+ align:start position:0%
+connected people um to each other and to
+ 
+
+ align:start position:0%
+connected people um to each other and to
+their work. It didn't just like hoover
+
+ align:start position:0%
+their work. It didn't just like hoover
+ 
+
+ align:start position:0%
+their work. It didn't just like hoover
+up your stuff, churn it through, grade
+
+ align:start position:0%
+up your stuff, churn it through, grade
+ 
+
+ align:start position:0%
+up your stuff, churn it through, grade
+it, and delete it, but it would be like
+
+ align:start position:0%
+it, and delete it, but it would be like
+ 
+
+ align:start position:0%
+it, and delete it, but it would be like
+something that you owned and cared about
+
+ align:start position:0%
+something that you owned and cared about
+ 
+
+ align:start position:0%
+something that you owned and cared about
+for a while. Um,
+
+ align:start position:0%
+for a while. Um,
+ 
+
+ align:start position:0%
+for a while. Um,
+uh, those are ice cream sandwiches. Um,
+
+ align:start position:0%
+uh, those are ice cream sandwiches. Um,
+ 
+
+ align:start position:0%
+uh, those are ice cream sandwiches. Um,
+uh, yeah. Good. Yeah. So, it's a good
+
+ align:start position:0%
+uh, yeah. Good. Yeah. So, it's a good
+ 
+
+ align:start position:0%
+uh, yeah. Good. Yeah. So, it's a good
+it's a good picture. It, you know, it
+
+ align:start position:0%
+it's a good picture. It, you know, it
+ 
+
+ align:start position:0%
+it's a good picture. It, you know, it
+definitely evokes some of these kinds of
+
+ align:start position:0%
+definitely evokes some of these kinds of
+ 
+
+ align:start position:0%
+definitely evokes some of these kinds of
+pictures. Like some of these kinds of
+
+ align:start position:0%
+pictures. Like some of these kinds of
+ 
+
+ align:start position:0%
+pictures. Like some of these kinds of
+pictures sort of ended up on like
+
+ align:start position:0%
+pictures sort of ended up on like
+ 
+
+ align:start position:0%
+pictures sort of ended up on like
+professor Twitter handles in the 2013.
+
+ align:start position:0%
+professor Twitter handles in the 2013.
+ 
+
+ align:start position:0%
+professor Twitter handles in the 2013.
+Um, I didn't make that picture. I had
+
+ align:start position:0%
+Um, I didn't make that picture. I had
+ 
+
+ align:start position:0%
+Um, I didn't make that picture. I had
+one semester um where I don't know some
+
+ align:start position:0%
+one semester um where I don't know some
+ 
+
+ align:start position:0%
+one semester um where I don't know some
+students just were like enjoying class
+
+ align:start position:0%
+students just were like enjoying class
+ 
+
+ align:start position:0%
+students just were like enjoying class
+and they sent me a whole bunch of p I
+
+ align:start position:0%
+and they sent me a whole bunch of p I
+ 
+
+ align:start position:0%
+and they sent me a whole bunch of p I
+don't know how quickly can I find these
+
+ align:start position:0%
+don't know how quickly can I find these
+ 
+
+ align:start position:0%
+don't know how quickly can I find these
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+Um there's one of
+
+ align:start position:0%
+Um there's one of
+ 
+
+ align:start position:0%
+Um there's one of
+me.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh are these going to be on here?
+
+ align:start position:0%
+Uh are these going to be on here?
+ 
+
+ align:start position:0%
+Uh are these going to be on here?
+Um. H there's a few. There's like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. This one. Oh, no. That's a real
+
+ align:start position:0%
+one. This one. Oh, no. That's a real
+ 
+
+ align:start position:0%
+one. This one. Oh, no. That's a real
+one. Justin is LeBron James. A little
+
+ align:start position:0%
+one. Justin is LeBron James. A little
+ 
+
+ align:start position:0%
+one. Justin is LeBron James. A little
+little dicey to be doing this one these
+
+ align:start position:0%
+little dicey to be doing this one these
+ 
+
+ align:start position:0%
+little dicey to be doing this one these
+days. I don't You probably wouldn't uh
+
+ align:start position:0%
+days. I don't You probably wouldn't uh
+ 
+
+ align:start position:0%
+days. I don't You probably wouldn't uh
+you probably wouldn't put white Justin
+
+ align:start position:0%
+you probably wouldn't put white Justin
+ 
+
+ align:start position:0%
+you probably wouldn't put white Justin
+into a black body anymore, but uh back
+
+ align:start position:0%
+into a black body anymore, but uh back
+ 
+
+ align:start position:0%
+into a black body anymore, but uh back
+in the day. Um yeah, I don't for one day
+
+ align:start position:0%
+in the day. Um yeah, I don't for one day
+ 
+
+ align:start position:0%
+in the day. Um yeah, I don't for one day
+for class uh I think something terrible
+
+ align:start position:0%
+for class uh I think something terrible
+ 
+
+ align:start position:0%
+for class uh I think something terrible
+had happened in the world and I made
+
+ align:start position:0%
+had happened in the world and I made
+ 
+
+ align:start position:0%
+had happened in the world and I made
+them ice cream sandwiches one day for
+
+ align:start position:0%
+them ice cream sandwiches one day for
+ 
+
+ align:start position:0%
+them ice cream sandwiches one day for
+class and so they uh um they made that
+
+ align:start position:0%
+class and so they uh um they made that
+ 
+
+ align:start position:0%
+class and so they uh um they made that
+picture there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It was for
+
+ align:start position:0%
+It was for
+ 
+
+ align:start position:0%
+It was for
+a we're get we're getting to the real
+
+ align:start position:0%
+a we're get we're getting to the real
+ 
+
+ align:start position:0%
+a we're get we're getting to the real
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+now. I think that I went to the
+
+ align:start position:0%
+now. I think that I went to the
+ 
+
+ align:start position:0%
+now. I think that I went to the
+International Society and Technology and
+
+ align:start position:0%
+International Society and Technology and
+ 
+
+ align:start position:0%
+International Society and Technology and
+Education conference and they basically
+
+ align:start position:0%
+Education conference and they basically
+ 
+
+ align:start position:0%
+Education conference and they basically
+grabbed a bunch of random people and
+
+ align:start position:0%
+grabbed a bunch of random people and
+ 
+
+ align:start position:0%
+grabbed a bunch of random people and
+took them to a photo shoot to generate
+
+ align:start position:0%
+took them to a photo shoot to generate
+ 
+
+ align:start position:0%
+took them to a photo shoot to generate
+their own stock photos. Um they they
+
+ align:start position:0%
+their own stock photos. Um they they
+ 
+
+ align:start position:0%
+their own stock photos. Um they they
+want they wanted to have a whole set of
+
+ align:start position:0%
+want they wanted to have a whole set of
+ 
+
+ align:start position:0%
+want they wanted to have a whole set of
+stock photos that were from the
+
+ align:start position:0%
+stock photos that were from the
+ 
+
+ align:start position:0%
+stock photos that were from the
+membership of this organization. And so
+
+ align:start position:0%
+membership of this organization. And so
+ 
+
+ align:start position:0%
+membership of this organization. And so
+it was just like I don't think I was
+
+ align:start position:0%
+it was just like I don't think I was
+ 
+
+ align:start position:0%
+it was just like I don't think I was
+holding any I think I I mean I like you
+
+ align:start position:0%
+holding any I think I I mean I like you
+ 
+
+ align:start position:0%
+holding any I think I I mean I like you
+could imagine this is like generic
+
+ align:start position:0%
+could imagine this is like generic
+ 
+
+ align:start position:0%
+could imagine this is like generic
+invitation to kind of thing. Um, but
+
+ align:start position:0%
+invitation to kind of thing. Um, but
+ 
+
+ align:start position:0%
+invitation to kind of thing. Um, but
+that's where all that came from.
+
+ align:start position:0%
+that's where all that came from.
+ 
+
+ align:start position:0%
+that's where all that came from.
+Um, is is this worth your learning time?
+
+ align:start position:0%
+Um, is is this worth your learning time?
+ 
+
+ align:start position:0%
+Um, is is this worth your learning time?
+Hard to say, but it's pretty fun. Okay,
+
+ align:start position:0%
+Hard to say, but it's pretty fun. Okay,
+ 
+
+ align:start position:0%
+Hard to say, but it's pretty fun. Okay,
+this you should remember a little bit.
+
+ align:start position:0%
+this you should remember a little bit.
+ 
+
+ align:start position:0%
+this you should remember a little bit.
+Um, this is another this is another
+
+ align:start position:0%
+Um, this is another this is another
+ 
+
+ align:start position:0%
+Um, this is another this is another
+branch of um uh of constructionism. You
+
+ align:start position:0%
+branch of um uh of constructionism. You
+ 
+
+ align:start position:0%
+branch of um uh of constructionism. You
+know, these ideas just repeat
+
+ align:start position:0%
+know, these ideas just repeat
+ 
+
+ align:start position:0%
+know, these ideas just repeat
+themselves. They get reinvented over and
+
+ align:start position:0%
+themselves. They get reinvented over and
+ 
+
+ align:start position:0%
+themselves. They get reinvented over and
+over again. um these two Canadian
+
+ align:start position:0%
+over again. um these two Canadian
+ 
+
+ align:start position:0%
+over again. um these two Canadian
+educators, people who sort of founded
+
+ align:start position:0%
+educators, people who sort of founded
+ 
+
+ align:start position:0%
+educators, people who sort of founded
+the 2007208 original mass of open online
+
+ align:start position:0%
+the 2007208 original mass of open online
+ 
+
+ align:start position:0%
+the 2007208 original mass of open online
+courses and they had this idea called
+
+ align:start position:0%
+courses and they had this idea called
+ 
+
+ align:start position:0%
+courses and they had this idea called
+connectivism. Um and they said, you
+
+ align:start position:0%
+connectivism. Um and they said, you
+ 
+
+ align:start position:0%
+connectivism. Um and they said, you
+know, part of the problem with learning
+
+ align:start position:0%
+know, part of the problem with learning
+ 
+
+ align:start position:0%
+know, part of the problem with learning
+theory is that it thinks that learning
+
+ align:start position:0%
+theory is that it thinks that learning
+ 
+
+ align:start position:0%
+theory is that it thinks that learning
+happens and knowledge exists inside
+
+ align:start position:0%
+happens and knowledge exists inside
+ 
+
+ align:start position:0%
+happens and knowledge exists inside
+people's heads. But learning and
+
+ align:start position:0%
+people's heads. But learning and
+ 
+
+ align:start position:0%
+people's heads. But learning and
+knowledge really exists between people
+
+ align:start position:0%
+knowledge really exists between people
+ 
+
+ align:start position:0%
+knowledge really exists between people
+more than exists within people. Um
+
+ align:start position:0%
+more than exists within people. Um
+ 
+
+ align:start position:0%
+more than exists within people. Um
+there's a famous line which is which you
+
+ align:start position:0%
+there's a famous line which is which you
+ 
+
+ align:start position:0%
+there's a famous line which is which you
+probably all would agree with in some
+
+ align:start position:0%
+probably all would agree with in some
+ 
+
+ align:start position:0%
+probably all would agree with in some
+way that the smartest person in the room
+
+ align:start position:0%
+way that the smartest person in the room
+ 
+
+ align:start position:0%
+way that the smartest person in the room
+is the room. Um that like the collective
+
+ align:start position:0%
+is the room. Um that like the collective
+ 
+
+ align:start position:0%
+is the room. Um that like the collective
+capacity of people is where kind of the
+
+ align:start position:0%
+capacity of people is where kind of the
+ 
+
+ align:start position:0%
+capacity of people is where kind of the
+heart of art intelligence is like
+
+ align:start position:0%
+heart of art intelligence is like
+ 
+
+ align:start position:0%
+heart of art intelligence is like
+connectivism almost went further and
+
+ align:start position:0%
+connectivism almost went further and
+ 
+
+ align:start position:0%
+connectivism almost went further and
+said like maybe the only intelligence in
+
+ align:start position:0%
+said like maybe the only intelligence in
+ 
+
+ align:start position:0%
+said like maybe the only intelligence in
+the room is the room. Um maybe your
+
+ align:start position:0%
+the room is the room. Um maybe your
+ 
+
+ align:start position:0%
+the room is the room. Um maybe your
+knowledge your understanding like
+
+ align:start position:0%
+knowledge your understanding like
+ 
+
+ align:start position:0%
+knowledge your understanding like
+doesn't exist without social convention
+
+ align:start position:0%
+doesn't exist without social convention
+ 
+
+ align:start position:0%
+doesn't exist without social convention
+like language um like culture other
+
+ align:start position:0%
+like language um like culture other
+ 
+
+ align:start position:0%
+like language um like culture other
+kinds of things like that. Um so this
+
+ align:start position:0%
+kinds of things like that. Um so this
+ 
+
+ align:start position:0%
+kinds of things like that. Um so this
+was so this was at first an educational
+
+ align:start position:0%
+was so this was at first an educational
+ 
+
+ align:start position:0%
+was so this was at first an educational
+philosophy. Um may you know may maybe it
+
+ align:start position:0%
+philosophy. Um may you know may maybe it
+ 
+
+ align:start position:0%
+philosophy. Um may you know may maybe it
+was a maybe it was an epistemology maybe
+
+ align:start position:0%
+was a maybe it was an epistemology maybe
+ 
+
+ align:start position:0%
+was a maybe it was an epistemology maybe
+it was a philosophy of knowledge but
+
+ align:start position:0%
+it was a philosophy of knowledge but
+ 
+
+ align:start position:0%
+it was a philosophy of knowledge but
+then it got translated into these
+
+ align:start position:0%
+then it got translated into these
+ 
+
+ align:start position:0%
+then it got translated into these
+pedagogical ideas. Um and the
+
+ align:start position:0%
+pedagogical ideas. Um and the
+ 
+
+ align:start position:0%
+pedagogical ideas. Um and the
+pedagogical ideas were say what if you
+
+ align:start position:0%
+pedagogical ideas were say what if you
+ 
+
+ align:start position:0%
+pedagogical ideas were say what if you
+defined courses where their primary
+
+ align:start position:0%
+defined courses where their primary
+ 
+
+ align:start position:0%
+defined courses where their primary
+value was creating connections between
+
+ align:start position:0%
+value was creating connections between
+ 
+
+ align:start position:0%
+value was creating connections between
+people and ideas. Um uh one of one of
+
+ align:start position:0%
+people and ideas. Um uh one of one of
+ 
+
+ align:start position:0%
+people and ideas. Um uh one of one of
+the things Stephen D said about this
+
+ align:start position:0%
+the things Stephen D said about this
+ 
+
+ align:start position:0%
+the things Stephen D said about this
+which you'll find it very connected to
+
+ align:start position:0%
+which you'll find it very connected to
+ 
+
+ align:start position:0%
+which you'll find it very connected to
+situated learning um he says you know
+
+ align:start position:0%
+situated learning um he says you know
+ 
+
+ align:start position:0%
+situated learning um he says you know
+like if you become a physicist what
+
+ align:start position:0%
+like if you become a physicist what
+ 
+
+ align:start position:0%
+like if you become a physicist what
+happens um well like you read physics
+
+ align:start position:0%
+happens um well like you read physics
+ 
+
+ align:start position:0%
+happens um well like you read physics
+papers and you follow new ideas in
+
+ align:start position:0%
+papers and you follow new ideas in
+ 
+
+ align:start position:0%
+papers and you follow new ideas in
+physics and you figure out where
+
+ align:start position:0%
+physics and you figure out where
+ 
+
+ align:start position:0%
+physics and you figure out where
+physicists talk to each other and like
+
+ align:start position:0%
+physicists talk to each other and like
+ 
+
+ align:start position:0%
+physicists talk to each other and like
+where the physics lounge is um and which
+
+ align:start position:0%
+where the physics lounge is um and which
+ 
+
+ align:start position:0%
+where the physics lounge is um and which
+physics conferences to go to I don't
+
+ align:start position:0%
+physics conferences to go to I don't
+ 
+
+ align:start position:0%
+physics conferences to go to I don't
+know what music physicists like what
+
+ align:start position:0%
+know what music physicists like what
+ 
+
+ align:start position:0%
+know what music physicists like what
+television shows they find funny all
+
+ align:start position:0%
+television shows they find funny all
+ 
+
+ align:start position:0%
+television shows they find funny all
+these kinds of things like that is as
+
+ align:start position:0%
+these kinds of things like that is as
+ 
+
+ align:start position:0%
+these kinds of things like that is as
+much a part of becoming a physicist as
+
+ align:start position:0%
+much a part of becoming a physicist as
+ 
+
+ align:start position:0%
+much a part of becoming a physicist as
+learning formulas and theories and
+
+ align:start position:0%
+learning formulas and theories and
+ 
+
+ align:start position:0%
+learning formulas and theories and
+knowledge and things like that. What if
+
+ align:start position:0%
+knowledge and things like that. What if
+ 
+
+ align:start position:0%
+knowledge and things like that. What if
+we had educational systems that took
+
+ align:start position:0%
+we had educational systems that took
+ 
+
+ align:start position:0%
+we had educational systems that took
+that really seriously? Like the job of a
+
+ align:start position:0%
+that really seriously? Like the job of a
+ 
+
+ align:start position:0%
+that really seriously? Like the job of a
+physics class is not just to have you,
+
+ align:start position:0%
+physics class is not just to have you,
+ 
+
+ align:start position:0%
+physics class is not just to have you,
+you know, be able to learn some formulas
+
+ align:start position:0%
+you know, be able to learn some formulas
+ 
+
+ align:start position:0%
+you know, be able to learn some formulas
+about Newton's three laws, but to
+
+ align:start position:0%
+about Newton's three laws, but to
+ 
+
+ align:start position:0%
+about Newton's three laws, but to
+connect to other physicists. That's kind
+
+ align:start position:0%
+connect to other physicists. That's kind
+ 
+
+ align:start position:0%
+connect to other physicists. That's kind
+of that's kind of a cool idea. Um, uh,
+
+ align:start position:0%
+of that's kind of a cool idea. Um, uh,
+ 
+
+ align:start position:0%
+of that's kind of a cool idea. Um, uh,
+Ste, one of the most radical things
+
+ align:start position:0%
+Ste, one of the most radical things
+ 
+
+ align:start position:0%
+Ste, one of the most radical things
+Steven DS ever said, he said something
+
+ align:start position:0%
+Steven DS ever said, he said something
+ 
+
+ align:start position:0%
+Steven DS ever said, he said something
+along the lines of, "In my class, the
+
+ align:start position:0%
+along the lines of, "In my class, the
+ 
+
+ align:start position:0%
+along the lines of, "In my class, the
+content is McGuffin." Um, a mcguffin is
+
+ align:start position:0%
+content is McGuffin." Um, a mcguffin is
+ 
+
+ align:start position:0%
+content is McGuffin." Um, a mcguffin is
+the thing in a movie that's not really
+
+ align:start position:0%
+the thing in a movie that's not really
+ 
+
+ align:start position:0%
+the thing in a movie that's not really
+important that drives the plot forward.
+
+ align:start position:0%
+important that drives the plot forward.
+ 
+
+ align:start position:0%
+important that drives the plot forward.
+Um, it's the briefcase that gets
+
+ align:start position:0%
+Um, it's the briefcase that gets
+ 
+
+ align:start position:0%
+Um, it's the briefcase that gets
+switched in the beginning which helps
+
+ align:start position:0%
+switched in the beginning which helps
+ 
+
+ align:start position:0%
+switched in the beginning which helps
+two people fall in love with each other
+
+ align:start position:0%
+two people fall in love with each other
+ 
+
+ align:start position:0%
+two people fall in love with each other
+or something like that. Um, the mcguffin
+
+ align:start position:0%
+or something like that. Um, the mcguffin
+ 
+
+ align:start position:0%
+or something like that. Um, the mcguffin
+is the thing that you're sort of chasing
+
+ align:start position:0%
+is the thing that you're sort of chasing
+ 
+
+ align:start position:0%
+is the thing that you're sort of chasing
+to make the plot move forward. This is a
+
+ align:start position:0%
+to make the plot move forward. This is a
+ 
+
+ align:start position:0%
+to make the plot move forward. This is a
+radical statement for an educator. The
+
+ align:start position:0%
+radical statement for an educator. The
+ 
+
+ align:start position:0%
+radical statement for an educator. The
+content is a mcguffin. The thing that I
+
+ align:start position:0%
+content is a mcguffin. The thing that I
+ 
+
+ align:start position:0%
+content is a mcguffin. The thing that I
+told you the class is about as a trick.
+
+ align:start position:0%
+told you the class is about as a trick.
+ 
+
+ align:start position:0%
+told you the class is about as a trick.
+The real part of the class is getting
+
+ align:start position:0%
+The real part of the class is getting
+ 
+
+ align:start position:0%
+The real part of the class is getting
+you connected to each other, to things
+
+ align:start position:0%
+you connected to each other, to things
+ 
+
+ align:start position:0%
+you connected to each other, to things
+that you're interested in, to other
+
+ align:start position:0%
+that you're interested in, to other
+ 
+
+ align:start position:0%
+that you're interested in, to other
+kinds of expertise is a very radical set
+
+ align:start position:0%
+kinds of expertise is a very radical set
+ 
+
+ align:start position:0%
+kinds of expertise is a very radical set
+of ideas. Um, and there are a lot of
+
+ align:start position:0%
+of ideas. Um, and there are a lot of
+ 
+
+ align:start position:0%
+of ideas. Um, and there are a lot of
+people who are sort of um profoundly
+
+ align:start position:0%
+people who are sort of um profoundly
+ 
+
+ align:start position:0%
+people who are sort of um profoundly
+influenced by them. Um, and people
+
+ align:start position:0%
+influenced by them. Um, and people
+ 
+
+ align:start position:0%
+influenced by them. Um, and people
+trying to say like, yeah, well, what
+
+ align:start position:0%
+trying to say like, yeah, well, what
+ 
+
+ align:start position:0%
+trying to say like, yeah, well, what
+what could some like genuine alternative
+
+ align:start position:0%
+what could some like genuine alternative
+ 
+
+ align:start position:0%
+what could some like genuine alternative
+architecture to canvas um that embraced
+
+ align:start position:0%
+architecture to canvas um that embraced
+ 
+
+ align:start position:0%
+architecture to canvas um that embraced
+some of these ideas of the open web, of
+
+ align:start position:0%
+some of these ideas of the open web, of
+ 
+
+ align:start position:0%
+some of these ideas of the open web, of
+web 2.0, of connectism, what might it
+
+ align:start position:0%
+web 2.0, of connectism, what might it
+ 
+
+ align:start position:0%
+web 2.0, of connectism, what might it
+look like? Um, and so this no longer
+
+ align:start position:0%
+look like? Um, and so this no longer
+ 
+
+ align:start position:0%
+look like? Um, and so this no longer
+exists. I don't I don't think either of
+
+ align:start position:0%
+exists. I don't I don't think either of
+ 
+
+ align:start position:0%
+exists. I don't I don't think either of
+those links are live anymore. Um, but
+
+ align:start position:0%
+those links are live anymore. Um, but
+ 
+
+ align:start position:0%
+those links are live anymore. Um, but
+this is what the website for this class,
+
+ align:start position:0%
+this is what the website for this class,
+ 
+
+ align:start position:0%
+this is what the website for this class,
+um, or an earlier version of this class
+
+ align:start position:0%
+um, or an earlier version of this class
+ 
+
+ align:start position:0%
+um, or an earlier version of this class
+used to look like. Um, and here's how
+
+ align:start position:0%
+used to look like. Um, and here's how
+ 
+
+ align:start position:0%
+used to look like. Um, and here's how
+the infrastructure of it worked. Um, at
+
+ align:start position:0%
+the infrastructure of it worked. Um, at
+ 
+
+ align:start position:0%
+the infrastructure of it worked. Um, at
+the beginning of class, um, folks were
+
+ align:start position:0%
+the beginning of class, um, folks were
+ 
+
+ align:start position:0%
+the beginning of class, um, folks were
+assigned to create spaces where they
+
+ align:start position:0%
+assigned to create spaces where they
+ 
+
+ align:start position:0%
+assigned to create spaces where they
+would do the work of this class. Um, so
+
+ align:start position:0%
+would do the work of this class. Um, so
+ 
+
+ align:start position:0%
+would do the work of this class. Um, so
+you wouldn't have a learning journal.
+
+ align:start position:0%
+you wouldn't have a learning journal.
+ 
+
+ align:start position:0%
+you wouldn't have a learning journal.
+You wouldn't have like a Canvas
+
+ align:start position:0%
+You wouldn't have like a Canvas
+ 
+
+ align:start position:0%
+You wouldn't have like a Canvas
+discussion page or something like that.
+
+ align:start position:0%
+discussion page or something like that.
+ 
+
+ align:start position:0%
+discussion page or something like that.
+Go make your own blog. Go make your own
+
+ align:start position:0%
+Go make your own blog. Go make your own
+ 
+
+ align:start position:0%
+Go make your own blog. Go make your own
+Tumblr page. Go make your own Twitter
+
+ align:start position:0%
+Tumblr page. Go make your own Twitter
+ 
+
+ align:start position:0%
+Tumblr page. Go make your own Twitter
+feed. Go make your own Flickr page. Make
+
+ align:start position:0%
+feed. Go make your own Flickr page. Make
+ 
+
+ align:start position:0%
+feed. Go make your own Flickr page. Make
+all kinds of other things like that. Um,
+
+ align:start position:0%
+all kinds of other things like that. Um,
+ 
+
+ align:start position:0%
+all kinds of other things like that. Um,
+and do all of the work for this class in
+
+ align:start position:0%
+and do all of the work for this class in
+ 
+
+ align:start position:0%
+and do all of the work for this class in
+your own space. Now, one problem with
+
+ align:start position:0%
+your own space. Now, one problem with
+ 
+
+ align:start position:0%
+your own space. Now, one problem with
+that is that nobody can find that stuff
+
+ align:start position:0%
+that is that nobody can find that stuff
+ 
+
+ align:start position:0%
+that is that nobody can find that stuff
+anymore. Now, it's all sort of on other
+
+ align:start position:0%
+anymore. Now, it's all sort of on other
+ 
+
+ align:start position:0%
+anymore. Now, it's all sort of on other
+people's things. But that's a solvable
+
+ align:start position:0%
+people's things. But that's a solvable
+ 
+
+ align:start position:0%
+people's things. But that's a solvable
+problem. Um, because we're going to
+
+ align:start position:0%
+problem. Um, because we're going to
+ 
+
+ align:start position:0%
+problem. Um, because we're going to
+build this thing called the syndication
+
+ align:start position:0%
+build this thing called the syndication
+ 
+
+ align:start position:0%
+build this thing called the syndication
+bus. Um and the syndication bus is gonna
+
+ align:start position:0%
+bus. Um and the syndication bus is gonna
+ 
+
+ align:start position:0%
+bus. Um and the syndication bus is gonna
+depend on this technology which how many
+
+ align:start position:0%
+depend on this technology which how many
+ 
+
+ align:start position:0%
+depend on this technology which how many
+of you are familiar with real simple
+
+ align:start position:0%
+of you are familiar with real simple
+ 
+
+ align:start position:0%
+of you are familiar with real simple
+syndication. Is that something that you
+
+ align:start position:0%
+syndication. Is that something that you
+ 
+
+ align:start position:0%
+syndication. Is that something that you
+like you like vaguely know exists? So
+
+ align:start position:0%
+like you like vaguely know exists? So
+ 
+
+ align:start position:0%
+like you like vaguely know exists? So
+again 10 or 15 years ago um this was
+
+ align:start position:0%
+again 10 or 15 years ago um this was
+ 
+
+ align:start position:0%
+again 10 or 15 years ago um this was
+considered like an essential part of the
+
+ align:start position:0%
+considered like an essential part of the
+ 
+
+ align:start position:0%
+considered like an essential part of the
+web and there are many people would have
+
+ align:start position:0%
+web and there are many people would have
+ 
+
+ align:start position:0%
+web and there are many people would have
+told you like this is the future of of
+
+ align:start position:0%
+told you like this is the future of of
+ 
+
+ align:start position:0%
+told you like this is the future of of
+how people will find things. So before
+
+ align:start position:0%
+how people will find things. So before
+ 
+
+ align:start position:0%
+how people will find things. So before
+um you know Jiren was telling us before
+
+ align:start position:0%
+um you know Jiren was telling us before
+ 
+
+ align:start position:0%
+um you know Jiren was telling us before
+about the YouTube algorithm kind of
+
+ align:start position:0%
+about the YouTube algorithm kind of
+ 
+
+ align:start position:0%
+about the YouTube algorithm kind of
+controlling what he watches and what he
+
+ align:start position:0%
+controlling what he watches and what he
+ 
+
+ align:start position:0%
+controlling what he watches and what he
+finds and things like that. An
+
+ align:start position:0%
+finds and things like that. An
+ 
+
+ align:start position:0%
+finds and things like that. An
+alternative to that was you subscribe to
+
+ align:start position:0%
+alternative to that was you subscribe to
+ 
+
+ align:start position:0%
+alternative to that was you subscribe to
+a series of feeds. Um so you would like
+
+ align:start position:0%
+a series of feeds. Um so you would like
+ 
+
+ align:start position:0%
+a series of feeds. Um so you would like
+find all the bloggers that you like or
+
+ align:start position:0%
+find all the bloggers that you like or
+ 
+
+ align:start position:0%
+find all the bloggers that you like or
+all the video bloggers you like or
+
+ align:start position:0%
+all the video bloggers you like or
+ 
+
+ align:start position:0%
+all the video bloggers you like or
+whatever else. You would choose their
+
+ align:start position:0%
+whatever else. You would choose their
+ 
+
+ align:start position:0%
+whatever else. You would choose their
+feeds and then you would have you know
+
+ align:start position:0%
+feeds and then you would have you know
+ 
+
+ align:start position:0%
+feeds and then you would have you know
+one really popular technology was called
+
+ align:start position:0%
+one really popular technology was called
+ 
+
+ align:start position:0%
+one really popular technology was called
+Google Reader which just gave you the
+
+ align:start position:0%
+Google Reader which just gave you the
+ 
+
+ align:start position:0%
+Google Reader which just gave you the
+things that came out of those feeds. So
+
+ align:start position:0%
+things that came out of those feeds. So
+ 
+
+ align:start position:0%
+things that came out of those feeds. So
+instead of instead of being sort of like
+
+ align:start position:0%
+instead of instead of being sort of like
+ 
+
+ align:start position:0%
+instead of instead of being sort of like
+bounced around by an algorithm to things
+
+ align:start position:0%
+bounced around by an algorithm to things
+ 
+
+ align:start position:0%
+bounced around by an algorithm to things
+that people think are popular,
+
+ align:start position:0%
+that people think are popular,
+ 
+
+ align:start position:0%
+that people think are popular,
+interesting and things like that um you
+
+ align:start position:0%
+interesting and things like that um you
+ 
+
+ align:start position:0%
+interesting and things like that um you
+sort of have more control over that. So
+
+ align:start position:0%
+sort of have more control over that. So
+ 
+
+ align:start position:0%
+sort of have more control over that. So
+basically what we did um was everyone
+
+ align:start position:0%
+basically what we did um was everyone
+ 
+
+ align:start position:0%
+basically what we did um was everyone
+would create their own online space and
+
+ align:start position:0%
+would create their own online space and
+ 
+
+ align:start position:0%
+would create their own online space and
+then we would use this signification bus
+
+ align:start position:0%
+then we would use this signification bus
+ 
+
+ align:start position:0%
+then we would use this signification bus
+to aggregate all those things. So
+
+ align:start position:0%
+to aggregate all those things. So
+ 
+
+ align:start position:0%
+to aggregate all those things. So
+effectively um we would oh there
+
+ align:start position:0%
+effectively um we would oh there
+ 
+
+ align:start position:0%
+effectively um we would oh there
+um there's an animation there that's
+
+ align:start position:0%
+um there's an animation there that's
+ 
+
+ align:start position:0%
+um there's an animation there that's
+missing. Um, we would make a copy of
+
+ align:start position:0%
+missing. Um, we would make a copy of
+ 
+
+ align:start position:0%
+missing. Um, we would make a copy of
+each of these pieces and we would pull
+
+ align:start position:0%
+each of these pieces and we would pull
+ 
+
+ align:start position:0%
+each of these pieces and we would pull
+the copy into the syndication bus. So,
+
+ align:start position:0%
+the copy into the syndication bus. So,
+ 
+
+ align:start position:0%
+the copy into the syndication bus. So,
+you owned your own thing, but we would
+
+ align:start position:0%
+you owned your own thing, but we would
+ 
+
+ align:start position:0%
+you owned your own thing, but we would
+use RSS to grab one copy of those
+
+ align:start position:0%
+use RSS to grab one copy of those
+ 
+
+ align:start position:0%
+use RSS to grab one copy of those
+things. Um, and then we would aggregate
+
+ align:start position:0%
+things. Um, and then we would aggregate
+ 
+
+ align:start position:0%
+things. Um, and then we would aggregate
+them in different kinds of ways. Um, so,
+
+ align:start position:0%
+them in different kinds of ways. Um, so,
+ 
+
+ align:start position:0%
+them in different kinds of ways. Um, so,
+um, imagine if every time you wrote in
+
+ align:start position:0%
+um, imagine if every time you wrote in
+ 
+
+ align:start position:0%
+um, imagine if every time you wrote in
+your learning journal, you didn't just
+
+ align:start position:0%
+your learning journal, you didn't just
+ 
+
+ align:start position:0%
+your learning journal, you didn't just
+write in your own Google Slides, um, but
+
+ align:start position:0%
+write in your own Google Slides, um, but
+ 
+
+ align:start position:0%
+write in your own Google Slides, um, but
+you wrote on a blog, um, anybody could
+
+ align:start position:0%
+you wrote on a blog, um, anybody could
+ 
+
+ align:start position:0%
+you wrote on a blog, um, anybody could
+subscribe to that blog, but the course
+
+ align:start position:0%
+subscribe to that blog, but the course
+ 
+
+ align:start position:0%
+subscribe to that blog, but the course
+subscribed to the blog. um and sort of
+
+ align:start position:0%
+subscribed to the blog. um and sort of
+ 
+
+ align:start position:0%
+subscribed to the blog. um and sort of
+hoovered all of those things up into one
+
+ align:start position:0%
+hoovered all of those things up into one
+ 
+
+ align:start position:0%
+hoovered all of those things up into one
+space. Um you could also um teach people
+
+ align:start position:0%
+space. Um you could also um teach people
+ 
+
+ align:start position:0%
+space. Um you could also um teach people
+other ways of aggregating things like
+
+ align:start position:0%
+other ways of aggregating things like
+ 
+
+ align:start position:0%
+other ways of aggregating things like
+anytime in any of the spaces that you're
+
+ align:start position:0%
+anytime in any of the spaces that you're
+ 
+
+ align:start position:0%
+anytime in any of the spaces that you're
+working you share something that we
+
+ align:start position:0%
+working you share something that we
+ 
+
+ align:start position:0%
+working you share something that we
+might be interested tag it with T509
+
+ align:start position:0%
+might be interested tag it with T509
+ 
+
+ align:start position:0%
+might be interested tag it with T509
+massive. Um and then what gets populated
+
+ align:start position:0%
+massive. Um and then what gets populated
+ 
+
+ align:start position:0%
+massive. Um and then what gets populated
+in this sort of syndication bust Twitter
+
+ align:start position:0%
+in this sort of syndication bust Twitter
+ 
+
+ align:start position:0%
+in this sort of syndication bust Twitter
+channel is like all the tweets that
+
+ align:start position:0%
+channel is like all the tweets that
+ 
+
+ align:start position:0%
+channel is like all the tweets that
+people have that are about T509 massive.
+
+ align:start position:0%
+people have that are about T509 massive.
+ 
+
+ align:start position:0%
+people have that are about T509 massive.
+Um there were
+
+ align:start position:0%
+Um there were
+ 
+
+ align:start position:0%
+Um there were
+uh the then um when you showed up on the
+
+ align:start position:0%
+uh the then um when you showed up on the
+ 
+
+ align:start position:0%
+uh the then um when you showed up on the
+homepage I as the instructor would pick
+
+ align:start position:0%
+homepage I as the instructor would pick
+ 
+
+ align:start position:0%
+homepage I as the instructor would pick
+a few of these things. So there was a
+
+ align:start position:0%
+a few of these things. So there was a
+ 
+
+ align:start position:0%
+a few of these things. So there was a
+section called the spotlight where I
+
+ align:start position:0%
+section called the spotlight where I
+ 
+
+ align:start position:0%
+section called the spotlight where I
+would sort of go through all the stuff
+
+ align:start position:0%
+would sort of go through all the stuff
+ 
+
+ align:start position:0%
+would sort of go through all the stuff
+that people were generating every week
+
+ align:start position:0%
+that people were generating every week
+ 
+
+ align:start position:0%
+that people were generating every week
+and pick a few things that I thought
+
+ align:start position:0%
+and pick a few things that I thought
+ 
+
+ align:start position:0%
+and pick a few things that I thought
+were like particularly interesting,
+
+ align:start position:0%
+were like particularly interesting,
+ 
+
+ align:start position:0%
+were like particularly interesting,
+particularly important, particularly
+
+ align:start position:0%
+particularly important, particularly
+ 
+
+ align:start position:0%
+particularly important, particularly
+funny, stuff like that, and sort of show
+
+ align:start position:0%
+funny, stuff like that, and sort of show
+ 
+
+ align:start position:0%
+funny, stuff like that, and sort of show
+them to people to feature them.
+
+ align:start position:0%
+them to people to feature them.
+ 
+
+ align:start position:0%
+them to people to feature them.
+Um and then uh that's probably kind of
+
+ align:start position:0%
+Um and then uh that's probably kind of
+ 
+
+ align:start position:0%
+Um and then uh that's probably kind of
+less important. Um, but then there were
+
+ align:start position:0%
+less important. Um, but then there were
+ 
+
+ align:start position:0%
+less important. Um, but then there were
+other spaces, you know, we I could
+
+ align:start position:0%
+other spaces, you know, we I could
+ 
+
+ align:start position:0%
+other spaces, you know, we I could
+create spaces that were about a
+
+ align:start position:0%
+create spaces that were about a
+ 
+
+ align:start position:0%
+create spaces that were about a
+particular assignment. Um, you could
+
+ align:start position:0%
+particular assignment. Um, you could
+ 
+
+ align:start position:0%
+particular assignment. Um, you could
+say, "Okay, everybody is working on your
+
+ align:start position:0%
+say, "Okay, everybody is working on your
+ 
+
+ align:start position:0%
+say, "Okay, everybody is working on your
+Oh, oh, I want to tell you about how I
+
+ align:start position:0%
+Oh, oh, I want to tell you about how I
+ 
+
+ align:start position:0%
+Oh, oh, I want to tell you about how I
+graded the class, but I could say,
+
+ align:start position:0%
+graded the class, but I could say,
+ 
+
+ align:start position:0%
+graded the class, but I could say,
+"Everybody create your rubric." Um, and
+
+ align:start position:0%
+"Everybody create your rubric." Um, and
+ 
+
+ align:start position:0%
+"Everybody create your rubric." Um, and
+then pull all of those things together,
+
+ align:start position:0%
+then pull all of those things together,
+ 
+
+ align:start position:0%
+then pull all of those things together,
+you know, like have a kind of rubric hub
+
+ align:start position:0%
+you know, like have a kind of rubric hub
+ 
+
+ align:start position:0%
+you know, like have a kind of rubric hub
+that everybody could see those things.
+
+ align:start position:0%
+that everybody could see those things.
+ 
+
+ align:start position:0%
+that everybody could see those things.
+And then we had a space, I think it was
+
+ align:start position:0%
+And then we had a space, I think it was
+ 
+
+ align:start position:0%
+And then we had a space, I think it was
+called the fire hose or something like
+
+ align:start position:0%
+called the fire hose or something like
+ 
+
+ align:start position:0%
+called the fire hose or something like
+that. Um, where it was everything that
+
+ align:start position:0%
+that. Um, where it was everything that
+ 
+
+ align:start position:0%
+that. Um, where it was everything that
+was coming in. Um there were probably 50
+
+ align:start position:0%
+was coming in. Um there were probably 50
+ 
+
+ align:start position:0%
+was coming in. Um there were probably 50
+or 60 people who took this version of
+
+ align:start position:0%
+or 60 people who took this version of
+ 
+
+ align:start position:0%
+or 60 people who took this version of
+the class and so there was no way that
+
+ align:start position:0%
+the class and so there was no way that
+ 
+
+ align:start position:0%
+the class and so there was no way that
+everybody was going to read everything
+
+ align:start position:0%
+everybody was going to read everything
+ 
+
+ align:start position:0%
+everybody was going to read everything
+that everyone else did but like a part
+
+ align:start position:0%
+that everyone else did but like a part
+ 
+
+ align:start position:0%
+that everyone else did but like a part
+of class every week was finding out um
+
+ align:start position:0%
+of class every week was finding out um
+ 
+
+ align:start position:0%
+of class every week was finding out um
+who are you connected with who are you
+
+ align:start position:0%
+who are you connected with who are you
+ 
+
+ align:start position:0%
+who are you connected with who are you
+finding interesting who are you learning
+
+ align:start position:0%
+finding interesting who are you learning
+ 
+
+ align:start position:0%
+finding interesting who are you learning
+from like oh you four were English
+
+ align:start position:0%
+from like oh you four were English
+ 
+
+ align:start position:0%
+from like oh you four were English
+teachers before you came in like this
+
+ align:start position:0%
+teachers before you came in like this
+ 
+
+ align:start position:0%
+teachers before you came in like this
+class like you should beworked with each
+
+ align:start position:0%
+class like you should beworked with each
+ 
+
+ align:start position:0%
+class like you should beworked with each
+other moreover you should beworked to
+
+ align:start position:0%
+other moreover you should beworked to
+ 
+
+ align:start position:0%
+other moreover you should beworked to
+other English teachers um the things
+
+ align:start position:0%
+other English teachers um the things
+ 
+
+ align:start position:0%
+other English teachers um the things
+that you're generating like if you're
+
+ align:start position:0%
+that you're generating like if you're
+ 
+
+ align:start position:0%
+that you're generating like if you're
+putting a bunch of work into this class
+
+ align:start position:0%
+putting a bunch of work into this class
+ 
+
+ align:start position:0%
+putting a bunch of work into this class
+why just have it sit in a, you know, in
+
+ align:start position:0%
+why just have it sit in a, you know, in
+ 
+
+ align:start position:0%
+why just have it sit in a, you know, in
+a discussion form that no one's ever
+
+ align:start position:0%
+a discussion form that no one's ever
+ 
+
+ align:start position:0%
+a discussion form that no one's ever
+going to see again, like put it in this
+
+ align:start position:0%
+going to see again, like put it in this
+ 
+
+ align:start position:0%
+going to see again, like put it in this
+space where you can share with other
+
+ align:start position:0%
+space where you can share with other
+ 
+
+ align:start position:0%
+space where you can share with other
+people and stuff like that. Um,
+
+ align:start position:0%
+people and stuff like that. Um,
+ 
+
+ align:start position:0%
+people and stuff like that. Um,
+uh,
+
+ align:start position:0%
+uh,
+ 
+
+ align:start position:0%
+uh,
+one, you know, if you if you if you if
+
+ align:start position:0%
+one, you know, if you if you if you if
+ 
+
+ align:start position:0%
+one, you know, if you if you if you if
+you take this idea, um, of letting
+
+ align:start position:0%
+you take this idea, um, of letting
+ 
+
+ align:start position:0%
+you take this idea, um, of letting
+people choose how they want to share who
+
+ align:start position:0%
+people choose how they want to share who
+ 
+
+ align:start position:0%
+people choose how they want to share who
+they want to connect with sort of
+
+ align:start position:0%
+they want to connect with sort of
+ 
+
+ align:start position:0%
+they want to connect with sort of
+seriously, the more and more you get to
+
+ align:start position:0%
+seriously, the more and more you get to
+ 
+
+ align:start position:0%
+seriously, the more and more you get to
+this idea of like there, you know,
+
+ align:start position:0%
+this idea of like there, you know,
+ 
+
+ align:start position:0%
+this idea of like there, you know,
+there's no right way to do this. Um,
+
+ align:start position:0%
+there's no right way to do this. Um,
+ 
+
+ align:start position:0%
+there's no right way to do this. Um,
+you're all coming into this class with
+
+ align:start position:0%
+you're all coming into this class with
+ 
+
+ align:start position:0%
+you're all coming into this class with
+different goals. Maybe some of you, you
+
+ align:start position:0%
+different goals. Maybe some of you, you
+ 
+
+ align:start position:0%
+different goals. Maybe some of you, you
+know, really want to connect with other
+
+ align:start position:0%
+know, really want to connect with other
+ 
+
+ align:start position:0%
+know, really want to connect with other
+edtech companies and are interested in
+
+ align:start position:0%
+edtech companies and are interested in
+ 
+
+ align:start position:0%
+edtech companies and are interested in
+being a founder or working for a
+
+ align:start position:0%
+being a founder or working for a
+ 
+
+ align:start position:0%
+being a founder or working for a
+startup. Maybe some of you want to go
+
+ align:start position:0%
+startup. Maybe some of you want to go
+ 
+
+ align:start position:0%
+startup. Maybe some of you want to go
+into education research. Maybe some want
+
+ align:start position:0%
+into education research. Maybe some want
+ 
+
+ align:start position:0%
+into education research. Maybe some want
+to go into teaching. Why should you all
+
+ align:start position:0%
+to go into teaching. Why should you all
+ 
+
+ align:start position:0%
+to go into teaching. Why should you all
+have the same criteria for what you're
+
+ align:start position:0%
+have the same criteria for what you're
+ 
+
+ align:start position:0%
+have the same criteria for what you're
+writing about or what you're sharing?
+
+ align:start position:0%
+writing about or what you're sharing?
+ 
+
+ align:start position:0%
+writing about or what you're sharing?
+Why don't you just tell me what it is
+
+ align:start position:0%
+Why don't you just tell me what it is
+ 
+
+ align:start position:0%
+Why don't you just tell me what it is
+that you want to learn about? Why don't
+
+ align:start position:0%
+that you want to learn about? Why don't
+ 
+
+ align:start position:0%
+that you want to learn about? Why don't
+you tell me what your goals are for this
+
+ align:start position:0%
+you tell me what your goals are for this
+ 
+
+ align:start position:0%
+you tell me what your goals are for this
+kind of communication? Um and so people
+
+ align:start position:0%
+kind of communication? Um and so people
+ 
+
+ align:start position:0%
+kind of communication? Um and so people
+would create uh their own rubrics about
+
+ align:start position:0%
+would create uh their own rubrics about
+ 
+
+ align:start position:0%
+would create uh their own rubrics about
+um you know essentially like you tell me
+
+ align:start position:0%
+um you know essentially like you tell me
+ 
+
+ align:start position:0%
+um you know essentially like you tell me
+what your blog is supposed to do
+
+ align:start position:0%
+what your blog is supposed to do
+ 
+
+ align:start position:0%
+what your blog is supposed to do
+supposed to accomplish. I think at one
+
+ align:start position:0%
+supposed to accomplish. I think at one
+ 
+
+ align:start position:0%
+supposed to accomplish. I think at one
+point um you know there was a part of
+
+ align:start position:0%
+point um you know there was a part of
+ 
+
+ align:start position:0%
+point um you know there was a part of
+the assignment which you had to say like
+
+ align:start position:0%
+the assignment which you had to say like
+ 
+
+ align:start position:0%
+the assignment which you had to say like
+describe how your writing is going to
+
+ align:start position:0%
+describe how your writing is going to
+ 
+
+ align:start position:0%
+describe how your writing is going to
+benefit you and your learning, how your
+
+ align:start position:0%
+benefit you and your learning, how your
+ 
+
+ align:start position:0%
+benefit you and your learning, how your
+writing is going to benefit the other
+
+ align:start position:0%
+writing is going to benefit the other
+ 
+
+ align:start position:0%
+writing is going to benefit the other
+people in this class and how your
+
+ align:start position:0%
+people in this class and how your
+ 
+
+ align:start position:0%
+people in this class and how your
+writing might plausibly benefit some
+
+ align:start position:0%
+writing might plausibly benefit some
+ 
+
+ align:start position:0%
+writing might plausibly benefit some
+other community somewhere else that
+
+ align:start position:0%
+other community somewhere else that
+ 
+
+ align:start position:0%
+other community somewhere else that
+you're connected to in some kind of way.
+
+ align:start position:0%
+you're connected to in some kind of way.
+ 
+
+ align:start position:0%
+you're connected to in some kind of way.
+This was a professional I taught this at
+
+ align:start position:0%
+This was a professional I taught this at
+ 
+
+ align:start position:0%
+This was a professional I taught this at
+the Harvard Graduate School of
+
+ align:start position:0%
+the Harvard Graduate School of
+ 
+
+ align:start position:0%
+the Harvard Graduate School of
+Education. So people were sort of for
+
+ align:start position:0%
+Education. So people were sort of for
+ 
+
+ align:start position:0%
+Education. So people were sort of for
+the most part already coming in with
+
+ align:start position:0%
+the most part already coming in with
+ 
+
+ align:start position:0%
+the most part already coming in with
+with some kind of professional
+
+ align:start position:0%
+with some kind of professional
+ 
+
+ align:start position:0%
+with some kind of professional
+communities from outside to to network.
+
+ align:start position:0%
+communities from outside to to network.
+ 
+
+ align:start position:0%
+communities from outside to to network.
+Um and
+
+ align:start position:0%
+Um and
+ 
+
+ align:start position:0%
+Um and
+um and there were there were lots of
+
+ align:start position:0%
+um and there were there were lots of
+ 
+
+ align:start position:0%
+um and there were there were lots of
+other people um who were doing this kind
+
+ align:start position:0%
+other people um who were doing this kind
+ 
+
+ align:start position:0%
+other people um who were doing this kind
+of thing. Um this was a course called
+
+ align:start position:0%
+of thing. Um this was a course called
+ 
+
+ align:start position:0%
+of thing. Um this was a course called
+connected courses which was basically
+
+ align:start position:0%
+connected courses which was basically
+ 
+
+ align:start position:0%
+connected courses which was basically
+teaching people across higher education
+
+ align:start position:0%
+teaching people across higher education
+ 
+
+ align:start position:0%
+teaching people across higher education
+how you would go about creating these
+
+ align:start position:0%
+how you would go about creating these
+ 
+
+ align:start position:0%
+how you would go about creating these
+courses. Um, but people built them in
+
+ align:start position:0%
+courses. Um, but people built them in
+ 
+
+ align:start position:0%
+courses. Um, but people built them in
+anthropology. You know, probably one of
+
+ align:start position:0%
+anthropology. You know, probably one of
+ 
+
+ align:start position:0%
+anthropology. You know, probably one of
+the most famous ones, which I think
+
+ align:start position:0%
+the most famous ones, which I think
+ 
+
+ align:start position:0%
+the most famous ones, which I think
+still has a bunch of stuff which exists,
+
+ align:start position:0%
+still has a bunch of stuff which exists,
+ 
+
+ align:start position:0%
+still has a bunch of stuff which exists,
+um, is called DS 106, digital
+
+ align:start position:0%
+um, is called DS 106, digital
+ 
+
+ align:start position:0%
+um, is called DS 106, digital
+storytelling 106, um, which was a course
+
+ align:start position:0%
+storytelling 106, um, which was a course
+ 
+
+ align:start position:0%
+storytelling 106, um, which was a course
+offered, um, at the University of Mary
+
+ align:start position:0%
+offered, um, at the University of Mary
+ 
+
+ align:start position:0%
+offered, um, at the University of Mary
+Washington, but like essentially
+
+ align:start position:0%
+Washington, but like essentially
+ 
+
+ align:start position:0%
+Washington, but like essentially
+syndicated to a bunch of other
+
+ align:start position:0%
+syndicated to a bunch of other
+ 
+
+ align:start position:0%
+syndicated to a bunch of other
+universities and also built in such a
+
+ align:start position:0%
+universities and also built in such a
+ 
+
+ align:start position:0%
+universities and also built in such a
+way I still, you can probably still go
+
+ align:start position:0%
+way I still, you can probably still go
+ 
+
+ align:start position:0%
+way I still, you can probably still go
+to ds 106.org right now. Um, and uh, it
+
+ align:start position:0%
+to ds 106.org right now. Um, and uh, it
+ 
+
+ align:start position:0%
+to ds 106.org right now. Um, and uh, it
+was mostly about creative assignments.
+
+ align:start position:0%
+was mostly about creative assignments.
+ 
+
+ align:start position:0%
+was mostly about creative assignments.
+Um, they had a uh they had a feature
+
+ align:start position:0%
+Um, they had a uh they had a feature
+ 
+
+ align:start position:0%
+Um, they had a uh they had a feature
+called the daily create where you know
+
+ align:start position:0%
+called the daily create where you know
+ 
+
+ align:start position:0%
+called the daily create where you know
+some if you took this class four days a
+
+ align:start position:0%
+some if you took this class four days a
+ 
+
+ align:start position:0%
+some if you took this class four days a
+week, you were supposed to do a daily
+
+ align:start position:0%
+week, you were supposed to do a daily
+ 
+
+ align:start position:0%
+week, you were supposed to do a daily
+create. It might be something like my
+
+ align:start position:0%
+create. It might be something like my
+ 
+
+ align:start position:0%
+create. It might be something like my
+favorite one was uh um pull out your
+
+ align:start position:0%
+favorite one was uh um pull out your
+ 
+
+ align:start position:0%
+favorite one was uh um pull out your
+keychain and make a short video where
+
+ align:start position:0%
+keychain and make a short video where
+ 
+
+ align:start position:0%
+keychain and make a short video where
+you tell the story of your keychain. Um
+
+ align:start position:0%
+you tell the story of your keychain. Um
+ 
+
+ align:start position:0%
+you tell the story of your keychain. Um
+where does each key come from? What does
+
+ align:start position:0%
+where does each key come from? What does
+ 
+
+ align:start position:0%
+where does each key come from? What does
+it mean to you? Other kinds of things
+
+ align:start position:0%
+it mean to you? Other kinds of things
+ 
+
+ align:start position:0%
+it mean to you? Other kinds of things
+like that. Um sort of figuring out how
+
+ align:start position:0%
+like that. Um sort of figuring out how
+ 
+
+ align:start position:0%
+like that. Um sort of figuring out how
+to make their way across the web.
+
+ align:start position:0%
+to make their way across the web.
+ 
+
+ align:start position:0%
+to make their way across the web.
+Um so I told you this was a story
+
+ align:start position:0%
+Um so I told you this was a story
+ 
+
+ align:start position:0%
+Um so I told you this was a story
+essentially of a failed enterprise. Um
+
+ align:start position:0%
+essentially of a failed enterprise. Um
+ 
+
+ align:start position:0%
+essentially of a failed enterprise. Um
+you won't f like clearly I'm not
+
+ align:start position:0%
+you won't f like clearly I'm not
+ 
+
+ align:start position:0%
+you won't f like clearly I'm not
+teaching like this anymore. Um you won't
+
+ align:start position:0%
+teaching like this anymore. Um you won't
+ 
+
+ align:start position:0%
+teaching like this anymore. Um you won't
+find many other classes. You'll find
+
+ align:start position:0%
+find many other classes. You'll find
+ 
+
+ align:start position:0%
+find many other classes. You'll find
+you'll find you know the ideas kind of
+
+ align:start position:0%
+you'll find you know the ideas kind of
+ 
+
+ align:start position:0%
+you'll find you know the ideas kind of
+out there percolating in different
+
+ align:start position:0%
+out there percolating in different
+ 
+
+ align:start position:0%
+out there percolating in different
+spaces. Um uh but like probably doesn't
+
+ align:start position:0%
+spaces. Um uh but like probably doesn't
+ 
+
+ align:start position:0%
+spaces. Um uh but like probably doesn't
+really exist. Um why did it fail?
+
+ align:start position:0%
+really exist. Um why did it fail?
+ 
+
+ align:start position:0%
+really exist. Um why did it fail?
+Probably two big reasons. Um one that
+
+ align:start position:0%
+Probably two big reasons. Um one that
+ 
+
+ align:start position:0%
+Probably two big reasons. Um one that
+we'll keep coming back to which I've
+
+ align:start position:0%
+we'll keep coming back to which I've
+ 
+
+ align:start position:0%
+we'll keep coming back to which I've
+termed the curse of the familiar which
+
+ align:start position:0%
+termed the curse of the familiar which
+ 
+
+ align:start position:0%
+termed the curse of the familiar which
+is it's just weird. Um, it's different.
+
+ align:start position:0%
+is it's just weird. Um, it's different.
+ 
+
+ align:start position:0%
+is it's just weird. Um, it's different.
+It's unusual. It takes a bunch of time
+
+ align:start position:0%
+It's unusual. It takes a bunch of time
+ 
+
+ align:start position:0%
+It's unusual. It takes a bunch of time
+to learn. On the one hand, I think
+
+ align:start position:0%
+to learn. On the one hand, I think
+ 
+
+ align:start position:0%
+to learn. On the one hand, I think
+people who are participating in these
+
+ align:start position:0%
+people who are participating in these
+ 
+
+ align:start position:0%
+people who are participating in these
+classes were like, "Ah man, I learned a
+
+ align:start position:0%
+classes were like, "Ah man, I learned a
+ 
+
+ align:start position:0%
+classes were like, "Ah man, I learned a
+lot of stuff about blogging, about using
+
+ align:start position:0%
+lot of stuff about blogging, about using
+ 
+
+ align:start position:0%
+lot of stuff about blogging, about using
+Twitter, about connecting with other
+
+ align:start position:0%
+Twitter, about connecting with other
+ 
+
+ align:start position:0%
+Twitter, about connecting with other
+people, about social networking." But
+
+ align:start position:0%
+people, about social networking." But
+ 
+
+ align:start position:0%
+people, about social networking." But
+like, you know, my guy the, you know,
+
+ align:start position:0%
+like, you know, my guy the, you know,
+ 
+
+ align:start position:0%
+like, you know, my guy the, you know,
+the the class was intermediate
+
+ align:start position:0%
+the the class was intermediate
+ 
+
+ align:start position:0%
+the the class was intermediate
+statistics. Like like that's not what
+
+ align:start position:0%
+statistics. Like like that's not what
+ 
+
+ align:start position:0%
+statistics. Like like that's not what
+you were supposed to be learning in this
+
+ align:start position:0%
+you were supposed to be learning in this
+ 
+
+ align:start position:0%
+you were supposed to be learning in this
+thing. Um there were a handful of
+
+ align:start position:0%
+thing. Um there were a handful of
+ 
+
+ align:start position:0%
+thing. Um there were a handful of
+universities that built a sort of
+
+ align:start position:0%
+universities that built a sort of
+ 
+
+ align:start position:0%
+universities that built a sort of
+collaborative infrastructure around this
+
+ align:start position:0%
+collaborative infrastructure around this
+ 
+
+ align:start position:0%
+collaborative infrastructure around this
+stuff in the hopes that you could drive
+
+ align:start position:0%
+stuff in the hopes that you could drive
+ 
+
+ align:start position:0%
+stuff in the hopes that you could drive
+down some of the complexity. So this guy
+
+ align:start position:0%
+down some of the complexity. So this guy
+ 
+
+ align:start position:0%
+down some of the complexity. So this guy
+Jim Groom built a company called Reclaim
+
+ align:start position:0%
+Jim Groom built a company called Reclaim
+ 
+
+ align:start position:0%
+Jim Groom built a company called Reclaim
+Hosting um which tried to make it really
+
+ align:start position:0%
+Hosting um which tried to make it really
+ 
+
+ align:start position:0%
+Hosting um which tried to make it really
+like universities could sign up to make
+
+ align:start position:0%
+like universities could sign up to make
+ 
+
+ align:start position:0%
+like universities could sign up to make
+it really easy for every student in the
+
+ align:start position:0%
+it really easy for every student in the
+ 
+
+ align:start position:0%
+it really easy for every student in the
+school to start a blog and then you like
+
+ align:start position:0%
+school to start a blog and then you like
+ 
+
+ align:start position:0%
+school to start a blog and then you like
+teach them all about blogging a little
+
+ align:start position:0%
+teach them all about blogging a little
+ 
+
+ align:start position:0%
+teach them all about blogging a little
+bit and then maybe you could get away
+
+ align:start position:0%
+bit and then maybe you could get away
+ 
+
+ align:start position:0%
+bit and then maybe you could get away
+from discussion forums and have people
+
+ align:start position:0%
+from discussion forums and have people
+ 
+
+ align:start position:0%
+from discussion forums and have people
+do more so of their short form writing
+
+ align:start position:0%
+do more so of their short form writing
+ 
+
+ align:start position:0%
+do more so of their short form writing
+on blogs. Um maybe there are some people
+
+ align:start position:0%
+on blogs. Um maybe there are some people
+ 
+
+ align:start position:0%
+on blogs. Um maybe there are some people
+out there that are still trying it but
+
+ align:start position:0%
+out there that are still trying it but
+ 
+
+ align:start position:0%
+out there that are still trying it but
+uh but not that much. Um and then
+
+ align:start position:0%
+uh but not that much. Um and then
+ 
+
+ align:start position:0%
+uh but not that much. Um and then
+um uh another huge challenge with asking
+
+ align:start position:0%
+um uh another huge challenge with asking
+ 
+
+ align:start position:0%
+um uh another huge challenge with asking
+people to write publicly uh is that we
+
+ align:start position:0%
+people to write publicly uh is that we
+ 
+
+ align:start position:0%
+people to write publicly uh is that we
+are not all equally vulnerable to the
+
+ align:start position:0%
+are not all equally vulnerable to the
+ 
+
+ align:start position:0%
+are not all equally vulnerable to the
+consequences of um having our writing be
+
+ align:start position:0%
+consequences of um having our writing be
+ 
+
+ align:start position:0%
+consequences of um having our writing be
+read. Anybody recognize this person? Um
+
+ align:start position:0%
+read. Anybody recognize this person? Um
+ 
+
+ align:start position:0%
+read. Anybody recognize this person? Um
+she's a woman named uh Anita Sarassian
+
+ align:start position:0%
+she's a woman named uh Anita Sarassian
+ 
+
+ align:start position:0%
+she's a woman named uh Anita Sarassian
+um who uh um had a website called
+
+ align:start position:0%
+um who uh um had a website called
+ 
+
+ align:start position:0%
+um who uh um had a website called
+Feminist Frequency which uh um was sort
+
+ align:start position:0%
+Feminist Frequency which uh um was sort
+ 
+
+ align:start position:0%
+Feminist Frequency which uh um was sort
+of one of one of the initial spaces that
+
+ align:start position:0%
+of one of one of the initial spaces that
+ 
+
+ align:start position:0%
+of one of one of the initial spaces that
+was related to um what became Gamergate.
+
+ align:start position:0%
+was related to um what became Gamergate.
+ 
+
+ align:start position:0%
+was related to um what became Gamergate.
+Um she uh she made a bunch of videos
+
+ align:start position:0%
+Um she uh she made a bunch of videos
+ 
+
+ align:start position:0%
+Um she uh she made a bunch of videos
+basically about sort of anti-feminist
+
+ align:start position:0%
+basically about sort of anti-feminist
+ 
+
+ align:start position:0%
+basically about sort of anti-feminist
+themes in video games like how uh um how
+
+ align:start position:0%
+themes in video games like how uh um how
+ 
+
+ align:start position:0%
+themes in video games like how uh um how
+like you know there's always a princess
+
+ align:start position:0%
+like you know there's always a princess
+ 
+
+ align:start position:0%
+like you know there's always a princess
+that needs to be saved and the princess
+
+ align:start position:0%
+that needs to be saved and the princess
+ 
+
+ align:start position:0%
+that needs to be saved and the princess
+doesn't actually have to like doesn't
+
+ align:start position:0%
+doesn't actually have to like doesn't
+ 
+
+ align:start position:0%
+doesn't actually have to like doesn't
+get to have her own character and things
+
+ align:start position:0%
+get to have her own character and things
+ 
+
+ align:start position:0%
+get to have her own character and things
+like that. Um and uh just you know piled
+
+ align:start position:0%
+like that. Um and uh just you know piled
+ 
+
+ align:start position:0%
+like that. Um and uh just you know piled
+on ruthlessly um by by all kinds of
+
+ align:start position:0%
+on ruthlessly um by by all kinds of
+ 
+
+ align:start position:0%
+on ruthlessly um by by all kinds of
+people you know especially people who
+
+ align:start position:0%
+people you know especially people who
+ 
+
+ align:start position:0%
+people you know especially people who
+who saw gaming as a hobby who didn't
+
+ align:start position:0%
+who saw gaming as a hobby who didn't
+ 
+
+ align:start position:0%
+who saw gaming as a hobby who didn't
+want these tropes changed. Um, and so
+
+ align:start position:0%
+want these tropes changed. Um, and so
+ 
+
+ align:start position:0%
+want these tropes changed. Um, and so
+you know, people get doxed and swatted
+
+ align:start position:0%
+you know, people get doxed and swatted
+ 
+
+ align:start position:0%
+you know, people get doxed and swatted
+and all kinds of Are you all familiar
+
+ align:start position:0%
+and all kinds of Are you all familiar
+ 
+
+ align:start position:0%
+and all kinds of Are you all familiar
+with Gamergate? Is that a phrase? Okay.
+
+ align:start position:0%
+with Gamergate? Is that a phrase? Okay.
+ 
+
+ align:start position:0%
+with Gamergate? Is that a phrase? Okay.
+Um, so I don't even remember what year
+
+ align:start position:0%
+Um, so I don't even remember what year
+ 
+
+ align:start position:0%
+Um, so I don't even remember what year
+this was now, but uh um I don't know. We
+
+ align:start position:0%
+this was now, but uh um I don't know. We
+ 
+
+ align:start position:0%
+this was now, but uh um I don't know. We
+should in the media studies department,
+
+ align:start position:0%
+should in the media studies department,
+ 
+
+ align:start position:0%
+should in the media studies department,
+we should be teaching a class called
+
+ align:start position:0%
+we should be teaching a class called
+ 
+
+ align:start position:0%
+we should be teaching a class called
+Gamergate. It was it was kind of um it
+
+ align:start position:0%
+Gamergate. It was it was kind of um it
+ 
+
+ align:start position:0%
+Gamergate. It was it was kind of um it
+seemed ludicrous at the time, but it was
+
+ align:start position:0%
+seemed ludicrous at the time, but it was
+ 
+
+ align:start position:0%
+seemed ludicrous at the time, but it was
+uh it was a sort of way of you know
+
+ align:start position:0%
+uh it was a sort of way of you know
+ 
+
+ align:start position:0%
+uh it was a sort of way of you know
+organizing groups of people to
+
+ align:start position:0%
+organizing groups of people to
+ 
+
+ align:start position:0%
+organizing groups of people to
+effectively suppress communication from
+
+ align:start position:0%
+effectively suppress communication from
+ 
+
+ align:start position:0%
+effectively suppress communication from
+sort of subalter perspectives from
+
+ align:start position:0%
+sort of subalter perspectives from
+ 
+
+ align:start position:0%
+sort of subalter perspectives from
+people who are trying to say different
+
+ align:start position:0%
+people who are trying to say different
+ 
+
+ align:start position:0%
+people who are trying to say different
+kinds of things. Um, so yeah, anyway,
+
+ align:start position:0%
+kinds of things. Um, so yeah, anyway,
+ 
+
+ align:start position:0%
+kinds of things. Um, so yeah, anyway,
+for me as like a pretty privileged white
+
+ align:start position:0%
+for me as like a pretty privileged white
+ 
+
+ align:start position:0%
+for me as like a pretty privileged white
+dude like blogging my way through the
+
+ align:start position:0%
+dude like blogging my way through the
+ 
+
+ align:start position:0%
+dude like blogging my way through the
+world is relatively safe and relatively
+
+ align:start position:0%
+world is relatively safe and relatively
+ 
+
+ align:start position:0%
+world is relatively safe and relatively
+straightforward, but you know, if I have
+
+ align:start position:0%
+straightforward, but you know, if I have
+ 
+
+ align:start position:0%
+straightforward, but you know, if I have
+50 or 60 students in my class, they're
+
+ align:start position:0%
+50 or 60 students in my class, they're
+ 
+
+ align:start position:0%
+50 or 60 students in my class, they're
+all going to be coming from different
+
+ align:start position:0%
+all going to be coming from different
+ 
+
+ align:start position:0%
+all going to be coming from different
+perspectives and they're all going to be
+
+ align:start position:0%
+perspectives and they're all going to be
+ 
+
+ align:start position:0%
+perspectives and they're all going to be
+sort of inequitably vulnerable um to
+
+ align:start position:0%
+sort of inequitably vulnerable um to
+ 
+
+ align:start position:0%
+sort of inequitably vulnerable um to
+writing something which catches the
+
+ align:start position:0%
+writing something which catches the
+ 
+
+ align:start position:0%
+writing something which catches the
+attention in negative ways of big crowds
+
+ align:start position:0%
+attention in negative ways of big crowds
+ 
+
+ align:start position:0%
+attention in negative ways of big crowds
+um or offends people or messes up their
+
+ align:start position:0%
+um or offends people or messes up their
+ 
+
+ align:start position:0%
+um or offends people or messes up their
+relationship or other kinds of things. I
+
+ align:start position:0%
+relationship or other kinds of things. I
+ 
+
+ align:start position:0%
+relationship or other kinds of things. I
+mean, what part of what you want to do
+
+ align:start position:0%
+mean, what part of what you want to do
+ 
+
+ align:start position:0%
+mean, what part of what you want to do
+in writing in a class is let people be
+
+ align:start position:0%
+in writing in a class is let people be
+ 
+
+ align:start position:0%
+in writing in a class is let people be
+experimental and try on ideas that they
+
+ align:start position:0%
+experimental and try on ideas that they
+ 
+
+ align:start position:0%
+experimental and try on ideas that they
+don't agree with yet or don't understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yet, you know, and in when I was doing
+
+ align:start position:0%
+yet, you know, and in when I was doing
+ 
+
+ align:start position:0%
+yet, you know, and in when I was doing
+this in 2013, that felt like a little
+
+ align:start position:0%
+this in 2013, that felt like a little
+ 
+
+ align:start position:0%
+this in 2013, that felt like a little
+bit risky, maybe like yeah, I could I
+
+ align:start position:0%
+bit risky, maybe like yeah, I could I
+ 
+
+ align:start position:0%
+bit risky, maybe like yeah, I could I
+could imagine someone might like take
+
+ align:start position:0%
+could imagine someone might like take
+ 
+
+ align:start position:0%
+could imagine someone might like take
+down a post that they, you know, decide
+
+ align:start position:0%
+down a post that they, you know, decide
+ 
+
+ align:start position:0%
+down a post that they, you know, decide
+wasn't well worded or disagree with
+
+ align:start position:0%
+wasn't well worded or disagree with
+ 
+
+ align:start position:0%
+wasn't well worded or disagree with
+things like that. Um, in 2024, it seems
+
+ align:start position:0%
+things like that. Um, in 2024, it seems
+ 
+
+ align:start position:0%
+things like that. Um, in 2024, it seems
+substantially um more risky. Not not I
+
+ align:start position:0%
+substantially um more risky. Not not I
+ 
+
+ align:start position:0%
+substantially um more risky. Not not I
+would say not just because um of
+
+ align:start position:0%
+would say not just because um of
+ 
+
+ align:start position:0%
+would say not just because um of
+heightened sensitivities um but because
+
+ align:start position:0%
+heightened sensitivities um but because
+ 
+
+ align:start position:0%
+heightened sensitivities um but because
+you know because actors in society have
+
+ align:start position:0%
+you know because actors in society have
+ 
+
+ align:start position:0%
+you know because actors in society have
+learned how to
+
+ align:start position:0%
+learned how to
+ 
+
+ align:start position:0%
+learned how to
+um how to how to broadcast messages that
+
+ align:start position:0%
+um how to how to broadcast messages that
+ 
+
+ align:start position:0%
+um how to how to broadcast messages that
+appear online in various kinds of places
+
+ align:start position:0%
+appear online in various kinds of places
+ 
+
+ align:start position:0%
+appear online in various kinds of places
+um and to use them to generate outrage
+
+ align:start position:0%
+um and to use them to generate outrage
+ 
+
+ align:start position:0%
+um and to use them to generate outrage
+and drive traffic and and those kinds of
+
+ align:start position:0%
+and drive traffic and and those kinds of
+ 
+
+ align:start position:0%
+and drive traffic and and those kinds of
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+Um, oh, this was the company, uh,
+
+ align:start position:0%
+Um, oh, this was the company, uh,
+ 
+
+ align:start position:0%
+Um, oh, this was the company, uh,
+Reclaim Hosting. Um, and they're, uh,
+
+ align:start position:0%
+Reclaim Hosting. Um, and they're, uh,
+ 
+
+ align:start position:0%
+Reclaim Hosting. Um, and they're, uh,
+somebody should Google Reclaim Hosting
+
+ align:start position:0%
+somebody should Google Reclaim Hosting
+ 
+
+ align:start position:0%
+somebody should Google Reclaim Hosting
+and see if they're they're still, um,
+
+ align:start position:0%
+and see if they're they're still, um,
+ 
+
+ align:start position:0%
+and see if they're they're still, um,
+uh, known for education was a was a
+
+ align:start position:0%
+uh, known for education was a was a
+ 
+
+ align:start position:0%
+uh, known for education was a was a
+project that was basically it was sort
+
+ align:start position:0%
+project that was basically it was sort
+ 
+
+ align:start position:0%
+project that was basically it was sort
+of trying to take like everything that I
+
+ align:start position:0%
+of trying to take like everything that I
+ 
+
+ align:start position:0%
+of trying to take like everything that I
+just described and figure out like how
+
+ align:start position:0%
+just described and figure out like how
+ 
+
+ align:start position:0%
+just described and figure out like how
+do you make a really simple front end
+
+ align:start position:0%
+do you make a really simple front end
+ 
+
+ align:start position:0%
+do you make a really simple front end
+for it so it's not hard for people to
+
+ align:start position:0%
+for it so it's not hard for people to
+ 
+
+ align:start position:0%
+for it so it's not hard for people to
+build, but it still lets people own
+
+ align:start position:0%
+build, but it still lets people own
+ 
+
+ align:start position:0%
+build, but it still lets people own
+stuff. um it still lets people sort of
+
+ align:start position:0%
+stuff. um it still lets people sort of
+ 
+
+ align:start position:0%
+stuff. um it still lets people sort of
+you know be the be the owner of their
+
+ align:start position:0%
+you know be the be the owner of their
+ 
+
+ align:start position:0%
+you know be the be the owner of their
+own means of production.
+
+ align:start position:0%
+own means of production.
+ 
+
+ align:start position:0%
+own means of production.
+Um but it's something that I think will
+
+ align:start position:0%
+Um but it's something that I think will
+ 
+
+ align:start position:0%
+Um but it's something that I think will
+um this was you know by far the most
+
+ align:start position:0%
+um this was you know by far the most
+ 
+
+ align:start position:0%
+um this was you know by far the most
+exciting part of teaching these courses
+
+ align:start position:0%
+exciting part of teaching these courses
+ 
+
+ align:start position:0%
+exciting part of teaching these courses
+was realizing that people were still
+
+ align:start position:0%
+was realizing that people were still
+ 
+
+ align:start position:0%
+was realizing that people were still
+using this infrastructure in various
+
+ align:start position:0%
+using this infrastructure in various
+ 
+
+ align:start position:0%
+using this infrastructure in various
+kinds of ways years after the course
+
+ align:start position:0%
+kinds of ways years after the course
+ 
+
+ align:start position:0%
+kinds of ways years after the course
+ended. So I think I taught this course
+
+ align:start position:0%
+ended. So I think I taught this course
+ 
+
+ align:start position:0%
+ended. So I think I taught this course
+in 2013 and still in 2015 people were
+
+ align:start position:0%
+in 2013 and still in 2015 people were
+ 
+
+ align:start position:0%
+in 2013 and still in 2015 people were
+posting on their blogs connecting with
+
+ align:start position:0%
+posting on their blogs connecting with
+ 
+
+ align:start position:0%
+posting on their blogs connecting with
+each other like you know I don't know
+
+ align:start position:0%
+each other like you know I don't know
+ 
+
+ align:start position:0%
+each other like you know I don't know
+the equivalent of that would be like you
+
+ align:start position:0%
+the equivalent of that would be like you
+ 
+
+ align:start position:0%
+the equivalent of that would be like you
+know if you're in 1806 now and it has a
+
+ align:start position:0%
+know if you're in 1806 now and it has a
+ 
+
+ align:start position:0%
+know if you're in 1806 now and it has a
+piaza forum what if three years from now
+
+ align:start position:0%
+piaza forum what if three years from now
+ 
+
+ align:start position:0%
+piaza forum what if three years from now
+you were inspired to like hop back in
+
+ align:start position:0%
+you were inspired to like hop back in
+ 
+
+ align:start position:0%
+you were inspired to like hop back in
+there and
+
+ align:start position:0%
+there and
+ 
+
+ align:start position:0%
+there and
+still like good god I would never do
+
+ align:start position:0%
+still like good god I would never do
+ 
+
+ align:start position:0%
+still like good god I would never do
+such a thing but part you know you
+
+ align:start position:0%
+such a thing but part you know you
+ 
+
+ align:start position:0%
+such a thing but part you know you
+wouldn't do such a thing because you
+
+ align:start position:0%
+wouldn't do such a thing because you
+ 
+
+ align:start position:0%
+wouldn't do such a thing because you
+don't own it and it's not yours and you
+
+ align:start position:0%
+don't own it and it's not yours and you
+ 
+
+ align:start position:0%
+don't own it and it's not yours and you
+can't take it in the direction that
+
+ align:start position:0%
+can't take it in the direction that
+ 
+
+ align:start position:0%
+can't take it in the direction that
+you're interested in. But if we, you
+
+ align:start position:0%
+you're interested in. But if we, you
+ 
+
+ align:start position:0%
+you're interested in. But if we, you
+know, in higher education, if we gave
+
+ align:start position:0%
+know, in higher education, if we gave
+ 
+
+ align:start position:0%
+know, in higher education, if we gave
+you an infrastructure that you had some
+
+ align:start position:0%
+you an infrastructure that you had some
+ 
+
+ align:start position:0%
+you an infrastructure that you had some
+control over, um, you might be
+
+ align:start position:0%
+control over, um, you might be
+ 
+
+ align:start position:0%
+control over, um, you might be
+substantially more, I mean, at least the
+
+ align:start position:0%
+substantially more, I mean, at least the
+ 
+
+ align:start position:0%
+substantially more, I mean, at least the
+students at the time were, um, were were
+
+ align:start position:0%
+students at the time were, um, were were
+ 
+
+ align:start position:0%
+students at the time were, um, were were
+interested in in continuing to pursue
+
+ align:start position:0%
+interested in in continuing to pursue
+ 
+
+ align:start position:0%
+interested in in continuing to pursue
+these kinds of, uh, these kinds of
+
+ align:start position:0%
+these kinds of, uh, these kinds of
+ 
+
+ align:start position:0%
+these kinds of, uh, these kinds of
+learning experiences.
+
+ align:start position:0%
+learning experiences.
+ 
+
+ align:start position:0%
+learning experiences.
+Um but I would but I would say the sort
+
+ align:start position:0%
+Um but I would but I would say the sort
+ 
+
+ align:start position:0%
+Um but I would but I would say the sort
+of the the the degree to which people
+
+ align:start position:0%
+of the the the degree to which people
+ 
+
+ align:start position:0%
+of the the the degree to which people
+feel much more individual threat about
+
+ align:start position:0%
+feel much more individual threat about
+ 
+
+ align:start position:0%
+feel much more individual threat about
+sharing things um online especially in
+
+ align:start position:0%
+sharing things um online especially in
+ 
+
+ align:start position:0%
+sharing things um online especially in
+really sort of open spaces. Um and just
+
+ align:start position:0%
+really sort of open spaces. Um and just
+ 
+
+ align:start position:0%
+really sort of open spaces. Um and just
+the like difficulty of the ramp up time
+
+ align:start position:0%
+the like difficulty of the ramp up time
+ 
+
+ align:start position:0%
+the like difficulty of the ramp up time
+of building all this infrastructure has
+
+ align:start position:0%
+of building all this infrastructure has
+ 
+
+ align:start position:0%
+of building all this infrastructure has
+made it like more or less um an
+
+ align:start position:0%
+made it like more or less um an
+ 
+
+ align:start position:0%
+made it like more or less um an
+interesting dead end and something kind
+
+ align:start position:0%
+interesting dead end and something kind
+ 
+
+ align:start position:0%
+interesting dead end and something kind
+of fun to learn from and explore. It
+
+ align:start position:0%
+of fun to learn from and explore. It
+ 
+
+ align:start position:0%
+of fun to learn from and explore. It
+probably also illustrates um more of
+
+ align:start position:0%
+probably also illustrates um more of
+ 
+
+ align:start position:0%
+probably also illustrates um more of
+what you'll read about. This is like an
+
+ align:start position:0%
+what you'll read about. This is like an
+ 
+
+ align:start position:0%
+what you'll read about. This is like an
+effort in higher education that
+
+ align:start position:0%
+effort in higher education that
+ 
+
+ align:start position:0%
+effort in higher education that
+basically foundered. Um you'll read
+
+ align:start position:0%
+basically foundered. Um you'll read
+ 
+
+ align:start position:0%
+basically foundered. Um you'll read
+about other kinds of things that sort of
+
+ align:start position:0%
+about other kinds of things that sort of
+ 
+
+ align:start position:0%
+about other kinds of things that sort of
+foundered in different ways in K12 or
+
+ align:start position:0%
+foundered in different ways in K12 or
+ 
+
+ align:start position:0%
+foundered in different ways in K12 or
+the challenge to make them not founder
+
+ align:start position:0%
+the challenge to make them not founder
+ 
+
+ align:start position:0%
+the challenge to make them not founder
+for next week. Like there's all this
+
+ align:start position:0%
+for next week. Like there's all this
+ 
+
+ align:start position:0%
+for next week. Like there's all this
+amazing learning that happens um in
+
+ align:start position:0%
+amazing learning that happens um in
+ 
+
+ align:start position:0%
+amazing learning that happens um in
+people's informal learning experiences.
+
+ align:start position:0%
+people's informal learning experiences.
+ 
+
+ align:start position:0%
+people's informal learning experiences.
+How do we why is it so hard to bring
+
+ align:start position:0%
+How do we why is it so hard to bring
+ 
+
+ align:start position:0%
+How do we why is it so hard to bring
+those practices into school
+
+ align:start position:0%
+those practices into school
+ 
+
+ align:start position:0%
+those practices into school
+environments? What is the nature of
+
+ align:start position:0%
+environments? What is the nature of
+ 
+
+ align:start position:0%
+environments? What is the nature of
+school environments um that makes it
+
+ align:start position:0%
+school environments um that makes it
+ 
+
+ align:start position:0%
+school environments um that makes it
+difficult for that to happen?
+
+ align:start position:0%
+difficult for that to happen?
+ 
+
+ align:start position:0%
+difficult for that to happen?
+Um good. What qu maybe I think that's
+
+ align:start position:0%
+Um good. What qu maybe I think that's
+ 
+
+ align:start position:0%
+Um good. What qu maybe I think that's
+where I got to the end. what questions
+
+ align:start position:0%
+where I got to the end. what questions
+ 
+
+ align:start position:0%
+where I got to the end. what questions
+do folks have or what um um my question
+
+ align:start position:0%
+do folks have or what um um my question
+ 
+
+ align:start position:0%
+do folks have or what um um my question
+is um what place kind of does um like
+
+ align:start position:0%
+is um what place kind of does um like
+ 
+
+ align:start position:0%
+is um what place kind of does um like
+kind of online community building
+
+ align:start position:0%
+kind of online community building
+ 
+
+ align:start position:0%
+kind of online community building
+without the presence of like instructors
+
+ align:start position:0%
+without the presence of like instructors
+ 
+
+ align:start position:0%
+without the presence of like instructors
+have in this
+
+ align:start position:0%
+have in this
+ 
+
+ align:start position:0%
+have in this
+yeah if it was if if this worked
+
+ align:start position:0%
+yeah if it was if if this worked
+ 
+
+ align:start position:0%
+yeah if it was if if this worked
+um because you owned your own piece of
+
+ align:start position:0%
+um because you owned your own piece of
+ 
+
+ align:start position:0%
+um because you owned your own piece of
+writing you know I'm teaching this class
+
+ align:start position:0%
+writing you know I'm teaching this class
+ 
+
+ align:start position:0%
+writing you know I'm teaching this class
+at a professional school um you might
+
+ align:start position:0%
+at a professional school um you might
+ 
+
+ align:start position:0%
+at a professional school um you might
+find that actually what motivates you
+
+ align:start position:0%
+find that actually what motivates you
+ 
+
+ align:start position:0%
+find that actually what motivates you
+most to write these assignments is that
+
+ align:start position:0%
+most to write these assignments is that
+ 
+
+ align:start position:0%
+most to write these assignments is that
+you've found a bunch of other sixth
+
+ align:start position:0%
+you've found a bunch of other sixth
+ 
+
+ align:start position:0%
+you've found a bunch of other sixth
+grade science teachers that are reading
+
+ align:start position:0%
+grade science teachers that are reading
+ 
+
+ align:start position:0%
+grade science teachers that are reading
+your blog posts and you sort of
+
+ align:start position:0%
+your blog posts and you sort of
+ 
+
+ align:start position:0%
+your blog posts and you sort of
+increasingly care less that you know
+
+ align:start position:0%
+increasingly care less that you know
+ 
+
+ align:start position:0%
+increasingly care less that you know
+Justin the instructor of this class is
+
+ align:start position:0%
+Justin the instructor of this class is
+ 
+
+ align:start position:0%
+Justin the instructor of this class is
+reading your stuff and more like hey I'm
+
+ align:start position:0%
+reading your stuff and more like hey I'm
+ 
+
+ align:start position:0%
+reading your stuff and more like hey I'm
+getting my ideas out there and
+
+ align:start position:0%
+getting my ideas out there and
+ 
+
+ align:start position:0%
+getting my ideas out there and
+connecting more with other earth science
+
+ align:start position:0%
+connecting more with other earth science
+ 
+
+ align:start position:0%
+connecting more with other earth science
+teachers. Um and that I think for a lot
+
+ align:start position:0%
+teachers. Um and that I think for a lot
+ 
+
+ align:start position:0%
+teachers. Um and that I think for a lot
+of you know when it was most successful
+
+ align:start position:0%
+of you know when it was most successful
+ 
+
+ align:start position:0%
+of you know when it was most successful
+that for people just felt like work that
+
+ align:start position:0%
+that for people just felt like work that
+ 
+
+ align:start position:0%
+that for people just felt like work that
+was super real and urgent. Um you know
+
+ align:start position:0%
+was super real and urgent. Um you know
+ 
+
+ align:start position:0%
+was super real and urgent. Um you know
+the the other thing is most of the thing
+
+ align:start position:0%
+the the other thing is most of the thing
+ 
+
+ align:start position:0%
+the the other thing is most of the thing
+I don't know um when people got
+
+ align:start position:0%
+I don't know um when people got
+ 
+
+ align:start position:0%
+I don't know um when people got
+responses it it there there wasn't a
+
+ align:start position:0%
+responses it it there there wasn't a
+ 
+
+ align:start position:0%
+responses it it there there wasn't a
+whole lot of there's probably some but
+
+ align:start position:0%
+whole lot of there's probably some but
+ 
+
+ align:start position:0%
+whole lot of there's probably some but
+there wasn't a whole lot of like you are
+
+ align:start position:0%
+there wasn't a whole lot of like you are
+ 
+
+ align:start position:0%
+there wasn't a whole lot of like you are
+required to reply to at least two people
+
+ align:start position:0%
+required to reply to at least two people
+ 
+
+ align:start position:0%
+required to reply to at least two people
+um kinds of things. Um there was a lot
+
+ align:start position:0%
+um kinds of things. Um there was a lot
+ 
+
+ align:start position:0%
+um kinds of things. Um there was a lot
+of you know when like people would write
+
+ align:start position:0%
+of you know when like people would write
+ 
+
+ align:start position:0%
+of you know when like people would write
+blog posts but they would write blog
+
+ align:start position:0%
+blog posts but they would write blog
+ 
+
+ align:start position:0%
+blog posts but they would write blog
+posts that sort of tagged or or posted
+
+ align:start position:0%
+posts that sort of tagged or or posted
+ 
+
+ align:start position:0%
+posts that sort of tagged or or posted
+back to someone else's post. So it was
+
+ align:start position:0%
+back to someone else's post. So it was
+ 
+
+ align:start position:0%
+back to someone else's post. So it was
+just kind of like a natural um uh
+
+ align:start position:0%
+just kind of like a natural um uh
+ 
+
+ align:start position:0%
+just kind of like a natural um uh
+conversation that was that was happening
+
+ align:start position:0%
+conversation that was that was happening
+ 
+
+ align:start position:0%
+conversation that was that was happening
+and unfolding like where it was most
+
+ align:start position:0%
+and unfolding like where it was most
+ 
+
+ align:start position:0%
+and unfolding like where it was most
+successful
+
+ align:start position:0%
+successful
+ 
+
+ align:start position:0%
+successful
+um what you felt like as an instructor
+
+ align:start position:0%
+um what you felt like as an instructor
+ 
+
+ align:start position:0%
+um what you felt like as an instructor
+is you were you were just like put
+
+ align:start position:0%
+is you were you were just like put
+ 
+
+ align:start position:0%
+is you were you were just like put
+putting putting some fuel for this fire
+
+ align:start position:0%
+putting putting some fuel for this fire
+ 
+
+ align:start position:0%
+putting putting some fuel for this fire
+to burn on its own. you were just like,
+
+ align:start position:0%
+to burn on its own. you were just like,
+ 
+
+ align:start position:0%
+to burn on its own. you were just like,
+you know, here check out these things
+
+ align:start position:0%
+you know, here check out these things
+ 
+
+ align:start position:0%
+you know, here check out these things
+like, you know, and then but then people
+
+ align:start position:0%
+like, you know, and then but then people
+ 
+
+ align:start position:0%
+like, you know, and then but then people
+would take them in the directions that
+
+ align:start position:0%
+would take them in the directions that
+ 
+
+ align:start position:0%
+would take them in the directions that
+they were most interested and excited
+
+ align:start position:0%
+they were most interested and excited
+ 
+
+ align:start position:0%
+they were most interested and excited
+about. Does that answer your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question other thoughts or things that
+
+ align:start position:0%
+question other thoughts or things that
+ 
+
+ align:start position:0%
+question other thoughts or things that
+how does this play into the Google doc
+
+ align:start position:0%
+how does this play into the Google doc
+ 
+
+ align:start position:0%
+how does this play into the Google doc
+that runs this course? Huh? Yeah. So,
+
+ align:start position:0%
+that runs this course? Huh? Yeah. So,
+ 
+
+ align:start position:0%
+that runs this course? Huh? Yeah. So,
+well, some of it is I uh probably
+
+ align:start position:0%
+well, some of it is I uh probably
+ 
+
+ align:start position:0%
+well, some of it is I uh probably
+probably the main lingering piece um is
+
+ align:start position:0%
+probably the main lingering piece um is
+ 
+
+ align:start position:0%
+probably the main lingering piece um is
+that it's a is that it's a pain in the
+
+ align:start position:0%
+that it's a is that it's a pain in the
+ 
+
+ align:start position:0%
+that it's a is that it's a pain in the
+ass to show my Canvas site to someone
+
+ align:start position:0%
+ass to show my Canvas site to someone
+ 
+
+ align:start position:0%
+ass to show my Canvas site to someone
+else. And one of the main things that I
+
+ align:start position:0%
+else. And one of the main things that I
+ 
+
+ align:start position:0%
+else. And one of the main things that I
+want to do is, you know, I don't know,
+
+ align:start position:0%
+want to do is, you know, I don't know,
+ 
+
+ align:start position:0%
+want to do is, you know, I don't know,
+in in in my career of teaching is be
+
+ align:start position:0%
+in in in my career of teaching is be
+ 
+
+ align:start position:0%
+in in in my career of teaching is be
+able to like quickly to explain to other
+
+ align:start position:0%
+able to like quickly to explain to other
+ 
+
+ align:start position:0%
+able to like quickly to explain to other
+people how I teach. Um, so one, you
+
+ align:start position:0%
+people how I teach. Um, so one, you
+ 
+
+ align:start position:0%
+people how I teach. Um, so one, you
+know, one of the best things about
+
+ align:start position:0%
+know, one of the best things about
+ 
+
+ align:start position:0%
+know, one of the best things about
+having the whole course live on a Google
+
+ align:start position:0%
+having the whole course live on a Google
+ 
+
+ align:start position:0%
+having the whole course live on a Google
+doc is, you know, any new professor
+
+ align:start position:0%
+doc is, you know, any new professor
+ 
+
+ align:start position:0%
+doc is, you know, any new professor
+who's just starting teaching edtech and
+
+ align:start position:0%
+who's just starting teaching edtech and
+ 
+
+ align:start position:0%
+who's just starting teaching edtech and
+society, it's like here's a whole
+
+ align:start position:0%
+society, it's like here's a whole
+ 
+
+ align:start position:0%
+society, it's like here's a whole
+course, you know, take it and c I mean,
+
+ align:start position:0%
+course, you know, take it and c I mean,
+ 
+
+ align:start position:0%
+course, you know, take it and c I mean,
+they're probably taking it and like
+
+ align:start position:0%
+they're probably taking it and like
+ 
+
+ align:start position:0%
+they're probably taking it and like
+shoving it bit by bit into Canvas, which
+
+ align:start position:0%
+shoving it bit by bit into Canvas, which
+ 
+
+ align:start position:0%
+shoving it bit by bit into Canvas, which
+I've done periodically for some things.
+
+ align:start position:0%
+I've done periodically for some things.
+ 
+
+ align:start position:0%
+I've done periodically for some things.
+Um, that any of you, you know, who want
+
+ align:start position:0%
+Um, that any of you, you know, who want
+ 
+
+ align:start position:0%
+Um, that any of you, you know, who want
+to sign up for my, you know, future
+
+ align:start position:0%
+to sign up for my, you know, future
+ 
+
+ align:start position:0%
+to sign up for my, you know, future
+people who are interested in this class,
+
+ align:start position:0%
+people who are interested in this class,
+ 
+
+ align:start position:0%
+people who are interested in this class,
+you know, syllabus is there. You, you
+
+ align:start position:0%
+you know, syllabus is there. You, you
+ 
+
+ align:start position:0%
+you know, syllabus is there. You, you
+know, I mean, it's even got it's even
+
+ align:start position:0%
+know, I mean, it's even got it's even
+ 
+
+ align:start position:0%
+know, I mean, it's even got it's even
+got the revision history. You can now
+
+ align:start position:0%
+got the revision history. You can now
+ 
+
+ align:start position:0%
+got the revision history. You can now
+see, nobody does that, but you can now
+
+ align:start position:0%
+see, nobody does that, but you can now
+ 
+
+ align:start position:0%
+see, nobody does that, but you can now
+see what we did. I mean in I I would
+
+ align:start position:0%
+see what we did. I mean in I I would
+ 
+
+ align:start position:0%
+see what we did. I mean in I I would
+also say earlier versions of that like
+
+ align:start position:0%
+also say earlier versions of that like
+ 
+
+ align:start position:0%
+also say earlier versions of that like
+when the web was sort of more active in
+
+ align:start position:0%
+when the web was sort of more active in
+ 
+
+ align:start position:0%
+when the web was sort of more active in
+this way, you know, I would like over
+
+ align:start position:0%
+this way, you know, I would like over
+ 
+
+ align:start position:0%
+this way, you know, I would like over
+the summer I would post like here are
+
+ align:start position:0%
+the summer I would post like here are
+ 
+
+ align:start position:0%
+the summer I would post like here are
+all the changes that I made to my
+
+ align:start position:0%
+all the changes that I made to my
+ 
+
+ align:start position:0%
+all the changes that I made to my
+syllabus and like circulated around to
+
+ align:start position:0%
+syllabus and like circulated around to
+ 
+
+ align:start position:0%
+syllabus and like circulated around to
+hashtags or other networks of people
+
+ align:start position:0%
+hashtags or other networks of people
+ 
+
+ align:start position:0%
+hashtags or other networks of people
+that were active in those conversations
+
+ align:start position:0%
+that were active in those conversations
+ 
+
+ align:start position:0%
+that were active in those conversations
+and people would definitely jump in to
+
+ align:start position:0%
+and people would definitely jump in to
+ 
+
+ align:start position:0%
+and people would definitely jump in to
+the syllabus um and through and add
+
+ align:start position:0%
+the syllabus um and through and add
+ 
+
+ align:start position:0%
+the syllabus um and through and add
+comments and be like oh you this new
+
+ align:start position:0%
+comments and be like oh you this new
+ 
+
+ align:start position:0%
+comments and be like oh you this new
+book just came out or these new
+
+ align:start position:0%
+book just came out or these new
+ 
+
+ align:start position:0%
+book just came out or these new
+resources came out and things like that.
+
+ align:start position:0%
+resources came out and things like that.
+ 
+
+ align:start position:0%
+resources came out and things like that.
+I mean it existed as a for for a period
+
+ align:start position:0%
+I mean it existed as a for for a period
+ 
+
+ align:start position:0%
+I mean it existed as a for for a period
+of time a much more sort of social
+
+ align:start position:0%
+of time a much more sort of social
+ 
+
+ align:start position:0%
+of time a much more sort of social
+document. Um again when when yeah there
+
+ align:start position:0%
+document. Um again when when yeah there
+ 
+
+ align:start position:0%
+document. Um again when when yeah there
+were a lot of you know educators
+
+ align:start position:0%
+were a lot of you know educators
+ 
+
+ align:start position:0%
+were a lot of you know educators
+especially people interested in online
+
+ align:start position:0%
+especially people interested in online
+ 
+
+ align:start position:0%
+especially people interested in online
+learning and education technology who
+
+ align:start position:0%
+learning and education technology who
+ 
+
+ align:start position:0%
+learning and education technology who
+were pretty active in those kinds of
+
+ align:start position:0%
+were pretty active in those kinds of
+ 
+
+ align:start position:0%
+were pretty active in those kinds of
+communities. Um and so you could do
+
+ align:start position:0%
+communities. Um and so you could do
+ 
+
+ align:start position:0%
+communities. Um and so you could do
+stuff like that. Now it's mostly just a
+
+ align:start position:0%
+stuff like that. Now it's mostly just a
+ 
+
+ align:start position:0%
+stuff like that. Now it's mostly just a
+legacy of you know editing that thing is
+
+ align:start position:0%
+legacy of you know editing that thing is
+ 
+
+ align:start position:0%
+legacy of you know editing that thing is
+so much easier than editing canvas. Um
+
+ align:start position:0%
+so much easier than editing canvas. Um
+ 
+
+ align:start position:0%
+so much easier than editing canvas. Um
+anytime I want to change something in
+
+ align:start position:0%
+anytime I want to change something in
+ 
+
+ align:start position:0%
+anytime I want to change something in
+canvas I have to do it in three places
+
+ align:start position:0%
+canvas I have to do it in three places
+ 
+
+ align:start position:0%
+canvas I have to do it in three places
+and click 15 buttons like Google doc I
+
+ align:start position:0%
+and click 15 buttons like Google doc I
+ 
+
+ align:start position:0%
+and click 15 buttons like Google doc I
+just edit. Um good. So that was a little
+
+ align:start position:0%
+just edit. Um good. So that was a little
+ 
+
+ align:start position:0%
+just edit. Um good. So that was a little
+bit in uh some of these ideas of peer
+
+ align:start position:0%
+bit in uh some of these ideas of peer
+ 
+
+ align:start position:0%
+bit in uh some of these ideas of peer
+guided learning in higher education.
+
+ align:start position:0%
+guided learning in higher education.
+ 
+
+ align:start position:0%
+guided learning in higher education.
+We'll see some more of them. Um, in K12,
+
+ align:start position:0%
+We'll see some more of them. Um, in K12,
+ 
+
+ align:start position:0%
+We'll see some more of them. Um, in K12,
+I think you're going to read some stuff
+
+ align:start position:0%
+I think you're going to read some stuff
+ 
+
+ align:start position:0%
+I think you're going to read some stuff
+from Mimito and uh
+
+ align:start position:0%
+from Mimito and uh
+ 
+
+ align:start position:0%
+from Mimito and uh
+um what else did I make you do for next
+
+ align:start position:0%
+um what else did I make you do for next
+ 
+
+ align:start position:0%
+um what else did I make you do for next
+time? And and Mitch Resnik um about
+
+ align:start position:0%
+time? And and Mitch Resnik um about
+ 
+
+ align:start position:0%
+time? And and Mitch Resnik um about
+Scratch, which is Scratch is probably
+
+ align:start position:0%
+Scratch, which is Scratch is probably
+ 
+
+ align:start position:0%
+Scratch, which is Scratch is probably
+the um most successful peer-guided
+
+ align:start position:0%
+the um most successful peer-guided
+ 
+
+ align:start position:0%
+the um most successful peer-guided
+learning environment which has made its
+
+ align:start position:0%
+learning environment which has made its
+ 
+
+ align:start position:0%
+learning environment which has made its
+way into K12 schools. Although one of
+
+ align:start position:0%
+way into K12 schools. Although one of
+ 
+
+ align:start position:0%
+way into K12 schools. Although one of
+the things that we'll learn is that uh
+
+ align:start position:0%
+the things that we'll learn is that uh
+ 
+
+ align:start position:0%
+the things that we'll learn is that uh
+when it gets there it kind of gets uh
+
+ align:start position:0%
+when it gets there it kind of gets uh
+ 
+
+ align:start position:0%
+when it gets there it kind of gets uh
+schoolified in ways that are horrific to
+
+ align:start position:0%
+schoolified in ways that are horrific to
+ 
+
+ align:start position:0%
+schoolified in ways that are horrific to
+the people who made it. But uh more to
+
+ align:start position:0%
+the people who made it. But uh more to
+ 
+
+ align:start position:0%
+the people who made it. But uh more to
+follow when they discuss that uh on
+
+ align:start position:0%
+follow when they discuss that uh on
+ 
+
+ align:start position:0%
+follow when they discuss that uh on
+Monday. Great. Have a wonderful uh rest
+
+ align:start position:0%
+Monday. Great. Have a wonderful uh rest
+ 
+
+ align:start position:0%
+Monday. Great. Have a wonderful uh rest
+of your week and weekend and I will see
+
+ align:start position:0%
+of your week and weekend and I will see
+ 
+
+ align:start position:0%
+of your week and weekend and I will see
+you next week.
\ No newline at end of file
diff --git a/QCA3zOe2xdA.txt b/QCA3zOe2xdA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..128e65bd9c9f3da64337edd6af67af0ccba8e842
--- /dev/null
+++ b/QCA3zOe2xdA.txt
@@ -0,0 +1,1555 @@
+align:start position:0%
+ 
+we can consider a given coordinate
+
+ align:start position:0%
+we can consider a given coordinate
+ 
+
+ align:start position:0%
+we can consider a given coordinate
+system as a reference frame within which
+
+ align:start position:0%
+system as a reference frame within which
+ 
+
+ align:start position:0%
+system as a reference frame within which
+we can describe the kinematics of an
+
+ align:start position:0%
+we can describe the kinematics of an
+ 
+
+ align:start position:0%
+we can describe the kinematics of an
+object by the kinematics I mean the
+
+ align:start position:0%
+object by the kinematics I mean the
+ 
+
+ align:start position:0%
+object by the kinematics I mean the
+position the velocity and the
+
+ align:start position:0%
+position the velocity and the
+ 
+
+ align:start position:0%
+position the velocity and the
+acceleration as a function of time
+
+ align:start position:0%
+acceleration as a function of time
+ 
+
+ align:start position:0%
+acceleration as a function of time
+basically a geometric description of the
+
+ align:start position:0%
+basically a geometric description of the
+ 
+
+ align:start position:0%
+basically a geometric description of the
+motion some aspects of these kinematics
+
+ align:start position:0%
+motion some aspects of these kinematics
+ 
+
+ align:start position:0%
+motion some aspects of these kinematics
+will look different in different
+
+ align:start position:0%
+will look different in different
+ 
+
+ align:start position:0%
+will look different in different
+reference frames and I'd like to examine
+
+ align:start position:0%
+reference frames and I'd like to examine
+ 
+
+ align:start position:0%
+reference frames and I'd like to examine
+that now first I want to Define what I
+
+ align:start position:0%
+that now first I want to Define what I
+ 
+
+ align:start position:0%
+that now first I want to Define what I
+mean by an inertial reference frame an
+
+ align:start position:0%
+mean by an inertial reference frame an
+ 
+
+ align:start position:0%
+mean by an inertial reference frame an
+inertial reference frame is one in which
+
+ align:start position:0%
+inertial reference frame is one in which
+ 
+
+ align:start position:0%
+inertial reference frame is one in which
+an isolated body one with no net force
+
+ align:start position:0%
+an isolated body one with no net force
+ 
+
+ align:start position:0%
+an isolated body one with no net force
+acting on it moves at constant velocity
+
+ align:start position:0%
+acting on it moves at constant velocity
+ 
+
+ align:start position:0%
+acting on it moves at constant velocity
+where that constant velocity might be
+
+ align:start position:0%
+where that constant velocity might be
+ 
+
+ align:start position:0%
+where that constant velocity might be
+zero another way of saying this is that
+
+ align:start position:0%
+zero another way of saying this is that
+ 
+
+ align:start position:0%
+zero another way of saying this is that
+an inertial reference frame is one in
+
+ align:start position:0%
+an inertial reference frame is one in
+ 
+
+ align:start position:0%
+an inertial reference frame is one in
+which Newton's Laws of Motion apply
+
+ align:start position:0%
+which Newton's Laws of Motion apply
+ 
+
+ align:start position:0%
+which Newton's Laws of Motion apply
+recall that Newton's first law of motion
+
+ align:start position:0%
+recall that Newton's first law of motion
+ 
+
+ align:start position:0%
+recall that Newton's first law of motion
+states that an isolated object with no
+
+ align:start position:0%
+states that an isolated object with no
+ 
+
+ align:start position:0%
+states that an isolated object with no
+forces acting on it moves at constant
+
+ align:start position:0%
+forces acting on it moves at constant
+ 
+
+ align:start position:0%
+forces acting on it moves at constant
+velocity so let's begin by considering a
+
+ align:start position:0%
+velocity so let's begin by considering a
+ 
+
+ align:start position:0%
+velocity so let's begin by considering a
+an observer in a particular reference
+
+ align:start position:0%
+an observer in a particular reference
+ 
+
+ align:start position:0%
+an observer in a particular reference
+frame we'll call that reference frame s
+
+ align:start position:0%
+frame we'll call that reference frame s
+ 
+
+ align:start position:0%
+frame we'll call that reference frame s
+and denoted by uh cordoes X and Y
+
+ align:start position:0%
+and denoted by uh cordoes X and Y
+ 
+
+ align:start position:0%
+and denoted by uh cordoes X and Y
+and let's consider an
+
+ align:start position:0%
+and let's consider an
+ 
+
+ align:start position:0%
+and let's consider an
+object that in that in that reference
+
+ align:start position:0%
+object that in that in that reference
+ 
+
+ align:start position:0%
+object that in that in that reference
+frame is at a position Vector small R we
+
+ align:start position:0%
+frame is at a position Vector small R we
+ 
+
+ align:start position:0%
+frame is at a position Vector small R we
+can then consider a second reference
+
+ align:start position:0%
+can then consider a second reference
+ 
+
+ align:start position:0%
+can then consider a second reference
+frame which I'll call the frame S Prime
+
+ align:start position:0%
+frame which I'll call the frame S Prime
+ 
+
+ align:start position:0%
+frame which I'll call the frame S Prime
+and I'll denote that with coordinate
+
+ align:start position:0%
+and I'll denote that with coordinate
+ 
+
+ align:start position:0%
+and I'll denote that with coordinate
+axes X Prime and Y Prime in my example
+
+ align:start position:0%
+axes X Prime and Y Prime in my example
+ 
+
+ align:start position:0%
+axes X Prime and Y Prime in my example
+here I'm going to assume that the
+
+ align:start position:0%
+here I'm going to assume that the
+ 
+
+ align:start position:0%
+here I'm going to assume that the
+coordinate axes in frame S Prime are
+
+ align:start position:0%
+coordinate axes in frame S Prime are
+ 
+
+ align:start position:0%
+coordinate axes in frame S Prime are
+parallel to but displaced away from the
+
+ align:start position:0%
+parallel to but displaced away from the
+ 
+
+ align:start position:0%
+parallel to but displaced away from the
+coordinate axes in frame s more
+
+ align:start position:0%
+coordinate axes in frame s more
+ 
+
+ align:start position:0%
+coordinate axes in frame s more
+generally we could have the S Prime
+
+ align:start position:0%
+generally we could have the S Prime
+ 
+
+ align:start position:0%
+generally we could have the S Prime
+coordinate axes rotated with respect to
+
+ align:start position:0%
+coordinate axes rotated with respect to
+ 
+
+ align:start position:0%
+coordinate axes rotated with respect to
+the frame s axis that's a complication
+
+ align:start position:0%
+the frame s axis that's a complication
+ 
+
+ align:start position:0%
+the frame s axis that's a complication
+I'm not going to add now but
+
+ align:start position:0%
+I'm not going to add now but
+ 
+
+ align:start position:0%
+I'm not going to add now but
+conceptually it's not really different
+
+ align:start position:0%
+conceptually it's not really different
+ 
+
+ align:start position:0%
+conceptually it's not really different
+for Simplicity we'll uh stick to
+
+ align:start position:0%
+for Simplicity we'll uh stick to
+ 
+
+ align:start position:0%
+for Simplicity we'll uh stick to
+parallel axes in this example so imagine
+
+ align:start position:0%
+parallel axes in this example so imagine
+ 
+
+ align:start position:0%
+parallel axes in this example so imagine
+we have two observers one in frame S at
+
+ align:start position:0%
+we have two observers one in frame S at
+ 
+
+ align:start position:0%
+we have two observers one in frame S at
+the origin and one at the origin of
+
+ align:start position:0%
+the origin and one at the origin of
+ 
+
+ align:start position:0%
+the origin and one at the origin of
+frame S Prime both looking at the same
+
+ align:start position:0%
+frame S Prime both looking at the same
+ 
+
+ align:start position:0%
+frame S Prime both looking at the same
+object Observer s will measure a
+
+ align:start position:0%
+object Observer s will measure a
+ 
+
+ align:start position:0%
+object Observer s will measure a
+position Vector little r Observer S
+
+ align:start position:0%
+position Vector little r Observer S
+ 
+
+ align:start position:0%
+position Vector little r Observer S
+Prime will measure a position Vector
+
+ align:start position:0%
+Prime will measure a position Vector
+ 
+
+ align:start position:0%
+Prime will measure a position Vector
+little r Prime the two observers have a
+
+ align:start position:0%
+little r Prime the two observers have a
+ 
+
+ align:start position:0%
+little r Prime the two observers have a
+relative position Vector capital r which
+
+ align:start position:0%
+relative position Vector capital r which
+ 
+
+ align:start position:0%
+relative position Vector capital r which
+is the position of S Prime relative to
+
+ align:start position:0%
+is the position of S Prime relative to
+ 
+
+ align:start position:0%
+is the position of S Prime relative to
+the origin of frame s so what we'd like
+
+ align:start position:0%
+the origin of frame s so what we'd like
+ 
+
+ align:start position:0%
+the origin of frame s so what we'd like
+to see is how are these different
+
+ align:start position:0%
+to see is how are these different
+ 
+
+ align:start position:0%
+to see is how are these different
+position vectors related well from the
+
+ align:start position:0%
+position vectors related well from the
+ 
+
+ align:start position:0%
+position vectors related well from the
+geometry of the diagram we can see that
+
+ align:start position:0%
+geometry of the diagram we can see that
+ 
+
+ align:start position:0%
+geometry of the diagram we can see that
+the position measured by Observer s
+
+ align:start position:0%
+the position measured by Observer s
+ 
+
+ align:start position:0%
+the position measured by Observer s
+which is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R is equal to the position of Observer S
+
+ align:start position:0%
+R is equal to the position of Observer S
+ 
+
+ align:start position:0%
+R is equal to the position of Observer S
+Prime relative to Observer s which is
+
+ align:start position:0%
+Prime relative to Observer s which is
+ 
+
+ align:start position:0%
+Prime relative to Observer s which is
+capital r plus the position Vector
+
+ align:start position:0%
+capital r plus the position Vector
+ 
+
+ align:start position:0%
+capital r plus the position Vector
+measured by The Observer at S Prime
+
+ align:start position:0%
+measured by The Observer at S Prime
+ 
+
+ align:start position:0%
+measured by The Observer at S Prime
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is little r Prime I can rewrite that if
+
+ align:start position:0%
+is little r Prime I can rewrite that if
+ 
+
+ align:start position:0%
+is little r Prime I can rewrite that if
+I'd like to
+
+ align:start position:0%
+I'd like to
+ 
+
+ align:start position:0%
+I'd like to
+write the position measured by The
+
+ align:start position:0%
+write the position measured by The
+ 
+
+ align:start position:0%
+write the position measured by The
+Observer S Prime in terms of what's
+
+ align:start position:0%
+Observer S Prime in terms of what's
+ 
+
+ align:start position:0%
+Observer S Prime in terms of what's
+measured by The Observer at S I could
+
+ align:start position:0%
+measured by The Observer at S I could
+ 
+
+ align:start position:0%
+measured by The Observer at S I could
+just rearrange this and write that
+
+ align:start position:0%
+just rearrange this and write that
+ 
+
+ align:start position:0%
+just rearrange this and write that
+little r Prime time is equal to little r
+
+ align:start position:0%
+little r Prime time is equal to little r
+ 
+
+ align:start position:0%
+little r Prime time is equal to little r
+minus capital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r now let's add a further complication
+
+ align:start position:0%
+r now let's add a further complication
+ 
+
+ align:start position:0%
+r now let's add a further complication
+and assume that the Observer S Prime is
+
+ align:start position:0%
+and assume that the Observer S Prime is
+ 
+
+ align:start position:0%
+and assume that the Observer S Prime is
+not just at a different location from
+
+ align:start position:0%
+not just at a different location from
+ 
+
+ align:start position:0%
+not just at a different location from
+The Observer of s but is moving at
+
+ align:start position:0%
+The Observer of s but is moving at
+ 
+
+ align:start position:0%
+The Observer of s but is moving at
+constant velocity relative to frame s so
+
+ align:start position:0%
+constant velocity relative to frame s so
+ 
+
+ align:start position:0%
+constant velocity relative to frame s so
+we'll assume that frame S Prime is
+
+ align:start position:0%
+we'll assume that frame S Prime is
+ 
+
+ align:start position:0%
+we'll assume that frame S Prime is
+moving at constant velocity with respect
+
+ align:start position:0%
+moving at constant velocity with respect
+ 
+
+ align:start position:0%
+moving at constant velocity with respect
+to frame s at a constant velocity vector
+
+ align:start position:0%
+to frame s at a constant velocity vector
+ 
+
+ align:start position:0%
+to frame s at a constant velocity vector
+v okay
+
+ align:start position:0%
+v okay
+ 
+
+ align:start position:0%
+v okay
+so V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector is a constant and in that case my
+
+ align:start position:0%
+Vector is a constant and in that case my
+ 
+
+ align:start position:0%
+Vector is a constant and in that case my
+offset of Observer S Prime relative to
+
+ align:start position:0%
+offset of Observer S Prime relative to
+ 
+
+ align:start position:0%
+offset of Observer S Prime relative to
+Observer s which is the vector capital r
+
+ align:start position:0%
+Observer s which is the vector capital r
+ 
+
+ align:start position:0%
+Observer s which is the vector capital r
+is a function of
+
+ align:start position:0%
+is a function of
+ 
+
+ align:start position:0%
+is a function of
+time so capital r is a function of time
+
+ align:start position:0%
+time so capital r is a function of time
+ 
+
+ align:start position:0%
+time so capital r is a function of time
+and it's given by the offset at Time
+
+ align:start position:0%
+and it's given by the offset at Time
+ 
+
+ align:start position:0%
+and it's given by the offset at Time
+Zero which I will call all capital r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not plus the
+
+ align:start position:0%
+not plus the
+ 
+
+ align:start position:0%
+not plus the
+elapsed motion due to the constant
+
+ align:start position:0%
+elapsed motion due to the constant
+ 
+
+ align:start position:0%
+elapsed motion due to the constant
+velocity which is capital V time
+
+ align:start position:0%
+velocity which is capital V time
+ 
+
+ align:start position:0%
+velocity which is capital V time
+time so since capital r is a function of
+
+ align:start position:0%
+time so since capital r is a function of
+ 
+
+ align:start position:0%
+time so since capital r is a function of
+time that tells me that in this equation
+
+ align:start position:0%
+time that tells me that in this equation
+ 
+
+ align:start position:0%
+time that tells me that in this equation
+little RP Prime the position Vector
+
+ align:start position:0%
+little RP Prime the position Vector
+ 
+
+ align:start position:0%
+little RP Prime the position Vector
+measured by The Observer in frame S
+
+ align:start position:0%
+measured by The Observer in frame S
+ 
+
+ align:start position:0%
+measured by The Observer in frame S
+Prime is also going to be a function of
+
+ align:start position:0%
+Prime is also going to be a function of
+ 
+
+ align:start position:0%
+Prime is also going to be a function of
+time even if
+
+ align:start position:0%
+time even if
+ 
+
+ align:start position:0%
+time even if
+Capital sorry even if little r is a
+
+ align:start position:0%
+Capital sorry even if little r is a
+ 
+
+ align:start position:0%
+Capital sorry even if little r is a
+constant so notice what that means if
+
+ align:start position:0%
+constant so notice what that means if
+ 
+
+ align:start position:0%
+constant so notice what that means if
+the object is at rest in frame
+
+ align:start position:0%
+the object is at rest in frame
+ 
+
+ align:start position:0%
+the object is at rest in frame
+s the object will appear to be moving
+
+ align:start position:0%
+s the object will appear to be moving
+ 
+
+ align:start position:0%
+s the object will appear to be moving
+its position Vector will be time
+
+ align:start position:0%
+its position Vector will be time
+ 
+
+ align:start position:0%
+its position Vector will be time
+dependent in frame S Prime because
+
+ align:start position:0%
+dependent in frame S Prime because
+ 
+
+ align:start position:0%
+dependent in frame S Prime because
+capital r the location of S Prime
+
+ align:start position:0%
+capital r the location of S Prime
+ 
+
+ align:start position:0%
+capital r the location of S Prime
+relative to S is
+
+ align:start position:0%
+relative to S is
+ 
+
+ align:start position:0%
+relative to S is
+changing so this relation tells us how
+
+ align:start position:0%
+changing so this relation tells us how
+ 
+
+ align:start position:0%
+changing so this relation tells us how
+the position vectors in the two frames
+
+ align:start position:0%
+the position vectors in the two frames
+ 
+
+ align:start position:0%
+the position vectors in the two frames
+are related what about the veloc
+
+ align:start position:0%
+are related what about the veloc
+ 
+
+ align:start position:0%
+are related what about the veloc
+ities well to compute how the velocities
+
+ align:start position:0%
+ities well to compute how the velocities
+ 
+
+ align:start position:0%
+ities well to compute how the velocities
+are related we can just take the time
+
+ align:start position:0%
+are related we can just take the time
+ 
+
+ align:start position:0%
+are related we can just take the time
+derivative of the relation of the
+
+ align:start position:0%
+derivative of the relation of the
+ 
+
+ align:start position:0%
+derivative of the relation of the
+position vectors so in this particular
+
+ align:start position:0%
+position vectors so in this particular
+ 
+
+ align:start position:0%
+position vectors so in this particular
+case we have that the time
+
+ align:start position:0%
+case we have that the time
+ 
+
+ align:start position:0%
+case we have that the time
+derivative of the S Prime position D
+
+ align:start position:0%
+derivative of the S Prime position D
+ 
+
+ align:start position:0%
+derivative of the S Prime position D
+little r Prime DT is equal to the time
+
+ align:start position:0%
+little r Prime DT is equal to the time
+ 
+
+ align:start position:0%
+little r Prime DT is equal to the time
+derivative of the position in frame s
+
+ align:start position:0%
+derivative of the position in frame s
+ 
+
+ align:start position:0%
+derivative of the position in frame s
+which is D little r DT minus the time
+
+ align:start position:0%
+which is D little r DT minus the time
+ 
+
+ align:start position:0%
+which is D little r DT minus the time
+derivative of the offset of S Prime
+
+ align:start position:0%
+derivative of the offset of S Prime
+ 
+
+ align:start position:0%
+derivative of the offset of S Prime
+relative to S so that's minus D capital
+
+ align:start position:0%
+relative to S so that's minus D capital
+ 
+
+ align:start position:0%
+relative to S so that's minus D capital
+r DT and I can rewrite that in terms of
+
+ align:start position:0%
+r DT and I can rewrite that in terms of
+ 
+
+ align:start position:0%
+r DT and I can rewrite that in terms of
+symbols for the velocity so I have
+
+ align:start position:0%
+symbols for the velocity so I have
+ 
+
+ align:start position:0%
+symbols for the velocity so I have
+here the velocity Little V Prime which
+
+ align:start position:0%
+here the velocity Little V Prime which
+ 
+
+ align:start position:0%
+here the velocity Little V Prime which
+is the velocity measured by an observer
+
+ align:start position:0%
+is the velocity measured by an observer
+ 
+
+ align:start position:0%
+is the velocity measured by an observer
+in frame S Prime and that's equal to the
+
+ align:start position:0%
+in frame S Prime and that's equal to the
+ 
+
+ align:start position:0%
+in frame S Prime and that's equal to the
+velocity Little V which is the velocity
+
+ align:start position:0%
+velocity Little V which is the velocity
+ 
+
+ align:start position:0%
+velocity Little V which is the velocity
+measured by frame
+
+ align:start position:0%
+measured by frame
+ 
+
+ align:start position:0%
+measured by frame
+s minus D capital r DT which we see is
+
+ align:start position:0%
+s minus D capital r DT which we see is
+ 
+
+ align:start position:0%
+s minus D capital r DT which we see is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+capital V Vector which is the velocity
+
+ align:start position:0%
+capital V Vector which is the velocity
+ 
+
+ align:start position:0%
+capital V Vector which is the velocity
+of S Prime relative to S so this is how
+
+ align:start position:0%
+of S Prime relative to S so this is how
+ 
+
+ align:start position:0%
+of S Prime relative to S so this is how
+the velocities are related and again
+
+ align:start position:0%
+the velocities are related and again
+ 
+
+ align:start position:0%
+the velocities are related and again
+notice that if the object is stationary
+
+ align:start position:0%
+notice that if the object is stationary
+ 
+
+ align:start position:0%
+notice that if the object is stationary
+in one frame it will still have it will
+
+ align:start position:0%
+in one frame it will still have it will
+ 
+
+ align:start position:0%
+in one frame it will still have it will
+be so if it's zero in one frame it will
+
+ align:start position:0%
+be so if it's zero in one frame it will
+ 
+
+ align:start position:0%
+be so if it's zero in one frame it will
+be nonzero in the other frame so in
+
+ align:start position:0%
+be nonzero in the other frame so in
+ 
+
+ align:start position:0%
+be nonzero in the other frame so in
+general you will measure different
+
+ align:start position:0%
+general you will measure different
+ 
+
+ align:start position:0%
+general you will measure different
+velocities in the different frames even
+
+ align:start position:0%
+velocities in the different frames even
+ 
+
+ align:start position:0%
+velocities in the different frames even
+if one of those velocities is
+
+ align:start position:0%
+if one of those velocities is
+ 
+
+ align:start position:0%
+if one of those velocities is
+zero now how are the acceleration
+
+ align:start position:0%
+zero now how are the acceleration
+ 
+
+ align:start position:0%
+zero now how are the acceleration
+related well again we can just take the
+
+ align:start position:0%
+related well again we can just take the
+ 
+
+ align:start position:0%
+related well again we can just take the
+time derivative of the velocities to to
+
+ align:start position:0%
+time derivative of the velocities to to
+ 
+
+ align:start position:0%
+time derivative of the velocities to to
+figure out what the relationship of the
+
+ align:start position:0%
+figure out what the relationship of the
+ 
+
+ align:start position:0%
+figure out what the relationship of the
+accelerations is so differentiating this
+
+ align:start position:0%
+accelerations is so differentiating this
+ 
+
+ align:start position:0%
+accelerations is so differentiating this
+equation I have that D Little V Prime DT
+
+ align:start position:0%
+equation I have that D Little V Prime DT
+ 
+
+ align:start position:0%
+equation I have that D Little V Prime DT
+is equal to D Little V DT minus
+
+ align:start position:0%
+is equal to D Little V DT minus
+ 
+
+ align:start position:0%
+is equal to D Little V DT minus
+D capital V DT but here something
+
+ align:start position:0%
+D capital V DT but here something
+ 
+
+ align:start position:0%
+D capital V DT but here something
+interesting happens because remember we
+
+ align:start position:0%
+interesting happens because remember we
+ 
+
+ align:start position:0%
+interesting happens because remember we
+said that capital V is a constant vector
+
+ align:start position:0%
+said that capital V is a constant vector
+ 
+
+ align:start position:0%
+said that capital V is a constant vector
+and remember capital V is the velocity
+
+ align:start position:0%
+and remember capital V is the velocity
+ 
+
+ align:start position:0%
+and remember capital V is the velocity
+that frame S Prime has relative to frame
+
+ align:start position:0%
+that frame S Prime has relative to frame
+ 
+
+ align:start position:0%
+that frame S Prime has relative to frame
+s okay so since capital V is a constant
+
+ align:start position:0%
+s okay so since capital V is a constant
+ 
+
+ align:start position:0%
+s okay so since capital V is a constant
+that means that this term goes to zero
+
+ align:start position:0%
+that means that this term goes to zero
+ 
+
+ align:start position:0%
+that means that this term goes to zero
+and so we see that the acceleration in
+
+ align:start position:0%
+and so we see that the acceleration in
+ 
+
+ align:start position:0%
+and so we see that the acceleration in
+frame S Prime is equal to the
+
+ align:start position:0%
+frame S Prime is equal to the
+ 
+
+ align:start position:0%
+frame S Prime is equal to the
+acceleration in frame a so if I have two
+
+ align:start position:0%
+acceleration in frame a so if I have two
+ 
+
+ align:start position:0%
+acceleration in frame a so if I have two
+reference frames one moving at a
+
+ align:start position:0%
+reference frames one moving at a
+ 
+
+ align:start position:0%
+reference frames one moving at a
+constant velocity relative to the the
+
+ align:start position:0%
+constant velocity relative to the the
+ 
+
+ align:start position:0%
+constant velocity relative to the the
+other in general I will measure
+
+ align:start position:0%
+other in general I will measure
+ 
+
+ align:start position:0%
+other in general I will measure
+different positions and different
+
+ align:start position:0%
+different positions and different
+ 
+
+ align:start position:0%
+different positions and different
+velocities for an object as measured by
+
+ align:start position:0%
+velocities for an object as measured by
+ 
+
+ align:start position:0%
+velocities for an object as measured by
+the two frames however the accelerations
+
+ align:start position:0%
+the two frames however the accelerations
+ 
+
+ align:start position:0%
+the two frames however the accelerations
+measured in both frames will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identical because the accelerations are
+
+ align:start position:0%
+identical because the accelerations are
+ 
+
+ align:start position:0%
+identical because the accelerations are
+identical we'll see that Newton's Laws
+
+ align:start position:0%
+identical we'll see that Newton's Laws
+ 
+
+ align:start position:0%
+identical we'll see that Newton's Laws
+will look identical in the two
+
+ align:start position:0%
+will look identical in the two
+ 
+
+ align:start position:0%
+will look identical in the two
+frames and we can see that in the
+
+ align:start position:0%
+frames and we can see that in the
+ 
+
+ align:start position:0%
+frames and we can see that in the
+following way in frame s
+
+ align:start position:0%
+following way in frame s
+ 
+
+ align:start position:0%
+following way in frame s
+we have that the force is equal to the
+
+ align:start position:0%
+we have that the force is equal to the
+ 
+
+ align:start position:0%
+we have that the force is equal to the
+mass times the acceleration in frame S
+
+ align:start position:0%
+mass times the acceleration in frame S
+ 
+
+ align:start position:0%
+mass times the acceleration in frame S
+Prime the force F Prime is equal to the
+
+ align:start position:0%
+Prime the force F Prime is equal to the
+ 
+
+ align:start position:0%
+Prime the force F Prime is equal to the
+mass time a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime but a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime is equal to a as we calculated
+
+ align:start position:0%
+prime is equal to a as we calculated
+ 
+
+ align:start position:0%
+prime is equal to a as we calculated
+here so we see that the forces in the
+
+ align:start position:0%
+here so we see that the forces in the
+ 
+
+ align:start position:0%
+here so we see that the forces in the
+two frames are ident identical even
+
+ align:start position:0%
+two frames are ident identical even
+ 
+
+ align:start position:0%
+two frames are ident identical even
+though the positions and velocities in
+
+ align:start position:0%
+though the positions and velocities in
+ 
+
+ align:start position:0%
+though the positions and velocities in
+general will be different as measured in
+
+ align:start position:0%
+general will be different as measured in
+ 
+
+ align:start position:0%
+general will be different as measured in
+the two frames for the same
+
+ align:start position:0%
+the two frames for the same
+ 
+
+ align:start position:0%
+the two frames for the same
+object but the accelerations will be
+
+ align:start position:0%
+object but the accelerations will be
+ 
+
+ align:start position:0%
+object but the accelerations will be
+identical and so the forces will be
+
+ align:start position:0%
+identical and so the forces will be
+ 
+
+ align:start position:0%
+identical and so the forces will be
+identical so if one of these reference
+
+ align:start position:0%
+identical so if one of these reference
+ 
+
+ align:start position:0%
+identical so if one of these reference
+frames is an inertial frame one in which
+
+ align:start position:0%
+frames is an inertial frame one in which
+ 
+
+ align:start position:0%
+frames is an inertial frame one in which
+an isolated body moves at constant
+
+ align:start position:0%
+an isolated body moves at constant
+ 
+
+ align:start position:0%
+an isolated body moves at constant
+velocity then any other frame moving at
+
+ align:start position:0%
+velocity then any other frame moving at
+ 
+
+ align:start position:0%
+velocity then any other frame moving at
+constant velocity with respect to the
+
+ align:start position:0%
+constant velocity with respect to the
+ 
+
+ align:start position:0%
+constant velocity with respect to the
+first frame will also be an inertial
+
+ align:start position:0%
+first frame will also be an inertial
+ 
+
+ align:start position:0%
+first frame will also be an inertial
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+what this means is that you're always
+
+ align:start position:0%
+what this means is that you're always
+ 
+
+ align:start position:0%
+what this means is that you're always
+free to transform from one inertial
+
+ align:start position:0%
+free to transform from one inertial
+ 
+
+ align:start position:0%
+free to transform from one inertial
+frame to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another and what that means is that you
+
+ align:start position:0%
+another and what that means is that you
+ 
+
+ align:start position:0%
+another and what that means is that you
+can always transform to another frame
+
+ align:start position:0%
+can always transform to another frame
+ 
+
+ align:start position:0%
+can always transform to another frame
+that is moving at constant velocity with
+
+ align:start position:0%
+that is moving at constant velocity with
+ 
+
+ align:start position:0%
+that is moving at constant velocity with
+respect to an original inertial frame
\ No newline at end of file
diff --git a/QHaAoQQy07I.txt b/QHaAoQQy07I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..01f2fdeaaa369bde9e32be5344a812006ded9770
--- /dev/null
+++ b/QHaAoQQy07I.txt
@@ -0,0 +1,744 @@
+align:start position:0%
+ 
+hello and welcome back to recitation in
+
+ align:start position:0%
+hello and welcome back to recitation in
+ 
+
+ align:start position:0%
+hello and welcome back to recitation in
+this problem I'd like you to compute the
+
+ align:start position:0%
+this problem I'd like you to compute the
+ 
+
+ align:start position:0%
+this problem I'd like you to compute the
+area of a triangle this triangle sits in
+
+ align:start position:0%
+area of a triangle this triangle sits in
+ 
+
+ align:start position:0%
+area of a triangle this triangle sits in
+space and it has its three vertices uh
+
+ align:start position:0%
+space and it has its three vertices uh
+ 
+
+ align:start position:0%
+space and it has its three vertices uh
+labeled here as P1 P2 and P3 so we're
+
+ align:start position:0%
+labeled here as P1 P2 and P3 so we're
+ 
+
+ align:start position:0%
+labeled here as P1 P2 and P3 so we're
+going to compute this area and we're
+
+ align:start position:0%
+going to compute this area and we're
+ 
+
+ align:start position:0%
+going to compute this area and we're
+going to do it using the cross product
+
+ align:start position:0%
+going to do it using the cross product
+ 
+
+ align:start position:0%
+going to do it using the cross product
+which we learned about in lecture so why
+
+ align:start position:0%
+which we learned about in lecture so why
+ 
+
+ align:start position:0%
+which we learned about in lecture so why
+don't you take some time to work this
+
+ align:start position:0%
+don't you take some time to work this
+ 
+
+ align:start position:0%
+don't you take some time to work this
+out pause the video and we'll check back
+
+ align:start position:0%
+out pause the video and we'll check back
+ 
+
+ align:start position:0%
+out pause the video and we'll check back
+in a minute and see how did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it hello and welcome back so the first
+
+ align:start position:0%
+it hello and welcome back so the first
+ 
+
+ align:start position:0%
+it hello and welcome back so the first
+thing that I like to do with a problem
+
+ align:start position:0%
+thing that I like to do with a problem
+ 
+
+ align:start position:0%
+thing that I like to do with a problem
+like this is I like to uh draw a picture
+
+ align:start position:0%
+like this is I like to uh draw a picture
+ 
+
+ align:start position:0%
+like this is I like to uh draw a picture
+so I can kind of think about what's
+
+ align:start position:0%
+so I can kind of think about what's
+ 
+
+ align:start position:0%
+so I can kind of think about what's
+going on so we have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triangle we have this triangle sitting
+
+ align:start position:0%
+triangle we have this triangle sitting
+ 
+
+ align:start position:0%
+triangle we have this triangle sitting
+out in space and uh we know that we want
+
+ align:start position:0%
+out in space and uh we know that we want
+ 
+
+ align:start position:0%
+out in space and uh we know that we want
+to take a cross product in order to
+
+ align:start position:0%
+to take a cross product in order to
+ 
+
+ align:start position:0%
+to take a cross product in order to
+compute uh compute uh its area uh but we
+
+ align:start position:0%
+compute uh compute uh its area uh but we
+ 
+
+ align:start position:0%
+compute uh compute uh its area uh but we
+need to be careful cross product uh
+
+ align:start position:0%
+need to be careful cross product uh
+ 
+
+ align:start position:0%
+need to be careful cross product uh
+doesn't make sense to take cross product
+
+ align:start position:0%
+doesn't make sense to take cross product
+ 
+
+ align:start position:0%
+doesn't make sense to take cross product
+of points what makes sense is to take
+
+ align:start position:0%
+of points what makes sense is to take
+ 
+
+ align:start position:0%
+of points what makes sense is to take
+cross product of vectors so the first
+
+ align:start position:0%
+cross product of vectors so the first
+ 
+
+ align:start position:0%
+cross product of vectors so the first
+thing that we need to do is build some
+
+ align:start position:0%
+thing that we need to do is build some
+ 
+
+ align:start position:0%
+thing that we need to do is build some
+vectors that describe this triangle and
+
+ align:start position:0%
+vectors that describe this triangle and
+ 
+
+ align:start position:0%
+vectors that describe this triangle and
+the vectors that we need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+build are P1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P2 and P1 P3 since we're going to use
+
+ align:start position:0%
+P2 and P1 P3 since we're going to use
+ 
+
+ align:start position:0%
+P2 and P1 P3 since we're going to use
+these in a minute let's go ahead and
+
+ align:start position:0%
+these in a minute let's go ahead and
+ 
+
+ align:start position:0%
+these in a minute let's go ahead and
+compute them now so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P1 P2 is just the difference of P2 minus
+
+ align:start position:0%
+P1 P2 is just the difference of P2 minus
+ 
+
+ align:start position:0%
+P1 P2 is just the difference of P2 minus
+P1 so we get uh 0 minus a negative 1 so
+
+ align:start position:0%
+P1 so we get uh 0 minus a negative 1 so
+ 
+
+ align:start position:0%
+P1 so we get uh 0 minus a negative 1 so
+we get
+
+ align:start position:0%
+we get
+ 
+
+ align:start position:0%
+we get
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+2 and one let me just check my notes to
+
+ align:start position:0%
+2 and one let me just check my notes to
+ 
+
+ align:start position:0%
+2 and one let me just check my notes to
+make sure I do that right good and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P1 P3 we get again 0 minus a negative 1
+
+ align:start position:0%
+P1 P3 we get again 0 minus a negative 1
+ 
+
+ align:start position:0%
+P1 P3 we get again 0 minus a negative 1
+so 1 we get minus one and then we get
+
+ align:start position:0%
+so 1 we get minus one and then we get
+ 
+
+ align:start position:0%
+so 1 we get minus one and then we get
+one let me again check my notes very
+
+ align:start position:0%
+one let me again check my notes very
+ 
+
+ align:start position:0%
+one let me again check my notes very
+good okay so now that we have these
+
+ align:start position:0%
+good okay so now that we have these
+ 
+
+ align:start position:0%
+good okay so now that we have these
+vectors we need to remember that if we
+
+ align:start position:0%
+vectors we need to remember that if we
+ 
+
+ align:start position:0%
+vectors we need to remember that if we
+take the absolute
+
+ align:start position:0%
+take the absolute
+ 
+
+ align:start position:0%
+take the absolute
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+P1 P2 cross product with P1 P3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this will be equal to the
+
+ align:start position:0%
+this will be equal to the
+ 
+
+ align:start position:0%
+this will be equal to the
+area of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the
+
+ align:start position:0%
+um the
+ 
+
+ align:start position:0%
+um the
+parallelogram uh they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enclose so let's get started by
+
+ align:start position:0%
+enclose so let's get started by
+ 
+
+ align:start position:0%
+enclose so let's get started by
+Computing this cross product so
+
+ align:start position:0%
+Computing this cross product so
+ 
+
+ align:start position:0%
+Computing this cross product so
+P1
+
+ align:start position:0%
+P1
+ 
+
+ align:start position:0%
+P1
+P2 plus
+
+ align:start position:0%
+P2 plus
+ 
+
+ align:start position:0%
+P2 plus
+P2 P3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember to compute a cross product
+
+ align:start position:0%
+so remember to compute a cross product
+ 
+
+ align:start position:0%
+so remember to compute a cross product
+we uh take the determinant of a matrix
+
+ align:start position:0%
+we uh take the determinant of a matrix
+ 
+
+ align:start position:0%
+we uh take the determinant of a matrix
+where we put in our unit normal vectors
+
+ align:start position:0%
+where we put in our unit normal vectors
+ 
+
+ align:start position:0%
+where we put in our unit normal vectors
+i j and
+
+ align:start position:0%
+i j and
+ 
+
+ align:start position:0%
+i j and
+k and then we enter in uh the the
+
+ align:start position:0%
+k and then we enter in uh the the
+ 
+
+ align:start position:0%
+k and then we enter in uh the the
+remaining entries of the Matrix are just
+
+ align:start position:0%
+remaining entries of the Matrix are just
+ 
+
+ align:start position:0%
+remaining entries of the Matrix are just
+the entries of our vectors so we do 1 2
+
+ align:start position:0%
+the entries of our vectors so we do 1 2
+ 
+
+ align:start position:0%
+the entries of our vectors so we do 1 2
+1 and 1 - one
+
+ align:start position:0%
+1 and 1 - one
+ 
+
+ align:start position:0%
+1 and 1 - one
+1 okay and so we can compute
+
+ align:start position:0%
+1 okay and so we can compute
+ 
+
+ align:start position:0%
+1 okay and so we can compute
+this and we
+
+ align:start position:0%
+this and we
+ 
+
+ align:start position:0%
+this and we
+get so the I component we get 2 minus a
+
+ align:start position:0%
+get so the I component we get 2 minus a
+ 
+
+ align:start position:0%
+get so the I component we get 2 minus a
+- 1 so we get
+
+ align:start position:0%
+- 1 so we get
+ 
+
+ align:start position:0%
+- 1 so we get
+3 now the J component if we look at the
+
+ align:start position:0%
+3 now the J component if we look at the
+ 
+
+ align:start position:0%
+3 now the J component if we look at the
+co-actor matrix it's just one one one
+
+ align:start position:0%
+co-actor matrix it's just one one one
+ 
+
+ align:start position:0%
+co-actor matrix it's just one one one
+one and that has determinant zero so our
+
+ align:start position:0%
+one and that has determinant zero so our
+ 
+
+ align:start position:0%
+one and that has determinant zero so our
+middle component is just
+
+ align:start position:0%
+middle component is just
+ 
+
+ align:start position:0%
+middle component is just
+zero and finally the K component we get
+
+ align:start position:0%
+zero and finally the K component we get
+ 
+
+ align:start position:0%
+zero and finally the K component we get
+minus one uh minus another two so Al
+
+ align:start position:0%
+minus one uh minus another two so Al
+ 
+
+ align:start position:0%
+minus one uh minus another two so Al
+together we get minus
+
+ align:start position:0%
+together we get minus
+ 
+
+ align:start position:0%
+together we get minus
+3 so what that tells us now is that
+
+ align:start position:0%
+3 so what that tells us now is that
+ 
+
+ align:start position:0%
+3 so what that tells us now is that
+the um that this quantity here the the
+
+ align:start position:0%
+the um that this quantity here the the
+ 
+
+ align:start position:0%
+the um that this quantity here the the
+magnitude of the cross product is just
+
+ align:start position:0%
+magnitude of the cross product is just
+ 
+
+ align:start position:0%
+magnitude of the cross product is just
+uh 3 * the < TK of 2 just looking at the
+
+ align:start position:0%
+uh 3 * the < TK of 2 just looking at the
+ 
+
+ align:start position:0%
+uh 3 * the < TK of 2 just looking at the
+length of this Vector
+
+ align:start position:0%
+length of this Vector
+ 
+
+ align:start position:0%
+length of this Vector
+here so we're almost done but let's go
+
+ align:start position:0%
+here so we're almost done but let's go
+ 
+
+ align:start position:0%
+here so we're almost done but let's go
+back and look at what we had uh to start
+
+ align:start position:0%
+back and look at what we had uh to start
+ 
+
+ align:start position:0%
+back and look at what we had uh to start
+with we were interested in the Triangle
+
+ align:start position:0%
+with we were interested in the Triangle
+ 
+
+ align:start position:0%
+with we were interested in the Triangle
+over here uh which uh was enclosed by
+
+ align:start position:0%
+over here uh which uh was enclosed by
+ 
+
+ align:start position:0%
+over here uh which uh was enclosed by
+the vectors P1 P2 and the vectors P1 P3
+
+ align:start position:0%
+the vectors P1 P2 and the vectors P1 P3
+ 
+
+ align:start position:0%
+the vectors P1 P2 and the vectors P1 P3
+and what we just computed is actually
+
+ align:start position:0%
+and what we just computed is actually
+ 
+
+ align:start position:0%
+and what we just computed is actually
+the area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of this parallelogram which as you
+
+ align:start position:0%
+of of this parallelogram which as you
+ 
+
+ align:start position:0%
+of of this parallelogram which as you
+can see is twice the area of the
+
+ align:start position:0%
+can see is twice the area of the
+ 
+
+ align:start position:0%
+can see is twice the area of the
+triangle that we're actually interested
+
+ align:start position:0%
+triangle that we're actually interested
+ 
+
+ align:start position:0%
+triangle that we're actually interested
+in so going back over here we see that
+
+ align:start position:0%
+in so going back over here we see that
+ 
+
+ align:start position:0%
+in so going back over here we see that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+area of our
+
+ align:start position:0%
+area of our
+ 
+
+ align:start position:0%
+area of our
+triangle is equal to 3 < tk2 and we just
+
+ align:start position:0%
+triangle is equal to 3 < tk2 and we just
+ 
+
+ align:start position:0%
+triangle is equal to 3 < tk2 and we just
+need divide by two to get the triangle
+
+ align:start position:0%
+need divide by two to get the triangle
+ 
+
+ align:start position:0%
+need divide by two to get the triangle
+okay and I'll leave it at that
\ No newline at end of file
diff --git a/Qa7Xnn7ixpk.txt b/Qa7Xnn7ixpk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9f250bc28e9047051ec5caff305bb3e97dd561f2
--- /dev/null
+++ b/Qa7Xnn7ixpk.txt
@@ -0,0 +1,11691 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay welcome welcome to the uh
+
+ align:start position:0%
+okay welcome welcome to the uh
+ 
+
+ align:start position:0%
+okay welcome welcome to the uh
+second uh
+
+ align:start position:0%
+second uh
+ 
+
+ align:start position:0%
+second uh
+discussion of networks and the second to
+
+ align:start position:0%
+discussion of networks and the second to
+ 
+
+ align:start position:0%
+discussion of networks and the second to
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+talk of a lecture of this course there's
+
+ align:start position:0%
+talk of a lecture of this course there's
+ 
+
+ align:start position:0%
+talk of a lecture of this course there's
+a very important set of
+
+ align:start position:0%
+a very important set of
+ 
+
+ align:start position:0%
+a very important set of
+lectures after that from the students
+
+ align:start position:0%
+lectures after that from the students
+ 
+
+ align:start position:0%
+lectures after that from the students
+i'm looking forward to
+
+ align:start position:0%
+i'm looking forward to
+ 
+
+ align:start position:0%
+i'm looking forward to
+so last time we talked about the
+
+ align:start position:0%
+so last time we talked about the
+ 
+
+ align:start position:0%
+so last time we talked about the
+mock use of computers to model various
+
+ align:start position:0%
+mock use of computers to model various
+ 
+
+ align:start position:0%
+mock use of computers to model various
+complicated systems in in
+
+ align:start position:0%
+complicated systems in in
+ 
+
+ align:start position:0%
+complicated systems in in
+mainly cellular systems
+
+ align:start position:0%
+mainly cellular systems
+ 
+
+ align:start position:0%
+mainly cellular systems
+ranging from
+
+ align:start position:0%
+ranging from
+ 
+
+ align:start position:0%
+ranging from
+highly cooperative even buy stable
+
+ align:start position:0%
+highly cooperative even buy stable
+ 
+
+ align:start position:0%
+highly cooperative even buy stable
+bifurcations that's sort of where the
+
+ align:start position:0%
+bifurcations that's sort of where the
+ 
+
+ align:start position:0%
+bifurcations that's sort of where the
+cell makes a decision
+
+ align:start position:0%
+cell makes a decision
+ 
+
+ align:start position:0%
+cell makes a decision
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a discussion of chromosome copy number
+
+ align:start position:0%
+a discussion of chromosome copy number
+ 
+
+ align:start position:0%
+a discussion of chromosome copy number
+and its implications
+
+ align:start position:0%
+and its implications
+ 
+
+ align:start position:0%
+and its implications
+and a large
+
+ align:start position:0%
+and a large
+ 
+
+ align:start position:0%
+and a large
+chunk of time on flux balance
+
+ align:start position:0%
+chunk of time on flux balance
+ 
+
+ align:start position:0%
+chunk of time on flux balance
+optimization where we can look at
+
+ align:start position:0%
+optimization where we can look at
+ 
+
+ align:start position:0%
+optimization where we can look at
+many of these things from the standpoint
+
+ align:start position:0%
+many of these things from the standpoint
+ 
+
+ align:start position:0%
+many of these things from the standpoint
+of optimization
+
+ align:start position:0%
+of optimization
+ 
+
+ align:start position:0%
+of optimization
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+paraphrase a famous local politician we
+
+ align:start position:0%
+paraphrase a famous local politician we
+ 
+
+ align:start position:0%
+paraphrase a famous local politician we
+will ask not what computers can do for
+
+ align:start position:0%
+will ask not what computers can do for
+ 
+
+ align:start position:0%
+will ask not what computers can do for
+biology but for what biology can do for
+
+ align:start position:0%
+biology but for what biology can do for
+ 
+
+ align:start position:0%
+biology but for what biology can do for
+computers
+
+ align:start position:0%
+computers
+ 
+
+ align:start position:0%
+computers
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and of course we'll go back and forth
+
+ align:start position:0%
+and of course we'll go back and forth
+ 
+
+ align:start position:0%
+and of course we'll go back and forth
+and and try to look at what kind of ex
+
+ align:start position:0%
+and and try to look at what kind of ex
+ 
+
+ align:start position:0%
+and and try to look at what kind of ex
+the this interesting dynamic between the
+
+ align:start position:0%
+the this interesting dynamic between the
+ 
+
+ align:start position:0%
+the this interesting dynamic between the
+experimental and the computational side
+
+ align:start position:0%
+experimental and the computational side
+ 
+
+ align:start position:0%
+experimental and the computational side
+and so how can biology aid algorithm
+
+ align:start position:0%
+and so how can biology aid algorithm
+ 
+
+ align:start position:0%
+and so how can biology aid algorithm
+development
+
+ align:start position:0%
+development
+ 
+
+ align:start position:0%
+development
+to return the favor and aid biology
+
+ align:start position:0%
+to return the favor and aid biology
+ 
+
+ align:start position:0%
+to return the favor and aid biology
+but not only algorithm development to
+
+ align:start position:0%
+but not only algorithm development to
+ 
+
+ align:start position:0%
+but not only algorithm development to
+not only inspiring algorithm development
+
+ align:start position:0%
+not only inspiring algorithm development
+ 
+
+ align:start position:0%
+not only inspiring algorithm development
+but actually implementing
+
+ align:start position:0%
+but actually implementing
+ 
+
+ align:start position:0%
+but actually implementing
+uh hardware and software
+
+ align:start position:0%
+uh hardware and software
+ 
+
+ align:start position:0%
+uh hardware and software
+in in
+
+ align:start position:0%
+in in
+ 
+
+ align:start position:0%
+in in
+biological systems we'll talk about that
+
+ align:start position:0%
+biological systems we'll talk about that
+ 
+
+ align:start position:0%
+biological systems we'll talk about that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+ranging from molecular computing to
+
+ align:start position:0%
+ranging from molecular computing to
+ 
+
+ align:start position:0%
+ranging from molecular computing to
+cellular computing
+
+ align:start position:0%
+cellular computing
+ 
+
+ align:start position:0%
+cellular computing
+and then back to
+
+ align:start position:0%
+and then back to
+ 
+
+ align:start position:0%
+and then back to
+inspiring algorithms again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+slide three what is it that we're really
+
+ align:start position:0%
+slide three what is it that we're really
+ 
+
+ align:start position:0%
+slide three what is it that we're really
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+computation needs in terms of aid how do
+
+ align:start position:0%
+computation needs in terms of aid how do
+ 
+
+ align:start position:0%
+computation needs in terms of aid how do
+we get uh what what are the what are the
+
+ align:start position:0%
+we get uh what what are the what are the
+ 
+
+ align:start position:0%
+we get uh what what are the what are the
+real issues here and we've mentioned a
+
+ align:start position:0%
+real issues here and we've mentioned a
+ 
+
+ align:start position:0%
+real issues here and we've mentioned a
+couple times in the course probably
+
+ align:start position:0%
+couple times in the course probably
+ 
+
+ align:start position:0%
+couple times in the course probably
+initially when we were talking about
+
+ align:start position:0%
+initially when we were talking about
+ 
+
+ align:start position:0%
+initially when we were talking about
+dynamic programming and related topics
+
+ align:start position:0%
+dynamic programming and related topics
+ 
+
+ align:start position:0%
+dynamic programming and related topics
+of how a problem in computer science
+
+ align:start position:0%
+of how a problem in computer science
+ 
+
+ align:start position:0%
+of how a problem in computer science
+scales
+
+ align:start position:0%
+scales
+ 
+
+ align:start position:0%
+scales
+typically you'll have one key input
+
+ align:start position:0%
+typically you'll have one key input
+ 
+
+ align:start position:0%
+typically you'll have one key input
+size in
+
+ align:start position:0%
+size in
+ 
+
+ align:start position:0%
+size in
+and then the running time or sometimes
+
+ align:start position:0%
+and then the running time or sometimes
+ 
+
+ align:start position:0%
+and then the running time or sometimes
+the memory has an upper bound which
+
+ align:start position:0%
+the memory has an upper bound which
+ 
+
+ align:start position:0%
+the memory has an upper bound which
+we've been referring to as the order of
+
+ align:start position:0%
+we've been referring to as the order of
+ 
+
+ align:start position:0%
+we've been referring to as the order of
+some function of that n where n is the
+
+ align:start position:0%
+some function of that n where n is the
+ 
+
+ align:start position:0%
+some function of that n where n is the
+length of the of a string or the size of
+
+ align:start position:0%
+length of the of a string or the size of
+ 
+
+ align:start position:0%
+length of the of a string or the size of
+the problem
+
+ align:start position:0%
+the problem
+ 
+
+ align:start position:0%
+the problem
+there are other uh symbols that are
+
+ align:start position:0%
+there are other uh symbols that are
+ 
+
+ align:start position:0%
+there are other uh symbols that are
+slightly more rarely used there's a in
+
+ align:start position:0%
+slightly more rarely used there's a in
+ 
+
+ align:start position:0%
+slightly more rarely used there's a in
+addition to the upper bound there's
+
+ align:start position:0%
+addition to the upper bound there's
+ 
+
+ align:start position:0%
+addition to the upper bound there's
+lower bound
+
+ align:start position:0%
+lower bound
+ 
+
+ align:start position:0%
+lower bound
+sometimes you can get an exact bound or
+
+ align:start position:0%
+sometimes you can get an exact bound or
+ 
+
+ align:start position:0%
+sometimes you can get an exact bound or
+equal bound
+
+ align:start position:0%
+equal bound
+ 
+
+ align:start position:0%
+equal bound
+and how does this play out when you have
+
+ align:start position:0%
+and how does this play out when you have
+ 
+
+ align:start position:0%
+and how does this play out when you have
+specific instances of n now of course
+
+ align:start position:0%
+specific instances of n now of course
+ 
+
+ align:start position:0%
+specific instances of n now of course
+this when you say that something's on
+
+ align:start position:0%
+this when you say that something's on
+ 
+
+ align:start position:0%
+this when you say that something's on
+the order of or upper bound of a
+
+ align:start position:0%
+the order of or upper bound of a
+ 
+
+ align:start position:0%
+the order of or upper bound of a
+function of n
+
+ align:start position:0%
+function of n
+ 
+
+ align:start position:0%
+function of n
+you don't always necessarily describe
+
+ align:start position:0%
+you don't always necessarily describe
+ 
+
+ align:start position:0%
+you don't always necessarily describe
+with the constants but to give you a
+
+ align:start position:0%
+with the constants but to give you a
+ 
+
+ align:start position:0%
+with the constants but to give you a
+ballpark when you have n ranging from
+
+ align:start position:0%
+ballpark when you have n ranging from
+ 
+
+ align:start position:0%
+ballpark when you have n ranging from
+one to a thousand and the and the
+
+ align:start position:0%
+one to a thousand and the and the
+ 
+
+ align:start position:0%
+one to a thousand and the and the
+polynomial
+
+ align:start position:0%
+polynomial
+ 
+
+ align:start position:0%
+polynomial
+uh ranging from
+
+ align:start position:0%
+uh ranging from
+ 
+
+ align:start position:0%
+uh ranging from
+linear to quadratic to tenth power then
+
+ align:start position:0%
+linear to quadratic to tenth power then
+ 
+
+ align:start position:0%
+linear to quadratic to tenth power then
+the exponential or
+
+ align:start position:0%
+the exponential or
+ 
+
+ align:start position:0%
+the exponential or
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+factorial
+
+ align:start position:0%
+factorial
+ 
+
+ align:start position:0%
+factorial
+and you can see that that for very small
+
+ align:start position:0%
+and you can see that that for very small
+ 
+
+ align:start position:0%
+and you can see that that for very small
+n you can get cases where a polynomial
+
+ align:start position:0%
+n you can get cases where a polynomial
+ 
+
+ align:start position:0%
+n you can get cases where a polynomial
+performance computation time can be
+
+ align:start position:0%
+performance computation time can be
+ 
+
+ align:start position:0%
+performance computation time can be
+longer than an exponential
+
+ align:start position:0%
+longer than an exponential
+ 
+
+ align:start position:0%
+longer than an exponential
+computation time so exponential isn't
+
+ align:start position:0%
+computation time so exponential isn't
+ 
+
+ align:start position:0%
+computation time so exponential isn't
+necessarily bad news depending on the
+
+ align:start position:0%
+necessarily bad news depending on the
+ 
+
+ align:start position:0%
+necessarily bad news depending on the
+size of your problem
+
+ align:start position:0%
+size of your problem
+ 
+
+ align:start position:0%
+size of your problem
+but it gets to be madness very quickly
+
+ align:start position:0%
+but it gets to be madness very quickly
+ 
+
+ align:start position:0%
+but it gets to be madness very quickly
+as in it increases you quickly get
+
+ align:start position:0%
+as in it increases you quickly get
+ 
+
+ align:start position:0%
+as in it increases you quickly get
+over large
+
+ align:start position:0%
+over large
+ 
+
+ align:start position:0%
+over large
+numbers on the far right hand side that
+
+ align:start position:0%
+numbers on the far right hand side that
+ 
+
+ align:start position:0%
+numbers on the far right hand side that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+computationally intractable with any
+
+ align:start position:0%
+computationally intractable with any
+ 
+
+ align:start position:0%
+computationally intractable with any
+known computer
+
+ align:start position:0%
+known computer
+ 
+
+ align:start position:0%
+known computer
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we mentioned computational complexity is
+
+ align:start position:0%
+we mentioned computational complexity is
+ 
+
+ align:start position:0%
+we mentioned computational complexity is
+one of the various definitions of
+
+ align:start position:0%
+one of the various definitions of
+ 
+
+ align:start position:0%
+one of the various definitions of
+complexity at the beginning of course
+
+ align:start position:0%
+complexity at the beginning of course
+ 
+
+ align:start position:0%
+complexity at the beginning of course
+this is not the one we chose to to be
+
+ align:start position:0%
+this is not the one we chose to to be
+ 
+
+ align:start position:0%
+this is not the one we chose to to be
+closest to the definition of living
+
+ align:start position:0%
+closest to the definition of living
+ 
+
+ align:start position:0%
+closest to the definition of living
+complexity but it's one that's very
+
+ align:start position:0%
+complexity but it's one that's very
+ 
+
+ align:start position:0%
+complexity but it's one that's very
+frequently used in the
+
+ align:start position:0%
+frequently used in the
+ 
+
+ align:start position:0%
+frequently used in the
+computer science field i just want to
+
+ align:start position:0%
+computer science field i just want to
+ 
+
+ align:start position:0%
+computer science field i just want to
+introduce a few of the terms here just
+
+ align:start position:0%
+introduce a few of the terms here just
+ 
+
+ align:start position:0%
+introduce a few of the terms here just
+so you've kind of heard them in this
+
+ align:start position:0%
+so you've kind of heard them in this
+ 
+
+ align:start position:0%
+so you've kind of heard them in this
+context
+
+ align:start position:0%
+context
+ 
+
+ align:start position:0%
+context
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+and it basically refers to the
+
+ align:start position:0%
+and it basically refers to the
+ 
+
+ align:start position:0%
+and it basically refers to the
+issues brought up in the previous slide
+
+ align:start position:0%
+issues brought up in the previous slide
+ 
+
+ align:start position:0%
+issues brought up in the previous slide
+of whether it takes part whether it
+
+ align:start position:0%
+of whether it takes part whether it
+ 
+
+ align:start position:0%
+of whether it takes part whether it
+scales by a polynomial which is
+
+ align:start position:0%
+scales by a polynomial which is
+ 
+
+ align:start position:0%
+scales by a polynomial which is
+generally desirable whether it scales
+
+ align:start position:0%
+generally desirable whether it scales
+ 
+
+ align:start position:0%
+generally desirable whether it scales
+exponentially or worse
+
+ align:start position:0%
+exponentially or worse
+ 
+
+ align:start position:0%
+exponentially or worse
+and so we have a p of our problems that
+
+ align:start position:0%
+and so we have a p of our problems that
+ 
+
+ align:start position:0%
+and so we have a p of our problems that
+we can solve in polynomial deterministic
+
+ align:start position:0%
+we can solve in polynomial deterministic
+ 
+
+ align:start position:0%
+we can solve in polynomial deterministic
+time deterministic is just describes the
+
+ align:start position:0%
+time deterministic is just describes the
+ 
+
+ align:start position:0%
+time deterministic is just describes the
+fact that the algorithms will do the
+
+ align:start position:0%
+fact that the algorithms will do the
+ 
+
+ align:start position:0%
+fact that the algorithms will do the
+same thing time after time which is
+
+ align:start position:0%
+same thing time after time which is
+ 
+
+ align:start position:0%
+same thing time after time which is
+typical the sort of typical computer
+
+ align:start position:0%
+typical the sort of typical computer
+ 
+
+ align:start position:0%
+typical the sort of typical computer
+that we feel comfortable using
+
+ align:start position:0%
+that we feel comfortable using
+ 
+
+ align:start position:0%
+that we feel comfortable using
+and uh an example of this of problems in
+
+ align:start position:0%
+and uh an example of this of problems in
+ 
+
+ align:start position:0%
+and uh an example of this of problems in
+the p class the dynamic programming
+
+ align:start position:0%
+the p class the dynamic programming
+ 
+
+ align:start position:0%
+the p class the dynamic programming
+which we've used numerous times it
+
+ align:start position:0%
+which we've used numerous times it
+ 
+
+ align:start position:0%
+which we've used numerous times it
+scales polynomial and the polynomial
+
+ align:start position:0%
+scales polynomial and the polynomial
+ 
+
+ align:start position:0%
+scales polynomial and the polynomial
+just depends on the problem slightly
+
+ align:start position:0%
+just depends on the problem slightly
+ 
+
+ align:start position:0%
+just depends on the problem slightly
+from squared to the sixth power we've
+
+ align:start position:0%
+from squared to the sixth power we've
+ 
+
+ align:start position:0%
+from squared to the sixth power we've
+seen
+
+ align:start position:0%
+seen
+ 
+
+ align:start position:0%
+seen
+np
+
+ align:start position:0%
+np
+ 
+
+ align:start position:0%
+np
+is uh has a number of subsets but
+
+ align:start position:0%
+is uh has a number of subsets but
+ 
+
+ align:start position:0%
+is uh has a number of subsets but
+overall it means it's not
+
+ align:start position:0%
+overall it means it's not
+ 
+
+ align:start position:0%
+overall it means it's not
+determined as a polynomial time to get
+
+ align:start position:0%
+determined as a polynomial time to get
+ 
+
+ align:start position:0%
+determined as a polynomial time to get
+the solutions the solutions are
+
+ align:start position:0%
+the solutions the solutions are
+ 
+
+ align:start position:0%
+the solutions the solutions are
+checkable
+
+ align:start position:0%
+checkable
+ 
+
+ align:start position:0%
+checkable
+in polynomial time but uh
+
+ align:start position:0%
+in polynomial time but uh
+ 
+
+ align:start position:0%
+in polynomial time but uh
+are generally felt
+
+ align:start position:0%
+are generally felt
+ 
+
+ align:start position:0%
+are generally felt
+to to not be
+
+ align:start position:0%
+to to not be
+ 
+
+ align:start position:0%
+to to not be
+currently feasible in polynomial time
+
+ align:start position:0%
+currently feasible in polynomial time
+ 
+
+ align:start position:0%
+currently feasible in polynomial time
+for the determination as opposed to
+
+ align:start position:0%
+for the determination as opposed to
+ 
+
+ align:start position:0%
+for the determination as opposed to
+checking
+
+ align:start position:0%
+checking
+ 
+
+ align:start position:0%
+checking
+an example of this where we're actually
+
+ align:start position:0%
+an example of this where we're actually
+ 
+
+ align:start position:0%
+an example of this where we're actually
+the inventors of various
+
+ align:start position:0%
+the inventors of various
+ 
+
+ align:start position:0%
+the inventors of various
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+encryption schemes such as rsa they are
+
+ align:start position:0%
+encryption schemes such as rsa they are
+ 
+
+ align:start position:0%
+encryption schemes such as rsa they are
+in the sda referring to the last
+
+ align:start position:0%
+in the sda referring to the last
+ 
+
+ align:start position:0%
+in the sda referring to the last
+names of the authors
+
+ align:start position:0%
+names of the authors
+ 
+
+ align:start position:0%
+names of the authors
+in a certain sense they are banking on
+
+ align:start position:0%
+in a certain sense they are banking on
+ 
+
+ align:start position:0%
+in a certain sense they are banking on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+difficulty
+
+ align:start position:0%
+difficulty
+ 
+
+ align:start position:0%
+difficulty
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+cracking these codes
+
+ align:start position:0%
+cracking these codes
+ 
+
+ align:start position:0%
+cracking these codes
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+polynomial time you can you can use the
+
+ align:start position:0%
+polynomial time you can you can use the
+ 
+
+ align:start position:0%
+polynomial time you can you can use the
+codes if you know it you can check it
+
+ align:start position:0%
+codes if you know it you can check it
+ 
+
+ align:start position:0%
+codes if you know it you can check it
+that is to say you can but you can't
+
+ align:start position:0%
+that is to say you can but you can't
+ 
+
+ align:start position:0%
+that is to say you can but you can't
+crack it unless someone comes through
+
+ align:start position:0%
+crack it unless someone comes through
+ 
+
+ align:start position:0%
+crack it unless someone comes through
+with breakthrough on the np problems
+
+ align:start position:0%
+with breakthrough on the np problems
+ 
+
+ align:start position:0%
+with breakthrough on the np problems
+because if you solve one of them you can
+
+ align:start position:0%
+because if you solve one of them you can
+ 
+
+ align:start position:0%
+because if you solve one of them you can
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+all of them
+
+ align:start position:0%
+all of them
+ 
+
+ align:start position:0%
+all of them
+and then there's substance of this this
+
+ align:start position:0%
+and then there's substance of this this
+ 
+
+ align:start position:0%
+and then there's substance of this this
+is a little less critical for today's
+
+ align:start position:0%
+is a little less critical for today's
+ 
+
+ align:start position:0%
+is a little less critical for today's
+discussion but there's np complete
+
+ align:start position:0%
+discussion but there's np complete
+ 
+
+ align:start position:0%
+discussion but there's np complete
+which uh an example of which is so the
+
+ align:start position:0%
+which uh an example of which is so the
+ 
+
+ align:start position:0%
+which uh an example of which is so the
+traveling salesman
+
+ align:start position:0%
+traveling salesman
+ 
+
+ align:start position:0%
+traveling salesman
+can you get through all of all the
+
+ align:start position:0%
+can you get through all of all the
+ 
+
+ align:start position:0%
+can you get through all of all the
+vertices on the on the trip
+
+ align:start position:0%
+vertices on the on the trip
+ 
+
+ align:start position:0%
+vertices on the on the trip
+um with a mileage below certain some
+
+ align:start position:0%
+um with a mileage below certain some
+ 
+
+ align:start position:0%
+um with a mileage below certain some
+threshold
+
+ align:start position:0%
+threshold
+ 
+
+ align:start position:0%
+threshold
+and an mp hard version of that same
+
+ align:start position:0%
+and an mp hard version of that same
+ 
+
+ align:start position:0%
+and an mp hard version of that same
+thing is what's the minimum mileage that
+
+ align:start position:0%
+thing is what's the minimum mileage that
+ 
+
+ align:start position:0%
+thing is what's the minimum mileage that
+you can get not just less than x but
+
+ align:start position:0%
+you can get not just less than x but
+ 
+
+ align:start position:0%
+you can get not just less than x but
+you know how much less than x
+
+ align:start position:0%
+you know how much less than x
+ 
+
+ align:start position:0%
+you know how much less than x
+and the worst case scenario is
+
+ align:start position:0%
+and the worst case scenario is
+ 
+
+ align:start position:0%
+and the worst case scenario is
+undecidable where you really uh
+
+ align:start position:0%
+undecidable where you really uh
+ 
+
+ align:start position:0%
+undecidable where you really uh
+even given an unlimited amount of time
+
+ align:start position:0%
+even given an unlimited amount of time
+ 
+
+ align:start position:0%
+even given an unlimited amount of time
+and space you can't tell whether it is
+
+ align:start position:0%
+and space you can't tell whether it is
+ 
+
+ align:start position:0%
+and space you can't tell whether it is
+and the classic one is the program
+
+ align:start position:0%
+and the classic one is the program
+ 
+
+ align:start position:0%
+and the classic one is the program
+halting problem where you don't know
+
+ align:start position:0%
+halting problem where you don't know
+ 
+
+ align:start position:0%
+halting problem where you don't know
+whether your program is going to halt
+
+ align:start position:0%
+whether your program is going to halt
+ 
+
+ align:start position:0%
+whether your program is going to halt
+and probably all of you run into that
+
+ align:start position:0%
+and probably all of you run into that
+ 
+
+ align:start position:0%
+and probably all of you run into that
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+i'm just being funny
+
+ align:start position:0%
+i'm just being funny
+ 
+
+ align:start position:0%
+i'm just being funny
+so but but i mean it is a real it is the
+
+ align:start position:0%
+so but but i mean it is a real it is the
+ 
+
+ align:start position:0%
+so but but i mean it is a real it is the
+program healthy problem is serious
+
+ align:start position:0%
+program healthy problem is serious
+ 
+
+ align:start position:0%
+program healthy problem is serious
+mathematical construct
+
+ align:start position:0%
+mathematical construct
+ 
+
+ align:start position:0%
+mathematical construct
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+how do we deal with this how do we start
+
+ align:start position:0%
+how do we deal with this how do we start
+ 
+
+ align:start position:0%
+how do we deal with this how do we start
+thinking about um
+
+ align:start position:0%
+thinking about um
+ 
+
+ align:start position:0%
+thinking about um
+ways that we've dealt with it before in
+
+ align:start position:0%
+ways that we've dealt with it before in
+ 
+
+ align:start position:0%
+ways that we've dealt with it before in
+ways that biology could change the
+
+ align:start position:0%
+ways that biology could change the
+ 
+
+ align:start position:0%
+ways that biology could change the
+landscape a little bit
+
+ align:start position:0%
+landscape a little bit
+ 
+
+ align:start position:0%
+landscape a little bit
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+usually you can what we do to when we're
+
+ align:start position:0%
+usually you can what we do to when we're
+ 
+
+ align:start position:0%
+usually you can what we do to when we're
+faced with an empty hard problem is uh
+
+ align:start position:0%
+faced with an empty hard problem is uh
+ 
+
+ align:start position:0%
+faced with an empty hard problem is uh
+cheat in some way or another you
+
+ align:start position:0%
+cheat in some way or another you
+ 
+
+ align:start position:0%
+cheat in some way or another you
+redefine the problem so it's in class p
+
+ align:start position:0%
+redefine the problem so it's in class p
+ 
+
+ align:start position:0%
+redefine the problem so it's in class p
+uh sometimes sacrificing something so
+
+ align:start position:0%
+uh sometimes sacrificing something so
+ 
+
+ align:start position:0%
+uh sometimes sacrificing something so
+you might have uh
+
+ align:start position:0%
+you might have uh
+ 
+
+ align:start position:0%
+you might have uh
+if you're interested in tertiary
+
+ align:start position:0%
+if you're interested in tertiary
+ 
+
+ align:start position:0%
+if you're interested in tertiary
+structure we made it redefine it as a
+
+ align:start position:0%
+structure we made it redefine it as a
+ 
+
+ align:start position:0%
+structure we made it redefine it as a
+secondary and we showed the secondary
+
+ align:start position:0%
+secondary and we showed the secondary
+ 
+
+ align:start position:0%
+secondary and we showed the secondary
+structure for
+
+ align:start position:0%
+structure for
+ 
+
+ align:start position:0%
+structure for
+uh rnas
+
+ align:start position:0%
+uh rnas
+ 
+
+ align:start position:0%
+uh rnas
+it can be solved with a dynamic
+
+ align:start position:0%
+it can be solved with a dynamic
+ 
+
+ align:start position:0%
+it can be solved with a dynamic
+programming algorithm with an n squared
+
+ align:start position:0%
+programming algorithm with an n squared
+ 
+
+ align:start position:0%
+programming algorithm with an n squared
+and or worse in the sixth algorithm
+
+ align:start position:0%
+and or worse in the sixth algorithm
+ 
+
+ align:start position:0%
+and or worse in the sixth algorithm
+whether that is as
+
+ align:start position:0%
+whether that is as
+ 
+
+ align:start position:0%
+whether that is as
+precise as the
+
+ align:start position:0%
+precise as the
+ 
+
+ align:start position:0%
+precise as the
+most precise tertiary structure that one
+
+ align:start position:0%
+most precise tertiary structure that one
+ 
+
+ align:start position:0%
+most precise tertiary structure that one
+could get given you know sort of
+
+ align:start position:0%
+could get given you know sort of
+ 
+
+ align:start position:0%
+could get given you know sort of
+infinite at exponential time is an open
+
+ align:start position:0%
+infinite at exponential time is an open
+ 
+
+ align:start position:0%
+infinite at exponential time is an open
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+probably not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some you could
+
+ align:start position:0%
+some you could
+ 
+
+ align:start position:0%
+some you could
+if the pro if n is small enough we
+
+ align:start position:0%
+if the pro if n is small enough we
+ 
+
+ align:start position:0%
+if the pro if n is small enough we
+showed that exponential times can be
+
+ align:start position:0%
+showed that exponential times can be
+ 
+
+ align:start position:0%
+showed that exponential times can be
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+and so you just do an exhaustive search
+
+ align:start position:0%
+and so you just do an exhaustive search
+ 
+
+ align:start position:0%
+and so you just do an exhaustive search
+or if you can't do that then then you
+
+ align:start position:0%
+or if you can't do that then then you
+ 
+
+ align:start position:0%
+or if you can't do that then then you
+use some clever heuristic way of pruning
+
+ align:start position:0%
+use some clever heuristic way of pruning
+ 
+
+ align:start position:0%
+use some clever heuristic way of pruning
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's in a certain sense that's
+
+ align:start position:0%
+and that's in a certain sense that's
+ 
+
+ align:start position:0%
+and that's in a certain sense that's
+what most of the approximations are
+
+ align:start position:0%
+what most of the approximations are
+ 
+
+ align:start position:0%
+what most of the approximations are
+so what can biology do
+
+ align:start position:0%
+so what can biology do
+ 
+
+ align:start position:0%
+so what can biology do
+we'll talk about three examples in uh
+
+ align:start position:0%
+we'll talk about three examples in uh
+ 
+
+ align:start position:0%
+we'll talk about three examples in uh
+today one is dna computing one is
+
+ align:start position:0%
+today one is dna computing one is
+ 
+
+ align:start position:0%
+today one is dna computing one is
+genetic algorithms and neural networks
+
+ align:start position:0%
+genetic algorithms and neural networks
+ 
+
+ align:start position:0%
+genetic algorithms and neural networks
+the first one in a cert none of these
+
+ align:start position:0%
+the first one in a cert none of these
+ 
+
+ align:start position:0%
+the first one in a cert none of these
+really actually solve the problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first one is a way of just obtaining
+
+ align:start position:0%
+the first one is a way of just obtaining
+ 
+
+ align:start position:0%
+the first one is a way of just obtaining
+a lot more wrong computing power
+
+ align:start position:0%
+a lot more wrong computing power
+ 
+
+ align:start position:0%
+a lot more wrong computing power
+i'll show you a quote where they say
+
+ align:start position:0%
+i'll show you a quote where they say
+ 
+
+ align:start position:0%
+i'll show you a quote where they say
+they've solved an np complete problem
+
+ align:start position:0%
+they've solved an np complete problem
+ 
+
+ align:start position:0%
+they've solved an np complete problem
+but it's in the same sense that you can
+
+ align:start position:0%
+but it's in the same sense that you can
+ 
+
+ align:start position:0%
+but it's in the same sense that you can
+solve any exponential problem by by
+
+ align:start position:0%
+solve any exponential problem by by
+ 
+
+ align:start position:0%
+solve any exponential problem by by
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+that's not really finessing it out of np
+
+ align:start position:0%
+that's not really finessing it out of np
+ 
+
+ align:start position:0%
+that's not really finessing it out of np
+into into p
+
+ align:start position:0%
+into into p
+ 
+
+ align:start position:0%
+into into p
+genetic algorithms and neural networks
+
+ align:start position:0%
+genetic algorithms and neural networks
+ 
+
+ align:start position:0%
+genetic algorithms and neural networks
+are definitely heuristics they're
+
+ align:start position:0%
+are definitely heuristics they're
+ 
+
+ align:start position:0%
+are definitely heuristics they're
+beautifully inspired by two of the
+
+ align:start position:0%
+beautifully inspired by two of the
+ 
+
+ align:start position:0%
+beautifully inspired by two of the
+greatest
+
+ align:start position:0%
+greatest
+ 
+
+ align:start position:0%
+greatest
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+in the history of life
+
+ align:start position:0%
+in the history of life
+ 
+
+ align:start position:0%
+in the history of life
+on earth and that is evolution and um
+
+ align:start position:0%
+on earth and that is evolution and um
+ 
+
+ align:start position:0%
+on earth and that is evolution and um
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+uh brain networks and we'll get and uh
+
+ align:start position:0%
+uh brain networks and we'll get and uh
+ 
+
+ align:start position:0%
+uh brain networks and we'll get and uh
+and so genetic algorithms is based on
+
+ align:start position:0%
+and so genetic algorithms is based on
+ 
+
+ align:start position:0%
+and so genetic algorithms is based on
+the adaptation that occurs
+
+ align:start position:0%
+the adaptation that occurs
+ 
+
+ align:start position:0%
+the adaptation that occurs
+during evolution and recombination and
+
+ align:start position:0%
+during evolution and recombination and
+ 
+
+ align:start position:0%
+during evolution and recombination and
+immunogenesis and neural network is also
+
+ align:start position:0%
+immunogenesis and neural network is also
+ 
+
+ align:start position:0%
+immunogenesis and neural network is also
+about adaptation but this is on sort of
+
+ align:start position:0%
+about adaptation but this is on sort of
+ 
+
+ align:start position:0%
+about adaptation but this is on sort of
+the time scale of learning
+
+ align:start position:0%
+the time scale of learning
+ 
+
+ align:start position:0%
+the time scale of learning
+so we'll first dedicate ourselves to
+
+ align:start position:0%
+so we'll first dedicate ourselves to
+ 
+
+ align:start position:0%
+so we'll first dedicate ourselves to
+molecular computing
+
+ align:start position:0%
+molecular computing
+ 
+
+ align:start position:0%
+molecular computing
+and uh associated just kind of put it in
+
+ align:start position:0%
+and uh associated just kind of put it in
+ 
+
+ align:start position:0%
+and uh associated just kind of put it in
+the context of nano computing in general
+
+ align:start position:0%
+the context of nano computing in general
+ 
+
+ align:start position:0%
+the context of nano computing in general
+and you can see all the issues in
+
+ align:start position:0%
+and you can see all the issues in
+ 
+
+ align:start position:0%
+and you can see all the issues in
+computing not just the uh the math
+
+ align:start position:0%
+computing not just the uh the math
+ 
+
+ align:start position:0%
+computing not just the uh the math
+module so all the steps
+
+ align:start position:0%
+module so all the steps
+ 
+
+ align:start position:0%
+module so all the steps
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+assembly of of the requisite hardware
+
+ align:start position:0%
+assembly of of the requisite hardware
+ 
+
+ align:start position:0%
+assembly of of the requisite hardware
+this is some kind of factory operation
+
+ align:start position:0%
+this is some kind of factory operation
+ 
+
+ align:start position:0%
+this is some kind of factory operation
+typically
+
+ align:start position:0%
+typically
+ 
+
+ align:start position:0%
+typically
+then there's some sort of input module
+
+ align:start position:0%
+then there's some sort of input module
+ 
+
+ align:start position:0%
+then there's some sort of input module
+some hardware and software that's
+
+ align:start position:0%
+some hardware and software that's
+ 
+
+ align:start position:0%
+some hardware and software that's
+required for getting the data in then
+
+ align:start position:0%
+required for getting the data in then
+ 
+
+ align:start position:0%
+required for getting the data in then
+there's some sort of memory
+
+ align:start position:0%
+there's some sort of memory
+ 
+
+ align:start position:0%
+there's some sort of memory
+and then there's a central processor
+
+ align:start position:0%
+and then there's a central processor
+ 
+
+ align:start position:0%
+and then there's a central processor
+might have
+
+ align:start position:0%
+might have
+ 
+
+ align:start position:0%
+might have
+math components and output this is sort
+
+ align:start position:0%
+math components and output this is sort
+ 
+
+ align:start position:0%
+math components and output this is sort
+of like from our first lecture
+
+ align:start position:0%
+of like from our first lecture
+ 
+
+ align:start position:0%
+of like from our first lecture
+assembly input memory process and output
+
+ align:start position:0%
+assembly input memory process and output
+ 
+
+ align:start position:0%
+assembly input memory process and output
+and what we want to do with biology is
+
+ align:start position:0%
+and what we want to do with biology is
+ 
+
+ align:start position:0%
+and what we want to do with biology is
+we want to harvest things uh from
+
+ align:start position:0%
+we want to harvest things uh from
+ 
+
+ align:start position:0%
+we want to harvest things uh from
+genomics and from just biological
+
+ align:start position:0%
+genomics and from just biological
+ 
+
+ align:start position:0%
+genomics and from just biological
+research in general to use design better
+
+ align:start position:0%
+research in general to use design better
+ 
+
+ align:start position:0%
+research in general to use design better
+computers either in silico or in in a
+
+ align:start position:0%
+computers either in silico or in in a
+ 
+
+ align:start position:0%
+computers either in silico or in in a
+biological biochemical sense and then
+
+ align:start position:0%
+biological biochemical sense and then
+ 
+
+ align:start position:0%
+biological biochemical sense and then
+harness evolution either to make devices
+
+ align:start position:0%
+harness evolution either to make devices
+ 
+
+ align:start position:0%
+harness evolution either to make devices
+or or as part of algorithm development
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know we have uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different different people have
+
+ align:start position:0%
+different different people have
+ 
+
+ align:start position:0%
+different different people have
+different opinions about how much longer
+
+ align:start position:0%
+different opinions about how much longer
+ 
+
+ align:start position:0%
+different opinions about how much longer
+moore's law the scaling for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large-scale integrated circuits or
+
+ align:start position:0%
+large-scale integrated circuits or
+ 
+
+ align:start position:0%
+large-scale integrated circuits or
+curse files version that goes back to
+
+ align:start position:0%
+curse files version that goes back to
+ 
+
+ align:start position:0%
+curse files version that goes back to
+1900 about doubling every two years
+
+ align:start position:0%
+1900 about doubling every two years
+ 
+
+ align:start position:0%
+1900 about doubling every two years
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the ability to
+
+ align:start position:0%
+the ability to
+ 
+
+ align:start position:0%
+the ability to
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+calculations per second per thousand
+
+ align:start position:0%
+calculations per second per thousand
+ 
+
+ align:start position:0%
+calculations per second per thousand
+dollars there might be another decade
+
+ align:start position:0%
+dollars there might be another decade
+ 
+
+ align:start position:0%
+dollars there might be another decade
+left in in the silicon
+
+ align:start position:0%
+left in in the silicon
+ 
+
+ align:start position:0%
+left in in the silicon
+uh large scale integrated circuit that's
+
+ align:start position:0%
+uh large scale integrated circuit that's
+ 
+
+ align:start position:0%
+uh large scale integrated circuit that's
+what some people say or maybe more maybe
+
+ align:start position:0%
+what some people say or maybe more maybe
+ 
+
+ align:start position:0%
+what some people say or maybe more maybe
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so there are three real options here for
+
+ align:start position:0%
+so there are three real options here for
+ 
+
+ align:start position:0%
+so there are three real options here for
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that next step
+
+ align:start position:0%
+that next step
+ 
+
+ align:start position:0%
+that next step
+electro electronic
+
+ align:start position:0%
+electro electronic
+ 
+
+ align:start position:0%
+electro electronic
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+nano computing optical nano computing
+
+ align:start position:0%
+nano computing optical nano computing
+ 
+
+ align:start position:0%
+nano computing optical nano computing
+molecular nano computing and you could
+
+ align:start position:0%
+molecular nano computing and you could
+ 
+
+ align:start position:0%
+molecular nano computing and you could
+add to this quantum computing for maybe
+
+ align:start position:0%
+add to this quantum computing for maybe
+ 
+
+ align:start position:0%
+add to this quantum computing for maybe
+four different options for beating
+
+ align:start position:0%
+four different options for beating
+ 
+
+ align:start position:0%
+four different options for beating
+moore's law or extending moore's law i
+
+ align:start position:0%
+moore's law or extending moore's law i
+ 
+
+ align:start position:0%
+moore's law or extending moore's law i
+think how you look at it
+
+ align:start position:0%
+think how you look at it
+ 
+
+ align:start position:0%
+think how you look at it
+so let's just walk through them quickly
+
+ align:start position:0%
+so let's just walk through them quickly
+ 
+
+ align:start position:0%
+so let's just walk through them quickly
+one at a time optical
+
+ align:start position:0%
+one at a time optical
+ 
+
+ align:start position:0%
+one at a time optical
+computing you can think of is already
+
+ align:start position:0%
+computing you can think of is already
+ 
+
+ align:start position:0%
+computing you can think of is already
+here in a sense in our optical fiber
+
+ align:start position:0%
+here in a sense in our optical fiber
+ 
+
+ align:start position:0%
+here in a sense in our optical fiber
+networks have very fast switches that
+
+ align:start position:0%
+networks have very fast switches that
+ 
+
+ align:start position:0%
+networks have very fast switches that
+are required
+
+ align:start position:0%
+are required
+ 
+
+ align:start position:0%
+are required
+for a good deal of our fastest internet
+
+ align:start position:0%
+for a good deal of our fastest internet
+ 
+
+ align:start position:0%
+for a good deal of our fastest internet
+and there in their various
+
+ align:start position:0%
+and there in their various
+ 
+
+ align:start position:0%
+and there in their various
+demonstrations where you can do optical
+
+ align:start position:0%
+demonstrations where you can do optical
+ 
+
+ align:start position:0%
+demonstrations where you can do optical
+computing
+
+ align:start position:0%
+computing
+ 
+
+ align:start position:0%
+computing
+for many of the tasks not just the data
+
+ align:start position:0%
+for many of the tasks not just the data
+ 
+
+ align:start position:0%
+for many of the tasks not just the data
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+and and and just like many other things
+
+ align:start position:0%
+and and and just like many other things
+ 
+
+ align:start position:0%
+and and and just like many other things
+there's a desire to shrink this down for
+
+ align:start position:0%
+there's a desire to shrink this down for
+ 
+
+ align:start position:0%
+there's a desire to shrink this down for
+cost of manufacturing and quality and so
+
+ align:start position:0%
+cost of manufacturing and quality and so
+ 
+
+ align:start position:0%
+cost of manufacturing and quality and so
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+uh the advantages of the optical over um
+
+ align:start position:0%
+uh the advantages of the optical over um
+ 
+
+ align:start position:0%
+uh the advantages of the optical over um
+electronic typical computers is that
+
+ align:start position:0%
+electronic typical computers is that
+ 
+
+ align:start position:0%
+electronic typical computers is that
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+they uh for a given set of operations
+
+ align:start position:0%
+they uh for a given set of operations
+ 
+
+ align:start position:0%
+they uh for a given set of operations
+there's the general sentiment then it
+
+ align:start position:0%
+there's the general sentiment then it
+ 
+
+ align:start position:0%
+there's the general sentiment then it
+might be lower heat generation
+
+ align:start position:0%
+might be lower heat generation
+ 
+
+ align:start position:0%
+might be lower heat generation
+it it goes at the speed of light
+
+ align:start position:0%
+it it goes at the speed of light
+ 
+
+ align:start position:0%
+it it goes at the speed of light
+rather than the slightly lower than
+
+ align:start position:0%
+rather than the slightly lower than
+ 
+
+ align:start position:0%
+rather than the slightly lower than
+speed of light that typically comes into
+
+ align:start position:0%
+speed of light that typically comes into
+ 
+
+ align:start position:0%
+speed of light that typically comes into
+actual implementations in electronic
+
+ align:start position:0%
+actual implementations in electronic
+ 
+
+ align:start position:0%
+actual implementations in electronic
+circuits
+
+ align:start position:0%
+circuits
+ 
+
+ align:start position:0%
+circuits
+and there here's two examples taken from
+
+ align:start position:0%
+and there here's two examples taken from
+ 
+
+ align:start position:0%
+and there here's two examples taken from
+the literature of getting
+
+ align:start position:0%
+the literature of getting
+ 
+
+ align:start position:0%
+the literature of getting
+natural sort of self-assembly just as
+
+ align:start position:0%
+natural sort of self-assembly just as
+ 
+
+ align:start position:0%
+natural sort of self-assembly just as
+we've seen in many biological systems we
+
+ align:start position:0%
+we've seen in many biological systems we
+ 
+
+ align:start position:0%
+we've seen in many biological systems we
+get self-assembly of membranes
+
+ align:start position:0%
+get self-assembly of membranes
+ 
+
+ align:start position:0%
+get self-assembly of membranes
+self-assembly of multi-protein complexes
+
+ align:start position:0%
+self-assembly of multi-protein complexes
+ 
+
+ align:start position:0%
+self-assembly of multi-protein complexes
+here you have you want to make
+
+ align:start position:0%
+here you have you want to make
+ 
+
+ align:start position:0%
+here you have you want to make
+a particular kind a size of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optical of particles
+
+ align:start position:0%
+optical of particles
+ 
+
+ align:start position:0%
+optical of particles
+that have the right uh refractive index
+
+ align:start position:0%
+that have the right uh refractive index
+ 
+
+ align:start position:0%
+that have the right uh refractive index
+and spacing and shape and so forth and
+
+ align:start position:0%
+and spacing and shape and so forth and
+ 
+
+ align:start position:0%
+and spacing and shape and so forth and
+you can use self assembly here
+
+ align:start position:0%
+you can use self assembly here
+ 
+
+ align:start position:0%
+you can use self assembly here
+for that sort of thing
+
+ align:start position:0%
+for that sort of thing
+ 
+
+ align:start position:0%
+for that sort of thing
+that's this is these are examples of
+
+ align:start position:0%
+that's this is these are examples of
+ 
+
+ align:start position:0%
+that's this is these are examples of
+where we're getting sort of in a
+
+ align:start position:0%
+where we're getting sort of in a
+ 
+
+ align:start position:0%
+where we're getting sort of in a
+nanometer range here this is a five
+
+ align:start position:0%
+nanometer range here this is a five
+ 
+
+ align:start position:0%
+nanometer range here this is a five
+micron scale object here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i've chosen this particular example
+
+ align:start position:0%
+i've chosen this particular example
+ 
+
+ align:start position:0%
+i've chosen this particular example
+there are a number of uh examples of
+
+ align:start position:0%
+there are a number of uh examples of
+ 
+
+ align:start position:0%
+there are a number of uh examples of
+electronic
+
+ align:start position:0%
+electronic
+ 
+
+ align:start position:0%
+electronic
+nano computing where the electronics is
+
+ align:start position:0%
+nano computing where the electronics is
+ 
+
+ align:start position:0%
+nano computing where the electronics is
+getting down to the sort of size of
+
+ align:start position:0%
+getting down to the sort of size of
+ 
+
+ align:start position:0%
+getting down to the sort of size of
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+here the molecule chosen
+
+ align:start position:0%
+here the molecule chosen
+ 
+
+ align:start position:0%
+here the molecule chosen
+is a polymer of carbon not a hydrocarbon
+
+ align:start position:0%
+is a polymer of carbon not a hydrocarbon
+ 
+
+ align:start position:0%
+is a polymer of carbon not a hydrocarbon
+but carbon
+
+ align:start position:0%
+but carbon
+ 
+
+ align:start position:0%
+but carbon
+it's like the buckyballs which is carbon
+
+ align:start position:0%
+it's like the buckyballs which is carbon
+ 
+
+ align:start position:0%
+it's like the buckyballs which is carbon
+60 or graphite rolled up in the tubes
+
+ align:start position:0%
+60 or graphite rolled up in the tubes
+ 
+
+ align:start position:0%
+60 or graphite rolled up in the tubes
+the nanotubes can be used as
+
+ align:start position:0%
+the nanotubes can be used as
+ 
+
+ align:start position:0%
+the nanotubes can be used as
+transistor-like elements in very tiny
+
+ align:start position:0%
+transistor-like elements in very tiny
+ 
+
+ align:start position:0%
+transistor-like elements in very tiny
+circuits
+
+ align:start position:0%
+circuits
+ 
+
+ align:start position:0%
+circuits
+um this is this is just a schematic this
+
+ align:start position:0%
+um this is this is just a schematic this
+ 
+
+ align:start position:0%
+um this is this is just a schematic this
+isn't actually a micrograph right and uh
+
+ align:start position:0%
+isn't actually a micrograph right and uh
+ 
+
+ align:start position:0%
+isn't actually a micrograph right and uh
+and here four circuits that kind of
+
+ align:start position:0%
+and here four circuits that kind of
+ 
+
+ align:start position:0%
+and here four circuits that kind of
+reflect what you might that might be
+
+ align:start position:0%
+reflect what you might that might be
+ 
+
+ align:start position:0%
+reflect what you might that might be
+your first four projects in a an
+
+ align:start position:0%
+your first four projects in a an
+ 
+
+ align:start position:0%
+your first four projects in a an
+introductory electronics course um
+
+ align:start position:0%
+introductory electronics course um
+ 
+
+ align:start position:0%
+introductory electronics course um
+ignoring the fact that you might not use
+
+ align:start position:0%
+ignoring the fact that you might not use
+ 
+
+ align:start position:0%
+ignoring the fact that you might not use
+nanotubes but you you would uh you would
+
+ align:start position:0%
+nanotubes but you you would uh you would
+ 
+
+ align:start position:0%
+nanotubes but you you would uh you would
+have voltage in and voltage out there
+
+ align:start position:0%
+have voltage in and voltage out there
+ 
+
+ align:start position:0%
+have voltage in and voltage out there
+was uh this is a transistor light
+
+ align:start position:0%
+was uh this is a transistor light
+ 
+
+ align:start position:0%
+was uh this is a transistor light
+circuit or an inverter like circuit in
+
+ align:start position:0%
+circuit or an inverter like circuit in
+ 
+
+ align:start position:0%
+circuit or an inverter like circuit in
+the upper left hand corner of slide 10.
+
+ align:start position:0%
+the upper left hand corner of slide 10.
+ 
+
+ align:start position:0%
+the upper left hand corner of slide 10.
+and the nano tube here is in the middle
+
+ align:start position:0%
+and the nano tube here is in the middle
+ 
+
+ align:start position:0%
+and the nano tube here is in the middle
+in in
+
+ align:start position:0%
+in in
+ 
+
+ align:start position:0%
+in in
+series with a resistor going from high
+
+ align:start position:0%
+series with a resistor going from high
+ 
+
+ align:start position:0%
+series with a resistor going from high
+voltage to the ground at the lower part
+
+ align:start position:0%
+voltage to the ground at the lower part
+ 
+
+ align:start position:0%
+voltage to the ground at the lower part
+and the voltage in
+
+ align:start position:0%
+and the voltage in
+ 
+
+ align:start position:0%
+and the voltage in
+essentially modulates the voltage out in
+
+ align:start position:0%
+essentially modulates the voltage out in
+ 
+
+ align:start position:0%
+essentially modulates the voltage out in
+the non-linear curve and you can see
+
+ align:start position:0%
+the non-linear curve and you can see
+ 
+
+ align:start position:0%
+the non-linear curve and you can see
+this highly cooperative
+
+ align:start position:0%
+this highly cooperative
+ 
+
+ align:start position:0%
+this highly cooperative
+curve just like the ones that we've been
+
+ align:start position:0%
+curve just like the ones that we've been
+ 
+
+ align:start position:0%
+curve just like the ones that we've been
+talking about in a number of other
+
+ align:start position:0%
+talking about in a number of other
+ 
+
+ align:start position:0%
+talking about in a number of other
+biological and physical systems
+
+ align:start position:0%
+biological and physical systems
+ 
+
+ align:start position:0%
+biological and physical systems
+uh the upper right you have a nor gate
+
+ align:start position:0%
+uh the upper right you have a nor gate
+ 
+
+ align:start position:0%
+uh the upper right you have a nor gate
+almost every circuit can be made by
+
+ align:start position:0%
+almost every circuit can be made by
+ 
+
+ align:start position:0%
+almost every circuit can be made by
+combination simply by
+
+ align:start position:0%
+combination simply by
+ 
+
+ align:start position:0%
+combination simply by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+not ores this is a this is an inverter
+
+ align:start position:0%
+not ores this is a this is an inverter
+ 
+
+ align:start position:0%
+not ores this is a this is an inverter
+and plus a an ore so you can see that
+
+ align:start position:0%
+and plus a an ore so you can see that
+ 
+
+ align:start position:0%
+and plus a an ore so you can see that
+there there now have two inputs
+
+ align:start position:0%
+there there now have two inputs
+ 
+
+ align:start position:0%
+there there now have two inputs
+on the left and right in one and two and
+
+ align:start position:0%
+on the left and right in one and two and
+ 
+
+ align:start position:0%
+on the left and right in one and two and
+they can have states one one one zero
+
+ align:start position:0%
+they can have states one one one zero
+ 
+
+ align:start position:0%
+they can have states one one one zero
+zero one zero zero going from left to
+
+ align:start position:0%
+zero one zero zero going from left to
+ 
+
+ align:start position:0%
+zero one zero zero going from left to
+right and you can see only the in when
+
+ align:start position:0%
+right and you can see only the in when
+ 
+
+ align:start position:0%
+right and you can see only the in when
+they're both zero does the whole circuit
+
+ align:start position:0%
+they're both zero does the whole circuit
+ 
+
+ align:start position:0%
+they're both zero does the whole circuit
+down go output go down to zero or low
+
+ align:start position:0%
+down go output go down to zero or low
+ 
+
+ align:start position:0%
+down go output go down to zero or low
+voltage for output so input
+
+ align:start position:0%
+voltage for output so input
+ 
+
+ align:start position:0%
+voltage for output so input
+if there are three possible input
+
+ align:start position:0%
+if there are three possible input
+ 
+
+ align:start position:0%
+if there are three possible input
+combinations and and the last one gets
+
+ align:start position:0%
+combinations and and the last one gets
+ 
+
+ align:start position:0%
+combinations and and the last one gets
+low and this is all done this is all
+
+ align:start position:0%
+low and this is all done this is all
+ 
+
+ align:start position:0%
+low and this is all done this is all
+done with these kind of molecular scale
+
+ align:start position:0%
+done with these kind of molecular scale
+ 
+
+ align:start position:0%
+done with these kind of molecular scale
+nano
+
+ align:start position:0%
+nano
+ 
+
+ align:start position:0%
+nano
+tubes
+
+ align:start position:0%
+tubes
+ 
+
+ align:start position:0%
+tubes
+uh here's a ram and virus two nanotubes
+
+ align:start position:0%
+uh here's a ram and virus two nanotubes
+ 
+
+ align:start position:0%
+uh here's a ram and virus two nanotubes
+in order to store where it's either
+
+ align:start position:0%
+in order to store where it's either
+ 
+
+ align:start position:0%
+in order to store where it's either
+where you flip it from from open to to
+
+ align:start position:0%
+where you flip it from from open to to
+ 
+
+ align:start position:0%
+where you flip it from from open to to
+flip it from low to to high
+
+ align:start position:0%
+flip it from low to to high
+ 
+
+ align:start position:0%
+flip it from low to to high
+in the last example the lower right you
+
+ align:start position:0%
+in the last example the lower right you
+ 
+
+ align:start position:0%
+in the last example the lower right you
+now need three nanotubes you see we
+
+ align:start position:0%
+now need three nanotubes you see we
+ 
+
+ align:start position:0%
+now need three nanotubes you see we
+worked our way up in complexity from one
+
+ align:start position:0%
+worked our way up in complexity from one
+ 
+
+ align:start position:0%
+worked our way up in complexity from one
+to two to three and you need three in
+
+ align:start position:0%
+to two to three and you need three in
+ 
+
+ align:start position:0%
+to two to three and you need three in
+order to get a ring oscillator used i
+
+ align:start position:0%
+order to get a ring oscillator used i
+ 
+
+ align:start position:0%
+order to get a ring oscillator used i
+mean that's the way you would think
+
+ align:start position:0%
+mean that's the way you would think
+ 
+
+ align:start position:0%
+mean that's the way you would think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+most easily think about it where you
+
+ align:start position:0%
+most easily think about it where you
+ 
+
+ align:start position:0%
+most easily think about it where you
+have the first one's output uh
+
+ align:start position:0%
+have the first one's output uh
+ 
+
+ align:start position:0%
+have the first one's output uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+affecting the second one the second one
+
+ align:start position:0%
+affecting the second one the second one
+ 
+
+ align:start position:0%
+affecting the second one the second one
+affected the third and third one looping
+
+ align:start position:0%
+affected the third and third one looping
+ 
+
+ align:start position:0%
+affected the third and third one looping
+back to the first and the result of this
+
+ align:start position:0%
+back to the first and the result of this
+ 
+
+ align:start position:0%
+back to the first and the result of this
+is you get a series
+
+ align:start position:0%
+is you get a series
+ 
+
+ align:start position:0%
+is you get a series
+of uh peaks and troughs here which you
+
+ align:start position:0%
+of uh peaks and troughs here which you
+ 
+
+ align:start position:0%
+of uh peaks and troughs here which you
+use for synchronizing circuits or
+
+ align:start position:0%
+use for synchronizing circuits or
+ 
+
+ align:start position:0%
+use for synchronizing circuits or
+generating other useful sinusoidal
+
+ align:start position:0%
+generating other useful sinusoidal
+ 
+
+ align:start position:0%
+generating other useful sinusoidal
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+now that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one example of sort of optical
+
+ align:start position:0%
+one example of sort of optical
+ 
+
+ align:start position:0%
+one example of sort of optical
+electronic molecular includes a number
+
+ align:start position:0%
+electronic molecular includes a number
+ 
+
+ align:start position:0%
+electronic molecular includes a number
+of different possibilities including dna
+
+ align:start position:0%
+of different possibilities including dna
+ 
+
+ align:start position:0%
+of different possibilities including dna
+which is what will focus on dna
+
+ align:start position:0%
+which is what will focus on dna
+ 
+
+ align:start position:0%
+which is what will focus on dna
+computing and this was started by a
+
+ align:start position:0%
+computing and this was started by a
+ 
+
+ align:start position:0%
+computing and this was started by a
+person a physicist famous for thinking
+
+ align:start position:0%
+person a physicist famous for thinking
+ 
+
+ align:start position:0%
+person a physicist famous for thinking
+out of the box quite a bit uh feynman in
+
+ align:start position:0%
+out of the box quite a bit uh feynman in
+ 
+
+ align:start position:0%
+out of the box quite a bit uh feynman in
+1959 when he was still fairly young
+
+ align:start position:0%
+1959 when he was still fairly young
+ 
+
+ align:start position:0%
+1959 when he was still fairly young
+gave a
+
+ align:start position:0%
+gave a
+ 
+
+ align:start position:0%
+gave a
+talk entitled there's plenty of room at
+
+ align:start position:0%
+talk entitled there's plenty of room at
+ 
+
+ align:start position:0%
+talk entitled there's plenty of room at
+the bottom
+
+ align:start position:0%
+the bottom
+ 
+
+ align:start position:0%
+the bottom
+and by that he meant
+
+ align:start position:0%
+and by that he meant
+ 
+
+ align:start position:0%
+and by that he meant
+that we can just as we can
+
+ align:start position:0%
+that we can just as we can
+ 
+
+ align:start position:0%
+that we can just as we can
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+machine and manufacture
+
+ align:start position:0%
+machine and manufacture
+ 
+
+ align:start position:0%
+machine and manufacture
+objects uh under
+
+ align:start position:0%
+objects uh under
+ 
+
+ align:start position:0%
+objects uh under
+fairly automated fashion we should be
+
+ align:start position:0%
+fairly automated fashion we should be
+ 
+
+ align:start position:0%
+fairly automated fashion we should be
+able to scale that down
+
+ align:start position:0%
+able to scale that down
+ 
+
+ align:start position:0%
+able to scale that down
+to the point where we're manipulating
+
+ align:start position:0%
+to the point where we're manipulating
+ 
+
+ align:start position:0%
+to the point where we're manipulating
+individual atoms and he couldn't think
+
+ align:start position:0%
+individual atoms and he couldn't think
+ 
+
+ align:start position:0%
+individual atoms and he couldn't think
+of any
+
+ align:start position:0%
+of any
+ 
+
+ align:start position:0%
+of any
+physical reason
+
+ align:start position:0%
+physical reason
+ 
+
+ align:start position:0%
+physical reason
+such as the uncertainty principle or
+
+ align:start position:0%
+such as the uncertainty principle or
+ 
+
+ align:start position:0%
+such as the uncertainty principle or
+anything like that that would prevent
+
+ align:start position:0%
+anything like that that would prevent
+ 
+
+ align:start position:0%
+anything like that that would prevent
+one from doing that manipulating
+
+ align:start position:0%
+one from doing that manipulating
+ 
+
+ align:start position:0%
+one from doing that manipulating
+individual atoms and many years later
+
+ align:start position:0%
+individual atoms and many years later
+ 
+
+ align:start position:0%
+individual atoms and many years later
+now he's been proven right and that we
+
+ align:start position:0%
+now he's been proven right and that we
+ 
+
+ align:start position:0%
+now he's been proven right and that we
+are doing that albeit not in any really
+
+ align:start position:0%
+are doing that albeit not in any really
+ 
+
+ align:start position:0%
+are doing that albeit not in any really
+high production method
+
+ align:start position:0%
+high production method
+ 
+
+ align:start position:0%
+high production method
+drexler in his thesis and subsequently
+
+ align:start position:0%
+drexler in his thesis and subsequently
+ 
+
+ align:start position:0%
+drexler in his thesis and subsequently
+has championed uh is probably the right
+
+ align:start position:0%
+has championed uh is probably the right
+ 
+
+ align:start position:0%
+has championed uh is probably the right
+word uh this sort of notion and then and
+
+ align:start position:0%
+word uh this sort of notion and then and
+ 
+
+ align:start position:0%
+word uh this sort of notion and then and
+giving it the name nanotechnology
+
+ align:start position:0%
+giving it the name nanotechnology
+ 
+
+ align:start position:0%
+giving it the name nanotechnology
+nanosystems
+
+ align:start position:0%
+nanosystems
+ 
+
+ align:start position:0%
+nanosystems
+and and really fleshed out some of the
+
+ align:start position:0%
+and and really fleshed out some of the
+ 
+
+ align:start position:0%
+and and really fleshed out some of the
+things that one might be able to do if
+
+ align:start position:0%
+things that one might be able to do if
+ 
+
+ align:start position:0%
+things that one might be able to do if
+you had a much
+
+ align:start position:0%
+you had a much
+ 
+
+ align:start position:0%
+you had a much
+higher throughput way of dealing with
+
+ align:start position:0%
+higher throughput way of dealing with
+ 
+
+ align:start position:0%
+higher throughput way of dealing with
+manufacturing an atomic scale
+
+ align:start position:0%
+manufacturing an atomic scale
+ 
+
+ align:start position:0%
+manufacturing an atomic scale
+however even he did not
+
+ align:start position:0%
+however even he did not
+ 
+
+ align:start position:0%
+however even he did not
+really connect all the dots between
+
+ align:start position:0%
+really connect all the dots between
+ 
+
+ align:start position:0%
+really connect all the dots between
+where we are now and where we and how we
+
+ align:start position:0%
+where we are now and where we and how we
+ 
+
+ align:start position:0%
+where we are now and where we and how we
+get to the very first nano assemblers
+
+ align:start position:0%
+get to the very first nano assemblers
+ 
+
+ align:start position:0%
+get to the very first nano assemblers
+and nano technology
+
+ align:start position:0%
+and nano technology
+ 
+
+ align:start position:0%
+and nano technology
+um since then there's been kind of a
+
+ align:start position:0%
+um since then there's been kind of a
+ 
+
+ align:start position:0%
+um since then there's been kind of a
+renaissance of interest in this um with
+
+ align:start position:0%
+renaissance of interest in this um with
+ 
+
+ align:start position:0%
+renaissance of interest in this um with
+the recognition that biological systems
+
+ align:start position:0%
+the recognition that biological systems
+ 
+
+ align:start position:0%
+the recognition that biological systems
+actually are sort of naturally doing
+
+ align:start position:0%
+actually are sort of naturally doing
+ 
+
+ align:start position:0%
+actually are sort of naturally doing
+nanotech now tech scale atomic
+
+ align:start position:0%
+nanotech now tech scale atomic
+ 
+
+ align:start position:0%
+nanotech now tech scale atomic
+manipulations
+
+ align:start position:0%
+manipulations
+ 
+
+ align:start position:0%
+manipulations
+and you've seen a few examples that in
+
+ align:start position:0%
+and you've seen a few examples that in
+ 
+
+ align:start position:0%
+and you've seen a few examples that in
+this course
+
+ align:start position:0%
+this course
+ 
+
+ align:start position:0%
+this course
+also you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the particular instance that we'll
+
+ align:start position:0%
+but the particular instance that we'll
+ 
+
+ align:start position:0%
+but the particular instance that we'll
+use as a jumping off point
+
+ align:start position:0%
+use as a jumping off point
+ 
+
+ align:start position:0%
+use as a jumping off point
+for discussion of all the steps that
+
+ align:start position:0%
+for discussion of all the steps that
+ 
+
+ align:start position:0%
+for discussion of all the steps that
+could be where biology and molecular
+
+ align:start position:0%
+could be where biology and molecular
+ 
+
+ align:start position:0%
+could be where biology and molecular
+mining could give us
+
+ align:start position:0%
+mining could give us
+ 
+
+ align:start position:0%
+mining could give us
+new tools
+
+ align:start position:0%
+new tools
+ 
+
+ align:start position:0%
+new tools
+whether it's from
+
+ align:start position:0%
+whether it's from
+ 
+
+ align:start position:0%
+whether it's from
+assembly
+
+ align:start position:0%
+assembly
+ 
+
+ align:start position:0%
+assembly
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+memory
+
+ align:start position:0%
+memory
+ 
+
+ align:start position:0%
+memory
+computation output
+
+ align:start position:0%
+computation output
+ 
+
+ align:start position:0%
+computation output
+we'll start with
+
+ align:start position:0%
+we'll start with
+ 
+
+ align:start position:0%
+we'll start with
+lynn adelman's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paste changing paper in 1994 this this
+
+ align:start position:0%
+paste changing paper in 1994 this this
+ 
+
+ align:start position:0%
+paste changing paper in 1994 this this
+is the a of the rsa that that
+
+ align:start position:0%
+is the a of the rsa that that
+ 
+
+ align:start position:0%
+is the a of the rsa that that
+we talked about just a few minutes ago
+
+ align:start position:0%
+we talked about just a few minutes ago
+ 
+
+ align:start position:0%
+we talked about just a few minutes ago
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+he was obviously a hardcore
+
+ align:start position:0%
+he was obviously a hardcore
+ 
+
+ align:start position:0%
+he was obviously a hardcore
+and is uh algorithmics
+
+ align:start position:0%
+and is uh algorithmics
+ 
+
+ align:start position:0%
+and is uh algorithmics
+expert
+
+ align:start position:0%
+expert
+ 
+
+ align:start position:0%
+expert
+and decided in 1994
+
+ align:start position:0%
+and decided in 1994
+ 
+
+ align:start position:0%
+and decided in 1994
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to actually do a paper that required not
+
+ align:start position:0%
+to actually do a paper that required not
+ 
+
+ align:start position:0%
+to actually do a paper that required not
+only algorithmics but a huge change in
+
+ align:start position:0%
+only algorithmics but a huge change in
+ 
+
+ align:start position:0%
+only algorithmics but a huge change in
+the way you implemented the algorithms
+
+ align:start position:0%
+the way you implemented the algorithms
+ 
+
+ align:start position:0%
+the way you implemented the algorithms
+and then actually to go into the lab
+
+ align:start position:0%
+and then actually to go into the lab
+ 
+
+ align:start position:0%
+and then actually to go into the lab
+into a biochemical laboratory which he
+
+ align:start position:0%
+into a biochemical laboratory which he
+ 
+
+ align:start position:0%
+into a biochemical laboratory which he
+was not
+
+ align:start position:0%
+was not
+ 
+
+ align:start position:0%
+was not
+previously
+
+ align:start position:0%
+previously
+ 
+
+ align:start position:0%
+previously
+trained
+
+ align:start position:0%
+trained
+ 
+
+ align:start position:0%
+trained
+and to to author it's a single author
+
+ align:start position:0%
+and to to author it's a single author
+ 
+
+ align:start position:0%
+and to to author it's a single author
+paper that included such things as pcr
+
+ align:start position:0%
+paper that included such things as pcr
+ 
+
+ align:start position:0%
+paper that included such things as pcr
+as in 1994 there was no literature on
+
+ align:start position:0%
+as in 1994 there was no literature on
+ 
+
+ align:start position:0%
+as in 1994 there was no literature on
+the subject of dna
+
+ align:start position:0%
+the subject of dna
+ 
+
+ align:start position:0%
+the subject of dna
+computers before that a mere six years
+
+ align:start position:0%
+computers before that a mere six years
+ 
+
+ align:start position:0%
+computers before that a mere six years
+later there were 520 references on the
+
+ align:start position:0%
+later there were 520 references on the
+ 
+
+ align:start position:0%
+later there were 520 references on the
+subject so he obviously hit some kind of
+
+ align:start position:0%
+subject so he obviously hit some kind of
+ 
+
+ align:start position:0%
+subject so he obviously hit some kind of
+nerve
+
+ align:start position:0%
+nerve
+ 
+
+ align:start position:0%
+nerve
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+first few years of that after that were
+
+ align:start position:0%
+first few years of that after that were
+ 
+
+ align:start position:0%
+first few years of that after that were
+mainly theoretical but i'll show you
+
+ align:start position:0%
+mainly theoretical but i'll show you
+ 
+
+ align:start position:0%
+mainly theoretical but i'll show you
+some example but his paper was was had
+
+ align:start position:0%
+some example but his paper was was had
+ 
+
+ align:start position:0%
+some example but his paper was was had
+an experimental component and some
+
+ align:start position:0%
+an experimental component and some
+ 
+
+ align:start position:0%
+an experimental component and some
+others that i'll show you
+
+ align:start position:0%
+others that i'll show you
+ 
+
+ align:start position:0%
+others that i'll show you
+since this course is really about that
+
+ align:start position:0%
+since this course is really about that
+ 
+
+ align:start position:0%
+since this course is really about that
+interface constantly checking the theory
+
+ align:start position:0%
+interface constantly checking the theory
+ 
+
+ align:start position:0%
+interface constantly checking the theory
+with reality
+
+ align:start position:0%
+with reality
+ 
+
+ align:start position:0%
+with reality
+that's those are the ones that i'll
+
+ align:start position:0%
+that's those are the ones that i'll
+ 
+
+ align:start position:0%
+that's those are the ones that i'll
+emphasize here
+
+ align:start position:0%
+emphasize here
+ 
+
+ align:start position:0%
+emphasize here
+so the question that he asked in 1994
+
+ align:start position:0%
+so the question that he asked in 1994
+ 
+
+ align:start position:0%
+so the question that he asked in 1994
+and is still fresh today is is there a
+
+ align:start position:0%
+and is still fresh today is is there a
+ 
+
+ align:start position:0%
+and is still fresh today is is there a
+hamiltonian path through all the nodes
+
+ align:start position:0%
+hamiltonian path through all the nodes
+ 
+
+ align:start position:0%
+hamiltonian path through all the nodes
+in a network so we've been talking about
+
+ align:start position:0%
+in a network so we've been talking about
+ 
+
+ align:start position:0%
+in a network so we've been talking about
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+biological networks but here you know
+
+ align:start position:0%
+biological networks but here you know
+ 
+
+ align:start position:0%
+biological networks but here you know
+just in any network where the black
+
+ align:start position:0%
+just in any network where the black
+ 
+
+ align:start position:0%
+just in any network where the black
+nodes are connected by directed
+
+ align:start position:0%
+nodes are connected by directed
+ 
+
+ align:start position:0%
+nodes are connected by directed
+uh edges in this directed graph you want
+
+ align:start position:0%
+uh edges in this directed graph you want
+ 
+
+ align:start position:0%
+uh edges in this directed graph you want
+to go from the start s to the terminus t
+
+ align:start position:0%
+to go from the start s to the terminus t
+ 
+
+ align:start position:0%
+to go from the start s to the terminus t
+from 1 to 6
+
+ align:start position:0%
+from 1 to 6
+ 
+
+ align:start position:0%
+from 1 to 6
+obeying the arrows and going through
+
+ align:start position:0%
+obeying the arrows and going through
+ 
+
+ align:start position:0%
+obeying the arrows and going through
+every point once
+
+ align:start position:0%
+every point once
+ 
+
+ align:start position:0%
+every point once
+how do you do this
+
+ align:start position:0%
+how do you do this
+ 
+
+ align:start position:0%
+how do you do this
+and how do you do it in dna
+
+ align:start position:0%
+and how do you do it in dna
+ 
+
+ align:start position:0%
+and how do you do it in dna
+so an example of one here is going from
+
+ align:start position:0%
+so an example of one here is going from
+ 
+
+ align:start position:0%
+so an example of one here is going from
+s to three to five to two to the fourth
+
+ align:start position:0%
+s to three to five to two to the fourth
+ 
+
+ align:start position:0%
+s to three to five to two to the fourth
+to t
+
+ align:start position:0%
+to t
+ 
+
+ align:start position:0%
+to t
+okay so the way you do it
+
+ align:start position:0%
+okay so the way you do it
+ 
+
+ align:start position:0%
+okay so the way you do it
+first uh in broad strokes you encode the
+
+ align:start position:0%
+first uh in broad strokes you encode the
+ 
+
+ align:start position:0%
+first uh in broad strokes you encode the
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+both the nodes
+
+ align:start position:0%
+both the nodes
+ 
+
+ align:start position:0%
+both the nodes
+black spots and the edges into single
+
+ align:start position:0%
+black spots and the edges into single
+ 
+
+ align:start position:0%
+black spots and the edges into single
+stranded dna sequences
+
+ align:start position:0%
+stranded dna sequences
+ 
+
+ align:start position:0%
+stranded dna sequences
+then you create all possible paths
+
+ align:start position:0%
+then you create all possible paths
+ 
+
+ align:start position:0%
+then you create all possible paths
+as by using overlapping sequences to
+
+ align:start position:0%
+as by using overlapping sequences to
+ 
+
+ align:start position:0%
+as by using overlapping sequences to
+indicate which node is connected to
+
+ align:start position:0%
+indicate which node is connected to
+ 
+
+ align:start position:0%
+indicate which node is connected to
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+other node by what by an edge in which
+
+ align:start position:0%
+other node by what by an edge in which
+ 
+
+ align:start position:0%
+other node by what by an edge in which
+direction so you can actually have
+
+ align:start position:0%
+direction so you can actually have
+ 
+
+ align:start position:0%
+direction so you can actually have
+directionality just
+
+ align:start position:0%
+directionality just
+ 
+
+ align:start position:0%
+directionality just
+because you know dna has directionality
+
+ align:start position:0%
+because you know dna has directionality
+ 
+
+ align:start position:0%
+because you know dna has directionality
+and you use dna hybridization now to do
+
+ align:start position:0%
+and you use dna hybridization now to do
+ 
+
+ align:start position:0%
+and you use dna hybridization now to do
+that step
+
+ align:start position:0%
+that step
+ 
+
+ align:start position:0%
+that step
+now the first step is linear encoding
+
+ align:start position:0%
+now the first step is linear encoding
+ 
+
+ align:start position:0%
+now the first step is linear encoding
+the graph is linear with the number of
+
+ align:start position:0%
+the graph is linear with the number of
+ 
+
+ align:start position:0%
+the graph is linear with the number of
+points in the graph the number of places
+
+ align:start position:0%
+points in the graph the number of places
+ 
+
+ align:start position:0%
+points in the graph the number of places
+in the hamiltonian path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second step is not something and
+
+ align:start position:0%
+the second step is not something and
+ 
+
+ align:start position:0%
+the second step is not something and
+that you would do by having your
+
+ align:start position:0%
+that you would do by having your
+ 
+
+ align:start position:0%
+that you would do by having your
+computer program a dna synthesizer which
+
+ align:start position:0%
+computer program a dna synthesizer which
+ 
+
+ align:start position:0%
+computer program a dna synthesizer which
+is an automated machine that we've
+
+ align:start position:0%
+is an automated machine that we've
+ 
+
+ align:start position:0%
+is an automated machine that we've
+described
+
+ align:start position:0%
+described
+ 
+
+ align:start position:0%
+described
+a couple times
+
+ align:start position:0%
+a couple times
+ 
+
+ align:start position:0%
+a couple times
+the second step is
+
+ align:start position:0%
+the second step is
+ 
+
+ align:start position:0%
+the second step is
+is out of your hands this is something
+
+ align:start position:0%
+is out of your hands this is something
+ 
+
+ align:start position:0%
+is out of your hands this is something
+that's uh
+
+ align:start position:0%
+that's uh
+ 
+
+ align:start position:0%
+that's uh
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that happens automatically when you put
+
+ align:start position:0%
+that happens automatically when you put
+ 
+
+ align:start position:0%
+that happens automatically when you put
+dna in the solution if you design these
+
+ align:start position:0%
+dna in the solution if you design these
+ 
+
+ align:start position:0%
+dna in the solution if you design these
+sequences carefully so they don't cross
+
+ align:start position:0%
+sequences carefully so they don't cross
+ 
+
+ align:start position:0%
+sequences carefully so they don't cross
+hybridize very much then the only way
+
+ align:start position:0%
+hybridize very much then the only way
+ 
+
+ align:start position:0%
+hybridize very much then the only way
+they can assemble is the way you want it
+
+ align:start position:0%
+they can assemble is the way you want it
+ 
+
+ align:start position:0%
+they can assemble is the way you want it
+and then you then finally determine
+
+ align:start position:0%
+and then you then finally determine
+ 
+
+ align:start position:0%
+and then you then finally determine
+whether solution exists and this is
+
+ align:start position:0%
+whether solution exists and this is
+ 
+
+ align:start position:0%
+whether solution exists and this is
+something which is almost constant
+
+ align:start position:0%
+something which is almost constant
+ 
+
+ align:start position:0%
+something which is almost constant
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+complexity so the entire thing scales
+
+ align:start position:0%
+complexity so the entire thing scales
+ 
+
+ align:start position:0%
+complexity so the entire thing scales
+very gracefully
+
+ align:start position:0%
+very gracefully
+ 
+
+ align:start position:0%
+very gracefully
+instead of scaling
+
+ align:start position:0%
+instead of scaling
+ 
+
+ align:start position:0%
+instead of scaling
+exponentially as the hamiltonian path
+
+ align:start position:0%
+exponentially as the hamiltonian path
+ 
+
+ align:start position:0%
+exponentially as the hamiltonian path
+problem normally would this gives the
+
+ align:start position:0%
+problem normally would this gives the
+ 
+
+ align:start position:0%
+problem normally would this gives the
+appearance of a scaling
+
+ align:start position:0%
+appearance of a scaling
+ 
+
+ align:start position:0%
+appearance of a scaling
+linearly in time which is really
+
+ align:start position:0%
+linearly in time which is really
+ 
+
+ align:start position:0%
+linearly in time which is really
+one of the best case scenarios for
+
+ align:start position:0%
+one of the best case scenarios for
+ 
+
+ align:start position:0%
+one of the best case scenarios for
+polynomial time and certainly better
+
+ align:start position:0%
+polynomial time and certainly better
+ 
+
+ align:start position:0%
+polynomial time and certainly better
+than exponential
+
+ align:start position:0%
+than exponential
+ 
+
+ align:start position:0%
+than exponential
+so how do we actually do those broad
+
+ align:start position:0%
+so how do we actually do those broad
+ 
+
+ align:start position:0%
+so how do we actually do those broad
+strokes this is a more detailed view and
+
+ align:start position:0%
+strokes this is a more detailed view and
+ 
+
+ align:start position:0%
+strokes this is a more detailed view and
+you can see how this really seems like
+
+ align:start position:0%
+you can see how this really seems like
+ 
+
+ align:start position:0%
+you can see how this really seems like
+it's going to work you have
+
+ align:start position:0%
+it's going to work you have
+ 
+
+ align:start position:0%
+it's going to work you have
+each of the nodes
+
+ align:start position:0%
+each of the nodes
+ 
+
+ align:start position:0%
+each of the nodes
+encoded by sequences
+
+ align:start position:0%
+encoded by sequences
+ 
+
+ align:start position:0%
+encoded by sequences
+let's say the red
+
+ align:start position:0%
+let's say the red
+ 
+
+ align:start position:0%
+let's say the red
+and tan here on the top left of slide 14
+
+ align:start position:0%
+and tan here on the top left of slide 14
+ 
+
+ align:start position:0%
+and tan here on the top left of slide 14
+and you have
+
+ align:start position:0%
+and you have
+ 
+
+ align:start position:0%
+and you have
+if you want to connect node three
+
+ align:start position:0%
+if you want to connect node three
+ 
+
+ align:start position:0%
+if you want to connect node three
+with node four so that
+
+ align:start position:0%
+with node four so that
+ 
+
+ align:start position:0%
+with node four so that
+you take the right hand end the three
+
+ align:start position:0%
+you take the right hand end the three
+ 
+
+ align:start position:0%
+you take the right hand end the three
+prime ends which is sort of greenish can
+
+ align:start position:0%
+prime ends which is sort of greenish can
+ 
+
+ align:start position:0%
+prime ends which is sort of greenish can
+and you connect it now to the
+
+ align:start position:0%
+and you connect it now to the
+ 
+
+ align:start position:0%
+and you connect it now to the
+other end of uh that is to say the five
+
+ align:start position:0%
+other end of uh that is to say the five
+ 
+
+ align:start position:0%
+other end of uh that is to say the five
+prime end of node four just below it
+
+ align:start position:0%
+prime end of node four just below it
+ 
+
+ align:start position:0%
+prime end of node four just below it
+which is blue so now you have this
+
+ align:start position:0%
+which is blue so now you have this
+ 
+
+ align:start position:0%
+which is blue so now you have this
+hybrid um
+
+ align:start position:0%
+hybrid um
+ 
+
+ align:start position:0%
+hybrid um
+which is ordered so it has so it's an
+
+ align:start position:0%
+which is ordered so it has so it's an
+ 
+
+ align:start position:0%
+which is ordered so it has so it's an
+arrow going from three to four
+
+ align:start position:0%
+arrow going from three to four
+ 
+
+ align:start position:0%
+arrow going from three to four
+and um and that edge has this particular
+
+ align:start position:0%
+and um and that edge has this particular
+ 
+
+ align:start position:0%
+and um and that edge has this particular
+sequence going from 5 prime to 3 prime
+
+ align:start position:0%
+sequence going from 5 prime to 3 prime
+ 
+
+ align:start position:0%
+sequence going from 5 prime to 3 prime
+now in practice you want the edges to be
+
+ align:start position:0%
+now in practice you want the edges to be
+ 
+
+ align:start position:0%
+now in practice you want the edges to be
+complementary not identical to the nodes
+
+ align:start position:0%
+complementary not identical to the nodes
+ 
+
+ align:start position:0%
+complementary not identical to the nodes
+and so all the nodes are actually
+
+ align:start position:0%
+and so all the nodes are actually
+ 
+
+ align:start position:0%
+and so all the nodes are actually
+represented as reverse sequences um in
+
+ align:start position:0%
+represented as reverse sequences um in
+ 
+
+ align:start position:0%
+represented as reverse sequences um in
+the lower left-hand part of
+
+ align:start position:0%
+the lower left-hand part of
+ 
+
+ align:start position:0%
+the lower left-hand part of
+slide 14. and so represent all the
+
+ align:start position:0%
+slide 14. and so represent all the
+ 
+
+ align:start position:0%
+slide 14. and so represent all the
+edges that connect nodes by the in this
+
+ align:start position:0%
+edges that connect nodes by the in this
+ 
+
+ align:start position:0%
+edges that connect nodes by the in this
+directional manner
+
+ align:start position:0%
+directional manner
+ 
+
+ align:start position:0%
+directional manner
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+an example of
+
+ align:start position:0%
+an example of
+ 
+
+ align:start position:0%
+an example of
+how you would connect three nodes three
+
+ align:start position:0%
+how you would connect three nodes three
+ 
+
+ align:start position:0%
+how you would connect three nodes three
+to four to five
+
+ align:start position:0%
+to four to five
+ 
+
+ align:start position:0%
+to four to five
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+two connecting directional edges three
+
+ align:start position:0%
+two connecting directional edges three
+ 
+
+ align:start position:0%
+two connecting directional edges three
+four four five is shown here all the
+
+ align:start position:0%
+four four five is shown here all the
+ 
+
+ align:start position:0%
+four four five is shown here all the
+nodes are in reverse complements
+
+ align:start position:0%
+nodes are in reverse complements
+ 
+
+ align:start position:0%
+nodes are in reverse complements
+and all the edges
+
+ align:start position:0%
+and all the edges
+ 
+
+ align:start position:0%
+and all the edges
+are in the forward
+
+ align:start position:0%
+are in the forward
+ 
+
+ align:start position:0%
+are in the forward
+direction as arbitrarily defined here
+
+ align:start position:0%
+direction as arbitrarily defined here
+ 
+
+ align:start position:0%
+direction as arbitrarily defined here
+and you can see how these stitch these
+
+ align:start position:0%
+and you can see how these stitch these
+ 
+
+ align:start position:0%
+and you can see how these stitch these
+together and you make firm connections
+
+ align:start position:0%
+together and you make firm connections
+ 
+
+ align:start position:0%
+together and you make firm connections
+that are unambiguous not non-cross
+
+ align:start position:0%
+that are unambiguous not non-cross
+ 
+
+ align:start position:0%
+that are unambiguous not non-cross
+reacting
+
+ align:start position:0%
+reacting
+ 
+
+ align:start position:0%
+reacting
+and have a direct directionality
+
+ align:start position:0%
+and have a direct directionality
+ 
+
+ align:start position:0%
+and have a direct directionality
+now that
+
+ align:start position:0%
+now that
+ 
+
+ align:start position:0%
+now that
+you're starting to get the idea that now
+
+ align:start position:0%
+you're starting to get the idea that now
+ 
+
+ align:start position:0%
+you're starting to get the idea that now
+we can encode this in dna but how we're
+
+ align:start position:0%
+we can encode this in dna but how we're
+ 
+
+ align:start position:0%
+we can encode this in dna but how we're
+going to actually do the computation and
+
+ align:start position:0%
+going to actually do the computation and
+ 
+
+ align:start position:0%
+going to actually do the computation and
+how we're going to find out who the
+
+ align:start position:0%
+how we're going to find out who the
+ 
+
+ align:start position:0%
+how we're going to find out who the
+winner is
+
+ align:start position:0%
+winner is
+ 
+
+ align:start position:0%
+winner is
+so what what is done
+
+ align:start position:0%
+so what what is done
+ 
+
+ align:start position:0%
+so what what is done
+remember we want to create all the paths
+
+ align:start position:0%
+remember we want to create all the paths
+ 
+
+ align:start position:0%
+remember we want to create all the paths
+and then ask whether any of them go
+
+ align:start position:0%
+and then ask whether any of them go
+ 
+
+ align:start position:0%
+and then ask whether any of them go
+through all the points and then do any
+
+ align:start position:0%
+through all the points and then do any
+ 
+
+ align:start position:0%
+through all the points and then do any
+of them go through all the points
+
+ align:start position:0%
+of them go through all the points
+ 
+
+ align:start position:0%
+of them go through all the points
+exactly once so the first thing is to
+
+ align:start position:0%
+exactly once so the first thing is to
+ 
+
+ align:start position:0%
+exactly once so the first thing is to
+create all the paths from start to
+
+ align:start position:0%
+create all the paths from start to
+ 
+
+ align:start position:0%
+create all the paths from start to
+terminus and by and by just throwing in
+
+ align:start position:0%
+terminus and by and by just throwing in
+ 
+
+ align:start position:0%
+terminus and by and by just throwing in
+this mixture of all the all the edges
+
+ align:start position:0%
+this mixture of all the all the edges
+ 
+
+ align:start position:0%
+this mixture of all the all the edges
+and all the nodes you will create in
+
+ align:start position:0%
+and all the nodes you will create in
+ 
+
+ align:start position:0%
+and all the nodes you will create in
+principle all the paths now you want to
+
+ align:start position:0%
+principle all the paths now you want to
+ 
+
+ align:start position:0%
+principle all the paths now you want to
+right you will go from the prefix of one
+
+ align:start position:0%
+right you will go from the prefix of one
+ 
+
+ align:start position:0%
+right you will go from the prefix of one
+into the suffix the other
+
+ align:start position:0%
+into the suffix the other
+ 
+
+ align:start position:0%
+into the suffix the other
+in the same way that illustrated on the
+
+ align:start position:0%
+in the same way that illustrated on the
+ 
+
+ align:start position:0%
+in the same way that illustrated on the
+previous slide
+
+ align:start position:0%
+previous slide
+ 
+
+ align:start position:0%
+previous slide
+and here are some examples of some of
+
+ align:start position:0%
+and here are some examples of some of
+ 
+
+ align:start position:0%
+and here are some examples of some of
+the paths some are very short this only
+
+ align:start position:0%
+the paths some are very short this only
+ 
+
+ align:start position:0%
+the paths some are very short this only
+goes through four the one two four six
+
+ align:start position:0%
+goes through four the one two four six
+ 
+
+ align:start position:0%
+goes through four the one two four six
+uh only goes through four of the nodes
+
+ align:start position:0%
+uh only goes through four of the nodes
+ 
+
+ align:start position:0%
+uh only goes through four of the nodes
+that's not all six of them the bottom
+
+ align:start position:0%
+that's not all six of them the bottom
+ 
+
+ align:start position:0%
+that's not all six of them the bottom
+one goes through too many nodes and two
+
+ align:start position:0%
+one goes through too many nodes and two
+ 
+
+ align:start position:0%
+one goes through too many nodes and two
+minutes some of them it's going through
+
+ align:start position:0%
+minutes some of them it's going through
+ 
+
+ align:start position:0%
+minutes some of them it's going through
+repetitively
+
+ align:start position:0%
+repetitively
+ 
+
+ align:start position:0%
+repetitively
+but you get the idea is that you can
+
+ align:start position:0%
+but you get the idea is that you can
+ 
+
+ align:start position:0%
+but you get the idea is that you can
+define the path in terms of all these
+
+ align:start position:0%
+define the path in terms of all these
+ 
+
+ align:start position:0%
+define the path in terms of all these
+edges and the reverse complements which
+
+ align:start position:0%
+edges and the reverse complements which
+ 
+
+ align:start position:0%
+edges and the reverse complements which
+represent the nodes
+
+ align:start position:0%
+represent the nodes
+ 
+
+ align:start position:0%
+represent the nodes
+but here's the actual algorithm as
+
+ align:start position:0%
+but here's the actual algorithm as
+ 
+
+ align:start position:0%
+but here's the actual algorithm as
+encoded in dna
+
+ align:start position:0%
+encoded in dna
+ 
+
+ align:start position:0%
+encoded in dna
+and implemented by practical
+
+ align:start position:0%
+and implemented by practical
+ 
+
+ align:start position:0%
+and implemented by practical
+methods that a a computer scientist
+
+ align:start position:0%
+methods that a a computer scientist
+ 
+
+ align:start position:0%
+methods that a a computer scientist
+can do
+
+ align:start position:0%
+can do
+ 
+
+ align:start position:0%
+can do
+without too much help at least not
+
+ align:start position:0%
+without too much help at least not
+ 
+
+ align:start position:0%
+without too much help at least not
+enough help required for authorship
+
+ align:start position:0%
+enough help required for authorship
+ 
+
+ align:start position:0%
+enough help required for authorship
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you and go we've already encoded the
+
+ align:start position:0%
+you and go we've already encoded the
+ 
+
+ align:start position:0%
+you and go we've already encoded the
+graph in the dna sequences
+
+ align:start position:0%
+graph in the dna sequences
+ 
+
+ align:start position:0%
+graph in the dna sequences
+and this is done by automated
+
+ align:start position:0%
+and this is done by automated
+ 
+
+ align:start position:0%
+and this is done by automated
+oligonucleotide synthesis you create all
+
+ align:start position:0%
+oligonucleotide synthesis you create all
+ 
+
+ align:start position:0%
+oligonucleotide synthesis you create all
+the paths from s to t by pcr amplifying
+
+ align:start position:0%
+the paths from s to t by pcr amplifying
+ 
+
+ align:start position:0%
+the paths from s to t by pcr amplifying
+from the s end of the oligo to the t end
+
+ align:start position:0%
+from the s end of the oligo to the t end
+ 
+
+ align:start position:0%
+from the s end of the oligo to the t end
+so that means the mere fact that they
+
+ align:start position:0%
+so that means the mere fact that they
+ 
+
+ align:start position:0%
+so that means the mere fact that they
+pcr amplify means they must contain node
+
+ align:start position:0%
+pcr amplify means they must contain node
+ 
+
+ align:start position:0%
+pcr amplify means they must contain node
+one and six the start and determinants
+
+ align:start position:0%
+one and six the start and determinants
+ 
+
+ align:start position:0%
+one and six the start and determinants
+so that's good
+
+ align:start position:0%
+so that's good
+ 
+
+ align:start position:0%
+so that's good
+now you wanna get the ones that visit
+
+ align:start position:0%
+now you wanna get the ones that visit
+ 
+
+ align:start position:0%
+now you wanna get the ones that visit
+every node so by serial hybridization
+
+ align:start position:0%
+every node so by serial hybridization
+ 
+
+ align:start position:0%
+every node so by serial hybridization
+you can have
+
+ align:start position:0%
+you can have
+ 
+
+ align:start position:0%
+you can have
+you can have those two three four and
+
+ align:start position:0%
+you can have those two three four and
+ 
+
+ align:start position:0%
+you can have those two three four and
+five immobilized and you bind the pcr
+
+ align:start position:0%
+five immobilized and you bind the pcr
+ 
+
+ align:start position:0%
+five immobilized and you bind the pcr
+products to it and then you'll lose from
+
+ align:start position:0%
+products to it and then you'll lose from
+ 
+
+ align:start position:0%
+products to it and then you'll lose from
+two and then in series you bind to three
+
+ align:start position:0%
+two and then in series you bind to three
+ 
+
+ align:start position:0%
+two and then in series you bind to three
+from three find it four loop four or
+
+ align:start position:0%
+from three find it four loop four or
+ 
+
+ align:start position:0%
+from three find it four loop four or
+five so now you know it has one and six
+
+ align:start position:0%
+five so now you know it has one and six
+ 
+
+ align:start position:0%
+five so now you know it has one and six
+because that's the pcr primers it has
+
+ align:start position:0%
+because that's the pcr primers it has
+ 
+
+ align:start position:0%
+because that's the pcr primers it has
+two three four and five because it
+
+ align:start position:0%
+two three four and five because it
+ 
+
+ align:start position:0%
+two three four and five because it
+balances them in series by hybridization
+
+ align:start position:0%
+balances them in series by hybridization
+ 
+
+ align:start position:0%
+balances them in series by hybridization
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+but that you could get some of those
+
+ align:start position:0%
+but that you could get some of those
+ 
+
+ align:start position:0%
+but that you could get some of those
+long
+
+ align:start position:0%
+long
+ 
+
+ align:start position:0%
+long
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+paths that went through multiple those
+
+ align:start position:0%
+paths that went through multiple those
+ 
+
+ align:start position:0%
+paths that went through multiple those
+multiple times if you wanted to have
+
+ align:start position:0%
+multiple times if you wanted to have
+ 
+
+ align:start position:0%
+multiple times if you wanted to have
+exactly n nodes and what you do is some
+
+ align:start position:0%
+exactly n nodes and what you do is some
+ 
+
+ align:start position:0%
+exactly n nodes and what you do is some
+sort of electrophoretic sizing and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here if you have a calibration curve
+
+ align:start position:0%
+and here if you have a calibration curve
+ 
+
+ align:start position:0%
+and here if you have a calibration curve
+as shown at the bottom of slide 16 we
+
+ align:start position:0%
+as shown at the bottom of slide 16 we
+ 
+
+ align:start position:0%
+as shown at the bottom of slide 16 we
+have known dna size markers and no pcr
+
+ align:start position:0%
+have known dna size markers and no pcr
+ 
+
+ align:start position:0%
+have known dna size markers and no pcr
+products going um showing you have
+
+ align:start position:0%
+products going um showing you have
+ 
+
+ align:start position:0%
+products going um showing you have
+one of these dna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nodes two three all the way up to six
+
+ align:start position:0%
+nodes two three all the way up to six
+ 
+
+ align:start position:0%
+nodes two three all the way up to six
+and if you find a solution that has all
+
+ align:start position:0%
+and if you find a solution that has all
+ 
+
+ align:start position:0%
+and if you find a solution that has all
+these properties pcrs does serial
+
+ align:start position:0%
+these properties pcrs does serial
+ 
+
+ align:start position:0%
+these properties pcrs does serial
+hybridization to all the nodes and is
+
+ align:start position:0%
+hybridization to all the nodes and is
+ 
+
+ align:start position:0%
+hybridization to all the nodes and is
+the right length such as the one
+
+ align:start position:0%
+the right length such as the one
+ 
+
+ align:start position:0%
+the right length such as the one
+in column six then you know you've got a
+
+ align:start position:0%
+in column six then you know you've got a
+ 
+
+ align:start position:0%
+in column six then you know you've got a
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+and that was
+
+ align:start position:0%
+and that was
+ 
+
+ align:start position:0%
+and that was
+when edelman's argument that he had dna
+
+ align:start position:0%
+when edelman's argument that he had dna
+ 
+
+ align:start position:0%
+when edelman's argument that he had dna
+computing working
+
+ align:start position:0%
+computing working
+ 
+
+ align:start position:0%
+computing working
+six years later we now have or
+
+ align:start position:0%
+six years later we now have or
+ 
+
+ align:start position:0%
+six years later we now have or
+as of six years later there were now
+
+ align:start position:0%
+as of six years later there were now
+ 
+
+ align:start position:0%
+as of six years later there were now
+over 500
+
+ align:start position:0%
+over 500
+ 
+
+ align:start position:0%
+over 500
+examples of this i'll show you
+
+ align:start position:0%
+examples of this i'll show you
+ 
+
+ align:start position:0%
+examples of this i'll show you
+this example
+
+ align:start position:0%
+this example
+ 
+
+ align:start position:0%
+this example
+as both as an introduction to the
+
+ align:start position:0%
+as both as an introduction to the
+ 
+
+ align:start position:0%
+as both as an introduction to the
+satisfiability problem and also as uh
+
+ align:start position:0%
+satisfiability problem and also as uh
+ 
+
+ align:start position:0%
+satisfiability problem and also as uh
+showing that you can do rna computing
+
+ align:start position:0%
+showing that you can do rna computing
+ 
+
+ align:start position:0%
+showing that you can do rna computing
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and that you can encode two-dimensional
+
+ align:start position:0%
+and that you can encode two-dimensional
+ 
+
+ align:start position:0%
+and that you can encode two-dimensional
+objects and it illustrates a number of
+
+ align:start position:0%
+objects and it illustrates a number of
+ 
+
+ align:start position:0%
+objects and it illustrates a number of
+things the problem here is a chest
+
+ align:start position:0%
+things the problem here is a chest
+ 
+
+ align:start position:0%
+things the problem here is a chest
+problem very simple chess board it's not
+
+ align:start position:0%
+problem very simple chess board it's not
+ 
+
+ align:start position:0%
+problem very simple chess board it's not
+eight by eight but three by three as and
+
+ align:start position:0%
+eight by eight but three by three as and
+ 
+
+ align:start position:0%
+eight by eight but three by three as and
+the other and you've got an artifice
+
+ align:start position:0%
+the other and you've got an artifice
+ 
+
+ align:start position:0%
+the other and you've got an artifice
+you've got an artificial number of
+
+ align:start position:0%
+you've got an artificial number of
+ 
+
+ align:start position:0%
+you've got an artificial number of
+knights here and you those you know
+
+ align:start position:0%
+knights here and you those you know
+ 
+
+ align:start position:0%
+knights here and you those you know
+chess know that these knights can can
+
+ align:start position:0%
+chess know that these knights can can
+ 
+
+ align:start position:0%
+chess know that these knights can can
+attack in a curious combination of
+
+ align:start position:0%
+attack in a curious combination of
+ 
+
+ align:start position:0%
+attack in a curious combination of
+straight and diagonal it doesn't really
+
+ align:start position:0%
+straight and diagonal it doesn't really
+ 
+
+ align:start position:0%
+straight and diagonal it doesn't really
+matter the point is that this these are
+
+ align:start position:0%
+matter the point is that this these are
+ 
+
+ align:start position:0%
+matter the point is that this these are
+there are a variety of arrangements of
+
+ align:start position:0%
+there are a variety of arrangements of
+ 
+
+ align:start position:0%
+there are a variety of arrangements of
+of any number of knights such that none
+
+ align:start position:0%
+of any number of knights such that none
+ 
+
+ align:start position:0%
+of any number of knights such that none
+of them can attack each other and
+
+ align:start position:0%
+of them can attack each other and
+ 
+
+ align:start position:0%
+of them can attack each other and
+they're all kind of at peace here
+
+ align:start position:0%
+they're all kind of at peace here
+ 
+
+ align:start position:0%
+they're all kind of at peace here
+and the the object of this algorithm is
+
+ align:start position:0%
+and the the object of this algorithm is
+ 
+
+ align:start position:0%
+and the the object of this algorithm is
+to find those combinations and and
+
+ align:start position:0%
+to find those combinations and and
+ 
+
+ align:start position:0%
+to find those combinations and and
+here's uh and you do it by cloning so
+
+ align:start position:0%
+here's uh and you do it by cloning so
+ 
+
+ align:start position:0%
+here's uh and you do it by cloning so
+that was something that
+
+ align:start position:0%
+that was something that
+ 
+
+ align:start position:0%
+that was something that
+was not in the previous example by
+
+ align:start position:0%
+was not in the previous example by
+ 
+
+ align:start position:0%
+was not in the previous example by
+cloning you could find each of the
+
+ align:start position:0%
+cloning you could find each of the
+ 
+
+ align:start position:0%
+cloning you could find each of the
+solutions and you could then determine
+
+ align:start position:0%
+solutions and you could then determine
+ 
+
+ align:start position:0%
+solutions and you could then determine
+what is present in cis along that clones
+
+ align:start position:0%
+what is present in cis along that clones
+ 
+
+ align:start position:0%
+what is present in cis along that clones
+kind of like haplotyping or or splice
+
+ align:start position:0%
+kind of like haplotyping or or splice
+ 
+
+ align:start position:0%
+kind of like haplotyping or or splice
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+uh analysis you can really only analyze
+
+ align:start position:0%
+uh analysis you can really only analyze
+ 
+
+ align:start position:0%
+uh analysis you can really only analyze
+these things by looking at a single at
+
+ align:start position:0%
+these things by looking at a single at
+ 
+
+ align:start position:0%
+these things by looking at a single at
+the product of a single molecule and
+
+ align:start position:0%
+the product of a single molecule and
+ 
+
+ align:start position:0%
+the product of a single molecule and
+that's what cloning is about looking at
+
+ align:start position:0%
+that's what cloning is about looking at
+ 
+
+ align:start position:0%
+that's what cloning is about looking at
+amplifying that single molecule to the
+
+ align:start position:0%
+amplifying that single molecule to the
+ 
+
+ align:start position:0%
+amplifying that single molecule to the
+point where you can analyze it so that's
+
+ align:start position:0%
+point where you can analyze it so that's
+ 
+
+ align:start position:0%
+point where you can analyze it so that's
+one thing that's new the other thing is
+
+ align:start position:0%
+one thing that's new the other thing is
+ 
+
+ align:start position:0%
+one thing that's new the other thing is
+new is you start with
+
+ align:start position:0%
+new is you start with
+ 
+
+ align:start position:0%
+new is you start with
+with an rna
+
+ align:start position:0%
+with an rna
+ 
+
+ align:start position:0%
+with an rna
+in order that you can use this powerful
+
+ align:start position:0%
+in order that you can use this powerful
+ 
+
+ align:start position:0%
+in order that you can use this powerful
+method this enzyme called rna-h
+
+ align:start position:0%
+method this enzyme called rna-h
+ 
+
+ align:start position:0%
+method this enzyme called rna-h
+which will which has a property that
+
+ align:start position:0%
+which will which has a property that
+ 
+
+ align:start position:0%
+which will which has a property that
+when you bind a dna oligonucleotide
+
+ align:start position:0%
+when you bind a dna oligonucleotide
+ 
+
+ align:start position:0%
+when you bind a dna oligonucleotide
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+to an rna and they're complementary
+
+ align:start position:0%
+to an rna and they're complementary
+ 
+
+ align:start position:0%
+to an rna and they're complementary
+rna-sh will destroy the rna at
+
+ align:start position:0%
+rna-sh will destroy the rna at
+ 
+
+ align:start position:0%
+rna-sh will destroy the rna at
+at that point at the point of
+
+ align:start position:0%
+at that point at the point of
+ 
+
+ align:start position:0%
+at that point at the point of
+hybridization so it's a way of
+
+ align:start position:0%
+hybridization so it's a way of
+ 
+
+ align:start position:0%
+hybridization so it's a way of
+eliminating an entire molecule
+
+ align:start position:0%
+eliminating an entire molecule
+ 
+
+ align:start position:0%
+eliminating an entire molecule
+if it happens to have a particular
+
+ align:start position:0%
+if it happens to have a particular
+ 
+
+ align:start position:0%
+if it happens to have a particular
+sequence in it and so one of the ways
+
+ align:start position:0%
+sequence in it and so one of the ways
+ 
+
+ align:start position:0%
+sequence in it and so one of the ways
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+ask logical questions about each
+
+ align:start position:0%
+ask logical questions about each
+ 
+
+ align:start position:0%
+ask logical questions about each
+molecule in a large complex mixture
+
+ align:start position:0%
+molecule in a large complex mixture
+ 
+
+ align:start position:0%
+molecule in a large complex mixture
+molecules is using this rna stage
+
+ align:start position:0%
+molecules is using this rna stage
+ 
+
+ align:start position:0%
+molecules is using this rna stage
+elimination
+
+ align:start position:0%
+elimination
+ 
+
+ align:start position:0%
+elimination
+and in a way it's a way of of having of
+
+ align:start position:0%
+and in a way it's a way of of having of
+ 
+
+ align:start position:0%
+and in a way it's a way of of having of
+designing an infinite number of
+
+ align:start position:0%
+designing an infinite number of
+ 
+
+ align:start position:0%
+designing an infinite number of
+restriction enzymes the the rnas plus
+
+ align:start position:0%
+restriction enzymes the the rnas plus
+ 
+
+ align:start position:0%
+restriction enzymes the the rnas plus
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dna oligonucleotide provides in a
+
+ align:start position:0%
+dna oligonucleotide provides in a
+ 
+
+ align:start position:0%
+dna oligonucleotide provides in a
+certain sense a custom restriction
+
+ align:start position:0%
+certain sense a custom restriction
+ 
+
+ align:start position:0%
+certain sense a custom restriction
+enzyme
+
+ align:start position:0%
+enzyme
+ 
+
+ align:start position:0%
+enzyme
+any case the other thing that's unusual
+
+ align:start position:0%
+any case the other thing that's unusual
+ 
+
+ align:start position:0%
+any case the other thing that's unusual
+here is the idea of using split and pool
+
+ align:start position:0%
+here is the idea of using split and pool
+ 
+
+ align:start position:0%
+here is the idea of using split and pool
+or ligonite synthesis we introduced this
+
+ align:start position:0%
+or ligonite synthesis we introduced this
+ 
+
+ align:start position:0%
+or ligonite synthesis we introduced this
+in the in the lecture where we had we
+
+ align:start position:0%
+in the in the lecture where we had we
+ 
+
+ align:start position:0%
+in the in the lecture where we had we
+were introducing drug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protein interaction and
+
+ align:start position:0%
+protein interaction and
+ 
+
+ align:start position:0%
+protein interaction and
+ways of synthesizing drugs and and other
+
+ align:start position:0%
+ways of synthesizing drugs and and other
+ 
+
+ align:start position:0%
+ways of synthesizing drugs and and other
+molecules by pool synthesis and the idea
+
+ align:start position:0%
+molecules by pool synthesis and the idea
+ 
+
+ align:start position:0%
+molecules by pool synthesis and the idea
+behind split pool synthesis in this case
+
+ align:start position:0%
+behind split pool synthesis in this case
+ 
+
+ align:start position:0%
+behind split pool synthesis in this case
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+uh it for each of the
+
+ align:start position:0%
+uh it for each of the
+ 
+
+ align:start position:0%
+uh it for each of the
+each of the squares in this three by
+
+ align:start position:0%
+each of the squares in this three by
+ 
+
+ align:start position:0%
+each of the squares in this three by
+three matrix can have two states either
+
+ align:start position:0%
+three matrix can have two states either
+ 
+
+ align:start position:0%
+three matrix can have two states either
+has a knight or it doesn't each of those
+
+ align:start position:0%
+has a knight or it doesn't each of those
+ 
+
+ align:start position:0%
+has a knight or it doesn't each of those
+two states you can consider a zero or
+
+ align:start position:0%
+two states you can consider a zero or
+ 
+
+ align:start position:0%
+two states you can consider a zero or
+one you can represent them as two
+
+ align:start position:0%
+one you can represent them as two
+ 
+
+ align:start position:0%
+one you can represent them as two
+different sequences
+
+ align:start position:0%
+different sequences
+ 
+
+ align:start position:0%
+different sequences
+uh you know sequence a or c plus a prime
+
+ align:start position:0%
+uh you know sequence a or c plus a prime
+ 
+
+ align:start position:0%
+uh you know sequence a or c plus a prime
+representing presence or absence of
+
+ align:start position:0%
+representing presence or absence of
+ 
+
+ align:start position:0%
+representing presence or absence of
+something and so you basically have two
+
+ align:start position:0%
+something and so you basically have two
+ 
+
+ align:start position:0%
+something and so you basically have two
+to the uh
+
+ align:start position:0%
+to the uh
+ 
+
+ align:start position:0%
+to the uh
+you have nine squares since you have two
+
+ align:start position:0%
+you have nine squares since you have two
+ 
+
+ align:start position:0%
+you have nine squares since you have two
+to the ninth different possibilities and
+
+ align:start position:0%
+to the ninth different possibilities and
+ 
+
+ align:start position:0%
+to the ninth different possibilities and
+so down here below
+
+ align:start position:0%
+so down here below
+ 
+
+ align:start position:0%
+so down here below
+they synthesized
+
+ align:start position:0%
+they synthesized
+ 
+
+ align:start position:0%
+they synthesized
+a set of polymers where you have every
+
+ align:start position:0%
+a set of polymers where you have every
+ 
+
+ align:start position:0%
+a set of polymers where you have every
+possible binary state for this
+
+ align:start position:0%
+possible binary state for this
+ 
+
+ align:start position:0%
+possible binary state for this
+three by three grid
+
+ align:start position:0%
+three by three grid
+ 
+
+ align:start position:0%
+three by three grid
+and that's done by your synthesizing
+
+ align:start position:0%
+and that's done by your synthesizing
+ 
+
+ align:start position:0%
+and that's done by your synthesizing
+along and you come to where you're going
+
+ align:start position:0%
+along and you come to where you're going
+ 
+
+ align:start position:0%
+along and you come to where you're going
+to synthesize either a or a prime you
+
+ align:start position:0%
+to synthesize either a or a prime you
+ 
+
+ align:start position:0%
+to synthesize either a or a prime you
+split it
+
+ align:start position:0%
+split it
+ 
+
+ align:start position:0%
+split it
+half of this cool gets a half of it gets
+
+ align:start position:0%
+half of this cool gets a half of it gets
+ 
+
+ align:start position:0%
+half of this cool gets a half of it gets
+sequence a prime you pull them back
+
+ align:start position:0%
+sequence a prime you pull them back
+ 
+
+ align:start position:0%
+sequence a prime you pull them back
+together half gets b half gets b prime
+
+ align:start position:0%
+together half gets b half gets b prime
+ 
+
+ align:start position:0%
+together half gets b half gets b prime
+pull them and split them and c and c
+
+ align:start position:0%
+pull them and split them and c and c
+ 
+
+ align:start position:0%
+pull them and split them and c and c
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+you really only need nine of these they
+
+ align:start position:0%
+you really only need nine of these they
+ 
+
+ align:start position:0%
+you really only need nine of these they
+did ten for some reason or other but the
+
+ align:start position:0%
+did ten for some reason or other but the
+ 
+
+ align:start position:0%
+did ten for some reason or other but the
+point is to get two to the ninth power
+
+ align:start position:0%
+point is to get two to the ninth power
+ 
+
+ align:start position:0%
+point is to get two to the ninth power
+um you need nine of these and then as
+
+ align:start position:0%
+um you need nine of these and then as
+ 
+
+ align:start position:0%
+um you need nine of these and then as
+you can uh then you can read them out
+
+ align:start position:0%
+you can uh then you can read them out
+ 
+
+ align:start position:0%
+you can uh then you can read them out
+electrophoretically just as the
+
+ align:start position:0%
+electrophoretically just as the
+ 
+
+ align:start position:0%
+electrophoretically just as the
+electrophoretic readout gave a sizing
+
+ align:start position:0%
+electrophoretic readout gave a sizing
+ 
+
+ align:start position:0%
+electrophoretic readout gave a sizing
+in the in the in the first dna computing
+
+ align:start position:0%
+in the in the in the first dna computing
+ 
+
+ align:start position:0%
+in the in the in the first dna computing
+you can use it to get the sizes of these
+
+ align:start position:0%
+you can use it to get the sizes of these
+ 
+
+ align:start position:0%
+you can use it to get the sizes of these
+and you can see you can read out this
+
+ align:start position:0%
+and you can see you can read out this
+ 
+
+ align:start position:0%
+and you can see you can read out this
+solute here's two solutions b e f h
+
+ align:start position:0%
+solute here's two solutions b e f h
+ 
+
+ align:start position:0%
+solute here's two solutions b e f h
+referring to the squares on the three by
+
+ align:start position:0%
+referring to the squares on the three by
+ 
+
+ align:start position:0%
+referring to the squares on the three by
+three did and efc these are both
+
+ align:start position:0%
+three did and efc these are both
+ 
+
+ align:start position:0%
+three did and efc these are both
+solutions bdfh um the way of reading
+
+ align:start position:0%
+solutions bdfh um the way of reading
+ 
+
+ align:start position:0%
+solutions bdfh um the way of reading
+this off this combinatorial synthesis
+
+ align:start position:0%
+this off this combinatorial synthesis
+ 
+
+ align:start position:0%
+this off this combinatorial synthesis
+from the bottom is you've got
+
+ align:start position:0%
+from the bottom is you've got
+ 
+
+ align:start position:0%
+from the bottom is you've got
+a through i as the possible bit binary
+
+ align:start position:0%
+a through i as the possible bit binary
+ 
+
+ align:start position:0%
+a through i as the possible bit binary
+signatures and then you have
+
+ align:start position:0%
+signatures and then you have
+ 
+
+ align:start position:0%
+signatures and then you have
+two columns either the zero column or
+
+ align:start position:0%
+two columns either the zero column or
+ 
+
+ align:start position:0%
+two columns either the zero column or
+the one the two states the two sequences
+
+ align:start position:0%
+the one the two states the two sequences
+ 
+
+ align:start position:0%
+the one the two states the two sequences
+and as you
+
+ align:start position:0%
+and as you
+ 
+
+ align:start position:0%
+and as you
+pcr from the end tag
+
+ align:start position:0%
+pcr from the end tag
+ 
+
+ align:start position:0%
+pcr from the end tag
+out to each of these tags a or a prime b
+
+ align:start position:0%
+out to each of these tags a or a prime b
+ 
+
+ align:start position:0%
+out to each of these tags a or a prime b
+or b prime and so forth then you get
+
+ align:start position:0%
+or b prime and so forth then you get
+ 
+
+ align:start position:0%
+or b prime and so forth then you get
+these are all uh you'll get this
+
+ align:start position:0%
+these are all uh you'll get this
+ 
+
+ align:start position:0%
+these are all uh you'll get this
+graduated series it'll tell you you've
+
+ align:start position:0%
+graduated series it'll tell you you've
+ 
+
+ align:start position:0%
+graduated series it'll tell you you've
+got a little you've got you've got
+
+ align:start position:0%
+got a little you've got you've got
+ 
+
+ align:start position:0%
+got a little you've got you've got
+a is in the zero state b is in the one
+
+ align:start position:0%
+a is in the zero state b is in the one
+ 
+
+ align:start position:0%
+a is in the zero state b is in the one
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+uh c and d are in the zero state
+
+ align:start position:0%
+uh c and d are in the zero state
+ 
+
+ align:start position:0%
+uh c and d are in the zero state
+e is in the one state so forth and so
+
+ align:start position:0%
+e is in the one state so forth and so
+ 
+
+ align:start position:0%
+e is in the one state so forth and so
+i've circle b being in the one state
+
+ align:start position:0%
+i've circle b being in the one state
+ 
+
+ align:start position:0%
+i've circle b being in the one state
+showing there's night in that position
+
+ align:start position:0%
+showing there's night in that position
+ 
+
+ align:start position:0%
+showing there's night in that position
+in position b
+
+ align:start position:0%
+in position b
+ 
+
+ align:start position:0%
+in position b
+and you can go through the same thing
+
+ align:start position:0%
+and you can go through the same thing
+ 
+
+ align:start position:0%
+and you can go through the same thing
+for the other solutions um each of these
+
+ align:start position:0%
+for the other solutions um each of these
+ 
+
+ align:start position:0%
+for the other solutions um each of these
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+developed as a clone and there's an and
+
+ align:start position:0%
+developed as a clone and there's an and
+ 
+
+ align:start position:0%
+developed as a clone and there's an and
+the neat thing about all these problems
+
+ align:start position:0%
+the neat thing about all these problems
+ 
+
+ align:start position:0%
+the neat thing about all these problems
+is they have multiple representations
+
+ align:start position:0%
+is they have multiple representations
+ 
+
+ align:start position:0%
+is they have multiple representations
+you represent them in dna your graphics
+
+ align:start position:0%
+you represent them in dna your graphics
+ 
+
+ align:start position:0%
+you represent them in dna your graphics
+in them and data you can represent them
+
+ align:start position:0%
+in them and data you can represent them
+ 
+
+ align:start position:0%
+in them and data you can represent them
+as a boolean logical set of operations
+
+ align:start position:0%
+as a boolean logical set of operations
+ 
+
+ align:start position:0%
+as a boolean logical set of operations
+where these things represent hands and
+
+ align:start position:0%
+where these things represent hands and
+ 
+
+ align:start position:0%
+where these things represent hands and
+ors
+
+ align:start position:0%
+ors
+ 
+
+ align:start position:0%
+ors
+at the bottom of the slide
+
+ align:start position:0%
+at the bottom of the slide
+ 
+
+ align:start position:0%
+at the bottom of the slide
+and so on and you will see that in in
+
+ align:start position:0%
+and so on and you will see that in in
+ 
+
+ align:start position:0%
+and so on and you will see that in in
+the last in the last uh examples where
+
+ align:start position:0%
+the last in the last uh examples where
+ 
+
+ align:start position:0%
+the last in the last uh examples where
+just kind of breeze through um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where that that
+
+ align:start position:0%
+where that that
+ 
+
+ align:start position:0%
+where that that
+set of logical operations is probably
+
+ align:start position:0%
+set of logical operations is probably
+ 
+
+ align:start position:0%
+set of logical operations is probably
+one of the favorite
+
+ align:start position:0%
+one of the favorite
+ 
+
+ align:start position:0%
+one of the favorite
+points of attack for dna computing
+
+ align:start position:0%
+points of attack for dna computing
+ 
+
+ align:start position:0%
+points of attack for dna computing
+still today
+
+ align:start position:0%
+still today
+ 
+
+ align:start position:0%
+still today
+so what are the problems and advantages
+
+ align:start position:0%
+so what are the problems and advantages
+ 
+
+ align:start position:0%
+so what are the problems and advantages
+the problems are
+
+ align:start position:0%
+the problems are
+ 
+
+ align:start position:0%
+the problems are
+that yes it is polynomial time
+
+ align:start position:0%
+that yes it is polynomial time
+ 
+
+ align:start position:0%
+that yes it is polynomial time
+in fact it's close to linear time with a
+
+ align:start position:0%
+in fact it's close to linear time with a
+ 
+
+ align:start position:0%
+in fact it's close to linear time with a
+number of inputs in in terms of
+
+ align:start position:0%
+number of inputs in in terms of
+ 
+
+ align:start position:0%
+number of inputs in in terms of
+synthesis needs uh you you know your
+
+ align:start position:0%
+synthesis needs uh you you know your
+ 
+
+ align:start position:0%
+synthesis needs uh you you know your
+computer tells the synthesizer what to
+
+ align:start position:0%
+computer tells the synthesizer what to
+ 
+
+ align:start position:0%
+computer tells the synthesizer what to
+make and then uh enzymes will
+
+ align:start position:0%
+make and then uh enzymes will
+ 
+
+ align:start position:0%
+make and then uh enzymes will
+or hybridization will do we'll do this
+
+ align:start position:0%
+or hybridization will do we'll do this
+ 
+
+ align:start position:0%
+or hybridization will do we'll do this
+highly parallel reaction um independent
+
+ align:start position:0%
+highly parallel reaction um independent
+ 
+
+ align:start position:0%
+highly parallel reaction um independent
+of n so basically constant time
+
+ align:start position:0%
+of n so basically constant time
+ 
+
+ align:start position:0%
+of n so basically constant time
+so it's linear time for synthesis
+
+ align:start position:0%
+so it's linear time for synthesis
+ 
+
+ align:start position:0%
+so it's linear time for synthesis
+constant time for the computing and
+
+ align:start position:0%
+constant time for the computing and
+ 
+
+ align:start position:0%
+constant time for the computing and
+constant time for the
+
+ align:start position:0%
+constant time for the
+ 
+
+ align:start position:0%
+constant time for the
+getting the answer read out
+
+ align:start position:0%
+getting the answer read out
+ 
+
+ align:start position:0%
+getting the answer read out
+but you have exponential volumes for
+
+ align:start position:0%
+but you have exponential volumes for
+ 
+
+ align:start position:0%
+but you have exponential volumes for
+example a hundred node graph we've been
+
+ align:start position:0%
+example a hundred node graph we've been
+ 
+
+ align:start position:0%
+example a hundred node graph we've been
+talking about the various graph
+
+ align:start position:0%
+talking about the various graph
+ 
+
+ align:start position:0%
+talking about the various graph
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+might be
+
+ align:start position:0%
+might be
+ 
+
+ align:start position:0%
+might be
+10 to the 30th molecules and if any of
+
+ align:start position:0%
+10 to the 30th molecules and if any of
+ 
+
+ align:start position:0%
+10 to the 30th molecules and if any of
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+ever tried to synthesize a mole or 10 to
+
+ align:start position:0%
+ever tried to synthesize a mole or 10 to
+ 
+
+ align:start position:0%
+ever tried to synthesize a mole or 10 to
+the 24th molecules you realize it would
+
+ align:start position:0%
+the 24th molecules you realize it would
+ 
+
+ align:start position:0%
+the 24th molecules you realize it would
+it would uh bankrupt our planet to make
+
+ align:start position:0%
+it would uh bankrupt our planet to make
+ 
+
+ align:start position:0%
+it would uh bankrupt our planet to make
+the 30th molecules
+
+ align:start position:0%
+the 30th molecules
+ 
+
+ align:start position:0%
+the 30th molecules
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in addition the elementary steps are
+
+ align:start position:0%
+in addition the elementary steps are
+ 
+
+ align:start position:0%
+in addition the elementary steps are
+slow okay it's highly parallel
+
+ align:start position:0%
+slow okay it's highly parallel
+ 
+
+ align:start position:0%
+slow okay it's highly parallel
+you know you can imagine having
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trillions of molecules computing in
+
+ align:start position:0%
+trillions of molecules computing in
+ 
+
+ align:start position:0%
+trillions of molecules computing in
+parallel but the elementary steps of
+
+ align:start position:0%
+parallel but the elementary steps of
+ 
+
+ align:start position:0%
+parallel but the elementary steps of
+hybridization and dna polymerase or rna
+
+ align:start position:0%
+hybridization and dna polymerase or rna
+ 
+
+ align:start position:0%
+hybridization and dna polymerase or rna
+stage and support typically are in the
+
+ align:start position:0%
+stage and support typically are in the
+ 
+
+ align:start position:0%
+stage and support typically are in the
+millihertz range as to say you know it
+
+ align:start position:0%
+millihertz range as to say you know it
+ 
+
+ align:start position:0%
+millihertz range as to say you know it
+might take a thousand seconds rather
+
+ align:start position:0%
+might take a thousand seconds rather
+ 
+
+ align:start position:0%
+might take a thousand seconds rather
+than gigahertz which would be a
+
+ align:start position:0%
+than gigahertz which would be a
+ 
+
+ align:start position:0%
+than gigahertz which would be a
+billionth of a second so there might be
+
+ align:start position:0%
+billionth of a second so there might be
+ 
+
+ align:start position:0%
+billionth of a second so there might be
+a 10 to the 12th
+
+ align:start position:0%
+a 10 to the 12th
+ 
+
+ align:start position:0%
+a 10 to the 12th
+gap in rate of of executing the commands
+
+ align:start position:0%
+gap in rate of of executing the commands
+ 
+
+ align:start position:0%
+gap in rate of of executing the commands
+but there's more that the hope is
+
+ align:start position:0%
+but there's more that the hope is
+ 
+
+ align:start position:0%
+but there's more that the hope is
+there's more than a 10-12 advantage in
+
+ align:start position:0%
+there's more than a 10-12 advantage in
+ 
+
+ align:start position:0%
+there's more than a 10-12 advantage in
+parallelism
+
+ align:start position:0%
+parallelism
+ 
+
+ align:start position:0%
+parallelism
+in addition experimental errors um
+
+ align:start position:0%
+in addition experimental errors um
+ 
+
+ align:start position:0%
+in addition experimental errors um
+mustn't be swept under the rug you've
+
+ align:start position:0%
+mustn't be swept under the rug you've
+ 
+
+ align:start position:0%
+mustn't be swept under the rug you've
+got issues with mismatch there's a limit
+
+ align:start position:0%
+got issues with mismatch there's a limit
+ 
+
+ align:start position:0%
+got issues with mismatch there's a limit
+that just how cleverly you can design
+
+ align:start position:0%
+that just how cleverly you can design
+ 
+
+ align:start position:0%
+that just how cleverly you can design
+all these sequences
+
+ align:start position:0%
+all these sequences
+ 
+
+ align:start position:0%
+all these sequences
+as as the graph gets bigger you need to
+
+ align:start position:0%
+as as the graph gets bigger you need to
+ 
+
+ align:start position:0%
+as as the graph gets bigger you need to
+have more and more sequences involved
+
+ align:start position:0%
+have more and more sequences involved
+ 
+
+ align:start position:0%
+have more and more sequences involved
+and that that means that you're going to
+
+ align:start position:0%
+and that that means that you're going to
+ 
+
+ align:start position:0%
+and that that means that you're going to
+get more and more cross hybridization
+
+ align:start position:0%
+get more and more cross hybridization
+ 
+
+ align:start position:0%
+get more and more cross hybridization
+and complete cleavage and so forth
+
+ align:start position:0%
+and complete cleavage and so forth
+ 
+
+ align:start position:0%
+and complete cleavage and so forth
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+when i when this slide 18 says
+
+ align:start position:0%
+when i when this slide 18 says
+ 
+
+ align:start position:0%
+when i when this slide 18 says
+non-reusable there are reusable forms
+
+ align:start position:0%
+non-reusable there are reusable forms
+ 
+
+ align:start position:0%
+non-reusable there are reusable forms
+and we'll get to those in just a minute
+
+ align:start position:0%
+and we'll get to those in just a minute
+ 
+
+ align:start position:0%
+and we'll get to those in just a minute
+so those are the disadvantages what are
+
+ align:start position:0%
+so those are the disadvantages what are
+ 
+
+ align:start position:0%
+so those are the disadvantages what are
+the promises or the possible advantages
+
+ align:start position:0%
+the promises or the possible advantages
+ 
+
+ align:start position:0%
+the promises or the possible advantages
+high parallelism could be much more than
+
+ align:start position:0%
+high parallelism could be much more than
+ 
+
+ align:start position:0%
+high parallelism could be much more than
+the 10 to the 12th full loss in the
+
+ align:start position:0%
+the 10 to the 12th full loss in the
+ 
+
+ align:start position:0%
+the 10 to the 12th full loss in the
+speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+when computer hardware
+
+ align:start position:0%
+when computer hardware
+ 
+
+ align:start position:0%
+when computer hardware
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+people dream of
+
+ align:start position:0%
+people dream of
+ 
+
+ align:start position:0%
+people dream of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+next generation of computers they hope
+
+ align:start position:0%
+next generation of computers they hope
+ 
+
+ align:start position:0%
+next generation of computers they hope
+to get away from the current record
+
+ align:start position:0%
+to get away from the current record
+ 
+
+ align:start position:0%
+to get away from the current record
+which is around 10 to the ninth
+
+ align:start position:0%
+which is around 10 to the ninth
+ 
+
+ align:start position:0%
+which is around 10 to the ninth
+operations per joule
+
+ align:start position:0%
+operations per joule
+ 
+
+ align:start position:0%
+operations per joule
+for conventional computers
+
+ align:start position:0%
+for conventional computers
+ 
+
+ align:start position:0%
+for conventional computers
+maybe that's not a record but it's
+
+ align:start position:0%
+maybe that's not a record but it's
+ 
+
+ align:start position:0%
+maybe that's not a record but it's
+conventional computers um
+
+ align:start position:0%
+conventional computers um
+ 
+
+ align:start position:0%
+conventional computers um
+closer to the 34 times 10 of the 19th
+
+ align:start position:0%
+closer to the 34 times 10 of the 19th
+ 
+
+ align:start position:0%
+closer to the 34 times 10 of the 19th
+operations per joule you should be able
+
+ align:start position:0%
+operations per joule you should be able
+ 
+
+ align:start position:0%
+operations per joule you should be able
+to squeak out near the thermodynamic
+
+ align:start position:0%
+to squeak out near the thermodynamic
+ 
+
+ align:start position:0%
+to squeak out near the thermodynamic
+limit as it turns out
+
+ align:start position:0%
+limit as it turns out
+ 
+
+ align:start position:0%
+limit as it turns out
+many dna enzymes such as dna polymerase
+
+ align:start position:0%
+many dna enzymes such as dna polymerase
+ 
+
+ align:start position:0%
+many dna enzymes such as dna polymerase
+are already within a factor of 10 of
+
+ align:start position:0%
+are already within a factor of 10 of
+ 
+
+ align:start position:0%
+are already within a factor of 10 of
+that goal
+
+ align:start position:0%
+that goal
+ 
+
+ align:start position:0%
+that goal
+while conventional computers are off by
+
+ align:start position:0%
+while conventional computers are off by
+ 
+
+ align:start position:0%
+while conventional computers are off by
+10 factors of 10 or more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if one can quote solve or
+
+ align:start position:0%
+if one can quote solve or
+ 
+
+ align:start position:0%
+if one can quote solve or
+one mp complete solve problem you can
+
+ align:start position:0%
+one mp complete solve problem you can
+ 
+
+ align:start position:0%
+one mp complete solve problem you can
+get many
+
+ align:start position:0%
+get many
+ 
+
+ align:start position:0%
+get many
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+you know they're they're the
+
+ align:start position:0%
+you know they're they're the
+ 
+
+ align:start position:0%
+you know they're they're the
+improvements that we'll just kind of
+
+ align:start position:0%
+improvements that we'll just kind of
+ 
+
+ align:start position:0%
+improvements that we'll just kind of
+briefly talk about that are
+
+ align:start position:0%
+briefly talk about that are
+ 
+
+ align:start position:0%
+briefly talk about that are
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+keep people excited about this are that
+
+ align:start position:0%
+keep people excited about this are that
+ 
+
+ align:start position:0%
+keep people excited about this are that
+this is a natural way of talking to
+
+ align:start position:0%
+this is a natural way of talking to
+ 
+
+ align:start position:0%
+this is a natural way of talking to
+biological problems if there are
+
+ align:start position:0%
+biological problems if there are
+ 
+
+ align:start position:0%
+biological problems if there are
+biological problems
+
+ align:start position:0%
+biological problems
+ 
+
+ align:start position:0%
+biological problems
+you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it may be a smaller step to get to dna
+
+ align:start position:0%
+it may be a smaller step to get to dna
+ 
+
+ align:start position:0%
+it may be a smaller step to get to dna
+computing and there are faster readout
+
+ align:start position:0%
+computing and there are faster readout
+ 
+
+ align:start position:0%
+computing and there are faster readout
+methods just as there are faster and
+
+ align:start position:0%
+methods just as there are faster and
+ 
+
+ align:start position:0%
+methods just as there are faster and
+faster
+
+ align:start position:0%
+faster
+ 
+
+ align:start position:0%
+faster
+computational methods
+
+ align:start position:0%
+computational methods
+ 
+
+ align:start position:0%
+computational methods
+and natural selection evolution is
+
+ align:start position:0%
+and natural selection evolution is
+ 
+
+ align:start position:0%
+and natural selection evolution is
+something that you can use on dna
+
+ align:start position:0%
+something that you can use on dna
+ 
+
+ align:start position:0%
+something that you can use on dna
+computers which so far has not been
+
+ align:start position:0%
+computers which so far has not been
+ 
+
+ align:start position:0%
+computers which so far has not been
+extremely powerful in
+
+ align:start position:0%
+extremely powerful in
+ 
+
+ align:start position:0%
+extremely powerful in
+conventional computers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+although we'll talk about genetic
+
+ align:start position:0%
+although we'll talk about genetic
+ 
+
+ align:start position:0%
+although we'll talk about genetic
+algorithms shortly
+
+ align:start position:0%
+algorithms shortly
+ 
+
+ align:start position:0%
+algorithms shortly
+so one way of getting reuse is to have a
+
+ align:start position:0%
+so one way of getting reuse is to have a
+ 
+
+ align:start position:0%
+so one way of getting reuse is to have a
+so-called sticker-based model or
+
+ align:start position:0%
+so-called sticker-based model or
+ 
+
+ align:start position:0%
+so-called sticker-based model or
+something where you're basically just
+
+ align:start position:0%
+something where you're basically just
+ 
+
+ align:start position:0%
+something where you're basically just
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+hybridization properties without being
+
+ align:start position:0%
+hybridization properties without being
+ 
+
+ align:start position:0%
+hybridization properties without being
+destructive
+
+ align:start position:0%
+destructive
+ 
+
+ align:start position:0%
+destructive
+and and here's an example i'm not going
+
+ align:start position:0%
+and and here's an example i'm not going
+ 
+
+ align:start position:0%
+and and here's an example i'm not going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+walk through it too much i should point
+
+ align:start position:0%
+walk through it too much i should point
+ 
+
+ align:start position:0%
+walk through it too much i should point
+out the at all in here include that one
+
+ align:start position:0%
+out the at all in here include that one
+ 
+
+ align:start position:0%
+out the at all in here include that one
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and uh i'll have
+
+ align:start position:0%
+and uh i'll have
+ 
+
+ align:start position:0%
+and uh i'll have
+one more example of his work in just a
+
+ align:start position:0%
+one more example of his work in just a
+ 
+
+ align:start position:0%
+one more example of his work in just a
+just a moment here but that they're
+
+ align:start position:0%
+just a moment here but that they're
+ 
+
+ align:start position:0%
+just a moment here but that they're
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+they're examples now of of work
+
+ align:start position:0%
+they're examples now of of work
+ 
+
+ align:start position:0%
+they're examples now of of work
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+consider seriously the amount the
+
+ align:start position:0%
+consider seriously the amount the
+ 
+
+ align:start position:0%
+consider seriously the amount the
+volumes of dna that are needed and ways
+
+ align:start position:0%
+volumes of dna that are needed and ways
+ 
+
+ align:start position:0%
+volumes of dna that are needed and ways
+of dealing with
+
+ align:start position:0%
+of dealing with
+ 
+
+ align:start position:0%
+of dealing with
+fault tolerance or
+
+ align:start position:0%
+fault tolerance or
+ 
+
+ align:start position:0%
+fault tolerance or
+or error reduction algorithms where you
+
+ align:start position:0%
+or error reduction algorithms where you
+ 
+
+ align:start position:0%
+or error reduction algorithms where you
+actually go through and
+
+ align:start position:0%
+actually go through and
+ 
+
+ align:start position:0%
+actually go through and
+consciously say okay if we had an error
+
+ align:start position:0%
+consciously say okay if we had an error
+ 
+
+ align:start position:0%
+consciously say okay if we had an error
+here how would we
+
+ align:start position:0%
+here how would we
+ 
+
+ align:start position:0%
+here how would we
+compensate for it how would we dedicate
+
+ align:start position:0%
+compensate for it how would we dedicate
+ 
+
+ align:start position:0%
+compensate for it how would we dedicate
+a little more a few more bits
+
+ align:start position:0%
+a little more a few more bits
+ 
+
+ align:start position:0%
+a little more a few more bits
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+take the next step
+
+ align:start position:0%
+take the next step
+ 
+
+ align:start position:0%
+take the next step
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just like in the the night
+
+ align:start position:0%
+just like in the the night
+ 
+
+ align:start position:0%
+just like in the the night
+test problem we had a little bit before
+
+ align:start position:0%
+test problem we had a little bit before
+ 
+
+ align:start position:0%
+test problem we had a little bit before
+the idea of using and and ors of uh
+
+ align:start position:0%
+the idea of using and and ors of uh
+ 
+
+ align:start position:0%
+the idea of using and and ors of uh
+boolean variables these x's in slide 21
+
+ align:start position:0%
+boolean variables these x's in slide 21
+ 
+
+ align:start position:0%
+boolean variables these x's in slide 21
+which can have two states zero or one
+
+ align:start position:0%
+which can have two states zero or one
+ 
+
+ align:start position:0%
+which can have two states zero or one
+similar to the boolean variables that we
+
+ align:start position:0%
+similar to the boolean variables that we
+ 
+
+ align:start position:0%
+similar to the boolean variables that we
+run across time time and genetic models
+
+ align:start position:0%
+run across time time and genetic models
+ 
+
+ align:start position:0%
+run across time time and genetic models
+and you can have clauses which are
+
+ align:start position:0%
+and you can have clauses which are
+ 
+
+ align:start position:0%
+and you can have clauses which are
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+logical operations on the set of boolean
+
+ align:start position:0%
+logical operations on the set of boolean
+ 
+
+ align:start position:0%
+logical operations on the set of boolean
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+where you have
+
+ align:start position:0%
+where you have
+ 
+
+ align:start position:0%
+where you have
+knots and ors and ands okay and this
+
+ align:start position:0%
+knots and ors and ands okay and this
+ 
+
+ align:start position:0%
+knots and ors and ands okay and this
+kind of problem is a very general
+
+ align:start position:0%
+kind of problem is a very general
+ 
+
+ align:start position:0%
+kind of problem is a very general
+problem very interesting one and uh it
+
+ align:start position:0%
+problem very interesting one and uh it
+ 
+
+ align:start position:0%
+problem very interesting one and uh it
+has been tackled just in very analogous
+
+ align:start position:0%
+has been tackled just in very analogous
+ 
+
+ align:start position:0%
+has been tackled just in very analogous
+ways to the ways we've been talking
+
+ align:start position:0%
+ways to the ways we've been talking
+ 
+
+ align:start position:0%
+ways to the ways we've been talking
+about the previous ones
+
+ align:start position:0%
+about the previous ones
+ 
+
+ align:start position:0%
+about the previous ones
+where you encode the graph in dna
+
+ align:start position:0%
+where you encode the graph in dna
+ 
+
+ align:start position:0%
+where you encode the graph in dna
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+thereby creating all the paths by
+
+ align:start position:0%
+thereby creating all the paths by
+ 
+
+ align:start position:0%
+thereby creating all the paths by
+hybridization or something like that
+
+ align:start position:0%
+hybridization or something like that
+ 
+
+ align:start position:0%
+hybridization or something like that
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+and then you read it out
+
+ align:start position:0%
+and then you read it out
+ 
+
+ align:start position:0%
+and then you read it out
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with um
+
+ align:start position:0%
+with um
+ 
+
+ align:start position:0%
+with um
+pcr
+
+ align:start position:0%
+pcr
+ 
+
+ align:start position:0%
+pcr
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+and solid phase
+
+ align:start position:0%
+and solid phase
+ 
+
+ align:start position:0%
+and solid phase
+and you could say you see here's a quote
+
+ align:start position:0%
+and you could say you see here's a quote
+ 
+
+ align:start position:0%
+and you could say you see here's a quote
+where they say here we solve an np
+
+ align:start position:0%
+where they say here we solve an np
+ 
+
+ align:start position:0%
+where they say here we solve an np
+complete problem
+
+ align:start position:0%
+complete problem
+ 
+
+ align:start position:0%
+complete problem
+they have indeed solved one but
+
+ align:start position:0%
+they have indeed solved one but
+ 
+
+ align:start position:0%
+they have indeed solved one but
+you know they haven't
+
+ align:start position:0%
+you know they haven't
+ 
+
+ align:start position:0%
+you know they haven't
+they haven't really turned it into a a
+
+ align:start position:0%
+they haven't really turned it into a a
+ 
+
+ align:start position:0%
+they haven't really turned it into a a
+polynomial time problem they simply
+
+ align:start position:0%
+polynomial time problem they simply
+ 
+
+ align:start position:0%
+polynomial time problem they simply
+forced it out
+
+ align:start position:0%
+forced it out
+ 
+
+ align:start position:0%
+forced it out
+and this is the most recent one just it
+
+ align:start position:0%
+and this is the most recent one just it
+ 
+
+ align:start position:0%
+and this is the most recent one just it
+came out in science again when adelman
+
+ align:start position:0%
+came out in science again when adelman
+ 
+
+ align:start position:0%
+came out in science again when adelman
+on it and now up to 20 variables in a
+
+ align:start position:0%
+on it and now up to 20 variables in a
+ 
+
+ align:start position:0%
+on it and now up to 20 variables in a
+three-stat problem
+
+ align:start position:0%
+three-stat problem
+ 
+
+ align:start position:0%
+three-stat problem
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's all about computing it may not
+
+ align:start position:0%
+so that's all about computing it may not
+ 
+
+ align:start position:0%
+so that's all about computing it may not
+since
+
+ align:start position:0%
+since
+ 
+
+ align:start position:0%
+since
+dna is relatively slow at computing
+
+ align:start position:0%
+dna is relatively slow at computing
+ 
+
+ align:start position:0%
+dna is relatively slow at computing
+per step highly parallel it may not be
+
+ align:start position:0%
+per step highly parallel it may not be
+ 
+
+ align:start position:0%
+per step highly parallel it may not be
+the best of the various steps in
+
+ align:start position:0%
+the best of the various steps in
+ 
+
+ align:start position:0%
+the best of the various steps in
+computing assembly
+
+ align:start position:0%
+computing assembly
+ 
+
+ align:start position:0%
+computing assembly
+input memory
+
+ align:start position:0%
+input memory
+ 
+
+ align:start position:0%
+input memory
+computation and output so we'll explore
+
+ align:start position:0%
+computation and output so we'll explore
+ 
+
+ align:start position:0%
+computation and output so we'll explore
+some of the other ones in particular
+
+ align:start position:0%
+some of the other ones in particular
+ 
+
+ align:start position:0%
+some of the other ones in particular
+assembly to a certain extent assembling
+
+ align:start position:0%
+assembly to a certain extent assembling
+ 
+
+ align:start position:0%
+assembly to a certain extent assembling
+computers is slow and so it's something
+
+ align:start position:0%
+computers is slow and so it's something
+ 
+
+ align:start position:0%
+computers is slow and so it's something
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+molecular
+
+ align:start position:0%
+molecular
+ 
+
+ align:start position:0%
+molecular
+assembly might have some advantages
+
+ align:start position:0%
+assembly might have some advantages
+ 
+
+ align:start position:0%
+assembly might have some advantages
+now this particular example
+
+ align:start position:0%
+now this particular example
+ 
+
+ align:start position:0%
+now this particular example
+i'm i'm going to emphasize the assembly
+
+ align:start position:0%
+i'm i'm going to emphasize the assembly
+ 
+
+ align:start position:0%
+i'm i'm going to emphasize the assembly
+aspect of it but you can think of this
+
+ align:start position:0%
+aspect of it but you can think of this
+ 
+
+ align:start position:0%
+aspect of it but you can think of this
+as a way of mapping these authors have
+
+ align:start position:0%
+as a way of mapping these authors have
+ 
+
+ align:start position:0%
+as a way of mapping these authors have
+mapped
+
+ align:start position:0%
+mapped
+ 
+
+ align:start position:0%
+mapped
+a assembly of an actual two-dimensional
+
+ align:start position:0%
+a assembly of an actual two-dimensional
+ 
+
+ align:start position:0%
+a assembly of an actual two-dimensional
+piling
+
+ align:start position:0%
+piling
+ 
+
+ align:start position:0%
+piling
+onto
+
+ align:start position:0%
+onto
+ 
+
+ align:start position:0%
+onto
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+abstract but important and powerful
+
+ align:start position:0%
+abstract but important and powerful
+ 
+
+ align:start position:0%
+abstract but important and powerful
+computer science concept which is a
+
+ align:start position:0%
+computer science concept which is a
+ 
+
+ align:start position:0%
+computer science concept which is a
+general turing machine a machine a kind
+
+ align:start position:0%
+general turing machine a machine a kind
+ 
+
+ align:start position:0%
+general turing machine a machine a kind
+of a tape like structure that can
+
+ align:start position:0%
+of a tape like structure that can
+ 
+
+ align:start position:0%
+of a tape like structure that can
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+do any kind of general
+
+ align:start position:0%
+do any kind of general
+ 
+
+ align:start position:0%
+do any kind of general
+computing deterministic computing
+
+ align:start position:0%
+computing deterministic computing
+ 
+
+ align:start position:0%
+computing deterministic computing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so they've mapped a kind of a physical
+
+ align:start position:0%
+so they've mapped a kind of a physical
+ 
+
+ align:start position:0%
+so they've mapped a kind of a physical
+tiling as you might have a you know
+
+ align:start position:0%
+tiling as you might have a you know
+ 
+
+ align:start position:0%
+tiling as you might have a you know
+periodic or a periodic mosaic of tiles
+
+ align:start position:0%
+periodic or a periodic mosaic of tiles
+ 
+
+ align:start position:0%
+periodic or a periodic mosaic of tiles
+onto this computing machine
+
+ align:start position:0%
+onto this computing machine
+ 
+
+ align:start position:0%
+onto this computing machine
+and onto this kind of logical operation
+
+ align:start position:0%
+and onto this kind of logical operation
+ 
+
+ align:start position:0%
+and onto this kind of logical operation
+x4
+
+ align:start position:0%
+x4
+ 
+
+ align:start position:0%
+x4
+on a string of binary bits just as we
+
+ align:start position:0%
+on a string of binary bits just as we
+ 
+
+ align:start position:0%
+on a string of binary bits just as we
+had the previous couple of slides on the
+
+ align:start position:0%
+had the previous couple of slides on the
+ 
+
+ align:start position:0%
+had the previous couple of slides on the
+on the three-stat problem
+
+ align:start position:0%
+on the three-stat problem
+ 
+
+ align:start position:0%
+on the three-stat problem
+i'm going to emphasize the geometric
+
+ align:start position:0%
+i'm going to emphasize the geometric
+ 
+
+ align:start position:0%
+i'm going to emphasize the geometric
+physical version of it because we're
+
+ align:start position:0%
+physical version of it because we're
+ 
+
+ align:start position:0%
+physical version of it because we're
+trying to make a transition now in this
+
+ align:start position:0%
+trying to make a transition now in this
+ 
+
+ align:start position:0%
+trying to make a transition now in this
+paper which combines the dna computing
+
+ align:start position:0%
+paper which combines the dna computing
+ 
+
+ align:start position:0%
+paper which combines the dna computing
+with the dna assembly
+
+ align:start position:0%
+with the dna assembly
+ 
+
+ align:start position:0%
+with the dna assembly
+now up it
+
+ align:start position:0%
+now up it
+ 
+
+ align:start position:0%
+now up it
+we have three more or less equivalent
+
+ align:start position:0%
+we have three more or less equivalent
+ 
+
+ align:start position:0%
+we have three more or less equivalent
+ways of representing the same sort of
+
+ align:start position:0%
+ways of representing the same sort of
+ 
+
+ align:start position:0%
+ways of representing the same sort of
+sequences now these are called triple
+
+ align:start position:0%
+sequences now these are called triple
+ 
+
+ align:start position:0%
+sequences now these are called triple
+crossovers because you can see
+
+ align:start position:0%
+crossovers because you can see
+ 
+
+ align:start position:0%
+crossovers because you can see
+let's take a look at
+
+ align:start position:0%
+let's take a look at
+ 
+
+ align:start position:0%
+let's take a look at
+say y2 here and right in the middle of
+
+ align:start position:0%
+say y2 here and right in the middle of
+ 
+
+ align:start position:0%
+say y2 here and right in the middle of
+the slide
+
+ align:start position:0%
+the slide
+ 
+
+ align:start position:0%
+the slide
+you can see that there are these
+
+ align:start position:0%
+you can see that there are these
+ 
+
+ align:start position:0%
+you can see that there are these
+multiple crossovers where you have a
+
+ align:start position:0%
+multiple crossovers where you have a
+ 
+
+ align:start position:0%
+multiple crossovers where you have a
+kind of a recombination
+
+ align:start position:0%
+kind of a recombination
+ 
+
+ align:start position:0%
+kind of a recombination
+event where you've got two
+
+ align:start position:0%
+event where you've got two
+ 
+
+ align:start position:0%
+event where you've got two
+double-stranded dna molecules that are
+
+ align:start position:0%
+double-stranded dna molecules that are
+ 
+
+ align:start position:0%
+double-stranded dna molecules that are
+exchanging a strand and this is not a
+
+ align:start position:0%
+exchanging a strand and this is not a
+ 
+
+ align:start position:0%
+exchanging a strand and this is not a
+natural homologous recombination event
+
+ align:start position:0%
+natural homologous recombination event
+ 
+
+ align:start position:0%
+natural homologous recombination event
+in the since they're non-homologous and
+
+ align:start position:0%
+in the since they're non-homologous and
+ 
+
+ align:start position:0%
+in the since they're non-homologous and
+this thing is kind of trapped in this
+
+ align:start position:0%
+this thing is kind of trapped in this
+ 
+
+ align:start position:0%
+this thing is kind of trapped in this
+crossover and the crossover when you
+
+ align:start position:0%
+crossover and the crossover when you
+ 
+
+ align:start position:0%
+crossover and the crossover when you
+have a multiple crossovers you can make
+
+ align:start position:0%
+have a multiple crossovers you can make
+ 
+
+ align:start position:0%
+have a multiple crossovers you can make
+a piece of dna that now has more than
+
+ align:start position:0%
+a piece of dna that now has more than
+ 
+
+ align:start position:0%
+a piece of dna that now has more than
+just two ends you can have multiple
+
+ align:start position:0%
+just two ends you can have multiple
+ 
+
+ align:start position:0%
+just two ends you can have multiple
+sticky ends you can have say in this
+
+ align:start position:0%
+sticky ends you can have say in this
+ 
+
+ align:start position:0%
+sticky ends you can have say in this
+case in the upper part you can see four
+
+ align:start position:0%
+case in the upper part you can see four
+ 
+
+ align:start position:0%
+case in the upper part you can see four
+different ends
+
+ align:start position:0%
+different ends
+ 
+
+ align:start position:0%
+different ends
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one two three
+
+ align:start position:0%
+one two three
+ 
+
+ align:start position:0%
+one two three
+four crossover strands here and each of
+
+ align:start position:0%
+four crossover strands here and each of
+ 
+
+ align:start position:0%
+four crossover strands here and each of
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see on the far
+
+ align:start position:0%
+you can see on the far
+ 
+
+ align:start position:0%
+you can see on the far
+right a five base three prime overhang
+
+ align:start position:0%
+right a five base three prime overhang
+ 
+
+ align:start position:0%
+right a five base three prime overhang
+and a seven base five prime overhang and
+
+ align:start position:0%
+and a seven base five prime overhang and
+ 
+
+ align:start position:0%
+and a seven base five prime overhang and
+some flush ends on the far left and so
+
+ align:start position:0%
+some flush ends on the far left and so
+ 
+
+ align:start position:0%
+some flush ends on the far left and so
+each of these things has
+
+ align:start position:0%
+each of these things has
+ 
+
+ align:start position:0%
+each of these things has
+uh ability to stick stick to other uh
+
+ align:start position:0%
+uh ability to stick stick to other uh
+ 
+
+ align:start position:0%
+uh ability to stick stick to other uh
+tiling elements and you can see that you
+
+ align:start position:0%
+tiling elements and you can see that you
+ 
+
+ align:start position:0%
+tiling elements and you can see that you
+can put together a
+
+ align:start position:0%
+can put together a
+ 
+
+ align:start position:0%
+can put together a
+a two-dimensional
+
+ align:start position:0%
+a two-dimensional
+ 
+
+ align:start position:0%
+a two-dimensional
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+which can be as an intricate as a mosaic
+
+ align:start position:0%
+which can be as an intricate as a mosaic
+ 
+
+ align:start position:0%
+which can be as an intricate as a mosaic
+it does not have to repeat itself or it
+
+ align:start position:0%
+it does not have to repeat itself or it
+ 
+
+ align:start position:0%
+it does not have to repeat itself or it
+can repeat itself if you want to use um
+
+ align:start position:0%
+can repeat itself if you want to use um
+ 
+
+ align:start position:0%
+can repeat itself if you want to use um
+you know visual
+
+ align:start position:0%
+you know visual
+ 
+
+ align:start position:0%
+you know visual
+tools such as 40 transforms to look at a
+
+ align:start position:0%
+tools such as 40 transforms to look at a
+ 
+
+ align:start position:0%
+tools such as 40 transforms to look at a
+repeating structure and you can see you
+
+ align:start position:0%
+repeating structure and you can see you
+ 
+
+ align:start position:0%
+repeating structure and you can see you
+can you can engineer in restriction
+
+ align:start position:0%
+can you can engineer in restriction
+ 
+
+ align:start position:0%
+can you can engineer in restriction
+sites to help you analyze
+
+ align:start position:0%
+sites to help you analyze
+ 
+
+ align:start position:0%
+sites to help you analyze
+the structure on on a gel based assay on
+
+ align:start position:0%
+the structure on on a gel based assay on
+ 
+
+ align:start position:0%
+the structure on on a gel based assay on
+the far left
+
+ align:start position:0%
+the far left
+ 
+
+ align:start position:0%
+the far left
+we've seen enough gel based assays
+
+ align:start position:0%
+we've seen enough gel based assays
+ 
+
+ align:start position:0%
+we've seen enough gel based assays
+tonight already i will be labeled we're
+
+ align:start position:0%
+tonight already i will be labeled we're
+ 
+
+ align:start position:0%
+tonight already i will be labeled we're
+not going to walk you through it but you
+
+ align:start position:0%
+not going to walk you through it but you
+ 
+
+ align:start position:0%
+not going to walk you through it but you
+can see that there's even though this is
+
+ align:start position:0%
+can see that there's even though this is
+ 
+
+ align:start position:0%
+can see that there's even though this is
+not straight dna as the previous uh two
+
+ align:start position:0%
+not straight dna as the previous uh two
+ 
+
+ align:start position:0%
+not straight dna as the previous uh two
+or three examples where this is a much
+
+ align:start position:0%
+or three examples where this is a much
+ 
+
+ align:start position:0%
+or three examples where this is a much
+more complicated branch structure
+
+ align:start position:0%
+more complicated branch structure
+ 
+
+ align:start position:0%
+more complicated branch structure
+nevertheless you can
+
+ align:start position:0%
+nevertheless you can
+ 
+
+ align:start position:0%
+nevertheless you can
+turn it into a linear readout with
+
+ align:start position:0%
+turn it into a linear readout with
+ 
+
+ align:start position:0%
+turn it into a linear readout with
+electrophoretic sizes
+
+ align:start position:0%
+electrophoretic sizes
+ 
+
+ align:start position:0%
+electrophoretic sizes
+but you can also look at it as a truly
+
+ align:start position:0%
+but you can also look at it as a truly
+ 
+
+ align:start position:0%
+but you can also look at it as a truly
+two or three dimensional object here
+
+ align:start position:0%
+two or three dimensional object here
+ 
+
+ align:start position:0%
+two or three dimensional object here
+here we use atomic they use atomic force
+
+ align:start position:0%
+here we use atomic they use atomic force
+ 
+
+ align:start position:0%
+here we use atomic they use atomic force
+microscopy
+
+ align:start position:0%
+microscopy
+ 
+
+ align:start position:0%
+microscopy
+where a probe with a single atom at its
+
+ align:start position:0%
+where a probe with a single atom at its
+ 
+
+ align:start position:0%
+where a probe with a single atom at its
+tip
+
+ align:start position:0%
+tip
+ 
+
+ align:start position:0%
+tip
+is responsing to responding to the force
+
+ align:start position:0%
+is responsing to responding to the force
+ 
+
+ align:start position:0%
+is responsing to responding to the force
+that allows that as you touch an object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the feedback in the system with a
+
+ align:start position:0%
+the feedback in the system with a
+ 
+
+ align:start position:0%
+the feedback in the system with a
+scanning telling microscope usually as a
+
+ align:start position:0%
+scanning telling microscope usually as a
+ 
+
+ align:start position:0%
+scanning telling microscope usually as a
+part of the feedback
+
+ align:start position:0%
+part of the feedback
+ 
+
+ align:start position:0%
+part of the feedback
+tells you that you've just touched the
+
+ align:start position:0%
+tells you that you've just touched the
+ 
+
+ align:start position:0%
+tells you that you've just touched the
+surface and you bound to back off a
+
+ align:start position:0%
+surface and you bound to back off a
+ 
+
+ align:start position:0%
+surface and you bound to back off a
+little bit and then you scan along and
+
+ align:start position:0%
+little bit and then you scan along and
+ 
+
+ align:start position:0%
+little bit and then you scan along and
+just just profiling the surface
+
+ align:start position:0%
+just just profiling the surface
+ 
+
+ align:start position:0%
+just just profiling the surface
+and so here with two different tiling
+
+ align:start position:0%
+and so here with two different tiling
+ 
+
+ align:start position:0%
+and so here with two different tiling
+methods this is more repetitive rather
+
+ align:start position:0%
+methods this is more repetitive rather
+ 
+
+ align:start position:0%
+methods this is more repetitive rather
+than an aperiodic title tiling you can
+
+ align:start position:0%
+than an aperiodic title tiling you can
+ 
+
+ align:start position:0%
+than an aperiodic title tiling you can
+see that these little pink protrusions
+
+ align:start position:0%
+see that these little pink protrusions
+ 
+
+ align:start position:0%
+see that these little pink protrusions
+you can engineer into the tile
+
+ align:start position:0%
+you can engineer into the tile
+ 
+
+ align:start position:0%
+you can engineer into the tile
+not just the two-dimensional stickiness
+
+ align:start position:0%
+not just the two-dimensional stickiness
+ 
+
+ align:start position:0%
+not just the two-dimensional stickiness
+sticky
+
+ align:start position:0%
+sticky
+ 
+
+ align:start position:0%
+sticky
+tags but a third dimension which is a
+
+ align:start position:0%
+tags but a third dimension which is a
+ 
+
+ align:start position:0%
+tags but a third dimension which is a
+bump which might be a um
+
+ align:start position:0%
+bump which might be a um
+ 
+
+ align:start position:0%
+bump which might be a um
+a stem loop as we've seen in other
+
+ align:start position:0%
+a stem loop as we've seen in other
+ 
+
+ align:start position:0%
+a stem loop as we've seen in other
+secondary structures there's engineering
+
+ align:start position:0%
+secondary structures there's engineering
+ 
+
+ align:start position:0%
+secondary structures there's engineering
+into this dna so now that these bumps
+
+ align:start position:0%
+into this dna so now that these bumps
+ 
+
+ align:start position:0%
+into this dna so now that these bumps
+will stick up and the easy targets for
+
+ align:start position:0%
+will stick up and the easy targets for
+ 
+
+ align:start position:0%
+will stick up and the easy targets for
+the atomic force microscope and here you
+
+ align:start position:0%
+the atomic force microscope and here you
+ 
+
+ align:start position:0%
+the atomic force microscope and here you
+have a bump every every second uh tile
+
+ align:start position:0%
+have a bump every every second uh tile
+ 
+
+ align:start position:0%
+have a bump every every second uh tile
+and that's on the left and on the right
+
+ align:start position:0%
+and that's on the left and on the right
+ 
+
+ align:start position:0%
+and that's on the left and on the right
+of slide 27 you have a more complicated
+
+ align:start position:0%
+of slide 27 you have a more complicated
+ 
+
+ align:start position:0%
+of slide 27 you have a more complicated
+tiling where you have four different
+
+ align:start position:0%
+tiling where you have four different
+ 
+
+ align:start position:0%
+tiling where you have four different
+types of tiles
+
+ align:start position:0%
+types of tiles
+ 
+
+ align:start position:0%
+types of tiles
+and a bump every
+
+ align:start position:0%
+and a bump every
+ 
+
+ align:start position:0%
+and a bump every
+fourth one and so you expect you can
+
+ align:start position:0%
+fourth one and so you expect you can
+ 
+
+ align:start position:0%
+fourth one and so you expect you can
+calculate from the the uh
+
+ align:start position:0%
+calculate from the the uh
+ 
+
+ align:start position:0%
+calculate from the the uh
+watson crick model for dna or more
+
+ align:start position:0%
+watson crick model for dna or more
+ 
+
+ align:start position:0%
+watson crick model for dna or more
+advanced models of dna even though this
+
+ align:start position:0%
+advanced models of dna even though this
+ 
+
+ align:start position:0%
+advanced models of dna even though this
+is a a lattice of
+
+ align:start position:0%
+is a a lattice of
+ 
+
+ align:start position:0%
+is a a lattice of
+brain structures you can calculate it
+
+ align:start position:0%
+brain structures you can calculate it
+ 
+
+ align:start position:0%
+brain structures you can calculate it
+should be about 33 nanometers between
+
+ align:start position:0%
+should be about 33 nanometers between
+ 
+
+ align:start position:0%
+should be about 33 nanometers between
+the bumps that's what's observed and 65
+
+ align:start position:0%
+the bumps that's what's observed and 65
+ 
+
+ align:start position:0%
+the bumps that's what's observed and 65
+nanometers is calculated and observed
+
+ align:start position:0%
+nanometers is calculated and observed
+ 
+
+ align:start position:0%
+nanometers is calculated and observed
+you can see the bigger lattice facing in
+
+ align:start position:0%
+you can see the bigger lattice facing in
+ 
+
+ align:start position:0%
+you can see the bigger lattice facing in
+these admittedly somewhat fuzzy atomic
+
+ align:start position:0%
+these admittedly somewhat fuzzy atomic
+ 
+
+ align:start position:0%
+these admittedly somewhat fuzzy atomic
+force micrographs
+
+ align:start position:0%
+force micrographs
+ 
+
+ align:start position:0%
+force micrographs
+but you can see you get something
+
+ align:start position:0%
+but you can see you get something
+ 
+
+ align:start position:0%
+but you can see you get something
+experimental confirmation of the
+
+ align:start position:0%
+experimental confirmation of the
+ 
+
+ align:start position:0%
+experimental confirmation of the
+two-dimensional
+
+ align:start position:0%
+two-dimensional
+ 
+
+ align:start position:0%
+two-dimensional
+structures here
+
+ align:start position:0%
+structures here
+ 
+
+ align:start position:0%
+structures here
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this is a self-assembly nanofabrication
+
+ align:start position:0%
+this is a self-assembly nanofabrication
+ 
+
+ align:start position:0%
+this is a self-assembly nanofabrication
+and and at some extent it is inspired by
+
+ align:start position:0%
+and and at some extent it is inspired by
+ 
+
+ align:start position:0%
+and and at some extent it is inspired by
+and is and can be combined with
+
+ align:start position:0%
+and is and can be combined with
+ 
+
+ align:start position:0%
+and is and can be combined with
+microfabrication this is something where
+
+ align:start position:0%
+microfabrication this is something where
+ 
+
+ align:start position:0%
+microfabrication this is something where
+you basically use optics you go to the
+
+ align:start position:0%
+you basically use optics you go to the
+ 
+
+ align:start position:0%
+you basically use optics you go to the
+limit of current uh optical
+
+ align:start position:0%
+limit of current uh optical
+ 
+
+ align:start position:0%
+limit of current uh optical
+manufacturing
+
+ align:start position:0%
+manufacturing
+ 
+
+ align:start position:0%
+manufacturing
+as a micro fabrication where it's
+
+ align:start position:0%
+as a micro fabrication where it's
+ 
+
+ align:start position:0%
+as a micro fabrication where it's
+typically hard to get below
+
+ align:start position:0%
+typically hard to get below
+ 
+
+ align:start position:0%
+typically hard to get below
+say 100 nanometers or so in feature size
+
+ align:start position:0%
+say 100 nanometers or so in feature size
+ 
+
+ align:start position:0%
+say 100 nanometers or so in feature size
+here you can see this is uh
+
+ align:start position:0%
+here you can see this is uh
+ 
+
+ align:start position:0%
+here you can see this is uh
+and this is the sort of micro
+
+ align:start position:0%
+and this is the sort of micro
+ 
+
+ align:start position:0%
+and this is the sort of micro
+fabrication used to make your uh
+
+ align:start position:0%
+fabrication used to make your uh
+ 
+
+ align:start position:0%
+fabrication used to make your uh
+computer chips
+
+ align:start position:0%
+computer chips
+ 
+
+ align:start position:0%
+computer chips
+but it's uh
+
+ align:start position:0%
+but it's uh
+ 
+
+ align:start position:0%
+but it's uh
+in this case it's used to actually make
+
+ align:start position:0%
+in this case it's used to actually make
+ 
+
+ align:start position:0%
+in this case it's used to actually make
+moving parts parts that move relative to
+
+ align:start position:0%
+moving parts parts that move relative to
+ 
+
+ align:start position:0%
+moving parts parts that move relative to
+one another and that that motion
+
+ align:start position:0%
+one another and that that motion
+ 
+
+ align:start position:0%
+one another and that that motion
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+actually has useful um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applications the first such useful
+
+ align:start position:0%
+applications the first such useful
+ 
+
+ align:start position:0%
+applications the first such useful
+application that i'm aware
+
+ align:start position:0%
+application that i'm aware
+ 
+
+ align:start position:0%
+application that i'm aware
+is putting these things into airbag
+
+ align:start position:0%
+is putting these things into airbag
+ 
+
+ align:start position:0%
+is putting these things into airbag
+sensors and the idea is that when you're
+
+ align:start position:0%
+sensors and the idea is that when you're
+ 
+
+ align:start position:0%
+sensors and the idea is that when you're
+driving your large automobile and run
+
+ align:start position:0%
+driving your large automobile and run
+ 
+
+ align:start position:0%
+driving your large automobile and run
+into a even larger object
+
+ align:start position:0%
+into a even larger object
+ 
+
+ align:start position:0%
+into a even larger object
+you suddenly decelerate either by breaks
+
+ align:start position:0%
+you suddenly decelerate either by breaks
+ 
+
+ align:start position:0%
+you suddenly decelerate either by breaks
+or some other method
+
+ align:start position:0%
+or some other method
+ 
+
+ align:start position:0%
+or some other method
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+when you do
+
+ align:start position:0%
+when you do
+ 
+
+ align:start position:0%
+when you do
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this little bitty device
+
+ align:start position:0%
+this little bitty device
+ 
+
+ align:start position:0%
+this little bitty device
+ins sensor inside your somewhere in your
+
+ align:start position:0%
+ins sensor inside your somewhere in your
+ 
+
+ align:start position:0%
+ins sensor inside your somewhere in your
+car
+
+ align:start position:0%
+car
+ 
+
+ align:start position:0%
+car
+will shift one of its parts by at least
+
+ align:start position:0%
+will shift one of its parts by at least
+ 
+
+ align:start position:0%
+will shift one of its parts by at least
+point two angstroms meaning a tenth of
+
+ align:start position:0%
+point two angstroms meaning a tenth of
+ 
+
+ align:start position:0%
+point two angstroms meaning a tenth of
+an atomic diameter that doesn't seem
+
+ align:start position:0%
+an atomic diameter that doesn't seem
+ 
+
+ align:start position:0%
+an atomic diameter that doesn't seem
+like very much and it isn't it only
+
+ align:start position:0%
+like very much and it isn't it only
+ 
+
+ align:start position:0%
+like very much and it isn't it only
+causes a hundred femtofarads that means
+
+ align:start position:0%
+causes a hundred femtofarads that means
+ 
+
+ align:start position:0%
+causes a hundred femtofarads that means
+10 to the minus 13 farad capacitors
+
+ align:start position:0%
+10 to the minus 13 farad capacitors
+ 
+
+ align:start position:0%
+10 to the minus 13 farad capacitors
+change but that's quite enough to signal
+
+ align:start position:0%
+change but that's quite enough to signal
+ 
+
+ align:start position:0%
+change but that's quite enough to signal
+a uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a collision has occurred or will
+
+ align:start position:0%
+that a collision has occurred or will
+ 
+
+ align:start position:0%
+that a collision has occurred or will
+occur
+
+ align:start position:0%
+occur
+ 
+
+ align:start position:0%
+occur
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+with a very low false positive rate
+
+ align:start position:0%
+with a very low false positive rate
+ 
+
+ align:start position:0%
+with a very low false positive rate
+those of you who have driven large
+
+ align:start position:0%
+those of you who have driven large
+ 
+
+ align:start position:0%
+those of you who have driven large
+automobiles know how infrequently the
+
+ align:start position:0%
+automobiles know how infrequently the
+ 
+
+ align:start position:0%
+automobiles know how infrequently the
+airbag opens up accidentally
+
+ align:start position:0%
+airbag opens up accidentally
+ 
+
+ align:start position:0%
+airbag opens up accidentally
+but when it does deflect by 0.2
+
+ align:start position:0%
+but when it does deflect by 0.2
+ 
+
+ align:start position:0%
+but when it does deflect by 0.2
+angstroms then it does open up the
+
+ align:start position:0%
+angstroms then it does open up the
+ 
+
+ align:start position:0%
+angstroms then it does open up the
+airbag okay so this is a payoff of
+
+ align:start position:0%
+airbag okay so this is a payoff of
+ 
+
+ align:start position:0%
+airbag okay so this is a payoff of
+microfabrication but now we want to
+
+ align:start position:0%
+microfabrication but now we want to
+ 
+
+ align:start position:0%
+microfabrication but now we want to
+combine the sort of nano systems we saw
+
+ align:start position:0%
+combine the sort of nano systems we saw
+ 
+
+ align:start position:0%
+combine the sort of nano systems we saw
+in the dna computers and in the tiling
+
+ align:start position:0%
+in the dna computers and in the tiling
+ 
+
+ align:start position:0%
+in the dna computers and in the tiling
+with microfabrication
+
+ align:start position:0%
+with microfabrication
+ 
+
+ align:start position:0%
+with microfabrication
+and i think this is just one of the very
+
+ align:start position:0%
+and i think this is just one of the very
+ 
+
+ align:start position:0%
+and i think this is just one of the very
+few examples where microfab meets
+
+ align:start position:0%
+few examples where microfab meets
+ 
+
+ align:start position:0%
+few examples where microfab meets
+nanofabrication and we'll call it a
+
+ align:start position:0%
+nanofabrication and we'll call it a
+ 
+
+ align:start position:0%
+nanofabrication and we'll call it a
+nanoelectromechanical system
+
+ align:start position:0%
+nanoelectromechanical system
+ 
+
+ align:start position:0%
+nanoelectromechanical system
+and here so you've got the
+
+ align:start position:0%
+and here so you've got the
+ 
+
+ align:start position:0%
+and here so you've got the
+microfabrication of both the posts upon
+
+ align:start position:0%
+microfabrication of both the posts upon
+ 
+
+ align:start position:0%
+microfabrication of both the posts upon
+which these things stand which is sort
+
+ align:start position:0%
+which these things stand which is sort
+ 
+
+ align:start position:0%
+which these things stand which is sort
+of these nickel columns of of
+
+ align:start position:0%
+of these nickel columns of of
+ 
+
+ align:start position:0%
+of these nickel columns of of
+you know 80 nanometers and the little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bars metal bars
+
+ align:start position:0%
+bars metal bars
+ 
+
+ align:start position:0%
+bars metal bars
+which can be a sort of a micron range
+
+ align:start position:0%
+which can be a sort of a micron range
+ 
+
+ align:start position:0%
+which can be a sort of a micron range
+and that and you can see them visualized
+
+ align:start position:0%
+and that and you can see them visualized
+ 
+
+ align:start position:0%
+and that and you can see them visualized
+in the left-hand photograph where you
+
+ align:start position:0%
+in the left-hand photograph where you
+ 
+
+ align:start position:0%
+in the left-hand photograph where you
+have these bars at regular spacings
+
+ align:start position:0%
+have these bars at regular spacings
+ 
+
+ align:start position:0%
+have these bars at regular spacings
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you look at this publication or the
+
+ align:start position:0%
+if you look at this publication or the
+ 
+
+ align:start position:0%
+if you look at this publication or the
+the webs that go along with it these
+
+ align:start position:0%
+the webs that go along with it these
+ 
+
+ align:start position:0%
+the webs that go along with it these
+little bars will spin around
+
+ align:start position:0%
+little bars will spin around
+ 
+
+ align:start position:0%
+little bars will spin around
+and what they're spinning on is not a
+
+ align:start position:0%
+and what they're spinning on is not a
+ 
+
+ align:start position:0%
+and what they're spinning on is not a
+microfabricated motor but it is a
+
+ align:start position:0%
+microfabricated motor but it is a
+ 
+
+ align:start position:0%
+microfabricated motor but it is a
+nano biotech motor which and actually
+
+ align:start position:0%
+nano biotech motor which and actually
+ 
+
+ align:start position:0%
+nano biotech motor which and actually
+it's a protein that most people didn't
+
+ align:start position:0%
+it's a protein that most people didn't
+ 
+
+ align:start position:0%
+it's a protein that most people didn't
+think of on the motor
+
+ align:start position:0%
+think of on the motor
+ 
+
+ align:start position:0%
+think of on the motor
+when it was first discovered it is the
+
+ align:start position:0%
+when it was first discovered it is the
+ 
+
+ align:start position:0%
+when it was first discovered it is the
+the protein present in almost all
+
+ align:start position:0%
+the protein present in almost all
+ 
+
+ align:start position:0%
+the protein present in almost all
+organisms
+
+ align:start position:0%
+organisms
+ 
+
+ align:start position:0%
+organisms
+that is responsible for atp generation
+
+ align:start position:0%
+that is responsible for atp generation
+ 
+
+ align:start position:0%
+that is responsible for atp generation
+usually think of this as making atp for
+
+ align:start position:0%
+usually think of this as making atp for
+ 
+
+ align:start position:0%
+usually think of this as making atp for
+other motor for motors to use but this
+
+ align:start position:0%
+other motor for motors to use but this
+ 
+
+ align:start position:0%
+other motor for motors to use but this
+actually since it is capable of rotary
+
+ align:start position:0%
+actually since it is capable of rotary
+ 
+
+ align:start position:0%
+actually since it is capable of rotary
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+does does move this one micron bar
+
+ align:start position:0%
+does does move this one micron bar
+ 
+
+ align:start position:0%
+does does move this one micron bar
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+at the rate that you would expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for uh for those for a nano machine to
+
+ align:start position:0%
+for uh for those for a nano machine to
+ 
+
+ align:start position:0%
+for uh for those for a nano machine to
+be generating torque
+
+ align:start position:0%
+be generating torque
+ 
+
+ align:start position:0%
+be generating torque
+okay so that's uh so we're now we've
+
+ align:start position:0%
+okay so that's uh so we're now we've
+ 
+
+ align:start position:0%
+okay so that's uh so we're now we've
+talked about assembly that's an example
+
+ align:start position:0%
+talked about assembly that's an example
+ 
+
+ align:start position:0%
+talked about assembly that's an example
+of an output device what sort of input
+
+ align:start position:0%
+of an output device what sort of input
+ 
+
+ align:start position:0%
+of an output device what sort of input
+devices we have that will work at the
+
+ align:start position:0%
+devices we have that will work at the
+ 
+
+ align:start position:0%
+devices we have that will work at the
+single molecule level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is uh there are many examples we
+
+ align:start position:0%
+here is uh there are many examples we
+ 
+
+ align:start position:0%
+here is uh there are many examples we
+mentioned a few of them uh in the
+
+ align:start position:0%
+mentioned a few of them uh in the
+ 
+
+ align:start position:0%
+mentioned a few of them uh in the
+sequencing
+
+ align:start position:0%
+sequencing
+ 
+
+ align:start position:0%
+sequencing
+genotyping lecture where we were talking
+
+ align:start position:0%
+genotyping lecture where we were talking
+ 
+
+ align:start position:0%
+genotyping lecture where we were talking
+about single fluorophores
+
+ align:start position:0%
+about single fluorophores
+ 
+
+ align:start position:0%
+about single fluorophores
+here you can use another aspect of
+
+ align:start position:0%
+here you can use another aspect of
+ 
+
+ align:start position:0%
+here you can use another aspect of
+biology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a self-assembly of membranes to
+
+ align:start position:0%
+which is a self-assembly of membranes to
+ 
+
+ align:start position:0%
+which is a self-assembly of membranes to
+make a very
+
+ align:start position:0%
+make a very
+ 
+
+ align:start position:0%
+make a very
+very tight
+
+ align:start position:0%
+very tight
+ 
+
+ align:start position:0%
+very tight
+low conductance seal
+
+ align:start position:0%
+low conductance seal
+ 
+
+ align:start position:0%
+low conductance seal
+which is only on the order of two
+
+ align:start position:0%
+which is only on the order of two
+ 
+
+ align:start position:0%
+which is only on the order of two
+nanometers thick but it's enough to make
+
+ align:start position:0%
+nanometers thick but it's enough to make
+ 
+
+ align:start position:0%
+nanometers thick but it's enough to make
+a giga ohm seal a multi gig ohm seal and
+
+ align:start position:0%
+a giga ohm seal a multi gig ohm seal and
+ 
+
+ align:start position:0%
+a giga ohm seal a multi gig ohm seal and
+then you poke a little hole in it with a
+
+ align:start position:0%
+then you poke a little hole in it with a
+ 
+
+ align:start position:0%
+then you poke a little hole in it with a
+single molecule of a protein
+
+ align:start position:0%
+single molecule of a protein
+ 
+
+ align:start position:0%
+single molecule of a protein
+and they're they're
+
+ align:start position:0%
+and they're they're
+ 
+
+ align:start position:0%
+and they're they're
+growing ways to do this on inorganic
+
+ align:start position:0%
+growing ways to do this on inorganic
+ 
+
+ align:start position:0%
+growing ways to do this on inorganic
+substrates as well
+
+ align:start position:0%
+substrates as well
+ 
+
+ align:start position:0%
+substrates as well
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when you have a single protein pour
+
+ align:start position:0%
+when you have a single protein pour
+ 
+
+ align:start position:0%
+when you have a single protein pour
+which itself might be a one nanometer
+
+ align:start position:0%
+which itself might be a one nanometer
+ 
+
+ align:start position:0%
+which itself might be a one nanometer
+opening
+
+ align:start position:0%
+opening
+ 
+
+ align:start position:0%
+opening
+it will it will allow in the presence of
+
+ align:start position:0%
+it will it will allow in the presence of
+ 
+
+ align:start position:0%
+it will it will allow in the presence of
+electric field indicated by these
+
+ align:start position:0%
+electric field indicated by these
+ 
+
+ align:start position:0%
+electric field indicated by these
+negative and positive charges here
+
+ align:start position:0%
+negative and positive charges here
+ 
+
+ align:start position:0%
+negative and positive charges here
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+yellow negative and positive ions to go
+
+ align:start position:0%
+yellow negative and positive ions to go
+ 
+
+ align:start position:0%
+yellow negative and positive ions to go
+through it's like sodium chloride
+
+ align:start position:0%
+through it's like sodium chloride
+ 
+
+ align:start position:0%
+through it's like sodium chloride
+and they will go through it about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up to a million ions per second
+
+ align:start position:0%
+up to a million ions per second
+ 
+
+ align:start position:0%
+up to a million ions per second
+easily
+
+ align:start position:0%
+easily
+ 
+
+ align:start position:0%
+easily
+and when you
+
+ align:start position:0%
+and when you
+ 
+
+ align:start position:0%
+and when you
+have a larger molecule that's that's say
+
+ align:start position:0%
+have a larger molecule that's that's say
+ 
+
+ align:start position:0%
+have a larger molecule that's that's say
+a polyanion in the electric field it
+
+ align:start position:0%
+a polyanion in the electric field it
+ 
+
+ align:start position:0%
+a polyanion in the electric field it
+will slowly migrate through this pore
+
+ align:start position:0%
+will slowly migrate through this pore
+ 
+
+ align:start position:0%
+will slowly migrate through this pore
+and while it does so it blocks the rapid
+
+ align:start position:0%
+and while it does so it blocks the rapid
+ 
+
+ align:start position:0%
+and while it does so it blocks the rapid
+movement of the smaller ions like sodium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can record
+
+ align:start position:0%
+and you can record
+ 
+
+ align:start position:0%
+and you can record
+the uh it doesn't it doesn't necessarily
+
+ align:start position:0%
+the uh it doesn't it doesn't necessarily
+ 
+
+ align:start position:0%
+the uh it doesn't it doesn't necessarily
+completely block the channel you can
+
+ align:start position:0%
+completely block the channel you can
+ 
+
+ align:start position:0%
+completely block the channel you can
+record the rate which sodium will go
+
+ align:start position:0%
+record the rate which sodium will go
+ 
+
+ align:start position:0%
+record the rate which sodium will go
+through and how it's influenced by the
+
+ align:start position:0%
+through and how it's influenced by the
+ 
+
+ align:start position:0%
+through and how it's influenced by the
+composition of the of the polymer um
+
+ align:start position:0%
+composition of the of the polymer um
+ 
+
+ align:start position:0%
+composition of the of the polymer um
+going through and so here's an example
+
+ align:start position:0%
+going through and so here's an example
+ 
+
+ align:start position:0%
+going through and so here's an example
+of a bacterial protein
+
+ align:start position:0%
+of a bacterial protein
+ 
+
+ align:start position:0%
+of a bacterial protein
+this is mellor at all reference down
+
+ align:start position:0%
+this is mellor at all reference down
+ 
+
+ align:start position:0%
+this is mellor at all reference down
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+um a bacterial
+
+ align:start position:0%
+um a bacterial
+ 
+
+ align:start position:0%
+um a bacterial
+toxin actually from
+
+ align:start position:0%
+toxin actually from
+ 
+
+ align:start position:0%
+toxin actually from
+staphylococcus
+
+ align:start position:0%
+staphylococcus
+ 
+
+ align:start position:0%
+staphylococcus
+whose goal in life is not is to is you
+
+ align:start position:0%
+whose goal in life is not is to is you
+ 
+
+ align:start position:0%
+whose goal in life is not is to is you
+know is to kill other organisms it's not
+
+ align:start position:0%
+know is to kill other organisms it's not
+ 
+
+ align:start position:0%
+know is to kill other organisms it's not
+to provide a handy conduit for rna to go
+
+ align:start position:0%
+to provide a handy conduit for rna to go
+ 
+
+ align:start position:0%
+to provide a handy conduit for rna to go
+through a cell but nevertheless in this
+
+ align:start position:0%
+through a cell but nevertheless in this
+ 
+
+ align:start position:0%
+through a cell but nevertheless in this
+in this experiment when it does when
+
+ align:start position:0%
+in this experiment when it does when
+ 
+
+ align:start position:0%
+in this experiment when it does when
+when a nucleic acid does spew through
+
+ align:start position:0%
+when a nucleic acid does spew through
+ 
+
+ align:start position:0%
+when a nucleic acid does spew through
+this it blocks the the
+
+ align:start position:0%
+this it blocks the the
+ 
+
+ align:start position:0%
+this it blocks the the
+little red water molecules and similar
+
+ align:start position:0%
+little red water molecules and similar
+ 
+
+ align:start position:0%
+little red water molecules and similar
+sized ions
+
+ align:start position:0%
+sized ions
+ 
+
+ align:start position:0%
+sized ions
+are blocked and they're blocked in a way
+
+ align:start position:0%
+are blocked and they're blocked in a way
+ 
+
+ align:start position:0%
+are blocked and they're blocked in a way
+which is sensitive to the in the not
+
+ align:start position:0%
+which is sensitive to the in the not
+ 
+
+ align:start position:0%
+which is sensitive to the in the not
+only the the molecule but parts of the
+
+ align:start position:0%
+only the the molecule but parts of the
+ 
+
+ align:start position:0%
+only the the molecule but parts of the
+molecule so you can see here you've got
+
+ align:start position:0%
+molecule so you can see here you've got
+ 
+
+ align:start position:0%
+molecule so you can see here you've got
+a molecule with a poly a lego a
+
+ align:start position:0%
+a molecule with a poly a lego a
+ 
+
+ align:start position:0%
+a molecule with a poly a lego a
+part and a lego c part and you can
+
+ align:start position:0%
+part and a lego c part and you can
+ 
+
+ align:start position:0%
+part and a lego c part and you can
+actually discriminate between these both
+
+ align:start position:0%
+actually discriminate between these both
+ 
+
+ align:start position:0%
+actually discriminate between these both
+in terms of the rate at which they go
+
+ align:start position:0%
+in terms of the rate at which they go
+ 
+
+ align:start position:0%
+in terms of the rate at which they go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+each of the parts goes through and the
+
+ align:start position:0%
+each of the parts goes through and the
+ 
+
+ align:start position:0%
+each of the parts goes through and the
+conductance so if you look down in the
+
+ align:start position:0%
+conductance so if you look down in the
+ 
+
+ align:start position:0%
+conductance so if you look down in the
+lower right hand
+
+ align:start position:0%
+lower right hand
+ 
+
+ align:start position:0%
+lower right hand
+part you'll see a 5 peco ampere to the
+
+ align:start position:0%
+part you'll see a 5 peco ampere to the
+ 
+
+ align:start position:0%
+part you'll see a 5 peco ampere to the
+minus 12 ampere 20 ampere and 120 ampere
+
+ align:start position:0%
+minus 12 ampere 20 ampere and 120 ampere
+ 
+
+ align:start position:0%
+minus 12 ampere 20 ampere and 120 ampere
+levels for these individual molecules in
+
+ align:start position:0%
+levels for these individual molecules in
+ 
+
+ align:start position:0%
+levels for these individual molecules in
+each of these spikes
+
+ align:start position:0%
+each of these spikes
+ 
+
+ align:start position:0%
+each of these spikes
+it uh is
+
+ align:start position:0%
+it uh is
+ 
+
+ align:start position:0%
+it uh is
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+the the a30 half and then the c70 half
+
+ align:start position:0%
+the the a30 half and then the c70 half
+ 
+
+ align:start position:0%
+the the a30 half and then the c70 half
+going through
+
+ align:start position:0%
+going through
+ 
+
+ align:start position:0%
+going through
+and you can see that the uh
+
+ align:start position:0%
+and you can see that the uh
+ 
+
+ align:start position:0%
+and you can see that the uh
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+the two different conductance levels you
+
+ align:start position:0%
+the two different conductance levels you
+ 
+
+ align:start position:0%
+the two different conductance levels you
+get reproducibly going it's going
+
+ align:start position:0%
+get reproducibly going it's going
+ 
+
+ align:start position:0%
+get reproducibly going it's going
+through it typically in one direction
+
+ align:start position:0%
+through it typically in one direction
+ 
+
+ align:start position:0%
+through it typically in one direction
+first the a is in the c
+
+ align:start position:0%
+first the a is in the c
+ 
+
+ align:start position:0%
+first the a is in the c
+and uh different conductance levels
+
+ align:start position:0%
+and uh different conductance levels
+ 
+
+ align:start position:0%
+and uh different conductance levels
+different rates and then the 120
+
+ align:start position:0%
+different rates and then the 120
+ 
+
+ align:start position:0%
+different rates and then the 120
+pipeline appears is in between molecules
+
+ align:start position:0%
+pipeline appears is in between molecules
+ 
+
+ align:start position:0%
+pipeline appears is in between molecules
+where you're getting the full
+
+ align:start position:0%
+where you're getting the full
+ 
+
+ align:start position:0%
+where you're getting the full
+conductance capability
+
+ align:start position:0%
+conductance capability
+ 
+
+ align:start position:0%
+conductance capability
+lots of sodium is going through
+
+ align:start position:0%
+lots of sodium is going through
+ 
+
+ align:start position:0%
+lots of sodium is going through
+and uh just like with other methods that
+
+ align:start position:0%
+and uh just like with other methods that
+ 
+
+ align:start position:0%
+and uh just like with other methods that
+we've seen
+
+ align:start position:0%
+we've seen
+ 
+
+ align:start position:0%
+we've seen
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+the use of two dimensions helps get you
+
+ align:start position:0%
+the use of two dimensions helps get you
+ 
+
+ align:start position:0%
+the use of two dimensions helps get you
+better statistical resolution here the
+
+ align:start position:0%
+better statistical resolution here the
+ 
+
+ align:start position:0%
+better statistical resolution here the
+two dimensions are the conductance and
+
+ align:start position:0%
+two dimensions are the conductance and
+ 
+
+ align:start position:0%
+two dimensions are the conductance and
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+time on the vertical axis and
+
+ align:start position:0%
+time on the vertical axis and
+ 
+
+ align:start position:0%
+time on the vertical axis and
+conductance on the horizontal axis
+
+ align:start position:0%
+conductance on the horizontal axis
+ 
+
+ align:start position:0%
+conductance on the horizontal axis
+and you can see how you can discriminate
+
+ align:start position:0%
+and you can see how you can discriminate
+ 
+
+ align:start position:0%
+and you can see how you can discriminate
+different types of polymers by this
+
+ align:start position:0%
+different types of polymers by this
+ 
+
+ align:start position:0%
+different types of polymers by this
+method one molecule at a time each of
+
+ align:start position:0%
+method one molecule at a time each of
+ 
+
+ align:start position:0%
+method one molecule at a time each of
+these dots represents a single molecular
+
+ align:start position:0%
+these dots represents a single molecular
+ 
+
+ align:start position:0%
+these dots represents a single molecular
+event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll take a
+
+ align:start position:0%
+so we'll take a
+ 
+
+ align:start position:0%
+so we'll take a
+short break
+
+ align:start position:0%
+short break
+ 
+
+ align:start position:0%
+short break
+and then when we come back we'll talk
+
+ align:start position:0%
+and then when we come back we'll talk
+ 
+
+ align:start position:0%
+and then when we come back we'll talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+not molecular computing but
+
+ align:start position:0%
+not molecular computing but
+ 
+
+ align:start position:0%
+not molecular computing but
+designing cellular computers and
+
+ align:start position:0%
+designing cellular computers and
+ 
+
+ align:start position:0%
+designing cellular computers and
+revisit some of these same themes
+
+ align:start position:0%
+revisit some of these same themes
+ 
+
+ align:start position:0%
+revisit some of these same themes
+thanks
\ No newline at end of file
diff --git a/Qd-zK_1bEPM.txt b/Qd-zK_1bEPM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f159a37b1460433fd7aa7c83404bb47fa694c8c8
--- /dev/null
+++ b/Qd-zK_1bEPM.txt
@@ -0,0 +1,98 @@
+TAKAKO AIKAWA: So we had
+two different sessions.
+
+One is grammar session, and
+the other one is drill session.
+
+Grammar session is to teach or
+introduce new grammar items,
+
+and usually, we do
+this grammar session,
+
+we are using English, especially
+for beginners classes.
+
+The drill session is to practice
+what students have learned
+
+in grammar session,
+so lots of drills
+
+and interactive activities
+in class, and drills sessions
+
+are entirely in Japanese, even
+from day two of the first year.
+
+And in terms of
+proportion, we usually
+
+spend one day for
+grammar session
+
+and four to five days for
+drill sessions per each lesson.
+
+So for grammar
+session, the students
+
+are supposed to read grammar
+notes of the textbook, so
+
+each lesson, we have grammar
+notes on the textbook.
+
+And at the same
+time, each lesson
+
+introduces 40 to 50
+new vocabularies,
+
+so students are supposed to
+learn those new vocabularies as
+
+well.
+
+For drill sessions,
+we have a lot
+
+of online interactive
+exercises, so students
+
+are supposed to go
+to this online site
+
+and then do a lot of practice.
+
+So conducting drills
+sessions entirely in Japanese
+
+it's quite challenging
+for us, but I
+
+believe that language needs
+to be learned together
+
+with context.
+
+So as a language
+teacher, and then
+
+I believe that other
+colleagues do the same thing,
+
+too, we bring a
+lot of visual aids.
+
+so that the classroom becomes
+more like a real context,
+
+and then we try to create
+a so-called immersive
+
+environment in
+class, and that way
+
+we can conduct
+interactive drills.
\ No newline at end of file
diff --git a/QrzHB9_kHPE.txt b/QrzHB9_kHPE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6fda348cbded717177f09159be07b514ee40bab7
--- /dev/null
+++ b/QrzHB9_kHPE.txt
@@ -0,0 +1,1811 @@
+The following content is
+provided under a creative
+
+commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR NELSON: Over the last
+couple lectures through
+
+our consideration of a number of
+somewhat difficult topics,
+
+including these Carnot cycles
+and specific Carnot engine to
+
+represent them, we've tried to
+define and understand a little
+
+bit about this very special
+function, this entropy.
+
+Where we've got our dS.
+
+It's dq reversible over T. And
+our treatment of reversible
+
+and irreversible cyclic
+processes, what we saw is that
+
+if we go around a cycle and look
+at dq reversible over T,
+
+then this is zero.
+
+Now go all the way around a
+cycle, of course, this is just
+
+delta S for the cycle.
+
+And that's consistent
+with the idea that
+
+entropy is a state functions.
+
+So if we go around cycle the
+cycle, we have the same ending
+
+point, the starting point, same
+state, then the change in
+
+the state function
+has to be zero.
+
+But we saw that for an
+irreversible path around a
+
+cycle, then we have
+that, this gives
+
+something less than zero.
+
+And so that was expressed in
+Clausius inequality that
+
+includes both these cases.
+
+And now I just want to go
+through a number of
+
+calculations of entropy.
+
+How entropy changes for a number
+processes, both to just
+
+learn more about it in general
+terms and also just to see how
+
+it's calculated and what sort
+of changes in undergoes for
+
+different sorts of
+changes in state.
+
+So the first very general
+example that I want to show is
+
+the following.
+
+Let's say we've got an isolated
+system, and it
+
+undergoes some irreversible
+change.
+
+So we'll start at one, and we'll
+go irreversibly to some
+
+new state, two.
+
+OK, now we can always return the
+system back to the initial
+
+state reversibly.
+
+If we do that, then we can't
+keep the system isolated.
+
+So it won't be isolated
+anymore.
+
+In other words, in order to
+arrange things so that you
+
+could have a return
+along a reversible
+
+path, it can't be isolated.
+
+In some sense you know that,
+because when it was isolated
+
+it spontaneously irreversibly
+went from one to two.
+
+And example would be ice melting
+at some temperature
+
+that might be higher than
+the freezing point.
+
+So you've got solid ice, but the
+temperature is above zero
+
+degrees Celsius, so irreversibly
+it'll melt.
+
+Systems isolated, it'll melt.
+
+Then you could put the system
+in contact with a cold
+
+reservoir reversibly re-freeze
+the water to form ice again.
+
+But of course to do that you
+couldn't keep it isolated.
+
+You need to have it in contact
+with a low temperature bath.
+
+But again, this is
+just completely
+
+general at this point.
+
+It's some irreversible process
+returned then along a
+
+reversible path.
+
+So let's just look
+at what happens.
+
+So here's our path B.
+Along path A, well
+
+it's an isolated system.
+
+So the heat exchanged is zero.
+
+And then, for the cycle based
+on the Clausius inequality
+
+expressed here, the integral
+around the cycle of dq over T
+
+in general, it's less than
+or equal to zero.
+
+If there was an irreversible
+process involved, then in
+
+fact, it'll be less than zero.
+
+I'll write it here in the more
+general case, but we know what
+
+it's really going to be with
+the irreversible step.
+
+Well, so we can write this
+as the integral of dq
+
+irreversible over T, going from
+state one to state two.
+
+Oh, let me rewrite
+this down here.
+
+So around the cycle, dq over
+T, it's integral from state
+
+one to two of dq irreversible
+over T, plus the integral from
+
+two back to one of dq reversible
+over T. And of
+
+course, we know that that's less
+than or equal to zero.
+
+But this, we know is zero,
+right, because this
+
+irreversible step is
+taken in isolation.
+
+The system is isolated.
+
+We've already seen that there's
+no heat crossing the
+
+boundary of the system.
+
+So we just have this.
+
+So of course this dq reversible
+over T from two to
+
+one, that's, what now we've a
+reversible path, so that's
+
+just the entropy at the delta
+S going from two to one.
+
+It's S1 minus S2 it's delta S,
+we can write it as delta S
+
+backwards, right, we're
+going back along
+
+that reversible path.
+
+Which is of course negative
+delta S forward.
+
+Because around the whole cycle
+delta s has to be zero.
+
+So what that says is delta S
+forward is greater than or
+
+equal to zero.
+
+That's interesting.
+
+What that's saying is --
+remember, we didn't specify
+
+the process.
+
+It's just for any completely
+general irreversible process.
+
+For any such process, for any
+spontaneous process, this is
+
+going to be the case.
+
+So in other words, for an
+isolated system, delta S tells
+
+us the direction of spontaneous
+change.
+
+In particular, for the isolated
+system, delta S is
+
+greater than zero for something
+that's irreversible.
+
+Delta S equals zero for
+something that's reversible,
+
+and delta S is never
+less than zero.
+
+In a sense, this is a direct
+consequence of the Clausius
+
+inequality.
+
+That's a pretty useful result.
+
+So remember when we started this
+whole discussion, I tried
+
+to emphasize that the first law
+of thermodynamics told us
+
+about conservation of energy.
+
+But it didn't tell us which
+way something would go
+
+spontaneously if you just left
+the system to its own devices
+
+under certain conditions.
+
+This is telling us that.
+
+We can tell which way the system
+will evolve in which
+
+direction it'll go.
+
+This is for an isolated system
+and we'll generalize this in
+
+subsequent lectures.
+
+Now, let's look at what
+happens if the
+
+system isn't isolated.
+
+So now let's go from one
+to two not isolated.
+
+So of course, delta S I'm
+going to specify for the
+
+system for reasons that'll soon
+be obvious is S2 for the
+
+system minus S1 for
+the system.
+
+Of course it doesn't depend on
+the path, even though to
+
+calculate it, we need to
+find a reversible path.
+
+Just to add emphasis to what we
+just did here, of course,
+
+it was the same thing.
+
+In order to calculate delta S
+along that irreversible path
+
+for that irreversible process
+we needed to construct some
+
+reversible path.
+
+And what we did is imagined
+the reversible path going
+
+backwards and then said, OK,
+fine then delta S for the
+
+irreversible process must be the
+opposite of delta S that
+
+we calculated along the
+
+reversible bath going backwards.
+
+The point is that to calculate
+delta S in either direction,
+
+we needed to construct
+some reversible path.
+
+All right, and of course
+it'll be the same here.
+
+Now, in this case since the
+system isn't isolated, that
+
+means heat's going to flow
+across the boundary.
+
+So that means heat is going
+between, it's being exchanged
+
+between the system and
+the surroundings.
+
+So what's happening to
+the surroundings?
+
+Generally, we've worry a lot
+about the system, but not much
+
+in recent discussions about
+the surroundings.
+
+But delta S surroundings
+must be something.
+
+We could calculate it.
+
+And that's depends
+on the path.
+
+Not because it isn't the state
+function in the surroundings,
+
+of course it is, but because
+depending on the path, the
+
+final state of the
+
+surroundings will be different.
+
+After all, depending on how much
+heat got exchanged, the
+
+surroundings got more or
+less of that heat.
+
+Work might have been done
+on the surroundings.
+
+So the surroundings are going
+to respond, are going to
+
+change also, when the system
+changes in this way and it's
+
+not isolated.
+
+And how the surroundings change
+will depend on what
+
+path was taken.
+
+And you've seen that before
+in calculating things like
+
+pressure, volume, work along
+different paths.
+
+Where you calculated delta u for
+the system and saw that it
+
+was the same for different paths
+but q and w were not the
+
+same for the system, and
+therefore, of course, not for
+
+the surroundings either.
+
+So let's just consider
+an irreversible path.
+
+And in order to think about
+what happens to the
+
+surroundings, let's take the
+entire universe which consists
+
+of the system and the
+surroundings -- that is a big
+
+isolated system, because
+it's everything.
+
+So it's not somehow in contact
+with another additional body
+
+or universe.
+
+We can treat the
+entire universe
+
+as an isolated system.
+
+So, we're going to think about
+the entire universe.
+
+We can think about it as
+an isolated system.
+
+Great.
+
+And we know that delta S for
+an isolated system, for a
+
+spontaneous process, is
+greater than zero.
+
+That's right there.
+
+So delta S for the universe
+which is delta S for the
+
+system plus delta S for the
+surroundings, and I'll specify
+
+since we're considering an
+irreversible process, specify
+
+that, it's greater than zero.
+
+The whole thing happened
+spontaneously, and the whole
+
+universe is an isolated
+system.
+
+So if we wanted to, we can
+write that delta S
+
+irreversible for the
+surroundings must be bigger
+
+than minus delta S for the
+system in order that there sum
+
+be positive.
+
+All right?
+
+Now, if we consider a reversible
+process, then of
+
+course we already know what
+happens for an isolated system
+
+in a reversible process,
+delta S is zero.
+
+So delta S in this case of the
+whole universe, which is delta
+
+S for the system plus delta S
+for the surroundings in the
+
+reversible case must
+be equal to zero.
+
+In other words, delta S of the
+surroundings in the reversible
+
+case is exactly the opposite
+of delta S of the system.
+
+Delta S of the system is the
+same in either case because
+
+reversible or irreversible,
+we're specifying the system,
+
+goes between the same states,
+but what happens to the
+
+surroundings is different
+in the two cases.
+
+So one way of recasting this
+statement or the Clausius
+
+inequality is the entropy
+of the whole
+
+universe never decreases.
+
+Of course, in some sense,
+that's obvious from this
+
+statement, since we're
+considering the universe an
+
+isolated system.
+
+So the entropy in any process
+can, it can, the change in
+
+entropy can either be zero or
+positive and never negative.
+
+So entropy off the whole
+universe never decreases.
+
+That's actually a really quite
+profound conclusion.
+
+All sorts of philosophical and
+other consequences of it that
+
+are sometimes considered in
+things like evolutionary
+
+biology and other things.
+
+And how things can change
+altogether an
+
+entire system of things.
+
+Now, I'd like to just go through
+a few calculations of
+
+delta S for common processes.
+
+We've seen a few general
+features of entropy.
+
+Let's calculate it
+for a few things.
+
+So calculations of
+delta S. And we
+
+know the general procedure.
+
+Whatever the process is, we're
+going to need to find
+
+reversible paths, and along a
+reversible path then, we'll be
+
+able to calculate it.
+
+One, let's just take two
+pieces of material at
+
+different temperatures.
+
+The entire system is going
+to be isolated.
+
+And then let's connect them.
+
+And then let's connect them.
+
+Put some material
+between them.
+
+So now heat can flow from
+one to the other.
+
+And you know what's going to
+happen which is if they start
+
+out at unequal temperatures, and
+you wait a little while,
+
+eventually they're going
+to wind up at the same
+
+temperature.
+
+In other words, you
+know the direction
+
+of spontaneous change.
+
+So let's just see what
+happens to delta S.
+
+So isolated system, so there's
+no work being done.
+
+There's no heat that's
+being exchanged.
+
+So delta u is zero.
+
+What's dS?
+
+Well it's just the sum of the
+changes in entropy for the two
+
+sub-systems the two
+separate pieces.
+
+So it's dq1 over T1 plus dq2
+over T2, I think there's a
+
+type in your notes. it's plus
+not minus of course.
+
+But in this case, dq1 is just
+the opposite of dq2.
+
+Because whatever heat is flowing
+into T1, into this
+
+block, is coming out of this
+block, or vice versa,
+
+depending on which
+one is hotter.
+
+So this is just equal to dq1
+times one over T1 minus one
+
+over T2, which is T2 minus
+T1 over T1 times T2.
+
+So that's dS, and then we could
+integrate it to get the
+
+delta S, but this is sufficient
+for what I'd like
+
+to illustrate, which is just
+the sign of things.
+
+We know dS must be greater than
+zero for the spontaneous
+
+change that's going to occur.
+
+So let's just make sure that
+common sense prevails here.
+
+That says if T2 is greater than
+T1, right T2 is hotter.
+
+Then dq must be positive, so
+this is positive, this is
+
+positive, dS we know
+has to be positive.
+
+So, it says T2 is hotter.
+
+This being positive means heat
+is flowing in from this one to
+
+this one, from the hotter
+to the colder body.
+
+So it looks right.
+
+If T2 is lower than T1, if this
+one is colder, then in
+
+order for dS to be positive,
+which it has to be, this
+
+better be negative.
+
+In other words, again heat is
+going to flow from the hotter
+
+toward the colder, into
+the colder body.
+
+So, as promised, the condition
+that dS must be greater than
+
+zero, guides us and tells us the
+direction that spontaneous
+
+change is going to occur.
+
+We can tell just from this
+condition which way things
+
+have to evolve.
+
+All right, let's try another
+pretty simple process.
+
+Let's just take a gas in some
+volume V and over here is
+
+going to be vacuum of equal
+volume, and we're going to
+
+remove the barrier.
+
+You know what's going to happen
+spontaneously, right?
+
+The gas is going to fill the
+available volume once it
+
+becomes available.
+
+So this, we'll make this a Joule
+expansion, and we'll
+
+make it an ideal gas.
+
+So the process is one mole of
+gas at our initial volume and
+
+some temperature, and we'll make
+this adiabatic, and this
+
+goes to one mole of gas at a new
+volume, 2V and at the same
+
+temperature.
+
+All right, so there's
+no work done.
+
+It's adiabatic.
+
+There's no heat exchanged.
+
+Delta u is zero.
+
+Everything's zero.
+
+Almost everything is zero.
+
+What isn't zero?
+
+STUDENT: Entropy.
+
+PROFESSOR NELSON: Entropy.
+
+It's going to tell us which
+way this whole thing goes.
+
+So this is an irreversible
+process.
+
+In order to calculate delta
+S we need to construct a
+
+reversible path along
+which this can go.
+
+So here's a way to do it.
+
+We could compress it back,
+isothermally and reversibly.
+
+Just like the example I gave,
+the general example, where I
+
+mentioned the ice melting.
+
+In that case, it won't
+be adiabatic.
+
+We'd have to put it in
+contact with a heat
+
+source of some sort.
+
+So reversible process.
+
+We could compress it back to
+volume V, isothermally, and
+
+reversibly.
+
+Let me say, there's no -- we
+wouldn't have to consider this
+
+process in reverse.
+
+Of course, we could also
+consider the forward process
+
+in the presence of some heat
+source with isn't isolated and
+
+do this, but let's just consider
+the compression.
+
+So, OK, now we'll have
+the -- well, once
+
+again, delta u is zero.
+
+It's an ideal gas.
+
+There's no temperature change.
+
+But this time q and w aren't
+going to be zero.
+
+They're going to be some
+finite numbers that are
+
+opposites of each other.
+
+Because we're no longer
+isolated.
+
+So let's just write out delta
+S to go backward is dq
+
+reversible over T, and
+that's minus dw
+
+over T, not zero anymore.
+
+And where we're going is from
+2V to V, we're compressing,
+
+and it's an ideal gas.
+
+So this is the same as p dV, but
+it's p dV over T which is
+
+the same thing as going from
+2V to V. Now we're going to
+
+replace this with RT over V,
+and the T's will cancel.
+
+So it's R dV over V going from
+2V to one V. So it's just R
+
+times the log of 1/2.
+
+So now we've just calculated
+the value of delta S by
+
+constructing this
+reversible path.
+
+Now this is delta S backward.
+
+To do the compression, so of
+course delta S forward is just
+
+the opposite of that.
+
+So, delta S forward
+is R log 2.
+
+Reassuringly, that's
+a positive number.
+
+So this process that we
+considered originally, this
+
+irreversibly process in this
+isolated system, remember, for
+
+the irreversible expansion
+we considered the system
+
+isolated, Happened
+spontaneously, and of course
+
+you know that's the case.
+
+Now, I'll just mention, and
+later on we'll go into this in
+
+considerably more detail, but
+I'll just mention at this
+
+stage through a little bit of
+sort of foreshadowing that
+
+everything we've discussed so
+far about entropy is with a
+
+macroscopic picture.
+
+We started with heat engines
+and Carnot cycles and
+
+macroscopic processes,
+reversible and irreversible
+
+processes and so on.
+
+But there's a, and that's
+certainly the way it was all
+
+formulated originally.
+
+Part of the power of
+thermodynamics is that it
+
+doesn't depend on a specific
+microscopic model of matter.
+
+That said though, we
+have a pretty good
+
+microscopic model of matter.
+
+We know about atoms and
+molecules, and in fact there
+
+is an entirely microscopic
+formulation of entropy that
+
+has to do with disorder and
+the number of available
+
+states, microscopic states
+available to a system.
+
+So I'll just state what
+we'll see in much more
+
+detail later on.
+
+Which is in microscopic terms,
+it's going to turn out that
+
+the entropy of a system can be
+given by R over Avogadro's
+
+number times the log of the
+number of distinct microscopic
+
+states that are available
+to a system.
+
+Right so in this isolated
+system, when we double that
+
+volume, each molecule suddenly
+has twice as many states
+
+available to it.
+
+You could formulate that
+in a lot of ways.
+
+You can sort of divide up the
+volume into tiny little
+
+molecule-sized cubes and realize
+well, now, there are
+
+twice as many of them.
+
+Now if I have one molecule, the
+number of states doubles.
+
+If I have n molecules, the
+number of states goes
+
+up by 2 to the n.
+
+Because for each one of the
+molecules, I can select any
+
+one of those states, and
+then the next one I
+
+can select any one.
+
+So you have this enormous
+increase in
+
+the number of states.
+
+So delta S in this case looks
+like R over NA log of 2 to the
+
+power NA, it's Avogadro's
+number,
+
+for a mole of molecules.
+
+This can come out
+and cancel this.
+
+There's our R log 2 result.
+
+But the point I'm making here
+is that could actually be
+
+derived from entirely
+microscopic consideration.
+
+We haven't gone through
+that yet.
+
+We've done entirely macroscopic
+thermodynamics so
+
+far, but we'll do a little bit
+of treatment of statistical
+
+mechanics, is what is called
+the whole microscopic
+
+formulation of entropy
+in thermodynamics.
+
+And that's a really important
+fundamental result.
+
+And we'll get to it in much
+more detail in a while.
+
+But for now, I just want to
+continue calculating entropy
+
+changes for a few more
+kinds of processes.
+
+So, how about if we have two
+different substances and we
+
+mix them, entropy of mixing.
+
+So, we start with some number
+of moles of substance A in
+
+some volume VA, and some other
+number of moles of substance B
+
+in volume VB, separated.
+
+And then we remove the barrier,
+of course we know
+
+they're going to mix.
+
+So we'll have some total number
+of moles, nA plus nB,
+
+and they'll be filling some
+total volume, which is the sum
+
+of the two original volumes.
+
+Certainly this is what
+we expect to happen
+
+spontaneously.
+
+So are process is nA moles of A,
+gas, initial volume VA and
+
+T, plus nB of substance B, I
+think this is miswritten as A
+
+there in your notes.
+
+Gas VB and T goes to nA moles of
+A plus nB moles of B. Gas,
+
+total volume and T. And
+we'll have constant
+
+temperature and pressure.
+
+Well, there was no
+p v worked done.
+
+The temperature didn't change
+and it's ideal gases, so delta
+
+u is zero, but what
+about delta S?
+
+Well again, to calculate
+it, we need to find
+
+a reversible path.
+
+This is irreversible if we just
+remove the barrier and
+
+let it all go.
+
+But we could at least imagine
+a reversible path, and we
+
+could actually construct this
+for the right substances.
+
+We could imagine that we can
+find some sort of piston here.
+
+And we're going to prepare
+to push it inward, with a
+
+membrane that's permeable
+only to b.
+
+And over here we could set up
+the exact same thing, but this
+
+one's permeable only to a.
+
+And then we could just push them
+to recover this state.
+
+And we can do it reversibly.
+
+So we could construct a
+reversible process that does
+
+the reverse of this.
+
+And in this case, it'll be
+isothermal still, constant
+
+pressure, reversible compression
+of the two gases.
+
+So, reversible compression
+and demixing.
+
+All right, so what happens?
+
+Well, of course, our delta S
+of demixing is going to be
+
+minus delta S of mixing.
+
+Delta u of demixing
+is still zero.
+
+Temperature didn't change, ideal
+gases, and there's some
+
+reversible work and heat.
+
+So dw in this reversible case,
+is just minus pA dVA minus pB
+
+dVB, the infinitesimal amount
+of work done as these things
+
+are gradually moved
+toward each other.
+
+So delta S for demixing, of
+course it's dq reversible over
+
+T, but just like we did right
+there, of course, in this case
+
+that's just negative dw.
+
+So it's integral from V to VA,
+right, were compressing.
+
+So for substance a, we're going
+to go back to there.
+
+It was occupying the whole
+volume, and then it's going to
+
+end up in only part
+of the volume, VA.
+
+pA dVA over T. Same thing for
+B, going to volume B, pB dVB
+
+over T. And now we can
+substitute for pressure,
+
+right? pV is nRT, so it's nA
+times R log of VA over V plus
+
+nB of R log of VB over V.
+
+Now, so this is a suitable
+answer, but I'm going to make
+
+if a little easier by putting
+in terms of mole fractions.
+
+So, mole fractions, of course,
+XA is nA over n, and XB is nB
+
+over n and XA is also equal to
+VA over V and XB is equal to
+
+VB over V for ideal
+gases, right?
+
+The molar volumes
+are the same.
+
+We're at the same temperature
+and pressure.
+
+So that immediately gives us the
+delta X of demixing is nR
+
+times XA log XA plus
+XB log XB.
+
+And of course delta S of mixing
+is the opposite of
+
+this, minus nR XA log
+XA plus XB log XB.
+
+Now XA and XB are
+mole fractions.
+
+They are between zero and
+one, So their log
+
+rhythms are both negative.
+
+There's a negative sign.
+
+So delta S of mixing
+is positive.
+
+That's reassuring.
+
+That tells us as we expect that
+the mixing should happen
+
+spontaneously and irreversibly
+when we remove the barrier.
+
+Any questions so far about how
+we're going about these
+
+calculations of delta S?
+
+OK, let's just do a couple
+more examples.
+
+Here's a really straightforward
+one.
+
+What if we just heat stuff
+up or cool it down.
+
+It happens all the time, but
+it's pretty important, right?
+
+So let's just heat or cool
+at constant volume.
+
+So, we're going to go from
+substance A at T1 and some
+
+volume going to substance
+A at T2 at some volume.
+
+We can do this.
+
+Delta S is integral of dq
+reversible over T. Going from
+
+T1 to T2, but we know how
+to do this, right?
+
+It's the heat that we need.
+
+It's just given by the constant
+volume heat capacity
+
+times the change
+in temperature.
+
+So this is just T1 to T2, Cv dT
+over T. And that is just Cv
+
+times the log of T2 over T1 if
+Cv is temperature independent.
+
+That's not always the case.
+
+Usually if it's not too big an
+excursion of temperature then
+
+it's a reasonable
+approximation.
+
+So that's straightforward.
+
+By the way, notice that delta
+S is greater than zero if T2
+
+is greater than T1.
+
+In other words, if we heated
+it up, delta S is positive.
+
+Notice also delta S is
+less than zero if T2
+
+is less than T1.
+
+Delta S is negative
+if we cooled it.
+
+Now, under certain conditions
+we've seen that delta S can't
+
+be negative.
+
+Why can it be negative here?
+
+STUDENT: [UNINTELLIGIBLE].
+
+PROFESSOR NELSON:
+Yes, I heard it.
+
+It's because the system
+isn't isolated, right.
+
+It was for the isolated system
+that delta S is always greater
+
+than or equal to zero.
+
+And you know, for the whole
+universe entropy never
+
+decreases and so on.
+
+In this case, though, you know
+we're taking a system and
+
+we're putting it in contact
+with a cold bath
+
+and cooling it down.
+
+It's certainly not isolated.
+
+Heat is being exchanged.
+
+It's going from the system to
+the surroundings, to the bath.
+
+So it's fine.
+
+Delta S can be negative.
+
+What would happen if we
+calculated delta S of a new
+
+entire system consisting
+of the original system
+
+plus the heat bath?
+
+What would delta S be then?
+
+We already kind of did that with
+those two blocks, T1 and
+
+T2 in an isolated systems.
+
+What do you think is
+going to happen?
+
+In other words, if we call our
+system the stuff that is put
+
+in contact with the heat bath,
+well OK, then we've seen delta
+
+S can be plus, can be positive
+or negative.
+
+Now let's call our system the
+original system plus the heat
+
+bath, and we'll put them all in
+some isolating box, that's
+
+thermally isolating and so on.
+
+And now we'll put our original
+system, which is now sort of a
+
+sub, part of the system, and
+it's now going to be in
+
+contact with the cold bath.
+
+The bath that it's in contact
+with is colder than it is.
+
+That's why its delta S
+is less than zero.
+
+But what's delta S to be for
+the entire new system
+
+including the cold bath?
+
+STUDENT: Wouldn't it
+greater than zero?
+
+PROFESSOR NELSON: Yes, it's
+going to be positive, because
+
+it's an isolated system
+and something happened
+
+spontaneously in it, namely the
+original system got cooler
+
+and presumably the heat
+bath got at least
+
+a little bit warmer.
+
+And it happened spontaneously,
+which immediately means delta
+
+S had to be positive for that
+entire assembly, of you know
+
+the original system
+plus the bath.
+
+Here's another important
+sort of process.
+
+Reversible phase change, we'll
+melt something or freeze it.
+
+How about water -- liquid
+100 degrees Celsius
+
+one bar goes to water.
+
+Gas 100 degrees Celsius
+one bar.
+
+Well in that case, you know
+what the heat is.
+
+It's just the delta H of
+vaporization, right, at
+
+constant pressure.
+
+So there's nothing really
+much to calculate here.
+
+Delta S of vaporization for H2O
+at 100 degrees Celsius is
+
+just q of vaporization over the
+boiling temperature, which
+
+is delta H of vaporization over
+the boiling temperature.
+
+So that was easy.
+
+One last thing.
+
+What if we want to calculate the
+entropy of melting or some
+
+phase transition not
+at equilibrium?
+
+In this case it's at equilibrium
+because it's water
+
+and water vapor at 100 degrees
+Celsius and one
+
+atmosphere or one bar.
+
+So it's at its boiling point.
+
+But what if it isn't at
+its boiling point?
+
+So what if instead, let's take
+H2O, liquid, at minus ten
+
+degrees Celsius and one
+bar so it's cold.
+
+It's going to freeze.
+
+So it's going to turn into
+solid water at minus 10
+
+degrees Celsius and one bar,
+we're going to have it be
+
+isothermal.
+
+Now you know that's going to
+happen spontaneously, and it's
+
+irreversible.
+
+Irreversible, which means we
+can't just straight away
+
+calculate delta S along
+this path because it's
+
+irreversible.
+
+But what we can do, just like
+we've done before for making
+
+cycles, we can make some other
+set of events that are all
+
+reversible.
+
+We can construct a reversible
+pass that will get there.
+
+How do we do it?
+
+Well you know for the phase
+change, for the freezing to be
+
+reversible, it has to happen at
+zero degrees Celsius right.
+
+You know that's where
+you have reversible,
+
+freezing and melting.
+
+Reversible equilibrium between
+liquid and solid water.
+
+So surely that's got to
+get involved here.
+
+H2O liquid zero degrees
+Celsius, one bar, in
+
+equilibrium with H2O solid at
+zero degrees Celsius, one bar.
+
+Whatever reversible path we
+construct that's going to go
+
+from liquid to solid water,
+somewhere along the set of
+
+steps, that better
+be one of them.
+
+So now what we need to do is
+go from liquid at minus 10
+
+degrees Celsius and one bar to
+liquid at zero degrees Celsius
+
+and one bar.
+
+That's called heating.
+
+We have to heat it.
+
+And here we have to cool it.
+
+And we've already seen all these
+three processes, right.
+
+So for the phase change,
+it's reversible now.
+
+This is just delta
+heat of fusion.
+
+Great.
+
+Because this is now
+reversible.
+
+This is going to
+be reversible.
+
+This is going to be reversible.
+
+Great.
+
+So dq reversible, it's going
+to be the heat capacity at
+
+constant pressure, the example
+we did before it was constant
+
+volume for the liquid dT.
+
+Here, dq reversible is going
+to be Cp solid, dT.
+
+Those won't be the same right?
+
+It's one thing to say the heat
+capacity of something doesn't
+
+change over some small excursion
+in temperature, but
+
+it's another thing when the
+thing actually changes phase.
+
+The heat capacity of the
+solid and the liquid
+
+won't be the same.
+
+So this we can just finish up in
+a jiffy, because we're just
+
+going to add the three things.
+
+So delta S is delta S of
+heating, minus, I think
+
+there's a plus that should be
+a minus there, minus delta S
+
+of fusion because it's going in
+the direction of freezing
+
+the way we've written it.
+
+Plus delta S of cooling.
+
+So integral from T1 to the
+melting point of Cp of the
+
+liquid dT over T, minus delta
+H of fusion over the melting
+
+temperature.
+
+Plus the integral going from the
+heat of the temperature of
+
+melting to T1 of Cp of
+the solid dT over T.
+
+That's it, all right?
+
+So delta S is minus delta H of
+fusion over T. That's what it
+
+would be for just the reversible
+phase change
+
+happening at zero
+degrees Celsius.
+
+And then there's this additional
+part which is, we
+
+can write it from T1 to melting
+point of Cp of the
+
+liquid, minus Cp of the
+solid, dT over T.
+
+Now usually we can assume that
+these will be temperature
+
+independent in their
+own phases.
+
+So we can usually write this
+as minus delta H of fusion
+
+over the melting temperature
+plus Cp of the liquid minus Cp
+
+of the solid log of T
+of fusion over T1.
+
+Any questions?
+
+What did we do?
+
+We constructed a reversible path
+going from here to here
+
+and calculated delta S that way,
+and of course that has to
+
+be the same as delta S in the
+one irreversible step.
+
+All right, more on entropy and
+its consequences for how to
+
+figure out what happened
+spontaneously next time.
\ No newline at end of file
diff --git a/QyJkYF-L1Kg.txt b/QyJkYF-L1Kg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1122a98e6271a8b43b5e15f6be880b3fe3ae726
--- /dev/null
+++ b/QyJkYF-L1Kg.txt
@@ -0,0 +1,1346 @@
+PROFESSOR: Resume by going back
+to our one-dimensional
+
+body that has undergone some
+elastic deformation.
+
+And what I would like to do now
+is to distinguish between
+
+displacement of an object and
+fractional change of length,
+
+which turned out to be measured
+by the same thing,
+
+that thing that we're
+going to name strain
+
+when properly defined.
+
+OK, here is our one-dimensional
+case.
+
+And we said that originally some
+point, P, at a location x
+
+gets mapped to a point P prime
+that is at x plus some
+
+displacement U. So this is the
+displacement vector U.
+
+Our point Q, which is originally
+at some location x
+
+plus delta x, where delta x
+is the original separation
+
+between P and Q, gets mapped to
+a point Q prime, which is
+
+going to be equal to a whole
+collection of terms.
+
+It's going to be equal to x
+plus delta x, the original
+
+location, plus the linear
+variation of U with x that has
+
+to go U times x plus delta x.
+
+And if we simplify this a little
+bit, Q prime is going
+
+to be at a location, factoring
+out x plus delta x, x plus
+
+delta x times 1 plus e.
+
+AUDIENCE: Is e represented
+here?
+
+PROFESSOR: e is the linear
+relation between displacement
+
+U and position along the body.
+
+OK, so what has happened here?
+
+The relative change of length
+is going to be P prime
+
+Q prime minus PQ.
+
+And if we just substitute in
+our two expressions, the
+
+relative change of length is
+going to be equal to delta x
+
+times 1 plus e minus delta x.
+
+This is the relative
+change of length.
+
+And I should label this such.
+
+That's going to be equal to
+delta x times 1 plus e minus
+
+delta x divided by delta x.
+
+And that simply going to be
+e, which is equal to delta
+
+U over delta x.
+
+And that is what we
+define as strain.
+
+And that is a dimensionless
+quantity.
+
+Because it has units of
+length over length.
+
+All right, how can we patch this
+one-dimensional sort of
+
+behavior up to a
+three-dimensional situation?
+
+What we are saying in this
+one-dimensional case is that
+
+the displacement of a particular
+point P varies
+
+linearly with position
+in the body.
+
+So let's generalize that into
+three dimensions by saying
+
+that the component of
+displacement U1-- and this is
+
+going to look like an
+algebraic identity.
+
+It's going to be the way in
+which U changes with x1 times
+
+the position x1.
+
+So this is saying that the
+displacement will vary
+
+linearly with x1.
+
+And the rate will be du1 dx1.
+
+But also U1 is going to change
+with the coordinate x2.
+
+And the coefficient there
+will be du1 dx2.
+
+And there's going to be a third
+term that will be the
+
+way in which U1, the x1
+component of displacement,
+
+changes with x3 times the
+position in the body x3.
+
+So this is saying exactly the
+same thing that we did in one
+
+dimension, that displacement
+depends linearly with
+
+position, except that
+there's now three
+
+coordinates for position.
+
+And the displacement will change
+with an increment of a
+
+change in position along each
+of those three axes.
+
+Similarly, we can say that U2
+is going to be equal to the
+
+way in which U2 changes with x1
+times the position x1, the
+
+way in which U2 changes with x2
+times the coordinate within
+
+the body x2, and the same for
+U2 dx3 and the actual
+
+positional coordinate x3.
+
+And so, in general, we're going
+to propose that the i-th
+
+component of displacement is
+given by the way in which
+
+displacement changes with
+x sub j times x sub j.
+
+Or you could do the same thing,
+not in terms of actual
+
+displacement, but differences in
+displacement, the same way
+
+we could define strain as the
+fractional change of length of
+
+our line segment on the
+elastic band or,
+
+alternatively, as the
+shift in position.
+
+So we could define it also as
+the difference in distances or
+
+displacements let
+me call them.
+
+And that really is
+a trivial change.
+
+We'll say the change of a length
+along x1 delta U1 is
+
+going to be the way in which U1
+changes with x1 times delta
+
+x1 plus the way in which U2
+changes with x1 times the way
+
+in which U1 changes with x2
+times delta x2 plus the way in
+
+which U1 changes with x3 times
+delta x3 or, in general, that
+
+the fractional change in length
+is going to be equal to
+
+dui dxj times delta xj.
+
+All right, so what we're going
+to define now is dui.
+
+Dxj will be defined as something
+like strain.
+
+It's not exactly strain yet.
+
+And this is going to be a
+measure of deformation.
+
+I'm hedging my words because of
+something that we'll want
+
+to impose upon the proper
+strain tensor.
+
+But first, let's see what these
+
+three-dimensional terms mean.
+
+And to see that, let me look
+at a place within the body.
+
+And I'm going to look at a line
+segment that goes between
+
+a P and Q that is oriented
+along x1.
+
+And I'm picking that
+deliberately.
+
+Because I want to keep things
+simple and isolate one of
+
+these terms so we can identify
+its meaning.
+
+So let's say here we have two
+points P and Q separated by a
+
+distance delta x1 prior
+to deformation.
+
+And now we squish the body.
+
+And what happens is that
+P will move to
+
+a position P prime.
+
+Q will move to a position
+Q prime.
+
+And this will be the new line
+segment, P prime Q prime.
+
+This will be the original
+delta x1.
+
+To that we're going to
+tack on an instrument
+
+which is delta U1.
+
+But then there will also
+be a delta U2.
+
+And clearly what has happened is
+that the length of the line
+
+segment P prime Q prime
+has changed.
+
+But also the orientation of the
+line segment has changed
+
+by an angle, which I'll
+define as phi.
+
+So again, we have
+a line segment.
+
+We deform the body.
+
+P is displaced.
+
+Q is displaced.
+
+The component of that line
+segment along x1 has changed
+
+in length by an amount
+delta U1.
+
+The coordinate along x2 will
+change by an amount delta U2.
+
+So we not only change
+the length.
+
+But we rotate the
+line segment.
+
+We can express these in terms of
+our general relation that I
+
+proposed a moment ago.
+
+Delta U1 is going to be equal
+to du1 dx1 times delta x1.
+
+And that is going to be given
+by the element epsilon 1, 1
+
+times delta x1.
+
+The value of x2 was going
+to be equal to du2
+
+dx1 times delta x1.
+
+And that's going to be
+by definition e2,
+
+1 times delta x1.
+
+And the reason this is so simple
+is that I initially
+
+picked the line segment which
+was parallel to x1.
+
+So not all of the four terms
+that would be present in the
+
+x1, x2 system have come in.
+
+So there's no contribution of
+delta x2 because of the fact
+
+that I've picked this
+special orientation.
+
+OK, the fractional change of
+length resolved on x1 is going
+
+to be, well, it's going to be
+exactly delta x plus delta U1
+
+quantity squared, it's going
+to be this horizontal line
+
+segment, plus delta U2
+quantity squared all
+
+to the power 1/2.
+
+And now I'm going to say that
+delta U2 is negligible
+
+compared to this big delta
+x plus delta U1.
+
+And I'll say that this is
+approximately equal to delta x
+
+plus delta U1, OK, just taking
+the whole works outside of the
+
+square root sign.
+
+So delta U1 over delta x1 is
+going to be equal to the term
+
+e1, 1 from this expression
+here.
+
+So the term e1, 1 represents the
+tensile strain along x1.
+
+So we can see how these
+derivatives are going to enter
+
+into changes of length.
+
+The P prime Q prime has also
+been rotated by phi.
+
+And we can say exactly what that
+is that the tangent of
+
+phi is going to be given exactly
+by delta U2 divided by
+
+the original length of the line
+segment delta x1 plus the
+
+little increment of displacement
+along x1.
+
+And this is--
+
+I'll walk down here
+so I can see it.
+
+This is delta U1.
+
+This is delta U2 over
+times delta x1--
+
+sorry, I can't see what I've
+got down here-- delta
+
+U1 plus delta x1.
+
+OK, so it's the amount of
+displacement along x2 over the
+
+original line segment delta
+x1 plus the change in
+
+displacement delta U1.
+
+And clearly delta U1 can be
+claimed to be small with
+
+respect to delta x1.
+
+So this is approximately equal
+to delta U2 over delta x1.
+
+And tangent of phi is going
+to be tangent of
+
+a very small angle.
+
+So this will be delta
+U2 over delta x1.
+
+And so this angle phi is, for
+small strains, going to be
+
+equal to delta U2
+over delta x1.
+
+And that is the definition of
+our element of strain e1, 2.
+
+So e1, 2 corresponds to a
+rotation of a line segment
+
+that was originally parallel to
+x1 in the direction of x2--
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: e2, 1, I'm sorry, e2,
+1, yeah, along x1 in the
+
+direction of x2.
+
+And that is counterintuitive as
+I have just demonstrated.
+
+e2, 1 is a rotation of a line
+segment along x1 in the
+
+direction of x2, which is just
+the reverse of the subscript.
+
+So eij, a general off-diagonal
+element of the array eij, is
+
+going to be a rotation of a line
+segment initially along x
+
+sub j in the direction
+of x sub i.
+
+And for very small strains,
+numerically that term eij will
+
+give an angle in radiants.
+
+AUDIENCE: For the equation you
+have over there, should it be
+
+delta x plus delta x2?
+
+PROFESSOR: No, I would
+say this--
+
+AUDIENCE: Because aren't
+you saying delta U1?
+
+PROFESSOR: Oh, OK,
+you're right.
+
+Yeah, I didn't take the
+difference here.
+
+AUDIENCE: Delta U1 is basically
+negligible?
+
+PROFESSOR: Yep, yep, so I'm
+saying that that [INAUDIBLE]
+
+should be delta x1--
+
+AUDIENCE: Plus delta U2?
+
+PROFESSOR: --plus delta U2.
+
+You're right.
+
+No, I'm throwing this out.
+
+And that's right.
+
+So I'm saying that this
+is essentially delta
+
+x1 plus delta U1.
+
+I'm saying that this
+is negligible.
+
+So strictly speaking the
+distance between P prime and Q
+
+prime is the square
+root of this
+
+squared plus this squared.
+
+But if this thing is tiny, P
+prime Q prime is essentially
+
+going to be this distance,
+delta x1 plus delta U1.
+
+So that's right.
+
+OK, so we have something that
+looks like it measures
+
+deformation.
+
+But I would like to ask if this
+is a suitable measure of
+
+deformation.
+
+And I would like to show that,
+unless the tensor eij is
+
+symmetric, that we have included
+in our definition of
+
+strain rigid body rotation as
+well as true deformation.
+
+So in order to demonstrate that,
+what I'm going to look
+
+at is a case where we have
+actually, by the way in which
+
+we apply a stress to the
+material, actually done
+
+nothing more than rotate
+x1 to x1 prime and
+
+rotate x2 to x2 prime.
+
+And in general, for a real
+amount of deformation, that is
+
+something that is
+going to happen.
+
+Let's say I decide to deform
+this eraser in shear before
+
+your very eyes.
+
+And I try shearing it.
+
+Nothing much has happened.
+
+And I squeeze a little harder.
+
+And finally, I've got it
+wrestled down into an
+
+orientation like this.
+
+And when I finished, this
+was the original
+
+position of the eraser.
+
+Here's x1.
+
+Here's x2.
+
+And by the time I've wrestled it
+around to a deformed state,
+
+it sits down like this, maybe
+deformed a little bit.
+
+But would you say that this
+angle here is a measure of
+
+deformation?
+
+No, that's clearly a rigid
+body rotation.
+
+And what I would intuitively
+do, if I wanted to measure
+
+true deformation, if this were
+the original body and after
+
+deformation it went to a
+location with some deformation
+
+to be sure but this has
+been rotated to here.
+
+This has been rotated down.
+
+And I wouldn't want to say
+that this is a measure of
+
+deformation.
+
+This would be e1, 2.
+
+What I would want to do
+intuitively would be to
+
+position the body symmetrically
+between the axes
+
+and then say that this is a
+measure of shear strain.
+
+So let me show you now in a more
+rigorous treatment that,
+
+if there is a component of rigid
+body rotation, let me
+
+show you what a rotation of the
+coordinate system to a new
+
+orientation x1, x
+prime would do.
+
+So let's say that this is
+an original point Q1.
+
+And after deformation, it moves
+by a rotation phi that's
+
+equal to e2, 1 to a new
+location Q1 prime.
+
+Let's suppose that this
+is a position Q2.
+
+And after what we think is the
+deformation, this moves to a
+
+location Q2 prime.
+
+And this would be e1, 2.
+
+That's equal to minus phi.
+
+This is e2, 1.
+
+And that's equal to plus phi.
+
+So what we would do is
+like to get rid of
+
+that rigid body rotation.
+
+And what I'll do is to show
+that, if we have a point
+
+that's out at the end of a
+radial vector, R, which has
+
+coordinates xi, x1, x2, x3, and
+if we have a displacement,
+
+which is absolutely
+perpendicular to that radial
+
+vector, that this would
+be characteristic
+
+of rigid body rotation.
+
+And I will say that, if Ui is
+perpendicular to the radial
+
+vector xi, then U.R should
+be equal to 0 for
+
+every position xi.
+
+So if we just multiply this out,
+this is saying that Ui Ri
+
+should be equal to 0 for
+rigid body rotation.
+
+And let's simply carry
+out this expansion.
+
+And I will have then eij xi xj
+forming this dot product.
+
+And that is going to be 0 for
+a rigid body rotation.
+
+And if I expand this, this will
+contain terms like e1, 1
+
+times x1 x1 plus e2,
+2 times x2 x2 plus
+
+e3, 3 times x3 squared.
+
+And then they'll be cross-terms
+e1, 3 plus e3, 1
+
+times x1 x3 plus e1, 2 plus e2,
+1 times x1 x2 plus e2, 3
+
+plus e3, 2 times x2, x3.
+
+And my claim now is that, if
+this represents rigid body
+
+rotation, then that
+should be 0.
+
+That is to say the displacement
+is absolutely
+
+perpendicular to the radius
+vector for small
+
+displacements.
+
+This must be 0 for all xi.
+
+And the only way that's going
+to be possible for any value
+
+of x1, x2, x3 is that each
+of these six terms vanish
+
+individual.
+
+It's the only way I'm going to
+be able to get the whole thing
+
+to disappear for any value
+of coordinate x1, x2, x3.
+
+So we're going to have to then
+have e1, 1 equals e2, 2 equals
+
+e3, 3 equals 0.
+
+All the diagonal terms are
+going to have to be 0.
+
+In order to get the fourth term
+to vanish, I'm going to
+
+have to have e1, 3 equal to the
+negative of e3, 1 and e1,
+
+2 the negative of e2, 1 and e2,
+3 the negative of e3, 2.
+
+So what is this going to look
+like for the part of the e
+
+tensor that corresponds to
+rigid body rotation?
+
+The diagonal terms are
+all going to be 0.
+
+And the off-diagonal terms are
+going to be the negative of
+
+one another.
+
+So this is e1, 2.
+
+e2, 1 would have to be
+equal to minus e1, 2.
+
+e3, 1 would have to be equal
+to the negative of e1, 3.
+
+And so we will have something
+like this.
+
+So this suggests that our
+definition of the true
+
+deformation, which will be
+a tensor epsilon ij--
+
+I bet you kind of guessed I was
+going to call it epsilon
+
+and not E. I can write this
+as a sum of two parts.
+
+I'll turn that around and say
+I'll write epsilon ij plus
+
+another three by three array
+omega ij is equal to the
+
+tensor eij.
+
+That's a novel idea.
+
+This is addition of two tensors
+element by element.
+
+And if I do that and define
+epsilon ij equal to 1/2 of eij
+
+plus eji, so for the diagonal
+elements that is going to take
+
+1/2 of e1, 1 plus e1, 1.
+
+And that's just going to give
+me e 1, 1 back again.
+
+And I'm going to define the
+terms omega ij as 1/2
+
+of eij minus eji.
+
+And if I do that, the resulting
+
+tensor will be symmetric.
+
+OK, so from tensor eij we can
+split it up into two parts and
+
+a part omega ij.
+
+And I won't bother
+to write it out.
+
+But you can see that omega ij
+plus eij is going to be equal
+
+to eij minus 1/2 of 2eij
+minus 1/2 of 0.
+
+And that's just going
+to be eij.
+
+So this plus this is indeed
+going to give
+
+me the tensor eij.
+
+So given a tensor eij, which
+is not symmetric, I will
+
+define eij as the sum of two
+parts, a tensor epsilon ij,
+
+which is true strain, and a part
+omega ij, which is rigid
+
+body rotation.
+
+And now at last we have a
+satisfactory measure of true
+
+deformation in terms of the
+displacement of points within
+
+a deformed body where that
+displacement can arise from
+
+either rigid body rotation
+and or deformation.
+
+So finally, we have a tensor
+epsilon ij, which is the
+
+strain tensor.
+
+And now I can finally make my
+claim that, if this really is
+
+true deformation, that
+for cubic crystals--
+
+you can see the same
+[INAUDIBLE]
+
+window coming again--
+
+since second ranked tensors have
+to be symmetric for cubic
+
+crystals, the form of
+strain for a cubic
+
+crystal can only be this.
+
+It has to be diagonal
+if the tensor is to
+
+conform to cubic symmetry.
+
+And you say, ah, ah, you tried
+to pull that on us with
+
+stress, too.
+
+And I can squish a crystal
+anyway I want.
+
+But you can only develop
+a strain if
+
+you deform a crystal.
+
+And the symmetry of the crystal
+is going to determine
+
+how the crystal deforms.
+
+So therefore, a cubic crystal
+should be able to deform only
+
+in a way that stays invariant
+to the transformations of a
+
+cubic symmetry, right?
+
+So cubic crystals can only
+deform isotropically.
+
+So if I wanted to design springs
+for an automobile so
+
+that elastic energy could be
+stored most efficiently in a
+
+solid, I would want to make
+these automobile springs out
+
+of a triclinic metal.
+
+Because then the tensor could be
+one of general deformation.
+
+OK, well, this, obviously, is
+a swindle like my assertion
+
+that stress could only be an
+isotropic compressional stress
+
+for a cubic crystal.
+
+But the argument is a little
+more convoluted.
+
+And strain, indeed, is
+also a field tensor.
+
+Because, even though I can only
+create the deformation by
+
+application of a stress or
+perhaps an electric field or
+
+something of that sort in that
+the link between the
+
+deformation and what I do to
+the crystal is coupled by a
+
+property of the crystal, which
+has to conform to the symmetry
+
+of the crystal, nevertheless,
+given a tensor that describes
+
+deformation, I can always,
+independent of the symmetry of
+
+the crystal, devise a particular
+set of stresses
+
+that would produce any state
+of strain I want.
+
+I would have to design, though,
+a particular state of
+
+stress to produce a desired
+state of strain.
+
+And that coupling has
+to conform to the
+
+symmetry of the crystal.
+
+But there's no reason why strain
+itself has to conform
+
+to the symmetry of
+the crystal.
+
+I can create any state of strain
+I like by choosing the
+
+appropriate stress.
+
+OK, so that is a swindle.
+
+But everything now that I can
+say about the behavior of a
+
+second ranked tensor applies
+to the strain tensor.
+
+I can take a strain
+tensor epsilon ij.
+
+And I can perform the surface
+epsilon ij xi xj equals 1.
+
+And that will be the
+strain quadric.
+
+The strain quadric will have the
+property like any quadric
+
+constructed from a tensor that
+the value of the radius in a
+
+particular direction is going to
+be such that the strain in
+
+that direction is equal to 1
+over the radius squared.
+
+So what does that mean?
+
+Well, we have to look at what
+the strain tensor is relating.
+
+The direction, remember now
+that the definition of the
+
+strain tensor is that U
+sub i equals epsilon
+
+ij times x sub j.
+
+So the quote "applied vector"
+is the direction in a solid.
+
+And we will get, in general, a
+displacement, U, which is not
+
+parallel to the direction
+that we're considering.
+
+And the epsilon in a particular
+direction is going
+
+to be equal to the part of
+U that's parallel to the
+
+direction of interest divided by
+distance in that direction.
+
+And what this is going to give
+us is the tensile component of
+
+deformation in the direction
+that we're examining.
+
+Now, the radius normal property
+works in this case.
+
+And what the radius normal
+property says, if you look at
+
+a certain direction in the solid
+and then look at the
+
+normal to the surface at that
+particular point, this will be
+
+the direction of
+what happened.
+
+So I've not drawn
+this correctly.
+
+This should be the direction
+of U. And this
+
+is the radio vector.
+
+So the normal to the surface
+gives us the direction of the
+
+displacement that's
+going to occur.
+
+And the reason I can say that
+is by definition that that
+
+property holds only for
+a symmetric tensor.
+
+And by definition, we have
+defined the strained tensor
+
+such that it is symmetric.
+
+So the radius normal
+property holds.
+
+If we want to change from one
+coordinate system to another,
+
+we do that by the all for
+transformation of a second
+
+ranked tensor that, if we change
+coordinate system, the
+
+elements of strain change to
+new values epsilon ij prime
+
+that are given by cil cjm times
+epsilon lm, the same law
+
+for transformation of a second
+ranked tensor that we have
+
+seen earlier.
+
+Finally, we can, because there
+is a quadric, we can change
+
+that by finding eigenvectors
+and eigenvalues, take a
+
+general form of the tensor
+epsilon 1, 1, epsilon 1, 2,
+
+epsilon 1, 3, and so on, and
+by solving the eigenvalue
+
+problem, convert this to a value
+epsilon 1, 1 prime 0, 0,
+
+0, epsilon 2, 2 prime 0, 0, 0,
+epsilon 3, 3 prime to find out
+
+what the extreme values of
+tensile deformation are and
+
+the orientations within the
+original description of the
+
+body in which these extreme
+values occur.
+
+OK, I'm just about
+out of time.
+
+I'll save until next time
+another neat feature of the
+
+strain tensor.
+
+And that is contained within
+these elements is information
+
+on the volume change that
+the body undergoes.
+
+And this is something
+called the dilation.
+
+And we'll see that this is
+related in a very simple way
+
+to the elements of the
+strain tensor.
+
+OK, we've spent a lot of time
+developing the formalism of
+
+stress and strain.
+
+And next thing we'll do is to
+move on to some interesting
+
+properties of crystals, which
+are defined in terms of
+
+tensors of rank higher
+than two.
+
+So we'll look at some third
+ranked tensor properties.
+
+That will include things like
+piezoelectricity, the stress
+
+optical effect, and things
+of that sort.
+
+These are going to be
+really anisotropic.
+
+Second ranked tensors were
+anisotropic enough.
+
+But the variation of property
+with direction was a
+
+quasi-ellipsoidal variation When
+as 1 over the square of
+
+the radius of the quadric.
+
+For higher ranked tensor
+properties, we will encounter
+
+some absolutely weird surfaces
+with dimples and lumps and
+
+lobes, not this smooth
+quasi-ellipsoidal variation, a
+
+property with direction, which
+was the case for second ranked
+
+tensor properties.
+
+So we will get into some exotic
+anisotropies very
+
+shortly to finish
+up the semester.
+
+So I will probably see some
+of you at the MRS
+
+meeting next week.
+
+I won't see you on Thursday for
+reasons that I need not
+
+elaborate upon.
+
+So I hope you have
+a happy holiday.
+
+Relax, suck in air, and come
+back refreshed next Tuesday
+
+for some really wild anisotropy
+of physical
+
+properties.
\ No newline at end of file
diff --git a/R2vL2wLqGYg.txt b/R2vL2wLqGYg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..880cf9d656fb7cd2d0a6d5c9317b67f6170dd743
--- /dev/null
+++ b/R2vL2wLqGYg.txt
@@ -0,0 +1,9139 @@
+align:start position:0%
+ 
+okay so this is dive in and I'll just
+
+ align:start position:0%
+okay so this is dive in and I'll just
+ 
+
+ align:start position:0%
+okay so this is dive in and I'll just
+quickly recap where we were last time so
+
+ align:start position:0%
+quickly recap where we were last time so
+ 
+
+ align:start position:0%
+quickly recap where we were last time so
+what I did last time was we are now
+
+ align:start position:0%
+what I did last time was we are now
+ 
+
+ align:start position:0%
+what I did last time was we are now
+beginning the adventure so to speak of
+
+ align:start position:0%
+beginning the adventure so to speak of
+ 
+
+ align:start position:0%
+beginning the adventure so to speak of
+looking at how one examines how one
+
+ align:start position:0%
+looking at how one examines how one
+ 
+
+ align:start position:0%
+looking at how one examines how one
+finds and then studies the properties of
+
+ align:start position:0%
+finds and then studies the properties of
+ 
+
+ align:start position:0%
+finds and then studies the properties of
+solutions to the Einstein field
+
+ align:start position:0%
+solutions to the Einstein field
+ 
+
+ align:start position:0%
+solutions to the Einstein field
+equations in other words given a
+
+ align:start position:0%
+equations in other words given a
+ 
+
+ align:start position:0%
+equations in other words given a
+particular source what is the space-time
+
+ align:start position:0%
+particular source what is the space-time
+ 
+
+ align:start position:0%
+particular source what is the space-time
+that emerges
+
+ align:start position:0%
+that emerges
+ 
+
+ align:start position:0%
+that emerges
+what is the space-time that is
+
+ align:start position:0%
+what is the space-time that is
+ 
+
+ align:start position:0%
+what is the space-time that is
+consistent with that source of gravity
+
+ align:start position:0%
+consistent with that source of gravity
+ 
+
+ align:start position:0%
+consistent with that source of gravity
+in Einstein's relativistic theory here
+
+ align:start position:0%
+in Einstein's relativistic theory here
+ 
+
+ align:start position:0%
+in Einstein's relativistic theory here
+so we began we're gonna look at this in
+
+ align:start position:0%
+so we began we're gonna look at this in
+ 
+
+ align:start position:0%
+so we began we're gonna look at this in
+a couple of different ways and the first
+
+ align:start position:0%
+a couple of different ways and the first
+ 
+
+ align:start position:0%
+a couple of different ways and the first
+one is where we're going to what we do
+
+ align:start position:0%
+one is where we're going to what we do
+ 
+
+ align:start position:0%
+one is where we're going to what we do
+linearize the Einstein equations so
+
+ align:start position:0%
+linearize the Einstein equations so
+ 
+
+ align:start position:0%
+linearize the Einstein equations so
+we're gonna imagine that space-time is a
+
+ align:start position:0%
+we're gonna imagine that space-time is a
+ 
+
+ align:start position:0%
+we're gonna imagine that space-time is a
+small deviation from the flat space-time
+
+ align:start position:0%
+small deviation from the flat space-time
+ 
+
+ align:start position:0%
+small deviation from the flat space-time
+that contains no gravity and we are
+
+ align:start position:0%
+that contains no gravity and we are
+ 
+
+ align:start position:0%
+that contains no gravity and we are
+going to expand the Einstein field
+
+ align:start position:0%
+going to expand the Einstein field
+ 
+
+ align:start position:0%
+going to expand the Einstein field
+equations discarding all terms that are
+
+ align:start position:0%
+equations discarding all terms that are
+ 
+
+ align:start position:0%
+equations discarding all terms that are
+nonlinear in the perturbation away from
+
+ align:start position:0%
+nonlinear in the perturbation away from
+ 
+
+ align:start position:0%
+nonlinear in the perturbation away from
+flat space-time so last time we did this
+
+ align:start position:0%
+flat space-time so last time we did this
+ 
+
+ align:start position:0%
+flat space-time so last time we did this
+we developed our we developed our field
+
+ align:start position:0%
+we developed our we developed our field
+ 
+
+ align:start position:0%
+we developed our we developed our field
+equations we recast them in a form
+
+ align:start position:0%
+equations we recast them in a form
+ 
+
+ align:start position:0%
+equations we recast them in a form
+that's particularly convenient for
+
+ align:start position:0%
+that's particularly convenient for
+ 
+
+ align:start position:0%
+that's particularly convenient for
+making solutions and we noted that the
+
+ align:start position:0%
+making solutions and we noted that the
+ 
+
+ align:start position:0%
+making solutions and we noted that the
+coordinate degrees of freedom can be
+
+ align:start position:0%
+coordinate degrees of freedom can be
+ 
+
+ align:start position:0%
+coordinate degrees of freedom can be
+thought of as a kind of gauge freedom
+
+ align:start position:0%
+thought of as a kind of gauge freedom
+ 
+
+ align:start position:0%
+thought of as a kind of gauge freedom
+that in some ways it's very useful for
+
+ align:start position:0%
+that in some ways it's very useful for
+ 
+
+ align:start position:0%
+that in some ways it's very useful for
+us because it allows us to write the
+
+ align:start position:0%
+us because it allows us to write the
+ 
+
+ align:start position:0%
+us because it allows us to write the
+equations in a form that is particularly
+
+ align:start position:0%
+equations in a form that is particularly
+ 
+
+ align:start position:0%
+equations in a form that is particularly
+amenable to solving but can also be a
+
+ align:start position:0%
+amenable to solving but can also be a
+ 
+
+ align:start position:0%
+amenable to solving but can also be a
+little bit dangerous because you can
+
+ align:start position:0%
+little bit dangerous because you can
+ 
+
+ align:start position:0%
+little bit dangerous because you can
+sometimes wind up with a solution whose
+
+ align:start position:0%
+sometimes wind up with a solution whose
+ 
+
+ align:start position:0%
+sometimes wind up with a solution whose
+physical character is masked by the
+
+ align:start position:0%
+physical character is masked by the
+ 
+
+ align:start position:0%
+physical character is masked by the
+nature of that gauge I went through a
+
+ align:start position:0%
+nature of that gauge I went through a
+ 
+
+ align:start position:0%
+nature of that gauge I went through a
+somewhat advanced topic for the purposes
+
+ align:start position:0%
+somewhat advanced topic for the purposes
+ 
+
+ align:start position:0%
+somewhat advanced topic for the purposes
+of 89-62 and I do not expect students to
+
+ align:start position:0%
+of 89-62 and I do not expect students to
+ 
+
+ align:start position:0%
+of 89-62 and I do not expect students to
+follow this in detail but it's good to
+
+ align:start position:0%
+follow this in detail but it's good to
+ 
+
+ align:start position:0%
+follow this in detail but it's good to
+at least survey this and understand what
+
+ align:start position:0%
+at least survey this and understand what
+ 
+
+ align:start position:0%
+at least survey this and understand what
+was going off this what I did was I
+
+ align:start position:0%
+was going off this what I did was I
+ 
+
+ align:start position:0%
+was going off this what I did was I
+decomposed the perturbation of flat
+
+ align:start position:0%
+decomposed the perturbation of flat
+ 
+
+ align:start position:0%
+decomposed the perturbation of flat
+space-time into irreducible degrees of
+
+ align:start position:0%
+space-time into irreducible degrees of
+ 
+
+ align:start position:0%
+space-time into irreducible degrees of
+freedom I sort of chose a time
+
+ align:start position:0%
+freedom I sort of chose a time
+ 
+
+ align:start position:0%
+freedom I sort of chose a time
+coordinate I then imagine the other
+
+ align:start position:0%
+coordinate I then imagine the other
+ 
+
+ align:start position:0%
+coordinate I then imagine the other
+three coordinates are spaced and I
+
+ align:start position:0%
+three coordinates are spaced and I
+ 
+
+ align:start position:0%
+three coordinates are spaced and I
+looked at how having chosen time the
+
+ align:start position:0%
+looked at how having chosen time the
+ 
+
+ align:start position:0%
+looked at how having chosen time the
+different degrees of freedom decomposed
+
+ align:start position:0%
+different degrees of freedom decomposed
+ 
+
+ align:start position:0%
+different degrees of freedom decomposed
+into scalars with respect to coordinate
+
+ align:start position:0%
+into scalars with respect to coordinate
+ 
+
+ align:start position:0%
+into scalars with respect to coordinate
+rotations vectors with respect to
+
+ align:start position:0%
+rotations vectors with respect to
+ 
+
+ align:start position:0%
+rotations vectors with respect to
+coordinate rotations and to index
+
+ align:start position:0%
+coordinate rotations and to index
+ 
+
+ align:start position:0%
+coordinate rotations and to index
+tensors of the Vexin coordinate
+
+ align:start position:0%
+tensors of the Vexin coordinate
+ 
+
+ align:start position:0%
+tensors of the Vexin coordinate
+rotations I then took those particularly
+
+ align:start position:0%
+rotations I then took those particularly
+ 
+
+ align:start position:0%
+rotations I then took those particularly
+the vectors and the tensors
+
+ align:start position:0%
+the vectors and the tensors
+ 
+
+ align:start position:0%
+the vectors and the tensors
+and I further broke them up into degrees
+
+ align:start position:0%
+and I further broke them up into degrees
+ 
+
+ align:start position:0%
+and I further broke them up into degrees
+of freedom that are either divergence
+
+ align:start position:0%
+of freedom that are either divergence
+ 
+
+ align:start position:0%
+of freedom that are either divergence
+free divergence free vector fields or
+
+ align:start position:0%
+free divergence free vector fields or
+ 
+
+ align:start position:0%
+free divergence free vector fields or
+the gradients of scalar fields okay
+
+ align:start position:0%
+the gradients of scalar fields okay
+ 
+
+ align:start position:0%
+the gradients of scalar fields okay
+and in doing this what we found was that
+
+ align:start position:0%
+and in doing this what we found was that
+ 
+
+ align:start position:0%
+and in doing this what we found was that
+the ten degrees of freedom that are
+
+ align:start position:0%
+the ten degrees of freedom that are
+ 
+
+ align:start position:0%
+the ten degrees of freedom that are
+specified actually the ten degrees of
+
+ align:start position:0%
+specified actually the ten degrees of
+ 
+
+ align:start position:0%
+specified actually the ten degrees of
+freedom that are present in the
+
+ align:start position:0%
+freedom that are present in the
+ 
+
+ align:start position:0%
+freedom that are present in the
+perturbation the space-time can be
+
+ align:start position:0%
+perturbation the space-time can be
+ 
+
+ align:start position:0%
+perturbation the space-time can be
+broken down into six functions that are
+
+ align:start position:0%
+broken down into six functions that are
+ 
+
+ align:start position:0%
+broken down into six functions that are
+gauge invariants plus 4 gauge degrees of
+
+ align:start position:0%
+gauge invariants plus 4 gauge degrees of
+ 
+
+ align:start position:0%
+gauge invariants plus 4 gauge degrees of
+freedom applying a similar decomposition
+
+ align:start position:0%
+freedom applying a similar decomposition
+ 
+
+ align:start position:0%
+freedom applying a similar decomposition
+to the source we found that those six
+
+ align:start position:0%
+to the source we found that those six
+ 
+
+ align:start position:0%
+to the source we found that those six
+gauge invariant degrees of freedom are
+
+ align:start position:0%
+gauge invariant degrees of freedom are
+ 
+
+ align:start position:0%
+gauge invariant degrees of freedom are
+governed by four poisson type equations
+
+ align:start position:0%
+governed by four poisson type equations
+ 
+
+ align:start position:0%
+governed by four poisson type equations
+and I will refer you to the previous
+
+ align:start position:0%
+and I will refer you to the previous
+ 
+
+ align:start position:0%
+and I will refer you to the previous
+lecture for exact definitions of these
+
+ align:start position:0%
+lecture for exact definitions of these
+ 
+
+ align:start position:0%
+lecture for exact definitions of these
+things but there is a scalar field Phi
+
+ align:start position:0%
+things but there is a scalar field Phi
+ 
+
+ align:start position:0%
+things but there is a scalar field Phi
+that is related to the mean density of
+
+ align:start position:0%
+that is related to the mean density of
+ 
+
+ align:start position:0%
+that is related to the mean density of
+energy mean density of energy in your
+
+ align:start position:0%
+energy mean density of energy in your
+ 
+
+ align:start position:0%
+energy mean density of energy in your
+space-time and pressures in your space
+
+ align:start position:0%
+space-time and pressures in your space
+ 
+
+ align:start position:0%
+space-time and pressures in your space
+I'm sort of an isotropic stresses this
+
+ align:start position:0%
+I'm sort of an isotropic stresses this
+ 
+
+ align:start position:0%
+I'm sort of an isotropic stresses this
+DTS is an additional degree of freedom
+
+ align:start position:0%
+DTS is an additional degree of freedom
+ 
+
+ align:start position:0%
+DTS is an additional degree of freedom
+that is defined in that previous lecture
+
+ align:start position:0%
+that is defined in that previous lecture
+ 
+
+ align:start position:0%
+that is defined in that previous lecture
+you find that a placin equation for a
+
+ align:start position:0%
+you find that a placin equation for a
+ 
+
+ align:start position:0%
+you find that a placin equation for a
+scalar field I called theta is really
+
+ align:start position:0%
+scalar field I called theta is really
+ 
+
+ align:start position:0%
+scalar field I called theta is really
+directly related to the energy density
+
+ align:start position:0%
+directly related to the energy density
+ 
+
+ align:start position:0%
+directly related to the energy density
+there is there are two degrees of
+
+ align:start position:0%
+there is there are two degrees of
+ 
+
+ align:start position:0%
+there is there are two degrees of
+freedom associated with sort of off
+
+ align:start position:0%
+freedom associated with sort of off
+ 
+
+ align:start position:0%
+freedom associated with sort of off
+diagonal terms in the metric the
+
+ align:start position:0%
+diagonal terms in the metric the
+ 
+
+ align:start position:0%
+diagonal terms in the metric the
+time/space terms in the metric and
+
+ align:start position:0%
+time/space terms in the metric and
+ 
+
+ align:start position:0%
+time/space terms in the metric and
+they're related to the momentum flow
+
+ align:start position:0%
+they're related to the momentum flow
+ 
+
+ align:start position:0%
+they're related to the momentum flow
+these are only two degrees of freedom
+
+ align:start position:0%
+these are only two degrees of freedom
+ 
+
+ align:start position:0%
+these are only two degrees of freedom
+because this sigh is a divergence free
+
+ align:start position:0%
+because this sigh is a divergence free
+ 
+
+ align:start position:0%
+because this sigh is a divergence free
+field and finally what we found is if
+
+ align:start position:0%
+field and finally what we found is if
+ 
+
+ align:start position:0%
+field and finally what we found is if
+you take the spatial piece of the
+
+ align:start position:0%
+you take the spatial piece of the
+ 
+
+ align:start position:0%
+you take the spatial piece of the
+space-time metric you project out the
+
+ align:start position:0%
+space-time metric you project out the
+ 
+
+ align:start position:0%
+space-time metric you project out the
+bits that are transverse in other words
+
+ align:start position:0%
+bits that are transverse in other words
+ 
+
+ align:start position:0%
+bits that are transverse in other words
+it's divergence free we will come to a
+
+ align:start position:0%
+it's divergence free we will come to a
+ 
+
+ align:start position:0%
+it's divergence free we will come to a
+more physical meaning of this a little
+
+ align:start position:0%
+more physical meaning of this a little
+ 
+
+ align:start position:0%
+more physical meaning of this a little
+bit later in today's lecture and require
+
+ align:start position:0%
+bit later in today's lecture and require
+ 
+
+ align:start position:0%
+bit later in today's lecture and require
+that this be traceless then those
+
+ align:start position:0%
+that this be traceless then those
+ 
+
+ align:start position:0%
+that this be traceless then those
+components of the spatial space-time
+
+ align:start position:0%
+components of the spatial space-time
+ 
+
+ align:start position:0%
+components of the spatial space-time
+perturbation are already gauge
+
+ align:start position:0%
+perturbation are already gauge
+ 
+
+ align:start position:0%
+perturbation are already gauge
+invariants and they're related to sort
+
+ align:start position:0%
+invariants and they're related to sort
+ 
+
+ align:start position:0%
+invariants and they're related to sort
+of anisotropic stresses in our source
+
+ align:start position:0%
+of anisotropic stresses in our source
+ 
+
+ align:start position:0%
+of anisotropic stresses in our source
+they are governed by a wave equation and
+
+ align:start position:0%
+they are governed by a wave equation and
+ 
+
+ align:start position:0%
+they are governed by a wave equation and
+as such these represent a radiative
+
+ align:start position:0%
+as such these represent a radiative
+ 
+
+ align:start position:0%
+as such these represent a radiative
+degree of freedom
+
+ align:start position:0%
+degree of freedom
+ 
+
+ align:start position:0%
+degree of freedom
+cuz this is feeling because this is tres
+
+ align:start position:0%
+cuz this is feeling because this is tres
+ 
+
+ align:start position:0%
+cuz this is feeling because this is tres
+free and divergence trait this naively
+
+ align:start position:0%
+free and divergence trait this naively
+ 
+
+ align:start position:0%
+free and divergence trait this naively
+you would think that this that this has
+
+ align:start position:0%
+you would think that this that this has
+ 
+
+ align:start position:0%
+you would think that this that this has
+six numbers in it it's a symmetric 3x3
+
+ align:start position:0%
+six numbers in it it's a symmetric 3x3
+ 
+
+ align:start position:0%
+six numbers in it it's a symmetric 3x3
+matrix is how we would represent it but
+
+ align:start position:0%
+matrix is how we would represent it but
+ 
+
+ align:start position:0%
+matrix is how we would represent it but
+because it is trace free and because of
+
+ align:start position:0%
+because it is trace free and because of
+ 
+
+ align:start position:0%
+because it is trace free and because of
+this divergence list there are four
+
+ align:start position:0%
+this divergence list there are four
+ 
+
+ align:start position:0%
+this divergence list there are four
+constraints and so those six independent
+
+ align:start position:0%
+constraints and so those six independent
+ 
+
+ align:start position:0%
+constraints and so those six independent
+numbers are reduced to two and as we'll
+
+ align:start position:0%
+numbers are reduced to two and as we'll
+ 
+
+ align:start position:0%
+numbers are reduced to two and as we'll
+see in this lecture
+
+ align:start position:0%
+see in this lecture
+ 
+
+ align:start position:0%
+see in this lecture
+those two degrees of freedom correspond
+
+ align:start position:0%
+those two degrees of freedom correspond
+ 
+
+ align:start position:0%
+those two degrees of freedom correspond
+to the polarizations of gravitational
+
+ align:start position:0%
+to the polarizations of gravitational
+ 
+
+ align:start position:0%
+to the polarizations of gravitational
+waves today's lecture is all about
+
+ align:start position:0%
+waves today's lecture is all about
+ 
+
+ align:start position:0%
+waves today's lecture is all about
+understanding these guys okay given our
+
+ align:start position:0%
+understanding these guys okay given our
+ 
+
+ align:start position:0%
+understanding these guys okay given our
+kind of a funny schedule it we're on
+
+ align:start position:0%
+kind of a funny schedule it we're on
+ 
+
+ align:start position:0%
+kind of a funny schedule it we're on
+today I got up early have not had time
+
+ align:start position:0%
+today I got up early have not had time
+ 
+
+ align:start position:0%
+today I got up early have not had time
+to take a shower so I am wearing my LIGO
+
+ align:start position:0%
+to take a shower so I am wearing my LIGO
+ 
+
+ align:start position:0%
+to take a shower so I am wearing my LIGO
+hat and what are we doing today is the
+
+ align:start position:0%
+hat and what are we doing today is the
+ 
+
+ align:start position:0%
+hat and what are we doing today is the
+foundations of how one calculates this
+
+ align:start position:0%
+foundations of how one calculates this
+ 
+
+ align:start position:0%
+foundations of how one calculates this
+and why one builds an observatory like
+
+ align:start position:0%
+and why one builds an observatory like
+ 
+
+ align:start position:0%
+and why one builds an observatory like
+LIGO to measure these things all right
+
+ align:start position:0%
+LIGO to measure these things all right
+ 
+
+ align:start position:0%
+LIGO to measure these things all right
+so let me just write that out so our
+
+ align:start position:0%
+so let me just write that out so our
+ 
+
+ align:start position:0%
+so let me just write that out so our
+goal for today I shouldn't say our goal
+
+ align:start position:0%
+goal for today I shouldn't say our goal
+ 
+
+ align:start position:0%
+goal for today I shouldn't say our goal
+for this lecture because this is the
+
+ align:start position:0%
+for this lecture because this is the
+ 
+
+ align:start position:0%
+for this lecture because this is the
+first of three lectures I'm going to
+
+ align:start position:0%
+first of three lectures I'm going to
+ 
+
+ align:start position:0%
+first of three lectures I'm going to
+record today our goal is to understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hij tt in terms of quantities that we
+
+ align:start position:0%
+hij tt in terms of quantities that we
+ 
+
+ align:start position:0%
+hij tt in terms of quantities that we
+can observe and also to understand how
+
+ align:start position:0%
+can observe and also to understand how
+ 
+
+ align:start position:0%
+can observe and also to understand how
+to compute this field this h IJ t t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given a source so let's begin by just
+
+ align:start position:0%
+given a source so let's begin by just
+ 
+
+ align:start position:0%
+given a source so let's begin by just
+assuming let's begin by focusing on how
+
+ align:start position:0%
+assuming let's begin by focusing on how
+ 
+
+ align:start position:0%
+assuming let's begin by focusing on how
+we can understand what h IJ t t actually
+
+ align:start position:0%
+we can understand what h IJ t t actually
+ 
+
+ align:start position:0%
+we can understand what h IJ t t actually
+means how we can go and measure this so
+
+ align:start position:0%
+means how we can go and measure this so
+ 
+
+ align:start position:0%
+means how we can go and measure this so
+what I'm gonna do is just we'll start
+
+ align:start position:0%
+what I'm gonna do is just we'll start
+ 
+
+ align:start position:0%
+what I'm gonna do is just we'll start
+out by enlist as hand ourselves an H I J
+
+ align:start position:0%
+out by enlist as hand ourselves an H I J
+ 
+
+ align:start position:0%
+out by enlist as hand ourselves an H I J
+TT and study its properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm going to do is begin with a
+
+ align:start position:0%
+so what I'm going to do is begin with a
+ 
+
+ align:start position:0%
+so what I'm going to do is begin with a
+spacetime perturbation it has everything
+
+ align:start position:0%
+spacetime perturbation it has everything
+ 
+
+ align:start position:0%
+spacetime perturbation it has everything
+except hij tt equals zero so this is
+
+ align:start position:0%
+except hij tt equals zero so this is
+ 
+
+ align:start position:0%
+except hij tt equals zero so this is
+something that has Phi equals zero theta
+
+ align:start position:0%
+something that has Phi equals zero theta
+ 
+
+ align:start position:0%
+something that has Phi equals zero theta
+equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sigh equal to zero
+
+ align:start position:0%
+sigh equal to zero
+ 
+
+ align:start position:0%
+sigh equal to zero
+I am going to pick H I J tt we have a
+
+ align:start position:0%
+I am going to pick H I J tt we have a
+ 
+
+ align:start position:0%
+I am going to pick H I J tt we have a
+form such that it only depends it's a
+
+ align:start position:0%
+form such that it only depends it's a
+ 
+
+ align:start position:0%
+form such that it only depends it's a
+function that depends only on the
+
+ align:start position:0%
+function that depends only on the
+ 
+
+ align:start position:0%
+function that depends only on the
+combination T minus C so this represents
+
+ align:start position:0%
+combination T minus C so this represents
+ 
+
+ align:start position:0%
+combination T minus C so this represents
+something propagating as we see it
+
+ align:start position:0%
+something propagating as we see it
+ 
+
+ align:start position:0%
+something propagating as we see it
+actually describes radiation propagating
+
+ align:start position:0%
+actually describes radiation propagating
+ 
+
+ align:start position:0%
+actually describes radiation propagating
+in the Z direction okay so this assumed
+
+ align:start position:0%
+in the Z direction okay so this assumed
+ 
+
+ align:start position:0%
+in the Z direction okay so this assumed
+form can be represented by following
+
+ align:start position:0%
+form can be represented by following
+ 
+
+ align:start position:0%
+form can be represented by following
+matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you take a look at this I'm gonna
+
+ align:start position:0%
+so if you take a look at this I'm gonna
+ 
+
+ align:start position:0%
+so if you take a look at this I'm gonna
+justify a few details of this later
+
+ align:start position:0%
+justify a few details of this later
+ 
+
+ align:start position:0%
+justify a few details of this later
+there's a few constraints so it looks
+
+ align:start position:0%
+there's a few constraints so it looks
+ 
+
+ align:start position:0%
+there's a few constraints so it looks
+like I have four numbers here because my
+
+ align:start position:0%
+like I have four numbers here because my
+ 
+
+ align:start position:0%
+like I have four numbers here because my
+space-time metric is always symmetric
+
+ align:start position:0%
+space-time metric is always symmetric
+ 
+
+ align:start position:0%
+space-time metric is always symmetric
+under just a symmetry its symmetric
+
+ align:start position:0%
+under just a symmetry its symmetric
+ 
+
+ align:start position:0%
+under just a symmetry its symmetric
+under exchange of indices H X Y is the
+
+ align:start position:0%
+under exchange of indices H X Y is the
+ 
+
+ align:start position:0%
+under exchange of indices H X Y is the
+same thing as H Y X so these two things
+
+ align:start position:0%
+same thing as H Y X so these two things
+ 
+
+ align:start position:0%
+same thing as H Y X so these two things
+are the same and from the requirement
+
+ align:start position:0%
+are the same and from the requirement
+ 
+
+ align:start position:0%
+are the same and from the requirement
+that this construction betray straight
+
+ align:start position:0%
+that this construction betray straight
+ 
+
+ align:start position:0%
+that this construction betray straight
+so from the way I've written this here
+
+ align:start position:0%
+so from the way I've written this here
+ 
+
+ align:start position:0%
+so from the way I've written this here
+that tells me that H X X plus h YY must
+
+ align:start position:0%
+that tells me that H X X plus h YY must
+ 
+
+ align:start position:0%
+that tells me that H X X plus h YY must
+equal zero so these two quantities on
+
+ align:start position:0%
+equal zero so these two quantities on
+ 
+
+ align:start position:0%
+equal zero so these two quantities on
+the diagonal are not independent they
+
+ align:start position:0%
+the diagonal are not independent they
+ 
+
+ align:start position:0%
+the diagonal are not independent they
+must be of opposite sign so there are my
+
+ align:start position:0%
+must be of opposite sign so there are my
+ 
+
+ align:start position:0%
+must be of opposite sign so there are my
+two degrees of freedom
+
+ align:start position:0%
+two degrees of freedom
+ 
+
+ align:start position:0%
+two degrees of freedom
+why have I set the Z part equal to zero
+
+ align:start position:0%
+why have I set the Z part equal to zero
+ 
+
+ align:start position:0%
+why have I set the Z part equal to zero
+we'll look at that in a little bit more
+
+ align:start position:0%
+we'll look at that in a little bit more
+ 
+
+ align:start position:0%
+we'll look at that in a little bit more
+detail a little later in the lecture but
+
+ align:start position:0%
+detail a little later in the lecture but
+ 
+
+ align:start position:0%
+detail a little later in the lecture but
+essentially it comes from the fact that
+
+ align:start position:0%
+essentially it comes from the fact that
+ 
+
+ align:start position:0%
+essentially it comes from the fact that
+I'm making it propagate in the Z
+
+ align:start position:0%
+I'm making it propagate in the Z
+ 
+
+ align:start position:0%
+I'm making it propagate in the Z
+direction what we're going to see is
+
+ align:start position:0%
+direction what we're going to see is
+ 
+
+ align:start position:0%
+direction what we're going to see is
+that if whatever direction the wave is
+
+ align:start position:0%
+that if whatever direction the wave is
+ 
+
+ align:start position:0%
+that if whatever direction the wave is
+propagating in my field has to be
+
+ align:start position:0%
+propagating in my field has to be
+ 
+
+ align:start position:0%
+propagating in my field has to be
+orthogonal to it and we'll prove that a
+
+ align:start position:0%
+orthogonal to it and we'll prove that a
+ 
+
+ align:start position:0%
+orthogonal to it and we'll prove that a
+little bit more carefully later so for
+
+ align:start position:0%
+little bit more carefully later so for
+ 
+
+ align:start position:0%
+little bit more carefully later so for
+now let's just take this as handed to us
+
+ align:start position:0%
+now let's just take this as handed to us
+ 
+
+ align:start position:0%
+now let's just take this as handed to us
+okay we can see this is that leaves
+
+ align:start position:0%
+okay we can see this is that leaves
+ 
+
+ align:start position:0%
+okay we can see this is that leaves
+consistent with the properties I've
+
+ align:start position:0%
+consistent with the properties I've
+ 
+
+ align:start position:0%
+consistent with the properties I've
+written down here from the fact that it
+
+ align:start position:0%
+written down here from the fact that it
+ 
+
+ align:start position:0%
+written down here from the fact that it
+depends on T - Z it's not hard to show
+
+ align:start position:0%
+depends on T - Z it's not hard to show
+ 
+
+ align:start position:0%
+depends on T - Z it's not hard to show
+that this thing will satisfy the wave
+
+ align:start position:0%
+that this thing will satisfy the wave
+ 
+
+ align:start position:0%
+that this thing will satisfy the wave
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have a good source for exploration
+
+ align:start position:0%
+so we have a good source for exploration
+ 
+
+ align:start position:0%
+so we have a good source for exploration
+in front of us you mean a good space
+
+ align:start position:0%
+in front of us you mean a good space
+ 
+
+ align:start position:0%
+in front of us you mean a good space
+time for us to explore the properties of
+
+ align:start position:0%
+time for us to explore the properties of
+ 
+
+ align:start position:0%
+time for us to explore the properties of
+so let's begin by saying great one of
+
+ align:start position:0%
+so let's begin by saying great one of
+ 
+
+ align:start position:0%
+so let's begin by saying great one of
+the most important things we've learned
+
+ align:start position:0%
+the most important things we've learned
+ 
+
+ align:start position:0%
+the most important things we've learned
+how to do is given a space time I can
+
+ align:start position:0%
+how to do is given a space time I can
+ 
+
+ align:start position:0%
+how to do is given a space time I can
+compute how a freely falling body moves
+
+ align:start position:0%
+compute how a freely falling body moves
+ 
+
+ align:start position:0%
+compute how a freely falling body moves
+in that space-time so let's consider
+
+ align:start position:0%
+in that space-time so let's consider
+ 
+
+ align:start position:0%
+in that space-time so let's consider
+what happens if I have freely falling
+
+ align:start position:0%
+what happens if I have freely falling
+ 
+
+ align:start position:0%
+what happens if I have freely falling
+bodies in a space-time in a spacetime
+
+ align:start position:0%
+bodies in a space-time in a spacetime
+ 
+
+ align:start position:0%
+bodies in a space-time in a spacetime
+such that this you know in a space-time
+
+ align:start position:0%
+such that this you know in a space-time
+ 
+
+ align:start position:0%
+such that this you know in a space-time
+that is this so I'm not saying it's very
+
+ align:start position:0%
+that is this so I'm not saying it's very
+ 
+
+ align:start position:0%
+that is this so I'm not saying it's very
+slowly okay so here's what we want to do
+
+ align:start position:0%
+slowly okay so here's what we want to do
+ 
+
+ align:start position:0%
+slowly okay so here's what we want to do
+we're gonna consider freely falling
+
+ align:start position:0%
+we're gonna consider freely falling
+ 
+
+ align:start position:0%
+we're gonna consider freely falling
+bodies in a space-time that involves
+
+ align:start position:0%
+bodies in a space-time that involves
+ 
+
+ align:start position:0%
+bodies in a space-time that involves
+this HM you know the way I'm going to do
+
+ align:start position:0%
+this HM you know the way I'm going to do
+ 
+
+ align:start position:0%
+this HM you know the way I'm going to do
+this my first pass is sort of say okay I
+
+ align:start position:0%
+this my first pass is sort of say okay I
+ 
+
+ align:start position:0%
+this my first pass is sort of say okay I
+know all about the motion of freely
+
+ align:start position:0%
+know all about the motion of freely
+ 
+
+ align:start position:0%
+know all about the motion of freely
+falling bodies in space-time they are
+
+ align:start position:0%
+falling bodies in space-time they are
+ 
+
+ align:start position:0%
+falling bodies in space-time they are
+geodesics judy's X describes such bodies
+
+ align:start position:0%
+geodesics judy's X describes such bodies
+ 
+
+ align:start position:0%
+geodesics judy's X describes such bodies
+so let's go ahead and look at the judy's
+
+ align:start position:0%
+so let's go ahead and look at the judy's
+ 
+
+ align:start position:0%
+so let's go ahead and look at the judy's
+equation for this for this set up now I
+
+ align:start position:0%
+equation for this for this set up now I
+ 
+
+ align:start position:0%
+equation for this for this set up now I
+wanted to split let's give ourselves a
+
+ align:start position:0%
+wanted to split let's give ourselves a
+ 
+
+ align:start position:0%
+wanted to split let's give ourselves a
+couple of conditions to try to
+
+ align:start position:0%
+couple of conditions to try to
+ 
+
+ align:start position:0%
+couple of conditions to try to
+understand this let's imagine that these
+
+ align:start position:0%
+understand this let's imagine that these
+ 
+
+ align:start position:0%
+understand this let's imagine that these
+are we're initially in a space-time that
+
+ align:start position:0%
+are we're initially in a space-time that
+ 
+
+ align:start position:0%
+are we're initially in a space-time that
+is just flat space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're gonna imagine that h mu nu is
+
+ align:start position:0%
+so we're gonna imagine that h mu nu is
+ 
+
+ align:start position:0%
+so we're gonna imagine that h mu nu is
+zero initially and perhaps it then you
+
+ align:start position:0%
+zero initially and perhaps it then you
+ 
+
+ align:start position:0%
+zero initially and perhaps it then you
+know we're sort of imagining a spacetime
+
+ align:start position:0%
+know we're sort of imagining a spacetime
+ 
+
+ align:start position:0%
+know we're sort of imagining a spacetime
+in which there's just you're falling
+
+ align:start position:0%
+in which there's just you're falling
+ 
+
+ align:start position:0%
+in which there's just you're falling
+freely an empty space absolutely nothing
+
+ align:start position:0%
+freely an empty space absolutely nothing
+ 
+
+ align:start position:0%
+freely an empty space absolutely nothing
+going on here and this atria new field
+
+ align:start position:0%
+going on here and this atria new field
+ 
+
+ align:start position:0%
+going on here and this atria new field
+passes over you okay a wave packet
+
+ align:start position:0%
+passes over you okay a wave packet
+ 
+
+ align:start position:0%
+passes over you okay a wave packet
+passes over your freely falling
+
+ align:start position:0%
+passes over your freely falling
+ 
+
+ align:start position:0%
+passes over your freely falling
+particles so H mu nu naught equals zero
+
+ align:start position:0%
+particles so H mu nu naught equals zero
+ 
+
+ align:start position:0%
+particles so H mu nu naught equals zero
+comes along and passes over your
+
+ align:start position:0%
+comes along and passes over your
+ 
+
+ align:start position:0%
+comes along and passes over your
+particles I'm going to imagine that
+
+ align:start position:0%
+particles I'm going to imagine that
+ 
+
+ align:start position:0%
+particles I'm going to imagine that
+these bodies are initially at rest okay
+
+ align:start position:0%
+these bodies are initially at rest okay
+ 
+
+ align:start position:0%
+these bodies are initially at rest okay
+so when I'm in this route this regime
+
+ align:start position:0%
+so when I'm in this route this regime
+ 
+
+ align:start position:0%
+so when I'm in this route this regime
+where H V nu is equal to zero these guys
+
+ align:start position:0%
+where H V nu is equal to zero these guys
+ 
+
+ align:start position:0%
+where H V nu is equal to zero these guys
+are just sitting stationary with respect
+
+ align:start position:0%
+are just sitting stationary with respect
+ 
+
+ align:start position:0%
+are just sitting stationary with respect
+to whoever is making these measurements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're gonna say great I've got
+
+ align:start position:0%
+okay so we're gonna say great I've got
+ 
+
+ align:start position:0%
+okay so we're gonna say great I've got
+these bodies sitting at rest and what is
+
+ align:start position:0%
+these bodies sitting at rest and what is
+ 
+
+ align:start position:0%
+these bodies sitting at rest and what is
+initially empty space-time wave passes
+
+ align:start position:0%
+initially empty space-time wave passes
+ 
+
+ align:start position:0%
+initially empty space-time wave passes
+along what happens to these bodies so if
+
+ align:start position:0%
+along what happens to these bodies so if
+ 
+
+ align:start position:0%
+along what happens to these bodies so if
+these guys are at rest that I know that
+
+ align:start position:0%
+these guys are at rest that I know that
+ 
+
+ align:start position:0%
+these guys are at rest that I know that
+at initial times so let's just say that
+
+ align:start position:0%
+at initial times so let's just say that
+ 
+
+ align:start position:0%
+at initial times so let's just say that
+this comes along and it becomes H P nu
+
+ align:start position:0%
+this comes along and it becomes H P nu
+ 
+
+ align:start position:0%
+this comes along and it becomes H P nu
+not equal to zero at some time what is
+
+ align:start position:0%
+not equal to zero at some time what is
+ 
+
+ align:start position:0%
+not equal to zero at some time what is
+to find that is the origin of time so T
+
+ align:start position:0%
+to find that is the origin of time so T
+ 
+
+ align:start position:0%
+to find that is the origin of time so T
+equals zero is when the non-zero wave
+
+ align:start position:0%
+equals zero is when the non-zero wave
+ 
+
+ align:start position:0%
+equals zero is when the non-zero wave
+comes along so my space time is just
+
+ align:start position:0%
+comes along so my space time is just
+ 
+
+ align:start position:0%
+comes along so my space time is just
+eight mu nu for all earlier times my
+
+ align:start position:0%
+eight mu nu for all earlier times my
+ 
+
+ align:start position:0%
+eight mu nu for all earlier times my
+particles are sitting here at rest at
+
+ align:start position:0%
+particles are sitting here at rest at
+ 
+
+ align:start position:0%
+particles are sitting here at rest at
+all earlier times then H mu nu comes
+
+ align:start position:0%
+all earlier times then H mu nu comes
+ 
+
+ align:start position:0%
+all earlier times then H mu nu comes
+along so what we want to do then is look
+
+ align:start position:0%
+along so what we want to do then is look
+ 
+
+ align:start position:0%
+along so what we want to do then is look
+at how does this guy behave at T equals
+
+ align:start position:0%
+at how does this guy behave at T equals
+ 
+
+ align:start position:0%
+at how does this guy behave at T equals
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now initially the only component
+
+ align:start position:0%
+okay now initially the only component
+ 
+
+ align:start position:0%
+okay now initially the only component
+that will get picked out of this is the
+
+ align:start position:0%
+that will get picked out of this is the
+ 
+
+ align:start position:0%
+that will get picked out of this is the
+zero zero complement and working to
+
+ align:start position:0%
+zero zero complement and working to
+ 
+
+ align:start position:0%
+zero zero complement and working to
+linear order I can write this okay right
+
+ align:start position:0%
+linear order I can write this okay right
+ 
+
+ align:start position:0%
+linear order I can write this okay right
+one more step in here let's say that
+
+ align:start position:0%
+one more step in here let's say that
+ 
+
+ align:start position:0%
+one more step in here let's say that
+this I'm going to write as zero go back
+
+ align:start position:0%
+this I'm going to write as zero go back
+ 
+
+ align:start position:0%
+this I'm going to write as zero go back
+to your earlier lecture when we define
+
+ align:start position:0%
+to your earlier lecture when we define
+ 
+
+ align:start position:0%
+to your earlier lecture when we define
+the Christoffel symbol to look up the
+
+ align:start position:0%
+the Christoffel symbol to look up the
+ 
+
+ align:start position:0%
+the Christoffel symbol to look up the
+definition of this guy okay so these are
+
+ align:start position:0%
+definition of this guy okay so these are
+ 
+
+ align:start position:0%
+definition of this guy okay so these are
+all the only components of the
+
+ align:start position:0%
+all the only components of the
+ 
+
+ align:start position:0%
+all the only components of the
+space-time that enter into this
+
+ align:start position:0%
+space-time that enter into this
+ 
+
+ align:start position:0%
+space-time that enter into this
+Christoffel symbol every single one
+
+ align:start position:0%
+Christoffel symbol every single one
+ 
+
+ align:start position:0%
+Christoffel symbol every single one
+let's go back and take a look at the
+
+ align:start position:0%
+let's go back and take a look at the
+ 
+
+ align:start position:0%
+let's go back and take a look at the
+space-time that we're looking down here
+
+ align:start position:0%
+space-time that we're looking down here
+ 
+
+ align:start position:0%
+space-time that we're looking down here
+notice this involves beta 0 0 beta and 0
+
+ align:start position:0%
+notice this involves beta 0 0 beta and 0
+ 
+
+ align:start position:0%
+notice this involves beta 0 0 beta and 0
+0 that is the space-time parts all of
+
+ align:start position:0%
+0 that is the space-time parts all of
+ 
+
+ align:start position:0%
+0 that is the space-time parts all of
+which are 0 the other space-time parts
+
+ align:start position:0%
+which are 0 the other space-time parts
+ 
+
+ align:start position:0%
+which are 0 the other space-time parts
+all of which are 0 and the time time
+
+ align:start position:0%
+all of which are 0 and the time time
+ 
+
+ align:start position:0%
+all of which are 0 and the time time
+part which is 0 so the initial
+
+ align:start position:0%
+part which is 0 so the initial
+ 
+
+ align:start position:0%
+part which is 0 so the initial
+acceleration is 0 that means do u alpha
+
+ align:start position:0%
+acceleration is 0 that means do u alpha
+ 
+
+ align:start position:0%
+acceleration is 0 that means do u alpha
+D tau is equal to 0 which means that my
+
+ align:start position:0%
+D tau is equal to 0 which means that my
+ 
+
+ align:start position:0%
+D tau is equal to 0 which means that my
+particle begins on a judy's ik and it
+
+ align:start position:0%
+particle begins on a judy's ik and it
+ 
+
+ align:start position:0%
+particle begins on a judy's ik and it
+stays on the judy's ik in these
+
+ align:start position:0%
+stays on the judy's ik in these
+ 
+
+ align:start position:0%
+stays on the judy's ik in these
+coordinates it does not move at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this seems to suggest that gravitation
+
+ align:start position:0%
+this seems to suggest that gravitation
+ 
+
+ align:start position:0%
+this seems to suggest that gravitation
+waves have no effect I have a small body
+
+ align:start position:0%
+waves have no effect I have a small body
+ 
+
+ align:start position:0%
+waves have no effect I have a small body
+here gravitational waves come along
+
+ align:start position:0%
+here gravitational waves come along
+ 
+
+ align:start position:0%
+here gravitational waves come along
+it's unaccelerated so what's this for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if you think about this for a
+
+ align:start position:0%
+well if you think about this for a
+ 
+
+ align:start position:0%
+well if you think about this for a
+second what you should convince yourself
+
+ align:start position:0%
+second what you should convince yourself
+ 
+
+ align:start position:0%
+second what you should convince yourself
+is that the calculation I just did it's
+
+ align:start position:0%
+is that the calculation I just did it's
+ 
+
+ align:start position:0%
+is that the calculation I just did it's
+probably the first one you would think
+
+ align:start position:0%
+probably the first one you would think
+ 
+
+ align:start position:0%
+probably the first one you would think
+of doing when you're trying to ascertain
+
+ align:start position:0%
+of doing when you're trying to ascertain
+ 
+
+ align:start position:0%
+of doing when you're trying to ascertain
+how does a body move in a particular
+
+ align:start position:0%
+how does a body move in a particular
+ 
+
+ align:start position:0%
+how does a body move in a particular
+space-time but in some ways it was kind
+
+ align:start position:0%
+space-time but in some ways it was kind
+ 
+
+ align:start position:0%
+space-time but in some ways it was kind
+of a dumb calculation to do so let's
+
+ align:start position:0%
+of a dumb calculation to do so let's
+ 
+
+ align:start position:0%
+of a dumb calculation to do so let's
+bear in mind what this is doing is tell
+
+ align:start position:0%
+bear in mind what this is doing is tell
+ 
+
+ align:start position:0%
+bear in mind what this is doing is tell
+me the judaising equation describes
+
+ align:start position:0%
+me the judaising equation describes
+ 
+
+ align:start position:0%
+me the judaising equation describes
+motion with respect to some given
+
+ align:start position:0%
+motion with respect to some given
+ 
+
+ align:start position:0%
+motion with respect to some given
+coordinate system satisfying this
+
+ align:start position:0%
+coordinate system satisfying this
+ 
+
+ align:start position:0%
+coordinate system satisfying this
+equation is just saying yep
+
+ align:start position:0%
+equation is just saying yep
+ 
+
+ align:start position:0%
+equation is just saying yep
+you're falling at Judy's ik and guess
+
+ align:start position:0%
+you're falling at Judy's ik and guess
+ 
+
+ align:start position:0%
+you're falling at Judy's ik and guess
+what these are this the this radiation
+
+ align:start position:0%
+what these are this the this radiation
+ 
+
+ align:start position:0%
+what these are this the this radiation
+is a form of gravity even if the body
+
+ align:start position:0%
+is a form of gravity even if the body
+ 
+
+ align:start position:0%
+is a form of gravity even if the body
+responds to it it is still going to
+
+ align:start position:0%
+responds to it it is still going to
+ 
+
+ align:start position:0%
+responds to it it is still going to
+follow a judy's it is going to be in
+
+ align:start position:0%
+follow a judy's it is going to be in
+ 
+
+ align:start position:0%
+follow a judy's it is going to be in
+freefall the gravitational field may be
+
+ align:start position:0%
+freefall the gravitational field may be
+ 
+
+ align:start position:0%
+freefall the gravitational field may be
+a little bit different from the ones
+
+ align:start position:0%
+a little bit different from the ones
+ 
+
+ align:start position:0%
+a little bit different from the ones
+that you're more used to from your
+
+ align:start position:0%
+that you're more used to from your
+ 
+
+ align:start position:0%
+that you're more used to from your
+previous experiences with gravity but it
+
+ align:start position:0%
+previous experiences with gravity but it
+ 
+
+ align:start position:0%
+previous experiences with gravity but it
+is still just following the free fall
+
+ align:start position:0%
+is still just following the free fall
+ 
+
+ align:start position:0%
+is still just following the free fall
+trajectory that gravity demands
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so freefall in these coordinates means
+
+ align:start position:0%
+so freefall in these coordinates means
+ 
+
+ align:start position:0%
+so freefall in these coordinates means
+the body is remaining fixed in these
+
+ align:start position:0%
+the body is remaining fixed in these
+ 
+
+ align:start position:0%
+the body is remaining fixed in these
+coordinates okay this is one of the most
+
+ align:start position:0%
+coordinates okay this is one of the most
+ 
+
+ align:start position:0%
+coordinates okay this is one of the most
+important lessons in general relativity
+
+ align:start position:0%
+important lessons in general relativity
+ 
+
+ align:start position:0%
+important lessons in general relativity
+when you ask the statements that depends
+
+ align:start position:0%
+when you ask the statements that depends
+ 
+
+ align:start position:0%
+when you ask the statements that depends
+on the coordinate system you've written
+
+ align:start position:0%
+on the coordinate system you've written
+ 
+
+ align:start position:0%
+on the coordinate system you've written
+down you have to understand your
+
+ align:start position:0%
+down you have to understand your
+ 
+
+ align:start position:0%
+down you have to understand your
+coordinates and I would submit we don't
+
+ align:start position:0%
+coordinates and I would submit we don't
+ 
+
+ align:start position:0%
+coordinates and I would submit we don't
+really understand the coordinates that
+
+ align:start position:0%
+really understand the coordinates that
+ 
+
+ align:start position:0%
+really understand the coordinates that
+we wrote down here with this these
+
+ align:start position:0%
+we wrote down here with this these
+ 
+
+ align:start position:0%
+we wrote down here with this these
+coordinates essentially follow the body
+
+ align:start position:0%
+coordinates essentially follow the body
+ 
+
+ align:start position:0%
+coordinates essentially follow the body
+even if the body is moving they
+
+ align:start position:0%
+even if the body is moving they
+ 
+
+ align:start position:0%
+even if the body is moving they
+essentially wiggle right along with the
+
+ align:start position:0%
+essentially wiggle right along with the
+ 
+
+ align:start position:0%
+essentially wiggle right along with the
+body itself so if you want to understand
+
+ align:start position:0%
+body itself so if you want to understand
+ 
+
+ align:start position:0%
+body itself so if you want to understand
+what the impact of gravitational waves
+
+ align:start position:0%
+what the impact of gravitational waves
+ 
+
+ align:start position:0%
+what the impact of gravitational waves
+is on things you have to try to
+
+ align:start position:0%
+is on things you have to try to
+ 
+
+ align:start position:0%
+is on things you have to try to
+formulate what you're able to measure
+
+ align:start position:0%
+formulate what you're able to measure
+ 
+
+ align:start position:0%
+formulate what you're able to measure
+using coordinate independent language as
+
+ align:start position:0%
+using coordinate independent language as
+ 
+
+ align:start position:0%
+using coordinate independent language as
+much as possible at the very least you
+
+ align:start position:0%
+much as possible at the very least you
+ 
+
+ align:start position:0%
+much as possible at the very least you
+need to understand your coordinate
+
+ align:start position:0%
+need to understand your coordinate
+ 
+
+ align:start position:0%
+need to understand your coordinate
+system a lot better than I did in
+
+ align:start position:0%
+system a lot better than I did in
+ 
+
+ align:start position:0%
+system a lot better than I did in
+setting up this calculation over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's reframe the way we do this
+
+ align:start position:0%
+so let's reframe the way we do this
+ 
+
+ align:start position:0%
+so let's reframe the way we do this
+analysis let's imagine so what what one
+
+ align:start position:0%
+analysis let's imagine so what what one
+ 
+
+ align:start position:0%
+analysis let's imagine so what what one
+of the things that we learned in
+
+ align:start position:0%
+of the things that we learned in
+ 
+
+ align:start position:0%
+of the things that we learned in
+thinking about how gravity works in
+
+ align:start position:0%
+thinking about how gravity works in
+ 
+
+ align:start position:0%
+thinking about how gravity works in
+general relativity is I can always if
+
+ align:start position:0%
+general relativity is I can always if
+ 
+
+ align:start position:0%
+general relativity is I can always if
+I'm just focusing on a single body a
+
+ align:start position:0%
+I'm just focusing on a single body a
+ 
+
+ align:start position:0%
+I'm just focusing on a single body a
+single point mass I can always go into
+
+ align:start position:0%
+single point mass I can always go into
+ 
+
+ align:start position:0%
+single point mass I can always go into
+freely falling coordinates and
+
+ align:start position:0%
+freely falling coordinates and
+ 
+
+ align:start position:0%
+freely falling coordinates and
+space-time is essentially the space-time
+
+ align:start position:0%
+space-time is essentially the space-time
+ 
+
+ align:start position:0%
+space-time is essentially the space-time
+of special relativity I can find a
+
+ align:start position:0%
+of special relativity I can find a
+ 
+
+ align:start position:0%
+of special relativity I can find a
+representation so that everything looks
+
+ align:start position:0%
+representation so that everything looks
+ 
+
+ align:start position:0%
+representation so that everything looks
+just like special relativity near there
+
+ align:start position:0%
+just like special relativity near there
+ 
+
+ align:start position:0%
+just like special relativity near there
+gravity is basically completely thrown
+
+ align:start position:0%
+gravity is basically completely thrown
+ 
+
+ align:start position:0%
+gravity is basically completely thrown
+away at least as far as the mathematical
+
+ align:start position:0%
+away at least as far as the mathematical
+ 
+
+ align:start position:0%
+away at least as far as the mathematical
+representation is is concerned okay I'm
+
+ align:start position:0%
+representation is is concerned okay I'm
+ 
+
+ align:start position:0%
+representation is is concerned okay I'm
+in freefall
+
+ align:start position:0%
+in freefall
+ 
+
+ align:start position:0%
+in freefall
+I don't really see much if I want to see
+
+ align:start position:0%
+I don't really see much if I want to see
+ 
+
+ align:start position:0%
+I don't really see much if I want to see
+the impact of these waves what I need to
+
+ align:start position:0%
+the impact of these waves what I need to
+ 
+
+ align:start position:0%
+the impact of these waves what I need to
+do is think about how things behave over
+
+ align:start position:0%
+do is think about how things behave over
+ 
+
+ align:start position:0%
+do is think about how things behave over
+some finite region okay I want to put
+
+ align:start position:0%
+some finite region okay I want to put
+ 
+
+ align:start position:0%
+some finite region okay I want to put
+together a set up such that I have two
+
+ align:start position:0%
+together a set up such that I have two
+ 
+
+ align:start position:0%
+together a set up such that I have two
+bodies and those the relative effect of
+
+ align:start position:0%
+bodies and those the relative effect of
+ 
+
+ align:start position:0%
+bodies and those the relative effect of
+things between those two bodies will
+
+ align:start position:0%
+things between those two bodies will
+ 
+
+ align:start position:0%
+things between those two bodies will
+allow me to see the effect of space-time
+
+ align:start position:0%
+allow me to see the effect of space-time
+ 
+
+ align:start position:0%
+allow me to see the effect of space-time
+curvature in action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's now with this in mind let's
+
+ align:start position:0%
+so let's now with this in mind let's
+ 
+
+ align:start position:0%
+so let's now with this in mind let's
+consider two nearby bodies that each
+
+ align:start position:0%
+consider two nearby bodies that each
+ 
+
+ align:start position:0%
+consider two nearby bodies that each
+follow Judy's ex so body a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is right here and I'm going to find body
+
+ align:start position:0%
+is right here and I'm going to find body
+ 
+
+ align:start position:0%
+is right here and I'm going to find body
+a as living at the origin of my
+
+ align:start position:0%
+a as living at the origin of my
+ 
+
+ align:start position:0%
+a as living at the origin of my
+coordinates and we've got a body B over
+
+ align:start position:0%
+coordinates and we've got a body B over
+ 
+
+ align:start position:0%
+coordinates and we've got a body B over
+here and we're gonna say that this guy
+
+ align:start position:0%
+here and we're gonna say that this guy
+ 
+
+ align:start position:0%
+here and we're gonna say that this guy
+is displaced from the origin by a small
+
+ align:start position:0%
+is displaced from the origin by a small
+ 
+
+ align:start position:0%
+is displaced from the origin by a small
+amount some epsilon in what I will call
+
+ align:start position:0%
+amount some epsilon in what I will call
+ 
+
+ align:start position:0%
+amount some epsilon in what I will call
+the X direction and what I want to do is
+
+ align:start position:0%
+the X direction and what I want to do is
+ 
+
+ align:start position:0%
+the X direction and what I want to do is
+say okay I've got these two guys they
+
+ align:start position:0%
+say okay I've got these two guys they
+ 
+
+ align:start position:0%
+say okay I've got these two guys they
+are moving through a space-time let's
+
+ align:start position:0%
+are moving through a space-time let's
+ 
+
+ align:start position:0%
+are moving through a space-time let's
+make this be the space-time that we had
+
+ align:start position:0%
+make this be the space-time that we had
+ 
+
+ align:start position:0%
+make this be the space-time that we had
+discussed discussed a moment ago so they
+
+ align:start position:0%
+discussed discussed a moment ago so they
+ 
+
+ align:start position:0%
+discussed discussed a moment ago so they
+are each moving on judy's X of this
+
+ align:start position:0%
+are each moving on judy's X of this
+ 
+
+ align:start position:0%
+are each moving on judy's X of this
+space-time we know that if I set up my
+
+ align:start position:0%
+space-time we know that if I set up my
+ 
+
+ align:start position:0%
+space-time we know that if I set up my
+coordinate system and the way that I've
+
+ align:start position:0%
+coordinate system and the way that I've
+ 
+
+ align:start position:0%
+coordinate system and the way that I've
+done it here I am NOT going to see any
+
+ align:start position:0%
+done it here I am NOT going to see any
+ 
+
+ align:start position:0%
+done it here I am NOT going to see any
+acceleration on each of these bodies
+
+ align:start position:0%
+acceleration on each of these bodies
+ 
+
+ align:start position:0%
+acceleration on each of these bodies
+let's now try to focus on some kind of a
+
+ align:start position:0%
+let's now try to focus on some kind of a
+ 
+
+ align:start position:0%
+let's now try to focus on some kind of a
+some kind of a quantity that tells me
+
+ align:start position:0%
+some kind of a quantity that tells me
+ 
+
+ align:start position:0%
+some kind of a quantity that tells me
+about the separation between these two
+
+ align:start position:0%
+about the separation between these two
+ 
+
+ align:start position:0%
+about the separation between these two
+I'm going to do this in two ways so the
+
+ align:start position:0%
+I'm going to do this in two ways so the
+ 
+
+ align:start position:0%
+I'm going to do this in two ways so the
+first in which I'm going to do is say
+
+ align:start position:0%
+first in which I'm going to do is say
+ 
+
+ align:start position:0%
+first in which I'm going to do is say
+let's imagine let's imagine that I am
+
+ align:start position:0%
+let's imagine let's imagine that I am
+ 
+
+ align:start position:0%
+let's imagine let's imagine that I am
+bouncing a light pulse back and forth
+
+ align:start position:0%
+bouncing a light pulse back and forth
+ 
+
+ align:start position:0%
+bouncing a light pulse back and forth
+between a and B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'm going to do is write the for
+
+ align:start position:0%
+what I'm going to do is write the for
+ 
+
+ align:start position:0%
+what I'm going to do is write the for
+momentum so she with that white so
+
+ align:start position:0%
+momentum so she with that white so
+ 
+
+ align:start position:0%
+momentum so she with that white so
+recall I can't really define a for
+
+ align:start position:0%
+recall I can't really define a for
+ 
+
+ align:start position:0%
+recall I can't really define a for
+velocity for light because proper time
+
+ align:start position:0%
+velocity for light because proper time
+ 
+
+ align:start position:0%
+velocity for light because proper time
+is not defined but I can introduce some
+
+ align:start position:0%
+is not defined but I can introduce some
+ 
+
+ align:start position:0%
+is not defined but I can introduce some
+kind of an affine parameter such that D
+
+ align:start position:0%
+kind of an affine parameter such that D
+ 
+
+ align:start position:0%
+kind of an affine parameter such that D
+by D lambda tells me about motional on
+
+ align:start position:0%
+by D lambda tells me about motional on
+ 
+
+ align:start position:0%
+by D lambda tells me about motional on
+the world line that this light follows
+
+ align:start position:0%
+the world line that this light follows
+ 
+
+ align:start position:0%
+the world line that this light follows
+and this is just bouncing back and forth
+
+ align:start position:0%
+and this is just bouncing back and forth
+ 
+
+ align:start position:0%
+and this is just bouncing back and forth
+between these two so it moves on in the
+
+ align:start position:0%
+between these two so it moves on in the
+ 
+
+ align:start position:0%
+between these two so it moves on in the
+X direction because this is light T
+
+ align:start position:0%
+X direction because this is light T
+ 
+
+ align:start position:0%
+X direction because this is light T
+equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these components are the four
+
+ align:start position:0%
+so these components are the four
+ 
+
+ align:start position:0%
+so these components are the four
+momentum associates light the DTV lambda
+
+ align:start position:0%
+momentum associates light the DTV lambda
+ 
+
+ align:start position:0%
+momentum associates light the DTV lambda
+and the xdxd lambda they are related to
+
+ align:start position:0%
+and the xdxd lambda they are related to
+ 
+
+ align:start position:0%
+and the xdxd lambda they are related to
+each other like so and look the
+
+ align:start position:0%
+each other like so and look the
+ 
+
+ align:start position:0%
+each other like so and look the
+space-time metric the gauge invariant
+
+ align:start position:0%
+space-time metric the gauge invariant
+ 
+
+ align:start position:0%
+space-time metric the gauge invariant
+piece of the space-time hxx tt it is
+
+ align:start position:0%
+piece of the space-time hxx tt it is
+ 
+
+ align:start position:0%
+piece of the space-time hxx tt it is
+appearing in here so let's say okay what
+
+ align:start position:0%
+appearing in here so let's say okay what
+ 
+
+ align:start position:0%
+appearing in here so let's say okay what
+I am interested now is computing what
+
+ align:start position:0%
+I am interested now is computing what
+ 
+
+ align:start position:0%
+I am interested now is computing what
+suppose I'm sitting at a and I want to
+
+ align:start position:0%
+suppose I'm sitting at a and I want to
+ 
+
+ align:start position:0%
+suppose I'm sitting at a and I want to
+compute the time according to a clock
+
+ align:start position:0%
+compute the time according to a clock
+ 
+
+ align:start position:0%
+compute the time according to a clock
+that it takes for a pulse of light to
+
+ align:start position:0%
+that it takes for a pulse of light to
+ 
+
+ align:start position:0%
+that it takes for a pulse of light to
+travel from A to B maybe I'll make it
+
+ align:start position:0%
+travel from A to B maybe I'll make it
+ 
+
+ align:start position:0%
+travel from A to B maybe I'll make it
+bounce back okay may I want to know how
+
+ align:start position:0%
+bounce back okay may I want to know how
+ 
+
+ align:start position:0%
+bounce back okay may I want to know how
+much time it takes for the light poles
+
+ align:start position:0%
+much time it takes for the light poles
+ 
+
+ align:start position:0%
+much time it takes for the light poles
+to go from A to B and back to a so let's
+
+ align:start position:0%
+to go from A to B and back to a so let's
+ 
+
+ align:start position:0%
+to go from A to B and back to a so let's
+turn this into an equation for the
+
+ align:start position:0%
+turn this into an equation for the
+ 
+
+ align:start position:0%
+turn this into an equation for the
+interval DT DT so DT I can do a little
+
+ align:start position:0%
+interval DT DT so DT I can do a little
+ 
+
+ align:start position:0%
+interval DT DT so DT I can do a little
+bit of this trick called division here
+
+ align:start position:0%
+bit of this trick called division here
+ 
+
+ align:start position:0%
+bit of this trick called division here
+is yeah so I'm doing the old physicist
+
+ align:start position:0%
+is yeah so I'm doing the old physicist
+ 
+
+ align:start position:0%
+is yeah so I'm doing the old physicist
+trick I'm just imagining that an
+
+ align:start position:0%
+trick I'm just imagining that an
+ 
+
+ align:start position:0%
+trick I'm just imagining that an
+interval of time Daehyun interval of a
+
+ align:start position:0%
+interval of time Daehyun interval of a
+ 
+
+ align:start position:0%
+interval of time Daehyun interval of a
+fine parameter D lambda the amount of DT
+
+ align:start position:0%
+fine parameter D lambda the amount of DT
+ 
+
+ align:start position:0%
+fine parameter D lambda the amount of DT
+that accumulates as it moves to an
+
+ align:start position:0%
+that accumulates as it moves to an
+ 
+
+ align:start position:0%
+that accumulates as it moves to an
+interval DX they are related by so and
+
+ align:start position:0%
+interval DX they are related by so and
+ 
+
+ align:start position:0%
+interval DX they are related by so and
+remember I am assuming that the
+
+ align:start position:0%
+remember I am assuming that the
+ 
+
+ align:start position:0%
+remember I am assuming that the
+perturbation from space-time from flat
+
+ align:start position:0%
+perturbation from space-time from flat
+ 
+
+ align:start position:0%
+perturbation from space-time from flat
+space-time is small enough that I can
+
+ align:start position:0%
+space-time is small enough that I can
+ 
+
+ align:start position:0%
+space-time is small enough that I can
+always linearize so this can be I can
+
+ align:start position:0%
+always linearize so this can be I can
+ 
+
+ align:start position:0%
+always linearize so this can be I can
+take that square root using the binomial
+
+ align:start position:0%
+take that square root using the binomial
+ 
+
+ align:start position:0%
+take that square root using the binomial
+expansion so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose I want to integrate up the time
+
+ align:start position:0%
+suppose I want to integrate up the time
+ 
+
+ align:start position:0%
+suppose I want to integrate up the time
+it takes for this thing to go from A to
+
+ align:start position:0%
+it takes for this thing to go from A to
+ 
+
+ align:start position:0%
+it takes for this thing to go from A to
+B and then back from B well this is
+
+ align:start position:0%
+B and then back from B well this is
+ 
+
+ align:start position:0%
+B and then back from B well this is
+going to be given by integrating this
+
+ align:start position:0%
+going to be given by integrating this
+ 
+
+ align:start position:0%
+going to be given by integrating this
+guy's motion from zero to epsilon and
+
+ align:start position:0%
+guy's motion from zero to epsilon and
+ 
+
+ align:start position:0%
+guy's motion from zero to epsilon and
+then integrating it back again it's
+
+ align:start position:0%
+then integrating it back again it's
+ 
+
+ align:start position:0%
+then integrating it back again it's
+going to switch direction when I do that
+
+ align:start position:0%
+going to switch direction when I do that
+ 
+
+ align:start position:0%
+going to switch direction when I do that
+so I'm going to flip the sign on that DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'm leaving it written in this form
+
+ align:start position:0%
+okay I'm leaving it written in this form
+ 
+
+ align:start position:0%
+okay I'm leaving it written in this form
+to be a little bit careful you guys will
+
+ align:start position:0%
+to be a little bit careful you guys will
+ 
+
+ align:start position:0%
+to be a little bit careful you guys will
+play with this a little bit more on a
+
+ align:start position:0%
+play with this a little bit more on a
+ 
+
+ align:start position:0%
+play with this a little bit more on a
+problem set bear in mind that as I move
+
+ align:start position:0%
+problem set bear in mind that as I move
+ 
+
+ align:start position:0%
+problem set bear in mind that as I move
+through X the time argument of these
+
+ align:start position:0%
+through X the time argument of these
+ 
+
+ align:start position:0%
+through X the time argument of these
+guys is changing okay and so that's
+
+ align:start position:0%
+guys is changing okay and so that's
+ 
+
+ align:start position:0%
+guys is changing okay and so that's
+where there's a little bit of work that
+
+ align:start position:0%
+where there's a little bit of work that
+ 
+
+ align:start position:0%
+where there's a little bit of work that
+you'll explore on a problem set but I'm
+
+ align:start position:0%
+you'll explore on a problem set but I'm
+ 
+
+ align:start position:0%
+you'll explore on a problem set but I'm
+writing it in this form so that we get
+
+ align:start position:0%
+writing it in this form so that we get
+ 
+
+ align:start position:0%
+writing it in this form so that we get
+some you naively you might think oh okay
+
+ align:start position:0%
+some you naively you might think oh okay
+ 
+
+ align:start position:0%
+some you naively you might think oh okay
+I'll just flip the sign and I'll combine
+
+ align:start position:0%
+I'll just flip the sign and I'll combine
+ 
+
+ align:start position:0%
+I'll just flip the sign and I'll combine
+these and a certain limit that is indeed
+
+ align:start position:0%
+these and a certain limit that is indeed
+ 
+
+ align:start position:0%
+these and a certain limit that is indeed
+a good approximation got to be a little
+
+ align:start position:0%
+a good approximation got to be a little
+ 
+
+ align:start position:0%
+a good approximation got to be a little
+bit more careful in general though this
+
+ align:start position:0%
+bit more careful in general though this
+ 
+
+ align:start position:0%
+bit more careful in general though this
+is the time it would take for light to
+
+ align:start position:0%
+is the time it would take for light to
+ 
+
+ align:start position:0%
+is the time it would take for light to
+go from A to B in back in the absence of
+
+ align:start position:0%
+go from A to B in back in the absence of
+ 
+
+ align:start position:0%
+go from A to B in back in the absence of
+this gravitational wave this h XX TTA
+
+ align:start position:0%
+this gravitational wave this h XX TTA
+ 
+
+ align:start position:0%
+this gravitational wave this h XX TTA
+notice there is an inference on the time
+
+ align:start position:0%
+notice there is an inference on the time
+ 
+
+ align:start position:0%
+notice there is an inference on the time
+of arrival of these pulses that depends
+
+ align:start position:0%
+of arrival of these pulses that depends
+ 
+
+ align:start position:0%
+of arrival of these pulses that depends
+on HX xt t time arrival of the pulses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depends on this particular piece of the
+
+ align:start position:0%
+depends on this particular piece of the
+ 
+
+ align:start position:0%
+depends on this particular piece of the
+space-time metric one could imagine if
+
+ align:start position:0%
+space-time metric one could imagine if
+ 
+
+ align:start position:0%
+space-time metric one could imagine if
+you had a precise clock and you sat
+
+ align:start position:0%
+you had a precise clock and you sat
+ 
+
+ align:start position:0%
+you had a precise clock and you sat
+there and you time the arrival of these
+
+ align:start position:0%
+there and you time the arrival of these
+ 
+
+ align:start position:0%
+there and you time the arrival of these
+things let's say you sent a pulse of
+
+ align:start position:0%
+things let's say you sent a pulse of
+ 
+
+ align:start position:0%
+things let's say you sent a pulse of
+light out Boop and you kept track of how
+
+ align:start position:0%
+light out Boop and you kept track of how
+ 
+
+ align:start position:0%
+light out Boop and you kept track of how
+long it took with a very precise clock
+
+ align:start position:0%
+long it took with a very precise clock
+ 
+
+ align:start position:0%
+long it took with a very precise clock
+you could look for in the absolute
+
+ align:start position:0%
+you could look for in the absolute
+ 
+
+ align:start position:0%
+you could look for in the absolute
+gravitational wave that would be if you
+
+ align:start position:0%
+gravitational wave that would be if you
+ 
+
+ align:start position:0%
+gravitational wave that would be if you
+imagine that your pulse was sent out
+
+ align:start position:0%
+imagine that your pulse was sent out
+ 
+
+ align:start position:0%
+imagine that your pulse was sent out
+perfectly periodically let's say every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every millisecond or something like that
+
+ align:start position:0%
+every millisecond or something like that
+ 
+
+ align:start position:0%
+every millisecond or something like that
+you sent out a little pulse if it
+
+ align:start position:0%
+you sent out a little pulse if it
+ 
+
+ align:start position:0%
+you sent out a little pulse if it
+arrived back and your arrival pulses
+
+ align:start position:0%
+arrived back and your arrival pulses
+ 
+
+ align:start position:0%
+arrived back and your arrival pulses
+were just as spaced by one millisecond
+
+ align:start position:0%
+were just as spaced by one millisecond
+ 
+
+ align:start position:0%
+were just as spaced by one millisecond
+you would say great I am sitting in
+
+ align:start position:0%
+you would say great I am sitting in
+ 
+
+ align:start position:0%
+you would say great I am sitting in
+empty space time but if you found that
+
+ align:start position:0%
+empty space time but if you found that
+ 
+
+ align:start position:0%
+empty space time but if you found that
+their arrivals varied
+
+ align:start position:0%
+their arrivals varied
+ 
+
+ align:start position:0%
+their arrivals varied
+you'd say hmm there's something else
+
+ align:start position:0%
+you'd say hmm there's something else
+ 
+
+ align:start position:0%
+you'd say hmm there's something else
+going on here gravitational waves is one
+
+ align:start position:0%
+going on here gravitational waves is one
+ 
+
+ align:start position:0%
+going on here gravitational waves is one
+of things that could lead to that
+
+ align:start position:0%
+of things that could lead to that
+ 
+
+ align:start position:0%
+of things that could lead to that
+variation so this at least is kind of a
+
+ align:start position:0%
+variation so this at least is kind of a
+ 
+
+ align:start position:0%
+variation so this at least is kind of a
+proof this calculation I just did you
+
+ align:start position:0%
+proof this calculation I just did you
+ 
+
+ align:start position:0%
+proof this calculation I just did you
+guys are actually on one of the upcoming
+
+ align:start position:0%
+guys are actually on one of the upcoming
+ 
+
+ align:start position:0%
+guys are actually on one of the upcoming
+problem sets believe it's problems
+
+ align:start position:0%
+problem sets believe it's problems
+ 
+
+ align:start position:0%
+problem sets believe it's problems
+anywhere for seven or eight you do a
+
+ align:start position:0%
+anywhere for seven or eight you do a
+ 
+
+ align:start position:0%
+anywhere for seven or eight you do a
+little analysis where you will use this
+
+ align:start position:0%
+little analysis where you will use this
+ 
+
+ align:start position:0%
+little analysis where you will use this
+to understand how a detector like LIGO
+
+ align:start position:0%
+to understand how a detector like LIGO
+ 
+
+ align:start position:0%
+to understand how a detector like LIGO
+actually functions to measure out the
+
+ align:start position:0%
+actually functions to measure out the
+ 
+
+ align:start position:0%
+actually functions to measure out the
+effect due to gravitational wave on the
+
+ align:start position:0%
+effect due to gravitational wave on the
+ 
+
+ align:start position:0%
+effect due to gravitational wave on the
+arms of a detector like this let me just
+
+ align:start position:0%
+arms of a detector like this let me just
+ 
+
+ align:start position:0%
+arms of a detector like this let me just
+do one more way of understanding how it
+
+ align:start position:0%
+do one more way of understanding how it
+ 
+
+ align:start position:0%
+do one more way of understanding how it
+is the gravitational wave leaves an
+
+ align:start position:0%
+is the gravitational wave leaves an
+ 
+
+ align:start position:0%
+is the gravitational wave leaves an
+imprint on these two separated particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you look at that first naive
+
+ align:start position:0%
+so when you look at that first naive
+ 
+
+ align:start position:0%
+so when you look at that first naive
+calculation I did the fact that I got no
+
+ align:start position:0%
+calculation I did the fact that I got no
+ 
+
+ align:start position:0%
+calculation I did the fact that I got no
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+I sort of joked that we did a dumb
+
+ align:start position:0%
+I sort of joked that we did a dumb
+ 
+
+ align:start position:0%
+I sort of joked that we did a dumb
+calculation to be fair it wasn't that
+
+ align:start position:0%
+calculation to be fair it wasn't that
+ 
+
+ align:start position:0%
+calculation to be fair it wasn't that
+dumb okay what weird the first thing you
+
+ align:start position:0%
+dumb okay what weird the first thing you
+ 
+
+ align:start position:0%
+dumb okay what weird the first thing you
+usually think of doing when you want to
+
+ align:start position:0%
+usually think of doing when you want to
+ 
+
+ align:start position:0%
+usually think of doing when you want to
+understand the motion of the body in
+
+ align:start position:0%
+understand the motion of the body in
+ 
+
+ align:start position:0%
+understand the motion of the body in
+space-time as you look at Judy's ex
+
+ align:start position:0%
+space-time as you look at Judy's ex
+ 
+
+ align:start position:0%
+space-time as you look at Judy's ex
+Judy's acceleration with respect to the
+
+ align:start position:0%
+Judy's acceleration with respect to the
+ 
+
+ align:start position:0%
+Judy's acceleration with respect to the
+freefall frame is zero and that's
+
+ align:start position:0%
+freefall frame is zero and that's
+ 
+
+ align:start position:0%
+freefall frame is zero and that's
+exactly what we end up getting it's
+
+ align:start position:0%
+exactly what we end up getting it's
+ 
+
+ align:start position:0%
+exactly what we end up getting it's
+basically just saying ah even in a
+
+ align:start position:0%
+basically just saying ah even in a
+ 
+
+ align:start position:0%
+basically just saying ah even in a
+gravitational wave my two bodies are
+
+ align:start position:0%
+gravitational wave my two bodies are
+ 
+
+ align:start position:0%
+gravitational wave my two bodies are
+moving on Judy's ex if I have two
+
+ align:start position:0%
+moving on Judy's ex if I have two
+ 
+
+ align:start position:0%
+moving on Judy's ex if I have two
+separated bodies like I have in this
+
+ align:start position:0%
+separated bodies like I have in this
+ 
+
+ align:start position:0%
+separated bodies like I have in this
+calculation where I just calculated the
+
+ align:start position:0%
+calculation where I just calculated the
+ 
+
+ align:start position:0%
+calculation where I just calculated the
+variation in the time of arrival of
+
+ align:start position:0%
+variation in the time of arrival of
+ 
+
+ align:start position:0%
+variation in the time of arrival of
+light pulses one of the tools we learned
+
+ align:start position:0%
+light pulses one of the tools we learned
+ 
+
+ align:start position:0%
+light pulses one of the tools we learned
+is that I can have - Judy's x2 freefall
+
+ align:start position:0%
+is that I can have - Judy's x2 freefall
+ 
+
+ align:start position:0%
+is that I can have - Judy's x2 freefall
+trajectories that deviate from one
+
+ align:start position:0%
+trajectories that deviate from one
+ 
+
+ align:start position:0%
+trajectories that deviate from one
+another so let's look at the Judy's ik
+
+ align:start position:0%
+another so let's look at the Judy's ik
+ 
+
+ align:start position:0%
+another so let's look at the Judy's ik
+deviation of the freefall world lines of
+
+ align:start position:0%
+deviation of the freefall world lines of
+ 
+
+ align:start position:0%
+deviation of the freefall world lines of
+these two bodies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm gonna as I did when I did my
+
+ align:start position:0%
+so I'm gonna as I did when I did my
+ 
+
+ align:start position:0%
+so I'm gonna as I did when I did my
+Judy's a calculation I'm going to take
+
+ align:start position:0%
+Judy's a calculation I'm going to take
+ 
+
+ align:start position:0%
+Judy's a calculation I'm going to take
+them to initially be close enough that
+
+ align:start position:0%
+them to initially be close enough that
+ 
+
+ align:start position:0%
+them to initially be close enough that
+they have the same for velocity and if
+
+ align:start position:0%
+they have the same for velocity and if
+ 
+
+ align:start position:0%
+they have the same for velocity and if
+you want to be careful about counting
+
+ align:start position:0%
+you want to be careful about counting
+ 
+
+ align:start position:0%
+you want to be careful about counting
+orders here you can imagine when the
+
+ align:start position:0%
+orders here you can imagine when the
+ 
+
+ align:start position:0%
+orders here you can imagine when the
+gravitational wave comes along that one
+
+ align:start position:0%
+gravitational wave comes along that one
+ 
+
+ align:start position:0%
+gravitational wave comes along that one
+or both of them might pick up a
+
+ align:start position:0%
+or both of them might pick up a
+ 
+
+ align:start position:0%
+or both of them might pick up a
+correction of this that's an order H
+
+ align:start position:0%
+correction of this that's an order H
+ 
+
+ align:start position:0%
+correction of this that's an order H
+okay depends on what kind of coordinate
+
+ align:start position:0%
+okay depends on what kind of coordinate
+ 
+
+ align:start position:0%
+okay depends on what kind of coordinate
+system you pick up but the key thing is
+
+ align:start position:0%
+system you pick up but the key thing is
+ 
+
+ align:start position:0%
+system you pick up but the key thing is
+that they start out like this the
+
+ align:start position:0%
+that they start out like this the
+ 
+
+ align:start position:0%
+that they start out like this the
+gravitational wave may come along and it
+
+ align:start position:0%
+gravitational wave may come along and it
+ 
+
+ align:start position:0%
+gravitational wave may come along and it
+will move them around a little bit okay
+
+ align:start position:0%
+will move them around a little bit okay
+ 
+
+ align:start position:0%
+will move them around a little bit okay
+but the amount is going to move them the
+
+ align:start position:0%
+but the amount is going to move them the
+ 
+
+ align:start position:0%
+but the amount is going to move them the
+amount of velocity that they're gonna
+
+ align:start position:0%
+amount of velocity that they're gonna
+ 
+
+ align:start position:0%
+amount of velocity that they're gonna
+pick up not displacement they're going
+
+ align:start position:0%
+pick up not displacement they're going
+ 
+
+ align:start position:0%
+pick up not displacement they're going
+to get from their initial position if
+
+ align:start position:0%
+to get from their initial position if
+ 
+
+ align:start position:0%
+to get from their initial position if
+they're at rest it can only be of order
+
+ align:start position:0%
+they're at rest it can only be of order
+ 
+
+ align:start position:0%
+they're at rest it can only be of order
+the H that you're trying to measure
+
+ align:start position:0%
+the H that you're trying to measure
+ 
+
+ align:start position:0%
+the H that you're trying to measure
+there so I'll remind you the equation of
+
+ align:start position:0%
+there so I'll remind you the equation of
+ 
+
+ align:start position:0%
+there so I'll remind you the equation of
+daeviation equation of Gd is a deviation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it defines a sort of proper acceleration
+
+ align:start position:0%
+it defines a sort of proper acceleration
+ 
+
+ align:start position:0%
+it defines a sort of proper acceleration
+acting on whoops that's a typo it is the
+
+ align:start position:0%
+acting on whoops that's a typo it is the
+ 
+
+ align:start position:0%
+acting on whoops that's a typo it is the
+proper cell acceleration on a vector C
+
+ align:start position:0%
+proper cell acceleration on a vector C
+ 
+
+ align:start position:0%
+proper cell acceleration on a vector C
+that defines in a precise geometric way
+
+ align:start position:0%
+that defines in a precise geometric way
+ 
+
+ align:start position:0%
+that defines in a precise geometric way
+the separation of two geodesics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what it looks like is the Riemann
+
+ align:start position:0%
+and what it looks like is the Riemann
+ 
+
+ align:start position:0%
+and what it looks like is the Riemann
+curvature of your space-time contracted
+
+ align:start position:0%
+curvature of your space-time contracted
+ 
+
+ align:start position:0%
+curvature of your space-time contracted
+on the for velocity of your bodies and
+
+ align:start position:0%
+on the for velocity of your bodies and
+ 
+
+ align:start position:0%
+on the for velocity of your bodies and
+that separation vector C so linearizing
+
+ align:start position:0%
+that separation vector C so linearizing
+ 
+
+ align:start position:0%
+that separation vector C so linearizing
+everything bearing in mind that our will
+
+ align:start position:0%
+everything bearing in mind that our will
+ 
+
+ align:start position:0%
+everything bearing in mind that our will
+itself be of order H and that's any
+
+ align:start position:0%
+itself be of order H and that's any
+ 
+
+ align:start position:0%
+itself be of order H and that's any
+difference between the proper time along
+
+ align:start position:0%
+difference between the proper time along
+ 
+
+ align:start position:0%
+difference between the proper time along
+these things and the coordinate time if
+
+ align:start position:0%
+these things and the coordinate time if
+ 
+
+ align:start position:0%
+these things and the coordinate time if
+a particular clock is also gonna be of
+
+ align:start position:0%
+a particular clock is also gonna be of
+ 
+
+ align:start position:0%
+a particular clock is also gonna be of
+order H they are small enough that this
+
+ align:start position:0%
+order H they are small enough that this
+ 
+
+ align:start position:0%
+order H they are small enough that this
+equation becomes it looks like this
+
+ align:start position:0%
+equation becomes it looks like this
+ 
+
+ align:start position:0%
+equation becomes it looks like this
+notice I'm only looking at the spatial
+
+ align:start position:0%
+notice I'm only looking at the spatial
+ 
+
+ align:start position:0%
+notice I'm only looking at the spatial
+components of the separation vector C ok
+
+ align:start position:0%
+components of the separation vector C ok
+ 
+
+ align:start position:0%
+components of the separation vector C ok
+that's because since I'm working since
+
+ align:start position:0%
+that's because since I'm working since
+ 
+
+ align:start position:0%
+that's because since I'm working since
+this is what my floor velocity looks
+
+ align:start position:0%
+this is what my floor velocity looks
+ 
+
+ align:start position:0%
+this is what my floor velocity looks
+like I'm gonna pick out the 0 0
+
+ align:start position:0%
+like I'm gonna pick out the 0 0
+ 
+
+ align:start position:0%
+like I'm gonna pick out the 0 0
+components of these things and don't
+
+ align:start position:0%
+components of these things and don't
+ 
+
+ align:start position:0%
+components of these things and don't
+forget Limon is anti-symmetric when I
+
+ align:start position:0%
+forget Limon is anti-symmetric when I
+ 
+
+ align:start position:0%
+forget Limon is anti-symmetric when I
+exchange either indices 1 & 2 or indices
+
+ align:start position:0%
+exchange either indices 1 & 2 or indices
+ 
+
+ align:start position:0%
+exchange either indices 1 & 2 or indices
+3 & 4 and because of that it's just the
+
+ align:start position:0%
+3 & 4 and because of that it's just the
+ 
+
+ align:start position:0%
+3 & 4 and because of that it's just the
+time light component of this guy is
+
+ align:start position:0%
+time light component of this guy is
+ 
+
+ align:start position:0%
+time light component of this guy is
+going to be an uninteresting thing I
+
+ align:start position:0%
+going to be an uninteresting thing I
+ 
+
+ align:start position:0%
+going to be an uninteresting thing I
+will just get that is equal to the
+
+ align:start position:0%
+will just get that is equal to the
+ 
+
+ align:start position:0%
+will just get that is equal to the
+acceleration of the time light component
+
+ align:start position:0%
+acceleration of the time light component
+ 
+
+ align:start position:0%
+acceleration of the time light component
+is zero so it doesn't really matter okay
+
+ align:start position:0%
+is zero so it doesn't really matter okay
+ 
+
+ align:start position:0%
+is zero so it doesn't really matter okay
+so this is telling me that the judy's
+
+ align:start position:0%
+so this is telling me that the judy's
+ 
+
+ align:start position:0%
+so this is telling me that the judy's
+except eration of these two world lines
+
+ align:start position:0%
+except eration of these two world lines
+ 
+
+ align:start position:0%
+except eration of these two world lines
+is it's a second-order equation in time
+
+ align:start position:0%
+is it's a second-order equation in time
+ 
+
+ align:start position:0%
+is it's a second-order equation in time
+and it's proportional to the separation
+
+ align:start position:0%
+and it's proportional to the separation
+ 
+
+ align:start position:0%
+and it's proportional to the separation
+itself we need to work out all of these
+
+ align:start position:0%
+itself we need to work out all of these
+ 
+
+ align:start position:0%
+itself we need to work out all of these
+complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is a fairly straightforward
+
+ align:start position:0%
+that is a fairly straightforward
+ 
+
+ align:start position:0%
+that is a fairly straightforward
+exercise and I would just report to you
+
+ align:start position:0%
+exercise and I would just report to you
+ 
+
+ align:start position:0%
+exercise and I would just report to you
+the results brief aside if you wants to
+
+ align:start position:0%
+the results brief aside if you wants to
+ 
+
+ align:start position:0%
+the results brief aside if you wants to
+sort of verify the results I'm about to
+
+ align:start position:0%
+sort of verify the results I'm about to
+ 
+
+ align:start position:0%
+sort of verify the results I'm about to
+write out here you could go into you
+
+ align:start position:0%
+write out here you could go into you
+ 
+
+ align:start position:0%
+write out here you could go into you
+could look up the definition of the
+
+ align:start position:0%
+could look up the definition of the
+ 
+
+ align:start position:0%
+could look up the definition of the
+Riemann tensor bear in mind that you are
+
+ align:start position:0%
+Riemann tensor bear in mind that you are
+ 
+
+ align:start position:0%
+Riemann tensor bear in mind that you are
+doing things at linear orders you can
+
+ align:start position:0%
+doing things at linear orders you can
+ 
+
+ align:start position:0%
+doing things at linear orders you can
+throw away the terms of like connection
+
+ align:start position:0%
+throw away the terms of like connection
+ 
+
+ align:start position:0%
+throw away the terms of like connection
+times connection it's just derivatives
+
+ align:start position:0%
+times connection it's just derivatives
+ 
+
+ align:start position:0%
+times connection it's just derivatives
+of the connection that are going to
+
+ align:start position:0%
+of the connection that are going to
+ 
+
+ align:start position:0%
+of the connection that are going to
+matter at linear order but even so it's
+
+ align:start position:0%
+matter at linear order but even so it's
+ 
+
+ align:start position:0%
+matter at linear order but even so it's
+you know it's a bit of a bit of a grotty
+
+ align:start position:0%
+you know it's a bit of a bit of a grotty
+ 
+
+ align:start position:0%
+you know it's a bit of a bit of a grotty
+calculation I am as I begin to
+
+ align:start position:0%
+calculation I am as I begin to
+ 
+
+ align:start position:0%
+calculation I am as I begin to
+reorganize the problem sets associated
+
+ align:start position:0%
+reorganize the problem sets associated
+ 
+
+ align:start position:0%
+reorganize the problem sets associated
+with this class under the new system
+
+ align:start position:0%
+with this class under the new system
+ 
+
+ align:start position:0%
+with this class under the new system
+that MIT is currently operating on I
+
+ align:start position:0%
+that MIT is currently operating on I
+ 
+
+ align:start position:0%
+that MIT is currently operating on I
+will soon be releasing a few Mathematica
+
+ align:start position:0%
+will soon be releasing a few Mathematica
+ 
+
+ align:start position:0%
+will soon be releasing a few Mathematica
+notebooks that are very useful tools for
+
+ align:start position:0%
+notebooks that are very useful tools for
+ 
+
+ align:start position:0%
+notebooks that are very useful tools for
+doing tedious calculations like
+
+ align:start position:0%
+doing tedious calculations like
+ 
+
+ align:start position:0%
+doing tedious calculations like
+computation of Riemann curvature tensor
+
+ align:start position:0%
+computation of Riemann curvature tensor
+ 
+
+ align:start position:0%
+computation of Riemann curvature tensor
+components okay so I will put a few of
+
+ align:start position:0%
+components okay so I will put a few of
+ 
+
+ align:start position:0%
+components okay so I will put a few of
+those things up there if you would like
+
+ align:start position:0%
+those things up there if you would like
+ 
+
+ align:start position:0%
+those things up there if you would like
+to validate some of the things that I am
+
+ align:start position:0%
+to validate some of the things that I am
+ 
+
+ align:start position:0%
+to validate some of the things that I am
+computing that is where you will find a
+
+ align:start position:0%
+computing that is where you will find a
+ 
+
+ align:start position:0%
+computing that is where you will find a
+good way to test this so anyway the
+
+ align:start position:0%
+good way to test this so anyway the
+ 
+
+ align:start position:0%
+good way to test this so anyway the
+non-zero Riemann components so at linear
+
+ align:start position:0%
+non-zero Riemann components so at linear
+ 
+
+ align:start position:0%
+non-zero Riemann components so at linear
+order you have are X 0 X 0 bear in mind
+
+ align:start position:0%
+order you have are X 0 X 0 bear in mind
+ 
+
+ align:start position:0%
+order you have are X 0 X 0 bear in mind
+that linear order you are raising and
+
+ align:start position:0%
+that linear order you are raising and
+ 
+
+ align:start position:0%
+that linear order you are raising and
+lowering indices with the metric of flat
+
+ align:start position:0%
+lowering indices with the metric of flat
+ 
+
+ align:start position:0%
+lowering indices with the metric of flat
+space-time so that's the same thing as
+
+ align:start position:0%
+space-time so that's the same thing as
+ 
+
+ align:start position:0%
+space-time so that's the same thing as
+this and this turns out to be minus 1/2
+
+ align:start position:0%
+this and this turns out to be minus 1/2
+ 
+
+ align:start position:0%
+this and this turns out to be minus 1/2
+to time derivatives of H X X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y 0 y 0 your yo-yo component pretty much
+
+ align:start position:0%
+y 0 y 0 your yo-yo component pretty much
+ 
+
+ align:start position:0%
+y 0 y 0 your yo-yo component pretty much
+looks exactly the same but it's to time
+
+ align:start position:0%
+looks exactly the same but it's to time
+ 
+
+ align:start position:0%
+looks exactly the same but it's to time
+derivatives of the YY piece remember
+
+ align:start position:0%
+derivatives of the YY piece remember
+ 
+
+ align:start position:0%
+derivatives of the YY piece remember
+though I've erased it a while ago there
+
+ align:start position:0%
+though I've erased it a while ago there
+ 
+
+ align:start position:0%
+though I've erased it a while ago there
+are some constraints that we found due
+
+ align:start position:0%
+are some constraints that we found due
+ 
+
+ align:start position:0%
+are some constraints that we found due
+to the fact that my original H mu nu has
+
+ align:start position:0%
+to the fact that my original H mu nu has
+ 
+
+ align:start position:0%
+to the fact that my original H mu nu has
+to be its spatial piece has to be
+
+ align:start position:0%
+to be its spatial piece has to be
+ 
+
+ align:start position:0%
+to be its spatial piece has to be
+traceless in particular we found h YY
+
+ align:start position:0%
+traceless in particular we found h YY
+ 
+
+ align:start position:0%
+traceless in particular we found h YY
+was minus HX X so I can remove that
+
+ align:start position:0%
+was minus HX X so I can remove that
+ 
+
+ align:start position:0%
+was minus HX X so I can remove that
+additional function and just leave
+
+ align:start position:0%
+additional function and just leave
+ 
+
+ align:start position:0%
+additional function and just leave
+things in terms of HX X and our final
+
+ align:start position:0%
+things in terms of HX X and our final
+ 
+
+ align:start position:0%
+things in terms of HX X and our final
+nonzero component looks like this all
+
+ align:start position:0%
+nonzero component looks like this all
+ 
+
+ align:start position:0%
+nonzero component looks like this all
+others are either 0 or related by a
+
+ align:start position:0%
+others are either 0 or related by a
+ 
+
+ align:start position:0%
+others are either 0 or related by a
+symmetry so notice although I've written
+
+ align:start position:0%
+symmetry so notice although I've written
+ 
+
+ align:start position:0%
+symmetry so notice although I've written
+down three different components here
+
+ align:start position:0%
+down three different components here
+ 
+
+ align:start position:0%
+down three different components here
+there's only only two ok because the
+
+ align:start position:0%
+there's only only two ok because the
+ 
+
+ align:start position:0%
+there's only only two ok because the
+symmetry that that's you know it's not a
+
+ align:start position:0%
+symmetry that that's you know it's not a
+ 
+
+ align:start position:0%
+symmetry that that's you know it's not a
+symmetry of Rima but the symmetry
+
+ align:start position:0%
+symmetry of Rima but the symmetry
+ 
+
+ align:start position:0%
+symmetry of Rima but the symmetry
+associated with the trace free nature of
+
+ align:start position:0%
+associated with the trace free nature of
+ 
+
+ align:start position:0%
+associated with the trace free nature of
+h idat t made these two equal to each
+
+ align:start position:0%
+h idat t made these two equal to each
+ 
+
+ align:start position:0%
+h idat t made these two equal to each
+other so this and this are really the
+
+ align:start position:0%
+other so this and this are really the
+ 
+
+ align:start position:0%
+other so this and this are really the
+only independent degrees of freedom here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright let's plug this into the
+
+ align:start position:0%
+alright let's plug this into the
+ 
+
+ align:start position:0%
+alright let's plug this into the
+equation of G DS deviation this guy and
+
+ align:start position:0%
+equation of G DS deviation this guy and
+ 
+
+ align:start position:0%
+equation of G DS deviation this guy and
+see what we got
+
+ align:start position:0%
+see what we got
+ 
+
+ align:start position:0%
+see what we got
+so what we get is an equation governing
+
+ align:start position:0%
+so what we get is an equation governing
+ 
+
+ align:start position:0%
+so what we get is an equation governing
+the acceleration of the X component of
+
+ align:start position:0%
+the acceleration of the X component of
+ 
+
+ align:start position:0%
+the acceleration of the X component of
+deviation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it is let's make a couple of
+
+ align:start position:0%
+here it is let's make a couple of
+ 
+
+ align:start position:0%
+here it is let's make a couple of
+assumptions and try to understand what
+
+ align:start position:0%
+assumptions and try to understand what
+ 
+
+ align:start position:0%
+assumptions and try to understand what
+this is telling us so what I'm going to
+
+ align:start position:0%
+this is telling us so what I'm going to
+ 
+
+ align:start position:0%
+this is telling us so what I'm going to
+do is let's assume this is the first
+
+ align:start position:0%
+do is let's assume this is the first
+ 
+
+ align:start position:0%
+do is let's assume this is the first
+assumption is necessitated by the idea
+
+ align:start position:0%
+assumption is necessitated by the idea
+ 
+
+ align:start position:0%
+assumption is necessitated by the idea
+that I can do linearized gravity so I'm
+
+ align:start position:0%
+that I can do linearized gravity so I'm
+ 
+
+ align:start position:0%
+that I can do linearized gravity so I'm
+gonna assume that these guys are all
+
+ align:start position:0%
+gonna assume that these guys are all
+ 
+
+ align:start position:0%
+gonna assume that these guys are all
+very small and I will imagine that my
+
+ align:start position:0%
+very small and I will imagine that my
+ 
+
+ align:start position:0%
+very small and I will imagine that my
+displacement vectors have some piece
+
+ align:start position:0%
+displacement vectors have some piece
+ 
+
+ align:start position:0%
+displacement vectors have some piece
+which basically is time constant okay it
+
+ align:start position:0%
+which basically is time constant okay it
+ 
+
+ align:start position:0%
+which basically is time constant okay it
+does not change and that there's a bit
+
+ align:start position:0%
+does not change and that there's a bit
+ 
+
+ align:start position:0%
+does not change and that there's a bit
+that will be of order H that describes
+
+ align:start position:0%
+that will be of order H that describes
+ 
+
+ align:start position:0%
+that will be of order H that describes
+how the separation of my two bodies
+
+ align:start position:0%
+how the separation of my two bodies
+ 
+
+ align:start position:0%
+how the separation of my two bodies
+responds to this incoming field okay so
+
+ align:start position:0%
+responds to this incoming field okay so
+ 
+
+ align:start position:0%
+responds to this incoming field okay so
+what I'm gonna do when you go and you
+
+ align:start position:0%
+what I'm gonna do when you go and you
+ 
+
+ align:start position:0%
+what I'm gonna do when you go and you
+plug this in assume that this guy is
+
+ align:start position:0%
+plug this in assume that this guy is
+ 
+
+ align:start position:0%
+plug this in assume that this guy is
+constant in time and this one varies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'm going to do is imagine I don't
+
+ align:start position:0%
+what I'm going to do is imagine I don't
+ 
+
+ align:start position:0%
+what I'm going to do is imagine I don't
+just have two bodies imagine I have a
+
+ align:start position:0%
+just have two bodies imagine I have a
+ 
+
+ align:start position:0%
+just have two bodies imagine I have a
+ring of bodies okay so suppose I have
+
+ align:start position:0%
+ring of bodies okay so suppose I have
+ 
+
+ align:start position:0%
+ring of bodies okay so suppose I have
+got to make coordinate axes here
+
+ align:start position:0%
+got to make coordinate axes here
+ 
+
+ align:start position:0%
+got to make coordinate axes here
+horizontal is X vertical and the board
+
+ align:start position:0%
+horizontal is X vertical and the board
+ 
+
+ align:start position:0%
+horizontal is X vertical and the board
+is y and so imagine I have a ring of
+
+ align:start position:0%
+is y and so imagine I have a ring of
+ 
+
+ align:start position:0%
+is y and so imagine I have a ring of
+bodies like so and let's consider the
+
+ align:start position:0%
+bodies like so and let's consider the
+ 
+
+ align:start position:0%
+bodies like so and let's consider the
+following limit let's imagine that my HX
+
+ align:start position:0%
+following limit let's imagine that my HX
+ 
+
+ align:start position:0%
+following limit let's imagine that my HX
+X is some function that is sinusoidally
+
+ align:start position:0%
+X is some function that is sinusoidally
+ 
+
+ align:start position:0%
+X is some function that is sinusoidally
+varying in time and my H X Y is zero
+
+ align:start position:0%
+varying in time and my H X Y is zero
+ 
+
+ align:start position:0%
+varying in time and my H X Y is zero
+okay I just want to call at the as we
+
+ align:start position:0%
+okay I just want to call at the as we
+ 
+
+ align:start position:0%
+okay I just want to call at the as we
+saw there's really only two degrees of
+
+ align:start position:0%
+saw there's really only two degrees of
+ 
+
+ align:start position:0%
+saw there's really only two degrees of
+freedom in this field and in the way
+
+ align:start position:0%
+freedom in this field and in the way
+ 
+
+ align:start position:0%
+freedom in this field and in the way
+that we formulated it it's gonna be
+
+ align:start position:0%
+that we formulated it it's gonna be
+ 
+
+ align:start position:0%
+that we formulated it it's gonna be
+encapsulated by these two functions xx
+
+ align:start position:0%
+encapsulated by these two functions xx
+ 
+
+ align:start position:0%
+encapsulated by these two functions xx
+and XY so let's just look at one let's
+
+ align:start position:0%
+and XY so let's just look at one let's
+ 
+
+ align:start position:0%
+and XY so let's just look at one let's
+just look at the influence of the HX X
+
+ align:start position:0%
+just look at the influence of the HX X
+ 
+
+ align:start position:0%
+just look at the influence of the HX X
+okay so when you do this you essentially
+
+ align:start position:0%
+okay so when you do this you essentially
+ 
+
+ align:start position:0%
+okay so when you do this you essentially
+have the second derivative of CX looks
+
+ align:start position:0%
+have the second derivative of CX looks
+ 
+
+ align:start position:0%
+have the second derivative of CX looks
+like two derivatives of your X field
+
+ align:start position:0%
+like two derivatives of your X field
+ 
+
+ align:start position:0%
+like two derivatives of your X field
+your X X field x CX and two derivatives
+
+ align:start position:0%
+your X X field x CX and two derivatives
+ 
+
+ align:start position:0%
+your X X field x CX and two derivatives
+you're sort of acceleration in the Y
+
+ align:start position:0%
+you're sort of acceleration in the Y
+ 
+
+ align:start position:0%
+you're sort of acceleration in the Y
+Direction is minus those two derivatives
+
+ align:start position:0%
+Direction is minus those two derivatives
+ 
+
+ align:start position:0%
+Direction is minus those two derivatives
+of your field times CY so what this is
+
+ align:start position:0%
+of your field times CY so what this is
+ 
+
+ align:start position:0%
+of your field times CY so what this is
+going to do if you think about the way
+
+ align:start position:0%
+going to do if you think about the way
+ 
+
+ align:start position:0%
+going to do if you think about the way
+this is going to act on these things
+
+ align:start position:0%
+this is going to act on these things
+ 
+
+ align:start position:0%
+this is going to act on these things
+you're gonna get a sinusoidal
+
+ align:start position:0%
+you're gonna get a sinusoidal
+ 
+
+ align:start position:0%
+you're gonna get a sinusoidal
+acceleration associated with the
+
+ align:start position:0%
+acceleration associated with the
+ 
+
+ align:start position:0%
+acceleration associated with the
+displacement of this little sea of
+
+ align:start position:0%
+displacement of this little sea of
+ 
+
+ align:start position:0%
+displacement of this little sea of
+freely falling bodies as the gravitation
+
+ align:start position:0%
+freely falling bodies as the gravitation
+ 
+
+ align:start position:0%
+freely falling bodies as the gravitation
+wave comes along and it's going to do so
+
+ align:start position:0%
+wave comes along and it's going to do so
+ 
+
+ align:start position:0%
+wave comes along and it's going to do so
+in such a way that the displacement in
+
+ align:start position:0%
+in such a way that the displacement in
+ 
+
+ align:start position:0%
+in such a way that the displacement in
+the X direction does the opposite of
+
+ align:start position:0%
+the X direction does the opposite of
+ 
+
+ align:start position:0%
+the X direction does the opposite of
+what the displacement in the Y direction
+
+ align:start position:0%
+what the displacement in the Y direction
+ 
+
+ align:start position:0%
+what the displacement in the Y direction
+is doing so as time passes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you'll find that so initially let's say
+
+ align:start position:0%
+you'll find that so initially let's say
+ 
+
+ align:start position:0%
+you'll find that so initially let's say
+it stretches along X but then squeezes
+
+ align:start position:0%
+it stretches along X but then squeezes
+ 
+
+ align:start position:0%
+it stretches along X but then squeezes
+along Y it's a sinusoid so quarter of a
+
+ align:start position:0%
+along Y it's a sinusoid so quarter of a
+ 
+
+ align:start position:0%
+along Y it's a sinusoid so quarter of a
+cycle later it's back to being a circle
+
+ align:start position:0%
+cycle later it's back to being a circle
+ 
+
+ align:start position:0%
+cycle later it's back to being a circle
+and quarter of a second later it
+
+ align:start position:0%
+and quarter of a second later it
+ 
+
+ align:start position:0%
+and quarter of a second later it
+stretches along Y and squeeze those
+
+ align:start position:0%
+stretches along Y and squeeze those
+ 
+
+ align:start position:0%
+stretches along Y and squeeze those
+along X let's consider the limit now
+
+ align:start position:0%
+along X let's consider the limit now
+ 
+
+ align:start position:0%
+along X let's consider the limit now
+where H xx is equal to zero and H X Y is
+
+ align:start position:0%
+where H xx is equal to zero and H X Y is
+ 
+
+ align:start position:0%
+where H xx is equal to zero and H X Y is
+some sinusoid so I start out with my
+
+ align:start position:0%
+some sinusoid so I start out with my
+ 
+
+ align:start position:0%
+some sinusoid so I start out with my
+circle look at your equations over here
+
+ align:start position:0%
+circle look at your equations over here
+ 
+
+ align:start position:0%
+circle look at your equations over here
+think about what they're going to do now
+
+ align:start position:0%
+think about what they're going to do now
+ 
+
+ align:start position:0%
+think about what they're going to do now
+we're going to find that the change in X
+
+ align:start position:0%
+we're going to find that the change in X
+ 
+
+ align:start position:0%
+we're going to find that the change in X
+and the change in Y is correlated so
+
+ align:start position:0%
+and the change in Y is correlated so
+ 
+
+ align:start position:0%
+and the change in Y is correlated so
+this guy stretches it out into an
+
+ align:start position:0%
+this guy stretches it out into an
+ 
+
+ align:start position:0%
+this guy stretches it out into an
+ellipse along a 45-degree line cycle
+
+ align:start position:0%
+ellipse along a 45-degree line cycle
+ 
+
+ align:start position:0%
+ellipse along a 45-degree line cycle
+later it's back to being a circle and a
+
+ align:start position:0%
+later it's back to being a circle and a
+ 
+
+ align:start position:0%
+later it's back to being a circle and a
+quarter of a second later it does the
+
+ align:start position:0%
+quarter of a second later it does the
+ 
+
+ align:start position:0%
+quarter of a second later it does the
+same thing with opposite sign these two
+
+ align:start position:0%
+same thing with opposite sign these two
+ 
+
+ align:start position:0%
+same thing with opposite sign these two
+fields my HX X and my H XY are what we
+
+ align:start position:0%
+fields my HX X and my H XY are what we
+ 
+
+ align:start position:0%
+fields my HX X and my H XY are what we
+call the fundamental polarizations of
+
+ align:start position:0%
+call the fundamental polarizations of
+ 
+
+ align:start position:0%
+call the fundamental polarizations of
+the gravitational wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polarization states are only defined
+
+ align:start position:0%
+polarization states are only defined
+ 
+
+ align:start position:0%
+polarization states are only defined
+with respect to a particular set of
+
+ align:start position:0%
+with respect to a particular set of
+ 
+
+ align:start position:0%
+with respect to a particular set of
+basis basis vectors so if I make my
+
+ align:start position:0%
+basis basis vectors so if I make my
+ 
+
+ align:start position:0%
+basis basis vectors so if I make my
+basis vectors B this x and y we call
+
+ align:start position:0%
+basis vectors B this x and y we call
+ 
+
+ align:start position:0%
+basis vectors B this x and y we call
+this one for reasons that I hope are
+
+ align:start position:0%
+this one for reasons that I hope are
+ 
+
+ align:start position:0%
+this one for reasons that I hope are
+obvious the plus polarization okay
+
+ align:start position:0%
+obvious the plus polarization okay
+ 
+
+ align:start position:0%
+obvious the plus polarization okay
+the gravitational waves acts as a tidal
+
+ align:start position:0%
+the gravitational waves acts as a tidal
+ 
+
+ align:start position:0%
+the gravitational waves acts as a tidal
+stretch and squeeze notice what's going
+
+ align:start position:0%
+stretch and squeeze notice what's going
+ 
+
+ align:start position:0%
+stretch and squeeze notice what's going
+on here I stretch along this axis
+
+ align:start position:0%
+on here I stretch along this axis
+ 
+
+ align:start position:0%
+on here I stretch along this axis
+squeeze along this one quarter of a
+
+ align:start position:0%
+squeeze along this one quarter of a
+ 
+
+ align:start position:0%
+squeeze along this one quarter of a
+second ladle later I squeeze along this
+
+ align:start position:0%
+second ladle later I squeeze along this
+ 
+
+ align:start position:0%
+second ladle later I squeeze along this
+one stretch along that one so I get a
+
+ align:start position:0%
+one stretch along that one so I get a
+ 
+
+ align:start position:0%
+one stretch along that one so I get a
+title stretch and squeeze where the main
+
+ align:start position:0%
+title stretch and squeeze where the main
+ 
+
+ align:start position:0%
+title stretch and squeeze where the main
+directions along which the stretch and
+
+ align:start position:0%
+directions along which the stretch and
+ 
+
+ align:start position:0%
+directions along which the stretch and
+squeeze are happening is plus shaped
+
+ align:start position:0%
+squeeze are happening is plus shaped
+ 
+
+ align:start position:0%
+squeeze are happening is plus shaped
+with respect to these axes this one is
+
+ align:start position:0%
+with respect to these axes this one is
+ 
+
+ align:start position:0%
+with respect to these axes this one is
+known as the cross polarization you also
+
+ align:start position:0%
+known as the cross polarization you also
+ 
+
+ align:start position:0%
+known as the cross polarization you also
+have a tidal stretch and squeeze but the
+
+ align:start position:0%
+have a tidal stretch and squeeze but the
+ 
+
+ align:start position:0%
+have a tidal stretch and squeeze but the
+lines of force in this case are along
+
+ align:start position:0%
+lines of force in this case are along
+ 
+
+ align:start position:0%
+lines of force in this case are along
+axes that have a an X shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so level of eight 962 this is this is
+
+ align:start position:0%
+so level of eight 962 this is this is
+ 
+
+ align:start position:0%
+so level of eight 962 this is this is
+all we're gonna say about the way that
+
+ align:start position:0%
+all we're gonna say about the way that
+ 
+
+ align:start position:0%
+all we're gonna say about the way that
+these things act on how gravitational
+
+ align:start position:0%
+these things act on how gravitational
+ 
+
+ align:start position:0%
+these things act on how gravitational
+waves act and what their observables are
+
+ align:start position:0%
+waves act and what their observables are
+ 
+
+ align:start position:0%
+waves act and what their observables are
+and I deliberately chose to wear my LIGO
+
+ align:start position:0%
+and I deliberately chose to wear my LIGO
+ 
+
+ align:start position:0%
+and I deliberately chose to wear my LIGO
+hat today because what LIGO does is look
+
+ align:start position:0%
+hat today because what LIGO does is look
+ 
+
+ align:start position:0%
+hat today because what LIGO does is look
+for these tidal stretches and squeezes
+
+ align:start position:0%
+for these tidal stretches and squeezes
+ 
+
+ align:start position:0%
+for these tidal stretches and squeezes
+the way it does so so obviously you it's
+
+ align:start position:0%
+the way it does so so obviously you it's
+ 
+
+ align:start position:0%
+the way it does so so obviously you it's
+technologically not really feasible to
+
+ align:start position:0%
+technologically not really feasible to
+ 
+
+ align:start position:0%
+technologically not really feasible to
+set up a ring like this but what you can
+
+ align:start position:0%
+set up a ring like this but what you can
+ 
+
+ align:start position:0%
+set up a ring like this but what you can
+do is sample the ring here in here it's
+
+ align:start position:0%
+do is sample the ring here in here it's
+ 
+
+ align:start position:0%
+do is sample the ring here in here it's
+a little bit better to do on the plus
+
+ align:start position:0%
+a little bit better to do on the plus
+ 
+
+ align:start position:0%
+a little bit better to do on the plus
+crawl ization plot so you make an
+
+ align:start position:0%
+crawl ization plot so you make an
+ 
+
+ align:start position:0%
+crawl ization plot so you make an
+experimental setup that samples the ring
+
+ align:start position:0%
+experimental setup that samples the ring
+ 
+
+ align:start position:0%
+experimental setup that samples the ring
+here in here and if a gravitational wave
+
+ align:start position:0%
+here in here and if a gravitational wave
+ 
+
+ align:start position:0%
+here in here and if a gravitational wave
+comes along and it's lined up right you
+
+ align:start position:0%
+comes along and it's lined up right you
+ 
+
+ align:start position:0%
+comes along and it's lined up right you
+see oh look at that I'm getting that
+
+ align:start position:0%
+see oh look at that I'm getting that
+ 
+
+ align:start position:0%
+see oh look at that I'm getting that
+stretch and squeeze the way you actually
+
+ align:start position:0%
+stretch and squeeze the way you actually
+ 
+
+ align:start position:0%
+stretch and squeeze the way you actually
+measure it out is essentially a timing
+
+ align:start position:0%
+measure it out is essentially a timing
+ 
+
+ align:start position:0%
+measure it out is essentially a timing
+experiment exactly like this little
+
+ align:start position:0%
+experiment exactly like this little
+ 
+
+ align:start position:0%
+experiment exactly like this little
+calculation I did here you bounce light
+
+ align:start position:0%
+calculation I did here you bounce light
+ 
+
+ align:start position:0%
+calculation I did here you bounce light
+between mirrors and you very carefully
+
+ align:start position:0%
+between mirrors and you very carefully
+ 
+
+ align:start position:0%
+between mirrors and you very carefully
+time the the round-trip travel time from
+
+ align:start position:0%
+time the the round-trip travel time from
+ 
+
+ align:start position:0%
+time the the round-trip travel time from
+one mirror to the other and what's
+
+ align:start position:0%
+one mirror to the other and what's
+ 
+
+ align:start position:0%
+one mirror to the other and what's
+particularly cool is the experimental
+
+ align:start position:0%
+particularly cool is the experimental
+ 
+
+ align:start position:0%
+particularly cool is the experimental
+aspect of this so how does one measure
+
+ align:start position:0%
+aspect of this so how does one measure
+ 
+
+ align:start position:0%
+aspect of this so how does one measure
+the time so precisely well you use a
+
+ align:start position:0%
+the time so precisely well you use a
+ 
+
+ align:start position:0%
+the time so precisely well you use a
+laser beam as your clock and what's
+
+ align:start position:0%
+laser beam as your clock and what's
+ 
+
+ align:start position:0%
+laser beam as your clock and what's
+beautiful about doing that is the way
+
+ align:start position:0%
+beautiful about doing that is the way
+ 
+
+ align:start position:0%
+beautiful about doing that is the way
+that you can actually sort of do the
+
+ align:start position:0%
+that you can actually sort of do the
+ 
+
+ align:start position:0%
+that you can actually sort of do the
+metrology at the level necessary to get
+
+ align:start position:0%
+metrology at the level necessary to get
+ 
+
+ align:start position:0%
+metrology at the level necessary to get
+the precision to measure your HX X's in
+
+ align:start position:0%
+the precision to measure your HX X's in
+ 
+
+ align:start position:0%
+the precision to measure your HX X's in
+here is by interference okay so you can
+
+ align:start position:0%
+here is by interference okay so you can
+ 
+
+ align:start position:0%
+here is by interference okay so you can
+treat the incoming laser beam is
+
+ align:start position:0%
+treat the incoming laser beam is
+ 
+
+ align:start position:0%
+treat the incoming laser beam is
+defining your time standard and then by
+
+ align:start position:0%
+defining your time standard and then by
+ 
+
+ align:start position:0%
+defining your time standard and then by
+interfering the the light that has
+
+ align:start position:0%
+interfering the the light that has
+ 
+
+ align:start position:0%
+interfering the the light that has
+traveled down the arm and bounced back
+
+ align:start position:0%
+traveled down the arm and bounced back
+ 
+
+ align:start position:0%
+traveled down the arm and bounced back
+with that laser beam the basically
+
+ align:start position:0%
+with that laser beam the basically
+ 
+
+ align:start position:0%
+with that laser beam the basically
+the laws of nature allow you to
+
+ align:start position:0%
+the laws of nature allow you to
+ 
+
+ align:start position:0%
+the laws of nature allow you to
+automatically check and see whether
+
+ align:start position:0%
+automatically check and see whether
+ 
+
+ align:start position:0%
+automatically check and see whether
+there is a shift in the time of arrival
+
+ align:start position:0%
+there is a shift in the time of arrival
+ 
+
+ align:start position:0%
+there is a shift in the time of arrival
+associated with the action of the
+
+ align:start position:0%
+associated with the action of the
+ 
+
+ align:start position:0%
+associated with the action of the
+gravitational wave so I imagine there'll
+
+ align:start position:0%
+gravitational wave so I imagine there'll
+ 
+
+ align:start position:0%
+gravitational wave so I imagine there'll
+be some questions about this um there
+
+ align:start position:0%
+be some questions about this um there
+ 
+
+ align:start position:0%
+be some questions about this um there
+are there is a homework exercise that
+
+ align:start position:0%
+are there is a homework exercise that
+ 
+
+ align:start position:0%
+are there is a homework exercise that
+allows you to sort of test drive some of
+
+ align:start position:0%
+allows you to sort of test drive some of
+ 
+
+ align:start position:0%
+allows you to sort of test drive some of
+these concepts and allows you to see how
+
+ align:start position:0%
+these concepts and allows you to see how
+ 
+
+ align:start position:0%
+these concepts and allows you to see how
+it is that Lyle works it really just
+
+ align:start position:0%
+it is that Lyle works it really just
+ 
+
+ align:start position:0%
+it is that Lyle works it really just
+sort of touches this it just scratches
+
+ align:start position:0%
+sort of touches this it just scratches
+ 
+
+ align:start position:0%
+sort of touches this it just scratches
+the surface of what an amazing
+
+ align:start position:0%
+the surface of what an amazing
+ 
+
+ align:start position:0%
+the surface of what an amazing
+experimental feat that is but it should
+
+ align:start position:0%
+experimental feat that is but it should
+ 
+
+ align:start position:0%
+experimental feat that is but it should
+give you a good idea as to what goes
+
+ align:start position:0%
+give you a good idea as to what goes
+ 
+
+ align:start position:0%
+give you a good idea as to what goes
+into that now there's an important part
+
+ align:start position:0%
+into that now there's an important part
+ 
+
+ align:start position:0%
+into that now there's an important part
+to all this that we've not talked about
+
+ align:start position:0%
+to all this that we've not talked about
+ 
+
+ align:start position:0%
+to all this that we've not talked about
+yet I handed you
+
+ align:start position:0%
+yet I handed you
+ 
+
+ align:start position:0%
+yet I handed you
+hij really I handed uhm you know the big
+
+ align:start position:0%
+hij really I handed uhm you know the big
+ 
+
+ align:start position:0%
+hij really I handed uhm you know the big
+thing that we care about
+
+ align:start position:0%
+thing that we care about
+ 
+
+ align:start position:0%
+thing that we care about
+next is given a particular source how do
+
+ align:start position:0%
+next is given a particular source how do
+ 
+
+ align:start position:0%
+next is given a particular source how do
+i compute this radiation field so
+
+ align:start position:0%
+i compute this radiation field so
+ 
+
+ align:start position:0%
+i compute this radiation field so
+bearing in mind that h IJ t t this is
+
+ align:start position:0%
+bearing in mind that h IJ t t this is
+ 
+
+ align:start position:0%
+bearing in mind that h IJ t t this is
+the gauge invariant radiative degree of
+
+ align:start position:0%
+the gauge invariant radiative degree of
+ 
+
+ align:start position:0%
+the gauge invariant radiative degree of
+freedom in my space-time how do i
+
+ align:start position:0%
+freedom in my space-time how do i
+ 
+
+ align:start position:0%
+freedom in my space-time how do i
+compute this guy and what i'm going to
+
+ align:start position:0%
+compute this guy and what i'm going to
+ 
+
+ align:start position:0%
+compute this guy and what i'm going to
+do is borrow the sort of one most
+
+ align:start position:0%
+do is borrow the sort of one most
+ 
+
+ align:start position:0%
+do is borrow the sort of one most
+important lessons of that gauge
+
+ align:start position:0%
+important lessons of that gauge
+ 
+
+ align:start position:0%
+important lessons of that gauge
+invariant formalism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to be cautious of the fact
+
+ align:start position:0%
+so we need to be cautious of the fact
+ 
+
+ align:start position:0%
+so we need to be cautious of the fact
+that in some gauges for example the
+
+ align:start position:0%
+that in some gauges for example the
+ 
+
+ align:start position:0%
+that in some gauges for example the
+Lorentz gauge which is so convenient for
+
+ align:start position:0%
+Lorentz gauge which is so convenient for
+ 
+
+ align:start position:0%
+Lorentz gauge which is so convenient for
+solving the Einstein equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components of the metric appear to be
+
+ align:start position:0%
+components of the metric appear to be
+ 
+
+ align:start position:0%
+components of the metric appear to be
+radiative whether they are or they
+
+ align:start position:0%
+radiative whether they are or they
+ 
+
+ align:start position:0%
+radiative whether they are or they
+aren't this is a consequence of our
+
+ align:start position:0%
+aren't this is a consequence of our
+ 
+
+ align:start position:0%
+aren't this is a consequence of our
+gauge but we also know only hij TT is
+
+ align:start position:0%
+gauge but we also know only hij TT is
+ 
+
+ align:start position:0%
+gauge but we also know only hij TT is
+radiation in all gauges so that was what
+
+ align:start position:0%
+radiation in all gauges so that was what
+ 
+
+ align:start position:0%
+radiation in all gauges so that was what
+the previous lecture was about as I've
+
+ align:start position:0%
+the previous lecture was about as I've
+ 
+
+ align:start position:0%
+the previous lecture was about as I've
+emphasized it was a slightly advanced
+
+ align:start position:0%
+emphasized it was a slightly advanced
+ 
+
+ align:start position:0%
+emphasized it was a slightly advanced
+one I don't expect everyone to follow
+
+ align:start position:0%
+one I don't expect everyone to follow
+ 
+
+ align:start position:0%
+one I don't expect everyone to follow
+all details but if you can sort of grok
+
+ align:start position:0%
+all details but if you can sort of grok
+ 
+
+ align:start position:0%
+all details but if you can sort of grok
+these two main concepts you're ready to
+
+ align:start position:0%
+these two main concepts you're ready to
+ 
+
+ align:start position:0%
+these two main concepts you're ready to
+now exploit this in the following way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you do is a compute find some
+
+ align:start position:0%
+what you do is a compute find some
+ 
+
+ align:start position:0%
+what you do is a compute find some
+metric perturbation in any convenient
+
+ align:start position:0%
+metric perturbation in any convenient
+ 
+
+ align:start position:0%
+metric perturbation in any convenient
+gauge by any convenient method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once you have that extract hij TT you're
+
+ align:start position:0%
+once you have that extract hij TT you're
+ 
+
+ align:start position:0%
+once you have that extract hij TT you're
+done so that's what we're gonna do right
+
+ align:start position:0%
+done so that's what we're gonna do right
+ 
+
+ align:start position:0%
+done so that's what we're gonna do right
+now in the last 20 or so minutes of this
+
+ align:start position:0%
+now in the last 20 or so minutes of this
+ 
+
+ align:start position:0%
+now in the last 20 or so minutes of this
+recorded lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to do it is let's take
+
+ align:start position:0%
+so we're going to do it is let's take
+ 
+
+ align:start position:0%
+so we're going to do it is let's take
+the linear Eisenstein equation in
+
+ align:start position:0%
+the linear Eisenstein equation in
+ 
+
+ align:start position:0%
+the linear Eisenstein equation in
+Lorentz gauge as we showed in I believe
+
+ align:start position:0%
+Lorentz gauge as we showed in I believe
+ 
+
+ align:start position:0%
+Lorentz gauge as we showed in I believe
+it was two lectures ago the I sign field
+
+ align:start position:0%
+it was two lectures ago the I sign field
+ 
+
+ align:start position:0%
+it was two lectures ago the I sign field
+equations in this case we've used two
+
+ align:start position:0%
+equations in this case we've used two
+ 
+
+ align:start position:0%
+equations in this case we've used two
+flat space-time wave operator on the
+
+ align:start position:0%
+flat space-time wave operator on the
+ 
+
+ align:start position:0%
+flat space-time wave operator on the
+trace reversed metric perturbation being
+
+ align:start position:0%
+trace reversed metric perturbation being
+ 
+
+ align:start position:0%
+trace reversed metric perturbation being
+up to a factor of minus sixteen pi g the
+
+ align:start position:0%
+up to a factor of minus sixteen pi g the
+ 
+
+ align:start position:0%
+up to a factor of minus sixteen pi g the
+stress energy tensor and this has an
+
+ align:start position:0%
+stress energy tensor and this has an
+ 
+
+ align:start position:0%
+stress energy tensor and this has an
+exact solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll remind you this notation so this is
+
+ align:start position:0%
+I'll remind you this notation so this is
+ 
+
+ align:start position:0%
+I'll remind you this notation so this is
+the field at time T and spatial location
+
+ align:start position:0%
+the field at time T and spatial location
+ 
+
+ align:start position:0%
+the field at time T and spatial location
+X X and T well great like this T and X
+
+ align:start position:0%
+X X and T well great like this T and X
+ 
+
+ align:start position:0%
+X X and T well great like this T and X
+are my field point that is where I
+
+ align:start position:0%
+are my field point that is where I
+ 
+
+ align:start position:0%
+are my field point that is where I
+measure my field X prime is my source
+
+ align:start position:0%
+measure my field X prime is my source
+ 
+
+ align:start position:0%
+measure my field X prime is my source
+point that is where I'm looking at my
+
+ align:start position:0%
+point that is where I'm looking at my
+ 
+
+ align:start position:0%
+point that is where I'm looking at my
+particular contribution to the integral
+
+ align:start position:0%
+particular contribution to the integral
+ 
+
+ align:start position:0%
+particular contribution to the integral
+as we were doing this calculation there
+
+ align:start position:0%
+as we were doing this calculation there
+ 
+
+ align:start position:0%
+as we were doing this calculation there
+was a t prime but the rate of greens
+
+ align:start position:0%
+was a t prime but the rate of greens
+ 
+
+ align:start position:0%
+was a t prime but the rate of greens
+function turned that T prime into this
+
+ align:start position:0%
+function turned that T prime into this
+ 
+
+ align:start position:0%
+function turned that T prime into this
+ time so what we're seeing is
+
+ align:start position:0%
+ time so what we're seeing is
+ 
+
+ align:start position:0%
+ time so what we're seeing is
+that the field at T depends upon what's
+
+ align:start position:0%
+that the field at T depends upon what's
+ 
+
+ align:start position:0%
+that the field at T depends upon what's
+going on at the source at t minus the
+
+ align:start position:0%
+going on at the source at t minus the
+ 
+
+ align:start position:0%
+going on at the source at t minus the
+interval of time it takes for
+
+ align:start position:0%
+interval of time it takes for
+ 
+
+ align:start position:0%
+interval of time it takes for
+information to propagate from X prime to
+
+ align:start position:0%
+information to propagate from X prime to
+ 
+
+ align:start position:0%
+information to propagate from X prime to
+X so what I'm going to do is first I'm
+
+ align:start position:0%
+X so what I'm going to do is first I'm
+ 
+
+ align:start position:0%
+X so what I'm going to do is first I'm
+going to introduce a couple of
+
+ align:start position:0%
+going to introduce a couple of
+ 
+
+ align:start position:0%
+going to introduce a couple of
+approximations that reflect the reality
+
+ align:start position:0%
+approximations that reflect the reality
+ 
+
+ align:start position:0%
+approximations that reflect the reality
+of the conditions under which we
+
+ align:start position:0%
+of the conditions under which we
+ 
+
+ align:start position:0%
+of the conditions under which we
+typically evaluate this integral and
+
+ align:start position:0%
+typically evaluate this integral and
+ 
+
+ align:start position:0%
+typically evaluate this integral and
+then we're going to talk about how to
+
+ align:start position:0%
+then we're going to talk about how to
+ 
+
+ align:start position:0%
+then we're going to talk about how to
+solve this thing
+
+ align:start position:0%
+solve this thing
+ 
+
+ align:start position:0%
+solve this thing
+and given that we've now solved it how
+
+ align:start position:0%
+and given that we've now solved it how
+ 
+
+ align:start position:0%
+and given that we've now solved it how
+to project out the gauge invariant
+
+ align:start position:0%
+to project out the gauge invariant
+ 
+
+ align:start position:0%
+to project out the gauge invariant
+degrees of freedom associated with the
+
+ align:start position:0%
+degrees of freedom associated with the
+ 
+
+ align:start position:0%
+degrees of freedom associated with the
+radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first as I introduced its
+
+ align:start position:0%
+so first as I introduced its
+ 
+
+ align:start position:0%
+so first as I introduced its
+approximation it's worth bearing in mind
+
+ align:start position:0%
+approximation it's worth bearing in mind
+ 
+
+ align:start position:0%
+approximation it's worth bearing in mind
+that when you are calculating this X
+
+ align:start position:0%
+that when you are calculating this X
+ 
+
+ align:start position:0%
+that when you are calculating this X
+minus X prime which is kind of like the
+
+ align:start position:0%
+minus X prime which is kind of like the
+ 
+
+ align:start position:0%
+minus X prime which is kind of like the
+distance from a particular point in the
+
+ align:start position:0%
+distance from a particular point in the
+ 
+
+ align:start position:0%
+distance from a particular point in the
+source to where you're making your
+
+ align:start position:0%
+source to where you're making your
+ 
+
+ align:start position:0%
+source to where you're making your
+measurement it is generally a lot larger
+
+ align:start position:0%
+measurement it is generally a lot larger
+ 
+
+ align:start position:0%
+measurement it is generally a lot larger
+than the size of the source okay so the
+
+ align:start position:0%
+than the size of the source okay so the
+ 
+
+ align:start position:0%
+than the size of the source okay so the
+kind of situation we're thinking about
+
+ align:start position:0%
+kind of situation we're thinking about
+ 
+
+ align:start position:0%
+kind of situation we're thinking about
+is here we are making our measurements
+
+ align:start position:0%
+is here we are making our measurements
+ 
+
+ align:start position:0%
+is here we are making our measurements
+at some point X here here's my source
+
+ align:start position:0%
+at some point X here here's my source
+ 
+
+ align:start position:0%
+at some point X here here's my source
+and here's a point X Prime inside the
+
+ align:start position:0%
+and here's a point X Prime inside the
+ 
+
+ align:start position:0%
+and here's a point X Prime inside the
+source okay so the same to bear in mind
+
+ align:start position:0%
+source okay so the same to bear in mind
+ 
+
+ align:start position:0%
+source okay so the same to bear in mind
+is that for the kind of calculations
+
+ align:start position:0%
+is that for the kind of calculations
+ 
+
+ align:start position:0%
+is that for the kind of calculations
+where that you know and when one is
+
+ align:start position:0%
+where that you know and when one is
+ 
+
+ align:start position:0%
+where that you know and when one is
+actually doing this X minus X prime well
+
+ align:start position:0%
+actually doing this X minus X prime well
+ 
+
+ align:start position:0%
+actually doing this X minus X prime well
+if I think about the kind of
+
+ align:start position:0%
+if I think about the kind of
+ 
+
+ align:start position:0%
+if I think about the kind of
+measurements that LIGO is doing for
+
+ align:start position:0%
+measurements that LIGO is doing for
+ 
+
+ align:start position:0%
+measurements that LIGO is doing for
+example that is typically hundreds of
+
+ align:start position:0%
+example that is typically hundreds of
+ 
+
+ align:start position:0%
+example that is typically hundreds of
+millions to billions of light years the
+
+ align:start position:0%
+millions to billions of light years the
+ 
+
+ align:start position:0%
+millions to billions of light years the
+size of the source itself is of order
+
+ align:start position:0%
+size of the source itself is of order
+ 
+
+ align:start position:0%
+size of the source itself is of order
+tens to hundreds of kilometers bit of a
+
+ align:start position:0%
+tens to hundreds of kilometers bit of a
+ 
+
+ align:start position:0%
+tens to hundreds of kilometers bit of a
+separation of length scales there you
+
+ align:start position:0%
+separation of length scales there you
+ 
+
+ align:start position:0%
+separation of length scales there you
+would say so what I'm going to do is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximate the solution that integral
+
+ align:start position:0%
+approximate the solution that integral
+ 
+
+ align:start position:0%
+approximate the solution that integral
+and for pedantic sake I'm gonna use an
+
+ align:start position:0%
+and for pedantic sake I'm gonna use an
+ 
+
+ align:start position:0%
+and for pedantic sake I'm gonna use an
+approximately equal what I'm going to do
+
+ align:start position:0%
+approximately equal what I'm going to do
+ 
+
+ align:start position:0%
+approximately equal what I'm going to do
+is replace X minus X Prime with our
+
+ align:start position:0%
+is replace X minus X Prime with our
+ 
+
+ align:start position:0%
+is replace X minus X Prime with our
+let's just say that this distance here
+
+ align:start position:0%
+let's just say that this distance here
+ 
+
+ align:start position:0%
+let's just say that this distance here
+it's effectively the same for all points
+
+ align:start position:0%
+it's effectively the same for all points
+ 
+
+ align:start position:0%
+it's effectively the same for all points
+in the source I can pull that out of the
+
+ align:start position:0%
+in the source I can pull that out of the
+ 
+
+ align:start position:0%
+in the source I can pull that out of the
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you like you can refine this
+
+ align:start position:0%
+okay if you like you can refine this
+ 
+
+ align:start position:0%
+okay if you like you can refine this
+there's a more careful expansion and if
+
+ align:start position:0%
+there's a more careful expansion and if
+ 
+
+ align:start position:0%
+there's a more careful expansion and if
+you've done any electrodynamics you
+
+ align:start position:0%
+you've done any electrodynamics you
+ 
+
+ align:start position:0%
+you've done any electrodynamics you
+should be familiar with this and it uses
+
+ align:start position:0%
+should be familiar with this and it uses
+ 
+
+ align:start position:0%
+should be familiar with this and it uses
+the fact that 1 over X minus X prime can
+
+ align:start position:0%
+the fact that 1 over X minus X prime can
+ 
+
+ align:start position:0%
+the fact that 1 over X minus X prime can
+be expanded in Legendre polynomials in a
+
+ align:start position:0%
+be expanded in Legendre polynomials in a
+ 
+
+ align:start position:0%
+be expanded in Legendre polynomials in a
+sum over Legendre polynomials ok so if
+
+ align:start position:0%
+sum over Legendre polynomials ok so if
+ 
+
+ align:start position:0%
+sum over Legendre polynomials ok so if
+you do that you can introduce
+
+ align:start position:0%
+you do that you can introduce
+ 
+
+ align:start position:0%
+you do that you can introduce
+refinements to what I'm about to derive
+
+ align:start position:0%
+refinements to what I'm about to derive
+ 
+
+ align:start position:0%
+refinements to what I'm about to derive
+right here what this does then is it
+
+ align:start position:0%
+right here what this does then is it
+ 
+
+ align:start position:0%
+right here what this does then is it
+defines a multipolar expansion I am NOT
+
+ align:start position:0%
+defines a multipolar expansion I am NOT
+ 
+
+ align:start position:0%
+defines a multipolar expansion I am NOT
+going to do that I'm just going to look
+
+ align:start position:0%
+going to do that I'm just going to look
+ 
+
+ align:start position:0%
+going to do that I'm just going to look
+at the very first term and you can sort
+
+ align:start position:0%
+at the very first term and you can sort
+ 
+
+ align:start position:0%
+at the very first term and you can sort
+of think of that as saying that I am
+
+ align:start position:0%
+of think of that as saying that I am
+ 
+
+ align:start position:0%
+of think of that as saying that I am
+just doing the leading the most
+
+ align:start position:0%
+just doing the leading the most
+ 
+
+ align:start position:0%
+just doing the leading the most
+important multiple additional multiples
+
+ align:start position:0%
+important multiple additional multiples
+ 
+
+ align:start position:0%
+important multiple additional multiples
+beyond that are certainly important and
+
+ align:start position:0%
+beyond that are certainly important and
+ 
+
+ align:start position:0%
+beyond that are certainly important and
+people who work in the field of
+
+ align:start position:0%
+people who work in the field of
+ 
+
+ align:start position:0%
+people who work in the field of
+gravitational radiation we certainly do
+
+ align:start position:0%
+gravitational radiation we certainly do
+ 
+
+ align:start position:0%
+gravitational radiation we certainly do
+not neglect them in fact much of my
+
+ align:start position:0%
+not neglect them in fact much of my
+ 
+
+ align:start position:0%
+not neglect them in fact much of my
+current research is based on sort of
+
+ align:start position:0%
+current research is based on sort of
+ 
+
+ align:start position:0%
+current research is based on sort of
+high order calculations associated with
+
+ align:start position:0%
+high order calculations associated with
+ 
+
+ align:start position:0%
+high order calculations associated with
+looking at behavior some of those some
+
+ align:start position:0%
+looking at behavior some of those some
+ 
+
+ align:start position:0%
+looking at behavior some of those some
+of those multiples this will be fine for
+
+ align:start position:0%
+of those multiples this will be fine for
+ 
+
+ align:start position:0%
+of those multiples this will be fine for
+initial pedagogical purposes next we're
+
+ align:start position:0%
+initial pedagogical purposes next we're
+ 
+
+ align:start position:0%
+initial pedagogical purposes next we're
+gonna use the fact that only the spatial
+
+ align:start position:0%
+gonna use the fact that only the spatial
+ 
+
+ align:start position:0%
+gonna use the fact that only the spatial
+whoops that's not suppose to be an H
+
+ align:start position:0%
+whoops that's not suppose to be an H
+ 
+
+ align:start position:0%
+whoops that's not suppose to be an H
+tilde my apologies
+
+ align:start position:0%
+tilde my apologies
+ 
+
+ align:start position:0%
+tilde my apologies
+just be H bark this is the Tracy first
+
+ align:start position:0%
+just be H bark this is the Tracy first
+ 
+
+ align:start position:0%
+just be H bark this is the Tracy first
+thing weird times folks okay uh what was
+
+ align:start position:0%
+thing weird times folks okay uh what was
+ 
+
+ align:start position:0%
+thing weird times folks okay uh what was
+I at yes so I am only going to care
+
+ align:start position:0%
+I at yes so I am only going to care
+ 
+
+ align:start position:0%
+I at yes so I am only going to care
+about the spatial pieces of this okay
+
+ align:start position:0%
+about the spatial pieces of this okay
+ 
+
+ align:start position:0%
+about the spatial pieces of this okay
+you might protest hey isn't it the
+
+ align:start position:0%
+you might protest hey isn't it the
+ 
+
+ align:start position:0%
+you might protest hey isn't it the
+spatial part of the metric not the trace
+
+ align:start position:0%
+spatial part of the metric not the trace
+ 
+
+ align:start position:0%
+spatial part of the metric not the trace
+reverse metric that matters and you
+
+ align:start position:0%
+reverse metric that matters and you
+ 
+
+ align:start position:0%
+reverse metric that matters and you
+would be correct if you do this
+
+ align:start position:0%
+would be correct if you do this
+ 
+
+ align:start position:0%
+would be correct if you do this
+carefully to be perfectly blunt you have
+
+ align:start position:0%
+carefully to be perfectly blunt you have
+ 
+
+ align:start position:0%
+carefully to be perfectly blunt you have
+to sort of finish the calculation before
+
+ align:start position:0%
+to sort of finish the calculation before
+ 
+
+ align:start position:0%
+to sort of finish the calculation before
+you can kind of justify the step I'm
+
+ align:start position:0%
+you can kind of justify the step I'm
+ 
+
+ align:start position:0%
+you can kind of justify the step I'm
+about to make and we're not gonna have
+
+ align:start position:0%
+about to make and we're not gonna have
+ 
+
+ align:start position:0%
+about to make and we're not gonna have
+time to do that very carefully but I'll
+
+ align:start position:0%
+time to do that very carefully but I'll
+ 
+
+ align:start position:0%
+time to do that very carefully but I'll
+make a comment about it for now it
+
+ align:start position:0%
+make a comment about it for now it
+ 
+
+ align:start position:0%
+make a comment about it for now it
+suffice to say we only care about the
+
+ align:start position:0%
+suffice to say we only care about the
+ 
+
+ align:start position:0%
+suffice to say we only care about the
+spatial components so I'm gonna take my
+
+ align:start position:0%
+spatial components so I'm gonna take my
+ 
+
+ align:start position:0%
+spatial components so I'm gonna take my
+alpha beta over to an IJ okay so I now
+
+ align:start position:0%
+alpha beta over to an IJ okay so I now
+ 
+
+ align:start position:0%
+alpha beta over to an IJ okay so I now
+have something that involves the
+
+ align:start position:0%
+have something that involves the
+ 
+
+ align:start position:0%
+have something that involves the
+integral of the spatial pieces of the
+
+ align:start position:0%
+integral of the spatial pieces of the
+ 
+
+ align:start position:0%
+integral of the spatial pieces of the
+stress energy tensor over my source and
+
+ align:start position:0%
+stress energy tensor over my source and
+ 
+
+ align:start position:0%
+stress energy tensor over my source and
+now I'm going to take advantage of an
+
+ align:start position:0%
+now I'm going to take advantage of an
+ 
+
+ align:start position:0%
+now I'm going to take advantage of an
+Easter egg that was hidden in an early
+
+ align:start position:0%
+Easter egg that was hidden in an early
+ 
+
+ align:start position:0%
+Easter egg that was hidden in an early
+problem set back on problem set two I
+
+ align:start position:0%
+problem set back on problem set two I
+ 
+
+ align:start position:0%
+problem set back on problem set two I
+asked you to prove a result that I
+
+ align:start position:0%
+asked you to prove a result that I
+ 
+
+ align:start position:0%
+asked you to prove a result that I
+called the tensor virial theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the reasons why I signed that was
+
+ align:start position:0%
+one of the reasons why I signed that was
+ 
+
+ align:start position:0%
+one of the reasons why I signed that was
+that I knew I was going to need it in
+
+ align:start position:0%
+that I knew I was going to need it in
+ 
+
+ align:start position:0%
+that I knew I was going to need it in
+this lecture and what the tensor virial
+
+ align:start position:0%
+this lecture and what the tensor virial
+ 
+
+ align:start position:0%
+this lecture and what the tensor virial
+theorem told us is that if I integrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this ends up being equivalent to
+
+ align:start position:0%
+that this ends up being equivalent to
+ 
+
+ align:start position:0%
+that this ends up being equivalent to
+one half two time derivatives equal to
+
+ align:start position:0%
+one half two time derivatives equal to
+ 
+
+ align:start position:0%
+one half two time derivatives equal to
+the integral of two time derivatives
+
+ align:start position:0%
+the integral of two time derivatives
+ 
+
+ align:start position:0%
+the integral of two time derivatives
+assuming it's two time rhythms of the
+
+ align:start position:0%
+assuming it's two time rhythms of the
+ 
+
+ align:start position:0%
+assuming it's two time rhythms of the
+integral of the zero zero piece of my
+
+ align:start position:0%
+integral of the zero zero piece of my
+ 
+
+ align:start position:0%
+integral of the zero zero piece of my
+stress energy tensor sort of the second
+
+ align:start position:0%
+stress energy tensor sort of the second
+ 
+
+ align:start position:0%
+stress energy tensor sort of the second
+moment of that X I prime XJ prime okay
+
+ align:start position:0%
+moment of that X I prime XJ prime okay
+ 
+
+ align:start position:0%
+moment of that X I prime XJ prime okay
+this is great because what I've got on
+
+ align:start position:0%
+this is great because what I've got on
+ 
+
+ align:start position:0%
+this is great because what I've got on
+the left hand side here that's exactly
+
+ align:start position:0%
+the left hand side here that's exactly
+ 
+
+ align:start position:0%
+the left hand side here that's exactly
+what my integral is you know what this
+
+ align:start position:0%
+what my integral is you know what this
+ 
+
+ align:start position:0%
+what my integral is you know what this
+is going to give me a result that
+
+ align:start position:0%
+is going to give me a result that
+ 
+
+ align:start position:0%
+is going to give me a result that
+sufficiently clean I want a new board so
+
+ align:start position:0%
+sufficiently clean I want a new board so
+ 
+
+ align:start position:0%
+sufficiently clean I want a new board so
+when that is done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I finally see is that my H I J
+
+ align:start position:0%
+what I finally see is that my H I J
+ 
+
+ align:start position:0%
+what I finally see is that my H I J
+trace you first is to G over our two
+
+ align:start position:0%
+trace you first is to G over our two
+ 
+
+ align:start position:0%
+trace you first is to G over our two
+time derivatives of a tensor that I will
+
+ align:start position:0%
+time derivatives of a tensor that I will
+ 
+
+ align:start position:0%
+time derivatives of a tensor that I will
+call i IJ this is what I get when I
+
+ align:start position:0%
+call i IJ this is what I get when I
+ 
+
+ align:start position:0%
+call i IJ this is what I get when I
+integrate T 0 0 to moments of T 0 0 this
+
+ align:start position:0%
+integrate T 0 0 to moments of T 0 0 this
+ 
+
+ align:start position:0%
+integrate T 0 0 to moments of T 0 0 this
+is called the quadrupole moment the
+
+ align:start position:0%
+is called the quadrupole moment the
+ 
+
+ align:start position:0%
+is called the quadrupole moment the
+source the asterisk is because as you
+
+ align:start position:0%
+source the asterisk is because as you
+ 
+
+ align:start position:0%
+source the asterisk is because as you
+guys will see on one of the problem sets
+
+ align:start position:0%
+guys will see on one of the problem sets
+ 
+
+ align:start position:0%
+guys will see on one of the problem sets
+there's a slight tweak that goes into
+
+ align:start position:0%
+there's a slight tweak that goes into
+ 
+
+ align:start position:0%
+there's a slight tweak that goes into
+the exact definition of the quadrupole
+
+ align:start position:0%
+the exact definition of the quadrupole
+ 
+
+ align:start position:0%
+the exact definition of the quadrupole
+moment which has to do with the behavior
+
+ align:start position:0%
+moment which has to do with the behavior
+ 
+
+ align:start position:0%
+moment which has to do with the behavior
+of the trace of I I J I will just leave
+
+ align:start position:0%
+of the trace of I I J I will just leave
+ 
+
+ align:start position:0%
+of the trace of I I J I will just leave
+this like so for now and leave you guys
+
+ align:start position:0%
+this like so for now and leave you guys
+ 
+
+ align:start position:0%
+this like so for now and leave you guys
+to explore that on the problem set so
+
+ align:start position:0%
+to explore that on the problem set so
+ 
+
+ align:start position:0%
+to explore that on the problem set so
+we're almost done what I now need to do
+
+ align:start position:0%
+we're almost done what I now need to do
+ 
+
+ align:start position:0%
+we're almost done what I now need to do
+is pull out the transverse and traceless
+
+ align:start position:0%
+is pull out the transverse and traceless
+ 
+
+ align:start position:0%
+is pull out the transverse and traceless
+piece of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's consider the transverse condition
+
+ align:start position:0%
+let's consider the transverse condition
+ 
+
+ align:start position:0%
+let's consider the transverse condition
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to do the transverse condition I'm
+
+ align:start position:0%
+so to do the transverse condition I'm
+ 
+
+ align:start position:0%
+so to do the transverse condition I'm
+gonna take advantage of the fact that
+
+ align:start position:0%
+gonna take advantage of the fact that
+ 
+
+ align:start position:0%
+gonna take advantage of the fact that
+far from the source box h bar IJ is
+
+ align:start position:0%
+far from the source box h bar IJ is
+ 
+
+ align:start position:0%
+far from the source box h bar IJ is
+equal to zero these because I'm in a
+
+ align:start position:0%
+equal to zero these because I'm in a
+ 
+
+ align:start position:0%
+equal to zero these because I'm in a
+region where the source is equal to zero
+
+ align:start position:0%
+region where the source is equal to zero
+ 
+
+ align:start position:0%
+region where the source is equal to zero
+when I'm far away from it this suggests
+
+ align:start position:0%
+when I'm far away from it this suggests
+ 
+
+ align:start position:0%
+when I'm far away from it this suggests
+that what we ought to do is expand our
+
+ align:start position:0%
+that what we ought to do is expand our
+ 
+
+ align:start position:0%
+that what we ought to do is expand our
+solution implant in plain ways so what I
+
+ align:start position:0%
+solution implant in plain ways so what I
+ 
+
+ align:start position:0%
+solution implant in plain ways so what I
+can do is write H bar and choose my
+
+ align:start position:0%
+can do is write H bar and choose my
+ 
+
+ align:start position:0%
+can do is write H bar and choose my
+indices carefully here clot JL it's some
+
+ align:start position:0%
+indices carefully here clot JL it's some
+ 
+
+ align:start position:0%
+indices carefully here clot JL it's some
+amplitude that does not depend on space
+
+ align:start position:0%
+amplitude that does not depend on space
+ 
+
+ align:start position:0%
+amplitude that does not depend on space
+or time e to the I Omega t minus a wave
+
+ align:start position:0%
+or time e to the I Omega t minus a wave
+ 
+
+ align:start position:0%
+or time e to the I Omega t minus a wave
+vector dotted with X okay so this
+
+ align:start position:0%
+vector dotted with X okay so this
+ 
+
+ align:start position:0%
+vector dotted with X okay so this
+amplitude may depend on Omega it may
+
+ align:start position:0%
+amplitude may depend on Omega it may
+ 
+
+ align:start position:0%
+amplitude may depend on Omega it may
+depend on K it does not depend on T or
+
+ align:start position:0%
+depend on K it does not depend on T or
+ 
+
+ align:start position:0%
+depend on K it does not depend on T or
+on X and the reason I changed my indices
+
+ align:start position:0%
+on X and the reason I changed my indices
+ 
+
+ align:start position:0%
+on X and the reason I changed my indices
+from I and J - J and L I did not use the
+
+ align:start position:0%
+from I and J - J and L I did not use the
+ 
+
+ align:start position:0%
+from I and J - J and L I did not use the
+index K is just to avoid confusion
+
+ align:start position:0%
+index K is just to avoid confusion
+ 
+
+ align:start position:0%
+index K is just to avoid confusion
+between square root of -1 and the wave
+
+ align:start position:0%
+between square root of -1 and the wave
+ 
+
+ align:start position:0%
+between square root of -1 and the wave
+vector to be absolutely careful this is
+
+ align:start position:0%
+vector to be absolutely careful this is
+ 
+
+ align:start position:0%
+vector to be absolutely careful this is
+a single mode okay if you like maybe you
+
+ align:start position:0%
+a single mode okay if you like maybe you
+ 
+
+ align:start position:0%
+a single mode okay if you like maybe you
+should think about this as something
+
+ align:start position:0%
+should think about this as something
+ 
+
+ align:start position:0%
+should think about this as something
+that I have I'm doing a sum or an
+
+ align:start position:0%
+that I have I'm doing a sum or an
+ 
+
+ align:start position:0%
+that I have I'm doing a sum or an
+integral over Omega and K in order to
+
+ align:start position:0%
+integral over Omega and K in order to
+ 
+
+ align:start position:0%
+integral over Omega and K in order to
+reconstruct the whole thing this is just
+
+ align:start position:0%
+reconstruct the whole thing this is just
+ 
+
+ align:start position:0%
+reconstruct the whole thing this is just
+a single Fourier mode in the wave field
+
+ align:start position:0%
+a single Fourier mode in the wave field
+ 
+
+ align:start position:0%
+a single Fourier mode in the wave field
+so if I want this to be transverse that
+
+ align:start position:0%
+so if I want this to be transverse that
+ 
+
+ align:start position:0%
+so if I want this to be transverse that
+condition is that the divergence of this
+
+ align:start position:0%
+condition is that the divergence of this
+ 
+
+ align:start position:0%
+condition is that the divergence of this
+guy be equal to zero okay but when I
+
+ align:start position:0%
+guy be equal to zero okay but when I
+ 
+
+ align:start position:0%
+guy be equal to zero okay but when I
+take the divergence of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this becomes I pull down a factor of
+
+ align:start position:0%
+this becomes I pull down a factor of
+ 
+
+ align:start position:0%
+this becomes I pull down a factor of
+minus I and I pull down the J component
+
+ align:start position:0%
+minus I and I pull down the J component
+ 
+
+ align:start position:0%
+minus I and I pull down the J component
+of my wave vector K and I get my wave my
+
+ align:start position:0%
+of my wave vector K and I get my wave my
+ 
+
+ align:start position:0%
+of my wave vector K and I get my wave my
+for a term that can be thought of as so
+
+ align:start position:0%
+for a term that can be thought of as so
+ 
+
+ align:start position:0%
+for a term that can be thought of as so
+we can clear out the factor of minus I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the transverse condition boils down to
+
+ align:start position:0%
+the transverse condition boils down to
+ 
+
+ align:start position:0%
+the transverse condition boils down to
+saying that KJ KJ contracted on the wave
+
+ align:start position:0%
+saying that KJ KJ contracted on the wave
+ 
+
+ align:start position:0%
+saying that KJ KJ contracted on the wave
+field is equal to zero in other words
+
+ align:start position:0%
+field is equal to zero in other words
+ 
+
+ align:start position:0%
+field is equal to zero in other words
+the wave field is orthogonal to the wave
+
+ align:start position:0%
+the wave field is orthogonal to the wave
+ 
+
+ align:start position:0%
+the wave field is orthogonal to the wave
+vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have studied electrodynamics this
+
+ align:start position:0%
+if you have studied electrodynamics this
+ 
+
+ align:start position:0%
+if you have studied electrodynamics this
+should be familiar to you this is the
+
+ align:start position:0%
+should be familiar to you this is the
+ 
+
+ align:start position:0%
+should be familiar to you this is the
+same it's exactly the same as the idea
+
+ align:start position:0%
+same it's exactly the same as the idea
+ 
+
+ align:start position:0%
+same it's exactly the same as the idea
+that when I have an electromagnetic wave
+
+ align:start position:0%
+that when I have an electromagnetic wave
+ 
+
+ align:start position:0%
+that when I have an electromagnetic wave
+my e field in my B field are orthogonal
+
+ align:start position:0%
+my e field in my B field are orthogonal
+ 
+
+ align:start position:0%
+my e field in my B field are orthogonal
+to the direction of propagation let's
+
+ align:start position:0%
+to the direction of propagation let's
+ 
+
+ align:start position:0%
+to the direction of propagation let's
+define a unit vector and sub J to be KJ
+
+ align:start position:0%
+define a unit vector and sub J to be KJ
+ 
+
+ align:start position:0%
+define a unit vector and sub J to be KJ
+but just normalized okay so my wave is
+
+ align:start position:0%
+but just normalized okay so my wave is
+ 
+
+ align:start position:0%
+but just normalized okay so my wave is
+propagating in the direction of the unit
+
+ align:start position:0%
+propagating in the direction of the unit
+ 
+
+ align:start position:0%
+propagating in the direction of the unit
+vector n go back to another Easter egg
+
+ align:start position:0%
+vector n go back to another Easter egg
+ 
+
+ align:start position:0%
+vector n go back to another Easter egg
+that was hitting on an earlier problem
+
+ align:start position:0%
+that was hitting on an earlier problem
+ 
+
+ align:start position:0%
+that was hitting on an earlier problem
+set you guys studied projection tensors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I introduced the projection tensor P
+
+ align:start position:0%
+if I introduced the projection tensor P
+ 
+
+ align:start position:0%
+if I introduced the projection tensor P
+IJ P IJ will project any spatial vector
+
+ align:start position:0%
+IJ P IJ will project any spatial vector
+ 
+
+ align:start position:0%
+IJ P IJ will project any spatial vector
+it will project out the components
+
+ align:start position:0%
+it will project out the components
+ 
+
+ align:start position:0%
+it will project out the components
+normal orthogonal to the direction of
+
+ align:start position:0%
+normal orthogonal to the direction of
+ 
+
+ align:start position:0%
+normal orthogonal to the direction of
+propagation n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can in fact think of pIJ as defining
+
+ align:start position:0%
+you can in fact think of pIJ as defining
+ 
+
+ align:start position:0%
+you can in fact think of pIJ as defining
+the metric for the subspace that is
+
+ align:start position:0%
+the metric for the subspace that is
+ 
+
+ align:start position:0%
+the metric for the subspace that is
+orthogonal to end so if Majan that your
+
+ align:start position:0%
+orthogonal to end so if Majan that your
+ 
+
+ align:start position:0%
+orthogonal to end so if Majan that your
+wave is propagating in the n direction
+
+ align:start position:0%
+wave is propagating in the n direction
+ 
+
+ align:start position:0%
+wave is propagating in the n direction
+there's a plane being carried along that
+
+ align:start position:0%
+there's a plane being carried along that
+ 
+
+ align:start position:0%
+there's a plane being carried along that
+it's the plane that's orthogonal to N
+
+ align:start position:0%
+it's the plane that's orthogonal to N
+ 
+
+ align:start position:0%
+it's the plane that's orthogonal to N
+and P IJ is the metric you use to define
+
+ align:start position:0%
+and P IJ is the metric you use to define
+ 
+
+ align:start position:0%
+and P IJ is the metric you use to define
+spatial distances in that in that plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using P IJ we can now make my H trace
+
+ align:start position:0%
+using P IJ we can now make my H trace
+ 
+
+ align:start position:0%
+using P IJ we can now make my H trace
+assuming I can make it transverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all I need to do I'll put one T on this
+
+ align:start position:0%
+all I need to do I'll put one T on this
+ 
+
+ align:start position:0%
+all I need to do I'll put one T on this
+to denote transverse all I need to do is
+
+ align:start position:0%
+to denote transverse all I need to do is
+ 
+
+ align:start position:0%
+to denote transverse all I need to do is
+project each of its indices you think
+
+ align:start position:0%
+project each of its indices you think
+ 
+
+ align:start position:0%
+project each of its indices you think
+that tension so we're almost there
+
+ align:start position:0%
+that tension so we're almost there
+ 
+
+ align:start position:0%
+that tension so we're almost there
+it's transverse but it's not yet trace
+
+ align:start position:0%
+it's transverse but it's not yet trace
+ 
+
+ align:start position:0%
+it's transverse but it's not yet trace
+free so if I take the trace on this guy
+
+ align:start position:0%
+free so if I take the trace on this guy
+ 
+
+ align:start position:0%
+free so if I take the trace on this guy
+okay taking the trace on this guy
+
+ align:start position:0%
+okay taking the trace on this guy
+ 
+
+ align:start position:0%
+okay taking the trace on this guy
+amounts to I am going to require that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this be equal to zero okay now suppose I
+
+ align:start position:0%
+this be equal to zero okay now suppose I
+ 
+
+ align:start position:0%
+this be equal to zero okay now suppose I
+have some tensor that is not trace free
+
+ align:start position:0%
+have some tensor that is not trace free
+ 
+
+ align:start position:0%
+have some tensor that is not trace free
+and I want to remove its trace I'm going
+
+ align:start position:0%
+and I want to remove its trace I'm going
+ 
+
+ align:start position:0%
+and I want to remove its trace I'm going
+to make this it's a to index tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm not going to prove the following
+
+ align:start position:0%
+so I'm not going to prove the following
+ 
+
+ align:start position:0%
+so I'm not going to prove the following
+result it's you can easily verify for
+
+ align:start position:0%
+result it's you can easily verify for
+ 
+
+ align:start position:0%
+result it's you can easily verify for
+yourself the formula for doing so is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a IJ trace free it is a IJ minus 1
+
+ align:start position:0%
+that a IJ trace free it is a IJ minus 1
+ 
+
+ align:start position:0%
+that a IJ trace free it is a IJ minus 1
+over n a KL g KL g IJ g is the metric
+
+ align:start position:0%
+over n a KL g KL g IJ g is the metric
+ 
+
+ align:start position:0%
+over n a KL g KL g IJ g is the metric
+that describes the manifold in which
+
+ align:start position:0%
+that describes the manifold in which
+ 
+
+ align:start position:0%
+that describes the manifold in which
+this tensor lives and is its dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for us the tensor field whose trace
+
+ align:start position:0%
+now for us the tensor field whose trace
+ 
+
+ align:start position:0%
+now for us the tensor field whose trace
+i want to remove is h IJ t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so hij bar T is the field whose trace I
+
+ align:start position:0%
+so hij bar T is the field whose trace I
+ 
+
+ align:start position:0%
+so hij bar T is the field whose trace I
+wish to remove this lives in the two
+
+ align:start position:0%
+wish to remove this lives in the two
+ 
+
+ align:start position:0%
+wish to remove this lives in the two
+dimensional manifold whose metric is
+
+ align:start position:0%
+dimensional manifold whose metric is
+ 
+
+ align:start position:0%
+dimensional manifold whose metric is
+projection tensor pIJ and we are working
+
+ align:start position:0%
+projection tensor pIJ and we are working
+ 
+
+ align:start position:0%
+projection tensor pIJ and we are working
+in a space where raising and lowering
+
+ align:start position:0%
+in a space where raising and lowering
+ 
+
+ align:start position:0%
+in a space where raising and lowering
+indices there's really no important
+
+ align:start position:0%
+indices there's really no important
+ 
+
+ align:start position:0%
+indices there's really no important
+distinction between the two of them
+
+ align:start position:0%
+distinction between the two of them
+ 
+
+ align:start position:0%
+distinction between the two of them
+because we're working in linearized
+
+ align:start position:0%
+because we're working in linearized
+ 
+
+ align:start position:0%
+because we're working in linearized
+theory so I remove the trace by taking
+
+ align:start position:0%
+theory so I remove the trace by taking
+ 
+
+ align:start position:0%
+theory so I remove the trace by taking
+this guy and subtracting off pardon me
+
+ align:start position:0%
+this guy and subtracting off pardon me
+ 
+
+ align:start position:0%
+this guy and subtracting off pardon me
+just one moment yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tracting off like so pardon me
+
+ align:start position:0%
+tracting off like so pardon me
+ 
+
+ align:start position:0%
+tracting off like so pardon me
+GWT on it plugging in my various
+
+ align:start position:0%
+GWT on it plugging in my various
+ 
+
+ align:start position:0%
+GWT on it plugging in my various
+definitions this turns into HL k PL i PK
+
+ align:start position:0%
+definitions this turns into HL k PL i PK
+ 
+
+ align:start position:0%
+definitions this turns into HL k PL i PK
+j minus 1/2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you might want to go and check
+
+ align:start position:0%
+okay so you might want to go and check
+ 
+
+ align:start position:0%
+okay so you might want to go and check
+them outta there but this is all I'm
+
+ align:start position:0%
+them outta there but this is all I'm
+ 
+
+ align:start position:0%
+them outta there but this is all I'm
+very confident in this there's an
+
+ align:start position:0%
+very confident in this there's an
+ 
+
+ align:start position:0%
+very confident in this there's an
+overall factor of H bar LK and the last
+
+ align:start position:0%
+overall factor of H bar LK and the last
+ 
+
+ align:start position:0%
+overall factor of H bar LK and the last
+thing which I will note is that once I
+
+ align:start position:0%
+thing which I will note is that once I
+ 
+
+ align:start position:0%
+thing which I will note is that once I
+have removed the trace this bar becomes
+
+ align:start position:0%
+have removed the trace this bar becomes
+ 
+
+ align:start position:0%
+have removed the trace this bar becomes
+meaningless its trace free so the trace
+
+ align:start position:0%
+meaningless its trace free so the trace
+ 
+
+ align:start position:0%
+meaningless its trace free so the trace
+reversing of it has no action now you
+
+ align:start position:0%
+reversing of it has no action now you
+ 
+
+ align:start position:0%
+reversing of it has no action now you
+should be a little bit careful about
+
+ align:start position:0%
+should be a little bit careful about
+ 
+
+ align:start position:0%
+should be a little bit careful about
+that there's a few different notions of
+
+ align:start position:0%
+that there's a few different notions of
+ 
+
+ align:start position:0%
+that there's a few different notions of
+trace that went into this definition
+
+ align:start position:0%
+trace that went into this definition
+ 
+
+ align:start position:0%
+trace that went into this definition
+without proof and just stating that by
+
+ align:start position:0%
+without proof and just stating that by
+ 
+
+ align:start position:0%
+without proof and just stating that by
+being a little bit more careful with
+
+ align:start position:0%
+being a little bit more careful with
+ 
+
+ align:start position:0%
+being a little bit more careful with
+some of the definitions we put down the
+
+ align:start position:0%
+some of the definitions we put down the
+ 
+
+ align:start position:0%
+some of the definitions we put down the
+difference between when you when you
+
+ align:start position:0%
+difference between when you when you
+ 
+
+ align:start position:0%
+difference between when you when you
+count this up you'll find that you know
+
+ align:start position:0%
+count this up you'll find that you know
+ 
+
+ align:start position:0%
+count this up you'll find that you know
+you may be making a small error but it
+
+ align:start position:0%
+you may be making a small error but it
+ 
+
+ align:start position:0%
+you may be making a small error but it
+is on the order of terms that are
+
+ align:start position:0%
+is on the order of terms that are
+ 
+
+ align:start position:0%
+is on the order of terms that are
+quadratic in the perturbation putting
+
+ align:start position:0%
+quadratic in the perturbation putting
+ 
+
+ align:start position:0%
+quadratic in the perturbation putting
+all these pieces together we find we
+
+ align:start position:0%
+all these pieces together we find we
+ 
+
+ align:start position:0%
+all these pieces together we find we
+obtain our transverse and traceless
+
+ align:start position:0%
+obtain our transverse and traceless
+ 
+
+ align:start position:0%
+obtain our transverse and traceless
+metric perturbation which looks like
+
+ align:start position:0%
+metric perturbation which looks like
+ 
+
+ align:start position:0%
+metric perturbation which looks like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a result known as the quadrupole
+
+ align:start position:0%
+this is a result known as the quadrupole
+ 
+
+ align:start position:0%
+this is a result known as the quadrupole
+formula for gravitational waves this is
+
+ align:start position:0%
+formula for gravitational waves this is
+ 
+
+ align:start position:0%
+formula for gravitational waves this is
+so given just take a stock of the final
+
+ align:start position:0%
+so given just take a stock of the final
+ 
+
+ align:start position:0%
+so given just take a stock of the final
+result suppose you have some dynamic
+
+ align:start position:0%
+result suppose you have some dynamic
+ 
+
+ align:start position:0%
+result suppose you have some dynamic
+gravitating source this is telling me
+
+ align:start position:0%
+gravitating source this is telling me
+ 
+
+ align:start position:0%
+gravitating source this is telling me
+what I do is I compute the quadrupole
+
+ align:start position:0%
+what I do is I compute the quadrupole
+ 
+
+ align:start position:0%
+what I do is I compute the quadrupole
+moment associate that source I take two
+
+ align:start position:0%
+moment associate that source I take two
+ 
+
+ align:start position:0%
+moment associate that source I take two
+time derivatives I hit it with this
+
+ align:start position:0%
+time derivatives I hit it with this
+ 
+
+ align:start position:0%
+time derivatives I hit it with this
+combination of projection tensors which
+
+ align:start position:0%
+combination of projection tensors which
+ 
+
+ align:start position:0%
+combination of projection tensors which
+has to do that tells me something about
+
+ align:start position:0%
+has to do that tells me something about
+ 
+
+ align:start position:0%
+has to do that tells me something about
+the geometry of the source that's saying
+
+ align:start position:0%
+the geometry of the source that's saying
+ 
+
+ align:start position:0%
+the geometry of the source that's saying
+that my source the waves of come from
+
+ align:start position:0%
+that my source the waves of come from
+ 
+
+ align:start position:0%
+that my source the waves of come from
+the source propagating along a
+
+ align:start position:0%
+the source propagating along a
+ 
+
+ align:start position:0%
+the source propagating along a
+particular direction to me and this
+
+ align:start position:0%
+particular direction to me and this
+ 
+
+ align:start position:0%
+particular direction to me and this
+picks out the components that are
+
+ align:start position:0%
+picks out the components that are
+ 
+
+ align:start position:0%
+picks out the components that are
+transverse with respect to that
+
+ align:start position:0%
+transverse with respect to that
+ 
+
+ align:start position:0%
+transverse with respect to that
+direction and are our traceless so that
+
+ align:start position:0%
+direction and are our traceless so that
+ 
+
+ align:start position:0%
+direction and are our traceless so that
+I don't have any gauge degrees of
+
+ align:start position:0%
+I don't have any gauge degrees of
+ 
+
+ align:start position:0%
+I don't have any gauge degrees of
+freedom and what results multiply by
+
+ align:start position:0%
+freedom and what results multiply by
+ 
+
+ align:start position:0%
+freedom and what results multiply by
+twice Newton's constant divided by
+
+ align:start position:0%
+twice Newton's constant divided by
+ 
+
+ align:start position:0%
+twice Newton's constant divided by
+distance and this is the wave field that
+
+ align:start position:0%
+distance and this is the wave field that
+ 
+
+ align:start position:0%
+distance and this is the wave field that
+our friends over and building nw20 two
+
+ align:start position:0%
+our friends over and building nw20 two
+ 
+
+ align:start position:0%
+our friends over and building nw20 two
+can now measure pretty much everyday
+
+ align:start position:0%
+can now measure pretty much everyday
+ 
+
+ align:start position:0%
+can now measure pretty much everyday
+you're going to do a few homework
+
+ align:start position:0%
+you're going to do a few homework
+ 
+
+ align:start position:0%
+you're going to do a few homework
+exercises associate with this one thing
+
+ align:start position:0%
+exercises associate with this one thing
+ 
+
+ align:start position:0%
+exercises associate with this one thing
+which is worth commenting on before I
+
+ align:start position:0%
+which is worth commenting on before I
+ 
+
+ align:start position:0%
+which is worth commenting on before I
+move on is when you keep factors of C in
+
+ align:start position:0%
+move on is when you keep factors of C in
+ 
+
+ align:start position:0%
+move on is when you keep factors of C in
+this that G goes over to G over C to the
+
+ align:start position:0%
+this that G goes over to G over C to the
+ 
+
+ align:start position:0%
+this that G goes over to G over C to the
+let me double check that didn't you ever
+
+ align:start position:0%
+let me double check that didn't you ever
+ 
+
+ align:start position:0%
+let me double check that didn't you ever
+see the fourth or G over C squared
+
+ align:start position:0%
+see the fourth or G over C squared
+ 
+
+ align:start position:0%
+see the fourth or G over C squared
+anyhow it's G divided by C to some power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's just say that it's missing factors
+
+ align:start position:0%
+let's just say that it's missing factors
+ 
+
+ align:start position:0%
+let's just say that it's missing factors
+of C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm a comment on that in some notes that
+
+ align:start position:0%
+I'm a comment on that in some notes that
+ 
+
+ align:start position:0%
+I'm a comment on that in some notes that
+I will add to the to the board and so
+
+ align:start position:0%
+I will add to the to the board and so
+ 
+
+ align:start position:0%
+I will add to the to the board and so
+that kind of tells you that this is
+
+ align:start position:0%
+that kind of tells you that this is
+ 
+
+ align:start position:0%
+that kind of tells you that this is
+going to be a really small quantity
+
+ align:start position:0%
+going to be a really small quantity
+ 
+
+ align:start position:0%
+going to be a really small quantity
+makes it very hard for these things to
+
+ align:start position:0%
+makes it very hard for these things to
+ 
+
+ align:start position:0%
+makes it very hard for these things to
+be measured nonetheless it turns out
+
+ align:start position:0%
+be measured nonetheless it turns out
+ 
+
+ align:start position:0%
+be measured nonetheless it turns out
+even though they have you think about
+
+ align:start position:0%
+even though they have you think about
+ 
+
+ align:start position:0%
+even though they have you think about
+the impact they have on a detector even
+
+ align:start position:0%
+the impact they have on a detector even
+ 
+
+ align:start position:0%
+the impact they have on a detector even
+though it's small they carry a
+
+ align:start position:0%
+though it's small they carry a
+ 
+
+ align:start position:0%
+though it's small they carry a
+tremendous amount of energy I'm gonna
+
+ align:start position:0%
+tremendous amount of energy I'm gonna
+ 
+
+ align:start position:0%
+tremendous amount of energy I'm gonna
+take a break before I begin recording
+
+ align:start position:0%
+take a break before I begin recording
+ 
+
+ align:start position:0%
+take a break before I begin recording
+mine Lex lack my next lecture but the
+
+ align:start position:0%
+mine Lex lack my next lecture but the
+ 
+
+ align:start position:0%
+mine Lex lack my next lecture but the
+next lecture is actually going to lead
+
+ align:start position:0%
+next lecture is actually going to lead
+ 
+
+ align:start position:0%
+next lecture is actually going to lead
+us to an understanding of a different
+
+ align:start position:0%
+us to an understanding of a different
+ 
+
+ align:start position:0%
+us to an understanding of a different
+version of the quadrupole formula it's
+
+ align:start position:0%
+version of the quadrupole formula it's
+ 
+
+ align:start position:0%
+version of the quadrupole formula it's
+based on this but it describes the
+
+ align:start position:0%
+based on this but it describes the
+ 
+
+ align:start position:0%
+based on this but it describes the
+energy content of gravitational waves
+
+ align:start position:0%
+energy content of gravitational waves
+ 
+
+ align:start position:0%
+energy content of gravitational waves
+both of these formulas go by the name
+
+ align:start position:0%
+both of these formulas go by the name
+ 
+
+ align:start position:0%
+both of these formulas go by the name
+the quadrupole formula a little bit
+
+ align:start position:0%
+the quadrupole formula a little bit
+ 
+
+ align:start position:0%
+the quadrupole formula a little bit
+confusing sometimes that both are used
+
+ align:start position:0%
+confusing sometimes that both are used
+ 
+
+ align:start position:0%
+confusing sometimes that both are used
+and you're gonna use both of them on up
+
+ align:start position:0%
+and you're gonna use both of them on up
+ 
+
+ align:start position:0%
+and you're gonna use both of them on up
+chemical mark assignments all right so I
+
+ align:start position:0%
+chemical mark assignments all right so I
+ 
+
+ align:start position:0%
+chemical mark assignments all right so I
+will end this recording here
\ No newline at end of file
diff --git a/RbJV-g9Lob8.txt b/RbJV-g9Lob8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..354b8d451165ec3df182cd575edf7e8fce1d04b4
--- /dev/null
+++ b/RbJV-g9Lob8.txt
@@ -0,0 +1,146 @@
+Our final challenge is figuring out how to
+represent signed integers, for example, what
+
+should be our representation for the number
+-2000?
+
+In decimal notation, the convention is to
+precede the number with a "+" or "-" to indicate
+
+whether it's positive or negative, usually
+omitting the "+" to simplify the notation
+
+for positive numbers.
+We could adopt a similar notation -- called
+
+"signed magnitude" -- in binary, by allocating
+a separate bit at the front of the binary
+
+string to indicate the sign, say "0" for positive
+numbers and "1" for negative numbers.
+
+So the signed-magnitude representation for
+-2000 would be an initial "1" to indicate
+
+a negative number, followed by the representation
+for 2000 (as described on the previous two
+
+slides).
+However there are some complications in using
+
+a signed-magnitude representation.
+There are two possible binary representations
+
+for zero: "+0" and "-0".
+This makes the encoding slightly inefficient
+
+but, more importantly, the circuitry for doing
+addition of signed-magnitude numbers is different
+
+than the circuitry for doing subtraction.
+Of course, we're used to that – in elementary
+
+school we learned one technique for addition
+and another for subtraction.
+
+To keep the circuitry simple, most modern
+digital systems use the two's complement binary
+
+representation for signed numbers.
+In this representation, the high-order bit
+
+of an N-bit two's complement number has a
+negative weight, as shown in the figure.
+
+Thus all negative numbers have a 1 in the
+high-order bit and, in that sense, the high-order
+
+bit is serving as the "sign bit" – if it's
+1, the represented number is negative.
+
+The most negative N-bit number has a 1-bit
+in the high-order position, representing the
+
+value -2^(N-1).
+The most positive N-bit number has a 0 in
+
+the negative-weight high-order bit and 1's
+for all the positive-weight bits, representing
+
+the value 2^(N-1)-1.
+This gives us the range of possible values
+
+– for example, in an 8-bit two's complement
+representation, the most negative number is
+
+-2^7 = -128 and the most positive number is
+2^7 – 1 = 127.
+
+If all N bits are 1, think of that as the
+sum of the most negative number with the most
+
+positive number, i.e., -2^(N-1) + 2^(N-1)-1,
+which equals -1.
+
+And, of course, if all N bits are 0, that's
+the unique representation of 0.
+
+Let's see what happens when we add the N-bit
+values for -1 and 1, keeping an N-bit answer.
+
+In the rightmost column, 1 plus 1 is 0, carry
+the 1.
+
+In the second column, the carry of 1 plus
+1 plus 0 is 0, carry the 1.
+
+And so on – the result is all zero's, the
+representation for 0… perfect!
+
+Notice that we just used ordinary binary addition,
+even when one or both of the operands are
+
+negative.
+Two's complement is perfect for N-bit arithmetic!
+
+To compute B - A, we can just use addition
+and compute B + (-A).
+
+So now we just need to figure out the two's
+complement representation for –A, given
+
+the two's complement representation for A.
+Well, we know that A + (-A) = 0 and using
+
+the example above, we can rewrite 0 as 1 +
+(-1).
+
+Reorganizing terms, we see that –A equals
+1 plus the quantity (-1) – A.
+
+As we saw above, the two's complement representation
+for -1 is all 1-bits, so we can write that
+
+subtraction as all 1's minus the individual
+bits of A: A_0, A_1, … up to A_N-1.
+
+If a particular bit A_i is 0, then 1-A_i = 1
+and if A_i is 1, then 1-A_i = 0.
+
+So in each column, the result is the bitwise
+complement of A_i, which we'll write using
+
+the C-language bitwise complement operator
+tilde.
+
+So we see that –A equals the bitwise complement
+of A plus 1.
+
+Ta-dah!
+To practice your skill with two's complement,
+
+try your hand at the following exercises.
+All you need to remember is how to do binary
+
+addition and two's complement negation (which
+is "bitwise complement and add 1").
\ No newline at end of file
diff --git a/Rv1UBrGVGFk.txt b/Rv1UBrGVGFk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6270d4fc7ee34ccf6e91d94cdf703e342d57ebb
--- /dev/null
+++ b/Rv1UBrGVGFk.txt
@@ -0,0 +1,3089 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK, let's start.
+
+So we were talking about
+melting in two dimensions,
+
+and the picture that
+you had was something
+
+like a triangular lattice,
+which at zero temperature
+
+has particles sitting
+at precise sites--
+
+let's say, on this
+triangular lattice--
+
+but then at finite
+temperature, the particles
+
+will to start to deform.
+
+And the deformations were
+indicated by a vector u.
+
+And the idea was that this
+is like an elastic material,
+
+as long as we're thinking
+about these long wavelength
+
+deformations.
+
+u and the energy
+costs can be written
+
+for an isotropic material
+in two dimensions in terms
+
+of two invariants.
+
+And traditionally, it
+is written in terms
+
+of the so called lame
+coefficients, mu and lambda.
+
+Where this uij,
+which is the strain,
+
+is obtained by taking
+derivatives of the deformation,
+
+the iuj, and symmetrizing it.
+
+This symmetrization essentially
+eliminates an energy
+
+at a cost for rotations.
+
+And then because of this
+simple quadratic translation
+
+of invariant form,
+we could also express
+
+this in terms of fullier mode.
+
+And I'm going to write the
+fullier description slightly
+
+differently than last time.
+
+Basically, this
+whole form can be
+
+written as u plus 2 lambda over
+2 q dot u tilde of q squared.
+
+And the other term-- other than
+previously I had written things
+
+in terms of q dot
+u and q squared
+
+u squared-- we write it in terms
+of q crossed with u tilde of q
+
+squared.
+
+Essentially, you can see that
+this ratifies that they're
+
+going to have modes that
+are in the direction of q,
+
+the longitudinal modes.
+
+Cost is nu plus 2
+lambda, and those
+
+that are transfers or orthogonal
+to the direction of q,
+
+whose cost is just mu.
+
+And clearly if I were
+to go into real space,
+
+this is kind of related
+to a divergence of u.
+
+And the divergence
+of u corresponds
+
+to essentially squeezing or
+expanding this deformation.
+
+So what these measures
+is essentially
+
+the cost of changing
+the density.
+
+And this combination is
+related to the bark modulus.
+
+You have that even for a liquid.
+
+So if you have a liquid,
+you try to squeeze it.
+
+There will be a
+bulk energy cost.
+
+And this term, which in the
+real space is kind of related
+
+to kern u, you would say
+is corresponding to making
+
+the rotations.
+
+So if you try to rotate
+this material locally,
+
+then the corresponding
+sheer cost of the formation
+
+has a cost that is indicated
+by mu, the sheer modulus.
+
+And basically what really
+makes a solid is this term.
+
+Because as I said, a liquid
+also has the bark modulus,
+
+but lacks the resistance
+to try to sheer it,
+
+which is captured by this, that
+is unique and characteristic
+
+of a solid.
+
+So this is the energy cost.
+
+The other part of
+this whole story
+
+is that this
+structure has order.
+
+And we can
+characterize that order
+
+which makes it distinct from a
+liquid or gas a number of ways.
+
+One was to do an
+x-ray scattering,
+
+and then you would
+see the back peaks.
+
+And really that type of
+order is translational.
+
+And you characterize that
+by an order parameter.
+
+It's kind of like
+a spin that you
+
+have in the case of a
+magnet being up or down.
+
+In this case, this
+object was e to the i g
+
+dot u-- the deformation that
+you have that's on location r.
+
+And then these g's are chosen to
+be the inverse lattice vectors.
+
+It doesn't really matter
+whether I write here
+
+u of r or the actual position.
+
+Because the actual positions
+starts at zero temperature,
+
+we devalue r 0, such that
+the dot product of that g
+
+is a multiple of 2pi.
+
+And so essentially,
+that's what captures this.
+
+Clearly, if I start with
+a zero temperature picture
+
+and just move this
+around, the phase
+
+of this order parameter
+over here will change,
+
+but it will be the
+same across the system.
+
+And so this is long
+range correlation that
+
+is present at zero
+temperature, you
+
+can ask what happens to
+it at finite temperature.
+
+So we can look at the row
+g at some position, row g
+
+star at some other position.
+
+And so that was related to
+exponential of minus g squared
+
+over 2-- something
+like u squared
+
+x, or u of x minus 0 squared.
+
+And what we saw
+was that this thing
+
+had a characteristic that it
+was falling off with distance
+
+according to some
+kind of power law.
+
+The exponent of this power
+law, when calculated,
+
+clearly is related
+to this g squared.
+
+Because this is the quantity
+that goes logarithmically.
+
+And so the answer was
+g squared over 4 pi.
+
+Heat was dependent on these
+two modes being present.
+
+So you have nu 2 nu plus lambda,
+and then 2 nu plus lambda.
+
+You had a form such as this.
+
+Now this result was
+obtained as long
+
+as we were treating this
+field, u, as just the continuum
+
+field that satisfies this.
+
+And this result is
+really different, also,
+
+from the expectation that
+at very high temperature
+
+the particle in a liquid
+should not know anything
+
+about the particle
+further out in the liquid,
+
+as long as they're beyond
+some small correlation links.
+
+So we expect this to
+actually decay exponentially
+
+at high temperatures.
+
+And we found that
+we could account
+
+for that by addition
+of these locations,
+
+can cause a transition
+to a high temperature
+
+phase in which row g, row
+g star, between x and 0,
+
+decays exponentially.
+
+As opposed to this
+algebraic behavior,
+
+indicating that these
+locations-- once you
+
+go to sufficiently
+high temperature,
+
+such that the entropy of
+creating and rearranging
+
+these dislocations overcomes
+the large cost of creating them
+
+in the first place,
+then you'll have
+
+this absence of
+translational order,
+
+and some kind of exponential
+decay of this order parameter.
+
+So at this stage, you may
+feel comfortable enough
+
+to say that addition
+of these dislocation
+
+causes our solid to melt
+and become a liquid.
+
+Now, I indicated,
+however, that the sun also
+
+has an orientational role.
+
+What I could do is-- at
+each location in the solid,
+
+I can ask how much has
+the angle been deformed,
+
+and look at the bond angle.
+
+So maybe this
+particle moved here,
+
+and this particle moved here.
+
+Somewhere else, the
+particles may have
+
+moved in a different fashion.
+
+And the angle that
+was originally,
+
+say, along the x direction,
+had rotated somewhere else.
+
+And clearly, again,
+at zero temperature,
+
+I can look at the correlations
+of this angular order,
+
+and they would be the
+same across the system.
+
+I can ask what happens when
+I include these deformations
+
+and then the dislocations.
+
+So in the same way that we
+defined the translational order
+
+parameter, I can define an
+orientational order parameter.
+
+Let's call it sci
+at some location, r,
+
+which is e to the i.
+
+Theta at that location r--
+
+Except that when I look
+at the triangular lattice,
+
+it may be that the triangles
+have actually rotated
+
+by 60 degrees or 120 degrees.
+
+And I can't really tell whether
+I clicked once, zero times,
+
+twice, et cetera.
+
+So because of this symmetry of
+the original lattice on their
+
+on their theta going to
+theta plus 2 pi over 6,
+
+I have to use something
+like this that will not
+
+be modified if I make
+this transformation,
+
+even at zero temperature.
+
+If I miscount some angle by 60
+degrees, this will become fine.
+
+Now I want to calculate the
+correlations of this theta
+
+from one part of this system
+to another part of the system.
+
+So for that, what
+I need to do is
+
+to look at the
+relationship between theta
+
+and the distortion field,
+u, that I told you before.
+
+Now you can see that right
+on the top right corner
+
+I took the distortion field,
+and I took it's derivative,
+
+and then symmetrized
+the result in pencil.
+
+And that symmetrization
+actually removes any rotation
+
+that I would have.
+
+So in order to bring
+back the notation,
+
+I just have to put a minus sign.
+
+And indeed, one can show that
+the distortion or displacement
+
+u or r across my
+system-- let's call it
+
+u of x-- leads to a
+corresponding angular
+
+distortion, theta, at x, which
+is minus one half-- let's
+
+call it z hat dotted
+with curve of u.
+
+So if, rather than doing
+the i u j plus d j u i,
+
+if I put a minus sign,
+you can see that I
+
+have the structure of a curve.
+
+In two dimensions,
+actually curve
+
+would be something that
+would be pointing only
+
+along the z direction.
+
+And so I just make
+a scale on my dot,
+
+without taking that
+in the z direction.
+
+And so you can do
+some distortion,
+
+and convince yourself
+that for each distortion
+
+you will get an
+angle that is this.
+
+AUDIENCE: Do we need some
+kind of thermalization
+
+to fix the dimensions of this?
+
+Because that can go u has
+dimensions of fields, and u--
+
+PROFESSOR: I'm only talking
+about two dimensions.
+
+And in any case,
+you can see that u
+
+is a distortion--
+is a displacement--
+
+the gradient is reduced
+by the displacement,
+
+so this thing is
+dimensionless as long as you
+
+have these dimensions.
+
+AUDIENCE: Sorry.
+
+PROFESSOR: Yes?
+
+AUDIENCE: That's a 2, right?
+
+Not a c?
+
+PROFESSOR: That's a 2.
+
+It's the same 2 that I have for
+the definition of the strain.
+
+Rather than a plus,
+you put a minus.
+
+AUDIENCE: So can
+we think of these
+
+as two sets of Goldstone
+modes, or is that not a way
+
+to interpret it?
+
+Is it like two order parameters?
+
+I mean, you have a think
+that has u dependence, but--
+
+PROFESSOR: OK, so let's look
+at this picture over here.
+
+You do have two sets of
+Goldstone modes corresponding
+
+to longitudinal transfers.
+
+You can see that this
+curve is the thing
+
+is that I call the angle.
+
+So if you like, you can
+put the angle over here.
+
+But the difference between
+putting an angle here,
+
+and this term, is that
+in terms of the angle,
+
+there is no q dependence.
+
+So it is not a ghost.
+
+Because the cost of making a
+distortion of wave number q
+
+does not vanish as
+q squared works.
+
+All right, so then I can look
+at the correlation between, say,
+
+sci of x, sci star of zero.
+
+And what I will be calculating
+is expectation value of e
+
+to the i 6.
+
+And then I will have
+this factor of--
+
+So let me write it
+in this fashion.
+
+Theta of x minus theta of 0.
+
+Since u is Gaussian
+distributed, theta
+
+in the Gaussian distributor.
+
+So for any Gaussian
+distributed entity,
+
+we can write the
+exponential of e
+
+to the something as its average
+as exponential of minus 1/2
+
+the average of whatever
+is in the exponent.
+
+So I will get 36 divided by 2.
+
+I do have the expectation
+value of delta theta squared.
+
+But delta theta is related
+up to this factor of 1/4
+
+to some expectation
+value of kern u.
+
+So I would need to calculate
+kern mu at x minus kern u
+
+at 0, the whole thing squared
+with the Gaussian average.
+
+Now, this entity--
+clearly what I can do
+
+is to go back and
+look at these things
+
+in terms of Fourier space,
+rather than position space.
+
+So this becomes an integral
+d 2 q 2 pi to the d.
+
+I will get e to the
+i q dot x minus 1.
+
+And then I have something
+like q cross u tilde of q.
+
+And I have to do that twice.
+
+When I do that twice, I find
+that the different q's are
+
+uncorrelated.
+
+So I will get, rather than
+two of these integrals, one
+
+of these integrals.
+
+And because the q and q prime
+are said to be the same,
+
+the product of those two
+factors will be the integral 2
+
+minus 2 cosine of q dot x
+term that we are used to.
+
+And so that's where the
+x dependence appears.
+
+And then I need the
+average of q cross mu of q.
+
+And that I can read off
+the beta [INAUDIBLE],
+
+root the energy over here.
+
+You can see that there
+is a Gaussian cost
+
+for q plus u of q
+squared, which is simply
+
+1 of a lingering variance.
+
+So basically, this term
+you'll the sum of 1 over u.
+
+Now the difference between
+all of the calculations
+
+that we were doing previously,
+as was asked regarding
+
+Goldstone modes-- if I was just
+looking at u squared, which
+
+is what I was doing
+up here, I would
+
+need to put another factor of
+1 over q squared [INAUDIBLE].
+
+And then I would have
+the coulomb integral that
+
+would grow logarithmically.
+
+But here you can see that
+the whole thing-- the cosine
+
+integrated against
+the constant--
+
+will average out to 0.
+
+So I will think you
+have 2 over u times
+
+this integral is a constant.
+
+So the whole thing,
+at the end of the day,
+
+is exponential of-- that
+becomes a 9 divided by 2.
+
+There's a factor
+of 1 over the mu,
+
+and then I have twice the
+integral of d 2 q over 2 pi
+
+squared.
+
+Which is-- you can
+convince yourself
+
+simply the density of the
+system a number of times.
+
+So as opposed to the
+translational order, which
+
+was decaying as above
+our lot, then we
+
+include the phonon modes.
+
+When we include
+these phonon modes,
+
+we find that the orientational
+order decays much more weakly.
+
+So that was falling off as
+I went further and further.
+
+This, as I go
+further and further,
+
+eventually reaches a
+constant that is less than 1,
+
+but it is something.
+
+Using conversely
+proportional to temperature--
+
+so as I go to 0
+temperature, these go to 1.
+
+And basically because
+this order parameter,
+
+with respect to--
+well, this measure
+
+of distortion with respect
+to that measure of distortion
+
+has an additional
+factor of gradient.
+
+I will get an additional
+factor of q squared, and then
+
+everything changes accordingly.
+
+So orientational order
+is much more robust.
+
+This phase that we were
+calling the analogue of a two
+
+dimensional solid had only
+quasi long range order.
+
+The long range order was
+decaying as a power law.
+
+Yes?
+
+AUDIENCE: Is n dependent
+on the position, or--
+
+PROFESSOR: No.
+
+So basically, if you were to
+remember the number of points
+
+it should be the same as the
+number of allowed fullier
+
+modes.
+
+And this goes to
+an integral-- 2 q
+
+over 2 pi squared-- when I put
+the area in two dimensions.
+
+So the integral over
+whatever [INAUDIBLE]
+
+zone you have over
+the fullier modes
+
+is the same thing as
+the number of points
+
+that you have in the original
+lattice, divided by area,
+
+or 1 over the size of one
+of those triangles squared.
+
+Yes?
+
+AUDIENCE: Where is the x
+dependent in that expression?
+
+PROFESSOR: OK, the x
+dependence basically
+
+disappears because you integrate
+over the cosine of q x.
+
+And if x is sufficiently large,
+those fluctuations disappear.
+
+AUDIENCE: Oh, so we're really
+looking at the [INAUDIBLE].
+
+PROFESSOR: Yes, that's right.
+
+So at short distances,
+there are going
+
+to be some oscillations
+or whatever.
+
+But it gradually-- we are
+interested in the long distance
+
+behavior.
+
+At very short
+distances, I can't even
+
+use the continuum
+description for things
+
+that are three or
+lattice spacings apart.
+
+So maybe I should explicitly
+say that this is usually
+
+called quasi long range order,
+versus this dependence, which
+
+is two long ranges.
+
+So given that this is more
+robust than these forum-like
+
+fluctuations, the
+next question is, well
+
+does it completely disappear
+when I include these locations.
+
+So again, this calculation,
+based on Gaussian's, relies
+
+on just the fullier modes of
+that line that I have up there.
+
+It does not include the
+dislocations, which, in order
+
+to properly account,
+you saw that we
+
+need to look at a collections
+of these locations appearing
+
+at different positions
+on the lattice.
+
+And they had these vectorial
+nature of the fullier
+
+interactions among them.
+
+So presumably, when I
+go into the base where
+
+these locations unbind--
+and by unbinding--
+
+as I said, in the
+low temperature
+
+picture of the
+dislocations, they
+
+should appear very
+close to each other
+
+because it is costly to separate
+them by an amount that grows
+
+invariably in the separation.
+
+In the unbound phase, you
+have essentially a gas
+
+of dislocations that
+can be anywhere.
+
+So the picture here
+now is that indeed this
+
+is a phase, that if I just
+focus on the dislocations,
+
+there is a whole bunch of them.
+
+In a triangular
+lattice, they could
+
+be pointing in any one of three
+directions, plus or minus.
+
+And then there is certainly
+an additional contribution
+
+to the angle that comes from the
+presence of these dislocations.
+
+So you calculate-- if you
+have a dislocation that
+
+has inverse b, let's say at the
+origin, what kind of angular
+
+distortion does it cause.
+
+And you find that it goes
+like v dot x, divided
+
+by the absolute value of x.
+
+This is for one dislocation.
+
+This is the theta that you
+would get for that dislocation
+
+at location x.
+
+Essentially, you
+can see that if I
+
+were to replace the u that
+I have here with the u that
+
+was caused by dislocation,
+you would get something
+
+like this formula.
+
+Because remember the u that
+was caused by dislocation
+
+was something like the
+gradient of the log potential.
+
+It's kind of hard to
+work, but maybe I'll
+
+make an attempt to write it.
+
+So let's take a
+gradient of theta.
+
+Gradient of theta, if
+I use that formula,
+
+you would say, OK, I
+have minus 1/2 z hat dot
+
+kern of something.
+
+And if I take a gradient of the
+kern, the answer should be 0.
+
+But that's as long as this
+u is a well defined object.
+
+And our task was to say
+that this u, then you
+
+have these dislocations,
+is not a well defined
+
+object, in the sense
+that you take the kern,
+
+and the gradient
+then you would get 0.
+
+So essentially, I will
+transport the gradient
+
+all the way over here,
+and the part of u
+
+that will survive that is
+the one that is characterized
+
+by this dislocation feat.
+
+Now, you can see
+that this object
+
+kind of looks like a
+Laplacian of this distortion.
+
+It's two the derivatives
+of this distortion field
+
+that had this logarithm in it.
+
+And when you take two
+derivatives of a logarithm,
+
+you get the delta function.
+
+So if you do things
+correctly, you
+
+will find that this answer
+here becomes a sum over i
+
+v i delta function
+of x minus xi.
+
+So basically, each dislocation
+at location x i-- again,
+
+depending on its v being
+in each direction--
+
+gives a contribution to
+the gradient of theta.
+
+And if I were to take the
+gradient of the expression
+
+that I have over here, the
+gradient of this object
+
+is also-- this is like
+the field that you
+
+have for the
+logarithmic potential--
+
+will give you the data function.
+
+So that's where the
+similarity comes.
+
+So the full answer
+comes out to be--
+
+if you have a sum
+over the dislocations,
+
+the sum over the distortion
+fields that each one of them
+
+is causing-- and you will
+have a form such as this.
+
+Yes?
+
+AUDIENCE: Should the
+denominator be squared?
+
+PROFESSOR: Yes, that's right.
+
+The potential goes
+logarithmically.
+
+The field, which is the
+gradient of the potential,
+
+falls off as 1 over separation.
+
+So since I put the
+separation out there,
+
+I have to put the
+separation squared.
+
+So you can see that the
+singular part, the part that
+
+arises from dislocations-- if
+I have a soup of dislocations,
+
+I can figure out what theta is.
+
+Now what I did look
+for-- actually, I
+
+was kind of hinting at that-- if
+I take the gradient of theta--
+
+and I forgot to put
+the factor of 1/2pi
+
+here-- does the 4 vertices
+that had charged to pi--
+
+I had the potential.
+
+That was 1/r.
+
+So for dislocations
+it becomes d/2pi.
+
+If I take the gradient,
+then the gradient translates
+
+to sum over pi, the i
+data function of x minus x
+
+i-- the expression that I
+have written over there.
+
+And if I do the
+fullier transform,
+
+you see what I did over
+here was essentially
+
+to look at theta
+in fullier space.
+
+So let's do something
+similar here.
+
+So when I do the fullier
+transform of this,
+
+I will get pi q-- the fullier
+transform of this angular feat.
+
+And on the right hand
+side, what I would get
+
+is essentially the
+fullier transform
+
+of the field of dislocations.
+
+So I have defined my v of q to
+be sum over i into the i q dot
+
+position of the i
+dislocation, the vector that
+
+characterizes the dislocation.
+
+And it would make
+sense to also tap
+
+into the normalization
+that gives 1
+
+over the square root of area.
+
+If you don't do that,
+then at some other point
+
+you have to worry about
+the normalization.
+
+So if I just multiply
+both sides by q--
+
+and I think I forgot the
+minus sign throughout,
+
+which is not that important--
+but theta tilde of q
+
+becomes i q dot b of
+q, divided-- maybe
+
+I should've been calling this
+b tilde-- divided by q squared.
+
+So this is important.
+
+Essentially, you take the
+collection of dislocations
+
+in this picture
+and you calculate
+
+what the fullier transform
+is, call that the tilde of q.
+
+Essentially, you divide
+by 1 factor of q,
+
+and you can get the
+corresponding angle of feat.
+
+Now what I needed
+to evaluate for here
+
+was the average of theta
+tilde of q squared.
+
+And you can see that if I
+write this explicitly, let's
+
+say, q i for be tilde i 4,
+then the two of them I will
+
+get q beta b tilde of beta.
+
+And then I would
+have a q to the side.
+
+And the average over
+here becomes the average
+
+over all contributions
+of these dislocations
+
+that I can put across my system.
+
+Now, explicitly I'm interested
+in the limit where q goes to 0.
+
+So these things depend on q.
+
+What I'm interested
+in is the limit
+
+as q goes to 0, especially
+what happens to this average.
+
+It becomes-- multiplying two
+of these things together--
+
+actually, in the limit
+where q goes to 0,
+
+what I have is the sum
+over all of the b's.
+
+So in the limit
+where q goes to 0,
+
+this becomes an integral or sum.
+
+It doesn't matter which
+one of them I write.
+
+q has gone to 0,
+so I basically need
+
+to look at the average of
+the alpha of x, the beta of x
+
+[INAUDIBLE], divided by area.
+
+So what is there
+in the numerator?
+
+We can see that in the
+numerator, sq goes to 0.
+
+What I'm looking at is the sum
+of all of these dislocations
+
+that I have in the system.
+
+Now the average up the
+sum is 0, because in all
+
+of our calculations, we've been
+restricting the configurations
+
+that we moved from.
+
+Because if I go
+beyond that strategy,
+
+it's going to cost too much.
+
+But what I'm looking
+at is not the average
+
+of b, which is 0, but
+the average of b squared,
+
+which is the variance.
+
+So essentially I have a system
+that has a large area, a.
+
+It is on average neutral.
+
+And the question is, what is
+the variance of the net charge.
+
+And my claim is that the
+variance of the net charge
+
+is, by central limit theorem,
+proportional to the area--
+
+actually, it is proportional
+to the units that are
+
+independent from each other.
+
+So roughly I would expect that
+in this high temperature phase,
+
+I have a correlation that is c.
+
+And within each portion of
+side c, will be neutral.
+
+But when I go within things
+that are more than c apart,
+
+there's no reason to
+maintain the strategy.
+
+So overall I have something
+like throwing coins,
+
+but at each one of
+them, the average
+
+is 0, with probability
+being up or down.
+
+But when I look at the
+variance for the entire thing,
+
+the average will be
+proportional to the area
+
+in units of these things that
+are independent of each other.
+
+It was from the normalization
+factor of 1 over area.
+
+And these, really, I should
+write as a proportionality,
+
+because I don't
+know precisely what
+
+the relationship between
+these independent sides
+
+that correlation [INAUDIBLE].
+
+But they have to be
+roughly proportional.
+
+So what do you compute?
+
+You compute that
+the limit as q goes
+
+to 0, of the average of my
+theta tilde of q squared
+
+is a structure such as this.
+
+I forgot to put one
+more thing here.
+
+I don't expect to
+be any correlations
+
+between the x
+component and the y
+
+component of this
+answer-- the variance,
+
+the covariance of the
+dislocations in one
+
+direction and the
+other direction--
+
+so I put the delta
+function there.
+
+If I put this over here,
+I would get the q squared
+
+divided by q to the 4th.
+
+So I will get a 1
+over4 q squared.
+
+And I have the c squared and
+then some unknown coefficient
+
+up here.
+
+So it's interesting,
+because we started
+
+without thinking about
+dislocations, just in terms
+
+of the distortion field.
+
+And we said that this object
+is related to the angle.
+
+And indeed, we had
+this distortion,
+
+that energy cost of distortions
+is proportional to angle
+
+squared.
+
+And that angle, therefore,
+is not the Goldstone mode
+
+because it doesn't
+go like q squared.
+
+Now we go to this
+other phase now,
+
+with dislocations
+all over the place,
+
+and we calculate the expectation
+value of theta squared.
+
+And it looks like it
+came from a theory that
+
+was like Goldstone modes.
+
+So you would say that once
+I am in this phase, where
+
+the dislocations are unbound,
+there is an effective energy
+
+cost for these
+changes in angle that
+
+is proportional to the
+radiant of the angle squared.
+
+So that means fullier space,
+this would go to k a over 2,
+
+integral into q 2 pi squared,
+q squared theta tilde of q
+
+squared.
+
+So that if you had this
+theory, you would definitely
+
+say that the expectation value
+of theta tilde of q squared
+
+is 1 over k a q squared.
+
+The variance is k
+a q squared invers.
+
+You compare those two things
+and you find that once
+
+the dislocations have
+unbound, and there
+
+is a correlation lend
+that essentially tells you
+
+how far the dislocations
+are talking to each other
+
+and maintaining neutrality,
+that there is exactly
+
+an effective stiffness,
+like a Goldstone note,
+
+for angular distortions, that
+is proportional to c squared.
+
+And hence, if I were to look
+at the orientation of all
+
+their correlations,
+I would essentially
+
+have something like expectation
+value of theta q squared,
+
+which is 1 over q squared.
+
+If I fully transform
+that, I get the log.
+
+And so I will get
+something that falls off
+
+in the distance to some
+other exponent, if I recall
+
+[INAUDIBLE].
+
+If I have a true
+liquid-- in a liquid,
+
+again, maybe in a
+neighborhood of seven
+
+or eight particles,
+neighbors, et cetera,
+
+they talk to each other and the
+orientations are correlated.
+
+But then I go from
+one part of the liquid
+
+to another part of
+the liquid, there
+
+is no correlation
+between bond angles.
+
+I expect these things
+to decay exponentially.
+
+So what we've established
+is that neither the phonon
+
+nor the dislocations
+are sufficient to give
+
+the exponential decay that
+you expect for the bond.
+
+So this object has
+quasi long range order,
+
+versus what I expect to
+happen in the liquid, which
+
+is exponential of
+minus x over psi.
+
+So the unbinding of
+dislocations gives rise
+
+to the new phase of matter
+that has this quasi long range
+
+order in the orientations.
+
+It has no positional order.
+
+It's a kind of a liquid crystal
+that is called a hexatic.
+
+Yes?
+
+AUDIENCE: So your correlation
+where you got 1 over k q
+
+squared, doesn't that assume
+that you're allowing the angle
+
+to vary in minus [INAUDIBLE]
+when you do your averaging?
+
+What about the restriction--
+
+PROFESSOR: OK, so what is the
+variance of the angle here?
+
+There's a variance of the angle
+that is controlled by this 1
+
+over k a.
+
+So if I go back and calculate
+these in real space,
+
+I will find that if I look at
+theta at location x minus theta
+
+at location 0, the
+answer is going to go
+
+like 1 over k logarithm x.
+
+So what it says
+is that if things
+
+are close enough to each other--
+and this is in units of 1/a--
+
+up to some factor, let's
+say log 5, et cetera.
+
+So I don't go all
+the way to infinity.
+
+The fluctuations in angle are
+inversely set by a parameter
+
+that we see as I approach
+right after the transition is
+
+very large.
+
+So in the same sense
+that previously
+
+for the positional
+correlations I
+
+had the temperature being small
+and inverse temperature being
+
+large, limiting the size of
+the translational fluctuations,
+
+here the same thing happens for
+the bond angle fluctuations.
+
+Close to the transitions,
+they are actually small.
+
+So the question
+that you asked, you
+
+could have certainly
+also asked over here.
+
+That is, when I'm thinking
+about the distortion field,
+
+the distortion field is
+certainly going to be limited.
+
+If it becomes as big as this,
+then it doesn't make sense.
+
+So given that,
+what sense or what
+
+justification do I have
+in making these Gaussian
+
+integrals?
+
+And the answer is
+that while it is true
+
+that it is fluctuating, as
+I go to low temperature,
+
+the degree of fluctuations
+is very small.
+
+So effectively
+what I have is that
+
+I have to integrate over
+some finite interval
+
+a function that kind
+of looks like this.
+
+And the fact that I replaced
+that with an integration
+
+from minus infinity to infinity
+rather than from minus a
+
+to a just doesn't matter.
+
+So we know that ultimately
+we should get this,
+
+but so far we've only got
+this, so what should we do?
+
+Well, we say OK, we
+encountered this difficulty
+
+before in something that looked
+like an angle in the xy model--
+
+that low temperature
+had power-law decay,
+
+whereas we knew that
+at high temperatures
+
+they would have to
+have exponential decay.
+
+And what we said was that we
+need these topological defects
+
+in angle.
+
+So what you need-- topological
+defects-- or in our case,
+
+theta is a bond angle.
+
+And these topological defects
+in the bond angle have a name.
+
+They're called disconnections.
+
+And very roughly they correspond
+to something like this.
+
+Suppose this is the center
+one of these discriminations,
+
+and then maybe
+next to this, here
+
+I have locally at the distance
+r-- if I look at a point,
+
+I would see that the bonds
+that connect it to its neighbor
+
+have an orientation such as the
+one that I have indicated over
+
+here.
+
+Now what I want to do is, as I
+go around and make a circuit,
+
+that this angle theta
+that I have here to be 0,
+
+rotates and comes
+back up to 60 degrees.
+
+So essentially what I
+do is I take this line
+
+and I gradually shift it
+around so that by the time
+
+I come back, I have
+rotated by 60 degrees.
+
+It's kind of hard
+for me to draw that,
+
+but you can imagine
+what I have to do.
+
+So what I need to do
+is to have the integral
+
+over a circuit that encloses
+this discrimination such
+
+that when I do a d s dotted
+with the gradient of the bond
+
+orientational angle,
+I come back to pi over
+
+6 times some integer.
+
+And again, I expect the
+[INAUDIBLE] dislocations that
+
+correspond to minus plus 1.
+
+Then the cost of
+these is obtained
+
+by taking this distortion
+fee, gradient of theta,
+
+whose magnitude at a distance r
+from the center of this object
+
+is going to be 1 over 2
+pi r times pi over 6 times
+
+whatever this integer n is.
+
+And then if I substitute
+this 1 over r behavior
+
+in this expression, which
+is the effective energy
+
+of this entity, I will
+get the logarithmic cost
+
+for making a single
+disclination.
+
+Which means that
+at low temperature,
+
+I have to create
+disclination pairs.
+
+And then there will be
+an effective interaction
+
+between disclination
+pairs, that is
+
+[INAUDIBLE] in exactly the
+same way that we calculated
+
+for the x y model.
+
+So up to just this minor change
+that the charge of a refect
+
+is reduced by a factor
+of six, this theory
+
+is identical the theory of
+the unbinding of the x y
+
+model [INAUDIBLE] defects.
+
+Yes?
+
+AUDIENCE: Why is it pi
+over 6 and not 2 pi over 6?
+
+PROFESSOR: You are right.
+
+It should be 2 pi over 6.
+
+Thank you.
+
+Yes?
+
+AUDIENCE: So when
+you were saying that
+
+the-- so the distance of this
+hexatic phase would require
+
+the dislocations to occur
+to [INAUDIBLE] [INAUDIBLE]
+
+orientational defects.
+
+Is there an analogous
+case where--
+
+I guess you can't have
+dislocations in the orientation
+
+without the dislocation--
+
+PROFESSOR: So if you try
+to make these objects
+
+in the original case, in
+the origin of lattice,
+
+you will find that their
+cost grows actually
+
+like l squared log l, as
+opposed to dislocations,
+
+whose cost only grows as log l.
+
+So these entities are
+extremely unlikely to occur
+
+in the original system.
+
+If you sort of go back
+and ask what they actually
+
+correspond to, if you have a
+picture that you have generated
+
+on the computer,
+they're actually
+
+reasonably easy to identify.
+
+Because the centers
+of these disclinations
+
+correspond to
+having points, that
+
+have, rather than 6
+neighbors, 5 or 7 neighbors.
+
+So you generate the picture,
+and you find mostly you have
+
+neighborhoods with 6 neighbors,
+and then there's a site where
+
+there's 5 neighbours,
+and another site that's 7
+
+neighbors.
+
+5 and 7 come more
+or less in pairs,
+
+and you can identify these
+disclination pairs reasonably
+
+easy.
+
+So at the end of the day,
+the picture that we have
+
+is something like this.
+
+We are starting with
+the triangular lattice
+
+that I drew at the
+beginning, and you're
+
+increasing temperature.
+
+We're asking what happens.
+
+So this is 0 temperature.
+
+Close to 0 temperature,
+what we have
+
+is an entity that has
+translational quasi
+
+long range order.
+
+So this quantity goes like 1
+over x to this power a to g.
+
+Whereas the orientations
+go to a constant.
+
+Now, this a to g is
+there because there's
+
+a shear modulus.
+
+And so throughout this phase,
+I have a shear modulus.
+
+The parameter that
+I'm calling u,
+
+I had scaled inversely
+with temperature.
+
+So I have this
+shear modulus u that
+
+diverges once we scale
+by temperature as 1
+
+over temperature.
+
+But then as I come down, the
+reduction is more than one
+
+over temperature
+because I will have
+
+this effect of dislocations
+appearing in pairs,
+
+and the system becomes softer.
+
+And eventually you
+will find that there's
+
+a transition temperature at
+which the shear modulus drops
+
+down to 0.
+
+And we said that
+near this transition,
+
+there is this behavior
+that mu approaches mu
+
+c, whatever it is,
+with something-- let's
+
+call this t 1.
+
+T 1 minus t to this
+exponent mu bar
+
+which was planned to be 6963.
+
+Now, once we are beyond
+this temperature t 1, then
+
+our positional correlations
+decay exponentially
+
+at some correlation, like c.
+
+And this c is
+something that diverges
+
+on approaching this transition.
+
+So basically I have a c that
+goes up here to infinity.
+
+And the fact that if
+we calculate the c,
+
+it diverges according to
+this strange formula that
+
+was 1 over t minus t
+1 to this exponent mu
+
+bar Very strange
+type of divergence.
+
+But then, associated with
+the presence of this c
+
+is the fact that when you
+look at the orientational
+
+correlations, they don't
+decay as an exponential
+
+but as a power-law 8 of c.
+
+And this 8 of c is related to
+this k a, and falls off as 1
+
+over c squared.
+
+So here it diverges as you
+approach this transition.
+
+Now, as we go further
+and further on,
+
+the disclinations will
+appear-- disclinations
+
+with [INAUDIBLE]
+resolve of the angles
+
+to be parallel to each other.
+
+And there's another
+transition that
+
+is [INAUDIBLE], at which this is
+going to suddenly go down to 0.
+
+And close to here,
+we have that a to c
+
+reaches the critical
+value of 1/4 v
+
+to square root
+of-- let's call it
+
+t 2-- v the square
+root singularity.
+
+And then finally we have
+the ordinary liquid phase,
+
+where additionally I will find
+that psi 6 of x psi star 6 of 0
+
+decays exponentially.
+
+Let's call it psi 6.
+
+And this psi 6 is
+something that will diverge
+
+of this transition as an
+exponential of minus 1
+
+over square root of t minus t2.
+
+So this is the current
+scenario of how
+
+melting could occur for a system
+of particles in two dimensions.
+
+If it is a continuous
+phase transition,
+
+it has to go through
+these two transitions
+
+with the intermediate
+exotic phase.
+
+Of course, it is also
+possible-- and typically people
+
+were seeing numerically
+when they were doing hearts,
+
+spheres, et cetera,
+that there is
+
+a direct transition from here
+to here, which is discontinuous,
+
+like you have in
+three dimensions.
+
+So that's an area of a
+discontinuous transition
+
+that is not ruled out.
+
+But if you have
+continuous transitions,
+
+it has to have this intermediate
+phase in [INAUDIBLE].
+
+Any questions?
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+so the red one is mu.
+
+The yellow one is theta psi, and
+the purple one is [INAUDIBLE].
+
+PROFESSOR: The correlation,
+then, that I would put here.
+
+So they are three
+different entities.
+
+So throughout the
+course, we have
+
+been thinking about
+systems that are
+
+described by some kind of
+an equilibrium probability
+
+distribution.
+
+So what we did not
+discuss is how the system
+
+comes to that equilibrium.
+
+So we're going to now very
+briefly talk about dynamics,
+
+and the specific
+type of dynamics
+
+that is common to
+condensed matter
+
+systems at finite
+temperature, which I
+
+will call precipative dynamics.
+
+And the prototype of this
+is a Brownian particle
+
+that I will briefly
+review for you.
+
+So what you have is that
+you have a particle that
+
+is within some
+kind of a solvent,
+
+and this particle
+is moving around.
+
+So you would say,
+let's for simplicity
+
+actually focus on
+the one direction, x.
+
+And you would say that
+the mass of the particle
+
+times its acceleration
+is equal to the forces
+
+that it's experiencing.
+
+The forces-- well, if you
+are moving in a fluid,
+
+you are going to be
+subject to some kind
+
+of a dissipative force
+which is typically
+
+portional to your velocity.
+
+If you, for example,
+solve for the hydrodynamic
+
+of a sphere in a
+fluid, you find that mu
+
+is related to
+viscosity inversely
+
+to the size of the
+particle, et cetera.
+
+But that behavior is generic.
+
+You're not going be
+thinking about that.
+
+Now suppose that
+additionally I put
+
+some kind of an optical
+trap, or something that tries
+
+to localize this potential.
+
+So then there would be
+an additional force v
+
+2, the derivative of the
+potential with respect to x.
+
+And then we are talking
+about Brownian particles.
+
+Brownian particles are
+constantly jiggling.
+
+So there is also a random force
+that is a function of time.
+
+Now we are going to be
+interested in the dynamics that
+
+is very much controlled
+by the dissipation term.
+
+And acceleration we can forget.
+
+And if we are in that limit,
+we can write the equation
+
+as mu-- I can sort of rearrange
+it slightly as-- actually,
+
+let me change location to this.
+
+So that the eventual
+velocity x dot
+
+is going to be proportional
+to the external force.
+
+mu the coefficient
+that is the mobility.
+
+So mu essentially relates
+the force to the velocity.
+
+Of course, this is
+the average force.
+
+And there is a fluctuating
+part, so essentially, I
+
+call mu times this to be
+the a times function of t.
+
+Now, if I didn't have
+this external force,
+
+the fluctuations of the
+particles would be diffusive.
+
+And you can convince
+yourself that you
+
+can get the diffusive result
+provided that you relate
+
+the correlations of this
+force that fluctuating
+
+and have 0 average, the
+diffusion constant d
+
+of the particle in the medium
+through delta of t minus t.
+
+So if their track was not there,
+you solve of this equation
+
+without the track and find that
+the prohibitive distribution
+
+for x grows as a Gaussian whose
+width grows with time, as d t.
+
+d therefore must be
+the diffusion constant.
+
+Now, in the presence
+of the potential,
+
+this particle will
+start to fluctuate.
+
+Eventually if you
+wait long enough,
+
+there is a probability
+that it will be here,
+
+a probability to
+be somewhere else.
+
+So at long enough times,
+there's a probability p
+
+of x to find the particle.
+
+And you expect
+that t of x will be
+
+proportional to exponential
+of minus v of x divided
+
+by whatever the temperature is.
+
+And you can show that in
+order to have this occur,
+
+you need to relate mu and d
+through the so called Einstein
+
+relation.
+
+So this is a brief review
+of Brownian particles.
+
+Yes?
+
+AUDIENCE: The average and
+time correlation of eta
+
+can be found by saying
+the potential is 0, right?
+
+PROFESSOR: Mm hmm.
+
+AUDIENCE: Those
+will still be true
+
+even if the potential
+is not 0, right?
+
+PROFESSOR: Yes.
+
+So I just wanted to have an
+idea of where this d comes from.
+
+But more specifically, this
+is the important thing.
+
+That if at very
+long times you want
+
+to have a probability
+distribution coming
+
+from this equation, that
+has the Boltzmann form
+
+with k t, the coefficients
+of mu and the noise,
+
+you have to relate through the
+so called Einstein relation.
+
+And once you do
+that, this result
+
+is true no matter how
+complicated this v of x is.
+
+So in general, for a
+complicated v of x,
+
+you won't be able to solve
+this equation analytically.
+
+You can only do it numerically.
+
+Yet you are guaranteed that
+this equation with this noise
+
+correlator will have
+asymptotically a probability
+
+distribution of [INAUDIBLE].
+
+The problem that we
+have been looking at all
+
+along is something different.
+
+Let's say you have, let's
+say, a piece of magnet
+
+or some other system
+that we characterize,
+
+let's say, by something m of x.
+
+Again, you can do it for vector,
+but for simplicity, let's do it
+
+for the scalar case.
+
+So we know, or we have stated,
+that subject to the symmetries
+
+of the system, I
+know the probability.
+
+For some configuration of this
+field is governed by a form,
+
+let's say, that has
+Landau Ginzburg character.
+
+So that has been
+our starting point.
+
+We have said that I have a
+prohibitive distribution that
+
+is of this form.
+
+So that statement is kind
+of like this statement.
+
+But the way that I
+came to that statement
+
+was to say that there
+was a degree of freedom
+
+x, the position of the particle,
+that was fluctuating subject
+
+to forces and external
+variables from the particles
+
+of the fluid, that was given
+by this so called Langevin
+
+equation.
+
+So I had a time
+dependent prescription
+
+that eventually went to the
+Boltzmann way that I wanted.
+
+Here I have started with
+the final Boltzmann weight.
+
+And the question is, can
+I think about a dynamics
+
+for a field that will
+eventually give this state.
+
+So there are lots and
+lots of different dynamics
+
+that I can impose.
+
+But I want to look
+at the dynamics that
+
+is closest to the Brownian
+particle that I wrote,
+
+and that's where this
+word dissipative comes.
+
+So among the universe of
+all possible dynamics,
+
+I'm going to look at one
+that has a linear time
+
+derivative for the field n.
+
+So this is the
+analog of the x dot.
+
+And so I write that it is
+equal to some coefficient,
+
+that with their minds,
+the ease with which
+
+that particle-- well the
+field of that location x
+
+changes as a function of the
+forces that is exerted on it.
+
+I assume that mu is the
+same across my system.
+
+So here I'm already assuming
+there's no x dependence.
+
+This system is uniform.
+
+And then there was a d v by d x.
+
+So v was ultimately the
+thing that was appearing
+
+in the Boltzmann weight.
+
+So clearly the analog
+of the v that I have
+
+is this Landau Ginzburg.
+
+So I will do a function of the
+derivative of this quantity
+
+that I will call beta h,
+with respect to m of x.
+
+Again, over there, I
+had one variable, x.
+
+You can imagine that I could
+have had a system where
+
+two particles, x 1 and x 2, also
+have an interaction among them.
+
+Then the equation that I
+would have had over there
+
+would be the force that
+is acting on particle 1,
+
+by taking the total
+potential-- which
+
+is the external potential
+plus the potential that
+
+comes from the inter
+particle interaction.
+
+So I would have to
+take a derivative
+
+of the net potential energy
+v, divided with respect
+
+to either x 1 or x 2
+to calculate the force
+
+on the first one
+or the second one.
+
+So here for a
+particular configuration
+
+m of the field
+across the system,
+
+if I'm interested in the
+dynamics of this position x,
+
+I have to take this total
+internal potential energy,
+
+and take the
+derivative with respect
+
+to the variable that is
+sitting on that side.
+
+So that's why this
+is a functional
+
+derivative of this end.
+
+And then I will have
+to put a noise, eta.
+
+Well, again, if I had
+multiple particles,
+
+I would subject each one of
+them to an independent noise.
+
+So at each location, I
+have an independent noise.
+
+So the noise is a
+function of time,
+
+but it is also wearing
+across my system.
+
+So if I take that form and do
+the functional derivative--
+
+so if I take the derivative
+with respect to m of x,
+
+I have to take the
+derivative of these objects.
+
+So I will have minus derivative
+of t m squared is t m.
+
+The u m to the 4th is
+4 u m q, and so forth.
+
+Once I have gotten
+rid of these terms,
+
+then I would have terms
+that depend on the gradient.
+
+So I would have minus the
+derivative of this object
+
+with respect to the gradient.
+
+So here I would get
+k gradient of m.
+
+And then the next term would
+be Laplacian derivative,
+
+with respect to Laplacian.
+
+So I would put l Laplacian
+of m, and so forth
+
+with the methodologies of
+taking function derivatives.
+
+And then I have the noise.
+
+So this leads to
+an equation which
+
+is called a time
+dependent, Landau Ginzberg.
+
+Because we started with
+the Landau Ginzberg weight,
+
+and this equation,
+as we see shortly,
+
+subject to similar restrictions
+as we had before, will give us,
+
+eventually, this
+probability distribution.
+
+This is a difficult
+equation in the same sense
+
+that the original
+Landau Ginzberg
+
+is difficult to look at
+correlations, et cetera.
+
+This is a nonlinear equation,
+causes various difficulties,
+
+and we need approaches
+to be able to deal
+
+with the difficult,
+non linealities.
+
+So what we did for
+the Landau Ginzburg
+
+was to initially get insights
+and simplify the system
+
+by focusing on the linearized
+or Gaussian version.
+
+So let's look at the version
+of this equation that
+
+is linearized.
+
+And when it is linearized, what
+I have on the left hand side
+
+is d m by d t.
+
+What I have on the
+right hand side is mu.
+
+I have t m.
+
+I got rid of the
+non linear term,
+
+so the next term that I will
+have will be k Laplacian of m,
+
+and then will be minus l 4th
+derivative of m, and so forth.
+
+And then there will be
+a noise [INAUDIBLE].
+
+One thing that I
+can immediately do
+
+is to go to fullier transform.
+
+So m of x goes to m theta of q.
+
+And if I do that, but not
+fullier transform in time,
+
+I will get that the time
+derivative of m tilde of q
+
+is essentially what I have here.
+
+And I forgot the minus
+that I have here.
+
+So this minus is important.
+
+And then this becomes negative,
+this becomes positive.
+
+So that when I go fullier
+transform, what I will get
+
+is minus t plus k q squared plus
+l q to the 4th, and so forth.
+
+And tilde of q with
+this mu out front.
+
+And then the fullier
+transform of what my noise is.
+
+First thing to note is that
+even in the absence of noise,
+
+there is a set of
+relaxation times.
+
+That is, for eta it was to 0.
+
+Or in general, I would
+have n tilde of q and p.
+
+I can solve this
+equation kind of simply.
+
+It is the m by d t is
+some constant times
+
+n-- let's call it
+gama of q-- which
+
+has dimensions of 1 over time.
+
+So I can call that
+1 over tau of q.
+
+If I didn't have
+noise, if I started
+
+with some original
+value at time 0,
+
+it is going to
+decay exponentially
+
+with this characteristic time.
+
+And once I have
+noise, it is actually
+
+easy to convince yourself
+that the answer is
+
+0 2 t d t prime e to the minus
+this gamma of q or inversify.
+
+Tau of q times eta
+of q i t prime.
+
+So you see that you have a
+hierarchy of relaxation times,
+
+ta of q, which are 1 over u t
+plus k q squared, and so forth,
+
+which scale in two limits.
+
+Either the wavelength lambda,
+which is the inverse of q
+
+is much larger than the
+correlation length--
+
+and the correlation
+length of this model
+
+you have seen to be the
+square root of t over k,
+
+square root of k over
+t-- or the other limit,
+
+where lambda is
+much less than c.
+
+In this limit,
+where we are looking
+
+at modes that are much shorter
+than the correlation length,
+
+this term is dominant.
+
+This becomes 1 over
+mu k q squared.
+
+In the other limit, it goes
+to a constant 1 over u t.
+
+So this linear equation
+has a whole bunch
+
+of modes that can
+be characterized
+
+by their wavelength
+or their wave number.
+
+You find that the
+short wavelength modes
+
+have this characteristic, time,
+that becomes longer and longer
+
+as the wavelength increases.
+
+So if you make the
+wavelength twice as large,
+
+and you want to relax a
+system that is linearly
+
+twice as large, this says that
+it will take 4 times longer.
+
+Because the answer goes
+like lambda squared.
+
+Whereas eventually you reach the
+size of the correlation length.
+
+Once you are beyond the size
+of the correlation length,
+
+it doesn't matter.
+
+It's the same time.
+
+But the interesting
+thing, of course, to us
+
+is that there are
+phase transitions that
+
+are continuous.
+
+And close to that
+phase transition,
+
+the correlation length
+goes to infinity.
+
+Which means that the relaxation
+time also will go to infinity.
+
+So according to
+this theory, there's
+
+a particular divergence
+as 1 over t minus t c.
+
+But it will be modified, and
+as I will discuss next time,
+
+this is only-- even within
+to dissipative class--
+
+one type of dynamics
+that you can have.
+
+And there are
+additional dynamics,
+
+and this system
+characterizes criticality
+
+as single universality
+class in statics.
+
+There are many dynamic
+universality classes that
+
+correspond to this same static.
\ No newline at end of file
diff --git a/S6dw885-SZI.txt b/S6dw885-SZI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b8b4d9bd99fbb3ed929517bd422e509e7ea1dd99
--- /dev/null
+++ b/S6dw885-SZI.txt
@@ -0,0 +1,8616 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu well okay this is my lecture
+
+ align:start position:0%
+ocw.mit.edu well okay this is my lecture
+ 
+
+ align:start position:0%
+ocw.mit.edu well okay this is my lecture
+on uh section 6.1 of the
+
+ align:start position:0%
+on uh section 6.1 of the
+ 
+
+ align:start position:0%
+on uh section 6.1 of the
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+uh really the central problem of uh
+
+ align:start position:0%
+uh really the central problem of uh
+ 
+
+ align:start position:0%
+uh really the central problem of uh
+numerical linear algebra is solving ax
+
+ align:start position:0%
+numerical linear algebra is solving ax
+ 
+
+ align:start position:0%
+numerical linear algebra is solving ax
+equal B by elimination that's what is
+
+ align:start position:0%
+equal B by elimination that's what is
+ 
+
+ align:start position:0%
+equal B by elimination that's what is
+used much more often than anything else
+
+ align:start position:0%
+used much more often than anything else
+ 
+
+ align:start position:0%
+used much more often than anything else
+but we're talking about sparse matrices
+
+ align:start position:0%
+but we're talking about sparse matrices
+ 
+
+ align:start position:0%
+but we're talking about sparse matrices
+large sparse matrices that's what we're
+
+ align:start position:0%
+large sparse matrices that's what we're
+ 
+
+ align:start position:0%
+large sparse matrices that's what we're
+we have in mind from from for a long
+
+ align:start position:0%
+we have in mind from from for a long
+ 
+
+ align:start position:0%
+we have in mind from from for a long
+time now they're probably the all
+
+ align:start position:0%
+time now they're probably the all
+ 
+
+ align:start position:0%
+time now they're probably the all
+lectures coming up thinking of those
+
+ align:start position:0%
+lectures coming up thinking of those
+ 
+
+ align:start position:0%
+lectures coming up thinking of those
+matrices and this is the Prototype of a
+
+ align:start position:0%
+matrices and this is the Prototype of a
+ 
+
+ align:start position:0%
+matrices and this is the Prototype of a
+large sparse Matrix okay so the main
+
+ align:start position:0%
+large sparse Matrix okay so the main
+ 
+
+ align:start position:0%
+large sparse Matrix okay so the main
+point the lecture is if you take the
+
+ align:start position:0%
+point the lecture is if you take the
+ 
+
+ align:start position:0%
+point the lecture is if you take the
+unknowns in whatever order they're given
+
+ align:start position:0%
+unknowns in whatever order they're given
+ 
+
+ align:start position:0%
+unknowns in whatever order they're given
+here I took them uh numbering along the
+
+ align:start position:0%
+here I took them uh numbering along the
+ 
+
+ align:start position:0%
+here I took them uh numbering along the
+rows 1 2 3 4 5 6 seven eight and so on
+
+ align:start position:0%
+rows 1 2 3 4 5 6 seven eight and so on
+ 
+
+ align:start position:0%
+rows 1 2 3 4 5 6 seven eight and so on
+that's uh you you got to stop and think
+
+ align:start position:0%
+that's uh you you got to stop and think
+ 
+
+ align:start position:0%
+that's uh you you got to stop and think
+or get the computer to look at
+
+ align:start position:0%
+or get the computer to look at
+ 
+
+ align:start position:0%
+or get the computer to look at
+reorderings because the reorderings can
+
+ align:start position:0%
+reorderings because the reorderings can
+ 
+
+ align:start position:0%
+reorderings because the reorderings can
+make an enormous difference in the in
+
+ align:start position:0%
+make an enormous difference in the in
+ 
+
+ align:start position:0%
+make an enormous difference in the in
+the in the fill in so this is the
+
+ align:start position:0%
+the in the fill in so this is the
+ 
+
+ align:start position:0%
+the in the fill in so this is the
+actually the key word for this lecture
+
+ align:start position:0%
+actually the key word for this lecture
+ 
+
+ align:start position:0%
+actually the key word for this lecture
+is and the key concept is the fact that
+
+ align:start position:0%
+is and the key concept is the fact that
+ 
+
+ align:start position:0%
+is and the key concept is the fact that
+as elimination goes forward all a lot of
+
+ align:start position:0%
+as elimination goes forward all a lot of
+ 
+
+ align:start position:0%
+as elimination goes forward all a lot of
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zeros become
+
+ align:start position:0%
+zeros become
+ 
+
+ align:start position:0%
+zeros become
+nonzeros so let let me see it happen
+
+ align:start position:0%
+nonzeros so let let me see it happen
+ 
+
+ align:start position:0%
+nonzeros so let let me see it happen
+first of all so this is the whole idea
+
+ align:start position:0%
+first of all so this is the whole idea
+ 
+
+ align:start position:0%
+first of all so this is the whole idea
+of fill in what's going to be the very
+
+ align:start position:0%
+of fill in what's going to be the very
+ 
+
+ align:start position:0%
+of fill in what's going to be the very
+first entries that are filled in
+
+ align:start position:0%
+first entries that are filled in
+ 
+
+ align:start position:0%
+first entries that are filled in
+well uh let's see I guess that the very
+
+ align:start position:0%
+well uh let's see I guess that the very
+ 
+
+ align:start position:0%
+well uh let's see I guess that the very
+first row operation if if you took the m
+
+ align:start position:0%
+first row operation if if you took the m
+ 
+
+ align:start position:0%
+first row operation if if you took the m
+tricks like this and did did elimination
+
+ align:start position:0%
+tricks like this and did did elimination
+ 
+
+ align:start position:0%
+tricks like this and did did elimination
+four is the first pivot you would add
+
+ align:start position:0%
+four is the first pivot you would add
+ 
+
+ align:start position:0%
+four is the first pivot you would add
+1/4 of the first row to the second row
+
+ align:start position:0%
+1/4 of the first row to the second row
+ 
+
+ align:start position:0%
+1/4 of the first row to the second row
+to make that a zero right and then what
+
+ align:start position:0%
+to make that a zero right and then what
+ 
+
+ align:start position:0%
+to make that a zero right and then what
+would happen this would change that
+
+ align:start position:0%
+would happen this would change that
+ 
+
+ align:start position:0%
+would happen this would change that
+number that's
+
+ align:start position:0%
+number that's
+ 
+
+ align:start position:0%
+number that's
+okay but this would put a new number in
+
+ align:start position:0%
+okay but this would put a new number in
+ 
+
+ align:start position:0%
+okay but this would put a new number in
+there right so a new number would appear
+
+ align:start position:0%
+there right so a new number would appear
+ 
+
+ align:start position:0%
+there right so a new number would appear
+when we do that first row operation and
+
+ align:start position:0%
+when we do that first row operation and
+ 
+
+ align:start position:0%
+when we do that first row operation and
+then all Al working with this pivot I
+
+ align:start position:0%
+then all Al working with this pivot I
+ 
+
+ align:start position:0%
+then all Al working with this pivot I
+would operate on that row to make this a
+
+ align:start position:0%
+would operate on that row to make this a
+ 
+
+ align:start position:0%
+would operate on that row to make this a
+zero and then this would change that
+
+ align:start position:0%
+zero and then this would change that
+ 
+
+ align:start position:0%
+zero and then this would change that
+would fill in right and I guess that
+
+ align:start position:0%
+would fill in right and I guess that
+ 
+
+ align:start position:0%
+would fill in right and I guess that
+this already has something so that won't
+
+ align:start position:0%
+this already has something so that won't
+ 
+
+ align:start position:0%
+this already has something so that won't
+be new so each of those steps each of
+
+ align:start position:0%
+be new so each of those steps each of
+ 
+
+ align:start position:0%
+be new so each of those steps each of
+those row
+
+ align:start position:0%
+those row
+ 
+
+ align:start position:0%
+those row
+operations filled in a
+
+ align:start position:0%
+operations filled in a
+ 
+
+ align:start position:0%
+operations filled in a
+nonzero
+
+ align:start position:0%
+nonzero
+ 
+
+ align:start position:0%
+nonzero
+and reduce the the sparsity of the
+
+ align:start position:0%
+and reduce the the sparsity of the
+ 
+
+ align:start position:0%
+and reduce the the sparsity of the
+Matrix and the the sparsity is what
+
+ align:start position:0%
+Matrix and the the sparsity is what
+ 
+
+ align:start position:0%
+Matrix and the the sparsity is what
+we're living by so we want to know and
+
+ align:start position:0%
+we're living by so we want to know and
+ 
+
+ align:start position:0%
+we're living by so we want to know and
+and now if I continue and
+
+ align:start position:0%
+and now if I continue and
+ 
+
+ align:start position:0%
+and now if I continue and
+continue uh we'd actually we'd need
+
+ align:start position:0%
+continue uh we'd actually we'd need
+ 
+
+ align:start position:0%
+continue uh we'd actually we'd need
+matlb to use spy in mat lab to uh see
+
+ align:start position:0%
+matlb to use spy in mat lab to uh see
+ 
+
+ align:start position:0%
+matlb to use spy in mat lab to uh see
+what the picture would look like it's
+
+ align:start position:0%
+what the picture would look like it's
+ 
+
+ align:start position:0%
+what the picture would look like it's
+very interesting to see it Spy shows you
+
+ align:start position:0%
+very interesting to see it Spy shows you
+ 
+
+ align:start position:0%
+very interesting to see it Spy shows you
+the nonzeros we're we're we're very much
+
+ align:start position:0%
+the nonzeros we're we're we're very much
+ 
+
+ align:start position:0%
+the nonzeros we're we're we're very much
+focused on what's zero and what isn't
+
+ align:start position:0%
+focused on what's zero and what isn't
+ 
+
+ align:start position:0%
+focused on what's zero and what isn't
+zero in Matrix entry
+
+ align:start position:0%
+zero in Matrix entry
+ 
+
+ align:start position:0%
+zero in Matrix entry
+we we actually keep track of that the
+
+ align:start position:0%
+we we actually keep track of that the
+ 
+
+ align:start position:0%
+we we actually keep track of that the
+the the structure of the Matrix as well
+
+ align:start position:0%
+the the structure of the Matrix as well
+ 
+
+ align:start position:0%
+the the structure of the Matrix as well
+of course as separately keeping track of
+
+ align:start position:0%
+of course as separately keeping track of
+ 
+
+ align:start position:0%
+of course as separately keeping track of
+the actual numbers so one place we're
+
+ align:start position:0%
+the actual numbers so one place we're
+ 
+
+ align:start position:0%
+the actual numbers so one place we're
+keeping the actual numbers but in the
+
+ align:start position:0%
+keeping the actual numbers but in the
+ 
+
+ align:start position:0%
+keeping the actual numbers but in the
+decisions on ordering we're only
+
+ align:start position:0%
+decisions on ordering we're only
+ 
+
+ align:start position:0%
+decisions on ordering we're only
+interested in zeros and nonzeros so let
+
+ align:start position:0%
+interested in zeros and nonzeros so let
+ 
+
+ align:start position:0%
+interested in zeros and nonzeros so let
+me look even more at this fill in just
+
+ align:start position:0%
+me look even more at this fill in just
+ 
+
+ align:start position:0%
+me look even more at this fill in just
+now you saw it happen up there let me
+
+ align:start position:0%
+now you saw it happen up there let me
+ 
+
+ align:start position:0%
+now you saw it happen up there let me
+just look at a single fill-in step
+
+ align:start position:0%
+just look at a single fill-in step
+ 
+
+ align:start position:0%
+just look at a single fill-in step
+so I have a so I have a row J and a row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I and this is going to be the pivot that
+
+ align:start position:0%
+I and this is going to be the pivot that
+ 
+
+ align:start position:0%
+I and this is going to be the pivot that
+I'll use to eliminate this but in this
+
+ align:start position:0%
+I'll use to eliminate this but in this
+ 
+
+ align:start position:0%
+I'll use to eliminate this but in this
+row there's
+
+ align:start position:0%
+row there's
+ 
+
+ align:start position:0%
+row there's
+a another nonzero and in this Row the
+
+ align:start position:0%
+a another nonzero and in this Row the
+ 
+
+ align:start position:0%
+a another nonzero and in this Row the
+case entry is not nonzero it's zero so
+
+ align:start position:0%
+case entry is not nonzero it's zero so
+ 
+
+ align:start position:0%
+case entry is not nonzero it's zero so
+this is what we start with prior to
+
+ align:start position:0%
+this is what we start with prior to
+ 
+
+ align:start position:0%
+this is what we start with prior to
+elimination just as we did there I just
+
+ align:start position:0%
+elimination just as we did there I just
+ 
+
+ align:start position:0%
+elimination just as we did there I just
+want to see focus on the small on the
+
+ align:start position:0%
+want to see focus on the small on the
+ 
+
+ align:start position:0%
+want to see focus on the small on the
+the fill in uh occurring okay so what
+
+ align:start position:0%
+the fill in uh occurring okay so what
+ 
+
+ align:start position:0%
+the fill in uh occurring okay so what
+does of course these are this isn't on
+
+ align:start position:0%
+does of course these are this isn't on
+ 
+
+ align:start position:0%
+does of course these are this isn't on
+the diagonal this is in column this is
+
+ align:start position:0%
+the diagonal this is in column this is
+ 
+
+ align:start position:0%
+the diagonal this is in column this is
+in um uh column K which is somewhere far
+
+ align:start position:0%
+in um uh column K which is somewhere far
+ 
+
+ align:start position:0%
+in um uh column K which is somewhere far
+out in that case somewhere close by in
+
+ align:start position:0%
+out in that case somewhere close by in
+ 
+
+ align:start position:0%
+out in that case somewhere close by in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+case uh but we're just we're seeing
+
+ align:start position:0%
+case uh but we're just we're seeing
+ 
+
+ align:start position:0%
+case uh but we're just we're seeing
+this is on the diagonal that's the pivot
+
+ align:start position:0%
+this is on the diagonal that's the pivot
+ 
+
+ align:start position:0%
+this is on the diagonal that's the pivot
+the Jace pivot that I'm ready to use so
+
+ align:start position:0%
+the Jace pivot that I'm ready to use so
+ 
+
+ align:start position:0%
+the Jace pivot that I'm ready to use so
+I subtract a multiple of that to remove
+
+ align:start position:0%
+I subtract a multiple of that to remove
+ 
+
+ align:start position:0%
+I subtract a multiple of that to remove
+that so what does elimination will not
+
+ align:start position:0%
+that so what does elimination will not
+ 
+
+ align:start position:0%
+that so what does elimination will not
+change the pivot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row and it will produce a zero there
+
+ align:start position:0%
+row and it will produce a zero there
+ 
+
+ align:start position:0%
+row and it will produce a zero there
+that's the point but then the real point
+
+ align:start position:0%
+that's the point but then the real point
+ 
+
+ align:start position:0%
+that's the point but then the real point
+that I'm making is that when I multiply
+
+ align:start position:0%
+that I'm making is that when I multiply
+ 
+
+ align:start position:0%
+that I'm making is that when I multiply
+this by the right number to produce a
+
+ align:start position:0%
+this by the right number to produce a
+ 
+
+ align:start position:0%
+this by the right number to produce a
+zero and do the subtraction this zero
+
+ align:start position:0%
+zero and do the subtraction this zero
+ 
+
+ align:start position:0%
+zero and do the subtraction this zero
+disappears that fills in
+
+ align:start position:0%
+disappears that fills in
+ 
+
+ align:start position:0%
+disappears that fills in
+that's that's some a i k new new the the
+
+ align:start position:0%
+that's that's some a i k new new the the
+ 
+
+ align:start position:0%
+that's that's some a i k new new the the
+the new value in row I column K is not
+
+ align:start position:0%
+the new value in row I column K is not
+ 
+
+ align:start position:0%
+the new value in row I column K is not
+zero okay so we see
+
+ align:start position:0%
+zero okay so we see
+ 
+
+ align:start position:0%
+zero okay so we see
+that as we saw for numbers here we're
+
+ align:start position:0%
+that as we saw for numbers here we're
+ 
+
+ align:start position:0%
+that as we saw for numbers here we're
+see seeing it symbolically let me see it
+
+ align:start position:0%
+see seeing it symbolically let me see it
+ 
+
+ align:start position:0%
+see seeing it symbolically let me see it
+graphically because everybody sort of to
+
+ align:start position:0%
+graphically because everybody sort of to
+ 
+
+ align:start position:0%
+graphically because everybody sort of to
+visualize the big
+
+ align:start position:0%
+visualize the big
+ 
+
+ align:start position:0%
+visualize the big
+picture I think everybody finds the
+
+ align:start position:0%
+picture I think everybody finds the
+ 
+
+ align:start position:0%
+picture I think everybody finds the
+graph description
+
+ align:start position:0%
+graph description
+ 
+
+ align:start position:0%
+graph description
+of the nonzero structure the simplest to
+
+ align:start position:0%
+of the nonzero structure the simplest to
+ 
+
+ align:start position:0%
+of the nonzero structure the simplest to
+to imagine so the graph for this little
+
+ align:start position:0%
+to imagine so the graph for this little
+ 
+
+ align:start position:0%
+to imagine so the graph for this little
+problem would be so what's the graph
+
+ align:start position:0%
+problem would be so what's the graph
+ 
+
+ align:start position:0%
+problem would be so what's the graph
+that tells me where the nonzeros are
+
+ align:start position:0%
+that tells me where the nonzeros are
+ 
+
+ align:start position:0%
+that tells me where the nonzeros are
+again it doesn't tell me what numbers
+
+ align:start position:0%
+again it doesn't tell me what numbers
+ 
+
+ align:start position:0%
+again it doesn't tell me what numbers
+they are just tells me where they are
+
+ align:start position:0%
+they are just tells me where they are
+ 
+
+ align:start position:0%
+they are just tells me where they are
+which positions it's only the positions
+
+ align:start position:0%
+which positions it's only the positions
+ 
+
+ align:start position:0%
+which positions it's only the positions
+that I worry about in deciding on the
+
+ align:start position:0%
+that I worry about in deciding on the
+ 
+
+ align:start position:0%
+that I worry about in deciding on the
+ordering to use then I execute using the
+
+ align:start position:0%
+ordering to use then I execute using the
+ 
+
+ align:start position:0%
+ordering to use then I execute using the
+actual numbers but in deciding on the
+
+ align:start position:0%
+actual numbers but in deciding on the
+ 
+
+ align:start position:0%
+actual numbers but in deciding on the
+ordering it's just the positions okay so
+
+ align:start position:0%
+ordering it's just the positions okay so
+ 
+
+ align:start position:0%
+ordering it's just the positions okay so
+I think of my graph was having node a
+
+ align:start position:0%
+I think of my graph was having node a
+ 
+
+ align:start position:0%
+I think of my graph was having node a
+node for
+
+ align:start position:0%
+node for
+ 
+
+ align:start position:0%
+node for
+every uh row so that's node J for row J
+
+ align:start position:0%
+every uh row so that's node J for row J
+ 
+
+ align:start position:0%
+every uh row so that's node J for row J
+this is node I for row row I and
+
+ align:start position:0%
+this is node I for row row I and
+ 
+
+ align:start position:0%
+this is node I for row row I and
+somewhere we'll have uh a node
+
+ align:start position:0%
+somewhere we'll have uh a node
+ 
+
+ align:start position:0%
+somewhere we'll have uh a node
+K okay so at the start and now that so
+
+ align:start position:0%
+K okay so at the start and now that so
+ 
+
+ align:start position:0%
+K okay so at the start and now that so
+those are the nodes what are the edges
+
+ align:start position:0%
+those are the nodes what are the edges
+ 
+
+ align:start position:0%
+those are the nodes what are the edges
+well this there is a non so the edges
+
+ align:start position:0%
+well this there is a non so the edges
+ 
+
+ align:start position:0%
+well this there is a non so the edges
+come from the nonzeros in The Matrix so
+
+ align:start position:0%
+come from the nonzeros in The Matrix so
+ 
+
+ align:start position:0%
+come from the nonzeros in The Matrix so
+there's a there's an edge from J to K
+
+ align:start position:0%
+there's a there's an edge from J to K
+ 
+
+ align:start position:0%
+there's a there's an edge from J to K
+because this is not zero and there's an
+
+ align:start position:0%
+because this is not zero and there's an
+ 
+
+ align:start position:0%
+because this is not zero and there's an
+edge from I to J or J to I I'm not
+
+ align:start position:0%
+edge from I to J or J to I I'm not
+ 
+
+ align:start position:0%
+edge from I to J or J to I I'm not
+worrying about the dire this is not a
+
+ align:start position:0%
+worrying about the dire this is not a
+ 
+
+ align:start position:0%
+worrying about the dire this is not a
+directed graph right now so this is the
+
+ align:start position:0%
+directed graph right now so this is the
+ 
+
+ align:start position:0%
+directed graph right now so this is the
+start but there's no edge here initially
+
+ align:start position:0%
+start but there's no edge here initially
+ 
+
+ align:start position:0%
+start but there's no edge here initially
+because AI K is
+
+ align:start position:0%
+because AI K is
+ 
+
+ align:start position:0%
+because AI K is
+zero and now in this graph world well
+
+ align:start position:0%
+zero and now in this graph world well
+ 
+
+ align:start position:0%
+zero and now in this graph world well
+it's so small we can just focus on the
+
+ align:start position:0%
+it's so small we can just focus on the
+ 
+
+ align:start position:0%
+it's so small we can just focus on the
+part that's going to change a little the
+
+ align:start position:0%
+part that's going to change a little the
+ 
+
+ align:start position:0%
+part that's going to change a little the
+rest of all the other uh
+
+ align:start position:0%
+rest of all the other uh
+ 
+
+ align:start position:0%
+rest of all the other uh
+rows uh have their nodes and all the
+
+ align:start position:0%
+rows uh have their nodes and all the
+ 
+
+ align:start position:0%
+rows uh have their nodes and all the
+other nonzero entries have their edges
+
+ align:start position:0%
+other nonzero entries have their edges
+ 
+
+ align:start position:0%
+other nonzero entries have their edges
+so this is a tiny part of the the big
+
+ align:start position:0%
+so this is a tiny part of the the big
+ 
+
+ align:start position:0%
+so this is a tiny part of the the big
+graph uh but what happens to this tiny
+
+ align:start position:0%
+graph uh but what happens to this tiny
+ 
+
+ align:start position:0%
+graph uh but what happens to this tiny
+part okay so again I I want to see the
+
+ align:start position:0%
+part okay so again I I want to see the
+ 
+
+ align:start position:0%
+part okay so again I I want to see the
+same elimination step just uh this way
+
+ align:start position:0%
+same elimination step just uh this way
+ 
+
+ align:start position:0%
+same elimination step just uh this way
+in the graph world okay so after after
+
+ align:start position:0%
+in the graph world okay so after after
+ 
+
+ align:start position:0%
+in the graph world okay so after after
+what what edges are
+
+ align:start position:0%
+what what edges are
+ 
+
+ align:start position:0%
+what what edges are
+there so again it's j i and
+
+ align:start position:0%
+there so again it's j i and
+ 
+
+ align:start position:0%
+there so again it's j i and
+K and after I do elimination well J is
+
+ align:start position:0%
+K and after I do elimination well J is
+ 
+
+ align:start position:0%
+K and after I do elimination well J is
+still connected to K that's still there
+
+ align:start position:0%
+still connected to K that's still there
+ 
+
+ align:start position:0%
+still connected to K that's still there
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+change J is no longer connected to I
+
+ align:start position:0%
+change J is no longer connected to I
+ 
+
+ align:start position:0%
+change J is no longer connected to I
+because elimination killed that edge but
+
+ align:start position:0%
+because elimination killed that edge but
+ 
+
+ align:start position:0%
+because elimination killed that edge but
+elimination created a new Edge I de K so
+
+ align:start position:0%
+elimination created a new Edge I de K so
+ 
+
+ align:start position:0%
+elimination created a new Edge I de K so
+that's that's essentially what
+
+ align:start position:0%
+that's that's essentially what
+ 
+
+ align:start position:0%
+that's that's essentially what
+elimination does maybe we can say it in
+
+ align:start position:0%
+elimination does maybe we can say it in
+ 
+
+ align:start position:0%
+elimination does maybe we can say it in
+words when it so when when this when
+
+ align:start position:0%
+words when it so when when this when
+ 
+
+ align:start position:0%
+words when it so when when this when
+this Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disappears at the same time we
+
+ align:start position:0%
+disappears at the same time we
+ 
+
+ align:start position:0%
+disappears at the same time we
+create new
+
+ align:start position:0%
+create new
+ 
+
+ align:start position:0%
+create new
+edges from but connecting any two
+
+ align:start position:0%
+edges from but connecting any two
+ 
+
+ align:start position:0%
+edges from but connecting any two
+nodes that were both connected to J you
+
+ align:start position:0%
+nodes that were both connected to J you
+ 
+
+ align:start position:0%
+nodes that were both connected to J you
+see that point if if if I'm using J as
+
+ align:start position:0%
+see that point if if if I'm using J as
+ 
+
+ align:start position:0%
+see that point if if if I'm using J as
+the pivot row
+
+ align:start position:0%
+the pivot row
+ 
+
+ align:start position:0%
+the pivot row
+and I look on that row and say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what what non-zeros are there what edges
+
+ align:start position:0%
+what what non-zeros are there what edges
+ 
+
+ align:start position:0%
+what what non-zeros are there what edges
+are connected to J and I see
+
+ align:start position:0%
+are connected to J and I see
+ 
+
+ align:start position:0%
+are connected to J and I see
+one and then if I use if I when I do
+
+ align:start position:0%
+one and then if I use if I when I do
+ 
+
+ align:start position:0%
+one and then if I use if I when I do
+elimination I'm going to introduce
+
+ align:start position:0%
+elimination I'm going to introduce
+ 
+
+ align:start position:0%
+elimination I'm going to introduce
+exactly as happened here a new
+
+ align:start position:0%
+exactly as happened here a new
+ 
+
+ align:start position:0%
+exactly as happened here a new
+Edge between any pair that were both
+
+ align:start position:0%
+Edge between any pair that were both
+ 
+
+ align:start position:0%
+Edge between any pair that were both
+connected to J so we're kind of fighting
+
+ align:start position:0%
+connected to J so we're kind of fighting
+ 
+
+ align:start position:0%
+connected to J so we're kind of fighting
+against creeping
+
+ align:start position:0%
+against creeping
+ 
+
+ align:start position:0%
+against creeping
+uh fill
+
+ align:start position:0%
+uh fill
+ 
+
+ align:start position:0%
+uh fill
+in and the question is what order should
+
+ align:start position:0%
+in and the question is what order should
+ 
+
+ align:start position:0%
+in and the question is what order should
+we do these eliminations so now think of
+
+ align:start position:0%
+we do these eliminations so now think of
+ 
+
+ align:start position:0%
+we do these eliminations so now think of
+a larger
+
+ align:start position:0%
+a larger
+ 
+
+ align:start position:0%
+a larger
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+actually I guess we could somehow think
+
+ align:start position:0%
+actually I guess we could somehow think
+ 
+
+ align:start position:0%
+actually I guess we could somehow think
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+that I guess maybe we could try to
+
+ align:start position:0%
+that I guess maybe we could try to
+ 
+
+ align:start position:0%
+that I guess maybe we could try to
+visualize it but maybe not not succeed
+
+ align:start position:0%
+visualize it but maybe not not succeed
+ 
+
+ align:start position:0%
+visualize it but maybe not not succeed
+so the graph for this um for
+
+ align:start position:0%
+so the graph for this um for
+ 
+
+ align:start position:0%
+so the graph for this um for
+that problem
+
+ align:start position:0%
+that problem
+ 
+
+ align:start position:0%
+that problem
+well could that serve as the graph I
+
+ align:start position:0%
+well could that serve as the graph I
+ 
+
+ align:start position:0%
+well could that serve as the graph I
+guess it could really well I would
+
+ align:start position:0%
+guess it could really well I would
+ 
+
+ align:start position:0%
+guess it could really well I would
+remove i' whiz away the the uh if I'm
+
+ align:start position:0%
+remove i' whiz away the the uh if I'm
+ 
+
+ align:start position:0%
+remove i' whiz away the the uh if I'm
+given the values on the outer edges then
+
+ align:start position:0%
+given the values on the outer edges then
+ 
+
+ align:start position:0%
+given the values on the outer edges then
+I would remove all those but essentially
+
+ align:start position:0%
+I would remove all those but essentially
+ 
+
+ align:start position:0%
+I would remove all those but essentially
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+graph for that Matrix right well yeah
+
+ align:start position:0%
+graph for that Matrix right well yeah
+ 
+
+ align:start position:0%
+graph for that Matrix right well yeah
+yeah if I number each of the nodes 1 to
+
+ align:start position:0%
+yeah if I number each of the nodes 1 to
+ 
+
+ align:start position:0%
+yeah if I number each of the nodes 1 to
+16 and I would do the numbering the way
+
+ align:start position:0%
+16 and I would do the numbering the way
+ 
+
+ align:start position:0%
+16 and I would do the numbering the way
+I did to produce that Matrix now the the
+
+ align:start position:0%
+I did to produce that Matrix now the the
+ 
+
+ align:start position:0%
+I did to produce that Matrix now the the
+whole question is if I do some different
+
+ align:start position:0%
+whole question is if I do some different
+ 
+
+ align:start position:0%
+whole question is if I do some different
+numbering
+
+ align:start position:0%
+numbering
+ 
+
+ align:start position:0%
+numbering
+will I I'll still that will shift around
+
+ align:start position:0%
+will I I'll still that will shift around
+ 
+
+ align:start position:0%
+will I I'll still that will shift around
+that'll just be a permutation Matrix
+
+ align:start position:0%
+that'll just be a permutation Matrix
+ 
+
+ align:start position:0%
+that'll just be a permutation Matrix
+right if I do a different numbering so
+
+ align:start position:0%
+right if I do a different numbering so
+ 
+
+ align:start position:0%
+right if I do a different numbering so
+Matrix wise I have my Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k2d what what what happens Matrix wise
+
+ align:start position:0%
+k2d what what what happens Matrix wise
+ 
+
+ align:start position:0%
+k2d what what what happens Matrix wise
+for a if I do a a numbering a a
+
+ align:start position:0%
+for a if I do a a numbering a a
+ 
+
+ align:start position:0%
+for a if I do a a numbering a a
+different numbering a reordering that
+
+ align:start position:0%
+different numbering a reordering that
+ 
+
+ align:start position:0%
+different numbering a reordering that
+just permutes
+
+ align:start position:0%
+just permutes
+ 
+
+ align:start position:0%
+just permutes
+the uh unknowns and the
+
+ align:start position:0%
+the uh unknowns and the
+ 
+
+ align:start position:0%
+the uh unknowns and the
+equations so really what happens is some
+
+ align:start position:0%
+equations so really what happens is some
+ 
+
+ align:start position:0%
+equations so really what happens is some
+permutation multiplies k2d on the left
+
+ align:start position:0%
+permutation multiplies k2d on the left
+ 
+
+ align:start position:0%
+permutation multiplies k2d on the left
+and its transpose does the same thing to
+
+ align:start position:0%
+and its transpose does the same thing to
+ 
+
+ align:start position:0%
+and its transpose does the same thing to
+the columns on the right because the
+
+ align:start position:0%
+the columns on the right because the
+ 
+
+ align:start position:0%
+the columns on the right because the
+this permutation will change the order
+
+ align:start position:0%
+this permutation will change the order
+ 
+
+ align:start position:0%
+this permutation will change the order
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+equations this permutation will reorder
+
+ align:start position:0%
+equations this permutation will reorder
+ 
+
+ align:start position:0%
+equations this permutation will reorder
+The
+
+ align:start position:0%
+The
+ 
+
+ align:start position:0%
+The
+Columns to to come back to bring the
+
+ align:start position:0%
+Columns to to come back to bring the
+ 
+
+ align:start position:0%
+Columns to to come back to bring the
+diagonal back onto the diagonal but in a
+
+ align:start position:0%
+diagonal back onto the diagonal but in a
+ 
+
+ align:start position:0%
+diagonal back onto the diagonal but in a
+different order well we won't know it
+
+ align:start position:0%
+different order well we won't know it
+ 
+
+ align:start position:0%
+different order well we won't know it
+with all those fours but that that will
+
+ align:start position:0%
+with all those fours but that that will
+ 
+
+ align:start position:0%
+with all those fours but that that will
+have again all the fours on the diagonal
+
+ align:start position:0%
+have again all the fours on the diagonal
+ 
+
+ align:start position:0%
+have again all the fours on the diagonal
+but the minus ones are moved around of
+
+ align:start position:0%
+but the minus ones are moved around of
+ 
+
+ align:start position:0%
+but the minus ones are moved around of
+course none have disappeared or or been
+
+ align:start position:0%
+course none have disappeared or or been
+ 
+
+ align:start position:0%
+course none have disappeared or or been
+created by that it's just that's giving
+
+ align:start position:0%
+created by that it's just that's giving
+ 
+
+ align:start position:0%
+created by that it's just that's giving
+us a new order and so that's the order
+
+ align:start position:0%
+us a new order and so that's the order
+ 
+
+ align:start position:0%
+us a new order and so that's the order
+order reordering Matrix wise what's the
+
+ align:start position:0%
+order reordering Matrix wise what's the
+ 
+
+ align:start position:0%
+order reordering Matrix wise what's the
+reordering graph wise graph wise would
+
+ align:start position:0%
+reordering graph wise graph wise would
+ 
+
+ align:start position:0%
+reordering graph wise graph wise would
+be instead of this numbering of unknowns
+
+ align:start position:0%
+be instead of this numbering of unknowns
+ 
+
+ align:start position:0%
+be instead of this numbering of unknowns
+one 2 2 3 4 5 6 7 8 and so on 9 10 11 12
+
+ align:start position:0%
+one 2 2 3 4 5 6 7 8 and so on 9 10 11 12
+ 
+
+ align:start position:0%
+one 2 2 3 4 5 6 7 8 and so on 9 10 11 12
+13 14 15 16 we have a different order
+
+ align:start position:0%
+13 14 15 16 we have a different order
+ 
+
+ align:start position:0%
+13 14 15 16 we have a different order
+different numbering so there it's a the
+
+ align:start position:0%
+different numbering so there it's a the
+ 
+
+ align:start position:0%
+different numbering so there it's a the
+the computations the the computer
+
+ align:start position:0%
+the computations the the computer
+ 
+
+ align:start position:0%
+the computations the the computer
+science aspect you could say uh is not
+
+ align:start position:0%
+science aspect you could say uh is not
+ 
+
+ align:start position:0%
+science aspect you could say uh is not
+going to be difficult actually we should
+
+ align:start position:0%
+going to be difficult actually we should
+ 
+
+ align:start position:0%
+going to be difficult actually we should
+think and maybe we'll think in a
+
+ align:start position:0%
+think and maybe we'll think in a
+ 
+
+ align:start position:0%
+think and maybe we'll think in a
+minute from for the from the computer
+
+ align:start position:0%
+minute from for the from the computer
+ 
+
+ align:start position:0%
+minute from for the from the computer
+science aspect the the the actual
+
+ align:start position:0%
+science aspect the the the actual
+ 
+
+ align:start position:0%
+science aspect the the the actual
+execution I'm probably not I'm certainly
+
+ align:start position:0%
+execution I'm probably not I'm certainly
+ 
+
+ align:start position:0%
+execution I'm probably not I'm certainly
+not going to write out a permutation
+
+ align:start position:0%
+not going to write out a permutation
+ 
+
+ align:start position:0%
+not going to write out a permutation
+Matrix that's ridiculous I'm not going
+
+ align:start position:0%
+Matrix that's ridiculous I'm not going
+ 
+
+ align:start position:0%
+Matrix that's ridiculous I'm not going
+to draw a graph and keep
+
+ align:start position:0%
+to draw a graph and keep
+ 
+
+ align:start position:0%
+to draw a graph and keep
+that I I'll keep some list of of non of
+
+ align:start position:0%
+that I I'll keep some list of of non of
+ 
+
+ align:start position:0%
+that I I'll keep some list of of non of
+positions for nonzeros so we'll say a
+
+ align:start position:0%
+positions for nonzeros so we'll say a
+ 
+
+ align:start position:0%
+positions for nonzeros so we'll say a
+word about that list later so so I'm but
+
+ align:start position:0%
+word about that list later so so I'm but
+ 
+
+ align:start position:0%
+word about that list later so so I'm but
+here I'm trying to say how do we get an
+
+ align:start position:0%
+here I'm trying to say how do we get an
+ 
+
+ align:start position:0%
+here I'm trying to say how do we get an
+idea of what the effective reordering is
+
+ align:start position:0%
+idea of what the effective reordering is
+ 
+
+ align:start position:0%
+idea of what the effective reordering is
+and what a good reordering would be so
+
+ align:start position:0%
+and what a good reordering would be so
+ 
+
+ align:start position:0%
+and what a good reordering would be so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+here this is a specific reordering that
+
+ align:start position:0%
+here this is a specific reordering that
+ 
+
+ align:start position:0%
+here this is a specific reordering that
+I want to mention right
+
+ align:start position:0%
+I want to mention right
+ 
+
+ align:start position:0%
+I want to mention right
+away because it's so
+
+ align:start position:0%
+away because it's so
+ 
+
+ align:start position:0%
+away because it's so
+straightforward you you can get the idea
+
+ align:start position:0%
+straightforward you you can get the idea
+ 
+
+ align:start position:0%
+straightforward you you can get the idea
+uh of the red black
+
+ align:start position:0%
+uh of the red black
+ 
+
+ align:start position:0%
+uh of the red black
+ordering um without any big
+
+ align:start position:0%
+ordering um without any big
+ 
+
+ align:start position:0%
+ordering um without any big
+computation this is
+
+ align:start position:0%
+computation this is
+ 
+
+ align:start position:0%
+computation this is
+the fundamentally the the winner this is
+
+ align:start position:0%
+the fundamentally the the winner this is
+ 
+
+ align:start position:0%
+the fundamentally the the winner this is
+what people use all the time and and
+
+ align:start position:0%
+what people use all the time and and
+ 
+
+ align:start position:0%
+what people use all the time and and
+uh matlabs backslash is going to have
+
+ align:start position:0%
+uh matlabs backslash is going to have
+ 
+
+ align:start position:0%
+uh matlabs backslash is going to have
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+available um and uh in inside this the
+
+ align:start position:0%
+available um and uh in inside this the
+ 
+
+ align:start position:0%
+available um and uh in inside this the
+the the codes that are called are
+
+ align:start position:0%
+the the codes that are called are
+ 
+
+ align:start position:0%
+the the codes that are called are
+the column or symmetric Matrix
+
+ align:start position:0%
+the column or symmetric Matrix
+ 
+
+ align:start position:0%
+the column or symmetric Matrix
+approximate minimum
+
+ align:start position:0%
+approximate minimum
+ 
+
+ align:start position:0%
+approximate minimum
+degree so that's what this AMD means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximate minimum degree
+
+ align:start position:0%
+approximate minimum degree
+ 
+
+ align:start position:0%
+approximate minimum degree
+so that's the basic uh idea that uh I'll
+
+ align:start position:0%
+so that's the basic uh idea that uh I'll
+ 
+
+ align:start position:0%
+so that's the basic uh idea that uh I'll
+come back to as soon as I've just drawn
+
+ align:start position:0%
+come back to as soon as I've just drawn
+ 
+
+ align:start position:0%
+come back to as soon as I've just drawn
+the red black picture and then uh it's
+
+ align:start position:0%
+the red black picture and then uh it's
+ 
+
+ align:start position:0%
+the red black picture and then uh it's
+so important that people don't stop
+
+ align:start position:0%
+so important that people don't stop
+ 
+
+ align:start position:0%
+so important that people don't stop
+thinking uh and then so another uh sort
+
+ align:start position:0%
+thinking uh and then so another uh sort
+ 
+
+ align:start position:0%
+thinking uh and then so another uh sort
+of uh High Lev picture of what how to do
+
+ align:start position:0%
+of uh High Lev picture of what how to do
+ 
+
+ align:start position:0%
+of uh High Lev picture of what how to do
+an ordering is look for graph separator
+
+ align:start position:0%
+an ordering is look for graph separator
+ 
+
+ align:start position:0%
+an ordering is look for graph separator
+that's become a big a big uh uh step in
+
+ align:start position:0%
+that's become a big a big uh uh step in
+ 
+
+ align:start position:0%
+that's become a big a big uh uh step in
+the world of uh comp computational graph
+
+ align:start position:0%
+the world of uh comp computational graph
+ 
+
+ align:start position:0%
+the world of uh comp computational graph
+Theory and that leads to a something
+
+ align:start position:0%
+Theory and that leads to a something
+ 
+
+ align:start position:0%
+Theory and that leads to a something
+called Nesta dissection which is uh
+
+ align:start position:0%
+called Nesta dissection which is uh
+ 
+
+ align:start position:0%
+called Nesta dissection which is uh
+separators of separators of separators
+
+ align:start position:0%
+separators of separators of separators
+ 
+
+ align:start position:0%
+separators of separators of separators
+the usual uh keep going with the same
+
+ align:start position:0%
+the usual uh keep going with the same
+ 
+
+ align:start position:0%
+the usual uh keep going with the same
+idea that you see in in uh algorithms
+
+ align:start position:0%
+idea that you see in in uh algorithms
+ 
+
+ align:start position:0%
+idea that you see in in uh algorithms
+okay what about red
+
+ align:start position:0%
+okay what about red
+ 
+
+ align:start position:0%
+okay what about red
+black red black I'm simp simply going to
+
+ align:start position:0%
+black red black I'm simp simply going to
+ 
+
+ align:start position:0%
+black red black I'm simp simply going to
+imagine that this is a checker board
+
+ align:start position:0%
+imagine that this is a checker board
+ 
+
+ align:start position:0%
+imagine that this is a checker board
+well it's the nodes that I'm looking at
+
+ align:start position:0%
+well it's the nodes that I'm looking at
+ 
+
+ align:start position:0%
+well it's the nodes that I'm looking at
+not the squares so
+
+ align:start position:0%
+not the squares so
+ 
+
+ align:start position:0%
+not the squares so
+imagine so that's red black red black so
+
+ align:start position:0%
+imagine so that's red black red black so
+ 
+
+ align:start position:0%
+imagine so that's red black red black so
+I'm going to number first I'm going to
+
+ align:start position:0%
+I'm going to number first I'm going to
+ 
+
+ align:start position:0%
+I'm going to number first I'm going to
+take all the Reds first so so that uh
+
+ align:start position:0%
+take all the Reds first so so that uh
+ 
+
+ align:start position:0%
+take all the Reds first so so that uh
+I'm changing this numbering now to take
+
+ align:start position:0%
+I'm changing this numbering now to take
+ 
+
+ align:start position:0%
+I'm changing this numbering now to take
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+Reds
+
+ align:start position:0%
+Reds
+ 
+
+ align:start position:0%
+Reds
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+2 3 4 5 5 6 7 8 and now all the blacks 9
+
+ align:start position:0%
+2 3 4 5 5 6 7 8 and now all the blacks 9
+ 
+
+ align:start position:0%
+2 3 4 5 5 6 7 8 and now all the blacks 9
+10 11 12 and so on I'll stop there so
+
+ align:start position:0%
+10 11 12 and so on I'll stop there so
+ 
+
+ align:start position:0%
+10 11 12 and so on I'll stop there so
+you your eye will know how to fill in
+
+ align:start position:0%
+you your eye will know how to fill in
+ 
+
+ align:start position:0%
+you your eye will know how to fill in
+what what's the point of that if I take
+
+ align:start position:0%
+what what's the point of that if I take
+ 
+
+ align:start position:0%
+what what's the point of that if I take
+a red
+
+ align:start position:0%
+a red
+ 
+
+ align:start position:0%
+a red
+node and look suppose this first one is
+
+ align:start position:0%
+node and look suppose this first one is
+ 
+
+ align:start position:0%
+node and look suppose this first one is
+a red node as it
+
+ align:start position:0%
+a red node as it
+ 
+
+ align:start position:0%
+a red node as it
+is okay then what about the what do I
+
+ align:start position:0%
+is okay then what about the what do I
+ 
+
+ align:start position:0%
+is okay then what about the what do I
+know about the positions of those minus
+
+ align:start position:0%
+know about the positions of those minus
+ 
+
+ align:start position:0%
+know about the positions of those minus
+ones the the nonzeros in The Matrix
+
+ align:start position:0%
+ones the the nonzeros in The Matrix
+ 
+
+ align:start position:0%
+ones the the nonzeros in The Matrix
+they're associated
+
+ align:start position:0%
+they're associated
+ 
+
+ align:start position:0%
+they're associated
+with black nodes right the the neighbors
+
+ align:start position:0%
+with black nodes right the the neighbors
+ 
+
+ align:start position:0%
+with black nodes right the the neighbors
+of this node number one
+
+ align:start position:0%
+of this node number one
+ 
+
+ align:start position:0%
+of this node number one
+are black that's they have the black
+
+ align:start position:0%
+are black that's they have the black
+ 
+
+ align:start position:0%
+are black that's they have the black
+ones have numbers from 9 to 16 so the
+
+ align:start position:0%
+ones have numbers from 9 to 16 so the
+ 
+
+ align:start position:0%
+ones have numbers from 9 to 16 so the
+the black well everybody sees it that
+
+ align:start position:0%
+the black well everybody sees it that
+ 
+
+ align:start position:0%
+the black well everybody sees it that
+with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecule that has a four in the center
+
+ align:start position:0%
+molecule that has a four in the center
+ 
+
+ align:start position:0%
+molecule that has a four in the center
+and minus ones beside it those minus
+
+ align:start position:0%
+and minus ones beside it those minus
+ 
+
+ align:start position:0%
+and minus ones beside it those minus
+ones are associated with nodes of the
+
+ align:start position:0%
+ones are associated with nodes of the
+ 
+
+ align:start position:0%
+ones are associated with nodes of the
+opposite
+
+ align:start position:0%
+opposite
+ 
+
+ align:start position:0%
+opposite
+color and that's what we see here in the
+
+ align:start position:0%
+color and that's what we see here in the
+ 
+
+ align:start position:0%
+color and that's what we see here in the
+actual numbering so what does the Matrix
+
+ align:start position:0%
+actual numbering so what does the Matrix
+ 
+
+ align:start position:0%
+actual numbering so what does the Matrix
+become what does this if I do that
+
+ align:start position:0%
+become what does this if I do that
+ 
+
+ align:start position:0%
+become what does this if I do that
+permutation the permutation that's
+
+ align:start position:0%
+permutation the permutation that's
+ 
+
+ align:start position:0%
+permutation the permutation that's
+associated with that
+
+ align:start position:0%
+associated with that
+ 
+
+ align:start position:0%
+associated with that
+renumbering what will the same Matrix
+
+ align:start position:0%
+renumbering what will the same Matrix
+ 
+
+ align:start position:0%
+renumbering what will the same Matrix
+well here's the same Matrix but now I'm
+
+ align:start position:0%
+well here's the same Matrix but now I'm
+ 
+
+ align:start position:0%
+well here's the same Matrix but now I'm
+permuting it and so what does it look
+
+ align:start position:0%
+permuting it and so what does it look
+ 
+
+ align:start position:0%
+permuting it and so what does it look
+like maybe I can draw it small I think I
+
+ align:start position:0%
+like maybe I can draw it small I think I
+ 
+
+ align:start position:0%
+like maybe I can draw it small I think I
+probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can so in this pretty special situation
+
+ align:start position:0%
+can so in this pretty special situation
+ 
+
+ align:start position:0%
+can so in this pretty special situation
+where the red nodes are not connected to
+
+ align:start position:0%
+where the red nodes are not connected to
+ 
+
+ align:start position:0%
+where the red nodes are not connected to
+any other red nodes only to themselves I
+
+ align:start position:0%
+any other red nodes only to themselves I
+ 
+
+ align:start position:0%
+any other red nodes only to themselves I
+think I'll only see the 4i this is red
+
+ align:start position:0%
+think I'll only see the 4i this is red
+ 
+
+ align:start position:0%
+think I'll only see the 4i this is red
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Red those are the eight red nodes it's
+
+ align:start position:0%
+Red those are the eight red nodes it's
+ 
+
+ align:start position:0%
+Red those are the eight red nodes it's
+an 8 by8 identity Matrix times four and
+
+ align:start position:0%
+an 8 by8 identity Matrix times four and
+ 
+
+ align:start position:0%
+an 8 by8 identity Matrix times four and
+the blacks are only connected to the
+
+ align:start position:0%
+the blacks are only connected to the
+ 
+
+ align:start position:0%
+the blacks are only connected to the
+black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and all the minus
+
+ align:start position:0%
+and all the minus
+ 
+
+ align:start position:0%
+and all the minus
+ones are in the are in our connections
+
+ align:start position:0%
+ones are in the are in our connections
+ 
+
+ align:start position:0%
+ones are in the are in our connections
+between red and black that is this far
+
+ align:start position:0%
+between red and black that is this far
+ 
+
+ align:start position:0%
+between red and black that is this far
+off the diagonal what shall I call it B
+
+ align:start position:0%
+off the diagonal what shall I call it B
+ 
+
+ align:start position:0%
+off the diagonal what shall I call it B
+I'll just pick a letter b and be
+
+ align:start position:0%
+I'll just pick a letter b and be
+ 
+
+ align:start position:0%
+I'll just pick a letter b and be
+transposed probably because I know the
+
+ align:start position:0%
+transposed probably because I know the
+ 
+
+ align:start position:0%
+transposed probably because I know the
+Matrix is going to stay symmetric if it
+
+ align:start position:0%
+Matrix is going to stay symmetric if it
+ 
+
+ align:start position:0%
+Matrix is going to stay symmetric if it
+if it started symmetric as it did then
+
+ align:start position:0%
+if it started symmetric as it did then
+ 
+
+ align:start position:0%
+if it started symmetric as it did then
+this operation of reordering rows and
+
+ align:start position:0%
+this operation of reordering rows and
+ 
+
+ align:start position:0%
+this operation of reordering rows and
+columns compatibly is going to leave it
+
+ align:start position:0%
+columns compatibly is going to leave it
+ 
+
+ align:start position:0%
+columns compatibly is going to leave it
+symmetric and it must look something
+
+ align:start position:0%
+symmetric and it must look something
+ 
+
+ align:start position:0%
+symmetric and it must look something
+like this okay is that Matrix more
+
+ align:start position:0%
+like this okay is that Matrix more
+ 
+
+ align:start position:0%
+like this okay is that Matrix more
+sparse than before no it's got the same
+
+ align:start position:0%
+sparse than before no it's got the same
+ 
+
+ align:start position:0%
+sparse than before no it's got the same
+minus ones they're just all pushed up
+
+ align:start position:0%
+minus ones they're just all pushed up
+ 
+
+ align:start position:0%
+minus ones they're just all pushed up
+into this
+
+ align:start position:0%
+into this
+ 
+
+ align:start position:0%
+into this
+corner will it have fill some fill in as
+
+ align:start position:0%
+corner will it have fill some fill in as
+ 
+
+ align:start position:0%
+corner will it have fill some fill in as
+we go
+
+ align:start position:0%
+we go
+ 
+
+ align:start position:0%
+we go
+forward what's the answer on that one as
+
+ align:start position:0%
+forward what's the answer on that one as
+ 
+
+ align:start position:0%
+forward what's the answer on that one as
+I go
+
+ align:start position:0%
+I go
+ 
+
+ align:start position:0%
+I go
+forward maybe I should I haven't really
+
+ align:start position:0%
+forward maybe I should I haven't really
+ 
+
+ align:start position:0%
+forward maybe I should I haven't really
+thought that through my instinct is yes
+
+ align:start position:0%
+thought that through my instinct is yes
+ 
+
+ align:start position:0%
+thought that through my instinct is yes
+we'll have fill in
+
+ align:start position:0%
+we'll have fill in
+ 
+
+ align:start position:0%
+we'll have fill in
+will we have more fill in or less fill
+
+ align:start position:0%
+will we have more fill in or less fill
+ 
+
+ align:start position:0%
+will we have more fill in or less fill
+in than the than the uh row row by row
+
+ align:start position:0%
+in than the than the uh row row by row
+ 
+
+ align:start position:0%
+in than the than the uh row row by row
+ordering I should know the answer I
+
+ align:start position:0%
+ordering I should know the answer I
+ 
+
+ align:start position:0%
+ordering I should know the answer I
+think I'd probably ask uh the machine to
+
+ align:start position:0%
+think I'd probably ask uh the machine to
+ 
+
+ align:start position:0%
+think I'd probably ask uh the machine to
+tell
+
+ align:start position:0%
+tell
+ 
+
+ align:start position:0%
+tell
+me my guess is probably not more and we
+
+ align:start position:0%
+me my guess is probably not more and we
+ 
+
+ align:start position:0%
+me my guess is probably not more and we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+well why do I think probably this is
+
+ align:start position:0%
+well why do I think probably this is
+ 
+
+ align:start position:0%
+well why do I think probably this is
+better and of course I should know
+
+ align:start position:0%
+better and of course I should know
+ 
+
+ align:start position:0%
+better and of course I should know
+exactly in general it's better to put
+
+ align:start position:0%
+exactly in general it's better to put
+ 
+
+ align:start position:0%
+exactly in general it's better to put
+off the evil day here that is this this
+
+ align:start position:0%
+off the evil day here that is this this
+ 
+
+ align:start position:0%
+off the evil day here that is this this
+goes through the first half of
+
+ align:start position:0%
+goes through the first half of
+ 
+
+ align:start position:0%
+goes through the first half of
+elimination CL I
+
+ align:start position:0%
+elimination CL I
+ 
+
+ align:start position:0%
+elimination CL I
+mean that you you know what I'm think
+
+ align:start position:0%
+mean that you you know what I'm think
+ 
+
+ align:start position:0%
+mean that you you know what I'm think
+thinking here all the off diagonals have
+
+ align:start position:0%
+thinking here all the off diagonals have
+ 
+
+ align:start position:0%
+thinking here all the off diagonals have
+been sort of pushed down in The
+
+ align:start position:0%
+been sort of pushed down in The
+ 
+
+ align:start position:0%
+been sort of pushed down in The
+Matrix so that now let me do an example
+
+ align:start position:0%
+Matrix so that now let me do an example
+ 
+
+ align:start position:0%
+Matrix so that now let me do an example
+that's it shows that why that's good
+
+ align:start position:0%
+that's it shows that why that's good
+ 
+
+ align:start position:0%
+that's it shows that why that's good
+suppose my Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a nonzero diagonal and by the way
+
+ align:start position:0%
+has a nonzero diagonal and by the way
+ 
+
+ align:start position:0%
+has a nonzero diagonal and by the way
+the first uh step in
+
+ align:start position:0%
+the first uh step in
+ 
+
+ align:start position:0%
+the first uh step in
+um in the in the good codes for
+
+ align:start position:0%
+um in the in the good codes for
+ 
+
+ align:start position:0%
+um in the in the good codes for
+elimination do a permutation exactly to
+
+ align:start position:0%
+elimination do a permutation exactly to
+ 
+
+ align:start position:0%
+elimination do a permutation exactly to
+produce a non-zero diagonal so you're
+
+ align:start position:0%
+produce a non-zero diagonal so you're
+ 
+
+ align:start position:0%
+produce a non-zero diagonal so you're
+you're you're you're okay to start you
+
+ align:start position:0%
+you're you're you're okay to start you
+ 
+
+ align:start position:0%
+you're you're you're okay to start you
+know where you you are now
+
+ align:start position:0%
+know where you you are now
+ 
+
+ align:start position:0%
+know where you you are now
+suppose that the nonzeros
+
+ align:start position:0%
+suppose that the nonzeros
+ 
+
+ align:start position:0%
+suppose that the nonzeros
+all show up and I'll make the Matrix
+
+ align:start position:0%
+all show up and I'll make the Matrix
+ 
+
+ align:start position:0%
+all show up and I'll make the Matrix
+symmetric so th that's the nonzero
+
+ align:start position:0%
+symmetric so th that's the nonzero
+ 
+
+ align:start position:0%
+symmetric so th that's the nonzero
+pattern and and my point is that's a
+
+ align:start position:0%
+pattern and and my point is that's a
+ 
+
+ align:start position:0%
+pattern and and my point is that's a
+very good nonzero
+
+ align:start position:0%
+very good nonzero
+ 
+
+ align:start position:0%
+very good nonzero
+pattern why is it good it's good because
+
+ align:start position:0%
+pattern why is it good it's good because
+ 
+
+ align:start position:0%
+pattern why is it good it's good because
+there's no fill in whatever when I
+
+ align:start position:0%
+there's no fill in whatever when I
+ 
+
+ align:start position:0%
+there's no fill in whatever when I
+subtract some multiple when I go to make
+
+ align:start position:0%
+subtract some multiple when I go to make
+ 
+
+ align:start position:0%
+subtract some multiple when I go to make
+this zero to eliminate it I subtract a
+
+ align:start position:0%
+this zero to eliminate it I subtract a
+ 
+
+ align:start position:0%
+this zero to eliminate it I subtract a
+multiple using the first pivot it
+
+ align:start position:0%
+multiple using the first pivot it
+ 
+
+ align:start position:0%
+multiple using the first pivot it
+changes that but it doesn't fill in
+
+ align:start position:0%
+changes that but it doesn't fill in
+ 
+
+ align:start position:0%
+changes that but it doesn't fill in
+anything new all the the only operations
+
+ align:start position:0%
+anything new all the the only operations
+ 
+
+ align:start position:0%
+anything new all the the only operations
+required are are operating on the last
+
+ align:start position:0%
+required are are operating on the last
+ 
+
+ align:start position:0%
+required are are operating on the last
+row which is already full so there's an
+
+ align:start position:0%
+row which is already full so there's an
+ 
+
+ align:start position:0%
+row which is already full so there's an
+example in which the
+
+ align:start position:0%
+example in which the
+ 
+
+ align:start position:0%
+example in which the
+bandwidth see normally the bandwidth is
+
+ align:start position:0%
+bandwidth see normally the bandwidth is
+ 
+
+ align:start position:0%
+bandwidth see normally the bandwidth is
+a like a good guide but that's only for
+
+ align:start position:0%
+a like a good guide but that's only for
+ 
+
+ align:start position:0%
+a like a good guide but that's only for
+like pretty full bands here's a matrix
+
+ align:start position:0%
+like pretty full bands here's a matrix
+ 
+
+ align:start position:0%
+like pretty full bands here's a matrix
+that's not banded really it's bandwidth
+
+ align:start position:0%
+that's not banded really it's bandwidth
+ 
+
+ align:start position:0%
+that's not banded really it's bandwidth
+is the full uh five I have five I have
+
+ align:start position:0%
+is the full uh five I have five I have
+ 
+
+ align:start position:0%
+is the full uh five I have five I have
+to go out
+
+ align:start position:0%
+to go out
+ 
+
+ align:start position:0%
+to go out
+five to uh columns until I get the last
+
+ align:start position:0%
+five to uh columns until I get the last
+ 
+
+ align:start position:0%
+five to uh columns until I get the last
+until I get the the
+
+ align:start position:0%
+until I get the the
+ 
+
+ align:start position:0%
+until I get the the
+nonzeros so that has a big bandwidth so
+
+ align:start position:0%
+nonzeros so that has a big bandwidth so
+ 
+
+ align:start position:0%
+nonzeros so that has a big bandwidth so
+bandwidth W the bandwidth W is
+
+ align:start position:0%
+bandwidth W the bandwidth W is
+ 
+
+ align:start position:0%
+bandwidth W the bandwidth W is
+large but it's the right it's the
+
+ align:start position:0%
+large but it's the right it's the
+ 
+
+ align:start position:0%
+large but it's the right it's the
+perfect ordering but no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fill I I don't F anything you realize
+
+ align:start position:0%
+fill I I don't F anything you realize
+ 
+
+ align:start position:0%
+fill I I don't F anything you realize
+that for banded Matrix
+
+ align:start position:0%
+that for banded Matrix
+ 
+
+ align:start position:0%
+that for banded Matrix
+we won't have fill in outside the band
+
+ align:start position:0%
+we won't have fill in outside the band
+ 
+
+ align:start position:0%
+we won't have fill in outside the band
+our our our our concern is for fill in
+
+ align:start position:0%
+our our our our concern is for fill in
+ 
+
+ align:start position:0%
+our our our our concern is for fill in
+inside the band and here we don't have
+
+ align:start position:0%
+inside the band and here we don't have
+ 
+
+ align:start position:0%
+inside the band and here we don't have
+any because the the bad row and actually
+
+ align:start position:0%
+any because the the bad row and actually
+ 
+
+ align:start position:0%
+any because the the bad row and actually
+it often happens in
+
+ align:start position:0%
+it often happens in
+ 
+
+ align:start position:0%
+it often happens in
+um in some lease squares and other
+
+ align:start position:0%
+um in some lease squares and other
+ 
+
+ align:start position:0%
+um in some lease squares and other
+problems that you might this isn't quite
+
+ align:start position:0%
+problems that you might this isn't quite
+ 
+
+ align:start position:0%
+problems that you might this isn't quite
+as stupid a matrix as you might think uh
+
+ align:start position:0%
+as stupid a matrix as you might think uh
+ 
+
+ align:start position:0%
+as stupid a matrix as you might think uh
+these might be blocks rather than single
+
+ align:start position:0%
+these might be blocks rather than single
+ 
+
+ align:start position:0%
+these might be blocks rather than single
+entries you often want to think
+
+ align:start position:0%
+entries you often want to think
+ 
+
+ align:start position:0%
+entries you often want to think
+blockwise about a
+
+ align:start position:0%
+blockwise about a
+ 
+
+ align:start position:0%
+blockwise about a
+matrix and and when would you you might
+
+ align:start position:0%
+matrix and and when would you you might
+ 
+
+ align:start position:0%
+matrix and and when would you you might
+think how why would you have a have a
+
+ align:start position:0%
+think how why would you have a have a
+ 
+
+ align:start position:0%
+think how why would you have a have a
+matrix that was well well separated uh
+
+ align:start position:0%
+matrix that was well well separated uh
+ 
+
+ align:start position:0%
+matrix that was well well separated uh
+with block diagonal which is really good
+
+ align:start position:0%
+with block diagonal which is really good
+ 
+
+ align:start position:0%
+with block diagonal which is really good
+and then a few rows that are full that
+
+ align:start position:0%
+and then a few rows that are full that
+ 
+
+ align:start position:0%
+and then a few rows that are full that
+seems sort of unlikely but I guess I
+
+ align:start position:0%
+seems sort of unlikely but I guess I
+ 
+
+ align:start position:0%
+seems sort of unlikely but I guess I
+want to say it isn't if you had a
+
+ align:start position:0%
+want to say it isn't if you had a
+ 
+
+ align:start position:0%
+want to say it isn't if you had a
+problem in these squares
+
+ align:start position:0%
+problem in these squares
+ 
+
+ align:start position:0%
+problem in these squares
+minimizing some expression involving
+
+ align:start position:0%
+minimizing some expression involving
+ 
+
+ align:start position:0%
+minimizing some expression involving
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Matrix the block diagonal part but with
+
+ align:start position:0%
+Matrix the block diagonal part but with
+ 
+
+ align:start position:0%
+Matrix the block diagonal part but with
+a constraint that maybe the sum of all
+
+ align:start position:0%
+a constraint that maybe the sum of all
+ 
+
+ align:start position:0%
+a constraint that maybe the sum of all
+the unknowns has to be
+
+ align:start position:0%
+the unknowns has to be
+ 
+
+ align:start position:0%
+the unknowns has to be
+one then when you use a lrange
+
+ align:start position:0%
+one then when you use a lrange
+ 
+
+ align:start position:0%
+one then when you use a lrange
+multiplier to bring that constraint into
+
+ align:start position:0%
+multiplier to bring that constraint into
+ 
+
+ align:start position:0%
+multiplier to bring that constraint into
+the problem into the Matrix that's going
+
+ align:start position:0%
+the problem into the Matrix that's going
+ 
+
+ align:start position:0%
+the problem into the Matrix that's going
+to show like that and the beauty of the
+
+ align:start position:0%
+to show like that and the beauty of the
+ 
+
+ align:start position:0%
+to show like that and the beauty of the
+lron multiplier
+
+ align:start position:0%
+lron multiplier
+ 
+
+ align:start position:0%
+lron multiplier
+devices that also that it'll produce a
+
+ align:start position:0%
+devices that also that it'll produce a
+ 
+
+ align:start position:0%
+devices that also that it'll produce a
+symmetric uh column there well we'll see
+
+ align:start position:0%
+symmetric uh column there well we'll see
+ 
+
+ align:start position:0%
+symmetric uh column there well we'll see
+that in uh the third part of the course
+
+ align:start position:0%
+that in uh the third part of the course
+ 
+
+ align:start position:0%
+that in uh the third part of the course
+but I I'm just my point is that this
+
+ align:start position:0%
+but I I'm just my point is that this
+ 
+
+ align:start position:0%
+but I I'm just my point is that this
+example is not as artificial as it
+
+ align:start position:0%
+example is not as artificial as it
+ 
+
+ align:start position:0%
+example is not as artificial as it
+seems okay
+
+ align:start position:0%
+seems okay
+ 
+
+ align:start position:0%
+seems okay
+now suppose
+
+ align:start position:0%
+now suppose
+ 
+
+ align:start position:0%
+now suppose
+we had taken the bandwidth as
+
+ align:start position:0%
+we had taken the bandwidth as
+ 
+
+ align:start position:0%
+we had taken the bandwidth as
+our metric as our as our goal or
+
+ align:start position:0%
+our metric as our as our goal or
+ 
+
+ align:start position:0%
+our metric as our as our goal or
+reducing the bandwidth as our goal we
+
+ align:start position:0%
+reducing the bandwidth as our goal we
+ 
+
+ align:start position:0%
+reducing the bandwidth as our goal we
+would have made a bad
+
+ align:start position:0%
+would have made a bad
+ 
+
+ align:start position:0%
+would have made a bad
+mistake because if I if I want to do a
+
+ align:start position:0%
+mistake because if I if I want to do a
+ 
+
+ align:start position:0%
+mistake because if I if I want to do a
+permutation that reduces the bandwidth I
+
+ align:start position:0%
+permutation that reduces the bandwidth I
+ 
+
+ align:start position:0%
+permutation that reduces the bandwidth I
+better put this up in the middle
+
+ align:start position:0%
+better put this up in the middle
+ 
+
+ align:start position:0%
+better put this up in the middle
+somewhere so this is that that bad row
+
+ align:start position:0%
+somewhere so this is that that bad row
+ 
+
+ align:start position:0%
+somewhere so this is that that bad row
+comes up in the middle and then I guess
+
+ align:start position:0%
+comes up in the middle and then I guess
+ 
+
+ align:start position:0%
+comes up in the middle and then I guess
+that these are maybe whatever well
+
+ align:start position:0%
+that these are maybe whatever well
+ 
+
+ align:start position:0%
+that these are maybe whatever well
+didn't I guess I need 3 X's down
+
+ align:start position:0%
+didn't I guess I need 3 X's down
+ 
+
+ align:start position:0%
+didn't I guess I need 3 X's down
+here and what oh I'm going to do the
+
+ align:start position:0%
+here and what oh I'm going to do the
+ 
+
+ align:start position:0%
+here and what oh I'm going to do the
+same permutation from the right so that
+
+ align:start position:0%
+same permutation from the right so that
+ 
+
+ align:start position:0%
+same permutation from the right so that
+will move this column over to the
+
+ align:start position:0%
+will move this column over to the
+ 
+
+ align:start position:0%
+will move this column over to the
+middle so that would be this would be a
+
+ align:start position:0%
+middle so that would be this would be a
+ 
+
+ align:start position:0%
+middle so that would be this would be a
+a reordered this would be a p Matrix P
+
+ align:start position:0%
+a reordered this would be a p Matrix P
+ 
+
+ align:start position:0%
+a reordered this would be a p Matrix P
+transposed thing I
+
+ align:start position:0%
+transposed thing I
+ 
+
+ align:start position:0%
+transposed thing I
+think and it's got a better bandwidth
+
+ align:start position:0%
+think and it's got a better bandwidth
+ 
+
+ align:start position:0%
+think and it's got a better bandwidth
+right now now we have we're we're
+
+ align:start position:0%
+right now now we have we're we're
+ 
+
+ align:start position:0%
+right now now we have we're we're
+totally confident of all these zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here but
+
+ align:start position:0%
+here but
+ 
+
+ align:start position:0%
+here but
+it will fill in where where will we get
+
+ align:start position:0%
+it will fill in where where will we get
+ 
+
+ align:start position:0%
+it will fill in where where will we get
+fill in in that Matrix so as we start
+
+ align:start position:0%
+fill in in that Matrix so as we start
+ 
+
+ align:start position:0%
+fill in in that Matrix so as we start
+we're we're we're using elimination to
+
+ align:start position:0%
+we're we're we're using elimination to
+ 
+
+ align:start position:0%
+we're we're we're using elimination to
+remove those entries no problem cuz CU
+
+ align:start position:0%
+remove those entries no problem cuz CU
+ 
+
+ align:start position:0%
+remove those entries no problem cuz CU
+that upper left corner is the way this
+
+ align:start position:0%
+that upper left corner is the way this
+ 
+
+ align:start position:0%
+that upper left corner is the way this
+big the whole Matrix was no fill in up
+
+ align:start position:0%
+big the whole Matrix was no fill in up
+ 
+
+ align:start position:0%
+big the whole Matrix was no fill in up
+to there but just as soon as we reach
+
+ align:start position:0%
+to there but just as soon as we reach
+ 
+
+ align:start position:0%
+to there but just as soon as we reach
+this one as our pivot row and use it to
+
+ align:start position:0%
+this one as our pivot row and use it to
+ 
+
+ align:start position:0%
+this one as our pivot row and use it to
+subtract multiples to to knock out those
+
+ align:start position:0%
+subtract multiples to to knock out those
+ 
+
+ align:start position:0%
+subtract multiples to to knock out those
+when I make those Zero by using that
+
+ align:start position:0%
+when I make those Zero by using that
+ 
+
+ align:start position:0%
+when I make those Zero by using that
+pivot it's going to bring the whole this
+
+ align:start position:0%
+pivot it's going to bring the whole this
+ 
+
+ align:start position:0%
+pivot it's going to bring the whole this
+will be gone at that time but this will
+
+ align:start position:0%
+will be gone at that time but this will
+ 
+
+ align:start position:0%
+will be gone at that time but this will
+be non zero and that will produce new uh
+
+ align:start position:0%
+be non zero and that will produce new uh
+ 
+
+ align:start position:0%
+be non zero and that will produce new uh
+new edges in the graph might be fun to
+
+ align:start position:0%
+new edges in the graph might be fun to
+ 
+
+ align:start position:0%
+new edges in the graph might be fun to
+look at the graph that is associated
+
+ align:start position:0%
+look at the graph that is associated
+ 
+
+ align:start position:0%
+look at the graph that is associated
+with these with this Matrix and its
+
+ align:start position:0%
+with these with this Matrix and its
+ 
+
+ align:start position:0%
+with these with this Matrix and its
+permutations but anyway you see that
+
+ align:start position:0%
+permutations but anyway you see that
+ 
+
+ align:start position:0%
+permutations but anyway you see that
+this will all fill
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in okay so again
+
+ align:start position:0%
+in okay so again
+ 
+
+ align:start position:0%
+in okay so again
+in that small problem we could really
+
+ align:start position:0%
+in that small problem we could really
+ 
+
+ align:start position:0%
+in that small problem we could really
+see what was
+
+ align:start position:0%
+see what was
+ 
+
+ align:start position:0%
+see what was
+happening in the big problem we could we
+
+ align:start position:0%
+happening in the big problem we could we
+ 
+
+ align:start position:0%
+happening in the big problem we could we
+can almost see it when we take a very
+
+ align:start position:0%
+can almost see it when we take a very
+ 
+
+ align:start position:0%
+can almost see it when we take a very
+specific highly structured permutation
+
+ align:start position:0%
+specific highly structured permutation
+ 
+
+ align:start position:0%
+specific highly structured permutation
+like red
+
+ align:start position:0%
+like red
+ 
+
+ align:start position:0%
+like red
+black although I
+
+ align:start position:0%
+black although I
+ 
+
+ align:start position:0%
+black although I
+haven't pinned down exactly what the
+
+ align:start position:0%
+haven't pinned down exactly what the
+ 
+
+ align:start position:0%
+haven't pinned down exactly what the
+count is like now I I'd be glad if
+
+ align:start position:0%
+count is like now I I'd be glad if
+ 
+
+ align:start position:0%
+count is like now I I'd be glad if
+somebody would just run a computer
+
+ align:start position:0%
+somebody would just run a computer
+ 
+
+ align:start position:0%
+somebody would just run a computer
+experiment count nonzero
+
+ align:start position:0%
+experiment count nonzero
+ 
+
+ align:start position:0%
+experiment count nonzero
+count um yeah count so what what's the
+
+ align:start position:0%
+count um yeah count so what what's the
+ 
+
+ align:start position:0%
+count um yeah count so what what's the
+good thing to count uh what's how do you
+
+ align:start position:0%
+good thing to count uh what's how do you
+ 
+
+ align:start position:0%
+good thing to count uh what's how do you
+see what the fill in finally was when
+
+ align:start position:0%
+see what the fill in finally was when
+ 
+
+ align:start position:0%
+see what the fill in finally was when
+you've done an elimination well I guess
+
+ align:start position:0%
+you've done an elimination well I guess
+ 
+
+ align:start position:0%
+you've done an elimination well I guess
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the um the lnu factors which is what
+
+ align:start position:0%
+the um the lnu factors which is what
+ 
+
+ align:start position:0%
+the um the lnu factors which is what
+elimination produces that's where the
+
+ align:start position:0%
+elimination produces that's where the
+ 
+
+ align:start position:0%
+elimination produces that's where the
+Fillin will be so maybe I just make that
+
+ align:start position:0%
+Fillin will be so maybe I just make that
+ 
+
+ align:start position:0%
+Fillin will be so maybe I just make that
+point so that so that you could make
+
+ align:start position:0%
+point so that so that you could make
+ 
+
+ align:start position:0%
+point so that so that you could make
+these experiments that I have in mind
+
+ align:start position:0%
+these experiments that I have in mind
+ 
+
+ align:start position:0%
+these experiments that I have in mind
+and tell me what I ought to know about
+
+ align:start position:0%
+and tell me what I ought to know about
+ 
+
+ align:start position:0%
+and tell me what I ought to know about
+it so so if I have the Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k whatever whichever it is whether it's
+
+ align:start position:0%
+k whatever whichever it is whether it's
+ 
+
+ align:start position:0%
+k whatever whichever it is whether it's
+this one or this one or any
+
+ align:start position:0%
+this one or this one or any
+ 
+
+ align:start position:0%
+this one or this one or any
+other then the effect of
+
+ align:start position:0%
+other then the effect of
+ 
+
+ align:start position:0%
+other then the effect of
+elimination is to factor it into a lower
+
+ align:start position:0%
+elimination is to factor it into a lower
+ 
+
+ align:start position:0%
+elimination is to factor it into a lower
+times an upper triangular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and in the I'll just mention the
+
+ align:start position:0%
+Matrix and in the I'll just mention the
+ 
+
+ align:start position:0%
+Matrix and in the I'll just mention the
+special case while
+
+ align:start position:0%
+special case while
+ 
+
+ align:start position:0%
+special case while
+on special positive definite
+
+ align:start position:0%
+on special positive definite
+ 
+
+ align:start position:0%
+on special positive definite
+case we could we can adjust it so that K
+
+ align:start position:0%
+case we could we can adjust it so that K
+ 
+
+ align:start position:0%
+case we could we can adjust it so that K
+is L * L transpose this is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keski we can arrange the the well it
+
+ align:start position:0%
+keski we can arrange the the well it
+ 
+
+ align:start position:0%
+keski we can arrange the the well it
+will happen we we can arrange the
+
+ align:start position:0%
+will happen we we can arrange the
+ 
+
+ align:start position:0%
+will happen we we can arrange the
+scaling so that
+
+ align:start position:0%
+scaling so that
+ 
+
+ align:start position:0%
+scaling so that
+um by putting a square root of pivots
+
+ align:start position:0%
+um by putting a square root of pivots
+ 
+
+ align:start position:0%
+um by putting a square root of pivots
+with L and the other square root with L
+
+ align:start position:0%
+with L and the other square root with L
+ 
+
+ align:start position:0%
+with L and the other square root with L
+transpose so keski is a matlb command Co
+
+ align:start position:0%
+transpose so keski is a matlb command Co
+ 
+
+ align:start position:0%
+transpose so keski is a matlb command Co
+chol and actually matlb if you give mat
+
+ align:start position:0%
+chol and actually matlb if you give mat
+ 
+
+ align:start position:0%
+chol and actually matlb if you give mat
+lab
+
+ align:start position:0%
+lab
+ 
+
+ align:start position:0%
+lab
+a symmetric
+
+ align:start position:0%
+a symmetric
+ 
+
+ align:start position:0%
+a symmetric
+Matrix or if you give matlb a matrix to
+
+ align:start position:0%
+Matrix or if you give matlb a matrix to
+ 
+
+ align:start position:0%
+Matrix or if you give matlb a matrix to
+work with it will first ask well it will
+
+ align:start position:0%
+work with it will first ask well it will
+ 
+
+ align:start position:0%
+work with it will first ask well it will
+ask is it symmetric if it is symmetric
+
+ align:start position:0%
+ask is it symmetric if it is symmetric
+ 
+
+ align:start position:0%
+ask is it symmetric if it is symmetric
+it will hope that it's positive definite
+
+ align:start position:0%
+it will hope that it's positive definite
+ 
+
+ align:start position:0%
+it will hope that it's positive definite
+so it will begin in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keski it will begin to look for this
+
+ align:start position:0%
+keski it will begin to look for this
+ 
+
+ align:start position:0%
+keski it will begin to look for this
+it'll begin the the factorization which
+
+ align:start position:0%
+it'll begin the the factorization which
+ 
+
+ align:start position:0%
+it'll begin the the factorization which
+it is perfect for positive definite
+
+ align:start position:0%
+it is perfect for positive definite
+ 
+
+ align:start position:0%
+it is perfect for positive definite
+ones until
+
+ align:start position:0%
+ones until
+ 
+
+ align:start position:0%
+ones until
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+succeeds and finishes KES keski or until
+
+ align:start position:0%
+succeeds and finishes KES keski or until
+ 
+
+ align:start position:0%
+succeeds and finishes KES keski or until
+it discovers that nope a negative pivot
+
+ align:start position:0%
+it discovers that nope a negative pivot
+ 
+
+ align:start position:0%
+it discovers that nope a negative pivot
+appeared
+
+ align:start position:0%
+appeared
+ 
+
+ align:start position:0%
+appeared
+um which means which signals that the
+
+ align:start position:0%
+um which means which signals that the
+ 
+
+ align:start position:0%
+um which means which signals that the
+Matrix is not and was not originally
+
+ align:start position:0%
+Matrix is not and was not originally
+ 
+
+ align:start position:0%
+Matrix is not and was not originally
+positive definite and then then uh mat
+
+ align:start position:0%
+positive definite and then then uh mat
+ 
+
+ align:start position:0%
+positive definite and then then uh mat
+lab has to has to accept okay now I may
+
+ align:start position:0%
+lab has to has to accept okay now I may
+ 
+
+ align:start position:0%
+lab has to has to accept okay now I may
+have to do uh row exchanges pivoting
+
+ align:start position:0%
+have to do uh row exchanges pivoting
+ 
+
+ align:start position:0%
+have to do uh row exchanges pivoting
+operations and all the rest so mat lab
+
+ align:start position:0%
+operations and all the rest so mat lab
+ 
+
+ align:start position:0%
+operations and all the rest so mat lab
+sort of optimistic until it on a
+
+ align:start position:0%
+sort of optimistic until it on a
+ 
+
+ align:start position:0%
+sort of optimistic until it on a
+symmetric Matrix until it uh is told
+
+ align:start position:0%
+symmetric Matrix until it uh is told
+ 
+
+ align:start position:0%
+symmetric Matrix until it uh is told
+otherwise but not all matrices are
+
+ align:start position:0%
+otherwise but not all matrices are
+ 
+
+ align:start position:0%
+otherwise but not all matrices are
+symmetric so this would be the general
+
+ align:start position:0%
+symmetric so this would be the general
+ 
+
+ align:start position:0%
+symmetric so this would be the general
+case the general almost the general case
+
+ align:start position:0%
+case the general almost the general case
+ 
+
+ align:start position:0%
+case the general almost the general case
+I haven't included here the pivoting the
+
+ align:start position:0%
+I haven't included here the pivoting the
+ 
+
+ align:start position:0%
+I haven't included here the pivoting the
+the the row exchanges that matlb does as
+
+ align:start position:0%
+the the row exchanges that matlb does as
+ 
+
+ align:start position:0%
+the the row exchanges that matlb does as
+it as it executes elimination but let so
+
+ align:start position:0%
+it as it executes elimination but let so
+ 
+
+ align:start position:0%
+it as it executes elimination but let so
+let me just finish my sentence on L and
+
+ align:start position:0%
+let me just finish my sentence on L and
+ 
+
+ align:start position:0%
+let me just finish my sentence on L and
+u l will
+
+ align:start position:0%
+u l will
+ 
+
+ align:start position:0%
+u l will
+have the fill in in it it l will tell us
+
+ align:start position:0%
+have the fill in in it it l will tell us
+ 
+
+ align:start position:0%
+have the fill in in it it l will tell us
+and you will certainly I mean they both
+
+ align:start position:0%
+and you will certainly I mean they both
+ 
+
+ align:start position:0%
+and you will certainly I mean they both
+will you you will have these
+
+ align:start position:0%
+will you you will have these
+ 
+
+ align:start position:0%
+will you you will have these
+uh that that guy is going to be part of
+
+ align:start position:0%
+uh that that guy is going to be part of
+ 
+
+ align:start position:0%
+uh that that guy is going to be part of
+you and this
+
+ align:start position:0%
+you and this
+ 
+
+ align:start position:0%
+you and this
+one is I expect to see something there
+
+ align:start position:0%
+one is I expect to see something there
+ 
+
+ align:start position:0%
+one is I expect to see something there
+in L so so L and youu will actually
+
+ align:start position:0%
+in L so so L and youu will actually
+ 
+
+ align:start position:0%
+in L so so L and youu will actually
+exhibit the fill in so that you could
+
+ align:start position:0%
+exhibit the fill in so that you could
+ 
+
+ align:start position:0%
+exhibit the fill in so that you could
+find out how much fill in there is
+
+ align:start position:0%
+find out how much fill in there is
+ 
+
+ align:start position:0%
+find out how much fill in there is
+simply by uh counting the
+
+ align:start position:0%
+simply by uh counting the
+ 
+
+ align:start position:0%
+simply by uh counting the
+nonzeros in the matrices L and u i this
+
+ align:start position:0%
+nonzeros in the matrices L and u i this
+ 
+
+ align:start position:0%
+nonzeros in the matrices L and u i this
+is to encourage you because this is
+
+ align:start position:0%
+is to encourage you because this is
+ 
+
+ align:start position:0%
+is to encourage you because this is
+really a pretty experimental subject
+
+ align:start position:0%
+really a pretty experimental subject
+ 
+
+ align:start position:0%
+really a pretty experimental subject
+nobody
+
+ align:start position:0%
+nobody
+ 
+
+ align:start position:0%
+nobody
+um you know the best
+
+ align:start position:0%
+um you know the best
+ 
+
+ align:start position:0%
+um you know the best
+methods which or the favorite method I
+
+ align:start position:0%
+methods which or the favorite method I
+ 
+
+ align:start position:0%
+methods which or the favorite method I
+think nobody can say best probably but
+
+ align:start position:0%
+think nobody can say best probably but
+ 
+
+ align:start position:0%
+think nobody can say best probably but
+this approximate minimum degree the
+
+ align:start position:0%
+this approximate minimum degree the
+ 
+
+ align:start position:0%
+this approximate minimum degree the
+favorite method um we could prove some
+
+ align:start position:0%
+favorite method um we could prove some
+ 
+
+ align:start position:0%
+favorite method um we could prove some
+theorems to to show that it was better
+
+ align:start position:0%
+theorems to to show that it was better
+ 
+
+ align:start position:0%
+theorems to to show that it was better
+than something else but to really see is
+
+ align:start position:0%
+than something else but to really see is
+ 
+
+ align:start position:0%
+than something else but to really see is
+it successful or not in in on a wide
+
+ align:start position:0%
+it successful or not in in on a wide
+ 
+
+ align:start position:0%
+it successful or not in in on a wide
+variety of problems that's really
+
+ align:start position:0%
+variety of problems that's really
+ 
+
+ align:start position:0%
+variety of problems that's really
+experiment just try it okay now what
+
+ align:start position:0%
+experiment just try it okay now what
+ 
+
+ align:start position:0%
+experiment just try it okay now what
+does it
+
+ align:start position:0%
+does it
+ 
+
+ align:start position:0%
+does it
+mean so I looked at that specific one
+
+ align:start position:0%
+mean so I looked at that specific one
+ 
+
+ align:start position:0%
+mean so I looked at that specific one
+now I'm ready to look at the at the
+
+ align:start position:0%
+now I'm ready to look at the at the
+ 
+
+ align:start position:0%
+now I'm ready to look at the at the
+approximate minimum degree and I'll
+
+ align:start position:0%
+approximate minimum degree and I'll
+ 
+
+ align:start position:0%
+approximate minimum degree and I'll
+contrast it with the perfect minimum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree and there are codes for that and
+
+ align:start position:0%
+degree and there are codes for that and
+ 
+
+ align:start position:0%
+degree and there are codes for that and
+those A's become
+
+ align:start position:0%
+those A's become
+ 
+
+ align:start position:0%
+those A's become
+M's but it turns out and I don't know
+
+ align:start position:0%
+M's but it turns out and I don't know
+ 
+
+ align:start position:0%
+M's but it turns out and I don't know
+exactly why it's the case that the
+
+ align:start position:0%
+exactly why it's the case that the
+ 
+
+ align:start position:0%
+exactly why it's the case that the
+approximate minimum degree
+
+ align:start position:0%
+approximate minimum degree
+ 
+
+ align:start position:0%
+approximate minimum degree
+usually if anything it's Superior so
+
+ align:start position:0%
+usually if anything it's Superior so
+ 
+
+ align:start position:0%
+usually if anything it's Superior so
+these are the the ones to use so what
+
+ align:start position:0%
+these are the the ones to use so what
+ 
+
+ align:start position:0%
+these are the the ones to use so what
+does minimum degree mean minimum degree
+
+ align:start position:0%
+does minimum degree mean minimum degree
+ 
+
+ align:start position:0%
+does minimum degree mean minimum degree
+means let me if I took this problem oh
+
+ align:start position:0%
+means let me if I took this problem oh
+ 
+
+ align:start position:0%
+means let me if I took this problem oh
+well I should draw the graph for that
+
+ align:start position:0%
+well I should draw the graph for that
+ 
+
+ align:start position:0%
+well I should draw the graph for that
+for this Matrix so what's what does the
+
+ align:start position:0%
+for this Matrix so what's what does the
+ 
+
+ align:start position:0%
+for this Matrix so what's what does the
+graph look look like for this Matrix
+
+ align:start position:0%
+graph look look like for this Matrix
+ 
+
+ align:start position:0%
+graph look look like for this Matrix
+I've got
+
+ align:start position:0%
+I've got
+ 
+
+ align:start position:0%
+I've got
+six uh
+
+ align:start position:0%
+six uh
+ 
+
+ align:start position:0%
+six uh
+nodes so let me put six nodes in well
+
+ align:start position:0%
+nodes so let me put six nodes in well
+ 
+
+ align:start position:0%
+nodes so let me put six nodes in well
+let me put five and the and the node in
+
+ align:start position:0%
+let me put five and the and the node in
+ 
+
+ align:start position:0%
+let me put five and the and the node in
+the middle is will be the one that
+
+ align:start position:0%
+the middle is will be the one that
+ 
+
+ align:start position:0%
+the middle is will be the one that
+they're all connected to so these in
+
+ align:start position:0%
+they're all connected to so these in
+ 
+
+ align:start position:0%
+they're all connected to so these in
+this in this ordering those would be 1 2
+
+ align:start position:0%
+this in this ordering those would be 1 2
+ 
+
+ align:start position:0%
+this in this ordering those would be 1 2
+3 4 5 and six and all the connections go
+
+ align:start position:0%
+3 4 5 and six and all the connections go
+ 
+
+ align:start position:0%
+3 4 5 and six and all the connections go
+into six so that's the graph for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and the graph for this
+
+ align:start position:0%
+Matrix and the graph for this
+ 
+
+ align:start position:0%
+Matrix and the graph for this
+one what so you probably see it better
+
+ align:start position:0%
+one what so you probably see it better
+ 
+
+ align:start position:0%
+one what so you probably see it better
+than I do well what I had originally
+
+ align:start position:0%
+than I do well what I had originally
+ 
+
+ align:start position:0%
+than I do well what I had originally
+there uh I guess this is the graph with
+
+ align:start position:0%
+there uh I guess this is the graph with
+ 
+
+ align:start position:0%
+there uh I guess this is the graph with
+the numbering 1 2 3 4 5 six this what
+
+ align:start position:0%
+the numbering 1 2 3 4 5 six this what
+ 
+
+ align:start position:0%
+the numbering 1 2 3 4 5 six this what
+what was there before before the fill in
+
+ align:start position:0%
+what was there before before the fill in
+ 
+
+ align:start position:0%
+what was there before before the fill in
+happened would the graph would look the
+
+ align:start position:0%
+happened would the graph would look the
+ 
+
+ align:start position:0%
+happened would the graph would look the
+same but the nodes would have a
+
+ align:start position:0%
+same but the nodes would have a
+ 
+
+ align:start position:0%
+same but the nodes would have a
+different numbering right 1 2 3 4 5 6
+
+ align:start position:0%
+different numbering right 1 2 3 4 5 6
+ 
+
+ align:start position:0%
+different numbering right 1 2 3 4 5 6
+and then so shall I just shall I just
+
+ align:start position:0%
+and then so shall I just shall I just
+ 
+
+ align:start position:0%
+and then so shall I just shall I just
+put the bad guy here 1 2 3 4 five six
+
+ align:start position:0%
+put the bad guy here 1 2 3 4 five six
+ 
+
+ align:start position:0%
+put the bad guy here 1 2 3 4 five six
+and then what's the point that as soon
+
+ align:start position:0%
+and then what's the point that as soon
+ 
+
+ align:start position:0%
+and then what's the point that as soon
+as I um use number three to eliminate
+
+ align:start position:0%
+as I um use number three to eliminate
+ 
+
+ align:start position:0%
+as I um use number three to eliminate
+four well three was connected to five so
+
+ align:start position:0%
+four well three was connected to five so
+ 
+
+ align:start position:0%
+four well three was connected to five so
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+new Edge is going to appear there and
+
+ align:start position:0%
+new Edge is going to appear there and
+ 
+
+ align:start position:0%
+new Edge is going to appear there and
+three was connected to six three is
+
+ align:start position:0%
+three was connected to six three is
+ 
+
+ align:start position:0%
+three was connected to six three is
+connected to four when I use it a new 4
+
+ align:start position:0%
+connected to four when I use it a new 4
+ 
+
+ align:start position:0%
+connected to four when I use it a new 4
+six is going to appear here so those are
+
+ align:start position:0%
+six is going to appear here so those are
+ 
+
+ align:start position:0%
+six is going to appear here so those are
+a couple of the fill-ins those are the
+
+ align:start position:0%
+a couple of the fill-ins those are the
+ 
+
+ align:start position:0%
+a couple of the fill-ins those are the
+two fill-ins in row four then when I go
+
+ align:start position:0%
+two fill-ins in row four then when I go
+ 
+
+ align:start position:0%
+two fill-ins in row four then when I go
+on to row
+
+ align:start position:0%
+on to row
+ 
+
+ align:start position:0%
+on to row
+five uh well I'll fill in there those
+
+ align:start position:0%
+five uh well I'll fill in there those
+ 
+
+ align:start position:0%
+five uh well I'll fill in there those
+are so those are the three off three low
+
+ align:start position:0%
+are so those are the three off three low
+ 
+
+ align:start position:0%
+are so those are the three off three low
+above below the diagonal and above the
+
+ align:start position:0%
+above below the diagonal and above the
+ 
+
+ align:start position:0%
+above below the diagonal and above the
+diagonal nonzeros that come from the bad
+
+ align:start position:0%
+diagonal nonzeros that come from the bad
+ 
+
+ align:start position:0%
+diagonal nonzeros that come from the bad
+ordering I think I didn't prepare that
+
+ align:start position:0%
+ordering I think I didn't prepare that
+ 
+
+ align:start position:0%
+ordering I think I didn't prepare that
+but I hope it so I hope it's right
+
+ align:start position:0%
+but I hope it so I hope it's right
+ 
+
+ align:start position:0%
+but I hope it so I hope it's right
+yeah okay now so what's minimum degree
+
+ align:start position:0%
+yeah okay now so what's minimum degree
+ 
+
+ align:start position:0%
+yeah okay now so what's minimum degree
+minimum degree is
+
+ align:start position:0%
+minimum degree is
+ 
+
+ align:start position:0%
+minimum degree is
+simply uh sort of a greedy type
+
+ align:start position:0%
+simply uh sort of a greedy type
+ 
+
+ align:start position:0%
+simply uh sort of a greedy type
+algorithm because we have no way to look
+
+ align:start position:0%
+algorithm because we have no way to look
+ 
+
+ align:start position:0%
+algorithm because we have no way to look
+far far ahead and see what what nonzeros
+
+ align:start position:0%
+far far ahead and see what what nonzeros
+ 
+
+ align:start position:0%
+far far ahead and see what what nonzeros
+are coming way way down the line so
+
+ align:start position:0%
+are coming way way down the line so
+ 
+
+ align:start position:0%
+are coming way way down the line so
+let's just take it where we
+
+ align:start position:0%
+let's just take it where we
+ 
+
+ align:start position:0%
+let's just take it where we
+are uh we have to choose what should be
+
+ align:start position:0%
+are uh we have to choose what should be
+ 
+
+ align:start position:0%
+are uh we have to choose what should be
+the next pivot so we here maybe we let's
+
+ align:start position:0%
+the next pivot so we here maybe we let's
+ 
+
+ align:start position:0%
+the next pivot so we here maybe we let's
+say we take that first pivot good
+
+ align:start position:0%
+say we take that first pivot good
+ 
+
+ align:start position:0%
+say we take that first pivot good
+it's it does it's all the all the so
+
+ align:start position:0%
+it's it does it's all the all the so
+ 
+
+ align:start position:0%
+it's it does it's all the all the so
+what are the degrees of these of these
+
+ align:start position:0%
+what are the degrees of these of these
+ 
+
+ align:start position:0%
+what are the degrees of these of these
+um let let me redraw the graph before
+
+ align:start position:0%
+um let let me redraw the graph before
+ 
+
+ align:start position:0%
+um let let me redraw the graph before
+the fill in 1 2 3 four five six so I've
+
+ align:start position:0%
+the fill in 1 2 3 four five six so I've
+ 
+
+ align:start position:0%
+the fill in 1 2 3 four five six so I've
+got six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nodes that has degree one it's connected
+
+ align:start position:0%
+nodes that has degree one it's connected
+ 
+
+ align:start position:0%
+nodes that has degree one it's connected
+only to one other node actually all
+
+ align:start position:0%
+only to one other node actually all
+ 
+
+ align:start position:0%
+only to one other node actually all
+these have degree one and this one has
+
+ align:start position:0%
+these have degree one and this one has
+ 
+
+ align:start position:0%
+these have degree one and this one has
+degree five five edges are going out of
+
+ align:start position:0%
+degree five five edges are going out of
+ 
+
+ align:start position:0%
+degree five five edges are going out of
+it so the whole point of minimum degree
+
+ align:start position:0%
+it so the whole point of minimum degree
+ 
+
+ align:start position:0%
+it so the whole point of minimum degree
+is don't pick that one pick at each step
+
+ align:start position:0%
+is don't pick that one pick at each step
+ 
+
+ align:start position:0%
+is don't pick that one pick at each step
+create the new graph the graph expresses
+
+ align:start position:0%
+create the new graph the graph expresses
+ 
+
+ align:start position:0%
+create the new graph the graph expresses
+a fill in and we're not going to be able
+
+ align:start position:0%
+a fill in and we're not going to be able
+ 
+
+ align:start position:0%
+a fill in and we're not going to be able
+to avoid fill in some fill in normally
+
+ align:start position:0%
+to avoid fill in some fill in normally
+ 
+
+ align:start position:0%
+to avoid fill in some fill in normally
+but at every point take the graph as it
+
+ align:start position:0%
+but at every point take the graph as it
+ 
+
+ align:start position:0%
+but at every point take the graph as it
+is and choose as the next node to work
+
+ align:start position:0%
+is and choose as the next node to work
+ 
+
+ align:start position:0%
+is and choose as the next node to work
+on that means the next row to use in
+
+ align:start position:0%
+on that means the next row to use in
+ 
+
+ align:start position:0%
+on that means the next row to use in
+elimination the next pivot to choose
+
+ align:start position:0%
+elimination the next pivot to choose
+ 
+
+ align:start position:0%
+elimination the next pivot to choose
+choose choose one that has smallest
+
+ align:start position:0%
+choose choose one that has smallest
+ 
+
+ align:start position:0%
+choose choose one that has smallest
+degree don't choose this one so that the
+
+ align:start position:0%
+degree don't choose this one so that the
+ 
+
+ align:start position:0%
+degree don't choose this one so that the
+for for this very special case we could
+
+ align:start position:0%
+for for this very special case we could
+ 
+
+ align:start position:0%
+for for this very special case we could
+we have five choices for what comes
+
+ align:start position:0%
+we have five choices for what comes
+ 
+
+ align:start position:0%
+we have five choices for what comes
+first we make a choice like that one we
+
+ align:start position:0%
+first we make a choice like that one we
+ 
+
+ align:start position:0%
+first we make a choice like that one we
+do elimination in this case it doesn't
+
+ align:start position:0%
+do elimination in this case it doesn't
+ 
+
+ align:start position:0%
+do elimination in this case it doesn't
+fill in anything now I'm looking at the
+
+ align:start position:0%
+fill in anything now I'm looking at the
+ 
+
+ align:start position:0%
+fill in anything now I'm looking at the
+rest of the graph I have four nodes
+
+ align:start position:0%
+rest of the graph I have four nodes
+ 
+
+ align:start position:0%
+rest of the graph I have four nodes
+there with only degree with degree only
+
+ align:start position:0%
+there with only degree with degree only
+ 
+
+ align:start position:0%
+there with only degree with degree only
+one and a node there with high degree so
+
+ align:start position:0%
+one and a node there with high degree so
+ 
+
+ align:start position:0%
+one and a node there with high degree so
+I don't choose that so I choose two and
+
+ align:start position:0%
+I don't choose that so I choose two and
+ 
+
+ align:start position:0%
+I don't choose that so I choose two and
+so on so so of course minimum degree
+
+ align:start position:0%
+so on so so of course minimum degree
+ 
+
+ align:start position:0%
+so on so so of course minimum degree
+approximate or perfect or any dumb idea
+
+ align:start position:0%
+approximate or perfect or any dumb idea
+ 
+
+ align:start position:0%
+approximate or perfect or any dumb idea
+is going to uh create the right ordering
+
+ align:start position:0%
+is going to uh create the right ordering
+ 
+
+ align:start position:0%
+is going to uh create the right ordering
+that produces this Matrix okay so but
+
+ align:start position:0%
+that produces this Matrix okay so but
+ 
+
+ align:start position:0%
+that produces this Matrix okay so but
+hope you've seen what minimum degree is
+
+ align:start position:0%
+hope you've seen what minimum degree is
+ 
+
+ align:start position:0%
+hope you've seen what minimum degree is
+at every stage you look down the column
+
+ align:start position:0%
+at every stage you look down the column
+ 
+
+ align:start position:0%
+at every stage you look down the column
+just as here well actually what would
+
+ align:start position:0%
+just as here well actually what would
+ 
+
+ align:start position:0%
+just as here well actually what would
+what would minimum degree give here I
+
+ align:start position:0%
+what would minimum degree give here I
+ 
+
+ align:start position:0%
+what would minimum degree give here I
+would love to have a complete picture I
+
+ align:start position:0%
+would love to have a complete picture I
+ 
+
+ align:start position:0%
+would love to have a complete picture I
+think we could at least see at the start
+
+ align:start position:0%
+think we could at least see at the start
+ 
+
+ align:start position:0%
+think we could at least see at the start
+let me let me erase this red black
+
+ align:start position:0%
+let me let me erase this red black
+ 
+
+ align:start position:0%
+let me let me erase this red black
+ordering and prepare to write
+
+ align:start position:0%
+ordering and prepare to write
+ 
+
+ align:start position:0%
+ordering and prepare to write
+in um a minimum degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order if I can complete that recomplete
+
+ align:start position:0%
+order if I can complete that recomplete
+ 
+
+ align:start position:0%
+order if I can complete that recomplete
+that graph okay so what node do I take
+
+ align:start position:0%
+that graph okay so what node do I take
+ 
+
+ align:start position:0%
+that graph okay so what node do I take
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember the the graph really does not
+
+ align:start position:0%
+remember the the graph really does not
+ 
+
+ align:start position:0%
+remember the the graph really does not
+have these pieces I should should uh I
+
+ align:start position:0%
+have these pieces I should should uh I
+ 
+
+ align:start position:0%
+have these pieces I should should uh I
+might as well erase them now shall I
+
+ align:start position:0%
+might as well erase them now shall I
+ 
+
+ align:start position:0%
+might as well erase them now shall I
+just erase these are pieces that connect
+
+ align:start position:0%
+just erase these are pieces that connect
+ 
+
+ align:start position:0%
+just erase these are pieces that connect
+to known values that are on the right
+
+ align:start position:0%
+to known values that are on the right
+ 
+
+ align:start position:0%
+to known values that are on the right
+hand side so I think the graph doesn't
+
+ align:start position:0%
+hand side so I think the graph doesn't
+ 
+
+ align:start position:0%
+hand side so I think the graph doesn't
+have those connections those connections
+
+ align:start position:0%
+have those connections those connections
+ 
+
+ align:start position:0%
+have those connections those connections
+it's going to look pretty much as it did
+
+ align:start position:0%
+it's going to look pretty much as it did
+ 
+
+ align:start position:0%
+it's going to look pretty much as it did
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+but I think now we have the graph of
+
+ align:start position:0%
+but I think now we have the graph of
+ 
+
+ align:start position:0%
+but I think now we have the graph of
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+16 the graph that we should be looking
+
+ align:start position:0%
+16 the graph that we should be looking
+ 
+
+ align:start position:0%
+16 the graph that we should be looking
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+that's the graph of our Matrix the graph
+
+ align:start position:0%
+that's the graph of our Matrix the graph
+ 
+
+ align:start position:0%
+that's the graph of our Matrix the graph
+of the nonzero structure in the Matrix
+
+ align:start position:0%
+of the nonzero structure in the Matrix
+ 
+
+ align:start position:0%
+of the nonzero structure in the Matrix
+okay so what do you take as the first
+
+ align:start position:0%
+okay so what do you take as the first
+ 
+
+ align:start position:0%
+okay so what do you take as the first
+node you take the corners right the
+
+ align:start position:0%
+node you take the corners right the
+ 
+
+ align:start position:0%
+node you take the corners right the
+corners are going to win because they
+
+ align:start position:0%
+corners are going to win because they
+ 
+
+ align:start position:0%
+corners are going to win because they
+have degree two these guys have degree
+
+ align:start position:0%
+have degree two these guys have degree
+ 
+
+ align:start position:0%
+have degree two these guys have degree
+three there's a degree two so I might
+
+ align:start position:0%
+three there's a degree two so I might
+ 
+
+ align:start position:0%
+three there's a degree two so I might
+take that or well let's see what happens
+
+ align:start position:0%
+take that or well let's see what happens
+ 
+
+ align:start position:0%
+take that or well let's see what happens
+when I take this
+
+ align:start position:0%
+when I take this
+ 
+
+ align:start position:0%
+when I take this
+one then I then I have to see okay when
+
+ align:start position:0%
+one then I then I have to see okay when
+ 
+
+ align:start position:0%
+one then I then I have to see okay when
+I use use that as the pivot exactly what
+
+ align:start position:0%
+I use use that as the pivot exactly what
+ 
+
+ align:start position:0%
+I use use that as the pivot exactly what
+I did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here what's going to fill in well I
+
+ align:start position:0%
+here what's going to fill in well I
+ 
+
+ align:start position:0%
+here what's going to fill in well I
+guess explicitly I know that two two new
+
+ align:start position:0%
+guess explicitly I know that two two new
+ 
+
+ align:start position:0%
+guess explicitly I know that two two new
+edges fill in and what are they
+
+ align:start position:0%
+edges fill in and what are they
+ 
+
+ align:start position:0%
+edges fill in and what are they
+H well maybe they're the same I guess
+
+ align:start position:0%
+H well maybe they're the same I guess
+ 
+
+ align:start position:0%
+H well maybe they're the same I guess
+they are this is Edge number yeah so on
+
+ align:start position:0%
+they are this is Edge number yeah so on
+ 
+
+ align:start position:0%
+they are this is Edge number yeah so on
+the graph it's probably easier to see
+
+ align:start position:0%
+the graph it's probably easier to see
+ 
+
+ align:start position:0%
+the graph it's probably easier to see
+than in The Matrix what so I use this
+
+ align:start position:0%
+than in The Matrix what so I use this
+ 
+
+ align:start position:0%
+than in The Matrix what so I use this
+guy it by elimination I'm removing the
+
+ align:start position:0%
+guy it by elimination I'm removing the
+ 
+
+ align:start position:0%
+guy it by elimination I'm removing the
+connections so it's maybe sits there as
+
+ align:start position:0%
+connections so it's maybe sits there as
+ 
+
+ align:start position:0%
+connections so it's maybe sits there as
+surviving the the to remind me what
+
+ align:start position:0%
+surviving the the to remind me what
+ 
+
+ align:start position:0%
+surviving the the to remind me what
+which node was numbered one but these
+
+ align:start position:0%
+which node was numbered one but these
+ 
+
+ align:start position:0%
+which node was numbered one but these
+connections have been removed by
+
+ align:start position:0%
+connections have been removed by
+ 
+
+ align:start position:0%
+connections have been removed by
+elimination these that entry became a
+
+ align:start position:0%
+elimination these that entry became a
+ 
+
+ align:start position:0%
+elimination these that entry became a
+zero and that entry became a zero but
+
+ align:start position:0%
+zero and that entry became a zero but
+ 
+
+ align:start position:0%
+zero and that entry became a zero but
+there was a fill in here
+
+ align:start position:0%
+there was a fill in here
+ 
+
+ align:start position:0%
+there was a fill in here
+right okay that's the first step of
+
+ align:start position:0%
+right okay that's the first step of
+ 
+
+ align:start position:0%
+right okay that's the first step of
+minimum
+
+ align:start position:0%
+minimum
+ 
+
+ align:start position:0%
+minimum
+degree the Second
+
+ align:start position:0%
+degree the Second
+ 
+
+ align:start position:0%
+degree the Second
+Step as you
+
+ align:start position:0%
+Step as you
+ 
+
+ align:start position:0%
+Step as you
+say it's I'm going to do all the corners
+
+ align:start position:0%
+say it's I'm going to do all the corners
+ 
+
+ align:start position:0%
+say it's I'm going to do all the corners
+first right because that has degree two
+
+ align:start position:0%
+first right because that has degree two
+ 
+
+ align:start position:0%
+first right because that has degree two
+and these still have degree three no no
+
+ align:start position:0%
+and these still have degree three no no
+ 
+
+ align:start position:0%
+and these still have degree three no no
+no improvement it's kind of fun to do
+
+ align:start position:0%
+no improvement it's kind of fun to do
+ 
+
+ align:start position:0%
+no improvement it's kind of fun to do
+these two and that filled
+
+ align:start position:0%
+these two and that filled
+ 
+
+ align:start position:0%
+these two and that filled
+in number three and that filled in
+
+ align:start position:0%
+in number three and that filled in
+ 
+
+ align:start position:0%
+in number three and that filled in
+number four and that filled
+
+ align:start position:0%
+number four and that filled
+ 
+
+ align:start position:0%
+number four and that filled
+in okay what
+
+ align:start position:0%
+in okay what
+ 
+
+ align:start position:0%
+in okay what
+next well there going to be a bunch of
+
+ align:start position:0%
+next well there going to be a bunch of
+ 
+
+ align:start position:0%
+next well there going to be a bunch of
+choices
+
+ align:start position:0%
+choices
+ 
+
+ align:start position:0%
+choices
+now and as far as I know I could be
+
+ align:start position:0%
+now and as far as I know I could be
+ 
+
+ align:start position:0%
+now and as far as I know I could be
+wrong the I I don't know whether the I
+
+ align:start position:0%
+wrong the I I don't know whether the I
+ 
+
+ align:start position:0%
+wrong the I I don't know whether the I
+don't know what the choice decision how
+
+ align:start position:0%
+don't know what the choice decision how
+ 
+
+ align:start position:0%
+don't know what the choice decision how
+the decision is made when there is a
+
+ align:start position:0%
+the decision is made when there is a
+ 
+
+ align:start position:0%
+the decision is made when there is a
+choice when I have one two 3 four five
+
+ align:start position:0%
+choice when I have one two 3 four five
+ 
+
+ align:start position:0%
+choice when I have one two 3 four five
+six seven eight nodes all with degree
+
+ align:start position:0%
+six seven eight nodes all with degree
+ 
+
+ align:start position:0%
+six seven eight nodes all with degree
+three but let me just take this one so
+
+ align:start position:0%
+three but let me just take this one so
+ 
+
+ align:start position:0%
+three but let me just take this one so
+I'll take this as the next one as number
+
+ align:start position:0%
+I'll take this as the next one as number
+ 
+
+ align:start position:0%
+I'll take this as the next one as number
+five I guess that'll be number five that
+
+ align:start position:0%
+five I guess that'll be number five that
+ 
+
+ align:start position:0%
+five I guess that'll be number five that
+will kill all those connections and just
+
+ align:start position:0%
+will kill all those connections and just
+ 
+
+ align:start position:0%
+will kill all those connections and just
+leave the node but it will put in that
+
+ align:start position:0%
+leave the node but it will put in that
+ 
+
+ align:start position:0%
+leave the node but it will put in that
+one any others maybe only that
+
+ align:start position:0%
+one any others maybe only that
+ 
+
+ align:start position:0%
+one any others maybe only that
+one did I do that
+
+ align:start position:0%
+one did I do that
+ 
+
+ align:start position:0%
+one did I do that
+right yep I think I mean it would have
+
+ align:start position:0%
+right yep I think I mean it would have
+ 
+
+ align:start position:0%
+right yep I think I mean it would have
+put in this one because those are both
+
+ align:start position:0%
+put in this one because those are both
+ 
+
+ align:start position:0%
+put in this one because those are both
+connected to this but they that edge is
+
+ align:start position:0%
+connected to this but they that edge is
+ 
+
+ align:start position:0%
+connected to this but they that edge is
+already in there so nothing
+
+ align:start position:0%
+already in there so nothing
+ 
+
+ align:start position:0%
+already in there so nothing
+new okay so actually here I've created a
+
+ align:start position:0%
+new okay so actually here I've created a
+ 
+
+ align:start position:0%
+new okay so actually here I've created a
+node with it's o degree three so I'm
+
+ align:start position:0%
+node with it's o degree three so I'm
+ 
+
+ align:start position:0%
+node with it's o degree three so I'm
+going to do I have a lot of degree 3es
+
+ align:start position:0%
+going to do I have a lot of degree 3es
+ 
+
+ align:start position:0%
+going to do I have a lot of degree 3es
+here but then after a while I think when
+
+ align:start position:0%
+here but then after a while I think when
+ 
+
+ align:start position:0%
+here but then after a while I think when
+I get into the
+
+ align:start position:0%
+I get into the
+ 
+
+ align:start position:0%
+I get into the
+center uh I'm guessing that the degree
+
+ align:start position:0%
+center uh I'm guessing that the degree
+ 
+
+ align:start position:0%
+center uh I'm guessing that the degree
+will go up I don't think I I don't think
+
+ align:start position:0%
+will go up I don't think I I don't think
+ 
+
+ align:start position:0%
+will go up I don't think I I don't think
+I get away with degree 3 all the way in
+
+ align:start position:0%
+I get away with degree 3 all the way in
+ 
+
+ align:start position:0%
+I get away with degree 3 all the way in
+until the finish I don't
+
+ align:start position:0%
+until the finish I don't
+ 
+
+ align:start position:0%
+until the finish I don't
+think anyway you you see
+
+ align:start position:0%
+think anyway you you see
+ 
+
+ align:start position:0%
+think anyway you you see
+the point that there are there are
+
+ align:start position:0%
+the point that there are there are
+ 
+
+ align:start position:0%
+the point that there are there are
+choices to make among uh equal equal
+
+ align:start position:0%
+choices to make among uh equal equal
+ 
+
+ align:start position:0%
+choices to make among uh equal equal
+nodes with equal
+
+ align:start position:0%
+nodes with equal
+ 
+
+ align:start position:0%
+nodes with equal
+degree and then there's this calculation
+
+ align:start position:0%
+degree and then there's this calculation
+ 
+
+ align:start position:0%
+degree and then there's this calculation
+to make maybe I should uh this is a
+
+ align:start position:0%
+to make maybe I should uh this is a
+ 
+
+ align:start position:0%
+to make maybe I should uh this is a
+moment to just mention if I can do it
+
+ align:start position:0%
+moment to just mention if I can do it
+ 
+
+ align:start position:0%
+moment to just mention if I can do it
+how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh how you might keep how you might
+
+ align:start position:0%
+uh how you might keep how you might
+ 
+
+ align:start position:0%
+uh how you might keep how you might
+organize the the
+
+ align:start position:0%
+organize the the
+ 
+
+ align:start position:0%
+organize the the
+uh this pass through so this pass
+
+ align:start position:0%
+uh this pass through so this pass
+ 
+
+ align:start position:0%
+uh this pass through so this pass
+through the Matrix is really a just a
+
+ align:start position:0%
+through the Matrix is really a just a
+ 
+
+ align:start position:0%
+through the Matrix is really a just a
+pass through the graph it's not looking
+
+ align:start position:0%
+pass through the graph it's not looking
+ 
+
+ align:start position:0%
+pass through the graph it's not looking
+at the actual numbers it's just choosing
+
+ align:start position:0%
+at the actual numbers it's just choosing
+ 
+
+ align:start position:0%
+at the actual numbers it's just choosing
+the ordering and then then the next pass
+
+ align:start position:0%
+the ordering and then then the next pass
+ 
+
+ align:start position:0%
+the ordering and then then the next pass
+through we follow that ordering with the
+
+ align:start position:0%
+through we follow that ordering with the
+ 
+
+ align:start position:0%
+through we follow that ordering with the
+numbers finding the multipliers that go
+
+ align:start position:0%
+numbers finding the multipliers that go
+ 
+
+ align:start position:0%
+numbers finding the multipliers that go
+into L and the numbers that are left in
+
+ align:start position:0%
+into L and the numbers that are left in
+ 
+
+ align:start position:0%
+into L and the numbers that are left in
+the Matrix U okay so how would
+
+ align:start position:0%
+the Matrix U okay so how would
+ 
+
+ align:start position:0%
+the Matrix U okay so how would
+I how would anybody
+
+ align:start position:0%
+I how would anybody
+ 
+
+ align:start position:0%
+I how would anybody
+reasonably write down the original list
+
+ align:start position:0%
+reasonably write down the original list
+ 
+
+ align:start position:0%
+reasonably write down the original list
+so I have the nodes numbers 1 two 3 4 up
+
+ align:start position:0%
+so I have the nodes numbers 1 two 3 4 up
+ 
+
+ align:start position:0%
+so I have the nodes numbers 1 two 3 4 up
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+16 those are the node numbers and now
+
+ align:start position:0%
+16 those are the node numbers and now
+ 
+
+ align:start position:0%
+16 those are the node numbers and now
+with node one I'll list all the so this
+
+ align:start position:0%
+with node one I'll list all the so this
+ 
+
+ align:start position:0%
+with node one I'll list all the so this
+corresponds to row one of the Matrix so
+
+ align:start position:0%
+corresponds to row one of the Matrix so
+ 
+
+ align:start position:0%
+corresponds to row one of the Matrix so
+I list all the nodes that are connected
+
+ align:start position:0%
+I list all the nodes that are connected
+ 
+
+ align:start position:0%
+I list all the nodes that are connected
+to to row one to to node one well I node
+
+ align:start position:0%
+to to row one to to node one well I node
+ 
+
+ align:start position:0%
+to to row one to to node one well I node
+one itself is I don't know whether to
+
+ align:start position:0%
+one itself is I don't know whether to
+ 
+
+ align:start position:0%
+one itself is I don't know whether to
+put that in or not maybe I will just and
+
+ align:start position:0%
+put that in or not maybe I will just and
+ 
+
+ align:start position:0%
+put that in or not maybe I will just and
+number two is connected to it and number
+
+ align:start position:0%
+number two is connected to it and number
+ 
+
+ align:start position:0%
+number two is connected to it and number
+five above it I'm taking the original
+
+ align:start position:0%
+five above it I'm taking the original
+ 
+
+ align:start position:0%
+five above it I'm taking the original
+row order
+
+ align:start position:0%
+row order
+ 
+
+ align:start position:0%
+row order
+okay and then when I look at node two so
+
+ align:start position:0%
+okay and then when I look at node two so
+ 
+
+ align:start position:0%
+okay and then when I look at node two so
+I'm just it's just going to be a long
+
+ align:start position:0%
+I'm just it's just going to be a long
+ 
+
+ align:start position:0%
+I'm just it's just going to be a long
+list but I'll have to have a break there
+
+ align:start position:0%
+list but I'll have to have a break there
+ 
+
+ align:start position:0%
+list but I'll have to have a break there
+to tell me that these were the these
+
+ align:start position:0%
+to tell me that these were the these
+ 
+
+ align:start position:0%
+to tell me that these were the these
+numbers were associated with Row
+
+ align:start position:0%
+numbers were associated with Row
+ 
+
+ align:start position:0%
+numbers were associated with Row
+one now I want to know those associated
+
+ align:start position:0%
+one now I want to know those associated
+ 
+
+ align:start position:0%
+one now I want to know those associated
+with row two so row two had the
+
+ align:start position:0%
+with row two so row two had the
+ 
+
+ align:start position:0%
+with row two so row two had the
+connection back to
+
+ align:start position:0%
+connection back to
+ 
+
+ align:start position:0%
+connection back to
+one so this little group is going to be
+
+ align:start position:0%
+one so this little group is going to be
+ 
+
+ align:start position:0%
+one so this little group is going to be
+all the things connected to row two
+
+ align:start position:0%
+all the things connected to row two
+ 
+
+ align:start position:0%
+all the things connected to row two
+remember sorry since I've erased all
+
+ align:start position:0%
+remember sorry since I've erased all
+ 
+
+ align:start position:0%
+remember sorry since I've erased all
+those connections but you remember them
+
+ align:start position:0%
+those connections but you remember them
+ 
+
+ align:start position:0%
+those connections but you remember them
+two was connected to one it's connected
+
+ align:start position:0%
+two was connected to one it's connected
+ 
+
+ align:start position:0%
+two was connected to one it's connected
+forward to three and above it to
+
+ align:start position:0%
+forward to three and above it to
+ 
+
+ align:start position:0%
+forward to three and above it to
+probably six maybe that's 1 three and
+
+ align:start position:0%
+probably six maybe that's 1 three and
+ 
+
+ align:start position:0%
+probably six maybe that's 1 three and
+six and then a slash and then whatever
+
+ align:start position:0%
+six and then a slash and then whatever
+ 
+
+ align:start position:0%
+six and then a slash and then whatever
+node three so I
+
+ align:start position:0%
+node three so I
+ 
+
+ align:start position:0%
+node three so I
+need I need I I guess I need one more
+
+ align:start position:0%
+need I need I I guess I need one more
+ 
+
+ align:start position:0%
+need I need I I guess I need one more
+line there to tell me I need a pointer I
+
+ align:start position:0%
+line there to tell me I need a pointer I
+ 
+
+ align:start position:0%
+line there to tell me I need a pointer I
+need a line of a pointer that tells me
+
+ align:start position:0%
+need a line of a pointer that tells me
+ 
+
+ align:start position:0%
+need a line of a pointer that tells me
+okay number one start with the first one
+
+ align:start position:0%
+okay number one start with the first one
+ 
+
+ align:start position:0%
+okay number one start with the first one
+one two 3 number two start with the
+
+ align:start position:0%
+one two 3 number two start with the
+ 
+
+ align:start position:0%
+one two 3 number two start with the
+fourth one number three start with the
+
+ align:start position:0%
+fourth one number three start with the
+ 
+
+ align:start position:0%
+fourth one number three start with the
+seventh one so that number seven is
+
+ align:start position:0%
+seventh one so that number seven is
+ 
+
+ align:start position:0%
+seventh one so that number seven is
+pointing to the to the beginning of
+
+ align:start position:0%
+pointing to the to the beginning of
+ 
+
+ align:start position:0%
+pointing to the to the beginning of
+the the Su list the beginning of the of
+
+ align:start position:0%
+the the Su list the beginning of the of
+ 
+
+ align:start position:0%
+the the Su list the beginning of the of
+the short list that's associated to the
+
+ align:start position:0%
+the short list that's associated to the
+ 
+
+ align:start position:0%
+the short list that's associated to the
+to each separate
+
+ align:start position:0%
+to each separate
+ 
+
+ align:start position:0%
+to each separate
+node okay and I I guess what I'm saying
+
+ align:start position:0%
+node okay and I I guess what I'm saying
+ 
+
+ align:start position:0%
+node okay and I I guess what I'm saying
+is that this is a pretty compact
+
+ align:start position:0%
+is that this is a pretty compact
+ 
+
+ align:start position:0%
+is that this is a pretty compact
+description of the graph this will tell
+
+ align:start position:0%
+description of the graph this will tell
+ 
+
+ align:start position:0%
+description of the graph this will tell
+me all the edges in the graph because it
+
+ align:start position:0%
+me all the edges in the graph because it
+ 
+
+ align:start position:0%
+me all the edges in the graph because it
+tells me what two is connected to and
+
+ align:start position:0%
+tells me what two is connected to and
+ 
+
+ align:start position:0%
+tells me what two is connected to and
+this tells me where that
+
+ align:start position:0%
+this tells me where that
+ 
+
+ align:start position:0%
+this tells me where that
+little uh set
+
+ align:start position:0%
+little uh set
+ 
+
+ align:start position:0%
+little uh set
+lies and now if
+
+ align:start position:0%
+lies and now if
+ 
+
+ align:start position:0%
+lies and now if
+I as I will change the
+
+ align:start position:0%
+I as I will change the
+ 
+
+ align:start position:0%
+I as I will change the
+ordering then I just reorganize the
+
+ align:start position:0%
+ordering then I just reorganize the
+ 
+
+ align:start position:0%
+ordering then I just reorganize the
+pointers I'm going to speak roughly and
+
+ align:start position:0%
+pointers I'm going to speak roughly and
+ 
+
+ align:start position:0%
+pointers I'm going to speak roughly and
+not the detail
+
+ align:start position:0%
+not the detail
+ 
+
+ align:start position:0%
+not the detail
+just in in general in the large you
+
+ align:start position:0%
+just in in general in the large you
+ 
+
+ align:start position:0%
+just in in general in the large you
+could imagine that this is a pretty
+
+ align:start position:0%
+could imagine that this is a pretty
+ 
+
+ align:start position:0%
+could imagine that this is a pretty
+convenient um structure to uh to use for
+
+ align:start position:0%
+convenient um structure to uh to use for
+ 
+
+ align:start position:0%
+convenient um structure to uh to use for
+the for the for keeping the record of
+
+ align:start position:0%
+the for the for keeping the record of
+ 
+
+ align:start position:0%
+the for the for keeping the record of
+what the order what what the node
+
+ align:start position:0%
+what the order what what the node
+ 
+
+ align:start position:0%
+what the order what what the node
+numbering is okay so that's and the the
+
+ align:start position:0%
+numbering is okay so that's and the the
+ 
+
+ align:start position:0%
+numbering is okay so that's and the the
+uh command nnz is a useful one that
+
+ align:start position:0%
+uh command nnz is a useful one that
+ 
+
+ align:start position:0%
+uh command nnz is a useful one that
+that's a mat command that counts the
+
+ align:start position:0%
+that's a mat command that counts the
+ 
+
+ align:start position:0%
+that's a mat command that counts the
+number of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonzeros so n n and Z suggest exactly
+
+ align:start position:0%
+nonzeros so n n and Z suggest exactly
+ 
+
+ align:start position:0%
+nonzeros so n n and Z suggest exactly
+what that will do so if you pick an
+
+ align:start position:0%
+what that will do so if you pick an
+ 
+
+ align:start position:0%
+what that will do so if you pick an
+ordering like approximate minimum degree
+
+ align:start position:0%
+ordering like approximate minimum degree
+ 
+
+ align:start position:0%
+ordering like approximate minimum degree
+and you pick a matrix like this one and
+
+ align:start position:0%
+and you pick a matrix like this one and
+ 
+
+ align:start position:0%
+and you pick a matrix like this one and
+you run well I'd be very interested in
+
+ align:start position:0%
+you run well I'd be very interested in
+ 
+
+ align:start position:0%
+you run well I'd be very interested in
+that what if you run it you you take you
+
+ align:start position:0%
+that what if you run it you you take you
+ 
+
+ align:start position:0%
+that what if you run it you you take you
+take the Matrix k2d you take the
+
+ align:start position:0%
+take the Matrix k2d you take the
+ 
+
+ align:start position:0%
+take the Matrix k2d you take the
+permutation that comes from approximate
+
+ align:start position:0%
+permutation that comes from approximate
+ 
+
+ align:start position:0%
+permutation that comes from approximate
+minimum degree that gives you this
+
+ align:start position:0%
+minimum degree that gives you this
+ 
+
+ align:start position:0%
+minimum degree that gives you this
+reordered Matrix which you then factor
+
+ align:start position:0%
+reordered Matrix which you then factor
+ 
+
+ align:start position:0%
+reordered Matrix which you then factor
+into you then do elimination which
+
+ align:start position:0%
+into you then do elimination which
+ 
+
+ align:start position:0%
+into you then do elimination which
+factors it in L * U or probably L * L
+
+ align:start position:0%
+factors it in L * U or probably L * L
+ 
+
+ align:start position:0%
+factors it in L * U or probably L * L
+transpose because it's positive definite
+
+ align:start position:0%
+transpose because it's positive definite
+ 
+
+ align:start position:0%
+transpose because it's positive definite
+and then I would do an NZ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofl as a measure of filling
+
+ align:start position:0%
+ofl as a measure of filling
+ 
+
+ align:start position:0%
+ofl as a measure of filling
+that would count the fill in in L and
+
+ align:start position:0%
+that would count the fill in in L and
+ 
+
+ align:start position:0%
+that would count the fill in in L and
+with symmetry it would be the same in U
+
+ align:start position:0%
+with symmetry it would be the same in U
+ 
+
+ align:start position:0%
+with symmetry it would be the same in U
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh if you have a better idea than
+
+ align:start position:0%
+uh if you have a better idea than
+ 
+
+ align:start position:0%
+uh if you have a better idea than
+approximate minimum degree that's a
+
+ align:start position:0%
+approximate minimum degree that's a
+ 
+
+ align:start position:0%
+approximate minimum degree that's a
+measure to to try it to to to use as the
+
+ align:start position:0%
+measure to to try it to to to use as the
+ 
+
+ align:start position:0%
+measure to to try it to to to use as the
+Criterion okay uh just a little time to
+
+ align:start position:0%
+Criterion okay uh just a little time to
+ 
+
+ align:start position:0%
+Criterion okay uh just a little time to
+speak finally about this idea of graph
+
+ align:start position:0%
+speak finally about this idea of graph
+ 
+
+ align:start position:0%
+speak finally about this idea of graph
+separators so again I have to get back
+
+ align:start position:0%
+separators so again I have to get back
+ 
+
+ align:start position:0%
+separators so again I have to get back
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+graph uh let me draw a graph on so now
+
+ align:start position:0%
+graph uh let me draw a graph on so now
+ 
+
+ align:start position:0%
+graph uh let me draw a graph on so now
+I'm ready for for this one I'll put a
+
+ align:start position:0%
+I'm ready for for this one I'll put a
+ 
+
+ align:start position:0%
+I'm ready for for this one I'll put a
+little star next to it to say that it
+
+ align:start position:0%
+little star next to it to say that it
+ 
+
+ align:start position:0%
+little star next to it to say that it
+didn't look for a long time as if it
+
+ align:start position:0%
+didn't look for a long time as if it
+ 
+
+ align:start position:0%
+didn't look for a long time as if it
+could compete with number
+
+ align:start position:0%
+could compete with number
+ 
+
+ align:start position:0%
+could compete with number
+two but uh because it'll be a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ordering you could in a way it's going
+
+ align:start position:0%
+ordering you could in a way it's going
+ 
+
+ align:start position:0%
+ordering you could in a way it's going
+to be a block minimum degree ordering
+
+ align:start position:0%
+to be a block minimum degree ordering
+ 
+
+ align:start position:0%
+to be a block minimum degree ordering
+let me let me say what it is and as I
+
+ align:start position:0%
+let me let me say what it is and as I
+ 
+
+ align:start position:0%
+let me let me say what it is and as I
+draw the graph let me say when it might
+
+ align:start position:0%
+draw the graph let me say when it might
+ 
+
+ align:start position:0%
+draw the graph let me say when it might
+win it might win when the
+
+ align:start position:0%
+win it might win when the
+ 
+
+ align:start position:0%
+win it might win when the
+when the size goes Way Up 3D in
+
+ align:start position:0%
+when the size goes Way Up 3D in
+ 
+
+ align:start position:0%
+when the size goes Way Up 3D in
+2D minimum degree is on sparse matrices
+
+ align:start position:0%
+2D minimum degree is on sparse matrices
+ 
+
+ align:start position:0%
+2D minimum degree is on sparse matrices
+is quite
+
+ align:start position:0%
+is quite
+ 
+
+ align:start position:0%
+is quite
+successful so in in two Dimensions until
+
+ align:start position:0%
+successful so in in two Dimensions until
+ 
+
+ align:start position:0%
+successful so in in two Dimensions until
+the size really gets big um you that's
+
+ align:start position:0%
+the size really gets big um you that's
+ 
+
+ align:start position:0%
+the size really gets big um you that's
+going to be fine in three dimensions
+
+ align:start position:0%
+going to be fine in three dimensions
+ 
+
+ align:start position:0%
+going to be fine in three dimensions
+well I'm still going to draw only two
+
+ align:start position:0%
+well I'm still going to draw only two
+ 
+
+ align:start position:0%
+well I'm still going to draw only two
+but in three dimensions or very very
+
+ align:start position:0%
+but in three dimensions or very very
+ 
+
+ align:start position:0%
+but in three dimensions or very very
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+matrices I want to think about this
+
+ align:start position:0%
+matrices I want to think about this
+ 
+
+ align:start position:0%
+matrices I want to think about this
+graph separator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me I'll make it just so I really
+
+ align:start position:0%
+so let me I'll make it just so I really
+ 
+
+ align:start position:0%
+so let me I'll make it just so I really
+separate it perfectly let me make the
+
+ align:start position:0%
+separate it perfectly let me make the
+ 
+
+ align:start position:0%
+separate it perfectly let me make the
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah I so when when you look at that
+
+ align:start position:0%
+um yeah I so when when you look at that
+ 
+
+ align:start position:0%
+um yeah I so when when you look at that
+graph you might say if I look at that
+
+ align:start position:0%
+graph you might say if I look at that
+ 
+
+ align:start position:0%
+graph you might say if I look at that
+that set of nodes so a
+
+ align:start position:0%
+that set of nodes so a
+ 
+
+ align:start position:0%
+that set of nodes so a
+separator is a set of
+
+ align:start position:0%
+separator is a set of
+ 
+
+ align:start position:0%
+separator is a set of
+nodes that separates the rest of the
+
+ align:start position:0%
+nodes that separates the rest of the
+ 
+
+ align:start position:0%
+nodes that separates the rest of the
+nodes into two groups so I have a group
+
+ align:start position:0%
+nodes into two groups so I have a group
+ 
+
+ align:start position:0%
+nodes into two groups so I have a group
+of nodes p a group of nodes q and
+
+ align:start position:0%
+of nodes p a group of nodes q and
+ 
+
+ align:start position:0%
+of nodes p a group of nodes q and
+nothing no connections between p and q p
+
+ align:start position:0%
+nothing no connections between p and q p
+ 
+
+ align:start position:0%
+nothing no connections between p and q p
+is this
+
+ align:start position:0%
+is this
+ 
+
+ align:start position:0%
+is this
+part Q is a s similar part over there s
+
+ align:start position:0%
+part Q is a s similar part over there s
+ 
+
+ align:start position:0%
+part Q is a s similar part over there s
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+separator
+
+ align:start position:0%
+separator
+ 
+
+ align:start position:0%
+separator
+is the part with the with the connection
+
+ align:start position:0%
+is the part with the with the connection
+ 
+
+ align:start position:0%
+is the part with the with the connection
+so p is connected to Q only through S so
+
+ align:start position:0%
+so p is connected to Q only through S so
+ 
+
+ align:start position:0%
+so p is connected to Q only through S so
+now if I think of ordering in what order
+
+ align:start position:0%
+now if I think of ordering in what order
+ 
+
+ align:start position:0%
+now if I think of ordering in what order
+should I take the the P the Q and the
+
+ align:start position:0%
+should I take the the P the Q and the
+ 
+
+ align:start position:0%
+should I take the the P the Q and the
+S well our absolute rule
+
+ align:start position:0%
+S well our absolute rule
+ 
+
+ align:start position:0%
+S well our absolute rule
+is everything's connected to S put it
+
+ align:start position:0%
+is everything's connected to S put it
+ 
+
+ align:start position:0%
+is everything's connected to S put it
+last so you see that this is the block
+
+ align:start position:0%
+last so you see that this is the block
+ 
+
+ align:start position:0%
+last so you see that this is the block
+form of my small example here well I
+
+ align:start position:0%
+form of my small example here well I
+ 
+
+ align:start position:0%
+form of my small example here well I
+didn't particularly have a p or a q but
+
+ align:start position:0%
+didn't particularly have a p or a q but
+ 
+
+ align:start position:0%
+didn't particularly have a p or a q but
+I certainly wanted to put s less oh well
+
+ align:start position:0%
+I certainly wanted to put s less oh well
+ 
+
+ align:start position:0%
+I certainly wanted to put s less oh well
+maybe I did so maybe the separator here
+
+ align:start position:0%
+maybe I did so maybe the separator here
+ 
+
+ align:start position:0%
+maybe I did so maybe the separator here
+was uh so what's the separator well one
+
+ align:start position:0%
+was uh so what's the separator well one
+ 
+
+ align:start position:0%
+was uh so what's the separator well one
+possible separator would be like that as
+
+ align:start position:0%
+possible separator would be like that as
+ 
+
+ align:start position:0%
+possible separator would be like that as
+s p for these two nodes Q for these
+
+ align:start position:0%
+s p for these two nodes Q for these
+ 
+
+ align:start position:0%
+s p for these two nodes Q for these
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+nodes and the rule would be I haven't
+
+ align:start position:0%
+nodes and the rule would be I haven't
+ 
+
+ align:start position:0%
+nodes and the rule would be I haven't
+said what I'll do within P or within Q
+
+ align:start position:0%
+said what I'll do within P or within Q
+ 
+
+ align:start position:0%
+said what I'll do within P or within Q
+or within s but the rule would be put Q
+
+ align:start position:0%
+or within s but the rule would be put Q
+ 
+
+ align:start position:0%
+or within s but the rule would be put Q
+L and of course that was exactly the
+
+ align:start position:0%
+L and of course that was exactly the
+ 
+
+ align:start position:0%
+L and of course that was exactly the
+right thing to do and it's the we're
+
+ align:start position:0%
+right thing to do and it's the we're
+ 
+
+ align:start position:0%
+right thing to do and it's the we're
+following the same rule just blockwise
+
+ align:start position:0%
+following the same rule just blockwise
+ 
+
+ align:start position:0%
+following the same rule just blockwise
+so we have the block so so our Matrix
+
+ align:start position:0%
+so we have the block so so our Matrix
+ 
+
+ align:start position:0%
+so we have the block so so our Matrix
+what is our Matrix look like when you
+
+ align:start position:0%
+what is our Matrix look like when you
+ 
+
+ align:start position:0%
+what is our Matrix look like when you
+choose this ordering well you have
+
+ align:start position:0%
+choose this ordering well you have
+ 
+
+ align:start position:0%
+choose this ordering well you have
+whatever P whatever p is the block of
+
+ align:start position:0%
+whatever P whatever p is the block of
+ 
+
+ align:start position:0%
+whatever P whatever p is the block of
+all these P's you have the block of all
+
+ align:start position:0%
+all these P's you have the block of all
+ 
+
+ align:start position:0%
+all these P's you have the block of all
+these Q's which might be connected to
+
+ align:start position:0%
+these Q's which might be connected to
+ 
+
+ align:start position:0%
+these Q's which might be connected to
+each other and
+
+ align:start position:0%
+each other and
+ 
+
+ align:start position:0%
+each other and
+R but not to P so the main point is to
+
+ align:start position:0%
+R but not to P so the main point is to
+ 
+
+ align:start position:0%
+R but not to P so the main point is to
+have these zero blocks and then
+
+ align:start position:0%
+have these zero blocks and then
+ 
+
+ align:start position:0%
+have these zero blocks and then
+everything is connected to
+
+ align:start position:0%
+everything is connected to
+ 
+
+ align:start position:0%
+everything is connected to
+S and S is connected to itself so it's
+
+ align:start position:0%
+S and S is connected to itself so it's
+ 
+
+ align:start position:0%
+S and S is connected to itself so it's
+all you've achieved but it could be
+
+ align:start position:0%
+all you've achieved but it could be
+ 
+
+ align:start position:0%
+all you've achieved but it could be
+considered considerable is to take an
+
+ align:start position:0%
+considered considerable is to take an
+ 
+
+ align:start position:0%
+considered considerable is to take an
+ordering in which P
+
+ align:start position:0%
+ordering in which P
+ 
+
+ align:start position:0%
+ordering in which P
+was since p is not connected to q that
+
+ align:start position:0%
+was since p is not connected to q that
+ 
+
+ align:start position:0%
+was since p is not connected to q that
+produce these large zero blocks and of
+
+ align:start position:0%
+produce these large zero blocks and of
+ 
+
+ align:start position:0%
+produce these large zero blocks and of
+course they'll stay zero as elimination
+
+ align:start position:0%
+course they'll stay zero as elimination
+ 
+
+ align:start position:0%
+course they'll stay zero as elimination
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+forward those those zeros there will I
+
+ align:start position:0%
+forward those those zeros there will I
+ 
+
+ align:start position:0%
+forward those those zeros there will I
+don't have to do any pivoting operations
+
+ align:start position:0%
+don't have to do any pivoting operations
+ 
+
+ align:start position:0%
+don't have to do any pivoting operations
+any row operations to make those zero
+
+ align:start position:0%
+any row operations to make those zero
+ 
+
+ align:start position:0%
+any row operations to make those zero
+they're already zero and uh so the only
+
+ align:start position:0%
+they're already zero and uh so the only
+ 
+
+ align:start position:0%
+they're already zero and uh so the only
+operations will
+
+ align:start position:0%
+operations will
+ 
+
+ align:start position:0%
+operations will
+be p on to s q on to s s onto
+
+ align:start position:0%
+be p on to s q on to s s onto
+ 
+
+ align:start position:0%
+be p on to s q on to s s onto
+itself and in many problems it's the S
+
+ align:start position:0%
+itself and in many problems it's the S
+ 
+
+ align:start position:0%
+itself and in many problems it's the S
+onto itself part so what will happen
+
+ align:start position:0%
+onto itself part so what will happen
+ 
+
+ align:start position:0%
+onto itself part so what will happen
+then when when I do elimination on this
+
+ align:start position:0%
+then when when I do elimination on this
+ 
+
+ align:start position:0%
+then when when I do elimination on this
+when I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elimination well I'll have whatever work
+
+ align:start position:0%
+elimination well I'll have whatever work
+ 
+
+ align:start position:0%
+elimination well I'll have whatever work
+is necessary within
+
+ align:start position:0%
+is necessary within
+ 
+
+ align:start position:0%
+is necessary within
+P so I I I'll be factoring can I call
+
+ align:start position:0%
+P so I I I'll be factoring can I call
+ 
+
+ align:start position:0%
+P so I I I'll be factoring can I call
+that P that part of the Matrix just
+
+ align:start position:0%
+that P that part of the Matrix just
+ 
+
+ align:start position:0%
+that P that part of the Matrix just
+it's an abuse of notation and this is
+
+ align:start position:0%
+it's an abuse of notation and this is
+ 
+
+ align:start position:0%
+it's an abuse of notation and this is
+the connections of s to P this is the
+
+ align:start position:0%
+the connections of s to P this is the
+ 
+
+ align:start position:0%
+the connections of s to P this is the
+connections of s to q s to itself Q to s
+
+ align:start position:0%
+connections of s to q s to itself Q to s
+ 
+
+ align:start position:0%
+connections of s to q s to itself Q to s
+p to S probably symmetric but the so
+
+ align:start position:0%
+p to S probably symmetric but the so
+ 
+
+ align:start position:0%
+p to S probably symmetric but the so
+when I do elimination I'll if if I don't
+
+ align:start position:0%
+when I do elimination I'll if if I don't
+ 
+
+ align:start position:0%
+when I do elimination I'll if if I don't
+if I accept this
+
+ align:start position:0%
+if I accept this
+ 
+
+ align:start position:0%
+if I accept this
+ordering if I accept this ordering and
+
+ align:start position:0%
+ordering if I accept this ordering and
+ 
+
+ align:start position:0%
+ordering if I accept this ordering and
+just go for it elimination will Factor P
+
+ align:start position:0%
+just go for it elimination will Factor P
+ 
+
+ align:start position:0%
+just go for it elimination will Factor P
+into Lu because it'll work up in the
+
+ align:start position:0%
+into Lu because it'll work up in the
+ 
+
+ align:start position:0%
+into Lu because it'll work up in the
+corner as always does then
+
+ align:start position:0%
+corner as always does then
+ 
+
+ align:start position:0%
+corner as always does then
+no connection here so it'll Factor Q
+
+ align:start position:0%
+no connection here so it'll Factor Q
+ 
+
+ align:start position:0%
+no connection here so it'll Factor Q
+into its own Lu and of course all that
+
+ align:start position:0%
+into its own Lu and of course all that
+ 
+
+ align:start position:0%
+into its own Lu and of course all that
+all this stuff down here will change but
+
+ align:start position:0%
+all this stuff down here will change but
+ 
+
+ align:start position:0%
+all this stuff down here will change but
+effectively the these will become zeros
+
+ align:start position:0%
+effectively the these will become zeros
+ 
+
+ align:start position:0%
+effectively the these will become zeros
+when because then then there's a serious
+
+ align:start position:0%
+when because then then there's a serious
+ 
+
+ align:start position:0%
+when because then then there's a serious
+elimination p on to S will make that
+
+ align:start position:0%
+elimination p on to S will make that
+ 
+
+ align:start position:0%
+elimination p on to S will make that
+zero P Q on to s q will make that zero
+
+ align:start position:0%
+zero P Q on to s q will make that zero
+ 
+
+ align:start position:0%
+zero P Q on to s q will make that zero
+this will be some I'll call it
+
+ align:start position:0%
+this will be some I'll call it
+ 
+
+ align:start position:0%
+this will be some I'll call it
+SSS it's some much full
+
+ align:start position:0%
+SSS it's some much full
+ 
+
+ align:start position:0%
+SSS it's some much full
+Matrix block smaller though hopefully
+
+ align:start position:0%
+Matrix block smaller though hopefully
+ 
+
+ align:start position:0%
+Matrix block smaller though hopefully
+smaller and uh but pretty full so
+
+ align:start position:0%
+smaller and uh but pretty full so
+ 
+
+ align:start position:0%
+smaller and uh but pretty full so
+actually in the graph separator nested
+
+ align:start position:0%
+actually in the graph separator nested
+ 
+
+ align:start position:0%
+actually in the graph separator nested
+dissection World often the most of the
+
+ align:start position:0%
+dissection World often the most of the
+ 
+
+ align:start position:0%
+dissection World often the most of the
+time is spent on that uh third block
+
+ align:start position:0%
+time is spent on that uh third block
+ 
+
+ align:start position:0%
+time is spent on that uh third block
+just working with it because it's it's
+
+ align:start position:0%
+just working with it because it's it's
+ 
+
+ align:start position:0%
+just working with it because it's it's
+the one that's pretty full okay so so
+
+ align:start position:0%
+the one that's pretty full okay so so
+ 
+
+ align:start position:0%
+the one that's pretty full okay so so
+how do how do graph separators work
+
+ align:start position:0%
+how do how do graph separators work
+ 
+
+ align:start position:0%
+how do how do graph separators work
+first of all you need a an algorithm
+
+ align:start position:0%
+first of all you need a an algorithm
+ 
+
+ align:start position:0%
+first of all you need a an algorithm
+that finds a
+
+ align:start position:0%
+that finds a
+ 
+
+ align:start position:0%
+that finds a
+separator and a lot of computer science
+
+ align:start position:0%
+separator and a lot of computer science
+ 
+
+ align:start position:0%
+separator and a lot of computer science
+attention has gone onto that given a
+
+ align:start position:0%
+attention has gone onto that given a
+ 
+
+ align:start position:0%
+attention has gone onto that given a
+graph cut it in half find a by a short
+
+ align:start position:0%
+graph cut it in half find a by a short
+ 
+
+ align:start position:0%
+graph cut it in half find a by a short
+we don't want more nodes in the
+
+ align:start position:0%
+we don't want more nodes in the
+ 
+
+ align:start position:0%
+we don't want more nodes in the
+separator than necessary because the
+
+ align:start position:0%
+separator than necessary because the
+ 
+
+ align:start position:0%
+separator than necessary because the
+work is going to end up there so we want
+
+ align:start position:0%
+work is going to end up there so we want
+ 
+
+ align:start position:0%
+work is going to end up there so we want
+to cut the graph pretty nearly in
+
+ align:start position:0%
+to cut the graph pretty nearly in
+ 
+
+ align:start position:0%
+to cut the graph pretty nearly in
+half by a short separator
+
+ align:start position:0%
+half by a short separator
+ 
+
+ align:start position:0%
+half by a short separator
+and then uh so that's a if we only did
+
+ align:start position:0%
+and then uh so that's a if we only did
+ 
+
+ align:start position:0%
+and then uh so that's a if we only did
+the the algorithm did this did the
+
+ align:start position:0%
+the the algorithm did this did the
+ 
+
+ align:start position:0%
+the the algorithm did this did the
+separation the cut the dissection once
+
+ align:start position:0%
+separation the cut the dissection once
+ 
+
+ align:start position:0%
+separation the cut the dissection once
+that's that's what we need but this idea
+
+ align:start position:0%
+that's that's what we need but this idea
+ 
+
+ align:start position:0%
+that's that's what we need but this idea
+of nested dissection oh you know what's
+
+ align:start position:0%
+of nested dissection oh you know what's
+ 
+
+ align:start position:0%
+of nested dissection oh you know what's
+going to come before I say it the idea
+
+ align:start position:0%
+going to come before I say it the idea
+ 
+
+ align:start position:0%
+going to come before I say it the idea
+of nested dissection will be take this
+
+ align:start position:0%
+of nested dissection will be take this
+ 
+
+ align:start position:0%
+of nested dissection will be take this
+um take the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph can I just draw this way without
+
+ align:start position:0%
+graph can I just draw this way without
+ 
+
+ align:start position:0%
+graph can I just draw this way without
+drawing all the Ed put cut it by a
+
+ align:start position:0%
+drawing all the Ed put cut it by a
+ 
+
+ align:start position:0%
+drawing all the Ed put cut it by a
+separator
+
+ align:start position:0%
+separator
+ 
+
+ align:start position:0%
+separator
+S1 that gives a P1 and a q1 but now
+
+ align:start position:0%
+S1 that gives a P1 and a q1 but now
+ 
+
+ align:start position:0%
+S1 that gives a P1 and a q1 but now
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+coming you're going to separate P1 in
+
+ align:start position:0%
+coming you're going to separate P1 in
+ 
+
+ align:start position:0%
+coming you're going to separate P1 in
+order to do the work up in that left
+
+ align:start position:0%
+order to do the work up in that left
+ 
+
+ align:start position:0%
+order to do the work up in that left
+corner for the P
+
+ align:start position:0%
+corner for the P
+ 
+
+ align:start position:0%
+corner for the P
+Matrix that's itself a sparse Matrix so
+
+ align:start position:0%
+Matrix that's itself a sparse Matrix so
+ 
+
+ align:start position:0%
+Matrix that's itself a sparse Matrix so
+now I'll look for a separator and what
+
+ align:start position:0%
+now I'll look for a separator and what
+ 
+
+ align:start position:0%
+now I'll look for a separator and what
+separator will I choose for the left
+
+ align:start position:0%
+separator will I choose for the left
+ 
+
+ align:start position:0%
+separator will I choose for the left
+side of this
+
+ align:start position:0%
+side of this
+ 
+
+ align:start position:0%
+side of this
+graph I'll choose the horizontal Al
+
+ align:start position:0%
+graph I'll choose the horizontal Al
+ 
+
+ align:start position:0%
+graph I'll choose the horizontal Al
+separator this will be the second
+
+ align:start position:0%
+separator this will be the second
+ 
+
+ align:start position:0%
+separator this will be the second
+separator it'll separate the two bits of
+
+ align:start position:0%
+separator it'll separate the two bits of
+ 
+
+ align:start position:0%
+separator it'll separate the two bits of
+P the third separator will separate the
+
+ align:start position:0%
+P the third separator will separate the
+ 
+
+ align:start position:0%
+P the third separator will separate the
+two bits of
+
+ align:start position:0%
+two bits of
+ 
+
+ align:start position:0%
+two bits of
+Q now I have this part to work on a
+
+ align:start position:0%
+Q now I have this part to work on a
+ 
+
+ align:start position:0%
+Q now I have this part to work on a
+fourth separator will you see it's
+
+ align:start position:0%
+fourth separator will you see it's
+ 
+
+ align:start position:0%
+fourth separator will you see it's
+nested these separators become nested
+
+ align:start position:0%
+nested these separators become nested
+ 
+
+ align:start position:0%
+nested these separators become nested
+there's S5 there's S6 and so on okay I
+
+ align:start position:0%
+there's S5 there's S6 and so on okay I
+ 
+
+ align:start position:0%
+there's S5 there's S6 and so on okay I
+think everybody sees in principle what
+
+ align:start position:0%
+think everybody sees in principle what
+ 
+
+ align:start position:0%
+think everybody sees in principle what
+nested dissection should do and the
+
+ align:start position:0%
+nested dissection should do and the
+ 
+
+ align:start position:0%
+nested dissection should do and the
+question is how does it compare with
+
+ align:start position:0%
+question is how does it compare with
+ 
+
+ align:start position:0%
+question is how does it compare with
+minimum degree you see it's just like a
+
+ align:start position:0%
+minimum degree you see it's just like a
+ 
+
+ align:start position:0%
+minimum degree you see it's just like a
+different we're off on a different route
+
+ align:start position:0%
+different we're off on a different route
+ 
+
+ align:start position:0%
+different we're off on a different route
+here and uh you can compute ASM
+
+ align:start position:0%
+here and uh you can compute ASM
+ 
+
+ align:start position:0%
+here and uh you can compute ASM
+totically for large n what the what
+
+ align:start position:0%
+totically for large n what the what
+ 
+
+ align:start position:0%
+totically for large n what the what
+power of n appears there what power of n
+
+ align:start position:0%
+power of n appears there what power of n
+ 
+
+ align:start position:0%
+power of n appears there what power of n
+appears in minimum degree but I would
+
+ align:start position:0%
+appears in minimum degree but I would
+ 
+
+ align:start position:0%
+appears in minimum degree but I would
+love to know does
+
+ align:start position:0%
+love to know does
+ 
+
+ align:start position:0%
+love to know does
+the I I would be happy if
+
+ align:start position:0%
+the I I would be happy if
+ 
+
+ align:start position:0%
+the I I would be happy if
+somebody used approximate minimum degree
+
+ align:start position:0%
+somebody used approximate minimum degree
+ 
+
+ align:start position:0%
+somebody used approximate minimum degree
+on our model problem and maybe also on
+
+ align:start position:0%
+on our model problem and maybe also on
+ 
+
+ align:start position:0%
+on our model problem and maybe also on
+some other problem and uh we could see
+
+ align:start position:0%
+some other problem and uh we could see
+ 
+
+ align:start position:0%
+some other problem and uh we could see
+what U what power of n that's
+
+ align:start position:0%
+what U what power of n that's
+ 
+
+ align:start position:0%
+what U what power of n that's
+essentially what we're looking for so
+
+ align:start position:0%
+essentially what we're looking for so
+ 
+
+ align:start position:0%
+essentially what we're looking for so
+it's n to what power for fill
+
+ align:start position:0%
+it's n to what power for fill
+ 
+
+ align:start position:0%
+it's n to what power for fill
+in and for the operation count which
+
+ align:start position:0%
+in and for the operation count which
+ 
+
+ align:start position:0%
+in and for the operation count which
+which the number of flops which uh
+
+ align:start position:0%
+which the number of flops which uh
+ 
+
+ align:start position:0%
+which the number of flops which uh
+controls the the cost and the time
+
+ align:start position:0%
+controls the the cost and the time
+ 
+
+ align:start position:0%
+controls the the cost and the time
+yeah so it's what power ofan appears
+
+ align:start position:0%
+yeah so it's what power ofan appears
+ 
+
+ align:start position:0%
+yeah so it's what power ofan appears
+there and what power appears in any
+
+ align:start position:0%
+there and what power appears in any
+ 
+
+ align:start position:0%
+there and what power appears in any
+other method so that's there you have it
+
+ align:start position:0%
+other method so that's there you have it
+ 
+
+ align:start position:0%
+other method so that's there you have it
+for um direct elimination methods and
+
+ align:start position:0%
+for um direct elimination methods and
+ 
+
+ align:start position:0%
+for um direct elimination methods and
+I'll just mention the name of the guy
+
+ align:start position:0%
+I'll just mention the name of the guy
+ 
+
+ align:start position:0%
+I'll just mention the name of the guy
+he's at University of
+
+ align:start position:0%
+he's at University of
+ 
+
+ align:start position:0%
+he's at University of
+Florida and he's the one who wrote the
+
+ align:start position:0%
+Florida and he's the one who wrote the
+ 
+
+ align:start position:0%
+Florida and he's the one who wrote the
+contributed the code that MathWorks uses
+
+ align:start position:0%
+contributed the code that MathWorks uses
+ 
+
+ align:start position:0%
+contributed the code that MathWorks uses
+and has just announced a book coming on
+
+ align:start position:0%
+and has just announced a book coming on
+ 
+
+ align:start position:0%
+and has just announced a book coming on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+exact topic
+
+ align:start position:0%
+exact topic
+ 
+
+ align:start position:0%
+exact topic
+uh to be to come later this year from
+
+ align:start position:0%
+uh to be to come later this year from
+ 
+
+ align:start position:0%
+uh to be to come later this year from
+the from cam so there will be a book
+
+ align:start position:0%
+the from cam so there will be a book
+ 
+
+ align:start position:0%
+the from cam so there will be a book
+that from the the person I take to be
+
+ align:start position:0%
+that from the the person I take to be
+ 
+
+ align:start position:0%
+that from the the person I take to be
+the leader in this uh in this
+
+ align:start position:0%
+the leader in this uh in this
+ 
+
+ align:start position:0%
+the leader in this uh in this
+algorithmic
+
+ align:start position:0%
+algorithmic
+ 
+
+ align:start position:0%
+algorithmic
+development okay and just a reminder
+
+ align:start position:0%
+development okay and just a reminder
+ 
+
+ align:start position:0%
+development okay and just a reminder
+Friday is my guest former PhD student
+
+ align:start position:0%
+Friday is my guest former PhD student
+ 
+
+ align:start position:0%
+Friday is my guest former PhD student
+who's going to speak about numerical
+
+ align:start position:0%
+who's going to speak about numerical
+ 
+
+ align:start position:0%
+who's going to speak about numerical
+methods for finance black schools
+
+ align:start position:0%
+methods for finance black schools
+ 
+
+ align:start position:0%
+methods for finance black schools
+equations and other
+
+ align:start position:0%
+equations and other
+ 
+
+ align:start position:0%
+equations and other
+problems to uh find the value of
+
+ align:start position:0%
+problems to uh find the value of
+ 
+
+ align:start position:0%
+problems to uh find the value of
+financial derivatives okay see you
+
+ align:start position:0%
+financial derivatives okay see you
+ 
+
+ align:start position:0%
+financial derivatives okay see you
+Friday
\ No newline at end of file
diff --git a/SemWOqUfMAY.txt b/SemWOqUfMAY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fefbde7611395e678015058cb6c9d861ba8e42f6
--- /dev/null
+++ b/SemWOqUfMAY.txt
@@ -0,0 +1,2448 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Let's get started.
+
+So what I'm going to do next
+is switch gears to one
+
+interesting compiler, which
+is the StreamIt
+
+parallelizing compiler.
+
+The main idea about StreamIt
+is the need for a common
+
+machine language.
+
+What we want to do normally is,
+in a language, you want to
+
+represent common architecture
+properties so you get good
+
+performance.
+
+You don't do it at a very high
+level of abstraction, so you
+
+base a lot of cycles dealing
+with the abstraction.
+
+But you want to abstract out
+the differences between
+
+machines to get the portability,
+otherwise you are
+
+going to just do
+
+assembly-hacking for one machine.
+
+Also you can't have things too
+complex, because a typical
+
+programmer cannot deal with very
+complex things that we
+
+ask them to do.
+
+C and Fortran was a really nice
+common assembly language
+
+for imperative languages
+running
+
+on the unicore machines.
+
+The problem is this type of
+language is not a good common
+
+language for multicores, because
+it doesn't deal with,
+
+first of all, multiple cores.
+
+And as you keep changing
+the number of cores --
+
+for example, automatic
+parallelizing compilers are
+
+not good to basically get really
+good parallelism out of
+
+that, even though we
+talk about that.
+
+Still a lot of work has
+to be done in there.
+
+So what's the correct
+abstraction if you have
+
+multicore machines?
+
+The current offering, what you
+guys are doing, is things like
+
+OpenMP, MPI type stuff.
+
+You are hand-hacking
+the parallelism.
+
+Well, the issue with that.
+
+It's basically this explicit
+parallel construct.
+
+It's kind of added to languages
+like C -- that's
+
+what you're working on.
+
+And what this does is all these
+nice properties about
+
+composability, malleability,
+debuggability, portability --
+
+all those things were kind
+of out of the window.
+
+And this is why this
+parallelizing is hard, because
+
+all these things makes life
+very difficult for the
+
+programmer.
+
+And it's a huge additional
+program burden.
+
+The programmer has to introduce
+parallelism,
+
+correctness, optimization --
+
+it's all left to
+the programmer.
+
+So what the program has to do in
+this kind of world -- what
+
+you are doing right now --
+
+you have to feed all the
+granularity decisions.
+
+If things are too small
+you might get too much
+
+communication.
+
+If things are too large you
+might not get good load
+
+balancing, and stuff like.
+
+And then you deal with all the
+load balancing decisions.
+
+All those decisions are
+left for you guys.
+
+You need to figure out what's
+local, what's not.
+
+And if you make a wrong decision
+it can cost you.
+
+All the synchronization, and
+all the pain and suffering
+
+that comes from making
+a wrong decision.
+
+Things like race conditions,
+deadlocks,
+
+and stuff like that.
+
+And this, while MIT students can
+hack it, you can't go and
+
+convince a dull programmer to
+convert from writing nice
+
+simple Java application code
+to dealing with all these
+
+complexities.
+
+So this is what kind of led to
+our research for the last five
+
+years to do StreamIt.
+
+What you want to do is move a
+bunch of these decisions to
+
+the compiler.
+
+Granularity, load balancing,
+locality, and
+
+synchronization --
+
+[OBSCURED]
+
+And in today's talk I am going
+to talk to you about, after
+
+you write a StreamIt program
+-- as Bill pointed out, the
+
+nice parallel properties -- how
+do you actually go about
+
+getting this kind
+of parallelism.
+
+So in StreamIt , in summary, it
+basically has regular and
+
+repeating computation
+in these filters.
+
+This is called a synchronous
+data flow model, because we
+
+know at compile time exactly how
+the data moves, how much
+
+each produces and consumes.
+
+And this has natural
+parallelism, and it exposes
+
+exactly what's going to happen
+to the compiler.
+
+And the compiler can do a lot
+of powerful transformations,
+
+as yesterday I pointed out.
+
+The first thing is, because of
+synchronous data flow, we know
+
+at compile time exactly who
+needs to do what when.
+
+And that really helps
+transform.
+
+It's not like everything happens
+run-time dynamically.
+
+So what does that mean?
+
+So what that means is each
+filter knows exactly how much
+
+to push and pop --
+
+that's in a repeatable
+execution.
+
+And so what we can do is, we
+can come up to the static
+
+schedule that can be repeated
+multiple times.
+
+So let me tell you a little
+bit about what a static
+
+schedule means.
+
+So assume this filter pushes
+two, this filter pops three
+
+but pushes one, that
+filter pops two.
+
+So these are kind of rate
+pushes, it's not everybody
+
+producing-consuming at once.
+
+So what's the schedule?
+
+So you can say --
+
+OK, at the beginning it produces
+two items, but I
+
+can't consume that because I
+need three items. And then I
+
+do two of them, and I can
+consume the first three and
+
+then produce one there.
+
+And I have two left behind.
+
+I do one more that, and
+now I got three.
+
+And it consumes that
+and produces that.
+
+And then I can fire C. So the
+neat thing about this is, when
+
+I started there was nothing
+inside any of these buffers.
+
+And if I ran A, A, B, A, B, C,
+there's nothing inside the
+
+buffers again.
+
+So what I have is, I'm back to
+the starting positioning.
+
+And if I repeat this millions
+of times --
+
+I keep the computation running
+nicely without any buffers
+
+accumulating or anything
+like that.
+
+So I can come up with this very
+nice schedule that says
+
+-- here's what I have to do.
+
+I have to run A actually three
+times, B twice, and C once, in
+
+this order, and if I
+do that I have a
+
+computation that keeps running.
+
+And that gives me a good global
+view on what can I
+
+parallelize, what can I load
+balance, all those things.
+
+Because things don't change.
+
+One more additional thing about
+StreamIt is we can look
+
+at more elements than
+I am consuming.
+
+Question?
+
+AUDIENCE: How common is it in
+your typical code that you can
+
+actually produce a static
+schedule like that?
+
+PROFESSOR: In a lot of DSV
+code this is very common.
+
+A lot of DSV code right now that
+goes into hardware and
+
+software, they have very
+common properties.
+
+But even things that are not
+common, what has a very large
+
+chunk of the program has this
+static property, and there are
+
+some few places that has
+dynamic property.
+
+So it's like, when you write a
+normal program you don't write
+
+a branch instruction after
+every instruction.
+
+You have a few hundred
+instructions and a branch, a
+
+few tens of instructions and
+a branch type thing.
+
+So what you can think about it
+is that those instructions
+
+without a branch can get
+optimized the hell out of
+
+them, and then you do a
+branch dynamically.
+
+So you can think about
+it like this.
+
+What's the largest chunks you
+can find that you don't have
+
+this uncertainty
+until run-time?
+
+Then you can optimize the hell
+out of it, and then you can
+
+deal with this run-time
+issues --
+
+basically branches, or control
+for changes, or direct your
+
+rate changes at run-time.
+
+If we have 10-90 rule, if you
+get 90% of the things are in a
+
+nice thing, and if you get good
+performance on that --
+
+hey, it has a big impact.
+
+So in our language you can deal
+with dynamism, but our
+
+analysis is basically trying
+to find the largest static
+
+chunk and analyze.
+
+So most of the time that
+basically said we start with
+
+empty and end with empty.
+
+But the trouble is, a lot of
+times we actually can look
+
+beyond the number of
+what we consume.
+
+So what you have to do is kind
+of do initial schedule that
+
+you don't start with empty,
+you basically consume
+
+something -- you start with
+something like this.
+
+So the next time in
+something comes --
+
+three things come
+into this one --
+
+I can actually pick four
+and pop three.
+
+So you go through the first
+thing kind of priming
+
+everything with the amount of
+data needed, and then you go
+
+to the static schedule.
+
+This kind of gives you a feel
+for what you'll get.
+
+This is a neat thing,
+I know exactly
+
+what's going on in here.
+
+So now how do I run
+this parallelism?
+
+This is something actually
+Rodric pointed out before,
+
+there are three types of
+parallelism we can deal with.
+
+So here's my stream program in
+here, and I do some filters,
+
+scatter-gather in here.
+
+The first site of parallelism
+is task parallelism.
+
+What that means is the
+programmer said, there are
+
+three things that can
+run parallelly
+
+before I join them together.
+
+So this is a
+programmer-specified
+
+parallelism.
+
+And you have a nice data
+parallel messenger
+
+presentation.
+
+The second part is
+data parallelism.
+
+What that means is, you have
+some of these things that
+
+don't depend on the previous
+run of that one.
+
+So there's no invocation,
+dependency across multiple
+
+invocations.
+
+These are called stateless
+filters, there's no state that
+
+keeps changing.
+
+If the state kept changing,
+you had to wait till the
+
+previous one finishes
+to run the next one.
+
+So if you have a stateless
+filter --
+
+assume that it's data
+parallel --
+
+what you can do is you can
+basically take that, replicate
+
+it many, many times, and
+when the data comes --
+
+parallel is in it
+every data --
+
+and it will compute and
+parallelly get out here.
+
+The final thing is pipeline
+parallelism.
+
+So you can feed this one into
+this one, this one into this
+
+one, and then douse across
+in a pipeline fashion.
+
+And you can get multiple
+things execution.
+
+So we have these three types
+of parallelism in here, and
+
+the interesting thing is if you
+have stateful filters, you
+
+can't run this data parallel.
+
+Actually the only parallelism
+you can get is pipeline
+
+parallelism.
+
+So traditionally task
+parallelism is fork/join
+
+parallelism, that you guys
+are doing right now.
+
+Data parallelism is
+loop parallelism.
+
+And pipeline parallelism mainly
+was done in hardware.
+
+If you have done something like
+Verilog or VHDL you'll do
+
+a lot of pipeline parallelism.
+
+So kind of combining these three
+ideas from different
+
+communities all into one,
+because I think programs can
+
+have each part in there.
+
+So now, how do you go
+and exploit this?
+
+How do you go take advantage
+of that?
+
+So I'll talk a little bit of
+baseline techniques, and then
+
+talk about what StreamIt
+compiler does today.
+
+So assume I have a program
+like this.
+
+The hardest thing is there
+are two tasks in here.
+
+The programs are given, you
+don't have to worry anything
+
+about that.
+
+And what you can do is assign
+them into different
+
+cores and run it.
+
+Neat.
+
+You can think what a fork /join
+parallelism is, you come
+
+here you fork, you do this
+thing, and you join in here.
+
+So the interesting thing is
+if you have two cores.
+
+You probably got a 2x
+speedup in this one.
+
+This is really neat because
+there are two things in here.
+
+The problem is, how about if you
+have a lot more different
+
+number of cores?
+
+Or if the next generation has
+double the number of cores,
+
+and I'm stuck with the program
+you've written for the current
+
+generation?
+
+So this not that great,
+interesting.
+
+So we ran it on the Raw
+processor we have -- it has 16
+
+cores in there --
+
+that we have been building, and
+this is actually running a
+
+simulator of that.
+
+What you find is, is a bunch of
+StreamIt programs we have
+
+we kind of get performance like
+basically close to two,
+
+because that's the kind of
+
+parallelism people have written.
+
+In fact, some programs even
+slowed down in there, because
+
+what happens in here is
+the parallelism and
+
+synchronization is not matched
+with the target --
+
+because it's matched
+with the program.
+
+Because you wrote a program
+because your parallelism in
+
+there was what you thought was
+right for the algorithm.
+
+We didn't want you to give any
+consideration to the machine
+
+you are running, and it didn't
+match the machine, basically,
+
+if you just got the
+parallelism.
+
+And you just don't
+do that right.
+
+So one thing we have noticed
+for a lot of streaming
+
+programs, to answer your
+question, is there are a lot
+
+of data parallelism.
+
+In fact, in this filter --
+
+in this program --
+
+what you can do is you can find
+data parallel filters,
+
+and parallelize them.
+
+So you can take each
+filter, run it on
+
+every core for awile.
+
+Get the data back.
+
+Go to the next filter,
+write on every
+
+go-while, get that back.
+
+So what you can do is, if you
+have four cores in here, you
+
+can each replicate all
+this four times.
+
+Run these four for a while,
+and then these four, these
+
+four, these four, these four.
+
+OK?
+
+So that's the nice
+way to do that.
+
+So the nice thing about doing
+that is you have a lot of nice
+
+in the load balancing, because
+each are doing the same amount
+
+of work for a while.
+
+And after it accumulates enough
+data you go to the next
+
+one, do for a while,
+and then like that.
+
+And each group basically will
+occupy the entire machine --
+
+you just go down this
+group like that.
+
+And so we ran it, it started
+even slower.
+
+Why?
+
+It should have a lot more
+parallelism, because all those
+
+filters were data-parallel.
+
+So you sort of gettting stuck
+with two, now we can easily
+
+run a parallelism of 16, because
+data parallelism you
+
+can just put it any
+amount in there.
+
+But we are running slow.
+
+AUDIENCE: Communication
+overhead?
+
+PROFESSOR: Yeah, it could
+mainly be communication
+
+overhead, because what happens
+is you run this for a small
+
+amount of time.
+
+You had to send it all over
+the place, collect it back
+
+again, send it all over the
+place, collect it back again.
+
+The problem is there's too
+much synchronization and
+
+communication.
+
+Because every person at the
+end is like this global
+
+barrier, and the data has
+to go shuffling around.
+
+And that doesn't help.
+
+So the other part, what you can
+do in the baseline is what
+
+you call hardware pipeline.
+
+What that means is you can
+actually do pipeline
+
+parallelism.
+
+The way you can do that is you
+can look at the amount of work
+
+each filters contain, and you
+can combine them together in a
+
+way that the number of filters
+is going to be just about the
+
+number of tiles available.
+
+Most programs have
+more filters than
+
+the number of cores.
+
+So you review combined filters,
+to give us a number
+
+of filters, is just either the
+same, or one or two less than
+
+the number of cores available.
+
+In a way that you combine them
+so each of them will probably
+
+have close to the same
+amount of work.
+
+The problem is if when you
+combine it's very hard to get
+
+the same amount of work.
+
+And if you assume eight cores,
+you can do this combination
+
+and we can say --
+
+aha, if I do this combination,
+I have one, two, three, four,
+
+five, six, seven.
+
+Eight cores, I can get
+seven of them.
+
+Hopefully each of them have the
+same amount of work, and I
+
+can run that.
+
+And then we assign this to one
+filter and say -- "You own
+
+this one, you run it forever.
+
+You get the data from the guy
+who owns this one, and you
+
+produce at this one." And if
+you have more cores you can
+
+actually keep doing
+some of that.
+
+If you have enough filters
+you can each
+
+combine them and do that.
+
+So we perform, and
+we got this.
+
+Not that bad.
+
+So what might be the
+problems here?
+
+AUDIENCE: Hardware locality.
+
+You want to make sure that the
+communicating filters are
+
+close to each other.
+
+PROFESSOR: Yeah, that
+we can deal with.
+
+It's not a big locality
+[OBSCURED]
+
+What's the other problem?
+
+The bigger problem.
+
+AUDIENCE: [NOISE]
+
+load balance.
+
+PROFESSOR: Load balance is the
+biggest problem, because the
+
+problem is you are combining
+different types of things
+
+together, and you are hoping
+that each chunk you get
+
+combined togeher will
+have an almost
+
+identical amount of work.
+
+And that's very hard to achieve
+most of the time,
+
+because dynamically things
+keep changing.
+
+The nice thing about loops is,
+most of the time if you have a
+
+loop or state if you replicate
+it many times, it's the same
+
+amount of code, same
+amount of work.
+
+It nicely balances out.
+
+Hardware --
+
+combining different things
+becomes actually much harder.
+
+So again, parallelism and
+synchronization are not really
+
+matched to the target.
+
+So the StreamIt compiler right
+now does two, three things.
+
+I'll go through details.
+
+Coarsen the granularity
+of things.
+
+So what happens is if you have
+small filters it combines them
+
+together to get the large
+stateless areas.
+
+It data parallelizes
+when possible.
+
+And it does software pipelining,
+that's a pipeline
+
+parallelism.
+
+I'll go through all these
+things in detail.
+
+And you can get about
+11x's speedup by
+
+doing all those things.
+
+So coarsen the stream graph.
+
+So you look at this stream
+graph and say -- wait a
+
+minute, I have a bunch of
+data-parallel parts.
+
+And before what I did was I take
+each data-parallel part,
+
+when 16 then came or get
+together, went 16 came
+
+together, went 16.
+
+Why?
+
+I have put too much
+communication.
+
+Can I combine data-parallel
+things into one gigantic unit
+
+when possible?
+
+Of course, you don't want to
+combine a data-parallel part
+
+with a non-data-parallel part.
+
+Then the entire thing
+becomes sequential,
+
+and that's not helpful.
+
+So in here what we found is
+these four cannot be combined,
+
+because if you combime them
+the entire thing becomes
+
+sequential.
+
+So what we have to do is, you
+can combine this way.
+
+So all those things are
+data-parallel, all those
+
+things are data-parallel.
+
+And even though they are
+data-parallel if you combine
+
+them they become
+non-data-parallel, because
+
+this is actually doing peeking,
+it's looking at more
+
+than one, and so it's
+looking at somebody
+
+else's iteration work.
+
+So you can't combine them.
+
+So what the benefits of doing
+this is you reduce global
+
+communication basically.
+
+And the next thing
+is you want data
+
+parallelizing to four cores.
+
+And this one fits four
+ways in there.
+
+But the interesting thing is,
+when you go in this one you
+
+realize there's some
+task parallelism.
+
+We know there are two tasks that
+have the same amount of
+
+work in here.
+
+So facing this four ways, and
+facing this four ways, and
+
+giving the entire machine to
+this one, and giving the
+
+entire machine to this one,
+might not be the best idea.
+
+What you want to do is you
+want to face it two ways.
+
+And then basically give the
+entire machine to all of these
+
+running at the same time,
+because they're
+
+load balanced --
+
+because they are the same
+thing repeated.
+
+And you can do the same
+thing in here.
+
+OK.
+
+So that's what the compiler
+does automatically, and it
+
+preserves task parallelism.
+
+So if you are task parallelism
+you don't need --
+
+the thing about that is the
+parallelism you need, you
+
+don't need too much
+parallelism.
+
+You need enough parallelism
+to make the machine happy.
+
+If you have too much parallelism
+you end up in
+
+other problems, like
+synchronization.
+
+So this gives enough parallelism
+to keep the entire
+
+machine happy, but
+not too much.
+
+And by doing that actually we
+get pretty good performance.
+
+There are a few cases where this
+hardware parallelism wins
+
+out, these two, but
+most of them --
+
+actually this last one
+we can recover --
+
+do it pretty well.
+
+OK.
+
+So what's left here is -- so
+this is good parallelism and
+
+low synchronization.
+
+But there's one thing, when you
+are doing data parallelism
+
+there are places where there
+are filters that cannot be
+
+parallelized -- they are
+stateful filters.
+
+Because you can't run the data
+parallelism, and according to
+
+Amdahl's Law that's actually
+going to basically kill you,
+
+because that's just waiting
+there and you
+
+can't do too much.
+
+I'm going to show that using
+this separate program -- so
+
+this number is the amount
+of work that each
+
+of them has to do.
+
+So this is actually a lot of
+work, a lot of work -- this
+
+does a little work in each
+of these filters.
+
+So if you look at that, these
+are data parallel but it
+
+doesn't do any much work.
+
+Just parallelizing this
+doesn't help you.
+
+And these are data parallel.
+
+And these actually
+do enough work.
+
+Actually we can go and say I
+am replicating this four
+
+times, and I'm OK.
+
+I'm getting actually good
+performance in here.
+
+Now what we have is a
+program like this.
+
+And so if you are not doing
+anything else that we have
+
+data parallelism in.
+
+So what happens in the first
+cycle you run these two.
+
+And then you run data parallel
+this one, and then you run
+
+these, and then you run data
+parallel this one.
+
+And if you look at that, what
+happens is we have a bunch of
+
+holes in here.
+
+Because at that point when you
+are running that part of the
+
+program there's not enough
+parallelism, and you only have
+
+two things in there.
+
+And when you're running this
+you can run this task
+
+parallelism in here, but there's
+nothing else you can
+
+do in here.
+
+And so you get basically
+21 time steps each --
+
+time minutes basically will
+run into that program.
+
+But here we can do better.
+
+What we can do is we can take
+and try to move that there,
+
+and kind of compress them.
+
+But the interesting thing
+is these things
+
+are not data parallel.
+
+So how do I do that?
+
+So the way to do that is taking
+advantage of pipeline
+
+parallelism.
+
+So what you can do is you can
+take this filter in here.
+
+Since each of the entire graph
+can run only sequentially --
+
+this has to run after this --
+you can look at the filters
+
+running separately like that,
+and kind of say, instead of
+
+running this and this and this,
+why don't I run this
+
+iterations of this one.
+
+This iterations of
+this invocation.
+
+And this interations
+of this one.
+
+And this iterations
+on the next one.
+
+And I'm still maintaining --
+because when I'm running this
+
+even though the --
+
+I'm not running anything data
+parallel here because these
+
+ones were already done
+previously, so I can actually
+
+use that value.
+
+And so I can maintain that
+dependency, but I'm running
+
+things from the different
+iterations.
+
+And so what I need to do is, I
+need to kind of do a prologue
+
+to kind of set everything
+up in there.
+
+And then I can do that and
+I don't have any kind of
+
+dependence among these things.
+
+So now what I can do is I can
+basically take thes two and
+
+basically lay out anything
+anywhere in those groups,
+
+because they are in different
+iterations and since I am
+
+pipelining these I don't have
+any dependence in there.
+
+So I end up in this kind of a
+thing, and basically much
+
+compress in here.
+
+And by doing that what you
+actually get is a really nice
+
+performance.
+
+The only place that this
+actually wins -- hardware
+
+pipelining, and this little
+bit in there.
+
+But the rest you get a really
+good win in here.
+
+OK.
+
+So what this does is basically
+now we got a program that when
+
+the programmer never thought
+anything about what the
+
+hardware is --
+
+just wrote abstract graph
+and data streaming.
+
+And given Raw, we automatically
+actually mapped
+
+into it, and figured out what
+is the right balance, right
+
+communication, right
+synchronization, and got
+
+really good performance.
+
+And you're getting something
+like 11x performance.
+
+If you do hard hand, if you work
+hard probably you can do
+
+a little bit better.
+
+But this is good, because you
+don't hand-do anything.
+
+The killer thing is now I can
+probably take this set of
+
+programs -- which we are
+actually working on -- is you
+
+can take them to Cell which has,
+depending on the day, six
+
+cores, seven cores, eight cores,
+and we can basically
+
+get to matching the number
+of cores in there.
+
+So this is it because right now
+what happens is you have
+
+to basically hand code all those
+things, and this can
+
+automate all that process.
+
+So that's the idea, is can you
+do this -- which we haven't
+
+really proved and this
+is our research --
+
+write once, use anywhere.
+
+So write this program once
+in this abstract way.
+
+You have to really don't think
+about full parallelism.
+
+You have to think about some
+amount of parallelism, how
+
+this can be put into a stream
+graph, but you are not dealing
+
+with synchronization, load
+balancing, performance.
+
+You don't have to
+deal with that.
+
+And then the compiler will
+automatically do all these
+
+things behind you, and get
+really good performance.
+
+And the reason I showed
+this was --
+
+I'll just play one more
+slide I think --
+
+showed this was it's
+not a simple thing.
+
+The compiler actually has to do
+a bunch of work, the work
+
+that you used to do before.
+
+Things like figuring out what's
+the right granularity,
+
+what's the right mix of
+operations, what type of
+
+transformations you need
+to do to get there.
+
+But at some point we did three
+things -- coarse-grained, data
+
+parallel, and software
+pipelining.
+
+And by doing these three we can
+actually get a really good
+
+performance in most of the
+programs we have. So what we
+
+are hoping is basically this
+kind of techniques can in fact
+
+help programmers to get
+multicore performance without
+
+really going and dealing in the
+grunge level of details
+
+you guys do.
+
+You guys will appreciate that,
+and hopefully will
+
+think of making --
+
+because now at the end of this
+class, you will know all the
+
+pain and suffering the
+programmers go
+
+through to get there.
+
+And the interesting thing would
+be to in fact look at
+
+the ways to basically reduce
+that pain and suffering.
+
+So that's what I have today.
+
+So this was, as I promised,
+a short lecture --
+
+the second one.
+
+Any questions?
+
+AUDIENCE: So if we've got enough
+data parallelism we'll
+
+have the same software pipeline
+jumping on each tile?
+
+Is that right?
+
+PROFESSOR: Yes.
+
+AUDIENCE: OK.
+
+So if you do that how does it
+scale up to something that has
+
+higher communication
+costs than Raw?
+
+By doing this software
+pipelining you have to do all
+
+of your communication
+off tile.
+
+PROFESSOR: So the interest in
+there right now is we haven't
+
+done any kind of hardware
+pipelining.
+
+We are kind of doing --
+everybody's getting a lot of
+
+data moving in there.
+
+The neat thing about right now
+is, even with the SP in Cell
+
+and even Raw, the number of
+tiles are still small enough
+
+that a lot of communication
+-- unless way too much
+
+communication -- it doesn't
+really overwhelm you.
+
+Because everybody's nearby,
+you can send things.
+
+They talk a little bit about in
+Cell that near enableness
+
+helps, but not that much.
+
+But as we go into larger and
+larger cores, it's going to
+
+become an issue.
+
+Near enables become much easier
+to communicate, and you
+
+can't do global things
+in there.
+
+And at that point you will
+actually have to do some
+
+hardware pipelining.
+
+You can't just assume that at
+some point everybody's going
+
+to get some data and
+go to something.
+
+So what you need to do is have
+different chunks that the only
+
+communication that would be
+between these chunks would be
+
+kind of a pipeline
+communication.
+
+So you don't mix data around.
+
+So as we go into larger and
+larger cores you need to start
+
+doing techniques like that.
+
+The interesting thing here is
+even though what you had to
+
+change was the compiler --
+hopefully the program stays
+
+the same --
+
+right now it's not an easy
+issue, because our compiler
+
+has 10 times more core than the
+program, so it's easier in
+
+the program.
+
+But if you look at something C,
+the core base is millions
+
+of times larger than the
+size of the compiler.
+
+So at some point they'll
+be switched.
+
+It's easier to change
+the compiler to kind
+
+of keep up to date.
+
+That's what happened in C. Every
+generation you change
+
+the compiler, you don't ask
+programmers where to code the
+
+application.
+
+So can you make these kind of
+things as the multicores
+
+become different --
+
+bigger, have different
+features.
+
+You change the compiler to get
+the performance, but have the
+
+same code base.
+
+That's the goal for
+portability.
+
+AUDIENCE: Have you tried
+applying StreamIt or the
+
+streaming model in general, to
+codes that are not not very
+
+clearly stream-based but using
+the streaming model to make
+
+communication explicit, such
+as scientific codes.
+
+Or, for example, the kinds of
+parallelizable loops that you
+
+covered in the first half
+of the lecture.
+
+PROFESSOR: Some of those things,
+when you have free
+
+form simple communication
+can map into streaming.
+
+So for example, one thing
+we are doing is things
+
+like right now MPEG.
+
+Some part of the MPEG is nicely
+StreamIt, but when you
+
+actually go inside the MPEG and
+dealing with the frame,
+
+it's basically a big array,
+and you're doing that.
+
+So how do you chunkify the
+arrays, and basically deal
+
+with it in a streaming order?
+
+There's some interesting
+things you can do.
+
+There will be some stuff
+that doesn't fit that.
+
+Things like pattern recognition
+type stuff, where
+
+what you want to do
+is you want to --
+
+assume you're trying to --
+
+good example.
+
+You're trying to feature
+a condition in a video.
+
+And what happens is the number
+of features, can you match or
+
+connect two features,
+or match and
+
+connect a thousand features.
+
+And then each feature you need
+to do some processing.
+
+And that is a very
+dynamic thing.
+
+And that doesn't
+really fit into
+
+streaming order right now.
+
+And so the interesting thing is,
+the problem we have been
+
+doing is we are trying to
+fit everything into one.
+
+So right now the object-oriented
+model is it
+
+basically -- everything
+has to fit in there.
+
+But what you're finding is there
+are many things that
+
+don't really fit nicely.
+
+And you'll do these very crazy
+looking things just to get
+
+every program to fit into the
+object-oriented model.
+
+That doesn't really work.
+
+I think the right way
+to work is, is there
+
+might be multiple models.
+
+There's a streaming model,
+there's some kind of a
+
+threaded model, there might
+be different ones --
+
+I don't know what other
+models are.
+
+So the key thing is your program
+might have a large
+
+chunky model, another
+chunky model.
+
+Don't try to come up with --
+
+right now what we have
+is we have a kitchen
+
+sink type of language.
+
+It tries to support everything
+at the same time.
+
+And that doesn't really work
+because then you have to think
+
+about and say --
+
+OK done, can I have
+a pointer here?
+
+And I need to think about all
+the possible models kind of
+
+colliding in the same space.
+
+AUDIENCE: On the other hand, the
+object-oriented model is
+
+much more generalized to me.
+
+It's not the best model for
+many things, but it's much
+
+more generalizable
+than some models.
+
+And having a single model cuts
+down on the number of semantic
+
+barriers you have to cross --
+
+PROFESSOR: I don't know but --
+
+AUDIENCE: Semantic barriers
+incur both programmer overhead
+
+and run-time overhead.
+
+PROFESSOR: See the problem with
+right now with all the
+
+semantic barriers, is
+object-oriented model plus a
+
+huge number of libraries.
+
+If you want to do OpenGL, it's
+object-oriented but you have
+
+no library.
+
+If you want to do something
+else, you have
+
+to learn the library.
+
+What the right thing would be,
+instead of trying to learn the
+
+libraries is learn kind
+of a subset language.
+
+So you have nice semantics, you
+have nice syntax in there,
+
+you have nice error
+checking, nice
+
+optimization within that syntax.
+
+Because the trouble is right now
+everything is in this just
+
+gigantic language, and you
+can't do anything.
+
+And in the program you don't
+even know, because you can mix
+
+and match in really bad ways.
+
+The mix and match gives you
+a lot of power, but it can
+
+actually really hurt.
+
+And a lot of people
+don't need it.
+
+Like for example in C, people
+doubt it was really crucial
+
+for you to access any part of
+memory anywhere you want.
+
+You just can go and just access
+any program, anywhere,
+
+anytime in there.
+
+If you look at it, nobody
+takes advantage of that.
+
+How many times do you write the
+program an say -- "Hey, I
+
+want to go access the other
+guy's stack from this part."
+
+That doesn't work.
+
+You have a variable and
+you use a variable.
+
+AUDIENCE: It still [OBSCURED]
+
+PROFESSOR: Yeah, but the thing
+is because of that power, it
+
+creates a lot of problems
+for a compiler --
+
+because it needs to prove
+that you're not doing
+
+that, which is hard.
+
+And also, if you make a mistake
+the program is like --
+
+"Yeah, this looks like right.
+
+It still matches my semantics
+and syntax, I'll let you do
+
+that." But what you realize is
+that's not something people do
+
+-- just stick with
+your variable.
+
+And if you don't go
+to variables --
+
+that's what type-safe languages
+do -- it's probably
+
+more for bugs than a feature.
+
+And the same kind of thing
+having efficiency in language,
+
+is you can do everything
+at the same time.
+
+Why can't you have a language
+that you can go with this kind
+
+of context.
+
+I'm in the streaming
+context now.
+
+I say this is my streaming
+context.
+
+I am in a threaded context.
+
+Then what that does is, I have
+to learn the full set of
+
+features, but I restrict
+what I'm using here.
+
+That can probably realistically
+improve your
+
+program building, because you
+don't have to worry about --
+
+AUDIENCE: It gives the
+programmer time to get to know
+
+each language.
+
+PROFESSOR: But right now
+you have to do that.
+
+If you look at C# it has
+all these features.
+
+It has streaming features, it
+has threaded features, it has
+
+every possible object-oriented
+feature.
+
+AUDIENCE: Right, but there's a
+compact central model which
+
+covers most things.
+
+You can pull in additional
+features and fit them
+
+[OBSCURED].
+
+You can do pointer manipulation
+in C#, but you
+
+bracket things into
+an unsafe block.
+
+And then the compiler knows
+in there you're
+
+doing really bad things.
+
+PROFESSOR: That's a nice
+thing, because
+
+you can have unsafe.
+
+But can you have something
+like -- this is
+
+my streaming part.
+
+OK.
+
+Can I do something like
+that, so I don't have
+
+to worry about other?
+
+The key thing is, is there a
+way where -- because right
+
+now, my feeling is if you look
+at the object-oriented part.
+
+So if you are doing, for
+example, Windows programming,
+
+you can spend about a week
+and learn all the
+
+object-oriented concepts.
+
+And you have to spend probably
+a year to learn all the
+
+libraries on top of that.
+
+That's the old action
+these days.
+
+It's basically the building
+blocks have become too low,
+
+and then everything else is kind
+of an unorganized mess on
+
+top of that.
+
+Can you put more abstraction
+things that easy?
+
+Hey, I'm talking about
+research, this is
+
+one possible angle.
+
+I mean there might -- you can
+think, I know there are messes
+
+that I think in there.
+
+My feeling is what we do well
+is when things get too
+
+complicated we build
+abstraction layers.
+
+And the interesting thing there
+is, we build this high
+
+level programming language
+abstraction layer.
+
+And then now we have built so
+much crud on top of that
+
+without any nice abstraction
+layers, I think it's probably
+
+time to think through what
+there could be at the
+
+abstraction level.
+
+Things like, it's hitting --
+
+that is where parallelism
+is really hitting.
+
+Because that layer, the
+object-oriented layer, doesn't
+
+really support that well.
+
+And it's all kind of ad
+hoc on top of that.
+
+And so that says something.
+
+Yes, it's usable.
+
+We had this argument --
+
+assembly languages programmers
+-- for two decades.
+
+There are people who were
+
+swearing by assembly languages.
+
+They could write it two times
+smaller, two times faster than
+
+anything you can write in
+high level language.
+
+It's probably still
+true today.
+
+But at the end there were
+things that high level
+
+languages won out.
+
+I think we are probably in
+another layer like that.
+
+I don't know, probably will
+go with that argument.
+
+You can always point to
+something saying this is
+
+something you cannot do.
+
+If there are still things --
+like structured programs and
+
+unstructured programs,
+we talked about that.
+
+That argument went
+for a decade.
+
+AUDIENCE: The question I would
+pose is can you formulate a
+
+kitchen sink language at a
+parallelizable level of
+
+abstraction?
+
+PROFESSOR: Ah.
+
+That's interesting, because
+parallelization is -- one of
+
+the biggest things people
+have to figure out is
+
+composability.
+
+You can't have two parallel
+regions as a
+
+black box put together.
+
+You start running into deadlocks
+and all those other
+
+issues in there.
+
+Most of the things that you work
+is the abstraction works,
+
+because then you can compose at
+a higher level abstraction.
+
+You can have interface and
+say -- here are something
+
+interface, I don't know what's
+underneath, I compose at the
+
+interface level.
+
+And then the next guy composes
+at the higher level, and
+
+everything is hidden.
+
+We don't know how to do that
+in parallelism right now.
+
+We need to combine two things,
+it runs into problems. And the
+
+minute you figure that one out
+-- if somebody can figure out
+
+what's the right abstraction
+that is composable, parallel
+
+abstraction --
+
+I think that will solve a
+huge amount of problems.
+
+AUDIENCE: Isn't it Fortress that
+attempted to do something
+
+that's parallelizable and the
+kitchen sink, but that then
+
+leaves all the parallelizable
+--
+
+AUDIENCE: I'm saying how
+terrible [OBSCURED]
+
+programmers.
+
+PROFESSOR: But I would say right
+now is a very exciting
+
+time, because there's
+a big problem and
+
+nobody knows the solution.
+
+And I think for industry they
+lose a lot of sleep over that,
+
+but for academia it's
+the best time.
+
+Because we don't care, we don't
+have to make money out
+
+of these things, we don't have
+to get production out of it.
+
+But these actually have a very
+open problem that a lot of
+
+people care about.
+
+And I think this is fun partly
+because of that.
+
+I think this huge open problem
+that if you talk to people
+
+like Intels and Microsoft, a
+lot of people worry a lot
+
+about they don't know how to
+deal with the future in 5-10
+
+years time.
+
+They don't see this is scaling
+what they're doing.
+
+And from Intel's point of
+view, they made money by
+
+making Moore's Law available
+for people to use.
+
+They know how to make it
+available, but they don't know
+
+how to make people use it.
+
+From Microsoft's point of
+view, their current
+
+development methodology is
+almost at this breaking point.
+
+And if you look at the last
+time this happening -- so
+
+things like Windows 3.0, where
+their current development
+
+methodology doesn't really
+scale, and they really
+
+revamped it.
+
+They came up with all this
+process, and that had
+
+lasted until now.
+
+For the last two Office and
+Vista, just realized they
+
+can't really scale that up.
+
+So they are already in trouble,
+because they can't
+
+write the next big goal is just
+two times bigger than
+
+Vista, and hopefully
+get it working.
+
+But on top of that, they have
+it thrown this multicore
+
+thing, and that really puts
+huge amount of burden.
+
+So they are worried
+about that.
+
+So from both their point of
+view, everybody's clamoring
+
+for a solution.
+
+And things like last
+time around --
+
+I'll talk about this in the
+future -- last time around
+
+when that happened, it created
+a huge amount of
+
+opportunities, and bunch of
+people who sold it kind of
+
+became famous.
+
+Becuase they say -- we came up
+with a solution, and that
+
+people started using and
+stuff like that.
+
+Right now, everybody's kind of
+waiting for somebody to come
+
+up and say here's the solution,
+here's a solution.
+
+And there are a lot of --
+
+Fortress type exports is one,
+and what we are doing is one.
+
+And hopefully some of you will
+end up doing something
+
+interesting that
+might solve it.
+
+This is why it's fun.
+
+I think we haven't had this much
+of an interesting time in
+
+programming languages,
+parallelism, architecture in
+
+the last two decades.
+
+With that, I'll stop my talk.
\ No newline at end of file
diff --git a/SsCeVABM4Mo.txt b/SsCeVABM4Mo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6dfd3eccead51a238873a3658bd3cfc0f6dc7520
--- /dev/null
+++ b/SsCeVABM4Mo.txt
@@ -0,0 +1,5092 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Any questions
+from last lecture
+
+from before spring break?
+
+No questions, nothing?
+
+Nothing at all?
+
+We you all still on vacation?
+
+Thank you.
+
+Yeah.
+
+AUDIENCE: Could you talk
+about coherence states?
+
+PROFESSOR: Ah.
+
+OK, well, that's
+a great question.
+
+So coherence states--
+actually, how many people
+
+have looked at the
+optional problems?
+
+Nice, OK, good.
+
+Good, so coherence
+states were a topic
+
+that we touched on
+the problem sets
+
+and on the optional problems,
+and the optional problems
+
+are mostly on the harmonic
+oscillator and nice problems
+
+revealing some of the structure
+of the harmonic oscillator,
+
+and it generalizes quite boldly.
+
+But here's the basic
+idea of coherence states.
+
+Let me just talk you
+through the basic ideas
+
+rather than do any calculations.
+
+So what's the ground state
+of a harmonic oscillator?
+
+What does its wave
+function look like?
+
+AUDIENCE: Gaussian.
+
+PROFESSOR: It's a
+Gaussian, exactly.
+
+It's minimum
+uncertainty wave packet.
+
+How does it evolve in time?
+
+AUDIENCE: Phase.
+
+PROFESSOR: Yeah, phase.
+
+It's an energy eigenstate,
+it's the ground state,
+
+so it just evolves in
+time with the phase.
+
+So if we look at the wave
+function for the ground
+
+state, phi naught, it's
+something like e to the minus x
+
+squared over 2a squared with
+some normalization coefficient,
+
+which I'm not going
+to worry about.
+
+So this is a minimal
+uncertainty wave packet.
+
+Its position distribution
+is time independent,
+
+because it's a
+stationary statement.
+
+It's momentum distribution,
+which is also a Gaussian,
+
+the Fourier transform,
+is time independent.
+
+And so this thing up to its
+rotation by the overall phase
+
+just sits there and
+remains a Gaussian.
+
+Now, here's a question.
+
+Suppose I take my harmonic
+oscillator potential,
+
+and I take my Gaussian, but
+I displace it a little bit.
+
+It's the same ground
+state, it's the same state
+
+but I've just displaced
+it over a little.
+
+What do you expect to happen?
+
+How will this state
+evolve in time?
+
+So, we know how to
+solve that problem.
+
+We take this state, it's a
+known wave function at time 0.
+
+We expand it in the basis
+of energy eigenstates,
+
+each energy eigenstate
+evolves in time with a phase,
+
+so we put in that
+phase and redo the sum,
+
+and recover the time
+evolution of the full state.
+
+And we've done this a number
+of time on the problem sets.
+
+Yeah.
+
+AUDIENCE: Would the Gaussian,
+the displaced Gaussian
+
+evolve the same
+way, keep its width,
+
+if it had any
+other initial width
+
+other than the one
+of the ground state?
+
+PROFESSOR: Let me
+come back to that,
+
+because it's a little more
+of a precise question.
+
+So we know how to solve
+this problem practically,
+
+algorithmically.
+
+But here's a nice fact.
+
+I'm not going to derive
+any equations, that's
+
+part of the point of
+the optional problems,
+
+but here's a nice
+fact about this state.
+
+So it's clearly a minimum
+uncertainty wave packet
+
+because at time 0,
+because it's just
+
+the same Gaussian just
+translated over a little bit.
+
+So what we'd expect,
+naively, from solving
+
+is we expand this
+in Fourier modes
+
+and then we let this the
+system evolve in time.
+
+We let each individual
+Fourier mode--
+
+or, sorry, Fourier mode-- we
+let each individual energy
+
+eigenstate evolve in time, pick
+up a phase, and now what we get
+
+is a superposition.
+
+Instead of sum over
+n at time 0, we'd
+
+have sum over n cn phi n of x.
+
+Now, as a function of time,
+we get e minus I omega nt,
+
+and these phases are going
+to change the interference
+
+from summing up all
+these energy eigenstates,
+
+and so the system
+will change in time.
+
+Because the way that the various
+terms in the superposition
+
+interfere will change in time.
+
+So very naively, what you
+might expect, if you just
+
+took a random
+function-- for example,
+
+if I took a harmonic
+oscillator potential
+
+and I took some stupid function
+that did something like this.
+
+What would you expect
+it to do over time?
+
+Well, due to all the complicated
+interference effects,
+
+you'd expect this to turn
+into, basically, some schmutz.
+
+Just some crazy
+interference pattern.
+
+The thing that's nice
+about a coherent state,
+
+and this is where
+it gets its name,
+
+is the way that all of
+these interference effects
+
+conspire together to evolve
+the state is to leave it
+
+a Gaussian that does nothing
+but translates in time.
+
+A coherent state is coherent
+because it remains coherently
+
+a Gaussian as it moves along.
+
+It oscillates back and forth.
+
+And in fact, the peak, the
+center of this Gaussian wave
+
+packet, oscillates with
+precisely the frequency
+
+of the trap.
+
+It behaves just as a classical
+particle would have had you
+
+displaced it from the center of
+the harmonic oscillator trap,
+
+it oscillates back and forth.
+
+Now, on the other hand,
+you know that its momentum
+
+is changing in time, right.
+
+And at any given
+point, as you've
+
+shown on the problem set
+that's due tomorrow--
+
+or you will have shown-- at
+any given moment in time,
+
+the momentum can be understood
+as the overall phase.
+
+You could just change that
+momentum by the overall phase,
+
+so it's the spatial rate
+of change of the phase, e
+
+to the ikx.
+
+So you know that the way the
+phase depends on position
+
+is changing over time.
+
+So it can't be quite so simple
+that the wave function, rather
+
+than the probability
+distribution,
+
+is remaining a
+Gaussian over time.
+
+It's not, it's got all
+sorts of complicated phases.
+
+But the upshot is that the
+probability distribution
+
+oscillates back and forth
+perfectly coherently.
+
+So that seems a little
+magical, and there's a nice way
+
+to understand how
+that magic arises,
+
+and it's to understand
+the following.
+
+If I take a state, phi 0, but
+I translate it x minus x0.
+
+OK.
+
+So we know that this
+state, phi 0 of x,
+
+was the ground
+state, what does it
+
+mean to be the ground state
+of the harmonic oscillator?
+
+How do I check if
+I'm the ground state
+
+of the harmonic oscillator?
+
+Look, I walk up to
+you, I'm like, hey,
+
+I'm the ground state of
+the harmonic oscillator.
+
+You're suspicious.
+
+What do you do?
+
+AUDIENCE: Annihilate.
+
+PROFESSOR: Annihilate.
+
+Exactly.
+
+You act with the
+annihilation operator.
+
+Curse you.
+
+So you act with the annihilation
+operator and you get 0, right.
+
+What happens if I act with the
+annihilation operator on this?
+
+Is this the ground state?
+
+No, it's been displaced by x0.
+
+And meanwhile, I told you that
+it oscillates back and forth.
+
+So what happens if you act
+with the annihilation operator?
+
+Should you get 0?
+
+No, what are you going to get?
+
+AUDIENCE: Something weird.
+
+PROFESSOR: Some
+random schmutz, right?
+
+If you just take a and you
+act on some stupid state,
+
+you'll just get some
+other stupid state.
+
+Except for Gaussians
+that have been displaced,
+
+you get a constant
+times the same wave
+
+function, phi 0 of x minus x0.
+
+Aha.
+
+It turns out that these
+displaced Gaussians
+
+are eigenstates of the
+annihilation operator.
+
+What does that mean?
+
+Well, it means they're
+coherent states.
+
+And so the optional
+problems are a working
+
+through of the study
+of the eigenfunctions
+
+of the annihilation operator,
+the coherent states.
+
+Is that cool?
+
+It's a state, it's
+a superposition.
+
+You can think
+about it like this.
+
+It's a superposition of
+the energy eigenstate.
+
+Any state is a superposition
+of energy eigenstates,
+
+and a coherent state is
+just some particularly
+
+special superposition
+of energy eigenstates.
+
+So you can think about
+it literally as c0 phi
+
+0 plus c1 phi 1 plus c2
+phi 2, blah blah blah.
+
+What does the
+annihilation operator
+
+do, what does the
+lowering operator do?
+
+It takes any state
+and then lowers it
+
+with some coefficient.
+
+So a coherent state, an
+eigenstate of the annihilation
+
+operator, must be a
+state such that if you
+
+take c 0 phi 0 plus
+c1 phi 1 plus c2 phi 2
+
+and you hit it with the
+annihilation operator, which
+
+will give you see c1 phi 0 plus
+c2 phi 1 divided by root 2 plus
+
+dot, dot, dot-- or times
+root 2 plus dot, dot, dot.
+
+It gives you the
+same state back.
+
+So that gave you a relation
+between the coefficients c0
+
+and c1, c1 and c2, c2 and c3.
+
+They've all got to be suitable
+multiples of each other.
+
+And what you can show-- and this
+is something you work through,
+
+not quite in this order, on
+the optional problems-- what
+
+you can show is that
+doing so it gives you
+
+a translated Gaussian.
+
+OK.
+
+So physically, that's
+what a coherent state is.
+
+Another way to say what
+a coherent state is,
+
+it's as close to
+a classical object
+
+as you're going
+to get by building
+
+a quantum mechanical
+wave function.
+
+It's something that behaves
+just like a classical particle
+
+in that potential
+would have behaved,
+
+in the harmonic
+oscillator potential.
+
+Did that answer your question?
+
+OK.
+
+Anything else?
+
+So, Matt works with
+these for a living.
+
+Matt, do you want
+to add anything?
+
+All right.
+
+I like these.
+
+They show up all over the place.
+
+This is like the spherical
+cow of wave functions
+
+because it's awesome.
+
+It's an eigenfunction, it's
+an annihilation operator,
+
+it behaves like a
+classical particle.
+
+AUDIENCE: Is there an easy
+way to define coherent states
+
+in potentials where you don't
+have nice operators like a?
+
+PROFESSOR: No, I
+mean, that's usually
+
+what we mean by
+a coherent state.
+
+So the term coherent state
+is often used interchangeably
+
+to mean many different
+things, which
+
+in the case of the harmonic
+oscillator, are identical.
+
+One is a state
+which is a Gaussian.
+
+OK.
+
+So in the harmonic
+oscillator system,
+
+that's a particularly nice
+state because it oscillates
+
+particularly nicely and it
+maintains its probability
+
+distribution as a function of
+time roughly by translating,
+
+possibly, some phases.
+
+But people often use the
+phrase coherent state
+
+even when you're not harmonic.
+
+And it's useful to keep in mind
+that we're often not harmonic,
+
+nothing's truly harmonic.
+
+You had another question
+a moment ago though,
+
+and your question
+was about the width.
+
+Yeah.
+
+AUDIENCE: It just translates
+without changing its width,
+
+with or without changing
+its shape at all.
+
+If the Gaussian were
+of a different width,
+
+would that still happen?
+
+PROFESSOR: Yeah, it does,
+although the details of how
+
+it does so are
+slightly different.
+
+That's called a squeeze state.
+
+The basic idea of a
+squeeze state is this.
+
+Suppose I have a
+harmonic oscillator--
+
+and this is actually
+one way people
+
+build squeeze
+states in labs-- so
+
+suppose I have a
+harmonic oscillator
+
+and I put the system
+in a ground state.
+
+So there's its ground state.
+
+And its width is correlated with
+the frequency of the potential.
+
+Now, suppose I
+take this potential
+
+at some moment in time and
+I control the potential,
+
+the potential is created by
+some laser field, for example.
+
+And some annoying grad student
+walks over to the control panel
+
+and doubles the
+power of the laser.
+
+All of a sudden, I've
+squeezed the potential.
+
+But my system is already in
+a state which is a Gaussian,
+
+it's just the wrong Gaussian.
+
+So what does this guy do?
+
+Well, this is funny.
+
+The true ground state,
+once we've squeezed,
+
+the true ground state
+would be something
+
+that's much narrower
+in position space.
+
+I didn't draw that
+very well, but it
+
+would be much narrower
+in position space,
+
+and thus its
+distribution would be
+
+much broader in momentum space.
+
+So the state that
+we put the system,
+
+or we've left the system in, has
+too much position uncertainty
+
+and too little
+momentum uncertainty.
+
+It's been squeezed compared
+to the normal state
+
+in the delta x delta p plane.
+
+It's uncertainty relation
+is still extreme,
+
+it still saturates the
+uncertainty bound because it's
+
+a Gaussian, but it doesn't have
+the specific delta x and delta
+
+p associated with
+the true ground
+
+state of the squeezed potential.
+
+OK, so now you can ask what
+does this guy do in time.
+
+And that's one of the
+optional problems, too,
+
+and it has many of the nice
+properties of coherent states,
+
+it's periodic, it evolves much
+like a classical particle,
+
+but it's uncertainties
+are different
+
+and they change shape.
+
+It's an interesting story,
+that's the squeezed state.
+
+Yeah.
+
+AUDIENCE: Do other
+potentials have
+
+coherent states
+that are Gaussian?
+
+PROFESSOR: It sort of depends.
+
+So other potentials have
+states that behave classically.
+
+Yeah.
+
+There are generally-- so
+systems that aren't the harmonic
+
+oscillator do have very
+special states that
+
+behave like a
+classical particle.
+
+But they're not as
+simple as annihilations
+
+by the annihilation operator.
+
+Come to my office
+and I'll tell you
+
+about analogous
+toys for something
+
+called supersymmetric
+quantum models,
+
+where there's a
+nice story there.
+
+OK.
+
+I'm going to cut off coherent
+states for the moment
+
+and move on to where we are now.
+
+OK, so last time we
+talked about scattering
+
+of a particle, a quantum
+particle of mass m
+
+against a barrier.
+
+And we made a
+classical prediction,
+
+which I didn't quite
+phrase this way.
+
+But we made a
+classical prediction
+
+that if you took this
+particle of mass m
+
+and threw it against a
+barrier of height v0,
+
+that the probability
+that it will transmit
+
+across this barrier to
+infinity is basically 0.
+
+So this is the
+classical prediction.
+
+It will not transmit to
+infinity until the energy goes
+
+above the potential.
+
+And when the energy is above the
+potential, it will slow down,
+
+but it will transmit
+100% of the time.
+
+So this is our
+classical prediction.
+
+And so we sought to solve
+this problem, we did.
+
+It was pretty straightforward.
+
+And the energy eigenstate
+took the form-- well,
+
+we know how to
+solve it out here,
+
+we know how to
+solve it out here,
+
+because these are just
+constant potentials
+
+so it's just plain waves.
+
+Let's take the
+case of the energy
+
+is less than the potential.
+
+So this guy.
+
+Then out here, it's in a
+classically disallowed state,
+
+so it's got to be a exponential.
+
+If we want it to be
+normalized, well, we
+
+need it to be a
+decaying exponential.
+
+Out here it's
+oscillatory, because it's
+
+a classically allowed region.
+
+And so the general form of the
+wave function of the energy
+
+eigenstate is a superposition
+of a wave moving this way
+
+with positive momentum, a
+wave with negative momentum,
+
+a contribution with
+minus k, and out here it
+
+had to be the
+decaying exponential.
+
+And then by matching, requiring
+that the wave function was
+
+oscillatory and then
+exponentially decaying out
+
+here, and requiring that it was
+continuous and differentiably
+
+continuous-- that its
+derivative was continuous--
+
+we found matching
+conditions between
+
+the various
+coefficients, and this
+
+was the solution in general.
+
+OK.
+
+Now, in particular,
+this term, which
+
+corresponds to the component
+of the wave function moving
+
+towards the barrier on the left
+hand side, has amplitude 1.
+
+This term, which corresponds
+to a wave on the left
+
+with negative momentum,
+so moving to the left,
+
+has amplitude k minus i
+alpha over k plus i alpha,
+
+where h bar squared
+k squared upon 2m
+
+is equal to-- that's just the
+energy, e-- and h bar squared
+
+alpha squared over 2m--
+that's on this side-- is
+
+equal to v0 minus e.
+
+But this, notably,
+is a pure phase.
+
+And we understood that, so
+we'll call this parameter r,
+
+because this is
+the reflected wave
+
+and this is an amplitude
+rather than a probability,
+
+so we'll call it little r.
+
+And we notice that
+the probability
+
+that we get out-- good.
+
+So if we want to ask
+the question, what
+
+is the transmission probability,
+the probability that I get
+
+from far out here to far out
+here, what is that probability?
+
+So if I consider a state that
+starts out as a localized wave
+
+packet way out here and I
+send it in but with energy
+
+below the barrier,
+what's the probability
+
+that I'll get
+arbitrarily far out here,
+
+that I will subsequently find
+the particle very far out here?
+
+0, right, exactly.
+
+And you can see that because
+here's the probability
+
+amplitude, the norm
+squared is the probability
+
+density as a function
+of the position.
+
+And it goes like a constant
+times e to the minus alpha x.
+
+For large x, this
+exponential kills us.
+
+And we made that more precise
+by talking about the current.
+
+We said look, the
+current that gets
+
+transmitted is equal to-- that's
+a funny way to write things.
+
+H bar-- sorry.
+
+The current that
+gets transmitted,
+
+which equal to h bar upon
+2mi psi complex conjugate dx
+
+psi minus psi dx psi complex
+conjugate on the right.
+
+So we'll put right,
+right, right, right.
+
+This is just equal to
+0, and the easiest way
+
+to see that is
+something you already
+
+showed on a problem set.
+
+The current vanishes
+when the wave function
+
+can be made real up to a phase.
+
+And since this is some
+number, but in particular it's
+
+an overall constant
+complex number,
+
+and this is a real
+wave function,
+
+we know that this is 0.
+
+So the transmitted
+current out here is 0.
+
+The flux of particles moving
+out to the right is 0.
+
+So nothing gets
+out to the right.
+
+So that was for the energy
+less than the potential,
+
+and we've now
+re-derived this result,
+
+the classical prediction.
+
+So the classical prediction
+worked pretty well.
+
+Now, importantly,
+in general, we also
+
+wanted to define the
+transmission probability
+
+a little more
+carefully, and I'm going
+
+to define the
+transmission probability
+
+as the current of
+transmitted particles
+
+on the right divided by the
+current of probability that
+
+was incident.
+
+And similarly, we can
+define a probability
+
+that the particle
+reflects, which
+
+is the ratio of the reflected
+current, the current
+
+of the reflected beam,
+to the incident current.
+
+So this is going to be the
+transmission probability
+
+and the reflection probability.
+
+Yeah.
+
+AUDIENCE: Is there
+a square on t?
+
+PROFESSOR: Thank you.
+
+OK.
+
+So let's do a slightly
+different example.
+
+In this example, I want to
+study the same system, the wall,
+
+but I want to consider
+a ball incident
+
+from the left-- a ball.
+
+An object, a quantum particle
+incident from the left,
+
+with energy greater
+than v. Greater than v0.
+
+So again, classically, what
+do you expect in this case.
+
+You send in the particle, it
+loses a little bit of energy
+
+going up the potential
+barrier, but it's still
+
+got a positive kinetic energy,
+and so it just keeps rolling.
+
+Just like my car making
+it up the driveway,
+
+just barely makes it.
+
+OK.
+
+So here again, what's the
+form of the wave function.
+
+Phi e can be put in
+the form on the left.
+
+It's going to be e to the
+ikx plus b to the minus ikx,
+
+and that's over
+here on the left.
+
+And on the right it's
+going in the form ce
+
+to the ik-- in fact, let me call
+this k1x and k2x-- or sorry,
+
+k1x, which is on the left.
+
+H bar squared k1 squared
+upon 2m is equal to e.
+
+And on the right, we're going
+to have k2x because it's, again,
+
+a classically
+allowed region, it's
+
+going to be oscillatory but
+with a different momentum.
+
+e to the ik2x plus
+de to the minus ik2x
+
+where h bar squared
+k2 squared upon 2m
+
+is equal to e minus v0,
+which is a positive number,
+
+so that's good.
+
+So here's our wave function.
+
+Now, before we do
+anything else, I
+
+want to just interpret
+this quickly.
+
+So again, this is like a wave
+that has positive momentum,
+
+and I'm going to say that it's
+like a contribution, a term
+
+in the superposition, that
+is moving to the right,
+
+and the way to think of it
+as moving to the right, well,
+
+first off, it's got
+positive momentum.
+
+But more to the point, this
+is an energy eigenstate.
+
+So how does this
+state evolve in time?
+
+It's an energy
+eigenstate with energy,
+
+how does it evolve in time.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: It rotates by
+an overall phase, exactly.
+
+So we just get this
+times an e to the minus
+
+i omega t, where h bar omega
+is equal to e, the energy.
+
+And that's true on
+the left or right,
+
+because the energy
+is just a constant.
+
+So this term goes as
+e to the ikx minus i
+
+omega t, or kx minus omega t.
+
+And this is a point
+of constant phase
+
+in this move to the right.
+
+As t increases-- in order
+for the phase to be constant
+
+or for the phase, for example,
+to be 0-- as t increases,
+
+x must increase.
+
+By assumption here, k
+is a positive number.
+
+On the other hand, this guy--
+that was a k1-- the second term
+
+is of the form e
+to the minus ik1x,
+
+and when I add the omega
+t, minus i omega t,
+
+this becomes kx plus omega t.
+
+So point of constant
+phase, for example, phase
+
+equals 0, in order for this to
+stay 0 then, as t increases,
+
+x must become negative.
+x must decrease.
+
+So that's why we
+say this corresponds
+
+to a component of
+the wave function,
+
+a term in the superposition
+which is moving to the left.
+
+And this is one which
+is moving to the right.
+
+Sorry, my right, your left.
+
+Sorry, this is
+moving to your right
+
+and this is moving to your left.
+
+OK?
+
+It's that little z2, it's
+harder than it seems.
+
+OK.
+
+In this set up, we could
+imagine two different kinds
+
+of scattering experiments.
+
+We can imagine a
+scattering experiment
+
+where we send in a particle from
+the left and ask what happens.
+
+So if you send in a
+particle from the left,
+
+what are the logical
+possibilities?
+
+AUDIENCE: It can go through.
+
+PROFESSOR: It could
+go through, or?
+
+AUDIENCE: Reflect back.
+
+PROFESSOR: Reflect back.
+
+Are you ever going to get a
+particle spontaneously coming
+
+from infinity out here?
+
+Not so much.
+
+So if you're sending a
+particle in from the left,
+
+what can you say about
+these coefficients?
+
+d equals 0 and a
+is not 0, right.
+
+Because d corresponds to a
+particle on the right hand
+
+side coming in this way.
+
+So that's a different
+scattering experiment.
+
+So in particular,
+coming in from the left
+
+means d equals 0 and
+a not equal to 0.
+
+Coming in from the right
+means a equals 0 and d
+
+not equal to 0 by
+exactly the same token.
+
+Cool?
+
+So I want to emphasize this.
+
+a and d, when you think of
+this as a scattering process, a
+
+and d are in guys.
+
+In, in.
+
+And c and b are out.
+
+This term corresponds to
+moving away from the barrier,
+
+this term corresponds to
+moving away from the barrier,
+
+just on the left
+or on the right.
+
+OK?
+
+Out and out.
+
+Everyone happy with that?
+
+Yeah.
+
+AUDIENCE: According to that
+graph, if d is-- no, that one.
+
+Yeah.
+
+If d is bigger than [INAUDIBLE]
+then the transplants will be 1.
+
+Doesn't that mean
+that d is also 0?
+
+PROFESSOR: So this is
+the classical prediction.
+
+I've written it,
+classical prediction.
+
+So let me rephrase.
+
+The question was
+basically, look,
+
+that classical
+prediction implies
+
+that b must be 0 on the
+other scattering process,
+
+and that doesn't sound right.
+
+So is that true?
+
+No, it's not true, and we'll
+see it again in a second.
+
+So very good intuition.
+
+That was good.
+
+OK, good.
+
+So in general, if we have
+a general wave function,
+
+general superposition of the
+two states with energy e with
+
+a,b,c, and d all
+non-0, that's fine.
+
+That just corresponds
+to sending some stuff
+
+in from the right and
+some stuff in-- sorry,
+
+some stuff in from the left and
+some stuff in from the right.
+
+Yeah?
+
+But it's, of course,
+going to be easier
+
+if we can just do a
+simpler experiment.
+
+If we send in stuff
+from the left or send in
+
+stuff from the right.
+
+And if we solve those
+problems independently,
+
+we can then just
+superpose the results
+
+to get the general solution.
+
+Yeah.
+
+So it will suffice
+to always either set
+
+d to 0 or a to 0,
+corresponding to sending things
+
+in from the left or sending
+things in from the right.
+
+And then we can just take
+a general superposition
+
+to get the general answer.
+
+Everyone happy with that?
+
+So let's do that in this set up.
+
+So here's our wave function.
+
+And you guys are now adept at
+solving the energy eigenvalue
+
+equation, it's just the matching
+conditions for a,b,c, and d.
+
+I'm not going to
+solve it for you,
+
+I'm just going to
+write down the results.
+
+So the results-- in fact,
+I'll use a new border.
+
+The results for this guy,
+now for e greater than v,
+
+are that-- doo doo doo,
+what just happened.
+
+Right, OK, good.
+
+So let's look at the case
+d equal 0 corresponding
+
+to coming in from the left.
+
+So in the case of
+in from the left,
+
+c is equal to 2k1
+over k1 plus k2,
+
+and b is equal to k1
+minus k2 over k1 plus k2.
+
+And this tells us, running
+through the definition of j,
+
+the currents, and t and r, gives
+us that, at the end of the day,
+
+the reflection coefficient is
+equal to k1 minus k2 upon k1
+
+plus k2 [INAUDIBLE] squared,
+whereas the transmission
+
+amplitude or probability
+is equal to 4k1 k2 over k1
+
+plus k2 squared.
+
+And a good exercise for
+yourself is to re-derive this,
+
+you're going to have to do that
+on the problem set as a warm
+
+up for a problem.
+
+So at this point
+we've got an answer,
+
+but it's not terribly satisfying
+because k1 and k2, what's
+
+the-- so let's put
+this in terms of a more
+
+easily interpretable form.
+
+k1 and k2 are nothing other
+than code for the energy
+
+and the energy
+minus the potential.
+
+Right, so we must be able to
+rewrite this purely in terms
+
+of the energy in the
+potential e and v. In fact,
+
+if we go through and
+divide both top and bottom
+
+by k1 squared for
+both r and t, this
+
+has a nice expression
+in terms of the ratio
+
+of the potential to the energy.
+
+And the nice expression is
+1 minus the square root of 1
+
+minus v0 over e over
+1 plus the square root
+
+of 1 minus v0 over
+e norm squared.
+
+And suddenly, the
+transmission amplitude
+
+has the form 4 root 1
+minus v0 over e over 1
+
+plus the square root of 1
+minus v0 over e squared.
+
+I don't remember which
+version of the notes
+
+I posted for this year's course.
+
+In the version from
+2011 there is a typo
+
+that had here e over v, and
+in the version from 2012, that
+
+was corrected in the
+notes to being v0 over e.
+
+So I'll check, but let me
+just warn you about that.
+
+On one or two pages of
+the notes, at some point,
+
+these guys were inverted
+with respect to each other.
+
+But the reason to
+write this out is now
+
+we can plot the following.
+
+We can now plot the quantum
+version of this plot.
+
+We can plot the actual
+quantum transmission
+
+as a function of energy,
+and the classical prediction
+
+was that at energy
+is equal to v0,
+
+we should have a step function.
+
+But now you can see that
+this is not a step function,
+
+and that's related to the fact
+that b was not actually 0,
+
+as you pointed out.
+
+Hold on one sec.
+
+Sorry, was it quick?
+
+AUDIENCE: The notes are wrong.
+
+PROFESSOR: OK, the notes
+are wrong, good, thank you.
+
+That's great.
+
+OK, so the notes are wrong.
+
+It should be v0 over e,
+not e over v0 on the notes
+
+that are posted.
+
+We're in the process
+of teching them up,
+
+so eventually a beautiful set
+of nice notes will be available.
+
+Extra elbow grease.
+
+OK.
+
+So what do we actually see?
+
+Here we got for e
+less than v0, we
+
+got in d that the transmission
+probability was exactly 0.
+
+So that's a result for
+the quantum result.
+
+But when e is equal
+to v0, what do we get?
+
+Well, when e is equal
+to v0, this is 1.
+
+And we get square
+root of 1 minus 1,
+
+which is square root of
+0, over square root of 1
+
+plus square root of 1
+minus 1, which is 0.
+
+That's 0 over-- OK, good.
+
+So that's not so bad.
+
+Except for this 1 over this e,
+this is a little bit worrying.
+
+If you actually
+plot this guy out,
+
+it does this, where
+it asymptotes to 1.
+
+And to see that it
+asymptotes to 1,
+
+to see that it asymptotes
+to 1, just take e0 gigantic.
+
+If you know it's gigantic,
+this becomes v0 over e,
+
+which goes to 0, and if e is
+much larger than the potential.
+
+So this becomes
+square root of 1.
+
+And in the denominator, this
+becomes square root of 1, 1
+
+plus 1, that's 2 squared, 4, 4
+divided by 4, that goes to 1.
+
+So for large e much larger
+than v0, this goes to 1.
+
+So we do recover the
+classical prediction
+
+if we look at energy
+scales very large
+
+compared to the
+potential height.
+
+Yeah?
+
+OK.
+
+So that's nice.
+
+Another thing
+that's nice to note
+
+is that if you take this
+reflection probability
+
+and this transmission
+probability,
+
+then they sum up to 1.
+
+This turns out to
+be a general fact
+
+and it's a necessary
+condition in order for those
+
+to be interpretable
+as reflection
+
+in transition probabilities.
+
+The probability
+that it transmits
+
+and the probability that it
+reflects had better add to 1,
+
+or something is eating
+your particles, which
+
+is probably not what
+you're looking for.
+
+So this turns out to be true
+in this case, just explicitly.
+
+But you can also, as you
+will in your problem set,
+
+prove that from that definition
+r and t, it's always true.
+
+A check on the sensibility
+of our definition.
+
+If it weren't true,
+it wouldn't tell you
+
+that quantum
+mechanics is wrong, it
+
+would tell you that we
+chose a stupid definition
+
+of the transmission and
+reflection probabilities.
+
+So in this case, we actually
+chose quite an enlightened one.
+
+OK, questions at this point?
+
+Yeah.
+
+AUDIENCE: Does
+this analysis even
+
+hold for classical particles?
+
+If we're talking about the
+difference between-- like
+
+if I threw a baseball and
+I happened to throw it
+
+at a potential that had height
+one millionth of a joule
+
+less than the energy
+of the baseball,
+
+would we observe this also?
+
+PROFESSOR: No.
+
+AUDIENCE: No?
+
+PROFESSOR: No, for
+the following reason.
+
+So here's my classical system.
+
+Classical system is
+literally some hill.
+
+So where I was
+growing up as a kid,
+
+there was a hill not
+far from our house.
+
+I'm not even going to go
+into it, but it was horrible.
+
+If you have energy just
+ever so slightly greater
+
+than the hill-- he said
+from some experience--
+
+if you have energy that's
+ever so slightly greater-- OK.
+
+I'm going resist the temptation.
+
+So one of these days.
+
+If you have ever so slightly
+greater than the hill,
+
+and you start up here,
+what does that tell you?
+
+What does it mean to
+say you have energy
+
+just ever so slightly greater
+than the potential energy
+
+at that point?
+
+AUDIENCE: Up more slowly.
+
+PROFESSOR: Little tiny velocity.
+
+OK, and I'm going to say I
+have a little tiny velocity
+
+this way.
+
+OK.
+
+So what happens?
+
+We follow Newton's equations.
+
+They are totally unambiguous,
+and what they tell you is,
+
+with 100% certainty, this thing
+will roll and roll and roll,
+
+and then all hell
+will break loose.
+
+And then if you're
+very lucky, your car
+
+gets caught in the trees on
+the side of the cliff, which
+
+is later referred to by the
+policeman who helps you tow it
+
+out as nature's guard rail.
+
+I was young, it
+won't happen again.
+
+And So with 100% certainty,
+Newton's equations
+
+send you right off the cliff.
+
+And for style points, backward.
+
+So now I'm going to
+do the second thing.
+
+Newton's laws satisfy
+time reversal invariance.
+
+So the time reversal of
+this is, this thing has
+
+this much energy, and
+it shoots up the cliff.
+
+And ever so slowly,
+it just eventually
+
+goes up to the top,
+where everything is fine.
+
+OK, but does it ever
+reflect back downhill?
+
+No.
+
+And does it ever--
+classically, when
+
+you roll the thing--
+does it ever actually not
+
+go off the cliff
+and hit the trees,
+
+but instead reflect backwards.
+
+I wish the answer were yes.
+
+But sadly, the answer is no.
+
+Now, if that car had been
+quantum mechanically small,
+
+my insurance would have
+been much more manageable.
+
+But sadly, it wasn't.
+
+OK, so this is a pretty
+stark and vivid-- this
+
+is a pretty stark difference
+between the quantum
+
+mechanical prediction and
+the classical prediction.
+
+Everyone cool with that?
+
+Other questions?
+
+Yeah.
+
+AUDIENCE: I understand why
+it works out that r plus t
+
+equals 1, but I'm
+not sure I understand
+
+the motivation to use the
+square with the ratios.
+
+PROFESSOR: Excellent, OK.
+
+So the reason to do it,
+so great, excellent.
+
+How to say.
+
+Here's one way to
+think about it.
+
+The first thing
+we want is we want
+
+a-- so this is a
+very good question,
+
+let me repeat the question.
+
+The question is, look,
+why is it squared?
+
+Why isn't it linear?
+
+So let's think about that.
+
+Ah, ah, ah.
+
+The reason it's squared
+is because of a typo.
+
+So let's think about--
+
+[LAUGHTER]
+
+PROFESSOR: Let's
+step back for second
+
+and let's think, OK, it's
+a very good question.
+
+So let's think about
+what it should be.
+
+OK.
+
+For the moment, put an
+arbitrary power there.
+
+OK.
+
+And let's think about
+what it should be.
+
+Thank you so much
+for this question.
+
+I owe you, like, a plate
+of cheese or something.
+
+That's high praise, guys.
+
+France, cheese.
+
+So should it be linear or
+should it be quadratic?
+
+What is that supposed
+to represent?
+
+What is T, the capital
+T, supposed to represent?
+
+AUDIENCE: The probability
+of transmission.
+
+PROFESSOR: The probability
+of transmission, exactly.
+
+The wave function.
+
+Is the wave function,
+the value of the wave
+
+function at some point,
+is that a probability?
+
+It's a--
+
+AUDIENCE: Probability
+of density.
+
+No, it's the square root.
+
+PROFESSOR: Is it a
+probability of density?
+
+It is a probability amplitude.
+
+It is a thing whose norm
+squared is a probability.
+
+So we want something that's
+quadratic in the wave function,
+
+right.
+
+Meanwhile, some time before,
+we wanted a definition
+
+of how much stuff is moving
+past a point in the given
+
+moment in time.
+
+What's the probability
+density moving past a point
+
+at a given moment in time.
+
+And that's where we got the
+current j from the first place.
+
+j was the probability
+density moving past a point
+
+at a given moment in time.
+
+So notice that j is quadratic
+in the wave function,
+
+so it's how much stuff is moving
+past any particular direction--
+
+we chose it to be the incident
+to the reflected bit--
+
+at a moment in time.
+
+So it's a probability density--
+it's actually a current--
+
+and it's quadratic
+in the wave function.
+
+So it has the right units
+and the right structure
+
+to be a probability.
+
+If we squared that, we would be
+in trouble, because it wouldn't
+
+be a probability, it would
+be a probability squared.
+
+And in particular, it
+wouldn't normalize correctly.
+
+So that typo was
+actually a bad typo.
+
+So what happened, now
+thinking back to-- you
+
+have a video someday,
+so you can scroll back.
+
+What happened was I didn't
+put the squared on the first,
+
+I put the squared on the
+second, and then someone said
+
+squared on the first?
+
+Like, yes.
+
+But the correct answer is
+no squared on the second.
+
+So there are no squareds.
+
+Thank you for the question.
+
+Very good question.
+
+In particular,
+the thing that was
+
+so awesome about
+that question was it
+
+was motivated by physics.
+
+It was like, look, why is this
+thing squared the right thing?
+
+That's two factors
+of the wave function,
+
+it's already quadratic.
+
+It should be like a probability.
+
+Why are you squaring it?
+
+Very good question.
+
+Yeah.
+
+AUDIENCE: So in the
+transmission probability,
+
+why do we know it's 0 if
+the energy is less than v0?
+
+I mean, is there any rule?
+
+PROFESSOR: Yeah, OK, good.
+
+We'll come back to that
+question in a little bit,
+
+but let me just quickly
+say that we calculated it,
+
+and we see explicitly
+that it's 0.
+
+Now you might say well,
+look, the true wave function
+
+has a little bit of a tail.
+
+So there's some
+[INAUDIBLE] probability
+
+you'll find it here if
+you do a measurement.
+
+But the question we want
+to ask in transmission
+
+is, if you send it in
+from far away over here,
+
+how likely are you to catch
+it far away over here?
+
+And the answer is, you are not.
+
+That make sense?
+
+OK, good.
+
+OK, so so much for that one.
+
+Now, here's a fun
+fact, I'm not going
+
+to go through this
+in any detail.
+
+We could have done exactly
+the same calculation-- OK,
+
+we could have done
+the same calculation
+
+sending something
+in from the right.
+
+And sending something in from
+the right, in on the right,
+
+corresponds to d not
+equal to 0 and nothing
+
+coming in from the
+left, that's a equals 0.
+
+So we could have done
+the case a equals 0,
+
+which is in from the right.
+
+And if you do that
+calculus, what you find
+
+is c is equal to k1 minus
+k2 upon k1 plus k2 d.
+
+And b is equal to 2k1
+upon k1 plus k2 d.
+
+And this says that
+plugging these guys in,
+
+the reflection and the
+transmission are the same.
+
+In particular, physically,
+what does that mean?
+
+That means the reflection
+and transmission
+
+are the same uphill as downhill.
+
+Downhill is uphill,
+they're the same both ways.
+
+But that's truly weird, right?
+
+What's the probability to
+transmit quantum mechanically
+
+if you have just a
+little bit of energy
+
+and you send the particle in?
+
+How likely are you
+to go off the cliff.
+
+If we have energy ever so
+slightly greater the potential,
+
+and the transmission
+amplitude is the same downhill
+
+as it was uphill, how likely are
+you to fall off the potential?
+
+AUDIENCE: Always.
+
+PROFESSOR: Never.
+
+Because if energy is just
+slightly greater than v0,
+
+then the transmission
+probability is very, very low.
+
+The transmission to
+go from here to here
+
+is extremely low
+if the energy is
+
+close to the height
+of the barrier.
+
+So had I only been on a
+quantum mechanical hill,
+
+I would have been just fine.
+
+This is a really
+striking result,
+
+but this thing, the
+fact that you're
+
+unlikely to scatter uphill,
+that's maybe not so shocking.
+
+But you're really unlikely
+to scatter downhill,
+
+that is surprising.
+
+So I'll leave it to you
+to check that, in fact,
+
+the transmission, when we
+do it in from the right,
+
+the transmission and reflection
+probabilities are the same.
+
+Recalling that transmission
+means going this way,
+
+reflection means bouncing
+back to the right.
+
+Cool?
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Uh, because, again.
+
+Jeez, today is just a disaster.
+
+Because there's a typo.
+
+This should be times a.
+
+God.
+
+And the reason you know it
+should be times a, first off,
+
+is that these should have
+the appropriate dimensions.
+
+So there should be an
+appropriate power of a.
+
+And the second thing is that
+if you double this stuff in,
+
+you'd better double
+this stuff out.
+
+So if you double a,
+you'd better double c.
+
+So you know there had better
+be a factor of a here.
+
+And that's just a typo again.
+
+I'm sorry, today is a bad
+day at the chalkboard.
+
+Thank you for that question.
+
+Yeah.
+
+AUDIENCE: Is there
+a physical reason
+
+for why r and t are the same
+and so different from what
+
+you would classically expect,
+or is that just the way the math
+
+works?
+
+PROFESSOR: There is.
+
+I want you to ponder that,
+and either at the end of today
+
+or at the beginning
+of tomorrow, we'll
+
+talk about that
+more in detail when
+
+we've done a little
+more technology.
+
+It's a good question
+and you should
+
+have that tingling
+sensation in your belly
+
+that something is
+confusing and surprising
+
+and requires more explanation,
+and we'll get there.
+
+But I want you to just think
+about it in the background
+
+first.
+
+Yeah.
+
+AUDIENCE: Is there any
+physical experiment
+
+where r and t don't sum up to 1?
+
+PROFESSOR: Mm mm.
+
+Nope.
+
+So the question is, is
+there any experiment
+
+in which r and t
+don't sum up to 1?
+
+And there are two
+ways to answer that.
+
+The first way to answer
+that is, it turns out
+
+that r and t adding up to 1
+follows from the definitions.
+
+So one of the things you'll
+do on the problem set
+
+is you'll show that using these
+definitions of the transmission
+
+and reflection of
+probabilities, they necessarily
+
+add up to 1, strictly.
+
+They have to.
+
+It follows from the
+Schrodinger equation.
+
+The second answer
+is, let's think
+
+about what it would mean if
+r and t didn't add up to 1.
+
+If r and t didn't
+add up to 1, then
+
+that would say,
+look, if you throw
+
+a particle at a barrier, at
+some feature in a potential,
+
+some wall, then the
+probability that it
+
+goes this way at the end
+versus the probability
+
+that it goes that way at the
+end if you wait long enough
+
+is not 1.
+
+So what could have happened?
+
+What could have
+gotten stuck in there?
+
+But that doesn't even
+conserve momentum,
+
+not even approximately.
+
+And we know that the
+expectation of momentum
+
+is time independent
+for a free particle.
+
+In between while it's
+actually in the potential,
+
+it's not actually
+time independent,
+
+there's a potential,
+there's a force.
+
+AUDIENCE: I mean, if it's whole
+particles, can't some of them
+
+get annihilated or something?
+
+PROFESSOR: Ah, well OK.
+
+So if you're talking
+about multiple particles
+
+and interactions amongst
+multiple particles,
+
+then it's a slightly more
+complicated question.
+
+The answer there
+is still yes, it
+
+has to be that the
+total probability in
+
+is the total probability out.
+
+But we're only going to talk
+about single particles here.
+
+But it's always true
+that for-- we're
+
+going to take this
+as an assumption,
+
+that things don't
+just disappear,
+
+that the number of particles
+or the total probability
+
+is conserved.
+
+There's a third way to
+say this, this really
+
+isn't independent
+from the first.
+
+Remember that these were
+defined in terms of the current?
+
+The current satisfies--
+the current concept
+
+of probability conservation
+equation dt of rho
+
+is equal to the gradient minus
+the gradient of the current.
+
+So the probability
+is always conserved,
+
+the integral of probability
+density is always conserved,
+
+it's time independent.
+
+AUDIENCE: So it's
+by [INAUDIBLE].
+
+PROFESSOR: Yeah,
+it's by construction.
+
+Exactly.
+
+Yeah?
+
+AUDIENCE: Looking at your
+expression for the transition
+
+probability, I'm having trouble
+seeing how that works out to 0
+
+when e is less than v0?
+
+PROFESSOR: Oh, this
+expression is only
+
+defined when e is equal to v0.
+
+Because we derived this--
+excellent question--
+
+we derived this assuming that
+we had an energy greater than v0
+
+and then that the wave
+function had this form.
+
+You cannot use this form of the
+wave function if the energy is
+
+less than v0.
+
+If the energy is
+less than v0, you've
+
+got use that form of
+the wave function.
+
+And in this form of
+the wave function,
+
+we derived that the
+transition amplitude is 0,
+
+because the current on the
+right, the transmitted current,
+
+is 0.
+
+So this calculation
+is appropriate
+
+when e is less than v0 and
+this calculation is appropriate
+
+when e is greater than v0.
+
+So you're absolutely correct.
+
+You can't use this
+one e is less than v0,
+
+it gives you not
+the same answer.
+
+In fact, it gives
+you a complex--
+
+it's kind of confusing.
+
+The factors cancel.
+
+So it's not really a
+probability at all,
+
+and indeed, this is just not
+the right quantity to use.
+
+AUDIENCE: All right, cool.
+
+PROFESSOR: Cool?
+
+All right.
+
+So there are a
+bunch of nice things
+
+I want to deduce from
+what we've done so far.
+
+So the first is,
+look, I pointed out
+
+that this can be
+derived just explicitly
+
+and it gives the same
+results as before.
+
+That's not an accident.
+
+If you take this
+system and you just
+
+reverse the roles of k1
+and k2, what happens?
+
+Well that's just
+replaces e by e minus v0,
+
+we can do that by doing this,
+replacing e by e minus v0
+
+and e minus v0 by e, it
+swaps the role of a and d,
+
+and it gives you exactly
+the same things back.
+
+So if you're careful
+about that, you never
+
+have to do this calculation.
+
+You can just do the
+appropriate transformation
+
+on that calculation and it gives
+you the exactly the same thing.
+
+It's the same algebraic steps.
+
+But the other thing
+that's nice is
+
+that you can actually do
+the same thing from here.
+
+So as long as you
+set the d equals 0--
+
+so there's another term
+here that we neglected,
+
+the plus delta x,
+we got rid of it.
+
+But you can analytically
+continue this calculation
+
+by noting that look,
+if we just set alpha,
+
+we want minus alpha
+equals ik2, then
+
+the algebra is all
+going to be the same.
+
+We just have ik2
+instead of minus alpha.
+
+So we can just replace
+alpha with minus ik2
+
+everywhere in our
+expressions, being
+
+careful about
+exactly how we do so,
+
+being careful to
+take care of factors
+
+of i and such correctly.
+
+And you derive the same
+results for both cases, which
+
+is a nice check on
+the calculation.
+
+So often, when you get a little
+bit of experience with these,
+
+you don't actually have
+to do the calculation.
+
+Again, you can
+just take what you
+
+know from a previous
+calculation and write down
+
+the correct answer.
+
+So it's a fun
+thing to play with,
+
+exactly how do you do that.
+
+So I invite you to think
+through that process
+
+while you're doing
+your problem set.
+
+Another thing is the
+reflection downhill
+
+thing which is
+pretty surprising.
+
+But here's the thing that
+I really want to emphasize.
+
+What this calculation
+shows you is not so much
+
+that-- it's not just that
+transmission downhill
+
+is highly unlikely
+when the energy is
+
+very close to the height
+of the potential barrier.
+
+That's true, but it's not
+the most interesting thing
+
+about this calculation.
+
+The most interesting thing about
+this calculation, to my mind,
+
+is the fact that from
+the detailed shape
+
+of the transmission as
+a function of energy,
+
+we can deduce what
+the potential is.
+
+Think about what that tells you.
+
+If you do an experiment,
+you have a barrier,
+
+and you want to know the
+shape of the barrier.
+
+Is it straight,
+is it wiggly, does
+
+it have some complicated shape.
+
+How do you measure that?
+
+Well, you might measure
+it by just looking.
+
+But imagine you can't,
+for some reason.
+
+For whatever, it's in a box
+or you can't look at it.
+
+Maybe it's just
+preposterously small.
+
+How can you deduce what
+the shape of that hill is?
+
+Well, one way to
+do it is to send
+
+in particles as a function of
+energy, more and more energy,
+
+and measure the probability
+that they transmit.
+
+OK.
+
+Now if you do so and you get
+this graph as a function of e,
+
+what do you deduce?
+
+You deduce that the barrier
+that you're scattering off of
+
+is a square step
+with this height v0.
+
+Are we cool with that?
+
+So apparently, just
+look at the transmission
+
+amplitudes, the
+transition probabilities,
+
+you can deduce at
+least something
+
+of the form of the potential.
+
+Which is kind of cool.
+
+If you didn't know
+the potential,
+
+you could figure
+out what it was.
+
+And this turns out to be a
+very general statement that you
+
+can deduce an enormous
+amount, and as we'll see,
+
+you can, in fact,
+deduce basically
+
+everything you want
+of the potential
+
+from knowing about the
+transmission probabilities
+
+as well as the phase shift,
+the transmission amplitudes.
+
+So this is the basic
+goal of scattering.
+
+And so the way I
+want you to think
+
+about it is imagine, for
+example, that someone
+
+hands you an object.
+
+A box.
+
+And the box has an in port
+and it has an out port.
+
+And they allow you
+to send in particles
+
+as a function of energy
+and measure transmission
+
+and reflection, you can measure
+transmission and reflection.
+
+Just like I'm measuring
+transmission off of your faces
+
+right now, from the
+light from above.
+
+So suppose that you do so, put
+it on your test stand and you
+
+measure transmission.
+
+You measure transmission
+as a function of energy,
+
+and you observe the following.
+
+The transmission as
+a function of energy
+
+is small up until some point,
+and then at some point,
+
+which may be the minimum energy
+you can meaningfully probe,
+
+you get something like this.
+
+So here's the transmission
+as a function of energy.
+
+So what can you say?
+
+If this is all the
+information you
+
+have about what's going
+on inside the box,
+
+what can you deduce about
+the thing inside the box?
+
+One thing you can
+deduce is that it
+
+looks kind of like a potential
+with height around v0.
+
+It looks kind of like a
+potential step with some height
+
+v0.
+
+This is asymptoting to 1.
+
+However, it's not, because it
+has these oscillations in it.
+
+So there's more to the potential
+than just a barrier of height
+
+v0.
+
+What I want to show you is
+that you can deduce everything
+
+about that potential, and
+that's the point of scattering.
+
+So let's do it.
+
+So the goal here, again, to say
+it differently, is what's v0?
+
+What is v of x?
+
+Not just the height,
+but the total potential.
+
+So another way to say
+this, let me set up
+
+a precise version
+of this question.
+
+I want to be able
+to do the following.
+
+I want to take a system that has
+a potential which is constant
+
+up to some point
+which I'll call 0,
+
+and then again from some
+point, which I'll call L,
+
+is constant again.
+
+And inside, I don't know
+what the potential is.
+
+So in here, there's
+some unknown potential,
+
+v of x, which is
+some crazy thing.
+
+It could be doing anything.
+
+It could be some crazy-- it
+could have horns and whatever.
+
+It could be awful.
+
+But the potential is constant
+if you go far enough away,
+
+and the potential is constant
+if you go far enough away.
+
+A good example of this
+is a hydrogen atom.
+
+It's neutral but there's
+a clearly and complicated
+
+potential inside because
+the proton and the electron
+
+are moving around in there in
+some quantum state, anyway,
+
+and if you send something
+at it, far away, it's
+
+as if it's not there.
+
+But close by, you know there
+are strong electrostatic forces.
+
+And so the question is what
+you learn about those forces,
+
+what can you learn
+about the potential
+
+by throwing things in from
+far away, from either side.
+
+Now one thing we know already
+is that out here, the wave
+
+function always-- because it's
+a constant potential-- always
+
+takes the form e to the ikx
+plus b e to the minus ikx.
+
+And out here it takes the
+form c e to the ikx plus d
+
+e to the minus ikx.
+
+And again, this
+corresponds to moving in.
+
+d is in from the right.
+
+c is out to the right.
+
+b is out to the left.
+
+And a is in from the left.
+
+So again, there are
+basically four kind
+
+of scattering
+experiments we can do.
+
+We can send things in
+from the right, which
+
+corresponds to setting a to 0.
+
+We can send things in
+from the left, which
+
+corresponds to
+setting t equal to 0.
+
+And all the information
+about what happens in v
+
+is going to be encoded
+in what's coming out,
+
+the b and c coefficients.
+
+And the way to make
+that sharp is just
+
+to notice that the transmission
+probability, if we compute
+
+for this system, assuming
+it's forming the wave function
+
+asymptotically away from the
+potential, the transmission
+
+amplitude is just
+c over a squared
+
+when you're sending
+in from the left.
+
+And the reflection is equal
+to b over a norm squared.
+
+This squared is a squared.
+
+[INAUDIBLE] function over
+amplitude squared, good.
+
+To learn about the transmission
+and reflection coefficients,
+
+it's enough-- suffices--
+to compute, to know b and c
+
+as a function of a and d.
+
+All of the scattering
+information
+
+is in those coefficients
+b and c for a and d.
+
+And here I'm assuming that I'm
+sending in a monochromatic wave
+
+with a single, well
+defined energy.
+
+I'm sending in a beam of
+particles with energy e.
+
+I don't know where
+they are, but I sure
+
+know what their momentum is.
+
+So some well defined beam
+of particles with energy e.
+
+And these
+probabilities are going
+
+to contain all the data I want.
+
+So this is the basic
+project of scattering.
+
+Questions?
+
+AUDIENCE: So basically,
+it only depends
+
+on the transmission-- it
+only depends on the edges?
+
+PROFESSOR: That's
+a good question.
+
+The question is, does the
+transmission depend only
+
+on what you do with the edges.
+
+And here's the important thing.
+
+The transmission
+depends crucially
+
+on what happens in here.
+
+For example, if this is an
+infinitely high barrier,
+
+nothing's going across.
+
+So this transmission
+depends on what's in here.
+
+But the point is we can deduce
+just by looking far away,
+
+we can deduce the
+transmission probability
+
+and amplitude just by
+measuring b and c far away,
+
+b and c far away.
+
+OK.
+
+So the transmission
+amplitude is something
+
+you measure when very far away.
+
+You measure-- if I throw
+something in from very far
+
+out here to the left, how likely
+is it to get out here very
+
+far to the right?
+
+And in order to answer
+that, if someone
+
+hands you the
+answer to that, they
+
+must have solved
+for what's inside.
+
+That the point.
+
+So knowing the answer
+to that question
+
+encodes information about
+what happened in between.
+
+AUDIENCE: So I guess
+initially, your potential's
+
+going to-- so say it's
+stuff you did earlier.
+
+The potential drops down to
+the [INAUDIBLE] in the box.
+
+Is that going to be problematic?
+
+PROFESSOR: Yeah,
+for simplicity, I'm
+
+going to assume that the
+potential always goes to 0 when
+
+we're far away, because that's
+going to be useful for modeling
+
+things like hydrogen
+and, exactly.
+
+Carbon, we're going
+to do diamond later
+
+in the semester,
+that'll be useful.
+
+But we could repeat
+this analysis
+
+by adding an extra change
+in the asymptotic potential,
+
+it doesn't really change
+anything important.
+
+Yeah.
+
+AUDIENCE: It looks like even
+for just the simple step up
+
+[INAUDIBLE] you can't tell
+from just the probabilities why
+
+the step is going
+up or going down.
+
+PROFESSOR: Ah, excellent.
+
+Excellent, excellent.
+
+So good, thank you for that
+question, that's really great.
+
+So already, it seems
+like we can't uniquely
+
+identify the potential from
+the transmission probability
+
+if the transmission probability
+is the same for step up
+
+or step down.
+
+So what's missing?
+
+AUDIENCE: Maybe the
+energy [INAUDIBLE]
+
+PROFESSOR: But we're working
+with an energy [INAUDIBLE].
+
+So the energy is just
+a global constant.
+
+We'll see what's
+missing, and what's
+
+missing is something
+called the phase shift.
+
+So very good question, yes.
+
+AUDIENCE: It looks like when we
+did the example for the step,
+
+that t equals [INAUDIBLE]
+over a squared.
+
+PROFESSOR: Yeah, it is,
+because it's the ratio.
+
+That's why I wrote
+t is c over here.
+
+So t is the ratio of j over ji.
+
+And in fact, jt here is
+equal to c squared times--
+
+so this is the
+probability density,
+
+so it's the probability density
+times the velocity, what's
+
+the effect of velocity here?
+
+H bar k 2 over m, whereas
+j incident is equal
+
+to a squared--
+probability density
+
+times the momentum there,
+the velocity there--
+
+which is h bar k1 upon m.
+
+So here the ratio of j
+transmitted to j incident
+
+is norm c squared k2
+over norm a squared k1.
+
+AUDIENCE: So because
+it's not level--
+
+PROFESSOR: Exactly, it's
+because it's not level.
+
+So here, they
+happen to be level,
+
+so they're only
+[INAUDIBLE] factor, cancel,
+
+and the only thing that
+survives is the amplitude.
+
+Good question.
+
+Yeah.
+
+AUDIENCE: For the
+lead box example,
+
+is it sufficient
+just to know what's
+
+reflected back to
+solve the situation?
+
+PROFESSOR: So for
+precisely for this reason,
+
+it's not sufficient to know t.
+
+It's not sufficient
+to know t and r.
+
+But, of course, once
+you know r, you know t,
+
+so you're exactly right.
+
+Once you know the
+reflection probability,
+
+you know the
+transmission probability,
+
+but there's one more
+bit of information
+
+which we're going to
+also need in order
+
+to specify the potential, which
+is going to be the phase shift.
+
+But you're right, you don't
+need to independently compute
+
+r and t, you can
+just compute one.
+
+AUDIENCE: You need sensors
+on both sides of the box,
+
+to answer my question.
+
+PROFESSOR: You
+don't need sensors
+
+on both sides of the box, but
+you need to do more than just
+
+do the counting problem.
+
+We'll see that.
+
+OK.
+
+So let's work out a simple
+example, the simplest
+
+example of a barrier
+of this kind.
+
+We want constant potential,
+and then ending at 0,
+
+and we want a constant again
+from L going off to infinity.
+
+So what's the easiest
+possible thing we could do?
+
+Step, step.
+
+We're just doing what
+we've done before twice.
+
+So this is an example of
+this kind of potential.
+
+It's sort of ridiculously
+simple, but let's work it out.
+
+So we want scattering,
+let's start out,
+
+we could do either
+scattering from the left
+
+or scattering from the right.
+
+Let's start out scattering
+from the left, so d equals 0,
+
+and let's study this problem.
+
+So what we know--
+and let's also note
+
+that we have a choice to make.
+
+We could either study
+energy below the height
+
+of the potential or
+we can study energy
+
+above the height
+of the potential.
+
+And so for simplicity,
+I'm also going
+
+to start with energy
+greater than the height
+
+of the potential, v0, and
+then we'll do e less than v0
+
+afterwards.
+
+It'll be an easy extension
+of what we've done.
+
+OK, so this will be our
+first case to study.
+
+So we know the form of the
+wave function out here,
+
+it's a e to the ikx,
+b to the minus ikx.
+
+We know that for the
+potential out here
+
+it's c e to the ikx and
+d e to the minus ikx.
+
+The only thing we
+don't know is the form
+
+of the potential in here.
+
+And in here it's
+actually very simple.
+
+It's got to be something
+of the form-- I
+
+think I called it
+f and g, I did.
+
+f e to the ik prime
+x-- I'm calling this k,
+
+so I'll just call this
+k prime x-- plus g
+
+e to the minus ik prime x.
+
+And the reason I
+chose k prime is
+
+because we're working
+with energy greater
+
+than the potential, so this is
+a classically allowed region.
+
+It's an oscillatory domain
+but with a different k prime.
+
+So here, k squared, h bar
+squared over 2m is equal to e,
+
+and h bar squared k
+prime squared over 2m
+
+is equal to e minus
+v0, which is positive
+
+when e is greater than v0.
+
+This analysis will not obtain
+when e is less than v0,
+
+we'll have to treat
+it separately.
+
+So now what do we do?
+
+We do the same thing we did
+before, we just do it twice.
+
+We'll do the matching
+conditions here,
+
+the matching conditions here.
+
+That's going to give us 1,
+2, 3, 4 matching conditions.
+
+We have 1, 2, 3, 4, 5,
+6 unknown coefficients,
+
+so we'll have two
+independent ones.
+
+That's great.
+
+We set d equal to 0
+to specify that it's
+
+coming in from the left and
+not from the right, that's 5.
+
+And then we have
+normalization, which is 6,
+
+so this should uniquely
+specify our wave function.
+
+Yeah.
+
+Once we've fixed e, we
+have enough conditions.
+
+So I'm not going to go
+through the derivation
+
+because it's just an extension
+of what we did for the first.
+
+It's just a whole
+bunch of algebra.
+
+And let me just emphasize this.
+
+The algebra is not interesting.
+
+It's just algebra.
+
+You have to be
+able to do it, you
+
+have to develop some
+familiarity with it,
+
+and it's easy to
+get good at this.
+
+You just practice.
+
+It's just algebra.
+
+But once you get the idea,
+don't ever do it again.
+
+Once you get
+reasonably quick at it,
+
+learn to use Mathematica, Maple,
+whatever package you want,
+
+and use computer algebra
+to check your analysis.
+
+And use your physics
+to check the answer
+
+you get from Mathematica or
+Maple or whatever you use.
+
+Always check against
+physical reasonability,
+
+but use Mathematica.
+
+So posted on the website
+are Mathematica files
+
+that walk through the
+computation of the transmission
+
+and reflection amplitudes
+and probabilities
+
+for this potential, and I
+think maybe another one,
+
+I don't remember exactly.
+
+But I encourage you strongly
+to use computer algebra tools,
+
+because it's just
+a waste of time
+
+to spend three hours doing
+an algebra calculation.
+
+In particular, on your
+problem set this week,
+
+you will do a scattering problem
+similar to the bound state
+
+probably you did last week, the
+quantum glue problem-- which
+
+you may be doing tonight,
+the one due tomorrow.
+
+Which is two delta
+function wells
+
+and find the bound
+states, so that
+
+involves a fair
+amount of algebra.
+
+The scattering
+problem will involve
+
+a similar amount of algebra.
+
+Do not do it.
+
+Use Mathematica or
+computer algebra
+
+just to simplify your life.
+
+So if we go through and
+compute the-- so what
+
+are we going to do, we're
+going to use the matching
+
+conditions here to determine
+f and g in terms of a and b,
+
+then we'll use the
+matching conditions here
+
+to determine c-- d is 0--
+c in terms of f and g.
+
+So that's going to give us an
+effective constraint relating
+
+a and b, leaving us with an
+overall unknown coefficient
+
+a, which we'll use
+for normalization.
+
+The upshot of all of
+which is the answers
+
+are that, I'm not even going
+to write down-- they're
+
+in the notes.
+
+Should I write this down?
+
+I will skip.
+
+So the upshot is that the
+transmission amplitude,
+
+as a function of k and k prime--
+the transmission probability, I
+
+should say, is 1
+over-- actually,
+
+I'm going to need
+the whole amplitude.
+
+Shoot.
+
+The transmission
+probability is equal to--
+
+and this is a horribly
+long expression--
+
+the transmission probability,
+which is c over a norm squared,
+
+is equal to 4 k squared k prime
+squared cosine squared of k
+
+prime l plus k squared plus
+k prime squared sine squared
+
+of k prime l under 4k
+squared k prime squared.
+
+Seriously.
+
+So we can simplify this out,
+so you can do some algebra.
+
+This is just what
+you get when you just
+
+naively do the algebra.
+
+I want to do two things.
+
+First off, this is horrible.
+
+There's a cosine squared,
+there's a sine squared,
+
+surely we can all be
+friends and put it together.
+
+So let's use some trig.
+
+But the second thing, and
+the more important thing,
+
+is I want to put this
+in dimensionless form.
+
+This is horrible.
+
+Here we have ks and we have ls,
+and these all have dimensions,
+
+and they're inside the sines
+and the cosines it's kl.
+
+That's good, because this
+has units of one over length,
+
+this has units of length,
+so that's dimensions.
+
+Let's put everything
+in dimensionless form.
+
+And in particular, what are
+the parameters of my system?
+
+The parameters of my system
+are, well, there's a mass,
+
+there's an h bar, there's a
+v0, and then there's an energy,
+
+and there's a length l.
+
+So it's easy to make a
+dimensionless parameter out
+
+of these guys, and a
+ratio of energies--
+
+a dimensionless ratio of
+energies-- out of these guys.
+
+So I'm going to do that, and
+the parameters I'm going to use
+
+are coming from here.
+
+I'm going to define the
+parameters g0 squared, which
+
+is a dimensionless measure of
+the depth of the potential.
+
+We've actually run
+into this guy before.
+
+2m l squared v0
+over h bar squared.
+
+So this is h bar squared, 1 over
+l squared is k squared over 2m,
+
+so that's an energy.
+
+So this is a ratio of the
+height of the potential
+
+to the characteristic energy
+corresponding to length scale
+
+l.
+
+So the width, there's an
+energy corresponding to it
+
+because you take a momentum
+which has 1 over that width.
+
+You can build an energy out of
+that h bar k squared over 2m.
+
+And we have an energy which
+is the height of the barrier,
+
+we take the ratio of those.
+
+So that's a dimensionless
+quantity, g0.
+
+And the other dimensionless
+quantity I want to consider
+
+is a ratio of the
+energy, e, to v0,
+
+which is what showed up
+before in our energy plot.
+
+Or in our transmission
+plot over there, e over v0.
+
+So when we take this and we
+do a little bit of algebra
+
+to simplify our life, again, use
+Mathematica, it's your friend.
+
+The result is much
+more palatable.
+
+It's t-- again, for the
+energy greater than v0--
+
+is equal to, still long.
+
+But 1 plus 1 over 4 epsilon,
+epsilon minus 1 sine
+
+squared of g0 square
+root of epsilon minus 1.
+
+And upstairs is a one.
+
+So remember this is only
+valid for e greater than v0,
+
+or equivalently,
+epsilon greater than 1.
+
+And I guess we can
+put an equal in.
+
+So when you get an
+expression like this,
+
+this is as easy as you're
+going to make this expression.
+
+It's not going to
+get any easier.
+
+It's 1 over a sine
+times a function plus 1.
+
+There's really no great
+way to simplify this.
+
+So what you need when you
+get an expression like this
+
+is try to figure out
+what it's telling you.
+
+The useful thing to
+do is to plot it.
+
+So let's just look
+at this function
+
+and see what it's telling us.
+
+Let's plot this t as
+a function of epsilon
+
+and for some fixed g0.
+
+Keep in mind that this only
+makes sense for e greater
+
+than v0 or for epsilon
+greater than 1, so here's 1.
+
+And we're going
+to remain agnostic
+
+as to what happens below 1.
+
+And just for normalization,
+we know that the transmission
+
+probability can never
+be greater than 1,
+
+so it's got to be
+between 1 and 0.
+
+So here's 0 and 0.
+
+We're remaining agnostic
+about this for the moment.
+
+So let's start thinking about
+what this plot looks like.
+
+First off, what does
+it look like at 1?
+
+So when epsilon
+goes to 1, this is
+
+going to 0, that's bad
+because it's in a denominator.
+
+But upstairs, this
+is going to 0,
+
+and sine squared of something
+when it's becoming small
+
+goes like-- well, sine
+goes like that thing.
+
+So sine squared goes like
+this quantity squared.
+
+So sine squared goes
+like g0 squared,
+
+this goes like 1
+over-- this is going
+
+like g0 squared epsilon
+minus 1 square root quantity
+
+squared, which is
+epsilon minus 1.
+
+So this is going to 0 and
+this, the denominator,
+
+is going to 0 exactly
+in the same way.
+
+Epsilon minus 1 from
+here, epsilon minus 1
+
+downstairs from here.
+
+So the epsilon minus
+ones precisely cancel.
+
+From the sine squared
+we get a g0 squared,
+
+and from here we
+get a 4 epsilon.
+
+So we get 1 plus g0
+squared over 4 epsilon.
+
+But 4 epsilon, what
+was epsilon here?
+
+1.
+
+We're looking at
+epsilon goes to 1,
+
+so this is just
+g0 squared over 4.
+
+So the height, the value of t--
+so we're not looking in here.
+
+But at energy is equal to
+v0 or epsilon is equal to 1,
+
+we know that the transmission
+amplitude is not 0,
+
+but it's also strictly
+smaller than 1.
+
+Which is good,
+because if it were 6,
+
+you'd be really worried.
+
+So g0 squared, if g0 squared
+is 0, what do we get?
+
+1.
+
+Fantastic, there's no barrier.
+
+We just keep right on going
+through, perfect transmission.
+
+If g0 is not zero, however,
+the transmission is suppressed.
+
+Like 1 over g0 squared.
+
+What does this actually
+look like with some value.
+
+And what is this value,
+it's just 1 over 1
+
+plus 1/4 g0 squared.
+
+Cool?
+
+OK.
+
+And now what
+happens, for example,
+
+for a very large epsilon?
+
+Well, when epsilon is gigantic,
+sine squared of this-- well,
+
+sine squared is
+oscillating rapidly,
+
+so that's kind of worrying.
+
+If this is very,
+very large, this
+
+is a rapidly
+oscillating function.
+
+However, it's being divided
+by roughly epsilon squared.
+
+So something that goes between
+0 and 1 divided by epsilon
+
+squared, as epsilon
+gets large, becomes 0.
+
+And so we get 1 over
+1 plus 0, we get 1.
+
+So for very large values
+it's asymptoting to 1.
+
+So naively, it's going to
+do something like this.
+
+However, there's
+this sine squared.
+
+And in fact, this
+is exactly what
+
+it would do if we just had
+the 1 over epsilon times
+
+some constant.
+
+But in fact, we have
+the sine squared,
+
+and the sine squared
+is making it wiggle.
+
+And the frequency
+of the wiggle is g0,
+
+except that it's not
+linear in epsilon,
+
+it's linear in square
+root of epsilon.
+
+So as epsilon gets larger,
+the square root of epsilon
+
+is getting larger
+less than linearly.
+
+So what that's telling you is
+if you looked at root epsilon,
+
+you would see it
+with even period.
+
+But we don't have
+root epsilon, we're
+
+plugging this as a
+function of epsilon.
+
+So it's not even period,
+it's getting wider and wider.
+
+Meanwhile, there's a
+nice fact about this.
+
+For special values of epsilon,
+what happens to sine squared?
+
+It goes to zero.
+
+And what happens
+when this is zero?
+
+Yeah, t is 1.
+
+So every time sine is 0,
+i.e., for sufficient values
+
+when root epsilon is a multiple
+of pi determined by g0,
+
+transmission goes to 1.
+
+It becomes perfect.
+
+So in fact, instead
+of doing-- wow.
+
+Instead of doing this, what
+it does is it does this.
+
+So let's check that
+I'm not lying to you.
+
+So let me draw it
+slightly different.
+
+To check, so it's going to
+0, and the period of the 0
+
+is getting further
+and further along.
+
+That's because this is
+square root, not squared.
+
+So epsilon has to get much
+larger to hit the next period.
+
+That's why it's getting
+larger and larger spacing.
+
+However, the amplitude
+goes down from 1,
+
+that's when this gets largest.
+
+Well, at large values of
+epsilon, this is suppressed.
+
+As epsilon goes
+larger and larger,
+
+this deviation become
+smaller and smaller.
+
+So that's what this
+plot is telling us.
+
+This plot is telling
+us a bunch of things.
+
+First off, we see that
+at large energies,
+
+we transmit perfectly.
+
+That makes sense.
+
+This was a finitely
+high barrier.
+
+Large energies, we
+don't even notice it.
+
+It tells you at low
+energies-- well,
+
+we don't know yet what
+happens at very low energies.
+
+But at reasonably low energies,
+the transmission is suppressed.
+
+And if you sort of
+squint, this roughly
+
+does what we'd expect
+from the step barrier.
+
+However, something
+really special
+
+is happening at special
+values of epsilon.
+
+We're getting
+perfect transmission.
+
+We get perfect transmission of
+these points, t is equal to 1.
+
+Perfect.
+
+Star.
+
+Happy with a big nose.
+
+I don't know.
+
+Perfect transmission
+at all these points.
+
+So this leaves us with
+a question of why.
+
+Why the perfect
+transmission, what's
+
+the mechanism making
+transmission perfect.
+
+But it also does something
+really lovely for us.
+
+Suppose you see a spectrum, you
+see a transmission amplitude
+
+or transmission probability
+that looks like this.
+
+You may get crappy data.
+
+You may see that
+it's smudged out
+
+and you see all
+sorts of messy stuff.
+
+But if you know that
+there's perfect transmission
+
+at some particular
+epsilon 1, there's
+
+more perfect transmission at
+another epsilon 2, more perfect
+
+transmission at
+epsilon 3, and they
+
+scale, they fit to
+this prediction.
+
+What do you know?
+
+That you've got a
+finite high barrier,
+
+and it's probably pretty well
+approximated by a square step.
+
+So in your problem set, you're
+going to get experimental data,
+
+and you're going to have to
+match to the experimental data.
+
+You're going to have
+to predict something
+
+about the potential that created
+a particular transmission
+
+probability distribution.
+
+And knowing where
+these resonances are,
+
+where these points of
+perfect transmission,
+
+is going to be very
+useful for you.
+
+Yeah.
+
+AUDIENCE: Wasn't there
+another potential
+
+that will also
+create periodic 1s?
+
+PROFESSOR: A very good question.
+
+So I'm going to turn
+that around to you.
+
+Can you orchestrate a potential
+that gives you the same thing?
+
+That's an interesting
+empirical question.
+
+So, on the problem set, you'll
+study a double well potential.
+
+So the question
+was, how do I know
+
+isn't another potential that
+gives me the same answer?
+
+At this point, we don't know.
+
+Maybe there is
+another potential.
+
+In fact, you can do
+all sorts of things
+
+to make a potential that's
+very arbitrarily close that
+
+gives you an arbitrarily
+similar profile.
+
+So if they're
+significantly different,
+
+how different do they look?
+
+So then the students
+say, well, I don't know.
+
+What about a double
+well potential?
+
+So, in fact, we'll be doing
+a double well potential
+
+on the problem set.
+
+A good question.
+
+And we certainly
+haven't proven anything
+
+like this is the
+only potentially
+
+that gives you this
+transmission amplitude.
+
+What we can say is if you get
+transmission amplitude that
+
+looks like this, it's
+probably pretty reasonable
+
+to say it's probably
+well modeled.
+
+We seem to be reproducing
+the data reasonably well.
+
+So it's not a proof of
+anything, but it's a nice model.
+
+And we're physicists,
+we build models.
+
+We don't tell you
+what's true, we
+
+tell you what are good models.
+
+If a theorist ever
+walks up on you
+
+and he says, here's the
+truth, punch him in the gut.
+
+That's not how it works.
+
+Experimentalists,
+on the other hand.
+
+We'll just punch
+them too, I guess.
+
+[LAUGHTER]
+
+PROFESSOR: We build models.
+
+OK, so this leaves us
+with an obvious question,
+
+which we've answer
+in the case of energy
+
+grade in the potential.
+
+What about the case of the
+energy less than the potential.
+
+So we haven't filled out
+that part of the graph.
+
+Let's fill out that
+part of the graph.
+
+What happens if the energy
+is less than the potential?
+
+And for this, I'm going to
+use the trick that I mentioned
+
+earlier that, look,
+if the energy is
+
+less than the potential,
+that just means that
+
+in the intervening
+regime, in here,
+
+instead of being
+oscillatory, it's
+
+going to be exponentially
+growing [INAUDIBLE]
+
+because we're in a
+classically disallowed region.
+
+So if the energy
+is less than v0,
+
+here we have instead of
+ikx, we have minus alpha x.
+
+And instead of minus ikx
+we have plus alpha x.
+
+So if you go through
+that whole analysis
+
+and plug in those values for
+the k prime, the answer you get
+
+is really quite nice.
+
+We find that t for energy
+less than v0 is equal to--
+
+and it's just a direct
+analytic continuation of what
+
+you get here-- 1 plus 1 over
+4 epsilon 1 minus epsilon.
+
+So epsilon is less than 1 now.
+
+1 sinh squared of g0 1
+minus epsilon under 1.
+
+OK, so now this lets
+us complete the plot.
+
+And you can check, it's
+pretty straightforward,
+
+that because sinh, again,
+goes like its argument
+
+at very small values
+of its argument,
+
+we get g0 squared
+1 minus epsilon.
+
+Sorry, this should be
+square root 1 minus epsilon.
+
+Really?
+
+Is that a typo?
+
+Oh no, it's in there.
+
+OK, good.
+
+So again, we get g0
+squared 1 minus epsilon,
+
+the 1 minus epsilon cancels,
+and we get 1 over 4 g0 squared.
+
+Which is good, because
+if they disagreed,
+
+we'd be in real trouble.
+
+So they agree, but the sinh
+squared is just a strictly--
+
+or that function is just
+a strictly decreasing
+
+function as we approach
+epsilon goes to 0.
+
+It goes mostly to 0.
+
+So this is what we see.
+
+We see an exponential
+region and then
+
+we see oscillations
+with residences
+
+where the period is
+getting wider and wider.
+
+But this should trouble
+you a little bit.
+
+Here, what are we saying?
+
+We're saying look,
+if we have a barrier,
+
+and we send in a
+particle with energy way
+
+below the barrier,
+that's kind of troubling.
+
+If we send in a particle with
+energy way below the barrier,
+
+there's some probability
+that it gets out.
+
+It goes across.
+
+So for e less than v0,
+classically no transmission,
+
+we get transmission.
+
+Now, do we get resonances
+when e is less than v0?
+
+No, that's an interesting thing.
+
+We'll talk about resonances
+and where they come from,
+
+and we'll talk about the more
+generalized notion of a nest
+
+matrix in the next lecture.
+
+But for now I just want to say
+a couple of things about it.
+
+So I want to ask-- so
+this is called tunneling,
+
+this transmission across
+a disallowed barrier,
+
+a classically
+disallowed barrier--
+
+so this transmission
+across a disallowed barrier
+
+is called tunneling.
+
+And just a quick thing to notice
+is that if we hold e fixed
+
+and we vary l, we vary
+the width of the barrier,
+
+how does the tunneling
+amplitude depend
+
+on the width of the barrier?
+
+At fixed energy, if we vary the
+width of the barrier-- which
+
+is only contained
+in g0-- how does
+
+the transmission amplitude vary?
+
+And we find that for large
+l-- for l much greater than 1
+
+for a typical scale
+in the problem--
+
+the tunneling amplitude goes
+like e to the minus 2 alpha l
+
+where alpha just depends on
+the energy in the potential.
+
+So what we see is that the
+probability of transmitting,
+
+of tunneling through
+a wall, depends
+
+on the width of that wall.
+
+And it depends on
+it exponentially.
+
+The wider the wall, the
+exponentially less likely you
+
+are to tunnel across it.
+
+And this fits the
+simulation we ran
+
+where we saw that tunnelling
+through a very thin wall
+
+was actually quite efficient.
+
+And we also saw that
+tunnelling across a wall
+
+can have resonant peaks.
+
+At special values, it
+transmits perfectly.
+
+We saw that in the simulations.
+
+So at this point I can't resist
+telling you a very short story.
+
+I have a very good friend
+who is not a physicist,
+
+but who is a professor at MIT.
+
+So a smart person,
+and very smart.
+
+She's one of the
+smartest people I know.
+
+She broke her ankle.
+
+She's always losing stuff,
+she's constantly losing stuff.
+
+And she broke her ankle, and she
+was going to the rehab place,
+
+and she parked her car right
+in front of the rehab place.
+
+She parked her
+car right in front
+
+because she's got
+the broken ankle
+
+and she doesn't want to have to
+walk a long way to get the car,
+
+she parked right in front.
+
+She went in, she did
+her two hours of rehab,
+
+and she came outside,
+and her car was gone.
+
+And she's always
+misplacing her car,
+
+she's always
+misplacing her keys,
+
+she's always losing everything.
+
+But this time, this time
+she knew where it was.
+
+And it wasn't there.
+
+So first she thought, oh
+crap, my car's been stolen.
+
+How annoying, I've
+got a broken ankle.
+
+But she looks
+around, and there's
+
+her car on the other side
+of the street pointed
+
+the opposite direction.
+
+And she's like, finally.
+
+Finally.
+
+She was explaining this to
+me and a friend of mine who
+
+is also a physicist,
+she said finally, I
+
+knew I had incontrovertible
+proof that quantum
+
+effects happen to
+macroscopic objects.
+
+My car tunnelled
+across the street.
+
+[LAUGHTER]
+
+PROFESSOR: At this
+point, of course,
+
+my friend and I are
+just dying of laughter.
+
+But she said my car
+tunnelled across the street.
+
+But here's the problem,
+I couldn't tell anyone.
+
+Because if I told anyone, they
+would know that I was crazy.
+
+Clearly I'm crazy, because I
+lose my stuff all the time,
+
+but surely it's just
+gotten misplaced.
+
+So I went home, and
+I got home and I
+
+was sitting down to dinner with
+my partner and our daughter
+
+and I was burning up
+inside because I wanted
+
+to tell them this
+crazy thing happened.
+
+I know quantum
+mechanics, it happens.
+
+I couldn't tell them
+anything, so I was just
+
+fidgeting and dying.
+
+And finally my
+daughter said, mom,
+
+didn't you notice that we moved
+the car across the street?
+
+[LAUGHTER]
+
+PROFESSOR: See you next time.
\ No newline at end of file
diff --git a/TOLwmtn8Miw.txt b/TOLwmtn8Miw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ce46fd0096c5533cfc55f8c7fd90d60fd63b1b51
--- /dev/null
+++ b/TOLwmtn8Miw.txt
@@ -0,0 +1,16712 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
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+the following content is provided under
+a Creative Commons license your support
+
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+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
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+will help MIT open courseware continue
+ 
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+will help MIT open courseware continue
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+to offer highquality educational
+resources for free to make a donation or
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+resources for free to make a donation or
+ 
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+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencare at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so everyone's working on
+
+ align:start position:0%
+ocw.mit.edu so everyone's working on
+ 
+
+ align:start position:0%
+ocw.mit.edu so everyone's working on
+papers I suppose when are they due in
+
+ align:start position:0%
+papers I suppose when are they due in
+ 
+
+ align:start position:0%
+papers I suppose when are they due in
+they are due on Sunday
+
+ align:start position:0%
+they are due on Sunday
+ 
+
+ align:start position:0%
+they are due on Sunday
+Horrors
+
+ align:start position:0%
+Horrors
+ 
+
+ align:start position:0%
+Horrors
+well when I went to graduate school it
+
+ align:start position:0%
+well when I went to graduate school it
+ 
+
+ align:start position:0%
+well when I went to graduate school it
+was at
+
+ align:start position:0%
+was at
+ 
+
+ align:start position:0%
+was at
+Princeton in the math
+
+ align:start position:0%
+Princeton in the math
+ 
+
+ align:start position:0%
+Princeton in the math
+department
+
+ align:start position:0%
+department
+ 
+
+ align:start position:0%
+department
+and there were all sorts of courses
+
+ align:start position:0%
+and there were all sorts of courses
+ 
+
+ align:start position:0%
+and there were all sorts of courses
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+by very good professors because I think
+
+ align:start position:0%
+by very good professors because I think
+ 
+
+ align:start position:0%
+by very good professors because I think
+I've mentioned this this
+
+ align:start position:0%
+I've mentioned this this
+ 
+
+ align:start position:0%
+I've mentioned this this
+is sort of
+
+ align:start position:0%
+is sort of
+ 
+
+ align:start position:0%
+is sort of
+1950 and the
+
+ align:start position:0%
+1950 and the
+ 
+
+ align:start position:0%
+1950 and the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+universities in the United States were
+
+ align:start position:0%
+universities in the United States were
+ 
+
+ align:start position:0%
+universities in the United States were
+uh at least the science departments were
+
+ align:start position:0%
+uh at least the science departments were
+ 
+
+ align:start position:0%
+uh at least the science departments were
+filled with great mathematicians and
+
+ align:start position:0%
+filled with great mathematicians and
+ 
+
+ align:start position:0%
+filled with great mathematicians and
+physicists and people like that who had
+
+ align:start position:0%
+physicists and people like that who had
+ 
+
+ align:start position:0%
+physicists and people like that who had
+been
+
+ align:start position:0%
+been
+ 
+
+ align:start position:0%
+been
+uh extracted from Europe because of
+
+ align:start position:0%
+uh extracted from Europe because of
+ 
+
+ align:start position:0%
+uh extracted from Europe because of
+World War II
+
+ align:start position:0%
+World War II
+ 
+
+ align:start position:0%
+World War II
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh the masterart department at
+
+ align:start position:0%
+uh the masterart department at
+ 
+
+ align:start position:0%
+uh the masterart department at
+Princeton was very very very exciting
+
+ align:start position:0%
+Princeton was very very very exciting
+ 
+
+ align:start position:0%
+Princeton was very very very exciting
+because of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the if you had a question
+
+ align:start position:0%
+the if you had a question
+ 
+
+ align:start position:0%
+the if you had a question
+you you had a very good chance that the
+
+ align:start position:0%
+you you had a very good chance that the
+ 
+
+ align:start position:0%
+you you had a very good chance that the
+uh world's leading Authority on that
+
+ align:start position:0%
+uh world's leading Authority on that
+ 
+
+ align:start position:0%
+uh world's leading Authority on that
+subject would would be in the next room
+
+ align:start position:0%
+subject would would be in the next room
+ 
+
+ align:start position:0%
+subject would would be in the next room
+or two I was interested in the theory of
+
+ align:start position:0%
+or two I was interested in the theory of
+ 
+
+ align:start position:0%
+or two I was interested in the theory of
+knots and there was
+
+ align:start position:0%
+knots and there was
+ 
+
+ align:start position:0%
+knots and there was
+Professor Ralph Fox who was uh one of
+
+ align:start position:0%
+Professor Ralph Fox who was uh one of
+ 
+
+ align:start position:0%
+Professor Ralph Fox who was uh one of
+the world's experts on not
+
+ align:start position:0%
+the world's experts on not
+ 
+
+ align:start position:0%
+the world's experts on not
+Theory and in fact he was so good at it
+
+ align:start position:0%
+Theory and in fact he was so good at it
+ 
+
+ align:start position:0%
+Theory and in fact he was so good at it
+that I gave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up which is nice important thing to keep
+
+ align:start position:0%
+up which is nice important thing to keep
+ 
+
+ align:start position:0%
+up which is nice important thing to keep
+in mind always be ready to give up if
+
+ align:start position:0%
+in mind always be ready to give up if
+ 
+
+ align:start position:0%
+in mind always be ready to give up if
+there's someone doing something better
+
+ align:start position:0%
+there's someone doing something better
+ 
+
+ align:start position:0%
+there's someone doing something better
+than you and find the right Niche but
+
+ align:start position:0%
+than you and find the right Niche but
+ 
+
+ align:start position:0%
+than you and find the right Niche but
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+um they had courses
+
+ align:start position:0%
+um they had courses
+ 
+
+ align:start position:0%
+um they had courses
+and you would register for courses and
+
+ align:start position:0%
+and you would register for courses and
+ 
+
+ align:start position:0%
+and you would register for courses and
+everyone got an A in all
+
+ align:start position:0%
+everyone got an A in all
+ 
+
+ align:start position:0%
+everyone got an A in all
+courses I'm sorry there were no grades
+
+ align:start position:0%
+courses I'm sorry there were no grades
+ 
+
+ align:start position:0%
+courses I'm sorry there were no grades
+uh when I got
+
+ align:start position:0%
+uh when I got
+ 
+
+ align:start position:0%
+uh when I got
+there um because Professor lefets didn't
+
+ align:start position:0%
+there um because Professor lefets didn't
+ 
+
+ align:start position:0%
+there um because Professor lefets didn't
+like the IDE of grading
+
+ align:start position:0%
+like the IDE of grading
+ 
+
+ align:start position:0%
+like the IDE of grading
+people and his he was head of the
+
+ align:start position:0%
+people and his he was head of the
+ 
+
+ align:start position:0%
+people and his he was head of the
+department and his feeling was
+
+ align:start position:0%
+department and his feeling was
+ 
+
+ align:start position:0%
+department and his feeling was
+that if somebody wasn't doing good work
+
+ align:start position:0%
+that if somebody wasn't doing good work
+ 
+
+ align:start position:0%
+that if somebody wasn't doing good work
+then it wasn't n that person's fault it
+
+ align:start position:0%
+then it wasn't n that person's fault it
+ 
+
+ align:start position:0%
+then it wasn't n that person's fault it
+was the fault of the admissions
+
+ align:start position:0%
+was the fault of the admissions
+ 
+
+ align:start position:0%
+was the fault of the admissions
+committee and if
+
+ align:start position:0%
+committee and if
+ 
+
+ align:start position:0%
+committee and if
+anybody got through the hurdles to get
+
+ align:start position:0%
+anybody got through the hurdles to get
+ 
+
+ align:start position:0%
+anybody got through the hurdles to get
+there then they
+
+ align:start position:0%
+there then they
+ 
+
+ align:start position:0%
+there then they
+were uh assumed to be mathematicians and
+
+ align:start position:0%
+were uh assumed to be mathematicians and
+ 
+
+ align:start position:0%
+were uh assumed to be mathematicians and
+that was that and uh but after a couple
+
+ align:start position:0%
+that was that and uh but after a couple
+ 
+
+ align:start position:0%
+that was that and uh but after a couple
+of years the Provost of the
+
+ align:start position:0%
+of years the Provost of the
+ 
+
+ align:start position:0%
+of years the Provost of the
+University uh got annoyed with the math
+
+ align:start position:0%
+University uh got annoyed with the math
+ 
+
+ align:start position:0%
+University uh got annoyed with the math
+department and he sent down a message
+
+ align:start position:0%
+department and he sent down a message
+ 
+
+ align:start position:0%
+department and he sent down a message
+that there would have to be grades in
+
+ align:start position:0%
+that there would have to be grades in
+ 
+
+ align:start position:0%
+that there would have to be grades in
+Rec course and lefet said
+
+ align:start position:0%
+Rec course and lefet said
+ 
+
+ align:start position:0%
+Rec course and lefet said
+okay uh he didn't believe in fighting
+
+ align:start position:0%
+okay uh he didn't believe in fighting
+ 
+
+ align:start position:0%
+okay uh he didn't believe in fighting
+when there was a good
+
+ align:start position:0%
+when there was a good
+ 
+
+ align:start position:0%
+when there was a good
+alternative the alternative was
+
+ align:start position:0%
+alternative the alternative was
+ 
+
+ align:start position:0%
+alternative the alternative was
+everybody got A's in every course
+
+ align:start position:0%
+everybody got A's in every course
+ 
+
+ align:start position:0%
+everybody got A's in every course
+whether they took the course or
+
+ align:start position:0%
+whether they took the course or
+ 
+
+ align:start position:0%
+whether they took the course or
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+not and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I think the end of the story is that
+
+ align:start position:0%
+uh I think the end of the story is that
+ 
+
+ align:start position:0%
+uh I think the end of the story is that
+when he
+
+ align:start position:0%
+when he
+ 
+
+ align:start position:0%
+when he
+retired the new chairman wasn't as good
+
+ align:start position:0%
+retired the new chairman wasn't as good
+ 
+
+ align:start position:0%
+retired the new chairman wasn't as good
+at evading the authorities
+
+ align:start position:0%
+at evading the authorities
+ 
+
+ align:start position:0%
+at evading the authorities
+but so I have a little discomfort at
+
+ align:start position:0%
+but so I have a little discomfort at
+ 
+
+ align:start position:0%
+but so I have a little discomfort at
+grades myself and when I gave this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course in the 60s and SE in the
+
+ align:start position:0%
+course in the 60s and SE in the
+ 
+
+ align:start position:0%
+course in the 60s and SE in the
+70s uh everybody got an A and it took
+
+ align:start position:0%
+70s uh everybody got an A and it took
+ 
+
+ align:start position:0%
+70s uh everybody got an A and it took
+several years for the Departments to
+
+ align:start position:0%
+several years for the Departments to
+ 
+
+ align:start position:0%
+several years for the Departments to
+notice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway so any so we have to give
+
+ align:start position:0%
+anyway so any so we have to give
+ 
+
+ align:start position:0%
+anyway so any so we have to give
+grades
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MIT but all that's great fun uh
+
+ align:start position:0%
+MIT but all that's great fun uh
+ 
+
+ align:start position:0%
+MIT but all that's great fun uh
+anybody what didn't we cover in this
+
+ align:start position:0%
+anybody what didn't we cover in this
+ 
+
+ align:start position:0%
+anybody what didn't we cover in this
+course that you wish it we had and uh
+
+ align:start position:0%
+course that you wish it we had and uh
+ 
+
+ align:start position:0%
+course that you wish it we had and uh
+I'd like to know what some of you are
+
+ align:start position:0%
+I'd like to know what some of you are
+ 
+
+ align:start position:0%
+I'd like to know what some of you are
+doing also what's uh what's your plan to
+
+ align:start position:0%
+doing also what's uh what's your plan to
+ 
+
+ align:start position:0%
+doing also what's uh what's your plan to
+make machines smarter in the
+
+ align:start position:0%
+make machines smarter in the
+ 
+
+ align:start position:0%
+make machines smarter in the
+future
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how hard is it to find a job where
+
+ align:start position:0%
+and how hard is it to find a job where
+ 
+
+ align:start position:0%
+and how hard is it to find a job where
+you can do
+
+ align:start position:0%
+you can do
+ 
+
+ align:start position:0%
+you can do
+research I've I haven't tried getting a
+
+ align:start position:0%
+research I've I haven't tried getting a
+ 
+
+ align:start position:0%
+research I've I haven't tried getting a
+new job for a long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time I just tried to hire a former
+
+ align:start position:0%
+time I just tried to hire a former
+ 
+
+ align:start position:0%
+time I just tried to hire a former
+student but he's starting a huge start
+
+ align:start position:0%
+student but he's starting a huge start
+ 
+
+ align:start position:0%
+student but he's starting a huge start
+up and um if you can't find a job I
+
+ align:start position:0%
+up and um if you can't find a job I
+ 
+
+ align:start position:0%
+up and um if you can't find a job I
+guess you can make one if you can full
+
+ align:start position:0%
+guess you can make one if you can full
+ 
+
+ align:start position:0%
+guess you can make one if you can full
+enough investors
+
+ align:start position:0%
+enough investors
+ 
+
+ align:start position:0%
+enough investors
+into supporting a new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operation do is design around a very
+
+ align:start position:0%
+operation do is design around a very
+ 
+
+ align:start position:0%
+operation do is design around a very
+specific problem design what around a
+
+ align:start position:0%
+specific problem design what around a
+ 
+
+ align:start position:0%
+specific problem design what around a
+very specific problem so you're
+
+ align:start position:0%
+very specific problem so you're
+ 
+
+ align:start position:0%
+very specific problem so you're
+addressing getting a machine to solve
+
+ align:start position:0%
+addressing getting a machine to solve
+ 
+
+ align:start position:0%
+addressing getting a machine to solve
+some particular problem which is always
+
+ align:start position:0%
+some particular problem which is always
+ 
+
+ align:start position:0%
+some particular problem which is always
+there's always a fast path to that by
+
+ align:start position:0%
+there's always a fast path to that by
+ 
+
+ align:start position:0%
+there's always a fast path to that by
+finding the right set of data and
+
+ align:start position:0%
+finding the right set of data and
+ 
+
+ align:start position:0%
+finding the right set of data and
+finding the right model that will work
+
+ align:start position:0%
+finding the right model that will work
+ 
+
+ align:start position:0%
+finding the right model that will work
+reasonably
+
+ align:start position:0%
+reasonably
+ 
+
+ align:start position:0%
+reasonably
+well it's not
+
+ align:start position:0%
+well it's not
+ 
+
+ align:start position:0%
+well it's not
+really like a business yes case that can
+
+ align:start position:0%
+really like a business yes case that can
+ 
+
+ align:start position:0%
+really like a business yes case that can
+be made for making a general
+
+ align:start position:0%
+be made for making a general
+ 
+
+ align:start position:0%
+be made for making a general
+intelligence
+
+ align:start position:0%
+intelligence
+ 
+
+ align:start position:0%
+intelligence
+in when there's motivation some specific
+
+ align:start position:0%
+in when there's motivation some specific
+ 
+
+ align:start position:0%
+in when there's motivation some specific
+application
+
+ align:start position:0%
+application
+ 
+
+ align:start position:0%
+application
+something that's right and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the goes back to World War II again the
+
+ align:start position:0%
+the goes back to World War II again the
+ 
+
+ align:start position:0%
+the goes back to World War II again the
+the reason
+
+ align:start position:0%
+the reason
+ 
+
+ align:start position:0%
+the reason
+we could do so much in those early years
+
+ align:start position:0%
+we could do so much in those early years
+ 
+
+ align:start position:0%
+we could do so much in those early years
+about General theories was
+
+ align:start position:0%
+about General theories was
+ 
+
+ align:start position:0%
+about General theories was
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the defense department had cre
+
+ align:start position:0%
+uh the defense department had cre
+ 
+
+ align:start position:0%
+uh the defense department had cre
+created this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new Wing called arpa Advanced research
+
+ align:start position:0%
+new Wing called arpa Advanced research
+ 
+
+ align:start position:0%
+new Wing called arpa Advanced research
+projects
+
+ align:start position:0%
+projects
+ 
+
+ align:start position:0%
+projects
+agency and I actually don't know what
+
+ align:start position:0%
+agency and I actually don't know what
+ 
+
+ align:start position:0%
+agency and I actually don't know what
+caused it to to begin but uh a lot of it
+
+ align:start position:0%
+caused it to to begin but uh a lot of it
+ 
+
+ align:start position:0%
+caused it to to begin but uh a lot of it
+was involved
+
+ align:start position:0%
+was involved
+ 
+
+ align:start position:0%
+was involved
+with uh trying to make new kinds of
+
+ align:start position:0%
+with uh trying to make new kinds of
+ 
+
+ align:start position:0%
+with uh trying to make new kinds of
+instruments to detect InterContinental
+
+ align:start position:0%
+instruments to detect InterContinental
+ 
+
+ align:start position:0%
+instruments to detect InterContinental
+missiles and uh heaven knows what else
+
+ align:start position:0%
+missiles and uh heaven knows what else
+ 
+
+ align:start position:0%
+missiles and uh heaven knows what else
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh they decided to have a basic research
+
+ align:start position:0%
+uh they decided to have a basic research
+ 
+
+ align:start position:0%
+uh they decided to have a basic research
+Branch to uh because if you're in the
+
+ align:start position:0%
+Branch to uh because if you're in the
+ 
+
+ align:start position:0%
+Branch to uh because if you're in the
+military one of your concerns is defense
+
+ align:start position:0%
+military one of your concerns is defense
+ 
+
+ align:start position:0%
+military one of your concerns is defense
+and for some reason that uh I
+
+ align:start position:0%
+and for some reason that uh I
+ 
+
+ align:start position:0%
+and for some reason that uh I
+don't know how to I don't know how to
+
+ align:start position:0%
+don't know how to I don't know how to
+ 
+
+ align:start position:0%
+don't know how to I don't know how to
+explain but a group of people in the
+
+ align:start position:0%
+explain but a group of people in the
+ 
+
+ align:start position:0%
+explain but a group of people in the
+Office of Naval Research
+
+ align:start position:0%
+Office of Naval Research
+ 
+
+ align:start position:0%
+Office of Naval Research
+uh concluded
+
+ align:start position:0%
+uh concluded
+ 
+
+ align:start position:0%
+uh concluded
+that the best defense is to be way ahead
+
+ align:start position:0%
+that the best defense is to be way ahead
+ 
+
+ align:start position:0%
+that the best defense is to be way ahead
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+technology of everyone else and since
+
+ align:start position:0%
+technology of everyone else and since
+ 
+
+ align:start position:0%
+technology of everyone else and since
+there were no particular constraints on
+
+ align:start position:0%
+there were no particular constraints on
+ 
+
+ align:start position:0%
+there were no particular constraints on
+them they didn't have to
+
+ align:start position:0%
+them they didn't have to
+ 
+
+ align:start position:0%
+them they didn't have to
+say uh you have to write a progress
+
+ align:start position:0%
+say uh you have to write a progress
+ 
+
+ align:start position:0%
+say uh you have to write a progress
+report every three months and stuff like
+
+ align:start position:0%
+report every three months and stuff like
+ 
+
+ align:start position:0%
+report every three months and stuff like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+anyway another unique thing about the
+
+ align:start position:0%
+anyway another unique thing about the
+ 
+
+ align:start position:0%
+anyway another unique thing about the
+situation when I started was that the
+
+ align:start position:0%
+situation when I started was that the
+ 
+
+ align:start position:0%
+situation when I started was that the
+students knew more than the professors
+
+ align:start position:0%
+students knew more than the professors
+ 
+
+ align:start position:0%
+students knew more than the professors
+about computer
+
+ align:start position:0%
+about computer
+ 
+
+ align:start position:0%
+about computer
+science uh now there were a couple of
+
+ align:start position:0%
+science uh now there were a couple of
+ 
+
+ align:start position:0%
+science uh now there were a couple of
+there were people around uh MIT who knew
+
+ align:start position:0%
+there were people around uh MIT who knew
+ 
+
+ align:start position:0%
+there were people around uh MIT who knew
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+computers but uh we had the bad luck of
+
+ align:start position:0%
+computers but uh we had the bad luck of
+ 
+
+ align:start position:0%
+computers but uh we had the bad luck of
+having the best analog computers in the
+
+ align:start position:0%
+having the best analog computers in the
+ 
+
+ align:start position:0%
+having the best analog computers in the
+world uh vavar Bush and people like that
+
+ align:start position:0%
+world uh vavar Bush and people like that
+ 
+
+ align:start position:0%
+world uh vavar Bush and people like that
+uh so when things change suddenly enough
+
+ align:start position:0%
+uh so when things change suddenly enough
+ 
+
+ align:start position:0%
+uh so when things change suddenly enough
+uh your best people might be turn out to
+
+ align:start position:0%
+uh your best people might be turn out to
+ 
+
+ align:start position:0%
+uh your best people might be turn out to
+be the worst for a few years and the
+
+ align:start position:0%
+be the worst for a few years and the
+ 
+
+ align:start position:0%
+be the worst for a few years and the
+leaders in Innovation uh came from the
+
+ align:start position:0%
+leaders in Innovation uh came from the
+ 
+
+ align:start position:0%
+leaders in Innovation uh came from the
+tech Model Railroad Club and a few uh
+
+ align:start position:0%
+tech Model Railroad Club and a few uh
+ 
+
+ align:start position:0%
+tech Model Railroad Club and a few uh
+institutions like that uh I
+
+ align:start position:0%
+institutions like that uh I
+ 
+
+ align:start position:0%
+institutions like that uh I
+certainly knew something about
+
+ align:start position:0%
+certainly knew something about
+ 
+
+ align:start position:0%
+certainly knew something about
+computers at least the theory of
+
+ align:start position:0%
+computers at least the theory of
+ 
+
+ align:start position:0%
+computers at least the theory of
+them uh but I didn't know anything about
+
+ align:start position:0%
+them uh but I didn't know anything about
+ 
+
+ align:start position:0%
+them uh but I didn't know anything about
+modern programming and either did anyone
+
+ align:start position:0%
+modern programming and either did anyone
+ 
+
+ align:start position:0%
+modern programming and either did anyone
+else except Newell and Simon and
+
+ align:start position:0%
+else except Newell and Simon and
+ 
+
+ align:start position:0%
+else except Newell and Simon and
+Carnegie melan and John McCarthy
+
+ align:start position:0%
+Carnegie melan and John McCarthy
+ 
+
+ align:start position:0%
+Carnegie melan and John McCarthy
+who uh they invented list processing
+
+ align:start position:0%
+who uh they invented list processing
+ 
+
+ align:start position:0%
+who uh they invented list processing
+languages and John McCarthy refined them
+
+ align:start position:0%
+languages and John McCarthy refined them
+ 
+
+ align:start position:0%
+languages and John McCarthy refined them
+and uh basically combined a very clumsy
+
+ align:start position:0%
+and uh basically combined a very clumsy
+ 
+
+ align:start position:0%
+and uh basically combined a very clumsy
+logol likee list processing
+
+ align:start position:0%
+logol likee list processing
+ 
+
+ align:start position:0%
+logol likee list processing
+language uh with
+
+ align:start position:0%
+language uh with
+ 
+
+ align:start position:0%
+language uh with
+uh with a
+
+ align:start position:0%
+uh with a
+ 
+
+ align:start position:0%
+uh with a
+algebraic language and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so lisp came after uh there had been
+
+ align:start position:0%
+uh so lisp came after uh there had been
+ 
+
+ align:start position:0%
+uh so lisp came after uh there had been
+A Primitive list processors and all of
+
+ align:start position:0%
+A Primitive list processors and all of
+ 
+
+ align:start position:0%
+A Primitive list processors and all of
+new and Simon's work including a chess
+
+ align:start position:0%
+new and Simon's work including a chess
+ 
+
+ align:start position:0%
+new and Simon's work including a chess
+program had been done with
+
+ align:start position:0%
+program had been done with
+ 
+
+ align:start position:0%
+program had been done with
+uh just a programming language that had
+
+ align:start position:0%
+uh just a programming language that had
+ 
+
+ align:start position:0%
+uh just a programming language that had
+something like car cter and cons so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was U so it was about 10 years
+
+ align:start position:0%
+was U so it was about 10 years
+ 
+
+ align:start position:0%
+was U so it was about 10 years
+after uh the
+
+ align:start position:0%
+after uh the
+ 
+
+ align:start position:0%
+after uh the
+be the first computers in at MIT came
+
+ align:start position:0%
+be the first computers in at MIT came
+ 
+
+ align:start position:0%
+be the first computers in at MIT came
+mainly from Lincoln lab who had the job
+
+ align:start position:0%
+mainly from Lincoln lab who had the job
+ 
+
+ align:start position:0%
+mainly from Lincoln lab who had the job
+of building supercomputers to uh analyze
+
+ align:start position:0%
+of building supercomputers to uh analyze
+ 
+
+ align:start position:0%
+of building supercomputers to uh analyze
+radar data and stuff like that uh which
+
+ align:start position:0%
+radar data and stuff like that uh which
+ 
+
+ align:start position:0%
+radar data and stuff like that uh which
+were indeed connected with National
+
+ align:start position:0%
+were indeed connected with National
+ 
+
+ align:start position:0%
+were indeed connected with National
+Defense and uh try to get combined radar
+
+ align:start position:0%
+Defense and uh try to get combined radar
+ 
+
+ align:start position:0%
+Defense and uh try to get combined radar
+reports from all sorts of places to uh
+
+ align:start position:0%
+reports from all sorts of places to uh
+ 
+
+ align:start position:0%
+reports from all sorts of places to uh
+get early warnings of uh activities in
+
+ align:start position:0%
+get early warnings of uh activities in
+ 
+
+ align:start position:0%
+get early warnings of uh activities in
+space and so forth um
+
+ align:start position:0%
+space and so forth um
+ 
+
+ align:start position:0%
+space and so forth um
+when the first Sputnik was launched for
+
+ align:start position:0%
+when the first Sputnik was launched for
+ 
+
+ align:start position:0%
+when the first Sputnik was launched for
+by the Russians there was just a little
+
+ align:start position:0%
+by the Russians there was just a little
+ 
+
+ align:start position:0%
+by the Russians there was just a little
+thing going beep beep beep in low earth
+
+ align:start position:0%
+thing going beep beep beep in low earth
+ 
+
+ align:start position:0%
+thing going beep beep beep in low earth
+orbit and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh within a couple of hours of
+
+ align:start position:0%
+uh within a couple of hours of
+ 
+
+ align:start position:0%
+uh within a couple of hours of
+after uh the Russians announced that
+
+ align:start position:0%
+after uh the Russians announced that
+ 
+
+ align:start position:0%
+after uh the Russians announced that
+Sputnik was
+
+ align:start position:0%
+Sputnik was
+ 
+
+ align:start position:0%
+Sputnik was
+there uh and they announced its orbit
+
+ align:start position:0%
+there uh and they announced its orbit
+ 
+
+ align:start position:0%
+there uh and they announced its orbit
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the a couple of hackers at Lincoln
+
+ align:start position:0%
+the a couple of hackers at Lincoln
+ 
+
+ align:start position:0%
+the a couple of hackers at Lincoln
+laboratory uh managed
+
+ align:start position:0%
+laboratory uh managed
+ 
+
+ align:start position:0%
+laboratory uh managed
+to uh track The Thing
+
+ align:start position:0%
+to uh track The Thing
+ 
+
+ align:start position:0%
+to uh track The Thing
+by hooking a couple of radio it was
+
+ align:start position:0%
+by hooking a couple of radio it was
+ 
+
+ align:start position:0%
+by hooking a couple of radio it was
+going beep beep beep and they guy named
+
+ align:start position:0%
+going beep beep beep and they guy named
+ 
+
+ align:start position:0%
+going beep beep beep and they guy named
+Brad Howland who was a teenager I think
+
+ align:start position:0%
+Brad Howland who was a teenager I think
+ 
+
+ align:start position:0%
+Brad Howland who was a teenager I think
+then hooked a couple of radio receivers
+
+ align:start position:0%
+then hooked a couple of radio receivers
+ 
+
+ align:start position:0%
+then hooked a couple of radio receivers
+up with some flip-flops and things and
+
+ align:start position:0%
+up with some flip-flops and things and
+ 
+
+ align:start position:0%
+up with some flip-flops and things and
+uh was able to get its exact traj trory
+
+ align:start position:0%
+uh was able to get its exact traj trory
+ 
+
+ align:start position:0%
+uh was able to get its exact traj trory
+from the Doppler shifts of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh then I think I've talked about that
+
+ align:start position:0%
+uh then I think I've talked about that
+ 
+
+ align:start position:0%
+uh then I think I've talked about that
+history at some point
+
+ align:start position:0%
+history at some point
+ 
+
+ align:start position:0%
+history at some point
+about early 1970 or so 10 or 15 years
+
+ align:start position:0%
+about early 1970 or so 10 or 15 years
+ 
+
+ align:start position:0%
+about early 1970 or so 10 or 15 years
+after uh arpa started well the big arpa
+
+ align:start position:0%
+after uh arpa started well the big arpa
+ 
+
+ align:start position:0%
+after uh arpa started well the big arpa
+uh project was called project Mac in
+
+ align:start position:0%
+uh project was called project Mac in
+ 
+
+ align:start position:0%
+uh project was called project Mac in
+1963 and MIT got $3 million a year uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for Designing and building a time
+
+ align:start position:0%
+for Designing and building a time
+ 
+
+ align:start position:0%
+for Designing and building a time
+sharing system the idea for a time
+
+ align:start position:0%
+sharing system the idea for a time
+ 
+
+ align:start position:0%
+sharing system the idea for a time
+sharing system had bubbled up in a few
+
+ align:start position:0%
+sharing system had bubbled up in a few
+ 
+
+ align:start position:0%
+sharing system had bubbled up in a few
+places but it was mainly uh a couple of
+
+ align:start position:0%
+places but it was mainly uh a couple of
+ 
+
+ align:start position:0%
+places but it was mainly uh a couple of
+other youngsters John McCarthy and
+
+ align:start position:0%
+other youngsters John McCarthy and
+ 
+
+ align:start position:0%
+other youngsters John McCarthy and
+Edward fredkin who uh
+
+ align:start position:0%
+Edward fredkin who uh
+ 
+
+ align:start position:0%
+Edward fredkin who uh
+recognize that if a computer could
+
+ align:start position:0%
+recognize that if a computer could
+ 
+
+ align:start position:0%
+recognize that if a computer could
+compute thousands of operations per
+
+ align:start position:0%
+compute thousands of operations per
+ 
+
+ align:start position:0%
+compute thousands of operations per
+second then it should be able to compute
+
+ align:start position:0%
+second then it should be able to compute
+ 
+
+ align:start position:0%
+second then it should be able to compute
+hundreds of operations per second for
+
+ align:start position:0%
+hundreds of operations per second for
+ 
+
+ align:start position:0%
+hundreds of operations per second for
+tens of people and when it gets to a
+
+ align:start position:0%
+tens of people and when it gets to a
+ 
+
+ align:start position:0%
+tens of people and when it gets to a
+billion operations per second then it
+
+ align:start position:0%
+billion operations per second then it
+ 
+
+ align:start position:0%
+billion operations per second then it
+should be able to compute a million
+
+ align:start position:0%
+should be able to compute a million
+ 
+
+ align:start position:0%
+should be able to compute a million
+operations per second for a thousand
+
+ align:start position:0%
+operations per second for a thousand
+ 
+
+ align:start position:0%
+operations per second for a thousand
+people and so forth and uh MIT was the
+
+ align:start position:0%
+people and so forth and uh MIT was the
+ 
+
+ align:start position:0%
+people and so forth and uh MIT was the
+first place to develop time sharing
+
+ align:start position:0%
+first place to develop time sharing
+ 
+
+ align:start position:0%
+first place to develop time sharing
+system and as I said uh they sent this
+
+ align:start position:0%
+system and as I said uh they sent this
+ 
+
+ align:start position:0%
+system and as I said uh they sent this
+$3 million a year to get that project to
+
+ align:start position:0%
+$3 million a year to get that project to
+ 
+
+ align:start position:0%
+$3 million a year to get that project to
+work and because the guy in charge of
+
+ align:start position:0%
+work and because the guy in charge of
+ 
+
+ align:start position:0%
+work and because the guy in charge of
+that was a former professor of
+
+ align:start position:0%
+that was a former professor of
+ 
+
+ align:start position:0%
+that was a former professor of
+psychology named uh Joe
+
+ align:start position:0%
+psychology named uh Joe
+ 
+
+ align:start position:0%
+psychology named uh Joe
+licklider uh had been a friend of mine
+
+ align:start position:0%
+licklider uh had been a friend of mine
+ 
+
+ align:start position:0%
+licklider uh had been a friend of mine
+when I was an
+
+ align:start position:0%
+when I was an
+ 
+
+ align:start position:0%
+when I was an
+undergraduate uh he added another
+
+ align:start position:0%
+undergraduate uh he added another
+ 
+
+ align:start position:0%
+undergraduate uh he added another
+million dollars a year and uh gave it to
+
+ align:start position:0%
+million dollars a year and uh gave it to
+ 
+
+ align:start position:0%
+million dollars a year and uh gave it to
+us to start the AI
+
+ align:start position:0%
+us to start the AI
+ 
+
+ align:start position:0%
+us to start the AI
+lab and
+
+ align:start position:0%
+lab and
+ 
+
+ align:start position:0%
+lab and
+uh if that ever happens to you uh I hope
+
+ align:start position:0%
+uh if that ever happens to you uh I hope
+ 
+
+ align:start position:0%
+uh if that ever happens to you uh I hope
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will anyway uh as I've complained a lot
+
+ align:start position:0%
+will anyway uh as I've complained a lot
+ 
+
+ align:start position:0%
+will anyway uh as I've complained a lot
+during the
+
+ align:start position:0%
+during the
+ 
+
+ align:start position:0%
+during the
+course uh we were able
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to sort of do anything we thought was
+
+ align:start position:0%
+to sort of do anything we thought was
+ 
+
+ align:start position:0%
+to sort of do anything we thought was
+possible and we didn't worry about
+
+ align:start position:0%
+possible and we didn't worry about
+ 
+
+ align:start position:0%
+possible and we didn't worry about
+whether it could be done in a year or
+
+ align:start position:0%
+whether it could be done in a year or
+ 
+
+ align:start position:0%
+whether it could be done in a year or
+two or
+
+ align:start position:0%
+two or
+ 
+
+ align:start position:0%
+two or
+20 uh we just had enough money and
+
+ align:start position:0%
+20 uh we just had enough money and
+ 
+
+ align:start position:0%
+20 uh we just had enough money and
+enough uh adventurous people to to just
+
+ align:start position:0%
+enough uh adventurous people to to just
+ 
+
+ align:start position:0%
+enough uh adventurous people to to just
+uh start doing those things so in the
+
+ align:start position:0%
+uh start doing those things so in the
+ 
+
+ align:start position:0%
+uh start doing those things so in the
+very first year uh we had Jim slagel
+
+ align:start position:0%
+very first year uh we had Jim slagel
+ 
+
+ align:start position:0%
+very first year uh we had Jim slagel
+making the program that
+
+ align:start position:0%
+making the program that
+ 
+
+ align:start position:0%
+making the program that
+uh could uh do
+
+ align:start position:0%
+uh could uh do
+ 
+
+ align:start position:0%
+uh could uh do
+integrals at the level of uh that
+
+ align:start position:0%
+integrals at the level of uh that
+ 
+
+ align:start position:0%
+integrals at the level of uh that
+student students in
+
+ align:start position:0%
+student students in
+ 
+
+ align:start position:0%
+student students in
+1801 uh were learning to do uh I think I
+
+ align:start position:0%
+1801 uh were learning to do uh I think I
+ 
+
+ align:start position:0%
+1801 uh were learning to do uh I think I
+mentioned I made the first program that
+
+ align:start position:0%
+mentioned I made the first program that
+ 
+
+ align:start position:0%
+mentioned I made the first program that
+computed derivatives and it was just
+
+ align:start position:0%
+computed derivatives and it was just
+ 
+
+ align:start position:0%
+computed derivatives and it was just
+five or 10 lines of code because it it
+
+ align:start position:0%
+five or 10 lines of code because it it
+ 
+
+ align:start position:0%
+five or 10 lines of code because it it
+said it worked lexically it said if you
+
+ align:start position:0%
+said it worked lexically it said if you
+ 
+
+ align:start position:0%
+said it worked lexically it said if you
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+XY replace it by the symbols
+
+ align:start position:0%
+XY replace it by the symbols
+ 
+
+ align:start position:0%
+XY replace it by the symbols
+xdy plus y
+
+ align:start position:0%
+xdy plus y
+ 
+
+ align:start position:0%
+xdy plus y
+DX and so
+
+ align:start position:0%
+DX and so
+ 
+
+ align:start position:0%
+DX and so
+forth uh that's how you do derivatives
+
+ align:start position:0%
+forth uh that's how you do derivatives
+ 
+
+ align:start position:0%
+forth uh that's how you do derivatives
+where d means derivative and since it's
+
+ align:start position:0%
+where d means derivative and since it's
+ 
+
+ align:start position:0%
+where d means derivative and since it's
+operating on the names of functions then
+
+ align:start position:0%
+operating on the names of functions then
+ 
+
+ align:start position:0%
+operating on the names of functions then
+you just recurse until all the function
+
+ align:start position:0%
+you just recurse until all the function
+ 
+
+ align:start position:0%
+you just recurse until all the function
+names have
+
+ align:start position:0%
+names have
+ 
+
+ align:start position:0%
+names have
+disappeared and
+
+ align:start position:0%
+disappeared and
+ 
+
+ align:start position:0%
+disappeared and
+uh so that was just a page of code and
+
+ align:start position:0%
+uh so that was just a page of code and
+ 
+
+ align:start position:0%
+uh so that was just a page of code and
+then slagel uh who was blind wrote 20
+
+ align:start position:0%
+then slagel uh who was blind wrote 20
+ 
+
+ align:start position:0%
+then slagel uh who was blind wrote 20
+pages of code and uh Joel Moses
+
+ align:start position:0%
+pages of code and uh Joel Moses
+ 
+
+ align:start position:0%
+pages of code and uh Joel Moses
+who what's he now Provost or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he did he retire or go back to work I'm
+
+ align:start position:0%
+he did he retire or go back to work I'm
+ 
+
+ align:start position:0%
+he did he retire or go back to work I'm
+not probably
+
+ align:start position:0%
+not probably
+ 
+
+ align:start position:0%
+not probably
+both uh Institute Professor yep and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh he mentioned that it took him a very
+
+ align:start position:0%
+uh he mentioned that it took him a very
+ 
+
+ align:start position:0%
+uh he mentioned that it took him a very
+long time to decode slagel's 20 Pages
+
+ align:start position:0%
+long time to decode slagel's 20 Pages
+ 
+
+ align:start position:0%
+long time to decode slagel's 20 Pages
+because since slagel is writing in brail
+
+ align:start position:0%
+because since slagel is writing in brail
+ 
+
+ align:start position:0%
+because since slagel is writing in brail
+uh poor slagel has to understand his
+
+ align:start position:0%
+uh poor slagel has to understand his
+ 
+
+ align:start position:0%
+uh poor slagel has to understand his
+code too and
+
+ align:start position:0%
+code too and
+ 
+
+ align:start position:0%
+code too and
+uh you can't just glance at a page so he
+
+ align:start position:0%
+uh you can't just glance at a page so he
+ 
+
+ align:start position:0%
+uh you can't just glance at a page so he
+wrote this incredibly intricate
+
+ align:start position:0%
+wrote this incredibly intricate
+ 
+
+ align:start position:0%
+wrote this incredibly intricate
+compressed stuff and it had the weird
+
+ align:start position:0%
+compressed stuff and it had the weird
+ 
+
+ align:start position:0%
+compressed stuff and it had the weird
+property that it solved
+
+ align:start position:0%
+property that it solved
+ 
+
+ align:start position:0%
+property that it solved
+integrals it did integrals at just about
+
+ align:start position:0%
+integrals it did integrals at just about
+ 
+
+ align:start position:0%
+integrals it did integrals at just about
+the same speed as good math students so
+
+ align:start position:0%
+the same speed as good math students so
+ 
+
+ align:start position:0%
+the same speed as good math students so
+uh if you gave it an expression with a
+
+ align:start position:0%
+uh if you gave it an expression with a
+ 
+
+ align:start position:0%
+uh if you gave it an expression with a
+couple of signs and cosiness and things
+
+ align:start position:0%
+couple of signs and cosiness and things
+ 
+
+ align:start position:0%
+couple of signs and cosiness and things
+it might take 10 or 15 minutes and uh
+
+ align:start position:0%
+it might take 10 or 15 minutes and uh
+ 
+
+ align:start position:0%
+it might take 10 or 15 minutes and uh
+everybody was very impressed that this
+
+ align:start position:0%
+everybody was very impressed that this
+ 
+
+ align:start position:0%
+everybody was very impressed that this
+computer could keep up with a human but
+
+ align:start position:0%
+computer could keep up with a human but
+ 
+
+ align:start position:0%
+computer could keep up with a human but
+uh of
+
+ align:start position:0%
+uh of
+ 
+
+ align:start position:0%
+uh of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+that that fact had no meaning whatever
+
+ align:start position:0%
+that that fact had no meaning whatever
+ 
+
+ align:start position:0%
+that that fact had no meaning whatever
+it was just that happened to be how slow
+
+ align:start position:0%
+it was just that happened to be how slow
+ 
+
+ align:start position:0%
+it was just that happened to be how slow
+computers were at that
+
+ align:start position:0%
+computers were at that
+ 
+
+ align:start position:0%
+computers were at that
+time uh the IBM 704 which was I guess we
+
+ align:start position:0%
+time uh the IBM 704 which was I guess we
+ 
+
+ align:start position:0%
+time uh the IBM 704 which was I guess we
+had a 701 and then a 704
+
+ align:start position:0%
+had a 701 and then a 704
+ 
+
+ align:start position:0%
+had a 701 and then a 704
+and I think that machine was uh doing
+
+ align:start position:0%
+and I think that machine was uh doing
+ 
+
+ align:start position:0%
+and I think that machine was uh doing
+about 20,000 operations per second which
+
+ align:start position:0%
+about 20,000 operations per second which
+ 
+
+ align:start position:0%
+about 20,000 operations per second which
+is probably more than a person can do
+
+ align:start position:0%
+is probably more than a person can do
+ 
+
+ align:start position:0%
+is probably more than a person can do
+but no one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so who has an idea on what what
+
+ align:start position:0%
+well so who has an idea on what what
+ 
+
+ align:start position:0%
+well so who has an idea on what what
+should be done next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what would you like to do uh a
+
+ align:start position:0%
+yeah what would you like to do uh a
+ 
+
+ align:start position:0%
+yeah what would you like to do uh a
+robot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that AI system that would interact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the well we're going to need robots
+
+ align:start position:0%
+the well we're going to need robots
+ 
+
+ align:start position:0%
+the well we're going to need robots
+pretty soon if you look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the just for example this aging problem
+
+ align:start position:0%
+the just for example this aging problem
+ 
+
+ align:start position:0%
+the just for example this aging problem
+uh We've getting more and more people
+
+ align:start position:0%
+uh We've getting more and more people
+ 
+
+ align:start position:0%
+uh We've getting more and more people
+who are uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crippled in one way or another
+
+ align:start position:0%
+crippled in one way or another
+ 
+
+ align:start position:0%
+crippled in one way or another
+handicapped
+
+ align:start position:0%
+handicapped
+ 
+
+ align:start position:0%
+handicapped
+uh a huge population of people uh with
+
+ align:start position:0%
+uh a huge population of people uh with
+ 
+
+ align:start position:0%
+uh a huge population of people uh with
+with mild brain disorders of course
+
+ align:start position:0%
+with mild brain disorders of course
+ 
+
+ align:start position:0%
+with mild brain disorders of course
+serious ones
+
+ align:start position:0%
+serious ones
+ 
+
+ align:start position:0%
+serious ones
+also and they're not enough uh nurses to
+
+ align:start position:0%
+also and they're not enough uh nurses to
+ 
+
+ align:start position:0%
+also and they're not enough uh nurses to
+take care of
+
+ align:start position:0%
+take care of
+ 
+
+ align:start position:0%
+take care of
+the U disabled aged
+
+ align:start position:0%
+the U disabled aged
+ 
+
+ align:start position:0%
+the U disabled aged
+people and u i I think that's probably
+
+ align:start position:0%
+people and u i I think that's probably
+ 
+
+ align:start position:0%
+people and u i I think that's probably
+the going to be a
+
+ align:start position:0%
+the going to be a
+ 
+
+ align:start position:0%
+the going to be a
+major need for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+robotics as I see it the problem with
+
+ align:start position:0%
+robotics as I see it the problem with
+ 
+
+ align:start position:0%
+robotics as I see it the problem with
+robotics is that people build
+
+ align:start position:0%
+robotics is that people build
+ 
+
+ align:start position:0%
+robotics is that people build
+robots and you look at any laboratory
+
+ align:start position:0%
+robots and you look at any laboratory
+ 
+
+ align:start position:0%
+robots and you look at any laboratory
+that has built a physical
+
+ align:start position:0%
+that has built a physical
+ 
+
+ align:start position:0%
+that has built a physical
+robot and media lab is a perfect example
+
+ align:start position:0%
+robot and media lab is a perfect example
+ 
+
+ align:start position:0%
+robot and media lab is a perfect example
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+it or Rod Brooks
+
+ align:start position:0%
+it or Rod Brooks
+ 
+
+ align:start position:0%
+it or Rod Brooks
+uh had a wonderful robot called Cog with
+
+ align:start position:0%
+uh had a wonderful robot called Cog with
+ 
+
+ align:start position:0%
+uh had a wonderful robot called Cog with
+a head and two
+
+ align:start position:0%
+a head and two
+ 
+
+ align:start position:0%
+a head and two
+hands took a lot of engineering and
+
+ align:start position:0%
+hands took a lot of engineering and
+ 
+
+ align:start position:0%
+hands took a lot of engineering and
+there was only one of it and it only
+
+ align:start position:0%
+there was only one of it and it only
+ 
+
+ align:start position:0%
+there was only one of it and it only
+worked for a few hours a week because
+
+ align:start position:0%
+worked for a few hours a week because
+ 
+
+ align:start position:0%
+worked for a few hours a week because
+it's very complicated and it breaks and
+
+ align:start position:0%
+it's very complicated and it breaks and
+ 
+
+ align:start position:0%
+it's very complicated and it breaks and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh so the
+
+ align:start position:0%
+uh so the
+ 
+
+ align:start position:0%
+uh so the
+joke is that if I were starting a
+
+ align:start position:0%
+joke is that if I were starting a
+ 
+
+ align:start position:0%
+joke is that if I were starting a
+robotic slab I would not permit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+robots once you simulate the robots and
+
+ align:start position:0%
+robots once you simulate the robots and
+ 
+
+ align:start position:0%
+robots once you simulate the robots and
+get them to do
+
+ align:start position:0%
+get them to do
+ 
+
+ align:start position:0%
+get them to do
+do what you want uh then you take it out
+
+ align:start position:0%
+do what you want uh then you take it out
+ 
+
+ align:start position:0%
+do what you want uh then you take it out
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+university and hire some good mechanical
+
+ align:start position:0%
+university and hire some good mechanical
+ 
+
+ align:start position:0%
+university and hire some good mechanical
+engineers to make the robot you want but
+
+ align:start position:0%
+engineers to make the robot you want but
+ 
+
+ align:start position:0%
+engineers to make the robot you want but
+you don't want to robotics research
+
+ align:start position:0%
+you don't want to robotics research
+ 
+
+ align:start position:0%
+you don't want to robotics research
+should not involve robots and I
+
+ align:start position:0%
+should not involve robots and I
+ 
+
+ align:start position:0%
+should not involve robots and I
+think I have sort of mixed feelings
+
+ align:start position:0%
+think I have sort of mixed feelings
+ 
+
+ align:start position:0%
+think I have sort of mixed feelings
+about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what's the great basketball robot
+
+ align:start position:0%
+uh what's the great basketball robot
+ 
+
+ align:start position:0%
+uh what's the great basketball robot
+event called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bas mean soccer well whatever you call
+
+ align:start position:0%
+Bas mean soccer well whatever you call
+ 
+
+ align:start position:0%
+Bas mean soccer well whatever you call
+it they kick a ball and try to get it's
+
+ align:start position:0%
+it they kick a ball and try to get it's
+ 
+
+ align:start position:0%
+it they kick a ball and try to get it's
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+it's they try to get it through to a
+
+ align:start position:0%
+it's they try to get it through to a
+ 
+
+ align:start position:0%
+it's they try to get it through to a
+goal so it is it is soccer
+
+ align:start position:0%
+goal so it is it is soccer
+ 
+
+ align:start position:0%
+goal so it is it is soccer
+RoboCop yeah
+
+ align:start position:0%
+RoboCop yeah
+ 
+
+ align:start position:0%
+RoboCop yeah
+whatever uh that's probably a plus for
+
+ align:start position:0%
+whatever uh that's probably a plus for
+ 
+
+ align:start position:0%
+whatever uh that's probably a plus for
+the high school students who are
+
+ align:start position:0%
+the high school students who are
+ 
+
+ align:start position:0%
+the high school students who are
+involved in it but yes why don't you
+
+ align:start position:0%
+involved in it but yes why don't you
+ 
+
+ align:start position:0%
+involved in it but yes why don't you
+would have like uh uh robots that all
+
+ align:start position:0%
+would have like uh uh robots that all
+ 
+
+ align:start position:0%
+would have like uh uh robots that all
+like University use as like a base why
+
+ align:start position:0%
+like University use as like a base why
+ 
+
+ align:start position:0%
+like University use as like a base why
+why do we do we keep building Hardware
+
+ align:start position:0%
+why do we do we keep building Hardware
+ 
+
+ align:start position:0%
+why do we do we keep building Hardware
+like is is it necessary to keep building
+
+ align:start position:0%
+like is is it necessary to keep building
+ 
+
+ align:start position:0%
+like is is it necessary to keep building
+Hardware all back again I'm not sure
+
+ align:start position:0%
+Hardware all back again I'm not sure
+ 
+
+ align:start position:0%
+Hardware all back again I'm not sure
+what what's your question like when we
+
+ align:start position:0%
+what what's your question like when we
+ 
+
+ align:start position:0%
+what what's your question like when we
+use computers we don't build the
+
+ align:start position:0%
+use computers we don't build the
+ 
+
+ align:start position:0%
+use computers we don't build the
+computers like again we
+
+ align:start position:0%
+computers like again we
+ 
+
+ align:start position:0%
+computers like again we
+use the like we just create software yes
+
+ align:start position:0%
+use the like we just create software yes
+ 
+
+ align:start position:0%
+use the like we just create software yes
+aren't we doing the same for for r and
+
+ align:start position:0%
+aren't we doing the same for for r and
+ 
+
+ align:start position:0%
+aren't we doing the same for for r and
+if not why are we just programming the
+
+ align:start position:0%
+if not why are we just programming the
+ 
+
+ align:start position:0%
+if not why are we just programming the
+robot to do stuff that we want what I'm
+
+ align:start position:0%
+robot to do stuff that we want what I'm
+ 
+
+ align:start position:0%
+robot to do stuff that we want what I'm
+say what I'm saying is that if people
+
+ align:start position:0%
+say what I'm saying is that if people
+ 
+
+ align:start position:0%
+say what I'm saying is that if people
+program the
+
+ align:start position:0%
+program the
+ 
+
+ align:start position:0%
+program the
+robot then it takes them two weeks to do
+
+ align:start position:0%
+robot then it takes them two weeks to do
+ 
+
+ align:start position:0%
+robot then it takes them two weeks to do
+the simplest
+
+ align:start position:0%
+the simplest
+ 
+
+ align:start position:0%
+the simplest
+thing if you're programming a simulated
+
+ align:start position:0%
+thing if you're programming a simulated
+ 
+
+ align:start position:0%
+thing if you're programming a simulated
+robot then it takes two minutes why does
+
+ align:start position:0%
+robot then it takes two minutes why does
+ 
+
+ align:start position:0%
+robot then it takes two minutes why does
+it take
+
+ align:start position:0%
+it take
+ 
+
+ align:start position:0%
+it take
+more because the robot's broken and
+
+ align:start position:0%
+more because the robot's broken and
+ 
+
+ align:start position:0%
+more because the robot's broken and
+there's only one in the lab and there
+
+ align:start position:0%
+there's only one in the lab and there
+ 
+
+ align:start position:0%
+there's only one in the lab and there
+are eight people who want to use it and
+
+ align:start position:0%
+are eight people who want to use it and
+ 
+
+ align:start position:0%
+are eight people who want to use it and
+3/4 of the time it's down because some
+
+ align:start position:0%
+3/4 of the time it's down because some
+ 
+
+ align:start position:0%
+3/4 of the time it's down because some
+motor because it's not in mass
+
+ align:start position:0%
+motor because it's not in mass
+ 
+
+ align:start position:0%
+motor because it's not in mass
+production if you have a machine that
+
+ align:start position:0%
+production if you have a machine that
+ 
+
+ align:start position:0%
+production if you have a machine that
+somebody
+
+ align:start position:0%
+somebody
+ 
+
+ align:start position:0%
+somebody
+made it's probably the first machine
+
+ align:start position:0%
+made it's probably the first machine
+ 
+
+ align:start position:0%
+made it's probably the first machine
+that person ever
+
+ align:start position:0%
+that person ever
+ 
+
+ align:start position:0%
+that person ever
+made so it's no
+
+ align:start position:0%
+made so it's no
+ 
+
+ align:start position:0%
+made so it's no
+good look at the Honda robot called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Asimo have you you've all seen it but
+
+ align:start position:0%
+Asimo have you you've all seen it but
+ 
+
+ align:start position:0%
+Asimo have you you've all seen it but
+you all saw it 10 years ago
+
+ align:start position:0%
+you all saw it 10 years ago
+ 
+
+ align:start position:0%
+you all saw it 10 years ago
+go it has not changed but they they say
+
+ align:start position:0%
+go it has not changed but they they say
+ 
+
+ align:start position:0%
+go it has not changed but they they say
+it doesn't fall over so often
+
+ align:start position:0%
+it doesn't fall over so often
+ 
+
+ align:start position:0%
+it doesn't fall over so often
+anymore so like there is a company a
+
+ align:start position:0%
+anymore so like there is a company a
+ 
+
+ align:start position:0%
+anymore so like there is a company a
+French company that there a robot called
+
+ align:start position:0%
+French company that there a robot called
+ 
+
+ align:start position:0%
+French company that there a robot called
+now robot that like it works pretty good
+
+ align:start position:0%
+now robot that like it works pretty good
+ 
+
+ align:start position:0%
+now robot that like it works pretty good
+I don't know why why don't we use a we
+
+ align:start position:0%
+I don't know why why don't we use a we
+ 
+
+ align:start position:0%
+I don't know why why don't we use a we
+buy some robots from some company
+
+ align:start position:0%
+buy some robots from some company
+ 
+
+ align:start position:0%
+buy some robots from some company
+because they're no
+
+ align:start position:0%
+because they're no
+ 
+
+ align:start position:0%
+because they're no
+good they don't do any they've only got
+
+ align:start position:0%
+good they don't do any they've only got
+ 
+
+ align:start position:0%
+good they don't do any they've only got
+one elbow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they can't reach around they don't have
+
+ align:start position:0%
+they can't reach around they don't have
+ 
+
+ align:start position:0%
+they can't reach around they don't have
+they don't not you can buy a hand for 30
+
+ align:start position:0%
+they don't not you can buy a hand for 30
+ 
+
+ align:start position:0%
+they don't not you can buy a hand for 30
+or $40,000 that has three or four
+
+ align:start position:0%
+or $40,000 that has three or four
+ 
+
+ align:start position:0%
+or $40,000 that has three or four
+fingers
+
+ align:start position:0%
+fingers
+ 
+
+ align:start position:0%
+fingers
+but tradeoff though
+
+ align:start position:0%
+but tradeoff though
+ 
+
+ align:start position:0%
+but tradeoff though
+between you know making a more complex
+
+ align:start position:0%
+between you know making a more complex
+ 
+
+ align:start position:0%
+between you know making a more complex
+robot that has more interaction you can
+
+ align:start position:0%
+robot that has more interaction you can
+ 
+
+ align:start position:0%
+robot that has more interaction you can
+make you know that gets more you're
+
+ align:start position:0%
+make you know that gets more you're
+ 
+
+ align:start position:0%
+make you know that gets more you're
+building an actual robot but for a
+
+ align:start position:0%
+building an actual robot but for a
+ 
+
+ align:start position:0%
+building an actual robot but for a
+simulator simulating the Real
+
+ align:start position:0%
+simulator simulating the Real
+ 
+
+ align:start position:0%
+simulator simulating the Real
+Environment gravity and those sort of
+
+ align:start position:0%
+Environment gravity and those sort of
+ 
+
+ align:start position:0%
+Environment gravity and those sort of
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+can also be difficult to create so that
+
+ align:start position:0%
+can also be difficult to create so that
+ 
+
+ align:start position:0%
+can also be difficult to create so that
+you're sure that whatever the reaction
+
+ align:start position:0%
+you're sure that whatever the reaction
+ 
+
+ align:start position:0%
+you're sure that whatever the reaction
+so your program robot you need to make
+
+ align:start position:0%
+so your program robot you need to make
+ 
+
+ align:start position:0%
+so your program robot you need to make
+sure the environment in is somewh real
+
+ align:start position:0%
+sure the environment in is somewh real
+ 
+
+ align:start position:0%
+sure the environment in is somewh real
+well it depends what you mean by real uh
+
+ align:start position:0%
+well it depends what you mean by real uh
+ 
+
+ align:start position:0%
+well it depends what you mean by real uh
+it seems to me if if the robot is smart
+
+ align:start position:0%
+it seems to me if if the robot is smart
+ 
+
+ align:start position:0%
+it seems to me if if the robot is smart
+and can learn and is adaptable and uh
+
+ align:start position:0%
+and can learn and is adaptable and uh
+ 
+
+ align:start position:0%
+and can learn and is adaptable and uh
+when a piece of piece of its software
+
+ align:start position:0%
+when a piece of piece of its software
+ 
+
+ align:start position:0%
+when a piece of piece of its software
+doesn't work then it modifies it
+
+ align:start position:0%
+doesn't work then it modifies it
+ 
+
+ align:start position:0%
+doesn't work then it modifies it
+uh in other words if you had a higher
+
+ align:start position:0%
+uh in other words if you had a higher
+ 
+
+ align:start position:0%
+uh in other words if you had a higher
+level learning machine in the in the uh
+
+ align:start position:0%
+level learning machine in the in the uh
+ 
+
+ align:start position:0%
+level learning machine in the in the uh
+processor of the
+
+ align:start position:0%
+processor of the
+ 
+
+ align:start position:0%
+processor of the
+robot then it could work in a real
+
+ align:start position:0%
+robot then it could work in a real
+ 
+
+ align:start position:0%
+robot then it could work in a real
+environment by learning that if you do
+
+ align:start position:0%
+environment by learning that if you do
+ 
+
+ align:start position:0%
+environment by learning that if you do
+this on a slippery floor you might uh
+
+ align:start position:0%
+this on a slippery floor you might uh
+ 
+
+ align:start position:0%
+this on a slippery floor you might uh
+maybe you should lean the other way
+
+ align:start position:0%
+maybe you should lean the other way
+ 
+
+ align:start position:0%
+maybe you should lean the other way
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+you uh Patty Mays did a little bit of
+
+ align:start position:0%
+you uh Patty Mays did a little bit of
+ 
+
+ align:start position:0%
+you uh Patty Mays did a little bit of
+that 20 years
+
+ align:start position:0%
+that 20 years
+ 
+
+ align:start position:0%
+that 20 years
+ago uh with
+
+ align:start position:0%
+ago uh with
+ 
+
+ align:start position:0%
+ago uh with
+what rule system that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving yeah but you see if you have a
+
+ align:start position:0%
+moving yeah but you see if you have a
+ 
+
+ align:start position:0%
+moving yeah but you see if you have a
+real robot you've only got an hour a
+
+ align:start position:0%
+real robot you've only got an hour a
+ 
+
+ align:start position:0%
+real robot you've only got an hour a
+week uh to debug this thing and and the
+
+ align:start position:0%
+week uh to debug this thing and and the
+ 
+
+ align:start position:0%
+week uh to debug this thing and and the
+program is working in real time if you
+
+ align:start position:0%
+program is working in real time if you
+ 
+
+ align:start position:0%
+program is working in real time if you
+look at real
+
+ align:start position:0%
+look at real
+ 
+
+ align:start position:0%
+look at real
+robots whereas if you're simulating a
+
+ align:start position:0%
+robots whereas if you're simulating a
+ 
+
+ align:start position:0%
+robots whereas if you're simulating a
+stick figure robot then you can simulate
+
+ align:start position:0%
+stick figure robot then you can simulate
+ 
+
+ align:start position:0%
+stick figure robot then you can simulate
+friction and slipping but uh you can
+
+ align:start position:0%
+friction and slipping but uh you can
+ 
+
+ align:start position:0%
+friction and slipping but uh you can
+move it as at
+
+ align:start position:0%
+move it as at
+ 
+
+ align:start position:0%
+move it as at
+uh 100,000 operations per second maybe
+
+ align:start position:0%
+uh 100,000 operations per second maybe
+ 
+
+ align:start position:0%
+uh 100,000 operations per second maybe
+another thing is uh there's something
+
+ align:start position:0%
+another thing is uh there's something
+ 
+
+ align:start position:0%
+another thing is uh there's something
+weird about the robot people they tell
+
+ align:start position:0%
+weird about the robot people they tell
+ 
+
+ align:start position:0%
+weird about the robot people they tell
+me there's so much uh feedback needed
+
+ align:start position:0%
+me there's so much uh feedback needed
+ 
+
+ align:start position:0%
+me there's so much uh feedback needed
+that they need a separate computer for
+
+ align:start position:0%
+that they need a separate computer for
+ 
+
+ align:start position:0%
+that they need a separate computer for
+each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joint I hear this everywhere they say
+
+ align:start position:0%
+joint I hear this everywhere they say
+ 
+
+ align:start position:0%
+joint I hear this everywhere they say
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+distributed it's really good of course
+
+ align:start position:0%
+distributed it's really good of course
+ 
+
+ align:start position:0%
+distributed it's really good of course
+it's still falling
+
+ align:start position:0%
+it's still falling
+ 
+
+ align:start position:0%
+it's still falling
+over agre there lot about robots that um
+
+ align:start position:0%
+over agre there lot about robots that um
+ 
+
+ align:start position:0%
+over agre there lot about robots that um
+can be simulated on a computer and I
+
+ align:start position:0%
+can be simulated on a computer and I
+ 
+
+ align:start position:0%
+can be simulated on a computer and I
+agree that a lot of the good things that
+
+ align:start position:0%
+agree that a lot of the good things that
+ 
+
+ align:start position:0%
+agree that a lot of the good things that
+people are currently working on with
+
+ align:start position:0%
+people are currently working on with
+ 
+
+ align:start position:0%
+people are currently working on with
+real robots would better be um first
+
+ align:start position:0%
+real robots would better be um first
+ 
+
+ align:start position:0%
+real robots would better be um first
+done simulated but I think that when you
+
+ align:start position:0%
+done simulated but I think that when you
+ 
+
+ align:start position:0%
+done simulated but I think that when you
+have a robot especially when you have
+
+ align:start position:0%
+have a robot especially when you have
+ 
+
+ align:start position:0%
+have a robot especially when you have
+situations where it interacts with the
+
+ align:start position:0%
+situations where it interacts with the
+ 
+
+ align:start position:0%
+situations where it interacts with the
+human being the reaction of the human
+
+ align:start position:0%
+human being the reaction of the human
+ 
+
+ align:start position:0%
+human being the reaction of the human
+being is sort of is really different um
+
+ align:start position:0%
+being is sort of is really different um
+ 
+
+ align:start position:0%
+being is sort of is really different um
+depending on whether it's a simulation
+
+ align:start position:0%
+depending on whether it's a simulation
+ 
+
+ align:start position:0%
+depending on whether it's a simulation
+or a physical being because I think I
+
+ align:start position:0%
+or a physical being because I think I
+ 
+
+ align:start position:0%
+or a physical being because I think I
+guess human beings inherently have
+
+ align:start position:0%
+guess human beings inherently have
+ 
+
+ align:start position:0%
+guess human beings inherently have
+different reactions to objects with
+
+ align:start position:0%
+different reactions to objects with
+ 
+
+ align:start position:0%
+different reactions to objects with
+physical monuments so so I feel like at
+
+ align:start position:0%
+physical monuments so so I feel like at
+ 
+
+ align:start position:0%
+physical monuments so so I feel like at
+a certain point especially when it
+
+ align:start position:0%
+a certain point especially when it
+ 
+
+ align:start position:0%
+a certain point especially when it
+interfaces with humans such as caretaker
+
+ align:start position:0%
+interfaces with humans such as caretaker
+ 
+
+ align:start position:0%
+interfaces with humans such as caretaker
+robots you do have to switch to the real
+
+ align:start position:0%
+robots you do have to switch to the real
+ 
+
+ align:start position:0%
+robots you do have to switch to the real
+robots well the caretaker robot has to
+
+ align:start position:0%
+robots well the caretaker robot has to
+ 
+
+ align:start position:0%
+robots well the caretaker robot has to
+uh be a smart program that's running a
+
+ align:start position:0%
+uh be a smart program that's running a
+ 
+
+ align:start position:0%
+uh be a smart program that's running a
+physical robot eventually it's just that
+
+ align:start position:0%
+physical robot eventually it's just that
+ 
+
+ align:start position:0%
+physical robot eventually it's just that
+we don't have the smart programs and we
+
+ align:start position:0%
+we don't have the smart programs and we
+ 
+
+ align:start position:0%
+we don't have the smart programs and we
+could have had them 25 years ago if the
+
+ align:start position:0%
+could have had them 25 years ago if the
+ 
+
+ align:start position:0%
+could have had them 25 years ago if the
+people wanting to make a helper robot
+
+ align:start position:0%
+people wanting to make a helper robot
+ 
+
+ align:start position:0%
+people wanting to make a helper robot
+didn't have a physical robot in their
+
+ align:start position:0%
+didn't have a physical robot in their
+ 
+
+ align:start position:0%
+didn't have a physical robot in their
+lab uh look at Cog which Cog is proudly
+
+ align:start position:0%
+lab uh look at Cog which Cog is proudly
+ 
+
+ align:start position:0%
+lab uh look at Cog which Cog is proudly
+displayed in the MIT
+
+ align:start position:0%
+displayed in the MIT
+ 
+
+ align:start position:0%
+displayed in the MIT
+Museum I don't know of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+single fact or technique or idea that
+
+ align:start position:0%
+single fact or technique or idea that
+ 
+
+ align:start position:0%
+single fact or technique or idea that
+came out of that project in the decade
+
+ align:start position:0%
+came out of that project in the decade
+ 
+
+ align:start position:0%
+came out of that project in the decade
+when graduate students wrote bad thesis
+
+ align:start position:0%
+when graduate students wrote bad thesis
+ 
+
+ align:start position:0%
+when graduate students wrote bad thesis
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+it so I guess then ultimately it's sort
+
+ align:start position:0%
+it so I guess then ultimately it's sort
+ 
+
+ align:start position:0%
+it so I guess then ultimately it's sort
+of like a division of um labor problem
+
+ align:start position:0%
+of like a division of um labor problem
+ 
+
+ align:start position:0%
+of like a division of um labor problem
+where it's like because it seems like
+
+ align:start position:0%
+where it's like because it seems like
+ 
+
+ align:start position:0%
+where it's like because it seems like
+when people are their code on actual
+
+ align:start position:0%
+when people are their code on actual
+ 
+
+ align:start position:0%
+when people are their code on actual
+robots it's like they have too many
+
+ align:start position:0%
+robots it's like they have too many
+ 
+
+ align:start position:0%
+robots it's like they have too many
+problems at the same time whereas you're
+
+ align:start position:0%
+problems at the same time whereas you're
+ 
+
+ align:start position:0%
+problems at the same time whereas you're
+saying they should focus on the software
+
+ align:start position:0%
+saying they should focus on the software
+ 
+
+ align:start position:0%
+saying they should focus on the software
+and after the software is like all good
+
+ align:start position:0%
+and after the software is like all good
+ 
+
+ align:start position:0%
+and after the software is like all good
+then they can move on to like
+
+ align:start position:0%
+then they can move on to like
+ 
+
+ align:start position:0%
+then they can move on to like
+integrating the software with the
+
+ align:start position:0%
+integrating the software with the
+ 
+
+ align:start position:0%
+integrating the software with the
+hardware yeah well the robots in uh
+
+ align:start position:0%
+hardware yeah well the robots in uh
+ 
+
+ align:start position:0%
+hardware yeah well the robots in uh
+Second Life but we're pretty good uh I
+
+ align:start position:0%
+Second Life but we're pretty good uh I
+ 
+
+ align:start position:0%
+Second Life but we're pretty good uh I
+don't know of any people who complained
+
+ align:start position:0%
+don't know of any people who complained
+ 
+
+ align:start position:0%
+don't know of any people who complained
+that they wanted real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones not familiar with the
+
+ align:start position:0%
+ones not familiar with the
+ 
+
+ align:start position:0%
+ones not familiar with the
+what did they do well you could make one
+
+ align:start position:0%
+what did they do well you could make one
+ 
+
+ align:start position:0%
+what did they do well you could make one
+because there was a a language for I
+
+ align:start position:0%
+because there was a a language for I
+ 
+
+ align:start position:0%
+because there was a a language for I
+don't think they did anything much but
+
+ align:start position:0%
+don't think they did anything much but
+ 
+
+ align:start position:0%
+don't think they did anything much but
+but they don't fall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over but I guess a good example might
+
+ align:start position:0%
+over but I guess a good example might
+ 
+
+ align:start position:0%
+over but I guess a good example might
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh well the dean
+
+ align:start position:0%
+uh well the dean
+ 
+
+ align:start position:0%
+uh well the dean
+cayman's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+robot soccer project
+
+ align:start position:0%
+robot soccer project
+ 
+
+ align:start position:0%
+robot soccer project
+and Carnegie melon has a had a robot so
+
+ align:start position:0%
+and Carnegie melon has a had a robot so
+ 
+
+ align:start position:0%
+and Carnegie melon has a had a robot so
+socker project for many years and I
+
+ align:start position:0%
+socker project for many years and I
+ 
+
+ align:start position:0%
+socker project for many years and I
+don't know that
+
+ align:start position:0%
+don't know that
+ 
+
+ align:start position:0%
+don't know that
+any I've never heard of any interesting
+
+ align:start position:0%
+any I've never heard of any interesting
+ 
+
+ align:start position:0%
+any I've never heard of any interesting
+discovery that came from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh the media lab
+
+ align:start position:0%
+that uh the media lab
+ 
+
+ align:start position:0%
+that uh the media lab
+also they're the Nic looking robots that
+
+ align:start position:0%
+also they're the Nic looking robots that
+ 
+
+ align:start position:0%
+also they're the Nic looking robots that
+smile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and people are impressed
+
+ align:start position:0%
+and people are impressed
+ 
+
+ align:start position:0%
+and people are impressed
+by uh the way that humans are attracted
+
+ align:start position:0%
+by uh the way that humans are attracted
+ 
+
+ align:start position:0%
+by uh the way that humans are attracted
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+these uh to interact with these
+
+ align:start position:0%
+these uh to interact with these
+ 
+
+ align:start position:0%
+these uh to interact with these
+robots
+
+ align:start position:0%
+robots
+ 
+
+ align:start position:0%
+robots
+but I think once we know that it's
+
+ align:start position:0%
+but I think once we know that it's
+ 
+
+ align:start position:0%
+but I think once we know that it's
+something to avoid rather than to
+
+ align:start position:0%
+something to avoid rather than to
+ 
+
+ align:start position:0%
+something to avoid rather than to
+exploit until when the robot says please
+
+ align:start position:0%
+exploit until when the robot says please
+ 
+
+ align:start position:0%
+exploit until when the robot says please
+to meet you uh wouldn't it be nice if it
+
+ align:start position:0%
+to meet you uh wouldn't it be nice if it
+ 
+
+ align:start position:0%
+to meet you uh wouldn't it be nice if it
+were at actually pleased to meet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you the intelligent welcome mat should
+
+ align:start position:0%
+you the intelligent welcome mat should
+ 
+
+ align:start position:0%
+you the intelligent welcome mat should
+be our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Target even if it doesn't move if it
+
+ align:start position:0%
+Target even if it doesn't move if it
+ 
+
+ align:start position:0%
+Target even if it doesn't move if it
+just sat there and felt good about
+
+ align:start position:0%
+just sat there and felt good about
+ 
+
+ align:start position:0%
+just sat there and felt good about
+seeing you that would be a great
+
+ align:start position:0%
+seeing you that would be a great
+ 
+
+ align:start position:0%
+seeing you that would be a great
+achievement I don't know how you would
+
+ align:start position:0%
+achievement I don't know how you would
+ 
+
+ align:start position:0%
+achievement I don't know how you would
+test for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it have you ever played with the Cleo
+
+ align:start position:0%
+it have you ever played with the Cleo
+ 
+
+ align:start position:0%
+it have you ever played with the Cleo
+dinosaur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yes and there was a cat that
+
+ align:start position:0%
+yes and there was a cat that
+ 
+
+ align:start position:0%
+yes and there was a cat that
+uh Itachi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+made in fact we ordered a pleo but we
+
+ align:start position:0%
+made in fact we ordered a pleo but we
+ 
+
+ align:start position:0%
+made in fact we ordered a pleo but we
+never got it do they are they still in
+
+ align:start position:0%
+never got it do they are they still in
+ 
+
+ align:start position:0%
+never got it do they are they still in
+production uh I believe so I don't I
+
+ align:start position:0%
+production uh I believe so I don't I
+ 
+
+ align:start position:0%
+production uh I believe so I don't I
+don't know I believe
+
+ align:start position:0%
+don't know I believe
+ 
+
+ align:start position:0%
+don't know I believe
+so they like they appear to be what they
+
+ align:start position:0%
+so they like they appear to be what they
+ 
+
+ align:start position:0%
+so they like they appear to be what they
+appear to be yeah it beautiful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+job somebody made a cat I'm trying to
+
+ align:start position:0%
+job somebody made a cat I'm trying to
+ 
+
+ align:start position:0%
+job somebody made a cat I'm trying to
+remember another Japanese
+
+ align:start position:0%
+remember another Japanese
+ 
+
+ align:start position:0%
+remember another Japanese
+company it was an awfully good
+
+ align:start position:0%
+company it was an awfully good
+ 
+
+ align:start position:0%
+company it was an awfully good
+cat it wouldn't do much but every now
+
+ align:start position:0%
+cat it wouldn't do much but every now
+ 
+
+ align:start position:0%
+cat it wouldn't do much but every now
+and then it would Mew and sort of look
+
+ align:start position:0%
+and then it would Mew and sort of look
+ 
+
+ align:start position:0%
+and then it would Mew and sort of look
+at look at you and beg for something but
+
+ align:start position:0%
+at look at you and beg for something but
+ 
+
+ align:start position:0%
+at look at you and beg for something but
+you you couldn't resist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah
+
+ align:start position:0%
+it yeah
+ 
+
+ align:start position:0%
+it yeah
+do you know how long would you take to
+
+ align:start position:0%
+do you know how long would you take to
+ 
+
+ align:start position:0%
+do you know how long would you take to
+kind of simulate a real world to like
+
+ align:start position:0%
+kind of simulate a real world to like
+ 
+
+ align:start position:0%
+kind of simulate a real world to like
+kind of great uh to create simulation
+
+ align:start position:0%
+kind of great uh to create simulation
+ 
+
+ align:start position:0%
+kind of great uh to create simulation
+simple simulation the well what and how
+
+ align:start position:0%
+simple simulation the well what and how
+ 
+
+ align:start position:0%
+simple simulation the well what and how
+many people because I you're saying that
+
+ align:start position:0%
+many people because I you're saying that
+ 
+
+ align:start position:0%
+many people because I you're saying that
+we should simulate robots in the
+
+ align:start position:0%
+we should simulate robots in the
+ 
+
+ align:start position:0%
+we should simulate robots in the
+computer create software for that
+
+ align:start position:0%
+computer create software for that
+ 
+
+ align:start position:0%
+computer create software for that
+instead of creating real robots and so
+
+ align:start position:0%
+instead of creating real robots and so
+ 
+
+ align:start position:0%
+instead of creating real robots and so
+we need to create a software that
+
+ align:start position:0%
+we need to create a software that
+ 
+
+ align:start position:0%
+we need to create a software that
+simulates the real world
+
+ align:start position:0%
+simulates the real world
+ 
+
+ align:start position:0%
+simulates the real world
+mhm that's complicated for me you know
+
+ align:start position:0%
+mhm that's complicated for me you know
+ 
+
+ align:start position:0%
+mhm that's complicated for me you know
+like have some ideas like how long would
+
+ align:start position:0%
+like have some ideas like how long would
+ 
+
+ align:start position:0%
+like have some ideas like how long would
+you take would it take how many people
+
+ align:start position:0%
+you take would it take how many people
+ 
+
+ align:start position:0%
+you take would it take how many people
+and why are why aren't we doing that or
+
+ align:start position:0%
+and why are why aren't we doing that or
+ 
+
+ align:start position:0%
+and why are why aren't we doing that or
+why isn't there somebody do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I wish somebody would explain to me
+
+ align:start position:0%
+that I wish somebody would explain to me
+ 
+
+ align:start position:0%
+that I wish somebody would explain to me
+why why the majority of you know there
+
+ align:start position:0%
+why why the majority of you know there
+ 
+
+ align:start position:0%
+why why the majority of you know there
+there are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there are epidemics of
+
+ align:start position:0%
+uh there are epidemics of
+ 
+
+ align:start position:0%
+uh there are epidemics of
+ideologies so that uh around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+the dominant idea of making machines
+
+ align:start position:0%
+the dominant idea of making machines
+ 
+
+ align:start position:0%
+the dominant idea of making machines
+better was to build rule-based
+
+ align:start position:0%
+better was to build rule-based
+ 
+
+ align:start position:0%
+better was to build rule-based
+systems and uh that's probably still
+
+ align:start position:0%
+systems and uh that's probably still
+ 
+
+ align:start position:0%
+systems and uh that's probably still
+the uh most
+
+ align:start position:0%
+the uh most
+ 
+
+ align:start position:0%
+the uh most
+popular way to program a computer for a
+
+ align:start position:0%
+popular way to program a computer for a
+ 
+
+ align:start position:0%
+popular way to program a computer for a
+complicated commercial application like
+
+ align:start position:0%
+complicated commercial application like
+ 
+
+ align:start position:0%
+complicated commercial application like
+making airplane reservations and keeping
+
+ align:start position:0%
+making airplane reservations and keeping
+ 
+
+ align:start position:0%
+making airplane reservations and keeping
+keeping stock of
+
+ align:start position:0%
+keeping stock of
+ 
+
+ align:start position:0%
+keeping stock of
+uh Parts in the factory and on and on
+
+ align:start position:0%
+uh Parts in the factory and on and on
+ 
+
+ align:start position:0%
+uh Parts in the factory and on and on
+uh now when the first rule-based systems
+
+ align:start position:0%
+uh now when the first rule-based systems
+ 
+
+ align:start position:0%
+uh now when the first rule-based systems
+appeared they were called production
+
+ align:start position:0%
+appeared they were called production
+ 
+
+ align:start position:0%
+appeared they were called production
+based languages production is just
+
+ align:start position:0%
+based languages production is just
+ 
+
+ align:start position:0%
+based languages production is just
+uh I think the word comes from Amo post
+
+ align:start position:0%
+uh I think the word comes from Amo post
+ 
+
+ align:start position:0%
+uh I think the word comes from Amo post
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+1920s and the idea is you you have a set
+
+ align:start position:0%
+1920s and the idea is you you have a set
+ 
+
+ align:start position:0%
+1920s and the idea is you you have a set
+of symbols x
+
+ align:start position:0%
+of symbols x
+ 
+
+ align:start position:0%
+of symbols x
+a y p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z where XY
+
+ align:start position:0%
+z where XY
+ 
+
+ align:start position:0%
+z where XY
+and I meant
+
+ align:start position:0%
+and I meant
+ 
+
+ align:start position:0%
+and I meant
+Z XY and z are variables and a and b are
+
+ align:start position:0%
+Z XY and z are variables and a and b are
+ 
+
+ align:start position:0%
+Z XY and z are variables and a and b are
+constants in other words an algebraic
+
+ align:start position:0%
+constants in other words an algebraic
+ 
+
+ align:start position:0%
+constants in other words an algebraic
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+basically and if the state of the world
+
+ align:start position:0%
+basically and if the state of the world
+ 
+
+ align:start position:0%
+basically and if the state of the world
+or the state of some process is
+
+ align:start position:0%
+or the state of some process is
+ 
+
+ align:start position:0%
+or the state of some process is
+described by this expression then uh
+
+ align:start position:0%
+described by this expression then uh
+ 
+
+ align:start position:0%
+described by this expression then uh
+then you change it into
+
+ align:start position:0%
+then you change it into
+ 
+
+ align:start position:0%
+then you change it into
+uh um something else like
+
+ align:start position:0%
+uh um something else like
+ 
+
+ align:start position:0%
+uh um something else like
+ax so one operation might be if if
+
+ align:start position:0%
+ax so one operation might be if if
+ 
+
+ align:start position:0%
+ax so one operation might be if if
+there's an ace anywhere let's move it uh
+
+ align:start position:0%
+there's an ace anywhere let's move it uh
+ 
+
+ align:start position:0%
+there's an ace anywhere let's move it uh
+to the left that's that's just a simple
+
+ align:start position:0%
+to the left that's that's just a simple
+ 
+
+ align:start position:0%
+to the left that's that's just a simple
+production C uh anyway if you read my
+
+ align:start position:0%
+production C uh anyway if you read my
+ 
+
+ align:start position:0%
+production C uh anyway if you read my
+old book on
+
+ align:start position:0%
+old book on
+ 
+
+ align:start position:0%
+old book on
+computation there's a couple of chapters
+
+ align:start position:0%
+computation there's a couple of chapters
+ 
+
+ align:start position:0%
+computation there's a couple of chapters
+about production systems
+
+ align:start position:0%
+about production systems
+ 
+
+ align:start position:0%
+about production systems
+and uh those were
+
+ align:start position:0%
+and uh those were
+ 
+
+ align:start position:0%
+and uh those were
+the the first Universal logical systems
+
+ align:start position:0%
+the the first Universal logical systems
+ 
+
+ align:start position:0%
+the the first Universal logical systems
+that could be applied to computers so
+
+ align:start position:0%
+that could be applied to computers so
+ 
+
+ align:start position:0%
+that could be applied to computers so
+although there were no computers in the
+
+ align:start position:0%
+although there were no computers in the
+ 
+
+ align:start position:0%
+although there were no computers in the
+1920s when Amil post started working on
+
+ align:start position:0%
+1920s when Amil post started working on
+ 
+
+ align:start position:0%
+1920s when Amil post started working on
+that there had been some
+
+ align:start position:0%
+that there had been some
+ 
+
+ align:start position:0%
+that there had been some
+discussion uh back in 1900 or so when
+
+ align:start position:0%
+discussion uh back in 1900 or so when
+ 
+
+ align:start position:0%
+discussion uh back in 1900 or so when
+mathematicians like Hilbert uh who were
+
+ align:start position:0%
+mathematicians like Hilbert uh who were
+ 
+
+ align:start position:0%
+mathematicians like Hilbert uh who were
+interested both in Applied Mathematics
+
+ align:start position:0%
+interested both in Applied Mathematics
+ 
+
+ align:start position:0%
+interested both in Applied Mathematics
+and basic uh
+
+ align:start position:0%
+and basic uh
+ 
+
+ align:start position:0%
+and basic uh
+logic logic
+
+ align:start position:0%
+logic logic
+ 
+
+ align:start position:0%
+logic logic
+theories uh we're trying to say what
+
+ align:start position:0%
+theories uh we're trying to say what
+ 
+
+ align:start position:0%
+theories uh we're trying to say what
+kinds of processes can be represented by
+
+ align:start position:0%
+kinds of processes can be represented by
+ 
+
+ align:start position:0%
+kinds of processes can be represented by
+what kinds of algebraic or uh production
+
+ align:start position:0%
+what kinds of algebraic or uh production
+ 
+
+ align:start position:0%
+what kinds of algebraic or uh production
+like systems so so there was a lot of
+
+ align:start position:0%
+like systems so so there was a lot of
+ 
+
+ align:start position:0%
+like systems so so there was a lot of
+research before well not a lot but quite
+
+ align:start position:0%
+research before well not a lot but quite
+ 
+
+ align:start position:0%
+research before well not a lot but quite
+a bit of research before computers even
+
+ align:start position:0%
+a bit of research before computers even
+ 
+
+ align:start position:0%
+a bit of research before computers even
+appeared and in the
+
+ align:start position:0%
+appeared and in the
+ 
+
+ align:start position:0%
+appeared and in the
+1950s uh making rule-based
+
+ align:start position:0%
+1950s uh making rule-based
+ 
+
+ align:start position:0%
+1950s uh making rule-based
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+uh just out of uh transforming sequences
+
+ align:start position:0%
+uh just out of uh transforming sequences
+ 
+
+ align:start position:0%
+uh just out of uh transforming sequences
+of symbols became popular and uh that
+
+ align:start position:0%
+of symbols became popular and uh that
+ 
+
+ align:start position:0%
+of symbols became popular and uh that
+was fine because those systems are sort
+
+ align:start position:0%
+was fine because those systems are sort
+ 
+
+ align:start position:0%
+was fine because those systems are sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+universal however to make a
+
+ align:start position:0%
+universal however to make a
+ 
+
+ align:start position:0%
+universal however to make a
+uh a production system to play a good
+
+ align:start position:0%
+uh a production system to play a good
+ 
+
+ align:start position:0%
+uh a production system to play a good
+game of chess there might be some point
+
+ align:start position:0%
+game of chess there might be some point
+ 
+
+ align:start position:0%
+game of chess there might be some point
+at which just making rules saying if
+
+ align:start position:0%
+at which just making rules saying if
+ 
+
+ align:start position:0%
+at which just making rules saying if
+there's a pawn here and a queen here and
+
+ align:start position:0%
+there's a pawn here and a queen here and
+ 
+
+ align:start position:0%
+there's a pawn here and a queen here and
+a bishop here do this uh maybe you can't
+
+ align:start position:0%
+a bishop here do this uh maybe you can't
+ 
+
+ align:start position:0%
+a bishop here do this uh maybe you can't
+express things that way and you might
+
+ align:start position:0%
+express things that way and you might
+ 
+
+ align:start position:0%
+express things that way and you might
+have to have a higher level expression
+
+ align:start position:0%
+have to have a higher level expression
+ 
+
+ align:start position:0%
+have to have a higher level expression
+such as if two pieces are under attack
+
+ align:start position:0%
+such as if two pieces are under attack
+ 
+
+ align:start position:0%
+such as if two pieces are under attack
+at distant parts of the board then uh
+
+ align:start position:0%
+at distant parts of the board then uh
+ 
+
+ align:start position:0%
+at distant parts of the board then uh
+you should decide to make a move that
+
+ align:start position:0%
+you should decide to make a move that
+ 
+
+ align:start position:0%
+you should decide to make a move that
+improves your situation
+
+ align:start position:0%
+improves your situation
+ 
+
+ align:start position:0%
+improves your situation
+in in one what do you call these in one
+
+ align:start position:0%
+in in one what do you call these in one
+ 
+
+ align:start position:0%
+in in one what do you call these in one
+of these uh
+
+ align:start position:0%
+of these uh
+ 
+
+ align:start position:0%
+of these uh
+situations and blocks a way of the
+
+ align:start position:0%
+situations and blocks a way of the
+ 
+
+ align:start position:0%
+situations and blocks a way of the
+opponent improving his situation on the
+
+ align:start position:0%
+opponent improving his situation on the
+ 
+
+ align:start position:0%
+opponent improving his situation on the
+other one so you can't express that as a
+
+ align:start position:0%
+other one so you can't express that as a
+ 
+
+ align:start position:0%
+other one so you can't express that as a
+uh in terms of this position of the
+
+ align:start position:0%
+uh in terms of this position of the
+ 
+
+ align:start position:0%
+uh in terms of this position of the
+pieces you have to have a higher level
+
+ align:start position:0%
+pieces you have to have a higher level
+ 
+
+ align:start position:0%
+pieces you have to have a higher level
+abstraction and what happened in the
+
+ align:start position:0%
+abstraction and what happened in the
+ 
+
+ align:start position:0%
+abstraction and what happened in the
+development of rule-based systems is
+
+ align:start position:0%
+development of rule-based systems is
+ 
+
+ align:start position:0%
+development of rule-based systems is
+that you could make rules about rules
+
+ align:start position:0%
+that you could make rules about rules
+ 
+
+ align:start position:0%
+that you could make rules about rules
+but nobody ever got very good at it and
+
+ align:start position:0%
+but nobody ever got very good at it and
+ 
+
+ align:start position:0%
+but nobody ever got very good at it and
+you didn't
+
+ align:start position:0%
+you didn't
+ 
+
+ align:start position:0%
+you didn't
+find and you still don't find six level
+
+ align:start position:0%
+find and you still don't find six level
+ 
+
+ align:start position:0%
+find and you still don't find six level
+systems like the kind proposed in the in
+
+ align:start position:0%
+systems like the kind proposed in the in
+ 
+
+ align:start position:0%
+systems like the kind proposed in the in
+the Society of Mind book which says
+
+ align:start position:0%
+the Society of Mind book which says
+ 
+
+ align:start position:0%
+the Society of Mind book which says
+whatever you do you ought to have
+
+ align:start position:0%
+whatever you do you ought to have
+ 
+
+ align:start position:0%
+whatever you do you ought to have
+multiple
+
+ align:start position:0%
+multiple
+ 
+
+ align:start position:0%
+multiple
+levels uh and at the third or fourth
+
+ align:start position:0%
+levels uh and at the third or fourth
+ 
+
+ align:start position:0%
+levels uh and at the third or fourth
+level the system should have some
+
+ align:start position:0%
+level the system should have some
+ 
+
+ align:start position:0%
+level the system should have some
+reflective ability so that it's keeping
+
+ align:start position:0%
+reflective ability so that it's keeping
+ 
+
+ align:start position:0%
+reflective ability so that it's keeping
+track of how successful it's been at
+
+ align:start position:0%
+track of how successful it's been at
+ 
+
+ align:start position:0%
+track of how successful it's been at
+something that's a simple kind of
+
+ align:start position:0%
+something that's a simple kind of
+ 
+
+ align:start position:0%
+something that's a simple kind of
+learning or it's noticing that
+
+ align:start position:0%
+learning or it's noticing that
+ 
+
+ align:start position:0%
+learning or it's noticing that
+abstractions of a certain sort have been
+
+ align:start position:0%
+abstractions of a certain sort have been
+ 
+
+ align:start position:0%
+abstractions of a certain sort have been
+very productive in a certain kind of
+
+ align:start position:0%
+very productive in a certain kind of
+ 
+
+ align:start position:0%
+very productive in a certain kind of
+situation described by some other
+
+ align:start position:0%
+situation described by some other
+ 
+
+ align:start position:0%
+situation described by some other
+abstraction nobody's ever uh
+
+ align:start position:0%
+abstraction nobody's ever uh
+ 
+
+ align:start position:0%
+abstraction nobody's ever uh
+build any programs that go up four or
+
+ align:start position:0%
+build any programs that go up four or
+ 
+
+ align:start position:0%
+build any programs that go up four or
+five levels of that
+
+ align:start position:0%
+five levels of that
+ 
+
+ align:start position:0%
+five levels of that
+sort and I suppose the reason is that
+
+ align:start position:0%
+sort and I suppose the reason is that
+ 
+
+ align:start position:0%
+sort and I suppose the reason is that
+nobody uh virtually no one has a job
+
+ align:start position:0%
+nobody uh virtually no one has a job
+ 
+
+ align:start position:0%
+nobody uh virtually no one has a job
+where they could uh definitely plan to
+
+ align:start position:0%
+where they could uh definitely plan to
+ 
+
+ align:start position:0%
+where they could uh definitely plan to
+spend four or five years I think David
+
+ align:start position:0%
+spend four or five years I think David
+ 
+
+ align:start position:0%
+spend four or five years I think David
+here said he's did you say three or four
+
+ align:start position:0%
+here said he's did you say three or four
+ 
+
+ align:start position:0%
+here said he's did you say three or four
+years to to map out this animal that's
+
+ align:start position:0%
+years to to map out this animal that's
+ 
+
+ align:start position:0%
+years to to map out this animal that's
+my hope all right and then you should
+
+ align:start position:0%
+my hope all right and then you should
+ 
+
+ align:start position:0%
+my hope all right and then you should
+have a meta hope that you'll have such a
+
+ align:start position:0%
+have a meta hope that you'll have such a
+ 
+
+ align:start position:0%
+have a meta hope that you'll have such a
+good student or two that uh you'll only
+
+ align:start position:0%
+good student or two that uh you'll only
+ 
+
+ align:start position:0%
+good student or two that uh you'll only
+have to spend a year of it in this uh
+
+ align:start position:0%
+have to spend a year of it in this uh
+ 
+
+ align:start position:0%
+have to spend a year of it in this uh
+this young Richard green bladder bill
+
+ align:start position:0%
+this young Richard green bladder bill
+ 
+
+ align:start position:0%
+this young Richard green bladder bill
+gosper or uh Peter Samson will come up
+
+ align:start position:0%
+gosper or uh Peter Samson will come up
+ 
+
+ align:start position:0%
+gosper or uh Peter Samson will come up
+and you'll notice that he's better than
+
+ align:start position:0%
+and you'll notice that he's better than
+ 
+
+ align:start position:0%
+and you'll notice that he's better than
+you at this and that's the best thing
+
+ align:start position:0%
+you at this and that's the best thing
+ 
+
+ align:start position:0%
+you at this and that's the best thing
+and then you can uh quit and go to a
+
+ align:start position:0%
+and then you can uh quit and go to a
+ 
+
+ align:start position:0%
+and then you can uh quit and go to a
+higher level true but
+
+ align:start position:0%
+higher level true but
+ 
+
+ align:start position:0%
+higher level true but
+uh there aren't any jobs like
+
+ align:start position:0%
+uh there aren't any jobs like
+ 
+
+ align:start position:0%
+uh there aren't any jobs like
+that uh we had a lab sublab that split
+
+ align:start position:0%
+that uh we had a lab sublab that split
+ 
+
+ align:start position:0%
+that uh we had a lab sublab that split
+off from the media
+
+ align:start position:0%
+off from the media
+ 
+
+ align:start position:0%
+off from the media
+lab that uh I won't mention its name but
+
+ align:start position:0%
+lab that uh I won't mention its name but
+ 
+
+ align:start position:0%
+lab that uh I won't mention its name but
+its director got into the habit of
+
+ align:start position:0%
+its director got into the habit of
+ 
+
+ align:start position:0%
+its director got into the habit of
+wanning a progress report each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+month
+
+ align:start position:0%
+month
+ 
+
+ align:start position:0%
+month
+well uh when we were funded by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arpa there was something about a
+
+ align:start position:0%
+arpa there was something about a
+ 
+
+ align:start position:0%
+arpa there was something about a
+proposal each year and guess what our
+
+ align:start position:0%
+proposal each year and guess what our
+ 
+
+ align:start position:0%
+proposal each year and guess what our
+proposal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was anybody want to guess we intelligent
+
+ align:start position:0%
+was anybody want to guess we intelligent
+ 
+
+ align:start position:0%
+was anybody want to guess we intelligent
+machines it was what we had done we
+
+ align:start position:0%
+machines it was what we had done we
+ 
+
+ align:start position:0%
+machines it was what we had done we
+proposed to do what we had done last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+uh of course it's nice when when the
+
+ align:start position:0%
+uh of course it's nice when when the
+ 
+
+ align:start position:0%
+uh of course it's nice when when the
+head of the agency is an old buddy of
+
+ align:start position:0%
+head of the agency is an old buddy of
+ 
+
+ align:start position:0%
+head of the agency is an old buddy of
+yours from undergraduate years that was
+
+ align:start position:0%
+yours from undergraduate years that was
+ 
+
+ align:start position:0%
+yours from undergraduate years that was
+licklider but uh that worked out fine
+
+ align:start position:0%
+licklider but uh that worked out fine
+ 
+
+ align:start position:0%
+licklider but uh that worked out fine
+and so our proposals were in fact
+
+ align:start position:0%
+and so our proposals were in fact
+ 
+
+ align:start position:0%
+and so our proposals were in fact
+progress
+
+ align:start position:0%
+progress
+ 
+
+ align:start position:0%
+progress
+reports and
+
+ align:start position:0%
+reports and
+ 
+
+ align:start position:0%
+reports and
+uh that way uh you could do anything you
+
+ align:start position:0%
+uh that way uh you could do anything you
+ 
+
+ align:start position:0%
+uh that way uh you could do anything you
+want now if you had to do that every
+
+ align:start position:0%
+want now if you had to do that every
+ 
+
+ align:start position:0%
+want now if you had to do that every
+month then those uh proposals would
+
+ align:start position:0%
+month then those uh proposals would
+ 
+
+ align:start position:0%
+month then those uh proposals would
+would look so flimsy and sick that uh
+
+ align:start position:0%
+would look so flimsy and sick that uh
+ 
+
+ align:start position:0%
+would look so flimsy and sick that uh
+any good executive would say you should
+
+ align:start position:0%
+any good executive would say you should
+ 
+
+ align:start position:0%
+any good executive would say you should
+squash that project it's not getting
+
+ align:start position:0%
+squash that project it's not getting
+ 
+
+ align:start position:0%
+squash that project it's not getting
+anything done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I don't know how to fix that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U if we try to deal with
+
+ align:start position:0%
+U if we try to deal with
+ 
+
+ align:start position:0%
+U if we try to deal with
+the economic collapse of the
+
+ align:start position:0%
+the economic collapse of the
+ 
+
+ align:start position:0%
+the economic collapse of the
+civilization we're
+
+ align:start position:0%
+civilization we're
+ 
+
+ align:start position:0%
+civilization we're
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh we
+
+ align:start position:0%
+uh we
+ 
+
+ align:start position:0%
+uh we
+may it may be politically hard to have
+
+ align:start position:0%
+may it may be politically hard to have
+ 
+
+ align:start position:0%
+may it may be politically hard to have
+five or 10 year research projects so I
+
+ align:start position:0%
+five or 10 year research projects so I
+ 
+
+ align:start position:0%
+five or 10 year research projects so I
+have no idea what's going to happen
+
+ align:start position:0%
+have no idea what's going to happen
+ 
+
+ align:start position:0%
+have no idea what's going to happen
+in in the next decade
+
+ align:start position:0%
+in in the next decade
+ 
+
+ align:start position:0%
+in in the next decade
+yes so two questions one what do you
+
+ align:start position:0%
+yes so two questions one what do you
+ 
+
+ align:start position:0%
+yes so two questions one what do you
+think is the most effective format for
+
+ align:start position:0%
+think is the most effective format for
+ 
+
+ align:start position:0%
+think is the most effective format for
+people to make progress in is it in
+
+ align:start position:0%
+people to make progress in is it in
+ 
+
+ align:start position:0%
+people to make progress in is it in
+universities would it be within
+
+ align:start position:0%
+universities would it be within
+ 
+
+ align:start position:0%
+universities would it be within
+corporations like what I is doing or
+
+ align:start position:0%
+corporations like what I is doing or
+ 
+
+ align:start position:0%
+corporations like what I is doing or
+what and also who do you think should be
+
+ align:start position:0%
+what and also who do you think should be
+ 
+
+ align:start position:0%
+what and also who do you think should be
+working on these
+
+ align:start position:0%
+working on these
+ 
+
+ align:start position:0%
+working on these
+problems well the
+
+ align:start position:0%
+problems well the
+ 
+
+ align:start position:0%
+problems well the
+problem it looks like this
+
+ align:start position:0%
+problem it looks like this
+ 
+
+ align:start position:0%
+problem it looks like this
+uh what do you call the IBM
+
+ align:start position:0%
+uh what do you call the IBM
+ 
+
+ align:start position:0%
+uh what do you call the IBM
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+Watson that might be a good thing uh
+
+ align:start position:0%
+Watson that might be a good thing uh
+ 
+
+ align:start position:0%
+Watson that might be a good thing uh
+it's the
+
+ align:start position:0%
+it's the
+ 
+
+ align:start position:0%
+it's the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+uh substantial AI
+
+ align:start position:0%
+uh substantial AI
+ 
+
+ align:start position:0%
+uh substantial AI
+project uh that is trying to combine
+
+ align:start position:0%
+project uh that is trying to combine
+ 
+
+ align:start position:0%
+project uh that is trying to combine
+more than one method but I don't know I
+
+ align:start position:0%
+more than one method but I don't know I
+ 
+
+ align:start position:0%
+more than one method but I don't know I
+actually haven't read uh even what's
+
+ align:start position:0%
+actually haven't read uh even what's
+ 
+
+ align:start position:0%
+actually haven't read uh even what's
+available about it
+
+ align:start position:0%
+available about it
+ 
+
+ align:start position:0%
+available about it
+but uh IBM did have ai researchers for
+
+ align:start position:0%
+but uh IBM did have ai researchers for
+ 
+
+ align:start position:0%
+but uh IBM did have ai researchers for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there was a group in
+
+ align:start position:0%
+uh there was a group in
+ 
+
+ align:start position:0%
+uh there was a group in
+the middle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1950s you've all read about this uh
+
+ align:start position:0%
+1950s you've all read about this uh
+ 
+
+ align:start position:0%
+1950s you've all read about this uh
+Dartmouth AI conference in
+
+ align:start position:0%
+Dartmouth AI conference in
+ 
+
+ align:start position:0%
+Dartmouth AI conference in
+1954 and uh that
+
+ align:start position:0%
+1954 and uh that
+ 
+
+ align:start position:0%
+1954 and uh that
+had uh McCarthy and me from around
+
+ align:start position:0%
+had uh McCarthy and me from around
+ 
+
+ align:start position:0%
+had uh McCarthy and me from around
+around here and Newell and Simon who
+
+ align:start position:0%
+around here and Newell and Simon who
+ 
+
+ align:start position:0%
+around here and Newell and Simon who
+were at Carnegie
+
+ align:start position:0%
+were at Carnegie
+ 
+
+ align:start position:0%
+were at Carnegie
+melon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I think it was called Carnegie
+
+ align:start position:0%
+uh I think it was called Carnegie
+ 
+
+ align:start position:0%
+uh I think it was called Carnegie
+Institute of Technology then but
+
+ align:start position:0%
+Institute of Technology then but
+ 
+
+ align:start position:0%
+Institute of Technology then but
+whatever and uh it had a couple of
+
+ align:start position:0%
+whatever and uh it had a couple of
+ 
+
+ align:start position:0%
+whatever and uh it had a couple of
+people from IBM and it had about six or
+
+ align:start position:0%
+people from IBM and it had about six or
+ 
+
+ align:start position:0%
+people from IBM and it had about six or
+seven assorted
+
+ align:start position:0%
+seven assorted
+ 
+
+ align:start position:0%
+seven assorted
+individuals um from here and there so
+
+ align:start position:0%
+individuals um from here and there so
+ 
+
+ align:start position:0%
+individuals um from here and there so
+IBM uh had a guy named Nat Roch who had
+
+ align:start position:0%
+IBM uh had a guy named Nat Roch who had
+ 
+
+ align:start position:0%
+IBM uh had a guy named Nat Roch who had
+been involved in
+
+ align:start position:0%
+been involved in
+ 
+
+ align:start position:0%
+been involved in
+designing
+
+ align:start position:0%
+designing
+ 
+
+ align:start position:0%
+designing
+computers and he had a lot of good
+
+ align:start position:0%
+computers and he had a lot of good
+ 
+
+ align:start position:0%
+computers and he had a lot of good
+ideas and uh I had written a on paper a
+
+ align:start position:0%
+ideas and uh I had written a on paper a
+ 
+
+ align:start position:0%
+ideas and uh I had written a on paper a
+geometry theorem proving program and he
+
+ align:start position:0%
+geometry theorem proving program and he
+ 
+
+ align:start position:0%
+geometry theorem proving program and he
+started a project to actually put that
+
+ align:start position:0%
+started a project to actually put that
+ 
+
+ align:start position:0%
+started a project to actually put that
+on a computer and it uh so for a few
+
+ align:start position:0%
+on a computer and it uh so for a few
+ 
+
+ align:start position:0%
+on a computer and it uh so for a few
+years IBM had a few people working
+
+ align:start position:0%
+years IBM had a few people working
+ 
+
+ align:start position:0%
+years IBM had a few people working
+on uh different small AI projects
+
+ align:start position:0%
+on uh different small AI projects
+ 
+
+ align:start position:0%
+on uh different small AI projects
+then that
+
+ align:start position:0%
+then that
+ 
+
+ align:start position:0%
+then that
+disappeared after about 10 or 15 years
+
+ align:start position:0%
+disappeared after about 10 or 15 years
+ 
+
+ align:start position:0%
+disappeared after about 10 or 15 years
+and there was essentially no artificial
+
+ align:start position:0%
+and there was essentially no artificial
+ 
+
+ align:start position:0%
+and there was essentially no artificial
+very little programming research at IBM
+
+ align:start position:0%
+very little programming research at IBM
+ 
+
+ align:start position:0%
+very little programming research at IBM
+and they were mostly into hardware and
+
+ align:start position:0%
+and they were mostly into hardware and
+ 
+
+ align:start position:0%
+and they were mostly into hardware and
+Commercial software so
+
+ align:start position:0%
+Commercial software so
+ 
+
+ align:start position:0%
+Commercial software so
+forth uh this Watson thing is apparently
+
+ align:start position:0%
+forth uh this Watson thing is apparently
+ 
+
+ align:start position:0%
+forth uh this Watson thing is apparently
+three or four years old and it looks
+
+ align:start position:0%
+three or four years old and it looks
+ 
+
+ align:start position:0%
+three or four years old and it looks
+like a substantial project and I'm a
+
+ align:start position:0%
+like a substantial project and I'm a
+ 
+
+ align:start position:0%
+like a substantial project and I'm a
+little worried that uh since they're not
+
+ align:start position:0%
+little worried that uh since they're not
+ 
+
+ align:start position:0%
+little worried that uh since they're not
+very academic they might not have the
+
+ align:start position:0%
+very academic they might not have the
+ 
+
+ align:start position:0%
+very academic they might not have the
+idea that if you've discovered something
+
+ align:start position:0%
+idea that if you've discovered something
+ 
+
+ align:start position:0%
+idea that if you've discovered something
+the first thing you should do is publish
+
+ align:start position:0%
+the first thing you should do is publish
+ 
+
+ align:start position:0%
+the first thing you should do is publish
+all its details so that you get credit
+
+ align:start position:0%
+all its details so that you get credit
+ 
+
+ align:start position:0%
+all its details so that you get credit
+for it well
+
+ align:start position:0%
+for it well
+ 
+
+ align:start position:0%
+for it well
+uh it's hard not very many companies
+
+ align:start position:0%
+uh it's hard not very many companies
+ 
+
+ align:start position:0%
+uh it's hard not very many companies
+encourage the individuals getting credit
+
+ align:start position:0%
+encourage the individuals getting credit
+ 
+
+ align:start position:0%
+encourage the individuals getting credit
+and it looks like uh the guys in that
+
+ align:start position:0%
+and it looks like uh the guys in that
+ 
+
+ align:start position:0%
+and it looks like uh the guys in that
+project are are able to publish a
+
+ align:start position:0%
+project are are able to publish a
+ 
+
+ align:start position:0%
+project are are able to publish a
+substantial amount
+
+ align:start position:0%
+substantial amount
+ 
+
+ align:start position:0%
+substantial amount
+but I think the first sign of uh first
+
+ align:start position:0%
+but I think the first sign of uh first
+ 
+
+ align:start position:0%
+but I think the first sign of uh first
+good sign will be if they uh just dump
+
+ align:start position:0%
+good sign will be if they uh just dump
+ 
+
+ align:start position:0%
+good sign will be if they uh just dump
+their code out too and uh let people go
+
+ align:start position:0%
+their code out too and uh let people go
+ 
+
+ align:start position:0%
+their code out too and uh let people go
+over it and copy it and see if see if
+
+ align:start position:0%
+over it and copy it and see if see if
+ 
+
+ align:start position:0%
+over it and copy it and see if see if
+there's anything there they can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use it's very rare for any AI researcher
+
+ align:start position:0%
+use it's very rare for any AI researcher
+ 
+
+ align:start position:0%
+use it's very rare for any AI researcher
+to use anyone else's code as far as I
+
+ align:start position:0%
+to use anyone else's code as far as I
+ 
+
+ align:start position:0%
+to use anyone else's code as far as I
+know it's almost never
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happened I don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know the best example almost was
+
+ align:start position:0%
+know the best example almost was
+ 
+
+ align:start position:0%
+know the best example almost was
+Winter's Shido program which uh was
+
+ align:start position:0%
+Winter's Shido program which uh was
+ 
+
+ align:start position:0%
+Winter's Shido program which uh was
+exported to Carnegie melon and to
+
+ align:start position:0%
+exported to Carnegie melon and to
+ 
+
+ align:start position:0%
+exported to Carnegie melon and to
+Stanford and both of them uh ran ran
+
+ align:start position:0%
+Stanford and both of them uh ran ran
+ 
+
+ align:start position:0%
+Stanford and both of them uh ran ran
+that program quite a bit but it wasn't I
+
+ align:start position:0%
+that program quite a bit but it wasn't I
+ 
+
+ align:start position:0%
+that program quite a bit but it wasn't I
+don't know why why it it died but
+
+ align:start position:0%
+don't know why why it it died but
+ 
+
+ align:start position:0%
+don't know why why it it died but
+apparently winegrad himself hadn't
+
+ align:start position:0%
+apparently winegrad himself hadn't
+ 
+
+ align:start position:0%
+apparently winegrad himself hadn't
+commented enough to remember how it
+
+ align:start position:0%
+commented enough to remember how it
+ 
+
+ align:start position:0%
+commented enough to remember how it
+worked and uh the beginners uh
+
+ align:start position:0%
+worked and uh the beginners uh
+ 
+
+ align:start position:0%
+worked and uh the beginners uh
+never uh got very far in improving
+
+ align:start position:0%
+never uh got very far in improving
+ 
+
+ align:start position:0%
+never uh got very far in improving
+either its robotic ability which
+
+ align:start position:0%
+either its robotic ability which
+ 
+
+ align:start position:0%
+either its robotic ability which
+was uh non-trivial or its linguistic
+
+ align:start position:0%
+was uh non-trivial or its linguistic
+ 
+
+ align:start position:0%
+was uh non-trivial or its linguistic
+ability which was unique uh it had
+
+ align:start position:0%
+ability which was unique uh it had
+ 
+
+ align:start position:0%
+ability which was unique uh it had
+better parsers and better semantic
+
+ align:start position:0%
+better parsers and better semantic
+ 
+
+ align:start position:0%
+better parsers and better semantic
+operations if only for a limited blocks
+
+ align:start position:0%
+operations if only for a limited blocks
+ 
+
+ align:start position:0%
+operations if only for a limited blocks
+Sr put the big red block on top of the
+
+ align:start position:0%
+Sr put the big red block on top of the
+ 
+
+ align:start position:0%
+Sr put the big red block on top of the
+little green block and uh it would do
+
+ align:start position:0%
+little green block and uh it would do
+ 
+
+ align:start position:0%
+little green block and uh it would do
+things like that so it
+
+ align:start position:0%
+things like that so it
+ 
+
+ align:start position:0%
+things like that so it
+uh and you could say put the block which
+
+ align:start position:0%
+uh and you could say put the block which
+ 
+
+ align:start position:0%
+uh and you could say put the block which
+is on top of the big red
+
+ align:start position:0%
+is on top of the big red
+ 
+
+ align:start position:0%
+is on top of the big red
+block uh and do such and such with it so
+
+ align:start position:0%
+block uh and do such and such with it so
+ 
+
+ align:start position:0%
+block uh and do such and such with it so
+it had uh fairly complicated ways to
+
+ align:start position:0%
+it had uh fairly complicated ways to
+ 
+
+ align:start position:0%
+it had uh fairly complicated ways to
+refer and refer to and describe things
+
+ align:start position:0%
+refer and refer to and describe things
+ 
+
+ align:start position:0%
+refer and refer to and describe things
+uh but it became a showpiece where you
+
+ align:start position:0%
+uh but it became a showpiece where you
+ 
+
+ align:start position:0%
+uh but it became a showpiece where you
+you could demonstrated it and after a
+
+ align:start position:0%
+you could demonstrated it and after a
+ 
+
+ align:start position:0%
+you could demonstrated it and after a
+few years uh you couldn't even has
+
+ align:start position:0%
+few years uh you couldn't even has
+ 
+
+ align:start position:0%
+few years uh you couldn't even has
+anyone tried
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I haven't I've looked into it but it
+
+ align:start position:0%
+it I haven't I've looked into it but it
+ 
+
+ align:start position:0%
+it I haven't I've looked into it but it
+it's I mean it's in Mac list so it's not
+
+ align:start position:0%
+it's I mean it's in Mac list so it's not
+ 
+
+ align:start position:0%
+it's I mean it's in Mac list so it's not
+even there isn't even have to run it so
+
+ align:start position:0%
+even there isn't even have to run it so
+ 
+
+ align:start position:0%
+even there isn't even have to run it so
+there's no interpreter to run it yeah it
+
+ align:start position:0%
+there's no interpreter to run it yeah it
+ 
+
+ align:start position:0%
+there's no interpreter to run it yeah it
+should have had the whole package of
+
+ align:start position:0%
+should have had the whole package of
+ 
+
+ align:start position:0%
+should have had the whole package of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+but because that program was big and
+
+ align:start position:0%
+but because that program was big and
+ 
+
+ align:start position:0%
+but because that program was big and
+maist would have only been 2% of the
+
+ align:start position:0%
+maist would have only been 2% of the
+ 
+
+ align:start position:0%
+maist would have only been 2% of the
+right the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing when you gret had quite a number
+
+ align:start position:0%
+thing when you gret had quite a number
+ 
+
+ align:start position:0%
+thing when you gret had quite a number
+of graduate students who finally left
+
+ align:start position:0%
+of graduate students who finally left
+ 
+
+ align:start position:0%
+of graduate students who finally left
+and did something else
+
+ align:start position:0%
+and did something else
+ 
+
+ align:start position:0%
+and did something else
+because the project was they just found
+
+ align:start position:0%
+because the project was they just found
+ 
+
+ align:start position:0%
+because the project was they just found
+it too hard to understand the code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but who has an idea what to do next
+
+ align:start position:0%
+but who has an idea what to do next
+ 
+
+ align:start position:0%
+but who has an idea what to do next
+that's I bet you all have
+
+ align:start position:0%
+that's I bet you all have
+ 
+
+ align:start position:0%
+that's I bet you all have
+some fantasy of how to make machines
+
+ align:start position:0%
+some fantasy of how to make machines
+ 
+
+ align:start position:0%
+some fantasy of how to make machines
+smarter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could wake for the human brain
+
+ align:start position:0%
+you could wake for the human brain
+ 
+
+ align:start position:0%
+you could wake for the human brain
+people to
+
+ align:start position:0%
+people to
+ 
+
+ align:start position:0%
+people to
+yes I was thinking you could get more
+
+ align:start position:0%
+yes I was thinking you could get more
+ 
+
+ align:start position:0%
+yes I was thinking you could get more
+funding for science fiction
+
+ align:start position:0%
+funding for science fiction
+ 
+
+ align:start position:0%
+funding for science fiction
+writers and then hopefully one of them
+
+ align:start position:0%
+writers and then hopefully one of them
+ 
+
+ align:start position:0%
+writers and then hopefully one of them
+will come up with a brilliant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea ah yes Greg Egan had a
+
+ align:start position:0%
+idea ah yes Greg Egan had a
+ 
+
+ align:start position:0%
+idea ah yes Greg Egan had a
+computer how many of you know the name
+
+ align:start position:0%
+computer how many of you know the name
+ 
+
+ align:start position:0%
+computer how many of you know the name
+of Greg
+
+ align:start position:0%
+of Greg
+ 
+
+ align:start position:0%
+of Greg
+Egan uh look at
+
+ align:start position:0%
+Egan uh look at
+ 
+
+ align:start position:0%
+Egan uh look at
+his his web page has more exciting
+
+ align:start position:0%
+his his web page has more exciting
+ 
+
+ align:start position:0%
+his his web page has more exciting
+mathematical demonstrations and is as
+
+ align:start position:0%
+mathematical demonstrations and is as
+ 
+
+ align:start position:0%
+mathematical demonstrations and is as
+far as I know I've never I don't know
+
+ align:start position:0%
+far as I know I've never I don't know
+ 
+
+ align:start position:0%
+far as I know I've never I don't know
+anything like it uh well yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh Ken
+
+ align:start position:0%
+uh Ken
+ 
+
+ align:start position:0%
+uh Ken
+plin uh type Ken perlin into your Google
+
+ align:start position:0%
+plin uh type Ken perlin into your Google
+ 
+
+ align:start position:0%
+plin uh type Ken perlin into your Google
+and get his web page and he
+
+ align:start position:0%
+and get his web page and he
+ 
+
+ align:start position:0%
+and get his web page and he
+has I think he must invent two or three
+
+ align:start position:0%
+has I think he must invent two or three
+ 
+
+ align:start position:0%
+has I think he must invent two or three
+incredibly brilliant small programs
+
+ align:start position:0%
+incredibly brilliant small programs
+ 
+
+ align:start position:0%
+incredibly brilliant small programs
+every week because there are quite a few
+
+ align:start position:0%
+every week because there are quite a few
+ 
+
+ align:start position:0%
+every week because there are quite a few
+hundred of these gorgeous demonstrations
+
+ align:start position:0%
+hundred of these gorgeous demonstrations
+ 
+
+ align:start position:0%
+hundred of these gorgeous demonstrations
+of one principle after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another oh
+
+ align:start position:0%
+another oh
+ 
+
+ align:start position:0%
+another oh
+dear I didn't look ahead
+
+ align:start position:0%
+dear I didn't look ahead
+ 
+
+ align:start position:0%
+dear I didn't look ahead
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another feature of Greg Egan is that he
+
+ align:start position:0%
+another feature of Greg Egan is that he
+ 
+
+ align:start position:0%
+another feature of Greg Egan is that he
+read the Society of Mind and worked a
+
+ align:start position:0%
+read the Society of Mind and worked a
+ 
+
+ align:start position:0%
+read the Society of Mind and worked a
+lot of ideas that I hadn't thought of
+
+ align:start position:0%
+lot of ideas that I hadn't thought of
+ 
+
+ align:start position:0%
+lot of ideas that I hadn't thought of
+into some of his stories so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but another feature of him is that no
+
+ align:start position:0%
+but another feature of him is that no
+ 
+
+ align:start position:0%
+but another feature of him is that no
+one has ever met
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+him uh that is if you knock on his door
+
+ align:start position:0%
+him uh that is if you knock on his door
+ 
+
+ align:start position:0%
+him uh that is if you knock on his door
+which is in Perth it he won't answer
+
+ align:start position:0%
+which is in Perth it he won't answer
+ 
+
+ align:start position:0%
+which is in Perth it he won't answer
+and uh I was discussing this with Greg
+
+ align:start position:0%
+and uh I was discussing this with Greg
+ 
+
+ align:start position:0%
+and uh I was discussing this with Greg
+Benford apparently there are a couple of
+
+ align:start position:0%
+Benford apparently there are a couple of
+ 
+
+ align:start position:0%
+Benford apparently there are a couple of
+people who have seen him but uh nobody
+
+ align:start position:0%
+people who have seen him but uh nobody
+ 
+
+ align:start position:0%
+people who have seen him but uh nobody
+knows anyone who knows him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could do
+
+ align:start position:0%
+you could do
+ 
+
+ align:start position:0%
+you could do
+that maybe that's the way to get a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done uh make a list of all your friends
+
+ align:start position:0%
+done uh make a list of all your friends
+ 
+
+ align:start position:0%
+done uh make a list of all your friends
+and abandon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them just think of all the free time
+
+ align:start position:0%
+them just think of all the free time
+ 
+
+ align:start position:0%
+them just think of all the free time
+you'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have there any other Gregs oh well Greg
+
+ align:start position:0%
+have there any other Gregs oh well Greg
+ 
+
+ align:start position:0%
+have there any other Gregs oh well Greg
+Benford
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this isn't fair I've lost the big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chalk among the science fiction writers
+
+ align:start position:0%
+chalk among the science fiction writers
+ 
+
+ align:start position:0%
+chalk among the science fiction writers
+there are only a few who actually know a
+
+ align:start position:0%
+there are only a few who actually know a
+ 
+
+ align:start position:0%
+there are only a few who actually know a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+uh uh Benford is quite a good physicist
+
+ align:start position:0%
+uh uh Benford is quite a good physicist
+ 
+
+ align:start position:0%
+uh uh Benford is quite a good physicist
+and uh knows a lot and publishes serious
+
+ align:start position:0%
+and uh knows a lot and publishes serious
+ 
+
+ align:start position:0%
+and uh knows a lot and publishes serious
+physics
+
+ align:start position:0%
+physics
+ 
+
+ align:start position:0%
+physics
+papers um Larry
+
+ align:start position:0%
+papers um Larry
+ 
+
+ align:start position:0%
+papers um Larry
+nien uh knew quite a bit of science but
+
+ align:start position:0%
+nien uh knew quite a bit of science but
+ 
+
+ align:start position:0%
+nien uh knew quite a bit of science but
+uh was never practicing one and so in
+
+ align:start position:0%
+uh was never practicing one and so in
+ 
+
+ align:start position:0%
+uh was never practicing one and so in
+His science fiction there occasional
+
+ align:start position:0%
+His science fiction there occasional
+ 
+
+ align:start position:0%
+His science fiction there occasional
+technical
+
+ align:start position:0%
+technical
+ 
+
+ align:start position:0%
+technical
+errors like in Ring
+
+ align:start position:0%
+errors like in Ring
+ 
+
+ align:start position:0%
+errors like in Ring
+World ring world was a big ring
+
+ align:start position:0%
+World ring world was a big ring
+ 
+
+ align:start position:0%
+World ring world was a big ring
+shaped planet around the
+
+ align:start position:0%
+shaped planet around the
+ 
+
+ align:start position:0%
+shaped planet around the
+Sun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so here's the Sun and here's this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ring and the ring is about 8,000 miles
+
+ align:start position:0%
+ring and the ring is about 8,000 miles
+ 
+
+ align:start position:0%
+ring and the ring is about 8,000 miles
+wide and goes all the way around uh its
+
+ align:start position:0%
+wide and goes all the way around uh its
+ 
+
+ align:start position:0%
+wide and goes all the way around uh its
+sun in something like Earth's
+
+ align:start position:0%
+sun in something like Earth's
+ 
+
+ align:start position:0%
+sun in something like Earth's
+orbit uh which means that it has an area
+
+ align:start position:0%
+orbit uh which means that it has an area
+ 
+
+ align:start position:0%
+orbit uh which means that it has an area
+of the orbit
+
+ align:start position:0%
+of the orbit
+ 
+
+ align:start position:0%
+of the orbit
+of 100,000
+
+ align:start position:0%
+of 100,000
+ 
+
+ align:start position:0%
+of 100,000
+Earths U well Larry didn't realize that
+
+ align:start position:0%
+Earths U well Larry didn't realize that
+ 
+
+ align:start position:0%
+Earths U well Larry didn't realize that
+there was a
+
+ align:start position:0%
+there was a
+ 
+
+ align:start position:0%
+there was a
+bug and
+
+ align:start position:0%
+bug and
+ 
+
+ align:start position:0%
+bug and
+uh if you make a ring that's rotating
+
+ align:start position:0%
+uh if you make a ring that's rotating
+ 
+
+ align:start position:0%
+uh if you make a ring that's rotating
+around the Sun well first of all there's
+
+ align:start position:0%
+around the Sun well first of all there's
+ 
+
+ align:start position:0%
+around the Sun well first of all there's
+no particular reason why it should
+
+ align:start position:0%
+no particular reason why it should
+ 
+
+ align:start position:0%
+no particular reason why it should
+rotate uh but uh if it didn't it would
+
+ align:start position:0%
+rotate uh but uh if it didn't it would
+ 
+
+ align:start position:0%
+rotate uh but uh if it didn't it would
+squash
+
+ align:start position:0%
+squash
+ 
+
+ align:start position:0%
+squash
+uh but it's not gravitationally stable
+
+ align:start position:0%
+uh but it's not gravitationally stable
+ 
+
+ align:start position:0%
+uh but it's not gravitationally stable
+so as soon as it gets slightly off
+
+ align:start position:0%
+so as soon as it gets slightly off
+ 
+
+ align:start position:0%
+so as soon as it gets slightly off
+center then uh this part if this is
+
+ align:start position:0%
+center then uh this part if this is
+ 
+
+ align:start position:0%
+center then uh this part if this is
+closer it gets folded in and so finally
+
+ align:start position:0%
+closer it gets folded in and so finally
+ 
+
+ align:start position:0%
+closer it gets folded in and so finally
+one part of it falls into the sun and
+
+ align:start position:0%
+one part of it falls into the sun and
+ 
+
+ align:start position:0%
+one part of it falls into the sun and
+the rest follows it so in the sequel to
+
+ align:start position:0%
+the rest follows it so in the sequel to
+ 
+
+ align:start position:0%
+the rest follows it so in the sequel to
+Ring World some physicist pointed this
+
+ align:start position:0%
+Ring World some physicist pointed this
+ 
+
+ align:start position:0%
+Ring World some physicist pointed this
+out to Larry Nan and
+
+ align:start position:0%
+out to Larry Nan and
+ 
+
+ align:start position:0%
+out to Larry Nan and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh now Larry nien
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had he had little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wires I forget what they're connected to
+
+ align:start position:0%
+wires I forget what they're connected to
+ 
+
+ align:start position:0%
+wires I forget what they're connected to
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+anybody they're made of something called
+
+ align:start position:0%
+anybody they're made of something called
+ 
+
+ align:start position:0%
+anybody they're made of something called
+scri which is 10 to the 50th times
+
+ align:start position:0%
+scri which is 10 to the 50th times
+ 
+
+ align:start position:0%
+scri which is 10 to the 50th times
+stronger than anything
+
+ align:start position:0%
+stronger than anything
+ 
+
+ align:start position:0%
+stronger than anything
+real because it's pretty hard to hold
+
+ align:start position:0%
+real because it's pretty hard to hold
+ 
+
+ align:start position:0%
+real because it's pretty hard to hold
+the thing that
+
+ align:start position:0%
+the thing that
+ 
+
+ align:start position:0%
+the thing that
+massive and so oh oh then they're little
+
+ align:start position:0%
+massive and so oh oh then they're little
+ 
+
+ align:start position:0%
+massive and so oh oh then they're little
+Jets which have been built by the
+
+ align:start position:0%
+Jets which have been built by the
+ 
+
+ align:start position:0%
+Jets which have been built by the
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+inhabitants now forgot all the geometry
+
+ align:start position:0%
+inhabitants now forgot all the geometry
+ 
+
+ align:start position:0%
+inhabitants now forgot all the geometry
+but uh so now there's an active system
+
+ align:start position:0%
+but uh so now there's an active system
+ 
+
+ align:start position:0%
+but uh so now there's an active system
+for maintaining the Ring World to not
+
+ align:start position:0%
+for maintaining the Ring World to not
+ 
+
+ align:start position:0%
+for maintaining the Ring World to not
+fall into the sun and the sequel the uh
+
+ align:start position:0%
+fall into the sun and the sequel the uh
+ 
+
+ align:start position:0%
+fall into the sun and the sequel the uh
+this was built by some disappeared
+
+ align:start position:0%
+this was built by some disappeared
+ 
+
+ align:start position:0%
+this was built by some disappeared
+aliens millions of years ago and the
+
+ align:start position:0%
+aliens millions of years ago and the
+ 
+
+ align:start position:0%
+aliens millions of years ago and the
+hardware is beginning to break down so
+
+ align:start position:0%
+hardware is beginning to break down so
+ 
+
+ align:start position:0%
+hardware is beginning to break down so
+they need to find an alien race with
+
+ align:start position:0%
+they need to find an alien race with
+ 
+
+ align:start position:0%
+they need to find an alien race with
+enough engineering to fix it and blah
+
+ align:start position:0%
+enough engineering to fix it and blah
+ 
+
+ align:start position:0%
+enough engineering to fix it and blah
+blah any anyway Larry nien is awfully
+
+ align:start position:0%
+blah any anyway Larry nien is awfully
+ 
+
+ align:start position:0%
+blah any anyway Larry nien is awfully
+good at making up things with a pretty
+
+ align:start position:0%
+good at making up things with a pretty
+ 
+
+ align:start position:0%
+good at making up things with a pretty
+good scientific
+
+ align:start position:0%
+good scientific
+ 
+
+ align:start position:0%
+good scientific
+background and then when he makes a
+
+ align:start position:0%
+background and then when he makes a
+ 
+
+ align:start position:0%
+background and then when he makes a
+mistake uh he writes a sequel to correct
+
+ align:start position:0%
+mistake uh he writes a sequel to correct
+ 
+
+ align:start position:0%
+mistake uh he writes a sequel to correct
+it so uh maybe that's actually better
+
+ align:start position:0%
+it so uh maybe that's actually better
+ 
+
+ align:start position:0%
+it so uh maybe that's actually better
+than getting it right the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time he has a machine you know the
+
+ align:start position:0%
+time he has a machine you know the
+ 
+
+ align:start position:0%
+time he has a machine you know the
+Transporters in Star Trek
+
+ align:start position:0%
+Transporters in Star Trek
+ 
+
+ align:start position:0%
+Transporters in Star Trek
+uh nien Transporters are nice because
+
+ align:start position:0%
+uh nien Transporters are nice because
+ 
+
+ align:start position:0%
+uh nien Transporters are nice because
+they take out all the
+
+ align:start position:0%
+they take out all the
+ 
+
+ align:start position:0%
+they take out all the
+chemicals uh in your cells that
+
+ align:start position:0%
+chemicals uh in your cells that
+ 
+
+ align:start position:0%
+chemicals uh in your cells that
+shouldn't be there so once they have
+
+ align:start position:0%
+shouldn't be there so once they have
+ 
+
+ align:start position:0%
+shouldn't be there so once they have
+Transporters automatically the people
+
+ align:start position:0%
+Transporters automatically the people
+ 
+
+ align:start position:0%
+Transporters automatically the people
+now become nearly Immortal because if
+
+ align:start position:0%
+now become nearly Immortal because if
+ 
+
+ align:start position:0%
+now become nearly Immortal because if
+you're being scanned and reconstructed
+
+ align:start position:0%
+you're being scanned and reconstructed
+ 
+
+ align:start position:0%
+you're being scanned and reconstructed
+by a transporter it might as well fix
+
+ align:start position:0%
+by a transporter it might as well fix
+ 
+
+ align:start position:0%
+by a transporter it might as well fix
+all your bugs while it's at
+
+ align:start position:0%
+all your bugs while it's at
+ 
+
+ align:start position:0%
+all your bugs while it's at
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so and anyway uh there's a good idea on
+
+ align:start position:0%
+so and anyway uh there's a good idea on
+ 
+
+ align:start position:0%
+so and anyway uh there's a good idea on
+every page of this guy uh even if it's
+
+ align:start position:0%
+every page of this guy uh even if it's
+ 
+
+ align:start position:0%
+every page of this guy uh even if it's
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+so when I read a regular
+
+ align:start position:0%
+so when I read a regular
+ 
+
+ align:start position:0%
+so when I read a regular
+novel which is very rare there's usually
+
+ align:start position:0%
+novel which is very rare there's usually
+ 
+
+ align:start position:0%
+novel which is very rare there's usually
+a good idea every chapter
+
+ align:start position:0%
+a good idea every chapter
+ 
+
+ align:start position:0%
+a good idea every chapter
+maybe but
+
+ align:start position:0%
+maybe but
+ 
+
+ align:start position:0%
+maybe but
+uh I didn't write Larry nen's name
+
+ align:start position:0%
+uh I didn't write Larry nen's name
+ 
+
+ align:start position:0%
+uh I didn't write Larry nen's name
+probably he had more ideas than any
+
+ align:start position:0%
+probably he had more ideas than any
+ 
+
+ align:start position:0%
+probably he had more ideas than any
+other writer but they're not all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct so how many of you are going to
+
+ align:start position:0%
+correct so how many of you are going to
+ 
+
+ align:start position:0%
+correct so how many of you are going to
+pursue AI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or are you going to work on trying to
+
+ align:start position:0%
+or are you going to work on trying to
+ 
+
+ align:start position:0%
+or are you going to work on trying to
+make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smarter here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one we sure could use
+
+ align:start position:0%
+one we sure could use
+ 
+
+ align:start position:0%
+one we sure could use
+them I'm sort of amused at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the there are a couple of
+
+ align:start position:0%
+uh the there are a couple of
+ 
+
+ align:start position:0%
+uh the there are a couple of
+transhumanist communities whatever that
+
+ align:start position:0%
+transhumanist communities whatever that
+ 
+
+ align:start position:0%
+transhumanist communities whatever that
+means and they're worried that the AI
+
+ align:start position:0%
+means and they're worried that the AI
+ 
+
+ align:start position:0%
+means and they're worried that the AI
+will uh as many science fiction writers
+
+ align:start position:0%
+will uh as many science fiction writers
+ 
+
+ align:start position:0%
+will uh as many science fiction writers
+have uh be hostile and take over and uh
+
+ align:start position:0%
+have uh be hostile and take over and uh
+ 
+
+ align:start position:0%
+have uh be hostile and take over and uh
+want everything for itself and so uh
+
+ align:start position:0%
+want everything for itself and so uh
+ 
+
+ align:start position:0%
+want everything for itself and so uh
+there are serious discussions on how to
+
+ align:start position:0%
+there are serious discussions on how to
+ 
+
+ align:start position:0%
+there are serious discussions on how to
+make friendly
+
+ align:start position:0%
+make friendly
+ 
+
+ align:start position:0%
+make friendly
+AIS and of course the master of that was
+
+ align:start position:0%
+AIS and of course the master of that was
+ 
+
+ align:start position:0%
+AIS and of course the master of that was
+Isaac
+
+ align:start position:0%
+Isaac
+ 
+
+ align:start position:0%
+Isaac
+aimof who said that uh a robot should
+
+ align:start position:0%
+aimof who said that uh a robot should
+ 
+
+ align:start position:0%
+aimof who said that uh a robot should
+always put its
+
+ align:start position:0%
+always put its
+ 
+
+ align:start position:0%
+always put its
+interests uh beneath those of its owner
+
+ align:start position:0%
+interests uh beneath those of its owner
+ 
+
+ align:start position:0%
+interests uh beneath those of its owner
+or whatever how many of you know
+
+ align:start position:0%
+or whatever how many of you know
+ 
+
+ align:start position:0%
+or whatever how many of you know
+asimov's
+
+ align:start position:0%
+asimov's
+ 
+
+ align:start position:0%
+asimov's
+laws and then there was the fourth law
+
+ align:start position:0%
+laws and then there was the fourth law
+ 
+
+ align:start position:0%
+laws and then there was the fourth law
+that he
+
+ align:start position:0%
+that he
+ 
+
+ align:start position:0%
+that he
+had to make which is that it's all right
+
+ align:start position:0%
+had to make which is that it's all right
+ 
+
+ align:start position:0%
+had to make which is that it's all right
+to harm a human if if if it's to save a
+
+ align:start position:0%
+to harm a human if if if it's to save a
+ 
+
+ align:start position:0%
+to harm a human if if if it's to save a
+large number of
+
+ align:start position:0%
+large number of
+ 
+
+ align:start position:0%
+large number of
+others uh from being harmed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and but you know
+
+ align:start position:0%
+and but you know
+ 
+
+ align:start position:0%
+and but you know
+uh it's like saying we shouldn't eat
+
+ align:start position:0%
+uh it's like saying we shouldn't eat
+ 
+
+ align:start position:0%
+uh it's like saying we shouldn't eat
+meat it's very hard to
+
+ align:start position:0%
+meat it's very hard to
+ 
+
+ align:start position:0%
+meat it's very hard to
+make up ethical principles that are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foolproof I'm not sure what the uh the
+
+ align:start position:0%
+foolproof I'm not sure what the uh the
+ 
+
+ align:start position:0%
+foolproof I'm not sure what the uh the
+safe AI people have as their asof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laws but if you walk around the uh AI
+
+ align:start position:0%
+laws but if you walk around the uh AI
+ 
+
+ align:start position:0%
+laws but if you walk around the uh AI
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+today it's hard to take ser iously the
+
+ align:start position:0%
+today it's hard to take ser iously the
+ 
+
+ align:start position:0%
+today it's hard to take ser iously the
+idea that they might form some sort of
+
+ align:start position:0%
+idea that they might form some sort of
+ 
+
+ align:start position:0%
+idea that they might form some sort of
+threat of course it could happen
+
+ align:start position:0%
+threat of course it could happen
+ 
+
+ align:start position:0%
+threat of course it could happen
+overnight but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh well we discussed the big threat the
+
+ align:start position:0%
+uh well we discussed the big threat the
+ 
+
+ align:start position:0%
+uh well we discussed the big threat the
+other day when somebody making a virus
+
+ align:start position:0%
+other day when somebody making a virus
+ 
+
+ align:start position:0%
+other day when somebody making a virus
+that kills
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything that's the road toward
+
+ align:start position:0%
+everything that's the road toward
+ 
+
+ align:start position:0%
+everything that's the road toward
+nanotechnology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can't get them to propose
+
+ align:start position:0%
+I can't get them to propose
+ 
+
+ align:start position:0%
+I can't get them to propose
+anything what happens in your class Pat
+
+ align:start position:0%
+anything what happens in your class Pat
+ 
+
+ align:start position:0%
+anything what happens in your class Pat
+I haven't been there for a long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time I don't know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you think efforts to augment human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intell people more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intelligent that's a great question
+
+ align:start position:0%
+intelligent that's a great question
+ 
+
+ align:start position:0%
+intelligent that's a great question
+because uh we're
+
+ align:start position:0%
+because uh we're
+ 
+
+ align:start position:0%
+because uh we're
+probably fairly close to the technology
+
+ align:start position:0%
+probably fairly close to the technology
+ 
+
+ align:start position:0%
+probably fairly close to the technology
+to do do something exciting in that
+
+ align:start position:0%
+to do do something exciting in that
+ 
+
+ align:start position:0%
+to do do something exciting in that
+direction except that we're afraid to
+
+ align:start position:0%
+direction except that we're afraid to
+ 
+
+ align:start position:0%
+direction except that we're afraid to
+because it seems to me
+
+ align:start position:0%
+because it seems to me
+ 
+
+ align:start position:0%
+because it seems to me
+that suppose you just wanted to do
+
+ align:start position:0%
+that suppose you just wanted to do
+ 
+
+ align:start position:0%
+that suppose you just wanted to do
+something modest like
+
+ align:start position:0%
+something modest like
+ 
+
+ align:start position:0%
+something modest like
+improve some person's
+
+ align:start position:0%
+improve some person's
+ 
+
+ align:start position:0%
+improve some person's
+memory I'll bet that with a few million
+
+ align:start position:0%
+memory I'll bet that with a few million
+ 
+
+ align:start position:0%
+memory I'll bet that with a few million
+dollars
+
+ align:start position:0%
+dollars
+ 
+
+ align:start position:0%
+dollars
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh I don't know how many
+
+ align:start position:0%
+uh I don't know how many
+ 
+
+ align:start position:0%
+uh I don't know how many
+years you could do something without
+
+ align:start position:0%
+years you could do something without
+ 
+
+ align:start position:0%
+years you could do something without
+understanding how the brain works
+
+ align:start position:0%
+understanding how the brain works
+ 
+
+ align:start position:0%
+understanding how the brain works
+to attach uh accessories to
+
+ align:start position:0%
+to attach uh accessories to
+ 
+
+ align:start position:0%
+to attach uh accessories to
+it uh I think I mentioned brindley's
+
+ align:start position:0%
+it uh I think I mentioned brindley's
+ 
+
+ align:start position:0%
+it uh I think I mentioned brindley's
+first experiment
+
+ align:start position:0%
+first experiment
+ 
+
+ align:start position:0%
+first experiment
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on trying to restore Vision to a blind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+uh I think I mentioned that last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l e y I
+
+ align:start position:0%
+l e y I
+ 
+
+ align:start position:0%
+l e y I
+think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so what he did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was here's his
+
+ align:start position:0%
+was here's his
+ 
+
+ align:start position:0%
+was here's his
+secretary who's
+
+ align:start position:0%
+secretary who's
+ 
+
+ align:start position:0%
+secretary who's
+blind and here's her aital
+
+ align:start position:0%
+blind and here's her aital
+ 
+
+ align:start position:0%
+blind and here's her aital
+lobe
+
+ align:start position:0%
+lobe
+ 
+
+ align:start position:0%
+lobe
+which of the brain
+
+ align:start position:0%
+which of the brain
+ 
+
+ align:start position:0%
+which of the brain
+and here's this area which is the
+
+ align:start position:0%
+and here's this area which is the
+ 
+
+ align:start position:0%
+and here's this area which is the
+primary uh
+
+ align:start position:0%
+primary uh
+ 
+
+ align:start position:0%
+primary uh
+visual I think it's called area 17 for
+
+ align:start position:0%
+visual I think it's called area 17 for
+ 
+
+ align:start position:0%
+visual I think it's called area 17 for
+no good
+
+ align:start position:0%
+no good
+ 
+
+ align:start position:0%
+no good
+reason that's the place where the
+
+ align:start position:0%
+reason that's the place where the
+ 
+
+ align:start position:0%
+reason that's the place where the
+signals get into the brain from the
+
+ align:start position:0%
+signals get into the brain from the
+ 
+
+ align:start position:0%
+signals get into the brain from the
+eye stupid isn't
+
+ align:start position:0%
+eye stupid isn't
+ 
+
+ align:start position:0%
+eye stupid isn't
+it here's the eye and here's the optic
+
+ align:start position:0%
+it here's the eye and here's the optic
+ 
+
+ align:start position:0%
+it here's the eye and here's the optic
+nerve and then here's some other stuff
+
+ align:start position:0%
+nerve and then here's some other stuff
+ 
+
+ align:start position:0%
+nerve and then here's some other stuff
+and it's all the way back
+
+ align:start position:0%
+and it's all the way back
+ 
+
+ align:start position:0%
+and it's all the way back
+here I presume this is because we used
+
+ align:start position:0%
+here I presume this is because we used
+ 
+
+ align:start position:0%
+here I presume this is because we used
+to be an octopus or something and the
+
+ align:start position:0%
+to be an octopus or something and the
+ 
+
+ align:start position:0%
+to be an octopus or something and the
+eye was here but uh
+
+ align:start position:0%
+eye was here but uh
+ 
+
+ align:start position:0%
+eye was here but uh
+anyway what's
+
+ align:start position:0%
+anyway what's
+ 
+
+ align:start position:0%
+anyway what's
+more the wires cross and all sorts of
+
+ align:start position:0%
+more the wires cross and all sorts of
+ 
+
+ align:start position:0%
+more the wires cross and all sorts of
+things but anyway so here's this piece
+
+ align:start position:0%
+things but anyway so here's this piece
+ 
+
+ align:start position:0%
+things but anyway so here's this piece
+of brain and what Brindley does is he
+
+ align:start position:0%
+of brain and what Brindley does is he
+ 
+
+ align:start position:0%
+of brain and what Brindley does is he
+makes a little uh Gadget with 64
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrodes and I forgotten the details
+
+ align:start position:0%
+electrodes and I forgotten the details
+ 
+
+ align:start position:0%
+electrodes and I forgotten the details
+but I think that these
+
+ align:start position:0%
+but I think that these
+ 
+
+ align:start position:0%
+but I think that these
+are actually uh has little
+
+ align:start position:0%
+are actually uh has little
+ 
+
+ align:start position:0%
+are actually uh has little
+coils I believe that the thing was
+
+ align:start position:0%
+coils I believe that the thing was
+ 
+
+ align:start position:0%
+coils I believe that the thing was
+there's no wire coming out of her head
+
+ align:start position:0%
+there's no wire coming out of her head
+ 
+
+ align:start position:0%
+there's no wire coming out of her head
+uh but these little uh wires little
+
+ align:start position:0%
+uh but these little uh wires little
+ 
+
+ align:start position:0%
+uh but these little uh wires little
+coils and electrodes are in uh
+
+ align:start position:0%
+coils and electrodes are in uh
+ 
+
+ align:start position:0%
+coils and electrodes are in uh
+this is in the
+
+ align:start position:0%
+this is in the
+ 
+
+ align:start position:0%
+this is in the
+1950s and silicone had just
+
+ align:start position:0%
+1950s and silicone had just
+ 
+
+ align:start position:0%
+1950s and silicone had just
+appeared uh and it looked pretty
+
+ align:start position:0%
+appeared uh and it looked pretty
+ 
+
+ align:start position:0%
+appeared uh and it looked pretty
+harmless so there's this a little pad of
+
+ align:start position:0%
+harmless so there's this a little pad of
+ 
+
+ align:start position:0%
+harmless so there's this a little pad of
+silicone he has to take the bone off the
+
+ align:start position:0%
+silicone he has to take the bone off the
+ 
+
+ align:start position:0%
+silicone he has to take the bone off the
+back of her skull which is risky and uh
+
+ align:start position:0%
+back of her skull which is risky and uh
+ 
+
+ align:start position:0%
+back of her skull which is risky and uh
+so there's the
+
+ align:start position:0%
+so there's the
+ 
+
+ align:start position:0%
+so there's the
+gadget and uh as I said uh when you
+
+ align:start position:0%
+gadget and uh as I said uh when you
+ 
+
+ align:start position:0%
+gadget and uh as I said uh when you
+stimulate
+
+ align:start position:0%
+stimulate
+ 
+
+ align:start position:0%
+stimulate
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+uh I believe 48 of them worked
+
+ align:start position:0%
+uh I believe 48 of them worked
+ 
+
+ align:start position:0%
+uh I believe 48 of them worked
+and about eight of them
+
+ align:start position:0%
+and about eight of them
+ 
+
+ align:start position:0%
+and about eight of them
+hurt and uh about eight of them didn't
+
+ align:start position:0%
+hurt and uh about eight of them didn't
+ 
+
+ align:start position:0%
+hurt and uh about eight of them didn't
+do anything but if you fired up this one
+
+ align:start position:0%
+do anything but if you fired up this one
+ 
+
+ align:start position:0%
+do anything but if you fired up this one
+then she described it as being like half
+
+ align:start position:0%
+then she described it as being like half
+ 
+
+ align:start position:0%
+then she described it as being like half
+a match stick at arms length and they
+
+ align:start position:0%
+a match stick at arms length and they
+ 
+
+ align:start position:0%
+a match stick at arms length and they
+were little bars which is interesting
+
+ align:start position:0%
+were little bars which is interesting
+ 
+
+ align:start position:0%
+were little bars which is interesting
+they were not little round dots but
+
+ align:start position:0%
+they were not little round dots but
+ 
+
+ align:start position:0%
+they were not little round dots but
+there were enough of them that she could
+
+ align:start position:0%
+there were enough of them that she could
+ 
+
+ align:start position:0%
+there were enough of them that she could
+read letters one at a time and so that's
+
+ align:start position:0%
+read letters one at a time and so that's
+ 
+
+ align:start position:0%
+read letters one at a time and so that's
+the 1950s and as far as I know it's
+
+ align:start position:0%
+the 1950s and as far as I know it's
+ 
+
+ align:start position:0%
+the 1950s and as far as I know it's
+never been done
+
+ align:start position:0%
+never been done
+ 
+
+ align:start position:0%
+never been done
+again uh maybe there some way to look
+
+ align:start position:0%
+again uh maybe there some way to look
+ 
+
+ align:start position:0%
+again uh maybe there some way to look
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+up yes so they I think improveed the
+
+ align:start position:0%
+up yes so they I think improveed the
+ 
+
+ align:start position:0%
+up yes so they I think improveed the
+memory of rats recently of rats yeah
+
+ align:start position:0%
+memory of rats recently of rats yeah
+ 
+
+ align:start position:0%
+memory of rats recently of rats yeah
+they turn off and turn off okay yeah uh
+
+ align:start position:0%
+they turn off and turn off okay yeah uh
+ 
+
+ align:start position:0%
+they turn off and turn off okay yeah uh
+but anyway I suspect that uh if you got
+
+ align:start position:0%
+but anyway I suspect that uh if you got
+ 
+
+ align:start position:0%
+but anyway I suspect that uh if you got
+permission to
+
+ align:start position:0%
+permission to
+ 
+
+ align:start position:0%
+permission to
+try I'll bet you could put a th000
+
+ align:start position:0%
+try I'll bet you could put a th000
+ 
+
+ align:start position:0%
+try I'll bet you could put a th000
+electrodes
+
+ align:start position:0%
+electrodes
+ 
+
+ align:start position:0%
+electrodes
+uh maybe in a couple of places on the
+
+ align:start position:0%
+uh maybe in a couple of places on the
+ 
+
+ align:start position:0%
+uh maybe in a couple of places on the
+cortex and just poke around and I'll bet
+
+ align:start position:0%
+cortex and just poke around and I'll bet
+ 
+
+ align:start position:0%
+cortex and just poke around and I'll bet
+that you could do it without much
+
+ align:start position:0%
+that you could do it without much
+ 
+
+ align:start position:0%
+that you could do it without much
+danger and
+
+ align:start position:0%
+danger and
+ 
+
+ align:start position:0%
+danger and
+eventually uh get enough inputs and
+
+ align:start position:0%
+eventually uh get enough inputs and
+ 
+
+ align:start position:0%
+eventually uh get enough inputs and
+outputs uh to hook it up to something
+
+ align:start position:0%
+outputs uh to hook it up to something
+ 
+
+ align:start position:0%
+outputs uh to hook it up to something
+stupid like the Oxford
+
+ align:start position:0%
+stupid like the Oxford
+ 
+
+ align:start position:0%
+stupid like the Oxford
+dictionary which would be about that
+
+ align:start position:0%
+dictionary which would be about that
+ 
+
+ align:start position:0%
+dictionary which would be about that
+big and uh
+
+ align:start position:0%
+big and uh
+ 
+
+ align:start position:0%
+big and uh
+or make it a memory retrieval system
+
+ align:start position:0%
+or make it a memory retrieval system
+ 
+
+ align:start position:0%
+or make it a memory retrieval system
+where you
+
+ align:start position:0%
+where you
+ 
+
+ align:start position:0%
+where you
+think I I don't know what you'd think
+
+ align:start position:0%
+think I I don't know what you'd think
+ 
+
+ align:start position:0%
+think I I don't know what you'd think
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+people having this gadget for in their
+
+ align:start position:0%
+people having this gadget for in their
+ 
+
+ align:start position:0%
+people having this gadget for in their
+head for a long time with a with a
+
+ align:start position:0%
+head for a long time with a with a
+ 
+
+ align:start position:0%
+head for a long time with a with a
+screen producing outputs would learn how
+
+ align:start position:0%
+screen producing outputs would learn how
+ 
+
+ align:start position:0%
+screen producing outputs would learn how
+to control some of those little spots
+
+ align:start position:0%
+to control some of those little spots
+ 
+
+ align:start position:0%
+to control some of those little spots
+and uh then another part of their brain
+
+ align:start position:0%
+and uh then another part of their brain
+ 
+
+ align:start position:0%
+and uh then another part of their brain
+would learn to control groups of them
+
+ align:start position:0%
+would learn to control groups of them
+ 
+
+ align:start position:0%
+would learn to control groups of them
+and so forth and maybe after a few days
+
+ align:start position:0%
+and so forth and maybe after a few days
+ 
+
+ align:start position:0%
+and so forth and maybe after a few days
+or weeks or
+
+ align:start position:0%
+or weeks or
+ 
+
+ align:start position:0%
+or weeks or
+months uh you'd be able to operate this
+
+ align:start position:0%
+months uh you'd be able to operate this
+ 
+
+ align:start position:0%
+months uh you'd be able to operate this
+uh as like the touch screen on your
+
+ align:start position:0%
+uh as like the touch screen on your
+ 
+
+ align:start position:0%
+uh as like the touch screen on your
+iPhone and uh uh it would provide you
+
+ align:start position:0%
+iPhone and uh uh it would provide you
+ 
+
+ align:start position:0%
+iPhone and uh uh it would provide you
+with a huge uh inexhaustible amount of
+
+ align:start position:0%
+with a huge uh inexhaustible amount of
+ 
+
+ align:start position:0%
+with a huge uh inexhaustible amount of
+memory that that uh and for one in a
+
+ align:start position:0%
+memory that that uh and for one in a
+ 
+
+ align:start position:0%
+memory that that uh and for one in a
+dozen people it it might produce outputs
+
+ align:start position:0%
+dozen people it it might produce outputs
+ 
+
+ align:start position:0%
+dozen people it it might produce outputs
+that uh get right into your mind in some
+
+ align:start position:0%
+that uh get right into your mind in some
+ 
+
+ align:start position:0%
+that uh get right into your mind in some
+graphic or auditory or uh unspeakably
+
+ align:start position:0%
+graphic or auditory or uh unspeakably
+ 
+
+ align:start position:0%
+graphic or auditory or uh unspeakably
+Alien sense uh and you'd know know
+
+ align:start position:0%
+Alien sense uh and you'd know know
+ 
+
+ align:start position:0%
+Alien sense uh and you'd know know
+something that you didn't know before so
+
+ align:start position:0%
+something that you didn't know before so
+ 
+
+ align:start position:0%
+something that you didn't know before so
+that would be very thrilling uh area and
+
+ align:start position:0%
+that would be very thrilling uh area and
+ 
+
+ align:start position:0%
+that would be very thrilling uh area and
+there lots of epileptics who are having
+
+ align:start position:0%
+there lots of epileptics who are having
+ 
+
+ align:start position:0%
+there lots of epileptics who are having
+pieces of their brain removed
+
+ align:start position:0%
+pieces of their brain removed
+ 
+
+ align:start position:0%
+pieces of their brain removed
+because uh it's saving their life and it
+
+ align:start position:0%
+because uh it's saving their life and it
+ 
+
+ align:start position:0%
+because uh it's saving their life and it
+would be almost risk-free to slide this
+
+ align:start position:0%
+would be almost risk-free to slide this
+ 
+
+ align:start position:0%
+would be almost risk-free to slide this
+little Gadget in while you're at it
+
+ align:start position:0%
+little Gadget in while you're at it
+ 
+
+ align:start position:0%
+little Gadget in while you're at it
+because now it's 60 years later and we
+
+ align:start position:0%
+because now it's 60 years later and we
+ 
+
+ align:start position:0%
+because now it's 60 years later and we
+know which kinds of silicone implants
+
+ align:start position:0%
+know which kinds of silicone implants
+ 
+
+ align:start position:0%
+know which kinds of silicone implants
+are tolerated and I'm sure there are
+
+ align:start position:0%
+are tolerated and I'm sure there are
+ 
+
+ align:start position:0%
+are tolerated and I'm sure there are
+other things what substances can you put
+
+ align:start position:0%
+other things what substances can you put
+ 
+
+ align:start position:0%
+other things what substances can you put
+in the body that don't irritate it must
+
+ align:start position:0%
+in the body that don't irritate it must
+ 
+
+ align:start position:0%
+in the body that don't irritate it must
+be quite a
+
+ align:start position:0%
+be quite a
+ 
+
+ align:start position:0%
+be quite a
+few I mean in a sense we're sort of
+
+ align:start position:0%
+few I mean in a sense we're sort of
+ 
+
+ align:start position:0%
+few I mean in a sense we're sort of
+already doing this like bring
+
+ align:start position:0%
+already doing this like bring
+ 
+
+ align:start position:0%
+already doing this like bring
+augmentation thing right ex like with
+
+ align:start position:0%
+augmentation thing right ex like with
+ 
+
+ align:start position:0%
+augmentation thing right ex like with
+our computers or with our smartphones
+
+ align:start position:0%
+our computers or with our smartphones
+ 
+
+ align:start position:0%
+our computers or with our smartphones
+except for the interface between us and
+
+ align:start position:0%
+except for the interface between us and
+ 
+
+ align:start position:0%
+except for the interface between us and
+the devices a lot Fier this is just like
+
+ align:start position:0%
+the devices a lot Fier this is just like
+ 
+
+ align:start position:0%
+the devices a lot Fier this is just like
+more direct whereas right now it's like
+
+ align:start position:0%
+more direct whereas right now it's like
+ 
+
+ align:start position:0%
+more direct whereas right now it's like
+we have to like I guess use our bodies
+
+ align:start position:0%
+we have to like I guess use our bodies
+ 
+
+ align:start position:0%
+we have to like I guess use our bodies
+actuate the machine and then like use
+
+ align:start position:0%
+actuate the machine and then like use
+ 
+
+ align:start position:0%
+actuate the machine and then like use
+our sentences to get the information
+
+ align:start position:0%
+our sentences to get the information
+ 
+
+ align:start position:0%
+our sentences to get the information
+back into our mind right and we're being
+
+ align:start position:0%
+back into our mind right and we're being
+ 
+
+ align:start position:0%
+back into our mind right and we're being
+very sluggish about it I don't see why
+
+ align:start position:0%
+very sluggish about it I don't see why
+ 
+
+ align:start position:0%
+very sluggish about it I don't see why
+you couldn't put little pads in the toes
+
+ align:start position:0%
+you couldn't put little pads in the toes
+ 
+
+ align:start position:0%
+you couldn't put little pads in the toes
+of your shoes so you wouldn't need a
+
+ align:start position:0%
+of your shoes so you wouldn't need a
+ 
+
+ align:start position:0%
+of your shoes so you wouldn't need a
+mouse or they have like tongue
+
+ align:start position:0%
+mouse or they have like tongue
+ 
+
+ align:start position:0%
+mouse or they have like tongue
+interfaces where like well yes tongue
+
+ align:start position:0%
+interfaces where like well yes tongue
+ 
+
+ align:start position:0%
+interfaces where like well yes tongue
+displays um where it sort of um send
+
+ align:start position:0%
+displays um where it sort of um send
+ 
+
+ align:start position:0%
+displays um where it sort of um send
+like electric signals um on your tongue
+
+ align:start position:0%
+like electric signals um on your tongue
+ 
+
+ align:start position:0%
+like electric signals um on your tongue
+in a 2d grid so that you can like I
+
+ align:start position:0%
+in a 2d grid so that you can like I
+ 
+
+ align:start position:0%
+in a 2d grid so that you can like I
+guess feel like some shape and there's
+
+ align:start position:0%
+guess feel like some shape and there's
+ 
+
+ align:start position:0%
+guess feel like some shape and there's
+also um I saw this talk last week of
+
+ align:start position:0%
+also um I saw this talk last week of
+ 
+
+ align:start position:0%
+also um I saw this talk last week of
+Microsoft research um working on this
+
+ align:start position:0%
+Microsoft research um working on this
+ 
+
+ align:start position:0%
+Microsoft research um working on this
+like tongue controlling interface where
+
+ align:start position:0%
+like tongue controlling interface where
+ 
+
+ align:start position:0%
+like tongue controlling interface where
+you can use no seriously like they gave
+
+ align:start position:0%
+you can use no seriously like they gave
+ 
+
+ align:start position:0%
+you can use no seriously like they gave
+this to disabled people and put them in
+
+ align:start position:0%
+this to disabled people and put them in
+ 
+
+ align:start position:0%
+this to disabled people and put them in
+this wheelchair and they could use their
+
+ align:start position:0%
+this wheelchair and they could use their
+ 
+
+ align:start position:0%
+this wheelchair and they could use their
+tongue to control the wheelchair and
+
+ align:start position:0%
+tongue to control the wheelchair and
+ 
+
+ align:start position:0%
+tongue to control the wheelchair and
+it's almost like their mind control yes
+
+ align:start position:0%
+it's almost like their mind control yes
+ 
+
+ align:start position:0%
+it's almost like their mind control yes
+right it's
+
+ align:start position:0%
+right it's
+ 
+
+ align:start position:0%
+right it's
+uh I think they something that does it
+
+ align:start position:0%
+uh I think they something that does it
+ 
+
+ align:start position:0%
+uh I think they something that does it
+with scanning the activity in the brain
+
+ align:start position:0%
+with scanning the activity in the brain
+ 
+
+ align:start position:0%
+with scanning the activity in the brain
+so I saw on it a while um oh thetive
+
+ align:start position:0%
+so I saw on it a while um oh thetive
+ 
+
+ align:start position:0%
+so I saw on it a while um oh thetive
+device I actually tried it it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that of left and right and
+
+ align:start position:0%
+that of left and right and
+ 
+
+ align:start position:0%
+that of left and right and
+they way I don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know I at a video game company and use
+
+ align:start position:0%
+know I at a video game company and use
+ 
+
+ align:start position:0%
+know I at a video game company and use
+that exact device to make a video and
+
+ align:start position:0%
+that exact device to make a video and
+ 
+
+ align:start position:0%
+that exact device to make a video and
+you have to train it except for it's
+
+ align:start position:0%
+you have to train it except for it's
+ 
+
+ align:start position:0%
+you have to train it except for it's
+sort of finicky because basically the
+
+ align:start position:0%
+sort of finicky because basically the
+ 
+
+ align:start position:0%
+sort of finicky because basically the
+way it works is like you have this
+
+ align:start position:0%
+way it works is like you have this
+ 
+
+ align:start position:0%
+way it works is like you have this
+training interface where um they tell
+
+ align:start position:0%
+training interface where um they tell
+ 
+
+ align:start position:0%
+training interface where um they tell
+you to like push or pull and like it
+
+ align:start position:0%
+you to like push or pull and like it
+ 
+
+ align:start position:0%
+you to like push or pull and like it
+Associates like your certain like
+
+ align:start position:0%
+Associates like your certain like
+ 
+
+ align:start position:0%
+Associates like your certain like
+thought patterns with like the push or
+
+ align:start position:0%
+thought patterns with like the push or
+ 
+
+ align:start position:0%
+thought patterns with like the push or
+with the pull but I don't know it's like
+
+ align:start position:0%
+with the pull but I don't know it's like
+ 
+
+ align:start position:0%
+with the pull but I don't know it's like
+maybe I just didn't practice it enough
+
+ align:start position:0%
+maybe I just didn't practice it enough
+ 
+
+ align:start position:0%
+maybe I just didn't practice it enough
+um it it's not that reliable so it's
+
+ align:start position:0%
+um it it's not that reliable so it's
+ 
+
+ align:start position:0%
+um it it's not that reliable so it's
+like for video game or for like toy
+
+ align:start position:0%
+like for video game or for like toy
+ 
+
+ align:start position:0%
+like for video game or for like toy
+applications it's okay but if you
+
+ align:start position:0%
+applications it's okay but if you
+ 
+
+ align:start position:0%
+applications it's okay but if you
+actually want to use that to like
+
+ align:start position:0%
+actually want to use that to like
+ 
+
+ align:start position:0%
+actually want to use that to like
+control I don't know like an evelon
+
+ align:start position:0%
+control I don't know like an evelon
+ 
+
+ align:start position:0%
+control I don't know like an evelon
+style giant robot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like uh this is an old thing I don't
+
+ align:start position:0%
+like uh this is an old thing I don't
+ 
+
+ align:start position:0%
+like uh this is an old thing I don't
+know if there are any better ones yes
+
+ align:start position:0%
+know if there are any better ones yes
+ 
+
+ align:start position:0%
+know if there are any better ones yes
+uh the people with the tongue Gadget
+
+ align:start position:0%
+uh the people with the tongue Gadget
+ 
+
+ align:start position:0%
+uh the people with the tongue Gadget
+claim very good results I don't know
+
+ align:start position:0%
+claim very good results I don't know
+ 
+
+ align:start position:0%
+claim very good results I don't know
+what it's like to go around with that
+
+ align:start position:0%
+what it's like to go around with that
+ 
+
+ align:start position:0%
+what it's like to go around with that
+thing in your mouth
+
+ align:start position:0%
+thing in your mouth
+ 
+
+ align:start position:0%
+thing in your mouth
+but they made a wireless one it's like
+
+ align:start position:0%
+but they made a wireless one it's like
+ 
+
+ align:start position:0%
+but they made a wireless one it's like
+in the shape of Aer oh okay is is it
+
+ align:start position:0%
+in the shape of Aer oh okay is is it
+ 
+
+ align:start position:0%
+in the shape of Aer oh okay is is it
+anchored to the teeth or something uh
+
+ align:start position:0%
+anchored to the teeth or something uh
+ 
+
+ align:start position:0%
+anchored to the teeth or something uh
+it's basically like a retener with you
+
+ align:start position:0%
+it's basically like a retener with you
+ 
+
+ align:start position:0%
+it's basically like a retener with you
+know wires to hold it on your teeth and
+
+ align:start position:0%
+know wires to hold it on your teeth and
+ 
+
+ align:start position:0%
+know wires to hold it on your teeth and
+it sticks on the your mouth oh so you
+
+ align:start position:0%
+it sticks on the your mouth oh so you
+ 
+
+ align:start position:0%
+it sticks on the your mouth oh so you
+just that that doesn't sound so bad is
+
+ align:start position:0%
+just that that doesn't sound so bad is
+ 
+
+ align:start position:0%
+just that that doesn't sound so bad is
+it Wireless that would be yeah yeah um
+
+ align:start position:0%
+it Wireless that would be yeah yeah um
+ 
+
+ align:start position:0%
+it Wireless that would be yeah yeah um
+okay by tan from Microsoft research and
+
+ align:start position:0%
+okay by tan from Microsoft research and
+ 
+
+ align:start position:0%
+okay by tan from Microsoft research and
+he showed stuff about that this guy I
+
+ align:start position:0%
+he showed stuff about that this guy I
+ 
+
+ align:start position:0%
+he showed stuff about that this guy I
+think it's spelled right but I'm not
+
+ align:start position:0%
+think it's spelled right but I'm not
+ 
+
+ align:start position:0%
+think it's spelled right but I'm not
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+um uh is a professor at Stanford and he
+
+ align:start position:0%
+um uh is a professor at Stanford and he
+ 
+
+ align:start position:0%
+um uh is a professor at Stanford and he
+made a uh an array of vibrators that go
+
+ align:start position:0%
+made a uh an array of vibrators that go
+ 
+
+ align:start position:0%
+made a uh an array of vibrators that go
+on your
+
+ align:start position:0%
+on your
+ 
+
+ align:start position:0%
+on your
+back and uh I put it on once uh it's 20
+
+ align:start position:0%
+back and uh I put it on once uh it's 20
+ 
+
+ align:start position:0%
+back and uh I put it on once uh it's 20
+by 20 I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think and they all work so it's uh
+
+ align:start position:0%
+think and they all work so it's uh
+ 
+
+ align:start position:0%
+think and they all work so it's uh
+that's better than the 8 by8 thing and I
+
+ align:start position:0%
+that's better than the 8 by8 thing and I
+ 
+
+ align:start position:0%
+that's better than the 8 by8 thing and I
+was able to recognize a
+
+ align:start position:0%
+was able to recognize a
+ 
+
+ align:start position:0%
+was able to recognize a
+telephone it's connected to a video
+
+ align:start position:0%
+telephone it's connected to a video
+ 
+
+ align:start position:0%
+telephone it's connected to a video
+camera and it's uh and it's just a pad
+
+ align:start position:0%
+camera and it's uh and it's just a pad
+ 
+
+ align:start position:0%
+camera and it's uh and it's just a pad
+on your back and if um you have a TV
+
+ align:start position:0%
+on your back and if um you have a TV
+ 
+
+ align:start position:0%
+on your back and if um you have a TV
+camera with the right kind of contrast
+
+ align:start position:0%
+camera with the right kind of contrast
+ 
+
+ align:start position:0%
+camera with the right kind of contrast
+and you can uh you can find the
+
+ align:start position:0%
+and you can uh you can find the
+ 
+
+ align:start position:0%
+and you can uh you can find the
+door and stuff like that it's easy and
+
+ align:start position:0%
+door and stuff like that it's easy and
+ 
+
+ align:start position:0%
+door and stuff like that it's easy and
+and I recognized a couple of objects I
+
+ align:start position:0%
+and I recognized a couple of objects I
+ 
+
+ align:start position:0%
+and I recognized a couple of objects I
+was only in it for about five minutes
+
+ align:start position:0%
+was only in it for about five minutes
+ 
+
+ align:start position:0%
+was only in it for about five minutes
+but uh the interesting thing is that uh
+
+ align:start position:0%
+but uh the interesting thing is that uh
+ 
+
+ align:start position:0%
+but uh the interesting thing is that uh
+it didn't take take any time
+
+ align:start position:0%
+it didn't take take any time
+ 
+
+ align:start position:0%
+it didn't take take any time
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh feel this in input as a shape I was
+
+ align:start position:0%
+uh feel this in input as a shape I was
+ 
+
+ align:start position:0%
+uh feel this in input as a shape I was
+pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surprised um that was many years ago uh
+
+ align:start position:0%
+surprised um that was many years ago uh
+ 
+
+ align:start position:0%
+surprised um that was many years ago uh
+I don't
+
+ align:start position:0%
+I don't
+ 
+
+ align:start position:0%
+I don't
+know what's happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since uh there's reading devices for the
+
+ align:start position:0%
+since uh there's reading devices for the
+ 
+
+ align:start position:0%
+since uh there's reading devices for the
+blind that uh go on your finger so
+
+ align:start position:0%
+blind that uh go on your finger so
+ 
+
+ align:start position:0%
+blind that uh go on your finger so
+instead of Braille
+
+ align:start position:0%
+instead of Braille
+ 
+
+ align:start position:0%
+instead of Braille
+uh you go like this and it can make make
+
+ align:start position:0%
+uh you go like this and it can make make
+ 
+
+ align:start position:0%
+uh you go like this and it can make make
+a sound or it can make a vibration in
+
+ align:start position:0%
+a sound or it can make a vibration in
+ 
+
+ align:start position:0%
+a sound or it can make a vibration in
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+fingertip see the trouble with Braille
+
+ align:start position:0%
+fingertip see the trouble with Braille
+ 
+
+ align:start position:0%
+fingertip see the trouble with Braille
+is you have to have
+
+ align:start position:0%
+is you have to have
+ 
+
+ align:start position:0%
+is you have to have
+Braille but this
+
+ align:start position:0%
+Braille but this
+ 
+
+ align:start position:0%
+Braille but this
+device I can't remember who makes
+
+ align:start position:0%
+device I can't remember who makes
+ 
+
+ align:start position:0%
+device I can't remember who makes
+it uh you just put this little thimble
+
+ align:start position:0%
+it uh you just put this little thimble
+ 
+
+ align:start position:0%
+it uh you just put this little thimble
+on and it has tiny
+
+ align:start position:0%
+on and it has tiny
+ 
+
+ align:start position:0%
+on and it has tiny
+vibrators so that it's like Braille it
+
+ align:start position:0%
+vibrators so that it's like Braille it
+ 
+
+ align:start position:0%
+vibrators so that it's like Braille it
+makes and you can feel the letters go by
+
+ align:start position:0%
+makes and you can feel the letters go by
+ 
+
+ align:start position:0%
+makes and you can feel the letters go by
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+uh as you move your
+
+ align:start position:0%
+uh as you move your
+ 
+
+ align:start position:0%
+uh as you move your
+finger and I've forgotten the
+
+ align:start position:0%
+finger and I've forgotten the
+ 
+
+ align:start position:0%
+finger and I've forgotten the
+professor's name for this do that
+
+ align:start position:0%
+professor's name for this do that
+ 
+
+ align:start position:0%
+professor's name for this do that
+ringabell uh anyway only about 10% of
+
+ align:start position:0%
+ringabell uh anyway only about 10% of
+ 
+
+ align:start position:0%
+ringabell uh anyway only about 10% of
+blind people find uh it easy to learn to
+
+ align:start position:0%
+blind people find uh it easy to learn to
+ 
+
+ align:start position:0%
+blind people find uh it easy to learn to
+to read this way
+
+ align:start position:0%
+to read this way
+ 
+
+ align:start position:0%
+to read this way
+so it hasn't it's not widely in
+
+ align:start position:0%
+so it hasn't it's not widely in
+ 
+
+ align:start position:0%
+so it hasn't it's not widely in
+production
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that's all beside the point I think
+
+ align:start position:0%
+but that's all beside the point I think
+ 
+
+ align:start position:0%
+but that's all beside the point I think
+at some
+
+ align:start position:0%
+at some
+ 
+
+ align:start position:0%
+at some
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+uh somebody's in some country will will
+
+ align:start position:0%
+uh somebody's in some country will will
+ 
+
+ align:start position:0%
+uh somebody's in some country will will
+uh want to try
+
+ align:start position:0%
+uh want to try
+ 
+
+ align:start position:0%
+uh want to try
+this uh direct brain connection thing
+
+ align:start position:0%
+this uh direct brain connection thing
+ 
+
+ align:start position:0%
+this uh direct brain connection thing
+might be great might be really good for
+
+ align:start position:0%
+might be great might be really good for
+ 
+
+ align:start position:0%
+might be great might be really good for
+an older person who's become
+
+ align:start position:0%
+an older person who's become
+ 
+
+ align:start position:0%
+an older person who's become
+blind
+
+ align:start position:0%
+blind
+ 
+
+ align:start position:0%
+blind
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+a senior person who's lost Vision might
+
+ align:start position:0%
+a senior person who's lost Vision might
+ 
+
+ align:start position:0%
+a senior person who's lost Vision might
+not be able to soup up their hearing and
+
+ align:start position:0%
+not be able to soup up their hearing and
+ 
+
+ align:start position:0%
+not be able to soup up their hearing and
+and other senses well enough or or learn
+
+ align:start position:0%
+and other senses well enough or or learn
+ 
+
+ align:start position:0%
+and other senses well enough or or learn
+fast enough uh to get
+
+ align:start position:0%
+fast enough uh to get
+ 
+
+ align:start position:0%
+fast enough uh to get
+around uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+being if you're if you become blind deaf
+
+ align:start position:0%
+being if you're if you become blind deaf
+ 
+
+ align:start position:0%
+being if you're if you become blind deaf
+like Helen Keller when you're a few
+
+ align:start position:0%
+like Helen Keller when you're a few
+ 
+
+ align:start position:0%
+like Helen Keller when you're a few
+months old or was she three years old
+
+ align:start position:0%
+months old or was she three years old
+ 
+
+ align:start position:0%
+months old or was she three years old
+anybody
+
+ align:start position:0%
+anybody
+ 
+
+ align:start position:0%
+anybody
+remember oh but
+
+ align:start position:0%
+remember oh but
+ 
+
+ align:start position:0%
+remember oh but
+uh so she just adapted and became quite
+
+ align:start position:0%
+uh so she just adapted and became quite
+ 
+
+ align:start position:0%
+uh so she just adapted and became quite
+a good writer
+
+ align:start position:0%
+a good writer
+ 
+
+ align:start position:0%
+a good writer
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh I think when thinking about like
+
+ align:start position:0%
+uh I think when thinking about like
+ 
+
+ align:start position:0%
+uh I think when thinking about like
+augmenting human intelligence there are
+
+ align:start position:0%
+augmenting human intelligence there are
+ 
+
+ align:start position:0%
+augmenting human intelligence there are
+really like two big rounds um to to
+
+ align:start position:0%
+really like two big rounds um to to
+ 
+
+ align:start position:0%
+really like two big rounds um to to
+think about one realm is sort of like
+
+ align:start position:0%
+think about one realm is sort of like
+ 
+
+ align:start position:0%
+think about one realm is sort of like
+developing the external device that like
+
+ align:start position:0%
+developing the external device that like
+ 
+
+ align:start position:0%
+developing the external device that like
+does the things for you that retrieves
+
+ align:start position:0%
+does the things for you that retrieves
+ 
+
+ align:start position:0%
+does the things for you that retrieves
+information and then the other realm is
+
+ align:start position:0%
+information and then the other realm is
+ 
+
+ align:start position:0%
+information and then the other realm is
+like the interface between the external
+
+ align:start position:0%
+like the interface between the external
+ 
+
+ align:start position:0%
+like the interface between the external
+thing and the human being yes what's the
+
+ align:start position:0%
+thing and the human being yes what's the
+ 
+
+ align:start position:0%
+thing and the human being yes what's the
+representations and it'd be wonderful to
+
+ align:start position:0%
+representations and it'd be wonderful to
+ 
+
+ align:start position:0%
+representations and it'd be wonderful to
+have a a gadget with a bunch of brain
+
+ align:start position:0%
+have a a gadget with a bunch of brain
+ 
+
+ align:start position:0%
+have a a gadget with a bunch of brain
+electrodes so you could you could
+
+ align:start position:0%
+electrodes so you could you could
+ 
+
+ align:start position:0%
+electrodes so you could you could
+discover uh what kinds of symbols can
+
+ align:start position:0%
+discover uh what kinds of symbols can
+ 
+
+ align:start position:0%
+discover uh what kinds of symbols can
+people learn to
+
+ align:start position:0%
+people learn to
+ 
+
+ align:start position:0%
+people learn to
+distinguish and uh we'd probably learn
+
+ align:start position:0%
+distinguish and uh we'd probably learn
+ 
+
+ align:start position:0%
+distinguish and uh we'd probably learn
+more about the brain in a couple of
+
+ align:start position:0%
+more about the brain in a couple of
+ 
+
+ align:start position:0%
+more about the brain in a couple of
+years than in the previous
+
+ align:start position:0%
+years than in the previous
+ 
+
+ align:start position:0%
+years than in the previous
+Century uh because we could we could get
+
+ align:start position:0%
+Century uh because we could we could get
+ 
+
+ align:start position:0%
+Century uh because we could we could get
+some idea of representations to to
+
+ align:start position:0%
+some idea of representations to to
+ 
+
+ align:start position:0%
+some idea of representations to to
+people represent things as list struct
+
+ align:start position:0%
+people represent things as list struct
+ 
+
+ align:start position:0%
+people represent things as list struct
+or as Productions or uh computer science
+
+ align:start position:0%
+or as Productions or uh computer science
+ 
+
+ align:start position:0%
+or as Productions or uh computer science
+has come up with lots of ways to
+
+ align:start position:0%
+has come up with lots of ways to
+ 
+
+ align:start position:0%
+has come up with lots of ways to
+represent
+
+ align:start position:0%
+represent
+ 
+
+ align:start position:0%
+represent
+knowledge I've never met a
+
+ align:start position:0%
+knowledge I've never met a
+ 
+
+ align:start position:0%
+knowledge I've never met a
+neuroscientist who even knows what what
+
+ align:start position:0%
+neuroscientist who even knows what what
+ 
+
+ align:start position:0%
+neuroscientist who even knows what what
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh your smirk uh maybe there are some I
+
+ align:start position:0%
+uh your smirk uh maybe there are some I
+ 
+
+ align:start position:0%
+uh your smirk uh maybe there are some I
+haven't met I'm sure well there's me
+
+ align:start position:0%
+haven't met I'm sure well there's me
+ 
+
+ align:start position:0%
+haven't met I'm sure well there's me
+that's why I
+
+ align:start position:0%
+that's why I
+ 
+
+ align:start position:0%
+that's why I
+smirk uh
+
+ align:start position:0%
+smirk uh
+ 
+
+ align:start position:0%
+smirk uh
+but I've complained about this about
+
+ align:start position:0%
+but I've complained about this about
+ 
+
+ align:start position:0%
+but I've complained about this about
+four times already but uh the best
+
+ align:start position:0%
+four times already but uh the best
+ 
+
+ align:start position:0%
+four times already but uh the best
+example is to look at the review of the
+
+ align:start position:0%
+example is to look at the review of the
+ 
+
+ align:start position:0%
+example is to look at the review of the
+emotion machine on my on the Amazon uh
+
+ align:start position:0%
+emotion machine on my on the Amazon uh
+ 
+
+ align:start position:0%
+emotion machine on my on the Amazon uh
+book page for it course there's this
+
+ align:start position:0%
+book page for it course there's this
+ 
+
+ align:start position:0%
+book page for it course there's this
+neurologist who
+
+ align:start position:0%
+neurologist who
+ 
+
+ align:start position:0%
+neurologist who
+says he writes all about these Kines and
+
+ align:start position:0%
+says he writes all about these Kines and
+ 
+
+ align:start position:0%
+says he writes all about these Kines and
+and and penies and
+
+ align:start position:0%
+and and penies and
+ 
+
+ align:start position:0%
+and and penies and
+isomes and he has no evidence they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist and it's just so funny because I'm
+
+ align:start position:0%
+exist and it's just so funny because I'm
+ 
+
+ align:start position:0%
+exist and it's just so funny because I'm
+writing this book to help those here
+
+ align:start position:0%
+writing this book to help those here
+ 
+
+ align:start position:0%
+writing this book to help those here
+they're drowning in ignorance and I've
+
+ align:start position:0%
+they're drowning in ignorance and I've
+ 
+
+ align:start position:0%
+they're drowning in ignorance and I've
+just taught them this life raft and they
+
+ align:start position:0%
+just taught them this life raft and they
+ 
+
+ align:start position:0%
+just taught them this life raft and they
+say well uh he hasn't tested this life
+
+ align:start position:0%
+say well uh he hasn't tested this life
+ 
+
+ align:start position:0%
+say well uh he hasn't tested this life
+raft to see if
+
+ align:start position:0%
+raft to see if
+ 
+
+ align:start position:0%
+raft to see if
+it they don't like the idea of a
+
+ align:start position:0%
+it they don't like the idea of a
+ 
+
+ align:start position:0%
+it they don't like the idea of a
+suggestion if you haven't proved it it's
+
+ align:start position:0%
+suggestion if you haven't proved it it's
+ 
+
+ align:start position:0%
+suggestion if you haven't proved it it's
+a that is not the way to do
+
+ align:start position:0%
+a that is not the way to do
+ 
+
+ align:start position:0%
+a that is not the way to do
+science uh you have to make
+
+ align:start position:0%
+science uh you have to make
+ 
+
+ align:start position:0%
+science uh you have to make
+hypothesis and if you're neuroscientist
+
+ align:start position:0%
+hypothesis and if you're neuroscientist
+ 
+
+ align:start position:0%
+hypothesis and if you're neuroscientist
+you can't do that because it's not in
+
+ align:start position:0%
+you can't do that because it's not in
+ 
+
+ align:start position:0%
+you can't do that because it's not in
+your nature so you have to get them from
+
+ align:start position:0%
+your nature so you have to get them from
+ 
+
+ align:start position:0%
+your nature so you have to get them from
+someone else it's very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple how come there are no programming
+
+ align:start position:0%
+simple how come there are no programming
+ 
+
+ align:start position:0%
+simple how come there are no programming
+languages that have decent
+
+ align:start position:0%
+languages that have decent
+ 
+
+ align:start position:0%
+languages that have decent
+representations of
+
+ align:start position:0%
+representations of
+ 
+
+ align:start position:0%
+representations of
+anything I people tell me they use C++
+
+ align:start position:0%
+anything I people tell me they use C++
+ 
+
+ align:start position:0%
+anything I people tell me they use C++
+whatever that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is I think when wrote a book on how to
+
+ align:start position:0%
+is I think when wrote a book on how to
+ 
+
+ align:start position:0%
+is I think when wrote a book on how to
+program in that and I asked him do you
+
+ align:start position:0%
+program in that and I asked him do you
+ 
+
+ align:start position:0%
+program in that and I asked him do you
+actually know how to program in that
+
+ align:start position:0%
+actually know how to program in that
+ 
+
+ align:start position:0%
+actually know how to program in that
+language he said of course not but I
+
+ align:start position:0%
+language he said of course not but I
+ 
+
+ align:start position:0%
+language he said of course not but I
+know how to write books on how to
+
+ align:start position:0%
+know how to write books on how to
+ 
+
+ align:start position:0%
+know how to write books on how to
+program do you remember that it's a
+
+ align:start position:0%
+program do you remember that it's a
+ 
+
+ align:start position:0%
+program do you remember that it's a
+great learning experience you actually
+
+ align:start position:0%
+great learning experience you actually
+ 
+
+ align:start position:0%
+great learning experience you actually
+said something like
+
+ align:start position:0%
+said something like
+ 
+
+ align:start position:0%
+said something like
+that because you write the book and then
+
+ align:start position:0%
+that because you write the book and then
+ 
+
+ align:start position:0%
+that because you write the book and then
+you can get other people to put in the
+
+ align:start position:0%
+you can get other people to put in the
+ 
+
+ align:start position:0%
+you can get other people to put in the
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+uh you should all read some of my I
+
+ align:start position:0%
+uh you should all read some of my I
+ 
+
+ align:start position:0%
+uh you should all read some of my I
+couldn't force myself to learn C without
+
+ align:start position:0%
+couldn't force myself to learn C without
+ 
+
+ align:start position:0%
+couldn't force myself to learn C without
+writing a book about it it was too
+
+ align:start position:0%
+writing a book about it it was too
+ 
+
+ align:start position:0%
+writing a book about it it was too
+boring that's
+
+ align:start position:0%
+boring that's
+ 
+
+ align:start position:0%
+boring that's
+right right um if you if you read my
+
+ align:start position:0%
+right right um if you if you read my
+ 
+
+ align:start position:0%
+right right um if you if you read my
+book on
+
+ align:start position:0%
+book on
+ 
+
+ align:start position:0%
+book on
+computation which is still actually
+
+ align:start position:0%
+computation which is still actually
+ 
+
+ align:start position:0%
+computation which is still actually
+current because it's about things that
+
+ align:start position:0%
+current because it's about things that
+ 
+
+ align:start position:0%
+current because it's about things that
+they don't teach
+
+ align:start position:0%
+they don't teach
+ 
+
+ align:start position:0%
+they don't teach
+much uh and uh the best thing about the
+
+ align:start position:0%
+much uh and uh the best thing about the
+ 
+
+ align:start position:0%
+much uh and uh the best thing about the
+book is that it's full of problems that
+
+ align:start position:0%
+book is that it's full of problems that
+ 
+
+ align:start position:0%
+book is that it's full of problems that
+you can actually solve and most but I
+
+ align:start position:0%
+you can actually solve and most but I
+ 
+
+ align:start position:0%
+you can actually solve and most but I
+wasn't good at making up problems so
+
+ align:start position:0%
+wasn't good at making up problems so
+ 
+
+ align:start position:0%
+wasn't good at making up problems so
+most of the problems there are U Were
+
+ align:start position:0%
+most of the problems there are U Were
+ 
+
+ align:start position:0%
+most of the problems there are U Were
+Made Up by a gradu young graduate
+
+ align:start position:0%
+Made Up by a gradu young graduate
+ 
+
+ align:start position:0%
+Made Up by a gradu young graduate
+student named Manuel
+
+ align:start position:0%
+student named Manuel
+ 
+
+ align:start position:0%
+student named Manuel
+Bloom uh and I don't think I gave him
+
+ align:start position:0%
+Bloom uh and I don't think I gave him
+ 
+
+ align:start position:0%
+Bloom uh and I don't think I gave him
+enough credit in the book I just took it
+
+ align:start position:0%
+enough credit in the book I just took it
+ 
+
+ align:start position:0%
+enough credit in the book I just took it
+for granted that people are good at
+
+ align:start position:0%
+for granted that people are good at
+ 
+
+ align:start position:0%
+for granted that people are good at
+making up problems and I didn't realize
+
+ align:start position:0%
+making up problems and I didn't realize
+ 
+
+ align:start position:0%
+making up problems and I didn't realize
+how rare this
+
+ align:start position:0%
+how rare this
+ 
+
+ align:start position:0%
+how rare this
+was he now has the property
+
+ align:start position:0%
+was he now has the property
+ 
+
+ align:start position:0%
+was he now has the property
+that Manuel and his wife Lenor and his
+
+ align:start position:0%
+that Manuel and his wife Lenor and his
+ 
+
+ align:start position:0%
+that Manuel and his wife Lenor and his
+son whose name I forgot are all
+
+ align:start position:0%
+son whose name I forgot are all
+ 
+
+ align:start position:0%
+son whose name I forgot are all
+professors at
+
+ align:start position:0%
+professors at
+ 
+
+ align:start position:0%
+professors at
+CMU so
+
+ align:start position:0%
+CMU so
+ 
+
+ align:start position:0%
+CMU so
+that's yes is do you know any are there
+
+ align:start position:0%
+that's yes is do you know any are there
+ 
+
+ align:start position:0%
+that's yes is do you know any are there
+any other such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+families but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as far as I can tell Winston's book
+
+ align:start position:0%
+and as far as I can tell Winston's book
+ 
+
+ align:start position:0%
+and as far as I can tell Winston's book
+has been substantially replaced by this
+
+ align:start position:0%
+has been substantially replaced by this
+ 
+
+ align:start position:0%
+has been substantially replaced by this
+noran what's his name but there's right
+
+ align:start position:0%
+noran what's his name but there's right
+ 
+
+ align:start position:0%
+noran what's his name but there's right
+but there's almost no ideas about AI in
+
+ align:start position:0%
+but there's almost no ideas about AI in
+ 
+
+ align:start position:0%
+but there's almost no ideas about AI in
+in that book so we have a text
+
+ align:start position:0%
+in that book so we have a text
+ 
+
+ align:start position:0%
+in that book so we have a text
+book that is not helping the field
+
+ align:start position:0%
+book that is not helping the field
+ 
+
+ align:start position:0%
+book that is not helping the field
+progress very much because it's giving a
+
+ align:start position:0%
+progress very much because it's giving a
+ 
+
+ align:start position:0%
+progress very much because it's giving a
+lot of details about methods that I do
+
+ align:start position:0%
+lot of details about methods that I do
+ 
+
+ align:start position:0%
+lot of details about methods that I do
+well you know like lots of stuff about
+
+ align:start position:0%
+well you know like lots of stuff about
+ 
+
+ align:start position:0%
+well you know like lots of stuff about
+probabilistic
+
+ align:start position:0%
+probabilistic
+ 
+
+ align:start position:0%
+probabilistic
+learning which is very nice but I don't
+
+ align:start position:0%
+learning which is very nice but I don't
+ 
+
+ align:start position:0%
+learning which is very nice but I don't
+think it has much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future so if you meet anybody who's
+
+ align:start position:0%
+future so if you meet anybody who's
+ 
+
+ align:start position:0%
+future so if you meet anybody who's
+interested in AI get them to read Pat's
+
+ align:start position:0%
+interested in AI get them to read Pat's
+ 
+
+ align:start position:0%
+interested in AI get them to read Pat's
+book yes so what happened like why did
+
+ align:start position:0%
+book yes so what happened like why did
+ 
+
+ align:start position:0%
+book yes so what happened like why did
+MIT change like so much why like so many
+
+ align:start position:0%
+MIT change like so much why like so many
+ 
+
+ align:start position:0%
+MIT change like so much why like so many
+machine learning people
+
+ align:start position:0%
+machine learning people
+ 
+
+ align:start position:0%
+machine learning people
+well there was a very strange phenomenon
+
+ align:start position:0%
+well there was a very strange phenomenon
+ 
+
+ align:start position:0%
+well there was a very strange phenomenon
+called Rodney
+
+ align:start position:0%
+called Rodney
+ 
+
+ align:start position:0%
+called Rodney
+Brooks who
+
+ align:start position:0%
+Brooks who
+ 
+
+ align:start position:0%
+Brooks who
+uh somehow got a worldwide
+
+ align:start position:0%
+uh somehow got a worldwide
+ 
+
+ align:start position:0%
+uh somehow got a worldwide
+reputation for
+
+ align:start position:0%
+reputation for
+ 
+
+ align:start position:0%
+reputation for
+inventing
+
+ align:start position:0%
+inventing
+ 
+
+ align:start position:0%
+inventing
+uh what was it called subsumption
+
+ align:start position:0%
+uh what was it called subsumption
+ 
+
+ align:start position:0%
+uh what was it called subsumption
+subsumption subsumption was
+
+ align:start position:0%
+subsumption subsumption was
+ 
+
+ align:start position:0%
+subsumption subsumption was
+a formulation related to what the first
+
+ align:start position:0%
+a formulation related to what the first
+ 
+
+ align:start position:0%
+a formulation related to what the first
+computer people called priority
+
+ align:start position:0%
+computer people called priority
+ 
+
+ align:start position:0%
+computer people called priority
+interrupt so uh instead of having
+
+ align:start position:0%
+interrupt so uh instead of having
+ 
+
+ align:start position:0%
+interrupt so uh instead of having
+highlevel programming
+
+ align:start position:0%
+highlevel programming
+ 
+
+ align:start position:0%
+highlevel programming
+languages Brook pointed out that if you
+
+ align:start position:0%
+languages Brook pointed out that if you
+ 
+
+ align:start position:0%
+languages Brook pointed out that if you
+just have a bunch of statements and give
+
+ align:start position:0%
+just have a bunch of statements and give
+ 
+
+ align:start position:0%
+just have a bunch of statements and give
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+priorities uh and then take the one that
+
+ align:start position:0%
+priorities uh and then take the one that
+ 
+
+ align:start position:0%
+priorities uh and then take the one that
+uh you take all the statements that
+
+ align:start position:0%
+uh you take all the statements that
+ 
+
+ align:start position:0%
+uh you take all the statements that
+apply to a situation and take the one
+
+ align:start position:0%
+apply to a situation and take the one
+ 
+
+ align:start position:0%
+apply to a situation and take the one
+with the highest priority and do that uh
+
+ align:start position:0%
+with the highest priority and do that uh
+ 
+
+ align:start position:0%
+with the highest priority and do that uh
+then you can write a PhD thesis
+
+ align:start position:0%
+then you can write a PhD thesis
+ 
+
+ align:start position:0%
+then you can write a PhD thesis
+uh and make a movie of an experiment in
+
+ align:start position:0%
+uh and make a movie of an experiment in
+ 
+
+ align:start position:0%
+uh and make a movie of an experiment in
+which a robot actually found a coke
+
+ align:start position:0%
+which a robot actually found a coke
+ 
+
+ align:start position:0%
+which a robot actually found a coke
+bottle now the fact that the first 40
+
+ align:start position:0%
+bottle now the fact that the first 40
+ 
+
+ align:start position:0%
+bottle now the fact that the first 40
+times it didn't find the coke
+
+ align:start position:0%
+times it didn't find the coke
+ 
+
+ align:start position:0%
+times it didn't find the coke
+bottle uh because when it got near the
+
+ align:start position:0%
+bottle uh because when it got near the
+ 
+
+ align:start position:0%
+bottle uh because when it got near the
+table it couldn't see it anymore and it
+
+ align:start position:0%
+table it couldn't see it anymore and it
+ 
+
+ align:start position:0%
+table it couldn't see it anymore and it
+had no
+
+ align:start position:0%
+had no
+ 
+
+ align:start position:0%
+had no
+memory is uh was ignored by the
+
+ align:start position:0%
+memory is uh was ignored by the
+ 
+
+ align:start position:0%
+memory is uh was ignored by the
+worldwide
+
+ align:start position:0%
+worldwide
+ 
+
+ align:start position:0%
+worldwide
+community and so uh
+
+ align:start position:0%
+community and so uh
+ 
+
+ align:start position:0%
+community and so uh
+some of Rodney Brook's ideas swept the
+
+ align:start position:0%
+some of Rodney Brook's ideas swept the
+ 
+
+ align:start position:0%
+some of Rodney Brook's ideas swept the
+entire world stopped research in
+
+ align:start position:0%
+entire world stopped research in
+ 
+
+ align:start position:0%
+entire world stopped research in
+Japan
+
+ align:start position:0%
+Japan
+ 
+
+ align:start position:0%
+Japan
+uh because they all turned toward saying
+
+ align:start position:0%
+uh because they all turned toward saying
+ 
+
+ align:start position:0%
+uh because they all turned toward saying
+if you just observe the environment
+
+ align:start position:0%
+if you just observe the environment
+ 
+
+ align:start position:0%
+if you just observe the environment
+properly you can solve a lot of problems
+
+ align:start position:0%
+properly you can solve a lot of problems
+ 
+
+ align:start position:0%
+properly you can solve a lot of problems
+without making
+
+ align:start position:0%
+without making
+ 
+
+ align:start position:0%
+without making
+plans uh and he won
+
+ align:start position:0%
+plans uh and he won
+ 
+
+ align:start position:0%
+plans uh and he won
+the top prize that the uh AI
+
+ align:start position:0%
+the top prize that the uh AI
+ 
+
+ align:start position:0%
+the top prize that the uh AI
+Society gave out it's a complete mystery
+
+ align:start position:0%
+Society gave out it's a complete mystery
+ 
+
+ align:start position:0%
+Society gave out it's a complete mystery
+to me here is four or five really bad
+
+ align:start position:0%
+to me here is four or five really bad
+ 
+
+ align:start position:0%
+to me here is four or five really bad
+ideas that swept the world and replaced
+
+ align:start position:0%
+ideas that swept the world and replaced
+ 
+
+ align:start position:0%
+ideas that swept the world and replaced
+almost all other AI research for a
+
+ align:start position:0%
+almost all other AI research for a
+ 
+
+ align:start position:0%
+almost all other AI research for a
+decade or two
+
+ align:start position:0%
+decade or two
+ 
+
+ align:start position:0%
+decade or two
+wonderful uh that's why there are no
+
+ align:start position:0%
+wonderful uh that's why there are no
+ 
+
+ align:start position:0%
+wonderful uh that's why there are no
+robots that can go into the
+
+ align:start position:0%
+robots that can go into the
+ 
+
+ align:start position:0%
+robots that can go into the
+reactors in uh Japan and fix
+
+ align:start position:0%
+reactors in uh Japan and fix
+ 
+
+ align:start position:0%
+reactors in uh Japan and fix
+things because all the robots we have
+
+ align:start position:0%
+things because all the robots we have
+ 
+
+ align:start position:0%
+things because all the robots we have
+only react
+
+ align:start position:0%
+only react
+ 
+
+ align:start position:0%
+only react
+to never mind
+
+ align:start position:0%
+to never mind
+ 
+
+ align:start position:0%
+to never mind
+yeah uh so how do you see we changing
+
+ align:start position:0%
+yeah uh so how do you see we changing
+ 
+
+ align:start position:0%
+yeah uh so how do you see we changing
+that from now now we have a problem that
+
+ align:start position:0%
+that from now now we have a problem that
+ 
+
+ align:start position:0%
+that from now now we have a problem that
+most of
+
+ align:start position:0%
+most of
+ 
+
+ align:start position:0%
+most of
+the maybe most of the stuff in computer
+
+ align:start position:0%
+the maybe most of the stuff in computer
+ 
+
+ align:start position:0%
+the maybe most of the stuff in computer
+science or more people
+
+ align:start position:0%
+science or more people
+ 
+
+ align:start position:0%
+science or more people
+AI real estate I don't know inference or
+
+ align:start position:0%
+AI real estate I don't know inference or
+ 
+
+ align:start position:0%
+AI real estate I don't know inference or
+I don't know some kind of
+
+ align:start position:0%
+I don't know some kind of
+ 
+
+ align:start position:0%
+I don't know some kind of
+uh supervised learning or supervised
+
+ align:start position:0%
+uh supervised learning or supervised
+ 
+
+ align:start position:0%
+uh supervised learning or supervised
+learning and that makes a lot of money I
+
+ align:start position:0%
+learning and that makes a lot of money I
+ 
+
+ align:start position:0%
+learning and that makes a lot of money I
+mean if you well that's the problem
+
+ align:start position:0%
+mean if you well that's the problem
+ 
+
+ align:start position:0%
+mean if you well that's the problem
+uh the best way to make money is to
+
+ align:start position:0%
+uh the best way to make money is to
+ 
+
+ align:start position:0%
+uh the best way to make money is to
+steal it so why doesn't everybody just
+
+ align:start position:0%
+steal it so why doesn't everybody just
+ 
+
+ align:start position:0%
+steal it so why doesn't everybody just
+turn and go down this corner and mug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+someone I mean they're thinking long ter
+
+ align:start position:0%
+someone I mean they're thinking long ter
+ 
+
+ align:start position:0%
+someone I mean they're thinking long ter
+yeah there's a real problem here because
+
+ align:start position:0%
+yeah there's a real problem here because
+ 
+
+ align:start position:0%
+yeah there's a real problem here because
+you can mug a lot of people in parallel
+
+ align:start position:0%
+you can mug a lot of people in parallel
+ 
+
+ align:start position:0%
+you can mug a lot of people in parallel
+using uh
+
+ align:start position:0%
+using uh
+ 
+
+ align:start position:0%
+using uh
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really you got
+
+ align:start position:0%
+really you got
+ 
+
+ align:start position:0%
+really you got
+it and isn't there any like smart other
+
+ align:start position:0%
+it and isn't there any like smart other
+ 
+
+ align:start position:0%
+it and isn't there any like smart other
+smart professors
+
+ align:start position:0%
+smart professors
+ 
+
+ align:start position:0%
+smart professors
+that like what can they see that why
+
+ align:start position:0%
+that like what can they see that why
+ 
+
+ align:start position:0%
+that like what can they see that why
+they see that it beats me I
+
+ align:start position:0%
+they see that it beats me I
+ 
+
+ align:start position:0%
+they see that it beats me I
+I'd like to hear some theories of
+
+ align:start position:0%
+I'd like to hear some theories of
+ 
+
+ align:start position:0%
+I'd like to hear some theories of
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+uh why the textbook by Russell and
+
+ align:start position:0%
+uh why the textbook by Russell and
+ 
+
+ align:start position:0%
+uh why the textbook by Russell and
+Norwood doesn't mention the Society of
+
+ align:start position:0%
+Norwood doesn't mention the Society of
+ 
+
+ align:start position:0%
+Norwood doesn't mention the Society of
+Mind theories for example I mean they've
+
+ align:start position:0%
+Mind theories for example I mean they've
+ 
+
+ align:start position:0%
+Mind theories for example I mean they've
+been out there for 30
+
+ align:start position:0%
+been out there for 30
+ 
+
+ align:start position:0%
+been out there for 30
+years so there's
+
+ align:start position:0%
+years so there's
+ 
+
+ align:start position:0%
+years so there's
+something I don't know what what the
+
+ align:start position:0%
+something I don't know what what the
+ 
+
+ align:start position:0%
+something I don't know what what the
+problem is but 250,000 people are taking
+
+ align:start position:0%
+problem is but 250,000 people are taking
+ 
+
+ align:start position:0%
+problem is but 250,000 people are taking
+that course well so that things are
+
+ align:start position:0%
+that course well so that things are
+ 
+
+ align:start position:0%
+that course well so that things are
+going to get worse or better worse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has anybody watched some of this course
+
+ align:start position:0%
+has anybody watched some of this course
+ 
+
+ align:start position:0%
+has anybody watched some of this course
+has it started yet oh it's Sil okay has
+
+ align:start position:0%
+has it started yet oh it's Sil okay has
+ 
+
+ align:start position:0%
+has it started yet oh it's Sil okay has
+it have any of you
+
+ align:start position:0%
+it have any of you
+ 
+
+ align:start position:0%
+it have any of you
+looked no one here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I couldn't hear I think have moreal we
+
+ align:start position:0%
+I couldn't hear I think have moreal we
+ 
+
+ align:start position:0%
+I couldn't hear I think have moreal we
+weren't already taking classes here most
+
+ align:start position:0%
+weren't already taking classes here most
+ 
+
+ align:start position:0%
+weren't already taking classes here most
+people I know taking
+
+ align:start position:0%
+people I know taking
+ 
+
+ align:start position:0%
+people I know taking
+that working industry
+
+ align:start position:0%
+that working industry
+ 
+
+ align:start position:0%
+that working industry
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uhhuh it it it seems to me that for
+
+ align:start position:0%
+uhhuh it it it seems to me that for
+ 
+
+ align:start position:0%
+uhhuh it it it seems to me that for
+example machine learning when people
+
+ align:start position:0%
+example machine learning when people
+ 
+
+ align:start position:0%
+example machine learning when people
+take machine learning they think they
+
+ align:start position:0%
+take machine learning they think they
+ 
+
+ align:start position:0%
+take machine learning they think they
+are very smart because they can do
+
+ align:start position:0%
+are very smart because they can do
+ 
+
+ align:start position:0%
+are very smart because they can do
+calculations with like a lot of symbols
+
+ align:start position:0%
+calculations with like a lot of symbols
+ 
+
+ align:start position:0%
+calculations with like a lot of symbols
+and they think oh I'm such a genius like
+
+ align:start position:0%
+and they think oh I'm such a genius like
+ 
+
+ align:start position:0%
+and they think oh I'm such a genius like
+I'm not saying that I'm smart but like
+
+ align:start position:0%
+I'm not saying that I'm smart but like
+ 
+
+ align:start position:0%
+I'm not saying that I'm smart but like
+it seems to me that dealing with
+
+ align:start position:0%
+it seems to me that dealing with
+ 
+
+ align:start position:0%
+it seems to me that dealing with
+symbols make people think that they are
+
+ align:start position:0%
+symbols make people think that they are
+ 
+
+ align:start position:0%
+symbols make people think that they are
+very smart and that makes the situation
+
+ align:start position:0%
+very smart and that makes the situation
+ 
+
+ align:start position:0%
+very smart and that makes the situation
+even worse because you have maybe people
+
+ align:start position:0%
+even worse because you have maybe people
+ 
+
+ align:start position:0%
+even worse because you have maybe people
+that could
+
+ align:start position:0%
+that could
+ 
+
+ align:start position:0%
+that could
+solve like this problem and they are oh
+
+ align:start position:0%
+solve like this problem and they are oh
+ 
+
+ align:start position:0%
+solve like this problem and they are oh
+I can do like a lot of calculation there
+
+ align:start position:0%
+I can do like a lot of calculation there
+ 
+
+ align:start position:0%
+I can do like a lot of calculation there
+the there are these really hard formulas
+
+ align:start position:0%
+the there are these really hard formulas
+ 
+
+ align:start position:0%
+the there are these really hard formulas
+that only I know
+
+ align:start position:0%
+that only I know
+ 
+
+ align:start position:0%
+that only I know
+and well
+
+ align:start position:0%
+and well
+ 
+
+ align:start position:0%
+and well
+I like it seems that theory of symbols
+
+ align:start position:0%
+I like it seems that theory of symbols
+ 
+
+ align:start position:0%
+I like it seems that theory of symbols
+is like more complex and harder and
+
+ align:start position:0%
+is like more complex and harder and
+ 
+
+ align:start position:0%
+is like more complex and harder and
+people tend to stick to MH theories that
+
+ align:start position:0%
+people tend to stick to MH theories that
+ 
+
+ align:start position:0%
+people tend to stick to MH theories that
+have symbols and formulas
+
+ align:start position:0%
+have symbols and formulas
+ 
+
+ align:start position:0%
+have symbols and formulas
+and I guess so but it somehow it doesn't
+
+ align:start position:0%
+and I guess so but it somehow it doesn't
+ 
+
+ align:start position:0%
+and I guess so but it somehow it doesn't
+to me mathematics is really hard and
+
+ align:start position:0%
+to me mathematics is really hard and
+ 
+
+ align:start position:0%
+to me mathematics is really hard and
+symbols are easy it's sort of
+
+ align:start position:0%
+symbols are easy it's sort of
+ 
+
+ align:start position:0%
+symbols are easy it's sort of
+funny yeah but there's still symbols
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well
+
+ align:start position:0%
+yeah well
+ 
+
+ align:start position:0%
+yeah well
+does the machine course ever
+
+ align:start position:0%
+does the machine course ever
+ 
+
+ align:start position:0%
+does the machine course ever
+mention uh like Pat
+
+ align:start position:0%
+mention uh like Pat
+ 
+
+ align:start position:0%
+mention uh like Pat
+Winston's it's all about
+
+ align:start position:0%
+Winston's it's all about
+ 
+
+ align:start position:0%
+Winston's it's all about
+techniques machine
+
+ align:start position:0%
+techniques machine
+ 
+
+ align:start position:0%
+techniques machine
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+because what Winston does is he looks at
+
+ align:start position:0%
+because what Winston does is he looks at
+ 
+
+ align:start position:0%
+because what Winston does is he looks at
+the differences between things and gets
+
+ align:start position:0%
+the differences between things and gets
+ 
+
+ align:start position:0%
+the differences between things and gets
+rid of them and you can think of it as a
+
+ align:start position:0%
+rid of them and you can think of it as a
+ 
+
+ align:start position:0%
+rid of them and you can think of it as a
+sort of symbolic
+
+ align:start position:0%
+sort of symbolic
+ 
+
+ align:start position:0%
+sort of symbolic
+Servo but there are a lot of very simple
+
+ align:start position:0%
+Servo but there are a lot of very simple
+ 
+
+ align:start position:0%
+Servo but there are a lot of very simple
+Common Sense sensical operations in the
+
+ align:start position:0%
+Common Sense sensical operations in the
+ 
+
+ align:start position:0%
+Common Sense sensical operations in the
+methods that he describes but none of
+
+ align:start position:0%
+methods that he describes but none of
+ 
+
+ align:start position:0%
+methods that he describes but none of
+them are easy to express as
+
+ align:start position:0%
+them are easy to express as
+ 
+
+ align:start position:0%
+them are easy to express as
+equations and maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's maybe programming isn't technical
+
+ align:start position:0%
+that's maybe programming isn't technical
+ 
+
+ align:start position:0%
+that's maybe programming isn't technical
+enough and you need to dress things up
+
+ align:start position:0%
+enough and you need to dress things up
+ 
+
+ align:start position:0%
+enough and you need to dress things up
+in in uh algebra to make I should redo
+
+ align:start position:0%
+in in uh algebra to make I should redo
+ 
+
+ align:start position:0%
+in in uh algebra to make I should redo
+that pces as an energy minimization
+
+ align:start position:0%
+that pces as an energy minimization
+ 
+
+ align:start position:0%
+that pces as an energy minimization
+principle or something oh that's cute
+
+ align:start position:0%
+principle or something oh that's cute
+ 
+
+ align:start position:0%
+principle or something oh that's cute
+yes getting closer to the goal that's
+
+ align:start position:0%
+yes getting closer to the goal that's
+ 
+
+ align:start position:0%
+yes getting closer to the goal that's
+all it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is I think I mentioned the new and Simon
+
+ align:start position:0%
+is I think I mentioned the new and Simon
+ 
+
+ align:start position:0%
+is I think I mentioned the new and Simon
+had this great idea of of uh getting
+
+ align:start position:0%
+had this great idea of of uh getting
+ 
+
+ align:start position:0%
+had this great idea of of uh getting
+closer to the goal and they gave up with
+
+ align:start position:0%
+closer to the goal and they gave up with
+ 
+
+ align:start position:0%
+closer to the goal and they gave up with
+when they couldn't solve the missionary
+
+ align:start position:0%
+when they couldn't solve the missionary
+ 
+
+ align:start position:0%
+when they couldn't solve the missionary
+and cannibals problem because uh because
+
+ align:start position:0%
+and cannibals problem because uh because
+ 
+
+ align:start position:0%
+and cannibals problem because uh because
+there's a step where you have to take
+
+ align:start position:0%
+there's a step where you have to take
+ 
+
+ align:start position:0%
+there's a step where you have to take
+three people back in the
+
+ align:start position:0%
+three people back in the
+ 
+
+ align:start position:0%
+three people back in the
+boat and their program uh refused to do
+
+ align:start position:0%
+boat and their program uh refused to do
+ 
+
+ align:start position:0%
+boat and their program uh refused to do
+that because it wasn't getting them
+
+ align:start position:0%
+that because it wasn't getting them
+ 
+
+ align:start position:0%
+that because it wasn't getting them
+closer to the goal and the funny part is
+
+ align:start position:0%
+closer to the goal and the funny part is
+ 
+
+ align:start position:0%
+closer to the goal and the funny part is
+that if
+
+ align:start position:0%
+that if
+ 
+
+ align:start position:0%
+that if
+you if you used pairs of operations as
+
+ align:start position:0%
+you if you used pairs of operations as
+ 
+
+ align:start position:0%
+you if you used pairs of operations as
+the unit then then their method would
+
+ align:start position:0%
+the unit then then their method would
+ 
+
+ align:start position:0%
+the unit then then their method would
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but nice question is why people how do
+
+ align:start position:0%
+but nice question is why people how do
+ 
+
+ align:start position:0%
+but nice question is why people how do
+people make a very beautiful Theory and
+
+ align:start position:0%
+people make a very beautiful Theory and
+ 
+
+ align:start position:0%
+people make a very beautiful Theory and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh not take the next step and someone
+
+ align:start position:0%
+uh not take the next step and someone
+ 
+
+ align:start position:0%
+uh not take the next step and someone
+else does it n years later
+
+ align:start position:0%
+else does it n years later
+ 
+
+ align:start position:0%
+else does it n years later
+so I
+
+ align:start position:0%
+so I
+ 
+
+ align:start position:0%
+so I
+guess it always happens
+
+ align:start position:0%
+guess it always happens
+ 
+
+ align:start position:0%
+guess it always happens
+yes I just go and say I think machine
+
+ align:start position:0%
+yes I just go and say I think machine
+ 
+
+ align:start position:0%
+yes I just go and say I think machine
+learning is incredibly useful and we
+
+ align:start position:0%
+learning is incredibly useful and we
+ 
+
+ align:start position:0%
+learning is incredibly useful and we
+should discredit it because it really
+
+ align:start position:0%
+should discredit it because it really
+ 
+
+ align:start position:0%
+should discredit it because it really
+isn't Ai and I think a lot of the
+
+ align:start position:0%
+isn't Ai and I think a lot of the
+ 
+
+ align:start position:0%
+isn't Ai and I think a lot of the
+problems between machine learning people
+
+ align:start position:0%
+problems between machine learning people
+ 
+
+ align:start position:0%
+problems between machine learning people
+and AI people is that they're trying to
+
+ align:start position:0%
+and AI people is that they're trying to
+ 
+
+ align:start position:0%
+and AI people is that they're trying to
+do different things and they just have
+
+ align:start position:0%
+do different things and they just have
+ 
+
+ align:start position:0%
+do different things and they just have
+share this
+
+ align:start position:0%
+share this
+ 
+
+ align:start position:0%
+share this
+um and see different different important
+
+ align:start position:0%
+um and see different different important
+ 
+
+ align:start position:0%
+um and see different different important
+problems because well it's not they're
+
+ align:start position:0%
+problems because well it's not they're
+ 
+
+ align:start position:0%
+problems because well it's not they're
+not doing different things one is doing
+
+ align:start position:0%
+not doing different things one is doing
+ 
+
+ align:start position:0%
+not doing different things one is doing
+a subset of the other yes
+
+ align:start position:0%
+a subset of the other yes
+ 
+
+ align:start position:0%
+a subset of the other yes
+I the main problems intelligence and
+
+ align:start position:0%
+I the main problems intelligence and
+ 
+
+ align:start position:0%
+I the main problems intelligence and
+cognition but they are making a lot of
+
+ align:start position:0%
+cognition but they are making a lot of
+ 
+
+ align:start position:0%
+cognition but they are making a lot of
+good progress in solving certain types
+
+ align:start position:0%
+good progress in solving certain types
+ 
+
+ align:start position:0%
+good progress in solving certain types
+of really hard problems and this can be
+
+ align:start position:0%
+of really hard problems and this can be
+ 
+
+ align:start position:0%
+of really hard problems and this can be
+really useful because a lot of these are
+
+ align:start position:0%
+really useful because a lot of these are
+ 
+
+ align:start position:0%
+really useful because a lot of these are
+problems that people aren't able to
+
+ align:start position:0%
+problems that people aren't able to
+ 
+
+ align:start position:0%
+problems that people aren't able to
+solve themselves and aren't good at um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the science one at a time yeah
+
+ align:start position:0%
+is the science one at a time yeah
+ 
+
+ align:start position:0%
+is the science one at a time yeah
+sorry uh you could say that about
+
+ align:start position:0%
+sorry uh you could say that about
+ 
+
+ align:start position:0%
+sorry uh you could say that about
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+surely uh what's really important is not
+
+ align:start position:0%
+surely uh what's really important is not
+ 
+
+ align:start position:0%
+surely uh what's really important is not
+solving all sorts of useful things but
+
+ align:start position:0%
+solving all sorts of useful things but
+ 
+
+ align:start position:0%
+solving all sorts of useful things but
+getting to a higher level where you can
+
+ align:start position:0%
+getting to a higher level where you can
+ 
+
+ align:start position:0%
+getting to a higher level where you can
+solve things that no one else can
+
+ align:start position:0%
+solve things that no one else can
+ 
+
+ align:start position:0%
+solve things that no one else can
+solve what you mean important for what
+
+ align:start position:0%
+solve what you mean important for what
+ 
+
+ align:start position:0%
+solve what you mean important for what
+important for the advancement of science
+
+ align:start position:0%
+important for the advancement of science
+ 
+
+ align:start position:0%
+important for the advancement of science
+yes important for like miscellaneous
+
+ align:start position:0%
+yes important for like miscellaneous
+ 
+
+ align:start position:0%
+yes important for like miscellaneous
+applications that are useful
+
+ align:start position:0%
+applications that are useful
+ 
+
+ align:start position:0%
+applications that are useful
+people well in the long run you're dead
+
+ align:start position:0%
+people well in the long run you're dead
+ 
+
+ align:start position:0%
+people well in the long run you're dead
+so uh things like say that everything
+
+ align:start position:0%
+so uh things like say that everything
+ 
+
+ align:start position:0%
+so uh things like say that everything
+that doesn't just Advanced science is
+
+ align:start position:0%
+that doesn't just Advanced science is
+ 
+
+ align:start position:0%
+that doesn't just Advanced science is
+completely useless just crazy I don't no
+
+ align:start position:0%
+completely useless just crazy I don't no
+ 
+
+ align:start position:0%
+completely useless just crazy I don't no
+I'm saying science science has
+
+ align:start position:0%
+I'm saying science science has
+ 
+
+ align:start position:0%
+I'm saying science science has
+disappeared because the Dark Ages so
+
+ align:start position:0%
+disappeared because the Dark Ages so
+ 
+
+ align:start position:0%
+disappeared because the Dark Ages so
+it's interesting but if you say it's
+
+ align:start position:0%
+it's interesting but if you say it's
+ 
+
+ align:start position:0%
+it's interesting but if you say it's
+just advancing
+
+ align:start position:0%
+just advancing
+ 
+
+ align:start position:0%
+just advancing
+science uh yes I take the position that
+
+ align:start position:0%
+science uh yes I take the position that
+ 
+
+ align:start position:0%
+science uh yes I take the position that
+we should spend a fraction of our uh
+
+ align:start position:0%
+we should spend a fraction of our uh
+ 
+
+ align:start position:0%
+we should spend a fraction of our uh
+World Resources on long-term
+
+ align:start position:0%
+World Resources on long-term
+ 
+
+ align:start position:0%
+World Resources on long-term
+things and it's no excuse and and no one
+
+ align:start position:0%
+things and it's no excuse and and no one
+ 
+
+ align:start position:0%
+things and it's no excuse and and no one
+should say let's spend all our resources
+
+ align:start position:0%
+should say let's spend all our resources
+ 
+
+ align:start position:0%
+should say let's spend all our resources
+on immediate useful moneymaking labor
+
+ align:start position:0%
+on immediate useful moneymaking labor
+ 
+
+ align:start position:0%
+on immediate useful moneymaking labor
+saving processes I'm not saying that I
+
+ align:start position:0%
+saving processes I'm not saying that I
+ 
+
+ align:start position:0%
+saving processes I'm not saying that I
+think we should spend quite a bit of
+
+ align:start position:0%
+think we should spend quite a bit of
+ 
+
+ align:start position:0%
+think we should spend quite a bit of
+money on science but I'm saying it
+
+ align:start position:0%
+money on science but I'm saying it
+ 
+
+ align:start position:0%
+money on science but I'm saying it
+doesn't mean that anything that's not
+
+ align:start position:0%
+doesn't mean that anything that's not
+ 
+
+ align:start position:0%
+doesn't mean that anything that's not
+science is yeah but if you look at AI no
+
+ align:start position:0%
+science is yeah but if you look at AI no
+ 
+
+ align:start position:0%
+science is yeah but if you look at AI no
+money I only know about 10 people in the
+
+ align:start position:0%
+money I only know about 10 people in the
+ 
+
+ align:start position:0%
+money I only know about 10 people in the
+entire country who are thinking about
+
+ align:start position:0%
+entire country who are thinking about
+ 
+
+ align:start position:0%
+entire country who are thinking about
+hard problems in AI so it is it's not
+
+ align:start position:0%
+hard problems in AI so it is it's not
+ 
+
+ align:start position:0%
+hard problems in AI so it is it's not
+just a mild complaint there's some kind
+
+ align:start position:0%
+just a mild complaint there's some kind
+ 
+
+ align:start position:0%
+just a mild complaint there's some kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+pathology there's no support I don't
+
+ align:start position:0%
+pathology there's no support I don't
+ 
+
+ align:start position:0%
+pathology there's no support I don't
+think anybody's denying that machine
+
+ align:start position:0%
+think anybody's denying that machine
+ 
+
+ align:start position:0%
+think anybody's denying that machine
+learning is useful it's just the problem
+
+ align:start position:0%
+learning is useful it's just the problem
+ 
+
+ align:start position:0%
+learning is useful it's just the problem
+is that it seems like the obsession with
+
+ align:start position:0%
+is that it seems like the obsession with
+ 
+
+ align:start position:0%
+is that it seems like the obsession with
+machine learning is sort of like
+
+ align:start position:0%
+machine learning is sort of like
+ 
+
+ align:start position:0%
+machine learning is sort of like
+overtaking anyone like trying to make
+
+ align:start position:0%
+overtaking anyone like trying to make
+ 
+
+ align:start position:0%
+overtaking anyone like trying to make
+progress in AI so so it's like okay in
+
+ align:start position:0%
+progress in AI so so it's like okay in
+ 
+
+ align:start position:0%
+progress in AI so so it's like okay in
+the ideal world it's like they're the
+
+ align:start position:0%
+the ideal world it's like they're the
+ 
+
+ align:start position:0%
+the ideal world it's like they're the
+people who work on machine learning but
+
+ align:start position:0%
+people who work on machine learning but
+ 
+
+ align:start position:0%
+people who work on machine learning but
+then they're also the people who are
+
+ align:start position:0%
+then they're also the people who are
+ 
+
+ align:start position:0%
+then they're also the people who are
+solving the big AI problems but it seems
+
+ align:start position:0%
+solving the big AI problems but it seems
+ 
+
+ align:start position:0%
+solving the big AI problems but it seems
+like in the current world like so many
+
+ align:start position:0%
+like in the current world like so many
+ 
+
+ align:start position:0%
+like in the current world like so many
+people are doing machine learning that
+
+ align:start position:0%
+people are doing machine learning that
+ 
+
+ align:start position:0%
+people are doing machine learning that
+like and there's so many resources for
+
+ align:start position:0%
+like and there's so many resources for
+ 
+
+ align:start position:0%
+like and there's so many resources for
+it such that there's like not enough for
+
+ align:start position:0%
+it such that there's like not enough for
+ 
+
+ align:start position:0%
+it such that there's like not enough for
+people who are doing
+
+ align:start position:0%
+people who are doing
+ 
+
+ align:start position:0%
+people who are doing
+AI yeah well the complaint my complaint
+
+ align:start position:0%
+AI yeah well the complaint my complaint
+ 
+
+ align:start position:0%
+AI yeah well the complaint my complaint
+is that there's almost no one doing
+
+ align:start position:0%
+is that there's almost no one doing
+ 
+
+ align:start position:0%
+is that there's almost no one doing
+AI it's very peculiar so uh what is it
+
+ align:start position:0%
+AI it's very peculiar so uh what is it
+ 
+
+ align:start position:0%
+AI it's very peculiar so uh what is it
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the uh current
+
+ align:start position:0%
+the uh current
+ 
+
+ align:start position:0%
+the uh current
+culture of science and technology that
+
+ align:start position:0%
+culture of science and technology that
+ 
+
+ align:start position:0%
+culture of science and technology that
+that causes this to
+
+ align:start position:0%
+that causes this to
+ 
+
+ align:start position:0%
+that causes this to
+happen a great example would be uh
+
+ align:start position:0%
+happen a great example would be uh
+ 
+
+ align:start position:0%
+happen a great example would be uh
+what's the gross product of what's the
+
+ align:start position:0%
+what's the gross product of what's the
+ 
+
+ align:start position:0%
+what's the gross product of what's the
+income of
+
+ align:start position:0%
+income of
+ 
+
+ align:start position:0%
+income of
+IBM it's big company how come they're
+
+ align:start position:0%
+IBM it's big company how come they're
+ 
+
+ align:start position:0%
+IBM it's big company how come they're
+doing that funny thing I keep forgetting
+
+ align:start position:0%
+doing that funny thing I keep forgetting
+ 
+
+ align:start position:0%
+doing that funny thing I keep forgetting
+how come they're doing
+
+ align:start position:0%
+how come they're doing
+ 
+
+ align:start position:0%
+how come they're doing
+Watson isn't that because it's cheaper
+
+ align:start position:0%
+Watson isn't that because it's cheaper
+ 
+
+ align:start position:0%
+Watson isn't that because it's cheaper
+than Super Bowl has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're getting kid they got a lot more
+
+ align:start position:0%
+they're getting kid they got a lot more
+ 
+
+ align:start position:0%
+they're getting kid they got a lot more
+publicity out of it than they would have
+
+ align:start position:0%
+publicity out of it than they would have
+ 
+
+ align:start position:0%
+publicity out of it than they would have
+gotten if a lot Super Bowl
+
+ align:start position:0%
+gotten if a lot Super Bowl
+ 
+
+ align:start position:0%
+gotten if a lot Super Bowl
+mhm I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but it's a serious company it fired
+
+ align:start position:0%
+so but it's a serious company it fired
+ 
+
+ align:start position:0%
+so but it's a serious company it fired
+its real AI
+
+ align:start position:0%
+its real AI
+ 
+
+ align:start position:0%
+its real AI
+group and
+
+ align:start position:0%
+group and
+ 
+
+ align:start position:0%
+group and
+what maybe properly question is um
+
+ align:start position:0%
+what maybe properly question is um
+ 
+
+ align:start position:0%
+what maybe properly question is um
+perhaps supplementary observation is
+
+ align:start position:0%
+perhaps supplementary observation is
+ 
+
+ align:start position:0%
+perhaps supplementary observation is
+that when
+
+ align:start position:0%
+that when
+ 
+
+ align:start position:0%
+that when
+we were doing stuff a long time ago it
+
+ align:start position:0%
+we were doing stuff a long time ago it
+ 
+
+ align:start position:0%
+we were doing stuff a long time ago it
+was regarded as a great success if you
+
+ align:start position:0%
+was regarded as a great success if you
+ 
+
+ align:start position:0%
+was regarded as a great success if you
+could get a program to do something for
+
+ align:start position:0%
+could get a program to do something for
+ 
+
+ align:start position:0%
+could get a program to do something for
+the first time and the feel taken over
+
+ align:start position:0%
+the first time and the feel taken over
+ 
+
+ align:start position:0%
+the first time and the feel taken over
+by people want to measure how much
+
+ align:start position:0%
+by people want to measure how much
+ 
+
+ align:start position:0%
+by people want to measure how much
+better your thing is than the next thing
+
+ align:start position:0%
+better your thing is than the next thing
+ 
+
+ align:start position:0%
+better your thing is than the next thing
+and there only a few kinds of problems
+
+ align:start position:0%
+and there only a few kinds of problems
+ 
+
+ align:start position:0%
+and there only a few kinds of problems
+that are suscep to kind scoring
+
+ align:start position:0%
+that are suscep to kind scoring
+ 
+
+ align:start position:0%
+that are suscep to kind scoring
+comparison as a consequence people
+
+ align:start position:0%
+comparison as a consequence people
+ 
+
+ align:start position:0%
+comparison as a consequence people
+working on those of problems are not
+
+ align:start position:0%
+working on those of problems are not
+ 
+
+ align:start position:0%
+working on those of problems are not
+doing things that ought to be
+
+ align:start position:0%
+doing things that ought to be
+ 
+
+ align:start position:0%
+doing things that ought to be
+done like doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm so it's a lot easier to write an
+
+ align:start position:0%
+mhm so it's a lot easier to write an
+ 
+
+ align:start position:0%
+mhm so it's a lot easier to write an
+article about how your par is 1% better
+
+ align:start position:0%
+article about how your par is 1% better
+ 
+
+ align:start position:0%
+article about how your par is 1% better
+than somebody else's part to get a
+
+ align:start position:0%
+than somebody else's part to get a
+ 
+
+ align:start position:0%
+than somebody else's part to get a
+program have common sense
+
+ align:start position:0%
+program have common sense
+ 
+
+ align:start position:0%
+program have common sense
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+yeah well now there are four or five
+
+ align:start position:0%
+yeah well now there are four or five
+ 
+
+ align:start position:0%
+yeah well now there are four or five
+common sense research groups I
+
+ align:start position:0%
+common sense research groups I
+ 
+
+ align:start position:0%
+common sense research groups I
+think how many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know if any of them make a
+
+ align:start position:0%
+I don't know if any of them make a
+ 
+
+ align:start position:0%
+I don't know if any of them make a
+living
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yet they're collecting common sense I'm
+
+ align:start position:0%
+yet they're collecting common sense I'm
+ 
+
+ align:start position:0%
+yet they're collecting common sense I'm
+not sure they have common sense
+
+ align:start position:0%
+not sure they have common sense
+ 
+
+ align:start position:0%
+not sure they have common sense
+mhm and you can measure how many how
+
+ align:start position:0%
+mhm and you can measure how many how
+ 
+
+ align:start position:0%
+mhm and you can measure how many how
+many things you know
+
+ align:start position:0%
+many things you know
+ 
+
+ align:start position:0%
+many things you know
+but it's not they're measuring how
+
+ align:start position:0%
+but it's not they're measuring how
+ 
+
+ align:start position:0%
+but it's not they're measuring how
+effective they
+
+ align:start position:0%
+effective they
+ 
+
+ align:start position:0%
+effective they
+are yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wonder how hard it would be to make a
+
+ align:start position:0%
+I wonder how hard it would be to make a
+ 
+
+ align:start position:0%
+I wonder how hard it would be to make a
+program that that knows
+
+ align:start position:0%
+program that that knows
+ 
+
+ align:start position:0%
+program that that knows
+mathematics and a lot of
+
+ align:start position:0%
+mathematics and a lot of
+ 
+
+ align:start position:0%
+mathematics and a lot of
+mathematics and does the kinds of things
+
+ align:start position:0%
+mathematics and does the kinds of things
+ 
+
+ align:start position:0%
+mathematics and does the kinds of things
+that that mathematicians
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do but somebody would have to pay them
+
+ align:start position:0%
+do but somebody would have to pay them
+ 
+
+ align:start position:0%
+do but somebody would have to pay them
+to do it and that's where do you get
+
+ align:start position:0%
+to do it and that's where do you get
+ 
+
+ align:start position:0%
+to do it and that's where do you get
+support for common sense of in
+
+ align:start position:0%
+support for common sense of in
+ 
+
+ align:start position:0%
+support for common sense of in
+mathematical
+
+ align:start position:0%
+mathematical
+ 
+
+ align:start position:0%
+mathematical
+reasoning it's a beautiful
+
+ align:start position:0%
+reasoning it's a beautiful
+ 
+
+ align:start position:0%
+reasoning it's a beautiful
+subject well there was L and there was
+
+ align:start position:0%
+subject well there was L and there was
+ 
+
+ align:start position:0%
+subject well there was L and there was
+Maxima and there was slal and there was
+
+ align:start position:0%
+Maxima and there was slal and there was
+ 
+
+ align:start position:0%
+Maxima and there was slal and there was
+Moses mhm so lots
+
+ align:start position:0%
+Moses mhm so lots
+ 
+
+ align:start position:0%
+Moses mhm so lots
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+and right and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wol it might be for all its faults well
+
+ align:start position:0%
+wol it might be for all its faults well
+ 
+
+ align:start position:0%
+wol it might be for all its faults well
+wfrs going to get people to work on real
+
+ align:start position:0%
+wfrs going to get people to work on real
+ 
+
+ align:start position:0%
+wfrs going to get people to work on real
+AI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+he's he's hired some people to try to
+
+ align:start position:0%
+he's he's hired some people to try to
+ 
+
+ align:start position:0%
+he's he's hired some people to try to
+make what's it called Wolfram Alpha at
+
+ align:start position:0%
+make what's it called Wolfram Alpha at
+ 
+
+ align:start position:0%
+make what's it called Wolfram Alpha at
+school to make it have more and more
+
+ align:start position:0%
+school to make it have more and more
+ 
+
+ align:start position:0%
+school to make it have more and more
+common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense yeah
+
+ align:start position:0%
+sense yeah
+ 
+
+ align:start position:0%
+sense yeah
+um I also think the
+
+ align:start position:0%
+um I also think the
+ 
+
+ align:start position:0%
+um I also think the
+big the challenges to try to make
+
+ align:start position:0%
+big the challenges to try to make
+ 
+
+ align:start position:0%
+big the challenges to try to make
+systems that want to do math or things
+
+ align:start position:0%
+systems that want to do math or things
+ 
+
+ align:start position:0%
+systems that want to do math or things
+that mathematicians do is deciding what
+
+ align:start position:0%
+that mathematicians do is deciding what
+ 
+
+ align:start position:0%
+that mathematicians do is deciding what
+problems are interesting wants to work
+
+ align:start position:0%
+problems are interesting wants to work
+ 
+
+ align:start position:0%
+problems are interesting wants to work
+on is there are there is automatic proof
+
+ align:start position:0%
+on is there are there is automatic proof
+ 
+
+ align:start position:0%
+on is there are there is automatic proof
+verification improving although those
+
+ align:start position:0%
+verification improving although those
+ 
+
+ align:start position:0%
+verification improving although those
+are also rather difficult problems when
+
+ align:start position:0%
+are also rather difficult problems when
+ 
+
+ align:start position:0%
+are also rather difficult problems when
+you get complicated things that don't
+
+ align:start position:0%
+you get complicated things that don't
+ 
+
+ align:start position:0%
+you get complicated things that don't
+seem to work out as well
+
+ align:start position:0%
+seem to work out as well
+ 
+
+ align:start position:0%
+seem to work out as well
+but what should be proven is something
+
+ align:start position:0%
+but what should be proven is something
+ 
+
+ align:start position:0%
+but what should be proven is something
+that I've never seen T tackled and
+
+ align:start position:0%
+that I've never seen T tackled and
+ 
+
+ align:start position:0%
+that I've never seen T tackled and
+doesn't seem
+
+ align:start position:0%
+doesn't seem
+ 
+
+ align:start position:0%
+doesn't seem
+all that P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the well Doug L's first piece of work
+
+ align:start position:0%
+the well Doug L's first piece of work
+ 
+
+ align:start position:0%
+the well Doug L's first piece of work
+was on a thesis that um did a kind of
+
+ align:start position:0%
+was on a thesis that um did a kind of
+ 
+
+ align:start position:0%
+was on a thesis that um did a kind of
+mathematical exploration on the basis
+
+ align:start position:0%
+mathematical exploration on the basis
+ 
+
+ align:start position:0%
+mathematical exploration on the basis
+of some theory of why a piece of math
+
+ align:start position:0%
+of some theory of why a piece of math
+ 
+
+ align:start position:0%
+of some theory of why a piece of math
+why why an expression or a
+
+ align:start position:0%
+why why an expression or a
+ 
+
+ align:start position:0%
+why why an expression or a
+transformation might be interesting so
+
+ align:start position:0%
+transformation might be interesting so
+ 
+
+ align:start position:0%
+transformation might be interesting so
+even that had had some prec oh really
+
+ align:start position:0%
+even that had had some prec oh really
+ 
+
+ align:start position:0%
+even that had had some prec oh really
+and it was
+
+ align:start position:0%
+and it was
+ 
+
+ align:start position:0%
+and it was
+uh it was a system that started from
+
+ align:start position:0%
+uh it was a system that started from
+ 
+
+ align:start position:0%
+uh it was a system that started from
+scratch and proved a few theorems and
+
+ align:start position:0%
+scratch and proved a few theorems and
+ 
+
+ align:start position:0%
+scratch and proved a few theorems and
+looked around for things that were
+
+ align:start position:0%
+looked around for things that were
+ 
+
+ align:start position:0%
+looked around for things that were
+interesting and invented the opposite of
+
+ align:start position:0%
+interesting and invented the opposite of
+ 
+
+ align:start position:0%
+interesting and invented the opposite of
+uh police com advisor or something like
+
+ align:start position:0%
+uh police com advisor or something like
+ 
+
+ align:start position:0%
+uh police com advisor or something like
+that yeah that was
+
+ align:start position:0%
+that yeah that was
+ 
+
+ align:start position:0%
+that yeah that was
+am yeah and it was pretty exciting
+
+ align:start position:0%
+am yeah and it was pretty exciting
+ 
+
+ align:start position:0%
+am yeah and it was pretty exciting
+and that's something that uh anybody
+
+ align:start position:0%
+and that's something that uh anybody
+ 
+
+ align:start position:0%
+and that's something that uh anybody
+could could take up again any time and U
+
+ align:start position:0%
+could could take up again any time and U
+ 
+
+ align:start position:0%
+could could take up again any time and U
+be a great thesis topic
+
+ align:start position:0%
+be a great thesis topic
+ 
+
+ align:start position:0%
+be a great thesis topic
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+lenet the phenomenon in am was that it
+
+ align:start position:0%
+lenet the phenomenon in am was that it
+ 
+
+ align:start position:0%
+lenet the phenomenon in am was that it
+did it discovered Division and prime
+
+ align:start position:0%
+did it discovered Division and prime
+ 
+
+ align:start position:0%
+did it discovered Division and prime
+numbers and and a number I think I
+
+ align:start position:0%
+numbers and and a number I think I
+ 
+
+ align:start position:0%
+numbers and and a number I think I
+talked about it uh and as as Pat says it
+
+ align:start position:0%
+talked about it uh and as as Pat says it
+ 
+
+ align:start position:0%
+talked about it uh and as as Pat says it
+was it had a bunch of Criterion for
+
+ align:start position:0%
+was it had a bunch of Criterion for
+ 
+
+ align:start position:0%
+was it had a bunch of Criterion for
+interestingness and it would find you
+
+ align:start position:0%
+interestingness and it would find you
+ 
+
+ align:start position:0%
+interestingness and it would find you
+know sets that were unusually large or
+
+ align:start position:0%
+know sets that were unusually large or
+ 
+
+ align:start position:0%
+know sets that were unusually large or
+unusually
+
+ align:start position:0%
+unusually
+ 
+
+ align:start position:0%
+unusually
+small uh and uh try to make more things
+
+ align:start position:0%
+small uh and uh try to make more things
+ 
+
+ align:start position:0%
+small uh and uh try to make more things
+like them and that sort of thing but uh
+
+ align:start position:0%
+like them and that sort of thing but uh
+ 
+
+ align:start position:0%
+like them and that sort of thing but uh
+it it's never been followed up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and school
+
+ align:start position:0%
+and school
+ 
+
+ align:start position:0%
+and school
+olyp yeah high school algebra is a
+
+ align:start position:0%
+olyp yeah high school algebra is a
+ 
+
+ align:start position:0%
+olyp yeah high school algebra is a
+wonderful area and there was BOS thesis
+
+ align:start position:0%
+wonderful area and there was BOS thesis
+ 
+
+ align:start position:0%
+wonderful area and there was BOS thesis
+which did a little bit of it and I've
+
+ align:start position:0%
+which did a little bit of it and I've
+ 
+
+ align:start position:0%
+which did a little bit of it and I've
+never seen now there's so much more
+
+ align:start position:0%
+never seen now there's so much more
+ 
+
+ align:start position:0%
+never seen now there's so much more
+known about natural language You' think
+
+ align:start position:0%
+known about natural language You' think
+ 
+
+ align:start position:0%
+known about natural language You' think
+some somebody would do a super babro
+
+ align:start position:0%
+some somebody would do a super babro
+ 
+
+ align:start position:0%
+some somebody would do a super babro
+program that might actually be good
+
+ align:start position:0%
+program that might actually be good
+ 
+
+ align:start position:0%
+program that might actually be good
+enough to connect into Google so that it
+
+ align:start position:0%
+enough to connect into Google so that it
+ 
+
+ align:start position:0%
+enough to connect into Google so that it
+would solve problems that people real
+
+ align:start position:0%
+would solve problems that people real
+ 
+
+ align:start position:0%
+would solve problems that people real
+people face every now and
+
+ align:start position:0%
+people face every now and
+ 
+
+ align:start position:0%
+people face every now and
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah the appearance
+
+ align:start position:0%
+so yeah the appearance
+ 
+
+ align:start position:0%
+so yeah the appearance
+of of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the new Siri and dragon things which
+
+ align:start position:0%
+uh the new Siri and dragon things which
+ 
+
+ align:start position:0%
+uh the new Siri and dragon things which
+actually answer useful questions and wol
+
+ align:start position:0%
+actually answer useful questions and wol
+ 
+
+ align:start position:0%
+actually answer useful questions and wol
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+alpha uh might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change there might be an industry in in
+
+ align:start position:0%
+change there might be an industry in in
+ 
+
+ align:start position:0%
+change there might be an industry in in
+common sense
+
+ align:start position:0%
+common sense
+ 
+
+ align:start position:0%
+common sense
+AI uh that's actually useful because a
+
+ align:start position:0%
+AI uh that's actually useful because a
+ 
+
+ align:start position:0%
+AI uh that's actually useful because a
+few million people might start using it
+
+ align:start position:0%
+few million people might start using it
+ 
+
+ align:start position:0%
+few million people might start using it
+as soon as it gets just a little bit
+
+ align:start position:0%
+as soon as it gets just a little bit
+ 
+
+ align:start position:0%
+as soon as it gets just a little bit
+better and uh I find that dragon and
+
+ align:start position:0%
+better and uh I find that dragon and
+ 
+
+ align:start position:0%
+better and uh I find that dragon and
+Siri I haven't used Siri but dragon now
+
+ align:start position:0%
+Siri I haven't used Siri but dragon now
+ 
+
+ align:start position:0%
+Siri I haven't used Siri but dragon now
+uh has a thing called Dragon search you
+
+ align:start position:0%
+uh has a thing called Dragon search you
+ 
+
+ align:start position:0%
+uh has a thing called Dragon search you
+talk to it and
+
+ align:start position:0%
+talk to it and
+ 
+
+ align:start position:0%
+talk to it and
+uh ask a question in ordinary English
+
+ align:start position:0%
+uh ask a question in ordinary English
+ 
+
+ align:start position:0%
+uh ask a question in ordinary English
+and it goes to the web and makes a uh
+
+ align:start position:0%
+and it goes to the web and makes a uh
+ 
+
+ align:start position:0%
+and it goes to the web and makes a uh
+Google search sentence out of what you
+
+ align:start position:0%
+Google search sentence out of what you
+ 
+
+ align:start position:0%
+Google search sentence out of what you
+said and good fraction of the time it
+
+ align:start position:0%
+said and good fraction of the time it
+ 
+
+ align:start position:0%
+said and good fraction of the time it
+saves you a half hour of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+search none of those really have any
+
+ align:start position:0%
+search none of those really have any
+ 
+
+ align:start position:0%
+search none of those really have any
+idea of context though like a very
+
+ align:start position:0%
+idea of context though like a very
+ 
+
+ align:start position:0%
+idea of context though like a very
+simple Improvement would be and wolf
+
+ align:start position:0%
+simple Improvement would be and wolf
+ 
+
+ align:start position:0%
+simple Improvement would be and wolf
+from Mal already does this a little bit
+
+ align:start position:0%
+from Mal already does this a little bit
+ 
+
+ align:start position:0%
+from Mal already does this a little bit
+as to say it assuming that you meant X
+
+ align:start position:0%
+as to say it assuming that you meant X
+ 
+
+ align:start position:0%
+as to say it assuming that you meant X
+did you mean y or Z and you can click
+
+ align:start position:0%
+did you mean y or Z and you can click
+ 
+
+ align:start position:0%
+did you mean y or Z and you can click
+those instead and that's as far as the
+
+ align:start position:0%
+those instead and that's as far as the
+ 
+
+ align:start position:0%
+those instead and that's as far as the
+conversation we pull from out right but
+
+ align:start position:0%
+conversation we pull from out right but
+ 
+
+ align:start position:0%
+conversation we pull from out right but
+you're a person and if it had a lot of
+
+ align:start position:0%
+you're a person and if it had a lot of
+ 
+
+ align:start position:0%
+you're a person and if it had a lot of
+information about
+
+ align:start position:0%
+information about
+ 
+
+ align:start position:0%
+information about
+you uh uh you could collect first of all
+
+ align:start position:0%
+you uh uh you could collect first of all
+ 
+
+ align:start position:0%
+you uh uh you could collect first of all
+it would say what kind of person are you
+
+ align:start position:0%
+it would say what kind of person are you
+ 
+
+ align:start position:0%
+it would say what kind of person are you
+and you'd give your biography and maybe
+
+ align:start position:0%
+and you'd give your biography and maybe
+ 
+
+ align:start position:0%
+and you'd give your biography and maybe
+we'll get comments sense databases that
+
+ align:start position:0%
+we'll get comments sense databases that
+ 
+
+ align:start position:0%
+we'll get comments sense databases that
+say well here are the kinds of things
+
+ align:start position:0%
+say well here are the kinds of things
+ 
+
+ align:start position:0%
+say well here are the kinds of things
+that uh somebody who likes pole vating
+
+ align:start position:0%
+that uh somebody who likes pole vating
+ 
+
+ align:start position:0%
+that uh somebody who likes pole vating
+is likely to
+
+ align:start position:0%
+is likely to
+ 
+
+ align:start position:0%
+is likely to
+know we already have the the what kind
+
+ align:start position:0%
+know we already have the the what kind
+ 
+
+ align:start position:0%
+know we already have the the what kind
+of person are you uh databases in social
+
+ align:start position:0%
+of person are you uh databases in social
+ 
+
+ align:start position:0%
+of person are you uh databases in social
+networks that's what it is right M or
+
+ align:start position:0%
+networks that's what it is right M or
+ 
+
+ align:start position:0%
+networks that's what it is right M or
+Google's personalized search
+
+ align:start position:0%
+Google's personalized search
+ 
+
+ align:start position:0%
+Google's personalized search
+yeah well I just joined Facebook by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mistake and all sorts of people want to
+
+ align:start position:0%
+mistake and all sorts of people want to
+ 
+
+ align:start position:0%
+mistake and all sorts of people want to
+link and all you have to do is look at
+
+ align:start position:0%
+link and all you have to do is look at
+ 
+
+ align:start position:0%
+link and all you have to do is look at
+their biography and see what music they
+
+ align:start position:0%
+their biography and see what music they
+ 
+
+ align:start position:0%
+their biography and see what music they
+like and you can see you don't want to
+
+ align:start position:0%
+like and you can see you don't want to
+ 
+
+ align:start position:0%
+like and you can see you don't want to
+have that person as a
+
+ align:start position:0%
+have that person as a
+ 
+
+ align:start position:0%
+have that person as a
+friend but I wish uh has anybody written
+
+ align:start position:0%
+friend but I wish uh has anybody written
+ 
+
+ align:start position:0%
+friend but I wish uh has anybody written
+a program to automate
+
+ align:start position:0%
+a program to automate
+ 
+
+ align:start position:0%
+a program to automate
+this I could tell them I don't like
+
+ align:start position:0%
+this I could tell them I don't like
+ 
+
+ align:start position:0%
+this I could tell them I don't like
+music written in the last 20
+
+ align:start position:0%
+music written in the last 20
+ 
+
+ align:start position:0%
+music written in the last 20
+years uh and that would get rid of about
+
+ align:start position:0%
+years uh and that would get rid of about
+ 
+
+ align:start position:0%
+years uh and that would get rid of about
+half of them right off
+
+ align:start position:0%
+half of them right off
+ 
+
+ align:start position:0%
+half of them right off
+of course there might be Freeman Dyson
+
+ align:start position:0%
+of course there might be Freeman Dyson
+ 
+
+ align:start position:0%
+of course there might be Freeman Dyson
+or somebody happens to like one of these
+
+ align:start position:0%
+or somebody happens to like one of these
+ 
+
+ align:start position:0%
+or somebody happens to like one of these
+Tunes I don't know so then you have
+
+ align:start position:0%
+Tunes I don't know so then you have
+ 
+
+ align:start position:0%
+Tunes I don't know so then you have
+to so you have to make a
+
+ align:start position:0%
+to so you have to make a
+ 
+
+ align:start position:0%
+to so you have to make a
+hierarchy if the person happens to be a
+
+ align:start position:0%
+hierarchy if the person happens to be a
+ 
+
+ align:start position:0%
+hierarchy if the person happens to be a
+really good physicist then then we'll
+
+ align:start position:0%
+really good physicist then then we'll
+ 
+
+ align:start position:0%
+really good physicist then then we'll
+flush that particular filter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah also Google's personalized search
+
+ align:start position:0%
+yeah also Google's personalized search
+ 
+
+ align:start position:0%
+yeah also Google's personalized search
+profile thinks that I'm a man because
+
+ align:start position:0%
+profile thinks that I'm a man because
+ 
+
+ align:start position:0%
+profile thinks that I'm a man because
+apparently I've searched too many
+
+ align:start position:0%
+apparently I've searched too many
+ 
+
+ align:start position:0%
+apparently I've searched too many
+computer science things in the
+
+ align:start position:0%
+computer science things in the
+ 
+
+ align:start position:0%
+computer science things in the
+past that's pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good maybe thinks most people are a man
+
+ align:start position:0%
+good maybe thinks most people are a man
+ 
+
+ align:start position:0%
+good maybe thinks most people are a man
+oh I don't know like with with other
+
+ align:start position:0%
+oh I don't know like with with other
+ 
+
+ align:start position:0%
+oh I don't know like with with other
+women they they get it right but like if
+
+ align:start position:0%
+women they they get it right but like if
+ 
+
+ align:start position:0%
+women they they get it right but like if
+you're if you happen to be you know um a
+
+ align:start position:0%
+you're if you happen to be you know um a
+ 
+
+ align:start position:0%
+you're if you happen to be you know um a
+woman who does computer techage stuff
+
+ align:start position:0%
+woman who does computer techage stuff
+ 
+
+ align:start position:0%
+woman who does computer techage stuff
+and if you happen to do a lot of search
+
+ align:start position:0%
+and if you happen to do a lot of search
+ 
+
+ align:start position:0%
+and if you happen to do a lot of search
+on like programming for instance like
+
+ align:start position:0%
+on like programming for instance like
+ 
+
+ align:start position:0%
+on like programming for instance like
+looking up apis of things then it it
+
+ align:start position:0%
+looking up apis of things then it it
+ 
+
+ align:start position:0%
+looking up apis of things then it it
+tends to try to think that you're a man
+
+ align:start position:0%
+tends to try to think that you're a man
+ 
+
+ align:start position:0%
+tends to try to think that you're a man
+does it store the gender as a Boolean or
+
+ align:start position:0%
+does it store the gender as a Boolean or
+ 
+
+ align:start position:0%
+does it store the gender as a Boolean or
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+it I I saw this like a while ago and it
+
+ align:start position:0%
+it I I saw this like a while ago and it
+ 
+
+ align:start position:0%
+it I I saw this like a while ago and it
+was just like according to this it
+
+ align:start position:0%
+was just like according to this it
+ 
+
+ align:start position:0%
+was just like according to this it
+here's what they think that you are and
+
+ align:start position:0%
+here's what they think that you are and
+ 
+
+ align:start position:0%
+here's what they think that you are and
+at the top it was like we think you're a
+
+ align:start position:0%
+at the top it was like we think you're a
+ 
+
+ align:start position:0%
+at the top it was like we think you're a
+man I I'm interested to know though like
+
+ align:start position:0%
+man I I'm interested to know though like
+ 
+
+ align:start position:0%
+man I I'm interested to know though like
+how manly exactly you
+
+ align:start position:0%
+how manly exactly you
+ 
+
+ align:start position:0%
+how manly exactly you
+become so I don't think they actually
+
+ align:start position:0%
+become so I don't think they actually
+ 
+
+ align:start position:0%
+become so I don't think they actually
+tell you like their internal
+
+ align:start position:0%
+tell you like their internal
+ 
+
+ align:start position:0%
+tell you like their internal
+representation of of who you are um but
+
+ align:start position:0%
+representation of of who you are um but
+ 
+
+ align:start position:0%
+representation of of who you are um but
+you just get to see like a couple
+
+ align:start position:0%
+you just get to see like a couple
+ 
+
+ align:start position:0%
+you just get to see like a couple
+categories like male 25 to 35 um
+
+ align:start position:0%
+categories like male 25 to 35 um
+ 
+
+ align:start position:0%
+categories like male 25 to 35 um
+interested in computers interested in in
+
+ align:start position:0%
+interested in computers interested in in
+ 
+
+ align:start position:0%
+interested in computers interested in in
+ETC um I'm sure they they keep it as
+
+ align:start position:0%
+ETC um I'm sure they they keep it as
+ 
+
+ align:start position:0%
+ETC um I'm sure they they keep it as
+flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somewhere you could cross correlate that
+
+ align:start position:0%
+somewhere you could cross correlate that
+ 
+
+ align:start position:0%
+somewhere you could cross correlate that
+with geography and be like this is the
+
+ align:start position:0%
+with geography and be like this is the
+ 
+
+ align:start position:0%
+with geography and be like this is the
+man cleanest level in a certain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is there anything in Facebook that would
+
+ align:start position:0%
+is there anything in Facebook that would
+ 
+
+ align:start position:0%
+is there anything in Facebook that would
+help us get a common sense database or
+
+ align:start position:0%
+help us get a common sense database or
+ 
+
+ align:start position:0%
+help us get a common sense database or
+is it
+
+ align:start position:0%
+is it
+ 
+
+ align:start position:0%
+is it
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+there's or is there
+
+ align:start position:0%
+there's or is there
+ 
+
+ align:start position:0%
+there's or is there
+no no useful
+
+ align:start position:0%
+no no useful
+ 
+
+ align:start position:0%
+no no useful
+knowledge must be something that well
+
+ align:start position:0%
+knowledge must be something that well
+ 
+
+ align:start position:0%
+knowledge must be something that well
+apparently a few years back for Hon's
+
+ align:start position:0%
+apparently a few years back for Hon's
+ 
+
+ align:start position:0%
+apparently a few years back for Hon's
+class somebody made um a program that
+
+ align:start position:0%
+class somebody made um a program that
+ 
+
+ align:start position:0%
+class somebody made um a program that
+could find out who was gay or not um
+
+ align:start position:0%
+could find out who was gay or not um
+ 
+
+ align:start position:0%
+could find out who was gay or not um
+even if they don't put gay or not gay on
+
+ align:start position:0%
+even if they don't put gay or not gay on
+ 
+
+ align:start position:0%
+even if they don't put gay or not gay on
+their profile like based on who their
+
+ align:start position:0%
+their profile like based on who their
+ 
+
+ align:start position:0%
+their profile like based on who their
+friends
+
+ align:start position:0%
+friends
+ 
+
+ align:start position:0%
+friends
+are yeah my friend is most gay they fall
+
+ align:start position:0%
+are yeah my friend is most gay they fall
+ 
+
+ align:start position:0%
+are yeah my friend is most gay they fall
+out this is my statistical is actually
+
+ align:start position:0%
+out this is my statistical is actually
+ 
+
+ align:start position:0%
+out this is my statistical is actually
+useful because you could specify that
+
+ align:start position:0%
+useful because you could specify that
+ 
+
+ align:start position:0%
+useful because you could specify that
+you're looking for someone who is 75
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+female how many women's names begin with
+
+ align:start position:0%
+female how many women's names begin with
+ 
+
+ align:start position:0%
+female how many women's names begin with
+the letter X begin with the letter x X
+
+ align:start position:0%
+the letter X begin with the letter x X
+ 
+
+ align:start position:0%
+the letter X begin with the letter x X
+that may be your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem yes it could
+
+ align:start position:0%
+problem yes it could
+ 
+
+ align:start position:0%
+problem yes it could
+be I heard that China is allowing more
+
+ align:start position:0%
+be I heard that China is allowing more
+ 
+
+ align:start position:0%
+be I heard that China is allowing more
+names is
+
+ align:start position:0%
+names is
+ 
+
+ align:start position:0%
+names is
+allowing well I read an article which
+
+ align:start position:0%
+allowing well I read an article which
+ 
+
+ align:start position:0%
+allowing well I read an article which
+said there only there are only about a
+
+ align:start position:0%
+said there only there are only about a
+ 
+
+ align:start position:0%
+said there only there are only about a
+hundred
+
+ align:start position:0%
+hundred
+ 
+
+ align:start position:0%
+hundred
+names
+
+ align:start position:0%
+names
+ 
+
+ align:start position:0%
+names
+in most of
+
+ align:start position:0%
+in most of
+ 
+
+ align:start position:0%
+in most of
+China and
+
+ align:start position:0%
+China and
+ 
+
+ align:start position:0%
+China and
+and uh in fact there was a law that that
+
+ align:start position:0%
+and uh in fact there was a law that that
+ 
+
+ align:start position:0%
+and uh in fact there was a law that that
+both your names have to be from this
+
+ align:start position:0%
+both your names have to be from this
+ 
+
+ align:start position:0%
+both your names have to be from this
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+set and so there are only 10,000
+
+ align:start position:0%
+set and so there are only 10,000
+ 
+
+ align:start position:0%
+set and so there are only 10,000
+different pairs of
+
+ align:start position:0%
+different pairs of
+ 
+
+ align:start position:0%
+different pairs of
+names do I mean that yeah family names
+
+ align:start position:0%
+names do I mean that yeah family names
+ 
+
+ align:start position:0%
+names do I mean that yeah family names
+are there a lot of family names um well
+
+ align:start position:0%
+are there a lot of family names um well
+ 
+
+ align:start position:0%
+are there a lot of family names um well
+I feel like there aren't really
+
+ align:start position:0%
+I feel like there aren't really
+ 
+
+ align:start position:0%
+I feel like there aren't really
+restrictions for uh name as long as
+
+ align:start position:0%
+restrictions for uh name as long as
+ 
+
+ align:start position:0%
+restrictions for uh name as long as
+they're Chinese characters right I I
+
+ align:start position:0%
+they're Chinese characters right I I
+ 
+
+ align:start position:0%
+they're Chinese characters right I I
+heard about like a lawsuit in China
+
+ align:start position:0%
+heard about like a lawsuit in China
+ 
+
+ align:start position:0%
+heard about like a lawsuit in China
+where somebody wanted to named their kid
+
+ align:start position:0%
+where somebody wanted to named their kid
+ 
+
+ align:start position:0%
+where somebody wanted to named their kid
+something something.com in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+government but as long as you pick you
+
+ align:start position:0%
+government but as long as you pick you
+ 
+
+ align:start position:0%
+government but as long as you pick you
+know like real Chinese characters you
+
+ align:start position:0%
+know like real Chinese characters you
+ 
+
+ align:start position:0%
+know like real Chinese characters you
+can name your kid like big poopy head
+
+ align:start position:0%
+can name your kid like big poopy head
+ 
+
+ align:start position:0%
+can name your kid like big poopy head
+and it's okay in fact naming your kid
+
+ align:start position:0%
+and it's okay in fact naming your kid
+ 
+
+ align:start position:0%
+and it's okay in fact naming your kid
+big poopy head is actually rather common
+
+ align:start position:0%
+big poopy head is actually rather common
+ 
+
+ align:start position:0%
+big poopy head is actually rather common
+in the countryside because there's some
+
+ align:start position:0%
+in the countryside because there's some
+ 
+
+ align:start position:0%
+in the countryside because there's some
+Superstition that believes that if your
+
+ align:start position:0%
+Superstition that believes that if your
+ 
+
+ align:start position:0%
+Superstition that believes that if your
+kid has a really terrible name then uh
+
+ align:start position:0%
+kid has a really terrible name then uh
+ 
+
+ align:start position:0%
+kid has a really terrible name then uh
+he won't die during childhood because
+
+ align:start position:0%
+he won't die during childhood because
+ 
+
+ align:start position:0%
+he won't die during childhood because
+even the devil won't want want him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for all we know it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true say knowledge are you only allowed
+
+ align:start position:0%
+true say knowledge are you only allowed
+ 
+
+ align:start position:0%
+true say knowledge are you only allowed
+to one first and last name though
+
+ align:start position:0%
+to one first and last name though
+ 
+
+ align:start position:0%
+to one first and last name though
+because it seems like you should only
+
+ align:start position:0%
+because it seems like you should only
+ 
+
+ align:start position:0%
+because it seems like you should only
+need two names and then just give
+
+ align:start position:0%
+need two names and then just give
+ 
+
+ align:start position:0%
+need two names and then just give
+everyone at most 64 names and that
+
+ align:start position:0%
+everyone at most 64 names and that
+ 
+
+ align:start position:0%
+everyone at most 64 names and that
+should cover all China I think in
+
+ align:start position:0%
+should cover all China I think in
+ 
+
+ align:start position:0%
+should cover all China I think in
+Chinese it's like um there's a set of
+
+ align:start position:0%
+Chinese it's like um there's a set of
+ 
+
+ align:start position:0%
+Chinese it's like um there's a set of
+last names that's pretty much standard
+
+ align:start position:0%
+last names that's pretty much standard
+ 
+
+ align:start position:0%
+last names that's pretty much standard
+um and I'm not sure how many maybe a few
+
+ align:start position:0%
+um and I'm not sure how many maybe a few
+ 
+
+ align:start position:0%
+um and I'm not sure how many maybe a few
+hundred um and then given names um so
+
+ align:start position:0%
+hundred um and then given names um so
+ 
+
+ align:start position:0%
+hundred um and then given names um so
+family names are usually one character
+
+ align:start position:0%
+family names are usually one character
+ 
+
+ align:start position:0%
+family names are usually one character
+but occasionally they're two characters
+
+ align:start position:0%
+but occasionally they're two characters
+ 
+
+ align:start position:0%
+but occasionally they're two characters
+and um given names are either one or two
+
+ align:start position:0%
+and um given names are either one or two
+ 
+
+ align:start position:0%
+and um given names are either one or two
+characters and you just get those two uh
+
+ align:start position:0%
+characters and you just get those two uh
+ 
+
+ align:start position:0%
+characters and you just get those two uh
+and you can pick any character oh well
+
+ align:start position:0%
+and you can pick any character oh well
+ 
+
+ align:start position:0%
+and you can pick any character oh well
+there are a lot of characters yeah like
+
+ align:start position:0%
+there are a lot of characters yeah like
+ 
+
+ align:start position:0%
+there are a lot of characters yeah like
+several thousand yeah but so it's it's
+
+ align:start position:0%
+several thousand yeah but so it's it's
+ 
+
+ align:start position:0%
+several thousand yeah but so it's it's
+something like a thousand by a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th000 300
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+35 maybe another 3000 the British
+
+ align:start position:0%
+35 maybe another 3000 the British
+ 
+
+ align:start position:0%
+35 maybe another 3000 the British
+solution is to just keep add simple
+
+ align:start position:0%
+solution is to just keep add simple
+ 
+
+ align:start position:0%
+solution is to just keep add simple
+names like my brother's name is Dylan
+
+ align:start position:0%
+names like my brother's name is Dylan
+ 
+
+ align:start position:0%
+names like my brother's name is Dylan
+Neville Thomas
+
+ align:start position:0%
+Neville Thomas
+ 
+
+ align:start position:0%
+Neville Thomas
+Bedford and you can just keep changing
+
+ align:start position:0%
+Bedford and you can just keep changing
+ 
+
+ align:start position:0%
+Bedford and you can just keep changing
+names and then if you get stuck with too
+
+ align:start position:0%
+names and then if you get stuck with too
+ 
+
+ align:start position:0%
+names and then if you get stuck with too
+many John Smiths you just do thirds
+
+ align:start position:0%
+many John Smiths you just do thirds
+ 
+
+ align:start position:0%
+many John Smiths you just do thirds
+fourths
+
+ align:start position:0%
+fourths
+ 
+
+ align:start position:0%
+fourths
+fifths well the article I read must have
+
+ align:start position:0%
+fifths well the article I read must have
+ 
+
+ align:start position:0%
+fifths well the article I read must have
+been wrong then or I misunderstood it
+
+ align:start position:0%
+been wrong then or I misunderstood it
+ 
+
+ align:start position:0%
+been wrong then or I misunderstood it
+because it said somewhere areas of China
+
+ align:start position:0%
+because it said somewhere areas of China
+ 
+
+ align:start position:0%
+because it said somewhere areas of China
+there are only a hundred names so if you
+
+ align:start position:0%
+there are only a hundred names so if you
+ 
+
+ align:start position:0%
+there are only a hundred names so if you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+more than 10,000 people you get people
+
+ align:start position:0%
+more than 10,000 people you get people
+ 
+
+ align:start position:0%
+more than 10,000 people you get people
+with the same name
+
+ align:start position:0%
+with the same name
+ 
+
+ align:start position:0%
+with the same name
+and anyway that's their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem maybe the person who wrote the
+
+ align:start position:0%
+problem maybe the person who wrote the
+ 
+
+ align:start position:0%
+problem maybe the person who wrote the
+article couldn't tell the difference
+
+ align:start position:0%
+article couldn't tell the difference
+ 
+
+ align:start position:0%
+article couldn't tell the difference
+between their friend shoe and their
+
+ align:start position:0%
+between their friend shoe and their
+ 
+
+ align:start position:0%
+between their friend shoe and their
+friend
+
+ align:start position:0%
+friend
+ 
+
+ align:start position:0%
+friend
+Sho yeah well one thing that they also
+
+ align:start position:0%
+Sho yeah well one thing that they also
+ 
+
+ align:start position:0%
+Sho yeah well one thing that they also
+did historically in China is that
+
+ align:start position:0%
+did historically in China is that
+ 
+
+ align:start position:0%
+did historically in China is that
+sometimes people have m names and the
+
+ align:start position:0%
+sometimes people have m names and the
+ 
+
+ align:start position:0%
+sometimes people have m names and the
+middle names is based on this uh thing
+
+ align:start position:0%
+middle names is based on this uh thing
+ 
+
+ align:start position:0%
+middle names is based on this uh thing
+that was like written centuries ago that
+
+ align:start position:0%
+that was like written centuries ago that
+ 
+
+ align:start position:0%
+that was like written centuries ago that
+for each generation it has a set
+
+ align:start position:0%
+for each generation it has a set
+ 
+
+ align:start position:0%
+for each generation it has a set
+character that must be your middle name
+
+ align:start position:0%
+character that must be your middle name
+ 
+
+ align:start position:0%
+character that must be your middle name
+so your name will be like family name um
+
+ align:start position:0%
+so your name will be like family name um
+ 
+
+ align:start position:0%
+so your name will be like family name um
+this middle name and then your actual
+
+ align:start position:0%
+this middle name and then your actual
+ 
+
+ align:start position:0%
+this middle name and then your actual
+given name so I don't know maybe that
+
+ align:start position:0%
+given name so I don't know maybe that
+ 
+
+ align:start position:0%
+given name so I don't know maybe that
+but that's sort of like becoming more
+
+ align:start position:0%
+but that's sort of like becoming more
+ 
+
+ align:start position:0%
+but that's sort of like becoming more
+obsolete nowadays mhm well in English we
+
+ align:start position:0%
+obsolete nowadays mhm well in English we
+ 
+
+ align:start position:0%
+obsolete nowadays mhm well in English we
+have lots of names like farmer and
+
+ align:start position:0%
+have lots of names like farmer and
+ 
+
+ align:start position:0%
+have lots of names like farmer and
+painter and so forth but people don't
+
+ align:start position:0%
+painter and so forth but people don't
+ 
+
+ align:start position:0%
+painter and so forth but people don't
+live up to them much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm because it's difficult to tell what
+
+ align:start position:0%
+mhm because it's difficult to tell what
+ 
+
+ align:start position:0%
+mhm because it's difficult to tell what
+a given baby is going to
+
+ align:start position:0%
+a given baby is going to
+ 
+
+ align:start position:0%
+a given baby is going to
+do but you can order it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around but actually the the historic
+
+ align:start position:0%
+around but actually the the historic
+ 
+
+ align:start position:0%
+around but actually the the historic
+Chinese system is kind of an interesting
+
+ align:start position:0%
+Chinese system is kind of an interesting
+ 
+
+ align:start position:0%
+Chinese system is kind of an interesting
+way of addressing um people like
+
+ align:start position:0%
+way of addressing um people like
+ 
+
+ align:start position:0%
+way of addressing um people like
+indexing people cuz you have the first
+
+ align:start position:0%
+indexing people cuz you have the first
+ 
+
+ align:start position:0%
+indexing people cuz you have the first
+character which is the family and then
+
+ align:start position:0%
+character which is the family and then
+ 
+
+ align:start position:0%
+character which is the family and then
+the second character is the generation
+
+ align:start position:0%
+the second character is the generation
+ 
+
+ align:start position:0%
+the second character is the generation
+and then the third character is you so
+
+ align:start position:0%
+and then the third character is you so
+ 
+
+ align:start position:0%
+and then the third character is you so
+it's like you know if your family is X
+
+ align:start position:0%
+it's like you know if your family is X
+ 
+
+ align:start position:0%
+it's like you know if your family is X
+and you're from generation a then um
+
+ align:start position:0%
+and you're from generation a then um
+ 
+
+ align:start position:0%
+and you're from generation a then um
+your siblings will be like X AA or xab
+
+ align:start position:0%
+your siblings will be like X AA or xab
+ 
+
+ align:start position:0%
+your siblings will be like X AA or xab
+xac whatever um and then like the next
+
+ align:start position:0%
+xac whatever um and then like the next
+ 
+
+ align:start position:0%
+xac whatever um and then like the next
+generation will be like
+
+ align:start position:0%
+generation will be like
+ 
+
+ align:start position:0%
+generation will be like
+XB whatever okay maybe I should have
+
+ align:start position:0%
+XB whatever okay maybe I should have
+ 
+
+ align:start position:0%
+XB whatever okay maybe I should have
+picked different
+
+ align:start position:0%
+picked different
+ 
+
+ align:start position:0%
+picked different
+uh but you know what I mean oh
+
+ align:start position:0%
+uh but you know what I mean oh
+ 
+
+ align:start position:0%
+uh but you know what I mean oh
+generation number kind of except for
+
+ align:start position:0%
+generation number kind of except for
+ 
+
+ align:start position:0%
+generation number kind of except for
+it's a character
+
+ align:start position:0%
+it's a character
+ 
+
+ align:start position:0%
+it's a character
+mhm there should be enough IPv6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as I feel like you're just going to end
+
+ align:start position:0%
+as I feel like you're just going to end
+ 
+
+ align:start position:0%
+as I feel like you're just going to end
+up with us all being numbers X
+
+ align:start position:0%
+up with us all being numbers X
+ 
+
+ align:start position:0%
+up with us all being numbers X
+so that being said i' I've always wanted
+
+ align:start position:0%
+so that being said i' I've always wanted
+ 
+
+ align:start position:0%
+so that being said i' I've always wanted
+to name my kids something that rhym with
+
+ align:start position:0%
+to name my kids something that rhym with
+ 
+
+ align:start position:0%
+to name my kids something that rhym with
+the letter like 1 two 3 4 so that like I
+
+ align:start position:0%
+the letter like 1 two 3 4 so that like I
+ 
+
+ align:start position:0%
+the letter like 1 two 3 4 so that like I
+can just call them by their their
+
+ align:start position:0%
+can just call them by their their
+ 
+
+ align:start position:0%
+can just call them by their their
+number without realizing that I'm
+
+ align:start position:0%
+number without realizing that I'm
+ 
+
+ align:start position:0%
+number without realizing that I'm
+calling them by number that's good great
+
+ align:start position:0%
+calling them by number that's good great
+ 
+
+ align:start position:0%
+calling them by number that's good great
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+yeah I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think name it could be the number of
+
+ align:start position:0%
+think name it could be the number of
+ 
+
+ align:start position:0%
+think name it could be the number of
+letters in the
+
+ align:start position:0%
+letters in the
+ 
+
+ align:start position:0%
+letters in the
+name like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four you name your fourth kid
+
+ align:start position:0%
+four you name your fourth kid
+ 
+
+ align:start position:0%
+four you name your fourth kid
+Forest come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here or name your third kid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trade eventually the name name could be
+
+ align:start position:0%
+trade eventually the name name could be
+ 
+
+ align:start position:0%
+trade eventually the name name could be
+longer and it could be a whole little
+
+ align:start position:0%
+longer and it could be a whole little
+ 
+
+ align:start position:0%
+longer and it could be a whole little
+semantic net with little list structure
+
+ align:start position:0%
+semantic net with little list structure
+ 
+
+ align:start position:0%
+semantic net with little list structure
+in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there was a nice science fiction
+
+ align:start position:0%
+and there was a nice science fiction
+ 
+
+ align:start position:0%
+and there was a nice science fiction
+story about some culture where
+
+ align:start position:0%
+story about some culture where
+ 
+
+ align:start position:0%
+story about some culture where
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+to where you had to know your
+
+ align:start position:0%
+to where you had to know your
+ 
+
+ align:start position:0%
+to where you had to know your
+genealogy back hundreds of generations I
+
+ align:start position:0%
+genealogy back hundreds of generations I
+ 
+
+ align:start position:0%
+genealogy back hundreds of generations I
+forgot the
+
+ align:start position:0%
+forgot the
+ 
+
+ align:start position:0%
+forgot the
+author but it was made into a movie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well who wants the last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DUS someone else can have it yeah do we
+
+ align:start position:0%
+DUS someone else can have it yeah do we
+ 
+
+ align:start position:0%
+DUS someone else can have it yeah do we
+have any announcement to make
+
+ align:start position:0%
+have any announcement to make
+ 
+
+ align:start position:0%
+have any announcement to make
+no just final projects would do on
+
+ align:start position:0%
+no just final projects would do on
+ 
+
+ align:start position:0%
+no just final projects would do on
+Sunday
+
+ align:start position:0%
+Sunday
+ 
+
+ align:start position:0%
+Sunday
+that's do you know what you're teaching
+
+ align:start position:0%
+that's do you know what you're teaching
+ 
+
+ align:start position:0%
+that's do you know what you're teaching
+next semester we're trying to make a
+
+ align:start position:0%
+next semester we're trying to make a
+ 
+
+ align:start position:0%
+next semester we're trying to make a
+plan for a some kind of weekly seminar
+
+ align:start position:0%
+plan for a some kind of weekly seminar
+ 
+
+ align:start position:0%
+plan for a some kind of weekly seminar
+that's not for
+
+ align:start position:0%
+that's not for
+ 
+
+ align:start position:0%
+that's not for
+credit
+
+ align:start position:0%
+credit
+ 
+
+ align:start position:0%
+credit
+uh although I might have to make it for
+
+ align:start position:0%
+uh although I might have to make it for
+ 
+
+ align:start position:0%
+uh although I might have to make it for
+credit for financial reasons or nobody
+
+ align:start position:0%
+credit for financial reasons or nobody
+ 
+
+ align:start position:0%
+credit for financial reasons or nobody
+will pay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me but uh we could go back to giving
+
+ align:start position:0%
+me but uh we could go back to giving
+ 
+
+ align:start position:0%
+me but uh we could go back to giving
+everyone A's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so you won't be teaching this
+
+ align:start position:0%
+again so you won't be teaching this
+ 
+
+ align:start position:0%
+again so you won't be teaching this
+subject until next fall I guess not uh I
+
+ align:start position:0%
+subject until next fall I guess not uh I
+ 
+
+ align:start position:0%
+subject until next fall I guess not uh I
+haven't absolutely decided but I'm
+
+ align:start position:0%
+haven't absolutely decided but I'm
+ 
+
+ align:start position:0%
+haven't absolutely decided but I'm
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+sure can they take your
+
+ align:start position:0%
+sure can they take your
+ 
+
+ align:start position:0%
+sure can they take your
+class how much how many students do you
+
+ align:start position:0%
+class how much how many students do you
+ 
+
+ align:start position:0%
+class how much how many students do you
+have each
+
+ align:start position:0%
+have each
+ 
+
+ align:start position:0%
+have each
+year well we've got room for about 40
+
+ align:start position:0%
+year well we've got room for about 40
+ 
+
+ align:start position:0%
+year well we've got room for about 40
+and usually about 120 sign up mhm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you weed them
+
+ align:start position:0%
+and then you weed them
+ 
+
+ align:start position:0%
+and then you weed them
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I'd like to borrow your reading
+
+ align:start position:0%
+yes I'd like to borrow your reading
+ 
+
+ align:start position:0%
+yes I'd like to borrow your reading
+program okay well thank you all for
+
+ align:start position:0%
+program okay well thank you all for
+ 
+
+ align:start position:0%
+program okay well thank you all for
+coming it's been fun
+
+ align:start position:0%
+coming it's been fun
+ 
+
+ align:start position:0%
+coming it's been fun
+[Applause]
\ No newline at end of file
diff --git a/TV6AtNbmLBE.txt b/TV6AtNbmLBE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4aa9052296c92972e5dbe84518b30afdd8c76662
--- /dev/null
+++ b/TV6AtNbmLBE.txt
@@ -0,0 +1,219 @@
+Okay, let's review our plan.
+
+The processor starts an access by sending
+an address to the cache.
+
+If data for the requested address is held
+in the cache, it's quickly returned to the
+
+CPU.
+
+If the data we request is not in the cache,
+we have a cache miss, so the cache has to
+
+make a request to main memory to get the data,
+which it then returns to processor.
+
+Typically the cache will remember the newly
+fetched data, possibly replacing some older
+
+data in the cache.
+
+Suppose a cache access takes 4 ns and a main
+memory access takes 40 ns.
+
+Then an access that hits in the cache has
+a latency of 4 ns, but an access that misses
+
+in the cache has a latency of 44 ns.
+
+The processor has to deal with the variable
+memory access time, perhaps by simply waiting
+
+for the access to complete, or, in modern
+hyper-threaded processors, it might execute
+
+an instruction or two from another programming
+thread.
+
+The hit and miss ratios tell us the fraction
+of accesses which are cache hits and the fraction
+
+of accesses which are cache misses.
+
+Of course, the ratios will sum to 1.
+
+Using these metrics we can compute the average
+memory access time (AMAT).
+
+Since we always check in the cache first,
+every access includes the cache access time
+
+(called the hit time).
+
+If we miss in the cache, we have to take the
+additional time needed to access main memory
+
+(called the miss penalty).
+
+But the main memory access only happens on
+some fraction of the accesses: the miss ratio
+
+tells us how often that occurs.
+
+So the AMAT can be computed using the formula
+shown here.
+
+The lower the miss ratio (or, equivalently,
+the higher the hit ratio), the smaller the
+
+average access time.
+
+Our design goal for the cache is to achieve
+a high hit ratio.
+
+If we have multiple levels of cache, we can
+apply the formula recursively to calculate
+
+the AMAT at each level of the memory.
+
+Each successive level of the cache is slower,
+i.e., has a longer hit time, which is offset
+
+by lower miss ratio because of its increased
+size.
+
+Let's try out some numbers.
+
+Suppose the cache takes 4 processor cycles
+to respond, and main memory takes 100 cycles.
+
+Without the cache, each memory access would
+take 100 cycles.
+
+With the cache, a cache hit takes 4 cycles,
+and a cache miss takes 104 cycles.
+
+What hit ratio is needed to so that the AMAT
+with the cache is 100 cycles, the break-even
+
+point?
+
+Using the AMAT formula from the previously
+slide, we see that we only need a hit ratio
+
+of 4% in order for memory system of the Cache
++ Main Memory to perform as well as Main Memory
+
+alone.
+
+The idea, of course, is that we'll be able
+to do much better than that.
+
+Suppose we wanted an AMAT of 5 cycles.
+
+Clearly most of the accesses would have to
+be cache hits.
+
+We can use the AMAT formula to compute the
+necessary hit ratio.
+
+Working through the arithmetic we see that
+99% of the accesses must be cache hits in
+
+order to achieve an average access time of
+5 cycles.
+
+Could we expect to do that well when running
+actual programs?
+
+Happily, we can come close.
+
+In a simulation of the Spec CPU2000 Benchmark,
+the hit ratio for a standard-size level 1
+
+cache was measured to be 97.5% over some ~10
+trillion accesses.
+
+[See the "All benchmarks" arithmetic-mean
+table at http://research.cs.wisc.edu/multifacet/misc/spec2000cache-data/]
+
+Here's a start at building a cache.
+
+The cache will hold many different blocks
+of data.
+
+For now let's assume each block is an individual
+memory location.
+
+Each data block is "tagged" with its address.
+
+A combination of a data block and its associated
+address tag is called a cache line.
+
+When an address is received from the CPU,
+we'll search the cache looking for a block
+
+with a matching address tag.
+
+If we find a matching address tag, we have
+a cache hit.
+
+On a read access, we'll return the data from
+the matching cache line.
+
+On a write access, we'll update the data stored
+in the cache line and, at some point, update
+
+the corresponding location in main memory.
+
+If no matching tag is found, we have a cache
+miss.
+
+So we'll have to choose a cache line to use
+to hold the requested data, which means that
+
+some previously cached location will no longer
+be found in the cache.
+
+For a read operation, we'll fetch the requested
+data from main memory, add it to the cache
+
+(updating the tag and data fields of the cache
+line) and, of course, return the data to the
+
+CPU.
+
+On a write, we'll update the tag and data
+in the selected cache line and, at some point,
+
+update the corresponding location in main
+memory.
+
+So the contents of the cache is determined
+by the memory requests made by the CPU.
+
+If the CPU requests a recently-used address,
+chances are good the data will still be in
+
+the cache from the previous access to the
+same location.
+
+As the working set slowly changes, the cache
+contents will be updated as needed.
+
+If the entire working set can fit into the
+cache, most of the requests will be hits and
+
+the AMAT will be close to the cache access
+time.
+
+So far, so good!
+
+Of course, we'll need to figure how to quickly
+search the cache, i.e., we'll a need fast
+
+way to answer the question of whether a particular
+address tag can be found in some cache line.
+
+That's our next topic.
\ No newline at end of file
diff --git a/Tyajd1ZddcQ.txt b/Tyajd1ZddcQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b4ebacc7df2996d2debbc94222724fb2335d7138
--- /dev/null
+++ b/Tyajd1ZddcQ.txt
@@ -0,0 +1,4403 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah look you can see the little
+
+ align:start position:0%
+oh yeah look you can see the little
+ 
+
+ align:start position:0%
+oh yeah look you can see the little
+C oh yeah sure you
+
+ align:start position:0%
+C oh yeah sure you
+ 
+
+ align:start position:0%
+C oh yeah sure you
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down all
+
+ align:start position:0%
+down all
+ 
+
+ align:start position:0%
+down all
+right and we don't have the right sample
+
+ align:start position:0%
+right and we don't have the right sample
+ 
+
+ align:start position:0%
+right and we don't have the right sample
+on right that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+what's oh yeah I think that that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glass glassa right yep so one the little
+
+ align:start position:0%
+glass glassa right yep so one the little
+ 
+
+ align:start position:0%
+glass glassa right yep so one the little
+ones I guess oh yeah you can actually
+
+ align:start position:0%
+ones I guess oh yeah you can actually
+ 
+
+ align:start position:0%
+ones I guess oh yeah you can actually
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quite so when you when you switch to
+
+ align:start position:0%
+quite so when you when you switch to
+ 
+
+ align:start position:0%
+quite so when you when you switch to
+these P leers it's fairly typical for
+
+ align:start position:0%
+these P leers it's fairly typical for
+ 
+
+ align:start position:0%
+these P leers it's fairly typical for
+them to require refocusing okay cuz
+
+ align:start position:0%
+them to require refocusing okay cuz
+ 
+
+ align:start position:0%
+them to require refocusing okay cuz
+they're significantly shorter than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um he's
+
+ align:start position:0%
+um he's
+ 
+
+ align:start position:0%
+um he's
+coming toward you you have to loosen the
+
+ align:start position:0%
+coming toward you you have to loosen the
+ 
+
+ align:start position:0%
+coming toward you you have to loosen the
+knobs yeah
+
+ align:start position:0%
+knobs yeah
+ 
+
+ align:start position:0%
+knobs yeah
+okay all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we I love this that is such a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great not supposed to
+
+ align:start position:0%
+great not supposed to
+ 
+
+ align:start position:0%
+great not supposed to
+touch what is it that you got huh you
+
+ align:start position:0%
+touch what is it that you got huh you
+ 
+
+ align:start position:0%
+touch what is it that you got huh you
+said you must that the you color code
+
+ align:start position:0%
+said you must that the you color code
+ 
+
+ align:start position:0%
+said you must that the you color code
+which pizo power source goes with which
+
+ align:start position:0%
+which pizo power source goes with which
+ 
+
+ align:start position:0%
+which pizo power source goes with which
+switch yeah that was when they were all
+
+ align:start position:0%
+switch yeah that was when they were all
+ 
+
+ align:start position:0%
+switch yeah that was when they were all
+on the same table we had uh two
+
+ align:start position:0%
+on the same table we had uh two
+ 
+
+ align:start position:0%
+on the same table we had uh two
+incarnations of the classic basically
+
+ align:start position:0%
+incarnations of the classic basically
+ 
+
+ align:start position:0%
+incarnations of the classic basically
+one huge object set
+
+ align:start position:0%
+one huge object set
+ 
+
+ align:start position:0%
+one huge object set
+up set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up well these three tables inside
+
+ align:start position:0%
+up well these three tables inside
+ 
+
+ align:start position:0%
+up well these three tables inside
+my it's still useful yeah all right so
+
+ align:start position:0%
+my it's still useful yeah all right so
+ 
+
+ align:start position:0%
+my it's still useful yeah all right so
+probably want to the uh
+
+ align:start position:0%
+probably want to the uh
+ 
+
+ align:start position:0%
+probably want to the uh
+down the
+
+ align:start position:0%
+down the
+ 
+
+ align:start position:0%
+down the
+scope oh yeah can get the you're still
+
+ align:start position:0%
+scope oh yeah can get the you're still
+ 
+
+ align:start position:0%
+scope oh yeah can get the you're still
+doing it with the scope I guess you're
+
+ align:start position:0%
+doing it with the scope I guess you're
+ 
+
+ align:start position:0%
+doing it with the scope I guess you're
+right who oh we took that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ey there's a missing eye piece
+
+ align:start position:0%
+ey there's a missing eye piece
+ 
+
+ align:start position:0%
+ey there's a missing eye piece
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+not I just gave it the old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all
+
+ align:start position:0%
+one all
+ 
+
+ align:start position:0%
+one all
+right and so then I guess we should hit
+
+ align:start position:0%
+right and so then I guess we should hit
+ 
+
+ align:start position:0%
+right and so then I guess we should hit
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh align the spot on
+
+ align:start position:0%
+uh align the spot on
+ 
+
+ align:start position:0%
+uh align the spot on
+the yeah so adjust the height would you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+cuz well I guess I can just do it by
+
+ align:start position:0%
+cuz well I guess I can just do it by
+ 
+
+ align:start position:0%
+cuz well I guess I can just do it by
+ey
+
+ align:start position:0%
+ey
+ 
+
+ align:start position:0%
+ey
+right for you're adjusting the height
+
+ align:start position:0%
+right for you're adjusting the height
+ 
+
+ align:start position:0%
+right for you're adjusting the height
+of I was thinking about adjusting the
+
+ align:start position:0%
+of I was thinking about adjusting the
+ 
+
+ align:start position:0%
+of I was thinking about adjusting the
+height of the
+
+ align:start position:0%
+height of the
+ 
+
+ align:start position:0%
+height of the
+tecture well uh okay but we could hit
+
+ align:start position:0%
+tecture well uh okay but we could hit
+ 
+
+ align:start position:0%
+tecture well uh okay but we could hit
+this uh we could try getting the L are
+
+ align:start position:0%
+this uh we could try getting the L are
+ 
+
+ align:start position:0%
+this uh we could try getting the L are
+on the uh close to the spot also yeah
+
+ align:start position:0%
+on the uh close to the spot also yeah
+ 
+
+ align:start position:0%
+on the uh close to the spot also yeah
+yeah right that's that's and that's what
+
+ align:start position:0%
+yeah right that's that's and that's what
+ 
+
+ align:start position:0%
+yeah right that's that's and that's what
+I meant sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I think you're going want these yeah
+
+ align:start position:0%
+so I think you're going want these yeah
+ 
+
+ align:start position:0%
+so I think you're going want these yeah
+I'm the stage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this surface of glass out so FP it over
+
+ align:start position:0%
+this surface of glass out so FP it over
+ 
+
+ align:start position:0%
+this surface of glass out so FP it over
+the first thing to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+touch all
+
+ align:start position:0%
+touch all
+ 
+
+ align:start position:0%
+touch all
+right yeah you're on the lever yeah
+
+ align:start position:0%
+right yeah you're on the lever yeah
+ 
+
+ align:start position:0%
+right yeah you're on the lever yeah
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+middle but you can also push with your
+
+ align:start position:0%
+middle but you can also push with your
+ 
+
+ align:start position:0%
+middle but you can also push with your
+finger and turn and it gets the clip out
+
+ align:start position:0%
+finger and turn and it gets the clip out
+ 
+
+ align:start position:0%
+finger and turn and it gets the clip out
+of the way and then you can turn the
+
+ align:start position:0%
+of the way and then you can turn the
+ 
+
+ align:start position:0%
+of the way and then you can turn the
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign that makes a lot of sense it
+
+ align:start position:0%
+sign that makes a lot of sense it
+ 
+
+ align:start position:0%
+sign that makes a lot of sense it
+position here but then you look at it
+
+ align:start position:0%
+position here but then you look at it
+ 
+
+ align:start position:0%
+position here but then you look at it
+put it back or rotate it don't yeah so
+
+ align:start position:0%
+put it back or rotate it don't yeah so
+ 
+
+ align:start position:0%
+put it back or rotate it don't yeah so
+so you see the pocket goes in this
+
+ align:start position:0%
+so you see the pocket goes in this
+ 
+
+ align:start position:0%
+so you see the pocket goes in this
+direction you want to just drop the
+
+ align:start position:0%
+direction you want to just drop the
+ 
+
+ align:start position:0%
+direction you want to just drop the
+back talking a
+
+ align:start position:0%
+back talking a
+ 
+
+ align:start position:0%
+back talking a
+camera and to clamp it you just push
+
+ align:start position:0%
+camera and to clamp it you just push
+ 
+
+ align:start position:0%
+camera and to clamp it you just push
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+idea and you can actually you know get
+
+ align:start position:0%
+idea and you can actually you know get
+ 
+
+ align:start position:0%
+idea and you can actually you know get
+it so that the field of view is is
+
+ align:start position:0%
+it so that the field of view is is
+ 
+
+ align:start position:0%
+it so that the field of view is is
+pretty small and so I think that I'll
+
+ align:start position:0%
+pretty small and so I think that I'll
+ 
+
+ align:start position:0%
+pretty small and so I think that I'll
+keep it's not exactly what people
+
+ align:start position:0%
+keep it's not exactly what people
+ 
+
+ align:start position:0%
+keep it's not exactly what people
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easic to see
+
+ align:start position:0%
+easic to see
+ 
+
+ align:start position:0%
+easic to see
+the yeah but you know
+
+ align:start position:0%
+the yeah but you know
+ 
+
+ align:start position:0%
+the yeah but you know
+what I once you do it five
+
+ align:start position:0%
+what I once you do it five
+ 
+
+ align:start position:0%
+what I once you do it five
+times for me to in
+
+ align:start position:0%
+times for me to in
+ 
+
+ align:start position:0%
+times for me to in
+so he's the he is our uh he he's the lab
+
+ align:start position:0%
+so he's the he is our uh he he's the lab
+ 
+
+ align:start position:0%
+so he's the he is our uh he he's the lab
+manager for DM for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+materials so anyway when we were
+
+ align:start position:0%
+materials so anyway when we were
+ 
+
+ align:start position:0%
+materials so anyway when we were
+developing forc put we
+
+ align:start position:0%
+developing forc put we
+ 
+
+ align:start position:0%
+developing forc put we
+got firewire ceras direct the of all our
+
+ align:start position:0%
+got firewire ceras direct the of all our
+ 
+
+ align:start position:0%
+got firewire ceras direct the of all our
+mic and they work really well
+
+ align:start position:0%
+mic and they work really well
+ 
+
+ align:start position:0%
+mic and they work really well
+for so you know when he's used to tring
+
+ align:start position:0%
+for so you know when he's used to tring
+ 
+
+ align:start position:0%
+for so you know when he's used to tring
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+outc yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjust you want to put f
+
+ align:start position:0%
+adjust you want to put f
+ 
+
+ align:start position:0%
+adjust you want to put f
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use fingers to take it out or tweezers
+
+ align:start position:0%
+use fingers to take it out or tweezers
+ 
+
+ align:start position:0%
+use fingers to take it out or tweezers
+um tweezers are best if you want to use
+
+ align:start position:0%
+um tweezers are best if you want to use
+ 
+
+ align:start position:0%
+um tweezers are best if you want to use
+your fingers I'd recommend the glove
+
+ align:start position:0%
+your fingers I'd recommend the glove
+ 
+
+ align:start position:0%
+your fingers I'd recommend the glove
+just so you don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use want to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you the
+
+ align:start position:0%
+do you the
+ 
+
+ align:start position:0%
+do you the
+twers um we have another
+
+ align:start position:0%
+twers um we have another
+ 
+
+ align:start position:0%
+twers um we have another
+pair blue or
+
+ align:start position:0%
+pair blue or
+ 
+
+ align:start position:0%
+pair blue or
+red that's probably red go on the left
+
+ align:start position:0%
+red that's probably red go on the left
+ 
+
+ align:start position:0%
+red that's probably red go on the left
+side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so we'll take so you said the
+
+ align:start position:0%
+there so we'll take so you said the
+ 
+
+ align:start position:0%
+there so we'll take so you said the
+softer ones it doesn't matteress like
+
+ align:start position:0%
+softer ones it doesn't matteress like
+ 
+
+ align:start position:0%
+softer ones it doesn't matteress like
+it's the hard ones first yeah you want
+
+ align:start position:0%
+it's the hard ones first yeah you want
+ 
+
+ align:start position:0%
+it's the hard ones first yeah you want
+the hard ones first to give your your
+
+ align:start position:0%
+the hard ones first to give your your
+ 
+
+ align:start position:0%
+the hard ones first to give your your
+calibration measurement basically and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we should try before we adjust the
+
+ align:start position:0%
+so we should try before we adjust the
+ 
+
+ align:start position:0%
+so we should try before we adjust the
+focus to position the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spot nearest tip is the best is the best
+
+ align:start position:0%
+spot nearest tip is the best is the best
+ 
+
+ align:start position:0%
+spot nearest tip is the best is the best
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so now we have to adjust
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the keep all of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these Max do you do you keep all four
+
+ align:start position:0%
+these Max do you do you keep all four
+ 
+
+ align:start position:0%
+these Max do you do you keep all four
+screws set screws on the oh no I
+
+ align:start position:0%
+screws set screws on the oh no I
+ 
+
+ align:start position:0%
+screws set screws on the oh no I
+typically just Tien one so and this SC
+
+ align:start position:0%
+typically just Tien one so and this SC
+ 
+
+ align:start position:0%
+typically just Tien one so and this SC
+might be on on the other side there we
+
+ align:start position:0%
+might be on on the other side there we
+ 
+
+ align:start position:0%
+might be on on the other side there we
+go this one yeah that's better one
+
+ align:start position:0%
+go this one yeah that's better one
+ 
+
+ align:start position:0%
+go this one yeah that's better one
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+sh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh no I don't think that was okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and
+
+ align:start position:0%
+right and
+ 
+
+ align:start position:0%
+right and
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CL do position
+
+ align:start position:0%
+CL do position
+ 
+
+ align:start position:0%
+CL do position
+it to see if you're right position it
+
+ align:start position:0%
+it to see if you're right position it
+ 
+
+ align:start position:0%
+it to see if you're right position it
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving side to
+
+ align:start position:0%
+moving side to
+ 
+
+ align:start position:0%
+moving side to
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side right way
+
+ align:start position:0%
+side right way
+ 
+
+ align:start position:0%
+side right way
+now oh
+
+ align:start position:0%
+now oh
+ 
+
+ align:start position:0%
+now oh
+nice good little lower we
+
+ align:start position:0%
+nice good little lower we
+ 
+
+ align:start position:0%
+nice good little lower we
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good oh I think we went too far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally that's how you make an
+
+ align:start position:0%
+finally that's how you make an
+ 
+
+ align:start position:0%
+finally that's how you make an
+adjustment all
+
+ align:start position:0%
+adjustment all
+ 
+
+ align:start position:0%
+adjustment all
+right now your challenge is to tighten
+
+ align:start position:0%
+right now your challenge is to tighten
+ 
+
+ align:start position:0%
+right now your challenge is to tighten
+that set screw without moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything the challeng is to not even to
+
+ align:start position:0%
+anything the challeng is to not even to
+ 
+
+ align:start position:0%
+anything the challeng is to not even to
+not move anything even before it okay is
+
+ align:start position:0%
+not move anything even before it okay is
+ 
+
+ align:start position:0%
+not move anything even before it okay is
+this good now yeah that looks great all
+
+ align:start position:0%
+this good now yeah that looks great all
+ 
+
+ align:start position:0%
+this good now yeah that looks great all
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you can check it once you think you
+
+ align:start position:0%
+here you can check it once you think you
+ 
+
+ align:start position:0%
+here you can check it once you think you
+the tight
+
+ align:start position:0%
+the tight
+ 
+
+ align:start position:0%
+the tight
+okay beautiful all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+nice just make sure we've got it on
+
+ align:start position:0%
+nice just make sure we've got it on
+ 
+
+ align:start position:0%
+nice just make sure we've got it on
+the bright
+
+ align:start position:0%
+the bright
+ 
+
+ align:start position:0%
+the bright
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+do then the light go to the right to the
+
+ align:start position:0%
+do then the light go to the right to the
+ 
+
+ align:start position:0%
+do then the light go to the right to the
+where we fell off just that we fell off
+
+ align:start position:0%
+where we fell off just that we fell off
+ 
+
+ align:start position:0%
+where we fell off just that we fell off
+the end
+
+ align:start position:0%
+the end
+ 
+
+ align:start position:0%
+the end
+again yeah I didn't move that one so
+
+ align:start position:0%
+again yeah I didn't move that one so
+ 
+
+ align:start position:0%
+again yeah I didn't move that one so
+okay that's right right okay
+
+ align:start position:0%
+okay that's right right okay
+ 
+
+ align:start position:0%
+okay that's right right okay
+nice okay so yeah let's run oh uh let's
+
+ align:start position:0%
+nice okay so yeah let's run oh uh let's
+ 
+
+ align:start position:0%
+nice okay so yeah let's run oh uh let's
+run the software and get the sample in
+
+ align:start position:0%
+run the software and get the sample in
+ 
+
+ align:start position:0%
+run the software and get the sample in
+contact yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we have miles to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+upfor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mod
+
+ align:start position:0%
+mod
+ 
+
+ align:start position:0%
+mod
+okay all right so start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure so I don't think we're that close
+
+ align:start position:0%
+sure so I don't think we're that close
+ 
+
+ align:start position:0%
+sure so I don't think we're that close
+yet but you see I've got the disc up
+
+ align:start position:0%
+yet but you see I've got the disc up
+ 
+
+ align:start position:0%
+yet but you see I've got the disc up
+inside the
+
+ align:start position:0%
+inside the
+ 
+
+ align:start position:0%
+inside the
+uhhuh so I don't know if that's too
+
+ align:start position:0%
+uhhuh so I don't know if that's too
+ 
+
+ align:start position:0%
+uhhuh so I don't know if that's too
+cautious as a place to start using the
+
+ align:start position:0%
+cautious as a place to start using the
+ 
+
+ align:start position:0%
+cautious as a place to start using the
+joystick but it I it takes a long time
+
+ align:start position:0%
+joystick but it I it takes a long time
+ 
+
+ align:start position:0%
+joystick but it I it takes a long time
+it's worth getting it it's worth getting
+
+ align:start position:0%
+it's worth getting it it's worth getting
+ 
+
+ align:start position:0%
+it's worth getting it it's worth getting
+it a little closer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not seeing the reflection of the C
+
+ align:start position:0%
+I'm not seeing the reflection of the C
+ 
+
+ align:start position:0%
+I'm not seeing the reflection of the C
+no you can't tell what you you can see
+
+ align:start position:0%
+no you can't tell what you you can see
+ 
+
+ align:start position:0%
+no you can't tell what you you can see
+the tip move but this with the short one
+
+ align:start position:0%
+the tip move but this with the short one
+ 
+
+ align:start position:0%
+the tip move but this with the short one
+actually you might can be pretty
+
+ align:start position:0%
+actually you might can be pretty
+ 
+
+ align:start position:0%
+actually you might can be pretty
+hard all right so let's go to the see
+
+ align:start position:0%
+hard all right so let's go to the see
+ 
+
+ align:start position:0%
+hard all right so let's go to the see
+under cautious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you can also see it on here when
+
+ align:start position:0%
+yeah you can also see it on here when
+ 
+
+ align:start position:0%
+yeah you can also see it on here when
+you hit you can see the oh yeah see the
+
+ align:start position:0%
+you hit you can see the oh yeah see the
+ 
+
+ align:start position:0%
+you hit you can see the oh yeah see the
+spots would here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can I
+
+ align:start position:0%
+you can I
+ 
+
+ align:start position:0%
+you can I
+mean now I think I can actually see what
+
+ align:start position:0%
+mean now I think I can actually see what
+ 
+
+ align:start position:0%
+mean now I think I can actually see what
+the reflection is
+
+ align:start position:0%
+the reflection is
+ 
+
+ align:start position:0%
+the reflection is
+okay that's the hardest part just
+
+ align:start position:0%
+okay that's the hardest part just
+ 
+
+ align:start position:0%
+okay that's the hardest part just
+getting your bearings on how close are
+
+ align:start position:0%
+getting your bearings on how close are
+ 
+
+ align:start position:0%
+getting your bearings on how close are
+you yeah now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I no I know I'm close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not that close am I well you can
+
+ align:start position:0%
+I'm not that close am I well you can
+ 
+
+ align:start position:0%
+I'm not that close am I well you can
+also go I mean you can crank it fast you
+
+ align:start position:0%
+also go I mean you can crank it fast you
+ 
+
+ align:start position:0%
+also go I mean you can crank it fast you
+can go faster too on the joystick you to
+
+ align:start position:0%
+can go faster too on the joystick you to
+ 
+
+ align:start position:0%
+can go faster too on the joystick you to
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go that yeah you're going pretty slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before Oh I saw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something it's not it
+
+ align:start position:0%
+something it's not it
+ 
+
+ align:start position:0%
+something it's not it
+Shi yeah something
+
+ align:start position:0%
+Shi yeah something
+ 
+
+ align:start position:0%
+Shi yeah something
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this bringing into contact is a delicate
+
+ align:start position:0%
+this bringing into contact is a delicate
+ 
+
+ align:start position:0%
+this bringing into contact is a delicate
+musn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M good is to we the uh machine parts we
+
+ align:start position:0%
+M good is to we the uh machine parts we
+ 
+
+ align:start position:0%
+M good is to we the uh machine parts we
+need for our sces as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can see why the froes get brok it now
+
+ align:start position:0%
+I can see why the froes get brok it now
+ 
+
+ align:start position:0%
+I can see why the froes get brok it now
+yeah cuz you probably get impatient look
+
+ align:start position:0%
+yeah cuz you probably get impatient look
+ 
+
+ align:start position:0%
+yeah cuz you probably get impatient look
+see I lost my
+
+ align:start position:0%
+see I lost my
+ 
+
+ align:start position:0%
+see I lost my
+defraction the
+
+ align:start position:0%
+defraction the
+ 
+
+ align:start position:0%
+defraction the
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+breako see it loed off
+
+ align:start position:0%
+breako see it loed off
+ 
+
+ align:start position:0%
+breako see it loed off
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+how's that possible I'm not sure what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right well should I should I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not you don't think I actually I don't
+
+ align:start position:0%
+not you don't think I actually I don't
+ 
+
+ align:start position:0%
+not you don't think I actually I don't
+know see the thing is now I'm moving
+
+ align:start position:0%
+know see the thing is now I'm moving
+ 
+
+ align:start position:0%
+know see the thing is now I'm moving
+down and I got my defraction spot back
+
+ align:start position:0%
+down and I got my defraction spot back
+ 
+
+ align:start position:0%
+down and I got my defraction spot back
+oh so maybe we did hit it long ago yeah
+
+ align:start position:0%
+oh so maybe we did hit it long ago yeah
+ 
+
+ align:start position:0%
+oh so maybe we did hit it long ago yeah
+but maybe we just don't have look at
+
+ align:start position:0%
+but maybe we just don't have look at
+ 
+
+ align:start position:0%
+but maybe we just don't have look at
+that oh there we go oh it looks like
+
+ align:start position:0%
+that oh there we go oh it looks like
+ 
+
+ align:start position:0%
+that oh there we go oh it looks like
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+hitting so maybe I missed it was just
+
+ align:start position:0%
+hitting so maybe I missed it was just
+ 
+
+ align:start position:0%
+hitting so maybe I missed it was just
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+done yeah I think that's probably right
+
+ align:start position:0%
+done yeah I think that's probably right
+ 
+
+ align:start position:0%
+done yeah I think that's probably right
+okay but I think we didn't break it
+
+ align:start position:0%
+okay but I think we didn't break it
+ 
+
+ align:start position:0%
+okay but I think we didn't break it
+yet hard
+
+ align:start position:0%
+yet hard
+ 
+
+ align:start position:0%
+yet hard
+to no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look how about that that's no joystick
+
+ align:start position:0%
+look how about that that's no joystick
+ 
+
+ align:start position:0%
+look how about that that's no joystick
+Conta
+
+ align:start position:0%
+Conta
+ 
+
+ align:start position:0%
+Conta
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right you might want to back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off that's almost exactly how I did it
+
+ align:start position:0%
+off that's almost exactly how I did it
+ 
+
+ align:start position:0%
+off that's almost exactly how I did it
+last time is I went and it was actually
+
+ align:start position:0%
+last time is I went and it was actually
+ 
+
+ align:start position:0%
+last time is I went and it was actually
+in very good contact and then I backed
+
+ align:start position:0%
+in very good contact and then I backed
+ 
+
+ align:start position:0%
+in very good contact and then I backed
+off yeah that's yeah another reason why
+
+ align:start position:0%
+off yeah that's yeah another reason why
+ 
+
+ align:start position:0%
+off yeah that's yeah another reason why
+you won't get good images with the hard
+
+ align:start position:0%
+you won't get good images with the hard
+ 
+
+ align:start position:0%
+you won't get good images with the hard
+Conta yeah so out of cont
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cont okay so now as far as the biasing
+
+ align:start position:0%
+cont okay so now as far as the biasing
+ 
+
+ align:start position:0%
+cont okay so now as far as the biasing
+right now we're down at the bottom of
+
+ align:start position:0%
+right now we're down at the bottom of
+ 
+
+ align:start position:0%
+right now we're down at the bottom of
+the way versus yeah the
+
+ align:start position:0%
+the way versus yeah the
+ 
+
+ align:start position:0%
+the way versus yeah the
+bottom it's not a big it's not really a
+
+ align:start position:0%
+bottom it's not a big it's not really a
+ 
+
+ align:start position:0%
+bottom it's not a big it's not really a
+big win is it because as long as you
+
+ align:start position:0%
+big win is it because as long as you
+ 
+
+ align:start position:0%
+big win is it because as long as you
+know you're as long as you come from
+
+ align:start position:0%
+know you're as long as you come from
+ 
+
+ align:start position:0%
+know you're as long as you come from
+place the same place the same place yeah
+
+ align:start position:0%
+place the same place the same place yeah
+ 
+
+ align:start position:0%
+place the same place the same place yeah
+yeah maybe that's maybe that's why he
+
+ align:start position:0%
+yeah maybe that's maybe that's why he
+ 
+
+ align:start position:0%
+yeah maybe that's maybe that's why he
+suggests the center it's easy to figure
+
+ align:start position:0%
+suggests the center it's easy to figure
+ 
+
+ align:start position:0%
+suggests the center it's easy to figure
+out where the center is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I was thinking it would be easier
+
+ align:start position:0%
+then I was thinking it would be easier
+ 
+
+ align:start position:0%
+then I was thinking it would be easier
+to fool yourself about what CER was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too kind weird
+
+ align:start position:0%
+too kind weird
+ 
+
+ align:start position:0%
+too kind weird
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just going to back out of contact
+
+ align:start position:0%
+so just going to back out of contact
+ 
+
+ align:start position:0%
+so just going to back out of contact
+okay so now I'm not in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contact a
+
+ align:start position:0%
+contact a
+ 
+
+ align:start position:0%
+contact a
+little get to contact yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is what's happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there top of the W it's hard when to
+
+ align:start position:0%
+there top of the W it's hard when to
+ 
+
+ align:start position:0%
+there top of the W it's hard when to
+when to trace the traes are the same
+
+ align:start position:0%
+when to trace the traes are the same
+ 
+
+ align:start position:0%
+when to trace the traes are the same
+color
+
+ align:start position:0%
+color
+ 
+
+ align:start position:0%
+color
+uh so I just move the th closer so we
+
+ align:start position:0%
+uh so I just move the th closer so we
+ 
+
+ align:start position:0%
+uh so I just move the th closer so we
+can get some more uh yeah hers I think
+
+ align:start position:0%
+can get some more uh yeah hers I think
+ 
+
+ align:start position:0%
+can get some more uh yeah hers I think
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also you know honestly if you look at
+
+ align:start position:0%
+also you know honestly if you look at
+ 
+
+ align:start position:0%
+also you know honestly if you look at
+the detector I'm not sure we're
+
+ align:start position:0%
+the detector I'm not sure we're
+ 
+
+ align:start position:0%
+the detector I'm not sure we're
+fully capturing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+making me much happier
+
+ align:start position:0%
+making me much happier
+ 
+
+ align:start position:0%
+making me much happier
+though all right well at least we
+
+ align:start position:0%
+though all right well at least we
+ 
+
+ align:start position:0%
+though all right well at least we
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+now so
+
+ align:start position:0%
+now so
+ 
+
+ align:start position:0%
+now so
+now see
+
+ align:start position:0%
+now see
+ 
+
+ align:start position:0%
+now see
+oh we want to make sure
+
+ align:start position:0%
+oh we want to make sure
+ 
+
+ align:start position:0%
+oh we want to make sure
+we're do we're not on high gain right
+
+ align:start position:0%
+we're do we're not on high gain right
+ 
+
+ align:start position:0%
+we're do we're not on high gain right
+yeah what are we on 100 divide by 100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right why don't we ground this for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there we go what did you do uh if we
+
+ align:start position:0%
+but there we go what did you do uh if we
+ 
+
+ align:start position:0%
+but there we go what did you do uh if we
+were grounding one oh yeah
+
+ align:start position:0%
+were grounding one oh yeah
+ 
+
+ align:start position:0%
+were grounding one oh yeah
+so now put that back in the middle there
+
+ align:start position:0%
+so now put that back in the middle there
+ 
+
+ align:start position:0%
+so now put that back in the middle there
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go out of contact right now
+
+ align:start position:0%
+go out of contact right now
+ 
+
+ align:start position:0%
+go out of contact right now
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay slightly in Conta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you guys we didn't have the the
+
+ align:start position:0%
+yeah you guys we didn't have the the
+ 
+
+ align:start position:0%
+yeah you guys we didn't have the the
+sauce proper sitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on oh no same thing as last is this a
+
+ align:start position:0%
+on oh no same thing as last is this a
+ 
+
+ align:start position:0%
+on oh no same thing as last is this a
+bad clip is
+
+ align:start position:0%
+bad clip is
+ 
+
+ align:start position:0%
+bad clip is
+that this one of the clips is a little
+
+ align:start position:0%
+that this one of the clips is a little
+ 
+
+ align:start position:0%
+that this one of the clips is a little
+weak
+
+ align:start position:0%
+weak
+ 
+
+ align:start position:0%
+weak
+right a little bit well we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk a
+
+ align:start position:0%
+talk a
+ 
+
+ align:start position:0%
+talk a
+little go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+wide yeah I'd expect to see more
+
+ align:start position:0%
+wide yeah I'd expect to see more
+ 
+
+ align:start position:0%
+wide yeah I'd expect to see more
+yeah so that's what
+
+ align:start position:0%
+yeah so that's what
+ 
+
+ align:start position:0%
+yeah so that's what
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+we that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those parts are bad for us they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you so are you trying to focus on the
+
+ align:start position:0%
+you so are you trying to focus on the
+ 
+
+ align:start position:0%
+you so are you trying to focus on the
+closer one are you trying to focus on
+
+ align:start position:0%
+closer one are you trying to focus on
+ 
+
+ align:start position:0%
+closer one are you trying to focus on
+The Closer account
+
+ align:start position:0%
+The Closer account
+ 
+
+ align:start position:0%
+The Closer account
+La first of all
+
+ align:start position:0%
+La first of all
+ 
+
+ align:start position:0%
+La first of all
+I don't know don't remember like which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one yeah just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does it look like that one of them might
+
+ align:start position:0%
+does it look like that one of them might
+ 
+
+ align:start position:0%
+does it look like that one of them might
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broken yeah the tips I think the poster
+
+ align:start position:0%
+broken yeah the tips I think the poster
+ 
+
+ align:start position:0%
+broken yeah the tips I think the poster
+one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broken there we
+
+ align:start position:0%
+broken there we
+ 
+
+ align:start position:0%
+broken there we
+go yeah this is what we were seeed not
+
+ align:start position:0%
+go yeah this is what we were seeed not
+ 
+
+ align:start position:0%
+go yeah this is what we were seeed not
+quite this St that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Ripple in the flat part yeah that
+
+ align:start position:0%
+the Ripple in the flat part yeah that
+ 
+
+ align:start position:0%
+the Ripple in the flat part yeah that
+that there's some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bizarre count to much but the basically
+
+ align:start position:0%
+bizarre count to much but the basically
+ 
+
+ align:start position:0%
+bizarre count to much but the basically
+be able to overlap the three different
+
+ align:start position:0%
+be able to overlap the three different
+ 
+
+ align:start position:0%
+be able to overlap the three different
+measurements that you make and then
+
+ align:start position:0%
+measurements that you make and then
+ 
+
+ align:start position:0%
+measurements that you make and then
+compare compare your stage motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+exct yeah because you can see that okay
+
+ align:start position:0%
+exct yeah because you can see that okay
+ 
+
+ align:start position:0%
+exct yeah because you can see that okay
+here the can is coming in contact well
+
+ align:start position:0%
+here the can is coming in contact well
+ 
+
+ align:start position:0%
+here the can is coming in contact well
+no it's not at all but
+
+ align:start position:0%
+no it's not at all but
+ 
+
+ align:start position:0%
+no it's not at all but
+um it's it's the place where it's
+
+ align:start position:0%
+um it's it's the place where it's
+ 
+
+ align:start position:0%
+um it's it's the place where it's
+clearest where the can comes in contact
+
+ align:start position:0%
+clearest where the can comes in contact
+ 
+
+ align:start position:0%
+clearest where the can comes in contact
+with the surface okay that Mak sense um
+
+ align:start position:0%
+with the surface okay that Mak sense um
+ 
+
+ align:start position:0%
+with the surface okay that Mak sense um
+you might also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check yeah let's see if the other
+
+ align:start position:0%
+check yeah let's see if the other
+ 
+
+ align:start position:0%
+check yeah let's see if the other
+grading is a little bit happier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you think maybe theor was bit angle
+
+ align:start position:0%
+did you think maybe theor was bit angle
+ 
+
+ align:start position:0%
+did you think maybe theor was bit angle
+yeah it was a little bit angled so you
+
+ align:start position:0%
+yeah it was a little bit angled so you
+ 
+
+ align:start position:0%
+yeah it was a little bit angled so you
+can probably improve some more tiny
+
+ align:start position:0%
+can probably improve some more tiny
+ 
+
+ align:start position:0%
+can probably improve some more tiny
+bit Yeah you see how well
+
+ align:start position:0%
+bit Yeah you see how well
+ 
+
+ align:start position:0%
+bit Yeah you see how well
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a better shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is because you're on the other
+
+ align:start position:0%
+so this is because you're on the other
+ 
+
+ align:start position:0%
+so this is because you're on the other
+Fringe now or because you adjusted the
+
+ align:start position:0%
+Fringe now or because you adjusted the
+ 
+
+ align:start position:0%
+Fringe now or because you adjusted the
+protector um it's part well so i' I've
+
+ align:start position:0%
+protector um it's part well so i' I've
+ 
+
+ align:start position:0%
+protector um it's part well so i' I've
+switched to the other set of fingers
+
+ align:start position:0%
+switched to the other set of fingers
+ 
+
+ align:start position:0%
+switched to the other set of fingers
+sorry that's they are a little bit
+
+ align:start position:0%
+sorry that's they are a little bit
+ 
+
+ align:start position:0%
+sorry that's they are a little bit
+better it looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like I also
+
+ align:start position:0%
+like I also
+ 
+
+ align:start position:0%
+like I also
+uh yeah I also slightly like improved
+
+ align:start position:0%
+uh yeah I also slightly like improved
+ 
+
+ align:start position:0%
+uh yeah I also slightly like improved
+the detector
+
+ align:start position:0%
+the detector
+ 
+
+ align:start position:0%
+the detector
+alignment so now the shape looks pretty
+
+ align:start position:0%
+alignment so now the shape looks pretty
+ 
+
+ align:start position:0%
+alignment so now the shape looks pretty
+decent the the the problem here that I
+
+ align:start position:0%
+decent the the the problem here that I
+ 
+
+ align:start position:0%
+decent the the the problem here that I
+anticipate
+
+ align:start position:0%
+anticipate
+ 
+
+ align:start position:0%
+anticipate
+is oh here we are yeah now we're getting
+
+ align:start position:0%
+is oh here we are yeah now we're getting
+ 
+
+ align:start position:0%
+is oh here we are yeah now we're getting
+a full
+
+ align:start position:0%
+a full
+ 
+
+ align:start position:0%
+a full
+Fringe
+
+ align:start position:0%
+Fringe
+ 
+
+ align:start position:0%
+Fringe
+okay so that's actually that's
+
+ align:start position:0%
+okay so that's actually that's
+ 
+
+ align:start position:0%
+okay so that's actually that's
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+um yeah so now you have a very nice
+
+ align:start position:0%
+um yeah so now you have a very nice
+ 
+
+ align:start position:0%
+um yeah so now you have a very nice
+sinos soy that you can get a full Fringe
+
+ align:start position:0%
+sinos soy that you can get a full Fringe
+ 
+
+ align:start position:0%
+sinos soy that you can get a full Fringe
+of this in contact portion so I would uh
+
+ align:start position:0%
+of this in contact portion so I would uh
+ 
+
+ align:start position:0%
+of this in contact portion so I would uh
+I would actually record that okay and
+
+ align:start position:0%
+I would actually record that okay and
+ 
+
+ align:start position:0%
+I would actually record that okay and
+keep that as a reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I think you can ALS sometimes you
+
+ align:start position:0%
+yeah I think you can ALS sometimes you
+ 
+
+ align:start position:0%
+yeah I think you can ALS sometimes you
+can use the retraction part also
+
+ align:start position:0%
+can use the retraction part also
+ 
+
+ align:start position:0%
+can use the retraction part also
+sometime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's it helps you interpret whether this
+
+ align:start position:0%
+it's it helps you interpret whether this
+ 
+
+ align:start position:0%
+it's it helps you interpret whether this
+is giving a good day that okay so um to
+
+ align:start position:0%
+is giving a good day that okay so um to
+ 
+
+ align:start position:0%
+is giving a good day that okay so um to
+actually record it I often times will do
+
+ align:start position:0%
+actually record it I often times will do
+ 
+
+ align:start position:0%
+actually record it I often times will do
+a slower Trace like at a half a Hertz so
+
+ align:start position:0%
+a slower Trace like at a half a Hertz so
+ 
+
+ align:start position:0%
+a slower Trace like at a half a Hertz so
+that so that there's no it minimizes
+
+ align:start position:0%
+that so that there's no it minimizes
+ 
+
+ align:start position:0%
+that so that there's no it minimizes
+hysteresis a little
+
+ align:start position:0%
+hysteresis a little
+ 
+
+ align:start position:0%
+hysteresis a little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+um we should make recorded yeah you can
+
+ align:start position:0%
+um we should make recorded yeah you can
+ 
+
+ align:start position:0%
+um we should make recorded yeah you can
+actually you can you can save a force
+
+ align:start position:0%
+actually you can you can save a force
+ 
+
+ align:start position:0%
+actually you can you can save a force
+curve when it's not
+
+ align:start position:0%
+curve when it's not
+ 
+
+ align:start position:0%
+curve when it's not
+scanning um whatever you see on the
+
+ align:start position:0%
+scanning um whatever you see on the
+ 
+
+ align:start position:0%
+scanning um whatever you see on the
+screen is what it put in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+file yeah yeah
+
+ align:start position:0%
+file yeah yeah
+ 
+
+ align:start position:0%
+file yeah yeah
+oh it's it's a little there's more
+
+ align:start position:0%
+oh it's it's a little there's more
+ 
+
+ align:start position:0%
+oh it's it's a little there's more
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically good yeah just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it's badly or it wasn't I think it
+
+ align:start position:0%
+say it's badly or it wasn't I think it
+ 
+
+ align:start position:0%
+say it's badly or it wasn't I think it
+was flipped yeah I think so couldn't
+
+ align:start position:0%
+was flipped yeah I think so couldn't
+ 
+
+ align:start position:0%
+was flipped yeah I think so couldn't
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see shall I start taking the sample out
+
+ align:start position:0%
+see shall I start taking the sample out
+ 
+
+ align:start position:0%
+see shall I start taking the sample out
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure yeah that looks
+
+ align:start position:0%
+sure yeah that looks
+ 
+
+ align:start position:0%
+sure yeah that looks
+good oh well did you reverse
+
+ align:start position:0%
+good oh well did you reverse
+ 
+
+ align:start position:0%
+good oh well did you reverse
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+it yeah so now what you've got you
+
+ align:start position:0%
+it yeah so now what you've got you
+ 
+
+ align:start position:0%
+it yeah so now what you've got you
+actually got these levers that are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular yeah
+
+ align:start position:0%
+particular yeah
+ 
+
+ align:start position:0%
+particular yeah
+which they might be now dead in the
+
+ align:start position:0%
+which they might be now dead in the
+ 
+
+ align:start position:0%
+which they might be now dead in the
+background but that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mic yeah let's just change to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simp okay thank you let's give it a shot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay those compressed a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+why isn't it saving
+
+ align:start position:0%
+why isn't it saving
+ 
+
+ align:start position:0%
+why isn't it saving
+yeah is there no file being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+created say that again I the full
+
+ align:start position:0%
+created say that again I the full
+ 
+
+ align:start position:0%
+created say that again I the full
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+uh you got to make sure there's a full
+
+ align:start position:0%
+uh you got to make sure there's a full
+ 
+
+ align:start position:0%
+uh you got to make sure there's a full
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path oh
+
+ align:start position:0%
+path oh
+ 
+
+ align:start position:0%
+path oh
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+the text is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good it just saves an uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+text do you export this to the the M lab
+
+ align:start position:0%
+text do you export this to the the M lab
+ 
+
+ align:start position:0%
+text do you export this to the the M lab
+desktop you can just load it as um it's
+
+ align:start position:0%
+desktop you can just load it as um it's
+ 
+
+ align:start position:0%
+desktop you can just load it as um it's
+should be a two colum file of data okay
+
+ align:start position:0%
+should be a two colum file of data okay
+ 
+
+ align:start position:0%
+should be a two colum file of data okay
+you should be able to just plot X versus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y sorry
+
+ align:start position:0%
+y sorry
+ 
+
+ align:start position:0%
+y sorry
+the gr SLE that should be
+
+ align:start position:0%
+the gr SLE that should be
+ 
+
+ align:start position:0%
+the gr SLE that should be
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and that'll help you position it
+
+ align:start position:0%
+yeah and that'll help you position it
+ 
+
+ align:start position:0%
+yeah and that'll help you position it
+and then you can load it back down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have to do you have to do one
+
+ align:start position:0%
+I have to do you have to do one
+ 
+
+ align:start position:0%
+I have to do you have to do one
+vers this is the driving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh oh uh there that's better
+
+ align:start position:0%
+uh oh uh there that's better
+ 
+
+ align:start position:0%
+uh oh uh there that's better
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh just want
+
+ align:start position:0%
+uh just want
+ 
+
+ align:start position:0%
+uh just want
+open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seal all right um oh and what yeah what
+
+ align:start position:0%
+seal all right um oh and what yeah what
+ 
+
+ align:start position:0%
+seal all right um oh and what yeah what
+actually the best thing to do is open
+
+ align:start position:0%
+actually the best thing to do is open
+ 
+
+ align:start position:0%
+actually the best thing to do is open
+yeah one thing I in the bolab is I just
+
+ align:start position:0%
+yeah one thing I in the bolab is I just
+ 
+
+ align:start position:0%
+yeah one thing I in the bolab is I just
+had all those variables like that appear
+
+ align:start position:0%
+had all those variables like that appear
+ 
+
+ align:start position:0%
+had all those variables like that appear
+in the workspace so you didn't have to
+
+ align:start position:0%
+in the workspace so you didn't have to
+ 
+
+ align:start position:0%
+in the workspace so you didn't have to
+export them and reort them oh should you
+
+ align:start position:0%
+export them and reort them oh should you
+ 
+
+ align:start position:0%
+export them and reort them oh should you
+click on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+workpace oh yeah so you got you got to
+
+ align:start position:0%
+workpace oh yeah so you got you got to
+ 
+
+ align:start position:0%
+workpace oh yeah so you got you got to
+you actually have to um they're in the
+
+ align:start position:0%
+you actually have to um they're in the
+ 
+
+ align:start position:0%
+you actually have to um they're in the
+name space of the that GOI application
+
+ align:start position:0%
+name space of the that GOI application
+ 
+
+ align:start position:0%
+name space of the that GOI application
+there's a
+
+ align:start position:0%
+there's a
+ 
+
+ align:start position:0%
+there's a
+command uh there's a command that
+
+ align:start position:0%
+command uh there's a command that
+ 
+
+ align:start position:0%
+command uh there's a command that
+exports it to the oh really I don't
+
+ align:start position:0%
+exports it to the oh really I don't
+ 
+
+ align:start position:0%
+exports it to the oh really I don't
+remember the name of it off off my head
+
+ align:start position:0%
+remember the name of it off off my head
+ 
+
+ align:start position:0%
+remember the name of it off off my head
+but there's a some stupid the long list
+
+ align:start position:0%
+but there's a some stupid the long list
+ 
+
+ align:start position:0%
+but there's a some stupid the long list
+of stupid that lb
+
+ align:start position:0%
+of stupid that lb
+ 
+
+ align:start position:0%
+of stupid that lb
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+con there's uh there's there's one and
+
+ align:start position:0%
+con there's uh there's there's one and
+ 
+
+ align:start position:0%
+con there's uh there's there's one and
+so what right what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I see
+
+ align:start position:0%
+I see
+ 
+
+ align:start position:0%
+I see
+where's still starting
+
+ align:start position:0%
+where's still starting
+ 
+
+ align:start position:0%
+where's still starting
+can I going be trying to put it in the
+
+ align:start position:0%
+can I going be trying to put it in the
+ 
+
+ align:start position:0%
+can I going be trying to put it in the
+same window or
+
+ align:start position:0%
+same window or
+ 
+
+ align:start position:0%
+same window or
+something thatb is really a pathetic
+
+ align:start position:0%
+something thatb is really a pathetic
+ 
+
+ align:start position:0%
+something thatb is really a pathetic
+program isn't it all right hey hey no I
+
+ align:start position:0%
+program isn't it all right hey hey no I
+ 
+
+ align:start position:0%
+program isn't it all right hey hey no I
+didn't say your stuff I said that
+
+ align:start position:0%
+didn't say your stuff I said that
+ 
+
+ align:start position:0%
+didn't say your stuff I said that
+notel that's
+
+ align:start position:0%
+notel that's
+ 
+
+ align:start position:0%
+notel that's
+right all right all right uh are we
+
+ align:start position:0%
+right all right all right uh are we
+ 
+
+ align:start position:0%
+right all right all right uh are we
+ready yes all right so we're
+
+ align:start position:0%
+ready yes all right so we're
+ 
+
+ align:start position:0%
+ready yes all right so we're
+do don't put the part where I said bat
+
+ align:start position:0%
+do don't put the part where I said bat
+ 
+
+ align:start position:0%
+do don't put the part where I said bat
+loveb is pathetic up all
+
+ align:start position:0%
+loveb is pathetic up all
+ 
+
+ align:start position:0%
+loveb is pathetic up all
+right all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it's a soft sample it's
+
+ align:start position:0%
+right it's a soft sample it's
+ 
+
+ align:start position:0%
+right it's a soft sample it's
+noted pretty sure I already touched it
+
+ align:start position:0%
+noted pretty sure I already touched it
+ 
+
+ align:start position:0%
+noted pretty sure I already touched it
+oh all right and so I can
+
+ align:start position:0%
+oh all right and so I can
+ 
+
+ align:start position:0%
+oh all right and so I can
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are so I'm just backing away from the
+
+ align:start position:0%
+are so I'm just backing away from the
+ 
+
+ align:start position:0%
+are so I'm just backing away from the
+surface now
+
+ align:start position:0%
+surface now
+ 
+
+ align:start position:0%
+surface now
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+contact out of
+
+ align:start position:0%
+contact out of
+ 
+
+ align:start position:0%
+contact out of
+contact just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contact contact all
+
+ align:start position:0%
+contact contact all
+ 
+
+ align:start position:0%
+contact contact all
+right yay all right let me uh maybe back
+
+ align:start position:0%
+right yay all right let me uh maybe back
+ 
+
+ align:start position:0%
+right yay all right let me uh maybe back
+off just a few
+
+ align:start position:0%
+off just a few
+ 
+
+ align:start position:0%
+off just a few
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+clicks uh
+
+ align:start position:0%
+clicks uh
+ 
+
+ align:start position:0%
+clicks uh
+yeah perfect all right so let's slow
+
+ align:start position:0%
+yeah perfect all right so let's slow
+ 
+
+ align:start position:0%
+yeah perfect all right so let's slow
+this down again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't see just one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spot oh this is cool you should uh can
+
+ align:start position:0%
+spot oh this is cool you should uh can
+ 
+
+ align:start position:0%
+spot oh this is cool you should uh can
+you run that again because since you're
+
+ align:start position:0%
+you run that again because since you're
+ 
+
+ align:start position:0%
+you run that again because since you're
+scanning so much more slowly now you can
+
+ align:start position:0%
+scanning so much more slowly now you can
+ 
+
+ align:start position:0%
+scanning so much more slowly now you can
+see the whole Fringe up and down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah that's really
+
+ align:start position:0%
+oh yeah that's really
+ 
+
+ align:start position:0%
+oh yeah that's really
+nice so this is indenting cyclically
+
+ align:start position:0%
+nice so this is indenting cyclically
+ 
+
+ align:start position:0%
+nice so this is indenting cyclically
+into the pdms so The Fringe moving shows
+
+ align:start position:0%
+into the pdms so The Fringe moving shows
+ 
+
+ align:start position:0%
+into the pdms so The Fringe moving shows
+that he's moving in and out of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sample did you stop it yeah I I'll sa
+
+ align:start position:0%
+sample did you stop it yeah I I'll sa
+ 
+
+ align:start position:0%
+sample did you stop it yeah I I'll sa
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+and this is art or the soft we don't
+
+ align:start position:0%
+and this is art or the soft we don't
+ 
+
+ align:start position:0%
+and this is art or the soft we don't
+know actually so this I'll save this as
+
+ align:start position:0%
+know actually so this I'll save this as
+ 
+
+ align:start position:0%
+know actually so this I'll save this as
+unknown you can save it as left because
+
+ align:start position:0%
+unknown you can save it as left because
+ 
+
+ align:start position:0%
+unknown you can save it as left because
+left okay that's good oh you know what
+
+ align:start position:0%
+left okay that's good oh you know what
+ 
+
+ align:start position:0%
+left okay that's good oh you know what
+it is the box is labeled I think he
+
+ align:start position:0%
+it is the box is labeled I think he
+ 
+
+ align:start position:0%
+it is the box is labeled I think he
+didn't think it was but it's 25 pdms so
+
+ align:start position:0%
+didn't think it was but it's 25 pdms so
+ 
+
+ align:start position:0%
+didn't think it was but it's 25 pdms so
+that should be the stiffer one I laed it
+
+ align:start position:0%
+that should be the stiffer one I laed it
+ 
+
+ align:start position:0%
+that should be the stiffer one I laed it
+now oh okay 25 is actually the sof oh is
+
+ align:start position:0%
+now oh okay 25 is actually the sof oh is
+ 
+
+ align:start position:0%
+now oh okay 25 is actually the sof oh is
+it yeah
+
+ align:start position:0%
+it yeah
+ 
+
+ align:start position:0%
+it yeah
+because that represents the ratio in
+
+ align:start position:0%
+because that represents the ratio in
+ 
+
+ align:start position:0%
+because that represents the ratio in
+which I Mi the
+
+ align:start position:0%
+which I Mi the
+ 
+
+ align:start position:0%
+which I Mi the
+um puring agent to uh base polymer so
+
+ align:start position:0%
+um puring agent to uh base polymer so
+ 
+
+ align:start position:0%
+um puring agent to uh base polymer so
+it's Mally it's mixed 1 to 10 oh okay
+
+ align:start position:0%
+it's Mally it's mixed 1 to 10 oh okay
+ 
+
+ align:start position:0%
+it's Mally it's mixed 1 to 10 oh okay
+for like the standard recipe and I mixed
+
+ align:start position:0%
+for like the standard recipe and I mixed
+ 
+
+ align:start position:0%
+for like the standard recipe and I mixed
+one to 25 so this I thought it was 10%
+
+ align:start position:0%
+one to 25 so this I thought it was 10%
+ 
+
+ align:start position:0%
+one to 25 so this I thought it was 10%
+25% we don't use standardized things
+
+ align:start position:0%
+25% we don't use standardized things
+ 
+
+ align:start position:0%
+25% we don't use standardized things
+like per that's a silly way to
\ No newline at end of file
diff --git a/U8R54zOTVLw.txt b/U8R54zOTVLw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ca74468da247f0df5a4c9ec2e57a19656464701c
--- /dev/null
+++ b/U8R54zOTVLw.txt
@@ -0,0 +1,1571 @@
+align:start position:0%
+ 
+okay more about igen values and igen
+
+ align:start position:0%
+okay more about igen values and igen
+ 
+
+ align:start position:0%
+okay more about igen values and igen
+vectors well actually it's going to be
+
+ align:start position:0%
+vectors well actually it's going to be
+ 
+
+ align:start position:0%
+vectors well actually it's going to be
+the same thing about igen values and
+
+ align:start position:0%
+the same thing about igen values and
+ 
+
+ align:start position:0%
+the same thing about igen values and
+igen vectors but I'm going to use Matrix
+
+ align:start position:0%
+igen vectors but I'm going to use Matrix
+ 
+
+ align:start position:0%
+igen vectors but I'm going to use Matrix
+notation so you remember I have a matrix
+
+ align:start position:0%
+notation so you remember I have a matrix
+ 
+
+ align:start position:0%
+notation so you remember I have a matrix
+a 2X two for example it's got two igen
+
+ align:start position:0%
+a 2X two for example it's got two igen
+ 
+
+ align:start position:0%
+a 2X two for example it's got two igen
+vectors each igen Vector has its igen
+
+ align:start position:0%
+vectors each igen Vector has its igen
+ 
+
+ align:start position:0%
+vectors each igen Vector has its igen
+value so I could write
+
+ align:start position:0%
+value so I could write
+ 
+
+ align:start position:0%
+value so I could write
+the the IG Value World that that way I
+
+ align:start position:0%
+the the IG Value World that that way I
+ 
+
+ align:start position:0%
+the the IG Value World that that way I
+want to write it in Matrix form I want
+
+ align:start position:0%
+want to write it in Matrix form I want
+ 
+
+ align:start position:0%
+want to write it in Matrix form I want
+to create an igen Vector matrix by
+
+ align:start position:0%
+to create an igen Vector matrix by
+ 
+
+ align:start position:0%
+to create an igen Vector matrix by
+taking the two I vectors and putting
+
+ align:start position:0%
+taking the two I vectors and putting
+ 
+
+ align:start position:0%
+taking the two I vectors and putting
+them in The Columns of my Matrix so
+
+ align:start position:0%
+them in The Columns of my Matrix so
+ 
+
+ align:start position:0%
+them in The Columns of my Matrix so
+that's uh that if I have n of them that
+
+ align:start position:0%
+that's uh that if I have n of them that
+ 
+
+ align:start position:0%
+that's uh that if I have n of them that
+allows me to give one name the I Vector
+
+ align:start position:0%
+allows me to give one name the I Vector
+ 
+
+ align:start position:0%
+allows me to give one name the I Vector
+Matrix maybe I'll call it V for
+
+ align:start position:0%
+Matrix maybe I'll call it V for
+ 
+
+ align:start position:0%
+Matrix maybe I'll call it V for
+vectors so that's a * V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now just bear with me while I do
+
+ align:start position:0%
+and now just bear with me while I do
+ 
+
+ align:start position:0%
+and now just bear with me while I do
+that multiplication of a * the I Vector
+
+ align:start position:0%
+that multiplication of a * the I Vector
+ 
+
+ align:start position:0%
+that multiplication of a * the I Vector
+Matrix so what do I get I get a matrix
+
+ align:start position:0%
+Matrix so what do I get I get a matrix
+ 
+
+ align:start position:0%
+Matrix so what do I get I get a matrix
+that's 2x two that's 2x two I'm getting
+
+ align:start position:0%
+that's 2x two that's 2x two I'm getting
+ 
+
+ align:start position:0%
+that's 2x two that's 2x two I'm getting
+a 2X two Matrix what's the First Column
+
+ align:start position:0%
+a 2X two Matrix what's the First Column
+ 
+
+ align:start position:0%
+a 2X two Matrix what's the First Column
+the First Column of the output is a *
+
+ align:start position:0%
+the First Column of the output is a *
+ 
+
+ align:start position:0%
+the First Column of the output is a *
+the First Column of the input and what
+
+ align:start position:0%
+the First Column of the input and what
+ 
+
+ align:start position:0%
+the First Column of the input and what
+is a * X1 well a * X X1 is Lambda 1 * X1
+
+ align:start position:0%
+is a * X1 well a * X X1 is Lambda 1 * X1
+ 
+
+ align:start position:0%
+is a * X1 well a * X X1 is Lambda 1 * X1
+so that First Column is Lambda 1 X1 and
+
+ align:start position:0%
+so that First Column is Lambda 1 X1 and
+ 
+
+ align:start position:0%
+so that First Column is Lambda 1 X1 and
+a times the second column is ax2 which
+
+ align:start position:0%
+a times the second column is ax2 which
+ 
+
+ align:start position:0%
+a times the second column is ax2 which
+is Lambda 2x2 so I'm seeing Lambda 2 x2
+
+ align:start position:0%
+is Lambda 2x2 so I'm seeing Lambda 2 x2
+ 
+
+ align:start position:0%
+is Lambda 2x2 so I'm seeing Lambda 2 x2
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+column okay Matrix notation those were
+
+ align:start position:0%
+column okay Matrix notation those were
+ 
+
+ align:start position:0%
+column okay Matrix notation those were
+the I vectors this is the result of a *
+
+ align:start position:0%
+the I vectors this is the result of a *
+ 
+
+ align:start position:0%
+the I vectors this is the result of a *
+V but but I can look at this a little
+
+ align:start position:0%
+V but but I can look at this a little
+ 
+
+ align:start position:0%
+V but but I can look at this a little
+differently I can say wait a minute that
+
+ align:start position:0%
+differently I can say wait a minute that
+ 
+
+ align:start position:0%
+differently I can say wait a minute that
+is my ion Vector Matrix X1 and X2 those
+
+ align:start position:0%
+is my ion Vector Matrix X1 and X2 those
+ 
+
+ align:start position:0%
+is my ion Vector Matrix X1 and X2 those
+two columns times a
+
+ align:start position:0%
+two columns times a
+ 
+
+ align:start position:0%
+two columns times a
+matrix ah yes I want to I'm I'm just
+
+ align:start position:0%
+matrix ah yes I want to I'm I'm just
+ 
+
+ align:start position:0%
+matrix ah yes I want to I'm I'm just
+taking this First Column Lambda 1x1
+
+ align:start position:0%
+taking this First Column Lambda 1x1
+ 
+
+ align:start position:0%
+taking this First Column Lambda 1x1
+is Lambda 1 * X1 + 0 * X2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right there I did a matrix
+
+ align:start position:0%
+right there I did a matrix
+ 
+
+ align:start position:0%
+right there I did a matrix
+multiplication I did it without
+
+ align:start position:0%
+multiplication I did it without
+ 
+
+ align:start position:0%
+multiplication I did it without
+preparing you for it I'll I'll go back
+
+ align:start position:0%
+preparing you for it I'll I'll go back
+ 
+
+ align:start position:0%
+preparing you for it I'll I'll go back
+and do that preparation in a moment
+
+ align:start position:0%
+and do that preparation in a moment
+ 
+
+ align:start position:0%
+and do that preparation in a moment
+but when I multiply a matrix by a vector
+
+ align:start position:0%
+but when I multiply a matrix by a vector
+ 
+
+ align:start position:0%
+but when I multiply a matrix by a vector
+I take Lambda 1 time that one 0 * that
+
+ align:start position:0%
+I take Lambda 1 time that one 0 * that
+ 
+
+ align:start position:0%
+I take Lambda 1 time that one 0 * that
+one I get Lambda 1x1 which is what I
+
+ align:start position:0%
+one I get Lambda 1x1 which is what I
+ 
+
+ align:start position:0%
+one I get Lambda 1x1 which is what I
+want can you see what I want in the
+
+ align:start position:0%
+want can you see what I want in the
+ 
+
+ align:start position:0%
+want can you see what I want in the
+second column here
+
+ align:start position:0%
+second column here
+ 
+
+ align:start position:0%
+second column here
+I the result I want is Lambda
+
+ align:start position:0%
+I the result I want is Lambda
+ 
+
+ align:start position:0%
+I the result I want is Lambda
+2x2 so I want no
+
+ align:start position:0%
+2x2 so I want no
+ 
+
+ align:start position:0%
+2x2 so I want no
+x1's and Lambda
+
+ align:start position:0%
+x1's and Lambda
+ 
+
+ align:start position:0%
+x1's and Lambda
+2 of that column so that's 0 * that
+
+ align:start position:0%
+2 of that column so that's 0 * that
+ 
+
+ align:start position:0%
+2 of that column so that's 0 * that
+column plus Lambda 2 * that
+
+ align:start position:0%
+column plus Lambda 2 * that
+ 
+
+ align:start position:0%
+column plus Lambda 2 * that
+column are we okay so what do I have now
+
+ align:start position:0%
+column are we okay so what do I have now
+ 
+
+ align:start position:0%
+column are we okay so what do I have now
+I have the whole thing in a beautiful
+
+ align:start position:0%
+I have the whole thing in a beautiful
+ 
+
+ align:start position:0%
+I have the whole thing in a beautiful
+form as is a * the igon vector Matrix
+
+ align:start position:0%
+form as is a * the igon vector Matrix
+ 
+
+ align:start position:0%
+form as is a * the igon vector Matrix
+equals there's the igon vector Matrix
+
+ align:start position:0%
+equals there's the igon vector Matrix
+ 
+
+ align:start position:0%
+equals there's the igon vector Matrix
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+V and here is a new Matrix that I'm
+
+ align:start position:0%
+V and here is a new Matrix that I'm
+ 
+
+ align:start position:0%
+V and here is a new Matrix that I'm
+going to that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+igon value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and
+
+ align:start position:0%
+Matrix and
+ 
+
+ align:start position:0%
+Matrix and
+everybody calls that because those are
+
+ align:start position:0%
+everybody calls that because those are
+ 
+
+ align:start position:0%
+everybody calls that because those are
+Lambda 1 and Lambda 2 so the natural
+
+ align:start position:0%
+Lambda 1 and Lambda 2 so the natural
+ 
+
+ align:start position:0%
+Lambda 1 and Lambda 2 so the natural
+letter is a capital Lambda that's a
+
+ align:start position:0%
+letter is a capital Lambda that's a
+ 
+
+ align:start position:0%
+letter is a capital Lambda that's a
+capital Greek Lambda there the best I
+
+ align:start position:0%
+capital Greek Lambda there the best I
+ 
+
+ align:start position:0%
+capital Greek Lambda there the best I
+could do so you see that the two
+
+ align:start position:0%
+could do so you see that the two
+ 
+
+ align:start position:0%
+could do so you see that the two
+equations SE written separately or the
+
+ align:start position:0%
+equations SE written separately or the
+ 
+
+ align:start position:0%
+equations SE written separately or the
+four equations or the N
+
+ align:start position:0%
+four equations or the N
+ 
+
+ align:start position:0%
+four equations or the N
+equations combine into one Matrix
+
+ align:start position:0%
+equations combine into one Matrix
+ 
+
+ align:start position:0%
+equations combine into one Matrix
+equation this is the same as those two
+
+ align:start position:0%
+equation this is the same as those two
+ 
+
+ align:start position:0%
+equation this is the same as those two
+together good good but now now that I
+
+ align:start position:0%
+together good good but now now that I
+ 
+
+ align:start position:0%
+together good good but now now that I
+have it in Matrix form I can mess around
+
+ align:start position:0%
+have it in Matrix form I can mess around
+ 
+
+ align:start position:0%
+have it in Matrix form I can mess around
+with it I can multiply both sides by V
+
+ align:start position:0%
+with it I can multiply both sides by V
+ 
+
+ align:start position:0%
+with it I can multiply both sides by V
+inverse If I multiply both sides by V
+
+ align:start position:0%
+inverse If I multiply both sides by V
+ 
+
+ align:start position:0%
+inverse If I multiply both sides by V
+inverse I I discover well shall I
+
+ align:start position:0%
+inverse I I discover well shall I
+ 
+
+ align:start position:0%
+inverse I I discover well shall I
+multiply on the left by V inverse yes
+
+ align:start position:0%
+multiply on the left by V inverse yes
+ 
+
+ align:start position:0%
+multiply on the left by V inverse yes
+I'll do that if I multiply on the left
+
+ align:start position:0%
+I'll do that if I multiply on the left
+ 
+
+ align:start position:0%
+I'll do that if I multiply on the left
+by V inverse that's V inverse a
+
+ align:start position:0%
+by V inverse that's V inverse a
+ 
+
+ align:start position:0%
+by V inverse that's V inverse a
+v so this the matrix multiplication and
+
+ align:start position:0%
+v so this the matrix multiplication and
+ 
+
+ align:start position:0%
+v so this the matrix multiplication and
+my next video is going to recap
+
+ align:start position:0%
+my next video is going to recap
+ 
+
+ align:start position:0%
+my next video is going to recap
+Matrix uh multiplication so I multiply
+
+ align:start position:0%
+Matrix uh multiplication so I multiply
+ 
+
+ align:start position:0%
+Matrix uh multiplication so I multiply
+both sides by V inverse V inverse time V
+
+ align:start position:0%
+both sides by V inverse V inverse time V
+ 
+
+ align:start position:0%
+both sides by V inverse V inverse time V
+is the identity that's what the inverse
+
+ align:start position:0%
+is the identity that's what the inverse
+ 
+
+ align:start position:0%
+is the identity that's what the inverse
+Matrix is V inverse V is the identity so
+
+ align:start position:0%
+Matrix is V inverse V is the identity so
+ 
+
+ align:start position:0%
+Matrix is V inverse V is the identity so
+there you go let me push that up that's
+
+ align:start position:0%
+there you go let me push that up that's
+ 
+
+ align:start position:0%
+there you go let me push that up that's
+really nice that's really nice that's
+
+ align:start position:0%
+really nice that's really nice that's
+ 
+
+ align:start position:0%
+really nice that's really nice that's
+called diagonalizing a i diagonalize a
+
+ align:start position:0%
+called diagonalizing a i diagonalize a
+ 
+
+ align:start position:0%
+called diagonalizing a i diagonalize a
+by taking the I Vector Matrix on the
+
+ align:start position:0%
+by taking the I Vector Matrix on the
+ 
+
+ align:start position:0%
+by taking the I Vector Matrix on the
+right its inverse on the left multiply
+
+ align:start position:0%
+right its inverse on the left multiply
+ 
+
+ align:start position:0%
+right its inverse on the left multiply
+those three matrices and I get this
+
+ align:start position:0%
+those three matrices and I get this
+ 
+
+ align:start position:0%
+those three matrices and I get this
+diagonal matrix this is the diagonal
+
+ align:start position:0%
+diagonal matrix this is the diagonal
+ 
+
+ align:start position:0%
+diagonal matrix this is the diagonal
+matrix Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or other times I might want to multiply
+
+ align:start position:0%
+or other times I might want to multiply
+ 
+
+ align:start position:0%
+or other times I might want to multiply
+by both sides here by V inverse on the
+
+ align:start position:0%
+by both sides here by V inverse on the
+ 
+
+ align:start position:0%
+by both sides here by V inverse on the
+coming on the right so that would give
+
+ align:start position:0%
+coming on the right so that would give
+ 
+
+ align:start position:0%
+coming on the right so that would give
+me a v v inverse is the identity so I'm
+
+ align:start position:0%
+me a v v inverse is the identity so I'm
+ 
+
+ align:start position:0%
+me a v v inverse is the identity so I'm
+I'm moving V I can move V over there as
+
+ align:start position:0%
+I'm moving V I can move V over there as
+ 
+
+ align:start position:0%
+I'm moving V I can move V over there as
+V inverse that's what it amounts to I
+
+ align:start position:0%
+V inverse that's what it amounts to I
+ 
+
+ align:start position:0%
+V inverse that's what it amounts to I
+multiply both sides by V inverse so this
+
+ align:start position:0%
+multiply both sides by V inverse so this
+ 
+
+ align:start position:0%
+multiply both sides by V inverse so this
+is just a and this is the V and the
+
+ align:start position:0%
+is just a and this is the V and the
+ 
+
+ align:start position:0%
+is just a and this is the V and the
+Lambda and now the V
+
+ align:start position:0%
+Lambda and now the V
+ 
+
+ align:start position:0%
+Lambda and now the V
+inverse that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great so that is that's a way to see
+
+ align:start position:0%
+great so that is that's a way to see
+ 
+
+ align:start position:0%
+great so that is that's a way to see
+what a how a is built
+
+ align:start position:0%
+what a how a is built
+ 
+
+ align:start position:0%
+what a how a is built
+up or broken down into the IG Vector
+
+ align:start position:0%
+up or broken down into the IG Vector
+ 
+
+ align:start position:0%
+up or broken down into the IG Vector
+Matrix times the igon value Matrix times
+
+ align:start position:0%
+Matrix times the igon value Matrix times
+ 
+
+ align:start position:0%
+Matrix times the igon value Matrix times
+the inverse of the I Vector Matrix okay
+
+ align:start position:0%
+the inverse of the I Vector Matrix okay
+ 
+
+ align:start position:0%
+the inverse of the I Vector Matrix okay
+let me just use that for a moment uh
+
+ align:start position:0%
+let me just use that for a moment uh
+ 
+
+ align:start position:0%
+let me just use that for a moment uh
+just so you see how it connects with
+
+ align:start position:0%
+just so you see how it connects with
+ 
+
+ align:start position:0%
+just so you see how it connects with
+what we already know about igen values
+
+ align:start position:0%
+what we already know about igen values
+ 
+
+ align:start position:0%
+what we already know about igen values
+and I vectors okay so I'll copy that
+
+ align:start position:0%
+and I vectors okay so I'll copy that
+ 
+
+ align:start position:0%
+and I vectors okay so I'll copy that
+great fact that
+
+ align:start position:0%
+great fact that
+ 
+
+ align:start position:0%
+great fact that
+a is V Lambda
+
+ align:start position:0%
+a is V Lambda
+ 
+
+ align:start position:0%
+a is V Lambda
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+inverse oh what do I want to do I want
+
+ align:start position:0%
+inverse oh what do I want to do I want
+ 
+
+ align:start position:0%
+inverse oh what do I want to do I want
+to look at a squ so if I look at a squ
+
+ align:start position:0%
+to look at a squ so if I look at a squ
+ 
+
+ align:start position:0%
+to look at a squ so if I look at a squ
+that's V V inverse
+
+ align:start position:0%
+that's V V inverse
+ 
+
+ align:start position:0%
+that's V V inverse
+times another
+
+ align:start position:0%
+times another
+ 
+
+ align:start position:0%
+times another
+one right there's an a there's an A so
+
+ align:start position:0%
+one right there's an a there's an A so
+ 
+
+ align:start position:0%
+one right there's an a there's an A so
+that's a s well you may say I've made a
+
+ align:start position:0%
+that's a s well you may say I've made a
+ 
+
+ align:start position:0%
+that's a s well you may say I've made a
+mess out of a squ but not true V inverse
+
+ align:start position:0%
+mess out of a squ but not true V inverse
+ 
+
+ align:start position:0%
+mess out of a squ but not true V inverse
+V is the
+
+ align:start position:0%
+V is the
+ 
+
+ align:start position:0%
+V is the
+identity so that's just the identity
+
+ align:start position:0%
+identity so that's just the identity
+ 
+
+ align:start position:0%
+identity so that's just the identity
+sitting in the middle so the V at the
+
+ align:start position:0%
+sitting in the middle so the V at the
+ 
+
+ align:start position:0%
+sitting in the middle so the V at the
+far left then I have the Lambda and then
+
+ align:start position:0%
+far left then I have the Lambda and then
+ 
+
+ align:start position:0%
+far left then I have the Lambda and then
+I have the other Lambda Lambda s squ and
+
+ align:start position:0%
+I have the other Lambda Lambda s squ and
+ 
+
+ align:start position:0%
+I have the other Lambda Lambda s squ and
+then the V inverse at the far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's a
+
+ align:start position:0%
+right that's a
+ 
+
+ align:start position:0%
+right that's a
+2 and if I did it n times I would have a
+
+ align:start position:0%
+2 and if I did it n times I would have a
+ 
+
+ align:start position:0%
+2 and if I did it n times I would have a
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+N would be
+
+ align:start position:0%
+N would be
+ 
+
+ align:start position:0%
+N would be
+V Lambda to the N power V inverse what
+
+ align:start position:0%
+V Lambda to the N power V inverse what
+ 
+
+ align:start position:0%
+V Lambda to the N power V inverse what
+is this what is this saying about this
+
+ align:start position:0%
+is this what is this saying about this
+ 
+
+ align:start position:0%
+is this what is this saying about this
+is a s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what what how do I understand that
+
+ align:start position:0%
+what what how do I understand that
+ 
+
+ align:start position:0%
+what what how do I understand that
+equation I to me that says that the I
+
+ align:start position:0%
+equation I to me that says that the I
+ 
+
+ align:start position:0%
+equation I to me that says that the I
+values of a s are Lambda squar I'm just
+
+ align:start position:0%
+values of a s are Lambda squar I'm just
+ 
+
+ align:start position:0%
+values of a s are Lambda squar I'm just
+squaring each igen value and the igen
+
+ align:start position:0%
+squaring each igen value and the igen
+ 
+
+ align:start position:0%
+squaring each igen value and the igen
+vectors what are the I vectors of a s
+
+ align:start position:0%
+vectors what are the I vectors of a s
+ 
+
+ align:start position:0%
+vectors what are the I vectors of a s
+they're the same V the same vectors X1
+
+ align:start position:0%
+they're the same V the same vectors X1
+ 
+
+ align:start position:0%
+they're the same V the same vectors X1
+X2 that went into V they they're also
+
+ align:start position:0%
+X2 that went into V they they're also
+ 
+
+ align:start position:0%
+X2 that went into V they they're also
+the ion vectors of a squ of a cubed of a
+
+ align:start position:0%
+the ion vectors of a squ of a cubed of a
+ 
+
+ align:start position:0%
+the ion vectors of a squ of a cubed of a
+to the N of a inverse and so that's the
+
+ align:start position:0%
+to the N of a inverse and so that's the
+ 
+
+ align:start position:0%
+to the N of a inverse and so that's the
+point of diagonalizing a matrix
+
+ align:start position:0%
+point of diagonalizing a matrix
+ 
+
+ align:start position:0%
+point of diagonalizing a matrix
+diagonalizing a matrix is another way to
+
+ align:start position:0%
+diagonalizing a matrix is another way to
+ 
+
+ align:start position:0%
+diagonalizing a matrix is another way to
+see that when I Square The Matrix which
+
+ align:start position:0%
+see that when I Square The Matrix which
+ 
+
+ align:start position:0%
+see that when I Square The Matrix which
+is usually a big
+
+ align:start position:0%
+is usually a big
+ 
+
+ align:start position:0%
+is usually a big
+mess look looking at the igen values and
+
+ align:start position:0%
+mess look looking at the igen values and
+ 
+
+ align:start position:0%
+mess look looking at the igen values and
+igen vectors it's the opposite of a big
+
+ align:start position:0%
+igen vectors it's the opposite of a big
+ 
+
+ align:start position:0%
+igen vectors it's the opposite of a big
+mess it's very clear the ion vectors are
+
+ align:start position:0%
+mess it's very clear the ion vectors are
+ 
+
+ align:start position:0%
+mess it's very clear the ion vectors are
+the same as for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the igen values are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squares of the I
+
+ align:start position:0%
+squares of the I
+ 
+
+ align:start position:0%
+squares of the I
+values of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a in other
+
+ align:start position:0%
+a in other
+ 
+
+ align:start position:0%
+a in other
+words we can take the N power and we
+
+ align:start position:0%
+words we can take the N power and we
+ 
+
+ align:start position:0%
+words we can take the N power and we
+have a nice notation for it we we
+
+ align:start position:0%
+have a nice notation for it we we
+ 
+
+ align:start position:0%
+have a nice notation for it we we
+learned already that the N power has the
+
+ align:start position:0%
+learned already that the N power has the
+ 
+
+ align:start position:0%
+learned already that the N power has the
+igen values to the n power and the igen
+
+ align:start position:0%
+igen values to the n power and the igen
+ 
+
+ align:start position:0%
+igen values to the n power and the igen
+vector is the same but now I just see it
+
+ align:start position:0%
+vector is the same but now I just see it
+ 
+
+ align:start position:0%
+vector is the same but now I just see it
+here and there it is for the ins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power so if I took the same Matrix step
+
+ align:start position:0%
+power so if I took the same Matrix step
+ 
+
+ align:start position:0%
+power so if I took the same Matrix step
+a thousand times what would be important
+
+ align:start position:0%
+a thousand times what would be important
+ 
+
+ align:start position:0%
+a thousand times what would be important
+what controls the thousandth power of a
+
+ align:start position:0%
+what controls the thousandth power of a
+ 
+
+ align:start position:0%
+what controls the thousandth power of a
+matrix the ion vectors
+
+ align:start position:0%
+matrix the ion vectors
+ 
+
+ align:start position:0%
+matrix the ion vectors
+stay they're just set it would be the
+
+ align:start position:0%
+stay they're just set it would be the
+ 
+
+ align:start position:0%
+stay they're just set it would be the
+thousandth power of the igen value so if
+
+ align:start position:0%
+thousandth power of the igen value so if
+ 
+
+ align:start position:0%
+thousandth power of the igen value so if
+this is a matrix with an igen value
+
+ align:start position:0%
+this is a matrix with an igen value
+ 
+
+ align:start position:0%
+this is a matrix with an igen value
+larger than one then the thousandth
+
+ align:start position:0%
+larger than one then the thousandth
+ 
+
+ align:start position:0%
+larger than one then the thousandth
+power is going to be much larger than
+
+ align:start position:0%
+power is going to be much larger than
+ 
+
+ align:start position:0%
+power is going to be much larger than
+one if this is a matrix with igen values
+
+ align:start position:0%
+one if this is a matrix with igen values
+ 
+
+ align:start position:0%
+one if this is a matrix with igen values
+smaller than one they're going to be
+
+ align:start position:0%
+smaller than one they're going to be
+ 
+
+ align:start position:0%
+smaller than one they're going to be
+very small for lamb when I take the
+
+ align:start position:0%
+very small for lamb when I take the
+ 
+
+ align:start position:0%
+very small for lamb when I take the
+thousandth power if if there's an IG
+
+ align:start position:0%
+thousandth power if if there's an IG
+ 
+
+ align:start position:0%
+thousandth power if if there's an IG
+value that's exactly one that will be a
+
+ align:start position:0%
+value that's exactly one that will be a
+ 
+
+ align:start position:0%
+value that's exactly one that will be a
+steady state and one to the thousandth
+
+ align:start position:0%
+steady state and one to the thousandth
+ 
+
+ align:start position:0%
+steady state and one to the thousandth
+power will still be one and nothing will
+
+ align:start position:0%
+power will still be one and nothing will
+ 
+
+ align:start position:0%
+power will still be one and nothing will
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+so the stability what happens as I
+
+ align:start position:0%
+so the stability what happens as I
+ 
+
+ align:start position:0%
+so the stability what happens as I
+multiply take powers of a matrix is a
+
+ align:start position:0%
+multiply take powers of a matrix is a
+ 
+
+ align:start position:0%
+multiply take powers of a matrix is a
+basic question parallel to the question
+
+ align:start position:0%
+basic question parallel to the question
+ 
+
+ align:start position:0%
+basic question parallel to the question
+what happens with a differential
+
+ align:start position:0%
+what happens with a differential
+ 
+
+ align:start position:0%
+what happens with a differential
+equation when I take the the solve
+
+ align:start position:0%
+equation when I take the the solve
+ 
+
+ align:start position:0%
+equation when I take the the solve
+forward in time I I think of those two
+
+ align:start position:0%
+forward in time I I think of those two
+ 
+
+ align:start position:0%
+forward in time I I think of those two
+problems as quite parallel this is
+
+ align:start position:0%
+problems as quite parallel this is
+ 
+
+ align:start position:0%
+problems as quite parallel this is
+taking steps single steps discrete steps
+
+ align:start position:0%
+taking steps single steps discrete steps
+ 
+
+ align:start position:0%
+taking steps single steps discrete steps
+the differential equation is moving
+
+ align:start position:0%
+the differential equation is moving
+ 
+
+ align:start position:0%
+the differential equation is moving
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+continuously this the difference between
+
+ align:start position:0%
+continuously this the difference between
+ 
+
+ align:start position:0%
+continuously this the difference between
+hop hop hop in the discrete case and run
+
+ align:start position:0%
+hop hop hop in the discrete case and run
+ 
+
+ align:start position:0%
+hop hop hop in the discrete case and run
+forward continuously in the differential
+
+ align:start position:0%
+forward continuously in the differential
+ 
+
+ align:start position:0%
+forward continuously in the differential
+case in both cases the I vectors and the
+
+ align:start position:0%
+case in both cases the I vectors and the
+ 
+
+ align:start position:0%
+case in both cases the I vectors and the
+igen values are the guide to what
+
+ align:start position:0%
+igen values are the guide to what
+ 
+
+ align:start position:0%
+igen values are the guide to what
+happens as time goes forward okay I have
+
+ align:start position:0%
+happens as time goes forward okay I have
+ 
+
+ align:start position:0%
+happens as time goes forward okay I have
+to do more about matric working with
+
+ align:start position:0%
+to do more about matric working with
+ 
+
+ align:start position:0%
+to do more about matric working with
+matrices uh let me come to that
+
+ align:start position:0%
+matrices uh let me come to that
+ 
+
+ align:start position:0%
+matrices uh let me come to that
+next thanks
\ No newline at end of file
diff --git a/UDow47-q5KI.txt b/UDow47-q5KI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..28368913bb021df494af5c17525e7ed03fe378e4
--- /dev/null
+++ b/UDow47-q5KI.txt
@@ -0,0 +1,417 @@
+We'll describe the operation of the FSM for
+our combination lock using a state transition
+
+diagram.
+
+Initially, the FSM has received no bits of
+the combination, a state we'll call SX.
+
+In the state transition diagram, states are
+represented as circles, each labeled for now
+
+with a symbolic name chosen to remind us of
+what history it represents.
+
+For this FSM, the unlock output U will be
+a function of the current state, so we'll
+
+indicate the value of U inside the circle.
+
+Since in state SX we know nothing about past
+input bits, the lock should stay locked and
+
+so U = 0.
+
+We'll indicate the initial state with a wide
+border on the circle.
+
+We'll use the successive states to remember
+what we've seen so far of the input combination.
+
+So if the FSM is in state SX and it receives
+a 0 input, it should transition to state S0
+
+to remind us that we've seen the first bit
+of the combination of 0-1-1-0.
+
+We use arrows to indicate transitions between
+states and each arrow has a label telling
+
+us when that transition should occur.
+
+So this particular arrow is telling us that
+when the FSM is in state SX and the next input
+
+is a 0, the FSM should transition to state
+S0.
+
+Transitions are triggered by the rising edge
+of the FSM's clock input.
+
+Let's add the states for the remainder of
+the specified combination.
+
+The rightmost state, S0110, represents the
+point at which the FSM has detected the specified
+
+sequence of inputs, so the unlock signal is
+1 in this state.
+
+Looking at the state transition diagram, we
+see that if the FSM starts in state SX, the
+
+input sequence 0-1-1-0 will leave the FSM
+in state S0110.
+
+So far, so good.
+
+What should the FSM do if an input bit is
+not the next bit in the combination?
+
+For example, if the FSM is in state SX and
+the input bit is a 1, it still has not received
+
+any correct combination bits, so the next
+state is SX again.
+
+Here are the appropriate non-combination transitions
+for the other states.
+
+Note that an incorrect combination entry doesn't
+necessarily take the FSM to state SX.
+
+For example, if the FSM is in state S0110,
+the last four input bits have been 0-1-1-0.
+
+If the next input is a 1, then the last four
+inputs bits are now 1-1-0-1, which won't lead
+
+to an open lock.
+
+But the last two bits might be the first two
+bits of a valid combination sequence and so
+
+the FSM transitions to S01, indicating that
+a sequence of 0-1 has been entered over the
+
+last two bits.
+
+We've been working with an FSM where the outputs
+are function of the current state, called
+
+a Moore machine.
+
+Here the outputs are written inside the state
+circle.
+
+If the outputs are a function of both the
+current state and the current inputs, it's
+
+called a Mealy machine.
+
+Since the transitions are also a function
+of the current state and current inputs, we'll
+
+label each transition with appropriate output
+values using a slash to separate input values
+
+from output values.
+
+So, looking at the state transition diagram
+on the right, suppose the FSM is in state
+
+S3.
+
+If the input is a 0, look for the arrow leaving
+S3 labeled "0/".
+
+The value after the slash tells us the output
+value, in this case 1.
+
+If the input had been a 1, the output value
+would be 0.
+
+There are some simple rules we can use to
+check that a state transition diagram is well
+
+formed.
+
+The transitions from a particular state must
+be mutually exclusive, i.e., for a each state,
+
+there can't be more than one transition with
+the same input label.
+
+This makes sense: if the FSM is to operate
+consistently there can't be any ambiguity
+
+about the next state for a given current state
+and input.
+
+By "consistently" we mean that the FSM should
+make the same transitions if it's restarted
+
+at the same starting state and given the same
+input sequences.
+
+Moreover, the transitions leaving each state
+should be collectively exhaustive, i.e., there
+
+should a transition specified for each possible
+input value.
+
+If we wish the FSM to stay in it's current
+state for that particular input value, we
+
+need to show a transition from the current
+state back to itself.
+
+With these rules there will be exactly one
+transition selected for every combination
+
+of current state and input value.
+
+All the information in a state transition
+diagram can be represented in tabular form
+
+as a truth table.
+
+The rows of the truth table list all the possible
+combinations of current state and inputs.
+
+And the output columns of the truth table
+tell us the next state and output value associated
+
+with each row.
+
+If we substitute binary values for the symbolic
+state names, we end up with a truth table
+
+just like the ones we saw in Chapter 4.
+
+If we have K states in our state transition
+diagram we'll need log_2(K) state bits, rounded
+
+up to the next integer since we don't have
+fractional bits!
+
+In our example, we have a 5-state FSM, so
+we'll need 3 state bits.
+
+We can assign the state encodings in any convenient
+way, e.g., 000 for the first state, 001 for
+
+the second state, and so on.
+
+But the choice of state encodings can have
+a big effect on the logic needed to implement
+
+the truth table.
+
+It's actually fun to figure out the state
+encoding that produces the simplest possible
+
+logic.
+
+With a truth table in hand, we can use the
+techniques from Chapter 4 to design logic
+
+circuits that implement the combinational
+logic for the FSM.
+
+Of course, we can take the easy way out and
+simply use a read-only memory to do the job!
+
+In this circuit, a read-only memory is used
+to compute the next state and outputs from
+
+the current state and inputs.
+
+We're encoding the 5 states of the FSM using
+a 3-bit binary value, so we have a 3-bit state
+
+register.
+
+The rectangle with the edge-triggered input
+is schematic shorthand for a multi-bit register.
+
+If a wire in the diagram represents a multi-bit
+signal, we use a little slash across the wire
+
+with a number to indicate how many bits are
+in the signal.
+
+In this example, both current_state and next_state
+are 3-bit signals.
+
+The read-only memory has a total of 4 input
+signals - 3 for the current state and 1 for
+
+the input value -
+so the read-only memory has 2^4 or 16 locations,
+
+which correspond to the 16 rows in the truth
+table.
+
+Each location in the ROM supplies the output
+values for a particular row of the truth table.
+
+Since we have 4 output signals - 3 for the
+next state and 1 for the output value - each
+
+location supplies 4 bits of information.
+
+Memories are often annotated with their number
+of locations and the number of bits in each
+
+location.
+
+So our memory is a 16-by-4 ROM: 16 locations
+of 4-bits each.
+
+Of course, in order for the state registers
+to work correctly, we need to ensure that
+
+the dynamic discipline is obeyed.
+
+We can use the timing analysis techniques
+described at the end of Chapter 5 to check
+
+that this is so.
+
+For now, we'll assume that the timing of transitions
+on the inputs are properly synchronized with
+
+the rising edges of the clock.
+
+So now we have the FSM abstraction to use
+when designing the functionality of a sequential
+
+logic system, and a general-purpose circuit
+implementation of the FSM using a ROM and
+
+a multi-bit state register.
+
+Recapping our design choices: the output bits
+can be strictly a function of the current
+
+state (the FSM would then be called a Moore
+machine),
+
+or they can be a function of both the current
+state and current inputs, in which case the
+
+FSM is called a Mealy machine.
+
+We can choose the number of state bits - S
+state bits will give us the ability to encode
+
+2^S possible states.
+
+Note that each extra state bit DOUBLES the
+number of locations in the ROM!
+
+So when using ROMs to implement the necessary
+logic, we're very interested in minimizing
+
+the number of state bits.
+
+The waveforms for our circuitry are pretty
+straightforward.
+
+The rising edge of the clock triggers a transition
+in the state register outputs.
+
+The ROM then does its thing, calculating the
+next state, which becomes valid at some point
+
+in the clock cycle.
+
+This is the value that gets loaded into the
+state registers at the next rising clock edge.
+
+This process repeats over-and-over as the
+FSM follows the state transitions dictated
+
+by the state transition diagram.
+
+There are a few housekeeping details that
+need our attention.
+
+On start-up we need some way to set the initial
+contents of the state register to the correct
+
+encoding for the initial state.
+
+Many designs use a RESET signal that's set
+to 1 to force some initial state and then
+
+set to 0 to start execution.
+
+We could adopt that approach here, using the
+RESET signal to select an initial value to
+
+be loaded into the state register.
+
+In our example, we used a 3-bit state encoding
+which would allow us to implement an FSM with
+
+up to 2^3 = 8 states.
+
+We're only using 5 of these encodings, which
+means there are locations in the ROM we'll
+
+never access.
+
+If that's a concern, we can always use logic
+gates to implement the necessary combinational
+
+logic instead of ROMs.
+
+Suppose the state register somehow got loaded
+with one of the unused encodings?
+
+Well, that would be like being in a state
+that's not listed in our state transition
+
+diagram.
+
+One way to defend against this problem is
+design the ROM contents so that unused states
+
+always point to the initial state.
+
+In theory the problem should never arise,
+but with this fix at least it won't lead to
+
+unknown behavior.
+
+We mentioned earlier the interesting problem
+of finding a state encoding that minimized
+
+the combinational logic.
+
+There are computer-aided design tools to help
+do this as part of the larger problem of finding
+
+minimal logic implementations for Boolean
+functions.
+
+Mr. Blue is showing us another approach to
+building the state register for the combination
+
+lock:
+use a shift register to capture the last four
+
+input bits, then simply look at the recorded
+history to determine if it matches the combination.
+
+No fancy next0state logic here!
+
+Finally, we still have to address the problem
+of ensuring that input transitions don't violate
+
+the dynamic discipline for the state register.
+
+We'll get to this in the last section of this
+chapter.
\ No newline at end of file
diff --git a/UmLCGjbeeJ8.txt b/UmLCGjbeeJ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..441916bf1e3021c45a3b209a4238b5e81dcb254e
--- /dev/null
+++ b/UmLCGjbeeJ8.txt
@@ -0,0 +1,2443 @@
+align:start position:0%
+ 
+our discussion about the future of the
+
+ align:start position:0%
+our discussion about the future of the
+ 
+
+ align:start position:0%
+our discussion about the future of the
+workforce would not be complete without
+
+ align:start position:0%
+workforce would not be complete without
+ 
+
+ align:start position:0%
+workforce would not be complete without
+an exploration of what impact the
+
+ align:start position:0%
+an exploration of what impact the
+ 
+
+ align:start position:0%
+an exploration of what impact the
+current innovations in technology will
+
+ align:start position:0%
+current innovations in technology will
+ 
+
+ align:start position:0%
+current innovations in technology will
+have specifically artificial
+
+ align:start position:0%
+have specifically artificial
+ 
+
+ align:start position:0%
+have specifically artificial
+intelligence over the past few years
+
+ align:start position:0%
+intelligence over the past few years
+ 
+
+ align:start position:0%
+intelligence over the past few years
+there have been significant innovations
+
+ align:start position:0%
+there have been significant innovations
+ 
+
+ align:start position:0%
+there have been significant innovations
+in big data database architecture and
+
+ align:start position:0%
+in big data database architecture and
+ 
+
+ align:start position:0%
+in big data database architecture and
+artificial intelligence that are
+
+ align:start position:0%
+artificial intelligence that are
+ 
+
+ align:start position:0%
+artificial intelligence that are
+enabling new business models and
+
+ align:start position:0%
+enabling new business models and
+ 
+
+ align:start position:0%
+enabling new business models and
+products and simplest terms the
+
+ align:start position:0%
+products and simplest terms the
+ 
+
+ align:start position:0%
+products and simplest terms the
+innovations and artificial intelligence
+
+ align:start position:0%
+innovations and artificial intelligence
+ 
+
+ align:start position:0%
+innovations and artificial intelligence
+are equipping algorithms to make smarter
+
+ align:start position:0%
+are equipping algorithms to make smarter
+ 
+
+ align:start position:0%
+are equipping algorithms to make smarter
+decisions about tasks and problems that
+
+ align:start position:0%
+decisions about tasks and problems that
+ 
+
+ align:start position:0%
+decisions about tasks and problems that
+have so far been thought only to be
+
+ align:start position:0%
+have so far been thought only to be
+ 
+
+ align:start position:0%
+have so far been thought only to be
+reserved for humans the accompanying
+
+ align:start position:0%
+reserved for humans the accompanying
+ 
+
+ align:start position:0%
+reserved for humans the accompanying
+innovations and cheapening of hardware
+
+ align:start position:0%
+innovations and cheapening of hardware
+ 
+
+ align:start position:0%
+innovations and cheapening of hardware
+that enables artificial intelligence
+
+ align:start position:0%
+that enables artificial intelligence
+ 
+
+ align:start position:0%
+that enables artificial intelligence
+algorithms to read in process incredibly
+
+ align:start position:0%
+algorithms to read in process incredibly
+ 
+
+ align:start position:0%
+algorithms to read in process incredibly
+large data sets has motivated more
+
+ align:start position:0%
+large data sets has motivated more
+ 
+
+ align:start position:0%
+large data sets has motivated more
+entrepreneurs and technologists to
+
+ align:start position:0%
+entrepreneurs and technologists to
+ 
+
+ align:start position:0%
+entrepreneurs and technologists to
+innovate with artificial intelligence
+
+ align:start position:0%
+innovate with artificial intelligence
+ 
+
+ align:start position:0%
+innovate with artificial intelligence
+many think that the implications for the
+
+ align:start position:0%
+many think that the implications for the
+ 
+
+ align:start position:0%
+many think that the implications for the
+workplace will hurt workers similar to
+
+ align:start position:0%
+workplace will hurt workers similar to
+ 
+
+ align:start position:0%
+workplace will hurt workers similar to
+how the Industrial Revolution displaced
+
+ align:start position:0%
+how the Industrial Revolution displaced
+ 
+
+ align:start position:0%
+how the Industrial Revolution displaced
+many workers through the creation of
+
+ align:start position:0%
+many workers through the creation of
+ 
+
+ align:start position:0%
+many workers through the creation of
+tech that was cheaper and overall more
+
+ align:start position:0%
+tech that was cheaper and overall more
+ 
+
+ align:start position:0%
+tech that was cheaper and overall more
+efficient than people people believe
+
+ align:start position:0%
+efficient than people people believe
+ 
+
+ align:start position:0%
+efficient than people people believe
+that AI will replace and not just
+
+ align:start position:0%
+that AI will replace and not just
+ 
+
+ align:start position:0%
+that AI will replace and not just
+blue-collar workers but also
+
+ align:start position:0%
+blue-collar workers but also
+ 
+
+ align:start position:0%
+blue-collar workers but also
+white-collar workers however the fact is
+
+ align:start position:0%
+white-collar workers however the fact is
+ 
+
+ align:start position:0%
+white-collar workers however the fact is
+that the impact on workers is under our
+
+ align:start position:0%
+that the impact on workers is under our
+ 
+
+ align:start position:0%
+that the impact on workers is under our
+control the control of entrepreneurs
+
+ align:start position:0%
+control the control of entrepreneurs
+ 
+
+ align:start position:0%
+control the control of entrepreneurs
+technologists and everyday citizens that
+
+ align:start position:0%
+technologists and everyday citizens that
+ 
+
+ align:start position:0%
+technologists and everyday citizens that
+are part of the workforce business
+
+ align:start position:0%
+are part of the workforce business
+ 
+
+ align:start position:0%
+are part of the workforce business
+owners and workers can harness AI to
+
+ align:start position:0%
+owners and workers can harness AI to
+ 
+
+ align:start position:0%
+owners and workers can harness AI to
+augment human intelligence in the
+
+ align:start position:0%
+augment human intelligence in the
+ 
+
+ align:start position:0%
+augment human intelligence in the
+workplace to creatively improve
+
+ align:start position:0%
+workplace to creatively improve
+ 
+
+ align:start position:0%
+workplace to creatively improve
+decision-making instead of replacing it
+
+ align:start position:0%
+decision-making instead of replacing it
+ 
+
+ align:start position:0%
+decision-making instead of replacing it
+here is Rob hi the CTO of IBM Watson one
+
+ align:start position:0%
+here is Rob hi the CTO of IBM Watson one
+ 
+
+ align:start position:0%
+here is Rob hi the CTO of IBM Watson one
+of the primary rd leaders in the AI
+
+ align:start position:0%
+of the primary rd leaders in the AI
+ 
+
+ align:start position:0%
+of the primary rd leaders in the AI
+space making this exact point at the
+
+ align:start position:0%
+space making this exact point at the
+ 
+
+ align:start position:0%
+space making this exact point at the
+2016 MIT technology conference right if
+
+ align:start position:0%
+2016 MIT technology conference right if
+ 
+
+ align:start position:0%
+2016 MIT technology conference right if
+we if we become experts and everything
+
+ align:start position:0%
+we if we become experts and everything
+ 
+
+ align:start position:0%
+we if we become experts and everything
+we're experts in nothing and so the same
+
+ align:start position:0%
+we're experts in nothing and so the same
+ 
+
+ align:start position:0%
+we're experts in nothing and so the same
+phenomenon occurs within these cognitive
+
+ align:start position:0%
+phenomenon occurs within these cognitive
+ 
+
+ align:start position:0%
+phenomenon occurs within these cognitive
+systems as well they can actually begin
+
+ align:start position:0%
+systems as well they can actually begin
+ 
+
+ align:start position:0%
+systems as well they can actually begin
+to get a little bit confused and in how
+
+ align:start position:0%
+to get a little bit confused and in how
+ 
+
+ align:start position:0%
+to get a little bit confused and in how
+to how to disambiguate question so a
+
+ align:start position:0%
+to how to disambiguate question so a
+ 
+
+ align:start position:0%
+to how to disambiguate question so a
+couple points to be made about that that
+
+ align:start position:0%
+couple points to be made about that that
+ 
+
+ align:start position:0%
+couple points to be made about that that
+said because each of these are distinct
+
+ align:start position:0%
+said because each of these are distinct
+ 
+
+ align:start position:0%
+said because each of these are distinct
+we can actually set the system up based
+
+ align:start position:0%
+we can actually set the system up based
+ 
+
+ align:start position:0%
+we can actually set the system up based
+on whatever is appropriate for the
+
+ align:start position:0%
+on whatever is appropriate for the
+ 
+
+ align:start position:0%
+on whatever is appropriate for the
+application we're trying to solve for
+
+ align:start position:0%
+application we're trying to solve for
+ 
+
+ align:start position:0%
+application we're trying to solve for
+for the case of oncology treatment
+
+ align:start position:0%
+for the case of oncology treatment
+ 
+
+ align:start position:0%
+for the case of oncology treatment
+advice it's the goal is actually about
+
+ align:start position:0%
+advice it's the goal is actually about
+ 
+
+ align:start position:0%
+advice it's the goal is actually about
+trying to identify
+
+ align:start position:0%
+trying to identify
+ 
+
+ align:start position:0%
+trying to identify
+best treatment based on outcomes based
+
+ align:start position:0%
+best treatment based on outcomes based
+ 
+
+ align:start position:0%
+best treatment based on outcomes based
+on standard of care practices and
+
+ align:start position:0%
+on standard of care practices and
+ 
+
+ align:start position:0%
+on standard of care practices and
+clinical expertise based on similarity
+
+ align:start position:0%
+clinical expertise based on similarity
+ 
+
+ align:start position:0%
+clinical expertise based on similarity
+this patient to other patients and all
+
+ align:start position:0%
+this patient to other patients and all
+ 
+
+ align:start position:0%
+this patient to other patients and all
+this contribute to help Watson come back
+
+ align:start position:0%
+this contribute to help Watson come back
+ 
+
+ align:start position:0%
+this contribute to help Watson come back
+with an ordered list of potential
+
+ align:start position:0%
+with an ordered list of potential
+ 
+
+ align:start position:0%
+with an ordered list of potential
+treatments but we again we're not trying
+
+ align:start position:0%
+treatments but we again we're not trying
+ 
+
+ align:start position:0%
+treatments but we again we're not trying
+to make the decision for the human right
+
+ align:start position:0%
+to make the decision for the human right
+ 
+
+ align:start position:0%
+to make the decision for the human right
+we're not trying to think for the human
+
+ align:start position:0%
+we're not trying to think for the human
+ 
+
+ align:start position:0%
+we're not trying to think for the human
+we're trying to do is do the research
+
+ align:start position:0%
+we're trying to do is do the research
+ 
+
+ align:start position:0%
+we're trying to do is do the research
+for the human so the human can then go
+
+ align:start position:0%
+for the human so the human can then go
+ 
+
+ align:start position:0%
+for the human so the human can then go
+make the better sort of better in this
+
+ align:start position:0%
+make the better sort of better in this
+ 
+
+ align:start position:0%
+make the better sort of better in this
+case the doctor so we're not going to
+
+ align:start position:0%
+case the doctor so we're not going to
+ 
+
+ align:start position:0%
+case the doctor so we're not going to
+take we're not going to you know Watson
+
+ align:start position:0%
+take we're not going to you know Watson
+ 
+
+ align:start position:0%
+take we're not going to you know Watson
+doesn't make the decision about what
+
+ align:start position:0%
+doesn't make the decision about what
+ 
+
+ align:start position:0%
+doesn't make the decision about what
+treatment to give for the doctor it
+
+ align:start position:0%
+treatment to give for the doctor it
+ 
+
+ align:start position:0%
+treatment to give for the doctor it
+presents the doctor a set of relevant
+
+ align:start position:0%
+presents the doctor a set of relevant
+ 
+
+ align:start position:0%
+presents the doctor a set of relevant
+treatments that has been rationalized
+
+ align:start position:0%
+treatments that has been rationalized
+ 
+
+ align:start position:0%
+treatments that has been rationalized
+based on all their information at a
+
+ align:start position:0%
+based on all their information at a
+ 
+
+ align:start position:0%
+based on all their information at a
+speed that a doctor could not do on
+
+ align:start position:0%
+speed that a doctor could not do on
+ 
+
+ align:start position:0%
+speed that a doctor could not do on
+their own including finding all the
+
+ align:start position:0%
+their own including finding all the
+ 
+
+ align:start position:0%
+their own including finding all the
+literature that's relevant to support
+
+ align:start position:0%
+literature that's relevant to support
+ 
+
+ align:start position:0%
+literature that's relevant to support
+why they should believe in that
+
+ align:start position:0%
+why they should believe in that
+ 
+
+ align:start position:0%
+why they should believe in that
+treatment or not okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what specific types of disruptions
+
+ align:start position:0%
+so what specific types of disruptions
+ 
+
+ align:start position:0%
+so what specific types of disruptions
+can we expect a I to cause for employers
+
+ align:start position:0%
+can we expect a I to cause for employers
+ 
+
+ align:start position:0%
+can we expect a I to cause for employers
+and employees let's take a look at what
+
+ align:start position:0%
+and employees let's take a look at what
+ 
+
+ align:start position:0%
+and employees let's take a look at what
+David otter a professor of economics at
+
+ align:start position:0%
+David otter a professor of economics at
+ 
+
+ align:start position:0%
+David otter a professor of economics at
+MIT said in the future work panel at the
+
+ align:start position:0%
+MIT said in the future work panel at the
+ 
+
+ align:start position:0%
+MIT said in the future work panel at the
+Nobel week dialogue of 2015 in terms of
+
+ align:start position:0%
+Nobel week dialogue of 2015 in terms of
+ 
+
+ align:start position:0%
+Nobel week dialogue of 2015 in terms of
+employment as we said earlier people
+
+ align:start position:0%
+employment as we said earlier people
+ 
+
+ align:start position:0%
+employment as we said earlier people
+have been worried for centuries about
+
+ align:start position:0%
+have been worried for centuries about
+ 
+
+ align:start position:0%
+have been worried for centuries about
+displacement of labor and labor has been
+
+ align:start position:0%
+displacement of labor and labor has been
+ 
+
+ align:start position:0%
+displacement of labor and labor has been
+vastly displaced right in the start of
+
+ align:start position:0%
+vastly displaced right in the start of
+ 
+
+ align:start position:0%
+vastly displaced right in the start of
+the 20th century forty percent of us
+
+ align:start position:0%
+the 20th century forty percent of us
+ 
+
+ align:start position:0%
+the 20th century forty percent of us
+employment was on in farms now it's
+
+ align:start position:0%
+employment was on in farms now it's
+ 
+
+ align:start position:0%
+employment was on in farms now it's
+under two percent we had no idea what
+
+ align:start position:0%
+under two percent we had no idea what
+ 
+
+ align:start position:0%
+under two percent we had no idea what
+was coming but it came we find uses for
+
+ align:start position:0%
+was coming but it came we find uses for
+ 
+
+ align:start position:0%
+was coming but it came we find uses for
+ourselves and that's partly because the
+
+ align:start position:0%
+ourselves and that's partly because the
+ 
+
+ align:start position:0%
+ourselves and that's partly because the
+technology augments us it doesn't just
+
+ align:start position:0%
+technology augments us it doesn't just
+ 
+
+ align:start position:0%
+technology augments us it doesn't just
+replace us it makes the rest of what we
+
+ align:start position:0%
+replace us it makes the rest of what we
+ 
+
+ align:start position:0%
+replace us it makes the rest of what we
+do more valuable right so you know I can
+
+ align:start position:0%
+do more valuable right so you know I can
+ 
+
+ align:start position:0%
+do more valuable right so you know I can
+make more as an uber driver then as a
+
+ align:start position:0%
+make more as an uber driver then as a
+ 
+
+ align:start position:0%
+make more as an uber driver then as a
+rickshaw driver not just because I'm in
+
+ align:start position:0%
+rickshaw driver not just because I'm in
+ 
+
+ align:start position:0%
+rickshaw driver not just because I'm in
+in the rich world but because I have a
+
+ align:start position:0%
+in the rich world but because I have a
+ 
+
+ align:start position:0%
+in the rich world but because I have a
+tool that makes me able to transport
+
+ align:start position:0%
+tool that makes me able to transport
+ 
+
+ align:start position:0%
+tool that makes me able to transport
+people much faster and further and more
+
+ align:start position:0%
+people much faster and further and more
+ 
+
+ align:start position:0%
+people much faster and further and more
+safely and more comfortably in a given
+
+ align:start position:0%
+safely and more comfortably in a given
+ 
+
+ align:start position:0%
+safely and more comfortably in a given
+amount of time in many many ways tools
+
+ align:start position:0%
+amount of time in many many ways tools
+ 
+
+ align:start position:0%
+amount of time in many many ways tools
+we make make our time more valuable
+
+ align:start position:0%
+we make make our time more valuable
+ 
+
+ align:start position:0%
+we make make our time more valuable
+because there's always some piece that
+
+ align:start position:0%
+because there's always some piece that
+ 
+
+ align:start position:0%
+because there's always some piece that
+we still have to supply and because that
+
+ align:start position:0%
+we still have to supply and because that
+ 
+
+ align:start position:0%
+we still have to supply and because that
+that becomes the scarce factor that
+
+ align:start position:0%
+that becomes the scarce factor that
+ 
+
+ align:start position:0%
+that becomes the scarce factor that
+raises our labor value so there's a
+
+ align:start position:0%
+raises our labor value so there's a
+ 
+
+ align:start position:0%
+raises our labor value so there's a
+challenge so now let me say but let's
+
+ align:start position:0%
+challenge so now let me say but let's
+ 
+
+ align:start position:0%
+challenge so now let me say but let's
+say I'm wrong and that we're going to be
+
+ align:start position:0%
+say I'm wrong and that we're going to be
+ 
+
+ align:start position:0%
+say I'm wrong and that we're going to be
+all replaced by robots right that they
+
+ align:start position:0%
+all replaced by robots right that they
+ 
+
+ align:start position:0%
+all replaced by robots right that they
+can do all the work we want is that a
+
+ align:start position:0%
+can do all the work we want is that a
+ 
+
+ align:start position:0%
+can do all the work we want is that a
+problem well if it's a problem it's a
+
+ align:start position:0%
+problem well if it's a problem it's a
+ 
+
+ align:start position:0%
+problem well if it's a problem it's a
+very unusual historical problem most
+
+ align:start position:0%
+very unusual historical problem most
+ 
+
+ align:start position:0%
+very unusual historical problem most
+problems economic problems societal
+
+ align:start position:0%
+problems economic problems societal
+ 
+
+ align:start position:0%
+problems economic problems societal
+problems are problems of scarcity of not
+
+ align:start position:0%
+problems are problems of scarcity of not
+ 
+
+ align:start position:0%
+problems are problems of scarcity of not
+having enough of something enough food
+
+ align:start position:0%
+having enough of something enough food
+ 
+
+ align:start position:0%
+having enough of something enough food
+enough power enough safety enough
+
+ align:start position:0%
+enough power enough safety enough
+ 
+
+ align:start position:0%
+enough power enough safety enough
+shelter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in addition to changing the kinds of
+
+ align:start position:0%
+in addition to changing the kinds of
+ 
+
+ align:start position:0%
+in addition to changing the kinds of
+roles that workers can take on in the
+
+ align:start position:0%
+roles that workers can take on in the
+ 
+
+ align:start position:0%
+roles that workers can take on in the
+workplace hey I based innovation can
+
+ align:start position:0%
+workplace hey I based innovation can
+ 
+
+ align:start position:0%
+workplace hey I based innovation can
+also impact social inequality for better
+
+ align:start position:0%
+also impact social inequality for better
+ 
+
+ align:start position:0%
+also impact social inequality for better
+or worse to be determined by how we
+
+ align:start position:0%
+or worse to be determined by how we
+ 
+
+ align:start position:0%
+or worse to be determined by how we
+choose to behave for example women and
+
+ align:start position:0%
+choose to behave for example women and
+ 
+
+ align:start position:0%
+choose to behave for example women and
+people of color are very
+
+ align:start position:0%
+people of color are very
+ 
+
+ align:start position:0%
+people of color are very
+underrepresented among technology
+
+ align:start position:0%
+underrepresented among technology
+ 
+
+ align:start position:0%
+underrepresented among technology
+entrepreneurs that receive funding from
+
+ align:start position:0%
+entrepreneurs that receive funding from
+ 
+
+ align:start position:0%
+entrepreneurs that receive funding from
+venture capitalists for their
+
+ align:start position:0%
+venture capitalists for their
+ 
+
+ align:start position:0%
+venture capitalists for their
+enterprises adventure capital investment
+
+ align:start position:0%
+enterprises adventure capital investment
+ 
+
+ align:start position:0%
+enterprises adventure capital investment
+goes towards a more diverse set of
+
+ align:start position:0%
+goes towards a more diverse set of
+ 
+
+ align:start position:0%
+goes towards a more diverse set of
+entrepreneurs then we will see social
+
+ align:start position:0%
+entrepreneurs then we will see social
+ 
+
+ align:start position:0%
+entrepreneurs then we will see social
+inequality improved positively here is
+
+ align:start position:0%
+inequality improved positively here is
+ 
+
+ align:start position:0%
+inequality improved positively here is
+Amanda callow CEO of six sons a
+
+ align:start position:0%
+Amanda callow CEO of six sons a
+ 
+
+ align:start position:0%
+Amanda callow CEO of six sons a
+predictive intelligence platform for
+
+ align:start position:0%
+predictive intelligence platform for
+ 
+
+ align:start position:0%
+predictive intelligence platform for
+marketing and sales expanding on the
+
+ align:start position:0%
+marketing and sales expanding on the
+ 
+
+ align:start position:0%
+marketing and sales expanding on the
+current under representation based on
+
+ align:start position:0%
+current under representation based on
+ 
+
+ align:start position:0%
+current under representation based on
+her experiences the short answer is yes
+
+ align:start position:0%
+her experiences the short answer is yes
+ 
+
+ align:start position:0%
+her experiences the short answer is yes
+I feel supported but I do feel so I go
+
+ align:start position:0%
+I feel supported but I do feel so I go
+ 
+
+ align:start position:0%
+I feel supported but I do feel so I go
+to a lot of CEO events instead I mean
+
+ align:start position:0%
+to a lot of CEO events instead I mean
+ 
+
+ align:start position:0%
+to a lot of CEO events instead I mean
+like on a panel like this last I was in
+
+ align:start position:0%
+like on a panel like this last I was in
+ 
+
+ align:start position:0%
+like on a panel like this last I was in
+Hawaii just a little while ago 250 CEOs
+
+ align:start position:0%
+Hawaii just a little while ago 250 CEOs
+ 
+
+ align:start position:0%
+Hawaii just a little while ago 250 CEOs
+as the only woman an enterprise tech on
+
+ align:start position:0%
+as the only woman an enterprise tech on
+ 
+
+ align:start position:0%
+as the only woman an enterprise tech on
+less than one percent in this world and
+
+ align:start position:0%
+less than one percent in this world and
+ 
+
+ align:start position:0%
+less than one percent in this world and
+it's it's crazy and it's it doesn't feel
+
+ align:start position:0%
+it's it's crazy and it's it doesn't feel
+ 
+
+ align:start position:0%
+it's it's crazy and it's it doesn't feel
+right and I think it's because we're
+
+ align:start position:0%
+right and I think it's because we're
+ 
+
+ align:start position:0%
+right and I think it's because we're
+missing that confidence and the passion
+
+ align:start position:0%
+missing that confidence and the passion
+ 
+
+ align:start position:0%
+missing that confidence and the passion
+to go forward and want to dream big do I
+
+ align:start position:0%
+to go forward and want to dream big do I
+ 
+
+ align:start position:0%
+to go forward and want to dream big do I
+feel supported by the men i think yes
+
+ align:start position:0%
+feel supported by the men i think yes
+ 
+
+ align:start position:0%
+feel supported by the men i think yes
+I'm supported I think pretty much I feel
+
+ align:start position:0%
+I'm supported I think pretty much I feel
+ 
+
+ align:start position:0%
+I'm supported I think pretty much I feel
+very supported especially my mail
+
+ align:start position:0%
+very supported especially my mail
+ 
+
+ align:start position:0%
+very supported especially my mail
+co-founders are ridiculously supportive
+
+ align:start position:0%
+co-founders are ridiculously supportive
+ 
+
+ align:start position:0%
+co-founders are ridiculously supportive
+and actually I think that they have more
+
+ align:start position:0%
+and actually I think that they have more
+ 
+
+ align:start position:0%
+and actually I think that they have more
+faith and confidence in me than I do
+
+ align:start position:0%
+faith and confidence in me than I do
+ 
+
+ align:start position:0%
+faith and confidence in me than I do
+myself which is amazing I think I have
+
+ align:start position:0%
+myself which is amazing I think I have
+ 
+
+ align:start position:0%
+myself which is amazing I think I have
+had to maybe guide and teach some of my
+
+ align:start position:0%
+had to maybe guide and teach some of my
+ 
+
+ align:start position:0%
+had to maybe guide and teach some of my
+VCS and other people in the world like
+
+ align:start position:0%
+VCS and other people in the world like
+ 
+
+ align:start position:0%
+VCS and other people in the world like
+what's important and it's not always
+
+ align:start position:0%
+what's important and it's not always
+ 
+
+ align:start position:0%
+what's important and it's not always
+just about like I think we're talking
+
+ align:start position:0%
+just about like I think we're talking
+ 
+
+ align:start position:0%
+just about like I think we're talking
+earlier about the end goal of the
+
+ align:start position:0%
+earlier about the end goal of the
+ 
+
+ align:start position:0%
+earlier about the end goal of the
+business and growing the business but
+
+ align:start position:0%
+business and growing the business but
+ 
+
+ align:start position:0%
+business and growing the business but
+creating a sustainable company is also
+
+ align:start position:0%
+creating a sustainable company is also
+ 
+
+ align:start position:0%
+creating a sustainable company is also
+about the culture and the people and I
+
+ align:start position:0%
+about the culture and the people and I
+ 
+
+ align:start position:0%
+about the culture and the people and I
+think that what what we're missing in
+
+ align:start position:0%
+think that what what we're missing in
+ 
+
+ align:start position:0%
+think that what what we're missing in
+today's workforce is putting an emphasis
+
+ align:start position:0%
+today's workforce is putting an emphasis
+ 
+
+ align:start position:0%
+today's workforce is putting an emphasis
+on that in addition to all the great
+
+ align:start position:0%
+on that in addition to all the great
+ 
+
+ align:start position:0%
+on that in addition to all the great
+technologies that we can do and that's
+
+ align:start position:0%
+technologies that we can do and that's
+ 
+
+ align:start position:0%
+technologies that we can do and that's
+the thing that the women bring to the
+
+ align:start position:0%
+the thing that the women bring to the
+ 
+
+ align:start position:0%
+the thing that the women bring to the
+table and you know I'm super proud of
+
+ align:start position:0%
+table and you know I'm super proud of
+ 
+
+ align:start position:0%
+table and you know I'm super proud of
+our lack of attrition rate at six cents
+
+ align:start position:0%
+our lack of attrition rate at six cents
+ 
+
+ align:start position:0%
+our lack of attrition rate at six cents
+like we don't have people leave and it's
+
+ align:start position:0%
+like we don't have people leave and it's
+ 
+
+ align:start position:0%
+like we don't have people leave and it's
+because they feel supported supported
+
+ align:start position:0%
+because they feel supported supported
+ 
+
+ align:start position:0%
+because they feel supported supported
+and heard and they can also be creative
+
+ align:start position:0%
+and heard and they can also be creative
+ 
+
+ align:start position:0%
+and heard and they can also be creative
+and do amazing things in the work that
+
+ align:start position:0%
+and do amazing things in the work that
+ 
+
+ align:start position:0%
+and do amazing things in the work that
+we're providing but I think there's I
+
+ align:start position:0%
+we're providing but I think there's I
+ 
+
+ align:start position:0%
+we're providing but I think there's I
+mean I think we're all it's not
+
+ align:start position:0%
+mean I think we're all it's not
+ 
+
+ align:start position:0%
+mean I think we're all it's not
+intentional when men aren't supporting
+
+ align:start position:0%
+intentional when men aren't supporting
+ 
+
+ align:start position:0%
+intentional when men aren't supporting
+you know I was actually sitting on a
+
+ align:start position:0%
+you know I was actually sitting on a
+ 
+
+ align:start position:0%
+you know I was actually sitting on a
+plane the other day talking to a
+
+ align:start position:0%
+plane the other day talking to a
+ 
+
+ align:start position:0%
+plane the other day talking to a
+gentleman and he asked me what I did and
+
+ align:start position:0%
+gentleman and he asked me what I did and
+ 
+
+ align:start position:0%
+gentleman and he asked me what I did and
+I never come out and say I'm a CEO this
+
+ align:start position:0%
+I never come out and say I'm a CEO this
+ 
+
+ align:start position:0%
+I never come out and say I'm a CEO this
+company I say I work for a software
+
+ align:start position:0%
+company I say I work for a software
+ 
+
+ align:start position:0%
+company I say I work for a software
+company I started talking about the
+
+ align:start position:0%
+company I started talking about the
+ 
+
+ align:start position:0%
+company I started talking about the
+stuff that we're doing and then two
+
+ align:start position:0%
+stuff that we're doing and then two
+ 
+
+ align:start position:0%
+stuff that we're doing and then two
+hours into the Congress
+
+ align:start position:0%
+hours into the Congress
+ 
+
+ align:start position:0%
+hours into the Congress
+hey it's like what do you do there and
+
+ align:start position:0%
+hey it's like what do you do there and
+ 
+
+ align:start position:0%
+hey it's like what do you do there and
+he's like are you in marketing and it's
+
+ align:start position:0%
+he's like are you in marketing and it's
+ 
+
+ align:start position:0%
+he's like are you in marketing and it's
+like no I'm the CEO and he got up from
+
+ align:start position:0%
+like no I'm the CEO and he got up from
+ 
+
+ align:start position:0%
+like no I'm the CEO and he got up from
+his seat and he had this like visceral
+
+ align:start position:0%
+his seat and he had this like visceral
+ 
+
+ align:start position:0%
+his seat and he had this like visceral
+reaction like he and he didn't mean to
+
+ align:start position:0%
+reaction like he and he didn't mean to
+ 
+
+ align:start position:0%
+reaction like he and he didn't mean to
+him then he sat down he's like I'm so
+
+ align:start position:0%
+him then he sat down he's like I'm so
+ 
+
+ align:start position:0%
+him then he sat down he's like I'm so
+sorry I didn't mean to react like that
+
+ align:start position:0%
+sorry I didn't mean to react like that
+ 
+
+ align:start position:0%
+sorry I didn't mean to react like that
+and it didn't intend to wait you're
+
+ align:start position:0%
+and it didn't intend to wait you're
+ 
+
+ align:start position:0%
+and it didn't intend to wait you're
+missing it you know it was it was just a
+
+ align:start position:0%
+missing it you know it was it was just a
+ 
+
+ align:start position:0%
+missing it you know it was it was just a
+lack of filter which we all have
+
+ align:start position:0%
+lack of filter which we all have
+ 
+
+ align:start position:0%
+lack of filter which we all have
+sometimes you know when he was realizing
+
+ align:start position:0%
+sometimes you know when he was realizing
+ 
+
+ align:start position:0%
+sometimes you know when he was realizing
+who I was in the company and I wear
+
+ align:start position:0%
+who I was in the company and I wear
+ 
+
+ align:start position:0%
+who I was in the company and I wear
+braids and pigtails and I don't always
+
+ align:start position:0%
+braids and pigtails and I don't always
+ 
+
+ align:start position:0%
+braids and pigtails and I don't always
+you know dress the part of you know
+
+ align:start position:0%
+you know dress the part of you know
+ 
+
+ align:start position:0%
+you know dress the part of you know
+something else I always struggle with
+
+ align:start position:0%
+something else I always struggle with
+ 
+
+ align:start position:0%
+something else I always struggle with
+being my authentic women's self I want
+
+ align:start position:0%
+being my authentic women's self I want
+ 
+
+ align:start position:0%
+being my authentic women's self I want
+to maintain that while dominating in the
+
+ align:start position:0%
+to maintain that while dominating in the
+ 
+
+ align:start position:0%
+to maintain that while dominating in the
+mail world that I'm in so I think there
+
+ align:start position:0%
+mail world that I'm in so I think there
+ 
+
+ align:start position:0%
+mail world that I'm in so I think there
+are just there are levels of education
+
+ align:start position:0%
+are just there are levels of education
+ 
+
+ align:start position:0%
+are just there are levels of education
+that we can give others for taking
+
+ align:start position:0%
+that we can give others for taking
+ 
+
+ align:start position:0%
+that we can give others for taking
+income and social inequality between
+
+ align:start position:0%
+income and social inequality between
+ 
+
+ align:start position:0%
+income and social inequality between
+genders will not improve unless we
+
+ align:start position:0%
+genders will not improve unless we
+ 
+
+ align:start position:0%
+genders will not improve unless we
+choose to make fair decisions about who
+
+ align:start position:0%
+choose to make fair decisions about who
+ 
+
+ align:start position:0%
+choose to make fair decisions about who
+gets opportunities to create and run
+
+ align:start position:0%
+gets opportunities to create and run
+ 
+
+ align:start position:0%
+gets opportunities to create and run
+companies in the tech industry if we do
+
+ align:start position:0%
+companies in the tech industry if we do
+ 
+
+ align:start position:0%
+companies in the tech industry if we do
+not actively monitor our biases we will
+
+ align:start position:0%
+not actively monitor our biases we will
+ 
+
+ align:start position:0%
+not actively monitor our biases we will
+not be able to take advantage of this
+
+ align:start position:0%
+not be able to take advantage of this
+ 
+
+ align:start position:0%
+not be able to take advantage of this
+period of innovation and wealth creation
+
+ align:start position:0%
+period of innovation and wealth creation
+ 
+
+ align:start position:0%
+period of innovation and wealth creation
+towards a more equitable future there is
+
+ align:start position:0%
+towards a more equitable future there is
+ 
+
+ align:start position:0%
+towards a more equitable future there is
+also an opportunity gap among people for
+
+ align:start position:0%
+also an opportunity gap among people for
+ 
+
+ align:start position:0%
+also an opportunity gap among people for
+who gets to work within companies in the
+
+ align:start position:0%
+who gets to work within companies in the
+ 
+
+ align:start position:0%
+who gets to work within companies in the
+tech industry Layla Jenna founder and
+
+ align:start position:0%
+tech industry Layla Jenna founder and
+ 
+
+ align:start position:0%
+tech industry Layla Jenna founder and
+CEO of summer group an organization that
+
+ align:start position:0%
+CEO of summer group an organization that
+ 
+
+ align:start position:0%
+CEO of summer group an organization that
+lift people out of poverty by enabling
+
+ align:start position:0%
+lift people out of poverty by enabling
+ 
+
+ align:start position:0%
+lift people out of poverty by enabling
+them to do work in the digital economy
+
+ align:start position:0%
+them to do work in the digital economy
+ 
+
+ align:start position:0%
+them to do work in the digital economy
+discusses this opportunity gap and how
+
+ align:start position:0%
+discusses this opportunity gap and how
+ 
+
+ align:start position:0%
+discusses this opportunity gap and how
+we can mitigate it now interestingly
+
+ align:start position:0%
+we can mitigate it now interestingly
+ 
+
+ align:start position:0%
+we can mitigate it now interestingly
+traditionally in the informal sector if
+
+ align:start position:0%
+traditionally in the informal sector if
+ 
+
+ align:start position:0%
+traditionally in the informal sector if
+you're doing say construction work and
+
+ align:start position:0%
+you're doing say construction work and
+ 
+
+ align:start position:0%
+you're doing say construction work and
+you go and you find your job by standing
+
+ align:start position:0%
+you go and you find your job by standing
+ 
+
+ align:start position:0%
+you go and you find your job by standing
+on the side of the road and waiting for
+
+ align:start position:0%
+on the side of the road and waiting for
+ 
+
+ align:start position:0%
+on the side of the road and waiting for
+someone to hire you as a labor
+
+ align:start position:0%
+someone to hire you as a labor
+ 
+
+ align:start position:0%
+someone to hire you as a labor
+contractor there is no such thing as
+
+ align:start position:0%
+contractor there is no such thing as
+ 
+
+ align:start position:0%
+contractor there is no such thing as
+getting rewarded for good work you might
+
+ align:start position:0%
+getting rewarded for good work you might
+ 
+
+ align:start position:0%
+getting rewarded for good work you might
+put in a wonderful 10-hour shift but you
+
+ align:start position:0%
+put in a wonderful 10-hour shift but you
+ 
+
+ align:start position:0%
+put in a wonderful 10-hour shift but you
+will get no five-star rating on a
+
+ align:start position:0%
+will get no five-star rating on a
+ 
+
+ align:start position:0%
+will get no five-star rating on a
+website you go back to zero the next day
+
+ align:start position:0%
+website you go back to zero the next day
+ 
+
+ align:start position:0%
+website you go back to zero the next day
+standing on the side of the road waiting
+
+ align:start position:0%
+standing on the side of the road waiting
+ 
+
+ align:start position:0%
+standing on the side of the road waiting
+for your next job so I think that that
+
+ align:start position:0%
+for your next job so I think that that
+ 
+
+ align:start position:0%
+for your next job so I think that that
+technology actually brings a lot more
+
+ align:start position:0%
+technology actually brings a lot more
+ 
+
+ align:start position:0%
+technology actually brings a lot more
+transparency in areas like wages and
+
+ align:start position:0%
+transparency in areas like wages and
+ 
+
+ align:start position:0%
+transparency in areas like wages and
+reviews and feedback that are very good
+
+ align:start position:0%
+reviews and feedback that are very good
+ 
+
+ align:start position:0%
+reviews and feedback that are very good
+for low-income workers and I'll say one
+
+ align:start position:0%
+for low-income workers and I'll say one
+ 
+
+ align:start position:0%
+for low-income workers and I'll say one
+last thing on this which is that Dave
+
+ align:start position:0%
+last thing on this which is that Dave
+ 
+
+ align:start position:0%
+last thing on this which is that Dave
+and I were talking about this just
+
+ align:start position:0%
+and I were talking about this just
+ 
+
+ align:start position:0%
+and I were talking about this just
+before the panel we so often assume that
+
+ align:start position:0%
+before the panel we so often assume that
+ 
+
+ align:start position:0%
+before the panel we so often assume that
+technology has some kind of morality
+
+ align:start position:0%
+technology has some kind of morality
+ 
+
+ align:start position:0%
+technology has some kind of morality
+built into it right technology in fact
+
+ align:start position:0%
+built into it right technology in fact
+ 
+
+ align:start position:0%
+built into it right technology in fact
+is agnostic it's as agnostic as roads
+
+ align:start position:0%
+is agnostic it's as agnostic as roads
+ 
+
+ align:start position:0%
+is agnostic it's as agnostic as roads
+waterways it's all about what we do with
+
+ align:start position:0%
+waterways it's all about what we do with
+ 
+
+ align:start position:0%
+waterways it's all about what we do with
+technology we can choose to inject
+
+ align:start position:0%
+technology we can choose to inject
+ 
+
+ align:start position:0%
+technology we can choose to inject
+morality into the technology we build we
+
+ align:start position:0%
+morality into the technology we build we
+ 
+
+ align:start position:0%
+morality into the technology we build we
+can choose to build systems that
+
+ align:start position:0%
+can choose to build systems that
+ 
+
+ align:start position:0%
+can choose to build systems that
+enfranchise the poor or we can choose
+
+ align:start position:0%
+enfranchise the poor or we can choose
+ 
+
+ align:start position:0%
+enfranchise the poor or we can choose
+not to but we're not victims of
+
+ align:start position:0%
+not to but we're not victims of
+ 
+
+ align:start position:0%
+not to but we're not victims of
+technological progress it's not
+
+ align:start position:0%
+technological progress it's not
+ 
+
+ align:start position:0%
+technological progress it's not
+happening you know in a way that we
+
+ align:start position:0%
+happening you know in a way that we
+ 
+
+ align:start position:0%
+happening you know in a way that we
+can't control at least until the
+
+ align:start position:0%
+can't control at least until the
+ 
+
+ align:start position:0%
+can't control at least until the
+singularity happens at which point all
+
+ align:start position:0%
+singularity happens at which point all
+ 
+
+ align:start position:0%
+singularity happens at which point all
+bets are off the first is job training
+
+ align:start position:0%
+bets are off the first is job training
+ 
+
+ align:start position:0%
+bets are off the first is job training
+needs to completely change in the US
+
+ align:start position:0%
+needs to completely change in the US
+ 
+
+ align:start position:0%
+needs to completely change in the US
+which is the best example I know it's
+
+ align:start position:0%
+which is the best example I know it's
+ 
+
+ align:start position:0%
+which is the best example I know it's
+abysmal we are still training people for
+
+ align:start position:0%
+abysmal we are still training people for
+ 
+
+ align:start position:0%
+abysmal we are still training people for
+jobs that are disappearing at an
+
+ align:start position:0%
+jobs that are disappearing at an
+ 
+
+ align:start position:0%
+jobs that are disappearing at an
+alarming rate we are not training them
+
+ align:start position:0%
+alarming rate we are not training them
+ 
+
+ align:start position:0%
+alarming rate we are not training them
+in how to be entrepreneurial and
+
+ align:start position:0%
+in how to be entrepreneurial and
+ 
+
+ align:start position:0%
+in how to be entrepreneurial and
+marketing themselves the skill that you
+
+ align:start position:0%
+marketing themselves the skill that you
+ 
+
+ align:start position:0%
+marketing themselves the skill that you
+need for 21st century jobs is marketing
+
+ align:start position:0%
+need for 21st century jobs is marketing
+ 
+
+ align:start position:0%
+need for 21st century jobs is marketing
+yourself if Kim Kardashian can teach us
+
+ align:start position:0%
+yourself if Kim Kardashian can teach us
+ 
+
+ align:start position:0%
+yourself if Kim Kardashian can teach us
+anything it's probably only that but
+
+ align:start position:0%
+anything it's probably only that but
+ 
+
+ align:start position:0%
+anything it's probably only that but
+interestingly you know we're see all of
+
+ align:start position:0%
+interestingly you know we're see all of
+ 
+
+ align:start position:0%
+interestingly you know we're see all of
+these new platforms require you to be
+
+ align:start position:0%
+these new platforms require you to be
+ 
+
+ align:start position:0%
+these new platforms require you to be
+able to set up a profile to choose the
+
+ align:start position:0%
+able to set up a profile to choose the
+ 
+
+ align:start position:0%
+able to set up a profile to choose the
+right kind of a photograph that will
+
+ align:start position:0%
+right kind of a photograph that will
+ 
+
+ align:start position:0%
+right kind of a photograph that will
+attract customers to send a follow up
+
+ align:start position:0%
+attract customers to send a follow up
+ 
+
+ align:start position:0%
+attract customers to send a follow up
+email to have customer service skills
+
+ align:start position:0%
+email to have customer service skills
+ 
+
+ align:start position:0%
+email to have customer service skills
+and you're absolutely right that many
+
+ align:start position:0%
+and you're absolutely right that many
+ 
+
+ align:start position:0%
+and you're absolutely right that many
+low income people and just to give you
+
+ align:start position:0%
+low income people and just to give you
+ 
+
+ align:start position:0%
+low income people and just to give you
+an idea of how profound this is in the
+
+ align:start position:0%
+an idea of how profound this is in the
+ 
+
+ align:start position:0%
+an idea of how profound this is in the
+u.s. we have one of our centers which is
+
+ align:start position:0%
+u.s. we have one of our centers which is
+ 
+
+ align:start position:0%
+u.s. we have one of our centers which is
+less than a mile from the facebook
+
+ align:start position:0%
+less than a mile from the facebook
+ 
+
+ align:start position:0%
+less than a mile from the facebook
+headquarters in Silicon Valley in East
+
+ align:start position:0%
+headquarters in Silicon Valley in East
+ 
+
+ align:start position:0%
+headquarters in Silicon Valley in East
+Palo Alto which is a very poor community
+
+ align:start position:0%
+Palo Alto which is a very poor community
+ 
+
+ align:start position:0%
+Palo Alto which is a very poor community
+and fully twenty five percent of our
+
+ align:start position:0%
+and fully twenty five percent of our
+ 
+
+ align:start position:0%
+and fully twenty five percent of our
+incoming class for one of our trainings
+
+ align:start position:0%
+incoming class for one of our trainings
+ 
+
+ align:start position:0%
+incoming class for one of our trainings
+last year had people who had zero
+
+ align:start position:0%
+last year had people who had zero
+ 
+
+ align:start position:0%
+last year had people who had zero
+internet access at home and no
+
+ align:start position:0%
+internet access at home and no
+ 
+
+ align:start position:0%
+internet access at home and no
+smartphone a mile from the Facebook
+
+ align:start position:0%
+smartphone a mile from the Facebook
+ 
+
+ align:start position:0%
+smartphone a mile from the Facebook
+campus so we can talk all we want about
+
+ align:start position:0%
+campus so we can talk all we want about
+ 
+
+ align:start position:0%
+campus so we can talk all we want about
+how technology is going to make
+
+ align:start position:0%
+how technology is going to make
+ 
+
+ align:start position:0%
+how technology is going to make
+everyone's lives better but the reality
+
+ align:start position:0%
+everyone's lives better but the reality
+ 
+
+ align:start position:0%
+everyone's lives better but the reality
+is that many people are disconnected and
+
+ align:start position:0%
+is that many people are disconnected and
+ 
+
+ align:start position:0%
+is that many people are disconnected and
+if you didn't grow up having the
+
+ align:start position:0%
+if you didn't grow up having the
+ 
+
+ align:start position:0%
+if you didn't grow up having the
+internet at home how can you possibly
+
+ align:start position:0%
+internet at home how can you possibly
+ 
+
+ align:start position:0%
+internet at home how can you possibly
+understand how to market yourself you're
+
+ align:start position:0%
+understand how to market yourself you're
+ 
+
+ align:start position:0%
+understand how to market yourself you're
+it's not easy to be an autodidact and to
+
+ align:start position:0%
+it's not easy to be an autodidact and to
+ 
+
+ align:start position:0%
+it's not easy to be an autodidact and to
+learn how to teach yourself yourself
+
+ align:start position:0%
+learn how to teach yourself yourself
+ 
+
+ align:start position:0%
+learn how to teach yourself yourself
+things on YouTube if you didn't grow up
+
+ align:start position:0%
+things on YouTube if you didn't grow up
+ 
+
+ align:start position:0%
+things on YouTube if you didn't grow up
+with the internet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+advancements in technology taking place
+
+ align:start position:0%
+advancements in technology taking place
+ 
+
+ align:start position:0%
+advancements in technology taking place
+right now are incredibly exciting and we
+
+ align:start position:0%
+right now are incredibly exciting and we
+ 
+
+ align:start position:0%
+right now are incredibly exciting and we
+all stand to gain from the most
+
+ align:start position:0%
+all stand to gain from the most
+ 
+
+ align:start position:0%
+all stand to gain from the most
+consumers however as with other periods
+
+ align:start position:0%
+consumers however as with other periods
+ 
+
+ align:start position:0%
+consumers however as with other periods
+of societal change we citizens and the
+
+ align:start position:0%
+of societal change we citizens and the
+ 
+
+ align:start position:0%
+of societal change we citizens and the
+government have to ensure that the
+
+ align:start position:0%
+government have to ensure that the
+ 
+
+ align:start position:0%
+government have to ensure that the
+opportunities to launch run and work in
+
+ align:start position:0%
+opportunities to launch run and work in
+ 
+
+ align:start position:0%
+opportunities to launch run and work in
+these new enterprises is made available
+
+ align:start position:0%
+these new enterprises is made available
+ 
+
+ align:start position:0%
+these new enterprises is made available
+to all members of society
\ No newline at end of file
diff --git a/UswuSLKQVK4.txt b/UswuSLKQVK4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..372c594172ff8d2b8836932ede3629492c862ea5
--- /dev/null
+++ b/UswuSLKQVK4.txt
@@ -0,0 +1,715 @@
+align:start position:0%
+ 
+I'm having our students be prepared to
+
+ align:start position:0%
+I'm having our students be prepared to
+ 
+
+ align:start position:0%
+I'm having our students be prepared to
+face fail it's really important because
+
+ align:start position:0%
+face fail it's really important because
+ 
+
+ align:start position:0%
+face fail it's really important because
+I think it's essential to the design
+
+ align:start position:0%
+I think it's essential to the design
+ 
+
+ align:start position:0%
+I think it's essential to the design
+process and I uh we have uh Professor
+
+ align:start position:0%
+process and I uh we have uh Professor
+ 
+
+ align:start position:0%
+process and I uh we have uh Professor
+Rob Miller came in to do a lecture on
+
+ align:start position:0%
+Rob Miller came in to do a lecture on
+ 
+
+ align:start position:0%
+Rob Miller came in to do a lecture on
+user Center design very early on in the
+
+ align:start position:0%
+user Center design very early on in the
+ 
+
+ align:start position:0%
+user Center design very early on in the
+semester where we basically present to
+
+ align:start position:0%
+semester where we basically present to
+ 
+
+ align:start position:0%
+semester where we basically present to
+them this design model of of you know
+
+ align:start position:0%
+them this design model of of you know
+ 
+
+ align:start position:0%
+them this design model of of you know
+where you do iterative design which
+
+ align:start position:0%
+where you do iterative design which
+ 
+
+ align:start position:0%
+where you do iterative design which
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+you quickly come up with a prototype you
+
+ align:start position:0%
+you quickly come up with a prototype you
+ 
+
+ align:start position:0%
+you quickly come up with a prototype you
+fail as fast as possible you figure out
+
+ align:start position:0%
+fail as fast as possible you figure out
+ 
+
+ align:start position:0%
+fail as fast as possible you figure out
+where everything's going wrong and then
+
+ align:start position:0%
+where everything's going wrong and then
+ 
+
+ align:start position:0%
+where everything's going wrong and then
+you make a second prototype you know and
+
+ align:start position:0%
+you make a second prototype you know and
+ 
+
+ align:start position:0%
+you make a second prototype you know and
+you keep going round and round and round
+
+ align:start position:0%
+you keep going round and round and round
+ 
+
+ align:start position:0%
+you keep going round and round and round
+this circle until you reach that perfect
+
+ align:start position:0%
+this circle until you reach that perfect
+ 
+
+ align:start position:0%
+this circle until you reach that perfect
+Prototype at the end of the day um and
+
+ align:start position:0%
+Prototype at the end of the day um and
+ 
+
+ align:start position:0%
+Prototype at the end of the day um and
+so I think they knew from the start that
+
+ align:start position:0%
+so I think they knew from the start that
+ 
+
+ align:start position:0%
+so I think they knew from the start that
+they were going to have to just keep
+
+ align:start position:0%
+they were going to have to just keep
+ 
+
+ align:start position:0%
+they were going to have to just keep
+making things and seeing how they were
+
+ align:start position:0%
+making things and seeing how they were
+ 
+
+ align:start position:0%
+making things and seeing how they were
+going to go wrong um and so yeah failure
+
+ align:start position:0%
+going to go wrong um and so yeah failure
+ 
+
+ align:start position:0%
+going to go wrong um and so yeah failure
+became very entrench as part of the
+
+ align:start position:0%
+became very entrench as part of the
+ 
+
+ align:start position:0%
+became very entrench as part of the
+design process in fact we told them
+
+ align:start position:0%
+design process in fact we told them
+ 
+
+ align:start position:0%
+design process in fact we told them
+right from the start we expect you to
+
+ align:start position:0%
+right from the start we expect you to
+ 
+
+ align:start position:0%
+right from the start we expect you to
+have three prototypes at least by the
+
+ align:start position:0%
+have three prototypes at least by the
+ 
+
+ align:start position:0%
+have three prototypes at least by the
+end of the semester and these are when
+
+ align:start position:0%
+end of the semester and these are when
+ 
+
+ align:start position:0%
+end of the semester and these are when
+your prototypes should be ready by and
+
+ align:start position:0%
+your prototypes should be ready by and
+ 
+
+ align:start position:0%
+your prototypes should be ready by and
+these are the weeks where you will get
+
+ align:start position:0%
+these are the weeks where you will get
+ 
+
+ align:start position:0%
+these are the weeks where you will get
+to test them and every week they had to
+
+ align:start position:0%
+to test them and every week they had to
+ 
+
+ align:start position:0%
+to test them and every week they had to
+come back and tell the mentors where
+
+ align:start position:0%
+come back and tell the mentors where
+ 
+
+ align:start position:0%
+come back and tell the mentors where
+things went well and where things didn't
+
+ align:start position:0%
+things went well and where things didn't
+ 
+
+ align:start position:0%
+things went well and where things didn't
+go well according to some uh set of
+
+ align:start position:0%
+go well according to some uh set of
+ 
+
+ align:start position:0%
+go well according to some uh set of
+success
+
+ align:start position:0%
+success
+ 
+
+ align:start position:0%
+success
+metrics yeah I think the design review
+
+ align:start position:0%
+metrics yeah I think the design review
+ 
+
+ align:start position:0%
+metrics yeah I think the design review
+these midterm panels were really just
+
+ align:start position:0%
+these midterm panels were really just
+ 
+
+ align:start position:0%
+these midterm panels were really just
+that to try to get feedback on the
+
+ align:start position:0%
+that to try to get feedback on the
+ 
+
+ align:start position:0%
+that to try to get feedback on the
+design or really explain the progress
+
+ align:start position:0%
+design or really explain the progress
+ 
+
+ align:start position:0%
+design or really explain the progress
+that they had made
+
+ align:start position:0%
+that they had made
+ 
+
+ align:start position:0%
+that they had made
+uh so far and so I think that that was a
+
+ align:start position:0%
+uh so far and so I think that that was a
+ 
+
+ align:start position:0%
+uh so far and so I think that that was a
+big reason why we did that I think
+
+ align:start position:0%
+big reason why we did that I think
+ 
+
+ align:start position:0%
+big reason why we did that I think
+having mentors this year was helpful on
+
+ align:start position:0%
+having mentors this year was helpful on
+ 
+
+ align:start position:0%
+having mentors this year was helpful on
+this front as well the mentors were
+
+ align:start position:0%
+this front as well the mentors were
+ 
+
+ align:start position:0%
+this front as well the mentors were
+pretty in touch with how teams were
+
+ align:start position:0%
+pretty in touch with how teams were
+ 
+
+ align:start position:0%
+pretty in touch with how teams were
+progressing we had uh each team fill out
+
+ align:start position:0%
+progressing we had uh each team fill out
+ 
+
+ align:start position:0%
+progressing we had uh each team fill out
+this little form um every week
+
+ align:start position:0%
+this little form um every week
+ 
+
+ align:start position:0%
+this little form um every week
+explaining what was going well and what
+
+ align:start position:0%
+explaining what was going well and what
+ 
+
+ align:start position:0%
+explaining what was going well and what
+they needed help with so I think a big
+
+ align:start position:0%
+they needed help with so I think a big
+ 
+
+ align:start position:0%
+they needed help with so I think a big
+part of it was kind of creating the
+
+ align:start position:0%
+part of it was kind of creating the
+ 
+
+ align:start position:0%
+part of it was kind of creating the
+culture that it doesn't have to go
+
+ align:start position:0%
+culture that it doesn't have to go
+ 
+
+ align:start position:0%
+culture that it doesn't have to go
+perfectly well every week there can be
+
+ align:start position:0%
+perfectly well every week there can be
+ 
+
+ align:start position:0%
+perfectly well every week there can be
+setbacks there can be different
+
+ align:start position:0%
+setbacks there can be different
+ 
+
+ align:start position:0%
+setbacks there can be different
+challenges or obstacles to over come but
+
+ align:start position:0%
+challenges or obstacles to over come but
+ 
+
+ align:start position:0%
+challenges or obstacles to over come but
+we're here to uh you know work through
+
+ align:start position:0%
+we're here to uh you know work through
+ 
+
+ align:start position:0%
+we're here to uh you know work through
+them and figure out how to deal with
+
+ align:start position:0%
+them and figure out how to deal with
+ 
+
+ align:start position:0%
+them and figure out how to deal with
+this uh situation or brainstorm some
+
+ align:start position:0%
+this uh situation or brainstorm some
+ 
+
+ align:start position:0%
+this uh situation or brainstorm some
+ideas one of the other things that we
+
+ align:start position:0%
+ideas one of the other things that we
+ 
+
+ align:start position:0%
+ideas one of the other things that we
+tried this year was to have these
+
+ align:start position:0%
+tried this year was to have these
+ 
+
+ align:start position:0%
+tried this year was to have these
+lightning updates at the end of every uh
+
+ align:start position:0%
+lightning updates at the end of every uh
+ 
+
+ align:start position:0%
+lightning updates at the end of every uh
+week's uh lab just to keep uh uh just to
+
+ align:start position:0%
+week's uh lab just to keep uh uh just to
+ 
+
+ align:start position:0%
+week's uh lab just to keep uh uh just to
+inform the rest of the class where
+
+ align:start position:0%
+inform the rest of the class where
+ 
+
+ align:start position:0%
+inform the rest of the class where
+you're at and what you were trying um uh
+
+ align:start position:0%
+you're at and what you were trying um uh
+ 
+
+ align:start position:0%
+you're at and what you were trying um uh
+what progress you were making I think
+
+ align:start position:0%
+what progress you were making I think
+ 
+
+ align:start position:0%
+what progress you were making I think
+this maybe set up a little bit of sort
+
+ align:start position:0%
+this maybe set up a little bit of sort
+ 
+
+ align:start position:0%
+this maybe set up a little bit of sort
+of friendly competition to kind of see
+
+ align:start position:0%
+of friendly competition to kind of see
+ 
+
+ align:start position:0%
+of friendly competition to kind of see
+where other projects are at but it also
+
+ align:start position:0%
+where other projects are at but it also
+ 
+
+ align:start position:0%
+where other projects are at but it also
+I think uh helped maybe the class feel
+
+ align:start position:0%
+I think uh helped maybe the class feel
+ 
+
+ align:start position:0%
+I think uh helped maybe the class feel
+like um We're All in This Together I
+
+ align:start position:0%
+like um We're All in This Together I
+ 
+
+ align:start position:0%
+like um We're All in This Together I
+suppose it's not always going to be easy
+
+ align:start position:0%
+suppose it's not always going to be easy
+ 
+
+ align:start position:0%
+suppose it's not always going to be easy
+maybe there's Logistics challenges maybe
+
+ align:start position:0%
+maybe there's Logistics challenges maybe
+ 
+
+ align:start position:0%
+maybe there's Logistics challenges maybe
+there's design challenges maybe there's
+
+ align:start position:0%
+there's design challenges maybe there's
+ 
+
+ align:start position:0%
+there's design challenges maybe there's
+um other sorts of things so I think um
+
+ align:start position:0%
+um other sorts of things so I think um
+ 
+
+ align:start position:0%
+um other sorts of things so I think um
+students were pretty open to sharing
+
+ align:start position:0%
+students were pretty open to sharing
+ 
+
+ align:start position:0%
+students were pretty open to sharing
+honestly what their progress was and
+
+ align:start position:0%
+honestly what their progress was and
+ 
+
+ align:start position:0%
+honestly what their progress was and
+what they were what they were doing at
+
+ align:start position:0%
+what they were what they were doing at
+ 
+
+ align:start position:0%
+what they were what they were doing at
+least that's what we we tried to do we
+
+ align:start position:0%
+least that's what we we tried to do we
+ 
+
+ align:start position:0%
+least that's what we we tried to do we
+hope so we did get feedback from
+
+ align:start position:0%
+hope so we did get feedback from
+ 
+
+ align:start position:0%
+hope so we did get feedback from
+students though that the lightning
+
+ align:start position:0%
+students though that the lightning
+ 
+
+ align:start position:0%
+students though that the lightning
+updates might have been too regular and
+
+ align:start position:0%
+updates might have been too regular and
+ 
+
+ align:start position:0%
+updates might have been too regular and
+they did say that it would have been
+
+ align:start position:0%
+they did say that it would have been
+ 
+
+ align:start position:0%
+they did say that it would have been
+nice to have it once every two weeks
+
+ align:start position:0%
+nice to have it once every two weeks
+ 
+
+ align:start position:0%
+nice to have it once every two weeks
+instead of every week um and that that
+
+ align:start position:0%
+instead of every week um and that that
+ 
+
+ align:start position:0%
+instead of every week um and that that
+would just give them more time to work
+
+ align:start position:0%
+would just give them more time to work
+ 
+
+ align:start position:0%
+would just give them more time to work
+together as a team and we realized too
+
+ align:start position:0%
+together as a team and we realized too
+ 
+
+ align:start position:0%
+together as a team and we realized too
+that for our students being able to do
+
+ align:start position:0%
+that for our students being able to do
+ 
+
+ align:start position:0%
+that for our students being able to do
+group work outside of class is actually
+
+ align:start position:0%
+group work outside of class is actually
+ 
+
+ align:start position:0%
+group work outside of class is actually
+difficult because they all have such
+
+ align:start position:0%
+difficult because they all have such
+ 
+
+ align:start position:0%
+difficult because they all have such
+busy schedules so anytime they had like
+
+ align:start position:0%
+busy schedules so anytime they had like
+ 
+
+ align:start position:0%
+busy schedules so anytime they had like
+structure time within a class to just do
+
+ align:start position:0%
+structure time within a class to just do
+ 
+
+ align:start position:0%
+structure time within a class to just do
+group work together that was really
+
+ align:start position:0%
+group work together that was really
+ 
+
+ align:start position:0%
+group work together that was really
+valuable for them
\ No newline at end of file
diff --git a/Uux0VkKaoxY.txt b/Uux0VkKaoxY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c8523c28ea31878e8573bce3957792b317ce704
--- /dev/null
+++ b/Uux0VkKaoxY.txt
@@ -0,0 +1,987 @@
+align:start position:0%
+ 
+so that's part of the story let's try to
+
+ align:start position:0%
+so that's part of the story let's try to
+ 
+
+ align:start position:0%
+so that's part of the story let's try to
+understand it a little better still so
+
+ align:start position:0%
+understand it a little better still so
+ 
+
+ align:start position:0%
+understand it a little better still so
+what does the state look like well the
+
+ align:start position:0%
+what does the state look like well the
+ 
+
+ align:start position:0%
+what does the state look like well the
+state looks like e to the ikx x times a
+
+ align:start position:0%
+state looks like e to the ikx x times a
+ 
+
+ align:start position:0%
+state looks like e to the ikx x times a
+state of the oscillator and Y okay so
+
+ align:start position:0%
+state of the oscillator and Y okay so
+ 
+
+ align:start position:0%
+state of the oscillator and Y okay so
+what what is happening here we could we
+
+ align:start position:0%
+what what is happening here we could we
+ 
+
+ align:start position:0%
+what what is happening here we could we
+solve this problem using a different
+
+ align:start position:0%
+solve this problem using a different
+ 
+
+ align:start position:0%
+solve this problem using a different
+gauge and you will you will solve it at
+
+ align:start position:0%
+gauge and you will you will solve it at
+ 
+
+ align:start position:0%
+gauge and you will you will solve it at
+least once or twice again this problem
+
+ align:start position:0%
+least once or twice again this problem
+ 
+
+ align:start position:0%
+least once or twice again this problem
+using a different gauge and the
+
+ align:start position:0%
+using a different gauge and the
+ 
+
+ align:start position:0%
+using a different gauge and the
+solutions are going to be looking a
+
+ align:start position:0%
+solutions are going to be looking a
+ 
+
+ align:start position:0%
+solutions are going to be looking a
+little different but of course you're
+
+ align:start position:0%
+little different but of course you're
+ 
+
+ align:start position:0%
+little different but of course you're
+going to find the same Landau levels and
+
+ align:start position:0%
+going to find the same Landau levels and
+ 
+
+ align:start position:0%
+going to find the same Landau levels and
+the same infinite degeneracy the wave
+
+ align:start position:0%
+the same infinite degeneracy the wave
+ 
+
+ align:start position:0%
+the same infinite degeneracy the wave
+functions will look sometimes a little
+
+ align:start position:0%
+functions will look sometimes a little
+ 
+
+ align:start position:0%
+functions will look sometimes a little
+more intuitive so in this case of one
+
+ align:start position:0%
+more intuitive so in this case of one
+ 
+
+ align:start position:0%
+more intuitive so in this case of one
+calculation that is interesting to try
+
+ align:start position:0%
+calculation that is interesting to try
+ 
+
+ align:start position:0%
+calculation that is interesting to try
+to understand the physics of this
+
+ align:start position:0%
+to understand the physics of this
+ 
+
+ align:start position:0%
+to understand the physics of this
+degeneracy is to work roughly a little
+
+ align:start position:0%
+degeneracy is to work roughly a little
+ 
+
+ align:start position:0%
+degeneracy is to work roughly a little
+heuristic aliy on a finite size sample
+
+ align:start position:0%
+heuristic aliy on a finite size sample
+ 
+
+ align:start position:0%
+heuristic aliy on a finite size sample
+you imagine a material but it's now
+
+ align:start position:0%
+you imagine a material but it's now
+ 
+
+ align:start position:0%
+you imagine a material but it's now
+finite size so let me remark to you what
+
+ align:start position:0%
+finite size so let me remark to you what
+ 
+
+ align:start position:0%
+finite size so let me remark to you what
+are the degrees of freedom you have here
+
+ align:start position:0%
+are the degrees of freedom you have here
+ 
+
+ align:start position:0%
+are the degrees of freedom you have here
+suppose you solve the Schrodinger
+
+ align:start position:0%
+suppose you solve the Schrodinger
+ 
+
+ align:start position:0%
+suppose you solve the Schrodinger
+equation in a different gauge a
+
+ align:start position:0%
+equation in a different gauge a
+ 
+
+ align:start position:0%
+equation in a different gauge a
+symmetric gauge in which there is an A Y
+
+ align:start position:0%
+symmetric gauge in which there is an A Y
+ 
+
+ align:start position:0%
+symmetric gauge in which there is an A Y
+and an ax solutions then are going to
+
+ align:start position:0%
+and an ax solutions then are going to
+ 
+
+ align:start position:0%
+and an ax solutions then are going to
+look a little more like circular orbits
+
+ align:start position:0%
+look a little more like circular orbits
+ 
+
+ align:start position:0%
+look a little more like circular orbits
+there's a little more mathematics
+
+ align:start position:0%
+there's a little more mathematics
+ 
+
+ align:start position:0%
+there's a little more mathematics
+involved in solving it but they're going
+
+ align:start position:0%
+involved in solving it but they're going
+ 
+
+ align:start position:0%
+involved in solving it but they're going
+to look a little nicer but how are they
+
+ align:start position:0%
+to look a little nicer but how are they
+ 
+
+ align:start position:0%
+to look a little nicer but how are they
+related to this ones well anyone with a
+
+ align:start position:0%
+related to this ones well anyone with a
+ 
+
+ align:start position:0%
+related to this ones well anyone with a
+circular orbit must be related to these
+
+ align:start position:0%
+circular orbit must be related to these
+ 
+
+ align:start position:0%
+circular orbit must be related to these
+solutions by first forming a
+
+ align:start position:0%
+solutions by first forming a
+ 
+
+ align:start position:0%
+solutions by first forming a
+superposition of those solutions maybe
+
+ align:start position:0%
+superposition of those solutions maybe
+ 
+
+ align:start position:0%
+superposition of those solutions maybe
+localizing it or doing something and
+
+ align:start position:0%
+localizing it or doing something and
+ 
+
+ align:start position:0%
+localizing it or doing something and
+then doing engage transformation so in
+
+ align:start position:0%
+then doing engage transformation so in
+ 
+
+ align:start position:0%
+then doing engage transformation so in
+order to compare your solution
+
+ align:start position:0%
+order to compare your solution
+ 
+
+ align:start position:0%
+order to compare your solution
+in different gauges you have to take
+
+ align:start position:0%
+in different gauges you have to take
+ 
+
+ align:start position:0%
+in different gauges you have to take
+into account you have an infant in
+
+ align:start position:0%
+into account you have an infant in
+ 
+
+ align:start position:0%
+into account you have an infant in
+degeneracy and you have gauge
+
+ align:start position:0%
+degeneracy and you have gauge
+ 
+
+ align:start position:0%
+degeneracy and you have gauge
+transformation so to see what state here
+
+ align:start position:0%
+transformation so to see what state here
+ 
+
+ align:start position:0%
+transformation so to see what state here
+corresponds to a particular state here
+
+ align:start position:0%
+corresponds to a particular state here
+ 
+
+ align:start position:0%
+corresponds to a particular state here
+it may be the gauge transformation of a
+
+ align:start position:0%
+it may be the gauge transformation of a
+ 
+
+ align:start position:0%
+it may be the gauge transformation of a
+particular superposition in this side so
+
+ align:start position:0%
+particular superposition in this side so
+ 
+
+ align:start position:0%
+particular superposition in this side so
+it's in general not all that easy to do
+
+ align:start position:0%
+it's in general not all that easy to do
+ 
+
+ align:start position:0%
+it's in general not all that easy to do
+okay so let's take of count state in a
+
+ align:start position:0%
+okay so let's take of count state in a
+ 
+
+ align:start position:0%
+okay so let's take of count state in a
+finite sample sum so same picture but
+
+ align:start position:0%
+finite sample sum so same picture but
+ 
+
+ align:start position:0%
+finite sample sum so same picture but
+now the material is here and we'll put
+
+ align:start position:0%
+now the material is here and we'll put
+ 
+
+ align:start position:0%
+now the material is here and we'll put
+LX and ly here so finite size in a legs
+
+ align:start position:0%
+LX and ly here so finite size in a legs
+ 
+
+ align:start position:0%
+LX and ly here so finite size in a legs
+finite size in ly so given our intuition
+
+ align:start position:0%
+finite size in ly so given our intuition
+ 
+
+ align:start position:0%
+finite size in ly so given our intuition
+with quantization this suggests that we
+
+ align:start position:0%
+with quantization this suggests that we
+ 
+
+ align:start position:0%
+with quantization this suggests that we
+impose periodic boundary conditions in X
+
+ align:start position:0%
+impose periodic boundary conditions in X
+ 
+
+ align:start position:0%
+impose periodic boundary conditions in X
+and try to quantize the KX here in
+
+ align:start position:0%
+and try to quantize the KX here in
+ 
+
+ align:start position:0%
+and try to quantize the KX here in
+general if you're imposing thinking of
+
+ align:start position:0%
+general if you're imposing thinking of
+ 
+
+ align:start position:0%
+general if you're imposing thinking of
+very large boxes which is the case here
+
+ align:start position:0%
+very large boxes which is the case here
+ 
+
+ align:start position:0%
+very large boxes which is the case here
+it doesn't matter much whether you
+
+ align:start position:0%
+it doesn't matter much whether you
+ 
+
+ align:start position:0%
+it doesn't matter much whether you
+impose periodic or vanishing boundary
+
+ align:start position:0%
+impose periodic or vanishing boundary
+ 
+
+ align:start position:0%
+impose periodic or vanishing boundary
+conditions or anything essentially at
+
+ align:start position:0%
+conditions or anything essentially at
+ 
+
+ align:start position:0%
+conditions or anything essentially at
+large number of states it makes no
+
+ align:start position:0%
+large number of states it makes no
+ 
+
+ align:start position:0%
+large number of states it makes no
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+so we quantize in X so we want e to the
+
+ align:start position:0%
+so we quantize in X so we want e to the
+ 
+
+ align:start position:0%
+so we quantize in X so we want e to the
+I I KX times X to be periodic under X
+
+ align:start position:0%
+I I KX times X to be periodic under X
+ 
+
+ align:start position:0%
+I I KX times X to be periodic under X
+goes to X plus LX
+
+ align:start position:0%
+goes to X plus LX
+ 
+
+ align:start position:0%
+goes to X plus LX
+I'm almost done with Sun so KX LX
+
+ align:start position:0%
+I'm almost done with Sun so KX LX
+ 
+
+ align:start position:0%
+I'm almost done with Sun so KX LX
+will have to be equal to a multiple with
+
+ align:start position:0%
+will have to be equal to a multiple with
+ 
+
+ align:start position:0%
+will have to be equal to a multiple with
+MX since we know that
+
+ align:start position:0%
+MX since we know that
+ 
+
+ align:start position:0%
+MX since we know that
+why naught is equal to minus KX l B
+
+ align:start position:0%
+why naught is equal to minus KX l B
+ 
+
+ align:start position:0%
+why naught is equal to minus KX l B
+squared we should take an x- so that
+
+ align:start position:0%
+squared we should take an x- so that
+ 
+
+ align:start position:0%
+squared we should take an x- so that
+you're within the sample you must be in
+
+ align:start position:0%
+you're within the sample you must be in
+ 
+
+ align:start position:0%
+you're within the sample you must be in
+Y positive and therefore KX should be
+
+ align:start position:0%
+Y positive and therefore KX should be
+ 
+
+ align:start position:0%
+Y positive and therefore KX should be
+negative and X should be negative and
+
+ align:start position:0%
+negative and X should be negative and
+ 
+
+ align:start position:0%
+negative and X should be negative and
+now I have a way to count because I can
+
+ align:start position:0%
+now I have a way to count because I can
+ 
+
+ align:start position:0%
+now I have a way to count because I can
+take an X negative up to some value
+
+ align:start position:0%
+take an X negative up to some value
+ 
+
+ align:start position:0%
+take an X negative up to some value
+minus NX bar and when NX grows
+
+ align:start position:0%
+minus NX bar and when NX grows
+ 
+
+ align:start position:0%
+minus NX bar and when NX grows
+KX grows and Y grow so I can take the
+
+ align:start position:0%
+KX grows and Y grow so I can take the
+ 
+
+ align:start position:0%
+KX grows and Y grow so I can take the
+last NX that I can use is the one in
+
+ align:start position:0%
+last NX that I can use is the one in
+ 
+
+ align:start position:0%
+last NX that I can use is the one in
+which the orbit is still in the sample
+
+ align:start position:0%
+which the orbit is still in the sample
+ 
+
+ align:start position:0%
+which the orbit is still in the sample
+up to the value y naught so this is this
+
+ align:start position:0%
+up to the value y naught so this is this
+ 
+
+ align:start position:0%
+up to the value y naught so this is this
+number is really the degeneracy because
+
+ align:start position:0%
+number is really the degeneracy because
+ 
+
+ align:start position:0%
+number is really the degeneracy because
+this is how many values of NX I can have
+
+ align:start position:0%
+this is how many values of NX I can have
+ 
+
+ align:start position:0%
+this is how many values of NX I can have
+from minus NX up to zero are the number
+
+ align:start position:0%
+from minus NX up to zero are the number
+ 
+
+ align:start position:0%
+from minus NX up to zero are the number
+of values that are consistent with a
+
+ align:start position:0%
+of values that are consistent with a
+ 
+
+ align:start position:0%
+of values that are consistent with a
+state still in the sample so why not
+
+ align:start position:0%
+state still in the sample so why not
+ 
+
+ align:start position:0%
+state still in the sample so why not
+equal to L Y should be equal to minus KX
+
+ align:start position:0%
+equal to L Y should be equal to minus KX
+ 
+
+ align:start position:0%
+equal to L Y should be equal to minus KX
+times L B squared so it's minus 2 pi NX
+
+ align:start position:0%
+times L B squared so it's minus 2 pi NX
+ 
+
+ align:start position:0%
+times L B squared so it's minus 2 pi NX
+bar over LX x lb squared and this gives
+
+ align:start position:0%
+bar over LX x lb squared and this gives
+ 
+
+ align:start position:0%
+bar over LX x lb squared and this gives
+you an X we can solve for an X there MX
+
+ align:start position:0%
+you an X we can solve for an X there MX
+ 
+
+ align:start position:0%
+you an X we can solve for an X there MX
+is ly L x over L B squared over 1 over 2
+
+ align:start position:0%
+is ly L x over L B squared over 1 over 2
+ 
+
+ align:start position:0%
+is ly L x over L B squared over 1 over 2
+pi so NX is the degeneracy this is the
+
+ align:start position:0%
+pi so NX is the degeneracy this is the
+ 
+
+ align:start position:0%
+pi so NX is the degeneracy this is the
+degeneracy and it's equal to the
+
+ align:start position:0%
+degeneracy and it's equal to the
+ 
+
+ align:start position:0%
+degeneracy and it's equal to the
+area / lb square which is H bar C over
+
+ align:start position:0%
+area / lb square which is H bar C over
+ 
+
+ align:start position:0%
+area / lb square which is H bar C over
+QB times 1 over 2 pi so it's equal to
+
+ align:start position:0%
+QB times 1 over 2 pi so it's equal to
+ 
+
+ align:start position:0%
+QB times 1 over 2 pi so it's equal to
+area times B divided by 2 pi H bar C
+
+ align:start position:0%
+area times B divided by 2 pi H bar C
+ 
+
+ align:start position:0%
+area times B divided by 2 pi H bar C
+over cube so we're back to the kind of
+
+ align:start position:0%
+over cube so we're back to the kind of
+ 
+
+ align:start position:0%
+over cube so we're back to the kind of
+thing we were saying before in which the
+
+ align:start position:0%
+thing we were saying before in which the
+ 
+
+ align:start position:0%
+thing we were saying before in which the
+degeneracy degeneracy is equal to the
+
+ align:start position:0%
+degeneracy degeneracy is equal to the
+ 
+
+ align:start position:0%
+degeneracy degeneracy is equal to the
+flux divided by the flux quantum that we
+
+ align:start position:0%
+flux divided by the flux quantum that we
+ 
+
+ align:start position:0%
+flux divided by the flux quantum that we
+figured out earlier today so this is how
+
+ align:start position:0%
+figured out earlier today so this is how
+ 
+
+ align:start position:0%
+figured out earlier today so this is how
+much how much states you can put on the
+
+ align:start position:0%
+much how much states you can put on the
+ 
+
+ align:start position:0%
+much how much states you can put on the
+sample so you find you're given a
+
+ align:start position:0%
+sample so you find you're given a
+ 
+
+ align:start position:0%
+sample so you find you're given a
+magnetic field at Tesla and you have
+
+ align:start position:0%
+magnetic field at Tesla and you have
+ 
+
+ align:start position:0%
+magnetic field at Tesla and you have
+some area you find the Phi u divided by
+
+ align:start position:0%
+some area you find the Phi u divided by
+ 
+
+ align:start position:0%
+some area you find the Phi u divided by
+Phi naught and that's the number of
+
+ align:start position:0%
+Phi naught and that's the number of
+ 
+
+ align:start position:0%
+Phi naught and that's the number of
+degenerate states of each Landau level
+
+ align:start position:0%
+degenerate states of each Landau level
+ 
+
+ align:start position:0%
+degenerate states of each Landau level
+so in particular given that we have that
+
+ align:start position:0%
+so in particular given that we have that
+ 
+
+ align:start position:0%
+so in particular given that we have that
+number that Phi naught is equal to about
+
+ align:start position:0%
+number that Phi naught is equal to about
+ 
+
+ align:start position:0%
+number that Phi naught is equal to about
+2 times 10 to the minus 7 Gauss then
+
+ align:start position:0%
+2 times 10 to the minus 7 Gauss then
+ 
+
+ align:start position:0%
+2 times 10 to the minus 7 Gauss then
+centimeter squared if you have a sample
+
+ align:start position:0%
+centimeter squared if you have a sample
+ 
+
+ align:start position:0%
+centimeter squared if you have a sample
+of 1 centimeter squared and you put one
+
+ align:start position:0%
+of 1 centimeter squared and you put one
+ 
+
+ align:start position:0%
+of 1 centimeter squared and you put one
+Gauss the value of the flux over Phi
+
+ align:start position:0%
+Gauss the value of the flux over Phi
+ 
+
+ align:start position:0%
+Gauss the value of the flux over Phi
+naught would be 1 Gauss centimeter
+
+ align:start position:0%
+naught would be 1 Gauss centimeter
+ 
+
+ align:start position:0%
+naught would be 1 Gauss centimeter
+squared over 2 times 10 to the minus 7
+
+ align:start position:0%
+squared over 2 times 10 to the minus 7
+ 
+
+ align:start position:0%
+squared over 2 times 10 to the minus 7
+same units so it's about five million
+
+ align:start position:0%
+same units so it's about five million
+ 
+
+ align:start position:0%
+same units so it's about five million
+states that's just to give you an idea
+
+ align:start position:0%
+states that's just to give you an idea
+ 
+
+ align:start position:0%
+states that's just to give you an idea
+of how big the numbers are that's the
+
+ align:start position:0%
+of how big the numbers are that's the
+ 
+
+ align:start position:0%
+of how big the numbers are that's the
+degeneracy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a classic problem very
+
+ align:start position:0%
+so this is a classic problem very
+ 
+
+ align:start position:0%
+so this is a classic problem very
+important in condensed matter physics is
+
+ align:start position:0%
+important in condensed matter physics is
+ 
+
+ align:start position:0%
+important in condensed matter physics is
+the first step in trying to understand
+
+ align:start position:0%
+the first step in trying to understand
+ 
+
+ align:start position:0%
+the first step in trying to understand
+quantum Hall effect and and many things
+
+ align:start position:0%
+quantum Hall effect and and many things
+ 
+
+ align:start position:0%
+quantum Hall effect and and many things
+and it's important to solve it and think
+
+ align:start position:0%
+and it's important to solve it and think
+ 
+
+ align:start position:0%
+and it's important to solve it and think
+it in several ways and I think you will
+
+ align:start position:0%
+it in several ways and I think you will
+ 
+
+ align:start position:0%
+it in several ways and I think you will
+be doing that in homework and recitation
\ No newline at end of file
diff --git a/VTWmccDMlDw.txt b/VTWmccDMlDw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1dd2533a83e498db887218ef738bbb7f2db4b31d
--- /dev/null
+++ b/VTWmccDMlDw.txt
@@ -0,0 +1,1311 @@
+Thanksgivings.  We're talking today about rational  
+
+medicine, and really what we're talking about is an understanding of  
+
+the molecular biology of disease has actually helped to revolutionize the  
+
+new science of therapeutic medicine.  And here, more often than not, the  
+
+discussions are focused around cancer.  And so,   
+
+I will therefore talk about an interesting story,   
+
+vis-à-vis the modern treatment of cancer, and how our understanding of  
+
+the molecular biology of the disease really helps in developing radically  
+
+new kinds of therapies.  By way of background,   
+
+let's just mention that most of the chemotherapeutics that we use today  
+
+to treat cancer were developed over the last 40-50 years at a time when  
+
+the molecular and biochemical defects inside cancer cells  
+
+were totally obscure.  And therefore,   
+
+to the extent that one developed chemotherapeutics,   
+
+they were developed simply empirically, trial and error.   
+
+For example, some of the most effective chemotherapeutics against  
+
+childhood leukemia are alkylating agents,   
+
+  which attach methyl and ethyl groups  
+
+to target molecules inside cells.  And their utility in cancer was  
+
+first discerned because of an explosion in a container.   
+
+I think it was in a ship off Naples in World War II where a bin of  
+
+alkylating agents was dispersed.  Many people were exposed to it, and  
+
+these people, as a consequence of that, came down with what's  
+
+called leucopoenia.  Poenia generally means a depression,   
+
+in this case, a depression of their white blood cells.   
+
+Such alkylating agents had actually been used during the First World War  
+
+in gas warfare because during the First World War,   
+
+one used so-called mustard gases,  which was a very effective way, even  
+
+more effective than artillery in killing vast numbers  
+
+of enemy soldiers.  And, somebody noticed this  
+
+leucopoenia in 1946-47 as a consequence of inadvertent exposure  
+
+to these alkylating agents,  which became dispersed as a gas.   
+
+And about five years later,  somebody made the logical leap that  
+
+if these agents were able to suppress normal white blood  
+
+concentrations that perhaps they might also be effective against what  
+
+seemed to be ostensibly a related problem, which is the problem  
+
+of leukemia.  And keep in mind that when we talk  
+
+about leukemia,  the suffix -emia refers to blood  
+
+generally, and leuk- once again refers to white blood,   
+
+i.e. an excess of white blood cells in the blood.  And so,   
+
+through this accidental discovery,  one began to develop alkylating  
+
+agents that turned out to be extremely successful in treating,   
+
+and often curing, childhood leukemias, most notably acute  
+
+lymphocytic leukemia,  which turns out to be very sensitive  
+
+to this and other related agents.  So, this is a very common form of  
+
+childhood leukemia,  which is now actually cured in 60 or  
+
+70% of the children who were treated,  which would have been unheard of  
+
+half a century ago.  But I return to what I said before,   
+
+which is that this kind of treatment was developed in the face of total  
+
+ignorance concerning the nature of the disease, the molecular defects  
+
+that were present in the disease,  and that were responsible for the  
+
+runaway, can you still hear me OK,  were responsible for the runaway  
+
+proliferation of the cancer cells.  So having said that,   
+
+I want to go to a different kind of leukemia, and this is called chronic  
+
+myelogenous leukemia,  to give you an indication of the  
+
+path of discovery that led from its original description to the  
+
+development of rather successful treatments.   
+
+So, chronic myelogenous leukemia,  I mentioned the prefix myelo- last  
+
+time or the time before referring to bone marrow, and this is a leukemia  
+
+of cells coming from the bone marrow from the myeloid cells in the bone  
+
+marrow, which are the precursors of things like macrophages  
+
+and granulocytes.  So, these are cells which are  
+
+playing an important role in the immune response,   
+
+and during this chronic myelogenous leukemia disease,   
+
+which is called CML,  there could be a period of three or  
+
+four years where individuals develop large numbers of these cells in  
+
+their blood stream.  And after a period of about three or  
+
+four years, all of a sudden there is an eruption into what's called blast  
+
+crisis.  And you may recall I mentioned the word blast also on one  
+
+occasion earlier.  This all fits together in a nice  
+
+puzzle.  Blast refers to primitive,  embryonic-like cells, and all of a  
+
+sudden there is an eruption of primitive, embryonic-like cells,   
+
+less differentiated like these macrophages and granulocytes,   
+
+which until this point had been present in vastly excessive numbers  
+
+in the blood.  There's blast crisis.   
+
+This leads to acute myelogenous leukemia, and death ensues usually  
+
+within a year or two,  or that's been traditionally the  
+
+case.  No one really had any idea about the possible causative  
+
+mechanisms of the disease,  and that allows me to use another  
+
+word which you might one day come across if you should stay in  
+
+biomedical research.  And that is the etiologic agents.   
+
+When we talk about etiologic agents,  we talk about the agents which are  
+
+causally responsible for inducing a disease.  These can be external  
+
+agents, or they could even be internal agents,   
+
+molecules inside cells which are responsible for the creation of the  
+
+disease.  And the key discovery was made in 1960 when individuals were  
+
+looking at the chromosomal makeup of the CML cells.   
+
+The chromosomal makeup,  I'll use another word just so we  
+
+could expand our vocabulary this morning, the chromosomal makeup is  
+
+often called the karyotype,  that is to say the constellation of  
+
+chromosomes that one can see at mitosis under the microscope.   
+
+Keep in mind, as we've said before,  that during the interphase of the  
+
+cell cycle, chromosomes are essentially invisible,   
+
+but during the metaphase of mitosis they become condensed,   
+
+and on that occasion, individuals noticed a 9-22 translocation.   
+
+So here is chromosome nine normally.  Here's chromosome 22.  And as you  
+
+may know, the numbering system with human chromosomes goes from the  
+
+largest number one all the way down to the smallest.   
+
+So, this is the smallest,  with the exception of the Y  
+
+chromosome.  And what they notice was instead of  
+
+seeing this regular chromosomal array, they noticed instead what  
+
+looked very much like a structure of this sort here, i.e.   
+
+a translocation.    
+
+And this translocation resulted in a swapping of sequences between these  
+
+two chromosomes.  Note, by the way,   
+
+this is reciprocal,  i.e. in the sense that nine donates  
+
+something to 22,  and 22 donates something to nine.   
+
+However, the segments that are swapped are not necessarily of equal  
+
+size.  So, it turns out here that in this case, chromosome nine has  
+
+actually gained a lot more than chromosome 22 gained as a  
+
+consequence of this exchange of genetic segments.   
+
+And this 9-22 translocation made the smallest chromosome even smaller.   
+
+So, this was already the smallest chromosome as I mentioned besides  
+
+the smallest autosome,  the smallest non-sex chromosome.   
+
+Now it got even smaller because it lost some of its bulk as a  
+
+consequence of this chromosomal translocation.   
+
+And because this discovery was made in Philadelphia,   
+
+it became known as the Philadelphia chromosome.  This is now about 40  
+
+years ago, or as it's sometimes called, PH-1 for reasons,   
+
+I don't know why it's called PH-1 except for Philadelphia.   
+
+And, as investigators began to look at other cases of chronic  
+
+myelogenous leukemia,  they discovered that this  
+
+translocation was present at the Philadelphia chromosome most  
+
+importantly was identifiable in virtually all cases,   
+
+more than 95% of the cases of chronic myelogenous leukemia.   
+
+And moreover, this chromosome was present as well in the more  
+
+differentiated macrophages and granulocytes that were present and  
+
+circulating in the blood of the CML patients.  And that began to suggest  
+
+the notion that there was a stem cell of some sort,   
+
+oligopotential stem cell that created various kinds of more  
+
+differentiated white blood cells that had sustained this chromosomal  
+
+translocation because that's what it is, a translocalization,   
+
+a translocation, that all the cells of these patients had sustained this  
+
+chromosomal translocation.  And that began to suggest the  
+
+notion that somehow as a consequence of a random genetic accident  
+
+happening in these people's blood,  this particular chromosome was  
+
+repeatedly identified.  And it was with great likelihood  
+
+causally or etiologically important in the genesis of the disease.   
+
+But that in itself led nowhere.  One could simply talk about its  
+
+association until work from a totally unrelated area,   
+
+which is to say the study of retroviruses discovered Abelson  
+
+murine leukemia virus.  And Abelson was named after the  
+
+fellow, Herb Abelson,  who first discovered it at NIH and  
+
+undertook its molecular characterization here in our own  
+
+cancer center,  and Abelson discovered that this  
+
+virus which he studied carried the ends of the murine leukemia virus,   
+
+which was a parental virus.  It was as hybrid virus.   
+
+And into the middle of it,  Abelson leukemia virus has acquired  
+
+a cellular proto-oncogene,  which it had activated into an  
+
+oncogene.  And therefore,  here we have a situation where a  
+
+cellular gene like sarc in the case of Rous Sarcoma Virus has been  
+
+activated.  This became called ABL for obvious reasons.   
+
+And this gene, it turned out,  was critically important in  
+
+understanding hwo the chromosomal translocation led to cancer.   
+
+In fact, if one infected mice with a retrovirus carrying this genome,   
+
+this is just to indicate the fact that the repeat ends,   
+
+the long terminal repeat ends of this provirus,   
+
+they occur twice at the ends of this retrovirus.  If one infected a mouse  
+
+with the Abelson virus,  out came a disease which was  
+
+superficially similar at least to chronic myelogenous leukemia.   
+
+And that began a search,  then, for the chromosomal  
+
+localization of the Abel proto-oncogene.   
+
+And what was discovered subsequently, fascinatingly enough,   
+
+was that the Abel proto-oncogene was right at the break point between two  
+
+chromosomes, nine and 22.  And what happened as a consequence  
+
+of this translocation,  and the resulting fusion of this  
+
+chromosome with this chromosome was the creation of a fuse gene,   
+
+a hybrid gene that now carried the reading frames of two previously  
+
+unconnected gene,  one on chromosome nine,   
+
+and one on chromosome 22.  Here's the normal, Abel protein.   
+
+It's called C Abel, meaning the cellular or the normal form of Abel.   
+
+And you see it up here.  It's shown in a very schematic way.   
+
+And here's a second protein which is encoded on the other chromosome.   
+
+So, Abel is encoded here, and the other gene, which is called BCR is  
+
+encoded here, and as a consequence of the translocation,   
+
+Abel is encoded here.  BCR is encoded here.  As a consequence of  
+
+the translocation,  one now has not only the fusion of  
+
+chromosomal segments.  But one has the fusion of the  
+
+reading frames of two previously unlinked genes.   
+
+And here, one creates as a consequence of these fusions,   
+
+any one of a series of three quite distinct fusion proteins,   
+
+which do not naturally preexist in the normal cell.   
+
+And there shown here is P-1 85,  P-2 10, and P-2 30.  These  
+
+translocations allow different parts of a second gene called BCR.   
+
+BCR refers to breakpoint cluster region.  The area of the point of  
+
+fusion is called the breakpoint between the two genes.   
+
+So, the point where each gene is cut and fused with the other is  
+
+called the breakpoint.  And it turns out that within the  
+
+region of the chromosome where BCR maps, there's actually three sites  
+
+at which the fusion can occur.  If you look carefully at this  
+
+diagram, you see that there's differing extents of the BCR protein,   
+
+which can be contributed to the fusion protein.   
+
+And, what this says,  in effect, is the following,   
+
+that here, let's just refer to this diagram right up here.   
+
+Notice, by the way, in all three of these, that the Abel protein is  
+
+present at the C terminal end of the protein.  The BCR is present at the  
+
+end terminal end.  So, here's the BCR gene.   
+
+Here's the Abel gene down here.  And what investigators found is that  
+
+there could be a break at this part of the BCR gene,   
+
+at this part of the BCR gene,  or at this part of the BCR gene,   
+
+resulting always in the fusion of Abel, to one, or two,   
+
+or three different kinds of BCR proteins.  And,   
+
+breakpoint cluster region signified the fact that there was a whole  
+
+cluster of sites in the previously existing BCR gene to which this  
+
+fusion could take place,  resulting, if the break occurred  
+
+here, the breakpoint occurred here,  and BCR to get the longer one.   
+
+Here you get the medium-sized one; here you'd get the shortest one.   
+
+And, interestingly enough, as one explored virtually,   
+
+other kinds of different leukemias,  one could see different of these  
+
+fusion proteins that were produced.  Here's chronic, myelogenous  
+
+leukemia, which I talked to you about before.  Here is acute  
+
+lymphocytic leukemia,  and here's chronic and neutrophylic  
+
+leukemia, three different kinds of leukemia.  We don't have to worry  
+
+about the details of these diseases,  aside from the fact to say that the  
+
+structure of this fusion protein encourages the outgrowth of  
+
+different kinds of stem cells in the bone marrow, which in turn create  
+
+three different kinds of diseases.  Most importantly for our discussion  
+
+was an attempt to understand the nature of the resulting fusion  
+
+protein, which as a consequence of this fusion caused by the  
+
+chromosomal translocation now clearly acquired biological powers  
+
+that did not preexist in either of the two parental proteins.   
+
+These various notations here indicate a whole series of different  
+
+functions which are associated with the Abel protein,   
+
+and alternatively with the BCR protein.  And we don't need to get  
+
+into them, except to say that each one of these different names here  
+
+allows the protein on its own to associate with other proteins and do  
+
+activated downstream signaling cascade.   
+
+What's most important about our discussion is the realization that  
+
+this SH-1 domain,  indicated here, SH-1 refers to the  
+
+sarcomology domain,  equals sarcomology, equals a  
+
+tyrosine kinase.  And therefore, what one has here is  
+
+a protein, which is much more elaborate than sarc,   
+
+has vastly more signaling capabilities,   
+
+by virtue of the fact that these different domains that are indicated  
+
+here allow the resulting fusion protein to grab hold of a whole  
+
+bunch of different signally partners so that it can send out a diverse  
+
+array of downstream activating signals.  If one examined the  
+
+structure of the SH-1 domain,  it had a tyrosine kinase activity  
+
+very much like sarc,  and most importantly,   
+
+if one introduced this fusion protein into a retrovirus,   
+
+now instead of Abel, one could make a BCR Abel fusion protein.   
+
+One could put this into a retrovirus as before, just like up here.   
+
+One could infect mice with it,  and now get out of a disease which  
+
+was indistinguishable,  in essence, from chronic myelogenous  
+
+leukemia in humans.  If one put a subtle point mutation  
+
+in the tyrosine kinase domain,  all of the able protein, here is the  
+
+tyrosine kinase domain,  SH-1, up here.  Here, we see the  
+
+tyrosine kinase domains represented in the three different fusion  
+
+proteins.  Keep in mind SH-1 is always the tyrosine kinase domain.   
+
+If one put a subtle, inactivating point mutation in the tyrosine  
+
+kinase domain,  that immediately wiped out all  
+
+biological powers of creating leukemias on the part of this  
+
+retrovirus here,  or any one of the other closely  
+
+related kinds of fusion proteins.  And therefore,   
+
+that indicated that the tyrosine kinase domain indicated right here  
+
+was really critical to creating the tumor, and that any effects on its  
+
+tyrosine kinase signaling ability would, in the end,   
+
+result in the collapse of the tumor,  or the inability of the resulting  
+
+retrovirus to actually create cancer.   
+
+And so, now one had,  really for the first time,   
+
+a clear demonstration of how a commonly occurring human cancer,   
+
+chronic myelogenous leukemia, is unfortunately not so rare,   
+
+could arise as a consequence of some random, chromosomal translocation  
+
+event.  You might ask,  why does one always get this  
+
+particular kind of translocation?  Well, the answer is, we don't  
+
+really know.  It would almost seem as if there's a homing device which  
+
+causes this fragment and this fragment to target each other and to  
+
+exchange one another.  It's probably not the case.   
+
+What probably happens is that chromosomal translocations take  
+
+place rather randomly within the bone marrow, and on rare occasion  
+
+there is a chromosomal translocation that creates exactly this kind of  
+
+fusion.  And this kind of fusion,  in turn, is what's responsible for  
+
+creating this fusion protein,  and this fusion protein in turn  
+
+creates the outgrowth of this CML,  the chronic myelogenous leukemia  
+
+disease.  So what that means is really that a  
+
+randomly occurring chromosomal translocation on rare occasion hits  
+
+a genetic jackpot,  and the cell which happens to have  
+
+acquired this kind of chromosomal translocation now begins to  
+
+proliferate wildly,  creating first chronic myelogenous  
+
+leukemia, and then subsequently erupting into a subsequent acute  
+
+phase where there are seemingly additional genetic alterations  
+
+beyond this chromosomal translocation that conspire with the  
+
+initially present chromosomal translocation to create a very  
+
+aggressive disease which rapidly leads to the death of the  
+
+leukemia patient.  That offered, in principle,   
+
+an attractive way of beginning to develop an anti-cancer therapeutic  
+
+because what one might imagine was that one could develop a tyrosine  
+
+kinase inhibitor.    
+
+Now keep in mind that tyrosine kinases are a class of enzymes which  
+
+attach phosphate groups onto the tyrosine residues of various  
+
+substrate proteins.  And keep in mind as well the fact  
+
+that we drew a series of growth factor receptors which have tyrosine  
+
+kinase domains in them.  And I'm drawing the tyrosine kinase  
+
+domains here like this,  that when these growth factor  
+
+receptors become activated,  they attach phosphate groups onto  
+
+the tails of one another.  And I'll draw those phosphate  
+
+groups like this,  i.e. the binding of ligand or let's  
+
+say epidermal growth factor ligand or plate ligand causes the two  
+
+receptors, which are normally mobilized in the plasma membrane to  
+
+come together to transphosphorylate one another,   
+
+and having done so,  to acquire actively signaling powers,   
+
+because once these phosphates become attached, they now represent sites  
+
+where other molecules can anchor themselves and send out downstream  
+
+signals.  In fact,  there are altogether 90 different  
+
+tyrosine kinases encoded in the human genome.   
+
+And so, to the extent that these tyrosine kinases become  
+
+hyperactivated in various kinds of human cancers,   
+
+this represents in principle a very attractive way of developing an  
+
+anti-cancer therapeutic.  But let's think about the problems  
+
+that are inherent in such a compound.  First of all,   
+
+if one wants to develop an anti-cancer therapeutic,   
+
+it must be reasonably specific for the Abelson tyrosine kinase,   
+
+and not the 89 kinds of tyrosine kinases that also coexist in the  
+
+human genome, and are active,  and apparently responsible for  
+
+normal cell metabolism in a whole variety of normal cell types.   
+
+So, one has to begin to think about the issue of cell activity.   
+
+How can one possibly make a low molecular weight compound,   
+
+which is selectively able to inactivate the Abelson tyrosine  
+
+kinase as indicated here,  the SH-1 group,   
+
+but doesn't disturb a whole variety of other tyrosine kinases that are  
+
+responsible for other normal physiological mechanisms.   
+
+Well, you'll say that's pretty easy.  We have 90 different genes.   
+
+Each of the 90 different genes makes a distinct protein,   
+
+and these proteins should be very different.  And therefore,   
+
+if one can, in fact, if one does the three-dimensional structure of these  
+
+proteins, all the tyrosine kinases look quite similar.   
+
+They have a biload structure.  Here is the active site of the  
+
+enzyme.  That is to say,  in here is the catalytic cleft,   
+
+the site where the actual catalysis takes place, the site where the  
+
+gamma phosphate of ATP is taken from the ATP and attached to a substrate  
+
+protein to the hydroxyl of a tyrosine of a protein that's about  
+
+to be phosphorylated.  So, you just make a low moleculoid  
+
+chemical that's specific for the tyrosine kinase domain of the Abel  
+
+protein.  And when I draw this biload structure,   
+
+this biload structure is carried here within the SH-1 domain right  
+
+here.  So, this has a biload structure.  It's obviously not  
+
+indicated here in this very schematic drawing.   
+
+The problem with that is the following.   
+
+All of the SH-1 domains,  all of the tyrosine kinase domains  
+
+are evolutionarily closely related to one another.   
+
+They're all derived from the precursors of the tyrosine kinase  
+
+domain that probably existed maybe 600 or 700 million years ago,   
+
+and has as a consequence of gene duplication been diversified to make  
+
+90 different tyrosine kinases.  And if you look under x-ray  
+
+crystallography at the three dimensional structure of all these  
+
+tyrosine kinases,  they all pretty much look like this,   
+
+i.e. they all have rather similar catalytic clefts because they  
+
+diverge from a common ancestral protein, and they retain this three  
+
+dimensional configuration because this three dimensional configuration  
+
+seems to be important for the retention of their function.   
+
+You could imagine, conversely,  that if there were some descendants  
+
+of the ancestral tyrosine kinase domain that some of them became  
+
+mutant and lost its three dimensional structure.   
+
+Those descendant kinases would lose their ability to phosphorylate  
+
+tyrosines on substrate proteins,  and therefore would be eliminated  
+
+from the gene pool because they would be defective.   
+
+And that explains the strong conservatism in the structure of  
+
+these 90 different enzymes.  They all look very similar to one  
+
+another, and that creates a great difficulty for the drug developer  
+
+because a low molecular weight drug,  which one would like to develop,   
+
+that fits in here.  So, here I'll draw a low molecular  
+
+weight drug that interacts in a stereo-specific fashion with the  
+
+amino acid residues that are aligning this pocket,   
+
+this catalytic cleft, might bind and nicely inactivate the tyrosine  
+
+kinase domain of Abel.  But at the same time,   
+
+it might also bind and inactivate a whole series of other tyrosine  
+
+kinases, and that in turn could lead to therapeutic disaster.   
+
+For instance, if you had a non-selective agent,   
+
+you could treat a chronic myelogenous leukemia patient with a  
+
+low molecular weight inhibitor,  a low molecular weight compound,   
+
+which would get into this pocket of the BCR Abel protein.   
+
+But it might similarly get into the catalytic cleft of the EGF receptor.   
+
+And if it shot down the EGF receptor, it might cause a fatal  
+
+diarrhea because after all,  the EGF receptor, I will tell you,   
+
+is needed to maintain the structure of the epithelial lining of the  
+
+colon.  And so,  you might kill the patient simply  
+
+because you had deprived the cells in that person's colon of their  
+
+ability to maintain themselves.  There are a whole series of growth  
+
+factor receptors that are required for hematapoeisis that we discussed  
+
+last time.  And there,  once again, if you had a  
+
+nonselective compound,  which got into the domain of one of  
+
+the growth factor receptors that is responsible for hematapoeisis,   
+
+you might shut down the entire bone marrow, and once again kill the  
+
+patient.  I'm just giving you those as overly dramatic examples of the  
+
+fact that cell activity is an extremely important consideration in  
+
+developing such a drug.  The other thing is affinity for the  
+
+target, for the catalytic cleft that is being targeted.   
+
+What do I mean by affinity?  If you look at those response  
+
+curves of various compounds,  what you see is the following.   
+
+You can draw out a line that looks like this, a graph that looks like  
+
+this, where here we have log of drug concentration.   
+
+And here is 10-4,  here, let's do the other one,   
+
+10-8 molar, 10-7 molar, 10-6, 10-5,  10-4.   
+
+And this is molar drug concentration.  And here is the percentage of  
+
+inhibition.  Let's say,  for example, we were able to take  
+
+the BCR Abel protein and study it in a test tube.  And let's say we were  
+
+interested in studying how well its tyrosine kinase activity responded  
+
+to an applied drug that we developed against it.   
+
+So, here's the percentage of inhibition of tyrosine kinase  
+
+activity of BCR Abel protein.  Now, I might be able to develop a  
+
+drug whose dose response curve would look like this.   
+
+And you'll say,  well, that's terrific.   
+
+That's a drug which shuts down BCR Abel.  We haven't even dealt with  
+
+the issue of cell activity,  but let's look at where one begins  
+
+to see a dose response right here,  10-5 molar.  And if you calculate  
+
+back as to how much of the drug you need to deliver in order to shut  
+
+down the BCR Abel protein in a patient, the size of the pill they'd  
+
+have to get would probably be this big everyday.   
+
+So, what you need to do is you need to be an acceptable range of drug  
+
+concentrations is down in this area here.  And therefore,   
+
+only until you get a drug which has a dose response curve that looks  
+
+like this, which is two or three orders of magnitude more potent  
+
+where it's able to shut down the kinase activity already at 10-7 in a,   
+
+this is called a submicromolar concentration.   
+
+Micromolar is 10-6.  Here already at a tenth of a  
+
+micromolar, 10-7 molar,  we're already getting a shutdown of  
+
+the enzyme function.  And if one can do that,   
+
+then one might in principle be able to develop a pill that's this big  
+
+and give that to the patient rather than a pill that's a size of a  
+
+football.  And by the way,  if you have to make lots of a very  
+
+complex, organic molecule through organic synthesis that has an  
+
+affinity of this,  it's also very expensive.   
+
+Obviously, if you can make a compound that's a hundredfold more  
+
+potent and requires a hundredfold less material to deliver to the  
+
+patient body, then you might have some success in treating  
+
+the patient.  Here's another issue.   
+
+So, we've talked about cell activity.  We've talked about  
+
+potency or affinity,  affinity for the substrate or  
+
+potency.  So, this would be an acceptable drug.   
+
+It works already at molar concentration where the inflection  
+
+point of this curve is.  This is an unacceptable drug at  
+
+10-5.  We can also talk about  
+
+pharmacokinetics.  I want to give you a feeling for  
+
+how complex drug development is,  and why it so rarely succeeds.  By  
+
+the way, you know how much it costs to develop a drug that's useful in  
+
+the clinic these days and test it on people?  Anybody have any idea?   
+
+How much?  Yeah.  It's pretty close to $1 billion,   
+
+between $900 million and $1 billion.  That's a lot of money.  That's more  
+
+money than you and I are going to earn together, all of us  
+
+maybe, in a lifetime.  OK, anyhow, pharmacokinetics,   
+
+well what's pharmacokinetics?  Glad I asked that question.   
+
+How long does the drug stay inside of you after you take it if you're a  
+
+cancer patient?  What happens if the drug is  
+
+excreted by the kidneys within minutes of its being taken,   
+
+let's say, either by injection or orally?   
+
+So here we can imagine,  let's talk about drug concentration.   
+
+I'll use the word drug concentration in blood.   
+
+And here's time.  And here's what some drugs look like when you give  
+
+them, let's say,  orally.  Here's what they look like.   
+
+So, let's say here's the effective drug concentration: effective  
+
+concentration.  And we know the effective  
+
+concentration from doing measurements like this.   
+
+We just measure it, work that out.  So, let's say we develop a drug  
+
+which is able to hit the BCR Abel protein.  What are the kinetics with  
+
+which the drug becomes soluble in the blood stream?   
+
+And it might look like this,  where I'm drawing here now, this is  
+
+one hour.  This is two hours.  This is three hours, four hours.   
+
+ Is that long enough?   
+
+Well, the fact of the matter is,  if you're going to try to kill a  
+
+cancer cell, and that's what the name of this game is,   
+
+you want to have it around for a while because it turns out,   
+
+as one learned, the continued viability of the CML cancer cells of  
+
+the leukemia cells was dependent on the continued firing by the BCR Abel  
+
+kinase protein.  In fact, as one learned,   
+
+if one shut off firing by the tyrosine kinase molecule in a  
+
+chronic myelogenous leukemia cell,  the cells would implode.   
+
+They would undergo apitosis.  So, this began to reveal that in  
+
+fact the BCR Abel protein is not only responsible for forcing these  
+
+cells to proliferate,  but it also independently provides  
+
+them with anti-apoptotic signal.  It keeps them from falling over the  
+
+cliff into apitosis.  It keeps them from killing  
+
+themselves, and that's obviously critical for the ability of this  
+
+tumor to proliferate,  for the number of cells to expand in  
+
+the body of a patient.  It turns out that if you provide  
+
+these cancer cells with an effective way of shutting down their BCR Abel  
+
+protein for 30 or 40 or 50 minutes,  not much happens to them.  You need  
+
+to deprive them of the drug for a very long period of time,   
+
+well, 15-20 hours, and therefore you need pharmacokinetics that look like  
+
+this.  It needs to be present for an extended period of time,   
+
+or even better, let me re-draw that,  even better look like this.   
+
+It stays in the blood for an extended period of time.   
+
+Some drugs stay in the circulation for a long time.   
+
+Other drugs stay in the circulation for a very short period of time.   
+
+There's another problem which we haven't even begun to talk about,   
+
+and that is the metabolism of the drug.  It turns out that many drugs  
+
+that you give a patient are rapidly converted by the enzymes and the  
+
+liver which are normally responsible for detoxifying chemicals that come  
+
+into our body.  And therefore,   
+
+many of the drugs that come into our bodies are with greater or lesser  
+
+speed altered into something else,  detoxified, and therefore rendered  
+
+innocuous.  Now you'll say,  well, you can figure that out too,   
+
+but here's an additional fly in the ointment.  Because we are a  
+
+polymorphic population,  because we humans are genetically  
+
+heterogeneous,  one from the other,   
+
+some of us metabolize a given drug much more rapidly than others do.   
+
+And here, we have a situation where potentially, most of us might  
+
+metabolize a drug very quickly,  in which case the physicians would  
+
+want to give us a very high dose of the drug so that we have enough of  
+
+the drug around for a long enough period of time to do some effect.   
+
+So let's say that 97% of us are able to metabolize the drug very  
+
+quickly, and as a consequence,  we're given a very high dosage in  
+
+order to have some effective dosage reaching the tumor to compensate for  
+
+the fact that much of this drug is rapidly eliminated by metabolism  
+
+in the liver.  It's inter-converted into another  
+
+chemically innocuous compound.  Well, you'll say, that's good.   
+
+We'll just take a large dose of that compound,   
+
+but let's think about the other 3% in the population who metabolize  
+
+this compound very slowly.  Like the other 97%, these  
+
+individuals will be given a high dose of the drug because experience  
+
+shows that in general,  most human beings metabolize a drug  
+
+very quickly.  These individuals metabolize the  
+
+drug very slowly,  and what's going to happen to them?   
+
+Well, they might croak.  Why?  Because that drug is going to be  
+
+around in potent biologically active form for an extended period of time  
+
+in their bodies,  and might have in them a lethal  
+
+outcome.  So therefore,  we have to deal with the effects of  
+
+variability in drug metabolism,  variability in metabolism because it  
+
+turns out that different people metabolize the drug differently and  
+
+that variability in drug metabolism is vastly greater if you compare the  
+
+way we metabolize drugs to the way that laboratory mice metabolize  
+
+drugs.  Well, you'll say,  why should we care about how  
+
+laboratory mice metabolize this or that drug?   
+
+Why is it important?  The fact is, the first tryouts of a  
+
+candidate drug are tried out in laboratory mice where laboratory  
+
+mice are given a tumor,  and they're injected with the drug  
+
+to see whether the tumor begins to shrink.  But if it's the case,   
+
+if the laboratory mice metabolize a drug in a vastly different way than  
+
+do humans, then the outcome of working with laboratory mice might  
+
+be enormously misleading.  And these are just some of the  
+
+problems that bedevil the development of a drug.   
+
+In any case, around 1994,  at a company which was a precursor  
+
+of Novartis, it was called Ciba-Geigy in Basel,   
+
+Switzerland.  They developed a highly specific and potent anti-Abel,   
+
+low molecular weight compound,  which came to be called Leveck.   
+
+Or in Europe it's called Gleveck.  It's also pronounced Leveck, but  
+
+it's spelled differently.  In fact, it was one of the other  
+
+difficulties of developing this drug was the following.   
+
+The higher ups in the drug company who were paying for this research  
+
+wanted on repeated occasion to scrub this entire drug development  
+
+program.  Why?  Because the number of cases of  
+
+chronic myelogenous leukemia overall worldwide is relatively small.   
+
+How many are in this country every year?  I don't know,   
+
+10 or 15,000.  So, the question was,  economically speaking, would the  
+
+relatively small number of cases of this disease justify their investing  
+
+$1 billion in the development of the drug.  Maybe it would take them a  
+
+generation to get any payback from their initial investment.   
+
+And so, they tried time after time,  time and again, to shut down this  
+
+development program because it didn't seem to have any clear,   
+
+long-term economic benefit.  Of course, now we're not talking about  
+
+biology.  We're talking about economics, and rational economics.   
+
+This is not avarice on their part.  A drug company like that cannot go  
+
+on spending $1 billion here and $1 billion there without at one point  
+
+or another leading to a major financial hemorrhage.   
+
+So, Gleveck turned out to be highly specific for the Abel kinase,   
+
+and as it turned out, for two other kinds of kinases as well.   
+
+Another kind of kinase is against a tyrosine kinase receptor called KIT,   
+
+this is a receptor tyrosine kinase,  and another receptor tyrosine kinase  
+
+called the PDGF receptor,  which we've also encountered in  
+
+passing earlier.  These two other growth factor  
+
+receptors, KIT and the PDGF receptor also have tyrosine kinase domains.   
+
+They therefore follow this overall structural plan here,   
+
+and it turns out by evolutionary quirk that the structures of their  
+
+tyrosine kinase domains are actually similar in certain ways to the  
+
+tyrosine kinase domain of Abel,  and therefore of BCR Abel.   
+
+So, in fact, they didn't actually have a totally specific drug which  
+
+would attack only one out of the 90-tyrosine kinases encoded in their  
+
+genome.  It attacked three of the 90-tyrosine kinases,   
+
+the Abel, the KITT, and the PDGF receptor.  And this might,   
+
+on its own, have already proven to be the death nail for the protein,   
+
+except they began to try it out for patients, and they saw some  
+
+remarkable responses.  It turned out that the great  
+
+majority of CML patients who were treated with Gleveck at therapeutic  
+
+concentrations ended up having a rapid remission of their chronic  
+
+myelogenous leukemia disease,  which ultimately resulted in their  
+
+being outwardly free of the disease.  This is your question of the day.   
+
+So, Gleveck goes into the catalytic cleft of the Abel tyrosine kinase.   
+
+It blocks the ATP binding site because keep in mind that these  
+
+enzymes need to grab the gamma phosphate off of ATP and transfer it  
+
+to a protein substrate,  and it does so because it hydrogen  
+
+bonds to the amino acids which are lining this catalytic cleft.   
+
+In other words,  this catalytic cleft up here is  
+
+obviously made of amino acids,  and there are hydrogen bonds which  
+
+Gleveck can form with the amino acid resides that you're lining on both  
+
+sides of the cleft.  I should have brought you a picture  
+
+of that.  And,  a similar kind of hydrogen bonding  
+
+can occur with the amino acids that are aligning the catalytic clefts of  
+
+the PDGF receptor and KIT,  and that hydrogen bonding can occur  
+
+already at concentrations that are submicromolar,   
+
+less than 10-6 molar,  10-7, even sometimes 10-8 molar  
+
+under certain conditions.  So, it's a high affinity binding,   
+
+and it's relatively specific.  Only three out of the 90 different  
+
+kinases are bound.  We can do the following kind of  
+
+experiment.  If I were to add Gleveck to cells  
+
+with BCR Abel function,  this is the response that BCR Abel  
+
+would show.  Here is the response that the EGF receptor would show.   
+
+So, if I dose the patient at this concentration of drug,   
+
+Gleveck will shut down the BCR Abel protein.   
+
+But it won't shut down the EGF receptor, which requires vastly  
+
+higher concentrations of drug in order to shut down its tyrosine  
+
+kinase domain.  And right here,   
+
+we can see what we call selectivity.  The fact that this enzyme responds  
+
+at very log drug concentration,  this enzyme EGF receptor and its  
+
+tyrosine kinase,  it's a growth factor receptor once  
+
+again, requires a vastly higher concentration drug in order to  
+
+elicit an outcome.  So, what happened to the chronic  
+
+myelogenous leukemia patients.  The great majority of them between  
+
+70-80% had a miraculous collapse of their disease.   
+
+In most cases,  this disease could be monitored  
+
+microscopically.  One could look for the immature  
+
+myeloid cells in their blood and see where they were previously present  
+
+in vast numbers.  They were microscopically now  
+
+indetectable (sic).  However, in those patients where the  
+
+disease seemed to collapse,  one could still use the PCR test to  
+
+demonstrate there were residual cancer cells in their blood.   
+
+How could one do that?  Well,  let's imagine that here is the PCR  
+
+Abel fusion protein.  So, here's PCR, and here's Abel  
+
+over here.  You can make PCR primers,   
+
+one of which is specific for a PCR sequence, and the other of which is  
+
+specific for an Abel sequence,  and the only time that you'll get a  
+
+PCR product is if these two sequences exist on the same  
+
+messenger RNA molecule that's reverse transcribed into a CDNA.   
+
+You could even do this genomic DNA as well, and so one can specifically  
+
+detect using this PCR test the presence of cells which have this  
+
+chromosomal translocation.  If one of the PCR primers is against  
+
+BCR and the other is Abel,  and the distances between these two  
+
+primers is not too far away,  not more than, let's say, kilobase,   
+
+so you get rather efficient PCR amplification.   
+
+So, it turned out that the great majority of patients who were  
+
+cytologically cured,  cytology means a cytological  
+
+analysis represents what you see through in microscopes.   
+
+So these patients,  if you looked at a smear of their  
+
+blood, cytologically they were cured.  But if you used PCR analysis,   
+
+which is far more sensitive, one could detect residual cancer cells  
+
+that might be present in one out of 105 or one out of 106 cells moving  
+
+around in circulation,  which are almost invisible if you're  
+
+looking through a very complex mixture of cells through the light  
+
+microscope.  And so,  what happened was that patients  
+
+began to relapse,  and after a period of several years,   
+
+a number of patients began to show a restoration of their CML condition.   
+
+In fact, in one recent European study, indicates that between 10-12%  
+
+of the CML patients who were treated with Gleveck relapsed every year.   
+
+What do I mean by relapse?  I mean they show a resurgence of their  
+
+disease.  The disease comes back to life, and they once again  
+
+have the disease.  And interestingly enough,   
+
+if one now looks at their cancer cells, what do you see?   
+
+In virtually every case you see some alteration in the BCR Abel  
+
+protein.  In the great majority of instances, you see point mutations  
+
+that affect amino acid residues lining the cavity here,   
+
+lining the cavity of the Abel kinase protein.   
+
+Those amino acid substitutions do not compromise the tyrosine kinase  
+
+activity of this enzyme.  But they do prevent Gleveck from  
+
+binding, and as a consequence,  now you begin to have patients whose  
+
+tumors are no longer responsive to Gleveck.  And what's happened now is  
+
+one has developed a new generation of compounds which binds into this  
+
+pocket even in the presence of these amino acid substitutions to retreat  
+
+these patients.  See you on Wednesday.
\ No newline at end of file
diff --git a/VVOazB6_D3Q.txt b/VVOazB6_D3Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..136ad61fe843567bf9cb4ec41458969bd57d530b
--- /dev/null
+++ b/VVOazB6_D3Q.txt
@@ -0,0 +1,635 @@
+align:start position:0%
+ 
+the following content is provided under
+
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+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
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+a Creative Commons license your support
+ 
+
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+a Creative Commons license your support
+will help MIT open courseware continue
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+will help MIT open courseware continue
+ 
+
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+will help MIT open courseware continue
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+to offer high quality educational
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+
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+to offer high quality educational
+resources for free to make a donation or
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+resources for free to make a donation or
+ 
+
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+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu hi everybody um you're in
+
+ align:start position:0%
+ocw.mit.edu hi everybody um you're in
+ 
+
+ align:start position:0%
+ocw.mit.edu hi everybody um you're in
+507 and if you look at your syllabus
+
+ align:start position:0%
+507 and if you look at your syllabus
+ 
+
+ align:start position:0%
+507 and if you look at your syllabus
+you'll find one of the things in the
+
+ align:start position:0%
+you'll find one of the things in the
+ 
+
+ align:start position:0%
+you'll find one of the things in the
+front page of your syllabus is called a
+
+ align:start position:0%
+front page of your syllabus is called a
+ 
+
+ align:start position:0%
+front page of your syllabus is called a
+lexicon
+
+ align:start position:0%
+lexicon
+ 
+
+ align:start position:0%
+lexicon
+um and I'd like to introduce you to why
+
+ align:start position:0%
+um and I'd like to introduce you to why
+ 
+
+ align:start position:0%
+um and I'd like to introduce you to why
+um we've chosen to have a lexicon for
+
+ align:start position:0%
+um we've chosen to have a lexicon for
+ 
+
+ align:start position:0%
+um we've chosen to have a lexicon for
+this course so if you look at this
+
+ align:start position:0%
+this course so if you look at this
+ 
+
+ align:start position:0%
+this course so if you look at this
+particular slide or overhead this is
+
+ align:start position:0%
+particular slide or overhead this is
+ 
+
+ align:start position:0%
+particular slide or overhead this is
+what John is going to teach you this
+
+ align:start position:0%
+what John is going to teach you this
+ 
+
+ align:start position:0%
+what John is going to teach you this
+semester introduct metabolism the
+
+ align:start position:0%
+semester introduct metabolism the
+ 
+
+ align:start position:0%
+semester introduct metabolism the
+glycolysis pathway fatty acid
+
+ align:start position:0%
+glycolysis pathway fatty acid
+ 
+
+ align:start position:0%
+glycolysis pathway fatty acid
+biosynthesis fatty acid oxidation amino
+
+ align:start position:0%
+biosynthesis fatty acid oxidation amino
+ 
+
+ align:start position:0%
+biosynthesis fatty acid oxidation amino
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+metabolism a complete jungle how are you
+
+ align:start position:0%
+metabolism a complete jungle how are you
+ 
+
+ align:start position:0%
+metabolism a complete jungle how are you
+ever going to learn anything out of this
+
+ align:start position:0%
+ever going to learn anything out of this
+ 
+
+ align:start position:0%
+ever going to learn anything out of this
+myth well it's that's actually exactly
+
+ align:start position:0%
+myth well it's that's actually exactly
+ 
+
+ align:start position:0%
+myth well it's that's actually exactly
+the point so what we're going to do over
+
+ align:start position:0%
+the point so what we're going to do over
+ 
+
+ align:start position:0%
+the point so what we're going to do over
+the course of this semester is convince
+
+ align:start position:0%
+the course of this semester is convince
+ 
+
+ align:start position:0%
+the course of this semester is convince
+you that all of this mess can be um
+
+ align:start position:0%
+you that all of this mess can be um
+ 
+
+ align:start position:0%
+you that all of this mess can be um
+simplified to 10 basic reactions and
+
+ align:start position:0%
+simplified to 10 basic reactions and
+ 
+
+ align:start position:0%
+simplified to 10 basic reactions and
+those 10 basic
+
+ align:start position:0%
+those 10 basic
+ 
+
+ align:start position:0%
+those 10 basic
+reactions are what's in the Lexicon so
+
+ align:start position:0%
+reactions are what's in the Lexicon so
+ 
+
+ align:start position:0%
+reactions are what's in the Lexicon so
+it turns
+
+ align:start position:0%
+it turns
+ 
+
+ align:start position:0%
+it turns
+out all of biochemistry um for primary
+
+ align:start position:0%
+out all of biochemistry um for primary
+ 
+
+ align:start position:0%
+out all of biochemistry um for primary
+metabolism
+
+ align:start position:0%
+metabolism
+ 
+
+ align:start position:0%
+metabolism
+can be described using 10 different sets
+
+ align:start position:0%
+can be described using 10 different sets
+ 
+
+ align:start position:0%
+can be described using 10 different sets
+of reactions and vitam your vitamin
+
+ align:start position:0%
+of reactions and vitam your vitamin
+ 
+
+ align:start position:0%
+of reactions and vitam your vitamin
+bottle and so if you look at your
+
+ align:start position:0%
+bottle and so if you look at your
+ 
+
+ align:start position:0%
+bottle and so if you look at your
+vitamin bottle what do you see most of
+
+ align:start position:0%
+vitamin bottle what do you see most of
+ 
+
+ align:start position:0%
+vitamin bottle what do you see most of
+you probably take vitamins you have
+
+ align:start position:0%
+you probably take vitamins you have
+ 
+
+ align:start position:0%
+you probably take vitamins you have
+vitamin B1 vitamin B2 vitamin B3 vitamin
+
+ align:start position:0%
+vitamin B1 vitamin B2 vitamin B3 vitamin
+ 
+
+ align:start position:0%
+vitamin B1 vitamin B2 vitamin B3 vitamin
+B6 vitamin B12 all of those um provide
+
+ align:start position:0%
+B6 vitamin B12 all of those um provide
+ 
+
+ align:start position:0%
+B6 vitamin B12 all of those um provide
+enzymes the catalysts for all the
+
+ align:start position:0%
+enzymes the catalysts for all the
+ 
+
+ align:start position:0%
+enzymes the catalysts for all the
+reactions in these this complex
+
+ align:start position:0%
+reactions in these this complex
+ 
+
+ align:start position:0%
+reactions in these this complex
+metabolic pathway I showed you um on the
+
+ align:start position:0%
+metabolic pathway I showed you um on the
+ 
+
+ align:start position:0%
+metabolic pathway I showed you um on the
+previous slide um they expand the
+
+ align:start position:0%
+previous slide um they expand the
+ 
+
+ align:start position:0%
+previous slide um they expand the
+repertoire of
+
+ align:start position:0%
+repertoire of
+ 
+
+ align:start position:0%
+repertoire of
+reactions um that enzymes can actually
+
+ align:start position:0%
+reactions um that enzymes can actually
+ 
+
+ align:start position:0%
+reactions um that enzymes can actually
+catalyze and So within the Lexicon what
+
+ align:start position:0%
+catalyze and So within the Lexicon what
+ 
+
+ align:start position:0%
+catalyze and So within the Lexicon what
+we're going to show you is the chemistry
+
+ align:start position:0%
+we're going to show you is the chemistry
+ 
+
+ align:start position:0%
+we're going to show you is the chemistry
+of actually how these vitamins work so
+
+ align:start position:0%
+of actually how these vitamins work so
+ 
+
+ align:start position:0%
+of actually how these vitamins work so
+again if we come back to the Lexicon um
+
+ align:start position:0%
+again if we come back to the Lexicon um
+ 
+
+ align:start position:0%
+again if we come back to the Lexicon um
+we'll talk about how carbon carbon bonds
+
+ align:start position:0%
+we'll talk about how carbon carbon bonds
+ 
+
+ align:start position:0%
+we'll talk about how carbon carbon bonds
+are made and broken fatty acid
+
+ align:start position:0%
+are made and broken fatty acid
+ 
+
+ align:start position:0%
+are made and broken fatty acid
+metabolism um sugar metabolism we'll
+
+ align:start position:0%
+metabolism um sugar metabolism we'll
+ 
+
+ align:start position:0%
+metabolism um sugar metabolism we'll
+talk about oxidation reduction reactions
+
+ align:start position:0%
+talk about oxidation reduction reactions
+ 
+
+ align:start position:0%
+talk about oxidation reduction reactions
+and the vitamins that are used for that
+
+ align:start position:0%
+and the vitamins that are used for that
+ 
+
+ align:start position:0%
+and the vitamins that are used for that
+transformation we'll talk about the
+
+ align:start position:0%
+transformation we'll talk about the
+ 
+
+ align:start position:0%
+transformation we'll talk about the
+energy storage and the energy currency
+
+ align:start position:0%
+energy storage and the energy currency
+ 
+
+ align:start position:0%
+energy storage and the energy currency
+in the cell ATP Etc so what the Lexicon
+
+ align:start position:0%
+in the cell ATP Etc so what the Lexicon
+ 
+
+ align:start position:0%
+in the cell ATP Etc so what the Lexicon
+is meant to do is sort of be an aid when
+
+ align:start position:0%
+is meant to do is sort of be an aid when
+ 
+
+ align:start position:0%
+is meant to do is sort of be an aid when
+you can't remember what does oxidation
+
+ align:start position:0%
+you can't remember what does oxidation
+ 
+
+ align:start position:0%
+you can't remember what does oxidation
+and reduction you can go back to your
+
+ align:start position:0%
+and reduction you can go back to your
+ 
+
+ align:start position:0%
+and reduction you can go back to your
+Lexicon and look up what are the Redux
+
+ align:start position:0%
+Lexicon and look up what are the Redux
+ 
+
+ align:start position:0%
+Lexicon and look up what are the Redux
+co-actors that are involved in
+
+ align:start position:0%
+co-actors that are involved in
+ 
+
+ align:start position:0%
+co-actors that are involved in
+transformation and by practicing the
+
+ align:start position:0%
+transformation and by practicing the
+ 
+
+ align:start position:0%
+transformation and by practicing the
+chemistry in the first part of the
+
+ align:start position:0%
+chemistry in the first part of the
+ 
+
+ align:start position:0%
+chemistry in the first part of the
+semester of all these reactions
+
+ align:start position:0%
+semester of all these reactions
+ 
+
+ align:start position:0%
+semester of all these reactions
+metabolism should be very
+
+ align:start position:0%
+metabolism should be very
+ 
+
+ align:start position:0%
+metabolism should be very
+straightforward in terms of all the cond
+
+ align:start position:0%
+straightforward in terms of all the cond
+ 
+
+ align:start position:0%
+straightforward in terms of all the cond
+activities so um what hopefully what you
+
+ align:start position:0%
+activities so um what hopefully what you
+ 
+
+ align:start position:0%
+activities so um what hopefully what you
+will do is look through your Lexicon
+
+ align:start position:0%
+will do is look through your Lexicon
+ 
+
+ align:start position:0%
+will do is look through your Lexicon
+tonight see what these reactions are and
+
+ align:start position:0%
+tonight see what these reactions are and
+ 
+
+ align:start position:0%
+tonight see what these reactions are and
+then keep it by your side during the
+
+ align:start position:0%
+then keep it by your side during the
+ 
+
+ align:start position:0%
+then keep it by your side during the
+rest of the semester and when you're
+
+ align:start position:0%
+rest of the semester and when you're
+ 
+
+ align:start position:0%
+rest of the semester and when you're
+having trouble understanding some
+
+ align:start position:0%
+having trouble understanding some
+ 
+
+ align:start position:0%
+having trouble understanding some
+chemical transformation you can use the
+
+ align:start position:0%
+chemical transformation you can use the
+ 
+
+ align:start position:0%
+chemical transformation you can use the
+Lexicon as a GU guide to think about the
+
+ align:start position:0%
+Lexicon as a GU guide to think about the
+ 
+
+ align:start position:0%
+Lexicon as a GU guide to think about the
+chemical Transformations that you'll be
+
+ align:start position:0%
+chemical Transformations that you'll be
+ 
+
+ align:start position:0%
+chemical Transformations that you'll be
+looking at over the course of the
+
+ align:start position:0%
+looking at over the course of the
+ 
+
+ align:start position:0%
+looking at over the course of the
+semester
\ No newline at end of file
diff --git a/VYS9EYZ3gCo.txt b/VYS9EYZ3gCo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..47afcf810f4924622e76559cb24870e947c0618e
--- /dev/null
+++ b/VYS9EYZ3gCo.txt
@@ -0,0 +1,1891 @@
+align:start position:0%
+ 
+hi everyone welcome back so today we're
+
+ align:start position:0%
+hi everyone welcome back so today we're
+ 
+
+ align:start position:0%
+hi everyone welcome back so today we're
+going to tackle a problem in complex
+
+ align:start position:0%
+going to tackle a problem in complex
+ 
+
+ align:start position:0%
+going to tackle a problem in complex
+matrices and specifically we're going to
+
+ align:start position:0%
+matrices and specifically we're going to
+ 
+
+ align:start position:0%
+matrices and specifically we're going to
+look at diagonalizing a complex matrix
+
+ align:start position:0%
+look at diagonalizing a complex matrix
+ 
+
+ align:start position:0%
+look at diagonalizing a complex matrix
+so given this matrix a we're asked to
+
+ align:start position:0%
+so given this matrix a we're asked to
+ 
+
+ align:start position:0%
+so given this matrix a we're asked to
+find its eigenvalue matrix lambda and
+
+ align:start position:0%
+find its eigenvalue matrix lambda and
+ 
+
+ align:start position:0%
+find its eigenvalue matrix lambda and
+its eigenvector matrix x and one thing
+
+ align:start position:0%
+its eigenvector matrix x and one thing
+ 
+
+ align:start position:0%
+its eigenvector matrix x and one thing
+to note about this matrix a is that if
+
+ align:start position:0%
+to note about this matrix a is that if
+ 
+
+ align:start position:0%
+to note about this matrix a is that if
+we take its conjugate transpose it's
+
+ align:start position:0%
+we take its conjugate transpose it's
+ 
+
+ align:start position:0%
+we take its conjugate transpose it's
+actually equal to itself so in professor
+
+ align:start position:0%
+actually equal to itself so in professor
+ 
+
+ align:start position:0%
+actually equal to itself so in professor
+Strang's
+
+ align:start position:0%
+Strang's
+ 
+
+ align:start position:0%
+Strang's
+book he combines this notation to be a
+
+ align:start position:0%
+book he combines this notation to be a
+ 
+
+ align:start position:0%
+book he combines this notation to be a
+superscript H to mean conjugate
+
+ align:start position:0%
+superscript H to mean conjugate
+ 
+
+ align:start position:0%
+superscript H to mean conjugate
+transpose so if you were to take the
+
+ align:start position:0%
+transpose so if you were to take the
+ 
+
+ align:start position:0%
+transpose so if you were to take the
+transpose of this matrix and then
+
+ align:start position:0%
+transpose of this matrix and then
+ 
+
+ align:start position:0%
+transpose of this matrix and then
+conjugate all the elements you would
+
+ align:start position:0%
+conjugate all the elements you would
+ 
+
+ align:start position:0%
+conjugate all the elements you would
+find that a equals its conjugate
+
+ align:start position:0%
+find that a equals its conjugate
+ 
+
+ align:start position:0%
+find that a equals its conjugate
+transpose and we call this property
+
+ align:start position:0%
+transpose and we call this property
+ 
+
+ align:start position:0%
+transpose and we call this property
+hermitian okay so let you think about
+
+ align:start position:0%
+hermitian okay so let you think about
+ 
+
+ align:start position:0%
+hermitian okay so let you think about
+this for a moment and I'll be back in a
+
+ align:start position:0%
+this for a moment and I'll be back in a
+ 
+
+ align:start position:0%
+this for a moment and I'll be back in a
+sec
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay welcome back so what's the first
+
+ align:start position:0%
+okay welcome back so what's the first
+ 
+
+ align:start position:0%
+okay welcome back so what's the first
+step in computing the eigenvectors and
+
+ align:start position:0%
+step in computing the eigenvectors and
+ 
+
+ align:start position:0%
+step in computing the eigenvectors and
+eigenvalues of a matrix it's to take a
+
+ align:start position:0%
+eigenvalues of a matrix it's to take a
+ 
+
+ align:start position:0%
+eigenvalues of a matrix it's to take a
+look at the characteristic equation so
+
+ align:start position:0%
+look at the characteristic equation so
+ 
+
+ align:start position:0%
+look at the characteristic equation so
+specifically we take DET of a minus
+
+ align:start position:0%
+specifically we take DET of a minus
+ 
+
+ align:start position:0%
+specifically we take DET of a minus
+lambda i and quite possibly the only
+
+ align:start position:0%
+lambda i and quite possibly the only
+ 
+
+ align:start position:0%
+lambda i and quite possibly the only
+thing new with this problem is that the
+
+ align:start position:0%
+thing new with this problem is that the
+ 
+
+ align:start position:0%
+thing new with this problem is that the
+entries of the matrix a are complex now
+
+ align:start position:0%
+entries of the matrix a are complex now
+ 
+
+ align:start position:0%
+entries of the matrix a are complex now
+you may have already seen that lambdas
+
+ align:start position:0%
+you may have already seen that lambdas
+ 
+
+ align:start position:0%
+you may have already seen that lambdas
+being complex but we're going to work
+
+ align:start position:0%
+being complex but we're going to work
+ 
+
+ align:start position:0%
+being complex but we're going to work
+this out explicitly so if I take the
+
+ align:start position:0%
+this out explicitly so if I take the
+ 
+
+ align:start position:0%
+this out explicitly so if I take the
+determinant we get DET of 2 minus lambda
+
+ align:start position:0%
+determinant we get DET of 2 minus lambda
+ 
+
+ align:start position:0%
+determinant we get DET of 2 minus lambda
+3 minus lambda we have 1 minus I 1 plus
+
+ align:start position:0%
+3 minus lambda we have 1 minus I 1 plus
+ 
+
+ align:start position:0%
+3 minus lambda we have 1 minus I 1 plus
+I we want to set this to 0 this then
+
+ align:start position:0%
+I we want to set this to 0 this then
+ 
+
+ align:start position:0%
+I we want to set this to 0 this then
+gives us a polynomial for lambda 1 plus
+
+ align:start position:0%
+gives us a polynomial for lambda 1 plus
+ 
+
+ align:start position:0%
+gives us a polynomial for lambda 1 plus
+I 1 minus I we set it equal to 0 we can
+
+ align:start position:0%
+I 1 minus I we set it equal to 0 we can
+ 
+
+ align:start position:0%
+I 1 minus I we set it equal to 0 we can
+expand out this term we get 6 minus 5
+
+ align:start position:0%
+expand out this term we get 6 minus 5
+ 
+
+ align:start position:0%
+expand out this term we get 6 minus 5
+lambda plus lambda squared these 2 terms
+
+ align:start position:0%
+lambda plus lambda squared these 2 terms
+ 
+
+ align:start position:0%
+lambda plus lambda squared these 2 terms
+you'll note are complex conjugates of
+
+ align:start position:0%
+you'll note are complex conjugates of
+ 
+
+ align:start position:0%
+you'll note are complex conjugates of
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+this tends to make things simple so we
+
+ align:start position:0%
+this tends to make things simple so we
+ 
+
+ align:start position:0%
+this tends to make things simple so we
+have minus 1 minus I squared is going to
+
+ align:start position:0%
+have minus 1 minus I squared is going to
+ 
+
+ align:start position:0%
+have minus 1 minus I squared is going to
+give us 2 because there are differences
+
+ align:start position:0%
+give us 2 because there are differences
+ 
+
+ align:start position:0%
+give us 2 because there are differences
+of squares the cross terms involving I
+
+ align:start position:0%
+of squares the cross terms involving I
+ 
+
+ align:start position:0%
+of squares the cross terms involving I
+cancel and we get the characteristic
+
+ align:start position:0%
+cancel and we get the characteristic
+ 
+
+ align:start position:0%
+cancel and we get the characteristic
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lambda squared minus 5 lambda plus 4
+
+ align:start position:0%
+lambda squared minus 5 lambda plus 4
+ 
+
+ align:start position:0%
+lambda squared minus 5 lambda plus 4
+equals 0 and specifically we can
+
+ align:start position:0%
+equals 0 and specifically we can
+ 
+
+ align:start position:0%
+equals 0 and specifically we can
+factorize this equation we see that
+
+ align:start position:0%
+factorize this equation we see that
+ 
+
+ align:start position:0%
+factorize this equation we see that
+there's roots of minus 1 there
+
+ align:start position:0%
+there's roots of minus 1 there
+ 
+
+ align:start position:0%
+there's roots of minus 1 there
+factorizes into factors of lambda minus
+
+ align:start position:0%
+factorizes into factors of lambda minus
+ 
+
+ align:start position:0%
+factorizes into factors of lambda minus
+1 and lambda minus 4 which then give us
+
+ align:start position:0%
+1 and lambda minus 4 which then give us
+ 
+
+ align:start position:0%
+1 and lambda minus 4 which then give us
+roots of lambda is 1 and lambda is 4 so
+
+ align:start position:0%
+roots of lambda is 1 and lambda is 4 so
+ 
+
+ align:start position:0%
+roots of lambda is 1 and lambda is 4 so
+when one curious point to note is that
+
+ align:start position:0%
+when one curious point to note is that
+ 
+
+ align:start position:0%
+when one curious point to note is that
+the eigenvalues are real in this case 1
+
+ align:start position:0%
+the eigenvalues are real in this case 1
+ 
+
+ align:start position:0%
+the eigenvalues are real in this case 1
+and 4 are real whereas the matrix that
+
+ align:start position:0%
+and 4 are real whereas the matrix that
+ 
+
+ align:start position:0%
+and 4 are real whereas the matrix that
+we started with was complex and this is
+
+ align:start position:0%
+we started with was complex and this is
+ 
+
+ align:start position:0%
+we started with was complex and this is
+a general property of hermitian matrices
+
+ align:start position:0%
+a general property of hermitian matrices
+ 
+
+ align:start position:0%
+a general property of hermitian matrices
+so even though they might be complex
+
+ align:start position:0%
+so even though they might be complex
+ 
+
+ align:start position:0%
+so even though they might be complex
+matrices hermitian matrices always have
+
+ align:start position:0%
+matrices hermitian matrices always have
+ 
+
+ align:start position:0%
+matrices hermitian matrices always have
+real eigenvalues ok so this is the first
+
+ align:start position:0%
+real eigenvalues ok so this is the first
+ 
+
+ align:start position:0%
+real eigenvalues ok so this is the first
+step when I ask to diagonalize a matrix
+
+ align:start position:0%
+step when I ask to diagonalize a matrix
+ 
+
+ align:start position:0%
+step when I ask to diagonalize a matrix
+the second step is to find the
+
+ align:start position:0%
+the second step is to find the
+ 
+
+ align:start position:0%
+the second step is to find the
+eigenvectors and to do that what we have
+
+ align:start position:0%
+eigenvectors and to do that what we have
+ 
+
+ align:start position:0%
+eigenvectors and to do that what we have
+to do is we have to look at the cases
+
+ align:start position:0%
+to do is we have to look at the cases
+ 
+
+ align:start position:0%
+to do is we have to look at the cases
+for lambda equals 1 and lambda is equal
+
+ align:start position:0%
+for lambda equals 1 and lambda is equal
+ 
+
+ align:start position:0%
+for lambda equals 1 and lambda is equal
+4 separately so let's first look at the
+
+ align:start position:0%
+4 separately so let's first look at the
+ 
+
+ align:start position:0%
+4 separately so let's first look at the
+case of lambda is equal to 1 and
+
+ align:start position:0%
+case of lambda is equal to 1 and
+ 
+
+ align:start position:0%
+case of lambda is equal to 1 and
+specifically we're going to be looking
+
+ align:start position:0%
+specifically we're going to be looking
+ 
+
+ align:start position:0%
+specifically we're going to be looking
+for a vector such that a minus lambda I
+
+ align:start position:0%
+for a vector such that a minus lambda I
+ 
+
+ align:start position:0%
+for a vector such that a minus lambda I
+times the vector V is 0 and if we've
+
+ align:start position:0%
+times the vector V is 0 and if we've
+ 
+
+ align:start position:0%
+times the vector V is 0 and if we've
+done things properly this matrix lambda
+
+ align:start position:0%
+done things properly this matrix lambda
+ 
+
+ align:start position:0%
+done things properly this matrix lambda
+minus or sorry a minus lambda I should
+
+ align:start position:0%
+minus or sorry a minus lambda I should
+ 
+
+ align:start position:0%
+minus or sorry a minus lambda I should
+be singular so if we take a minus lambda
+
+ align:start position:0%
+be singular so if we take a minus lambda
+ 
+
+ align:start position:0%
+be singular so if we take a minus lambda
+I we're going to get 1 1 minus I 1 plus
+
+ align:start position:0%
+I we're going to get 1 1 minus I 1 plus
+ 
+
+ align:start position:0%
+I we're going to get 1 1 minus I 1 plus
+I 3 minus 1 is 2 and I'll write out
+
+ align:start position:0%
+I 3 minus 1 is 2 and I'll write out
+ 
+
+ align:start position:0%
+I 3 minus 1 is 2 and I'll write out
+components of V which are V 1 and V 2
+
+ align:start position:0%
+components of V which are V 1 and V 2
+ 
+
+ align:start position:0%
+components of V which are V 1 and V 2
+and we want this to be 0 and you'll note
+
+ align:start position:0%
+and we want this to be 0 and you'll note
+ 
+
+ align:start position:0%
+and we want this to be 0 and you'll note
+that it's it's always the case it's
+
+ align:start position:0%
+that it's it's always the case it's
+ 
+
+ align:start position:0%
+that it's it's always the case it's
+almost always the case that when we work
+
+ align:start position:0%
+almost always the case that when we work
+ 
+
+ align:start position:0%
+almost always the case that when we work
+out a minus lambda I the second row is
+
+ align:start position:0%
+out a minus lambda I the second row is
+ 
+
+ align:start position:0%
+out a minus lambda I the second row is
+going to be a constant multiple of the
+
+ align:start position:0%
+going to be a constant multiple of the
+ 
+
+ align:start position:0%
+going to be a constant multiple of the
+first row and this must be the case
+
+ align:start position:0%
+first row and this must be the case
+ 
+
+ align:start position:0%
+first row and this must be the case
+because these two rows must be linearly
+
+ align:start position:0%
+because these two rows must be linearly
+ 
+
+ align:start position:0%
+because these two rows must be linearly
+depend
+
+ align:start position:0%
+depend
+ 
+
+ align:start position:0%
+depend
+on each other for the matrix a minus
+
+ align:start position:0%
+on each other for the matrix a minus
+ 
+
+ align:start position:0%
+on each other for the matrix a minus
+lambda I to be singular so if you look
+
+ align:start position:0%
+lambda I to be singular so if you look
+ 
+
+ align:start position:0%
+lambda I to be singular so if you look
+at this you might think that these two
+
+ align:start position:0%
+at this you might think that these two
+ 
+
+ align:start position:0%
+at this you might think that these two
+rows aren't necessarily linearly
+
+ align:start position:0%
+rows aren't necessarily linearly
+ 
+
+ align:start position:0%
+rows aren't necessarily linearly
+independent but the point is that
+
+ align:start position:0%
+independent but the point is that
+ 
+
+ align:start position:0%
+independent but the point is that
+there's complex numbers involved and
+
+ align:start position:0%
+there's complex numbers involved and
+ 
+
+ align:start position:0%
+there's complex numbers involved and
+indeed actually if we were to multiply
+
+ align:start position:0%
+indeed actually if we were to multiply
+ 
+
+ align:start position:0%
+indeed actually if we were to multiply
+this first row by 1 plus lambda we would
+
+ align:start position:0%
+this first row by 1 plus lambda we would
+ 
+
+ align:start position:0%
+this first row by 1 plus lambda we would
+get 1 plus lambda and 2 and you note
+
+ align:start position:0%
+get 1 plus lambda and 2 and you note
+ 
+
+ align:start position:0%
+get 1 plus lambda and 2 and you note
+that that's exactly the second row so
+
+ align:start position:0%
+that that's exactly the second row so
+ 
+
+ align:start position:0%
+that that's exactly the second row so
+this second row is actually 1 plus
+
+ align:start position:0%
+this second row is actually 1 plus
+ 
+
+ align:start position:0%
+this second row is actually 1 plus
+lambda times the first row so these rows
+
+ align:start position:0%
+lambda times the first row so these rows
+ 
+
+ align:start position:0%
+lambda times the first row so these rows
+are actually linearly dependent on each
+
+ align:start position:0%
+are actually linearly dependent on each
+ 
+
+ align:start position:0%
+are actually linearly dependent on each
+other okay so what values of V 1 and V 2
+
+ align:start position:0%
+other okay so what values of V 1 and V 2
+ 
+
+ align:start position:0%
+other okay so what values of V 1 and V 2
+can we take well we just need to make
+
+ align:start position:0%
+can we take well we just need to make
+ 
+
+ align:start position:0%
+can we take well we just need to make
+this top row multiplied by V 1 and V 2
+
+ align:start position:0%
+this top row multiplied by V 1 and V 2
+ 
+
+ align:start position:0%
+this top row multiplied by V 1 and V 2
+equal to 0 and then because the second
+
+ align:start position:0%
+equal to 0 and then because the second
+ 
+
+ align:start position:0%
+equal to 0 and then because the second
+row is a constant multiple of the first
+
+ align:start position:0%
+row is a constant multiple of the first
+ 
+
+ align:start position:0%
+row is a constant multiple of the first
+row were automatically guaranteed that
+
+ align:start position:0%
+row were automatically guaranteed that
+ 
+
+ align:start position:0%
+row were automatically guaranteed that
+the second equation holds so just by
+
+ align:start position:0%
+the second equation holds so just by
+ 
+
+ align:start position:0%
+the second equation holds so just by
+looking at it I'm going to take V 1 is
+
+ align:start position:0%
+looking at it I'm going to take V 1 is
+ 
+
+ align:start position:0%
+looking at it I'm going to take V 1 is
+equal to 1 minus I and V 2 is negative 1
+
+ align:start position:0%
+equal to 1 minus I and V 2 is negative 1
+ 
+
+ align:start position:0%
+equal to 1 minus I and V 2 is negative 1
+so we see that 1 times 1 minus I minus 1
+
+ align:start position:0%
+so we see that 1 times 1 minus I minus 1
+ 
+
+ align:start position:0%
+so we see that 1 times 1 minus I minus 1
+times 1 minus I is going to give us 0 so
+
+ align:start position:0%
+times 1 minus I is going to give us 0 so
+ 
+
+ align:start position:0%
+times 1 minus I is going to give us 0 so
+this is one solution and of course we
+
+ align:start position:0%
+this is one solution and of course we
+ 
+
+ align:start position:0%
+this is one solution and of course we
+can take any constant multiple times
+
+ align:start position:0%
+can take any constant multiple times
+ 
+
+ align:start position:0%
+can take any constant multiple times
+this eigenvector and that's also going
+
+ align:start position:0%
+this eigenvector and that's also going
+ 
+
+ align:start position:0%
+this eigenvector and that's also going
+to be an eigenvector so I'll just write
+
+ align:start position:0%
+to be an eigenvector so I'll just write
+ 
+
+ align:start position:0%
+to be an eigenvector so I'll just write
+this out 1 minus I minus 1 is the
+
+ align:start position:0%
+this out 1 minus I minus 1 is the
+ 
+
+ align:start position:0%
+this out 1 minus I minus 1 is the
+eigenvector for lambda is equal to 1 for
+
+ align:start position:0%
+eigenvector for lambda is equal to 1 for
+ 
+
+ align:start position:0%
+eigenvector for lambda is equal to 1 for
+lambda is equal to 4 again a minus
+
+ align:start position:0%
+lambda is equal to 4 again a minus
+ 
+
+ align:start position:0%
+lambda is equal to 4 again a minus
+lambda I is going to give us negative 2
+
+ align:start position:0%
+lambda I is going to give us negative 2
+ 
+
+ align:start position:0%
+lambda I is going to give us negative 2
+1 minus I 1 plus I 3 minus lambda is
+
+ align:start position:0%
+1 minus I 1 plus I 3 minus lambda is
+ 
+
+ align:start position:0%
+1 minus I 1 plus I 3 minus lambda is
+going to be minus 1 and I'll call this
+
+ align:start position:0%
+going to be minus 1 and I'll call this
+ 
+
+ align:start position:0%
+going to be minus 1 and I'll call this
+vector u 1 and u 2 and again we want u 1
+
+ align:start position:0%
+vector u 1 and u 2 and again we want u 1
+ 
+
+ align:start position:0%
+vector u 1 and u 2 and again we want u 1
+u 2 equal to 0 or sorry the matrix
+
+ align:start position:0%
+u 2 equal to 0 or sorry the matrix
+ 
+
+ align:start position:0%
+u 2 equal to 0 or sorry the matrix
+multiplied by u 1 u 2 is equal to 0 and
+
+ align:start position:0%
+multiplied by u 1 u 2 is equal to 0 and
+ 
+
+ align:start position:0%
+multiplied by u 1 u 2 is equal to 0 and
+just by looking at this again we see
+
+ align:start position:0%
+just by looking at this again we see
+ 
+
+ align:start position:0%
+just by looking at this again we see
+that the second row is actually a
+
+ align:start position:0%
+that the second row is actually a
+ 
+
+ align:start position:0%
+that the second row is actually a
+constant multiple of the first row for
+
+ align:start position:0%
+constant multiple of the first row for
+ 
+
+ align:start position:0%
+constant multiple of the first row for
+example if we were to multiply this this
+
+ align:start position:0%
+example if we were to multiply this this
+ 
+
+ align:start position:0%
+example if we were to multiply this this
+row by negative 2 and this row by 1 plus
+
+ align:start position:0%
+row by negative 2 and this row by 1 plus
+ 
+
+ align:start position:0%
+row by negative 2 and this row by 1 plus
+I we would see that there constant
+
+ align:start position:0%
+I we would see that there constant
+ 
+
+ align:start position:0%
+I we would see that there constant
+multiples of each
+
+ align:start position:0%
+multiples of each
+ 
+
+ align:start position:0%
+multiples of each
+so I can take you to B for example 1 + 1
+
+ align:start position:0%
+so I can take you to B for example 1 + 1
+ 
+
+ align:start position:0%
+so I can take you to B for example 1 + 1
++ I how did I get this well I just
+
+ align:start position:0%
++ I how did I get this well I just
+ 
+
+ align:start position:0%
++ I how did I get this well I just
+looked at the second equation because
+
+ align:start position:0%
+looked at the second equation because
+ 
+
+ align:start position:0%
+looked at the second equation because
+it's a little simpler and I said well if
+
+ align:start position:0%
+it's a little simpler and I said well if
+ 
+
+ align:start position:0%
+it's a little simpler and I said well if
+I have 1 plus I here
+
+ align:start position:0%
+I have 1 plus I here
+ 
+
+ align:start position:0%
+I have 1 plus I here
+I can just say multiply by 1 and then
+
+ align:start position:0%
+I can just say multiply by 1 and then
+ 
+
+ align:start position:0%
+I can just say multiply by 1 and then
+minus 1 times 1 plus I when I add them
+
+ align:start position:0%
+minus 1 times 1 plus I when I add them
+ 
+
+ align:start position:0%
+minus 1 times 1 plus I when I add them
+up is going to vanish so this is how I
+
+ align:start position:0%
+up is going to vanish so this is how I
+ 
+
+ align:start position:0%
+up is going to vanish so this is how I
+get the second one now there's something
+
+ align:start position:0%
+get the second one now there's something
+ 
+
+ align:start position:0%
+get the second one now there's something
+curious going on and this is going to be
+
+ align:start position:0%
+curious going on and this is going to be
+ 
+
+ align:start position:0%
+curious going on and this is going to be
+another property of hermitian matrices
+
+ align:start position:0%
+another property of hermitian matrices
+ 
+
+ align:start position:0%
+another property of hermitian matrices
+but if you actually take a look at this
+
+ align:start position:0%
+but if you actually take a look at this
+ 
+
+ align:start position:0%
+but if you actually take a look at this
+eigenvector it will be orthogonal to
+
+ align:start position:0%
+eigenvector it will be orthogonal to
+ 
+
+ align:start position:0%
+eigenvector it will be orthogonal to
+this eigenvector when we conjugate the
+
+ align:start position:0%
+this eigenvector when we conjugate the
+ 
+
+ align:start position:0%
+this eigenvector when we conjugate the
+elements and dot the two vectors
+
+ align:start position:0%
+elements and dot the two vectors
+ 
+
+ align:start position:0%
+elements and dot the two vectors
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+so this is another very special property
+
+ align:start position:0%
+so this is another very special property
+ 
+
+ align:start position:0%
+so this is another very special property
+of complex hermitian matrices ok so the
+
+ align:start position:0%
+of complex hermitian matrices ok so the
+ 
+
+ align:start position:0%
+of complex hermitian matrices ok so the
+last step now is to construct these
+
+ align:start position:0%
+last step now is to construct these
+ 
+
+ align:start position:0%
+last step now is to construct these
+matrices lambda n s now we already know
+
+ align:start position:0%
+matrices lambda n s now we already know
+ 
+
+ align:start position:0%
+matrices lambda n s now we already know
+what lambda is because it's just the
+
+ align:start position:0%
+what lambda is because it's just the
+ 
+
+ align:start position:0%
+what lambda is because it's just the
+matrix it's the diagonal matrix with the
+
+ align:start position:0%
+matrix it's the diagonal matrix with the
+ 
+
+ align:start position:0%
+matrix it's the diagonal matrix with the
+eigenvalues 1 in 4 so we have 1 0 0 and
+
+ align:start position:0%
+eigenvalues 1 in 4 so we have 1 0 0 and
+ 
+
+ align:start position:0%
+eigenvalues 1 in 4 so we have 1 0 0 and
+for now I'm going to do something
+
+ align:start position:0%
+for now I'm going to do something
+ 
+
+ align:start position:0%
+for now I'm going to do something
+special for s I've noticed I've noted
+
+ align:start position:0%
+special for s I've noticed I've noted
+ 
+
+ align:start position:0%
+special for s I've noticed I've noted
+that these two vectors U and V are
+
+ align:start position:0%
+that these two vectors U and V are
+ 
+
+ align:start position:0%
+that these two vectors U and V are
+orthogonal to each other so what do I
+
+ align:start position:0%
+orthogonal to each other so what do I
+ 
+
+ align:start position:0%
+orthogonal to each other so what do I
+mean by orthogonal specifically if I
+
+ align:start position:0%
+mean by orthogonal specifically if I
+ 
+
+ align:start position:0%
+mean by orthogonal specifically if I
+were to take V conjugate transpose and
+
+ align:start position:0%
+were to take V conjugate transpose and
+ 
+
+ align:start position:0%
+were to take V conjugate transpose and
+multiply it by u we would end up getting
+
+ align:start position:0%
+multiply it by u we would end up getting
+ 
+
+ align:start position:0%
+multiply it by u we would end up getting
+1 plus I minus 1 this would be the
+
+ align:start position:0%
+1 plus I minus 1 this would be the
+ 
+
+ align:start position:0%
+1 plus I minus 1 this would be the
+conjugate transpose 1 1 plus I and we
+
+ align:start position:0%
+conjugate transpose 1 1 plus I and we
+ 
+
+ align:start position:0%
+conjugate transpose 1 1 plus I and we
+see that when we multiply these out we
+
+ align:start position:0%
+see that when we multiply these out we
+ 
+
+ align:start position:0%
+see that when we multiply these out we
+get 0 so when we have orthogonal eigen
+
+ align:start position:0%
+get 0 so when we have orthogonal eigen
+ 
+
+ align:start position:0%
+get 0 so when we have orthogonal eigen
+vectors there's a trick that we can do
+
+ align:start position:0%
+vectors there's a trick that we can do
+ 
+
+ align:start position:0%
+vectors there's a trick that we can do
+to build up this matrix s and s inverse
+
+ align:start position:0%
+to build up this matrix s and s inverse
+ 
+
+ align:start position:0%
+to build up this matrix s and s inverse
+what we can do is we can normalize U and
+
+ align:start position:0%
+what we can do is we can normalize U and
+ 
+
+ align:start position:0%
+what we can do is we can normalize U and
+V so specifically we can take any
+
+ align:start position:0%
+V so specifically we can take any
+ 
+
+ align:start position:0%
+V so specifically we can take any
+constant multiple of U and V and it's
+
+ align:start position:0%
+constant multiple of U and V and it's
+ 
+
+ align:start position:0%
+constant multiple of U and V and it's
+still going to be an eigen vector so
+
+ align:start position:0%
+still going to be an eigen vector so
+ 
+
+ align:start position:0%
+still going to be an eigen vector so
+what I'm going to do is I'm going to
+
+ align:start position:0%
+what I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+what I'm going to do is I'm going to
+take U and V and multiply them by their
+
+ align:start position:0%
+take U and V and multiply them by their
+ 
+
+ align:start position:0%
+take U and V and multiply them by their
+length so for example you
+
+ align:start position:0%
+length so for example you
+ 
+
+ align:start position:0%
+length so for example you
+the amplitude of its top component is 1
+
+ align:start position:0%
+the amplitude of its top component is 1
+ 
+
+ align:start position:0%
+the amplitude of its top component is 1
+the amplitude of its bottom component is
+
+ align:start position:0%
+the amplitude of its bottom component is
+ 
+
+ align:start position:0%
+the amplitude of its bottom component is
+2 so notice that the modulus of the
+
+ align:start position:0%
+2 so notice that the modulus of the
+ 
+
+ align:start position:0%
+2 so notice that the modulus of the
+complex number 1 + I is 2 so we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry it's it's root to the complex
+
+ align:start position:0%
+sorry it's it's root to the complex
+ 
+
+ align:start position:0%
+sorry it's it's root to the complex
+modulus is root 2 so the amplitude of
+
+ align:start position:0%
+modulus is root 2 so the amplitude of
+ 
+
+ align:start position:0%
+modulus is root 2 so the amplitude of
+the entire vector is root 3 it's 1 plus
+
+ align:start position:0%
+the entire vector is root 3 it's 1 plus
+ 
+
+ align:start position:0%
+the entire vector is root 3 it's 1 plus
+2 squared quantity square rooting so
+
+ align:start position:0%
+2 squared quantity square rooting so
+ 
+
+ align:start position:0%
+2 squared quantity square rooting so
+it's root 3 so what we can do is we can
+
+ align:start position:0%
+it's root 3 so what we can do is we can
+ 
+
+ align:start position:0%
+it's root 3 so what we can do is we can
+build up this matrix s using a
+
+ align:start position:0%
+build up this matrix s using a
+ 
+
+ align:start position:0%
+build up this matrix s using a
+normalization factor of 1 over root 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to take the the first
+
+ align:start position:0%
+and I'm going to take the the first
+ 
+
+ align:start position:0%
+and I'm going to take the the first
+column is the first eigenvector that
+
+ align:start position:0%
+column is the first eigenvector that
+ 
+
+ align:start position:0%
+column is the first eigenvector that
+corresponds to eigenvalue 1 and then the
+
+ align:start position:0%
+corresponds to eigenvalue 1 and then the
+ 
+
+ align:start position:0%
+corresponds to eigenvalue 1 and then the
+second column is the second eigen vector
+
+ align:start position:0%
+second column is the second eigen vector
+ 
+
+ align:start position:0%
+second column is the second eigen vector
+which corresponds to eigenvalue 4 and
+
+ align:start position:0%
+which corresponds to eigenvalue 4 and
+ 
+
+ align:start position:0%
+which corresponds to eigenvalue 4 and
+the reason I've put in this root 3 here
+
+ align:start position:0%
+the reason I've put in this root 3 here
+ 
+
+ align:start position:0%
+the reason I've put in this root 3 here
+is to make this column unit length 1 and
+
+ align:start position:0%
+is to make this column unit length 1 and
+ 
+
+ align:start position:0%
+is to make this column unit length 1 and
+this column unit length 1 and the reason
+
+ align:start position:0%
+this column unit length 1 and the reason
+ 
+
+ align:start position:0%
+this column unit length 1 and the reason
+I do this is because now this matrix S
+
+ align:start position:0%
+I do this is because now this matrix S
+ 
+
+ align:start position:0%
+I do this is because now this matrix S
+it's it's it's possible to check that
+
+ align:start position:0%
+it's it's it's possible to check that
+ 
+
+ align:start position:0%
+it's it's it's possible to check that
+this matrix S is actually unitary which
+
+ align:start position:0%
+this matrix S is actually unitary which
+ 
+
+ align:start position:0%
+this matrix S is actually unitary which
+means that its inverse is actually just
+
+ align:start position:0%
+means that its inverse is actually just
+ 
+
+ align:start position:0%
+means that its inverse is actually just
+equal to its conjugate transpose so this
+
+ align:start position:0%
+equal to its conjugate transpose so this
+ 
+
+ align:start position:0%
+equal to its conjugate transpose so this
+is a very special property of the of the
+
+ align:start position:0%
+is a very special property of the of the
+ 
+
+ align:start position:0%
+is a very special property of the of the
+eigenvectors of a hermitian matrix ok
+
+ align:start position:0%
+eigenvectors of a hermitian matrix ok
+ 
+
+ align:start position:0%
+eigenvectors of a hermitian matrix ok
+and then lastly I'm just going to write
+
+ align:start position:0%
+and then lastly I'm just going to write
+ 
+
+ align:start position:0%
+and then lastly I'm just going to write
+down the diagonalization of a so if I
+
+ align:start position:0%
+down the diagonalization of a so if I
+ 
+
+ align:start position:0%
+down the diagonalization of a so if I
+have a because I have its eigenvector
+
+ align:start position:0%
+have a because I have its eigenvector
+ 
+
+ align:start position:0%
+have a because I have its eigenvector
+matrix s and its eigenvalue matrix
+
+ align:start position:0%
+matrix s and its eigenvalue matrix
+ 
+
+ align:start position:0%
+matrix s and its eigenvalue matrix
+lambda it's possible to decompose a into
+
+ align:start position:0%
+lambda it's possible to decompose a into
+ 
+
+ align:start position:0%
+lambda it's possible to decompose a into
+a product of s lambda s inverse and
+
+ align:start position:0%
+a product of s lambda s inverse and
+ 
+
+ align:start position:0%
+a product of s lambda s inverse and
+because s is for me or s is unitary its
+
+ align:start position:0%
+because s is for me or s is unitary its
+ 
+
+ align:start position:0%
+because s is for me or s is unitary its
+inverse is actually its conjugate
+
+ align:start position:0%
+inverse is actually its conjugate
+ 
+
+ align:start position:0%
+inverse is actually its conjugate
+transpose so just to put the pieces
+
+ align:start position:0%
+transpose so just to put the pieces
+ 
+
+ align:start position:0%
+transpose so just to put the pieces
+together we
+
+ align:start position:0%
+together we
+ 
+
+ align:start position:0%
+together we
+a is equal to s which is 1 over root 3 1
+
+ align:start position:0%
+a is equal to s which is 1 over root 3 1
+ 
+
+ align:start position:0%
+a is equal to s which is 1 over root 3 1
+minus I minus 1 1 1 plus I times the
+
+ align:start position:0%
+minus I minus 1 1 1 plus I times the
+ 
+
+ align:start position:0%
+minus I minus 1 1 1 plus I times the
+diagonal matrix 1 0 0 4 times s inverse
+
+ align:start position:0%
+diagonal matrix 1 0 0 4 times s inverse
+ 
+
+ align:start position:0%
+diagonal matrix 1 0 0 4 times s inverse
+which is going to be its conjugate
+
+ align:start position:0%
+which is going to be its conjugate
+ 
+
+ align:start position:0%
+which is going to be its conjugate
+transpose so what I do is I conjugate
+
+ align:start position:0%
+transpose so what I do is I conjugate
+ 
+
+ align:start position:0%
+transpose so what I do is I conjugate
+each element so 1 minus I becomes 1 plus
+
+ align:start position:0%
+each element so 1 minus I becomes 1 plus
+ 
+
+ align:start position:0%
+each element so 1 minus I becomes 1 plus
+I and vice versa and then I take the
+
+ align:start position:0%
+I and vice versa and then I take the
+ 
+
+ align:start position:0%
+I and vice versa and then I take the
+transpose so I get 1 plus I transposing
+
+ align:start position:0%
+transpose so I get 1 plus I transposing
+ 
+
+ align:start position:0%
+transpose so I get 1 plus I transposing
+swaps the minus 1 and 1 and at the end
+
+ align:start position:0%
+swaps the minus 1 and 1 and at the end
+ 
+
+ align:start position:0%
+swaps the minus 1 and 1 and at the end
+of the day I get s inverse is just this
+
+ align:start position:0%
+of the day I get s inverse is just this
+ 
+
+ align:start position:0%
+of the day I get s inverse is just this
+matrix here ok
+
+ align:start position:0%
+matrix here ok
+ 
+
+ align:start position:0%
+matrix here ok
+and if you were to multiply these
+
+ align:start position:0%
+and if you were to multiply these
+ 
+
+ align:start position:0%
+and if you were to multiply these
+matrices out you would see that you
+
+ align:start position:0%
+matrices out you would see that you
+ 
+
+ align:start position:0%
+matrices out you would see that you
+actually do recover a ok so just to
+
+ align:start position:0%
+actually do recover a ok so just to
+ 
+
+ align:start position:0%
+actually do recover a ok so just to
+summarize quickly even though we were
+
+ align:start position:0%
+summarize quickly even though we were
+ 
+
+ align:start position:0%
+summarize quickly even though we were
+given a complex matrix a the the process
+
+ align:start position:0%
+given a complex matrix a the the process
+ 
+
+ align:start position:0%
+given a complex matrix a the the process
+to diagonalize a was this is the same as
+
+ align:start position:0%
+to diagonalize a was this is the same as
+ 
+
+ align:start position:0%
+to diagonalize a was this is the same as
+what we've seen before the first step is
+
+ align:start position:0%
+what we've seen before the first step is
+ 
+
+ align:start position:0%
+what we've seen before the first step is
+to find the characteristic equation and
+
+ align:start position:0%
+to find the characteristic equation and
+ 
+
+ align:start position:0%
+to find the characteristic equation and
+the eigenvalues and then the second step
+
+ align:start position:0%
+the eigenvalues and then the second step
+ 
+
+ align:start position:0%
+the eigenvalues and then the second step
+is to find the eigenvectors and you do
+
+ align:start position:0%
+is to find the eigenvectors and you do
+ 
+
+ align:start position:0%
+is to find the eigenvectors and you do
+this in the same procedure but in
+
+ align:start position:0%
+this in the same procedure but in
+ 
+
+ align:start position:0%
+this in the same procedure but in
+general the eigenvectors can be complex
+
+ align:start position:0%
+general the eigenvectors can be complex
+ 
+
+ align:start position:0%
+general the eigenvectors can be complex
+and for this very special case when a is
+
+ align:start position:0%
+and for this very special case when a is
+ 
+
+ align:start position:0%
+and for this very special case when a is
+hermitian the eigenvalues are real and
+
+ align:start position:0%
+hermitian the eigenvalues are real and
+ 
+
+ align:start position:0%
+hermitian the eigenvalues are real and
+the eigenvectors are orthogonal to each
+
+ align:start position:0%
+the eigenvectors are orthogonal to each
+ 
+
+ align:start position:0%
+the eigenvectors are orthogonal to each
+other ok so I think I'll conclude here
+
+ align:start position:0%
+other ok so I think I'll conclude here
+ 
+
+ align:start position:0%
+other ok so I think I'll conclude here
+and I'll see you next time
\ No newline at end of file
diff --git a/VqXKa11IA6A.txt b/VqXKa11IA6A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0d7578995387d15aecb5e2ee049902b2d6271340
--- /dev/null
+++ b/VqXKa11IA6A.txt
@@ -0,0 +1,2531 @@
+align:start position:0%
+ 
+okay uh this is the second video for
+
+ align:start position:0%
+okay uh this is the second video for
+ 
+
+ align:start position:0%
+okay uh this is the second video for
+chapter three and it's going to be
+
+ align:start position:0%
+chapter three and it's going to be
+ 
+
+ align:start position:0%
+chapter three and it's going to be
+pictures again but it's pictures for a
+
+ align:start position:0%
+pictures again but it's pictures for a
+ 
+
+ align:start position:0%
+pictures again but it's pictures for a
+second order
+
+ align:start position:0%
+second order
+ 
+
+ align:start position:0%
+second order
+equation uh and in and I'll make them
+
+ align:start position:0%
+equation uh and in and I'll make them
+ 
+
+ align:start position:0%
+equation uh and in and I'll make them
+these will be nice we'll know formulas
+
+ align:start position:0%
+these will be nice we'll know formulas
+ 
+
+ align:start position:0%
+these will be nice we'll know formulas
+here these will be constant coefficient
+
+ align:start position:0%
+here these will be constant coefficient
+ 
+
+ align:start position:0%
+here these will be constant coefficient
+linear second order equations and we
+
+ align:start position:0%
+linear second order equations and we
+ 
+
+ align:start position:0%
+linear second order equations and we
+know that the solution there are
+
+ align:start position:0%
+know that the solution there are
+ 
+
+ align:start position:0%
+know that the solution there are
+two uh special Solutions e to the s 1 T
+
+ align:start position:0%
+two uh special Solutions e to the s 1 T
+ 
+
+ align:start position:0%
+two uh special Solutions e to the s 1 T
+and e to the s2t two null Solutions and
+
+ align:start position:0%
+and e to the s2t two null Solutions and
+ 
+
+ align:start position:0%
+and e to the s2t two null Solutions and
+any combination is a null solution so
+
+ align:start position:0%
+any combination is a null solution so
+ 
+
+ align:start position:0%
+any combination is a null solution so
+we're talking about null equations zero
+
+ align:start position:0%
+we're talking about null equations zero
+ 
+
+ align:start position:0%
+we're talking about null equations zero
+on the right hand side and we just want
+
+ align:start position:0%
+on the right hand side and we just want
+ 
+
+ align:start position:0%
+on the right hand side and we just want
+to draw that picture that goes with
+
+ align:start position:0%
+to draw that picture that goes with
+ 
+
+ align:start position:0%
+to draw that picture that goes with
+Solutions like that so the here is the
+
+ align:start position:0%
+Solutions like that so the here is the
+ 
+
+ align:start position:0%
+Solutions like that so the here is the
+magic word phase
+
+ align:start position:0%
+magic word phase
+ 
+
+ align:start position:0%
+magic word phase
+plane phase plane we're going to draw
+
+ align:start position:0%
+plane phase plane we're going to draw
+ 
+
+ align:start position:0%
+plane phase plane we're going to draw
+the pictures in a plane because that's
+
+ align:start position:0%
+the pictures in a plane because that's
+ 
+
+ align:start position:0%
+the pictures in a plane because that's
+what I'm Blackboard is and the axes we
+
+ align:start position:0%
+what I'm Blackboard is and the axes we
+ 
+
+ align:start position:0%
+what I'm Blackboard is and the axes we
+choose will be Y and Y Prime not
+
+ align:start position:0%
+choose will be Y and Y Prime not
+ 
+
+ align:start position:0%
+choose will be Y and Y Prime not
+t you'll see how T time comes into the
+
+ align:start position:0%
+t you'll see how T time comes into the
+ 
+
+ align:start position:0%
+t you'll see how T time comes into the
+picture but we have the two axes will be
+
+ align:start position:0%
+picture but we have the two axes will be
+ 
+
+ align:start position:0%
+picture but we have the two axes will be
+Y and Y Prime so I had to figure out
+
+ align:start position:0%
+Y and Y Prime so I had to figure out
+ 
+
+ align:start position:0%
+Y and Y Prime so I had to figure out
+what y Prime was it just brings down an
+
+ align:start position:0%
+what y Prime was it just brings down an
+ 
+
+ align:start position:0%
+what y Prime was it just brings down an
+S1 from that term and brings down an S2
+
+ align:start position:0%
+S1 from that term and brings down an S2
+ 
+
+ align:start position:0%
+S1 from that term and brings down an S2
+from that term and now here's the
+
+ align:start position:0%
+from that term and now here's the
+ 
+
+ align:start position:0%
+from that term and now here's the
+example here's the first
+
+ align:start position:0%
+example here's the first
+ 
+
+ align:start position:0%
+example here's the first
+example uh so I made this took this
+
+ align:start position:0%
+example uh so I made this took this
+ 
+
+ align:start position:0%
+example uh so I made this took this
+particular equation notice that the uh
+
+ align:start position:0%
+particular equation notice that the uh
+ 
+
+ align:start position:0%
+particular equation notice that the uh
+damping term is negative I have negative
+
+ align:start position:0%
+damping term is negative I have negative
+ 
+
+ align:start position:0%
+damping term is negative I have negative
+damping this will be unstable Solutions
+
+ align:start position:0%
+damping this will be unstable Solutions
+ 
+
+ align:start position:0%
+damping this will be unstable Solutions
+will go out to infinity and I can find
+
+ align:start position:0%
+will go out to infinity and I can find
+ 
+
+ align:start position:0%
+will go out to infinity and I can find
+those Solutions because you know that I
+
+ align:start position:0%
+those Solutions because you know that I
+ 
+
+ align:start position:0%
+those Solutions because you know that I
+look for e to the St I always look for e
+
+ align:start position:0%
+look for e to the St I always look for e
+ 
+
+ align:start position:0%
+look for e to the St I always look for e
+to the St I plug in e to the St I get an
+
+ align:start position:0%
+to the St I plug in e to the St I get an
+ 
+
+ align:start position:0%
+to the St I plug in e to the St I get an
+s squar from two derivatives - 3S from
+
+ align:start position:0%
+s squar from two derivatives - 3S from
+ 
+
+ align:start position:0%
+s squar from two derivatives - 3S from
+one derivative + 2 equaling 0 I factor
+
+ align:start position:0%
+one derivative + 2 equaling 0 I factor
+ 
+
+ align:start position:0%
+one derivative + 2 equaling 0 I factor
+that and I find the two S1 is one and S2
+
+ align:start position:0%
+that and I find the two S1 is one and S2
+ 
+
+ align:start position:0%
+that and I find the two S1 is one and S2
+is two and now I'm ready for the phase
+
+ align:start position:0%
+is two and now I'm ready for the phase
+ 
+
+ align:start position:0%
+is two and now I'm ready for the phase
+plane picture Okay phase plane
+
+ align:start position:0%
+plane picture Okay phase plane
+ 
+
+ align:start position:0%
+plane picture Okay phase plane
+picture so here are my Solutions s is
+
+ align:start position:0%
+picture so here are my Solutions s is
+ 
+
+ align:start position:0%
+picture so here are my Solutions s is
+one or two then the derivative has a one
+
+ align:start position:0%
+one or two then the derivative has a one
+ 
+
+ align:start position:0%
+one or two then the derivative has a one
+or a two and here's my plane here's my
+
+ align:start position:0%
+or a two and here's my plane here's my
+ 
+
+ align:start position:0%
+or a two and here's my plane here's my
+plane and I want to draw on that the
+
+ align:start position:0%
+plane and I want to draw on that the
+ 
+
+ align:start position:0%
+plane and I want to draw on that the
+solutions these Solutions I actually
+
+ align:start position:0%
+solutions these Solutions I actually
+ 
+
+ align:start position:0%
+solutions these Solutions I actually
+have formulas I just want to draw them
+
+ align:start position:0%
+have formulas I just want to draw them
+ 
+
+ align:start position:0%
+have formulas I just want to draw them
+so I'm plotting the one example would be
+
+ align:start position:0%
+so I'm plotting the one example would be
+ 
+
+ align:start position:0%
+so I'm plotting the one example would be
+let C1 be one and let C2 be zero so
+
+ align:start position:0%
+let C1 be one and let C2 be zero so
+ 
+
+ align:start position:0%
+let C1 be one and let C2 be zero so
+that's gone C1 is one I I just have that
+
+ align:start position:0%
+that's gone C1 is one I I just have that
+ 
+
+ align:start position:0%
+that's gone C1 is one I I just have that
+picture what kind of a picture do I have
+
+ align:start position:0%
+picture what kind of a picture do I have
+ 
+
+ align:start position:0%
+picture what kind of a picture do I have
+in the phase plane in the y y Prime
+
+ align:start position:0%
+in the phase plane in the y y Prime
+ 
+
+ align:start position:0%
+in the phase plane in the y y Prime
+plane when that's Y and that's y Prime
+
+ align:start position:0%
+plane when that's Y and that's y Prime
+ 
+
+ align:start position:0%
+plane when that's Y and that's y Prime
+well those are
+
+ align:start position:0%
+well those are
+ 
+
+ align:start position:0%
+well those are
+equal so y equals y y Prime for that
+
+ align:start position:0%
+equal so y equals y y Prime for that
+ 
+
+ align:start position:0%
+equal so y equals y y Prime for that
+solution y = y Prime along the 45° line
+
+ align:start position:0%
+solution y = y Prime along the 45° line
+ 
+
+ align:start position:0%
+solution y = y Prime along the 45° line
+it's just like yal x y y Prime is y and
+
+ align:start position:0%
+it's just like yal x y y Prime is y and
+ 
+
+ align:start position:0%
+it's just like yal x y y Prime is y and
+what's happening on this 45 Dee line the
+
+ align:start position:0%
+what's happening on this 45 Dee line the
+ 
+
+ align:start position:0%
+what's happening on this 45 Dee line the
+solution is this
+
+ align:start position:0%
+solution is this
+ 
+
+ align:start position:0%
+solution is this
+solution is going straight out the line
+
+ align:start position:0%
+solution is going straight out the line
+ 
+
+ align:start position:0%
+solution is going straight out the line
+as T increases Y and Y Prime both
+
+ align:start position:0%
+as T increases Y and Y Prime both
+ 
+
+ align:start position:0%
+as T increases Y and Y Prime both
+increase I go out to so as T this is T
+
+ align:start position:0%
+increase I go out to so as T this is T
+ 
+
+ align:start position:0%
+increase I go out to so as T this is T
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity and what about t going to minus
+
+ align:start position:0%
+infinity and what about t going to minus
+ 
+
+ align:start position:0%
+infinity and what about t going to minus
+infinity cuz we got the whole picture
+
+ align:start position:0%
+infinity cuz we got the whole picture
+ 
+
+ align:start position:0%
+infinity cuz we got the whole picture
+here when T goes to minus infinity that
+
+ align:start position:0%
+here when T goes to minus infinity that
+ 
+
+ align:start position:0%
+here when T goes to minus infinity that
+goes to zero that goes to zero here
+
+ align:start position:0%
+goes to zero that goes to zero here
+ 
+
+ align:start position:0%
+goes to zero that goes to zero here
+here's the point
+
+ align:start position:0%
+here's the point
+ 
+
+ align:start position:0%
+here's the point
+where where the universe began the Big
+
+ align:start position:0%
+where where the universe began the Big
+ 
+
+ align:start position:0%
+where where the universe began the Big
+Bang is right there at t equal minus
+
+ align:start position:0%
+Bang is right there at t equal minus
+ 
+
+ align:start position:0%
+Bang is right there at t equal minus
+infinity and as T
+
+ align:start position:0%
+infinity and as T
+ 
+
+ align:start position:0%
+infinity and as T
+increases this these this point y y
+
+ align:start position:0%
+increases this these this point y y
+ 
+
+ align:start position:0%
+increases this these this point y y
+Prime is is traveling along that 45°
+
+ align:start position:0%
+Prime is is traveling along that 45°
+ 
+
+ align:start position:0%
+Prime is is traveling along that 45°
+line because y equals y Prime and out
+
+ align:start position:0%
+line because y equals y Prime and out
+ 
+
+ align:start position:0%
+line because y equals y Prime and out
+there and what about the rest of the
+
+ align:start position:0%
+there and what about the rest of the
+ 
+
+ align:start position:0%
+there and what about the rest of the
+line well if if I if C1 was negative if
+
+ align:start position:0%
+line well if if I if C1 was negative if
+ 
+
+ align:start position:0%
+line well if if I if C1 was negative if
+C1 was negative I'd have a minus there
+
+ align:start position:0%
+C1 was negative I'd have a minus there
+ 
+
+ align:start position:0%
+C1 was negative I'd have a minus there
+and a minus there I would just have
+
+ align:start position:0%
+and a minus there I would just have
+ 
+
+ align:start position:0%
+and a minus there I would just have
+minuses and I'd be going out that
+
+ align:start position:0%
+minuses and I'd be going out that
+ 
+
+ align:start position:0%
+minuses and I'd be going out that
+line well that's one line in my whole
+
+ align:start position:0%
+line well that's one line in my whole
+ 
+
+ align:start position:0%
+line well that's one line in my whole
+plane but not all now let me take as a
+
+ align:start position:0%
+plane but not all now let me take as a
+ 
+
+ align:start position:0%
+plane but not all now let me take as a
+second line uh C1 equals z so nothing
+
+ align:start position:0%
+second line uh C1 equals z so nothing
+ 
+
+ align:start position:0%
+second line uh C1 equals z so nothing
+from e to the T and let me take y1 as y
+
+ align:start position:0%
+from e to the T and let me take y1 as y
+ 
+
+ align:start position:0%
+from e to the T and let me take y1 as y
+as e to the 2T and Y Prime then would be
+
+ align:start position:0%
+as e to the 2T and Y Prime then would be
+ 
+
+ align:start position:0%
+as e to the 2T and Y Prime then would be
+2 e to
+
+ align:start position:0%
+2 e to
+ 
+
+ align:start position:0%
+2 e to
+2T okay what's happening in the phase
+
+ align:start position:0%
+2T okay what's happening in the phase
+ 
+
+ align:start position:0%
+2T okay what's happening in the phase
+plane for this solution now looking at
+
+ align:start position:0%
+plane for this solution now looking at
+ 
+
+ align:start position:0%
+plane for this solution now looking at
+this one well along in this solution in
+
+ align:start position:0%
+this one well along in this solution in
+ 
+
+ align:start position:0%
+this one well along in this solution in
+this case y Prime is 2 * y y Prime is 2
+
+ align:start position:0%
+this case y Prime is 2 * y y Prime is 2
+ 
+
+ align:start position:0%
+this case y Prime is 2 * y y Prime is 2
+* y so I'm staying on the line Y Prime
+
+ align:start position:0%
+* y so I'm staying on the line Y Prime
+ 
+
+ align:start position:0%
+* y so I'm staying on the line Y Prime
+where y Prime is 2 * y it's a steeper
+
+ align:start position:0%
+where y Prime is 2 * y it's a steeper
+ 
+
+ align:start position:0%
+where y Prime is 2 * y it's a steeper
+line steeper
+
+ align:start position:0%
+line steeper
+ 
+
+ align:start position:0%
+line steeper
+Line This is the case so that was the
+
+ align:start position:0%
+Line This is the case so that was the
+ 
+
+ align:start position:0%
+Line This is the case so that was the
+case this was the line where C2 was Zero
+
+ align:start position:0%
+case this was the line where C2 was Zero
+ 
+
+ align:start position:0%
+case this was the line where C2 was Zero
+there was no e to the 2T on that first
+
+ align:start position:0%
+there was no e to the 2T on that first
+ 
+
+ align:start position:0%
+there was no e to the 2T on that first
+line that we
+
+ align:start position:0%
+line that we
+ 
+
+ align:start position:0%
+line that we
+drew and the second line that we drew
+
+ align:start position:0%
+drew and the second line that we drew
+ 
+
+ align:start position:0%
+drew and the second line that we drew
+C1 is zero there's no e to the T
+
+ align:start position:0%
+C1 is zero there's no e to the T
+ 
+
+ align:start position:0%
+C1 is zero there's no e to the T
+everything is in e to the 2T so now C1
+
+ align:start position:0%
+everything is in e to the 2T so now C1
+ 
+
+ align:start position:0%
+everything is in e to the 2T so now C1
+is zero on this line okay and we just go
+
+ align:start position:0%
+is zero on this line okay and we just go
+ 
+
+ align:start position:0%
+is zero on this line okay and we just go
+out it as T increases y Prime increases
+
+ align:start position:0%
+out it as T increases y Prime increases
+ 
+
+ align:start position:0%
+out it as T increases y Prime increases
+faster because of the factor two so it
+
+ align:start position:0%
+faster because of the factor two so it
+ 
+
+ align:start position:0%
+faster because of the factor two so it
+goes up steeply and it goes this way
+
+ align:start position:0%
+goes up steeply and it goes this way
+ 
+
+ align:start position:0%
+goes up steeply and it goes this way
+when T is negative going to oh no or
+
+ align:start position:0%
+when T is negative going to oh no or
+ 
+
+ align:start position:0%
+when T is negative going to oh no or
+when sorry when C2 is negative if I if
+
+ align:start position:0%
+when sorry when C2 is negative if I if
+ 
+
+ align:start position:0%
+when sorry when C2 is negative if I if
+if I took a minus and a minus I would
+
+ align:start position:0%
+if I took a minus and a minus I would
+ 
+
+ align:start position:0%
+if I took a minus and a minus I would
+just go down uh the other way on the
+
+ align:start position:0%
+just go down uh the other way on the
+ 
+
+ align:start position:0%
+just go down uh the other way on the
+same line and this is still the Big
+
+ align:start position:0%
+same line and this is still the Big
+ 
+
+ align:start position:0%
+same line and this is still the Big
+Bang t equal minus infinity where
+
+ align:start position:0%
+Bang t equal minus infinity where
+ 
+
+ align:start position:0%
+Bang t equal minus infinity where
+everything starts okay so that is two
+
+ align:start position:0%
+everything starts okay so that is two
+ 
+
+ align:start position:0%
+everything starts okay so that is two
+lines two very the two special lines in
+
+ align:start position:0%
+lines two very the two special lines in
+ 
+
+ align:start position:0%
+lines two very the two special lines in
+the phase plane but now I have to draw
+
+ align:start position:0%
+the phase plane but now I have to draw
+ 
+
+ align:start position:0%
+the phase plane but now I have to draw
+all the other curves and they will be
+
+ align:start position:0%
+all the other curves and they will be
+ 
+
+ align:start position:0%
+all the other curves and they will be
+curves and where will they come from
+
+ align:start position:0%
+curves and where will they come from
+ 
+
+ align:start position:0%
+curves and where will they come from
+they will come from a combination
+
+ align:start position:0%
+they will come from a combination
+ 
+
+ align:start position:0%
+they will come from a combination
+now so now I'm ready for that one let me
+
+ align:start position:0%
+now so now I'm ready for that one let me
+ 
+
+ align:start position:0%
+now so now I'm ready for that one let me
+take the case C1 equal 1 C2 equal 1 yeah
+
+ align:start position:0%
+take the case C1 equal 1 C2 equal 1 yeah
+ 
+
+ align:start position:0%
+take the case C1 equal 1 C2 equal 1 yeah
+why not C1 equal 1 so I can erase
+
+ align:start position:0%
+why not C1 equal 1 so I can erase
+ 
+
+ align:start position:0%
+why not C1 equal 1 so I can erase
+C1 C2 equal 1 I can erase
+
+ align:start position:0%
+C1 C2 equal 1 I can erase
+ 
+
+ align:start position:0%
+C1 C2 equal 1 I can erase
+C2 and now I have another solution Y and
+
+ align:start position:0%
+C2 and now I have another solution Y and
+ 
+
+ align:start position:0%
+C2 and now I have another solution Y and
+Y Prime and I want to put it in the
+
+ align:start position:0%
+Y Prime and I want to put it in the
+ 
+
+ align:start position:0%
+Y Prime and I want to put it in the
+phase plane so at every value of t
+
+ align:start position:0%
+phase plane so at every value of t
+ 
+
+ align:start position:0%
+phase plane so at every value of t
+at every value of T that's a point
+
+ align:start position:0%
+at every value of T that's a point
+ 
+
+ align:start position:0%
+at every value of T that's a point
+that's a value of y this is a value of y
+
+ align:start position:0%
+that's a value of y this is a value of y
+ 
+
+ align:start position:0%
+that's a value of y this is a value of y
+Prime I plot the points Y and Y Prime
+
+ align:start position:0%
+Prime I plot the points Y and Y Prime
+ 
+
+ align:start position:0%
+Prime I plot the points Y and Y Prime
+and I look at the picture and again as T
+
+ align:start position:0%
+and I look at the picture and again as T
+ 
+
+ align:start position:0%
+and I look at the picture and again as T
+changes as T changes I'll travel along
+
+ align:start position:0%
+changes as T changes I'll travel along
+ 
+
+ align:start position:0%
+changes as T changes I'll travel along
+the solution curve in the phase plane
+
+ align:start position:0%
+the solution curve in the phase plane
+ 
+
+ align:start position:0%
+the solution curve in the phase plane
+I'll travel along as T changes y will
+
+ align:start position:0%
+I'll travel along as T changes y will
+ 
+
+ align:start position:0%
+I'll travel along as T changes y will
+grow y Prime will grow I'll head out
+
+ align:start position:0%
+grow y Prime will grow I'll head out
+ 
+
+ align:start position:0%
+grow y Prime will grow I'll head out
+here but I won't be on that straight
+
+ align:start position:0%
+here but I won't be on that straight
+ 
+
+ align:start position:0%
+here but I won't be on that straight
+line or that straight line because those
+
+ align:start position:0%
+line or that straight line because those
+ 
+
+ align:start position:0%
+line or that straight line because those
+were the cases when I had only one of
+
+ align:start position:0%
+were the cases when I had only one of
+ 
+
+ align:start position:0%
+were the cases when I had only one of
+the two solutions these were the special
+
+ align:start position:0%
+the two solutions these were the special
+ 
+
+ align:start position:0%
+the two solutions these were the special
+Solutions and now I have a com
+
+ align:start position:0%
+Solutions and now I have a com
+ 
+
+ align:start position:0%
+Solutions and now I have a com
+combination so what happens as T goes to
+
+ align:start position:0%
+combination so what happens as T goes to
+ 
+
+ align:start position:0%
+combination so what happens as T goes to
+Infinity as T goes to Infinity this
+
+ align:start position:0%
+Infinity as T goes to Infinity this
+ 
+
+ align:start position:0%
+Infinity as T goes to Infinity this
+wins as as T goes to
+
+ align:start position:0%
+wins as as T goes to
+ 
+
+ align:start position:0%
+wins as as T goes to
+Infinity the e to the 2T is bigger than
+
+ align:start position:0%
+Infinity the e to the 2T is bigger than
+ 
+
+ align:start position:0%
+Infinity the e to the 2T is bigger than
+e to the T so this is the larger term so
+
+ align:start position:0%
+e to the T so this is the larger term so
+ 
+
+ align:start position:0%
+e to the T so this is the larger term so
+it it approaches this curve now will
+
+ align:start position:0%
+it it approaches this curve now will
+ 
+
+ align:start position:0%
+it it approaches this curve now will
+approach closer and closer to the one
+
+ align:start position:0%
+approach closer and closer to the one
+ 
+
+ align:start position:0%
+approach closer and closer to the one
+when the the the line with slope two the
+
+ align:start position:0%
+when the the the line with slope two the
+ 
+
+ align:start position:0%
+when the the the line with slope two the
+two will be the winner out here but at
+
+ align:start position:0%
+two will be the winner out here but at
+ 
+
+ align:start position:0%
+two will be the winner out here but at
+tal minus infinity near the Big Bang at
+
+ align:start position:0%
+tal minus infinity near the Big Bang at
+ 
+
+ align:start position:0%
+tal minus infinity near the Big Bang at
+tal minus infinity e to the 2T is even
+
+ align:start position:0%
+tal minus infinity e to the 2T is even
+ 
+
+ align:start position:0%
+tal minus infinity e to the 2T is even
+more small so at tal minus infinity
+
+ align:start position:0%
+more small so at tal minus infinity
+ 
+
+ align:start position:0%
+more small so at tal minus infinity
+or tal minus 10 let's say this is eus 10
+
+ align:start position:0%
+or tal minus 10 let's say this is eus 10
+ 
+
+ align:start position:0%
+or tal minus 10 let's say this is eus 10
+this would be eus 20 very very very
+
+ align:start position:0%
+this would be eus 20 very very very
+ 
+
+ align:start position:0%
+this would be eus 20 very very very
+small these would win so what happens
+
+ align:start position:0%
+small these would win so what happens
+ 
+
+ align:start position:0%
+small these would win so what happens
+for this solution is it starts out along
+
+ align:start position:0%
+for this solution is it starts out along
+ 
+
+ align:start position:0%
+for this solution is it starts out along
+the the the line given by the the not so
+
+ align:start position:0%
+the the the line given by the the not so
+ 
+
+ align:start position:0%
+the the the line given by the the not so
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+T the not so small exponent it starts up
+
+ align:start position:0%
+T the not so small exponent it starts up
+ 
+
+ align:start position:0%
+T the not so small exponent it starts up
+that line but T is increasing as T when
+
+ align:start position:0%
+that line but T is increasing as T when
+ 
+
+ align:start position:0%
+that line but T is increasing as T when
+T passes some point this 2T will be
+
+ align:start position:0%
+T passes some point this 2T will be
+ 
+
+ align:start position:0%
+T passes some point this 2T will be
+bigger than T and uh uh it will I guess
+
+ align:start position:0%
+bigger than T and uh uh it will I guess
+ 
+
+ align:start position:0%
+bigger than T and uh uh it will I guess
+T at T equals zero 2T will be bigger
+
+ align:start position:0%
+T at T equals zero 2T will be bigger
+ 
+
+ align:start position:0%
+T at T equals zero 2T will be bigger
+than T and from that point on from the T
+
+ align:start position:0%
+than T and from that point on from the T
+ 
+
+ align:start position:0%
+than T and from that point on from the T
+equals z point oh I could even plot that
+
+ align:start position:0%
+equals z point oh I could even plot that
+ 
+
+ align:start position:0%
+equals z point oh I could even plot that
+t equals z so at t equal 0 Y is 2 and Y
+
+ align:start position:0%
+t equals z so at t equal 0 Y is 2 and Y
+ 
+
+ align:start position:0%
+t equals z so at t equal 0 Y is 2 and Y
+Prime is 3 so 1 two one two 3 somewhere
+
+ align:start position:0%
+Prime is 3 so 1 two one two 3 somewhere
+ 
+
+ align:start position:0%
+Prime is 3 so 1 two one two 3 somewhere
+in there is so you see it the the curve
+
+ align:start position:0%
+in there is so you see it the the curve
+ 
+
+ align:start position:0%
+in there is so you see it the the curve
+starts
+
+ align:start position:0%
+starts
+ 
+
+ align:start position:0%
+starts
+up along the line
+
+ align:start position:0%
+up along the line
+ 
+
+ align:start position:0%
+up along the line
+where where e to the t is
+
+ align:start position:0%
+where where e to the t is
+ 
+
+ align:start position:0%
+where where e to the t is
+bigger they they have the same size at T
+
+ align:start position:0%
+bigger they they have the same size at T
+ 
+
+ align:start position:0%
+bigger they they have the same size at T
+equals 0 both equal one this is at T
+
+ align:start position:0%
+equals 0 both equal one this is at T
+ 
+
+ align:start position:0%
+equals 0 both equal one this is at T
+equals 0 and
+
+ align:start position:0%
+equals 0 and
+ 
+
+ align:start position:0%
+equals 0 and
+then the for large times this one wins
+
+ align:start position:0%
+then the for large times this one wins
+ 
+
+ align:start position:0%
+then the for large times this one wins
+so I approach that line I don't know if
+
+ align:start position:0%
+so I approach that line I don't know if
+ 
+
+ align:start position:0%
+so I approach that line I don't know if
+you can see that curve I I and I don't
+
+ align:start position:0%
+you can see that curve I I and I don't
+ 
+
+ align:start position:0%
+you can see that curve I I and I don't
+swear to the slopes of that curve but in
+
+ align:start position:0%
+swear to the slopes of that curve but in
+ 
+
+ align:start position:0%
+swear to the slopes of that curve but in
+between in in there is filled with
+
+ align:start position:0%
+between in in there is filled with
+ 
+
+ align:start position:0%
+between in in there is filled with
+curves that start out with this slope
+
+ align:start position:0%
+curves that start out with this slope
+ 
+
+ align:start position:0%
+curves that start out with this slope
+and end with that slope and the same
+
+ align:start position:0%
+and end with that slope and the same
+ 
+
+ align:start position:0%
+and end with that slope and the same
+here it'll start with this slope but
+
+ align:start position:0%
+here it'll start with this slope but
+ 
+
+ align:start position:0%
+here it'll start with this slope but
+then go yeah probably this is a better
+
+ align:start position:0%
+then go yeah probably this is a better
+ 
+
+ align:start position:0%
+then go yeah probably this is a better
+picture yeah yeah that's a better
+
+ align:start position:0%
+picture yeah yeah that's a better
+ 
+
+ align:start position:0%
+picture yeah yeah that's a better
+picture yeah it doesn't it it will just
+
+ align:start position:0%
+picture yeah it doesn't it it will just
+ 
+
+ align:start position:0%
+picture yeah it doesn't it it will just
+go up with
+
+ align:start position:0%
+go up with
+ 
+
+ align:start position:0%
+go up with
+slope at the end it will have slope two
+
+ align:start position:0%
+slope at the end it will have slope two
+ 
+
+ align:start position:0%
+slope at the end it will have slope two
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+upwards yeah that looks good well you
+
+ align:start position:0%
+upwards yeah that looks good well you
+ 
+
+ align:start position:0%
+upwards yeah that looks good well you
+could say I only Drew part of the phase
+
+ align:start position:0%
+could say I only Drew part of the phase
+ 
+
+ align:start position:0%
+could say I only Drew part of the phase
+plane and you're completely right if I
+
+ align:start position:0%
+plane and you're completely right if I
+ 
+
+ align:start position:0%
+plane and you're completely right if I
+start somewhere here what would you
+
+ align:start position:0%
+start somewhere here what would you
+ 
+
+ align:start position:0%
+start somewhere here what would you
+think would happen what would you think
+
+ align:start position:0%
+think would happen what would you think
+ 
+
+ align:start position:0%
+think would happen what would you think
+would happen if I start with that value
+
+ align:start position:0%
+would happen if I start with that value
+ 
+
+ align:start position:0%
+would happen if I start with that value
+of y that much and that value of y prime
+
+ align:start position:0%
+of y that much and that value of y prime
+ 
+
+ align:start position:0%
+of y that much and that value of y prime
+it would have some mixture
+
+ align:start position:0%
+it would have some mixture
+ 
+
+ align:start position:0%
+it would have some mixture
+of of there would be a C1 and a
+
+ align:start position:0%
+of of there would be a C1 and a
+ 
+
+ align:start position:0%
+of of there would be a C1 and a
+C2 so the other curves that I haven't
+
+ align:start position:0%
+C2 so the other curves that I haven't
+ 
+
+ align:start position:0%
+C2 so the other curves that I haven't
+drawn yet come from the other C1 and C2
+
+ align:start position:0%
+drawn yet come from the other C1 and C2
+ 
+
+ align:start position:0%
+drawn yet come from the other C1 and C2
+I've done C1 equal 1 and C2 equal 1 and
+
+ align:start position:0%
+I've done C1 equal 1 and C2 equal 1 and
+ 
+
+ align:start position:0%
+I've done C1 equal 1 and C2 equal 1 and
+C1 equal C2 equal 1 but now I have many
+
+ align:start position:0%
+C1 equal C2 equal 1 but now I have many
+ 
+
+ align:start position:0%
+C1 equal C2 equal 1 but now I have many
+more possibilities and what they do is
+
+ align:start position:0%
+more possibilities and what they do is
+ 
+
+ align:start position:0%
+more possibilities and what they do is
+they will uh so suppose I start there it
+
+ align:start position:0%
+they will uh so suppose I start there it
+ 
+
+ align:start position:0%
+they will uh so suppose I start there it
+will start out uh at it will approach
+
+ align:start position:0%
+will start out uh at it will approach
+ 
+
+ align:start position:0%
+will start out uh at it will approach
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the this is the winner this is the
+
+ align:start position:0%
+the this is the winner this is the
+ 
+
+ align:start position:0%
+the this is the winner this is the
+winner this is this is the where C1 is
+
+ align:start position:0%
+winner this is this is the where C1 is
+ 
+
+ align:start position:0%
+winner this is this is the where C1 is
+one where where this is happening there
+
+ align:start position:0%
+one where where this is happening there
+ 
+
+ align:start position:0%
+one where where this is happening there
+there is the winner for a large time so
+
+ align:start position:0%
+there is the winner for a large time so
+ 
+
+ align:start position:0%
+there is the winner for a large time so
+all curves swing up toward that to
+
+ align:start position:0%
+all curves swing up toward that to
+ 
+
+ align:start position:0%
+all curves swing up toward that to
+parallel to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line or down here they swing down
+
+ align:start position:0%
+line or down here they swing down
+ 
+
+ align:start position:0%
+line or down here they swing down
+parallel to that line so things here
+
+ align:start position:0%
+parallel to that line so things here
+ 
+
+ align:start position:0%
+parallel to that line so things here
+will swing down this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way that's the phase plane may I do one
+
+ align:start position:0%
+way that's the phase plane may I do one
+ 
+
+ align:start position:0%
+way that's the phase plane may I do one
+more example to show that this was a
+
+ align:start position:0%
+more example to show that this was a
+ 
+
+ align:start position:0%
+more example to show that this was a
+source this is called a source
+
+ align:start position:0%
+source this is called a source
+ 
+
+ align:start position:0%
+source this is called a source
+because the
+
+ align:start position:0%
+because the
+ 
+
+ align:start position:0%
+because the
+the the solution goes to Infinity
+
+ align:start position:0%
+the the solution goes to Infinity
+ 
+
+ align:start position:0%
+the the solution goes to Infinity
+wherever you start the solution goes to
+
+ align:start position:0%
+wherever you start the solution goes to
+ 
+
+ align:start position:0%
+wherever you start the solution goes to
+Infinity it's un totally
+
+ align:start position:0%
+Infinity it's un totally
+ 
+
+ align:start position:0%
+Infinity it's un totally
+unstable now if I changed to a positive
+
+ align:start position:0%
+unstable now if I changed to a positive
+ 
+
+ align:start position:0%
+unstable now if I changed to a positive
+damping then I would have a plus sign
+
+ align:start position:0%
+damping then I would have a plus sign
+ 
+
+ align:start position:0%
+damping then I would have a plus sign
+there these would be plus signs I would
+
+ align:start position:0%
+there these would be plus signs I would
+ 
+
+ align:start position:0%
+there these would be plus signs I would
+have S = minus1 or S equal -2 so with
+
+ align:start position:0%
+have S = minus1 or S equal -2 so with
+ 
+
+ align:start position:0%
+have S = minus1 or S equal -2 so with
+positive damping I damp out naturally
+
+ align:start position:0%
+positive damping I damp out naturally
+ 
+
+ align:start position:0%
+positive damping I damp out naturally
+and the all the this picture would be
+
+ align:start position:0%
+and the all the this picture would be
+ 
+
+ align:start position:0%
+and the all the this picture would be
+the same except all the lines are coming
+
+ align:start position:0%
+the same except all the lines are coming
+ 
+
+ align:start position:0%
+the same except all the lines are coming
+into to 0 0 the solutions are damping to
+
+ align:start position:0%
+into to 0 0 the solutions are damping to
+ 
+
+ align:start position:0%
+into to 0 0 the solutions are damping to
+0 0 to nothing happen happening so I
+
+ align:start position:0%
+0 0 to nothing happen happening so I
+ 
+
+ align:start position:0%
+0 0 to nothing happen happening so I
+just track the same lines but in the
+
+ align:start position:0%
+just track the same lines but in the
+ 
+
+ align:start position:0%
+just track the same lines but in the
+opposite direction into so instead of
+
+ align:start position:0%
+opposite direction into so instead of
+ 
+
+ align:start position:0%
+opposite direction into so instead of
+this being the Big Bang it's the end of
+
+ align:start position:0%
+this being the Big Bang it's the end of
+ 
+
+ align:start position:0%
+this being the Big Bang it's the end of
+the universe t equal
+
+ align:start position:0%
+the universe t equal
+ 
+
+ align:start position:0%
+the universe t equal
+Infinity okay I'm up for one more
+
+ align:start position:0%
+Infinity okay I'm up for one more
+ 
+
+ align:start position:0%
+Infinity okay I'm up for one more
+picture of this uh possibility and let
+
+ align:start position:0%
+picture of this uh possibility and let
+ 
+
+ align:start position:0%
+picture of this uh possibility and let
+me take the equation Y
+
+ align:start position:0%
+me take the equation Y
+ 
+
+ align:start position:0%
+me take the equation Y
+Prime = 4
+
+ align:start position:0%
+Prime = 4
+ 
+
+ align:start position:0%
+Prime = 4
+y so my equation will be
+
+ align:start position:0%
+y so my equation will be
+ 
+
+ align:start position:0%
+y so my equation will be
+s² = 4 4 S = 2 or -2 and when I draw the
+
+ align:start position:0%
+s² = 4 4 S = 2 or -2 and when I draw the
+ 
+
+ align:start position:0%
+s² = 4 4 S = 2 or -2 and when I draw the
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+plane when the and the solutions the
+
+ align:start position:0%
+plane when the and the solutions the
+ 
+
+ align:start position:0%
+plane when the and the solutions the
+solutions will be C1 e to the
+
+ align:start position:0%
+solutions will be C1 e to the
+ 
+
+ align:start position:0%
+solutions will be C1 e to the
+2T and C2 e to Theus 2T from a two and a
+
+ align:start position:0%
+2T and C2 e to Theus 2T from a two and a
+ 
+
+ align:start position:0%
+2T and C2 e to Theus 2T from a two and a
+minus 2 that's the that's the solution
+
+ align:start position:0%
+minus 2 that's the that's the solution
+ 
+
+ align:start position:0%
+minus 2 that's the that's the solution
+we all know and now I should compute its
+
+ align:start position:0%
+we all know and now I should compute its
+ 
+
+ align:start position:0%
+we all know and now I should compute its
+slope y Prime will be 2 C1 1 E to 2T
+
+ align:start position:0%
+slope y Prime will be 2 C1 1 E to 2T
+ 
+
+ align:start position:0%
+slope y Prime will be 2 C1 1 E to 2T
+minus 2 C2 e to 2T and now you just want
+
+ align:start position:0%
+minus 2 C2 e to 2T and now you just want
+ 
+
+ align:start position:0%
+minus 2 C2 e to 2T and now you just want
+me to draw those pictures you just want
+
+ align:start position:0%
+me to draw those pictures you just want
+ 
+
+ align:start position:0%
+me to draw those pictures you just want
+me to draw those pictures and let me try
+
+ align:start position:0%
+me to draw those pictures and let me try
+ 
+
+ align:start position:0%
+me to draw those pictures and let me try
+to say what happens here uh this is this
+
+ align:start position:0%
+to say what happens here uh this is this
+ 
+
+ align:start position:0%
+to say what happens here uh this is this
+is a saddle point it's called a saddle
+
+ align:start position:0%
+is a saddle point it's called a saddle
+ 
+
+ align:start position:0%
+is a saddle point it's called a saddle
+when we have in One Direction things are
+
+ align:start position:0%
+when we have in One Direction things are
+ 
+
+ align:start position:0%
+when we have in One Direction things are
+growing but in the other things are
+
+ align:start position:0%
+growing but in the other things are
+ 
+
+ align:start position:0%
+growing but in the other things are
+decreasing so uh mostly
+
+ align:start position:0%
+decreasing so uh mostly
+ 
+
+ align:start position:0%
+decreasing so uh mostly
+most solutions if C1 is not zero then
+
+ align:start position:0%
+most solutions if C1 is not zero then
+ 
+
+ align:start position:0%
+most solutions if C1 is not zero then
+the growth is going to win and that will
+
+ align:start position:0%
+the growth is going to win and that will
+ 
+
+ align:start position:0%
+the growth is going to win and that will
+disappear but there is the possibility
+
+ align:start position:0%
+disappear but there is the possibility
+ 
+
+ align:start position:0%
+disappear but there is the possibility
+that C1 is zero so there will be one
+
+ align:start position:0%
+that C1 is zero so there will be one
+ 
+
+ align:start position:0%
+that C1 is zero so there will be one
+line coming from there there' be one
+
+ align:start position:0%
+line coming from there there' be one
+ 
+
+ align:start position:0%
+line coming from there there' be one
+line coming from there maybe I can try
+
+ align:start position:0%
+line coming from there maybe I can try
+ 
+
+ align:start position:0%
+line coming from there maybe I can try
+to draw that I'll again I'll draw that
+
+ align:start position:0%
+to draw that I'll again I'll draw that
+ 
+
+ align:start position:0%
+to draw that I'll again I'll draw that
+Pure Line where where C1 is zero so that
+
+ align:start position:0%
+Pure Line where where C1 is zero so that
+ 
+
+ align:start position:0%
+Pure Line where where C1 is zero so that
+Pure Line is coming these are minuses
+
+ align:start position:0%
+Pure Line is coming these are minuses
+ 
+
+ align:start position:0%
+Pure Line is coming these are minuses
+here so that line is coming into the
+
+ align:start position:0%
+here so that line is coming into the
+ 
+
+ align:start position:0%
+here so that line is coming into the
+center so that's why we have a saddle we
+
+ align:start position:0%
+center so that's why we have a saddle we
+ 
+
+ align:start position:0%
+center so that's why we have a saddle we
+we approach the saddle uh if along this
+
+ align:start position:0%
+we approach the saddle uh if along this
+ 
+
+ align:start position:0%
+we approach the saddle uh if along this
+where where where this is minus two of
+
+ align:start position:0%
+where where where this is minus two of
+ 
+
+ align:start position:0%
+where where where this is minus two of
+that so I think it would be so it's a
+
+ align:start position:0%
+that so I think it would be so it's a
+ 
+
+ align:start position:0%
+that so I think it would be so it's a
+slope of Min
+
+ align:start position:0%
+slope of Min
+ 
+
+ align:start position:0%
+slope of Min
+-2 so I think so slope like
+
+ align:start position:0%
+-2 so I think so slope like
+ 
+
+ align:start position:0%
+-2 so I think so slope like
+that so again this is y this is y Prime
+
+ align:start position:0%
+that so again this is y this is y Prime
+ 
+
+ align:start position:0%
+that so again this is y this is y Prime
+this is the slope of Min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-2 and that's this curve and
+
+ align:start position:0%
+-2 and that's this curve and
+ 
+
+ align:start position:0%
+-2 and that's this curve and
+uh uh yeah so so it will be very
+
+ align:start position:0%
+uh uh yeah so so it will be very
+ 
+
+ align:start position:0%
+uh uh yeah so so it will be very
+exceptional that we're just follow that
+
+ align:start position:0%
+exceptional that we're just follow that
+ 
+
+ align:start position:0%
+exceptional that we're just follow that
+we're right on that line all
+
+ align:start position:0%
+we're right on that line all
+ 
+
+ align:start position:0%
+we're right on that line all
+other points all other Curves in this
+
+ align:start position:0%
+other points all other Curves in this
+ 
+
+ align:start position:0%
+other points all other Curves in this
+phase plane are going to have a little
+
+ align:start position:0%
+phase plane are going to have a little
+ 
+
+ align:start position:0%
+phase plane are going to have a little
+C1 in them and then this will take over
+
+ align:start position:0%
+C1 in them and then this will take over
+ 
+
+ align:start position:0%
+C1 in them and then this will take over
+and that is gives us as we saw before
+
+ align:start position:0%
+and that is gives us as we saw before
+ 
+
+ align:start position:0%
+and that is gives us as we saw before
+this slope is this is two times that so
+
+ align:start position:0%
+this slope is this is two times that so
+ 
+
+ align:start position:0%
+this slope is this is two times that so
+that line is the is where everybody
+
+ align:start position:0%
+that line is the is where everybody
+ 
+
+ align:start position:0%
+that line is the is where everybody
+wants to go and only if you start
+
+ align:start position:0%
+wants to go and only if you start
+ 
+
+ align:start position:0%
+wants to go and only if you start
+exactly on this line do you do you get
+
+ align:start position:0%
+exactly on this line do you do you get
+ 
+
+ align:start position:0%
+exactly on this line do you do you get
+this picture and you come in to the S
+
+ align:start position:0%
+this picture and you come in to the S
+ 
+
+ align:start position:0%
+this picture and you come in to the S
+there's the instead of the Big Bang or
+
+ align:start position:0%
+there's the instead of the Big Bang or
+ 
+
+ align:start position:0%
+there's the instead of the Big Bang or
+the end of the universe this is now the
+
+ align:start position:0%
+the end of the universe this is now the
+ 
+
+ align:start position:0%
+the end of the universe this is now the
+saddle point where we come in on this
+
+ align:start position:0%
+saddle point where we come in on this
+ 
+
+ align:start position:0%
+saddle point where we come in on this
+most special of all lines coming from
+
+ align:start position:0%
+most special of all lines coming from
+ 
+
+ align:start position:0%
+most special of all lines coming from
+this picture but almost always this is
+
+ align:start position:0%
+this picture but almost always this is
+ 
+
+ align:start position:0%
+this picture but almost always this is
+the dominant thing and we go out so so
+
+ align:start position:0%
+the dominant thing and we go out so so
+ 
+
+ align:start position:0%
+the dominant thing and we go out so so
+if I take a typical starting point I'll
+
+ align:start position:0%
+if I take a typical starting point I'll
+ 
+
+ align:start position:0%
+if I take a typical starting point I'll
+go out
+
+ align:start position:0%
+go out
+ 
+
+ align:start position:0%
+go out
+this like
+
+ align:start position:0%
+this like
+ 
+
+ align:start position:0%
+this like
+that or like this oh no uh yep no I'll
+
+ align:start position:0%
+that or like this oh no uh yep no I'll
+ 
+
+ align:start position:0%
+that or like this oh no uh yep no I'll
+go out it'll have to go out so if I
+
+ align:start position:0%
+go out it'll have to go out so if I
+ 
+
+ align:start position:0%
+go out it'll have to go out so if I
+start anywhere here these are probably
+
+ align:start position:0%
+start anywhere here these are probably
+ 
+
+ align:start position:0%
+start anywhere here these are probably
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+hyperbolas uh going out in that
+
+ align:start position:0%
+hyperbolas uh going out in that
+ 
+
+ align:start position:0%
+hyperbolas uh going out in that
+direction I don't swear that they're
+
+ align:start position:0%
+direction I don't swear that they're
+ 
+
+ align:start position:0%
+direction I don't swear that they're
+hyperbolas here again we might start in
+
+ align:start position:0%
+hyperbolas here again we might start in
+ 
+
+ align:start position:0%
+hyperbolas here again we might start in
+because we have a big numers here but
+
+ align:start position:0%
+because we have a big numers here but
+ 
+
+ align:start position:0%
+because we have a big numers here but
+then e to the T takes over and we go out
+
+ align:start position:0%
+then e to the T takes over and we go out
+ 
+
+ align:start position:0%
+then e to the T takes over and we go out
+so those go out these go
+
+ align:start position:0%
+so those go out these go
+ 
+
+ align:start position:0%
+so those go out these go
+out and these go out yeah so this is the
+
+ align:start position:0%
+out and these go out yeah so this is the
+ 
+
+ align:start position:0%
+out and these go out yeah so this is the
+big line that's the line coming from
+
+ align:start position:0%
+big line that's the line coming from
+ 
+
+ align:start position:0%
+big line that's the line coming from
+here and that's where everything wants
+
+ align:start position:0%
+here and that's where everything wants
+ 
+
+ align:start position:0%
+here and that's where everything wants
+to go and everything eventually goes
+
+ align:start position:0%
+to go and everything eventually goes
+ 
+
+ align:start position:0%
+to go and everything eventually goes
+that way except the one line where C1 is
+
+ align:start position:0%
+that way except the one line where C1 is
+ 
+
+ align:start position:0%
+that way except the one line where C1 is
+zero so the that this dominant term is
+
+ align:start position:0%
+zero so the that this dominant term is
+ 
+
+ align:start position:0%
+zero so the that this dominant term is
+not even here then and then we come
+
+ align:start position:0%
+not even here then and then we come
+ 
+
+ align:start position:0%
+not even here then and then we come
+inwards so that saddle point is a a the
+
+ align:start position:0%
+inwards so that saddle point is a a the
+ 
+
+ align:start position:0%
+inwards so that saddle point is a a the
+special point where you could go out if
+
+ align:start position:0%
+special point where you could go out if
+ 
+
+ align:start position:0%
+special point where you could go out if
+if you go the right way or you could
+
+ align:start position:0%
+if you go the right way or you could
+ 
+
+ align:start position:0%
+if you go the right way or you could
+come in if you go the other special
+
+ align:start position:0%
+come in if you go the other special
+ 
+
+ align:start position:0%
+come in if you go the other special
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+way okay so that's sources sinks and
+
+ align:start position:0%
+way okay so that's sources sinks and
+ 
+
+ align:start position:0%
+way okay so that's sources sinks and
+Saddles and I still have to draw the
+
+ align:start position:0%
+Saddles and I still have to draw the
+ 
+
+ align:start position:0%
+Saddles and I still have to draw the
+pictures which involve spirals that come
+
+ align:start position:0%
+pictures which involve spirals that come
+ 
+
+ align:start position:0%
+pictures which involve spirals that come
+from complex s where we have oscillation
+
+ align:start position:0%
+from complex s where we have oscillation
+ 
+
+ align:start position:0%
+from complex s where we have oscillation
+that'll be the next video
\ No newline at end of file
diff --git a/W-7gI87IG1A.txt b/W-7gI87IG1A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ebb15cbf36ba1d07c2d1eb6cf6329c4d3fac459
--- /dev/null
+++ b/W-7gI87IG1A.txt
@@ -0,0 +1,18344 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
+ align:start position:0%
+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
+
+ align:start position:0%
+will help mit opencourseware continue to
+ 
+
+ align:start position:0%
+will help mit opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so today's class we are going to
+
+ align:start position:0%
+yeah so today's class we are going to
+ 
+
+ align:start position:0%
+yeah so today's class we are going to
+talk about uh
+
+ align:start position:0%
+talk about uh
+ 
+
+ align:start position:0%
+talk about uh
+coherence and
+
+ align:start position:0%
+coherence and
+ 
+
+ align:start position:0%
+coherence and
+basically as
+
+ align:start position:0%
+basically as
+ 
+
+ align:start position:0%
+basically as
+foreign system within current imaging so
+
+ align:start position:0%
+foreign system within current imaging so
+ 
+
+ align:start position:0%
+foreign system within current imaging so
+particularly this topic is very
+
+ align:start position:0%
+particularly this topic is very
+ 
+
+ align:start position:0%
+particularly this topic is very
+important if you want to take optic
+
+ align:start position:0%
+important if you want to take optic
+ 
+
+ align:start position:0%
+important if you want to take optic
+score because you know we're dealing
+
+ align:start position:0%
+score because you know we're dealing
+ 
+
+ align:start position:0%
+score because you know we're dealing
+with coherence and in korean so
+
+ align:start position:0%
+with coherence and in korean so
+ 
+
+ align:start position:0%
+with coherence and in korean so
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so far we have deal with the 4f system
+
+ align:start position:0%
+so far we have deal with the 4f system
+ 
+
+ align:start position:0%
+so far we have deal with the 4f system
+with the with a coherent illumination
+
+ align:start position:0%
+with the with a coherent illumination
+ 
+
+ align:start position:0%
+with the with a coherent illumination
+basically a laser light
+
+ align:start position:0%
+basically a laser light
+ 
+
+ align:start position:0%
+basically a laser light
+from a point source i mean pinhole so
+
+ align:start position:0%
+from a point source i mean pinhole so
+ 
+
+ align:start position:0%
+from a point source i mean pinhole so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the coherent
+
+ align:start position:0%
+the coherent
+ 
+
+ align:start position:0%
+the coherent
+coherent plane waves are illuminating
+
+ align:start position:0%
+coherent plane waves are illuminating
+ 
+
+ align:start position:0%
+coherent plane waves are illuminating
+the voice system
+
+ align:start position:0%
+the voice system
+ 
+
+ align:start position:0%
+the voice system
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the frequency content appear at the free
+
+ align:start position:0%
+the frequency content appear at the free
+ 
+
+ align:start position:0%
+the frequency content appear at the free
+up plane and you can put the put the
+
+ align:start position:0%
+up plane and you can put the put the
+ 
+
+ align:start position:0%
+up plane and you can put the put the
+pupil mask to play with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know the spatial filtering and
+
+ align:start position:0%
+you know the spatial filtering and
+ 
+
+ align:start position:0%
+you know the spatial filtering and
+you're going to get some
+
+ align:start position:0%
+you're going to get some
+ 
+
+ align:start position:0%
+you're going to get some
+image at the alpha plane but
+
+ align:start position:0%
+image at the alpha plane but
+ 
+
+ align:start position:0%
+image at the alpha plane but
+you know in everyday life if you
+
+ align:start position:0%
+you know in everyday life if you
+ 
+
+ align:start position:0%
+you know in everyday life if you
+use your digital camera you're not using
+
+ align:start position:0%
+use your digital camera you're not using
+ 
+
+ align:start position:0%
+use your digital camera you're not using
+the really
+
+ align:start position:0%
+the really
+ 
+
+ align:start position:0%
+the really
+laser elimination right you mostly use
+
+ align:start position:0%
+laser elimination right you mostly use
+ 
+
+ align:start position:0%
+laser elimination right you mostly use
+this ambient light or
+
+ align:start position:0%
+this ambient light or
+ 
+
+ align:start position:0%
+this ambient light or
+if it's too dark then you're use you're
+
+ align:start position:0%
+if it's too dark then you're use you're
+ 
+
+ align:start position:0%
+if it's too dark then you're use you're
+going to use the flash uh light
+
+ align:start position:0%
+going to use the flash uh light
+ 
+
+ align:start position:0%
+going to use the flash uh light
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so today we are going to talk about more
+
+ align:start position:0%
+so today we are going to talk about more
+ 
+
+ align:start position:0%
+so today we are going to talk about more
+realistic case we use the in korean
+
+ align:start position:0%
+realistic case we use the in korean
+ 
+
+ align:start position:0%
+realistic case we use the in korean
+light by the way the difference between
+
+ align:start position:0%
+light by the way the difference between
+ 
+
+ align:start position:0%
+light by the way the difference between
+coherent and in colon is
+
+ align:start position:0%
+coherent and in colon is
+ 
+
+ align:start position:0%
+coherent and in colon is
+basically you can make the interference
+
+ align:start position:0%
+basically you can make the interference
+ 
+
+ align:start position:0%
+basically you can make the interference
+with the coherent light right so if you
+
+ align:start position:0%
+with the coherent light right so if you
+ 
+
+ align:start position:0%
+with the coherent light right so if you
+want to make interference you're using
+
+ align:start position:0%
+want to make interference you're using
+ 
+
+ align:start position:0%
+want to make interference you're using
+laser
+
+ align:start position:0%
+laser
+ 
+
+ align:start position:0%
+laser
+but in most cases like this white light
+
+ align:start position:0%
+but in most cases like this white light
+ 
+
+ align:start position:0%
+but in most cases like this white light
+source you are not going to see
+
+ align:start position:0%
+source you are not going to see
+ 
+
+ align:start position:0%
+source you are not going to see
+interference so
+
+ align:start position:0%
+interference so
+ 
+
+ align:start position:0%
+interference so
+we are going to first we are going to
+
+ align:start position:0%
+we are going to first we are going to
+ 
+
+ align:start position:0%
+we are going to first we are going to
+define what coherence is and there are
+
+ align:start position:0%
+define what coherence is and there are
+ 
+
+ align:start position:0%
+define what coherence is and there are
+actually there are two kind of coherence
+
+ align:start position:0%
+actually there are two kind of coherence
+ 
+
+ align:start position:0%
+actually there are two kind of coherence
+temporal coherence and spatial coherence
+
+ align:start position:0%
+temporal coherence and spatial coherence
+ 
+
+ align:start position:0%
+temporal coherence and spatial coherence
+and the rest of the topic is pretty
+
+ align:start position:0%
+and the rest of the topic is pretty
+ 
+
+ align:start position:0%
+and the rest of the topic is pretty
+straightforward we are going to define
+
+ align:start position:0%
+straightforward we are going to define
+ 
+
+ align:start position:0%
+straightforward we are going to define
+incoherent poinsettia function and
+
+ align:start position:0%
+incoherent poinsettia function and
+ 
+
+ align:start position:0%
+incoherent poinsettia function and
+and is free transform pair which is
+
+ align:start position:0%
+and is free transform pair which is
+ 
+
+ align:start position:0%
+and is free transform pair which is
+optical transfer function and modulation
+
+ align:start position:0%
+optical transfer function and modulation
+ 
+
+ align:start position:0%
+optical transfer function and modulation
+transfer function which is
+
+ align:start position:0%
+transfer function which is
+ 
+
+ align:start position:0%
+transfer function which is
+modulus of otf
+
+ align:start position:0%
+modulus of otf
+ 
+
+ align:start position:0%
+modulus of otf
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're gonna see what mtf mean and
+
+ align:start position:0%
+we're gonna see what mtf mean and
+ 
+
+ align:start position:0%
+we're gonna see what mtf mean and
+we're gonna compare the difference
+
+ align:start position:0%
+we're gonna compare the difference
+ 
+
+ align:start position:0%
+we're gonna compare the difference
+between especially in core hand and
+
+ align:start position:0%
+between especially in core hand and
+ 
+
+ align:start position:0%
+between especially in core hand and
+especially kohen and current imaging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+so as i just described the coherence is
+
+ align:start position:0%
+so as i just described the coherence is
+ 
+
+ align:start position:0%
+so as i just described the coherence is
+basically uh popular ability to make
+
+ align:start position:0%
+basically uh popular ability to make
+ 
+
+ align:start position:0%
+basically uh popular ability to make
+interference so if you have incoherent
+
+ align:start position:0%
+interference so if you have incoherent
+ 
+
+ align:start position:0%
+interference so if you have incoherent
+light you cannot make interference and
+
+ align:start position:0%
+light you cannot make interference and
+ 
+
+ align:start position:0%
+light you cannot make interference and
+if you have coherent light then you can
+
+ align:start position:0%
+if you have coherent light then you can
+ 
+
+ align:start position:0%
+if you have coherent light then you can
+make the interference
+
+ align:start position:0%
+make the interference
+ 
+
+ align:start position:0%
+make the interference
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i'm going to describe later but the
+
+ align:start position:0%
+i'm going to describe later but the
+ 
+
+ align:start position:0%
+i'm going to describe later but the
+mathematically
+
+ align:start position:0%
+mathematically
+ 
+
+ align:start position:0%
+mathematically
+actually the coherence is nothing but
+
+ align:start position:0%
+actually the coherence is nothing but
+ 
+
+ align:start position:0%
+actually the coherence is nothing but
+the correlation of
+
+ align:start position:0%
+the correlation of
+ 
+
+ align:start position:0%
+the correlation of
+wave at two
+
+ align:start position:0%
+wave at two
+ 
+
+ align:start position:0%
+wave at two
+time space point which means we have
+
+ align:start position:0%
+time space point which means we have
+ 
+
+ align:start position:0%
+time space point which means we have
+some light and you just
+
+ align:start position:0%
+some light and you just
+ 
+
+ align:start position:0%
+some light and you just
+sample two uh point it could be
+
+ align:start position:0%
+sample two uh point it could be
+ 
+
+ align:start position:0%
+sample two uh point it could be
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+different time points but you combine
+
+ align:start position:0%
+different time points but you combine
+ 
+
+ align:start position:0%
+different time points but you combine
+them and if you see interference then
+
+ align:start position:0%
+them and if you see interference then
+ 
+
+ align:start position:0%
+them and if you see interference then
+you can say it is coherent but if you
+
+ align:start position:0%
+you can say it is coherent but if you
+ 
+
+ align:start position:0%
+you can say it is coherent but if you
+don't see interference then
+
+ align:start position:0%
+don't see interference then
+ 
+
+ align:start position:0%
+don't see interference then
+in korean
+
+ align:start position:0%
+in korean
+ 
+
+ align:start position:0%
+in korean
+so first let me describe uh what's going
+
+ align:start position:0%
+so first let me describe uh what's going
+ 
+
+ align:start position:0%
+so first let me describe uh what's going
+to happen if i use the incurrent light
+
+ align:start position:0%
+to happen if i use the incurrent light
+ 
+
+ align:start position:0%
+to happen if i use the incurrent light
+in microsoft interferometer so here we
+
+ align:start position:0%
+in microsoft interferometer so here we
+ 
+
+ align:start position:0%
+in microsoft interferometer so here we
+have the microsoft interferometer so
+
+ align:start position:0%
+have the microsoft interferometer so
+ 
+
+ align:start position:0%
+have the microsoft interferometer so
+with the from the point source the light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the point source light is coming in
+
+ align:start position:0%
+from the point source light is coming in
+ 
+
+ align:start position:0%
+from the point source light is coming in
+this direction this direction and at the
+
+ align:start position:0%
+this direction this direction and at the
+ 
+
+ align:start position:0%
+this direction this direction and at the
+beam spiritual a half of the light just
+
+ align:start position:0%
+beam spiritual a half of the light just
+ 
+
+ align:start position:0%
+beam spiritual a half of the light just
+transmit the beam splitter but the other
+
+ align:start position:0%
+transmit the beam splitter but the other
+ 
+
+ align:start position:0%
+transmit the beam splitter but the other
+half is reflected
+
+ align:start position:0%
+half is reflected
+ 
+
+ align:start position:0%
+half is reflected
+so this path they reflect again at the
+
+ align:start position:0%
+so this path they reflect again at the
+ 
+
+ align:start position:0%
+so this path they reflect again at the
+mirror and pass through the vm splitter
+
+ align:start position:0%
+mirror and pass through the vm splitter
+ 
+
+ align:start position:0%
+mirror and pass through the vm splitter
+and arrives at the detector and the
+
+ align:start position:0%
+and arrives at the detector and the
+ 
+
+ align:start position:0%
+and arrives at the detector and the
+other path
+
+ align:start position:0%
+other path
+ 
+
+ align:start position:0%
+other path
+is reflected again and reflected at the
+
+ align:start position:0%
+is reflected again and reflected at the
+ 
+
+ align:start position:0%
+is reflected again and reflected at the
+beam filler and
+
+ align:start position:0%
+beam filler and
+ 
+
+ align:start position:0%
+beam filler and
+again you get i mean it is it arrives at
+
+ align:start position:0%
+again you get i mean it is it arrives at
+ 
+
+ align:start position:0%
+again you get i mean it is it arrives at
+the detector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's just suppose that we have the
+
+ align:start position:0%
+let's just suppose that we have the
+ 
+
+ align:start position:0%
+let's just suppose that we have the
+laser uh source here then what we want
+
+ align:start position:0%
+laser uh source here then what we want
+ 
+
+ align:start position:0%
+laser uh source here then what we want
+to see at the detector is nice
+
+ align:start position:0%
+to see at the detector is nice
+ 
+
+ align:start position:0%
+to see at the detector is nice
+sinusoidal pattern if i move one of the
+
+ align:start position:0%
+sinusoidal pattern if i move one of the
+ 
+
+ align:start position:0%
+sinusoidal pattern if i move one of the
+mirror right because i can i tune the
+
+ align:start position:0%
+mirror right because i can i tune the
+ 
+
+ align:start position:0%
+mirror right because i can i tune the
+uh optical pass differ actually
+
+ align:start position:0%
+uh optical pass differ actually
+ 
+
+ align:start position:0%
+uh optical pass differ actually
+optical fast length
+
+ align:start position:0%
+optical fast length
+ 
+
+ align:start position:0%
+optical fast length
+that light travels and if the distance
+
+ align:start position:0%
+that light travels and if the distance
+ 
+
+ align:start position:0%
+that light travels and if the distance
+match then
+
+ align:start position:0%
+match then
+ 
+
+ align:start position:0%
+match then
+i get the constructive interference and
+
+ align:start position:0%
+i get the constructive interference and
+ 
+
+ align:start position:0%
+i get the constructive interference and
+the base delay uh
+
+ align:start position:0%
+the base delay uh
+ 
+
+ align:start position:0%
+the base delay uh
+pi then i get destructive interference
+
+ align:start position:0%
+pi then i get destructive interference
+ 
+
+ align:start position:0%
+pi then i get destructive interference
+so as i move to one of the mirror i get
+
+ align:start position:0%
+so as i move to one of the mirror i get
+ 
+
+ align:start position:0%
+so as i move to one of the mirror i get
+nice sinusoidal pattern with the full
+
+ align:start position:0%
+nice sinusoidal pattern with the full
+ 
+
+ align:start position:0%
+nice sinusoidal pattern with the full
+contrast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+let's suppose instead of the laser i
+
+ align:start position:0%
+let's suppose instead of the laser i
+ 
+
+ align:start position:0%
+let's suppose instead of the laser i
+have uh in current source which means so
+
+ align:start position:0%
+have uh in current source which means so
+ 
+
+ align:start position:0%
+have uh in current source which means so
+the horizontal axis is time and the
+
+ align:start position:0%
+the horizontal axis is time and the
+ 
+
+ align:start position:0%
+the horizontal axis is time and the
+vertical axis is amplitude but the the
+
+ align:start position:0%
+vertical axis is amplitude but the the
+ 
+
+ align:start position:0%
+vertical axis is amplitude but the the
+phase or amplitudes are varying randomly
+
+ align:start position:0%
+phase or amplitudes are varying randomly
+ 
+
+ align:start position:0%
+phase or amplitudes are varying randomly
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+over time time the amplitudes are very
+
+ align:start position:0%
+over time time the amplitudes are very
+ 
+
+ align:start position:0%
+over time time the amplitudes are very
+very very
+
+ align:start position:0%
+very very
+ 
+
+ align:start position:0%
+very very
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+randomly
+
+ align:start position:0%
+randomly
+ 
+
+ align:start position:0%
+randomly
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even though it's random this wave trend
+
+ align:start position:0%
+even though it's random this wave trend
+ 
+
+ align:start position:0%
+even though it's random this wave trend
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+travel
+
+ align:start position:0%
+travel
+ 
+
+ align:start position:0%
+travel
+through the interferometer so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this path
+
+ align:start position:0%
+in this path
+ 
+
+ align:start position:0%
+in this path
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+optical path
+
+ align:start position:0%
+optical path
+ 
+
+ align:start position:0%
+optical path
+length is actually constant which is i
+
+ align:start position:0%
+length is actually constant which is i
+ 
+
+ align:start position:0%
+length is actually constant which is i
+mean these paths are the they're common
+
+ align:start position:0%
+mean these paths are the they're common
+ 
+
+ align:start position:0%
+mean these paths are the they're common
+in two paths so constant plus 2 d 1 over
+
+ align:start position:0%
+in two paths so constant plus 2 d 1 over
+ 
+
+ align:start position:0%
+in two paths so constant plus 2 d 1 over
+c which is time speed of light
+
+ align:start position:0%
+c which is time speed of light
+ 
+
+ align:start position:0%
+c which is time speed of light
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in the second path i have the same this
+
+ align:start position:0%
+in the second path i have the same this
+ 
+
+ align:start position:0%
+in the second path i have the same this
+little trim also travel but
+
+ align:start position:0%
+little trim also travel but
+ 
+
+ align:start position:0%
+little trim also travel but
+due to the difference between a t1 and
+
+ align:start position:0%
+due to the difference between a t1 and
+ 
+
+ align:start position:0%
+due to the difference between a t1 and
+d2 i mean at a detector
+
+ align:start position:0%
+d2 i mean at a detector
+ 
+
+ align:start position:0%
+d2 i mean at a detector
+essentially i'm going to sample a
+
+ align:start position:0%
+essentially i'm going to sample a
+ 
+
+ align:start position:0%
+essentially i'm going to sample a
+different time point right so
+
+ align:start position:0%
+different time point right so
+ 
+
+ align:start position:0%
+different time point right so
+even though it's random
+
+ align:start position:0%
+even though it's random
+ 
+
+ align:start position:0%
+even though it's random
+i basically choose two time
+
+ align:start position:0%
+i basically choose two time
+ 
+
+ align:start position:0%
+i basically choose two time
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+here and here and combine them at the
+
+ align:start position:0%
+here and here and combine them at the
+ 
+
+ align:start position:0%
+here and here and combine them at the
+detector right
+
+ align:start position:0%
+detector right
+ 
+
+ align:start position:0%
+detector right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if d1 and d2 are same then basically two
+
+ align:start position:0%
+if d1 and d2 are same then basically two
+ 
+
+ align:start position:0%
+if d1 and d2 are same then basically two
+basically identical two waves are coming
+
+ align:start position:0%
+basically identical two waves are coming
+ 
+
+ align:start position:0%
+basically identical two waves are coming
+together so i always get constructed
+
+ align:start position:0%
+together so i always get constructed
+ 
+
+ align:start position:0%
+together so i always get constructed
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+but what if d1 and d2 are not same
+
+ align:start position:0%
+but what if d1 and d2 are not same
+ 
+
+ align:start position:0%
+but what if d1 and d2 are not same
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then basically they get different phase
+
+ align:start position:0%
+then basically they get different phase
+ 
+
+ align:start position:0%
+then basically they get different phase
+shifts right and since it's random so
+
+ align:start position:0%
+shifts right and since it's random so
+ 
+
+ align:start position:0%
+shifts right and since it's random so
+they are kind of the average out so d1
+
+ align:start position:0%
+they are kind of the average out so d1
+ 
+
+ align:start position:0%
+they are kind of the average out so d1
+and d2 are getting bigger then
+
+ align:start position:0%
+and d2 are getting bigger then
+ 
+
+ align:start position:0%
+and d2 are getting bigger then
+basically the degree of correlation is
+
+ align:start position:0%
+basically the degree of correlation is
+ 
+
+ align:start position:0%
+basically the degree of correlation is
+get is getting decreased and which means
+
+ align:start position:0%
+get is getting decreased and which means
+ 
+
+ align:start position:0%
+get is getting decreased and which means
+at the detector the contrast
+
+ align:start position:0%
+at the detector the contrast
+ 
+
+ align:start position:0%
+at the detector the contrast
+will also get decreased
+
+ align:start position:0%
+will also get decreased
+ 
+
+ align:start position:0%
+will also get decreased
+so if i plot the intensity at the
+
+ align:start position:0%
+so if i plot the intensity at the
+ 
+
+ align:start position:0%
+so if i plot the intensity at the
+detector
+
+ align:start position:0%
+detector
+ 
+
+ align:start position:0%
+detector
+with respect to d2 minus t1 which is the
+
+ align:start position:0%
+with respect to d2 minus t1 which is the
+ 
+
+ align:start position:0%
+with respect to d2 minus t1 which is the
+the distance difference of true arm
+
+ align:start position:0%
+the distance difference of true arm
+ 
+
+ align:start position:0%
+the distance difference of true arm
+then the intensity is going to be like
+
+ align:start position:0%
+then the intensity is going to be like
+ 
+
+ align:start position:0%
+then the intensity is going to be like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+remember that if we if if i have the
+
+ align:start position:0%
+remember that if we if if i have the
+ 
+
+ align:start position:0%
+remember that if we if if i have the
+laser at
+
+ align:start position:0%
+laser at
+ 
+
+ align:start position:0%
+laser at
+point source then i will get
+
+ align:start position:0%
+point source then i will get
+ 
+
+ align:start position:0%
+point source then i will get
+the sinusoidal pattern with the full
+
+ align:start position:0%
+the sinusoidal pattern with the full
+ 
+
+ align:start position:0%
+the sinusoidal pattern with the full
+contrast but
+
+ align:start position:0%
+contrast but
+ 
+
+ align:start position:0%
+contrast but
+since now i have random randomly varying
+
+ align:start position:0%
+since now i have random randomly varying
+ 
+
+ align:start position:0%
+since now i have random randomly varying
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+those this envelope is getting
+
+ align:start position:0%
+those this envelope is getting
+ 
+
+ align:start position:0%
+those this envelope is getting
+attenuated like this so if i have the
+
+ align:start position:0%
+attenuated like this so if i have the
+ 
+
+ align:start position:0%
+attenuated like this so if i have the
+rapid more rapid decay curve which means
+
+ align:start position:0%
+rapid more rapid decay curve which means
+ 
+
+ align:start position:0%
+rapid more rapid decay curve which means
+i have more incoherent light right and
+
+ align:start position:0%
+i have more incoherent light right and
+ 
+
+ align:start position:0%
+i have more incoherent light right and
+if i have the
+
+ align:start position:0%
+if i have the
+ 
+
+ align:start position:0%
+if i have the
+slowly decaying envelope then it's more
+
+ align:start position:0%
+slowly decaying envelope then it's more
+ 
+
+ align:start position:0%
+slowly decaying envelope then it's more
+coherent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there is another
+
+ align:start position:0%
+there is another
+ 
+
+ align:start position:0%
+there is another
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+kind of coherence which is special
+
+ align:start position:0%
+kind of coherence which is special
+ 
+
+ align:start position:0%
+kind of coherence which is special
+coherence so basically the concept is
+
+ align:start position:0%
+coherence so basically the concept is
+ 
+
+ align:start position:0%
+coherence so basically the concept is
+same but we only define the correlation
+
+ align:start position:0%
+same but we only define the correlation
+ 
+
+ align:start position:0%
+same but we only define the correlation
+in space domain
+
+ align:start position:0%
+in space domain
+ 
+
+ align:start position:0%
+in space domain
+so now we i i have the young
+
+ align:start position:0%
+so now we i i have the young
+ 
+
+ align:start position:0%
+so now we i i have the young
+interferometer i have the two pin on x1
+
+ align:start position:0%
+interferometer i have the two pin on x1
+ 
+
+ align:start position:0%
+interferometer i have the two pin on x1
+and x2 and i put a detector at the
+
+ align:start position:0%
+and x2 and i put a detector at the
+ 
+
+ align:start position:0%
+and x2 and i put a detector at the
+center of the two pinhole so
+
+ align:start position:0%
+center of the two pinhole so
+ 
+
+ align:start position:0%
+center of the two pinhole so
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+so from this panel
+
+ align:start position:0%
+so from this panel
+ 
+
+ align:start position:0%
+so from this panel
+you see i mean
+
+ align:start position:0%
+you see i mean
+ 
+
+ align:start position:0%
+you see i mean
+the spherical wave
+
+ align:start position:0%
+the spherical wave
+ 
+
+ align:start position:0%
+the spherical wave
+is going to be emanating but
+
+ align:start position:0%
+is going to be emanating but
+ 
+
+ align:start position:0%
+is going to be emanating but
+since it is at the center these paths
+
+ align:start position:0%
+since it is at the center these paths
+ 
+
+ align:start position:0%
+since it is at the center these paths
+are exactly the same
+
+ align:start position:0%
+are exactly the same
+ 
+
+ align:start position:0%
+are exactly the same
+and first let's suppose we have a laser
+
+ align:start position:0%
+and first let's suppose we have a laser
+ 
+
+ align:start position:0%
+and first let's suppose we have a laser
+illumination so i have
+
+ align:start position:0%
+illumination so i have
+ 
+
+ align:start position:0%
+illumination so i have
+the plane f coming in then this
+
+ align:start position:0%
+the plane f coming in then this
+ 
+
+ align:start position:0%
+the plane f coming in then this
+spherical wave will make the young's
+
+ align:start position:0%
+spherical wave will make the young's
+ 
+
+ align:start position:0%
+spherical wave will make the young's
+interference right so i'm going to have
+
+ align:start position:0%
+interference right so i'm going to have
+ 
+
+ align:start position:0%
+interference right so i'm going to have
+a sinusoidal
+
+ align:start position:0%
+a sinusoidal
+ 
+
+ align:start position:0%
+a sinusoidal
+pattern with the full contrast at this
+
+ align:start position:0%
+pattern with the full contrast at this
+ 
+
+ align:start position:0%
+pattern with the full contrast at this
+plane but i'm just seeing at one point
+
+ align:start position:0%
+plane but i'm just seeing at one point
+ 
+
+ align:start position:0%
+plane but i'm just seeing at one point
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+again if i have the random randomly
+
+ align:start position:0%
+again if i have the random randomly
+ 
+
+ align:start position:0%
+again if i have the random randomly
+varying uh
+
+ align:start position:0%
+varying uh
+ 
+
+ align:start position:0%
+varying uh
+wave here
+
+ align:start position:0%
+wave here
+ 
+
+ align:start position:0%
+wave here
+so in this case
+
+ align:start position:0%
+so in this case
+ 
+
+ align:start position:0%
+so in this case
+this horizontal axis
+
+ align:start position:0%
+this horizontal axis
+ 
+
+ align:start position:0%
+this horizontal axis
+amplitude and vertical axis is space
+
+ align:start position:0%
+amplitude and vertical axis is space
+ 
+
+ align:start position:0%
+amplitude and vertical axis is space
+instead of time
+
+ align:start position:0%
+instead of time
+ 
+
+ align:start position:0%
+instead of time
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+amplitude and phase are varying randomly
+
+ align:start position:0%
+amplitude and phase are varying randomly
+ 
+
+ align:start position:0%
+amplitude and phase are varying randomly
+varying over space
+
+ align:start position:0%
+varying over space
+ 
+
+ align:start position:0%
+varying over space
+since i have two pinots
+
+ align:start position:0%
+since i have two pinots
+ 
+
+ align:start position:0%
+since i have two pinots
+so i essentially sample at two point
+
+ align:start position:0%
+so i essentially sample at two point
+ 
+
+ align:start position:0%
+so i essentially sample at two point
+here and there and
+
+ align:start position:0%
+here and there and
+ 
+
+ align:start position:0%
+here and there and
+combine them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again if these two panels are very
+
+ align:start position:0%
+so again if these two panels are very
+ 
+
+ align:start position:0%
+so again if these two panels are very
+close then these sampling points also
+
+ align:start position:0%
+close then these sampling points also
+ 
+
+ align:start position:0%
+close then these sampling points also
+very close right so the
+
+ align:start position:0%
+very close right so the
+ 
+
+ align:start position:0%
+very close right so the
+the amplitude and phase are more likely
+
+ align:start position:0%
+the amplitude and phase are more likely
+ 
+
+ align:start position:0%
+the amplitude and phase are more likely
+uh similar
+
+ align:start position:0%
+uh similar
+ 
+
+ align:start position:0%
+uh similar
+i mean there is big change right but if
+
+ align:start position:0%
+i mean there is big change right but if
+ 
+
+ align:start position:0%
+i mean there is big change right but if
+if i move this two pin in i mean to
+
+ align:start position:0%
+if i move this two pin in i mean to
+ 
+
+ align:start position:0%
+if i move this two pin in i mean to
+abort and downward so like this
+
+ align:start position:0%
+abort and downward so like this
+ 
+
+ align:start position:0%
+abort and downward so like this
+then the the spacing between two pins
+
+ align:start position:0%
+then the the spacing between two pins
+ 
+
+ align:start position:0%
+then the the spacing between two pins
+are getting bigger and basically i lose
+
+ align:start position:0%
+are getting bigger and basically i lose
+ 
+
+ align:start position:0%
+are getting bigger and basically i lose
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+correlation which means the special
+
+ align:start position:0%
+correlation which means the special
+ 
+
+ align:start position:0%
+correlation which means the special
+coherence is getting attenuated getting
+
+ align:start position:0%
+coherence is getting attenuated getting
+ 
+
+ align:start position:0%
+coherence is getting attenuated getting
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again if i plot the intensity at the
+
+ align:start position:0%
+again if i plot the intensity at the
+ 
+
+ align:start position:0%
+again if i plot the intensity at the
+detector with respect to
+
+ align:start position:0%
+detector with respect to
+ 
+
+ align:start position:0%
+detector with respect to
+x2 minus x1 which is the spacing between
+
+ align:start position:0%
+x2 minus x1 which is the spacing between
+ 
+
+ align:start position:0%
+x2 minus x1 which is the spacing between
+two pinholes
+
+ align:start position:0%
+two pinholes
+ 
+
+ align:start position:0%
+two pinholes
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+intensity varying like this
+
+ align:start position:0%
+intensity varying like this
+ 
+
+ align:start position:0%
+intensity varying like this
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+again remember if i have the laser then
+
+ align:start position:0%
+again remember if i have the laser then
+ 
+
+ align:start position:0%
+again remember if i have the laser then
+it doesn't really matter i mean i always
+
+ align:start position:0%
+it doesn't really matter i mean i always
+ 
+
+ align:start position:0%
+it doesn't really matter i mean i always
+get the full contrast right even though
+
+ align:start position:0%
+get the full contrast right even though
+ 
+
+ align:start position:0%
+get the full contrast right even though
+those frequencies of the uh i'm at the
+
+ align:start position:0%
+those frequencies of the uh i'm at the
+ 
+
+ align:start position:0%
+those frequencies of the uh i'm at the
+observation plane the frequency of the
+
+ align:start position:0%
+observation plane the frequency of the
+ 
+
+ align:start position:0%
+observation plane the frequency of the
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+is changing but i always get the full
+
+ align:start position:0%
+is changing but i always get the full
+ 
+
+ align:start position:0%
+is changing but i always get the full
+contrast but contrast getting smaller if
+
+ align:start position:0%
+contrast but contrast getting smaller if
+ 
+
+ align:start position:0%
+contrast but contrast getting smaller if
+you have the in current source
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+let me describe mathematically why this
+
+ align:start position:0%
+let me describe mathematically why this
+ 
+
+ align:start position:0%
+let me describe mathematically why this
+happened
+
+ align:start position:0%
+happened
+ 
+
+ align:start position:0%
+happened
+it doesn't really matter if i i mean
+
+ align:start position:0%
+it doesn't really matter if i i mean
+ 
+
+ align:start position:0%
+it doesn't really matter if i i mean
+whether i used in my cursing
+
+ align:start position:0%
+whether i used in my cursing
+ 
+
+ align:start position:0%
+whether i used in my cursing
+interferement or young
+
+ align:start position:0%
+interferement or young
+ 
+
+ align:start position:0%
+interferement or young
+interferometer basically in the thermal
+
+ align:start position:0%
+interferometer basically in the thermal
+ 
+
+ align:start position:0%
+interferometer basically in the thermal
+we have uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have two waves right so a1 e to the
+
+ align:start position:0%
+we have two waves right so a1 e to the
+ 
+
+ align:start position:0%
+we have two waves right so a1 e to the
+pi 1 and a2 e to the pi 2 basically we
+
+ align:start position:0%
+pi 1 and a2 e to the pi 2 basically we
+ 
+
+ align:start position:0%
+pi 1 and a2 e to the pi 2 basically we
+have two wave i can sample in space or
+
+ align:start position:0%
+have two wave i can sample in space or
+ 
+
+ align:start position:0%
+have two wave i can sample in space or
+time domain but anyway i'm going to have
+
+ align:start position:0%
+time domain but anyway i'm going to have
+ 
+
+ align:start position:0%
+time domain but anyway i'm going to have
+two waves and just add them together and
+
+ align:start position:0%
+two waves and just add them together and
+ 
+
+ align:start position:0%
+two waves and just add them together and
+take the magnitude square which is
+
+ align:start position:0%
+take the magnitude square which is
+ 
+
+ align:start position:0%
+take the magnitude square which is
+intensity right
+
+ align:start position:0%
+intensity right
+ 
+
+ align:start position:0%
+intensity right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+vacation interferometer this is
+
+ align:start position:0%
+vacation interferometer this is
+ 
+
+ align:start position:0%
+vacation interferometer this is
+i mean basically these two waves came
+
+ align:start position:0%
+i mean basically these two waves came
+ 
+
+ align:start position:0%
+i mean basically these two waves came
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+different the uh path length d1 and d2
+
+ align:start position:0%
+different the uh path length d1 and d2
+ 
+
+ align:start position:0%
+different the uh path length d1 and d2
+and young's interferometer basically
+
+ align:start position:0%
+and young's interferometer basically
+ 
+
+ align:start position:0%
+and young's interferometer basically
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+they came from the two different point p
+
+ align:start position:0%
+they came from the two different point p
+ 
+
+ align:start position:0%
+they came from the two different point p
+notes x1 and x2 but anyway i can always
+
+ align:start position:0%
+notes x1 and x2 but anyway i can always
+ 
+
+ align:start position:0%
+notes x1 and x2 but anyway i can always
+write the interference of two waves as
+
+ align:start position:0%
+write the interference of two waves as
+ 
+
+ align:start position:0%
+write the interference of two waves as
+like this so
+
+ align:start position:0%
+like this so
+ 
+
+ align:start position:0%
+like this so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+wave one and wave two
+
+ align:start position:0%
+wave one and wave two
+ 
+
+ align:start position:0%
+wave one and wave two
+its negative square is gonna be i naught
+
+ align:start position:0%
+its negative square is gonna be i naught
+ 
+
+ align:start position:0%
+its negative square is gonna be i naught
+and one plus m cosine the phase
+
+ align:start position:0%
+and one plus m cosine the phase
+ 
+
+ align:start position:0%
+and one plus m cosine the phase
+difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we are assuming monochromatic yes
+
+ align:start position:0%
+yeah we are assuming monochromatic yes
+ 
+
+ align:start position:0%
+yeah we are assuming monochromatic yes
+i mean you can write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the one uh we use assuming monochromatic
+
+ align:start position:0%
+the one uh we use assuming monochromatic
+ 
+
+ align:start position:0%
+the one uh we use assuming monochromatic
+because we are using phase notation
+
+ align:start position:0%
+because we are using phase notation
+ 
+
+ align:start position:0%
+because we are using phase notation
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+we write this this and we rewrite phasor
+
+ align:start position:0%
+we write this this and we rewrite phasor
+ 
+
+ align:start position:0%
+we write this this and we rewrite phasor
+but actually there is e to the i omega t
+
+ align:start position:0%
+but actually there is e to the i omega t
+ 
+
+ align:start position:0%
+but actually there is e to the i omega t
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+from we assume it's monochromatic but
+
+ align:start position:0%
+from we assume it's monochromatic but
+ 
+
+ align:start position:0%
+from we assume it's monochromatic but
+even though it's it's normal commander
+
+ align:start position:0%
+even though it's it's normal commander
+ 
+
+ align:start position:0%
+even though it's it's normal commander
+you can always write just addition of
+
+ align:start position:0%
+you can always write just addition of
+ 
+
+ align:start position:0%
+you can always write just addition of
+two apps right
+
+ align:start position:0%
+two apps right
+ 
+
+ align:start position:0%
+two apps right
+it really doesn't matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah so interference is basically the d
+
+ align:start position:0%
+yeah so interference is basically the d
+ 
+
+ align:start position:0%
+yeah so interference is basically the d
+system which is i naught so i naught is
+
+ align:start position:0%
+system which is i naught so i naught is
+ 
+
+ align:start position:0%
+system which is i naught so i naught is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+a1 square plus a2 square which is
+
+ align:start position:0%
+a1 square plus a2 square which is
+ 
+
+ align:start position:0%
+a1 square plus a2 square which is
+intensity of the wave one and intensity
+
+ align:start position:0%
+intensity of the wave one and intensity
+ 
+
+ align:start position:0%
+intensity of the wave one and intensity
+of the wave two so
+
+ align:start position:0%
+of the wave two so
+ 
+
+ align:start position:0%
+of the wave two so
+this this term is just addition of
+
+ align:start position:0%
+this this term is just addition of
+ 
+
+ align:start position:0%
+this this term is just addition of
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+and we have some
+
+ align:start position:0%
+and we have some
+ 
+
+ align:start position:0%
+and we have some
+cosine modulation term
+
+ align:start position:0%
+cosine modulation term
+ 
+
+ align:start position:0%
+cosine modulation term
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is basically
+
+ align:start position:0%
+so this is basically
+ 
+
+ align:start position:0%
+so this is basically
+interference so we if you have uh if you
+
+ align:start position:0%
+interference so we if you have uh if you
+ 
+
+ align:start position:0%
+interference so we if you have uh if you
+have a coherent light then
+
+ align:start position:0%
+have a coherent light then
+ 
+
+ align:start position:0%
+have a coherent light then
+we have some d term and have a
+
+ align:start position:0%
+we have some d term and have a
+ 
+
+ align:start position:0%
+we have some d term and have a
+sinusoidal modulation right
+
+ align:start position:0%
+sinusoidal modulation right
+ 
+
+ align:start position:0%
+sinusoidal modulation right
+and it
+
+ align:start position:0%
+and it
+ 
+
+ align:start position:0%
+and it
+had to fit and as the phase very and
+
+ align:start position:0%
+had to fit and as the phase very and
+ 
+
+ align:start position:0%
+had to fit and as the phase very and
+we're going to see the sinusoidal
+
+ align:start position:0%
+we're going to see the sinusoidal
+ 
+
+ align:start position:0%
+we're going to see the sinusoidal
+pattern is changing
+
+ align:start position:0%
+pattern is changing
+ 
+
+ align:start position:0%
+pattern is changing
+but remember that
+
+ align:start position:0%
+but remember that
+ 
+
+ align:start position:0%
+but remember that
+this optical frequency is very fast
+
+ align:start position:0%
+this optical frequency is very fast
+ 
+
+ align:start position:0%
+this optical frequency is very fast
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+the tens of gigahertz are more than that
+
+ align:start position:0%
+the tens of gigahertz are more than that
+ 
+
+ align:start position:0%
+the tens of gigahertz are more than that
+so actually what we measure i mean
+
+ align:start position:0%
+so actually what we measure i mean
+ 
+
+ align:start position:0%
+so actually what we measure i mean
+intensity is time average of this guy so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're gonna take the time average of
+
+ align:start position:0%
+we're gonna take the time average of
+ 
+
+ align:start position:0%
+we're gonna take the time average of
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+do the math
+
+ align:start position:0%
+do the math
+ 
+
+ align:start position:0%
+do the math
+actually we we have the this term and
+
+ align:start position:0%
+actually we we have the this term and
+ 
+
+ align:start position:0%
+actually we we have the this term and
+this kind of
+
+ align:start position:0%
+this kind of
+ 
+
+ align:start position:0%
+this kind of
+modulation term which is time average of
+
+ align:start position:0%
+modulation term which is time average of
+ 
+
+ align:start position:0%
+modulation term which is time average of
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+with the phase difference but remember
+
+ align:start position:0%
+with the phase difference but remember
+ 
+
+ align:start position:0%
+with the phase difference but remember
+that if we i have increased like this
+
+ align:start position:0%
+that if we i have increased like this
+ 
+
+ align:start position:0%
+that if we i have increased like this
+phase difference is random so
+
+ align:start position:0%
+phase difference is random so
+ 
+
+ align:start position:0%
+phase difference is random so
+what is the average of
+
+ align:start position:0%
+what is the average of
+ 
+
+ align:start position:0%
+what is the average of
+cosine of random phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exported
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the average of
+
+ align:start position:0%
+what is the average of
+ 
+
+ align:start position:0%
+what is the average of
+cosine of random phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero yeah zero right cosine is
+
+ align:start position:0%
+zero yeah zero right cosine is
+ 
+
+ align:start position:0%
+zero yeah zero right cosine is
+oscillating between one and
+
+ align:start position:0%
+oscillating between one and
+ 
+
+ align:start position:0%
+oscillating between one and
+plus one to minus one so
+
+ align:start position:0%
+plus one to minus one so
+ 
+
+ align:start position:0%
+plus one to minus one so
+if you have random phase and average
+
+ align:start position:0%
+if you have random phase and average
+ 
+
+ align:start position:0%
+if you have random phase and average
+then you get zero right
+
+ align:start position:0%
+then you get zero right
+ 
+
+ align:start position:0%
+then you get zero right
+so if you have equivalent light
+
+ align:start position:0%
+so if you have equivalent light
+ 
+
+ align:start position:0%
+so if you have equivalent light
+and basically intensity is just
+
+ align:start position:0%
+and basically intensity is just
+ 
+
+ align:start position:0%
+and basically intensity is just
+addition of
+
+ align:start position:0%
+addition of
+ 
+
+ align:start position:0%
+addition of
+intensity of two f and we don't have any
+
+ align:start position:0%
+intensity of two f and we don't have any
+ 
+
+ align:start position:0%
+intensity of two f and we don't have any
+interference term
+
+ align:start position:0%
+interference term
+ 
+
+ align:start position:0%
+interference term
+so that's the difference between
+
+ align:start position:0%
+so that's the difference between
+ 
+
+ align:start position:0%
+so that's the difference between
+coherent and incranolite so coherent we
+
+ align:start position:0%
+coherent and incranolite so coherent we
+ 
+
+ align:start position:0%
+coherent and incranolite so coherent we
+always have
+
+ align:start position:0%
+always have
+ 
+
+ align:start position:0%
+always have
+a modulation term i mean it could be
+
+ align:start position:0%
+a modulation term i mean it could be
+ 
+
+ align:start position:0%
+a modulation term i mean it could be
+zero it depending on phase difference
+
+ align:start position:0%
+zero it depending on phase difference
+ 
+
+ align:start position:0%
+zero it depending on phase difference
+right but
+
+ align:start position:0%
+right but
+ 
+
+ align:start position:0%
+right but
+in corona you always have just addition
+
+ align:start position:0%
+in corona you always have just addition
+ 
+
+ align:start position:0%
+in corona you always have just addition
+of this term i mean addition of
+
+ align:start position:0%
+of this term i mean addition of
+ 
+
+ align:start position:0%
+of this term i mean addition of
+intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so if it's perfectly in current
+
+ align:start position:0%
+yeah so if it's perfectly in current
+ 
+
+ align:start position:0%
+yeah so if it's perfectly in current
+then we have just addition of intensity
+
+ align:start position:0%
+then we have just addition of intensity
+ 
+
+ align:start position:0%
+then we have just addition of intensity
+and actually
+
+ align:start position:0%
+and actually
+ 
+
+ align:start position:0%
+and actually
+coherent and encoding is very actually
+
+ align:start position:0%
+coherent and encoding is very actually
+ 
+
+ align:start position:0%
+coherent and encoding is very actually
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+opposite extreme case right
+
+ align:start position:0%
+opposite extreme case right
+ 
+
+ align:start position:0%
+opposite extreme case right
+so i mean it's just like monochromatic
+
+ align:start position:0%
+so i mean it's just like monochromatic
+ 
+
+ align:start position:0%
+so i mean it's just like monochromatic
+we are not gonna i mean in real case we
+
+ align:start position:0%
+we are not gonna i mean in real case we
+ 
+
+ align:start position:0%
+we are not gonna i mean in real case we
+are not gonna have really uh
+
+ align:start position:0%
+are not gonna have really uh
+ 
+
+ align:start position:0%
+are not gonna have really uh
+monochromatic source our source is
+
+ align:start position:0%
+monochromatic source our source is
+ 
+
+ align:start position:0%
+monochromatic source our source is
+always finite bandwidth right it's not
+
+ align:start position:0%
+always finite bandwidth right it's not
+ 
+
+ align:start position:0%
+always finite bandwidth right it's not
+gonna be delta function so it's same
+
+ align:start position:0%
+gonna be delta function so it's same
+ 
+
+ align:start position:0%
+gonna be delta function so it's same
+thing we are not gonna have
+
+ align:start position:0%
+thing we are not gonna have
+ 
+
+ align:start position:0%
+thing we are not gonna have
+the perfectly coherent or perfectly in
+
+ align:start position:0%
+the perfectly coherent or perfectly in
+ 
+
+ align:start position:0%
+the perfectly coherent or perfectly in
+queen everything is a partially coherent
+
+ align:start position:0%
+queen everything is a partially coherent
+ 
+
+ align:start position:0%
+queen everything is a partially coherent
+so you if you want to deal with that and
+
+ align:start position:0%
+so you if you want to deal with that and
+ 
+
+ align:start position:0%
+so you if you want to deal with that and
+you have to apply
+
+ align:start position:0%
+you have to apply
+ 
+
+ align:start position:0%
+you have to apply
+basically statistics
+
+ align:start position:0%
+basically statistics
+ 
+
+ align:start position:0%
+basically statistics
+all to all these uh fresnel and frontal
+
+ align:start position:0%
+all to all these uh fresnel and frontal
+ 
+
+ align:start position:0%
+all to all these uh fresnel and frontal
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+i mean this kind of free optics so
+
+ align:start position:0%
+i mean this kind of free optics so
+ 
+
+ align:start position:0%
+i mean this kind of free optics so
+it's called the statistical optics and
+
+ align:start position:0%
+it's called the statistical optics and
+ 
+
+ align:start position:0%
+it's called the statistical optics and
+it's covered in
+
+ align:start position:0%
+it's covered in
+ 
+
+ align:start position:0%
+it's covered in
+2.717 so if you want to
+
+ align:start position:0%
+2.717 so if you want to
+ 
+
+ align:start position:0%
+2.717 so if you want to
+learn more more about it then you can
+
+ align:start position:0%
+learn more more about it then you can
+ 
+
+ align:start position:0%
+learn more more about it then you can
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+2717.
+
+ align:start position:0%
+2717.
+ 
+
+ align:start position:0%
+2717.
+nevertheless the korean and in current
+
+ align:start position:0%
+nevertheless the korean and in current
+ 
+
+ align:start position:0%
+nevertheless the korean and in current
+case is enough they are enough to
+
+ align:start position:0%
+case is enough they are enough to
+ 
+
+ align:start position:0%
+case is enough they are enough to
+describe uh many many uh phenomena so
+
+ align:start position:0%
+describe uh many many uh phenomena so
+ 
+
+ align:start position:0%
+describe uh many many uh phenomena so
+we are focused on coherent and
+
+ align:start position:0%
+we are focused on coherent and
+ 
+
+ align:start position:0%
+we are focused on coherent and
+increasing uh equal and current uh state
+
+ align:start position:0%
+increasing uh equal and current uh state
+ 
+
+ align:start position:0%
+increasing uh equal and current uh state
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+really fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since we have two kind of coherence
+
+ align:start position:0%
+so since we have two kind of coherence
+ 
+
+ align:start position:0%
+so since we have two kind of coherence
+so temporal coherence and special
+
+ align:start position:0%
+so temporal coherence and special
+ 
+
+ align:start position:0%
+so temporal coherence and special
+coherence
+
+ align:start position:0%
+coherence
+ 
+
+ align:start position:0%
+coherence
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+actually we have four different
+
+ align:start position:0%
+actually we have four different
+ 
+
+ align:start position:0%
+actually we have four different
+combinations right so temporally
+
+ align:start position:0%
+combinations right so temporally
+ 
+
+ align:start position:0%
+combinations right so temporally
+especially korean and
+
+ align:start position:0%
+especially korean and
+ 
+
+ align:start position:0%
+especially korean and
+temporary especially in korean and
+
+ align:start position:0%
+temporary especially in korean and
+ 
+
+ align:start position:0%
+temporary especially in korean and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+temporarily korean especially korean
+
+ align:start position:0%
+temporarily korean especially korean
+ 
+
+ align:start position:0%
+temporarily korean especially korean
+temporary coherence especially in queen
+
+ align:start position:0%
+temporary coherence especially in queen
+ 
+
+ align:start position:0%
+temporary coherence especially in queen
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the rule of thumb
+
+ align:start position:0%
+the rule of thumb
+ 
+
+ align:start position:0%
+the rule of thumb
+so temporal coherence is related to the
+
+ align:start position:0%
+so temporal coherence is related to the
+ 
+
+ align:start position:0%
+so temporal coherence is related to the
+bandwidth of the
+
+ align:start position:0%
+bandwidth of the
+ 
+
+ align:start position:0%
+bandwidth of the
+your source and basically the color of
+
+ align:start position:0%
+your source and basically the color of
+ 
+
+ align:start position:0%
+your source and basically the color of
+your source so if you have one color in
+
+ align:start position:0%
+your source so if you have one color in
+ 
+
+ align:start position:0%
+your source so if you have one color in
+monochromatic then it's
+
+ align:start position:0%
+monochromatic then it's
+ 
+
+ align:start position:0%
+monochromatic then it's
+question yeah
+
+ align:start position:0%
+question yeah
+ 
+
+ align:start position:0%
+question yeah
+where do diode lasers go in that chart
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diode laser is more like
+
+ align:start position:0%
+diode laser is more like
+ 
+
+ align:start position:0%
+diode laser is more like
+temporary and special equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so oh yeah let me just continue so
+
+ align:start position:0%
+so oh yeah let me just continue so
+ 
+
+ align:start position:0%
+so oh yeah let me just continue so
+temporal aquarius is related to color so
+
+ align:start position:0%
+temporal aquarius is related to color so
+ 
+
+ align:start position:0%
+temporal aquarius is related to color so
+if you have laser like single color
+
+ align:start position:0%
+if you have laser like single color
+ 
+
+ align:start position:0%
+if you have laser like single color
+monochromatic then it's more like
+
+ align:start position:0%
+monochromatic then it's more like
+ 
+
+ align:start position:0%
+monochromatic then it's more like
+coherent but if you have white light
+
+ align:start position:0%
+coherent but if you have white light
+ 
+
+ align:start position:0%
+coherent but if you have white light
+like this fluorescent lamp or halogen
+
+ align:start position:0%
+like this fluorescent lamp or halogen
+ 
+
+ align:start position:0%
+like this fluorescent lamp or halogen
+lamp then you know it's broadband so
+
+ align:start position:0%
+lamp then you know it's broadband so
+ 
+
+ align:start position:0%
+lamp then you know it's broadband so
+it's temporarily increasing
+
+ align:start position:0%
+it's temporarily increasing
+ 
+
+ align:start position:0%
+it's temporarily increasing
+and special occurrence is related to
+
+ align:start position:0%
+and special occurrence is related to
+ 
+
+ align:start position:0%
+and special occurrence is related to
+actually the size of the source and the
+
+ align:start position:0%
+actually the size of the source and the
+ 
+
+ align:start position:0%
+actually the size of the source and the
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+so everything coming from the points of
+
+ align:start position:0%
+so everything coming from the points of
+ 
+
+ align:start position:0%
+so everything coming from the points of
+especially especially cohen because you
+
+ align:start position:0%
+especially especially cohen because you
+ 
+
+ align:start position:0%
+especially especially cohen because you
+know they are basically coming from the
+
+ align:start position:0%
+know they are basically coming from the
+ 
+
+ align:start position:0%
+know they are basically coming from the
+same point
+
+ align:start position:0%
+same point
+ 
+
+ align:start position:0%
+same point
+but if your source is extended like
+
+ align:start position:0%
+but if your source is extended like
+ 
+
+ align:start position:0%
+but if your source is extended like
+or you know you have a filament in the
+
+ align:start position:0%
+or you know you have a filament in the
+ 
+
+ align:start position:0%
+or you know you have a filament in the
+bulb or
+
+ align:start position:0%
+bulb or
+ 
+
+ align:start position:0%
+bulb or
+this kind of fluorescent light then
+
+ align:start position:0%
+this kind of fluorescent light then
+ 
+
+ align:start position:0%
+this kind of fluorescent light then
+especially in korean
+
+ align:start position:0%
+especially in korean
+ 
+
+ align:start position:0%
+especially in korean
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the monochromatic laser source you know
+
+ align:start position:0%
+the monochromatic laser source you know
+ 
+
+ align:start position:0%
+the monochromatic laser source you know
+laser is very
+
+ align:start position:0%
+laser is very
+ 
+
+ align:start position:0%
+laser is very
+monochromatic and it's the uh the output
+
+ align:start position:0%
+monochromatic and it's the uh the output
+ 
+
+ align:start position:0%
+monochromatic and it's the uh the output
+is very small so
+
+ align:start position:0%
+is very small so
+ 
+
+ align:start position:0%
+is very small so
+laser is typically very temporary and
+
+ align:start position:0%
+laser is typically very temporary and
+ 
+
+ align:start position:0%
+laser is typically very temporary and
+especially in korean and that's why
+
+ align:start position:0%
+especially in korean and that's why
+ 
+
+ align:start position:0%
+especially in korean and that's why
+people use it in interferometry
+
+ align:start position:0%
+people use it in interferometry
+ 
+
+ align:start position:0%
+people use it in interferometry
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+white light source and if you
+
+ align:start position:0%
+white light source and if you
+ 
+
+ align:start position:0%
+white light source and if you
+if you are nearby the wide wildlife
+
+ align:start position:0%
+if you are nearby the wide wildlife
+ 
+
+ align:start position:0%
+if you are nearby the wide wildlife
+source then it's more like temporary and
+
+ align:start position:0%
+source then it's more like temporary and
+ 
+
+ align:start position:0%
+source then it's more like temporary and
+in temporary and especially in korean
+
+ align:start position:0%
+in temporary and especially in korean
+ 
+
+ align:start position:0%
+in temporary and especially in korean
+and actually these two are a little bit
+
+ align:start position:0%
+and actually these two are a little bit
+ 
+
+ align:start position:0%
+and actually these two are a little bit
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+so temporarily in korean but especially
+
+ align:start position:0%
+so temporarily in korean but especially
+ 
+
+ align:start position:0%
+so temporarily in korean but especially
+kohen
+
+ align:start position:0%
+kohen
+ 
+
+ align:start position:0%
+kohen
+so if you put a pinhole small pinhole in
+
+ align:start position:0%
+so if you put a pinhole small pinhole in
+ 
+
+ align:start position:0%
+so if you put a pinhole small pinhole in
+in front of the white light then it's
+
+ align:start position:0%
+in front of the white light then it's
+ 
+
+ align:start position:0%
+in front of the white light then it's
+temporarily in korean because it's
+
+ align:start position:0%
+temporarily in korean because it's
+ 
+
+ align:start position:0%
+temporarily in korean because it's
+broadband but it's coming from pinhole
+
+ align:start position:0%
+broadband but it's coming from pinhole
+ 
+
+ align:start position:0%
+broadband but it's coming from pinhole
+so especially korean
+
+ align:start position:0%
+so especially korean
+ 
+
+ align:start position:0%
+so especially korean
+at the same reason the sunlight is very
+
+ align:start position:0%
+at the same reason the sunlight is very
+ 
+
+ align:start position:0%
+at the same reason the sunlight is very
+especially
+
+ align:start position:0%
+especially
+ 
+
+ align:start position:0%
+especially
+coherent but temporarily in korean but
+
+ align:start position:0%
+coherent but temporarily in korean but
+ 
+
+ align:start position:0%
+coherent but temporarily in korean but
+sun is very huge but also the distance
+
+ align:start position:0%
+sun is very huge but also the distance
+ 
+
+ align:start position:0%
+sun is very huge but also the distance
+very huge right so if you see the sun
+
+ align:start position:0%
+very huge right so if you see the sun
+ 
+
+ align:start position:0%
+very huge right so if you see the sun
+then it looks you know it's sunlight
+
+ align:start position:0%
+then it looks you know it's sunlight
+ 
+
+ align:start position:0%
+then it looks you know it's sunlight
+it's coming from point source right so
+
+ align:start position:0%
+it's coming from point source right so
+ 
+
+ align:start position:0%
+it's coming from point source right so
+that's why
+
+ align:start position:0%
+that's why
+ 
+
+ align:start position:0%
+that's why
+especially korean
+
+ align:start position:0%
+especially korean
+ 
+
+ align:start position:0%
+especially korean
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah the live from
+
+ align:start position:0%
+yeah the live from
+ 
+
+ align:start position:0%
+yeah the live from
+press the button
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doesn't work yeah oh yeah
+
+ align:start position:0%
+doesn't work yeah oh yeah
+ 
+
+ align:start position:0%
+doesn't work yeah oh yeah
+so anyway so one of the terms i heard
+
+ align:start position:0%
+so anyway so one of the terms i heard
+ 
+
+ align:start position:0%
+so anyway so one of the terms i heard
+come off this computer flights which i
+
+ align:start position:0%
+come off this computer flights which i
+ 
+
+ align:start position:0%
+come off this computer flights which i
+guess really is abandonment
+
+ align:start position:0%
+guess really is abandonment
+ 
+
+ align:start position:0%
+guess really is abandonment
+to measure clearance but what
+
+ align:start position:0%
+to measure clearance but what
+ 
+
+ align:start position:0%
+to measure clearance but what
+exactly is
+
+ align:start position:0%
+exactly is
+ 
+
+ align:start position:0%
+exactly is
+overhearing those so here in points uh
+
+ align:start position:0%
+overhearing those so here in points uh
+ 
+
+ align:start position:0%
+overhearing those so here in points uh
+describing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah that's an exclusion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so actually
+
+ align:start position:0%
+so actually
+ 
+
+ align:start position:0%
+so actually
+uh it's it's a little bit
+
+ align:start position:0%
+uh it's it's a little bit
+ 
+
+ align:start position:0%
+uh it's it's a little bit
+lengthy to explain but what essentially
+
+ align:start position:0%
+lengthy to explain but what essentially
+ 
+
+ align:start position:0%
+lengthy to explain but what essentially
+the light i mean this kind of light is
+
+ align:start position:0%
+the light i mean this kind of light is
+ 
+
+ align:start position:0%
+the light i mean this kind of light is
+you know you excite some atom and when
+
+ align:start position:0%
+you know you excite some atom and when
+ 
+
+ align:start position:0%
+you know you excite some atom and when
+they are going down you get the energy
+
+ align:start position:0%
+they are going down you get the energy
+ 
+
+ align:start position:0%
+they are going down you get the energy
+right i mean
+
+ align:start position:0%
+right i mean
+ 
+
+ align:start position:0%
+right i mean
+basically light energy by
+
+ align:start position:0%
+basically light energy by
+ 
+
+ align:start position:0%
+basically light energy by
+e e to the i mean the energy is h new
+
+ align:start position:0%
+e e to the i mean the energy is h new
+ 
+
+ align:start position:0%
+e e to the i mean the energy is h new
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's not i mean this kind of
+
+ align:start position:0%
+but it's not i mean this kind of
+ 
+
+ align:start position:0%
+but it's not i mean this kind of
+spontaneous emission it's not correlated
+
+ align:start position:0%
+spontaneous emission it's not correlated
+ 
+
+ align:start position:0%
+spontaneous emission it's not correlated
+you have many many items but they are
+
+ align:start position:0%
+you have many many items but they are
+ 
+
+ align:start position:0%
+you have many many items but they are
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+synchronized right it's they're very
+
+ align:start position:0%
+synchronized right it's they're very
+ 
+
+ align:start position:0%
+synchronized right it's they're very
+emitting randomly
+
+ align:start position:0%
+emitting randomly
+ 
+
+ align:start position:0%
+emitting randomly
+so you basically you have some finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a wave train so in that a wave trend you
+
+ align:start position:0%
+a wave train so in that a wave trend you
+ 
+
+ align:start position:0%
+a wave train so in that a wave trend you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+basically coherently but you have many
+
+ align:start position:0%
+basically coherently but you have many
+ 
+
+ align:start position:0%
+basically coherently but you have many
+many of them
+
+ align:start position:0%
+many of them
+ 
+
+ align:start position:0%
+many of them
+with the random phase that's why you add
+
+ align:start position:0%
+with the random phase that's why you add
+ 
+
+ align:start position:0%
+with the random phase that's why you add
+them together then you get in current so
+
+ align:start position:0%
+them together then you get in current so
+ 
+
+ align:start position:0%
+them together then you get in current so
+coherence length is essentially what is
+
+ align:start position:0%
+coherence length is essentially what is
+ 
+
+ align:start position:0%
+coherence length is essentially what is
+the length of the a finite wave train
+
+ align:start position:0%
+the length of the a finite wave train
+ 
+
+ align:start position:0%
+the length of the a finite wave train
+that you can define uh deterministic
+
+ align:start position:0%
+that you can define uh deterministic
+ 
+
+ align:start position:0%
+that you can define uh deterministic
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+d1 so in the just imagine the
+
+ align:start position:0%
+d1 so in the just imagine the
+ 
+
+ align:start position:0%
+d1 so in the just imagine the
+microscience theorem if you have you
+
+ align:start position:0%
+microscience theorem if you have you
+ 
+
+ align:start position:0%
+microscience theorem if you have you
+have the
+
+ align:start position:0%
+have the
+ 
+
+ align:start position:0%
+have the
+optic capacity first d1 minus t2 but
+
+ align:start position:0%
+optic capacity first d1 minus t2 but
+ 
+
+ align:start position:0%
+optic capacity first d1 minus t2 but
+that difference is within the uh that
+
+ align:start position:0%
+that difference is within the uh that
+ 
+
+ align:start position:0%
+that difference is within the uh that
+the distance then you get
+
+ align:start position:0%
+the distance then you get
+ 
+
+ align:start position:0%
+the distance then you get
+interference right that's why we call
+
+ align:start position:0%
+interference right that's why we call
+ 
+
+ align:start position:0%
+interference right that's why we call
+the coherence length and coordinates
+
+ align:start position:0%
+the coherence length and coordinates
+ 
+
+ align:start position:0%
+the coherence length and coordinates
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah essentially that's it
+
+ align:start position:0%
+yeah essentially that's it
+ 
+
+ align:start position:0%
+yeah essentially that's it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+remember that if we have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh excuse me yep
+
+ align:start position:0%
+uh excuse me yep
+ 
+
+ align:start position:0%
+uh excuse me yep
+uh here i also have one question so i
+
+ align:start position:0%
+uh here i also have one question so i
+ 
+
+ align:start position:0%
+uh here i also have one question so i
+want to check whether this understanding
+
+ align:start position:0%
+want to check whether this understanding
+ 
+
+ align:start position:0%
+want to check whether this understanding
+is correct so let's see if the light
+
+ align:start position:0%
+is correct so let's see if the light
+ 
+
+ align:start position:0%
+is correct so let's see if the light
+come at the perfect parallel direction
+
+ align:start position:0%
+come at the perfect parallel direction
+ 
+
+ align:start position:0%
+come at the perfect parallel direction
+even though they have different
+
+ align:start position:0%
+even though they have different
+ 
+
+ align:start position:0%
+even though they have different
+wavelengths it's considered as
+
+ align:start position:0%
+wavelengths it's considered as
+ 
+
+ align:start position:0%
+wavelengths it's considered as
+especially coherent
+
+ align:start position:0%
+especially coherent
+ 
+
+ align:start position:0%
+especially coherent
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+even if life go into different direction
+
+ align:start position:0%
+even if life go into different direction
+ 
+
+ align:start position:0%
+even if life go into different direction
+but if they have perfect the single
+
+ align:start position:0%
+but if they have perfect the single
+ 
+
+ align:start position:0%
+but if they have perfect the single
+wavelengths they consider as a
+
+ align:start position:0%
+wavelengths they consider as a
+ 
+
+ align:start position:0%
+wavelengths they consider as a
+time coherent it is understanding
+
+ align:start position:0%
+time coherent it is understanding
+ 
+
+ align:start position:0%
+time coherent it is understanding
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+so actually if you have plane wave then
+
+ align:start position:0%
+so actually if you have plane wave then
+ 
+
+ align:start position:0%
+so actually if you have plane wave then
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+already assume your wave is specially
+
+ align:start position:0%
+already assume your wave is specially
+ 
+
+ align:start position:0%
+already assume your wave is specially
+coherent
+
+ align:start position:0%
+coherent
+ 
+
+ align:start position:0%
+coherent
+because plainly
+
+ align:start position:0%
+because plainly
+ 
+
+ align:start position:0%
+because plainly
+it doesn't really matter where you
+
+ align:start position:0%
+it doesn't really matter where you
+ 
+
+ align:start position:0%
+it doesn't really matter where you
+sample right they have always in phase
+
+ align:start position:0%
+sample right they have always in phase
+ 
+
+ align:start position:0%
+sample right they have always in phase
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+your assumption is especially coherent
+
+ align:start position:0%
+your assumption is especially coherent
+ 
+
+ align:start position:0%
+your assumption is especially coherent
+if you assume especially in a special
+
+ align:start position:0%
+if you assume especially in a special
+ 
+
+ align:start position:0%
+if you assume especially in a special
+coherent life
+
+ align:start position:0%
+coherent life
+ 
+
+ align:start position:0%
+coherent life
+and you mean even if they have different
+
+ align:start position:0%
+and you mean even if they have different
+ 
+
+ align:start position:0%
+and you mean even if they have different
+wavelengths
+
+ align:start position:0%
+wavelengths
+ 
+
+ align:start position:0%
+wavelengths
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yeah even yeah even though you have
+
+ align:start position:0%
+yeah even yeah even though you have
+ 
+
+ align:start position:0%
+yeah even yeah even though you have
+different wavelengths that's temporary
+
+ align:start position:0%
+different wavelengths that's temporary
+ 
+
+ align:start position:0%
+different wavelengths that's temporary
+in current but in space domain you have
+
+ align:start position:0%
+in current but in space domain you have
+ 
+
+ align:start position:0%
+in current but in space domain you have
+specially coherent
+
+ align:start position:0%
+specially coherent
+ 
+
+ align:start position:0%
+specially coherent
+yeah another way to think of especially
+
+ align:start position:0%
+yeah another way to think of especially
+ 
+
+ align:start position:0%
+yeah another way to think of especially
+in korean is you have many many plane
+
+ align:start position:0%
+in korean is you have many many plane
+ 
+
+ align:start position:0%
+in korean is you have many many plane
+waves
+
+ align:start position:0%
+waves
+ 
+
+ align:start position:0%
+waves
+and propagating all the different
+
+ align:start position:0%
+and propagating all the different
+ 
+
+ align:start position:0%
+and propagating all the different
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+but they are randomly
+
+ align:start position:0%
+but they are randomly
+ 
+
+ align:start position:0%
+but they are randomly
+they have random initial interface
+
+ align:start position:0%
+they have random initial interface
+ 
+
+ align:start position:0%
+they have random initial interface
+so you know
+
+ align:start position:0%
+so you know
+ 
+
+ align:start position:0%
+so you know
+basically especially in coin light you
+
+ align:start position:0%
+basically especially in coin light you
+ 
+
+ align:start position:0%
+basically especially in coin light you
+cannot really define unique uh
+
+ align:start position:0%
+cannot really define unique uh
+ 
+
+ align:start position:0%
+cannot really define unique uh
+propagation direction
+
+ align:start position:0%
+propagation direction
+ 
+
+ align:start position:0%
+propagation direction
+yeah but
+
+ align:start position:0%
+yeah but
+ 
+
+ align:start position:0%
+yeah but
+especially coherent light you can always
+
+ align:start position:0%
+especially coherent light you can always
+ 
+
+ align:start position:0%
+especially coherent light you can always
+define direction i mean even though
+
+ align:start position:0%
+define direction i mean even though
+ 
+
+ align:start position:0%
+define direction i mean even though
+wave it has all the direction but you
+
+ align:start position:0%
+wave it has all the direction but you
+ 
+
+ align:start position:0%
+wave it has all the direction but you
+can always say
+
+ align:start position:0%
+can always say
+ 
+
+ align:start position:0%
+can always say
+if you put if you define the position
+
+ align:start position:0%
+if you put if you define the position
+ 
+
+ align:start position:0%
+if you put if you define the position
+then that position you have a k vector
+
+ align:start position:0%
+then that position you have a k vector
+ 
+
+ align:start position:0%
+then that position you have a k vector
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+you can define the direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so let me yeah so let me just
+
+ align:start position:0%
+yeah so let me yeah so let me just
+ 
+
+ align:start position:0%
+yeah so let me yeah so let me just
+finish this
+
+ align:start position:0%
+finish this
+ 
+
+ align:start position:0%
+finish this
+thing so if if d1 and d2 are within the
+
+ align:start position:0%
+thing so if if d1 and d2 are within the
+ 
+
+ align:start position:0%
+thing so if if d1 and d2 are within the
+coherence length or current time then
+
+ align:start position:0%
+coherence length or current time then
+ 
+
+ align:start position:0%
+coherence length or current time then
+you get some
+
+ align:start position:0%
+you get some
+ 
+
+ align:start position:0%
+you get some
+interference but after that so basically
+
+ align:start position:0%
+interference but after that so basically
+ 
+
+ align:start position:0%
+interference but after that so basically
+this is essentially the coherence length
+
+ align:start position:0%
+this is essentially the coherence length
+ 
+
+ align:start position:0%
+this is essentially the coherence length
+of this particular source
+
+ align:start position:0%
+of this particular source
+ 
+
+ align:start position:0%
+of this particular source
+and remember that
+
+ align:start position:0%
+and remember that
+ 
+
+ align:start position:0%
+and remember that
+i mean this always happens so even
+
+ align:start position:0%
+i mean this always happens so even
+ 
+
+ align:start position:0%
+i mean this always happens so even
+though you have a white light you you
+
+ align:start position:0%
+though you have a white light you you
+ 
+
+ align:start position:0%
+though you have a white light you you
+can get interference but
+
+ align:start position:0%
+can get interference but
+ 
+
+ align:start position:0%
+can get interference but
+with within a very limited range okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how where did i stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah and
+
+ align:start position:0%
+okay yeah and
+ 
+
+ align:start position:0%
+okay yeah and
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+excuse me so another interesting is
+
+ align:start position:0%
+excuse me so another interesting is
+ 
+
+ align:start position:0%
+excuse me so another interesting is
+there is a laser
+
+ align:start position:0%
+there is a laser
+ 
+
+ align:start position:0%
+there is a laser
+that has a broadband which is per
+
+ align:start position:0%
+that has a broadband which is per
+ 
+
+ align:start position:0%
+that has a broadband which is per
+continuum laser
+
+ align:start position:0%
+continuum laser
+ 
+
+ align:start position:0%
+continuum laser
+so especially coherent but
+
+ align:start position:0%
+so especially coherent but
+ 
+
+ align:start position:0%
+so especially coherent but
+it's broadband so you have temporary
+
+ align:start position:0%
+it's broadband so you have temporary
+ 
+
+ align:start position:0%
+it's broadband so you have temporary
+inquiry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the other kind of
+
+ align:start position:0%
+and the other kind of
+ 
+
+ align:start position:0%
+and the other kind of
+this combination is temporary coherent
+
+ align:start position:0%
+this combination is temporary coherent
+ 
+
+ align:start position:0%
+this combination is temporary coherent
+but especially in korean
+
+ align:start position:0%
+but especially in korean
+ 
+
+ align:start position:0%
+but especially in korean
+so it's typically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+referred to quasim monochromatic
+
+ align:start position:0%
+referred to quasim monochromatic
+ 
+
+ align:start position:0%
+referred to quasim monochromatic
+temporary cohere
+
+ align:start position:0%
+temporary cohere
+ 
+
+ align:start position:0%
+temporary cohere
+and especially in korean
+
+ align:start position:0%
+and especially in korean
+ 
+
+ align:start position:0%
+and especially in korean
+so if you put a rotating diffuser which
+
+ align:start position:0%
+so if you put a rotating diffuser which
+ 
+
+ align:start position:0%
+so if you put a rotating diffuser which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+mean you rotate the uh
+
+ align:start position:0%
+mean you rotate the uh
+ 
+
+ align:start position:0%
+mean you rotate the uh
+ground glass or like milky glass in
+
+ align:start position:0%
+ground glass or like milky glass in
+ 
+
+ align:start position:0%
+ground glass or like milky glass in
+front of the razor in front of the laser
+
+ align:start position:0%
+front of the razor in front of the laser
+ 
+
+ align:start position:0%
+front of the razor in front of the laser
+then basically
+
+ align:start position:0%
+then basically
+ 
+
+ align:start position:0%
+then basically
+it induces some random phase to the
+
+ align:start position:0%
+it induces some random phase to the
+ 
+
+ align:start position:0%
+it induces some random phase to the
+laser beam or you can say it destroy the
+
+ align:start position:0%
+laser beam or you can say it destroy the
+ 
+
+ align:start position:0%
+laser beam or you can say it destroy the
+correlation of the laser beam so it's
+
+ align:start position:0%
+correlation of the laser beam so it's
+ 
+
+ align:start position:0%
+correlation of the laser beam so it's
+monochromatic so temporary coherent but
+
+ align:start position:0%
+monochromatic so temporary coherent but
+ 
+
+ align:start position:0%
+monochromatic so temporary coherent but
+in space domain it has a random phase so
+
+ align:start position:0%
+in space domain it has a random phase so
+ 
+
+ align:start position:0%
+in space domain it has a random phase so
+you get you can have the uh especially
+
+ align:start position:0%
+you get you can have the uh especially
+ 
+
+ align:start position:0%
+you get you can have the uh especially
+in current life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so these are lists of optical instrument
+
+ align:start position:0%
+so these are lists of optical instrument
+ 
+
+ align:start position:0%
+so these are lists of optical instrument
+uh using special coherence on imaging
+
+ align:start position:0%
+uh using special coherence on imaging
+ 
+
+ align:start position:0%
+uh using special coherence on imaging
+microsoft and stellar interferometer and
+
+ align:start position:0%
+microsoft and stellar interferometer and
+ 
+
+ align:start position:0%
+microsoft and stellar interferometer and
+the radio telescope they are basically
+
+ align:start position:0%
+the radio telescope they are basically
+ 
+
+ align:start position:0%
+the radio telescope they are basically
+uh measuring special coherence
+
+ align:start position:0%
+uh measuring special coherence
+ 
+
+ align:start position:0%
+uh measuring special coherence
+of the light coming from a distant star
+
+ align:start position:0%
+of the light coming from a distant star
+ 
+
+ align:start position:0%
+of the light coming from a distant star
+or sun or yeah they're basically for
+
+ align:start position:0%
+or sun or yeah they're basically for
+ 
+
+ align:start position:0%
+or sun or yeah they're basically for
+externally so they can measure
+
+ align:start position:0%
+externally so they can measure
+ 
+
+ align:start position:0%
+externally so they can measure
+for example diameter of a distant star
+
+ align:start position:0%
+for example diameter of a distant star
+ 
+
+ align:start position:0%
+for example diameter of a distant star
+you remember the spatial coherence is
+
+ align:start position:0%
+you remember the spatial coherence is
+ 
+
+ align:start position:0%
+you remember the spatial coherence is
+related to the source size and the
+
+ align:start position:0%
+related to the source size and the
+ 
+
+ align:start position:0%
+related to the source size and the
+distance so if you properly measure
+
+ align:start position:0%
+distance so if you properly measure
+ 
+
+ align:start position:0%
+distance so if you properly measure
+special coherence actually the envelope
+
+ align:start position:0%
+special coherence actually the envelope
+ 
+
+ align:start position:0%
+special coherence actually the envelope
+of the special coherence then you can
+
+ align:start position:0%
+of the special coherence then you can
+ 
+
+ align:start position:0%
+of the special coherence then you can
+estimate the diameter of the star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i believe microsoft are normal
+
+ align:start position:0%
+yeah i believe microsoft are normal
+ 
+
+ align:start position:0%
+yeah i believe microsoft are normal
+price for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and optical current tomography is
+
+ align:start position:0%
+and optical current tomography is
+ 
+
+ align:start position:0%
+and optical current tomography is
+actually uh utilizing temporal
+
+ align:start position:0%
+actually uh utilizing temporal
+ 
+
+ align:start position:0%
+actually uh utilizing temporal
+incurrence so as i just described if you
+
+ align:start position:0%
+incurrence so as i just described if you
+ 
+
+ align:start position:0%
+incurrence so as i just described if you
+even though you have y light
+
+ align:start position:0%
+even though you have y light
+ 
+
+ align:start position:0%
+even though you have y light
+if you are properly matched optical path
+
+ align:start position:0%
+if you are properly matched optical path
+ 
+
+ align:start position:0%
+if you are properly matched optical path
+difference then you can get interference
+
+ align:start position:0%
+difference then you can get interference
+ 
+
+ align:start position:0%
+difference then you can get interference
+within the very
+
+ align:start position:0%
+within the very
+ 
+
+ align:start position:0%
+within the very
+small range
+
+ align:start position:0%
+small range
+ 
+
+ align:start position:0%
+small range
+so let's say you have multiple layer
+
+ align:start position:0%
+so let's say you have multiple layer
+ 
+
+ align:start position:0%
+so let's say you have multiple layer
+like tissue and you construct a
+
+ align:start position:0%
+like tissue and you construct a
+ 
+
+ align:start position:0%
+like tissue and you construct a
+microscope interferometer with the white
+
+ align:start position:0%
+microscope interferometer with the white
+ 
+
+ align:start position:0%
+microscope interferometer with the white
+light and as you move the other mirror
+
+ align:start position:0%
+light and as you move the other mirror
+ 
+
+ align:start position:0%
+light and as you move the other mirror
+then if the optical pacifiers match then
+
+ align:start position:0%
+then if the optical pacifiers match then
+ 
+
+ align:start position:0%
+then if the optical pacifiers match then
+you get interference but if you slightly
+
+ align:start position:0%
+you get interference but if you slightly
+ 
+
+ align:start position:0%
+you get interference but if you slightly
+off that point then you don't get the
+
+ align:start position:0%
+off that point then you don't get the
+ 
+
+ align:start position:0%
+off that point then you don't get the
+interference right so if you plot the
+
+ align:start position:0%
+interference right so if you plot the
+ 
+
+ align:start position:0%
+interference right so if you plot the
+interference versus the distance of the
+
+ align:start position:0%
+interference versus the distance of the
+ 
+
+ align:start position:0%
+interference versus the distance of the
+mirror then you can
+
+ align:start position:0%
+mirror then you can
+ 
+
+ align:start position:0%
+mirror then you can
+see kind of the peak whenever you have
+
+ align:start position:0%
+see kind of the peak whenever you have
+ 
+
+ align:start position:0%
+see kind of the peak whenever you have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right position
+
+ align:start position:0%
+right position
+ 
+
+ align:start position:0%
+right position
+i mean whenever you have the right
+
+ align:start position:0%
+i mean whenever you have the right
+ 
+
+ align:start position:0%
+i mean whenever you have the right
+position to the t to each layer right so
+
+ align:start position:0%
+position to the t to each layer right so
+ 
+
+ align:start position:0%
+position to the t to each layer right so
+you can kind of do the optical
+
+ align:start position:0%
+you can kind of do the optical
+ 
+
+ align:start position:0%
+you can kind of do the optical
+sectioning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in
+
+ align:start position:0%
+and in
+ 
+
+ align:start position:0%
+and in
+the lithography like verification
+
+ align:start position:0%
+the lithography like verification
+ 
+
+ align:start position:0%
+the lithography like verification
+technique people
+
+ align:start position:0%
+technique people
+ 
+
+ align:start position:0%
+technique people
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+some special coils to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make basically make some uh
+
+ align:start position:0%
+make basically make some uh
+ 
+
+ align:start position:0%
+make basically make some uh
+it's a nice pattern
+
+ align:start position:0%
+it's a nice pattern
+ 
+
+ align:start position:0%
+it's a nice pattern
+because as we describe special currency
+
+ align:start position:0%
+because as we describe special currency
+ 
+
+ align:start position:0%
+because as we describe special currency
+is essentially
+
+ align:start position:0%
+is essentially
+ 
+
+ align:start position:0%
+is essentially
+affecting uh basically resolution and
+
+ align:start position:0%
+affecting uh basically resolution and
+ 
+
+ align:start position:0%
+affecting uh basically resolution and
+the the contrast of your image so
+
+ align:start position:0%
+the the contrast of your image so
+ 
+
+ align:start position:0%
+the the contrast of your image so
+yeah there are these kind of things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah even though we deal with the
+
+ align:start position:0%
+yeah even though we deal with the
+ 
+
+ align:start position:0%
+yeah even though we deal with the
+especially coherent with the wave system
+
+ align:start position:0%
+especially coherent with the wave system
+ 
+
+ align:start position:0%
+especially coherent with the wave system
+so what if we change the elimination
+
+ align:start position:0%
+so what if we change the elimination
+ 
+
+ align:start position:0%
+so what if we change the elimination
+with to
+
+ align:start position:0%
+with to
+ 
+
+ align:start position:0%
+with to
+especially in korean or
+
+ align:start position:0%
+especially in korean or
+ 
+
+ align:start position:0%
+especially in korean or
+temporary current
+
+ align:start position:0%
+temporary current
+ 
+
+ align:start position:0%
+temporary current
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know obviously my image will be
+
+ align:start position:0%
+you know obviously my image will be
+ 
+
+ align:start position:0%
+you know obviously my image will be
+different the way depending on the spec
+
+ align:start position:0%
+different the way depending on the spec
+ 
+
+ align:start position:0%
+different the way depending on the spec
+depending on the coherent state actually
+
+ align:start position:0%
+depending on the coherent state actually
+ 
+
+ align:start position:0%
+depending on the coherent state actually
+that's the bottom line of the uh today's
+
+ align:start position:0%
+that's the bottom line of the uh today's
+ 
+
+ align:start position:0%
+that's the bottom line of the uh today's
+course today's lecture
+
+ align:start position:0%
+course today's lecture
+ 
+
+ align:start position:0%
+course today's lecture
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so the first if we have the temporary
+
+ align:start position:0%
+so the first if we have the temporary
+ 
+
+ align:start position:0%
+so the first if we have the temporary
+current basically we if you have the
+
+ align:start position:0%
+current basically we if you have the
+ 
+
+ align:start position:0%
+current basically we if you have the
+broadband or many many colors
+
+ align:start position:0%
+broadband or many many colors
+ 
+
+ align:start position:0%
+broadband or many many colors
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the chromatic aberration is typical
+
+ align:start position:0%
+the chromatic aberration is typical
+ 
+
+ align:start position:0%
+the chromatic aberration is typical
+evidence that i have uh
+
+ align:start position:0%
+evidence that i have uh
+ 
+
+ align:start position:0%
+evidence that i have uh
+temporarily in current source
+
+ align:start position:0%
+temporarily in current source
+ 
+
+ align:start position:0%
+temporarily in current source
+and how to delete how to deal with it if
+
+ align:start position:0%
+and how to delete how to deal with it if
+ 
+
+ align:start position:0%
+and how to delete how to deal with it if
+you have many many colors
+
+ align:start position:0%
+you have many many colors
+ 
+
+ align:start position:0%
+you have many many colors
+it's pretty straightforward right so you
+
+ align:start position:0%
+it's pretty straightforward right so you
+ 
+
+ align:start position:0%
+it's pretty straightforward right so you
+can define point step function or atf or
+
+ align:start position:0%
+can define point step function or atf or
+ 
+
+ align:start position:0%
+can define point step function or atf or
+out or
+
+ align:start position:0%
+out or
+ 
+
+ align:start position:0%
+out or
+whatever it is you can define that thing
+
+ align:start position:0%
+whatever it is you can define that thing
+ 
+
+ align:start position:0%
+whatever it is you can define that thing
+for each wavelength so for example if i
+
+ align:start position:0%
+for each wavelength so for example if i
+ 
+
+ align:start position:0%
+for each wavelength so for example if i
+can define point sphere function for red
+
+ align:start position:0%
+can define point sphere function for red
+ 
+
+ align:start position:0%
+can define point sphere function for red
+wavelengths i can define points function
+
+ align:start position:0%
+wavelengths i can define points function
+ 
+
+ align:start position:0%
+wavelengths i can define points function
+for blue wavelengths so it's just you
+
+ align:start position:0%
+for blue wavelengths so it's just you
+ 
+
+ align:start position:0%
+for blue wavelengths so it's just you
+can do the straightforward fashion
+
+ align:start position:0%
+can do the straightforward fashion
+ 
+
+ align:start position:0%
+can do the straightforward fashion
+and special coherence is a little bit
+
+ align:start position:0%
+and special coherence is a little bit
+ 
+
+ align:start position:0%
+and special coherence is a little bit
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i mean you need to be careful
+
+ align:start position:0%
+i mean you need to be careful
+ 
+
+ align:start position:0%
+i mean you need to be careful
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the bottom actually this is the taken
+
+ align:start position:0%
+the bottom actually this is the taken
+ 
+
+ align:start position:0%
+the bottom actually this is the taken
+message of the lecture if the
+
+ align:start position:0%
+message of the lecture if the
+ 
+
+ align:start position:0%
+message of the lecture if the
+illumination is specially coherent then
+
+ align:start position:0%
+illumination is specially coherent then
+ 
+
+ align:start position:0%
+illumination is specially coherent then
+input field is
+
+ align:start position:0%
+input field is
+ 
+
+ align:start position:0%
+input field is
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+of the actually output field sorry after
+
+ align:start position:0%
+of the actually output field sorry after
+ 
+
+ align:start position:0%
+of the actually output field sorry after
+field is a convolution of input field
+
+ align:start position:0%
+field is a convolution of input field
+ 
+
+ align:start position:0%
+field is a convolution of input field
+with the coherent point spray function
+
+ align:start position:0%
+with the coherent point spray function
+ 
+
+ align:start position:0%
+with the coherent point spray function
+as we all know right
+
+ align:start position:0%
+as we all know right
+ 
+
+ align:start position:0%
+as we all know right
+but if the illumination is specially in
+
+ align:start position:0%
+but if the illumination is specially in
+ 
+
+ align:start position:0%
+but if the illumination is specially in
+coherent then
+
+ align:start position:0%
+coherent then
+ 
+
+ align:start position:0%
+coherent then
+output intensity not the output field so
+
+ align:start position:0%
+output intensity not the output field so
+ 
+
+ align:start position:0%
+output intensity not the output field so
+output intensity is a convolution
+
+ align:start position:0%
+output intensity is a convolution
+ 
+
+ align:start position:0%
+output intensity is a convolution
+of the input intensity
+
+ align:start position:0%
+of the input intensity
+ 
+
+ align:start position:0%
+of the input intensity
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+in current 0.5 function
+
+ align:start position:0%
+in current 0.5 function
+ 
+
+ align:start position:0%
+in current 0.5 function
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah so that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means
+
+ align:start position:0%
+which means
+ 
+
+ align:start position:0%
+which means
+if you have uh especially coherent
+
+ align:start position:0%
+if you have uh especially coherent
+ 
+
+ align:start position:0%
+if you have uh especially coherent
+imaging then
+
+ align:start position:0%
+imaging then
+ 
+
+ align:start position:0%
+imaging then
+field a linear system right you can do
+
+ align:start position:0%
+field a linear system right you can do
+ 
+
+ align:start position:0%
+field a linear system right you can do
+the convolution in field
+
+ align:start position:0%
+the convolution in field
+ 
+
+ align:start position:0%
+the convolution in field
+but if you
+
+ align:start position:0%
+but if you
+ 
+
+ align:start position:0%
+but if you
+if the elimination is in coherent then
+
+ align:start position:0%
+if the elimination is in coherent then
+ 
+
+ align:start position:0%
+if the elimination is in coherent then
+intensity is a linear system so you can
+
+ align:start position:0%
+intensity is a linear system so you can
+ 
+
+ align:start position:0%
+intensity is a linear system so you can
+deal with the intensity with the
+
+ align:start position:0%
+deal with the intensity with the
+ 
+
+ align:start position:0%
+deal with the intensity with the
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+so yeah so rest of the lecture we're
+
+ align:start position:0%
+so yeah so rest of the lecture we're
+ 
+
+ align:start position:0%
+so yeah so rest of the lecture we're
+gonna deal with the
+
+ align:start position:0%
+gonna deal with the
+ 
+
+ align:start position:0%
+gonna deal with the
+uh special in coin elimination so how we
+
+ align:start position:0%
+uh special in coin elimination so how we
+ 
+
+ align:start position:0%
+uh special in coin elimination so how we
+can define uh point five function and
+
+ align:start position:0%
+can define uh point five function and
+ 
+
+ align:start position:0%
+can define uh point five function and
+transfer function and etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so first let's review uh what we
+
+ align:start position:0%
+so first let's review uh what we
+ 
+
+ align:start position:0%
+so first let's review uh what we
+have learned so far
+
+ align:start position:0%
+have learned so far
+ 
+
+ align:start position:0%
+have learned so far
+so we have four four f system with the
+
+ align:start position:0%
+so we have four four f system with the
+ 
+
+ align:start position:0%
+so we have four four f system with the
+two lengths
+
+ align:start position:0%
+two lengths
+ 
+
+ align:start position:0%
+two lengths
+whose focal lengths are f1 and f2
+
+ align:start position:0%
+whose focal lengths are f1 and f2
+ 
+
+ align:start position:0%
+whose focal lengths are f1 and f2
+and typically we put our input
+
+ align:start position:0%
+and typically we put our input
+ 
+
+ align:start position:0%
+and typically we put our input
+transparency a grading at the input
+
+ align:start position:0%
+transparency a grading at the input
+ 
+
+ align:start position:0%
+transparency a grading at the input
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+and we illuminate with the with
+
+ align:start position:0%
+and we illuminate with the with
+ 
+
+ align:start position:0%
+and we illuminate with the with
+especially coherent elimination and also
+
+ align:start position:0%
+especially coherent elimination and also
+ 
+
+ align:start position:0%
+especially coherent elimination and also
+temporary coherence right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the input field just arrived after
+
+ align:start position:0%
+so the input field just arrived after
+ 
+
+ align:start position:0%
+so the input field just arrived after
+the input transparency is going to be
+
+ align:start position:0%
+the input transparency is going to be
+ 
+
+ align:start position:0%
+the input transparency is going to be
+just product of the illumination field
+
+ align:start position:0%
+just product of the illumination field
+ 
+
+ align:start position:0%
+just product of the illumination field
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+complex transparency that's the the
+
+ align:start position:0%
+complex transparency that's the the
+ 
+
+ align:start position:0%
+complex transparency that's the the
+input field and we're going to take the
+
+ align:start position:0%
+input field and we're going to take the
+ 
+
+ align:start position:0%
+input field and we're going to take the
+phase transform
+
+ align:start position:0%
+phase transform
+ 
+
+ align:start position:0%
+phase transform
+to get the field at the free plane and
+
+ align:start position:0%
+to get the field at the free plane and
+ 
+
+ align:start position:0%
+to get the field at the free plane and
+another fret transform you'll get the
+
+ align:start position:0%
+another fret transform you'll get the
+ 
+
+ align:start position:0%
+another fret transform you'll get the
+final image
+
+ align:start position:0%
+final image
+ 
+
+ align:start position:0%
+final image
+and from that we all know that
+
+ align:start position:0%
+and from that we all know that
+ 
+
+ align:start position:0%
+and from that we all know that
+uh amplitude transfer function is
+
+ align:start position:0%
+uh amplitude transfer function is
+ 
+
+ align:start position:0%
+uh amplitude transfer function is
+nothing but
+
+ align:start position:0%
+nothing but
+ 
+
+ align:start position:0%
+nothing but
+the purple
+
+ align:start position:0%
+the purple
+ 
+
+ align:start position:0%
+the purple
+uh ppl mask function with the
+
+ align:start position:0%
+uh ppl mask function with the
+ 
+
+ align:start position:0%
+uh ppl mask function with the
+coordinate scaling right so atf h of u
+
+ align:start position:0%
+coordinate scaling right so atf h of u
+ 
+
+ align:start position:0%
+coordinate scaling right so atf h of u
+and v is
+
+ align:start position:0%
+and v is
+ 
+
+ align:start position:0%
+and v is
+some constant and
+
+ align:start position:0%
+some constant and
+ 
+
+ align:start position:0%
+some constant and
+p mass function
+
+ align:start position:0%
+p mass function
+ 
+
+ align:start position:0%
+p mass function
+and lambda f 1 u and lambda 1 v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+point function in field is
+
+ align:start position:0%
+point function in field is
+ 
+
+ align:start position:0%
+point function in field is
+just free transform of the
+
+ align:start position:0%
+just free transform of the
+ 
+
+ align:start position:0%
+just free transform of the
+atf so
+
+ align:start position:0%
+atf so
+ 
+
+ align:start position:0%
+atf so
+or you can say it's free transform the
+
+ align:start position:0%
+or you can say it's free transform the
+ 
+
+ align:start position:0%
+or you can say it's free transform the
+purple function
+
+ align:start position:0%
+purple function
+ 
+
+ align:start position:0%
+purple function
+so this is the coherent points function
+
+ align:start position:0%
+so this is the coherent points function
+ 
+
+ align:start position:0%
+so this is the coherent points function
+and you can define coincident function
+
+ align:start position:0%
+and you can define coincident function
+ 
+
+ align:start position:0%
+and you can define coincident function
+in reduced coordinate
+
+ align:start position:0%
+in reduced coordinate
+ 
+
+ align:start position:0%
+in reduced coordinate
+and the relation in between input and
+
+ align:start position:0%
+and the relation in between input and
+ 
+
+ align:start position:0%
+and the relation in between input and
+output field is
+
+ align:start position:0%
+output field is
+ 
+
+ align:start position:0%
+output field is
+this convolution right so g output i
+
+ align:start position:0%
+this convolution right so g output i
+ 
+
+ align:start position:0%
+this convolution right so g output i
+mean output field is convolutional input
+
+ align:start position:0%
+mean output field is convolutional input
+ 
+
+ align:start position:0%
+mean output field is convolutional input
+field and this is coherent point
+
+ align:start position:0%
+field and this is coherent point
+ 
+
+ align:start position:0%
+field and this is coherent point
+function which is defined in field
+
+ align:start position:0%
+function which is defined in field
+ 
+
+ align:start position:0%
+function which is defined in field
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+this is the stuff that we all know
+
+ align:start position:0%
+this is the stuff that we all know
+ 
+
+ align:start position:0%
+this is the stuff that we all know
+so the next thing is
+
+ align:start position:0%
+so the next thing is
+ 
+
+ align:start position:0%
+so the next thing is
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+let me put the two pin holes at the
+
+ align:start position:0%
+let me put the two pin holes at the
+ 
+
+ align:start position:0%
+let me put the two pin holes at the
+input plane so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and illuminate with especially coherent
+
+ align:start position:0%
+and illuminate with especially coherent
+ 
+
+ align:start position:0%
+and illuminate with especially coherent
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+so basically we have young
+
+ align:start position:0%
+so basically we have young
+ 
+
+ align:start position:0%
+so basically we have young
+interferometer here and
+
+ align:start position:0%
+interferometer here and
+ 
+
+ align:start position:0%
+interferometer here and
+i'm gonna image that
+
+ align:start position:0%
+i'm gonna image that
+ 
+
+ align:start position:0%
+i'm gonna image that
+pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since it is coherent you see it is
+
+ align:start position:0%
+and since it is coherent you see it is
+ 
+
+ align:start position:0%
+and since it is coherent you see it is
+illuminated with the coherent line so
+
+ align:start position:0%
+illuminated with the coherent line so
+ 
+
+ align:start position:0%
+illuminated with the coherent line so
+what essentially
+
+ align:start position:0%
+what essentially
+ 
+
+ align:start position:0%
+what essentially
+i have at the image plane is actually
+
+ align:start position:0%
+i have at the image plane is actually
+ 
+
+ align:start position:0%
+i have at the image plane is actually
+2.3 function
+
+ align:start position:0%
+2.3 function
+ 
+
+ align:start position:0%
+2.3 function
+coming from two pin all right so in the
+
+ align:start position:0%
+coming from two pin all right so in the
+ 
+
+ align:start position:0%
+coming from two pin all right so in the
+upper image actually coming from the
+
+ align:start position:0%
+upper image actually coming from the
+ 
+
+ align:start position:0%
+upper image actually coming from the
+lower panel and the lower image actually
+
+ align:start position:0%
+lower panel and the lower image actually
+ 
+
+ align:start position:0%
+lower panel and the lower image actually
+coming from the upper pinout but i have
+
+ align:start position:0%
+coming from the upper pinout but i have
+ 
+
+ align:start position:0%
+coming from the upper pinout but i have
+the addition
+
+ align:start position:0%
+the addition
+ 
+
+ align:start position:0%
+the addition
+of two
+
+ align:start position:0%
+of two
+ 
+
+ align:start position:0%
+of two
+point three function which is shifted by
+
+ align:start position:0%
+point three function which is shifted by
+ 
+
+ align:start position:0%
+point three function which is shifted by
+the position of the p-troop signal and i
+
+ align:start position:0%
+the position of the p-troop signal and i
+ 
+
+ align:start position:0%
+the position of the p-troop signal and i
+may have some initial phase a one e to
+
+ align:start position:0%
+may have some initial phase a one e to
+ 
+
+ align:start position:0%
+may have some initial phase a one e to
+the e to the phi one and a two e to the
+
+ align:start position:0%
+the e to the phi one and a two e to the
+ 
+
+ align:start position:0%
+the e to the phi one and a two e to the
+phi two but the bottom line is in quran
+
+ align:start position:0%
+phi two but the bottom line is in quran
+ 
+
+ align:start position:0%
+phi two but the bottom line is in quran
+case i just have
+
+ align:start position:0%
+case i just have
+ 
+
+ align:start position:0%
+case i just have
+coherent addition of 2.3 function like
+
+ align:start position:0%
+coherent addition of 2.3 function like
+ 
+
+ align:start position:0%
+coherent addition of 2.3 function like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and to get the intensity
+
+ align:start position:0%
+and to get the intensity
+ 
+
+ align:start position:0%
+and to get the intensity
+as you all know you just
+
+ align:start position:0%
+as you all know you just
+ 
+
+ align:start position:0%
+as you all know you just
+take the magnitude square
+
+ align:start position:0%
+take the magnitude square
+ 
+
+ align:start position:0%
+take the magnitude square
+of the sum and if we expand it then we
+
+ align:start position:0%
+of the sum and if we expand it then we
+ 
+
+ align:start position:0%
+of the sum and if we expand it then we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+two dc term which is intensity of the
+
+ align:start position:0%
+two dc term which is intensity of the
+ 
+
+ align:start position:0%
+two dc term which is intensity of the
+first point sphere function and
+
+ align:start position:0%
+first point sphere function and
+ 
+
+ align:start position:0%
+first point sphere function and
+intensity of the second point function
+
+ align:start position:0%
+intensity of the second point function
+ 
+
+ align:start position:0%
+intensity of the second point function
+and we have some additional
+
+ align:start position:0%
+and we have some additional
+ 
+
+ align:start position:0%
+and we have some additional
+modulation term which means i have some
+
+ align:start position:0%
+modulation term which means i have some
+ 
+
+ align:start position:0%
+modulation term which means i have some
+interference right so it's a1 a2 and
+
+ align:start position:0%
+interference right so it's a1 a2 and
+ 
+
+ align:start position:0%
+interference right so it's a1 a2 and
+rear part of this guy
+
+ align:start position:0%
+rear part of this guy
+ 
+
+ align:start position:0%
+rear part of this guy
+but you know real part is always cosine
+
+ align:start position:0%
+but you know real part is always cosine
+ 
+
+ align:start position:0%
+but you know real part is always cosine
+right so if you change the face
+
+ align:start position:0%
+right so if you change the face
+ 
+
+ align:start position:0%
+right so if you change the face
+you have some cos sinusoidal modulation
+
+ align:start position:0%
+you have some cos sinusoidal modulation
+ 
+
+ align:start position:0%
+you have some cos sinusoidal modulation
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so this is sometimes called
+
+ align:start position:0%
+yeah so this is sometimes called
+ 
+
+ align:start position:0%
+yeah so this is sometimes called
+interference term or
+
+ align:start position:0%
+interference term or
+ 
+
+ align:start position:0%
+interference term or
+cluster
+
+ align:start position:0%
+cluster
+ 
+
+ align:start position:0%
+cluster
+implies that you have interference
+
+ align:start position:0%
+implies that you have interference
+ 
+
+ align:start position:0%
+implies that you have interference
+so with
+
+ align:start position:0%
+so with
+ 
+
+ align:start position:0%
+so with
+this parameter so initial phase is just
+
+ align:start position:0%
+this parameter so initial phase is just
+ 
+
+ align:start position:0%
+this parameter so initial phase is just
+e to the uh negative pi over 3 and
+
+ align:start position:0%
+e to the uh negative pi over 3 and
+ 
+
+ align:start position:0%
+e to the uh negative pi over 3 and
+the other one is pi the positive pi over
+
+ align:start position:0%
+the other one is pi the positive pi over
+ 
+
+ align:start position:0%
+the other one is pi the positive pi over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+then if i plot this intensity
+
+ align:start position:0%
+then if i plot this intensity
+ 
+
+ align:start position:0%
+then if i plot this intensity
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+i'm going to have this kind this blue
+
+ align:start position:0%
+i'm going to have this kind this blue
+ 
+
+ align:start position:0%
+i'm going to have this kind this blue
+line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so this is the case of especially
+
+ align:start position:0%
+yeah so this is the case of especially
+ 
+
+ align:start position:0%
+yeah so this is the case of especially
+coherent illumination
+
+ align:start position:0%
+coherent illumination
+ 
+
+ align:start position:0%
+coherent illumination
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so next let's suppose if i illuminate
+
+ align:start position:0%
+so next let's suppose if i illuminate
+ 
+
+ align:start position:0%
+so next let's suppose if i illuminate
+with the in current in coin elimination
+
+ align:start position:0%
+with the in current in coin elimination
+ 
+
+ align:start position:0%
+with the in current in coin elimination
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh as i as
+
+ align:start position:0%
+uh as i as
+ 
+
+ align:start position:0%
+uh as i as
+as i described earlier so the difference
+
+ align:start position:0%
+as i described earlier so the difference
+ 
+
+ align:start position:0%
+as i described earlier so the difference
+between in korean and korean is you know
+
+ align:start position:0%
+between in korean and korean is you know
+ 
+
+ align:start position:0%
+between in korean and korean is you know
+i don't have interference term if i
+
+ align:start position:0%
+i don't have interference term if i
+ 
+
+ align:start position:0%
+i don't have interference term if i
+eliminate with the
+
+ align:start position:0%
+eliminate with the
+ 
+
+ align:start position:0%
+eliminate with the
+incoherent source right so at the
+
+ align:start position:0%
+incoherent source right so at the
+ 
+
+ align:start position:0%
+incoherent source right so at the
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+i only have these two terms just
+
+ align:start position:0%
+i only have these two terms just
+ 
+
+ align:start position:0%
+i only have these two terms just
+intensity of the first position function
+
+ align:start position:0%
+intensity of the first position function
+ 
+
+ align:start position:0%
+intensity of the first position function
+and intensity of the second point
+
+ align:start position:0%
+and intensity of the second point
+ 
+
+ align:start position:0%
+and intensity of the second point
+function and i don't have this the extra
+
+ align:start position:0%
+function and i don't have this the extra
+ 
+
+ align:start position:0%
+function and i don't have this the extra
+cosine term
+
+ align:start position:0%
+cosine term
+ 
+
+ align:start position:0%
+cosine term
+so this is just
+
+ align:start position:0%
+so this is just
+ 
+
+ align:start position:0%
+so this is just
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i plot the intensity with the same
+
+ align:start position:0%
+if i plot the intensity with the same
+ 
+
+ align:start position:0%
+if i plot the intensity with the same
+parameter then this is how it looks like
+
+ align:start position:0%
+parameter then this is how it looks like
+ 
+
+ align:start position:0%
+parameter then this is how it looks like
+and if i put together
+
+ align:start position:0%
+and if i put together
+ 
+
+ align:start position:0%
+and if i put together
+then the upper left is the
+
+ align:start position:0%
+then the upper left is the
+ 
+
+ align:start position:0%
+then the upper left is the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the two intensity uh profile
+
+ align:start position:0%
+the two intensity uh profile
+ 
+
+ align:start position:0%
+the two intensity uh profile
+of cohen and in current elimination
+
+ align:start position:0%
+of cohen and in current elimination
+ 
+
+ align:start position:0%
+of cohen and in current elimination
+so they are slightly different right
+
+ align:start position:0%
+so they are slightly different right
+ 
+
+ align:start position:0%
+so they are slightly different right
+and if i play with a different parameter
+
+ align:start position:0%
+and if i play with a different parameter
+ 
+
+ align:start position:0%
+and if i play with a different parameter
+like uh with different an interface
+
+ align:start position:0%
+like uh with different an interface
+ 
+
+ align:start position:0%
+like uh with different an interface
+and in this case
+
+ align:start position:0%
+and in this case
+ 
+
+ align:start position:0%
+and in this case
+my positive function is as extra linear
+
+ align:start position:0%
+my positive function is as extra linear
+ 
+
+ align:start position:0%
+my positive function is as extra linear
+phase term then the difference is quite
+
+ align:start position:0%
+phase term then the difference is quite
+ 
+
+ align:start position:0%
+phase term then the difference is quite
+dramatic
+
+ align:start position:0%
+dramatic
+ 
+
+ align:start position:0%
+dramatic
+so you always have to careful what kind
+
+ align:start position:0%
+so you always have to careful what kind
+ 
+
+ align:start position:0%
+so you always have to careful what kind
+of coherence
+
+ align:start position:0%
+of coherence
+ 
+
+ align:start position:0%
+of coherence
+your elimination is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in previous case which is especially
+
+ align:start position:0%
+in previous case which is especially
+ 
+
+ align:start position:0%
+in previous case which is especially
+coherent then the input field and output
+
+ align:start position:0%
+coherent then the input field and output
+ 
+
+ align:start position:0%
+coherent then the input field and output
+field is
+
+ align:start position:0%
+field is
+ 
+
+ align:start position:0%
+field is
+they are linear so you can use the
+
+ align:start position:0%
+they are linear so you can use the
+ 
+
+ align:start position:0%
+they are linear so you can use the
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+especially in coherent case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we deal with the input intensity
+
+ align:start position:0%
+so we deal with the input intensity
+ 
+
+ align:start position:0%
+so we deal with the input intensity
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+uh which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know so we're gonna deal with
+
+ align:start position:0%
+i don't know so we're gonna deal with
+ 
+
+ align:start position:0%
+i don't know so we're gonna deal with
+the input intensity and output intensity
+
+ align:start position:0%
+the input intensity and output intensity
+ 
+
+ align:start position:0%
+the input intensity and output intensity
+and at the image plane
+
+ align:start position:0%
+and at the image plane
+ 
+
+ align:start position:0%
+and at the image plane
+the intensity will be
+
+ align:start position:0%
+the intensity will be
+ 
+
+ align:start position:0%
+the intensity will be
+will be summed in currently
+
+ align:start position:0%
+will be summed in currently
+ 
+
+ align:start position:0%
+will be summed in currently
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i used i illuminate with a
+
+ align:start position:0%
+so i used i illuminate with a
+ 
+
+ align:start position:0%
+so i used i illuminate with a
+intensity i mean increasing in coherent
+
+ align:start position:0%
+intensity i mean increasing in coherent
+ 
+
+ align:start position:0%
+intensity i mean increasing in coherent
+illumination with the intensity i illume
+
+ align:start position:0%
+illumination with the intensity i illume
+ 
+
+ align:start position:0%
+illumination with the intensity i illume
+and g sub t is the complex transparency
+
+ align:start position:0%
+and g sub t is the complex transparency
+ 
+
+ align:start position:0%
+and g sub t is the complex transparency
+but you know this is in this is field so
+
+ align:start position:0%
+but you know this is in this is field so
+ 
+
+ align:start position:0%
+but you know this is in this is field so
+you have to take
+
+ align:start position:0%
+you have to take
+ 
+
+ align:start position:0%
+you have to take
+negative square so
+
+ align:start position:0%
+negative square so
+ 
+
+ align:start position:0%
+negative square so
+product of this guy
+
+ align:start position:0%
+product of this guy
+ 
+
+ align:start position:0%
+product of this guy
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+is basically your input intensity right
+
+ align:start position:0%
+is basically your input intensity right
+ 
+
+ align:start position:0%
+is basically your input intensity right
+so this illumination intensity and
+
+ align:start position:0%
+so this illumination intensity and
+ 
+
+ align:start position:0%
+so this illumination intensity and
+intensity of your grading
+
+ align:start position:0%
+intensity of your grading
+ 
+
+ align:start position:0%
+intensity of your grading
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is point square function
+
+ align:start position:0%
+this is point square function
+ 
+
+ align:start position:0%
+this is point square function
+actually coherent points function but
+
+ align:start position:0%
+actually coherent points function but
+ 
+
+ align:start position:0%
+actually coherent points function but
+you take the magnitude square
+
+ align:start position:0%
+you take the magnitude square
+ 
+
+ align:start position:0%
+you take the magnitude square
+right because you know you take the
+
+ align:start position:0%
+right because you know you take the
+ 
+
+ align:start position:0%
+right because you know you take the
+magnitude square to get intensity so we
+
+ align:start position:0%
+magnitude square to get intensity so we
+ 
+
+ align:start position:0%
+magnitude square to get intensity so we
+define
+
+ align:start position:0%
+define
+ 
+
+ align:start position:0%
+define
+excuse me the defined equivalent points
+
+ align:start position:0%
+excuse me the defined equivalent points
+ 
+
+ align:start position:0%
+excuse me the defined equivalent points
+of function
+
+ align:start position:0%
+of function
+ 
+
+ align:start position:0%
+of function
+which is ipsf is actually negative
+
+ align:start position:0%
+which is ipsf is actually negative
+ 
+
+ align:start position:0%
+which is ipsf is actually negative
+square of the coherent pointer function
+
+ align:start position:0%
+square of the coherent pointer function
+ 
+
+ align:start position:0%
+square of the coherent pointer function
+it's pretty simple right you have
+
+ align:start position:0%
+it's pretty simple right you have
+ 
+
+ align:start position:0%
+it's pretty simple right you have
+coins um
+
+ align:start position:0%
+coins um
+ 
+
+ align:start position:0%
+coins um
+points a function in fair and if you
+
+ align:start position:0%
+points a function in fair and if you
+ 
+
+ align:start position:0%
+points a function in fair and if you
+just take the intensity then that's the
+
+ align:start position:0%
+just take the intensity then that's the
+ 
+
+ align:start position:0%
+just take the intensity then that's the
+you know intensity points for function
+
+ align:start position:0%
+you know intensity points for function
+ 
+
+ align:start position:0%
+you know intensity points for function
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you you probably already noticed the
+
+ align:start position:0%
+you you probably already noticed the
+ 
+
+ align:start position:0%
+you you probably already noticed the
+difference right so if you use the
+
+ align:start position:0%
+difference right so if you use the
+ 
+
+ align:start position:0%
+difference right so if you use the
+coherent case if you use the coherent
+
+ align:start position:0%
+coherent case if you use the coherent
+ 
+
+ align:start position:0%
+coherent case if you use the coherent
+elimination then
+
+ align:start position:0%
+elimination then
+ 
+
+ align:start position:0%
+elimination then
+the fields are
+
+ align:start position:0%
+the fields are
+ 
+
+ align:start position:0%
+the fields are
+related to convolution but in current
+
+ align:start position:0%
+related to convolution but in current
+ 
+
+ align:start position:0%
+related to convolution but in current
+case intensity are related to
+
+ align:start position:0%
+case intensity are related to
+ 
+
+ align:start position:0%
+case intensity are related to
+convolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and points of function are different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any question
+
+ align:start position:0%
+any question
+ 
+
+ align:start position:0%
+any question
+i'm going to a little bit fast so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we just defined the intensity
+
+ align:start position:0%
+so we just defined the intensity
+ 
+
+ align:start position:0%
+so we just defined the intensity
+intensity points function which is
+
+ align:start position:0%
+intensity points function which is
+ 
+
+ align:start position:0%
+intensity points function which is
+magnitude square of current point side
+
+ align:start position:0%
+magnitude square of current point side
+ 
+
+ align:start position:0%
+magnitude square of current point side
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and by analogy that i mean
+
+ align:start position:0%
+and by analogy that i mean
+ 
+
+ align:start position:0%
+and by analogy that i mean
+uh in
+
+ align:start position:0%
+uh in
+ 
+
+ align:start position:0%
+uh in
+the coherence case we had the current
+
+ align:start position:0%
+the coherence case we had the current
+ 
+
+ align:start position:0%
+the coherence case we had the current
+point spread function and if you take
+
+ align:start position:0%
+point spread function and if you take
+ 
+
+ align:start position:0%
+point spread function and if you take
+the free transform of the coherent point
+
+ align:start position:0%
+the free transform of the coherent point
+ 
+
+ align:start position:0%
+the free transform of the coherent point
+function then there is that is atf right
+
+ align:start position:0%
+function then there is that is atf right
+ 
+
+ align:start position:0%
+function then there is that is atf right
+amplitude transfer function
+
+ align:start position:0%
+amplitude transfer function
+ 
+
+ align:start position:0%
+amplitude transfer function
+so we can define the same transfer
+
+ align:start position:0%
+so we can define the same transfer
+ 
+
+ align:start position:0%
+so we can define the same transfer
+function for in core in coherent point
+
+ align:start position:0%
+function for in core in coherent point
+ 
+
+ align:start position:0%
+function for in core in coherent point
+function which is otf here
+
+ align:start position:0%
+function which is otf here
+ 
+
+ align:start position:0%
+function which is otf here
+so that's derivation that
+
+ align:start position:0%
+so that's derivation that
+ 
+
+ align:start position:0%
+so that's derivation that
+deviation says that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so actually
+
+ align:start position:0%
+so actually
+ 
+
+ align:start position:0%
+so actually
+the small h is the
+
+ align:start position:0%
+the small h is the
+ 
+
+ align:start position:0%
+the small h is the
+coherent point function and
+
+ align:start position:0%
+coherent point function and
+ 
+
+ align:start position:0%
+coherent point function and
+the capital h is
+
+ align:start position:0%
+the capital h is
+ 
+
+ align:start position:0%
+the capital h is
+atf
+
+ align:start position:0%
+atf
+ 
+
+ align:start position:0%
+atf
+which is so they are
+
+ align:start position:0%
+which is so they are
+ 
+
+ align:start position:0%
+which is so they are
+free to some pair
+
+ align:start position:0%
+free to some pair
+ 
+
+ align:start position:0%
+free to some pair
+and h i which is intensity point three
+
+ align:start position:0%
+and h i which is intensity point three
+ 
+
+ align:start position:0%
+and h i which is intensity point three
+function is the magnitude square of the
+
+ align:start position:0%
+function is the magnitude square of the
+ 
+
+ align:start position:0%
+function is the magnitude square of the
+coherent point of function
+
+ align:start position:0%
+coherent point of function
+ 
+
+ align:start position:0%
+coherent point of function
+but h i and
+
+ align:start position:0%
+but h i and
+ 
+
+ align:start position:0%
+but h i and
+otf which is
+
+ align:start position:0%
+otf which is
+ 
+
+ align:start position:0%
+otf which is
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+weird h
+
+ align:start position:0%
+weird h
+ 
+
+ align:start position:0%
+weird h
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+here actually they are also transform a
+
+ align:start position:0%
+here actually they are also transform a
+ 
+
+ align:start position:0%
+here actually they are also transform a
+free transform pair
+
+ align:start position:0%
+free transform pair
+ 
+
+ align:start position:0%
+free transform pair
+so if you go through this derivation
+
+ align:start position:0%
+so if you go through this derivation
+ 
+
+ align:start position:0%
+so if you go through this derivation
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+it will prove actually they are
+
+ align:start position:0%
+it will prove actually they are
+ 
+
+ align:start position:0%
+it will prove actually they are
+actually to prove that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otf is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otf is actually
+
+ align:start position:0%
+otf is actually
+ 
+
+ align:start position:0%
+otf is actually
+this integration of
+
+ align:start position:0%
+this integration of
+ 
+
+ align:start position:0%
+this integration of
+atf
+
+ align:start position:0%
+atf
+ 
+
+ align:start position:0%
+atf
+so if you once you have atf and you can
+
+ align:start position:0%
+so if you once you have atf and you can
+ 
+
+ align:start position:0%
+so if you once you have atf and you can
+compute and
+
+ align:start position:0%
+compute and
+ 
+
+ align:start position:0%
+compute and
+after you compute this integration then
+
+ align:start position:0%
+after you compute this integration then
+ 
+
+ align:start position:0%
+after you compute this integration then
+you get rtf which is autocorrelation
+
+ align:start position:0%
+you get rtf which is autocorrelation
+ 
+
+ align:start position:0%
+you get rtf which is autocorrelation
+and i'm gonna
+
+ align:start position:0%
+and i'm gonna
+ 
+
+ align:start position:0%
+and i'm gonna
+derive
+
+ align:start position:0%
+derive
+ 
+
+ align:start position:0%
+derive
+in different way here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so can i use darken please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we start with h i of x
+
+ align:start position:0%
+we start with h i of x
+ 
+
+ align:start position:0%
+we start with h i of x
+which is intensity point function is
+
+ align:start position:0%
+which is intensity point function is
+ 
+
+ align:start position:0%
+which is intensity point function is
+magnitude square of the coherent point
+
+ align:start position:0%
+magnitude square of the coherent point
+ 
+
+ align:start position:0%
+magnitude square of the coherent point
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and yes
+
+ align:start position:0%
+and yes
+ 
+
+ align:start position:0%
+and yes
+much bigger
+
+ align:start position:0%
+much bigger
+ 
+
+ align:start position:0%
+much bigger
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me
+
+ align:start position:0%
+okay let me
+ 
+
+ align:start position:0%
+okay let me
+try
+
+ align:start position:0%
+try
+ 
+
+ align:start position:0%
+try
+that's too big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's too small okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it will get smaller
+
+ align:start position:0%
+it will get smaller
+ 
+
+ align:start position:0%
+it will get smaller
+yeah we start with this thing and
+
+ align:start position:0%
+yeah we start with this thing and
+ 
+
+ align:start position:0%
+yeah we start with this thing and
+we know that the otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+free transform
+
+ align:start position:0%
+free transform
+ 
+
+ align:start position:0%
+free transform
+of intensity
+
+ align:start position:0%
+of intensity
+ 
+
+ align:start position:0%
+of intensity
+point spread function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i can just plug in here so is fret
+
+ align:start position:0%
+and i can just plug in here so is fret
+ 
+
+ align:start position:0%
+and i can just plug in here so is fret
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+magnitude square
+
+ align:start position:0%
+magnitude square
+ 
+
+ align:start position:0%
+magnitude square
+of the points of coherent points of
+
+ align:start position:0%
+of the points of coherent points of
+ 
+
+ align:start position:0%
+of the points of coherent points of
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and free transform
+
+ align:start position:0%
+and free transform
+ 
+
+ align:start position:0%
+and free transform
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+since this is complex quantity i can
+
+ align:start position:0%
+since this is complex quantity i can
+ 
+
+ align:start position:0%
+since this is complex quantity i can
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+h of x
+
+ align:start position:0%
+h of x
+ 
+
+ align:start position:0%
+h of x
+and it's complex conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and since these two are product
+
+ align:start position:0%
+and since these two are product
+ 
+
+ align:start position:0%
+and since these two are product
+then i can write as convolution
+
+ align:start position:0%
+then i can write as convolution
+ 
+
+ align:start position:0%
+then i can write as convolution
+of two guys so it's first transform
+
+ align:start position:0%
+of two guys so it's first transform
+ 
+
+ align:start position:0%
+of two guys so it's first transform
+of h of x
+
+ align:start position:0%
+of h of x
+ 
+
+ align:start position:0%
+of h of x
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+with fret transform
+
+ align:start position:0%
+with fret transform
+ 
+
+ align:start position:0%
+with fret transform
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a complex conjugate
+
+ align:start position:0%
+a complex conjugate
+ 
+
+ align:start position:0%
+a complex conjugate
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up pretty straightforward right
+
+ align:start position:0%
+up pretty straightforward right
+ 
+
+ align:start position:0%
+up pretty straightforward right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+flat transform of the age is actually
+
+ align:start position:0%
+flat transform of the age is actually
+ 
+
+ align:start position:0%
+flat transform of the age is actually
+h of u
+
+ align:start position:0%
+h of u
+ 
+
+ align:start position:0%
+h of u
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atf is just nothing but frequencies of
+
+ align:start position:0%
+atf is just nothing but frequencies of
+ 
+
+ align:start position:0%
+atf is just nothing but frequencies of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+coherent points function
+
+ align:start position:0%
+coherent points function
+ 
+
+ align:start position:0%
+coherent points function
+and what about this guy
+
+ align:start position:0%
+and what about this guy
+ 
+
+ align:start position:0%
+and what about this guy
+the transform of
+
+ align:start position:0%
+the transform of
+ 
+
+ align:start position:0%
+the transform of
+complex conjugate of h
+
+ align:start position:0%
+complex conjugate of h
+ 
+
+ align:start position:0%
+complex conjugate of h
+small h
+
+ align:start position:0%
+small h
+ 
+
+ align:start position:0%
+small h
+so i can write this in integral form so
+
+ align:start position:0%
+so i can write this in integral form so
+ 
+
+ align:start position:0%
+so i can write this in integral form so
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+each complex conjugate of x
+
+ align:start position:0%
+each complex conjugate of x
+ 
+
+ align:start position:0%
+each complex conjugate of x
+e to the
+
+ align:start position:0%
+e to the
+ 
+
+ align:start position:0%
+e to the
+minus j 2 pi
+
+ align:start position:0%
+minus j 2 pi
+ 
+
+ align:start position:0%
+minus j 2 pi
+x u
+
+ align:start position:0%
+x u
+ 
+
+ align:start position:0%
+x u
+d x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since it is complex conjugate i can
+
+ align:start position:0%
+and since it is complex conjugate i can
+ 
+
+ align:start position:0%
+and since it is complex conjugate i can
+write as
+
+ align:start position:0%
+write as
+ 
+
+ align:start position:0%
+write as
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+h of x
+
+ align:start position:0%
+h of x
+ 
+
+ align:start position:0%
+h of x
+e to the i 2 pi
+
+ align:start position:0%
+e to the i 2 pi
+ 
+
+ align:start position:0%
+e to the i 2 pi
+x u
+
+ align:start position:0%
+x u
+ 
+
+ align:start position:0%
+x u
+d x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so i can
+
+ align:start position:0%
+so i can
+ 
+
+ align:start position:0%
+so i can
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+otf
+
+ align:start position:0%
+otf
+ 
+
+ align:start position:0%
+otf
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+hou
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex conjugate or free transform of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+inverse spread transform yes
+
+ align:start position:0%
+inverse spread transform yes
+ 
+
+ align:start position:0%
+inverse spread transform yes
+thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so actually this inverse transform if
+
+ align:start position:0%
+so actually this inverse transform if
+ 
+
+ align:start position:0%
+so actually this inverse transform if
+you remember
+
+ align:start position:0%
+you remember
+ 
+
+ align:start position:0%
+you remember
+the definition of the fret transform is
+
+ align:start position:0%
+the definition of the fret transform is
+ 
+
+ align:start position:0%
+the definition of the fret transform is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+integral h of x
+
+ align:start position:0%
+integral h of x
+ 
+
+ align:start position:0%
+integral h of x
+e to the i 2 pi x u d x when you can
+
+ align:start position:0%
+e to the i 2 pi x u d x when you can
+ 
+
+ align:start position:0%
+e to the i 2 pi x u d x when you can
+write as uh
+
+ align:start position:0%
+write as uh
+ 
+
+ align:start position:0%
+write as uh
+h of x
+
+ align:start position:0%
+h of x
+ 
+
+ align:start position:0%
+h of x
+e to the
+
+ align:start position:0%
+e to the
+ 
+
+ align:start position:0%
+e to the
+minus 2 pi
+
+ align:start position:0%
+minus 2 pi
+ 
+
+ align:start position:0%
+minus 2 pi
+x minus u dx so actually it is fret
+
+ align:start position:0%
+x minus u dx so actually it is fret
+ 
+
+ align:start position:0%
+x minus u dx so actually it is fret
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+and h of x
+
+ align:start position:0%
+and h of x
+ 
+
+ align:start position:0%
+and h of x
+but you change the spatial frequency
+
+ align:start position:0%
+but you change the spatial frequency
+ 
+
+ align:start position:0%
+but you change the spatial frequency
+variable as a minus u so it's going to
+
+ align:start position:0%
+variable as a minus u so it's going to
+ 
+
+ align:start position:0%
+variable as a minus u so it's going to
+be h of minus u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so at the end we have we have
+
+ align:start position:0%
+so at the end we have we have
+ 
+
+ align:start position:0%
+so at the end we have we have
+h of u
+
+ align:start position:0%
+h of u
+ 
+
+ align:start position:0%
+h of u
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+and complex conjugate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+h complex conjugate or minus uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+where i can write as an integral form
+
+ align:start position:0%
+where i can write as an integral form
+ 
+
+ align:start position:0%
+where i can write as an integral form
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+h of u prime
+
+ align:start position:0%
+h of u prime
+ 
+
+ align:start position:0%
+h of u prime
+h of
+
+ align:start position:0%
+h of
+ 
+
+ align:start position:0%
+h of
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h of minus
+
+ align:start position:0%
+h of minus
+ 
+
+ align:start position:0%
+h of minus
+u minus u prime
+
+ align:start position:0%
+u minus u prime
+ 
+
+ align:start position:0%
+u minus u prime
+complex conjugate
+
+ align:start position:0%
+complex conjugate
+ 
+
+ align:start position:0%
+complex conjugate
+and d u prime so essentially
+
+ align:start position:0%
+and d u prime so essentially
+ 
+
+ align:start position:0%
+and d u prime so essentially
+integration h complex conjugate
+
+ align:start position:0%
+integration h complex conjugate
+ 
+
+ align:start position:0%
+integration h complex conjugate
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i have com
+
+ align:start position:0%
+i have com
+ 
+
+ align:start position:0%
+i have com
+h of
+
+ align:start position:0%
+h of
+ 
+
+ align:start position:0%
+h of
+u prime
+
+ align:start position:0%
+u prime
+ 
+
+ align:start position:0%
+u prime
+complex conjugate
+
+ align:start position:0%
+complex conjugate
+ 
+
+ align:start position:0%
+complex conjugate
+u prime
+
+ align:start position:0%
+u prime
+ 
+
+ align:start position:0%
+u prime
+minus u
+
+ align:start position:0%
+minus u
+ 
+
+ align:start position:0%
+minus u
+d u prime
+
+ align:start position:0%
+d u prime
+ 
+
+ align:start position:0%
+d u prime
+which is essentially
+
+ align:start position:0%
+which is essentially
+ 
+
+ align:start position:0%
+which is essentially
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+in one
+
+ align:start position:0%
+in one
+ 
+
+ align:start position:0%
+in one
+1d
+
+ align:start position:0%
+1d
+ 
+
+ align:start position:0%
+1d
+one dimensional geometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and sometimes we denote
+
+ align:start position:0%
+and sometimes we denote
+ 
+
+ align:start position:0%
+and sometimes we denote
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+h of u
+
+ align:start position:0%
+h of u
+ 
+
+ align:start position:0%
+h of u
+and star
+
+ align:start position:0%
+and star
+ 
+
+ align:start position:0%
+and star
+h of u
+
+ align:start position:0%
+h of u
+ 
+
+ align:start position:0%
+h of u
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+auto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correlation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any question in the derivation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so before uh we move on uh can anyone
+
+ align:start position:0%
+so before uh we move on uh can anyone
+ 
+
+ align:start position:0%
+so before uh we move on uh can anyone
+guess what this integration means
+
+ align:start position:0%
+guess what this integration means
+ 
+
+ align:start position:0%
+guess what this integration means
+so you have your own computer in otf
+
+ align:start position:0%
+so you have your own computer in otf
+ 
+
+ align:start position:0%
+so you have your own computer in otf
+which is autocorrelation or the atf but
+
+ align:start position:0%
+which is autocorrelation or the atf but
+ 
+
+ align:start position:0%
+which is autocorrelation or the atf but
+this integration is basically you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+and you take the complex conjugate but
+
+ align:start position:0%
+and you take the complex conjugate but
+ 
+
+ align:start position:0%
+and you take the complex conjugate but
+you shift right and take the integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so next slide i'm gonna explain how we
+
+ align:start position:0%
+so next slide i'm gonna explain how we
+ 
+
+ align:start position:0%
+so next slide i'm gonna explain how we
+can compute i mean
+
+ align:start position:0%
+can compute i mean
+ 
+
+ align:start position:0%
+can compute i mean
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the bottom line of this slide is you
+
+ align:start position:0%
+the bottom line of this slide is you
+ 
+
+ align:start position:0%
+the bottom line of this slide is you
+know otf is nothing but autocorrelation
+
+ align:start position:0%
+know otf is nothing but autocorrelation
+ 
+
+ align:start position:0%
+know otf is nothing but autocorrelation
+of your atf
+
+ align:start position:0%
+of your atf
+ 
+
+ align:start position:0%
+of your atf
+and the next slide is how to compute
+
+ align:start position:0%
+and the next slide is how to compute
+ 
+
+ align:start position:0%
+and the next slide is how to compute
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+you can simply compute this integration
+
+ align:start position:0%
+you can simply compute this integration
+ 
+
+ align:start position:0%
+you can simply compute this integration
+but there is another easy way
+
+ align:start position:0%
+but there is another easy way
+ 
+
+ align:start position:0%
+but there is another easy way
+to guess the otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conceptually yes i mean actually the
+
+ align:start position:0%
+conceptually yes i mean actually the
+ 
+
+ align:start position:0%
+conceptually yes i mean actually the
+transform of the
+
+ align:start position:0%
+transform of the
+ 
+
+ align:start position:0%
+transform of the
+input intensity and flex ratio of the
+
+ align:start position:0%
+input intensity and flex ratio of the
+ 
+
+ align:start position:0%
+input intensity and flex ratio of the
+upper intensity and the rate of the two
+
+ align:start position:0%
+upper intensity and the rate of the two
+ 
+
+ align:start position:0%
+upper intensity and the rate of the two
+likes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's first compute the otf for the
+
+ align:start position:0%
+so let's first compute the otf for the
+ 
+
+ align:start position:0%
+so let's first compute the otf for the
+simple case
+
+ align:start position:0%
+simple case
+ 
+
+ align:start position:0%
+simple case
+i have the rectangular aperture in my
+
+ align:start position:0%
+i have the rectangular aperture in my
+ 
+
+ align:start position:0%
+i have the rectangular aperture in my
+purple from trippy plane at the free
+
+ align:start position:0%
+purple from trippy plane at the free
+ 
+
+ align:start position:0%
+purple from trippy plane at the free
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+and from that i know that the atf h of u
+
+ align:start position:0%
+and from that i know that the atf h of u
+ 
+
+ align:start position:0%
+and from that i know that the atf h of u
+is just vector function and u over u max
+
+ align:start position:0%
+is just vector function and u over u max
+ 
+
+ align:start position:0%
+is just vector function and u over u max
+so u max is defined by the physical size
+
+ align:start position:0%
+so u max is defined by the physical size
+ 
+
+ align:start position:0%
+so u max is defined by the physical size
+of the previous function right and
+
+ align:start position:0%
+of the previous function right and
+ 
+
+ align:start position:0%
+of the previous function right and
+so which is x double prime x and
+
+ align:start position:0%
+so which is x double prime x and
+ 
+
+ align:start position:0%
+so which is x double prime x and
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+the scaling vector of lambda f1
+
+ align:start position:0%
+the scaling vector of lambda f1
+ 
+
+ align:start position:0%
+the scaling vector of lambda f1
+so this is the at
+
+ align:start position:0%
+so this is the at
+ 
+
+ align:start position:0%
+so this is the at
+atf
+
+ align:start position:0%
+atf
+ 
+
+ align:start position:0%
+atf
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we just i just proved that otf is
+
+ align:start position:0%
+we just i just proved that otf is
+ 
+
+ align:start position:0%
+we just i just proved that otf is
+autocorrelation of atf
+
+ align:start position:0%
+autocorrelation of atf
+ 
+
+ align:start position:0%
+autocorrelation of atf
+in integra integral form i have this
+
+ align:start position:0%
+in integra integral form i have this
+ 
+
+ align:start position:0%
+in integra integral form i have this
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh let's just take a look at this in
+
+ align:start position:0%
+uh let's just take a look at this in
+ 
+
+ align:start position:0%
+uh let's just take a look at this in
+this equation actually so otf is
+
+ align:start position:0%
+this equation actually so otf is
+ 
+
+ align:start position:0%
+this equation actually so otf is
+function of u
+
+ align:start position:0%
+function of u
+ 
+
+ align:start position:0%
+function of u
+but this integration i mean inside of
+
+ align:start position:0%
+but this integration i mean inside of
+ 
+
+ align:start position:0%
+but this integration i mean inside of
+this integration i have function of u
+
+ align:start position:0%
+this integration i have function of u
+ 
+
+ align:start position:0%
+this integration i have function of u
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+h of u prime
+
+ align:start position:0%
+h of u prime
+ 
+
+ align:start position:0%
+h of u prime
+and h complex conjugate u prime minus u
+
+ align:start position:0%
+and h complex conjugate u prime minus u
+ 
+
+ align:start position:0%
+and h complex conjugate u prime minus u
+so i have the first function which is
+
+ align:start position:0%
+so i have the first function which is
+ 
+
+ align:start position:0%
+so i have the first function which is
+essentially same as my original function
+
+ align:start position:0%
+essentially same as my original function
+ 
+
+ align:start position:0%
+essentially same as my original function
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+or even though i change the variable u
+
+ align:start position:0%
+or even though i change the variable u
+ 
+
+ align:start position:0%
+or even though i change the variable u
+from u to u prime
+
+ align:start position:0%
+from u to u prime
+ 
+
+ align:start position:0%
+from u to u prime
+but this guy is function of u prime but
+
+ align:start position:0%
+but this guy is function of u prime but
+ 
+
+ align:start position:0%
+but this guy is function of u prime but
+you shift by u
+
+ align:start position:0%
+you shift by u
+ 
+
+ align:start position:0%
+you shift by u
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and take the integration and this whole
+
+ align:start position:0%
+and take the integration and this whole
+ 
+
+ align:start position:0%
+and take the integration and this whole
+thing is function of u
+
+ align:start position:0%
+thing is function of u
+ 
+
+ align:start position:0%
+thing is function of u
+which means you're gonna take you're
+
+ align:start position:0%
+which means you're gonna take you're
+ 
+
+ align:start position:0%
+which means you're gonna take you're
+gonna compute this integration for every
+
+ align:start position:0%
+gonna compute this integration for every
+ 
+
+ align:start position:0%
+gonna compute this integration for every
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+and then you get otf right
+
+ align:start position:0%
+and then you get otf right
+ 
+
+ align:start position:0%
+and then you get otf right
+and this integration is basically you
+
+ align:start position:0%
+and this integration is basically you
+ 
+
+ align:start position:0%
+and this integration is basically you
+have two functions one is shifted by you
+
+ align:start position:0%
+have two functions one is shifted by you
+ 
+
+ align:start position:0%
+have two functions one is shifted by you
+and multiply them and take the
+
+ align:start position:0%
+and multiply them and take the
+ 
+
+ align:start position:0%
+and multiply them and take the
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+essentially you
+
+ align:start position:0%
+essentially you
+ 
+
+ align:start position:0%
+essentially you
+compute the area of the overlapped i
+
+ align:start position:0%
+compute the area of the overlapped i
+ 
+
+ align:start position:0%
+compute the area of the overlapped i
+mean overlapped area of the true
+
+ align:start position:0%
+mean overlapped area of the true
+ 
+
+ align:start position:0%
+mean overlapped area of the true
+function right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so graphically
+
+ align:start position:0%
+so graphically
+ 
+
+ align:start position:0%
+so graphically
+if i have the wrapped function and
+
+ align:start position:0%
+if i have the wrapped function and
+ 
+
+ align:start position:0%
+if i have the wrapped function and
+plugging in this integration i have
+
+ align:start position:0%
+plugging in this integration i have
+ 
+
+ align:start position:0%
+plugging in this integration i have
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+integration but i can imagine four
+
+ align:start position:0%
+integration but i can imagine four
+ 
+
+ align:start position:0%
+integration but i can imagine four
+different situations the first
+
+ align:start position:0%
+different situations the first
+ 
+
+ align:start position:0%
+different situations the first
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this first vector function is uh the
+
+ align:start position:0%
+so this first vector function is uh the
+ 
+
+ align:start position:0%
+so this first vector function is uh the
+green vector function
+
+ align:start position:0%
+green vector function
+ 
+
+ align:start position:0%
+green vector function
+and the second one which is moving is a
+
+ align:start position:0%
+and the second one which is moving is a
+ 
+
+ align:start position:0%
+and the second one which is moving is a
+green rec function
+
+ align:start position:0%
+green rec function
+ 
+
+ align:start position:0%
+green rec function
+so if they are not overlapped then i get
+
+ align:start position:0%
+so if they are not overlapped then i get
+ 
+
+ align:start position:0%
+so if they are not overlapped then i get
+simply zero right the first situation
+
+ align:start position:0%
+simply zero right the first situation
+ 
+
+ align:start position:0%
+simply zero right the first situation
+and as soon as they are overlapped and
+
+ align:start position:0%
+and as soon as they are overlapped and
+ 
+
+ align:start position:0%
+and as soon as they are overlapped and
+then the overlapped area is getting
+
+ align:start position:0%
+then the overlapped area is getting
+ 
+
+ align:start position:0%
+then the overlapped area is getting
+linearly increased right
+
+ align:start position:0%
+linearly increased right
+ 
+
+ align:start position:0%
+linearly increased right
+so i get this u plus u max until they
+
+ align:start position:0%
+so i get this u plus u max until they
+ 
+
+ align:start position:0%
+so i get this u plus u max until they
+are completely overlapped and then
+
+ align:start position:0%
+are completely overlapped and then
+ 
+
+ align:start position:0%
+are completely overlapped and then
+so this is a concentration
+
+ align:start position:0%
+so this is a concentration
+ 
+
+ align:start position:0%
+so this is a concentration
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once you move uh
+
+ align:start position:0%
+once you move uh
+ 
+
+ align:start position:0%
+once you move uh
+a little bit far then basically this
+
+ align:start position:0%
+a little bit far then basically this
+ 
+
+ align:start position:0%
+a little bit far then basically this
+overlap area is getting decreased so
+
+ align:start position:0%
+overlap area is getting decreased so
+ 
+
+ align:start position:0%
+overlap area is getting decreased so
+this is third situation which is this
+
+ align:start position:0%
+this is third situation which is this
+ 
+
+ align:start position:0%
+this is third situation which is this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+and eventually
+
+ align:start position:0%
+and eventually
+ 
+
+ align:start position:0%
+and eventually
+they are not going to overlap so i get 0
+
+ align:start position:0%
+they are not going to overlap so i get 0
+ 
+
+ align:start position:0%
+they are not going to overlap so i get 0
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+remember that this otf is function of u
+
+ align:start position:0%
+remember that this otf is function of u
+ 
+
+ align:start position:0%
+remember that this otf is function of u
+which is the amount of shift of this
+
+ align:start position:0%
+which is the amount of shift of this
+ 
+
+ align:start position:0%
+which is the amount of shift of this
+green leg function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any question
+
+ align:start position:0%
+any question
+ 
+
+ align:start position:0%
+any question
+yeah so if you plot
+
+ align:start position:0%
+yeah so if you plot
+ 
+
+ align:start position:0%
+yeah so if you plot
+this overlapped area like i mean this
+
+ align:start position:0%
+this overlapped area like i mean this
+ 
+
+ align:start position:0%
+this overlapped area like i mean this
+guy and this guy
+
+ align:start position:0%
+guy and this guy
+ 
+
+ align:start position:0%
+guy and this guy
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+u then actually we are going to get a
+
+ align:start position:0%
+u then actually we are going to get a
+ 
+
+ align:start position:0%
+u then actually we are going to get a
+triangular function
+
+ align:start position:0%
+triangular function
+ 
+
+ align:start position:0%
+triangular function
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he it looks like
+
+ align:start position:0%
+he it looks like
+ 
+
+ align:start position:0%
+he it looks like
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we of course we normalize at the
+
+ align:start position:0%
+and we of course we normalize at the
+ 
+
+ align:start position:0%
+and we of course we normalize at the
+zero frequency
+
+ align:start position:0%
+zero frequency
+ 
+
+ align:start position:0%
+zero frequency
+so at a zero we always have a one
+
+ align:start position:0%
+so at a zero we always have a one
+ 
+
+ align:start position:0%
+so at a zero we always have a one
+so you know you notice the difference
+
+ align:start position:0%
+so you know you notice the difference
+ 
+
+ align:start position:0%
+so you know you notice the difference
+between these two
+
+ align:start position:0%
+between these two
+ 
+
+ align:start position:0%
+between these two
+so atf
+
+ align:start position:0%
+so atf
+ 
+
+ align:start position:0%
+so atf
+my activity is nothing but my pupil
+
+ align:start position:0%
+my activity is nothing but my pupil
+ 
+
+ align:start position:0%
+my activity is nothing but my pupil
+function right just wrapped function and
+
+ align:start position:0%
+function right just wrapped function and
+ 
+
+ align:start position:0%
+function right just wrapped function and
+the color frequency u max is defined by
+
+ align:start position:0%
+the color frequency u max is defined by
+ 
+
+ align:start position:0%
+the color frequency u max is defined by
+my physical size of the pupil with the
+
+ align:start position:0%
+my physical size of the pupil with the
+ 
+
+ align:start position:0%
+my physical size of the pupil with the
+scaling factor
+
+ align:start position:0%
+scaling factor
+ 
+
+ align:start position:0%
+scaling factor
+but otf is autocorrelation so the shape
+
+ align:start position:0%
+but otf is autocorrelation so the shape
+ 
+
+ align:start position:0%
+but otf is autocorrelation so the shape
+is now
+
+ align:start position:0%
+is now
+ 
+
+ align:start position:0%
+is now
+the triangular shape but also the color
+
+ align:start position:0%
+the triangular shape but also the color
+ 
+
+ align:start position:0%
+the triangular shape but also the color
+frequency the umx is twice of the umax
+
+ align:start position:0%
+frequency the umx is twice of the umax
+ 
+
+ align:start position:0%
+frequency the umx is twice of the umax
+because you know
+
+ align:start position:0%
+because you know
+ 
+
+ align:start position:0%
+because you know
+basically you basically you
+
+ align:start position:0%
+basically you basically you
+ 
+
+ align:start position:0%
+basically you basically you
+go through all this process so
+
+ align:start position:0%
+go through all this process so
+ 
+
+ align:start position:0%
+go through all this process so
+you get twice of the color frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so whatever yeah
+
+ align:start position:0%
+so whatever yeah
+ 
+
+ align:start position:0%
+so whatever yeah
+so whatever triple you have if you
+
+ align:start position:0%
+so whatever triple you have if you
+ 
+
+ align:start position:0%
+so whatever triple you have if you
+compute this kind of uh overlapped area
+
+ align:start position:0%
+compute this kind of uh overlapped area
+ 
+
+ align:start position:0%
+compute this kind of uh overlapped area
+then you can get
+
+ align:start position:0%
+then you can get
+ 
+
+ align:start position:0%
+then you can get
+otf
+
+ align:start position:0%
+otf
+ 
+
+ align:start position:0%
+otf
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in convincebook if you have a
+
+ align:start position:0%
+in convincebook if you have a
+ 
+
+ align:start position:0%
+in convincebook if you have a
+rectangular scale aperture then you know
+
+ align:start position:0%
+rectangular scale aperture then you know
+ 
+
+ align:start position:0%
+rectangular scale aperture then you know
+if you go through this uh
+
+ align:start position:0%
+if you go through this uh
+ 
+
+ align:start position:0%
+if you go through this uh
+autocorrelation then you can get this
+
+ align:start position:0%
+autocorrelation then you can get this
+ 
+
+ align:start position:0%
+autocorrelation then you can get this
+kind of otf so this is just linear
+
+ align:start position:0%
+kind of otf so this is just linear
+ 
+
+ align:start position:0%
+kind of otf so this is just linear
+completely linear in
+
+ align:start position:0%
+completely linear in
+ 
+
+ align:start position:0%
+completely linear in
+u and v direction
+
+ align:start position:0%
+u and v direction
+ 
+
+ align:start position:0%
+u and v direction
+so yeah again the f x and f y they are u
+
+ align:start position:0%
+so yeah again the f x and f y they are u
+ 
+
+ align:start position:0%
+so yeah again the f x and f y they are u
+and v uh in our electron
+
+ align:start position:0%
+and v uh in our electron
+ 
+
+ align:start position:0%
+and v uh in our electron
+and if you have the circular aperture
+
+ align:start position:0%
+and if you have the circular aperture
+ 
+
+ align:start position:0%
+and if you have the circular aperture
+it's almost linear but it's slightly
+
+ align:start position:0%
+it's almost linear but it's slightly
+ 
+
+ align:start position:0%
+it's almost linear but it's slightly
+curved at the edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah but
+
+ align:start position:0%
+yeah but
+ 
+
+ align:start position:0%
+yeah but
+you know essentially base is essentially
+
+ align:start position:0%
+you know essentially base is essentially
+ 
+
+ align:start position:0%
+you know essentially base is essentially
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+same thing so if you
+
+ align:start position:0%
+same thing so if you
+ 
+
+ align:start position:0%
+same thing so if you
+move around two circles and compute the
+
+ align:start position:0%
+move around two circles and compute the
+ 
+
+ align:start position:0%
+move around two circles and compute the
+overlapped area then you will end up
+
+ align:start position:0%
+overlapped area then you will end up
+ 
+
+ align:start position:0%
+overlapped area then you will end up
+with this uh
+
+ align:start position:0%
+with this uh
+ 
+
+ align:start position:0%
+with this uh
+you'll end up with this function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i guess this is a good time to
+
+ align:start position:0%
+i guess this is a good time to
+ 
+
+ align:start position:0%
+i guess this is a good time to
+take a break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all righty uh any questions so far
+
+ align:start position:0%
+all righty uh any questions so far
+ 
+
+ align:start position:0%
+all righty uh any questions so far
+so we uh so we discussed that
+
+ align:start position:0%
+so we uh so we discussed that
+ 
+
+ align:start position:0%
+so we uh so we discussed that
+so what the difference between temporal
+
+ align:start position:0%
+so what the difference between temporal
+ 
+
+ align:start position:0%
+so what the difference between temporal
+and special coherence
+
+ align:start position:0%
+and special coherence
+ 
+
+ align:start position:0%
+and special coherence
+and define the intensity point three
+
+ align:start position:0%
+and define the intensity point three
+ 
+
+ align:start position:0%
+and define the intensity point three
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and also define the otf which is spread
+
+ align:start position:0%
+and also define the otf which is spread
+ 
+
+ align:start position:0%
+and also define the otf which is spread
+transform of the intensity point
+
+ align:start position:0%
+transform of the intensity point
+ 
+
+ align:start position:0%
+transform of the intensity point
+function and
+
+ align:start position:0%
+function and
+ 
+
+ align:start position:0%
+function and
+at the last
+
+ align:start position:0%
+at the last
+ 
+
+ align:start position:0%
+at the last
+excuse me
+
+ align:start position:0%
+excuse me
+ 
+
+ align:start position:0%
+excuse me
+otf is autocorrelation of the atf and i
+
+ align:start position:0%
+otf is autocorrelation of the atf and i
+ 
+
+ align:start position:0%
+otf is autocorrelation of the atf and i
+visually
+
+ align:start position:0%
+visually
+ 
+
+ align:start position:0%
+visually
+show that how to compute the otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's just summarize uh what we
+
+ align:start position:0%
+so let's just summarize uh what we
+ 
+
+ align:start position:0%
+so let's just summarize uh what we
+discussed so far
+
+ align:start position:0%
+discussed so far
+ 
+
+ align:start position:0%
+discussed so far
+so first
+
+ align:start position:0%
+so first
+ 
+
+ align:start position:0%
+so first
+we know and we already we all know that
+
+ align:start position:0%
+we know and we already we all know that
+ 
+
+ align:start position:0%
+we know and we already we all know that
+i mean cohen points a function is
+
+ align:start position:0%
+i mean cohen points a function is
+ 
+
+ align:start position:0%
+i mean cohen points a function is
+nothing but an optical field generated
+
+ align:start position:0%
+nothing but an optical field generated
+ 
+
+ align:start position:0%
+nothing but an optical field generated
+by a point source at the input plane
+
+ align:start position:0%
+by a point source at the input plane
+ 
+
+ align:start position:0%
+by a point source at the input plane
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah that's the
+
+ align:start position:0%
+yeah that's the
+ 
+
+ align:start position:0%
+yeah that's the
+field and by and also you know that
+
+ align:start position:0%
+field and by and also you know that
+ 
+
+ align:start position:0%
+field and by and also you know that
+point coherent points of function is
+
+ align:start position:0%
+point coherent points of function is
+ 
+
+ align:start position:0%
+point coherent points of function is
+fret transform of your perfect function
+
+ align:start position:0%
+fret transform of your perfect function
+ 
+
+ align:start position:0%
+fret transform of your perfect function
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+coordinate scaling
+
+ align:start position:0%
+coordinate scaling
+ 
+
+ align:start position:0%
+coordinate scaling
+and in cohere in coherent points
+
+ align:start position:0%
+and in cohere in coherent points
+ 
+
+ align:start position:0%
+and in cohere in coherent points
+function is
+
+ align:start position:0%
+function is
+ 
+
+ align:start position:0%
+function is
+magnitude square of
+
+ align:start position:0%
+magnitude square of
+ 
+
+ align:start position:0%
+magnitude square of
+forehand point function
+
+ align:start position:0%
+forehand point function
+ 
+
+ align:start position:0%
+forehand point function
+or another way to say is
+
+ align:start position:0%
+or another way to say is
+ 
+
+ align:start position:0%
+or another way to say is
+intensity function function is intensity
+
+ align:start position:0%
+intensity function function is intensity
+ 
+
+ align:start position:0%
+intensity function function is intensity
+of the field
+
+ align:start position:0%
+of the field
+ 
+
+ align:start position:0%
+of the field
+of coherent points function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we define that we define the
+
+ align:start position:0%
+and we define that we define the
+ 
+
+ align:start position:0%
+and we define that we define the
+amplitude transfer function atf which is
+
+ align:start position:0%
+amplitude transfer function atf which is
+ 
+
+ align:start position:0%
+amplitude transfer function atf which is
+free transform of the
+
+ align:start position:0%
+free transform of the
+ 
+
+ align:start position:0%
+free transform of the
+coherent points function
+
+ align:start position:0%
+coherent points function
+ 
+
+ align:start position:0%
+coherent points function
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+nothing but the pupil
+
+ align:start position:0%
+nothing but the pupil
+ 
+
+ align:start position:0%
+nothing but the pupil
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+prepare function with the scaling factor
+
+ align:start position:0%
+prepare function with the scaling factor
+ 
+
+ align:start position:0%
+prepare function with the scaling factor
+i mean coordinate scaling
+
+ align:start position:0%
+i mean coordinate scaling
+ 
+
+ align:start position:0%
+i mean coordinate scaling
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just derived that the otf which is
+
+ align:start position:0%
+we just derived that the otf which is
+ 
+
+ align:start position:0%
+we just derived that the otf which is
+free transform of the intensity points
+
+ align:start position:0%
+free transform of the intensity points
+ 
+
+ align:start position:0%
+free transform of the intensity points
+function is actually correlate
+
+ align:start position:0%
+function is actually correlate
+ 
+
+ align:start position:0%
+function is actually correlate
+autocorrelation of the atf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in the rest of the lecture we will
+
+ align:start position:0%
+in the rest of the lecture we will
+ 
+
+ align:start position:0%
+in the rest of the lecture we will
+probably um we most we are going to
+
+ align:start position:0%
+probably um we most we are going to
+ 
+
+ align:start position:0%
+probably um we most we are going to
+mostly deal with the the mtf which is uh
+
+ align:start position:0%
+mostly deal with the the mtf which is uh
+ 
+
+ align:start position:0%
+mostly deal with the the mtf which is uh
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+modulus of the mt otf actually it should
+
+ align:start position:0%
+modulus of the mt otf actually it should
+ 
+
+ align:start position:0%
+modulus of the mt otf actually it should
+be otf so mtf is the magnitude component
+
+ align:start position:0%
+be otf so mtf is the magnitude component
+ 
+
+ align:start position:0%
+be otf so mtf is the magnitude component
+of the otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in terms of
+
+ align:start position:0%
+uh in terms of
+ 
+
+ align:start position:0%
+uh in terms of
+inputed output you know we are dealing
+
+ align:start position:0%
+inputed output you know we are dealing
+ 
+
+ align:start position:0%
+inputed output you know we are dealing
+with linear system approach so
+
+ align:start position:0%
+with linear system approach so
+ 
+
+ align:start position:0%
+with linear system approach so
+if we have especially coherent
+
+ align:start position:0%
+if we have especially coherent
+ 
+
+ align:start position:0%
+if we have especially coherent
+illumination
+
+ align:start position:0%
+illumination
+ 
+
+ align:start position:0%
+illumination
+so this sub illumina is the
+
+ align:start position:0%
+so this sub illumina is the
+ 
+
+ align:start position:0%
+so this sub illumina is the
+illumination field and i have the thin
+
+ align:start position:0%
+illumination field and i have the thin
+ 
+
+ align:start position:0%
+illumination field and i have the thin
+transparency the complex transparency g
+
+ align:start position:0%
+transparency the complex transparency g
+ 
+
+ align:start position:0%
+transparency the complex transparency g
+sub t then my input field is just
+
+ align:start position:0%
+sub t then my input field is just
+ 
+
+ align:start position:0%
+sub t then my input field is just
+product of my elimination field and
+
+ align:start position:0%
+product of my elimination field and
+ 
+
+ align:start position:0%
+product of my elimination field and
+complex transparency so g sub in that's
+
+ align:start position:0%
+complex transparency so g sub in that's
+ 
+
+ align:start position:0%
+complex transparency so g sub in that's
+the input field and if i convolve with
+
+ align:start position:0%
+the input field and if i convolve with
+ 
+
+ align:start position:0%
+the input field and if i convolve with
+the coherent point function that's going
+
+ align:start position:0%
+the coherent point function that's going
+ 
+
+ align:start position:0%
+the coherent point function that's going
+to be my
+
+ align:start position:0%
+to be my
+ 
+
+ align:start position:0%
+to be my
+output field which is g sub out
+
+ align:start position:0%
+output field which is g sub out
+ 
+
+ align:start position:0%
+output field which is g sub out
+and i can think of i mean this whole
+
+ align:start position:0%
+and i can think of i mean this whole
+ 
+
+ align:start position:0%
+and i can think of i mean this whole
+thing in frequency domain right so if i
+
+ align:start position:0%
+thing in frequency domain right so if i
+ 
+
+ align:start position:0%
+thing in frequency domain right so if i
+take a transfer transform
+
+ align:start position:0%
+take a transfer transform
+ 
+
+ align:start position:0%
+take a transfer transform
+capital g in is actually free transform
+
+ align:start position:0%
+capital g in is actually free transform
+ 
+
+ align:start position:0%
+capital g in is actually free transform
+of the o
+
+ align:start position:0%
+of the o
+ 
+
+ align:start position:0%
+of the o
+of small g in which is
+
+ align:start position:0%
+of small g in which is
+ 
+
+ align:start position:0%
+of small g in which is
+a free free component of my input field
+
+ align:start position:0%
+a free free component of my input field
+ 
+
+ align:start position:0%
+a free free component of my input field
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know convolution is multiplication
+
+ align:start position:0%
+you know convolution is multiplication
+ 
+
+ align:start position:0%
+you know convolution is multiplication
+and frequency domain so i multiply by
+
+ align:start position:0%
+and frequency domain so i multiply by
+ 
+
+ align:start position:0%
+and frequency domain so i multiply by
+atf
+
+ align:start position:0%
+atf
+ 
+
+ align:start position:0%
+atf
+then i'm going to get
+
+ align:start position:0%
+then i'm going to get
+ 
+
+ align:start position:0%
+then i'm going to get
+g sub capital g sub r which is
+
+ align:start position:0%
+g sub capital g sub r which is
+ 
+
+ align:start position:0%
+g sub capital g sub r which is
+phase transform of my upper field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if i have the
+
+ align:start position:0%
+if i have the
+ 
+
+ align:start position:0%
+if i have the
+specially in chronic elimination then i
+
+ align:start position:0%
+specially in chronic elimination then i
+ 
+
+ align:start position:0%
+specially in chronic elimination then i
+deal with the intensity
+
+ align:start position:0%
+deal with the intensity
+ 
+
+ align:start position:0%
+deal with the intensity
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i have the intensity
+
+ align:start position:0%
+i have the intensity
+ 
+
+ align:start position:0%
+i have the intensity
+of illumination and i have the still
+
+ align:start position:0%
+of illumination and i have the still
+ 
+
+ align:start position:0%
+of illumination and i have the still
+complex transparency so actually my
+
+ align:start position:0%
+complex transparency so actually my
+ 
+
+ align:start position:0%
+complex transparency so actually my
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+intensity is
+
+ align:start position:0%
+intensity is
+ 
+
+ align:start position:0%
+intensity is
+elimination intensity times
+
+ align:start position:0%
+elimination intensity times
+ 
+
+ align:start position:0%
+elimination intensity times
+magnitude square of g sub t so
+
+ align:start position:0%
+magnitude square of g sub t so
+ 
+
+ align:start position:0%
+magnitude square of g sub t so
+remember that gt is complex transparency
+
+ align:start position:0%
+remember that gt is complex transparency
+ 
+
+ align:start position:0%
+remember that gt is complex transparency
+so to make the intensity you have to
+
+ align:start position:0%
+so to make the intensity you have to
+ 
+
+ align:start position:0%
+so to make the intensity you have to
+take magnitude square so this is my
+
+ align:start position:0%
+take magnitude square so this is my
+ 
+
+ align:start position:0%
+take magnitude square so this is my
+input intensity
+
+ align:start position:0%
+input intensity
+ 
+
+ align:start position:0%
+input intensity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in coherent case
+
+ align:start position:0%
+in coherent case
+ 
+
+ align:start position:0%
+in coherent case
+it is linear in intensity so you have to
+
+ align:start position:0%
+it is linear in intensity so you have to
+ 
+
+ align:start position:0%
+it is linear in intensity so you have to
+convolve with the intensity point
+
+ align:start position:0%
+convolve with the intensity point
+ 
+
+ align:start position:0%
+convolve with the intensity point
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+magnitude square of the coherent point
+
+ align:start position:0%
+magnitude square of the coherent point
+ 
+
+ align:start position:0%
+magnitude square of the coherent point
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+you're gonna get in output intensity
+
+ align:start position:0%
+you're gonna get in output intensity
+ 
+
+ align:start position:0%
+you're gonna get in output intensity
+and again in the frequency domain
+
+ align:start position:0%
+and again in the frequency domain
+ 
+
+ align:start position:0%
+and again in the frequency domain
+we can take the phase transform so g sub
+
+ align:start position:0%
+we can take the phase transform so g sub
+ 
+
+ align:start position:0%
+we can take the phase transform so g sub
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+i cannot see
+
+ align:start position:0%
+i cannot see
+ 
+
+ align:start position:0%
+i cannot see
+capital g i
+
+ align:start position:0%
+capital g i
+ 
+
+ align:start position:0%
+capital g i
+input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital g
+
+ align:start position:0%
+capital g
+ 
+
+ align:start position:0%
+capital g
+sub i
+
+ align:start position:0%
+sub i
+ 
+
+ align:start position:0%
+sub i
+which is uh input free transform of the
+
+ align:start position:0%
+which is uh input free transform of the
+ 
+
+ align:start position:0%
+which is uh input free transform of the
+input intensity and you're going to
+
+ align:start position:0%
+input intensity and you're going to
+ 
+
+ align:start position:0%
+input intensity and you're going to
+multiply by otf
+
+ align:start position:0%
+multiply by otf
+ 
+
+ align:start position:0%
+multiply by otf
+which is autocorrelation of the atf
+
+ align:start position:0%
+which is autocorrelation of the atf
+ 
+
+ align:start position:0%
+which is autocorrelation of the atf
+and you will get the free transform free
+
+ align:start position:0%
+and you will get the free transform free
+ 
+
+ align:start position:0%
+and you will get the free transform free
+transform of the output intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so actually
+
+ align:start position:0%
+so actually
+ 
+
+ align:start position:0%
+so actually
+if you're familiar with
+
+ align:start position:0%
+if you're familiar with
+ 
+
+ align:start position:0%
+if you're familiar with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+control theory then you probably know
+
+ align:start position:0%
+control theory then you probably know
+ 
+
+ align:start position:0%
+control theory then you probably know
+the body plot so body plot is nothing
+
+ align:start position:0%
+the body plot so body plot is nothing
+ 
+
+ align:start position:0%
+the body plot so body plot is nothing
+but you have
+
+ align:start position:0%
+but you have
+ 
+
+ align:start position:0%
+but you have
+you know in frequency domain you
+
+ align:start position:0%
+you know in frequency domain you
+ 
+
+ align:start position:0%
+you know in frequency domain you
+describe the weighting function that is
+
+ align:start position:0%
+describe the weighting function that is
+ 
+
+ align:start position:0%
+describe the weighting function that is
+going to be multiplied by your input and
+
+ align:start position:0%
+going to be multiplied by your input and
+ 
+
+ align:start position:0%
+going to be multiplied by your input and
+produce your output right so this atf
+
+ align:start position:0%
+produce your output right so this atf
+ 
+
+ align:start position:0%
+produce your output right so this atf
+and otf and also mtf they are basically
+
+ align:start position:0%
+and otf and also mtf they are basically
+ 
+
+ align:start position:0%
+and otf and also mtf they are basically
+the same thing you
+
+ align:start position:0%
+the same thing you
+ 
+
+ align:start position:0%
+the same thing you
+uh you can you multiply your
+
+ align:start position:0%
+uh you can you multiply your
+ 
+
+ align:start position:0%
+uh you can you multiply your
+uh so basically this trans uh fluid
+
+ align:start position:0%
+uh so basically this trans uh fluid
+ 
+
+ align:start position:0%
+uh so basically this trans uh fluid
+transfer function in frequency domain
+
+ align:start position:0%
+transfer function in frequency domain
+ 
+
+ align:start position:0%
+transfer function in frequency domain
+describe the weighting function that is
+
+ align:start position:0%
+describe the weighting function that is
+ 
+
+ align:start position:0%
+describe the weighting function that is
+going to be multiplied by your input and
+
+ align:start position:0%
+going to be multiplied by your input and
+ 
+
+ align:start position:0%
+going to be multiplied by your input and
+you can just you know compare the
+
+ align:start position:0%
+you can just you know compare the
+ 
+
+ align:start position:0%
+you can just you know compare the
+bit and also another way to say is the
+
+ align:start position:0%
+bit and also another way to say is the
+ 
+
+ align:start position:0%
+bit and also another way to say is the
+ratio between input and output okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+mtf so yeah so as i just described this
+
+ align:start position:0%
+mtf so yeah so as i just described this
+ 
+
+ align:start position:0%
+mtf so yeah so as i just described this
+frequency uh this transform transfer
+
+ align:start position:0%
+frequency uh this transform transfer
+ 
+
+ align:start position:0%
+frequency uh this transform transfer
+function is nothing but you know the
+
+ align:start position:0%
+function is nothing but you know the
+ 
+
+ align:start position:0%
+function is nothing but you know the
+weighting function in frequency domain
+
+ align:start position:0%
+weighting function in frequency domain
+ 
+
+ align:start position:0%
+weighting function in frequency domain
+frequency domain so uh let me show how
+
+ align:start position:0%
+frequency domain so uh let me show how
+ 
+
+ align:start position:0%
+frequency domain so uh let me show how
+to use it because you know if you if you
+
+ align:start position:0%
+to use it because you know if you if you
+ 
+
+ align:start position:0%
+to use it because you know if you if you
+buy or lens for your digital camera i
+
+ align:start position:0%
+buy or lens for your digital camera i
+ 
+
+ align:start position:0%
+buy or lens for your digital camera i
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+typically the slr camera
+
+ align:start position:0%
+typically the slr camera
+ 
+
+ align:start position:0%
+typically the slr camera
+the lens makers provide the mtf data
+
+ align:start position:0%
+the lens makers provide the mtf data
+ 
+
+ align:start position:0%
+the lens makers provide the mtf data
+which is the weight you know this
+
+ align:start position:0%
+which is the weight you know this
+ 
+
+ align:start position:0%
+which is the weight you know this
+weighting function with the special
+
+ align:start position:0%
+weighting function with the special
+ 
+
+ align:start position:0%
+weighting function with the special
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+and with the color frequency or i mean
+
+ align:start position:0%
+and with the color frequency or i mean
+ 
+
+ align:start position:0%
+and with the color frequency or i mean
+basically you can say what kind of image
+
+ align:start position:0%
+basically you can say what kind of image
+ 
+
+ align:start position:0%
+basically you can say what kind of image
+quality i can expect with the lens
+
+ align:start position:0%
+quality i can expect with the lens
+ 
+
+ align:start position:0%
+quality i can expect with the lens
+so first let's consider i have the
+
+ align:start position:0%
+so first let's consider i have the
+ 
+
+ align:start position:0%
+so first let's consider i have the
+gradient which
+
+ align:start position:0%
+gradient which
+ 
+
+ align:start position:0%
+gradient which
+whose amplitude transmission function is
+
+ align:start position:0%
+whose amplitude transmission function is
+ 
+
+ align:start position:0%
+whose amplitude transmission function is
+given by this equation
+
+ align:start position:0%
+given by this equation
+ 
+
+ align:start position:0%
+given by this equation
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the input intensity is going to be
+
+ align:start position:0%
+the input intensity is going to be
+ 
+
+ align:start position:0%
+the input intensity is going to be
+you know i mean
+
+ align:start position:0%
+you know i mean
+ 
+
+ align:start position:0%
+you know i mean
+intensity of the gradient is going to be
+
+ align:start position:0%
+intensity of the gradient is going to be
+ 
+
+ align:start position:0%
+intensity of the gradient is going to be
+negative square so i have one over two
+
+ align:start position:0%
+negative square so i have one over two
+ 
+
+ align:start position:0%
+negative square so i have one over two
+then one plus m modulation and cosine
+
+ align:start position:0%
+then one plus m modulation and cosine
+ 
+
+ align:start position:0%
+then one plus m modulation and cosine
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+and the phase vector
+
+ align:start position:0%
+and the phase vector
+ 
+
+ align:start position:0%
+and the phase vector
+e to the i phi doesn't matter right
+
+ align:start position:0%
+e to the i phi doesn't matter right
+ 
+
+ align:start position:0%
+e to the i phi doesn't matter right
+because you take the negative square
+
+ align:start position:0%
+because you take the negative square
+ 
+
+ align:start position:0%
+because you take the negative square
+it's always
+
+ align:start position:0%
+it's always
+ 
+
+ align:start position:0%
+it's always
+one and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the free transform transform free
+
+ align:start position:0%
+the free transform transform free
+ 
+
+ align:start position:0%
+the free transform transform free
+transform of this intensity
+
+ align:start position:0%
+transform of this intensity
+ 
+
+ align:start position:0%
+transform of this intensity
+input intensity is you know we all know
+
+ align:start position:0%
+input intensity is you know we all know
+ 
+
+ align:start position:0%
+input intensity is you know we all know
+that it has three uh
+
+ align:start position:0%
+that it has three uh
+ 
+
+ align:start position:0%
+that it has three uh
+three orders so so zeroth order and the
+
+ align:start position:0%
+three orders so so zeroth order and the
+ 
+
+ align:start position:0%
+three orders so so zeroth order and the
+one over capital lambda and minus one of
+
+ align:start position:0%
+one over capital lambda and minus one of
+ 
+
+ align:start position:0%
+one over capital lambda and minus one of
+the lambda we have three different
+
+ align:start position:0%
+the lambda we have three different
+ 
+
+ align:start position:0%
+the lambda we have three different
+orders
+
+ align:start position:0%
+orders
+ 
+
+ align:start position:0%
+orders
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it's going to be multiplied by the otf
+
+ align:start position:0%
+it's going to be multiplied by the otf
+ 
+
+ align:start position:0%
+it's going to be multiplied by the otf
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+at this h right
+
+ align:start position:0%
+at this h right
+ 
+
+ align:start position:0%
+at this h right
+and since this uh delta function which
+
+ align:start position:0%
+and since this uh delta function which
+ 
+
+ align:start position:0%
+and since this uh delta function which
+means this one is one only at
+
+ align:start position:0%
+means this one is one only at
+ 
+
+ align:start position:0%
+means this one is one only at
+u equals zero and on at
+
+ align:start position:0%
+u equals zero and on at
+ 
+
+ align:start position:0%
+u equals zero and on at
+u equal one over capital lambda and at
+
+ align:start position:0%
+u equal one over capital lambda and at
+ 
+
+ align:start position:0%
+u equal one over capital lambda and at
+-1 capital lambda so if you multiply the
+
+ align:start position:0%
+-1 capital lambda so if you multiply the
+ 
+
+ align:start position:0%
+-1 capital lambda so if you multiply the
+otf and actually you still have the
+
+ align:start position:0%
+otf and actually you still have the
+ 
+
+ align:start position:0%
+otf and actually you still have the
+three components
+
+ align:start position:0%
+three components
+ 
+
+ align:start position:0%
+three components
+so at zero component you have the
+
+ align:start position:0%
+so at zero component you have the
+ 
+
+ align:start position:0%
+so at zero component you have the
+otf at the zero frequency
+
+ align:start position:0%
+otf at the zero frequency
+ 
+
+ align:start position:0%
+otf at the zero frequency
+but and these two delta functions are
+
+ align:start position:0%
+but and these two delta functions are
+ 
+
+ align:start position:0%
+but and these two delta functions are
+multiplied by otf at
+
+ align:start position:0%
+multiplied by otf at
+ 
+
+ align:start position:0%
+multiplied by otf at
+the one over capital lambda and minus
+
+ align:start position:0%
+the one over capital lambda and minus
+ 
+
+ align:start position:0%
+the one over capital lambda and minus
+one over capital lambda we still have
+
+ align:start position:0%
+one over capital lambda we still have
+ 
+
+ align:start position:0%
+one over capital lambda we still have
+the uh three diffraction orders
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since this is your
+
+ align:start position:0%
+so since this is your
+ 
+
+ align:start position:0%
+so since this is your
+first transform of the output intensity
+
+ align:start position:0%
+first transform of the output intensity
+ 
+
+ align:start position:0%
+first transform of the output intensity
+so you can just take the inverse flat
+
+ align:start position:0%
+so you can just take the inverse flat
+ 
+
+ align:start position:0%
+so you can just take the inverse flat
+transform to get to it compute the
+
+ align:start position:0%
+transform to get to it compute the
+ 
+
+ align:start position:0%
+transform to get to it compute the
+output intensity right but there is
+
+ align:start position:0%
+output intensity right but there is
+ 
+
+ align:start position:0%
+output intensity right but there is
+another uh
+
+ align:start position:0%
+another uh
+ 
+
+ align:start position:0%
+another uh
+there is
+
+ align:start position:0%
+there is
+ 
+
+ align:start position:0%
+there is
+important property of the otf so this
+
+ align:start position:0%
+important property of the otf so this
+ 
+
+ align:start position:0%
+important property of the otf so this
+guy and this guy
+
+ align:start position:0%
+guy and this guy
+ 
+
+ align:start position:0%
+guy and this guy
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so otf is actually
+
+ align:start position:0%
+so otf is actually
+ 
+
+ align:start position:0%
+so otf is actually
+you know intensity point function which
+
+ align:start position:0%
+you know intensity point function which
+ 
+
+ align:start position:0%
+you know intensity point function which
+is h sub i
+
+ align:start position:0%
+is h sub i
+ 
+
+ align:start position:0%
+is h sub i
+is negative square of the coherent point
+
+ align:start position:0%
+is negative square of the coherent point
+ 
+
+ align:start position:0%
+is negative square of the coherent point
+function so it is always positive
+
+ align:start position:0%
+function so it is always positive
+ 
+
+ align:start position:0%
+function so it is always positive
+i mean it's not non-negative i should
+
+ align:start position:0%
+i mean it's not non-negative i should
+ 
+
+ align:start position:0%
+i mean it's not non-negative i should
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+so it's non-negative so it's free
+
+ align:start position:0%
+so it's non-negative so it's free
+ 
+
+ align:start position:0%
+so it's non-negative so it's free
+transform is actually formation which is
+
+ align:start position:0%
+transform is actually formation which is
+ 
+
+ align:start position:0%
+transform is actually formation which is
+mathematically you can write h of minus
+
+ align:start position:0%
+mathematically you can write h of minus
+ 
+
+ align:start position:0%
+mathematically you can write h of minus
+u is actually h complex conjugate of u
+
+ align:start position:0%
+u is actually h complex conjugate of u
+ 
+
+ align:start position:0%
+u is actually h complex conjugate of u
+or you can say
+
+ align:start position:0%
+or you can say
+ 
+
+ align:start position:0%
+or you can say
+this real part is even function but this
+
+ align:start position:0%
+this real part is even function but this
+ 
+
+ align:start position:0%
+this real part is even function but this
+imaginary part is odd function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so otf of the physically realizable
+
+ align:start position:0%
+so otf of the physically realizable
+ 
+
+ align:start position:0%
+so otf of the physically realizable
+optical system must be hermitian so most
+
+ align:start position:0%
+optical system must be hermitian so most
+ 
+
+ align:start position:0%
+optical system must be hermitian so most
+i mean this condition should be
+
+ align:start position:0%
+i mean this condition should be
+ 
+
+ align:start position:0%
+i mean this condition should be
+satisfied always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in previous slide i had
+
+ align:start position:0%
+so in previous slide i had
+ 
+
+ align:start position:0%
+so in previous slide i had
+let me just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+1 over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otf at 0 and delta u
+
+ align:start position:0%
+otf at 0 and delta u
+ 
+
+ align:start position:0%
+otf at 0 and delta u
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m over 2
+
+ align:start position:0%
+m over 2
+ 
+
+ align:start position:0%
+m over 2
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+1 over capital lambda
+
+ align:start position:0%
+1 over capital lambda
+ 
+
+ align:start position:0%
+1 over capital lambda
+and delta
+
+ align:start position:0%
+and delta
+ 
+
+ align:start position:0%
+and delta
+u 1 over lambda plus
+
+ align:start position:0%
+u 1 over lambda plus
+ 
+
+ align:start position:0%
+u 1 over lambda plus
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+minus 1 lambda delta u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the otf is hermitian which means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+i mean at otf over
+
+ align:start position:0%
+i mean at otf over
+ 
+
+ align:start position:0%
+i mean at otf over
+minus one over capital lambda is
+
+ align:start position:0%
+minus one over capital lambda is
+ 
+
+ align:start position:0%
+minus one over capital lambda is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+a complex conjugate of h
+
+ align:start position:0%
+a complex conjugate of h
+ 
+
+ align:start position:0%
+a complex conjugate of h
+one over capital lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this hermitian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so g out i mean the capital g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i out
+
+ align:start position:0%
+i out
+ 
+
+ align:start position:0%
+i out
+i can write as
+
+ align:start position:0%
+i can write as
+ 
+
+ align:start position:0%
+i can write as
+1 over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otf at 0 still delta function
+
+ align:start position:0%
+otf at 0 still delta function
+ 
+
+ align:start position:0%
+otf at 0 still delta function
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+m over 2
+
+ align:start position:0%
+m over 2
+ 
+
+ align:start position:0%
+m over 2
+h 1 over capital lambda delta u 1 over
+
+ align:start position:0%
+h 1 over capital lambda delta u 1 over
+ 
+
+ align:start position:0%
+h 1 over capital lambda delta u 1 over
+capital lambda
+
+ align:start position:0%
+capital lambda
+ 
+
+ align:start position:0%
+capital lambda
+but the last delta function i can write
+
+ align:start position:0%
+but the last delta function i can write
+ 
+
+ align:start position:0%
+but the last delta function i can write
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+h complex conjugate
+
+ align:start position:0%
+h complex conjugate
+ 
+
+ align:start position:0%
+h complex conjugate
+one over capital lambda
+
+ align:start position:0%
+one over capital lambda
+ 
+
+ align:start position:0%
+one over capital lambda
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+plus omega lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first data function i mean if you
+
+ align:start position:0%
+so the first data function i mean if you
+ 
+
+ align:start position:0%
+so the first data function i mean if you
+take the inverse phase transform or free
+
+ align:start position:0%
+take the inverse phase transform or free
+ 
+
+ align:start position:0%
+take the inverse phase transform or free
+transform the first data function you
+
+ align:start position:0%
+transform the first data function you
+ 
+
+ align:start position:0%
+transform the first data function you
+know it just generated this term right
+
+ align:start position:0%
+know it just generated this term right
+ 
+
+ align:start position:0%
+know it just generated this term right
+just one or something so it's pretty
+
+ align:start position:0%
+just one or something so it's pretty
+ 
+
+ align:start position:0%
+just one or something so it's pretty
+straightforward the question is still
+
+ align:start position:0%
+straightforward the question is still
+ 
+
+ align:start position:0%
+straightforward the question is still
+what happened
+
+ align:start position:0%
+what happened
+ 
+
+ align:start position:0%
+what happened
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+these two data functions because this
+
+ align:start position:0%
+these two data functions because this
+ 
+
+ align:start position:0%
+these two data functions because this
+one has
+
+ align:start position:0%
+one has
+ 
+
+ align:start position:0%
+one has
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+h of one i mean the otf at capital one
+
+ align:start position:0%
+h of one i mean the otf at capital one
+ 
+
+ align:start position:0%
+h of one i mean the otf at capital one
+over capital lambda and
+
+ align:start position:0%
+over capital lambda and
+ 
+
+ align:start position:0%
+over capital lambda and
+the other one is actually complex
+
+ align:start position:0%
+the other one is actually complex
+ 
+
+ align:start position:0%
+the other one is actually complex
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if i just write
+
+ align:start position:0%
+if i just write
+ 
+
+ align:start position:0%
+if i just write
+this the two delta function part
+
+ align:start position:0%
+this the two delta function part
+ 
+
+ align:start position:0%
+this the two delta function part
+then and i'm going to take the inverse
+
+ align:start position:0%
+then and i'm going to take the inverse
+ 
+
+ align:start position:0%
+then and i'm going to take the inverse
+spread transform so
+
+ align:start position:0%
+spread transform so
+ 
+
+ align:start position:0%
+spread transform so
+inverse fluid transform
+
+ align:start position:0%
+inverse fluid transform
+ 
+
+ align:start position:0%
+inverse fluid transform
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+m over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital lambda
+
+ align:start position:0%
+capital lambda
+ 
+
+ align:start position:0%
+capital lambda
+delta u 1 over lambda plus
+
+ align:start position:0%
+delta u 1 over lambda plus
+ 
+
+ align:start position:0%
+delta u 1 over lambda plus
+h complex conjugate capital lambda delta
+
+ align:start position:0%
+h complex conjugate capital lambda delta
+ 
+
+ align:start position:0%
+h complex conjugate capital lambda delta
+u plus 1 over capital lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is
+
+ align:start position:0%
+what is
+ 
+
+ align:start position:0%
+what is
+inverse frequency of the delta function
+
+ align:start position:0%
+inverse frequency of the delta function
+ 
+
+ align:start position:0%
+inverse frequency of the delta function
+is going to be exponential right so
+
+ align:start position:0%
+is going to be exponential right so
+ 
+
+ align:start position:0%
+is going to be exponential right so
+mr2 is just scalar so it's just outside
+
+ align:start position:0%
+mr2 is just scalar so it's just outside
+ 
+
+ align:start position:0%
+mr2 is just scalar so it's just outside
+and i'm going to have
+
+ align:start position:0%
+and i'm going to have
+ 
+
+ align:start position:0%
+and i'm going to have
+h of
+
+ align:start position:0%
+h of
+ 
+
+ align:start position:0%
+h of
+1 over capital lambda
+
+ align:start position:0%
+1 over capital lambda
+ 
+
+ align:start position:0%
+1 over capital lambda
+and exponent e to the
+
+ align:start position:0%
+and exponent e to the
+ 
+
+ align:start position:0%
+and exponent e to the
+i 2 pi
+
+ align:start position:0%
+i 2 pi
+ 
+
+ align:start position:0%
+i 2 pi
+x over capital lambda
+
+ align:start position:0%
+x over capital lambda
+ 
+
+ align:start position:0%
+x over capital lambda
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+h complex conjugate
+
+ align:start position:0%
+h complex conjugate
+ 
+
+ align:start position:0%
+h complex conjugate
+1 over capital lambda e to the minus i
+
+ align:start position:0%
+1 over capital lambda e to the minus i
+ 
+
+ align:start position:0%
+1 over capital lambda e to the minus i
+2 pi
+
+ align:start position:0%
+2 pi
+ 
+
+ align:start position:0%
+2 pi
+x of capital lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i can write
+
+ align:start position:0%
+and i can write
+ 
+
+ align:start position:0%
+and i can write
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital
+
+ align:start position:0%
+capital
+ 
+
+ align:start position:0%
+capital
+lambda
+
+ align:start position:0%
+lambda
+ 
+
+ align:start position:0%
+lambda
+lambda e to the i 2 pi
+
+ align:start position:0%
+lambda e to the i 2 pi
+ 
+
+ align:start position:0%
+lambda e to the i 2 pi
+x over lambda
+
+ align:start position:0%
+x over lambda
+ 
+
+ align:start position:0%
+x over lambda
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+actually same thing
+
+ align:start position:0%
+actually same thing
+ 
+
+ align:start position:0%
+actually same thing
+h 1 over capital lambda e to the i 2 pi
+
+ align:start position:0%
+h 1 over capital lambda e to the i 2 pi
+ 
+
+ align:start position:0%
+h 1 over capital lambda e to the i 2 pi
+x over lambda
+
+ align:start position:0%
+x over lambda
+ 
+
+ align:start position:0%
+x over lambda
+and complex
+
+ align:start position:0%
+and complex
+ 
+
+ align:start position:0%
+and complex
+conjugate like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so what is the
+
+ align:start position:0%
+so what is the
+ 
+
+ align:start position:0%
+so what is the
+what happen if you add
+
+ align:start position:0%
+what happen if you add
+ 
+
+ align:start position:0%
+what happen if you add
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and it's complex conjugate so for
+
+ align:start position:0%
+and it's complex conjugate so for
+ 
+
+ align:start position:0%
+and it's complex conjugate so for
+example this is a and this is a complex
+
+ align:start position:0%
+example this is a and this is a complex
+ 
+
+ align:start position:0%
+example this is a and this is a complex
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+and if you add them together then
+
+ align:start position:0%
+and if you add them together then
+ 
+
+ align:start position:0%
+and if you add them together then
+you get only real part right because you
+
+ align:start position:0%
+you get only real part right because you
+ 
+
+ align:start position:0%
+you get only real part right because you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+real part of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so i'm gonna have
+
+ align:start position:0%
+so i'm gonna have
+ 
+
+ align:start position:0%
+so i'm gonna have
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+the real part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otf at capital one over capital lambda
+
+ align:start position:0%
+otf at capital one over capital lambda
+ 
+
+ align:start position:0%
+otf at capital one over capital lambda
+e to the
+
+ align:start position:0%
+e to the
+ 
+
+ align:start position:0%
+e to the
+i two pi x over lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which i can write as m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and bring it to the this magnitude is
+
+ align:start position:0%
+and bring it to the this magnitude is
+ 
+
+ align:start position:0%
+and bring it to the this magnitude is
+you know this h is just non-zero so it
+
+ align:start position:0%
+you know this h is just non-zero so it
+ 
+
+ align:start position:0%
+you know this h is just non-zero so it
+only it it could have i mean it
+
+ align:start position:0%
+only it it could have i mean it
+ 
+
+ align:start position:0%
+only it it could have i mean it
+you can have
+
+ align:start position:0%
+you can have
+ 
+
+ align:start position:0%
+you can have
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+zero or minus basically so i can write
+
+ align:start position:0%
+zero or minus basically so i can write
+ 
+
+ align:start position:0%
+zero or minus basically so i can write
+as a magnitude here and this will be
+
+ align:start position:0%
+as a magnitude here and this will be
+ 
+
+ align:start position:0%
+as a magnitude here and this will be
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+2 pi
+
+ align:start position:0%
+2 pi
+ 
+
+ align:start position:0%
+2 pi
+x over lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's why
+
+ align:start position:0%
+so that's why
+ 
+
+ align:start position:0%
+so that's why
+my g is i mean the output intensity is
+
+ align:start position:0%
+my g is i mean the output intensity is
+ 
+
+ align:start position:0%
+my g is i mean the output intensity is
+just one plus
+
+ align:start position:0%
+just one plus
+ 
+
+ align:start position:0%
+just one plus
+m which is original modulation
+
+ align:start position:0%
+m which is original modulation
+ 
+
+ align:start position:0%
+m which is original modulation
+but i have extra modulation due to otf
+
+ align:start position:0%
+but i have extra modulation due to otf
+ 
+
+ align:start position:0%
+but i have extra modulation due to otf
+and cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should i prove why otf is formation
+
+ align:start position:0%
+should i prove why otf is formation
+ 
+
+ align:start position:0%
+should i prove why otf is formation
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me prove why otf is hormone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so otf
+
+ align:start position:0%
+so otf
+ 
+
+ align:start position:0%
+so otf
+is autocorrelation of atf which is
+
+ align:start position:0%
+is autocorrelation of atf which is
+ 
+
+ align:start position:0%
+is autocorrelation of atf which is
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and integration
+
+ align:start position:0%
+and integration
+ 
+
+ align:start position:0%
+and integration
+with the integral form i can write as
+
+ align:start position:0%
+with the integral form i can write as
+ 
+
+ align:start position:0%
+with the integral form i can write as
+h of
+
+ align:start position:0%
+h of
+ 
+
+ align:start position:0%
+h of
+u prime
+
+ align:start position:0%
+u prime
+ 
+
+ align:start position:0%
+u prime
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+complex conjugate
+
+ align:start position:0%
+complex conjugate
+ 
+
+ align:start position:0%
+complex conjugate
+u prime minus u
+
+ align:start position:0%
+u prime minus u
+ 
+
+ align:start position:0%
+u prime minus u
+and v u prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i want to compute
+
+ align:start position:0%
+and i want to compute
+ 
+
+ align:start position:0%
+and i want to compute
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+i mean otf
+
+ align:start position:0%
+i mean otf
+ 
+
+ align:start position:0%
+i mean otf
+and complex conjugate of u
+
+ align:start position:0%
+and complex conjugate of u
+ 
+
+ align:start position:0%
+and complex conjugate of u
+so i can write as uh
+
+ align:start position:0%
+so i can write as uh
+ 
+
+ align:start position:0%
+so i can write as uh
+the total thing
+
+ align:start position:0%
+the total thing
+ 
+
+ align:start position:0%
+the total thing
+h of u prime
+
+ align:start position:0%
+h of u prime
+ 
+
+ align:start position:0%
+h of u prime
+x h complex conjugate u prime u
+
+ align:start position:0%
+x h complex conjugate u prime u
+ 
+
+ align:start position:0%
+x h complex conjugate u prime u
+d u u prime
+
+ align:start position:0%
+d u u prime
+ 
+
+ align:start position:0%
+d u u prime
+and complex
+
+ align:start position:0%
+and complex
+ 
+
+ align:start position:0%
+and complex
+excuse me yes uh we're not able to see
+
+ align:start position:0%
+excuse me yes uh we're not able to see
+ 
+
+ align:start position:0%
+excuse me yes uh we're not able to see
+what you are writing means uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay now okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so i just take the complex
+
+ align:start position:0%
+yeah so i just take the complex
+ 
+
+ align:start position:0%
+yeah so i just take the complex
+conjugate on both sides okay
+
+ align:start position:0%
+conjugate on both sides okay
+ 
+
+ align:start position:0%
+conjugate on both sides okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i can change the complex conjugate
+
+ align:start position:0%
+i can change the complex conjugate
+ 
+
+ align:start position:0%
+i can change the complex conjugate
+so it's gonna be
+
+ align:start position:0%
+so it's gonna be
+ 
+
+ align:start position:0%
+so it's gonna be
+h complex conjugate over u prime
+
+ align:start position:0%
+h complex conjugate over u prime
+ 
+
+ align:start position:0%
+h complex conjugate over u prime
+h and u prime and u
+
+ align:start position:0%
+h and u prime and u
+ 
+
+ align:start position:0%
+h and u prime and u
+and d u prime
+
+ align:start position:0%
+and d u prime
+ 
+
+ align:start position:0%
+and d u prime
+so i just replied i mean just put the
+
+ align:start position:0%
+so i just replied i mean just put the
+ 
+
+ align:start position:0%
+so i just replied i mean just put the
+complex conjugate inside of the
+
+ align:start position:0%
+complex conjugate inside of the
+ 
+
+ align:start position:0%
+complex conjugate inside of the
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+and here i define the new variable so
+
+ align:start position:0%
+and here i define the new variable so
+ 
+
+ align:start position:0%
+and here i define the new variable so
+u double prime is
+
+ align:start position:0%
+u double prime is
+ 
+
+ align:start position:0%
+u double prime is
+u prime minus u
+
+ align:start position:0%
+u prime minus u
+ 
+
+ align:start position:0%
+u prime minus u
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u prime
+
+ align:start position:0%
+u prime
+ 
+
+ align:start position:0%
+u prime
+is u plus u double prime
+
+ align:start position:0%
+is u plus u double prime
+ 
+
+ align:start position:0%
+is u plus u double prime
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+d u prime is actually d u double prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+h complex conjugate is
+
+ align:start position:0%
+h complex conjugate is
+ 
+
+ align:start position:0%
+h complex conjugate is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h complex conjugate
+
+ align:start position:0%
+h complex conjugate
+ 
+
+ align:start position:0%
+h complex conjugate
+u plus u double prime
+
+ align:start position:0%
+u plus u double prime
+ 
+
+ align:start position:0%
+u plus u double prime
+h of u double prime
+
+ align:start position:0%
+h of u double prime
+ 
+
+ align:start position:0%
+h of u double prime
+and d u double prime
+
+ align:start position:0%
+and d u double prime
+ 
+
+ align:start position:0%
+and d u double prime
+which i can write as
+
+ align:start position:0%
+which i can write as
+ 
+
+ align:start position:0%
+which i can write as
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+u double prime
+
+ align:start position:0%
+u double prime
+ 
+
+ align:start position:0%
+u double prime
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+complex conjugate
+
+ align:start position:0%
+complex conjugate
+ 
+
+ align:start position:0%
+complex conjugate
+u double prime
+
+ align:start position:0%
+u double prime
+ 
+
+ align:start position:0%
+u double prime
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+minus u
+
+ align:start position:0%
+minus u
+ 
+
+ align:start position:0%
+minus u
+d u double prime so is
+
+ align:start position:0%
+d u double prime so is
+ 
+
+ align:start position:0%
+d u double prime so is
+h of
+
+ align:start position:0%
+h of
+ 
+
+ align:start position:0%
+h of
+minus u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i just proved
+
+ align:start position:0%
+yeah i just proved
+ 
+
+ align:start position:0%
+yeah i just proved
+you know you can easily do that so the
+
+ align:start position:0%
+you know you can easily do that so the
+ 
+
+ align:start position:0%
+you know you can easily do that so the
+bottom line is
+
+ align:start position:0%
+bottom line is
+ 
+
+ align:start position:0%
+bottom line is
+uh at the output plane i mean output
+
+ align:start position:0%
+uh at the output plane i mean output
+ 
+
+ align:start position:0%
+uh at the output plane i mean output
+intensity i have extra modulation uh
+
+ align:start position:0%
+intensity i have extra modulation uh
+ 
+
+ align:start position:0%
+intensity i have extra modulation uh
+coming from the otf i mean you can say
+
+ align:start position:0%
+coming from the otf i mean you can say
+ 
+
+ align:start position:0%
+coming from the otf i mean you can say
+this is magnitude so you can say it's
+
+ align:start position:0%
+this is magnitude so you can say it's
+ 
+
+ align:start position:0%
+this is magnitude so you can say it's
+mtf
+
+ align:start position:0%
+mtf
+ 
+
+ align:start position:0%
+mtf
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you compare in terms of the
+
+ align:start position:0%
+if you compare in terms of the
+ 
+
+ align:start position:0%
+if you compare in terms of the
+contrast or visibility so the contract
+
+ align:start position:0%
+contrast or visibility so the contract
+ 
+
+ align:start position:0%
+contrast or visibility so the contract
+is defined by
+
+ align:start position:0%
+is defined by
+ 
+
+ align:start position:0%
+is defined by
+imx minus i min over i max plus i mean
+
+ align:start position:0%
+imx minus i min over i max plus i mean
+ 
+
+ align:start position:0%
+imx minus i min over i max plus i mean
+but at the output plane uh we have the
+
+ align:start position:0%
+but at the output plane uh we have the
+ 
+
+ align:start position:0%
+but at the output plane uh we have the
+extra uh modulation term so if you
+
+ align:start position:0%
+extra uh modulation term so if you
+ 
+
+ align:start position:0%
+extra uh modulation term so if you
+compute the same thing then actually
+
+ align:start position:0%
+compute the same thing then actually
+ 
+
+ align:start position:0%
+compute the same thing then actually
+your contract is going to be on the
+
+ align:start position:0%
+your contract is going to be on the
+ 
+
+ align:start position:0%
+your contract is going to be on the
+original modulation multiplied by
+
+ align:start position:0%
+original modulation multiplied by
+ 
+
+ align:start position:0%
+original modulation multiplied by
+mtf at the
+
+ align:start position:0%
+mtf at the
+ 
+
+ align:start position:0%
+mtf at the
+that spatial frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+yeah mtf is just contrast at the special
+
+ align:start position:0%
+yeah mtf is just contrast at the special
+ 
+
+ align:start position:0%
+yeah mtf is just contrast at the special
+frequency and relative to the
+
+ align:start position:0%
+frequency and relative to the
+ 
+
+ align:start position:0%
+frequency and relative to the
+transmission to the discussion
+
+ align:start position:0%
+transmission to the discussion
+ 
+
+ align:start position:0%
+transmission to the discussion
+so what does it mean
+
+ align:start position:0%
+so what does it mean
+ 
+
+ align:start position:0%
+so what does it mean
+so for example i have
+
+ align:start position:0%
+so for example i have
+ 
+
+ align:start position:0%
+so for example i have
+mtf
+
+ align:start position:0%
+mtf
+ 
+
+ align:start position:0%
+mtf
+looks like this
+
+ align:start position:0%
+looks like this
+ 
+
+ align:start position:0%
+looks like this
+i initially had the grading
+
+ align:start position:0%
+i initially had the grading
+ 
+
+ align:start position:0%
+i initially had the grading
+intensity of the grading is actually one
+
+ align:start position:0%
+intensity of the grading is actually one
+ 
+
+ align:start position:0%
+intensity of the grading is actually one
+over two one plus m cosine two pi x over
+
+ align:start position:0%
+over two one plus m cosine two pi x over
+ 
+
+ align:start position:0%
+over two one plus m cosine two pi x over
+capital lambda so if i draw in greyscale
+
+ align:start position:0%
+capital lambda so if i draw in greyscale
+ 
+
+ align:start position:0%
+capital lambda so if i draw in greyscale
+so the white is one and black is zero
+
+ align:start position:0%
+so the white is one and black is zero
+ 
+
+ align:start position:0%
+so the white is one and black is zero
+right so i have nice sinusoid with the
+
+ align:start position:0%
+right so i have nice sinusoid with the
+ 
+
+ align:start position:0%
+right so i have nice sinusoid with the
+full contrast like this
+
+ align:start position:0%
+full contrast like this
+ 
+
+ align:start position:0%
+full contrast like this
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the output intensity i'm going to have
+
+ align:start position:0%
+the output intensity i'm going to have
+ 
+
+ align:start position:0%
+the output intensity i'm going to have
+one plus m
+
+ align:start position:0%
+one plus m
+ 
+
+ align:start position:0%
+one plus m
+and additional modulation and cosine
+
+ align:start position:0%
+and additional modulation and cosine
+ 
+
+ align:start position:0%
+and additional modulation and cosine
+term so
+
+ align:start position:0%
+term so
+ 
+
+ align:start position:0%
+term so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this factor you can find at the graph
+
+ align:start position:0%
+this factor you can find at the graph
+ 
+
+ align:start position:0%
+this factor you can find at the graph
+right so if you have the vulnerable log
+
+ align:start position:0%
+right so if you have the vulnerable log
+ 
+
+ align:start position:0%
+right so if you have the vulnerable log
+capital lambda then you can find the the
+
+ align:start position:0%
+capital lambda then you can find the the
+ 
+
+ align:start position:0%
+capital lambda then you can find the the
+value at that
+
+ align:start position:0%
+value at that
+ 
+
+ align:start position:0%
+value at that
+point right i mean mtf at that point
+
+ align:start position:0%
+point right i mean mtf at that point
+ 
+
+ align:start position:0%
+point right i mean mtf at that point
+this point so if that value is 0.6
+
+ align:start position:0%
+this point so if that value is 0.6
+ 
+
+ align:start position:0%
+this point so if that value is 0.6
+in this case so this
+
+ align:start position:0%
+in this case so this
+ 
+
+ align:start position:0%
+in this case so this
+sine so the pattern
+
+ align:start position:0%
+sine so the pattern
+ 
+
+ align:start position:0%
+sine so the pattern
+will look like this
+
+ align:start position:0%
+will look like this
+ 
+
+ align:start position:0%
+will look like this
+but if the modulation is 0.2 then
+
+ align:start position:0%
+but if the modulation is 0.2 then
+ 
+
+ align:start position:0%
+but if the modulation is 0.2 then
+you know the black become uh brighter
+
+ align:start position:0%
+you know the black become uh brighter
+ 
+
+ align:start position:0%
+you know the black become uh brighter
+and white become darker so you kind of
+
+ align:start position:0%
+and white become darker so you kind of
+ 
+
+ align:start position:0%
+and white become darker so you kind of
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+the gray scale
+
+ align:start position:0%
+the gray scale
+ 
+
+ align:start position:0%
+the gray scale
+the broad version of the grading like
+
+ align:start position:0%
+the broad version of the grading like
+ 
+
+ align:start position:0%
+the broad version of the grading like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so basically this mtf tells you that
+
+ align:start position:0%
+so basically this mtf tells you that
+ 
+
+ align:start position:0%
+so basically this mtf tells you that
+what kind of
+
+ align:start position:0%
+what kind of
+ 
+
+ align:start position:0%
+what kind of
+contrast i expect with that
+
+ align:start position:0%
+contrast i expect with that
+ 
+
+ align:start position:0%
+contrast i expect with that
+i mean at this particular special
+
+ align:start position:0%
+i mean at this particular special
+ 
+
+ align:start position:0%
+i mean at this particular special
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+it specifies the maximum special
+
+ align:start position:0%
+it specifies the maximum special
+ 
+
+ align:start position:0%
+it specifies the maximum special
+frequency you can resolve i mean you can
+
+ align:start position:0%
+frequency you can resolve i mean you can
+ 
+
+ align:start position:0%
+frequency you can resolve i mean you can
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so far we just deal with the ideal
+
+ align:start position:0%
+so so far we just deal with the ideal
+ 
+
+ align:start position:0%
+so so far we just deal with the ideal
+thin length with the clear aperture like
+
+ align:start position:0%
+thin length with the clear aperture like
+ 
+
+ align:start position:0%
+thin length with the clear aperture like
+the rectangular aperture circular
+
+ align:start position:0%
+the rectangular aperture circular
+ 
+
+ align:start position:0%
+the rectangular aperture circular
+aperture
+
+ align:start position:0%
+aperture
+ 
+
+ align:start position:0%
+aperture
+so in the case of rectangular aperture
+
+ align:start position:0%
+so in the case of rectangular aperture
+ 
+
+ align:start position:0%
+so in the case of rectangular aperture
+we know that the otf is just
+
+ align:start position:0%
+we know that the otf is just
+ 
+
+ align:start position:0%
+we know that the otf is just
+autocorrelation of the two red function
+
+ align:start position:0%
+autocorrelation of the two red function
+ 
+
+ align:start position:0%
+autocorrelation of the two red function
+which is it's just triangular function
+
+ align:start position:0%
+which is it's just triangular function
+ 
+
+ align:start position:0%
+which is it's just triangular function
+so it's
+
+ align:start position:0%
+so it's
+ 
+
+ align:start position:0%
+so it's
+just linear from one to uh color
+
+ align:start position:0%
+just linear from one to uh color
+ 
+
+ align:start position:0%
+just linear from one to uh color
+frequency which is twice of the outer
+
+ align:start position:0%
+frequency which is twice of the outer
+ 
+
+ align:start position:0%
+frequency which is twice of the outer
+frequency at otf
+
+ align:start position:0%
+frequency at otf
+ 
+
+ align:start position:0%
+frequency at otf
+no the atf
+
+ align:start position:0%
+no the atf
+ 
+
+ align:start position:0%
+no the atf
+and if you have the circular aperture
+
+ align:start position:0%
+and if you have the circular aperture
+ 
+
+ align:start position:0%
+and if you have the circular aperture
+it's almost linear except at the
+
+ align:start position:0%
+it's almost linear except at the
+ 
+
+ align:start position:0%
+it's almost linear except at the
+edge region you slide you have slightly
+
+ align:start position:0%
+edge region you slide you have slightly
+ 
+
+ align:start position:0%
+edge region you slide you have slightly
+curved
+
+ align:start position:0%
+curved
+ 
+
+ align:start position:0%
+curved
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+but you know basically same thing so
+
+ align:start position:0%
+but you know basically same thing so
+ 
+
+ align:start position:0%
+but you know basically same thing so
+this blue line
+
+ align:start position:0%
+this blue line
+ 
+
+ align:start position:0%
+this blue line
+and the black line we call uh diffracted
+
+ align:start position:0%
+and the black line we call uh diffracted
+ 
+
+ align:start position:0%
+and the black line we call uh diffracted
+uh deflection limited otf
+
+ align:start position:0%
+uh deflection limited otf
+ 
+
+ align:start position:0%
+uh deflection limited otf
+because we assume the ideal a thin lens
+
+ align:start position:0%
+because we assume the ideal a thin lens
+ 
+
+ align:start position:0%
+because we assume the ideal a thin lens
+without any aberration so this is kind
+
+ align:start position:0%
+without any aberration so this is kind
+ 
+
+ align:start position:0%
+without any aberration so this is kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a maximum otf i mean best rtf you can
+
+ align:start position:0%
+a maximum otf i mean best rtf you can
+ 
+
+ align:start position:0%
+a maximum otf i mean best rtf you can
+achieve
+
+ align:start position:0%
+achieve
+ 
+
+ align:start position:0%
+achieve
+but you know in practice you always have
+
+ align:start position:0%
+but you know in practice you always have
+ 
+
+ align:start position:0%
+but you know in practice you always have
+aeration right i mean chromatic
+
+ align:start position:0%
+aeration right i mean chromatic
+ 
+
+ align:start position:0%
+aeration right i mean chromatic
+aberration or any higher vibration or
+
+ align:start position:0%
+aberration or any higher vibration or
+ 
+
+ align:start position:0%
+aberration or any higher vibration or
+you know you can't have the difficult or
+
+ align:start position:0%
+you know you can't have the difficult or
+ 
+
+ align:start position:0%
+you know you can't have the difficult or
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+imperfect uh factor in length so
+
+ align:start position:0%
+imperfect uh factor in length so
+ 
+
+ align:start position:0%
+imperfect uh factor in length so
+typically
+
+ align:start position:0%
+typically
+ 
+
+ align:start position:0%
+typically
+typical lens has this kind of
+
+ align:start position:0%
+typical lens has this kind of
+ 
+
+ align:start position:0%
+typical lens has this kind of
+distorted or degraded otf like this the
+
+ align:start position:0%
+distorted or degraded otf like this the
+ 
+
+ align:start position:0%
+distorted or degraded otf like this the
+red one like here or here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know in terms of of this
+
+ align:start position:0%
+so you know in terms of of this
+ 
+
+ align:start position:0%
+so you know in terms of of this
+deflection limit you want to buy your
+
+ align:start position:0%
+deflection limit you want to buy your
+ 
+
+ align:start position:0%
+deflection limit you want to buy your
+lens that
+
+ align:start position:0%
+lens that
+ 
+
+ align:start position:0%
+lens that
+otf is similar to this blue line because
+
+ align:start position:0%
+otf is similar to this blue line because
+ 
+
+ align:start position:0%
+otf is similar to this blue line because
+you know this is deflection limited
+
+ align:start position:0%
+you know this is deflection limited
+ 
+
+ align:start position:0%
+you know this is deflection limited
+which means the best
+
+ align:start position:0%
+which means the best
+ 
+
+ align:start position:0%
+which means the best
+otf we can achieve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so i described i mean this is this
+
+ align:start position:0%
+yeah so i described i mean this is this
+ 
+
+ align:start position:0%
+yeah so i described i mean this is this
+uh slope is linear and
+
+ align:start position:0%
+uh slope is linear and
+ 
+
+ align:start position:0%
+uh slope is linear and
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah circular aperture and
+
+ align:start position:0%
+yeah circular aperture and
+ 
+
+ align:start position:0%
+yeah circular aperture and
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+i mean locally it can have a higher
+
+ align:start position:0%
+i mean locally it can have a higher
+ 
+
+ align:start position:0%
+i mean locally it can have a higher
+value but you know overall
+
+ align:start position:0%
+value but you know overall
+ 
+
+ align:start position:0%
+value but you know overall
+the overall shape should be smaller than
+
+ align:start position:0%
+the overall shape should be smaller than
+ 
+
+ align:start position:0%
+the overall shape should be smaller than
+this blue line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's just apply the all this concept
+
+ align:start position:0%
+uh let's just apply the all this concept
+ 
+
+ align:start position:0%
+uh let's just apply the all this concept
+in you know the in real voice system
+
+ align:start position:0%
+in you know the in real voice system
+ 
+
+ align:start position:0%
+in you know the in real voice system
+so we have first system was focal length
+
+ align:start position:0%
+so we have first system was focal length
+ 
+
+ align:start position:0%
+so we have first system was focal length
+iphone f2 again
+
+ align:start position:0%
+iphone f2 again
+ 
+
+ align:start position:0%
+iphone f2 again
+and i put a input transparency which is
+
+ align:start position:0%
+and i put a input transparency which is
+ 
+
+ align:start position:0%
+and i put a input transparency which is
+a binary amplitude grading right here
+
+ align:start position:0%
+a binary amplitude grading right here
+ 
+
+ align:start position:0%
+a binary amplitude grading right here
+and illuminate with a
+
+ align:start position:0%
+and illuminate with a
+ 
+
+ align:start position:0%
+and illuminate with a
+quasi-monochromatic
+
+ align:start position:0%
+quasi-monochromatic
+ 
+
+ align:start position:0%
+quasi-monochromatic
+which is from a single color and
+
+ align:start position:0%
+which is from a single color and
+ 
+
+ align:start position:0%
+which is from a single color and
+especially in current illumination
+
+ align:start position:0%
+especially in current illumination
+ 
+
+ align:start position:0%
+especially in current illumination
+and uniform intensity typically we
+
+ align:start position:0%
+and uniform intensity typically we
+ 
+
+ align:start position:0%
+and uniform intensity typically we
+assume the intensity variation is
+
+ align:start position:0%
+assume the intensity variation is
+ 
+
+ align:start position:0%
+assume the intensity variation is
+uniform
+
+ align:start position:0%
+uniform
+ 
+
+ align:start position:0%
+uniform
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+the possible question is what kind of
+
+ align:start position:0%
+the possible question is what kind of
+ 
+
+ align:start position:0%
+the possible question is what kind of
+image we can expect at the image plane
+
+ align:start position:0%
+image we can expect at the image plane
+ 
+
+ align:start position:0%
+image we can expect at the image plane
+or you know what is the
+
+ align:start position:0%
+or you know what is the
+ 
+
+ align:start position:0%
+or you know what is the
+otf or
+
+ align:start position:0%
+otf or
+ 
+
+ align:start position:0%
+otf or
+yeah what is atf and otf and blah blah
+
+ align:start position:0%
+yeah what is atf and otf and blah blah
+ 
+
+ align:start position:0%
+yeah what is atf and otf and blah blah
+blah so let's go through it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the binary amplitude
+
+ align:start position:0%
+okay so this is the binary amplitude
+ 
+
+ align:start position:0%
+okay so this is the binary amplitude
+grading so it is
+
+ align:start position:0%
+grading so it is
+ 
+
+ align:start position:0%
+grading so it is
+still complex transparency
+
+ align:start position:0%
+still complex transparency
+ 
+
+ align:start position:0%
+still complex transparency
+in field so
+
+ align:start position:0%
+in field so
+ 
+
+ align:start position:0%
+in field so
+you know if you have in uh in current
+
+ align:start position:0%
+you know if you have in uh in current
+ 
+
+ align:start position:0%
+you know if you have in uh in current
+elimination you want to compute the
+
+ align:start position:0%
+elimination you want to compute the
+ 
+
+ align:start position:0%
+elimination you want to compute the
+intensity so you have to take the
+
+ align:start position:0%
+intensity so you have to take the
+ 
+
+ align:start position:0%
+intensity so you have to take the
+magnitude square but this is just 0 or 1
+
+ align:start position:0%
+magnitude square but this is just 0 or 1
+ 
+
+ align:start position:0%
+magnitude square but this is just 0 or 1
+so basically you have the same thing in
+
+ align:start position:0%
+so basically you have the same thing in
+ 
+
+ align:start position:0%
+so basically you have the same thing in
+intensity right
+
+ align:start position:0%
+intensity right
+ 
+
+ align:start position:0%
+intensity right
+so that's the input intensity the upper
+
+ align:start position:0%
+so that's the input intensity the upper
+ 
+
+ align:start position:0%
+so that's the input intensity the upper
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and this is the
+
+ align:start position:0%
+and this is the
+ 
+
+ align:start position:0%
+and this is the
+face mask located at the free plane
+
+ align:start position:0%
+face mask located at the free plane
+ 
+
+ align:start position:0%
+face mask located at the free plane
+and we know that the atf is
+
+ align:start position:0%
+and we know that the atf is
+ 
+
+ align:start position:0%
+and we know that the atf is
+basically the same function with
+
+ align:start position:0%
+basically the same function with
+ 
+
+ align:start position:0%
+basically the same function with
+different uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different coordinates right
+
+ align:start position:0%
+different coordinates right
+ 
+
+ align:start position:0%
+different coordinates right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+atf is face mask
+
+ align:start position:0%
+atf is face mask
+ 
+
+ align:start position:0%
+atf is face mask
+but the function is the x double prime i
+
+ align:start position:0%
+but the function is the x double prime i
+ 
+
+ align:start position:0%
+but the function is the x double prime i
+mean you have this coordinate scaling
+
+ align:start position:0%
+mean you have this coordinate scaling
+ 
+
+ align:start position:0%
+mean you have this coordinate scaling
+factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you
+
+ align:start position:0%
+so if you
+ 
+
+ align:start position:0%
+so if you
+compute the otf from this a-tip
+
+ align:start position:0%
+compute the otf from this a-tip
+ 
+
+ align:start position:0%
+compute the otf from this a-tip
+basically what you do is you have two uh
+
+ align:start position:0%
+basically what you do is you have two uh
+ 
+
+ align:start position:0%
+basically what you do is you have two uh
+you have two that two-rect function
+
+ align:start position:0%
+you have two that two-rect function
+ 
+
+ align:start position:0%
+you have two that two-rect function
+actually you have so you you're gonna
+
+ align:start position:0%
+actually you have so you you're gonna
+ 
+
+ align:start position:0%
+actually you have so you you're gonna
+have actually four vector functions
+
+ align:start position:0%
+have actually four vector functions
+ 
+
+ align:start position:0%
+have actually four vector functions
+right and you move one uh two of them
+
+ align:start position:0%
+right and you move one uh two of them
+ 
+
+ align:start position:0%
+right and you move one uh two of them
+so whenever they overlap you get some uh
+
+ align:start position:0%
+so whenever they overlap you get some uh
+ 
+
+ align:start position:0%
+so whenever they overlap you get some uh
+value right
+
+ align:start position:0%
+value right
+ 
+
+ align:start position:0%
+value right
+so if you do uh that autocorrelation
+
+ align:start position:0%
+so if you do uh that autocorrelation
+ 
+
+ align:start position:0%
+so if you do uh that autocorrelation
+then actually
+
+ align:start position:0%
+then actually
+ 
+
+ align:start position:0%
+then actually
+you're going to have
+
+ align:start position:0%
+you're going to have
+ 
+
+ align:start position:0%
+you're going to have
+three triangular so remember that if you
+
+ align:start position:0%
+three triangular so remember that if you
+ 
+
+ align:start position:0%
+three triangular so remember that if you
+have the one right function
+
+ align:start position:0%
+have the one right function
+ 
+
+ align:start position:0%
+have the one right function
+i mean yeah one like function then you
+
+ align:start position:0%
+i mean yeah one like function then you
+ 
+
+ align:start position:0%
+i mean yeah one like function then you
+move two left function so you're going
+
+ align:start position:0%
+move two left function so you're going
+ 
+
+ align:start position:0%
+move two left function so you're going
+to have one triangulation one triangular
+
+ align:start position:0%
+to have one triangulation one triangular
+ 
+
+ align:start position:0%
+to have one triangulation one triangular
+so since we have two vector functions so
+
+ align:start position:0%
+so since we have two vector functions so
+ 
+
+ align:start position:0%
+so since we have two vector functions so
+whenever they first meet
+
+ align:start position:0%
+whenever they first meet
+ 
+
+ align:start position:0%
+whenever they first meet
+that we have the one train one triangle
+
+ align:start position:0%
+that we have the one train one triangle
+ 
+
+ align:start position:0%
+that we have the one train one triangle
+but the second and
+
+ align:start position:0%
+but the second and
+ 
+
+ align:start position:0%
+but the second and
+the two red functions are overlapped and
+
+ align:start position:0%
+the two red functions are overlapped and
+ 
+
+ align:start position:0%
+the two red functions are overlapped and
+we have the center triangle and
+
+ align:start position:0%
+we have the center triangle and
+ 
+
+ align:start position:0%
+we have the center triangle and
+like this we have the another triangle
+
+ align:start position:0%
+like this we have the another triangle
+ 
+
+ align:start position:0%
+like this we have the another triangle
+so we get the three triangles
+
+ align:start position:0%
+so we get the three triangles
+ 
+
+ align:start position:0%
+so we get the three triangles
+so that's the otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you expand with the frequencies of
+
+ align:start position:0%
+if you expand with the frequencies of
+ 
+
+ align:start position:0%
+if you expand with the frequencies of
+your input intensity then we are going
+
+ align:start position:0%
+your input intensity then we are going
+ 
+
+ align:start position:0%
+your input intensity then we are going
+to have infinite number of deflection
+
+ align:start position:0%
+to have infinite number of deflection
+ 
+
+ align:start position:0%
+to have infinite number of deflection
+but in atf case
+
+ align:start position:0%
+but in atf case
+ 
+
+ align:start position:0%
+but in atf case
+we have uh
+
+ align:start position:0%
+we have uh
+ 
+
+ align:start position:0%
+we have uh
+only first order and the minus first
+
+ align:start position:0%
+only first order and the minus first
+ 
+
+ align:start position:0%
+only first order and the minus first
+order and minus first order
+
+ align:start position:0%
+order and minus first order
+ 
+
+ align:start position:0%
+order and minus first order
+are going to be transmitted but in otf
+
+ align:start position:0%
+are going to be transmitted but in otf
+ 
+
+ align:start position:0%
+are going to be transmitted but in otf
+actually they are blocked because this
+
+ align:start position:0%
+actually they are blocked because this
+ 
+
+ align:start position:0%
+actually they are blocked because this
+is zero
+
+ align:start position:0%
+is zero
+ 
+
+ align:start position:0%
+is zero
+actually plus two and zero and minus two
+
+ align:start position:0%
+actually plus two and zero and minus two
+ 
+
+ align:start position:0%
+actually plus two and zero and minus two
+they are going to be transmitted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you just multiply
+
+ align:start position:0%
+you just multiply
+ 
+
+ align:start position:0%
+you just multiply
+these three data functions by the
+
+ align:start position:0%
+these three data functions by the
+ 
+
+ align:start position:0%
+these three data functions by the
+value of the atf i mean this this this
+
+ align:start position:0%
+value of the atf i mean this this this
+ 
+
+ align:start position:0%
+value of the atf i mean this this this
+and that's going to be your
+
+ align:start position:0%
+and that's going to be your
+ 
+
+ align:start position:0%
+and that's going to be your
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+the free transform of your output
+
+ align:start position:0%
+the free transform of your output
+ 
+
+ align:start position:0%
+the free transform of your output
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so 1 over 3 is just came from the the
+
+ align:start position:0%
+so 1 over 3 is just came from the the
+ 
+
+ align:start position:0%
+so 1 over 3 is just came from the the
+central data function because this is 1
+
+ align:start position:0%
+central data function because this is 1
+ 
+
+ align:start position:0%
+central data function because this is 1
+so just 1 over three
+
+ align:start position:0%
+so just 1 over three
+ 
+
+ align:start position:0%
+so just 1 over three
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for the first order
+
+ align:start position:0%
+for the first order
+ 
+
+ align:start position:0%
+for the first order
+at the point one and
+
+ align:start position:0%
+at the point one and
+ 
+
+ align:start position:0%
+at the point one and
+the minus point one and minus point one
+
+ align:start position:0%
+the minus point one and minus point one
+ 
+
+ align:start position:0%
+the minus point one and minus point one
+micrometer actually a vulnerable
+
+ align:start position:0%
+micrometer actually a vulnerable
+ 
+
+ align:start position:0%
+micrometer actually a vulnerable
+micrometer actually they have zero value
+
+ align:start position:0%
+micrometer actually they have zero value
+ 
+
+ align:start position:0%
+micrometer actually they have zero value
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i multiply by zero
+
+ align:start position:0%
+i multiply by zero
+ 
+
+ align:start position:0%
+i multiply by zero
+and this for the second order
+
+ align:start position:0%
+and this for the second order
+ 
+
+ align:start position:0%
+and this for the second order
+i have one over two which is
+
+ align:start position:0%
+i have one over two which is
+ 
+
+ align:start position:0%
+i have one over two which is
+this value here and here
+
+ align:start position:0%
+this value here and here
+ 
+
+ align:start position:0%
+this value here and here
+so that is the you know free transfer of
+
+ align:start position:0%
+so that is the you know free transfer of
+ 
+
+ align:start position:0%
+so that is the you know free transfer of
+the output intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you
+
+ align:start position:0%
+so if you
+ 
+
+ align:start position:0%
+so if you
+compute the inverse spread transform of
+
+ align:start position:0%
+compute the inverse spread transform of
+ 
+
+ align:start position:0%
+compute the inverse spread transform of
+this equation then we are going to have
+
+ align:start position:0%
+this equation then we are going to have
+ 
+
+ align:start position:0%
+this equation then we are going to have
+1 over 3 and 1 over 2 and two exponent
+
+ align:start position:0%
+1 over 3 and 1 over 2 and two exponent
+ 
+
+ align:start position:0%
+1 over 3 and 1 over 2 and two exponent
+two exponential which is actually
+
+ align:start position:0%
+two exponential which is actually
+ 
+
+ align:start position:0%
+two exponential which is actually
+uh cosine
+
+ align:start position:0%
+uh cosine
+ 
+
+ align:start position:0%
+uh cosine
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+so in terms of grayscale image we have
+
+ align:start position:0%
+so in terms of grayscale image we have
+ 
+
+ align:start position:0%
+so in terms of grayscale image we have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+binary amplitude gradient which vary
+
+ align:start position:0%
+binary amplitude gradient which vary
+ 
+
+ align:start position:0%
+binary amplitude gradient which vary
+just black or white like this
+
+ align:start position:0%
+just black or white like this
+ 
+
+ align:start position:0%
+just black or white like this
+but if you go through this 4-f system at
+
+ align:start position:0%
+but if you go through this 4-f system at
+ 
+
+ align:start position:0%
+but if you go through this 4-f system at
+the image you're going to have this kind
+
+ align:start position:0%
+the image you're going to have this kind
+ 
+
+ align:start position:0%
+the image you're going to have this kind
+of gray scale
+
+ align:start position:0%
+of gray scale
+ 
+
+ align:start position:0%
+of gray scale
+because you know contrast is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three 0.1.1034
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one or three four so it's very little
+
+ align:start position:0%
+one or three four so it's very little
+ 
+
+ align:start position:0%
+one or three four so it's very little
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+and uh the average value is about point
+
+ align:start position:0%
+and uh the average value is about point
+ 
+
+ align:start position:0%
+and uh the average value is about point
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+three or something so basically it looks
+
+ align:start position:0%
+three or something so basically it looks
+ 
+
+ align:start position:0%
+three or something so basically it looks
+great with the little uh wiggling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know atf basically tells you the
+
+ align:start position:0%
+so you know atf basically tells you the
+ 
+
+ align:start position:0%
+so you know atf basically tells you the
+contrast i mean contrast of the
+
+ align:start position:0%
+contrast i mean contrast of the
+ 
+
+ align:start position:0%
+contrast i mean contrast of the
+particular spatial frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what happened i mean the orders at
+
+ align:start position:0%
+yeah what happened i mean the orders at
+ 
+
+ align:start position:0%
+yeah what happened i mean the orders at
+this side so if my
+
+ align:start position:0%
+this side so if my
+ 
+
+ align:start position:0%
+this side so if my
+you know otf is zero then what kind of
+
+ align:start position:0%
+you know otf is zero then what kind of
+ 
+
+ align:start position:0%
+you know otf is zero then what kind of
+image i can expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not white right
+
+ align:start position:0%
+it's not white right
+ 
+
+ align:start position:0%
+it's not white right
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so if it is zero
+
+ align:start position:0%
+so if it is zero
+ 
+
+ align:start position:0%
+so if it is zero
+i mean if the value are zero
+
+ align:start position:0%
+i mean if the value are zero
+ 
+
+ align:start position:0%
+i mean if the value are zero
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i still have dc term right so some
+
+ align:start position:0%
+but i still have dc term right so some
+ 
+
+ align:start position:0%
+but i still have dc term right so some
+kind of gray scale
+
+ align:start position:0%
+kind of gray scale
+ 
+
+ align:start position:0%
+kind of gray scale
+but i don't see any uh
+
+ align:start position:0%
+but i don't see any uh
+ 
+
+ align:start position:0%
+but i don't see any uh
+demodulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know otf is autocorrelation so you
+
+ align:start position:0%
+you know otf is autocorrelation so you
+ 
+
+ align:start position:0%
+you know otf is autocorrelation so you
+always have
+
+ align:start position:0%
+always have
+ 
+
+ align:start position:0%
+always have
+one at the dc frequency
+
+ align:start position:0%
+one at the dc frequency
+ 
+
+ align:start position:0%
+one at the dc frequency
+you know because you know you should
+
+ align:start position:0%
+you know because you know you should
+ 
+
+ align:start position:0%
+you know because you know you should
+move the two function but so they when
+
+ align:start position:0%
+move the two function but so they when
+ 
+
+ align:start position:0%
+move the two function but so they when
+they are exactly overlapped you always
+
+ align:start position:0%
+they are exactly overlapped you always
+ 
+
+ align:start position:0%
+they are exactly overlapped you always
+have a maximum value so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you always have a dc term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually there is slightly different in
+
+ align:start position:0%
+actually there is slightly different in
+ 
+
+ align:start position:0%
+actually there is slightly different in
+current case right so atf case you can
+
+ align:start position:0%
+current case right so atf case you can
+ 
+
+ align:start position:0%
+current case right so atf case you can
+actually cancel this system right but
+
+ align:start position:0%
+actually cancel this system right but
+ 
+
+ align:start position:0%
+actually cancel this system right but
+otf you cannot cancel this term because
+
+ align:start position:0%
+otf you cannot cancel this term because
+ 
+
+ align:start position:0%
+otf you cannot cancel this term because
+it's autocorrelation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+again we have a
+
+ align:start position:0%
+again we have a
+ 
+
+ align:start position:0%
+again we have a
+simulation with the mit layer so this
+
+ align:start position:0%
+simulation with the mit layer so this
+ 
+
+ align:start position:0%
+simulation with the mit layer so this
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+circular aperture
+
+ align:start position:0%
+circular aperture
+ 
+
+ align:start position:0%
+circular aperture
+if i use if i illuminate with the
+
+ align:start position:0%
+if i use if i illuminate with the
+ 
+
+ align:start position:0%
+if i use if i illuminate with the
+coherent illumination then this is the
+
+ align:start position:0%
+coherent illumination then this is the
+ 
+
+ align:start position:0%
+coherent illumination then this is the
+image actually yes
+
+ align:start position:0%
+image actually yes
+ 
+
+ align:start position:0%
+image actually yes
+yeah in singapore side the
+
+ align:start position:0%
+yeah in singapore side the
+ 
+
+ align:start position:0%
+yeah in singapore side the
+ppt slides are not means they are
+
+ align:start position:0%
+ppt slides are not means they are
+ 
+
+ align:start position:0%
+ppt slides are not means they are
+phrased
+
+ align:start position:0%
+phrased
+ 
+
+ align:start position:0%
+phrased
+means still it is showing this example
+
+ align:start position:0%
+means still it is showing this example
+ 
+
+ align:start position:0%
+means still it is showing this example
+of band pass filtering
+
+ align:start position:0%
+of band pass filtering
+ 
+
+ align:start position:0%
+of band pass filtering
+slide number
+
+ align:start position:0%
+slide number
+ 
+
+ align:start position:0%
+slide number
+here or maybe it takes time or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it even didn't show that
+
+ align:start position:0%
+no it even didn't show that
+ 
+
+ align:start position:0%
+no it even didn't show that
+that input
+
+ align:start position:0%
+that input
+ 
+
+ align:start position:0%
+that input
+and output image
+
+ align:start position:0%
+and output image
+ 
+
+ align:start position:0%
+and output image
+when you explained about that contrast
+
+ align:start position:0%
+when you explained about that contrast
+ 
+
+ align:start position:0%
+when you explained about that contrast
+uh-huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh just let me ask control
+
+ align:start position:0%
+uh just let me ask control
+ 
+
+ align:start position:0%
+uh just let me ask control
+hello
+
+ align:start position:0%
+hello
+ 
+
+ align:start position:0%
+hello
+hey control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes uh the same singapore side they
+
+ align:start position:0%
+yes uh the same singapore side they
+ 
+
+ align:start position:0%
+yes uh the same singapore side they
+their screen is freezed
+
+ align:start position:0%
+their screen is freezed
+ 
+
+ align:start position:0%
+their screen is freezed
+it's frozen yeah
+
+ align:start position:0%
+it's frozen yeah
+ 
+
+ align:start position:0%
+it's frozen yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are they gonna reset the system so yeah
+
+ align:start position:0%
+are they gonna reset the system so yeah
+ 
+
+ align:start position:0%
+are they gonna reset the system so yeah
+so let me just take a few moments
+
+ align:start position:0%
+so let me just take a few moments
+ 
+
+ align:start position:0%
+so let me just take a few moments
+any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah actually i'm going to talk about
+
+ align:start position:0%
+uh yeah actually i'm going to talk about
+ 
+
+ align:start position:0%
+uh yeah actually i'm going to talk about
+it but you know
+
+ align:start position:0%
+it but you know
+ 
+
+ align:start position:0%
+it but you know
+in general if you use the equivalent
+
+ align:start position:0%
+in general if you use the equivalent
+ 
+
+ align:start position:0%
+in general if you use the equivalent
+light then you don't see any phase
+
+ align:start position:0%
+light then you don't see any phase
+ 
+
+ align:start position:0%
+light then you don't see any phase
+effect right because you know you're
+
+ align:start position:0%
+effect right because you know you're
+ 
+
+ align:start position:0%
+effect right because you know you're
+going to take the magnitude square so
+
+ align:start position:0%
+going to take the magnitude square so
+ 
+
+ align:start position:0%
+going to take the magnitude square so
+it doesn't really matter so you don't
+
+ align:start position:0%
+it doesn't really matter so you don't
+ 
+
+ align:start position:0%
+it doesn't really matter so you don't
+see any i mean you barely see some
+
+ align:start position:0%
+see any i mean you barely see some
+ 
+
+ align:start position:0%
+see any i mean you barely see some
+variation but usually
+
+ align:start position:0%
+variation but usually
+ 
+
+ align:start position:0%
+variation but usually
+it's not traumatic as coherent
+
+ align:start position:0%
+it's not traumatic as coherent
+ 
+
+ align:start position:0%
+it's not traumatic as coherent
+elimination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what i was about to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah so mtf is just making to the
+
+ align:start position:0%
+oh yeah so mtf is just making to the
+ 
+
+ align:start position:0%
+oh yeah so mtf is just making to the
+magnitude of the otf right so we we
+
+ align:start position:0%
+magnitude of the otf right so we we
+ 
+
+ align:start position:0%
+magnitude of the otf right so we we
+haven't talked about any
+
+ align:start position:0%
+haven't talked about any
+ 
+
+ align:start position:0%
+haven't talked about any
+phase of the rtf so what's the effect of
+
+ align:start position:0%
+phase of the rtf so what's the effect of
+ 
+
+ align:start position:0%
+phase of the rtf so what's the effect of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+what is what does it mean i mean if i
+
+ align:start position:0%
+what is what does it mean i mean if i
+ 
+
+ align:start position:0%
+what is what does it mean i mean if i
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+some phase variation in otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can anyone guess
+
+ align:start position:0%
+can anyone guess
+ 
+
+ align:start position:0%
+can anyone guess
+so for example otf is always nine nine
+
+ align:start position:0%
+so for example otf is always nine nine
+ 
+
+ align:start position:0%
+so for example otf is always nine nine
+zero right is
+
+ align:start position:0%
+zero right is
+ 
+
+ align:start position:0%
+zero right is
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+zero or positive
+
+ align:start position:0%
+zero or positive
+ 
+
+ align:start position:0%
+zero or positive
+but you know his face can be zero or pi
+
+ align:start position:0%
+but you know his face can be zero or pi
+ 
+
+ align:start position:0%
+but you know his face can be zero or pi
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so what if i have
+
+ align:start position:0%
+so what if i have
+ 
+
+ align:start position:0%
+so what if i have
+pi phase shift in otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example i have
+
+ align:start position:0%
+for example i have
+ 
+
+ align:start position:0%
+for example i have
+assigned to the grading and at the
+
+ align:start position:0%
+assigned to the grading and at the
+ 
+
+ align:start position:0%
+assigned to the grading and at the
+output i have the sinusoidal gradient
+
+ align:start position:0%
+output i have the sinusoidal gradient
+ 
+
+ align:start position:0%
+output i have the sinusoidal gradient
+but what does it mean i have the pi
+
+ align:start position:0%
+but what does it mean i have the pi
+ 
+
+ align:start position:0%
+but what does it mean i have the pi
+phase shift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not really yeah
+
+ align:start position:0%
+not really yeah
+ 
+
+ align:start position:0%
+not really yeah
+what money what happens if you
+
+ align:start position:0%
+what money what happens if you
+ 
+
+ align:start position:0%
+what money what happens if you
+shift by
+
+ align:start position:0%
+shift by
+ 
+
+ align:start position:0%
+shift by
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+i mean if you move the cosine by pi
+
+ align:start position:0%
+i mean if you move the cosine by pi
+ 
+
+ align:start position:0%
+i mean if you move the cosine by pi
+you get sine right
+
+ align:start position:0%
+you get sine right
+ 
+
+ align:start position:0%
+you get sine right
+so you you have cosine pattern here
+
+ align:start position:0%
+so you you have cosine pattern here
+ 
+
+ align:start position:0%
+so you you have cosine pattern here
+and if you have pi phase shift then
+
+ align:start position:0%
+and if you have pi phase shift then
+ 
+
+ align:start position:0%
+and if you have pi phase shift then
+you're going to have the sine pattern
+
+ align:start position:0%
+you're going to have the sine pattern
+ 
+
+ align:start position:0%
+you're going to have the sine pattern
+which means
+
+ align:start position:0%
+which means
+ 
+
+ align:start position:0%
+which means
+you flip the black and white at the
+
+ align:start position:0%
+you flip the black and white at the
+ 
+
+ align:start position:0%
+you flip the black and white at the
+image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so i flipped the black but still i
+
+ align:start position:0%
+yeah so i flipped the black but still i
+ 
+
+ align:start position:0%
+yeah so i flipped the black but still i
+change the black and white right yeah
+
+ align:start position:0%
+change the black and white right yeah
+ 
+
+ align:start position:0%
+change the black and white right yeah
+not the sine to cosine that's why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i singapore uh otherwise can you guys
+
+ align:start position:0%
+i singapore uh otherwise can you guys
+ 
+
+ align:start position:0%
+i singapore uh otherwise can you guys
+see the side right now or
+
+ align:start position:0%
+see the side right now or
+ 
+
+ align:start position:0%
+see the side right now or
+yes all right yeah thanks yeah uh i have
+
+ align:start position:0%
+yes all right yeah thanks yeah uh i have
+ 
+
+ align:start position:0%
+yes all right yeah thanks yeah uh i have
+one question uh how do you enter this
+
+ align:start position:0%
+one question uh how do you enter this
+ 
+
+ align:start position:0%
+one question uh how do you enter this
+five phase shift in otf
+
+ align:start position:0%
+five phase shift in otf
+ 
+
+ align:start position:0%
+five phase shift in otf
+uh so if you have five phase shift in
+
+ align:start position:0%
+uh so if you have five phase shift in
+ 
+
+ align:start position:0%
+uh so if you have five phase shift in
+otf then basically you flip the black
+
+ align:start position:0%
+otf then basically you flip the black
+ 
+
+ align:start position:0%
+otf then basically you flip the black
+and white
+
+ align:start position:0%
+and white
+ 
+
+ align:start position:0%
+and white
+so your input image is
+
+ align:start position:0%
+so your input image is
+ 
+
+ align:start position:0%
+so your input image is
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+let's say the black white black white
+
+ align:start position:0%
+let's say the black white black white
+ 
+
+ align:start position:0%
+let's say the black white black white
+and your image is going to be white
+
+ align:start position:0%
+and your image is going to be white
+ 
+
+ align:start position:0%
+and your image is going to be white
+black white black
+
+ align:start position:0%
+black white black
+ 
+
+ align:start position:0%
+black white black
+now my question is like uh
+
+ align:start position:0%
+now my question is like uh
+ 
+
+ align:start position:0%
+now my question is like uh
+physically how means how how do you
+
+ align:start position:0%
+physically how means how how do you
+ 
+
+ align:start position:0%
+physically how means how how do you
+introduce that controllable phase shift
+
+ align:start position:0%
+introduce that controllable phase shift
+ 
+
+ align:start position:0%
+introduce that controllable phase shift
+in otf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+this atf can be complex right so if you
+
+ align:start position:0%
+this atf can be complex right so if you
+ 
+
+ align:start position:0%
+this atf can be complex right so if you
+come if you compute the autocorrelation
+
+ align:start position:0%
+come if you compute the autocorrelation
+ 
+
+ align:start position:0%
+come if you compute the autocorrelation
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+actually you can have a negative value
+
+ align:start position:0%
+actually you can have a negative value
+ 
+
+ align:start position:0%
+actually you can have a negative value
+of otf
+
+ align:start position:0%
+of otf
+ 
+
+ align:start position:0%
+of otf
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and if you have the negative value in
+
+ align:start position:0%
+and if you have the negative value in
+ 
+
+ align:start position:0%
+and if you have the negative value in
+otf which means you have still positive
+
+ align:start position:0%
+otf which means you have still positive
+ 
+
+ align:start position:0%
+otf which means you have still positive
+magnitude but you have some negative uh
+
+ align:start position:0%
+magnitude but you have some negative uh
+ 
+
+ align:start position:0%
+magnitude but you have some negative uh
+i mean pi basically pi phase right so if
+
+ align:start position:0%
+i mean pi basically pi phase right so if
+ 
+
+ align:start position:0%
+i mean pi basically pi phase right so if
+you want to do that kind of thing
+
+ align:start position:0%
+you want to do that kind of thing
+ 
+
+ align:start position:0%
+you want to do that kind of thing
+basically you have some complex
+
+ align:start position:0%
+basically you have some complex
+ 
+
+ align:start position:0%
+basically you have some complex
+transparency at your pp mask
+
+ align:start position:0%
+transparency at your pp mask
+ 
+
+ align:start position:0%
+transparency at your pp mask
+yeah but if you have clear aperture then
+
+ align:start position:0%
+yeah but if you have clear aperture then
+ 
+
+ align:start position:0%
+yeah but if you have clear aperture then
+you don't you don't get that
+
+ align:start position:0%
+you don't you don't get that
+ 
+
+ align:start position:0%
+you don't you don't get that
+effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so let me continue this slide so
+
+ align:start position:0%
+yeah so let me continue this slide so
+ 
+
+ align:start position:0%
+yeah so let me continue this slide so
+this i mean these two image we already
+
+ align:start position:0%
+this i mean these two image we already
+ 
+
+ align:start position:0%
+this i mean these two image we already
+seen
+
+ align:start position:0%
+seen
+ 
+
+ align:start position:0%
+seen
+maybe two or three lectures ago so this
+
+ align:start position:0%
+maybe two or three lectures ago so this
+ 
+
+ align:start position:0%
+maybe two or three lectures ago so this
+is mit lecture i mean the image of the
+
+ align:start position:0%
+is mit lecture i mean the image of the
+ 
+
+ align:start position:0%
+is mit lecture i mean the image of the
+mit ladder with the coherent elimination
+
+ align:start position:0%
+mit ladder with the coherent elimination
+ 
+
+ align:start position:0%
+mit ladder with the coherent elimination
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this the right to
+
+ align:start position:0%
+this the right to
+ 
+
+ align:start position:0%
+this the right to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right two images are
+
+ align:start position:0%
+right two images are
+ 
+
+ align:start position:0%
+right two images are
+obtained with the in query elimination
+
+ align:start position:0%
+obtained with the in query elimination
+ 
+
+ align:start position:0%
+obtained with the in query elimination
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i can notice two main difference here so
+
+ align:start position:0%
+i can notice two main difference here so
+ 
+
+ align:start position:0%
+i can notice two main difference here so
+so if i use the in-query elimination i
+
+ align:start position:0%
+so if i use the in-query elimination i
+ 
+
+ align:start position:0%
+so if i use the in-query elimination i
+basically the image looks sharper than
+
+ align:start position:0%
+basically the image looks sharper than
+ 
+
+ align:start position:0%
+basically the image looks sharper than
+the one with the cohen
+
+ align:start position:0%
+the one with the cohen
+ 
+
+ align:start position:0%
+the one with the cohen
+and that's because
+
+ align:start position:0%
+and that's because
+ 
+
+ align:start position:0%
+and that's because
+your you know otf has a higher choice of
+
+ align:start position:0%
+your you know otf has a higher choice of
+ 
+
+ align:start position:0%
+your you know otf has a higher choice of
+higher quarter frequency right even
+
+ align:start position:0%
+higher quarter frequency right even
+ 
+
+ align:start position:0%
+higher quarter frequency right even
+though they get attenuated but basically
+
+ align:start position:0%
+though they get attenuated but basically
+ 
+
+ align:start position:0%
+though they get attenuated but basically
+it can pass through the higher special
+
+ align:start position:0%
+it can pass through the higher special
+ 
+
+ align:start position:0%
+it can pass through the higher special
+frequencies so that's why
+
+ align:start position:0%
+frequencies so that's why
+ 
+
+ align:start position:0%
+frequencies so that's why
+it preserves higher frequency more
+
+ align:start position:0%
+it preserves higher frequency more
+ 
+
+ align:start position:0%
+it preserves higher frequency more
+increases more higher frequency
+
+ align:start position:0%
+increases more higher frequency
+ 
+
+ align:start position:0%
+increases more higher frequency
+preserve higher frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's same thing here so with the cohen
+
+ align:start position:0%
+it's same thing here so with the cohen
+ 
+
+ align:start position:0%
+it's same thing here so with the cohen
+light you barely see the eye
+
+ align:start position:0%
+light you barely see the eye
+ 
+
+ align:start position:0%
+light you barely see the eye
+letter i but you can still see the mit
+
+ align:start position:0%
+letter i but you can still see the mit
+ 
+
+ align:start position:0%
+letter i but you can still see the mit
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and another difference is actually if
+
+ align:start position:0%
+and another difference is actually if
+ 
+
+ align:start position:0%
+and another difference is actually if
+you see the n or t there are some
+
+ align:start position:0%
+you see the n or t there are some
+ 
+
+ align:start position:0%
+you see the n or t there are some
+variations
+
+ align:start position:0%
+variations
+ 
+
+ align:start position:0%
+variations
+like black or white some wiggling in m
+
+ align:start position:0%
+like black or white some wiggling in m
+ 
+
+ align:start position:0%
+like black or white some wiggling in m
+and t here
+
+ align:start position:0%
+and t here
+ 
+
+ align:start position:0%
+and t here
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+in in coordinate case you
+
+ align:start position:0%
+in in coordinate case you
+ 
+
+ align:start position:0%
+in in coordinate case you
+intensity is more like uniform you don't
+
+ align:start position:0%
+intensity is more like uniform you don't
+ 
+
+ align:start position:0%
+intensity is more like uniform you don't
+see any
+
+ align:start position:0%
+see any
+ 
+
+ align:start position:0%
+see any
+some weird variation so
+
+ align:start position:0%
+some weird variation so
+ 
+
+ align:start position:0%
+some weird variation so
+that's the another difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so so if you use the incoherent in
+
+ align:start position:0%
+so so if you use the incoherent in
+ 
+
+ align:start position:0%
+so so if you use the incoherent in
+current light generally
+
+ align:start position:0%
+current light generally
+ 
+
+ align:start position:0%
+current light generally
+you don't have
+
+ align:start position:0%
+you don't have
+ 
+
+ align:start position:0%
+you don't have
+the ringing artifact as i just described
+
+ align:start position:0%
+the ringing artifact as i just described
+ 
+
+ align:start position:0%
+the ringing artifact as i just described
+and also no speckle is in korean so you
+
+ align:start position:0%
+and also no speckle is in korean so you
+ 
+
+ align:start position:0%
+and also no speckle is in korean so you
+know you're not going to see any
+
+ align:start position:0%
+know you're not going to see any
+ 
+
+ align:start position:0%
+know you're not going to see any
+you know interference
+
+ align:start position:0%
+you know interference
+ 
+
+ align:start position:0%
+you know interference
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it has higher bandwidth because you know
+
+ align:start position:0%
+it has higher bandwidth because you know
+ 
+
+ align:start position:0%
+it has higher bandwidth because you know
+the quarter frequency is twice higher
+
+ align:start position:0%
+the quarter frequency is twice higher
+ 
+
+ align:start position:0%
+the quarter frequency is twice higher
+than the color frequency in atm
+
+ align:start position:0%
+than the color frequency in atm
+ 
+
+ align:start position:0%
+than the color frequency in atm
+so you know you can see basically higher
+
+ align:start position:0%
+so you know you can see basically higher
+ 
+
+ align:start position:0%
+so you know you can see basically higher
+the smaller feature
+
+ align:start position:0%
+the smaller feature
+ 
+
+ align:start position:0%
+the smaller feature
+i mean the two
+
+ align:start position:0%
+i mean the two
+ 
+
+ align:start position:0%
+i mean the two
+uh point
+
+ align:start position:0%
+uh point
+ 
+
+ align:start position:0%
+uh point
+the closer okay so you can see the hot
+
+ align:start position:0%
+the closer okay so you can see the hot
+ 
+
+ align:start position:0%
+the closer okay so you can see the hot
+the smaller feature
+
+ align:start position:0%
+the smaller feature
+ 
+
+ align:start position:0%
+the smaller feature
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah but if i describe as i answered to
+
+ align:start position:0%
+yeah but if i describe as i answered to
+ 
+
+ align:start position:0%
+yeah but if i describe as i answered to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+javascription uh in current imaging is
+
+ align:start position:0%
+javascription uh in current imaging is
+ 
+
+ align:start position:0%
+javascription uh in current imaging is
+insensitive to phase variation so
+
+ align:start position:0%
+insensitive to phase variation so
+ 
+
+ align:start position:0%
+insensitive to phase variation so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yeah so mostly we just deal with the
+
+ align:start position:0%
+yeah so mostly we just deal with the
+ 
+
+ align:start position:0%
+yeah so mostly we just deal with the
+monochromatic especially in korean but
+
+ align:start position:0%
+monochromatic especially in korean but
+ 
+
+ align:start position:0%
+monochromatic especially in korean but
+if you have polychromatic which is
+
+ align:start position:0%
+if you have polychromatic which is
+ 
+
+ align:start position:0%
+if you have polychromatic which is
+broadband and you
+
+ align:start position:0%
+broadband and you
+ 
+
+ align:start position:0%
+broadband and you
+and you're gonna have some chromatic
+
+ align:start position:0%
+and you're gonna have some chromatic
+ 
+
+ align:start position:0%
+and you're gonna have some chromatic
+aberration but
+
+ align:start position:0%
+aberration but
+ 
+
+ align:start position:0%
+aberration but
+again you can define
+
+ align:start position:0%
+again you can define
+ 
+
+ align:start position:0%
+again you can define
+all this otf or mtf or poinsettia
+
+ align:start position:0%
+all this otf or mtf or poinsettia
+ 
+
+ align:start position:0%
+all this otf or mtf or poinsettia
+function for each different wavelength
+
+ align:start position:0%
+function for each different wavelength
+ 
+
+ align:start position:0%
+function for each different wavelength
+so you know you can just extend this in
+
+ align:start position:0%
+so you know you can just extend this in
+ 
+
+ align:start position:0%
+so you know you can just extend this in
+straightforward fashion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's the end of show so
+
+ align:start position:0%
+it's the end of show so
+ 
+
+ align:start position:0%
+it's the end of show so
+any question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so the second message of the
+
+ align:start position:0%
+yeah so the second message of the
+ 
+
+ align:start position:0%
+yeah so the second message of the
+today's lecture is you know
+
+ align:start position:0%
+today's lecture is you know
+ 
+
+ align:start position:0%
+today's lecture is you know
+if you have coherent illumination then
+
+ align:start position:0%
+if you have coherent illumination then
+ 
+
+ align:start position:0%
+if you have coherent illumination then
+you have linear uh convolution in field
+
+ align:start position:0%
+you have linear uh convolution in field
+ 
+
+ align:start position:0%
+you have linear uh convolution in field
+but if you have incoherent case
+
+ align:start position:0%
+but if you have incoherent case
+ 
+
+ align:start position:0%
+but if you have incoherent case
+and you have
+
+ align:start position:0%
+and you have
+ 
+
+ align:start position:0%
+and you have
+the linear linear relation in intensity
+
+ align:start position:0%
+the linear linear relation in intensity
+ 
+
+ align:start position:0%
+the linear linear relation in intensity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for in coin coinlight you have to deal
+
+ align:start position:0%
+for in coin coinlight you have to deal
+ 
+
+ align:start position:0%
+for in coin coinlight you have to deal
+with the otf which is autocorrelation of
+
+ align:start position:0%
+with the otf which is autocorrelation of
+ 
+
+ align:start position:0%
+with the otf which is autocorrelation of
+atf
+
+ align:start position:0%
+atf
+ 
+
+ align:start position:0%
+atf
+and that's pretty much about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah if you don't have question then
+
+ align:start position:0%
+yeah if you don't have question then
+ 
+
+ align:start position:0%
+yeah if you don't have question then
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+next monday
\ No newline at end of file
diff --git a/WCw7gzz5RZY.txt b/WCw7gzz5RZY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa9acacd08a92730a7d64170beeb85e3263874aa
--- /dev/null
+++ b/WCw7gzz5RZY.txt
@@ -0,0 +1,4008 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
+ align:start position:0%
+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
+
+ align:start position:0%
+will help mit opencourseware continue to
+ 
+
+ align:start position:0%
+will help mit opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so our group is going to talk
+
+ align:start position:0%
+all right so our group is going to talk
+ 
+
+ align:start position:0%
+all right so our group is going to talk
+about the accuracy requirements in the
+
+ align:start position:0%
+about the accuracy requirements in the
+ 
+
+ align:start position:0%
+about the accuracy requirements in the
+mechanical assembly of photonic crystals
+
+ align:start position:0%
+mechanical assembly of photonic crystals
+ 
+
+ align:start position:0%
+mechanical assembly of photonic crystals
+um so to do so
+
+ align:start position:0%
+um so to do so
+ 
+
+ align:start position:0%
+um so to do so
+we'll definitely have to introduce what
+
+ align:start position:0%
+we'll definitely have to introduce what
+ 
+
+ align:start position:0%
+we'll definitely have to introduce what
+a photonic crystal is
+
+ align:start position:0%
+a photonic crystal is
+ 
+
+ align:start position:0%
+a photonic crystal is
+um then martin is going to talk about
+
+ align:start position:0%
+um then martin is going to talk about
+ 
+
+ align:start position:0%
+um then martin is going to talk about
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+the fabrication process
+
+ align:start position:0%
+the fabrication process
+ 
+
+ align:start position:0%
+the fabrication process
+of 3d photonic crystals and corey is
+
+ align:start position:0%
+of 3d photonic crystals and corey is
+ 
+
+ align:start position:0%
+of 3d photonic crystals and corey is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+have this little application
+
+ align:start position:0%
+have this little application
+ 
+
+ align:start position:0%
+have this little application
+that it carried out
+
+ align:start position:0%
+that it carried out
+ 
+
+ align:start position:0%
+that it carried out
+to see the influence of
+
+ align:start position:0%
+to see the influence of
+ 
+
+ align:start position:0%
+to see the influence of
+misalignment in a 3d structure on the
+
+ align:start position:0%
+misalignment in a 3d structure on the
+ 
+
+ align:start position:0%
+misalignment in a 3d structure on the
+properties of
+
+ align:start position:0%
+properties of
+ 
+
+ align:start position:0%
+properties of
+photonics so an intuitive way to
+
+ align:start position:0%
+photonics so an intuitive way to
+ 
+
+ align:start position:0%
+photonics so an intuitive way to
+introduce photonic crystal is to use the
+
+ align:start position:0%
+introduce photonic crystal is to use the
+ 
+
+ align:start position:0%
+introduce photonic crystal is to use the
+analogy with elect semiconductors in
+
+ align:start position:0%
+analogy with elect semiconductors in
+ 
+
+ align:start position:0%
+analogy with elect semiconductors in
+electronics because photonic crystals
+
+ align:start position:0%
+electronics because photonic crystals
+ 
+
+ align:start position:0%
+electronics because photonic crystals
+are two optics what um semiconductors
+
+ align:start position:0%
+are two optics what um semiconductors
+ 
+
+ align:start position:0%
+are two optics what um semiconductors
+are to electronics which means that
+
+ align:start position:0%
+are to electronics which means that
+ 
+
+ align:start position:0%
+are to electronics which means that
+in uh
+
+ align:start position:0%
+in uh
+ 
+
+ align:start position:0%
+in uh
+semiconductors depending on the electron
+
+ align:start position:0%
+semiconductors depending on the electron
+ 
+
+ align:start position:0%
+semiconductors depending on the electron
+energy you can or cannot propagate a
+
+ align:start position:0%
+energy you can or cannot propagate a
+ 
+
+ align:start position:0%
+energy you can or cannot propagate a
+current in it
+
+ align:start position:0%
+current in it
+ 
+
+ align:start position:0%
+current in it
+in photonic crystal depending on the the
+
+ align:start position:0%
+in photonic crystal depending on the the
+ 
+
+ align:start position:0%
+in photonic crystal depending on the the
+frequency of your wave you will or will
+
+ align:start position:0%
+frequency of your wave you will or will
+ 
+
+ align:start position:0%
+frequency of your wave you will or will
+not propagate
+
+ align:start position:0%
+not propagate
+ 
+
+ align:start position:0%
+not propagate
+waves in it and so to understand this
+
+ align:start position:0%
+waves in it and so to understand this
+ 
+
+ align:start position:0%
+waves in it and so to understand this
+interesting property
+
+ align:start position:0%
+interesting property
+ 
+
+ align:start position:0%
+interesting property
+uh you have to go back to maxwell
+
+ align:start position:0%
+uh you have to go back to maxwell
+ 
+
+ align:start position:0%
+uh you have to go back to maxwell
+equations i'd be quick on this slide
+
+ align:start position:0%
+equations i'd be quick on this slide
+ 
+
+ align:start position:0%
+equations i'd be quick on this slide
+don't worry
+
+ align:start position:0%
+don't worry
+ 
+
+ align:start position:0%
+don't worry
+uh but
+
+ align:start position:0%
+uh but
+ 
+
+ align:start position:0%
+uh but
+you know that
+
+ align:start position:0%
+you know that
+ 
+
+ align:start position:0%
+you know that
+from the the set of the four maxwell's
+
+ align:start position:0%
+from the the set of the four maxwell's
+ 
+
+ align:start position:0%
+from the the set of the four maxwell's
+equation you can write it as a
+
+ align:start position:0%
+equation you can write it as a
+ 
+
+ align:start position:0%
+equation you can write it as a
+eigenvalue problem if you assume that
+
+ align:start position:0%
+eigenvalue problem if you assume that
+ 
+
+ align:start position:0%
+eigenvalue problem if you assume that
+your waves are
+
+ align:start position:0%
+your waves are
+ 
+
+ align:start position:0%
+your waves are
+sinusoidal
+
+ align:start position:0%
+sinusoidal
+ 
+
+ align:start position:0%
+sinusoidal
+and now if you
+
+ align:start position:0%
+and now if you
+ 
+
+ align:start position:0%
+and now if you
+introduce periodicity in your crystal
+
+ align:start position:0%
+introduce periodicity in your crystal
+ 
+
+ align:start position:0%
+introduce periodicity in your crystal
+and the block theorem says that you can
+
+ align:start position:0%
+and the block theorem says that you can
+ 
+
+ align:start position:0%
+and the block theorem says that you can
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+the magnetic field
+
+ align:start position:0%
+the magnetic field
+ 
+
+ align:start position:0%
+the magnetic field
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+where uh the k vector is in the
+
+ align:start position:0%
+where uh the k vector is in the
+ 
+
+ align:start position:0%
+where uh the k vector is in the
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+times a periodic function where
+
+ align:start position:0%
+times a periodic function where
+ 
+
+ align:start position:0%
+times a periodic function where
+u is a
+
+ align:start position:0%
+u is a
+ 
+
+ align:start position:0%
+u is a
+a periodic function
+
+ align:start position:0%
+a periodic function
+ 
+
+ align:start position:0%
+a periodic function
+r is the periodicity of your crystal
+
+ align:start position:0%
+r is the periodicity of your crystal
+ 
+
+ align:start position:0%
+r is the periodicity of your crystal
+lattice
+
+ align:start position:0%
+lattice
+ 
+
+ align:start position:0%
+lattice
+and so the first eigenvalue problem
+
+ align:start position:0%
+and so the first eigenvalue problem
+ 
+
+ align:start position:0%
+and so the first eigenvalue problem
+because becomes this one which can be
+
+ align:start position:0%
+because becomes this one which can be
+ 
+
+ align:start position:0%
+because becomes this one which can be
+solved numerically
+
+ align:start position:0%
+solved numerically
+ 
+
+ align:start position:0%
+solved numerically
+which is what a corey uh
+
+ align:start position:0%
+which is what a corey uh
+ 
+
+ align:start position:0%
+which is what a corey uh
+has done in the simulations
+
+ align:start position:0%
+has done in the simulations
+ 
+
+ align:start position:0%
+has done in the simulations
+and you manage to extract these those
+
+ align:start position:0%
+and you manage to extract these those
+ 
+
+ align:start position:0%
+and you manage to extract these those
+eigenvalues
+
+ align:start position:0%
+eigenvalues
+ 
+
+ align:start position:0%
+eigenvalues
+which are the dispersion relation
+
+ align:start position:0%
+which are the dispersion relation
+ 
+
+ align:start position:0%
+which are the dispersion relation
+between the frequency and the k vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we take the example of a 1d
+
+ align:start position:0%
+so if we take the example of a 1d
+ 
+
+ align:start position:0%
+so if we take the example of a 1d
+photonic crystal like this
+
+ align:start position:0%
+photonic crystal like this
+ 
+
+ align:start position:0%
+photonic crystal like this
+with no periodicity which means that all
+
+ align:start position:0%
+with no periodicity which means that all
+ 
+
+ align:start position:0%
+with no periodicity which means that all
+the permittivity in the in the crystal
+
+ align:start position:0%
+the permittivity in the in the crystal
+ 
+
+ align:start position:0%
+the permittivity in the in the crystal
+are the same equals one for example we
+
+ align:start position:0%
+are the same equals one for example we
+ 
+
+ align:start position:0%
+are the same equals one for example we
+have this relation which is uh
+
+ align:start position:0%
+have this relation which is uh
+ 
+
+ align:start position:0%
+have this relation which is uh
+proportional the frequency is
+
+ align:start position:0%
+proportional the frequency is
+ 
+
+ align:start position:0%
+proportional the frequency is
+proportional to the 2k
+
+ align:start position:0%
+proportional to the 2k
+ 
+
+ align:start position:0%
+proportional to the 2k
+but now if you take different
+
+ align:start position:0%
+but now if you take different
+ 
+
+ align:start position:0%
+but now if you take different
+permittivity in the crystal you
+
+ align:start position:0%
+permittivity in the crystal you
+ 
+
+ align:start position:0%
+permittivity in the crystal you
+introduce those range of frequency in
+
+ align:start position:0%
+introduce those range of frequency in
+ 
+
+ align:start position:0%
+introduce those range of frequency in
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+cannot propagate and the width the size
+
+ align:start position:0%
+cannot propagate and the width the size
+ 
+
+ align:start position:0%
+cannot propagate and the width the size
+and the position of those gaps the band
+
+ align:start position:0%
+and the position of those gaps the band
+ 
+
+ align:start position:0%
+and the position of those gaps the band
+gaps
+
+ align:start position:0%
+gaps
+ 
+
+ align:start position:0%
+gaps
+are a function of the permeability or
+
+ align:start position:0%
+are a function of the permeability or
+ 
+
+ align:start position:0%
+are a function of the permeability or
+the geometry of your lattice in the
+
+ align:start position:0%
+the geometry of your lattice in the
+ 
+
+ align:start position:0%
+the geometry of your lattice in the
+crystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh note that we're only interested uh
+
+ align:start position:0%
+uh note that we're only interested uh
+ 
+
+ align:start position:0%
+uh note that we're only interested uh
+because of the shape of those uh
+
+ align:start position:0%
+because of the shape of those uh
+ 
+
+ align:start position:0%
+because of the shape of those uh
+magnetic field as exponential of ikr
+
+ align:start position:0%
+magnetic field as exponential of ikr
+ 
+
+ align:start position:0%
+magnetic field as exponential of ikr
+then we're only interested and because
+
+ align:start position:0%
+then we're only interested and because
+ 
+
+ align:start position:0%
+then we're only interested and because
+of the the the paradisity in the crystal
+
+ align:start position:0%
+of the the the paradisity in the crystal
+ 
+
+ align:start position:0%
+of the the the paradisity in the crystal
+we aren't interested in this small range
+
+ align:start position:0%
+we aren't interested in this small range
+ 
+
+ align:start position:0%
+we aren't interested in this small range
+of k vectors from
+
+ align:start position:0%
+of k vectors from
+ 
+
+ align:start position:0%
+of k vectors from
+minus k over pi to plus k over pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+to illustrate this interesting property
+
+ align:start position:0%
+to illustrate this interesting property
+ 
+
+ align:start position:0%
+to illustrate this interesting property
+we brought
+
+ align:start position:0%
+we brought
+ 
+
+ align:start position:0%
+we brought
+1d photonic crystal
+
+ align:start position:0%
+1d photonic crystal
+ 
+
+ align:start position:0%
+1d photonic crystal
+which can only pass blue light which
+
+ align:start position:0%
+which can only pass blue light which
+ 
+
+ align:start position:0%
+which can only pass blue light which
+means that it will the the vein gaps are
+
+ align:start position:0%
+means that it will the the vein gaps are
+ 
+
+ align:start position:0%
+means that it will the the vein gaps are
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+where you don't propagate blue
+
+ align:start position:0%
+where you don't propagate blue
+ 
+
+ align:start position:0%
+where you don't propagate blue
+so which you can see if you if you shine
+
+ align:start position:0%
+so which you can see if you if you shine
+ 
+
+ align:start position:0%
+so which you can see if you if you shine
+it's going to be easy
+
+ align:start position:0%
+it's going to be easy
+ 
+
+ align:start position:0%
+it's going to be easy
+if you shine blue light
+
+ align:start position:0%
+if you shine blue light
+ 
+
+ align:start position:0%
+if you shine blue light
+if you shine sorry if you eliminate it
+
+ align:start position:0%
+if you shine sorry if you eliminate it
+ 
+
+ align:start position:0%
+if you shine sorry if you eliminate it
+with a white
+
+ align:start position:0%
+with a white
+ 
+
+ align:start position:0%
+with a white
+white light you will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you will
+
+ align:start position:0%
+you will
+ 
+
+ align:start position:0%
+you will
+transmit only blue now if you
+
+ align:start position:0%
+transmit only blue now if you
+ 
+
+ align:start position:0%
+transmit only blue now if you
+shine if you eliminate with a red light
+
+ align:start position:0%
+shine if you eliminate with a red light
+ 
+
+ align:start position:0%
+shine if you eliminate with a red light
+then it will block almost everything
+
+ align:start position:0%
+then it will block almost everything
+ 
+
+ align:start position:0%
+then it will block almost everything
+as you can see on the second i don't
+
+ align:start position:0%
+as you can see on the second i don't
+ 
+
+ align:start position:0%
+as you can see on the second i don't
+know if you can see it but
+
+ align:start position:0%
+know if you can see it but
+ 
+
+ align:start position:0%
+know if you can see it but
+basically there's nothing to see
+
+ align:start position:0%
+basically there's nothing to see
+ 
+
+ align:start position:0%
+basically there's nothing to see
+the only problem with the 1d photonic
+
+ align:start position:0%
+the only problem with the 1d photonic
+ 
+
+ align:start position:0%
+the only problem with the 1d photonic
+crystal if you shine off axis then it
+
+ align:start position:0%
+crystal if you shine off axis then it
+ 
+
+ align:start position:0%
+crystal if you shine off axis then it
+loses its property
+
+ align:start position:0%
+loses its property
+ 
+
+ align:start position:0%
+loses its property
+and now you should be able to see this
+
+ align:start position:0%
+and now you should be able to see this
+ 
+
+ align:start position:0%
+and now you should be able to see this
+red spot over there
+
+ align:start position:0%
+red spot over there
+ 
+
+ align:start position:0%
+red spot over there
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+is the reason why people are trying to
+
+ align:start position:0%
+is the reason why people are trying to
+ 
+
+ align:start position:0%
+is the reason why people are trying to
+now create 2d or 3d photonic
+
+ align:start position:0%
+now create 2d or 3d photonic
+ 
+
+ align:start position:0%
+now create 2d or 3d photonic
+crystals to keep this
+
+ align:start position:0%
+crystals to keep this
+ 
+
+ align:start position:0%
+crystals to keep this
+property in all the directions and with
+
+ align:start position:0%
+property in all the directions and with
+ 
+
+ align:start position:0%
+property in all the directions and with
+all polarization
+
+ align:start position:0%
+all polarization
+ 
+
+ align:start position:0%
+all polarization
+the applications of photon photonic
+
+ align:start position:0%
+the applications of photon photonic
+ 
+
+ align:start position:0%
+the applications of photon photonic
+crystals are well as you saw
+
+ align:start position:0%
+crystals are well as you saw
+ 
+
+ align:start position:0%
+crystals are well as you saw
+to filter some of the frequencies but
+
+ align:start position:0%
+to filter some of the frequencies but
+ 
+
+ align:start position:0%
+to filter some of the frequencies but
+also to use it as a perfect mirror
+
+ align:start position:0%
+also to use it as a perfect mirror
+ 
+
+ align:start position:0%
+also to use it as a perfect mirror
+can also use it as wave guides
+
+ align:start position:0%
+can also use it as wave guides
+ 
+
+ align:start position:0%
+can also use it as wave guides
+or cavities or
+
+ align:start position:0%
+or cavities or
+ 
+
+ align:start position:0%
+or cavities or
+light shaping
+
+ align:start position:0%
+light shaping
+ 
+
+ align:start position:0%
+light shaping
+and now martin's going to talk about the
+
+ align:start position:0%
+and now martin's going to talk about the
+ 
+
+ align:start position:0%
+and now martin's going to talk about the
+fabrication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you sebastian so this really
+
+ align:start position:0%
+thank you sebastian so this really
+ 
+
+ align:start position:0%
+thank you sebastian so this really
+photonic crystal seems really
+
+ align:start position:0%
+photonic crystal seems really
+ 
+
+ align:start position:0%
+photonic crystal seems really
+interesting but the main problem is how
+
+ align:start position:0%
+interesting but the main problem is how
+ 
+
+ align:start position:0%
+interesting but the main problem is how
+can you fabricate them so we can there
+
+ align:start position:0%
+can you fabricate them so we can there
+ 
+
+ align:start position:0%
+can you fabricate them so we can there
+are lots of techniques
+
+ align:start position:0%
+are lots of techniques
+ 
+
+ align:start position:0%
+are lots of techniques
+lots of techniques out there but we can
+
+ align:start position:0%
+lots of techniques out there but we can
+ 
+
+ align:start position:0%
+lots of techniques out there but we can
+categorize this
+
+ align:start position:0%
+categorize this
+ 
+
+ align:start position:0%
+categorize this
+in three main categories the first one
+
+ align:start position:0%
+in three main categories the first one
+ 
+
+ align:start position:0%
+in three main categories the first one
+is a full 3d fabrication when you where
+
+ align:start position:0%
+is a full 3d fabrication when you where
+ 
+
+ align:start position:0%
+is a full 3d fabrication when you where
+you create the whole 3d uh structure all
+
+ align:start position:0%
+you create the whole 3d uh structure all
+ 
+
+ align:start position:0%
+you create the whole 3d uh structure all
+at once or you can do a point by point
+
+ align:start position:0%
+at once or you can do a point by point
+ 
+
+ align:start position:0%
+at once or you can do a point by point
+fabrication where you create every
+
+ align:start position:0%
+fabrication where you create every
+ 
+
+ align:start position:0%
+fabrication where you create every
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+aspect in the crystal
+
+ align:start position:0%
+aspect in the crystal
+ 
+
+ align:start position:0%
+aspect in the crystal
+by scanning the whole 3d
+
+ align:start position:0%
+by scanning the whole 3d
+ 
+
+ align:start position:0%
+by scanning the whole 3d
+structure or you can have a layer by
+
+ align:start position:0%
+structure or you can have a layer by
+ 
+
+ align:start position:0%
+structure or you can have a layer by
+layer approach
+
+ align:start position:0%
+layer approach
+ 
+
+ align:start position:0%
+layer approach
+to make a whole 3d structure
+
+ align:start position:0%
+to make a whole 3d structure
+ 
+
+ align:start position:0%
+to make a whole 3d structure
+so first example of full 3d fabrication
+
+ align:start position:0%
+so first example of full 3d fabrication
+ 
+
+ align:start position:0%
+so first example of full 3d fabrication
+is to use colloidal particles so you can
+
+ align:start position:0%
+is to use colloidal particles so you can
+ 
+
+ align:start position:0%
+is to use colloidal particles so you can
+assemble
+
+ align:start position:0%
+assemble
+ 
+
+ align:start position:0%
+assemble
+colloidal particles like different ways
+
+ align:start position:0%
+colloidal particles like different ways
+ 
+
+ align:start position:0%
+colloidal particles like different ways
+you can either use mac you can either
+
+ align:start position:0%
+you can either use mac you can either
+ 
+
+ align:start position:0%
+you can either use mac you can either
+micromanipulate your sphere to put
+
+ align:start position:0%
+micromanipulate your sphere to put
+ 
+
+ align:start position:0%
+micromanipulate your sphere to put
+whatever sphere you want where you want
+
+ align:start position:0%
+whatever sphere you want where you want
+ 
+
+ align:start position:0%
+whatever sphere you want where you want
+or you can use a self-assembly property
+
+ align:start position:0%
+or you can use a self-assembly property
+ 
+
+ align:start position:0%
+or you can use a self-assembly property
+of colloidal particles to make a whole
+
+ align:start position:0%
+of colloidal particles to make a whole
+ 
+
+ align:start position:0%
+of colloidal particles to make a whole
+stack of particles and then you can do
+
+ align:start position:0%
+stack of particles and then you can do
+ 
+
+ align:start position:0%
+stack of particles and then you can do
+different processes to make a whole
+
+ align:start position:0%
+different processes to make a whole
+ 
+
+ align:start position:0%
+different processes to make a whole
+3d structure
+
+ align:start position:0%
+3d structure
+ 
+
+ align:start position:0%
+3d structure
+that can be used as a photonic crystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a second full 3d fabrication process is
+
+ align:start position:0%
+a second full 3d fabrication process is
+ 
+
+ align:start position:0%
+a second full 3d fabrication process is
+to use what's called holographic
+
+ align:start position:0%
+to use what's called holographic
+ 
+
+ align:start position:0%
+to use what's called holographic
+lithography so in this case you have
+
+ align:start position:0%
+lithography so in this case you have
+ 
+
+ align:start position:0%
+lithography so in this case you have
+four laser beams interfering
+
+ align:start position:0%
+four laser beams interfering
+ 
+
+ align:start position:0%
+four laser beams interfering
+and they create a whole 3d interference
+
+ align:start position:0%
+and they create a whole 3d interference
+ 
+
+ align:start position:0%
+and they create a whole 3d interference
+pattern that can if you stand in this
+
+ align:start position:0%
+pattern that can if you stand in this
+ 
+
+ align:start position:0%
+pattern that can if you stand in this
+into a photoresist you would have
+
+ align:start position:0%
+into a photoresist you would have
+ 
+
+ align:start position:0%
+into a photoresist you would have
+some region which are
+
+ align:start position:0%
+some region which are
+ 
+
+ align:start position:0%
+some region which are
+exposed and some not and if you develop
+
+ align:start position:0%
+exposed and some not and if you develop
+ 
+
+ align:start position:0%
+exposed and some not and if you develop
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+photoresist you would end up having a
+
+ align:start position:0%
+photoresist you would end up having a
+ 
+
+ align:start position:0%
+photoresist you would end up having a
+whole 3d structure that have been made
+
+ align:start position:0%
+whole 3d structure that have been made
+ 
+
+ align:start position:0%
+whole 3d structure that have been made
+like all
+
+ align:start position:0%
+like all
+ 
+
+ align:start position:0%
+like all
+uh like in three dimension all at once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you move on now to a point by point
+
+ align:start position:0%
+if you move on now to a point by point
+ 
+
+ align:start position:0%
+if you move on now to a point by point
+fabrication process we can use
+
+ align:start position:0%
+fabrication process we can use
+ 
+
+ align:start position:0%
+fabrication process we can use
+multi-photon polymerization
+
+ align:start position:0%
+multi-photon polymerization
+ 
+
+ align:start position:0%
+multi-photon polymerization
+in the sense where here you can expose a
+
+ align:start position:0%
+in the sense where here you can expose a
+ 
+
+ align:start position:0%
+in the sense where here you can expose a
+single dot
+
+ align:start position:0%
+single dot
+ 
+
+ align:start position:0%
+single dot
+exactly where you want so in this case
+
+ align:start position:0%
+exactly where you want so in this case
+ 
+
+ align:start position:0%
+exactly where you want so in this case
+if for example if you shine light with a
+
+ align:start position:0%
+if for example if you shine light with a
+ 
+
+ align:start position:0%
+if for example if you shine light with a
+very tight focus point here you can have
+
+ align:start position:0%
+very tight focus point here you can have
+ 
+
+ align:start position:0%
+very tight focus point here you can have
+a multi multiphoton polymerization in
+
+ align:start position:0%
+a multi multiphoton polymerization in
+ 
+
+ align:start position:0%
+a multi multiphoton polymerization in
+your photoresist that a single photon
+
+ align:start position:0%
+your photoresist that a single photon
+ 
+
+ align:start position:0%
+your photoresist that a single photon
+cannot achieve and so then if you scan
+
+ align:start position:0%
+cannot achieve and so then if you scan
+ 
+
+ align:start position:0%
+cannot achieve and so then if you scan
+your whole three-dimensional structure
+
+ align:start position:0%
+your whole three-dimensional structure
+ 
+
+ align:start position:0%
+your whole three-dimensional structure
+you can make whatever shape you want and
+
+ align:start position:0%
+you can make whatever shape you want and
+ 
+
+ align:start position:0%
+you can make whatever shape you want and
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+this can be combined with holographic
+
+ align:start position:0%
+this can be combined with holographic
+ 
+
+ align:start position:0%
+this can be combined with holographic
+lithography for example
+
+ align:start position:0%
+lithography for example
+ 
+
+ align:start position:0%
+lithography for example
+where in the holographic lithography you
+
+ align:start position:0%
+where in the holographic lithography you
+ 
+
+ align:start position:0%
+where in the holographic lithography you
+make the whole 3d pattern and then with
+
+ align:start position:0%
+make the whole 3d pattern and then with
+ 
+
+ align:start position:0%
+make the whole 3d pattern and then with
+multiphoton primerization you can put
+
+ align:start position:0%
+multiphoton primerization you can put
+ 
+
+ align:start position:0%
+multiphoton primerization you can put
+some defects where you want or correct
+
+ align:start position:0%
+some defects where you want or correct
+ 
+
+ align:start position:0%
+some defects where you want or correct
+for errors that that could have been
+
+ align:start position:0%
+for errors that that could have been
+ 
+
+ align:start position:0%
+for errors that that could have been
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+but another promising approach is to use
+
+ align:start position:0%
+but another promising approach is to use
+ 
+
+ align:start position:0%
+but another promising approach is to use
+a layer by layer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technique so this is an example uh this
+
+ align:start position:0%
+technique so this is an example uh this
+ 
+
+ align:start position:0%
+technique so this is an example uh this
+is called the wood pie structure as you
+
+ align:start position:0%
+is called the wood pie structure as you
+ 
+
+ align:start position:0%
+is called the wood pie structure as you
+can see so this is done
+
+ align:start position:0%
+can see so this is done
+ 
+
+ align:start position:0%
+can see so this is done
+so layer by layer where you uh pattern a
+
+ align:start position:0%
+so layer by layer where you uh pattern a
+ 
+
+ align:start position:0%
+so layer by layer where you uh pattern a
+whole two-dimensional pattern on your
+
+ align:start position:0%
+whole two-dimensional pattern on your
+ 
+
+ align:start position:0%
+whole two-dimensional pattern on your
+substrate and then
+
+ align:start position:0%
+substrate and then
+ 
+
+ align:start position:0%
+substrate and then
+you you move on building the whole stack
+
+ align:start position:0%
+you you move on building the whole stack
+ 
+
+ align:start position:0%
+you you move on building the whole stack
+and this here is a noticeable you we
+
+ align:start position:0%
+and this here is a noticeable you we
+ 
+
+ align:start position:0%
+and this here is a noticeable you we
+have a fcc
+
+ align:start position:0%
+have a fcc
+ 
+
+ align:start position:0%
+have a fcc
+crystal lattice when every other
+
+ align:start position:0%
+crystal lattice when every other
+ 
+
+ align:start position:0%
+crystal lattice when every other
+layer is shifted by half a period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another interesting ladder is we can
+
+ align:start position:0%
+another interesting ladder is we can
+ 
+
+ align:start position:0%
+another interesting ladder is we can
+form with this layer of a layer approach
+
+ align:start position:0%
+form with this layer of a layer approach
+ 
+
+ align:start position:0%
+form with this layer of a layer approach
+is a so-called holes rod structure we
+
+ align:start position:0%
+is a so-called holes rod structure we
+ 
+
+ align:start position:0%
+is a so-called holes rod structure we
+can see here on the right
+
+ align:start position:0%
+can see here on the right
+ 
+
+ align:start position:0%
+can see here on the right
+and how you can
+
+ align:start position:0%
+and how you can
+ 
+
+ align:start position:0%
+and how you can
+make these is to use the same process of
+
+ align:start position:0%
+make these is to use the same process of
+ 
+
+ align:start position:0%
+make these is to use the same process of
+patterning each layer at a time and
+
+ align:start position:0%
+patterning each layer at a time and
+ 
+
+ align:start position:0%
+patterning each layer at a time and
+repeating the process to and you
+
+ align:start position:0%
+repeating the process to and you
+ 
+
+ align:start position:0%
+repeating the process to and you
+actually have this multiple layer
+
+ align:start position:0%
+actually have this multiple layer
+ 
+
+ align:start position:0%
+actually have this multiple layer
+on top of each other
+
+ align:start position:0%
+on top of each other
+ 
+
+ align:start position:0%
+on top of each other
+and with this technique you can also
+
+ align:start position:0%
+and with this technique you can also
+ 
+
+ align:start position:0%
+and with this technique you can also
+make defects uh in whatever layer you
+
+ align:start position:0%
+make defects uh in whatever layer you
+ 
+
+ align:start position:0%
+make defects uh in whatever layer you
+want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can also use a membrane stacking
+
+ align:start position:0%
+you can also use a membrane stacking
+ 
+
+ align:start position:0%
+you can also use a membrane stacking
+technique so in this case you pattern uh
+
+ align:start position:0%
+technique so in this case you pattern uh
+ 
+
+ align:start position:0%
+technique so in this case you pattern uh
+all your 2d uh
+
+ align:start position:0%
+all your 2d uh
+ 
+
+ align:start position:0%
+all your 2d uh
+structure your 2d membranes uh
+
+ align:start position:0%
+structure your 2d membranes uh
+ 
+
+ align:start position:0%
+structure your 2d membranes uh
+first and you can make whatever shape
+
+ align:start position:0%
+first and you can make whatever shape
+ 
+
+ align:start position:0%
+first and you can make whatever shape
+you want with defects or not and then
+
+ align:start position:0%
+you want with defects or not and then
+ 
+
+ align:start position:0%
+you want with defects or not and then
+you can stack them together
+
+ align:start position:0%
+you can stack them together
+ 
+
+ align:start position:0%
+you can stack them together
+using some alignment techniques
+
+ align:start position:0%
+using some alignment techniques
+ 
+
+ align:start position:0%
+using some alignment techniques
+that here is used uh
+
+ align:start position:0%
+that here is used uh
+ 
+
+ align:start position:0%
+that here is used uh
+by microspheres
+
+ align:start position:0%
+by microspheres
+ 
+
+ align:start position:0%
+by microspheres
+so basically you
+
+ align:start position:0%
+so basically you
+ 
+
+ align:start position:0%
+so basically you
+you come with all these 2d
+
+ align:start position:0%
+you come with all these 2d
+ 
+
+ align:start position:0%
+you come with all these 2d
+two-dimensional structure and you stack
+
+ align:start position:0%
+two-dimensional structure and you stack
+ 
+
+ align:start position:0%
+two-dimensional structure and you stack
+them together using this microsphere for
+
+ align:start position:0%
+them together using this microsphere for
+ 
+
+ align:start position:0%
+them together using this microsphere for
+alignment another promising technique to
+
+ align:start position:0%
+alignment another promising technique to
+ 
+
+ align:start position:0%
+alignment another promising technique to
+align and stack this structure is to use
+
+ align:start position:0%
+align and stack this structure is to use
+ 
+
+ align:start position:0%
+align and stack this structure is to use
+nanomagnets on these membranes and this
+
+ align:start position:0%
+nanomagnets on these membranes and this
+ 
+
+ align:start position:0%
+nanomagnets on these membranes and this
+memory can help you first to align
+
+ align:start position:0%
+memory can help you first to align
+ 
+
+ align:start position:0%
+memory can help you first to align
+each layer uh on the on the other and
+
+ align:start position:0%
+each layer uh on the on the other and
+ 
+
+ align:start position:0%
+each layer uh on the on the other and
+also because the magnetic force can be
+
+ align:start position:0%
+also because the magnetic force can be
+ 
+
+ align:start position:0%
+also because the magnetic force can be
+used to break uh each membrane from the
+
+ align:start position:0%
+used to break uh each membrane from the
+ 
+
+ align:start position:0%
+used to break uh each membrane from the
+from the mainframe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you want to build this one of
+
+ align:start position:0%
+and if you want to build this one of
+ 
+
+ align:start position:0%
+and if you want to build this one of
+these layers we can use for
+
+ align:start position:0%
+these layers we can use for
+ 
+
+ align:start position:0%
+these layers we can use for
+this stacking uh a really promising
+
+ align:start position:0%
+this stacking uh a really promising
+ 
+
+ align:start position:0%
+this stacking uh a really promising
+technique is to use coherent diffraction
+
+ align:start position:0%
+technique is to use coherent diffraction
+ 
+
+ align:start position:0%
+technique is to use coherent diffraction
+lithography so here we
+
+ align:start position:0%
+lithography so here we
+ 
+
+ align:start position:0%
+lithography so here we
+we shine light through a mask which is a
+
+ align:start position:0%
+we shine light through a mask which is a
+ 
+
+ align:start position:0%
+we shine light through a mask which is a
+grating for example and
+
+ align:start position:0%
+grating for example and
+ 
+
+ align:start position:0%
+grating for example and
+and you have your uh you have your
+
+ align:start position:0%
+and you have your uh you have your
+ 
+
+ align:start position:0%
+and you have your uh you have your
+substrate below at a specific uh
+
+ align:start position:0%
+substrate below at a specific uh
+ 
+
+ align:start position:0%
+substrate below at a specific uh
+position a specific height below which
+
+ align:start position:0%
+position a specific height below which
+ 
+
+ align:start position:0%
+position a specific height below which
+corresponds to one of the towable plane
+
+ align:start position:0%
+corresponds to one of the towable plane
+ 
+
+ align:start position:0%
+corresponds to one of the towable plane
+for example so here you can see the
+
+ align:start position:0%
+for example so here you can see the
+ 
+
+ align:start position:0%
+for example so here you can see the
+field below the mask or you can see
+
+ align:start position:0%
+field below the mask or you can see
+ 
+
+ align:start position:0%
+field below the mask or you can see
+different double plane and here is an
+
+ align:start position:0%
+different double plane and here is an
+ 
+
+ align:start position:0%
+different double plane and here is an
+example of
+
+ align:start position:0%
+example of
+ 
+
+ align:start position:0%
+example of
+so self-imaging for grading at the first
+
+ align:start position:0%
+so self-imaging for grading at the first
+ 
+
+ align:start position:0%
+so self-imaging for grading at the first
+elbow plane
+
+ align:start position:0%
+elbow plane
+ 
+
+ align:start position:0%
+elbow plane
+so but one of the main problem is this
+
+ align:start position:0%
+so but one of the main problem is this
+ 
+
+ align:start position:0%
+so but one of the main problem is this
+2d
+
+ align:start position:0%
+2d
+ 
+
+ align:start position:0%
+2d
+layer by layer fabrication is how
+
+ align:start position:0%
+layer by layer fabrication is how
+ 
+
+ align:start position:0%
+layer by layer fabrication is how
+accurate do you need an alignment to be
+
+ align:start position:0%
+accurate do you need an alignment to be
+ 
+
+ align:start position:0%
+accurate do you need an alignment to be
+between your different 2d uh
+
+ align:start position:0%
+between your different 2d uh
+ 
+
+ align:start position:0%
+between your different 2d uh
+2d layers so that's really a big big
+
+ align:start position:0%
+2d layers so that's really a big big
+ 
+
+ align:start position:0%
+2d layers so that's really a big big
+problem in the fabrication of this 3d
+
+ align:start position:0%
+problem in the fabrication of this 3d
+ 
+
+ align:start position:0%
+problem in the fabrication of this 3d
+photonic crystal uses this layer by
+
+ align:start position:0%
+photonic crystal uses this layer by
+ 
+
+ align:start position:0%
+photonic crystal uses this layer by
+layer approach and that's why we run
+
+ align:start position:0%
+layer approach and that's why we run
+ 
+
+ align:start position:0%
+layer approach and that's why we run
+some simulation to see how accurate we
+
+ align:start position:0%
+some simulation to see how accurate we
+ 
+
+ align:start position:0%
+some simulation to see how accurate we
+should we need to be
+
+ align:start position:0%
+should we need to be
+ 
+
+ align:start position:0%
+should we need to be
+in a in this layer-by-layer approach i
+
+ align:start position:0%
+in a in this layer-by-layer approach i
+ 
+
+ align:start position:0%
+in a in this layer-by-layer approach i
+got it
+
+ align:start position:0%
+got it
+ 
+
+ align:start position:0%
+got it
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right thank you martin so
+
+ align:start position:0%
+all right thank you martin so
+ 
+
+ align:start position:0%
+all right thank you martin so
+one of the structures that martin
+
+ align:start position:0%
+one of the structures that martin
+ 
+
+ align:start position:0%
+one of the structures that martin
+mentioned was the diamond lattice which
+
+ align:start position:0%
+mentioned was the diamond lattice which
+ 
+
+ align:start position:0%
+mentioned was the diamond lattice which
+is just the same as the face center
+
+ align:start position:0%
+is just the same as the face center
+ 
+
+ align:start position:0%
+is just the same as the face center
+cubic but there's two atoms in the
+
+ align:start position:0%
+cubic but there's two atoms in the
+ 
+
+ align:start position:0%
+cubic but there's two atoms in the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+so what i mean by that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this atom and this atom this is
+
+ align:start position:0%
+is this atom and this atom this is
+ 
+
+ align:start position:0%
+is this atom and this atom this is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+eight unit cells in this picture now
+
+ align:start position:0%
+eight unit cells in this picture now
+ 
+
+ align:start position:0%
+eight unit cells in this picture now
+this image and this image were taken
+
+ align:start position:0%
+this image and this image were taken
+ 
+
+ align:start position:0%
+this image and this image were taken
+from a program mit photonic bands which
+
+ align:start position:0%
+from a program mit photonic bands which
+ 
+
+ align:start position:0%
+from a program mit photonic bands which
+allows you to calculate the band gap in
+
+ align:start position:0%
+allows you to calculate the band gap in
+ 
+
+ align:start position:0%
+allows you to calculate the band gap in
+three-dimensional structures
+
+ align:start position:0%
+three-dimensional structures
+ 
+
+ align:start position:0%
+three-dimensional structures
+for this particular structure
+
+ align:start position:0%
+for this particular structure
+ 
+
+ align:start position:0%
+for this particular structure
+the band gap is 10.62 percent and this
+
+ align:start position:0%
+the band gap is 10.62 percent and this
+ 
+
+ align:start position:0%
+the band gap is 10.62 percent and this
+band gap is actually the range of
+
+ align:start position:0%
+band gap is actually the range of
+ 
+
+ align:start position:0%
+band gap is actually the range of
+frequencies here divided by the mid
+
+ align:start position:0%
+frequencies here divided by the mid
+ 
+
+ align:start position:0%
+frequencies here divided by the mid
+frequency so that's what gives us these
+
+ align:start position:0%
+frequency so that's what gives us these
+ 
+
+ align:start position:0%
+frequency so that's what gives us these
+percentages
+
+ align:start position:0%
+percentages
+ 
+
+ align:start position:0%
+percentages
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+one of the things that uh
+
+ align:start position:0%
+one of the things that uh
+ 
+
+ align:start position:0%
+one of the things that uh
+we notice is that it's centered about
+
+ align:start position:0%
+we notice is that it's centered about
+ 
+
+ align:start position:0%
+we notice is that it's centered about
+0.42
+
+ align:start position:0%
+0.42
+ 
+
+ align:start position:0%
+0.42
+and obviously the gap is defined in this
+
+ align:start position:0%
+and obviously the gap is defined in this
+ 
+
+ align:start position:0%
+and obviously the gap is defined in this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+what we are concerned with is
+
+ align:start position:0%
+what we are concerned with is
+ 
+
+ align:start position:0%
+what we are concerned with is
+what happens if we change this parameter
+
+ align:start position:0%
+what happens if we change this parameter
+ 
+
+ align:start position:0%
+what happens if we change this parameter
+delta so that corresponds to
+
+ align:start position:0%
+delta so that corresponds to
+ 
+
+ align:start position:0%
+delta so that corresponds to
+shifting this sphere this sphere this
+
+ align:start position:0%
+shifting this sphere this sphere this
+ 
+
+ align:start position:0%
+shifting this sphere this sphere this
+sphere and this fear by
+
+ align:start position:0%
+sphere and this fear by
+ 
+
+ align:start position:0%
+sphere and this fear by
+an amount delta in a linear direction
+
+ align:start position:0%
+an amount delta in a linear direction
+ 
+
+ align:start position:0%
+an amount delta in a linear direction
+so what we did was we looked at you know
+
+ align:start position:0%
+so what we did was we looked at you know
+ 
+
+ align:start position:0%
+so what we did was we looked at you know
+say it's 10 20 30 40 what happens to the
+
+ align:start position:0%
+say it's 10 20 30 40 what happens to the
+ 
+
+ align:start position:0%
+say it's 10 20 30 40 what happens to the
+overall band gap
+
+ align:start position:0%
+overall band gap
+ 
+
+ align:start position:0%
+overall band gap
+and so these are the simulations that i
+
+ align:start position:0%
+and so these are the simulations that i
+ 
+
+ align:start position:0%
+and so these are the simulations that i
+ran
+
+ align:start position:0%
+ran
+ 
+
+ align:start position:0%
+ran
+and you can see that at no displacement
+
+ align:start position:0%
+and you can see that at no displacement
+ 
+
+ align:start position:0%
+and you can see that at no displacement
+you've got that nice band gap
+
+ align:start position:0%
+you've got that nice band gap
+ 
+
+ align:start position:0%
+you've got that nice band gap
+and then as you shift it by ten percent
+
+ align:start position:0%
+and then as you shift it by ten percent
+ 
+
+ align:start position:0%
+and then as you shift it by ten percent
+the gap decreases substantially and as
+
+ align:start position:0%
+the gap decreases substantially and as
+ 
+
+ align:start position:0%
+the gap decreases substantially and as
+you go beyond that the gap pretty much
+
+ align:start position:0%
+you go beyond that the gap pretty much
+ 
+
+ align:start position:0%
+you go beyond that the gap pretty much
+goes away
+
+ align:start position:0%
+goes away
+ 
+
+ align:start position:0%
+goes away
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+one of the things that's curious is
+
+ align:start position:0%
+one of the things that's curious is
+ 
+
+ align:start position:0%
+one of the things that's curious is
+what's happening in this you know zero
+
+ align:start position:0%
+what's happening in this you know zero
+ 
+
+ align:start position:0%
+what's happening in this you know zero
+to say 15 percent regime so we ran a
+
+ align:start position:0%
+to say 15 percent regime so we ran a
+ 
+
+ align:start position:0%
+to say 15 percent regime so we ran a
+finer simulation to uh give us that and
+
+ align:start position:0%
+finer simulation to uh give us that and
+ 
+
+ align:start position:0%
+finer simulation to uh give us that and
+plotted the
+
+ align:start position:0%
+plotted the
+ 
+
+ align:start position:0%
+plotted the
+gap
+
+ align:start position:0%
+gap
+ 
+
+ align:start position:0%
+gap
+normalized by that maximum gap that you
+
+ align:start position:0%
+normalized by that maximum gap that you
+ 
+
+ align:start position:0%
+normalized by that maximum gap that you
+could get for those you know percent
+
+ align:start position:0%
+could get for those you know percent
+ 
+
+ align:start position:0%
+could get for those you know percent
+displacements and you can see that
+
+ align:start position:0%
+displacements and you can see that
+ 
+
+ align:start position:0%
+displacements and you can see that
+at around five percent displacement the
+
+ align:start position:0%
+at around five percent displacement the
+ 
+
+ align:start position:0%
+at around five percent displacement the
+gaps about 67 percent of what it was
+
+ align:start position:0%
+gaps about 67 percent of what it was
+ 
+
+ align:start position:0%
+gaps about 67 percent of what it was
+originally so a small displacement can
+
+ align:start position:0%
+originally so a small displacement can
+ 
+
+ align:start position:0%
+originally so a small displacement can
+substantially affect your band gap
+
+ align:start position:0%
+substantially affect your band gap
+ 
+
+ align:start position:0%
+substantially affect your band gap
+and to the extent that you may want that
+
+ align:start position:0%
+and to the extent that you may want that
+ 
+
+ align:start position:0%
+and to the extent that you may want that
+it's not necessarily a bad thing
+
+ align:start position:0%
+it's not necessarily a bad thing
+ 
+
+ align:start position:0%
+it's not necessarily a bad thing
+but you
+
+ align:start position:0%
+but you
+ 
+
+ align:start position:0%
+but you
+need to be aware of it when you're
+
+ align:start position:0%
+need to be aware of it when you're
+ 
+
+ align:start position:0%
+need to be aware of it when you're
+engineering these things
+
+ align:start position:0%
+engineering these things
+ 
+
+ align:start position:0%
+engineering these things
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+these are just some numbers that you
+
+ align:start position:0%
+these are just some numbers that you
+ 
+
+ align:start position:0%
+these are just some numbers that you
+know kind of give you a better handle on
+
+ align:start position:0%
+know kind of give you a better handle on
+ 
+
+ align:start position:0%
+know kind of give you a better handle on
+what that graph means but you know i
+
+ align:start position:0%
+what that graph means but you know i
+ 
+
+ align:start position:0%
+what that graph means but you know i
+like this one the best if you want to
+
+ align:start position:0%
+like this one the best if you want to
+ 
+
+ align:start position:0%
+like this one the best if you want to
+keep your gap above 10 or 95 percent
+
+ align:start position:0%
+keep your gap above 10 or 95 percent
+ 
+
+ align:start position:0%
+keep your gap above 10 or 95 percent
+then that's really a displacement of
+
+ align:start position:0%
+then that's really a displacement of
+ 
+
+ align:start position:0%
+then that's really a displacement of
+around one to two percent which is
+
+ align:start position:0%
+around one to two percent which is
+ 
+
+ align:start position:0%
+around one to two percent which is
+pretty small
+
+ align:start position:0%
+pretty small
+ 
+
+ align:start position:0%
+pretty small
+so a real example of this you know in
+
+ align:start position:0%
+so a real example of this you know in
+ 
+
+ align:start position:0%
+so a real example of this you know in
+the telecom
+
+ align:start position:0%
+the telecom
+ 
+
+ align:start position:0%
+the telecom
+wavelengths and frequencies
+
+ align:start position:0%
+wavelengths and frequencies
+ 
+
+ align:start position:0%
+wavelengths and frequencies
+is you know frequency is 1.9 times 10 to
+
+ align:start position:0%
+is you know frequency is 1.9 times 10 to
+ 
+
+ align:start position:0%
+is you know frequency is 1.9 times 10 to
+the 14 hertz
+
+ align:start position:0%
+the 14 hertz
+ 
+
+ align:start position:0%
+the 14 hertz
+and if you look at the displacement in
+
+ align:start position:0%
+and if you look at the displacement in
+ 
+
+ align:start position:0%
+and if you look at the displacement in
+nanometers now so we've multiplied it by
+
+ align:start position:0%
+nanometers now so we've multiplied it by
+ 
+
+ align:start position:0%
+nanometers now so we've multiplied it by
+our lattice spacing in
+
+ align:start position:0%
+our lattice spacing in
+ 
+
+ align:start position:0%
+our lattice spacing in
+sebastian slides this was the r
+
+ align:start position:0%
+sebastian slides this was the r
+ 
+
+ align:start position:0%
+sebastian slides this was the r
+but in this case it's 663 nanometers you
+
+ align:start position:0%
+but in this case it's 663 nanometers you
+ 
+
+ align:start position:0%
+but in this case it's 663 nanometers you
+multiply the percent by that number you
+
+ align:start position:0%
+multiply the percent by that number you
+ 
+
+ align:start position:0%
+multiply the percent by that number you
+find that you know the bandwidth
+
+ align:start position:0%
+find that you know the bandwidth
+ 
+
+ align:start position:0%
+find that you know the bandwidth
+decreases rapidly as you go out to like
+
+ align:start position:0%
+decreases rapidly as you go out to like
+ 
+
+ align:start position:0%
+decreases rapidly as you go out to like
+you know 40 or 60 nanometers the
+
+ align:start position:0%
+you know 40 or 60 nanometers the
+ 
+
+ align:start position:0%
+you know 40 or 60 nanometers the
+bandwidth is dropped almost 50 percent
+
+ align:start position:0%
+bandwidth is dropped almost 50 percent
+ 
+
+ align:start position:0%
+bandwidth is dropped almost 50 percent
+so in this case
+
+ align:start position:0%
+so in this case
+ 
+
+ align:start position:0%
+so in this case
+we might want to narrow the band gap if
+
+ align:start position:0%
+we might want to narrow the band gap if
+ 
+
+ align:start position:0%
+we might want to narrow the band gap if
+we want to have like a very very uh
+
+ align:start position:0%
+we want to have like a very very uh
+ 
+
+ align:start position:0%
+we want to have like a very very uh
+narrow band filter but we might want to
+
+ align:start position:0%
+narrow band filter but we might want to
+ 
+
+ align:start position:0%
+narrow band filter but we might want to
+have lots of frequencies being reflected
+
+ align:start position:0%
+have lots of frequencies being reflected
+ 
+
+ align:start position:0%
+have lots of frequencies being reflected
+from this particular crystal at which
+
+ align:start position:0%
+from this particular crystal at which
+ 
+
+ align:start position:0%
+from this particular crystal at which
+point we'd want to be operating over
+
+ align:start position:0%
+point we'd want to be operating over
+ 
+
+ align:start position:0%
+point we'd want to be operating over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so i hope that this gives you a sense
+
+ align:start position:0%
+so i hope that this gives you a sense
+ 
+
+ align:start position:0%
+so i hope that this gives you a sense
+for how important misalignment is and
+
+ align:start position:0%
+for how important misalignment is and
+ 
+
+ align:start position:0%
+for how important misalignment is and
+how you can use it to engineer your band
+
+ align:start position:0%
+how you can use it to engineer your band
+ 
+
+ align:start position:0%
+how you can use it to engineer your band
+gap appropriately
+
+ align:start position:0%
+gap appropriately
+ 
+
+ align:start position:0%
+gap appropriately
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the things that was mentioned was
+
+ align:start position:0%
+one of the things that was mentioned was
+ 
+
+ align:start position:0%
+one of the things that was mentioned was
+that certain fabrication techniques will
+
+ align:start position:0%
+that certain fabrication techniques will
+ 
+
+ align:start position:0%
+that certain fabrication techniques will
+allow you to put defects in why would
+
+ align:start position:0%
+allow you to put defects in why would
+ 
+
+ align:start position:0%
+allow you to put defects in why would
+you want is it the same principle that
+
+ align:start position:0%
+you want is it the same principle that
+ 
+
+ align:start position:0%
+you want is it the same principle that
+you want
+
+ align:start position:0%
+you want
+ 
+
+ align:start position:0%
+you want
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+um if you add defects into the photonic
+
+ align:start position:0%
+um if you add defects into the photonic
+ 
+
+ align:start position:0%
+um if you add defects into the photonic
+crystal then essentially you make a pass
+
+ align:start position:0%
+crystal then essentially you make a pass
+ 
+
+ align:start position:0%
+crystal then essentially you make a pass
+band in the band gap and light can
+
+ align:start position:0%
+band in the band gap and light can
+ 
+
+ align:start position:0%
+band in the band gap and light can
+propagate if it's like a line defect you
+
+ align:start position:0%
+propagate if it's like a line defect you
+ 
+
+ align:start position:0%
+propagate if it's like a line defect you
+make a waveguide
+
+ align:start position:0%
+make a waveguide
+ 
+
+ align:start position:0%
+make a waveguide
+if it's like a point defect then light
+
+ align:start position:0%
+if it's like a point defect then light
+ 
+
+ align:start position:0%
+if it's like a point defect then light
+will resonate inside that defect and you
+
+ align:start position:0%
+will resonate inside that defect and you
+ 
+
+ align:start position:0%
+will resonate inside that defect and you
+know there's obviously other structures
+
+ align:start position:0%
+know there's obviously other structures
+ 
+
+ align:start position:0%
+know there's obviously other structures
+you could do but those are two of the
+
+ align:start position:0%
+you could do but those are two of the
+ 
+
+ align:start position:0%
+you could do but those are two of the
+simpler ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this for a given thickness of
+
+ align:start position:0%
+is this for a given thickness of
+ 
+
+ align:start position:0%
+is this for a given thickness of
+photonic crystal or is it like an
+
+ align:start position:0%
+photonic crystal or is it like an
+ 
+
+ align:start position:0%
+photonic crystal or is it like an
+infinite photonic crystal this is
+
+ align:start position:0%
+infinite photonic crystal this is
+ 
+
+ align:start position:0%
+infinite photonic crystal this is
+actually one of my big caveats about the
+
+ align:start position:0%
+actually one of my big caveats about the
+ 
+
+ align:start position:0%
+actually one of my big caveats about the
+simulation so
+
+ align:start position:0%
+simulation so
+ 
+
+ align:start position:0%
+simulation so
+this software assumes that it's
+
+ align:start position:0%
+this software assumes that it's
+ 
+
+ align:start position:0%
+this software assumes that it's
+infinitely periodic and so
+
+ align:start position:0%
+infinitely periodic and so
+ 
+
+ align:start position:0%
+infinitely periodic and so
+what i've done here
+
+ align:start position:0%
+what i've done here
+ 
+
+ align:start position:0%
+what i've done here
+is actually shifted every other layer
+
+ align:start position:0%
+is actually shifted every other layer
+ 
+
+ align:start position:0%
+is actually shifted every other layer
+not just a single layer and that's an
+
+ align:start position:0%
+not just a single layer and that's an
+ 
+
+ align:start position:0%
+not just a single layer and that's an
+artifact of the simulation software if i
+
+ align:start position:0%
+artifact of the simulation software if i
+ 
+
+ align:start position:0%
+artifact of the simulation software if i
+wanted to try and model just one layer
+
+ align:start position:0%
+wanted to try and model just one layer
+ 
+
+ align:start position:0%
+wanted to try and model just one layer
+it becomes much much more complicated
+
+ align:start position:0%
+it becomes much much more complicated
+ 
+
+ align:start position:0%
+it becomes much much more complicated
+but yeah it is infinite in extent and
+
+ align:start position:0%
+but yeah it is infinite in extent and
+ 
+
+ align:start position:0%
+but yeah it is infinite in extent and
+one of the things that the holographic
+
+ align:start position:0%
+one of the things that the holographic
+ 
+
+ align:start position:0%
+one of the things that the holographic
+lithography is limited by is the actual
+
+ align:start position:0%
+lithography is limited by is the actual
+ 
+
+ align:start position:0%
+lithography is limited by is the actual
+thickness of the photoresist that they
+
+ align:start position:0%
+thickness of the photoresist that they
+ 
+
+ align:start position:0%
+thickness of the photoresist that they
+can expose because after a little while
+
+ align:start position:0%
+can expose because after a little while
+ 
+
+ align:start position:0%
+can expose because after a little while
+the light stops interfering in the right
+
+ align:start position:0%
+the light stops interfering in the right
+ 
+
+ align:start position:0%
+the light stops interfering in the right
+way and you don't get that interference
+
+ align:start position:0%
+way and you don't get that interference
+ 
+
+ align:start position:0%
+way and you don't get that interference
+pattern that you want anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in real life how could such a defect
+
+ align:start position:0%
+in real life how could such a defect
+ 
+
+ align:start position:0%
+in real life how could such a defect
+come about
+
+ align:start position:0%
+come about
+ 
+
+ align:start position:0%
+come about
+so it's displacement
+
+ align:start position:0%
+so it's displacement
+ 
+
+ align:start position:0%
+so it's displacement
+yeah there's there's a couple ways right
+
+ align:start position:0%
+yeah there's there's a couple ways right
+ 
+
+ align:start position:0%
+yeah there's there's a couple ways right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+one of the things that um
+
+ align:start position:0%
+one of the things that um
+ 
+
+ align:start position:0%
+one of the things that um
+martin was showing was this coherent
+
+ align:start position:0%
+martin was showing was this coherent
+ 
+
+ align:start position:0%
+martin was showing was this coherent
+diffraction lithography stuff and i'm
+
+ align:start position:0%
+diffraction lithography stuff and i'm
+ 
+
+ align:start position:0%
+diffraction lithography stuff and i'm
+going to talk about it a little bit
+
+ align:start position:0%
+going to talk about it a little bit
+ 
+
+ align:start position:0%
+going to talk about it a little bit
+because i know very well
+
+ align:start position:0%
+because i know very well
+ 
+
+ align:start position:0%
+because i know very well
+so you can imagine you know if you
+
+ align:start position:0%
+so you can imagine you know if you
+ 
+
+ align:start position:0%
+so you can imagine you know if you
+had your substrate at an angle here
+
+ align:start position:0%
+had your substrate at an angle here
+ 
+
+ align:start position:0%
+had your substrate at an angle here
+you know you pass through a few tablet
+
+ align:start position:0%
+you know you pass through a few tablet
+ 
+
+ align:start position:0%
+you know you pass through a few tablet
+planes and so the actual
+
+ align:start position:0%
+planes and so the actual
+ 
+
+ align:start position:0%
+planes and so the actual
+shape of your grating
+
+ align:start position:0%
+shape of your grating
+ 
+
+ align:start position:0%
+shape of your grating
+wouldn't be just periodic there'd be
+
+ align:start position:0%
+wouldn't be just periodic there'd be
+ 
+
+ align:start position:0%
+wouldn't be just periodic there'd be
+regions where you'd go to frequency
+
+ align:start position:0%
+regions where you'd go to frequency
+ 
+
+ align:start position:0%
+regions where you'd go to frequency
+doubling there'd be regions where you
+
+ align:start position:0%
+doubling there'd be regions where you
+ 
+
+ align:start position:0%
+doubling there'd be regions where you
+didn't
+
+ align:start position:0%
+didn't
+ 
+
+ align:start position:0%
+didn't
+so that alignment capability is really
+
+ align:start position:0%
+so that alignment capability is really
+ 
+
+ align:start position:0%
+so that alignment capability is really
+an important thing and if you imagine
+
+ align:start position:0%
+an important thing and if you imagine
+ 
+
+ align:start position:0%
+an important thing and if you imagine
+stacking in the membrane stacking sense
+
+ align:start position:0%
+stacking in the membrane stacking sense
+ 
+
+ align:start position:0%
+stacking in the membrane stacking sense
+these printed patterns on top of each
+
+ align:start position:0%
+these printed patterns on top of each
+ 
+
+ align:start position:0%
+these printed patterns on top of each
+other you have to be able to align those
+
+ align:start position:0%
+other you have to be able to align those
+ 
+
+ align:start position:0%
+other you have to be able to align those
+patterns relative to each other and if
+
+ align:start position:0%
+patterns relative to each other and if
+ 
+
+ align:start position:0%
+patterns relative to each other and if
+your alignment is off by say 25
+
+ align:start position:0%
+your alignment is off by say 25
+ 
+
+ align:start position:0%
+your alignment is off by say 25
+nanometers then you get something like
+
+ align:start position:0%
+nanometers then you get something like
+ 
+
+ align:start position:0%
+nanometers then you get something like
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+decrease in your band gap
+
+ align:start position:0%
+decrease in your band gap
+ 
+
+ align:start position:0%
+decrease in your band gap
+so one of the examples of misalignment
+
+ align:start position:0%
+so one of the examples of misalignment
+ 
+
+ align:start position:0%
+so one of the examples of misalignment
+is actually in the stacking part of the
+
+ align:start position:0%
+is actually in the stacking part of the
+ 
+
+ align:start position:0%
+is actually in the stacking part of the
+fabrication and one of the things that
+
+ align:start position:0%
+fabrication and one of the things that
+ 
+
+ align:start position:0%
+fabrication and one of the things that
+you know in this particular case this
+
+ align:start position:0%
+you know in this particular case this
+ 
+
+ align:start position:0%
+you know in this particular case this
+stacking is all dependent on how good
+
+ align:start position:0%
+stacking is all dependent on how good
+ 
+
+ align:start position:0%
+stacking is all dependent on how good
+these spheres are
+
+ align:start position:0%
+these spheres are
+ 
+
+ align:start position:0%
+these spheres are
+you know so the misalignment's not i
+
+ align:start position:0%
+you know so the misalignment's not i
+ 
+
+ align:start position:0%
+you know so the misalignment's not i
+don't believe it was reported in this
+
+ align:start position:0%
+don't believe it was reported in this
+ 
+
+ align:start position:0%
+don't believe it was reported in this
+paper but you know
+
+ align:start position:0%
+paper but you know
+ 
+
+ align:start position:0%
+paper but you know
+it could be 20 or 30 nanometers they
+
+ align:start position:0%
+it could be 20 or 30 nanometers they
+ 
+
+ align:start position:0%
+it could be 20 or 30 nanometers they
+don't say
+
+ align:start position:0%
+don't say
+ 
+
+ align:start position:0%
+don't say
+and so that's where the misalignment
+
+ align:start position:0%
+and so that's where the misalignment
+ 
+
+ align:start position:0%
+and so that's where the misalignment
+comes from but you know in ming howe's
+
+ align:start position:0%
+comes from but you know in ming howe's
+ 
+
+ align:start position:0%
+comes from but you know in ming howe's
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+in this one the misalignment comes from
+
+ align:start position:0%
+in this one the misalignment comes from
+ 
+
+ align:start position:0%
+in this one the misalignment comes from
+the e-beam
+
+ align:start position:0%
+the e-beam
+ 
+
+ align:start position:0%
+the e-beam
+right so as the e-beam is writing each
+
+ align:start position:0%
+right so as the e-beam is writing each
+ 
+
+ align:start position:0%
+right so as the e-beam is writing each
+one of these uh
+
+ align:start position:0%
+one of these uh
+ 
+
+ align:start position:0%
+one of these uh
+each one of these hole layers or each
+
+ align:start position:0%
+each one of these hole layers or each
+ 
+
+ align:start position:0%
+each one of these hole layers or each
+one of these rod layers there's a
+
+ align:start position:0%
+one of these rod layers there's a
+ 
+
+ align:start position:0%
+one of these rod layers there's a
+certain few nanometers off error that
+
+ align:start position:0%
+certain few nanometers off error that
+ 
+
+ align:start position:0%
+certain few nanometers off error that
+you know it misplaces a rod or it
+
+ align:start position:0%
+you know it misplaces a rod or it
+ 
+
+ align:start position:0%
+you know it misplaces a rod or it
+misplaces a hole
+
+ align:start position:0%
+misplaces a hole
+ 
+
+ align:start position:0%
+misplaces a hole
+so i guess the answer to your question
+
+ align:start position:0%
+so i guess the answer to your question
+ 
+
+ align:start position:0%
+so i guess the answer to your question
+is that there's a lot of different ways
+
+ align:start position:0%
+is that there's a lot of different ways
+ 
+
+ align:start position:0%
+is that there's a lot of different ways
+that misalignment can happen but it's
+
+ align:start position:0%
+that misalignment can happen but it's
+ 
+
+ align:start position:0%
+that misalignment can happen but it's
+controlling that misalignment
+
+ align:start position:0%
+controlling that misalignment
+ 
+
+ align:start position:0%
+controlling that misalignment
+and if we use diffractive optics we can
+
+ align:start position:0%
+and if we use diffractive optics we can
+ 
+
+ align:start position:0%
+and if we use diffractive optics we can
+control it very well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so how does a crystal that's designed
+
+ align:start position:0%
+so how does a crystal that's designed
+ 
+
+ align:start position:0%
+so how does a crystal that's designed
+for a wider band gap but like has
+
+ align:start position:0%
+for a wider band gap but like has
+ 
+
+ align:start position:0%
+for a wider band gap but like has
+misalignment so you have an effectively
+
+ align:start position:0%
+misalignment so you have an effectively
+ 
+
+ align:start position:0%
+misalignment so you have an effectively
+shorter one how does that compare to one
+
+ align:start position:0%
+shorter one how does that compare to one
+ 
+
+ align:start position:0%
+shorter one how does that compare to one
+that's actually designed for the
+
+ align:start position:0%
+that's actually designed for the
+ 
+
+ align:start position:0%
+that's actually designed for the
+smaller band gap and is accurately
+
+ align:start position:0%
+smaller band gap and is accurately
+ 
+
+ align:start position:0%
+smaller band gap and is accurately
+aligned
+
+ align:start position:0%
+aligned
+ 
+
+ align:start position:0%
+aligned
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i think the answer to the question is if
+
+ align:start position:0%
+i think the answer to the question is if
+ 
+
+ align:start position:0%
+i think the answer to the question is if
+i were designing it
+
+ align:start position:0%
+i were designing it
+ 
+
+ align:start position:0%
+i were designing it
+i'd want to go with the one that's
+
+ align:start position:0%
+i'd want to go with the one that's
+ 
+
+ align:start position:0%
+i'd want to go with the one that's
+designed to have a smaller band gap
+
+ align:start position:0%
+designed to have a smaller band gap
+ 
+
+ align:start position:0%
+designed to have a smaller band gap
+without misalignment than one that's
+
+ align:start position:0%
+without misalignment than one that's
+ 
+
+ align:start position:0%
+without misalignment than one that's
+designed to have a smaller gap with
+
+ align:start position:0%
+designed to have a smaller gap with
+ 
+
+ align:start position:0%
+designed to have a smaller gap with
+misalignment like i wouldn't
+
+ align:start position:0%
+misalignment like i wouldn't
+ 
+
+ align:start position:0%
+misalignment like i wouldn't
+screw up my pattern to make the band gap
+
+ align:start position:0%
+screw up my pattern to make the band gap
+ 
+
+ align:start position:0%
+screw up my pattern to make the band gap
+get smaller i'd try and design it to
+
+ align:start position:0%
+get smaller i'd try and design it to
+ 
+
+ align:start position:0%
+get smaller i'd try and design it to
+have that band gap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/WIKsL9tPoAE.txt b/WIKsL9tPoAE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2bbc5b2927461e19ac0a1a31713a37fdd0b65e68
--- /dev/null
+++ b/WIKsL9tPoAE.txt
@@ -0,0 +1,1171 @@
+align:start position:0%
+ 
+we'll call from our last video that it
+
+ align:start position:0%
+we'll call from our last video that it
+ 
+
+ align:start position:0%
+we'll call from our last video that it
+was impossible for us to use
+
+ align:start position:0%
+was impossible for us to use
+ 
+
+ align:start position:0%
+was impossible for us to use
+hierarchical clustering because of the
+
+ align:start position:0%
+hierarchical clustering because of the
+ 
+
+ align:start position:0%
+hierarchical clustering because of the
+high resolution of our image so in this
+
+ align:start position:0%
+high resolution of our image so in this
+ 
+
+ align:start position:0%
+high resolution of our image so in this
+video we will try to segment the MRI
+
+ align:start position:0%
+video we will try to segment the MRI
+ 
+
+ align:start position:0%
+video we will try to segment the MRI
+image using the canyons clustering
+
+ align:start position:0%
+image using the canyons clustering
+ 
+
+ align:start position:0%
+image using the canyons clustering
+algorithm the first step in k-means
+
+ align:start position:0%
+algorithm the first step in k-means
+ 
+
+ align:start position:0%
+algorithm the first step in k-means
+clustering involves specifying the
+
+ align:start position:0%
+clustering involves specifying the
+ 
+
+ align:start position:0%
+clustering involves specifying the
+number of clusters k but how do we
+
+ align:start position:0%
+number of clusters k but how do we
+ 
+
+ align:start position:0%
+number of clusters k but how do we
+select K while our clusters would
+
+ align:start position:0%
+select K while our clusters would
+ 
+
+ align:start position:0%
+select K while our clusters would
+ideally assign each point in the image
+
+ align:start position:0%
+ideally assign each point in the image
+ 
+
+ align:start position:0%
+ideally assign each point in the image
+to a tissue class or a particular
+
+ align:start position:0%
+to a tissue class or a particular
+ 
+
+ align:start position:0%
+to a tissue class or a particular
+substance for instance gray matter or
+
+ align:start position:0%
+substance for instance gray matter or
+ 
+
+ align:start position:0%
+substance for instance gray matter or
+white matter and so on and these
+
+ align:start position:0%
+white matter and so on and these
+ 
+
+ align:start position:0%
+white matter and so on and these
+substances are known to the medical
+
+ align:start position:0%
+substances are known to the medical
+ 
+
+ align:start position:0%
+substances are known to the medical
+community so setting the number of
+
+ align:start position:0%
+community so setting the number of
+ 
+
+ align:start position:0%
+community so setting the number of
+clusters depends on exactly what you are
+
+ align:start position:0%
+clusters depends on exactly what you are
+ 
+
+ align:start position:0%
+clusters depends on exactly what you are
+trying to extract from the image for the
+
+ align:start position:0%
+trying to extract from the image for the
+ 
+
+ align:start position:0%
+trying to extract from the image for the
+sake of our example let's set the number
+
+ align:start position:0%
+sake of our example let's set the number
+ 
+
+ align:start position:0%
+sake of our example let's set the number
+of clusters here K to 5 and since the
+
+ align:start position:0%
+of clusters here K to 5 and since the
+ 
+
+ align:start position:0%
+of clusters here K to 5 and since the
+k-means clustering algorithm starts by
+
+ align:start position:0%
+k-means clustering algorithm starts by
+ 
+
+ align:start position:0%
+k-means clustering algorithm starts by
+randomly assigning points to clusters we
+
+ align:start position:0%
+randomly assigning points to clusters we
+ 
+
+ align:start position:0%
+randomly assigning points to clusters we
+should set the seed so that we all
+
+ align:start position:0%
+should set the seed so that we all
+ 
+
+ align:start position:0%
+should set the seed so that we all
+obtain the same clusters so let's
+
+ align:start position:0%
+obtain the same clusters so let's
+ 
+
+ align:start position:0%
+obtain the same clusters so let's
+dissect that seed and give it a value of
+
+ align:start position:0%
+dissect that seed and give it a value of
+ 
+
+ align:start position:0%
+dissect that seed and give it a value of
+1/2 of the k-means clustering algorithm
+
+ align:start position:0%
+1/2 of the k-means clustering algorithm
+ 
+
+ align:start position:0%
+1/2 of the k-means clustering algorithm
+or KMC in short we need to use the
+
+ align:start position:0%
+or KMC in short we need to use the
+ 
+
+ align:start position:0%
+or KMC in short we need to use the
+k-means function in our and the first
+
+ align:start position:0%
+k-means function in our and the first
+ 
+
+ align:start position:0%
+k-means function in our and the first
+input is whatever we are trying to
+
+ align:start position:0%
+input is whatever we are trying to
+ 
+
+ align:start position:0%
+input is whatever we are trying to
+cluster in this case it is the healthy
+
+ align:start position:0%
+cluster in this case it is the healthy
+ 
+
+ align:start position:0%
+cluster in this case it is the healthy
+vector the second argument is the number
+
+ align:start position:0%
+vector the second argument is the number
+ 
+
+ align:start position:0%
+vector the second argument is the number
+of clusters and we can specify it using
+
+ align:start position:0%
+of clusters and we can specify it using
+ 
+
+ align:start position:0%
+of clusters and we can specify it using
+the argument centers and that would be
+
+ align:start position:0%
+the argument centers and that would be
+ 
+
+ align:start position:0%
+the argument centers and that would be
+equal to K and then finally since the
+
+ align:start position:0%
+equal to K and then finally since the
+ 
+
+ align:start position:0%
+equal to K and then finally since the
+k-means is an iterative method that
+
+ align:start position:0%
+k-means is an iterative method that
+ 
+
+ align:start position:0%
+k-means is an iterative method that
+could take very long to converge we need
+
+ align:start position:0%
+could take very long to converge we need
+ 
+
+ align:start position:0%
+could take very long to converge we need
+to set a maximum number of iterations
+
+ align:start position:0%
+to set a maximum number of iterations
+ 
+
+ align:start position:0%
+to set a maximum number of iterations
+and we can do this by typing by chopped
+
+ align:start position:0%
+and we can do this by typing by chopped
+ 
+
+ align:start position:0%
+and we can do this by typing by chopped
+Max and give it for instance the value
+
+ align:start position:0%
+Max and give it for instance the value
+ 
+
+ align:start position:0%
+Max and give it for instance the value
+thousand and now let's run the k-means
+
+ align:start position:0%
+thousand and now let's run the k-means
+ 
+
+ align:start position:0%
+thousand and now let's run the k-means
+algorithm the k-means algorithm is
+
+ align:start position:0%
+algorithm the k-means algorithm is
+ 
+
+ align:start position:0%
+algorithm the k-means algorithm is
+actually quite fast even though we have
+
+ align:start position:0%
+actually quite fast even though we have
+ 
+
+ align:start position:0%
+actually quite fast even though we have
+a high-resolution image now to see the
+
+ align:start position:0%
+a high-resolution image now to see the
+ 
+
+ align:start position:0%
+a high-resolution image now to see the
+result of the k-means clustering
+
+ align:start position:0%
+result of the k-means clustering
+ 
+
+ align:start position:0%
+result of the k-means clustering
+algorithm we can output the structure of
+
+ align:start position:0%
+algorithm we can output the structure of
+ 
+
+ align:start position:0%
+algorithm we can output the structure of
+the KFC variable the first thing most
+
+ align:start position:0%
+the KFC variable the first thing most
+ 
+
+ align:start position:0%
+the KFC variable the first thing most
+important piece of information that we
+
+ align:start position:0%
+important piece of information that we
+ 
+
+ align:start position:0%
+important piece of information that we
+get is the cluster vector which assigns
+
+ align:start position:0%
+get is the cluster vector which assigns
+ 
+
+ align:start position:0%
+get is the cluster vector which assigns
+each intensity value in the healthy that
+
+ align:start position:0%
+each intensity value in the healthy that
+ 
+
+ align:start position:0%
+each intensity value in the healthy that
+to a cluster in this case it will be
+
+ align:start position:0%
+to a cluster in this case it will be
+ 
+
+ align:start position:0%
+to a cluster in this case it will be
+given them values one through five since
+
+ align:start position:0%
+given them values one through five since
+ 
+
+ align:start position:0%
+given them values one through five since
+we have five clusters now recall that to
+
+ align:start position:0%
+we have five clusters now recall that to
+ 
+
+ align:start position:0%
+we have five clusters now recall that to
+output the segmented image we need to
+
+ align:start position:0%
+output the segmented image we need to
+ 
+
+ align:start position:0%
+output the segmented image we need to
+extract this vector the way to do this
+
+ align:start position:0%
+extract this vector the way to do this
+ 
+
+ align:start position:0%
+extract this vector the way to do this
+is by using the dollar notation for
+
+ align:start position:0%
+is by using the dollar notation for
+ 
+
+ align:start position:0%
+is by using the dollar notation for
+instance let us define healthy clusters
+
+ align:start position:0%
+instance let us define healthy clusters
+ 
+
+ align:start position:0%
+instance let us define healthy clusters
+and then set it equal to K and C dollar
+
+ align:start position:0%
+and then set it equal to K and C dollar
+ 
+
+ align:start position:0%
+and then set it equal to K and C dollar
+sign cluster and what we're basically
+
+ align:start position:0%
+sign cluster and what we're basically
+ 
+
+ align:start position:0%
+sign cluster and what we're basically
+doing here is that we are taking the
+
+ align:start position:0%
+doing here is that we are taking the
+ 
+
+ align:start position:0%
+doing here is that we are taking the
+information extracting the information
+
+ align:start position:0%
+information extracting the information
+ 
+
+ align:start position:0%
+information extracting the information
+of the cluster vector and putting it in
+
+ align:start position:0%
+of the cluster vector and putting it in
+ 
+
+ align:start position:0%
+of the cluster vector and putting it in
+the new variable that is called healthy
+
+ align:start position:0%
+the new variable that is called healthy
+ 
+
+ align:start position:0%
+the new variable that is called healthy
+clusters now how can we obtain the mean
+
+ align:start position:0%
+clusters now how can we obtain the mean
+ 
+
+ align:start position:0%
+clusters now how can we obtain the mean
+intensity value within each of our five
+
+ align:start position:0%
+intensity value within each of our five
+ 
+
+ align:start position:0%
+intensity value within each of our five
+clusters in hierarchical clustering we
+
+ align:start position:0%
+clusters in hierarchical clustering we
+ 
+
+ align:start position:0%
+clusters in hierarchical clustering we
+needed to do some manual work and use
+
+ align:start position:0%
+needed to do some manual work and use
+ 
+
+ align:start position:0%
+needed to do some manual work and use
+the T apply function to extract this
+
+ align:start position:0%
+the T apply function to extract this
+ 
+
+ align:start position:0%
+the T apply function to extract this
+information in this case we have the
+
+ align:start position:0%
+information in this case we have the
+ 
+
+ align:start position:0%
+information in this case we have the
+answers ready under the vector centers
+
+ align:start position:0%
+answers ready under the vector centers
+ 
+
+ align:start position:0%
+answers ready under the vector centers
+in fact for instance the mean intensity
+
+ align:start position:0%
+in fact for instance the mean intensity
+ 
+
+ align:start position:0%
+in fact for instance the mean intensity
+value of the first cluster is 0.40 a
+
+ align:start position:0%
+value of the first cluster is 0.40 a
+ 
+
+ align:start position:0%
+value of the first cluster is 0.40 a
+then the mean intensity value of the
+
+ align:start position:0%
+then the mean intensity value of the
+ 
+
+ align:start position:0%
+then the mean intensity value of the
+last cluster is 0.18 we can also extract
+
+ align:start position:0%
+last cluster is 0.18 we can also extract
+ 
+
+ align:start position:0%
+last cluster is 0.18 we can also extract
+this information using the dollar sign
+
+ align:start position:0%
+this information using the dollar sign
+ 
+
+ align:start position:0%
+this information using the dollar sign
+for instance KFC dollar sign centers and
+
+ align:start position:0%
+for instance KFC dollar sign centers and
+ 
+
+ align:start position:0%
+for instance KFC dollar sign centers and
+then between brackets the index to this
+
+ align:start position:0%
+then between brackets the index to this
+ 
+
+ align:start position:0%
+then between brackets the index to this
+should give us the mean intensity value
+
+ align:start position:0%
+should give us the mean intensity value
+ 
+
+ align:start position:0%
+should give us the mean intensity value
+of the second cluster which is 0.1 and
+
+ align:start position:0%
+of the second cluster which is 0.1 and
+ 
+
+ align:start position:0%
+of the second cluster which is 0.1 and
+indeed this is what we obtained before
+
+ align:start position:0%
+indeed this is what we obtained before
+ 
+
+ align:start position:0%
+indeed this is what we obtained before
+we move on I would like to point your
+
+ align:start position:0%
+we move on I would like to point your
+ 
+
+ align:start position:0%
+we move on I would like to point your
+attention to one last interesting piece
+
+ align:start position:0%
+attention to one last interesting piece
+ 
+
+ align:start position:0%
+attention to one last interesting piece
+of information that we can get here and
+
+ align:start position:0%
+of information that we can get here and
+ 
+
+ align:start position:0%
+of information that we can get here and
+that is the size of the cluster for
+
+ align:start position:0%
+that is the size of the cluster for
+ 
+
+ align:start position:0%
+that is the size of the cluster for
+instance the largest cluster that we
+
+ align:start position:0%
+instance the largest cluster that we
+ 
+
+ align:start position:0%
+instance the largest cluster that we
+have is the third one which combines
+
+ align:start position:0%
+have is the third one which combines
+ 
+
+ align:start position:0%
+have is the third one which combines
+133,000 values in it and interestingly
+
+ align:start position:0%
+133,000 values in it and interestingly
+ 
+
+ align:start position:0%
+133,000 values in it and interestingly
+it's the one that has the smallest mean
+
+ align:start position:0%
+it's the one that has the smallest mean
+ 
+
+ align:start position:0%
+it's the one that has the smallest mean
+intensity value which means that it
+
+ align:start position:0%
+intensity value which means that it
+ 
+
+ align:start position:0%
+intensity value which means that it
+corresponds to the darkest shade in our
+
+ align:start position:0%
+corresponds to the darkest shade in our
+ 
+
+ align:start position:0%
+corresponds to the darkest shade in our
+image actually if we look at all the
+
+ align:start position:0%
+image actually if we look at all the
+ 
+
+ align:start position:0%
+image actually if we look at all the
+mean intensity values we can see that
+
+ align:start position:0%
+mean intensity values we can see that
+ 
+
+ align:start position:0%
+mean intensity values we can see that
+they're all less than 0.5 so they're all
+
+ align:start position:0%
+they're all less than 0.5 so they're all
+ 
+
+ align:start position:0%
+they're all less than 0.5 so they're all
+pretty close to 0 and this means that
+
+ align:start position:0%
+pretty close to 0 and this means that
+ 
+
+ align:start position:0%
+pretty close to 0 and this means that
+our image is pretty dark if we look at
+
+ align:start position:0%
+our image is pretty dark if we look at
+ 
+
+ align:start position:0%
+our image is pretty dark if we look at
+our image again it's indeed very dark
+
+ align:start position:0%
+our image again it's indeed very dark
+ 
+
+ align:start position:0%
+our image again it's indeed very dark
+and we have very few points that are
+
+ align:start position:0%
+and we have very few points that are
+ 
+
+ align:start position:0%
+and we have very few points that are
+now the exciting part
+
+ align:start position:0%
+now the exciting part
+ 
+
+ align:start position:0%
+now the exciting part
+let us output the segmented image and
+
+ align:start position:0%
+let us output the segmented image and
+ 
+
+ align:start position:0%
+let us output the segmented image and
+see what we get
+
+ align:start position:0%
+see what we get
+ 
+
+ align:start position:0%
+see what we get
+recall that we first need to convert the
+
+ align:start position:0%
+recall that we first need to convert the
+ 
+
+ align:start position:0%
+recall that we first need to convert the
+vector healthy clusters to a matrix to
+
+ align:start position:0%
+vector healthy clusters to a matrix to
+ 
+
+ align:start position:0%
+vector healthy clusters to a matrix to
+do this we will use the dimension
+
+ align:start position:0%
+do this we will use the dimension
+ 
+
+ align:start position:0%
+do this we will use the dimension
+function that takes an input the healthy
+
+ align:start position:0%
+function that takes an input the healthy
+ 
+
+ align:start position:0%
+function that takes an input the healthy
+clusters vector and now we're going to
+
+ align:start position:0%
+clusters vector and now we're going to
+ 
+
+ align:start position:0%
+clusters vector and now we're going to
+turn it into a matrix so we have to
+
+ align:start position:0%
+turn it into a matrix so we have to
+ 
+
+ align:start position:0%
+turn it into a matrix so we have to
+specify using the combined function the
+
+ align:start position:0%
+specify using the combined function the
+ 
+
+ align:start position:0%
+specify using the combined function the
+number of rows and the number of columns
+
+ align:start position:0%
+number of rows and the number of columns
+ 
+
+ align:start position:0%
+number of rows and the number of columns
+that we want we should make sure that it
+
+ align:start position:0%
+that we want we should make sure that it
+ 
+
+ align:start position:0%
+that we want we should make sure that it
+corresponds to the same size as the
+
+ align:start position:0%
+corresponds to the same size as the
+ 
+
+ align:start position:0%
+corresponds to the same size as the
+healthy matrix and since we forgot the
+
+ align:start position:0%
+healthy matrix and since we forgot the
+ 
+
+ align:start position:0%
+healthy matrix and since we forgot the
+number of rows and the number of columns
+
+ align:start position:0%
+number of rows and the number of columns
+ 
+
+ align:start position:0%
+number of rows and the number of columns
+and be healthy matrix we can simply use
+
+ align:start position:0%
+and be healthy matrix we can simply use
+ 
+
+ align:start position:0%
+and be healthy matrix we can simply use
+the n row and M call function to get
+
+ align:start position:0%
+the n row and M call function to get
+ 
+
+ align:start position:0%
+the n row and M call function to get
+them so the first input right now would
+
+ align:start position:0%
+them so the first input right now would
+ 
+
+ align:start position:0%
+them so the first input right now would
+be n row of healthy matrix and then the
+
+ align:start position:0%
+be n row of healthy matrix and then the
+ 
+
+ align:start position:0%
+be n row of healthy matrix and then the
+second input would be the number of
+
+ align:start position:0%
+second input would be the number of
+ 
+
+ align:start position:0%
+second input would be the number of
+columns of the healthy matrix and now we
+
+ align:start position:0%
+columns of the healthy matrix and now we
+ 
+
+ align:start position:0%
+columns of the healthy matrix and now we
+are assigning these numbers of rows and
+
+ align:start position:0%
+are assigning these numbers of rows and
+ 
+
+ align:start position:0%
+are assigning these numbers of rows and
+columns to our new matrix healthy
+
+ align:start position:0%
+columns to our new matrix healthy
+ 
+
+ align:start position:0%
+columns to our new matrix healthy
+clusters and now we can visualize our
+
+ align:start position:0%
+clusters and now we can visualize our
+ 
+
+ align:start position:0%
+clusters and now we can visualize our
+clusters by using the function image
+
+ align:start position:0%
+clusters by using the function image
+ 
+
+ align:start position:0%
+clusters by using the function image
+which takes as an input the healthy
+
+ align:start position:0%
+which takes as an input the healthy
+ 
+
+ align:start position:0%
+which takes as an input the healthy
+clusters matrix then let's turn off the
+
+ align:start position:0%
+clusters matrix then let's turn off the
+ 
+
+ align:start position:0%
+clusters matrix then let's turn off the
+axes and then let's be creative and use
+
+ align:start position:0%
+axes and then let's be creative and use
+ 
+
+ align:start position:0%
+axes and then let's be creative and use
+a fancy color scheme well going to
+
+ align:start position:0%
+a fancy color scheme well going to
+ 
+
+ align:start position:0%
+a fancy color scheme well going to
+invoke for color here the rainbow
+
+ align:start position:0%
+invoke for color here the rainbow
+ 
+
+ align:start position:0%
+invoke for color here the rainbow
+palette and on and the rainbow fat
+
+ align:start position:0%
+palette and on and the rainbow fat
+ 
+
+ align:start position:0%
+palette and on and the rainbow fat
+select or the function rainbow takes as
+
+ align:start position:0%
+select or the function rainbow takes as
+ 
+
+ align:start position:0%
+select or the function rainbow takes as
+an input the number of colors that we
+
+ align:start position:0%
+an input the number of colors that we
+ 
+
+ align:start position:0%
+an input the number of colors that we
+want in this case the number of colors
+
+ align:start position:0%
+want in this case the number of colors
+ 
+
+ align:start position:0%
+want in this case the number of colors
+would correspond to the number of
+
+ align:start position:0%
+would correspond to the number of
+ 
+
+ align:start position:0%
+would correspond to the number of
+clusters so the input would be K and now
+
+ align:start position:0%
+clusters so the input would be K and now
+ 
+
+ align:start position:0%
+clusters so the input would be K and now
+let's output the segmented image going
+
+ align:start position:0%
+let's output the segmented image going
+ 
+
+ align:start position:0%
+let's output the segmented image going
+back to the graphics window we see that
+
+ align:start position:0%
+back to the graphics window we see that
+ 
+
+ align:start position:0%
+back to the graphics window we see that
+the k-means algorithm was able to
+
+ align:start position:0%
+the k-means algorithm was able to
+ 
+
+ align:start position:0%
+the k-means algorithm was able to
+segment the image in five different
+
+ align:start position:0%
+segment the image in five different
+ 
+
+ align:start position:0%
+segment the image in five different
+clusters more refinement maybe needs to
+
+ align:start position:0%
+clusters more refinement maybe needs to
+ 
+
+ align:start position:0%
+clusters more refinement maybe needs to
+be made to our clustering algorithm to
+
+ align:start position:0%
+be made to our clustering algorithm to
+ 
+
+ align:start position:0%
+be made to our clustering algorithm to
+appropriately capture all the anatomical
+
+ align:start position:0%
+appropriately capture all the anatomical
+ 
+
+ align:start position:0%
+appropriately capture all the anatomical
+structures but this seems like a good
+
+ align:start position:0%
+structures but this seems like a good
+ 
+
+ align:start position:0%
+structures but this seems like a good
+starting point the question now is can
+
+ align:start position:0%
+starting point the question now is can
+ 
+
+ align:start position:0%
+starting point the question now is can
+we use the clusters or the classes found
+
+ align:start position:0%
+we use the clusters or the classes found
+ 
+
+ align:start position:0%
+we use the clusters or the classes found
+by our k-means algorithm
+
+ align:start position:0%
+by our k-means algorithm
+ 
+
+ align:start position:0%
+by our k-means algorithm
+on the healthy MRI in it to identify
+
+ align:start position:0%
+on the healthy MRI in it to identify
+ 
+
+ align:start position:0%
+on the healthy MRI in it to identify
+tumors in another MRI image of a sick
+
+ align:start position:0%
+tumors in another MRI image of a sick
+ 
+
+ align:start position:0%
+tumors in another MRI image of a sick
+patient we will see if this is possible
+
+ align:start position:0%
+patient we will see if this is possible
+ 
+
+ align:start position:0%
+patient we will see if this is possible
+in the next video
\ No newline at end of file
diff --git a/WVOIk8en6YE.txt b/WVOIk8en6YE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..87a8c2a82b33b6df6bd27232227ecce4137a2f7c
--- /dev/null
+++ b/WVOIk8en6YE.txt
@@ -0,0 +1,10411 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay let us start so let me
+
+ align:start position:0%
+ocw.mit.edu okay let us start so let me
+ 
+
+ align:start position:0%
+ocw.mit.edu okay let us start so let me
+first remind you what we did uh uh in N
+
+ align:start position:0%
+first remind you what we did uh uh in N
+ 
+
+ align:start position:0%
+first remind you what we did uh uh in N
+neure we proved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we showed that the wber we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forbids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+existence of mes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spin two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles matx spin two particles are
+
+ align:start position:0%
+particles matx spin two particles are
+ 
+
+ align:start position:0%
+particles matx spin two particles are
+whole Mark of of gravity so that's why
+
+ align:start position:0%
+whole Mark of of gravity so that's why
+ 
+
+ align:start position:0%
+whole Mark of of gravity so that's why
+we look for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them in the
+
+ align:start position:0%
+them in the
+ 
+
+ align:start position:0%
+them in the
+same so emphasiz in the same space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time say a
+
+ align:start position:0%
+time say a
+ 
+
+ align:start position:0%
+time say a
+qft leaves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this theem essentially say
+
+ align:start position:0%
+okay so this theem essentially say
+ 
+
+ align:start position:0%
+okay so this theem essentially say
+this you will never have emerging
+
+ align:start position:0%
+this you will never have emerging
+ 
+
+ align:start position:0%
+this you will never have emerging
+gravity start from low ranging variant
+
+ align:start position:0%
+gravity start from low ranging variant
+ 
+
+ align:start position:0%
+gravity start from low ranging variant
+Quantum field Theory with a well defined
+
+ align:start position:0%
+Quantum field Theory with a well defined
+ 
+
+ align:start position:0%
+Quantum field Theory with a well defined
+stress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tensor so as we already
+
+ align:start position:0%
+tensor so as we already
+ 
+
+ align:start position:0%
+tensor so as we already
+mentioned is a nohole of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Serum is
+
+ align:start position:0%
+Serum is
+ 
+
+ align:start position:0%
+Serum is
+that actually a emerging space emerging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity can actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leave in the different space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+as in holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duality in fact in holographic
+
+ align:start position:0%
+duality in fact in holographic
+ 
+
+ align:start position:0%
+duality in fact in holographic
+Duality the gravity leaves in one
+
+ align:start position:0%
+Duality the gravity leaves in one
+ 
+
+ align:start position:0%
+Duality the gravity leaves in one
+dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher but we are not ready to go there
+
+ align:start position:0%
+higher but we are not ready to go there
+ 
+
+ align:start position:0%
+higher but we are not ready to go there
+yet so in order to describe this thing
+
+ align:start position:0%
+yet so in order to describe this thing
+ 
+
+ align:start position:0%
+yet so in order to describe this thing
+we still lead to um do some
+
+ align:start position:0%
+we still lead to um do some
+ 
+
+ align:start position:0%
+we still lead to um do some
+preparations so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preparations let me just outline the
+
+ align:start position:0%
+preparations let me just outline the
+ 
+
+ align:start position:0%
+preparations let me just outline the
+preparations we need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do so the first thing we will do is
+
+ align:start position:0%
+do so the first thing we will do is
+ 
+
+ align:start position:0%
+do so the first thing we will do is
+black hole thermodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this will give
+
+ align:start position:0%
+okay so this will give
+ 
+
+ align:start position:0%
+okay so this will give
+hint for something called holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle which is actually more
+
+ align:start position:0%
+principle which is actually more
+ 
+
+ align:start position:0%
+principle which is actually more
+General than the holographic Duality
+
+ align:start position:0%
+General than the holographic Duality
+ 
+
+ align:start position:0%
+General than the holographic Duality
+discovered so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far and the second thing is we will also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quickly go over the larg engage series
+
+ align:start position:0%
+quickly go over the larg engage series
+ 
+
+ align:start position:0%
+quickly go over the larg engage series
+the properties of the Marg say a G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Series so this give
+
+ align:start position:0%
+Series so this give
+ 
+
+ align:start position:0%
+Series so this give
+hint something called the gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings parity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the behavior of the Lage
+
+ align:start position:0%
+so the behavior of the Lage
+ 
+
+ align:start position:0%
+so the behavior of the Lage
+the give you a strong
+
+ align:start position:0%
+the give you a strong
+ 
+
+ align:start position:0%
+the give you a strong
+hint that actually this a string series
+
+ align:start position:0%
+hint that actually this a string series
+ 
+
+ align:start position:0%
+hint that actually this a string series
+description for ordinary gauge series
+
+ align:start position:0%
+description for ordinary gauge series
+ 
+
+ align:start position:0%
+description for ordinary gauge series
+okay and when you combine this these two
+
+ align:start position:0%
+okay and when you combine this these two
+ 
+
+ align:start position:0%
+okay and when you combine this these two
+things together then you get what we
+
+ align:start position:0%
+things together then you get what we
+ 
+
+ align:start position:0%
+things together then you get what we
+have currently the holographic
+
+ align:start position:0%
+have currently the holographic
+ 
+
+ align:start position:0%
+have currently the holographic
+Duality and
+
+ align:start position:0%
+Duality and
+ 
+
+ align:start position:0%
+Duality and
+uh then a then we will also talk a
+
+ align:start position:0%
+uh then a then we will also talk a
+ 
+
+ align:start position:0%
+uh then a then we will also talk a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+of scen theory a tiny bit not a lot so
+
+ align:start position:0%
+of scen theory a tiny bit not a lot so
+ 
+
+ align:start position:0%
+of scen theory a tiny bit not a lot so
+don't be
+
+ align:start position:0%
+don't be
+ 
+
+ align:start position:0%
+don't be
+scared so we also will talk a little bit
+
+ align:start position:0%
+scared so we also will talk a little bit
+ 
+
+ align:start position:0%
+scared so we also will talk a little bit
+about screen
+
+ align:start position:0%
+about screen
+ 
+
+ align:start position:0%
+about screen
+Theory so in principle actually I can
+
+ align:start position:0%
+Theory so in principle actually I can
+ 
+
+ align:start position:0%
+Theory so in principle actually I can
+talk about holographic Duality right now
+
+ align:start position:0%
+talk about holographic Duality right now
+ 
+
+ align:start position:0%
+talk about holographic Duality right now
+but going over those aspects can help
+
+ align:start position:0%
+but going over those aspects can help
+ 
+
+ align:start position:0%
+but going over those aspects can help
+you to build some intuitions and also to
+
+ align:start position:0%
+you to build some intuitions and also to
+ 
+
+ align:start position:0%
+you to build some intuitions and also to
+have a broader uh uh perspective than um
+
+ align:start position:0%
+have a broader uh uh perspective than um
+ 
+
+ align:start position:0%
+have a broader uh uh perspective than um
+than just presenting the uh uh uh
+
+ align:start position:0%
+than just presenting the uh uh uh
+ 
+
+ align:start position:0%
+than just presenting the uh uh uh
+Duality
+
+ align:start position:0%
+Duality
+ 
+
+ align:start position:0%
+Duality
+directory so before I start uh today's
+
+ align:start position:0%
+directory so before I start uh today's
+ 
+
+ align:start position:0%
+directory so before I start uh today's
+uh uh lecture do you have any questions
+
+ align:start position:0%
+uh uh lecture do you have any questions
+ 
+
+ align:start position:0%
+uh uh lecture do you have any questions
+regarding our last lecture and regarding
+
+ align:start position:0%
+regarding our last lecture and regarding
+ 
+
+ align:start position:0%
+regarding our last lecture and regarding
+uh uh this um um yeah General remarks
+
+ align:start position:0%
+uh uh this um um yeah General remarks
+ 
+
+ align:start position:0%
+uh uh this um um yeah General remarks
+here yes so moving forward are we going
+
+ align:start position:0%
+here yes so moving forward are we going
+ 
+
+ align:start position:0%
+here yes so moving forward are we going
+to Define uh emerging gravity as the
+
+ align:start position:0%
+to Define uh emerging gravity as the
+ 
+
+ align:start position:0%
+to Define uh emerging gravity as the
+existence of a massless v 2 particle uh
+
+ align:start position:0%
+existence of a massless v 2 particle uh
+ 
+
+ align:start position:0%
+existence of a massless v 2 particle uh
+no that we will not do so how are we
+
+ align:start position:0%
+no that we will not do so how are we
+ 
+
+ align:start position:0%
+no that we will not do so how are we
+defining emerging gravity
+
+ align:start position:0%
+defining emerging gravity
+ 
+
+ align:start position:0%
+defining emerging gravity
+um um you construct newon La
+
+ align:start position:0%
+um um you construct newon La
+ 
+
+ align:start position:0%
+um um you construct newon La
+yeah you will see it you will see it
+
+ align:start position:0%
+yeah you will see it you will see it
+ 
+
+ align:start position:0%
+yeah you will see it you will see it
+when we have it yeah essentially you see
+
+ align:start position:0%
+when we have it yeah essentially you see
+ 
+
+ align:start position:0%
+when we have it yeah essentially you see
+the uh you see um essentially it's
+
+ align:start position:0%
+the uh you see um essentially it's
+ 
+
+ align:start position:0%
+the uh you see um essentially it's
+handed over to you you don't have to go
+
+ align:start position:0%
+handed over to you you don't have to go
+ 
+
+ align:start position:0%
+handed over to you you don't have to go
+through that step yeah you don't have to
+
+ align:start position:0%
+through that step yeah you don't have to
+ 
+
+ align:start position:0%
+through that step yeah you don't have to
+go through that step uh um yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay okay good good let's
+
+ align:start position:0%
+questions okay okay good good let's
+ 
+
+ align:start position:0%
+questions okay okay good good let's
+start with black hole some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamics so let me we start by doing a
+
+ align:start position:0%
+Dynamics so let me we start by doing a
+ 
+
+ align:start position:0%
+Dynamics so let me we start by doing a
+little bit um dimensional
+
+ align:start position:0%
+little bit um dimensional
+ 
+
+ align:start position:0%
+little bit um dimensional
+analysis just to remind
+
+ align:start position:0%
+analysis just to remind
+ 
+
+ align:start position:0%
+analysis just to remind
+you important scales for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity okay so the first thing is what
+
+ align:start position:0%
+gravity okay so the first thing is what
+ 
+
+ align:start position:0%
+gravity okay so the first thing is what
+we call the plank scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in nature we have fundamental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constants H Bar Newton constant and the
+
+ align:start position:0%
+constants H Bar Newton constant and the
+ 
+
+ align:start position:0%
+constants H Bar Newton constant and the
+C speed of
+
+ align:start position:0%
+C speed of
+ 
+
+ align:start position:0%
+C speed of
+light and
+
+ align:start position:0%
+light and
+ 
+
+ align:start position:0%
+light and
+immediately after
+
+ align:start position:0%
+immediately after
+ 
+
+ align:start position:0%
+immediately after
+plunk himself introduced this H
+
+ align:start position:0%
+plunk himself introduced this H
+ 
+
+ align:start position:0%
+plunk himself introduced this H
+bar he realized you can actually combine
+
+ align:start position:0%
+bar he realized you can actually combine
+ 
+
+ align:start position:0%
+bar he realized you can actually combine
+the three of them to come up with a map
+
+ align:start position:0%
+the three of them to come up with a map
+ 
+
+ align:start position:0%
+the three of them to come up with a map
+scale which is just
+
+ align:start position:0%
+scale which is just
+ 
+
+ align:start position:0%
+scale which is just
+hc/ by
+
+ align:start position:0%
+hc/ by
+ 
+
+ align:start position:0%
+hc/ by
+GN and this if you plug in the exessive
+
+ align:start position:0%
+GN and this if you plug in the exessive
+ 
+
+ align:start position:0%
+GN and this if you plug in the exessive
+numerical value is about 1.2 to the 10
+
+ align:start position:0%
+numerical value is about 1.2 to the 10
+ 
+
+ align:start position:0%
+numerical value is about 1.2 to the 10
+to the 19 G
+
+ align:start position:0%
+to the 19 G
+ 
+
+ align:start position:0%
+to the 19 G
+v/ by
+
+ align:start position:0%
+v/ by
+ 
+
+ align:start position:0%
+v/ by
+c² you can also write it in terms of the
+
+ align:start position:0%
+c² you can also write it in terms of the
+ 
+
+ align:start position:0%
+c² you can also write it in terms of the
+gram which is about
+
+ align:start position:0%
+gram which is about
+ 
+
+ align:start position:0%
+gram which is about
+2.2 10 Theus 5 GR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can also have you can also
+
+ align:start position:0%
+and then you can also have you can also
+ 
+
+ align:start position:0%
+and then you can also have you can also
+construct the lens
+
+ align:start position:0%
+construct the lens
+ 
+
+ align:start position:0%
+construct the lens
+scale which is H GN divide C
+
+ align:start position:0%
+scale which is H GN divide C
+ 
+
+ align:start position:0%
+scale which is H GN divide C
+Cube which is about 1.6 to 10 Theus 33
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cm and uh
+
+ align:start position:0%
+cm and uh
+ 
+
+ align:start position:0%
+cm and uh
+PP which is l/ C okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this was discovered so this
+
+ align:start position:0%
+so so this was discovered so this
+ 
+
+ align:start position:0%
+so so this was discovered so this
+was plank introduced them in 19 in 1899
+
+ align:start position:0%
+was plank introduced them in 19 in 1899
+ 
+
+ align:start position:0%
+was plank introduced them in 19 in 1899
+so you may most of you may know the
+
+ align:start position:0%
+so you may most of you may know the
+ 
+
+ align:start position:0%
+so you may most of you may know the
+story and just immediately after he
+
+ align:start position:0%
+story and just immediately after he
+ 
+
+ align:start position:0%
+story and just immediately after he
+introduced HB so so he discovered so
+
+ align:start position:0%
+introduced HB so so he discovered so
+ 
+
+ align:start position:0%
+introduced HB so so he discovered so
+introduced H bar in 1899 in the same
+
+ align:start position:0%
+introduced H bar in 1899 in the same
+ 
+
+ align:start position:0%
+introduced H bar in 1899 in the same
+year he realized you can write down
+
+ align:start position:0%
+year he realized you can write down
+ 
+
+ align:start position:0%
+year he realized you can write down
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+numbers and of course those numbers
+
+ align:start position:0%
+numbers and of course those numbers
+ 
+
+ align:start position:0%
+numbers and of course those numbers
+meant nothing to him because that time
+
+ align:start position:0%
+meant nothing to him because that time
+ 
+
+ align:start position:0%
+meant nothing to him because that time
+we don't know special Rel at that time
+
+ align:start position:0%
+we don't know special Rel at that time
+ 
+
+ align:start position:0%
+we don't know special Rel at that time
+he didn't know special relativity he
+
+ align:start position:0%
+he didn't know special relativity he
+ 
+
+ align:start position:0%
+he didn't know special relativity he
+didn't know quantum mechanics he didn't
+
+ align:start position:0%
+didn't know quantum mechanics he didn't
+ 
+
+ align:start position:0%
+didn't know quantum mechanics he didn't
+he essenti he didn't know
+
+ align:start position:0%
+he essenti he didn't know
+ 
+
+ align:start position:0%
+he essenti he didn't know
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+but but he famously
+
+ align:start position:0%
+but but he famously
+ 
+
+ align:start position:0%
+but but he famously
+said that these
+
+ align:start position:0%
+said that these
+ 
+
+ align:start position:0%
+said that these
+units so he claimed those should be
+
+ align:start position:0%
+units so he claimed those should be
+ 
+
+ align:start position:0%
+units so he claimed those should be
+basic units of
+
+ align:start position:0%
+basic units of
+ 
+
+ align:start position:0%
+basic units of
+physics and he also said these are the
+
+ align:start position:0%
+physics and he also said these are the
+ 
+
+ align:start position:0%
+physics and he also said these are the
+units that would retain the significant
+
+ align:start position:0%
+units that would retain the significant
+ 
+
+ align:start position:0%
+units that would retain the significant
+for all times and all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cultures he even he even said the even
+
+ align:start position:0%
+cultures he even he even said the even
+ 
+
+ align:start position:0%
+cultures he even he even said the even
+will apply to um to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aliens but only after 50 years so after
+
+ align:start position:0%
+aliens but only after 50 years so after
+ 
+
+ align:start position:0%
+aliens but only after 50 years so after
+1950s people uh get some sense so many
+
+ align:start position:0%
+1950s people uh get some sense so many
+ 
+
+ align:start position:0%
+1950s people uh get some sense so many
+years after special
+
+ align:start position:0%
+years after special
+ 
+
+ align:start position:0%
+years after special
+relativity many years after general
+
+ align:start position:0%
+relativity many years after general
+ 
+
+ align:start position:0%
+relativity many years after general
+relativity and also quantum mechanics
+
+ align:start position:0%
+relativity and also quantum mechanics
+ 
+
+ align:start position:0%
+relativity and also quantum mechanics
+Etc
+
+ align:start position:0%
+Etc
+ 
+
+ align:start position:0%
+Etc
+people started grasping the meaning of
+
+ align:start position:0%
+people started grasping the meaning of
+ 
+
+ align:start position:0%
+people started grasping the meaning of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+scales and uh so uh so let me uh briefly
+
+ align:start position:0%
+scales and uh so uh so let me uh briefly
+ 
+
+ align:start position:0%
+scales and uh so uh so let me uh briefly
+review
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so you
+
+ align:start position:0%
+them so you
+ 
+
+ align:start position:0%
+them so you
+can get the feeling of the meaning of
+
+ align:start position:0%
+can get the feeling of the meaning of
+ 
+
+ align:start position:0%
+can get the feeling of the meaning of
+those scales by looking at the strength
+
+ align:start position:0%
+those scales by looking at the strength
+ 
+
+ align:start position:0%
+those scales by looking at the strength
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+gravity so let me first start this
+
+ align:start position:0%
+gravity so let me first start this
+ 
+
+ align:start position:0%
+gravity so let me first start this
+example for
+
+ align:start position:0%
+example for
+ 
+
+ align:start position:0%
+example for
+electromagnetism which you have a
+
+ align:start position:0%
+electromagnetism which you have a
+ 
+
+ align:start position:0%
+electromagnetism which you have a
+potential which is e s/ r okay
+
+ align:start position:0%
+potential which is e s/ r okay
+ 
+
+ align:start position:0%
+potential which is e s/ r okay
+say if you have two charge particle of
+
+ align:start position:0%
+say if you have two charge particle of
+ 
+
+ align:start position:0%
+say if you have two charge particle of
+charge e then the potential between them
+
+ align:start position:0%
+charge e then the potential between them
+ 
+
+ align:start position:0%
+charge e then the potential between them
+is e s/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r and for for particle of mass m then
+
+ align:start position:0%
+r and for for particle of mass m then
+ 
+
+ align:start position:0%
+r and for for particle of mass m then
+you also have competent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wavelength say if you have a particle
+
+ align:start position:0%
+wavelength say if you have a particle
+ 
+
+ align:start position:0%
+wavelength say if you have a particle
+with mass m you also have Conant
+
+ align:start position:0%
+with mass m you also have Conant
+ 
+
+ align:start position:0%
+with mass m you also have Conant
+wavelength each H baride by
+
+ align:start position:0%
+wavelength each H baride by
+ 
+
+ align:start position:0%
+wavelength each H baride by
+MC
+
+ align:start position:0%
+MC
+ 
+
+ align:start position:0%
+MC
+okay so you can get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a rough measure of the
+
+ align:start position:0%
+a rough measure of the
+ 
+
+ align:start position:0%
+a rough measure of the
+strings of
+
+ align:start position:0%
+strings of
+ 
+
+ align:start position:0%
+strings of
+electromagnetism the interaction
+
+ align:start position:0%
+electromagnetism the interaction
+ 
+
+ align:start position:0%
+electromagnetism the interaction
+strength of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electromagnetism by considering the
+
+ align:start position:0%
+electromagnetism by considering the
+ 
+
+ align:start position:0%
+electromagnetism by considering the
+following Dimension is
+
+ align:start position:0%
+following Dimension is
+ 
+
+ align:start position:0%
+following Dimension is
+number so which I call Lambda e which is
+
+ align:start position:0%
+number so which I call Lambda e which is
+ 
+
+ align:start position:0%
+number so which I call Lambda e which is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+evaluated at the minimal in Quantum
+
+ align:start position:0%
+evaluated at the minimal in Quantum
+ 
+
+ align:start position:0%
+evaluated at the minimal in Quantum
+mechanic X essentially this is the
+
+ align:start position:0%
+mechanic X essentially this is the
+ 
+
+ align:start position:0%
+mechanic X essentially this is the
+minimal distance you can make sense
+
+ align:start position:0%
+minimal distance you can make sense
+ 
+
+ align:start position:0%
+minimal distance you can make sense
+of because once you go distance smaller
+
+ align:start position:0%
+of because once you go distance smaller
+ 
+
+ align:start position:0%
+of because once you go distance smaller
+than this you can no longer and and then
+
+ align:start position:0%
+than this you can no longer and and then
+ 
+
+ align:start position:0%
+than this you can no longer and and then
+the quantum uncertainty will create the
+
+ align:start position:0%
+the quantum uncertainty will create the
+ 
+
+ align:start position:0%
+the quantum uncertainty will create the
+energy uncertainty bigger than M you can
+
+ align:start position:0%
+energy uncertainty bigger than M you can
+ 
+
+ align:start position:0%
+energy uncertainty bigger than M you can
+no longer talk about the particle
+
+ align:start position:0%
+no longer talk about the particle
+ 
+
+ align:start position:0%
+no longer talk about the particle
+sensity then you can no longer talk
+
+ align:start position:0%
+sensity then you can no longer talk
+ 
+
+ align:start position:0%
+sensity then you can no longer talk
+about single particle in a sensible way
+
+ align:start position:0%
+about single particle in a sensible way
+ 
+
+ align:start position:0%
+about single particle in a sensible way
+so this is essentially the minimal then
+
+ align:start position:0%
+so this is essentially the minimal then
+ 
+
+ align:start position:0%
+so this is essentially the minimal then
+scale you can talk about single
+
+ align:start position:0%
+scale you can talk about single
+ 
+
+ align:start position:0%
+scale you can talk about single
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+so so this is essentially some energy
+
+ align:start position:0%
+so so this is essentially some energy
+ 
+
+ align:start position:0%
+so so this is essentially some energy
+scale so you can compare this to the say
+
+ align:start position:0%
+scale so you can compare this to the say
+ 
+
+ align:start position:0%
+scale so you can compare this to the say
+the static mass of the particle so this
+
+ align:start position:0%
+the static mass of the particle so this
+ 
+
+ align:start position:0%
+the static mass of the particle so this
+give you a a measure of the strength of
+
+ align:start position:0%
+give you a a measure of the strength of
+ 
+
+ align:start position:0%
+give you a a measure of the strength of
+the electrom
+
+ align:start position:0%
+the electrom
+ 
+
+ align:start position:0%
+the electrom
+magnetism of course if you plug this in
+
+ align:start position:0%
+magnetism of course if you plug this in
+ 
+
+ align:start position:0%
+magnetism of course if you plug this in
+you just get e s / H+ C and of course we
+
+ align:start position:0%
+you just get e s / H+ C and of course we
+ 
+
+ align:start position:0%
+you just get e s / H+ C and of course we
+know this is the fine structure constant
+
+ align:start position:0%
+know this is the fine structure constant
+ 
+
+ align:start position:0%
+know this is the fine structure constant
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+indeed the the
+
+ align:start position:0%
+indeed the the
+ 
+
+ align:start position:0%
+indeed the the
+coupling say you would do um indeed is
+
+ align:start position:0%
+coupling say you would do um indeed is
+ 
+
+ align:start position:0%
+coupling say you would do um indeed is
+the coupling Q okay so you can do the
+
+ align:start position:0%
+the coupling Q okay so you can do the
+ 
+
+ align:start position:0%
+the coupling Q okay so you can do the
+same thing for
+
+ align:start position:0%
+same thing for
+ 
+
+ align:start position:0%
+same thing for
+Gravity so you can do the same thing for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gravity so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gravity we have essentially
+
+ align:start position:0%
+Gravity we have essentially
+ 
+
+ align:start position:0%
+Gravity we have essentially
+G and say if you take two particle of
+
+ align:start position:0%
+G and say if you take two particle of
+ 
+
+ align:start position:0%
+G and say if you take two particle of
+mass m
+
+ align:start position:0%
+mass m
+ 
+
+ align:start position:0%
+mass m
+then then then the potential between
+
+ align:start position:0%
+then then then the potential between
+ 
+
+ align:start position:0%
+then then then the potential between
+them is GM m² /
+
+ align:start position:0%
+them is GM m² /
+ 
+
+ align:start position:0%
+them is GM m² /
+R and then again you can Define
+
+ align:start position:0%
+R and then again you can Define
+ 
+
+ align:start position:0%
+R and then again you can Define
+effective strength for the Gravity by
+
+ align:start position:0%
+effective strength for the Gravity by
+ 
+
+ align:start position:0%
+effective strength for the Gravity by
+evaluate this potential at compant wave
+
+ align:start position:0%
+evaluate this potential at compant wave
+ 
+
+ align:start position:0%
+evaluate this potential at compant wave
+lens divided by the static energy of the
+
+ align:start position:0%
+lens divided by the static energy of the
+ 
+
+ align:start position:0%
+lens divided by the static energy of the
+particle and then you can just plug this
+
+ align:start position:0%
+particle and then you can just plug this
+ 
+
+ align:start position:0%
+particle and then you can just plug this
+in so so this is GN m² / by h bar / by
+
+ align:start position:0%
+in so so this is GN m² / by h bar / by
+ 
+
+ align:start position:0%
+in so so this is GN m² / by h bar / by
+MC then / by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mc² and then you find this is just equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to this is equal to
+
+ align:start position:0%
+to this is equal to
+ 
+
+ align:start position:0%
+to this is equal to
+GN m² divided by H Bar
+
+ align:start position:0%
+GN m² divided by H Bar
+ 
+
+ align:start position:0%
+GN m² divided by H Bar
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+okay so now if you
+
+ align:start position:0%
+okay so now if you
+ 
+
+ align:start position:0%
+okay so now if you
+compare with this
+
+ align:start position:0%
+compare with this
+ 
+
+ align:start position:0%
+compare with this
+equation so so this is just given by m
+
+ align:start position:0%
+equation so so this is just given by m
+ 
+
+ align:start position:0%
+equation so so this is just given by m
+Square MP
+
+ align:start position:0%
+Square MP
+ 
+
+ align:start position:0%
+Square MP
+s okay so for
+
+ align:start position:0%
+s okay so for
+ 
+
+ align:start position:0%
+s okay so for
+Gravity this effective
+
+ align:start position:0%
+Gravity this effective
+ 
+
+ align:start position:0%
+Gravity this effective
+strength is just given by the mass of
+
+ align:start position:0%
+strength is just given by the mass of
+ 
+
+ align:start position:0%
+strength is just given by the mass of
+the particle so because for Gravity the
+
+ align:start position:0%
+the particle so because for Gravity the
+ 
+
+ align:start position:0%
+the particle so because for Gravity the
+Mass is like some kind of effective
+
+ align:start position:0%
+Mass is like some kind of effective
+ 
+
+ align:start position:0%
+Mass is like some kind of effective
+charge and divided by plank scale this
+
+ align:start position:0%
+charge and divided by plank scale this
+ 
+
+ align:start position:0%
+charge and divided by plank scale this
+plank mass square
+
+ align:start position:0%
+plank mass square
+ 
+
+ align:start position:0%
+plank mass square
+okay and you can also write
+
+ align:start position:0%
+okay and you can also write
+ 
+
+ align:start position:0%
+okay and you can also write
+it you can also write it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as LP
+
+ align:start position:0%
+as LP
+ 
+
+ align:start position:0%
+as LP
+s divided by RC
+
+ align:start position:0%
+s divided by RC
+ 
+
+ align:start position:0%
+s divided by RC
+sare or or just as this plank
+
+ align:start position:0%
+sare or or just as this plank
+ 
+
+ align:start position:0%
+sare or or just as this plank
+lens divided by component wavelength of
+
+ align:start position:0%
+lens divided by component wavelength of
+ 
+
+ align:start position:0%
+lens divided by component wavelength of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+okay so for most Elementary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles so so for typical Elementary
+
+ align:start position:0%
+particles so so for typical Elementary
+ 
+
+ align:start position:0%
+particles so so for typical Elementary
+particles we know the m is always much
+
+ align:start position:0%
+particles we know the m is always much
+ 
+
+ align:start position:0%
+particles we know the m is always much
+smaller than MP
+
+ align:start position:0%
+smaller than MP
+ 
+
+ align:start position:0%
+smaller than MP
+okay and then the Lambda G will be
+
+ align:start position:0%
+okay and then the Lambda G will be
+ 
+
+ align:start position:0%
+okay and then the Lambda G will be
+typically much smaller than
+
+ align:start position:0%
+typically much smaller than
+ 
+
+ align:start position:0%
+typically much smaller than
+one so for
+
+ align:start position:0%
+one so for
+ 
+
+ align:start position:0%
+one so for
+example say if you can see the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron the electron Mass would be say
+
+ align:start position:0%
+electron the electron Mass would be say
+ 
+
+ align:start position:0%
+electron the electron Mass would be say
+5 to the 10 Theus 4 G v/
+
+ align:start position:0%
+5 to the 10 Theus 4 G v/
+ 
+
+ align:start position:0%
+5 to the 10 Theus 4 G v/
+c² of course this is much smaller than
+
+ align:start position:0%
+c² of course this is much smaller than
+ 
+
+ align:start position:0%
+c² of course this is much smaller than
+this plankk
+
+ align:start position:0%
+this plankk
+ 
+
+ align:start position:0%
+this plankk
+mass and then you find this ratio
+
+ align:start position:0%
+mass and then you find this ratio
+ 
+
+ align:start position:0%
+mass and then you find this ratio
+so you can work out this ratio so let's
+
+ align:start position:0%
+so you can work out this ratio so let's
+ 
+
+ align:start position:0%
+so you can work out this ratio so let's
+compare it to the to the corresponding
+
+ align:start position:0%
+compare it to the to the corresponding
+ 
+
+ align:start position:0%
+compare it to the to the corresponding
+strings for the
+
+ align:start position:0%
+strings for the
+ 
+
+ align:start position:0%
+strings for the
+electromagnetic so this is about 10
+
+ align:start position:0%
+electromagnetic so this is about 10
+ 
+
+ align:start position:0%
+electromagnetic so this is about 10
+Theus
+
+ align:start position:0%
+Theus
+ 
+
+ align:start position:0%
+Theus
+43 if you work this
+
+ align:start position:0%
+43 if you work this
+ 
+
+ align:start position:0%
+43 if you work this
+out okay so this tells you the gravity
+
+ align:start position:0%
+out okay so this tells you the gravity
+ 
+
+ align:start position:0%
+out okay so this tells you the gravity
+is really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weak so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ordinary Elementary
+
+ align:start position:0%
+Ordinary Elementary
+ 
+
+ align:start position:0%
+Ordinary Elementary
+particles so the gravity is really weak
+
+ align:start position:0%
+particles so the gravity is really weak
+ 
+
+ align:start position:0%
+particles so the gravity is really weak
+and so so we can forget all about
+
+ align:start position:0%
+and so so we can forget all about
+ 
+
+ align:start position:0%
+and so so we can forget all about
+gravity
+
+ align:start position:0%
+gravity
+ 
+
+ align:start position:0%
+gravity
+until you reach the plank
+
+ align:start position:0%
+until you reach the plank
+ 
+
+ align:start position:0%
+until you reach the plank
+Mass all your compant wavelengths reach
+
+ align:start position:0%
+Mass all your compant wavelengths reach
+ 
+
+ align:start position:0%
+Mass all your compant wavelengths reach
+the plank lens and then um then the
+
+ align:start position:0%
+the plank lens and then um then the
+ 
+
+ align:start position:0%
+the plank lens and then um then the
+gravity then effect of the quantum
+
+ align:start position:0%
+gravity then effect of the quantum
+ 
+
+ align:start position:0%
+gravity then effect of the quantum
+gravity will be
+
+ align:start position:0%
+gravity will be
+ 
+
+ align:start position:0%
+gravity will be
+important so so from this exercise we
+
+ align:start position:0%
+important so so from this exercise we
+ 
+
+ align:start position:0%
+important so so from this exercise we
+know that the MP is the energy scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the effective gravity strengths
+
+ align:start position:0%
+that the effective gravity strengths
+ 
+
+ align:start position:0%
+that the effective gravity strengths
+become of order
+
+ align:start position:0%
+become of order
+ 
+
+ align:start position:0%
+become of order
+one come of order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that
+
+ align:start position:0%
+one that
+ 
+
+ align:start position:0%
+one that
+is quantum gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effect become significant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh and similarly so so
+
+ align:start position:0%
+okay and uh and similarly so so
+ 
+
+ align:start position:0%
+okay and uh and similarly so so
+a is the corresponding lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale associate with such energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this give you a
+
+ align:start position:0%
+okay so this give you a
+ 
+
+ align:start position:0%
+okay so this give you a
+heris fit in
+
+ align:start position:0%
+heris fit in
+ 
+
+ align:start position:0%
+heris fit in
+give you her istic
+
+ align:start position:0%
+give you her istic
+ 
+
+ align:start position:0%
+give you her istic
+indication that the meaning of those
+
+ align:start position:0%
+indication that the meaning of those
+ 
+
+ align:start position:0%
+indication that the meaning of those
+plank scales
+
+ align:start position:0%
+plank scales
+ 
+
+ align:start position:0%
+plank scales
+okay so there's another important scale
+
+ align:start position:0%
+okay so there's another important scale
+ 
+
+ align:start position:0%
+okay so there's another important scale
+associate with
+
+ align:start position:0%
+associate with
+ 
+
+ align:start position:0%
+associate with
+gravity so any questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this good there's another important
+
+ align:start position:0%
+this good there's another important
+ 
+
+ align:start position:0%
+this good there's another important
+scale associated with gravity it's
+
+ align:start position:0%
+scale associated with gravity it's
+ 
+
+ align:start position:0%
+scale associated with gravity it's
+called swal radius
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I should
+
+ align:start position:0%
+so I should
+ 
+
+ align:start position:0%
+so I should
+radius so the just from dimensional
+
+ align:start position:0%
+radius so the just from dimensional
+ 
+
+ align:start position:0%
+radius so the just from dimensional
+lysis the stral radius can be argued as
+
+ align:start position:0%
+lysis the stral radius can be argued as
+ 
+
+ align:start position:0%
+lysis the stral radius can be argued as
+follows so consider again we can just uh
+
+ align:start position:0%
+follows so consider again we can just uh
+ 
+
+ align:start position:0%
+follows so consider again we can just uh
+even see it from Newtonian
+
+ align:start position:0%
+even see it from Newtonian
+ 
+
+ align:start position:0%
+even see it from Newtonian
+gravity so say let's consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m okay
+
+ align:start position:0%
+m okay
+ 
+
+ align:start position:0%
+m okay
+then we
+
+ align:start position:0%
+then we
+ 
+
+ align:start position:0%
+then we
+ask then we ask
+
+ align:start position:0%
+ask then we ask
+ 
+
+ align:start position:0%
+ask then we ask
+what is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance at what distance maybe I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should at what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it the classical gravity becomes strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so for this purpose let's consider say a
+
+ align:start position:0%
+so for this purpose let's consider say a
+ 
+
+ align:start position:0%
+so for this purpose let's consider say a
+pro Mass say m
+
+ align:start position:0%
+pro Mass say m
+ 
+
+ align:start position:0%
+pro Mass say m
+Prime so can see the pro Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I Define a scale which I call r
+
+ align:start position:0%
+okay so I Define a scale which I call r
+ 
+
+ align:start position:0%
+okay so I Define a scale which I call r
+s is I require the potential energy
+
+ align:start position:0%
+s is I require the potential energy
+ 
+
+ align:start position:0%
+s is I require the potential energy
+between M and M Prime at such a scale r
+
+ align:start position:0%
+between M and M Prime at such a scale r
+ 
+
+ align:start position:0%
+between M and M Prime at such a scale r
+s then this become of
+
+ align:start position:0%
+s then this become of
+ 
+
+ align:start position:0%
+s then this become of
+order say the again the energy the
+
+ align:start position:0%
+order say the again the energy the
+ 
+
+ align:start position:0%
+order say the again the energy the
+static energy of this probe
+
+ align:start position:0%
+static energy of this probe
+ 
+
+ align:start position:0%
+static energy of this probe
+particle of this probe
+
+ align:start position:0%
+particle of this probe
+ 
+
+ align:start position:0%
+particle of this probe
+Mass so if you cancel things out then
+
+ align:start position:0%
+Mass so if you cancel things out then
+ 
+
+ align:start position:0%
+Mass so if you cancel things out then
+you find is s is of order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+GM m /
+
+ align:start position:0%
+GM m /
+ 
+
+ align:start position:0%
+GM m /
+c²
+
+ align:start position:0%
+c²
+ 
+
+ align:start position:0%
+c²
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this give you a a
+
+ align:start position:0%
+so so this give you a a
+ 
+
+ align:start position:0%
+so so this give you a a
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um uh give you a scale you can also ask
+
+ align:start position:0%
+um uh give you a scale you can also ask
+ 
+
+ align:start position:0%
+um uh give you a scale you can also ask
+so this is from neonian
+
+ align:start position:0%
+so this is from neonian
+ 
+
+ align:start position:0%
+so this is from neonian
+gravity of course the um when your
+
+ align:start position:0%
+gravity of course the um when your
+ 
+
+ align:start position:0%
+gravity of course the um when your
+gravity becomes strong uh you should
+
+ align:start position:0%
+gravity becomes strong uh you should
+ 
+
+ align:start position:0%
+gravity becomes strong uh you should
+replace the ding Gravity by by Einstein
+
+ align:start position:0%
+replace the ding Gravity by by Einstein
+ 
+
+ align:start position:0%
+replace the ding Gravity by by Einstein
+relativity and when you go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relativity when you go to relativity
+
+ align:start position:0%
+relativity when you go to relativity
+ 
+
+ align:start position:0%
+relativity when you go to relativity
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+relativity then you find then this swal
+
+ align:start position:0%
+relativity then you find then this swal
+ 
+
+ align:start position:0%
+relativity then you find then this swal
+radius so uh this saral radius which
+
+ align:start position:0%
+radius so uh this saral radius which
+ 
+
+ align:start position:0%
+radius so uh this saral radius which
+given by 2
+
+ align:start position:0%
+given by 2
+ 
+
+ align:start position:0%
+given by 2
+gmid by
+
+ align:start position:0%
+gmid by
+ 
+
+ align:start position:0%
+gmid by
+c² which corresponding to the side of a
+
+ align:start position:0%
+c² which corresponding to the side of a
+ 
+
+ align:start position:0%
+c² which corresponding to the side of a
+black hole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay corresponding to the Sid of a black
+
+ align:start position:0%
+okay corresponding to the Sid of a black
+ 
+
+ align:start position:0%
+okay corresponding to the Sid of a black
+ho so this is a classical scale purely
+
+ align:start position:0%
+ho so this is a classical scale purely
+ 
+
+ align:start position:0%
+ho so this is a classical scale purely
+classical Gale just the scale which the
+
+ align:start position:0%
+classical Gale just the scale which the
+ 
+
+ align:start position:0%
+classical Gale just the scale which the
+classical gravity becomes
+
+ align:start position:0%
+classical gravity becomes
+ 
+
+ align:start position:0%
+classical gravity becomes
+strong and in
+
+ align:start position:0%
+strong and in
+ 
+
+ align:start position:0%
+strong and in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+RS can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+considered as the minimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale one can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pro a par an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object of mass
+
+ align:start position:0%
+object of mass
+ 
+
+ align:start position:0%
+object of mass
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so classically black absorb everything
+
+ align:start position:0%
+so classically black absorb everything
+ 
+
+ align:start position:0%
+so classically black absorb everything
+so once you four into black ho you can
+
+ align:start position:0%
+so once you four into black ho you can
+ 
+
+ align:start position:0%
+so once you four into black ho you can
+never come
+
+ align:start position:0%
+never come
+ 
+
+ align:start position:0%
+never come
+back and uh so so the minimal distance
+
+ align:start position:0%
+back and uh so so the minimal distance
+ 
+
+ align:start position:0%
+back and uh so so the minimal distance
+you can uh approach a and object of mass
+
+ align:start position:0%
+you can uh approach a and object of mass
+ 
+
+ align:start position:0%
+you can uh approach a and object of mass
+m it just given by the SWAT your radius
+
+ align:start position:0%
+m it just given by the SWAT your radius
+ 
+
+ align:start position:0%
+m it just given by the SWAT your radius
+so when you go inside SWAT your radius
+
+ align:start position:0%
+so when you go inside SWAT your radius
+ 
+
+ align:start position:0%
+so when you go inside SWAT your radius
+you just fall into the black ho and you
+
+ align:start position:0%
+you just fall into the black ho and you
+ 
+
+ align:start position:0%
+you just fall into the black ho and you
+can never send information out
+
+ align:start position:0%
+can never send information out
+ 
+
+ align:start position:0%
+can never send information out
+okay and the why interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compare yeah one thing regarding this
+
+ align:start position:0%
+compare yeah one thing regarding this
+ 
+
+ align:start position:0%
+compare yeah one thing regarding this
+wasal radius you said raal radius
+
+ align:start position:0%
+wasal radius you said raal radius
+ 
+
+ align:start position:0%
+wasal radius you said raal radius
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+with mass okay if you increase Mass the
+
+ align:start position:0%
+with mass okay if you increase Mass the
+ 
+
+ align:start position:0%
+with mass okay if you increase Mass the
+spal radius
+
+ align:start position:0%
+spal radius
+ 
+
+ align:start position:0%
+spal radius
+increases okay so in principle can be
+
+ align:start position:0%
+increases okay so in principle can be
+ 
+
+ align:start position:0%
+increases okay so in principle can be
+very large uh when you can see the very
+
+ align:start position:0%
+very large uh when you can see the very
+ 
+
+ align:start position:0%
+very large uh when you can see the very
+large object when you can see the very
+
+ align:start position:0%
+large object when you can see the very
+ 
+
+ align:start position:0%
+large object when you can see the very
+massive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object so now so let us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+summarize let us
+
+ align:start position:0%
+summarize let us
+ 
+
+ align:start position:0%
+summarize let us
+summarize so for for object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m there are two important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scales two important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scales so why is just the standard
+
+ align:start position:0%
+scales so why is just the standard
+ 
+
+ align:start position:0%
+scales so why is just the standard
+compon wavelength
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the other is the swal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radius okay so one is quantum and the
+
+ align:start position:0%
+radius okay so one is quantum and the
+ 
+
+ align:start position:0%
+radius okay so one is quantum and the
+other is
+
+ align:start position:0%
+other is
+ 
+
+ align:start position:0%
+other is
+classical yeah the classical so let's
+
+ align:start position:0%
+classical yeah the classical so let's
+ 
+
+ align:start position:0%
+classical yeah the classical so let's
+take the ratio between them okay let's
+
+ align:start position:0%
+take the ratio between them okay let's
+ 
+
+ align:start position:0%
+take the ratio between them okay let's
+take the ratio between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so if you take the ratio between
+
+ align:start position:0%
+them so if you take the ratio between
+ 
+
+ align:start position:0%
+them so if you take the ratio between
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so um yeah so so let's forget about this
+
+ align:start position:0%
+so um yeah so so let's forget about this
+ 
+
+ align:start position:0%
+so um yeah so so let's forget about this
+two just to consider of
+
+ align:start position:0%
+two just to consider of
+ 
+
+ align:start position:0%
+two just to consider of
+order up to order one so c² / H baride
+
+ align:start position:0%
+order up to order one so c² / H baride
+ 
+
+ align:start position:0%
+order up to order one so c² / H baride
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+MC and then this again give
+
+ align:start position:0%
+MC and then this again give
+ 
+
+ align:start position:0%
+MC and then this again give
+you GM
+
+ align:start position:0%
+you GM
+ 
+
+ align:start position:0%
+you GM
+m² divided by H Bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C and this is
+
+ align:start position:0%
+C and this is
+ 
+
+ align:start position:0%
+C and this is
+again just m² / m p
+
+ align:start position:0%
+again just m² / m p
+ 
+
+ align:start position:0%
+again just m² / m p
+sare
+
+ align:start position:0%
+sare
+ 
+
+ align:start position:0%
+sare
+okay this again just m Square MP Square
+
+ align:start position:0%
+okay this again just m Square MP Square
+ 
+
+ align:start position:0%
+okay this again just m Square MP Square
+MP is the plankk
+
+ align:start position:0%
+MP is the plankk
+ 
+
+ align:start position:0%
+MP is the plankk
+mass so so let's consider the different
+
+ align:start position:0%
+mass so so let's consider the different
+ 
+
+ align:start position:0%
+mass so so let's consider the different
+scenarios so the first let's consider
+
+ align:start position:0%
+scenarios so the first let's consider
+ 
+
+ align:start position:0%
+scenarios so the first let's consider
+just suppose the mass of the object is
+
+ align:start position:0%
+just suppose the mass of the object is
+ 
+
+ align:start position:0%
+just suppose the mass of the object is
+much much greater than
+
+ align:start position:0%
+much much greater than
+ 
+
+ align:start position:0%
+much much greater than
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+okay so in this
+
+ align:start position:0%
+okay so in this
+ 
+
+ align:start position:0%
+okay so in this
+case then the swal radius much ner than
+
+ align:start position:0%
+case then the swal radius much ner than
+ 
+
+ align:start position:0%
+case then the swal radius much ner than
+the compant wavelength
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much larger than the comant
+
+ align:start position:0%
+much larger than the comant
+ 
+
+ align:start position:0%
+much larger than the comant
+wavelength and essentially all the
+
+ align:start position:0%
+wavelength and essentially all the
+ 
+
+ align:start position:0%
+wavelength and essentially all the
+physics is controlled by the classical
+
+ align:start position:0%
+physics is controlled by the classical
+ 
+
+ align:start position:0%
+physics is controlled by the classical
+gravity because you can because you can
+
+ align:start position:0%
+gravity because you can because you can
+ 
+
+ align:start position:0%
+gravity because you can because you can
+no longer because you can no longer Pro
+
+ align:start position:0%
+no longer because you can no longer Pro
+ 
+
+ align:start position:0%
+no longer because you can no longer Pro
+yeah because this compant wavelength is
+
+ align:start position:0%
+yeah because this compant wavelength is
+ 
+
+ align:start position:0%
+yeah because this compant wavelength is
+much much inside the swash radius which
+
+ align:start position:0%
+much much inside the swash radius which
+ 
+
+ align:start position:0%
+much much inside the swash radius which
+you cannot prob okay so the physic is
+
+ align:start position:0%
+you cannot prob okay so the physic is
+ 
+
+ align:start position:0%
+you cannot prob okay so the physic is
+essentially classical gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and the um Quantum effect fact
+
+ align:start position:0%
+and uh and the um Quantum effect fact
+ 
+
+ align:start position:0%
+and uh and the um Quantum effect fact
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+important so you don't have to worry
+
+ align:start position:0%
+important so you don't have to worry
+ 
+
+ align:start position:0%
+important so you don't have to worry
+about the quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effect so I will put code
+
+ align:start position:0%
+effect so I will put code
+ 
+
+ align:start position:0%
+effect so I will put code
+here uh uh not code I will put some uh
+
+ align:start position:0%
+here uh uh not code I will put some uh
+ 
+
+ align:start position:0%
+here uh uh not code I will put some uh
+yeah put some code here uh just to yeah
+
+ align:start position:0%
+yeah put some code here uh just to yeah
+ 
+
+ align:start position:0%
+yeah put some code here uh just to yeah
+you will see what this means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the second possibility is for Mass
+
+ align:start position:0%
+and the second possibility is for Mass
+ 
+
+ align:start position:0%
+and the second possibility is for Mass
+much much smaller than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P so in this case then the compant
+
+ align:start position:0%
+P so in this case then the compant
+ 
+
+ align:start position:0%
+P so in this case then the compant
+wavelength will be much much greater
+
+ align:start position:0%
+wavelength will be much much greater
+ 
+
+ align:start position:0%
+wavelength will be much much greater
+than the the swater
+
+ align:start position:0%
+than the the swater
+ 
+
+ align:start position:0%
+than the the swater
+radius okay so this is a Quantum object
+
+ align:start position:0%
+radius okay so this is a Quantum object
+ 
+
+ align:start position:0%
+radius okay so this is a Quantum object
+so the quantum size is much larger than
+
+ align:start position:0%
+so the quantum size is much larger than
+ 
+
+ align:start position:0%
+so the quantum size is much larger than
+S
+
+ align:start position:0%
+S
+ 
+
+ align:start position:0%
+S
+radius but we also know precisely in
+
+ align:start position:0%
+radius but we also know precisely in
+ 
+
+ align:start position:0%
+radius but we also know precisely in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this Lambda G is also very small the
+
+ align:start position:0%
+this Lambda G is also very small the
+ 
+
+ align:start position:0%
+this Lambda G is also very small the
+effective strength of the gravity is
+
+ align:start position:0%
+effective strength of the gravity is
+ 
+
+ align:start position:0%
+effective strength of the gravity is
+also very very
+
+ align:start position:0%
+also very very
+ 
+
+ align:start position:0%
+also very very
+small so we also have found before that
+
+ align:start position:0%
+small so we also have found before that
+ 
+
+ align:start position:0%
+small so we also have found before that
+the Lambda G is also very very
+
+ align:start position:0%
+the Lambda G is also very very
+ 
+
+ align:start position:0%
+the Lambda G is also very very
+small so in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case as what we said here the gravity is
+
+ align:start position:0%
+case as what we said here the gravity is
+ 
+
+ align:start position:0%
+case as what we said here the gravity is
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weak and notot important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's much much weaker than other
+
+ align:start position:0%
+it's much much weaker than other
+ 
+
+ align:start position:0%
+it's much much weaker than other
+interactions so you can essentially
+
+ align:start position:0%
+interactions so you can essentially
+ 
+
+ align:start position:0%
+interactions so you can essentially
+ignore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them then then that only left with this
+
+ align:start position:0%
+them then then that only left with this
+ 
+
+ align:start position:0%
+them then then that only left with this
+single Square which mass is off all the
+
+ align:start position:0%
+single Square which mass is off all the
+ 
+
+ align:start position:0%
+single Square which mass is off all the
+MP and then as we said before the
+
+ align:start position:0%
+MP and then as we said before the
+ 
+
+ align:start position:0%
+MP and then as we said before the
+quantum gravity is important so let me
+
+ align:start position:0%
+quantum gravity is important so let me
+ 
+
+ align:start position:0%
+quantum gravity is important so let me
+just say quantum gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If This Were the full
+
+ align:start position:0%
+If This Were the full
+ 
+
+ align:start position:0%
+If This Were the full
+story then the life will be very boring
+
+ align:start position:0%
+story then the life will be very boring
+ 
+
+ align:start position:0%
+story then the life will be very boring
+even though it would be very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple because then the only scale you
+
+ align:start position:0%
+simple because then the only scale you
+ 
+
+ align:start position:0%
+simple because then the only scale you
+need to worry about quantum
+
+ align:start position:0%
+need to worry about quantum
+ 
+
+ align:start position:0%
+need to worry about quantum
+gravity is essentially matal zero it's
+
+ align:start position:0%
+gravity is essentially matal zero it's
+ 
+
+ align:start position:0%
+gravity is essentially matal zero it's
+only one
+
+ align:start position:0%
+only one
+ 
+
+ align:start position:0%
+only one
+scale and it will took us maybe 100 if
+
+ align:start position:0%
+scale and it will took us maybe 100 if
+ 
+
+ align:start position:0%
+scale and it will took us maybe 100 if
+not thousand years to reach that scale
+
+ align:start position:0%
+not thousand years to reach that scale
+ 
+
+ align:start position:0%
+not thousand years to reach that scale
+but whatever acceleration or other
+
+ align:start position:0%
+but whatever acceleration or other
+ 
+
+ align:start position:0%
+but whatever acceleration or other
+propes and so there's really low urgency
+
+ align:start position:0%
+propes and so there's really low urgency
+ 
+
+ align:start position:0%
+propes and so there's really low urgency
+to think about the quantum
+
+ align:start position:0%
+to think about the quantum
+ 
+
+ align:start position:0%
+to think about the quantum
+gravity because the um yeah right now we
+
+ align:start position:0%
+gravity because the um yeah right now we
+ 
+
+ align:start position:0%
+gravity because the um yeah right now we
+are at this kind of scale right now we
+
+ align:start position:0%
+are at this kind of scale right now we
+ 
+
+ align:start position:0%
+are at this kind of scale right now we
+are at this kind of scale it's very very
+
+ align:start position:0%
+are at this kind of scale it's very very
+ 
+
+ align:start position:0%
+are at this kind of scale it's very very
+far from this kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale but the remarkable
+
+ align:start position:0%
+scale but the remarkable
+ 
+
+ align:start position:0%
+scale but the remarkable
+thing about black
+
+ align:start position:0%
+thing about black
+ 
+
+ align:start position:0%
+thing about black
+hole so this part of the physics is
+
+ align:start position:0%
+hole so this part of the physics is
+ 
+
+ align:start position:0%
+hole so this part of the physics is
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+controlled Say by swal read because the
+
+ align:start position:0%
+controlled Say by swal read because the
+ 
+
+ align:start position:0%
+controlled Say by swal read because the
+S radius is the
+
+ align:start position:0%
+S radius is the
+ 
+
+ align:start position:0%
+S radius is the
+minimal classical radius you
+
+ align:start position:0%
+minimal classical radius you
+ 
+
+ align:start position:0%
+minimal classical radius you
+can you can achieve uh yeah you can you
+
+ align:start position:0%
+can you can achieve uh yeah you can you
+ 
+
+ align:start position:0%
+can you can achieve uh yeah you can you
+can probe the system and the quantum
+
+ align:start position:0%
+can probe the system and the quantum
+ 
+
+ align:start position:0%
+can probe the system and the quantum
+physics is
+
+ align:start position:0%
+physics is
+ 
+
+ align:start position:0%
+physics is
+relevant but the remarkable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing is that it turns out this
+
+ align:start position:0%
+thing is that it turns out this
+ 
+
+ align:start position:0%
+thing is that it turns out this
+statement is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct this statement is not correct
+
+ align:start position:0%
+correct this statement is not correct
+ 
+
+ align:start position:0%
+correct this statement is not correct
+actually Quantum effect is
+
+ align:start position:0%
+actually Quantum effect is
+ 
+
+ align:start position:0%
+actually Quantum effect is
+important so the remarkable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing you said the black
+
+ align:start position:0%
+thing you said the black
+ 
+
+ align:start position:0%
+thing you said the black
+ho can have Quantum effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manifest at the microscopic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level so at then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale of
+
+ align:start position:0%
+scale of
+ 
+
+ align:start position:0%
+scale of
+order SW your radius okay so that's why
+
+ align:start position:0%
+order SW your radius okay so that's why
+ 
+
+ align:start position:0%
+order SW your radius okay so that's why
+it makes the black hole so
+
+ align:start position:0%
+it makes the black hole so
+ 
+
+ align:start position:0%
+it makes the black hole so
+interesting and also makes the why black
+
+ align:start position:0%
+interesting and also makes the why black
+ 
+
+ align:start position:0%
+interesting and also makes the why black
+ho is such a rich
+
+ align:start position:0%
+ho is such a rich
+ 
+
+ align:start position:0%
+ho is such a rich
+source of insight and information if you
+
+ align:start position:0%
+source of insight and information if you
+ 
+
+ align:start position:0%
+source of insight and information if you
+want to know about quantum
+
+ align:start position:0%
+want to know about quantum
+ 
+
+ align:start position:0%
+want to know about quantum
+gravity and as we will see actually we
+
+ align:start position:0%
+gravity and as we will see actually we
+ 
+
+ align:start position:0%
+gravity and as we will see actually we
+also contain a rich source information
+
+ align:start position:0%
+also contain a rich source information
+ 
+
+ align:start position:0%
+also contain a rich source information
+about ordinary manying body systems due
+
+ align:start position:0%
+about ordinary manying body systems due
+ 
+
+ align:start position:0%
+about ordinary manying body systems due
+to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Duality any questions regarding
+
+ align:start position:0%
+Duality any questions regarding
+ 
+
+ align:start position:0%
+Duality any questions regarding
+this yes so when we talk about M much
+
+ align:start position:0%
+this yes so when we talk about M much
+ 
+
+ align:start position:0%
+this yes so when we talk about M much
+larger than MP so the m is not only a
+
+ align:start position:0%
+larger than MP so the m is not only a
+ 
+
+ align:start position:0%
+larger than MP so the m is not only a
+elementary particle it can be just an
+
+ align:start position:0%
+elementary particle it can be just an
+ 
+
+ align:start position:0%
+elementary particle it can be just an
+object yeah yeah but if it can be a
+
+ align:start position:0%
+object yeah yeah but if it can be a
+ 
+
+ align:start position:0%
+object yeah yeah but if it can be a
+bound state so it can be a here we
+
+ align:start position:0%
+bound state so it can be a here we
+ 
+
+ align:start position:0%
+bound state so it can be a here we
+always talking about Quantum object Say
+
+ align:start position:0%
+always talking about Quantum object Say
+ 
+
+ align:start position:0%
+always talking about Quantum object Say
+Say Yeah Quantum object but can have
+
+ align:start position:0%
+Say Yeah Quantum object but can have
+ 
+
+ align:start position:0%
+Say Yeah Quantum object but can have
+mass very large that's still and Quantum
+
+ align:start position:0%
+mass very large that's still and Quantum
+ 
+
+ align:start position:0%
+mass very large that's still and Quantum
+object yeah but but you will not see
+
+ align:start position:0%
+object yeah but but you will not see
+ 
+
+ align:start position:0%
+object yeah but but you will not see
+from the from a traditional way for such
+
+ align:start position:0%
+from the from a traditional way for such
+ 
+
+ align:start position:0%
+from the from a traditional way for such
+a large mass object you will not see its
+
+ align:start position:0%
+a large mass object you will not see its
+ 
+
+ align:start position:0%
+a large mass object you will not see its
+of quantum uncertainty because Quantum
+
+ align:start position:0%
+of quantum uncertainty because Quantum
+ 
+
+ align:start position:0%
+of quantum uncertainty because Quantum
+uncertainty is Tiny the contant
+
+ align:start position:0%
+uncertainty is Tiny the contant
+ 
+
+ align:start position:0%
+uncertainty is Tiny the contant
+wavelength is very tiny so the
+
+ align:start position:0%
+wavelength is very tiny so the
+ 
+
+ align:start position:0%
+wavelength is very tiny so the
+fluctuation is very small and so you
+
+ align:start position:0%
+fluctuation is very small and so you
+ 
+
+ align:start position:0%
+fluctuation is very small and so you
+have to Pro very very small lens scale
+
+ align:start position:0%
+have to Pro very very small lens scale
+ 
+
+ align:start position:0%
+have to Pro very very small lens scale
+to see it's content from traditional
+
+ align:start position:0%
+to see it's content from traditional
+ 
+
+ align:start position:0%
+to see it's content from traditional
+point of view you have to Pro very very
+
+ align:start position:0%
+point of view you have to Pro very very
+ 
+
+ align:start position:0%
+point of view you have to Pro very very
+small lens scale to to see it quantum
+
+ align:start position:0%
+small lens scale to to see it quantum
+ 
+
+ align:start position:0%
+small lens scale to to see it quantum
+fluctuations and that lens scale is much
+
+ align:start position:0%
+fluctuations and that lens scale is much
+ 
+
+ align:start position:0%
+fluctuations and that lens scale is much
+much smaller than SWAT your radius okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah any another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question good so let me before we talk
+
+ align:start position:0%
+question good so let me before we talk
+ 
+
+ align:start position:0%
+question good so let me before we talk
+more about talk more specific about
+
+ align:start position:0%
+more about talk more specific about
+ 
+
+ align:start position:0%
+more about talk more specific about
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+holes then let me just make one
+
+ align:start position:0%
+holes then let me just make one
+ 
+
+ align:start position:0%
+holes then let me just make one
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+remark is said in the
+
+ align:start position:0%
+remark is said in the
+ 
+
+ align:start position:0%
+remark is said in the
+sense this plank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lens has defined this L scale as defined
+
+ align:start position:0%
+lens has defined this L scale as defined
+ 
+
+ align:start position:0%
+lens has defined this L scale as defined
+by plank can be considered as a minimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+localization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lens okay for the following reason so
+
+ align:start position:0%
+lens okay for the following reason so
+ 
+
+ align:start position:0%
+lens okay for the following reason so
+let's first imagine in in
+
+ align:start position:0%
+let's first imagine in in
+ 
+
+ align:start position:0%
+let's first imagine in in
+non-gravitational
+
+ align:start position:0%
+non-gravitational
+ 
+
+ align:start position:0%
+non-gravitational
+physics say in non-gravitational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics if you want to Pro some short
+
+ align:start position:0%
+physics if you want to Pro some short
+ 
+
+ align:start position:0%
+physics if you want to Pro some short
+distance scales okay then it's easy if
+
+ align:start position:0%
+distance scales okay then it's easy if
+ 
+
+ align:start position:0%
+distance scales okay then it's easy if
+you are rich
+
+ align:start position:0%
+you are rich
+ 
+
+ align:start position:0%
+you are rich
+enough then then you just accelerate the
+
+ align:start position:0%
+enough then then you just accelerate the
+ 
+
+ align:start position:0%
+enough then then you just accelerate the
+particles to very high
+
+ align:start position:0%
+particles to very high
+ 
+
+ align:start position:0%
+particles to very high
+energies say say say e plus e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus with p and minus
+
+ align:start position:0%
+minus with p and minus
+ 
+
+ align:start position:0%
+minus with p and minus
+P so you can then that can Pro the
+
+ align:start position:0%
+P so you can then that can Pro the
+ 
+
+ align:start position:0%
+P so you can then that can Pro the
+distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale then then prob then this can prob
+
+ align:start position:0%
+scale then then prob then this can prob
+ 
+
+ align:start position:0%
+scale then then prob then this can prob
+length scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say of
+
+ align:start position:0%
+say of
+ 
+
+ align:start position:0%
+say of
+order h /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+okay so so if you make make the
+
+ align:start position:0%
+okay so so if you make make the
+ 
+
+ align:start position:0%
+okay so so if you make make the
+particle energy high enough you can in
+
+ align:start position:0%
+particle energy high enough you can in
+ 
+
+ align:start position:0%
+particle energy high enough you can in
+principle prob as short as any scale as
+
+ align:start position:0%
+principle prob as short as any scale as
+ 
+
+ align:start position:0%
+principle prob as short as any scale as
+you want okay you
+
+ align:start position:0%
+you want okay you
+ 
+
+ align:start position:0%
+you want okay you
+can anything uh as far as you can make
+
+ align:start position:0%
+can anything uh as far as you can make
+ 
+
+ align:start position:0%
+can anything uh as far as you can make
+this p as large as you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle you can take L all the way to
+
+ align:start position:0%
+principle you can take L all the way to
+ 
+
+ align:start position:0%
+principle you can take L all the way to
+zero so this scale you can all the way
+
+ align:start position:0%
+zero so this scale you can all the way
+ 
+
+ align:start position:0%
+zero so this scale you can all the way
+to zero if you take P go to
+
+ align:start position:0%
+to zero if you take P go to
+ 
+
+ align:start position:0%
+to zero if you take P go to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+okay but in gravity this is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so so with gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with gravity this is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when your energ is much much greater
+
+ align:start position:0%
+so when your energ is much much greater
+ 
+
+ align:start position:0%
+so when your energ is much much greater
+than EP say say the plankk
+
+ align:start position:0%
+than EP say say the plankk
+ 
+
+ align:start position:0%
+than EP say say the plankk
+mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then as we discuss from
+
+ align:start position:0%
+okay then as we discuss from
+ 
+
+ align:start position:0%
+okay then as we discuss from
+there so so this is a center of mass
+
+ align:start position:0%
+there so so this is a center of mass
+ 
+
+ align:start position:0%
+there so so this is a center of mass
+energy okay so if your center of mass
+
+ align:start position:0%
+energy okay so if your center of mass
+ 
+
+ align:start position:0%
+energy okay so if your center of mass
+energy become much much larger than the
+
+ align:start position:0%
+energy become much much larger than the
+ 
+
+ align:start position:0%
+energy become much much larger than the
+plank scale plank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass then RS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+controlled by the energ yeah let me call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P yeah let me just forget about C let me
+
+ align:start position:0%
+P yeah let me just forget about C let me
+ 
+
+ align:start position:0%
+P yeah let me just forget about C let me
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say okay then the SWAT your radius from
+
+ align:start position:0%
+say okay then the SWAT your radius from
+ 
+
+ align:start position:0%
+say okay then the SWAT your radius from
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on equal to one
+
+ align:start position:0%
+on equal to one
+ 
+
+ align:start position:0%
+on equal to one
+okay so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the swal radius we'll take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minimal L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale okay so what's going to
+
+ align:start position:0%
+scale okay so what's going to
+ 
+
+ align:start position:0%
+scale okay so what's going to
+happen is that if you cide these two
+
+ align:start position:0%
+happen is that if you cide these two
+ 
+
+ align:start position:0%
+happen is that if you cide these two
+particle at very high
+
+ align:start position:0%
+particle at very high
+ 
+
+ align:start position:0%
+particle at very high
+energies then at certain point even
+
+ align:start position:0%
+energies then at certain point even
+ 
+
+ align:start position:0%
+energies then at certain point even
+before these two particle meets together
+
+ align:start position:0%
+before these two particle meets together
+ 
+
+ align:start position:0%
+before these two particle meets together
+they will already form a black hole of
+
+ align:start position:0%
+they will already form a black hole of
+ 
+
+ align:start position:0%
+they will already form a black hole of
+the swal sides okay if this energy is
+
+ align:start position:0%
+the swal sides okay if this energy is
+ 
+
+ align:start position:0%
+the swal sides okay if this energy is
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+enough then we form black ho and then
+
+ align:start position:0%
+enough then we form black ho and then
+ 
+
+ align:start position:0%
+enough then we form black ho and then
+you cannot then you can no longer prob
+
+ align:start position:0%
+you cannot then you can no longer prob
+ 
+
+ align:start position:0%
+you cannot then you can no longer prob
+inside the swal radius of that black ho
+
+ align:start position:0%
+inside the swal radius of that black ho
+ 
+
+ align:start position:0%
+inside the swal radius of that black ho
+so that Define a new
+
+ align:start position:0%
+so that Define a new
+ 
+
+ align:start position:0%
+so that Define a new
+scale which you can prob
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so the funny thing about this
+
+ align:start position:0%
+okay so so the funny thing about this
+ 
+
+ align:start position:0%
+okay so so the funny thing about this
+was radius is that is proportional to
+
+ align:start position:0%
+was radius is that is proportional to
+ 
+
+ align:start position:0%
+was radius is that is proportional to
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+rather than inverse propor to energy as
+
+ align:start position:0%
+rather than inverse propor to energy as
+ 
+
+ align:start position:0%
+rather than inverse propor to energy as
+a standard compant wavelength okay so
+
+ align:start position:0%
+a standard compant wavelength okay so
+ 
+
+ align:start position:0%
+a standard compant wavelength okay so
+after a certain point when you go beyond
+
+ align:start position:0%
+after a certain point when you go beyond
+ 
+
+ align:start position:0%
+after a certain point when you go beyond
+the plank
+
+ align:start position:0%
+the plank
+ 
+
+ align:start position:0%
+the plank
+Mass when you further increase the
+
+ align:start position:0%
+Mass when you further increase the
+ 
+
+ align:start position:0%
+Mass when you further increase the
+energy then you actually prob in the
+
+ align:start position:0%
+energy then you actually prob in the
+ 
+
+ align:start position:0%
+energy then you actually prob in the
+larger distance scales rather than
+
+ align:start position:0%
+larger distance scales rather than
+ 
+
+ align:start position:0%
+larger distance scales rather than
+smaller distance scales okay due to the
+
+ align:start position:0%
+smaller distance scales okay due to the
+ 
+
+ align:start position:0%
+smaller distance scales okay due to the
+funny thing about the gravity and the
+
+ align:start position:0%
+funny thing about the gravity and the
+ 
+
+ align:start position:0%
+funny thing about the gravity and the
+funny thing about black
+
+ align:start position:0%
+funny thing about black
+ 
+
+ align:start position:0%
+funny thing about black
+hole okay so so
+
+ align:start position:0%
+hole okay so so
+ 
+
+ align:start position:0%
+hole okay so so
+so actually uh this scale increases with
+
+ align:start position:0%
+so actually uh this scale increases with
+ 
+
+ align:start position:0%
+so actually uh this scale increases with
+P increase with your center of mass
+
+ align:start position:0%
+P increase with your center of mass
+ 
+
+ align:start position:0%
+P increase with your center of mass
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energies go to longer length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scales okay
+
+ align:start position:0%
+scales okay
+ 
+
+ align:start position:0%
+scales okay
+so this essentially defines the plank
+
+ align:start position:0%
+so this essentially defines the plank
+ 
+
+ align:start position:0%
+so this essentially defines the plank
+lens as a minimal scale one can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pro okay so when your center of mass
+
+ align:start position:0%
+Pro okay so when your center of mass
+ 
+
+ align:start position:0%
+Pro okay so when your center of mass
+energy smaller than the plank scale than
+
+ align:start position:0%
+energy smaller than the plank scale than
+ 
+
+ align:start position:0%
+energy smaller than the plank scale than
+the plank mass then you count the
+
+ align:start position:0%
+the plank mass then you count the
+ 
+
+ align:start position:0%
+the plank mass then you count the
+wavelength of course n than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LP but when this is greater than
+
+ align:start position:0%
+LP but when this is greater than
+ 
+
+ align:start position:0%
+LP but when this is greater than
+MP then then as we discussed here then
+
+ align:start position:0%
+MP then then as we discussed here then
+ 
+
+ align:start position:0%
+MP then then as we discussed here then
+the swater radius of corresponding
+
+ align:start position:0%
+the swater radius of corresponding
+ 
+
+ align:start position:0%
+the swater radius of corresponding
+object will be greater
+
+ align:start position:0%
+object will be greater
+ 
+
+ align:start position:0%
+object will be greater
+than the the the plunk
+
+ align:start position:0%
+than the the the plunk
+ 
+
+ align:start position:0%
+than the the the plunk
+side and will will greater than the comp
+
+ align:start position:0%
+side and will will greater than the comp
+ 
+
+ align:start position:0%
+side and will will greater than the comp
+wavelength and will be greater than the
+
+ align:start position:0%
+wavelength and will be greater than the
+ 
+
+ align:start position:0%
+wavelength and will be greater than the
+uh uh plank
+
+ align:start position:0%
+uh uh plank
+ 
+
+ align:start position:0%
+uh uh plank
+sides and this give you essentially the
+
+ align:start position:0%
+sides and this give you essentially the
+ 
+
+ align:start position:0%
+sides and this give you essentially the
+uh the minimum radius to Pro
+
+ align:start position:0%
+uh the minimum radius to Pro
+ 
+
+ align:start position:0%
+uh the minimum radius to Pro
+okay and uh so so in alternatively we
+
+ align:start position:0%
+okay and uh so so in alternatively we
+ 
+
+ align:start position:0%
+okay and uh so so in alternatively we
+can also
+
+ align:start position:0%
+can also
+ 
+
+ align:start position:0%
+can also
+just reach the same
+
+ align:start position:0%
+just reach the same
+ 
+
+ align:start position:0%
+just reach the same
+argument uh uh simply I can just write
+
+ align:start position:0%
+argument uh uh simply I can just write
+ 
+
+ align:start position:0%
+argument uh uh simply I can just write
+down a couple of equations so let's
+
+ align:start position:0%
+down a couple of equations so let's
+ 
+
+ align:start position:0%
+down a couple of equations so let's
+consider you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncertainty say suppose you have a
+
+ align:start position:0%
+uncertainty say suppose you have a
+ 
+
+ align:start position:0%
+uncertainty say suppose you have a
+position uncertainty data
+
+ align:start position:0%
+position uncertainty data
+ 
+
+ align:start position:0%
+position uncertainty data
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+okay and then the then the
+
+ align:start position:0%
+okay and then the then the
+ 
+
+ align:start position:0%
+okay and then the then the
+the uncertainty energy or momentum
+
+ align:start position:0%
+the uncertainty energy or momentum
+ 
+
+ align:start position:0%
+the uncertainty energy or momentum
+associated with the this Delta s is
+
+ align:start position:0%
+associated with the this Delta s is
+ 
+
+ align:start position:0%
+associated with the this Delta s is
+Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P but on the other hand the distance you
+
+ align:start position:0%
+P but on the other hand the distance you
+ 
+
+ align:start position:0%
+P but on the other hand the distance you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+prop must be greater
+
+ align:start position:0%
+prop must be greater
+ 
+
+ align:start position:0%
+prop must be greater
+than then the SWAT radius associate with
+
+ align:start position:0%
+than then the SWAT radius associate with
+ 
+
+ align:start position:0%
+than then the SWAT radius associate with
+LP Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P okay Delta p
+
+ align:start position:0%
+P okay Delta p
+ 
+
+ align:start position:0%
+P okay Delta p
+so so if you combine this two equation
+
+ align:start position:0%
+so so if you combine this two equation
+ 
+
+ align:start position:0%
+so so if you combine this two equation
+together so this is greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+GN H bar divided by Del P so so now I
+
+ align:start position:0%
+GN H bar divided by Del P so so now I
+ 
+
+ align:start position:0%
+GN H bar divided by Del P so so now I
+have suppressed the C so you can see
+
+ align:start position:0%
+have suppressed the C so you can see
+ 
+
+ align:start position:0%
+have suppressed the C so you can see
+from this equation you can see that
+
+ align:start position:0%
+from this equation you can see that
+ 
+
+ align:start position:0%
+from this equation you can see that
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X must be greater
+
+ align:start position:0%
+X must be greater
+ 
+
+ align:start position:0%
+X must be greater
+than H bar
+
+ align:start position:0%
+than H bar
+ 
+
+ align:start position:0%
+than H bar
+GM which is
+
+ align:start position:0%
+GM which is
+ 
+
+ align:start position:0%
+GM which is
+LP
+
+ align:start position:0%
+LP
+ 
+
+ align:start position:0%
+LP
+okay which is the lp here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah this is the same argument as this
+
+ align:start position:0%
+yeah this is the same argument as this
+ 
+
+ align:start position:0%
+yeah this is the same argument as this
+one uh but this is a little bit formal
+
+ align:start position:0%
+one uh but this is a little bit formal
+ 
+
+ align:start position:0%
+one uh but this is a little bit formal
+and so so the essence is that once your
+
+ align:start position:0%
+and so so the essence is that once your
+ 
+
+ align:start position:0%
+and so so the essence is that once your
+energy is big enough then you create a
+
+ align:start position:0%
+energy is big enough then you create a
+ 
+
+ align:start position:0%
+energy is big enough then you create a
+black hole and then your physics will
+
+ align:start position:0%
+black hole and then your physics will
+ 
+
+ align:start position:0%
+black hole and then your physics will
+completely change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay black hole evaporate so they not
+
+ align:start position:0%
+okay black hole evaporate so they not
+ 
+
+ align:start position:0%
+okay black hole evaporate so they not
+cont
+
+ align:start position:0%
+cont
+ 
+
+ align:start position:0%
+cont
+information right yeah so uh uh we yeah
+
+ align:start position:0%
+information right yeah so uh uh we yeah
+ 
+
+ align:start position:0%
+information right yeah so uh uh we yeah
+let's uh uh uh uh uh uh yeah we will go
+
+ align:start position:0%
+let's uh uh uh uh uh uh yeah we will go
+ 
+
+ align:start position:0%
+let's uh uh uh uh uh uh yeah we will go
+into that uh when the Black ho evaporate
+
+ align:start position:0%
+into that uh when the Black ho evaporate
+ 
+
+ align:start position:0%
+into that uh when the Black ho evaporate
+actually you still don't probe the short
+
+ align:start position:0%
+actually you still don't probe the short
+ 
+
+ align:start position:0%
+actually you still don't probe the short
+still harder to Pro the short distance
+
+ align:start position:0%
+still harder to Pro the short distance
+ 
+
+ align:start position:0%
+still harder to Pro the short distance
+scale because if I yeah we will talk
+
+ align:start position:0%
+scale because if I yeah we will talk
+ 
+
+ align:start position:0%
+scale because if I yeah we will talk
+about that later
+
+ align:start position:0%
+about that later
+ 
+
+ align:start position:0%
+about that later
+yeah so yeah here just a heric argument
+
+ align:start position:0%
+yeah so yeah here just a heric argument
+ 
+
+ align:start position:0%
+yeah so yeah here just a heric argument
+to tell you that the because of
+
+ align:start position:0%
+to tell you that the because of
+ 
+
+ align:start position:0%
+to tell you that the because of
+this the actually uh the physic is very
+
+ align:start position:0%
+this the actually uh the physic is very
+ 
+
+ align:start position:0%
+this the actually uh the physic is very
+special okay uh uh the the physic of the
+
+ align:start position:0%
+special okay uh uh the the physic of the
+ 
+
+ align:start position:0%
+special okay uh uh the the physic of the
+gravity is very special
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions yes um so as a pro for Ming
+
+ align:start position:0%
+questions yes um so as a pro for Ming
+ 
+
+ align:start position:0%
+questions yes um so as a pro for Ming
+gravity I was thinking what if there
+
+ align:start position:0%
+gravity I was thinking what if there
+ 
+
+ align:start position:0%
+gravity I was thinking what if there
+were some um phenomenon in which gravity
+
+ align:start position:0%
+were some um phenomenon in which gravity
+ 
+
+ align:start position:0%
+were some um phenomenon in which gravity
+is weak but and it's a macroscopic scale
+
+ align:start position:0%
+is weak but and it's a macroscopic scale
+ 
+
+ align:start position:0%
+is weak but and it's a macroscopic scale
+but there's some kind of um coherence
+
+ align:start position:0%
+but there's some kind of um coherence
+ 
+
+ align:start position:0%
+but there's some kind of um coherence
+happening that will maybe on the scale
+
+ align:start position:0%
+happening that will maybe on the scale
+ 
+
+ align:start position:0%
+happening that will maybe on the scale
+of galaxies or something like that that
+
+ align:start position:0%
+of galaxies or something like that that
+ 
+
+ align:start position:0%
+of galaxies or something like that that
+will allow Quantum effects to be me
+
+ align:start position:0%
+will allow Quantum effects to be me
+ 
+
+ align:start position:0%
+will allow Quantum effects to be me
+like an analogy of what happens in a
+
+ align:start position:0%
+like an analogy of what happens in a
+ 
+
+ align:start position:0%
+like an analogy of what happens in a
+laser or something like that
+
+ align:start position:0%
+laser or something like that
+ 
+
+ align:start position:0%
+laser or something like that
+um yeah uh that is black hole the black
+
+ align:start position:0%
+um yeah uh that is black hole the black
+ 
+
+ align:start position:0%
+um yeah uh that is black hole the black
+hole is the way which black uh black
+
+ align:start position:0%
+hole is the way which black uh black
+ 
+
+ align:start position:0%
+hole is the way which black uh black
+hole is the way which gravity can
+
+ align:start position:0%
+hole is the way which gravity can
+ 
+
+ align:start position:0%
+hole is the way which gravity can
+manifest the quantum effect at lar
+
+ align:start position:0%
+manifest the quantum effect at lar
+ 
+
+ align:start position:0%
+manifest the quantum effect at lar
+scales and we don't know any other ways
+
+ align:start position:0%
+scales and we don't know any other ways
+ 
+
+ align:start position:0%
+scales and we don't know any other ways
+to for for Gravity to manifest such
+
+ align:start position:0%
+to for for Gravity to manifest such
+ 
+
+ align:start position:0%
+to for for Gravity to manifest such
+quantum physics at large decent scales
+
+ align:start position:0%
+quantum physics at large decent scales
+ 
+
+ align:start position:0%
+quantum physics at large decent scales
+yeah okay so
+
+ align:start position:0%
+yeah okay so
+ 
+
+ align:start position:0%
+yeah okay so
+so so let me conclude this General
+
+ align:start position:0%
+so so let me conclude this General
+ 
+
+ align:start position:0%
+so so let me conclude this General
+discussion Again by reminding
+
+ align:start position:0%
+discussion Again by reminding
+ 
+
+ align:start position:0%
+discussion Again by reminding
+you what is regimes of
+
+ align:start position:0%
+you what is regimes of
+ 
+
+ align:start position:0%
+you what is regimes of
+gravity what is regimes of uh the
+
+ align:start position:0%
+gravity what is regimes of uh the
+ 
+
+ align:start position:0%
+gravity what is regimes of uh the
+gravity or quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in this
+
+ align:start position:0%
+okay so in this
+ 
+
+ align:start position:0%
+okay so in this
+discussion you should always in the
+
+ align:start position:0%
+discussion you should always in the
+ 
+
+ align:start position:0%
+discussion you should always in the
+discussion I'm going to do in the next
+
+ align:start position:0%
+discussion I'm going to do in the next
+ 
+
+ align:start position:0%
+discussion I'm going to do in the next
+minutes you should
+
+ align:start position:0%
+minutes you should
+ 
+
+ align:start position:0%
+minutes you should
+always think when I take the limit I
+
+ align:start position:0%
+always think when I take the limit I
+ 
+
+ align:start position:0%
+always think when I take the limit I
+always keep my energy fixed okay I keep
+
+ align:start position:0%
+always keep my energy fixed okay I keep
+ 
+
+ align:start position:0%
+always keep my energy fixed okay I keep
+the the energy scale I'm interested in
+
+ align:start position:0%
+the the energy scale I'm interested in
+ 
+
+ align:start position:0%
+the the energy scale I'm interested in
+fixed I keep that fixed okay so the
+
+ align:start position:0%
+fixed I keep that fixed okay so the
+ 
+
+ align:start position:0%
+fixed I keep that fixed okay so the
+classical gravity regime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the regime which you take H bar go
+
+ align:start position:0%
+is the regime which you take H bar go
+ 
+
+ align:start position:0%
+is the regime which you take H bar go
+zero take the Newton constant
+
+ align:start position:0%
+zero take the Newton constant
+ 
+
+ align:start position:0%
+zero take the Newton constant
+finite
+
+ align:start position:0%
+finite
+ 
+
+ align:start position:0%
+finite
+okay and the regime of a particle
+
+ align:start position:0%
+okay and the regime of a particle
+ 
+
+ align:start position:0%
+okay and the regime of a particle
+physics which normally be sometimes say
+
+ align:start position:0%
+physics which normally be sometimes say
+ 
+
+ align:start position:0%
+physics which normally be sometimes say
+qft in the fixed space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so this is the Quantum F in the in
+
+ align:start position:0%
+time so this is the Quantum F in the in
+ 
+
+ align:start position:0%
+time so this is the Quantum F in the in
+the fixed space time including curved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay including cured so this is a regime
+
+ align:start position:0%
+okay including cured so this is a regime
+ 
+
+ align:start position:0%
+okay including cured so this is a regime
+which H bar is
+
+ align:start position:0%
+which H bar is
+ 
+
+ align:start position:0%
+which H bar is
+finite but you take the Newton constant
+
+ align:start position:0%
+finite but you take the Newton constant
+ 
+
+ align:start position:0%
+finite but you take the Newton constant
+go to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then there's of course the
+
+ align:start position:0%
+okay and then there's of course the
+ 
+
+ align:start position:0%
+okay and then there's of course the
+quantum gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regime which is the GM and H bar both
+
+ align:start position:0%
+regime which is the GM and H bar both
+ 
+
+ align:start position:0%
+regime which is the GM and H bar both
+finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's a very interesting regime
+
+ align:start position:0%
+and there's a very interesting regime
+ 
+
+ align:start position:0%
+and there's a very interesting regime
+which is actually the the regime in most
+
+ align:start position:0%
+which is actually the the regime in most
+ 
+
+ align:start position:0%
+which is actually the the regime in most
+of us work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with so there's also something called
+
+ align:start position:0%
+with so there's also something called
+ 
+
+ align:start position:0%
+with so there's also something called
+the semil classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regime for quantum
+
+ align:start position:0%
+regime for quantum
+ 
+
+ align:start position:0%
+regime for quantum
+gravity so this is the regime you
+
+ align:start position:0%
+gravity so this is the regime you
+ 
+
+ align:start position:0%
+gravity so this is the regime you
+keep H bar finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expand you expand the
+
+ align:start position:0%
+expand you expand the
+ 
+
+ align:start position:0%
+expand you expand the
+system in Newton constant
+
+ align:start position:0%
+system in Newton constant
+ 
+
+ align:start position:0%
+system in Newton constant
+okay so around say expand the whatever
+
+ align:start position:0%
+okay so around say expand the whatever
+ 
+
+ align:start position:0%
+okay so around say expand the whatever
+quantity Newton constant
+
+ align:start position:0%
+quantity Newton constant
+ 
+
+ align:start position:0%
+quantity Newton constant
+around say gon equal to
+
+ align:start position:0%
+around say gon equal to
+ 
+
+ align:start position:0%
+around say gon equal to
+zero so gon equal to zero is the
+
+ align:start position:0%
+zero so gon equal to zero is the
+ 
+
+ align:start position:0%
+zero so gon equal to zero is the
+classical reg is the classical regime no
+
+ align:start position:0%
+classical reg is the classical regime no
+ 
+
+ align:start position:0%
+classical reg is the classical regime no
+is the is the uh is the regime the
+
+ align:start position:0%
+is the is the uh is the regime the
+ 
+
+ align:start position:0%
+is the is the uh is the regime the
+gravity is not important but including H
+
+ align:start position:0%
+gravity is not important but including H
+ 
+
+ align:start position:0%
+gravity is not important but including H
+bar and now you can take into
+
+ align:start position:0%
+bar and now you can take into
+ 
+
+ align:start position:0%
+bar and now you can take into
+account the quantum gravity effect
+
+ align:start position:0%
+account the quantum gravity effect
+ 
+
+ align:start position:0%
+account the quantum gravity effect
+semiclassically by expanding around the
+
+ align:start position:0%
+semiclassically by expanding around the
+ 
+
+ align:start position:0%
+semiclassically by expanding around the
+GN okay so this is normally what we call
+
+ align:start position:0%
+GN okay so this is normally what we call
+ 
+
+ align:start position:0%
+GN okay so this is normally what we call
+semiclassical regime of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity yes do we know that g goes to Z
+
+ align:start position:0%
+gravity yes do we know that g goes to Z
+ 
+
+ align:start position:0%
+gravity yes do we know that g goes to Z
+the smooth limit
+
+ align:start position:0%
+the smooth limit
+ 
+
+ align:start position:0%
+the smooth limit
+it's not sing Point
+
+ align:start position:0%
+it's not sing Point
+ 
+
+ align:start position:0%
+it's not sing Point
+yeah this is a very good question so so
+
+ align:start position:0%
+yeah this is a very good question so so
+ 
+
+ align:start position:0%
+yeah this is a very good question so so
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+indeed so this is indeed the
+
+ align:start position:0%
+indeed so this is indeed the
+ 
+
+ align:start position:0%
+indeed so this is indeed the
+question uh indeed the most of the
+
+ align:start position:0%
+question uh indeed the most of the
+ 
+
+ align:start position:0%
+question uh indeed the most of the
+puzzles regarding black hole is in this
+
+ align:start position:0%
+puzzles regarding black hole is in this
+ 
+
+ align:start position:0%
+puzzles regarding black hole is in this
+regime so our current understanding of
+
+ align:start position:0%
+regime so our current understanding of
+ 
+
+ align:start position:0%
+regime so our current understanding of
+quantum physics of black ho is in this
+
+ align:start position:0%
+quantum physics of black ho is in this
+ 
+
+ align:start position:0%
+quantum physics of black ho is in this
+semi classical regime and uh you you
+
+ align:start position:0%
+semi classical regime and uh you you
+ 
+
+ align:start position:0%
+semi classical regime and uh you you
+treat the any matter field H bar finite
+
+ align:start position:0%
+treat the any matter field H bar finite
+ 
+
+ align:start position:0%
+treat the any matter field H bar finite
+but the gravity is weak and uh so so
+
+ align:start position:0%
+but the gravity is weak and uh so so
+ 
+
+ align:start position:0%
+but the gravity is weak and uh so so
+there are various indication that this
+
+ align:start position:0%
+there are various indication that this
+ 
+
+ align:start position:0%
+there are various indication that this
+limit is actually not smooth but but
+
+ align:start position:0%
+limit is actually not smooth but but
+ 
+
+ align:start position:0%
+limit is actually not smooth but but
+only for very subtle questions for for
+
+ align:start position:0%
+only for very subtle questions for for
+ 
+
+ align:start position:0%
+only for very subtle questions for for
+gener for simple questions for typical
+
+ align:start position:0%
+gener for simple questions for typical
+ 
+
+ align:start position:0%
+gener for simple questions for typical
+questions actually this is a limit this
+
+ align:start position:0%
+questions actually this is a limit this
+ 
+
+ align:start position:0%
+questions actually this is a limit this
+limit is smooth but they can be very
+
+ align:start position:0%
+limit is smooth but they can be very
+ 
+
+ align:start position:0%
+limit is smooth but they can be very
+subtle questions which this limit is not
+
+ align:start position:0%
+subtle questions which this limit is not
+ 
+
+ align:start position:0%
+subtle questions which this limit is not
+smooth and one such question is this
+
+ align:start position:0%
+smooth and one such question is this
+ 
+
+ align:start position:0%
+smooth and one such question is this
+so-call black ho information no and
+
+ align:start position:0%
+so-call black ho information no and
+ 
+
+ align:start position:0%
+so-call black ho information no and
+involving and the subtle limit of taking
+
+ align:start position:0%
+involving and the subtle limit of taking
+ 
+
+ align:start position:0%
+involving and the subtle limit of taking
+this uh yeah involving subt of taking
+
+ align:start position:0%
+this uh yeah involving subt of taking
+ 
+
+ align:start position:0%
+this uh yeah involving subt of taking
+this limit
+
+ align:start position:0%
+this limit
+ 
+
+ align:start position:0%
+this limit
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay and this is the regime
+
+ align:start position:0%
+questions okay and this is the regime
+ 
+
+ align:start position:0%
+questions okay and this is the regime
+actually we will work with most okay
+
+ align:start position:0%
+actually we will work with most okay
+ 
+
+ align:start position:0%
+actually we will work with most okay
+this is the regime we will work with
+
+ align:start position:0%
+this is the regime we will work with
+ 
+
+ align:start position:0%
+this is the regime we will work with
+most and so so we will always uh in
+
+ align:start position:0%
+most and so so we will always uh in
+ 
+
+ align:start position:0%
+most and so so we will always uh in
+particular later so right now I'm
+
+ align:start position:0%
+particular later so right now I'm
+ 
+
+ align:start position:0%
+particular later so right now I'm
+keeping the H bar explicited but later I
+
+ align:start position:0%
+keeping the H bar explicited but later I
+ 
+
+ align:start position:0%
+keeping the H bar explicited but later I
+will also set H bar equal to one and so
+
+ align:start position:0%
+will also set H bar equal to one and so
+ 
+
+ align:start position:0%
+will also set H bar equal to one and so
+H bar will equal to so we always
+
+ align:start position:0%
+H bar will equal to so we always
+ 
+
+ align:start position:0%
+H bar will equal to so we always
+typically work with this regime H bar
+
+ align:start position:0%
+typically work with this regime H bar
+ 
+
+ align:start position:0%
+typically work with this regime H bar
+equal to one and then you will have
+
+ align:start position:0%
+equal to one and then you will have
+ 
+
+ align:start position:0%
+equal to one and then you will have
+uh um uh
+
+ align:start position:0%
+uh um uh
+ 
+
+ align:start position:0%
+uh um uh
+uh yeah then then you take into account
+
+ align:start position:0%
+uh yeah then then you take into account
+ 
+
+ align:start position:0%
+uh yeah then then you take into account
+the effect of GN uh in the peration
+
+ align:start position:0%
+the effect of GN uh in the peration
+ 
+
+ align:start position:0%
+the effect of GN uh in the peration
+theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good good so now let's move to the
+
+ align:start position:0%
+okay good good so now let's move to the
+ 
+
+ align:start position:0%
+okay good good so now let's move to the
+black hole okay so with
+
+ align:start position:0%
+black hole okay so with
+ 
+
+ align:start position:0%
+black hole okay so with
+this uh yes just some random top do
+
+ align:start position:0%
+this uh yes just some random top do
+ 
+
+ align:start position:0%
+this uh yes just some random top do
+people also work in the other semic reg
+
+ align:start position:0%
+people also work in the other semic reg
+ 
+
+ align:start position:0%
+people also work in the other semic reg
+I mean finite butand HR yeah this is not
+
+ align:start position:0%
+I mean finite butand HR yeah this is not
+ 
+
+ align:start position:0%
+I mean finite butand HR yeah this is not
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um not so much um it's because the
+
+ align:start position:0%
+um not so much um it's because the
+ 
+
+ align:start position:0%
+um not so much um it's because the
+um it's because it's easy in some sense
+
+ align:start position:0%
+um it's because it's easy in some sense
+ 
+
+ align:start position:0%
+um it's because it's easy in some sense
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+easy so so in the sense we are doing a
+
+ align:start position:0%
+easy so so in the sense we are doing a
+ 
+
+ align:start position:0%
+easy so so in the sense we are doing a
+little bit both uh uh
+
+ align:start position:0%
+little bit both uh uh
+ 
+
+ align:start position:0%
+little bit both uh uh
+so yeah so later right now I don't want
+
+ align:start position:0%
+so yeah so later right now I don't want
+ 
+
+ align:start position:0%
+so yeah so later right now I don't want
+to go into that you will see the
+
+ align:start position:0%
+to go into that you will see the
+ 
+
+ align:start position:0%
+to go into that you will see the
+effective uh the effective coupling
+
+ align:start position:0%
+effective uh the effective coupling
+ 
+
+ align:start position:0%
+effective uh the effective coupling
+constant control the the quantum gravity
+
+ align:start position:0%
+constant control the the quantum gravity
+ 
+
+ align:start position:0%
+constant control the the quantum gravity
+effect is in fact the H Bar times
+
+ align:start position:0%
+effect is in fact the H Bar times
+ 
+
+ align:start position:0%
+effect is in fact the H Bar times
+GN is H Bar times GN and so so the
+
+ align:start position:0%
+GN is H Bar times GN and so so the
+ 
+
+ align:start position:0%
+GN is H Bar times GN and so so the
+quantum gravity effect will be important
+
+ align:start position:0%
+quantum gravity effect will be important
+ 
+
+ align:start position:0%
+quantum gravity effect will be important
+when the H Bar times when you do
+
+ align:start position:0%
+when the H Bar times when you do
+ 
+
+ align:start position:0%
+when the H Bar times when you do
+putation Ser in h Bar times GN yeah yeah
+
+ align:start position:0%
+putation Ser in h Bar times GN yeah yeah
+ 
+
+ align:start position:0%
+putation Ser in h Bar times GN yeah yeah
+so when I say uh you are doing things in
+
+ align:start position:0%
+so when I say uh you are doing things in
+ 
+
+ align:start position:0%
+so when I say uh you are doing things in
+GN essentially because I'm fixing H bar
+
+ align:start position:0%
+GN essentially because I'm fixing H bar
+ 
+
+ align:start position:0%
+GN essentially because I'm fixing H bar
+so you're actually doing pation Theory H
+
+ align:start position:0%
+so you're actually doing pation Theory H
+ 
+
+ align:start position:0%
+so you're actually doing pation Theory H
+bar GN yeah so you have to do both yeah
+
+ align:start position:0%
+bar GN yeah so you have to do both yeah
+ 
+
+ align:start position:0%
+bar GN yeah so you have to do both yeah
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so now let's talk about the black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hole so let's first talk about classical
+
+ align:start position:0%
+hole so let's first talk about classical
+ 
+
+ align:start position:0%
+hole so let's first talk about classical
+geometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here will assume you already
+
+ align:start position:0%
+okay so here will assume you already
+ 
+
+ align:start position:0%
+okay so here will assume you already
+have some background in GR in
+
+ align:start position:0%
+have some background in GR in
+ 
+
+ align:start position:0%
+have some background in GR in
+generativity and for example you have
+
+ align:start position:0%
+generativity and for example you have
+ 
+
+ align:start position:0%
+generativity and for example you have
+seen things like swashi matric
+
+ align:start position:0%
+seen things like swashi matric
+ 
+
+ align:start position:0%
+seen things like swashi matric
+Etc and if you have not seen swashi
+
+ align:start position:0%
+Etc and if you have not seen swashi
+ 
+
+ align:start position:0%
+Etc and if you have not seen swashi
+matric it's also okay uh um I think uh
+
+ align:start position:0%
+matric it's also okay uh um I think uh
+ 
+
+ align:start position:0%
+matric it's also okay uh um I think uh
+uh you should be able to uh to follow uh
+
+ align:start position:0%
+uh you should be able to uh to follow uh
+ 
+
+ align:start position:0%
+uh you should be able to uh to follow uh
+uh what I'm going to say so so for
+
+ align:start position:0%
+uh what I'm going to say so so for
+ 
+
+ align:start position:0%
+uh what I'm going to say so so for
+Simplicity let me consider zero cos mod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant okay zero cosmology constant
+
+ align:start position:0%
+constant okay zero cosmology constant
+ 
+
+ align:start position:0%
+constant okay zero cosmology constant
+cosmological
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant okay Z cosmological constant
+
+ align:start position:0%
+constant okay Z cosmological constant
+ 
+
+ align:start position:0%
+constant okay Z cosmological constant
+corresponding to we can see the SYM
+
+ align:start position:0%
+corresponding to we can see the SYM
+ 
+
+ align:start position:0%
+corresponding to we can see the SYM
+totically um minkovski space
+
+ align:start position:0%
+totically um minkovski space
+ 
+
+ align:start position:0%
+totically um minkovski space
+time and uh so so in the space time of
+
+ align:start position:0%
+time and uh so so in the space time of
+ 
+
+ align:start position:0%
+time and uh so so in the space time of
+zero coso constant and then the space
+
+ align:start position:0%
+zero coso constant and then the space
+ 
+
+ align:start position:0%
+zero coso constant and then the space
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric due
+
+ align:start position:0%
+matric due
+ 
+
+ align:start position:0%
+matric due
+to an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+okay can be written as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the famous was magic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh so so of course here we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assuming this is a a SP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metric and the neutral ex there's not
+
+ align:start position:0%
+metric and the neutral ex there's not
+ 
+
+ align:start position:0%
+metric and the neutral ex there's not
+say this all object does not carry any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge and then this m and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F is given by 1 - 2
+
+ align:start position:0%
+F is given by 1 - 2
+ 
+
+ align:start position:0%
+F is given by 1 - 2
+n m/ r or is equal to r s/ r okay so
+
+ align:start position:0%
+n m/ r or is equal to r s/ r okay so
+ 
+
+ align:start position:0%
+n m/ r or is equal to r s/ r okay so
+this RS is the SW radius so now C is
+
+ align:start position:0%
+this RS is the SW radius so now C is
+ 
+
+ align:start position:0%
+this RS is the SW radius so now C is
+always equal to
+
+ align:start position:0%
+always equal to
+ 
+
+ align:start position:0%
+always equal to
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if this
+
+ align:start position:0%
+okay so if this
+ 
+
+ align:start position:0%
+okay so if this
+object so we consider this object is
+
+ align:start position:0%
+object so we consider this object is
+ 
+
+ align:start position:0%
+object so we consider this object is
+verical symmetric if this object have a
+
+ align:start position:0%
+verical symmetric if this object have a
+ 
+
+ align:start position:0%
+verical symmetric if this object have a
+fight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sides then then of course this matric
+
+ align:start position:0%
+sides then then of course this matric
+ 
+
+ align:start position:0%
+sides then then of course this matric
+only is valid outside this object
+
+ align:start position:0%
+only is valid outside this object
+ 
+
+ align:start position:0%
+only is valid outside this object
+okay but if the side of this
+
+ align:start position:0%
+okay but if the side of this
+ 
+
+ align:start position:0%
+okay but if the side of this
+object is
+
+ align:start position:0%
+object is
+ 
+
+ align:start position:0%
+object is
+smaller than this wasal radius then this
+
+ align:start position:0%
+smaller than this wasal radius then this
+ 
+
+ align:start position:0%
+smaller than this wasal radius then this
+is a black hole okay and the black hole
+
+ align:start position:0%
+is a black hole okay and the black hole
+ 
+
+ align:start position:0%
+is a black hole okay and the black hole
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+distinguished by even Horizon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at I to r
+
+ align:start position:0%
+at I to r
+ 
+
+ align:start position:0%
+at I to r
+s okay at I to i s so at I to i s you
+
+ align:start position:0%
+s okay at I to i s so at I to i s you
+ 
+
+ align:start position:0%
+s okay at I to i s so at I to i s you
+you see that this F become
+
+ align:start position:0%
+you see that this F become
+ 
+
+ align:start position:0%
+you see that this F become
+zero okay so FAL become zero so
+
+ align:start position:0%
+zero okay so FAL become zero so
+ 
+
+ align:start position:0%
+zero okay so FAL become zero so
+essentially and here
+
+ align:start position:0%
+essentially and here
+ 
+
+ align:start position:0%
+essentially and here
+gtt so the metric for the TT compon
+
+ align:start position:0%
+gtt so the metric for the TT compon
+ 
+
+ align:start position:0%
+gtt so the metric for the TT compon
+component is become
+
+ align:start position:0%
+component is become
+ 
+
+ align:start position:0%
+component is become
+zero and
+
+ align:start position:0%
+zero and
+ 
+
+ align:start position:0%
+zero and
+grr the matric before the the r
+
+ align:start position:0%
+grr the matric before the the r
+ 
+
+ align:start position:0%
+grr the matric before the the r
+component it become
+
+ align:start position:0%
+component it become
+ 
+
+ align:start position:0%
+component it become
+infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and another thing is that when R
+
+ align:start position:0%
+okay and another thing is that when R
+ 
+
+ align:start position:0%
+okay and another thing is that when R
+become smaller than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RS then F switch sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so s become
+
+ align:start position:0%
+so s become
+ 
+
+ align:start position:0%
+so s become
+negative and then in this case then R
+
+ align:start position:0%
+negative and then in this case then R
+ 
+
+ align:start position:0%
+negative and then in this case then R
+become time coordinates then the T
+
+ align:start position:0%
+become time coordinates then the T
+ 
+
+ align:start position:0%
+become time coordinates then the T
+become spatial coordinates okay when you
+
+ align:start position:0%
+become spatial coordinates okay when you
+ 
+
+ align:start position:0%
+become spatial coordinates okay when you
+go inside the IAL to i
+
+ align:start position:0%
+go inside the IAL to i
+ 
+
+ align:start position:0%
+go inside the IAL to i
+s okay this is just a feature of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric so now let me say some simple uh
+
+ align:start position:0%
+matric so now let me say some simple uh
+ 
+
+ align:start position:0%
+matric so now let me say some simple uh
+now let me uh list some uh uh some
+
+ align:start position:0%
+now let me uh list some uh uh some
+ 
+
+ align:start position:0%
+now let me uh list some uh uh some
+facts about this magic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so most of them I expect to be
+
+ align:start position:0%
+so most of them I expect to be
+ 
+
+ align:start position:0%
+so most of them I expect to be
+low actually I I expect to be low all of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them but it's
+
+ align:start position:0%
+them but it's
+ 
+
+ align:start position:0%
+them but it's
+um just remind
+
+ align:start position:0%
+um just remind
+ 
+
+ align:start position:0%
+um just remind
+you some of those facts will be
+
+ align:start position:0%
+you some of those facts will be
+ 
+
+ align:start position:0%
+you some of those facts will be
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+later okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are mostly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reminders so first this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric if you look at this Matrix
+
+ align:start position:0%
+matric if you look at this Matrix
+ 
+
+ align:start position:0%
+matric if you look at this Matrix
+itself is time reversal in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+warrant
+
+ align:start position:0%
+warrant
+ 
+
+ align:start position:0%
+warrant
+okay because you can if you take T go to
+
+ align:start position:0%
+okay because you can if you take T go to
+ 
+
+ align:start position:0%
+okay because you can if you take T go to
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+t of course the uh uh yeah envirment on
+
+ align:start position:0%
+t of course the uh uh yeah envirment on
+ 
+
+ align:start position:0%
+t of course the uh uh yeah envirment on
+the T goes minus
+
+ align:start position:0%
+the T goes minus
+ 
+
+ align:start position:0%
+the T goes minus
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+Okay so this actually because of this
+
+ align:start position:0%
+Okay so this actually because of this
+ 
+
+ align:start position:0%
+Okay so this actually because of this
+this cannot describe a real black hole
+
+ align:start position:0%
+this cannot describe a real black hole
+ 
+
+ align:start position:0%
+this cannot describe a real black hole
+so the real life black hole
+
+ align:start position:0%
+so the real life black hole
+ 
+
+ align:start position:0%
+so the real life black hole
+arise from gravitational collapse and
+
+ align:start position:0%
+arise from gravitational collapse and
+ 
+
+ align:start position:0%
+arise from gravitational collapse and
+the gravitational collapse cannot be a
+
+ align:start position:0%
+the gravitational collapse cannot be a
+ 
+
+ align:start position:0%
+the gravitational collapse cannot be a
+time symmetric process okay so this
+
+ align:start position:0%
+time symmetric process okay so this
+ 
+
+ align:start position:0%
+time symmetric process okay so this
+cannot describe so this does not
+
+ align:start position:0%
+cannot describe so this does not
+ 
+
+ align:start position:0%
+cannot describe so this does not
+describe a real black
+
+ align:start position:0%
+describe a real black
+ 
+
+ align:start position:0%
+describe a real black
+ho but it's a good approximation to the
+
+ align:start position:0%
+ho but it's a good approximation to the
+ 
+
+ align:start position:0%
+ho but it's a good approximation to the
+real life black hole after this object
+
+ align:start position:0%
+real life black hole after this object
+ 
+
+ align:start position:0%
+real life black hole after this object
+have stabilized so after the
+
+ align:start position:0%
+have stabilized so after the
+ 
+
+ align:start position:0%
+have stabilized so after the
+gravitational collapse has
+
+ align:start position:0%
+gravitational collapse has
+ 
+
+ align:start position:0%
+gravitational collapse has
+finished um yeah so this is the
+
+ align:start position:0%
+finished um yeah so this is the
+ 
+
+ align:start position:0%
+finished um yeah so this is the
+um so this is a mathematical in some
+
+ align:start position:0%
+um so this is a mathematical in some
+ 
+
+ align:start position:0%
+um so this is a mathematical in some
+sense it's a
+
+ align:start position:0%
+sense it's a
+ 
+
+ align:start position:0%
+sense it's a
+mathematical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idealization of real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+life back ho
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remark so the second
+
+ align:start position:0%
+remark so the second
+ 
+
+ align:start position:0%
+remark so the second
+remark is that despite this grr goes
+
+ align:start position:0%
+remark is that despite this grr goes
+ 
+
+ align:start position:0%
+remark is that despite this grr goes
+Infinity this MATC component goes
+
+ align:start position:0%
+Infinity this MATC component goes
+ 
+
+ align:start position:0%
+Infinity this MATC component goes
+Infinity so the space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time is non single Horizon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you can check it by Computing
+
+ align:start position:0%
+okay so you can check it by Computing
+ 
+
+ align:start position:0%
+okay so you can check it by Computing
+say curvature
+
+ align:start position:0%
+say curvature
+ 
+
+ align:start position:0%
+say curvature
+invariant of this metric you find none
+
+ align:start position:0%
+invariant of this metric you find none
+ 
+
+ align:start position:0%
+invariant of this metric you find none
+of the all the curvature in warant they
+
+ align:start position:0%
+of the all the curvature in warant they
+ 
+
+ align:start position:0%
+of the all the curvature in warant they
+are well
+
+ align:start position:0%
+are well
+ 
+
+ align:start position:0%
+are well
+defined so so this Horizon is just a
+
+ align:start position:0%
+defined so so this Horizon is just a
+ 
+
+ align:start position:0%
+defined so so this Horizon is just a
+coordinate uh you can show that this
+
+ align:start position:0%
+coordinate uh you can show that this
+ 
+
+ align:start position:0%
+coordinate uh you can show that this
+corizon just a coordinate singularity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we
+
+ align:start position:0%
+which we
+ 
+
+ align:start position:0%
+which we
+C actually we will see it
+
+ align:start position:0%
+C actually we will see it
+ 
+
+ align:start position:0%
+C actually we will see it
+maybe in next lecture or or maybe at the
+
+ align:start position:0%
+maybe in next lecture or or maybe at the
+ 
+
+ align:start position:0%
+maybe in next lecture or or maybe at the
+end of today's lecture that it just this
+
+ align:start position:0%
+end of today's lecture that it just this
+ 
+
+ align:start position:0%
+end of today's lecture that it just this
+coordinates R and the T coordinate
+
+ align:start position:0%
+coordinates R and the T coordinate
+ 
+
+ align:start position:0%
+coordinates R and the T coordinate
+become singular the coordinate cell
+
+ align:start position:0%
+become singular the coordinate cell
+ 
+
+ align:start position:0%
+become singular the coordinate cell
+become singular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this T we normally call it swash
+
+ align:start position:0%
+okay so this T we normally call it swash
+ 
+
+ align:start position:0%
+okay so this T we normally call it swash
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+time so let me just introduce the L so
+
+ align:start position:0%
+time so let me just introduce the L so
+ 
+
+ align:start position:0%
+time so let me just introduce the L so
+this T we call the swash your time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so swash found a this solution while
+
+ align:start position:0%
+so swash found a this solution while
+ 
+
+ align:start position:0%
+so swash found a this solution while
+fighting first world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+war in the really in the
+
+ align:start position:0%
+war in the really in the
+ 
+
+ align:start position:0%
+war in the really in the
+battlefield and uh and a couple months
+
+ align:start position:0%
+battlefield and uh and a couple months
+ 
+
+ align:start position:0%
+battlefield and uh and a couple months
+after he finished this metric he he he
+
+ align:start position:0%
+after he finished this metric he he he
+ 
+
+ align:start position:0%
+after he finished this metric he he he
+died from some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disease right this is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so L
+
+ align:start position:0%
+so so L
+ 
+
+ align:start position:0%
+so so L
+thing you can easily check
+
+ align:start position:0%
+thing you can easily check
+ 
+
+ align:start position:0%
+thing you can easily check
+yourself that IAL to RS The Horizon is a
+
+ align:start position:0%
+yourself that IAL to RS The Horizon is a
+ 
+
+ align:start position:0%
+yourself that IAL to RS The Horizon is a
+LW
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface it's a not hypers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface so nor hypers Surface by now
+
+ align:start position:0%
+surface so nor hypers Surface by now
+ 
+
+ align:start position:0%
+surface so nor hypers Surface by now
+hypersurface just say this surface
+
+ align:start position:0%
+hypersurface just say this surface
+ 
+
+ align:start position:0%
+hypersurface just say this surface
+contains
+
+ align:start position:0%
+contains
+ 
+
+ align:start position:0%
+contains
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+contain
+
+ align:start position:0%
+contain
+ 
+
+ align:start position:0%
+contain
+um geodesics which allow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this is a the thir remark is
+
+ align:start position:0%
+okay and this is a the thir remark is
+ 
+
+ align:start position:0%
+okay and this is a the thir remark is
+extremely important one which we
+
+ align:start position:0%
+extremely important one which we
+ 
+
+ align:start position:0%
+extremely important one which we
+will use many times in the
+
+ align:start position:0%
+will use many times in the
+ 
+
+ align:start position:0%
+will use many times in the
+future is that the
+
+ align:start position:0%
+future is that the
+ 
+
+ align:start position:0%
+future is that the
+Horizon is a surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of infinite R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shift compared to
+
+ align:start position:0%
+shift compared to
+ 
+
+ align:start position:0%
+shift compared to
+the infinite red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shift from the perspective of Observer
+
+ align:start position:0%
+shift from the perspective of Observer
+ 
+
+ align:start position:0%
+shift from the perspective of Observer
+at Infinity
+
+ align:start position:0%
+at Infinity
+ 
+
+ align:start position:0%
+at Infinity
+okay so let me save time not to add this
+
+ align:start position:0%
+okay so let me save time not to add this
+ 
+
+ align:start position:0%
+okay so let me save time not to add this
+qualifying remark from from the
+
+ align:start position:0%
+qualifying remark from from the
+ 
+
+ align:start position:0%
+qualifying remark from from the
+perspective of the observe by
+
+ align:start position:0%
+perspective of the observe by
+ 
+
+ align:start position:0%
+perspective of the observe by
+Infinity so so let me just illustrate
+
+ align:start position:0%
+Infinity so so let me just illustrate
+ 
+
+ align:start position:0%
+Infinity so so let me just illustrate
+this point
+
+ align:start position:0%
+this point
+ 
+
+ align:start position:0%
+this point
+a little bit more
+
+ align:start position:0%
+a little bit more
+ 
+
+ align:start position:0%
+a little bit more
+explicitly so let's consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Observer consider an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observer so let me call
+
+ align:start position:0%
+observer so let me call
+ 
+
+ align:start position:0%
+observer so let me call
+O so this is at some hypers surface R
+
+ align:start position:0%
+O so this is at some hypers surface R
+ 
+
+ align:start position:0%
+O so this is at some hypers surface R
+which is close
+
+ align:start position:0%
+which is close
+ 
+
+ align:start position:0%
+which is close
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Horizon yeah uh some say some as some
+
+ align:start position:0%
+Horizon yeah uh some say some as some
+ 
+
+ align:start position:0%
+Horizon yeah uh some say some as some
+place which is close to the Horizon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay slightly outside
+
+ align:start position:0%
+okay slightly outside
+ 
+
+ align:start position:0%
+okay slightly outside
+Horizon and let's consider another
+
+ align:start position:0%
+Horizon and let's consider another
+ 
+
+ align:start position:0%
+Horizon and let's consider another
+Observer which I call O
+
+ align:start position:0%
+Observer which I call O
+ 
+
+ align:start position:0%
+Observer which I call O
+Infinity which
+
+ align:start position:0%
+Infinity which
+ 
+
+ align:start position:0%
+Infinity which
+add I equal to
+
+ align:start position:0%
+add I equal to
+ 
+
+ align:start position:0%
+add I equal to
+Infinity okay very far away from the
+
+ align:start position:0%
+Infinity okay very far away from the
+ 
+
+ align:start position:0%
+Infinity okay very far away from the
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+hole so at so let's first look at this
+
+ align:start position:0%
+hole so at so let's first look at this
+ 
+
+ align:start position:0%
+hole so at so let's first look at this
+Observer
+
+ align:start position:0%
+Observer
+ 
+
+ align:start position:0%
+Observer
+so I equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity then your
+
+ align:start position:0%
+Infinity then your
+ 
+
+ align:start position:0%
+Infinity then your
+matric so at I go to Infinity this F
+
+ align:start position:0%
+matric so at I go to Infinity this F
+ 
+
+ align:start position:0%
+matric so at I go to Infinity this F
+just become one because when you R go to
+
+ align:start position:0%
+just become one because when you R go to
+ 
+
+ align:start position:0%
+just become one because when you R go to
+Infinity this R just become one and then
+
+ align:start position:0%
+Infinity this R just become one and then
+ 
+
+ align:start position:0%
+Infinity this R just become one and then
+this become the standard
+
+ align:start position:0%
+this become the standard
+ 
+
+ align:start position:0%
+this become the standard
+minkovski space time written in the
+
+ align:start position:0%
+minkovski space time written in the
+ 
+
+ align:start position:0%
+minkovski space time written in the
+spherical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates so so we just have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah just standard the mosi's time
+
+ align:start position:0%
+yeah just standard the mosi's time
+ 
+
+ align:start position:0%
+yeah just standard the mosi's time
+written the spical
+
+ align:start position:0%
+written the spical
+ 
+
+ align:start position:0%
+written the spical
+coordinates and uh and from here you can
+
+ align:start position:0%
+coordinates and uh and from here you can
+ 
+
+ align:start position:0%
+coordinates and uh and from here you can
+immediately see so this T this what we
+
+ align:start position:0%
+immediately see so this T this what we
+ 
+
+ align:start position:0%
+immediately see so this T this what we
+call swal time T is the proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time for this observe at Infinity say
+
+ align:start position:0%
+time for this observe at Infinity say
+ 
+
+ align:start position:0%
+time for this observe at Infinity say
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+okay so now let's look
+
+ align:start position:0%
+okay so now let's look
+ 
+
+ align:start position:0%
+okay so now let's look
+at at some some place IAL to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RH so at IAL to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RH then the the matric is given by minus
+
+ align:start position:0%
+RH then the the matric is given by minus
+ 
+
+ align:start position:0%
+RH then the the matric is given by minus
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+RH DT
+
+ align:start position:0%
+RH DT
+ 
+
+ align:start position:0%
+RH DT
+s with the
+
+ align:start position:0%
+s with the
+ 
+
+ align:start position:0%
+s with the
+rest
+
+ align:start position:0%
+rest
+ 
+
+ align:start position:0%
+rest
+okay and to to define the proper
+
+ align:start position:0%
+okay and to to define the proper
+ 
+
+ align:start position:0%
+okay and to to define the proper
+time for The Observer at we can just
+
+ align:start position:0%
+time for The Observer at we can just
+ 
+
+ align:start position:0%
+time for The Observer at we can just
+directly write it as minus d square so
+
+ align:start position:0%
+directly write it as minus d square so
+ 
+
+ align:start position:0%
+directly write it as minus d square so
+that's the prop time observed by
+
+ align:start position:0%
+that's the prop time observed by
+ 
+
+ align:start position:0%
+that's the prop time observed by
+Observer at this
+
+ align:start position:0%
+Observer at this
+ 
+
+ align:start position:0%
+Observer at this
+hypersurface okay so so then we conclude
+
+ align:start position:0%
+hypersurface okay so so then we conclude
+ 
+
+ align:start position:0%
+hypersurface okay so so then we conclude
+so let me call it to H so we conclude
+
+ align:start position:0%
+so let me call it to H so we conclude
+ 
+
+ align:start position:0%
+so let me call it to H so we conclude
+that the proper time at for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+o is given by
+
+ align:start position:0%
+o is given by
+ 
+
+ align:start position:0%
+o is given by
+F12 I RH *
+
+ align:start position:0%
+F12 I RH *
+ 
+
+ align:start position:0%
+F12 I RH *
+DT okay so relates to the proper time at
+
+ align:start position:0%
+DT okay so relates to the proper time at
+ 
+
+ align:start position:0%
+DT okay so relates to the proper time at
+Infinity by this Factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so if I write it more explicitly so
+
+ align:start position:0%
+so so if I write it more explicitly so
+ 
+
+ align:start position:0%
+so so if I write it more explicitly so
+this is 1 minus RH / by RS 12 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT so we see that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we see that
+
+ align:start position:0%
+so we see that
+ 
+
+ align:start position:0%
+so we see that
+as RH suppose this
+
+ align:start position:0%
+as RH suppose this
+ 
+
+ align:start position:0%
+as RH suppose this
+Observer the location of this Ober the
+
+ align:start position:0%
+Observer the location of this Ober the
+ 
+
+ align:start position:0%
+Observer the location of this Ober the
+the location of this Observer approach
+
+ align:start position:0%
+the location of this Observer approach
+ 
+
+ align:start position:0%
+the location of this Observer approach
+The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Horizon say if I H approaches to
+
+ align:start position:0%
+Horizon say if I H approaches to
+ 
+
+ align:start position:0%
+Horizon say if I H approaches to
+is then this d h
+
+ align:start position:0%
+is then this d h
+ 
+
+ align:start position:0%
+is then this d h
+divid by DT will goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compare to the time at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity the time
+
+ align:start position:0%
+Infinity the time
+ 
+
+ align:start position:0%
+Infinity the time
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+r equal to r
+
+ align:start position:0%
+r equal to r
+ 
+
+ align:start position:0%
+r equal to r
+s becomes infinite snow okay so so
+
+ align:start position:0%
+s becomes infinite snow okay so so
+ 
+
+ align:start position:0%
+s becomes infinite snow okay so so
+approximate let me say becomes infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+snow
+
+ align:start position:0%
+snow
+ 
+
+ align:start position:0%
+snow
+okay so that
+
+ align:start position:0%
+okay so that
+ 
+
+ align:start position:0%
+okay so that
+means any finite
+
+ align:start position:0%
+means any finite
+ 
+
+ align:start position:0%
+means any finite
+interval any finite proper time
+
+ align:start position:0%
+interval any finite proper time
+ 
+
+ align:start position:0%
+interval any finite proper time
+interval for Observer at o for this
+
+ align:start position:0%
+interval for Observer at o for this
+ 
+
+ align:start position:0%
+interval for Observer at o for this
+o when you viewed from
+
+ align:start position:0%
+o when you viewed from
+ 
+
+ align:start position:0%
+o when you viewed from
+Infinity uh become infinitely long okay
+
+ align:start position:0%
+Infinity uh become infinitely long okay
+ 
+
+ align:start position:0%
+Infinity uh become infinitely long okay
+become very long time scale okay become
+
+ align:start position:0%
+become very long time scale okay become
+ 
+
+ align:start position:0%
+become very long time scale okay become
+very long time scale so you can also
+
+ align:start position:0%
+very long time scale so you can also
+ 
+
+ align:start position:0%
+very long time scale so you can also
+invert this you can also
+
+ align:start position:0%
+invert this you can also
+ 
+
+ align:start position:0%
+invert this you can also
+invert this
+
+ align:start position:0%
+invert this
+ 
+
+ align:start position:0%
+invert this
+relation okay you can also re invert re
+
+ align:start position:0%
+relation okay you can also re invert re
+ 
+
+ align:start position:0%
+relation okay you can also re invert re
+relation say say suppose some event of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energ with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energ EH with proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy with proper
+
+ align:start position:0%
+energy with proper
+ 
+
+ align:start position:0%
+energy with proper
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+eh say for this Observer at o for this
+
+ align:start position:0%
+eh say for this Observer at o for this
+ 
+
+ align:start position:0%
+eh say for this Observer at o for this
+observe o
+
+ align:start position:0%
+observe o
+ 
+
+ align:start position:0%
+observe o
+h then because of this time because of
+
+ align:start position:0%
+h then because of this time because of
+ 
+
+ align:start position:0%
+h then because of this time because of
+the time relation between
+
+ align:start position:0%
+the time relation between
+ 
+
+ align:start position:0%
+the time relation between
+them okay because of the time relation
+
+ align:start position:0%
+them okay because of the time relation
+ 
+
+ align:start position:0%
+them okay because of the time relation
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+them then then from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perspective from the perspective of this
+
+ align:start position:0%
+perspective from the perspective of this
+ 
+
+ align:start position:0%
+perspective from the perspective of this
+obser
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity the
+
+ align:start position:0%
+Infinity the
+ 
+
+ align:start position:0%
+Infinity the
+energe is given just by by you inverted
+
+ align:start position:0%
+energe is given just by by you inverted
+ 
+
+ align:start position:0%
+energe is given just by by you inverted
+viation between the time okay because
+
+ align:start position:0%
+viation between the time okay because
+ 
+
+ align:start position:0%
+viation between the time okay because
+the energy and time conjugate so the E
+
+ align:start position:0%
+the energy and time conjugate so the E
+ 
+
+ align:start position:0%
+the energy and time conjugate so the E
+Infinity e times this F12
+
+ align:start position:0%
+Infinity e times this F12
+ 
+
+ align:start position:0%
+Infinity e times this F12
+RH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so this just again say in the
+
+ align:start position:0%
+okay so so this just again say in the
+ 
+
+ align:start position:0%
+okay so so this just again say in the
+slightly different way that for any
+
+ align:start position:0%
+slightly different way that for any
+ 
+
+ align:start position:0%
+slightly different way that for any
+finite any
+
+ align:start position:0%
+finite any
+ 
+
+ align:start position:0%
+finite any
+finite eh prop noal proper energy okay
+
+ align:start position:0%
+finite eh prop noal proper energy okay
+ 
+
+ align:start position:0%
+finite eh prop noal proper energy okay
+so this is a local proper energy for the
+
+ align:start position:0%
+so this is a local proper energy for the
+ 
+
+ align:start position:0%
+so this is a local proper energy for the
+Observer at o
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this e
+
+ align:start position:0%
+this e
+ 
+
+ align:start position:0%
+this e
+Infinity the same event viewed from the
+
+ align:start position:0%
+Infinity the same event viewed from the
+ 
+
+ align:start position:0%
+Infinity the same event viewed from the
+from the perspective of the obser
+
+ align:start position:0%
+from the perspective of the obser
+ 
+
+ align:start position:0%
+from the perspective of the obser
+infinity goes
+
+ align:start position:0%
+infinity goes
+ 
+
+ align:start position:0%
+infinity goes
+zero as I goes to I
+
+ align:start position:0%
+zero as I goes to I
+ 
+
+ align:start position:0%
+zero as I goes to I
+okay so that so that is this is
+
+ align:start position:0%
+okay so that so that is this is
+ 
+
+ align:start position:0%
+okay so that so that is this is
+infinitely ref red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shifted okay become infinite R shift so
+
+ align:start position:0%
+shifted okay become infinite R shift so
+ 
+
+ align:start position:0%
+shifted okay become infinite R shift so
+any process
+
+ align:start position:0%
+any process
+ 
+
+ align:start position:0%
+any process
+so any process with noal proper energy
+
+ align:start position:0%
+so any process with noal proper energy
+ 
+
+ align:start position:0%
+so any process with noal proper energy
+Bu from Infinity corresponding to very
+
+ align:start position:0%
+Bu from Infinity corresponding to very
+ 
+
+ align:start position:0%
+Bu from Infinity corresponding to very
+very low energy process okay so this
+
+ align:start position:0%
+very low energy process okay so this
+ 
+
+ align:start position:0%
+very low energy process okay so this
+actually will play a very important role
+
+ align:start position:0%
+actually will play a very important role
+ 
+
+ align:start position:0%
+actually will play a very important role
+this feature will play very important
+
+ align:start position:0%
+this feature will play very important
+ 
+
+ align:start position:0%
+this feature will play very important
+role when later we talk about
+
+ align:start position:0%
+role when later we talk about
+ 
+
+ align:start position:0%
+role when later we talk about
+holographic Duality and its
+
+ align:start position:0%
+holographic Duality and its
+ 
+
+ align:start position:0%
+holographic Duality and its
+simplification say say for the field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ET yes so this is just a tic comment I
+
+ align:start position:0%
+ET yes so this is just a tic comment I
+ 
+
+ align:start position:0%
+ET yes so this is just a tic comment I
+think you need a minus in Fr of your s
+
+ align:start position:0%
+think you need a minus in Fr of your s
+ 
+
+ align:start position:0%
+think you need a minus in Fr of your s
+just to make sure proper time isn't
+
+ align:start position:0%
+just to make sure proper time isn't
+ 
+
+ align:start position:0%
+just to make sure proper time isn't
+imaginary uh sorry which Mal sign um in
+
+ align:start position:0%
+imaginary uh sorry which Mal sign um in
+ 
+
+ align:start position:0%
+imaginary uh sorry which Mal sign um in
+the you mean
+
+ align:start position:0%
+the you mean
+ 
+
+ align:start position:0%
+the you mean
+here you mean here or here below that
+
+ align:start position:0%
+here you mean here or here below that
+ 
+
+ align:start position:0%
+here you mean here or here below that
+below that below that yeah R iser oh no
+
+ align:start position:0%
+below that below that yeah R iser oh no
+ 
+
+ align:start position:0%
+below that below that yeah R iser oh no
+sorry sorry sorry
+
+ align:start position:0%
+sorry sorry sorry
+ 
+
+ align:start position:0%
+sorry sorry sorry
+sorry thank you I wrote it wrong should
+
+ align:start position:0%
+sorry thank you I wrote it wrong should
+ 
+
+ align:start position:0%
+sorry thank you I wrote it wrong should
+be i s i
+
+ align:start position:0%
+be i s i
+ 
+
+ align:start position:0%
+be i s i
+yeah yeah yeah because I S is above
+
+ align:start position:0%
+yeah yeah yeah because I S is above
+ 
+
+ align:start position:0%
+yeah yeah yeah because I S is above
+sorry yeah so r s is above so I Val as I
+
+ align:start position:0%
+sorry yeah so r s is above so I Val as I
+ 
+
+ align:start position:0%
+sorry yeah so r s is above so I Val as I
+so I is downstairs yeah thank you so so
+
+ align:start position:0%
+so I is downstairs yeah thank you so so
+ 
+
+ align:start position:0%
+so I is downstairs yeah thank you so so
+I stand so I always consider RH is great
+
+ align:start position:0%
+I stand so I always consider RH is great
+ 
+
+ align:start position:0%
+I stand so I always consider RH is great
+equal to r s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh so some other fact and again
+
+ align:start position:0%
+okay and uh so some other fact and again
+ 
+
+ align:start position:0%
+okay and uh so some other fact and again
+I will just list
+
+ align:start position:0%
+I will just list
+ 
+
+ align:start position:0%
+I will just list
+them I will just list them if you're not
+
+ align:start position:0%
+them I will just list them if you're not
+ 
+
+ align:start position:0%
+them I will just list them if you're not
+not familiar with them uh it should be
+
+ align:start position:0%
+not familiar with them uh it should be
+ 
+
+ align:start position:0%
+not familiar with them uh it should be
+very easy for you to go through them to
+
+ align:start position:0%
+very easy for you to go through them to
+ 
+
+ align:start position:0%
+very easy for you to go through them to
+rederive them with a little bit
+
+ align:start position:0%
+rederive them with a little bit
+ 
+
+ align:start position:0%
+rederive them with a little bit
+knowledge in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gr so number
+
+ align:start position:0%
+gr so number
+ 
+
+ align:start position:0%
+gr so number
+four is that it takes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four fre four means we just follow
+
+ align:start position:0%
+four fre four means we just follow
+ 
+
+ align:start position:0%
+four fre four means we just follow
+geodesics okay fre four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traveler a finite proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time to reach the Horizon say from the
+
+ align:start position:0%
+time to reach the Horizon say from the
+ 
+
+ align:start position:0%
+time to reach the Horizon say from the
+infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite s short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so so you can easily check that
+
+ align:start position:0%
+okay so so you can easily check that
+ 
+
+ align:start position:0%
+okay so so you can easily check that
+actually take infinite spal time for
+
+ align:start position:0%
+actually take infinite spal time for
+ 
+
+ align:start position:0%
+actually take infinite spal time for
+object to Force Through The Horizon
+
+ align:start position:0%
+object to Force Through The Horizon
+ 
+
+ align:start position:0%
+object to Force Through The Horizon
+but from the from the free four obser
+
+ align:start position:0%
+but from the from the free four obser
+ 
+
+ align:start position:0%
+but from the from the free four obser
+itself it's actually just fin at proper
+
+ align:start position:0%
+itself it's actually just fin at proper
+ 
+
+ align:start position:0%
+itself it's actually just fin at proper
+time and so from the perspective of the
+
+ align:start position:0%
+time and so from the perspective of the
+ 
+
+ align:start position:0%
+time and so from the perspective of the
+Observer and infinity looks like this
+
+ align:start position:0%
+Observer and infinity looks like this
+ 
+
+ align:start position:0%
+Observer and infinity looks like this
+object never fall into the black
+
+ align:start position:0%
+object never fall into the black
+ 
+
+ align:start position:0%
+object never fall into the black
+hole it just Frozen at the
+
+ align:start position:0%
+hole it just Frozen at the
+ 
+
+ align:start position:0%
+hole it just Frozen at the
+Horizon so and the and
+
+ align:start position:0%
+Horizon so and the and
+ 
+
+ align:start position:0%
+Horizon so and the and
+the another remark is that
+
+ align:start position:0%
+the another remark is that
+ 
+
+ align:start position:0%
+the another remark is that
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+inside the horizon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means when R BEC smaller than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RS The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Traveler
+
+ align:start position:0%
+Traveler
+ 
+
+ align:start position:0%
+Traveler
+canot send signals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+signals to outs side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no can
+
+ align:start position:0%
+no can
+ 
+
+ align:start position:0%
+no can
+he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+escape okay so that's why this is called
+
+ align:start position:0%
+escape okay so that's why this is called
+ 
+
+ align:start position:0%
+escape okay so that's why this is called
+even Horizon so we will see this uh uh
+
+ align:start position:0%
+even Horizon so we will see this uh uh
+ 
+
+ align:start position:0%
+even Horizon so we will see this uh uh
+slightly
+
+ align:start position:0%
+slightly
+ 
+
+ align:start position:0%
+slightly
+later in next neure we will see this
+
+ align:start position:0%
+later in next neure we will see this
+ 
+
+ align:start position:0%
+later in next neure we will see this
+explicitly
+
+ align:start position:0%
+explicitly
+ 
+
+ align:start position:0%
+explicitly
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+finally there two important geometric
+
+ align:start position:0%
+finally there two important geometric
+ 
+
+ align:start position:0%
+finally there two important geometric
+quantities associated with a
+
+ align:start position:0%
+quantities associated with a
+ 
+
+ align:start position:0%
+quantities associated with a
+horizon two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometric
+
+ align:start position:0%
+geometric
+ 
+
+ align:start position:0%
+geometric
+okay so the first one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the area of the spatial section so
+
+ align:start position:0%
+it's the area of the spatial section so
+ 
+
+ align:start position:0%
+it's the area of the spatial section so
+suppose so let's consider we are at IAL
+
+ align:start position:0%
+suppose so let's consider we are at IAL
+ 
+
+ align:start position:0%
+suppose so let's consider we are at IAL
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+RS and then and here you just set this
+
+ align:start position:0%
+RS and then and here you just set this
+ 
+
+ align:start position:0%
+RS and then and here you just set this
+IAL to r s and then this is a two
+
+ align:start position:0%
+IAL to r s and then this is a two
+ 
+
+ align:start position:0%
+IAL to r s and then this is a two
+dimensional sphere okay so this two
+
+ align:start position:0%
+dimensional sphere okay so this two
+ 
+
+ align:start position:0%
+dimensional sphere okay so this two
+dimensional sphere corresponding to a
+
+ align:start position:0%
+dimensional sphere corresponding to a
+ 
+
+ align:start position:0%
+dimensional sphere corresponding to a
+spatial section say of the
+
+ align:start position:0%
+spatial section say of the
+ 
+
+ align:start position:0%
+spatial section say of the
+Horizon so um so
+
+ align:start position:0%
+Horizon so um so
+ 
+
+ align:start position:0%
+Horizon so um so
+first is this is the
+
+ align:start position:0%
+first is this is the
+ 
+
+ align:start position:0%
+first is this is the
+a is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area of a spatial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+section
+
+ align:start position:0%
+section
+ 
+
+ align:start position:0%
+section
+okay so so you can just say let's look
+
+ align:start position:0%
+okay so so you can just say let's look
+ 
+
+ align:start position:0%
+okay so so you can just say let's look
+at the area of this
+
+ align:start position:0%
+at the area of this
+ 
+
+ align:start position:0%
+at the area of this
+part um with the r equal to the Horizon
+
+ align:start position:0%
+part um with the r equal to the Horizon
+ 
+
+ align:start position:0%
+part um with the r equal to the Horizon
+radius so so this just give you a equal
+
+ align:start position:0%
+radius so so this just give you a equal
+ 
+
+ align:start position:0%
+radius so so this just give you a equal
+to ah equal to 4 pi r
+
+ align:start position:0%
+to ah equal to 4 pi r
+ 
+
+ align:start position:0%
+to ah equal to 4 pi r
+s² and this
+
+ align:start position:0%
+s² and this
+ 
+
+ align:start position:0%
+s² and this
+RS is 2
+
+ align:start position:0%
+RS is 2
+ 
+
+ align:start position:0%
+RS is 2
+GM so this
+
+ align:start position:0%
+GM so this
+ 
+
+ align:start position:0%
+GM so this
+become 16
+
+ align:start position:0%
+become 16
+ 
+
+ align:start position:0%
+become 16
+Pi GM
+
+ align:start position:0%
+Pi GM
+ 
+
+ align:start position:0%
+Pi GM
+squ Square okay so this is one of the
+
+ align:start position:0%
+squ Square okay so this is one of the
+ 
+
+ align:start position:0%
+squ Square okay so this is one of the
+key quantities of a black Horizon is it
+
+ align:start position:0%
+key quantities of a black Horizon is it
+ 
+
+ align:start position:0%
+key quantities of a black Horizon is it
+is what we call Horizon area
+
+ align:start position:0%
+is what we call Horizon area
+ 
+
+ align:start position:0%
+is what we call Horizon area
+okay let we call this Horizon area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+B is called the surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity is called surface
+
+ align:start position:0%
+gravity is called surface
+ 
+
+ align:start position:0%
+gravity is called surface
+gravity so the surface gravity is
+
+ align:start position:0%
+gravity so the surface gravity is
+ 
+
+ align:start position:0%
+gravity so the surface gravity is
+defined by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration of a stationary Observer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Horizon has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measured at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity okay at Infinity means that the
+
+ align:start position:0%
+Infinity okay at Infinity means that the
+ 
+
+ align:start position:0%
+Infinity okay at Infinity means that the
+yeah spatial
+
+ align:start position:0%
+yeah spatial
+ 
+
+ align:start position:0%
+yeah spatial
+Infinity so so you can uh if you're not
+
+ align:start position:0%
+Infinity so so you can uh if you're not
+ 
+
+ align:start position:0%
+Infinity so so you can uh if you're not
+familiar with the this concept of
+
+ align:start position:0%
+familiar with the this concept of
+ 
+
+ align:start position:0%
+familiar with the this concept of
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+gravity you can find it in standard
+
+ align:start position:0%
+gravity you can find it in standard
+ 
+
+ align:start position:0%
+gravity you can find it in standard
+Textbooks For
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example the
+
+ align:start position:0%
+example the
+ 
+
+ align:start position:0%
+example the
+W say page
+
+ align:start position:0%
+W say page
+ 
+
+ align:start position:0%
+W say page
+158 and
+
+ align:start position:0%
+158 and
+ 
+
+ align:start position:0%
+158 and
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+section five okay let's try to check it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so say suppose you have a black
+
+ align:start position:0%
+there so say suppose you have a black
+ 
+
+ align:start position:0%
+there so say suppose you have a black
+hole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say this is a SWAT of
+
+ align:start position:0%
+say this is a SWAT of
+ 
+
+ align:start position:0%
+say this is a SWAT of
+radius of course since want to fall into
+
+ align:start position:0%
+radius of course since want to fall into
+ 
+
+ align:start position:0%
+radius of course since want to fall into
+the black hole so if you want to
+
+ align:start position:0%
+the black hole so if you want to
+ 
+
+ align:start position:0%
+the black hole so if you want to
+remain at a fixed location outside the
+
+ align:start position:0%
+remain at a fixed location outside the
+ 
+
+ align:start position:0%
+remain at a fixed location outside the
+black Co then you really have to
+
+ align:start position:0%
+black Co then you really have to
+ 
+
+ align:start position:0%
+black Co then you really have to
+accelerate okay you have to file some
+
+ align:start position:0%
+accelerate okay you have to file some
+ 
+
+ align:start position:0%
+accelerate okay you have to file some
+engine to keep yourself to stay there
+
+ align:start position:0%
+engine to keep yourself to stay there
+ 
+
+ align:start position:0%
+engine to keep yourself to stay there
+and you can yeah you can calculate what
+
+ align:start position:0%
+and you can yeah you can calculate what
+ 
+
+ align:start position:0%
+and you can yeah you can calculate what
+is acceleration you need to be able to
+
+ align:start position:0%
+is acceleration you need to be able to
+ 
+
+ align:start position:0%
+is acceleration you need to be able to
+stay here still okay
+
+ align:start position:0%
+stay here still okay
+ 
+
+ align:start position:0%
+stay here still okay
+and once you are closer and closer to
+
+ align:start position:0%
+and once you are closer and closer to
+ 
+
+ align:start position:0%
+and once you are closer and closer to
+the Horizon that acceleration become
+
+ align:start position:0%
+the Horizon that acceleration become
+ 
+
+ align:start position:0%
+the Horizon that acceleration become
+bigger and bigger eventually become
+
+ align:start position:0%
+bigger and bigger eventually become
+ 
+
+ align:start position:0%
+bigger and bigger eventually become
+Infinity when you approach The
+
+ align:start position:0%
+Infinity when you approach The
+ 
+
+ align:start position:0%
+Infinity when you approach The
+Horizon but because of this red shift
+
+ align:start position:0%
+Horizon but because of this red shift
+ 
+
+ align:start position:0%
+Horizon but because of this red shift
+effect okay because of this red shift
+
+ align:start position:0%
+effect okay because of this red shift
+ 
+
+ align:start position:0%
+effect okay because of this red shift
+effect when this acceleration is viewed
+
+ align:start position:0%
+effect when this acceleration is viewed
+ 
+
+ align:start position:0%
+effect when this acceleration is viewed
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+units for observe and infinite and
+
+ align:start position:0%
+units for observe and infinite and
+ 
+
+ align:start position:0%
+units for observe and infinite and
+infinity then you have Infinity divide
+
+ align:start position:0%
+infinity then you have Infinity divide
+ 
+
+ align:start position:0%
+infinity then you have Infinity divide
+by Infinity then tends out to be
+
+ align:start position:0%
+by Infinity then tends out to be
+ 
+
+ align:start position:0%
+by Infinity then tends out to be
+finite and
+
+ align:start position:0%
+finite and
+ 
+
+ align:start position:0%
+finite and
+and this is called surface gravity is
+
+ align:start position:0%
+and this is called surface gravity is
+ 
+
+ align:start position:0%
+and this is called surface gravity is
+normally called
+
+ align:start position:0%
+normally called
+ 
+
+ align:start position:0%
+normally called
+Kappa normally called Kappa and this is
+
+ align:start position:0%
+Kappa normally called Kappa and this is
+ 
+
+ align:start position:0%
+Kappa normally called Kappa and this is
+one of basic quantities basic geometric
+
+ align:start position:0%
+one of basic quantities basic geometric
+ 
+
+ align:start position:0%
+one of basic quantities basic geometric
+quantity of the Horizon so so we're not
+
+ align:start position:0%
+quantity of the Horizon so so we're not
+ 
+
+ align:start position:0%
+quantity of the Horizon so so we're not
+derive it here I don't have
+
+ align:start position:0%
+derive it here I don't have
+ 
+
+ align:start position:0%
+derive it here I don't have
+time and if you want to see it uh see
+
+ align:start position:0%
+time and if you want to see it uh see
+ 
+
+ align:start position:0%
+time and if you want to see it uh see
+this WS book so you can calculate that
+
+ align:start position:0%
+this WS book so you can calculate that
+ 
+
+ align:start position:0%
+this WS book so you can calculate that
+this is just given by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one2 the derivative of this function
+
+ align:start position:0%
+one2 the derivative of this function
+ 
+
+ align:start position:0%
+one2 the derivative of this function
+f you validated at the Horizon uh
+
+ align:start position:0%
+f you validated at the Horizon uh
+ 
+
+ align:start position:0%
+f you validated at the Horizon uh
+invited at the Horizon location okay so
+
+ align:start position:0%
+invited at the Horizon location okay so
+ 
+
+ align:start position:0%
+invited at the Horizon location okay so
+f is equal to zero at the Horizon but F
+
+ align:start position:0%
+f is equal to zero at the Horizon but F
+ 
+
+ align:start position:0%
+f is equal to zero at the Horizon but F
+Prime is not okay so so you can easily
+
+ align:start position:0%
+Prime is not okay so so you can easily
+ 
+
+ align:start position:0%
+Prime is not okay so so you can easily
+calculate so this is 1 over 2
+
+ align:start position:0%
+calculate so this is 1 over 2
+ 
+
+ align:start position:0%
+calculate so this is 1 over 2
+RS from
+
+ align:start position:0%
+RS from
+ 
+
+ align:start position:0%
+RS from
+here and uh is equal to 1 over 4 g
+
+ align:start position:0%
+here and uh is equal to 1 over 4 g
+ 
+
+ align:start position:0%
+here and uh is equal to 1 over 4 g
+m okay this is another very important
+
+ align:start position:0%
+m okay this is another very important
+ 
+
+ align:start position:0%
+m okay this is another very important
+quantity for the for the black ho
+
+ align:start position:0%
+quantity for the for the black ho
+ 
+
+ align:start position:0%
+quantity for the for the black ho
+actually I think right now it's
+
+ align:start position:0%
+actually I think right now it's
+ 
+
+ align:start position:0%
+actually I think right now it's
+a good place to
+
+ align:start position:0%
+a good place to
+ 
+
+ align:start position:0%
+a good place to
+stop
+
+ align:start position:0%
+stop
+ 
+
+ align:start position:0%
+stop
+um okay so let's stop here for today and
+
+ align:start position:0%
+um okay so let's stop here for today and
+ 
+
+ align:start position:0%
+um okay so let's stop here for today and
+next time we will describe then we will
+
+ align:start position:0%
+next time we will describe then we will
+ 
+
+ align:start position:0%
+next time we will describe then we will
+from here we will discuss the Cal
+
+ align:start position:0%
+from here we will discuss the Cal
+ 
+
+ align:start position:0%
+from here we will discuss the Cal
+structure of the black hole and then you
+
+ align:start position:0%
+structure of the black hole and then you
+ 
+
+ align:start position:0%
+structure of the black hole and then you
+will see uh explicitely some of those
+
+ align:start position:0%
+will see uh explicitely some of those
+ 
+
+ align:start position:0%
+will see uh explicitely some of those
+statement if you if you have not seen
+
+ align:start position:0%
+statement if you if you have not seen
+ 
+
+ align:start position:0%
+statement if you if you have not seen
+them before
\ No newline at end of file
diff --git a/X86s94ylybQ.txt b/X86s94ylybQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..123d83d65b187879854a8689e8bb6c7d4c5ac836
--- /dev/null
+++ b/X86s94ylybQ.txt
@@ -0,0 +1,7779 @@
+align:start position:0%
+ 
+sorry okay what
+
+ align:start position:0%
+sorry okay what
+ 
+
+ align:start position:0%
+sorry okay what
+now all right so before I begin I just
+
+ align:start position:0%
+now all right so before I begin I just
+ 
+
+ align:start position:0%
+now all right so before I begin I just
+want to say I want to keep this pretty
+
+ align:start position:0%
+want to say I want to keep this pretty
+ 
+
+ align:start position:0%
+want to say I want to keep this pretty
+informal you know so feel free to jump
+
+ align:start position:0%
+informal you know so feel free to jump
+ 
+
+ align:start position:0%
+informal you know so feel free to jump
+in if you have comments questions if you
+
+ align:start position:0%
+in if you have comments questions if you
+ 
+
+ align:start position:0%
+in if you have comments questions if you
+disagree with me you know which
+
+ align:start position:0%
+disagree with me you know which
+ 
+
+ align:start position:0%
+disagree with me you know which
+hopefully you will you know so okay so
+
+ align:start position:0%
+hopefully you will you know so okay so
+ 
+
+ align:start position:0%
+hopefully you will you know so okay so
+I'm the first presentation here and I
+
+ align:start position:0%
+I'm the first presentation here and I
+ 
+
+ align:start position:0%
+I'm the first presentation here and I
+kind of like being the first because
+
+ align:start position:0%
+kind of like being the first because
+ 
+
+ align:start position:0%
+kind of like being the first because
+we're just getting introduced to the
+
+ align:start position:0%
+we're just getting introduced to the
+ 
+
+ align:start position:0%
+we're just getting introduced to the
+class so I have a chance to kind of say
+
+ align:start position:0%
+class so I have a chance to kind of say
+ 
+
+ align:start position:0%
+class so I have a chance to kind of say
+my own opinions my own viewpoints on why
+
+ align:start position:0%
+my own opinions my own viewpoints on why
+ 
+
+ align:start position:0%
+my own opinions my own viewpoints on why
+we study film why we're studying
+
+ align:start position:0%
+we study film why we're studying
+ 
+
+ align:start position:0%
+we study film why we're studying
+philosophy of film um and so we've all
+
+ align:start position:0%
+philosophy of film um and so we've all
+ 
+
+ align:start position:0%
+philosophy of film um and so we've all
+done the reading you know so I kind of
+
+ align:start position:0%
+done the reading you know so I kind of
+ 
+
+ align:start position:0%
+done the reading you know so I kind of
+want to present my own views my own
+
+ align:start position:0%
+want to present my own views my own
+ 
+
+ align:start position:0%
+want to present my own views my own
+reactions to the reading you know I
+
+ align:start position:0%
+reactions to the reading you know I
+ 
+
+ align:start position:0%
+reactions to the reading you know I
+agree with a lot of it disagree with
+
+ align:start position:0%
+agree with a lot of it disagree with
+ 
+
+ align:start position:0%
+agree with a lot of it disagree with
+some of it I understand hopefully most
+
+ align:start position:0%
+some of it I understand hopefully most
+ 
+
+ align:start position:0%
+some of it I understand hopefully most
+of it and I'm sure I misunderstood some
+
+ align:start position:0%
+of it and I'm sure I misunderstood some
+ 
+
+ align:start position:0%
+of it and I'm sure I misunderstood some
+of it but I mean it definitely brought
+
+ align:start position:0%
+of it but I mean it definitely brought
+ 
+
+ align:start position:0%
+of it but I mean it definitely brought
+up a lot of questions in my mind and
+
+ align:start position:0%
+up a lot of questions in my mind and
+ 
+
+ align:start position:0%
+up a lot of questions in my mind and
+hopefully my my talk will bring up some
+
+ align:start position:0%
+hopefully my my talk will bring up some
+ 
+
+ align:start position:0%
+hopefully my my talk will bring up some
+more questions that we'll go over um
+
+ align:start position:0%
+more questions that we'll go over um
+ 
+
+ align:start position:0%
+more questions that we'll go over um
+through the rest of the term because I
+
+ align:start position:0%
+through the rest of the term because I
+ 
+
+ align:start position:0%
+through the rest of the term because I
+can't I can't possibly answer all the
+
+ align:start position:0%
+can't I can't possibly answer all the
+ 
+
+ align:start position:0%
+can't I can't possibly answer all the
+questions that came into my head let me
+
+ align:start position:0%
+questions that came into my head let me
+ 
+
+ align:start position:0%
+questions that came into my head let me
+interrupt briefly um if you have any
+
+ align:start position:0%
+interrupt briefly um if you have any
+ 
+
+ align:start position:0%
+interrupt briefly um if you have any
+ideas about the movie we watched last
+
+ align:start position:0%
+ideas about the movie we watched last
+ 
+
+ align:start position:0%
+ideas about the movie we watched last
+time Beauty and the Beast yeah I have
+
+ align:start position:0%
+time Beauty and the Beast yeah I have
+ 
+
+ align:start position:0%
+time Beauty and the Beast yeah I have
+some ideas on that and also feel free to
+
+ align:start position:0%
+some ideas on that and also feel free to
+ 
+
+ align:start position:0%
+some ideas on that and also feel free to
+bring that in okay um so one one of the
+
+ align:start position:0%
+bring that in okay um so one one of the
+ 
+
+ align:start position:0%
+bring that in okay um so one one of the
+major questions that I have that's kind
+
+ align:start position:0%
+major questions that I have that's kind
+ 
+
+ align:start position:0%
+major questions that I have that's kind
+of a recurring theme in my life is why
+
+ align:start position:0%
+of a recurring theme in my life is why
+ 
+
+ align:start position:0%
+of a recurring theme in my life is why
+study film because I've been studying
+
+ align:start position:0%
+study film because I've been studying
+ 
+
+ align:start position:0%
+study film because I've been studying
+film all through MIT you know and
+
+ align:start position:0%
+film all through MIT you know and
+ 
+
+ align:start position:0%
+film all through MIT you know and
+obviously all of us have chosen to study
+
+ align:start position:0%
+obviously all of us have chosen to study
+ 
+
+ align:start position:0%
+obviously all of us have chosen to study
+film too and I didn't really know why
+
+ align:start position:0%
+film too and I didn't really know why
+ 
+
+ align:start position:0%
+film too and I didn't really know why
+you know um it's not like my parents
+
+ align:start position:0%
+you know um it's not like my parents
+ 
+
+ align:start position:0%
+you know um it's not like my parents
+made me or I need to do it to graduate
+
+ align:start position:0%
+made me or I need to do it to graduate
+ 
+
+ align:start position:0%
+made me or I need to do it to graduate
+or something you know it's just
+
+ align:start position:0%
+or something you know it's just
+ 
+
+ align:start position:0%
+or something you know it's just
+something that I choose to do and it's a
+
+ align:start position:0%
+something that I choose to do and it's a
+ 
+
+ align:start position:0%
+something that I choose to do and it's a
+it's a very personal question for all of
+
+ align:start position:0%
+it's a very personal question for all of
+ 
+
+ align:start position:0%
+it's a very personal question for all of
+us and we probably each have our own
+
+ align:start position:0%
+us and we probably each have our own
+ 
+
+ align:start position:0%
+us and we probably each have our own
+answers and I'm going to talk about why
+
+ align:start position:0%
+answers and I'm going to talk about why
+ 
+
+ align:start position:0%
+answers and I'm going to talk about why
+I choose to study film because I thought
+
+ align:start position:0%
+I choose to study film because I thought
+ 
+
+ align:start position:0%
+I choose to study film because I thought
+about it a lot and to answer that you
+
+ align:start position:0%
+about it a lot and to answer that you
+ 
+
+ align:start position:0%
+about it a lot and to answer that you
+know I need to tell you a little bit
+
+ align:start position:0%
+know I need to tell you a little bit
+ 
+
+ align:start position:0%
+know I need to tell you a little bit
+about my personal life and I'll get to
+
+ align:start position:0%
+about my personal life and I'll get to
+ 
+
+ align:start position:0%
+about my personal life and I'll get to
+that but first uh some definitions like
+
+ align:start position:0%
+that but first uh some definitions like
+ 
+
+ align:start position:0%
+that but first uh some definitions like
+uh realism and formalism were mentioned
+
+ align:start position:0%
+uh realism and formalism were mentioned
+ 
+
+ align:start position:0%
+uh realism and formalism were mentioned
+in the text and at MIT I've taken I
+
+ align:start position:0%
+in the text and at MIT I've taken I
+ 
+
+ align:start position:0%
+in the text and at MIT I've taken I
+don't know like three or four film
+
+ align:start position:0%
+don't know like three or four film
+ 
+
+ align:start position:0%
+don't know like three or four film
+classes now and in each of those classes
+
+ align:start position:0%
+classes now and in each of those classes
+ 
+
+ align:start position:0%
+classes now and in each of those classes
+we generally use a combination of those
+
+ align:start position:0%
+we generally use a combination of those
+ 
+
+ align:start position:0%
+we generally use a combination of those
+two techniques and honestly I think
+
+ align:start position:0%
+two techniques and honestly I think
+ 
+
+ align:start position:0%
+two techniques and honestly I think
+they're pretty hard to Define they seem
+
+ align:start position:0%
+they're pretty hard to Define they seem
+ 
+
+ align:start position:0%
+they're pretty hard to Define they seem
+to be um the opposite ends of a spectrum
+
+ align:start position:0%
+to be um the opposite ends of a spectrum
+ 
+
+ align:start position:0%
+to be um the opposite ends of a spectrum
+in which you can analyze film and so
+
+ align:start position:0%
+in which you can analyze film and so
+ 
+
+ align:start position:0%
+in which you can analyze film and so
+there's two different ways you can look
+
+ align:start position:0%
+there's two different ways you can look
+ 
+
+ align:start position:0%
+there's two different ways you can look
+at each aspect of film so that that
+
+ align:start position:0%
+at each aspect of film so that that
+ 
+
+ align:start position:0%
+at each aspect of film so that that
+means U for example story editing um uh
+
+ align:start position:0%
+means U for example story editing um uh
+ 
+
+ align:start position:0%
+means U for example story editing um uh
+costumes everything you know there's two
+
+ align:start position:0%
+costumes everything you know there's two
+ 
+
+ align:start position:0%
+costumes everything you know there's two
+different ways you can look at it so
+
+ align:start position:0%
+different ways you can look at it so
+ 
+
+ align:start position:0%
+different ways you can look at it so
+it's hard to Define since they overlaps
+
+ align:start position:0%
+it's hard to Define since they overlaps
+ 
+
+ align:start position:0%
+it's hard to Define since they overlaps
+so much but still I try to Define them
+
+ align:start position:0%
+so much but still I try to Define them
+ 
+
+ align:start position:0%
+so much but still I try to Define them
+you know because I want to have a clear
+
+ align:start position:0%
+you know because I want to have a clear
+ 
+
+ align:start position:0%
+you know because I want to have a clear
+picture of what exactly they mean so in
+
+ align:start position:0%
+picture of what exactly they mean so in
+ 
+
+ align:start position:0%
+picture of what exactly they mean so in
+realism it seems like what that means is
+
+ align:start position:0%
+realism it seems like what that means is
+ 
+
+ align:start position:0%
+realism it seems like what that means is
+the film is capturing an aspect of real
+
+ align:start position:0%
+the film is capturing an aspect of real
+ 
+
+ align:start position:0%
+the film is capturing an aspect of real
+life and that's what makes it powerful
+
+ align:start position:0%
+life and that's what makes it powerful
+ 
+
+ align:start position:0%
+life and that's what makes it powerful
+basically the um I'm sure you've all
+
+ align:start position:0%
+basically the um I'm sure you've all
+ 
+
+ align:start position:0%
+basically the um I'm sure you've all
+heard that art imitates life um so
+
+ align:start position:0%
+heard that art imitates life um so
+ 
+
+ align:start position:0%
+heard that art imitates life um so
+something about film is reflecting the
+
+ align:start position:0%
+something about film is reflecting the
+ 
+
+ align:start position:0%
+something about film is reflecting the
+actual world and maybe maybe even more
+
+ align:start position:0%
+actual world and maybe maybe even more
+ 
+
+ align:start position:0%
+actual world and maybe maybe even more
+than reflecting it's representing the
+
+ align:start position:0%
+than reflecting it's representing the
+ 
+
+ align:start position:0%
+than reflecting it's representing the
+world or being the world now let's talk
+
+ align:start position:0%
+world or being the world now let's talk
+ 
+
+ align:start position:0%
+world or being the world now let's talk
+about formalism um to me that means that
+
+ align:start position:0%
+about formalism um to me that means that
+ 
+
+ align:start position:0%
+about formalism um to me that means that
+you're using the power of film you're
+
+ align:start position:0%
+you're using the power of film you're
+ 
+
+ align:start position:0%
+you're using the power of film you're
+using technology to extend real life
+
+ align:start position:0%
+using technology to extend real life
+ 
+
+ align:start position:0%
+using technology to extend real life
+um so for example with editing of course
+
+ align:start position:0%
+um so for example with editing of course
+ 
+
+ align:start position:0%
+um so for example with editing of course
+a realist would have something different
+
+ align:start position:0%
+a realist would have something different
+ 
+
+ align:start position:0%
+a realist would have something different
+to say about this but but for editing
+
+ align:start position:0%
+to say about this but but for editing
+ 
+
+ align:start position:0%
+to say about this but but for editing
+you're you're able to change um
+
+ align:start position:0%
+you're you're able to change um
+ 
+
+ align:start position:0%
+you're you're able to change um
+temporality you know you can you can
+
+ align:start position:0%
+temporality you know you can you can
+ 
+
+ align:start position:0%
+temporality you know you can you can
+rearrange time you can rearrange space
+
+ align:start position:0%
+rearrange time you can rearrange space
+ 
+
+ align:start position:0%
+rearrange time you can rearrange space
+and that's power part of the power of
+
+ align:start position:0%
+and that's power part of the power of
+ 
+
+ align:start position:0%
+and that's power part of the power of
+film in which you in which you can
+
+ align:start position:0%
+film in which you in which you can
+ 
+
+ align:start position:0%
+film in which you in which you can
+change reality and give people something
+
+ align:start position:0%
+change reality and give people something
+ 
+
+ align:start position:0%
+change reality and give people something
+more um okay so as I said we analyzed
+
+ align:start position:0%
+more um okay so as I said we analyzed
+ 
+
+ align:start position:0%
+more um okay so as I said we analyzed
+film in my previous classes using
+
+ align:start position:0%
+film in my previous classes using
+ 
+
+ align:start position:0%
+film in my previous classes using
+combination of the two things because
+
+ align:start position:0%
+combination of the two things because
+ 
+
+ align:start position:0%
+combination of the two things because
+you want see how it relates to the real
+
+ align:start position:0%
+you want see how it relates to the real
+ 
+
+ align:start position:0%
+you want see how it relates to the real
+world but you also want to see what
+
+ align:start position:0%
+world but you also want to see what
+ 
+
+ align:start position:0%
+world but you also want to see what
+directors can do to harness the power of
+
+ align:start position:0%
+directors can do to harness the power of
+ 
+
+ align:start position:0%
+directors can do to harness the power of
+the media of the medium um so which way
+
+ align:start position:0%
+the media of the medium um so which way
+ 
+
+ align:start position:0%
+the media of the medium um so which way
+is the best I really don't know but I
+
+ align:start position:0%
+is the best I really don't know but I
+ 
+
+ align:start position:0%
+is the best I really don't know but I
+think a combination of the two is useful
+
+ align:start position:0%
+think a combination of the two is useful
+ 
+
+ align:start position:0%
+think a combination of the two is useful
+because at least then you can see what
+
+ align:start position:0%
+because at least then you can see what
+ 
+
+ align:start position:0%
+because at least then you can see what
+you can try to get the advantages of
+
+ align:start position:0%
+you can try to get the advantages of
+ 
+
+ align:start position:0%
+you can try to get the advantages of
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+approaches okay
+
+ align:start position:0%
+approaches okay
+ 
+
+ align:start position:0%
+approaches okay
+so I want to I want to say a quote from
+
+ align:start position:0%
+so I want to I want to say a quote from
+ 
+
+ align:start position:0%
+so I want to I want to say a quote from
+a movie actually um there's a quote from
+
+ align:start position:0%
+a movie actually um there's a quote from
+ 
+
+ align:start position:0%
+a movie actually um there's a quote from
+the player which was I think it came out
+
+ align:start position:0%
+the player which was I think it came out
+ 
+
+ align:start position:0%
+the player which was I think it came out
+in the 80s directed by Alman and the
+
+ align:start position:0%
+in the 80s directed by Alman and the
+ 
+
+ align:start position:0%
+in the 80s directed by Alman and the
+quote I want to say is movies are art
+
+ align:start position:0%
+quote I want to say is movies are art
+ 
+
+ align:start position:0%
+quote I want to say is movies are art
+now more than ever and that's a quote by
+
+ align:start position:0%
+now more than ever and that's a quote by
+ 
+
+ align:start position:0%
+now more than ever and that's a quote by
+the main character and um so to me
+
+ align:start position:0%
+the main character and um so to me
+ 
+
+ align:start position:0%
+the main character and um so to me
+that's one of the central reasons why we
+
+ align:start position:0%
+that's one of the central reasons why we
+ 
+
+ align:start position:0%
+that's one of the central reasons why we
+study film because we think that it's
+
+ align:start position:0%
+study film because we think that it's
+ 
+
+ align:start position:0%
+study film because we think that it's
+art and that's great ex how do you
+
+ align:start position:0%
+art and that's great ex how do you
+ 
+
+ align:start position:0%
+art and that's great ex how do you
+define art because that's really hard to
+
+ align:start position:0%
+define art because that's really hard to
+ 
+
+ align:start position:0%
+define art because that's really hard to
+Define too and in fact it's an ongoing
+
+ align:start position:0%
+Define too and in fact it's an ongoing
+ 
+
+ align:start position:0%
+Define too and in fact it's an ongoing
+battle with modern art you know um a lot
+
+ align:start position:0%
+battle with modern art you know um a lot
+ 
+
+ align:start position:0%
+battle with modern art you know um a lot
+of people go to an art museum and see a
+
+ align:start position:0%
+of people go to an art museum and see a
+ 
+
+ align:start position:0%
+of people go to an art museum and see a
+piece of mod and say oh that's not art
+
+ align:start position:0%
+piece of mod and say oh that's not art
+ 
+
+ align:start position:0%
+piece of mod and say oh that's not art
+well why you know it's really hard to
+
+ align:start position:0%
+well why you know it's really hard to
+ 
+
+ align:start position:0%
+well why you know it's really hard to
+Define um so let me tell you a little
+
+ align:start position:0%
+Define um so let me tell you a little
+ 
+
+ align:start position:0%
+Define um so let me tell you a little
+bit about my own personal background I
+
+ align:start position:0%
+bit about my own personal background I
+ 
+
+ align:start position:0%
+bit about my own personal background I
+started playing piano and violin when I
+
+ align:start position:0%
+started playing piano and violin when I
+ 
+
+ align:start position:0%
+started playing piano and violin when I
+was four years old so and all the way up
+
+ align:start position:0%
+was four years old so and all the way up
+ 
+
+ align:start position:0%
+was four years old so and all the way up
+to MIT when I became too busy with
+
+ align:start position:0%
+to MIT when I became too busy with
+ 
+
+ align:start position:0%
+to MIT when I became too busy with
+problem sets to to really play much
+
+ align:start position:0%
+problem sets to to really play much
+ 
+
+ align:start position:0%
+problem sets to to really play much
+anymore but um so To Me music was my
+
+ align:start position:0%
+anymore but um so To Me music was my
+ 
+
+ align:start position:0%
+anymore but um so To Me music was my
+first my first art you know my first
+
+ align:start position:0%
+first my first art you know my first
+ 
+
+ align:start position:0%
+first my first art you know my first
+love of art came from music now if you
+
+ align:start position:0%
+love of art came from music now if you
+ 
+
+ align:start position:0%
+love of art came from music now if you
+look at music you can't really use
+
+ align:start position:0%
+look at music you can't really use
+ 
+
+ align:start position:0%
+look at music you can't really use
+realism and formalism to analyze music
+
+ align:start position:0%
+realism and formalism to analyze music
+ 
+
+ align:start position:0%
+realism and formalism to analyze music
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well go ahead you want to say something
+
+ align:start position:0%
+well go ahead you want to say something
+ 
+
+ align:start position:0%
+well go ahead you want to say something
+well you can talk about leaving aside
+
+ align:start position:0%
+well you can talk about leaving aside
+ 
+
+ align:start position:0%
+well you can talk about leaving aside
+representational music which is
+
+ align:start position:0%
+representational music which is
+ 
+
+ align:start position:0%
+representational music which is
+obviously going to be patterned upon
+
+ align:start position:0%
+obviously going to be patterned upon
+ 
+
+ align:start position:0%
+obviously going to be patterned upon
+some reality right yeah um a tone poem
+
+ align:start position:0%
+some reality right yeah um a tone poem
+ 
+
+ align:start position:0%
+some reality right yeah um a tone poem
+by Richard Strauss wants you
+
+ align:start position:0%
+by Richard Strauss wants you
+ 
+
+ align:start position:0%
+by Richard Strauss wants you
+to hear or imagine sonically what um the
+
+ align:start position:0%
+to hear or imagine sonically what um the
+ 
+
+ align:start position:0%
+to hear or imagine sonically what um the
+Sheep are in
+
+ align:start position:0%
+Sheep are in
+ 
+
+ align:start position:0%
+Sheep are in
+donot or what the adventures are of Don
+
+ align:start position:0%
+donot or what the adventures are of Don
+ 
+
+ align:start position:0%
+donot or what the adventures are of Don
+Juan that's the nature of
+
+ align:start position:0%
+Juan that's the nature of
+ 
+
+ align:start position:0%
+Juan that's the nature of
+programmatic tone poems of that sort now
+
+ align:start position:0%
+programmatic tone poems of that sort now
+ 
+
+ align:start position:0%
+programmatic tone poems of that sort now
+that that would be a realistic effect uh
+
+ align:start position:0%
+that that would be a realistic effect uh
+ 
+
+ align:start position:0%
+that that would be a realistic effect uh
+but over and above that uh almost
+
+ align:start position:0%
+but over and above that uh almost
+ 
+
+ align:start position:0%
+but over and above that uh almost
+everybody recognizes that music is
+
+ align:start position:0%
+everybody recognizes that music is
+ 
+
+ align:start position:0%
+everybody recognizes that music is
+important for what it expresses
+
+ align:start position:0%
+important for what it expresses
+ 
+
+ align:start position:0%
+important for what it expresses
+shuminsky said somewhere music doesn't
+
+ align:start position:0%
+shuminsky said somewhere music doesn't
+ 
+
+ align:start position:0%
+shuminsky said somewhere music doesn't
+Express anything it expresses
+
+ align:start position:0%
+Express anything it expresses
+ 
+
+ align:start position:0%
+Express anything it expresses
+itself which is a way of denying that it
+
+ align:start position:0%
+itself which is a way of denying that it
+ 
+
+ align:start position:0%
+itself which is a way of denying that it
+expresses anything in the composer or in
+
+ align:start position:0%
+expresses anything in the composer or in
+ 
+
+ align:start position:0%
+expresses anything in the composer or in
+the world feelings
+
+ align:start position:0%
+the world feelings
+ 
+
+ align:start position:0%
+the world feelings
+or an a theory of the world an attitude
+
+ align:start position:0%
+or an a theory of the world an attitude
+ 
+
+ align:start position:0%
+or an a theory of the world an attitude
+toward the world it's not expressive at
+
+ align:start position:0%
+toward the world it's not expressive at
+ 
+
+ align:start position:0%
+toward the world it's not expressive at
+all um the OD what's amusing however is
+
+ align:start position:0%
+all um the OD what's amusing however is
+ 
+
+ align:start position:0%
+all um the OD what's amusing however is
+that Stravinsky's music it is often very
+
+ align:start position:0%
+that Stravinsky's music it is often very
+ 
+
+ align:start position:0%
+that Stravinsky's music it is often very
+very expressive and he went through
+
+ align:start position:0%
+very expressive and he went through
+ 
+
+ align:start position:0%
+very expressive and he went through
+Romantic Period and then uh Classical
+
+ align:start position:0%
+Romantic Period and then uh Classical
+ 
+
+ align:start position:0%
+Romantic Period and then uh Classical
+period and in The Classical period
+
+ align:start position:0%
+period and in The Classical period
+ 
+
+ align:start position:0%
+period and in The Classical period
+there's a great emphasis on technique
+
+ align:start position:0%
+there's a great emphasis on technique
+ 
+
+ align:start position:0%
+there's a great emphasis on technique
+but it still it nevertheless remains
+
+ align:start position:0%
+but it still it nevertheless remains
+ 
+
+ align:start position:0%
+but it still it nevertheless remains
+expressive the uh
+
+ align:start position:0%
+expressive the uh
+ 
+
+ align:start position:0%
+expressive the uh
+formalist view would emphasize music as
+
+ align:start position:0%
+formalist view would emphasize music as
+ 
+
+ align:start position:0%
+formalist view would emphasize music as
+a series of techniques as requiring a
+
+ align:start position:0%
+a series of techniques as requiring a
+ 
+
+ align:start position:0%
+a series of techniques as requiring a
+knowledge of the scales of of different
+
+ align:start position:0%
+knowledge of the scales of of different
+ 
+
+ align:start position:0%
+knowledge of the scales of of different
+ways of manipulating the notes of
+
+ align:start position:0%
+ways of manipulating the notes of
+ 
+
+ align:start position:0%
+ways of manipulating the notes of
+different forms musical forms and that's
+
+ align:start position:0%
+different forms musical forms and that's
+ 
+
+ align:start position:0%
+different forms musical forms and that's
+what's usually taught in music classes
+
+ align:start position:0%
+what's usually taught in music classes
+ 
+
+ align:start position:0%
+what's usually taught in music classes
+introductory ones because they're afraid
+
+ align:start position:0%
+introductory ones because they're afraid
+ 
+
+ align:start position:0%
+introductory ones because they're afraid
+the students are going to have Daydreams
+
+ align:start position:0%
+the students are going to have Daydreams
+ 
+
+ align:start position:0%
+the students are going to have Daydreams
+about um some romantic moment or or you
+
+ align:start position:0%
+about um some romantic moment or or you
+ 
+
+ align:start position:0%
+about um some romantic moment or or you
+know something in Schubert which is very
+
+ align:start position:0%
+know something in Schubert which is very
+ 
+
+ align:start position:0%
+know something in Schubert which is very
+sad or very you know something like that
+
+ align:start position:0%
+sad or very you know something like that
+ 
+
+ align:start position:0%
+sad or very you know something like that
+and never hear the music so that there
+
+ align:start position:0%
+and never hear the music so that there
+ 
+
+ align:start position:0%
+and never hear the music so that there
+too you get the same problem about the
+
+ align:start position:0%
+too you get the same problem about the
+ 
+
+ align:start position:0%
+too you get the same problem about the
+formalistic element and the realistic
+
+ align:start position:0%
+formalistic element and the realistic
+ 
+
+ align:start position:0%
+formalistic element and the realistic
+one and the difficulty for the theorist
+
+ align:start position:0%
+one and the difficulty for the theorist
+ 
+
+ align:start position:0%
+one and the difficulty for the theorist
+or the philosopher is to make sense out
+
+ align:start position:0%
+or the philosopher is to make sense out
+ 
+
+ align:start position:0%
+or the philosopher is to make sense out
+of what these different Alternatives
+
+ align:start position:0%
+of what these different Alternatives
+ 
+
+ align:start position:0%
+of what these different Alternatives
+might be so it's not entirely different
+
+ align:start position:0%
+might be so it's not entirely different
+ 
+
+ align:start position:0%
+might be so it's not entirely different
+from film okay but I don't mean I didn't
+
+ align:start position:0%
+from film okay but I don't mean I didn't
+ 
+
+ align:start position:0%
+from film okay but I don't mean I didn't
+mean to interrupt you that long oh no
+
+ align:start position:0%
+mean to interrupt you that long oh no
+ 
+
+ align:start position:0%
+mean to interrupt you that long oh no
+that's okay um so when I was growing up
+
+ align:start position:0%
+that's okay um so when I was growing up
+ 
+
+ align:start position:0%
+that's okay um so when I was growing up
+though of course I didn't approach music
+
+ align:start position:0%
+though of course I didn't approach music
+ 
+
+ align:start position:0%
+though of course I didn't approach music
+with such a with such a philosophy you
+
+ align:start position:0%
+with such a with such a philosophy you
+ 
+
+ align:start position:0%
+with such a with such a philosophy you
+know I was just trying to enjoy it and
+
+ align:start position:0%
+know I was just trying to enjoy it and
+ 
+
+ align:start position:0%
+know I was just trying to enjoy it and
+and try to see how it's an art form and
+
+ align:start position:0%
+and try to see how it's an art form and
+ 
+
+ align:start position:0%
+and try to see how it's an art form and
+one of the things that I noticed is just
+
+ align:start position:0%
+one of the things that I noticed is just
+ 
+
+ align:start position:0%
+one of the things that I noticed is just
+that art I mean music Sorry music is
+
+ align:start position:0%
+that art I mean music Sorry music is
+ 
+
+ align:start position:0%
+that art I mean music Sorry music is
+highly capable of of producing emotion
+
+ align:start position:0%
+highly capable of of producing emotion
+ 
+
+ align:start position:0%
+highly capable of of producing emotion
+in someone you know and that's something
+
+ align:start position:0%
+in someone you know and that's something
+ 
+
+ align:start position:0%
+in someone you know and that's something
+strange you know why should why should
+
+ align:start position:0%
+strange you know why should why should
+ 
+
+ align:start position:0%
+strange you know why should why should
+these noises produce an emotional
+
+ align:start position:0%
+these noises produce an emotional
+ 
+
+ align:start position:0%
+these noises produce an emotional
+response in a human being and that's
+
+ align:start position:0%
+response in a human being and that's
+ 
+
+ align:start position:0%
+response in a human being and that's
+probably never going to be explained but
+
+ align:start position:0%
+probably never going to be explained but
+ 
+
+ align:start position:0%
+probably never going to be explained but
+I mean that's that's one of the reasons
+
+ align:start position:0%
+I mean that's that's one of the reasons
+ 
+
+ align:start position:0%
+I mean that's that's one of the reasons
+to me that it makes it art it it is able
+
+ align:start position:0%
+to me that it makes it art it it is able
+ 
+
+ align:start position:0%
+to me that it makes it art it it is able
+to evolve this emotion and so um I think
+
+ align:start position:0%
+to evolve this emotion and so um I think
+ 
+
+ align:start position:0%
+to evolve this emotion and so um I think
+my personal um definition of art like
+
+ align:start position:0%
+my personal um definition of art like
+ 
+
+ align:start position:0%
+my personal um definition of art like
+what is art to me well I would say that
+
+ align:start position:0%
+what is art to me well I would say that
+ 
+
+ align:start position:0%
+what is art to me well I would say that
+it's something that can either provoke a
+
+ align:start position:0%
+it's something that can either provoke a
+ 
+
+ align:start position:0%
+it's something that can either provoke a
+cognitive or an effective response so
+
+ align:start position:0%
+cognitive or an effective response so
+ 
+
+ align:start position:0%
+cognitive or an effective response so
+what does that mean it either makes me
+
+ align:start position:0%
+what does that mean it either makes me
+ 
+
+ align:start position:0%
+what does that mean it either makes me
+think or it makes me have an emotional
+
+ align:start position:0%
+think or it makes me have an emotional
+ 
+
+ align:start position:0%
+think or it makes me have an emotional
+response to it of which music can do
+
+ align:start position:0%
+response to it of which music can do
+ 
+
+ align:start position:0%
+response to it of which music can do
+both and so to me art is all about the
+
+ align:start position:0%
+both and so to me art is all about the
+ 
+
+ align:start position:0%
+both and so to me art is all about the
+ception you know I don't I don't
+
+ align:start position:0%
+ception you know I don't I don't
+ 
+
+ align:start position:0%
+ception you know I don't I don't
+really um actually let me let me uh save
+
+ align:start position:0%
+really um actually let me let me uh save
+ 
+
+ align:start position:0%
+really um actually let me let me uh save
+that for a little bit later but um so
+
+ align:start position:0%
+that for a little bit later but um so
+ 
+
+ align:start position:0%
+that for a little bit later but um so
+what is it about perception you know why
+
+ align:start position:0%
+what is it about perception you know why
+ 
+
+ align:start position:0%
+what is it about perception you know why
+why would we enjoy something that makes
+
+ align:start position:0%
+why would we enjoy something that makes
+ 
+
+ align:start position:0%
+why would we enjoy something that makes
+us think something that makes us feel
+
+ align:start position:0%
+us think something that makes us feel
+ 
+
+ align:start position:0%
+us think something that makes us feel
+emotions well I think that's just one of
+
+ align:start position:0%
+emotions well I think that's just one of
+ 
+
+ align:start position:0%
+emotions well I think that's just one of
+the basic basic aspects of humanity that
+
+ align:start position:0%
+the basic basic aspects of humanity that
+ 
+
+ align:start position:0%
+the basic basic aspects of humanity that
+we want to learn we want to experience
+
+ align:start position:0%
+we want to learn we want to experience
+ 
+
+ align:start position:0%
+we want to learn we want to experience
+so art makes us learn and it makes us
+
+ align:start position:0%
+so art makes us learn and it makes us
+ 
+
+ align:start position:0%
+so art makes us learn and it makes us
+experience and that satisfies one of our
+
+ align:start position:0%
+experience and that satisfies one of our
+ 
+
+ align:start position:0%
+experience and that satisfies one of our
+basic desires
+
+ align:start position:0%
+basic desires
+ 
+
+ align:start position:0%
+basic desires
+let me interrupt you again one of the
+
+ align:start position:0%
+let me interrupt you again one of the
+ 
+
+ align:start position:0%
+let me interrupt you again one of the
+burdens the main burden of the book
+
+ align:start position:0%
+burdens the main burden of the book
+ 
+
+ align:start position:0%
+burdens the main burden of the book
+which you'll realize when you finish it
+
+ align:start position:0%
+which you'll realize when you finish it
+ 
+
+ align:start position:0%
+which you'll realize when you finish it
+is to say that our way of formulating
+
+ align:start position:0%
+is to say that our way of formulating
+ 
+
+ align:start position:0%
+is to say that our way of formulating
+the problem between the realistic and
+
+ align:start position:0%
+the problem between the realistic and
+ 
+
+ align:start position:0%
+the problem between the realistic and
+the formalistic is itself self deficient
+
+ align:start position:0%
+the formalistic is itself self deficient
+ 
+
+ align:start position:0%
+the formalistic is itself self deficient
+and that's the job of the philosopher to
+
+ align:start position:0%
+and that's the job of the philosopher to
+ 
+
+ align:start position:0%
+and that's the job of the philosopher to
+help us make our ideas clear and my
+
+ align:start position:0%
+help us make our ideas clear and my
+ 
+
+ align:start position:0%
+help us make our ideas clear and my
+suggestion is that the two alternatives
+
+ align:start position:0%
+suggestion is that the two alternatives
+ 
+
+ align:start position:0%
+suggestion is that the two alternatives
+are not really separate it's an
+
+ align:start position:0%
+are not really separate it's an
+ 
+
+ align:start position:0%
+are not really separate it's an
+artificial distinction the way most
+
+ align:start position:0%
+artificial distinction the way most
+ 
+
+ align:start position:0%
+artificial distinction the way most
+philosophical distinctions are and in
+
+ align:start position:0%
+philosophical distinctions are and in
+ 
+
+ align:start position:0%
+philosophical distinctions are and in
+reality the two interpenetrate and so
+
+ align:start position:0%
+reality the two interpenetrate and so
+ 
+
+ align:start position:0%
+reality the two interpenetrate and so
+one has to find a way
+
+ align:start position:0%
+one has to find a way
+ 
+
+ align:start position:0%
+one has to find a way
+of explaining and understanding and
+
+ align:start position:0%
+of explaining and understanding and
+ 
+
+ align:start position:0%
+of explaining and understanding and
+experiencing the
+
+ align:start position:0%
+experiencing the
+ 
+
+ align:start position:0%
+experiencing the
+interpenetration so that it's not just a
+
+ align:start position:0%
+interpenetration so that it's not just a
+ 
+
+ align:start position:0%
+interpenetration so that it's not just a
+question of Music doing both the
+
+ align:start position:0%
+question of Music doing both the
+ 
+
+ align:start position:0%
+question of Music doing both the
+formalistic and the non- formalistic one
+
+ align:start position:0%
+formalistic and the non- formalistic one
+ 
+
+ align:start position:0%
+formalistic and the non- formalistic one
+both uh making sounds and also
+
+ align:start position:0%
+both uh making sounds and also
+ 
+
+ align:start position:0%
+both uh making sounds and also
+expressing emotions but the two are
+
+ align:start position:0%
+expressing emotions but the two are
+ 
+
+ align:start position:0%
+expressing emotions but the two are
+interwoven and then how does one make
+
+ align:start position:0%
+interwoven and then how does one make
+ 
+
+ align:start position:0%
+interwoven and then how does one make
+sense out of the concept of the into W
+
+ align:start position:0%
+sense out of the concept of the into W
+ 
+
+ align:start position:0%
+sense out of the concept of the into W
+woing into weaving and what are
+
+ align:start position:0%
+woing into weaving and what are
+ 
+
+ align:start position:0%
+woing into weaving and what are
+different ways of doing that briefly in
+
+ align:start position:0%
+different ways of doing that briefly in
+ 
+
+ align:start position:0%
+different ways of doing that briefly in
+terms of your two instruments there are
+
+ align:start position:0%
+terms of your two instruments there are
+ 
+
+ align:start position:0%
+terms of your two instruments there are
+pianists and
+
+ align:start position:0%
+pianists and
+ 
+
+ align:start position:0%
+pianists and
+violinists who seem to have a very
+
+ align:start position:0%
+violinists who seem to have a very
+ 
+
+ align:start position:0%
+violinists who seem to have a very
+profound understanding of the music in
+
+ align:start position:0%
+profound understanding of the music in
+ 
+
+ align:start position:0%
+profound understanding of the music in
+terms of the feelings like yudi Manu
+
+ align:start position:0%
+terms of the feelings like yudi Manu
+ 
+
+ align:start position:0%
+terms of the feelings like yudi Manu
+would be a good example um on the other
+
+ align:start position:0%
+would be a good example um on the other
+ 
+
+ align:start position:0%
+would be a good example um on the other
+hand in Violin other hand on the other
+
+ align:start position:0%
+hand in Violin other hand on the other
+ 
+
+ align:start position:0%
+hand in Violin other hand on the other
+hand there are those whose technique is
+
+ align:start position:0%
+hand there are those whose technique is
+ 
+
+ align:start position:0%
+hand there are those whose technique is
+absolutely perfect and they don't seem
+
+ align:start position:0%
+absolutely perfect and they don't seem
+ 
+
+ align:start position:0%
+absolutely perfect and they don't seem
+to express very much they really know
+
+ align:start position:0%
+to express very much they really know
+ 
+
+ align:start position:0%
+to express very much they really know
+how to use the instrument but they don't
+
+ align:start position:0%
+how to use the instrument but they don't
+ 
+
+ align:start position:0%
+how to use the instrument but they don't
+use it with any profound Insight well
+
+ align:start position:0%
+use it with any profound Insight well
+ 
+
+ align:start position:0%
+use it with any profound Insight well
+for me as a listener as observing the
+
+ align:start position:0%
+for me as a listener as observing the
+ 
+
+ align:start position:0%
+for me as a listener as observing the
+situation it tells me something about
+
+ align:start position:0%
+situation it tells me something about
+ 
+
+ align:start position:0%
+situation it tells me something about
+them as people you know I want to say
+
+ align:start position:0%
+them as people you know I want to say
+ 
+
+ align:start position:0%
+them as people you know I want to say
+yudi minu in order to play like that has
+
+ align:start position:0%
+yudi minu in order to play like that has
+ 
+
+ align:start position:0%
+yudi minu in order to play like that has
+not only learned the how how to use the
+
+ align:start position:0%
+not only learned the how how to use the
+ 
+
+ align:start position:0%
+not only learned the how how to use the
+technique but he has developed
+
+ align:start position:0%
+technique but he has developed
+ 
+
+ align:start position:0%
+technique but he has developed
+in his personality and so if one says
+
+ align:start position:0%
+in his personality and so if one says
+ 
+
+ align:start position:0%
+in his personality and so if one says
+about his music it's very spiritual very
+
+ align:start position:0%
+about his music it's very spiritual very
+ 
+
+ align:start position:0%
+about his music it's very spiritual very
+Soulful very filled with a kind of
+
+ align:start position:0%
+Soulful very filled with a kind of
+ 
+
+ align:start position:0%
+Soulful very filled with a kind of
+natural acceptance of the world and of
+
+ align:start position:0%
+natural acceptance of the world and of
+ 
+
+ align:start position:0%
+natural acceptance of the world and of
+other people and that in that sense he's
+
+ align:start position:0%
+other people and that in that sense he's
+ 
+
+ align:start position:0%
+other people and that in that sense he's
+a very beautiful person I've never met
+
+ align:start position:0%
+a very beautiful person I've never met
+ 
+
+ align:start position:0%
+a very beautiful person I've never met
+him but just listening I've I've seen
+
+ align:start position:0%
+him but just listening I've I've seen
+ 
+
+ align:start position:0%
+him but just listening I've I've seen
+him on screen of course but listening to
+
+ align:start position:0%
+him on screen of course but listening to
+ 
+
+ align:start position:0%
+him on screen of course but listening to
+the music I feel like in touch with that
+
+ align:start position:0%
+the music I feel like in touch with that
+ 
+
+ align:start position:0%
+the music I feel like in touch with that
+aspect of his being well that's because
+
+ align:start position:0%
+aspect of his being well that's because
+ 
+
+ align:start position:0%
+aspect of his being well that's because
+of the way in which he integrates the
+
+ align:start position:0%
+of the way in which he integrates the
+ 
+
+ align:start position:0%
+of the way in which he integrates the
+formal and the technical the formal and
+
+ align:start position:0%
+formal and the technical the formal and
+ 
+
+ align:start position:0%
+formal and the technical the formal and
+the realistic and that others um do it
+
+ align:start position:0%
+the realistic and that others um do it
+ 
+
+ align:start position:0%
+the realistic and that others um do it
+in a different way and that tells me
+
+ align:start position:0%
+in a different way and that tells me
+ 
+
+ align:start position:0%
+in a different way and that tells me
+something about them in either event the
+
+ align:start position:0%
+something about them in either event the
+ 
+
+ align:start position:0%
+something about them in either event the
+art is a function of the humanity the
+
+ align:start position:0%
+art is a function of the humanity the
+ 
+
+ align:start position:0%
+art is a function of the humanity the
+total Humanity of the practitioner and
+
+ align:start position:0%
+total Humanity of the practitioner and
+ 
+
+ align:start position:0%
+total Humanity of the practitioner and
+the difficulty is that you can teach
+
+ align:start position:0%
+the difficulty is that you can teach
+ 
+
+ align:start position:0%
+the difficulty is that you can teach
+people scales and exercises you can't
+
+ align:start position:0%
+people scales and exercises you can't
+ 
+
+ align:start position:0%
+people scales and exercises you can't
+teach them how to be human they've got
+
+ align:start position:0%
+teach them how to be human they've got
+ 
+
+ align:start position:0%
+teach them how to be human they've got
+somehow to be lucky enough to grow up in
+
+ align:start position:0%
+somehow to be lucky enough to grow up in
+ 
+
+ align:start position:0%
+somehow to be lucky enough to grow up in
+a world in which it comes out of them
+
+ align:start position:0%
+a world in which it comes out of them
+ 
+
+ align:start position:0%
+a world in which it comes out of them
+maybe they had a suffer or maybe they
+
+ align:start position:0%
+maybe they had a suffer or maybe they
+ 
+
+ align:start position:0%
+maybe they had a suffer or maybe they
+had to have a a loving parent especially
+
+ align:start position:0%
+had to have a a loving parent especially
+ 
+
+ align:start position:0%
+had to have a a loving parent especially
+a loving woman you know uh that I don't
+
+ align:start position:0%
+a loving woman you know uh that I don't
+ 
+
+ align:start position:0%
+a loving woman you know uh that I don't
+mean a loving mother um I haven't done
+
+ align:start position:0%
+mean a loving mother um I haven't done
+ 
+
+ align:start position:0%
+mean a loving mother um I haven't done
+the sociology but um I'll bet one finds
+
+ align:start position:0%
+the sociology but um I'll bet one finds
+ 
+
+ align:start position:0%
+the sociology but um I'll bet one finds
+that a great many of the really
+
+ align:start position:0%
+that a great many of the really
+ 
+
+ align:start position:0%
+that a great many of the really
+outstanding musicians learn music from
+
+ align:start position:0%
+outstanding musicians learn music from
+ 
+
+ align:start position:0%
+outstanding musicians learn music from
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+mothers particularly if they were men I
+
+ align:start position:0%
+mothers particularly if they were men I
+ 
+
+ align:start position:0%
+mothers particularly if they were men I
+don't know what about the girls but the
+
+ align:start position:0%
+don't know what about the girls but the
+ 
+
+ align:start position:0%
+don't know what about the girls but the
+being a little boy sitting at your
+
+ align:start position:0%
+being a little boy sitting at your
+ 
+
+ align:start position:0%
+being a little boy sitting at your
+mother's lap while she's playing the
+
+ align:start position:0%
+mother's lap while she's playing the
+ 
+
+ align:start position:0%
+mother's lap while she's playing the
+piano and teaching you affects them as
+
+ align:start position:0%
+piano and teaching you affects them as
+ 
+
+ align:start position:0%
+piano and teaching you affects them as
+human beings and also uh accelerates
+
+ align:start position:0%
+human beings and also uh accelerates
+ 
+
+ align:start position:0%
+human beings and also uh accelerates
+their ability to become uh proficient
+
+ align:start position:0%
+their ability to become uh proficient
+ 
+
+ align:start position:0%
+their ability to become uh proficient
+technicians in their art form so there
+
+ align:start position:0%
+technicians in their art form so there
+ 
+
+ align:start position:0%
+technicians in their art form so there
+there are all sorts of causes about the
+
+ align:start position:0%
+there are all sorts of causes about the
+ 
+
+ align:start position:0%
+there are all sorts of causes about the
+expressiveness but the two are not going
+
+ align:start position:0%
+expressiveness but the two are not going
+ 
+
+ align:start position:0%
+expressiveness but the two are not going
+to be separable ultimately and that's
+
+ align:start position:0%
+to be separable ultimately and that's
+ 
+
+ align:start position:0%
+to be separable ultimately and that's
+what I tried to argue that was my
+
+ align:start position:0%
+what I tried to argue that was my
+ 
+
+ align:start position:0%
+what I tried to argue that was my
+inspiration when I try to argue uh the
+
+ align:start position:0%
+inspiration when I try to argue uh the
+ 
+
+ align:start position:0%
+inspiration when I try to argue uh the
+um thesis in reality
+
+ align:start position:0%
+um thesis in reality
+ 
+
+ align:start position:0%
+um thesis in reality
+transformed you noticed in the first
+
+ align:start position:0%
+transformed you noticed in the first
+ 
+
+ align:start position:0%
+transformed you noticed in the first
+chapter I set up the positions in terms
+
+ align:start position:0%
+chapter I set up the positions in terms
+ 
+
+ align:start position:0%
+chapter I set up the positions in terms
+of theorists who have maintained that
+
+ align:start position:0%
+of theorists who have maintained that
+ 
+
+ align:start position:0%
+of theorists who have maintained that
+they were realists or formalists and I
+
+ align:start position:0%
+they were realists or formalists and I
+ 
+
+ align:start position:0%
+they were realists or formalists and I
+attack both of them with the idea that
+
+ align:start position:0%
+attack both of them with the idea that
+ 
+
+ align:start position:0%
+attack both of them with the idea that
+what they're saying isn't wrong but
+
+ align:start position:0%
+what they're saying isn't wrong but
+ 
+
+ align:start position:0%
+what they're saying isn't wrong but
+having limited themselves they're
+
+ align:start position:0%
+having limited themselves they're
+ 
+
+ align:start position:0%
+having limited themselves they're
+ignoring something else and then in the
+
+ align:start position:0%
+ignoring something else and then in the
+ 
+
+ align:start position:0%
+ignoring something else and then in the
+last chap I suggest the integration and
+
+ align:start position:0%
+last chap I suggest the integration and
+ 
+
+ align:start position:0%
+last chap I suggest the integration and
+how difficult it is to understand the
+
+ align:start position:0%
+how difficult it is to understand the
+ 
+
+ align:start position:0%
+how difficult it is to understand the
+the second book you of mine you'll be
+
+ align:start position:0%
+the second book you of mine you'll be
+ 
+
+ align:start position:0%
+the second book you of mine you'll be
+reading tries to start from that except
+
+ align:start position:0%
+reading tries to start from that except
+ 
+
+ align:start position:0%
+reading tries to start from that except
+starting with exemplars of cinematic
+
+ align:start position:0%
+starting with exemplars of cinematic
+ 
+
+ align:start position:0%
+starting with exemplars of cinematic
+greatness three great filmmakers none of
+
+ align:start position:0%
+greatness three great filmmakers none of
+ 
+
+ align:start position:0%
+greatness three great filmmakers none of
+whom people would have called
+
+ align:start position:0%
+whom people would have called
+ 
+
+ align:start position:0%
+whom people would have called
+philosophers because they don't come in
+
+ align:start position:0%
+philosophers because they don't come in
+ 
+
+ align:start position:0%
+philosophers because they don't come in
+with thesis like some U European in
+
+ align:start position:0%
+with thesis like some U European in
+ 
+
+ align:start position:0%
+with thesis like some U European in
+particular filmmakers uh but there
+
+ align:start position:0%
+particular filmmakers uh but there
+ 
+
+ align:start position:0%
+particular filmmakers uh but there
+they're great men
+
+ align:start position:0%
+they're great men
+ 
+
+ align:start position:0%
+they're great men
+and approached properly one can see what
+
+ align:start position:0%
+and approached properly one can see what
+ 
+
+ align:start position:0%
+and approached properly one can see what
+the depths of their souls are and that's
+
+ align:start position:0%
+the depths of their souls are and that's
+ 
+
+ align:start position:0%
+the depths of their souls are and that's
+all I care about is when I talk about
+
+ align:start position:0%
+all I care about is when I talk about
+ 
+
+ align:start position:0%
+all I care about is when I talk about
+philosophical I don't care whether
+
+ align:start position:0%
+philosophical I don't care whether
+ 
+
+ align:start position:0%
+philosophical I don't care whether
+they've take taken courses called
+
+ align:start position:0%
+they've take taken courses called
+ 
+
+ align:start position:0%
+they've take taken courses called
+philosophy in some University or whether
+
+ align:start position:0%
+philosophy in some University or whether
+ 
+
+ align:start position:0%
+philosophy in some University or whether
+they've written the equivalent of
+
+ align:start position:0%
+they've written the equivalent of
+ 
+
+ align:start position:0%
+they've written the equivalent of
+consecrate of pure reason it's their
+
+ align:start position:0%
+consecrate of pure reason it's their
+ 
+
+ align:start position:0%
+consecrate of pure reason it's their
+having a deep awareness and sensitivity
+
+ align:start position:0%
+having a deep awareness and sensitivity
+ 
+
+ align:start position:0%
+having a deep awareness and sensitivity
+to human what it is to be a human being
+
+ align:start position:0%
+to human what it is to be a human being
+ 
+
+ align:start position:0%
+to human what it is to be a human being
+and then without they knowing
+
+ align:start position:0%
+and then without they knowing
+ 
+
+ align:start position:0%
+and then without they knowing
+necessarily what they're
+
+ align:start position:0%
+necessarily what they're
+ 
+
+ align:start position:0%
+necessarily what they're
+doing introducing that into the
+
+ align:start position:0%
+doing introducing that into the
+ 
+
+ align:start position:0%
+doing introducing that into the
+expressiveness and the meaningfulness of
+
+ align:start position:0%
+expressiveness and the meaningfulness of
+ 
+
+ align:start position:0%
+expressiveness and the meaningfulness of
+their of their work of art but doing it
+
+ align:start position:0%
+their of their work of art but doing it
+ 
+
+ align:start position:0%
+their of their work of art but doing it
+on the basis of absolute technical
+
+ align:start position:0%
+on the basis of absolute technical
+ 
+
+ align:start position:0%
+on the basis of absolute technical
+Mastery since the two cannot be
+
+ align:start position:0%
+Mastery since the two cannot be
+ 
+
+ align:start position:0%
+Mastery since the two cannot be
+separated okay so um I want to go back
+
+ align:start position:0%
+separated okay so um I want to go back
+ 
+
+ align:start position:0%
+separated okay so um I want to go back
+again to that question on why we study
+
+ align:start position:0%
+again to that question on why we study
+ 
+
+ align:start position:0%
+again to that question on why we study
+film you know and so I'll I'll tell you
+
+ align:start position:0%
+film you know and so I'll I'll tell you
+ 
+
+ align:start position:0%
+film you know and so I'll I'll tell you
+a little bit about my own personal view
+
+ align:start position:0%
+a little bit about my own personal view
+ 
+
+ align:start position:0%
+a little bit about my own personal view
+um I'm an engineer um I'm at MIT to do
+
+ align:start position:0%
+um I'm an engineer um I'm at MIT to do
+ 
+
+ align:start position:0%
+um I'm an engineer um I'm at MIT to do
+electrical engineering and what does
+
+ align:start position:0%
+electrical engineering and what does
+ 
+
+ align:start position:0%
+electrical engineering and what does
+that involve that involves solving a lot
+
+ align:start position:0%
+that involve that involves solving a lot
+ 
+
+ align:start position:0%
+that involve that involves solving a lot
+of problems and in general they're
+
+ align:start position:0%
+of problems and in general they're
+ 
+
+ align:start position:0%
+of problems and in general they're
+pretty easy you know like one of the
+
+ align:start position:0%
+pretty easy you know like one of the
+ 
+
+ align:start position:0%
+pretty easy you know like one of the
+hardest problems would probably take
+
+ align:start position:0%
+hardest problems would probably take
+ 
+
+ align:start position:0%
+hardest problems would probably take
+like you know like a couple days to
+
+ align:start position:0%
+like you know like a couple days to
+ 
+
+ align:start position:0%
+like you know like a couple days to
+solve before you figure it out and then
+
+ align:start position:0%
+solve before you figure it out and then
+ 
+
+ align:start position:0%
+solve before you figure it out and then
+you go on and build something as an
+
+ align:start position:0%
+you go on and build something as an
+ 
+
+ align:start position:0%
+you go on and build something as an
+engineer and the attraction of Art and
+
+ align:start position:0%
+engineer and the attraction of Art and
+ 
+
+ align:start position:0%
+engineer and the attraction of Art and
+philosophy is that the problem can never
+
+ align:start position:0%
+philosophy is that the problem can never
+ 
+
+ align:start position:0%
+philosophy is that the problem can never
+really be solved as far as we know you
+
+ align:start position:0%
+really be solved as far as we know you
+ 
+
+ align:start position:0%
+really be solved as far as we know you
+know you can keep on working on it
+
+ align:start position:0%
+know you can keep on working on it
+ 
+
+ align:start position:0%
+know you can keep on working on it
+forever you can keep on trying to figure
+
+ align:start position:0%
+forever you can keep on trying to figure
+ 
+
+ align:start position:0%
+forever you can keep on trying to figure
+out why film is so powerful and you'll
+
+ align:start position:0%
+out why film is so powerful and you'll
+ 
+
+ align:start position:0%
+out why film is so powerful and you'll
+you'll come up with a lot of reasons but
+
+ align:start position:0%
+you'll come up with a lot of reasons but
+ 
+
+ align:start position:0%
+you'll come up with a lot of reasons but
+you won't ever know for sure and as
+
+ align:start position:0%
+you won't ever know for sure and as
+ 
+
+ align:start position:0%
+you won't ever know for sure and as
+problem solvers you know that's
+
+ align:start position:0%
+problem solvers you know that's
+ 
+
+ align:start position:0%
+problem solvers you know that's
+that's I mean we we chose to challenge
+
+ align:start position:0%
+that's I mean we we chose to challenge
+ 
+
+ align:start position:0%
+that's I mean we we chose to challenge
+exactly you know we live on the
+
+ align:start position:0%
+exactly you know we live on the
+ 
+
+ align:start position:0%
+exactly you know we live on the
+challenge and that for me that's why I
+
+ align:start position:0%
+challenge and that for me that's why I
+ 
+
+ align:start position:0%
+challenge and that for me that's why I
+enjoy the challenge as opposed to say
+
+ align:start position:0%
+enjoy the challenge as opposed to say
+ 
+
+ align:start position:0%
+enjoy the challenge as opposed to say
+studying economics or something where
+
+ align:start position:0%
+studying economics or something where
+ 
+
+ align:start position:0%
+studying economics or something where
+the problems are generally solved and
+
+ align:start position:0%
+the problems are generally solved and
+ 
+
+ align:start position:0%
+the problems are generally solved and
+you just learn how to solve problems
+
+ align:start position:0%
+you just learn how to solve problems
+ 
+
+ align:start position:0%
+you just learn how to solve problems
+that have been solved or mathematics
+
+ align:start position:0%
+that have been solved or mathematics
+ 
+
+ align:start position:0%
+that have been solved or mathematics
+yeah where which is an art form based on
+
+ align:start position:0%
+yeah where which is an art form based on
+ 
+
+ align:start position:0%
+yeah where which is an art form based on
+the possibility of of a solution and
+
+ align:start position:0%
+the possibility of of a solution and
+ 
+
+ align:start position:0%
+the possibility of of a solution and
+then the achievement of
+
+ align:start position:0%
+then the achievement of
+ 
+
+ align:start position:0%
+then the achievement of
+it yes Am I Wrong is there are there any
+
+ align:start position:0%
+it yes Am I Wrong is there are there any
+ 
+
+ align:start position:0%
+it yes Am I Wrong is there are there any
+mathematicians here I you came in late
+
+ align:start position:0%
+mathematicians here I you came in late
+ 
+
+ align:start position:0%
+mathematicians here I you came in late
+you I I talked a little about life not
+
+ align:start position:0%
+you I I talked a little about life not
+ 
+
+ align:start position:0%
+you I I talked a little about life not
+being like a mathematical problem with
+
+ align:start position:0%
+being like a mathematical problem with
+ 
+
+ align:start position:0%
+being like a mathematical problem with
+you did I or was that my other class U
+
+ align:start position:0%
+you did I or was that my other class U
+ 
+
+ align:start position:0%
+you did I or was that my other class U
+why it is that I'm a humanist and
+
+ align:start position:0%
+why it is that I'm a humanist and
+ 
+
+ align:start position:0%
+why it is that I'm a humanist and
+pluralist U but in the context of that
+
+ align:start position:0%
+pluralist U but in the context of that
+ 
+
+ align:start position:0%
+pluralist U but in the context of that
+what I believed and what I must have
+
+ align:start position:0%
+what I believed and what I must have
+ 
+
+ align:start position:0%
+what I believed and what I must have
+said to the other class this term was
+
+ align:start position:0%
+said to the other class this term was
+ 
+
+ align:start position:0%
+said to the other class this term was
+that mathematics is a great art form
+
+ align:start position:0%
+that mathematics is a great art form
+ 
+
+ align:start position:0%
+that mathematics is a great art form
+it's a an abstract art form and
+
+ align:start position:0%
+it's a an abstract art form and
+ 
+
+ align:start position:0%
+it's a an abstract art form and
+therefore possibly the greatest of any
+
+ align:start position:0%
+therefore possibly the greatest of any
+ 
+
+ align:start position:0%
+therefore possibly the greatest of any
+pure art form it's pure
+
+ align:start position:0%
+pure art form it's pure
+ 
+
+ align:start position:0%
+pure art form it's pure
+art I'm not talking about useful
+
+ align:start position:0%
+art I'm not talking about useful
+ 
+
+ align:start position:0%
+art I'm not talking about useful
+mathematics I'm talking about um
+
+ align:start position:0%
+mathematics I'm talking about um
+ 
+
+ align:start position:0%
+mathematics I'm talking about um
+mathematics that is not useful uh it
+
+ align:start position:0%
+mathematics that is not useful uh it
+ 
+
+ align:start position:0%
+mathematics that is not useful uh it
+pure mathematics is pure art because it
+
+ align:start position:0%
+pure mathematics is pure art because it
+ 
+
+ align:start position:0%
+pure mathematics is pure art because it
+is purely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+abstract and that's because it can be
+
+ align:start position:0%
+abstract and that's because it can be
+ 
+
+ align:start position:0%
+abstract and that's because it can be
+solved and therefore it can be solved
+
+ align:start position:0%
+solved and therefore it can be solved
+ 
+
+ align:start position:0%
+solved and therefore it can be solved
+life is not like that and therefore um
+
+ align:start position:0%
+life is not like that and therefore um
+ 
+
+ align:start position:0%
+life is not like that and therefore um
+apart from the art of mathematics usual
+
+ align:start position:0%
+apart from the art of mathematics usual
+ 
+
+ align:start position:0%
+apart from the art of mathematics usual
+Arts like film and music and literature
+
+ align:start position:0%
+Arts like film and music and literature
+ 
+
+ align:start position:0%
+Arts like film and music and literature
+are are challenging and intriguing
+
+ align:start position:0%
+are are challenging and intriguing
+ 
+
+ align:start position:0%
+are are challenging and intriguing
+particularly to MIT students because you
+
+ align:start position:0%
+particularly to MIT students because you
+ 
+
+ align:start position:0%
+particularly to MIT students because you
+can recognize the problem and it's not
+
+ align:start position:0%
+can recognize the problem and it's not
+ 
+
+ align:start position:0%
+can recognize the problem and it's not
+clear that there is a solution to
+
+ align:start position:0%
+clear that there is a solution to
+ 
+
+ align:start position:0%
+clear that there is a solution to
+it which doesn't mean you shouldn't work
+
+ align:start position:0%
+it which doesn't mean you shouldn't work
+ 
+
+ align:start position:0%
+it which doesn't mean you shouldn't work
+at it um how much time do we have to I
+
+ align:start position:0%
+at it um how much time do we have to I
+ 
+
+ align:start position:0%
+at it um how much time do we have to I
+don't want to have to we have we can go
+
+ align:start position:0%
+don't want to have to we have we can go
+ 
+
+ align:start position:0%
+don't want to have to we have we can go
+on for an hour this way this is very
+
+ align:start position:0%
+on for an hour this way this is very
+ 
+
+ align:start position:0%
+on for an hour this way this is very
+profitable I think okay no do any of you
+
+ align:start position:0%
+profitable I think okay no do any of you
+ 
+
+ align:start position:0%
+profitable I think okay no do any of you
+feel differently than well I just meant
+
+ align:start position:0%
+feel differently than well I just meant
+ 
+
+ align:start position:0%
+feel differently than well I just meant
+because of the movie that we want what
+
+ align:start position:0%
+because of the movie that we want what
+ 
+
+ align:start position:0%
+because of the movie that we want what
+um because we have to watch the movie we
+
+ align:start position:0%
+um because we have to watch the movie we
+ 
+
+ align:start position:0%
+um because we have to watch the movie we
+have an hour before okay okay great um
+
+ align:start position:0%
+have an hour before okay okay great um
+ 
+
+ align:start position:0%
+have an hour before okay okay great um
+so I want to talk a little bit about the
+
+ align:start position:0%
+so I want to talk a little bit about the
+ 
+
+ align:start position:0%
+so I want to talk a little bit about the
+uni uniqueness and power of film as
+
+ align:start position:0%
+uni uniqueness and power of film as
+ 
+
+ align:start position:0%
+uni uniqueness and power of film as
+opposed to other media um so what is
+
+ align:start position:0%
+opposed to other media um so what is
+ 
+
+ align:start position:0%
+opposed to other media um so what is
+what is different about film you know
+
+ align:start position:0%
+what is different about film you know
+ 
+
+ align:start position:0%
+what is different about film you know
+first of all I can display any image
+
+ align:start position:0%
+first of all I can display any image
+ 
+
+ align:start position:0%
+first of all I can display any image
+it's not limited say an artist a paint
+
+ align:start position:0%
+it's not limited say an artist a paint
+ 
+
+ align:start position:0%
+it's not limited say an artist a paint
+artist is limited by the colors he can
+
+ align:start position:0%
+artist is limited by the colors he can
+ 
+
+ align:start position:0%
+artist is limited by the colors he can
+use or the brush I don't know much about
+
+ align:start position:0%
+use or the brush I don't know much about
+ 
+
+ align:start position:0%
+use or the brush I don't know much about
+painting but um the technique that he
+
+ align:start position:0%
+painting but um the technique that he
+ 
+
+ align:start position:0%
+painting but um the technique that he
+has he can't just put anything up there
+
+ align:start position:0%
+has he can't just put anything up there
+ 
+
+ align:start position:0%
+has he can't just put anything up there
+um of course there's sound in film which
+
+ align:start position:0%
+um of course there's sound in film which
+ 
+
+ align:start position:0%
+um of course there's sound in film which
+can be very powerful there's editing
+
+ align:start position:0%
+can be very powerful there's editing
+ 
+
+ align:start position:0%
+can be very powerful there's editing
+special effects and the experience of
+
+ align:start position:0%
+special effects and the experience of
+ 
+
+ align:start position:0%
+special effects and the experience of
+watching film is very different and
+
+ align:start position:0%
+watching film is very different and
+ 
+
+ align:start position:0%
+watching film is very different and
+that's that's unique to film and we
+
+ align:start position:0%
+that's that's unique to film and we
+ 
+
+ align:start position:0%
+that's that's unique to film and we
+there's definitely um advantage and
+
+ align:start position:0%
+there's definitely um advantage and
+ 
+
+ align:start position:0%
+there's definitely um advantage and
+disadvantages I'll mention a few and
+
+ align:start position:0%
+disadvantages I'll mention a few and
+ 
+
+ align:start position:0%
+disadvantages I'll mention a few and
+finally one of the great powers of film
+
+ align:start position:0%
+finally one of the great powers of film
+ 
+
+ align:start position:0%
+finally one of the great powers of film
+to me is that it's just socially
+
+ align:start position:0%
+to me is that it's just socially
+ 
+
+ align:start position:0%
+to me is that it's just socially
+pervasive and acceptable you know like
+
+ align:start position:0%
+pervasive and acceptable you know like
+ 
+
+ align:start position:0%
+pervasive and acceptable you know like
+it's a great tool as an artist a
+
+ align:start position:0%
+it's a great tool as an artist a
+ 
+
+ align:start position:0%
+it's a great tool as an artist a
+director as an artist and that he can
+
+ align:start position:0%
+director as an artist and that he can
+ 
+
+ align:start position:0%
+director as an artist and that he can
+release a film and instantly worldwide
+
+ align:start position:0%
+release a film and instantly worldwide
+ 
+
+ align:start position:0%
+release a film and instantly worldwide
+it's accessible to everyone and
+
+ align:start position:0%
+it's accessible to everyone and
+ 
+
+ align:start position:0%
+it's accessible to everyone and
+I mean that's that's really every
+
+ align:start position:0%
+I mean that's that's really every
+ 
+
+ align:start position:0%
+I mean that's that's really every
+artist's dream you know if if you're an
+
+ align:start position:0%
+artist's dream you know if if you're an
+ 
+
+ align:start position:0%
+artist's dream you know if if you're an
+artist right now and you want to get
+
+ align:start position:0%
+artist right now and you want to get
+ 
+
+ align:start position:0%
+artist right now and you want to get
+your work out film is probably the best
+
+ align:start position:0%
+your work out film is probably the best
+ 
+
+ align:start position:0%
+your work out film is probably the best
+media in which medium in which to do it
+
+ align:start position:0%
+media in which medium in which to do it
+ 
+
+ align:start position:0%
+media in which medium in which to do it
+but there's another dream and that is
+
+ align:start position:0%
+but there's another dream and that is
+ 
+
+ align:start position:0%
+but there's another dream and that is
+once you've achieved that kind of
+
+ align:start position:0%
+once you've achieved that kind of
+ 
+
+ align:start position:0%
+once you've achieved that kind of
+success you care about the audience you
+
+ align:start position:0%
+success you care about the audience you
+ 
+
+ align:start position:0%
+success you care about the audience you
+want to make sure that they know how to
+
+ align:start position:0%
+want to make sure that they know how to
+ 
+
+ align:start position:0%
+want to make sure that they know how to
+look at film exactly and that's that's
+
+ align:start position:0%
+look at film exactly and that's that's
+ 
+
+ align:start position:0%
+look at film exactly and that's that's
+what this kind of course addresses
+
+ align:start position:0%
+what this kind of course addresses
+ 
+
+ align:start position:0%
+what this kind of course addresses
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+to okay so I want to also compare film
+
+ align:start position:0%
+to okay so I want to also compare film
+ 
+
+ align:start position:0%
+to okay so I want to also compare film
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+photography um because similar in some
+
+ align:start position:0%
+photography um because similar in some
+ 
+
+ align:start position:0%
+photography um because similar in some
+ways and very different in other ways so
+
+ align:start position:0%
+ways and very different in other ways so
+ 
+
+ align:start position:0%
+ways and very different in other ways so
+I think the chief difference between
+
+ align:start position:0%
+I think the chief difference between
+ 
+
+ align:start position:0%
+I think the chief difference between
+film and between movies and photography
+
+ align:start position:0%
+film and between movies and photography
+ 
+
+ align:start position:0%
+film and between movies and photography
+is the way they're experienced now in a
+
+ align:start position:0%
+is the way they're experienced now in a
+ 
+
+ align:start position:0%
+is the way they're experienced now in a
+photograph the image is self-sufficient
+
+ align:start position:0%
+photograph the image is self-sufficient
+ 
+
+ align:start position:0%
+photograph the image is self-sufficient
+and the way it's experienced is you look
+
+ align:start position:0%
+and the way it's experienced is you look
+ 
+
+ align:start position:0%
+and the way it's experienced is you look
+at it and your eye may be drawn around
+
+ align:start position:0%
+at it and your eye may be drawn around
+ 
+
+ align:start position:0%
+at it and your eye may be drawn around
+the film I'm sure you've heard I mean
+
+ align:start position:0%
+the film I'm sure you've heard I mean
+ 
+
+ align:start position:0%
+the film I'm sure you've heard I mean
+the photograph sorry and I'm sure you've
+
+ align:start position:0%
+the photograph sorry and I'm sure you've
+ 
+
+ align:start position:0%
+the photograph sorry and I'm sure you've
+heard about artwork which paintings
+
+ align:start position:0%
+heard about artwork which paintings
+ 
+
+ align:start position:0%
+heard about artwork which paintings
+which draw your gaze to a piece of the
+
+ align:start position:0%
+which draw your gaze to a piece of the
+ 
+
+ align:start position:0%
+which draw your gaze to a piece of the
+artwork that's commonly analyzed
+
+ align:start position:0%
+artwork that's commonly analyzed
+ 
+
+ align:start position:0%
+artwork that's commonly analyzed
+something similar is done with
+
+ align:start position:0%
+something similar is done with
+ 
+
+ align:start position:0%
+something similar is done with
+Photography in film it can still be done
+
+ align:start position:0%
+Photography in film it can still be done
+ 
+
+ align:start position:0%
+Photography in film it can still be done
+but not to the same extent because
+
+ align:start position:0%
+but not to the same extent because
+ 
+
+ align:start position:0%
+but not to the same extent because
+you're experiencing constant stream of
+
+ align:start position:0%
+you're experiencing constant stream of
+ 
+
+ align:start position:0%
+you're experiencing constant stream of
+pictures instead of one self-sufficient
+
+ align:start position:0%
+pictures instead of one self-sufficient
+ 
+
+ align:start position:0%
+pictures instead of one self-sufficient
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+um and also the the experience in which
+
+ align:start position:0%
+um and also the the experience in which
+ 
+
+ align:start position:0%
+um and also the the experience in which
+you which you have at a movie theer is
+
+ align:start position:0%
+you which you have at a movie theer is
+ 
+
+ align:start position:0%
+you which you have at a movie theer is
+completely different than um looking at
+
+ align:start position:0%
+completely different than um looking at
+ 
+
+ align:start position:0%
+completely different than um looking at
+a photograph so how do we look at movies
+
+ align:start position:0%
+a photograph so how do we look at movies
+ 
+
+ align:start position:0%
+a photograph so how do we look at movies
+in general you go to a movie theater you
+
+ align:start position:0%
+in general you go to a movie theater you
+ 
+
+ align:start position:0%
+in general you go to a movie theater you
+sit down and you for 2 hours or however
+
+ align:start position:0%
+sit down and you for 2 hours or however
+ 
+
+ align:start position:0%
+sit down and you for 2 hours or however
+long and you watch the film on the
+
+ align:start position:0%
+long and you watch the film on the
+ 
+
+ align:start position:0%
+long and you watch the film on the
+screen what about photography you go to
+
+ align:start position:0%
+screen what about photography you go to
+ 
+
+ align:start position:0%
+screen what about photography you go to
+an art gallery or maybe it's in a
+
+ align:start position:0%
+an art gallery or maybe it's in a
+ 
+
+ align:start position:0%
+an art gallery or maybe it's in a
+magazine at home and so that experience
+
+ align:start position:0%
+magazine at home and so that experience
+ 
+
+ align:start position:0%
+magazine at home and so that experience
+is completely different and I want to
+
+ align:start position:0%
+is completely different and I want to
+ 
+
+ align:start position:0%
+is completely different and I want to
+bring up um an example of a horror movie
+
+ align:start position:0%
+bring up um an example of a horror movie
+ 
+
+ align:start position:0%
+bring up um an example of a horror movie
+now I was actually talking about this
+
+ align:start position:0%
+now I was actually talking about this
+ 
+
+ align:start position:0%
+now I was actually talking about this
+with my roommates yesterday which is why
+
+ align:start position:0%
+with my roommates yesterday which is why
+ 
+
+ align:start position:0%
+with my roommates yesterday which is why
+I bring this up but so why what what is
+
+ align:start position:0%
+I bring this up but so why what what is
+ 
+
+ align:start position:0%
+I bring this up but so why what what is
+it about a horror movie that is so
+
+ align:start position:0%
+it about a horror movie that is so
+ 
+
+ align:start position:0%
+it about a horror movie that is so
+appealing to people um because so so my
+
+ align:start position:0%
+appealing to people um because so so my
+ 
+
+ align:start position:0%
+appealing to people um because so so my
+roommates said that well it's because
+
+ align:start position:0%
+roommates said that well it's because
+ 
+
+ align:start position:0%
+roommates said that well it's because
+makes you feel scared
+
+ align:start position:0%
+makes you feel scared
+ 
+
+ align:start position:0%
+makes you feel scared
+and and to me that kind of makes sense
+
+ align:start position:0%
+and and to me that kind of makes sense
+ 
+
+ align:start position:0%
+and and to me that kind of makes sense
+but why would you want to feel scared
+
+ align:start position:0%
+but why would you want to feel scared
+ 
+
+ align:start position:0%
+but why would you want to feel scared
+you know that you could just go outside
+
+ align:start position:0%
+you know that you could just go outside
+ 
+
+ align:start position:0%
+you know that you could just go outside
+and walk alone at night you know then
+
+ align:start position:0%
+and walk alone at night you know then
+ 
+
+ align:start position:0%
+and walk alone at night you know then
+you feel scared but that's not enjoyable
+
+ align:start position:0%
+you feel scared but that's not enjoyable
+ 
+
+ align:start position:0%
+you feel scared but that's not enjoyable
+so what is it about a a scary movie
+
+ align:start position:0%
+so what is it about a a scary movie
+ 
+
+ align:start position:0%
+so what is it about a a scary movie
+that's enjoyable well I think it's
+
+ align:start position:0%
+that's enjoyable well I think it's
+ 
+
+ align:start position:0%
+that's enjoyable well I think it's
+because you know you're in the theater
+
+ align:start position:0%
+because you know you're in the theater
+ 
+
+ align:start position:0%
+because you know you're in the theater
+you know you're safe but you can still
+
+ align:start position:0%
+you know you're safe but you can still
+ 
+
+ align:start position:0%
+you know you're safe but you can still
+sympathize with the characters that
+
+ align:start position:0%
+sympathize with the characters that
+ 
+
+ align:start position:0%
+sympathize with the characters that
+you're seeing and so I I just bring up
+
+ align:start position:0%
+you're seeing and so I I just bring up
+ 
+
+ align:start position:0%
+you're seeing and so I I just bring up
+this example because it's one of the uh
+
+ align:start position:0%
+this example because it's one of the uh
+ 
+
+ align:start position:0%
+this example because it's one of the uh
+it's something that that the um director
+
+ align:start position:0%
+it's something that that the um director
+ 
+
+ align:start position:0%
+it's something that that the um director
+has to keep in mind for the mental state
+
+ align:start position:0%
+has to keep in mind for the mental state
+ 
+
+ align:start position:0%
+has to keep in mind for the mental state
+of his audience they know they're safe
+
+ align:start position:0%
+of his audience they know they're safe
+ 
+
+ align:start position:0%
+of his audience they know they're safe
+they know they're probably in a theater
+
+ align:start position:0%
+they know they're probably in a theater
+ 
+
+ align:start position:0%
+they know they're probably in a theater
+or at home watching it on TV and and
+
+ align:start position:0%
+or at home watching it on TV and and
+ 
+
+ align:start position:0%
+or at home watching it on TV and and
+this is part of the experience that they
+
+ align:start position:0%
+this is part of the experience that they
+ 
+
+ align:start position:0%
+this is part of the experience that they
+get as they're watching the film and
+
+ align:start position:0%
+get as they're watching the film and
+ 
+
+ align:start position:0%
+get as they're watching the film and
+that's part of the art form that's part
+
+ align:start position:0%
+that's part of the art form that's part
+ 
+
+ align:start position:0%
+that's part of the art form that's part
+of the medium okay we can discuss this
+
+ align:start position:0%
+of the medium okay we can discuss this
+ 
+
+ align:start position:0%
+of the medium okay we can discuss this
+further when you read my chapter on
+
+ align:start position:0%
+further when you read my chapter on
+ 
+
+ align:start position:0%
+further when you read my chapter on
+Hitchcock who who talks a great deal
+
+ align:start position:0%
+Hitchcock who who talks a great deal
+ 
+
+ align:start position:0%
+Hitchcock who who talks a great deal
+about this uh the principle that he
+
+ align:start position:0%
+about this uh the principle that he
+ 
+
+ align:start position:0%
+about this uh the principle that he
+develops is fear and fear not
+
+ align:start position:0%
+develops is fear and fear not
+ 
+
+ align:start position:0%
+develops is fear and fear not
+go ahead okay and um one thing that is
+
+ align:start position:0%
+go ahead okay and um one thing that is
+ 
+
+ align:start position:0%
+go ahead okay and um one thing that is
+really really important about film to me
+
+ align:start position:0%
+really really important about film to me
+ 
+
+ align:start position:0%
+really really important about film to me
+is that it's influenced by all other
+
+ align:start position:0%
+is that it's influenced by all other
+ 
+
+ align:start position:0%
+is that it's influenced by all other
+films that I've seen it's influenced by
+
+ align:start position:0%
+films that I've seen it's influenced by
+ 
+
+ align:start position:0%
+films that I've seen it's influenced by
+everything that I've seen you know
+
+ align:start position:0%
+everything that I've seen you know
+ 
+
+ align:start position:0%
+everything that I've seen you know
+because my experience watching a movie
+
+ align:start position:0%
+because my experience watching a movie
+ 
+
+ align:start position:0%
+because my experience watching a movie
+is going to be different than okay let's
+
+ align:start position:0%
+is going to be different than okay let's
+ 
+
+ align:start position:0%
+is going to be different than okay let's
+take an example of Beauty and the Beast
+
+ align:start position:0%
+take an example of Beauty and the Beast
+ 
+
+ align:start position:0%
+take an example of Beauty and the Beast
+our experience last week watching Beauty
+
+ align:start position:0%
+our experience last week watching Beauty
+ 
+
+ align:start position:0%
+our experience last week watching Beauty
+and the Beast I'm sure was vastly
+
+ align:start position:0%
+and the Beast I'm sure was vastly
+ 
+
+ align:start position:0%
+and the Beast I'm sure was vastly
+different than audiences watching it
+
+ align:start position:0%
+different than audiences watching it
+ 
+
+ align:start position:0%
+different than audiences watching it
+when it first came out and does that
+
+ align:start position:0%
+when it first came out and does that
+ 
+
+ align:start position:0%
+when it first came out and does that
+mean we got a less we saw less of an
+
+ align:start position:0%
+mean we got a less we saw less of an
+ 
+
+ align:start position:0%
+mean we got a less we saw less of an
+artwork I don't think so does it really
+
+ align:start position:0%
+artwork I don't think so does it really
+ 
+
+ align:start position:0%
+artwork I don't think so does it really
+matter to us um does it it's the point
+
+ align:start position:0%
+matter to us um does it it's the point
+ 
+
+ align:start position:0%
+matter to us um does it it's the point
+of our watching that film to try to
+
+ align:start position:0%
+of our watching that film to try to
+ 
+
+ align:start position:0%
+of our watching that film to try to
+recreate the experience of the original
+
+ align:start position:0%
+recreate the experience of the original
+ 
+
+ align:start position:0%
+recreate the experience of the original
+audiences at the time when it came out
+
+ align:start position:0%
+audiences at the time when it came out
+ 
+
+ align:start position:0%
+audiences at the time when it came out
+no I don't think so either I think to us
+
+ align:start position:0%
+no I don't think so either I think to us
+ 
+
+ align:start position:0%
+no I don't think so either I think to us
+it's a it's a whole different piece of
+
+ align:start position:0%
+it's a it's a whole different piece of
+ 
+
+ align:start position:0%
+it's a it's a whole different piece of
+art than to the people back then or even
+
+ align:start position:0%
+art than to the people back then or even
+ 
+
+ align:start position:0%
+art than to the people back then or even
+say me versus someone else in this room
+
+ align:start position:0%
+say me versus someone else in this room
+ 
+
+ align:start position:0%
+say me versus someone else in this room
+we have a completely different way of
+
+ align:start position:0%
+we have a completely different way of
+ 
+
+ align:start position:0%
+we have a completely different way of
+thinking about the movie it it drew out
+
+ align:start position:0%
+thinking about the movie it it drew out
+ 
+
+ align:start position:0%
+thinking about the movie it it drew out
+different emotions in us but I think
+
+ align:start position:0%
+different emotions in us but I think
+ 
+
+ align:start position:0%
+different emotions in us but I think
+that's okay and that's part of that's
+
+ align:start position:0%
+that's okay and that's part of that's
+ 
+
+ align:start position:0%
+that's okay and that's part of that's
+part of the power of art is that it can
+
+ align:start position:0%
+part of the power of art is that it can
+ 
+
+ align:start position:0%
+part of the power of art is that it can
+draw out different emotions different
+
+ align:start position:0%
+draw out different emotions different
+ 
+
+ align:start position:0%
+draw out different emotions different
+thinking from every single person from
+
+ align:start position:0%
+thinking from every single person from
+ 
+
+ align:start position:0%
+thinking from every single person from
+every single time with different
+
+ align:start position:0%
+every single time with different
+ 
+
+ align:start position:0%
+every single time with different
+experiences that watches the movie well
+
+ align:start position:0%
+experiences that watches the movie well
+ 
+
+ align:start position:0%
+experiences that watches the movie well
+let me inter up that uh that movie was
+
+ align:start position:0%
+let me inter up that uh that movie was
+ 
+
+ align:start position:0%
+let me inter up that uh that movie was
+made what 60 years ago almost and it in
+
+ align:start position:0%
+made what 60 years ago almost and it in
+ 
+
+ align:start position:0%
+made what 60 years ago almost and it in
+a world that you can't possibly
+
+ align:start position:0%
+a world that you can't possibly
+ 
+
+ align:start position:0%
+a world that you can't possibly
+appreciate because even your parents
+
+ align:start position:0%
+appreciate because even your parents
+ 
+
+ align:start position:0%
+appreciate because even your parents
+probably weren't born then um and that's
+
+ align:start position:0%
+probably weren't born then um and that's
+ 
+
+ align:start position:0%
+probably weren't born then um and that's
+the difference and people then for the
+
+ align:start position:0%
+the difference and people then for the
+ 
+
+ align:start position:0%
+the difference and people then for the
+people that who saw it they they were
+
+ align:start position:0%
+people that who saw it they they were
+ 
+
+ align:start position:0%
+people that who saw it they they were
+living in that world and you aren't
+
+ align:start position:0%
+living in that world and you aren't
+ 
+
+ align:start position:0%
+living in that world and you aren't
+anymore at the same time and also so
+
+ align:start position:0%
+anymore at the same time and also so
+ 
+
+ align:start position:0%
+anymore at the same time and also so
+that's a big difference another
+
+ align:start position:0%
+that's a big difference another
+ 
+
+ align:start position:0%
+that's a big difference another
+difference is the version you saw last
+
+ align:start position:0%
+difference is the version you saw last
+ 
+
+ align:start position:0%
+difference is the version you saw last
+week uh has been digitalized cleaned up
+
+ align:start position:0%
+week uh has been digitalized cleaned up
+ 
+
+ align:start position:0%
+week uh has been digitalized cleaned up
+restored looks better than it ever did
+
+ align:start position:0%
+restored looks better than it ever did
+ 
+
+ align:start position:0%
+restored looks better than it ever did
+including the first time it was shown it
+
+ align:start position:0%
+including the first time it was shown it
+ 
+
+ align:start position:0%
+including the first time it was shown it
+was probably much more grainy then and
+
+ align:start position:0%
+was probably much more grainy then and
+ 
+
+ align:start position:0%
+was probably much more grainy then and
+here you saw it as a beautiful perfect
+
+ align:start position:0%
+here you saw it as a beautiful perfect
+ 
+
+ align:start position:0%
+here you saw it as a beautiful perfect
+entity in itself true to its spirit
+
+ align:start position:0%
+entity in itself true to its spirit
+ 
+
+ align:start position:0%
+entity in itself true to its spirit
+but not identical to the first seeing so
+
+ align:start position:0%
+but not identical to the first seeing so
+ 
+
+ align:start position:0%
+but not identical to the first seeing so
+that in that sense too it's very
+
+ align:start position:0%
+that in that sense too it's very
+ 
+
+ align:start position:0%
+that in that sense too it's very
+different but I think what's most
+
+ align:start position:0%
+different but I think what's most
+ 
+
+ align:start position:0%
+different but I think what's most
+important is the fact that you're
+
+ align:start position:0%
+important is the fact that you're
+ 
+
+ align:start position:0%
+important is the fact that you're
+different that uh this is happens
+
+ align:start position:0%
+different that uh this is happens
+ 
+
+ align:start position:0%
+different that uh this is happens
+inevitably in the passage of time uh
+
+ align:start position:0%
+inevitably in the passage of time uh
+ 
+
+ align:start position:0%
+inevitably in the passage of time uh
+life um in a sense never repeats itself
+
+ align:start position:0%
+life um in a sense never repeats itself
+ 
+
+ align:start position:0%
+life um in a sense never repeats itself
+you know there is saying about history
+
+ align:start position:0%
+you know there is saying about history
+ 
+
+ align:start position:0%
+you know there is saying about history
+repeating itself but history doesn't
+
+ align:start position:0%
+repeating itself but history doesn't
+ 
+
+ align:start position:0%
+repeating itself but history doesn't
+repeat itself because every moment is a
+
+ align:start position:0%
+repeat itself because every moment is a
+ 
+
+ align:start position:0%
+repeat itself because every moment is a
+function of what happened before and
+
+ align:start position:0%
+function of what happened before and
+ 
+
+ align:start position:0%
+function of what happened before and
+that affects the novelty of that moment
+
+ align:start position:0%
+that affects the novelty of that moment
+ 
+
+ align:start position:0%
+that affects the novelty of that moment
+which then becomes the past for the next
+
+ align:start position:0%
+which then becomes the past for the next
+ 
+
+ align:start position:0%
+which then becomes the past for the next
+moment that life is dynamic it's
+
+ align:start position:0%
+moment that life is dynamic it's
+ 
+
+ align:start position:0%
+moment that life is dynamic it's
+developing and consequently uh in a
+
+ align:start position:0%
+developing and consequently uh in a
+ 
+
+ align:start position:0%
+developing and consequently uh in a
+sense we can't live the past anymore but
+
+ align:start position:0%
+sense we can't live the past anymore but
+ 
+
+ align:start position:0%
+sense we can't live the past anymore but
+we don't have to because as we change
+
+ align:start position:0%
+we don't have to because as we change
+ 
+
+ align:start position:0%
+we don't have to because as we change
+we're capable of aesthetic um aptitudes
+
+ align:start position:0%
+we're capable of aesthetic um aptitudes
+ 
+
+ align:start position:0%
+we're capable of aesthetic um aptitudes
+that didn't exist before so that it's a
+
+ align:start position:0%
+that didn't exist before so that it's a
+ 
+
+ align:start position:0%
+that didn't exist before so that it's a
+very complicated thing because of the
+
+ align:start position:0%
+very complicated thing because of the
+ 
+
+ align:start position:0%
+very complicated thing because of the
+presence of time uh in relation to
+
+ align:start position:0%
+presence of time uh in relation to
+ 
+
+ align:start position:0%
+presence of time uh in relation to
+particularly a temporal uh phenomenon
+
+ align:start position:0%
+particularly a temporal uh phenomenon
+ 
+
+ align:start position:0%
+particularly a temporal uh phenomenon
+like the movie uh the movies it's also
+
+ align:start position:0%
+like the movie uh the movies it's also
+ 
+
+ align:start position:0%
+like the movie uh the movies it's also
+true of uh non-temporal Arts like poetry
+
+ align:start position:0%
+true of uh non-temporal Arts like poetry
+ 
+
+ align:start position:0%
+true of uh non-temporal Arts like poetry
+but wanted to go on okay adding on to
+
+ align:start position:0%
+but wanted to go on okay adding on to
+ 
+
+ align:start position:0%
+but wanted to go on okay adding on to
+that I I strongly believe that recording
+
+ align:start position:0%
+that I I strongly believe that recording
+ 
+
+ align:start position:0%
+that I I strongly believe that recording
+doesn't reproduce reality and a large
+
+ align:start position:0%
+doesn't reproduce reality and a large
+ 
+
+ align:start position:0%
+doesn't reproduce reality and a large
+part of that is based on the experience
+
+ align:start position:0%
+part of that is based on the experience
+ 
+
+ align:start position:0%
+part of that is based on the experience
+that you have as you're as you're
+
+ align:start position:0%
+that you have as you're as you're
+ 
+
+ align:start position:0%
+that you have as you're as you're
+watching whatever has been recorded so
+
+ align:start position:0%
+watching whatever has been recorded so
+ 
+
+ align:start position:0%
+watching whatever has been recorded so
+for example um this class is being
+
+ align:start position:0%
+for example um this class is being
+ 
+
+ align:start position:0%
+for example um this class is being
+recorded and someone somewhere is
+
+ align:start position:0%
+recorded and someone somewhere is
+ 
+
+ align:start position:0%
+recorded and someone somewhere is
+probably going to watch this tap
+
+ align:start position:0%
+probably going to watch this tap
+ 
+
+ align:start position:0%
+probably going to watch this tap
+and their experience is going to be very
+
+ align:start position:0%
+and their experience is going to be very
+ 
+
+ align:start position:0%
+and their experience is going to be very
+different than the experience of
+
+ align:start position:0%
+different than the experience of
+ 
+
+ align:start position:0%
+different than the experience of
+everyone in this class and so they're
+
+ align:start position:0%
+everyone in this class and so they're
+ 
+
+ align:start position:0%
+everyone in this class and so they're
+it's not like by watching the tape
+
+ align:start position:0%
+it's not like by watching the tape
+ 
+
+ align:start position:0%
+it's not like by watching the tape
+they're suddenly sitting in an empty
+
+ align:start position:0%
+they're suddenly sitting in an empty
+ 
+
+ align:start position:0%
+they're suddenly sitting in an empty
+seat in this in this room as realistic
+
+ align:start position:0%
+seat in this in this room as realistic
+ 
+
+ align:start position:0%
+seat in this in this room as realistic
+as a tape may be and that's something to
+
+ align:start position:0%
+as a tape may be and that's something to
+ 
+
+ align:start position:0%
+as a tape may be and that's something to
+keep in mind also and that applies to
+
+ align:start position:0%
+keep in mind also and that applies to
+ 
+
+ align:start position:0%
+keep in mind also and that applies to
+photography as well that that definitely
+
+ align:start position:0%
+photography as well that that definitely
+ 
+
+ align:start position:0%
+photography as well that that definitely
+applies to film so finally I just want
+
+ align:start position:0%
+applies to film so finally I just want
+ 
+
+ align:start position:0%
+applies to film so finally I just want
+to talk a little bit about uh Beauty and
+
+ align:start position:0%
+to talk a little bit about uh Beauty and
+ 
+
+ align:start position:0%
+to talk a little bit about uh Beauty and
+the Beast and also citizen C so Beauty
+
+ align:start position:0%
+the Beast and also citizen C so Beauty
+ 
+
+ align:start position:0%
+the Beast and also citizen C so Beauty
+and the Beast um it's clear that not
+
+ align:start position:0%
+and the Beast um it's clear that not
+ 
+
+ align:start position:0%
+and the Beast um it's clear that not
+supposed to reflect reality since
+
+ align:start position:0%
+supposed to reflect reality since
+ 
+
+ align:start position:0%
+supposed to reflect reality since
+there's a beast you know it's fictional
+
+ align:start position:0%
+there's a beast you know it's fictional
+ 
+
+ align:start position:0%
+there's a beast you know it's fictional
+characters it's AIC Beast who talks yeah
+
+ align:start position:0%
+characters it's AIC Beast who talks yeah
+ 
+
+ align:start position:0%
+characters it's AIC Beast who talks yeah
+fictional fairy tale story you know
+
+ align:start position:0%
+fictional fairy tale story you know
+ 
+
+ align:start position:0%
+fictional fairy tale story you know
+there's the girl that can that can
+
+ align:start position:0%
+there's the girl that can that can
+ 
+
+ align:start position:0%
+there's the girl that can that can
+transport herself with the uh Power of
+
+ align:start position:0%
+transport herself with the uh Power of
+ 
+
+ align:start position:0%
+transport herself with the uh Power of
+the glove and so it's not a realistic
+
+ align:start position:0%
+the glove and so it's not a realistic
+ 
+
+ align:start position:0%
+the glove and so it's not a realistic
+story but it's still powerful at least I
+
+ align:start position:0%
+story but it's still powerful at least I
+ 
+
+ align:start position:0%
+story but it's still powerful at least I
+found it very powerful and why because
+
+ align:start position:0%
+found it very powerful and why because
+ 
+
+ align:start position:0%
+found it very powerful and why because
+it doesn't really reflect real life well
+
+ align:start position:0%
+it doesn't really reflect real life well
+ 
+
+ align:start position:0%
+it doesn't really reflect real life well
+to me it it does reflect real human them
+
+ align:start position:0%
+to me it it does reflect real human them
+ 
+
+ align:start position:0%
+to me it it does reflect real human them
+um most notably the love conquers all
+
+ align:start position:0%
+um most notably the love conquers all
+ 
+
+ align:start position:0%
+um most notably the love conquers all
+theme the the Beast and and Bell are in
+
+ align:start position:0%
+theme the the Beast and and Bell are in
+ 
+
+ align:start position:0%
+theme the the Beast and and Bell are in
+love and this is this you see in real
+
+ align:start position:0%
+love and this is this you see in real
+ 
+
+ align:start position:0%
+love and this is this you see in real
+life and you also see in the movie
+
+ align:start position:0%
+life and you also see in the movie
+ 
+
+ align:start position:0%
+life and you also see in the movie
+and in the movie love wins in the end
+
+ align:start position:0%
+and in the movie love wins in the end
+ 
+
+ align:start position:0%
+and in the movie love wins in the end
+and so in love of some sort that's
+
+ align:start position:0%
+and so in love of some sort that's
+ 
+
+ align:start position:0%
+and so in love of some sort that's
+something we can discuss go ahead and um
+
+ align:start position:0%
+something we can discuss go ahead and um
+ 
+
+ align:start position:0%
+something we can discuss go ahead and um
+so this kind of movie seems to trigger
+
+ align:start position:0%
+so this kind of movie seems to trigger
+ 
+
+ align:start position:0%
+so this kind of movie seems to trigger
+just H basic human humanistic concerns
+
+ align:start position:0%
+just H basic human humanistic concerns
+ 
+
+ align:start position:0%
+just H basic human humanistic concerns
+you know and I I'll just name a couple
+
+ align:start position:0%
+you know and I I'll just name a couple
+ 
+
+ align:start position:0%
+you know and I I'll just name a couple
+things um that the movie that the movie
+
+ align:start position:0%
+things um that the movie that the movie
+ 
+
+ align:start position:0%
+things um that the movie that the movie
+has in it um physical Beauty uh
+
+ align:start position:0%
+has in it um physical Beauty uh
+ 
+
+ align:start position:0%
+has in it um physical Beauty uh
+Forbidden Love These are these are
+
+ align:start position:0%
+Forbidden Love These are these are
+ 
+
+ align:start position:0%
+Forbidden Love These are these are
+common themes that people think about
+
+ align:start position:0%
+common themes that people think about
+ 
+
+ align:start position:0%
+common themes that people think about
+and can easily see reflected in real
+
+ align:start position:0%
+and can easily see reflected in real
+ 
+
+ align:start position:0%
+and can easily see reflected in real
+life no you're not forbidden to love a a
+
+ align:start position:0%
+life no you're not forbidden to love a a
+ 
+
+ align:start position:0%
+life no you're not forbidden to love a a
+monster it's just it's not ordinary it
+
+ align:start position:0%
+monster it's just it's not ordinary it
+ 
+
+ align:start position:0%
+monster it's just it's not ordinary it
+usually doesn't happen it's socially
+
+ align:start position:0%
+usually doesn't happen it's socially
+ 
+
+ align:start position:0%
+usually doesn't happen it's socially
+unacceptable in in the movie which which
+
+ align:start position:0%
+unacceptable in in the movie which which
+ 
+
+ align:start position:0%
+unacceptable in in the movie which which
+is a common theme in real life too um
+
+ align:start position:0%
+is a common theme in real life too um
+ 
+
+ align:start position:0%
+is a common theme in real life too um
+okay so citizen came no let's discuss
+
+ align:start position:0%
+okay so citizen came no let's discuss
+ 
+
+ align:start position:0%
+okay so citizen came no let's discuss
+this first does anybody want to say
+
+ align:start position:0%
+this first does anybody want to say
+ 
+
+ align:start position:0%
+this first does anybody want to say
+anything about Beauty and the
+
+ align:start position:0%
+anything about Beauty and the
+ 
+
+ align:start position:0%
+anything about Beauty and the
+Beast let me make a couple of remarks um
+
+ align:start position:0%
+Beast let me make a couple of remarks um
+ 
+
+ align:start position:0%
+Beast let me make a couple of remarks um
+ to who directed it wrote it who was
+
+ align:start position:0%
+ to who directed it wrote it who was
+ 
+
+ align:start position:0%
+ to who directed it wrote it who was
+this great genius really um told the
+
+ align:start position:0%
+this great genius really um told the
+ 
+
+ align:start position:0%
+this great genius really um told the
+crew particularly the cinematographer
+
+ align:start position:0%
+crew particularly the cinematographer
+ 
+
+ align:start position:0%
+crew particularly the cinematographer
+alak Kon who does a wonderful job and
+
+ align:start position:0%
+alak Kon who does a wonderful job and
+ 
+
+ align:start position:0%
+alak Kon who does a wonderful job and
+Chan Kant
+
+ align:start position:0%
+Chan Kant
+ 
+
+ align:start position:0%
+Chan Kant
+barah um who was the set designer he
+
+ align:start position:0%
+barah um who was the set designer he
+ 
+
+ align:start position:0%
+barah um who was the set designer he
+said what I want to do is to make a
+
+ align:start position:0%
+said what I want to do is to make a
+ 
+
+ align:start position:0%
+said what I want to do is to make a
+documentary of another world of a
+
+ align:start position:0%
+documentary of another world of a
+ 
+
+ align:start position:0%
+documentary of another world of a
+magical world I don't want it to be uh
+
+ align:start position:0%
+magical world I don't want it to be uh
+ 
+
+ align:start position:0%
+magical world I don't want it to be uh
+have Frills and look look like magic I
+
+ align:start position:0%
+have Frills and look look like magic I
+ 
+
+ align:start position:0%
+have Frills and look look like magic I
+wanted to be another world which is
+
+ align:start position:0%
+wanted to be another world which is
+ 
+
+ align:start position:0%
+wanted to be another world which is
+different from ours because it is Magic
+
+ align:start position:0%
+different from ours because it is Magic
+ 
+
+ align:start position:0%
+different from ours because it is Magic
+now he he couldn't have had in mind
+
+ align:start position:0%
+now he he couldn't have had in mind
+ 
+
+ align:start position:0%
+now he he couldn't have had in mind
+beauty and beast that the Disney Studio
+
+ align:start position:0%
+beauty and beast that the Disney Studio
+ 
+
+ align:start position:0%
+beauty and beast that the Disney Studio
+made about 15 years ago which most of
+
+ align:start position:0%
+made about 15 years ago which most of
+ 
+
+ align:start position:0%
+made about 15 years ago which most of
+you may have seen that is that's not a
+
+ align:start position:0%
+you may have seen that is that's not a
+ 
+
+ align:start position:0%
+you may have seen that is that's not a
+documentary of anything that is uh
+
+ align:start position:0%
+documentary of anything that is uh
+ 
+
+ align:start position:0%
+documentary of anything that is uh
+touching your sense of fancy and the
+
+ align:start position:0%
+touching your sense of fancy and the
+ 
+
+ align:start position:0%
+touching your sense of fancy and the
+fantasy uh and that's not what I I read
+
+ align:start position:0%
+fantasy uh and that's not what I I read
+ 
+
+ align:start position:0%
+fantasy uh and that's not what I I read
+a lot about that in my chapter but I
+
+ align:start position:0%
+a lot about that in my chapter but I
+ 
+
+ align:start position:0%
+a lot about that in my chapter but I
+don't want to get into it right now but
+
+ align:start position:0%
+don't want to get into it right now but
+ 
+
+ align:start position:0%
+don't want to get into it right now but
+I want want to mention that as an
+
+ align:start position:0%
+I want want to mention that as an
+ 
+
+ align:start position:0%
+I want want to mention that as an
+alternative to what kto tried for and I
+
+ align:start position:0%
+alternative to what kto tried for and I
+ 
+
+ align:start position:0%
+alternative to what kto tried for and I
+think succeeded he gets us into the mood
+
+ align:start position:0%
+think succeeded he gets us into the mood
+ 
+
+ align:start position:0%
+think succeeded he gets us into the mood
+that of course this is what a beast
+
+ align:start position:0%
+that of course this is what a beast
+ 
+
+ align:start position:0%
+that of course this is what a beast
+would look like and would be talk like
+
+ align:start position:0%
+would look like and would be talk like
+ 
+
+ align:start position:0%
+would look like and would be talk like
+if he were if he were um able to talk
+
+ align:start position:0%
+if he were if he were um able to talk
+ 
+
+ align:start position:0%
+if he were if he were um able to talk
+you know you're involved in that other
+
+ align:start position:0%
+you know you're involved in that other
+ 
+
+ align:start position:0%
+you know you're involved in that other
+reality and um the whole fantasy of it
+
+ align:start position:0%
+reality and um the whole fantasy of it
+ 
+
+ align:start position:0%
+reality and um the whole fantasy of it
+the Magic The Magic Castle and and the
+
+ align:start position:0%
+the Magic The Magic Castle and and the
+ 
+
+ align:start position:0%
+the Magic The Magic Castle and and the
+the Articles like the glove and the
+
+ align:start position:0%
+the Articles like the glove and the
+ 
+
+ align:start position:0%
+the Articles like the glove and the
+mirror that have magical properties uh
+
+ align:start position:0%
+mirror that have magical properties uh
+ 
+
+ align:start position:0%
+mirror that have magical properties uh
+but they're real articles they're real
+
+ align:start position:0%
+but they're real articles they're real
+ 
+
+ align:start position:0%
+but they're real articles they're real
+things in the world and you get a
+
+ align:start position:0%
+things in the world and you get a
+ 
+
+ align:start position:0%
+things in the world and you get a
+feeling for the real
+
+ align:start position:0%
+feeling for the real
+ 
+
+ align:start position:0%
+feeling for the real
+world um
+
+ align:start position:0%
+world um
+ 
+
+ align:start position:0%
+world um
+why did clo do this that itself is a big
+
+ align:start position:0%
+why did clo do this that itself is a big
+ 
+
+ align:start position:0%
+why did clo do this that itself is a big
+story uh and briefly it's
+
+ align:start position:0%
+story uh and briefly it's
+ 
+
+ align:start position:0%
+story uh and briefly it's
+because he was talking about what he
+
+ align:start position:0%
+because he was talking about what he
+ 
+
+ align:start position:0%
+because he was talking about what he
+calls the Poetry of film his his life
+
+ align:start position:0%
+calls the Poetry of film his his life
+ 
+
+ align:start position:0%
+calls the Poetry of film his his life
+output is mainly as a poet he made
+
+ align:start position:0%
+output is mainly as a poet he made
+ 
+
+ align:start position:0%
+output is mainly as a poet he made
+movies starting with the blood of the
+
+ align:start position:0%
+movies starting with the blood of the
+ 
+
+ align:start position:0%
+movies starting with the blood of the
+poet uh which is um uh what's called a
+
+ align:start position:0%
+poet uh which is um uh what's called a
+ 
+
+ align:start position:0%
+poet uh which is um uh what's called a
+surrealist movie but it isn't really but
+
+ align:start position:0%
+surrealist movie but it isn't really but
+ 
+
+ align:start position:0%
+surrealist movie but it isn't really but
+I'll give you an idea and in 1930
+
+ align:start position:0%
+I'll give you an idea and in 1930
+ 
+
+ align:start position:0%
+I'll give you an idea and in 1930
+when he was already over 40 I think and
+
+ align:start position:0%
+when he was already over 40 I think and
+ 
+
+ align:start position:0%
+when he was already over 40 I think and
+then he didn't make another movie for 15
+
+ align:start position:0%
+then he didn't make another movie for 15
+ 
+
+ align:start position:0%
+then he didn't make another movie for 15
+years and that second movie was Beauty
+
+ align:start position:0%
+years and that second movie was Beauty
+ 
+
+ align:start position:0%
+years and that second movie was Beauty
+and the Beast in the meantime he was
+
+ align:start position:0%
+and the Beast in the meantime he was
+ 
+
+ align:start position:0%
+and the Beast in the meantime he was
+turning out volume after volume of
+
+ align:start position:0%
+turning out volume after volume of
+ 
+
+ align:start position:0%
+turning out volume after volume of
+poetry uh stage plays novels stories
+
+ align:start position:0%
+poetry uh stage plays novels stories
+ 
+
+ align:start position:0%
+poetry uh stage plays novels stories
+everything but always as a poet and uh
+
+ align:start position:0%
+everything but always as a poet and uh
+ 
+
+ align:start position:0%
+everything but always as a poet and uh
+his uh attraction to the film was that
+
+ align:start position:0%
+his uh attraction to the film was that
+ 
+
+ align:start position:0%
+his uh attraction to the film was that
+he saw that there's an aspect of film
+
+ align:start position:0%
+he saw that there's an aspect of film
+ 
+
+ align:start position:0%
+he saw that there's an aspect of film
+that is or can be
+
+ align:start position:0%
+that is or can be
+ 
+
+ align:start position:0%
+that is or can be
+poetic but
+
+ align:start position:0%
+poetic but
+ 
+
+ align:start position:0%
+poetic but
+he distinguishes between poetry itself
+
+ align:start position:0%
+he distinguishes between poetry itself
+ 
+
+ align:start position:0%
+he distinguishes between poetry itself
+and the poetic he says the poetic is
+
+ align:start position:0%
+and the poetic he says the poetic is
+ 
+
+ align:start position:0%
+and the poetic he says the poetic is
+what people uh uh try to emulate when
+
+ align:start position:0%
+what people uh uh try to emulate when
+ 
+
+ align:start position:0%
+what people uh uh try to emulate when
+they're being superficial they're trying
+
+ align:start position:0%
+they're being superficial they're trying
+ 
+
+ align:start position:0%
+they're being superficial they're trying
+to act poetically you know you get the
+
+ align:start position:0%
+to act poetically you know you get the
+ 
+
+ align:start position:0%
+to act poetically you know you get the
+that mood that is being expressed uh and
+
+ align:start position:0%
+that mood that is being expressed uh and
+ 
+
+ align:start position:0%
+that mood that is being expressed uh and
+that's not what that's not what real
+
+ align:start position:0%
+that's not what that's not what real
+ 
+
+ align:start position:0%
+that's not what that's not what real
+life poetry is like that's not what
+
+ align:start position:0%
+life poetry is like that's not what
+ 
+
+ align:start position:0%
+life poetry is like that's not what
+poetry is really like in real life
+
+ align:start position:0%
+poetry is really like in real life
+ 
+
+ align:start position:0%
+poetry is really like in real life
+poetry comes out of the things of
+
+ align:start position:0%
+poetry comes out of the things of
+ 
+
+ align:start position:0%
+poetry comes out of the things of
+everyday life out of common existence
+
+ align:start position:0%
+everyday life out of common existence
+ 
+
+ align:start position:0%
+everyday life out of common existence
+and it comes out in unpr predictable
+
+ align:start position:0%
+and it comes out in unpr predictable
+ 
+
+ align:start position:0%
+and it comes out in unpr predictable
+ways if you look for it you won't find
+
+ align:start position:0%
+ways if you look for it you won't find
+ 
+
+ align:start position:0%
+ways if you look for it you won't find
+it because it hides but if you
+
+ align:start position:0%
+it because it hides but if you
+ 
+
+ align:start position:0%
+it because it hides but if you
+are perceptive and aware of the the
+
+ align:start position:0%
+are perceptive and aware of the the
+ 
+
+ align:start position:0%
+are perceptive and aware of the the
+difference it'll suddenly appear in
+
+ align:start position:0%
+difference it'll suddenly appear in
+ 
+
+ align:start position:0%
+difference it'll suddenly appear in
+unexpected places and for him the
+
+ align:start position:0%
+unexpected places and for him the
+ 
+
+ align:start position:0%
+unexpected places and for him the
+attraction of film is that film lends
+
+ align:start position:0%
+attraction of film is that film lends
+ 
+
+ align:start position:0%
+attraction of film is that film lends
+itself to
+
+ align:start position:0%
+itself to
+ 
+
+ align:start position:0%
+itself to
+that bringing forth of poetry I'll come
+
+ align:start position:0%
+that bringing forth of poetry I'll come
+ 
+
+ align:start position:0%
+that bringing forth of poetry I'll come
+back to this more when we talk about
+
+ align:start position:0%
+back to this more when we talk about
+ 
+
+ align:start position:0%
+back to this more when we talk about
+Wells um and renoa both of whom speak of
+
+ align:start position:0%
+Wells um and renoa both of whom speak of
+ 
+
+ align:start position:0%
+Wells um and renoa both of whom speak of
+poetic effects but they don't analyze it
+
+ align:start position:0%
+poetic effects but they don't analyze it
+ 
+
+ align:start position:0%
+poetic effects but they don't analyze it
+and haven't thought it through as well
+
+ align:start position:0%
+and haven't thought it through as well
+ 
+
+ align:start position:0%
+and haven't thought it through as well
+as cck cck to did uh in in the film uh
+
+ align:start position:0%
+as cck cck to did uh in in the film uh
+ 
+
+ align:start position:0%
+as cck cck to did uh in in the film uh
+there everything is as if it were real
+
+ align:start position:0%
+there everything is as if it were real
+ 
+
+ align:start position:0%
+there everything is as if it were real
+The Farmhouse at the beginning the
+
+ align:start position:0%
+The Farmhouse at the beginning the
+ 
+
+ align:start position:0%
+The Farmhouse at the beginning the
+ordinary life that we accept oh yeah
+
+ align:start position:0%
+ordinary life that we accept oh yeah
+ 
+
+ align:start position:0%
+ordinary life that we accept oh yeah
+that's real a real Farmhouse and it was
+
+ align:start position:0%
+that's real a real Farmhouse and it was
+ 
+
+ align:start position:0%
+that's real a real Farmhouse and it was
+a real Farmhouse um and then the castle
+
+ align:start position:0%
+a real Farmhouse um and then the castle
+ 
+
+ align:start position:0%
+a real Farmhouse um and then the castle
+the castle the Enchanted Castle
+
+ align:start position:0%
+the castle the Enchanted Castle
+ 
+
+ align:start position:0%
+the castle the Enchanted Castle
+uh looks like a real thing except that
+
+ align:start position:0%
+uh looks like a real thing except that
+ 
+
+ align:start position:0%
+uh looks like a real thing except that
+unreal things happen in it but they
+
+ align:start position:0%
+unreal things happen in it but they
+ 
+
+ align:start position:0%
+unreal things happen in it but they
+happen in a way that make it as if in
+
+ align:start position:0%
+happen in a way that make it as if in
+ 
+
+ align:start position:0%
+happen in a way that make it as if in
+another reality there could be arms
+
+ align:start position:0%
+another reality there could be arms
+ 
+
+ align:start position:0%
+another reality there could be arms
+coming out of the walls that hold on
+
+ align:start position:0%
+coming out of the walls that hold on
+ 
+
+ align:start position:0%
+coming out of the walls that hold on
+hold the chandel uh you know candles or
+
+ align:start position:0%
+hold the chandel uh you know candles or
+ 
+
+ align:start position:0%
+hold the chandel uh you know candles or
+that uh pour the wine for you or that
+
+ align:start position:0%
+that uh pour the wine for you or that
+ 
+
+ align:start position:0%
+that uh pour the wine for you or that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+uh faces embedded in the lle piece that
+
+ align:start position:0%
+uh faces embedded in the lle piece that
+ 
+
+ align:start position:0%
+uh faces embedded in the lle piece that
+keep moving around you remember all that
+
+ align:start position:0%
+keep moving around you remember all that
+ 
+
+ align:start position:0%
+keep moving around you remember all that
+uh all of that is real but in an unreal
+
+ align:start position:0%
+uh all of that is real but in an unreal
+ 
+
+ align:start position:0%
+uh all of that is real but in an unreal
+use and unreal context which is just
+
+ align:start position:0%
+use and unreal context which is just
+ 
+
+ align:start position:0%
+use and unreal context which is just
+what CTO wants um and as a way of
+
+ align:start position:0%
+what CTO wants um and as a way of
+ 
+
+ align:start position:0%
+what CTO wants um and as a way of
+enforcing that he avoided all special
+
+ align:start position:0%
+enforcing that he avoided all special
+ 
+
+ align:start position:0%
+enforcing that he avoided all special
+effects now we live in a world in which
+
+ align:start position:0%
+effects now we live in a world in which
+ 
+
+ align:start position:0%
+effects now we live in a world in which
+special effects have taken over the uh
+
+ align:start position:0%
+special effects have taken over the uh
+ 
+
+ align:start position:0%
+special effects have taken over the uh
+film industry and all visual uh
+
+ align:start position:0%
+film industry and all visual uh
+ 
+
+ align:start position:0%
+film industry and all visual uh
+experiences that we have uh in in his
+
+ align:start position:0%
+experiences that we have uh in in his
+ 
+
+ align:start position:0%
+experiences that we have uh in in his
+day when the movie was made 1945 they
+
+ align:start position:0%
+day when the movie was made 1945 they
+ 
+
+ align:start position:0%
+day when the movie was made 1945 they
+existed though they hadn't gone as far
+
+ align:start position:0%
+existed though they hadn't gone as far
+ 
+
+ align:start position:0%
+existed though they hadn't gone as far
+because they didn't have the computers
+
+ align:start position:0%
+because they didn't have the computers
+ 
+
+ align:start position:0%
+because they didn't have the computers
+at that time uh and he doesn't want it
+
+ align:start position:0%
+at that time uh and he doesn't want it
+ 
+
+ align:start position:0%
+at that time uh and he doesn't want it
+he didn't there's only one special
+
+ align:start position:0%
+he didn't there's only one special
+ 
+
+ align:start position:0%
+he didn't there's only one special
+effect in the movie does anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spotted when she disappeared there's the
+
+ align:start position:0%
+spotted when she disappeared there's the
+ 
+
+ align:start position:0%
+spotted when she disappeared there's the
+moment that U Belle has come back to the
+
+ align:start position:0%
+moment that U Belle has come back to the
+ 
+
+ align:start position:0%
+moment that U Belle has come back to the
+farm and dressed gorgeously with her
+
+ align:start position:0%
+farm and dressed gorgeously with her
+ 
+
+ align:start position:0%
+farm and dressed gorgeously with her
+magnificent what is it Collard or
+
+ align:start position:0%
+magnificent what is it Collard or
+ 
+
+ align:start position:0%
+magnificent what is it Collard or
+bracelet you that's necklace that's
+
+ align:start position:0%
+bracelet you that's necklace that's
+ 
+
+ align:start position:0%
+bracelet you that's necklace that's
+right and U uh her sister obviously
+
+ align:start position:0%
+right and U uh her sister obviously
+ 
+
+ align:start position:0%
+right and U uh her sister obviously
+envies it and she takes it off to hand
+
+ align:start position:0%
+envies it and she takes it off to hand
+ 
+
+ align:start position:0%
+envies it and she takes it off to hand
+it to her sister the minute it leaves
+
+ align:start position:0%
+it to her sister the minute it leaves
+ 
+
+ align:start position:0%
+it to her sister the minute it leaves
+her hands it turns into a cluster of
+
+ align:start position:0%
+her hands it turns into a cluster of
+ 
+
+ align:start position:0%
+her hands it turns into a cluster of
+rope that falls to the ground that's a
+
+ align:start position:0%
+rope that falls to the ground that's a
+ 
+
+ align:start position:0%
+rope that falls to the ground that's a
+special effect it's the only
+
+ align:start position:0%
+special effect it's the only
+ 
+
+ align:start position:0%
+special effect it's the only
+one uh and we don't we're used to that
+
+ align:start position:0%
+one uh and we don't we're used to that
+ 
+
+ align:start position:0%
+one uh and we don't we're used to that
+so we don't even notice it um so the
+
+ align:start position:0%
+so we don't even notice it um so the
+ 
+
+ align:start position:0%
+so we don't even notice it um so the
+tuo's idea what's interesting in the
+
+ align:start position:0%
+tuo's idea what's interesting in the
+ 
+
+ align:start position:0%
+tuo's idea what's interesting in the
+movie is that it is like the doc a
+
+ align:start position:0%
+movie is that it is like the doc a
+ 
+
+ align:start position:0%
+movie is that it is like the doc a
+documentary of of another world and that
+
+ align:start position:0%
+documentary of of another world and that
+ 
+
+ align:start position:0%
+documentary of of another world and that
+poses questions about the meaningfulness
+
+ align:start position:0%
+poses questions about the meaningfulness
+ 
+
+ align:start position:0%
+poses questions about the meaningfulness
+which uh I mustn't start because um you
+
+ align:start position:0%
+which uh I mustn't start because um you
+ 
+
+ align:start position:0%
+which uh I mustn't start because um you
+know I've written n 9,000 words already
+
+ align:start position:0%
+know I've written n 9,000 words already
+ 
+
+ align:start position:0%
+know I've written n 9,000 words already
+and I'm only half
+
+ align:start position:0%
+and I'm only half
+ 
+
+ align:start position:0%
+and I'm only half
+finished go ahead okay so I just want to
+
+ align:start position:0%
+finished go ahead okay so I just want to
+ 
+
+ align:start position:0%
+finished go ahead okay so I just want to
+say to wrap up a few words on citizen K
+
+ align:start position:0%
+say to wrap up a few words on citizen K
+ 
+
+ align:start position:0%
+say to wrap up a few words on citizen K
+okay let's go to Citizen K unless
+
+ align:start position:0%
+okay let's go to Citizen K unless
+ 
+
+ align:start position:0%
+okay let's go to Citizen K unless
+somebody wants to say something about it
+
+ align:start position:0%
+somebody wants to say something about it
+ 
+
+ align:start position:0%
+somebody wants to say something about it
+did you all get something out of that
+
+ align:start position:0%
+did you all get something out of that
+ 
+
+ align:start position:0%
+did you all get something out of that
+movie I thought it would be get
+
+ align:start position:0%
+movie I thought it would be get
+ 
+
+ align:start position:0%
+movie I thought it would be get
+increasingly more meaningful to you
+
+ align:start position:0%
+increasingly more meaningful to you
+ 
+
+ align:start position:0%
+increasingly more meaningful to you
+especially after you've had a chance to
+
+ align:start position:0%
+especially after you've had a chance to
+ 
+
+ align:start position:0%
+especially after you've had a chance to
+read the discussion about formalism and
+
+ align:start position:0%
+read the discussion about formalism and
+ 
+
+ align:start position:0%
+read the discussion about formalism and
+realism because it uses both it use it
+
+ align:start position:0%
+realism because it uses both it use it
+ 
+
+ align:start position:0%
+realism because it uses both it use it
+has trick formal tricks like uh uh the
+
+ align:start position:0%
+has trick formal tricks like uh uh the
+ 
+
+ align:start position:0%
+has trick formal tricks like uh uh the
+Beast carrying Beauty into her room did
+
+ align:start position:0%
+Beast carrying Beauty into her room did
+ 
+
+ align:start position:0%
+Beast carrying Beauty into her room did
+you notice she's attired the way she was
+
+ align:start position:0%
+you notice she's attired the way she was
+ 
+
+ align:start position:0%
+you notice she's attired the way she was
+on the farm until she goes through the
+
+ align:start position:0%
+on the farm until she goes through the
+ 
+
+ align:start position:0%
+on the farm until she goes through the
+door and then she ends up gorgeously
+
+ align:start position:0%
+door and then she ends up gorgeously
+ 
+
+ align:start position:0%
+door and then she ends up gorgeously
+dressed now that's a formal technique
+
+ align:start position:0%
+dressed now that's a formal technique
+ 
+
+ align:start position:0%
+dressed now that's a formal technique
+it's it's very inventive Citizen Cane is
+
+ align:start position:0%
+it's it's very inventive Citizen Cane is
+ 
+
+ align:start position:0%
+it's it's very inventive Citizen Cane is
+considered the greatest movie ever made
+
+ align:start position:0%
+considered the greatest movie ever made
+ 
+
+ align:start position:0%
+considered the greatest movie ever made
+by many people because it has so many of
+
+ align:start position:0%
+by many people because it has so many of
+ 
+
+ align:start position:0%
+by many people because it has so many of
+those inventive techniques and yet they
+
+ align:start position:0%
+those inventive techniques and yet they
+ 
+
+ align:start position:0%
+those inventive techniques and yet they
+work on another level as well in Cen
+
+ align:start position:0%
+work on another level as well in Cen
+ 
+
+ align:start position:0%
+work on another level as well in Cen
+Kane and also in Beauty and and the
+
+ align:start position:0%
+Kane and also in Beauty and and the
+ 
+
+ align:start position:0%
+Kane and also in Beauty and and the
+Beast anything else any anything any of
+
+ align:start position:0%
+Beast anything else any anything any of
+ 
+
+ align:start position:0%
+Beast anything else any anything any of
+you want to say about that okay let's go
+
+ align:start position:0%
+you want to say about that okay let's go
+ 
+
+ align:start position:0%
+you want to say about that okay let's go
+on to citiz Kane okay I don't know I
+
+ align:start position:0%
+on to citiz Kane okay I don't know I
+ 
+
+ align:start position:0%
+on to citiz Kane okay I don't know I
+don't want to give away too much about
+
+ align:start position:0%
+don't want to give away too much about
+ 
+
+ align:start position:0%
+don't want to give away too much about
+the movie because how many have not seen
+
+ align:start position:0%
+the movie because how many have not seen
+ 
+
+ align:start position:0%
+the movie because how many have not seen
+it I think about half I think
+
+ align:start position:0%
+it I think about half I think
+ 
+
+ align:start position:0%
+it I think about half I think
+but um I've studied it in several other
+
+ align:start position:0%
+but um I've studied it in several other
+ 
+
+ align:start position:0%
+but um I've studied it in several other
+classes and one thing that's often
+
+ align:start position:0%
+classes and one thing that's often
+ 
+
+ align:start position:0%
+classes and one thing that's often
+brought up is just the history of the
+
+ align:start position:0%
+brought up is just the history of the
+ 
+
+ align:start position:0%
+brought up is just the history of the
+film Orson Wells who's the director was
+
+ align:start position:0%
+film Orson Wells who's the director was
+ 
+
+ align:start position:0%
+film Orson Wells who's the director was
+a radio star at the time but had I think
+
+ align:start position:0%
+a radio star at the time but had I think
+ 
+
+ align:start position:0%
+a radio star at the time but had I think
+no experience at all in movies and this
+
+ align:start position:0%
+no experience at all in movies and this
+ 
+
+ align:start position:0%
+no experience at all in movies and this
+was his first film that's true goad and
+
+ align:start position:0%
+was his first film that's true goad and
+ 
+
+ align:start position:0%
+was his first film that's true goad and
+it was a huge success and at the time at
+
+ align:start position:0%
+it was a huge success and at the time at
+ 
+
+ align:start position:0%
+it was a huge success and at the time at
+the time it was just groundbreaking for
+
+ align:start position:0%
+the time it was just groundbreaking for
+ 
+
+ align:start position:0%
+the time it was just groundbreaking for
+things that he did in editing in special
+
+ align:start position:0%
+things that he did in editing in special
+ 
+
+ align:start position:0%
+things that he did in editing in special
+effects especially and also the the
+
+ align:start position:0%
+effects especially and also the the
+ 
+
+ align:start position:0%
+effects especially and also the the
+camera work that's those are the main
+
+ align:start position:0%
+camera work that's those are the main
+ 
+
+ align:start position:0%
+camera work that's those are the main
+things that we studied um one thing that
+
+ align:start position:0%
+things that we studied um one thing that
+ 
+
+ align:start position:0%
+things that we studied um one thing that
+you hear time and time again is deep
+
+ align:start position:0%
+you hear time and time again is deep
+ 
+
+ align:start position:0%
+you hear time and time again is deep
+focus which is Poss I think this is the
+
+ align:start position:0%
+focus which is Poss I think this is the
+ 
+
+ align:start position:0%
+focus which is Poss I think this is the
+first film that really used it people
+
+ align:start position:0%
+first film that really used it people
+ 
+
+ align:start position:0%
+first film that really used it people
+say that and it's not true but it's not
+
+ align:start position:0%
+say that and it's not true but it's not
+ 
+
+ align:start position:0%
+say that and it's not true but it's not
+your fault it's a common mistake um when
+
+ align:start position:0%
+your fault it's a common mistake um when
+ 
+
+ align:start position:0%
+your fault it's a common mistake um when
+you see the movie by renoa called rules
+
+ align:start position:0%
+you see the movie by renoa called rules
+ 
+
+ align:start position:0%
+you see the movie by renoa called rules
+of the game which is also treated as one
+
+ align:start position:0%
+of the game which is also treated as one
+ 
+
+ align:start position:0%
+of the game which is also treated as one
+of the two or three greatest movies ever
+
+ align:start position:0%
+of the two or three greatest movies ever
+ 
+
+ align:start position:0%
+of the two or three greatest movies ever
+made and that you'll be seeing it in
+
+ align:start position:0%
+made and that you'll be seeing it in
+ 
+
+ align:start position:0%
+made and that you'll be seeing it in
+this course you will see examples of
+
+ align:start position:0%
+this course you will see examples of
+ 
+
+ align:start position:0%
+this course you will see examples of
+deep focus and the movie was was made in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1939 before Orson
+
+ align:start position:0%
+1939 before Orson
+ 
+
+ align:start position:0%
+1939 before Orson
+Wells but Orson Wells developed it
+
+ align:start position:0%
+Wells but Orson Wells developed it
+ 
+
+ align:start position:0%
+Wells but Orson Wells developed it
+further and he gets the credit but um
+
+ align:start position:0%
+further and he gets the credit but um
+ 
+
+ align:start position:0%
+further and he gets the credit but um
+not he wasn't the first one go ahead
+
+ align:start position:0%
+not he wasn't the first one go ahead
+ 
+
+ align:start position:0%
+not he wasn't the first one go ahead
+okay so I mean this historical
+
+ align:start position:0%
+okay so I mean this historical
+ 
+
+ align:start position:0%
+okay so I mean this historical
+background is nice but it doesn't really
+
+ align:start position:0%
+background is nice but it doesn't really
+ 
+
+ align:start position:0%
+background is nice but it doesn't really
+affect our viewing experience of the
+
+ align:start position:0%
+affect our viewing experience of the
+ 
+
+ align:start position:0%
+affect our viewing experience of the
+movie and it's still a very powerful
+
+ align:start position:0%
+movie and it's still a very powerful
+ 
+
+ align:start position:0%
+movie and it's still a very powerful
+movie otherwise why would people say
+
+ align:start position:0%
+movie otherwise why would people say
+ 
+
+ align:start position:0%
+movie otherwise why would people say
+it's the greatest movie of all time and
+
+ align:start position:0%
+it's the greatest movie of all time and
+ 
+
+ align:start position:0%
+it's the greatest movie of all time and
+so um as I was watching the movie you
+
+ align:start position:0%
+so um as I was watching the movie you
+ 
+
+ align:start position:0%
+so um as I was watching the movie you
+know I wasn't really impressed by the
+
+ align:start position:0%
+know I wasn't really impressed by the
+ 
+
+ align:start position:0%
+know I wasn't really impressed by the
+special effect of it all because I've
+
+ align:start position:0%
+special effect of it all because I've
+ 
+
+ align:start position:0%
+special effect of it all because I've
+seen them now I've seen them hundreds of
+
+ align:start position:0%
+seen them now I've seen them hundreds of
+ 
+
+ align:start position:0%
+seen them now I've seen them hundreds of
+times already give an
+
+ align:start position:0%
+times already give an
+ 
+
+ align:start position:0%
+times already give an
+example okay um so there's there's one
+
+ align:start position:0%
+example okay um so there's there's one
+ 
+
+ align:start position:0%
+example okay um so there's there's one
+scene where the camera will scroll up um
+
+ align:start position:0%
+scene where the camera will scroll up um
+ 
+
+ align:start position:0%
+scene where the camera will scroll up um
+okay so they'll be on a stage the camera
+
+ align:start position:0%
+okay so they'll be on a stage the camera
+ 
+
+ align:start position:0%
+okay so they'll be on a stage the camera
+will scroll up and then suddenly it'll
+
+ align:start position:0%
+will scroll up and then suddenly it'll
+ 
+
+ align:start position:0%
+will scroll up and then suddenly it'll
+be another another scene it'll show a
+
+ align:start position:0%
+be another another scene it'll show a
+ 
+
+ align:start position:0%
+be another another scene it'll show a
+person clapping and so at the time that
+
+ align:start position:0%
+person clapping and so at the time that
+ 
+
+ align:start position:0%
+person clapping and so at the time that
+was a tough special effect to do without
+
+ align:start position:0%
+was a tough special effect to do without
+ 
+
+ align:start position:0%
+was a tough special effect to do without
+computers without ways of editing now
+
+ align:start position:0%
+computers without ways of editing now
+ 
+
+ align:start position:0%
+computers without ways of editing now
+it's you know it's you see it all the
+
+ align:start position:0%
+it's you know it's you see it all the
+ 
+
+ align:start position:0%
+it's you know it's you see it all the
+time you know a camera will pan and
+
+ align:start position:0%
+time you know a camera will pan and
+ 
+
+ align:start position:0%
+time you know a camera will pan and
+suddenly you'll be in a different scene
+
+ align:start position:0%
+suddenly you'll be in a different scene
+ 
+
+ align:start position:0%
+suddenly you'll be in a different scene
+and that's really easy to do nowadays um
+
+ align:start position:0%
+and that's really easy to do nowadays um
+ 
+
+ align:start position:0%
+and that's really easy to do nowadays um
+uh what you're referring to perhaps is
+
+ align:start position:0%
+uh what you're referring to perhaps is
+ 
+
+ align:start position:0%
+uh what you're referring to perhaps is
+when Kane gives a political speech and
+
+ align:start position:0%
+when Kane gives a political speech and
+ 
+
+ align:start position:0%
+when Kane gives a political speech and
+so you see him on the stage with his
+
+ align:start position:0%
+so you see him on the stage with his
+ 
+
+ align:start position:0%
+so you see him on the stage with his
+this is one of the images that's often
+
+ align:start position:0%
+this is one of the images that's often
+ 
+
+ align:start position:0%
+this is one of the images that's often
+copied uh even on the cover of my that's
+
+ align:start position:0%
+copied uh even on the cover of my that's
+ 
+
+ align:start position:0%
+copied uh even on the cover of my that's
+right the dusk jacket of my book in the
+
+ align:start position:0%
+right the dusk jacket of my book in the
+ 
+
+ align:start position:0%
+right the dusk jacket of my book in the
+wreath where there are excerpts from
+
+ align:start position:0%
+wreath where there are excerpts from
+ 
+
+ align:start position:0%
+wreath where there are excerpts from
+films by Hitchcock and Renoir as well as
+
+ align:start position:0%
+films by Hitchcock and Renoir as well as
+ 
+
+ align:start position:0%
+films by Hitchcock and Renoir as well as
+Wells there's one um vignette that shows
+
+ align:start position:0%
+Wells there's one um vignette that shows
+ 
+
+ align:start position:0%
+Wells there's one um vignette that shows
+Wells with his arm stretched out
+
+ align:start position:0%
+Wells with his arm stretched out
+ 
+
+ align:start position:0%
+Wells with his arm stretched out
+pointing to his own photograph that
+
+ align:start position:0%
+pointing to his own photograph that
+ 
+
+ align:start position:0%
+pointing to his own photograph that
+happens in this scene it's part of his
+
+ align:start position:0%
+happens in this scene it's part of his
+ 
+
+ align:start position:0%
+happens in this scene it's part of his
+political speech it's done in a big
+
+ align:start position:0%
+political speech it's done in a big
+ 
+
+ align:start position:0%
+political speech it's done in a big
+audience a big theater and you
+
+ align:start position:0%
+audience a big theater and you
+ 
+
+ align:start position:0%
+audience a big theater and you
+occasionally get quick shots of people
+
+ align:start position:0%
+occasionally get quick shots of people
+ 
+
+ align:start position:0%
+occasionally get quick shots of people
+in the audience well there were no
+
+ align:start position:0%
+in the audience well there were no
+ 
+
+ align:start position:0%
+in the audience well there were no
+people in the audience that that was
+
+ align:start position:0%
+people in the audience that that was
+ 
+
+ align:start position:0%
+people in the audience that that was
+done with photographs that saved a lot
+
+ align:start position:0%
+done with photographs that saved a lot
+ 
+
+ align:start position:0%
+done with photographs that saved a lot
+of money and uh they there was no need
+
+ align:start position:0%
+of money and uh they there was no need
+ 
+
+ align:start position:0%
+of money and uh they there was no need
+for there to be real people so they did
+
+ align:start position:0%
+for there to be real people so they did
+ 
+
+ align:start position:0%
+for there to be real people so they did
+it that way um in a movie like Titanic
+
+ align:start position:0%
+it that way um in a movie like Titanic
+ 
+
+ align:start position:0%
+it that way um in a movie like Titanic
+um where they have hordes of people in
+
+ align:start position:0%
+um where they have hordes of people in
+ 
+
+ align:start position:0%
+um where they have hordes of people in
+all sorts of scenes a lot of them are
+
+ align:start position:0%
+all sorts of scenes a lot of them are
+ 
+
+ align:start position:0%
+all sorts of scenes a lot of them are
+not real but rather um uh special
+
+ align:start position:0%
+not real but rather um uh special
+ 
+
+ align:start position:0%
+not real but rather um uh special
+effects with with the computer you can
+
+ align:start position:0%
+effects with with the computer you can
+ 
+
+ align:start position:0%
+effects with with the computer you can
+do more of that uh I myself think that
+
+ align:start position:0%
+do more of that uh I myself think that
+ 
+
+ align:start position:0%
+do more of that uh I myself think that
+the computerized things uh for instance
+
+ align:start position:0%
+the computerized things uh for instance
+ 
+
+ align:start position:0%
+the computerized things uh for instance
+in the movie in Titanic but also the one
+
+ align:start position:0%
+in the movie in Titanic but also the one
+ 
+
+ align:start position:0%
+in the movie in Titanic but also the one
+called Pearl Harbor um where they do
+
+ align:start position:0%
+called Pearl Harbor um where they do
+ 
+
+ align:start position:0%
+called Pearl Harbor um where they do
+that a lot at the end for instance that
+
+ align:start position:0%
+that a lot at the end for instance that
+ 
+
+ align:start position:0%
+that a lot at the end for instance that
+it's so obvious that it for me it
+
+ align:start position:0%
+it's so obvious that it for me it
+ 
+
+ align:start position:0%
+it's so obvious that it for me it
+attracted from the value of the movie in
+
+ align:start position:0%
+attracted from the value of the movie in
+ 
+
+ align:start position:0%
+attracted from the value of the movie in
+the case of Wells I don't think I would
+
+ align:start position:0%
+the case of Wells I don't think I would
+ 
+
+ align:start position:0%
+the case of Wells I don't think I would
+ever have noticed this if I hadn't read
+
+ align:start position:0%
+ever have noticed this if I hadn't read
+ 
+
+ align:start position:0%
+ever have noticed this if I hadn't read
+about it uh I'm telling to you now so
+
+ align:start position:0%
+about it uh I'm telling to you now so
+ 
+
+ align:start position:0%
+about it uh I'm telling to you now so
+you can see for yourself that's an
+
+ align:start position:0%
+you can see for yourself that's an
+ 
+
+ align:start position:0%
+you can see for yourself that's an
+example of a special effect and Wells
+
+ align:start position:0%
+example of a special effect and Wells
+ 
+
+ align:start position:0%
+example of a special effect and Wells
+was very Artful in doing that right I
+
+ align:start position:0%
+was very Artful in doing that right I
+ 
+
+ align:start position:0%
+was very Artful in doing that right I
+agree with that I without a computer all
+
+ align:start position:0%
+agree with that I without a computer all
+ 
+
+ align:start position:0%
+agree with that I without a computer all
+all of the effects I really wouldn't
+
+ align:start position:0%
+all of the effects I really wouldn't
+ 
+
+ align:start position:0%
+all of the effects I really wouldn't
+have known if I hadn't listened to the
+
+ align:start position:0%
+have known if I hadn't listened to the
+ 
+
+ align:start position:0%
+have known if I hadn't listened to the
+director's commentary you know where he
+
+ align:start position:0%
+director's commentary you know where he
+ 
+
+ align:start position:0%
+director's commentary you know where he
+talks about how he had to saw a table in
+
+ align:start position:0%
+talks about how he had to saw a table in
+ 
+
+ align:start position:0%
+talks about how he had to saw a table in
+half so that he could open it as he
+
+ align:start position:0%
+half so that he could open it as he
+ 
+
+ align:start position:0%
+half so that he could open it as he
+moved the camera through things like
+
+ align:start position:0%
+moved the camera through things like
+ 
+
+ align:start position:0%
+moved the camera through things like
+that are just nowadays they probably
+
+ align:start position:0%
+that are just nowadays they probably
+ 
+
+ align:start position:0%
+that are just nowadays they probably
+would have some fancier way of doing it
+
+ align:start position:0%
+would have some fancier way of doing it
+ 
+
+ align:start position:0%
+would have some fancier way of doing it
+but it's not something that that is
+
+ align:start position:0%
+but it's not something that that is
+ 
+
+ align:start position:0%
+but it's not something that that is
+really impressive to the modern audience
+
+ align:start position:0%
+really impressive to the modern audience
+ 
+
+ align:start position:0%
+really impressive to the modern audience
+yet Citizen Kane is still a very
+
+ align:start position:0%
+yet Citizen Kane is still a very
+ 
+
+ align:start position:0%
+yet Citizen Kane is still a very
+powerful film and um I don't really know
+
+ align:start position:0%
+powerful film and um I don't really know
+ 
+
+ align:start position:0%
+powerful film and um I don't really know
+exactly why but to me it it there's some
+
+ align:start position:0%
+exactly why but to me it it there's some
+ 
+
+ align:start position:0%
+exactly why but to me it it there's some
+there's some questions and there's some
+
+ align:start position:0%
+there's some questions and there's some
+ 
+
+ align:start position:0%
+there's some questions and there's some
+mysteries in the movie that aren't
+
+ align:start position:0%
+mysteries in the movie that aren't
+ 
+
+ align:start position:0%
+mysteries in the movie that aren't
+really answered and to me that just
+
+ align:start position:0%
+really answered and to me that just
+ 
+
+ align:start position:0%
+really answered and to me that just
+keeps me thinking about it long after
+
+ align:start position:0%
+keeps me thinking about it long after
+ 
+
+ align:start position:0%
+keeps me thinking about it long after
+after I I leave the theater or leave the
+
+ align:start position:0%
+after I I leave the theater or leave the
+ 
+
+ align:start position:0%
+after I I leave the theater or leave the
+room where I've been watching it you
+
+ align:start position:0%
+room where I've been watching it you
+ 
+
+ align:start position:0%
+room where I've been watching it you
+know I just keep reflecting on the movie
+
+ align:start position:0%
+know I just keep reflecting on the movie
+ 
+
+ align:start position:0%
+know I just keep reflecting on the movie
+and to me that's that's the real power
+
+ align:start position:0%
+and to me that's that's the real power
+ 
+
+ align:start position:0%
+and to me that's that's the real power
+of Citizen Kane was the example about
+
+ align:start position:0%
+of Citizen Kane was the example about
+ 
+
+ align:start position:0%
+of Citizen Kane was the example about
+the sewing of the table out of Citizen
+
+ align:start position:0%
+the sewing of the table out of Citizen
+ 
+
+ align:start position:0%
+the sewing of the table out of Citizen
+Kane yeah when he's in the uh when
+
+ align:start position:0%
+Kane yeah when he's in the uh when
+ 
+
+ align:start position:0%
+Kane yeah when he's in the uh when
+Kane's in the in the window off playing
+
+ align:start position:0%
+Kane's in the in the window off playing
+ 
+
+ align:start position:0%
+Kane's in the in the window off playing
+in the snow in the distance as a boy and
+
+ align:start position:0%
+in the snow in the distance as a boy and
+ 
+
+ align:start position:0%
+in the snow in the distance as a boy and
+his his parents are talking and the
+
+ align:start position:0%
+his his parents are talking and the
+ 
+
+ align:start position:0%
+his his parents are talking and the
+camera is behind the table you'll notice
+
+ align:start position:0%
+camera is behind the table you'll notice
+ 
+
+ align:start position:0%
+camera is behind the table you'll notice
+it and then the camera moves forward I
+
+ align:start position:0%
+it and then the camera moves forward I
+ 
+
+ align:start position:0%
+it and then the camera moves forward I
+see and they had to chop the table in
+
+ align:start position:0%
+see and they had to chop the table in
+ 
+
+ align:start position:0%
+see and they had to chop the table in
+half to get
+
+ align:start position:0%
+half to get
+ 
+
+ align:start position:0%
+half to get
+Wells was a professional magician and
+
+ align:start position:0%
+Wells was a professional magician and
+ 
+
+ align:start position:0%
+Wells was a professional magician and
+that shows up in various
+
+ align:start position:0%
+that shows up in various
+ 
+
+ align:start position:0%
+that shows up in various
+ways you you know he saw ladies in
+
+ align:start position:0%
+ways you you know he saw ladies in
+ 
+
+ align:start position:0%
+ways you you know he saw ladies in
+half go ahead okay so I I think that's I
+
+ align:start position:0%
+half go ahead okay so I I think that's I
+ 
+
+ align:start position:0%
+half go ahead okay so I I think that's I
+think I hit all the main points that I
+
+ align:start position:0%
+think I hit all the main points that I
+ 
+
+ align:start position:0%
+think I hit all the main points that I
+want well that's Splendid I think that's
+
+ align:start position:0%
+want well that's Splendid I think that's
+ 
+
+ align:start position:0%
+want well that's Splendid I think that's
+a very good presentation and we have
+
+ align:start position:0%
+a very good presentation and we have
+ 
+
+ align:start position:0%
+a very good presentation and we have
+time for anybody else to say
+
+ align:start position:0%
+time for anybody else to say
+ 
+
+ align:start position:0%
+time for anybody else to say
+something um I just wanted to say
+
+ align:start position:0%
+something um I just wanted to say
+ 
+
+ align:start position:0%
+something um I just wanted to say
+something about um Beauty and the Beast
+
+ align:start position:0%
+something about um Beauty and the Beast
+ 
+
+ align:start position:0%
+something about um Beauty and the Beast
+like something that I thought was
+
+ align:start position:0%
+like something that I thought was
+ 
+
+ align:start position:0%
+like something that I thought was
+interesting was the communication that
+
+ align:start position:0%
+interesting was the communication that
+ 
+
+ align:start position:0%
+interesting was the communication that
+um he tried to have with the audience
+
+ align:start position:0%
+um he tried to have with the audience
+ 
+
+ align:start position:0%
+um he tried to have with the audience
+especially like even just the beginning
+
+ align:start position:0%
+especially like even just the beginning
+ 
+
+ align:start position:0%
+especially like even just the beginning
+before the movie started you know how he
+
+ align:start position:0%
+before the movie started you know how he
+ 
+
+ align:start position:0%
+before the movie started you know how he
+was like well um just take your
+
+ align:start position:0%
+was like well um just take your
+ 
+
+ align:start position:0%
+was like well um just take your
+preconceptions of Beauty and the Beast
+
+ align:start position:0%
+preconceptions of Beauty and the Beast
+ 
+
+ align:start position:0%
+preconceptions of Beauty and the Beast
+and just humor me in this film and watch
+
+ align:start position:0%
+and just humor me in this film and watch
+ 
+
+ align:start position:0%
+and just humor me in this film and watch
+it in a different way I thought that was
+
+ align:start position:0%
+it in a different way I thought that was
+ 
+
+ align:start position:0%
+it in a different way I thought that was
+very interesting that he he set up the
+
+ align:start position:0%
+very interesting that he he set up the
+ 
+
+ align:start position:0%
+very interesting that he he set up the
+movie like that and actually came out
+
+ align:start position:0%
+movie like that and actually came out
+ 
+
+ align:start position:0%
+movie like that and actually came out
+and said that and then um I don't know
+
+ align:start position:0%
+and said that and then um I don't know
+ 
+
+ align:start position:0%
+and said that and then um I don't know
+well he he says that in order to uh
+
+ align:start position:0%
+well he he says that in order to uh
+ 
+
+ align:start position:0%
+well he he says that in order to uh
+awaken your imagination the way he
+
+ align:start position:0%
+awaken your imagination the way he
+ 
+
+ align:start position:0%
+awaken your imagination the way he
+thinks it would be for children in other
+
+ align:start position:0%
+thinks it would be for children in other
+ 
+
+ align:start position:0%
+thinks it would be for children in other
+words be a child but it's not a movie
+
+ align:start position:0%
+words be a child but it's not a movie
+ 
+
+ align:start position:0%
+words be a child but it's not a movie
+for children I don't think children
+
+ align:start position:0%
+for children I don't think children
+ 
+
+ align:start position:0%
+for children I don't think children
+would get much out of it but that's
+
+ align:start position:0%
+would get much out of it but that's
+ 
+
+ align:start position:0%
+would get much out of it but that's
+that's the mode of expression notice
+
+ align:start position:0%
+that's the mode of expression notice
+ 
+
+ align:start position:0%
+that's the mode of expression notice
+that the credits are put on in a school
+
+ align:start position:0%
+that the credits are put on in a school
+ 
+
+ align:start position:0%
+that the credits are put on in a school
+room and he is like the teacher who
+
+ align:start position:0%
+room and he is like the teacher who
+ 
+
+ align:start position:0%
+room and he is like the teacher who
+writes it on the Blackboard but then the
+
+ align:start position:0%
+writes it on the Blackboard but then the
+ 
+
+ align:start position:0%
+writes it on the Blackboard but then the
+actors who are dressed not in their
+
+ align:start position:0%
+actors who are dressed not in their
+ 
+
+ align:start position:0%
+actors who are dressed not in their
+costumes but as real people they come up
+
+ align:start position:0%
+costumes but as real people they come up
+ 
+
+ align:start position:0%
+costumes but as real people they come up
+and they erase it so there is that play
+
+ align:start position:0%
+and they erase it so there is that play
+ 
+
+ align:start position:0%
+and they erase it so there is that play
+uh which is very clever I think yeah so
+
+ align:start position:0%
+uh which is very clever I think yeah so
+ 
+
+ align:start position:0%
+uh which is very clever I think yeah so
+it's also like the reality of like
+
+ align:start position:0%
+it's also like the reality of like
+ 
+
+ align:start position:0%
+it's also like the reality of like
+trying to show the reality of magic like
+
+ align:start position:0%
+trying to show the reality of magic like
+ 
+
+ align:start position:0%
+trying to show the reality of magic like
+trying to put yourself in that and that
+
+ align:start position:0%
+trying to put yourself in that and that
+ 
+
+ align:start position:0%
+trying to put yourself in that and that
+I thought that was something in a theme
+
+ align:start position:0%
+I thought that was something in a theme
+ 
+
+ align:start position:0%
+I thought that was something in a theme
+through the whole movie you
+
+ align:start position:0%
+through the whole movie you
+ 
+
+ align:start position:0%
+through the whole movie you
+know why don't we go because otherwise
+
+ align:start position:0%
+know why don't we go because otherwise
+ 
+
+ align:start position:0%
+know why don't we go because otherwise
+it'll run after um
+
+ align:start position:0%
+it'll run after um
+ 
+
+ align:start position:0%
+it'll run after um
+I made myself be in a little late who
+
+ align:start position:0%
+I made myself be in a little late who
+ 
+
+ align:start position:0%
+I made myself be in a little late who
+was it put the movie in last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time person who put it in I say uh he's
+
+ align:start position:0%
+time person who put it in I say uh he's
+ 
+
+ align:start position:0%
+time person who put it in I say uh he's
+the person who put it in the last time
+
+ align:start position:0%
+the person who put it in the last time
+ 
+
+ align:start position:0%
+the person who put it in the last time
+he's not here today oh he's not here
+
+ align:start position:0%
+he's not here today oh he's not here
+ 
+
+ align:start position:0%
+he's not here today oh he's not here
+today yeah can any of you manage this or
+
+ align:start position:0%
+today yeah can any of you manage this or
+ 
+
+ align:start position:0%
+today yeah can any of you manage this or
+you really know because there's some
+
+ align:start position:0%
+you really know because there's some
+ 
+
+ align:start position:0%
+you really know because there's some
+trouble with the DVD there okay put it
+
+ align:start position:0%
+trouble with the DVD there okay put it
+ 
+
+ align:start position:0%
+trouble with the DVD there okay put it
+in and uh if I'm not back started anyhow
+
+ align:start position:0%
+in and uh if I'm not back started anyhow
+ 
+
+ align:start position:0%
+in and uh if I'm not back started anyhow
+but I'll try very hard to get back in
+
+ align:start position:0%
+but I'll try very hard to get back in
+ 
+
+ align:start position:0%
+but I'll try very hard to get back in
+time in the meantime could you make out
+
+ align:start position:0%
+time in the meantime could you make out
+ 
+
+ align:start position:0%
+time in the meantime could you make out
+um a card
\ No newline at end of file
diff --git a/X9eErxRjQEI.txt b/X9eErxRjQEI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4476502a7e22afa515b6de55e9bd214bdb9337f2
--- /dev/null
+++ b/X9eErxRjQEI.txt
@@ -0,0 +1,12121 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer high quality educational
+
+ align:start position:0%
+to offer high quality educational
+ 
+
+ align:start position:0%
+to offer high quality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay let's get
+
+ align:start position:0%
+ocw.mit.edu okay let's get
+ 
+
+ align:start position:0%
+ocw.mit.edu okay let's get
+started uh last time we looked at a
+
+ align:start position:0%
+started uh last time we looked at a
+ 
+
+ align:start position:0%
+started uh last time we looked at a
+variety of ways to analyze sums and
+
+ align:start position:0%
+variety of ways to analyze sums and
+ 
+
+ align:start position:0%
+variety of ways to analyze sums and
+Define closed form expressions for the
+
+ align:start position:0%
+Define closed form expressions for the
+ 
+
+ align:start position:0%
+Define closed form expressions for the
+sums and today we're going to use those
+
+ align:start position:0%
+sums and today we're going to use those
+ 
+
+ align:start position:0%
+sums and today we're going to use those
+methods to solve uh a variety of famous
+
+ align:start position:0%
+methods to solve uh a variety of famous
+ 
+
+ align:start position:0%
+methods to solve uh a variety of famous
+problems one of them involving uh Center
+
+ align:start position:0%
+problems one of them involving uh Center
+ 
+
+ align:start position:0%
+problems one of them involving uh Center
+of mass and and stacking blocks uh we
+
+ align:start position:0%
+of mass and and stacking blocks uh we
+ 
+
+ align:start position:0%
+of mass and and stacking blocks uh we
+saw a version of that yesterday in
+
+ align:start position:0%
+saw a version of that yesterday in
+ 
+
+ align:start position:0%
+saw a version of that yesterday in
+recitation where you solved the problem
+
+ align:start position:0%
+recitation where you solved the problem
+ 
+
+ align:start position:0%
+recitation where you solved the problem
+of figuring out how many uh L's you need
+
+ align:start position:0%
+of figuring out how many uh L's you need
+ 
+
+ align:start position:0%
+of figuring out how many uh L's you need
+to make something like this balanced
+
+ align:start position:0%
+to make something like this balanced
+ 
+
+ align:start position:0%
+to make something like this balanced
+perfectly uh now in this case I didn't
+
+ align:start position:0%
+perfectly uh now in this case I didn't
+ 
+
+ align:start position:0%
+perfectly uh now in this case I didn't
+actually get an interg number of L's
+
+ align:start position:0%
+actually get an interg number of L's
+ 
+
+ align:start position:0%
+actually get an interg number of L's
+which is possible because I didn't quite
+
+ align:start position:0%
+which is possible because I didn't quite
+ 
+
+ align:start position:0%
+which is possible because I didn't quite
+get it stacked right at the bottom so I
+
+ align:start position:0%
+get it stacked right at the bottom so I
+ 
+
+ align:start position:0%
+get it stacked right at the bottom so I
+got 10 and a half L's here there's an
+
+ align:start position:0%
+got 10 and a half L's here there's an
+ 
+
+ align:start position:0%
+got 10 and a half L's here there's an
+extra vertical here now in theory there
+
+ align:start position:0%
+extra vertical here now in theory there
+ 
+
+ align:start position:0%
+extra vertical here now in theory there
+are two integer ways of doing it and you
+
+ align:start position:0%
+are two integer ways of doing it and you
+ 
+
+ align:start position:0%
+are two integer ways of doing it and you
+Pro that yesterday in recitation So in
+
+ align:start position:0%
+Pro that yesterday in recitation So in
+ 
+
+ align:start position:0%
+Pro that yesterday in recitation So in
+theory 10 and 11 should work but in
+
+ align:start position:0%
+theory 10 and 11 should work but in
+ 
+
+ align:start position:0%
+theory 10 and 11 should work but in
+practice the blocks aren't perfect I
+
+ align:start position:0%
+practice the blocks aren't perfect I
+ 
+
+ align:start position:0%
+practice the blocks aren't perfect I
+didn't get them perfectly lined up and
+
+ align:start position:0%
+didn't get them perfectly lined up and
+ 
+
+ align:start position:0%
+didn't get them perfectly lined up and
+so 10 wouldn't quite work and 11 tended
+
+ align:start position:0%
+so 10 wouldn't quite work and 11 tended
+ 
+
+ align:start position:0%
+so 10 wouldn't quite work and 11 tended
+to pitch it the other way and of course
+
+ align:start position:0%
+to pitch it the other way and of course
+ 
+
+ align:start position:0%
+to pitch it the other way and of course
+in theory as long as the center of mass
+
+ align:start position:0%
+in theory as long as the center of mass
+ 
+
+ align:start position:0%
+in theory as long as the center of mass
+is just anywhere over this block it's
+
+ align:start position:0%
+is just anywhere over this block it's
+ 
+
+ align:start position:0%
+is just anywhere over this block it's
+going to be stable you know in practice
+
+ align:start position:0%
+going to be stable you know in practice
+ 
+
+ align:start position:0%
+going to be stable you know in practice
+there's air moving around and bouncing
+
+ align:start position:0%
+there's air moving around and bouncing
+ 
+
+ align:start position:0%
+there's air moving around and bouncing
+and stuff and so if you're close to the
+
+ align:start position:0%
+and stuff and so if you're close to the
+ 
+
+ align:start position:0%
+and stuff and so if you're close to the
+edge it's it's going
+
+ align:start position:0%
+edge it's it's going
+ 
+
+ align:start position:0%
+edge it's it's going
+over okay so now if you want to build
+
+ align:start position:0%
+over okay so now if you want to build
+ 
+
+ align:start position:0%
+over okay so now if you want to build
+one of these yourself it's not hard to
+
+ align:start position:0%
+one of these yourself it's not hard to
+ 
+
+ align:start position:0%
+one of these yourself it's not hard to
+do um you just start with an extra block
+
+ align:start position:0%
+do um you just start with an extra block
+ 
+
+ align:start position:0%
+do um you just start with an extra block
+here all right and then you build up and
+
+ align:start position:0%
+here all right and then you build up and
+ 
+
+ align:start position:0%
+here all right and then you build up and
+that's easy and then you notice when
+
+ align:start position:0%
+that's easy and then you notice when
+ 
+
+ align:start position:0%
+that's easy and then you notice when
+it's about right you know and you can
+
+ align:start position:0%
+it's about right you know and you can
+ 
+
+ align:start position:0%
+it's about right you know and you can
+start wiggling this block out and then
+
+ align:start position:0%
+start wiggling this block out and then
+ 
+
+ align:start position:0%
+start wiggling this block out and then
+then it looks pretty cool at that point
+
+ align:start position:0%
+then it looks pretty cool at that point
+ 
+
+ align:start position:0%
+then it looks pretty cool at that point
+uh actually it was a student in the
+
+ align:start position:0%
+uh actually it was a student in the
+ 
+
+ align:start position:0%
+uh actually it was a student in the
+class showed me this
+
+ align:start position:0%
+class showed me this
+ 
+
+ align:start position:0%
+class showed me this
+um a couple years ago because we were
+
+ align:start position:0%
+um a couple years ago because we were
+ 
+
+ align:start position:0%
+um a couple years ago because we were
+doing the blocks the next thing we're
+
+ align:start position:0%
+doing the blocks the next thing we're
+ 
+
+ align:start position:0%
+doing the blocks the next thing we're
+going to do we were doing that and he
+
+ align:start position:0%
+going to do we were doing that and he
+ 
+
+ align:start position:0%
+going to do we were doing that and he
+said hey there's this thing and it's
+
+ align:start position:0%
+said hey there's this thing and it's
+ 
+
+ align:start position:0%
+said hey there's this thing and it's
+pretty cool uh so today we're going to
+
+ align:start position:0%
+pretty cool uh so today we're going to
+ 
+
+ align:start position:0%
+pretty cool uh so today we're going to
+look at a different problem and that's
+
+ align:start position:0%
+look at a different problem and that's
+ 
+
+ align:start position:0%
+look at a different problem and that's
+the problem of getting the blocks
+
+ align:start position:0%
+the problem of getting the blocks
+ 
+
+ align:start position:0%
+the problem of getting the blocks
+stacked up so they go out over the edge
+
+ align:start position:0%
+stacked up so they go out over the edge
+ 
+
+ align:start position:0%
+stacked up so they go out over the edge
+of the table if that's
+
+ align:start position:0%
+of the table if that's
+ 
+
+ align:start position:0%
+of the table if that's
+doable uh so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal is
+
+ align:start position:0%
+goal is
+ 
+
+ align:start position:0%
+goal is
+to stack the blocks up
+
+ align:start position:0%
+to stack the blocks up
+ 
+
+ align:start position:0%
+to stack the blocks up
+like this we go farther and farther out
+
+ align:start position:0%
+like this we go farther and farther out
+ 
+
+ align:start position:0%
+like this we go farther and farther out
+and the question we're going to look at
+
+ align:start position:0%
+and the question we're going to look at
+ 
+
+ align:start position:0%
+and the question we're going to look at
+is is it
+
+ align:start position:0%
+is is it
+ 
+
+ align:start position:0%
+is is it
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+whoa almost is it possible to get a
+
+ align:start position:0%
+whoa almost is it possible to get a
+ 
+
+ align:start position:0%
+whoa almost is it possible to get a
+block all the way off the table that's
+
+ align:start position:0%
+block all the way off the table that's
+ 
+
+ align:start position:0%
+block all the way off the table that's
+the question we're going to look at and
+
+ align:start position:0%
+the question we're going to look at and
+ 
+
+ align:start position:0%
+the question we're going to look at and
+here I got I got close and you can see
+
+ align:start position:0%
+here I got I got close and you can see
+ 
+
+ align:start position:0%
+here I got I got close and you can see
+it's getting a little Tippy oh it's not
+
+ align:start position:0%
+it's getting a little Tippy oh it's not
+ 
+
+ align:start position:0%
+it's getting a little Tippy oh it's not
+going to go it's going to fall over if I
+
+ align:start position:0%
+going to go it's going to fall over if I
+ 
+
+ align:start position:0%
+going to go it's going to fall over if I
+so that's so I didn't do it this time um
+
+ align:start position:0%
+so that's so I didn't do it this time um
+ 
+
+ align:start position:0%
+so that's so I didn't do it this time um
+you're only allowed one block per level
+
+ align:start position:0%
+you're only allowed one block per level
+ 
+
+ align:start position:0%
+you're only allowed one block per level
+so you can't you can't do uh you know
+
+ align:start position:0%
+so you can't you can't do uh you know
+ 
+
+ align:start position:0%
+so you can't you can't do uh you know
+anything like this that's not allowed
+
+ align:start position:0%
+anything like this that's not allowed
+ 
+
+ align:start position:0%
+anything like this that's not allowed
+you can go
+
+ align:start position:0%
+you can go
+ 
+
+ align:start position:0%
+you can go
+backwards you know if that helps you you
+
+ align:start position:0%
+backwards you know if that helps you you
+ 
+
+ align:start position:0%
+backwards you know if that helps you you
+well it's got to be stable on both sides
+
+ align:start position:0%
+well it's got to be stable on both sides
+ 
+
+ align:start position:0%
+well it's got to be stable on both sides
+but you can go back and forth um so the
+
+ align:start position:0%
+but you can go back and forth um so the
+ 
+
+ align:start position:0%
+but you can go back and forth um so the
+question is can you get out one block
+
+ align:start position:0%
+question is can you get out one block
+ 
+
+ align:start position:0%
+question is can you get out one block
+totally out over the table how many
+
+ align:start position:0%
+totally out over the table how many
+ 
+
+ align:start position:0%
+totally out over the table how many
+people think it can't be
+
+ align:start position:0%
+people think it can't be
+ 
+
+ align:start position:0%
+people think it can't be
+done right a few doubs oh more doubs how
+
+ align:start position:0%
+done right a few doubs oh more doubs how
+ 
+
+ align:start position:0%
+done right a few doubs oh more doubs how
+many think it can be done oh a lot of
+
+ align:start position:0%
+many think it can be done oh a lot of
+ 
+
+ align:start position:0%
+many think it can be done oh a lot of
+people think it can be done okay well
+
+ align:start position:0%
+people think it can be done okay well
+ 
+
+ align:start position:0%
+people think it can be done okay well
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right how many people think you can get
+
+ align:start position:0%
+right how many people think you can get
+ 
+
+ align:start position:0%
+right how many people think you can get
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+block two blocks out over the
+
+ align:start position:0%
+block two blocks out over the
+ 
+
+ align:start position:0%
+block two blocks out over the
+table a few of you how many think you
+
+ align:start position:0%
+table a few of you how many think you
+ 
+
+ align:start position:0%
+table a few of you how many think you
+can get it three blocks
+
+ align:start position:0%
+can get it three blocks
+ 
+
+ align:start position:0%
+can get it three blocks
+out ah you're Believers okay how many
+
+ align:start position:0%
+out ah you're Believers okay how many
+ 
+
+ align:start position:0%
+out ah you're Believers okay how many
+people think I can reach that
+
+ align:start position:0%
+people think I can reach that
+ 
+
+ align:start position:0%
+people think I can reach that
+wall well I got to tell you I can't
+
+ align:start position:0%
+wall well I got to tell you I can't
+ 
+
+ align:start position:0%
+wall well I got to tell you I can't
+reach the wall
+
+ align:start position:0%
+reach the wall
+ 
+
+ align:start position:0%
+reach the wall
+because yeah you know that's going to be
+
+ align:start position:0%
+because yeah you know that's going to be
+ 
+
+ align:start position:0%
+because yeah you know that's going to be
+hard to do uh but this is what we're
+
+ align:start position:0%
+hard to do uh but this is what we're
+ 
+
+ align:start position:0%
+hard to do uh but this is what we're
+going to we're going to try to figure
+
+ align:start position:0%
+going to we're going to try to figure
+ 
+
+ align:start position:0%
+going to we're going to try to figure
+out and we're going to do it with a
+
+ align:start position:0%
+out and we're going to do it with a
+ 
+
+ align:start position:0%
+out and we're going to do it with a
+little competition so we're going to
+
+ align:start position:0%
+little competition so we're going to
+ 
+
+ align:start position:0%
+little competition so we're going to
+have a team of you go up against the
+
+ align:start position:0%
+have a team of you go up against the
+ 
+
+ align:start position:0%
+have a team of you go up against the
+Tas and the winner gets candy to
+
+ align:start position:0%
+Tas and the winner gets candy to
+ 
+
+ align:start position:0%
+Tas and the winner gets candy to
+share the losing team gets the infamous
+
+ align:start position:0%
+share the losing team gets the infamous
+ 
+
+ align:start position:0%
+share the losing team gets the infamous
+6042 nerd Pride pocket
+
+ align:start position:0%
+6042 nerd Pride pocket
+ 
+
+ align:start position:0%
+6042 nerd Pride pocket
+protectors very nice you know shiny
+
+ align:start position:0%
+protectors very nice you know shiny
+ 
+
+ align:start position:0%
+protectors very nice you know shiny
+plastic has the MIT logo on them very
+
+ align:start position:0%
+plastic has the MIT logo on them very
+ 
+
+ align:start position:0%
+plastic has the MIT logo on them very
+handy all right so I need four
+
+ align:start position:0%
+handy all right so I need four
+ 
+
+ align:start position:0%
+handy all right so I need four
+volunteers so come on down if you'd like
+
+ align:start position:0%
+volunteers so come on down if you'd like
+ 
+
+ align:start position:0%
+volunteers so come on down if you'd like
+to volunteer you can win some candy for
+
+ align:start position:0%
+to volunteer you can win some candy for
+ 
+
+ align:start position:0%
+to volunteer you can win some candy for
+the class or at least win yourself a
+
+ align:start position:0%
+the class or at least win yourself a
+ 
+
+ align:start position:0%
+the class or at least win yourself a
+pocket
+
+ align:start position:0%
+pocket
+ 
+
+ align:start position:0%
+pocket
+protector and we'll put the class over
+
+ align:start position:0%
+protector and we'll put the class over
+ 
+
+ align:start position:0%
+protector and we'll put the class over
+there and we get the Tas to come
+
+ align:start position:0%
+there and we get the Tas to come
+ 
+
+ align:start position:0%
+there and we get the Tas to come
+down so come on down I got a couple of
+
+ align:start position:0%
+down so come on down I got a couple of
+ 
+
+ align:start position:0%
+down so come on down I got a couple of
+people who else wants to join them all
+
+ align:start position:0%
+people who else wants to join them all
+ 
+
+ align:start position:0%
+people who else wants to join them all
+right come on down we got a fourth
+
+ align:start position:0%
+right come on down we got a fourth
+ 
+
+ align:start position:0%
+right come on down we got a fourth
+volunteer out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there all right we got some people
+
+ align:start position:0%
+there all right we got some people
+ 
+
+ align:start position:0%
+there all right we got some people
+coming down all right come on over
+
+ align:start position:0%
+coming down all right come on over
+ 
+
+ align:start position:0%
+coming down all right come on over
+all right you got all the blocks you
+
+ align:start position:0%
+all right you got all the blocks you
+ 
+
+ align:start position:0%
+all right you got all the blocks you
+want we can even take this thing down so
+
+ align:start position:0%
+want we can even take this thing down so
+ 
+
+ align:start position:0%
+want we can even take this thing down so
+here's your here's your
+
+ align:start position:0%
+here's your here's your
+ 
+
+ align:start position:0%
+here's your here's your
+supply all right now the Tas have a
+
+ align:start position:0%
+supply all right now the Tas have a
+ 
+
+ align:start position:0%
+supply all right now the Tas have a
+little bit of an advantage because
+
+ align:start position:0%
+little bit of an advantage because
+ 
+
+ align:start position:0%
+little bit of an advantage because
+they've done this before some of them uh
+
+ align:start position:0%
+they've done this before some of them uh
+ 
+
+ align:start position:0%
+they've done this before some of them uh
+so you can give some advice to your
+
+ align:start position:0%
+so you can give some advice to your
+ 
+
+ align:start position:0%
+so you can give some advice to your
+colleagues here so you got to get some
+
+ align:start position:0%
+colleagues here so you got to get some
+ 
+
+ align:start position:0%
+colleagues here so you got to get some
+blocks out of the block supply maybe we
+
+ align:start position:0%
+blocks out of the block supply maybe we
+ 
+
+ align:start position:0%
+blocks out of the block supply maybe we
+should take this down it's about to fall
+
+ align:start position:0%
+should take this down it's about to fall
+ 
+
+ align:start position:0%
+should take this down it's about to fall
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+anyway so yeah how do we get this down
+
+ align:start position:0%
+anyway so yeah how do we get this down
+ 
+
+ align:start position:0%
+anyway so yeah how do we get this down
+not sure
+
+ align:start position:0%
+not sure
+ 
+
+ align:start position:0%
+not sure
+all right I got this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end whoa there we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who all
+
+ align:start position:0%
+who all
+ 
+
+ align:start position:0%
+who all
+right there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go so whoever gets a block out over the
+
+ align:start position:0%
+go so whoever gets a block out over the
+ 
+
+ align:start position:0%
+go so whoever gets a block out over the
+farthest wins one block per level you
+
+ align:start position:0%
+farthest wins one block per level you
+ 
+
+ align:start position:0%
+farthest wins one block per level you
+can't do two blocks on a level believe
+
+ align:start position:0%
+can't do two blocks on a level believe
+ 
+
+ align:start position:0%
+can't do two blocks on a level believe
+me it's a lot easier if you can do multi
+
+ align:start position:0%
+me it's a lot easier if you can do multi
+ 
+
+ align:start position:0%
+me it's a lot easier if you can do multi
+M blocks per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level you can go back and forth go ahead
+
+ align:start position:0%
+level you can go back and forth go ahead
+ 
+
+ align:start position:0%
+level you can go back and forth go ahead
+and give them some advice they look like
+
+ align:start position:0%
+and give them some advice they look like
+ 
+
+ align:start position:0%
+and give them some advice they look like
+they need
+
+ align:start position:0%
+they need
+ 
+
+ align:start position:0%
+they need
+it they're only about half a block out
+
+ align:start position:0%
+it they're only about half a block out
+ 
+
+ align:start position:0%
+it they're only about half a block out
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far how are the Tas doing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right the Tas are getting scientific
+
+ align:start position:0%
+all right the Tas are getting scientific
+ 
+
+ align:start position:0%
+all right the Tas are getting scientific
+here you know it's not looking good for
+
+ align:start position:0%
+here you know it's not looking good for
+ 
+
+ align:start position:0%
+here you know it's not looking good for
+you guys to get the candy today I gotta
+
+ align:start position:0%
+you guys to get the candy today I gotta
+ 
+
+ align:start position:0%
+you guys to get the candy today I gotta
+tell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you oh Tas are close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right you got oh you're about two3
+
+ align:start position:0%
+all right you got oh you're about two3
+ 
+
+ align:start position:0%
+all right you got oh you're about two3
+of the way over we got one
+
+ align:start position:0%
+of the way over we got one
+ 
+
+ align:start position:0%
+of the way over we got one
+2/3 got an inch to go yeah maybe it's
+
+ align:start position:0%
+2/3 got an inch to go yeah maybe it's
+ 
+
+ align:start position:0%
+2/3 got an inch to go yeah maybe it's
+not doable it's not the first time we've
+
+ align:start position:0%
+not doable it's not the first time we've
+ 
+
+ align:start position:0%
+not doable it's not the first time we've
+done this
+
+ align:start position:0%
+done this
+ 
+
+ align:start position:0%
+done this
+and and the problem has not been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solvable oh Tas are close they're
+
+ align:start position:0%
+solvable oh Tas are close they're
+ 
+
+ align:start position:0%
+solvable oh Tas are close they're
+definitely within an
+
+ align:start position:0%
+definitely within an
+ 
+
+ align:start position:0%
+definitely within an
+inch uh maybe an inch and a half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you can't hold it it's got to stand
+
+ align:start position:0%
+yeah you can't hold it it's got to stand
+ 
+
+ align:start position:0%
+yeah you can't hold it it's got to stand
+up by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself now the bottom block can go out
+
+ align:start position:0%
+itself now the bottom block can go out
+ 
+
+ align:start position:0%
+itself now the bottom block can go out
+over the edge if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want oh they're getting
+
+ align:start position:0%
+want oh they're getting
+ 
+
+ align:start position:0%
+want oh they're getting
+close oh I think you might you might
+
+ align:start position:0%
+close oh I think you might you might
+ 
+
+ align:start position:0%
+close oh I think you might you might
+have the but the top block out over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe how you guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doing not good this is this is trouble
+
+ align:start position:0%
+doing not good this is this is trouble
+ 
+
+ align:start position:0%
+doing not good this is this is trouble
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the you got it yeah oh all right you
+
+ align:start position:0%
+the you got it yeah oh all right you
+ 
+
+ align:start position:0%
+the you got it yeah oh all right you
+gota you got to work fast now if you're
+
+ align:start position:0%
+gota you got to work fast now if you're
+ 
+
+ align:start position:0%
+gota you got to work fast now if you're
+gonna beat that ta's got it out over the
+
+ align:start position:0%
+gonna beat that ta's got it out over the
+ 
+
+ align:start position:0%
+gonna beat that ta's got it out over the
+edge you see that they're out over the
+
+ align:start position:0%
+edge you see that they're out over the
+ 
+
+ align:start position:0%
+edge you see that they're out over the
+edge all right I think they did it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to have a hard time
+
+ align:start position:0%
+we're going to have a hard time
+ 
+
+ align:start position:0%
+we're going to have a hard time
+analyzing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no all right we'll try another block or
+
+ align:start position:0%
+no all right we'll try another block or
+ 
+
+ align:start position:0%
+no all right we'll try another block or
+two and then we'll uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vote looks like the stat Center yeah
+
+ align:start position:0%
+vote looks like the stat Center yeah
+ 
+
+ align:start position:0%
+vote looks like the stat Center yeah
+that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close you're not the most efficient
+
+ align:start position:0%
+close you're not the most efficient
+ 
+
+ align:start position:0%
+close you're not the most efficient
+that's for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure yeah the Tas are already munching
+
+ align:start position:0%
+sure yeah the Tas are already munching
+ 
+
+ align:start position:0%
+sure yeah the Tas are already munching
+down here this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sol now there's an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea all right well I think it's time
+
+ align:start position:0%
+idea all right well I think it's time
+ 
+
+ align:start position:0%
+idea all right well I think it's time
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+vote but let the class see what you did
+
+ align:start position:0%
+vote but let the class see what you did
+ 
+
+ align:start position:0%
+vote but let the class see what you did
+REM yeah you got to take your hands off
+
+ align:start position:0%
+REM yeah you got to take your hands off
+ 
+
+ align:start position:0%
+REM yeah you got to take your hands off
+that's you know we're just choosing not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to I'll get some good top balancing on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there I don't know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right can you let it go all right
+
+ align:start position:0%
+all right can you let it go all right
+ 
+
+ align:start position:0%
+all right can you let it go all right
+they let it go all right let's see did
+
+ align:start position:0%
+they let it go all right let's see did
+ 
+
+ align:start position:0%
+they let it go all right let's see did
+you get one
+
+ align:start position:0%
+you get one
+ 
+
+ align:start position:0%
+you get one
+out all right we're going to do a vote
+
+ align:start position:0%
+out all right we're going to do a vote
+ 
+
+ align:start position:0%
+out all right we're going to do a vote
+who thinks they got the one farthest
+
+ align:start position:0%
+who thinks they got the one farthest
+ 
+
+ align:start position:0%
+who thinks they got the one farthest
+out oh it's close oh look at that we
+
+ align:start position:0%
+out oh it's close oh look at that we
+ 
+
+ align:start position:0%
+out oh it's close oh look at that we
+need some glasses out there who thinks
+
+ align:start position:0%
+need some glasses out there who thinks
+ 
+
+ align:start position:0%
+need some glasses out there who thinks
+the TA has got it farther
+
+ align:start position:0%
+the TA has got it farther
+ 
+
+ align:start position:0%
+the TA has got it farther
+out oh man all rightor tower all right
+
+ align:start position:0%
+out oh man all rightor tower all right
+ 
+
+ align:start position:0%
+out oh man all rightor tower all right
+so you guys here you go very nice pocket
+
+ align:start position:0%
+so you guys here you go very nice pocket
+ 
+
+ align:start position:0%
+so you guys here you go very nice pocket
+protect a good effort right there you
+
+ align:start position:0%
+protect a good effort right there you
+ 
+
+ align:start position:0%
+protect a good effort right there you
+are well
+
+ align:start position:0%
+are well
+ 
+
+ align:start position:0%
+are well
+done and I'm afraid they get the candy
+
+ align:start position:0%
+done and I'm afraid they get the candy
+ 
+
+ align:start position:0%
+done and I'm afraid they get the candy
+here so you can take these out and share
+
+ align:start position:0%
+here so you can take these out and share
+ 
+
+ align:start position:0%
+here so you can take these out and share
+them with the
+
+ align:start position:0%
+them with the
+ 
+
+ align:start position:0%
+them with the
+class oh leave it that way leave it
+
+ align:start position:0%
+class oh leave it that way leave it
+ 
+
+ align:start position:0%
+class oh leave it that way leave it
+there I'm we're going to analyze yours
+
+ align:start position:0%
+there I'm we're going to analyze yours
+ 
+
+ align:start position:0%
+there I'm we're going to analyze yours
+because I can't begin to analyze
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all right now watching this how
+
+ align:start position:0%
+that all right now watching this how
+ 
+
+ align:start position:0%
+that all right now watching this how
+many people still think we can get it
+
+ align:start position:0%
+many people still think we can get it
+ 
+
+ align:start position:0%
+many people still think we can get it
+all the way to the
+
+ align:start position:0%
+all the way to the
+ 
+
+ align:start position:0%
+all the way to the
+wall a few people in fact if you stack
+
+ align:start position:0%
+wall a few people in fact if you stack
+ 
+
+ align:start position:0%
+wall a few people in fact if you stack
+this high enough and we're going to
+
+ align:start position:0%
+this high enough and we're going to
+ 
+
+ align:start position:0%
+this high enough and we're going to
+analyze how high it has to go you could
+
+ align:start position:0%
+analyze how high it has to go you could
+ 
+
+ align:start position:0%
+analyze how high it has to go you could
+reach the wall now in fact we're going
+
+ align:start position:0%
+reach the wall now in fact we're going
+ 
+
+ align:start position:0%
+reach the wall now in fact we're going
+to find that you probably got to go out
+
+ align:start position:0%
+to find that you probably got to go out
+ 
+
+ align:start position:0%
+to find that you probably got to go out
+to the Stars to get that high before you
+
+ align:start position:0%
+to the Stars to get that high before you
+ 
+
+ align:start position:0%
+to the Stars to get that high before you
+can reach the wall so it's not too
+
+ align:start position:0%
+can reach the wall so it's not too
+ 
+
+ align:start position:0%
+can reach the wall so it's not too
+practical now what I want to do is
+
+ align:start position:0%
+practical now what I want to do is
+ 
+
+ align:start position:0%
+practical now what I want to do is
+analyze this strategy and this sort of
+
+ align:start position:0%
+analyze this strategy and this sort of
+ 
+
+ align:start position:0%
+analyze this strategy and this sort of
+looks like a nice design they got out
+
+ align:start position:0%
+looks like a nice design they got out
+ 
+
+ align:start position:0%
+looks like a nice design they got out
+there with just five and they did a a
+
+ align:start position:0%
+there with just five and they did a a
+ 
+
+ align:start position:0%
+there with just five and they did a a
+particular approach using what we could
+
+ align:start position:0%
+particular approach using what we could
+ 
+
+ align:start position:0%
+particular approach using what we could
+call as the greedy algorithm you know
+
+ align:start position:0%
+call as the greedy algorithm you know
+ 
+
+ align:start position:0%
+call as the greedy algorithm you know
+we've seen greedy algorithms before and
+
+ align:start position:0%
+we've seen greedy algorithms before and
+ 
+
+ align:start position:0%
+we've seen greedy algorithms before and
+they used another greedy algorithm here
+
+ align:start position:0%
+they used another greedy algorithm here
+ 
+
+ align:start position:0%
+they used another greedy algorithm here
+now what their greedy strategy did and
+
+ align:start position:0%
+now what their greedy strategy did and
+ 
+
+ align:start position:0%
+now what their greedy strategy did and
+I'm going to redo it
+
+ align:start position:0%
+I'm going to redo it
+ 
+
+ align:start position:0%
+I'm going to redo it
+here is stack all the blocks right at
+
+ align:start position:0%
+here is stack all the blocks right at
+ 
+
+ align:start position:0%
+here is stack all the blocks right at
+the edge line it up
+
+ align:start position:0%
+the edge line it up
+ 
+
+ align:start position:0%
+the edge line it up
+here and starting at the Top push it out
+
+ align:start position:0%
+here and starting at the Top push it out
+ 
+
+ align:start position:0%
+here and starting at the Top push it out
+as far as you can go now in this case we
+
+ align:start position:0%
+as far as you can go now in this case we
+ 
+
+ align:start position:0%
+as far as you can go now in this case we
+can get it out about halfway because the
+
+ align:start position:0%
+can get it out about halfway because the
+ 
+
+ align:start position:0%
+can get it out about halfway because the
+center of mass of this block is at
+
+ align:start position:0%
+center of mass of this block is at
+ 
+
+ align:start position:0%
+center of mass of this block is at
+halfway point and that better be sitting
+
+ align:start position:0%
+halfway point and that better be sitting
+ 
+
+ align:start position:0%
+halfway point and that better be sitting
+over this block or it's going to
+
+ align:start position:0%
+over this block or it's going to
+ 
+
+ align:start position:0%
+over this block or it's going to
+tip so the top block goes out here now
+
+ align:start position:0%
+tip so the top block goes out here now
+ 
+
+ align:start position:0%
+tip so the top block goes out here now
+I'm going to slide the top two blocks
+
+ align:start position:0%
+I'm going to slide the top two blocks
+ 
+
+ align:start position:0%
+I'm going to slide the top two blocks
+out as far as they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go all right that's about the tip then I
+
+ align:start position:0%
+go all right that's about the tip then I
+ 
+
+ align:start position:0%
+go all right that's about the tip then I
+slide the top three out as far as they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+almost oops theory is always easier than
+
+ align:start position:0%
+almost oops theory is always easier than
+ 
+
+ align:start position:0%
+almost oops theory is always easier than
+practice and now we do the top four
+
+ align:start position:0%
+practice and now we do the top four
+ 
+
+ align:start position:0%
+practice and now we do the top four
+blocks and they did a better job than I
+
+ align:start position:0%
+blocks and they did a better job than I
+ 
+
+ align:start position:0%
+blocks and they did a better job than I
+did but that's the algorithm okay the
+
+ align:start position:0%
+did but that's the algorithm okay the
+ 
+
+ align:start position:0%
+did but that's the algorithm okay the
+greedy algorithm you just the top ey
+
+ align:start position:0%
+greedy algorithm you just the top ey
+ 
+
+ align:start position:0%
+greedy algorithm you just the top ey
+blocks from I goes one to n push it out
+
+ align:start position:0%
+blocks from I goes one to n push it out
+ 
+
+ align:start position:0%
+blocks from I goes one to n push it out
+as far as you can go all right and we're
+
+ align:start position:0%
+as far as you can go all right and we're
+ 
+
+ align:start position:0%
+as far as you can go all right and we're
+going to analyze that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy and see how far it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goes so we're given
+
+ align:start position:0%
+goes so we're given
+ 
+
+ align:start position:0%
+goes so we're given
+n blocks and let's say they all have
+
+ align:start position:0%
+n blocks and let's say they all have
+ 
+
+ align:start position:0%
+n blocks and let's say they all have
+length one to make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easy and we're going to
+
+ align:start position:0%
+easy and we're going to
+ 
+
+ align:start position:0%
+easy and we're going to
+Define r sub I to be the amount by which
+
+ align:start position:0%
+Define r sub I to be the amount by which
+ 
+
+ align:start position:0%
+Define r sub I to be the amount by which
+the I block hangs out over the edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to count from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+top all right so let's see this on a
+
+ align:start position:0%
+top all right so let's see this on a
+ 
+
+ align:start position:0%
+top all right so let's see this on a
+picture so I got the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then I'm stacking the blocks
+
+ align:start position:0%
+here and then I'm stacking the blocks
+ 
+
+ align:start position:0%
+here and then I'm stacking the blocks
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+in some way like
+
+ align:start position:0%
+in some way like
+ 
+
+ align:start position:0%
+in some way like
+this and with the greedy strategy you
+
+ align:start position:0%
+this and with the greedy strategy you
+ 
+
+ align:start position:0%
+this and with the greedy strategy you
+don't ever go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backwards all right so I'm
+
+ align:start position:0%
+backwards all right so I'm
+ 
+
+ align:start position:0%
+backwards all right so I'm
+defining this distance this is block
+
+ align:start position:0%
+defining this distance this is block
+ 
+
+ align:start position:0%
+defining this distance this is block
+one this distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+R1 this
+
+ align:start position:0%
+R1 this
+ 
+
+ align:start position:0%
+R1 this
+distance is
+
+ align:start position:0%
+distance is
+ 
+
+ align:start position:0%
+distance is
+R2 this one is R3 and so forth until you
+
+ align:start position:0%
+R2 this one is R3 and so forth until you
+ 
+
+ align:start position:0%
+R2 this one is R3 and so forth until you
+get down to here this is
+
+ align:start position:0%
+get down to here this is
+ 
+
+ align:start position:0%
+get down to here this is
+RN because this is the nth block and it
+
+ align:start position:0%
+RN because this is the nth block and it
+ 
+
+ align:start position:0%
+RN because this is the nth block and it
+extends out RN from the table and this
+
+ align:start position:0%
+extends out RN from the table and this
+ 
+
+ align:start position:0%
+extends out RN from the table and this
+is zero here which in the table we'll
+
+ align:start position:0%
+is zero here which in the table we'll
+ 
+
+ align:start position:0%
+is zero here which in the table we'll
+consider the table to be the N plus
+
+ align:start position:0%
+consider the table to be the N plus
+ 
+
+ align:start position:0%
+consider the table to be the N plus
+first block so RN + one is
+
+ align:start position:0%
+first block so RN + one is
+ 
+
+ align:start position:0%
+first block so RN + one is
+zero okay and so using the strategy the
+
+ align:start position:0%
+zero okay and so using the strategy the
+ 
+
+ align:start position:0%
+zero okay and so using the strategy the
+greedy strategy we want to know what's
+
+ align:start position:0%
+greedy strategy we want to know what's
+ 
+
+ align:start position:0%
+greedy strategy we want to know what's
+R1 we want to compute that if I keep
+
+ align:start position:0%
+R1 we want to compute that if I keep
+ 
+
+ align:start position:0%
+R1 we want to compute that if I keep
+pushing the the blocks out in a topw
+
+ align:start position:0%
+pushing the the blocks out in a topw
+ 
+
+ align:start position:0%
+pushing the the blocks out in a topw
+fashion as far as they'll go now the
+
+ align:start position:0%
+fashion as far as they'll go now the
+ 
+
+ align:start position:0%
+fashion as far as they'll go now the
+constraint is the stability constraint
+
+ align:start position:0%
+constraint is the stability constraint
+ 
+
+ align:start position:0%
+constraint is the stability constraint
+so it won't fall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over the stability constraint says that
+
+ align:start position:0%
+over the stability constraint says that
+ 
+
+ align:start position:0%
+over the stability constraint says that
+the center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass we'll call it
+
+ align:start position:0%
+mass we'll call it
+ 
+
+ align:start position:0%
+mass we'll call it
+CK of the top K block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X must lie on the K plus first block
+
+ align:start position:0%
+X must lie on the K plus first block
+ 
+
+ align:start position:0%
+X must lie on the K plus first block
+otherwise it'll tip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over and of course the table is block n
+
+ align:start position:0%
+over and of course the table is block n
+ 
+
+ align:start position:0%
+over and of course the table is block n
+plus one in this context
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if at any point we've got K
+
+ align:start position:0%
+okay so if at any point we've got K
+ 
+
+ align:start position:0%
+okay so if at any point we've got K
+blocks and their Center of mass is out
+
+ align:start position:0%
+blocks and their Center of mass is out
+ 
+
+ align:start position:0%
+blocks and their Center of mass is out
+here they'll fall over at that point or
+
+ align:start position:0%
+here they'll fall over at that point or
+ 
+
+ align:start position:0%
+here they'll fall over at that point or
+if you were building it this way they
+
+ align:start position:0%
+if you were building it this way they
+ 
+
+ align:start position:0%
+if you were building it this way they
+would fall over that way right so for
+
+ align:start position:0%
+would fall over that way right so for
+ 
+
+ align:start position:0%
+would fall over that way right so for
+each set of the top K blocks the center
+
+ align:start position:0%
+each set of the top K blocks the center
+ 
+
+ align:start position:0%
+each set of the top K blocks the center
+of mass has to be on the Block below and
+
+ align:start position:0%
+of mass has to be on the Block below and
+ 
+
+ align:start position:0%
+of mass has to be on the Block below and
+if it is we're fine it won't fall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over now for the greedy stacking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where is the center of mass of the top K
+
+ align:start position:0%
+where is the center of mass of the top K
+ 
+
+ align:start position:0%
+where is the center of mass of the top K
+blocks in the greedy stacking the way we
+
+ align:start position:0%
+blocks in the greedy stacking the way we
+ 
+
+ align:start position:0%
+blocks in the greedy stacking the way we
+defin
+
+ align:start position:0%
+defin
+ 
+
+ align:start position:0%
+defin
+it in terms of these variables what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CK right so I got the top K blocks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r k + one the center of mass of the top
+
+ align:start position:0%
+r k + one the center of mass of the top
+ 
+
+ align:start position:0%
+r k + one the center of mass of the top
+K blocks by the greedy strategy is right
+
+ align:start position:0%
+K blocks by the greedy strategy is right
+ 
+
+ align:start position:0%
+K blocks by the greedy strategy is right
+at the edge of the K block so if this is
+
+ align:start position:0%
+at the edge of the K block so if this is
+ 
+
+ align:start position:0%
+at the edge of the K block so if this is
+block K here then this is RK +
+
+ align:start position:0%
+block K here then this is RK +
+ 
+
+ align:start position:0%
+block K here then this is RK +
+one that's where the center of mass has
+
+ align:start position:0%
+one that's where the center of mass has
+ 
+
+ align:start position:0%
+one that's where the center of mass has
+to be of all these blocks the top K
+
+ align:start position:0%
+to be of all these blocks the top K
+ 
+
+ align:start position:0%
+to be of all these blocks the top K
+blocks if it's a little bit more it's
+
+ align:start position:0%
+blocks if it's a little bit more it's
+ 
+
+ align:start position:0%
+blocks if it's a little bit more it's
+going to fall over if it's less then
+
+ align:start position:0%
+going to fall over if it's less then
+ 
+
+ align:start position:0%
+going to fall over if it's less then
+it's not greedy we didn't push it out as
+
+ align:start position:0%
+it's not greedy we didn't push it out as
+ 
+
+ align:start position:0%
+it's not greedy we didn't push it out as
+far as it could go all right
+
+ align:start position:0%
+far as it could go all right
+ 
+
+ align:start position:0%
+far as it could go all right
+so for the greedy stacking CK is equal
+
+ align:start position:0%
+so for the greedy stacking CK is equal
+ 
+
+ align:start position:0%
+so for the greedy stacking CK is equal
+to RK +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and RN + one of course is the edge of
+
+ align:start position:0%
+and RN + one of course is the edge of
+ 
+
+ align:start position:0%
+and RN + one of course is the edge of
+the table that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero any questions so
+
+ align:start position:0%
+zero any questions so
+ 
+
+ align:start position:0%
+zero any questions so
+far what we're
+
+ align:start position:0%
+far what we're
+ 
+
+ align:start position:0%
+far what we're
+doing okay all right so let's figure out
+
+ align:start position:0%
+doing okay all right so let's figure out
+ 
+
+ align:start position:0%
+doing okay all right so let's figure out
+where the center of mass of the top K
+
+ align:start position:0%
+where the center of mass of the top K
+ 
+
+ align:start position:0%
+where the center of mass of the top K
+blocks is you know a formula for that a
+
+ align:start position:0%
+blocks is you know a formula for that a
+ 
+
+ align:start position:0%
+blocks is you know a formula for that a
+recursive formula
+
+ align:start position:0%
+recursive formula
+ 
+
+ align:start position:0%
+recursive formula
+so to do that we look at the center of
+
+ align:start position:0%
+so to do that we look at the center of
+ 
+
+ align:start position:0%
+so to do that we look at the center of
+mass of the kith block by itself and
+
+ align:start position:0%
+mass of the kith block by itself and
+ 
+
+ align:start position:0%
+mass of the kith block by itself and
+then average it in with the center of
+
+ align:start position:0%
+then average it in with the center of
+ 
+
+ align:start position:0%
+then average it in with the center of
+mass of the top K minus one
+
+ align:start position:0%
+mass of the top K minus one
+ 
+
+ align:start position:0%
+mass of the top K minus one
+blocks okay so we're going to set up a
+
+ align:start position:0%
+blocks okay so we're going to set up a
+ 
+
+ align:start position:0%
+blocks okay so we're going to set up a
+recursion to compute
+
+ align:start position:0%
+recursion to compute
+ 
+
+ align:start position:0%
+recursion to compute
+CK where is the center of mass of the
+
+ align:start position:0%
+CK where is the center of mass of the
+ 
+
+ align:start position:0%
+CK where is the center of mass of the
+kith
+
+ align:start position:0%
+kith
+ 
+
+ align:start position:0%
+kith
+block just by itself the center of mass
+
+ align:start position:0%
+block just by itself the center of mass
+ 
+
+ align:start position:0%
+block just by itself the center of mass
+of the kith
+
+ align:start position:0%
+of the kith
+ 
+
+ align:start position:0%
+of the kith
+block this guy where's it Center of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah RK +1 minus 0.5 because it's the
+
+ align:start position:0%
+yeah RK +1 minus 0.5 because it's the
+ 
+
+ align:start position:0%
+yeah RK +1 minus 0.5 because it's the
+center of mass of this block is a half
+
+ align:start position:0%
+center of mass of this block is a half
+ 
+
+ align:start position:0%
+center of mass of this block is a half
+from the right Edge and the right Edge
+
+ align:start position:0%
+from the right Edge and the right Edge
+ 
+
+ align:start position:0%
+from the right Edge and the right Edge
+is oh it's
+
+ align:start position:0%
+is oh it's
+ 
+
+ align:start position:0%
+is oh it's
+RK sorry right the top yeah this is what
+
+ align:start position:0%
+RK sorry right the top yeah this is what
+ 
+
+ align:start position:0%
+RK sorry right the top yeah this is what
+did I do here oh the top k sorry this is
+
+ align:start position:0%
+did I do here oh the top k sorry this is
+ 
+
+ align:start position:0%
+did I do here oh the top k sorry this is
+the Ki block the way I had it here's the
+
+ align:start position:0%
+the Ki block the way I had it here's the
+ 
+
+ align:start position:0%
+the Ki block the way I had it here's the
+K so it is RK minus a half that's right
+
+ align:start position:0%
+K so it is RK minus a half that's right
+ 
+
+ align:start position:0%
+K so it is RK minus a half that's right
+this is RK plus one down here
+
+ align:start position:0%
+this is RK plus one down here
+ 
+
+ align:start position:0%
+this is RK plus one down here
+all right because the right edge of the
+
+ align:start position:0%
+all right because the right edge of the
+ 
+
+ align:start position:0%
+all right because the right edge of the
+C block is at RK the center of mass is a
+
+ align:start position:0%
+C block is at RK the center of mass is a
+ 
+
+ align:start position:0%
+C block is at RK the center of mass is a
+half left of
+
+ align:start position:0%
+half left of
+ 
+
+ align:start position:0%
+half left of
+that all right so we know that the
+
+ align:start position:0%
+that all right so we know that the
+ 
+
+ align:start position:0%
+that all right so we know that the
+center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass of the Ki
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+block is at RK minus a
+
+ align:start position:0%
+block is at RK minus a
+ 
+
+ align:start position:0%
+block is at RK minus a
+half all right now we can compute
+
+ align:start position:0%
+half all right now we can compute
+ 
+
+ align:start position:0%
+half all right now we can compute
+another expression for CK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass of the top K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blocks
+
+ align:start position:0%
+blocks
+ 
+
+ align:start position:0%
+blocks
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+CK equals well there's K minus one
+
+ align:start position:0%
+CK equals well there's K minus one
+ 
+
+ align:start position:0%
+CK equals well there's K minus one
+blocks centered at CK
+
+ align:start position:0%
+blocks centered at CK
+ 
+
+ align:start position:0%
+blocks centered at CK
+minus1 because the center of mass of the
+
+ align:start position:0%
+minus1 because the center of mass of the
+ 
+
+ align:start position:0%
+minus1 because the center of mass of the
+top K minus1 blocks by definition is C
+
+ align:start position:0%
+top K minus1 blocks by definition is C
+ 
+
+ align:start position:0%
+top K minus1 blocks by definition is C
+kus1 and they have weight K
+
+ align:start position:0%
+kus1 and they have weight K
+ 
+
+ align:start position:0%
+kus1 and they have weight K
+minus1 and then we average that with a
+
+ align:start position:0%
+minus1 and then we average that with a
+ 
+
+ align:start position:0%
+minus1 and then we average that with a
+Ki block that has weight one at position
+
+ align:start position:0%
+Ki block that has weight one at position
+ 
+
+ align:start position:0%
+Ki block that has weight one at position
+r k minus a
+
+ align:start position:0%
+r k minus a
+ 
+
+ align:start position:0%
+r k minus a
+half and the total weight of this is K
+
+ align:start position:0%
+half and the total weight of this is K
+ 
+
+ align:start position:0%
+half and the total weight of this is K
+minus one here and one for this block so
+
+ align:start position:0%
+minus one here and one for this block so
+ 
+
+ align:start position:0%
+minus one here and one for this block so
+this equals K CK minus one plus sorry
+
+ align:start position:0%
+this equals K CK minus one plus sorry
+ 
+
+ align:start position:0%
+this equals K CK minus one plus sorry
+minus let me write it better here k
+
+ align:start position:0%
+minus let me write it better here k
+ 
+
+ align:start position:0%
+minus let me write it better here k
+minus1 c k -
+
+ align:start position:0%
+minus1 c k -
+ 
+
+ align:start position:0%
+minus1 c k -
+1+ r k - a half all over
+
+ align:start position:0%
+1+ r k - a half all over
+ 
+
+ align:start position:0%
+1+ r k - a half all over
+K all right so now we' got an expression
+
+ align:start position:0%
+K all right so now we' got an expression
+ 
+
+ align:start position:0%
+K all right so now we' got an expression
+a recursive expression for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CK and to simplify it we're going to
+
+ align:start position:0%
+CK and to simplify it we're going to
+ 
+
+ align:start position:0%
+CK and to simplify it we're going to
+plug in that CK as rk+ one for the
+
+ align:start position:0%
+plug in that CK as rk+ one for the
+ 
+
+ align:start position:0%
+plug in that CK as rk+ one for the
+greedy strategy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah L is one the length of the blocks
+
+ align:start position:0%
+yeah L is one the length of the blocks
+ 
+
+ align:start position:0%
+yeah L is one the length of the blocks
+is one here all right to make it simpler
+
+ align:start position:0%
+is one here all right to make it simpler
+ 
+
+ align:start position:0%
+is one here all right to make it simpler
+otherwise it would have been a half l so
+
+ align:start position:0%
+otherwise it would have been a half l so
+ 
+
+ align:start position:0%
+otherwise it would have been a half l so
+yesterday we talked about length L
+
+ align:start position:0%
+yesterday we talked about length L
+ 
+
+ align:start position:0%
+yesterday we talked about length L
+blocks today they're length one to be
+
+ align:start position:0%
+blocks today they're length one to be
+ 
+
+ align:start position:0%
+blocks today they're length one to be
+simple all right so now for the greedy
+
+ align:start position:0%
+simple all right so now for the greedy
+ 
+
+ align:start position:0%
+simple all right so now for the greedy
+strategy I'm just going to plug in CK as
+
+ align:start position:0%
+strategy I'm just going to plug in CK as
+ 
+
+ align:start position:0%
+strategy I'm just going to plug in CK as
+RK + one so let's do
+
+ align:start position:0%
+RK + one so let's do
+ 
+
+ align:start position:0%
+RK + one so let's do
+that so I got CK is RK + 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals uh K minus one well CK minus one
+
+ align:start position:0%
+equals uh K minus one well CK minus one
+ 
+
+ align:start position:0%
+equals uh K minus one well CK minus one
+is just RK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus rkus a
+
+ align:start position:0%
+plus rkus a
+ 
+
+ align:start position:0%
+plus rkus a
+half over K and this simplifies to K
+
+ align:start position:0%
+half over K and this simplifies to K
+ 
+
+ align:start position:0%
+half over K and this simplifies to K
+RK minus RK plus RK they cancel minus a
+
+ align:start position:0%
+RK minus RK plus RK they cancel minus a
+ 
+
+ align:start position:0%
+RK minus RK plus RK they cancel minus a
+half over
+
+ align:start position:0%
+half over
+ 
+
+ align:start position:0%
+half over
+K this equals RK minus a half so getting
+
+ align:start position:0%
+K this equals RK minus a half so getting
+ 
+
+ align:start position:0%
+K this equals RK minus a half so getting
+very simple
+
+ align:start position:0%
+very simple
+ 
+
+ align:start position:0%
+very simple
+now and I'm just going to rewrite this
+
+ align:start position:0%
+now and I'm just going to rewrite this
+ 
+
+ align:start position:0%
+now and I'm just going to rewrite this
+to look at the difference between RK and
+
+ align:start position:0%
+to look at the difference between RK and
+ 
+
+ align:start position:0%
+to look at the difference between RK and
+RK + 1 so RK minus RK +
+
+ align:start position:0%
+RK + 1 so RK minus RK +
+ 
+
+ align:start position:0%
+RK + 1 so RK minus RK +
+1 oops I made a mistake that's 1 over 2K
+
+ align:start position:0%
+1 oops I made a mistake that's 1 over 2K
+ 
+
+ align:start position:0%
+1 oops I made a mistake that's 1 over 2K
+half over K is 1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2K any questions about the math we
+
+ align:start position:0%
+2K any questions about the math we
+ 
+
+ align:start position:0%
+2K any questions about the math we
+did interesting this is one of those
+
+ align:start position:0%
+did interesting this is one of those
+ 
+
+ align:start position:0%
+did interesting this is one of those
+problems where the math this way is easy
+
+ align:start position:0%
+problems where the math this way is easy
+ 
+
+ align:start position:0%
+problems where the math this way is easy
+there are other ways to try to solve
+
+ align:start position:0%
+there are other ways to try to solve
+ 
+
+ align:start position:0%
+there are other ways to try to solve
+this problem the math gets pretty hairy
+
+ align:start position:0%
+this problem the math gets pretty hairy
+ 
+
+ align:start position:0%
+this problem the math gets pretty hairy
+uh but this one's a a simple
+
+ align:start position:0%
+uh but this one's a a simple
+ 
+
+ align:start position:0%
+uh but this one's a a simple
+approach what's the meaning of this
+
+ align:start position:0%
+approach what's the meaning of this
+ 
+
+ align:start position:0%
+approach what's the meaning of this
+what's an interpretation of RK minus RK
+
+ align:start position:0%
+what's an interpretation of RK minus RK
+ 
+
+ align:start position:0%
+what's an interpretation of RK minus RK
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah this is how much further the K
+
+ align:start position:0%
+yeah yeah this is how much further the K
+ 
+
+ align:start position:0%
+yeah yeah this is how much further the K
+block sticks out over the K plus first
+
+ align:start position:0%
+block sticks out over the K plus first
+ 
+
+ align:start position:0%
+block sticks out over the K plus first
+block so let's see
+
+ align:start position:0%
+block so let's see
+ 
+
+ align:start position:0%
+block so let's see
+that right so here's R1 here's R2 R1
+
+ align:start position:0%
+that right so here's R1 here's R2 R1
+ 
+
+ align:start position:0%
+that right so here's R1 here's R2 R1
+minus R2 is the the amount by which the
+
+ align:start position:0%
+minus R2 is the the amount by which the
+ 
+
+ align:start position:0%
+minus R2 is the the amount by which the
+first block sticks out over the second
+
+ align:start position:0%
+first block sticks out over the second
+ 
+
+ align:start position:0%
+first block sticks out over the second
+here's R2 minus R3 it's that
+
+ align:start position:0%
+here's R2 minus R3 it's that
+ 
+
+ align:start position:0%
+here's R2 minus R3 it's that
+distance all right so we've gotten a
+
+ align:start position:0%
+distance all right so we've gotten a
+ 
+
+ align:start position:0%
+distance all right so we've gotten a
+formula for the greedy
+
+ align:start position:0%
+formula for the greedy
+ 
+
+ align:start position:0%
+formula for the greedy
+strategy of how much the Ki block sticks
+
+ align:start position:0%
+strategy of how much the Ki block sticks
+ 
+
+ align:start position:0%
+strategy of how much the Ki block sticks
+out over the K plus first block and it's
+
+ align:start position:0%
+out over the K plus first block and it's
+ 
+
+ align:start position:0%
+out over the K plus first block and it's
+pretty simple all right so now we can
+
+ align:start position:0%
+pretty simple all right so now we can
+ 
+
+ align:start position:0%
+pretty simple all right so now we can
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+down this expression for all the values
+
+ align:start position:0%
+down this expression for all the values
+ 
+
+ align:start position:0%
+down this expression for all the values
+of K so what's R1 minus R2 going to be
+
+ align:start position:0%
+of K so what's R1 minus R2 going to be
+ 
+
+ align:start position:0%
+of K so what's R1 minus R2 going to be
+in the greedy strategy how much is the
+
+ align:start position:0%
+in the greedy strategy how much is the
+ 
+
+ align:start position:0%
+in the greedy strategy how much is the
+top block sticking out over the second
+
+ align:start position:0%
+top block sticking out over the second
+ 
+
+ align:start position:0%
+top block sticking out over the second
+Block in the greedy
+
+ align:start position:0%
+Block in the greedy
+ 
+
+ align:start position:0%
+Block in the greedy
+Strat 1 12 just plug in K =
+
+ align:start position:0%
+Strat 1 12 just plug in K =
+ 
+
+ align:start position:0%
+Strat 1 12 just plug in K =
+1 R2 - R3
+
+ align:start position:0%
+1 R2 - R3
+ 
+
+ align:start position:0%
+1 R2 - R3
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+= qu quarter one quter R3 -
+
+ align:start position:0%
+= qu quarter one quter R3 -
+ 
+
+ align:start position:0%
+= qu quarter one quter R3 -
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+R4 is what a six all right so now you
+
+ align:start position:0%
+R4 is what a six all right so now you
+ 
+
+ align:start position:0%
+R4 is what a six all right so now you
+can start to see what the T did how it
+
+ align:start position:0%
+can start to see what the T did how it
+ 
+
+ align:start position:0%
+can start to see what the T did how it
+got smaller each step going down all the
+
+ align:start position:0%
+got smaller each step going down all the
+ 
+
+ align:start position:0%
+got smaller each step going down all the
+way to the end here you get
+
+ align:start position:0%
+way to the end here you get
+ 
+
+ align:start position:0%
+way to the end here you get
+RN the nth block minus the the
+
+ align:start position:0%
+RN the nth block minus the the
+ 
+
+ align:start position:0%
+RN the nth block minus the the
+table is 1 over 2
+
+ align:start position:0%
+table is 1 over 2
+ 
+
+ align:start position:0%
+table is 1 over 2
+N all right now there's a very easy way
+
+ align:start position:0%
+N all right now there's a very easy way
+ 
+
+ align:start position:0%
+N all right now there's a very easy way
+to figure out what R1
+
+ align:start position:0%
+to figure out what R1
+ 
+
+ align:start position:0%
+to figure out what R1
+is which is what we're after how far out
+
+ align:start position:0%
+is which is what we're after how far out
+ 
+
+ align:start position:0%
+is which is what we're after how far out
+of the top block what do I
+
+ align:start position:0%
+of the top block what do I
+ 
+
+ align:start position:0%
+of the top block what do I
+do add them all
+
+ align:start position:0%
+do add them all
+ 
+
+ align:start position:0%
+do add them all
+together and and everything
+
+ align:start position:0%
+together and and everything
+ 
+
+ align:start position:0%
+together and and everything
+cancels so I get R1 - r n + 1
+
+ align:start position:0%
+cancels so I get R1 - r n + 1
+ 
+
+ align:start position:0%
+cancels so I get R1 - r n + 1
+equals a half plus A4 plus a
+
+ align:start position:0%
+equals a half plus A4 plus a
+ 
+
+ align:start position:0%
+equals a half plus A4 plus a
+6 out to 1 over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N all right so that's just equal to the
+
+ align:start position:0%
+N all right so that's just equal to the
+ 
+
+ align:start position:0%
+N all right so that's just equal to the
+sum I = 1 to n 1 over 2
+
+ align:start position:0%
+sum I = 1 to n 1 over 2
+ 
+
+ align:start position:0%
+sum I = 1 to n 1 over 2
+I all right
+
+ align:start position:0%
+I all right
+ 
+
+ align:start position:0%
+I all right
+now I got R1 RN + 1 but what's RN
+
+ align:start position:0%
+now I got R1 RN + 1 but what's RN
+ 
+
+ align:start position:0%
+now I got R1 RN + 1 but what's RN
+plus1 zero that's the table the table
+
+ align:start position:0%
+plus1 zero that's the table the table
+ 
+
+ align:start position:0%
+plus1 zero that's the table the table
+doesn't hang out over itself so in fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R1 equals a half of the
+
+ align:start position:0%
+R1 equals a half of the
+ 
+
+ align:start position:0%
+R1 equals a half of the
+sum of the inverses of the first and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers okay and so now alls we have to
+
+ align:start position:0%
+integers okay and so now alls we have to
+ 
+
+ align:start position:0%
+integers okay and so now alls we have to
+do is to compute this sum to know how
+
+ align:start position:0%
+do is to compute this sum to know how
+ 
+
+ align:start position:0%
+do is to compute this sum to know how
+far out it is uh in fact this sum comes
+
+ align:start position:0%
+far out it is uh in fact this sum comes
+ 
+
+ align:start position:0%
+far out it is uh in fact this sum comes
+up so often in mathematics and computer
+
+ align:start position:0%
+up so often in mathematics and computer
+ 
+
+ align:start position:0%
+up so often in mathematics and computer
+science that it has a special name it's
+
+ align:start position:0%
+science that it has a special name it's
+ 
+
+ align:start position:0%
+science that it has a special name it's
+called the harmonic sum and the numbers
+
+ align:start position:0%
+called the harmonic sum and the numbers
+ 
+
+ align:start position:0%
+called the harmonic sum and the numbers
+are called the harmonic numbers and in
+
+ align:start position:0%
+are called the harmonic numbers and in
+ 
+
+ align:start position:0%
+are called the harmonic numbers and in
+particular the nth harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number is typically denoted
+
+ align:start position:0%
+number is typically denoted
+ 
+
+ align:start position:0%
+number is typically denoted
+hn just equals the sum of the first n
+
+ align:start position:0%
+hn just equals the sum of the first n
+ 
+
+ align:start position:0%
+hn just equals the sum of the first n
+reciprocals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so for example the first
+
+ align:start position:0%
+all right so for example the first
+ 
+
+ align:start position:0%
+all right so for example the first
+harmonic number is one the second is 1+
+
+ align:start position:0%
+harmonic number is one the second is 1+
+ 
+
+ align:start position:0%
+harmonic number is one the second is 1+
+a half =
+
+ align:start position:0%
+a half =
+ 
+
+ align:start position:0%
+a half =
+3es the 3 is 3es plus a
+
+ align:start position:0%
+3es the 3 is 3es plus a
+ 
+
+ align:start position:0%
+3es the 3 is 3es plus a
+3 which
+
+ align:start position:0%
+3 which
+ 
+
+ align:start position:0%
+3 which
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+116 the fourth harmonic number is that
+
+ align:start position:0%
+116 the fourth harmonic number is that
+ 
+
+ align:start position:0%
+116 the fourth harmonic number is that
+plus a
+
+ align:start position:0%
+plus a
+ 
+
+ align:start position:0%
+plus a
+quarter 22+ 3 12th is 25
+
+ align:start position:0%
+quarter 22+ 3 12th is 25
+ 
+
+ align:start position:0%
+quarter 22+ 3 12th is 25
+12ths that's sort of an interesting
+
+ align:start position:0%
+12ths that's sort of an interesting
+ 
+
+ align:start position:0%
+12ths that's sort of an interesting
+number because it's bigger than
+
+ align:start position:0%
+number because it's bigger than
+ 
+
+ align:start position:0%
+number because it's bigger than
+two what does that tell
+
+ align:start position:0%
+two what does that tell
+ 
+
+ align:start position:0%
+two what does that tell
+us why is that interesting from this
+
+ align:start position:0%
+us why is that interesting from this
+ 
+
+ align:start position:0%
+us why is that interesting from this
+perspective what we're doing
+
+ align:start position:0%
+perspective what we're doing
+ 
+
+ align:start position:0%
+perspective what we're doing
+here now you can get a block off the
+
+ align:start position:0%
+here now you can get a block off the
+ 
+
+ align:start position:0%
+here now you can get a block off the
+table because R1 the distance that the
+
+ align:start position:0%
+table because R1 the distance that the
+ 
+
+ align:start position:0%
+table because R1 the distance that the
+top block hangs out off the table is
+
+ align:start position:0%
+top block hangs out off the table is
+ 
+
+ align:start position:0%
+top block hangs out off the table is
+half the harmonic number half of H4 is a
+
+ align:start position:0%
+half the harmonic number half of H4 is a
+ 
+
+ align:start position:0%
+half the harmonic number half of H4 is a
+little bit bigger than one which means
+
+ align:start position:0%
+little bit bigger than one which means
+ 
+
+ align:start position:0%
+little bit bigger than one which means
+means with four blocks the top block can
+
+ align:start position:0%
+means with four blocks the top block can
+ 
+
+ align:start position:0%
+means with four blocks the top block can
+be off the table now the T did it using
+
+ align:start position:0%
+be off the table now the T did it using
+ 
+
+ align:start position:0%
+be off the table now the T did it using
+five I didn't even get it to work with
+
+ align:start position:0%
+five I didn't even get it to work with
+ 
+
+ align:start position:0%
+five I didn't even get it to work with
+five in theory it'll work with 12 you
+
+ align:start position:0%
+five in theory it'll work with 12 you
+ 
+
+ align:start position:0%
+five in theory it'll work with 12 you
+can hang one out there just a 24th
+
+ align:start position:0%
+can hang one out there just a 24th
+ 
+
+ align:start position:0%
+can hang one out there just a 24th
+Beyond the Edge of the table in
+
+ align:start position:0%
+Beyond the Edge of the table in
+ 
+
+ align:start position:0%
+Beyond the Edge of the table in
+theory all right if we kept on
+
+ align:start position:0%
+theory all right if we kept on
+ 
+
+ align:start position:0%
+theory all right if we kept on
+going h of a million the million tonic
+
+ align:start position:0%
+going h of a million the million tonic
+ 
+
+ align:start position:0%
+going h of a million the million tonic
+number if you were to go comput it is
+
+ align:start position:0%
+number if you were to go comput it is
+ 
+
+ align:start position:0%
+number if you were to go comput it is
+14392 7 and some other stuff
+
+ align:start position:0%
+14392 7 and some other stuff
+ 
+
+ align:start position:0%
+14392 7 and some other stuff
+so if I had a million blocks stacked up
+
+ align:start position:0%
+so if I had a million blocks stacked up
+ 
+
+ align:start position:0%
+so if I had a million blocks stacked up
+in theory how far would I get the top
+
+ align:start position:0%
+in theory how far would I get the top
+ 
+
+ align:start position:0%
+in theory how far would I get the top
+block out off the
+
+ align:start position:0%
+block out off the
+ 
+
+ align:start position:0%
+block out off the
+table seven blocks all right so that
+
+ align:start position:0%
+table seven blocks all right so that
+ 
+
+ align:start position:0%
+table seven blocks all right so that
+gives you an idea you got to do a lot of
+
+ align:start position:0%
+gives you an idea you got to do a lot of
+ 
+
+ align:start position:0%
+gives you an idea you got to do a lot of
+work to get seven um and in fact it's
+
+ align:start position:0%
+work to get seven um and in fact it's
+ 
+
+ align:start position:0%
+work to get seven um and in fact it's
+hard because the bottom block would be
+
+ align:start position:0%
+hard because the bottom block would be
+ 
+
+ align:start position:0%
+hard because the bottom block would be
+hanging out one two millionth of a block
+
+ align:start position:0%
+hanging out one two millionth of a block
+ 
+
+ align:start position:0%
+hanging out one two millionth of a block
+right so you're adding up a lot of tiny
+
+ align:start position:0%
+right so you're adding up a lot of tiny
+ 
+
+ align:start position:0%
+right so you're adding up a lot of tiny
+things to get to Seven out
+
+ align:start position:0%
+things to get to Seven out
+ 
+
+ align:start position:0%
+things to get to Seven out
+there now it turns out that the harmonic
+
+ align:start position:0%
+there now it turns out that the harmonic
+ 
+
+ align:start position:0%
+there now it turns out that the harmonic
+numbers grow to Infinity
+
+ align:start position:0%
+numbers grow to Infinity
+ 
+
+ align:start position:0%
+numbers grow to Infinity
+and we'll see that but they grow very
+
+ align:start position:0%
+and we'll see that but they grow very
+ 
+
+ align:start position:0%
+and we'll see that but they grow very
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+slowly uh and to see that we need to get
+
+ align:start position:0%
+slowly uh and to see that we need to get
+ 
+
+ align:start position:0%
+slowly uh and to see that we need to get
+a closed form expression for this
+
+ align:start position:0%
+a closed form expression for this
+ 
+
+ align:start position:0%
+a closed form expression for this
+sum now does anybody know a closed form
+
+ align:start position:0%
+sum now does anybody know a closed form
+ 
+
+ align:start position:0%
+sum now does anybody know a closed form
+expression for the sum of 1 over
+
+ align:start position:0%
+expression for the sum of 1 over
+ 
+
+ align:start position:0%
+expression for the sum of 1 over
+I I don't think so because I don't I
+
+ align:start position:0%
+I I don't think so because I don't I
+ 
+
+ align:start position:0%
+I I don't think so because I don't I
+don't know I don't know anybody who
+
+ align:start position:0%
+don't know I don't know anybody who
+ 
+
+ align:start position:0%
+don't know I don't know anybody who
+knows
+
+ align:start position:0%
+knows
+ 
+
+ align:start position:0%
+knows
+that uh in fact it's probably believed
+
+ align:start position:0%
+that uh in fact it's probably believed
+ 
+
+ align:start position:0%
+that uh in fact it's probably believed
+that it doesn't
+
+ align:start position:0%
+that it doesn't
+ 
+
+ align:start position:0%
+that it doesn't
+exist so what do we do to get a good
+
+ align:start position:0%
+exist so what do we do to get a good
+ 
+
+ align:start position:0%
+exist so what do we do to get a good
+estimation of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum what do we do integration bounds
+
+ align:start position:0%
+sum what do we do integration bounds
+ 
+
+ align:start position:0%
+sum what do we do integration bounds
+integration bounds yeah because we're
+
+ align:start position:0%
+integration bounds yeah because we're
+ 
+
+ align:start position:0%
+integration bounds yeah because we're
+not going to get a closed form at least
+
+ align:start position:0%
+not going to get a closed form at least
+ 
+
+ align:start position:0%
+not going to get a closed form at least
+I don't know if anybody who knows how to
+
+ align:start position:0%
+I don't know if anybody who knows how to
+ 
+
+ align:start position:0%
+I don't know if anybody who knows how to
+do it uh so we'll use the integration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounds and what kind of function are we
+
+ align:start position:0%
+bounds and what kind of function are we
+ 
+
+ align:start position:0%
+bounds and what kind of function are we
+summing is it increasing or
+
+ align:start position:0%
+summing is it increasing or
+ 
+
+ align:start position:0%
+summing is it increasing or
+decreasing decreasing
+
+ align:start position:0%
+decreasing decreasing
+ 
+
+ align:start position:0%
+decreasing decreasing
+yeah so we use the formula we did last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time all right and that formula is that
+
+ align:start position:0%
+time all right and that formula is that
+ 
+
+ align:start position:0%
+time all right and that formula is that
+the sum I = 1 to
+
+ align:start position:0%
+the sum I = 1 to
+ 
+
+ align:start position:0%
+the sum I = 1 to
+n of f of
+
+ align:start position:0%
+n of f of
+ 
+
+ align:start position:0%
+n of f of
+I is at most the first term plus the
+
+ align:start position:0%
+I is at most the first term plus the
+ 
+
+ align:start position:0%
+I is at most the first term plus the
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's at least the last term plus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral all right in this case we have
+
+ align:start position:0%
+integral all right in this case we have
+ 
+
+ align:start position:0%
+integral all right in this case we have
+F of I is 1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I so the first step is to compute the
+
+ align:start position:0%
+I so the first step is to compute the
+ 
+
+ align:start position:0%
+I so the first step is to compute the
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's pretty easy that's just the
+
+ align:start position:0%
+and that's pretty easy that's just the
+ 
+
+ align:start position:0%
+and that's pretty easy that's just the
+natural log of
+
+ align:start position:0%
+natural log of
+ 
+
+ align:start position:0%
+natural log of
+x evaluated at n and one and that's easy
+
+ align:start position:0%
+x evaluated at n and one and that's easy
+ 
+
+ align:start position:0%
+x evaluated at n and one and that's easy
+that's just a natural log of
+
+ align:start position:0%
+that's just a natural log of
+ 
+
+ align:start position:0%
+that's just a natural log of
+n so the integral is very easy here and
+
+ align:start position:0%
+n so the integral is very easy here and
+ 
+
+ align:start position:0%
+n so the integral is very easy here and
+now we actually can just plug in and get
+
+ align:start position:0%
+now we actually can just plug in and get
+ 
+
+ align:start position:0%
+now we actually can just plug in and get
+really good
+
+ align:start position:0%
+really good
+ 
+
+ align:start position:0%
+really good
+bounds um maybe I'll save that just in
+
+ align:start position:0%
+bounds um maybe I'll save that just in
+ 
+
+ align:start position:0%
+bounds um maybe I'll save that just in
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so plugging in into the bounds F of
+
+ align:start position:0%
+okay so plugging in into the bounds F of
+ 
+
+ align:start position:0%
+okay so plugging in into the bounds F of
+n is 1 /
+
+ align:start position:0%
+n is 1 /
+ 
+
+ align:start position:0%
+n is 1 /
+n plus the integral is log of n is less
+
+ align:start position:0%
+n plus the integral is log of n is less
+ 
+
+ align:start position:0%
+n plus the integral is log of n is less
+than or equal to the nth harmonic number
+
+ align:start position:0%
+than or equal to the nth harmonic number
+ 
+
+ align:start position:0%
+than or equal to the nth harmonic number
+and it's upper bounded by F of one which
+
+ align:start position:0%
+and it's upper bounded by F of one which
+ 
+
+ align:start position:0%
+and it's upper bounded by F of one which
+is one
+
+ align:start position:0%
+is one
+ 
+
+ align:start position:0%
+is one
+plus the
+
+ align:start position:0%
+plus the
+ 
+
+ align:start position:0%
+plus the
+integral all right so that's really good
+
+ align:start position:0%
+integral all right so that's really good
+ 
+
+ align:start position:0%
+integral all right so that's really good
+we got very tight bounds and now you can
+
+ align:start position:0%
+we got very tight bounds and now you can
+ 
+
+ align:start position:0%
+we got very tight bounds and now you can
+see that the nth harmonic number how
+
+ align:start position:0%
+see that the nth harmonic number how
+ 
+
+ align:start position:0%
+see that the nth harmonic number how
+fast is it growing if I were to use
+
+ align:start position:0%
+fast is it growing if I were to use
+ 
+
+ align:start position:0%
+fast is it growing if I were to use
+Tilda notation what would I
+
+ align:start position:0%
+Tilda notation what would I
+ 
+
+ align:start position:0%
+Tilda notation what would I
+write as log n yeah so this means that h
+
+ align:start position:0%
+write as log n yeah so this means that h
+ 
+
+ align:start position:0%
+write as log n yeah so this means that h
+of n is Tilda log of
+
+ align:start position:0%
+of n is Tilda log of
+ 
+
+ align:start position:0%
+of n is Tilda log of
+n okay now this is such an important
+
+ align:start position:0%
+n okay now this is such an important
+ 
+
+ align:start position:0%
+n okay now this is such an important
+function that people have gone to a lot
+
+ align:start position:0%
+function that people have gone to a lot
+ 
+
+ align:start position:0%
+function that people have gone to a lot
+of extra work which we can't do in this
+
+ align:start position:0%
+of extra work which we can't do in this
+ 
+
+ align:start position:0%
+of extra work which we can't do in this
+class um to really nail down the value
+
+ align:start position:0%
+class um to really nail down the value
+ 
+
+ align:start position:0%
+class um to really nail down the value
+get it much closer and in
+
+ align:start position:0%
+get it much closer and in
+ 
+
+ align:start position:0%
+get it much closer and in
+fact it's now known that it's the
+
+ align:start position:0%
+fact it's now known that it's the
+ 
+
+ align:start position:0%
+fact it's now known that it's the
+natural log of n + 1 over 2
+
+ align:start position:0%
+natural log of n + 1 over 2
+ 
+
+ align:start position:0%
+natural log of n + 1 over 2
+n + 1 over 12
+
+ align:start position:0%
+n + 1 over 12
+ 
+
+ align:start position:0%
+n + 1 over 12
+n^2 plus Epsilon of n over 120 n
+
+ align:start position:0%
+n^2 plus Epsilon of n over 120 n
+ 
+
+ align:start position:0%
+n^2 plus Epsilon of n over 120 n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where for all n Epsilon n is between
+
+ align:start position:0%
+where for all n Epsilon n is between
+ 
+
+ align:start position:0%
+where for all n Epsilon n is between
+zero and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one oh and I laugh lost left one piece
+
+ align:start position:0%
+one oh and I laugh lost left one piece
+ 
+
+ align:start position:0%
+one oh and I laugh lost left one piece
+out actually there's a constant term in
+
+ align:start position:0%
+out actually there's a constant term in
+ 
+
+ align:start position:0%
+out actually there's a constant term in
+here Delta that's called Oiler
+
+ align:start position:0%
+here Delta that's called Oiler
+ 
+
+ align:start position:0%
+here Delta that's called Oiler
+constant all right
+
+ align:start position:0%
+constant all right
+ 
+
+ align:start position:0%
+constant all right
+Delta is called Oiler
+
+ align:start position:0%
+Delta is called Oiler
+ 
+
+ align:start position:0%
+Delta is called Oiler
+constant and
+
+ align:start position:0%
+constant and
+ 
+
+ align:start position:0%
+constant and
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+0.577 21
+
+ align:start position:0%
+0.577 21
+ 
+
+ align:start position:0%
+0.577 21
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+664 and some other stuff and in fact to
+
+ align:start position:0%
+664 and some other stuff and in fact to
+ 
+
+ align:start position:0%
+664 and some other stuff and in fact to
+this day people don't know if this
+
+ align:start position:0%
+this day people don't know if this
+ 
+
+ align:start position:0%
+this day people don't know if this
+constant is rational or
+
+ align:start position:0%
+constant is rational or
+ 
+
+ align:start position:0%
+constant is rational or
+irrational but they know it to a lot of
+
+ align:start position:0%
+irrational but they know it to a lot of
+ 
+
+ align:start position:0%
+irrational but they know it to a lot of
+decimal
+
+ align:start position:0%
+decimal
+ 
+
+ align:start position:0%
+decimal
+places uh so basically hn is the log of
+
+ align:start position:0%
+places uh so basically hn is the log of
+ 
+
+ align:start position:0%
+places uh so basically hn is the log of
+n plus some fixed value between zero and
+
+ align:start position:0%
+n plus some fixed value between zero and
+ 
+
+ align:start position:0%
+n plus some fixed value between zero and
+one as we knew it had to be plus even
+
+ align:start position:0%
+one as we knew it had to be plus even
+ 
+
+ align:start position:0%
+one as we knew it had to be plus even
+some tail terms here that get very small
+
+ align:start position:0%
+some tail terms here that get very small
+ 
+
+ align:start position:0%
+some tail terms here that get very small
+as n gets
+
+ align:start position:0%
+as n gets
+ 
+
+ align:start position:0%
+as n gets
+large all right so say I wanted to know
+
+ align:start position:0%
+large all right so say I wanted to know
+ 
+
+ align:start position:0%
+large all right so say I wanted to know
+using this greedy strategy how many
+
+ align:start position:0%
+using this greedy strategy how many
+ 
+
+ align:start position:0%
+using this greedy strategy how many
+blocks I would need to get a block a
+
+ align:start position:0%
+blocks I would need to get a block a
+ 
+
+ align:start position:0%
+blocks I would need to get a block a
+hundred blocks out over the end of the
+
+ align:start position:0%
+hundred blocks out over the end of the
+ 
+
+ align:start position:0%
+hundred blocks out over the end of the
+table so I want to go a 100 blocks out
+
+ align:start position:0%
+table so I want to go a 100 blocks out
+ 
+
+ align:start position:0%
+table so I want to go a 100 blocks out
+how many blocks do I need using this
+
+ align:start position:0%
+how many blocks do I need using this
+ 
+
+ align:start position:0%
+how many blocks do I need using this
+strategy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly what is
+
+ align:start position:0%
+roughly what is
+ 
+
+ align:start position:0%
+roughly what is
+it think somebody said
+
+ align:start position:0%
+it think somebody said
+ 
+
+ align:start position:0%
+it think somebody said
+it so I want to
+
+ align:start position:0%
+it so I want to
+ 
+
+ align:start position:0%
+it so I want to
+get R1 to be 100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I need the harmonic number to be
+
+ align:start position:0%
+so I need the harmonic number to be
+ 
+
+ align:start position:0%
+so I need the harmonic number to be
+200 and what does this tell me about n
+
+ align:start position:0%
+200 and what does this tell me about n
+ 
+
+ align:start position:0%
+200 and what does this tell me about n
+to get this to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+200 e to the 200 right so you're going
+
+ align:start position:0%
+200 e to the 200 right so you're going
+ 
+
+ align:start position:0%
+200 e to the 200 right so you're going
+to need an exponential in 200 number of
+
+ align:start position:0%
+to need an exponential in 200 number of
+ 
+
+ align:start position:0%
+to need an exponential in 200 number of
+blocks which now we're past the Stars
+
+ align:start position:0%
+blocks which now we're past the Stars
+ 
+
+ align:start position:0%
+blocks which now we're past the Stars
+right to get that many right all right
+
+ align:start position:0%
+right to get that many right all right
+ 
+
+ align:start position:0%
+right to get that many right all right
+now we won't prove it in class but this
+
+ align:start position:0%
+now we won't prove it in class but this
+ 
+
+ align:start position:0%
+now we won't prove it in class but this
+strategy the TA greedy strategy is
+
+ align:start position:0%
+strategy the TA greedy strategy is
+ 
+
+ align:start position:0%
+strategy the TA greedy strategy is
+optimal there is no way to get a block
+
+ align:start position:0%
+optimal there is no way to get a block
+ 
+
+ align:start position:0%
+optimal there is no way to get a block
+farther out over the
+
+ align:start position:0%
+farther out over the
+ 
+
+ align:start position:0%
+farther out over the
+edge uh that said there is a second way
+
+ align:start position:0%
+edge uh that said there is a second way
+ 
+
+ align:start position:0%
+edge uh that said there is a second way
+to get there and in the second way the
+
+ align:start position:0%
+to get there and in the second way the
+ 
+
+ align:start position:0%
+to get there and in the second way the
+top block is not the optimal Block in
+
+ align:start position:0%
+top block is not the optimal Block in
+ 
+
+ align:start position:0%
+top block is not the optimal Block in
+the second way it's the second block
+
+ align:start position:0%
+the second way it's the second block
+ 
+
+ align:start position:0%
+the second way it's the second block
+that goes out so it looks something like
+
+ align:start position:0%
+that goes out so it looks something like
+ 
+
+ align:start position:0%
+that goes out so it looks something like
+that so there's a counterweight on it
+
+ align:start position:0%
+that so there's a counterweight on it
+ 
+
+ align:start position:0%
+that so there's a counterweight on it
+and in the text when you read chapter 9
+
+ align:start position:0%
+and in the text when you read chapter 9
+ 
+
+ align:start position:0%
+and in the text when you read chapter 9
+you will see the proof that shows that
+
+ align:start position:0%
+you will see the proof that shows that
+ 
+
+ align:start position:0%
+you will see the proof that shows that
+there's two solutions that are optimal
+
+ align:start position:0%
+there's two solutions that are optimal
+ 
+
+ align:start position:0%
+there's two solutions that are optimal
+one's the greedy and one's this other
+
+ align:start position:0%
+one's the greedy and one's this other
+ 
+
+ align:start position:0%
+one's the greedy and one's this other
+one that sort of is mostly the greedy
+
+ align:start position:0%
+one that sort of is mostly the greedy
+ 
+
+ align:start position:0%
+one that sort of is mostly the greedy
+except the top couple of blocks are
+
+ align:start position:0%
+except the top couple of blocks are
+ 
+
+ align:start position:0%
+except the top couple of blocks are
+different and it proves that's optimal
+
+ align:start position:0%
+different and it proves that's optimal
+ 
+
+ align:start position:0%
+different and it proves that's optimal
+we won't we won't cover that in
+
+ align:start position:0%
+we won't we won't cover that in
+ 
+
+ align:start position:0%
+we won't we won't cover that in
+class uh now actually in the literature
+
+ align:start position:0%
+class uh now actually in the literature
+ 
+
+ align:start position:0%
+class uh now actually in the literature
+today people have been studying how far
+
+ align:start position:0%
+today people have been studying how far
+ 
+
+ align:start position:0%
+today people have been studying how far
+a block can go out if you're allowed to
+
+ align:start position:0%
+a block can go out if you're allowed to
+ 
+
+ align:start position:0%
+a block can go out if you're allowed to
+do more than one block per level like
+
+ align:start position:0%
+do more than one block per level like
+ 
+
+ align:start position:0%
+do more than one block per level like
+one of the students wanted to do so if
+
+ align:start position:0%
+one of the students wanted to do so if
+ 
+
+ align:start position:0%
+one of the students wanted to do so if
+you're allowed to have multiple blocks
+
+ align:start position:0%
+you're allowed to have multiple blocks
+ 
+
+ align:start position:0%
+you're allowed to have multiple blocks
+on the same level it turns out you can
+
+ align:start position:0%
+on the same level it turns out you can
+ 
+
+ align:start position:0%
+on the same level it turns out you can
+get much farther out then blocks and
+
+ align:start position:0%
+get much farther out then blocks and
+ 
+
+ align:start position:0%
+get much farther out then blocks and
+right now it's known that it's uh
+
+ align:start position:0%
+right now it's known that it's uh
+ 
+
+ align:start position:0%
+right now it's known that it's uh
+something like n the3 is how far you can
+
+ align:start position:0%
+something like n the3 is how far you can
+ 
+
+ align:start position:0%
+something like n the3 is how far you can
+get out which is much better than log of
+
+ align:start position:0%
+get out which is much better than log of
+ 
+
+ align:start position:0%
+get out which is much better than log of
+N and so mathematicians have been
+
+ align:start position:0%
+N and so mathematicians have been
+ 
+
+ align:start position:0%
+N and so mathematicians have been
+studying that
+
+ align:start position:0%
+studying that
+ 
+
+ align:start position:0%
+studying that
+problem any
+
+ align:start position:0%
+problem any
+ 
+
+ align:start position:0%
+problem any
+questions about the block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stacking okay all right so um that's
+
+ align:start position:0%
+stacking okay all right so um that's
+ 
+
+ align:start position:0%
+stacking okay all right so um that's
+basically it for sums I do want to spend
+
+ align:start position:0%
+basically it for sums I do want to spend
+ 
+
+ align:start position:0%
+basically it for sums I do want to spend
+a little time talking about products and
+
+ align:start position:0%
+a little time talking about products and
+ 
+
+ align:start position:0%
+a little time talking about products and
+that may get us back into sums pretty
+
+ align:start position:0%
+that may get us back into sums pretty
+ 
+
+ align:start position:0%
+that may get us back into sums pretty
+quick
+
+ align:start position:0%
+quick
+ 
+
+ align:start position:0%
+quick
+um the most famous product out there is
+
+ align:start position:0%
+um the most famous product out there is
+ 
+
+ align:start position:0%
+um the most famous product out there is
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+factorial and once we get to counting
+
+ align:start position:0%
+factorial and once we get to counting
+ 
+
+ align:start position:0%
+factorial and once we get to counting
+and probability probably every lecture
+
+ align:start position:0%
+and probability probably every lecture
+ 
+
+ align:start position:0%
+and probability probably every lecture
+we're going to be looking at n factorial
+
+ align:start position:0%
+we're going to be looking at n factorial
+ 
+
+ align:start position:0%
+we're going to be looking at n factorial
+one way or another just comes up all the
+
+ align:start position:0%
+one way or another just comes up all the
+ 
+
+ align:start position:0%
+one way or another just comes up all the
+time n factorial is the
+
+ align:start position:0%
+time n factorial is the
+ 
+
+ align:start position:0%
+time n factorial is the
+product of I = 1 to n of I it's the
+
+ align:start position:0%
+product of I = 1 to n of I it's the
+ 
+
+ align:start position:0%
+product of I = 1 to n of I it's the
+product of the first n now natural
+
+ align:start position:0%
+product of the first n now natural
+ 
+
+ align:start position:0%
+product of the first n now natural
+numbers after
+
+ align:start position:0%
+numbers after
+ 
+
+ align:start position:0%
+numbers after
+zero now we'd like to be able to get a
+
+ align:start position:0%
+zero now we'd like to be able to get a
+ 
+
+ align:start position:0%
+zero now we'd like to be able to get a
+closed form expression for this because
+
+ align:start position:0%
+closed form expression for this because
+ 
+
+ align:start position:0%
+closed form expression for this because
+factorial is really not closed form
+
+ align:start position:0%
+factorial is really not closed form
+ 
+
+ align:start position:0%
+factorial is really not closed form
+because it's it's hiding this
+
+ align:start position:0%
+because it's it's hiding this
+ 
+
+ align:start position:0%
+because it's it's hiding this
+thing and if I ask you how big is n
+
+ align:start position:0%
+thing and if I ask you how big is n
+ 
+
+ align:start position:0%
+thing and if I ask you how big is n
+factorial sort of hard to to say how big
+
+ align:start position:0%
+factorial sort of hard to to say how big
+ 
+
+ align:start position:0%
+factorial sort of hard to to say how big
+it is how fast it
+
+ align:start position:0%
+it is how fast it
+ 
+
+ align:start position:0%
+it is how fast it
+grows any ideas about how we might go
+
+ align:start position:0%
+grows any ideas about how we might go
+ 
+
+ align:start position:0%
+grows any ideas about how we might go
+about doing a
+
+ align:start position:0%
+about doing a
+ 
+
+ align:start position:0%
+about doing a
+product to get a closed form expression
+
+ align:start position:0%
+product to get a closed form expression
+ 
+
+ align:start position:0%
+product to get a closed form expression
+yeah LM of a product you get a sum yeah
+
+ align:start position:0%
+yeah LM of a product you get a sum yeah
+ 
+
+ align:start position:0%
+yeah LM of a product you get a sum yeah
+good take the log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it well that's just let's write that out
+
+ align:start position:0%
+it well that's just let's write that out
+ 
+
+ align:start position:0%
+it well that's just let's write that out
+1 * 2 * 3 to n that equals the log of
+
+ align:start position:0%
+1 * 2 * 3 to n that equals the log of
+ 
+
+ align:start position:0%
+1 * 2 * 3 to n that equals the log of
+one plus the log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops all right so I've now got a sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now that I got a sum we can use all
+
+ align:start position:0%
+and now that I got a sum we can use all
+ 
+
+ align:start position:0%
+and now that I got a sum we can use all
+the tools we had for sums so really
+
+ align:start position:0%
+the tools we had for sums so really
+ 
+
+ align:start position:0%
+the tools we had for sums so really
+products look hairy but they're no
+
+ align:start position:0%
+products look hairy but they're no
+ 
+
+ align:start position:0%
+products look hairy but they're no
+different than sums because we're going
+
+ align:start position:0%
+different than sums because we're going
+ 
+
+ align:start position:0%
+different than sums because we're going
+to get an approximation or get an answer
+
+ align:start position:0%
+to get an approximation or get an answer
+ 
+
+ align:start position:0%
+to get an approximation or get an answer
+for log of n factorial then we'll
+
+ align:start position:0%
+for log of n factorial then we'll
+ 
+
+ align:start position:0%
+for log of n factorial then we'll
+exponentiate it we'll have the
+
+ align:start position:0%
+exponentiate it we'll have the
+ 
+
+ align:start position:0%
+exponentiate it we'll have the
+answer all right so we're looking at
+
+ align:start position:0%
+answer all right so we're looking at
+ 
+
+ align:start position:0%
+answer all right so we're looking at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+sum and uh so how do I get a closed form
+
+ align:start position:0%
+sum and uh so how do I get a closed form
+ 
+
+ align:start position:0%
+sum and uh so how do I get a closed form
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+that turns out nobody knows a closed
+
+ align:start position:0%
+that turns out nobody knows a closed
+ 
+
+ align:start position:0%
+that turns out nobody knows a closed
+form but we do know a method that
+
+ align:start position:0%
+form but we do know a method that
+ 
+
+ align:start position:0%
+form but we do know a method that
+approximates it very
+
+ align:start position:0%
+approximates it very
+ 
+
+ align:start position:0%
+approximates it very
+well which is the integration
+
+ align:start position:0%
+well which is the integration
+ 
+
+ align:start position:0%
+well which is the integration
+bounds only in this case it's an
+
+ align:start position:0%
+bounds only in this case it's an
+ 
+
+ align:start position:0%
+bounds only in this case it's an
+increasing
+
+ align:start position:0%
+increasing
+ 
+
+ align:start position:0%
+increasing
+function so let's do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and the formula is easy it's
+
+ align:start position:0%
+that and the formula is easy it's
+ 
+
+ align:start position:0%
+that and the formula is easy it's
+basically the same formula we had there
+
+ align:start position:0%
+basically the same formula we had there
+ 
+
+ align:start position:0%
+basically the same formula we had there
+that the sum
+
+ align:start position:0%
+that the sum
+ 
+
+ align:start position:0%
+that the sum
+I = 1 to n of f of I is at most the nth
+
+ align:start position:0%
+I = 1 to n of f of I is at most the nth
+ 
+
+ align:start position:0%
+I = 1 to n of f of I is at most the nth
+term plus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral and it's at least the first
+
+ align:start position:0%
+integral and it's at least the first
+ 
+
+ align:start position:0%
+integral and it's at least the first
+term plus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral all right now in this case f of
+
+ align:start position:0%
+integral all right now in this case f of
+ 
+
+ align:start position:0%
+integral all right now in this case f of
+I is the log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I and so we need to compute the integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of log of
+
+ align:start position:0%
+of log of
+ 
+
+ align:start position:0%
+of log of
+x and that's easy that's X Ln of x minus
+
+ align:start position:0%
+x and that's easy that's X Ln of x minus
+ 
+
+ align:start position:0%
+x and that's easy that's X Ln of x minus
+X evaluated at n and
+
+ align:start position:0%
+X evaluated at n and
+ 
+
+ align:start position:0%
+X evaluated at n and
+one and that's just NL n log of n minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n if I plug in one I get a zero here and
+
+ align:start position:0%
+n if I plug in one I get a zero here and
+ 
+
+ align:start position:0%
+n if I plug in one I get a zero here and
+I'm subtracting negative one
+
+ align:start position:0%
+I'm subtracting negative one
+ 
+
+ align:start position:0%
+I'm subtracting negative one
+there all right and so now we'll just
+
+ align:start position:0%
+there all right and so now we'll just
+ 
+
+ align:start position:0%
+there all right and so now we'll just
+plug this into the integral and we'll
+
+ align:start position:0%
+plug this into the integral and we'll
+ 
+
+ align:start position:0%
+plug this into the integral and we'll
+get our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounce so F of
+
+ align:start position:0%
+bounce so F of
+ 
+
+ align:start position:0%
+bounce so F of
+one what is f of
+
+ align:start position:0%
+one what is f of
+ 
+
+ align:start position:0%
+one what is f of
+one in this
+
+ align:start position:0%
+one in this
+ 
+
+ align:start position:0%
+one in this
+case yeah
+
+ align:start position:0%
+case yeah
+ 
+
+ align:start position:0%
+case yeah
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+plus n
+
+ align:start position:0%
+plus n
+ 
+
+ align:start position:0%
+plus n
+Ln and - n + 1 less than equal
+
+ align:start position:0%
+Ln and - n + 1 less than equal
+ 
+
+ align:start position:0%
+Ln and - n + 1 less than equal
+to log of n factorial
+
+ align:start position:0%
+to log of n factorial
+ 
+
+ align:start position:0%
+to log of n factorial
+or equal to F of n is log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay so to get bounds on N factorial
+
+ align:start position:0%
+n okay so to get bounds on N factorial
+ 
+
+ align:start position:0%
+n okay so to get bounds on N factorial
+we just exponentiate both
+
+ align:start position:0%
+we just exponentiate both
+ 
+
+ align:start position:0%
+we just exponentiate both
+sides so I take e to this gives me well
+
+ align:start position:0%
+sides so I take e to this gives me well
+ 
+
+ align:start position:0%
+sides so I take e to this gives me well
+that's going to
+
+ align:start position:0%
+that's going to
+ 
+
+ align:start position:0%
+that's going to
+give n to the N here and then this is
+
+ align:start position:0%
+give n to the N here and then this is
+ 
+
+ align:start position:0%
+give n to the N here and then this is
+negative that'll be e to the N minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here I've
+
+ align:start position:0%
+and here I've
+ 
+
+ align:start position:0%
+and here I've
+got uh n +1 * the log of n so it's n the
+
+ align:start position:0%
+got uh n +1 * the log of n so it's n the
+ 
+
+ align:start position:0%
+got uh n +1 * the log of n so it's n the
+n + one over the same thing e to the N
+
+ align:start position:0%
+n + one over the same thing e to the N
+ 
+
+ align:start position:0%
+n + one over the same thing e to the N
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one so we got very close bounds they're
+
+ align:start position:0%
+one so we got very close bounds they're
+ 
+
+ align:start position:0%
+one so we got very close bounds they're
+within a factor of
+
+ align:start position:0%
+within a factor of
+ 
+
+ align:start position:0%
+within a factor of
+n which sounds like a lot but compared
+
+ align:start position:0%
+n which sounds like a lot but compared
+ 
+
+ align:start position:0%
+n which sounds like a lot but compared
+to how big n factorial is not so bad
+
+ align:start position:0%
+to how big n factorial is not so bad
+ 
+
+ align:start position:0%
+to how big n factorial is not so bad
+pretty pretty good bounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay it's about so n factorial is about
+
+ align:start position:0%
+okay it's about so n factorial is about
+ 
+
+ align:start position:0%
+okay it's about so n factorial is about
+n over e to the N
+
+ align:start position:0%
+n over e to the N
+ 
+
+ align:start position:0%
+n over e to the N
+power now this is so important that that
+
+ align:start position:0%
+power now this is so important that that
+ 
+
+ align:start position:0%
+power now this is so important that that
+even more important than harmonic
+
+ align:start position:0%
+even more important than harmonic
+ 
+
+ align:start position:0%
+even more important than harmonic
+numbers people have gone to a lot of
+
+ align:start position:0%
+numbers people have gone to a lot of
+ 
+
+ align:start position:0%
+numbers people have gone to a lot of
+effort to get very tight bounds on N
+
+ align:start position:0%
+effort to get very tight bounds on N
+ 
+
+ align:start position:0%
+effort to get very tight bounds on N
+factorial so let me tell you what those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are it's called Sterling's formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that says that n
+
+ align:start position:0%
+and that says that n
+ 
+
+ align:start position:0%
+and that says that n
+factorial equals n / e to the N Power
+
+ align:start position:0%
+factorial equals n / e to the N Power
+ 
+
+ align:start position:0%
+factorial equals n / e to the N Power
+Times the < TK of 2 piun
+
+ align:start position:0%
+Times the < TK of 2 piun
+ 
+
+ align:start position:0%
+Times the < TK of 2 piun
+N time e to the Epsilon
+
+ align:start position:0%
+N time e to the Epsilon
+ 
+
+ align:start position:0%
+N time e to the Epsilon
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where Epsilon n is between 1 over 12 n +
+
+ align:start position:0%
+where Epsilon n is between 1 over 12 n +
+ 
+
+ align:start position:0%
+where Epsilon n is between 1 over 12 n +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and 1 over
+
+ align:start position:0%
+and 1 over
+ 
+
+ align:start position:0%
+and 1 over
+12n so it's Epsilon n is going to zero
+
+ align:start position:0%
+12n so it's Epsilon n is going to zero
+ 
+
+ align:start position:0%
+12n so it's Epsilon n is going to zero
+as n gets big so e is something going to
+
+ align:start position:0%
+as n gets big so e is something going to
+ 
+
+ align:start position:0%
+as n gets big so e is something going to
+zero is going to one all right so
+
+ align:start position:0%
+zero is going to one all right so
+ 
+
+ align:start position:0%
+zero is going to one all right so
+another way of looking at this is you
+
+ align:start position:0%
+another way of looking at this is you
+ 
+
+ align:start position:0%
+another way of looking at this is you
+could put a Tilda here all right and
+
+ align:start position:0%
+could put a Tilda here all right and
+ 
+
+ align:start position:0%
+could put a Tilda here all right and
+ignore that term that's called
+
+ align:start position:0%
+ignore that term that's called
+ 
+
+ align:start position:0%
+ignore that term that's called
+Sterling's formula this is a good thing
+
+ align:start position:0%
+Sterling's formula this is a good thing
+ 
+
+ align:start position:0%
+Sterling's formula this is a good thing
+to have on your crib sheet all right for
+
+ align:start position:0%
+to have on your crib sheet all right for
+ 
+
+ align:start position:0%
+to have on your crib sheet all right for
+the midterm so very likely there'll be
+
+ align:start position:0%
+the midterm so very likely there'll be
+ 
+
+ align:start position:0%
+the midterm so very likely there'll be
+something where you got to have some
+
+ align:start position:0%
+something where you got to have some
+ 
+
+ align:start position:0%
+something where you got to have some
+kind of analysis of n factorial and to
+
+ align:start position:0%
+kind of analysis of n factorial and to
+ 
+
+ align:start position:0%
+kind of analysis of n factorial and to
+know how fast it's
+
+ align:start position:0%
+know how fast it's
+ 
+
+ align:start position:0%
+know how fast it's
+growing now this these bounds you get
+
+ align:start position:0%
+growing now this these bounds you get
+ 
+
+ align:start position:0%
+growing now this these bounds you get
+here are very tight for
+
+ align:start position:0%
+here are very tight for
+ 
+
+ align:start position:0%
+here are very tight for
+example 100
+
+ align:start position:0%
+example 100
+ 
+
+ align:start position:0%
+example 100
+factorial is at
+
+ align:start position:0%
+factorial is at
+ 
+
+ align:start position:0%
+factorial is at
+least 100 over e to 100 * < TK 200
+
+ align:start position:0%
+least 100 over e to 100 * < TK 200
+ 
+
+ align:start position:0%
+least 100 over e to 100 * < TK 200
+piun time e to 1 over
+
+ align:start position:0%
+piun time e to 1 over
+ 
+
+ align:start position:0%
+piun time e to 1 over
+1201 this thing is is just really tiny
+
+ align:start position:0%
+1201 this thing is is just really tiny
+ 
+
+ align:start position:0%
+1201 this thing is is just really tiny
+this thing here is
+
+ align:start position:0%
+this thing here is
+ 
+
+ align:start position:0%
+this thing here is
+1.0
+
+ align:start position:0%
+1.0
+ 
+
+ align:start position:0%
+1.0
+8329 and something and 100 factorial is
+
+ align:start position:0%
+8329 and something and 100 factorial is
+ 
+
+ align:start position:0%
+8329 and something and 100 factorial is
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+bounded by the same
+
+ align:start position:0%
+bounded by the same
+ 
+
+ align:start position:0%
+bounded by the same
+things only here it's e to the 1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1200 and that is very close to one
+
+ align:start position:0%
+1200 and that is very close to one
+ 
+
+ align:start position:0%
+1200 and that is very close to one
+1.008 33 6 8 so the difference in these
+
+ align:start position:0%
+1.008 33 6 8 so the difference in these
+ 
+
+ align:start position:0%
+1.008 33 6 8 so the difference in these
+bounds is a tiny fraction of
+
+ align:start position:0%
+bounds is a tiny fraction of
+ 
+
+ align:start position:0%
+bounds is a tiny fraction of
+1% so the bound you get from Sterling's
+
+ align:start position:0%
+1% so the bound you get from Sterling's
+ 
+
+ align:start position:0%
+1% so the bound you get from Sterling's
+formula is very very close to the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer any
+
+ align:start position:0%
+answer any
+ 
+
+ align:start position:0%
+answer any
+questions on Sterling's formula we won't
+
+ align:start position:0%
+questions on Sterling's formula we won't
+ 
+
+ align:start position:0%
+questions on Sterling's formula we won't
+derive it you can derive that in a
+
+ align:start position:0%
+derive it you can derive that in a
+ 
+
+ align:start position:0%
+derive it you can derive that in a
+graduate math class they do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sometimes well typically you'll see it
+
+ align:start position:0%
+sometimes well typically you'll see it
+ 
+
+ align:start position:0%
+sometimes well typically you'll see it
+without that e to the error term and you
+
+ align:start position:0%
+without that e to the error term and you
+ 
+
+ align:start position:0%
+without that e to the error term and you
+just see n factorial written as Tilda n
+
+ align:start position:0%
+just see n factorial written as Tilda n
+ 
+
+ align:start position:0%
+just see n factorial written as Tilda n
+/ e to the N < TK 2 piun
+
+ align:start position:0%
+/ e to the N < TK 2 piun
+ 
+
+ align:start position:0%
+/ e to the N < TK 2 piun
+N all right because that e to the
+
+ align:start position:0%
+N all right because that e to the
+ 
+
+ align:start position:0%
+N all right because that e to the
+Epsilon n goes to one in the limit so it
+
+ align:start position:0%
+Epsilon n goes to one in the limit so it
+ 
+
+ align:start position:0%
+Epsilon n goes to one in the limit so it
+sort of disappears when you go to the
+
+ align:start position:0%
+sort of disappears when you go to the
+ 
+
+ align:start position:0%
+sort of disappears when you go to the
+TAA
+
+ align:start position:0%
+TAA
+ 
+
+ align:start position:0%
+TAA
+notation and this in fact is a lower
+
+ align:start position:0%
+notation and this in fact is a lower
+ 
+
+ align:start position:0%
+notation and this in fact is a lower
+bound on N factorial and very close to
+
+ align:start position:0%
+bound on N factorial and very close to
+ 
+
+ align:start position:0%
+bound on N factorial and very close to
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+answer now this is sort of this is sort
+
+ align:start position:0%
+answer now this is sort of this is sort
+ 
+
+ align:start position:0%
+answer now this is sort of this is sort
+of an amazing formula I mean who would
+
+ align:start position:0%
+of an amazing formula I mean who would
+ 
+
+ align:start position:0%
+of an amazing formula I mean who would
+think that when you look at n
+
+ align:start position:0%
+think that when you look at n
+ 
+
+ align:start position:0%
+think that when you look at n
+factorial that the expression would have
+
+ align:start position:0%
+factorial that the expression would have
+ 
+
+ align:start position:0%
+factorial that the expression would have
+e and Pi in the expression for it maybe
+
+ align:start position:0%
+e and Pi in the expression for it maybe
+ 
+
+ align:start position:0%
+e and Pi in the expression for it maybe
+e maybe but what's pi doing in N
+
+ align:start position:0%
+e maybe but what's pi doing in N
+ 
+
+ align:start position:0%
+e maybe but what's pi doing in N
+factorial it's just sort of a bizarre
+
+ align:start position:0%
+factorial it's just sort of a bizarre
+ 
+
+ align:start position:0%
+factorial it's just sort of a bizarre
+thing okay that's it for products we're
+
+ align:start position:0%
+thing okay that's it for products we're
+ 
+
+ align:start position:0%
+thing okay that's it for products we're
+just going to do the one example because
+
+ align:start position:0%
+just going to do the one example because
+ 
+
+ align:start position:0%
+just going to do the one example because
+really any product just becomes a sum
+
+ align:start position:0%
+really any product just becomes a sum
+ 
+
+ align:start position:0%
+really any product just becomes a sum
+through the log and that makes it really
+
+ align:start position:0%
+through the log and that makes it really
+ 
+
+ align:start position:0%
+through the log and that makes it really
+easy any questions on sums and
+
+ align:start position:0%
+easy any questions on sums and
+ 
+
+ align:start position:0%
+easy any questions on sums and
+products I'm I'm going to totally change
+
+ align:start position:0%
+products I'm I'm going to totally change
+ 
+
+ align:start position:0%
+products I'm I'm going to totally change
+gears now and talk about things more
+
+ align:start position:0%
+gears now and talk about things more
+ 
+
+ align:start position:0%
+gears now and talk about things more
+things like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tilda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're going to talk today and
+
+ align:start position:0%
+okay so we're going to talk today and
+ 
+
+ align:start position:0%
+okay so we're going to talk today and
+tomorrow and
+
+ align:start position:0%
+tomorrow and
+ 
+
+ align:start position:0%
+tomorrow and
+recitation about asymptotic
+
+ align:start position:0%
+recitation about asymptotic
+ 
+
+ align:start position:0%
+recitation about asymptotic
+notation it is used all over the place
+
+ align:start position:0%
+notation it is used all over the place
+ 
+
+ align:start position:0%
+notation it is used all over the place
+in computer
+
+ align:start position:0%
+in computer
+ 
+
+ align:start position:0%
+in computer
+science we've already seen one example
+
+ align:start position:0%
+science we've already seen one example
+ 
+
+ align:start position:0%
+science we've already seen one example
+which is the tied notation
+
+ align:start position:0%
+which is the tied notation
+ 
+
+ align:start position:0%
+which is the tied notation
+and it turns out there's five more
+
+ align:start position:0%
+and it turns out there's five more
+ 
+
+ align:start position:0%
+and it turns out there's five more
+things like that which we're going to
+
+ align:start position:0%
+things like that which we're going to
+ 
+
+ align:start position:0%
+things like that which we're going to
+learn what they are and how they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work they all they're used to explain or
+
+ align:start position:0%
+work they all they're used to explain or
+ 
+
+ align:start position:0%
+work they all they're used to explain or
+describe how a function grows in the
+
+ align:start position:0%
+describe how a function grows in the
+ 
+
+ align:start position:0%
+describe how a function grows in the
+limit so for example we had the Tia
+
+ align:start position:0%
+limit so for example we had the Tia
+ 
+
+ align:start position:0%
+limit so for example we had the Tia
+notation and we wrote FX is a g of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x if the
+
+ align:start position:0%
+x if the
+ 
+
+ align:start position:0%
+x if the
+limit as X goes to
+
+ align:start position:0%
+limit as X goes to
+ 
+
+ align:start position:0%
+limit as X goes to
+Infinity of f over
+
+ align:start position:0%
+Infinity of f over
+ 
+
+ align:start position:0%
+Infinity of f over
+G is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now the next one and most commonly
+
+ align:start position:0%
+one now the next one and most commonly
+ 
+
+ align:start position:0%
+one now the next one and most commonly
+used one in computer science is called
+
+ align:start position:0%
+used one in computer science is called
+ 
+
+ align:start position:0%
+used one in computer science is called
+the O notation or the Big
+
+ align:start position:0%
+the O notation or the Big
+ 
+
+ align:start position:0%
+the O notation or the Big
+O and it's written like this f ofx
+
+ align:start position:0%
+O and it's written like this f ofx
+ 
+
+ align:start position:0%
+O and it's written like this f ofx
+equals o of G
+
+ align:start position:0%
+equals o of G
+ 
+
+ align:start position:0%
+equals o of G
+ofx and it
+
+ align:start position:0%
+ofx and it
+ 
+
+ align:start position:0%
+ofx and it
+means that the
+
+ align:start position:0%
+means that the
+ 
+
+ align:start position:0%
+means that the
+limit as X goes to
+
+ align:start position:0%
+limit as X goes to
+ 
+
+ align:start position:0%
+limit as X goes to
+Infinity of the absolute value of f ofx
+
+ align:start position:0%
+Infinity of the absolute value of f ofx
+ 
+
+ align:start position:0%
+Infinity of the absolute value of f ofx
+over G
+
+ align:start position:0%
+over G
+ 
+
+ align:start position:0%
+over G
+ofx is converges is less than infinity
+
+ align:start position:0%
+ofx is converges is less than infinity
+ 
+
+ align:start position:0%
+ofx is converges is less than infinity
+so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite it can't
+
+ align:start position:0%
+finite it can't
+ 
+
+ align:start position:0%
+finite it can't
+diverge the interpretation is that this
+
+ align:start position:0%
+diverge the interpretation is that this
+ 
+
+ align:start position:0%
+diverge the interpretation is that this
+function is up to constant factors upper
+
+ align:start position:0%
+function is up to constant factors upper
+ 
+
+ align:start position:0%
+function is up to constant factors upper
+bounded by this
+
+ align:start position:0%
+bounded by this
+ 
+
+ align:start position:0%
+bounded by this
+one that this grows the same rate or
+
+ align:start position:0%
+one that this grows the same rate or
+ 
+
+ align:start position:0%
+one that this grows the same rate or
+slower than this one grows as X gets
+
+ align:start position:0%
+slower than this one grows as X gets
+ 
+
+ align:start position:0%
+slower than this one grows as X gets
+large because if if F was growing a lot
+
+ align:start position:0%
+large because if if F was growing a lot
+ 
+
+ align:start position:0%
+large because if if F was growing a lot
+faster than G in the limit then the
+
+ align:start position:0%
+faster than G in the limit then the
+ 
+
+ align:start position:0%
+faster than G in the limit then the
+limit would be the ratio infinity and
+
+ align:start position:0%
+limit would be the ratio infinity and
+ 
+
+ align:start position:0%
+limit would be the ratio infinity and
+we're saying that doesn't happen right
+
+ align:start position:0%
+we're saying that doesn't happen right
+ 
+
+ align:start position:0%
+we're saying that doesn't happen right
+I'm going to do a lot of examples for
+
+ align:start position:0%
+I'm going to do a lot of examples for
+ 
+
+ align:start position:0%
+I'm going to do a lot of examples for
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that's fact let's go over here
+
+ align:start position:0%
+um that's fact let's go over here
+ 
+
+ align:start position:0%
+um that's fact let's go over here
+there's several other ways you'll see it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+written for example you'll see people
+
+ align:start position:0%
+written for example you'll see people
+ 
+
+ align:start position:0%
+written for example you'll see people
+write f ofx is less than or equal to o
+
+ align:start position:0%
+write f ofx is less than or equal to o
+ 
+
+ align:start position:0%
+write f ofx is less than or equal to o
+of G of
+
+ align:start position:0%
+of G of
+ 
+
+ align:start position:0%
+of G of
+X because the natural interpretation is
+
+ align:start position:0%
+X because the natural interpretation is
+ 
+
+ align:start position:0%
+X because the natural interpretation is
+f is not growing faster than G sort of
+
+ align:start position:0%
+f is not growing faster than G sort of
+ 
+
+ align:start position:0%
+f is not growing faster than G sort of
+upper bounded by G you'll see people
+
+ align:start position:0%
+upper bounded by G you'll see people
+ 
+
+ align:start position:0%
+upper bounded by G you'll see people
+write f ofx is O of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx and the formal math way that people
+
+ align:start position:0%
+ofx and the formal math way that people
+ 
+
+ align:start position:0%
+ofx and the formal math way that people
+don't use but it's the formally correct
+
+ align:start position:0%
+don't use but it's the formally correct
+ 
+
+ align:start position:0%
+don't use but it's the formally correct
+one is f ofx is an element of O of G
+
+ align:start position:0%
+one is f ofx is an element of O of G
+ 
+
+ align:start position:0%
+one is f ofx is an element of O of G
+ofx and the interpretation there is that
+
+ align:start position:0%
+ofx and the interpretation there is that
+ 
+
+ align:start position:0%
+ofx and the interpretation there is that
+o of G ofx is a set of functions that
+
+ align:start position:0%
+o of G ofx is a set of functions that
+ 
+
+ align:start position:0%
+o of G ofx is a set of functions that
+don't grow any faster than G and F is
+
+ align:start position:0%
+don't grow any faster than G and F is
+ 
+
+ align:start position:0%
+don't grow any faster than G and F is
+one of them you can use any of these and
+
+ align:start position:0%
+one of them you can use any of these and
+ 
+
+ align:start position:0%
+one of them you can use any of these and
+that's fine people will know what you
+
+ align:start position:0%
+that's fine people will know what you
+ 
+
+ align:start position:0%
+that's fine people will know what you
+mean and it'll be fine for the
+
+ align:start position:0%
+mean and it'll be fine for the
+ 
+
+ align:start position:0%
+mean and it'll be fine for the
+class all right let's see some
+
+ align:start position:0%
+class all right let's see some
+ 
+
+ align:start position:0%
+class all right let's see some
+examples and see how to prove a big O
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation let F
+
+ align:start position:0%
+relation let F
+ 
+
+ align:start position:0%
+relation let F
+ofx be the function X and G of X be the
+
+ align:start position:0%
+ofx be the function X and G of X be the
+ 
+
+ align:start position:0%
+ofx be the function X and G of X be the
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+X2 then
+
+ align:start position:0%
+X2 then
+ 
+
+ align:start position:0%
+X2 then
+in this case f ofx is O of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx because X doesn't gr any faster than
+
+ align:start position:0%
+ofx because X doesn't gr any faster than
+ 
+
+ align:start position:0%
+ofx because X doesn't gr any faster than
+x squ as X gets large to prove
+
+ align:start position:0%
+x squ as X gets large to prove
+ 
+
+ align:start position:0%
+x squ as X gets large to prove
+it we take the limit as X goes to
+
+ align:start position:0%
+it we take the limit as X goes to
+ 
+
+ align:start position:0%
+it we take the limit as X goes to
+Infinity of X over
+
+ align:start position:0%
+Infinity of X over
+ 
+
+ align:start position:0%
+Infinity of X over
+X2 that is equal to what what is the
+
+ align:start position:0%
+X2 that is equal to what what is the
+ 
+
+ align:start position:0%
+X2 that is equal to what what is the
+limit of xx2 as X goes to
+
+ align:start position:0%
+limit of xx2 as X goes to
+ 
+
+ align:start position:0%
+limit of xx2 as X goes to
+Infinity zero
+
+ align:start position:0%
+Infinity zero
+ 
+
+ align:start position:0%
+Infinity zero
+and that is less than
+
+ align:start position:0%
+and that is less than
+ 
+
+ align:start position:0%
+and that is less than
+infinity so we proved it so if you get
+
+ align:start position:0%
+infinity so we proved it so if you get
+ 
+
+ align:start position:0%
+infinity so we proved it so if you get
+asked to
+
+ align:start position:0%
+asked to
+ 
+
+ align:start position:0%
+asked to
+prove f is O of G what you do is you
+
+ align:start position:0%
+prove f is O of G what you do is you
+ 
+
+ align:start position:0%
+prove f is O of G what you do is you
+take the limit of f over G as X goes to
+
+ align:start position:0%
+take the limit of f over G as X goes to
+ 
+
+ align:start position:0%
+take the limit of f over G as X goes to
+infinity and show that it doesn't
+
+ align:start position:0%
+infinity and show that it doesn't
+ 
+
+ align:start position:0%
+infinity and show that it doesn't
+diverge all right let's do do another
+
+ align:start position:0%
+diverge all right let's do do another
+ 
+
+ align:start position:0%
+diverge all right let's do do another
+example this case we'll show that f is
+
+ align:start position:0%
+example this case we'll show that f is
+ 
+
+ align:start position:0%
+example this case we'll show that f is
+not o of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2 is not o of
+
+ align:start position:0%
+X2 is not o of
+ 
+
+ align:start position:0%
+X2 is not o of
+X of course X squ grows faster than x
+
+ align:start position:0%
+X of course X squ grows faster than x
+ 
+
+ align:start position:0%
+X of course X squ grows faster than x
+but let's see why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not well we take the
+
+ align:start position:0%
+not well we take the
+ 
+
+ align:start position:0%
+not well we take the
+limit as X goes to Infinity of
+
+ align:start position:0%
+limit as X goes to Infinity of
+ 
+
+ align:start position:0%
+limit as X goes to Infinity of
+X2
+
+ align:start position:0%
+X2
+ 
+
+ align:start position:0%
+X2
+overx and what is that
+
+ align:start position:0%
+overx and what is that
+ 
+
+ align:start position:0%
+overx and what is that
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+infinity and so it can't be true that
+
+ align:start position:0%
+infinity and so it can't be true that
+ 
+
+ align:start position:0%
+infinity and so it can't be true that
+it's X2 is O of X because it has to be
+
+ align:start position:0%
+it's X2 is O of X because it has to be
+ 
+
+ align:start position:0%
+it's X2 is O of X because it has to be
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+Infinity sorry Infinity there we go
+
+ align:start position:0%
+Infinity sorry Infinity there we go
+ 
+
+ align:start position:0%
+Infinity sorry Infinity there we go
+that's important in the definition yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good all right what about
+
+ align:start position:0%
+good all right what about
+ 
+
+ align:start position:0%
+good all right what about
+this is X2 = o of a million times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x yes
+
+ align:start position:0%
+x yes
+ 
+
+ align:start position:0%
+x yes
+no what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think this looks pretty darn big that's
+
+ align:start position:0%
+think this looks pretty darn big that's
+ 
+
+ align:start position:0%
+think this looks pretty darn big that's
+a constant that's a
+
+ align:start position:0%
+a constant that's a
+ 
+
+ align:start position:0%
+a constant that's a
+constant so in the limit as X goes to
+
+ align:start position:0%
+constant so in the limit as X goes to
+ 
+
+ align:start position:0%
+constant so in the limit as X goes to
+Infinity this over that is
+
+ align:start position:0%
+Infinity this over that is
+ 
+
+ align:start position:0%
+Infinity this over that is
+infinite all right so
+
+ align:start position:0%
+infinite all right so
+ 
+
+ align:start position:0%
+infinite all right so
+no because the
+
+ align:start position:0%
+no because the
+ 
+
+ align:start position:0%
+no because the
+limit X goes to Infinity of x^2 over 10
+
+ align:start position:0%
+limit X goes to Infinity of x^2 over 10
+ 
+
+ align:start position:0%
+limit X goes to Infinity of x^2 over 10
+6X at equals
+
+ align:start position:0%
+6X at equals
+ 
+
+ align:start position:0%
+6X at equals
+infinity all right so the thing with
+
+ align:start position:0%
+infinity all right so the thing with
+ 
+
+ align:start position:0%
+infinity all right so the thing with
+these Big O notation is you just ignore
+
+ align:start position:0%
+these Big O notation is you just ignore
+ 
+
+ align:start position:0%
+these Big O notation is you just ignore
+constant factors they don't do anything
+
+ align:start position:0%
+constant factors they don't do anything
+ 
+
+ align:start position:0%
+constant factors they don't do anything
+just forget about
+
+ align:start position:0%
+just forget about
+ 
+
+ align:start position:0%
+just forget about
+them all
+
+ align:start position:0%
+them all
+ 
+
+ align:start position:0%
+them all
+right what about this
+
+ align:start position:0%
+right what about this
+ 
+
+ align:start position:0%
+right what about this
+is 10 6 x equal o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x^2
+
+ align:start position:0%
+x^2
+ 
+
+ align:start position:0%
+x^2
+yes because you just ignore the constant
+
+ align:start position:0%
+yes because you just ignore the constant
+ 
+
+ align:start position:0%
+yes because you just ignore the constant
+that's what the Big O is for and why
+
+ align:start position:0%
+that's what the Big O is for and why
+ 
+
+ align:start position:0%
+that's what the Big O is for and why
+it's used all the time in computer
+
+ align:start position:0%
+it's used all the time in computer
+ 
+
+ align:start position:0%
+it's used all the time in computer
+science so yes that's true proof is very
+
+ align:start position:0%
+science so yes that's true proof is very
+ 
+
+ align:start position:0%
+science so yes that's true proof is very
+simple the limit as X goes to Infinity
+
+ align:start position:0%
+simple the limit as X goes to Infinity
+ 
+
+ align:start position:0%
+simple the limit as X goes to Infinity
+of 100 X2 whoops I you can even put a
+
+ align:start position:0%
+of 100 X2 whoops I you can even put a
+ 
+
+ align:start position:0%
+of 100 X2 whoops I you can even put a
+square there 10 6 X2
+
+ align:start position:0%
+square there 10 6 X2
+ 
+
+ align:start position:0%
+square there 10 6 X2
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+x^2 is 10
+
+ align:start position:0%
+x^2 is 10
+ 
+
+ align:start position:0%
+x^2 is 10
+6 that's less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity in fact I could take any
+
+ align:start position:0%
+infinity in fact I could take any
+ 
+
+ align:start position:0%
+infinity in fact I could take any
+quadratic
+
+ align:start position:0%
+quadratic
+ 
+
+ align:start position:0%
+quadratic
+polinomial x^2 + 100x + 10 7th is O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x^2 right because smaller order terms
+
+ align:start position:0%
+x^2 right because smaller order terms
+ 
+
+ align:start position:0%
+x^2 right because smaller order terms
+don't matter the limit of this here over
+
+ align:start position:0%
+don't matter the limit of this here over
+ 
+
+ align:start position:0%
+don't matter the limit of this here over
+that in that case is one so it's less
+
+ align:start position:0%
+that in that case is one so it's less
+ 
+
+ align:start position:0%
+that in that case is one so it's less
+than infinity as X gets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big all right let's do a few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more this really is not so hard it's a
+
+ align:start position:0%
+more this really is not so hard it's a
+ 
+
+ align:start position:0%
+more this really is not so hard it's a
+little dull uh but it's you got to you
+
+ align:start position:0%
+little dull uh but it's you got to you
+ 
+
+ align:start position:0%
+little dull uh but it's you got to you
+got to know it for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later in fact you take classes like 6046
+
+ align:start position:0%
+later in fact you take classes like 6046
+ 
+
+ align:start position:0%
+later in fact you take classes like 6046
+and you'll you'll never see any
+
+ align:start position:0%
+and you'll you'll never see any
+ 
+
+ align:start position:0%
+and you'll you'll never see any
+constants because everything is
+
+ align:start position:0%
+constants because everything is
+ 
+
+ align:start position:0%
+constants because everything is
+things like Big O and in the other
+
+ align:start position:0%
+things like Big O and in the other
+ 
+
+ align:start position:0%
+things like Big O and in the other
+notation we'll talk
+
+ align:start position:0%
+notation we'll talk
+ 
+
+ align:start position:0%
+notation we'll talk
+about what about this x to the
+
+ align:start position:0%
+about what about this x to the
+ 
+
+ align:start position:0%
+about what about this x to the
+10th equal o of e to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is x 10 o of e to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X yeah it is because so this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+proof limit as X goes to INF infinity x
+
+ align:start position:0%
+proof limit as X goes to INF infinity x
+ 
+
+ align:start position:0%
+proof limit as X goes to INF infinity x
+10 e x that equals z which is certainly
+
+ align:start position:0%
+10 e x that equals z which is certainly
+ 
+
+ align:start position:0%
+10 e x that equals z which is certainly
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+infinity all right now the reason this
+
+ align:start position:0%
+infinity all right now the reason this
+ 
+
+ align:start position:0%
+infinity all right now the reason this
+stuff is useful when you're doing the
+
+ align:start position:0%
+stuff is useful when you're doing the
+ 
+
+ align:start position:0%
+stuff is useful when you're doing the
+analysis of algorithms is because when
+
+ align:start position:0%
+analysis of algorithms is because when
+ 
+
+ align:start position:0%
+analysis of algorithms is because when
+you're talking about things like matrix
+
+ align:start position:0%
+you're talking about things like matrix
+ 
+
+ align:start position:0%
+you're talking about things like matrix
+multiplication algorithms or things like
+
+ align:start position:0%
+multiplication algorithms or things like
+ 
+
+ align:start position:0%
+multiplication algorithms or things like
+that the actual running time depends on
+
+ align:start position:0%
+that the actual running time depends on
+ 
+
+ align:start position:0%
+that the actual running time depends on
+the machine you're dealing with the
+
+ align:start position:0%
+the machine you're dealing with the
+ 
+
+ align:start position:0%
+the machine you're dealing with the
+machine characteristics you know details
+
+ align:start position:0%
+machine characteristics you know details
+ 
+
+ align:start position:0%
+machine characteristics you know details
+in how you count steps of the algorithm
+
+ align:start position:0%
+in how you count steps of the algorithm
+ 
+
+ align:start position:0%
+in how you count steps of the algorithm
+for example in doing matrix
+
+ align:start position:0%
+for example in doing matrix
+ 
+
+ align:start position:0%
+for example in doing matrix
+multiplication do you count multiply
+
+ align:start position:0%
+multiplication do you count multiply
+ 
+
+ align:start position:0%
+multiplication do you count multiply
+different than you count plus addition
+
+ align:start position:0%
+different than you count plus addition
+ 
+
+ align:start position:0%
+different than you count plus addition
+and it just if you start getting caught
+
+ align:start position:0%
+and it just if you start getting caught
+ 
+
+ align:start position:0%
+and it just if you start getting caught
+up in all those details you lose the
+
+ align:start position:0%
+up in all those details you lose the
+ 
+
+ align:start position:0%
+up in all those details you lose the
+important fact of the algorithm for
+
+ align:start position:0%
+important fact of the algorithm for
+ 
+
+ align:start position:0%
+important fact of the algorithm for
+example matrix multiplication the
+
+ align:start position:0%
+example matrix multiplication the
+ 
+
+ align:start position:0%
+example matrix multiplication the
+elementary algorithm takes order o of n
+
+ align:start position:0%
+elementary algorithm takes order o of n
+ 
+
+ align:start position:0%
+elementary algorithm takes order o of n
+Cub
+
+ align:start position:0%
+Cub
+ 
+
+ align:start position:0%
+Cub
+steps and and that's the important fact
+
+ align:start position:0%
+steps and and that's the important fact
+ 
+
+ align:start position:0%
+steps and and that's the important fact
+and it tells you that if you double the
+
+ align:start position:0%
+and it tells you that if you double the
+ 
+
+ align:start position:0%
+and it tells you that if you double the
+size of the Matrix the running time will
+
+ align:start position:0%
+size of the Matrix the running time will
+ 
+
+ align:start position:0%
+size of the Matrix the running time will
+increase by at most a factor of eight in
+
+ align:start position:0%
+increase by at most a factor of eight in
+ 
+
+ align:start position:0%
+increase by at most a factor of eight in
+the limit
+
+ align:start position:0%
+the limit
+ 
+
+ align:start position:0%
+the limit
+as n gets large and so you might write
+
+ align:start position:0%
+as n gets large and so you might write
+ 
+
+ align:start position:0%
+as n gets large and so you might write
+things like the time to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiply n byn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices you might call that t of N and
+
+ align:start position:0%
+matrices you might call that t of N and
+ 
+
+ align:start position:0%
+matrices you might call that t of N and
+then state that is O of n
+
+ align:start position:0%
+then state that is O of n
+ 
+
+ align:start position:0%
+then state that is O of n
+cubed all right and you don't have to
+
+ align:start position:0%
+cubed all right and you don't have to
+ 
+
+ align:start position:0%
+cubed all right and you don't have to
+worry about what computer it's running
+
+ align:start position:0%
+worry about what computer it's running
+ 
+
+ align:start position:0%
+worry about what computer it's running
+on you know exactly how you're counting
+
+ align:start position:0%
+on you know exactly how you're counting
+ 
+
+ align:start position:0%
+on you know exactly how you're counting
+the details of what a step is or what
+
+ align:start position:0%
+the details of what a step is or what
+ 
+
+ align:start position:0%
+the details of what a step is or what
+time is the important thing is that it's
+
+ align:start position:0%
+time is the important thing is that it's
+ 
+
+ align:start position:0%
+time is the important thing is that it's
+growing at most as a cubic of the size
+
+ align:start position:0%
+growing at most as a cubic of the size
+ 
+
+ align:start position:0%
+growing at most as a cubic of the size
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+matrices and so in 6046 and in
+
+ align:start position:0%
+matrices and so in 6046 and in
+ 
+
+ align:start position:0%
+matrices and so in 6046 and in
+66 you will spend lots of time proving
+
+ align:start position:0%
+66 you will spend lots of time proving
+ 
+
+ align:start position:0%
+66 you will spend lots of time proving
+that things are running time or the size
+
+ align:start position:0%
+that things are running time or the size
+ 
+
+ align:start position:0%
+that things are running time or the size
+is O of some function of the input
+
+ align:start position:0%
+is O of some function of the input
+ 
+
+ align:start position:0%
+is O of some function of the input
+size all
+
+ align:start position:0%
+size all
+ 
+
+ align:start position:0%
+size all
+right any
+
+ align:start position:0%
+right any
+ 
+
+ align:start position:0%
+right any
+questions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you know gets all dicey if you do
+
+ align:start position:0%
+yeah you know gets all dicey if you do
+ 
+
+ align:start position:0%
+yeah you know gets all dicey if you do
+oscillatory things and depends how you
+
+ align:start position:0%
+oscillatory things and depends how you
+ 
+
+ align:start position:0%
+oscillatory things and depends how you
+define it so we're going to stay away
+
+ align:start position:0%
+define it so we're going to stay away
+ 
+
+ align:start position:0%
+define it so we're going to stay away
+from that um and just stick with this
+
+ align:start position:0%
+from that um and just stick with this
+ 
+
+ align:start position:0%
+from that um and just stick with this
+definition so if this guy oscillates
+
+ align:start position:0%
+definition so if this guy oscillates
+ 
+
+ align:start position:0%
+definition so if this guy oscillates
+like f is a sign s of x s of X is O of X
+
+ align:start position:0%
+like f is a sign s of x s of X is O of X
+ 
+
+ align:start position:0%
+like f is a sign s of x s of X is O of X
+all right doesn't have to converge but
+
+ align:start position:0%
+all right doesn't have to converge but
+ 
+
+ align:start position:0%
+all right doesn't have to converge but
+as long as the ratio is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity yeah everything you do maybe
+
+ align:start position:0%
+Infinity yeah everything you do maybe
+ 
+
+ align:start position:0%
+Infinity yeah everything you do maybe
+you'll see sign functions sometimes but
+
+ align:start position:0%
+you'll see sign functions sometimes but
+ 
+
+ align:start position:0%
+you'll see sign functions sometimes but
+everything you do in algorithms is going
+
+ align:start position:0%
+everything you do in algorithms is going
+ 
+
+ align:start position:0%
+everything you do in algorithms is going
+to be growing monotonically yeah nothing
+
+ align:start position:0%
+to be growing monotonically yeah nothing
+ 
+
+ align:start position:0%
+to be growing monotonically yeah nothing
+no wacky stuff in math usually any other
+
+ align:start position:0%
+no wacky stuff in math usually any other
+ 
+
+ align:start position:0%
+no wacky stuff in math usually any other
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah it's upper bounded so it's not
+
+ align:start position:0%
+yeah yeah it's upper bounded so it's not
+ 
+
+ align:start position:0%
+yeah yeah it's upper bounded so it's not
+the same we'll get to the same in a
+
+ align:start position:0%
+the same we'll get to the same in a
+ 
+
+ align:start position:0%
+the same we'll get to the same in a
+minute but it's upper bounded f is upper
+
+ align:start position:0%
+minute but it's upper bounded f is upper
+ 
+
+ align:start position:0%
+minute but it's upper bounded f is upper
+bounded by G up to a fixed constant as
+
+ align:start position:0%
+bounded by G up to a fixed constant as
+ 
+
+ align:start position:0%
+bounded by G up to a fixed constant as
+you go to infinity and all constants get
+
+ align:start position:0%
+you go to infinity and all constants get
+ 
+
+ align:start position:0%
+you go to infinity and all constants get
+washed away by
+
+ align:start position:0%
+washed away by
+ 
+
+ align:start position:0%
+washed away by
+o
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh ah why is this true well uh
+
+ align:start position:0%
+yeah uh ah why is this true well uh
+ 
+
+ align:start position:0%
+yeah uh ah why is this true well uh
+technically we'd have to go back to
+
+ align:start position:0%
+technically we'd have to go back to
+ 
+
+ align:start position:0%
+technically we'd have to go back to
+calculus and use lal's rule or something
+
+ align:start position:0%
+calculus and use lal's rule or something
+ 
+
+ align:start position:0%
+calculus and use lal's rule or something
+like that because this function
+
+ align:start position:0%
+like that because this function
+ 
+
+ align:start position:0%
+like that because this function
+exponential grows a lot faster than x to
+
+ align:start position:0%
+exponential grows a lot faster than x to
+ 
+
+ align:start position:0%
+exponential grows a lot faster than x to
+the 10th so lal's rule is you take the
+
+ align:start position:0%
+the 10th so lal's rule is you take the
+ 
+
+ align:start position:0%
+the 10th so lal's rule is you take the
+derivative of this over the derivative
+
+ align:start position:0%
+derivative of this over the derivative
+ 
+
+ align:start position:0%
+derivative of this over the derivative
+of that then you'd have x to the 9th
+
+ align:start position:0%
+of that then you'd have x to the 9th
+ 
+
+ align:start position:0%
+of that then you'd have x to the 9th
+over e to X You' do it n more times and
+
+ align:start position:0%
+over e to X You' do it n more times and
+ 
+
+ align:start position:0%
+over e to X You' do it n more times and
+you'd get 10 factorial over e to X and
+
+ align:start position:0%
+you'd get 10 factorial over e to X and
+ 
+
+ align:start position:0%
+you'd get 10 factorial over e to X and
+that limit is zero so that's how you'd
+
+ align:start position:0%
+that limit is zero so that's how you'd
+ 
+
+ align:start position:0%
+that limit is zero so that's how you'd
+actually do it using lal's
+
+ align:start position:0%
+actually do it using lal's
+ 
+
+ align:start position:0%
+actually do it using lal's
+rule yeah any polinomial grows slower
+
+ align:start position:0%
+rule yeah any polinomial grows slower
+ 
+
+ align:start position:0%
+rule yeah any polinomial grows slower
+than any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential all right let's uh let's now
+
+ align:start position:0%
+exponential all right let's uh let's now
+ 
+
+ align:start position:0%
+exponential all right let's uh let's now
+do some examples that can get you
+
+ align:start position:0%
+do some examples that can get you
+ 
+
+ align:start position:0%
+do some examples that can get you
+screwed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up what about this one
+
+ align:start position:0%
+up what about this one
+ 
+
+ align:start position:0%
+up what about this one
+is 4 the x o of 2 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is that
+
+ align:start position:0%
+x is that
+ 
+
+ align:start position:0%
+x is that
+true no it's not true I mean the mistake
+
+ align:start position:0%
+true no it's not true I mean the mistake
+ 
+
+ align:start position:0%
+true no it's not true I mean the mistake
+you might make is say oh four and two
+
+ align:start position:0%
+you might make is say oh four and two
+ 
+
+ align:start position:0%
+you might make is say oh four and two
+four is only double two Big O wipes out
+
+ align:start position:0%
+four is only double two Big O wipes out
+ 
+
+ align:start position:0%
+four is only double two Big O wipes out
+constant factors so the answer is yes
+
+ align:start position:0%
+constant factors so the answer is yes
+ 
+
+ align:start position:0%
+constant factors so the answer is yes
+that would be bad better to look at the
+
+ align:start position:0%
+that would be bad better to look at the
+ 
+
+ align:start position:0%
+that would be bad better to look at the
+limit so we'll State the correct theorem
+
+ align:start position:0%
+limit so we'll State the correct theorem
+ 
+
+ align:start position:0%
+limit so we'll State the correct theorem
+4 X is not o of 2 x and the proof is
+
+ align:start position:0%
+4 X is not o of 2 x and the proof is
+ 
+
+ align:start position:0%
+4 X is not o of 2 x and the proof is
+obtained by looking at the
+
+ align:start position:0%
+obtained by looking at the
+ 
+
+ align:start position:0%
+obtained by looking at the
+limit as X goes to Infinity of 4 x over
+
+ align:start position:0%
+limit as X goes to Infinity of 4 x over
+ 
+
+ align:start position:0%
+limit as X goes to Infinity of 4 x over
+2 x that is just the limit 4 x over 2 x
+
+ align:start position:0%
+2 x that is just the limit 4 x over 2 x
+ 
+
+ align:start position:0%
+2 x that is just the limit 4 x over 2 x
+is 2 X that's
+
+ align:start position:0%
+is 2 X that's
+ 
+
+ align:start position:0%
+is 2 X that's
+Infinity so the limit is not
+
+ align:start position:0%
+Infinity so the limit is not
+ 
+
+ align:start position:0%
+Infinity so the limit is not
+bounded right so it is not Big O
+
+ align:start position:0%
+bounded right so it is not Big O
+ 
+
+ align:start position:0%
+bounded right so it is not Big O
+there right here's one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is 10 o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one I've purposely written it this
+
+ align:start position:0%
+one I've purposely written it this
+ 
+
+ align:start position:0%
+one I've purposely written it this
+way yes it is and in fact the
+
+ align:start position:0%
+way yes it is and in fact the
+ 
+
+ align:start position:0%
+way yes it is and in fact the
+interpretation here is that you've got
+
+ align:start position:0%
+interpretation here is that you've got
+ 
+
+ align:start position:0%
+interpretation here is that you've got
+some function f ofx that's just always
+
+ align:start position:0%
+some function f ofx that's just always
+ 
+
+ align:start position:0%
+some function f ofx that's just always
+equal to 10 and some function G ofx
+
+ align:start position:0%
+equal to 10 and some function G ofx
+ 
+
+ align:start position:0%
+equal to 10 and some function G ofx
+that's always equal to one and then it
+
+ align:start position:0%
+that's always equal to one and then it
+ 
+
+ align:start position:0%
+that's always equal to one and then it
+is true in this case that f ofx is O of
+
+ align:start position:0%
+is true in this case that f ofx is O of
+ 
+
+ align:start position:0%
+is true in this case that f ofx is O of
+G of x
+
+ align:start position:0%
+G of x
+ 
+
+ align:start position:0%
+G of x
+X all right but any constant function is
+
+ align:start position:0%
+X all right but any constant function is
+ 
+
+ align:start position:0%
+X all right but any constant function is
+O of any other constant
+
+ align:start position:0%
+O of any other constant
+ 
+
+ align:start position:0%
+O of any other constant
+function we're going to revisit this in
+
+ align:start position:0%
+function we're going to revisit this in
+ 
+
+ align:start position:0%
+function we're going to revisit this in
+a nastier scenario in a little
+
+ align:start position:0%
+a nastier scenario in a little
+ 
+
+ align:start position:0%
+a nastier scenario in a little
+bit okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um sometimes you'll see notation like
+
+ align:start position:0%
+um sometimes you'll see notation like
+ 
+
+ align:start position:0%
+um sometimes you'll see notation like
+this h of n in fact we saw this earlier
+
+ align:start position:0%
+this h of n in fact we saw this earlier
+ 
+
+ align:start position:0%
+this h of n in fact we saw this earlier
+is the log of n Plus
+
+ align:start position:0%
+is the log of n Plus
+ 
+
+ align:start position:0%
+is the log of n Plus
+Delta plus o of 1/ n when we wrote out
+
+ align:start position:0%
+Delta plus o of 1/ n when we wrote out
+ 
+
+ align:start position:0%
+Delta plus o of 1/ n when we wrote out
+the formula for the nth harmonic number
+
+ align:start position:0%
+the formula for the nth harmonic number
+ 
+
+ align:start position:0%
+the formula for the nth harmonic number
+it was log of n plus Oiler constant plus
+
+ align:start position:0%
+it was log of n plus Oiler constant plus
+ 
+
+ align:start position:0%
+it was log of n plus Oiler constant plus
+something like 1/ n constant time 1/ n
+
+ align:start position:0%
+something like 1/ n constant time 1/ n
+ 
+
+ align:start position:0%
+something like 1/ n constant time 1/ n
+and then some even smaller terms and so
+
+ align:start position:0%
+and then some even smaller terms and so
+ 
+
+ align:start position:0%
+and then some even smaller terms and so
+people will write it like this and it
+
+ align:start position:0%
+people will write it like this and it
+ 
+
+ align:start position:0%
+people will write it like this and it
+tells you that the error terms grow no
+
+ align:start position:0%
+tells you that the error terms grow no
+ 
+
+ align:start position:0%
+tells you that the error terms grow no
+faster than a constant * 1 n technically
+
+ align:start position:0%
+faster than a constant * 1 n technically
+ 
+
+ align:start position:0%
+faster than a constant * 1 n technically
+this is the wrong way to write it but
+
+ align:start position:0%
+this is the wrong way to write it but
+ 
+
+ align:start position:0%
+this is the wrong way to write it but
+everybody does it so you can
+
+ align:start position:0%
+everybody does it so you can
+ 
+
+ align:start position:0%
+everybody does it so you can
+too what it means is this h of n minus
+
+ align:start position:0%
+too what it means is this h of n minus
+ 
+
+ align:start position:0%
+too what it means is this h of n minus
+Ln of n minus Delta is O of
+
+ align:start position:0%
+Ln of n minus Delta is O of
+ 
+
+ align:start position:0%
+Ln of n minus Delta is O of
+1/n all right that's the correct way to
+
+ align:start position:0%
+1/n all right that's the correct way to
+ 
+
+ align:start position:0%
+1/n all right that's the correct way to
+write it because you're taking the ratio
+
+ align:start position:0%
+write it because you're taking the ratio
+ 
+
+ align:start position:0%
+write it because you're taking the ratio
+of this over that uh this is how people
+
+ align:start position:0%
+of this over that uh this is how people
+ 
+
+ align:start position:0%
+of this over that uh this is how people
+will do it all right so just know make
+
+ align:start position:0%
+will do it all right so just know make
+ 
+
+ align:start position:0%
+will do it all right so just know make
+sure you understand that um what it
+
+ align:start position:0%
+sure you understand that um what it
+ 
+
+ align:start position:0%
+sure you understand that um what it
+means when we put it over there same
+
+ align:start position:0%
+means when we put it over there same
+ 
+
+ align:start position:0%
+means when we put it over there same
+thing with tiled notation people will
+
+ align:start position:0%
+thing with tiled notation people will
+ 
+
+ align:start position:0%
+thing with tiled notation people will
+write this a h of n is Tilda Ln of n
+
+ align:start position:0%
+write this a h of n is Tilda Ln of n
+ 
+
+ align:start position:0%
+write this a h of n is Tilda Ln of n
+plus Oiler constant the right way to
+
+ align:start position:0%
+plus Oiler constant the right way to
+ 
+
+ align:start position:0%
+plus Oiler constant the right way to
+write it is hn minus Oilers constant is
+
+ align:start position:0%
+write it is hn minus Oilers constant is
+ 
+
+ align:start position:0%
+write it is hn minus Oilers constant is
+TAA L of
+
+ align:start position:0%
+TAA L of
+ 
+
+ align:start position:0%
+TAA L of
+n now can anybody tell me
+
+ align:start position:0%
+n now can anybody tell me
+ 
+
+ align:start position:0%
+n now can anybody tell me
+why this is really not a good thing to
+
+ align:start position:0%
+why this is really not a good thing to
+ 
+
+ align:start position:0%
+why this is really not a good thing to
+do you think of how things get really
+
+ align:start position:0%
+do you think of how things get really
+ 
+
+ align:start position:0%
+do you think of how things get really
+screwed up if you allow to start doing
+
+ align:start position:0%
+screwed up if you allow to start doing
+ 
+
+ align:start position:0%
+screwed up if you allow to start doing
+this can you think of anything
+
+ align:start position:0%
+this can you think of anything
+ 
+
+ align:start position:0%
+this can you think of anything
+that what if what if I did this is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 the nth harmonic is harmonic number
+
+ align:start position:0%
+10 the nth harmonic is harmonic number
+ 
+
+ align:start position:0%
+10 the nth harmonic is harmonic number
+is tilled of log of n+
+
+ align:start position:0%
+is tilled of log of n+
+ 
+
+ align:start position:0%
+is tilled of log of n+
+10 is that
+
+ align:start position:0%
+10 is that
+ 
+
+ align:start position:0%
+10 is that
+true think about that people are shaking
+
+ align:start position:0%
+true think about that people are shaking
+ 
+
+ align:start position:0%
+true think about that people are shaking
+their heads I mean how can it be true
+
+ align:start position:0%
+their heads I mean how can it be true
+ 
+
+ align:start position:0%
+their heads I mean how can it be true
+because that we know this is we know
+
+ align:start position:0%
+because that we know this is we know
+ 
+
+ align:start position:0%
+because that we know this is we know
+that's what it
+
+ align:start position:0%
+that's what it
+ 
+
+ align:start position:0%
+that's what it
+is in fact this is true I could even
+
+ align:start position:0%
+is in fact this is true I could even
+ 
+
+ align:start position:0%
+is in fact this is true I could even
+make it you know a million 10 the six
+
+ align:start position:0%
+make it you know a million 10 the six
+ 
+
+ align:start position:0%
+make it you know a million 10 the six
+here it's
+
+ align:start position:0%
+here it's
+ 
+
+ align:start position:0%
+here it's
+true because the ratio of this over that
+
+ align:start position:0%
+true because the ratio of this over that
+ 
+
+ align:start position:0%
+true because the ratio of this over that
+and the limit is
+
+ align:start position:0%
+and the limit is
+ 
+
+ align:start position:0%
+and the limit is
+what one and that's all I need for
+
+ align:start position:0%
+what one and that's all I need for
+ 
+
+ align:start position:0%
+what one and that's all I need for
+Tilda all right so when I wrote this
+
+ align:start position:0%
+Tilda all right so when I wrote this
+ 
+
+ align:start position:0%
+Tilda all right so when I wrote this
+everybody knew what I
+
+ align:start position:0%
+everybody knew what I
+ 
+
+ align:start position:0%
+everybody knew what I
+meant but I could write this and be just
+
+ align:start position:0%
+meant but I could write this and be just
+ 
+
+ align:start position:0%
+meant but I could write this and be just
+as true
+
+ align:start position:0%
+as true
+ 
+
+ align:start position:0%
+as true
+mathematically and so you got to be sort
+
+ align:start position:0%
+mathematically and so you got to be sort
+ 
+
+ align:start position:0%
+mathematically and so you got to be sort
+of careful you know about this really
+
+ align:start position:0%
+of careful you know about this really
+ 
+
+ align:start position:0%
+of careful you know about this really
+the right way to do it is this because
+
+ align:start position:0%
+the right way to do it is this because
+ 
+
+ align:start position:0%
+the right way to do it is this because
+now we're taking off that term and it's
+
+ align:start position:0%
+now we're taking off that term and it's
+ 
+
+ align:start position:0%
+now we're taking off that term and it's
+then it's actually I did this wrong I
+
+ align:start position:0%
+then it's actually I did this wrong I
+ 
+
+ align:start position:0%
+then it's actually I did this wrong I
+should have put the L in oops I should
+
+ align:start position:0%
+should have put the L in oops I should
+ 
+
+ align:start position:0%
+should have put the L in oops I should
+have done this way let me rewrite that
+
+ align:start position:0%
+have done this way let me rewrite that
+ 
+
+ align:start position:0%
+have done this way let me rewrite that
+the right way to do it is H of n yeah is
+
+ align:start position:0%
+the right way to do it is H of n yeah is
+ 
+
+ align:start position:0%
+the right way to do it is H of n yeah is
+this you put the small term out over
+
+ align:start position:0%
+this you put the small term out over
+ 
+
+ align:start position:0%
+this you put the small term out over
+here that's the right way because now
+
+ align:start position:0%
+here that's the right way because now
+ 
+
+ align:start position:0%
+here that's the right way because now
+it's not true that it's 10 the 6 out
+
+ align:start position:0%
+it's not true that it's 10 the 6 out
+ 
+
+ align:start position:0%
+it's not true that it's 10 the 6 out
+here all right for the ratio of that
+
+ align:start position:0%
+here all right for the ratio of that
+ 
+
+ align:start position:0%
+here all right for the ratio of that
+over this
+
+ align:start position:0%
+over this
+ 
+
+ align:start position:0%
+over this
+guy all right so you can do it but be
+
+ align:start position:0%
+guy all right so you can do it but be
+ 
+
+ align:start position:0%
+guy all right so you can do it but be
+careful because you might write WR wrong
+
+ align:start position:0%
+careful because you might write WR wrong
+ 
+
+ align:start position:0%
+careful because you might write WR wrong
+things that technically would fit the
+
+ align:start position:0%
+things that technically would fit the
+ 
+
+ align:start position:0%
+things that technically would fit the
+definition same thing with Big O same
+
+ align:start position:0%
+definition same thing with Big O same
+ 
+
+ align:start position:0%
+definition same thing with Big O same
+same problem there any
+
+ align:start position:0%
+same problem there any
+ 
+
+ align:start position:0%
+same problem there any
+questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all
+
+ align:start position:0%
+that all
+ 
+
+ align:start position:0%
+that all
+right all right now one thing that
+
+ align:start position:0%
+right all right now one thing that
+ 
+
+ align:start position:0%
+right all right now one thing that
+people do all the time that you cannot
+
+ align:start position:0%
+people do all the time that you cannot
+ 
+
+ align:start position:0%
+people do all the time that you cannot
+do is to use Big O as a lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound all right so that's one abuse that
+
+ align:start position:0%
+bound all right so that's one abuse that
+ 
+
+ align:start position:0%
+bound all right so that's one abuse that
+we won't you'll get marked wrong for
+
+ align:start position:0%
+we won't you'll get marked wrong for
+ 
+
+ align:start position:0%
+we won't you'll get marked wrong for
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+that even though famous researchers will
+
+ align:start position:0%
+that even though famous researchers will
+ 
+
+ align:start position:0%
+that even though famous researchers will
+do it you'll probably even have a
+
+ align:start position:0%
+do it you'll probably even have a
+ 
+
+ align:start position:0%
+do it you'll probably even have a
+professor do it
+
+ align:start position:0%
+professor do it
+ 
+
+ align:start position:0%
+professor do it
+sometime
+
+ align:start position:0%
+sometime
+ 
+
+ align:start position:0%
+sometime
+uh so you may not do this F ofx is
+
+ align:start position:0%
+uh so you may not do this F ofx is
+ 
+
+ align:start position:0%
+uh so you may not do this F ofx is
+bigger than or equal to O of G of X that
+
+ align:start position:0%
+bigger than or equal to O of G of X that
+ 
+
+ align:start position:0%
+bigger than or equal to O of G of X that
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaningless because the whole point of
+
+ align:start position:0%
+meaningless because the whole point of
+ 
+
+ align:start position:0%
+meaningless because the whole point of
+Big O is that it's an upper bound so you
+
+ align:start position:0%
+Big O is that it's an upper bound so you
+ 
+
+ align:start position:0%
+Big O is that it's an upper bound so you
+can't use it as a lower bound and the
+
+ align:start position:0%
+can't use it as a lower bound and the
+ 
+
+ align:start position:0%
+can't use it as a lower bound and the
+reason you can't do it is because there
+
+ align:start position:0%
+reason you can't do it is because there
+ 
+
+ align:start position:0%
+reason you can't do it is because there
+is another symbol to do what you want to
+
+ align:start position:0%
+is another symbol to do what you want to
+ 
+
+ align:start position:0%
+is another symbol to do what you want to
+do and that's called the Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symbol and it's written like
+
+ align:start position:0%
+symbol and it's written like
+ 
+
+ align:start position:0%
+symbol and it's written like
+this it's a capital
+
+ align:start position:0%
+this it's a capital
+ 
+
+ align:start position:0%
+this it's a capital
+Omega and it's if the limit as X goes to
+
+ align:start position:0%
+Omega and it's if the limit as X goes to
+ 
+
+ align:start position:0%
+Omega and it's if the limit as X goes to
+Infinity of f ofx
+
+ align:start position:0%
+Infinity of f ofx
+ 
+
+ align:start position:0%
+Infinity of f ofx
+over G ofx is greater than
+
+ align:start position:0%
+over G ofx is greater than
+ 
+
+ align:start position:0%
+over G ofx is greater than
+zero okay so now we're getting the lower
+
+ align:start position:0%
+zero okay so now we're getting the lower
+ 
+
+ align:start position:0%
+zero okay so now we're getting the lower
+bound version in fact it's just the
+
+ align:start position:0%
+bound version in fact it's just the
+ 
+
+ align:start position:0%
+bound version in fact it's just the
+opposite of Big
+
+ align:start position:0%
+opposite of Big
+ 
+
+ align:start position:0%
+opposite of Big
+O fact state of theorem not hard to
+
+ align:start position:0%
+O fact state of theorem not hard to
+ 
+
+ align:start position:0%
+O fact state of theorem not hard to
+prove we won't do it f ofx equals o of G
+
+ align:start position:0%
+prove we won't do it f ofx equals o of G
+ 
+
+ align:start position:0%
+prove we won't do it f ofx equals o of G
+ofx if and only if G of x equals big
+
+ align:start position:0%
+ofx if and only if G of x equals big
+ 
+
+ align:start position:0%
+ofx if and only if G of x equals big
+Omega of f ofx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words F grows no faster than
+
+ align:start position:0%
+in other words F grows no faster than
+ 
+
+ align:start position:0%
+in other words F grows no faster than
+G if and only if G grows at least as
+
+ align:start position:0%
+G if and only if G grows at least as
+ 
+
+ align:start position:0%
+G if and only if G grows at least as
+fast as
+
+ align:start position:0%
+fast as
+ 
+
+ align:start position:0%
+fast as
+F one's an upper bound one's a lower
+
+ align:start position:0%
+F one's an upper bound one's a lower
+ 
+
+ align:start position:0%
+F one's an upper bound one's a lower
+bound and you just got to use the symbol
+
+ align:start position:0%
+bound and you just got to use the symbol
+ 
+
+ align:start position:0%
+bound and you just got to use the symbol
+the right way now you can do this you
+
+ align:start position:0%
+the right way now you can do this you
+ 
+
+ align:start position:0%
+the right way now you can do this you
+can write F ofx bigger than or equal to
+
+ align:start position:0%
+can write F ofx bigger than or equal to
+ 
+
+ align:start position:0%
+can write F ofx bigger than or equal to
+G of Omega G ofx that's
+
+ align:start position:0%
+G of Omega G ofx that's
+ 
+
+ align:start position:0%
+G of Omega G ofx that's
+okay all right that's all right to do
+
+ align:start position:0%
+okay all right that's all right to do
+ 
+
+ align:start position:0%
+okay all right that's all right to do
+all right let's do some examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so X2 is Omega of X because it grows
+
+ align:start position:0%
+so X2 is Omega of X because it grows
+ 
+
+ align:start position:0%
+so X2 is Omega of X because it grows
+faster than
+
+ align:start position:0%
+faster than
+ 
+
+ align:start position:0%
+faster than
+x 2 to the
+
+ align:start position:0%
+x 2 to the
+ 
+
+ align:start position:0%
+x 2 to the
+x is Omega of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x^2 all right
+
+ align:start position:0%
+x^2 all right
+ 
+
+ align:start position:0%
+x^2 all right
+X over
+
+ align:start position:0%
+X over
+ 
+
+ align:start position:0%
+X over
+100 is Omega of 100 x +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+25 because constants don't matter X over
+
+ align:start position:0%
+25 because constants don't matter X over
+ 
+
+ align:start position:0%
+25 because constants don't matter X over
+100 grows at least as fast as 100x does
+
+ align:start position:0%
+100 grows at least as fast as 100x does
+ 
+
+ align:start position:0%
+100 grows at least as fast as 100x does
+in terms because we're measuring the
+
+ align:start position:0%
+in terms because we're measuring the
+ 
+
+ align:start position:0%
+in terms because we're measuring the
+growth so constants go
+
+ align:start position:0%
+growth so constants go
+ 
+
+ align:start position:0%
+growth so constants go
+away if you want to say the running time
+
+ align:start position:0%
+away if you want to say the running time
+ 
+
+ align:start position:0%
+away if you want to say the running time
+of that algorithm is at least
+
+ align:start position:0%
+of that algorithm is at least
+ 
+
+ align:start position:0%
+of that algorithm is at least
+quadratic you would write T of n is
+
+ align:start position:0%
+quadratic you would write T of n is
+ 
+
+ align:start position:0%
+quadratic you would write T of n is
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+n^2 all right and that says that the
+
+ align:start position:0%
+n^2 all right and that says that the
+ 
+
+ align:start position:0%
+n^2 all right and that says that the
+running time is at least
+
+ align:start position:0%
+running time is at least
+ 
+
+ align:start position:0%
+running time is at least
+n^2 any questions on big
+
+ align:start position:0%
+n^2 any questions on big
+ 
+
+ align:start position:0%
+n^2 any questions on big
+Omega not too hard once you have big O
+
+ align:start position:0%
+Omega not too hard once you have big O
+ 
+
+ align:start position:0%
+Omega not too hard once you have big O
+it's just the
+
+ align:start position:0%
+it's just the
+ 
+
+ align:start position:0%
+it's just the
+opposite all right the next symbol is
+
+ align:start position:0%
+opposite all right the next symbol is
+ 
+
+ align:start position:0%
+opposite all right the next symbol is
+the version of equality where you're
+
+ align:start position:0%
+the version of equality where you're
+ 
+
+ align:start position:0%
+the version of equality where you're
+bigger at least as big as and at most as
+
+ align:start position:0%
+bigger at least as big as and at most as
+ 
+
+ align:start position:0%
+bigger at least as big as and at most as
+big as there's a special symbol for
+
+ align:start position:0%
+big as there's a special symbol for
+ 
+
+ align:start position:0%
+big as there's a special symbol for
+that so in that case we use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and we say that f ofx equals Theta
+
+ align:start position:0%
+Theta and we say that f ofx equals Theta
+ 
+
+ align:start position:0%
+Theta and we say that f ofx equals Theta
+of G
+
+ align:start position:0%
+of G
+ 
+
+ align:start position:0%
+of G
+ofx if the
+
+ align:start position:0%
+ofx if the
+ 
+
+ align:start position:0%
+ofx if the
+limit is both bigger than
+
+ align:start position:0%
+limit is both bigger than
+ 
+
+ align:start position:0%
+limit is both bigger than
+zero and less than
+
+ align:start position:0%
+zero and less than
+ 
+
+ align:start position:0%
+zero and less than
+infinity all right so it's just a
+
+ align:start position:0%
+infinity all right so it's just a
+ 
+
+ align:start position:0%
+infinity all right so it's just a
+shorthand way of saying Big O and big
+
+ align:start position:0%
+shorthand way of saying Big O and big
+ 
+
+ align:start position:0%
+shorthand way of saying Big O and big
+Omega that's what Theta means it just
+
+ align:start position:0%
+Omega that's what Theta means it just
+ 
+
+ align:start position:0%
+Omega that's what Theta means it just
+both hold
+
+ align:start position:0%
+both hold
+ 
+
+ align:start position:0%
+both hold
+true all right that's a theorem which is
+
+ align:start position:0%
+true all right that's a theorem which is
+ 
+
+ align:start position:0%
+true all right that's a theorem which is
+not hard to prove but we won't do it f
+
+ align:start position:0%
+not hard to prove but we won't do it f
+ 
+
+ align:start position:0%
+not hard to prove but we won't do it f
+ofx equals Theta of G
+
+ align:start position:0%
+ofx equals Theta of G
+ 
+
+ align:start position:0%
+ofx equals Theta of G
+ofx if and only
+
+ align:start position:0%
+ofx if and only
+ 
+
+ align:start position:0%
+ofx if and only
+if F ofx equal o of G
+
+ align:start position:0%
+if F ofx equal o of G
+ 
+
+ align:start position:0%
+if F ofx equal o of G
+ofx
+
+ align:start position:0%
+ofx
+ 
+
+ align:start position:0%
+ofx
+and F
+
+ align:start position:0%
+and F
+ 
+
+ align:start position:0%
+and F
+ofx equal Omega G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx all right so let's do some examples
+
+ align:start position:0%
+ofx all right so let's do some examples
+ 
+
+ align:start position:0%
+ofx all right so let's do some examples
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thea so for example 10 x Cub - 20x + 1
+
+ align:start position:0%
+Thea so for example 10 x Cub - 20x + 1
+ 
+
+ align:start position:0%
+Thea so for example 10 x Cub - 20x + 1
+is more easily written as Theta of X
+
+ align:start position:0%
+is more easily written as Theta of X
+ 
+
+ align:start position:0%
+is more easily written as Theta of X
+Cub because the constants don't matter
+
+ align:start position:0%
+Cub because the constants don't matter
+ 
+
+ align:start position:0%
+Cub because the constants don't matter
+the low or term terms don't matter what
+
+ align:start position:0%
+the low or term terms don't matter what
+ 
+
+ align:start position:0%
+the low or term terms don't matter what
+about this is X over log of
+
+ align:start position:0%
+about this is X over log of
+ 
+
+ align:start position:0%
+about this is X over log of
+x is that Theta of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x x over log of x is that Theta of
+
+ align:start position:0%
+x x over log of x is that Theta of
+ 
+
+ align:start position:0%
+x x over log of x is that Theta of
+X people are nodding their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heads let's see let's
+
+ align:start position:0%
+heads let's see let's
+ 
+
+ align:start position:0%
+heads let's see let's
+check um the limit as X goes to Infinity
+
+ align:start position:0%
+check um the limit as X goes to Infinity
+ 
+
+ align:start position:0%
+check um the limit as X goes to Infinity
+of X over log of x /
+
+ align:start position:0%
+of X over log of x /
+ 
+
+ align:start position:0%
+of X over log of x /
+X well the x is cancel that's the limit
+
+ align:start position:0%
+X well the x is cancel that's the limit
+ 
+
+ align:start position:0%
+X well the x is cancel that's the limit
+as X goes to Infinity of 1 over log of
+
+ align:start position:0%
+as X goes to Infinity of 1 over log of
+ 
+
+ align:start position:0%
+as X goes to Infinity of 1 over log of
+x what's
+
+ align:start position:0%
+x what's
+ 
+
+ align:start position:0%
+x what's
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+zero uh oh it is not Theta I got to be
+
+ align:start position:0%
+zero uh oh it is not Theta I got to be
+ 
+
+ align:start position:0%
+zero uh oh it is not Theta I got to be
+bigger than
+
+ align:start position:0%
+bigger than
+ 
+
+ align:start position:0%
+bigger than
+zero in
+
+ align:start position:0%
+zero in
+ 
+
+ align:start position:0%
+zero in
+fact this grows more slowly than that
+
+ align:start position:0%
+fact this grows more slowly than that
+ 
+
+ align:start position:0%
+fact this grows more slowly than that
+strictly more
+
+ align:start position:0%
+strictly more
+ 
+
+ align:start position:0%
+strictly more
+slowly all right a little more slowly
+
+ align:start position:0%
+slowly all right a little more slowly
+ 
+
+ align:start position:0%
+slowly all right a little more slowly
+but strictly more
+
+ align:start position:0%
+but strictly more
+ 
+
+ align:start position:0%
+but strictly more
+slowly all right if I use for an an
+
+ align:start position:0%
+slowly all right if I use for an an
+ 
+
+ align:start position:0%
+slowly all right if I use for an an
+algorithm if you want to say the
+
+ align:start position:0%
+algorithm if you want to say the
+ 
+
+ align:start position:0%
+algorithm if you want to say the
+algorithm runs in quadratic time namely
+
+ align:start position:0%
+algorithm runs in quadratic time namely
+ 
+
+ align:start position:0%
+algorithm runs in quadratic time namely
+at least quadratic time and at most
+
+ align:start position:0%
+at least quadratic time and at most
+ 
+
+ align:start position:0%
+at least quadratic time and at most
+quadratic time then you'd say t of n is
+
+ align:start position:0%
+quadratic time then you'd say t of n is
+ 
+
+ align:start position:0%
+quadratic time then you'd say t of n is
+Theta of
+
+ align:start position:0%
+Theta of
+ 
+
+ align:start position:0%
+Theta of
+n^2 so let me write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so T of Nal Theta
+
+ align:start position:0%
+that so T of Nal Theta
+ 
+
+ align:start position:0%
+that so T of Nal Theta
+N2
+
+ align:start position:0%
+N2
+ 
+
+ align:start position:0%
+N2
+means T
+
+ align:start position:0%
+means T
+ 
+
+ align:start position:0%
+means T
+grows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quadratically in
+
+ align:start position:0%
+quadratically in
+ 
+
+ align:start position:0%
+quadratically in
+N both upper and lower
+
+ align:start position:0%
+N both upper and lower
+ 
+
+ align:start position:0%
+N both upper and lower
+bound okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and for these three guys to
+
+ align:start position:0%
+so and for these three guys to
+ 
+
+ align:start position:0%
+so and for these three guys to
+summarize
+
+ align:start position:0%
+summarize
+ 
+
+ align:start position:0%
+summarize
+that's so you can keep track of them
+
+ align:start position:0%
+that's so you can keep track of them
+ 
+
+ align:start position:0%
+that's so you can keep track of them
+pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simply
+
+ align:start position:0%
+simply
+ 
+
+ align:start position:0%
+simply
+o
+
+ align:start position:0%
+o
+ 
+
+ align:start position:0%
+o
+means less than or equal Omega means
+
+ align:start position:0%
+means less than or equal Omega means
+ 
+
+ align:start position:0%
+means less than or equal Omega means
+greater than or equal Theta means equal
+
+ align:start position:0%
+greater than or equal Theta means equal
+ 
+
+ align:start position:0%
+greater than or equal Theta means equal
+up to constant factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there's two more symbols
+
+ align:start position:0%
+now there's two more symbols
+ 
+
+ align:start position:0%
+now there's two more symbols
+here and they correspond very naturally
+
+ align:start position:0%
+here and they correspond very naturally
+ 
+
+ align:start position:0%
+here and they correspond very naturally
+to this setup what two symbols are
+
+ align:start position:0%
+to this setup what two symbols are
+ 
+
+ align:start position:0%
+to this setup what two symbols are
+missing from here that would you
+
+ align:start position:0%
+missing from here that would you
+ 
+
+ align:start position:0%
+missing from here that would you
+naturally add to
+
+ align:start position:0%
+naturally add to
+ 
+
+ align:start position:0%
+naturally add to
+here yeah less than and greater than so
+
+ align:start position:0%
+here yeah less than and greater than so
+ 
+
+ align:start position:0%
+here yeah less than and greater than so
+less than is little
+
+ align:start position:0%
+less than is little
+ 
+
+ align:start position:0%
+less than is little
+o greater than is little
+
+ align:start position:0%
+o greater than is little
+ 
+
+ align:start position:0%
+o greater than is little
+Omega and less than means it's less than
+
+ align:start position:0%
+Omega and less than means it's less than
+ 
+
+ align:start position:0%
+Omega and less than means it's less than
+or equal but not equal and this means
+
+ align:start position:0%
+or equal but not equal and this means
+ 
+
+ align:start position:0%
+or equal but not equal and this means
+greater than or equal not
+
+ align:start position:0%
+greater than or equal not
+ 
+
+ align:start position:0%
+greater than or equal not
+equal and let me put them up over here
+
+ align:start position:0%
+equal and let me put them up over here
+ 
+
+ align:start position:0%
+equal and let me put them up over here
+and give you the formal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+racer okay so little o
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is we have f ofx equals little of G of
+
+ align:start position:0%
+is we have f ofx equals little of G of
+ 
+
+ align:start position:0%
+is we have f ofx equals little of G of
+x if the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit of f ofx over g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx equals zero so f is growing strictly
+
+ align:start position:0%
+ofx equals zero so f is growing strictly
+ 
+
+ align:start position:0%
+ofx equals zero so f is growing strictly
+smaller than G so that when I take the
+
+ align:start position:0%
+smaller than G so that when I take the
+ 
+
+ align:start position:0%
+smaller than G so that when I take the
+ratio the limit goes to zero and the
+
+ align:start position:0%
+ratio the limit goes to zero and the
+ 
+
+ align:start position:0%
+ratio the limit goes to zero and the
+reverse is little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega and we say that f ofx is little
+
+ align:start position:0%
+Omega and we say that f ofx is little
+ 
+
+ align:start position:0%
+Omega and we say that f ofx is little
+Omega whoops of G of
+
+ align:start position:0%
+Omega whoops of G of
+ 
+
+ align:start position:0%
+Omega whoops of G of
+x if this is
+
+ align:start position:0%
+x if this is
+ 
+
+ align:start position:0%
+x if this is
+infinity because now f is growing
+
+ align:start position:0%
+infinity because now f is growing
+ 
+
+ align:start position:0%
+infinity because now f is growing
+strictly faster than G so I take the
+
+ align:start position:0%
+strictly faster than G so I take the
+ 
+
+ align:start position:0%
+strictly faster than G so I take the
+limit of the ratio and it goes to
+
+ align:start position:0%
+limit of the ratio and it goes to
+ 
+
+ align:start position:0%
+limit of the ratio and it goes to
+Infinity all right so we can do some
+
+ align:start position:0%
+Infinity all right so we can do some
+ 
+
+ align:start position:0%
+Infinity all right so we can do some
+simple examples
+
+ align:start position:0%
+simple examples
+ 
+
+ align:start position:0%
+simple examples
+then we're almost done with all this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation what about this one X over Ln
+
+ align:start position:0%
+notation what about this one X over Ln
+ 
+
+ align:start position:0%
+notation what about this one X over Ln
+of X we just looked at
+
+ align:start position:0%
+of X we just looked at
+ 
+
+ align:start position:0%
+of X we just looked at
+it and x what symbol do I put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there what symbols missing
+
+ align:start position:0%
+there what symbols missing
+ 
+
+ align:start position:0%
+there what symbols missing
+here little little o this grows strictly
+
+ align:start position:0%
+here little little o this grows strictly
+ 
+
+ align:start position:0%
+here little little o this grows strictly
+smaller than that if I took the ratio
+
+ align:start position:0%
+smaller than that if I took the ratio
+ 
+
+ align:start position:0%
+smaller than that if I took the ratio
+and I took the limit we got zero so
+
+ align:start position:0%
+and I took the limit we got zero so
+ 
+
+ align:start position:0%
+and I took the limit we got zero so
+that's little
+
+ align:start position:0%
+that's little
+ 
+
+ align:start position:0%
+that's little
+o
+
+ align:start position:0%
+o
+ 
+
+ align:start position:0%
+o
+okay is this true X over 100 is that
+
+ align:start position:0%
+okay is this true X over 100 is that
+ 
+
+ align:start position:0%
+okay is this true X over 100 is that
+little o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+no the limit of the ratio is 1 over 100
+
+ align:start position:0%
+no the limit of the ratio is 1 over 100
+ 
+
+ align:start position:0%
+no the limit of the ratio is 1 over 100
+that's bigger than zero constants don't
+
+ align:start position:0%
+that's bigger than zero constants don't
+ 
+
+ align:start position:0%
+that's bigger than zero constants don't
+matter all right so what symbol would go
+
+ align:start position:0%
+matter all right so what symbol would go
+ 
+
+ align:start position:0%
+matter all right so what symbol would go
+here Theta goes here good also Big O and
+
+ align:start position:0%
+here Theta goes here good also Big O and
+ 
+
+ align:start position:0%
+here Theta goes here good also Big O and
+big Omega but Theta captures
+
+ align:start position:0%
+big Omega but Theta captures
+ 
+
+ align:start position:0%
+big Omega but Theta captures
+everything all right what symbol goes
+
+ align:start position:0%
+everything all right what symbol goes
+ 
+
+ align:start position:0%
+everything all right what symbol goes
+here X2 equals something
+
+ align:start position:0%
+here X2 equals something
+ 
+
+ align:start position:0%
+here X2 equals something
+x what symbol goes
+
+ align:start position:0%
+x what symbol goes
+ 
+
+ align:start position:0%
+x what symbol goes
+there little Omega you could would also
+
+ align:start position:0%
+there little Omega you could would also
+ 
+
+ align:start position:0%
+there little Omega you could would also
+be true to put big Omega but little
+
+ align:start position:0%
+be true to put big Omega but little
+ 
+
+ align:start position:0%
+be true to put big Omega but little
+Omega tells you more because the limit
+
+ align:start position:0%
+Omega tells you more because the limit
+ 
+
+ align:start position:0%
+Omega tells you more because the limit
+of x2x goes to
+
+ align:start position:0%
+of x2x goes to
+ 
+
+ align:start position:0%
+of x2x goes to
+Infinity okay any questions about these
+
+ align:start position:0%
+Infinity okay any questions about these
+ 
+
+ align:start position:0%
+Infinity okay any questions about these
+things so you know a natural thing on
+
+ align:start position:0%
+things so you know a natural thing on
+ 
+
+ align:start position:0%
+things so you know a natural thing on
+the midterm is we do some of that for
+
+ align:start position:0%
+the midterm is we do some of that for
+ 
+
+ align:start position:0%
+the midterm is we do some of that for
+example all right you'll certainly see
+
+ align:start position:0%
+example all right you'll certainly see
+ 
+
+ align:start position:0%
+example all right you'll certainly see
+some of that on
+
+ align:start position:0%
+some of that on
+ 
+
+ align:start position:0%
+some of that on
+homework you might see some of that on
+
+ align:start position:0%
+homework you might see some of that on
+ 
+
+ align:start position:0%
+homework you might see some of that on
+the test you'll certainly see all this
+
+ align:start position:0%
+the test you'll certainly see all this
+ 
+
+ align:start position:0%
+the test you'll certainly see all this
+stuff little Omega not very often in
+
+ align:start position:0%
+stuff little Omega not very often in
+ 
+
+ align:start position:0%
+stuff little Omega not very often in
+6046 and later algorithms courses but
+
+ align:start position:0%
+6046 and later algorithms courses but
+ 
+
+ align:start position:0%
+6046 and later algorithms courses but
+all the rest you'll see
+
+ align:start position:0%
+all the rest you'll see
+ 
+
+ align:start position:0%
+all the rest you'll see
+there any
+
+ align:start position:0%
+there any
+ 
+
+ align:start position:0%
+there any
+questions all right now I'm going to
+
+ align:start position:0%
+questions all right now I'm going to
+ 
+
+ align:start position:0%
+questions all right now I'm going to
+show you something that is sort of
+
+ align:start position:0%
+show you something that is sort of
+ 
+
+ align:start position:0%
+show you something that is sort of
+scary yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals little Omega it corresponds to a
+
+ align:start position:0%
+equals little Omega it corresponds to a
+ 
+
+ align:start position:0%
+equals little Omega it corresponds to a
+greater than which means a greater than
+
+ align:start position:0%
+greater than which means a greater than
+ 
+
+ align:start position:0%
+greater than which means a greater than
+or equal to but not an equal
+
+ align:start position:0%
+or equal to but not an equal
+ 
+
+ align:start position:0%
+or equal to but not an equal
+to and the way we can see that is
+
+ align:start position:0%
+to and the way we can see that is
+ 
+
+ align:start position:0%
+to and the way we can see that is
+looking at the definitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and the greater than or equal to is
+
+ align:start position:0%
+here and the greater than or equal to is
+ 
+
+ align:start position:0%
+here and the greater than or equal to is
+the big Omega
+
+ align:start position:0%
+the big Omega
+ 
+
+ align:start position:0%
+the big Omega
+and that just
+
+ align:start position:0%
+and that just
+ 
+
+ align:start position:0%
+and that just
+says you're bigger than
+
+ align:start position:0%
+says you're bigger than
+ 
+
+ align:start position:0%
+says you're bigger than
+zero uh let's see right so I'm bigger
+
+ align:start position:0%
+zero uh let's see right so I'm bigger
+ 
+
+ align:start position:0%
+zero uh let's see right so I'm bigger
+than or equal to is Omega but I'm not
+
+ align:start position:0%
+than or equal to is Omega but I'm not
+ 
+
+ align:start position:0%
+than or equal to is Omega but I'm not
+equal to which is
+
+ align:start position:0%
+equal to which is
+ 
+
+ align:start position:0%
+equal to which is
+Theta so if I know that I'm this but not
+
+ align:start position:0%
+Theta so if I know that I'm this but not
+ 
+
+ align:start position:0%
+Theta so if I know that I'm this but not
+that the only conclusion is that I'm
+
+ align:start position:0%
+that the only conclusion is that I'm
+ 
+
+ align:start position:0%
+that the only conclusion is that I'm
+Infinity in the
+
+ align:start position:0%
+Infinity in the
+ 
+
+ align:start position:0%
+Infinity in the
+ratio all right so that's another way of
+
+ align:start position:0%
+ratio all right so that's another way of
+ 
+
+ align:start position:0%
+ratio all right so that's another way of
+saying it that's why
+
+ align:start position:0%
+saying it that's why
+ 
+
+ align:start position:0%
+saying it that's why
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right now I'm going to
+
+ align:start position:0%
+questions all right now I'm going to
+ 
+
+ align:start position:0%
+questions all right now I'm going to
+show you something that is commonly done
+
+ align:start position:0%
+show you something that is commonly done
+ 
+
+ align:start position:0%
+show you something that is commonly done
+and that many students will attempt to
+
+ align:start position:0%
+and that many students will attempt to
+ 
+
+ align:start position:0%
+and that many students will attempt to
+do after seeing this notation because a
+
+ align:start position:0%
+do after seeing this notation because a
+ 
+
+ align:start position:0%
+do after seeing this notation because a
+notation is pretty simple take your
+
+ align:start position:0%
+notation is pretty simple take your
+ 
+
+ align:start position:0%
+notation is pretty simple take your
+limits everything you know goes fine
+
+ align:start position:0%
+limits everything you know goes fine
+ 
+
+ align:start position:0%
+limits everything you know goes fine
+then you start you know cruising along
+
+ align:start position:0%
+then you start you know cruising along
+ 
+
+ align:start position:0%
+then you start you know cruising along
+with it so now I'm going to show you how
+
+ align:start position:0%
+with it so now I'm going to show you how
+ 
+
+ align:start position:0%
+with it so now I'm going to show you how
+to prove something that's false using
+
+ align:start position:0%
+to prove something that's false using
+ 
+
+ align:start position:0%
+to prove something that's false using
+this notation in a way that people often
+
+ align:start position:0%
+this notation in a way that people often
+ 
+
+ align:start position:0%
+this notation in a way that people often
+do and the hope is by showing you you
+
+ align:start position:0%
+do and the hope is by showing you you
+ 
+
+ align:start position:0%
+do and the hope is by showing you you
+won't do it
+
+ align:start position:0%
+won't do it
+ 
+
+ align:start position:0%
+won't do it
+it will confuse you which is why
+
+ align:start position:0%
+it will confuse you which is why
+ 
+
+ align:start position:0%
+it will confuse you which is why
+sometimes we worry about showing you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but let F of i f of
+
+ align:start position:0%
+but let F of i f of
+ 
+
+ align:start position:0%
+but let F of i f of
+n equal the sum I = 1 to n of
+
+ align:start position:0%
+n equal the sum I = 1 to n of
+ 
+
+ align:start position:0%
+n equal the sum I = 1 to n of
+I now we all know what that is
+
+ align:start position:0%
+I now we all know what that is
+ 
+
+ align:start position:0%
+I now we all know what that is
+right all right so I'm going to prove to
+
+ align:start position:0%
+right all right so I'm going to prove to
+ 
+
+ align:start position:0%
+right all right so I'm going to prove to
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that F of n is O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n now what really what what should be
+
+ align:start position:0%
+n now what really what what should be
+ 
+
+ align:start position:0%
+n now what really what what should be
+here instead of
+
+ align:start position:0%
+here instead of
+ 
+
+ align:start position:0%
+here instead of
+n n s so it can't n squ can't be o of n
+
+ align:start position:0%
+n n s so it can't n squ can't be o of n
+ 
+
+ align:start position:0%
+n n s so it can't n squ can't be o of n
+so this can't be true all right well
+
+ align:start position:0%
+so this can't be true all right well
+ 
+
+ align:start position:0%
+so this can't be true all right well
+let's see how we do
+
+ align:start position:0%
+let's see how we do
+ 
+
+ align:start position:0%
+let's see how we do
+it all right so the false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof is by induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+N my induction
+
+ align:start position:0%
+N my induction
+ 
+
+ align:start position:0%
+N my induction
+hypothesis is p of n is going to be that
+
+ align:start position:0%
+hypothesis is p of n is going to be that
+ 
+
+ align:start position:0%
+hypothesis is p of n is going to be that
+F of
+
+ align:start position:0%
+F of
+ 
+
+ align:start position:0%
+F of
+n is O of
+
+ align:start position:0%
+n is O of
+ 
+
+ align:start position:0%
+n is O of
+n right that's what we when we want to
+
+ align:start position:0%
+n right that's what we when we want to
+ 
+
+ align:start position:0%
+n right that's what we when we want to
+prove something by induction typically
+
+ align:start position:0%
+prove something by induction typically
+ 
+
+ align:start position:0%
+prove something by induction typically
+that's what you do becomes the induction
+
+ align:start position:0%
+that's what you do becomes the induction
+ 
+
+ align:start position:0%
+that's what you do becomes the induction
+hypothesis let's look at the base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case well well F of
+
+ align:start position:0%
+case well well F of
+ 
+
+ align:start position:0%
+case well well F of
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+one and one is O of one
+
+ align:start position:0%
+one and one is O of one
+ 
+
+ align:start position:0%
+one and one is O of one
+surely right even 10 was O of
+
+ align:start position:0%
+surely right even 10 was O of
+ 
+
+ align:start position:0%
+surely right even 10 was O of
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right now we do the inductive
+
+ align:start position:0%
+okay all right now we do the inductive
+ 
+
+ align:start position:0%
+okay all right now we do the inductive
+step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+assume PN is
+
+ align:start position:0%
+assume PN is
+ 
+
+ align:start position:0%
+assume PN is
+true to
+
+ align:start position:0%
+true to
+ 
+
+ align:start position:0%
+true to
+prove PN + one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true well
+
+ align:start position:0%
+true well
+ 
+
+ align:start position:0%
+true well
+PN means that F of n is O of
+
+ align:start position:0%
+PN means that F of n is O of
+ 
+
+ align:start position:0%
+PN means that F of n is O of
+n now I look at F of n +
+
+ align:start position:0%
+n now I look at F of n +
+ 
+
+ align:start position:0%
+n now I look at F of n +
+one that equals the sum of the first n+
+
+ align:start position:0%
+one that equals the sum of the first n+
+ 
+
+ align:start position:0%
+one that equals the sum of the first n+
+one number so that'll be f n plus n
+
+ align:start position:0%
+one number so that'll be f n plus n
+ 
+
+ align:start position:0%
+one number so that'll be f n plus n
++1 the induction hypothesis says this is
+
+ align:start position:0%
++1 the induction hypothesis says this is
+ 
+
+ align:start position:0%
++1 the induction hypothesis says this is
+O of
+
+ align:start position:0%
+O of
+ 
+
+ align:start position:0%
+O of
+n clearly this is O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n well I got o of n plus o of n that's
+
+ align:start position:0%
+n well I got o of n plus o of n that's
+ 
+
+ align:start position:0%
+n well I got o of n plus o of n that's
+at most twice o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N and constants don't matter so that's o
+
+ align:start position:0%
+N and constants don't matter so that's o
+ 
+
+ align:start position:0%
+N and constants don't matter so that's o
+of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right this
+
+ align:start position:0%
+all right this
+ 
+
+ align:start position:0%
+all right this
+should begin to cause Panic you know I
+
+ align:start position:0%
+should begin to cause Panic you know I
+ 
+
+ align:start position:0%
+should begin to cause Panic you know I
+don't is induction wrong what's going on
+
+ align:start position:0%
+don't is induction wrong what's going on
+ 
+
+ align:start position:0%
+don't is induction wrong what's going on
+with a big
+
+ align:start position:0%
+with a big
+ 
+
+ align:start position:0%
+with a big
+O you will see this done all the time
+
+ align:start position:0%
+O you will see this done all the time
+ 
+
+ align:start position:0%
+O you will see this done all the time
+people will will do this kind of an
+
+ align:start position:0%
+people will will do this kind of an
+ 
+
+ align:start position:0%
+people will will do this kind of an
+argument looks pretty good
+
+ align:start position:0%
+argument looks pretty good
+ 
+
+ align:start position:0%
+argument looks pretty good
+right can anybody see
+
+ align:start position:0%
+right can anybody see
+ 
+
+ align:start position:0%
+right can anybody see
+where I got off track this is a really
+
+ align:start position:0%
+where I got off track this is a really
+ 
+
+ align:start position:0%
+where I got off track this is a really
+hard one to figure out where things went
+
+ align:start position:0%
+hard one to figure out where things went
+ 
+
+ align:start position:0%
+hard one to figure out where things went
+wrong yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great that's a great observation ASM
+
+ align:start position:0%
+great that's a great observation ASM
+ 
+
+ align:start position:0%
+great that's a great observation ASM
+totic
+
+ align:start position:0%
+totic
+ 
+
+ align:start position:0%
+totic
+notation only works for functions now
+
+ align:start position:0%
+notation only works for functions now
+ 
+
+ align:start position:0%
+notation only works for functions now
+here when we say one is O of one well
+
+ align:start position:0%
+here when we say one is O of one well
+ 
+
+ align:start position:0%
+here when we say one is O of one well
+you could think of it as F ofx being one
+
+ align:start position:0%
+you could think of it as F ofx being one
+ 
+
+ align:start position:0%
+you could think of it as F ofx being one
+the function and so forth so that's okay
+
+ align:start position:0%
+the function and so forth so that's okay
+ 
+
+ align:start position:0%
+the function and so forth so that's okay
+that's a great point now let's figure
+
+ align:start position:0%
+that's a great point now let's figure
+ 
+
+ align:start position:0%
+that's a great point now let's figure
+out using that how we got in trouble
+
+ align:start position:0%
+out using that how we got in trouble
+ 
+
+ align:start position:0%
+out using that how we got in trouble
+we're not quite done yet that's a great
+
+ align:start position:0%
+we're not quite done yet that's a great
+ 
+
+ align:start position:0%
+we're not quite done yet that's a great
+observation but how does where's the
+
+ align:start position:0%
+observation but how does where's the
+ 
+
+ align:start position:0%
+observation but how does where's the
+step that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong uh no 2 * o of n is O of n if I
+
+ align:start position:0%
+wrong uh no 2 * o of n is O of n if I
+ 
+
+ align:start position:0%
+wrong uh no 2 * o of n is O of n if I
+have a function that's f is O of G twice
+
+ align:start position:0%
+have a function that's f is O of G twice
+ 
+
+ align:start position:0%
+have a function that's f is O of G twice
+f is O of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah is it so what what's the problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now well F of n plus one this statement
+
+ align:start position:0%
+now well F of n plus one this statement
+ 
+
+ align:start position:0%
+now well F of n plus one this statement
+is true because F of n + 1 is the sum of
+
+ align:start position:0%
+is true because F of n + 1 is the sum of
+ 
+
+ align:start position:0%
+is true because F of n + 1 is the sum of
+I = 1 to n + 1 of I that's 1 + 2 + n + n
+
+ align:start position:0%
+I = 1 to n + 1 of I that's 1 + 2 + n + n
+ 
+
+ align:start position:0%
+I = 1 to n + 1 of I that's 1 + 2 + n + n
++ 1 and this is f of
+
+ align:start position:0%
++ 1 and this is f of
+ 
+
+ align:start position:0%
++ 1 and this is f of
+n so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you know uh you're getting
+
+ align:start position:0%
+yeah you know uh you're getting
+ 
+
+ align:start position:0%
+yeah you know uh you're getting
+closer yeah I've only got a yeah sort of
+
+ align:start position:0%
+closer yeah I've only got a yeah sort of
+ 
+
+ align:start position:0%
+closer yeah I've only got a yeah sort of
+that's a little flaky because I've just
+
+ align:start position:0%
+that's a little flaky because I've just
+ 
+
+ align:start position:0%
+that's a little flaky because I've just
+got a single value saying it's O of one
+
+ align:start position:0%
+got a single value saying it's O of one
+ 
+
+ align:start position:0%
+got a single value saying it's O of one
+but we sort of argued before that 10 was
+
+ align:start position:0%
+but we sort of argued before that 10 was
+ 
+
+ align:start position:0%
+but we sort of argued before that 10 was
+O of one now really there's a function
+
+ align:start position:0%
+O of one now really there's a function
+ 
+
+ align:start position:0%
+O of one now really there's a function
+behind here that matters so you're on
+
+ align:start position:0%
+behind here that matters so you're on
+ 
+
+ align:start position:0%
+behind here that matters so you're on
+the right Trail but there's an even
+
+ align:start position:0%
+the right Trail but there's an even
+ 
+
+ align:start position:0%
+the right Trail but there's an even
+bigger Whopper hiding
+
+ align:start position:0%
+bigger Whopper hiding
+ 
+
+ align:start position:0%
+bigger Whopper hiding
+yeah oh yeah this is really really
+
+ align:start position:0%
+yeah oh yeah this is really really
+ 
+
+ align:start position:0%
+yeah oh yeah this is really really
+bad all right so now explain to me why
+
+ align:start position:0%
+bad all right so now explain to me why
+ 
+
+ align:start position:0%
+bad all right so now explain to me why
+this is really bad what I did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here yeah and why isn't this looks like
+
+ align:start position:0%
+here yeah and why isn't this looks like
+ 
+
+ align:start position:0%
+here yeah and why isn't this looks like
+a function why isn't it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function it's not but it looks like one
+
+ align:start position:0%
+function it's not but it looks like one
+ 
+
+ align:start position:0%
+function it's not but it looks like one
+F of n sure looks like one why is it not
+
+ align:start position:0%
+F of n sure looks like one why is it not
+ 
+
+ align:start position:0%
+F of n sure looks like one why is it not
+a function when it's sitting in this
+
+ align:start position:0%
+a function when it's sitting in this
+ 
+
+ align:start position:0%
+a function when it's sitting in this
+thing because P of
+
+ align:start position:0%
+thing because P of
+ 
+
+ align:start position:0%
+thing because P of
+n right because I've fixed the value of
+
+ align:start position:0%
+n right because I've fixed the value of
+ 
+
+ align:start position:0%
+n right because I've fixed the value of
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+here and so this is now just to scaler
+
+ align:start position:0%
+here and so this is now just to scaler
+ 
+
+ align:start position:0%
+here and so this is now just to scaler
+in fact you know I could State the
+
+ align:start position:0%
+in fact you know I could State the
+ 
+
+ align:start position:0%
+in fact you know I could State the
+following F of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+million right is O of one because this
+
+ align:start position:0%
+million right is O of one because this
+ 
+
+ align:start position:0%
+million right is O of one because this
+is really some function H ofx that
+
+ align:start position:0%
+is really some function H ofx that
+ 
+
+ align:start position:0%
+is really some function H ofx that
+always is this value it's a difference
+
+ align:start position:0%
+always is this value it's a difference
+ 
+
+ align:start position:0%
+always is this value it's a difference
+between a scalar and a function and this
+
+ align:start position:0%
+between a scalar and a function and this
+ 
+
+ align:start position:0%
+between a scalar and a function and this
+is just so nasty looking because we see
+
+ align:start position:0%
+is just so nasty looking because we see
+ 
+
+ align:start position:0%
+is just so nasty looking because we see
+F ofn that's a function but you can
+
+ align:start position:0%
+F ofn that's a function but you can
+ 
+
+ align:start position:0%
+F ofn that's a function but you can
+never use Big O in a predicate
+
+ align:start position:0%
+never use Big O in a predicate
+ 
+
+ align:start position:0%
+never use Big O in a predicate
+right because we've lost the function
+
+ align:start position:0%
+right because we've lost the function
+ 
+
+ align:start position:0%
+right because we've lost the function
+here this is just the F evalu at n
+
+ align:start position:0%
+here this is just the F evalu at n
+ 
+
+ align:start position:0%
+here this is just the F evalu at n
+period the only that single instance is
+
+ align:start position:0%
+period the only that single instance is
+ 
+
+ align:start position:0%
+period the only that single instance is
+all that's happened here it's not a
+
+ align:start position:0%
+all that's happened here it's not a
+ 
+
+ align:start position:0%
+all that's happened here it's not a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+anymore all right if you know if we had
+
+ align:start position:0%
+anymore all right if you know if we had
+ 
+
+ align:start position:0%
+anymore all right if you know if we had
+FN of X or something that might be okay
+
+ align:start position:0%
+FN of X or something that might be okay
+ 
+
+ align:start position:0%
+FN of X or something that might be okay
+but there's no function left all right
+
+ align:start position:0%
+but there's no function left all right
+ 
+
+ align:start position:0%
+but there's no function left all right
+so never ever use asymptotic notation
+
+ align:start position:0%
+so never ever use asymptotic notation
+ 
+
+ align:start position:0%
+so never ever use asymptotic notation
+with inductive proofs because you will
+
+ align:start position:0%
+with inductive proofs because you will
+ 
+
+ align:start position:0%
+with inductive proofs because you will
+just invariably stick Big O into your
+
+ align:start position:0%
+just invariably stick Big O into your
+ 
+
+ align:start position:0%
+just invariably stick Big O into your
+predicate and you can prove all sorts of
+
+ align:start position:0%
+predicate and you can prove all sorts of
+ 
+
+ align:start position:0%
+predicate and you can prove all sorts of
+false things once you do
+
+ align:start position:0%
+false things once you do
+ 
+
+ align:start position:0%
+false things once you do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay all right never use ASM totic
+
+ align:start position:0%
+okay all right never use ASM totic
+ 
+
+ align:start position:0%
+okay all right never use ASM totic
+notation in induction or predicates
+
+ align:start position:0%
+notation in induction or predicates
+ 
+
+ align:start position:0%
+notation in induction or predicates
+thanks
\ No newline at end of file
diff --git a/XQKV-hpsurs.txt b/XQKV-hpsurs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d710d804df79dafae4efcd9f655b457df98603c3
--- /dev/null
+++ b/XQKV-hpsurs.txt
@@ -0,0 +1,3547 @@
+align:start position:0%
+ 
+expectation
+
+ align:start position:0%
+expectation
+ 
+
+ align:start position:0%
+expectation
+values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation values of
+
+ align:start position:0%
+expectation values of
+ 
+
+ align:start position:0%
+expectation values of
+operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators so this is in a sense one of
+
+ align:start position:0%
+operators so this is in a sense one of
+ 
+
+ align:start position:0%
+operators so this is in a sense one of
+our first steps that we're going to take
+
+ align:start position:0%
+our first steps that we're going to take
+ 
+
+ align:start position:0%
+our first steps that we're going to take
+towards the interpretation of quantum
+
+ align:start position:0%
+towards the interpretation of quantum
+ 
+
+ align:start position:0%
+towards the interpretation of quantum
+mechanics we've had already that the way
+
+ align:start position:0%
+mechanics we've had already that the way
+ 
+
+ align:start position:0%
+mechanics we've had already that the way
+function tells you about probabilities
+
+ align:start position:0%
+function tells you about probabilities
+ 
+
+ align:start position:0%
+function tells you about probabilities
+but that's not quite enough to have the
+
+ align:start position:0%
+but that's not quite enough to have the
+ 
+
+ align:start position:0%
+but that's not quite enough to have the
+full interpretation of what we're doing
+
+ align:start position:0%
+full interpretation of what we're doing
+ 
+
+ align:start position:0%
+full interpretation of what we're doing
+so let's uh think of operators and
+
+ align:start position:0%
+so let's uh think of operators and
+ 
+
+ align:start position:0%
+so let's uh think of operators and
+expectation values that we can motivate
+
+ align:start position:0%
+expectation values that we can motivate
+ 
+
+ align:start position:0%
+expectation values that we can motivate
+so for example if you have a random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+q that can take values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this could be a coin that can take
+
+ align:start position:0%
+so this could be a coin that can take
+ 
+
+ align:start position:0%
+so this could be a coin that can take
+values head and tail could be a pair of
+
+ align:start position:0%
+values head and tail could be a pair of
+ 
+
+ align:start position:0%
+values head and tail could be a pair of
+D that takes many values of can take
+
+ align:start position:0%
+D that takes many values of can take
+ 
+
+ align:start position:0%
+D that takes many values of can take
+values in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set q1 up to
+
+ align:start position:0%
+set q1 up to
+ 
+
+ align:start position:0%
+set q1 up to
+qn with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+abilities p
+
+ align:start position:0%
+abilities p
+ 
+
+ align:start position:0%
+abilities p
+P1 up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PN then in statistics or in
+
+ align:start position:0%
+PN then in statistics or in
+ 
+
+ align:start position:0%
+PN then in statistics or in
+8044 uh you would say that this variable
+
+ align:start position:0%
+8044 uh you would say that this variable
+ 
+
+ align:start position:0%
+8044 uh you would say that this variable
+this random variable has an expectation
+
+ align:start position:0%
+this random variable has an expectation
+ 
+
+ align:start position:0%
+this random variable has an expectation
+value and the expectation
+
+ align:start position:0%
+value and the expectation
+ 
+
+ align:start position:0%
+value and the expectation
+value denoted by this um
+
+ align:start position:0%
+value denoted by this um
+ 
+
+ align:start position:0%
+value denoted by this um
+angular symbols over here left and right
+
+ align:start position:0%
+angular symbols over here left and right
+ 
+
+ align:start position:0%
+angular symbols over here left and right
+um it's given by the sum over I IAL 1 to
+
+ align:start position:0%
+um it's given by the sum over I IAL 1 to
+ 
+
+ align:start position:0%
+um it's given by the sum over I IAL 1 to
+n of the possible values the random
+
+ align:start position:0%
+n of the possible values the random
+ 
+
+ align:start position:0%
+n of the possible values the random
+variable can take times the
+
+ align:start position:0%
+variable can take times the
+ 
+
+ align:start position:0%
+variable can take times the
+probabilities it's a
+
+ align:start position:0%
+probabilities it's a
+ 
+
+ align:start position:0%
+probabilities it's a
+definition that makes sense and it's
+
+ align:start position:0%
+definition that makes sense and it's
+ 
+
+ align:start position:0%
+definition that makes sense and it's
+thought to be this expectation value is
+
+ align:start position:0%
+thought to be this expectation value is
+ 
+
+ align:start position:0%
+thought to be this expectation value is
+the expected value or average value that
+
+ align:start position:0%
+the expected value or average value that
+ 
+
+ align:start position:0%
+the expected value or average value that
+you would obtain if you did the
+
+ align:start position:0%
+you would obtain if you did the
+ 
+
+ align:start position:0%
+you would obtain if you did the
+experiment of tossing the random
+
+ align:start position:0%
+experiment of tossing the random
+ 
+
+ align:start position:0%
+experiment of tossing the random
+variable many times for each value of
+
+ align:start position:0%
+variable many times for each value of
+ 
+
+ align:start position:0%
+variable many times for each value of
+the random variable you multiply by the
+
+ align:start position:0%
+the random variable you multiply by the
+ 
+
+ align:start position:0%
+the random variable you multiply by the
+probability and that's the number you
+
+ align:start position:0%
+probability and that's the number you
+ 
+
+ align:start position:0%
+probability and that's the number you
+expect to
+
+ align:start position:0%
+expect to
+ 
+
+ align:start position:0%
+expect to
+get so in a Quantum system we follow
+
+ align:start position:0%
+get so in a Quantum system we follow
+ 
+
+ align:start position:0%
+get so in a Quantum system we follow
+this analogy very closely so what do we
+
+ align:start position:0%
+this analogy very closely so what do we
+ 
+
+ align:start position:0%
+this analogy very closely so what do we
+have in a Quantum system in a Quantum
+
+ align:start position:0%
+have in a Quantum system in a Quantum
+ 
+
+ align:start position:0%
+have in a Quantum system in a Quantum
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system you have that s
+
+ align:start position:0%
+system you have that s
+ 
+
+ align:start position:0%
+system you have that s
+star of
+
+ align:start position:0%
+star of
+ 
+
+ align:start position:0%
+star of
+x and t now SI of x and t
+
+ align:start position:0%
+x and t now SI of x and t
+ 
+
+ align:start position:0%
+x and t now SI of x and t
+DX is the
+
+ align:start position:0%
+DX is the
+ 
+
+ align:start position:0%
+DX is the
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+particle is
+
+ align:start position:0%
+particle is
+ 
+
+ align:start position:0%
+particle is
+in X comma x +
+
+ align:start position:0%
+in X comma x +
+ 
+
+ align:start position:0%
+in X comma x +
+DX okay so that's the probability that
+
+ align:start position:0%
+DX okay so that's the probability that
+ 
+
+ align:start position:0%
+DX okay so that's the probability that
+the particle is going to be found
+
+ align:start position:0%
+the particle is going to be found
+ 
+
+ align:start position:0%
+the particle is going to be found
+between X and X Plus DX the position of
+
+ align:start position:0%
+between X and X Plus DX the position of
+ 
+
+ align:start position:0%
+between X and X Plus DX the position of
+this particle is like a random variable
+
+ align:start position:0%
+this particle is like a random variable
+ 
+
+ align:start position:0%
+this particle is like a random variable
+you never know where you're going to
+
+ align:start position:0%
+you never know where you're going to
+ 
+
+ align:start position:0%
+you never know where you're going to
+find it but it has different
+
+ align:start position:0%
+find it but it has different
+ 
+
+ align:start position:0%
+find it but it has different
+probabilities to find it so we could now
+
+ align:start position:0%
+probabilities to find it so we could now
+ 
+
+ align:start position:0%
+probabilities to find it so we could now
+Define in complete analogy to here the
+
+ align:start position:0%
+Define in complete analogy to here the
+ 
+
+ align:start position:0%
+Define in complete analogy to here the
+expectation value of the position
+
+ align:start position:0%
+expectation value of the position
+ 
+
+ align:start position:0%
+expectation value of the position
+operator or the expectation value of the
+
+ align:start position:0%
+operator or the expectation value of the
+ 
+
+ align:start position:0%
+operator or the expectation value of the
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+expectation
+
+ align:start position:0%
+expectation
+ 
+
+ align:start position:0%
+expectation
+value of x hat or the position and say
+
+ align:start position:0%
+value of x hat or the position and say
+ 
+
+ align:start position:0%
+value of x hat or the position and say
+well I'm going to do exactly what I'm
+
+ align:start position:0%
+well I'm going to do exactly what I'm
+ 
+
+ align:start position:0%
+well I'm going to do exactly what I'm
+have here I will
+
+ align:start position:0%
+have here I will
+ 
+
+ align:start position:0%
+have here I will
+sum the products of the position times
+
+ align:start position:0%
+sum the products of the position times
+ 
+
+ align:start position:0%
+sum the products of the position times
+the probability for the position so I
+
+ align:start position:0%
+the probability for the position so I
+ 
+
+ align:start position:0%
+the probability for the position so I
+have to do it as an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral and in this integral I have to
+
+ align:start position:0%
+integral and in this integral I have to
+ 
+
+ align:start position:0%
+integral and in this integral I have to
+multiply the
+
+ align:start position:0%
+multiply the
+ 
+
+ align:start position:0%
+multiply the
+position times the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position so the probability that it is
+
+ align:start position:0%
+position so the probability that it is
+ 
+
+ align:start position:0%
+position so the probability that it is
+takes a value
+
+ align:start position:0%
+takes a value
+ 
+
+ align:start position:0%
+takes a value
+X basically or that is in the
+
+ align:start position:0%
+X basically or that is in the
+ 
+
+ align:start position:0%
+X basically or that is in the
+interval DX X about X is this quantity
+
+ align:start position:0%
+interval DX X about X is this quantity
+ 
+
+ align:start position:0%
+interval DX X about X is this quantity
+and that's the position that you get
+
+ align:start position:0%
+and that's the position that you get
+ 
+
+ align:start position:0%
+and that's the position that you get
+when you estimate this probability so
+
+ align:start position:0%
+when you estimate this probability so
+ 
+
+ align:start position:0%
+when you estimate this probability so
+you must sum the values of the random
+
+ align:start position:0%
+you must sum the values of the random
+ 
+
+ align:start position:0%
+you must sum the values of the random
+variable times its
+
+ align:start position:0%
+variable times its
+ 
+
+ align:start position:0%
+variable times its
+probability and that is taken in quantum
+
+ align:start position:0%
+probability and that is taken in quantum
+ 
+
+ align:start position:0%
+probability and that is taken in quantum
+mechanics to be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition we can def find the
+
+ align:start position:0%
+definition we can def find the
+ 
+
+ align:start position:0%
+definition we can def find the
+expectation value of x by this
+
+ align:start position:0%
+expectation value of x by this
+ 
+
+ align:start position:0%
+expectation value of x by this
+quantity and what does it mean
+
+ align:start position:0%
+quantity and what does it mean
+ 
+
+ align:start position:0%
+quantity and what does it mean
+experimentally it means that in quantum
+
+ align:start position:0%
+experimentally it means that in quantum
+ 
+
+ align:start position:0%
+experimentally it means that in quantum
+mechanics if you have a system
+
+ align:start position:0%
+mechanics if you have a system
+ 
+
+ align:start position:0%
+mechanics if you have a system
+represented by a wave function you
+
+ align:start position:0%
+represented by a wave function you
+ 
+
+ align:start position:0%
+represented by a wave function you
+should build many copies of the system
+
+ align:start position:0%
+should build many copies of the system
+ 
+
+ align:start position:0%
+should build many copies of the system
+100 copies of the system in all of these
+
+ align:start position:0%
+100 copies of the system in all of these
+ 
+
+ align:start position:0%
+100 copies of the system in all of these
+copies you measure the position and you
+
+ align:start position:0%
+copies you measure the position and you
+ 
+
+ align:start position:0%
+copies you measure the position and you
+make a table of the values that you
+
+ align:start position:0%
+make a table of the values that you
+ 
+
+ align:start position:0%
+make a table of the values that you
+measure the position and you measure
+
+ align:start position:0%
+measure the position and you measure
+ 
+
+ align:start position:0%
+measure the position and you measure
+them at the same time in the 100 copies
+
+ align:start position:0%
+them at the same time in the 100 copies
+ 
+
+ align:start position:0%
+them at the same time in the 100 copies
+there's an experimental list on each one
+
+ align:start position:0%
+there's an experimental list on each one
+ 
+
+ align:start position:0%
+there's an experimental list on each one
+and it measures the position of X you
+
+ align:start position:0%
+and it measures the position of X you
+ 
+
+ align:start position:0%
+and it measures the position of X you
+construct the table take the average and
+
+ align:start position:0%
+construct the table take the average and
+ 
+
+ align:start position:0%
+construct the table take the average and
+that's what this quantity should be
+
+ align:start position:0%
+that's what this quantity should be
+ 
+
+ align:start position:0%
+that's what this quantity should be
+telling
+
+ align:start position:0%
+telling
+ 
+
+ align:start position:0%
+telling
+you so this quantity as you can see may
+
+ align:start position:0%
+you so this quantity as you can see may
+ 
+
+ align:start position:0%
+you so this quantity as you can see may
+depend on
+
+ align:start position:0%
+depend on
+ 
+
+ align:start position:0%
+depend on
+time may depend on time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it does give
+
+ align:start position:0%
+but it does give
+ 
+
+ align:start position:0%
+but it does give
+you the interpretation of uh expected
+
+ align:start position:0%
+you the interpretation of uh expected
+ 
+
+ align:start position:0%
+you the interpretation of uh expected
+value coinciding with a system now the
+
+ align:start position:0%
+value coinciding with a system now the
+ 
+
+ align:start position:0%
+value coinciding with a system now the
+quantum mechanical system for which the
+
+ align:start position:0%
+quantum mechanical system for which the
+ 
+
+ align:start position:0%
+quantum mechanical system for which the
+position is not anymore a quantity that
+
+ align:start position:0%
+position is not anymore a quantity that
+ 
+
+ align:start position:0%
+position is not anymore a quantity that
+is well defined and it's always the same
+
+ align:start position:0%
+is well defined and it's always the same
+ 
+
+ align:start position:0%
+is well defined and it's always the same
+it's a random variable and each
+
+ align:start position:0%
+it's a random variable and each
+ 
+
+ align:start position:0%
+it's a random variable and each
+measurement can give you a different
+
+ align:start position:0%
+measurement can give you a different
+ 
+
+ align:start position:0%
+measurement can give you a different
+value of the position Quantum
+
+ align:start position:0%
+value of the position Quantum
+ 
+
+ align:start position:0%
+value of the position Quantum
+mechanically this is the expect
+
+ align:start position:0%
+mechanically this is the expect
+ 
+
+ align:start position:0%
+mechanically this is the expect
+value and the interpretation is again if
+
+ align:start position:0%
+value and the interpretation is again if
+ 
+
+ align:start position:0%
+value and the interpretation is again if
+you measure many times that is the value
+
+ align:start position:0%
+you measure many times that is the value
+ 
+
+ align:start position:0%
+you measure many times that is the value
+the average value you will
+
+ align:start position:0%
+the average value you will
+ 
+
+ align:start position:0%
+the average value you will
+observe but now we can do the same thing
+
+ align:start position:0%
+observe but now we can do the same thing
+ 
+
+ align:start position:0%
+observe but now we can do the same thing
+to understand
+
+ align:start position:0%
+to understand
+ 
+
+ align:start position:0%
+to understand
+the expectation values we can do it with
+
+ align:start position:0%
+the expectation values we can do it with
+ 
+
+ align:start position:0%
+the expectation values we can do it with
+a momentum and this is a little more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nontrivial so we have also Al just like
+
+ align:start position:0%
+nontrivial so we have also Al just like
+ 
+
+ align:start position:0%
+nontrivial so we have also Al just like
+we said here that s star DX is the
+
+ align:start position:0%
+we said here that s star DX is the
+ 
+
+ align:start position:0%
+we said here that s star DX is the
+probability that the particle is in
+
+ align:start position:0%
+probability that the particle is in
+ 
+
+ align:start position:0%
+probability that the particle is in
+there you also have that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fi of P
+
+ align:start position:0%
+fi of P
+ 
+
+ align:start position:0%
+fi of P
+Squared DP is the
+
+ align:start position:0%
+Squared DP is the
+ 
+
+ align:start position:0%
+Squared DP is the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+probability to find the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+particle with with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range P p+
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DP so
+
+ align:start position:0%
+DP so
+ 
+
+ align:start position:0%
+DP so
+um how do we Define the expected value
+
+ align:start position:0%
+um how do we Define the expected value
+ 
+
+ align:start position:0%
+um how do we Define the expected value
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+momentum the expected value of the
+
+ align:start position:0%
+momentum the expected value of the
+ 
+
+ align:start position:0%
+momentum the expected value of the
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+would be given by again the
+
+ align:start position:0%
+would be given by again the
+ 
+
+ align:start position:0%
+would be given by again the
+sum of the random variable which is the
+
+ align:start position:0%
+sum of the random variable which is the
+ 
+
+ align:start position:0%
+sum of the random variable which is the
+momentum times the
+
+ align:start position:0%
+momentum times the
+ 
+
+ align:start position:0%
+momentum times the
+probability that you get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value so this is it is very
+
+ align:start position:0%
+value so this is it is very
+ 
+
+ align:start position:0%
+value so this is it is very
+analogous to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expression but it's now with momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this is a pretty nice thing but uh
+
+ align:start position:0%
+well this is a pretty nice thing but uh
+ 
+
+ align:start position:0%
+well this is a pretty nice thing but uh
+we can learn more about it by pushing
+
+ align:start position:0%
+we can learn more about it by pushing
+ 
+
+ align:start position:0%
+we can learn more about it by pushing
+the analogy more and you could say look
+
+ align:start position:0%
+the analogy more and you could say look
+ 
+
+ align:start position:0%
+the analogy more and you could say look
+uh this is perfect
+
+ align:start position:0%
+uh this is perfect
+ 
+
+ align:start position:0%
+uh this is perfect
+but it's all done in momentum space What
+
+ align:start position:0%
+but it's all done in momentum space What
+ 
+
+ align:start position:0%
+but it's all done in momentum space What
+would happen if you would try to do this
+
+ align:start position:0%
+would happen if you would try to do this
+ 
+
+ align:start position:0%
+would happen if you would try to do this
+in position
+
+ align:start position:0%
+in position
+ 
+
+ align:start position:0%
+in position
+space that is you know how F of p is
+
+ align:start position:0%
+space that is you know how F of p is
+ 
+
+ align:start position:0%
+space that is you know how F of p is
+related to P of X so write everything in
+
+ align:start position:0%
+related to P of X so write everything in
+ 
+
+ align:start position:0%
+related to P of X so write everything in
+terms of X I would like to see this
+
+ align:start position:0%
+terms of X I would like to see this
+ 
+
+ align:start position:0%
+terms of X I would like to see this
+formula in terms of X it would be a very
+
+ align:start position:0%
+formula in terms of X it would be a very
+ 
+
+ align:start position:0%
+formula in terms of X it would be a very
+good thing to have so let's try to do
+
+ align:start position:0%
+good thing to have so let's try to do
+ 
+
+ align:start position:0%
+good thing to have so let's try to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so we have to do a little bit of work
+
+ align:start position:0%
+so we have to do a little bit of work
+ 
+
+ align:start position:0%
+so we have to do a little bit of work
+here with integral so but it's not so
+
+ align:start position:0%
+here with integral so but it's not so
+ 
+
+ align:start position:0%
+here with integral so but it's not so
+bad
+
+ align:start position:0%
+bad
+ 
+
+ align:start position:0%
+bad
+P five
+
+ align:start position:0%
+P five
+ 
+
+ align:start position:0%
+P five
+star of P
+
+ align:start position:0%
+star of P
+ 
+
+ align:start position:0%
+star of P
+5 of
+
+ align:start position:0%
+5 of
+ 
+
+ align:start position:0%
+5 of
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+DP and for this one you have to write it
+
+ align:start position:0%
+DP and for this one you have to write it
+ 
+
+ align:start position:0%
+DP and for this one you have to write it
+as an integral over some position so let
+
+ align:start position:0%
+as an integral over some position so let
+ 
+
+ align:start position:0%
+as an integral over some position so let
+me call it over position X Prime this
+
+ align:start position:0%
+me call it over position X Prime this
+ 
+
+ align:start position:0%
+me call it over position X Prime this
+you will write as an integral over some
+
+ align:start position:0%
+you will write as an integral over some
+ 
+
+ align:start position:0%
+you will write as an integral over some
+position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and then we're going to try to rewrite
+
+ align:start position:0%
+X and then we're going to try to rewrite
+ 
+
+ align:start position:0%
+X and then we're going to try to rewrite
+the whole thing in terms of
+
+ align:start position:0%
+the whole thing in terms of
+ 
+
+ align:start position:0%
+the whole thing in terms of
+um coordinates coordinate space so what
+
+ align:start position:0%
+um coordinates coordinate space so what
+ 
+
+ align:start position:0%
+um coordinates coordinate space so what
+do we have here we have integral P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DP and the first five star would be the
+
+ align:start position:0%
+DP and the first five star would be the
+ 
+
+ align:start position:0%
+DP and the first five star would be the
+integral over DX Prime we said there's
+
+ align:start position:0%
+integral over DX Prime we said there's
+ 
+
+ align:start position:0%
+integral over DX Prime we said there's
+the square root of 2 pi H bar that we
+
+ align:start position:0%
+the square root of 2 pi H bar that we
+ 
+
+ align:start position:0%
+the square root of 2 pi H bar that we
+can't
+
+ align:start position:0%
+can't
+ 
+
+ align:start position:0%
+can't
+forget five P um it would have an e to
+
+ align:start position:0%
+forget five P um it would have an e to
+ 
+
+ align:start position:0%
+forget five P um it would have an e to
+the i p b x Prime over H
+
+ align:start position:0%
+the i p b x Prime over H
+ 
+
+ align:start position:0%
+the i p b x Prime over H
+bar and uh aze star of X
+
+ align:start position:0%
+bar and uh aze star of X
+ 
+
+ align:start position:0%
+bar and uh aze star of X
+Prime so I did conjugate um this five
+
+ align:start position:0%
+Prime so I did conjugate um this five
+ 
+
+ align:start position:0%
+Prime so I did conjugate um this five
+star of P that I may have it here yes
+
+ align:start position:0%
+star of P that I may have it here yes
+ 
+
+ align:start position:0%
+star of P that I may have it here yes
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+here I conjugated it and uh did the
+
+ align:start position:0%
+here I conjugated it and uh did the
+ 
+
+ align:start position:0%
+here I conjugated it and uh did the
+integral over X
+
+ align:start position:0%
+integral over X
+ 
+
+ align:start position:0%
+integral over X
+Prime and now we have another one
+
+ align:start position:0%
+Prime and now we have another one
+ 
+
+ align:start position:0%
+Prime and now we have another one
+integral DX over 2 pi H
+
+ align:start position:0%
+integral DX over 2 pi H
+ 
+
+ align:start position:0%
+integral DX over 2 pi H
+bar e to the- I PX over H bar and you
+
+ align:start position:0%
+bar e to the- I PX over H bar and you
+ 
+
+ align:start position:0%
+bar e to the- I PX over H bar and you
+have S of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X okay now there's a lot of integrals
+
+ align:start position:0%
+X okay now there's a lot of integrals
+ 
+
+ align:start position:0%
+X okay now there's a lot of integrals
+there and
+
+ align:start position:0%
+there and
+ 
+
+ align:start position:0%
+there and
+uh let's try to get them simplified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um we're going to try to do
+
+ align:start position:0%
+okay so um we're going to try to do
+ 
+
+ align:start position:0%
+okay so um we're going to try to do
+first the P
+
+ align:start position:0%
+first the P
+ 
+
+ align:start position:0%
+first the P
+integral so let's try to clean up
+
+ align:start position:0%
+integral so let's try to clean up
+ 
+
+ align:start position:0%
+integral so let's try to clean up
+everything in such a way that we have
+
+ align:start position:0%
+everything in such a way that we have
+ 
+
+ align:start position:0%
+everything in such a way that we have
+only P done first
+
+ align:start position:0%
+only P done first
+ 
+
+ align:start position:0%
+only P done first
+so we'll have a one over 2 pi H bar from
+
+ align:start position:0%
+so we'll have a one over 2 pi H bar from
+ 
+
+ align:start position:0%
+so we'll have a one over 2 pi H bar from
+the two square roots and I'll have the
+
+ align:start position:0%
+the two square roots and I'll have the
+ 
+
+ align:start position:0%
+the two square roots and I'll have the
+two integrals DX Prime SI of X
+
+ align:start position:0%
+two integrals DX Prime SI of X
+ 
+
+ align:start position:0%
+two integrals DX Prime SI of X
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+Star d x s of
+
+ align:start position:0%
+Star d x s of
+ 
+
+ align:start position:0%
+Star d x s of
+X okay
+
+ align:start position:0%
+X okay
+ 
+
+ align:start position:0%
+X okay
+so look uh again as we said these
+
+ align:start position:0%
+so look uh again as we said these
+ 
+
+ align:start position:0%
+so look uh again as we said these
+integrals we just wrote them out they
+
+ align:start position:0%
+integrals we just wrote them out they
+ 
+
+ align:start position:0%
+integrals we just wrote them out they
+cannot be done so our only hope is to
+
+ align:start position:0%
+cannot be done so our only hope is to
+ 
+
+ align:start position:0%
+cannot be done so our only hope is to
+simplify first the PDP
+
+ align:start position:0%
+simplify first the PDP
+ 
+
+ align:start position:0%
+simplify first the PDP
+integral so um here we would have
+
+ align:start position:0%
+integral so um here we would have
+ 
+
+ align:start position:0%
+integral so um here we would have
+integral of
+
+ align:start position:0%
+integral of
+ 
+
+ align:start position:0%
+integral of
+DP * P * e to the i p x Prime over
+
+ align:start position:0%
+DP * P * e to the i p x Prime over
+ 
+
+ align:start position:0%
+DP * P * e to the i p x Prime over
+H and E to the- i
+
+ align:start position:0%
+H and E to the- i
+ 
+
+ align:start position:0%
+H and E to the- i
+p x over h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+okay now we need a little bit of
+
+ align:start position:0%
+okay now we need a little bit of
+ 
+
+ align:start position:0%
+okay now we need a little bit of
+probably you were doing this um would
+
+ align:start position:0%
+probably you were doing this um would
+ 
+
+ align:start position:0%
+probably you were doing this um would
+not be obvious what to do unless you
+
+ align:start position:0%
+not be obvious what to do unless you
+ 
+
+ align:start position:0%
+not be obvious what to do unless you
+have some intuition of what the momentum
+
+ align:start position:0%
+have some intuition of what the momentum
+ 
+
+ align:start position:0%
+have some intuition of what the momentum
+operator used to be um the momentum
+
+ align:start position:0%
+operator used to be um the momentum
+ 
+
+ align:start position:0%
+operator used to be um the momentum
+operator used to be
+
+ align:start position:0%
+operator used to be
+ 
+
+ align:start position:0%
+operator used to be
+um DDX basically now this integral would
+
+ align:start position:0%
+um DDX basically now this integral would
+ 
+
+ align:start position:0%
+um DDX basically now this integral would
+be a Delta function if the P was not
+
+ align:start position:0%
+be a Delta function if the P was not
+ 
+
+ align:start position:0%
+be a Delta function if the P was not
+here but here is the P so what I should
+
+ align:start position:0%
+here but here is the P so what I should
+ 
+
+ align:start position:0%
+here but here is the P so what I should
+try to do is get rid of that P in order
+
+ align:start position:0%
+try to do is get rid of that P in order
+ 
+
+ align:start position:0%
+try to do is get rid of that P in order
+to understand what we have
+
+ align:start position:0%
+to understand what we have
+ 
+
+ align:start position:0%
+to understand what we have
+so here we'll do integral
+
+ align:start position:0%
+so here we'll do integral
+ 
+
+ align:start position:0%
+so here we'll do integral
+DP and look I'll put here minus H bar r/
+
+ align:start position:0%
+DP and look I'll put here minus H bar r/
+ 
+
+ align:start position:0%
+DP and look I'll put here minus H bar r/
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DDX and leave everything here to the
+
+ align:start position:0%
+DDX and leave everything here to the
+ 
+
+ align:start position:0%
+DDX and leave everything here to the
+right e to the i p x Prime over h e to
+
+ align:start position:0%
+right e to the i p x Prime over h e to
+ 
+
+ align:start position:0%
+right e to the i p x Prime over h e to
+the minus i p x over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H I claim this is the same because this
+
+ align:start position:0%
+H I claim this is the same because this
+ 
+
+ align:start position:0%
+H I claim this is the same because this
+operator H over I DDX well it doesn't
+
+ align:start position:0%
+operator H over I DDX well it doesn't
+ 
+
+ align:start position:0%
+operator H over I DDX well it doesn't
+act on X Prime but it acts here and when
+
+ align:start position:0%
+act on X Prime but it acts here and when
+ 
+
+ align:start position:0%
+act on X Prime but it acts here and when
+it does it will produce just the factor
+
+ align:start position:0%
+it does it will produce just the factor
+ 
+
+ align:start position:0%
+it does it will produce just the factor
+of P that you have because the minus I
+
+ align:start position:0%
+of P that you have because the minus I
+ 
+
+ align:start position:0%
+of P that you have because the minus I
+and the minus I will cancel the H bar
+
+ align:start position:0%
+and the minus I will cancel the H bar
+ 
+
+ align:start position:0%
+and the minus I will cancel the H bar
+will cancel and the DDX will just bring
+
+ align:start position:0%
+will cancel and the DDX will just bring
+ 
+
+ align:start position:0%
+will cancel and the DDX will just bring
+down a p so this is the way to have this
+
+ align:start position:0%
+down a p so this is the way to have this
+ 
+
+ align:start position:0%
+down a p so this is the way to have this
+work out quite
+
+ align:start position:0%
+work out quite
+ 
+
+ align:start position:0%
+work out quite
+nicely
+
+ align:start position:0%
+nicely
+ 
+
+ align:start position:0%
+nicely
+now all right now this
+
+ align:start position:0%
+now all right now this
+ 
+
+ align:start position:0%
+now all right now this
+thing is inside the integral but it
+
+ align:start position:0%
+thing is inside the integral but it
+ 
+
+ align:start position:0%
+thing is inside the integral but it
+could as well be outside the integral it
+
+ align:start position:0%
+could as well be outside the integral it
+ 
+
+ align:start position:0%
+could as well be outside the integral it
+has nothing to do with DP so I'll
+
+ align:start position:0%
+has nothing to do with DP so I'll
+ 
+
+ align:start position:0%
+has nothing to do with DP so I'll
+rewrite this
+
+ align:start position:0%
+rewrite this
+ 
+
+ align:start position:0%
+rewrite this
+again I'll write it as DX Prime SI of X
+
+ align:start position:0%
+again I'll write it as DX Prime SI of X
+ 
+
+ align:start position:0%
+again I'll write it as DX Prime SI of X
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+Star integral DX s of
+
+ align:start position:0%
+Star integral DX s of
+ 
+
+ align:start position:0%
+Star integral DX s of
+X and I'll put this here minus h/ I DDX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in front of the integral the 1 2 pi H
+
+ align:start position:0%
+in front of the integral the 1 2 pi H
+ 
+
+ align:start position:0%
+in front of the integral the 1 2 pi H
+bar here integral
+
+ align:start position:0%
+bar here integral
+ 
+
+ align:start position:0%
+bar here integral
+DP e to the i p x Prime - x over H
+
+ align:start position:0%
+DP e to the i p x Prime - x over H
+ 
+
+ align:start position:0%
+DP e to the i p x Prime - x over H
+bar okay so I simply did a couple of
+
+ align:start position:0%
+bar okay so I simply did a couple of
+ 
+
+ align:start position:0%
+bar okay so I simply did a couple of
+things I moved it one over 2 pi H to the
+
+ align:start position:0%
+things I moved it one over 2 pi H to the
+ 
+
+ align:start position:0%
+things I moved it one over 2 pi H to the
+right and then I set this this
+
+ align:start position:0%
+right and then I set this this
+ 
+
+ align:start position:0%
+right and then I set this this
+derivative could be outside the integral
+
+ align:start position:0%
+derivative could be outside the integral
+ 
+
+ align:start position:0%
+derivative could be outside the integral
+because it's an integral over P doesn't
+
+ align:start position:0%
+because it's an integral over P doesn't
+ 
+
+ align:start position:0%
+because it's an integral over P doesn't
+interfere with X derivative so I took it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay now the final two steps we're
+
+ align:start position:0%
+out okay now the final two steps we're
+ 
+
+ align:start position:0%
+out okay now the final two steps we're
+almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there the first step is to say with this
+
+ align:start position:0%
+there the first step is to say with this
+ 
+
+ align:start position:0%
+there the first step is to say with this
+is a DDX and yes this is a function of X
+
+ align:start position:0%
+is a DDX and yes this is a function of X
+ 
+
+ align:start position:0%
+is a DDX and yes this is a function of X
+and X Prime but I don't want to take
+
+ align:start position:0%
+and X Prime but I don't want to take
+ 
+
+ align:start position:0%
+and X Prime but I don't want to take
+that der ative because I'm going to
+
+ align:start position:0%
+that der ative because I'm going to
+ 
+
+ align:start position:0%
+that der ative because I'm going to
+complicate things in fact this is
+
+ align:start position:0%
+complicate things in fact this is
+ 
+
+ align:start position:0%
+complicate things in fact this is
+already looking like a Delta function
+
+ align:start position:0%
+already looking like a Delta function
+ 
+
+ align:start position:0%
+already looking like a Delta function
+there's a DP DP and the H bars that
+
+ align:start position:0%
+there's a DP DP and the H bars that
+ 
+
+ align:start position:0%
+there's a DP DP and the H bars that
+actually would cancel so this is a
+
+ align:start position:0%
+actually would cancel so this is a
+ 
+
+ align:start position:0%
+actually would cancel so this is a
+perfectly nice Delta function you can
+
+ align:start position:0%
+perfectly nice Delta function you can
+ 
+
+ align:start position:0%
+perfectly nice Delta function you can
+change variables do p equal U * H bar
+
+ align:start position:0%
+change variables do p equal U * H bar
+ 
+
+ align:start position:0%
+change variables do p equal U * H bar
+and see that actually the H bar doesn't
+
+ align:start position:0%
+and see that actually the H bar doesn't
+ 
+
+ align:start position:0%
+and see that actually the H bar doesn't
+matter and this is just Delta of x Prime
+
+ align:start position:0%
+matter and this is just Delta of x Prime
+ 
+
+ align:start position:0%
+matter and this is just Delta of x Prime
+-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and in here you will do you could act
+
+ align:start position:0%
+x and in here you will do you could act
+ 
+
+ align:start position:0%
+x and in here you will do you could act
+on the Delta function but you could say
+
+ align:start position:0%
+on the Delta function but you could say
+ 
+
+ align:start position:0%
+on the Delta function but you could say
+no let me do integration by parts and
+
+ align:start position:0%
+no let me do integration by parts and
+ 
+
+ align:start position:0%
+no let me do integration by parts and
+act on this
+
+ align:start position:0%
+act on this
+ 
+
+ align:start position:0%
+act on this
+one integration by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parts when you do integration by parts
+
+ align:start position:0%
+parts when you do integration by parts
+ 
+
+ align:start position:0%
+parts when you do integration by parts
+you have to worry about the term at the
+
+ align:start position:0%
+you have to worry about the term at the
+ 
+
+ align:start position:0%
+you have to worry about the term at the
+boundary but if you're way functions
+
+ align:start position:0%
+boundary but if you're way functions
+ 
+
+ align:start position:0%
+boundary but if you're way functions
+vanish sufficiently fast at Infinity
+
+ align:start position:0%
+vanish sufficiently fast at Infinity
+ 
+
+ align:start position:0%
+vanish sufficiently fast at Infinity
+there's no problem so let's assume we're
+
+ align:start position:0%
+there's no problem so let's assume we're
+ 
+
+ align:start position:0%
+there's no problem so let's assume we're
+in that case we will integrate by parts
+
+ align:start position:0%
+in that case we will integrate by parts
+ 
+
+ align:start position:0%
+in that case we will integrate by parts
+and then do the Delta function so what
+
+ align:start position:0%
+and then do the Delta function so what
+ 
+
+ align:start position:0%
+and then do the Delta function so what
+do we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I have integral DX
+
+ align:start position:0%
+here I have integral DX
+ 
+
+ align:start position:0%
+here I have integral DX
+Prime s star of X
+
+ align:start position:0%
+Prime s star of X
+ 
+
+ align:start position:0%
+Prime s star of X
+Prime integral DX and now I have because
+
+ align:start position:0%
+Prime integral DX and now I have because
+ 
+
+ align:start position:0%
+Prime integral DX and now I have because
+of the sign of integration by Parts h/ I
+
+ align:start position:0%
+of the sign of integration by Parts h/ I
+ 
+
+ align:start position:0%
+of the sign of integration by Parts h/ I
+DDX of
+
+ align:start position:0%
+DDX of
+ 
+
+ align:start position:0%
+DDX of
+p and then we have the Delta function of
+
+ align:start position:0%
+p and then we have the Delta function of
+ 
+
+ align:start position:0%
+p and then we have the Delta function of
+x - x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime it's probably better still to
+
+ align:start position:0%
+Prime it's probably better still to
+ 
+
+ align:start position:0%
+Prime it's probably better still to
+write the integral like this DX H bar
+
+ align:start position:0%
+write the integral like this DX H bar
+ 
+
+ align:start position:0%
+write the integral like this DX H bar
+over i d DX of
+
+ align:start position:0%
+over i d DX of
+ 
+
+ align:start position:0%
+over i d DX of
+s time integral DX Prime P
+
+ align:start position:0%
+s time integral DX Prime P
+ 
+
+ align:start position:0%
+s time integral DX Prime P
+star of X Prime Delta of x - x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime and we're almost
+
+ align:start position:0%
+Prime and we're almost
+ 
+
+ align:start position:0%
+Prime and we're almost
+done so that's
+
+ align:start position:0%
+done so that's
+ 
+
+ align:start position:0%
+done so that's
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um we're almost done we can do the
+
+ align:start position:0%
+um we're almost done we can do the
+ 
+
+ align:start position:0%
+um we're almost done we can do the
+integral over X Prime and it will
+
+ align:start position:0%
+integral over X Prime and it will
+ 
+
+ align:start position:0%
+integral over X Prime and it will
+evaluate that wave
+
+ align:start position:0%
+evaluate that wave
+ 
+
+ align:start position:0%
+evaluate that wave
+function at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X so at the end of the day what have we
+
+ align:start position:0%
+X so at the end of the day what have we
+ 
+
+ align:start position:0%
+X so at the end of the day what have we
+found we found that P expectation value
+
+ align:start position:0%
+found we found that P expectation value
+ 
+
+ align:start position:0%
+found we found that P expectation value
+of P equal integral of P 5 of
+
+ align:start position:0%
+of P equal integral of P 5 of
+ 
+
+ align:start position:0%
+of P equal integral of P 5 of
+p^ squ
+
+ align:start position:0%
+p^ squ
+ 
+
+ align:start position:0%
+p^ squ
+DP is equal
+
+ align:start position:0%
+DP is equal
+ 
+
+ align:start position:0%
+DP is equal
+to we do this integral so we have
+
+ align:start position:0%
+to we do this integral so we have
+ 
+
+ align:start position:0%
+to we do this integral so we have
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+DX I'll write it two times H over i d DX
+
+ align:start position:0%
+DX I'll write it two times H over i d DX
+ 
+
+ align:start position:0%
+DX I'll write it two times H over i d DX
+of x and t and Si
+
+ align:start position:0%
+of x and t and Si
+ 
+
+ align:start position:0%
+of x and t and Si
+star of x and
+
+ align:start position:0%
+star of x and
+ 
+
+ align:start position:0%
+star of x and
+t um I not sure I carried the times I
+
+ align:start position:0%
+t um I not sure I carried the times I
+ 
+
+ align:start position:0%
+t um I not sure I carried the times I
+didn't put the time anywhere so maybe I
+
+ align:start position:0%
+didn't put the time anywhere so maybe I
+ 
+
+ align:start position:0%
+didn't put the time anywhere so maybe I
+shouldn't put it
+
+ align:start position:0%
+shouldn't put it
+ 
+
+ align:start position:0%
+shouldn't put it
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+yet this is what we did it and might as
+
+ align:start position:0%
+yet this is what we did it and might as
+ 
+
+ align:start position:0%
+yet this is what we did it and might as
+well write it in the standard order
+
+ align:start position:0%
+well write it in the standard order
+ 
+
+ align:start position:0%
+well write it in the standard order
+where the complex conjugate function
+
+ align:start position:0%
+where the complex conjugate function
+ 
+
+ align:start position:0%
+where the complex conjugate function
+appears
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first okay this is what we
+
+ align:start position:0%
+first okay this is what we
+ 
+
+ align:start position:0%
+first okay this is what we
+found
+
+ align:start position:0%
+found
+ 
+
+ align:start position:0%
+found
+so this is actually very neat um let me
+
+ align:start position:0%
+so this is actually very neat um let me
+ 
+
+ align:start position:0%
+so this is actually very neat um let me
+put the time back everywhere you could
+
+ align:start position:0%
+put the time back everywhere you could
+ 
+
+ align:start position:0%
+put the time back everywhere you could
+put time because this is a Time
+
+ align:start position:0%
+put time because this is a Time
+ 
+
+ align:start position:0%
+put time because this is a Time
+dependent thing so P expectation value
+
+ align:start position:0%
+dependent thing so P expectation value
+ 
+
+ align:start position:0%
+dependent thing so P expectation value
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+p f of p and
+
+ align:start position:0%
+p f of p and
+ 
+
+ align:start position:0%
+p f of p and
+t squar d p is equal to integral
+
+ align:start position:0%
+t squar d p is equal to integral
+ 
+
+ align:start position:0%
+t squar d p is equal to integral
+DX s
+
+ align:start position:0%
+DX s
+ 
+
+ align:start position:0%
+DX s
+star of X and now we have if you wish P
+
+ align:start position:0%
+star of X and now we have if you wish P
+ 
+
+ align:start position:0%
+star of X and now we have if you wish P
+hat s of X where P hat
+
+ align:start position:0%
+hat s of X where P hat
+ 
+
+ align:start position:0%
+hat s of X where P hat
+is what we used to call the momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator so look what has happened uh we
+
+ align:start position:0%
+operator so look what has happened uh we
+ 
+
+ align:start position:0%
+operator so look what has happened uh we
+started with this
+
+ align:start position:0%
+started with this
+ 
+
+ align:start position:0%
+started with this
+expression for the expectation value of
+
+ align:start position:0%
+expression for the expectation value of
+ 
+
+ align:start position:0%
+expression for the expectation value of
+the momentum justified by the
+
+ align:start position:0%
+the momentum justified by the
+ 
+
+ align:start position:0%
+the momentum justified by the
+probabilistic interpretation of
+
+ align:start position:0%
+probabilistic interpretation of
+ 
+
+ align:start position:0%
+probabilistic interpretation of
+fi and we were led to this expression
+
+ align:start position:0%
+fi and we were led to this expression
+ 
+
+ align:start position:0%
+fi and we were led to this expression
+which is very similar to this one you
+
+ align:start position:0%
+which is very similar to this one you
+ 
+
+ align:start position:0%
+which is very similar to this one you
+see you have the star the and the X
+
+ align:start position:0%
+see you have the star the and the X
+ 
+
+ align:start position:0%
+see you have the star the and the X
+there but here the momentum appeared at
+
+ align:start position:0%
+there but here the momentum appeared at
+ 
+
+ align:start position:0%
+there but here the momentum appeared at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+position acting on the wave function P
+
+ align:start position:0%
+position acting on the wave function P
+ 
+
+ align:start position:0%
+position acting on the wave function P
+not on P
+
+ align:start position:0%
+not on P
+ 
+
+ align:start position:0%
+not on P
+star and that's the way in quantum
+
+ align:start position:0%
+star and that's the way in quantum
+ 
+
+ align:start position:0%
+star and that's the way in quantum
+mechanics people Define expectation
+
+ align:start position:0%
+mechanics people Define expectation
+ 
+
+ align:start position:0%
+mechanics people Define expectation
+values of operators in general
+
+ align:start position:0%
+values of operators in general
+ 
+
+ align:start position:0%
+values of operators in general
+so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+around for an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+Q will Define the expectation value of
+
+ align:start position:0%
+Q will Define the expectation value of
+ 
+
+ align:start position:0%
+Q will Define the expectation value of
+Q to be
+
+ align:start position:0%
+Q to be
+ 
+
+ align:start position:0%
+Q to be
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+DX P star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of x and
+
+ align:start position:0%
+of x and
+ 
+
+ align:start position:0%
+of x and
+t q acting on S of x and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t so you will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always do this of putting the operator
+
+ align:start position:0%
+always do this of putting the operator
+ 
+
+ align:start position:0%
+always do this of putting the operator
+to act on the second part of the wave
+
+ align:start position:0%
+to act on the second part of the wave
+ 
+
+ align:start position:0%
+to act on the second part of the wave
+function on the second appearance of the
+
+ align:start position:0%
+function on the second appearance of the
+ 
+
+ align:start position:0%
+function on the second appearance of the
+wave function not on the P star
+
+ align:start position:0%
+wave function not on the P star
+ 
+
+ align:start position:0%
+wave function not on the P star
+but on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side um we can do other ex examples of
+
+ align:start position:0%
+side um we can do other ex examples of
+ 
+
+ align:start position:0%
+side um we can do other ex examples of
+this and uh our final
+
+ align:start position:0%
+this and uh our final
+ 
+
+ align:start position:0%
+this and uh our final
+theorem that um this is of course time
+
+ align:start position:0%
+theorem that um this is of course time
+ 
+
+ align:start position:0%
+theorem that um this is of course time
+dependent time
+
+ align:start position:0%
+dependent time
+ 
+
+ align:start position:0%
+dependent time
+dependent so let me do one example and
+
+ align:start position:0%
+dependent so let me do one example and
+ 
+
+ align:start position:0%
+dependent so let me do one example and
+uh our final um time dependence analysis
+
+ align:start position:0%
+uh our final um time dependence analysis
+ 
+
+ align:start position:0%
+uh our final um time dependence analysis
+of this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minutes so for example if you would
+
+ align:start position:0%
+minutes so for example if you would
+ 
+
+ align:start position:0%
+minutes so for example if you would
+think of the kinetic operator example
+
+ align:start position:0%
+think of the kinetic operator example
+ 
+
+ align:start position:0%
+think of the kinetic operator example
+kinetic operator
+
+ align:start position:0%
+kinetic operator
+ 
+
+ align:start position:0%
+kinetic operator
+T is p^ 2/ 2
+
+ align:start position:0%
+T is p^ 2/ 2
+ 
+
+ align:start position:0%
+T is p^ 2/ 2
+m is a kinetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator how would you compute its
+
+ align:start position:0%
+operator how would you compute its
+ 
+
+ align:start position:0%
+operator how would you compute its
+expectation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value expectation value of the kinetic
+
+ align:start position:0%
+value expectation value of the kinetic
+ 
+
+ align:start position:0%
+value expectation value of the kinetic
+operator is
+
+ align:start position:0%
+operator is
+ 
+
+ align:start position:0%
+operator is
+what well I could do the position
+
+ align:start position:0%
+what well I could do the position
+ 
+
+ align:start position:0%
+what well I could do the position
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+calculation in which I'm think of the
+
+ align:start position:0%
+calculation in which I'm think of the
+ 
+
+ align:start position:0%
+calculation in which I'm think of the
+kinetic operator as an operator that
+
+ align:start position:0%
+kinetic operator as an operator that
+ 
+
+ align:start position:0%
+kinetic operator as an operator that
+acts in position space where the
+
+ align:start position:0%
+acts in position space where the
+ 
+
+ align:start position:0%
+acts in position space where the
+momentum is H bar over I DDX so then I
+
+ align:start position:0%
+momentum is H bar over I DDX so then I
+ 
+
+ align:start position:0%
+momentum is H bar over I DDX so then I
+would have integral
+
+ align:start position:0%
+would have integral
+ 
+
+ align:start position:0%
+would have integral
+DX SI star of x and t and then I would
+
+ align:start position:0%
+DX SI star of x and t and then I would
+ 
+
+ align:start position:0%
+DX SI star of x and t and then I would
+have Min - h^2 / 2 m DC D
+
+ align:start position:0%
+have Min - h^2 / 2 m DC D
+ 
+
+ align:start position:0%
+have Min - h^2 / 2 m DC D
+x² of s of X and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D so here I did exactly what I was
+
+ align:start position:0%
+D so here I did exactly what I was
+ 
+
+ align:start position:0%
+D so here I did exactly what I was
+supposed to do given this
+
+ align:start position:0%
+supposed to do given this
+ 
+
+ align:start position:0%
+supposed to do given this
+formula but you could do another thing
+
+ align:start position:0%
+formula but you could do another thing
+ 
+
+ align:start position:0%
+formula but you could do another thing
+if you wished uh you could say look I
+
+ align:start position:0%
+if you wished uh you could say look I
+ 
+
+ align:start position:0%
+if you wished uh you could say look I
+can work in momentum
+
+ align:start position:0%
+can work in momentum
+ 
+
+ align:start position:0%
+can work in momentum
+space this is a momentum uh
+
+ align:start position:0%
+space this is a momentum uh
+ 
+
+ align:start position:0%
+space this is a momentum uh
+operator P just like I defined the
+
+ align:start position:0%
+operator P just like I defined the
+ 
+
+ align:start position:0%
+operator P just like I defined the
+expectation value of p i could have the
+
+ align:start position:0%
+expectation value of p i could have the
+ 
+
+ align:start position:0%
+expectation value of p i could have the
+expectation value of p^ s so the other
+
+ align:start position:0%
+expectation value of p^ s so the other
+ 
+
+ align:start position:0%
+expectation value of p^ s so the other
+possibility is that you have
+
+ align:start position:0%
+possibility is that you have
+ 
+
+ align:start position:0%
+possibility is that you have
+t is equal to the
+
+ align:start position:0%
+t is equal to the
+ 
+
+ align:start position:0%
+t is equal to the
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+DP of p^ 2 / 2 m * 5
+
+ align:start position:0%
+DP of p^ 2 / 2 m * 5
+ 
+
+ align:start position:0%
+DP of p^ 2 / 2 m * 5
+of P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squar this is the operator and this is
+
+ align:start position:0%
+squar this is the operator and this is
+ 
+
+ align:start position:0%
+squar this is the operator and this is
+the probability or you could write it
+
+ align:start position:0%
+the probability or you could write it
+ 
+
+ align:start position:0%
+the probability or you could write it
+more elegantly perhaps
+
+ align:start position:0%
+more elegantly perhaps
+ 
+
+ align:start position:0%
+more elegantly perhaps
+DP 5 star of
+
+ align:start position:0%
+DP 5 star of
+ 
+
+ align:start position:0%
+DP 5 star of
+p p^ 2 / 2 m f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P this are just integrals of numbers all
+
+ align:start position:0%
+P this are just integrals of numbers all
+ 
+
+ align:start position:0%
+P this are just integrals of numbers all
+these are numbers
+
+ align:start position:0%
+these are numbers
+ 
+
+ align:start position:0%
+these are numbers
+already so in momentum space it's easier
+
+ align:start position:0%
+already so in momentum space it's easier
+ 
+
+ align:start position:0%
+already so in momentum space it's easier
+to find the expectation value of the
+
+ align:start position:0%
+to find the expectation value of the
+ 
+
+ align:start position:0%
+to find the expectation value of the
+kinetic
+
+ align:start position:0%
+kinetic
+ 
+
+ align:start position:0%
+kinetic
+operator in coordinate space you have to
+
+ align:start position:0%
+operator in coordinate space you have to
+ 
+
+ align:start position:0%
+operator in coordinate space you have to
+do this um you might even say look
+
+ align:start position:0%
+do this um you might even say look
+ 
+
+ align:start position:0%
+do this um you might even say look
+um this thing looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive because it's p squ and the
+
+ align:start position:0%
+positive because it's p squ and the
+ 
+
+ align:start position:0%
+positive because it's p squ and the
+numbers square and this inter here it
+
+ align:start position:0%
+numbers square and this inter here it
+ 
+
+ align:start position:0%
+numbers square and this inter here it
+looks negative but uh that's an
+
+ align:start position:0%
+looks negative but uh that's an
+ 
+
+ align:start position:0%
+looks negative but uh that's an
+illusion this second derivative can be
+
+ align:start position:0%
+illusion this second derivative can be
+ 
+
+ align:start position:0%
+illusion this second derivative can be
+partially integrated one of the two
+
+ align:start position:0%
+partially integrated one of the two
+ 
+
+ align:start position:0%
+partially integrated one of the two
+derivatives can be integrated to act on
+
+ align:start position:0%
+derivatives can be integrated to act on
+ 
+
+ align:start position:0%
+derivatives can be integrated to act on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one so if you do an partial integration
+
+ align:start position:0%
+one so if you do an partial integration
+ 
+
+ align:start position:0%
+one so if you do an partial integration
+by parts you would have integral
+
+ align:start position:0%
+by parts you would have integral
+ 
+
+ align:start position:0%
+by parts you would have integral
+DX h^2 / 2 m and then you would have d
+
+ align:start position:0%
+DX h^2 / 2 m and then you would have d
+ 
+
+ align:start position:0%
+DX h^2 / 2 m and then you would have d
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+squared by integration by
+
+ align:start position:0%
+squared by integration by
+ 
+
+ align:start position:0%
+squared by integration by
+parts and that's clearly positive as
+
+ align:start position:0%
+parts and that's clearly positive as
+ 
+
+ align:start position:0%
+parts and that's clearly positive as
+well so it's similar to this
\ No newline at end of file
diff --git a/XW9xERSeenI.txt b/XW9xERSeenI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ffc1646cda98ceb85c1265c1cf14354d25fae311
--- /dev/null
+++ b/XW9xERSeenI.txt
@@ -0,0 +1,12730 @@
+align:start position:0%
+ 
+all right welcome back to 61200 today we
+
+ align:start position:0%
+all right welcome back to 61200 today we
+ 
+
+ align:start position:0%
+all right welcome back to 61200 today we
+are talking about number Theory uh and
+
+ align:start position:0%
+are talking about number Theory uh and
+ 
+
+ align:start position:0%
+are talking about number Theory uh and
+number is I guess an old word here for
+
+ align:start position:0%
+number is I guess an old word here for
+ 
+
+ align:start position:0%
+number is I guess an old word here for
+integers in modern terminology um you
+
+ align:start position:0%
+integers in modern terminology um you
+ 
+
+ align:start position:0%
+integers in modern terminology um you
+know this Set uh Blackboard bold Z which
+
+ align:start position:0%
+know this Set uh Blackboard bold Z which
+ 
+
+ align:start position:0%
+know this Set uh Blackboard bold Z which
+is all positive and negative integers
+
+ align:start position:0%
+is all positive and negative integers
+ 
+
+ align:start position:0%
+is all positive and negative integers
+although mostly we think about natural
+
+ align:start position:0%
+although mostly we think about natural
+ 
+
+ align:start position:0%
+although mostly we think about natural
+numbers the non- negative integers uh
+
+ align:start position:0%
+numbers the non- negative integers uh
+ 
+
+ align:start position:0%
+numbers the non- negative integers uh
+number theory is a a big topic we're
+
+ align:start position:0%
+number theory is a a big topic we're
+ 
+
+ align:start position:0%
+number theory is a a big topic we're
+going to spend three lectures on it
+
+ align:start position:0%
+going to spend three lectures on it
+ 
+
+ align:start position:0%
+going to spend three lectures on it
+today and to next week um and it's a
+
+ align:start position:0%
+today and to next week um and it's a
+ 
+
+ align:start position:0%
+today and to next week um and it's a
+really important branch of sub Branch I
+
+ align:start position:0%
+really important branch of sub Branch I
+ 
+
+ align:start position:0%
+really important branch of sub Branch I
+guess or related branch of discrete
+
+ align:start position:0%
+guess or related branch of discrete
+ 
+
+ align:start position:0%
+guess or related branch of discrete
+mathematics uh in particular because
+
+ align:start position:0%
+mathematics uh in particular because
+ 
+
+ align:start position:0%
+mathematics uh in particular because
+it's found a lot of applications in
+
+ align:start position:0%
+it's found a lot of applications in
+ 
+
+ align:start position:0%
+it's found a lot of applications in
+modern days in cryptography and error
+
+ align:start position:0%
+modern days in cryptography and error
+ 
+
+ align:start position:0%
+modern days in cryptography and error
+correction every when you use your cell
+
+ align:start position:0%
+correction every when you use your cell
+ 
+
+ align:start position:0%
+correction every when you use your cell
+phone probably several different things
+
+ align:start position:0%
+phone probably several different things
+ 
+
+ align:start position:0%
+phone probably several different things
+uh in your in that software is using
+
+ align:start position:0%
+uh in your in that software is using
+ 
+
+ align:start position:0%
+uh in your in that software is using
+number Theory at some level to do crypto
+
+ align:start position:0%
+number Theory at some level to do crypto
+ 
+
+ align:start position:0%
+number Theory at some level to do crypto
+to access your bank to do uh error
+
+ align:start position:0%
+to access your bank to do uh error
+ 
+
+ align:start position:0%
+to access your bank to do uh error
+correction to talk over radio waves all
+
+ align:start position:0%
+correction to talk over radio waves all
+ 
+
+ align:start position:0%
+correction to talk over radio waves all
+sorts of fun things uh number three is
+
+ align:start position:0%
+sorts of fun things uh number three is
+ 
+
+ align:start position:0%
+sorts of fun things uh number three is
+also extremely old it's probably the
+
+ align:start position:0%
+also extremely old it's probably the
+ 
+
+ align:start position:0%
+also extremely old it's probably the
+oldest branch of mathematics though you
+
+ align:start position:0%
+oldest branch of mathematics though you
+ 
+
+ align:start position:0%
+oldest branch of mathematics though you
+know past 4,000 years it's a little hard
+
+ align:start position:0%
+know past 4,000 years it's a little hard
+ 
+
+ align:start position:0%
+know past 4,000 years it's a little hard
+to tell exactly what people were doing
+
+ align:start position:0%
+to tell exactly what people were doing
+ 
+
+ align:start position:0%
+to tell exactly what people were doing
+uh but in particular the Babylonians uh
+
+ align:start position:0%
+uh but in particular the Babylonians uh
+ 
+
+ align:start position:0%
+uh but in particular the Babylonians uh
+3,800 years ago were uh doing number
+
+ align:start position:0%
+3,800 years ago were uh doing number
+ 
+
+ align:start position:0%
+3,800 years ago were uh doing number
+Theory uh Pythagoras uh 25 200 years ago
+
+ align:start position:0%
+Theory uh Pythagoras uh 25 200 years ago
+ 
+
+ align:start position:0%
+Theory uh Pythagoras uh 25 200 years ago
+was doing number Theory um in the it had
+
+ align:start position:0%
+was doing number Theory um in the it had
+ 
+
+ align:start position:0%
+was doing number Theory um in the it had
+a a lot of exciting activity in the
+
+ align:start position:0%
+a a lot of exciting activity in the
+ 
+
+ align:start position:0%
+a a lot of exciting activity in the
+middle of last century uh Hardy is one
+
+ align:start position:0%
+middle of last century uh Hardy is one
+ 
+
+ align:start position:0%
+middle of last century uh Hardy is one
+of the famous uh number theories number
+
+ align:start position:0%
+of the famous uh number theories number
+ 
+
+ align:start position:0%
+of the famous uh number theories number
+theorists of sort of near our time um he
+
+ align:start position:0%
+theorists of sort of near our time um he
+ 
+
+ align:start position:0%
+theorists of sort of near our time um he
+wrote uh number theory is great because
+
+ align:start position:0%
+wrote uh number theory is great because
+ 
+
+ align:start position:0%
+wrote uh number theory is great because
+it's one science whose very remoteness
+
+ align:start position:0%
+it's one science whose very remoteness
+ 
+
+ align:start position:0%
+it's one science whose very remoteness
+very remoteness from human activities
+
+ align:start position:0%
+very remoteness from human activities
+ 
+
+ align:start position:0%
+very remoteness from human activities
+should keep it gentle and clean he was a
+
+ align:start position:0%
+should keep it gentle and clean he was a
+ 
+
+ align:start position:0%
+should keep it gentle and clean he was a
+pacifist and he wanted to do math that
+
+ align:start position:0%
+pacifist and he wanted to do math that
+ 
+
+ align:start position:0%
+pacifist and he wanted to do math that
+was completely useless from the
+
+ align:start position:0%
+was completely useless from the
+ 
+
+ align:start position:0%
+was completely useless from the
+perspective of warfare sadly uh that's
+
+ align:start position:0%
+perspective of warfare sadly uh that's
+ 
+
+ align:start position:0%
+perspective of warfare sadly uh that's
+not the case for number Theory anymore
+
+ align:start position:0%
+not the case for number Theory anymore
+ 
+
+ align:start position:0%
+not the case for number Theory anymore
+but it used to be um
+
+ align:start position:0%
+but it used to be um
+ 
+
+ align:start position:0%
+but it used to be um
+so uh but the things we'll be doing here
+
+ align:start position:0%
+so uh but the things we'll be doing here
+ 
+
+ align:start position:0%
+so uh but the things we'll be doing here
+are pretty fundamental uh today we're
+
+ align:start position:0%
+are pretty fundamental uh today we're
+ 
+
+ align:start position:0%
+are pretty fundamental uh today we're
+going to talk about divisibility and
+
+ align:start position:0%
+going to talk about divisibility and
+ 
+
+ align:start position:0%
+going to talk about divisibility and
+something called gcd which you may have
+
+ align:start position:0%
+something called gcd which you may have
+ 
+
+ align:start position:0%
+something called gcd which you may have
+heard of before it's a pretty basic
+
+ align:start position:0%
+heard of before it's a pretty basic
+ 
+
+ align:start position:0%
+heard of before it's a pretty basic
+notion both of these are but we're going
+
+ align:start position:0%
+notion both of these are but we're going
+ 
+
+ align:start position:0%
+notion both of these are but we're going
+to Define everything carefully and prove
+
+ align:start position:0%
+to Define everything carefully and prove
+ 
+
+ align:start position:0%
+to Define everything carefully and prove
+uh all sorts of cool properties about
+
+ align:start position:0%
+uh all sorts of cool properties about
+ 
+
+ align:start position:0%
+uh all sorts of cool properties about
+divisibility and use it to solve at
+
+ align:start position:0%
+divisibility and use it to solve at
+ 
+
+ align:start position:0%
+divisibility and use it to solve at
+least one fun
+
+ align:start position:0%
+least one fun
+ 
+
+ align:start position:0%
+least one fun
+problem so uh the notation for
+
+ align:start position:0%
+problem so uh the notation for
+ 
+
+ align:start position:0%
+problem so uh the notation for
+divisibility is a divides
+
+ align:start position:0%
+divisibility is a divides
+ 
+
+ align:start position:0%
+divisibility is a divides
+B uh we use a vertical bar we use a
+
+ align:start position:0%
+B uh we use a vertical bar we use a
+ 
+
+ align:start position:0%
+B uh we use a vertical bar we use a
+vertical Bar for a few other things like
+
+ align:start position:0%
+vertical Bar for a few other things like
+ 
+
+ align:start position:0%
+vertical Bar for a few other things like
+absolute value and set notation so try
+
+ align:start position:0%
+absolute value and set notation so try
+ 
+
+ align:start position:0%
+absolute value and set notation so try
+not to be too confused uh this will only
+
+ align:start position:0%
+not to be too confused uh this will only
+ 
+
+ align:start position:0%
+not to be too confused uh this will only
+be for uh a couple weeks um divisibility
+
+ align:start position:0%
+be for uh a couple weeks um divisibility
+ 
+
+ align:start position:0%
+be for uh a couple weeks um divisibility
+means uh a evenly divides b or B is
+
+ align:start position:0%
+means uh a evenly divides b or B is
+ 
+
+ align:start position:0%
+means uh a evenly divides b or B is
+evenly divisible by a okay so for
+
+ align:start position:0%
+evenly divisible by a okay so for
+ 
+
+ align:start position:0%
+evenly divisible by a okay so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+uh let's say uh two divides 4 as an
+
+ align:start position:0%
+uh let's say uh two divides 4 as an
+ 
+
+ align:start position:0%
+uh let's say uh two divides 4 as an
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but in general what we would like is
+
+ align:start position:0%
+uh but in general what we would like is
+ 
+
+ align:start position:0%
+uh but in general what we would like is
+a a def a formal definition of
+
+ align:start position:0%
+a a def a formal definition of
+ 
+
+ align:start position:0%
+a a def a formal definition of
+this um so we'll say a divides B if
+
+ align:start position:0%
+this um so we'll say a divides B if
+ 
+
+ align:start position:0%
+this um so we'll say a divides B if
+there exists some integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiple
+
+ align:start position:0%
+multiple
+ 
+
+ align:start position:0%
+multiple
+K such that uh B is that multiple of a
+
+ align:start position:0%
+K such that uh B is that multiple of a
+ 
+
+ align:start position:0%
+K such that uh B is that multiple of a
+so b equal K * a very important that
+
+ align:start position:0%
+so b equal K * a very important that
+ 
+
+ align:start position:0%
+so b equal K * a very important that
+this is an integer otherwise over reals
+
+ align:start position:0%
+this is an integer otherwise over reals
+ 
+
+ align:start position:0%
+this is an integer otherwise over reals
+this is always the case pretty
+
+ align:start position:0%
+this is always the case pretty
+ 
+
+ align:start position:0%
+this is always the case pretty
+much um and we Define divisibility in
+
+ align:start position:0%
+much um and we Define divisibility in
+ 
+
+ align:start position:0%
+much um and we Define divisibility in
+terms of multiplication instead of
+
+ align:start position:0%
+terms of multiplication instead of
+ 
+
+ align:start position:0%
+terms of multiplication instead of
+division I mean you could divide both
+
+ align:start position:0%
+division I mean you could divide both
+ 
+
+ align:start position:0%
+division I mean you could divide both
+sides by uh a here and so for example
+
+ align:start position:0%
+sides by uh a here and so for example
+ 
+
+ align:start position:0%
+sides by uh a here and so for example
+this is saying B divided by a is an
+
+ align:start position:0%
+this is saying B divided by a is an
+ 
+
+ align:start position:0%
+this is saying B divided by a is an
+integer but that's not such a great
+
+ align:start position:0%
+integer but that's not such a great
+ 
+
+ align:start position:0%
+integer but that's not such a great
+definition because it doesn't work well
+
+ align:start position:0%
+definition because it doesn't work well
+ 
+
+ align:start position:0%
+definition because it doesn't work well
+when you try to divide by zero this
+
+ align:start position:0%
+when you try to divide by zero this
+ 
+
+ align:start position:0%
+when you try to divide by zero this
+definition works even when B is when a
+
+ align:start position:0%
+definition works even when B is when a
+ 
+
+ align:start position:0%
+definition works even when B is when a
+is zero and uh otherwi if you do
+
+ align:start position:0%
+is zero and uh otherwi if you do
+ 
+
+ align:start position:0%
+is zero and uh otherwi if you do
+division it doesn't so that's why we
+
+ align:start position:0%
+division it doesn't so that's why we
+ 
+
+ align:start position:0%
+division it doesn't so that's why we
+Define divisibility this way so more
+
+ align:start position:0%
+Define divisibility this way so more
+ 
+
+ align:start position:0%
+Define divisibility this way so more
+interesting examples are 2 ID n uh means
+
+ align:start position:0%
+interesting examples are 2 ID n uh means
+ 
+
+ align:start position:0%
+interesting examples are 2 ID n uh means
+what we have been saying n is
+
+ align:start position:0%
+what we have been saying n is
+ 
+
+ align:start position:0%
+what we have been saying n is
+even whenever we say n is even what we
+
+ align:start position:0%
+even whenever we say n is even what we
+ 
+
+ align:start position:0%
+even whenever we say n is even what we
+really mean is two divides n there's
+
+ align:start position:0%
+really mean is two divides n there's
+ 
+
+ align:start position:0%
+really mean is two divides n there's
+some integer multiple of two that equals
+
+ align:start position:0%
+some integer multiple of two that equals
+ 
+
+ align:start position:0%
+some integer multiple of two that equals
+n okay uh some other weirder
+
+ align:start position:0%
+n okay uh some other weirder
+ 
+
+ align:start position:0%
+n okay uh some other weirder
+cases every natural
+
+ align:start position:0%
+cases every natural
+ 
+
+ align:start position:0%
+cases every natural
+number uh n divides n
+
+ align:start position:0%
+number uh n divides n
+ 
+
+ align:start position:0%
+number uh n divides n
+it's maybe not so intuitive what
+
+ align:start position:0%
+it's maybe not so intuitive what
+ 
+
+ align:start position:0%
+it's maybe not so intuitive what
+divisibility means for negative numbers
+
+ align:start position:0%
+divisibility means for negative numbers
+ 
+
+ align:start position:0%
+divisibility means for negative numbers
+but here are some examples we allow this
+
+ align:start position:0%
+but here are some examples we allow this
+ 
+
+ align:start position:0%
+but here are some examples we allow this
+integer multiple K to be negative so in
+
+ align:start position:0%
+integer multiple K to be negative so in
+ 
+
+ align:start position:0%
+integer multiple K to be negative so in
+particular K can be minus1 and minus1 *
+
+ align:start position:0%
+particular K can be minus1 and minus1 *
+ 
+
+ align:start position:0%
+particular K can be minus1 and minus1 *
+negative n is n okay also n divides n
+
+ align:start position:0%
+negative n is n okay also n divides n
+ 
+
+ align:start position:0%
+negative n is n okay also n divides n
+but that's a little less exciting uh
+
+ align:start position:0%
+but that's a little less exciting uh
+ 
+
+ align:start position:0%
+but that's a little less exciting uh
+another fun fact is that every number
+
+ align:start position:0%
+another fun fact is that every number
+ 
+
+ align:start position:0%
+another fun fact is that every number
+divides
+
+ align:start position:0%
+divides
+ 
+
+ align:start position:0%
+divides
+zero this is also maybe not the most
+
+ align:start position:0%
+zero this is also maybe not the most
+ 
+
+ align:start position:0%
+zero this is also maybe not the most
+intuitive but it comes from the
+
+ align:start position:0%
+intuitive but it comes from the
+ 
+
+ align:start position:0%
+intuitive but it comes from the
+definition K in particular can be zero
+
+ align:start position:0%
+definition K in particular can be zero
+ 
+
+ align:start position:0%
+definition K in particular can be zero
+and if you take 0 * n you get zero so
+
+ align:start position:0%
+and if you take 0 * n you get zero so
+ 
+
+ align:start position:0%
+and if you take 0 * n you get zero so
+everything divides zero uh number also
+
+ align:start position:0%
+everything divides zero uh number also
+ 
+
+ align:start position:0%
+everything divides zero uh number also
+divides its negative things like that um
+
+ align:start position:0%
+divides its negative things like that um
+ 
+
+ align:start position:0%
+divides its negative things like that um
+a consequence of these two things
+
+ align:start position:0%
+a consequence of these two things
+ 
+
+ align:start position:0%
+a consequence of these two things
+together is that zero is even if you
+
+ align:start position:0%
+together is that zero is even if you
+ 
+
+ align:start position:0%
+together is that zero is even if you
+were ever worried about whether zero was
+
+ align:start position:0%
+were ever worried about whether zero was
+ 
+
+ align:start position:0%
+were ever worried about whether zero was
+an exception to evenness in the
+
+ align:start position:0%
+an exception to evenness in the
+ 
+
+ align:start position:0%
+an exception to evenness in the
+alternation of of these numbers yes uh
+
+ align:start position:0%
+alternation of of these numbers yes uh
+ 
+
+ align:start position:0%
+alternation of of these numbers yes uh
+this is even this is even this is even
+
+ align:start position:0%
+this is even this is even this is even
+ 
+
+ align:start position:0%
+this is even this is even this is even
+because uh in particular 2 divides 0
+
+ align:start position:0%
+because uh in particular 2 divides 0
+ 
+
+ align:start position:0%
+because uh in particular 2 divides 0
+everything divides Z but in particular
+
+ align:start position:0%
+everything divides Z but in particular
+ 
+
+ align:start position:0%
+everything divides Z but in particular
+two divid Z that's the meaning of
+
+ align:start position:0%
+two divid Z that's the meaning of
+ 
+
+ align:start position:0%
+two divid Z that's the meaning of
+even okay great uh
+
+ align:start position:0%
+even okay great uh
+ 
+
+ align:start position:0%
+even okay great uh
+let's State some theorems about
+
+ align:start position:0%
+let's State some theorems about
+ 
+
+ align:start position:0%
+let's State some theorems about
+divisibility I'm going to call these
+
+ align:start position:0%
+divisibility I'm going to call these
+ 
+
+ align:start position:0%
+divisibility I'm going to call these
+divisibility facts we're going to use
+
+ align:start position:0%
+divisibility facts we're going to use
+ 
+
+ align:start position:0%
+divisibility facts we're going to use
+them several times
+
+ align:start position:0%
+them several times
+ 
+
+ align:start position:0%
+them several times
+today uh let's say we have
+
+ align:start position:0%
+today uh let's say we have
+ 
+
+ align:start position:0%
+today uh let's say we have
+two numbers divisible by the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we call this uh D is a
+
+ align:start position:0%
+uh we call this uh D is a
+ 
+
+ align:start position:0%
+uh we call this uh D is a
+common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisor of A and B so D divides A and D
+
+ align:start position:0%
+divisor of A and B so D divides A and D
+ 
+
+ align:start position:0%
+divisor of A and B so D divides A and D
+divides B we call it a common
+
+ align:start position:0%
+divides B we call it a common
+ 
+
+ align:start position:0%
+divides B we call it a common
+divisor uh
+
+ align:start position:0%
+divisor uh
+ 
+
+ align:start position:0%
+divisor uh
+then I claim uh for example D divides a
+
+ align:start position:0%
+then I claim uh for example D divides a
+ 
+
+ align:start position:0%
+then I claim uh for example D divides a
+plus b their
+
+ align:start position:0%
+plus b their
+ 
+
+ align:start position:0%
+plus b their
+sum why this is very easy to prove if
+
+ align:start position:0%
+sum why this is very easy to prove if
+ 
+
+ align:start position:0%
+sum why this is very easy to prove if
+you just work through the definition so
+
+ align:start position:0%
+you just work through the definition so
+ 
+
+ align:start position:0%
+you just work through the definition so
+let's say um a = j * D and Bal K * D for
+
+ align:start position:0%
+let's say um a = j * D and Bal K * D for
+ 
+
+ align:start position:0%
+let's say um a = j * D and Bal K * D for
+some integers J and K they might be the
+
+ align:start position:0%
+some integers J and K they might be the
+ 
+
+ align:start position:0%
+some integers J and K they might be the
+same they might be different uh then a
+
+ align:start position:0%
+same they might be different uh then a
+ 
+
+ align:start position:0%
+same they might be different uh then a
+plus b well it's it's just the sum of
+
+ align:start position:0%
+plus b well it's it's just the sum of
+ 
+
+ align:start position:0%
+plus b well it's it's just the sum of
+these two things right it's j + K *
+
+ align:start position:0%
+these two things right it's j + K *
+ 
+
+ align:start position:0%
+these two things right it's j + K *
+D not very hard uh more generally uh D
+
+ align:start position:0%
+D not very hard uh more generally uh D
+ 
+
+ align:start position:0%
+D not very hard uh more generally uh D
+divides
+
+ align:start position:0%
+divides
+ 
+
+ align:start position:0%
+divides
+uh sa a + TB for any integers s and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t uh this is just a a simple extension
+
+ align:start position:0%
+t uh this is just a a simple extension
+ 
+
+ align:start position:0%
+t uh this is just a a simple extension
+of this property um I guess you can
+
+ align:start position:0%
+of this property um I guess you can
+ 
+
+ align:start position:0%
+of this property um I guess you can
+write uh this thing equals uh SJ + TK *
+
+ align:start position:0%
+write uh this thing equals uh SJ + TK *
+ 
+
+ align:start position:0%
+write uh this thing equals uh SJ + TK *
+D um and it turns out this
+
+ align:start position:0%
+D um and it turns out this
+ 
+
+ align:start position:0%
+D um and it turns out this
+structure is interesting it's what we
+
+ align:start position:0%
+structure is interesting it's what we
+ 
+
+ align:start position:0%
+structure is interesting it's what we
+call an integer linear
+
+ align:start position:0%
+call an integer linear
+ 
+
+ align:start position:0%
+call an integer linear
+combination this is a concept we will
+
+ align:start position:0%
+combination this is a concept we will
+ 
+
+ align:start position:0%
+combination this is a concept we will
+also be using throughout
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today so much so that uh I'm going to
+
+ align:start position:0%
+today so much so that uh I'm going to
+ 
+
+ align:start position:0%
+today so much so that uh I'm going to
+give an acronym I don't usually like
+
+ align:start position:0%
+give an acronym I don't usually like
+ 
+
+ align:start position:0%
+give an acronym I don't usually like
+acronyms but this is so long that it's
+
+ align:start position:0%
+acronyms but this is so long that it's
+ 
+
+ align:start position:0%
+acronyms but this is so long that it's
+going to save me a ton of work to write
+
+ align:start position:0%
+going to save me a ton of work to write
+ 
+
+ align:start position:0%
+going to save me a ton of work to write
+ilc for integer linear combination uh if
+
+ align:start position:0%
+ilc for integer linear combination uh if
+ 
+
+ align:start position:0%
+ilc for integer linear combination uh if
+you know linear algebra this is just
+
+ align:start position:0%
+you know linear algebra this is just
+ 
+
+ align:start position:0%
+you know linear algebra this is just
+linear combination but where the
+
+ align:start position:0%
+linear combination but where the
+ 
+
+ align:start position:0%
+linear combination but where the
+coefficients need to be integers so it's
+
+ align:start position:0%
+coefficients need to be integers so it's
+ 
+
+ align:start position:0%
+coefficients need to be integers so it's
+exactly this notion so an integer linear
+
+ align:start position:0%
+exactly this notion so an integer linear
+ 
+
+ align:start position:0%
+exactly this notion so an integer linear
+combination of A and B uh is some number
+
+ align:start position:0%
+combination of A and B uh is some number
+ 
+
+ align:start position:0%
+combination of A and B uh is some number
+s * a plus T * B uh for
+
+ align:start position:0%
+s * a plus T * B uh for
+ 
+
+ align:start position:0%
+s * a plus T * B uh for
+any uh s and t that are integers okay so
+
+ align:start position:0%
+any uh s and t that are integers okay so
+ 
+
+ align:start position:0%
+any uh s and t that are integers okay so
+if I give you two numbers A and B we'll
+
+ align:start position:0%
+if I give you two numbers A and B we'll
+ 
+
+ align:start position:0%
+if I give you two numbers A and B we'll
+only be doing integer linear
+
+ align:start position:0%
+only be doing integer linear
+ 
+
+ align:start position:0%
+only be doing integer linear
+combinations today of two
+
+ align:start position:0%
+combinations today of two
+ 
+
+ align:start position:0%
+combinations today of two
+numbers uh then this is what they always
+
+ align:start position:0%
+numbers uh then this is what they always
+ 
+
+ align:start position:0%
+numbers uh then this is what they always
+look like and given two numbers there's
+
+ align:start position:0%
+look like and given two numbers there's
+ 
+
+ align:start position:0%
+look like and given two numbers there's
+some numbers you can construct VI
+
+ align:start position:0%
+some numbers you can construct VI
+ 
+
+ align:start position:0%
+some numbers you can construct VI
+integer linear combinations and some you
+
+ align:start position:0%
+integer linear combinations and some you
+ 
+
+ align:start position:0%
+integer linear combinations and some you
+can't uh actually fun fact divis
+
+ align:start position:0%
+can't uh actually fun fact divis
+ 
+
+ align:start position:0%
+can't uh actually fun fact divis
+is like integer linear combinations of
+
+ align:start position:0%
+is like integer linear combinations of
+ 
+
+ align:start position:0%
+is like integer linear combinations of
+one number this is saying B is an
+
+ align:start position:0%
+one number this is saying B is an
+ 
+
+ align:start position:0%
+one number this is saying B is an
+integer linear combination of just a uh
+
+ align:start position:0%
+integer linear combination of just a uh
+ 
+
+ align:start position:0%
+integer linear combination of just a uh
+but we that's so special we call it
+
+ align:start position:0%
+but we that's so special we call it
+ 
+
+ align:start position:0%
+but we that's so special we call it
+divisibility U two numbers is where
+
+ align:start position:0%
+divisibility U two numbers is where
+ 
+
+ align:start position:0%
+divisibility U two numbers is where
+integer linear combinations really get
+
+ align:start position:0%
+integer linear combinations really get
+ 
+
+ align:start position:0%
+integer linear combinations really get
+interesting all right so to motivate
+
+ align:start position:0%
+interesting all right so to motivate
+ 
+
+ align:start position:0%
+interesting all right so to motivate
+these Concepts more turns out these are
+
+ align:start position:0%
+these Concepts more turns out these are
+ 
+
+ align:start position:0%
+these Concepts more turns out these are
+key Concepts to solving a famous puzzle
+
+ align:start position:0%
+key Concepts to solving a famous puzzle
+ 
+
+ align:start position:0%
+key Concepts to solving a famous puzzle
+uh it's at least 80 90 years old called
+
+ align:start position:0%
+uh it's at least 80 90 years old called
+ 
+
+ align:start position:0%
+uh it's at least 80 90 years old called
+the water uh water pouring puzzle but it
+
+ align:start position:0%
+the water uh water pouring puzzle but it
+ 
+
+ align:start position:0%
+the water uh water pouring puzzle but it
+became particularly famous uh through
+
+ align:start position:0%
+became particularly famous uh through
+ 
+
+ align:start position:0%
+became particularly famous uh through
+Die Hard three Die Hard with a Vengeance
+
+ align:start position:0%
+Die Hard three Die Hard with a Vengeance
+ 
+
+ align:start position:0%
+Die Hard three Die Hard with a Vengeance
+so we're going to watch a little clip uh
+
+ align:start position:0%
+so we're going to watch a little clip uh
+ 
+
+ align:start position:0%
+so we're going to watch a little clip uh
+and if you uh if this clip is not
+
+ align:start position:0%
+and if you uh if this clip is not
+ 
+
+ align:start position:0%
+and if you uh if this clip is not
+included in this video you can go uh
+
+ align:start position:0%
+included in this video you can go uh
+ 
+
+ align:start position:0%
+included in this video you can go uh
+stream or uh purchase Die Hard with a
+
+ align:start position:0%
+stream or uh purchase Die Hard with a
+ 
+
+ align:start position:0%
+stream or uh purchase Die Hard with a
+Vengeance and start at the one hour mark
+
+ align:start position:0%
+Vengeance and start at the one hour mark
+ 
+
+ align:start position:0%
+Vengeance and start at the one hour mark
+and you will see an exchange like the
+
+ align:start position:0%
+and you will see an exchange like the
+ 
+
+ align:start position:0%
+and you will see an exchange like the
+following so we have uh of course John
+
+ align:start position:0%
+following so we have uh of course John
+ 
+
+ align:start position:0%
+following so we have uh of course John
+mlan here uh who's uh trying to save
+
+ align:start position:0%
+mlan here uh who's uh trying to save
+ 
+
+ align:start position:0%
+mlan here uh who's uh trying to save
+Manhattan uh along with his friend Zeus
+
+ align:start position:0%
+Manhattan uh along with his friend Zeus
+ 
+
+ align:start position:0%
+Manhattan uh along with his friend Zeus
+who's like an electrician who just
+
+ align:start position:0%
+who's like an electrician who just
+ 
+
+ align:start position:0%
+who's like an electrician who just
+happens to get uh brought into this
+
+ align:start position:0%
+happens to get uh brought into this
+ 
+
+ align:start position:0%
+happens to get uh brought into this
+whole chaos basically the bad guys are
+
+ align:start position:0%
+whole chaos basically the bad guys are
+ 
+
+ align:start position:0%
+whole chaos basically the bad guys are
+trying to distract the good guys by
+
+ align:start position:0%
+trying to distract the good guys by
+ 
+
+ align:start position:0%
+trying to distract the good guys by
+solving forcing them to solve puzzles so
+
+ align:start position:0%
+solving forcing them to solve puzzles so
+ 
+
+ align:start position:0%
+solving forcing them to solve puzzles so
+here we go all right so we're going to
+
+ align:start position:0%
+here we go all right so we're going to
+ 
+
+ align:start position:0%
+here we go all right so we're going to
+focus on the problem at hand uh which uh
+
+ align:start position:0%
+focus on the problem at hand uh which uh
+ 
+
+ align:start position:0%
+focus on the problem at hand uh which uh
+we can formalize as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows uh so we have two
+
+ align:start position:0%
+follows uh so we have two
+ 
+
+ align:start position:0%
+follows uh so we have two
+jugs uh we'll say of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacity A and B and we'll assume
+
+ align:start position:0%
+capacity A and B and we'll assume
+ 
+
+ align:start position:0%
+capacity A and B and we'll assume
+they're integers and in the
+
+ align:start position:0%
+they're integers and in the
+ 
+
+ align:start position:0%
+they're integers and in the
+example uh that saves Manhattan we have
+
+ align:start position:0%
+example uh that saves Manhattan we have
+ 
+
+ align:start position:0%
+example uh that saves Manhattan we have
+a equals 5 and b equals 3 and we'd like
+
+ align:start position:0%
+a equals 5 and b equals 3 and we'd like
+ 
+
+ align:start position:0%
+a equals 5 and b equals 3 and we'd like
+to represent some number uh in this case
+
+ align:start position:0%
+to represent some number uh in this case
+ 
+
+ align:start position:0%
+to represent some number uh in this case
+four by a sequence of pouring
+
+ align:start position:0%
+four by a sequence of pouring
+ 
+
+ align:start position:0%
+four by a sequence of pouring
+operations uh so um how could we
+
+ align:start position:0%
+operations uh so um how could we
+ 
+
+ align:start position:0%
+operations uh so um how could we
+represent this water porn in problem
+
+ align:start position:0%
+represent this water porn in problem
+ 
+
+ align:start position:0%
+represent this water porn in problem
+using techniques that we have from
+
+ align:start position:0%
+using techniques that we have from
+ 
+
+ align:start position:0%
+using techniques that we have from
+previous
+
+ align:start position:0%
+previous
+ 
+
+ align:start position:0%
+previous
+lectures any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas I heard
+
+ align:start position:0%
+ideas I heard
+ 
+
+ align:start position:0%
+ideas I heard
+something yeah State machines good so
+
+ align:start position:0%
+something yeah State machines good so
+ 
+
+ align:start position:0%
+something yeah State machines good so
+we'll use a state machine um and so
+
+ align:start position:0%
+we'll use a state machine um and so
+ 
+
+ align:start position:0%
+we'll use a state machine um and so
+we'll have a
+
+ align:start position:0%
+we'll have a
+ 
+
+ align:start position:0%
+we'll have a
+state x and y means that there's
+
+ align:start position:0%
+state x and y means that there's
+ 
+
+ align:start position:0%
+state x and y means that there's
+currently X gallons in the first jug and
+
+ align:start position:0%
+currently X gallons in the first jug and
+ 
+
+ align:start position:0%
+currently X gallons in the first jug and
+Y gallons in the second jck
+
+ align:start position:0%
+Y gallons in the second jck
+ 
+
+ align:start position:0%
+Y gallons in the second jck
+uh or let's say the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amounts in uh
+
+ align:start position:0%
+amounts in uh
+ 
+
+ align:start position:0%
+amounts in uh
+each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joke okay so uh we
+
+ align:start position:0%
+joke okay so uh we
+ 
+
+ align:start position:0%
+joke okay so uh we
+start at the state z z let's say the
+
+ align:start position:0%
+start at the state z z let's say the
+ 
+
+ align:start position:0%
+start at the state z z let's say the
+drug started empty uh we're given an
+
+ align:start position:0%
+drug started empty uh we're given an
+ 
+
+ align:start position:0%
+drug started empty uh we're given an
+infinite water supply because they're at
+
+ align:start position:0%
+infinite water supply because they're at
+ 
+
+ align:start position:0%
+infinite water supply because they're at
+a fountain
+
+ align:start position:0%
+a fountain
+ 
+
+ align:start position:0%
+a fountain
+conveniently um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's see we want to finish at a
+
+ align:start position:0%
+and let's see we want to finish at a
+ 
+
+ align:start position:0%
+and let's see we want to finish at a
+state that has four in one of the two
+
+ align:start position:0%
+state that has four in one of the two
+ 
+
+ align:start position:0%
+state that has four in one of the two
+values and as John mlan said uh it has
+
+ align:start position:0%
+values and as John mlan said uh it has
+ 
+
+ align:start position:0%
+values and as John mlan said uh it has
+to be in the bigger one in this case
+
+ align:start position:0%
+to be in the bigger one in this case
+ 
+
+ align:start position:0%
+to be in the bigger one in this case
+because four is bigger than
+
+ align:start position:0%
+because four is bigger than
+ 
+
+ align:start position:0%
+because four is bigger than
+three so we'd like
+
+ align:start position:0%
+three so we'd like
+ 
+
+ align:start position:0%
+three so we'd like
+to uh goal is to get to uh four comma
+
+ align:start position:0%
+to uh goal is to get to uh four comma
+ 
+
+ align:start position:0%
+to uh goal is to get to uh four comma
+something and the tricky part is to
+
+ align:start position:0%
+something and the tricky part is to
+ 
+
+ align:start position:0%
+something and the tricky part is to
+write down the transitions here so let's
+
+ align:start position:0%
+write down the transitions here so let's
+ 
+
+ align:start position:0%
+write down the transitions here so let's
+write down some of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transitions so given X and
+
+ align:start position:0%
+transitions so given X and
+ 
+
+ align:start position:0%
+transitions so given X and
+Y uh what are the some of the things I
+
+ align:start position:0%
+Y uh what are the some of the things I
+ 
+
+ align:start position:0%
+Y uh what are the some of the things I
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+do any
+
+ align:start position:0%
+do any
+ 
+
+ align:start position:0%
+do any
+suggestions I have some partially filled
+
+ align:start position:0%
+suggestions I have some partially filled
+ 
+
+ align:start position:0%
+suggestions I have some partially filled
+jars these are two jars of uh five and
+
+ align:start position:0%
+jars these are two jars of uh five and
+ 
+
+ align:start position:0%
+jars these are two jars of uh five and
+three pumpkins capacity respectively uh
+
+ align:start position:0%
+three pumpkins capacity respectively uh
+ 
+
+ align:start position:0%
+three pumpkins capacity respectively uh
+maybe I'm at some position here what
+
+ align:start position:0%
+maybe I'm at some position here what
+ 
+
+ align:start position:0%
+maybe I'm at some position here what
+could I do to these trugs yeah the back
+
+ align:start position:0%
+could I do to these trugs yeah the back
+ 
+
+ align:start position:0%
+could I do to these trugs yeah the back
+fill one to the top I I go to the
+
+ align:start position:0%
+fill one to the top I I go to the
+ 
+
+ align:start position:0%
+fill one to the top I I go to the
+Fountain I pour it up until it's
+
+ align:start position:0%
+Fountain I pour it up until it's
+ 
+
+ align:start position:0%
+Fountain I pour it up until it's
+completely fill or or this one I could
+
+ align:start position:0%
+completely fill or or this one I could
+ 
+
+ align:start position:0%
+completely fill or or this one I could
+go to the fill Point other suggestions
+
+ align:start position:0%
+go to the fill Point other suggestions
+ 
+
+ align:start position:0%
+go to the fill Point other suggestions
+yeah empty I could empty one of the jars
+
+ align:start position:0%
+yeah empty I could empty one of the jars
+ 
+
+ align:start position:0%
+yeah empty I could empty one of the jars
+hopefully I won't need that so in the
+
+ align:start position:0%
+hopefully I won't need that so in the
+ 
+
+ align:start position:0%
+hopefully I won't need that so in the
+transitions this is this corresponds to
+
+ align:start position:0%
+transitions this is this corresponds to
+ 
+
+ align:start position:0%
+transitions this is this corresponds to
+going to uh I guess a comma y if I fill
+
+ align:start position:0%
+going to uh I guess a comma y if I fill
+ 
+
+ align:start position:0%
+going to uh I guess a comma y if I fill
+the first one um or I could go to x
+
+ align:start position:0%
+the first one um or I could go to x
+ 
+
+ align:start position:0%
+the first one um or I could go to x
+comma B if I fill the second one um I
+
+ align:start position:0%
+comma B if I fill the second one um I
+ 
+
+ align:start position:0%
+comma B if I fill the second one um I
+could empty by going to uh 0 comma y if
+
+ align:start position:0%
+could empty by going to uh 0 comma y if
+ 
+
+ align:start position:0%
+could empty by going to uh 0 comma y if
+I empty the first one or I could go to x
+
+ align:start position:0%
+I empty the first one or I could go to x
+ 
+
+ align:start position:0%
+I empty the first one or I could go to x
+comma 0 so these are all sorry this is
+
+ align:start position:0%
+comma 0 so these are all sorry this is
+ 
+
+ align:start position:0%
+comma 0 so these are all sorry this is
+all transitions from
+
+ align:start position:0%
+all transitions from
+ 
+
+ align:start position:0%
+all transitions from
+XY uh anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I can pour the contents of one jug
+
+ align:start position:0%
+yeah I can pour the contents of one jug
+ 
+
+ align:start position:0%
+yeah I can pour the contents of one jug
+into the other cool yeah so here for
+
+ align:start position:0%
+into the other cool yeah so here for
+ 
+
+ align:start position:0%
+into the other cool yeah so here for
+example I filled up a three I poured in
+
+ align:start position:0%
+example I filled up a three I poured in
+ 
+
+ align:start position:0%
+example I filled up a three I poured in
+three uh I could fill this one up again
+
+ align:start position:0%
+three uh I could fill this one up again
+ 
+
+ align:start position:0%
+three uh I could fill this one up again
+and pour it in again and at some point
+
+ align:start position:0%
+and pour it in again and at some point
+ 
+
+ align:start position:0%
+and pour it in again and at some point
+uh I'll run out of capacity in this jug
+
+ align:start position:0%
+uh I'll run out of capacity in this jug
+ 
+
+ align:start position:0%
+uh I'll run out of capacity in this jug
+and that's an event that I can detect
+
+ align:start position:0%
+and that's an event that I can detect
+ 
+
+ align:start position:0%
+and that's an event that I can detect
+when I reach level Che okay so to write
+
+ align:start position:0%
+when I reach level Che okay so to write
+ 
+
+ align:start position:0%
+when I reach level Che okay so to write
+that down more carefully given
+
+ align:start position:0%
+that down more carefully given
+ 
+
+ align:start position:0%
+that down more carefully given
+XY we can transition to one of two cases
+
+ align:start position:0%
+XY we can transition to one of two cases
+ 
+
+ align:start position:0%
+XY we can transition to one of two cases
+either we get to completely empty the
+
+ align:start position:0%
+either we get to completely empty the
+ 
+
+ align:start position:0%
+either we get to completely empty the
+left jug into the right jug so this
+
+ align:start position:0%
+left jug into the right jug so this
+ 
+
+ align:start position:0%
+left jug into the right jug so this
+would be uh x + y but that's only
+
+ align:start position:0%
+would be uh x + y but that's only
+ 
+
+ align:start position:0%
+would be uh x + y but that's only
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+if it fits in the second jug If X Plus Y
+
+ align:start position:0%
+if it fits in the second jug If X Plus Y
+ 
+
+ align:start position:0%
+if it fits in the second jug If X Plus Y
+is less than or equal to B otherwise to
+
+ align:start position:0%
+is less than or equal to B otherwise to
+ 
+
+ align:start position:0%
+is less than or equal to B otherwise to
+do arithmetic this too hard uh we move
+
+ align:start position:0%
+do arithmetic this too hard uh we move
+ 
+
+ align:start position:0%
+do arithmetic this too hard uh we move
+over B minus y or something um so we
+
+ align:start position:0%
+over B minus y or something um so we
+ 
+
+ align:start position:0%
+over B minus y or something um so we
+have x minus B minus y comma B
+
+ align:start position:0%
+have x minus B minus y comma B
+ 
+
+ align:start position:0%
+have x minus B minus y comma B
+otherwise okay if we end up filling up
+
+ align:start position:0%
+otherwise okay if we end up filling up
+ 
+
+ align:start position:0%
+otherwise okay if we end up filling up
+the second one then this is how much uh
+
+ align:start position:0%
+the second one then this is how much uh
+ 
+
+ align:start position:0%
+the second one then this is how much uh
+of the original X that I started with
+
+ align:start position:0%
+of the original X that I started with
+ 
+
+ align:start position:0%
+of the original X that I started with
+remains
+
+ align:start position:0%
+remains
+ 
+
+ align:start position:0%
+remains
+okay uh and you can do the there's one
+
+ align:start position:0%
+okay uh and you can do the there's one
+ 
+
+ align:start position:0%
+okay uh and you can do the there's one
+more rule which is if I pour from right
+
+ align:start position:0%
+more rule which is if I pour from right
+ 
+
+ align:start position:0%
+more rule which is if I pour from right
+to left those are the available uh State
+
+ align:start position:0%
+to left those are the available uh State
+ 
+
+ align:start position:0%
+to left those are the available uh State
+transitions in this puzzle uh and now
+
+ align:start position:0%
+transitions in this puzzle uh and now
+ 
+
+ align:start position:0%
+transitions in this puzzle uh and now
+maybe I've talked about it long enough
+
+ align:start position:0%
+maybe I've talked about it long enough
+ 
+
+ align:start position:0%
+maybe I've talked about it long enough
+you have some intuition on how to solve
+
+ align:start position:0%
+you have some intuition on how to solve
+ 
+
+ align:start position:0%
+you have some intuition on how to solve
+this start
+
+ align:start position:0%
+this start
+ 
+
+ align:start position:0%
+this start
+empty any suggestions on how to
+
+ align:start position:0%
+empty any suggestions on how to
+ 
+
+ align:start position:0%
+empty any suggestions on how to
+construct the number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let fill up the five gallon
+
+ align:start position:0%
+let fill up the five gallon
+ 
+
+ align:start position:0%
+let fill up the five gallon
+jug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay we're going to transfer the
+
+ align:start position:0%
+okay okay we're going to transfer the
+ 
+
+ align:start position:0%
+okay okay we're going to transfer the
+three gallon jug until the three gallon
+
+ align:start position:0%
+three gallon jug until the three gallon
+ 
+
+ align:start position:0%
+three gallon jug until the three gallon
+jug is exactly empty which if you're
+
+ align:start position:0%
+jug is exactly empty which if you're
+ 
+
+ align:start position:0%
+jug is exactly empty which if you're
+using water it would be
+
+ align:start position:0%
+using water it would be
+ 
+
+ align:start position:0%
+using water it would be
+level okay empty the three gallon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jug okay move the two over this now
+
+ align:start position:0%
+jug okay move the two over this now
+ 
+
+ align:start position:0%
+jug okay move the two over this now
+feels like towers of anoi
+
+ align:start position:0%
+feels like towers of anoi
+ 
+
+ align:start position:0%
+feels like towers of anoi
+okay fill the five
+
+ align:start position:0%
+okay fill the five
+ 
+
+ align:start position:0%
+okay fill the five
+and then transfer like
+
+ align:start position:0%
+and then transfer like
+ 
+
+ align:start position:0%
+and then transfer like
+this from five to did I get the right
+
+ align:start position:0%
+this from five to did I get the right
+ 
+
+ align:start position:0%
+this from five to did I get the right
+number there we go water's water's
+
+ align:start position:0%
+number there we go water's water's
+ 
+
+ align:start position:0%
+number there we go water's water's
+particularly unsettled today all right
+
+ align:start position:0%
+particularly unsettled today all right
+ 
+
+ align:start position:0%
+particularly unsettled today all right
+so we've got uh five on the right if I
+
+ align:start position:0%
+so we've got uh five on the right if I
+ 
+
+ align:start position:0%
+so we've got uh five on the right if I
+can count and we fill over here until
+
+ align:start position:0%
+can count and we fill over here until
+ 
+
+ align:start position:0%
+can count and we fill over here until
+this one is filled and now we've got the
+
+ align:start position:0%
+this one is filled and now we've got the
+ 
+
+ align:start position:0%
+this one is filled and now we've got the
+number four
+
+ align:start position:0%
+number four
+ 
+
+ align:start position:0%
+number four
+yay uh that's how we solve that's how we
+
+ align:start position:0%
+yay uh that's how we solve that's how we
+ 
+
+ align:start position:0%
+yay uh that's how we solve that's how we
+save Manhattan with uh with this water
+
+ align:start position:0%
+save Manhattan with uh with this water
+ 
+
+ align:start position:0%
+save Manhattan with uh with this water
+pouring problem but uh while the bad
+
+ align:start position:0%
+pouring problem but uh while the bad
+ 
+
+ align:start position:0%
+pouring problem but uh while the bad
+guys are off uh stealing
+
+ align:start position:0%
+guys are off uh stealing
+ 
+
+ align:start position:0%
+guys are off uh stealing
+money from the bank um but sometimes
+
+ align:start position:0%
+money from the bank um but sometimes
+ 
+
+ align:start position:0%
+money from the bank um but sometimes
+this puzzle isn't solvable so let's take
+
+ align:start position:0%
+this puzzle isn't solvable so let's take
+ 
+
+ align:start position:0%
+this puzzle isn't solvable so let's take
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+example uh let's say we want uh AAL 6
+
+ align:start position:0%
+example uh let's say we want uh AAL 6
+ 
+
+ align:start position:0%
+example uh let's say we want uh AAL 6
+bals 4 and we want the number
+
+ align:start position:0%
+bals 4 and we want the number
+ 
+
+ align:start position:0%
+bals 4 and we want the number
+three is this possible I already gave
+
+ align:start position:0%
+three is this possible I already gave
+ 
+
+ align:start position:0%
+three is this possible I already gave
+away that this is impossible why is it
+
+ align:start position:0%
+away that this is impossible why is it
+ 
+
+ align:start position:0%
+away that this is impossible why is it
+impossible any
+
+ align:start position:0%
+impossible any
+ 
+
+ align:start position:0%
+impossible any
+feelings hint it has something to do
+
+ align:start position:0%
+feelings hint it has something to do
+ 
+
+ align:start position:0%
+feelings hint it has something to do
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay you said there are no integer
+
+ align:start position:0%
+yeah okay you said there are no integer
+ 
+
+ align:start position:0%
+yeah okay you said there are no integer
+linear combinations where of six and
+
+ align:start position:0%
+linear combinations where of six and
+ 
+
+ align:start position:0%
+linear combinations where of six and
+four that make three that is true but uh
+
+ align:start position:0%
+four that make three that is true but uh
+ 
+
+ align:start position:0%
+four that make three that is true but uh
+this problem isn't directly about
+
+ align:start position:0%
+this problem isn't directly about
+ 
+
+ align:start position:0%
+this problem isn't directly about
+integer linear combinations is it I
+
+ align:start position:0%
+integer linear combinations is it I
+ 
+
+ align:start position:0%
+integer linear combinations is it I
+don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there's no way to get an odd number
+
+ align:start position:0%
+yeah there's no way to get an odd number
+ 
+
+ align:start position:0%
+yeah there's no way to get an odd number
+from these two
+
+ align:start position:0%
+from these two
+ 
+
+ align:start position:0%
+from these two
+gallons that's the simp both of you are
+
+ align:start position:0%
+gallons that's the simp both of you are
+ 
+
+ align:start position:0%
+gallons that's the simp both of you are
+correct uh the simpler reason in this
+
+ align:start position:0%
+correct uh the simpler reason in this
+ 
+
+ align:start position:0%
+correct uh the simpler reason in this
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+uh is it's impossible to get an odd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amount um I guess the proof of both of
+
+ align:start position:0%
+amount um I guess the proof of both of
+ 
+
+ align:start position:0%
+amount um I guess the proof of both of
+these things is you look at all the
+
+ align:start position:0%
+these things is you look at all the
+ 
+
+ align:start position:0%
+these things is you look at all the
+possible Transitions and uh You observe
+
+ align:start position:0%
+possible Transitions and uh You observe
+ 
+
+ align:start position:0%
+possible Transitions and uh You observe
+that if you start with A and B being
+
+ align:start position:0%
+that if you start with A and B being
+ 
+
+ align:start position:0%
+that if you start with A and B being
+even you can never construct an odd
+
+ align:start position:0%
+even you can never construct an odd
+ 
+
+ align:start position:0%
+even you can never construct an odd
+number by adding and subtracting all
+
+ align:start position:0%
+number by adding and subtracting all
+ 
+
+ align:start position:0%
+number by adding and subtracting all
+we're doing here taking numbers that
+
+ align:start position:0%
+we're doing here taking numbers that
+ 
+
+ align:start position:0%
+we're doing here taking numbers that
+we've constructed adding them and or
+
+ align:start position:0%
+we've constructed adding them and or
+ 
+
+ align:start position:0%
+we've constructed adding them and or
+subtracting them with a and b or each
+
+ align:start position:0%
+subtracting them with a and b or each
+ 
+
+ align:start position:0%
+subtracting them with a and b or each
+other and so if you start with even
+
+ align:start position:0%
+other and so if you start with even
+ 
+
+ align:start position:0%
+other and so if you start with even
+numbers you add and subtract them you
+
+ align:start position:0%
+numbers you add and subtract them you
+ 
+
+ align:start position:0%
+numbers you add and subtract them you
+always stay within the even numbers but
+
+ align:start position:0%
+always stay within the even numbers but
+ 
+
+ align:start position:0%
+always stay within the even numbers but
+also as you're saying if you start with
+
+ align:start position:0%
+also as you're saying if you start with
+ 
+
+ align:start position:0%
+also as you're saying if you start with
+an integer linear combination of A and B
+
+ align:start position:0%
+an integer linear combination of A and B
+ 
+
+ align:start position:0%
+an integer linear combination of A and B
+all you can get are integer linear
+
+ align:start position:0%
+all you can get are integer linear
+ 
+
+ align:start position:0%
+all you can get are integer linear
+combinations of A and B so here is uh a
+
+ align:start position:0%
+combinations of A and B so here is uh a
+ 
+
+ align:start position:0%
+combinations of A and B so here is uh a
+key Lemma about this puzzle and why that
+
+ align:start position:0%
+key Lemma about this puzzle and why that
+ 
+
+ align:start position:0%
+key Lemma about this puzzle and why that
+is impossible more
+
+ align:start position:0%
+is impossible more
+ 
+
+ align:start position:0%
+is impossible more
+generally is uh all reachable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amounts in this puzzle are integer
+
+ align:start position:0%
+amounts in this puzzle are integer
+ 
+
+ align:start position:0%
+amounts in this puzzle are integer
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+combinations of A and
+
+ align:start position:0%
+combinations of A and
+ 
+
+ align:start position:0%
+combinations of A and
+B let's prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this any suggestions on how to prove a
+
+ align:start position:0%
+this any suggestions on how to prove a
+ 
+
+ align:start position:0%
+this any suggestions on how to prove a
+property like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this you remember all the way back to
+
+ align:start position:0%
+this you remember all the way back to
+ 
+
+ align:start position:0%
+this you remember all the way back to
+State machines hopefully you've been
+
+ align:start position:0%
+State machines hopefully you've been
+ 
+
+ align:start position:0%
+State machines hopefully you've been
+studying for the test State machines are
+
+ align:start position:0%
+studying for the test State machines are
+ 
+
+ align:start position:0%
+studying for the test State machines are
+on the test this lecture is not it will
+
+ align:start position:0%
+on the test this lecture is not it will
+ 
+
+ align:start position:0%
+on the test this lecture is not it will
+be on quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two invariance yeah in particular
+
+ align:start position:0%
+two invariance yeah in particular
+ 
+
+ align:start position:0%
+two invariance yeah in particular
+uh this this is a statement about
+
+ align:start position:0%
+uh this this is a statement about
+ 
+
+ align:start position:0%
+uh this this is a statement about
+invariance this is saying uh for all
+
+ align:start position:0%
+invariance this is saying uh for all
+ 
+
+ align:start position:0%
+invariance this is saying uh for all
+reachable uh X comma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y um X and Y are integer linear
+
+ align:start position:0%
+y um X and Y are integer linear
+ 
+
+ align:start position:0%
+y um X and Y are integer linear
+combinations of A and B so this is an
+
+ align:start position:0%
+combinations of A and B so this is an
+ 
+
+ align:start position:0%
+combinations of A and B so this is an
+invariant property this is a state
+
+ align:start position:0%
+invariant property this is a state
+ 
+
+ align:start position:0%
+invariant property this is a state
+predicate we want to prove that it's
+
+ align:start position:0%
+predicate we want to prove that it's
+ 
+
+ align:start position:0%
+predicate we want to prove that it's
+invariant that is true for all reachable
+
+ align:start position:0%
+invariant that is true for all reachable
+ 
+
+ align:start position:0%
+invariant that is true for all reachable
+states starting from 0 0 um and we
+
+ align:start position:0%
+states starting from 0 0 um and we
+ 
+
+ align:start position:0%
+states starting from 0 0 um and we
+usually do that using the invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle which has requires two steps
+
+ align:start position:0%
+principle which has requires two steps
+ 
+
+ align:start position:0%
+principle which has requires two steps
+one is base case we need to check that
+
+ align:start position:0%
+one is base case we need to check that
+ 
+
+ align:start position:0%
+one is base case we need to check that
+this predicate holds
+
+ align:start position:0%
+this predicate holds
+ 
+
+ align:start position:0%
+this predicate holds
+initially uh and the initial state for
+
+ align:start position:0%
+initially uh and the initial state for
+ 
+
+ align:start position:0%
+initially uh and the initial state for
+us is 0 comma 0 and we observe that zero
+
+ align:start position:0%
+us is 0 comma 0 and we observe that zero
+ 
+
+ align:start position:0%
+us is 0 comma 0 and we observe that zero
+is indeed a linear combination of A and
+
+ align:start position:0%
+is indeed a linear combination of A and
+ 
+
+ align:start position:0%
+is indeed a linear combination of A and
+B namely 0 * a uh plus 0 * B great base
+
+ align:start position:0%
+B namely 0 * a uh plus 0 * B great base
+ 
+
+ align:start position:0%
+B namely 0 * a uh plus 0 * B great base
+case is true and so now we just need the
+
+ align:start position:0%
+case is true and so now we just need the
+ 
+
+ align:start position:0%
+case is true and so now we just need the
+inductive step or the I guess the
+
+ align:start position:0%
+inductive step or the I guess the
+ 
+
+ align:start position:0%
+inductive step or the I guess the
+preserved the fact that this predicate
+
+ align:start position:0%
+preserved the fact that this predicate
+ 
+
+ align:start position:0%
+preserved the fact that this predicate
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preserved uh so suppose that we're at
+
+ align:start position:0%
+preserved uh so suppose that we're at
+ 
+
+ align:start position:0%
+preserved uh so suppose that we're at
+some State X and Y where the predicate
+
+ align:start position:0%
+some State X and Y where the predicate
+ 
+
+ align:start position:0%
+some State X and Y where the predicate
+is true uh so xal sa a + TB and y = s
+
+ align:start position:0%
+is true uh so xal sa a + TB and y = s
+ 
+
+ align:start position:0%
+is true uh so xal sa a + TB and y = s
+prime a + T Prime B
+
+ align:start position:0%
+prime a + T Prime B
+ 
+
+ align:start position:0%
+prime a + T Prime B
+um and then we just look at all of the
+
+ align:start position:0%
+um and then we just look at all of the
+ 
+
+ align:start position:0%
+um and then we just look at all of the
+available
+
+ align:start position:0%
+available
+ 
+
+ align:start position:0%
+available
+Transitions and we show that every
+
+ align:start position:0%
+Transitions and we show that every
+ 
+
+ align:start position:0%
+Transitions and we show that every
+number that you can make uh is indeed an
+
+ align:start position:0%
+number that you can make uh is indeed an
+ 
+
+ align:start position:0%
+number that you can make uh is indeed an
+integer linear combination of uh A and B
+
+ align:start position:0%
+integer linear combination of uh A and B
+ 
+
+ align:start position:0%
+integer linear combination of uh A and B
+so let's do one example we can construct
+
+ align:start position:0%
+so let's do one example we can construct
+ 
+
+ align:start position:0%
+so let's do one example we can construct
+X + Y X + Y uh we can rewrite as um s +
+
+ align:start position:0%
+X + Y X + Y uh we can rewrite as um s +
+ 
+
+ align:start position:0%
+X + Y X + Y uh we can rewrite as um s +
+S Prime * a and t + T Prime * B so
+
+ align:start position:0%
+S Prime * a and t + T Prime * B so
+ 
+
+ align:start position:0%
+S Prime * a and t + T Prime * B so
+that's uh if this transition happens to
+
+ align:start position:0%
+that's uh if this transition happens to
+ 
+
+ align:start position:0%
+that's uh if this transition happens to
+be possible it may not be possible
+
+ align:start position:0%
+be possible it may not be possible
+ 
+
+ align:start position:0%
+be possible it may not be possible
+because there's this if condition but if
+
+ align:start position:0%
+because there's this if condition but if
+ 
+
+ align:start position:0%
+because there's this if condition but if
+we show that every thing every number we
+
+ align:start position:0%
+we show that every thing every number we
+ 
+
+ align:start position:0%
+we show that every thing every number we
+could possibly build has this property
+
+ align:start position:0%
+could possibly build has this property
+ 
+
+ align:start position:0%
+could possibly build has this property
+then of course all the ones that we can
+
+ align:start position:0%
+then of course all the ones that we can
+ 
+
+ align:start position:0%
+then of course all the ones that we can
+actually reach also have this property
+
+ align:start position:0%
+actually reach also have this property
+ 
+
+ align:start position:0%
+actually reach also have this property
+uh so X+ Y is indeed an integer linear
+
+ align:start position:0%
+uh so X+ Y is indeed an integer linear
+ 
+
+ align:start position:0%
+uh so X+ Y is indeed an integer linear
+combination of a uh A and
+
+ align:start position:0%
+combination of a uh A and
+ 
+
+ align:start position:0%
+combination of a uh A and
+B um Etc and of proof okay I don't want
+
+ align:start position:0%
+B um Etc and of proof okay I don't want
+ 
+
+ align:start position:0%
+B um Etc and of proof okay I don't want
+to prove it for for every single
+
+ align:start position:0%
+to prove it for for every single
+ 
+
+ align:start position:0%
+to prove it for for every single
+transition here uh just because there's
+
+ align:start position:0%
+transition here uh just because there's
+ 
+
+ align:start position:0%
+transition here uh just because there's
+a bunch of them but for example a is
+
+ align:start position:0%
+a bunch of them but for example a is
+ 
+
+ align:start position:0%
+a bunch of them but for example a is
+indeed an integer linear combination of
+
+ align:start position:0%
+indeed an integer linear combination of
+ 
+
+ align:start position:0%
+indeed an integer linear combination of
+A and B it's 1 * a plus 0 * B this one
+
+ align:start position:0%
+A and B it's 1 * a plus 0 * B this one
+ 
+
+ align:start position:0%
+A and B it's 1 * a plus 0 * B this one
+looks mess here it's actually just X+ y
+
+ align:start position:0%
+looks mess here it's actually just X+ y
+ 
+
+ align:start position:0%
+looks mess here it's actually just X+ y
+minus B so it's almost the same you just
+
+ align:start position:0%
+minus B so it's almost the same you just
+ 
+
+ align:start position:0%
+minus B so it's almost the same you just
+add a minus one here but the general
+
+ align:start position:0%
+add a minus one here but the general
+ 
+
+ align:start position:0%
+add a minus one here but the general
+property we're using here is that all of
+
+ align:start position:0%
+property we're using here is that all of
+ 
+
+ align:start position:0%
+property we're using here is that all of
+the constructible numbers here are
+
+ align:start position:0%
+the constructible numbers here are
+ 
+
+ align:start position:0%
+the constructible numbers here are
+integer linear combinations of X Y A and
+
+ align:start position:0%
+integer linear combinations of X Y A and
+ 
+
+ align:start position:0%
+integer linear combinations of X Y A and
+B Okay I lied we're using integer linear
+
+ align:start position:0%
+B Okay I lied we're using integer linear
+ 
+
+ align:start position:0%
+B Okay I lied we're using integer linear
+combinations of four things but all of
+
+ align:start position:0%
+combinations of four things but all of
+ 
+
+ align:start position:0%
+combinations of four things but all of
+the X and y's are also integer linear
+
+ align:start position:0%
+the X and y's are also integer linear
+ 
+
+ align:start position:0%
+the X and y's are also integer linear
+combinations of a and B so what we're
+
+ align:start position:0%
+combinations of a and B so what we're
+ 
+
+ align:start position:0%
+combinations of a and B so what we're
+really taking is integer linear
+
+ align:start position:0%
+really taking is integer linear
+ 
+
+ align:start position:0%
+really taking is integer linear
+combinations of integer linear
+
+ align:start position:0%
+combinations of integer linear
+ 
+
+ align:start position:0%
+combinations of integer linear
+combinations of A and B and it turns out
+
+ align:start position:0%
+combinations of A and B and it turns out
+ 
+
+ align:start position:0%
+combinations of A and B and it turns out
+that if you take two integer linear
+
+ align:start position:0%
+that if you take two integer linear
+ 
+
+ align:start position:0%
+that if you take two integer linear
+combinations of A and B like X and Y and
+
+ align:start position:0%
+combinations of A and B like X and Y and
+ 
+
+ align:start position:0%
+combinations of A and B like X and Y and
+you add them together or in general take
+
+ align:start position:0%
+you add them together or in general take
+ 
+
+ align:start position:0%
+you add them together or in general take
+an integer linear combination of them
+
+ align:start position:0%
+an integer linear combination of them
+ 
+
+ align:start position:0%
+an integer linear combination of them
+you still get an integer linear
+
+ align:start position:0%
+you still get an integer linear
+ 
+
+ align:start position:0%
+you still get an integer linear
+combination of A and B as you can see
+
+ align:start position:0%
+combination of A and B as you can see
+ 
+
+ align:start position:0%
+combination of A and B as you can see
+from this proof it's actually pretty
+
+ align:start position:0%
+from this proof it's actually pretty
+ 
+
+ align:start position:0%
+from this proof it's actually pretty
+much the same proof we were doing over
+
+ align:start position:0%
+much the same proof we were doing over
+ 
+
+ align:start position:0%
+much the same proof we were doing over
+here uh this was integer linear
+
+ align:start position:0%
+here uh this was integer linear
+ 
+
+ align:start position:0%
+here uh this was integer linear
+combinations of one number D and
+
+ align:start position:0%
+combinations of one number D and
+ 
+
+ align:start position:0%
+combinations of one number D and
+divisibility was preserved even when you
+
+ align:start position:0%
+divisibility was preserved even when you
+ 
+
+ align:start position:0%
+divisibility was preserved even when you
+took inte linear combinations so same
+
+ align:start position:0%
+took inte linear combinations so same
+ 
+
+ align:start position:0%
+took inte linear combinations so same
+idea and for any puzzle where you have
+
+ align:start position:0%
+idea and for any puzzle where you have
+ 
+
+ align:start position:0%
+idea and for any puzzle where you have
+that property you can only construct
+
+ align:start position:0%
+that property you can only construct
+ 
+
+ align:start position:0%
+that property you can only construct
+numbers that are integer linear
+
+ align:start position:0%
+numbers that are integer linear
+ 
+
+ align:start position:0%
+numbers that are integer linear
+combinations of A and B now for this
+
+ align:start position:0%
+combinations of A and B now for this
+ 
+
+ align:start position:0%
+combinations of A and B now for this
+puzzle you can actually construct all of
+
+ align:start position:0%
+puzzle you can actually construct all of
+ 
+
+ align:start position:0%
+puzzle you can actually construct all of
+them that fit in the
+
+ align:start position:0%
+them that fit in the
+ 
+
+ align:start position:0%
+them that fit in the
+jars uh
+
+ align:start position:0%
+jars uh
+ 
+
+ align:start position:0%
+jars uh
+so I'll just mention this as a claim and
+
+ align:start position:0%
+so I'll just mention this as a claim and
+ 
+
+ align:start position:0%
+so I'll just mention this as a claim and
+if we have time at the end we'll come
+
+ align:start position:0%
+if we have time at the end we'll come
+ 
+
+ align:start position:0%
+if we have time at the end we'll come
+back to
+
+ align:start position:0%
+back to
+ 
+
+ align:start position:0%
+back to
+it uh we
+
+ align:start position:0%
+it uh we
+ 
+
+ align:start position:0%
+it uh we
+can we can
+
+ align:start position:0%
+can we can
+ 
+
+ align:start position:0%
+can we can
+obtain uh a value
+
+ align:start position:0%
+obtain uh a value
+ 
+
+ align:start position:0%
+obtain uh a value
+X um if and only
+
+ align:start position:0%
+X um if and only
+ 
+
+ align:start position:0%
+X um if and only
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's say x is an integer linear
+
+ align:start position:0%
+uh let's say x is an integer linear
+ 
+
+ align:start position:0%
+uh let's say x is an integer linear
+combination of A and
+
+ align:start position:0%
+combination of A and
+ 
+
+ align:start position:0%
+combination of A and
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh Z is less than equal to X is less
+
+ align:start position:0%
+uh Z is less than equal to X is less
+ 
+
+ align:start position:0%
+uh Z is less than equal to X is less
+than equal to Max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of okay so we might try to um prove that
+
+ align:start position:0%
+of okay so we might try to um prove that
+ 
+
+ align:start position:0%
+of okay so we might try to um prove that
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+uh so now the central question is how do
+
+ align:start position:0%
+uh so now the central question is how do
+ 
+
+ align:start position:0%
+uh so now the central question is how do
+we know whether one number is an integer
+
+ align:start position:0%
+we know whether one number is an integer
+ 
+
+ align:start position:0%
+we know whether one number is an integer
+linear combination of two other numbers
+
+ align:start position:0%
+linear combination of two other numbers
+ 
+
+ align:start position:0%
+linear combination of two other numbers
+and when it is can we actually construct
+
+ align:start position:0%
+and when it is can we actually construct
+ 
+
+ align:start position:0%
+and when it is can we actually construct
+the values s and t so that sa a plus TB
+
+ align:start position:0%
+the values s and t so that sa a plus TB
+ 
+
+ align:start position:0%
+the values s and t so that sa a plus TB
+equals x because that's what we needed
+
+ align:start position:0%
+equals x because that's what we needed
+ 
+
+ align:start position:0%
+equals x because that's what we needed
+to solve this puzzle was some way to uh
+
+ align:start position:0%
+to solve this puzzle was some way to uh
+ 
+
+ align:start position:0%
+to solve this puzzle was some way to uh
+we were only given the capacities of the
+
+ align:start position:0%
+we were only given the capacities of the
+ 
+
+ align:start position:0%
+we were only given the capacities of the
+jars and the target value and now we
+
+ align:start position:0%
+jars and the target value and now we
+ 
+
+ align:start position:0%
+jars and the target value and now we
+want to represent oh let's check that
+
+ align:start position:0%
+want to represent oh let's check that
+ 
+
+ align:start position:0%
+want to represent oh let's check that
+this is actually possible for this
+
+ align:start position:0%
+this is actually possible for this
+ 
+
+ align:start position:0%
+this is actually possible for this
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so if we um sorry not this example
+
+ align:start position:0%
+uh so if we um sorry not this example
+ 
+
+ align:start position:0%
+uh so if we um sorry not this example
+the one that's actually solvable so for
+
+ align:start position:0%
+the one that's actually solvable so for
+ 
+
+ align:start position:0%
+the one that's actually solvable so for
+this solvable puzzle uh 4 equals 2 * 5
+
+ align:start position:0%
+this solvable puzzle uh 4 equals 2 * 5
+ 
+
+ align:start position:0%
+this solvable puzzle uh 4 equals 2 * 5
+that's 10 minus 2 * 3 that's
+
+ align:start position:0%
+that's 10 minus 2 * 3 that's
+ 
+
+ align:start position:0%
+that's 10 minus 2 * 3 that's
+six right 10 - 6 is four so that's
+
+ align:start position:0%
+six right 10 - 6 is four so that's
+ 
+
+ align:start position:0%
+six right 10 - 6 is four so that's
+intuitively why this puzzle is solvable
+
+ align:start position:0%
+intuitively why this puzzle is solvable
+ 
+
+ align:start position:0%
+intuitively why this puzzle is solvable
+although that's not a proof I mean we
+
+ align:start position:0%
+although that's not a proof I mean we
+ 
+
+ align:start position:0%
+although that's not a proof I mean we
+just saw that it wasn't limited by this
+
+ align:start position:0%
+just saw that it wasn't limited by this
+ 
+
+ align:start position:0%
+just saw that it wasn't limited by this
+same issue uh so for example if we
+
+ align:start position:0%
+same issue uh so for example if we
+ 
+
+ align:start position:0%
+same issue uh so for example if we
+started with six and
+
+ align:start position:0%
+started with six and
+ 
+
+ align:start position:0%
+started with six and
+four We Know by this Lemma because two
+
+ align:start position:0%
+four We Know by this Lemma because two
+ 
+
+ align:start position:0%
+four We Know by this Lemma because two
+divides four and two divides six two
+
+ align:start position:0%
+divides four and two divides six two
+ 
+
+ align:start position:0%
+divides four and two divides six two
+will divide any integer linear
+
+ align:start position:0%
+will divide any integer linear
+ 
+
+ align:start position:0%
+will divide any integer linear
+combination and therefore any
+
+ align:start position:0%
+combination and therefore any
+ 
+
+ align:start position:0%
+combination and therefore any
+reachable uh value in this puzzle and
+
+ align:start position:0%
+reachable uh value in this puzzle and
+ 
+
+ align:start position:0%
+reachable uh value in this puzzle and
+two does not divide three three is odd
+
+ align:start position:0%
+two does not divide three three is odd
+ 
+
+ align:start position:0%
+two does not divide three three is odd
+not even and so we will never be able to
+
+ align:start position:0%
+not even and so we will never be able to
+ 
+
+ align:start position:0%
+not even and so we will never be able to
+reach three because all the reachable
+
+ align:start position:0%
+reach three because all the reachable
+ 
+
+ align:start position:0%
+reach three because all the reachable
+states are even that's a corollary now
+
+ align:start position:0%
+states are even that's a corollary now
+ 
+
+ align:start position:0%
+states are even that's a corollary now
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+Lemma okay um
+
+ align:start position:0%
+Lemma okay um
+ 
+
+ align:start position:0%
+Lemma okay um
+okay but how when in the good case in
+
+ align:start position:0%
+okay but how when in the good case in
+ 
+
+ align:start position:0%
+okay but how when in the good case in
+the bad case it's easy to see I guess uh
+
+ align:start position:0%
+the bad case it's easy to see I guess uh
+ 
+
+ align:start position:0%
+the bad case it's easy to see I guess uh
+how how do we know whether we're in a
+
+ align:start position:0%
+how how do we know whether we're in a
+ 
+
+ align:start position:0%
+how how do we know whether we're in a
+good case or a bad case how do we know
+
+ align:start position:0%
+good case or a bad case how do we know
+ 
+
+ align:start position:0%
+good case or a bad case how do we know
+whether X is a integer linear
+
+ align:start position:0%
+whether X is a integer linear
+ 
+
+ align:start position:0%
+whether X is a integer linear
+combination of A and B given X and A and
+
+ align:start position:0%
+combination of A and B given X and A and
+ 
+
+ align:start position:0%
+combination of A and B given X and A and
+B that is kind of the purpose of the
+
+ align:start position:0%
+B that is kind of the purpose of the
+ 
+
+ align:start position:0%
+B that is kind of the purpose of the
+well some motivation for the rest of
+
+ align:start position:0%
+well some motivation for the rest of
+ 
+
+ align:start position:0%
+well some motivation for the rest of
+this lecture we can use it for all sorts
+
+ align:start position:0%
+this lecture we can use it for all sorts
+ 
+
+ align:start position:0%
+this lecture we can use it for all sorts
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+things all right and I claim that this
+
+ align:start position:0%
+things all right and I claim that this
+ 
+
+ align:start position:0%
+things all right and I claim that this
+is going to be true um if and only
+
+ align:start position:0%
+is going to be true um if and only
+ 
+
+ align:start position:0%
+is going to be true um if and only
+if uh
+
+ align:start position:0%
+if uh
+ 
+
+ align:start position:0%
+if uh
+this property is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true so now I'm going to restate this in
+
+ align:start position:0%
+true so now I'm going to restate this in
+ 
+
+ align:start position:0%
+true so now I'm going to restate this in
+terms of divisibility this is this
+
+ align:start position:0%
+terms of divisibility this is this
+ 
+
+ align:start position:0%
+terms of divisibility this is this
+equivalence is not obvious we'll prove
+
+ align:start position:0%
+equivalence is not obvious we'll prove
+ 
+
+ align:start position:0%
+equivalence is not obvious we'll prove
+it by the end of today um so I claim
+
+ align:start position:0%
+it by the end of today um so I claim
+ 
+
+ align:start position:0%
+it by the end of today um so I claim
+what what we really want to shows that
+
+ align:start position:0%
+what what we really want to shows that
+ 
+
+ align:start position:0%
+what what we really want to shows that
+every common divisor of A and B remember
+
+ align:start position:0%
+every common divisor of A and B remember
+ 
+
+ align:start position:0%
+every common divisor of A and B remember
+this is our definition of d is a common
+
+ align:start position:0%
+this is our definition of d is a common
+ 
+
+ align:start position:0%
+this is our definition of d is a common
+divisor
+
+ align:start position:0%
+divisor
+ 
+
+ align:start position:0%
+divisor
+uh common divisor of A and B divides a
+
+ align:start position:0%
+uh common divisor of A and B divides a
+ 
+
+ align:start position:0%
+uh common divisor of A and B divides a
+and it divides B um then it should also
+
+ align:start position:0%
+and it divides B um then it should also
+ 
+
+ align:start position:0%
+and it divides B um then it should also
+divide X so in the example uh we saw
+
+ align:start position:0%
+divide X so in the example uh we saw
+ 
+
+ align:start position:0%
+divide X so in the example uh we saw
+that two was a common divisor of four
+
+ align:start position:0%
+that two was a common divisor of four
+ 
+
+ align:start position:0%
+that two was a common divisor of four
+and six and so two better divide
+
+ align:start position:0%
+and six and so two better divide
+ 
+
+ align:start position:0%
+and six and so two better divide
+anything that we make uh what are the
+
+ align:start position:0%
+anything that we make uh what are the
+ 
+
+ align:start position:0%
+anything that we make uh what are the
+common divisors of five and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three three doesn't work five doesn't
+
+ align:start position:0%
+three three doesn't work five doesn't
+ 
+
+ align:start position:0%
+three three doesn't work five doesn't
+work two doesn't work four doesn't work
+
+ align:start position:0%
+work two doesn't work four doesn't work
+ 
+
+ align:start position:0%
+work two doesn't work four doesn't work
+I guess one is a common divisor one
+
+ align:start position:0%
+I guess one is a common divisor one
+ 
+
+ align:start position:0%
+I guess one is a common divisor one
+divides
+
+ align:start position:0%
+divides
+ 
+
+ align:start position:0%
+divides
+everything uh
+
+ align:start position:0%
+everything uh
+ 
+
+ align:start position:0%
+everything uh
+so yeah that's also this is true in our
+
+ align:start position:0%
+so yeah that's also this is true in our
+ 
+
+ align:start position:0%
+so yeah that's also this is true in our
+in our good case
+
+ align:start position:0%
+in our good case
+ 
+
+ align:start position:0%
+in our good case
+uh and this we can rewrite in yet
+
+ align:start position:0%
+uh and this we can rewrite in yet
+ 
+
+ align:start position:0%
+uh and this we can rewrite in yet
+another way which motivates our next
+
+ align:start position:0%
+another way which motivates our next
+ 
+
+ align:start position:0%
+another way which motivates our next
+topic uh the gcd of A and B divides X
+
+ align:start position:0%
+topic uh the gcd of A and B divides X
+ 
+
+ align:start position:0%
+topic uh the gcd of A and B divides X
+okay so I claim in particular this is
+
+ align:start position:0%
+okay so I claim in particular this is
+ 
+
+ align:start position:0%
+okay so I claim in particular this is
+going to be a way to tell whether X is
+
+ align:start position:0%
+going to be a way to tell whether X is
+ 
+
+ align:start position:0%
+going to be a way to tell whether X is
+an integer linear combination of A and B
+
+ align:start position:0%
+an integer linear combination of A and B
+ 
+
+ align:start position:0%
+an integer linear combination of A and B
+you compute something called the gcd of
+
+ align:start position:0%
+you compute something called the gcd of
+ 
+
+ align:start position:0%
+you compute something called the gcd of
+A and B and you see whether it divides X
+
+ align:start position:0%
+A and B and you see whether it divides X
+ 
+
+ align:start position:0%
+A and B and you see whether it divides X
+so let's talk about gcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gcd is another acronym it stands for uh
+
+ align:start position:0%
+gcd is another acronym it stands for uh
+ 
+
+ align:start position:0%
+gcd is another acronym it stands for uh
+greatest common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisor I assume it comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from uh Britain in particular where they
+
+ align:start position:0%
+from uh Britain in particular where they
+ 
+
+ align:start position:0%
+from uh Britain in particular where they
+use great to to indicate large uh so we
+
+ align:start position:0%
+use great to to indicate large uh so we
+ 
+
+ align:start position:0%
+use great to to indicate large uh so we
+might call call this the largest common
+
+ align:start position:0%
+might call call this the largest common
+ 
+
+ align:start position:0%
+might call call this the largest common
+divisor uh or the biggest common divisor
+
+ align:start position:0%
+divisor uh or the biggest common divisor
+ 
+
+ align:start position:0%
+divisor uh or the biggest common divisor
+all synonyms for the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so this is the I'm going to give two
+
+ align:start position:0%
+um so this is the I'm going to give two
+ 
+
+ align:start position:0%
+um so this is the I'm going to give two
+equivalent definitions of
+
+ align:start position:0%
+equivalent definitions of
+ 
+
+ align:start position:0%
+equivalent definitions of
+gcd to me the more intuitive one is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's a little bit uglier because it
+
+ align:start position:0%
+but it's a little bit uglier because it
+ 
+
+ align:start position:0%
+but it's a little bit uglier because it
+has a special case so what I'd like to
+
+ align:start position:0%
+has a special case so what I'd like to
+ 
+
+ align:start position:0%
+has a special case so what I'd like to
+say is the gcd of A and B is the largest
+
+ align:start position:0%
+say is the gcd of A and B is the largest
+ 
+
+ align:start position:0%
+say is the gcd of A and B is the largest
+integer D such that D divides A and D
+
+ align:start position:0%
+integer D such that D divides A and D
+ 
+
+ align:start position:0%
+integer D such that D divides A and D
+divides B again this is common common
+
+ align:start position:0%
+divides B again this is common common
+ 
+
+ align:start position:0%
+divides B again this is common common
+divisor D is a common divisor of A and B
+
+ align:start position:0%
+divisor D is a common divisor of A and B
+ 
+
+ align:start position:0%
+divisor D is a common divisor of A and B
+I want it to be the largest common
+
+ align:start position:0%
+I want it to be the largest common
+ 
+
+ align:start position:0%
+I want it to be the largest common
+diviser that would be gcd uh but there's
+
+ align:start position:0%
+diviser that would be gcd uh but there's
+ 
+
+ align:start position:0%
+diviser that would be gcd uh but there's
+one annoying special case which really
+
+ align:start position:0%
+one annoying special case which really
+ 
+
+ align:start position:0%
+one annoying special case which really
+won't matter for the rest of lecture but
+
+ align:start position:0%
+won't matter for the rest of lecture but
+ 
+
+ align:start position:0%
+won't matter for the rest of lecture but
+to be technically correct we should say
+
+ align:start position:0%
+to be technically correct we should say
+ 
+
+ align:start position:0%
+to be technically correct we should say
+what happens when you compute the gcd of
+
+ align:start position:0%
+what happens when you compute the gcd of
+ 
+
+ align:start position:0%
+what happens when you compute the gcd of
+Z and zero because remember every
+
+ align:start position:0%
+Z and zero because remember every
+ 
+
+ align:start position:0%
+Z and zero because remember every
+integer D divides zero everything
+
+ align:start position:0%
+integer D divides zero everything
+ 
+
+ align:start position:0%
+integer D divides zero everything
+divides zero so what's the largest
+
+ align:start position:0%
+divides zero so what's the largest
+ 
+
+ align:start position:0%
+divides zero so what's the largest
+diviser of zero and zero I mean Infinity
+
+ align:start position:0%
+diviser of zero and zero I mean Infinity
+ 
+
+ align:start position:0%
+diviser of zero and zero I mean Infinity
+I don't know it's like there is no such
+
+ align:start position:0%
+I don't know it's like there is no such
+ 
+
+ align:start position:0%
+I don't know it's like there is no such
+integer that's the largest so there is
+
+ align:start position:0%
+integer that's the largest so there is
+ 
+
+ align:start position:0%
+integer that's the largest so there is
+no largest integer uh so in this case it
+
+ align:start position:0%
+no largest integer uh so in this case it
+ 
+
+ align:start position:0%
+no largest integer uh so in this case it
+turns out the right thing is to Define
+
+ align:start position:0%
+turns out the right thing is to Define
+ 
+
+ align:start position:0%
+turns out the right thing is to Define
+gcd of 0 comma 0 to be zero that will be
+
+ align:start position:0%
+gcd of 0 comma 0 to be zero that will be
+ 
+
+ align:start position:0%
+gcd of 0 comma 0 to be zero that will be
+a little counterintuitive maybe uh until
+
+ align:start position:0%
+a little counterintuitive maybe uh until
+ 
+
+ align:start position:0%
+a little counterintuitive maybe uh until
+you see the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition Okay so
+
+ align:start position:0%
+definition Okay so
+ 
+
+ align:start position:0%
+definition Okay so
+here's another
+
+ align:start position:0%
+here's another
+ 
+
+ align:start position:0%
+here's another
+definition gcd is uh the only non-
+
+ align:start position:0%
+definition gcd is uh the only non-
+ 
+
+ align:start position:0%
+definition gcd is uh the only non-
+negative common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisor of A and
+
+ align:start position:0%
+divisor of A and
+ 
+
+ align:start position:0%
+divisor of A and
+B uh divisible by all common divisors of
+
+ align:start position:0%
+B uh divisible by all common divisors of
+ 
+
+ align:start position:0%
+B uh divisible by all common divisors of
+A and B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh another way to think about
+
+ align:start position:0%
+okay so uh another way to think about
+ 
+
+ align:start position:0%
+okay so uh another way to think about
+the large the greatest common divisor is
+
+ align:start position:0%
+the large the greatest common divisor is
+ 
+
+ align:start position:0%
+the large the greatest common divisor is
+it's greatest in terms of the
+
+ align:start position:0%
+it's greatest in terms of the
+ 
+
+ align:start position:0%
+it's greatest in terms of the
+divisibility relation um the one that is
+
+ align:start position:0%
+divisibility relation um the one that is
+ 
+
+ align:start position:0%
+divisibility relation um the one that is
+uh the most divisible by by other common
+
+ align:start position:0%
+uh the most divisible by by other common
+ 
+
+ align:start position:0%
+uh the most divisible by by other common
+divisors so it turns out there's going
+
+ align:start position:0%
+divisors so it turns out there's going
+ 
+
+ align:start position:0%
+divisors so it turns out there's going
+to be one common divisor that's both
+
+ align:start position:0%
+to be one common divisor that's both
+ 
+
+ align:start position:0%
+to be one common divisor that's both
+non- negative and is divisible by all
+
+ align:start position:0%
+non- negative and is divisible by all
+ 
+
+ align:start position:0%
+non- negative and is divisible by all
+common divisor of A and B uh so in these
+
+ align:start position:0%
+common divisor of A and B uh so in these
+ 
+
+ align:start position:0%
+common divisor of A and B uh so in these
+examples uh for four and six gcd
+
+ align:start position:0%
+examples uh for four and six gcd
+ 
+
+ align:start position:0%
+examples uh for four and six gcd
+of of 6 and four is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two uh because the only let's see the
+
+ align:start position:0%
+two uh because the only let's see the
+ 
+
+ align:start position:0%
+two uh because the only let's see the
+the common divisors if we think what are
+
+ align:start position:0%
+the common divisors if we think what are
+ 
+
+ align:start position:0%
+the common divisors if we think what are
+all the common
+
+ align:start position:0%
+all the common
+ 
+
+ align:start position:0%
+all the common
+divisors between four and
+
+ align:start position:0%
+divisors between four and
+ 
+
+ align:start position:0%
+divisors between four and
+six uh maybe obvious there there's two
+
+ align:start position:0%
+six uh maybe obvious there there's two
+ 
+
+ align:start position:0%
+six uh maybe obvious there there's two
+there's minus two uh there's one and
+
+ align:start position:0%
+there's minus two uh there's one and
+ 
+
+ align:start position:0%
+there's minus two uh there's one and
+minus one zero divides nothing except
+
+ align:start position:0%
+minus one zero divides nothing except
+ 
+
+ align:start position:0%
+minus one zero divides nothing except
+itself and all you can check all the
+
+ align:start position:0%
+itself and all you can check all the
+ 
+
+ align:start position:0%
+itself and all you can check all the
+numbers between like6 and six uh those
+
+ align:start position:0%
+numbers between like6 and six uh those
+ 
+
+ align:start position:0%
+numbers between like6 and six uh those
+are the possible divisors um and uh
+
+ align:start position:0%
+are the possible divisors um and uh
+ 
+
+ align:start position:0%
+are the possible divisors um and uh
+these are the only ones that divide both
+
+ align:start position:0%
+these are the only ones that divide both
+ 
+
+ align:start position:0%
+these are the only ones that divide both
+A and B and the
+
+ align:start position:0%
+A and B and the
+ 
+
+ align:start position:0%
+A and B and the
+largest uh non- negative one here is two
+
+ align:start position:0%
+largest uh non- negative one here is two
+ 
+
+ align:start position:0%
+largest uh non- negative one here is two
+and also it has the property that all of
+
+ align:start position:0%
+and also it has the property that all of
+ 
+
+ align:start position:0%
+and also it has the property that all of
+these other common divisors divide
+
+ align:start position:0%
+these other common divisors divide
+ 
+
+ align:start position:0%
+these other common divisors divide
+two okay so uh whichever way you want to
+
+ align:start position:0%
+two okay so uh whichever way you want to
+ 
+
+ align:start position:0%
+two okay so uh whichever way you want to
+think about it you can use either
+
+ align:start position:0%
+think about it you can use either
+ 
+
+ align:start position:0%
+think about it you can use either
+definition I'm not going to prove that
+
+ align:start position:0%
+definition I'm not going to prove that
+ 
+
+ align:start position:0%
+definition I'm not going to prove that
+these definitions are equivalent we're
+
+ align:start position:0%
+these definitions are equivalent we're
+ 
+
+ align:start position:0%
+these definitions are equivalent we're
+just going to take it as an axiom but
+
+ align:start position:0%
+just going to take it as an axiom but
+ 
+
+ align:start position:0%
+just going to take it as an axiom but
+you can prove it uh this maybe an
+
+ align:start position:0%
+you can prove it uh this maybe an
+ 
+
+ align:start position:0%
+you can prove it uh this maybe an
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+uh so we but when we're proving things
+
+ align:start position:0%
+uh so we but when we're proving things
+ 
+
+ align:start position:0%
+uh so we but when we're proving things
+about gcd we can use either of these
+
+ align:start position:0%
+about gcd we can use either of these
+ 
+
+ align:start position:0%
+about gcd we can use either of these
+definitions whichever is more
+
+ align:start position:0%
+definitions whichever is more
+ 
+
+ align:start position:0%
+definitions whichever is more
+convenient so let's um do one more
+
+ align:start position:0%
+convenient so let's um do one more
+ 
+
+ align:start position:0%
+convenient so let's um do one more
+interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example which
+
+ align:start position:0%
+example which
+ 
+
+ align:start position:0%
+example which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+gcd of I think I want to do zero first Z
+
+ align:start position:0%
+gcd of I think I want to do zero first Z
+ 
+
+ align:start position:0%
+gcd of I think I want to do zero first Z
+comma a so suppose I want to compute gcd
+
+ align:start position:0%
+comma a so suppose I want to compute gcd
+ 
+
+ align:start position:0%
+comma a so suppose I want to compute gcd
+of two numbers maybe I should put a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there uh and one of them is
+
+ align:start position:0%
+there uh and one of them is
+ 
+
+ align:start position:0%
+there uh and one of them is
+zero any
+
+ align:start position:0%
+zero any
+ 
+
+ align:start position:0%
+zero any
+guesses what the gcd of zero and B
+
+ align:start position:0%
+guesses what the gcd of zero and B
+ 
+
+ align:start position:0%
+guesses what the gcd of zero and B
+should be remember everything divides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero B is a good guess almost right what
+
+ align:start position:0%
+zero B is a good guess almost right what
+ 
+
+ align:start position:0%
+zero B is a good guess almost right what
+if B was -7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should be absolute value of B so uh if
+
+ align:start position:0%
+should be absolute value of B so uh if
+ 
+
+ align:start position:0%
+should be absolute value of B so uh if
+we want to handle positive and negative
+
+ align:start position:0%
+we want to handle positive and negative
+ 
+
+ align:start position:0%
+we want to handle positive and negative
+things this turns out to be the right
+
+ align:start position:0%
+things this turns out to be the right
+ 
+
+ align:start position:0%
+things this turns out to be the right
+answer uh here is a mini
+
+ align:start position:0%
+answer uh here is a mini
+ 
+
+ align:start position:0%
+answer uh here is a mini
+proof uh there are two things we want to
+
+ align:start position:0%
+proof uh there are two things we want to
+ 
+
+ align:start position:0%
+proof uh there are two things we want to
+check one is that absolute value of B is
+
+ align:start position:0%
+check one is that absolute value of B is
+ 
+
+ align:start position:0%
+check one is that absolute value of B is
+a common divisor of zero and B uh so
+
+ align:start position:0%
+a common divisor of zero and B uh so
+ 
+
+ align:start position:0%
+a common divisor of zero and B uh so
+well the absolute value of B this gets
+
+ align:start position:0%
+well the absolute value of B this gets
+ 
+
+ align:start position:0%
+well the absolute value of B this gets
+notationally pretty gross divides zero
+
+ align:start position:0%
+notationally pretty gross divides zero
+ 
+
+ align:start position:0%
+notationally pretty gross divides zero
+that's true because everything divides
+
+ align:start position:0%
+that's true because everything divides
+ 
+
+ align:start position:0%
+that's true because everything divides
+zero uh and absolute value of B divides
+
+ align:start position:0%
+zero uh and absolute value of B divides
+ 
+
+ align:start position:0%
+zero uh and absolute value of B divides
+B namely when we let K be uh1 or one
+
+ align:start position:0%
+B namely when we let K be uh1 or one
+ 
+
+ align:start position:0%
+B namely when we let K be uh1 or one
+depending on whether B was positive or
+
+ align:start position:0%
+depending on whether B was positive or
+ 
+
+ align:start position:0%
+depending on whether B was positive or
+negative or
+
+ align:start position:0%
+negative or
+ 
+
+ align:start position:0%
+negative or
+zero um cool so uh good it is a common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisor and now I want to claim that
+
+ align:start position:0%
+divisor and now I want to claim that
+ 
+
+ align:start position:0%
+divisor and now I want to claim that
+it's the greatest common divisor
+
+ align:start position:0%
+it's the greatest common divisor
+ 
+
+ align:start position:0%
+it's the greatest common divisor
+according to the second definition so
+
+ align:start position:0%
+according to the second definition so
+ 
+
+ align:start position:0%
+according to the second definition so
+let's suppose that we had some number D
+
+ align:start position:0%
+let's suppose that we had some number D
+ 
+
+ align:start position:0%
+let's suppose that we had some number D
+which divides zero and which divides
+
+ align:start position:0%
+which divides zero and which divides
+ 
+
+ align:start position:0%
+which divides zero and which divides
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+B so d divid z and d divides B then uh I
+
+ align:start position:0%
+B so d divid z and d divides B then uh I
+ 
+
+ align:start position:0%
+B so d divid z and d divides B then uh I
+claim in particular D also
+
+ align:start position:0%
+claim in particular D also
+ 
+
+ align:start position:0%
+claim in particular D also
+divides uh the absolute value of
+
+ align:start position:0%
+divides uh the absolute value of
+ 
+
+ align:start position:0%
+divides uh the absolute value of
+B Because if you divide a number you
+
+ align:start position:0%
+B Because if you divide a number you
+ 
+
+ align:start position:0%
+B Because if you divide a number you
+also divide its negation just by
+
+ align:start position:0%
+also divide its negation just by
+ 
+
+ align:start position:0%
+also divide its negation just by
+negating the value K that you're
+
+ align:start position:0%
+negating the value K that you're
+ 
+
+ align:start position:0%
+negating the value K that you're
+multiplying by right if I take K * D and
+
+ align:start position:0%
+multiplying by right if I take K * D and
+ 
+
+ align:start position:0%
+multiplying by right if I take K * D and
+I get b i then I take negative K * D and
+
+ align:start position:0%
+I get b i then I take negative K * D and
+ 
+
+ align:start position:0%
+I get b i then I take negative K * D and
+I get absolute value of B if B happened
+
+ align:start position:0%
+I get absolute value of B if B happened
+ 
+
+ align:start position:0%
+I get absolute value of B if B happened
+to be negative okay so that means if
+
+ align:start position:0%
+to be negative okay so that means if
+ 
+
+ align:start position:0%
+to be negative okay so that means if
+you're a common diviser of zero and B
+
+ align:start position:0%
+you're a common diviser of zero and B
+ 
+
+ align:start position:0%
+you're a common diviser of zero and B
+then you're also a common diviser of
+
+ align:start position:0%
+then you're also a common diviser of
+ 
+
+ align:start position:0%
+then you're also a common diviser of
+this thing and that was our defin second
+
+ align:start position:0%
+this thing and that was our defin second
+ 
+
+ align:start position:0%
+this thing and that was our defin second
+definition of gcd uh so great uh this
+
+ align:start position:0%
+definition of gcd uh so great uh this
+ 
+
+ align:start position:0%
+definition of gcd uh so great uh this
+means we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greatest okay uh now the the question
+
+ align:start position:0%
+greatest okay uh now the the question
+ 
+
+ align:start position:0%
+greatest okay uh now the the question
+arises how do we compute gcd of A and B
+
+ align:start position:0%
+arises how do we compute gcd of A and B
+ 
+
+ align:start position:0%
+arises how do we compute gcd of A and B
+because I claimed uh
+
+ align:start position:0%
+because I claimed uh
+ 
+
+ align:start position:0%
+because I claimed uh
+over here that what we need to check is
+
+ align:start position:0%
+over here that what we need to check is
+ 
+
+ align:start position:0%
+over here that what we need to check is
+whether gcd of ab divides X so given a
+
+ align:start position:0%
+whether gcd of ab divides X so given a
+ 
+
+ align:start position:0%
+whether gcd of ab divides X so given a
+and b we need to be able to compute this
+
+ align:start position:0%
+and b we need to be able to compute this
+ 
+
+ align:start position:0%
+and b we need to be able to compute this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+how do we find the greatest common
+
+ align:start position:0%
+how do we find the greatest common
+ 
+
+ align:start position:0%
+how do we find the greatest common
+divisor turns out there's a great
+
+ align:start position:0%
+divisor turns out there's a great
+ 
+
+ align:start position:0%
+divisor turns out there's a great
+algorithm to do it and the base case of
+
+ align:start position:0%
+algorithm to do it and the base case of
+ 
+
+ align:start position:0%
+algorithm to do it and the base case of
+that algorithm is this if we can get one
+
+ align:start position:0%
+that algorithm is this if we can get one
+ 
+
+ align:start position:0%
+that algorithm is this if we can get one
+of the numbers down to zero then that we
+
+ align:start position:0%
+of the numbers down to zero then that we
+ 
+
+ align:start position:0%
+of the numbers down to zero then that we
+found the
+
+ align:start position:0%
+found the
+ 
+
+ align:start position:0%
+found the
+gcd okay so our goal now is given some
+
+ align:start position:0%
+gcd okay so our goal now is given some
+ 
+
+ align:start position:0%
+gcd okay so our goal now is given some
+big numbers to make them smaller
+
+ align:start position:0%
+big numbers to make them smaller
+ 
+
+ align:start position:0%
+big numbers to make them smaller
+somehow and the big idea here to make a
+
+ align:start position:0%
+somehow and the big idea here to make a
+ 
+
+ align:start position:0%
+somehow and the big idea here to make a
+gcd algorithm is
+
+ align:start position:0%
+gcd algorithm is
+ 
+
+ align:start position:0%
+gcd algorithm is
+subtraction how do we make numbers
+
+ align:start position:0%
+subtraction how do we make numbers
+ 
+
+ align:start position:0%
+subtraction how do we make numbers
+smaller with arithmetic subtraction or
+
+ align:start position:0%
+smaller with arithmetic subtraction or
+ 
+
+ align:start position:0%
+smaller with arithmetic subtraction or
+division seem like good ideas we're
+
+ align:start position:0%
+division seem like good ideas we're
+ 
+
+ align:start position:0%
+division seem like good ideas we're
+going to use both starting with
+
+ align:start position:0%
+going to use both starting with
+ 
+
+ align:start position:0%
+going to use both starting with
+subtraction
+
+ align:start position:0%
+subtraction
+ 
+
+ align:start position:0%
+subtraction
+so I
+
+ align:start position:0%
+so I
+ 
+
+ align:start position:0%
+so I
+claim gcd of ab equals gcd of a minus B
+
+ align:start position:0%
+claim gcd of ab equals gcd of a minus B
+ 
+
+ align:start position:0%
+claim gcd of ab equals gcd of a minus B
+comma B comma
+
+ align:start position:0%
+comma B comma
+ 
+
+ align:start position:0%
+comma B comma
+B uh for all integers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so if a and b are big numbers this is
+
+ align:start position:0%
+a so if a and b are big numbers this is
+ 
+
+ align:start position:0%
+a so if a and b are big numbers this is
+pretty cool this is saying we can
+
+ align:start position:0%
+pretty cool this is saying we can
+ 
+
+ align:start position:0%
+pretty cool this is saying we can
+subtract one of the numbers from the
+
+ align:start position:0%
+subtract one of the numbers from the
+ 
+
+ align:start position:0%
+subtract one of the numbers from the
+other and we get the same gcd somehow
+
+ align:start position:0%
+other and we get the same gcd somehow
+ 
+
+ align:start position:0%
+other and we get the same gcd somehow
+okay we'll prove this in a
+
+ align:start position:0%
+okay we'll prove this in a
+ 
+
+ align:start position:0%
+okay we'll prove this in a
+second now actually going leave a little
+
+ align:start position:0%
+second now actually going leave a little
+ 
+
+ align:start position:0%
+second now actually going leave a little
+bit of space let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof okay so um then we're going to
+
+ align:start position:0%
+proof okay so um then we're going to
+ 
+
+ align:start position:0%
+proof okay so um then we're going to
+turn this into an algorithm but let's
+
+ align:start position:0%
+turn this into an algorithm but let's
+ 
+
+ align:start position:0%
+turn this into an algorithm but let's
+first see why this is the case so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we this is a statement about GC CD
+
+ align:start position:0%
+um we this is a statement about GC CD
+ 
+
+ align:start position:0%
+um we this is a statement about GC CD
+gcd is this complicated definition uh
+
+ align:start position:0%
+gcd is this complicated definition uh
+ 
+
+ align:start position:0%
+gcd is this complicated definition uh
+it's a little easier to think about all
+
+ align:start position:0%
+it's a little easier to think about all
+ 
+
+ align:start position:0%
+it's a little easier to think about all
+common divisors you think about the
+
+ align:start position:0%
+common divisors you think about the
+ 
+
+ align:start position:0%
+common divisors you think about the
+common divisors of A and B those are all
+
+ align:start position:0%
+common divisors of A and B those are all
+ 
+
+ align:start position:0%
+common divisors of A and B those are all
+the numbers D where D divides A and D
+
+ align:start position:0%
+the numbers D where D divides A and D
+ 
+
+ align:start position:0%
+the numbers D where D divides A and D
+divides B and you think of the common
+
+ align:start position:0%
+divides B and you think of the common
+ 
+
+ align:start position:0%
+divides B and you think of the common
+divisors of a minus B and B I claim
+
+ align:start position:0%
+divisors of a minus B and B I claim
+ 
+
+ align:start position:0%
+divisors of a minus B and B I claim
+these sets are the same so the set of
+
+ align:start position:0%
+these sets are the same so the set of
+ 
+
+ align:start position:0%
+these sets are the same so the set of
+common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisors of a and
+
+ align:start position:0%
+divisors of a and
+ 
+
+ align:start position:0%
+divisors of a and
+b equals the set of common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divisors of a minus B and
+
+ align:start position:0%
+divisors of a minus B and
+ 
+
+ align:start position:0%
+divisors of a minus B and
+B okay this is a kind of proof we
+
+ align:start position:0%
+B okay this is a kind of proof we
+ 
+
+ align:start position:0%
+B okay this is a kind of proof we
+actually haven't seen in this class yet
+
+ align:start position:0%
+actually haven't seen in this class yet
+ 
+
+ align:start position:0%
+actually haven't seen in this class yet
+uh this is the brace not a minus sign uh
+
+ align:start position:0%
+uh this is the brace not a minus sign uh
+ 
+
+ align:start position:0%
+uh this is the brace not a minus sign uh
+when you want to prove two sets are
+
+ align:start position:0%
+when you want to prove two sets are
+ 
+
+ align:start position:0%
+when you want to prove two sets are
+equal a very common template for such a
+
+ align:start position:0%
+equal a very common template for such a
+ 
+
+ align:start position:0%
+equal a very common template for such a
+proof is to show that every element of
+
+ align:start position:0%
+proof is to show that every element of
+ 
+
+ align:start position:0%
+proof is to show that every element of
+this set is also an element of this set
+
+ align:start position:0%
+this set is also an element of this set
+ 
+
+ align:start position:0%
+this set is also an element of this set
+that if you recall back to our set
+
+ align:start position:0%
+that if you recall back to our set
+ 
+
+ align:start position:0%
+that if you recall back to our set
+definitions in lecture one is that this
+
+ align:start position:0%
+definitions in lecture one is that this
+ 
+
+ align:start position:0%
+definitions in lecture one is that this
+set is contained in this set and also to
+
+ align:start position:0%
+set is contained in this set and also to
+ 
+
+ align:start position:0%
+set is contained in this set and also to
+prove that every element of the second
+
+ align:start position:0%
+prove that every element of the second
+ 
+
+ align:start position:0%
+prove that every element of the second
+set is an element of the first set
+
+ align:start position:0%
+set is an element of the first set
+ 
+
+ align:start position:0%
+set is an element of the first set
+that's saying the second set is a subset
+
+ align:start position:0%
+that's saying the second set is a subset
+ 
+
+ align:start position:0%
+that's saying the second set is a subset
+of the first set so uh we're going to do
+
+ align:start position:0%
+of the first set so uh we're going to do
+ 
+
+ align:start position:0%
+of the first set so uh we're going to do
+a proof in two parts one part one is to
+
+ align:start position:0%
+a proof in two parts one part one is to
+ 
+
+ align:start position:0%
+a proof in two parts one part one is to
+show containment that the first set is
+
+ align:start position:0%
+show containment that the first set is
+ 
+
+ align:start position:0%
+show containment that the first set is
+contained in the second set uh part two
+
+ align:start position:0%
+contained in the second set uh part two
+ 
+
+ align:start position:0%
+contained in the second set uh part two
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here is to show containment in the other
+
+ align:start position:0%
+here is to show containment in the other
+ 
+
+ align:start position:0%
+here is to show containment in the other
+direction this set is a suet of this set
+
+ align:start position:0%
+direction this set is a suet of this set
+ 
+
+ align:start position:0%
+direction this set is a suet of this set
+okay if I can prove that these sets are
+
+ align:start position:0%
+okay if I can prove that these sets are
+ 
+
+ align:start position:0%
+okay if I can prove that these sets are
+equal then in particular the maximum
+
+ align:start position:0%
+equal then in particular the maximum
+ 
+
+ align:start position:0%
+equal then in particular the maximum
+element of these sets if it exists is
+
+ align:start position:0%
+element of these sets if it exists is
+ 
+
+ align:start position:0%
+element of these sets if it exists is
+also going to be equal right if you have
+
+ align:start position:0%
+also going to be equal right if you have
+ 
+
+ align:start position:0%
+also going to be equal right if you have
+two identical sets you take the max
+
+ align:start position:0%
+two identical sets you take the max
+ 
+
+ align:start position:0%
+two identical sets you take the max
+you're going to get the same thing now
+
+ align:start position:0%
+you're going to get the same thing now
+ 
+
+ align:start position:0%
+you're going to get the same thing now
+there's this one I'm using the first
+
+ align:start position:0%
+there's this one I'm using the first
+ 
+
+ align:start position:0%
+there's this one I'm using the first
+definition here of course there's this
+
+ align:start position:0%
+definition here of course there's this
+ 
+
+ align:start position:0%
+definition here of course there's this
+one case when the two numbers are zero
+
+ align:start position:0%
+one case when the two numbers are zero
+ 
+
+ align:start position:0%
+one case when the two numbers are zero
+then there is no maximum because all
+
+ align:start position:0%
+then there is no maximum because all
+ 
+
+ align:start position:0%
+then there is no maximum because all
+integers actually will be common
+
+ align:start position:0%
+integers actually will be common
+ 
+
+ align:start position:0%
+integers actually will be common
+divisors of zero and zero but in that
+
+ align:start position:0%
+divisors of zero and zero but in that
+ 
+
+ align:start position:0%
+divisors of zero and zero but in that
+case again if the sets are equal that
+
+ align:start position:0%
+case again if the sets are equal that
+ 
+
+ align:start position:0%
+case again if the sets are equal that
+means that A and B or these numbers must
+
+ align:start position:0%
+means that A and B or these numbers must
+ 
+
+ align:start position:0%
+means that A and B or these numbers must
+be zero and then of course these numbers
+
+ align:start position:0%
+be zero and then of course these numbers
+ 
+
+ align:start position:0%
+be zero and then of course these numbers
+are also all zero and this this
+
+ align:start position:0%
+are also all zero and this this
+ 
+
+ align:start position:0%
+are also all zero and this this
+statement is trivially true when
+
+ align:start position:0%
+statement is trivially true when
+ 
+
+ align:start position:0%
+statement is trivially true when
+everything's zero okay it's just saying
+
+ align:start position:0%
+everything's zero okay it's just saying
+ 
+
+ align:start position:0%
+everything's zero okay it's just saying
+gcd of 0 comma 0 equals gcd of 0 comma 0
+
+ align:start position:0%
+gcd of 0 comma 0 equals gcd of 0 comma 0
+ 
+
+ align:start position:0%
+gcd of 0 comma 0 equals gcd of 0 comma 0
+that one I'm fine with but as long as
+
+ align:start position:0%
+that one I'm fine with but as long as
+ 
+
+ align:start position:0%
+that one I'm fine with but as long as
+we're not in the z z case these sets
+
+ align:start position:0%
+we're not in the z z case these sets
+ 
+
+ align:start position:0%
+we're not in the z z case these sets
+will be finite and if they're equal then
+
+ align:start position:0%
+will be finite and if they're equal then
+ 
+
+ align:start position:0%
+will be finite and if they're equal then
+their maximums will be the same so this
+
+ align:start position:0%
+their maximums will be the same so this
+ 
+
+ align:start position:0%
+their maximums will be the same so this
+is all I need to show let's do it in two
+
+ align:start position:0%
+is all I need to show let's do it in two
+ 
+
+ align:start position:0%
+is all I need to show let's do it in two
+parts so first we suppose that we have a
+
+ align:start position:0%
+parts so first we suppose that we have a
+ 
+
+ align:start position:0%
+parts so first we suppose that we have a
+common diviser of A and B so that means
+
+ align:start position:0%
+common diviser of A and B so that means
+ 
+
+ align:start position:0%
+common diviser of A and B so that means
+D divides A and D divides B for some
+
+ align:start position:0%
+D divides A and D divides B for some
+ 
+
+ align:start position:0%
+D divides A and D divides B for some
+number number
+
+ align:start position:0%
+number number
+ 
+
+ align:start position:0%
+number number
+B um well I claim that also D divides a
+
+ align:start position:0%
+B um well I claim that also D divides a
+ 
+
+ align:start position:0%
+B um well I claim that also D divides a
+minus B because a minus B is an integer
+
+ align:start position:0%
+minus B because a minus B is an integer
+ 
+
+ align:start position:0%
+minus B because a minus B is an integer
+linear combination of A and B and we had
+
+ align:start position:0%
+linear combination of A and B and we had
+ 
+
+ align:start position:0%
+linear combination of A and B and we had
+over here in our divisibility fact if D
+
+ align:start position:0%
+over here in our divisibility fact if D
+ 
+
+ align:start position:0%
+over here in our divisibility fact if D
+divides A and D divides B then D divides
+
+ align:start position:0%
+divides A and D divides B then D divides
+ 
+
+ align:start position:0%
+divides A and D divides B then D divides
+every integer linear combination of A
+
+ align:start position:0%
+every integer linear combination of A
+ 
+
+ align:start position:0%
+every integer linear combination of A
+and B so we're plugging in s equal 1
+
+ align:start position:0%
+and B so we're plugging in s equal 1
+ 
+
+ align:start position:0%
+and B so we're plugging in s equal 1
+tals minus one here and we get the D
+
+ align:start position:0%
+tals minus one here and we get the D
+ 
+
+ align:start position:0%
+tals minus one here and we get the D
+divides a minus
+
+ align:start position:0%
+divides a minus
+ 
+
+ align:start position:0%
+divides a minus
+B great so uh we have d divides A and D
+
+ align:start position:0%
+B great so uh we have d divides A and D
+ 
+
+ align:start position:0%
+B great so uh we have d divides A and D
+divid A minus B so in other words uh we
+
+ align:start position:0%
+divid A minus B so in other words uh we
+ 
+
+ align:start position:0%
+divid A minus B so in other words uh we
+have D divid A and D divides a minus B
+
+ align:start position:0%
+have D divid A and D divides a minus B
+ 
+
+ align:start position:0%
+have D divid A and D divides a minus B
+and that sorry wrong one I want to D
+
+ align:start position:0%
+and that sorry wrong one I want to D
+ 
+
+ align:start position:0%
+and that sorry wrong one I want to D
+divides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B and this is the meaning of a common
+
+ align:start position:0%
+B and this is the meaning of a common
+ 
+
+ align:start position:0%
+B and this is the meaning of a common
+divisor of a minus B and B so we we
+
+ align:start position:0%
+divisor of a minus B and B so we we
+ 
+
+ align:start position:0%
+divisor of a minus B and B so we we
+assumed that D was a common divisor of
+
+ align:start position:0%
+assumed that D was a common divisor of
+ 
+
+ align:start position:0%
+assumed that D was a common divisor of
+this we proved that D was a common
+
+ align:start position:0%
+this we proved that D was a common
+ 
+
+ align:start position:0%
+this we proved that D was a common
+divisor of these two numbers therefore
+
+ align:start position:0%
+divisor of these two numbers therefore
+ 
+
+ align:start position:0%
+divisor of these two numbers therefore
+we have containment every element in
+
+ align:start position:0%
+we have containment every element in
+ 
+
+ align:start position:0%
+we have containment every element in
+this set is contained in this set now
+
+ align:start position:0%
+this set is contained in this set now
+ 
+
+ align:start position:0%
+this set is contained in this set now
+let's prove the reverse and that will
+
+ align:start position:0%
+let's prove the reverse and that will
+ 
+
+ align:start position:0%
+let's prove the reverse and that will
+imply that these sets are equal so now
+
+ align:start position:0%
+imply that these sets are equal so now
+ 
+
+ align:start position:0%
+imply that these sets are equal so now
+suppose that D divides a minus B and D
+
+ align:start position:0%
+suppose that D divides a minus B and D
+ 
+
+ align:start position:0%
+suppose that D divides a minus B and D
+divides
+
+ align:start position:0%
+divides
+ 
+
+ align:start position:0%
+divides
+B then I want to show that D divides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+why any
+
+ align:start position:0%
+why any
+ 
+
+ align:start position:0%
+why any
+suggestions can I use integer linear
+
+ align:start position:0%
+suggestions can I use integer linear
+ 
+
+ align:start position:0%
+suggestions can I use integer linear
+combinations yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T equals z I agree if if I put T equals
+
+ align:start position:0%
+T equals z I agree if if I put T equals
+ 
+
+ align:start position:0%
+T equals z I agree if if I put T equals
+0 and S equals 1 then integer this is an
+
+ align:start position:0%
+0 and S equals 1 then integer this is an
+ 
+
+ align:start position:0%
+0 and S equals 1 then integer this is an
+integer linear combination of A and B
+
+ align:start position:0%
+integer linear combination of A and B
+ 
+
+ align:start position:0%
+integer linear combination of A and B
+but in this case I don't know that D
+
+ align:start position:0%
+but in this case I don't know that D
+ 
+
+ align:start position:0%
+but in this case I don't know that D
+divides a that's actually what I want to
+
+ align:start position:0%
+divides a that's actually what I want to
+ 
+
+ align:start position:0%
+divides a that's actually what I want to
+prove so I can't use integer linear
+
+ align:start position:0%
+prove so I can't use integer linear
+ 
+
+ align:start position:0%
+prove so I can't use integer linear
+combinations of A and B but you do Aus I
+
+ align:start position:0%
+combinations of A and B but you do Aus I
+ 
+
+ align:start position:0%
+combinations of A and B but you do Aus I
+can take an integer linear combination
+
+ align:start position:0%
+can take an integer linear combination
+ 
+
+ align:start position:0%
+can take an integer linear combination
+of a minus B and B if I do 1 * this uh
+
+ align:start position:0%
+of a minus B and B if I do 1 * this uh
+ 
+
+ align:start position:0%
+of a minus B and B if I do 1 * this uh
+Plus 1 * this a - b * 1 + 1 * B is
+
+ align:start position:0%
+Plus 1 * this a - b * 1 + 1 * B is
+ 
+
+ align:start position:0%
+Plus 1 * this a - b * 1 + 1 * B is
+a uh so in other words because this
+
+ align:start position:0%
+a uh so in other words because this
+ 
+
+ align:start position:0%
+a uh so in other words because this
+equals the sum a minus B plus
+
+ align:start position:0%
+equals the sum a minus B plus
+ 
+
+ align:start position:0%
+equals the sum a minus B plus
+b and because I know that D is a common
+
+ align:start position:0%
+b and because I know that D is a common
+ 
+
+ align:start position:0%
+b and because I know that D is a common
+divisor of a minus B and B I know that D
+
+ align:start position:0%
+divisor of a minus B and B I know that D
+ 
+
+ align:start position:0%
+divisor of a minus B and B I know that D
+also divides any interger linear
+
+ align:start position:0%
+also divides any interger linear
+ 
+
+ align:start position:0%
+also divides any interger linear
+combination of those two numbers and in
+
+ align:start position:0%
+combination of those two numbers and in
+ 
+
+ align:start position:0%
+combination of those two numbers and in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+a cool so so both of these are using the
+
+ align:start position:0%
+a cool so so both of these are using the
+ 
+
+ align:start position:0%
+a cool so so both of these are using the
+uh divisibility facts that if you have a
+
+ align:start position:0%
+uh divisibility facts that if you have a
+ 
+
+ align:start position:0%
+uh divisibility facts that if you have a
+common divisor you also divide all
+
+ align:start position:0%
+common divisor you also divide all
+ 
+
+ align:start position:0%
+common divisor you also divide all
+integer linear combinations of those two
+
+ align:start position:0%
+integer linear combinations of those two
+ 
+
+ align:start position:0%
+integer linear combinations of those two
+numbers uh so in particular this means
+
+ align:start position:0%
+numbers uh so in particular this means
+ 
+
+ align:start position:0%
+numbers uh so in particular this means
+we have D divides A and D divides B I'm
+
+ align:start position:0%
+we have D divides A and D divides B I'm
+ 
+
+ align:start position:0%
+we have D divides A and D divides B I'm
+just taking this thing that we proved
+
+ align:start position:0%
+just taking this thing that we proved
+ 
+
+ align:start position:0%
+just taking this thing that we proved
+and this thing that we
+
+ align:start position:0%
+and this thing that we
+ 
+
+ align:start position:0%
+and this thing that we
+assumed and this says we have a common
+
+ align:start position:0%
+assumed and this says we have a common
+ 
+
+ align:start position:0%
+assumed and this says we have a common
+if we had saying if we had a common
+
+ align:start position:0%
+if we had saying if we had a common
+ 
+
+ align:start position:0%
+if we had saying if we had a common
+divisor of a minus B and B we also have
+
+ align:start position:0%
+divisor of a minus B and B we also have
+ 
+
+ align:start position:0%
+divisor of a minus B and B we also have
+a common divisor of A and B so that says
+
+ align:start position:0%
+a common divisor of A and B so that says
+ 
+
+ align:start position:0%
+a common divisor of A and B so that says
+every element in this second set is an
+
+ align:start position:0%
+every element in this second set is an
+ 
+
+ align:start position:0%
+every element in this second set is an
+element of the first set and because we
+
+ align:start position:0%
+element of the first set and because we
+ 
+
+ align:start position:0%
+element of the first set and because we
+have containment in both directions in
+
+ align:start position:0%
+have containment in both directions in
+ 
+
+ align:start position:0%
+have containment in both directions in
+fact these two sets must be exactly the
+
+ align:start position:0%
+fact these two sets must be exactly the
+ 
+
+ align:start position:0%
+fact these two sets must be exactly the
+same set so if you ever have to prove
+
+ align:start position:0%
+same set so if you ever have to prove
+ 
+
+ align:start position:0%
+same set so if you ever have to prove
+the two sets are equal I recommend a
+
+ align:start position:0%
+the two sets are equal I recommend a
+ 
+
+ align:start position:0%
+the two sets are equal I recommend a
+common template is to do it in two
+
+ align:start position:0%
+common template is to do it in two
+ 
+
+ align:start position:0%
+common template is to do it in two
+halves like
+
+ align:start position:0%
+halves like
+ 
+
+ align:start position:0%
+halves like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay great uh so I claim we can get an
+
+ align:start position:0%
+okay great uh so I claim we can get an
+ 
+
+ align:start position:0%
+okay great uh so I claim we can get an
+algorithm out of
+
+ align:start position:0%
+algorithm out of
+ 
+
+ align:start position:0%
+algorithm out of
+this out of this subtraction idea and
+
+ align:start position:0%
+this out of this subtraction idea and
+ 
+
+ align:start position:0%
+this out of this subtraction idea and
+gcd of 0 comma B
+
+ align:start position:0%
+gcd of 0 comma B
+ 
+
+ align:start position:0%
+gcd of 0 comma B
+so let's just do an example of that I
+
+ align:start position:0%
+so let's just do an example of that I
+ 
+
+ align:start position:0%
+so let's just do an example of that I
+won't write a careful algorithm because
+
+ align:start position:0%
+won't write a careful algorithm because
+ 
+
+ align:start position:0%
+won't write a careful algorithm because
+we're going to do
+
+ align:start position:0%
+we're going to do
+ 
+
+ align:start position:0%
+we're going to do
+better let's say we want to do uh gcd of
+
+ align:start position:0%
+better let's say we want to do uh gcd of
+ 
+
+ align:start position:0%
+better let's say we want to do uh gcd of
+9 comma
+
+ align:start position:0%
+9 comma
+ 
+
+ align:start position:0%
+9 comma
+6 okay uh oh and maybe I want to write
+
+ align:start position:0%
+6 okay uh oh and maybe I want to write
+ 
+
+ align:start position:0%
+6 okay uh oh and maybe I want to write
+another fact
+
+ align:start position:0%
+another fact
+ 
+
+ align:start position:0%
+another fact
+here um does it
+
+ align:start position:0%
+here um does it
+ 
+
+ align:start position:0%
+here um does it
+matter yeah I do uh so gcd of a comma B
+
+ align:start position:0%
+matter yeah I do uh so gcd of a comma B
+ 
+
+ align:start position:0%
+matter yeah I do uh so gcd of a comma B
+is also equal to uh gcd of B comma a by
+
+ align:start position:0%
+is also equal to uh gcd of B comma a by
+ 
+
+ align:start position:0%
+is also equal to uh gcd of B comma a by
+symmetry of this definition A and B
+
+ align:start position:0%
+symmetry of this definition A and B
+ 
+
+ align:start position:0%
+symmetry of this definition A and B
+could be swapped and you get exactly the
+
+ align:start position:0%
+could be swapped and you get exactly the
+ 
+
+ align:start position:0%
+could be swapped and you get exactly the
+same things we're talking about and if I
+
+ align:start position:0%
+same things we're talking about and if I
+ 
+
+ align:start position:0%
+same things we're talking about and if I
+apply this subtraction Lemma uh with the
+
+ align:start position:0%
+apply this subtraction Lemma uh with the
+ 
+
+ align:start position:0%
+apply this subtraction Lemma uh with the
+elements swapped what I get is uh gcd of
+
+ align:start position:0%
+elements swapped what I get is uh gcd of
+ 
+
+ align:start position:0%
+elements swapped what I get is uh gcd of
+the first argument which is B minus the
+
+ align:start position:0%
+the first argument which is B minus the
+ 
+
+ align:start position:0%
+the first argument which is B minus the
+second argument which is a comma the
+
+ align:start position:0%
+second argument which is a comma the
+ 
+
+ align:start position:0%
+second argument which is a comma the
+second argument which is a
+
+ align:start position:0%
+second argument which is a
+ 
+
+ align:start position:0%
+second argument which is a
+so um all these things are equal just
+
+ align:start position:0%
+so um all these things are equal just
+ 
+
+ align:start position:0%
+so um all these things are equal just
+from the same subtraction LMA and using
+
+ align:start position:0%
+from the same subtraction LMA and using
+ 
+
+ align:start position:0%
+from the same subtraction LMA and using
+the Symmetry uh but what this is saying
+
+ align:start position:0%
+the Symmetry uh but what this is saying
+ 
+
+ align:start position:0%
+the Symmetry uh but what this is saying
+is either I can subtract the second
+
+ align:start position:0%
+is either I can subtract the second
+ 
+
+ align:start position:0%
+is either I can subtract the second
+argument from the first and get a minus
+
+ align:start position:0%
+argument from the first and get a minus
+ 
+
+ align:start position:0%
+argument from the first and get a minus
+b or uh I I can also rewrite this as gcd
+
+ align:start position:0%
+b or uh I I can also rewrite this as gcd
+ 
+
+ align:start position:0%
+b or uh I I can also rewrite this as gcd
+of a comma B minus a alternatively I
+
+ align:start position:0%
+of a comma B minus a alternatively I
+ 
+
+ align:start position:0%
+of a comma B minus a alternatively I
+could leave the first argument alone and
+
+ align:start position:0%
+could leave the first argument alone and
+ 
+
+ align:start position:0%
+could leave the first argument alone and
+subtract it from the second argument so
+
+ align:start position:0%
+subtract it from the second argument so
+ 
+
+ align:start position:0%
+subtract it from the second argument so
+I'm free to subtract whichever way I
+
+ align:start position:0%
+I'm free to subtract whichever way I
+ 
+
+ align:start position:0%
+I'm free to subtract whichever way I
+want and I find it much easier to think
+
+ align:start position:0%
+want and I find it much easier to think
+ 
+
+ align:start position:0%
+want and I find it much easier to think
+about non- negative numbers so I'm
+
+ align:start position:0%
+about non- negative numbers so I'm
+ 
+
+ align:start position:0%
+about non- negative numbers so I'm
+always going to subtract the smaller
+
+ align:start position:0%
+always going to subtract the smaller
+ 
+
+ align:start position:0%
+always going to subtract the smaller
+number from the bigger number I can do
+
+ align:start position:0%
+number from the bigger number I can do
+ 
+
+ align:start position:0%
+number from the bigger number I can do
+it either way so let's do it
+
+ align:start position:0%
+it either way so let's do it
+ 
+
+ align:start position:0%
+it either way so let's do it
+for uh 9 comma
+
+ align:start position:0%
+for uh 9 comma
+ 
+
+ align:start position:0%
+for uh 9 comma
+6 so I'm going to subtract six from 9
+
+ align:start position:0%
+6 so I'm going to subtract six from 9
+ 
+
+ align:start position:0%
+6 so I'm going to subtract six from 9
+and I get this is equal to so this would
+
+ align:start position:0%
+and I get this is equal to so this would
+ 
+
+ align:start position:0%
+and I get this is equal to so this would
+be uh a minus B this one minus this one
+
+ align:start position:0%
+be uh a minus B this one minus this one
+ 
+
+ align:start position:0%
+be uh a minus B this one minus this one
+uh is three 9 - 6 is three second
+
+ align:start position:0%
+uh is three 9 - 6 is three second
+ 
+
+ align:start position:0%
+uh is three 9 - 6 is three second
+argument stays the same okay I still
+
+ align:start position:0%
+argument stays the same okay I still
+ 
+
+ align:start position:0%
+argument stays the same okay I still
+don't know the answer so I'm going to
+
+ align:start position:0%
+don't know the answer so I'm going to
+ 
+
+ align:start position:0%
+don't know the answer so I'm going to
+keep subtracting in this case I'll take
+
+ align:start position:0%
+keep subtracting in this case I'll take
+ 
+
+ align:start position:0%
+keep subtracting in this case I'll take
+the smaller number subtract it from the
+
+ align:start position:0%
+the smaller number subtract it from the
+ 
+
+ align:start position:0%
+the smaller number subtract it from the
+larger number so this is uh B minus a I
+
+ align:start position:0%
+larger number so this is uh B minus a I
+ 
+
+ align:start position:0%
+larger number so this is uh B minus a I
+guess replacing B with B minus a I get
+
+ align:start position:0%
+guess replacing B with B minus a I get
+ 
+
+ align:start position:0%
+guess replacing B with B minus a I get
+gcd
+
+ align:start position:0%
+gcd
+ 
+
+ align:start position:0%
+gcd
+of sorry uh I wanted yeah 3 comma
+
+ align:start position:0%
+of sorry uh I wanted yeah 3 comma
+ 
+
+ align:start position:0%
+of sorry uh I wanted yeah 3 comma
+3 subtract three from six I get three
+
+ align:start position:0%
+3 subtract three from six I get three
+ 
+
+ align:start position:0%
+3 subtract three from six I get three
+okay this that looks pretty easy I'm
+
+ align:start position:0%
+okay this that looks pretty easy I'm
+ 
+
+ align:start position:0%
+okay this that looks pretty easy I'm
+guessing gcd of three and three is three
+
+ align:start position:0%
+guessing gcd of three and three is three
+ 
+
+ align:start position:0%
+guessing gcd of three and three is three
+uh but if we go all the way uh we can
+
+ align:start position:0%
+uh but if we go all the way uh we can
+ 
+
+ align:start position:0%
+uh but if we go all the way uh we can
+subtract one of them from the other I
+
+ align:start position:0%
+subtract one of them from the other I
+ 
+
+ align:start position:0%
+subtract one of them from the other I
+guess I want to do B minus a again and
+
+ align:start position:0%
+guess I want to do B minus a again and
+ 
+
+ align:start position:0%
+guess I want to do B minus a again and
+we get 3 comma 0 and this we actually
+
+ align:start position:0%
+we get 3 comma 0 and this we actually
+ 
+
+ align:start position:0%
+we get 3 comma 0 and this we actually
+analyzed over here uh we said gcd oh I
+
+ align:start position:0%
+analyzed over here uh we said gcd oh I
+ 
+
+ align:start position:0%
+analyzed over here uh we said gcd oh I
+got it backwards but of zero comma
+
+ align:start position:0%
+got it backwards but of zero comma
+ 
+
+ align:start position:0%
+got it backwards but of zero comma
+something is the absolute value of
+
+ align:start position:0%
+something is the absolute value of
+ 
+
+ align:start position:0%
+something is the absolute value of
+something so absolute value of three is
+
+ align:start position:0%
+something so absolute value of three is
+ 
+
+ align:start position:0%
+something so absolute value of three is
+three and so gcd of three comma 0 is
+
+ align:start position:0%
+three and so gcd of three comma 0 is
+ 
+
+ align:start position:0%
+three and so gcd of three comma 0 is
+three okay great uh another
+
+ align:start position:0%
+three okay great uh another
+ 
+
+ align:start position:0%
+three okay great uh another
+example gcd of 1 comma
+
+ align:start position:0%
+example gcd of 1 comma
+ 
+
+ align:start position:0%
+example gcd of 1 comma
+100 okay well I take the smaller one
+
+ align:start position:0%
+100 okay well I take the smaller one
+ 
+
+ align:start position:0%
+100 okay well I take the smaller one
+subtract it from the larger one I get
+
+ align:start position:0%
+subtract it from the larger one I get
+ 
+
+ align:start position:0%
+subtract it from the larger one I get
+gcd of 1 comma
+
+ align:start position:0%
+gcd of 1 comma
+ 
+
+ align:start position:0%
+gcd of 1 comma
+99 H okay now I subtract one from the
+
+ align:start position:0%
+99 H okay now I subtract one from the
+ 
+
+ align:start position:0%
+99 H okay now I subtract one from the
+larger number I get gcd of 1 comma
+
+ align:start position:0%
+larger number I get gcd of 1 comma
+ 
+
+ align:start position:0%
+larger number I get gcd of 1 comma
+98 and so on I won't bore you with the
+
+ align:start position:0%
+98 and so on I won't bore you with the
+ 
+
+ align:start position:0%
+98 and so on I won't bore you with the
+details in the end the answer is one but
+
+ align:start position:0%
+details in the end the answer is one but
+ 
+
+ align:start position:0%
+details in the end the answer is one but
+uh this is a very slow way to arrive at
+
+ align:start position:0%
+uh this is a very slow way to arrive at
+ 
+
+ align:start position:0%
+uh this is a very slow way to arrive at
+the answer of one um I have to do a 100
+
+ align:start position:0%
+the answer of one um I have to do a 100
+ 
+
+ align:start position:0%
+the answer of one um I have to do a 100
+steps to figure out the gcd of 1 comma
+
+ align:start position:0%
+steps to figure out the gcd of 1 comma
+ 
+
+ align:start position:0%
+steps to figure out the gcd of 1 comma
+100 so the number of steps you get in
+
+ align:start position:0%
+100 so the number of steps you get in
+ 
+
+ align:start position:0%
+100 so the number of steps you get in
+this algorithm which I haven't precis
+
+ align:start position:0%
+this algorithm which I haven't precis
+ 
+
+ align:start position:0%
+this algorithm which I haven't precis
+defined is going to be uh roughly at
+
+ align:start position:0%
+defined is going to be uh roughly at
+ 
+
+ align:start position:0%
+defined is going to be uh roughly at
+least in the worst case um the sum of a
+
+ align:start position:0%
+least in the worst case um the sum of a
+ 
+
+ align:start position:0%
+least in the worst case um the sum of a
+and b or the maximum of A and B it
+
+ align:start position:0%
+and b or the maximum of A and B it
+ 
+
+ align:start position:0%
+and b or the maximum of A and B it
+doesn't matter up to constant factors uh
+
+ align:start position:0%
+doesn't matter up to constant factors uh
+ 
+
+ align:start position:0%
+doesn't matter up to constant factors uh
+and this is what we would call a slow
+
+ align:start position:0%
+and this is what we would call a slow
+ 
+
+ align:start position:0%
+and this is what we would call a slow
+algorithm for in number
+
+ align:start position:0%
+algorithm for in number
+ 
+
+ align:start position:0%
+algorithm for in number
+Theory because generally we want to
+
+ align:start position:0%
+Theory because generally we want to
+ 
+
+ align:start position:0%
+Theory because generally we want to
+think about numbers that are huge you
+
+ align:start position:0%
+think about numbers that are huge you
+ 
+
+ align:start position:0%
+think about numbers that are huge you
+know uh 100 bits long if you have a 100
+
+ align:start position:0%
+know uh 100 bits long if you have a 100
+ 
+
+ align:start position:0%
+know uh 100 bits long if you have a 100
+bit long number that is as large as two
+
+ align:start position:0%
+bit long number that is as large as two
+ 
+
+ align:start position:0%
+bit long number that is as large as two
+to the 100
+
+ align:start position:0%
+to the 100
+ 
+
+ align:start position:0%
+to the 100
+and that's a very large number uh
+
+ align:start position:0%
+and that's a very large number uh
+ 
+
+ align:start position:0%
+and that's a very large number uh
+it's big roughly the number of particles
+
+ align:start position:0%
+it's big roughly the number of particles
+ 
+
+ align:start position:0%
+it's big roughly the number of particles
+in the known universe I think that's
+
+ align:start position:0%
+in the known universe I think that's
+ 
+
+ align:start position:0%
+in the known universe I think that's
+about to the 128 or something so we
+
+ align:start position:0%
+about to the 128 or something so we
+ 
+
+ align:start position:0%
+about to the 128 or something so we
+don't want to spend that much time uh to
+
+ align:start position:0%
+don't want to spend that much time uh to
+ 
+
+ align:start position:0%
+don't want to spend that much time uh to
+compute this in fact we can do a lot
+
+ align:start position:0%
+compute this in fact we can do a lot
+ 
+
+ align:start position:0%
+compute this in fact we can do a lot
+better using
+
+ align:start position:0%
+better using
+ 
+
+ align:start position:0%
+better using
+a better technique which is division so
+
+ align:start position:0%
+a better technique which is division so
+ 
+
+ align:start position:0%
+a better technique which is division so
+we've seen here uh the idea that we can
+
+ align:start position:0%
+we've seen here uh the idea that we can
+ 
+
+ align:start position:0%
+we've seen here uh the idea that we can
+subtract one number from the other but
+
+ align:start position:0%
+subtract one number from the other but
+ 
+
+ align:start position:0%
+subtract one number from the other but
+if we subtract and then subtract and
+
+ align:start position:0%
+if we subtract and then subtract and
+ 
+
+ align:start position:0%
+if we subtract and then subtract and
+then we subtract and we subtract that
+
+ align:start position:0%
+then we subtract and we subtract that
+ 
+
+ align:start position:0%
+then we subtract and we subtract that
+sounds a lot like division right this is
+
+ align:start position:0%
+sounds a lot like division right this is
+ 
+
+ align:start position:0%
+sounds a lot like division right this is
+like the bad way to do division is to
+
+ align:start position:0%
+like the bad way to do division is to
+ 
+
+ align:start position:0%
+like the bad way to do division is to
+repeatedly subtract one number from the
+
+ align:start position:0%
+repeatedly subtract one number from the
+ 
+
+ align:start position:0%
+repeatedly subtract one number from the
+other and that's exactly what happens in
+
+ align:start position:0%
+other and that's exactly what happens in
+ 
+
+ align:start position:0%
+other and that's exactly what happens in
+the 100 comma one case we have to
+
+ align:start position:0%
+the 100 comma one case we have to
+ 
+
+ align:start position:0%
+the 100 comma one case we have to
+subtract one from 100 subtract it from
+
+ align:start position:0%
+subtract one from 100 subtract it from
+ 
+
+ align:start position:0%
+subtract one from 100 subtract it from
+99 keep subtracting one until the left
+
+ align:start position:0%
+99 keep subtracting one until the left
+ 
+
+ align:start position:0%
+99 keep subtracting one until the left
+hand side uh becomes larger than the
+
+ align:start position:0%
+hand side uh becomes larger than the
+ 
+
+ align:start position:0%
+hand side uh becomes larger than the
+right hand side and then we can stop in
+
+ align:start position:0%
+right hand side and then we can stop in
+ 
+
+ align:start position:0%
+right hand side and then we can stop in
+fact they become equal because one
+
+ align:start position:0%
+fact they become equal because one
+ 
+
+ align:start position:0%
+fact they become equal because one
+divides 100 uh but in general we want to
+
+ align:start position:0%
+divides 100 uh but in general we want to
+ 
+
+ align:start position:0%
+divides 100 uh but in general we want to
+keep subtracting on until we go beyond
+
+ align:start position:0%
+keep subtracting on until we go beyond
+ 
+
+ align:start position:0%
+keep subtracting on until we go beyond
+or we would go beyond what we can afford
+
+ align:start position:0%
+or we would go beyond what we can afford
+ 
+
+ align:start position:0%
+or we would go beyond what we can afford
+and that's exactly division so let me
+
+ align:start position:0%
+and that's exactly division so let me
+ 
+
+ align:start position:0%
+and that's exactly division so let me
+give
+
+ align:start position:0%
+give
+ 
+
+ align:start position:0%
+give
+you a very precise version of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+division with something called the
+
+ align:start position:0%
+division with something called the
+ 
+
+ align:start position:0%
+division with something called the
+division theorem this is one of the core
+
+ align:start position:0%
+division theorem this is one of the core
+ 
+
+ align:start position:0%
+division theorem this is one of the core
+theorems
+
+ align:start position:0%
+theorems
+ 
+
+ align:start position:0%
+theorems
+in number Theory we won't prove it here
+
+ align:start position:0%
+in number Theory we won't prove it here
+ 
+
+ align:start position:0%
+in number Theory we won't prove it here
+it's kind of TS um for every integer n
+
+ align:start position:0%
+it's kind of TS um for every integer n
+ 
+
+ align:start position:0%
+it's kind of TS um for every integer n
+and for every positive integer D so I'm
+
+ align:start position:0%
+and for every positive integer D so I'm
+ 
+
+ align:start position:0%
+and for every positive integer D so I'm
+going to write z+ to mean uh D is
+
+ align:start position:0%
+going to write z+ to mean uh D is
+ 
+
+ align:start position:0%
+going to write z+ to mean uh D is
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
+unique
+um and usually we would write this as
+
+ align:start position:0%
+um and usually we would write this as
+ 
+
+ align:start position:0%
+um and usually we would write this as
+exists exclamation mark there is a
+
+ align:start position:0%
+exists exclamation mark there is a
+ 
+
+ align:start position:0%
+exists exclamation mark there is a
+unique so you know this means there is
+
+ align:start position:0%
+unique so you know this means there is
+ 
+
+ align:start position:0%
+unique so you know this means there is
+exclamation mark it's really exists but
+
+ align:start position:0%
+exclamation mark it's really exists but
+ 
+
+ align:start position:0%
+exclamation mark it's really exists but
+there's only one of them uh there exists
+
+ align:start position:0%
+there's only one of them uh there exists
+ 
+
+ align:start position:0%
+there's only one of them uh there exists
+a unique uh pair of
+
+ align:start position:0%
+a unique uh pair of
+ 
+
+ align:start position:0%
+a unique uh pair of
+integers uh q and
+
+ align:start position:0%
+integers uh q and
+ 
+
+ align:start position:0%
+integers uh q and
+R uh I don't want the parentheses
+
+ align:start position:0%
+R uh I don't want the parentheses
+ 
+
+ align:start position:0%
+R uh I don't want the parentheses
+actually uh I want to say those are both
+
+ align:start position:0%
+actually uh I want to say those are both
+ 
+
+ align:start position:0%
+actually uh I want to say those are both
+integers um such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and n = q * D +
+
+ align:start position:0%
+that and n = q * D +
+ 
+
+ align:start position:0%
+that and n = q * D +
+R and R is between zero and strictly
+
+ align:start position:0%
+R and R is between zero and strictly
+ 
+
+ align:start position:0%
+R and R is between zero and strictly
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+D okay you actually have seen this in
+
+ align:start position:0%
+D okay you actually have seen this in
+ 
+
+ align:start position:0%
+D okay you actually have seen this in
+other terms probably before uh this Q is
+
+ align:start position:0%
+other terms probably before uh this Q is
+ 
+
+ align:start position:0%
+other terms probably before uh this Q is
+what we would call the
+
+ align:start position:0%
+what we would call the
+ 
+
+ align:start position:0%
+what we would call the
+quotient and this R is what we call the
+
+ align:start position:0%
+quotient and this R is what we call the
+ 
+
+ align:start position:0%
+quotient and this R is what we call the
+remainder I'm sure you've heard those
+
+ align:start position:0%
+remainder I'm sure you've heard those
+ 
+
+ align:start position:0%
+remainder I'm sure you've heard those
+terms before this is like a very precise
+
+ align:start position:0%
+terms before this is like a very precise
+ 
+
+ align:start position:0%
+terms before this is like a very precise
+way to say what division gives us in all
+
+ align:start position:0%
+way to say what division gives us in all
+ 
+
+ align:start position:0%
+way to say what division gives us in all
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+given uh a numerator and a
+
+ align:start position:0%
+given uh a numerator and a
+ 
+
+ align:start position:0%
+given uh a numerator and a
+denominator that's why they're called n
+
+ align:start position:0%
+denominator that's why they're called n
+ 
+
+ align:start position:0%
+denominator that's why they're called n
+and D here um and as long as D is uh not
+
+ align:start position:0%
+and D here um and as long as D is uh not
+ 
+
+ align:start position:0%
+and D here um and as long as D is uh not
+zero we're going to furthermore assume
+
+ align:start position:0%
+zero we're going to furthermore assume
+ 
+
+ align:start position:0%
+zero we're going to furthermore assume
+that it's positive so it's easier to
+
+ align:start position:0%
+that it's positive so it's easier to
+ 
+
+ align:start position:0%
+that it's positive so it's easier to
+think about um then there's a unique
+
+ align:start position:0%
+think about um then there's a unique
+ 
+
+ align:start position:0%
+think about um then there's a unique
+quotient and remainder you get from
+
+ align:start position:0%
+quotient and remainder you get from
+ 
+
+ align:start position:0%
+quotient and remainder you get from
+dividing A over
+
+ align:start position:0%
+dividing A over
+ 
+
+ align:start position:0%
+dividing A over
+B right Q is how many whole copies of D
+
+ align:start position:0%
+B right Q is how many whole copies of D
+ 
+
+ align:start position:0%
+B right Q is how many whole copies of D
+you can fit inside n and R is whatever
+
+ align:start position:0%
+you can fit inside n and R is whatever
+ 
+
+ align:start position:0%
+you can fit inside n and R is whatever
+is left over so that's roughly a proof
+
+ align:start position:0%
+is left over so that's roughly a proof
+ 
+
+ align:start position:0%
+is left over so that's roughly a proof
+that this is true um and it if you think
+
+ align:start position:0%
+that this is true um and it if you think
+ 
+
+ align:start position:0%
+that this is true um and it if you think
+about what the remainder should be it
+
+ align:start position:0%
+about what the remainder should be it
+ 
+
+ align:start position:0%
+about what the remainder should be it
+could be zero in the zero case that's
+
+ align:start position:0%
+could be zero in the zero case that's
+ 
+
+ align:start position:0%
+could be zero in the zero case that's
+when we have divisibility right if D
+
+ align:start position:0%
+when we have divisibility right if D
+ 
+
+ align:start position:0%
+when we have divisibility right if D
+divides n if n equals Q * D that's
+
+ align:start position:0%
+divides n if n equals Q * D that's
+ 
+
+ align:start position:0%
+divides n if n equals Q * D that's
+exactly divisibility if there's no R
+
+ align:start position:0%
+exactly divisibility if there's no R
+ 
+
+ align:start position:0%
+exactly divisibility if there's no R
+that's when R equals z that's what we
+
+ align:start position:0%
+that's when R equals z that's what we
+ 
+
+ align:start position:0%
+that's when R equals z that's what we
+get uh but in general we know R should
+
+ align:start position:0%
+get uh but in general we know R should
+ 
+
+ align:start position:0%
+get uh but in general we know R should
+also be less than D because if if there
+
+ align:start position:0%
+also be less than D because if if there
+ 
+
+ align:start position:0%
+also be less than D because if if there
+was D left over we would just increase Q
+
+ align:start position:0%
+was D left over we would just increase Q
+ 
+
+ align:start position:0%
+was D left over we would just increase Q
+one that would be a whole copy of D so
+
+ align:start position:0%
+one that would be a whole copy of D so
+ 
+
+ align:start position:0%
+one that would be a whole copy of D so
+the remainder is always going to be
+
+ align:start position:0%
+the remainder is always going to be
+ 
+
+ align:start position:0%
+the remainder is always going to be
+between zero and strictly less than
+
+ align:start position:0%
+between zero and strictly less than
+ 
+
+ align:start position:0%
+between zero and strictly less than
+D okay uh I guess the the interesting
+
+ align:start position:0%
+D okay uh I guess the the interesting
+ 
+
+ align:start position:0%
+D okay uh I guess the the interesting
+part here is that there's only one sorry
+
+ align:start position:0%
+part here is that there's only one sorry
+ 
+
+ align:start position:0%
+part here is that there's only one sorry
+I should have put an i in unique uh
+
+ align:start position:0%
+I should have put an i in unique uh
+ 
+
+ align:start position:0%
+I should have put an i in unique uh
+there's only one way to do this um that
+
+ align:start position:0%
+there's only one way to do this um that
+ 
+
+ align:start position:0%
+there's only one way to do this um that
+with these conditions there's only one
+
+ align:start position:0%
+with these conditions there's only one
+ 
+
+ align:start position:0%
+with these conditions there's only one
+uh quotient and
+
+ align:start position:0%
+uh quotient and
+ 
+
+ align:start position:0%
+uh quotient and
+remainder okay uh I also want to give
+
+ align:start position:0%
+remainder okay uh I also want to give
+ 
+
+ align:start position:0%
+remainder okay uh I also want to give
+you some definitions some notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is uh for the quotient we write
+
+ align:start position:0%
+which is uh for the quotient we write
+ 
+
+ align:start position:0%
+which is uh for the quotient we write
+the numerator div D div for division uh
+
+ align:start position:0%
+the numerator div D div for division uh
+ 
+
+ align:start position:0%
+the numerator div D div for division uh
+and for the remainder we write n remd
+
+ align:start position:0%
+and for the remainder we write n remd
+ 
+
+ align:start position:0%
+and for the remainder we write n remd
+REM for
+
+ align:start position:0%
+REM for
+ 
+
+ align:start position:0%
+REM for
+remainder uh this is also sometimes
+
+ align:start position:0%
+remainder uh this is also sometimes
+ 
+
+ align:start position:0%
+remainder uh this is also sometimes
+called n mod D so if you ever see that
+
+ align:start position:0%
+called n mod D so if you ever see that
+ 
+
+ align:start position:0%
+called n mod D so if you ever see that
+we probably won't use it in this form
+
+ align:start position:0%
+we probably won't use it in this form
+ 
+
+ align:start position:0%
+we probably won't use it in this form
+we're going to use mod to mean a
+
+ align:start position:0%
+we're going to use mod to mean a
+ 
+
+ align:start position:0%
+we're going to use mod to mean a
+slightly related slightly different
+
+ align:start position:0%
+slightly related slightly different
+ 
+
+ align:start position:0%
+slightly related slightly different
+notion um also the textbook uh they
+
+ align:start position:0%
+notion um also the textbook uh they
+ 
+
+ align:start position:0%
+notion um also the textbook uh they
+write REM as a as a two argument
+
+ align:start position:0%
+write REM as a as a two argument
+ 
+
+ align:start position:0%
+write REM as a as a two argument
+function but same
+
+ align:start position:0%
+function but same
+ 
+
+ align:start position:0%
+function but same
+idea okay so uh we're going to use
+
+ align:start position:0%
+idea okay so uh we're going to use
+ 
+
+ align:start position:0%
+idea okay so uh we're going to use
+division theorem a lot from now on and
+
+ align:start position:0%
+division theorem a lot from now on and
+ 
+
+ align:start position:0%
+division theorem a lot from now on and
+as a way to uh reduce our numbers again
+
+ align:start position:0%
+as a way to uh reduce our numbers again
+ 
+
+ align:start position:0%
+as a way to uh reduce our numbers again
+in a more powerful way than subtraction
+
+ align:start position:0%
+in a more powerful way than subtraction
+ 
+
+ align:start position:0%
+in a more powerful way than subtraction
+so we would like to do subtraction
+
+ align:start position:0%
+so we would like to do subtraction
+ 
+
+ align:start position:0%
+so we would like to do subtraction
+repeatedly and what will we be left with
+
+ align:start position:0%
+repeatedly and what will we be left with
+ 
+
+ align:start position:0%
+repeatedly and what will we be left with
+we'll be left with the remainder if you
+
+ align:start position:0%
+we'll be left with the remainder if you
+ 
+
+ align:start position:0%
+we'll be left with the remainder if you
+keep subtracting until you can't
+
+ align:start position:0%
+keep subtracting until you can't
+ 
+
+ align:start position:0%
+keep subtracting until you can't
+subtract anymore that's remainder
+
+ align:start position:0%
+subtract anymore that's remainder
+ 
+
+ align:start position:0%
+subtract anymore that's remainder
+okay so let's do
+
+ align:start position:0%
+okay so let's do
+ 
+
+ align:start position:0%
+okay so let's do
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+that probably still need this
+
+ align:start position:0%
+that probably still need this
+ 
+
+ align:start position:0%
+that probably still need this
+divisibility facts I'll leave it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is gcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+division
+
+ align:start position:0%
+division
+ 
+
+ align:start position:0%
+division
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+um if let's suppose a is less than or
+
+ align:start position:0%
+um if let's suppose a is less than or
+ 
+
+ align:start position:0%
+um if let's suppose a is less than or
+equal to B is less than or equal to
+
+ align:start position:0%
+equal to B is less than or equal to
+ 
+
+ align:start position:0%
+equal to B is less than or equal to
+one that what I want no way around that
+
+ align:start position:0%
+one that what I want no way around that
+ 
+
+ align:start position:0%
+one that what I want no way around that
+seems weird be weird to be at most one I
+
+ align:start position:0%
+seems weird be weird to be at most one I
+ 
+
+ align:start position:0%
+seems weird be weird to be at most one I
+want things to be non- negative so I'm
+
+ align:start position:0%
+want things to be non- negative so I'm
+ 
+
+ align:start position:0%
+want things to be non- negative so I'm
+going to assume a is the bigger one of A
+
+ align:start position:0%
+going to assume a is the bigger one of A
+ 
+
+ align:start position:0%
+going to assume a is the bigger one of A
+and B and I want to compute gcd of a
+
+ align:start position:0%
+and B and I want to compute gcd of a
+ 
+
+ align:start position:0%
+and B and I want to compute gcd of a
+comma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B and I'm going to assume we haven't
+
+ align:start position:0%
+B and I'm going to assume we haven't
+ 
+
+ align:start position:0%
+B and I'm going to assume we haven't
+gotten down to zero in particular
+
+ align:start position:0%
+gotten down to zero in particular
+ 
+
+ align:start position:0%
+gotten down to zero in particular
+because I can't divide by zero uh but
+
+ align:start position:0%
+because I can't divide by zero uh but
+ 
+
+ align:start position:0%
+because I can't divide by zero uh but
+also because when we get to zero we're
+
+ align:start position:0%
+also because when we get to zero we're
+ 
+
+ align:start position:0%
+also because when we get to zero we're
+done if one of the numbers is zero we're
+
+ align:start position:0%
+done if one of the numbers is zero we're
+ 
+
+ align:start position:0%
+done if one of the numbers is zero we're
+happy so let's assume they're both at
+
+ align:start position:0%
+happy so let's assume they're both at
+ 
+
+ align:start position:0%
+happy so let's assume they're both at
+least one and let's assume by symmetry
+
+ align:start position:0%
+least one and let's assume by symmetry
+ 
+
+ align:start position:0%
+least one and let's assume by symmetry
+that a the one on the left is bigger or
+
+ align:start position:0%
+that a the one on the left is bigger or
+ 
+
+ align:start position:0%
+that a the one on the left is bigger or
+equal uh then I claim gcd of a is gcd of
+
+ align:start position:0%
+equal uh then I claim gcd of a is gcd of
+ 
+
+ align:start position:0%
+equal uh then I claim gcd of a is gcd of
+a remainder B comma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay uh so before we had a minus B and
+
+ align:start position:0%
+B okay uh so before we had a minus B and
+ 
+
+ align:start position:0%
+B okay uh so before we had a minus B and
+now we have a remainder B seems like a
+
+ align:start position:0%
+now we have a remainder B seems like a
+ 
+
+ align:start position:0%
+now we have a remainder B seems like a
+small difference and indeed the proof is
+
+ align:start position:0%
+small difference and indeed the proof is
+ 
+
+ align:start position:0%
+small difference and indeed the proof is
+basically the same
+
+ align:start position:0%
+basically the same
+ 
+
+ align:start position:0%
+basically the same
+um I'm going to do a proof sketch which
+
+ align:start position:0%
+um I'm going to do a proof sketch which
+ 
+
+ align:start position:0%
+um I'm going to do a proof sketch which
+is to say well gcd of a comma B is equal
+
+ align:start position:0%
+is to say well gcd of a comma B is equal
+ 
+
+ align:start position:0%
+is to say well gcd of a comma B is equal
+to gcd of a minus B comma B uh and if we
+
+ align:start position:0%
+to gcd of a minus B comma B uh and if we
+ 
+
+ align:start position:0%
+to gcd of a minus B comma B uh and if we
+apply by the subtraction theorem uh
+
+ align:start position:0%
+apply by the subtraction theorem uh
+ 
+
+ align:start position:0%
+apply by the subtraction theorem uh
+which we just did over over there um and
+
+ align:start position:0%
+which we just did over over there um and
+ 
+
+ align:start position:0%
+which we just did over over there um and
+if we apply the subtraction theorem
+
+ align:start position:0%
+if we apply the subtraction theorem
+ 
+
+ align:start position:0%
+if we apply the subtraction theorem
+again we can subtract the right argument
+
+ align:start position:0%
+again we can subtract the right argument
+ 
+
+ align:start position:0%
+again we can subtract the right argument
+from the left one again A minus 2 B
+
+ align:start position:0%
+from the left one again A minus 2 B
+ 
+
+ align:start position:0%
+from the left one again A minus 2 B
+comma B and so on eventually we get to
+
+ align:start position:0%
+comma B and so on eventually we get to
+ 
+
+ align:start position:0%
+comma B and so on eventually we get to
+to gcd of a minus um a div B *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B right a div B is how many whole copies
+
+ align:start position:0%
+B right a div B is how many whole copies
+ 
+
+ align:start position:0%
+B right a div B is how many whole copies
+of B I can fit into a and so if I take
+
+ align:start position:0%
+of B I can fit into a and so if I take
+ 
+
+ align:start position:0%
+of B I can fit into a and so if I take
+that number multiply it by B that's how
+
+ align:start position:0%
+that number multiply it by B that's how
+ 
+
+ align:start position:0%
+that number multiply it by B that's how
+much uh I can subtract away before a
+
+ align:start position:0%
+much uh I can subtract away before a
+ 
+
+ align:start position:0%
+much uh I can subtract away before a
+would go negative if I subtracted one
+
+ align:start position:0%
+would go negative if I subtracted one
+ 
+
+ align:start position:0%
+would go negative if I subtracted one
+more time and what I'll be left with is
+
+ align:start position:0%
+more time and what I'll be left with is
+ 
+
+ align:start position:0%
+more time and what I'll be left with is
+exactly the remainder a minus uh a remb
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times uh oh no times comma B If I
+
+ align:start position:0%
+times uh oh no times comma B If I
+ 
+
+ align:start position:0%
+times uh oh no times comma B If I
+subtract off that many copies of B I
+
+ align:start position:0%
+subtract off that many copies of B I
+ 
+
+ align:start position:0%
+subtract off that many copies of B I
+will be left with uh a remainder B sorry
+
+ align:start position:0%
+will be left with uh a remainder B sorry
+ 
+
+ align:start position:0%
+will be left with uh a remainder B sorry
+no a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus okay that's
+
+ align:start position:0%
+minus okay that's
+ 
+
+ align:start position:0%
+minus okay that's
+uh that's what we're writing here in
+
+ align:start position:0%
+uh that's what we're writing here in
+ 
+
+ align:start position:0%
+uh that's what we're writing here in
+fact so we wrote uh let me rewrite this
+
+ align:start position:0%
+fact so we wrote uh let me rewrite this
+ 
+
+ align:start position:0%
+fact so we wrote uh let me rewrite this
+um we have n or maybe I'll write it as
+
+ align:start position:0%
+um we have n or maybe I'll write it as
+ 
+
+ align:start position:0%
+um we have n or maybe I'll write it as
+uh Want A or
+
+ align:start position:0%
+uh Want A or
+ 
+
+ align:start position:0%
+uh Want A or
+B I'll stick with that what this over
+
+ align:start position:0%
+B I'll stick with that what this over
+ 
+
+ align:start position:0%
+B I'll stick with that what this over
+here is saying is uh n div D * D plus n
+
+ align:start position:0%
+here is saying is uh n div D * D plus n
+ 
+
+ align:start position:0%
+here is saying is uh n div D * D plus n
+RM D equals to n okay I'm just rewriting
+
+ align:start position:0%
+RM D equals to n okay I'm just rewriting
+ 
+
+ align:start position:0%
+RM D equals to n okay I'm just rewriting
+this formula using the notations for Q
+
+ align:start position:0%
+this formula using the notations for Q
+ 
+
+ align:start position:0%
+this formula using the notations for Q
+and R and if I rearrange this I get that
+
+ align:start position:0%
+and R and if I rearrange this I get that
+ 
+
+ align:start position:0%
+and R and if I rearrange this I get that
+n minus n divd
+
+ align:start position:0%
+n minus n divd
+ 
+
+ align:start position:0%
+n minus n divd
+* D equals
+
+ align:start position:0%
+* D equals
+ 
+
+ align:start position:0%
+* D equals
+ND okay and that's exactly what I'm
+
+ align:start position:0%
+ND okay and that's exactly what I'm
+ 
+
+ align:start position:0%
+ND okay and that's exactly what I'm
+using here the remainder is what you get
+
+ align:start position:0%
+using here the remainder is what you get
+ 
+
+ align:start position:0%
+using here the remainder is what you get
+what's left over if you take uh the
+
+ align:start position:0%
+what's left over if you take uh the
+ 
+
+ align:start position:0%
+what's left over if you take uh the
+numerator and subtract off uh the div
+
+ align:start position:0%
+numerator and subtract off uh the div
+ 
+
+ align:start position:0%
+numerator and subtract off uh the div
+many copies of the denominator so I use
+
+ align:start position:0%
+many copies of the denominator so I use
+ 
+
+ align:start position:0%
+many copies of the denominator so I use
+dot dot dot here you can't really use
+
+ align:start position:0%
+dot dot dot here you can't really use
+ 
+
+ align:start position:0%
+dot dot dot here you can't really use
+dot dot dot in a proof technically this
+
+ align:start position:0%
+dot dot dot in a proof technically this
+ 
+
+ align:start position:0%
+dot dot dot in a proof technically this
+is a proof by induction but I think
+
+ align:start position:0%
+is a proof by induction but I think
+ 
+
+ align:start position:0%
+is a proof by induction but I think
+hopefully you're familiar enough with
+
+ align:start position:0%
+hopefully you're familiar enough with
+ 
+
+ align:start position:0%
+hopefully you're familiar enough with
+induction that you could turn this into
+
+ align:start position:0%
+induction that you could turn this into
+ 
+
+ align:start position:0%
+induction that you could turn this into
+a formal proof it's not hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can
+
+ align:start position:0%
+okay so we can
+ 
+
+ align:start position:0%
+okay so we can
+divide and uh this will make this gcd
+
+ align:start position:0%
+divide and uh this will make this gcd
+ 
+
+ align:start position:0%
+divide and uh this will make this gcd
+algorithm much faster because now if I
+
+ align:start position:0%
+algorithm much faster because now if I
+ 
+
+ align:start position:0%
+algorithm much faster because now if I
+want to uh say to compute gcd of 1 comma
+
+ align:start position:0%
+want to uh say to compute gcd of 1 comma
+ 
+
+ align:start position:0%
+want to uh say to compute gcd of 1 comma
+100 this is the same thing as gcd of 100
+
+ align:start position:0%
+100 this is the same thing as gcd of 100
+ 
+
+ align:start position:0%
+100 this is the same thing as gcd of 100
+comma
+
+ align:start position:0%
+comma
+ 
+
+ align:start position:0%
+comma
+1 and what that says is I can divide 100
+
+ align:start position:0%
+1 and what that says is I can divide 100
+ 
+
+ align:start position:0%
+1 and what that says is I can divide 100
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+one and see what the remainder is well
+
+ align:start position:0%
+one and see what the remainder is well
+ 
+
+ align:start position:0%
+one and see what the remainder is well
+one divides 100 so the remainder is zero
+
+ align:start position:0%
+one divides 100 so the remainder is zero
+ 
+
+ align:start position:0%
+one divides 100 so the remainder is zero
+so I instantly get that this is gcd of 0
+
+ align:start position:0%
+so I instantly get that this is gcd of 0
+ 
+
+ align:start position:0%
+so I instantly get that this is gcd of 0
+comma 1
+
+ align:start position:0%
+comma 1
+ 
+
+ align:start position:0%
+comma 1
+boom uh I'm done this gcd of Zer comma
+
+ align:start position:0%
+boom uh I'm done this gcd of Zer comma
+ 
+
+ align:start position:0%
+boom uh I'm done this gcd of Zer comma
+anything is the
+
+ align:start position:0%
+anything is the
+ 
+
+ align:start position:0%
+anything is the
+anything so in like one step now one
+
+ align:start position:0%
+anything so in like one step now one
+ 
+
+ align:start position:0%
+anything so in like one step now one
+division instead of having to do a bunch
+
+ align:start position:0%
+division instead of having to do a bunch
+ 
+
+ align:start position:0%
+division instead of having to do a bunch
+of subtractions I compute the
+
+ align:start position:0%
+of subtractions I compute the
+ 
+
+ align:start position:0%
+of subtractions I compute the
+gcd great let's write this down as an
+
+ align:start position:0%
+gcd great let's write this down as an
+ 
+
+ align:start position:0%
+gcd great let's write this down as an
+algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is called ukis algorithm or the
+
+ align:start position:0%
+this is called ukis algorithm or the
+ 
+
+ align:start position:0%
+this is called ukis algorithm or the
+ukian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm it's called UK's algorithm
+
+ align:start position:0%
+algorithm it's called UK's algorithm
+ 
+
+ align:start position:0%
+algorithm it's called UK's algorithm
+because uclid was not the first to
+
+ align:start position:0%
+because uclid was not the first to
+ 
+
+ align:start position:0%
+because uclid was not the first to
+discover it of course uh but he was
+
+ align:start position:0%
+discover it of course uh but he was
+ 
+
+ align:start position:0%
+discover it of course uh but he was
+still pretty early uh around 300C C uh
+
+ align:start position:0%
+still pretty early uh around 300C C uh
+ 
+
+ align:start position:0%
+still pretty early uh around 300C C uh
+but I'll mention an earlier version in
+
+ align:start position:0%
+but I'll mention an earlier version in
+ 
+
+ align:start position:0%
+but I'll mention an earlier version in
+in a moment uh so what this does is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computes gcd of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ab uh
+
+ align:start position:0%
+ab uh
+ 
+
+ align:start position:0%
+ab uh
+for a greater than or equal to B greater
+
+ align:start position:0%
+for a greater than or equal to B greater
+ 
+
+ align:start position:0%
+for a greater than or equal to B greater
+than or equal to zero okay I'm going to
+
+ align:start position:0%
+than or equal to zero okay I'm going to
+ 
+
+ align:start position:0%
+than or equal to zero okay I'm going to
+assume everything's not negative if it's
+
+ align:start position:0%
+assume everything's not negative if it's
+ 
+
+ align:start position:0%
+assume everything's not negative if it's
+negative just negate it I'm going to
+
+ align:start position:0%
+negative just negate it I'm going to
+ 
+
+ align:start position:0%
+negative just negate it I'm going to
+assume the left argument is is bigger
+
+ align:start position:0%
+assume the left argument is is bigger
+ 
+
+ align:start position:0%
+assume the left argument is is bigger
+than the right one or equal uh if it's
+
+ align:start position:0%
+than the right one or equal uh if it's
+ 
+
+ align:start position:0%
+than the right one or equal uh if it's
+the other way around swap A and B okay
+
+ align:start position:0%
+the other way around swap A and B okay
+ 
+
+ align:start position:0%
+the other way around swap A and B okay
+so this is enough for computing gcd of
+
+ align:start position:0%
+so this is enough for computing gcd of
+ 
+
+ align:start position:0%
+so this is enough for computing gcd of
+any two
+
+ align:start position:0%
+any two
+ 
+
+ align:start position:0%
+any two
+integers um and I'm going to write this
+
+ align:start position:0%
+integers um and I'm going to write this
+ 
+
+ align:start position:0%
+integers um and I'm going to write this
+of course as a state
+
+ align:start position:0%
+of course as a state
+ 
+
+ align:start position:0%
+of course as a state
+machine so in general I'm going to have
+
+ align:start position:0%
+machine so in general I'm going to have
+ 
+
+ align:start position:0%
+machine so in general I'm going to have
+a pair of integers A and B where a is
+
+ align:start position:0%
+a pair of integers A and B where a is
+ 
+
+ align:start position:0%
+a pair of integers A and B where a is
+greater than equal to B uh greater equal
+
+ align:start position:0%
+greater than equal to B uh greater equal
+ 
+
+ align:start position:0%
+greater than equal to B uh greater equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+zero uh so I guess I should say the
+
+ align:start position:0%
+zero uh so I guess I should say the
+ 
+
+ align:start position:0%
+zero uh so I guess I should say the
+states are X comma y uh
+
+ align:start position:0%
+states are X comma y uh
+ 
+
+ align:start position:0%
+states are X comma y uh
+where X is greater equal to Y is greater
+
+ align:start position:0%
+where X is greater equal to Y is greater
+ 
+
+ align:start position:0%
+where X is greater equal to Y is greater
+than equal to zero and then the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transitions go from X comma y to X REM
+
+ align:start position:0%
+transitions go from X comma y to X REM
+ 
+
+ align:start position:0%
+transitions go from X comma y to X REM
+y Oh wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order y comma X Ram
+
+ align:start position:0%
+order y comma X Ram
+ 
+
+ align:start position:0%
+order y comma X Ram
+y okay almost the same as this theorem
+
+ align:start position:0%
+y okay almost the same as this theorem
+ 
+
+ align:start position:0%
+y okay almost the same as this theorem
+except I'm going to rewrite this as gcd
+
+ align:start position:0%
+except I'm going to rewrite this as gcd
+ 
+
+ align:start position:0%
+except I'm going to rewrite this as gcd
+of B comma a rem B just flip the
+
+ align:start position:0%
+of B comma a rem B just flip the
+ 
+
+ align:start position:0%
+of B comma a rem B just flip the
+arguments because I would like the left
+
+ align:start position:0%
+arguments because I would like the left
+ 
+
+ align:start position:0%
+arguments because I would like the left
+argument to always be greater than or
+
+ align:start position:0%
+argument to always be greater than or
+ 
+
+ align:start position:0%
+argument to always be greater than or
+equal to I would like the left argument
+
+ align:start position:0%
+equal to I would like the left argument
+ 
+
+ align:start position:0%
+equal to I would like the left argument
+to be always greater than or equal to
+
+ align:start position:0%
+to be always greater than or equal to
+ 
+
+ align:start position:0%
+to be always greater than or equal to
+the right argument um and if I do them
+
+ align:start position:0%
+the right argument um and if I do them
+ 
+
+ align:start position:0%
+the right argument um and if I do them
+in this order if x was greater than
+
+ align:start position:0%
+in this order if x was greater than
+ 
+
+ align:start position:0%
+in this order if x was greater than
+equal to Y I do this division this
+
+ align:start position:0%
+equal to Y I do this division this
+ 
+
+ align:start position:0%
+equal to Y I do this division this
+division will of course be less than y
+
+ align:start position:0%
+division will of course be less than y
+ 
+
+ align:start position:0%
+division will of course be less than y
+and so the left one will be bigger than
+
+ align:start position:0%
+and so the left one will be bigger than
+ 
+
+ align:start position:0%
+and so the left one will be bigger than
+the right one actually
+
+ align:start position:0%
+the right one actually
+ 
+
+ align:start position:0%
+the right one actually
+strictly in that case
+
+ align:start position:0%
+strictly in that case
+ 
+
+ align:start position:0%
+strictly in that case
+okay uh so that's basically just
+
+ align:start position:0%
+okay uh so that's basically just
+ 
+
+ align:start position:0%
+okay uh so that's basically just
+following this rule
+
+ align:start position:0%
+following this rule
+ 
+
+ align:start position:0%
+following this rule
+repeatedly and those are my
+
+ align:start position:0%
+repeatedly and those are my
+ 
+
+ align:start position:0%
+repeatedly and those are my
+transitions uh now this only
+
+ align:start position:0%
+transitions uh now this only
+ 
+
+ align:start position:0%
+transitions uh now this only
+works uh when Y is bigger than
+
+ align:start position:0%
+works uh when Y is bigger than
+ 
+
+ align:start position:0%
+works uh when Y is bigger than
+zero if Y is
+
+ align:start position:0%
+zero if Y is
+ 
+
+ align:start position:0%
+zero if Y is
+zero uh at um X comma 0 we
+
+ align:start position:0%
+zero uh at um X comma 0 we
+ 
+
+ align:start position:0%
+zero uh at um X comma 0 we
+return
+
+ align:start position:0%
+return
+ 
+
+ align:start position:0%
+return
+X as the
+
+ align:start position:0%
+X as the
+ 
+
+ align:start position:0%
+X as the
+gcd that's the final state or there
+
+ align:start position:0%
+gcd that's the final state or there
+ 
+
+ align:start position:0%
+gcd that's the final state or there
+these these are various final States any
+
+ align:start position:0%
+these these are various final States any
+ 
+
+ align:start position:0%
+these these are various final States any
+X comma 0 is going to be a final State
+
+ align:start position:0%
+X comma 0 is going to be a final State
+ 
+
+ align:start position:0%
+X comma 0 is going to be a final State
+there's no transition out of there
+
+ align:start position:0%
+there's no transition out of there
+ 
+
+ align:start position:0%
+there's no transition out of there
+because we're not allowed to divide by
+
+ align:start position:0%
+because we're not allowed to divide by
+ 
+
+ align:start position:0%
+because we're not allowed to divide by
+zero because I wrote this for all y
+
+ align:start position:0%
+zero because I wrote this for all y
+ 
+
+ align:start position:0%
+zero because I wrote this for all y
+greater than zero rule but at that in
+
+ align:start position:0%
+greater than zero rule but at that in
+ 
+
+ align:start position:0%
+greater than zero rule but at that in
+that situation we know the gcd of 0
+
+ align:start position:0%
+that situation we know the gcd of 0
+ 
+
+ align:start position:0%
+that situation we know the gcd of 0
+comma b or B comma 0 is the absolute
+
+ align:start position:0%
+comma b or B comma 0 is the absolute
+ 
+
+ align:start position:0%
+comma b or B comma 0 is the absolute
+value of B because everything here is
+
+ align:start position:0%
+value of B because everything here is
+ 
+
+ align:start position:0%
+value of B because everything here is
+non- negative uh the answer is X at that
+
+ align:start position:0%
+non- negative uh the answer is X at that
+ 
+
+ align:start position:0%
+non- negative uh the answer is X at that
+point so why does this
+
+ align:start position:0%
+point so why does this
+ 
+
+ align:start position:0%
+point so why does this
+work well because we just proved an
+
+ align:start position:0%
+work well because we just proved an
+ 
+
+ align:start position:0%
+work well because we just proved an
+invariant that uh as this machine
+
+ align:start position:0%
+invariant that uh as this machine
+ 
+
+ align:start position:0%
+invariant that uh as this machine
+runs um I want to say p of
+
+ align:start position:0%
+runs um I want to say p of
+ 
+
+ align:start position:0%
+runs um I want to say p of
+XY is the state predicate which is uh
+
+ align:start position:0%
+XY is the state predicate which is uh
+ 
+
+ align:start position:0%
+XY is the state predicate which is uh
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gcd of X comma y equals the gcd of a
+
+ align:start position:0%
+gcd of X comma y equals the gcd of a
+ 
+
+ align:start position:0%
+gcd of X comma y equals the gcd of a
+comma
+
+ align:start position:0%
+comma
+ 
+
+ align:start position:0%
+comma
+B right whatever we designed the change
+
+ align:start position:0%
+B right whatever we designed the change
+ 
+
+ align:start position:0%
+B right whatever we designed the change
+in arguments here we started with a
+
+ align:start position:0%
+in arguments here we started with a
+ 
+
+ align:start position:0%
+in arguments here we started with a
+comma B so this is true initially in our
+
+ align:start position:0%
+comma B so this is true initially in our
+ 
+
+ align:start position:0%
+comma B so this is true initially in our
+initial State a comma B of course gcd of
+
+ align:start position:0%
+initial State a comma B of course gcd of
+ 
+
+ align:start position:0%
+initial State a comma B of course gcd of
+a comma b equals gcd of a comma B and
+
+ align:start position:0%
+a comma b equals gcd of a comma B and
+ 
+
+ align:start position:0%
+a comma b equals gcd of a comma B and
+then every time we do a transition and
+
+ align:start position:0%
+then every time we do a transition and
+ 
+
+ align:start position:0%
+then every time we do a transition and
+we do this Division and take the
+
+ align:start position:0%
+we do this Division and take the
+ 
+
+ align:start position:0%
+we do this Division and take the
+remainder we still have we know that the
+
+ align:start position:0%
+remainder we still have we know that the
+ 
+
+ align:start position:0%
+remainder we still have we know that the
+gcds are equal by this
+
+ align:start position:0%
+gcds are equal by this
+ 
+
+ align:start position:0%
+gcds are equal by this
+theorem right that's exactly what this
+
+ align:start position:0%
+theorem right that's exactly what this
+ 
+
+ align:start position:0%
+theorem right that's exactly what this
+tells us and so this is saying this
+
+ align:start position:0%
+tells us and so this is saying this
+ 
+
+ align:start position:0%
+tells us and so this is saying this
+theorem tells us that this state
+
+ align:start position:0%
+theorem tells us that this state
+ 
+
+ align:start position:0%
+theorem tells us that this state
+predicate is preserved and because it
+
+ align:start position:0%
+predicate is preserved and because it
+ 
+
+ align:start position:0%
+predicate is preserved and because it
+holds initially that means it's
+
+ align:start position:0%
+holds initially that means it's
+ 
+
+ align:start position:0%
+holds initially that means it's
+invariant okay uh true initially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preserved by this theorem and so by the
+
+ align:start position:0%
+preserved by this theorem and so by the
+ 
+
+ align:start position:0%
+preserved by this theorem and so by the
+invariant principle we know that this
+
+ align:start position:0%
+invariant principle we know that this
+ 
+
+ align:start position:0%
+invariant principle we know that this
+will remain true for any reachable state
+
+ align:start position:0%
+will remain true for any reachable state
+ 
+
+ align:start position:0%
+will remain true for any reachable state
+XY we'll have gcd of XY equal gcd of ab
+
+ align:start position:0%
+XY we'll have gcd of XY equal gcd of ab
+ 
+
+ align:start position:0%
+XY we'll have gcd of XY equal gcd of ab
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+furthermore uh when we get to a final
+
+ align:start position:0%
+furthermore uh when we get to a final
+ 
+
+ align:start position:0%
+furthermore uh when we get to a final
+state so this is a final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State uh we know that this answer is
+
+ align:start position:0%
+State uh we know that this answer is
+ 
+
+ align:start position:0%
+State uh we know that this answer is
+correct because gcd of X comma 0 equals
+
+ align:start position:0%
+correct because gcd of X comma 0 equals
+ 
+
+ align:start position:0%
+correct because gcd of X comma 0 equals
+X for non- Negative X so this was this
+
+ align:start position:0%
+X for non- Negative X so this was this
+ 
+
+ align:start position:0%
+X for non- Negative X so this was this
+is partial
+
+ align:start position:0%
+is partial
+ 
+
+ align:start position:0%
+is partial
+correctness if we get to a final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State uh
+
+ align:start position:0%
+State uh
+ 
+
+ align:start position:0%
+State uh
+gcd of X comma 0 equals
+
+ align:start position:0%
+gcd of X comma 0 equals
+ 
+
+ align:start position:0%
+gcd of X comma 0 equals
+X for X greater than equal to Z by this
+
+ align:start position:0%
+X for X greater than equal to Z by this
+ 
+
+ align:start position:0%
+X for X greater than equal to Z by this
+theorem that we
+
+ align:start position:0%
+theorem that we
+ 
+
+ align:start position:0%
+theorem that we
+proved Okay so if this machine
+
+ align:start position:0%
+proved Okay so if this machine
+ 
+
+ align:start position:0%
+proved Okay so if this machine
+terminates we're
+
+ align:start position:0%
+terminates we're
+ 
+
+ align:start position:0%
+terminates we're
+done and I claim this machine does
+
+ align:start position:0%
+done and I claim this machine does
+ 
+
+ align:start position:0%
+done and I claim this machine does
+terminate so let's prove
+
+ align:start position:0%
+terminate so let's prove
+ 
+
+ align:start position:0%
+terminate so let's prove
+termination in a couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways so how do we prove termination of
+
+ align:start position:0%
+ways so how do we prove termination of
+ 
+
+ align:start position:0%
+ways so how do we prove termination of
+State machines we
+
+ align:start position:0%
+State machines we
+ 
+
+ align:start position:0%
+State machines we
+Define uh some value some function of
+
+ align:start position:0%
+Define uh some value some function of
+ 
+
+ align:start position:0%
+Define uh some value some function of
+States that's an integer a non- negative
+
+ align:start position:0%
+States that's an integer a non- negative
+ 
+
+ align:start position:0%
+States that's an integer a non- negative
+integer and we show that it strictly
+
+ align:start position:0%
+integer and we show that it strictly
+ 
+
+ align:start position:0%
+integer and we show that it strictly
+decreases that's our main tool for
+
+ align:start position:0%
+decreases that's our main tool for
+ 
+
+ align:start position:0%
+decreases that's our main tool for
+proving termination of algorithms uh so
+
+ align:start position:0%
+proving termination of algorithms uh so
+ 
+
+ align:start position:0%
+proving termination of algorithms uh so
+for example we could uh take the
+
+ align:start position:0%
+for example we could uh take the
+ 
+
+ align:start position:0%
+for example we could uh take the
+function X+
+
+ align:start position:0%
+function X+
+ 
+
+ align:start position:0%
+function X+
+y this strictly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreases why uh just think about a
+
+ align:start position:0%
+decreases why uh just think about a
+ 
+
+ align:start position:0%
+decreases why uh just think about a
+transition we start with X comma y y
+
+ align:start position:0%
+transition we start with X comma y y
+ 
+
+ align:start position:0%
+transition we start with X comma y y
+doesn't change and then the other term
+
+ align:start position:0%
+doesn't change and then the other term
+ 
+
+ align:start position:0%
+doesn't change and then the other term
+in the sum used to be X and then it
+
+ align:start position:0%
+in the sum used to be X and then it
+ 
+
+ align:start position:0%
+in the sum used to be X and then it
+becomes X remainder y so we're dividing
+
+ align:start position:0%
+becomes X remainder y so we're dividing
+ 
+
+ align:start position:0%
+becomes X remainder y so we're dividing
+X by y so X gets smaller in that process
+
+ align:start position:0%
+X by y so X gets smaller in that process
+ 
+
+ align:start position:0%
+X by y so X gets smaller in that process
+and so the sum of these two values is
+
+ align:start position:0%
+and so the sum of these two values is
+ 
+
+ align:start position:0%
+and so the sum of these two values is
+going to be smaller than the sum of X
+
+ align:start position:0%
+going to be smaller than the sum of X
+ 
+
+ align:start position:0%
+going to be smaller than the sum of X
+and Y so that's cool we now know that
+
+ align:start position:0%
+and Y so that's cool we now know that
+ 
+
+ align:start position:0%
+and Y so that's cool we now know that
+this algorithm terminates um but stating
+
+ align:start position:0%
+this algorithm terminates um but stating
+ 
+
+ align:start position:0%
+this algorithm terminates um but stating
+it using this
+
+ align:start position:0%
+it using this
+ 
+
+ align:start position:0%
+it using this
+uh function is not so great because it
+
+ align:start position:0%
+uh function is not so great because it
+ 
+
+ align:start position:0%
+uh function is not so great because it
+tells us that the number of
+
+ align:start position:0%
+tells us that the number of
+ 
+
+ align:start position:0%
+tells us that the number of
+steps uh is uh at most a plus b
+
+ align:start position:0%
+steps uh is uh at most a plus b
+ 
+
+ align:start position:0%
+steps uh is uh at most a plus b
+but that's not great that's that's what
+
+ align:start position:0%
+but that's not great that's that's what
+ 
+
+ align:start position:0%
+but that's not great that's that's what
+we had before uh from our slow algorithm
+
+ align:start position:0%
+we had before uh from our slow algorithm
+ 
+
+ align:start position:0%
+we had before uh from our slow algorithm
+we got a running time of a plus b like
+
+ align:start position:0%
+we got a running time of a plus b like
+ 
+
+ align:start position:0%
+we got a running time of a plus b like
+so that's still true it's an upper bound
+
+ align:start position:0%
+so that's still true it's an upper bound
+ 
+
+ align:start position:0%
+so that's still true it's an upper bound
+on the running time but I claim that in
+
+ align:start position:0%
+on the running time but I claim that in
+ 
+
+ align:start position:0%
+on the running time but I claim that in
+fact our running time is much
+
+ align:start position:0%
+fact our running time is much
+ 
+
+ align:start position:0%
+fact our running time is much
+smaller by a more clever proof let me
+
+ align:start position:0%
+smaller by a more clever proof let me
+ 
+
+ align:start position:0%
+smaller by a more clever proof let me
+erase subtraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I
+
+ align:start position:0%
+okay so I
+ 
+
+ align:start position:0%
+okay so I
+claim uh in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact if we look at the bit count of X
+
+ align:start position:0%
+fact if we look at the bit count of X
+ 
+
+ align:start position:0%
+fact if we look at the bit count of X
+and the bit count of Y in summation this
+
+ align:start position:0%
+and the bit count of Y in summation this
+ 
+
+ align:start position:0%
+and the bit count of Y in summation this
+also strictly decreases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is a bit count this is if you write
+
+ align:start position:0%
+what is a bit count this is if you write
+ 
+
+ align:start position:0%
+what is a bit count this is if you write
+X in binary how many bits are there
+
+ align:start position:0%
+X in binary how many bits are there
+ 
+
+ align:start position:0%
+X in binary how many bits are there
+what's the length of the binary
+
+ align:start position:0%
+what's the length of the binary
+ 
+
+ align:start position:0%
+what's the length of the binary
+representation of X um this is
+
+ align:start position:0%
+representation of X um this is
+ 
+
+ align:start position:0%
+representation of X um this is
+essentially 1 + log base 2 of X
+
+ align:start position:0%
+essentially 1 + log base 2 of X
+ 
+
+ align:start position:0%
+essentially 1 + log base 2 of X
+ceiling a little gross but uh ASM
+
+ align:start position:0%
+ceiling a little gross but uh ASM
+ 
+
+ align:start position:0%
+ceiling a little gross but uh ASM
+totically this is log base 2 of
+
+ align:start position:0%
+totically this is log base 2 of
+ 
+
+ align:start position:0%
+totically this is log base 2 of
+x or when you use ASM totic notation you
+
+ align:start position:0%
+x or when you use ASM totic notation you
+ 
+
+ align:start position:0%
+x or when you use ASM totic notation you
+don't even need the base because it only
+
+ align:start position:0%
+don't even need the base because it only
+ 
+
+ align:start position:0%
+don't even need the base because it only
+makes uh constant Factor difference so
+
+ align:start position:0%
+makes uh constant Factor difference so
+ 
+
+ align:start position:0%
+makes uh constant Factor difference so
+this is roughly log of x it's Theta log
+
+ align:start position:0%
+this is roughly log of x it's Theta log
+ 
+
+ align:start position:0%
+this is roughly log of x it's Theta log
+of x this is Theta log of Y so uh the
+
+ align:start position:0%
+of x this is Theta log of Y so uh the
+ 
+
+ align:start position:0%
+of x this is Theta log of Y so uh the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+steps is order log X Plus log
+
+ align:start position:0%
+steps is order log X Plus log
+ 
+
+ align:start position:0%
+steps is order log X Plus log
+Y and that's really good that's
+
+ align:start position:0%
+Y and that's really good that's
+ 
+
+ align:start position:0%
+Y and that's really good that's
+exponentially faster sorry I should have
+
+ align:start position:0%
+exponentially faster sorry I should have
+ 
+
+ align:start position:0%
+exponentially faster sorry I should have
+written uh log a plus log B because
+
+ align:start position:0%
+written uh log a plus log B because
+ 
+
+ align:start position:0%
+written uh log a plus log B because
+that's where we start is a a comma B so
+
+ align:start position:0%
+that's where we start is a a comma B so
+ 
+
+ align:start position:0%
+that's where we start is a a comma B so
+if I give you two numbers A and B I can
+
+ align:start position:0%
+if I give you two numbers A and B I can
+ 
+
+ align:start position:0%
+if I give you two numbers A and B I can
+compute the gcd in roughly
+
+ align:start position:0%
+compute the gcd in roughly
+ 
+
+ align:start position:0%
+compute the gcd in roughly
+logarithmically many divisions whereas
+
+ align:start position:0%
+logarithmically many divisions whereas
+ 
+
+ align:start position:0%
+logarithmically many divisions whereas
+before we did a plus b now we have log a
+
+ align:start position:0%
+before we did a plus b now we have log a
+ 
+
+ align:start position:0%
+before we did a plus b now we have log a
+plus log B so that's what we call an
+
+ align:start position:0%
+plus log B so that's what we call an
+ 
+
+ align:start position:0%
+plus log B so that's what we call an
+exponential Improvement and this is a
+
+ align:start position:0%
+exponential Improvement and this is a
+ 
+
+ align:start position:0%
+exponential Improvement and this is a
+what we would call a fast algorithm
+
+ align:start position:0%
+what we would call a fast algorithm
+ 
+
+ align:start position:0%
+what we would call a fast algorithm
+because now if I have a 100 bit integer
+
+ align:start position:0%
+because now if I have a 100 bit integer
+ 
+
+ align:start position:0%
+because now if I have a 100 bit integer
+it only takes me like or or two 100 bit
+
+ align:start position:0%
+it only takes me like or or two 100 bit
+ 
+
+ align:start position:0%
+it only takes me like or or two 100 bit
+integers it only takes me around 100
+
+ align:start position:0%
+integers it only takes me around 100
+ 
+
+ align:start position:0%
+integers it only takes me around 100
+steps whereas before is taking me two to
+
+ align:start position:0%
+steps whereas before is taking me two to
+ 
+
+ align:start position:0%
+steps whereas before is taking me two to
+the 100 steps big difference
+
+ align:start position:0%
+the 100 steps big difference
+ 
+
+ align:start position:0%
+the 100 steps big difference
+okay uh why is this true why is bit
+
+ align:start position:0%
+okay uh why is this true why is bit
+ 
+
+ align:start position:0%
+okay uh why is this true why is bit
+count of X Plus bit count of Y strictly
+
+ align:start position:0%
+count of X Plus bit count of Y strictly
+ 
+
+ align:start position:0%
+count of X Plus bit count of Y strictly
+decreasing um
+
+ align:start position:0%
+decreasing um
+ 
+
+ align:start position:0%
+decreasing um
+because I
+
+ align:start position:0%
+because I
+ 
+
+ align:start position:0%
+because I
+claim so I should say
+
+ align:start position:0%
+claim so I should say
+ 
+
+ align:start position:0%
+claim so I should say
+because XR Y is less than x over2 this
+
+ align:start position:0%
+because XR Y is less than x over2 this
+ 
+
+ align:start position:0%
+because XR Y is less than x over2 this
+is another fact about division um I
+
+ align:start position:0%
+is another fact about division um I
+ 
+
+ align:start position:0%
+is another fact about division um I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+the intuition here is uh Y is smaller
+
+ align:start position:0%
+the intuition here is uh Y is smaller
+ 
+
+ align:start position:0%
+the intuition here is uh Y is smaller
+than x when we're doing this Division
+
+ align:start position:0%
+than x when we're doing this Division
+ 
+
+ align:start position:0%
+than x when we're doing this Division
+and so we can remove at least one whole
+
+ align:start position:0%
+and so we can remove at least one whole
+ 
+
+ align:start position:0%
+and so we can remove at least one whole
+copy of Y from X and maybe we remove
+
+ align:start position:0%
+copy of Y from X and maybe we remove
+ 
+
+ align:start position:0%
+copy of Y from X and maybe we remove
+more but um yeah you can think about
+
+ align:start position:0%
+more but um yeah you can think about
+ 
+
+ align:start position:0%
+more but um yeah you can think about
+when y if Y is more than half X then
+
+ align:start position:0%
+when y if Y is more than half X then
+ 
+
+ align:start position:0%
+when y if Y is more than half X then
+just in the first step we've removed
+
+ align:start position:0%
+just in the first step we've removed
+ 
+
+ align:start position:0%
+just in the first step we've removed
+half of X and so we've gotten down to
+
+ align:start position:0%
+half of X and so we've gotten down to
+ 
+
+ align:start position:0%
+half of X and so we've gotten down to
+less than x over two um if x is smaller
+
+ align:start position:0%
+less than x over two um if x is smaller
+ 
+
+ align:start position:0%
+less than x over two um if x is smaller
+if Y is really small like one then we're
+
+ align:start position:0%
+if Y is really small like one then we're
+ 
+
+ align:start position:0%
+if Y is really small like one then we're
+going to be able to eat all of x uh in
+
+ align:start position:0%
+going to be able to eat all of x uh in
+ 
+
+ align:start position:0%
+going to be able to eat all of x uh in
+both cases you'll end up uh eating at
+
+ align:start position:0%
+both cases you'll end up uh eating at
+ 
+
+ align:start position:0%
+both cases you'll end up uh eating at
+least half of X and so in general the
+
+ align:start position:0%
+least half of X and so in general the
+ 
+
+ align:start position:0%
+least half of X and so in general the
+remainder will be less than half of X
+
+ align:start position:0%
+remainder will be less than half of X
+ 
+
+ align:start position:0%
+remainder will be less than half of X
+over2 and so if we start with X and we
+
+ align:start position:0%
+over2 and so if we start with X and we
+ 
+
+ align:start position:0%
+over2 and so if we start with X and we
+in the next step we get to X over2 or
+
+ align:start position:0%
+in the next step we get to X over2 or
+ 
+
+ align:start position:0%
+in the next step we get to X over2 or
+smaller that means we removed one bit
+
+ align:start position:0%
+smaller that means we removed one bit
+ 
+
+ align:start position:0%
+smaller that means we removed one bit
+from the binary representation or if you
+
+ align:start position:0%
+from the binary representation or if you
+ 
+
+ align:start position:0%
+from the binary representation or if you
+think about it in log base 2 we've if we
+
+ align:start position:0%
+think about it in log base 2 we've if we
+ 
+
+ align:start position:0%
+think about it in log base 2 we've if we
+have the number log base two goes down
+
+ align:start position:0%
+have the number log base two goes down
+ 
+
+ align:start position:0%
+have the number log base two goes down
+by one so even with the ceiling it goes
+
+ align:start position:0%
+by one so even with the ceiling it goes
+ 
+
+ align:start position:0%
+by one so even with the ceiling it goes
+down by
+
+ align:start position:0%
+down by
+ 
+
+ align:start position:0%
+down by
+one okay so that's why this uclid
+
+ align:start position:0%
+one okay so that's why this uclid
+ 
+
+ align:start position:0%
+one okay so that's why this uclid
+algorithm is fast and good that's why we
+
+ align:start position:0%
+algorithm is fast and good that's why we
+ 
+
+ align:start position:0%
+algorithm is fast and good that's why we
+love it um I have for you a little of
+
+ align:start position:0%
+love it um I have for you a little of
+ 
+
+ align:start position:0%
+love it um I have for you a little of
+the algorithm and then we'll talk about
+
+ align:start position:0%
+the algorithm and then we'll talk about
+ 
+
+ align:start position:0%
+the algorithm and then we'll talk about
+extensions so here uh on the screen
+
+ align:start position:0%
+extensions so here uh on the screen
+ 
+
+ align:start position:0%
+extensions so here uh on the screen
+we're Computing gcd of 189 and
+
+ align:start position:0%
+we're Computing gcd of 189 and
+ 
+
+ align:start position:0%
+we're Computing gcd of 189 and
+66 if we think of that as a rectangle
+
+ align:start position:0%
+66 if we think of that as a rectangle
+ 
+
+ align:start position:0%
+66 if we think of that as a rectangle
+189 by
+
+ align:start position:0%
+189 by
+ 
+
+ align:start position:0%
+189 by
+606 uh then doing a division is like
+
+ align:start position:0%
+606 uh then doing a division is like
+ 
+
+ align:start position:0%
+606 uh then doing a division is like
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+packing um so
+
+ align:start position:0%
+packing um so
+ 
+
+ align:start position:0%
+packing um so
+here if we have an A by B rectangle and
+
+ align:start position:0%
+here if we have an A by B rectangle and
+ 
+
+ align:start position:0%
+here if we have an A by B rectangle and
+a and b is the smaller one uh then a b
+
+ align:start position:0%
+a and b is the smaller one uh then a b
+ 
+
+ align:start position:0%
+a and b is the smaller one uh then a b
+by B squ like subtracting off B and so
+
+ align:start position:0%
+by B squ like subtracting off B and so
+ 
+
+ align:start position:0%
+by B squ like subtracting off B and so
+uh if you think of the whole rectangle
+
+ align:start position:0%
+uh if you think of the whole rectangle
+ 
+
+ align:start position:0%
+uh if you think of the whole rectangle
+it's how many squares can I subtract off
+
+ align:start position:0%
+it's how many squares can I subtract off
+ 
+
+ align:start position:0%
+it's how many squares can I subtract off
+and what we'll be left with is the
+
+ align:start position:0%
+and what we'll be left with is the
+ 
+
+ align:start position:0%
+and what we'll be left with is the
+remainder because one dimension stays
+
+ align:start position:0%
+remainder because one dimension stays
+ 
+
+ align:start position:0%
+remainder because one dimension stays
+the same the other dimension gets
+
+ align:start position:0%
+the same the other dimension gets
+ 
+
+ align:start position:0%
+the same the other dimension gets
+reduced to the remainder so hopefully
+
+ align:start position:0%
+reduced to the remainder so hopefully
+ 
+
+ align:start position:0%
+reduced to the remainder so hopefully
+that's clear why the geometric view of
+
+ align:start position:0%
+that's clear why the geometric view of
+ 
+
+ align:start position:0%
+that's clear why the geometric view of
+squares is the same as what we've been
+
+ align:start position:0%
+squares is the same as what we've been
+ 
+
+ align:start position:0%
+squares is the same as what we've been
+doing with UK's algorithm makes for a
+
+ align:start position:0%
+doing with UK's algorithm makes for a
+ 
+
+ align:start position:0%
+doing with UK's algorithm makes for a
+much nicer picture and then you take
+
+ align:start position:0%
+much nicer picture and then you take
+ 
+
+ align:start position:0%
+much nicer picture and then you take
+that rectangle and you flip it so that
+
+ align:start position:0%
+that rectangle and you flip it so that
+ 
+
+ align:start position:0%
+that rectangle and you flip it so that
+the horizontal Dimensions bigger you
+
+ align:start position:0%
+the horizontal Dimensions bigger you
+ 
+
+ align:start position:0%
+the horizontal Dimensions bigger you
+take off as many squares as you can and
+
+ align:start position:0%
+take off as many squares as you can and
+ 
+
+ align:start position:0%
+take off as many squares as you can and
+you flip and you take off as many
+
+ align:start position:0%
+you flip and you take off as many
+ 
+
+ align:start position:0%
+you flip and you take off as many
+squares as you can here's just just one
+
+ align:start position:0%
+squares as you can here's just just one
+ 
+
+ align:start position:0%
+squares as you can here's just just one
+that's just a subtraction you flip uh
+
+ align:start position:0%
+that's just a subtraction you flip uh
+ 
+
+ align:start position:0%
+that's just a subtraction you flip uh
+you take off as many squares as you can
+
+ align:start position:0%
+you take off as many squares as you can
+ 
+
+ align:start position:0%
+you take off as many squares as you can
+you left with a remainder of three by
+
+ align:start position:0%
+you left with a remainder of three by
+ 
+
+ align:start position:0%
+you left with a remainder of three by
+six uh and now here we get even Division
+
+ align:start position:0%
+six uh and now here we get even Division
+ 
+
+ align:start position:0%
+six uh and now here we get even Division
+and so one of the dimensions becomes
+
+ align:start position:0%
+and so one of the dimensions becomes
+ 
+
+ align:start position:0%
+and so one of the dimensions becomes
+zero and then the gcd of three and zero
+
+ align:start position:0%
+zero and then the gcd of three and zero
+ 
+
+ align:start position:0%
+zero and then the gcd of three and zero
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+cool so if that helps great if not don't
+
+ align:start position:0%
+cool so if that helps great if not don't
+ 
+
+ align:start position:0%
+cool so if that helps great if not don't
+worry uh hopefully you can now compute
+
+ align:start position:0%
+worry uh hopefully you can now compute
+ 
+
+ align:start position:0%
+worry uh hopefully you can now compute
+gcd uh we will do another example in a
+
+ align:start position:0%
+gcd uh we will do another example in a
+ 
+
+ align:start position:0%
+gcd uh we will do another example in a
+second I would like to first uh
+
+ align:start position:0%
+second I would like to first uh
+ 
+
+ align:start position:0%
+second I would like to first uh
+strengthen this algorithm and make it uh
+
+ align:start position:0%
+strengthen this algorithm and make it uh
+ 
+
+ align:start position:0%
+strengthen this algorithm and make it uh
+do more
+
+ align:start position:0%
+do more
+ 
+
+ align:start position:0%
+do more
+because remember we wanted to compute
+
+ align:start position:0%
+because remember we wanted to compute
+ 
+
+ align:start position:0%
+because remember we wanted to compute
+gcd uh why we wanted to see whether gcd
+
+ align:start position:0%
+gcd uh why we wanted to see whether gcd
+ 
+
+ align:start position:0%
+gcd uh why we wanted to see whether gcd
+of ab divided X because if the gcd of ab
+
+ align:start position:0%
+of ab divided X because if the gcd of ab
+ 
+
+ align:start position:0%
+of ab divided X because if the gcd of ab
+divides X then all common divisors of A
+
+ align:start position:0%
+divides X then all common divisors of A
+ 
+
+ align:start position:0%
+divides X then all common divisors of A
+and B will divide x uh and what the
+
+ align:start position:0%
+and B will divide x uh and what the
+ 
+
+ align:start position:0%
+and B will divide x uh and what the
+reason we cared about that is I claimed
+
+ align:start position:0%
+reason we cared about that is I claimed
+ 
+
+ align:start position:0%
+reason we cared about that is I claimed
+it was the same thing as X being an
+
+ align:start position:0%
+it was the same thing as X being an
+ 
+
+ align:start position:0%
+it was the same thing as X being an
+integer linear combination of A and B
+
+ align:start position:0%
+integer linear combination of A and B
+ 
+
+ align:start position:0%
+integer linear combination of A and B
+but where did the integer linear
+
+ align:start position:0%
+but where did the integer linear
+ 
+
+ align:start position:0%
+but where did the integer linear
+combinations go all we've done so far is
+
+ align:start position:0%
+combinations go all we've done so far is
+ 
+
+ align:start position:0%
+combinations go all we've done so far is
+compute gcd of ab well it turns out
+
+ align:start position:0%
+compute gcd of ab well it turns out
+ 
+
+ align:start position:0%
+compute gcd of ab well it turns out
+there's a connection
+
+ align:start position:0%
+there's a connection
+ 
+
+ align:start position:0%
+there's a connection
+and the connection is called bezus
+
+ align:start position:0%
+and the connection is called bezus
+ 
+
+ align:start position:0%
+and the connection is called bezus
+theorem or
+
+ align:start position:0%
+theorem or
+ 
+
+ align:start position:0%
+theorem or
+LMA it's called bazus Lemma because B is
+
+ align:start position:0%
+LMA it's called bazus Lemma because B is
+ 
+
+ align:start position:0%
+LMA it's called bazus Lemma because B is
+like the last person to discover it
+
+ align:start position:0%
+like the last person to discover it
+ 
+
+ align:start position:0%
+like the last person to discover it
+after uh in
+
+ align:start position:0%
+after uh in
+ 
+
+ align:start position:0%
+after uh in
+1779 after another French mathematician
+
+ align:start position:0%
+1779 after another French mathematician
+ 
+
+ align:start position:0%
+1779 after another French mathematician
+mesak uh in 1624 and after uh two Indian
+
+ align:start position:0%
+mesak uh in 1624 and after uh two Indian
+ 
+
+ align:start position:0%
+mesak uh in 1624 and after uh two Indian
+mathematicians around 500 uh AC so uh
+
+ align:start position:0%
+mathematicians around 500 uh AC so uh
+ 
+
+ align:start position:0%
+mathematicians around 500 uh AC so uh
+but we call it Biz LMA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+connection uh gcd of ab is an integer
+
+ align:start position:0%
+connection uh gcd of ab is an integer
+ 
+
+ align:start position:0%
+connection uh gcd of ab is an integer
+linear combination of A and B and we can
+
+ align:start position:0%
+linear combination of A and B and we can
+ 
+
+ align:start position:0%
+linear combination of A and B and we can
+prove this using UK's
+
+ align:start position:0%
+prove this using UK's
+ 
+
+ align:start position:0%
+prove this using UK's
+algorithm is pretty
+
+ align:start position:0%
+algorithm is pretty
+ 
+
+ align:start position:0%
+algorithm is pretty
+cool we're going
+
+ align:start position:0%
+cool we're going
+ 
+
+ align:start position:0%
+cool we're going
+to uh buy ukids algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh let me do this
+
+ align:start position:0%
+okay uh let me do this
+ 
+
+ align:start position:0%
+okay uh let me do this
+quickly let's assume a is greater equal
+
+ align:start position:0%
+quickly let's assume a is greater equal
+ 
+
+ align:start position:0%
+quickly let's assume a is greater equal
+to B again if not we can just swap A and
+
+ align:start position:0%
+to B again if not we can just swap A and
+ 
+
+ align:start position:0%
+to B again if not we can just swap A and
+B and I guess we'll assume greater equal
+
+ align:start position:0%
+B and I guess we'll assume greater equal
+ 
+
+ align:start position:0%
+B and I guess we'll assume greater equal
+to zero so we can apply ul's
+
+ align:start position:0%
+to zero so we can apply ul's
+ 
+
+ align:start position:0%
+to zero so we can apply ul's
+algorithm uh UK's algorithm tells us or
+
+ align:start position:0%
+algorithm uh UK's algorithm tells us or
+ 
+
+ align:start position:0%
+algorithm uh UK's algorithm tells us or
+the theorem we proved before UK's
+
+ align:start position:0%
+the theorem we proved before UK's
+ 
+
+ align:start position:0%
+the theorem we proved before UK's
+algorithm tells us gcd of ab equals gcd
+
+ align:start position:0%
+algorithm tells us gcd of ab equals gcd
+ 
+
+ align:start position:0%
+algorithm tells us gcd of ab equals gcd
+of B comma a rem B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and we can use induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now by strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction on a plus b so this is very
+
+ align:start position:0%
+induction on a plus b so this is very
+ 
+
+ align:start position:0%
+induction on a plus b so this is very
+similar to what we were saying here uh X
+
+ align:start position:0%
+similar to what we were saying here uh X
+ 
+
+ align:start position:0%
+similar to what we were saying here uh X
+Plus y strictly decreases it's all we
+
+ align:start position:0%
+Plus y strictly decreases it's all we
+ 
+
+ align:start position:0%
+Plus y strictly decreases it's all we
+need for induction to work here so we're
+
+ align:start position:0%
+need for induction to work here so we're
+ 
+
+ align:start position:0%
+need for induction to work here so we're
+assuming by induction
+
+ align:start position:0%
+assuming by induction
+ 
+
+ align:start position:0%
+assuming by induction
+that if a plus b is smaller than the
+
+ align:start position:0%
+that if a plus b is smaller than the
+ 
+
+ align:start position:0%
+that if a plus b is smaller than the
+current value then gcd of AA B is an
+
+ align:start position:0%
+current value then gcd of AA B is an
+ 
+
+ align:start position:0%
+current value then gcd of AA B is an
+integ linear combination of A and B and
+
+ align:start position:0%
+integ linear combination of A and B and
+ 
+
+ align:start position:0%
+integ linear combination of A and B and
+so here we have gcd of A and B and we've
+
+ align:start position:0%
+so here we have gcd of A and B and we've
+ 
+
+ align:start position:0%
+so here we have gcd of A and B and we've
+reduced it to gcd of some smaller values
+
+ align:start position:0%
+reduced it to gcd of some smaller values
+ 
+
+ align:start position:0%
+reduced it to gcd of some smaller values
+or whose sum is smaller and so we can
+
+ align:start position:0%
+or whose sum is smaller and so we can
+ 
+
+ align:start position:0%
+or whose sum is smaller and so we can
+apply strong induction to the this
+
+ align:start position:0%
+apply strong induction to the this
+ 
+
+ align:start position:0%
+apply strong induction to the this
+pair uh and so we'll get that this gcd
+
+ align:start position:0%
+pair uh and so we'll get that this gcd
+ 
+
+ align:start position:0%
+pair uh and so we'll get that this gcd
+is an integer linear combination of its
+
+ align:start position:0%
+is an integer linear combination of its
+ 
+
+ align:start position:0%
+is an integer linear combination of its
+arguments so
+
+ align:start position:0%
+arguments so
+ 
+
+ align:start position:0%
+arguments so
+let's continue here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by strong induction we get that uh
+
+ align:start position:0%
+so by strong induction we get that uh
+ 
+
+ align:start position:0%
+so by strong induction we get that uh
+gcd of B comma a ram
+
+ align:start position:0%
+gcd of B comma a ram
+ 
+
+ align:start position:0%
+gcd of B comma a ram
+B uh is an integer linear
+
+ align:start position:0%
+B uh is an integer linear
+ 
+
+ align:start position:0%
+B uh is an integer linear
+combination of b and a rem
+
+ align:start position:0%
+combination of b and a rem
+ 
+
+ align:start position:0%
+combination of b and a rem
+B okay and this value of course is equal
+
+ align:start position:0%
+B okay and this value of course is equal
+ 
+
+ align:start position:0%
+B okay and this value of course is equal
+to gcd of
+
+ align:start position:0%
+to gcd of
+ 
+
+ align:start position:0%
+to gcd of
+ab by this equality and so uh we get
+
+ align:start position:0%
+ab by this equality and so uh we get
+ 
+
+ align:start position:0%
+ab by this equality and so uh we get
+that the gcd we care about is integer
+
+ align:start position:0%
+that the gcd we care about is integer
+ 
+
+ align:start position:0%
+that the gcd we care about is integer
+linear combination not of A and B but of
+
+ align:start position:0%
+linear combination not of A and B but of
+ 
+
+ align:start position:0%
+linear combination not of A and B but of
+this reduced version b and a rem B okay
+
+ align:start position:0%
+this reduced version b and a rem B okay
+ 
+
+ align:start position:0%
+this reduced version b and a rem B okay
+that's kind of annoying but it turns out
+
+ align:start position:0%
+that's kind of annoying but it turns out
+ 
+
+ align:start position:0%
+that's kind of annoying but it turns out
+uh a r
+
+ align:start position:0%
+uh a r
+ 
+
+ align:start position:0%
+uh a r
+b is an integer linear combination of A
+
+ align:start position:0%
+b is an integer linear combination of A
+ 
+
+ align:start position:0%
+b is an integer linear combination of A
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+B Why by the division
+
+ align:start position:0%
+B Why by the division
+ 
+
+ align:start position:0%
+B Why by the division
+theorem actually wrote it out over here
+
+ align:start position:0%
+theorem actually wrote it out over here
+ 
+
+ align:start position:0%
+theorem actually wrote it out over here
+we wrote that NR D is n minus something
+
+ align:start position:0%
+we wrote that NR D is n minus something
+ 
+
+ align:start position:0%
+we wrote that NR D is n minus something
+time D that is this thing is an integer
+
+ align:start position:0%
+time D that is this thing is an integer
+ 
+
+ align:start position:0%
+time D that is this thing is an integer
+linear combination of N and
+
+ align:start position:0%
+linear combination of N and
+ 
+
+ align:start position:0%
+linear combination of N and
+d and so if I'm if I'm doing a rem B I
+
+ align:start position:0%
+d and so if I'm if I'm doing a rem B I
+ 
+
+ align:start position:0%
+d and so if I'm if I'm doing a rem B I
+get that it's a
+
+ align:start position:0%
+get that it's a
+ 
+
+ align:start position:0%
+get that it's a
+minus uh something the div times uh B so
+
+ align:start position:0%
+minus uh something the div times uh B so
+ 
+
+ align:start position:0%
+minus uh something the div times uh B so
+that's an integer linear combination of
+
+ align:start position:0%
+that's an integer linear combination of
+ 
+
+ align:start position:0%
+that's an integer linear combination of
+A and
+
+ align:start position:0%
+A and
+ 
+
+ align:start position:0%
+A and
+B okay so what we're left with is we
+
+ align:start position:0%
+B okay so what we're left with is we
+ 
+
+ align:start position:0%
+B okay so what we're left with is we
+have that this gcd that we care about is
+
+ align:start position:0%
+have that this gcd that we care about is
+ 
+
+ align:start position:0%
+have that this gcd that we care about is
+an integer linear combination of B and
+
+ align:start position:0%
+an integer linear combination of B and
+ 
+
+ align:start position:0%
+an integer linear combination of B and
+something else that is an integer linear
+
+ align:start position:0%
+something else that is an integer linear
+ 
+
+ align:start position:0%
+something else that is an integer linear
+combination of A and B so in other words
+
+ align:start position:0%
+combination of A and B so in other words
+ 
+
+ align:start position:0%
+combination of A and B so in other words
+we have an integer linear combination of
+
+ align:start position:0%
+we have an integer linear combination of
+ 
+
+ align:start position:0%
+we have an integer linear combination of
+two integer linear combinations of A and
+
+ align:start position:0%
+two integer linear combinations of A and
+ 
+
+ align:start position:0%
+two integer linear combinations of A and
+B Because B is definitely an integer
+
+ align:start position:0%
+B Because B is definitely an integer
+ 
+
+ align:start position:0%
+B Because B is definitely an integer
+linear combination of A and B it's 0 * a
+
+ align:start position:0%
+linear combination of A and B it's 0 * a
+ 
+
+ align:start position:0%
+linear combination of A and B it's 0 * a
+plus 1 time b a rem B is an integer
+
+ align:start position:0%
+plus 1 time b a rem B is an integer
+ 
+
+ align:start position:0%
+plus 1 time b a rem B is an integer
+linear combination as written over there
+
+ align:start position:0%
+linear combination as written over there
+ 
+
+ align:start position:0%
+linear combination as written over there
+and so now we're just taking an integer
+
+ align:start position:0%
+and so now we're just taking an integer
+ 
+
+ align:start position:0%
+and so now we're just taking an integer
+linear combination of those two things
+
+ align:start position:0%
+linear combination of those two things
+ 
+
+ align:start position:0%
+linear combination of those two things
+and that's also an integer linear
+
+ align:start position:0%
+and that's also an integer linear
+ 
+
+ align:start position:0%
+and that's also an integer linear
+combination
+
+ align:start position:0%
+combination
+ 
+
+ align:start position:0%
+combination
+of A and B as we showed
+
+ align:start position:0%
+of A and B as we showed
+ 
+
+ align:start position:0%
+of A and B as we showed
+before okay so that's maybe a little
+
+ align:start position:0%
+before okay so that's maybe a little
+ 
+
+ align:start position:0%
+before okay so that's maybe a little
+abstract but it does prove the theorem
+
+ align:start position:0%
+abstract but it does prove the theorem
+ 
+
+ align:start position:0%
+abstract but it does prove the theorem
+now I'm going to turn that into an
+
+ align:start position:0%
+now I'm going to turn that into an
+ 
+
+ align:start position:0%
+now I'm going to turn that into an
+algorithm cool
+
+ align:start position:0%
+algorithm cool
+ 
+
+ align:start position:0%
+algorithm cool
+algorithm uh maybe over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+here which is called the pulverizer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mentioned ucl's algorithm was
+
+ align:start position:0%
+I mentioned ucl's algorithm was
+ 
+
+ align:start position:0%
+I mentioned ucl's algorithm was
+discovered before uid in fact a stronger
+
+ align:start position:0%
+discovered before uid in fact a stronger
+ 
+
+ align:start position:0%
+discovered before uid in fact a stronger
+version of ID's algorithm called the
+
+ align:start position:0%
+version of ID's algorithm called the
+ 
+
+ align:start position:0%
+version of ID's algorithm called the
+pulverizer was Des uh described by Arab
+
+ align:start position:0%
+pulverizer was Des uh described by Arab
+ 
+
+ align:start position:0%
+pulverizer was Des uh described by Arab
+Bata an Indian mathematician around 500
+
+ align:start position:0%
+Bata an Indian mathematician around 500
+ 
+
+ align:start position:0%
+Bata an Indian mathematician around 500
+AC so uh long time ago and he called it
+
+ align:start position:0%
+AC so uh long time ago and he called it
+ 
+
+ align:start position:0%
+AC so uh long time ago and he called it
+kutaka which is sanskrit for
+
+ align:start position:0%
+kutaka which is sanskrit for
+ 
+
+ align:start position:0%
+kutaka which is sanskrit for
+pulverization so we're going to call
+
+ align:start position:0%
+pulverization so we're going to call
+ 
+
+ align:start position:0%
+pulverization so we're going to call
+this the pulverizer most people call
+
+ align:start position:0%
+this the pulverizer most people call
+ 
+
+ align:start position:0%
+this the pulverizer most people call
+this the extended ukian algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and it's basically run ID's algorithm
+
+ align:start position:0%
+uh and it's basically run ID's algorithm
+ 
+
+ align:start position:0%
+uh and it's basically run ID's algorithm
+but also keep in mind what's going on in
+
+ align:start position:0%
+but also keep in mind what's going on in
+ 
+
+ align:start position:0%
+but also keep in mind what's going on in
+beus LMA and always keep track of X and
+
+ align:start position:0%
+beus LMA and always keep track of X and
+ 
+
+ align:start position:0%
+beus LMA and always keep track of X and
+Y as an integer linear combination of A
+
+ align:start position:0%
+Y as an integer linear combination of A
+ 
+
+ align:start position:0%
+Y as an integer linear combination of A
+and B okay so that's the
+
+ align:start position:0%
+and B okay so that's the
+ 
+
+ align:start position:0%
+and B okay so that's the
+intuition uh as a state machine it's
+
+ align:start position:0%
+intuition uh as a state machine it's
+ 
+
+ align:start position:0%
+intuition uh as a state machine it's
+quite simple kind of simple
+
+ align:start position:0%
+quite simple kind of simple
+ 
+
+ align:start position:0%
+quite simple kind of simple
+A10 B 01 is where we start because a
+
+ align:start position:0%
+A10 B 01 is where we start because a
+ 
+
+ align:start position:0%
+A10 B 01 is where we start because a
+equal 1 * a + 0 * B and B = 0 * a + 1 *
+
+ align:start position:0%
+equal 1 * a + 0 * B and B = 0 * a + 1 *
+ 
+
+ align:start position:0%
+equal 1 * a + 0 * B and B = 0 * a + 1 *
+B so that's how we represent a and b as
+
+ align:start position:0%
+B so that's how we represent a and b as
+ 
+
+ align:start position:0%
+B so that's how we represent a and b as
+integer linear combinations of A and B
+
+ align:start position:0%
+integer linear combinations of A and B
+ 
+
+ align:start position:0%
+integer linear combinations of A and B
+pretty trivial and then our transitions
+
+ align:start position:0%
+pretty trivial and then our transitions
+ 
+
+ align:start position:0%
+pretty trivial and then our transitions
+if we have X
+
+ align:start position:0%
+if we have X
+ 
+
+ align:start position:0%
+if we have X
+St so this means u x = s * a + T *
+
+ align:start position:0%
+St so this means u x = s * a + T *
+ 
+
+ align:start position:0%
+St so this means u x = s * a + T *
+B and we have uh y u v so in other words
+
+ align:start position:0%
+B and we have uh y u v so in other words
+ 
+
+ align:start position:0%
+B and we have uh y u v so in other words
+we've represented y as U * s plus v *
+
+ align:start position:0%
+we've represented y as U * s plus v *
+ 
+
+ align:start position:0%
+we've represented y as U * s plus v *
+sorry uh V time U * a plus v *
+
+ align:start position:0%
+sorry uh V time U * a plus v *
+ 
+
+ align:start position:0%
+sorry uh V time U * a plus v *
+B then we transition
+
+ align:start position:0%
+B then we transition
+ 
+
+ align:start position:0%
+B then we transition
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that's a mistake this should be y UV
+
+ align:start position:0%
+uh that's a mistake this should be y UV
+ 
+
+ align:start position:0%
+uh that's a mistake this should be y UV
+uh we we as usual we just copy y to the
+
+ align:start position:0%
+uh we we as usual we just copy y to the
+ 
+
+ align:start position:0%
+uh we we as usual we just copy y to the
+left argument we don't change it and
+
+ align:start position:0%
+left argument we don't change it and
+ 
+
+ align:start position:0%
+left argument we don't change it and
+then X changes to um x r
+
+ align:start position:0%
+then X changes to um x r
+ 
+
+ align:start position:0%
+then X changes to um x r
+y and then it turns out you can
+
+ align:start position:0%
+y and then it turns out you can
+ 
+
+ align:start position:0%
+y and then it turns out you can
+write uh you can figure out how XR Y is
+
+ align:start position:0%
+write uh you can figure out how XR Y is
+ 
+
+ align:start position:0%
+write uh you can figure out how XR Y is
+relative to the as a linear combination
+
+ align:start position:0%
+relative to the as a linear combination
+ 
+
+ align:start position:0%
+relative to the as a linear combination
+of A and B like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this it's kind of a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gross okay so we started with
+
+ align:start position:0%
+gross okay so we started with
+ 
+
+ align:start position:0%
+gross okay so we started with
+representing X as uh s * a plus T * B
+
+ align:start position:0%
+representing X as uh s * a plus T * B
+ 
+
+ align:start position:0%
+representing X as uh s * a plus T * B
+and we take s and we subtract off a
+
+ align:start position:0%
+and we take s and we subtract off a
+ 
+
+ align:start position:0%
+and we take s and we subtract off a
+corrective term which is XD y time
+
+ align:start position:0%
+corrective term which is XD y time
+ 
+
+ align:start position:0%
+corrective term which is XD y time
+either U or V where U or V is what
+
+ align:start position:0%
+either U or V where U or V is what
+ 
+
+ align:start position:0%
+either U or V where U or V is what
+represented y okay if you work it out
+
+ align:start position:0%
+represented y okay if you work it out
+ 
+
+ align:start position:0%
+represented y okay if you work it out
+that's exactly what we were doing here
+
+ align:start position:0%
+that's exactly what we were doing here
+ 
+
+ align:start position:0%
+that's exactly what we were doing here
+we started with one number and we uh
+
+ align:start position:0%
+we started with one number and we uh
+ 
+
+ align:start position:0%
+we started with one number and we uh
+subtracted off the div times what we had
+
+ align:start position:0%
+subtracted off the div times what we had
+ 
+
+ align:start position:0%
+subtracted off the div times what we had
+before so if you stare at it at this
+
+ align:start position:0%
+before so if you stare at it at this
+ 
+
+ align:start position:0%
+before so if you stare at it at this
+equation long enough uh this is exactly
+
+ align:start position:0%
+equation long enough uh this is exactly
+ 
+
+ align:start position:0%
+equation long enough uh this is exactly
+what we're doing but in uh integer
+
+ align:start position:0%
+what we're doing but in uh integer
+ 
+
+ align:start position:0%
+what we're doing but in uh integer
+linear combination space of A and B
+
+ align:start position:0%
+linear combination space of A and B
+ 
+
+ align:start position:0%
+linear combination space of A and B
+um so I'm not going to justify this
+
+ align:start position:0%
+um so I'm not going to justify this
+ 
+
+ align:start position:0%
+um so I'm not going to justify this
+anymore and I won't even show an example
+
+ align:start position:0%
+anymore and I won't even show an example
+ 
+
+ align:start position:0%
+anymore and I won't even show an example
+but it gives you this is a particular
+
+ align:start position:0%
+but it gives you this is a particular
+ 
+
+ align:start position:0%
+but it gives you this is a particular
+way to compute it um and I I'll say at
+
+ align:start position:0%
+way to compute it um and I I'll say at
+ 
+
+ align:start position:0%
+way to compute it um and I I'll say at
+the beginning of an example if you have
+
+ align:start position:0%
+the beginning of an example if you have
+ 
+
+ align:start position:0%
+the beginning of an example if you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0301 and you run this a few times you
+
+ align:start position:0%
+0301 and you run this a few times you
+ 
+
+ align:start position:0%
+0301 and you run this a few times you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um 2 1us
+
+ align:start position:0%
+um 2 1us
+ 
+
+ align:start position:0%
+um 2 1us
+1 1 -1 2 and this part tells us that 1
+
+ align:start position:0%
+1 1 -1 2 and this part tells us that 1
+ 
+
+ align:start position:0%
+1 1 -1 2 and this part tells us that 1
+equals -1 * 5 + 2 * 3 I hope that is
+
+ align:start position:0%
+equals -1 * 5 + 2 * 3 I hope that is
+ 
+
+ align:start position:0%
+equals -1 * 5 + 2 * 3 I hope that is
+correct uh - 5 + 6 is 1 yep okay so this
+
+ align:start position:0%
+correct uh - 5 + 6 is 1 yep okay so this
+ 
+
+ align:start position:0%
+correct uh - 5 + 6 is 1 yep okay so this
+is how you represent one as an integer
+
+ align:start position:0%
+is how you represent one as an integer
+ 
+
+ align:start position:0%
+is how you represent one as an integer
+linear combination of five and three one
+
+ align:start position:0%
+linear combination of five and three one
+ 
+
+ align:start position:0%
+linear combination of five and three one
+is interesting because it's the gcd of
+
+ align:start position:0%
+is interesting because it's the gcd of
+ 
+
+ align:start position:0%
+is interesting because it's the gcd of
+five and three I'm this is connecting to
+
+ align:start position:0%
+five and three I'm this is connecting to
+ 
+
+ align:start position:0%
+five and three I'm this is connecting to
+the water pouring right with water
+
+ align:start position:0%
+the water pouring right with water
+ 
+
+ align:start position:0%
+the water pouring right with water
+pouring we had a container of size five
+
+ align:start position:0%
+pouring we had a container of size five
+ 
+
+ align:start position:0%
+pouring we had a container of size five
+container of size three their gcd is one
+
+ align:start position:0%
+container of size three their gcd is one
+ 
+
+ align:start position:0%
+container of size three their gcd is one
+they have basically no common divisors
+
+ align:start position:0%
+they have basically no common divisors
+ 
+
+ align:start position:0%
+they have basically no common divisors
+except one and minus one uh and we can
+
+ align:start position:0%
+except one and minus one uh and we can
+ 
+
+ align:start position:0%
+except one and minus one uh and we can
+represent the gcd as an integer linear
+
+ align:start position:0%
+represent the gcd as an integer linear
+ 
+
+ align:start position:0%
+represent the gcd as an integer linear
+combination of five and three namely
+
+ align:start position:0%
+combination of five and three namely
+ 
+
+ align:start position:0%
+combination of five and three namely
+this one therefore we can represent four
+
+ align:start position:0%
+this one therefore we can represent four
+ 
+
+ align:start position:0%
+this one therefore we can represent four
+as an integer linear combination of 5
+
+ align:start position:0%
+as an integer linear combination of 5
+ 
+
+ align:start position:0%
+as an integer linear combination of 5
+and three we just multiply both sides by
+
+ align:start position:0%
+and three we just multiply both sides by
+ 
+
+ align:start position:0%
+and three we just multiply both sides by
+four and we get minus 4 * 5 plus 8 * 3
+
+ align:start position:0%
+four and we get minus 4 * 5 plus 8 * 3
+ 
+
+ align:start position:0%
+four and we get minus 4 * 5 plus 8 * 3
+is one way to do it and uh that gives
+
+ align:start position:0%
+is one way to do it and uh that gives
+ 
+
+ align:start position:0%
+is one way to do it and uh that gives
+you at least a way to solve this problem
+
+ align:start position:0%
+you at least a way to solve this problem
+ 
+
+ align:start position:0%
+you at least a way to solve this problem
+problem it turns out you can take uh
+
+ align:start position:0%
+problem it turns out you can take uh
+ 
+
+ align:start position:0%
+problem it turns out you can take uh
+eight copies of three and subtract out
+
+ align:start position:0%
+eight copies of three and subtract out
+ 
+
+ align:start position:0%
+eight copies of three and subtract out
+four copies of five how do I do that um
+
+ align:start position:0%
+four copies of five how do I do that um
+ 
+
+ align:start position:0%
+four copies of five how do I do that um
+well I just fill this up eight times in
+
+ align:start position:0%
+well I just fill this up eight times in
+ 
+
+ align:start position:0%
+well I just fill this up eight times in
+total and each time I pour in uh all
+
+ align:start position:0%
+total and each time I pour in uh all
+ 
+
+ align:start position:0%
+total and each time I pour in uh all
+that I can into the thing of size five
+
+ align:start position:0%
+that I can into the thing of size five
+ 
+
+ align:start position:0%
+that I can into the thing of size five
+and each time it overflows I empty out
+
+ align:start position:0%
+and each time it overflows I empty out
+ 
+
+ align:start position:0%
+and each time it overflows I empty out
+the five and so that's exactly how I can
+
+ align:start position:0%
+the five and so that's exactly how I can
+ 
+
+ align:start position:0%
+the five and so that's exactly how I can
+build any integer linear combination of
+
+ align:start position:0%
+build any integer linear combination of
+ 
+
+ align:start position:0%
+build any integer linear combination of
+five and three by start as long as one
+
+ align:start position:0%
+five and three by start as long as one
+ 
+
+ align:start position:0%
+five and three by start as long as one
+side is positive and the other is
+
+ align:start position:0%
+side is positive and the other is
+ 
+
+ align:start position:0%
+side is positive and the other is
+negative which turns out to be necessary
+
+ align:start position:0%
+negative which turns out to be necessary
+ 
+
+ align:start position:0%
+negative which turns out to be necessary
+um then you can just take that many
+
+ align:start position:0%
+um then you can just take that many
+ 
+
+ align:start position:0%
+um then you can just take that many
+copies of filling up one bucket pouring
+
+ align:start position:0%
+copies of filling up one bucket pouring
+ 
+
+ align:start position:0%
+copies of filling up one bucket pouring
+it into the other removing whenever it
+
+ align:start position:0%
+it into the other removing whenever it
+ 
+
+ align:start position:0%
+it into the other removing whenever it
+overflows and you will get uh exactly
+
+ align:start position:0%
+overflows and you will get uh exactly
+ 
+
+ align:start position:0%
+overflows and you will get uh exactly
+the number you wanted for these numbers
+
+ align:start position:0%
+the number you wanted for these numbers
+ 
+
+ align:start position:0%
+the number you wanted for these numbers
+one two pores of three uh into five will
+
+ align:start position:0%
+one two pores of three uh into five will
+ 
+
+ align:start position:0%
+one two pores of three uh into five will
+give you one uh if you multiply this by
+
+ align:start position:0%
+give you one uh if you multiply this by
+ 
+
+ align:start position:0%
+give you one uh if you multiply this by
+four I get the number four and I save
+
+ align:start position:0%
+four I get the number four and I save
+ 
+
+ align:start position:0%
+four I get the number four and I save
+Manhattan
+
+ align:start position:0%
+Manhattan
+ 
+
+ align:start position:0%
+Manhattan
+great good luck on your quiz on Thursday
\ No newline at end of file
diff --git a/Xj4nKgJW5yE.txt b/Xj4nKgJW5yE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..107aaafe1039994859443f3a52379eeb7f46eef7
--- /dev/null
+++ b/Xj4nKgJW5yE.txt
@@ -0,0 +1,8795 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+now for a different entirely different
+
+ align:start position:0%
+now for a different entirely different
+ 
+
+ align:start position:0%
+now for a different entirely different
+type of issue that has more to do with
+
+ align:start position:0%
+type of issue that has more to do with
+ 
+
+ align:start position:0%
+type of issue that has more to do with
+recognition some psychophysics on
+
+ align:start position:0%
+recognition some psychophysics on
+ 
+
+ align:start position:0%
+recognition some psychophysics on
+computer vision but you will see at the
+
+ align:start position:0%
+computer vision but you will see at the
+ 
+
+ align:start position:0%
+computer vision but you will see at the
+end the motivation was really to be able
+
+ align:start position:0%
+end the motivation was really to be able
+ 
+
+ align:start position:0%
+end the motivation was really to be able
+to be able to recognize and understand
+
+ align:start position:0%
+to be able to recognize and understand
+ 
+
+ align:start position:0%
+to be able to recognize and understand
+really complicated things that are
+
+ align:start position:0%
+really complicated things that are
+ 
+
+ align:start position:0%
+really complicated things that are
+happening in natural images now when we
+
+ align:start position:0%
+happening in natural images now when we
+ 
+
+ align:start position:0%
+happening in natural images now when we
+look at it objects in the world people
+
+ align:start position:0%
+look at it objects in the world people
+ 
+
+ align:start position:0%
+look at it objects in the world people
+have worked a lot and object recognition
+
+ align:start position:0%
+have worked a lot and object recognition
+ 
+
+ align:start position:0%
+have worked a lot and object recognition
+and we can recognize we can recognize
+
+ align:start position:0%
+and we can recognize we can recognize
+ 
+
+ align:start position:0%
+and we can recognize we can recognize
+well complete objects but we can also
+
+ align:start position:0%
+well complete objects but we can also
+ 
+
+ align:start position:0%
+well complete objects but we can also
+recognize very limited configuration of
+
+ align:start position:0%
+recognize very limited configuration of
+ 
+
+ align:start position:0%
+recognize very limited configuration of
+objects so we are very good at using
+
+ align:start position:0%
+objects so we are very good at using
+ 
+
+ align:start position:0%
+objects so we are very good at using
+limited information if this is what's
+
+ align:start position:0%
+limited information if this is what's
+ 
+
+ align:start position:0%
+limited information if this is what's
+available in order to recognize what's
+
+ align:start position:0%
+available in order to recognize what's
+ 
+
+ align:start position:0%
+available in order to recognize what's
+in this is some arbitrary collection I
+
+ align:start position:0%
+in this is some arbitrary collection I
+ 
+
+ align:start position:0%
+in this is some arbitrary collection I
+guess you can recognize all of them some
+
+ align:start position:0%
+guess you can recognize all of them some
+ 
+
+ align:start position:0%
+guess you can recognize all of them some
+of them if you think about a person or
+
+ align:start position:0%
+of them if you think about a person or
+ 
+
+ align:start position:0%
+of them if you think about a person or
+even a face this is a very small part of
+
+ align:start position:0%
+even a face this is a very small part of
+ 
+
+ align:start position:0%
+even a face this is a very small part of
+a face everybody I guess knows what it
+
+ align:start position:0%
+a face everybody I guess knows what it
+ 
+
+ align:start position:0%
+a face everybody I guess knows what it
+is right it's not even a recognizable
+
+ align:start position:0%
+is right it's not even a recognizable
+ 
+
+ align:start position:0%
+is right it's not even a recognizable
+well delineated part like an eye you see
+
+ align:start position:0%
+well delineated part like an eye you see
+ 
+
+ align:start position:0%
+well delineated part like an eye you see
+a part of a person you know we know what
+
+ align:start position:0%
+a part of a person you know we know what
+ 
+
+ align:start position:0%
+a part of a person you know we know what
+it is right we don't I mean everybody
+
+ align:start position:0%
+it is right we don't I mean everybody
+ 
+
+ align:start position:0%
+it is right we don't I mean everybody
+recognizes and so on now I think that
+
+ align:start position:0%
+recognizes and so on now I think that
+ 
+
+ align:start position:0%
+recognizes and so on now I think that
+the ability to be able to get all the
+
+ align:start position:0%
+the ability to be able to get all the
+ 
+
+ align:start position:0%
+the ability to be able to get all the
+information out even from a limited
+
+ align:start position:0%
+information out even from a limited
+ 
+
+ align:start position:0%
+information out even from a limited
+region plays an important role in
+
+ align:start position:0%
+region plays an important role in
+ 
+
+ align:start position:0%
+region plays an important role in
+understanding images and let me motivate
+
+ align:start position:0%
+understanding images and let me motivate
+ 
+
+ align:start position:0%
+understanding images and let me motivate
+it by by one example I'll go back to it
+
+ align:start position:0%
+it by by one example I'll go back to it
+ 
+
+ align:start position:0%
+it by by one example I'll go back to it
+at the end when we look at these images
+
+ align:start position:0%
+at the end when we look at these images
+ 
+
+ align:start position:0%
+at the end when we look at these images
+we know what's happening we know what
+
+ align:start position:0%
+we know what's happening we know what
+ 
+
+ align:start position:0%
+we know what's happening we know what
+the action here is all the people are
+
+ align:start position:0%
+the action here is all the people are
+ 
+
+ align:start position:0%
+the action here is all the people are
+performing the same action all drinking
+
+ align:start position:0%
+performing the same action all drinking
+ 
+
+ align:start position:0%
+performing the same action all drinking
+even drinking from a bottle right but
+
+ align:start position:0%
+even drinking from a bottle right but
+ 
+
+ align:start position:0%
+even drinking from a bottle right but
+the images as images are very different
+
+ align:start position:0%
+the images as images are very different
+ 
+
+ align:start position:0%
+the images as images are very different
+if you look at each image if you stored
+
+ align:start position:0%
+if you look at each image if you stored
+ 
+
+ align:start position:0%
+if you look at each image if you stored
+one image and you try to recognize
+
+ align:start position:0%
+one image and you try to recognize
+ 
+
+ align:start position:0%
+one image and you try to recognize
+another image based on
+
+ align:start position:0%
+another image based on
+ 
+
+ align:start position:0%
+another image based on
+first one it would be difficult the
+
+ align:start position:0%
+first one it would be difficult the
+ 
+
+ align:start position:0%
+first one it would be difficult the
+variability here can be huge
+
+ align:start position:0%
+variability here can be huge
+ 
+
+ align:start position:0%
+variability here can be huge
+but if you focus on where the action
+
+ align:start position:0%
+but if you focus on where the action
+ 
+
+ align:start position:0%
+but if you focus on where the action
+really takes place the most informative
+
+ align:start position:0%
+really takes place the most informative
+ 
+
+ align:start position:0%
+really takes place the most informative
+part where most of the answer is already
+
+ align:start position:0%
+part where most of the answer is already
+ 
+
+ align:start position:0%
+part where most of the answer is already
+given to you what's happening here which
+
+ align:start position:0%
+given to you what's happening here which
+ 
+
+ align:start position:0%
+given to you what's happening here which
+is where the bottle is docked into the
+
+ align:start position:0%
+is where the bottle is docked into the
+ 
+
+ align:start position:0%
+is where the bottle is docked into the
+mouth you can see that now this diverse
+
+ align:start position:0%
+mouth you can see that now this diverse
+ 
+
+ align:start position:0%
+mouth you can see that now this diverse
+images becomes virtually almost a copy
+
+ align:start position:0%
+images becomes virtually almost a copy
+ 
+
+ align:start position:0%
+images becomes virtually almost a copy
+of one another right now almost the same
+
+ align:start position:0%
+of one another right now almost the same
+ 
+
+ align:start position:0%
+of one another right now almost the same
+so if you manage to understand this and
+
+ align:start position:0%
+so if you manage to understand this and
+ 
+
+ align:start position:0%
+so if you manage to understand this and
+extract the most informative part and
+
+ align:start position:0%
+extract the most informative part and
+ 
+
+ align:start position:0%
+extract the most informative part and
+although it's limited and so on the
+
+ align:start position:0%
+although it's limited and so on the
+ 
+
+ align:start position:0%
+although it's limited and so on the
+variability will be much much reduced
+
+ align:start position:0%
+variability will be much much reduced
+ 
+
+ align:start position:0%
+variability will be much much reduced
+variability here is much much reduced
+
+ align:start position:0%
+variability here is much much reduced
+ 
+
+ align:start position:0%
+variability here is much much reduced
+compared to variability that you have in
+
+ align:start position:0%
+compared to variability that you have in
+ 
+
+ align:start position:0%
+compared to variability that you have in
+the entire image so most of the other
+
+ align:start position:0%
+the entire image so most of the other
+ 
+
+ align:start position:0%
+the entire image so most of the other
+stuff is much less relevant but this is
+
+ align:start position:0%
+stuff is much less relevant but this is
+ 
+
+ align:start position:0%
+stuff is much less relevant but this is
+where the information is concentrated
+
+ align:start position:0%
+where the information is concentrated
+ 
+
+ align:start position:0%
+where the information is concentrated
+and in the limited restricted
+
+ align:start position:0%
+and in the limited restricted
+ 
+
+ align:start position:0%
+and in the limited restricted
+configuration recognition will be much
+
+ align:start position:0%
+configuration recognition will be much
+ 
+
+ align:start position:0%
+configuration recognition will be much
+easier and will generalize much better
+
+ align:start position:0%
+easier and will generalize much better
+ 
+
+ align:start position:0%
+easier and will generalize much better
+from one situation to another because of
+
+ align:start position:0%
+from one situation to another because of
+ 
+
+ align:start position:0%
+from one situation to another because of
+this principle of highly reduced
+
+ align:start position:0%
+this principle of highly reduced
+ 
+
+ align:start position:0%
+this principle of highly reduced
+variability in the in the limited image
+
+ align:start position:0%
+variability in the in the limited image
+ 
+
+ align:start position:0%
+variability in the in the limited image
+so we became interested as I say it's as
+
+ align:start position:0%
+so we became interested as I say it's as
+ 
+
+ align:start position:0%
+so we became interested as I say it's as
+you see it's useful but it's also to
+
+ align:start position:0%
+you see it's useful but it's also to
+ 
+
+ align:start position:0%
+you see it's useful but it's also to
+deal with small images and still
+
+ align:start position:0%
+deal with small images and still
+ 
+
+ align:start position:0%
+deal with small images and still
+recognize them limited images you will
+
+ align:start position:0%
+recognize them limited images you will
+ 
+
+ align:start position:0%
+recognize them limited images you will
+see it's much more there are some very
+
+ align:start position:0%
+see it's much more there are some very
+ 
+
+ align:start position:0%
+see it's much more there are some very
+challenging issues and I want to discuss
+
+ align:start position:0%
+challenging issues and I want to discuss
+ 
+
+ align:start position:0%
+challenging issues and I want to discuss
+it a little bit and then also discuss
+
+ align:start position:0%
+it a little bit and then also discuss
+ 
+
+ align:start position:0%
+it a little bit and then also discuss
+what it's good for
+
+ align:start position:0%
+what it's good for
+ 
+
+ align:start position:0%
+what it's good for
+a little bit more I will show you some
+
+ align:start position:0%
+a little bit more I will show you some
+ 
+
+ align:start position:0%
+a little bit more I will show you some
+human studies what we wanted to see is
+
+ align:start position:0%
+human studies what we wanted to see is
+ 
+
+ align:start position:0%
+human studies what we wanted to see is
+what are the sort of the minimal images
+
+ align:start position:0%
+what are the sort of the minimal images
+ 
+
+ align:start position:0%
+what are the sort of the minimal images
+that people can still recognize we
+
+ align:start position:0%
+that people can still recognize we
+ 
+
+ align:start position:0%
+that people can still recognize we
+examine some computation and models and
+
+ align:start position:0%
+examine some computation and models and
+ 
+
+ align:start position:0%
+examine some computation and models and
+I will give you sort of was not keep the
+
+ align:start position:0%
+I will give you sort of was not keep the
+ 
+
+ align:start position:0%
+I will give you sort of was not keep the
+secret it turns out that well performing
+
+ align:start position:0%
+secret it turns out that well performing
+ 
+
+ align:start position:0%
+secret it turns out that well performing
+current schemes including deep networks
+
+ align:start position:0%
+current schemes including deep networks
+ 
+
+ align:start position:0%
+current schemes including deep networks
+cannot deal well with such minimal
+
+ align:start position:0%
+cannot deal well with such minimal
+ 
+
+ align:start position:0%
+cannot deal well with such minimal
+images and from this I want to discuss
+
+ align:start position:0%
+images and from this I want to discuss
+ 
+
+ align:start position:0%
+images and from this I want to discuss
+some implications in terms of
+
+ align:start position:0%
+some implications in terms of
+ 
+
+ align:start position:0%
+some implications in terms of
+representations you know system brain
+
+ align:start position:0%
+representations you know system brain
+ 
+
+ align:start position:0%
+representations you know system brain
+processing and things like this and
+
+ align:start position:0%
+processing and things like this and
+ 
+
+ align:start position:0%
+processing and things like this and
+quite a number of people have been
+
+ align:start position:0%
+quite a number of people have been
+ 
+
+ align:start position:0%
+quite a number of people have been
+involved in this here are the names some
+
+ align:start position:0%
+involved in this here are the names some
+ 
+
+ align:start position:0%
+involved in this here are the names some
+of them are at the Weitzman Institute in
+
+ align:start position:0%
+of them are at the Weitzman Institute in
+ 
+
+ align:start position:0%
+of them are at the Weitzman Institute in
+Israel and a few lies here I see
+
+ align:start position:0%
+Israel and a few lies here I see
+ 
+
+ align:start position:0%
+Israel and a few lies here I see
+is here in the in the summer school and
+
+ align:start position:0%
+is here in the in the summer school and
+ 
+
+ align:start position:0%
+is here in the in the summer school and
+a student here Nahanni at MIT doing some
+
+ align:start position:0%
+a student here Nahanni at MIT doing some
+ 
+
+ align:start position:0%
+a student here Nahanni at MIT doing some
+brain imaging on this which I will
+
+ align:start position:0%
+brain imaging on this which I will
+ 
+
+ align:start position:0%
+brain imaging on this which I will
+mention very very briefly so I start
+
+ align:start position:0%
+mention very very briefly so I start
+ 
+
+ align:start position:0%
+mention very very briefly so I start
+with the human study we're looking for
+
+ align:start position:0%
+with the human study we're looking for
+ 
+
+ align:start position:0%
+with the human study we're looking for
+minimal sort of atomic things in
+
+ align:start position:0%
+minimal sort of atomic things in
+ 
+
+ align:start position:0%
+minimal sort of atomic things in
+recognition and the experiment goes like
+
+ align:start position:0%
+recognition and the experiment goes like
+ 
+
+ align:start position:0%
+recognition and the experiment goes like
+this you so subject an image and ask
+
+ align:start position:0%
+this you so subject an image and ask
+ 
+
+ align:start position:0%
+this you so subject an image and ask
+them to recognize it
+
+ align:start position:0%
+them to recognize it
+ 
+
+ align:start position:0%
+them to recognize it
+just put use a label so this is a dog if
+
+ align:start position:0%
+just put use a label so this is a dog if
+ 
+
+ align:start position:0%
+just put use a label so this is a dog if
+they say dog they recognized it and if
+
+ align:start position:0%
+they say dog they recognized it and if
+ 
+
+ align:start position:0%
+they say dog they recognized it and if
+they recognize it correctly we generate
+
+ align:start position:0%
+they recognize it correctly we generate
+ 
+
+ align:start position:0%
+they recognize it correctly we generate
+five descendants from this initial image
+
+ align:start position:0%
+five descendants from this initial image
+ 
+
+ align:start position:0%
+five descendants from this initial image
+if this image was say fifty by fifty
+
+ align:start position:0%
+if this image was say fifty by fifty
+ 
+
+ align:start position:0%
+if this image was say fifty by fifty
+pixels and tell you about pixels in a
+
+ align:start position:0%
+pixels and tell you about pixels in a
+ 
+
+ align:start position:0%
+pixels and tell you about pixels in a
+minute but say it's 50 by 50 pixels we
+
+ align:start position:0%
+minute but say it's 50 by 50 pixels we
+ 
+
+ align:start position:0%
+minute but say it's 50 by 50 pixels we
+make it somewhat smaller we reduce it
+
+ align:start position:0%
+make it somewhat smaller we reduce it
+ 
+
+ align:start position:0%
+make it somewhat smaller we reduce it
+because it's still not minimal and we
+
+ align:start position:0%
+because it's still not minimal and we
+ 
+
+ align:start position:0%
+because it's still not minimal and we
+reduce it in five ways we either copied
+
+ align:start position:0%
+reduce it in five ways we either copied
+ 
+
+ align:start position:0%
+reduce it in five ways we either copied
+in at one of the four corners to create
+
+ align:start position:0%
+in at one of the four corners to create
+ 
+
+ align:start position:0%
+in at one of the four corners to create
+say 48 by 48 image by taking two pixels
+
+ align:start position:0%
+say 48 by 48 image by taking two pixels
+ 
+
+ align:start position:0%
+say 48 by 48 image by taking two pixels
+from this corner here or this corner
+
+ align:start position:0%
+from this corner here or this corner
+ 
+
+ align:start position:0%
+from this corner here or this corner
+here and so on so for descendants and we
+
+ align:start position:0%
+here and so on so for descendants and we
+ 
+
+ align:start position:0%
+here and so on so for descendants and we
+generate we also take the full image
+
+ align:start position:0%
+generate we also take the full image
+ 
+
+ align:start position:0%
+generate we also take the full image
+keep it as is we do not crop it we just
+
+ align:start position:0%
+keep it as is we do not crop it we just
+ 
+
+ align:start position:0%
+keep it as is we do not crop it we just
+reduce the resolution so you release we
+
+ align:start position:0%
+reduce the resolution so you release we
+ 
+
+ align:start position:0%
+reduce the resolution so you release we
+resample it so some details start to
+
+ align:start position:0%
+resample it so some details start to
+ 
+
+ align:start position:0%
+resample it so some details start to
+become lost instead of 50 by 50 pixels
+
+ align:start position:0%
+become lost instead of 50 by 50 pixels
+ 
+
+ align:start position:0%
+become lost instead of 50 by 50 pixels
+it's also full image but 40 48 by 48 and
+
+ align:start position:0%
+it's also full image but 40 48 by 48 and
+ 
+
+ align:start position:0%
+it's also full image but 40 48 by 48 and
+then we give each one of these images
+
+ align:start position:0%
+then we give each one of these images
+ 
+
+ align:start position:0%
+then we give each one of these images
+now we have 5 we give each now 1 this is
+
+ align:start position:0%
+now we have 5 we give each now 1 this is
+ 
+
+ align:start position:0%
+now we have 5 we give each now 1 this is
+beginning to explained as a 3 each one
+
+ align:start position:0%
+beginning to explained as a 3 each one
+ 
+
+ align:start position:0%
+beginning to explained as a 3 each one
+of the 5 is given again to a subject if
+
+ align:start position:0%
+of the 5 is given again to a subject if
+ 
+
+ align:start position:0%
+of the 5 is given again to a subject if
+they recognize it again 5 descendants of
+
+ align:start position:0%
+they recognize it again 5 descendants of
+ 
+
+ align:start position:0%
+they recognize it again 5 descendants of
+being generated and we explore the
+
+ align:start position:0%
+being generated and we explore the
+ 
+
+ align:start position:0%
+being generated and we explore the
+entire tree until we find all the sub
+
+ align:start position:0%
+entire tree until we find all the sub
+ 
+
+ align:start position:0%
+entire tree until we find all the sub
+images which are minimal and can be
+
+ align:start position:0%
+images which are minimal and can be
+ 
+
+ align:start position:0%
+images which are minimal and can be
+recognizable in this original
+
+ align:start position:0%
+recognizable in this original
+ 
+
+ align:start position:0%
+recognizable in this original
+configuration now this is challenging
+
+ align:start position:0%
+configuration now this is challenging
+ 
+
+ align:start position:0%
+configuration now this is challenging
+psycho physically in terms of number of
+
+ align:start position:0%
+psycho physically in terms of number of
+ 
+
+ align:start position:0%
+psycho physically in terms of number of
+subjects because you can use a subject
+
+ align:start position:0%
+subjects because you can use a subject
+ 
+
+ align:start position:0%
+subjects because you can use a subject
+only once because if you show a subject
+
+ align:start position:0%
+only once because if you show a subject
+ 
+
+ align:start position:0%
+only once because if you show a subject
+this and you recognize it if you show
+
+ align:start position:0%
+this and you recognize it if you show
+ 
+
+ align:start position:0%
+this and you recognize it if you show
+him the same subject a reduced image he
+
+ align:start position:0%
+him the same subject a reduced image he
+ 
+
+ align:start position:0%
+him the same subject a reduced image he
+will recognize the image based on his
+
+ align:start position:0%
+will recognize the image based on his
+ 
+
+ align:start position:0%
+will recognize the image based on his
+previous exposure so you don't you do
+
+ align:start position:0%
+previous exposure so you don't you do
+ 
+
+ align:start position:0%
+previous exposure so you don't you do
+not want to use him again so you don't
+
+ align:start position:0%
+not want to use him again so you don't
+ 
+
+ align:start position:0%
+not want to use him again so you don't
+use him again and you show the other
+
+ align:start position:0%
+use him again and you show the other
+ 
+
+ align:start position:0%
+use him again and you show the other
+images to to new subject and this
+
+ align:start position:0%
+images to to new subject and this
+ 
+
+ align:start position:0%
+images to to new subject and this
+requires a large number of subjects or
+
+ align:start position:0%
+requires a large number of subjects or
+ 
+
+ align:start position:0%
+requires a large number of subjects or
+15 thousand subs
+
+ align:start position:0%
+15 thousand subs
+ 
+
+ align:start position:0%
+15 thousand subs
+participated in this experiment online
+
+ align:start position:0%
+participated in this experiment online
+ 
+
+ align:start position:0%
+participated in this experiment online
+by Mechanical Turk together with some
+
+ align:start position:0%
+by Mechanical Turk together with some
+ 
+
+ align:start position:0%
+by Mechanical Turk together with some
+laboratory controls to see that they are
+
+ align:start position:0%
+laboratory controls to see that they are
+ 
+
+ align:start position:0%
+laboratory controls to see that they are
+doing the right thing and how it
+
+ align:start position:0%
+doing the right thing and how it
+ 
+
+ align:start position:0%
+doing the right thing and how it
+compares with the same experiment done
+
+ align:start position:0%
+compares with the same experiment done
+ 
+
+ align:start position:0%
+compares with the same experiment done
+under laboratory conditions and so on so
+
+ align:start position:0%
+under laboratory conditions and so on so
+ 
+
+ align:start position:0%
+under laboratory conditions and so on so
+the way we define the minimal image for
+
+ align:start position:0%
+the way we define the minimal image for
+ 
+
+ align:start position:0%
+the way we define the minimal image for
+recognition is industry here is an image
+
+ align:start position:0%
+recognition is industry here is an image
+ 
+
+ align:start position:0%
+recognition is industry here is an image
+the image suppose if this image is
+
+ align:start position:0%
+the image suppose if this image is
+ 
+
+ align:start position:0%
+the image suppose if this image is
+recognizable and then we create the five
+
+ align:start position:0%
+recognizable and then we create the five
+ 
+
+ align:start position:0%
+recognizable and then we create the five
+descendants and none of the descendants
+
+ align:start position:0%
+descendants and none of the descendants
+ 
+
+ align:start position:0%
+descendants and none of the descendants
+is recognizable so this is recognizable
+
+ align:start position:0%
+is recognizable so this is recognizable
+ 
+
+ align:start position:0%
+is recognizable so this is recognizable
+nothing here is recognizable so it's
+
+ align:start position:0%
+nothing here is recognizable so it's
+ 
+
+ align:start position:0%
+nothing here is recognizable so it's
+minimal because you can no longer reduce
+
+ align:start position:0%
+minimal because you can no longer reduce
+ 
+
+ align:start position:0%
+minimal because you can no longer reduce
+it either by resolution going here or by
+
+ align:start position:0%
+it either by resolution going here or by
+ 
+
+ align:start position:0%
+it either by resolution going here or by
+reducing the size any manipulation like
+
+ align:start position:0%
+reducing the size any manipulation like
+ 
+
+ align:start position:0%
+reducing the size any manipulation like
+this we make it an unrecognizable
+
+ align:start position:0%
+this we make it an unrecognizable
+ 
+
+ align:start position:0%
+this we make it an unrecognizable
+technically when I'm am i measuring if
+
+ align:start position:0%
+technically when I'm am i measuring if
+ 
+
+ align:start position:0%
+technically when I'm am i measuring if
+I'm using numbers that the image is 50
+
+ align:start position:0%
+I'm using numbers that the image is 50
+ 
+
+ align:start position:0%
+I'm using numbers that the image is 50
+50 pixels or 35 pixels and so on what I
+
+ align:start position:0%
+50 pixels or 35 pixels and so on what I
+ 
+
+ align:start position:0%
+50 pixels or 35 pixels and so on what I
+it's actually well defined or I mean not
+
+ align:start position:0%
+it's actually well defined or I mean not
+ 
+
+ align:start position:0%
+it's actually well defined or I mean not
+the pixels on the screen you can take
+
+ align:start position:0%
+the pixels on the screen you can take
+ 
+
+ align:start position:0%
+the pixels on the screen you can take
+the image and make it bigger or smaller
+
+ align:start position:0%
+the image and make it bigger or smaller
+ 
+
+ align:start position:0%
+the image and make it bigger or smaller
+on this on the screen but the number of
+
+ align:start position:0%
+on this on the screen but the number of
+ 
+
+ align:start position:0%
+on this on the screen but the number of
+sampling points in the image is
+
+ align:start position:0%
+sampling points in the image is
+ 
+
+ align:start position:0%
+sampling points in the image is
+well-defined which give me an image
+
+ align:start position:0%
+well-defined which give me an image
+ 
+
+ align:start position:0%
+well-defined which give me an image
+particular image I can tell you how many
+
+ align:start position:0%
+particular image I can tell you how many
+ 
+
+ align:start position:0%
+particular image I can tell you how many
+sample points you need in order to
+
+ align:start position:0%
+sample points you need in order to
+ 
+
+ align:start position:0%
+sample points you need in order to
+capture this image technically for those
+
+ align:start position:0%
+capture this image technically for those
+ 
+
+ align:start position:0%
+capture this image technically for those
+of you who know it's twice the if you do
+
+ align:start position:0%
+of you who know it's twice the if you do
+ 
+
+ align:start position:0%
+of you who know it's twice the if you do
+a Fourier transform and take the twice
+
+ align:start position:0%
+a Fourier transform and take the twice
+ 
+
+ align:start position:0%
+a Fourier transform and take the twice
+the cutoff frequency the highest
+
+ align:start position:0%
+the cutoff frequency the highest
+ 
+
+ align:start position:0%
+the cutoff frequency the highest
+frequency in the free aspect this is by
+
+ align:start position:0%
+frequency in the free aspect this is by
+ 
+
+ align:start position:0%
+frequency in the free aspect this is by
+the sampling theorem of Shannon this is
+
+ align:start position:0%
+the sampling theorem of Shannon this is
+ 
+
+ align:start position:0%
+the sampling theorem of Shannon this is
+the number of points you need in order
+
+ align:start position:0%
+the number of points you need in order
+ 
+
+ align:start position:0%
+the number of points you need in order
+to so when I say that the image was 35
+
+ align:start position:0%
+to so when I say that the image was 35
+ 
+
+ align:start position:0%
+to so when I say that the image was 35
+pixels I don't really care you can make
+
+ align:start position:0%
+pixels I don't really care you can make
+ 
+
+ align:start position:0%
+pixels I don't really care you can make
+it somewhat smaller larger on the screen
+
+ align:start position:0%
+it somewhat smaller larger on the screen
+ 
+
+ align:start position:0%
+it somewhat smaller larger on the screen
+by interpolation it doesn't change the
+
+ align:start position:0%
+by interpolation it doesn't change the
+ 
+
+ align:start position:0%
+by interpolation it doesn't change the
+information content it's well defined
+
+ align:start position:0%
+information content it's well defined
+ 
+
+ align:start position:0%
+information content it's well defined
+the notion mathematically how many
+
+ align:start position:0%
+the notion mathematically how many
+ 
+
+ align:start position:0%
+the notion mathematically how many
+points in this discrete point for
+
+ align:start position:0%
+points in this discrete point for
+ 
+
+ align:start position:0%
+points in this discrete point for
+sampling points in this in these images
+
+ align:start position:0%
+sampling points in this in these images
+ 
+
+ align:start position:0%
+sampling points in this in these images
+so a very interesting thing that we we
+
+ align:start position:0%
+so a very interesting thing that we we
+ 
+
+ align:start position:0%
+so a very interesting thing that we we
+found when we found this minimal images
+
+ align:start position:0%
+found when we found this minimal images
+ 
+
+ align:start position:0%
+found when we found this minimal images
+is that there is a sharp transition when
+
+ align:start position:0%
+is that there is a sharp transition when
+ 
+
+ align:start position:0%
+is that there is a sharp transition when
+you get to live to the level of the
+
+ align:start position:0%
+you get to live to the level of the
+ 
+
+ align:start position:0%
+you get to live to the level of the
+minimal images so you go down and you
+
+ align:start position:0%
+minimal images so you go down and you
+ 
+
+ align:start position:0%
+minimal images so you go down and you
+recognize it and then there is a sharp
+
+ align:start position:0%
+recognize it and then there is a sharp
+ 
+
+ align:start position:0%
+recognize it and then there is a sharp
+transition that
+
+ align:start position:0%
+transition that
+ 
+
+ align:start position:0%
+transition that
+it suddenly becomes unrecognizable
+
+ align:start position:0%
+it suddenly becomes unrecognizable
+ 
+
+ align:start position:0%
+it suddenly becomes unrecognizable
+basically to the large majority of
+
+ align:start position:0%
+basically to the large majority of
+ 
+
+ align:start position:0%
+basically to the large majority of
+people so it can change a little bit and
+
+ align:start position:0%
+people so it can change a little bit and
+ 
+
+ align:start position:0%
+people so it can change a little bit and
+I'll show you some examples for you to
+
+ align:start position:0%
+I'll show you some examples for you to
+ 
+
+ align:start position:0%
+I'll show you some examples for you to
+try to see how this minimal images look
+
+ align:start position:0%
+try to see how this minimal images look
+ 
+
+ align:start position:0%
+try to see how this minimal images look
+like a recognizable level at the
+
+ align:start position:0%
+like a recognizable level at the
+ 
+
+ align:start position:0%
+like a recognizable level at the
+unrecognized but this is the recognizer
+
+ align:start position:0%
+unrecognized but this is the recognizer
+ 
+
+ align:start position:0%
+unrecognized but this is the recognizer
+believe that this is the unrecognizable
+
+ align:start position:0%
+believe that this is the unrecognizable
+ 
+
+ align:start position:0%
+believe that this is the unrecognizable
+level so to show it to you as examples
+
+ align:start position:0%
+level so to show it to you as examples
+ 
+
+ align:start position:0%
+level so to show it to you as examples
+here that I will show you first the
+
+ align:start position:0%
+here that I will show you first the
+ 
+
+ align:start position:0%
+here that I will show you first the
+unrecognizable one the one which people
+
+ align:start position:0%
+unrecognizable one the one which people
+ 
+
+ align:start position:0%
+unrecognizable one the one which people
+find on average more difficult to
+
+ align:start position:0%
+find on average more difficult to
+ 
+
+ align:start position:0%
+find on average more difficult to
+recognize if you recognize it raise your
+
+ align:start position:0%
+recognize if you recognize it raise your
+ 
+
+ align:start position:0%
+recognize if you recognize it raise your
+hand don't say what you see because this
+
+ align:start position:0%
+hand don't say what you see because this
+ 
+
+ align:start position:0%
+hand don't say what you see because this
+will influence other people just raise
+
+ align:start position:0%
+will influence other people just raise
+ 
+
+ align:start position:0%
+will influence other people just raise
+your hand if you recognize the image and
+
+ align:start position:0%
+your hand if you recognize the image and
+ 
+
+ align:start position:0%
+your hand if you recognize the image and
+then I'll show you the Molech ignitable
+
+ align:start position:0%
+then I'll show you the Molech ignitable
+ 
+
+ align:start position:0%
+then I'll show you the Molech ignitable
+one and let's see if more hands show up
+
+ align:start position:0%
+one and let's see if more hands show up
+ 
+
+ align:start position:0%
+one and let's see if more hands show up
+with the distinction between the
+
+ align:start position:0%
+with the distinction between the
+ 
+
+ align:start position:0%
+with the distinction between the
+recognizable in unrecognizable holes
+
+ align:start position:0%
+recognizable in unrecognizable holes
+ 
+
+ align:start position:0%
+recognizable in unrecognizable holes
+here I'll just show you a couple of
+
+ align:start position:0%
+here I'll just show you a couple of
+ 
+
+ align:start position:0%
+here I'll just show you a couple of
+example from the okay so okay so this is
+
+ align:start position:0%
+example from the okay so okay so this is
+ 
+
+ align:start position:0%
+example from the okay so okay so this is
+the one which is supposed to be
+
+ align:start position:0%
+the one which is supposed to be
+ 
+
+ align:start position:0%
+the one which is supposed to be
+difficult to recognize if you see what
+
+ align:start position:0%
+difficult to recognize if you see what
+ 
+
+ align:start position:0%
+difficult to recognize if you see what
+it is if you know what's the object
+
+ align:start position:0%
+it is if you know what's the object
+ 
+
+ align:start position:0%
+it is if you know what's the object
+raise your hand okay don't say what it
+
+ align:start position:0%
+raise your hand okay don't say what it
+ 
+
+ align:start position:0%
+raise your hand okay don't say what it
+is we have to let's see here okay
+
+ align:start position:0%
+is we have to let's see here okay
+ 
+
+ align:start position:0%
+is we have to let's see here okay
+certainly more hand what do you see what
+
+ align:start position:0%
+certainly more hand what do you see what
+ 
+
+ align:start position:0%
+certainly more hand what do you see what
+do you think okay
+
+ align:start position:0%
+do you think okay
+ 
+
+ align:start position:0%
+do you think okay
+now you can say because a horse right so
+
+ align:start position:0%
+now you can say because a horse right so
+ 
+
+ align:start position:0%
+now you can say because a horse right so
+let me show them side by side so you see
+
+ align:start position:0%
+let me show them side by side so you see
+ 
+
+ align:start position:0%
+let me show them side by side so you see
+that it's very difficult to recognize
+
+ align:start position:0%
+that it's very difficult to recognize
+ 
+
+ align:start position:0%
+that it's very difficult to recognize
+what not record this is you can see the
+
+ align:start position:0%
+what not record this is you can see the
+ 
+
+ align:start position:0%
+what not record this is you can see the
+statistic this is recognized by 93
+
+ align:start position:0%
+statistic this is recognized by 93
+ 
+
+ align:start position:0%
+statistic this is recognized by 93
+percent of the subjects 30 subjects so
+
+ align:start position:0%
+percent of the subjects 30 subjects so
+ 
+
+ align:start position:0%
+percent of the subjects 30 subjects so
+each one of these images 93 recognize
+
+ align:start position:0%
+each one of these images 93 recognize
+ 
+
+ align:start position:0%
+each one of these images 93 recognize
+this 3% recognized this and you look at
+
+ align:start position:0%
+this 3% recognized this and you look at
+ 
+
+ align:start position:0%
+this 3% recognized this and you look at
+the image and you see that a very very
+
+ align:start position:0%
+the image and you see that a very very
+ 
+
+ align:start position:0%
+the image and you see that a very very
+similar images and it drops on ninety
+
+ align:start position:0%
+similar images and it drops on ninety
+ 
+
+ align:start position:0%
+similar images and it drops on ninety
+two three so you can see the two images
+
+ align:start position:0%
+two three so you can see the two images
+ 
+
+ align:start position:0%
+two three so you can see the two images
+and you can see the similarity and you
+
+ align:start position:0%
+and you can see the similarity and you
+ 
+
+ align:start position:0%
+and you can see the similarity and you
+can see the large the loud drop this is
+
+ align:start position:0%
+can see the large the loud drop this is
+ 
+
+ align:start position:0%
+can see the large the loud drop this is
+part of the entire tree which is being
+
+ align:start position:0%
+part of the entire tree which is being
+ 
+
+ align:start position:0%
+part of the entire tree which is being
+explored this is the father this is the
+
+ align:start position:0%
+explored this is the father this is the
+ 
+
+ align:start position:0%
+explored this is the father this is the
+recognized one the minimal image and you
+
+ align:start position:0%
+recognized one the minimal image and you
+ 
+
+ align:start position:0%
+recognized one the minimal image and you
+can see that even reduce the resolution
+
+ align:start position:0%
+can see that even reduce the resolution
+ 
+
+ align:start position:0%
+can see that even reduce the resolution
+which is really not a big manipulation
+
+ align:start position:0%
+which is really not a big manipulation
+ 
+
+ align:start position:0%
+which is really not a big manipulation
+but it is a drop in performance and you
+
+ align:start position:0%
+but it is a drop in performance and you
+ 
+
+ align:start position:0%
+but it is a drop in performance and you
+can see all the so we used 50% as our
+
+ align:start position:0%
+can see all the so we used 50% as our
+ 
+
+ align:start position:0%
+can see all the so we used 50% as our
+criterion so the parent should be
+
+ align:start position:0%
+criterion so the parent should be
+ 
+
+ align:start position:0%
+criterion so the parent should be
+recognized at higher this should be
+
+ align:start position:0%
+recognized at higher this should be
+ 
+
+ align:start position:0%
+recognized at higher this should be
+recognized
+
+ align:start position:0%
+recognized
+ 
+
+ align:start position:0%
+recognized
+loyal but typically the the jump is very
+
+ align:start position:0%
+loyal but typically the the jump is very
+ 
+
+ align:start position:0%
+loyal but typically the the jump is very
+it's very sharp let's write two more or
+
+ align:start position:0%
+it's very sharp let's write two more or
+ 
+
+ align:start position:0%
+it's very sharp let's write two more or
+something and then just for fun if you
+
+ align:start position:0%
+something and then just for fun if you
+ 
+
+ align:start position:0%
+something and then just for fun if you
+can recognize it raise your hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody or just for the record okay look
+
+ align:start position:0%
+nobody or just for the record okay look
+ 
+
+ align:start position:0%
+nobody or just for the record okay look
+around you can see many what do you see
+
+ align:start position:0%
+around you can see many what do you see
+ 
+
+ align:start position:0%
+around you can see many what do you see
+both right so you can see the two images
+
+ align:start position:0%
+both right so you can see the two images
+ 
+
+ align:start position:0%
+both right so you can see the two images
+or 80% and this 0% here and you can see
+
+ align:start position:0%
+or 80% and this 0% here and you can see
+ 
+
+ align:start position:0%
+or 80% and this 0% here and you can see
+that what's really missing here is the
+
+ align:start position:0%
+that what's really missing here is the
+ 
+
+ align:start position:0%
+that what's really missing here is the
+tip here and clearly this tip is there
+
+ align:start position:0%
+tip here and clearly this tip is there
+ 
+
+ align:start position:0%
+tip here and clearly this tip is there
+are many contours in this image but this
+
+ align:start position:0%
+are many contours in this image but this
+ 
+
+ align:start position:0%
+are many contours in this image but this
+particular corner sharp makes an
+
+ align:start position:0%
+particular corner sharp makes an
+ 
+
+ align:start position:0%
+particular corner sharp makes an
+enormous different and it goes from 80%
+
+ align:start position:0%
+enormous different and it goes from 80%
+ 
+
+ align:start position:0%
+enormous different and it goes from 80%
+to to 0% okay just one more in this is
+
+ align:start position:0%
+to to 0% okay just one more in this is
+ 
+
+ align:start position:0%
+to to 0% okay just one more in this is
+somewhat easier okay this is some fun
+
+ align:start position:0%
+somewhat easier okay this is some fun
+ 
+
+ align:start position:0%
+somewhat easier okay this is some fun
+okay it is one two and three okay this
+
+ align:start position:0%
+okay it is one two and three okay this
+ 
+
+ align:start position:0%
+okay it is one two and three okay this
+one everybody I think or maybe we are
+
+ align:start position:0%
+one everybody I think or maybe we are
+ 
+
+ align:start position:0%
+one everybody I think or maybe we are
+missing one
+
+ align:start position:0%
+missing one
+ 
+
+ align:start position:0%
+missing one
+so again you can see that the difference
+
+ align:start position:0%
+so again you can see that the difference
+ 
+
+ align:start position:0%
+so again you can see that the difference
+if you look at the two there is a
+
+ align:start position:0%
+if you look at the two there is a
+ 
+
+ align:start position:0%
+if you look at the two there is a
+difference and it's this thing here but
+
+ align:start position:0%
+difference and it's this thing here but
+ 
+
+ align:start position:0%
+difference and it's this thing here but
+it's not a very big part of the image
+
+ align:start position:0%
+it's not a very big part of the image
+ 
+
+ align:start position:0%
+it's not a very big part of the image
+it's crucial you know it's you have to
+
+ align:start position:0%
+it's crucial you know it's you have to
+ 
+
+ align:start position:0%
+it's crucial you know it's you have to
+be trained on this you have it's part of
+
+ align:start position:0%
+be trained on this you have it's part of
+ 
+
+ align:start position:0%
+be trained on this you have it's part of
+your representation it's important you
+
+ align:start position:0%
+your representation it's important you
+ 
+
+ align:start position:0%
+your representation it's important you
+go from almost 90 percent or 15 percent
+
+ align:start position:0%
+go from almost 90 percent or 15 percent
+ 
+
+ align:start position:0%
+go from almost 90 percent or 15 percent
+roughly in its so it's an important so
+
+ align:start position:0%
+roughly in its so it's an important so
+ 
+
+ align:start position:0%
+roughly in its so it's an important so
+you can see that the drop is typically
+
+ align:start position:0%
+you can see that the drop is typically
+ 
+
+ align:start position:0%
+you can see that the drop is typically
+very very sharp and it's also into you
+
+ align:start position:0%
+very very sharp and it's also into you
+ 
+
+ align:start position:0%
+very very sharp and it's also into you
+know the sharp transition is also
+
+ align:start position:0%
+know the sharp transition is also
+ 
+
+ align:start position:0%
+know the sharp transition is also
+interesting in the sense that if it
+
+ align:start position:0%
+interesting in the sense that if it
+ 
+
+ align:start position:0%
+interesting in the sense that if it
+drops from like from 90% to Tempe to 3%
+
+ align:start position:0%
+drops from like from 90% to Tempe to 3%
+ 
+
+ align:start position:0%
+drops from like from 90% to Tempe to 3%
+or even here it also says that we all
+
+ align:start position:0%
+or even here it also says that we all
+ 
+
+ align:start position:0%
+or even here it also says that we all
+carry around in our head a very similar
+
+ align:start position:0%
+carry around in our head a very similar
+ 
+
+ align:start position:0%
+carry around in our head a very similar
+representation because if each one of us
+
+ align:start position:0%
+representation because if each one of us
+ 
+
+ align:start position:0%
+representation because if each one of us
+based on the history an expiry
+
+ align:start position:0%
+based on the history an expiry
+ 
+
+ align:start position:0%
+based on the history an expiry
+experience would be less of more
+
+ align:start position:0%
+experience would be less of more
+ 
+
+ align:start position:0%
+experience would be less of more
+sensitive to various feature then we
+
+ align:start position:0%
+sensitive to various feature then we
+ 
+
+ align:start position:0%
+sensitive to various feature then we
+will not find this sharp transition
+
+ align:start position:0%
+will not find this sharp transition
+ 
+
+ align:start position:0%
+will not find this sharp transition
+different people will lose it at
+
+ align:start position:0%
+different people will lose it at
+ 
+
+ align:start position:0%
+different people will lose it at
+different different points in the in the
+
+ align:start position:0%
+different different points in the in the
+ 
+
+ align:start position:0%
+different different points in the in the
+manipulation but at 90 percent 90
+
+ align:start position:0%
+manipulation but at 90 percent 90
+ 
+
+ align:start position:0%
+manipulation but at 90 percent 90
+percent of the people roughly everybody
+
+ align:start position:0%
+percent of the people roughly everybody
+ 
+
+ align:start position:0%
+percent of the people roughly everybody
+recognize it you remove a feature and it
+
+ align:start position:0%
+recognize it you remove a feature and it
+ 
+
+ align:start position:0%
+recognize it you remove a feature and it
+goes to 3 percent so everybody is using
+
+ align:start position:0%
+goes to 3 percent so everybody is using
+ 
+
+ align:start position:0%
+goes to 3 percent so everybody is using
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a very similar representation which I
+
+ align:start position:0%
+a very similar representation which I
+ 
+
+ align:start position:0%
+a very similar representation which I
+find somewhat surprising at least for
+
+ align:start position:0%
+find somewhat surprising at least for
+ 
+
+ align:start position:0%
+find somewhat surprising at least for
+some of these images you know that we
+
+ align:start position:0%
+some of these images you know that we
+ 
+
+ align:start position:0%
+some of these images you know that we
+don't all have the same kind of
+
+ align:start position:0%
+don't all have the same kind of
+ 
+
+ align:start position:0%
+don't all have the same kind of
+experience with horses or with
+
+ align:start position:0%
+experience with horses or with
+ 
+
+ align:start position:0%
+experience with horses or with
+battleships or things like that and
+
+ align:start position:0%
+battleships or things like that and
+ 
+
+ align:start position:0%
+battleships or things like that and
+still the representation is very
+
+ align:start position:0%
+still the representation is very
+ 
+
+ align:start position:0%
+still the representation is very
+strikingly similar across individuals
+
+ align:start position:0%
+strikingly similar across individuals
+ 
+
+ align:start position:0%
+strikingly similar across individuals
+the experiment was done on 10 different
+
+ align:start position:0%
+the experiment was done on 10 different
+ 
+
+ align:start position:0%
+the experiment was done on 10 different
+objects these are the initial objects or
+
+ align:start position:0%
+objects these are the initial objects or
+ 
+
+ align:start position:0%
+objects these are the initial objects or
+I showed you the object all right
+
+ align:start position:0%
+I showed you the object all right
+ 
+
+ align:start position:0%
+I showed you the object all right
+beginning of the hierarchy and then you
+
+ align:start position:0%
+beginning of the hierarchy and then you
+ 
+
+ align:start position:0%
+beginning of the hierarchy and then you
+start the manipulation to discover all
+
+ align:start position:0%
+start the manipulation to discover all
+ 
+
+ align:start position:0%
+start the manipulation to discover all
+the minimal images inside them and here
+
+ align:start position:0%
+the minimal images inside them and here
+ 
+
+ align:start position:0%
+the minimal images inside them and here
+so we ended up with a very nice catalog
+
+ align:start position:0%
+so we ended up with a very nice catalog
+ 
+
+ align:start position:0%
+so we ended up with a very nice catalog
+we have a database of all the minimal
+
+ align:start position:0%
+we have a database of all the minimal
+ 
+
+ align:start position:0%
+we have a database of all the minimal
+images in all of these ten images in all
+
+ align:start position:0%
+images in all of these ten images in all
+ 
+
+ align:start position:0%
+images in all of these ten images in all
+of the children the unrecognizable ones
+
+ align:start position:0%
+of the children the unrecognizable ones
+ 
+
+ align:start position:0%
+of the children the unrecognizable ones
+so in terms of modeling and in terms of
+
+ align:start position:0%
+so in terms of modeling and in terms of
+ 
+
+ align:start position:0%
+so in terms of modeling and in terms of
+exploring visual features and what is
+
+ align:start position:0%
+exploring visual features and what is
+ 
+
+ align:start position:0%
+exploring visual features and what is
+necessary in order to recognize and so
+
+ align:start position:0%
+necessary in order to recognize and so
+ 
+
+ align:start position:0%
+necessary in order to recognize and so
+on there is a very rich data set here of
+
+ align:start position:0%
+on there is a very rich data set here of
+ 
+
+ align:start position:0%
+on there is a very rich data set here of
+all the minimal images in all of these
+
+ align:start position:0%
+all the minimal images in all of these
+ 
+
+ align:start position:0%
+all the minimal images in all of these
+ten images here are some more pairs of
+
+ align:start position:0%
+ten images here are some more pairs of
+ 
+
+ align:start position:0%
+ten images here are some more pairs of
+recognizable and unrecognizable rocky
+
+ align:start position:0%
+recognizable and unrecognizable rocky
+ 
+
+ align:start position:0%
+recognizable and unrecognizable rocky
+bodies so this in principle but just to
+
+ align:start position:0%
+bodies so this in principle but just to
+ 
+
+ align:start position:0%
+bodies so this in principle but just to
+show some in some cases it's pretty
+
+ align:start position:0%
+show some in some cases it's pretty
+ 
+
+ align:start position:0%
+show some in some cases it's pretty
+clear what may be going on for example
+
+ align:start position:0%
+clear what may be going on for example
+ 
+
+ align:start position:0%
+clear what may be going on for example
+this is horse legs the front legs of the
+
+ align:start position:0%
+this is horse legs the front legs of the
+ 
+
+ align:start position:0%
+this is horse legs the front legs of the
+horse this seems to be important you can
+
+ align:start position:0%
+horse this seems to be important you can
+ 
+
+ align:start position:0%
+horse this seems to be important you can
+see that very often it's a tremendously
+
+ align:start position:0%
+see that very often it's a tremendously
+ 
+
+ align:start position:0%
+see that very often it's a tremendously
+small in this fly image very small
+
+ align:start position:0%
+small in this fly image very small
+ 
+
+ align:start position:0%
+small in this fly image very small
+differences very hard to pinpoint and
+
+ align:start position:0%
+differences very hard to pinpoint and
+ 
+
+ align:start position:0%
+differences very hard to pinpoint and
+it's drastic or in this in the
+
+ align:start position:0%
+it's drastic or in this in the
+ 
+
+ align:start position:0%
+it's drastic or in this in the
+eyeglasses something here is missing a
+
+ align:start position:0%
+eyeglasses something here is missing a
+ 
+
+ align:start position:0%
+eyeglasses something here is missing a
+little bit but very small things in very
+
+ align:start position:0%
+little bit but very small things in very
+ 
+
+ align:start position:0%
+little bit but very small things in very
+reliable way cause this dramatic change
+
+ align:start position:0%
+reliable way cause this dramatic change
+ 
+
+ align:start position:0%
+reliable way cause this dramatic change
+as was mentioned here somebody mentioned
+
+ align:start position:0%
+as was mentioned here somebody mentioned
+ 
+
+ align:start position:0%
+as was mentioned here somebody mentioned
+would say the inflection in point you
+
+ align:start position:0%
+would say the inflection in point you
+ 
+
+ align:start position:0%
+would say the inflection in point you
+can manipulate psycho physically a bit
+
+ align:start position:0%
+can manipulate psycho physically a bit
+ 
+
+ align:start position:0%
+can manipulate psycho physically a bit
+more for example here this was a this is
+
+ align:start position:0%
+more for example here this was a this is
+ 
+
+ align:start position:0%
+more for example here this was a this is
+another version of a minimal image it
+
+ align:start position:0%
+another version of a minimal image it
+ 
+
+ align:start position:0%
+another version of a minimal image it
+was co-opted two locations you can crop
+
+ align:start position:0%
+was co-opted two locations you can crop
+ 
+
+ align:start position:0%
+was co-opted two locations you can crop
+only the left side you can crop only the
+
+ align:start position:0%
+only the left side you can crop only the
+ 
+
+ align:start position:0%
+only the left side you can crop only the
+the bottom side and you can try to see
+
+ align:start position:0%
+the bottom side and you can try to see
+ 
+
+ align:start position:0%
+the bottom side and you can try to see
+what makes it different so you can
+
+ align:start position:0%
+what makes it different so you can
+ 
+
+ align:start position:0%
+what makes it different so you can
+really zoom in on the on the critical on
+
+ align:start position:0%
+really zoom in on the on the critical on
+ 
+
+ align:start position:0%
+really zoom in on the on the critical on
+the critical features in terms of number
+
+ align:start position:0%
+the critical features in terms of number
+ 
+
+ align:start position:0%
+the critical features in terms of number
+of pixels the impression is that it's
+
+ align:start position:0%
+of pixels the impression is that it's
+ 
+
+ align:start position:0%
+of pixels the impression is that it's
+surprisingly
+
+ align:start position:0%
+surprisingly
+ 
+
+ align:start position:0%
+surprisingly
+small so I guess you can recognize this
+
+ align:start position:0%
+small so I guess you can recognize this
+ 
+
+ align:start position:0%
+small so I guess you can recognize this
+is an ego this is an airplane and the
+
+ align:start position:0%
+is an ego this is an airplane and the
+ 
+
+ align:start position:0%
+is an ego this is an airplane and the
+number of pixels you know you're right
+
+ align:start position:0%
+number of pixels you know you're right
+ 
+
+ align:start position:0%
+number of pixels you know you're right
+in your you know those of you know
+
+ align:start position:0%
+in your you know those of you know
+ 
+
+ align:start position:0%
+in your you know those of you know
+vision your retinas has 120 million
+
+ align:start position:0%
+vision your retinas has 120 million
+ 
+
+ align:start position:0%
+vision your retinas has 120 million
+pixels the fovea which is the area of
+
+ align:start position:0%
+pixels the fovea which is the area of
+ 
+
+ align:start position:0%
+pixels the fovea which is the area of
+very high acuity is two degrees it's
+
+ align:start position:0%
+very high acuity is two degrees it's
+ 
+
+ align:start position:0%
+very high acuity is two degrees it's
+about 250 by 250 250 by 200 pixels this
+
+ align:start position:0%
+about 250 by 250 250 by 200 pixels this
+ 
+
+ align:start position:0%
+about 250 by 250 250 by 200 pixels this
+is the area the central area of high
+
+ align:start position:0%
+is the area the central area of high
+ 
+
+ align:start position:0%
+is the area the central area of high
+acuity but you can recognize things with
+
+ align:start position:0%
+acuity but you can recognize things with
+ 
+
+ align:start position:0%
+acuity but you can recognize things with
+I don't know 15 20 pixels it's one-tenth
+
+ align:start position:0%
+I don't know 15 20 pixels it's one-tenth
+ 
+
+ align:start position:0%
+I don't know 15 20 pixels it's one-tenth
+of your your fovea it's tiny time in
+
+ align:start position:0%
+of your your fovea it's tiny time in
+ 
+
+ align:start position:0%
+of your your fovea it's tiny time in
+terms of you can make it larger but in
+
+ align:start position:0%
+terms of you can make it larger but in
+ 
+
+ align:start position:0%
+terms of you can make it larger but in
+terms of how much visual information
+
+ align:start position:0%
+terms of how much visual information
+ 
+
+ align:start position:0%
+terms of how much visual information
+it's I find it surprising that you need
+
+ align:start position:0%
+it's I find it surprising that you need
+ 
+
+ align:start position:0%
+it's I find it surprising that you need
+very very little it's also interesting
+
+ align:start position:0%
+very very little it's also interesting
+ 
+
+ align:start position:0%
+very very little it's also interesting
+that it's it's very useful in the center
+
+ align:start position:0%
+that it's it's very useful in the center
+ 
+
+ align:start position:0%
+that it's it's very useful in the center
+it's it's very redundant if you if you
+
+ align:start position:0%
+it's it's very redundant if you if you
+ 
+
+ align:start position:0%
+it's it's very redundant if you if you
+have the capacity if you have a visual
+
+ align:start position:0%
+have the capacity if you have a visual
+ 
+
+ align:start position:0%
+have the capacity if you have a visual
+system that can recognize individually
+
+ align:start position:0%
+system that can recognize individually
+ 
+
+ align:start position:0%
+system that can recognize individually
+each one of these minimal images and in
+
+ align:start position:0%
+each one of these minimal images and in
+ 
+
+ align:start position:0%
+each one of these minimal images and in
+fact they can be recognized on their own
+
+ align:start position:0%
+fact they can be recognized on their own
+ 
+
+ align:start position:0%
+fact they can be recognized on their own
+then a full image like this contains a
+
+ align:start position:0%
+then a full image like this contains a
+ 
+
+ align:start position:0%
+then a full image like this contains a
+high number of partially overlapping
+
+ align:start position:0%
+high number of partially overlapping
+ 
+
+ align:start position:0%
+high number of partially overlapping
+minimal images some of them are large
+
+ align:start position:0%
+minimal images some of them are large
+ 
+
+ align:start position:0%
+minimal images some of them are large
+you can see each one of this frame
+
+ align:start position:0%
+you can see each one of this frame
+ 
+
+ align:start position:0%
+you can see each one of this frame
+colored frame is a minimal image shown
+
+ align:start position:0%
+colored frame is a minimal image shown
+ 
+
+ align:start position:0%
+colored frame is a minimal image shown
+not necessarily at the right resolution
+
+ align:start position:0%
+not necessarily at the right resolution
+ 
+
+ align:start position:0%
+not necessarily at the right resolution
+you can reduce the resolution of things
+
+ align:start position:0%
+you can reduce the resolution of things
+ 
+
+ align:start position:0%
+you can reduce the resolution of things
+but you can see that some images of
+
+ align:start position:0%
+but you can see that some images of
+ 
+
+ align:start position:0%
+but you can see that some images of
+essentially low resolution
+
+ align:start position:0%
+essentially low resolution
+ 
+
+ align:start position:0%
+essentially low resolution
+representations of the entire object
+
+ align:start position:0%
+representations of the entire object
+ 
+
+ align:start position:0%
+representations of the entire object
+like almost the entire eagle but some of
+
+ align:start position:0%
+like almost the entire eagle but some of
+ 
+
+ align:start position:0%
+like almost the entire eagle but some of
+them just contained something relatively
+
+ align:start position:0%
+them just contained something relatively
+ 
+
+ align:start position:0%
+them just contained something relatively
+small around the round around the head
+
+ align:start position:0%
+small around the round around the head
+ 
+
+ align:start position:0%
+small around the round around the head
+and the eye for the eye region you can
+
+ align:start position:0%
+and the eye for the eye region you can
+ 
+
+ align:start position:0%
+and the eye for the eye region you can
+see that some you can get a low
+
+ align:start position:0%
+see that some you can get a low
+ 
+
+ align:start position:0%
+see that some you can get a low
+resolution again saying of almost
+
+ align:start position:0%
+resolution again saying of almost
+ 
+
+ align:start position:0%
+resolution again saying of almost
+everything but you can just the corner
+
+ align:start position:0%
+everything but you can just the corner
+ 
+
+ align:start position:0%
+everything but you can just the corner
+of the eye and things like that are
+
+ align:start position:0%
+of the eye and things like that are
+ 
+
+ align:start position:0%
+of the eye and things like that are
+enough we find in general it seemed that
+
+ align:start position:0%
+enough we find in general it seemed that
+ 
+
+ align:start position:0%
+enough we find in general it seemed that
+things that are related to humans you
+
+ align:start position:0%
+things that are related to humans you
+ 
+
+ align:start position:0%
+things that are related to humans you
+have a large number of these minimal
+
+ align:start position:0%
+have a large number of these minimal
+ 
+
+ align:start position:0%
+have a large number of these minimal
+minimal images so they provide a
+
+ align:start position:0%
+minimal images so they provide a
+ 
+
+ align:start position:0%
+minimal images so they provide a
+sensitive tool to compare
+
+ align:start position:0%
+sensitive tool to compare
+ 
+
+ align:start position:0%
+sensitive tool to compare
+representations to see what's missing in
+
+ align:start position:0%
+representations to see what's missing in
+ 
+
+ align:start position:0%
+representations to see what's missing in
+the sub image which made the image
+
+ align:start position:0%
+the sub image which made the image
+ 
+
+ align:start position:0%
+the sub image which made the image
+become unrecognizable so
+
+ align:start position:0%
+become unrecognizable so
+ 
+
+ align:start position:0%
+become unrecognizable so
+we call them sometimes this economy
+
+ align:start position:0%
+we call them sometimes this economy
+ 
+
+ align:start position:0%
+we call them sometimes this economy
+minimal recognizable configuration we we
+
+ align:start position:0%
+minimal recognizable configuration we we
+ 
+
+ align:start position:0%
+minimal recognizable configuration we we
+call them configuration but not images
+
+ align:start position:0%
+call them configuration but not images
+ 
+
+ align:start position:0%
+call them configuration but not images
+not parts or not objects because now not
+
+ align:start position:0%
+not parts or not objects because now not
+ 
+
+ align:start position:0%
+not parts or not objects because now not
+objects and not parts because as we saw
+
+ align:start position:0%
+objects and not parts because as we saw
+ 
+
+ align:start position:0%
+objects and not parts because as we saw
+in the examples they do not have to be
+
+ align:start position:0%
+in the examples they do not have to be
+ 
+
+ align:start position:0%
+in the examples they do not have to be
+well delineated parts are more like
+
+ align:start position:0%
+well delineated parts are more like
+ 
+
+ align:start position:0%
+well delineated parts are more like
+local configuration but anyway minimal
+
+ align:start position:0%
+local configuration but anyway minimal
+ 
+
+ align:start position:0%
+local configuration but anyway minimal
+minimal images and the next thing that
+
+ align:start position:0%
+minimal images and the next thing that
+ 
+
+ align:start position:0%
+minimal images and the next thing that
+we did is we were wondering if this kind
+
+ align:start position:0%
+we did is we were wondering if this kind
+ 
+
+ align:start position:0%
+we did is we were wondering if this kind
+of behavior that the ability to
+
+ align:start position:0%
+of behavior that the ability to
+ 
+
+ align:start position:0%
+of behavior that the ability to
+recognize this the ability to recognize
+
+ align:start position:0%
+recognize this the ability to recognize
+ 
+
+ align:start position:0%
+recognize this the ability to recognize
+these images from such minimal
+
+ align:start position:0%
+these images from such minimal
+ 
+
+ align:start position:0%
+these images from such minimal
+information requires it places an
+
+ align:start position:0%
+information requires it places an
+ 
+
+ align:start position:0%
+information requires it places an
+interesting challenge in into
+
+ align:start position:0%
+interesting challenge in into
+ 
+
+ align:start position:0%
+interesting challenge in into
+interesting test of a recognition system
+
+ align:start position:0%
+interesting test of a recognition system
+ 
+
+ align:start position:0%
+interesting test of a recognition system
+because you really have to extract and
+
+ align:start position:0%
+because you really have to extract and
+ 
+
+ align:start position:0%
+because you really have to extract and
+use all the available information by
+
+ align:start position:0%
+use all the available information by
+ 
+
+ align:start position:0%
+use all the available information by
+definition this is minimal if you do not
+
+ align:start position:0%
+definition this is minimal if you do not
+ 
+
+ align:start position:0%
+definition this is minimal if you do not
+use all the information that's in this
+
+ align:start position:0%
+use all the information that's in this
+ 
+
+ align:start position:0%
+use all the information that's in this
+minimal image then you don't have the
+
+ align:start position:0%
+minimal image then you don't have the
+ 
+
+ align:start position:0%
+minimal image then you don't have the
+minimal information you have less than
+
+ align:start position:0%
+minimal information you have less than
+ 
+
+ align:start position:0%
+minimal information you have less than
+that and you will fail so a system that
+
+ align:start position:0%
+that and you will fail so a system that
+ 
+
+ align:start position:0%
+that and you will fail so a system that
+is not good enough will fail on this
+
+ align:start position:0%
+is not good enough will fail on this
+ 
+
+ align:start position:0%
+is not good enough will fail on this
+minimal images or the ability to
+
+ align:start position:0%
+minimal images or the ability to
+ 
+
+ align:start position:0%
+minimal images or the ability to
+recognize that means that you really can
+
+ align:start position:0%
+recognize that means that you really can
+ 
+
+ align:start position:0%
+recognize that means that you really can
+suck out all the all the relevant
+
+ align:start position:0%
+suck out all the all the relevant
+ 
+
+ align:start position:0%
+suck out all the all the relevant
+information out so we were wondering
+
+ align:start position:0%
+information out so we were wondering
+ 
+
+ align:start position:0%
+information out so we were wondering
+what will happen if we show it to
+
+ align:start position:0%
+what will happen if we show it to
+ 
+
+ align:start position:0%
+what will happen if we show it to
+various computation and algorithms that
+
+ align:start position:0%
+various computation and algorithms that
+ 
+
+ align:start position:0%
+various computation and algorithms that
+performs well perform well on full
+
+ align:start position:0%
+performs well perform well on full
+ 
+
+ align:start position:0%
+performs well perform well on full
+images what will happen when you
+
+ align:start position:0%
+images what will happen when you
+ 
+
+ align:start position:0%
+images what will happen when you
+challenge them with things which are by
+
+ align:start position:0%
+challenge them with things which are by
+ 
+
+ align:start position:0%
+challenge them with things which are by
+nature designed to be non redundant so
+
+ align:start position:0%
+nature designed to be non redundant so
+ 
+
+ align:start position:0%
+nature designed to be non redundant so
+here is I will do it it's not a computer
+
+ align:start position:0%
+here is I will do it it's not a computer
+ 
+
+ align:start position:0%
+here is I will do it it's not a computer
+vision school I will not go too much
+
+ align:start position:0%
+vision school I will not go too much
+ 
+
+ align:start position:0%
+vision school I will not go too much
+through the details of the computational
+
+ align:start position:0%
+through the details of the computational
+ 
+
+ align:start position:0%
+through the details of the computational
+scheme just to show you what what was
+
+ align:start position:0%
+scheme just to show you what what was
+ 
+
+ align:start position:0%
+scheme just to show you what what was
+happening and in the bottom line is that
+
+ align:start position:0%
+happening and in the bottom line is that
+ 
+
+ align:start position:0%
+happening and in the bottom line is that
+they are not doing a good job two things
+
+ align:start position:0%
+they are not doing a good job two things
+ 
+
+ align:start position:0%
+they are not doing a good job two things
+happen first of all when you train a
+
+ align:start position:0%
+happen first of all when you train a
+ 
+
+ align:start position:0%
+happen first of all when you train a
+computational system you do not see the
+
+ align:start position:0%
+computational system you do not see the
+ 
+
+ align:start position:0%
+computational system you do not see the
+same drop that you see here that it
+
+ align:start position:0%
+same drop that you see here that it
+ 
+
+ align:start position:0%
+same drop that you see here that it
+recognizes one it doesn't recognize the
+
+ align:start position:0%
+recognizes one it doesn't recognize the
+ 
+
+ align:start position:0%
+recognizes one it doesn't recognize the
+other you don't have a drop in
+
+ align:start position:0%
+other you don't have a drop in
+ 
+
+ align:start position:0%
+other you don't have a drop in
+recognition that the this sort of phase
+
+ align:start position:0%
+recognition that the this sort of phase
+ 
+
+ align:start position:0%
+recognition that the this sort of phase
+transition that characterizes the human
+
+ align:start position:0%
+transition that characterizes the human
+ 
+
+ align:start position:0%
+transition that characterizes the human
+visual system is not reproduced in any
+
+ align:start position:0%
+visual system is not reproduced in any
+ 
+
+ align:start position:0%
+visual system is not reproduced in any
+of the current recognition systems
+
+ align:start position:0%
+of the current recognition systems
+ 
+
+ align:start position:0%
+of the current recognition systems
+include
+
+ align:start position:0%
+include
+ 
+
+ align:start position:0%
+include
+did network in any any other ones and
+
+ align:start position:0%
+did network in any any other ones and
+ 
+
+ align:start position:0%
+did network in any any other ones and
+secondly they are not very good at
+
+ align:start position:0%
+secondly they are not very good at
+ 
+
+ align:start position:0%
+secondly they are not very good at
+recognizing them regardless of the gap
+
+ align:start position:0%
+recognizing them regardless of the gap
+ 
+
+ align:start position:0%
+recognizing them regardless of the gap
+that there is a sharp transition or not
+
+ align:start position:0%
+that there is a sharp transition or not
+ 
+
+ align:start position:0%
+that there is a sharp transition or not
+they do not get good recognition results
+
+ align:start position:0%
+they do not get good recognition results
+ 
+
+ align:start position:0%
+they do not get good recognition results
+on on this minimal images do not suck
+
+ align:start position:0%
+on on this minimal images do not suck
+ 
+
+ align:start position:0%
+on on this minimal images do not suck
+all the necessary information so in the
+
+ align:start position:0%
+all the necessary information so in the
+ 
+
+ align:start position:0%
+all the necessary information so in the
+fully images it's like we had a an image
+
+ align:start position:0%
+fully images it's like we had a an image
+ 
+
+ align:start position:0%
+fully images it's like we had a an image
+of a side view of a plane so we are
+
+ align:start position:0%
+of a side view of a plane so we are
+ 
+
+ align:start position:0%
+of a side view of a plane so we are
+training on airplane you can think about
+
+ align:start position:0%
+training on airplane you can think about
+ 
+
+ align:start position:0%
+training on airplane you can think about
+deep Network we actually try the whole
+
+ align:start position:0%
+deep Network we actually try the whole
+ 
+
+ align:start position:0%
+deep Network we actually try the whole
+range of good classifiers and in all of
+
+ align:start position:0%
+range of good classifiers and in all of
+ 
+
+ align:start position:0%
+range of good classifiers and in all of
+these good classifiers those of you are
+
+ align:start position:0%
+these good classifiers those of you are
+ 
+
+ align:start position:0%
+these good classifiers those of you are
+not in vision and probably got enough at
+
+ align:start position:0%
+not in vision and probably got enough at
+ 
+
+ align:start position:0%
+not in vision and probably got enough at
+the beginning of this summer school that
+
+ align:start position:0%
+the beginning of this summer school that
+ 
+
+ align:start position:0%
+the beginning of this summer school that
+they have a feeling for a classifier in
+
+ align:start position:0%
+they have a feeling for a classifier in
+ 
+
+ align:start position:0%
+they have a feeling for a classifier in
+computer vision it's a system that
+
+ align:start position:0%
+computer vision it's a system that
+ 
+
+ align:start position:0%
+computer vision it's a system that
+algorithm the system that scheme that
+
+ align:start position:0%
+algorithm the system that scheme that
+ 
+
+ align:start position:0%
+algorithm the system that scheme that
+you give it training images you don't
+
+ align:start position:0%
+you give it training images you don't
+ 
+
+ align:start position:0%
+you give it training images you don't
+have to specify you don't tell it what
+
+ align:start position:0%
+have to specify you don't tell it what
+ 
+
+ align:start position:0%
+have to specify you don't tell it what
+to look for you just give it lots of
+
+ align:start position:0%
+to look for you just give it lots of
+ 
+
+ align:start position:0%
+to look for you just give it lots of
+images and tell them all these are of
+
+ align:start position:0%
+images and tell them all these are of
+ 
+
+ align:start position:0%
+images and tell them all these are of
+the same class and then it calibrates
+
+ align:start position:0%
+the same class and then it calibrates
+ 
+
+ align:start position:0%
+the same class and then it calibrates
+itself and adjust parameters and so on
+
+ align:start position:0%
+itself and adjust parameters and so on
+ 
+
+ align:start position:0%
+itself and adjust parameters and so on
+and then you give it new images and the
+
+ align:start position:0%
+and then you give it new images and the
+ 
+
+ align:start position:0%
+and then you give it new images and the
+system is supposed to tell you if we
+
+ align:start position:0%
+system is supposed to tell you if we
+ 
+
+ align:start position:0%
+system is supposed to tell you if we
+belong it's a new member of the same
+
+ align:start position:0%
+belong it's a new member of the same
+ 
+
+ align:start position:0%
+belong it's a new member of the same
+class or not so in this case we train
+
+ align:start position:0%
+class or not so in this case we train
+ 
+
+ align:start position:0%
+class or not so in this case we train
+the system giving them full side views
+
+ align:start position:0%
+the system giving them full side views
+ 
+
+ align:start position:0%
+the system giving them full side views
+of airplane but then we gave them just
+
+ align:start position:0%
+of airplane but then we gave them just
+ 
+
+ align:start position:0%
+of airplane but then we gave them just
+the tails compared to random patches
+
+ align:start position:0%
+the tails compared to random patches
+ 
+
+ align:start position:0%
+the tails compared to random patches
+taking from long images the question is
+
+ align:start position:0%
+taking from long images the question is
+ 
+
+ align:start position:0%
+taking from long images the question is
+do they reliably can tell you that this
+
+ align:start position:0%
+do they reliably can tell you that this
+ 
+
+ align:start position:0%
+do they reliably can tell you that this
+is a tail of an airplane part of the
+
+ align:start position:0%
+is a tail of an airplane part of the
+ 
+
+ align:start position:0%
+is a tail of an airplane part of the
+previous plus a class or they would be
+
+ align:start position:0%
+previous plus a class or they would be
+ 
+
+ align:start position:0%
+previous plus a class or they would be
+confused and we will give even higher
+
+ align:start position:0%
+confused and we will give even higher
+ 
+
+ align:start position:0%
+confused and we will give even higher
+score to things which do not come from
+
+ align:start position:0%
+score to things which do not come from
+ 
+
+ align:start position:0%
+score to things which do not come from
+airplane at all so we started this when
+
+ align:start position:0%
+airplane at all so we started this when
+ 
+
+ align:start position:0%
+airplane at all so we started this when
+deep networks were still not the leaders
+
+ align:start position:0%
+deep networks were still not the leaders
+ 
+
+ align:start position:0%
+deep networks were still not the leaders
+and we had some other things like DPM
+
+ align:start position:0%
+and we had some other things like DPM
+ 
+
+ align:start position:0%
+and we had some other things like DPM
+and including H marks which is a very
+
+ align:start position:0%
+and including H marks which is a very
+ 
+
+ align:start position:0%
+and including H marks which is a very
+good model of the human visual system
+
+ align:start position:0%
+good model of the human visual system
+ 
+
+ align:start position:0%
+good model of the human visual system
+and performs very well and so we
+
+ align:start position:0%
+and performs very well and so we
+ 
+
+ align:start position:0%
+and performs very well and so we
+included it as well and deep networks as
+
+ align:start position:0%
+included it as well and deep networks as
+ 
+
+ align:start position:0%
+included it as well and deep networks as
+well this is the H marks
+
+ align:start position:0%
+well this is the H marks
+ 
+
+ align:start position:0%
+well this is the H marks
+this is convolutional neural networks
+
+ align:start position:0%
+this is convolutional neural networks
+ 
+
+ align:start position:0%
+this is convolutional neural networks
+you probably got the idea just worth
+
+ align:start position:0%
+you probably got the idea just worth
+ 
+
+ align:start position:0%
+you probably got the idea just worth
+pointing I find it interesting in the
+
+ align:start position:0%
+pointing I find it interesting in the
+ 
+
+ align:start position:0%
+pointing I find it interesting in the
+computer vision coming
+
+ align:start position:0%
+computer vision coming
+ 
+
+ align:start position:0%
+computer vision coming
+that it's a you have all implicates
+
+ align:start position:0%
+that it's a you have all implicates
+ 
+
+ align:start position:0%
+that it's a you have all implicates
+something which is very structured and
+
+ align:start position:0%
+something which is very structured and
+ 
+
+ align:start position:0%
+something which is very structured and
+very competitive and very nice in this
+
+ align:start position:0%
+very competitive and very nice in this
+ 
+
+ align:start position:0%
+very competitive and very nice in this
+regard that for that there is the Pascal
+
+ align:start position:0%
+regard that for that there is the Pascal
+ 
+
+ align:start position:0%
+regard that for that there is the Pascal
+challenge and the imagenet challenge and
+
+ align:start position:0%
+challenge and the imagenet challenge and
+ 
+
+ align:start position:0%
+challenge and the imagenet challenge and
+it's well run and people who think that
+
+ align:start position:0%
+it's well run and people who think that
+ 
+
+ align:start position:0%
+it's well run and people who think that
+they have a better algorithm than others
+
+ align:start position:0%
+they have a better algorithm than others
+ 
+
+ align:start position:0%
+they have a better algorithm than others
+can submit an entry can submit an
+
+ align:start position:0%
+can submit an entry can submit an
+ 
+
+ align:start position:0%
+can submit an entry can submit an
+algorithm everybody gets training images
+
+ align:start position:0%
+algorithm everybody gets training images
+ 
+
+ align:start position:0%
+algorithm everybody gets training images
+that are distributed publicly but there
+
+ align:start position:0%
+that are distributed publicly but there
+ 
+
+ align:start position:0%
+that are distributed publicly but there
+are secret images used for testing and
+
+ align:start position:0%
+are secret images used for testing and
+ 
+
+ align:start position:0%
+are secret images used for testing and
+you can train your algorithm on the
+
+ align:start position:0%
+you can train your algorithm on the
+ 
+
+ align:start position:0%
+you can train your algorithm on the
+available data everybody uses the same
+
+ align:start position:0%
+available data everybody uses the same
+ 
+
+ align:start position:0%
+available data everybody uses the same
+data and then you submit your algorithm
+
+ align:start position:0%
+data and then you submit your algorithm
+ 
+
+ align:start position:0%
+data and then you submit your algorithm
+and the algorithm is run by the Central
+
+ align:start position:0%
+and the algorithm is run by the Central
+ 
+
+ align:start position:0%
+and the algorithm is run by the Central
+Committee on the test images and the
+
+ align:start position:0%
+Committee on the test images and the
+ 
+
+ align:start position:0%
+Committee on the test images and the
+results are published and everybody
+
+ align:start position:0%
+results are published and everybody
+ 
+
+ align:start position:0%
+results are published and everybody
+knows who is number one with number two
+
+ align:start position:0%
+knows who is number one with number two
+ 
+
+ align:start position:0%
+knows who is number one with number two
+you have the gold medal and a silver
+
+ align:start position:0%
+you have the gold medal and a silver
+ 
+
+ align:start position:0%
+you have the gold medal and a silver
+model and medal
+
+ align:start position:0%
+model and medal
+ 
+
+ align:start position:0%
+model and medal
+it's it's very competitive and it's it
+
+ align:start position:0%
+it's it's very competitive and it's it
+ 
+
+ align:start position:0%
+it's it's very competitive and it's it
+in some sense it's doing very good
+
+ align:start position:0%
+in some sense it's doing very good
+ 
+
+ align:start position:0%
+in some sense it's doing very good
+things it's sort of driving the
+
+ align:start position:0%
+things it's sort of driving the
+ 
+
+ align:start position:0%
+things it's sort of driving the
+performance up it also has a negative
+
+ align:start position:0%
+performance up it also has a negative
+ 
+
+ align:start position:0%
+performance up it also has a negative
+effect on the I think on the way things
+
+ align:start position:0%
+effect on the I think on the way things
+ 
+
+ align:start position:0%
+effect on the I think on the way things
+are being done one negative it's very
+
+ align:start position:0%
+are being done one negative it's very
+ 
+
+ align:start position:0%
+are being done one negative it's very
+difficult to come up with an entirely
+
+ align:start position:0%
+difficult to come up with an entirely
+ 
+
+ align:start position:0%
+difficult to come up with an entirely
+new scheme which explores a completely
+
+ align:start position:0%
+new scheme which explores a completely
+ 
+
+ align:start position:0%
+new scheme which explores a completely
+new idea because initially before you
+
+ align:start position:0%
+new idea because initially before you
+ 
+
+ align:start position:0%
+new idea because initially before you
+find you need it will not be at the
+
+ align:start position:0%
+find you need it will not be at the
+ 
+
+ align:start position:0%
+find you need it will not be at the
+level of the high-performing winners
+
+ align:start position:0%
+level of the high-performing winners
+ 
+
+ align:start position:0%
+level of the high-performing winners
+until it establishes itself as a winner
+
+ align:start position:0%
+until it establishes itself as a winner
+ 
+
+ align:start position:0%
+until it establishes itself as a winner
+it will not get credit so it sort of
+
+ align:start position:0%
+it will not get credit so it sort of
+ 
+
+ align:start position:0%
+it will not get credit so it sort of
+becomes a little bit conservative in
+
+ align:start position:0%
+becomes a little bit conservative in
+ 
+
+ align:start position:0%
+becomes a little bit conservative in
+this in this regard which is the
+
+ align:start position:0%
+this in this regard which is the
+ 
+
+ align:start position:0%
+this in this regard which is the
+unfortunate part so as I told you and I
+
+ align:start position:0%
+unfortunate part so as I told you and I
+ 
+
+ align:start position:0%
+unfortunate part so as I told you and I
+will not go in great detail the two
+
+ align:start position:0%
+will not go in great detail the two
+ 
+
+ align:start position:0%
+will not go in great detail the two
+basic outcomes is that the gap between
+
+ align:start position:0%
+basic outcomes is that the gap between
+ 
+
+ align:start position:0%
+basic outcomes is that the gap between
+recognizable and unrecognizable these
+
+ align:start position:0%
+recognizable and unrecognizable these
+ 
+
+ align:start position:0%
+recognizable and unrecognizable these
+two bars or the gap for human vision
+
+ align:start position:0%
+two bars or the gap for human vision
+ 
+
+ align:start position:0%
+two bars or the gap for human vision
+that a whole group of horse images the
+
+ align:start position:0%
+that a whole group of horse images the
+ 
+
+ align:start position:0%
+that a whole group of horse images the
+parents are highly recognizable the
+
+ align:start position:0%
+parents are highly recognizable the
+ 
+
+ align:start position:0%
+parents are highly recognizable the
+children offspring are not recognizable
+
+ align:start position:0%
+children offspring are not recognizable
+ 
+
+ align:start position:0%
+children offspring are not recognizable
+very large dog this drop is not
+
+ align:start position:0%
+very large dog this drop is not
+ 
+
+ align:start position:0%
+very large dog this drop is not
+recapitulate recaptured in
+
+ align:start position:0%
+recapitulate recaptured in
+ 
+
+ align:start position:0%
+recapitulate recaptured in
+in this model in any any of the model if
+
+ align:start position:0%
+in this model in any any of the model if
+ 
+
+ align:start position:0%
+in this model in any any of the model if
+you have a deep network or you have one
+
+ align:start position:0%
+you have a deep network or you have one
+ 
+
+ align:start position:0%
+you have a deep network or you have one
+of these classifiers what is recognized
+
+ align:start position:0%
+of these classifiers what is recognized
+ 
+
+ align:start position:0%
+of these classifiers what is recognized
+and not recognized depend on the
+
+ align:start position:0%
+and not recognized depend on the
+ 
+
+ align:start position:0%
+and not recognized depend on the
+threshold you can decide that it gives
+
+ align:start position:0%
+threshold you can decide that it gives
+ 
+
+ align:start position:0%
+threshold you can decide that it gives
+you a number and it says that I have
+
+ align:start position:0%
+you a number and it says that I have
+ 
+
+ align:start position:0%
+you a number and it says that I have
+this and it's confident that this is
+
+ align:start position:0%
+this and it's confident that this is
+ 
+
+ align:start position:0%
+this and it's confident that this is
+belongs to the class so what we did here
+
+ align:start position:0%
+belongs to the class so what we did here
+ 
+
+ align:start position:0%
+belongs to the class so what we did here
+is that we try to match we had a class
+
+ align:start position:0%
+is that we try to match we had a class
+ 
+
+ align:start position:0%
+is that we try to match we had a class
+of images and people recognize them at
+
+ align:start position:0%
+of images and people recognize them at
+ 
+
+ align:start position:0%
+of images and people recognize them at
+80 percent recognition so we put the
+
+ align:start position:0%
+80 percent recognition so we put the
+ 
+
+ align:start position:0%
+80 percent recognition so we put the
+threshold in the artificial the computer
+
+ align:start position:0%
+threshold in the artificial the computer
+ 
+
+ align:start position:0%
+threshold in the artificial the computer
+vision system at such a level that it
+
+ align:start position:0%
+vision system at such a level that it
+ 
+
+ align:start position:0%
+vision system at such a level that it
+recognized correctly 80 percent of the
+
+ align:start position:0%
+recognized correctly 80 percent of the
+ 
+
+ align:start position:0%
+recognized correctly 80 percent of the
+of the of the minimal images so you
+
+ align:start position:0%
+of the of the minimal images so you
+ 
+
+ align:start position:0%
+of the of the minimal images so you
+match them and then we looked at how
+
+ align:start position:0%
+match them and then we looked at how
+ 
+
+ align:start position:0%
+match them and then we looked at how
+many of the sub images it passed the
+
+ align:start position:0%
+many of the sub images it passed the
+ 
+
+ align:start position:0%
+many of the sub images it passed the
+threshold and you get this is for bitmap
+
+ align:start position:0%
+threshold and you get this is for bitmap
+ 
+
+ align:start position:0%
+threshold and you get this is for bitmap
+that instead of a gap you actually got
+
+ align:start position:0%
+that instead of a gap you actually got
+ 
+
+ align:start position:0%
+that instead of a gap you actually got
+an up until gap it actually recognized a
+
+ align:start position:0%
+an up until gap it actually recognized a
+ 
+
+ align:start position:0%
+an up until gap it actually recognized a
+few more but this should not confuse you
+
+ align:start position:0%
+few more but this should not confuse you
+ 
+
+ align:start position:0%
+few more but this should not confuse you
+it does not mean that the deep network
+
+ align:start position:0%
+it does not mean that the deep network
+ 
+
+ align:start position:0%
+it does not mean that the deep network
+did better than humans it actually did
+
+ align:start position:0%
+did better than humans it actually did
+ 
+
+ align:start position:0%
+did better than humans it actually did
+much worse than humans although the bars
+
+ align:start position:0%
+much worse than humans although the bars
+ 
+
+ align:start position:0%
+much worse than humans although the bars
+here are higher and there is the
+
+ align:start position:0%
+here are higher and there is the
+ 
+
+ align:start position:0%
+here are higher and there is the
+following you can always even in very
+
+ align:start position:0%
+following you can always even in very
+ 
+
+ align:start position:0%
+following you can always even in very
+bad classifier you can get 80%
+
+ align:start position:0%
+bad classifier you can get 80%
+ 
+
+ align:start position:0%
+bad classifier you can get 80%
+recognition by just lowering the
+
+ align:start position:0%
+recognition by just lowering the
+ 
+
+ align:start position:0%
+recognition by just lowering the
+threshold and then 80 percent of the
+
+ align:start position:0%
+threshold and then 80 percent of the
+ 
+
+ align:start position:0%
+threshold and then 80 percent of the
+class examples will exceed the threshold
+
+ align:start position:0%
+class examples will exceed the threshold
+ 
+
+ align:start position:0%
+class examples will exceed the threshold
+the question is how many just garbage
+
+ align:start position:0%
+the question is how many just garbage
+ 
+
+ align:start position:0%
+the question is how many just garbage
+image non class images will also pass
+
+ align:start position:0%
+image non class images will also pass
+ 
+
+ align:start position:0%
+image non class images will also pass
+the threshold at the same time if you
+
+ align:start position:0%
+the threshold at the same time if you
+ 
+
+ align:start position:0%
+the threshold at the same time if you
+get 80 percent of the class but also
+
+ align:start position:0%
+get 80 percent of the class but also
+ 
+
+ align:start position:0%
+get 80 percent of the class but also
+lots and lots and lots of completely
+
+ align:start position:0%
+lots and lots and lots of completely
+ 
+
+ align:start position:0%
+lots and lots and lots of completely
+false positive negative images non class
+
+ align:start position:0%
+false positive negative images non class
+ 
+
+ align:start position:0%
+false positive negative images non class
+images are also saying I mean airplane
+
+ align:start position:0%
+images are also saying I mean airplane
+ 
+
+ align:start position:0%
+images are also saying I mean airplane
+then that's bad performance so just the
+
+ align:start position:0%
+then that's bad performance so just the
+ 
+
+ align:start position:0%
+then that's bad performance so just the
+these high bars do not say anything the
+
+ align:start position:0%
+these high bars do not say anything the
+ 
+
+ align:start position:0%
+these high bars do not say anything the
+the actual recognition levels will very
+
+ align:start position:0%
+the actual recognition levels will very
+ 
+
+ align:start position:0%
+the actual recognition levels will very
+low we can see here for deep networks
+
+ align:start position:0%
+low we can see here for deep networks
+ 
+
+ align:start position:0%
+low we can see here for deep networks
+that this high bar is the performance on
+
+ align:start position:0%
+that this high bar is the performance on
+ 
+
+ align:start position:0%
+that this high bar is the performance on
+new airplanes so for airplanes they did
+
+ align:start position:0%
+new airplanes so for airplanes they did
+ 
+
+ align:start position:0%
+new airplanes so for airplanes they did
+very well but the percent correct that
+
+ align:start position:0%
+very well but the percent correct that
+ 
+
+ align:start position:0%
+very well but the percent correct that
+he did on minimal images or 3% 4% very
+
+ align:start position:0%
+he did on minimal images or 3% 4% very
+ 
+
+ align:start position:0%
+he did on minimal images or 3% 4% very
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+very low so it did very bad recognition
+
+ align:start position:0%
+very low so it did very bad recognition
+ 
+
+ align:start position:0%
+very low so it did very bad recognition
+on the minimal on the minimal images so
+
+ align:start position:0%
+on the minimal on the minimal images so
+ 
+
+ align:start position:0%
+on the minimal on the minimal images so
+recognition of minimal image does not
+
+ align:start position:0%
+recognition of minimal image does not
+ 
+
+ align:start position:0%
+recognition of minimal image does not
+emerge by training any of the existing
+
+ align:start position:0%
+emerge by training any of the existing
+ 
+
+ align:start position:0%
+emerge by training any of the existing
+model that I know in in the world
+
+ align:start position:0%
+model that I know in in the world
+ 
+
+ align:start position:0%
+model that I know in in the world
+including not your deep network models
+
+ align:start position:0%
+including not your deep network models
+ 
+
+ align:start position:0%
+including not your deep network models
+now the tag the second test was as was
+
+ align:start position:0%
+now the tag the second test was as was
+ 
+
+ align:start position:0%
+now the tag the second test was as was
+asked here is that we we did another
+
+ align:start position:0%
+asked here is that we we did another
+ 
+
+ align:start position:0%
+asked here is that we we did another
+large test all of these things actually
+
+ align:start position:0%
+large test all of these things actually
+ 
+
+ align:start position:0%
+large test all of these things actually
+were a lot of effort and time consuming
+
+ align:start position:0%
+were a lot of effort and time consuming
+ 
+
+ align:start position:0%
+were a lot of effort and time consuming
+because now we have this this was in the
+
+ align:start position:0%
+because now we have this this was in the
+ 
+
+ align:start position:0%
+because now we have this this was in the
+original test was a minimal image I
+
+ align:start position:0%
+original test was a minimal image I
+ 
+
+ align:start position:0%
+original test was a minimal image I
+don't know this was a minimal image then
+
+ align:start position:0%
+don't know this was a minimal image then
+ 
+
+ align:start position:0%
+don't know this was a minimal image then
+we we collected a range of tales of
+
+ align:start position:0%
+we we collected a range of tales of
+ 
+
+ align:start position:0%
+we we collected a range of tales of
+planes like this for many other
+
+ align:start position:0%
+planes like this for many other
+ 
+
+ align:start position:0%
+planes like this for many other
+airplanes and we did run another Terk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment which was pretty large
+
+ align:start position:0%
+experiment which was pretty large
+ 
+
+ align:start position:0%
+experiment which was pretty large
+because we wanted to verify that each
+
+ align:start position:0%
+because we wanted to verify that each
+ 
+
+ align:start position:0%
+because we wanted to verify that each
+one of these patches that we added to
+
+ align:start position:0%
+one of these patches that we added to
+ 
+
+ align:start position:0%
+one of these patches that we added to
+our test and we were going to use for
+
+ align:start position:0%
+our test and we were going to use for
+ 
+
+ align:start position:0%
+our test and we were going to use for
+testing recognition was indeed a minimal
+
+ align:start position:0%
+testing recognition was indeed a minimal
+ 
+
+ align:start position:0%
+testing recognition was indeed a minimal
+image from recognition so each one of
+
+ align:start position:0%
+image from recognition so each one of
+ 
+
+ align:start position:0%
+image from recognition so each one of
+these patches and there were 60 of those
+
+ align:start position:0%
+these patches and there were 60 of those
+ 
+
+ align:start position:0%
+these patches and there were 60 of those
+we ran on psychophysical II and we saw
+
+ align:start position:0%
+we ran on psychophysical II and we saw
+ 
+
+ align:start position:0%
+we ran on psychophysical II and we saw
+that it's recognizable and if you make
+
+ align:start position:0%
+that it's recognizable and if you make
+ 
+
+ align:start position:0%
+that it's recognizable and if you make
+it small if you try to reduce it it's
+
+ align:start position:0%
+it small if you try to reduce it it's
+ 
+
+ align:start position:0%
+it small if you try to reduce it it's
+unrecognizable so each one of these is
+
+ align:start position:0%
+unrecognizable so each one of these is
+ 
+
+ align:start position:0%
+unrecognizable so each one of these is
+individually also a minimal image so
+
+ align:start position:0%
+individually also a minimal image so
+ 
+
+ align:start position:0%
+individually also a minimal image so
+here we did training and testing on so
+
+ align:start position:0%
+here we did training and testing on so
+ 
+
+ align:start position:0%
+here we did training and testing on so
+this is some examples of this so here
+
+ align:start position:0%
+this is some examples of this so here
+ 
+
+ align:start position:0%
+this is some examples of this so here
+various images of fly and each one of
+
+ align:start position:0%
+various images of fly and each one of
+ 
+
+ align:start position:0%
+various images of fly and each one of
+them was tested on 30 subject on the
+
+ align:start position:0%
+them was tested on 30 subject on the
+ 
+
+ align:start position:0%
+them was tested on 30 subject on the
+Mechanical Turk and the results that in
+
+ align:start position:0%
+Mechanical Turk and the results that in
+ 
+
+ align:start position:0%
+Mechanical Turk and the results that in
+terms of correct recognition there is a
+
+ align:start position:0%
+terms of correct recognition there is a
+ 
+
+ align:start position:0%
+terms of correct recognition there is a
+substantial improvement from 3 percent
+
+ align:start position:0%
+substantial improvement from 3 percent
+ 
+
+ align:start position:0%
+substantial improvement from 3 percent
+to 60 percent but 60 percent is not very
+
+ align:start position:0%
+to 60 percent but 60 percent is not very
+ 
+
+ align:start position:0%
+to 60 percent but 60 percent is not very
+large people recognize them 60 I should
+
+ align:start position:0%
+large people recognize them 60 I should
+ 
+
+ align:start position:0%
+large people recognize them 60 I should
+say you should look at the false alarm
+
+ align:start position:0%
+say you should look at the false alarm
+ 
+
+ align:start position:0%
+say you should look at the false alarm
+the number of arrows we'll show you
+
+ align:start position:0%
+the number of arrows we'll show you
+ 
+
+ align:start position:0%
+the number of arrows we'll show you
+later the number of arrows that even
+
+ align:start position:0%
+later the number of arrows that even
+ 
+
+ align:start position:0%
+later the number of arrows that even
+after training on minimal images the
+
+ align:start position:0%
+after training on minimal images the
+ 
+
+ align:start position:0%
+after training on minimal images the
+number of the performance of the deep
+
+ align:start position:0%
+number of the performance of the deep
+ 
+
+ align:start position:0%
+number of the performance of the deep
+network and all the other models on the
+
+ align:start position:0%
+network and all the other models on the
+ 
+
+ align:start position:0%
+network and all the other models on the
+minimum image
+
+ align:start position:0%
+minimum image
+ 
+
+ align:start position:0%
+minimum image
+is far worse than human recognition
+
+ align:start position:0%
+is far worse than human recognition
+ 
+
+ align:start position:0%
+is far worse than human recognition
+level human performance on the same
+
+ align:start position:0%
+level human performance on the same
+ 
+
+ align:start position:0%
+level human performance on the same
+images so it's not just the the gap is
+
+ align:start position:0%
+images so it's not just the the gap is
+ 
+
+ align:start position:0%
+images so it's not just the the gap is
+not reproduce even training with minimal
+
+ align:start position:0%
+not reproduce even training with minimal
+ 
+
+ align:start position:0%
+not reproduce even training with minimal
+images the performance is not is not
+
+ align:start position:0%
+images the performance is not is not
+ 
+
+ align:start position:0%
+images the performance is not is not
+reproduced the arrows or the accuracy is
+
+ align:start position:0%
+reproduced the arrows or the accuracy is
+ 
+
+ align:start position:0%
+reproduced the arrows or the accuracy is
+far worse in the in all the models
+
+ align:start position:0%
+far worse in the in all the models
+ 
+
+ align:start position:0%
+far worse in the in all the models
+including deep network compared to to
+
+ align:start position:0%
+including deep network compared to to
+ 
+
+ align:start position:0%
+including deep network compared to to
+human vision so these systems do not do
+
+ align:start position:0%
+human vision so these systems do not do
+ 
+
+ align:start position:0%
+human vision so these systems do not do
+it it remains to be you can always ask
+
+ align:start position:0%
+it it remains to be you can always ask
+ 
+
+ align:start position:0%
+it it remains to be you can always ask
+what happened if I train it with a
+
+ align:start position:0%
+what happened if I train it with a
+ 
+
+ align:start position:0%
+what happened if I train it with a
+hundred thousand images and I add an add
+
+ align:start position:0%
+hundred thousand images and I add an add
+ 
+
+ align:start position:0%
+hundred thousand images and I add an add
+more and more example this we couldn't
+
+ align:start position:0%
+more and more example this we couldn't
+ 
+
+ align:start position:0%
+more and more example this we couldn't
+this becomes more and larger but my with
+
+ align:start position:0%
+this becomes more and larger but my with
+ 
+
+ align:start position:0%
+this becomes more and larger but my with
+the experiment we've done which are
+
+ align:start position:0%
+the experiment we've done which are
+ 
+
+ align:start position:0%
+the experiment we've done which are
+quite extensive it does not a poet does
+
+ align:start position:0%
+quite extensive it does not a poet does
+ 
+
+ align:start position:0%
+quite extensive it does not a poet does
+not begin to approach human accuracy
+
+ align:start position:0%
+not begin to approach human accuracy
+ 
+
+ align:start position:0%
+not begin to approach human accuracy
+humans are much are much better and I'll
+
+ align:start position:0%
+humans are much are much better and I'll
+ 
+
+ align:start position:0%
+humans are much are much better and I'll
+show you I think it's not just the
+
+ align:start position:0%
+show you I think it's not just the
+ 
+
+ align:start position:0%
+show you I think it's not just the
+competition who does who does better I
+
+ align:start position:0%
+competition who does who does better I
+ 
+
+ align:start position:0%
+competition who does who does better I
+think there is something deeper there
+
+ align:start position:0%
+think there is something deeper there
+ 
+
+ align:start position:0%
+think there is something deeper there
+and that's what I want to go next let me
+
+ align:start position:0%
+and that's what I want to go next let me
+ 
+
+ align:start position:0%
+and that's what I want to go next let me
+skip some these are the arrow comparison
+
+ align:start position:0%
+skip some these are the arrow comparison
+ 
+
+ align:start position:0%
+skip some these are the arrow comparison
+and you can see it just to show in a lot
+
+ align:start position:0%
+and you can see it just to show in a lot
+ 
+
+ align:start position:0%
+and you can see it just to show in a lot
+of different examples zero zero arrows
+
+ align:start position:0%
+of different examples zero zero arrows
+ 
+
+ align:start position:0%
+of different examples zero zero arrows
+for humans 17% in the deep networks and
+
+ align:start position:0%
+for humans 17% in the deep networks and
+ 
+
+ align:start position:0%
+for humans 17% in the deep networks and
+so on so that's big big differences ok
+
+ align:start position:0%
+so on so that's big big differences ok
+ 
+
+ align:start position:0%
+so on so that's big big differences ok
+the related thing which I think gets to
+
+ align:start position:0%
+the related thing which I think gets to
+ 
+
+ align:start position:0%
+the related thing which I think gets to
+the heart of what's going on that humans
+
+ align:start position:0%
+the heart of what's going on that humans
+ 
+
+ align:start position:0%
+the heart of what's going on that humans
+can do with these minimal images and
+
+ align:start position:0%
+can do with these minimal images and
+ 
+
+ align:start position:0%
+can do with these minimal images and
+model at the moment cannot is that we do
+
+ align:start position:0%
+model at the moment cannot is that we do
+ 
+
+ align:start position:0%
+model at the moment cannot is that we do
+not only do not only recognize this
+
+ align:start position:0%
+not only do not only recognize this
+ 
+
+ align:start position:0%
+not only do not only recognize this
+image and say this is a man this is an
+
+ align:start position:0%
+image and say this is a man this is an
+ 
+
+ align:start position:0%
+image and say this is a man this is an
+eagle this is the horse once we
+
+ align:start position:0%
+eagle this is the horse once we
+ 
+
+ align:start position:0%
+eagle this is the horse once we
+recognize it although the image itself
+
+ align:start position:0%
+recognize it although the image itself
+ 
+
+ align:start position:0%
+recognize it although the image itself
+is sort of atomic in the sense that you
+
+ align:start position:0%
+is sort of atomic in the sense that you
+ 
+
+ align:start position:0%
+is sort of atomic in the sense that you
+would use it and the cognition goes away
+
+ align:start position:0%
+would use it and the cognition goes away
+ 
+
+ align:start position:0%
+would use it and the cognition goes away
+but once you recognize it we can
+
+ align:start position:0%
+but once you recognize it we can
+ 
+
+ align:start position:0%
+but once you recognize it we can
+recognize sort of subatomic particles we
+
+ align:start position:0%
+recognize sort of subatomic particles we
+ 
+
+ align:start position:0%
+recognize sort of subatomic particles we
+can recognize things inside it so if
+
+ align:start position:0%
+can recognize things inside it so if
+ 
+
+ align:start position:0%
+can recognize things inside it so if
+this is a person we asked again in a
+
+ align:start position:0%
+this is a person we asked again in a
+ 
+
+ align:start position:0%
+this is a person we asked again in a
+psycho physical test to tell us what you
+
+ align:start position:0%
+psycho physical test to tell us what you
+ 
+
+ align:start position:0%
+psycho physical test to tell us what you
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+inside the image in various using
+
+ align:start position:0%
+inside the image in various using
+ 
+
+ align:start position:0%
+inside the image in various using
+various methodologies which I'll not go
+
+ align:start position:0%
+various methodologies which I'll not go
+ 
+
+ align:start position:0%
+various methodologies which I'll not go
+into but people recognize this this is a
+
+ align:start position:0%
+into but people recognize this this is a
+ 
+
+ align:start position:0%
+into but people recognize this this is a
+person in Italian suit for those of you
+
+ align:start position:0%
+person in Italian suit for those of you
+ 
+
+ align:start position:0%
+person in Italian suit for those of you
+could not recognize it but once people
+
+ align:start position:0%
+could not recognize it but once people
+ 
+
+ align:start position:0%
+could not recognize it but once people
+recognize it they say this is the neck
+
+ align:start position:0%
+recognize it they say this is the neck
+ 
+
+ align:start position:0%
+recognize it they say this is the neck
+of the person this is the tie this is
+
+ align:start position:0%
+of the person this is the tie this is
+ 
+
+ align:start position:0%
+of the person this is the tie this is
+the this is the knot of the tie this is
+
+ align:start position:0%
+the this is the knot of the tie this is
+ 
+
+ align:start position:0%
+the this is the knot of the tie this is
+part of the jacket and so on and so
+
+ align:start position:0%
+part of the jacket and so on and so
+ 
+
+ align:start position:0%
+part of the jacket and so on and so
+forth I mean they recognize a whole lot
+
+ align:start position:0%
+forth I mean they recognize a whole lot
+ 
+
+ align:start position:0%
+forth I mean they recognize a whole lot
+of details semantic internal details
+
+ align:start position:0%
+of details semantic internal details
+ 
+
+ align:start position:0%
+of details semantic internal details
+inside if they see this is the horse so
+
+ align:start position:0%
+inside if they see this is the horse so
+ 
+
+ align:start position:0%
+inside if they see this is the horse so
+in the contrast is low but they see the
+
+ align:start position:0%
+in the contrast is low but they see the
+ 
+
+ align:start position:0%
+in the contrast is low but they see the
+ear and the other in the eye and the
+
+ align:start position:0%
+ear and the other in the eye and the
+ 
+
+ align:start position:0%
+ear and the other in the eye and the
+mouse but if you reduce the image they
+
+ align:start position:0%
+mouse but if you reduce the image they
+ 
+
+ align:start position:0%
+mouse but if you reduce the image they
+lose the recognition completely once you
+
+ align:start position:0%
+lose the recognition completely once you
+ 
+
+ align:start position:0%
+lose the recognition completely once you
+recognize it they recognize a whole lot
+
+ align:start position:0%
+recognize it they recognize a whole lot
+ 
+
+ align:start position:0%
+recognize it they recognize a whole lot
+of structure inside and I think that the
+
+ align:start position:0%
+of structure inside and I think that the
+ 
+
+ align:start position:0%
+of structure inside and I think that the
+structure by itself is the more
+
+ align:start position:0%
+structure by itself is the more
+ 
+
+ align:start position:0%
+structure by itself is the more
+interesting part because when we we
+
+ align:start position:0%
+interesting part because when we we
+ 
+
+ align:start position:0%
+interesting part because when we we
+don't want to say a horse we don't want
+
+ align:start position:0%
+don't want to say a horse we don't want
+ 
+
+ align:start position:0%
+don't want to say a horse we don't want
+to see a car we want to know where the
+
+ align:start position:0%
+to see a car we want to know where the
+ 
+
+ align:start position:0%
+to see a car we want to know where the
+car door where the knob is we want to
+
+ align:start position:0%
+car door where the knob is we want to
+ 
+
+ align:start position:0%
+car door where the knob is we want to
+recognize all the internal details but
+
+ align:start position:0%
+recognize all the internal details but
+ 
+
+ align:start position:0%
+recognize all the internal details but
+the ability to recognize all of these
+
+ align:start position:0%
+the ability to recognize all of these
+ 
+
+ align:start position:0%
+the ability to recognize all of these
+internal details is automatically it's
+
+ align:start position:0%
+internal details is automatically it's
+ 
+
+ align:start position:0%
+internal details is automatically it's
+also helping you with improving the
+
+ align:start position:0%
+also helping you with improving the
+ 
+
+ align:start position:0%
+also helping you with improving the
+recognition and rejecting sort of false
+
+ align:start position:0%
+recognition and rejecting sort of false
+ 
+
+ align:start position:0%
+recognition and rejecting sort of false
+detections because these are images the
+
+ align:start position:0%
+detections because these are images the
+ 
+
+ align:start position:0%
+detections because these are images the
+deep network thought that are good
+
+ align:start position:0%
+deep network thought that are good
+ 
+
+ align:start position:0%
+deep network thought that are good
+images of a man in a suit but once you
+
+ align:start position:0%
+images of a man in a suit but once you
+ 
+
+ align:start position:0%
+images of a man in a suit but once you
+dive inside and you say where exactly is
+
+ align:start position:0%
+dive inside and you say where exactly is
+ 
+
+ align:start position:0%
+dive inside and you say where exactly is
+the neck and where exactly is the tie
+
+ align:start position:0%
+the neck and where exactly is the tie
+ 
+
+ align:start position:0%
+the neck and where exactly is the tie
+and is it the right structure that I
+
+ align:start position:0%
+and is it the right structure that I
+ 
+
+ align:start position:0%
+and is it the right structure that I
+expect the answer is that it's not quite
+
+ align:start position:0%
+expect the answer is that it's not quite
+ 
+
+ align:start position:0%
+expect the answer is that it's not quite
+appropriate and you can use that so that
+
+ align:start position:0%
+appropriate and you can use that so that
+ 
+
+ align:start position:0%
+appropriate and you can use that so that
+this internal interpretation is first of
+
+ align:start position:0%
+this internal interpretation is first of
+ 
+
+ align:start position:0%
+this internal interpretation is first of
+all the more important goal of vision
+
+ align:start position:0%
+all the more important goal of vision
+ 
+
+ align:start position:0%
+all the more important goal of vision
+but in addition once you do it you can
+
+ align:start position:0%
+but in addition once you do it you can
+ 
+
+ align:start position:0%
+but in addition once you do it you can
+reject things that appeared based on the
+
+ align:start position:0%
+reject things that appeared based on the
+ 
+
+ align:start position:0%
+reject things that appeared based on the
+causal structure to be correct and in
+
+ align:start position:0%
+causal structure to be correct and in
+ 
+
+ align:start position:0%
+causal structure to be correct and in
+this in this way you can get the correct
+
+ align:start position:0%
+this in this way you can get the correct
+ 
+
+ align:start position:0%
+this in this way you can get the correct
+recognition and in this for this reason
+
+ align:start position:0%
+recognition and in this for this reason
+ 
+
+ align:start position:0%
+recognition and in this for this reason
+my prediction is that it would be very
+
+ align:start position:0%
+my prediction is that it would be very
+ 
+
+ align:start position:0%
+my prediction is that it would be very
+difficult to get it with current deep
+
+ align:start position:0%
+difficult to get it with current deep
+ 
+
+ align:start position:0%
+difficult to get it with current deep
+network because what you need is not
+
+ align:start position:0%
+network because what you need is not
+ 
+
+ align:start position:0%
+network because what you need is not
+only to get the label out but to be able
+
+ align:start position:0%
+only to get the label out but to be able
+ 
+
+ align:start position:0%
+only to get the label out but to be able
+to dive down and get the correct
+
+ align:start position:0%
+to dive down and get the correct
+ 
+
+ align:start position:0%
+to dive down and get the correct
+interpretation and inspect it and it has
+
+ align:start position:0%
+interpretation and inspect it and it has
+ 
+
+ align:start position:0%
+interpretation and inspect it and it has
+some property is what the pie
+
+ align:start position:0%
+some property is what the pie
+ 
+
+ align:start position:0%
+some property is what the pie
+the knot in the tie is slightly wider
+
+ align:start position:0%
+the knot in the tie is slightly wider
+ 
+
+ align:start position:0%
+the knot in the tie is slightly wider
+than the part under it and so on so you
+
+ align:start position:0%
+than the part under it and so on so you
+ 
+
+ align:start position:0%
+than the part under it and so on so you
+have to check for the you know these
+
+ align:start position:0%
+have to check for the you know these
+ 
+
+ align:start position:0%
+have to check for the you know these
+things and you check for them and if you
+
+ align:start position:0%
+things and you check for them and if you
+ 
+
+ align:start position:0%
+things and you check for them and if you
+don't do it then the recognition will
+
+ align:start position:0%
+don't do it then the recognition will
+ 
+
+ align:start position:0%
+don't do it then the recognition will
+remain remain limited now when you look
+
+ align:start position:0%
+remain remain limited now when you look
+ 
+
+ align:start position:0%
+remain remain limited now when you look
+at it and you say okay and we try to
+
+ align:start position:0%
+at it and you say okay and we try to
+ 
+
+ align:start position:0%
+at it and you say okay and we try to
+develop algorithm which will actually
+
+ align:start position:0%
+develop algorithm which will actually
+ 
+
+ align:start position:0%
+develop algorithm which will actually
+dive in and we'll do the interval
+
+ align:start position:0%
+dive in and we'll do the interval
+ 
+
+ align:start position:0%
+dive in and we'll do the interval
+internal interpretation and we'll do
+
+ align:start position:0%
+internal interpretation and we'll do
+ 
+
+ align:start position:0%
+internal interpretation and we'll do
+them correctly and we'll reject false
+
+ align:start position:0%
+them correctly and we'll reject false
+ 
+
+ align:start position:0%
+them correctly and we'll reject false
+and false alarms and so on it turns out
+
+ align:start position:0%
+and false alarms and so on it turns out
+ 
+
+ align:start position:0%
+and false alarms and so on it turns out
+that this is an interesting business you
+
+ align:start position:0%
+that this is an interesting business you
+ 
+
+ align:start position:0%
+that this is an interesting business you
+have to be very accurate and some of the
+
+ align:start position:0%
+have to be very accurate and some of the
+ 
+
+ align:start position:0%
+have to be very accurate and some of the
+properties and relations that you need
+
+ align:start position:0%
+properties and relations that you need
+ 
+
+ align:start position:0%
+properties and relations that you need
+to extract are very specific to certain
+
+ align:start position:0%
+to extract are very specific to certain
+ 
+
+ align:start position:0%
+to extract are very specific to certain
+categories and are very precise for
+
+ align:start position:0%
+categories and are very precise for
+ 
+
+ align:start position:0%
+categories and are very precise for
+example this was selected by deep
+
+ align:start position:0%
+example this was selected by deep
+ 
+
+ align:start position:0%
+example this was selected by deep
+Network is a very good example of a
+
+ align:start position:0%
+Network is a very good example of a
+ 
+
+ align:start position:0%
+Network is a very good example of a
+horse head and it's basically the right
+
+ align:start position:0%
+horse head and it's basically the right
+ 
+
+ align:start position:0%
+horse head and it's basically the right
+it does have the right shape but for
+
+ align:start position:0%
+it does have the right shape but for
+ 
+
+ align:start position:0%
+it does have the right shape but for
+example people reject it we ask as
+
+ align:start position:0%
+example people reject it we ask as
+ 
+
+ align:start position:0%
+example people reject it we ask as
+people did not accept it as a horse head
+
+ align:start position:0%
+people did not accept it as a horse head
+ 
+
+ align:start position:0%
+people did not accept it as a horse head
+and they said for example the dis lines
+
+ align:start position:0%
+and they said for example the dis lines
+ 
+
+ align:start position:0%
+and they said for example the dis lines
+are too straight it looks like a
+
+ align:start position:0%
+are too straight it looks like a
+ 
+
+ align:start position:0%
+are too straight it looks like a
+man-made palate rather than a part of a
+
+ align:start position:0%
+man-made palate rather than a part of a
+ 
+
+ align:start position:0%
+man-made palate rather than a part of a
+wheel of a real animal that that was a
+
+ align:start position:0%
+wheel of a real animal that that was a
+ 
+
+ align:start position:0%
+wheel of a real animal that that was a
+repeating answer for example but the
+
+ align:start position:0%
+repeating answer for example but the
+ 
+
+ align:start position:0%
+repeating answer for example but the
+creation how straight is it and so on
+
+ align:start position:0%
+creation how straight is it and so on
+ 
+
+ align:start position:0%
+creation how straight is it and so on
+this is a bit tricky and also it didn't
+
+ align:start position:0%
+this is a bit tricky and also it didn't
+ 
+
+ align:start position:0%
+this is a bit tricky and also it didn't
+have quite the ear that you do expect
+
+ align:start position:0%
+have quite the ear that you do expect
+ 
+
+ align:start position:0%
+have quite the ear that you do expect
+here so we think that the kind of
+
+ align:start position:0%
+here so we think that the kind of
+ 
+
+ align:start position:0%
+here so we think that the kind of
+feature that you need in order to do
+
+ align:start position:0%
+feature that you need in order to do
+ 
+
+ align:start position:0%
+feature that you need in order to do
+this internal interpretation of interest
+
+ align:start position:0%
+this internal interpretation of interest
+ 
+
+ align:start position:0%
+this internal interpretation of interest
+depends on relatively complicated
+
+ align:start position:0%
+depends on relatively complicated
+ 
+
+ align:start position:0%
+depends on relatively complicated
+properties and relations that you don't
+
+ align:start position:0%
+properties and relations that you don't
+ 
+
+ align:start position:0%
+properties and relations that you don't
+want to spend time and effort doing in a
+
+ align:start position:0%
+want to spend time and effort doing in a
+ 
+
+ align:start position:0%
+want to spend time and effort doing in a
+bottom-up way all over the all over the
+
+ align:start position:0%
+bottom-up way all over the all over the
+ 
+
+ align:start position:0%
+bottom-up way all over the all over the
+the entire visual field if certain two
+
+ align:start position:0%
+the entire visual field if certain two
+ 
+
+ align:start position:0%
+the entire visual field if certain two
+contours move smoothly or in a corner or
+
+ align:start position:0%
+contours move smoothly or in a corner or
+ 
+
+ align:start position:0%
+contours move smoothly or in a corner or
+if something is really straight only
+
+ align:start position:0%
+if something is really straight only
+ 
+
+ align:start position:0%
+if something is really straight only
+semi straight I mean to do all of these
+
+ align:start position:0%
+semi straight I mean to do all of these
+ 
+
+ align:start position:0%
+semi straight I mean to do all of these
+computations my subject my hunch is to
+
+ align:start position:0%
+computations my subject my hunch is to
+ 
+
+ align:start position:0%
+computations my subject my hunch is to
+do all of these complicated things you
+
+ align:start position:0%
+do all of these complicated things you
+ 
+
+ align:start position:0%
+do all of these complicated things you
+need them only in a small you need some
+
+ align:start position:0%
+need them only in a small you need some
+ 
+
+ align:start position:0%
+need them only in a small you need some
+specific ones for some specific classes
+
+ align:start position:0%
+specific ones for some specific classes
+ 
+
+ align:start position:0%
+specific ones for some specific classes
+at some specific locations so the right
+
+ align:start position:0%
+at some specific locations so the right
+ 
+
+ align:start position:0%
+at some specific locations so the right
+way to do to do this kind of computation
+
+ align:start position:0%
+way to do to do this kind of computation
+ 
+
+ align:start position:0%
+way to do to do this kind of computation
+the right architecture seems to me a
+
+ align:start position:0%
+the right architecture seems to me a
+ 
+
+ align:start position:0%
+the right architecture seems to me a
+combination of bottom-up and top-down
+
+ align:start position:0%
+combination of bottom-up and top-down
+ 
+
+ align:start position:0%
+combination of bottom-up and top-down
+processing and we know that in the
+
+ align:start position:0%
+processing and we know that in the
+ 
+
+ align:start position:0%
+processing and we know that in the
+visual system this is a diagram of the
+
+ align:start position:0%
+visual system this is a diagram of the
+ 
+
+ align:start position:0%
+visual system this is a diagram of the
+system which is supposed supposed to
+
+ align:start position:0%
+system which is supposed supposed to
+ 
+
+ align:start position:0%
+system which is supposed supposed to
+show that we have lots of connections
+
+ align:start position:0%
+show that we have lots of connections
+ 
+
+ align:start position:0%
+show that we have lots of connections
+going up but also a lot of connections
+
+ align:start position:0%
+going up but also a lot of connections
+ 
+
+ align:start position:0%
+going up but also a lot of connections
+going down and it's suggestion that I
+
+ align:start position:0%
+going down and it's suggestion that I
+ 
+
+ align:start position:0%
+going down and it's suggestion that I
+would like to put up and I think it's
+
+ align:start position:0%
+would like to put up and I think it's
+ 
+
+ align:start position:0%
+would like to put up and I think it's
+what's happening here is that we have
+
+ align:start position:0%
+what's happening here is that we have
+ 
+
+ align:start position:0%
+what's happening here is that we have
+something like deep network that does an
+
+ align:start position:0%
+something like deep network that does an
+ 
+
+ align:start position:0%
+something like deep network that does an
+initial generic classification it's
+
+ align:start position:0%
+initial generic classification it's
+ 
+
+ align:start position:0%
+initial generic classification it's
+bottom-up it has some kind of was
+
+ align:start position:0%
+bottom-up it has some kind of was
+ 
+
+ align:start position:0%
+bottom-up it has some kind of was
+trained on many categories it is not
+
+ align:start position:0%
+trained on many categories it is not
+ 
+
+ align:start position:0%
+trained on many categories it is not
+sensitive to all of this small and
+
+ align:start position:0%
+sensitive to all of this small and
+ 
+
+ align:start position:0%
+sensitive to all of this small and
+informative things that you need for
+
+ align:start position:0%
+informative things that you need for
+ 
+
+ align:start position:0%
+informative things that you need for
+internal classification and it proposes
+
+ align:start position:0%
+internal classification and it proposes
+ 
+
+ align:start position:0%
+internal classification and it proposes
+a lot of it gives you initialize initial
+
+ align:start position:0%
+a lot of it gives you initialize initial
+ 
+
+ align:start position:0%
+a lot of it gives you initialize initial
+recognition which is OK
+
+ align:start position:0%
+recognition which is OK
+ 
+
+ align:start position:0%
+recognition which is OK
+it's especially ok when you have a
+
+ align:start position:0%
+it's especially ok when you have a
+ 
+
+ align:start position:0%
+it's especially ok when you have a
+complete object and not something
+
+ align:start position:0%
+complete object and not something
+ 
+
+ align:start position:0%
+complete object and not something
+challenging like it's like a minimal
+
+ align:start position:0%
+challenging like it's like a minimal
+ 
+
+ align:start position:0%
+challenging like it's like a minimal
+image because you may be wrong on a
+
+ align:start position:0%
+image because you may be wrong on a
+ 
+
+ align:start position:0%
+image because you may be wrong on a
+couple of the minimal images but you
+
+ align:start position:0%
+couple of the minimal images but you
+ 
+
+ align:start position:0%
+couple of the minimal images but you
+have 20 of them in each object so 2 are
+
+ align:start position:0%
+have 20 of them in each object so 2 are
+ 
+
+ align:start position:0%
+have 20 of them in each object so 2 are
+wrong it's not too bad so under many
+
+ align:start position:0%
+wrong it's not too bad so under many
+ 
+
+ align:start position:0%
+wrong it's not too bad so under many
+circumstances you'll be okay in terms of
+
+ align:start position:0%
+circumstances you'll be okay in terms of
+ 
+
+ align:start position:0%
+circumstances you'll be okay in terms of
+general general recognition but what
+
+ align:start position:0%
+general general recognition but what
+ 
+
+ align:start position:0%
+general general recognition but what
+this does is it doesn't complete the
+
+ align:start position:0%
+this does is it doesn't complete the
+ 
+
+ align:start position:0%
+this does is it doesn't complete the
+process but it sort of triggers the
+
+ align:start position:0%
+process but it sort of triggers the
+ 
+
+ align:start position:0%
+process but it sort of triggers the
+application of something which is much
+
+ align:start position:0%
+application of something which is much
+ 
+
+ align:start position:0%
+application of something which is much
+more class specific that it says oh it
+
+ align:start position:0%
+more class specific that it says oh it
+ 
+
+ align:start position:0%
+more class specific that it says oh it
+looks like a horse let's check if it has
+
+ align:start position:0%
+looks like a horse let's check if it has
+ 
+
+ align:start position:0%
+looks like a horse let's check if it has
+so let's now complete the interpretation
+
+ align:start position:0%
+so let's now complete the interpretation
+ 
+
+ align:start position:0%
+so let's now complete the interpretation
+it's not just a validation but you
+
+ align:start position:0%
+it's not just a validation but you
+ 
+
+ align:start position:0%
+it's not just a validation but you
+really want to know where is the eye
+
+ align:start position:0%
+really want to know where is the eye
+ 
+
+ align:start position:0%
+really want to know where is the eye
+where is the ear where is the mouse and
+
+ align:start position:0%
+where is the ear where is the mouse and
+ 
+
+ align:start position:0%
+where is the ear where is the mouse and
+so on you want to know maybe if the
+
+ align:start position:0%
+so on you want to know maybe if the
+ 
+
+ align:start position:0%
+so on you want to know maybe if the
+mouse is open or closed you want to feed
+
+ align:start position:0%
+mouse is open or closed you want to feed
+ 
+
+ align:start position:0%
+mouse is open or closed you want to feed
+the horse you want to pet the horse I
+
+ align:start position:0%
+the horse you want to pet the horse I
+ 
+
+ align:start position:0%
+the horse you want to pet the horse I
+mean when you interact with object all
+
+ align:start position:0%
+mean when you interact with object all
+ 
+
+ align:start position:0%
+mean when you interact with object all
+of these things are important so you
+
+ align:start position:0%
+of these things are important so you
+ 
+
+ align:start position:0%
+of these things are important so you
+continue your understanding of the
+
+ align:start position:0%
+continue your understanding of the
+ 
+
+ align:start position:0%
+continue your understanding of the
+visual scene but this is not this
+
+ align:start position:0%
+visual scene but this is not this
+ 
+
+ align:start position:0%
+visual scene but this is not this
+generic bottom-up recognition but you
+
+ align:start position:0%
+generic bottom-up recognition but you
+ 
+
+ align:start position:0%
+generic bottom-up recognition but you
+are looking for specific structures that
+
+ align:start position:0%
+are looking for specific structures that
+ 
+
+ align:start position:0%
+are looking for specific structures that
+you you learned about when you interact
+
+ align:start position:0%
+you you learned about when you interact
+ 
+
+ align:start position:0%
+you you learned about when you interact
+with these objects before and then you
+
+ align:start position:0%
+with these objects before and then you
+ 
+
+ align:start position:0%
+with these objects before and then you
+test specific things I mean where is the
+
+ align:start position:0%
+test specific things I mean where is the
+ 
+
+ align:start position:0%
+test specific things I mean where is the
+eye this should be a round thing roughly
+
+ align:start position:0%
+eye this should be a round thing roughly
+ 
+
+ align:start position:0%
+eye this should be a round thing roughly
+here and so on and so forth so these are
+
+ align:start position:0%
+here and so on and so forth so these are
+ 
+
+ align:start position:0%
+here and so on and so forth so these are
+more extended routines that you're
+
+ align:start position:0%
+more extended routines that you're
+ 
+
+ align:start position:0%
+more extended routines that you're
+applying to the to the detected to the
+
+ align:start position:0%
+applying to the to the detected to the
+ 
+
+ align:start position:0%
+applying to the to the detected to the
+detected region sort of directed from
+
+ align:start position:0%
+detected region sort of directed from
+ 
+
+ align:start position:0%
+detected region sort of directed from
+above and you know what kind of feature
+
+ align:start position:0%
+above and you know what kind of feature
+ 
+
+ align:start position:0%
+above and you know what kind of feature
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+to look for at different locations with
+
+ align:start position:0%
+to look for at different locations with
+ 
+
+ align:start position:0%
+to look for at different locations with
+India within the minimal image and this
+
+ align:start position:0%
+India within the minimal image and this
+ 
+
+ align:start position:0%
+India within the minimal image and this
+kind of ongoing continuing
+
+ align:start position:0%
+kind of ongoing continuing
+ 
+
+ align:start position:0%
+kind of ongoing continuing
+interpretation is not just inside
+
+ align:start position:0%
+interpretation is not just inside
+ 
+
+ align:start position:0%
+interpretation is not just inside
+internally to the what you succeeded to
+
+ align:start position:0%
+internally to the what you succeeded to
+ 
+
+ align:start position:0%
+internally to the what you succeeded to
+recognize but start to spread over the
+
+ align:start position:0%
+recognize but start to spread over the
+ 
+
+ align:start position:0%
+recognize but start to spread over the
+entire image for example if you look at
+
+ align:start position:0%
+entire image for example if you look at
+ 
+
+ align:start position:0%
+entire image for example if you look at
+this image what do you see here in this
+
+ align:start position:0%
+this image what do you see here in this
+ 
+
+ align:start position:0%
+this image what do you see here in this
+image here anyone want to suggest what
+
+ align:start position:0%
+image here anyone want to suggest what
+ 
+
+ align:start position:0%
+image here anyone want to suggest what
+we see here sorry
+
+ align:start position:0%
+we see here sorry
+ 
+
+ align:start position:0%
+we see here sorry
+women's face what is it one doing
+
+ align:start position:0%
+women's face what is it one doing
+ 
+
+ align:start position:0%
+women's face what is it one doing
+drinking right so it's a woman drinking
+
+ align:start position:0%
+drinking right so it's a woman drinking
+ 
+
+ align:start position:0%
+drinking right so it's a woman drinking
+for those of you managed to recognize
+
+ align:start position:0%
+for those of you managed to recognize
+ 
+
+ align:start position:0%
+for those of you managed to recognize
+this is the woman she's drinking for
+
+ align:start position:0%
+this is the woman she's drinking for
+ 
+
+ align:start position:0%
+this is the woman she's drinking for
+from a cup but we tested e the woman is
+
+ align:start position:0%
+from a cup but we tested e the woman is
+ 
+
+ align:start position:0%
+from a cup but we tested e the woman is
+actually a minimal image it's if you
+
+ align:start position:0%
+actually a minimal image it's if you
+ 
+
+ align:start position:0%
+actually a minimal image it's if you
+remove the cup you show this image
+
+ align:start position:0%
+remove the cup you show this image
+ 
+
+ align:start position:0%
+remove the cup you show this image
+people recognize it at relatively high
+
+ align:start position:0%
+people recognize it at relatively high
+ 
+
+ align:start position:0%
+people recognize it at relatively high
+nobody you recognize this is a glass
+
+ align:start position:0%
+nobody you recognize this is a glass
+ 
+
+ align:start position:0%
+nobody you recognize this is a glass
+when you when you just show the glass on
+
+ align:start position:0%
+when you when you just show the glass on
+ 
+
+ align:start position:0%
+when you when you just show the glass on
+its own we think that you started actual
+
+ align:start position:0%
+its own we think that you started actual
+ 
+
+ align:start position:0%
+its own we think that you started actual
+recognition process in your head starts
+
+ align:start position:0%
+recognition process in your head starts
+ 
+
+ align:start position:0%
+recognition process in your head starts
+with recognizing the what is
+
+ align:start position:0%
+with recognizing the what is
+ 
+
+ align:start position:0%
+with recognizing the what is
+recognizable on its own sort of the
+
+ align:start position:0%
+recognizable on its own sort of the
+ 
+
+ align:start position:0%
+recognizable on its own sort of the
+minimal configuration but you know what
+
+ align:start position:0%
+minimal configuration but you know what
+ 
+
+ align:start position:0%
+minimal configuration but you know what
+it is you don't need help you don't need
+
+ align:start position:0%
+it is you don't need help you don't need
+ 
+
+ align:start position:0%
+it is you don't need help you don't need
+contact you don't need anything this is
+
+ align:start position:0%
+contact you don't need anything this is
+ 
+
+ align:start position:0%
+contact you don't need anything this is
+a woman this is the mouse and you can
+
+ align:start position:0%
+a woman this is the mouse and you can
+ 
+
+ align:start position:0%
+a woman this is the mouse and you can
+continue from there in the same way that
+
+ align:start position:0%
+continue from there in the same way that
+ 
+
+ align:start position:0%
+continue from there in the same way that
+you can recognize internally that this
+
+ align:start position:0%
+you can recognize internally that this
+ 
+
+ align:start position:0%
+you can recognize internally that this
+is the this is the nose and the nostril
+
+ align:start position:0%
+is the this is the nose and the nostril
+ 
+
+ align:start position:0%
+is the this is the nose and the nostril
+and this is the upper lip and lower lip
+
+ align:start position:0%
+and this is the upper lip and lower lip
+ 
+
+ align:start position:0%
+and this is the upper lip and lower lip
+you can in the same way that you can
+
+ align:start position:0%
+you can in the same way that you can
+ 
+
+ align:start position:0%
+you can in the same way that you can
+guide your interpretation process
+
+ align:start position:0%
+guide your interpretation process
+ 
+
+ align:start position:0%
+guide your interpretation process
+internally you can also say that the
+
+ align:start position:0%
+internally you can also say that the
+ 
+
+ align:start position:0%
+internally you can also say that the
+thing which is docked at her mouth is is
+
+ align:start position:0%
+thing which is docked at her mouth is is
+ 
+
+ align:start position:0%
+thing which is docked at her mouth is is
+a glass some results from this is has
+
+ align:start position:0%
+a glass some results from this is has
+ 
+
+ align:start position:0%
+a glass some results from this is has
+been implemented by guide when yourself
+
+ align:start position:0%
+been implemented by guide when yourself
+ 
+
+ align:start position:0%
+been implemented by guide when yourself
+who is also now a part of CBM and this
+
+ align:start position:0%
+who is also now a part of CBM and this
+ 
+
+ align:start position:0%
+who is also now a part of CBM and this
+internal interpretation begins to work
+
+ align:start position:0%
+internal interpretation begins to work
+ 
+
+ align:start position:0%
+internal interpretation begins to work
+interestingly where we started to do it
+
+ align:start position:0%
+interestingly where we started to do it
+ 
+
+ align:start position:0%
+interestingly where we started to do it
+MIT some Meg studies because if this is
+
+ align:start position:0%
+MIT some Meg studies because if this is
+ 
+
+ align:start position:0%
+MIT some Meg studies because if this is
+correct if the interpretation process in
+
+ align:start position:0%
+correct if the interpretation process in
+ 
+
+ align:start position:0%
+correct if the interpretation process in
+the correct recognition of minimal
+
+ align:start position:0%
+the correct recognition of minimal
+ 
+
+ align:start position:0%
+the correct recognition of minimal
+images and the following full
+
+ align:start position:0%
+images and the following full
+ 
+
+ align:start position:0%
+images and the following full
+interpretation process is driven by its
+
+ align:start position:0%
+interpretation process is driven by its
+ 
+
+ align:start position:0%
+interpretation process is driven by its
+requires for completion it requires the
+
+ align:start position:0%
+requires for completion it requires the
+ 
+
+ align:start position:0%
+requires for completion it requires the
+triggering of top-down processing that
+
+ align:start position:0%
+triggering of top-down processing that
+ 
+
+ align:start position:0%
+triggering of top-down processing that
+we could see it in using the right kind
+
+ align:start position:0%
+we could see it in using the right kind
+ 
+
+ align:start position:0%
+we could see it in using the right kind
+of imaging in this case the
+
+ align:start position:0%
+of imaging in this case the
+ 
+
+ align:start position:0%
+of imaging in this case the
+we started to do minimal images in meg
+
+ align:start position:0%
+we started to do minimal images in meg
+ 
+
+ align:start position:0%
+we started to do minimal images in meg
+Meg images with Meg is I think you was
+
+ align:start position:0%
+Meg images with Meg is I think you was
+ 
+
+ align:start position:0%
+Meg images with Meg is I think you was
+make already mentioned here and if the
+
+ align:start position:0%
+make already mentioned here and if the
+ 
+
+ align:start position:0%
+make already mentioned here and if the
+talk so Meg as you know it doesn't have
+
+ align:start position:0%
+talk so Meg as you know it doesn't have
+ 
+
+ align:start position:0%
+talk so Meg as you know it doesn't have
+very good spatial resolution it's not
+
+ align:start position:0%
+very good spatial resolution it's not
+ 
+
+ align:start position:0%
+very good spatial resolution it's not
+like fMRI but it has very good temporal
+
+ align:start position:0%
+like fMRI but it has very good temporal
+ 
+
+ align:start position:0%
+like fMRI but it has very good temporal
+resolution and what Lila was I was led
+
+ align:start position:0%
+resolution and what Lila was I was led
+ 
+
+ align:start position:0%
+resolution and what Lila was I was led
+by by Leila Isaac and what we've done
+
+ align:start position:0%
+by by Leila Isaac and what we've done
+ 
+
+ align:start position:0%
+by by Leila Isaac and what we've done
+here is trying to let subject in the Meg
+
+ align:start position:0%
+here is trying to let subject in the Meg
+ 
+
+ align:start position:0%
+here is trying to let subject in the Meg
+recognize minimal images and we took the
+
+ align:start position:0%
+recognize minimal images and we took the
+ 
+
+ align:start position:0%
+recognize minimal images and we took the
+electrodes from the meg and trained a
+
+ align:start position:0%
+electrodes from the meg and trained a
+ 
+
+ align:start position:0%
+electrodes from the meg and trained a
+decoder the decoder is trained to say
+
+ align:start position:0%
+decoder the decoder is trained to say
+ 
+
+ align:start position:0%
+decoder the decoder is trained to say
+whether or not the image contains say an
+
+ align:start position:0%
+whether or not the image contains say an
+ 
+
+ align:start position:0%
+whether or not the image contains say an
+eagle in this case and we had various
+
+ align:start position:0%
+eagle in this case and we had various
+ 
+
+ align:start position:0%
+eagle in this case and we had various
+images and the question is we can follow
+
+ align:start position:0%
+images and the question is we can follow
+ 
+
+ align:start position:0%
+images and the question is we can follow
+the performance of the computational
+
+ align:start position:0%
+the performance of the computational
+ 
+
+ align:start position:0%
+the performance of the computational
+decoder they tries to say now the image
+
+ align:start position:0%
+decoder they tries to say now the image
+ 
+
+ align:start position:0%
+decoder they tries to say now the image
+now the electrode the pattern of
+
+ align:start position:0%
+now the electrode the pattern of
+ 
+
+ align:start position:0%
+now the electrode the pattern of
+electrodes allow me to deduce that there
+
+ align:start position:0%
+electrodes allow me to deduce that there
+ 
+
+ align:start position:0%
+electrodes allow me to deduce that there
+is an eagle in there in the image and we
+
+ align:start position:0%
+is an eagle in there in the image and we
+ 
+
+ align:start position:0%
+is an eagle in there in the image and we
+see that the decoder is successful you
+
+ align:start position:0%
+see that the decoder is successful you
+ 
+
+ align:start position:0%
+see that the decoder is successful you
+can see about 400 milliseconds this is
+
+ align:start position:0%
+can see about 400 milliseconds this is
+ 
+
+ align:start position:0%
+can see about 400 milliseconds this is
+late for vision the initial bottom-up
+
+ align:start position:0%
+late for vision the initial bottom-up
+ 
+
+ align:start position:0%
+late for vision the initial bottom-up
+initial recognition is more like a
+
+ align:start position:0%
+initial recognition is more like a
+ 
+
+ align:start position:0%
+initial recognition is more like a
+hundred and fifty or something like this
+
+ align:start position:0%
+hundred and fifty or something like this
+ 
+
+ align:start position:0%
+hundred and fifty or something like this
+and we also get the same results when we
+
+ align:start position:0%
+and we also get the same results when we
+ 
+
+ align:start position:0%
+and we also get the same results when we
+do psychophysics that in normal images
+
+ align:start position:0%
+do psychophysics that in normal images
+ 
+
+ align:start position:0%
+do psychophysics that in normal images
+you can recognize them you can get good
+
+ align:start position:0%
+you can recognize them you can get good
+ 
+
+ align:start position:0%
+you can recognize them you can get good
+recognition after exposure of 100
+
+ align:start position:0%
+recognition after exposure of 100
+ 
+
+ align:start position:0%
+recognition after exposure of 100
+milliseconds followed by a mask in to
+
+ align:start position:0%
+milliseconds followed by a mask in to
+ 
+
+ align:start position:0%
+milliseconds followed by a mask in to
+recognize correctly at the human level
+
+ align:start position:0%
+recognize correctly at the human level
+ 
+
+ align:start position:0%
+recognize correctly at the human level
+to get to the human level that we get
+
+ align:start position:0%
+to get to the human level that we get
+ 
+
+ align:start position:0%
+to get to the human level that we get
+with minimal images you have to give
+
+ align:start position:0%
+with minimal images you have to give
+ 
+
+ align:start position:0%
+with minimal images you have to give
+enough time which we suspect that enough
+
+ align:start position:0%
+enough time which we suspect that enough
+ 
+
+ align:start position:0%
+enough time which we suspect that enough
+time is to allow the application of the
+
+ align:start position:0%
+time is to allow the application of the
+ 
+
+ align:start position:0%
+time is to allow the application of the
+top-down interpretation routine and it's
+
+ align:start position:0%
+top-down interpretation routine and it's
+ 
+
+ align:start position:0%
+top-down interpretation routine and it's
+even if you don't give enough time then
+
+ align:start position:0%
+even if you don't give enough time then
+ 
+
+ align:start position:0%
+even if you don't give enough time then
+people that generate and become deep
+
+ align:start position:0%
+people that generate and become deep
+ 
+
+ align:start position:0%
+people that generate and become deep
+networks and you get this the same kind
+
+ align:start position:0%
+networks and you get this the same kind
+ 
+
+ align:start position:0%
+networks and you get this the same kind
+of performance roughly but this is all
+
+ align:start position:0%
+of performance roughly but this is all
+ 
+
+ align:start position:0%
+of performance roughly but this is all
+still unpublished and
+
+ align:start position:0%
+still unpublished and
+ 
+
+ align:start position:0%
+still unpublished and
+still running and we need more subjects
+
+ align:start position:0%
+still running and we need more subjects
+ 
+
+ align:start position:0%
+still running and we need more subjects
+and all of this is looking in the right
+
+ align:start position:0%
+and all of this is looking in the right
+ 
+
+ align:start position:0%
+and all of this is looking in the right
+direction and looking in providing
+
+ align:start position:0%
+direction and looking in providing
+ 
+
+ align:start position:0%
+direction and looking in providing
+support for top-down processing for this
+
+ align:start position:0%
+support for top-down processing for this
+ 
+
+ align:start position:0%
+support for top-down processing for this
+and this by the way for it's interesting
+
+ align:start position:0%
+and this by the way for it's interesting
+ 
+
+ align:start position:0%
+and this by the way for it's interesting
+methodologically because it's very
+
+ align:start position:0%
+methodologically because it's very
+ 
+
+ align:start position:0%
+methodologically because it's very
+difficult with real images it's so rich
+
+ align:start position:0%
+difficult with real images it's so rich
+ 
+
+ align:start position:0%
+difficult with real images it's so rich
+and you get so much information already
+
+ align:start position:0%
+and you get so much information already
+ 
+
+ align:start position:0%
+and you get so much information already
+in the way of going up and because of
+
+ align:start position:0%
+in the way of going up and because of
+ 
+
+ align:start position:0%
+in the way of going up and because of
+this redundancy that even if you make
+
+ align:start position:0%
+this redundancy that even if you make
+ 
+
+ align:start position:0%
+this redundancy that even if you make
+20% arrow it doesn't really matter
+
+ align:start position:0%
+20% arrow it doesn't really matter
+ 
+
+ align:start position:0%
+20% arrow it doesn't really matter
+because you have redundancy many
+
+ align:start position:0%
+because you have redundancy many
+ 
+
+ align:start position:0%
+because you have redundancy many
+multiple sufficient minimal images
+
+ align:start position:0%
+multiple sufficient minimal images
+ 
+
+ align:start position:0%
+multiple sufficient minimal images
+within any object and so on so it's very
+
+ align:start position:0%
+within any object and so on so it's very
+ 
+
+ align:start position:0%
+within any object and so on so it's very
+difficult to tease out the effect of
+
+ align:start position:0%
+difficult to tease out the effect of
+ 
+
+ align:start position:0%
+difficult to tease out the effect of
+where exactly the top-down information
+
+ align:start position:0%
+where exactly the top-down information
+ 
+
+ align:start position:0%
+where exactly the top-down information
+starts what you need it where you where
+
+ align:start position:0%
+starts what you need it where you where
+ 
+
+ align:start position:0%
+starts what you need it where you where
+exactly you fail if you do if you don't
+
+ align:start position:0%
+exactly you fail if you do if you don't
+ 
+
+ align:start position:0%
+exactly you fail if you do if you don't
+have it so we think we you need it for
+
+ align:start position:0%
+have it so we think we you need it for
+ 
+
+ align:start position:0%
+have it so we think we you need it for
+this internal interpretation and for the
+
+ align:start position:0%
+this internal interpretation and for the
+ 
+
+ align:start position:0%
+this internal interpretation and for the
+correct recognition of minimum images
+
+ align:start position:0%
+correct recognition of minimum images
+ 
+
+ align:start position:0%
+correct recognition of minimum images
+and here you can start seeing good
+
+ align:start position:0%
+and here you can start seeing good
+ 
+
+ align:start position:0%
+and here you can start seeing good
+signals in the in the mag it provides
+
+ align:start position:0%
+signals in the in the mag it provides
+ 
+
+ align:start position:0%
+signals in the in the mag it provides
+you sort of a tool that is pretty unique
+
+ align:start position:0%
+you sort of a tool that is pretty unique
+ 
+
+ align:start position:0%
+you sort of a tool that is pretty unique
+and allows you to do to do these things
+
+ align:start position:0%
+and allows you to do to do these things
+ 
+
+ align:start position:0%
+and allows you to do to do these things
+so let me add with very informal thing
+
+ align:start position:0%
+so let me add with very informal thing
+ 
+
+ align:start position:0%
+so let me add with very informal thing
+but where I think this is going I think
+
+ align:start position:0%
+but where I think this is going I think
+ 
+
+ align:start position:0%
+but where I think this is going I think
+that when you look at difficult images
+
+ align:start position:0%
+that when you look at difficult images
+ 
+
+ align:start position:0%
+that when you look at difficult images
+like action recognition which we
+
+ align:start position:0%
+like action recognition which we
+ 
+
+ align:start position:0%
+like action recognition which we
+discussed below many things that we do
+
+ align:start position:0%
+discussed below many things that we do
+ 
+
+ align:start position:0%
+discussed below many things that we do
+depend not on sort of course level label
+
+ align:start position:0%
+depend not on sort of course level label
+ 
+
+ align:start position:0%
+depend not on sort of course level label
+of there is a person there is airplane
+
+ align:start position:0%
+of there is a person there is airplane
+ 
+
+ align:start position:0%
+of there is a person there is airplane
+or is a dog but really things depend on
+
+ align:start position:0%
+or is a dog but really things depend on
+ 
+
+ align:start position:0%
+or is a dog but really things depend on
+they flying details of the internal
+
+ align:start position:0%
+they flying details of the internal
+ 
+
+ align:start position:0%
+they flying details of the internal
+interpretation and so if you can turn
+
+ align:start position:0%
+interpretation and so if you can turn
+ 
+
+ align:start position:0%
+interpretation and so if you can turn
+off the what I think is the top-down
+
+ align:start position:0%
+off the what I think is the top-down
+ 
+
+ align:start position:0%
+off the what I think is the top-down
+part of class specific top-down
+
+ align:start position:0%
+part of class specific top-down
+ 
+
+ align:start position:0%
+part of class specific top-down
+processes I think that many of this fine
+
+ align:start position:0%
+processes I think that many of this fine
+ 
+
+ align:start position:0%
+processes I think that many of this fine
+distinction that we make all the time
+
+ align:start position:0%
+distinction that we make all the time
+ 
+
+ align:start position:0%
+distinction that we make all the time
+and it's what vision is all about vision
+
+ align:start position:0%
+and it's what vision is all about vision
+ 
+
+ align:start position:0%
+and it's what vision is all about vision
+is not about giving course categories
+
+ align:start position:0%
+is not about giving course categories
+ 
+
+ align:start position:0%
+is not about giving course categories
+will go away and so these things will
+
+ align:start position:0%
+will go away and so these things will
+ 
+
+ align:start position:0%
+will go away and so these things will
+become more and more an important part
+
+ align:start position:0%
+become more and more an important part
+ 
+
+ align:start position:0%
+become more and more an important part
+of vision let me look at this
+
+ align:start position:0%
+of vision let me look at this
+ 
+
+ align:start position:0%
+of vision let me look at this
+variability in action recognition but
+
+ align:start position:0%
+variability in action recognition but
+ 
+
+ align:start position:0%
+variability in action recognition but
+let me show you some specific examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is something that confuses current
+
+ align:start position:0%
+this is something that confuses current
+ 
+
+ align:start position:0%
+this is something that confuses current
+classifiers that in both of them it
+
+ align:start position:0%
+classifiers that in both of them it
+ 
+
+ align:start position:0%
+classifiers that in both of them it
+seemed that the person is drinking this
+
+ align:start position:0%
+seemed that the person is drinking this
+ 
+
+ align:start position:0%
+seemed that the person is drinking this
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+because there is you know person there
+
+ align:start position:0%
+because there is you know person there
+ 
+
+ align:start position:0%
+because there is you know person there
+is a bottle and the bottle is close to
+
+ align:start position:0%
+is a bottle and the bottle is close to
+ 
+
+ align:start position:0%
+is a bottle and the bottle is close to
+the to the mouse or the person is
+
+ align:start position:0%
+the to the mouse or the person is
+ 
+
+ align:start position:0%
+the to the mouse or the person is
+drinking at this rough level of
+
+ align:start position:0%
+drinking at this rough level of
+ 
+
+ align:start position:0%
+drinking at this rough level of
+description but obviously you know this
+
+ align:start position:0%
+description but obviously you know this
+ 
+
+ align:start position:0%
+description but obviously you know this
+person is drinking this person is
+
+ align:start position:0%
+person is drinking this person is
+ 
+
+ align:start position:0%
+person is drinking this person is
+pouring right something very is this
+
+ align:start position:0%
+pouring right something very is this
+ 
+
+ align:start position:0%
+pouring right something very is this
+person drinking at the moment yes or no
+
+ align:start position:0%
+person drinking at the moment yes or no
+ 
+
+ align:start position:0%
+person drinking at the moment yes or no
+no why not she is holding a cup and it's
+
+ align:start position:0%
+no why not she is holding a cup and it's
+ 
+
+ align:start position:0%
+no why not she is holding a cup and it's
+not you know maybe on the way to them we
+
+ align:start position:0%
+not you know maybe on the way to them we
+ 
+
+ align:start position:0%
+not you know maybe on the way to them we
+know that she's not drinking right but
+
+ align:start position:0%
+know that she's not drinking right but
+ 
+
+ align:start position:0%
+know that she's not drinking right but
+why exactly not and again this is
+
+ align:start position:0%
+why exactly not and again this is
+ 
+
+ align:start position:0%
+why exactly not and again this is
+something that is picked up with
+
+ align:start position:0%
+something that is picked up with
+ 
+
+ align:start position:0%
+something that is picked up with
+drinking by many recognition system but
+
+ align:start position:0%
+drinking by many recognition system but
+ 
+
+ align:start position:0%
+drinking by many recognition system but
+it's something is wrong here
+
+ align:start position:0%
+it's something is wrong here
+ 
+
+ align:start position:0%
+it's something is wrong here
+all of these things these are different
+
+ align:start position:0%
+all of these things these are different
+ 
+
+ align:start position:0%
+all of these things these are different
+objects and different actions that the
+
+ align:start position:0%
+objects and different actions that the
+ 
+
+ align:start position:0%
+objects and different actions that the
+people are performing this is drinking
+
+ align:start position:0%
+people are performing this is drinking
+ 
+
+ align:start position:0%
+people are performing this is drinking
+from a straw this is smoking and this is
+
+ align:start position:0%
+from a straw this is smoking and this is
+ 
+
+ align:start position:0%
+from a straw this is smoking and this is
+brushing their teeth but this depends on
+
+ align:start position:0%
+brushing their teeth but this depends on
+ 
+
+ align:start position:0%
+brushing their teeth but this depends on
+you know you have to go to the right
+
+ align:start position:0%
+you know you have to go to the right
+ 
+
+ align:start position:0%
+you know you have to go to the right
+location and decide exactly what's
+
+ align:start position:0%
+location and decide exactly what's
+ 
+
+ align:start position:0%
+location and decide exactly what's
+happening there it's the kind of thing
+
+ align:start position:0%
+happening there it's the kind of thing
+ 
+
+ align:start position:0%
+happening there it's the kind of thing
+that we do all the time some more
+
+ align:start position:0%
+that we do all the time some more
+ 
+
+ align:start position:0%
+that we do all the time some more
+challenges this is just sort of informal
+
+ align:start position:0%
+challenges this is just sort of informal
+ 
+
+ align:start position:0%
+challenges this is just sort of informal
+challenges to show you how we can deal
+
+ align:start position:0%
+challenges to show you how we can deal
+ 
+
+ align:start position:0%
+challenges to show you how we can deal
+with fine interpretation of details of
+
+ align:start position:0%
+with fine interpretation of details of
+ 
+
+ align:start position:0%
+with fine interpretation of details of
+interest in the image what is this arrow
+
+ align:start position:0%
+interest in the image what is this arrow
+ 
+
+ align:start position:0%
+interest in the image what is this arrow
+point pointing at sorry yeah but above
+
+ align:start position:0%
+point pointing at sorry yeah but above
+ 
+
+ align:start position:0%
+point pointing at sorry yeah but above
+the bottle there is something else there
+
+ align:start position:0%
+the bottle there is something else there
+ 
+
+ align:start position:0%
+the bottle there is something else there
+sorry fingers right let's see just what
+
+ align:start position:0%
+sorry fingers right let's see just what
+ 
+
+ align:start position:0%
+sorry fingers right let's see just what
+is this arrow pointing it zipper let's
+
+ align:start position:0%
+is this arrow pointing it zipper let's
+ 
+
+ align:start position:0%
+is this arrow pointing it zipper let's
+see this is your two challenging things
+
+ align:start position:0%
+see this is your two challenging things
+ 
+
+ align:start position:0%
+see this is your two challenging things
+you are - what what is this one pointing
+
+ align:start position:0%
+you are - what what is this one pointing
+ 
+
+ align:start position:0%
+you are - what what is this one pointing
+it alright not next to the cup right
+
+ align:start position:0%
+it alright not next to the cup right
+ 
+
+ align:start position:0%
+it alright not next to the cup right
+it's also this is really challenging
+
+ align:start position:0%
+it's also this is really challenging
+ 
+
+ align:start position:0%
+it's also this is really challenging
+let's see what is this one pointing at
+
+ align:start position:0%
+let's see what is this one pointing at
+ 
+
+ align:start position:0%
+let's see what is this one pointing at
+tray not really so the trace think about
+
+ align:start position:0%
+tray not really so the trace think about
+ 
+
+ align:start position:0%
+tray not really so the trace think about
+it this but you match it with this thing
+
+ align:start position:0%
+it this but you match it with this thing
+ 
+
+ align:start position:0%
+it this but you match it with this thing
+here in order to make sure to know that
+
+ align:start position:0%
+here in order to make sure to know that
+ 
+
+ align:start position:0%
+here in order to make sure to know that
+it's it's a tray it's not something that
+
+ align:start position:0%
+it's it's a tray it's not something that
+ 
+
+ align:start position:0%
+it's it's a tray it's not something that
+will be easily picked up but I mean I'm
+
+ align:start position:0%
+will be easily picked up but I mean I'm
+ 
+
+ align:start position:0%
+will be easily picked up but I mean I'm
+looking for difficult things which are a
+
+ align:start position:0%
+looking for difficult things which are a
+ 
+
+ align:start position:0%
+looking for difficult things which are a
+little bit challenging and you say oh I
+
+ align:start position:0%
+little bit challenging and you say oh I
+ 
+
+ align:start position:0%
+little bit challenging and you say oh I
+can get it but it's in this level of
+
+ align:start position:0%
+can get it but it's in this level of
+ 
+
+ align:start position:0%
+can get it but it's in this level of
+detail interpreting the fine details in
+
+ align:start position:0%
+detail interpreting the fine details in
+ 
+
+ align:start position:0%
+detail interpreting the fine details in
+images in a top-down fashion happens all
+
+ align:start position:0%
+images in a top-down fashion happens all
+ 
+
+ align:start position:0%
+images in a top-down fashion happens all
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+this person smoking of course not and we
+
+ align:start position:0%
+this person smoking of course not and we
+ 
+
+ align:start position:0%
+this person smoking of course not and we
+are not fooled by it and we immediately
+
+ align:start position:0%
+are not fooled by it and we immediately
+ 
+
+ align:start position:0%
+are not fooled by it and we immediately
+zoom on the right things and it's really
+
+ align:start position:0%
+zoom on the right things and it's really
+ 
+
+ align:start position:0%
+zoom on the right things and it's really
+all the information is here at the end
+
+ align:start position:0%
+all the information is here at the end
+ 
+
+ align:start position:0%
+all the information is here at the end
+so in so on zone and so forth I mean we
+
+ align:start position:0%
+so in so on zone and so forth I mean we
+ 
+
+ align:start position:0%
+so in so on zone and so forth I mean we
+were looking at dealing visually with
+
+ align:start position:0%
+were looking at dealing visually with
+ 
+
+ align:start position:0%
+were looking at dealing visually with
+social interactions understanding the
+
+ align:start position:0%
+social interactions understanding the
+ 
+
+ align:start position:0%
+social interactions understanding the
+social interactions between agents in
+
+ align:start position:0%
+social interactions between agents in
+ 
+
+ align:start position:0%
+social interactions between agents in
+there and again it's very difficult to
+
+ align:start position:0%
+there and again it's very difficult to
+ 
+
+ align:start position:0%
+there and again it's very difficult to
+do correctly and it depends on subtle
+
+ align:start position:0%
+do correctly and it depends on subtle
+ 
+
+ align:start position:0%
+do correctly and it depends on subtle
+subtle things I mean you can get
+
+ align:start position:0%
+subtle things I mean you can get
+ 
+
+ align:start position:0%
+subtle things I mean you can get
+something rough okay but for example is
+
+ align:start position:0%
+something rough okay but for example is
+ 
+
+ align:start position:0%
+something rough okay but for example is
+this sort of an intimate hug or is this
+
+ align:start position:0%
+this sort of an intimate hug or is this
+ 
+
+ align:start position:0%
+this sort of an intimate hug or is this
+just cordial hug of people who are not
+
+ align:start position:0%
+just cordial hug of people who are not
+ 
+
+ align:start position:0%
+just cordial hug of people who are not
+we know exactly what's going on right
+
+ align:start position:0%
+we know exactly what's going on right
+ 
+
+ align:start position:0%
+we know exactly what's going on right
+and it turns out that the features are
+
+ align:start position:0%
+and it turns out that the features are
+ 
+
+ align:start position:0%
+and it turns out that the features are
+not that easy to get this was picked up
+
+ align:start position:0%
+not that easy to get this was picked up
+ 
+
+ align:start position:0%
+not that easy to get this was picked up
+incorrectly by something that we
+
+ align:start position:0%
+incorrectly by something that we
+ 
+
+ align:start position:0%
+incorrectly by something that we
+designed for people hugging and it's not
+
+ align:start position:0%
+designed for people hugging and it's not
+ 
+
+ align:start position:0%
+designed for people hugging and it's not
+very far from people hugging but it
+
+ align:start position:0%
+very far from people hugging but it
+ 
+
+ align:start position:0%
+very far from people hugging but it
+doesn't fool doesn't fool us right I'm
+
+ align:start position:0%
+doesn't fool doesn't fool us right I'm
+ 
+
+ align:start position:0%
+doesn't fool doesn't fool us right I'm
+not not really hugging on social
+
+ align:start position:0%
+not not really hugging on social
+ 
+
+ align:start position:0%
+not not really hugging on social
+interaction we know interactions even
+
+ align:start position:0%
+interaction we know interactions even
+ 
+
+ align:start position:0%
+interaction we know interactions even
+between non-human agents I mean this
+
+ align:start position:0%
+between non-human agents I mean this
+ 
+
+ align:start position:0%
+between non-human agents I mean this
+interaction is this is threatening
+
+ align:start position:0%
+interaction is this is threatening
+ 
+
+ align:start position:0%
+interaction is this is threatening
+interaction or friendly interaction what
+
+ align:start position:0%
+interaction or friendly interaction what
+ 
+
+ align:start position:0%
+interaction or friendly interaction what
+do you think right I think anyway I
+
+ align:start position:0%
+do you think right I think anyway I
+ 
+
+ align:start position:0%
+do you think right I think anyway I
+think that all of this thing that we can
+
+ align:start position:0%
+think that all of this thing that we can
+ 
+
+ align:start position:0%
+think that all of this thing that we can
+do and I think that vision is about this
+
+ align:start position:0%
+do and I think that vision is about this
+ 
+
+ align:start position:0%
+do and I think that vision is about this
+it's not about looking at this room and
+
+ align:start position:0%
+it's not about looking at this room and
+ 
+
+ align:start position:0%
+it's not about looking at this room and
+saying that this is a computer and this
+
+ align:start position:0%
+saying that this is a computer and this
+ 
+
+ align:start position:0%
+saying that this is a computer and this
+is a chair it's about understanding the
+
+ align:start position:0%
+is a chair it's about understanding the
+ 
+
+ align:start position:0%
+is a chair it's about understanding the
+situation and making fine judgments and
+
+ align:start position:0%
+situation and making fine judgments and
+ 
+
+ align:start position:0%
+situation and making fine judgments and
+interacting with objects and in fact we
+
+ align:start position:0%
+interacting with objects and in fact we
+ 
+
+ align:start position:0%
+interacting with objects and in fact we
+are looking at the past part of doing
+
+ align:start position:0%
+are looking at the past part of doing
+ 
+
+ align:start position:0%
+are looking at the past part of doing
+CBMM we are looking at the problem of
+
+ align:start position:0%
+CBMM we are looking at the problem of
+ 
+
+ align:start position:0%
+CBMM we are looking at the problem of
+asking questions about images so we want
+
+ align:start position:0%
+asking questions about images so we want
+ 
+
+ align:start position:0%
+asking questions about images so we want
+a system that you can give it an image
+
+ align:start position:0%
+a system that you can give it an image
+ 
+
+ align:start position:0%
+a system that you can give it an image
+in a question and then we want the
+
+ align:start position:0%
+in a question and then we want the
+ 
+
+ align:start position:0%
+in a question and then we want the
+system to be able to process the image
+
+ align:start position:0%
+system to be able to process the image
+ 
+
+ align:start position:0%
+system to be able to process the image
+in such a way that will give you a good
+
+ align:start position:0%
+in such a way that will give you a good
+ 
+
+ align:start position:0%
+in such a way that will give you a good
+answer to the question and this is
+
+ align:start position:0%
+answer to the question and this is
+ 
+
+ align:start position:0%
+answer to the question and this is
+interesting because it means that it's
+
+ align:start position:0%
+interesting because it means that it's
+ 
+
+ align:start position:0%
+interesting because it means that it's
+not just a generic pipeline of running
+
+ align:start position:0%
+not just a generic pipeline of running
+ 
+
+ align:start position:0%
+not just a generic pipeline of running
+the imagery pipeline sort of fixed
+
+ align:start position:0%
+the imagery pipeline sort of fixed
+ 
+
+ align:start position:0%
+the imagery pipeline sort of fixed
+sequence of operations but depending on
+
+ align:start position:0%
+sequence of operations but depending on
+ 
+
+ align:start position:0%
+sequence of operations but depending on
+what you're interested in the whole
+
+ align:start position:0%
+what you're interested in the whole
+ 
+
+ align:start position:0%
+what you're interested in the whole
+visual process should be directed in a
+
+ align:start position:0%
+visual process should be directed in a
+ 
+
+ align:start position:0%
+visual process should be directed in a
+particular way to produce just the
+
+ align:start position:0%
+particular way to produce just the
+ 
+
+ align:start position:0%
+particular way to produce just the
+relevant answer and we looked at it set
+
+ align:start position:0%
+relevant answer and we looked at it set
+ 
+
+ align:start position:0%
+relevant answer and we looked at it set
+of with the student we looked at a set
+
+ align:start position:0%
+of with the student we looked at a set
+ 
+
+ align:start position:0%
+of with the student we looked at a set
+of some 600 question that we gave people
+
+ align:start position:0%
+of some 600 question that we gave people
+ 
+
+ align:start position:0%
+of some 600 question that we gave people
+on the mechanical torque images and they
+
+ align:start position:0%
+on the mechanical torque images and they
+ 
+
+ align:start position:0%
+on the mechanical torque images and they
+say imagine some questions about the
+
+ align:start position:0%
+say imagine some questions about the
+ 
+
+ align:start position:0%
+say imagine some questions about the
+images asked some question about these
+
+ align:start position:0%
+images asked some question about these
+ 
+
+ align:start position:0%
+images asked some question about these
+images and they came up with some images
+
+ align:start position:0%
+images and they came up with some images
+ 
+
+ align:start position:0%
+images and they came up with some images
+we looked at them in an informal
+
+ align:start position:0%
+we looked at them in an informal
+ 
+
+ align:start position:0%
+we looked at them in an informal
+observation initial observation is that
+
+ align:start position:0%
+observation initial observation is that
+ 
+
+ align:start position:0%
+observation initial observation is that
+most of this question that people
+
+ align:start position:0%
+most of this question that people
+ 
+
+ align:start position:0%
+most of this question that people
+invented to ask about images you needed
+
+ align:start position:0%
+invented to ask about images you needed
+ 
+
+ align:start position:0%
+invented to ask about images you needed
+some things which depended on precise
+
+ align:start position:0%
+some things which depended on precise
+ 
+
+ align:start position:0%
+some things which depended on precise
+internal interpretation of the details
+
+ align:start position:0%
+internal interpretation of the details
+ 
+
+ align:start position:0%
+internal interpretation of the details
+so it's saying it's things that come up
+
+ align:start position:0%
+so it's saying it's things that come up
+ 
+
+ align:start position:0%
+so it's saying it's things that come up
+all the time you have to dive into the
+
+ align:start position:0%
+all the time you have to dive into the
+ 
+
+ align:start position:0%
+all the time you have to dive into the
+image and analyze the subtle cues that
+
+ align:start position:0%
+image and analyze the subtle cues that
+ 
+
+ align:start position:0%
+image and analyze the subtle cues that
+will tell you that these are not hugging
+
+ align:start position:0%
+will tell you that these are not hugging
+ 
+
+ align:start position:0%
+will tell you that these are not hugging
+and this is not threatening and this is
+
+ align:start position:0%
+and this is not threatening and this is
+ 
+
+ align:start position:0%
+and this is not threatening and this is
+not an intimate hug and so on and so
+
+ align:start position:0%
+not an intimate hug and so on and so
+ 
+
+ align:start position:0%
+not an intimate hug and so on and so
+forth and this is what we are the whole
+
+ align:start position:0%
+forth and this is what we are the whole
+ 
+
+ align:start position:0%
+forth and this is what we are the whole
+story of the minimal images and internal
+
+ align:start position:0%
+story of the minimal images and internal
+ 
+
+ align:start position:0%
+story of the minimal images and internal
+interpretation is the the real goal
+
+ align:start position:0%
+interpretation is the the real goal
+ 
+
+ align:start position:0%
+interpretation is the the real goal
+eventually is to be able to identify the
+
+ align:start position:0%
+eventually is to be able to identify the
+ 
+
+ align:start position:0%
+eventually is to be able to identify the
+important visual features and structures
+
+ align:start position:0%
+important visual features and structures
+ 
+
+ align:start position:0%
+important visual features and structures
+which are important for this and
+
+ align:start position:0%
+which are important for this and
+ 
+
+ align:start position:0%
+which are important for this and
+thinking about the automatic learning of
+
+ align:start position:0%
+thinking about the automatic learning of
+ 
+
+ align:start position:0%
+thinking about the automatic learning of
+the how to extract the internal
+
+ align:start position:0%
+the how to extract the internal
+ 
+
+ align:start position:0%
+the how to extract the internal
+structure that will be support the
+
+ align:start position:0%
+structure that will be support the
+ 
+
+ align:start position:0%
+structure that will be support the
+interpretation of all these interesting
+
+ align:start position:0%
+interpretation of all these interesting
+ 
+
+ align:start position:0%
+interpretation of all these interesting
+and meaningful aspects of images that at
+
+ align:start position:0%
+and meaningful aspects of images that at
+ 
+
+ align:start position:0%
+and meaningful aspects of images that at
+the moment we do not have okay I think
+
+ align:start position:0%
+the moment we do not have okay I think
+ 
+
+ align:start position:0%
+the moment we do not have okay I think
+I've said I've said all of all of these
+
+ align:start position:0%
+I've said I've said all of all of these
+ 
+
+ align:start position:0%
+I've said I've said all of all of these
+conclusions already in the final comment
+
+ align:start position:0%
+conclusions already in the final comment
+ 
+
+ align:start position:0%
+conclusions already in the final comment
+so let me stop here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/Y9Awwqqc288.txt b/Y9Awwqqc288.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bee04f940323ee2d1f8b376eed2bbf0fe8b4c064
--- /dev/null
+++ b/Y9Awwqqc288.txt
@@ -0,0 +1,7008 @@
+align:start position:0%
+ 
+good okay so last time right at the end
+
+ align:start position:0%
+good okay so last time right at the end
+ 
+
+ align:start position:0%
+good okay so last time right at the end
+of the lecture I had um introduced a
+
+ align:start position:0%
+of the lecture I had um introduced a
+ 
+
+ align:start position:0%
+of the lecture I had um introduced a
+more General linear model the
+
+ align:start position:0%
+more General linear model the
+ 
+
+ align:start position:0%
+more General linear model the
+multivariant um linear model okay and I
+
+ align:start position:0%
+multivariant um linear model okay and I
+ 
+
+ align:start position:0%
+multivariant um linear model okay and I
+had just um gone through the first
+
+ align:start position:0%
+had just um gone through the first
+ 
+
+ align:start position:0%
+had just um gone through the first
+couple of these slides SL saying let's
+
+ align:start position:0%
+couple of these slides SL saying let's
+ 
+
+ align:start position:0%
+couple of these slides SL saying let's
+uh let's sort of analyze this model
+
+ align:start position:0%
+uh let's sort of analyze this model
+ 
+
+ align:start position:0%
+uh let's sort of analyze this model
+using a different notation in particular
+
+ align:start position:0%
+using a different notation in particular
+ 
+
+ align:start position:0%
+using a different notation in particular
+Matrix notation uh because the sort of
+
+ align:start position:0%
+Matrix notation uh because the sort of
+ 
+
+ align:start position:0%
+Matrix notation uh because the sort of
+summation notation was just too clunky
+
+ align:start position:0%
+summation notation was just too clunky
+ 
+
+ align:start position:0%
+summation notation was just too clunky
+it wasn't up for the job um and so let
+
+ align:start position:0%
+it wasn't up for the job um and so let
+ 
+
+ align:start position:0%
+it wasn't up for the job um and so let
+me just go through
+
+ align:start position:0%
+me just go through
+ 
+
+ align:start position:0%
+me just go through
+quickly let's see this was I think the
+
+ align:start position:0%
+quickly let's see this was I think the
+ 
+
+ align:start position:0%
+quickly let's see this was I think the
+next to last slide I had up um so if we
+
+ align:start position:0%
+next to last slide I had up um so if we
+ 
+
+ align:start position:0%
+next to last slide I had up um so if we
+let uh y be the column Vector of all of
+
+ align:start position:0%
+let uh y be the column Vector of all of
+ 
+
+ align:start position:0%
+let uh y be the column Vector of all of
+the object observations on the dependent
+
+ align:start position:0%
+the object observations on the dependent
+ 
+
+ align:start position:0%
+the object observations on the dependent
+variable then let uh Epsilon be the
+
+ align:start position:0%
+variable then let uh Epsilon be the
+ 
+
+ align:start position:0%
+variable then let uh Epsilon be the
+column Vector of all of the errors and
+
+ align:start position:0%
+column Vector of all of the errors and
+ 
+
+ align:start position:0%
+column Vector of all of the errors and
+then let X be the Matrix where across
+
+ align:start position:0%
+then let X be the Matrix where across
+ 
+
+ align:start position:0%
+then let X be the Matrix where across
+the rows of the Matrix we have uh all of
+
+ align:start position:0%
+the rows of the Matrix we have uh all of
+ 
+
+ align:start position:0%
+the rows of the Matrix we have uh all of
+the the uh first a column of ones and
+
+ align:start position:0%
+the the uh first a column of ones and
+ 
+
+ align:start position:0%
+the the uh first a column of ones and
+then a column of each of the um the
+
+ align:start position:0%
+then a column of each of the um the
+ 
+
+ align:start position:0%
+then a column of each of the um the
+explanatory variables and then sort of
+
+ align:start position:0%
+explanatory variables and then sort of
+ 
+
+ align:start position:0%
+explanatory variables and then sort of
+down uh you know sort of uh Down The
+
+ align:start position:0%
+down uh you know sort of uh Down The
+ 
+
+ align:start position:0%
+down uh you know sort of uh Down The
+Matrix we have uh observations on each
+
+ align:start position:0%
+Matrix we have uh observations on each
+ 
+
+ align:start position:0%
+Matrix we have uh observations on each
+of the well we have each of the
+
+ align:start position:0%
+of the well we have each of the
+ 
+
+ align:start position:0%
+of the well we have each of the
+observations each observation
+
+ align:start position:0%
+observations each observation
+ 
+
+ align:start position:0%
+observations each observation
+corresponds to a row so if we Define uh
+
+ align:start position:0%
+corresponds to a row so if we Define uh
+ 
+
+ align:start position:0%
+corresponds to a row so if we Define uh
+these this Matrix and vectors this way
+
+ align:start position:0%
+these this Matrix and vectors this way
+ 
+
+ align:start position:0%
+these this Matrix and vectors this way
+uh then we can write our
+
+ align:start position:0%
+uh then we can write our
+ 
+
+ align:start position:0%
+uh then we can write our
+multivariate linear model in the
+
+ align:start position:0%
+multivariate linear model in the
+ 
+
+ align:start position:0%
+multivariate linear model in the
+following very parsimonious fashion y
+
+ align:start position:0%
+following very parsimonious fashion y
+ 
+
+ align:start position:0%
+following very parsimonious fashion y
+equal x beta plus Epsilon
+
+ align:start position:0%
+equal x beta plus Epsilon
+ 
+
+ align:start position:0%
+equal x beta plus Epsilon
+okay okay so now um we have
+
+ align:start position:0%
+okay okay so now um we have
+ 
+
+ align:start position:0%
+okay okay so now um we have
+uh the we're we're B I'm basically going
+
+ align:start position:0%
+uh the we're we're B I'm basically going
+ 
+
+ align:start position:0%
+uh the we're we're B I'm basically going
+to go through the same assumptions but
+
+ align:start position:0%
+to go through the same assumptions but
+ 
+
+ align:start position:0%
+to go through the same assumptions but
+in a slightly more General way from uh
+
+ align:start position:0%
+in a slightly more General way from uh
+ 
+
+ align:start position:0%
+in a slightly more General way from uh
+when I discussed assumptions in the B
+
+ align:start position:0%
+when I discussed assumptions in the B
+ 
+
+ align:start position:0%
+when I discussed assumptions in the B
+variant model the assumptions have to be
+
+ align:start position:0%
+variant model the assumptions have to be
+ 
+
+ align:start position:0%
+variant model the assumptions have to be
+discussed in a more General way now
+
+ align:start position:0%
+discussed in a more General way now
+ 
+
+ align:start position:0%
+discussed in a more General way now
+because actually they're a little bit
+
+ align:start position:0%
+because actually they're a little bit
+ 
+
+ align:start position:0%
+because actually they're a little bit
+more complicated with the
+
+ align:start position:0%
+more complicated with the
+ 
+
+ align:start position:0%
+more complicated with the
+multivariate um the multivariate model
+
+ align:start position:0%
+multivariate um the multivariate model
+ 
+
+ align:start position:0%
+multivariate um the multivariate model
+okay so uh I'm going to condense all of
+
+ align:start position:0%
+okay so uh I'm going to condense all of
+ 
+
+ align:start position:0%
+okay so uh I'm going to condense all of
+the assumptions into two basic
+
+ align:start position:0%
+the assumptions into two basic
+ 
+
+ align:start position:0%
+the assumptions into two basic
+categories one is the identification
+
+ align:start position:0%
+categories one is the identification
+ 
+
+ align:start position:0%
+categories one is the identification
+assumptions and two is the assumptions
+
+ align:start position:0%
+assumptions and two is the assumptions
+ 
+
+ align:start position:0%
+assumptions and two is the assumptions
+in the error Behavior okay so in the
+
+ align:start position:0%
+in the error Behavior okay so in the
+ 
+
+ align:start position:0%
+in the error Behavior okay so in the
+multivariate linear model in order to
+
+ align:start position:0%
+multivariate linear model in order to
+ 
+
+ align:start position:0%
+multivariate linear model in order to
+have identification in order to be able
+
+ align:start position:0%
+have identification in order to be able
+ 
+
+ align:start position:0%
+have identification in order to be able
+to estimate our model we have to have n
+
+ align:start position:0%
+to estimate our model we have to have n
+ 
+
+ align:start position:0%
+to estimate our model we have to have n
+greater than k+ one that just means we
+
+ align:start position:0%
+greater than k+ one that just means we
+ 
+
+ align:start position:0%
+greater than k+ one that just means we
+have to have more observations than we
+
+ align:start position:0%
+have to have more observations than we
+ 
+
+ align:start position:0%
+have to have more observations than we
+have uh explanatory
+
+ align:start position:0%
+have uh explanatory
+ 
+
+ align:start position:0%
+have uh explanatory
+variables plus one
+
+ align:start position:0%
+variables plus one
+ 
+
+ align:start position:0%
+variables plus one
+okay and uh X has to have full column
+
+ align:start position:0%
+okay and uh X has to have full column
+ 
+
+ align:start position:0%
+okay and uh X has to have full column
+rank
+
+ align:start position:0%
+rank
+ 
+
+ align:start position:0%
+rank
+of k +
+
+ align:start position:0%
+of k +
+ 
+
+ align:start position:0%
+of k +
+1 and what does that mean in other words
+
+ align:start position:0%
+1 and what does that mean in other words
+ 
+
+ align:start position:0%
+1 and what does that mean in other words
+means that the regressors have to be
+
+ align:start position:0%
+means that the regressors have to be
+ 
+
+ align:start position:0%
+means that the regressors have to be
+linearly independent or another way of
+
+ align:start position:0%
+linearly independent or another way of
+ 
+
+ align:start position:0%
+linearly independent or another way of
+saying this is that the Matrix X prime
+
+ align:start position:0%
+saying this is that the Matrix X prime
+ 
+
+ align:start position:0%
+saying this is that the Matrix X prime
+or X transpose X is invertible okay I'm
+
+ align:start position:0%
+or X transpose X is invertible okay I'm
+ 
+
+ align:start position:0%
+or X transpose X is invertible okay I'm
+going to go through this in some more
+
+ align:start position:0%
+going to go through this in some more
+ 
+
+ align:start position:0%
+going to go through this in some more
+detail in just a
+
+ align:start position:0%
+detail in just a
+ 
+
+ align:start position:0%
+detail in just a
+second and then the second main
+
+ align:start position:0%
+second and then the second main
+ 
+
+ align:start position:0%
+second and then the second main
+assumption or main category of
+
+ align:start position:0%
+assumption or main category of
+ 
+
+ align:start position:0%
+assumption or main category of
+assumptions on the error behavior and
+
+ align:start position:0%
+assumptions on the error behavior and
+ 
+
+ align:start position:0%
+assumptions on the error behavior and
+these actually are exactly like the
+
+ align:start position:0%
+these actually are exactly like the
+ 
+
+ align:start position:0%
+these actually are exactly like the
+assumptions we saw before just using
+
+ align:start position:0%
+assumptions we saw before just using
+ 
+
+ align:start position:0%
+assumptions we saw before just using
+Matrix notation to to express them so
+
+ align:start position:0%
+Matrix notation to to express them so
+ 
+
+ align:start position:0%
+Matrix notation to to express them so
+here we have the expectation of Epsilon
+
+ align:start position:0%
+here we have the expectation of Epsilon
+ 
+
+ align:start position:0%
+here we have the expectation of Epsilon
+here Epsilon is a vector and that's the
+
+ align:start position:0%
+here Epsilon is a vector and that's the
+ 
+
+ align:start position:0%
+here Epsilon is a vector and that's the
+vector of zeros okay the expectation of
+
+ align:start position:0%
+vector of zeros okay the expectation of
+ 
+
+ align:start position:0%
+vector of zeros okay the expectation of
+Epsilon Epsilon transpose is equal to
+
+ align:start position:0%
+Epsilon Epsilon transpose is equal to
+ 
+
+ align:start position:0%
+Epsilon Epsilon transpose is equal to
+Sigma squar times the N byn identity
+
+ align:start position:0%
+Sigma squar times the N byn identity
+ 
+
+ align:start position:0%
+Sigma squar times the N byn identity
+Matrix okay and this is in fact this
+
+ align:start position:0%
+Matrix okay and this is in fact this
+ 
+
+ align:start position:0%
+Matrix okay and this is in fact this
+Matrix here is in fact just the Matrix
+
+ align:start position:0%
+Matrix here is in fact just the Matrix
+ 
+
+ align:start position:0%
+Matrix here is in fact just the Matrix
+uh that we denote co uh Co covariance of
+
+ align:start position:0%
+uh that we denote co uh Co covariance of
+ 
+
+ align:start position:0%
+uh that we denote co uh Co covariance of
+Epsilon which is I'll show you a picture
+
+ align:start position:0%
+Epsilon which is I'll show you a picture
+ 
+
+ align:start position:0%
+Epsilon which is I'll show you a picture
+of it in a second it's just a matrix
+
+ align:start position:0%
+of it in a second it's just a matrix
+ 
+
+ align:start position:0%
+of it in a second it's just a matrix
+that has the variances of Epsilon along
+
+ align:start position:0%
+that has the variances of Epsilon along
+ 
+
+ align:start position:0%
+that has the variances of Epsilon along
+the diagonal and the co-variances on the
+
+ align:start position:0%
+the diagonal and the co-variances on the
+ 
+
+ align:start position:0%
+the diagonal and the co-variances on the
+off diagonal okay and so what we're
+
+ align:start position:0%
+off diagonal okay and so what we're
+ 
+
+ align:start position:0%
+off diagonal okay and so what we're
+saying here is that the the diagonal is
+
+ align:start position:0%
+saying here is that the the diagonal is
+ 
+
+ align:start position:0%
+saying here is that the the diagonal is
+equal to Sigma
+
+ align:start position:0%
+equal to Sigma
+ 
+
+ align:start position:0%
+equal to Sigma
+squar okay and the off diagonals are
+
+ align:start position:0%
+squar okay and the off diagonals are
+ 
+
+ align:start position:0%
+squar okay and the off diagonals are
+zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a stronger version of this is that
+
+ align:start position:0%
+and a stronger version of this is that
+ 
+
+ align:start position:0%
+and a stronger version of this is that
+Epsilon uh the Epsilon Vector has this
+
+ align:start position:0%
+Epsilon uh the Epsilon Vector has this
+ 
+
+ align:start position:0%
+Epsilon uh the Epsilon Vector has this
+normal this multivariant normal
+
+ align:start position:0%
+normal this multivariant normal
+ 
+
+ align:start position:0%
+normal this multivariant normal
+distribution with this variance
+
+ align:start position:0%
+distribution with this variance
+ 
+
+ align:start position:0%
+distribution with this variance
+covariance
+
+ align:start position:0%
+covariance
+ 
+
+ align:start position:0%
+covariance
+Matrix okay I I'll go into more detail
+
+ align:start position:0%
+Matrix okay I I'll go into more detail
+ 
+
+ align:start position:0%
+Matrix okay I I'll go into more detail
+of in both of these in just a second
+
+ align:start position:0%
+of in both of these in just a second
+ 
+
+ align:start position:0%
+of in both of these in just a second
+okay so let's do the oh n by n identity
+
+ align:start position:0%
+okay so let's do the oh n by n identity
+ 
+
+ align:start position:0%
+okay so let's do the oh n by n identity
+Matrix okay so let's take a closer look
+
+ align:start position:0%
+Matrix okay so let's take a closer look
+ 
+
+ align:start position:0%
+Matrix okay so let's take a closer look
+at these assumptions so assumption one
+
+ align:start position:0%
+at these assumptions so assumption one
+ 
+
+ align:start position:0%
+at these assumptions so assumption one
+the identification assumption um what
+
+ align:start position:0%
+the identification assumption um what
+ 
+
+ align:start position:0%
+the identification assumption um what
+exactly does this mean well we need to
+
+ align:start position:0%
+exactly does this mean well we need to
+ 
+
+ align:start position:0%
+exactly does this mean well we need to
+have more observations than regressors
+
+ align:start position:0%
+have more observations than regressors
+ 
+
+ align:start position:0%
+have more observations than regressors
+that shouldn't come as a surprise
+
+ align:start position:0%
+that shouldn't come as a surprise
+ 
+
+ align:start position:0%
+that shouldn't come as a surprise
+especially if we think about the B
+
+ align:start position:0%
+especially if we think about the B
+ 
+
+ align:start position:0%
+especially if we think about the B
+variant model um you know we have one
+
+ align:start position:0%
+variant model um you know we have one
+ 
+
+ align:start position:0%
+variant model um you know we have one
+regressor you have to have at least two
+
+ align:start position:0%
+regressor you have to have at least two
+ 
+
+ align:start position:0%
+regressor you have to have at least two
+observations or else you can't draw a
+
+ align:start position:0%
+observations or else you can't draw a
+ 
+
+ align:start position:0%
+observations or else you can't draw a
+line okay so this just sort of
+
+ align:start position:0%
+line okay so this just sort of
+ 
+
+ align:start position:0%
+line okay so this just sort of
+generalizes that to to higher Dimensions
+
+ align:start position:0%
+generalizes that to to higher Dimensions
+ 
+
+ align:start position:0%
+generalizes that to to higher Dimensions
+uh we can't have any regressors that do
+
+ align:start position:0%
+uh we can't have any regressors that do
+ 
+
+ align:start position:0%
+uh we can't have any regressors that do
+not have positive sample variation so we
+
+ align:start position:0%
+not have positive sample variation so we
+ 
+
+ align:start position:0%
+not have positive sample variation so we
+saw this assumption in the B variant
+
+ align:start position:0%
+saw this assumption in the B variant
+ 
+
+ align:start position:0%
+saw this assumption in the B variant
+case remember I had a picture that
+
+ align:start position:0%
+case remember I had a picture that
+ 
+
+ align:start position:0%
+case remember I had a picture that
+looked
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like I had a picture that looked like
+
+ align:start position:0%
+like I had a picture that looked like
+ 
+
+ align:start position:0%
+like I had a picture that looked like
+this and I said if all of our
+
+ align:start position:0%
+this and I said if all of our
+ 
+
+ align:start position:0%
+this and I said if all of our
+observations are on the same value of x
+
+ align:start position:0%
+observations are on the same value of x
+ 
+
+ align:start position:0%
+observations are on the same value of x
+we can't uh we can't
+
+ align:start position:0%
+we can't uh we can't
+ 
+
+ align:start position:0%
+we can't uh we can't
+identify um
+
+ align:start position:0%
+identify um
+ 
+
+ align:start position:0%
+identify um
+the how the conditional mean of Y
+
+ align:start position:0%
+the how the conditional mean of Y
+ 
+
+ align:start position:0%
+the how the conditional mean of Y
+changes with X okay well again in the
+
+ align:start position:0%
+changes with X okay well again in the
+ 
+
+ align:start position:0%
+changes with X okay well again in the
+multivariant regression uh or the
+
+ align:start position:0%
+multivariant regression uh or the
+ 
+
+ align:start position:0%
+multivariant regression uh or the
+multivariant case we can't identify uh
+
+ align:start position:0%
+multivariant case we can't identify uh
+ 
+
+ align:start position:0%
+multivariant case we can't identify uh
+the a particular parameter if we have a
+
+ align:start position:0%
+the a particular parameter if we have a
+ 
+
+ align:start position:0%
+the a particular parameter if we have a
+regressor that doesn't have positive
+
+ align:start position:0%
+regressor that doesn't have positive
+ 
+
+ align:start position:0%
+regressor that doesn't have positive
+sample variation so all of our
+
+ align:start position:0%
+sample variation so all of our
+ 
+
+ align:start position:0%
+sample variation so all of our
+regressors have to have positive sample
+
+ align:start position:0%
+regressors have to have positive sample
+ 
+
+ align:start position:0%
+regressors have to have positive sample
+variation and then the third one and
+
+ align:start position:0%
+variation and then the third one and
+ 
+
+ align:start position:0%
+variation and then the third one and
+this is the one that actually trips
+
+ align:start position:0%
+this is the one that actually trips
+ 
+
+ align:start position:0%
+this is the one that actually trips
+people up sometimes is that we can't
+
+ align:start position:0%
+people up sometimes is that we can't
+ 
+
+ align:start position:0%
+people up sometimes is that we can't
+have any regressors that are linear
+
+ align:start position:0%
+have any regressors that are linear
+ 
+
+ align:start position:0%
+have any regressors that are linear
+functions of one or more other
+
+ align:start position:0%
+functions of one or more other
+ 
+
+ align:start position:0%
+functions of one or more other
+regressors okay and in Matrix notation
+
+ align:start position:0%
+regressors okay and in Matrix notation
+ 
+
+ align:start position:0%
+regressors okay and in Matrix notation
+that's just uh that's another way to say
+
+ align:start position:0%
+that's just uh that's another way to say
+ 
+
+ align:start position:0%
+that's just uh that's another way to say
+that is the regressors are linearly
+
+ align:start position:0%
+that is the regressors are linearly
+ 
+
+ align:start position:0%
+that is the regressors are linearly
+independent okay and that is turns out
+
+ align:start position:0%
+independent okay and that is turns out
+ 
+
+ align:start position:0%
+independent okay and that is turns out
+to be equivalent to X Prime X being
+
+ align:start position:0%
+to be equivalent to X Prime X being
+ 
+
+ align:start position:0%
+to be equivalent to X Prime X being
+invertible yep you give an example of
+
+ align:start position:0%
+invertible yep you give an example of
+ 
+
+ align:start position:0%
+invertible yep you give an example of
+that I will give two examples in
+
+ align:start position:0%
+that I will give two examples in
+ 
+
+ align:start position:0%
+that I will give two examples in
+fact okay so here is one example let's
+
+ align:start position:0%
+fact okay so here is one example let's
+ 
+
+ align:start position:0%
+fact okay so here is one example let's
+suppose let's imagine a case where we
+
+ align:start position:0%
+suppose let's imagine a case where we
+ 
+
+ align:start position:0%
+suppose let's imagine a case where we
+want to estimate the effect of schooling
+
+ align:start position:0%
+want to estimate the effect of schooling
+ 
+
+ align:start position:0%
+want to estimate the effect of schooling
+work experience and age on salary okay
+
+ align:start position:0%
+work experience and age on salary okay
+ 
+
+ align:start position:0%
+work experience and age on salary okay
+and we have individual level data so we
+
+ align:start position:0%
+and we have individual level data so we
+ 
+
+ align:start position:0%
+and we have individual level data so we
+have a we have sort of a data set we
+
+ align:start position:0%
+have a we have sort of a data set we
+ 
+
+ align:start position:0%
+have a we have sort of a data set we
+have a bunch of different salaries and
+
+ align:start position:0%
+have a bunch of different salaries and
+ 
+
+ align:start position:0%
+have a bunch of different salaries and
+then we also have each person's years of
+
+ align:start position:0%
+then we also have each person's years of
+ 
+
+ align:start position:0%
+then we also have each person's years of
+schooling each person's years of work
+
+ align:start position:0%
+schooling each person's years of work
+ 
+
+ align:start position:0%
+schooling each person's years of work
+experience each person's age and maybe
+
+ align:start position:0%
+experience each person's age and maybe
+ 
+
+ align:start position:0%
+experience each person's age and maybe
+some other stuff too doesn't matter well
+
+ align:start position:0%
+some other stuff too doesn't matter well
+ 
+
+ align:start position:0%
+some other stuff too doesn't matter well
+it could be in our particular sample
+
+ align:start position:0%
+it could be in our particular sample
+ 
+
+ align:start position:0%
+it could be in our particular sample
+quite possible that everyone in our
+
+ align:start position:0%
+quite possible that everyone in our
+ 
+
+ align:start position:0%
+quite possible that everyone in our
+sample started school at age six went to
+
+ align:start position:0%
+sample started school at age six went to
+ 
+
+ align:start position:0%
+sample started school at age six went to
+school until here or she finished school
+
+ align:start position:0%
+school until here or she finished school
+ 
+
+ align:start position:0%
+school until here or she finished school
+and then started
+
+ align:start position:0%
+and then started
+ 
+
+ align:start position:0%
+and then started
+working wouldn't be crazy if that
+
+ align:start position:0%
+working wouldn't be crazy if that
+ 
+
+ align:start position:0%
+working wouldn't be crazy if that
+happened well if in fact that was the
+
+ align:start position:0%
+happened well if in fact that was the
+ 
+
+ align:start position:0%
+happened well if in fact that was the
+case then the years of schooling plus
+
+ align:start position:0%
+case then the years of schooling plus
+ 
+
+ align:start position:0%
+case then the years of schooling plus
+the years of work experience plus six is
+
+ align:start position:0%
+the years of work experience plus six is
+ 
+
+ align:start position:0%
+the years of work experience plus six is
+equal to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+age okay so if that's the case we can't
+
+ align:start position:0%
+age okay so if that's the case we can't
+ 
+
+ align:start position:0%
+age okay so if that's the case we can't
+estimate this regression equation
+
+ align:start position:0%
+estimate this regression equation
+ 
+
+ align:start position:0%
+estimate this regression equation
+and that makes it sort of makes logical
+
+ align:start position:0%
+and that makes it sort of makes logical
+ 
+
+ align:start position:0%
+and that makes it sort of makes logical
+sense too in the sense that I if there's
+
+ align:start position:0%
+sense too in the sense that I if there's
+ 
+
+ align:start position:0%
+sense too in the sense that I if there's
+no there's nothing that helps
+
+ align:start position:0%
+no there's nothing that helps
+ 
+
+ align:start position:0%
+no there's nothing that helps
+us separately identify what the effect
+
+ align:start position:0%
+us separately identify what the effect
+ 
+
+ align:start position:0%
+us separately identify what the effect
+of schooling and work experience and age
+
+ align:start position:0%
+of schooling and work experience and age
+ 
+
+ align:start position:0%
+of schooling and work experience and age
+are there's nothing that that no
+
+ align:start position:0%
+are there's nothing that that no
+ 
+
+ align:start position:0%
+are there's nothing that that no
+variation that allows us to separately
+
+ align:start position:0%
+variation that allows us to separately
+ 
+
+ align:start position:0%
+variation that allows us to separately
+figure out the effects of all three of
+
+ align:start position:0%
+figure out the effects of all three of
+ 
+
+ align:start position:0%
+figure out the effects of all three of
+those if in fact they're collinear in
+
+ align:start position:0%
+those if in fact they're collinear in
+ 
+
+ align:start position:0%
+those if in fact they're collinear in
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+sample Okay so we just we can't estimate
+
+ align:start position:0%
+sample Okay so we just we can't estimate
+ 
+
+ align:start position:0%
+sample Okay so we just we can't estimate
+such a model is that clear so you would
+
+ align:start position:0%
+such a model is that clear so you would
+ 
+
+ align:start position:0%
+such a model is that clear so you would
+drop a regressor exactly you have to
+
+ align:start position:0%
+drop a regressor exactly you have to
+ 
+
+ align:start position:0%
+drop a regressor exactly you have to
+drop one of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regressors yeah does this make
+
+ align:start position:0%
+regressors yeah does this make
+ 
+
+ align:start position:0%
+regressors yeah does this make
+sense yes drop AG
+
+ align:start position:0%
+sense yes drop AG
+ 
+
+ align:start position:0%
+sense yes drop AG
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+still if you drop age it still wouldn't
+
+ align:start position:0%
+still if you drop age it still wouldn't
+ 
+
+ align:start position:0%
+still if you drop age it still wouldn't
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+yes it it would uh the it wouldn't work
+
+ align:start position:0%
+yes it it would uh the it wouldn't work
+ 
+
+ align:start position:0%
+yes it it would uh the it wouldn't work
+if everyone went to school until age
+
+ align:start position:0%
+if everyone went to school until age
+ 
+
+ align:start position:0%
+if everyone went to school until age
+18 so so it so we still need we would
+
+ align:start position:0%
+18 so so it so we still need we would
+ 
+
+ align:start position:0%
+18 so so it so we still need we would
+still need to have uh we couldn't have a
+
+ align:start position:0%
+still need to have uh we couldn't have a
+ 
+
+ align:start position:0%
+still need to have uh we couldn't have a
+a perfect linear relationship between um
+
+ align:start position:0%
+a perfect linear relationship between um
+ 
+
+ align:start position:0%
+a perfect linear relationship between um
+you know sort of number of years of
+
+ align:start position:0%
+you know sort of number of years of
+ 
+
+ align:start position:0%
+you know sort of number of years of
+schooling well actually that wouldn't be
+
+ align:start position:0%
+schooling well actually that wouldn't be
+ 
+
+ align:start position:0%
+schooling well actually that wouldn't be
+a perfect line that would just be no
+
+ align:start position:0%
+a perfect line that would just be no
+ 
+
+ align:start position:0%
+a perfect line that would just be no
+sample variation in years of
+
+ align:start position:0%
+sample variation in years of
+ 
+
+ align:start position:0%
+sample variation in years of
+schooling but if we did have if some
+
+ align:start position:0%
+schooling but if we did have if some
+ 
+
+ align:start position:0%
+schooling but if we did have if some
+people went to school until age 18 and
+
+ align:start position:0%
+people went to school until age 18 and
+ 
+
+ align:start position:0%
+people went to school until age 18 and
+some people went till age 20 and some
+
+ align:start position:0%
+some people went till age 20 and some
+ 
+
+ align:start position:0%
+some people went till age 20 and some
+went till age 25 then then if we dropped
+
+ align:start position:0%
+went till age 25 then then if we dropped
+ 
+
+ align:start position:0%
+went till age 25 then then if we dropped
+age from this regression and then we
+
+ align:start position:0%
+age from this regression and then we
+ 
+
+ align:start position:0%
+age from this regression and then we
+could estimate
+
+ align:start position:0%
+could estimate
+ 
+
+ align:start position:0%
+could estimate
+it we say that this is uh that why this
+
+ align:start position:0%
+it we say that this is uh that why this
+ 
+
+ align:start position:0%
+it we say that this is uh that why this
+doesn't hold is that if we took X1 X2
+
+ align:start position:0%
+doesn't hold is that if we took X1 X2
+ 
+
+ align:start position:0%
+doesn't hold is that if we took X1 X2
+and X3 we could get values of beta 1
+
+ align:start position:0%
+and X3 we could get values of beta 1
+ 
+
+ align:start position:0%
+and X3 we could get values of beta 1
+beta 2 and all of these which would
+
+ align:start position:0%
+beta 2 and all of these which would
+ 
+
+ align:start position:0%
+beta 2 and all of these which would
+essentially make y 0 so 1 1 and minus
+
+ align:start position:0%
+essentially make y 0 so 1 1 and minus
+ 
+
+ align:start position:0%
+essentially make y 0 so 1 1 and minus
+one for example so then this equation
+
+ align:start position:0%
+one for example so then this equation
+ 
+
+ align:start position:0%
+one for example so then this equation
+would hold two and then y would be zero
+
+ align:start position:0%
+would hold two and then y would be zero
+ 
+
+ align:start position:0%
+would hold two and then y would be zero
+in that case I don't so that's not the
+
+ align:start position:0%
+in that case I don't so that's not the
+ 
+
+ align:start position:0%
+in that case I don't so that's not the
+intuition I have um it that may be
+
+ align:start position:0%
+intuition I have um it that may be
+ 
+
+ align:start position:0%
+intuition I have um it that may be
+correct in some way but uh that's
+
+ align:start position:0%
+correct in some way but uh that's
+ 
+
+ align:start position:0%
+correct in some way but uh that's
+certainly not the intuition I have I
+
+ align:start position:0%
+certainly not the intuition I have I
+ 
+
+ align:start position:0%
+certainly not the intuition I have I
+mean I guess I would just say that my
+
+ align:start position:0%
+mean I guess I would just say that my
+ 
+
+ align:start position:0%
+mean I guess I would just say that my
+intuition is just that uh you know you
+
+ align:start position:0%
+intuition is just that uh you know you
+ 
+
+ align:start position:0%
+intuition is just that uh you know you
+can't we don't have any variation to
+
+ align:start position:0%
+can't we don't have any variation to
+ 
+
+ align:start position:0%
+can't we don't have any variation to
+separately identify the the effects of
+
+ align:start position:0%
+separately identify the the effects of
+ 
+
+ align:start position:0%
+separately identify the the effects of
+these three things if they're perfectly
+
+ align:start position:0%
+these three things if they're perfectly
+ 
+
+ align:start position:0%
+these three things if they're perfectly
+uh linearly associated with one another
+
+ align:start position:0%
+uh linearly associated with one another
+ 
+
+ align:start position:0%
+uh linearly associated with one another
+yes so what if the two regressor are
+
+ align:start position:0%
+yes so what if the two regressor are
+ 
+
+ align:start position:0%
+yes so what if the two regressor are
+somewh related U but they are not
+
+ align:start position:0%
+somewh related U but they are not
+ 
+
+ align:start position:0%
+somewh related U but they are not
+perfectly Rel relationship so that's an
+
+ align:start position:0%
+perfectly Rel relationship so that's an
+ 
+
+ align:start position:0%
+perfectly Rel relationship so that's an
+excellent question so the question was
+
+ align:start position:0%
+excellent question so the question was
+ 
+
+ align:start position:0%
+excellent question so the question was
+what if they are uh closely related so
+
+ align:start position:0%
+what if they are uh closely related so
+ 
+
+ align:start position:0%
+what if they are uh closely related so
+maybe this doesn't quite hold in our
+
+ align:start position:0%
+maybe this doesn't quite hold in our
+ 
+
+ align:start position:0%
+maybe this doesn't quite hold in our
+sample but it comes close to holding
+
+ align:start position:0%
+sample but it comes close to holding
+ 
+
+ align:start position:0%
+sample but it comes close to holding
+like we had a few people who went to
+
+ align:start position:0%
+like we had a few people who went to
+ 
+
+ align:start position:0%
+like we had a few people who went to
+school at age five instead of age six
+
+ align:start position:0%
+school at age five instead of age six
+ 
+
+ align:start position:0%
+school at age five instead of age six
+and we had like a couple people who took
+
+ align:start position:0%
+and we had like a couple people who took
+ 
+
+ align:start position:0%
+and we had like a couple people who took
+a year off and didn't work so so this
+
+ align:start position:0%
+a year off and didn't work so so this
+ 
+
+ align:start position:0%
+a year off and didn't work so so this
+linear relationship is close to holding
+
+ align:start position:0%
+linear relationship is close to holding
+ 
+
+ align:start position:0%
+linear relationship is close to holding
+but not quite that's something that
+
+ align:start position:0%
+but not quite that's something that
+ 
+
+ align:start position:0%
+but not quite that's something that
+Esther might be able to talk about next
+
+ align:start position:0%
+Esther might be able to talk about next
+ 
+
+ align:start position:0%
+Esther might be able to talk about next
+time I'm not sure so basically in that
+
+ align:start position:0%
+time I'm not sure so basically in that
+ 
+
+ align:start position:0%
+time I'm not sure so basically in that
+case you
+
+ align:start position:0%
+case you
+ 
+
+ align:start position:0%
+case you
+can maybe maybe not but but anyhow I
+
+ align:start position:0%
+can maybe maybe not but but anyhow I
+ 
+
+ align:start position:0%
+can maybe maybe not but but anyhow I
+I'll I'll tell you the answer in that
+
+ align:start position:0%
+I'll I'll tell you the answer in that
+ 
+
+ align:start position:0%
+I'll I'll tell you the answer in that
+case you can estimate this equation but
+
+ align:start position:0%
+case you can estimate this equation but
+ 
+
+ align:start position:0%
+case you can estimate this equation but
+you you end up having you end up sort of
+
+ align:start position:0%
+you you end up having you end up sort of
+ 
+
+ align:start position:0%
+you you end up having you end up sort of
+having trouble separately identifying
+
+ align:start position:0%
+having trouble separately identifying
+ 
+
+ align:start position:0%
+having trouble separately identifying
+the coefficients on these variables on
+
+ align:start position:0%
+the coefficients on these variables on
+ 
+
+ align:start position:0%
+the coefficients on these variables on
+these three variables and in fact
+
+ align:start position:0%
+these three variables and in fact
+ 
+
+ align:start position:0%
+these three variables and in fact
+they're going to be coefficients that
+
+ align:start position:0%
+they're going to be coefficients that
+ 
+
+ align:start position:0%
+they're going to be coefficients that
+have very that your estimator is going
+
+ align:start position:0%
+have very that your estimator is going
+ 
+
+ align:start position:0%
+have very that your estimator is going
+to be a very high variance estimator and
+
+ align:start position:0%
+to be a very high variance estimator and
+ 
+
+ align:start position:0%
+to be a very high variance estimator and
+so in that case what you might want to
+
+ align:start position:0%
+so in that case what you might want to
+ 
+
+ align:start position:0%
+so in that case what you might want to
+do is still drop one of them that's
+
+ align:start position:0%
+do is still drop one of them that's
+ 
+
+ align:start position:0%
+do is still drop one of them that's
+going to give you much lower variance
+
+ align:start position:0%
+going to give you much lower variance
+ 
+
+ align:start position:0%
+going to give you much lower variance
+estimators for the remaining two it's
+
+ align:start position:0%
+estimators for the remaining two it's
+ 
+
+ align:start position:0%
+estimators for the remaining two it's
+going to introduce a little bit of bias
+
+ align:start position:0%
+going to introduce a little bit of bias
+ 
+
+ align:start position:0%
+going to introduce a little bit of bias
+if that regressor belongs in there it's
+
+ align:start position:0%
+if that regressor belongs in there it's
+ 
+
+ align:start position:0%
+if that regressor belongs in there it's
+going to introduce a little bit of bias
+
+ align:start position:0%
+going to introduce a little bit of bias
+ 
+
+ align:start position:0%
+going to introduce a little bit of bias
+but you might be willing to accept that
+
+ align:start position:0%
+but you might be willing to accept that
+ 
+
+ align:start position:0%
+but you might be willing to accept that
+bias to have much lower variance
+
+ align:start position:0%
+bias to have much lower variance
+ 
+
+ align:start position:0%
+bias to have much lower variance
+estimators so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+question um what if you have a lar data
+
+ align:start position:0%
+question um what if you have a lar data
+ 
+
+ align:start position:0%
+question um what if you have a lar data
+set with a lot of variables and and we
+
+ align:start position:0%
+set with a lot of variables and and we
+ 
+
+ align:start position:0%
+set with a lot of variables and and we
+don't know that there are regression in
+
+ align:start position:0%
+don't know that there are regression in
+ 
+
+ align:start position:0%
+don't know that there are regression in
+there that do have
+
+ align:start position:0%
+there that do have
+ 
+
+ align:start position:0%
+there that do have
+what are the things
+
+ align:start position:0%
+what are the things
+ 
+
+ align:start position:0%
+what are the things
+that like this could be causing problems
+
+ align:start position:0%
+that like this could be causing problems
+ 
+
+ align:start position:0%
+that like this could be causing problems
+in my analysis or yeah so so first of
+
+ align:start position:0%
+in my analysis or yeah so so first of
+ 
+
+ align:start position:0%
+in my analysis or yeah so so first of
+all if you if I tried to run this
+
+ align:start position:0%
+all if you if I tried to run this
+ 
+
+ align:start position:0%
+all if you if I tried to run this
+regression and this linear relationship
+
+ align:start position:0%
+regression and this linear relationship
+ 
+
+ align:start position:0%
+regression and this linear relationship
+existed in my data set R would throw up
+
+ align:start position:0%
+existed in my data set R would throw up
+ 
+
+ align:start position:0%
+existed in my data set R would throw up
+its hands and say you can't do that okay
+
+ align:start position:0%
+its hands and say you can't do that okay
+ 
+
+ align:start position:0%
+its hands and say you can't do that okay
+so I I can't even do it so you you would
+
+ align:start position:0%
+so I I can't even do it so you you would
+ 
+
+ align:start position:0%
+so I I can't even do it so you you would
+you would find that out if this
+
+ align:start position:0%
+you would find that out if this
+ 
+
+ align:start position:0%
+you would find that out if this
+relationship didn't quite exist it was
+
+ align:start position:0%
+relationship didn't quite exist it was
+ 
+
+ align:start position:0%
+relationship didn't quite exist it was
+close to existing in the data set but
+
+ align:start position:0%
+close to existing in the data set but
+ 
+
+ align:start position:0%
+close to existing in the data set but
+not quite R would go ahead and give you
+
+ align:start position:0%
+not quite R would go ahead and give you
+ 
+
+ align:start position:0%
+not quite R would go ahead and give you
+the results of this but the one thing
+
+ align:start position:0%
+the results of this but the one thing
+ 
+
+ align:start position:0%
+the results of this but the one thing
+that you could do is you could sort of
+
+ align:start position:0%
+that you could do is you could sort of
+ 
+
+ align:start position:0%
+that you could do is you could sort of
+uh compute the correlation coefficients
+
+ align:start position:0%
+uh compute the correlation coefficients
+ 
+
+ align:start position:0%
+uh compute the correlation coefficients
+for all of your regressors before you
+
+ align:start position:0%
+for all of your regressors before you
+ 
+
+ align:start position:0%
+for all of your regressors before you
+run the regression and see if any are
+
+ align:start position:0%
+run the regression and see if any are
+ 
+
+ align:start position:0%
+run the regression and see if any are
+really highly correlated that doesn't
+
+ align:start position:0%
+really highly correlated that doesn't
+ 
+
+ align:start position:0%
+really highly correlated that doesn't
+wouldn't necessarily pick up a linear
+
+ align:start position:0%
+wouldn't necessarily pick up a linear
+ 
+
+ align:start position:0%
+wouldn't necessarily pick up a linear
+relationship like this but the other
+
+ align:start position:0%
+relationship like this but the other
+ 
+
+ align:start position:0%
+relationship like this but the other
+thing you could do is after you run the
+
+ align:start position:0%
+thing you could do is after you run the
+ 
+
+ align:start position:0%
+thing you could do is after you run the
+regression if you have really large
+
+ align:start position:0%
+regression if you have really large
+ 
+
+ align:start position:0%
+regression if you have really large
+standard errors that could be a signal
+
+ align:start position:0%
+standard errors that could be a signal
+ 
+
+ align:start position:0%
+standard errors that could be a signal
+to you that uh you could have this this
+
+ align:start position:0%
+to you that uh you could have this this
+ 
+
+ align:start position:0%
+to you that uh you could have this this
+uh situation that's close to perfect
+
+ align:start position:0%
+uh situation that's close to perfect
+ 
+
+ align:start position:0%
+uh situation that's close to perfect
+colinearity yes so if we had two regress
+
+ align:start position:0%
+colinearity yes so if we had two regress
+ 
+
+ align:start position:0%
+colinearity yes so if we had two regress
+X1 and X2 could we use the ratio X1 by
+
+ align:start position:0%
+X1 and X2 could we use the ratio X1 by
+ 
+
+ align:start position:0%
+X1 and X2 could we use the ratio X1 by
+X2 as a thir regress as a or would that
+
+ align:start position:0%
+X2 as a thir regress as a or would that
+ 
+
+ align:start position:0%
+X2 as a thir regress as a or would that
+also so uh so that you could sort of you
+
+ align:start position:0%
+also so uh so that you could sort of you
+ 
+
+ align:start position:0%
+also so uh so that you could sort of you
+know that wouldn't induce this sort of
+
+ align:start position:0%
+know that wouldn't induce this sort of
+ 
+
+ align:start position:0%
+know that wouldn't induce this sort of
+perfect linear um you know perfect
+
+ align:start position:0%
+perfect linear um you know perfect
+ 
+
+ align:start position:0%
+perfect linear um you know perfect
+linear cinear ity problem you could you
+
+ align:start position:0%
+linear cinear ity problem you could you
+ 
+
+ align:start position:0%
+linear cinear ity problem you could you
+might not want to do it for other
+
+ align:start position:0%
+might not want to do it for other
+ 
+
+ align:start position:0%
+might not want to do it for other
+reasons but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah question on if you had many
+
+ align:start position:0%
+yeah question on if you had many
+ 
+
+ align:start position:0%
+yeah question on if you had many
+regressor and you didn't
+
+ align:start position:0%
+regressor and you didn't
+ 
+
+ align:start position:0%
+regressor and you didn't
+know which one to pick sort of go away
+
+ align:start position:0%
+know which one to pick sort of go away
+ 
+
+ align:start position:0%
+know which one to pick sort of go away
+from traditional eometric it becomes
+
+ align:start position:0%
+from traditional eometric it becomes
+ 
+
+ align:start position:0%
+from traditional eometric it becomes
+then this is from what we're going to
+
+ align:start position:0%
+then this is from what we're going to
+ 
+
+ align:start position:0%
+then this is from what we're going to
+talk about when we talk about machine
+
+ align:start position:0%
+talk about when we talk about machine
+ 
+
+ align:start position:0%
+talk about when we talk about machine
+learning if you really don't want to
+
+ align:start position:0%
+learning if you really don't want to
+ 
+
+ align:start position:0%
+learning if you really don't want to
+traditional eometric assumes you have a
+
+ align:start position:0%
+traditional eometric assumes you have a
+ 
+
+ align:start position:0%
+traditional eometric assumes you have a
+model that you are trying to test so you
+
+ align:start position:0%
+model that you are trying to test so you
+ 
+
+ align:start position:0%
+model that you are trying to test so you
+don't go on a g fishing Expedition if
+
+ align:start position:0%
+don't go on a g fishing Expedition if
+ 
+
+ align:start position:0%
+don't go on a g fishing Expedition if
+you want to go on a giant fishing
+
+ align:start position:0%
+you want to go on a giant fishing
+ 
+
+ align:start position:0%
+you want to go on a giant fishing
+Expedition there are there are there are
+
+ align:start position:0%
+Expedition there are there are there are
+ 
+
+ align:start position:0%
+Expedition there are there are there are
+techniques for that that's F that's what
+
+ align:start position:0%
+techniques for that that's F that's what
+ 
+
+ align:start position:0%
+techniques for that that's F that's what
+we are going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+introduce good okay so that's one
+
+ align:start position:0%
+introduce good okay so that's one
+ 
+
+ align:start position:0%
+introduce good okay so that's one
+example a second example of this perfect
+
+ align:start position:0%
+example a second example of this perfect
+ 
+
+ align:start position:0%
+example a second example of this perfect
+multicolinearity
+
+ align:start position:0%
+multicolinearity
+ 
+
+ align:start position:0%
+multicolinearity
+uh is um and one that sort of
+
+ align:start position:0%
+uh is um and one that sort of
+ 
+
+ align:start position:0%
+uh is um and one that sort of
+researchers run a fowl of all the time
+
+ align:start position:0%
+researchers run a fowl of all the time
+ 
+
+ align:start position:0%
+researchers run a fowl of all the time
+um it is uh when
+
+ align:start position:0%
+um it is uh when
+ 
+
+ align:start position:0%
+um it is uh when
+they use dummy variables to indicate say
+
+ align:start position:0%
+they use dummy variables to indicate say
+ 
+
+ align:start position:0%
+they use dummy variables to indicate say
+observations falling into um exhaustive
+
+ align:start position:0%
+observations falling into um exhaustive
+ 
+
+ align:start position:0%
+observations falling into um exhaustive
+and mutually exclusive uh set of classes
+
+ align:start position:0%
+and mutually exclusive uh set of classes
+ 
+
+ align:start position:0%
+and mutually exclusive uh set of classes
+so here's an example let's suppose I
+
+ align:start position:0%
+so here's an example let's suppose I
+ 
+
+ align:start position:0%
+so here's an example let's suppose I
+have a data set let's say I go um you
+
+ align:start position:0%
+have a data set let's say I go um you
+ 
+
+ align:start position:0%
+have a data set let's say I go um you
+know sort of talk to all my friends in
+
+ align:start position:0%
+know sort of talk to all my friends in
+ 
+
+ align:start position:0%
+know sort of talk to all my friends in
+the dorm to collect my data set for 1431
+
+ align:start position:0%
+the dorm to collect my data set for 1431
+ 
+
+ align:start position:0%
+the dorm to collect my data set for 1431
+and I ask them what pets they have at
+
+ align:start position:0%
+and I ask them what pets they have at
+ 
+
+ align:start position:0%
+and I ask them what pets they have at
+home and um let's say all of them have
+
+ align:start position:0%
+home and um let's say all of them have
+ 
+
+ align:start position:0%
+home and um let's say all of them have
+pets we could have a category for no pet
+
+ align:start position:0%
+pets we could have a category for no pet
+ 
+
+ align:start position:0%
+pets we could have a category for no pet
+as well but anyhow let's say all of them
+
+ align:start position:0%
+as well but anyhow let's say all of them
+ 
+
+ align:start position:0%
+as well but anyhow let's say all of them
+have pets but they either either have a
+
+ align:start position:0%
+have pets but they either either have a
+ 
+
+ align:start position:0%
+have pets but they either either have a
+cat a dog or a fish and so then I create
+
+ align:start position:0%
+cat a dog or a fish and so then I create
+ 
+
+ align:start position:0%
+cat a dog or a fish and so then I create
+three different dummy variables one is
+
+ align:start position:0%
+three different dummy variables one is
+ 
+
+ align:start position:0%
+three different dummy variables one is
+equal to one if they have a cat and zero
+
+ align:start position:0%
+equal to one if they have a cat and zero
+ 
+
+ align:start position:0%
+equal to one if they have a cat and zero
+otherwise one is equal to one if they
+
+ align:start position:0%
+otherwise one is equal to one if they
+ 
+
+ align:start position:0%
+otherwise one is equal to one if they
+have a dog and zero otherwise and one is
+
+ align:start position:0%
+have a dog and zero otherwise and one is
+ 
+
+ align:start position:0%
+have a dog and zero otherwise and one is
+equal to one if they have a fish and
+
+ align:start position:0%
+equal to one if they have a fish and
+ 
+
+ align:start position:0%
+equal to one if they have a fish and
+zero otherwise and everyone has exactly
+
+ align:start position:0%
+zero otherwise and everyone has exactly
+ 
+
+ align:start position:0%
+zero otherwise and everyone has exactly
+one of those pets okay I cannot include
+
+ align:start position:0%
+one of those pets okay I cannot include
+ 
+
+ align:start position:0%
+one of those pets okay I cannot include
+all three of those dummy variables in
+
+ align:start position:0%
+all three of those dummy variables in
+ 
+
+ align:start position:0%
+all three of those dummy variables in
+the uh regression because if we add up
+
+ align:start position:0%
+the uh regression because if we add up
+ 
+
+ align:start position:0%
+the uh regression because if we add up
+those three dummy variables we get a
+
+ align:start position:0%
+those three dummy variables we get a
+ 
+
+ align:start position:0%
+those three dummy variables we get a
+column of ones and that's perfectly
+
+ align:start position:0%
+column of ones and that's perfectly
+ 
+
+ align:start position:0%
+column of ones and that's perfectly
+collinear with our uh column of ones
+
+ align:start position:0%
+collinear with our uh column of ones
+ 
+
+ align:start position:0%
+collinear with our uh column of ones
+that allows us to estimate the um The
+
+ align:start position:0%
+that allows us to estimate the um The
+ 
+
+ align:start position:0%
+that allows us to estimate the um The
+Intercept okay now it there there are
+
+ align:start position:0%
+Intercept okay now it there there are
+ 
+
+ align:start position:0%
+Intercept okay now it there there are
+sort of other ways you you can in fact
+
+ align:start position:0%
+sort of other ways you you can in fact
+ 
+
+ align:start position:0%
+sort of other ways you you can in fact
+um it you can in fact decide to include
+
+ align:start position:0%
+um it you can in fact decide to include
+ 
+
+ align:start position:0%
+um it you can in fact decide to include
+all three dummy variables and not
+
+ align:start position:0%
+all three dummy variables and not
+ 
+
+ align:start position:0%
+all three dummy variables and not
+include an intercept not estimate an
+
+ align:start position:0%
+include an intercept not estimate an
+ 
+
+ align:start position:0%
+include an intercept not estimate an
+Intercept in this regression it's
+
+ align:start position:0%
+Intercept in this regression it's
+ 
+
+ align:start position:0%
+Intercept in this regression it's
+entirely equivalent it would be a little
+
+ align:start position:0%
+entirely equivalent it would be a little
+ 
+
+ align:start position:0%
+entirely equivalent it would be a little
+troubling if it wasn't equivalent but it
+
+ align:start position:0%
+troubling if it wasn't equivalent but it
+ 
+
+ align:start position:0%
+troubling if it wasn't equivalent but it
+isn't in fact entirely equivalent it's
+
+ align:start position:0%
+isn't in fact entirely equivalent it's
+ 
+
+ align:start position:0%
+isn't in fact entirely equivalent it's
+just you have to interpret the
+
+ align:start position:0%
+just you have to interpret the
+ 
+
+ align:start position:0%
+just you have to interpret the
+coefficient estimates a different way
+
+ align:start position:0%
+coefficient estimates a different way
+ 
+
+ align:start position:0%
+coefficient estimates a different way
+but you can't have both an Intercept in
+
+ align:start position:0%
+but you can't have both an Intercept in
+ 
+
+ align:start position:0%
+but you can't have both an Intercept in
+your regression and a set of dummy
+
+ align:start position:0%
+your regression and a set of dummy
+ 
+
+ align:start position:0%
+your regression and a set of dummy
+variables that are a full set of
+
+ align:start position:0%
+variables that are a full set of
+ 
+
+ align:start position:0%
+variables that are a full set of
+exhaustive and mutually exclusive
+
+ align:start position:0%
+exhaustive and mutually exclusive
+ 
+
+ align:start position:0%
+exhaustive and mutually exclusive
+classes Okay and like I said R will not
+
+ align:start position:0%
+classes Okay and like I said R will not
+ 
+
+ align:start position:0%
+classes Okay and like I said R will not
+let you do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyhow okay so now the second um
+
+ align:start position:0%
+anyhow okay so now the second um
+ 
+
+ align:start position:0%
+anyhow okay so now the second um
+assumption or second yes does it change
+
+ align:start position:0%
+assumption or second yes does it change
+ 
+
+ align:start position:0%
+assumption or second yes does it change
+anything depending on which one
+
+ align:start position:0%
+anything depending on which one
+ 
+
+ align:start position:0%
+anything depending on which one
+it only changes the interpretation so
+
+ align:start position:0%
+it only changes the interpretation so
+ 
+
+ align:start position:0%
+it only changes the interpretation so
+basically uh I yeah I think I'll I'll
+
+ align:start position:0%
+basically uh I yeah I think I'll I'll
+ 
+
+ align:start position:0%
+basically uh I yeah I think I'll I'll
+leave I'll leave that question for
+
+ align:start position:0%
+leave I'll leave that question for
+ 
+
+ align:start position:0%
+leave I'll leave that question for
+Esther uh because she will be giving
+
+ align:start position:0%
+Esther uh because she will be giving
+ 
+
+ align:start position:0%
+Esther uh because she will be giving
+examples of uh you know how to use dummy
+
+ align:start position:0%
+examples of uh you know how to use dummy
+ 
+
+ align:start position:0%
+examples of uh you know how to use dummy
+variables in regressions and how to
+
+ align:start position:0%
+variables in regressions and how to
+ 
+
+ align:start position:0%
+variables in regressions and how to
+interpret the coefficients so we'll
+
+ align:start position:0%
+interpret the coefficients so we'll
+ 
+
+ align:start position:0%
+interpret the coefficients so we'll
+leave that to
+
+ align:start position:0%
+leave that to
+ 
+
+ align:start position:0%
+leave that to
+later okay um so then the second
+
+ align:start position:0%
+later okay um so then the second
+ 
+
+ align:start position:0%
+later okay um so then the second
+assumption was about the error of
+
+ align:start position:0%
+assumption was about the error of
+ 
+
+ align:start position:0%
+assumption was about the error of
+behavior and as I said before the these
+
+ align:start position:0%
+behavior and as I said before the these
+ 
+
+ align:start position:0%
+behavior and as I said before the these
+assumptions aren't different for the
+
+ align:start position:0%
+assumptions aren't different for the
+ 
+
+ align:start position:0%
+assumptions aren't different for the
+mult variant model it's just that uh
+
+ align:start position:0%
+mult variant model it's just that uh
+ 
+
+ align:start position:0%
+mult variant model it's just that uh
+I've expressed them using Matrix
+
+ align:start position:0%
+I've expressed them using Matrix
+ 
+
+ align:start position:0%
+I've expressed them using Matrix
+notation so let me just sort of go
+
+ align:start position:0%
+notation so let me just sort of go
+ 
+
+ align:start position:0%
+notation so let me just sort of go
+through um these exactly the same
+
+ align:start position:0%
+through um these exactly the same
+ 
+
+ align:start position:0%
+through um these exactly the same
+assumptions we saw in the B variant
+
+ align:start position:0%
+assumptions we saw in the B variant
+ 
+
+ align:start position:0%
+assumptions we saw in the B variant
+model here I'm using Matrix notation so
+
+ align:start position:0%
+model here I'm using Matrix notation so
+ 
+
+ align:start position:0%
+model here I'm using Matrix notation so
+I'll just go through and show you what
+
+ align:start position:0%
+I'll just go through and show you what
+ 
+
+ align:start position:0%
+I'll just go through and show you what
+what they mean so what I uh so first of
+
+ align:start position:0%
+what they mean so what I uh so first of
+ 
+
+ align:start position:0%
+what they mean so what I uh so first of
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+expectation of um Epsilon is equal to
+
+ align:start position:0%
+expectation of um Epsilon is equal to
+ 
+
+ align:start position:0%
+expectation of um Epsilon is equal to
+zero Epsilon is a vector um and so it's
+
+ align:start position:0%
+zero Epsilon is a vector um and so it's
+ 
+
+ align:start position:0%
+zero Epsilon is a vector um and so it's
+just equal to you know a vector of zeros
+
+ align:start position:0%
+just equal to you know a vector of zeros
+ 
+
+ align:start position:0%
+just equal to you know a vector of zeros
+and then for some reason we often write
+
+ align:start position:0%
+and then for some reason we often write
+ 
+
+ align:start position:0%
+and then for some reason we often write
+that the um instead of writing the
+
+ align:start position:0%
+that the um instead of writing the
+ 
+
+ align:start position:0%
+that the um instead of writing the
+Assumption as the covariance Matrix of
+
+ align:start position:0%
+Assumption as the covariance Matrix of
+ 
+
+ align:start position:0%
+Assumption as the covariance Matrix of
+Epsilon equals Sigma s time the identity
+
+ align:start position:0%
+Epsilon equals Sigma s time the identity
+ 
+
+ align:start position:0%
+Epsilon equals Sigma s time the identity
+the N byn identity Matrix we write it as
+
+ align:start position:0%
+the N byn identity Matrix we write it as
+ 
+
+ align:start position:0%
+the N byn identity Matrix we write it as
+the expectation of Epsilon Epsilon
+
+ align:start position:0%
+the expectation of Epsilon Epsilon
+ 
+
+ align:start position:0%
+the expectation of Epsilon Epsilon
+transpose is equal to that well it turns
+
+ align:start position:0%
+transpose is equal to that well it turns
+ 
+
+ align:start position:0%
+transpose is equal to that well it turns
+out because the expectation of Epsilon
+
+ align:start position:0%
+out because the expectation of Epsilon
+ 
+
+ align:start position:0%
+out because the expectation of Epsilon
+is is identically equal to zero this
+
+ align:start position:0%
+is is identically equal to zero this
+ 
+
+ align:start position:0%
+is is identically equal to zero this
+Matrix is equal to this Matrix you can
+
+ align:start position:0%
+Matrix is equal to this Matrix you can
+ 
+
+ align:start position:0%
+Matrix is equal to this Matrix you can
+just do you know you can sort of do the
+
+ align:start position:0%
+just do you know you can sort of do the
+ 
+
+ align:start position:0%
+just do you know you can sort of do the
+calculations it's just two lines to
+
+ align:start position:0%
+calculations it's just two lines to
+ 
+
+ align:start position:0%
+calculations it's just two lines to
+convince yourself but I could have
+
+ align:start position:0%
+convince yourself but I could have
+ 
+
+ align:start position:0%
+convince yourself but I could have
+expressed this assumption by just saying
+
+ align:start position:0%
+expressed this assumption by just saying
+ 
+
+ align:start position:0%
+expressed this assumption by just saying
+that this Matrix is equal to this okay
+
+ align:start position:0%
+that this Matrix is equal to this okay
+ 
+
+ align:start position:0%
+that this Matrix is equal to this okay
+but for whatever reason we often see it
+
+ align:start position:0%
+but for whatever reason we often see it
+ 
+
+ align:start position:0%
+but for whatever reason we often see it
+written as this Matrix is equal to this
+
+ align:start position:0%
+written as this Matrix is equal to this
+ 
+
+ align:start position:0%
+written as this Matrix is equal to this
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+okay does everyone understand
+
+ align:start position:0%
+okay does everyone understand
+ 
+
+ align:start position:0%
+okay does everyone understand
+why this Matrix equaling this is exactly
+
+ align:start position:0%
+why this Matrix equaling this is exactly
+ 
+
+ align:start position:0%
+why this Matrix equaling this is exactly
+the same assumptions we saw
+
+ align:start position:0%
+the same assumptions we saw
+ 
+
+ align:start position:0%
+the same assumptions we saw
+before so this Matrix is just simply the
+
+ align:start position:0%
+before so this Matrix is just simply the
+ 
+
+ align:start position:0%
+before so this Matrix is just simply the
+the a matrix containing the variances of
+
+ align:start position:0%
+the a matrix containing the variances of
+ 
+
+ align:start position:0%
+the a matrix containing the variances of
+the epsilons on the diagonal so remember
+
+ align:start position:0%
+the epsilons on the diagonal so remember
+ 
+
+ align:start position:0%
+the epsilons on the diagonal so remember
+before we said each Epsilon had variance
+
+ align:start position:0%
+before we said each Epsilon had variance
+ 
+
+ align:start position:0%
+before we said each Epsilon had variance
+Sigma squ that was our
+
+ align:start position:0%
+Sigma squ that was our
+ 
+
+ align:start position:0%
+Sigma squ that was our
+homoscedasticity assumption so each
+
+ align:start position:0%
+homoscedasticity assumption so each
+ 
+
+ align:start position:0%
+homoscedasticity assumption so each
+variance is Sigma squar and then all the
+
+ align:start position:0%
+variance is Sigma squar and then all the
+ 
+
+ align:start position:0%
+variance is Sigma squar and then all the
+co-variances were zero that was our no
+
+ align:start position:0%
+co-variances were zero that was our no
+ 
+
+ align:start position:0%
+co-variances were zero that was our no
+serial correlation assumption all all of
+
+ align:start position:0%
+serial correlation assumption all all of
+ 
+
+ align:start position:0%
+serial correlation assumption all all of
+the off diagonals here are zero
+
+ align:start position:0%
+the off diagonals here are zero
+ 
+
+ align:start position:0%
+the off diagonals here are zero
+okay so it's the same thing just in
+
+ align:start position:0%
+okay so it's the same thing just in
+ 
+
+ align:start position:0%
+okay so it's the same thing just in
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+okay and yeah I guess I think I said
+
+ align:start position:0%
+okay and yeah I guess I think I said
+ 
+
+ align:start position:0%
+okay and yeah I guess I think I said
+this verbally but this this thing is
+
+ align:start position:0%
+this verbally but this this thing is
+ 
+
+ align:start position:0%
+this verbally but this this thing is
+denoted coari of Epsilon and it's called
+
+ align:start position:0%
+denoted coari of Epsilon and it's called
+ 
+
+ align:start position:0%
+denoted coari of Epsilon and it's called
+the variance coari Matrix of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon okay fine we've got this linear
+
+ align:start position:0%
+Epsilon okay fine we've got this linear
+ 
+
+ align:start position:0%
+Epsilon okay fine we've got this linear
+model we've got the these assumptions
+
+ align:start position:0%
+model we've got the these assumptions
+ 
+
+ align:start position:0%
+model we've got the these assumptions
+just like four we're going to now ask
+
+ align:start position:0%
+just like four we're going to now ask
+ 
+
+ align:start position:0%
+just like four we're going to now ask
+the question how do we get beta hat and
+
+ align:start position:0%
+the question how do we get beta hat and
+ 
+
+ align:start position:0%
+the question how do we get beta hat and
+what distribution does beta hat have and
+
+ align:start position:0%
+what distribution does beta hat have and
+ 
+
+ align:start position:0%
+what distribution does beta hat have and
+the answers are not going to be
+
+ align:start position:0%
+the answers are not going to be
+ 
+
+ align:start position:0%
+the answers are not going to be
+surprising but they're going to be more
+
+ align:start position:0%
+surprising but they're going to be more
+ 
+
+ align:start position:0%
+surprising but they're going to be more
+beautiful than they were last time okay
+
+ align:start position:0%
+beautiful than they were last time okay
+ 
+
+ align:start position:0%
+beautiful than they were last time okay
+so what is beta hat well it's the vector
+
+ align:start position:0%
+so what is beta hat well it's the vector
+ 
+
+ align:start position:0%
+so what is beta hat well it's the vector
+that minimizes the sum of squared errors
+
+ align:start position:0%
+that minimizes the sum of squared errors
+ 
+
+ align:start position:0%
+that minimizes the sum of squared errors
+so we've got a vector of
+
+ align:start position:0%
+so we've got a vector of
+ 
+
+ align:start position:0%
+so we've got a vector of
+residuals transpose uh or you know
+
+ align:start position:0%
+residuals transpose uh or you know
+ 
+
+ align:start position:0%
+residuals transpose uh or you know
+transpose times a vector of residuals
+
+ align:start position:0%
+transpose times a vector of residuals
+ 
+
+ align:start position:0%
+transpose times a vector of residuals
+and uh that's that's sort of uh you know
+
+ align:start position:0%
+and uh that's that's sort of uh you know
+ 
+
+ align:start position:0%
+and uh that's that's sort of uh you know
+expanded out what it looks like
+
+ align:start position:0%
+expanded out what it looks like
+ 
+
+ align:start position:0%
+expanded out what it looks like
+okay so we want to choose the beta hat
+
+ align:start position:0%
+okay so we want to choose the beta hat
+ 
+
+ align:start position:0%
+okay so we want to choose the beta hat
+that minimizes that thing so what we do
+
+ align:start position:0%
+that minimizes that thing so what we do
+ 
+
+ align:start position:0%
+that minimizes that thing so what we do
+is we take the derivative with respect
+
+ align:start position:0%
+is we take the derivative with respect
+ 
+
+ align:start position:0%
+is we take the derivative with respect
+to Beta set it equal to zero and
+
+ align:start position:0%
+to Beta set it equal to zero and
+ 
+
+ align:start position:0%
+to Beta set it equal to zero and
+obtain this okay if you're not used to
+
+ align:start position:0%
+obtain this okay if you're not used to
+ 
+
+ align:start position:0%
+obtain this okay if you're not used to
+doing calculus with vectors and matrices
+
+ align:start position:0%
+doing calculus with vectors and matrices
+ 
+
+ align:start position:0%
+doing calculus with vectors and matrices
+you can sort of in the notes that I
+
+ align:start position:0%
+you can sort of in the notes that I
+ 
+
+ align:start position:0%
+you can sort of in the notes that I
+posted online I sort of write this out
+
+ align:start position:0%
+posted online I sort of write this out
+ 
+
+ align:start position:0%
+posted online I sort of write this out
+in more detail and you can take a look
+
+ align:start position:0%
+in more detail and you can take a look
+ 
+
+ align:start position:0%
+in more detail and you can take a look
+at that if you want but basically uh we
+
+ align:start position:0%
+at that if you want but basically uh we
+ 
+
+ align:start position:0%
+at that if you want but basically uh we
+get this um this sort of equation um set
+
+ align:start position:0%
+get this um this sort of equation um set
+ 
+
+ align:start position:0%
+get this um this sort of equation um set
+equal to zero and this is going to tell
+
+ align:start position:0%
+equal to zero and this is going to tell
+ 
+
+ align:start position:0%
+equal to zero and this is going to tell
+us what the beta hat that minimizes the
+
+ align:start position:0%
+us what the beta hat that minimizes the
+ 
+
+ align:start position:0%
+us what the beta hat that minimizes the
+sum of squared residuals is we then we
+
+ align:start position:0%
+sum of squared residuals is we then we
+ 
+
+ align:start position:0%
+sum of squared residuals is we then we
+solve for beta hat the -2 we can just
+
+ align:start position:0%
+solve for beta hat the -2 we can just
+ 
+
+ align:start position:0%
+solve for beta hat the -2 we can just
+divide you know both sides by -2 and so
+
+ align:start position:0%
+divide you know both sides by -2 and so
+ 
+
+ align:start position:0%
+divide you know both sides by -2 and so
+that goes away then we write uh this
+
+ align:start position:0%
+that goes away then we write uh this
+ 
+
+ align:start position:0%
+that goes away then we write uh this
+equation is X Prime y or X transpose
+
+ align:start position:0%
+equation is X Prime y or X transpose
+ 
+
+ align:start position:0%
+equation is X Prime y or X transpose
+yals Xpose x * beta hat
+
+ align:start position:0%
+yals Xpose x * beta hat
+ 
+
+ align:start position:0%
+yals Xpose x * beta hat
+okay and then if this is
+
+ align:start position:0%
+okay and then if this is
+ 
+
+ align:start position:0%
+okay and then if this is
+invertible and remember that was one of
+
+ align:start position:0%
+invertible and remember that was one of
+ 
+
+ align:start position:0%
+invertible and remember that was one of
+our assumptions that was our
+
+ align:start position:0%
+our assumptions that was our
+ 
+
+ align:start position:0%
+our assumptions that was our
+identification assumption that that
+
+ align:start position:0%
+identification assumption that that
+ 
+
+ align:start position:0%
+identification assumption that that
+thing was invertible if that's
+
+ align:start position:0%
+thing was invertible if that's
+ 
+
+ align:start position:0%
+thing was invertible if that's
+invertible then we get that beta hat is
+
+ align:start position:0%
+invertible then we get that beta hat is
+ 
+
+ align:start position:0%
+invertible then we get that beta hat is
+just equal to X Prime X inverse X Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y beautiful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I mean that was I mean that was
+
+ align:start position:0%
+okay so I mean that was I mean that was
+ 
+
+ align:start position:0%
+okay so I mean that was I mean that was
+literally the derivation of the the
+
+ align:start position:0%
+literally the derivation of the the
+ 
+
+ align:start position:0%
+literally the derivation of the the
+least squares estimators in Matrix
+
+ align:start position:0%
+least squares estimators in Matrix
+ 
+
+ align:start position:0%
+least squares estimators in Matrix
+notation if you look at my notes that
+
+ align:start position:0%
+notation if you look at my notes that
+ 
+
+ align:start position:0%
+notation if you look at my notes that
+I've posted online I mean it's just
+
+ align:start position:0%
+I've posted online I mean it's just
+ 
+
+ align:start position:0%
+I've posted online I mean it's just
+pages of algebra using that summation
+
+ align:start position:0%
+pages of algebra using that summation
+ 
+
+ align:start position:0%
+pages of algebra using that summation
+notation so this is why we love doing it
+
+ align:start position:0%
+notation so this is why we love doing it
+ 
+
+ align:start position:0%
+notation so this is why we love doing it
+in Matrix
+
+ align:start position:0%
+in Matrix
+ 
+
+ align:start position:0%
+in Matrix
+notation what do we want to know about
+
+ align:start position:0%
+notation what do we want to know about
+ 
+
+ align:start position:0%
+notation what do we want to know about
+beta hat what do we always want to know
+
+ align:start position:0%
+beta hat what do we always want to know
+ 
+
+ align:start position:0%
+beta hat what do we always want to know
+about an estimator so we can do
+
+ align:start position:0%
+about an estimator so we can do
+ 
+
+ align:start position:0%
+about an estimator so we can do
+inference it's distribution oh it's
+
+ align:start position:0%
+inference it's distribution oh it's
+ 
+
+ align:start position:0%
+inference it's distribution oh it's
+right up there
+
+ align:start position:0%
+right up there
+ 
+
+ align:start position:0%
+right up there
+okay okay fine so the expectation of
+
+ align:start position:0%
+okay okay fine so the expectation of
+ 
+
+ align:start position:0%
+okay okay fine so the expectation of
+beta hat is equal to Beta again this is
+
+ align:start position:0%
+beta hat is equal to Beta again this is
+ 
+
+ align:start position:0%
+beta hat is equal to Beta again this is
+in in Matrix notation it's very simple I
+
+ align:start position:0%
+in in Matrix notation it's very simple I
+ 
+
+ align:start position:0%
+in in Matrix notation it's very simple I
+haven't included the four lines or
+
+ align:start position:0%
+haven't included the four lines or
+ 
+
+ align:start position:0%
+haven't included the four lines or
+something like that but if you treat the
+
+ align:start position:0%
+something like that but if you treat the
+ 
+
+ align:start position:0%
+something like that but if you treat the
+X's as
+
+ align:start position:0%
+X's as
+ 
+
+ align:start position:0%
+X's as
+fixed um then that makes the sort of
+
+ align:start position:0%
+fixed um then that makes the sort of
+ 
+
+ align:start position:0%
+fixed um then that makes the sort of
+proof very simple okay they come outside
+
+ align:start position:0%
+proof very simple okay they come outside
+ 
+
+ align:start position:0%
+proof very simple okay they come outside
+the expectation operator and you
+
+ align:start position:0%
+the expectation operator and you
+ 
+
+ align:start position:0%
+the expectation operator and you
+basically just falls
+
+ align:start position:0%
+basically just falls
+ 
+
+ align:start position:0%
+basically just falls
+out so it is unbiased
+
+ align:start position:0%
+out so it is unbiased
+ 
+
+ align:start position:0%
+out so it is unbiased
+uh and the co-variance of beta hat
+
+ align:start position:0%
+uh and the co-variance of beta hat
+ 
+
+ align:start position:0%
+uh and the co-variance of beta hat
+remember this is the variance
+
+ align:start position:0%
+remember this is the variance
+ 
+
+ align:start position:0%
+remember this is the variance
+co-variance Matrix so it's the Matrix
+
+ align:start position:0%
+co-variance Matrix so it's the Matrix
+ 
+
+ align:start position:0%
+co-variance Matrix so it's the Matrix
+that has along the diagonal the
+
+ align:start position:0%
+that has along the diagonal the
+ 
+
+ align:start position:0%
+that has along the diagonal the
+variances of each of the beta hats and
+
+ align:start position:0%
+variances of each of the beta hats and
+ 
+
+ align:start position:0%
+variances of each of the beta hats and
+off the on the off diagonals the
+
+ align:start position:0%
+off the on the off diagonals the
+ 
+
+ align:start position:0%
+off the on the off diagonals the
+co-variances between them that is just
+
+ align:start position:0%
+co-variances between them that is just
+ 
+
+ align:start position:0%
+co-variances between them that is just
+equal to Sigma s time x Prime X
+
+ align:start position:0%
+equal to Sigma s time x Prime X
+ 
+
+ align:start position:0%
+equal to Sigma s time x Prime X
+inverse okay so again very elegant very
+
+ align:start position:0%
+inverse okay so again very elegant very
+ 
+
+ align:start position:0%
+inverse okay so again very elegant very
+beautiful and not too hard to show if
+
+ align:start position:0%
+beautiful and not too hard to show if
+ 
+
+ align:start position:0%
+beautiful and not too hard to show if
+you treat the X's as fixed
+
+ align:start position:0%
+you treat the X's as fixed
+ 
+
+ align:start position:0%
+you treat the X's as fixed
+and you can look on the website if
+
+ align:start position:0%
+and you can look on the website if
+ 
+
+ align:start position:0%
+and you can look on the website if
+you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interested and finally we often don't
+
+ align:start position:0%
+interested and finally we often don't
+ 
+
+ align:start position:0%
+interested and finally we often don't
+know what Sigma squar is for inference
+
+ align:start position:0%
+know what Sigma squar is for inference
+ 
+
+ align:start position:0%
+know what Sigma squar is for inference
+we need to know what Sigma squar is so
+
+ align:start position:0%
+we need to know what Sigma squar is so
+ 
+
+ align:start position:0%
+we need to know what Sigma squar is so
+or we need an estimate for Sigma squar
+
+ align:start position:0%
+or we need an estimate for Sigma squar
+ 
+
+ align:start position:0%
+or we need an estimate for Sigma squar
+so this is our uh this is our unbiased
+
+ align:start position:0%
+so this is our uh this is our unbiased
+ 
+
+ align:start position:0%
+so this is our uh this is our unbiased
+estimate uh for Sigma squared and as
+
+ align:start position:0%
+estimate uh for Sigma squared and as
+ 
+
+ align:start position:0%
+estimate uh for Sigma squared and as
+Esther uh uh
+
+ align:start position:0%
+Esther uh uh
+ 
+
+ align:start position:0%
+Esther uh uh
+anticipated uh here we have to subtract
+
+ align:start position:0%
+anticipated uh here we have to subtract
+ 
+
+ align:start position:0%
+anticipated uh here we have to subtract
+off a k instead of a two because instead
+
+ align:start position:0%
+off a k instead of a two because instead
+ 
+
+ align:start position:0%
+off a k instead of a two because instead
+of it being a uh byar model it's a
+
+ align:start position:0%
+of it being a uh byar model it's a
+ 
+
+ align:start position:0%
+of it being a uh byar model it's a
+Univar model or sorry multivar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model okay and then finally if we're
+
+ align:start position:0%
+model okay and then finally if we're
+ 
+
+ align:start position:0%
+model okay and then finally if we're
+willing to impose the more strict
+
+ align:start position:0%
+willing to impose the more strict
+ 
+
+ align:start position:0%
+willing to impose the more strict
+assumption on the error distribution the
+
+ align:start position:0%
+assumption on the error distribution the
+ 
+
+ align:start position:0%
+assumption on the error distribution the
+errors are normally distributed uh then
+
+ align:start position:0%
+errors are normally distributed uh then
+ 
+
+ align:start position:0%
+errors are normally distributed uh then
+the beta hats are also normally
+
+ align:start position:0%
+the beta hats are also normally
+ 
+
+ align:start position:0%
+the beta hats are also normally
+distributed so sometimes we want to
+
+ align:start position:0%
+distributed so sometimes we want to
+ 
+
+ align:start position:0%
+distributed so sometimes we want to
+impose that sometimes we want to be less
+
+ align:start position:0%
+impose that sometimes we want to be less
+ 
+
+ align:start position:0%
+impose that sometimes we want to be less
+uh Pro
+
+ align:start position:0%
+uh Pro
+ 
+
+ align:start position:0%
+uh Pro
+descriptive okay so now finally we get
+
+ align:start position:0%
+descriptive okay so now finally we get
+ 
+
+ align:start position:0%
+descriptive okay so now finally we get
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+inference so typically in the linear
+
+ align:start position:0%
+inference so typically in the linear
+ 
+
+ align:start position:0%
+inference so typically in the linear
+model we're going to want to test
+
+ align:start position:0%
+model we're going to want to test
+ 
+
+ align:start position:0%
+model we're going to want to test
+hypotheses involving the betas that's
+
+ align:start position:0%
+hypotheses involving the betas that's
+ 
+
+ align:start position:0%
+hypotheses involving the betas that's
+where the real action is I mean I Can
+
+ align:start position:0%
+where the real action is I mean I Can
+ 
+
+ align:start position:0%
+where the real action is I mean I Can
+Dream up hypotheses involving Sigma
+
+ align:start position:0%
+Dream up hypotheses involving Sigma
+ 
+
+ align:start position:0%
+Dream up hypotheses involving Sigma
+squar and things like that and that's
+
+ align:start position:0%
+squar and things like that and that's
+ 
+
+ align:start position:0%
+squar and things like that and that's
+fine and occasionally you might want to
+
+ align:start position:0%
+fine and occasionally you might want to
+ 
+
+ align:start position:0%
+fine and occasionally you might want to
+to test a hypothesis involving Sigma squ
+
+ align:start position:0%
+to test a hypothesis involving Sigma squ
+ 
+
+ align:start position:0%
+to test a hypothesis involving Sigma squ
+but really we care about the betas
+
+ align:start position:0%
+but really we care about the betas
+ 
+
+ align:start position:0%
+but really we care about the betas
+because the betas are the parameters in
+
+ align:start position:0%
+because the betas are the parameters in
+ 
+
+ align:start position:0%
+because the betas are the parameters in
+our conditional mean function of our
+
+ align:start position:0%
+our conditional mean function of our
+ 
+
+ align:start position:0%
+our conditional mean function of our
+outcome variable and the questions that
+
+ align:start position:0%
+outcome variable and the questions that
+ 
+
+ align:start position:0%
+outcome variable and the questions that
+we usually want to answer using a linear
+
+ align:start position:0%
+we usually want to answer using a linear
+ 
+
+ align:start position:0%
+we usually want to answer using a linear
+regression are about the nature of this
+
+ align:start position:0%
+regression are about the nature of this
+ 
+
+ align:start position:0%
+regression are about the nature of this
+conditional mean function okay so
+
+ align:start position:0%
+conditional mean function okay so
+ 
+
+ align:start position:0%
+conditional mean function okay so
+sometimes we might only be interested in
+
+ align:start position:0%
+sometimes we might only be interested in
+ 
+
+ align:start position:0%
+sometimes we might only be interested in
+one of the betas other times we might
+
+ align:start position:0%
+one of the betas other times we might
+ 
+
+ align:start position:0%
+one of the betas other times we might
+want to simultaneously test hypothesis
+
+ align:start position:0%
+want to simultaneously test hypothesis
+ 
+
+ align:start position:0%
+want to simultaneously test hypothesis
+about a whole bunch of them um and as we
+
+ align:start position:0%
+about a whole bunch of them um and as we
+ 
+
+ align:start position:0%
+about a whole bunch of them um and as we
+saw in the output that I showed you last
+
+ align:start position:0%
+saw in the output that I showed you last
+ 
+
+ align:start position:0%
+saw in the output that I showed you last
+lecture uh statistical packages
+
+ align:start position:0%
+lecture uh statistical packages
+ 
+
+ align:start position:0%
+lecture uh statistical packages
+typically perform some standard tests on
+
+ align:start position:0%
+typically perform some standard tests on
+ 
+
+ align:start position:0%
+typically perform some standard tests on
+the betas for free and just report them
+
+ align:start position:0%
+the betas for free and just report them
+ 
+
+ align:start position:0%
+the betas for free and just report them
+with uh with the output okay and you
+
+ align:start position:0%
+with uh with the output okay and you
+ 
+
+ align:start position:0%
+with uh with the output okay and you
+know that's fine and we can use those
+
+ align:start position:0%
+know that's fine and we can use those
+ 
+
+ align:start position:0%
+know that's fine and we can use those
+and they're often quite handy um but
+
+ align:start position:0%
+and they're often quite handy um but
+ 
+
+ align:start position:0%
+and they're often quite handy um but
+there may be other ones that we need to
+
+ align:start position:0%
+there may be other ones that we need to
+ 
+
+ align:start position:0%
+there may be other ones that we need to
+do ourselves so they don't perform every
+
+ align:start position:0%
+do ourselves so they don't perform every
+ 
+
+ align:start position:0%
+do ourselves so they don't perform every
+conceivable test we might be interested
+
+ align:start position:0%
+conceivable test we might be interested
+ 
+
+ align:start position:0%
+conceivable test we might be interested
+in okay so let's start with a pretty
+
+ align:start position:0%
+in okay so let's start with a pretty
+ 
+
+ align:start position:0%
+in okay so let's start with a pretty
+General framework for testing hypotheses
+
+ align:start position:0%
+General framework for testing hypotheses
+ 
+
+ align:start position:0%
+General framework for testing hypotheses
+about beta and it's not only quite
+
+ align:start position:0%
+about beta and it's not only quite
+ 
+
+ align:start position:0%
+about beta and it's not only quite
+General and flexible it's also super
+
+ align:start position:0%
+General and flexible it's also super
+ 
+
+ align:start position:0%
+General and flexible it's also super
+intuitive it's like one of my favorite
+
+ align:start position:0%
+intuitive it's like one of my favorite
+ 
+
+ align:start position:0%
+intuitive it's like one of my favorite
+tests I really like it okay so let's
+
+ align:start position:0%
+tests I really like it okay so let's
+ 
+
+ align:start position:0%
+tests I really like it okay so let's
+consider hypothesis the following
+
+ align:start position:0%
+consider hypothesis the following
+ 
+
+ align:start position:0%
+consider hypothesis the following
+form a matrix R Time beta is equal to a
+
+ align:start position:0%
+form a matrix R Time beta is equal to a
+ 
+
+ align:start position:0%
+form a matrix R Time beta is equal to a
+vector C that's the null hypothesis the
+
+ align:start position:0%
+vector C that's the null hypothesis the
+ 
+
+ align:start position:0%
+vector C that's the null hypothesis the
+alternative is that it's not equal to
+
+ align:start position:0%
+alternative is that it's not equal to
+ 
+
+ align:start position:0%
+alternative is that it's not equal to
+the vector C so what is this Matrix R
+
+ align:start position:0%
+the vector C so what is this Matrix R
+ 
+
+ align:start position:0%
+the vector C so what is this Matrix R
+it's a matrix of
+
+ align:start position:0%
+it's a matrix of
+ 
+
+ align:start position:0%
+it's a matrix of
+restrictions okay and its uh dimensions
+
+ align:start position:0%
+restrictions okay and its uh dimensions
+ 
+
+ align:start position:0%
+restrictions okay and its uh dimensions
+are R by k + 1 so it has the number of
+
+ align:start position:0%
+are R by k + 1 so it has the number of
+ 
+
+ align:start position:0%
+are R by k + 1 so it has the number of
+so it's the the number of columns is
+
+ align:start position:0%
+so it's the the number of columns is
+ 
+
+ align:start position:0%
+so it's the the number of columns is
+equal to the number of parameters the
+
+ align:start position:0%
+equal to the number of parameters the
+ 
+
+ align:start position:0%
+equal to the number of parameters the
+number of betas that we're estimating in
+
+ align:start position:0%
+number of betas that we're estimating in
+ 
+
+ align:start position:0%
+number of betas that we're estimating in
+the linear model and then the number of
+
+ align:start position:0%
+the linear model and then the number of
+ 
+
+ align:start position:0%
+the linear model and then the number of
+rows is the number of restrictions that
+
+ align:start position:0%
+rows is the number of restrictions that
+ 
+
+ align:start position:0%
+rows is the number of restrictions that
+we want to impose in our null hypothesis
+
+ align:start position:0%
+we want to impose in our null hypothesis
+ 
+
+ align:start position:0%
+we want to impose in our null hypothesis
+the number of restrictions we want to
+
+ align:start position:0%
+the number of restrictions we want to
+ 
+
+ align:start position:0%
+the number of restrictions we want to
+test so if R so we could have a matrix
+
+ align:start position:0%
+test so if R so we could have a matrix
+ 
+
+ align:start position:0%
+test so if R so we could have a matrix
+um that's just where R is equal to one
+
+ align:start position:0%
+um that's just where R is equal to one
+ 
+
+ align:start position:0%
+um that's just where R is equal to one
+and then we're just testing one
+
+ align:start position:0%
+and then we're just testing one
+ 
+
+ align:start position:0%
+and then we're just testing one
+restriction so that would correspond to
+
+ align:start position:0%
+restriction so that would correspond to
+ 
+
+ align:start position:0%
+restriction so that would correspond to
+something like beta 1 is equal to zero
+
+ align:start position:0%
+something like beta 1 is equal to zero
+ 
+
+ align:start position:0%
+something like beta 1 is equal to zero
+okay so let
+
+ align:start position:0%
+okay so let
+ 
+
+ align:start position:0%
+okay so let
+me oh so let me just say this I'll get
+
+ align:start position:0%
+me oh so let me just say this I'll get
+ 
+
+ align:start position:0%
+me oh so let me just say this I'll get
+to some examples in a minute okay so
+
+ align:start position:0%
+to some examples in a minute okay so
+ 
+
+ align:start position:0%
+to some examples in a minute okay so
+almost any hypothesis involving beta you
+
+ align:start position:0%
+almost any hypothesis involving beta you
+ 
+
+ align:start position:0%
+almost any hypothesis involving beta you
+can dream up in the context of the
+
+ align:start position:0%
+can dream up in the context of the
+ 
+
+ align:start position:0%
+can dream up in the context of the
+linear model can be captured in this
+
+ align:start position:0%
+linear model can be captured in this
+ 
+
+ align:start position:0%
+linear model can be captured in this
+framework not quite any but most of them
+
+ align:start position:0%
+framework not quite any but most of them
+ 
+
+ align:start position:0%
+framework not quite any but most of them
+you can test whether individual
+
+ align:start position:0%
+you can test whether individual
+ 
+
+ align:start position:0%
+you can test whether individual
+parameters are equal to zero you can
+
+ align:start position:0%
+parameters are equal to zero you can
+ 
+
+ align:start position:0%
+parameters are equal to zero you can
+test whether individual parameters are
+
+ align:start position:0%
+test whether individual parameters are
+ 
+
+ align:start position:0%
+test whether individual parameters are
+equal to something other than zero you
+
+ align:start position:0%
+equal to something other than zero you
+ 
+
+ align:start position:0%
+equal to something other than zero you
+can test multiple hypotheses
+
+ align:start position:0%
+can test multiple hypotheses
+ 
+
+ align:start position:0%
+can test multiple hypotheses
+simultaneously you can test hypothesis
+
+ align:start position:0%
+simultaneously you can test hypothesis
+ 
+
+ align:start position:0%
+simultaneously you can test hypothesis
+about linear combinations of parameters
+
+ align:start position:0%
+about linear combinations of parameters
+ 
+
+ align:start position:0%
+about linear combinations of parameters
+the world is your oyster okay so let me
+
+ align:start position:0%
+the world is your oyster okay so let me
+ 
+
+ align:start position:0%
+the world is your oyster okay so let me
+show you a few examples of these and
+
+ align:start position:0%
+show you a few examples of these and
+ 
+
+ align:start position:0%
+show you a few examples of these and
+exactly what the r Matrix looks like and
+
+ align:start position:0%
+exactly what the r Matrix looks like and
+ 
+
+ align:start position:0%
+exactly what the r Matrix looks like and
+what the C Vector looks like in these
+
+ align:start position:0%
+what the C Vector looks like in these
+ 
+
+ align:start position:0%
+what the C Vector looks like in these
+examples okay so let's say for instance
+
+ align:start position:0%
+examples okay so let's say for instance
+ 
+
+ align:start position:0%
+examples okay so let's say for instance
+that we set up the Matrix R to be just a
+
+ align:start position:0%
+that we set up the Matrix R to be just a
+ 
+
+ align:start position:0%
+that we set up the Matrix R to be just a
+row Vector with a zero in the first spot
+
+ align:start position:0%
+row Vector with a zero in the first spot
+ 
+
+ align:start position:0%
+row Vector with a zero in the first spot
+and then a one and then the rest zeros
+
+ align:start position:0%
+and then a one and then the rest zeros
+ 
+
+ align:start position:0%
+and then a one and then the rest zeros
+so what that Matrix is doing is it's
+
+ align:start position:0%
+so what that Matrix is doing is it's
+ 
+
+ align:start position:0%
+so what that Matrix is doing is it's
+picking out beta 1 okay remember it this
+
+ align:start position:0%
+picking out beta 1 okay remember it this
+ 
+
+ align:start position:0%
+picking out beta 1 okay remember it this
+this spot corresponds to Beta not okay
+
+ align:start position:0%
+this spot corresponds to Beta not okay
+ 
+
+ align:start position:0%
+this spot corresponds to Beta not okay
+so it's picking so being in the second
+
+ align:start position:0%
+so it's picking so being in the second
+ 
+
+ align:start position:0%
+so it's picking so being in the second
+spot it's picking out beta 1 and C is
+
+ align:start position:0%
+spot it's picking out beta 1 and C is
+ 
+
+ align:start position:0%
+spot it's picking out beta 1 and C is
+just what uh beta 1 is equal to under
+
+ align:start position:0%
+just what uh beta 1 is equal to under
+ 
+
+ align:start position:0%
+just what uh beta 1 is equal to under
+the null okay so that R and this C
+
+ align:start position:0%
+the null okay so that R and this C
+ 
+
+ align:start position:0%
+the null okay so that R and this C
+corresponds to the hypothesis that beta
+
+ align:start position:0%
+corresponds to the hypothesis that beta
+ 
+
+ align:start position:0%
+corresponds to the hypothesis that beta
+1 is equal to
+
+ align:start position:0%
+1 is equal to
+ 
+
+ align:start position:0%
+1 is equal to
+zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's suppose instead that we want to
+
+ align:start position:0%
+let's suppose instead that we want to
+ 
+
+ align:start position:0%
+let's suppose instead that we want to
+test a whole bunch of hypotheses
+
+ align:start position:0%
+test a whole bunch of hypotheses
+ 
+
+ align:start position:0%
+test a whole bunch of hypotheses
+simultaneously that beta 1 is equal to
+
+ align:start position:0%
+simultaneously that beta 1 is equal to
+ 
+
+ align:start position:0%
+simultaneously that beta 1 is equal to
+zero and beta 2 is equal to zero and
+
+ align:start position:0%
+zero and beta 2 is equal to zero and
+ 
+
+ align:start position:0%
+zero and beta 2 is equal to zero and
+beta 3 is equal to zero Etc well then
+
+ align:start position:0%
+beta 3 is equal to zero Etc well then
+ 
+
+ align:start position:0%
+beta 3 is equal to zero Etc well then
+this is what our R Matrix would look
+
+ align:start position:0%
+this is what our R Matrix would look
+ 
+
+ align:start position:0%
+this is what our R Matrix would look
+like okay so it would basically be an
+
+ align:start position:0%
+like okay so it would basically be an
+ 
+
+ align:start position:0%
+like okay so it would basically be an
+identity Matrix with a column of zeros
+
+ align:start position:0%
+identity Matrix with a column of zeros
+ 
+
+ align:start position:0%
+identity Matrix with a column of zeros
+tacked on the front the reason why the
+
+ align:start position:0%
+tacked on the front the reason why the
+ 
+
+ align:start position:0%
+tacked on the front the reason why the
+column of zeros is tacked on the front
+
+ align:start position:0%
+column of zeros is tacked on the front
+ 
+
+ align:start position:0%
+column of zeros is tacked on the front
+is because that corresponds to the
+
+ align:start position:0%
+is because that corresponds to the
+ 
+
+ align:start position:0%
+is because that corresponds to the
+intercept and we we're not interested at
+
+ align:start position:0%
+intercept and we we're not interested at
+ 
+
+ align:start position:0%
+intercept and we we're not interested at
+least here in testing a hypothesis about
+
+ align:start position:0%
+least here in testing a hypothesis about
+ 
+
+ align:start position:0%
+least here in testing a hypothesis about
+The Intercept
+
+ align:start position:0%
+The Intercept
+ 
+
+ align:start position:0%
+The Intercept
+okay and then the C Vector uh is just a
+
+ align:start position:0%
+okay and then the C Vector uh is just a
+ 
+
+ align:start position:0%
+okay and then the C Vector uh is just a
+vector of
+
+ align:start position:0%
+vector of
+ 
+
+ align:start position:0%
+vector of
+zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I do want to emphasize even
+
+ align:start position:0%
+okay so I do want to emphasize even
+ 
+
+ align:start position:0%
+okay so I do want to emphasize even
+though I've sort of written this as like
+
+ align:start position:0%
+though I've sort of written this as like
+ 
+
+ align:start position:0%
+though I've sort of written this as like
+one equation this is actually we're
+
+ align:start position:0%
+one equation this is actually we're
+ 
+
+ align:start position:0%
+one equation this is actually we're
+testing K hypotheses simultaneously here
+
+ align:start position:0%
+testing K hypotheses simultaneously here
+ 
+
+ align:start position:0%
+testing K hypotheses simultaneously here
+so we have K uh equal signs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's a more complicated
+
+ align:start position:0%
+okay so here's a more complicated
+ 
+
+ align:start position:0%
+okay so here's a more complicated
+example if our R Matrix has in the first
+
+ align:start position:0%
+example if our R Matrix has in the first
+ 
+
+ align:start position:0%
+example if our R Matrix has in the first
+row a one and a negative one and then
+
+ align:start position:0%
+row a one and a negative one and then
+ 
+
+ align:start position:0%
+row a one and a negative one and then
+the rest zeros sorry zero and then one
+
+ align:start position:0%
+the rest zeros sorry zero and then one
+ 
+
+ align:start position:0%
+the rest zeros sorry zero and then one
+negative one the rest zeros um and then
+
+ align:start position:0%
+negative one the rest zeros um and then
+ 
+
+ align:start position:0%
+negative one the rest zeros um and then
+the second row there's a one in the
+
+ align:start position:0%
+the second row there's a one in the
+ 
+
+ align:start position:0%
+the second row there's a one in the
+fourth
+
+ align:start position:0%
+fourth
+ 
+
+ align:start position:0%
+fourth
+spot
+
+ align:start position:0%
+spot
+ 
+
+ align:start position:0%
+spot
+Etc then and then the C Vector looks
+
+ align:start position:0%
+Etc then and then the C Vector looks
+ 
+
+ align:start position:0%
+Etc then and then the C Vector looks
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+what does this correspond to in terms of
+
+ align:start position:0%
+what does this correspond to in terms of
+ 
+
+ align:start position:0%
+what does this correspond to in terms of
+a a hypothesis we might want to test or
+
+ align:start position:0%
+a a hypothesis we might want to test or
+ 
+
+ align:start position:0%
+a a hypothesis we might want to test or
+a series of
+
+ align:start position:0%
+a series of
+ 
+
+ align:start position:0%
+a series of
+hypotheses well here the first row gives
+
+ align:start position:0%
+hypotheses well here the first row gives
+ 
+
+ align:start position:0%
+hypotheses well here the first row gives
+us the hypothesis that beta 1 minus beta
+
+ align:start position:0%
+us the hypothesis that beta 1 minus beta
+ 
+
+ align:start position:0%
+us the hypothesis that beta 1 minus beta
+2 is equal to zero so I could just write
+
+ align:start position:0%
+2 is equal to zero so I could just write
+ 
+
+ align:start position:0%
+2 is equal to zero so I could just write
+that as beta 1 is equal to Beta 2 right
+
+ align:start position:0%
+that as beta 1 is equal to Beta 2 right
+ 
+
+ align:start position:0%
+that as beta 1 is equal to Beta 2 right
+the second row corresponds to Beta 3
+
+ align:start position:0%
+the second row corresponds to Beta 3
+ 
+
+ align:start position:0%
+the second row corresponds to Beta 3
+this is beta 3 here being equal to five
+
+ align:start position:0%
+this is beta 3 here being equal to five
+ 
+
+ align:start position:0%
+this is beta 3 here being equal to five
+okay and and the third row corresponds
+
+ align:start position:0%
+okay and and the third row corresponds
+ 
+
+ align:start position:0%
+okay and and the third row corresponds
+to Beta K being equal to
+
+ align:start position:0%
+to Beta K being equal to
+ 
+
+ align:start position:0%
+to Beta K being equal to
+-2
+
+ align:start position:0%
+-2
+ 
+
+ align:start position:0%
+-2
+yes beta
+
+ align:start position:0%
+yes beta
+ 
+
+ align:start position:0%
+yes beta
+1sa okay so if I just wrote If I just uh
+
+ align:start position:0%
+1sa okay so if I just wrote If I just uh
+ 
+
+ align:start position:0%
+1sa okay so if I just wrote If I just uh
+wrote out what the you know just
+
+ align:start position:0%
+wrote out what the you know just
+ 
+
+ align:start position:0%
+wrote out what the you know just
+multiplied The Matrix um the r matrix by
+
+ align:start position:0%
+multiplied The Matrix um the r matrix by
+ 
+
+ align:start position:0%
+multiplied The Matrix um the r matrix by
+Beta And you know sort of wrote These
+
+ align:start position:0%
+Beta And you know sort of wrote These
+ 
+
+ align:start position:0%
+Beta And you know sort of wrote These
+out as equations I would get beta 1
+
+ align:start position:0%
+out as equations I would get beta 1
+ 
+
+ align:start position:0%
+out as equations I would get beta 1
+minus so this is beta 0 here so here's
+
+ align:start position:0%
+minus so this is beta 0 here so here's
+ 
+
+ align:start position:0%
+minus so this is beta 0 here so here's
+beta 1 minus beta 2 is equal to
+
+ align:start position:0%
+beta 1 minus beta 2 is equal to
+ 
+
+ align:start position:0%
+beta 1 minus beta 2 is equal to
+Z okay and then I just rewrote that is
+
+ align:start position:0%
+Z okay and then I just rewrote that is
+ 
+
+ align:start position:0%
+Z okay and then I just rewrote that is
+beta 1 is equal to Beta 2 that's all yep
+
+ align:start position:0%
+beta 1 is equal to Beta 2 that's all yep
+ 
+
+ align:start position:0%
+beta 1 is equal to Beta 2 that's all yep
+how often are we interested
+
+ align:start position:0%
+how often are we interested
+ 
+
+ align:start position:0%
+how often are we interested
+seea specific value rather than range
+
+ align:start position:0%
+seea specific value rather than range
+ 
+
+ align:start position:0%
+seea specific value rather than range
+and is there a way to that
+
+ align:start position:0%
+and is there a way to that
+ 
+
+ align:start position:0%
+and is there a way to that
+so yes and no so basically what if we're
+
+ align:start position:0%
+so yes and no so basically what if we're
+ 
+
+ align:start position:0%
+so yes and no so basically what if we're
+not interested in um if we're interested
+
+ align:start position:0%
+not interested in um if we're interested
+ 
+
+ align:start position:0%
+not interested in um if we're interested
+in whether beta is in a Range then what
+
+ align:start position:0%
+in whether beta is in a Range then what
+ 
+
+ align:start position:0%
+in whether beta is in a Range then what
+we might want to do is instead of doing
+
+ align:start position:0%
+we might want to do is instead of doing
+ 
+
+ align:start position:0%
+we might want to do is instead of doing
+a hypothesis test where the null was a
+
+ align:start position:0%
+a hypothesis test where the null was a
+ 
+
+ align:start position:0%
+a hypothesis test where the null was a
+single value and the alternative was
+
+ align:start position:0%
+single value and the alternative was
+ 
+
+ align:start position:0%
+single value and the alternative was
+everything else we might want to do say
+
+ align:start position:0%
+everything else we might want to do say
+ 
+
+ align:start position:0%
+everything else we might want to do say
+a one-sided test where the null is that
+
+ align:start position:0%
+a one-sided test where the null is that
+ 
+
+ align:start position:0%
+a one-sided test where the null is that
+beta is less than some value and the
+
+ align:start position:0%
+beta is less than some value and the
+ 
+
+ align:start position:0%
+beta is less than some value and the
+alternative is that it's greater than
+
+ align:start position:0%
+alternative is that it's greater than
+ 
+
+ align:start position:0%
+alternative is that it's greater than
+some value we can do those we can't do
+
+ align:start position:0%
+some value we can do those we can't do
+ 
+
+ align:start position:0%
+some value we can do those we can't do
+them in this framework so I'll talk
+
+ align:start position:0%
+them in this framework so I'll talk
+ 
+
+ align:start position:0%
+them in this framework so I'll talk
+about that in a second the other the
+
+ align:start position:0%
+about that in a second the other the
+ 
+
+ align:start position:0%
+about that in a second the other the
+other thing that you might be suggesting
+
+ align:start position:0%
+other thing that you might be suggesting
+ 
+
+ align:start position:0%
+other thing that you might be suggesting
+is instead of doing hypothesis testing
+
+ align:start position:0%
+is instead of doing hypothesis testing
+ 
+
+ align:start position:0%
+is instead of doing hypothesis testing
+we might want to just report confidence
+
+ align:start position:0%
+we might want to just report confidence
+ 
+
+ align:start position:0%
+we might want to just report confidence
+intervals as well so remember that that
+
+ align:start position:0%
+intervals as well so remember that that
+ 
+
+ align:start position:0%
+intervals as well so remember that that
+really hypothesis testing and
+
+ align:start position:0%
+really hypothesis testing and
+ 
+
+ align:start position:0%
+really hypothesis testing and
+constructing confidence intervals are
+
+ align:start position:0%
+constructing confidence intervals are
+ 
+
+ align:start position:0%
+constructing confidence intervals are
+kind of the same thing just reporting
+
+ align:start position:0%
+kind of the same thing just reporting
+ 
+
+ align:start position:0%
+kind of the same thing just reporting
+the same information in different forms
+
+ align:start position:0%
+the same information in different forms
+ 
+
+ align:start position:0%
+the same information in different forms
+and so um you know it can just be a
+
+ align:start position:0%
+and so um you know it can just be a
+ 
+
+ align:start position:0%
+and so um you know it can just be a
+matter of style or preference uh instead
+
+ align:start position:0%
+matter of style or preference uh instead
+ 
+
+ align:start position:0%
+matter of style or preference uh instead
+of uh reporting hypothesis tests you
+
+ align:start position:0%
+of uh reporting hypothesis tests you
+ 
+
+ align:start position:0%
+of uh reporting hypothesis tests you
+report confidence intervals and that's
+
+ align:start position:0%
+report confidence intervals and that's
+ 
+
+ align:start position:0%
+report confidence intervals and that's
+perfectly fine yeah confidence inter
+
+ align:start position:0%
+perfectly fine yeah confidence inter
+ 
+
+ align:start position:0%
+perfectly fine yeah confidence inter
+will be hard to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-4 is yeah in I mean it's kind of hard
+
+ align:start position:0%
+-4 is yeah in I mean it's kind of hard
+ 
+
+ align:start position:0%
+-4 is yeah in I mean it's kind of hard
+to see they don't really add up so yeah
+
+ align:start position:0%
+to see they don't really add up so yeah
+ 
+
+ align:start position:0%
+to see they don't really add up so yeah
+and I guess I guess the other the other
+
+ align:start position:0%
+and I guess I guess the other the other
+ 
+
+ align:start position:0%
+and I guess I guess the other the other
+sort of more fundamental answer to your
+
+ align:start position:0%
+sort of more fundamental answer to your
+ 
+
+ align:start position:0%
+sort of more fundamental answer to your
+question is that sometimes we actually
+
+ align:start position:0%
+question is that sometimes we actually
+ 
+
+ align:start position:0%
+question is that sometimes we actually
+do like there might be a theory that
+
+ align:start position:0%
+do like there might be a theory that
+ 
+
+ align:start position:0%
+do like there might be a theory that
+says beta should be equal to this number
+
+ align:start position:0%
+says beta should be equal to this number
+ 
+
+ align:start position:0%
+says beta should be equal to this number
+and we're in order to test that theory
+
+ align:start position:0%
+and we're in order to test that theory
+ 
+
+ align:start position:0%
+and we're in order to test that theory
+we want to perform a hypothesis test
+
+ align:start position:0%
+we want to perform a hypothesis test
+ 
+
+ align:start position:0%
+we want to perform a hypothesis test
+that beta is equal to that number so
+
+ align:start position:0%
+that beta is equal to that number so
+ 
+
+ align:start position:0%
+that beta is equal to that number so
+that does come up um and not every but
+
+ align:start position:0%
+that does come up um and not every but
+ 
+
+ align:start position:0%
+that does come up um and not every but
+yeah it is it is relevant other
+
+ align:start position:0%
+yeah it is it is relevant other
+ 
+
+ align:start position:0%
+yeah it is it is relevant other
+questions no you could also use it
+
+ align:start position:0%
+questions no you could also use it
+ 
+
+ align:start position:0%
+questions no you could also use it
+to if somebody came out with a paper say
+
+ align:start position:0%
+to if somebody came out with a paper say
+ 
+
+ align:start position:0%
+to if somebody came out with a paper say
+describing the treatment of valarian X
+
+ align:start position:0%
+describing the treatment of valarian X
+ 
+
+ align:start position:0%
+describing the treatment of valarian X
+and you wanted to see if that was true
+
+ align:start position:0%
+and you wanted to see if that was true
+ 
+
+ align:start position:0%
+and you wanted to see if that was true
+or not and you just take that beta test
+
+ align:start position:0%
+or not and you just take that beta test
+ 
+
+ align:start position:0%
+or not and you just take that beta test
+for do hypothesis Tes right yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay okay oh here's here's part of the
+
+ align:start position:0%
+okay okay oh here's here's part of the
+ 
+
+ align:start position:0%
+okay okay oh here's here's part of the
+answer to your question one thing you
+
+ align:start position:0%
+answer to your question one thing you
+ 
+
+ align:start position:0%
+answer to your question one thing you
+can't do in this framework as test
+
+ align:start position:0%
+can't do in this framework as test
+ 
+
+ align:start position:0%
+can't do in this framework as test
+one-sided hypothesis we'll get back to
+
+ align:start position:0%
+one-sided hypothesis we'll get back to
+ 
+
+ align:start position:0%
+one-sided hypothesis we'll get back to
+those okay so so now we have um we have
+
+ align:start position:0%
+those okay so so now we have um we have
+ 
+
+ align:start position:0%
+those okay so so now we have um we have
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+framework I mean it's not really
+
+ align:start position:0%
+framework I mean it's not really
+ 
+
+ align:start position:0%
+framework I mean it's not really
+framework just sort of a notation in
+
+ align:start position:0%
+framework just sort of a notation in
+ 
+
+ align:start position:0%
+framework just sort of a notation in
+some sense to set up you know the to
+
+ align:start position:0%
+some sense to set up you know the to
+ 
+
+ align:start position:0%
+some sense to set up you know the to
+deal with sort of um hypotheses of of
+
+ align:start position:0%
+deal with sort of um hypotheses of of
+ 
+
+ align:start position:0%
+deal with sort of um hypotheses of of
+all of the forms we just talked about
+
+ align:start position:0%
+all of the forms we just talked about
+ 
+
+ align:start position:0%
+all of the forms we just talked about
+and within the regression framework we
+
+ align:start position:0%
+and within the regression framework we
+ 
+
+ align:start position:0%
+and within the regression framework we
+have a super intuitive and cool way to
+
+ align:start position:0%
+have a super intuitive and cool way to
+ 
+
+ align:start position:0%
+have a super intuitive and cool way to
+test these hypotheses so first of all
+
+ align:start position:0%
+test these hypotheses so first of all
+ 
+
+ align:start position:0%
+test these hypotheses so first of all
+let's think of the null is describing a
+
+ align:start position:0%
+let's think of the null is describing a
+ 
+
+ align:start position:0%
+let's think of the null is describing a
+set of restrictions on the model okay so
+
+ align:start position:0%
+set of restrictions on the model okay so
+ 
+
+ align:start position:0%
+set of restrictions on the model okay so
+let me just go back for a second so in
+
+ align:start position:0%
+let me just go back for a second so in
+ 
+
+ align:start position:0%
+let me just go back for a second so in
+this case this null has three different
+
+ align:start position:0%
+this case this null has three different
+ 
+
+ align:start position:0%
+this case this null has three different
+restrictions that beta 1 is equal to
+
+ align:start position:0%
+restrictions that beta 1 is equal to
+ 
+
+ align:start position:0%
+restrictions that beta 1 is equal to
+Beta 2 that beta 3 is equal to 5 and
+
+ align:start position:0%
+Beta 2 that beta 3 is equal to 5 and
+ 
+
+ align:start position:0%
+Beta 2 that beta 3 is equal to 5 and
+that beta K is equal to minus two okay
+
+ align:start position:0%
+that beta K is equal to minus two okay
+ 
+
+ align:start position:0%
+that beta K is equal to minus two okay
+so we think of the null as imposing
+
+ align:start position:0%
+so we think of the null as imposing
+ 
+
+ align:start position:0%
+so we think of the null as imposing
+restrictions on the
+
+ align:start position:0%
+restrictions on the
+ 
+
+ align:start position:0%
+restrictions on the
+model then here's how we perform the
+
+ align:start position:0%
+model then here's how we perform the
+ 
+
+ align:start position:0%
+model then here's how we perform the
+test we estimate the unrestricted model
+
+ align:start position:0%
+test we estimate the unrestricted model
+ 
+
+ align:start position:0%
+test we estimate the unrestricted model
+we impose the restrictions of the null
+
+ align:start position:0%
+we impose the restrictions of the null
+ 
+
+ align:start position:0%
+we impose the restrictions of the null
+and estimate that model and then we
+
+ align:start position:0%
+and estimate that model and then we
+ 
+
+ align:start position:0%
+and estimate that model and then we
+compare the goodness of fit of those two
+
+ align:start position:0%
+compare the goodness of fit of those two
+ 
+
+ align:start position:0%
+compare the goodness of fit of those two
+models okay so that's why I love this
+
+ align:start position:0%
+models okay so that's why I love this
+ 
+
+ align:start position:0%
+models okay so that's why I love this
+test it's just it seems really intuitive
+
+ align:start position:0%
+test it's just it seems really intuitive
+ 
+
+ align:start position:0%
+test it's just it seems really intuitive
+to me that if you have a set of
+
+ align:start position:0%
+to me that if you have a set of
+ 
+
+ align:start position:0%
+to me that if you have a set of
+restrictions and they really
+
+ align:start position:0%
+restrictions and they really
+ 
+
+ align:start position:0%
+restrictions and they really
+bind and like the the they really sort
+
+ align:start position:0%
+bind and like the the they really sort
+ 
+
+ align:start position:0%
+bind and like the the they really sort
+of affect how good your fit is then that
+
+ align:start position:0%
+of affect how good your fit is then that
+ 
+
+ align:start position:0%
+of affect how good your fit is then that
+tells you well maybe those restrictions
+
+ align:start position:0%
+tells you well maybe those restrictions
+ 
+
+ align:start position:0%
+tells you well maybe those restrictions
+are not
+
+ align:start position:0%
+are not
+ 
+
+ align:start position:0%
+are not
+true if the restrictions on the other
+
+ align:start position:0%
+true if the restrictions on the other
+ 
+
+ align:start position:0%
+true if the restrictions on the other
+hand don't really bind that much if your
+
+ align:start position:0%
+hand don't really bind that much if your
+ 
+
+ align:start position:0%
+hand don't really bind that much if your
+your um model fil fits almost as well
+
+ align:start position:0%
+your um model fil fits almost as well
+ 
+
+ align:start position:0%
+your um model fil fits almost as well
+with the unrestricted model the
+
+ align:start position:0%
+with the unrestricted model the
+ 
+
+ align:start position:0%
+with the unrestricted model the
+restricted model as it does with the
+
+ align:start position:0%
+restricted model as it does with the
+ 
+
+ align:start position:0%
+restricted model as it does with the
+unrestricted model then that tells you
+
+ align:start position:0%
+unrestricted model then that tells you
+ 
+
+ align:start position:0%
+unrestricted model then that tells you
+maybe these restrictions are true or
+
+ align:start position:0%
+maybe these restrictions are true or
+ 
+
+ align:start position:0%
+maybe these restrictions are true or
+close to true and we don't want to
+
+ align:start position:0%
+close to true and we don't want to
+ 
+
+ align:start position:0%
+close to true and we don't want to
+reject them okay so that's the whole
+
+ align:start position:0%
+reject them okay so that's the whole
+ 
+
+ align:start position:0%
+reject them okay so that's the whole
+intuition and the idea behind this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+test okay
+
+ align:start position:0%
+test okay
+ 
+
+ align:start position:0%
+test okay
+so um estimating so a couple details
+
+ align:start position:0%
+so um estimating so a couple details
+ 
+
+ align:start position:0%
+so um estimating so a couple details
+before we get to sort of the
+
+ align:start position:0%
+before we get to sort of the
+ 
+
+ align:start position:0%
+before we get to sort of the
+distribution the test statistic
+
+ align:start position:0%
+distribution the test statistic
+ 
+
+ align:start position:0%
+distribution the test statistic
+estimating the unrestricted model is
+
+ align:start position:0%
+estimating the unrestricted model is
+ 
+
+ align:start position:0%
+estimating the unrestricted model is
+simple just run the regression but how
+
+ align:start position:0%
+simple just run the regression but how
+ 
+
+ align:start position:0%
+simple just run the regression but how
+do we estimate the restricted model well
+
+ align:start position:0%
+do we estimate the restricted model well
+ 
+
+ align:start position:0%
+do we estimate the restricted model well
+let's it depends on how what form the
+
+ align:start position:0%
+let's it depends on how what form the
+ 
+
+ align:start position:0%
+let's it depends on how what form the
+restrictions take so let's say we have
+
+ align:start position:0%
+restrictions take so let's say we have
+ 
+
+ align:start position:0%
+restrictions take so let's say we have
+we're testing hypothesis where uh just a
+
+ align:start position:0%
+we're testing hypothesis where uh just a
+ 
+
+ align:start position:0%
+we're testing hypothesis where uh just a
+bunch of the betas are equal to zero how
+
+ align:start position:0%
+bunch of the betas are equal to zero how
+ 
+
+ align:start position:0%
+bunch of the betas are equal to zero how
+do we run the restricted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model yes we just think the on the one
+
+ align:start position:0%
+model yes we just think the on the one
+ 
+
+ align:start position:0%
+model yes we just think the on the one
+Z yes exactly so we just leave out so so
+
+ align:start position:0%
+Z yes exactly so we just leave out so so
+ 
+
+ align:start position:0%
+Z yes exactly so we just leave out so so
+practically speaking what we do is we
+
+ align:start position:0%
+practically speaking what we do is we
+ 
+
+ align:start position:0%
+practically speaking what we do is we
+just run the regression leaving out all
+
+ align:start position:0%
+just run the regression leaving out all
+ 
+
+ align:start position:0%
+just run the regression leaving out all
+of those X's so that's the way we
+
+ align:start position:0%
+of those X's so that's the way we
+ 
+
+ align:start position:0%
+of those X's so that's the way we
+constrain the the coefficients to be
+
+ align:start position:0%
+constrain the the coefficients to be
+ 
+
+ align:start position:0%
+constrain the the coefficients to be
+equal to zero okay so we have the
+
+ align:start position:0%
+equal to zero okay so we have the
+ 
+
+ align:start position:0%
+equal to zero okay so we have the
+unrestricted the unrestricted regression
+
+ align:start position:0%
+unrestricted the unrestricted regression
+ 
+
+ align:start position:0%
+unrestricted the unrestricted regression
+is just sort of all of the X's are in
+
+ align:start position:0%
+is just sort of all of the X's are in
+ 
+
+ align:start position:0%
+is just sort of all of the X's are in
+there if we want to restrict that
+
+ align:start position:0%
+there if we want to restrict that
+ 
+
+ align:start position:0%
+there if we want to restrict that
+certain betas are equal to zero we just
+
+ align:start position:0%
+certain betas are equal to zero we just
+ 
+
+ align:start position:0%
+certain betas are equal to zero we just
+run another regression where we leave
+
+ align:start position:0%
+run another regression where we leave
+ 
+
+ align:start position:0%
+run another regression where we leave
+out the X's associated with the betas
+
+ align:start position:0%
+out the X's associated with the betas
+ 
+
+ align:start position:0%
+out the X's associated with the betas
+that that we want to have equal to zero
+
+ align:start position:0%
+that that we want to have equal to zero
+ 
+
+ align:start position:0%
+that that we want to have equal to zero
+okay so that's our our restricted
+
+ align:start position:0%
+okay so that's our our restricted
+ 
+
+ align:start position:0%
+okay so that's our our restricted
+model okay then let's say the
+
+ align:start position:0%
+model okay then let's say the
+ 
+
+ align:start position:0%
+model okay then let's say the
+Restriction is that the two betas are
+
+ align:start position:0%
+Restriction is that the two betas are
+ 
+
+ align:start position:0%
+Restriction is that the two betas are
+equal we have you know beta 1 equals
+
+ align:start position:0%
+equal we have you know beta 1 equals
+ 
+
+ align:start position:0%
+equal we have you know beta 1 equals
+beta 2 or something like that that's our
+
+ align:start position:0%
+beta 2 or something like that that's our
+ 
+
+ align:start position:0%
+beta 2 or something like that that's our
+null restriction um then how do we
+
+ align:start position:0%
+null restriction um then how do we
+ 
+
+ align:start position:0%
+null restriction um then how do we
+impose that restriction on a linear
+
+ align:start position:0%
+impose that restriction on a linear
+ 
+
+ align:start position:0%
+impose that restriction on a linear
+model well let me actually might help if
+
+ align:start position:0%
+model well let me actually might help if
+ 
+
+ align:start position:0%
+model well let me actually might help if
+I write the linear model so we have y
+
+ align:start position:0%
+I write the linear model so we have y
+ 
+
+ align:start position:0%
+I write the linear model so we have y
+subi
+
+ align:start position:0%
+subi
+ 
+
+ align:start position:0%
+subi
+equal beta KN plus beta
+
+ align:start position:0%
+equal beta KN plus beta
+ 
+
+ align:start position:0%
+equal beta KN plus beta
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+X1 ah I hope I'm using the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation do I have my subscripts in the
+
+ align:start position:0%
+notation do I have my subscripts in the
+ 
+
+ align:start position:0%
+notation do I have my subscripts in the
+same order I hope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so let's suppose this is our um
+
+ align:start position:0%
+so okay so let's suppose this is our um
+ 
+
+ align:start position:0%
+so okay so let's suppose this is our um
+this is our our uh unrestricted model we
+
+ align:start position:0%
+this is our our uh unrestricted model we
+ 
+
+ align:start position:0%
+this is our our uh unrestricted model we
+want to restrict beta one to be equal to
+
+ align:start position:0%
+want to restrict beta one to be equal to
+ 
+
+ align:start position:0%
+want to restrict beta one to be equal to
+Beta 2 well what do we do we just create
+
+ align:start position:0%
+Beta 2 well what do we do we just create
+ 
+
+ align:start position:0%
+Beta 2 well what do we do we just create
+a new variable that's the sum of these
+
+ align:start position:0%
+a new variable that's the sum of these
+ 
+
+ align:start position:0%
+a new variable that's the sum of these
+two so this is
+
+ align:start position:0%
+two so this is
+ 
+
+ align:start position:0%
+two so this is
+called X1 i+ x 2 I it's just a new
+
+ align:start position:0%
+called X1 i+ x 2 I it's just a new
+ 
+
+ align:start position:0%
+called X1 i+ x 2 I it's just a new
+variable and then we only
+
+ align:start position:0%
+variable and then we only
+ 
+
+ align:start position:0%
+variable and then we only
+estimate
+
+ align:start position:0%
+estimate
+ 
+
+ align:start position:0%
+estimate
+one coefficient on that so our
+
+ align:start position:0%
+one coefficient on that so our
+ 
+
+ align:start position:0%
+one coefficient on that so our
+restricted model is just that we create
+
+ align:start position:0%
+restricted model is just that we create
+ 
+
+ align:start position:0%
+restricted model is just that we create
+we don't don't include this variable as
+
+ align:start position:0%
+we don't don't include this variable as
+ 
+
+ align:start position:0%
+we don't don't include this variable as
+a regressor or this variable as a
+
+ align:start position:0%
+a regressor or this variable as a
+ 
+
+ align:start position:0%
+a regressor or this variable as a
+regressor we include their sum as a
+
+ align:start position:0%
+regressor we include their sum as a
+ 
+
+ align:start position:0%
+regressor we include their sum as a
+regressor okay and that's how we're
+
+ align:start position:0%
+regressor okay and that's how we're
+ 
+
+ align:start position:0%
+regressor okay and that's how we're
+imposing the null restriction because
+
+ align:start position:0%
+imposing the null restriction because
+ 
+
+ align:start position:0%
+imposing the null restriction because
+when we include their sum we're making
+
+ align:start position:0%
+when we include their sum we're making
+ 
+
+ align:start position:0%
+when we include their sum we're making
+their two coefficients equal we're
+
+ align:start position:0%
+their two coefficients equal we're
+ 
+
+ align:start position:0%
+their two coefficients equal we're
+forcing their two coefficients to be
+
+ align:start position:0%
+forcing their two coefficients to be
+ 
+
+ align:start position:0%
+forcing their two coefficients to be
+equal okay yep so are we testing the
+
+ align:start position:0%
+equal okay yep so are we testing the
+ 
+
+ align:start position:0%
+equal okay yep so are we testing the
+first beta one and the second beta one
+
+ align:start position:0%
+first beta one and the second beta one
+ 
+
+ align:start position:0%
+first beta one and the second beta one
+are the same exactly yes this is this is
+
+ align:start position:0%
+are the same exactly yes this is this is
+ 
+
+ align:start position:0%
+are the same exactly yes this is this is
+testing the hypothesis
+
+ align:start position:0%
+testing the hypothesis
+ 
+
+ align:start position:0%
+testing the hypothesis
+that beta 1 is equal to Beta 2 okay yep
+
+ align:start position:0%
+that beta 1 is equal to Beta 2 okay yep
+ 
+
+ align:start position:0%
+that beta 1 is equal to Beta 2 okay yep
+is that beta
+
+ align:start position:0%
+is that beta
+ 
+
+ align:start position:0%
+is that beta
+2 yeah it's definitely different yeah so
+
+ align:start position:0%
+2 yeah it's definitely different yeah so
+ 
+
+ align:start position:0%
+2 yeah it's definitely different yeah so
+here these these betas could be ver
+
+ align:start position:0%
+here these these betas could be ver
+ 
+
+ align:start position:0%
+here these these betas could be ver
+could be anything they could be a
+
+ align:start position:0%
+could be anything they could be a
+ 
+
+ align:start position:0%
+could be anything they could be a
+million we're just the hypo we're just
+
+ align:start position:0%
+million we're just the hypo we're just
+ 
+
+ align:start position:0%
+million we're just the hypo we're just
+testing the hypothesis that they're
+
+ align:start position:0%
+testing the hypothesis that they're
+ 
+
+ align:start position:0%
+testing the hypothesis that they're
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+okay so yes uh but if if it's
+
+ align:start position:0%
+okay so yes uh but if if it's
+ 
+
+ align:start position:0%
+okay so yes uh but if if it's
+a but if they're equal wouldn't it be
+
+ align:start position:0%
+a but if they're equal wouldn't it be
+ 
+
+ align:start position:0%
+a but if they're equal wouldn't it be
+like a linear combination of together
+
+ align:start position:0%
+like a linear combination of together
+ 
+
+ align:start position:0%
+like a linear combination of together
+and become Zer you know how like we have
+
+ align:start position:0%
+and become Zer you know how like we have
+ 
+
+ align:start position:0%
+and become Zer you know how like we have
+to they cannot be like a line
+
+ align:start position:0%
+to they cannot be like a line
+ 
+
+ align:start position:0%
+to they cannot be like a line
+some I'm not uh not sure if I understand
+
+ align:start position:0%
+some I'm not uh not sure if I understand
+ 
+
+ align:start position:0%
+some I'm not uh not sure if I understand
+your question so basically what what I'm
+
+ align:start position:0%
+your question so basically what what I'm
+ 
+
+ align:start position:0%
+your question so basically what what I'm
+trying to do here is impose just this
+
+ align:start position:0%
+trying to do here is impose just this
+ 
+
+ align:start position:0%
+trying to do here is impose just this
+hypothesis but not impose anything else
+
+ align:start position:0%
+hypothesis but not impose anything else
+ 
+
+ align:start position:0%
+hypothesis but not impose anything else
+about what the betas might be uh equal
+
+ align:start position:0%
+about what the betas might be uh equal
+ 
+
+ align:start position:0%
+about what the betas might be uh equal
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+identification restriction is not on the
+
+ align:start position:0%
+identification restriction is not on the
+ 
+
+ align:start position:0%
+identification restriction is not on the
+betas it's on the ex
+
+ align:start position:0%
+betas it's on the ex
+ 
+
+ align:start position:0%
+betas it's on the ex
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+whatever ahh you were confused about the
+
+ align:start position:0%
+whatever ahh you were confused about the
+ 
+
+ align:start position:0%
+whatever ahh you were confused about the
+identification assumption y yep y that's
+
+ align:start position:0%
+identification assumption y yep y that's
+ 
+
+ align:start position:0%
+identification assumption y yep y that's
+right okay um what if the if you we can
+
+ align:start position:0%
+right okay um what if the if you we can
+ 
+
+ align:start position:0%
+right okay um what if the if you we can
+re ask your question saying if you could
+
+ align:start position:0%
+re ask your question saying if you could
+ 
+
+ align:start position:0%
+re ask your question saying if you could
+OST the sum and just X and that in fact
+
+ align:start position:0%
+OST the sum and just X and that in fact
+ 
+
+ align:start position:0%
+OST the sum and just X and that in fact
+they were
+
+ align:start position:0%
+they were
+ 
+
+ align:start position:0%
+they were
+equal you can guess what the beta be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X okay what if the Restriction is that
+
+ align:start position:0%
+X okay what if the Restriction is that
+ 
+
+ align:start position:0%
+X okay what if the Restriction is that
+sum beta is equal to to a constant
+
+ align:start position:0%
+sum beta is equal to to a constant
+ 
+
+ align:start position:0%
+sum beta is equal to to a constant
+C how would we impose that restriction
+
+ align:start position:0%
+C how would we impose that restriction
+ 
+
+ align:start position:0%
+C how would we impose that restriction
+and then reestimate the restricted model
+
+ align:start position:0%
+and then reestimate the restricted model
+ 
+
+ align:start position:0%
+and then reestimate the restricted model
+well if we have let's suppose this is
+
+ align:start position:0%
+well if we have let's suppose this is
+ 
+
+ align:start position:0%
+well if we have let's suppose this is
+just a constant so we impose that this
+
+ align:start position:0%
+just a constant so we impose that this
+ 
+
+ align:start position:0%
+just a constant so we impose that this
+one's equal to a constant so then here
+
+ align:start position:0%
+one's equal to a constant so then here
+ 
+
+ align:start position:0%
+one's equal to a constant so then here
+that we have something we we there's no
+
+ align:start position:0%
+that we have something we we there's no
+ 
+
+ align:start position:0%
+that we have something we we there's no
+parameter in this term that we need to
+
+ align:start position:0%
+parameter in this term that we need to
+ 
+
+ align:start position:0%
+parameter in this term that we need to
+estimate under the null so we just
+
+ align:start position:0%
+estimate under the null so we just
+ 
+
+ align:start position:0%
+estimate under the null so we just
+subtract the constant times X1 from the
+
+ align:start position:0%
+subtract the constant times X1 from the
+ 
+
+ align:start position:0%
+subtract the constant times X1 from the
+dependent variable and rerun that
+
+ align:start position:0%
+dependent variable and rerun that
+ 
+
+ align:start position:0%
+dependent variable and rerun that
+regression that's our restricted
+
+ align:start position:0%
+regression that's our restricted
+ 
+
+ align:start position:0%
+regression that's our restricted
+regression okay does that make sense
+
+ align:start position:0%
+regression okay does that make sense
+ 
+
+ align:start position:0%
+regression okay does that make sense
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so going back we estimate the
+
+ align:start position:0%
+so so going back we estimate the
+ 
+
+ align:start position:0%
+so so going back we estimate the
+unrestricted model we estim we impose
+
+ align:start position:0%
+unrestricted model we estim we impose
+ 
+
+ align:start position:0%
+unrestricted model we estim we impose
+restrictions and estimate that model and
+
+ align:start position:0%
+restrictions and estimate that model and
+ 
+
+ align:start position:0%
+restrictions and estimate that model and
+then we compare the goodness of fit and
+
+ align:start position:0%
+then we compare the goodness of fit and
+ 
+
+ align:start position:0%
+then we compare the goodness of fit and
+if the goodness of fit is not very
+
+ align:start position:0%
+if the goodness of fit is not very
+ 
+
+ align:start position:0%
+if the goodness of fit is not very
+different we don't reject the null if
+
+ align:start position:0%
+different we don't reject the null if
+ 
+
+ align:start position:0%
+different we don't reject the null if
+it's very different we reject the null
+
+ align:start position:0%
+it's very different we reject the null
+ 
+
+ align:start position:0%
+it's very different we reject the null
+in particular this test statistic which
+
+ align:start position:0%
+in particular this test statistic which
+ 
+
+ align:start position:0%
+in particular this test statistic which
+which is basically on the the numerator
+
+ align:start position:0%
+which is basically on the the numerator
+ 
+
+ align:start position:0%
+which is basically on the the numerator
+has the difference in the sum of square
+
+ align:start position:0%
+has the difference in the sum of square
+ 
+
+ align:start position:0%
+has the difference in the sum of square
+the restricted and unrestricted sum of
+
+ align:start position:0%
+the restricted and unrestricted sum of
+ 
+
+ align:start position:0%
+the restricted and unrestricted sum of
+squares and then in the denominator has
+
+ align:start position:0%
+squares and then in the denominator has
+ 
+
+ align:start position:0%
+squares and then in the denominator has
+the unrestricted sum of squares this is
+
+ align:start position:0%
+the unrestricted sum of squares this is
+ 
+
+ align:start position:0%
+the unrestricted sum of squares this is
+how we form the test statistic and it
+
+ align:start position:0%
+how we form the test statistic and it
+ 
+
+ align:start position:0%
+how we form the test statistic and it
+turns out that that has an F
+
+ align:start position:0%
+turns out that that has an F
+ 
+
+ align:start position:0%
+turns out that that has an F
+distribution under the null and we
+
+ align:start position:0%
+distribution under the null and we
+ 
+
+ align:start position:0%
+distribution under the null and we
+reject uh the null for large values of
+
+ align:start position:0%
+reject uh the null for large values of
+ 
+
+ align:start position:0%
+reject uh the null for large values of
+this test statistic okay
\ No newline at end of file
diff --git a/YKfoSx16mXk.txt b/YKfoSx16mXk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f7ddf1e8ab4e028f8651d2b94b75386015c823ad
--- /dev/null
+++ b/YKfoSx16mXk.txt
@@ -0,0 +1,6499 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today I'm going to go over a lot of
+
+ align:start position:0%
+today I'm going to go over a lot of
+ 
+
+ align:start position:0%
+today I'm going to go over a lot of
+material that you already know and to
+
+ align:start position:0%
+material that you already know and to
+ 
+
+ align:start position:0%
+material that you already know and to
+work an example with non-degenerate
+
+ align:start position:0%
+work an example with non-degenerate
+ 
+
+ align:start position:0%
+work an example with non-degenerate
+perturbation theory at the this will
+
+ align:start position:0%
+perturbation theory at the this will
+ 
+
+ align:start position:0%
+perturbation theory at the this will
+give me an excuse to use interspersed
+
+ align:start position:0%
+give me an excuse to use interspersed
+ 
+
+ align:start position:0%
+give me an excuse to use interspersed
+matrix and operator notation and one of
+
+ align:start position:0%
+matrix and operator notation and one of
+ 
+
+ align:start position:0%
+matrix and operator notation and one of
+the things that you will be doing is
+
+ align:start position:0%
+the things that you will be doing is
+ 
+
+ align:start position:0%
+the things that you will be doing is
+dealing with infinite matrices and we
+
+ align:start position:0%
+dealing with infinite matrices and we
+ 
+
+ align:start position:0%
+dealing with infinite matrices and we
+don't diagonalize infinite matrices but
+
+ align:start position:0%
+don't diagonalize infinite matrices but
+ 
+
+ align:start position:0%
+don't diagonalize infinite matrices but
+the picture of an infinite matrix is
+
+ align:start position:0%
+the picture of an infinite matrix is
+ 
+
+ align:start position:0%
+the picture of an infinite matrix is
+useful in guiding intuition and and so
+
+ align:start position:0%
+useful in guiding intuition and and so
+ 
+
+ align:start position:0%
+useful in guiding intuition and and so
+we have to know about what those
+
+ align:start position:0%
+we have to know about what those
+ 
+
+ align:start position:0%
+we have to know about what those
+pictures mean and how to construct them
+
+ align:start position:0%
+pictures mean and how to construct them
+ 
+
+ align:start position:0%
+pictures mean and how to construct them
+from things that are seemed to be
+
+ align:start position:0%
+from things that are seemed to be
+ 
+
+ align:start position:0%
+from things that are seemed to be
+obvious okay the problem I want to spend
+
+ align:start position:0%
+obvious okay the problem I want to spend
+ 
+
+ align:start position:0%
+obvious okay the problem I want to spend
+most of my time on is an example of a
+
+ align:start position:0%
+most of my time on is an example of a
+ 
+
+ align:start position:0%
+most of my time on is an example of a
+real molecular potential which is
+
+ align:start position:0%
+real molecular potential which is
+ 
+
+ align:start position:0%
+real molecular potential which is
+quadratic but with a cubic and a quartic
+
+ align:start position:0%
+quadratic but with a cubic and a quartic
+ 
+
+ align:start position:0%
+quadratic but with a cubic and a quartic
+perturbation term and these are this is
+
+ align:start position:0%
+perturbation term and these are this is
+ 
+
+ align:start position:0%
+perturbation term and these are this is
+a simpler problem than what I talked
+
+ align:start position:0%
+a simpler problem than what I talked
+ 
+
+ align:start position:0%
+a simpler problem than what I talked
+about last time the last time I really
+
+ align:start position:0%
+about last time the last time I really
+ 
+
+ align:start position:0%
+about last time the last time I really
+wanted to set the stage for what you can
+
+ align:start position:0%
+wanted to set the stage for what you can
+ 
+
+ align:start position:0%
+wanted to set the stage for what you can
+do with with non degenerate perturbation
+
+ align:start position:0%
+do with with non degenerate perturbation
+ 
+
+ align:start position:0%
+do with with non degenerate perturbation
+theory and this is going to be more of a
+
+ align:start position:0%
+theory and this is going to be more of a
+ 
+
+ align:start position:0%
+theory and this is going to be more of a
+specific dealing with a specific problem
+
+ align:start position:0%
+specific dealing with a specific problem
+ 
+
+ align:start position:0%
+specific dealing with a specific problem
+and now the algebra does not get simpler
+
+ align:start position:0%
+and now the algebra does not get simpler
+ 
+
+ align:start position:0%
+and now the algebra does not get simpler
+and so it's easy to get lost in the
+
+ align:start position:0%
+and so it's easy to get lost in the
+ 
+
+ align:start position:0%
+and so it's easy to get lost in the
+algebra and so I will give you some
+
+ align:start position:0%
+algebra and so I will give you some
+ 
+
+ align:start position:0%
+algebra and so I will give you some
+rules about what to expect when you have
+
+ align:start position:0%
+rules about what to expect when you have
+ 
+
+ align:start position:0%
+rules about what to expect when you have
+a potential like this and how does that
+
+ align:start position:0%
+a potential like this and how does that
+ 
+
+ align:start position:0%
+a potential like this and how does that
+come out of time to have non degenerate
+
+ align:start position:0%
+come out of time to have non degenerate
+ 
+
+ align:start position:0%
+come out of time to have non degenerate
+perturbation theory now everything that
+
+ align:start position:0%
+perturbation theory now everything that
+ 
+
+ align:start position:0%
+perturbation theory now everything that
+we know about molecules comes from
+
+ align:start position:0%
+we know about molecules comes from
+ 
+
+ align:start position:0%
+we know about molecules comes from
+spectroscopy that means transitions
+
+ align:start position:0%
+spectroscopy that means transitions
+ 
+
+ align:start position:0%
+spectroscopy that means transitions
+between energy levels and so well what
+
+ align:start position:0%
+between energy levels and so well what
+ 
+
+ align:start position:0%
+between energy levels and so well what
+how does how do they happen
+
+ align:start position:0%
+how does how do they happen
+ 
+
+ align:start position:0%
+how does how do they happen
+we can lead into that by talking about
+
+ align:start position:0%
+we can lead into that by talking about
+ 
+
+ align:start position:0%
+we can lead into that by talking about
+the stark effect which is the
+
+ align:start position:0%
+the stark effect which is the
+ 
+
+ align:start position:0%
+the stark effect which is the
+interaction of an electric field with a
+
+ align:start position:0%
+interaction of an electric field with a
+ 
+
+ align:start position:0%
+interaction of an electric field with a
+dipole in the molecule and and so most
+
+ align:start position:0%
+dipole in the molecule and and so most
+ 
+
+ align:start position:0%
+dipole in the molecule and and so most
+transitions are caused by a time
+
+ align:start position:0%
+transitions are caused by a time
+ 
+
+ align:start position:0%
+transitions are caused by a time
+dependent electric field which somehow
+
+ align:start position:0%
+dependent electric field which somehow
+ 
+
+ align:start position:0%
+dependent electric field which somehow
+interacts with the the molecule through
+
+ align:start position:0%
+interacts with the the molecule through
+ 
+
+ align:start position:0%
+interacts with the the molecule through
+its dipole moment and so you'll begin to
+
+ align:start position:0%
+its dipole moment and so you'll begin to
+ 
+
+ align:start position:0%
+its dipole moment and so you'll begin to
+see that today okay last time
+
+ align:start position:0%
+see that today okay last time
+ 
+
+ align:start position:0%
+see that today okay last time
+I derived the formulas for a
+
+ align:start position:0%
+I derived the formulas for a
+ 
+
+ align:start position:0%
+I derived the formulas for a
+non-degenerate perturbation theory now
+
+ align:start position:0%
+non-degenerate perturbation theory now
+ 
+
+ align:start position:0%
+non-degenerate perturbation theory now
+I'm a little bit crazy and I really
+
+ align:start position:0%
+I'm a little bit crazy and I really
+ 
+
+ align:start position:0%
+I'm a little bit crazy and I really
+believe in perturbation theory most of
+
+ align:start position:0%
+believe in perturbation theory most of
+ 
+
+ align:start position:0%
+believe in perturbation theory most of
+the textbooks say well let's just stop
+
+ align:start position:0%
+the textbooks say well let's just stop
+ 
+
+ align:start position:0%
+the textbooks say well let's just stop
+here at the first order correction to
+
+ align:start position:0%
+here at the first order correction to
+ 
+
+ align:start position:0%
+here at the first order correction to
+the energy levels and you get nothing
+
+ align:start position:0%
+the energy levels and you get nothing
+ 
+
+ align:start position:0%
+the energy levels and you get nothing
+from that except the same on effect
+
+ align:start position:0%
+from that except the same on effect
+ 
+
+ align:start position:0%
+from that except the same on effect
+which is kind of important for NMR but
+
+ align:start position:0%
+which is kind of important for NMR but
+ 
+
+ align:start position:0%
+which is kind of important for NMR but
+in terms of what molecules do you you
+
+ align:start position:0%
+in terms of what molecules do you you
+ 
+
+ align:start position:0%
+in terms of what molecules do you you
+need this too okay and this is equal to
+
+ align:start position:0%
+need this too okay and this is equal to
+ 
+
+ align:start position:0%
+need this too okay and this is equal to
+the zero order energy the first I'm
+
+ align:start position:0%
+the zero order energy the first I'm
+ 
+
+ align:start position:0%
+the zero order energy the first I'm
+sorry the zero order energy which comes
+
+ align:start position:0%
+sorry the zero order energy which comes
+ 
+
+ align:start position:0%
+sorry the zero order energy which comes
+from an exactly cell problem and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the diagonal matrix element of the the
+
+ align:start position:0%
+the diagonal matrix element of the the
+ 
+
+ align:start position:0%
+the diagonal matrix element of the the
+everything that's bad in the world the
+
+ align:start position:0%
+everything that's bad in the world the
+ 
+
+ align:start position:0%
+everything that's bad in the world the
+first order Hamiltonian and then we have
+
+ align:start position:0%
+first order Hamiltonian and then we have
+ 
+
+ align:start position:0%
+first order Hamiltonian and then we have
+this complicated looking thing m92 the
+
+ align:start position:0%
+this complicated looking thing m92 the
+ 
+
+ align:start position:0%
+this complicated looking thing m92 the
+end of H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero now the only thing that you might
+
+ align:start position:0%
+zero now the only thing that you might
+ 
+
+ align:start position:0%
+zero now the only thing that you might
+forget about in this kind of a formula
+
+ align:start position:0%
+forget about in this kind of a formula
+ 
+
+ align:start position:0%
+forget about in this kind of a formula
+is is it n before M or the other way
+
+ align:start position:0%
+is is it n before M or the other way
+ 
+
+ align:start position:0%
+is is it n before M or the other way
+around and what we know is okay here's
+
+ align:start position:0%
+around and what we know is okay here's
+ 
+
+ align:start position:0%
+around and what we know is okay here's
+the nth level and here is the M flow and
+
+ align:start position:0%
+the nth level and here is the M flow and
+ 
+
+ align:start position:0%
+the nth level and here is the M flow and
+the interaction causes this level to be
+
+ align:start position:0%
+the interaction causes this level to be
+ 
+
+ align:start position:0%
+the interaction causes this level to be
+pushed down so if the M is above the nth
+
+ align:start position:0%
+pushed down so if the M is above the nth
+ 
+
+ align:start position:0%
+pushed down so if the M is above the nth
+level this denominator will be negative
+
+ align:start position:0%
+level this denominator will be negative
+ 
+
+ align:start position:0%
+level this denominator will be negative
+and that causes the pushing down and so
+
+ align:start position:0%
+and that causes the pushing down and so
+ 
+
+ align:start position:0%
+and that causes the pushing down and so
+if you remember the idea of perturbation
+
+ align:start position:0%
+if you remember the idea of perturbation
+ 
+
+ align:start position:0%
+if you remember the idea of perturbation
+theory that things interact and they one
+
+ align:start position:0%
+theory that things interact and they one
+ 
+
+ align:start position:0%
+theory that things interact and they one
+level gets pushed down the other level
+
+ align:start position:0%
+level gets pushed down the other level
+ 
+
+ align:start position:0%
+level gets pushed down the other level
+gets pushed up equal and opposite you
+
+ align:start position:0%
+gets pushed up equal and opposite you
+ 
+
+ align:start position:0%
+gets pushed up equal and opposite you
+can you can correct your flaws of memory
+
+ align:start position:0%
+can you can correct your flaws of memory
+ 
+
+ align:start position:0%
+can you can correct your flaws of memory
+on the witch which comes first and we
+
+ align:start position:0%
+on the witch which comes first and we
+ 
+
+ align:start position:0%
+on the witch which comes first and we
+can write the wave function as an eigen
+
+ align:start position:0%
+can write the wave function as an eigen
+ 
+
+ align:start position:0%
+can write the wave function as an eigen
+function of the exactly self problem
+
+ align:start position:0%
+function of the exactly self problem
+ 
+
+ align:start position:0%
+function of the exactly self problem
+plus a term M not equal to n of x sigh
+
+ align:start position:0%
+plus a term M not equal to n of x sigh
+ 
+
+ align:start position:0%
+plus a term M not equal to n of x sigh
+and now the reason this sum does not
+
+ align:start position:0%
+and now the reason this sum does not
+ 
+
+ align:start position:0%
+and now the reason this sum does not
+include the nth level is well if you did
+
+ align:start position:0%
+include the nth level is well if you did
+ 
+
+ align:start position:0%
+include the nth level is well if you did
+this denominator would blow up and you
+
+ align:start position:0%
+this denominator would blow up and you
+ 
+
+ align:start position:0%
+this denominator would blow up and you
+don't need the nth level because you've
+
+ align:start position:0%
+don't need the nth level because you've
+ 
+
+ align:start position:0%
+don't need the nth level because you've
+already got it here so these are the
+
+ align:start position:0%
+already got it here so these are the
+ 
+
+ align:start position:0%
+already got it here so these are the
+formulas and we had it we had said okay
+
+ align:start position:0%
+formulas and we had it we had said okay
+ 
+
+ align:start position:0%
+formulas and we had it we had said okay
+we're going to write the Hamiltonian as
+
+ align:start position:0%
+we're going to write the Hamiltonian as
+ 
+
+ align:start position:0%
+we're going to write the Hamiltonian as
+H 0 plus h 1 and this is an exactly
+
+ align:start position:0%
+H 0 plus h 1 and this is an exactly
+ 
+
+ align:start position:0%
+H 0 plus h 1 and this is an exactly
+solve problem
+
+ align:start position:0%
+solve problem
+ 
+
+ align:start position:0%
+solve problem
+this is everything else now some people
+
+ align:start position:0%
+this is everything else now some people
+ 
+
+ align:start position:0%
+this is everything else now some people
+will sort this out into small everything
+
+ align:start position:0%
+will sort this out into small everything
+ 
+
+ align:start position:0%
+will sort this out into small everything
+else and big everything else but it's
+
+ align:start position:0%
+else and big everything else but it's
+ 
+
+ align:start position:0%
+else and big everything else but it's
+foolish because all that does is
+
+ align:start position:0%
+foolish because all that does is
+ 
+
+ align:start position:0%
+foolish because all that does is
+multiply the algebra in a horrible way
+
+ align:start position:0%
+multiply the algebra in a horrible way
+ 
+
+ align:start position:0%
+multiply the algebra in a horrible way
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know care anyway you just know that
+
+ align:start position:0%
+you know care anyway you just know that
+ 
+
+ align:start position:0%
+you know care anyway you just know that
+the stuff that's not in this exactly
+
+ align:start position:0%
+the stuff that's not in this exactly
+ 
+
+ align:start position:0%
+the stuff that's not in this exactly
+cell problem it's treated here and
+
+ align:start position:0%
+cell problem it's treated here and
+ 
+
+ align:start position:0%
+cell problem it's treated here and
+you're going to know in principle how to
+
+ align:start position:0%
+you're going to know in principle how to
+ 
+
+ align:start position:0%
+you're going to know in principle how to
+deal with it and there'll be some small
+
+ align:start position:0%
+deal with it and there'll be some small
+ 
+
+ align:start position:0%
+deal with it and there'll be some small
+problems that you know how to deal with
+
+ align:start position:0%
+problems that you know how to deal with
+ 
+
+ align:start position:0%
+problems that you know how to deal with
+okay and there's a rule that H and M 1
+
+ align:start position:0%
+okay and there's a rule that H and M 1
+ 
+
+ align:start position:0%
+okay and there's a rule that H and M 1
+over E and 0 minus e m 0 absolute value
+
+ align:start position:0%
+over E and 0 minus e m 0 absolute value
+ 
+
+ align:start position:0%
+over E and 0 minus e m 0 absolute value
+it's much less than 1 that's what we
+
+ align:start position:0%
+it's much less than 1 that's what we
+ 
+
+ align:start position:0%
+it's much less than 1 that's what we
+mean yes ok you can say well we've got
+
+ align:start position:0%
+mean yes ok you can say well we've got
+ 
+
+ align:start position:0%
+mean yes ok you can say well we've got
+things that that are important that they
+
+ align:start position:0%
+things that that are important that they
+ 
+
+ align:start position:0%
+things that that are important that they
+obviously affect the energy levels and
+
+ align:start position:0%
+obviously affect the energy levels and
+ 
+
+ align:start position:0%
+obviously affect the energy levels and
+there's things that are smaller like
+
+ align:start position:0%
+there's things that are smaller like
+ 
+
+ align:start position:0%
+there's things that are smaller like
+hyperfine structure and when you use the
+
+ align:start position:0%
+hyperfine structure and when you use the
+ 
+
+ align:start position:0%
+hyperfine structure and when you use the
+word hyper you generally mean it's small
+
+ align:start position:0%
+word hyper you generally mean it's small
+ 
+
+ align:start position:0%
+word hyper you generally mean it's small
+and and so what ends up happening is
+
+ align:start position:0%
+and and so what ends up happening is
+ 
+
+ align:start position:0%
+and and so what ends up happening is
+that you do the big picture and then you
+
+ align:start position:0%
+that you do the big picture and then you
+ 
+
+ align:start position:0%
+that you do the big picture and then you
+see some more details but it's only a
+
+ align:start position:0%
+see some more details but it's only a
+ 
+
+ align:start position:0%
+see some more details but it's only a
+very small number of people who actually
+
+ align:start position:0%
+very small number of people who actually
+ 
+
+ align:start position:0%
+very small number of people who actually
+segregate the badness into real bad and
+
+ align:start position:0%
+segregate the badness into real bad and
+ 
+
+ align:start position:0%
+segregate the badness into real bad and
+not so bad ok so this works only when
+
+ align:start position:0%
+not so bad ok so this works only when
+ 
+
+ align:start position:0%
+not so bad ok so this works only when
+this off diagonal matrix element is
+
+ align:start position:0%
+this off diagonal matrix element is
+ 
+
+ align:start position:0%
+this off diagonal matrix element is
+smaller than the energy difference and
+
+ align:start position:0%
+smaller than the energy difference and
+ 
+
+ align:start position:0%
+smaller than the energy difference and
+that's going to be true and now here's
+
+ align:start position:0%
+that's going to be true and now here's
+ 
+
+ align:start position:0%
+that's going to be true and now here's
+an infinite matrix and we're interested
+
+ align:start position:0%
+an infinite matrix and we're interested
+ 
+
+ align:start position:0%
+an infinite matrix and we're interested
+in a certain space of quite a state
+
+ align:start position:0%
+in a certain space of quite a state
+ 
+
+ align:start position:0%
+in a certain space of quite a state
+space which are our experiments are
+
+ align:start position:0%
+space which are our experiments are
+ 
+
+ align:start position:0%
+space which are our experiments are
+designed to measure and it depends on
+
+ align:start position:0%
+designed to measure and it depends on
+ 
+
+ align:start position:0%
+designed to measure and it depends on
+what you what experiment you do this
+
+ align:start position:0%
+what you what experiment you do this
+ 
+
+ align:start position:0%
+what you what experiment you do this
+might be here it might be somewhere in
+
+ align:start position:0%
+might be here it might be somewhere in
+ 
+
+ align:start position:0%
+might be here it might be somewhere in
+the middle and the rest is we're not
+
+ align:start position:0%
+the middle and the rest is we're not
+ 
+
+ align:start position:0%
+the middle and the rest is we're not
+interested because it's far away because
+
+ align:start position:0%
+interested because it's far away because
+ 
+
+ align:start position:0%
+interested because it's far away because
+the energy denominator is so large that
+
+ align:start position:0%
+the energy denominator is so large that
+ 
+
+ align:start position:0%
+the energy denominator is so large that
+the effect on the energy levels can be
+
+ align:start position:0%
+the effect on the energy levels can be
+ 
+
+ align:start position:0%
+the effect on the energy levels can be
+ignored
+
+ align:start position:0%
+ignored
+ 
+
+ align:start position:0%
+ignored
+or you can say well we're not really
+
+ align:start position:0%
+or you can say well we're not really
+ 
+
+ align:start position:0%
+or you can say well we're not really
+ignoring it we're folding the effect of
+
+ align:start position:0%
+ignoring it we're folding the effect of
+ 
+
+ align:start position:0%
+ignoring it we're folding the effect of
+all these levels through the matrix
+
+ align:start position:0%
+all these levels through the matrix
+ 
+
+ align:start position:0%
+all these levels through the matrix
+elements in here into here by
+
+ align:start position:0%
+elements in here into here by
+ 
+
+ align:start position:0%
+elements in here into here by
+second-order perturbation theory we
+
+ align:start position:0%
+second-order perturbation theory we
+ 
+
+ align:start position:0%
+second-order perturbation theory we
+could in principle do that we certainly
+
+ align:start position:0%
+could in principle do that we certainly
+ 
+
+ align:start position:0%
+could in principle do that we certainly
+are allowed to think that we're getting
+
+ align:start position:0%
+are allowed to think that we're getting
+ 
+
+ align:start position:0%
+are allowed to think that we're getting
+rid of this state space by in principle
+
+ align:start position:0%
+rid of this state space by in principle
+ 
+
+ align:start position:0%
+rid of this state space by in principle
+folding it into this block now in this
+
+ align:start position:0%
+folding it into this block now in this
+ 
+
+ align:start position:0%
+folding it into this block now in this
+block of levels that we are we care
+
+ align:start position:0%
+block of levels that we are we care
+ 
+
+ align:start position:0%
+block of levels that we are we care
+about now I always like to draw these
+
+ align:start position:0%
+about now I always like to draw these
+ 
+
+ align:start position:0%
+about now I always like to draw these
+infinite matrices or these matrices by
+
+ align:start position:0%
+infinite matrices or these matrices by
+ 
+
+ align:start position:0%
+infinite matrices or these matrices by
+just saying okay here's the diagonal and
+
+ align:start position:0%
+just saying okay here's the diagonal and
+ 
+
+ align:start position:0%
+just saying okay here's the diagonal and
+there might be a couple of levels within
+
+ align:start position:0%
+there might be a couple of levels within
+ 
+
+ align:start position:0%
+there might be a couple of levels within
+this state space we're interested in
+
+ align:start position:0%
+this state space we're interested in
+ 
+
+ align:start position:0%
+this state space we're interested in
+which because of accident or because of
+
+ align:start position:0%
+which because of accident or because of
+ 
+
+ align:start position:0%
+which because of accident or because of
+something evil their energy denominator
+
+ align:start position:0%
+something evil their energy denominator
+ 
+
+ align:start position:0%
+something evil their energy denominator
+is small compared to the energy the zero
+
+ align:start position:0%
+is small compared to the energy the zero
+ 
+
+ align:start position:0%
+is small compared to the energy the zero
+order energy differences but that's
+
+ align:start position:0%
+order energy differences but that's
+ 
+
+ align:start position:0%
+order energy differences but that's
+usually true for only a couple of a few
+
+ align:start position:0%
+usually true for only a couple of a few
+ 
+
+ align:start position:0%
+usually true for only a couple of a few
+accidentally degenerate states and we
+
+ align:start position:0%
+accidentally degenerate states and we
+ 
+
+ align:start position:0%
+accidentally degenerate states and we
+deal with them by using the machinery we
+
+ align:start position:0%
+deal with them by using the machinery we
+ 
+
+ align:start position:0%
+deal with them by using the machinery we
+obtained from the two-level problem and
+
+ align:start position:0%
+obtained from the two-level problem and
+ 
+
+ align:start position:0%
+obtained from the two-level problem and
+so there we're actually diagonalizing a
+
+ align:start position:0%
+so there we're actually diagonalizing a
+ 
+
+ align:start position:0%
+so there we're actually diagonalizing a
+small dimension matrix we're not
+
+ align:start position:0%
+small dimension matrix we're not
+ 
+
+ align:start position:0%
+small dimension matrix we're not
+diagonally thinking our computer is
+
+ align:start position:0%
+diagonally thinking our computer is
+ 
+
+ align:start position:0%
+diagonally thinking our computer is
+diagonalize again you really don't care
+
+ align:start position:0%
+diagonalize again you really don't care
+ 
+
+ align:start position:0%
+diagonalize again you really don't care
+how it's done because you have a machine
+
+ align:start position:0%
+how it's done because you have a machine
+ 
+
+ align:start position:0%
+how it's done because you have a machine
+that will will will solve this like
+
+ align:start position:0%
+that will will will solve this like
+ 
+
+ align:start position:0%
+that will will will solve this like
+difficulty and so it's okay for this
+
+ align:start position:0%
+difficulty and so it's okay for this
+ 
+
+ align:start position:0%
+difficulty and so it's okay for this
+rule to be violated but so what happens
+
+ align:start position:0%
+rule to be violated but so what happens
+ 
+
+ align:start position:0%
+rule to be violated but so what happens
+suppose we have two levels and just want
+
+ align:start position:0%
+suppose we have two levels and just want
+ 
+
+ align:start position:0%
+suppose we have two levels and just want
+to make sure I use the same notation as
+
+ align:start position:0%
+to make sure I use the same notation as
+ 
+
+ align:start position:0%
+to make sure I use the same notation as
+in the notes so here we have the two
+
+ align:start position:0%
+in the notes so here we have the two
+ 
+
+ align:start position:0%
+in the notes so here we have the two
+zero order levels and they interact and
+
+ align:start position:0%
+zero order levels and they interact and
+ 
+
+ align:start position:0%
+zero order levels and they interact and
+repel each other equal and opposite
+
+ align:start position:0%
+repel each other equal and opposite
+ 
+
+ align:start position:0%
+repel each other equal and opposite
+amounts and these states which are D 2
+
+ align:start position:0%
+amounts and these states which are D 2
+ 
+
+ align:start position:0%
+amounts and these states which are D 2
+and E 1 are not pure state 2
+
+ align:start position:0%
+and E 1 are not pure state 2
+ 
+
+ align:start position:0%
+and E 1 are not pure state 2
+they have a mixture of state one in them
+
+ align:start position:0%
+they have a mixture of state one in them
+ 
+
+ align:start position:0%
+they have a mixture of state one in them
+now in spectroscopy we always observe
+
+ align:start position:0%
+now in spectroscopy we always observe
+ 
+
+ align:start position:0%
+now in spectroscopy we always observe
+these levels by transitions and so
+
+ align:start position:0%
+these levels by transitions and so
+ 
+
+ align:start position:0%
+these levels by transitions and so
+suppose we have state zero down here and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let us say that this transition between
+
+ align:start position:0%
+let us say that this transition between
+ 
+
+ align:start position:0%
+let us say that this transition between
+the the zero level and the zero order
+
+ align:start position:0%
+the the zero level and the zero order
+ 
+
+ align:start position:0%
+the the zero level and the zero order
+level one is allowed and I'll symbolize
+
+ align:start position:0%
+level one is allowed and I'll symbolize
+ 
+
+ align:start position:0%
+level one is allowed and I'll symbolize
+that by 1 0 mu 1 0 is not equal to 0 and
+
+ align:start position:0%
+that by 1 0 mu 1 0 is not equal to 0 and
+ 
+
+ align:start position:0%
+that by 1 0 mu 1 0 is not equal to 0 and
+the transition between this 0 this level
+
+ align:start position:0%
+the transition between this 0 this level
+ 
+
+ align:start position:0%
+the transition between this 0 this level
+and this is our order level is forbidden
+
+ align:start position:0%
+and this is our order level is forbidden
+ 
+
+ align:start position:0%
+and this is our order level is forbidden
+mu to 0 is equal to 0 so we call this a
+
+ align:start position:0%
+mu to 0 is equal to 0 so we call this a
+ 
+
+ align:start position:0%
+mu to 0 is equal to 0 so we call this a
+dark state and a bright state and now
+
+ align:start position:0%
+dark state and a bright state and now
+ 
+
+ align:start position:0%
+dark state and a bright state and now
+these two states interact and we have
+
+ align:start position:0%
+these two states interact and we have
+ 
+
+ align:start position:0%
+these two states interact and we have
+mixed States
+
+ align:start position:0%
+mixed States
+ 
+
+ align:start position:0%
+mixed States
+so the real eigenstates you wouldn't
+
+ align:start position:0%
+so the real eigenstates you wouldn't
+ 
+
+ align:start position:0%
+so the real eigenstates you wouldn't
+have expected to see this level in the
+
+ align:start position:0%
+have expected to see this level in the
+ 
+
+ align:start position:0%
+have expected to see this level in the
+spectrum but you do because it's
+
+ align:start position:0%
+spectrum but you do because it's
+ 
+
+ align:start position:0%
+spectrum but you do because it's
+borrowed some bright character through
+
+ align:start position:0%
+borrowed some bright character through
+ 
+
+ align:start position:0%
+borrowed some bright character through
+the perturbation interaction and so
+
+ align:start position:0%
+the perturbation interaction and so
+ 
+
+ align:start position:0%
+the perturbation interaction and so
+there's two surprises one is everything
+
+ align:start position:0%
+there's two surprises one is everything
+ 
+
+ align:start position:0%
+there's two surprises one is everything
+is sort of describable by a simple set
+
+ align:start position:0%
+is sort of describable by a simple set
+ 
+
+ align:start position:0%
+is sort of describable by a simple set
+of equations and then there's a couple
+
+ align:start position:0%
+of equations and then there's a couple
+ 
+
+ align:start position:0%
+of equations and then there's a couple
+of deviations and there's some extra
+
+ align:start position:0%
+of deviations and there's some extra
+ 
+
+ align:start position:0%
+of deviations and there's some extra
+levels that appear that's very that's
+
+ align:start position:0%
+levels that appear that's very that's
+ 
+
+ align:start position:0%
+levels that appear that's very that's
+information very rich because if it's
+
+ align:start position:0%
+information very rich because if it's
+ 
+
+ align:start position:0%
+information very rich because if it's
+dark you can't see it it's not a ghost
+
+ align:start position:0%
+dark you can't see it it's not a ghost
+ 
+
+ align:start position:0%
+dark you can't see it it's not a ghost
+it's there but you can't see it well the
+
+ align:start position:0%
+it's there but you can't see it well the
+ 
+
+ align:start position:0%
+it's there but you can't see it well the
+perturbation somehow pulls that
+
+ align:start position:0%
+perturbation somehow pulls that
+ 
+
+ align:start position:0%
+perturbation somehow pulls that
+sometimes pulls the curtain back and
+
+ align:start position:0%
+sometimes pulls the curtain back and
+ 
+
+ align:start position:0%
+sometimes pulls the curtain back and
+enables you to see stuff you need to
+
+ align:start position:0%
+enables you to see stuff you need to
+ 
+
+ align:start position:0%
+enables you to see stuff you need to
+know about now you can imagine exciting
+
+ align:start position:0%
+know about now you can imagine exciting
+ 
+
+ align:start position:0%
+know about now you can imagine exciting
+this two-level system with a short pulse
+
+ align:start position:0%
+this two-level system with a short pulse
+ 
+
+ align:start position:0%
+this two-level system with a short pulse
+of light where the uncertainty
+
+ align:start position:0%
+of light where the uncertainty
+ 
+
+ align:start position:0%
+of light where the uncertainty
+broadening of the short pulse of light
+
+ align:start position:0%
+broadening of the short pulse of light
+ 
+
+ align:start position:0%
+broadening of the short pulse of light
+covers these two eigenstates what
+
+ align:start position:0%
+covers these two eigenstates what
+ 
+
+ align:start position:0%
+covers these two eigenstates what
+happens then is you get quantum beats
+
+ align:start position:0%
+happens then is you get quantum beats
+ 
+
+ align:start position:0%
+happens then is you get quantum beats
+and that's going to be on the exam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a local perturbation
+
+ align:start position:0%
+okay so this is a local perturbation
+ 
+
+ align:start position:0%
+okay so this is a local perturbation
+it's just something in here that that
+
+ align:start position:0%
+it's just something in here that that
+ 
+
+ align:start position:0%
+it's just something in here that that
+spoils the general rule but it's very
+
+ align:start position:0%
+spoils the general rule but it's very
+ 
+
+ align:start position:0%
+spoils the general rule but it's very
+information-rich and it also is to
+
+ align:start position:0%
+information-rich and it also is to
+ 
+
+ align:start position:0%
+information-rich and it also is to
+pedagogically fun okay so now I'm going
+
+ align:start position:0%
+pedagogically fun okay so now I'm going
+ 
+
+ align:start position:0%
+pedagogically fun okay so now I'm going
+to talk about stuff that I've talked
+
+ align:start position:0%
+to talk about stuff that I've talked
+ 
+
+ align:start position:0%
+to talk about stuff that I've talked
+about before but I'm going to go a
+
+ align:start position:0%
+about before but I'm going to go a
+ 
+
+ align:start position:0%
+about before but I'm going to go a
+little deeper and slower and and so
+
+ align:start position:0%
+little deeper and slower and and so
+ 
+
+ align:start position:0%
+little deeper and slower and and so
+let's let's do this problem we have a
+
+ align:start position:0%
+let's let's do this problem we have a
+ 
+
+ align:start position:0%
+let's let's do this problem we have a
+potential and for molecules we tend to
+
+ align:start position:0%
+potential and for molecules we tend to
+ 
+
+ align:start position:0%
+potential and for molecules we tend to
+use Q rather than R or X as the
+
+ align:start position:0%
+use Q rather than R or X as the
+ 
+
+ align:start position:0%
+use Q rather than R or X as the
+displacement from equilibrium the
+
+ align:start position:0%
+displacement from equilibrium the
+ 
+
+ align:start position:0%
+displacement from equilibrium the
+harmonic oscillator coordinate and it's
+
+ align:start position:0%
+harmonic oscillator coordinate and it's
+ 
+
+ align:start position:0%
+harmonic oscillator coordinate and it's
+the same thing we have okay so this is
+
+ align:start position:0%
+the same thing we have okay so this is
+ 
+
+ align:start position:0%
+the same thing we have okay so this is
+an exactly solved problem and this is
+
+ align:start position:0%
+an exactly solved problem and this is
+ 
+
+ align:start position:0%
+an exactly solved problem and this is
+something extra and so this is a cubic
+
+ align:start position:0%
+something extra and so this is a cubic
+ 
+
+ align:start position:0%
+something extra and so this is a cubic
+anharmonicity and this is a quartic
+
+ align:start position:0%
+anharmonicity and this is a quartic
+ 
+
+ align:start position:0%
+anharmonicity and this is a quartic
+anharmonicity in the previous lecture I
+
+ align:start position:0%
+anharmonicity in the previous lecture I
+ 
+
+ align:start position:0%
+anharmonicity in the previous lecture I
+talked about a mnemonic couplings
+
+ align:start position:0%
+talked about a mnemonic couplings
+ 
+
+ align:start position:0%
+talked about a mnemonic couplings
+between different modes of the same
+
+ align:start position:0%
+between different modes of the same
+ 
+
+ align:start position:0%
+between different modes of the same
+polyatomic molecule here this is really
+
+ align:start position:0%
+polyatomic molecule here this is really
+ 
+
+ align:start position:0%
+polyatomic molecule here this is really
+a simpler problem and I probably should
+
+ align:start position:0%
+a simpler problem and I probably should
+ 
+
+ align:start position:0%
+a simpler problem and I probably should
+have talked about it first but I didn't
+
+ align:start position:0%
+have talked about it first but I didn't
+ 
+
+ align:start position:0%
+have talked about it first but I didn't
+because I'm going to go deeper here then
+
+ align:start position:0%
+because I'm going to go deeper here then
+ 
+
+ align:start position:0%
+because I'm going to go deeper here then
+just the big picture which I described
+
+ align:start position:0%
+just the big picture which I described
+ 
+
+ align:start position:0%
+just the big picture which I described
+last time so we're going to have two
+
+ align:start position:0%
+last time so we're going to have two
+ 
+
+ align:start position:0%
+last time so we're going to have two
+terms that we are going to treat by
+
+ align:start position:0%
+terms that we are going to treat by
+ 
+
+ align:start position:0%
+terms that we are going to treat by
+perturbation theory and there are
+
+ align:start position:0%
+perturbation theory and there are
+ 
+
+ align:start position:0%
+perturbation theory and there are
+several important things here molecular
+
+ align:start position:0%
+several important things here molecular
+ 
+
+ align:start position:0%
+several important things here molecular
+potential looks like this not like that
+
+ align:start position:0%
+potential looks like this not like that
+ 
+
+ align:start position:0%
+potential looks like this not like that
+right this is bond breaking and it
+
+ align:start position:0%
+right this is bond breaking and it
+ 
+
+ align:start position:0%
+right this is bond breaking and it
+breaks at large displacement there's no
+
+ align:start position:0%
+breaks at large displacement there's no
+ 
+
+ align:start position:0%
+breaks at large displacement there's no
+such thing as upon breaking as you
+
+ align:start position:0%
+such thing as upon breaking as you
+ 
+
+ align:start position:0%
+such thing as upon breaking as you
+squeeze the molecules together so this
+
+ align:start position:0%
+squeeze the molecules together so this
+ 
+
+ align:start position:0%
+squeeze the molecules together so this
+is a crazy idea and how do you get an
+
+ align:start position:0%
+is a crazy idea and how do you get an
+ 
+
+ align:start position:0%
+is a crazy idea and how do you get an
+asymmetric potential well it's cubic and
+
+ align:start position:0%
+asymmetric potential well it's cubic and
+ 
+
+ align:start position:0%
+asymmetric potential well it's cubic and
+which sign of B is going to lead to this
+
+ align:start position:0%
+which sign of B is going to lead to this
+ 
+
+ align:start position:0%
+which sign of B is going to lead to this
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+right okay now if we're really naive
+
+ align:start position:0%
+right okay now if we're really naive
+ 
+
+ align:start position:0%
+right okay now if we're really naive
+we're saying yeah negative is good but
+
+ align:start position:0%
+we're saying yeah negative is good but
+ 
+
+ align:start position:0%
+we're saying yeah negative is good but
+boom we ignore that we don't worry that
+
+ align:start position:0%
+boom we ignore that we don't worry that
+ 
+
+ align:start position:0%
+boom we ignore that we don't worry that
+if we took this seriously at large
+
+ align:start position:0%
+if we took this seriously at large
+ 
+
+ align:start position:0%
+if we took this seriously at large
+enough displacement the potential go to
+
+ align:start position:0%
+enough displacement the potential go to
+ 
+
+ align:start position:0%
+enough displacement the potential go to
+minus infinity we don't worry about
+
+ align:start position:0%
+minus infinity we don't worry about
+ 
+
+ align:start position:0%
+minus infinity we don't worry about
+tunneling through this barrier we just
+
+ align:start position:0%
+tunneling through this barrier we just
+ 
+
+ align:start position:0%
+tunneling through this barrier we just
+use this to give us something that has
+
+ align:start position:0%
+use this to give us something that has
+ 
+
+ align:start position:0%
+use this to give us something that has
+the right shape and that we can apply
+
+ align:start position:0%
+the right shape and that we can apply
+ 
+
+ align:start position:0%
+the right shape and that we can apply
+perturbation theory to and we're not
+
+ align:start position:0%
+perturbation theory to and we're not
+ 
+
+ align:start position:0%
+perturbation theory to and we're not
+going to worry about using perturbation
+
+ align:start position:0%
+going to worry about using perturbation
+ 
+
+ align:start position:0%
+going to worry about using perturbation
+theory to capture this tunneling at
+
+ align:start position:0%
+theory to capture this tunneling at
+ 
+
+ align:start position:0%
+theory to capture this tunneling at
+least not now and not in this course
+
+ align:start position:0%
+least not now and not in this course
+ 
+
+ align:start position:0%
+least not now and not in this course
+okay so so one thing is we have this
+
+ align:start position:0%
+okay so so one thing is we have this
+ 
+
+ align:start position:0%
+okay so so one thing is we have this
+term and there's there's something you
+
+ align:start position:0%
+term and there's there's something you
+ 
+
+ align:start position:0%
+term and there's there's something you
+know immediately about odd powers they
+
+ align:start position:0%
+know immediately about odd powers they
+ 
+
+ align:start position:0%
+know immediately about odd powers they
+never have Delta V equals zero matrix
+
+ align:start position:0%
+never have Delta V equals zero matrix
+ 
+
+ align:start position:0%
+never have Delta V equals zero matrix
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+they never have diagonal elements and so
+
+ align:start position:0%
+they never have diagonal elements and so
+ 
+
+ align:start position:0%
+they never have diagonal elements and so
+they do not contribute to the energy in
+
+ align:start position:0%
+they do not contribute to the energy in
+ 
+
+ align:start position:0%
+they do not contribute to the energy in
+first order the only way you know the
+
+ align:start position:0%
+first order the only way you know the
+ 
+
+ align:start position:0%
+first order the only way you know the
+sign of this perturbation is from a
+
+ align:start position:0%
+sign of this perturbation is from a
+ 
+
+ align:start position:0%
+sign of this perturbation is from a
+nonzero first order contribution because
+
+ align:start position:0%
+nonzero first order contribution because
+ 
+
+ align:start position:0%
+nonzero first order contribution because
+when you do second order perturbation
+
+ align:start position:0%
+when you do second order perturbation
+ 
+
+ align:start position:0%
+when you do second order perturbation
+Theory the matrix element gets squared
+
+ align:start position:0%
+Theory the matrix element gets squared
+ 
+
+ align:start position:0%
+Theory the matrix element gets squared
+and the sign information is lost so
+
+ align:start position:0%
+and the sign information is lost so
+ 
+
+ align:start position:0%
+and the sign information is lost so
+there's nothing so far that tells you
+
+ align:start position:0%
+there's nothing so far that tells you
+ 
+
+ align:start position:0%
+there's nothing so far that tells you
+what the sign of B is and the energy
+
+ align:start position:0%
+what the sign of B is and the energy
+ 
+
+ align:start position:0%
+what the sign of B is and the energy
+level pattern that you would obtain from
+
+ align:start position:0%
+level pattern that you would obtain from
+ 
+
+ align:start position:0%
+level pattern that you would obtain from
+either sign of B would be the same it's
+
+ align:start position:0%
+either sign of B would be the same it's
+ 
+
+ align:start position:0%
+either sign of B would be the same it's
+just one one of the signs is completely
+
+ align:start position:0%
+just one one of the signs is completely
+ 
+
+ align:start position:0%
+just one one of the signs is completely
+ridiculous
+
+ align:start position:0%
+ridiculous
+ 
+
+ align:start position:0%
+ridiculous
+now Q to the fourth has selection rules
+
+ align:start position:0%
+now Q to the fourth has selection rules
+ 
+
+ align:start position:0%
+now Q to the fourth has selection rules
+Delta V of 4 to 0 minus 2 and minus 4 so
+
+ align:start position:0%
+Delta V of 4 to 0 minus 2 and minus 4 so
+ 
+
+ align:start position:0%
+Delta V of 4 to 0 minus 2 and minus 4 so
+that Delta P of 0 term
+
+ align:start position:0%
+that Delta P of 0 term
+ 
+
+ align:start position:0%
+that Delta P of 0 term
+Center in first-order perturbation
+
+ align:start position:0%
+Center in first-order perturbation
+ 
+
+ align:start position:0%
+Center in first-order perturbation
+theory and so you can determine the sign
+
+ align:start position:0%
+theory and so you can determine the sign
+ 
+
+ align:start position:0%
+theory and so you can determine the sign
+of any even perturbation which is useful
+
+ align:start position:0%
+of any even perturbation which is useful
+ 
+
+ align:start position:0%
+of any even perturbation which is useful
+now what does this do well one thing
+
+ align:start position:0%
+now what does this do well one thing
+ 
+
+ align:start position:0%
+now what does this do well one thing
+that Q does is if this if if Q is if C
+
+ align:start position:0%
+that Q does is if this if if Q is if C
+ 
+
+ align:start position:0%
+that Q does is if this if if Q is if C
+is positive instead of having a harmonic
+
+ align:start position:0%
+is positive instead of having a harmonic
+ 
+
+ align:start position:0%
+is positive instead of having a harmonic
+oscillator it makes it steeper and if Q
+
+ align:start position:0%
+oscillator it makes it steeper and if Q
+ 
+
+ align:start position:0%
+oscillator it makes it steeper and if Q
+is negative it makes it flatter this is
+
+ align:start position:0%
+is negative it makes it flatter this is
+ 
+
+ align:start position:0%
+is negative it makes it flatter this is
+typical of bending vibrations and so
+
+ align:start position:0%
+typical of bending vibrations and so
+ 
+
+ align:start position:0%
+typical of bending vibrations and so
+bending vibrations tend to have flat
+
+ align:start position:0%
+bending vibrations tend to have flat
+ 
+
+ align:start position:0%
+bending vibrations tend to have flat
+bottom potentials but there's also
+
+ align:start position:0%
+bottom potentials but there's also
+ 
+
+ align:start position:0%
+bottom potentials but there's also
+something else suppose we have two
+
+ align:start position:0%
+something else suppose we have two
+ 
+
+ align:start position:0%
+something else suppose we have two
+electronic states now I'm cheating
+
+ align:start position:0%
+electronic states now I'm cheating
+ 
+
+ align:start position:0%
+electronic states now I'm cheating
+because I'm assuming you you'll accept
+
+ align:start position:0%
+because I'm assuming you you'll accept
+ 
+
+ align:start position:0%
+because I'm assuming you you'll accept
+the idea that there is something we
+
+ align:start position:0%
+the idea that there is something we
+ 
+
+ align:start position:0%
+the idea that there is something we
+haven't talked about yet but there are
+
+ align:start position:0%
+haven't talked about yet but there are
+ 
+
+ align:start position:0%
+haven't talked about yet but there are
+different potential curves and it's
+
+ align:start position:0%
+different potential curves and it's
+ 
+
+ align:start position:0%
+different potential curves and it's
+mostly true for polyatomic molecules
+
+ align:start position:0%
+mostly true for polyatomic molecules
+ 
+
+ align:start position:0%
+mostly true for polyatomic molecules
+these two states can't talk to each
+
+ align:start position:0%
+these two states can't talk to each
+ 
+
+ align:start position:0%
+these two states can't talk to each
+other at equilibrium because a symmetry
+
+ align:start position:0%
+other at equilibrium because a symmetry
+ 
+
+ align:start position:0%
+other at equilibrium because a symmetry
+exists that prevents that and as you
+
+ align:start position:0%
+exists that prevents that and as you
+ 
+
+ align:start position:0%
+exists that prevents that and as you
+move away from equilibrium there's a
+
+ align:start position:0%
+move away from equilibrium there's a
+ 
+
+ align:start position:0%
+move away from equilibrium there's a
+perturbation that gets larger and larger
+
+ align:start position:0%
+perturbation that gets larger and larger
+ 
+
+ align:start position:0%
+perturbation that gets larger and larger
+and as a result what happens is that
+
+ align:start position:0%
+and as a result what happens is that
+ 
+
+ align:start position:0%
+and as a result what happens is that
+this potential does something like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you get a either a flattening or an
+
+ align:start position:0%
+so you get a either a flattening or an
+ 
+
+ align:start position:0%
+so you get a either a flattening or an
+actual extra pair of minima and this one
+
+ align:start position:0%
+actual extra pair of minima and this one
+ 
+
+ align:start position:0%
+actual extra pair of minima and this one
+gets sharper that's called the vibronic
+
+ align:start position:0%
+gets sharper that's called the vibronic
+ 
+
+ align:start position:0%
+gets sharper that's called the vibronic
+interaction and that's fairly important
+
+ align:start position:0%
+interaction and that's fairly important
+ 
+
+ align:start position:0%
+interaction and that's fairly important
+in polyatomic molecules but so we can
+
+ align:start position:0%
+in polyatomic molecules but so we can
+ 
+
+ align:start position:0%
+in polyatomic molecules but so we can
+begin to understand these things just by
+
+ align:start position:0%
+begin to understand these things just by
+ 
+
+ align:start position:0%
+begin to understand these things just by
+dealing with these terms in the
+
+ align:start position:0%
+dealing with these terms in the
+ 
+
+ align:start position:0%
+dealing with these terms in the
+potential okay
+
+ align:start position:0%
+potential okay
+ 
+
+ align:start position:0%
+potential okay
+so now we're off to the races and my
+
+ align:start position:0%
+so now we're off to the races and my
+ 
+
+ align:start position:0%
+so now we're off to the races and my
+goal here is to make you comfortable
+
+ align:start position:0%
+goal here is to make you comfortable
+ 
+
+ align:start position:0%
+goal here is to make you comfortable
+with either the operator or the matrix
+
+ align:start position:0%
+with either the operator or the matrix
+ 
+
+ align:start position:0%
+with either the operator or the matrix
+notation and so I'm going to go back and
+
+ align:start position:0%
+notation and so I'm going to go back and
+ 
+
+ align:start position:0%
+notation and so I'm going to go back and
+forth between them you know what might
+
+ align:start position:0%
+forth between them you know what might
+ 
+
+ align:start position:0%
+forth between them you know what might
+seem to be a random manner but okay now
+
+ align:start position:0%
+seem to be a random manner but okay now
+ 
+
+ align:start position:0%
+seem to be a random manner but okay now
+you know that a dagger now we can call
+
+ align:start position:0%
+you know that a dagger now we can call
+ 
+
+ align:start position:0%
+you know that a dagger now we can call
+it a dagger with a hat or we can call it
+
+ align:start position:0%
+it a dagger with a hat or we can call it
+ 
+
+ align:start position:0%
+it a dagger with a hat or we can call it
+a dagger double underline the old hat
+
+ align:start position:0%
+a dagger double underline the old hat
+ 
+
+ align:start position:0%
+a dagger double underline the old hat
+matrix operator and you know that this
+
+ align:start position:0%
+matrix operator and you know that this
+ 
+
+ align:start position:0%
+matrix operator and you know that this
+operates on V to give V plus one Sparrow
+
+ align:start position:0%
+operates on V to give V plus one Sparrow
+ 
+
+ align:start position:0%
+operates on V to give V plus one Sparrow
+side B plus one or in bracket notation
+
+ align:start position:0%
+side B plus one or in bracket notation
+ 
+
+ align:start position:0%
+side B plus one or in bracket notation
+we could write this as V plus 1 a dagger
+
+ align:start position:0%
+we could write this as V plus 1 a dagger
+ 
+
+ align:start position:0%
+we could write this as V plus 1 a dagger
+V now this is a shorthand it's a
+
+ align:start position:0%
+V now this is a shorthand it's a
+ 
+
+ align:start position:0%
+V now this is a shorthand it's a
+wonderful shorthand it's easier to draw
+
+ align:start position:0%
+wonderful shorthand it's easier to draw
+ 
+
+ align:start position:0%
+wonderful shorthand it's easier to draw
+this than wavefunctions but we have to
+
+ align:start position:0%
+this than wavefunctions but we have to
+ 
+
+ align:start position:0%
+this than wavefunctions but we have to
+know okay what does this look like in
+
+ align:start position:0%
+know okay what does this look like in
+ 
+
+ align:start position:0%
+know okay what does this look like in
+the matrix for a dagger so here is a
+
+ align:start position:0%
+the matrix for a dagger so here is a
+ 
+
+ align:start position:0%
+the matrix for a dagger so here is a
+dagger and it's a matrix and what goes
+
+ align:start position:0%
+dagger and it's a matrix and what goes
+ 
+
+ align:start position:0%
+dagger and it's a matrix and what goes
+in here
+
+ align:start position:0%
+in here
+ 
+
+ align:start position:0%
+in here
+well the first thing you do this is
+
+ align:start position:0%
+well the first thing you do this is
+ 
+
+ align:start position:0%
+well the first thing you do this is
+infinite so you need some sort of a way
+
+ align:start position:0%
+infinite so you need some sort of a way
+ 
+
+ align:start position:0%
+infinite so you need some sort of a way
+of drawing something that's infinite so
+
+ align:start position:0%
+of drawing something that's infinite so
+ 
+
+ align:start position:0%
+of drawing something that's infinite so
+that you understand what it is and so
+
+ align:start position:0%
+that you understand what it is and so
+ 
+
+ align:start position:0%
+that you understand what it is and so
+the first thing you do is you know that
+
+ align:start position:0%
+the first thing you do is you know that
+ 
+
+ align:start position:0%
+the first thing you do is you know that
+there is no all of the diagonal elements
+
+ align:start position:0%
+there is no all of the diagonal elements
+ 
+
+ align:start position:0%
+there is no all of the diagonal elements
+are 0 now most of the elements in this
+
+ align:start position:0%
+are 0 now most of the elements in this
+ 
+
+ align:start position:0%
+are 0 now most of the elements in this
+matrix are 0 and you don't want to draw
+
+ align:start position:0%
+matrix are 0 and you don't want to draw
+ 
+
+ align:start position:0%
+matrix are 0 and you don't want to draw
+them and because you'll just be spending
+
+ align:start position:0%
+them and because you'll just be spending
+ 
+
+ align:start position:0%
+them and because you'll just be spending
+all your time make it writing zeroes so
+
+ align:start position:0%
+all your time make it writing zeroes so
+ 
+
+ align:start position:0%
+all your time make it writing zeroes so
+we want a shorthand and so now this is a
+
+ align:start position:0%
+we want a shorthand and so now this is a
+ 
+
+ align:start position:0%
+we want a shorthand and so now this is a
+matrix element this is the row and this
+
+ align:start position:0%
+matrix element this is the row and this
+ 
+
+ align:start position:0%
+matrix element this is the row and this
+is the column and so where do I put this
+
+ align:start position:0%
+is the column and so where do I put this
+ 
+
+ align:start position:0%
+is the column and so where do I put this
+square root of V plus 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here we have the Rosso I I get
+
+ align:start position:0%
+so here we have the Rosso I I get
+ 
+
+ align:start position:0%
+so here we have the Rosso I I get
+confused about this so before I accept
+
+ align:start position:0%
+confused about this so before I accept
+ 
+
+ align:start position:0%
+confused about this so before I accept
+your answer which I want to reject I
+
+ align:start position:0%
+your answer which I want to reject I
+ 
+
+ align:start position:0%
+your answer which I want to reject I
+have to think carefully about it so let
+
+ align:start position:0%
+have to think carefully about it so let
+ 
+
+ align:start position:0%
+have to think carefully about it so let
+us say this is 0 and this is 1 so we
+
+ align:start position:0%
+us say this is 0 and this is 1 so we
+ 
+
+ align:start position:0%
+us say this is 0 and this is 1 so we
+have the 1 you're right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so we have the square root of 1
+
+ align:start position:0%
+okay and so we have the square root of 1
+ 
+
+ align:start position:0%
+okay and so we have the square root of 1
+the square root of 2 square root of N
+
+ align:start position:0%
+the square root of 2 square root of N
+ 
+
+ align:start position:0%
+the square root of 2 square root of N
+and everything else is 0 so we can write
+
+ align:start position:0%
+and everything else is 0 so we can write
+ 
+
+ align:start position:0%
+and everything else is 0 so we can write
+big zeros so that's what this matrix
+
+ align:start position:0%
+big zeros so that's what this matrix
+ 
+
+ align:start position:0%
+big zeros so that's what this matrix
+looks like now if we're using computers
+
+ align:start position:0%
+looks like now if we're using computers
+ 
+
+ align:start position:0%
+looks like now if we're using computers
+instead of multiplying these matrices to
+
+ align:start position:0%
+instead of multiplying these matrices to
+ 
+
+ align:start position:0%
+instead of multiplying these matrices to
+have say Q to the 13th or via a dagger
+
+ align:start position:0%
+have say Q to the 13th or via a dagger
+ 
+
+ align:start position:0%
+have say Q to the 13th or via a dagger
+to the 13th you can just multiply these
+
+ align:start position:0%
+to the 13th you can just multiply these
+ 
+
+ align:start position:0%
+to the 13th you can just multiply these
+matrices it's an easy request for the
+
+ align:start position:0%
+matrices it's an easy request for the
+ 
+
+ align:start position:0%
+matrices it's an easy request for the
+computer it's a not such an easy request
+
+ align:start position:0%
+computer it's a not such an easy request
+ 
+
+ align:start position:0%
+computer it's a not such an easy request
+for you but you end up getting matrices
+
+ align:start position:0%
+for you but you end up getting matrices
+ 
+
+ align:start position:0%
+for you but you end up getting matrices
+when you have integer powers of these
+
+ align:start position:0%
+when you have integer powers of these
+ 
+
+ align:start position:0%
+when you have integer powers of these
+you get a matrix with a diagonal and
+
+ align:start position:0%
+you get a matrix with a diagonal and
+ 
+
+ align:start position:0%
+you get a matrix with a diagonal and
+then another diagonal separated by a
+
+ align:start position:0%
+then another diagonal separated by a
+ 
+
+ align:start position:0%
+then another diagonal separated by a
+diagonal of zeroes and so you know what
+
+ align:start position:0%
+diagonal of zeroes and so you know what
+ 
+
+ align:start position:0%
+diagonal of zeroes and so you know what
+these things are going to look like so
+
+ align:start position:0%
+these things are going to look like so
+ 
+
+ align:start position:0%
+these things are going to look like so
+you might ask okay what is it hey you
+
+ align:start position:0%
+you might ask okay what is it hey you
+ 
+
+ align:start position:0%
+you might ask okay what is it hey you
+look like and there are several ways to
+
+ align:start position:0%
+look like and there are several ways to
+ 
+
+ align:start position:0%
+look like and there are several ways to
+say what a is going to look like because
+
+ align:start position:0%
+say what a is going to look like because
+ 
+
+ align:start position:0%
+say what a is going to look like because
+it's the conjugate transpose of a dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well these are all real numbers and so
+
+ align:start position:0%
+well these are all real numbers and so
+ 
+
+ align:start position:0%
+well these are all real numbers and so
+all you do is flip this on a stye agonal
+
+ align:start position:0%
+all you do is flip this on a stye agonal
+ 
+
+ align:start position:0%
+all you do is flip this on a stye agonal
+now you get a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's another actor in this
+
+ align:start position:0%
+and then there's another actor in this
+ 
+
+ align:start position:0%
+and then there's another actor in this
+game that's n the number operator and
+
+ align:start position:0%
+game that's n the number operator and
+ 
+
+ align:start position:0%
+game that's n the number operator and
+the number operator is going to be a hey
+
+ align:start position:0%
+the number operator is going to be a hey
+ 
+
+ align:start position:0%
+the number operator is going to be a hey
+dagger or is it gonna be a dagger a so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is it this yes okay one way to
+
+ align:start position:0%
+which is it this yes okay one way to
+ 
+
+ align:start position:0%
+which is it this yes okay one way to
+remember this is when you operate with
+
+ align:start position:0%
+remember this is when you operate with
+ 
+
+ align:start position:0%
+remember this is when you operate with
+either a or a dagger it connects to
+
+ align:start position:0%
+either a or a dagger it connects to
+ 
+
+ align:start position:0%
+either a or a dagger it connects to
+vibrational levels and the thing you put
+
+ align:start position:0%
+vibrational levels and the thing you put
+ 
+
+ align:start position:0%
+vibrational levels and the thing you put
+in the square root is the larger of the
+
+ align:start position:0%
+in the square root is the larger of the
+ 
+
+ align:start position:0%
+in the square root is the larger of the
+two quantum numbers okay so what would
+
+ align:start position:0%
+two quantum numbers okay so what would
+ 
+
+ align:start position:0%
+two quantum numbers okay so what would
+the number operator matrix look like so
+
+ align:start position:0%
+the number operator matrix look like so
+ 
+
+ align:start position:0%
+the number operator matrix look like so
+what do I put here yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what's the lowest vibrational
+
+ align:start position:0%
+but what's the lowest vibrational
+ 
+
+ align:start position:0%
+but what's the lowest vibrational
+quantum number right okay and so you
+
+ align:start position:0%
+quantum number right okay and so you
+ 
+
+ align:start position:0%
+quantum number right okay and so you
+know once you've practiced a little bit
+
+ align:start position:0%
+know once you've practiced a little bit
+ 
+
+ align:start position:0%
+know once you've practiced a little bit
+you can write these things and it's it's
+
+ align:start position:0%
+you can write these things and it's it's
+ 
+
+ align:start position:0%
+you can write these things and it's it's
+not just an arbitrary thing because you
+
+ align:start position:0%
+not just an arbitrary thing because you
+ 
+
+ align:start position:0%
+not just an arbitrary thing because you
+want to be able to visualize what you're
+
+ align:start position:0%
+want to be able to visualize what you're
+ 
+
+ align:start position:0%
+want to be able to visualize what you're
+doing because you're dealing with
+
+ align:start position:0%
+doing because you're dealing with
+ 
+
+ align:start position:0%
+doing because you're dealing with
+multiple infinities of objects and you
+
+ align:start position:0%
+multiple infinities of objects and you
+ 
+
+ align:start position:0%
+multiple infinities of objects and you
+want to focus only on the ones you care
+
+ align:start position:0%
+want to focus only on the ones you care
+ 
+
+ align:start position:0%
+want to focus only on the ones you care
+about and you know with a little bit of
+
+ align:start position:0%
+about and you know with a little bit of
+ 
+
+ align:start position:0%
+about and you know with a little bit of
+guidance from these pictures you can do
+
+ align:start position:0%
+guidance from these pictures you can do
+ 
+
+ align:start position:0%
+guidance from these pictures you can do
+what you need to do okay so well we know
+
+ align:start position:0%
+what you need to do okay so well we know
+ 
+
+ align:start position:0%
+what you need to do okay so well we know
+what the operator cube is in terms of a
+
+ align:start position:0%
+what the operator cube is in terms of a
+ 
+
+ align:start position:0%
+what the operator cube is in terms of a
+dimensionless a version of QED and
+
+ align:start position:0%
+dimensionless a version of QED and
+ 
+
+ align:start position:0%
+dimensionless a version of QED and
+that's h-bar over now I'm going to be
+
+ align:start position:0%
+that's h-bar over now I'm going to be
+ 
+
+ align:start position:0%
+that's h-bar over now I'm going to be
+using this okay this is the
+
+ align:start position:0%
+using this okay this is the
+ 
+
+ align:start position:0%
+using this okay this is the
+dimensionless queue that's what the
+
+ align:start position:0%
+dimensionless queue that's what the
+ 
+
+ align:start position:0%
+dimensionless queue that's what the
+twiddle means and these are constants
+
+ align:start position:0%
+twiddle means and these are constants
+ 
+
+ align:start position:0%
+twiddle means and these are constants
+and now I'm using Omega twiddle because
+
+ align:start position:0%
+and now I'm using Omega twiddle because
+ 
+
+ align:start position:0%
+and now I'm using Omega twiddle because
+spectroscopy is always called Omega
+
+ align:start position:0%
+spectroscopy is always called Omega
+ 
+
+ align:start position:0%
+spectroscopy is always called Omega
+use Omega in wave number units
+
+ align:start position:0%
+use Omega in wave number units
+ 
+
+ align:start position:0%
+use Omega in wave number units
+reciprocal centimeter units which is a
+
+ align:start position:0%
+reciprocal centimeter units which is a
+ 
+
+ align:start position:0%
+reciprocal centimeter units which is a
+terrible thing because first of all wave
+
+ align:start position:0%
+terrible thing because first of all wave
+ 
+
+ align:start position:0%
+terrible thing because first of all wave
+number doesn't have a units of quantity
+
+ align:start position:0%
+number doesn't have a units of quantity
+ 
+
+ align:start position:0%
+number doesn't have a units of quantity
+and centimeters are things that we're
+
+ align:start position:0%
+and centimeters are things that we're
+ 
+
+ align:start position:0%
+and centimeters are things that we're
+not supposed to use because we use MKS
+
+ align:start position:0%
+not supposed to use because we use MKS
+ 
+
+ align:start position:0%
+not supposed to use because we use MKS
+but spectroscopy are stubborn and when
+
+ align:start position:0%
+but spectroscopy are stubborn and when
+ 
+
+ align:start position:0%
+but spectroscopy are stubborn and when
+we observe transitions we always talk
+
+ align:start position:0%
+we observe transitions we always talk
+ 
+
+ align:start position:0%
+we observe transitions we always talk
+about wave numbers not energy and so the
+
+ align:start position:0%
+about wave numbers not energy and so the
+ 
+
+ align:start position:0%
+about wave numbers not energy and so the
+difference between wave numbers and
+
+ align:start position:0%
+difference between wave numbers and
+ 
+
+ align:start position:0%
+difference between wave numbers and
+energies is the factor of h c not H bar
+
+ align:start position:0%
+energies is the factor of h c not H bar
+ 
+
+ align:start position:0%
+energies is the factor of h c not H bar
+C so anyway this is the conversion
+
+ align:start position:0%
+C so anyway this is the conversion
+ 
+
+ align:start position:0%
+C so anyway this is the conversion
+factor when Omega is in wave number
+
+ align:start position:0%
+factor when Omega is in wave number
+ 
+
+ align:start position:0%
+factor when Omega is in wave number
+units and so and we can go
+
+ align:start position:0%
+units and so and we can go
+ 
+
+ align:start position:0%
+units and so and we can go
+further and relate Q twiddle do let's
+
+ align:start position:0%
+further and relate Q twiddle do let's
+ 
+
+ align:start position:0%
+further and relate Q twiddle do let's
+just do that we can relate this to h-bar
+
+ align:start position:0%
+just do that we can relate this to h-bar
+ 
+
+ align:start position:0%
+just do that we can relate this to h-bar
+over 4 I see you Omega square what times
+
+ align:start position:0%
+over 4 I see you Omega square what times
+ 
+
+ align:start position:0%
+over 4 I see you Omega square what times
+a plus a dagger okay so this is
+
+ align:start position:0%
+a plus a dagger okay so this is
+ 
+
+ align:start position:0%
+a plus a dagger okay so this is
+something we did before
+
+ align:start position:0%
+something we did before
+ 
+
+ align:start position:0%
+something we did before
+Omega twiddle is K over nu Square 1 over
+
+ align:start position:0%
+Omega twiddle is K over nu Square 1 over
+ 
+
+ align:start position:0%
+Omega twiddle is K over nu Square 1 over
+2 pi C HC so this is this is what you're
+
+ align:start position:0%
+2 pi C HC so this is this is what you're
+ 
+
+ align:start position:0%
+2 pi C HC so this is this is what you're
+used to and this is the extra stuff that
+
+ align:start position:0%
+used to and this is the extra stuff that
+ 
+
+ align:start position:0%
+used to and this is the extra stuff that
+we have to carry along in order to work
+
+ align:start position:0%
+we have to carry along in order to work
+ 
+
+ align:start position:0%
+we have to carry along in order to work
+in wave number units
+
+ align:start position:0%
+in wave number units
+ 
+
+ align:start position:0%
+in wave number units
+okay so we have operators that can be
+
+ align:start position:0%
+okay so we have operators that can be
+ 
+
+ align:start position:0%
+okay so we have operators that can be
+expressed like a a a dagger a or a
+
+ align:start position:0%
+expressed like a a a dagger a or a
+ 
+
+ align:start position:0%
+expressed like a a a dagger a or a
+dagger a a a or anywhere you put the
+
+ align:start position:0%
+dagger a a a or anywhere you put the
+ 
+
+ align:start position:0%
+dagger a a a or anywhere you put the
+dagger anywhere you look at this and you
+
+ align:start position:0%
+dagger anywhere you look at this and you
+ 
+
+ align:start position:0%
+dagger anywhere you look at this and you
+say immediately I know two things I know
+
+ align:start position:0%
+say immediately I know two things I know
+ 
+
+ align:start position:0%
+say immediately I know two things I know
+the selection rule the selection rule is
+
+ align:start position:0%
+the selection rule the selection rule is
+ 
+
+ align:start position:0%
+the selection rule the selection rule is
+count up the A's and count up the a
+
+ align:start position:0%
+count up the A's and count up the a
+ 
+
+ align:start position:0%
+count up the A's and count up the a
+daggers and so this is Delta V of minus
+
+ align:start position:0%
+daggers and so this is Delta V of minus
+ 
+
+ align:start position:0%
+daggers and so this is Delta V of minus
+2 so is this all of the positions of the
+
+ align:start position:0%
+2 so is this all of the positions of the
+ 
+
+ align:start position:0%
+2 so is this all of the positions of the
+a dagger are Delta V of minus 2 but the
+
+ align:start position:0%
+a dagger are Delta V of minus 2 but the
+ 
+
+ align:start position:0%
+a dagger are Delta V of minus 2 but the
+numbers the matrix elements are
+
+ align:start position:0%
+numbers the matrix elements are
+ 
+
+ align:start position:0%
+numbers the matrix elements are
+different you know this from the last
+
+ align:start position:0%
+different you know this from the last
+ 
+
+ align:start position:0%
+different you know this from the last
+exam so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can have v- to be and whatever comes in
+
+ align:start position:0%
+can have v- to be and whatever comes in
+ 
+
+ align:start position:0%
+can have v- to be and whatever comes in
+here well in one of those forms so those
+
+ align:start position:0%
+here well in one of those forms so those
+ 
+
+ align:start position:0%
+here well in one of those forms so those
+are the only nonzero elements and you
+
+ align:start position:0%
+are the only nonzero elements and you
+ 
+
+ align:start position:0%
+are the only nonzero elements and you
+know how to mechanically figure out what
+
+ align:start position:0%
+know how to mechanically figure out what
+ 
+
+ align:start position:0%
+know how to mechanically figure out what
+is the value of the matrix element and
+
+ align:start position:0%
+is the value of the matrix element and
+ 
+
+ align:start position:0%
+is the value of the matrix element and
+now in order to simplify the algebra
+
+ align:start position:0%
+now in order to simplify the algebra
+ 
+
+ align:start position:0%
+now in order to simplify the algebra
+which is not essential to the physics
+
+ align:start position:0%
+which is not essential to the physics
+ 
+
+ align:start position:0%
+which is not essential to the physics
+you want to take all of the terms that
+
+ align:start position:0%
+you want to take all of the terms that
+ 
+
+ align:start position:0%
+you want to take all of the terms that
+result safe from Q to the fourth and and
+
+ align:start position:0%
+result safe from Q to the fourth and and
+ 
+
+ align:start position:0%
+result safe from Q to the fourth and and
+arrange them according to selection rule
+
+ align:start position:0%
+arrange them according to selection rule
+ 
+
+ align:start position:0%
+arrange them according to selection rule
+and then take all of the terms that have
+
+ align:start position:0%
+and then take all of the terms that have
+ 
+
+ align:start position:0%
+and then take all of the terms that have
+the same selection rule and combining
+
+ align:start position:0%
+the same selection rule and combining
+ 
+
+ align:start position:0%
+the same selection rule and combining
+them to a single number so you know and
+
+ align:start position:0%
+them to a single number so you know and
+ 
+
+ align:start position:0%
+them to a single number so you know and
+you use the commutation rule to be able
+
+ align:start position:0%
+you use the commutation rule to be able
+ 
+
+ align:start position:0%
+you use the commutation rule to be able
+to reverse the order of terms well I
+
+ align:start position:0%
+to reverse the order of terms well I
+ 
+
+ align:start position:0%
+to reverse the order of terms well I
+don't want to do that I do so suppose we
+
+ align:start position:0%
+don't want to do that I do so suppose we
+ 
+
+ align:start position:0%
+don't want to do that I do so suppose we
+have an a a dagger and we can write that
+
+ align:start position:0%
+have an a a dagger and we can write that
+ 
+
+ align:start position:0%
+have an a a dagger and we can write that
+as a a dagger plus a dagger okay and so
+
+ align:start position:0%
+as a a dagger plus a dagger okay and so
+ 
+
+ align:start position:0%
+as a a dagger plus a dagger okay and so
+if we want to convert something like
+
+ align:start position:0%
+if we want to convert something like
+ 
+
+ align:start position:0%
+if we want to convert something like
+this just something like that we know
+
+ align:start position:0%
+this just something like that we know
+ 
+
+ align:start position:0%
+this just something like that we know
+that this has a value of +1 so we can do
+
+ align:start position:0%
+that this has a value of +1 so we can do
+ 
+
+ align:start position:0%
+that this has a value of +1 so we can do
+that and that's tedious and you have to
+
+ align:start position:0%
+that and that's tedious and you have to
+ 
+
+ align:start position:0%
+that and that's tedious and you have to
+do it but one of the things that is kind
+
+ align:start position:0%
+do it but one of the things that is kind
+ 
+
+ align:start position:0%
+do it but one of the things that is kind
+of nice is when you have a problem
+
+ align:start position:0%
+of nice is when you have a problem
+ 
+
+ align:start position:0%
+of nice is when you have a problem
+that's cubic or quartic or quintic you
+
+ align:start position:0%
+that's cubic or quartic or quintic you
+ 
+
+ align:start position:0%
+that's cubic or quartic or quintic you
+do mess around with this operator l true
+
+ align:start position:0%
+do mess around with this operator l true
+ 
+
+ align:start position:0%
+do mess around with this operator l true
+once in your life and you put it on a
+
+ align:start position:0%
+once in your life and you put it on a
+ 
+
+ align:start position:0%
+once in your life and you put it on a
+sheet of paper and you refer to it it
+
+ align:start position:0%
+sheet of paper and you refer to it it
+ 
+
+ align:start position:0%
+sheet of paper and you refer to it it
+doesn't matter what the molecule is what
+
+ align:start position:0%
+doesn't matter what the molecule is what
+ 
+
+ align:start position:0%
+doesn't matter what the molecule is what
+the constant in front of Q to the third
+
+ align:start position:0%
+the constant in front of Q to the third
+ 
+
+ align:start position:0%
+the constant in front of Q to the third
+or fourth or 13th is if you've done the
+
+ align:start position:0%
+or fourth or 13th is if you've done the
+ 
+
+ align:start position:0%
+or fourth or 13th is if you've done the
+operator algebra you're fine now you
+
+ align:start position:0%
+operator algebra you're fine now you
+ 
+
+ align:start position:0%
+operator algebra you're fine now you
+might say well I don't want to do that
+
+ align:start position:0%
+might say well I don't want to do that
+ 
+
+ align:start position:0%
+might say well I don't want to do that
+I'm going to have the computer do that
+
+ align:start position:0%
+I'm going to have the computer do that
+ 
+
+ align:start position:0%
+I'm going to have the computer do that
+well fine you can have the computer do
+
+ align:start position:0%
+well fine you can have the computer do
+ 
+
+ align:start position:0%
+well fine you can have the computer do
+that and then a computer will tell you
+
+ align:start position:0%
+that and then a computer will tell you
+ 
+
+ align:start position:0%
+that and then a computer will tell you
+what the matrix looks like and
+
+ align:start position:0%
+what the matrix looks like and
+ 
+
+ align:start position:0%
+what the matrix looks like and
+you can do what you need to do okay so
+
+ align:start position:0%
+you can do what you need to do okay so
+ 
+
+ align:start position:0%
+you can do what you need to do okay so
+spectroscopy called the vibrational
+
+ align:start position:0%
+spectroscopy called the vibrational
+ 
+
+ align:start position:0%
+spectroscopy called the vibrational
+energy formula G of B I don't know why
+
+ align:start position:0%
+energy formula G of B I don't know why
+ 
+
+ align:start position:0%
+energy formula G of B I don't know why
+the letter G is always used but it is
+
+ align:start position:0%
+the letter G is always used but it is
+ 
+
+ align:start position:0%
+the letter G is always used but it is
+and so this is the same thing as
+
+ align:start position:0%
+and so this is the same thing as
+ 
+
+ align:start position:0%
+and so this is the same thing as
+vibrational energy and the vibrational
+
+ align:start position:0%
+vibrational energy and the vibrational
+ 
+
+ align:start position:0%
+vibrational energy and the vibrational
+energy I'm gonna put the tilt on it you
+
+ align:start position:0%
+energy I'm gonna put the tilt on it you
+ 
+
+ align:start position:0%
+energy I'm gonna put the tilt on it you
+will never find a tilde in any
+
+ align:start position:0%
+will never find a tilde in any
+ 
+
+ align:start position:0%
+will never find a tilde in any
+spectroscopy no paper we assume that you
+
+ align:start position:0%
+spectroscopy no paper we assume that you
+ 
+
+ align:start position:0%
+spectroscopy no paper we assume that you
+understand that the only units for
+
+ align:start position:0%
+understand that the only units for
+ 
+
+ align:start position:0%
+understand that the only units for
+spectroscopic quantities are reciprocal
+
+ align:start position:0%
+spectroscopic quantities are reciprocal
+ 
+
+ align:start position:0%
+spectroscopic quantities are reciprocal
+centimeters but for this purpose is I
+
+ align:start position:0%
+centimeters but for this purpose is I
+ 
+
+ align:start position:0%
+centimeters but for this purpose is I
+have I've finally caved and I said okay
+
+ align:start position:0%
+have I've finally caved and I said okay
+ 
+
+ align:start position:0%
+have I've finally caved and I said okay
+I'm gonna put the Tilda's on so the
+
+ align:start position:0%
+I'm gonna put the Tilda's on so the
+ 
+
+ align:start position:0%
+I'm gonna put the Tilda's on so the
+energy levels now you might ask why this
+
+ align:start position:0%
+energy levels now you might ask why this
+ 
+
+ align:start position:0%
+energy levels now you might ask why this
+this is the first n-terminus T constant
+
+ align:start position:0%
+this is the first n-terminus T constant
+ 
+
+ align:start position:0%
+this is the first n-terminus T constant
+it's not a product of two numbers it's
+
+ align:start position:0%
+it's not a product of two numbers it's
+ 
+
+ align:start position:0%
+it's not a product of two numbers it's
+just what people wrote originally
+
+ align:start position:0%
+just what people wrote originally
+ 
+
+ align:start position:0%
+just what people wrote originally
+because they sort of thought of it as a
+
+ align:start position:0%
+because they sort of thought of it as a
+ 
+
+ align:start position:0%
+because they sort of thought of it as a
+product of two numbers but it's really
+
+ align:start position:0%
+product of two numbers but it's really
+ 
+
+ align:start position:0%
+product of two numbers but it's really
+only one and and that's times V plus 1/2
+
+ align:start position:0%
+only one and and that's times V plus 1/2
+ 
+
+ align:start position:0%
+only one and and that's times V plus 1/2
+squared and then the next term is omega
+
+ align:start position:0%
+squared and then the next term is omega
+ 
+
+ align:start position:0%
+squared and then the next term is omega
+e ye b plus 1/2 cubed so this is a dumb
+
+ align:start position:0%
+e ye b plus 1/2 cubed so this is a dumb
+ 
+
+ align:start position:0%
+e ye b plus 1/2 cubed so this is a dumb
+power series in the vibrational quantum
+
+ align:start position:0%
+power series in the vibrational quantum
+ 
+
+ align:start position:0%
+power series in the vibrational quantum
+number and so in the spectrum one is
+
+ align:start position:0%
+number and so in the spectrum one is
+ 
+
+ align:start position:0%
+number and so in the spectrum one is
+able to fit the spectrum to these sorts
+
+ align:start position:0%
+able to fit the spectrum to these sorts
+ 
+
+ align:start position:0%
+able to fit the spectrum to these sorts
+of things so that's what you get
+
+ align:start position:0%
+of things so that's what you get
+ 
+
+ align:start position:0%
+of things so that's what you get
+experimentally but what you want to know
+
+ align:start position:0%
+experimentally but what you want to know
+ 
+
+ align:start position:0%
+experimentally but what you want to know
+is we want to know the force the force
+
+ align:start position:0%
+is we want to know the force the force
+ 
+
+ align:start position:0%
+is we want to know the force the force
+constant the reduced mass the cube again
+
+ align:start position:0%
+constant the reduced mass the cube again
+ 
+
+ align:start position:0%
+constant the reduced mass the cube again
+our ministry constant the court again
+
+ align:start position:0%
+our ministry constant the court again
+ 
+
+ align:start position:0%
+our ministry constant the court again
+i'm gonna see constant and whatever so
+
+ align:start position:0%
+i'm gonna see constant and whatever so
+ 
+
+ align:start position:0%
+i'm gonna see constant and whatever so
+these are structural parameters and
+
+ align:start position:0%
+these are structural parameters and
+ 
+
+ align:start position:0%
+these are structural parameters and
+these are molecular parameters or not
+
+ align:start position:0%
+these are molecular parameters or not
+ 
+
+ align:start position:0%
+these are molecular parameters or not
+people like to call them spectroscopic
+
+ align:start position:0%
+people like to call them spectroscopic
+ 
+
+ align:start position:0%
+people like to call them spectroscopic
+parameters but that implies something
+
+ align:start position:0%
+parameters but that implies something
+ 
+
+ align:start position:0%
+parameters but that implies something
+more fundamental these are just what you
+
+ align:start position:0%
+more fundamental these are just what you
+ 
+
+ align:start position:0%
+more fundamental these are just what you
+measure in the spectrum and so we want
+
+ align:start position:0%
+measure in the spectrum and so we want
+ 
+
+ align:start position:0%
+measure in the spectrum and so we want
+to know the relationship between the
+
+ align:start position:0%
+to know the relationship between the
+ 
+
+ align:start position:0%
+to know the relationship between the
+things we measure and the things we want
+
+ align:start position:0%
+things we measure and the things we want
+ 
+
+ align:start position:0%
+things we measure and the things we want
+to know and so that's what perturbation
+
+ align:start position:0%
+to know and so that's what perturbation
+ 
+
+ align:start position:0%
+to know and so that's what perturbation
+theory is for okay
+
+ align:start position:0%
+theory is for okay
+ 
+
+ align:start position:0%
+theory is for okay
+now to risk boring you I'm just going to
+
+ align:start position:0%
+now to risk boring you I'm just going to
+ 
+
+ align:start position:0%
+now to risk boring you I'm just going to
+go over material that we've done before
+
+ align:start position:0%
+go over material that we've done before
+ 
+
+ align:start position:0%
+go over material that we've done before
+so if we have Q to the N we have this
+
+ align:start position:0%
+so if we have Q to the N we have this
+ 
+
+ align:start position:0%
+so if we have Q to the N we have this
+constant out in front h-bar over 4 pi C
+
+ align:start position:0%
+constant out in front h-bar over 4 pi C
+ 
+
+ align:start position:0%
+constant out in front h-bar over 4 pi C
+mu Omega to the N over 2 a plus a dagger
+
+ align:start position:0%
+mu Omega to the N over 2 a plus a dagger
+ 
+
+ align:start position:0%
+mu Omega to the N over 2 a plus a dagger
+to the N and so we're going to be
+
+ align:start position:0%
+to the N and so we're going to be
+ 
+
+ align:start position:0%
+to the N and so we're going to be
+constantly dealing with earth like a
+
+ align:start position:0%
+constantly dealing with earth like a
+ 
+
+ align:start position:0%
+constantly dealing with earth like a
+plus a dagger squared and a plus a
+
+ align:start position:0%
+plus a dagger squared and a plus a
+ 
+
+ align:start position:0%
+plus a dagger squared and a plus a
+dagger cubed and so on these are the
+
+ align:start position:0%
+dagger cubed and so on these are the
+ 
+
+ align:start position:0%
+dagger cubed and so on these are the
+things I said you're going to work out
+
+ align:start position:0%
+things I said you're going to work out
+ 
+
+ align:start position:0%
+things I said you're going to work out
+once in your life and either remember or
+
+ align:start position:0%
+once in your life and either remember or
+ 
+
+ align:start position:0%
+once in your life and either remember or
+just be so come so practiced with it
+
+ align:start position:0%
+just be so come so practiced with it
+ 
+
+ align:start position:0%
+just be so come so practiced with it
+you'll do it faster okay and so these
+
+ align:start position:0%
+you'll do it faster okay and so these
+ 
+
+ align:start position:0%
+you'll do it faster okay and so these
+contain the values of the matrix
+
+ align:start position:0%
+contain the values of the matrix
+ 
+
+ align:start position:0%
+contain the values of the matrix
+elements and the selection rules okay
+
+ align:start position:0%
+elements and the selection rules okay
+ 
+
+ align:start position:0%
+elements and the selection rules okay
+so I'm going to do an example the cube
+
+ align:start position:0%
+so I'm going to do an example the cube
+ 
+
+ align:start position:0%
+so I'm going to do an example the cube
+and that's of course this thing in
+
+ align:start position:0%
+and that's of course this thing in
+ 
+
+ align:start position:0%
+and that's of course this thing in
+constant to the three-halves and then a
+
+ align:start position:0%
+constant to the three-halves and then a
+ 
+
+ align:start position:0%
+constant to the three-halves and then a
+cubed plus a dagger cubed plus a whole
+
+ align:start position:0%
+cubed plus a dagger cubed plus a whole
+ 
+
+ align:start position:0%
+cubed plus a dagger cubed plus a whole
+bunch of terms which have two A's in one
+
+ align:start position:0%
+bunch of terms which have two A's in one
+ 
+
+ align:start position:0%
+bunch of terms which have two A's in one
+a dagger so let's just put a squared + a
+
+ align:start position:0%
+a dagger so let's just put a squared + a
+ 
+
+ align:start position:0%
+a dagger so let's just put a squared + a
+dagger this isn't a commutation rule
+
+ align:start position:0%
+dagger this isn't a commutation rule
+ 
+
+ align:start position:0%
+dagger this isn't a commutation rule
+this is just three terms that you have
+
+ align:start position:0%
+this is just three terms that you have
+ 
+
+ align:start position:0%
+this is just three terms that you have
+to deal with and three terms that have a
+
+ align:start position:0%
+to deal with and three terms that have a
+ 
+
+ align:start position:0%
+to deal with and three terms that have a
+dagger squared and a and then
+
+ align:start position:0%
+dagger squared and a and then
+ 
+
+ align:start position:0%
+dagger squared and a and then
+so that's what you'd do your work on
+
+ align:start position:0%
+so that's what you'd do your work on
+ 
+
+ align:start position:0%
+so that's what you'd do your work on
+because you don't want to be messing
+
+ align:start position:0%
+because you don't want to be messing
+ 
+
+ align:start position:0%
+because you don't want to be messing
+around once you start doing this
+
+ align:start position:0%
+around once you start doing this
+ 
+
+ align:start position:0%
+around once you start doing this
+perturbation sums because it's ugly
+
+ align:start position:0%
+perturbation sums because it's ugly
+ 
+
+ align:start position:0%
+perturbation sums because it's ugly
+enough so you want to simplify this as
+
+ align:start position:0%
+enough so you want to simplify this as
+ 
+
+ align:start position:0%
+enough so you want to simplify this as
+much as possible and you do and so the
+
+ align:start position:0%
+much as possible and you do and so the
+ 
+
+ align:start position:0%
+much as possible and you do and so the
+purpose is this is Delta V of minus
+
+ align:start position:0%
+purpose is this is Delta V of minus
+ 
+
+ align:start position:0%
+purpose is this is Delta V of minus
+three this is Delta V of plus three this
+
+ align:start position:0%
+three this is Delta V of plus three this
+ 
+
+ align:start position:0%
+three this is Delta V of plus three this
+is Delta V of minus 1 this is Delta V of
+
+ align:start position:0%
+is Delta V of minus 1 this is Delta V of
+ 
+
+ align:start position:0%
+is Delta V of minus 1 this is Delta V of
+plus 1 you arrange the terms according
+
+ align:start position:0%
+plus 1 you arrange the terms according
+ 
+
+ align:start position:0%
+plus 1 you arrange the terms according
+to selection rules and so what you end
+
+ align:start position:0%
+to selection rules and so what you end
+ 
+
+ align:start position:0%
+to selection rules and so what you end
+up getting is Q cubed is equal to this
+
+ align:start position:0%
+up getting is Q cubed is equal to this
+ 
+
+ align:start position:0%
+up getting is Q cubed is equal to this
+thing to the three-halves times a cubed
+
+ align:start position:0%
+thing to the three-halves times a cubed
+ 
+
+ align:start position:0%
+thing to the three-halves times a cubed
+plus three a n plus three a dagger n
+
+ align:start position:0%
+plus three a n plus three a dagger n
+ 
+
+ align:start position:0%
+plus three a n plus three a dagger n
+plus one plus okay the algebra is
+
+ align:start position:0%
+plus one plus okay the algebra is
+ 
+
+ align:start position:0%
+plus one plus okay the algebra is
+tedious pretty simple and what you
+
+ align:start position:0%
+tedious pretty simple and what you
+ 
+
+ align:start position:0%
+tedious pretty simple and what you
+usually want to do is have the thing
+
+ align:start position:0%
+usually want to do is have the thing
+ 
+
+ align:start position:0%
+usually want to do is have the thing
+that changes the vibrational quantum
+
+ align:start position:0%
+that changes the vibrational quantum
+ 
+
+ align:start position:0%
+that changes the vibrational quantum
+number after the thing that preserves it
+
+ align:start position:0%
+number after the thing that preserves it
+ 
+
+ align:start position:0%
+number after the thing that preserves it
+because then it's easy just to write
+
+ align:start position:0%
+because then it's easy just to write
+ 
+
+ align:start position:0%
+because then it's easy just to write
+down these matrix elements just by
+
+ align:start position:0%
+down these matrix elements just by
+ 
+
+ align:start position:0%
+down these matrix elements just by
+inspection okay you could do it the
+
+ align:start position:0%
+inspection okay you could do it the
+ 
+
+ align:start position:0%
+inspection okay you could do it the
+other way around it's more complicated
+
+ align:start position:0%
+other way around it's more complicated
+ 
+
+ align:start position:0%
+other way around it's more complicated
+if you put the N first and then the a
+
+ align:start position:0%
+if you put the N first and then the a
+ 
+
+ align:start position:0%
+if you put the N first and then the a
+but it's not you know it's up to you so
+
+ align:start position:0%
+but it's not you know it's up to you so
+ 
+
+ align:start position:0%
+but it's not you know it's up to you so
+these then are what you work on and now
+
+ align:start position:0%
+these then are what you work on and now
+ 
+
+ align:start position:0%
+these then are what you work on and now
+we start doing non-degenerate
+
+ align:start position:0%
+we start doing non-degenerate
+ 
+
+ align:start position:0%
+we start doing non-degenerate
+perturbation Theory the first thing you
+
+ align:start position:0%
+perturbation Theory the first thing you
+ 
+
+ align:start position:0%
+perturbation Theory the first thing you
+do is you want to know well what is the
+
+ align:start position:0%
+do is you want to know well what is the
+ 
+
+ align:start position:0%
+do is you want to know well what is the
+first order correction to the energy and
+
+ align:start position:0%
+first order correction to the energy and
+ 
+
+ align:start position:0%
+first order correction to the energy and
+if this is Q Q to the third power
+
+ align:start position:0%
+if this is Q Q to the third power
+ 
+
+ align:start position:0%
+if this is Q Q to the third power
+then this that's zero so you like zeros
+
+ align:start position:0%
+then this that's zero so you like zeros
+ 
+
+ align:start position:0%
+then this that's zero so you like zeros
+but in this case you're kind of
+
+ align:start position:0%
+but in this case you're kind of
+ 
+
+ align:start position:0%
+but in this case you're kind of
+disappointed because you don't know what
+
+ align:start position:0%
+disappointed because you don't know what
+ 
+
+ align:start position:0%
+disappointed because you don't know what
+the sign of the coefficient of Q to the
+
+ align:start position:0%
+the sign of the coefficient of Q to the
+ 
+
+ align:start position:0%
+the sign of the coefficient of Q to the
+third power is
+
+ align:start position:0%
+third power is
+ 
+
+ align:start position:0%
+third power is
+from any experiment or at least any
+
+ align:start position:0%
+from any experiment or at least any
+ 
+
+ align:start position:0%
+from any experiment or at least any
+experiment at the level we've described
+
+ align:start position:0%
+experiment at the level we've described
+ 
+
+ align:start position:0%
+experiment at the level we've described
+when we introduced rotation as well as
+
+ align:start position:0%
+when we introduced rotation as well as
+ 
+
+ align:start position:0%
+when we introduced rotation as well as
+vibration there will be something that
+
+ align:start position:0%
+vibration there will be something that
+ 
+
+ align:start position:0%
+vibration there will be something that
+reports the sign of the coefficient of Q
+
+ align:start position:0%
+reports the sign of the coefficient of Q
+ 
+
+ align:start position:0%
+reports the sign of the coefficient of Q
+third so now we're we're stuck and we
+
+ align:start position:0%
+third so now we're we're stuck and we
+ 
+
+ align:start position:0%
+third so now we're we're stuck and we
+have to start doing all of this
+
+ align:start position:0%
+have to start doing all of this
+ 
+
+ align:start position:0%
+have to start doing all of this
+second-order stuff and okay well we have
+
+ align:start position:0%
+second-order stuff and okay well we have
+ 
+
+ align:start position:0%
+second-order stuff and okay well we have
+this V Q to the third power and so we
+
+ align:start position:0%
+this V Q to the third power and so we
+ 
+
+ align:start position:0%
+this V Q to the third power and so we
+get squares of the matrix elements so we
+
+ align:start position:0%
+get squares of the matrix elements so we
+ 
+
+ align:start position:0%
+get squares of the matrix elements so we
+get a B squared we get this thing to the
+
+ align:start position:0%
+get a B squared we get this thing to the
+ 
+
+ align:start position:0%
+get a B squared we get this thing to the
+third power because we're squaring the
+
+ align:start position:0%
+third power because we're squaring the
+ 
+
+ align:start position:0%
+third power because we're squaring the
+matrix M so this bunch of constants and
+
+ align:start position:0%
+matrix M so this bunch of constants and
+ 
+
+ align:start position:0%
+matrix M so this bunch of constants and
+then you get a matrix element V prime
+
+ align:start position:0%
+then you get a matrix element V prime
+ 
+
+ align:start position:0%
+then you get a matrix element V prime
+some operator B and then we get an
+
+ align:start position:0%
+some operator B and then we get an
+ 
+
+ align:start position:0%
+some operator B and then we get an
+energy denominator now we you know
+
+ align:start position:0%
+energy denominator now we you know
+ 
+
+ align:start position:0%
+energy denominator now we you know
+there's a lot of symbols but we want to
+
+ align:start position:0%
+there's a lot of symbols but we want to
+ 
+
+ align:start position:0%
+there's a lot of symbols but we want to
+simplify things as much as possible H C
+
+ align:start position:0%
+simplify things as much as possible H C
+ 
+
+ align:start position:0%
+simplify things as much as possible H C
+Omega times the minus V prime so this is
+
+ align:start position:0%
+Omega times the minus V prime so this is
+ 
+
+ align:start position:0%
+Omega times the minus V prime so this is
+matrix element squared over an energy
+
+ align:start position:0%
+matrix element squared over an energy
+ 
+
+ align:start position:0%
+matrix element squared over an energy
+denominator and what you really want to
+
+ align:start position:0%
+denominator and what you really want to
+ 
+
+ align:start position:0%
+denominator and what you really want to
+know is what is the quantum number
+
+ align:start position:0%
+know is what is the quantum number
+ 
+
+ align:start position:0%
+know is what is the quantum number
+dependence of everything okay so the
+
+ align:start position:0%
+dependence of everything okay so the
+ 
+
+ align:start position:0%
+dependence of everything okay so the
+operator here is either Q dagger cubed Q
+
+ align:start position:0%
+operator here is either Q dagger cubed Q
+ 
+
+ align:start position:0%
+operator here is either Q dagger cubed Q
+dagger I'm sorry a dagger a cubed a
+
+ align:start position:0%
+dagger I'm sorry a dagger a cubed a
+ 
+
+ align:start position:0%
+dagger I'm sorry a dagger a cubed a
+times n a dagger n plus 1 or a dagger
+
+ align:start position:0%
+times n a dagger n plus 1 or a dagger
+ 
+
+ align:start position:0%
+times n a dagger n plus 1 or a dagger
+cubed and so we we know how to write all
+
+ align:start position:0%
+cubed and so we we know how to write all
+ 
+
+ align:start position:0%
+cubed and so we we know how to write all
+of these matrix elements trivially no
+
+ align:start position:0%
+of these matrix elements trivially no
+ 
+
+ align:start position:0%
+of these matrix elements trivially no
+work once we've simplified here it's
+
+ align:start position:0%
+work once we've simplified here it's
+ 
+
+ align:start position:0%
+work once we've simplified here it's
+really trivial to write the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the squared matrix of it okay so we do
+
+ align:start position:0%
+the squared matrix of it okay so we do
+ 
+
+ align:start position:0%
+the squared matrix of it okay so we do
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we arrange things according to
+
+ align:start position:0%
+and so we arrange things according to
+ 
+
+ align:start position:0%
+and so we arrange things according to
+Delta V and we have Delta V a plus 3
+
+ align:start position:0%
+Delta V and we have Delta V a plus 3
+ 
+
+ align:start position:0%
+Delta V and we have Delta V a plus 3
+plus 1 minus 1 and minus 3 and so what
+
+ align:start position:0%
+plus 1 minus 1 and minus 3 and so what
+ 
+
+ align:start position:0%
+plus 1 minus 1 and minus 3 and so what
+we get from the square of the matrix
+
+ align:start position:0%
+we get from the square of the matrix
+ 
+
+ align:start position:0%
+we get from the square of the matrix
+element a dagger cubed we get V Plus 1 B
+
+ align:start position:0%
+element a dagger cubed we get V Plus 1 B
+ 
+
+ align:start position:0%
+element a dagger cubed we get V Plus 1 B
+plus 2 V Plus 3 and we also have an
+
+ align:start position:0%
+plus 2 V Plus 3 and we also have an
+ 
+
+ align:start position:0%
+plus 2 V Plus 3 and we also have an
+energy denominator and we're going to
+
+ align:start position:0%
+energy denominator and we're going to
+ 
+
+ align:start position:0%
+energy denominator and we're going to
+get for this one 1 over minus 3 because
+
+ align:start position:0%
+get for this one 1 over minus 3 because
+ 
+
+ align:start position:0%
+get for this one 1 over minus 3 because
+the initial quantum number is is V and
+
+ align:start position:0%
+the initial quantum number is is V and
+ 
+
+ align:start position:0%
+the initial quantum number is is V and
+the second quantum number V prime is V
+
+ align:start position:0%
+the second quantum number V prime is V
+ 
+
+ align:start position:0%
+the second quantum number V prime is V
+Plus 3 and so we get a minus 3 in the
+
+ align:start position:0%
+Plus 3 and so we get a minus 3 in the
+ 
+
+ align:start position:0%
+Plus 3 and so we get a minus 3 in the
+energy denominator and then the plus 1
+
+ align:start position:0%
+energy denominator and then the plus 1
+ 
+
+ align:start position:0%
+energy denominator and then the plus 1
+that comes out to be I've got it in a
+
+ align:start position:0%
+that comes out to be I've got it in a
+ 
+
+ align:start position:0%
+that comes out to be I've got it in a
+different order in my notes that comes
+
+ align:start position:0%
+different order in my notes that comes
+ 
+
+ align:start position:0%
+different order in my notes that comes
+out to be 9 v + 1 v + 2 v + 1 squared
+
+ align:start position:0%
+out to be 9 v + 1 v + 2 v + 1 squared
+ 
+
+ align:start position:0%
+out to be 9 v + 1 v + 2 v + 1 squared
+and the energy denominator for this is 1
+
+ align:start position:0%
+and the energy denominator for this is 1
+ 
+
+ align:start position:0%
+and the energy denominator for this is 1
+over minus 1 ok then we have the I'm
+
+ align:start position:0%
+over minus 1 ok then we have the I'm
+ 
+
+ align:start position:0%
+over minus 1 ok then we have the I'm
+going to skip this one we have the
+
+ align:start position:0%
+going to skip this one we have the
+ 
+
+ align:start position:0%
+going to skip this one we have the
+matrix element here and that's going to
+
+ align:start position:0%
+matrix element here and that's going to
+ 
+
+ align:start position:0%
+matrix element here and that's going to
+be V V minus 1 n minus 2
+
+ align:start position:0%
+be V V minus 1 n minus 2
+ 
+
+ align:start position:0%
+be V V minus 1 n minus 2
+remember we're squaring these things so
+
+ align:start position:0%
+remember we're squaring these things so
+ 
+
+ align:start position:0%
+remember we're squaring these things so
+that's why we don't have those square
+
+ align:start position:0%
+that's why we don't have those square
+ 
+
+ align:start position:0%
+that's why we don't have those square
+roots anymore and we have an energy
+
+ align:start position:0%
+roots anymore and we have an energy
+ 
+
+ align:start position:0%
+roots anymore and we have an energy
+denominator 1 over 3 okay now advice you
+
+ align:start position:0%
+denominator 1 over 3 okay now advice you
+ 
+
+ align:start position:0%
+denominator 1 over 3 okay now advice you
+don't like this and you want to minimize
+
+ align:start position:0%
+don't like this and you want to minimize
+ 
+
+ align:start position:0%
+don't like this and you want to minimize
+your effort
+
+ align:start position:0%
+your effort
+ 
+
+ align:start position:0%
+your effort
+and so it turns out that if you take the
+
+ align:start position:0%
+and so it turns out that if you take the
+ 
+
+ align:start position:0%
+and so it turns out that if you take the
+terms with the equal and opposite energy
+
+ align:start position:0%
+terms with the equal and opposite energy
+ 
+
+ align:start position:0%
+terms with the equal and opposite energy
+denominators and combine them
+
+ align:start position:0%
+denominators and combine them
+ 
+
+ align:start position:0%
+denominators and combine them
+simplifications occur one of the things
+
+ align:start position:0%
+simplifications occur one of the things
+ 
+
+ align:start position:0%
+simplifications occur one of the things
+you can see is you're going to have a V
+
+ align:start position:0%
+you can see is you're going to have a V
+ 
+
+ align:start position:0%
+you can see is you're going to have a V
+cubed here and you're going to have a V
+
+ align:start position:0%
+cubed here and you're going to have a V
+ 
+
+ align:start position:0%
+cubed here and you're going to have a V
+cubed here they're going to cancel right
+
+ align:start position:0%
+cubed here they're going to cancel right
+ 
+
+ align:start position:0%
+cubed here they're going to cancel right
+because we have them 1 over minus 3 and
+
+ align:start position:0%
+because we have them 1 over minus 3 and
+ 
+
+ align:start position:0%
+because we have them 1 over minus 3 and
+then 1 over plus 3 so you get an
+
+ align:start position:0%
+then 1 over plus 3 so you get an
+ 
+
+ align:start position:0%
+then 1 over plus 3 so you get an
+algebraic simplification when you take
+
+ align:start position:0%
+algebraic simplification when you take
+ 
+
+ align:start position:0%
+algebraic simplification when you take
+these terms pairwise and combine them
+
+ align:start position:0%
+these terms pairwise and combine them
+ 
+
+ align:start position:0%
+these terms pairwise and combine them
+now you're never in your life gonna do
+
+ align:start position:0%
+now you're never in your life gonna do
+ 
+
+ align:start position:0%
+now you're never in your life gonna do
+this but you know if you didn't do it
+
+ align:start position:0%
+this but you know if you didn't do it
+ 
+
+ align:start position:0%
+this but you know if you didn't do it
+you know this is how you end up with
+
+ align:start position:0%
+you know this is how you end up with
+ 
+
+ align:start position:0%
+you know this is how you end up with
+algebra which or formulas which are
+
+ align:start position:0%
+algebra which or formulas which are
+ 
+
+ align:start position:0%
+algebra which or formulas which are
+simple they're horrible getting there
+
+ align:start position:0%
+simple they're horrible getting there
+ 
+
+ align:start position:0%
+simple they're horrible getting there
+unless you know how to get there so now
+
+ align:start position:0%
+unless you know how to get there so now
+ 
+
+ align:start position:0%
+unless you know how to get there so now
+there's a rule so if the perturbation is
+
+ align:start position:0%
+there's a rule so if the perturbation is
+ 
+
+ align:start position:0%
+there's a rule so if the perturbation is
+2 to the N then the highest order term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involves V plus 1/2 to the N minus 1 the
+
+ align:start position:0%
+involves V plus 1/2 to the N minus 1 the
+ 
+
+ align:start position:0%
+involves V plus 1/2 to the N minus 1 the
+reason for that is in the matrix of them
+
+ align:start position:0%
+reason for that is in the matrix of them
+ 
+
+ align:start position:0%
+reason for that is in the matrix of them
+it the highest order term is V is V plus
+
+ align:start position:0%
+it the highest order term is V is V plus
+ 
+
+ align:start position:0%
+it the highest order term is V is V plus
+1/2 to V + 3 over 2 and then you square
+
+ align:start position:0%
+1/2 to V + 3 over 2 and then you square
+ 
+
+ align:start position:0%
+1/2 to V + 3 over 2 and then you square
+it you get to the third power and then
+
+ align:start position:0%
+it you get to the third power and then
+ 
+
+ align:start position:0%
+it you get to the third power and then
+the highest order term cancels so we
+
+ align:start position:0%
+the highest order term cancels so we
+ 
+
+ align:start position:0%
+the highest order term cancels so we
+know that if we have if we're dealing
+
+ align:start position:0%
+know that if we have if we're dealing
+ 
+
+ align:start position:0%
+know that if we have if we're dealing
+with Q to the third power
+
+ align:start position:0%
+with Q to the third power
+ 
+
+ align:start position:0%
+with Q to the third power
+we're going to get a term V plus 1/2
+
+ align:start position:0%
+we're going to get a term V plus 1/2
+ 
+
+ align:start position:0%
+we're going to get a term V plus 1/2
+squared if we're dealing with Q to the
+
+ align:start position:0%
+squared if we're dealing with Q to the
+ 
+
+ align:start position:0%
+squared if we're dealing with Q to the
+fourth power well then we get something
+
+ align:start position:0%
+fourth power well then we get something
+ 
+
+ align:start position:0%
+fourth power well then we get something
+from 2nd order from the first order
+
+ align:start position:0%
+from 2nd order from the first order
+ 
+
+ align:start position:0%
+from 2nd order from the first order
+correction to the energy a Delta V of 1
+
+ align:start position:0%
+correction to the energy a Delta V of 1
+ 
+
+ align:start position:0%
+correction to the energy a Delta V of 1
+matrix element where we done is square
+
+ align:start position:0%
+matrix element where we done is square
+ 
+
+ align:start position:0%
+matrix element where we done is square
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and we get 3 plus 1/2 squared also okay
+
+ align:start position:0%
+and we get 3 plus 1/2 squared also okay
+ 
+
+ align:start position:0%
+and we get 3 plus 1/2 squared also okay
+and the the off-diagonal matrix element
+
+ align:start position:0%
+and the the off-diagonal matrix element
+ 
+
+ align:start position:0%
+and the the off-diagonal matrix element
+we're going to get a from the the
+
+ align:start position:0%
+we're going to get a from the the
+ 
+
+ align:start position:0%
+we're going to get a from the the
+highest order from the off diagonal is V
+
+ align:start position:0%
+highest order from the off diagonal is V
+ 
+
+ align:start position:0%
+highest order from the off diagonal is V
+plus 1/2 cubed so one of the things that
+
+ align:start position:0%
+plus 1/2 cubed so one of the things that
+ 
+
+ align:start position:0%
+plus 1/2 cubed so one of the things that
+is great about the algebra is with a
+
+ align:start position:0%
+is great about the algebra is with a
+ 
+
+ align:start position:0%
+is great about the algebra is with a
+little bit of practice you know how to
+
+ align:start position:0%
+little bit of practice you know how to
+ 
+
+ align:start position:0%
+little bit of practice you know how to
+organize things and if you do the
+
+ align:start position:0%
+organize things and if you do the
+ 
+
+ align:start position:0%
+organize things and if you do the
+algebra you connect you you collect the
+
+ align:start position:0%
+algebra you connect you you collect the
+ 
+
+ align:start position:0%
+algebra you connect you you collect the
+highest order terms then there's that
+
+ align:start position:0%
+highest order terms then there's that
+ 
+
+ align:start position:0%
+highest order terms then there's that
+kind of cascading result and you get the
+
+ align:start position:0%
+kind of cascading result and you get the
+ 
+
+ align:start position:0%
+kind of cascading result and you get the
+lower lowest order terms in simplified
+
+ align:start position:0%
+lower lowest order terms in simplified
+ 
+
+ align:start position:0%
+lower lowest order terms in simplified
+form so this is this is irrelevant but
+
+ align:start position:0%
+form so this is this is irrelevant but
+ 
+
+ align:start position:0%
+form so this is this is irrelevant but
+this is how you do it if you're a
+
+ align:start position:0%
+this is how you do it if you're a
+ 
+
+ align:start position:0%
+this is how you do it if you're a
+professional
+
+ align:start position:0%
+professional
+ 
+
+ align:start position:0%
+professional
+so with these results we can determine
+
+ align:start position:0%
+so with these results we can determine
+ 
+
+ align:start position:0%
+so with these results we can determine
+the relationship between these molecular
+
+ align:start position:0%
+the relationship between these molecular
+ 
+
+ align:start position:0%
+the relationship between these molecular
+constants where did I put them
+
+ align:start position:0%
+constants where did I put them
+ 
+
+ align:start position:0%
+constants where did I put them
+well probably on this board know
+
+ align:start position:0%
+well probably on this board know
+ 
+
+ align:start position:0%
+well probably on this board know
+so we oh yeah it's right here so we have
+
+ align:start position:0%
+so we oh yeah it's right here so we have
+ 
+
+ align:start position:0%
+so we oh yeah it's right here so we have
+Omega e make the XE Omega Y E and we
+
+ align:start position:0%
+Omega e make the XE Omega Y E and we
+ 
+
+ align:start position:0%
+Omega e make the XE Omega Y E and we
+have then the relationships between
+
+ align:start position:0%
+have then the relationships between
+ 
+
+ align:start position:0%
+have then the relationships between
+these things which you measure and these
+
+ align:start position:0%
+these things which you measure and these
+ 
+
+ align:start position:0%
+these things which you measure and these
+things that you want to know so the
+
+ align:start position:0%
+things that you want to know so the
+ 
+
+ align:start position:0%
+things that you want to know so the
+stuff you want to know is encoded in the
+
+ align:start position:0%
+stuff you want to know is encoded in the
+ 
+
+ align:start position:0%
+stuff you want to know is encoded in the
+spectrum in a not particularly
+
+ align:start position:0%
+spectrum in a not particularly
+ 
+
+ align:start position:0%
+spectrum in a not particularly
+complicated way it's just not a very
+
+ align:start position:0%
+complicated way it's just not a very
+ 
+
+ align:start position:0%
+complicated way it's just not a very
+interesting way but you have to do it in
+
+ align:start position:0%
+interesting way but you have to do it in
+ 
+
+ align:start position:0%
+interesting way but you have to do it in
+order to get it okay so I've got just a
+
+ align:start position:0%
+order to get it okay so I've got just a
+ 
+
+ align:start position:0%
+order to get it okay so I've got just a
+few minutes left but I want to get to
+
+ align:start position:0%
+few minutes left but I want to get to
+ 
+
+ align:start position:0%
+few minutes left but I want to get to
+the really interesting stuff so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have some expression for the
+
+ align:start position:0%
+if you have some expression for the
+ 
+
+ align:start position:0%
+if you have some expression for the
+potential it's easy to go and get the
+
+ align:start position:0%
+potential it's easy to go and get the
+ 
+
+ align:start position:0%
+potential it's easy to go and get the
+expression for the energy levels and the
+
+ align:start position:0%
+expression for the energy levels and the
+ 
+
+ align:start position:0%
+expression for the energy levels and the
+wave functions and you can use the
+
+ align:start position:0%
+wave functions and you can use the
+ 
+
+ align:start position:0%
+wave functions and you can use the
+vector picture or the wave function
+
+ align:start position:0%
+vector picture or the wave function
+ 
+
+ align:start position:0%
+vector picture or the wave function
+picture it doesn't matter and so this is
+
+ align:start position:0%
+picture it doesn't matter and so this is
+ 
+
+ align:start position:0%
+picture it doesn't matter and so this is
+enough to do the spectroscopy it tells
+
+ align:start position:0%
+enough to do the spectroscopy it tells
+ 
+
+ align:start position:0%
+enough to do the spectroscopy it tells
+you not only where are the energies but
+
+ align:start position:0%
+you not only where are the energies but
+ 
+
+ align:start position:0%
+you not only where are the energies but
+because some transition are supposed to
+
+ align:start position:0%
+because some transition are supposed to
+ 
+
+ align:start position:0%
+because some transition are supposed to
+be weak because of the dipole selection
+
+ align:start position:0%
+be weak because of the dipole selection
+ 
+
+ align:start position:0%
+be weak because of the dipole selection
+rule or whatever it's as well there's
+
+ align:start position:0%
+rule or whatever it's as well there's
+ 
+
+ align:start position:0%
+rule or whatever it's as well there's
+some transitions that have borrowed
+
+ align:start position:0%
+some transitions that have borrowed
+ 
+
+ align:start position:0%
+some transitions that have borrowed
+intensity it also tells you suppose we
+
+ align:start position:0%
+intensity it also tells you suppose we
+ 
+
+ align:start position:0%
+intensity it also tells you suppose we
+make a coherent superposition state at T
+
+ align:start position:0%
+make a coherent superposition state at T
+ 
+
+ align:start position:0%
+make a coherent superposition state at T
+equals zero using a short pulse and
+
+ align:start position:0%
+equals zero using a short pulse and
+ 
+
+ align:start position:0%
+equals zero using a short pulse and
+suppose in the company in the linear
+
+ align:start position:0%
+suppose in the company in the linear
+ 
+
+ align:start position:0%
+suppose in the company in the linear
+combination of zero order states there's
+
+ align:start position:0%
+combination of zero order states there's
+ 
+
+ align:start position:0%
+combination of zero order states there's
+only one that is bright and so then it
+
+ align:start position:0%
+only one that is bright and so then it
+ 
+
+ align:start position:0%
+only one that is bright and so then it
+tells us if we know how to go from
+
+ align:start position:0%
+tells us if we know how to go from
+ 
+
+ align:start position:0%
+tells us if we know how to go from
+eigenstate from basis States to
+
+ align:start position:0%
+eigenstate from basis States to
+ 
+
+ align:start position:0%
+eigenstate from basis States to
+eigenstates we can go backwards and we
+
+ align:start position:0%
+eigenstates we can go backwards and we
+ 
+
+ align:start position:0%
+eigenstates we can go backwards and we
+can write with the expression for T
+
+ align:start position:0%
+can write with the expression for T
+ 
+
+ align:start position:0%
+can write with the expression for T
+equals the T equals zero superposition
+
+ align:start position:0%
+equals the T equals zero superposition
+ 
+
+ align:start position:0%
+equals the T equals zero superposition
+in terms of some sum over side V zero CV
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we have this as long as we are
+
+ align:start position:0%
+and if we have this as long as we are
+ 
+
+ align:start position:0%
+and if we have this as long as we are
+writing a superposition in terms of
+
+ align:start position:0%
+writing a superposition in terms of
+ 
+
+ align:start position:0%
+writing a superposition in terms of
+eigenstates we know immediately how to
+
+ align:start position:0%
+eigenstates we know immediately how to
+ 
+
+ align:start position:0%
+eigenstates we know immediately how to
+get this and then we've got all the
+
+ align:start position:0%
+get this and then we've got all the
+ 
+
+ align:start position:0%
+get this and then we've got all the
+dynamics so the perturbation Theory
+
+ align:start position:0%
+dynamics so the perturbation Theory
+ 
+
+ align:start position:0%
+dynamics so the perturbation Theory
+enables you to say if I want to work in
+
+ align:start position:0%
+enables you to say if I want to work in
+ 
+
+ align:start position:0%
+enables you to say if I want to work in
+the time domain I know what what to do
+
+ align:start position:0%
+the time domain I know what what to do
+ 
+
+ align:start position:0%
+the time domain I know what what to do
+and I know that certain you're going to
+
+ align:start position:0%
+and I know that certain you're going to
+ 
+
+ align:start position:0%
+and I know that certain you're going to
+get in the time domain you're going to
+
+ align:start position:0%
+get in the time domain you're going to
+ 
+
+ align:start position:0%
+get in the time domain you're going to
+get a signal that oscillates
+
+ align:start position:0%
+get a signal that oscillates
+ 
+
+ align:start position:0%
+get a signal that oscillates
+and it oscillates at frequencies
+
+ align:start position:0%
+and it oscillates at frequencies
+ 
+
+ align:start position:0%
+and it oscillates at frequencies
+corresponding to energy level
+
+ align:start position:0%
+corresponding to energy level
+ 
+
+ align:start position:0%
+corresponding to energy level
+differences divided by h-bar and so what
+
+ align:start position:0%
+differences divided by h-bar and so what
+ 
+
+ align:start position:0%
+differences divided by h-bar and so what
+frequencies will appear in the Fourier
+
+ align:start position:0%
+frequencies will appear in the Fourier
+ 
+
+ align:start position:0%
+frequencies will appear in the Fourier
+transform of the the spectrum and what
+
+ align:start position:0%
+transform of the the spectrum and what
+ 
+
+ align:start position:0%
+transform of the the spectrum and what
+are the amplitudes of those Fourier
+
+ align:start position:0%
+are the amplitudes of those Fourier
+ 
+
+ align:start position:0%
+are the amplitudes of those Fourier
+components you can calculate all those
+
+ align:start position:0%
+components you can calculate all those
+ 
+
+ align:start position:0%
+components you can calculate all those
+stuff it all comes from perturbation
+
+ align:start position:0%
+stuff it all comes from perturbation
+ 
+
+ align:start position:0%
+stuff it all comes from perturbation
+Theory these mixing coefficients you get
+
+ align:start position:0%
+Theory these mixing coefficients you get
+ 
+
+ align:start position:0%
+Theory these mixing coefficients you get
+by perturbation theory and remember if
+
+ align:start position:0%
+by perturbation theory and remember if
+ 
+
+ align:start position:0%
+by perturbation theory and remember if
+you have a transformation that
+
+ align:start position:0%
+you have a transformation that
+ 
+
+ align:start position:0%
+you have a transformation that
+diagonalizes the Hamiltonian that the
+
+ align:start position:0%
+diagonalizes the Hamiltonian that the
+ 
+
+ align:start position:0%
+diagonalizes the Hamiltonian that the
+eigenstates correspond to the columns of
+
+ align:start position:0%
+eigenstates correspond to the columns of
+ 
+
+ align:start position:0%
+eigenstates correspond to the columns of
+t dagger and the expression of the zero
+
+ align:start position:0%
+t dagger and the expression of the zero
+ 
+
+ align:start position:0%
+t dagger and the expression of the zero
+order states in terms of the eigenstates
+
+ align:start position:0%
+order states in terms of the eigenstates
+ 
+
+ align:start position:0%
+order states in terms of the eigenstates
+corresponds to either the columns of T
+
+ align:start position:0%
+corresponds to either the columns of T
+ 
+
+ align:start position:0%
+corresponds to either the columns of T
+or the rows of T dagger so once you do
+
+ align:start position:0%
+or the rows of T dagger so once you do
+ 
+
+ align:start position:0%
+or the rows of T dagger so once you do
+the perturbation Theory you can go to
+
+ align:start position:0%
+the perturbation Theory you can go to
+ 
+
+ align:start position:0%
+the perturbation Theory you can go to
+the time the frequency domain spectrum
+
+ align:start position:0%
+the time the frequency domain spectrum
+ 
+
+ align:start position:0%
+the time the frequency domain spectrum
+with intensities and frequencies or the
+
+ align:start position:0%
+with intensities and frequencies or the
+ 
+
+ align:start position:0%
+with intensities and frequencies or the
+time domain spectrum with amplitudes and
+
+ align:start position:0%
+time domain spectrum with amplitudes and
+ 
+
+ align:start position:0%
+time domain spectrum with amplitudes and
+frequencies it's all there
+
+ align:start position:0%
+frequencies it's all there
+ 
+
+ align:start position:0%
+frequencies it's all there
+this is a complete tool it's it's the
+
+ align:start position:0%
+this is a complete tool it's it's the
+ 
+
+ align:start position:0%
+this is a complete tool it's it's the
+kind of tool that you can use for an
+
+ align:start position:0%
+kind of tool that you can use for an
+ 
+
+ align:start position:0%
+kind of tool that you can use for an
+enormous number of problems and so you'd
+
+ align:start position:0%
+enormous number of problems and so you'd
+ 
+
+ align:start position:0%
+enormous number of problems and so you'd
+better get comfortable with perturbation
+
+ align:start position:0%
+better get comfortable with perturbation
+ 
+
+ align:start position:0%
+better get comfortable with perturbation
+theory because the people who don't
+
+ align:start position:0%
+theory because the people who don't
+ 
+
+ align:start position:0%
+theory because the people who don't
+aren't comfortable can't do anything
+
+ align:start position:0%
+aren't comfortable can't do anything
+ 
+
+ align:start position:0%
+aren't comfortable can't do anything
+except talk about it but if you want to
+
+ align:start position:0%
+except talk about it but if you want to
+ 
+
+ align:start position:0%
+except talk about it but if you want to
+actually solve problems especially
+
+ align:start position:0%
+actually solve problems especially
+ 
+
+ align:start position:0%
+actually solve problems especially
+problems on an exam you want to know how
+
+ align:start position:0%
+problems on an exam you want to know how
+ 
+
+ align:start position:0%
+problems on an exam you want to know how
+to use perturbation theory and you also
+
+ align:start position:0%
+to use perturbation theory and you also
+ 
+
+ align:start position:0%
+to use perturbation theory and you also
+want to know how to read and constructed
+
+ align:start position:0%
+want to know how to read and constructed
+ 
+
+ align:start position:0%
+want to know how to read and constructed
+the relevant notation in the vector
+
+ align:start position:0%
+the relevant notation in the vector
+ 
+
+ align:start position:0%
+the relevant notation in the vector
+picture because the vector picture and
+
+ align:start position:0%
+picture because the vector picture and
+ 
+
+ align:start position:0%
+picture because the vector picture and
+the matrix picture is the one where you
+
+ align:start position:0%
+the matrix picture is the one where you
+ 
+
+ align:start position:0%
+the matrix picture is the one where you
+see the entire structure of the problem
+
+ align:start position:0%
+see the entire structure of the problem
+ 
+
+ align:start position:0%
+see the entire structure of the problem
+and you can decide on how you're going
+
+ align:start position:0%
+and you can decide on how you're going
+ 
+
+ align:start position:0%
+and you can decide on how you're going
+to organize your time or what is you
+
+ align:start position:0%
+to organize your time or what is you
+ 
+
+ align:start position:0%
+to organize your time or what is you
+know what are the important things I'm
+
+ align:start position:0%
+know what are the important things I'm
+ 
+
+ align:start position:0%
+know what are the important things I'm
+going to get from this analysis and so
+
+ align:start position:0%
+going to get from this analysis and so
+ 
+
+ align:start position:0%
+going to get from this analysis and so
+it's much better than the Schrodinger
+
+ align:start position:0%
+it's much better than the Schrodinger
+ 
+
+ align:start position:0%
+it's much better than the Schrodinger
+picture because you would just have to
+
+ align:start position:0%
+picture because you would just have to
+ 
+
+ align:start position:0%
+picture because you would just have to
+you know with the Schrodinger picture
+
+ align:start position:0%
+you know with the Schrodinger picture
+ 
+
+ align:start position:0%
+you know with the Schrodinger picture
+you're just solving a differential
+
+ align:start position:0%
+you're just solving a differential
+ 
+
+ align:start position:0%
+you're just solving a differential
+equation and one problem at a time where
+
+ align:start position:0%
+equation and one problem at a time where
+ 
+
+ align:start position:0%
+equation and one problem at a time where
+it's you're with the matrix picture
+
+ align:start position:0%
+it's you're with the matrix picture
+ 
+
+ align:start position:0%
+it's you're with the matrix picture
+you're solving all problems at once this
+
+ align:start position:0%
+you're solving all problems at once this
+ 
+
+ align:start position:0%
+you're solving all problems at once this
+is really a wonderful thing and and so
+
+ align:start position:0%
+is really a wonderful thing and and so
+ 
+
+ align:start position:0%
+is really a wonderful thing and and so
+that's why I'm taking a very different
+
+ align:start position:0%
+that's why I'm taking a very different
+ 
+
+ align:start position:0%
+that's why I'm taking a very different
+path from what is in the textbooks
+
+ align:start position:0%
+path from what is in the textbooks
+ 
+
+ align:start position:0%
+path from what is in the textbooks
+your wonderful textbook Macquarie does
+
+ align:start position:0%
+your wonderful textbook Macquarie does
+ 
+
+ align:start position:0%
+your wonderful textbook Macquarie does
+not do second-order perturbation Theory
+
+ align:start position:0%
+not do second-order perturbation Theory
+ 
+
+ align:start position:0%
+not do second-order perturbation Theory
+so nothing you want can be calculated
+
+ align:start position:0%
+so nothing you want can be calculated
+ 
+
+ align:start position:0%
+so nothing you want can be calculated
+unless you're dealing with NMR and and
+
+ align:start position:0%
+unless you're dealing with NMR and and
+ 
+
+ align:start position:0%
+unless you're dealing with NMR and and
+you're dealing with magnetic dipole
+
+ align:start position:0%
+you're dealing with magnetic dipole
+ 
+
+ align:start position:0%
+you're dealing with magnetic dipole
+transitions and then you you can get a
+
+ align:start position:0%
+transitions and then you you can get a
+ 
+
+ align:start position:0%
+transitions and then you you can get a
+lot of good stuff from first-order
+
+ align:start position:0%
+lot of good stuff from first-order
+ 
+
+ align:start position:0%
+lot of good stuff from first-order
+perturbation theory and you can avoid
+
+ align:start position:0%
+perturbation theory and you can avoid
+ 
+
+ align:start position:0%
+perturbation theory and you can avoid
+second-order until you grow up okay I'm
+
+ align:start position:0%
+second-order until you grow up okay I'm
+ 
+
+ align:start position:0%
+second-order until you grow up okay I'm
+done I'll be talking about rigid rotor
+
+ align:start position:0%
+done I'll be talking about rigid rotor
+ 
+
+ align:start position:0%
+done I'll be talking about rigid rotor
+next time and I was talking about it
+
+ align:start position:0%
+next time and I was talking about it
+ 
+
+ align:start position:0%
+next time and I was talking about it
+also in an unconventional way
\ No newline at end of file
diff --git a/YZ9y4zcfCPs.txt b/YZ9y4zcfCPs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..418a04d620931c06a3288a5d9cd0c0e53b62aa01
--- /dev/null
+++ b/YZ9y4zcfCPs.txt
@@ -0,0 +1,9947 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu today we're going to talk
+
+ align:start position:0%
+ocw.mit.edu today we're going to talk
+ 
+
+ align:start position:0%
+ocw.mit.edu today we're going to talk
+all about moments of inera
+
+ align:start position:0%
+all about moments of inera
+ 
+
+ align:start position:0%
+all about moments of inera
+and the last time we did Muddy cards
+
+ align:start position:0%
+and the last time we did Muddy cards
+ 
+
+ align:start position:0%
+and the last time we did Muddy cards
+there were a lot of questions the most
+
+ align:start position:0%
+there were a lot of questions the most
+ 
+
+ align:start position:0%
+there were a lot of questions the most
+common question you know was where do
+
+ align:start position:0%
+common question you know was where do
+ 
+
+ align:start position:0%
+common question you know was where do
+all those terms come from and I'm going
+
+ align:start position:0%
+all those terms come from and I'm going
+ 
+
+ align:start position:0%
+all those terms come from and I'm going
+to do a brief kind of intro around that
+
+ align:start position:0%
+to do a brief kind of intro around that
+ 
+
+ align:start position:0%
+to do a brief kind of intro around that
+so as to get the rest of this to
+
+ align:start position:0%
+so as to get the rest of this to
+ 
+
+ align:start position:0%
+so as to get the rest of this to
+facilitate the rest of of the
+
+ align:start position:0%
+facilitate the rest of of the
+ 
+
+ align:start position:0%
+facilitate the rest of of the
+discussions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh kind of some basic assumptions here
+
+ align:start position:0%
+uh kind of some basic assumptions here
+ 
+
+ align:start position:0%
+uh kind of some basic assumptions here
+today we're going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodies that rotate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about their Center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass or fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points that's the kind of problems we're
+
+ align:start position:0%
+points that's the kind of problems we're
+ 
+
+ align:start position:0%
+points that's the kind of problems we're
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+secondly all through this lecture today
+
+ align:start position:0%
+secondly all through this lecture today
+ 
+
+ align:start position:0%
+secondly all through this lecture today
+there's four or five significant
+
+ align:start position:0%
+there's four or five significant
+ 
+
+ align:start position:0%
+there's four or five significant
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+or conditions that are really important
+
+ align:start position:0%
+or conditions that are really important
+ 
+
+ align:start position:0%
+or conditions that are really important
+to the whole discussion I'm going to
+
+ align:start position:0%
+to the whole discussion I'm going to
+ 
+
+ align:start position:0%
+to the whole discussion I'm going to
+really try to highlight them I'm
+
+ align:start position:0%
+really try to highlight them I'm
+ 
+
+ align:start position:0%
+really try to highlight them I'm
+starting with two here the other one is
+
+ align:start position:0%
+starting with two here the other one is
+ 
+
+ align:start position:0%
+starting with two here the other one is
+we're going to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frames attached to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodies it's why we did all that work in
+
+ align:start position:0%
+bodies it's why we did all that work in
+ 
+
+ align:start position:0%
+bodies it's why we did all that work in
+kinematics figuring out how to do
+
+ align:start position:0%
+kinematics figuring out how to do
+ 
+
+ align:start position:0%
+kinematics figuring out how to do
+velocities of things that are in have
+
+ align:start position:0%
+velocities of things that are in have
+ 
+
+ align:start position:0%
+velocities of things that are in have
+translating and rotating reference
+
+ align:start position:0%
+translating and rotating reference
+ 
+
+ align:start position:0%
+translating and rotating reference
+frames it's so that we can do these
+
+ align:start position:0%
+frames it's so that we can do these
+ 
+
+ align:start position:0%
+frames it's so that we can do these
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+okay now F so this
+
+ align:start position:0%
+okay now F so this
+ 
+
+ align:start position:0%
+okay now F so this
+said here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a inertial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame here's some rigid
+
+ align:start position:0%
+frame here's some rigid
+ 
+
+ align:start position:0%
+frame here's some rigid
+body here's a point on it that's my
+
+ align:start position:0%
+body here's a point on it that's my
+ 
+
+ align:start position:0%
+body here's a point on it that's my
+origin and here is a set of coordinates
+
+ align:start position:0%
+origin and here is a set of coordinates
+ 
+
+ align:start position:0%
+origin and here is a set of coordinates
+attached to the rigid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body the axyz system the body rotates
+
+ align:start position:0%
+body the axyz system the body rotates
+ 
+
+ align:start position:0%
+body the axyz system the body rotates
+and translates it goes with
+
+ align:start position:0%
+and translates it goes with
+ 
+
+ align:start position:0%
+and translates it goes with
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and if we have consider a little piece
+
+ align:start position:0%
+and if we have consider a little piece
+ 
+
+ align:start position:0%
+and if we have consider a little piece
+of this body a little Mass part I'll
+
+ align:start position:0%
+of this body a little Mass part I'll
+ 
+
+ align:start position:0%
+of this body a little Mass part I'll
+call it little Mass element
+
+ align:start position:0%
+call it little Mass element
+ 
+
+ align:start position:0%
+call it little Mass element
+mi from here to here is some distance r
+
+ align:start position:0%
+mi from here to here is some distance r
+ 
+
+ align:start position:0%
+mi from here to here is some distance r
+i with respect to
+
+ align:start position:0%
+i with respect to
+ 
+
+ align:start position:0%
+i with respect to
+a then the angular
+
+ align:start position:0%
+a then the angular
+ 
+
+ align:start position:0%
+a then the angular
+momentum of that little Mass particle
+
+ align:start position:0%
+momentum of that little Mass particle
+ 
+
+ align:start position:0%
+momentum of that little Mass particle
+is by just by definition of angular
+
+ align:start position:0%
+is by just by definition of angular
+ 
+
+ align:start position:0%
+is by just by definition of angular
+momentum R cross p i and the p i p is
+
+ align:start position:0%
+momentum R cross p i and the p i p is
+ 
+
+ align:start position:0%
+momentum R cross p i and the p i p is
+always the linear momentum defined in an
+
+ align:start position:0%
+always the linear momentum defined in an
+ 
+
+ align:start position:0%
+always the linear momentum defined in an
+inertial frame okay that's the
+
+ align:start position:0%
+inertial frame okay that's the
+ 
+
+ align:start position:0%
+inertial frame okay that's the
+definition of angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum so youve you've seen this this
+
+ align:start position:0%
+momentum so youve you've seen this this
+ 
+
+ align:start position:0%
+momentum so youve you've seen this this
+little demo before but now so this is
+
+ align:start position:0%
+little demo before but now so this is
+ 
+
+ align:start position:0%
+little demo before but now so this is
+now my rigid body that I'm talking
+
+ align:start position:0%
+now my rigid body that I'm talking
+ 
+
+ align:start position:0%
+now my rigid body that I'm talking
+about it I'm going to in this case the
+
+ align:start position:0%
+about it I'm going to in this case the
+ 
+
+ align:start position:0%
+about it I'm going to in this case the
+axis of rotation is this
+
+ align:start position:0%
+axis of rotation is this
+ 
+
+ align:start position:0%
+axis of rotation is this
+one and I'm just going to Define my
+
+ align:start position:0%
+one and I'm just going to Define my
+ 
+
+ align:start position:0%
+one and I'm just going to Define my
+rigid body as essentially rotating about
+
+ align:start position:0%
+rigid body as essentially rotating about
+ 
+
+ align:start position:0%
+rigid body as essentially rotating about
+this fixed point this is a now and my
+
+ align:start position:0%
+this fixed point this is a now and my
+ 
+
+ align:start position:0%
+this fixed point this is a now and my
+coordinate system is um x y z so the
+
+ align:start position:0%
+coordinate system is um x y z so the
+ 
+
+ align:start position:0%
+coordinate system is um x y z so the
+rotation is Omega Z and this rigid body
+
+ align:start position:0%
+rotation is Omega Z and this rigid body
+ 
+
+ align:start position:0%
+rotation is Omega Z and this rigid body
+this is massless considers consists of
+
+ align:start position:0%
+this is massless considers consists of
+ 
+
+ align:start position:0%
+this is massless considers consists of
+the single point Mass Okay so we've done
+
+ align:start position:0%
+the single point Mass Okay so we've done
+ 
+
+ align:start position:0%
+the single point Mass Okay so we've done
+this before but we tended to do this
+
+ align:start position:0%
+this before but we tended to do this
+ 
+
+ align:start position:0%
+this before but we tended to do this
+kind of problem using polar coordinates
+
+ align:start position:0%
+kind of problem using polar coordinates
+ 
+
+ align:start position:0%
+kind of problem using polar coordinates
+and now I really want to just strictly
+
+ align:start position:0%
+and now I really want to just strictly
+ 
+
+ align:start position:0%
+and now I really want to just strictly
+think in terms of XYZ the answers come
+
+ align:start position:0%
+think in terms of XYZ the answers come
+ 
+
+ align:start position:0%
+think in terms of XYZ the answers come
+out exactly the same polar coordinates
+
+ align:start position:0%
+out exactly the same polar coordinates
+ 
+
+ align:start position:0%
+out exactly the same polar coordinates
+also moved you could do this in R hat
+
+ align:start position:0%
+also moved you could do this in R hat
+ 
+
+ align:start position:0%
+also moved you could do this in R hat
+Theta hat Z we're going to do it an
+
+ align:start position:0%
+Theta hat Z we're going to do it an
+ 
+
+ align:start position:0%
+Theta hat Z we're going to do it an
+XYZ XYZ attach to the body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why is going into the board we
+
+ align:start position:0%
+and why is going into the board we
+ 
+
+ align:start position:0%
+and why is going into the board we
+have we'll have no values in the y
+
+ align:start position:0%
+have we'll have no values in the y
+ 
+
+ align:start position:0%
+have we'll have no values in the y
+direction for this problem here's our
+
+ align:start position:0%
+direction for this problem here's our
+ 
+
+ align:start position:0%
+direction for this problem here's our
+little Mass we'll call it
+
+ align:start position:0%
+little Mass we'll call it
+ 
+
+ align:start position:0%
+little Mass we'll call it
+M1 it's at a position out here
+
+ align:start position:0%
+M1 it's at a position out here
+ 
+
+ align:start position:0%
+M1 it's at a position out here
+X1 Z1 or its coordinates and Y is
+
+ align:start position:0%
+X1 Z1 or its coordinates and Y is
+ 
+
+ align:start position:0%
+X1 Z1 or its coordinates and Y is
+zero and we want to compute its angular
+
+ align:start position:0%
+zero and we want to compute its angular
+ 
+
+ align:start position:0%
+zero and we want to compute its angular
+momentum H1 with respect to
+
+ align:start position:0%
+momentum H1 with respect to
+ 
+
+ align:start position:0%
+momentum H1 with respect to
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's our R1 a cross P1 in O and
+
+ align:start position:0%
+okay that's our R1 a cross P1 in O and
+ 
+
+ align:start position:0%
+okay that's our R1 a cross P1 in O and
+for this problem that's X X1 in the I
+
+ align:start position:0%
+for this problem that's X X1 in the I
+ 
+
+ align:start position:0%
+for this problem that's X X1 in the I
+hat plus Z1 in the K hat that's the
+
+ align:start position:0%
+hat plus Z1 in the K hat that's the
+ 
+
+ align:start position:0%
+hat plus Z1 in the K hat that's the
+r cross p and p is mass time you know
+
+ align:start position:0%
+r cross p and p is mass time you know
+ 
+
+ align:start position:0%
+r cross p and p is mass time you know
+it's mass time velocity M1 and the
+
+ align:start position:0%
+it's mass time velocity M1 and the
+ 
+
+ align:start position:0%
+it's mass time velocity M1 and the
+velocity is just Omega cross R we've
+
+ align:start position:0%
+velocity is just Omega cross R we've
+ 
+
+ align:start position:0%
+velocity is just Omega cross R we've
+done this before so there's going to be
+
+ align:start position:0%
+done this before so there's going to be
+ 
+
+ align:start position:0%
+done this before so there's going to be
+a we need a length on this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've done this enough times before I'm
+
+ align:start position:0%
+we've done this enough times before I'm
+ 
+
+ align:start position:0%
+we've done this enough times before I'm
+assuming you can make this leap with me
+
+ align:start position:0%
+assuming you can make this leap with me
+ 
+
+ align:start position:0%
+assuming you can make this leap with me
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the momentum is into the board it's in
+
+ align:start position:0%
+the momentum is into the board it's in
+ 
+
+ align:start position:0%
+the momentum is into the board it's in
+the y
+
+ align:start position:0%
+the y
+ 
+
+ align:start position:0%
+the y
+direction the linear momentum is R cross
+
+ align:start position:0%
+direction the linear momentum is R cross
+ 
+
+ align:start position:0%
+direction the linear momentum is R cross
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+and that will give
+
+ align:start position:0%
+and that will give
+ 
+
+ align:start position:0%
+and that will give
+us let me write it little yeah Omega Z
+
+ align:start position:0%
+us let me write it little yeah Omega Z
+ 
+
+ align:start position:0%
+us let me write it little yeah Omega Z
+so that's the linear momentum it's in
+
+ align:start position:0%
+so that's the linear momentum it's in
+ 
+
+ align:start position:0%
+so that's the linear momentum it's in
+the J Direction its velocity is x 1
+
+ align:start position:0%
+the J Direction its velocity is x 1
+ 
+
+ align:start position:0%
+the J Direction its velocity is x 1
+Omega Z it's the radius times the
+
+ align:start position:0%
+Omega Z it's the radius times the
+ 
+
+ align:start position:0%
+Omega Z it's the radius times the
+rotation rate is the velocity the
+
+ align:start position:0%
+rotation rate is the velocity the
+ 
+
+ align:start position:0%
+rotation rate is the velocity the
+direction is that direction so this is
+
+ align:start position:0%
+direction is that direction so this is
+ 
+
+ align:start position:0%
+direction is that direction so this is
+your momentum you multiply out this
+
+ align:start position:0%
+your momentum you multiply out this
+ 
+
+ align:start position:0%
+your momentum you multiply out this
+cross product you get two
+
+ align:start position:0%
+cross product you get two
+ 
+
+ align:start position:0%
+cross product you get two
+terms M1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X12 Omega z k
+
+ align:start position:0%
+X12 Omega z k
+ 
+
+ align:start position:0%
+X12 Omega z k
+minus M1 X1 Z1 Omega z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i and these two terms then we would
+
+ align:start position:0%
+i and these two terms then we would
+ 
+
+ align:start position:0%
+i and these two terms then we would
+identify this is the angular momentum in
+
+ align:start position:0%
+identify this is the angular momentum in
+ 
+
+ align:start position:0%
+identify this is the angular momentum in
+the K Direction the angular momentum in
+
+ align:start position:0%
+the K Direction the angular momentum in
+ 
+
+ align:start position:0%
+the K Direction the angular momentum in
+the I Direction there doesn't happen to
+
+ align:start position:0%
+the I Direction there doesn't happen to
+ 
+
+ align:start position:0%
+the I Direction there doesn't happen to
+be any in the Z Direction in general
+
+ align:start position:0%
+be any in the Z Direction in general
+ 
+
+ align:start position:0%
+be any in the Z Direction in general
+there could be but this is H for this
+
+ align:start position:0%
+there could be but this is H for this
+ 
+
+ align:start position:0%
+there could be but this is H for this
+particle uh particle
+
+ align:start position:0%
+particle uh particle
+ 
+
+ align:start position:0%
+particle uh particle
+one um let me write it I'm just going to
+
+ align:start position:0%
+one um let me write it I'm just going to
+ 
+
+ align:start position:0%
+one um let me write it I'm just going to
+want to particularly emphasize this one
+
+ align:start position:0%
+want to particularly emphasize this one
+ 
+
+ align:start position:0%
+want to particularly emphasize this one
+is the this is excuse me Z and this is
+
+ align:start position:0%
+is the this is excuse me Z and this is
+ 
+
+ align:start position:0%
+is the this is excuse me Z and this is
+the piece we'd call
+
+ align:start position:0%
+the piece we'd call
+ 
+
+ align:start position:0%
+the piece we'd call
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+x so there's a component of the angular
+
+ align:start position:0%
+x so there's a component of the angular
+ 
+
+ align:start position:0%
+x so there's a component of the angular
+momentum that's in the Z direction
+
+ align:start position:0%
+momentum that's in the Z direction
+ 
+
+ align:start position:0%
+momentum that's in the Z direction
+there's a component in the X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction we know that if we compute
+
+ align:start position:0%
+direction we know that if we compute
+ 
+
+ align:start position:0%
+direction we know that if we compute
+just to carry the
+
+ align:start position:0%
+just to carry the
+ 
+
+ align:start position:0%
+just to carry the
+uh the previous word a tie it back to
+
+ align:start position:0%
+uh the previous word a tie it back to
+ 
+
+ align:start position:0%
+uh the previous word a tie it back to
+the previous work a little further d by
+
+ align:start position:0%
+the previous work a little further d by
+ 
+
+ align:start position:0%
+the previous work a little further d by
+DT of H1 a gives us the torqu the
+
+ align:start position:0%
+DT of H1 a gives us the torqu the
+ 
+
+ align:start position:0%
+DT of H1 a gives us the torqu the
+external torqu in the system a vector of
+
+ align:start position:0%
+external torqu in the system a vector of
+ 
+
+ align:start position:0%
+external torqu in the system a vector of
+torqus when we compute that out I don't
+
+ align:start position:0%
+torqus when we compute that out I don't
+ 
+
+ align:start position:0%
+torqus when we compute that out I don't
+I'm not going to calculate it we don't I
+
+ align:start position:0%
+I'm not going to calculate it we don't I
+ 
+
+ align:start position:0%
+I'm not going to calculate it we don't I
+don't need it for the purposes of the
+
+ align:start position:0%
+don't need it for the purposes of the
+ 
+
+ align:start position:0%
+don't need it for the purposes of the
+rest of the discussion this one gives
+
+ align:start position:0%
+rest of the discussion this one gives
+ 
+
+ align:start position:0%
+rest of the discussion this one gives
+you Omega Z dot term this one gets two
+
+ align:start position:0%
+you Omega Z dot term this one gets two
+ 
+
+ align:start position:0%
+you Omega Z dot term this one gets two
+terms because you have to take the
+
+ align:start position:0%
+terms because you have to take the
+ 
+
+ align:start position:0%
+terms because you have to take the
+derivative of I so you get three terms
+
+ align:start position:0%
+derivative of I so you get three terms
+ 
+
+ align:start position:0%
+derivative of I so you get three terms
+which are torque in the X torque in the
+
+ align:start position:0%
+which are torque in the X torque in the
+ 
+
+ align:start position:0%
+which are torque in the X torque in the
+Y torque in the Z directions two of them
+
+ align:start position:0%
+Y torque in the Z directions two of them
+ 
+
+ align:start position:0%
+Y torque in the Z directions two of them
+are static because it's trying to bend
+
+ align:start position:0%
+are static because it's trying to bend
+ 
+
+ align:start position:0%
+are static because it's trying to bend
+this thing back and out and one of them
+
+ align:start position:0%
+this thing back and out and one of them
+ 
+
+ align:start position:0%
+this thing back and out and one of them
+the Z Direction one is the one that
+
+ align:start position:0%
+the Z Direction one is the one that
+ 
+
+ align:start position:0%
+the Z Direction one is the one that
+makes it spin faster
+
+ align:start position:0%
+makes it spin faster
+ 
+
+ align:start position:0%
+makes it spin faster
+okay so You' we've seen that that's a
+
+ align:start position:0%
+okay so You' we've seen that that's a
+ 
+
+ align:start position:0%
+okay so You' we've seen that that's a
+review
+
+ align:start position:0%
+review
+ 
+
+ align:start position:0%
+review
+and to make the leap from that to rigid
+
+ align:start position:0%
+and to make the leap from that to rigid
+ 
+
+ align:start position:0%
+and to make the leap from that to rigid
+bodies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Capital H now a collection of particles
+
+ align:start position:0%
+Capital H now a collection of particles
+ 
+
+ align:start position:0%
+Capital H now a collection of particles
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+its the axis the origin attached to the
+
+ align:start position:0%
+its the axis the origin attached to the
+ 
+
+ align:start position:0%
+its the axis the origin attached to the
+rigid
+
+ align:start position:0%
+rigid
+ 
+
+ align:start position:0%
+rigid
+body is going to be the summation over
+
+ align:start position:0%
+body is going to be the summation over
+ 
+
+ align:start position:0%
+body is going to be the summation over
+all the little M particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+their position Vector crossed with the
+
+ align:start position:0%
+their position Vector crossed with the
+ 
+
+ align:start position:0%
+their position Vector crossed with the
+linear momentum of all those little Mass
+
+ align:start position:0%
+linear momentum of all those little Mass
+ 
+
+ align:start position:0%
+linear momentum of all those little Mass
+particles sum all that up because it's a
+
+ align:start position:0%
+particles sum all that up because it's a
+ 
+
+ align:start position:0%
+particles sum all that up because it's a
+rigid body this is always something of
+
+ align:start position:0%
+rigid body this is always something of
+ 
+
+ align:start position:0%
+rigid body this is always something of
+the form that looks like Omega cross r m
+
+ align:start position:0%
+the form that looks like Omega cross r m
+ 
+
+ align:start position:0%
+the form that looks like Omega cross r m
+Omega cross R and I can then write this
+
+ align:start position:0%
+Omega cross R and I can then write this
+ 
+
+ align:start position:0%
+Omega cross R and I can then write this
+as the
+
+ align:start position:0%
+as the
+ 
+
+ align:start position:0%
+as the
+summation
+
+ align:start position:0%
+summation
+ 
+
+ align:start position:0%
+summation
+of I of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MI r
+
+ align:start position:0%
+MI r
+ 
+
+ align:start position:0%
+MI r
+i a
+
+ align:start position:0%
+i a
+ 
+
+ align:start position:0%
+i a
+cross Omega with respect to O cross r i
+
+ align:start position:0%
+cross Omega with respect to O cross r i
+ 
+
+ align:start position:0%
+cross Omega with respect to O cross r i
+a that gives you the velocity times the
+
+ align:start position:0%
+a that gives you the velocity times the
+ 
+
+ align:start position:0%
+a that gives you the velocity times the
+moment M gives you the linear momentum
+
+ align:start position:0%
+moment M gives you the linear momentum
+ 
+
+ align:start position:0%
+moment M gives you the linear momentum
+times the cross with this one again
+
+ align:start position:0%
+times the cross with this one again
+ 
+
+ align:start position:0%
+times the cross with this one again
+makes it into an angular momentum so
+
+ align:start position:0%
+makes it into an angular momentum so
+ 
+
+ align:start position:0%
+makes it into an angular momentum so
+every M the angular momentum of every
+
+ align:start position:0%
+every M the angular momentum of every
+ 
+
+ align:start position:0%
+every M the angular momentum of every
+particle the term the bits of this come
+
+ align:start position:0%
+particle the term the bits of this come
+ 
+
+ align:start position:0%
+particle the term the bits of this come
+out looking like an like an R SAR
+
+ align:start position:0%
+out looking like an like an R SAR
+ 
+
+ align:start position:0%
+out looking like an like an R SAR
+Omega or at least has has
+
+ align:start position:0%
+Omega or at least has has
+ 
+
+ align:start position:0%
+Omega or at least has has
+um dimensions of R 2 Omega these can be
+
+ align:start position:0%
+um dimensions of R 2 Omega these can be
+ 
+
+ align:start position:0%
+um dimensions of R 2 Omega these can be
+like X1 SAR but these can also be ends
+
+ align:start position:0%
+like X1 SAR but these can also be ends
+ 
+
+ align:start position:0%
+like X1 SAR but these can also be ends
+up being terms like X1 Z1 those cross
+
+ align:start position:0%
+up being terms like X1 Z1 those cross
+ 
+
+ align:start position:0%
+up being terms like X1 Z1 those cross
+product terms but in general these
+
+ align:start position:0%
+product terms but in general these
+ 
+
+ align:start position:0%
+product terms but in general these
+things all add
+
+ align:start position:0%
+things all add
+ 
+
+ align:start position:0%
+things all add
+up and this is this is a vector
+
+ align:start position:0%
+up and this is this is a vector
+ 
+
+ align:start position:0%
+up and this is this is a vector
+this is a vector so this is a vector CR
+
+ align:start position:0%
+this is a vector so this is a vector CR
+ 
+
+ align:start position:0%
+this is a vector so this is a vector CR
+these are all vectors the results of
+
+ align:start position:0%
+these are all vectors the results of
+ 
+
+ align:start position:0%
+these are all vectors the results of
+vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and therefore we would break this
+
+ align:start position:0%
+right and therefore we would break this
+ 
+
+ align:start position:0%
+right and therefore we would break this
+down this whole thing once you write all
+
+ align:start position:0%
+down this whole thing once you write all
+ 
+
+ align:start position:0%
+down this whole thing once you write all
+that out and sum it all up you're going
+
+ align:start position:0%
+that out and sum it all up you're going
+ 
+
+ align:start position:0%
+that out and sum it all up you're going
+to get a piece of it that we would say
+
+ align:start position:0%
+to get a piece of it that we would say
+ 
+
+ align:start position:0%
+to get a piece of it that we would say
+is in that is in the IH hat Direction
+
+ align:start position:0%
+is in that is in the IH hat Direction
+ 
+
+ align:start position:0%
+is in that is in the IH hat Direction
+and we call that
+
+ align:start position:0%
+and we call that
+ 
+
+ align:start position:0%
+and we call that
+HX another piece that's in the J hat
+
+ align:start position:0%
+HX another piece that's in the J hat
+ 
+
+ align:start position:0%
+HX another piece that's in the J hat
+Direction which we call H1 Y and HZ in
+
+ align:start position:0%
+Direction which we call H1 Y and HZ in
+ 
+
+ align:start position:0%
+Direction which we call H1 Y and HZ in
+the K
+
+ align:start position:0%
+the K
+ 
+
+ align:start position:0%
+the K
+hat that's just how that'll all shake
+
+ align:start position:0%
+hat that's just how that'll all shake
+ 
+
+ align:start position:0%
+hat that's just how that'll all shake
+out you're going to get three in general
+
+ align:start position:0%
+out you're going to get three in general
+ 
+
+ align:start position:0%
+out you're going to get three in general
+you get three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah why do we have ma Mass multiplied
+
+ align:start position:0%
+yeah why do we have ma Mass multiplied
+ 
+
+ align:start position:0%
+yeah why do we have ma Mass multiplied
+by a position Vector times momentum
+
+ align:start position:0%
+by a position Vector times momentum
+ 
+
+ align:start position:0%
+by a position Vector times momentum
+because that is the definition of
+
+ align:start position:0%
+because that is the definition of
+ 
+
+ align:start position:0%
+because that is the definition of
+angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum it's R cross P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right ah I see what I've done yeah
+
+ align:start position:0%
+right ah I see what I've done yeah
+ 
+
+ align:start position:0%
+right ah I see what I've done yeah
+you're right this m doesn't belong I got
+
+ align:start position:0%
+you're right this m doesn't belong I got
+ 
+
+ align:start position:0%
+you're right this m doesn't belong I got
+ahead of myself it doesn't belong here
+
+ align:start position:0%
+ahead of myself it doesn't belong here
+ 
+
+ align:start position:0%
+ahead of myself it doesn't belong here
+when it pops out of this to here thanks
+
+ align:start position:0%
+when it pops out of this to here thanks
+ 
+
+ align:start position:0%
+when it pops out of this to here thanks
+for catching that
+
+ align:start position:0%
+for catching that
+ 
+
+ align:start position:0%
+for catching that
+absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so we're in the pract each of
+
+ align:start position:0%
+right so we're in the pract each of
+ 
+
+ align:start position:0%
+right so we're in the pract each of
+these each of these is every term here
+
+ align:start position:0%
+these each of these is every term here
+ 
+
+ align:start position:0%
+these each of these is every term here
+is made up of things that look like
+
+ align:start position:0%
+is made up of things that look like
+ 
+
+ align:start position:0%
+is made up of things that look like
+X1 Z1 M1 Omega X
+
+ align:start position:0%
+X1 Z1 M1 Omega X
+ 
+
+ align:start position:0%
+X1 Z1 M1 Omega X
+or Omega y or Omega Z because this is a
+
+ align:start position:0%
+or Omega y or Omega Z because this is a
+ 
+
+ align:start position:0%
+or Omega y or Omega Z because this is a
+vector and it can have three components
+
+ align:start position:0%
+vector and it can have three components
+ 
+
+ align:start position:0%
+vector and it can have three components
+a piece in the eye a piece in the J
+
+ align:start position:0%
+a piece in the eye a piece in the J
+ 
+
+ align:start position:0%
+a piece in the eye a piece in the J
+piece in the K Direction so when
+
+ align:start position:0%
+piece in the K Direction so when
+ 
+
+ align:start position:0%
+piece in the K Direction so when
+you there's a lot of possible terms and
+
+ align:start position:0%
+you there's a lot of possible terms and
+ 
+
+ align:start position:0%
+you there's a lot of possible terms and
+we're in the practice of writing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H Vector can be written WR then as a
+
+ align:start position:0%
+H Vector can be written WR then as a
+ 
+
+ align:start position:0%
+H Vector can be written WR then as a
+um I'm going to run out of room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so the HX term the piece that comes
+
+ align:start position:0%
+here so the HX term the piece that comes
+ 
+
+ align:start position:0%
+here so the HX term the piece that comes
+out with all little bits in the I
+
+ align:start position:0%
+out with all little bits in the I
+ 
+
+ align:start position:0%
+out with all little bits in the I
+Direction when you just break it apart
+
+ align:start position:0%
+Direction when you just break it apart
+ 
+
+ align:start position:0%
+Direction when you just break it apart
+we would write it
+
+ align:start position:0%
+we would write it
+ 
+
+ align:start position:0%
+we would write it
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+XX Omega x +
+
+ align:start position:0%
+XX Omega x +
+ 
+
+ align:start position:0%
+XX Omega x +
+ixy Omega y plus
+
+ align:start position:0%
+ixy Omega y plus
+ 
+
+ align:start position:0%
+ixy Omega y plus
+I X Z Omega
+
+ align:start position:0%
+I X Z Omega
+ 
+
+ align:start position:0%
+I X Z Omega
+Z these are all all the I terms that
+
+ align:start position:0%
+Z these are all all the I terms that
+ 
+
+ align:start position:0%
+Z these are all all the I terms that
+float out of
+
+ align:start position:0%
+float out of
+ 
+
+ align:start position:0%
+float out of
+this we just write them we just collect
+
+ align:start position:0%
+this we just write them we just collect
+ 
+
+ align:start position:0%
+this we just write them we just collect
+them together all the ones that are
+
+ align:start position:0%
+them together all the ones that are
+ 
+
+ align:start position:0%
+them together all the ones that are
+multiplied by om GA X ends up being some
+
+ align:start position:0%
+multiplied by om GA X ends up being some
+ 
+
+ align:start position:0%
+multiplied by om GA X ends up being some
+terms that look like sums of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mi xmi Z2 terms and there's some y s
+
+ align:start position:0%
+Mi xmi Z2 terms and there's some y s
+ 
+
+ align:start position:0%
+Mi xmi Z2 terms and there's some y s
+terms but we collect them all together
+
+ align:start position:0%
+terms but we collect them all together
+ 
+
+ align:start position:0%
+terms but we collect them all together
+and we call this constant in front of it
+
+ align:start position:0%
+and we call this constant in front of it
+ 
+
+ align:start position:0%
+and we call this constant in front of it
+ixx it's just what floats out of this
+
+ align:start position:0%
+ixx it's just what floats out of this
+ 
+
+ align:start position:0%
+ixx it's just what floats out of this
+stuff we break it into three pieces the
+
+ align:start position:0%
+stuff we break it into three pieces the
+ 
+
+ align:start position:0%
+stuff we break it into three pieces the
+part of the angular momentum due to the
+
+ align:start position:0%
+part of the angular momentum due to the
+ 
+
+ align:start position:0%
+part of the angular momentum due to the
+rotation in the X the part due to the
+
+ align:start position:0%
+rotation in the X the part due to the
+ 
+
+ align:start position:0%
+rotation in the X the part due to the
+rotation in the Y the part due to the
+
+ align:start position:0%
+rotation in the Y the part due to the
+ 
+
+ align:start position:0%
+rotation in the Y the part due to the
+rotation in the Z and you do the same
+
+ align:start position:0%
+rotation in the Z and you do the same
+ 
+
+ align:start position:0%
+rotation in the Z and you do the same
+thing for
+
+ align:start position:0%
+thing for
+ 
+
+ align:start position:0%
+thing for
+Hy you get an
+
+ align:start position:0%
+Hy you get an
+ 
+
+ align:start position:0%
+Hy you get an
+i y x Omega X plus an i y y Omega y plus
+
+ align:start position:0%
+i y x Omega X plus an i y y Omega y plus
+ 
+
+ align:start position:0%
+i y x Omega X plus an i y y Omega y plus
+an i y z Omega Z and you finally get an
+
+ align:start position:0%
+an i y z Omega Z and you finally get an
+ 
+
+ align:start position:0%
+an i y z Omega Z and you finally get an
+HZ
+
+ align:start position:0%
+HZ
+ 
+
+ align:start position:0%
+HZ
+term i z x Omega x i z z y Omega
+
+ align:start position:0%
+term i z x Omega x i z z y Omega
+ 
+
+ align:start position:0%
+term i z x Omega x i z z y Omega
+y i
+
+ align:start position:0%
+y i
+ 
+
+ align:start position:0%
+y i
+ZZ Omega Z okay that's everything that
+
+ align:start position:0%
+ZZ Omega Z okay that's everything that
+ 
+
+ align:start position:0%
+ZZ Omega Z okay that's everything that
+falls out of just doing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation and we are in the habit of
+
+ align:start position:0%
+calculation and we are in the habit of
+ 
+
+ align:start position:0%
+calculation and we are in the habit of
+writing that in a matrix notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the product of this thing called the
+
+ align:start position:0%
+as the product of this thing called the
+ 
+
+ align:start position:0%
+as the product of this thing called the
+inertia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and so forth with this bottom
+
+ align:start position:0%
+Matrix and so forth with this bottom
+ 
+
+ align:start position:0%
+Matrix and so forth with this bottom
+term here saying be i z z multiplied by
+
+ align:start position:0%
+term here saying be i z z multiplied by
+ 
+
+ align:start position:0%
+term here saying be i z z multiplied by
+Omega X Omega y Omega
+
+ align:start position:0%
+Omega X Omega y Omega
+ 
+
+ align:start position:0%
+Omega X Omega y Omega
+Z you multiply that times the top row
+
+ align:start position:0%
+Z you multiply that times the top row
+ 
+
+ align:start position:0%
+Z you multiply that times the top row
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+HX middle row you get Hy bottom row you
+
+ align:start position:0%
+HX middle row you get Hy bottom row you
+ 
+
+ align:start position:0%
+HX middle row you get Hy bottom row you
+get the
+
+ align:start position:0%
+get the
+ 
+
+ align:start position:0%
+get the
+HC so where this stuff comes from it's
+
+ align:start position:0%
+HC so where this stuff comes from it's
+ 
+
+ align:start position:0%
+HC so where this stuff comes from it's
+just from conducting carrying out this
+
+ align:start position:0%
+just from conducting carrying out this
+ 
+
+ align:start position:0%
+just from conducting carrying out this
+summation over all the mass
+
+ align:start position:0%
+summation over all the mass
+ 
+
+ align:start position:0%
+summation over all the mass
+bits so it basically starts with the
+
+ align:start position:0%
+bits so it basically starts with the
+ 
+
+ align:start position:0%
+bits so it basically starts with the
+definition of angular momentum and this
+
+ align:start position:0%
+definition of angular momentum and this
+ 
+
+ align:start position:0%
+definition of angular momentum and this
+is just a convenient way to write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so for
+
+ align:start position:0%
+it so for
+ 
+
+ align:start position:0%
+it so for
+example the I
+
+ align:start position:0%
+example the I
+ 
+
+ align:start position:0%
+example the I
+XZ term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the one in the upper right there that's
+
+ align:start position:0%
+the one in the upper right there that's
+ 
+
+ align:start position:0%
+the one in the upper right there that's
+part of HX the ixz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term is minus the
+
+ align:start position:0%
+term is minus the
+ 
+
+ align:start position:0%
+term is minus the
+summation of all the little Mass
+
+ align:start position:0%
+summation of all the little Mass
+ 
+
+ align:start position:0%
+summation of all the little Mass
+bits times their location XI
+
+ align:start position:0%
+bits times their location XI
+ 
+
+ align:start position:0%
+bits times their location XI
+zi and this see XZ always matches
+
+ align:start position:0%
+zi and this see XZ always matches
+ 
+
+ align:start position:0%
+zi and this see XZ always matches
+XZ and when you want to do this over a
+
+ align:start position:0%
+XZ and when you want to do this over a
+ 
+
+ align:start position:0%
+XZ and when you want to do this over a
+continuous object you integrate that
+
+ align:start position:0%
+continuous object you integrate that
+ 
+
+ align:start position:0%
+continuous object you integrate that
+and for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+izz this is the summation
+
+ align:start position:0%
+izz this is the summation
+ 
+
+ align:start position:0%
+izz this is the summation
+of over
+
+ align:start position:0%
+of over
+ 
+
+ align:start position:0%
+of over
+I all the bits of m
+
+ align:start position:0%
+I all the bits of m
+ 
+
+ align:start position:0%
+I all the bits of m
+i x i 2 + y i
+
+ align:start position:0%
+i x i 2 + y i
+ 
+
+ align:start position:0%
+i x i 2 + y i
+2 okay so in general this by as
+
+ align:start position:0%
+2 okay so in general this by as
+ 
+
+ align:start position:0%
+2 okay so in general this by as
+summations that's where these terms come
+
+ align:start position:0%
+summations that's where these terms come
+ 
+
+ align:start position:0%
+summations that's where these terms come
+from they've just come they' started
+
+ align:start position:0%
+from they've just come they' started
+ 
+
+ align:start position:0%
+from they've just come they' started
+with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation okay and in general from
+
+ align:start position:0%
+calculation okay and in general from
+ 
+
+ align:start position:0%
+calculation okay and in general from
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation so for our one particle
+
+ align:start position:0%
+calculation so for our one particle
+ 
+
+ align:start position:0%
+calculation so for our one particle
+system for this thing so this is x and z
+
+ align:start position:0%
+system for this thing so this is x and z
+ 
+
+ align:start position:0%
+system for this thing so this is x and z
+it's one single
+
+ align:start position:0%
+it's one single
+ 
+
+ align:start position:0%
+it's one single
+particle so for our one particle system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's no y one in here because
+
+ align:start position:0%
+and there's no y one in here because
+ 
+
+ align:start position:0%
+and there's no y one in here because
+it's zero in this problem right there's
+
+ align:start position:0%
+it's zero in this problem right there's
+ 
+
+ align:start position:0%
+it's zero in this problem right there's
+no it's coordinate of that little Mass
+
+ align:start position:0%
+no it's coordinate of that little Mass
+ 
+
+ align:start position:0%
+no it's coordinate of that little Mass
+particle is X1 0 y1 so in general this
+
+ align:start position:0%
+particle is X1 0 y1 so in general this
+ 
+
+ align:start position:0%
+particle is X1 0 y1 so in general this
+is x i^ 2 + y i^ s but that's zero so
+
+ align:start position:0%
+is x i^ 2 + y i^ s but that's zero so
+ 
+
+ align:start position:0%
+is x i^ 2 + y i^ s but that's zero so
+it's just mx1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so that's where all these things come
+
+ align:start position:0%
+2 so that's where all these things come
+ 
+
+ align:start position:0%
+2 so that's where all these things come
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+now let's kind of look at
+
+ align:start position:0%
+now let's kind of look at
+ 
+
+ align:start position:0%
+now let's kind of look at
+uh the units of these things are always
+
+ align:start position:0%
+uh the units of these things are always
+ 
+
+ align:start position:0%
+uh the units of these things are always
+masstimes length
+
+ align:start position:0%
+masstimes length
+ 
+
+ align:start position:0%
+masstimes length
+squ the diagonal
+
+ align:start position:0%
+squ the diagonal
+ 
+
+ align:start position:0%
+squ the diagonal
+terms the x ixx i y y i ZZ terms will
+
+ align:start position:0%
+terms the x ixx i y y i ZZ terms will
+ 
+
+ align:start position:0%
+terms the x ixx i y y i ZZ terms will
+all be of the form of something
+
+ align:start position:0%
+all be of the form of something
+ 
+
+ align:start position:0%
+all be of the form of something
+squared and what it is is it's always
+
+ align:start position:0%
+squared and what it is is it's always
+ 
+
+ align:start position:0%
+squared and what it is is it's always
+just the distance of the mass
+
+ align:start position:0%
+just the distance of the mass
+ 
+
+ align:start position:0%
+just the distance of the mass
+particles from the axis of rotation call
+
+ align:start position:0%
+particles from the axis of rotation call
+ 
+
+ align:start position:0%
+particles from the axis of rotation call
+that R it's just a summation of this
+
+ align:start position:0%
+that R it's just a summation of this
+ 
+
+ align:start position:0%
+that R it's just a summation of this
+perpendicular distance from the axis of
+
+ align:start position:0%
+perpendicular distance from the axis of
+ 
+
+ align:start position:0%
+perpendicular distance from the axis of
+rotation for izz the axis of rotation is
+
+ align:start position:0%
+rotation for izz the axis of rotation is
+ 
+
+ align:start position:0%
+rotation for izz the axis of rotation is
+z and this piece here is always the
+
+ align:start position:0%
+z and this piece here is always the
+ 
+
+ align:start position:0%
+z and this piece here is always the
+distance squared that the mass particle
+
+ align:start position:0%
+distance squared that the mass particle
+ 
+
+ align:start position:0%
+distance squared that the mass particle
+is from the axis of
+
+ align:start position:0%
+is from the axis of
+ 
+
+ align:start position:0%
+is from the axis of
+rotation okay now that that's kind of
+
+ align:start position:0%
+rotation okay now that that's kind of
+ 
+
+ align:start position:0%
+rotation okay now that that's kind of
+that's the setup for
+
+ align:start position:0%
+that's the setup for
+ 
+
+ align:start position:0%
+that's the setup for
+today and we want to get on the real
+
+ align:start position:0%
+today and we want to get on the real
+ 
+
+ align:start position:0%
+today and we want to get on the real
+meat of the discussion are talking about
+
+ align:start position:0%
+meat of the discussion are talking about
+ 
+
+ align:start position:0%
+meat of the discussion are talking about
+things like the
+
+ align:start position:0%
+things like the
+ 
+
+ align:start position:0%
+things like the
+uh what principal axes are and so forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so now we're going to move on to the
+
+ align:start position:0%
+so now we're going to move on to the
+ 
+
+ align:start position:0%
+so now we're going to move on to the
+part of this conversation about
+
+ align:start position:0%
+part of this conversation about
+ 
+
+ align:start position:0%
+part of this conversation about
+principal axes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so really important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point for every rigid
+
+ align:start position:0%
+point for every rigid
+ 
+
+ align:start position:0%
+point for every rigid
+body for even weird ones for every rigid
+
+ align:start position:0%
+body for even weird ones for every rigid
+ 
+
+ align:start position:0%
+body for even weird ones for every rigid
+body there is a coordinate system that
+
+ align:start position:0%
+body there is a coordinate system that
+ 
+
+ align:start position:0%
+body there is a coordinate system that
+you can attach to this body an XYZ set
+
+ align:start position:0%
+you can attach to this body an XYZ set
+ 
+
+ align:start position:0%
+you can attach to this body an XYZ set
+of orthogonal coordinates that you can
+
+ align:start position:0%
+of orthogonal coordinates that you can
+ 
+
+ align:start position:0%
+of orthogonal coordinates that you can
+fix in this body such that you can make
+
+ align:start position:0%
+fix in this body such that you can make
+ 
+
+ align:start position:0%
+fix in this body such that you can make
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+this inertia
+
+ align:start position:0%
+this inertia
+ 
+
+ align:start position:0%
+this inertia
+Matrix have be
+
+ align:start position:0%
+Matrix have be
+ 
+
+ align:start position:0%
+Matrix have be
+diagonal any weird body at all there is
+
+ align:start position:0%
+diagonal any weird body at all there is
+ 
+
+ align:start position:0%
+diagonal any weird body at all there is
+a set of coordinates that if you use
+
+ align:start position:0%
+a set of coordinates that if you use
+ 
+
+ align:start position:0%
+a set of coordinates that if you use
+that set this this Matrix turns out to
+
+ align:start position:0%
+that set this this Matrix turns out to
+ 
+
+ align:start position:0%
+that set this this Matrix turns out to
+be diagonal and in terms of what that
+
+ align:start position:0%
+be diagonal and in terms of what that
+ 
+
+ align:start position:0%
+be diagonal and in terms of what that
+means in Dynamics
+
+ align:start position:0%
+means in Dynamics
+ 
+
+ align:start position:0%
+means in Dynamics
+terms is if you then rotate the
+
+ align:start position:0%
+terms is if you then rotate the
+ 
+
+ align:start position:0%
+terms is if you then rotate the
+object about one of those axes it will
+
+ align:start position:0%
+object about one of those axes it will
+ 
+
+ align:start position:0%
+object about one of those axes it will
+be dynamically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balanced and so when you rotate a shaft
+
+ align:start position:0%
+balanced and so when you rotate a shaft
+ 
+
+ align:start position:0%
+balanced and so when you rotate a shaft
+this is a this is an an object for which
+
+ align:start position:0%
+this is a this is an an object for which
+ 
+
+ align:start position:0%
+this is a this is an an object for which
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+know it's a circular uniform disc one of
+
+ align:start position:0%
+know it's a circular uniform disc one of
+ 
+
+ align:start position:0%
+know it's a circular uniform disc one of
+the axes through the center is a
+
+ align:start position:0%
+the axes through the center is a
+ 
+
+ align:start position:0%
+the axes through the center is a
+principal axis and if I rotate the
+
+ align:start position:0%
+principal axis and if I rotate the
+ 
+
+ align:start position:0%
+principal axis and if I rotate the
+object about that this one the hole is
+
+ align:start position:0%
+object about that this one the hole is
+ 
+
+ align:start position:0%
+object about that this one the hole is
+kind of out around so wobbles a bit but
+
+ align:start position:0%
+kind of out around so wobbles a bit but
+ 
+
+ align:start position:0%
+kind of out around so wobbles a bit but
+if I rotate it about that it will have
+
+ align:start position:0%
+if I rotate it about that it will have
+ 
+
+ align:start position:0%
+if I rotate it about that it will have
+no it will make no torqus about this
+
+ align:start position:0%
+no it will make no torqus about this
+ 
+
+ align:start position:0%
+no it will make no torqus about this
+axis that are because it's
+
+ align:start position:0%
+axis that are because it's
+ 
+
+ align:start position:0%
+axis that are because it's
+unbalanced okay that's that's
+
+ align:start position:0%
+unbalanced okay that's that's
+ 
+
+ align:start position:0%
+unbalanced okay that's that's
+essentially the dynamic meaning of
+
+ align:start position:0%
+essentially the dynamic meaning of
+ 
+
+ align:start position:0%
+essentially the dynamic meaning of
+principal axis the axis about which you
+
+ align:start position:0%
+principal axis the axis about which you
+ 
+
+ align:start position:0%
+principal axis the axis about which you
+can rotate the thing and and it'll just
+
+ align:start position:0%
+can rotate the thing and and it'll just
+ 
+
+ align:start position:0%
+can rotate the thing and and it'll just
+be smooth no no out of away from the
+
+ align:start position:0%
+be smooth no no out of away from the
+ 
+
+ align:start position:0%
+be smooth no no out of away from the
+axis torqus okay so that's so those are
+
+ align:start position:0%
+axis torqus okay so that's so those are
+ 
+
+ align:start position:0%
+axis torqus okay so that's so those are
+pretty important we want to know what
+
+ align:start position:0%
+pretty important we want to know what
+ 
+
+ align:start position:0%
+pretty important we want to know what
+those are for rigid bodies and how to
+
+ align:start position:0%
+those are for rigid bodies and how to
+ 
+
+ align:start position:0%
+those are for rigid bodies and how to
+find them so there's a mathematical way
+
+ align:start position:0%
+find them so there's a mathematical way
+ 
+
+ align:start position:0%
+find them so there's a mathematical way
+to find them and you can just read about
+
+ align:start position:0%
+to find them and you can just read about
+ 
+
+ align:start position:0%
+to find them and you can just read about
+it in the textbook
+
+ align:start position:0%
+it in the textbook
+ 
+
+ align:start position:0%
+it in the textbook
+the uh you know it's
+
+ align:start position:0%
+the uh you know it's
+ 
+
+ align:start position:0%
+the uh you know it's
+a sort of a um trying to think the
+
+ align:start position:0%
+a sort of a um trying to think the
+ 
+
+ align:start position:0%
+a sort of a um trying to think the
+mathematical
+
+ align:start position:0%
+mathematical
+ 
+
+ align:start position:0%
+mathematical
+term I've forgotten it so the uh but
+
+ align:start position:0%
+term I've forgotten it so the uh but
+ 
+
+ align:start position:0%
+term I've forgotten it so the uh but
+what I want to teach you today is for
+
+ align:start position:0%
+what I want to teach you today is for
+ 
+
+ align:start position:0%
+what I want to teach you today is for
+many many objects if you just look at
+
+ align:start position:0%
+many many objects if you just look at
+ 
+
+ align:start position:0%
+many many objects if you just look at
+their symmetries you can figure out by
+
+ align:start position:0%
+their symmetries you can figure out by
+ 
+
+ align:start position:0%
+their symmetries you can figure out by
+Common Sense where the principal axes
+
+ align:start position:0%
+Common Sense where the principal axes
+ 
+
+ align:start position:0%
+Common Sense where the principal axes
+are so that's what we're going to do
+
+ align:start position:0%
+are so that's what we're going to do
+ 
+
+ align:start position:0%
+are so that's what we're going to do
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we started off saying that we're talking
+
+ align:start position:0%
+we started off saying that we're talking
+ 
+
+ align:start position:0%
+we started off saying that we're talking
+about bodies that are either rotating
+
+ align:start position:0%
+about bodies that are either rotating
+ 
+
+ align:start position:0%
+about bodies that are either rotating
+about their centers of mass or about
+
+ align:start position:0%
+about their centers of mass or about
+ 
+
+ align:start position:0%
+about their centers of mass or about
+some other fixed Point okay so we're now
+
+ align:start position:0%
+some other fixed Point okay so we're now
+ 
+
+ align:start position:0%
+some other fixed Point okay so we're now
+we're going to talk about we're going to
+
+ align:start position:0%
+we're going to talk about we're going to
+ 
+
+ align:start position:0%
+we're going to talk about we're going to
+Define our principal
+
+ align:start position:0%
+Define our principal
+ 
+
+ align:start position:0%
+Define our principal
+axis assuming we are rotating about the
+
+ align:start position:0%
+axis assuming we are rotating about the
+ 
+
+ align:start position:0%
+axis assuming we are rotating about the
+center of
+
+ align:start position:0%
+center of
+ 
+
+ align:start position:0%
+center of
+mass there's an easy easy method known
+
+ align:start position:0%
+mass there's an easy easy method known
+ 
+
+ align:start position:0%
+mass there's an easy easy method known
+as the parallel axis theorem to get any
+
+ align:start position:0%
+as the parallel axis theorem to get any
+ 
+
+ align:start position:0%
+as the parallel axis theorem to get any
+other point so why do we want to why do
+
+ align:start position:0%
+other point so why do we want to why do
+ 
+
+ align:start position:0%
+other point so why do we want to why do
+we care about doing it about the center
+
+ align:start position:0%
+we care about doing it about the center
+ 
+
+ align:start position:0%
+we care about doing it about the center
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass why is that useful to know about
+
+ align:start position:0%
+mass why is that useful to know about
+ 
+
+ align:start position:0%
+mass why is that useful to know about
+the properties around the center for
+
+ align:start position:0%
+the properties around the center for
+ 
+
+ align:start position:0%
+the properties around the center for
+Dynamics purposes what kind of Dynamics
+
+ align:start position:0%
+Dynamics purposes what kind of Dynamics
+ 
+
+ align:start position:0%
+Dynamics purposes what kind of Dynamics
+problems do you care about the center of
+
+ align:start position:0%
+problems do you care about the center of
+ 
+
+ align:start position:0%
+problems do you care about the center of
+mass rotation about the center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass okay so when I throw this thing in
+
+ align:start position:0%
+mass okay so when I throw this thing in
+ 
+
+ align:start position:0%
+mass okay so when I throw this thing in
+the air it's rotating it's translating
+
+ align:start position:0%
+the air it's rotating it's translating
+ 
+
+ align:start position:0%
+the air it's rotating it's translating
+and when it rotates what's it rotating
+
+ align:start position:0%
+and when it rotates what's it rotating
+ 
+
+ align:start position:0%
+and when it rotates what's it rotating
+about Center Mass so there's just lots
+
+ align:start position:0%
+about Center Mass so there's just lots
+ 
+
+ align:start position:0%
+about Center Mass so there's just lots
+and lots of problems in which in fact
+
+ align:start position:0%
+and lots of problems in which in fact
+ 
+
+ align:start position:0%
+and lots of problems in which in fact
+the rotation is going to occur around
+
+ align:start position:0%
+the rotation is going to occur around
+ 
+
+ align:start position:0%
+the rotation is going to occur around
+the center Mass anytime the thing is off
+
+ align:start position:0%
+the center Mass anytime the thing is off
+ 
+
+ align:start position:0%
+the center Mass anytime the thing is off
+there and there's no uh nothing
+
+ align:start position:0%
+there and there's no uh nothing
+ 
+
+ align:start position:0%
+there and there's no uh nothing
+constraining its rotational motion the
+
+ align:start position:0%
+constraining its rotational motion the
+ 
+
+ align:start position:0%
+constraining its rotational motion the
+rotation will will be about the center
+
+ align:start position:0%
+rotation will will be about the center
+ 
+
+ align:start position:0%
+rotation will will be about the center
+of mass so that's a good that's a good
+
+ align:start position:0%
+of mass so that's a good that's a good
+ 
+
+ align:start position:0%
+of mass so that's a good that's a good
+enough reason the pract and a very
+
+ align:start position:0%
+enough reason the pract and a very
+ 
+
+ align:start position:0%
+enough reason the pract and a very
+practical then reason for computing
+
+ align:start position:0%
+practical then reason for computing
+ 
+
+ align:start position:0%
+practical then reason for computing
+these things or knowing how to find
+
+ align:start position:0%
+these things or knowing how to find
+ 
+
+ align:start position:0%
+these things or knowing how to find
+these things about the Center of mass
+
+ align:start position:0%
+these things about the Center of mass
+ 
+
+ align:start position:0%
+these things about the Center of mass
+all right so we're now we're going to do
+
+ align:start position:0%
+all right so we're now we're going to do
+ 
+
+ align:start position:0%
+all right so we're now we're going to do
+so we're doing principal
+
+ align:start position:0%
+so we're doing principal
+ 
+
+ align:start position:0%
+so we're doing principal
+axes
+
+ align:start position:0%
+axes
+ 
+
+ align:start position:0%
+axes
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and I'm going to teach you some symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules maybe first a little Common
+
+ align:start position:0%
+rules maybe first a little Common
+ 
+
+ align:start position:0%
+rules maybe first a little Common
+Sense this thing is is this a principal
+
+ align:start position:0%
+Sense this thing is is this a principal
+ 
+
+ align:start position:0%
+Sense this thing is is this a principal
+axis no way right and we know for a fact
+
+ align:start position:0%
+axis no way right and we know for a fact
+ 
+
+ align:start position:0%
+axis no way right and we know for a fact
+that it doesn't have has off diagonal
+
+ align:start position:0%
+that it doesn't have has off diagonal
+ 
+
+ align:start position:0%
+that it doesn't have has off diagonal
+terms because I've defined my
+
+ align:start position:0%
+terms because I've defined my
+ 
+
+ align:start position:0%
+terms because I've defined my
+coordinates as being x y z like this and
+
+ align:start position:0%
+coordinates as being x y z like this and
+ 
+
+ align:start position:0%
+coordinates as being x y z like this and
+this is off at some strange angle so as
+
+ align:start position:0%
+this is off at some strange angle so as
+ 
+
+ align:start position:0%
+this is off at some strange angle so as
+a practical matter how could I make this
+
+ align:start position:0%
+a practical matter how could I make this
+ 
+
+ align:start position:0%
+a practical matter how could I make this
+the how could I make this object alter
+
+ align:start position:0%
+the how could I make this object alter
+ 
+
+ align:start position:0%
+the how could I make this object alter
+this object so that this is a principal
+
+ align:start position:0%
+this object so that this is a principal
+ 
+
+ align:start position:0%
+this object so that this is a principal
+axis it's essentially how would you
+
+ align:start position:0%
+axis it's essentially how would you
+ 
+
+ align:start position:0%
+axis it's essentially how would you
+balance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this thatass off take the mass off that
+
+ align:start position:0%
+this thatass off take the mass off that
+ 
+
+ align:start position:0%
+this thatass off take the mass off that
+fix it okay
+
+ align:start position:0%
+fix it okay
+ 
+
+ align:start position:0%
+fix it okay
+or all
+
+ align:start position:0%
+or all
+ 
+
+ align:start position:0%
+or all
+right where put it down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now you want it like this all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is steel going into
+
+ align:start position:0%
+right this is steel going into
+ 
+
+ align:start position:0%
+right this is steel going into
+aluminum I have to be careful that I
+
+ align:start position:0%
+aluminum I have to be careful that I
+ 
+
+ align:start position:0%
+aluminum I have to be careful that I
+don't strip the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+threads there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go all right and now test test one this
+
+ align:start position:0%
+go all right and now test test one this
+ 
+
+ align:start position:0%
+go all right and now test test one this
+is act rotation is a dynamically
+
+ align:start position:0%
+is act rotation is a dynamically
+ 
+
+ align:start position:0%
+is act rotation is a dynamically
+imbalance smooth as silk okay this now
+
+ align:start position:0%
+imbalance smooth as silk okay this now
+ 
+
+ align:start position:0%
+imbalance smooth as silk okay this now
+is a principal axis this thing has its
+
+ align:start position:0%
+is a principal axis this thing has its
+ 
+
+ align:start position:0%
+is a principal axis this thing has its
+mass distribution is
+
+ align:start position:0%
+mass distribution is
+ 
+
+ align:start position:0%
+mass distribution is
+symmetric and the plane of symmetry
+
+ align:start position:0%
+symmetric and the plane of symmetry
+ 
+
+ align:start position:0%
+symmetric and the plane of symmetry
+there's a plane where is there a plane
+
+ align:start position:0%
+there's a plane where is there a plane
+ 
+
+ align:start position:0%
+there's a plane where is there a plane
+of symmetry for this problem for this
+
+ align:start position:0%
+of symmetry for this problem for this
+ 
+
+ align:start position:0%
+of symmetry for this problem for this
+object so that's what we're going to
+
+ align:start position:0%
+object so that's what we're going to
+ 
+
+ align:start position:0%
+object so that's what we're going to
+talk about now planes of symmetry and
+
+ align:start position:0%
+talk about now planes of symmetry and
+ 
+
+ align:start position:0%
+talk about now planes of symmetry and
+axes of
+
+ align:start position:0%
+axes of
+ 
+
+ align:start position:0%
+axes of
+symmetry W you you see one like that
+
+ align:start position:0%
+symmetry W you you see one like that
+ 
+
+ align:start position:0%
+symmetry W you you see one like that
+you're right that's a PL of symmetry is
+
+ align:start position:0%
+you're right that's a PL of symmetry is
+ 
+
+ align:start position:0%
+you're right that's a PL of symmetry is
+there another one for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one like this so that's two planes of
+
+ align:start position:0%
+one like this so that's two planes of
+ 
+
+ align:start position:0%
+one like this so that's two planes of
+symmetry okay so let's let's let's come
+
+ align:start position:0%
+symmetry okay so let's let's let's come
+ 
+
+ align:start position:0%
+symmetry okay so let's let's let's come
+up with some rules for some symmetry
+
+ align:start position:0%
+up with some rules for some symmetry
+ 
+
+ align:start position:0%
+up with some rules for some symmetry
+rules
+
+ align:start position:0%
+rules
+ 
+
+ align:start position:0%
+rules
+um so this first one is there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by this I mean diagonal it's a diagonal
+
+ align:start position:0%
+by this I mean diagonal it's a diagonal
+ 
+
+ align:start position:0%
+by this I mean diagonal it's a diagonal
+matrix you can find a set of orthogonal
+
+ align:start position:0%
+matrix you can find a set of orthogonal
+ 
+
+ align:start position:0%
+matrix you can find a set of orthogonal
+axes such that this Matrix is diagonal
+
+ align:start position:0%
+axes such that this Matrix is diagonal
+ 
+
+ align:start position:0%
+axes such that this Matrix is diagonal
+that's what we mean when we go to find
+
+ align:start position:0%
+that's what we mean when we go to find
+ 
+
+ align:start position:0%
+that's what we mean when we go to find
+principal axes
+
+ align:start position:0%
+principal axes
+ 
+
+ align:start position:0%
+principal axes
+okay um going to pick a board here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules and we're going to have three of
+
+ align:start position:0%
+rules and we're going to have three of
+ 
+
+ align:start position:0%
+rules and we're going to have three of
+them so just leave room on your paper
+
+ align:start position:0%
+them so just leave room on your paper
+ 
+
+ align:start position:0%
+them so just leave room on your paper
+we're going to build these up and I'm
+
+ align:start position:0%
+we're going to build these up and I'm
+ 
+
+ align:start position:0%
+we're going to build these up and I'm
+going to talk about it and then add
+
+ align:start position:0%
+going to talk about it and then add
+ 
+
+ align:start position:0%
+going to talk about it and then add
+another one and so forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+yeah what the uh inertia matrix mean
+
+ align:start position:0%
+yeah what the uh inertia matrix mean
+ 
+
+ align:start position:0%
+yeah what the uh inertia matrix mean
+what is the inertia Matrix I mean the
+
+ align:start position:0%
+what is the inertia Matrix I mean the
+ 
+
+ align:start position:0%
+what is the inertia Matrix I mean the
+second one
+
+ align:start position:0%
+second one
+ 
+
+ align:start position:0%
+second one
+this thing with the diagonals this is
+
+ align:start position:0%
+this thing with the diagonals this is
+ 
+
+ align:start position:0%
+this thing with the diagonals this is
+going to have all the off diagonal terms
+
+ align:start position:0%
+going to have all the off diagonal terms
+ 
+
+ align:start position:0%
+going to have all the off diagonal terms
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zeros that's what I mean it's a diagonal
+
+ align:start position:0%
+zeros that's what I mean it's a diagonal
+ 
+
+ align:start position:0%
+zeros that's what I mean it's a diagonal
+matrix there the mass moments of inertia
+
+ align:start position:0%
+matrix there the mass moments of inertia
+ 
+
+ align:start position:0%
+matrix there the mass moments of inertia
+and products of inertia you only have
+
+ align:start position:0%
+and products of inertia you only have
+ 
+
+ align:start position:0%
+and products of inertia you only have
+iixx i y y izz if you properly pick this
+
+ align:start position:0%
+iixx i y y izz if you properly pick this
+ 
+
+ align:start position:0%
+iixx i y y izz if you properly pick this
+set of orthogonal coordinates attached
+
+ align:start position:0%
+set of orthogonal coordinates attached
+ 
+
+ align:start position:0%
+set of orthogonal coordinates attached
+to the body if you pick them right what
+
+ align:start position:0%
+to the body if you pick them right what
+ 
+
+ align:start position:0%
+to the body if you pick them right what
+it means is you then you spin that
+
+ align:start position:0%
+it means is you then you spin that
+ 
+
+ align:start position:0%
+it means is you then you spin that
+object about one of those axes it's it
+
+ align:start position:0%
+object about one of those axes it's it
+ 
+
+ align:start position:0%
+object about one of those axes it's it
+it's it's
+
+ align:start position:0%
+it's it's
+ 
+
+ align:start position:0%
+it's it's
+inbalance okay so rule
+
+ align:start position:0%
+inbalance okay so rule
+ 
+
+ align:start position:0%
+inbalance okay so rule
+one so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if there is an
+
+ align:start position:0%
+if there is an
+ 
+
+ align:start position:0%
+if there is an
+axis of symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay remember the caveat here we're
+
+ align:start position:0%
+okay remember the caveat here we're
+ 
+
+ align:start position:0%
+okay remember the caveat here we're
+talking about uniform density objects or
+
+ align:start position:0%
+talking about uniform density objects or
+ 
+
+ align:start position:0%
+talking about uniform density objects or
+at least objects in which the density is
+
+ align:start position:0%
+at least objects in which the density is
+ 
+
+ align:start position:0%
+at least objects in which the density is
+symmetrically
+
+ align:start position:0%
+symmetrically
+ 
+
+ align:start position:0%
+symmetrically
+distributed all right so the geometric
+
+ align:start position:0%
+distributed all right so the geometric
+ 
+
+ align:start position:0%
+distributed all right so the geometric
+Symmetry and mass symmetry mean the same
+
+ align:start position:0%
+Symmetry and mass symmetry mean the same
+ 
+
+ align:start position:0%
+Symmetry and mass symmetry mean the same
+thing okay what's what does that mean so
+
+ align:start position:0%
+thing okay what's what does that mean so
+ 
+
+ align:start position:0%
+thing okay what's what does that mean so
+axis of
+
+ align:start position:0%
+axis of
+ 
+
+ align:start position:0%
+axis of
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um does this have an axis of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+where it has multiple ones down the
+
+ align:start position:0%
+where it has multiple ones down the
+ 
+
+ align:start position:0%
+where it has multiple ones down the
+middle that's a plane of symmetry the
+
+ align:start position:0%
+middle that's a plane of symmetry the
+ 
+
+ align:start position:0%
+middle that's a plane of symmetry the
+other ones you think so axis of symmetry
+
+ align:start position:0%
+other ones you think so axis of symmetry
+ 
+
+ align:start position:0%
+other ones you think so axis of symmetry
+line right which
+
+ align:start position:0%
+line right which
+ 
+
+ align:start position:0%
+line right which
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+no okay a AIS of symmetry means that you
+
+ align:start position:0%
+no okay a AIS of symmetry means that you
+ 
+
+ align:start position:0%
+no okay a AIS of symmetry means that you
+can you know there a mirror image from
+
+ align:start position:0%
+can you know there a mirror image from
+ 
+
+ align:start position:0%
+can you know there a mirror image from
+that point that point Mirror Image over
+
+ align:start position:0%
+that point that point Mirror Image over
+ 
+
+ align:start position:0%
+that point that point Mirror Image over
+here is always identical but you can
+
+ align:start position:0%
+here is always identical but you can
+ 
+
+ align:start position:0%
+here is always identical but you can
+pick it any from any angle doesn't
+
+ align:start position:0%
+pick it any from any angle doesn't
+ 
+
+ align:start position:0%
+pick it any from any angle doesn't
+matter where you start it's reflected
+
+ align:start position:0%
+matter where you start it's reflected
+ 
+
+ align:start position:0%
+matter where you start it's reflected
+through the axis so things that are
+
+ align:start position:0%
+through the axis so things that are
+ 
+
+ align:start position:0%
+through the axis so things that are
+circularly shape tend to have axes of
+
+ align:start position:0%
+circularly shape tend to have axes of
+ 
+
+ align:start position:0%
+circularly shape tend to have axes of
+symmetry so this has an axis of symmetry
+
+ align:start position:0%
+symmetry so this has an axis of symmetry
+ 
+
+ align:start position:0%
+symmetry so this has an axis of symmetry
+any everything is reflected exactly just
+
+ align:start position:0%
+any everything is reflected exactly just
+ 
+
+ align:start position:0%
+any everything is reflected exactly just
+across the axis you don't have to pick
+
+ align:start position:0%
+across the axis you don't have to pick
+ 
+
+ align:start position:0%
+across the axis you don't have to pick
+any particular line so for an axis of
+
+ align:start position:0%
+any particular line so for an axis of
+ 
+
+ align:start position:0%
+any particular line so for an axis of
+symmetry what it's saying if it's an
+
+ align:start position:0%
+symmetry what it's saying if it's an
+ 
+
+ align:start position:0%
+symmetry what it's saying if it's an
+axis of symmetry then it is a principal
+
+ align:start position:0%
+axis of symmetry then it is a principal
+ 
+
+ align:start position:0%
+axis of symmetry then it is a principal
+axis and rotation about that axis the
+
+ align:start position:0%
+axis and rotation about that axis the
+ 
+
+ align:start position:0%
+axis and rotation about that axis the
+thing will be nice perfectly inbalance
+
+ align:start position:0%
+thing will be nice perfectly inbalance
+ 
+
+ align:start position:0%
+thing will be nice perfectly inbalance
+if you go through all the hairy details
+
+ align:start position:0%
+if you go through all the hairy details
+ 
+
+ align:start position:0%
+if you go through all the hairy details
+of calculating uh the hard way the iixx
+
+ align:start position:0%
+of calculating uh the hard way the iixx
+ 
+
+ align:start position:0%
+of calculating uh the hard way the iixx
+i y y Etc terms all of the off diagonal
+
+ align:start position:0%
+i y y Etc terms all of the off diagonal
+ 
+
+ align:start position:0%
+i y y Etc terms all of the off diagonal
+terms will come out zero and the reason
+
+ align:start position:0%
+terms will come out zero and the reason
+ 
+
+ align:start position:0%
+terms will come out zero and the reason
+is that for every Mass particle over
+
+ align:start position:0%
+is that for every Mass particle over
+ 
+
+ align:start position:0%
+is that for every Mass particle over
+here let's say there's a little bit
+
+ align:start position:0%
+here let's say there's a little bit
+ 
+
+ align:start position:0%
+here let's say there's a little bit
+right here in the corner there is one
+
+ align:start position:0%
+right here in the corner there is one
+ 
+
+ align:start position:0%
+right here in the corner there is one
+exactly like it on the other side so if
+
+ align:start position:0%
+exactly like it on the other side so if
+ 
+
+ align:start position:0%
+exactly like it on the other side so if
+this one were're trying to make Bend
+
+ align:start position:0%
+this one were're trying to make Bend
+ 
+
+ align:start position:0%
+this one were're trying to make Bend
+this thing up as it spins around this
+
+ align:start position:0%
+this thing up as it spins around this
+ 
+
+ align:start position:0%
+this thing up as it spins around this
+one over here is telling it to come
+
+ align:start position:0%
+one over here is telling it to come
+ 
+
+ align:start position:0%
+one over here is telling it to come
+back yeah how come this is not an a like
+
+ align:start position:0%
+back yeah how come this is not an a like
+ 
+
+ align:start position:0%
+back yeah how come this is not an a like
+if you hold it yeah straight to the so
+
+ align:start position:0%
+if you hold it yeah straight to the so
+ 
+
+ align:start position:0%
+if you hold it yeah straight to the so
+to do this so I think it's kind of just
+
+ align:start position:0%
+to do this so I think it's kind of just
+ 
+
+ align:start position:0%
+to do this so I think it's kind of just
+definition we're getting into an axis of
+
+ align:start position:0%
+definition we're getting into an axis of
+ 
+
+ align:start position:0%
+definition we're getting into an axis of
+symmetry because the object in kind of
+
+ align:start position:0%
+symmetry because the object in kind of
+ 
+
+ align:start position:0%
+symmetry because the object in kind of
+simple terms the the what the object
+
+ align:start position:0%
+simple terms the the what the object
+ 
+
+ align:start position:0%
+simple terms the the what the object
+looks like this way it's it's a narrow
+
+ align:start position:0%
+looks like this way it's it's a narrow
+ 
+
+ align:start position:0%
+looks like this way it's it's a narrow
+object it is in fact uh a mirror image
+
+ align:start position:0%
+object it is in fact uh a mirror image
+ 
+
+ align:start position:0%
+object it is in fact uh a mirror image
+reflection but it looks different when
+
+ align:start position:0%
+reflection but it looks different when
+ 
+
+ align:start position:0%
+reflection but it looks different when
+you go to this angle and it looks
+
+ align:start position:0%
+you go to this angle and it looks
+ 
+
+ align:start position:0%
+you go to this angle and it looks
+different when you go to this angle so
+
+ align:start position:0%
+different when you go to this angle so
+ 
+
+ align:start position:0%
+different when you go to this angle so
+it's not an axis of symmetry that's a
+
+ align:start position:0%
+it's not an axis of symmetry that's a
+ 
+
+ align:start position:0%
+it's not an axis of symmetry that's a
+plane of symmetry and we're going to
+
+ align:start position:0%
+plane of symmetry and we're going to
+ 
+
+ align:start position:0%
+plane of symmetry and we're going to
+talk about that next so axes of symmetry
+
+ align:start position:0%
+talk about that next so axes of symmetry
+ 
+
+ align:start position:0%
+talk about that next so axes of symmetry
+the thing essentially looks the same at
+
+ align:start position:0%
+the thing essentially looks the same at
+ 
+
+ align:start position:0%
+the thing essentially looks the same at
+all orientations about that axis okay so
+
+ align:start position:0%
+all orientations about that axis okay so
+ 
+
+ align:start position:0%
+all orientations about that axis okay so
+but it is certainly it's dynamically
+
+ align:start position:0%
+but it is certainly it's dynamically
+ 
+
+ align:start position:0%
+but it is certainly it's dynamically
+balanced it it doesn't have every Mass
+
+ align:start position:0%
+balanced it it doesn't have every Mass
+ 
+
+ align:start position:0%
+balanced it it doesn't have every Mass
+bit here it balances one over there it
+
+ align:start position:0%
+bit here it balances one over there it
+ 
+
+ align:start position:0%
+bit here it balances one over there it
+doesn't wobble all right so that's a
+
+ align:start position:0%
+doesn't wobble all right so that's a
+ 
+
+ align:start position:0%
+doesn't wobble all right so that's a
+that's for sure true now keep in fact
+
+ align:start position:0%
+that's for sure true now keep in fact
+ 
+
+ align:start position:0%
+that's for sure true now keep in fact
+keep in
+
+ align:start position:0%
+keep in
+ 
+
+ align:start position:0%
+keep in
+mind that there exists an orthogonal a
+
+ align:start position:0%
+mind that there exists an orthogonal a
+ 
+
+ align:start position:0%
+mind that there exists an orthogonal a
+set of orthogonal
+
+ align:start position:0%
+set of orthogonal
+ 
+
+ align:start position:0%
+set of orthogonal
+axes so that means once you find one you
+
+ align:start position:0%
+axes so that means once you find one you
+ 
+
+ align:start position:0%
+axes so that means once you find one you
+know that the other two are
+
+ align:start position:0%
+know that the other two are
+ 
+
+ align:start position:0%
+know that the other two are
+perpendicular to it and perpendicular to
+
+ align:start position:0%
+perpendicular to it and perpendicular to
+ 
+
+ align:start position:0%
+perpendicular to it and perpendicular to
+each other so for this system what I've
+
+ align:start position:0%
+each other so for this system what I've
+ 
+
+ align:start position:0%
+each other so for this system what I've
+got X and Y here there has to be an X
+
+ align:start position:0%
+got X and Y here there has to be an X
+ 
+
+ align:start position:0%
+got X and Y here there has to be an X
+and Y perpendicular that that are the
+
+ align:start position:0%
+and Y perpendicular that that are the
+ 
+
+ align:start position:0%
+and Y perpendicular that that are the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+two and for because it's actually
+
+ align:start position:0%
+two and for because it's actually
+ 
+
+ align:start position:0%
+two and for because it's actually
+symmetric then where you put them you
+
+ align:start position:0%
+symmetric then where you put them you
+ 
+
+ align:start position:0%
+symmetric then where you put them you
+could just say it's these two these two
+
+ align:start position:0%
+could just say it's these two these two
+ 
+
+ align:start position:0%
+could just say it's these two these two
+these two doesn't matter you just have
+
+ align:start position:0%
+these two doesn't matter you just have
+ 
+
+ align:start position:0%
+these two doesn't matter you just have
+to decide where you're going to put them
+
+ align:start position:0%
+to decide where you're going to put them
+ 
+
+ align:start position:0%
+to decide where you're going to put them
+on the object they're all the
+
+ align:start position:0%
+on the object they're all the
+ 
+
+ align:start position:0%
+on the object they're all the
+same okay so for
+
+ align:start position:0%
+same okay so for
+ 
+
+ align:start position:0%
+same okay so for
+uh this axis of symmetry there's just
+
+ align:start position:0%
+uh this axis of symmetry there's just
+ 
+
+ align:start position:0%
+uh this axis of symmetry there's just
+two more they're going to be in the body
+
+ align:start position:0%
+two more they're going to be in the body
+ 
+
+ align:start position:0%
+two more they're going to be in the body
+perpendicular to the first now we're
+
+ align:start position:0%
+perpendicular to the first now we're
+ 
+
+ align:start position:0%
+perpendicular to the first now we're
+going to do it about G
+
+ align:start position:0%
+going to do it about G
+ 
+
+ align:start position:0%
+going to do it about G
+so the book uses G to talk about as a
+
+ align:start position:0%
+so the book uses G to talk about as a
+ 
+
+ align:start position:0%
+so the book uses G to talk about as a
+cent Center Mass I'll use G so the
+
+ align:start position:0%
+cent Center Mass I'll use G so the
+ 
+
+ align:start position:0%
+cent Center Mass I'll use G so the
+center mass of this thing is is right in
+
+ align:start position:0%
+center mass of this thing is is right in
+ 
+
+ align:start position:0%
+center mass of this thing is is right in
+the middle of this and in the middle
+
+ align:start position:0%
+the middle of this and in the middle
+ 
+
+ align:start position:0%
+the middle of this and in the middle
+here so it's
+
+ align:start position:0%
+here so it's
+ 
+
+ align:start position:0%
+here so it's
+inside this body right in the dead
+
+ align:start position:0%
+inside this body right in the dead
+ 
+
+ align:start position:0%
+inside this body right in the dead
+center of it right okay so the pr
+
+ align:start position:0%
+center of it right okay so the pr
+ 
+
+ align:start position:0%
+center of it right okay so the pr
+principal axes are an orthogonal set one
+
+ align:start position:0%
+principal axes are an orthogonal set one
+ 
+
+ align:start position:0%
+principal axes are an orthogonal set one
+of which goes through it the other two
+
+ align:start position:0%
+of which goes through it the other two
+ 
+
+ align:start position:0%
+of which goes through it the other two
+are embedded in it at right angles so if
+
+ align:start position:0%
+are embedded in it at right angles so if
+ 
+
+ align:start position:0%
+are embedded in it at right angles so if
+you have this is the simplest rule if
+
+ align:start position:0%
+you have this is the simplest rule if
+ 
+
+ align:start position:0%
+you have this is the simplest rule if
+you have an axis of symmetry you know
+
+ align:start position:0%
+you have an axis of symmetry you know
+ 
+
+ align:start position:0%
+you have an axis of symmetry you know
+right away just about everything you
+
+ align:start position:0%
+right away just about everything you
+ 
+
+ align:start position:0%
+right away just about everything you
+need to know about the principal axes of
+
+ align:start position:0%
+need to know about the principal axes of
+ 
+
+ align:start position:0%
+need to know about the principal axes of
+the body um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shoot only symmetry in objects that are
+
+ align:start position:0%
+shoot only symmetry in objects that are
+ 
+
+ align:start position:0%
+shoot only symmetry in objects that are
+either round or spherical is that pretty
+
+ align:start position:0%
+either round or spherical is that pretty
+ 
+
+ align:start position:0%
+either round or spherical is that pretty
+much okay so it's very limited special
+
+ align:start position:0%
+much okay so it's very limited special
+ 
+
+ align:start position:0%
+much okay so it's very limited special
+case yeah but they sure appear an awful
+
+ align:start position:0%
+case yeah but they sure appear an awful
+ 
+
+ align:start position:0%
+case yeah but they sure appear an awful
+lot in machines because they have this
+
+ align:start position:0%
+lot in machines because they have this
+ 
+
+ align:start position:0%
+lot in machines because they have this
+beautiful property of just being
+
+ align:start position:0%
+beautiful property of just being
+ 
+
+ align:start position:0%
+beautiful property of just being
+balanced in all
+
+ align:start position:0%
+balanced in all
+ 
+
+ align:start position:0%
+balanced in all
+directions okay so everything rotating
+
+ align:start position:0%
+directions okay so everything rotating
+ 
+
+ align:start position:0%
+directions okay so everything rotating
+in the world tends to have almost
+
+ align:start position:0%
+in the world tends to have almost
+ 
+
+ align:start position:0%
+in the world tends to have almost
+perfect axial
+
+ align:start position:0%
+perfect axial
+ 
+
+ align:start position:0%
+perfect axial
+symmetry okay
+
+ align:start position:0%
+symmetry okay
+ 
+
+ align:start position:0%
+symmetry okay
+um just thinking about order here Let's
+
+ align:start position:0%
+um just thinking about order here Let's
+ 
+
+ align:start position:0%
+um just thinking about order here Let's
+do let's do this and then I'm going to
+
+ align:start position:0%
+do let's do this and then I'm going to
+ 
+
+ align:start position:0%
+do let's do this and then I'm going to
+go do a couple of examples the second
+
+ align:start position:0%
+go do a couple of examples the second
+ 
+
+ align:start position:0%
+go do a couple of examples the second
+rule if you have one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+plane of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry okay what a plane of symmetry
+
+ align:start position:0%
+symmetry okay what a plane of symmetry
+ 
+
+ align:start position:0%
+symmetry okay what a plane of symmetry
+so this kind of the simp the opposite
+
+ align:start position:0%
+so this kind of the simp the opposite
+ 
+
+ align:start position:0%
+so this kind of the simp the opposite
+direction this you have the least
+
+ align:start position:0%
+direction this you have the least
+ 
+
+ align:start position:0%
+direction this you have the least
+information here's an object does it
+
+ align:start position:0%
+information here's an object does it
+ 
+
+ align:start position:0%
+information here's an object does it
+have a plane of
+
+ align:start position:0%
+have a plane of
+ 
+
+ align:start position:0%
+have a plane of
+symmetry where Straight middle show
+
+ align:start position:0%
+symmetry where Straight middle show
+ 
+
+ align:start position:0%
+symmetry where Straight middle show
+me that cut all right so I've got the
+
+ align:start position:0%
+me that cut all right so I've got the
+ 
+
+ align:start position:0%
+me that cut all right so I've got the
+little dotted marks on this thing so if
+
+ align:start position:0%
+little dotted marks on this thing so if
+ 
+
+ align:start position:0%
+little dotted marks on this thing so if
+I cut if I slice through that I create
+
+ align:start position:0%
+I cut if I slice through that I create
+ 
+
+ align:start position:0%
+I cut if I slice through that I create
+two pieces that are identical so that's
+
+ align:start position:0%
+two pieces that are identical so that's
+ 
+
+ align:start position:0%
+two pieces that are identical so that's
+a plane of symmetry there's image match
+
+ align:start position:0%
+a plane of symmetry there's image match
+ 
+
+ align:start position:0%
+a plane of symmetry there's image match
+across that plane at every Point
+
+ align:start position:0%
+across that plane at every Point
+ 
+
+ align:start position:0%
+across that plane at every Point
+okay so if I have a plane of symmetry
+
+ align:start position:0%
+okay so if I have a plane of symmetry
+ 
+
+ align:start position:0%
+okay so if I have a plane of symmetry
+what do you think you can say about a
+
+ align:start position:0%
+what do you think you can say about a
+ 
+
+ align:start position:0%
+what do you think you can say about a
+principal axis one of the principal axes
+
+ align:start position:0%
+principal axis one of the principal axes
+ 
+
+ align:start position:0%
+principal axis one of the principal axes
+it will be on that it'll be on that
+
+ align:start position:0%
+it will be on that it'll be on that
+ 
+
+ align:start position:0%
+it will be on that it'll be on that
+plane that turns out to be true but
+
+ align:start position:0%
+plane that turns out to be true but
+ 
+
+ align:start position:0%
+plane that turns out to be true but
+that's the second point I want to make
+
+ align:start position:0%
+that's the second point I want to make
+ 
+
+ align:start position:0%
+that's the second point I want to make
+it might be perpendicular she says it
+
+ align:start position:0%
+it might be perpendicular she says it
+ 
+
+ align:start position:0%
+it might be perpendicular she says it
+might be there might be one
+
+ align:start position:0%
+might be there might be one
+ 
+
+ align:start position:0%
+might be there might be one
+perpendicular to it and that's the one I
+
+ align:start position:0%
+perpendicular to it and that's the one I
+ 
+
+ align:start position:0%
+perpendicular to it and that's the one I
+was searching for you're right too okay
+
+ align:start position:0%
+was searching for you're right too okay
+ 
+
+ align:start position:0%
+was searching for you're right too okay
+there's going to be an axis a principal
+
+ align:start position:0%
+there's going to be an axis a principal
+ 
+
+ align:start position:0%
+there's going to be an axis a principal
+axis that's perpendicular to that plane
+
+ align:start position:0%
+axis that's perpendicular to that plane
+ 
+
+ align:start position:0%
+axis that's perpendicular to that plane
+of symmetry and since we want to Define
+
+ align:start position:0%
+of symmetry and since we want to Define
+ 
+
+ align:start position:0%
+of symmetry and since we want to Define
+our moments of inertia for this to start
+
+ align:start position:0%
+our moments of inertia for this to start
+ 
+
+ align:start position:0%
+our moments of inertia for this to start
+with with respect to G where will it
+
+ align:start position:0%
+with with respect to G where will it
+ 
+
+ align:start position:0%
+with with respect to G where will it
+pass through g g okay kind of by
+
+ align:start position:0%
+pass through g g okay kind of by
+ 
+
+ align:start position:0%
+pass through g g okay kind of by
+definition so we're going to have it
+
+ align:start position:0%
+definition so we're going to have it
+ 
+
+ align:start position:0%
+definition so we're going to have it
+pass through G if there's a plane of
+
+ align:start position:0%
+pass through G if there's a plane of
+ 
+
+ align:start position:0%
+pass through G if there's a plane of
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+uh then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a principal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis perpendicular to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and we'll Define it for the purposes
+
+ align:start position:0%
+it and we'll Define it for the purposes
+ 
+
+ align:start position:0%
+it and we'll Define it for the purposes
+of our discussion
+
+ align:start position:0%
+of our discussion
+ 
+
+ align:start position:0%
+of our discussion
+we'll we'll just let it pass through G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so doesn't have to but that's how we're
+
+ align:start position:0%
+so doesn't have to but that's how we're
+ 
+
+ align:start position:0%
+so doesn't have to but that's how we're
+going about this discussion let it pass
+
+ align:start position:0%
+going about this discussion let it pass
+ 
+
+ align:start position:0%
+going about this discussion let it pass
+through the center of mass this point we
+
+ align:start position:0%
+through the center of mass this point we
+ 
+
+ align:start position:0%
+through the center of mass this point we
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+G all right all right so that means that
+
+ align:start position:0%
+G all right all right so that means that
+ 
+
+ align:start position:0%
+G all right all right so that means that
+there's a point there's a center there's
+
+ align:start position:0%
+there's a point there's a center there's
+ 
+
+ align:start position:0%
+there's a point there's a center there's
+a center of mass in this
+
+ align:start position:0%
+a center of mass in this
+ 
+
+ align:start position:0%
+a center of mass in this
+thing and I'm just guessing roughly
+
+ align:start position:0%
+thing and I'm just guessing roughly
+ 
+
+ align:start position:0%
+thing and I'm just guessing roughly
+where it is but in fact you know if I
+
+ align:start position:0%
+where it is but in fact you know if I
+ 
+
+ align:start position:0%
+where it is but in fact you know if I
+hung this thing up here like this
+
+ align:start position:0%
+hung this thing up here like this
+ 
+
+ align:start position:0%
+hung this thing up here like this
+and let gravity find its find its uh
+
+ align:start position:0%
+and let gravity find its find its uh
+ 
+
+ align:start position:0%
+and let gravity find its find its uh
+natural hanging angle and I drew a plum
+
+ align:start position:0%
+natural hanging angle and I drew a plum
+ 
+
+ align:start position:0%
+natural hanging angle and I drew a plum
+line down here and just drew a line
+
+ align:start position:0%
+line down here and just drew a line
+ 
+
+ align:start position:0%
+line down here and just drew a line
+that's the that that the string would
+
+ align:start position:0%
+that's the that that the string would
+ 
+
+ align:start position:0%
+that's the that that the string would
+take with a plum Bob then I went to some
+
+ align:start position:0%
+take with a plum Bob then I went to some
+ 
+
+ align:start position:0%
+take with a plum Bob then I went to some
+other point and did it again and hung a
+
+ align:start position:0%
+other point and did it again and hung a
+ 
+
+ align:start position:0%
+other point and did it again and hung a
+plum Bob on it and Drew the line where
+
+ align:start position:0%
+plum Bob on it and Drew the line where
+ 
+
+ align:start position:0%
+plum Bob on it and Drew the line where
+the intersect is Center of mass okay
+
+ align:start position:0%
+the intersect is Center of mass okay
+ 
+
+ align:start position:0%
+the intersect is Center of mass okay
+then you know since it's got symmetry
+
+ align:start position:0%
+then you know since it's got symmetry
+ 
+
+ align:start position:0%
+then you know since it's got symmetry
+this way that it's in the middle so I
+
+ align:start position:0%
+this way that it's in the middle so I
+ 
+
+ align:start position:0%
+this way that it's in the middle so I
+guessed that that's about where it is
+
+ align:start position:0%
+guessed that that's about where it is
+ 
+
+ align:start position:0%
+guessed that that's about where it is
+and there then is a a principal axis of
+
+ align:start position:0%
+and there then is a a principal axis of
+ 
+
+ align:start position:0%
+and there then is a a principal axis of
+this object that passes that's
+
+ align:start position:0%
+this object that passes that's
+ 
+
+ align:start position:0%
+this object that passes that's
+perpendicular to it P passing through
+
+ align:start position:0%
+perpendicular to it P passing through
+ 
+
+ align:start position:0%
+perpendicular to it P passing through
+the plane perpendicular to the plane and
+
+ align:start position:0%
+the plane perpendicular to the plane and
+ 
+
+ align:start position:0%
+the plane perpendicular to the plane and
+that means now there's two more that
+
+ align:start position:0%
+that means now there's two more that
+ 
+
+ align:start position:0%
+that means now there's two more that
+this gets a little more difficult and I
+
+ align:start position:0%
+this gets a little more difficult and I
+ 
+
+ align:start position:0%
+this gets a little more difficult and I
+I don't I have no
+
+ align:start position:0%
+I don't I have no
+ 
+
+ align:start position:0%
+I don't I have no
+clue there are two more because the
+
+ align:start position:0%
+clue there are two more because the
+ 
+
+ align:start position:0%
+clue there are two more because the
+principal axes are always coming in
+
+ align:start position:0%
+principal axes are always coming in
+ 
+
+ align:start position:0%
+principal axes are always coming in
+orthogonal set so now that I know one I
+
+ align:start position:0%
+orthogonal set so now that I know one I
+ 
+
+ align:start position:0%
+orthogonal set so now that I know one I
+know that there's two more
+
+ align:start position:0%
+know that there's two more
+ 
+
+ align:start position:0%
+know that there's two more
+somewhere around mounted you know
+
+ align:start position:0%
+somewhere around mounted you know
+ 
+
+ align:start position:0%
+somewhere around mounted you know
+oriented with this way someplace in this
+
+ align:start position:0%
+oriented with this way someplace in this
+ 
+
+ align:start position:0%
+oriented with this way someplace in this
+plane you know maybe one like that maybe
+
+ align:start position:0%
+plane you know maybe one like that maybe
+ 
+
+ align:start position:0%
+plane you know maybe one like that maybe
+one like like this such that if you spun
+
+ align:start position:0%
+one like like this such that if you spun
+ 
+
+ align:start position:0%
+one like like this such that if you spun
+it about one of those axes it would be
+
+ align:start position:0%
+it about one of those axes it would be
+ 
+
+ align:start position:0%
+it about one of those axes it would be
+inbalance and you can see that gets a
+
+ align:start position:0%
+inbalance and you can see that gets a
+ 
+
+ align:start position:0%
+inbalance and you can see that gets a
+little messy I can't guess where it
+
+ align:start position:0%
+little messy I can't guess where it
+ 
+
+ align:start position:0%
+little messy I can't guess where it
+is and so there are ways to find it one
+
+ align:start position:0%
+is and so there are ways to find it one
+ 
+
+ align:start position:0%
+is and so there are ways to find it one
+of them would be doing an experiment
+
+ align:start position:0%
+of them would be doing an experiment
+ 
+
+ align:start position:0%
+of them would be doing an experiment
+seeing which axis it spins nicely around
+
+ align:start position:0%
+seeing which axis it spins nicely around
+ 
+
+ align:start position:0%
+seeing which axis it spins nicely around
+so that's the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule but even just with that one plane
+
+ align:start position:0%
+rule but even just with that one plane
+ 
+
+ align:start position:0%
+rule but even just with that one plane
+of symmetry that's you you get some
+
+ align:start position:0%
+of symmetry that's you you get some
+ 
+
+ align:start position:0%
+of symmetry that's you you get some
+pretty good Insight okay now what if
+
+ align:start position:0%
+pretty good Insight okay now what if
+ 
+
+ align:start position:0%
+pretty good Insight okay now what if
+there are two planes of symmetry
+
+ align:start position:0%
+there are two planes of symmetry
+ 
+
+ align:start position:0%
+there are two planes of symmetry
+yeah um you said that your principal
+
+ align:start position:0%
+yeah um you said that your principal
+ 
+
+ align:start position:0%
+yeah um you said that your principal
+access does not have to pass through the
+
+ align:start position:0%
+access does not have to pass through the
+ 
+
+ align:start position:0%
+access does not have to pass through the
+center of mass no we're she asked about
+
+ align:start position:0%
+center of mass no we're she asked about
+ 
+
+ align:start position:0%
+center of mass no we're she asked about
+about I'm saying it doesn't have to pass
+
+ align:start position:0%
+about I'm saying it doesn't have to pass
+ 
+
+ align:start position:0%
+about I'm saying it doesn't have to pass
+through the center of mass the question
+
+ align:start position:0%
+through the center of mass the question
+ 
+
+ align:start position:0%
+through the center of mass the question
+is um how could it not because it' be
+
+ align:start position:0%
+is um how could it not because it' be
+ 
+
+ align:start position:0%
+is um how could it not because it' be
+unstable so she's saying it'd be
+
+ align:start position:0%
+unstable so she's saying it'd be
+ 
+
+ align:start position:0%
+unstable so she's saying it'd be
+unstable if it's not passing through
+
+ align:start position:0%
+unstable if it's not passing through
+ 
+
+ align:start position:0%
+unstable if it's not passing through
+there like if I put an axle through this
+
+ align:start position:0%
+there like if I put an axle through this
+ 
+
+ align:start position:0%
+there like if I put an axle through this
+wheel and I spun it about some point out
+
+ align:start position:0%
+wheel and I spun it about some point out
+ 
+
+ align:start position:0%
+wheel and I spun it about some point out
+here we you know cuz I had that Shaker
+
+ align:start position:0%
+here we you know cuz I had that Shaker
+ 
+
+ align:start position:0%
+here we you know cuz I had that Shaker
+in here that thing is going to shake
+
+ align:start position:0%
+in here that thing is going to shake
+ 
+
+ align:start position:0%
+in here that thing is going to shake
+like crazy right but it does it produce
+
+ align:start position:0%
+like crazy right but it does it produce
+ 
+
+ align:start position:0%
+like crazy right but it does it produce
+unbalance torqus about my rotation
+
+ align:start position:0%
+unbalance torqus about my rotation
+ 
+
+ align:start position:0%
+unbalance torqus about my rotation
+Point it'll produce a centrifugal force
+
+ align:start position:0%
+Point it'll produce a centrifugal force
+ 
+
+ align:start position:0%
+Point it'll produce a centrifugal force
+that you'll feel like crazy but does it
+
+ align:start position:0%
+that you'll feel like crazy but does it
+ 
+
+ align:start position:0%
+that you'll feel like crazy but does it
+produce a torque trying to that you'd
+
+ align:start position:0%
+produce a torque trying to that you'd
+ 
+
+ align:start position:0%
+produce a torque trying to that you'd
+have to resist with some static
+
+ align:start position:0%
+have to resist with some static
+ 
+
+ align:start position:0%
+have to resist with some static
+torque what do you
+
+ align:start position:0%
+torque what do you
+ 
+
+ align:start position:0%
+torque what do you
+think it won't so there's a new one to
+
+ align:start position:0%
+think it won't so there's a new one to
+ 
+
+ align:start position:0%
+think it won't so there's a new one to
+this unbalanced thing and I was going to
+
+ align:start position:0%
+this unbalanced thing and I was going to
+ 
+
+ align:start position:0%
+this unbalanced thing and I was going to
+get to it probably next lecture but and
+
+ align:start position:0%
+get to it probably next lecture but and
+ 
+
+ align:start position:0%
+get to it probably next lecture but and
+that is that when we say an object is
+
+ align:start position:0%
+that is that when we say an object is
+ 
+
+ align:start position:0%
+that is that when we say an object is
+dynamically balanced we mean that it
+
+ align:start position:0%
+dynamically balanced we mean that it
+ 
+
+ align:start position:0%
+dynamically balanced we mean that it
+doesn't have any unbalanced
+
+ align:start position:0%
+doesn't have any unbalanced
+ 
+
+ align:start position:0%
+doesn't have any unbalanced
+torqus if we if it is statically
+
+ align:start position:0%
+torqus if we if it is statically
+ 
+
+ align:start position:0%
+torqus if we if it is statically
+balanced it
+
+ align:start position:0%
+balanced it
+ 
+
+ align:start position:0%
+balanced it
+doesn't it's rotating about its Center
+
+ align:start position:0%
+doesn't it's rotating about its Center
+ 
+
+ align:start position:0%
+doesn't it's rotating about its Center
+of mass but you can be statically
+
+ align:start position:0%
+of mass but you can be statically
+ 
+
+ align:start position:0%
+of mass but you can be statically
+unbalanced and let it go around this
+
+ align:start position:0%
+unbalanced and let it go around this
+ 
+
+ align:start position:0%
+unbalanced and let it go around this
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+but it'll produce no torqus it's still
+
+ align:start position:0%
+but it'll produce no torqus it's still
+ 
+
+ align:start position:0%
+but it'll produce no torqus it's still
+dynamically balanced and the angular
+
+ align:start position:0%
+dynamically balanced and the angular
+ 
+
+ align:start position:0%
+dynamically balanced and the angular
+momentum of an object which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotating this we know has a principal
+
+ align:start position:0%
+rotating this we know has a principal
+ 
+
+ align:start position:0%
+rotating this we know has a principal
+axis here I just moved it off to the
+
+ align:start position:0%
+axis here I just moved it off to the
+ 
+
+ align:start position:0%
+axis here I just moved it off to the
+side it's rotating about
+
+ align:start position:0%
+side it's rotating about
+ 
+
+ align:start position:0%
+side it's rotating about
+this um it is dynamically balanced and
+
+ align:start position:0%
+this um it is dynamically balanced and
+ 
+
+ align:start position:0%
+this um it is dynamically balanced and
+if you computed the off D about this
+
+ align:start position:0%
+if you computed the off D about this
+ 
+
+ align:start position:0%
+if you computed the off D about this
+point now the IX y ixz off
+
+ align:start position:0%
+point now the IX y ixz off
+ 
+
+ align:start position:0%
+point now the IX y ixz off
+diagonal entries in that moment of
+
+ align:start position:0%
+diagonal entries in that moment of
+ 
+
+ align:start position:0%
+diagonal entries in that moment of
+inertia Matrix they're all
+
+ align:start position:0%
+inertia Matrix they're all
+ 
+
+ align:start position:0%
+inertia Matrix they're all
+zero you'd get no Tor no unbalanced
+
+ align:start position:0%
+zero you'd get no Tor no unbalanced
+ 
+
+ align:start position:0%
+zero you'd get no Tor no unbalanced
+torqu but you do have an unbalanced
+
+ align:start position:0%
+torqu but you do have an unbalanced
+ 
+
+ align:start position:0%
+torqu but you do have an unbalanced
+centrifugal force as this thing goes
+
+ align:start position:0%
+centrifugal force as this thing goes
+ 
+
+ align:start position:0%
+centrifugal force as this thing goes
+around we'll talk a little bit more is
+
+ align:start position:0%
+around we'll talk a little bit more is
+ 
+
+ align:start position:0%
+around we'll talk a little bit more is
+that sort of analogous to the homework
+
+ align:start position:0%
+that sort of analogous to the homework
+ 
+
+ align:start position:0%
+that sort of analogous to the homework
+problem we had if you keep this back
+
+ align:start position:0%
+problem we had if you keep this back
+ 
+
+ align:start position:0%
+problem we had if you keep this back
+with the um motorcycle wheel and you
+
+ align:start position:0%
+with the um motorcycle wheel and you
+ 
+
+ align:start position:0%
+with the um motorcycle wheel and you
+just had a MTH on one
+
+ align:start position:0%
+just had a MTH on one
+ 
+
+ align:start position:0%
+just had a MTH on one
+side right so she's asking about the
+
+ align:start position:0%
+side right so she's asking about the
+ 
+
+ align:start position:0%
+side right so she's asking about the
+motorcycle wheel problem where we had
+
+ align:start position:0%
+motorcycle wheel problem where we had
+ 
+
+ align:start position:0%
+motorcycle wheel problem where we had
+that little Mass stuck out there I think
+
+ align:start position:0%
+that little Mass stuck out there I think
+ 
+
+ align:start position:0%
+that little Mass stuck out there I think
+in the next lecture I'm going to bring
+
+ align:start position:0%
+in the next lecture I'm going to bring
+ 
+
+ align:start position:0%
+in the next lecture I'm going to bring
+I'm going to come back to that problem
+
+ align:start position:0%
+I'm going to come back to that problem
+ 
+
+ align:start position:0%
+I'm going to come back to that problem
+just so that we can tie a bow around
+
+ align:start position:0%
+just so that we can tie a bow around
+ 
+
+ align:start position:0%
+just so that we can tie a bow around
+this whole thing and understand how uh
+
+ align:start position:0%
+this whole thing and understand how uh
+ 
+
+ align:start position:0%
+this whole thing and understand how uh
+how you why it's unbalanced how you can
+
+ align:start position:0%
+how you why it's unbalanced how you can
+ 
+
+ align:start position:0%
+how you why it's unbalanced how you can
+balance it and the difference between
+
+ align:start position:0%
+balance it and the difference between
+ 
+
+ align:start position:0%
+balance it and the difference between
+static unbalance and dynamic unbalance
+
+ align:start position:0%
+static unbalance and dynamic unbalance
+ 
+
+ align:start position:0%
+static unbalance and dynamic unbalance
+but today we're talking about symmetry
+
+ align:start position:0%
+but today we're talking about symmetry
+ 
+
+ align:start position:0%
+but today we're talking about symmetry
+rules
+
+ align:start position:0%
+rules
+ 
+
+ align:start position:0%
+rules
+okay finally so I was saying let's talk
+
+ align:start position:0%
+okay finally so I was saying let's talk
+ 
+
+ align:start position:0%
+okay finally so I was saying let's talk
+about something that has two planes of
+
+ align:start position:0%
+about something that has two planes of
+ 
+
+ align:start position:0%
+about something that has two planes of
+symmetry this actually has three ples of
+
+ align:start position:0%
+symmetry this actually has three ples of
+ 
+
+ align:start position:0%
+symmetry this actually has three ples of
+symmetry but we'll settle for two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane of where where's a where's pick
+
+ align:start position:0%
+plane of where where's a where's pick
+ 
+
+ align:start position:0%
+plane of where where's a where's pick
+pick a plane of symmetry for this object
+
+ align:start position:0%
+pick a plane of symmetry for this object
+ 
+
+ align:start position:0%
+pick a plane of symmetry for this object
+if I okay she picks the one slice it
+
+ align:start position:0%
+if I okay she picks the one slice it
+ 
+
+ align:start position:0%
+if I okay she picks the one slice it
+this way all right that's a plan of
+
+ align:start position:0%
+this way all right that's a plan of
+ 
+
+ align:start position:0%
+this way all right that's a plan of
+symmetry do I have do I have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second like that okay and a third right
+
+ align:start position:0%
+second like that okay and a third right
+ 
+
+ align:start position:0%
+second like that okay and a third right
+there's even one like that so this has
+
+ align:start position:0%
+there's even one like that so this has
+ 
+
+ align:start position:0%
+there's even one like that so this has
+three planes of symmetry but if you have
+
+ align:start position:0%
+three planes of symmetry but if you have
+ 
+
+ align:start position:0%
+three planes of symmetry but if you have
+two planes of
+
+ align:start position:0%
+two planes of
+ 
+
+ align:start position:0%
+two planes of
+symmetry that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersect that are orthogonal to one
+
+ align:start position:0%
+intersect that are orthogonal to one
+ 
+
+ align:start position:0%
+intersect that are orthogonal to one
+another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you think you can say about that
+
+ align:start position:0%
+what do you think you can say about that
+ 
+
+ align:start position:0%
+what do you think you can say about that
+line of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersection you and it it sure is and
+
+ align:start position:0%
+intersection you and it it sure is and
+ 
+
+ align:start position:0%
+intersection you and it it sure is and
+it's probably right through
+
+ align:start position:0%
+it's probably right through
+ 
+
+ align:start position:0%
+it's probably right through
+G okay so if you have two uh planes of
+
+ align:start position:0%
+G okay so if you have two uh planes of
+ 
+
+ align:start position:0%
+G okay so if you have two uh planes of
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll make them orthogonal you can
+
+ align:start position:0%
+and I'll make them orthogonal you can
+ 
+
+ align:start position:0%
+and I'll make them orthogonal you can
+make all sorts of symmetry rules and I'm
+
+ align:start position:0%
+make all sorts of symmetry rules and I'm
+ 
+
+ align:start position:0%
+make all sorts of symmetry rules and I'm
+just picking these three to make to to
+
+ align:start position:0%
+just picking these three to make to to
+ 
+
+ align:start position:0%
+just picking these three to make to to
+help you out this just to help you see
+
+ align:start position:0%
+help you out this just to help you see
+ 
+
+ align:start position:0%
+help you out this just to help you see
+uh principal axes if you have two
+
+ align:start position:0%
+uh principal axes if you have two
+ 
+
+ align:start position:0%
+uh principal axes if you have two
+orthogonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planes of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+their intersection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and once you know
+
+ align:start position:0%
+and once you know
+ 
+
+ align:start position:0%
+and once you know
+that then you go back to rule two and it
+
+ align:start position:0%
+that then you go back to rule two and it
+ 
+
+ align:start position:0%
+that then you go back to rule two and it
+tells you everything else you need to
+
+ align:start position:0%
+tells you everything else you need to
+ 
+
+ align:start position:0%
+tells you everything else you need to
+know because you have one plan of
+
+ align:start position:0%
+know because you have one plan of
+ 
+
+ align:start position:0%
+know because you have one plan of
+symmetry you know that there is an a
+
+ align:start position:0%
+symmetry you know that there is an a
+ 
+
+ align:start position:0%
+symmetry you know that there is an a
+principal
+
+ align:start position:0%
+principal
+ 
+
+ align:start position:0%
+principal
+axis perpendicular to it well if you
+
+ align:start position:0%
+axis perpendicular to it well if you
+ 
+
+ align:start position:0%
+axis perpendicular to it well if you
+have two planes of symmetry rules still
+
+ align:start position:0%
+have two planes of symmetry rules still
+ 
+
+ align:start position:0%
+have two planes of symmetry rules still
+hold there's one perpendicular to each
+
+ align:start position:0%
+hold there's one perpendicular to each
+ 
+
+ align:start position:0%
+hold there's one perpendicular to each
+one the intersection let's say of this
+
+ align:start position:0%
+one the intersection let's say of this
+ 
+
+ align:start position:0%
+one the intersection let's say of this
+plane of symmetry and this plane of
+
+ align:start position:0%
+plane of symmetry and this plane of
+ 
+
+ align:start position:0%
+plane of symmetry and this plane of
+symmetry is a line which goes right
+
+ align:start position:0%
+symmetry is a line which goes right
+ 
+
+ align:start position:0%
+symmetry is a line which goes right
+through dead through the center of this
+
+ align:start position:0%
+through dead through the center of this
+ 
+
+ align:start position:0%
+through dead through the center of this
+thing that way so there's a principal
+
+ align:start position:0%
+thing that way so there's a principal
+ 
+
+ align:start position:0%
+thing that way so there's a principal
+axis this way but since there is a plane
+
+ align:start position:0%
+axis this way but since there is a plane
+ 
+
+ align:start position:0%
+axis this way but since there is a plane
+of symmetry here there must also be a
+
+ align:start position:0%
+of symmetry here there must also be a
+ 
+
+ align:start position:0%
+of symmetry here there must also be a
+principal axis perpendicular to it so
+
+ align:start position:0%
+principal axis perpendicular to it so
+ 
+
+ align:start position:0%
+principal axis perpendicular to it so
+sure enough The three principal axes for
+
+ align:start position:0%
+sure enough The three principal axes for
+ 
+
+ align:start position:0%
+sure enough The three principal axes for
+this thing are through the
+
+ align:start position:0%
+this thing are through the
+ 
+
+ align:start position:0%
+this thing are through the
+center per perpendicular this way
+
+ align:start position:0%
+center per perpendicular this way
+ 
+
+ align:start position:0%
+center per perpendicular this way
+perpendicular that way you instantly
+
+ align:start position:0%
+perpendicular that way you instantly
+ 
+
+ align:start position:0%
+perpendicular that way you instantly
+know two planes of symmetry you
+
+ align:start position:0%
+know two planes of symmetry you
+ 
+
+ align:start position:0%
+know two planes of symmetry you
+instantly know where the three
+
+ align:start position:0%
+instantly know where the three
+ 
+
+ align:start position:0%
+instantly know where the three
+orthogonal principal axes are that pass
+
+ align:start position:0%
+orthogonal principal axes are that pass
+ 
+
+ align:start position:0%
+orthogonal principal axes are that pass
+through the center of mass okay
+
+ align:start position:0%
+through the center of mass okay
+ 
+
+ align:start position:0%
+through the center of mass okay
+yeah constant Mass not
+
+ align:start position:0%
+yeah constant Mass not
+ 
+
+ align:start position:0%
+yeah constant Mass not
+constant symmetrically I symmetrically
+
+ align:start position:0%
+constant symmetrically I symmetrically
+ 
+
+ align:start position:0%
+constant symmetrically I symmetrically
+distributed
+
+ align:start position:0%
+distributed
+ 
+
+ align:start position:0%
+distributed
+density all right so I want what I'm
+
+ align:start position:0%
+density all right so I want what I'm
+ 
+
+ align:start position:0%
+density all right so I want what I'm
+trying to I'm choosing my words
+
+ align:start position:0%
+trying to I'm choosing my words
+ 
+
+ align:start position:0%
+trying to I'm choosing my words
+carefully so that I succeed in the
+
+ align:start position:0%
+carefully so that I succeed in the
+ 
+
+ align:start position:0%
+carefully so that I succeed in the
+following that the planes defining Mass
+
+ align:start position:0%
+following that the planes defining Mass
+ 
+
+ align:start position:0%
+following that the planes defining Mass
+symmetry will be the same as the planes
+
+ align:start position:0%
+symmetry will be the same as the planes
+ 
+
+ align:start position:0%
+symmetry will be the same as the planes
+defining geometric similarity but you
+
+ align:start position:0%
+defining geometric similarity but you
+ 
+
+ align:start position:0%
+defining geometric similarity but you
+actually don't have to have constant
+
+ align:start position:0%
+actually don't have to have constant
+ 
+
+ align:start position:0%
+actually don't have to have constant
+density it just has to be distributed so
+
+ align:start position:0%
+density it just has to be distributed so
+ 
+
+ align:start position:0%
+density it just has to be distributed so
+that what I just said is true so that
+
+ align:start position:0%
+that what I just said is true so that
+ 
+
+ align:start position:0%
+that what I just said is true so that
+the geometric symmetries are the same as
+
+ align:start position:0%
+the geometric symmetries are the same as
+ 
+
+ align:start position:0%
+the geometric symmetries are the same as
+the mass distribution
+
+ align:start position:0%
+the mass distribution
+ 
+
+ align:start position:0%
+the mass distribution
+symmetries all right so those are my
+
+ align:start position:0%
+symmetries all right so those are my
+ 
+
+ align:start position:0%
+symmetries all right so those are my
+three rules of symmetry you could make
+
+ align:start position:0%
+three rules of symmetry you could make
+ 
+
+ align:start position:0%
+three rules of symmetry you could make
+up others those are three that I've made
+
+ align:start position:0%
+up others those are three that I've made
+ 
+
+ align:start position:0%
+up others those are three that I've made
+up to help you see objects um okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that object it's a circular
+
+ align:start position:0%
+that object it's a circular
+ 
+
+ align:start position:0%
+that object it's a circular
+disc put on top of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a of another object such their CG their
+
+ align:start position:0%
+a of another object such their CG their
+ 
+
+ align:start position:0%
+a of another object such their CG their
+centers of mass
+
+ align:start position:0%
+centers of mass
+ 
+
+ align:start position:0%
+centers of mass
+lineup where are the principal axes of
+
+ align:start position:0%
+lineup where are the principal axes of
+ 
+
+ align:start position:0%
+lineup where are the principal axes of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+object using those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules you think you know one tell me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M all right dead through the middle of
+
+ align:start position:0%
+M all right dead through the middle of
+ 
+
+ align:start position:0%
+M all right dead through the middle of
+both of them all right probably it's
+
+ align:start position:0%
+both of them all right probably it's
+ 
+
+ align:start position:0%
+both of them all right probably it's
+good guess how about another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one mean where are there planes where
+
+ align:start position:0%
+one mean where are there planes where
+ 
+
+ align:start position:0%
+one mean where are there planes where
+does this thing at planes of
+
+ align:start position:0%
+does this thing at planes of
+ 
+
+ align:start position:0%
+does this thing at planes of
+symmetry so there's a plan of symmetry
+
+ align:start position:0%
+symmetry so there's a plan of symmetry
+ 
+
+ align:start position:0%
+symmetry so there's a plan of symmetry
+cut half access if you cut
+
+ align:start position:0%
+cut half access if you cut
+ 
+
+ align:start position:0%
+cut half access if you cut
+half okay and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one like that we just we've got all
+
+ align:start position:0%
+and one like that we just we've got all
+ 
+
+ align:start position:0%
+and one like that we just we've got all
+three but and if we're going to want it
+
+ align:start position:0%
+three but and if we're going to want it
+ 
+
+ align:start position:0%
+three but and if we're going to want it
+to go through the center of mass and
+
+ align:start position:0%
+to go through the center of mass and
+ 
+
+ align:start position:0%
+to go through the center of mass and
+we're going to have to find where the
+
+ align:start position:0%
+we're going to have to find where the
+ 
+
+ align:start position:0%
+we're going to have to find where the
+center of mass is this way but it's you
+
+ align:start position:0%
+center of mass is this way but it's you
+ 
+
+ align:start position:0%
+center of mass is this way but it's you
+know about there let's say okay so just
+
+ align:start position:0%
+know about there let's say okay so just
+ 
+
+ align:start position:0%
+know about there let's say okay so just
+using these symmetry ideas you can write
+
+ align:start position:0%
+using these symmetry ideas you can write
+ 
+
+ align:start position:0%
+using these symmetry ideas you can write
+away figure out where these principal
+
+ align:start position:0%
+away figure out where these principal
+ 
+
+ align:start position:0%
+away figure out where these principal
+axes be and that means that from a
+
+ align:start position:0%
+axes be and that means that from a
+ 
+
+ align:start position:0%
+axes be and that means that from a
+dynamic point of view if you spin it
+
+ align:start position:0%
+dynamic point of view if you spin it
+ 
+
+ align:start position:0%
+dynamic point of view if you spin it
+about one of those ax axes it's nice and
+
+ align:start position:0%
+about one of those ax axes it's nice and
+ 
+
+ align:start position:0%
+about one of those ax axes it's nice and
+dynamically balanced if you spin it off
+
+ align:start position:0%
+dynamically balanced if you spin it off
+ 
+
+ align:start position:0%
+dynamically balanced if you spin it off
+in some other weird direction is it
+
+ align:start position:0%
+in some other weird direction is it
+ 
+
+ align:start position:0%
+in some other weird direction is it
+necessar thly dynamically balanced about
+
+ align:start position:0%
+necessar thly dynamically balanced about
+ 
+
+ align:start position:0%
+necessar thly dynamically balanced about
+that axis of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spin so let me restate that
+
+ align:start position:0%
+spin so let me restate that
+ 
+
+ align:start position:0%
+spin so let me restate that
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we know that this thing has an axis
+
+ align:start position:0%
+um we know that this thing has an axis
+ 
+
+ align:start position:0%
+um we know that this thing has an axis
+of symmetry a principal axis through the
+
+ align:start position:0%
+of symmetry a principal axis through the
+ 
+
+ align:start position:0%
+of symmetry a principal axis through the
+center there another one this way and
+
+ align:start position:0%
+center there another one this way and
+ 
+
+ align:start position:0%
+center there another one this way and
+another one this way and if I spin it
+
+ align:start position:0%
+another one this way and if I spin it
+ 
+
+ align:start position:0%
+another one this way and if I spin it
+about any one of those it's dynamically
+
+ align:start position:0%
+about any one of those it's dynamically
+ 
+
+ align:start position:0%
+about any one of those it's dynamically
+balanced but if I pick some other
+
+ align:start position:0%
+balanced but if I pick some other
+ 
+
+ align:start position:0%
+balanced but if I pick some other
+strange direction for the spin and I
+
+ align:start position:0%
+strange direction for the spin and I
+ 
+
+ align:start position:0%
+strange direction for the spin and I
+spin it about that axis will I feel
+
+ align:start position:0%
+spin it about that axis will I feel
+ 
+
+ align:start position:0%
+spin it about that axis will I feel
+unbalanced torqus on this axle on the
+
+ align:start position:0%
+unbalanced torqus on this axle on the
+ 
+
+ align:start position:0%
+unbalanced torqus on this axle on the
+bearings having to hold this thing in
+
+ align:start position:0%
+bearings having to hold this thing in
+ 
+
+ align:start position:0%
+bearings having to hold this thing in
+place yeah you better believe it this
+
+ align:start position:0%
+place yeah you better believe it this
+ 
+
+ align:start position:0%
+place yeah you better believe it this
+thing wobbles like crazy so the
+
+ align:start position:0%
+thing wobbles like crazy so the
+ 
+
+ align:start position:0%
+thing wobbles like crazy so the
+fact the principal axes are a property
+
+ align:start position:0%
+fact the principal axes are a property
+ 
+
+ align:start position:0%
+fact the principal axes are a property
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+object they're not a property of the
+
+ align:start position:0%
+object they're not a property of the
+ 
+
+ align:start position:0%
+object they're not a property of the
+angular momentum the angular momentum
+
+ align:start position:0%
+angular momentum the angular momentum
+ 
+
+ align:start position:0%
+angular momentum the angular momentum
+comes then from
+
+ align:start position:0%
+comes then from
+ 
+
+ align:start position:0%
+comes then from
+multiplying the mass moment of inertia
+
+ align:start position:0%
+multiplying the mass moment of inertia
+ 
+
+ align:start position:0%
+multiplying the mass moment of inertia
+that you've determined
+
+ align:start position:0%
+that you've determined
+ 
+
+ align:start position:0%
+that you've determined
+times the actual rotation vector and
+
+ align:start position:0%
+times the actual rotation vector and
+ 
+
+ align:start position:0%
+times the actual rotation vector and
+you'll find out that you get uh angular
+
+ align:start position:0%
+you'll find out that you get uh angular
+ 
+
+ align:start position:0%
+you'll find out that you get uh angular
+components of angular momentum that are
+
+ align:start position:0%
+components of angular momentum that are
+ 
+
+ align:start position:0%
+components of angular momentum that are
+not in the direction of spin as soon as
+
+ align:start position:0%
+not in the direction of spin as soon as
+ 
+
+ align:start position:0%
+not in the direction of spin as soon as
+that happens you have unbalanced
+
+ align:start position:0%
+that happens you have unbalanced
+ 
+
+ align:start position:0%
+that happens you have unbalanced
+terms okay
+
+ align:start position:0%
+terms okay
+ 
+
+ align:start position:0%
+terms okay
+um I got to get on to something else
+
+ align:start position:0%
+um I got to get on to something else
+ 
+
+ align:start position:0%
+um I got to get on to something else
+before to help you do homework let's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dis with Z coming out of the
+
+ align:start position:0%
+dis with Z coming out of the
+ 
+
+ align:start position:0%
+dis with Z coming out of the
+board the izz so let's say here's x y z
+
+ align:start position:0%
+board the izz so let's say here's x y z
+ 
+
+ align:start position:0%
+board the izz so let's say here's x y z
+coming out of the board izz the mass
+
+ align:start position:0%
+coming out of the board izz the mass
+ 
+
+ align:start position:0%
+coming out of the board izz the mass
+dist Mass moment of inertia of about
+
+ align:start position:0%
+dist Mass moment of inertia of about
+ 
+
+ align:start position:0%
+dist Mass moment of inertia of about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+z-axis
+
+ align:start position:0%
+z-axis
+ 
+
+ align:start position:0%
+z-axis
+is from the basic definition the
+
+ align:start position:0%
+is from the basic definition the
+ 
+
+ align:start position:0%
+is from the basic definition the
+summation of the
+
+ align:start position:0%
+summation of the
+ 
+
+ align:start position:0%
+summation of the
+m x i 2 plus uh y i 2 it's just that for
+
+ align:start position:0%
+m x i 2 plus uh y i 2 it's just that for
+ 
+
+ align:start position:0%
+m x i 2 plus uh y i 2 it's just that for
+every little Mass particle it's the dist
+
+ align:start position:0%
+every little Mass particle it's the dist
+ 
+
+ align:start position:0%
+every little Mass particle it's the dist
+it's the radius squared away from the
+
+ align:start position:0%
+it's the radius squared away from the
+ 
+
+ align:start position:0%
+it's the radius squared away from the
+center of rotation that's what x^2 + y^
+
+ align:start position:0%
+center of rotation that's what x^2 + y^
+ 
+
+ align:start position:0%
+center of rotation that's what x^2 + y^
+is and we can turn this into an integral
+
+ align:start position:0%
+is and we can turn this into an integral
+ 
+
+ align:start position:0%
+is and we can turn this into an integral
+it's the integral of r² that distance
+
+ align:start position:0%
+it's the integral of r² that distance
+ 
+
+ align:start position:0%
+it's the integral of r² that distance
+times the little Mass bit that's
+
+ align:start position:0%
+times the little Mass bit that's
+ 
+
+ align:start position:0%
+times the little Mass bit that's
+there and
+
+ align:start position:0%
+there and
+ 
+
+ align:start position:0%
+there and
+if that's the same if you wanted to do
+
+ align:start position:0%
+if that's the same if you wanted to do
+ 
+
+ align:start position:0%
+if that's the same if you wanted to do
+the integral as x^2 +
+
+ align:start position:0%
+the integral as x^2 +
+ 
+
+ align:start position:0%
+the integral as x^2 +
+y^2 d m
+
+ align:start position:0%
+y^2 d m
+ 
+
+ align:start position:0%
+y^2 d m
+okay but to do this integral for a nice
+
+ align:start position:0%
+okay but to do this integral for a nice
+ 
+
+ align:start position:0%
+okay but to do this integral for a nice
+circularly symmetric
+
+ align:start position:0%
+circularly symmetric
+ 
+
+ align:start position:0%
+circularly symmetric
+dis all you can pick a little Mass bit
+
+ align:start position:0%
+dis all you can pick a little Mass bit
+ 
+
+ align:start position:0%
+dis all you can pick a little Mass bit
+that has
+
+ align:start position:0%
+that has
+ 
+
+ align:start position:0%
+that has
+thickness Dr
+
+ align:start position:0%
+thickness Dr
+ 
+
+ align:start position:0%
+thickness Dr
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+width r d Theta this angle here is D
+
+ align:start position:0%
+width r d Theta this angle here is D
+ 
+
+ align:start position:0%
+width r d Theta this angle here is D
+Theta and that's a little bit of area
+
+ align:start position:0%
+Theta and that's a little bit of area
+ 
+
+ align:start position:0%
+Theta and that's a little bit of area
+that's a little
+
+ align:start position:0%
+that's a little
+ 
+
+ align:start position:0%
+that's a little
+da which has area R Dr D Theta it's just
+
+ align:start position:0%
+da which has area R Dr D Theta it's just
+ 
+
+ align:start position:0%
+da which has area R Dr D Theta it's just
+length times width it's little when it's
+
+ align:start position:0%
+length times width it's little when it's
+ 
+
+ align:start position:0%
+length times width it's little when it's
+small enough it's a little rectangle and
+
+ align:start position:0%
+small enough it's a little rectangle and
+ 
+
+ align:start position:0%
+small enough it's a little rectangle and
+it has that
+
+ align:start position:0%
+it has that
+ 
+
+ align:start position:0%
+it has that
+area and it has a
+
+ align:start position:0%
+area and it has a
+ 
+
+ align:start position:0%
+area and it has a
+volume DV the volume of that thing is
+
+ align:start position:0%
+volume DV the volume of that thing is
+ 
+
+ align:start position:0%
+volume DV the volume of that thing is
+just the area times the thickness of it
+
+ align:start position:0%
+just the area times the thickness of it
+ 
+
+ align:start position:0%
+just the area times the thickness of it
+so here's our disc here but it has some
+
+ align:start position:0%
+so here's our disc here but it has some
+ 
+
+ align:start position:0%
+so here's our disc here but it has some
+thickness and I'll call that
+
+ align:start position:0%
+thickness and I'll call that
+ 
+
+ align:start position:0%
+thickness and I'll call that
+H so the volume is just HR Dr r d
+
+ align:start position:0%
+H so the volume is just HR Dr r d
+ 
+
+ align:start position:0%
+H so the volume is just HR Dr r d
+Theta okay and the mass
+
+ align:start position:0%
+Theta okay and the mass
+ 
+
+ align:start position:0%
+Theta okay and the mass
+DM is a density time DV
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to integrate this all I have
+
+ align:start position:0%
+so I want to integrate this all I have
+ 
+
+ align:start position:0%
+so I want to integrate this all I have
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+integrate the integral then of R2
+
+ align:start position:0%
+integrate the integral then of R2
+ 
+
+ align:start position:0%
+integrate the integral then of R2
+DM is the integral from 0 to 2
+
+ align:start position:0%
+DM is the integral from 0 to 2
+ 
+
+ align:start position:0%
+DM is the integral from 0 to 2
+pi 0 to
+
+ align:start position:0%
+pi 0 to
+ 
+
+ align:start position:0%
+pi 0 to
+R of row
+
+ align:start position:0%
+R of row
+ 
+
+ align:start position:0%
+R of row
+DV
+
+ align:start position:0%
+DV
+ 
+
+ align:start position:0%
+DV
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+H oh and I need an r squ r R 2 DV is row
+
+ align:start position:0%
+H oh and I need an r squ r R 2 DV is row
+ 
+
+ align:start position:0%
+H oh and I need an r squ r R 2 DV is row
+h r d r d Theta so this is 1802
+
+ align:start position:0%
+h r d r d Theta so this is 1802
+ 
+
+ align:start position:0%
+h r d r d Theta so this is 1802
+integrals right so this is then is this
+
+ align:start position:0%
+integrals right so this is then is this
+ 
+
+ align:start position:0%
+integrals right so this is then is this
+a any of this a function of theta Noe so
+
+ align:start position:0%
+a any of this a function of theta Noe so
+ 
+
+ align:start position:0%
+a any of this a function of theta Noe so
+it's a trivial integral just gives you
+
+ align:start position:0%
+it's a trivial integral just gives you
+ 
+
+ align:start position:0%
+it's a trivial integral just gives you
+integrate that over Theta you just get
+
+ align:start position:0%
+integrate that over Theta you just get
+ 
+
+ align:start position:0%
+integrate that over Theta you just get
+Theta evaluated 0 to 2 pi so this is 2
+
+ align:start position:0%
+Theta evaluated 0 to 2 pi so this is 2
+ 
+
+ align:start position:0%
+Theta evaluated 0 to 2 pi so this is 2
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+row H can all come to the outside
+
+ align:start position:0%
+row H can all come to the outside
+ 
+
+ align:start position:0%
+row H can all come to the outside
+integral 0 to R of R cubed d
+
+ align:start position:0%
+integral 0 to R of R cubed d
+ 
+
+ align:start position:0%
+integral 0 to R of R cubed d
+r and that ends up give the r Cub goes
+
+ align:start position:0%
+r and that ends up give the r Cub goes
+ 
+
+ align:start position:0%
+r and that ends up give the r Cub goes
+to R 4 over
+
+ align:start position:0%
+to R 4 over
+ 
+
+ align:start position:0%
+to R 4 over
+4 and the final result of this one is 2
+
+ align:start position:0%
+4 and the final result of this one is 2
+ 
+
+ align:start position:0%
+4 and the final result of this one is 2
+pi r 4th over
+
+ align:start position:0%
+pi r 4th over
+ 
+
+ align:start position:0%
+pi r 4th over
+4 row H and when you account for H * <
+
+ align:start position:0%
+4 row H and when you account for H * <
+ 
+
+ align:start position:0%
+4 row H and when you account for H * <
+r^ 2 is the volume * row is the mass
+
+ align:start position:0%
+r^ 2 is the volume * row is the mass
+ 
+
+ align:start position:0%
+r^ 2 is the volume * row is the mass
+this all works out to be m r 2/ 2 okay
+
+ align:start position:0%
+this all works out to be m r 2/ 2 okay
+ 
+
+ align:start position:0%
+this all works out to be m r 2/ 2 okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+izz so I needed to do this once for you
+
+ align:start position:0%
+izz so I needed to do this once for you
+ 
+
+ align:start position:0%
+izz so I needed to do this once for you
+for simple things to integrate izz in
+
+ align:start position:0%
+for simple things to integrate izz in
+ 
+
+ align:start position:0%
+for simple things to integrate izz in
+this case you just integrate it out
+
+ align:start position:0%
+this case you just integrate it out
+ 
+
+ align:start position:0%
+this case you just integrate it out
+count for all the little Mass bits that
+
+ align:start position:0%
+count for all the little Mass bits that
+ 
+
+ align:start position:0%
+count for all the little Mass bits that
+is the mass moment of inertia with
+
+ align:start position:0%
+is the mass moment of inertia with
+ 
+
+ align:start position:0%
+is the mass moment of inertia with
+respect to the axis passing through the
+
+ align:start position:0%
+respect to the axis passing through the
+ 
+
+ align:start position:0%
+respect to the axis passing through the
+center like
+
+ align:start position:0%
+center like
+ 
+
+ align:start position:0%
+center like
+this pardon
+
+ align:start position:0%
+this pardon
+ 
+
+ align:start position:0%
+this pardon
+it's this this is what I'm talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need this is moving on to the last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit so we need to know how to be able to
+
+ align:start position:0%
+bit so we need to know how to be able to
+ 
+
+ align:start position:0%
+bit so we need to know how to be able to
+rotate things about parts places other
+
+ align:start position:0%
+rotate things about parts places other
+ 
+
+ align:start position:0%
+rotate things about parts places other
+than their centers of mass so this is a
+
+ align:start position:0%
+than their centers of mass so this is a
+ 
+
+ align:start position:0%
+than their centers of mass so this is a
+stick I can rotate it about the center
+
+ align:start position:0%
+stick I can rotate it about the center
+ 
+
+ align:start position:0%
+stick I can rotate it about the center
+of mass but it's more interesting if I
+
+ align:start position:0%
+of mass but it's more interesting if I
+ 
+
+ align:start position:0%
+of mass but it's more interesting if I
+rotate it about some other point makes
+
+ align:start position:0%
+rotate it about some other point makes
+ 
+
+ align:start position:0%
+rotate it about some other point makes
+it pendulum when I do it around here so
+
+ align:start position:0%
+it pendulum when I do it around here so
+ 
+
+ align:start position:0%
+it pendulum when I do it around here so
+I need to be able to calculate mass
+
+ align:start position:0%
+I need to be able to calculate mass
+ 
+
+ align:start position:0%
+I need to be able to calculate mass
+moments of inertia about a point that's
+
+ align:start position:0%
+moments of inertia about a point that's
+ 
+
+ align:start position:0%
+moments of inertia about a point that's
+not through the center of mass now I
+
+ align:start position:0%
+not through the center of mass now I
+ 
+
+ align:start position:0%
+not through the center of mass now I
+know you've seen this before in uh in
+
+ align:start position:0%
+know you've seen this before in uh in
+ 
+
+ align:start position:0%
+know you've seen this before in uh in
+801 so this is going to be a quick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reminder but I'll show you where it
+
+ align:start position:0%
+reminder but I'll show you where it
+ 
+
+ align:start position:0%
+reminder but I'll show you where it
+comes from so here's my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stick and I'm going to has a center of
+
+ align:start position:0%
+stick and I'm going to has a center of
+ 
+
+ align:start position:0%
+stick and I'm going to has a center of
+mass and that's where G is located
+
+ align:start position:0%
+mass and that's where G is located
+ 
+
+ align:start position:0%
+mass and that's where G is located
+here has a length total length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L I'm going to give it a thickness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b a
+
+ align:start position:0%
+b a
+ 
+
+ align:start position:0%
+b a
+width a okay so just it's a
+
+ align:start position:0%
+width a okay so just it's a
+ 
+
+ align:start position:0%
+width a okay so just it's a
+stick a wide B thick L
+
+ align:start position:0%
+stick a wide B thick L
+ 
+
+ align:start position:0%
+stick a wide B thick L
+long uniform has a center of gravity
+
+ align:start position:0%
+long uniform has a center of gravity
+ 
+
+ align:start position:0%
+long uniform has a center of gravity
+right in the
+
+ align:start position:0%
+right in the
+ 
+
+ align:start position:0%
+right in the
+middle and I'm going
+
+ align:start position:0%
+middle and I'm going
+ 
+
+ align:start position:0%
+middle and I'm going
+to attach to this
+
+ align:start position:0%
+to attach to this
+ 
+
+ align:start position:0%
+to attach to this
+stick
+
+ align:start position:0%
+stick
+ 
+
+ align:start position:0%
+stick
+a and this this point is kind of hard to
+
+ align:start position:0%
+a and this this point is kind of hard to
+ 
+
+ align:start position:0%
+a and this this point is kind of hard to
+draw this point is at in the center of
+
+ align:start position:0%
+draw this point is at in the center of
+ 
+
+ align:start position:0%
+draw this point is at in the center of
+the stick okay I'm going to put my
+
+ align:start position:0%
+the stick okay I'm going to put my
+ 
+
+ align:start position:0%
+the stick okay I'm going to put my
+coordinate system attached at the center
+
+ align:start position:0%
+coordinate system attached at the center
+ 
+
+ align:start position:0%
+coordinate system attached at the center
+of gravity Center of mass and I'm going
+
+ align:start position:0%
+of gravity Center of mass and I'm going
+ 
+
+ align:start position:0%
+of gravity Center of mass and I'm going
+to make it the
+
+ align:start position:0%
+to make it the
+ 
+
+ align:start position:0%
+to make it the
+uh that's X Prime downward Z Prime and Y
+
+ align:start position:0%
+uh that's X Prime downward Z Prime and Y
+ 
+
+ align:start position:0%
+uh that's X Prime downward Z Prime and Y
+Prime is then going off that way so this
+
+ align:start position:0%
+Prime is then going off that way so this
+ 
+
+ align:start position:0%
+Prime is then going off that way so this
+is a body set of coordinates at the
+
+ align:start position:0%
+is a body set of coordinates at the
+ 
+
+ align:start position:0%
+is a body set of coordinates at the
+center of mass x Prime y Prime Z Prime
+
+ align:start position:0%
+center of mass x Prime y Prime Z Prime
+ 
+
+ align:start position:0%
+center of mass x Prime y Prime Z Prime
+and X happens to be down and I want to
+
+ align:start position:0%
+and X happens to be down and I want to
+ 
+
+ align:start position:0%
+and X happens to be down and I want to
+move I want to calculate my mass moment
+
+ align:start position:0%
+move I want to calculate my mass moment
+ 
+
+ align:start position:0%
+move I want to calculate my mass moment
+of inertia with respect to a point up
+
+ align:start position:0%
+of inertia with respect to a point up
+ 
+
+ align:start position:0%
+of inertia with respect to a point up
+here that is
+
+ align:start position:0%
+here that is
+ 
+
+ align:start position:0%
+here that is
+D this distance I've moved up the xaxis
+
+ align:start position:0%
+D this distance I've moved up the xaxis
+ 
+
+ align:start position:0%
+D this distance I've moved up the xaxis
+in amount
+
+ align:start position:0%
+in amount
+ 
+
+ align:start position:0%
+in amount
+D so I'm going to set a new coordinate
+
+ align:start position:0%
+D so I'm going to set a new coordinate
+ 
+
+ align:start position:0%
+D so I'm going to set a new coordinate
+system up here so if this was Z primed
+
+ align:start position:0%
+system up here so if this was Z primed
+ 
+
+ align:start position:0%
+system up here so if this was Z primed
+my new Z is here it's getting a little
+
+ align:start position:0%
+my new Z is here it's getting a little
+ 
+
+ align:start position:0%
+my new Z is here it's getting a little
+messy and maybe I'll
+
+ align:start position:0%
+messy and maybe I'll
+ 
+
+ align:start position:0%
+messy and maybe I'll
+uh just a face View
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if my previously y Prime and X Prime
+
+ align:start position:0%
+if my previously y Prime and X Prime
+ 
+
+ align:start position:0%
+if my previously y Prime and X Prime
+were like that Z coming out of the board
+
+ align:start position:0%
+were like that Z coming out of the board
+ 
+
+ align:start position:0%
+were like that Z coming out of the board
+now I have a new system that is Y and X
+
+ align:start position:0%
+now I have a new system that is Y and X
+ 
+
+ align:start position:0%
+now I have a new system that is Y and X
+like this Z still coming out of the
+
+ align:start position:0%
+like this Z still coming out of the
+ 
+
+ align:start position:0%
+like this Z still coming out of the
+board all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now the
+
+ align:start position:0%
+right now the
+ 
+
+ align:start position:0%
+right now the
+coordinate so how do I calculate mass
+
+ align:start position:0%
+coordinate so how do I calculate mass
+ 
+
+ align:start position:0%
+coordinate so how do I calculate mass
+moment of
+
+ align:start position:0%
+moment of
+ 
+
+ align:start position:0%
+moment of
+inertia well I want to I want to
+
+ align:start position:0%
+inertia well I want to I want to
+ 
+
+ align:start position:0%
+inertia well I want to I want to
+know I I
+
+ align:start position:0%
+know I I
+ 
+
+ align:start position:0%
+know I I
+want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+izz I probably know I Z Prime Z Prime i
+
+ align:start position:0%
+izz I probably know I Z Prime Z Prime i
+ 
+
+ align:start position:0%
+izz I probably know I Z Prime Z Prime i
+z Prime Z Prime is the mass moment of
+
+ align:start position:0%
+z Prime Z Prime is the mass moment of
+ 
+
+ align:start position:0%
+z Prime Z Prime is the mass moment of
+inertia about this point I know it's a
+
+ align:start position:0%
+inertia about this point I know it's a
+ 
+
+ align:start position:0%
+inertia about this point I know it's a
+principal axis from all the things we
+
+ align:start position:0%
+principal axis from all the things we
+ 
+
+ align:start position:0%
+principal axis from all the things we
+just that square block is the same as
+
+ align:start position:0%
+just that square block is the same as
+ 
+
+ align:start position:0%
+just that square block is the same as
+this that's a principal axis in the Z
+
+ align:start position:0%
+this that's a principal axis in the Z
+ 
+
+ align:start position:0%
+this that's a principal axis in the Z
+Prime Direction I know the izz Prime
+
+ align:start position:0%
+Prime Direction I know the izz Prime
+ 
+
+ align:start position:0%
+Prime Direction I know the izz Prime
+with respect to G I want to know it with
+
+ align:start position:0%
+with respect to G I want to know it with
+ 
+
+ align:start position:0%
+with respect to G I want to know it with
+respect to to this
+
+ align:start position:0%
+respect to to this
+ 
+
+ align:start position:0%
+respect to to this
+point so well izz which is my new
+
+ align:start position:0%
+point so well izz which is my new
+ 
+
+ align:start position:0%
+point so well izz which is my new
+location up here and we'll call it a so
+
+ align:start position:0%
+location up here and we'll call it a so
+ 
+
+ align:start position:0%
+location up here and we'll call it a so
+izz here with respect to
+
+ align:start position:0%
+izz here with respect to
+ 
+
+ align:start position:0%
+izz here with respect to
+a is the integral of R 2 DM got to do
+
+ align:start position:0%
+a is the integral of R 2 DM got to do
+ 
+
+ align:start position:0%
+a is the integral of R 2 DM got to do
+the same integral
+
+ align:start position:0%
+the same integral
+ 
+
+ align:start position:0%
+the same integral
+now and but that's
+
+ align:start position:0%
+now and but that's
+ 
+
+ align:start position:0%
+now and but that's
+the integral of x^2 + y^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DM but now I can look at this and I can
+
+ align:start position:0%
+DM but now I can look at this and I can
+ 
+
+ align:start position:0%
+DM but now I can look at this and I can
+say oh well these are D this is
+
+ align:start position:0%
+say oh well these are D this is
+ 
+
+ align:start position:0%
+say oh well these are D this is
+separated by D I only moved it in the X
+
+ align:start position:0%
+separated by D I only moved it in the X
+ 
+
+ align:start position:0%
+separated by D I only moved it in the X
+the Y's haven't moved and the Z's didn't
+
+ align:start position:0%
+the Y's haven't moved and the Z's didn't
+ 
+
+ align:start position:0%
+the Y's haven't moved and the Z's didn't
+change I just move my point only in the
+
+ align:start position:0%
+change I just move my point only in the
+ 
+
+ align:start position:0%
+change I just move my point only in the
+X Direction so I can now say that H in
+
+ align:start position:0%
+X Direction so I can now say that H in
+ 
+
+ align:start position:0%
+X Direction so I can now say that H in
+terms of my new
+
+ align:start position:0%
+terms of my new
+ 
+
+ align:start position:0%
+terms of my new
+coordinate it's the same as X Prime + D
+
+ align:start position:0%
+coordinate it's the same as X Prime + D
+ 
+
+ align:start position:0%
+coordinate it's the same as X Prime + D
+the distance from here to a point down
+
+ align:start position:0%
+the distance from here to a point down
+ 
+
+ align:start position:0%
+the distance from here to a point down
+here some Mass
+
+ align:start position:0%
+here some Mass
+ 
+
+ align:start position:0%
+here some Mass
+Point some arbitrary Mass Point XI is
+
+ align:start position:0%
+Point some arbitrary Mass Point XI is
+ 
+
+ align:start position:0%
+Point some arbitrary Mass Point XI is
+going to be x i prime plus
+
+ align:start position:0%
+going to be x i prime plus
+ 
+
+ align:start position:0%
+going to be x i prime plus
+d okay so to do this integral in the new
+
+ align:start position:0%
+d okay so to do this integral in the new
+ 
+
+ align:start position:0%
+d okay so to do this integral in the new
+coordinates this is going to be the
+
+ align:start position:0%
+coordinates this is going to be the
+ 
+
+ align:start position:0%
+coordinates this is going to be the
+integral of x Prime +
+
+ align:start position:0%
+integral of x Prime +
+ 
+
+ align:start position:0%
+integral of x Prime +
+D squared +
+
+ align:start position:0%
+D squared +
+ 
+
+ align:start position:0%
+D squared +
+y now y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime equal Y and Z Prime equals z those
+
+ align:start position:0%
+Prime equal Y and Z Prime equals z those
+ 
+
+ align:start position:0%
+Prime equal Y and Z Prime equals z those
+haven't changed I didn't move my
+
+ align:start position:0%
+haven't changed I didn't move my
+ 
+
+ align:start position:0%
+haven't changed I didn't move my
+coordinate system in the y direction or
+
+ align:start position:0%
+coordinate system in the y direction or
+ 
+
+ align:start position:0%
+coordinate system in the y direction or
+the Z Direction so the the coordinate in
+
+ align:start position:0%
+the Z Direction so the the coordinate in
+ 
+
+ align:start position:0%
+the Z Direction so the the coordinate in
+the new system in y is the same as
+
+ align:start position:0%
+the new system in y is the same as
+ 
+
+ align:start position:0%
+the new system in y is the same as
+before so this is just y Prime
+
+ align:start position:0%
+before so this is just y Prime
+ 
+
+ align:start position:0%
+before so this is just y Prime
+squar and this whole thing times
+
+ align:start position:0%
+squar and this whole thing times
+ 
+
+ align:start position:0%
+squar and this whole thing times
+integrated times every little Mass bit
+
+ align:start position:0%
+integrated times every little Mass bit
+ 
+
+ align:start position:0%
+integrated times every little Mass bit
+I'm going to if I expand if I Square
+
+ align:start position:0%
+I'm going to if I expand if I Square
+ 
+
+ align:start position:0%
+I'm going to if I expand if I Square
+this I get X Prime squ 2 x Prime d d ^ 2
+
+ align:start position:0%
+this I get X Prime squ 2 x Prime d d ^ 2
+ 
+
+ align:start position:0%
+this I get X Prime squ 2 x Prime d d ^ 2
++ y^2 so this
+
+ align:start position:0%
++ y^2 so this
+ 
+
+ align:start position:0%
++ y^2 so this
+integral izz with respect to a and you
+
+ align:start position:0%
+integral izz with respect to a and you
+ 
+
+ align:start position:0%
+integral izz with respect to a and you
+rearrange it looks
+
+ align:start position:0%
+rearrange it looks
+ 
+
+ align:start position:0%
+rearrange it looks
+like X Prime 2ar + y Prime squared DM
+
+ align:start position:0%
+like X Prime 2ar + y Prime squared DM
+ 
+
+ align:start position:0%
+like X Prime 2ar + y Prime squared DM
+and the sum uh integral of the sums the
+
+ align:start position:0%
+and the sum uh integral of the sums the
+ 
+
+ align:start position:0%
+and the sum uh integral of the sums the
+sum of the integrals so I break it into
+
+ align:start position:0%
+sum of the integrals so I break it into
+ 
+
+ align:start position:0%
+sum of the integrals so I break it into
+bits here there's a d^2 which is a
+
+ align:start position:0%
+bits here there's a d^2 which is a
+ 
+
+ align:start position:0%
+bits here there's a d^2 which is a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+DM and then the last term is
+
+ align:start position:0%
+DM and then the last term is
+ 
+
+ align:start position:0%
+DM and then the last term is
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+2D and it's X Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DM that's with this just multiply this
+
+ align:start position:0%
+DM that's with this just multiply this
+ 
+
+ align:start position:0%
+DM that's with this just multiply this
+out rewrite it break it
+
+ align:start position:0%
+out rewrite it break it
+ 
+
+ align:start position:0%
+out rewrite it break it
+apart integral of well let's do this one
+
+ align:start position:0%
+apart integral of well let's do this one
+ 
+
+ align:start position:0%
+apart integral of well let's do this one
+integral of x Prime s + y Prim s DM you
+
+ align:start position:0%
+integral of x Prime s + y Prim s DM you
+ 
+
+ align:start position:0%
+integral of x Prime s + y Prim s DM you
+know that's something that we already
+
+ align:start position:0%
+know that's something that we already
+ 
+
+ align:start position:0%
+know that's something that we already
+have a name
+
+ align:start position:0%
+have a name
+ 
+
+ align:start position:0%
+have a name
+for this is i g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in ZZ it's the original Mass moment of
+
+ align:start position:0%
+in ZZ it's the original Mass moment of
+ 
+
+ align:start position:0%
+in ZZ it's the original Mass moment of
+inertia with respect to the original
+
+ align:start position:0%
+inertia with respect to the original
+ 
+
+ align:start position:0%
+inertia with respect to the original
+coordinate system at g in the Z
+
+ align:start position:0%
+coordinate system at g in the Z
+ 
+
+ align:start position:0%
+coordinate system at g in the Z
+Direction so it's I
+
+ align:start position:0%
+Direction so it's I
+ 
+
+ align:start position:0%
+Direction so it's I
+zzg okay that's we already know that
+
+ align:start position:0%
+zzg okay that's we already know that
+ 
+
+ align:start position:0%
+zzg okay that's we already know that
+that's given for the object plus this is
+
+ align:start position:0%
+that's given for the object plus this is
+ 
+
+ align:start position:0%
+that's given for the object plus this is
+the integral of DM over the whole extent
+
+ align:start position:0%
+the integral of DM over the whole extent
+ 
+
+ align:start position:0%
+the integral of DM over the whole extent
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+object just the mass of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object and this integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the integral in terms of the x
+
+ align:start position:0%
+this is the integral in terms of the x
+ 
+
+ align:start position:0%
+this is the integral in terms of the x
+coordinate and every Mass bit from here
+
+ align:start position:0%
+coordinate and every Mass bit from here
+ 
+
+ align:start position:0%
+coordinate and every Mass bit from here
+if I go out here and find one there's an
+
+ align:start position:0%
+if I go out here and find one there's an
+ 
+
+ align:start position:0%
+if I go out here and find one there's an
+equal and opposite one up here this is
+
+ align:start position:0%
+equal and opposite one up here this is
+ 
+
+ align:start position:0%
+equal and opposite one up here this is
+the definition of the center of mass
+
+ align:start position:0%
+the definition of the center of mass
+ 
+
+ align:start position:0%
+the definition of the center of mass
+this integral if I'm at the center of
+
+ align:start position:0%
+this integral if I'm at the center of
+ 
+
+ align:start position:0%
+this integral if I'm at the center of
+mass integrating out from it this is
+
+ align:start position:0%
+mass integrating out from it this is
+ 
+
+ align:start position:0%
+mass integrating out from it this is
+zero because of the definition of the
+
+ align:start position:0%
+zero because of the definition of the
+ 
+
+ align:start position:0%
+zero because of the definition of the
+center of
+
+ align:start position:0%
+center of
+ 
+
+ align:start position:0%
+center of
+mass and I've just proven the parallel
+
+ align:start position:0%
+mass and I've just proven the parallel
+ 
+
+ align:start position:0%
+mass and I've just proven the parallel
+axis theorem
+
+ align:start position:0%
+axis theorem
+ 
+
+ align:start position:0%
+axis theorem
+izz about this new point is I about G+
+
+ align:start position:0%
+izz about this new point is I about G+
+ 
+
+ align:start position:0%
+izz about this new point is I about G+
+md^ 2 where d^2 is the distance I've
+
+ align:start position:0%
+md^ 2 where d^2 is the distance I've
+ 
+
+ align:start position:0%
+md^ 2 where d^2 is the distance I've
+moved the Z axis to a new place parallel
+
+ align:start position:0%
+moved the Z axis to a new place parallel
+ 
+
+ align:start position:0%
+moved the Z axis to a new place parallel
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+izz with for for with respect to
+
+ align:start position:0%
+izz with for for with respect to
+ 
+
+ align:start position:0%
+izz with for for with respect to
+G the original Mass moment of inertia
+
+ align:start position:0%
+G the original Mass moment of inertia
+ 
+
+ align:start position:0%
+G the original Mass moment of inertia
+for RO the for
+
+ align:start position:0%
+for RO the for
+ 
+
+ align:start position:0%
+for RO the for
+izz is um m
+
+ align:start position:0%
+izz is um m
+ 
+
+ align:start position:0%
+izz is um m
+l^2 + a 2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+12 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iixx
+
+ align:start position:0%
+iixx
+ 
+
+ align:start position:0%
+iixx
+M L 2 + b^
+
+ align:start position:0%
+M L 2 + b^
+ 
+
+ align:start position:0%
+M L 2 + b^
+2 over
+
+ align:start position:0%
+2 over
+ 
+
+ align:start position:0%
+2 over
+12 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I ZZ
+
+ align:start position:0%
+I ZZ
+ 
+
+ align:start position:0%
+I ZZ
+oh we already we already know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one oh wait a minute I don't haven't
+
+ align:start position:0%
+one oh wait a minute I don't haven't
+ 
+
+ align:start position:0%
+one oh wait a minute I don't haven't
+told you what that is it's izz iixx i y
+
+ align:start position:0%
+told you what that is it's izz iixx i y
+ 
+
+ align:start position:0%
+told you what that is it's izz iixx i y
+y I'm just a little messy here iy y for
+
+ align:start position:0%
+y I'm just a little messy here iy y for
+ 
+
+ align:start position:0%
+y I'm just a little messy here iy y for
+this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is I have made a mistake ixx is a 2 + b^
+
+ align:start position:0%
+is I have made a mistake ixx is a 2 + b^
+ 
+
+ align:start position:0%
+is I have made a mistake ixx is a 2 + b^
+2 i y y is m l 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus b^2 so those are the three all with
+
+ align:start position:0%
+plus b^2 so those are the three all with
+ 
+
+ align:start position:0%
+plus b^2 so those are the three all with
+respect to G for this stick okay and I'm
+
+ align:start position:0%
+respect to G for this stick okay and I'm
+ 
+
+ align:start position:0%
+respect to G for this stick okay and I'm
+going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that kind of sets us up where I can
+
+ align:start position:0%
+okay that kind of sets us up where I can
+ 
+
+ align:start position:0%
+okay that kind of sets us up where I can
+pick up next time so let's finish by
+
+ align:start position:0%
+pick up next time so let's finish by
+ 
+
+ align:start position:0%
+pick up next time so let's finish by
+asking ourselves
+
+ align:start position:0%
+asking ourselves
+ 
+
+ align:start position:0%
+asking ourselves
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question what do we think about if I've
+
+ align:start position:0%
+question what do we think about if I've
+ 
+
+ align:start position:0%
+question what do we think about if I've
+moved to this new po new
+
+ align:start position:0%
+moved to this new po new
+ 
+
+ align:start position:0%
+moved to this new po new
+position and I'm not rotating about the
+
+ align:start position:0%
+position and I'm not rotating about the
+ 
+
+ align:start position:0%
+position and I'm not rotating about the
+center is this new axis this one around
+
+ align:start position:0%
+center is this new axis this one around
+ 
+
+ align:start position:0%
+center is this new axis this one around
+around the center
+
+ align:start position:0%
+around the center
+ 
+
+ align:start position:0%
+around the center
+before that one we know is a principal
+
+ align:start position:0%
+before that one we know is a principal
+ 
+
+ align:start position:0%
+before that one we know is a principal
+axis is the new if I rotate about this
+
+ align:start position:0%
+axis is the new if I rotate about this
+ 
+
+ align:start position:0%
+axis is the new if I rotate about this
+new place which I've defined the mass
+
+ align:start position:0%
+new place which I've defined the mass
+ 
+
+ align:start position:0%
+new place which I've defined the mass
+moment inti about that place is this a
+
+ align:start position:0%
+moment inti about that place is this a
+ 
+
+ align:start position:0%
+moment inti about that place is this a
+principal
+
+ align:start position:0%
+principal
+ 
+
+ align:start position:0%
+principal
+axis how many think
+
+ align:start position:0%
+axis how many think
+ 
+
+ align:start position:0%
+axis how many think
+yes how many think
+
+ align:start position:0%
+yes how many think
+ 
+
+ align:start position:0%
+yes how many think
+no okay so a little and lots of people
+
+ align:start position:0%
+no okay so a little and lots of people
+ 
+
+ align:start position:0%
+no okay so a little and lots of people
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+sure so the dynamic my dynamic
+
+ align:start position:0%
+sure so the dynamic my dynamic
+ 
+
+ align:start position:0%
+sure so the dynamic my dynamic
+definition of principal axis is if you
+
+ align:start position:0%
+definition of principal axis is if you
+ 
+
+ align:start position:0%
+definition of principal axis is if you
+can rotate the object about that axis
+
+ align:start position:0%
+can rotate the object about that axis
+ 
+
+ align:start position:0%
+can rotate the object about that axis
+and produce no unbalanced Torx it's a
+
+ align:start position:0%
+and produce no unbalanced Torx it's a
+ 
+
+ align:start position:0%
+and produce no unbalanced Torx it's a
+principal axis and I can do that this
+
+ align:start position:0%
+principal axis and I can do that this
+ 
+
+ align:start position:0%
+principal axis and I can do that this
+thing will just spin all day long now
+
+ align:start position:0%
+thing will just spin all day long now
+ 
+
+ align:start position:0%
+thing will just spin all day long now
+there is a force there's you can think
+
+ align:start position:0%
+there is a force there's you can think
+ 
+
+ align:start position:0%
+there is a force there's you can think
+of the fictitious Force there's a center
+
+ align:start position:0%
+of the fictitious Force there's a center
+ 
+
+ align:start position:0%
+of the fictitious Force there's a center
+of mass out here as it spins around
+
+ align:start position:0%
+of mass out here as it spins around
+ 
+
+ align:start position:0%
+of mass out here as it spins around
+there's a centripetal acceleration
+
+ align:start position:0%
+there's a centripetal acceleration
+ 
+
+ align:start position:0%
+there's a centripetal acceleration
+making it go in the circle that means
+
+ align:start position:0%
+making it go in the circle that means
+ 
+
+ align:start position:0%
+making it go in the circle that means
+that fictitious force is like there is a
+
+ align:start position:0%
+that fictitious force is like there is a
+ 
+
+ align:start position:0%
+that fictitious force is like there is a
+centrifugal force pull pulling out on it
+
+ align:start position:0%
+centrifugal force pull pulling out on it
+ 
+
+ align:start position:0%
+centrifugal force pull pulling out on it
+do I feel that do I have to resist that
+
+ align:start position:0%
+do I feel that do I have to resist that
+ 
+
+ align:start position:0%
+do I feel that do I have to resist that
+Force as it goes round and round yes so
+
+ align:start position:0%
+Force as it goes round and round yes so
+ 
+
+ align:start position:0%
+Force as it goes round and round yes so
+there that is an imbalance of a kind we
+
+ align:start position:0%
+there that is an imbalance of a kind we
+ 
+
+ align:start position:0%
+there that is an imbalance of a kind we
+know as a static imbalance but it
+
+ align:start position:0%
+know as a static imbalance but it
+ 
+
+ align:start position:0%
+know as a static imbalance but it
+doesn't produce torqux about this my G
+
+ align:start position:0%
+doesn't produce torqux about this my G
+ 
+
+ align:start position:0%
+doesn't produce torqux about this my G
+my center of my Axis right lined up on
+
+ align:start position:0%
+my center of my Axis right lined up on
+ 
+
+ align:start position:0%
+my center of my Axis right lined up on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Center okay doesn't gravity p on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sure gravity does but that's now a
+
+ align:start position:0%
+the sure gravity does but that's now a
+ 
+
+ align:start position:0%
+the sure gravity does but that's now a
+different problem that's what makes this
+
+ align:start position:0%
+different problem that's what makes this
+ 
+
+ align:start position:0%
+different problem that's what makes this
+thing act like an
+
+ align:start position:0%
+thing act like an
+ 
+
+ align:start position:0%
+thing act like an
+oscillator okay the torqux of the kind
+
+ align:start position:0%
+oscillator okay the torqux of the kind
+ 
+
+ align:start position:0%
+oscillator okay the torqux of the kind
+I'm talking about is if I compute the
+
+ align:start position:0%
+I'm talking about is if I compute the
+ 
+
+ align:start position:0%
+I'm talking about is if I compute the
+angular
+
+ align:start position:0%
+angular
+ 
+
+ align:start position:0%
+angular
+momentum of this thing and take compute
+
+ align:start position:0%
+momentum of this thing and take compute
+ 
+
+ align:start position:0%
+momentum of this thing and take compute
+dhdt the time rate of change of the
+
+ align:start position:0%
+dhdt the time rate of change of the
+ 
+
+ align:start position:0%
+dhdt the time rate of change of the
+angular momentum is a torque on the
+
+ align:start position:0%
+angular momentum is a torque on the
+ 
+
+ align:start position:0%
+angular momentum is a torque on the
+system right I will get the term that
+
+ align:start position:0%
+system right I will get the term that
+ 
+
+ align:start position:0%
+system right I will get the term that
+makes it spin faster and I will get if
+
+ align:start position:0%
+makes it spin faster and I will get if
+ 
+
+ align:start position:0%
+makes it spin faster and I will get if
+they exist terms that make it want to
+
+ align:start position:0%
+they exist terms that make it want to
+ 
+
+ align:start position:0%
+they exist terms that make it want to
+bend this way or bend you know Bend back
+
+ align:start position:0%
+bend this way or bend you know Bend back
+ 
+
+ align:start position:0%
+bend this way or bend you know Bend back
+it only happens if if I if I if I hold
+
+ align:start position:0%
+it only happens if if I if I if I hold
+ 
+
+ align:start position:0%
+it only happens if if I if I if I hold
+this thing over
+
+ align:start position:0%
+this thing over
+ 
+
+ align:start position:0%
+this thing over
+here and spin it get it spinning and I
+
+ align:start position:0%
+here and spin it get it spinning and I
+ 
+
+ align:start position:0%
+here and spin it get it spinning and I
+compute the angular momentum with this
+
+ align:start position:0%
+compute the angular momentum with this
+ 
+
+ align:start position:0%
+compute the angular momentum with this
+back to this point will I get torqux
+
+ align:start position:0%
+back to this point will I get torqux
+ 
+
+ align:start position:0%
+back to this point will I get torqux
+yeah but that's not how I that's that's
+
+ align:start position:0%
+yeah but that's not how I that's that's
+ 
+
+ align:start position:0%
+yeah but that's not how I that's that's
+that's a different problem we computed I
+
+ align:start position:0%
+that's a different problem we computed I
+ 
+
+ align:start position:0%
+that's a different problem we computed I
+the IG is as if I were Computing the
+
+ align:start position:0%
+the IG is as if I were Computing the
+ 
+
+ align:start position:0%
+the IG is as if I were Computing the
+angular momentum I remember I started
+
+ align:start position:0%
+angular momentum I remember I started
+ 
+
+ align:start position:0%
+angular momentum I remember I started
+defining Mass moment of inertia Matrix
+
+ align:start position:0%
+defining Mass moment of inertia Matrix
+ 
+
+ align:start position:0%
+defining Mass moment of inertia Matrix
+based on an angular momentum computation
+
+ align:start position:0%
+based on an angular momentum computation
+ 
+
+ align:start position:0%
+based on an angular momentum computation
+at G so it's right there in the center
+
+ align:start position:0%
+at G so it's right there in the center
+ 
+
+ align:start position:0%
+at G so it's right there in the center
+of this object there's no moment arm
+
+ align:start position:0%
+of this object there's no moment arm
+ 
+
+ align:start position:0%
+of this object there's no moment arm
+that is causing torqux that's trying to
+
+ align:start position:0%
+that is causing torqux that's trying to
+ 
+
+ align:start position:0%
+that is causing torqux that's trying to
+twist this thing about that point okay
+
+ align:start position:0%
+twist this thing about that point okay
+ 
+
+ align:start position:0%
+twist this thing about that point okay
+so when the answer to question is this
+
+ align:start position:0%
+so when the answer to question is this
+ 
+
+ align:start position:0%
+so when the answer to question is this
+is a this is a principal axis yeah um so
+
+ align:start position:0%
+is a this is a principal axis yeah um so
+ 
+
+ align:start position:0%
+is a this is a principal axis yeah um so
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+take getor that are not in
+
+ align:start position:0%
+take getor that are not in
+ 
+
+ align:start position:0%
+take getor that are not in
+that then either if you get torqus that
+
+ align:start position:0%
+that then either if you get torqus that
+ 
+
+ align:start position:0%
+that then either if you get torqus that
+aren't in that direction you either you
+
+ align:start position:0%
+aren't in that direction you either you
+ 
+
+ align:start position:0%
+aren't in that direction you either you
+made a mistake doing the math or you
+
+ align:start position:0%
+made a mistake doing the math or you
+ 
+
+ align:start position:0%
+made a mistake doing the math or you
+started you were in error in identifying
+
+ align:start position:0%
+started you were in error in identifying
+ 
+
+ align:start position:0%
+started you were in error in identifying
+the mass moment of inertia Matrix to
+
+ align:start position:0%
+the mass moment of inertia Matrix to
+ 
+
+ align:start position:0%
+the mass moment of inertia Matrix to
+begin with because if you get torqus
+
+ align:start position:0%
+begin with because if you get torqus
+ 
+
+ align:start position:0%
+begin with because if you get torqus
+that must be nonzero off diagonal terms
+
+ align:start position:0%
+that must be nonzero off diagonal terms
+ 
+
+ align:start position:0%
+that must be nonzero off diagonal terms
+in the mass moment of inertia Matrix
+
+ align:start position:0%
+in the mass moment of inertia Matrix
+ 
+
+ align:start position:0%
+in the mass moment of inertia Matrix
+they are what account for the
+
+ align:start position:0%
+they are what account for the
+ 
+
+ align:start position:0%
+they are what account for the
+torqus okay so any by this parallel axis
+
+ align:start position:0%
+torqus okay so any by this parallel axis
+ 
+
+ align:start position:0%
+torqus okay so any by this parallel axis
+theem any other axis you go to if you
+
+ align:start position:0%
+theem any other axis you go to if you
+ 
+
+ align:start position:0%
+theem any other axis you go to if you
+started at a principal axis any other
+
+ align:start position:0%
+started at a principal axis any other
+ 
+
+ align:start position:0%
+started at a principal axis any other
+axis you create is also a principal axis
+
+ align:start position:0%
+axis you create is also a principal axis
+ 
+
+ align:start position:0%
+axis you create is also a principal axis
+that's the movement of just one axis if
+
+ align:start position:0%
+that's the movement of just one axis if
+ 
+
+ align:start position:0%
+that's the movement of just one axis if
+you do two if you move this way and this
+
+ align:start position:0%
+you do two if you move this way and this
+ 
+
+ align:start position:0%
+you do two if you move this way and this
+way is all bets are off you get a
+
+ align:start position:0%
+way is all bets are off you get a
+ 
+
+ align:start position:0%
+way is all bets are off you get a
+different answer and if you're
+
+ align:start position:0%
+different answer and if you're
+ 
+
+ align:start position:0%
+different answer and if you're
+interested in that more complicated
+
+ align:start position:0%
+interested in that more complicated
+ 
+
+ align:start position:0%
+interested in that more complicated
+problem read that Williams thing because
+
+ align:start position:0%
+problem read that Williams thing because
+ 
+
+ align:start position:0%
+problem read that Williams thing because
+he does the complete parallel axis
+
+ align:start position:0%
+he does the complete parallel axis
+ 
+
+ align:start position:0%
+he does the complete parallel axis
+parallel planes and comes with a super
+
+ align:start position:0%
+parallel planes and comes with a super
+ 
+
+ align:start position:0%
+parallel planes and comes with a super
+compact little way of calculating them
+
+ align:start position:0%
+compact little way of calculating them
+ 
+
+ align:start position:0%
+compact little way of calculating them
+okay see you on Thursday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
\ No newline at end of file
diff --git a/YgyshX9T3S4.txt b/YgyshX9T3S4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b5e98ab84218c6c05f4f4ae73a16a5bdce73e209
--- /dev/null
+++ b/YgyshX9T3S4.txt
@@ -0,0 +1,12643 @@
+align:start position:0%
+ 
+laughs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so last time
+
+ align:start position:0%
+okay so so last time
+ 
+
+ align:start position:0%
+okay so so last time
+we talked about the rock equation
+
+ align:start position:0%
+we talked about the rock equation
+ 
+
+ align:start position:0%
+we talked about the rock equation
+so the Iraq equation has the following
+
+ align:start position:0%
+so the Iraq equation has the following
+ 
+
+ align:start position:0%
+so the Iraq equation has the following
+form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gamma mu
+
+ align:start position:0%
+gamma mu
+ 
+
+ align:start position:0%
+gamma mu
+partial mu
+
+ align:start position:0%
+partial mu
+ 
+
+ align:start position:0%
+partial mu
+minus m
+
+ align:start position:0%
+minus m
+ 
+
+ align:start position:0%
+minus m
+PSI equal to zero
+
+ align:start position:0%
+PSI equal to zero
+ 
+
+ align:start position:0%
+PSI equal to zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so here we have two spaces
+
+ align:start position:0%
+so so here we have two spaces
+ 
+
+ align:start position:0%
+so so here we have two spaces
+so Y is your
+
+ align:start position:0%
+so Y is your
+ 
+
+ align:start position:0%
+so Y is your
+standard physical space time
+
+ align:start position:0%
+standard physical space time
+ 
+
+ align:start position:0%
+standard physical space time
+so with X mu
+
+ align:start position:0%
+so with X mu
+ 
+
+ align:start position:0%
+so with X mu
+and then we have a lot of internal space
+
+ align:start position:0%
+and then we have a lot of internal space
+ 
+
+ align:start position:0%
+and then we have a lot of internal space
+which is labeled by the index of The
+
+ align:start position:0%
+which is labeled by the index of The
+ 
+
+ align:start position:0%
+which is labeled by the index of The
+Upside and the gamma which has
+
+ align:start position:0%
+Upside and the gamma which has
+ 
+
+ align:start position:0%
+Upside and the gamma which has
+suppressed here so psi should be
+
+ align:start position:0%
+suppressed here so psi should be
+ 
+
+ align:start position:0%
+suppressed here so psi should be
+considered as a four vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the alpha equal to one two three four
+
+ align:start position:0%
+the alpha equal to one two three four
+ 
+
+ align:start position:0%
+the alpha equal to one two three four
+and the gamma mu
+
+ align:start position:0%
+and the gamma mu
+ 
+
+ align:start position:0%
+and the gamma mu
+should be considered as a matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay four by four Matrix
+
+ align:start position:0%
+okay four by four Matrix
+ 
+
+ align:start position:0%
+okay four by four Matrix
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so so this space labeled by by Alpha
+
+ align:start position:0%
+and so so this space labeled by by Alpha
+ 
+
+ align:start position:0%
+and so so this space labeled by by Alpha
+so this is called the spinner space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal spinner space so uh so you have
+
+ align:start position:0%
+is equal spinner space so uh so you have
+ 
+
+ align:start position:0%
+is equal spinner space so uh so you have
+to be careful that now we have two uh
+
+ align:start position:0%
+to be careful that now we have two uh
+ 
+
+ align:start position:0%
+to be careful that now we have two uh
+spaces in the time together okay one is
+
+ align:start position:0%
+spaces in the time together okay one is
+ 
+
+ align:start position:0%
+spaces in the time together okay one is
+your ordinary space time and so this is
+
+ align:start position:0%
+your ordinary space time and so this is
+ 
+
+ align:start position:0%
+your ordinary space time and so this is
+the function of the space time
+
+ align:start position:0%
+the function of the space time
+ 
+
+ align:start position:0%
+the function of the space time
+by this Carriage on index yeah uh
+
+ align:start position:0%
+by this Carriage on index yeah uh
+ 
+
+ align:start position:0%
+by this Carriage on index yeah uh
+carries on indices and so this is the a
+
+ align:start position:0%
+carries on indices and so this is the a
+ 
+
+ align:start position:0%
+carries on indices and so this is the a
+matrix equation
+
+ align:start position:0%
+matrix equation
+ 
+
+ align:start position:0%
+matrix equation
+so all together they are there are four
+
+ align:start position:0%
+so all together they are there are four
+ 
+
+ align:start position:0%
+so all together they are there are four
+four equations here for each component
+
+ align:start position:0%
+four equations here for each component
+ 
+
+ align:start position:0%
+four equations here for each component
+of PSI okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh yeah so let me call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let me call this equation one
+
+ align:start position:0%
+so let me call this equation one
+ 
+
+ align:start position:0%
+so let me call this equation one
+whichever this nature
+
+ align:start position:0%
+whichever this nature
+ 
+
+ align:start position:0%
+whichever this nature
+will be a lot ordinary images they
+
+ align:start position:0%
+will be a lot ordinary images they
+ 
+
+ align:start position:0%
+will be a lot ordinary images they
+satisfy this condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with new equal to Q is a blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means
+
+ align:start position:0%
+so that means
+ 
+
+ align:start position:0%
+so that means
+different gamma matrices when their
+
+ align:start position:0%
+different gamma matrices when their
+ 
+
+ align:start position:0%
+different gamma matrices when their
+index are not the same
+
+ align:start position:0%
+index are not the same
+ 
+
+ align:start position:0%
+index are not the same
+the anti-commute with each other
+
+ align:start position:0%
+the anti-commute with each other
+ 
+
+ align:start position:0%
+the anti-commute with each other
+okay so if you come uh you pass them
+
+ align:start position:0%
+okay so if you come uh you pass them
+ 
+
+ align:start position:0%
+okay so if you come uh you pass them
+through you get the minus sign okay so
+
+ align:start position:0%
+through you get the minus sign okay so
+ 
+
+ align:start position:0%
+through you get the minus sign okay so
+the anti-compute with each other because
+
+ align:start position:0%
+the anti-compute with each other because
+ 
+
+ align:start position:0%
+the anti-compute with each other because
+when we will not continue the right hand
+
+ align:start position:0%
+when we will not continue the right hand
+ 
+
+ align:start position:0%
+when we will not continue the right hand
+side is zero and uh when you pass
+
+ align:start position:0%
+side is zero and uh when you pass
+ 
+
+ align:start position:0%
+side is zero and uh when you pass
+through each other you get the minus
+
+ align:start position:0%
+through each other you get the minus
+ 
+
+ align:start position:0%
+through each other you get the minus
+under the square of them so gamma zero
+
+ align:start position:0%
+under the square of them so gamma zero
+ 
+
+ align:start position:0%
+under the square of them so gamma zero
+Square you get the minus one because
+
+ align:start position:0%
+Square you get the minus one because
+ 
+
+ align:start position:0%
+Square you get the minus one because
+this is zero zero it's minus one and the
+
+ align:start position:0%
+this is zero zero it's minus one and the
+ 
+
+ align:start position:0%
+this is zero zero it's minus one and the
+gamma I squared in this case one okay so
+
+ align:start position:0%
+gamma I squared in this case one okay so
+ 
+
+ align:start position:0%
+gamma I squared in this case one okay so
+so this is very simple
+
+ align:start position:0%
+so this is very simple
+ 
+
+ align:start position:0%
+so this is very simple
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's the identity Matrix yeah yeah
+
+ align:start position:0%
+yeah it's the identity Matrix yeah yeah
+ 
+
+ align:start position:0%
+yeah it's the identity Matrix yeah yeah
+when I say gamma zero squares minus one
+
+ align:start position:0%
+when I say gamma zero squares minus one
+ 
+
+ align:start position:0%
+when I say gamma zero squares minus one
+is also minus times identity Matrix
+
+ align:start position:0%
+is also minus times identity Matrix
+ 
+
+ align:start position:0%
+is also minus times identity Matrix
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and also not all gamma mu are Commission
+
+ align:start position:0%
+and also not all gamma mu are Commission
+ 
+
+ align:start position:0%
+and also not all gamma mu are Commission
+so so the relation is that the the gamma
+
+ align:start position:0%
+so so the relation is that the the gamma
+ 
+
+ align:start position:0%
+so so the relation is that the the gamma
+mu dagger is equal to gamma mu comma
+
+ align:start position:0%
+mu dagger is equal to gamma mu comma
+ 
+
+ align:start position:0%
+mu dagger is equal to gamma mu comma
+zero common mu comma zero okay
+
+ align:start position:0%
+zero common mu comma zero okay
+ 
+
+ align:start position:0%
+zero common mu comma zero okay
+so so again from here you can
+
+ align:start position:0%
+so so again from here you can
+ 
+
+ align:start position:0%
+so so again from here you can
+yeah so this is just a compact way to uh
+
+ align:start position:0%
+yeah so this is just a compact way to uh
+ 
+
+ align:start position:0%
+yeah so this is just a compact way to uh
+to to write the uh its properties when
+
+ align:start position:0%
+to to write the uh its properties when
+ 
+
+ align:start position:0%
+to to write the uh its properties when
+you have when when mu is equal to zero
+
+ align:start position:0%
+you have when when mu is equal to zero
+ 
+
+ align:start position:0%
+you have when when mu is equal to zero
+and then you have comma 0 times gamma
+
+ align:start position:0%
+and then you have comma 0 times gamma
+ 
+
+ align:start position:0%
+and then you have comma 0 times gamma
+zero square is -1 and then you get the
+
+ align:start position:0%
+zero square is -1 and then you get the
+ 
+
+ align:start position:0%
+zero square is -1 and then you get the
+minus comma zero tells you that gamma
+
+ align:start position:0%
+minus comma zero tells you that gamma
+ 
+
+ align:start position:0%
+minus comma zero tells you that gamma
+zero is anti-commission
+
+ align:start position:0%
+zero is anti-commission
+ 
+
+ align:start position:0%
+zero is anti-commission
+and if you take the index to be I here
+
+ align:start position:0%
+and if you take the index to be I here
+ 
+
+ align:start position:0%
+and if you take the index to be I here
+and then you have index I here and then
+
+ align:start position:0%
+and then you have index I here and then
+ 
+
+ align:start position:0%
+and then you have index I here and then
+when zero and I they're not the same so
+
+ align:start position:0%
+when zero and I they're not the same so
+ 
+
+ align:start position:0%
+when zero and I they're not the same so
+the anti-commute you can pass through
+
+ align:start position:0%
+the anti-commute you can pass through
+ 
+
+ align:start position:0%
+the anti-commute you can pass through
+this gamma zero through this gamma I you
+
+ align:start position:0%
+this gamma zero through this gamma I you
+ 
+
+ align:start position:0%
+this gamma zero through this gamma I you
+get the minus sign and then gamma zero
+
+ align:start position:0%
+get the minus sign and then gamma zero
+ 
+
+ align:start position:0%
+get the minus sign and then gamma zero
+Square give you another minus sign so
+
+ align:start position:0%
+Square give you another minus sign so
+ 
+
+ align:start position:0%
+Square give you another minus sign so
+you get one so that means that the gamma
+
+ align:start position:0%
+you get one so that means that the gamma
+ 
+
+ align:start position:0%
+you get one so that means that the gamma
+I dagger equal to gamma I okay so gamma
+
+ align:start position:0%
+I dagger equal to gamma I okay so gamma
+ 
+
+ align:start position:0%
+I dagger equal to gamma I okay so gamma
+I is commission okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so in my convention there's no I
+
+ align:start position:0%
+uh so in my convention there's no I
+ 
+
+ align:start position:0%
+uh so in my convention there's no I
+so with this
+
+ align:start position:0%
+so with this
+ 
+
+ align:start position:0%
+so with this
+so so it's a mu mu here is mostly plus
+
+ align:start position:0%
+so so it's a mu mu here is mostly plus
+ 
+
+ align:start position:0%
+so so it's a mu mu here is mostly plus
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+so some people when they use say mostly
+
+ align:start position:0%
+so some people when they use say mostly
+ 
+
+ align:start position:0%
+so some people when they use say mostly
+negative metric then there may be a i
+
+ align:start position:0%
+negative metric then there may be a i
+ 
+
+ align:start position:0%
+negative metric then there may be a i
+in in there yeah yeah yeah so it's
+
+ align:start position:0%
+in in there yeah yeah yeah so it's
+ 
+
+ align:start position:0%
+in in there yeah yeah yeah so it's
+depend on your convention in defining
+
+ align:start position:0%
+depend on your convention in defining
+ 
+
+ align:start position:0%
+depend on your convention in defining
+the gamma matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good other questions
+
+ align:start position:0%
+good other questions
+ 
+
+ align:start position:0%
+good other questions
+yeah as I mentioned last time different
+
+ align:start position:0%
+yeah as I mentioned last time different
+ 
+
+ align:start position:0%
+yeah as I mentioned last time different
+conventions are loined so but you just
+
+ align:start position:0%
+conventions are loined so but you just
+ 
+
+ align:start position:0%
+conventions are loined so but you just
+stick one convention should be fine
+
+ align:start position:0%
+stick one convention should be fine
+ 
+
+ align:start position:0%
+stick one convention should be fine
+stick to my convention would be fine yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah this is just a compact way to
+
+ align:start position:0%
+oh yeah this is just a compact way to
+ 
+
+ align:start position:0%
+oh yeah this is just a compact way to
+write down that gamma zero is
+
+ align:start position:0%
+write down that gamma zero is
+ 
+
+ align:start position:0%
+write down that gamma zero is
+anti-hubmission and Gamma I is formation
+
+ align:start position:0%
+anti-hubmission and Gamma I is formation
+ 
+
+ align:start position:0%
+anti-hubmission and Gamma I is formation
+okay yeah yeah just uh at least just
+
+ align:start position:0%
+okay yeah yeah just uh at least just
+ 
+
+ align:start position:0%
+okay yeah yeah just uh at least just
+compact yeah just this is useful so that
+
+ align:start position:0%
+compact yeah just this is useful so that
+ 
+
+ align:start position:0%
+compact yeah just this is useful so that
+you can treat all gamma mule in the same
+
+ align:start position:0%
+you can treat all gamma mule in the same
+ 
+
+ align:start position:0%
+you can treat all gamma mule in the same
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+so that you don't have to always
+
+ align:start position:0%
+so that you don't have to always
+ 
+
+ align:start position:0%
+so that you don't have to always
+separate them yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so last time we also said
+
+ align:start position:0%
+okay so last time we also said
+ 
+
+ align:start position:0%
+okay so last time we also said
+you have many many choices for gamma mu
+
+ align:start position:0%
+you have many many choices for gamma mu
+ 
+
+ align:start position:0%
+you have many many choices for gamma mu
+but they are all equivalent physically
+
+ align:start position:0%
+but they are all equivalent physically
+ 
+
+ align:start position:0%
+but they are all equivalent physically
+equivalent and so different choices they
+
+ align:start position:0%
+equivalent and so different choices they
+ 
+
+ align:start position:0%
+equivalent and so different choices they
+are convenient for different purposes
+
+ align:start position:0%
+are convenient for different purposes
+ 
+
+ align:start position:0%
+are convenient for different purposes
+okay so often we just pick one of them
+
+ align:start position:0%
+okay so often we just pick one of them
+ 
+
+ align:start position:0%
+okay so often we just pick one of them
+and depend on a depending on the problem
+
+ align:start position:0%
+and depend on a depending on the problem
+ 
+
+ align:start position:0%
+and depend on a depending on the problem
+we are yeah so that comes with
+
+ align:start position:0%
+we are yeah so that comes with
+ 
+
+ align:start position:0%
+we are yeah so that comes with
+experience so for certain problems
+
+ align:start position:0%
+experience so for certain problems
+ 
+
+ align:start position:0%
+experience so for certain problems
+certain choices of gamma become more
+
+ align:start position:0%
+certain choices of gamma become more
+ 
+
+ align:start position:0%
+certain choices of gamma become more
+useful yeah become more easier to
+
+ align:start position:0%
+useful yeah become more easier to
+ 
+
+ align:start position:0%
+useful yeah become more easier to
+manipulate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so now let's talk about the
+
+ align:start position:0%
+okay good so now let's talk about the
+ 
+
+ align:start position:0%
+okay good so now let's talk about the
+Lorenz covariance
+
+ align:start position:0%
+Lorenz covariance
+ 
+
+ align:start position:0%
+Lorenz covariance
+of the Iraq equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we started a little bit last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+Lorraine's quarries means that the
+
+ align:start position:0%
+Lorraine's quarries means that the
+ 
+
+ align:start position:0%
+Lorraine's quarries means that the
+equation looks the same
+
+ align:start position:0%
+equation looks the same
+ 
+
+ align:start position:0%
+equation looks the same
+in all orange frames okay so so when you
+
+ align:start position:0%
+in all orange frames okay so so when you
+ 
+
+ align:start position:0%
+in all orange frames okay so so when you
+make a chlorine transformation
+
+ align:start position:0%
+make a chlorine transformation
+ 
+
+ align:start position:0%
+make a chlorine transformation
+so imagine you make a
+
+ align:start position:0%
+so imagine you make a
+ 
+
+ align:start position:0%
+so imagine you make a
+go to another frame you start with your
+
+ align:start position:0%
+go to another frame you start with your
+ 
+
+ align:start position:0%
+go to another frame you start with your
+frame defined by this x mu so now
+
+ align:start position:0%
+frame defined by this x mu so now
+ 
+
+ align:start position:0%
+frame defined by this x mu so now
+imagine you go to another frame
+
+ align:start position:0%
+imagine you go to another frame
+ 
+
+ align:start position:0%
+imagine you go to another frame
+which you make a low range
+
+ align:start position:0%
+which you make a low range
+ 
+
+ align:start position:0%
+which you make a low range
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+the low range covariance means you you
+
+ align:start position:0%
+the low range covariance means you you
+ 
+
+ align:start position:0%
+the low range covariance means you you
+see your equation when written in this
+
+ align:start position:0%
+see your equation when written in this
+ 
+
+ align:start position:0%
+see your equation when written in this
+frame in terms of X Prime mu have the
+
+ align:start position:0%
+frame in terms of X Prime mu have the
+ 
+
+ align:start position:0%
+frame in terms of X Prime mu have the
+same form okay have the same form so
+
+ align:start position:0%
+same form okay have the same form so
+ 
+
+ align:start position:0%
+same form okay have the same form so
+last time we talked about the scalar
+
+ align:start position:0%
+last time we talked about the scalar
+ 
+
+ align:start position:0%
+last time we talked about the scalar
+equations at the end
+
+ align:start position:0%
+equations at the end
+ 
+
+ align:start position:0%
+equations at the end
+and a lot of the equation we have seen
+
+ align:start position:0%
+and a lot of the equation we have seen
+ 
+
+ align:start position:0%
+and a lot of the equation we have seen
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+is the is the Maxwell equation okay so
+
+ align:start position:0%
+is the is the Maxwell equation okay so
+ 
+
+ align:start position:0%
+is the is the Maxwell equation okay so
+so let me also very quickly mention uh
+
+ align:start position:0%
+so let me also very quickly mention uh
+ 
+
+ align:start position:0%
+so let me also very quickly mention uh
+for the Maxwell equation so so when you
+
+ align:start position:0%
+for the Maxwell equation so so when you
+ 
+
+ align:start position:0%
+for the Maxwell equation so so when you
+have a Maxwell equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the story for the
+
+ align:start position:0%
+which is the story for the
+ 
+
+ align:start position:0%
+which is the story for the
+Vector potential
+
+ align:start position:0%
+Vector potential
+ 
+
+ align:start position:0%
+Vector potential
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now in contrast we remember for the
+
+ align:start position:0%
+so now in contrast we remember for the
+ 
+
+ align:start position:0%
+so now in contrast we remember for the
+scalar case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so last time yeah let me just write
+
+ align:start position:0%
+so so last time yeah let me just write
+ 
+
+ align:start position:0%
+so so last time yeah let me just write
+it down here last time we said for the
+
+ align:start position:0%
+it down here last time we said for the
+ 
+
+ align:start position:0%
+it down here last time we said for the
+scalar case
+
+ align:start position:0%
+scalar case
+ 
+
+ align:start position:0%
+scalar case
+when you go to different frame
+
+ align:start position:0%
+when you go to different frame
+ 
+
+ align:start position:0%
+when you go to different frame
+the five Prime should be equal to
+
+ align:start position:0%
+the five Prime should be equal to
+ 
+
+ align:start position:0%
+the five Prime should be equal to
+evaluate to do coordinate should be
+
+ align:start position:0%
+evaluate to do coordinate should be
+ 
+
+ align:start position:0%
+evaluate to do coordinate should be
+equal to 5x okay so this is the
+
+ align:start position:0%
+equal to 5x okay so this is the
+ 
+
+ align:start position:0%
+equal to 5x okay so this is the
+transformation for scalar field
+
+ align:start position:0%
+transformation for scalar field
+ 
+
+ align:start position:0%
+transformation for scalar field
+but now if you want you to Max the
+
+ align:start position:0%
+but now if you want you to Max the
+ 
+
+ align:start position:0%
+but now if you want you to Max the
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+so we have to think about
+
+ align:start position:0%
+so we have to think about
+ 
+
+ align:start position:0%
+so we have to think about
+how this a mu transform under a lower
+
+ align:start position:0%
+how this a mu transform under a lower
+ 
+
+ align:start position:0%
+how this a mu transform under a lower
+end transformation and now a mu is a
+
+ align:start position:0%
+end transformation and now a mu is a
+ 
+
+ align:start position:0%
+end transformation and now a mu is a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+is a four Vector in the in space time
+
+ align:start position:0%
+is a four Vector in the in space time
+ 
+
+ align:start position:0%
+is a four Vector in the in space time
+okay and so
+
+ align:start position:0%
+okay and so
+ 
+
+ align:start position:0%
+okay and so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that means that the uh uh a mu should
+
+ align:start position:0%
+so that means that the uh uh a mu should
+ 
+
+ align:start position:0%
+so that means that the uh uh a mu should
+uh transform also as the a vector okay
+
+ align:start position:0%
+uh transform also as the a vector okay
+ 
+
+ align:start position:0%
+uh transform also as the a vector okay
+so so this means that when you go to new
+
+ align:start position:0%
+so so this means that when you go to new
+ 
+
+ align:start position:0%
+so so this means that when you go to new
+frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a mu transform
+
+ align:start position:0%
+a mu transform
+ 
+
+ align:start position:0%
+a mu transform
+as Lambda mu Nu
+
+ align:start position:0%
+as Lambda mu Nu
+ 
+
+ align:start position:0%
+as Lambda mu Nu
+a new
+
+ align:start position:0%
+a new
+ 
+
+ align:start position:0%
+a new
+X okay
+
+ align:start position:0%
+X okay
+ 
+
+ align:start position:0%
+X okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here not only so when a mu
+
+ align:start position:0%
+here not only so when a mu
+ 
+
+ align:start position:0%
+here not only so when a mu
+you evaluate the new position
+
+ align:start position:0%
+you evaluate the new position
+ 
+
+ align:start position:0%
+you evaluate the new position
+is can be written as a linear
+
+ align:start position:0%
+is can be written as a linear
+ 
+
+ align:start position:0%
+is can be written as a linear
+supervisition of the value at your
+
+ align:start position:0%
+supervisition of the value at your
+ 
+
+ align:start position:0%
+supervisition of the value at your
+original position
+
+ align:start position:0%
+original position
+ 
+
+ align:start position:0%
+original position
+and this linear position this linear
+
+ align:start position:0%
+and this linear position this linear
+ 
+
+ align:start position:0%
+and this linear position this linear
+superposition by itself is a low range
+
+ align:start position:0%
+superposition by itself is a low range
+ 
+
+ align:start position:0%
+superposition by itself is a low range
+transformation because a mu is a vector
+
+ align:start position:0%
+transformation because a mu is a vector
+ 
+
+ align:start position:0%
+transformation because a mu is a vector
+okay uh because mu is a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means just under Lauren
+
+ align:start position:0%
+that means just under Lauren
+ 
+
+ align:start position:0%
+that means just under Lauren
+transformation and the different
+
+ align:start position:0%
+transformation and the different
+ 
+
+ align:start position:0%
+transformation and the different
+components of a mu should also uh change
+
+ align:start position:0%
+components of a mu should also uh change
+ 
+
+ align:start position:0%
+components of a mu should also uh change
+under the transformation
+
+ align:start position:0%
+under the transformation
+ 
+
+ align:start position:0%
+under the transformation
+so so given this
+
+ align:start position:0%
+so so given this
+ 
+
+ align:start position:0%
+so so given this
+so I will not uh showed it now just I
+
+ align:start position:0%
+so I will not uh showed it now just I
+ 
+
+ align:start position:0%
+so I will not uh showed it now just I
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+take a couple minutes but you should
+
+ align:start position:0%
+take a couple minutes but you should
+ 
+
+ align:start position:0%
+take a couple minutes but you should
+convince yourself try to check yourself
+
+ align:start position:0%
+convince yourself try to check yourself
+ 
+
+ align:start position:0%
+convince yourself try to check yourself
+that the Maxwell equation which can be
+
+ align:start position:0%
+that the Maxwell equation which can be
+ 
+
+ align:start position:0%
+that the Maxwell equation which can be
+written so example as
+
+ align:start position:0%
+written so example as
+ 
+
+ align:start position:0%
+written so example as
+F mu mu Nu U equal to zero
+
+ align:start position:0%
+F mu mu Nu U equal to zero
+ 
+
+ align:start position:0%
+F mu mu Nu U equal to zero
+this implies
+
+ align:start position:0%
+this implies
+ 
+
+ align:start position:0%
+this implies
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that the partial mu Prime in the new
+
+ align:start position:0%
+that the partial mu Prime in the new
+ 
+
+ align:start position:0%
+that the partial mu Prime in the new
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+and then the F mu Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fmu Prime is a a obtained from this new
+
+ align:start position:0%
+fmu Prime is a a obtained from this new
+ 
+
+ align:start position:0%
+fmu Prime is a a obtained from this new
+a new Prime
+
+ align:start position:0%
+a new Prime
+ 
+
+ align:start position:0%
+a new Prime
+and these two equations are the same
+
+ align:start position:0%
+and these two equations are the same
+ 
+
+ align:start position:0%
+and these two equations are the same
+okay uh equivalent just in one frame and
+
+ align:start position:0%
+okay uh equivalent just in one frame and
+ 
+
+ align:start position:0%
+okay uh equivalent just in one frame and
+then when you go to different frame and
+
+ align:start position:0%
+then when you go to different frame and
+ 
+
+ align:start position:0%
+then when you go to different frame and
+then you get this equation so equation
+
+ align:start position:0%
+then you get this equation so equation
+ 
+
+ align:start position:0%
+then you get this equation so equation
+will be exactly the same form okay but
+
+ align:start position:0%
+will be exactly the same form okay but
+ 
+
+ align:start position:0%
+will be exactly the same form okay but
+now it's in the new frame okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so now let's go to the Rock equation
+
+ align:start position:0%
+so now let's go to the Rock equation
+ 
+
+ align:start position:0%
+so now let's go to the Rock equation
+so now I've got a a go to the Rock
+
+ align:start position:0%
+so now I've got a a go to the Rock
+ 
+
+ align:start position:0%
+so now I've got a a go to the Rock
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again this side
+
+ align:start position:0%
+again this side
+ 
+
+ align:start position:0%
+again this side
+we need to ask how the size should
+
+ align:start position:0%
+we need to ask how the size should
+ 
+
+ align:start position:0%
+we need to ask how the size should
+transform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+underly range transformation okay
+
+ align:start position:0%
+underly range transformation okay
+ 
+
+ align:start position:0%
+underly range transformation okay
+but now this side is a completely new
+
+ align:start position:0%
+but now this side is a completely new
+ 
+
+ align:start position:0%
+but now this side is a completely new
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+so this is another it's not like in the
+
+ align:start position:0%
+so this is another it's not like in the
+ 
+
+ align:start position:0%
+so this is another it's not like in the
+in the Maxwell case below this is a
+
+ align:start position:0%
+in the Maxwell case below this is a
+ 
+
+ align:start position:0%
+in the Maxwell case below this is a
+space-time Vector so you can easily
+
+ align:start position:0%
+space-time Vector so you can easily
+ 
+
+ align:start position:0%
+space-time Vector so you can easily
+guess how you should transform okay
+
+ align:start position:0%
+guess how you should transform okay
+ 
+
+ align:start position:0%
+guess how you should transform okay
+so now this upside this spinner space is
+
+ align:start position:0%
+so now this upside this spinner space is
+ 
+
+ align:start position:0%
+so now this upside this spinner space is
+completely new okay so so now we have to
+
+ align:start position:0%
+completely new okay so so now we have to
+ 
+
+ align:start position:0%
+completely new okay so so now we have to
+figure out
+
+ align:start position:0%
+figure out
+ 
+
+ align:start position:0%
+figure out
+half side transform okay helps I
+
+ align:start position:0%
+half side transform okay helps I
+ 
+
+ align:start position:0%
+half side transform okay helps I
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+so so let's suppose okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low range transformation namda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative PSI Transformer as follows
+
+ align:start position:0%
+negative PSI Transformer as follows
+ 
+
+ align:start position:0%
+negative PSI Transformer as follows
+PSI Prime
+
+ align:start position:0%
+PSI Prime
+ 
+
+ align:start position:0%
+PSI Prime
+alpha x Prime because now again you
+
+ align:start position:0%
+alpha x Prime because now again you
+ 
+
+ align:start position:0%
+alpha x Prime because now again you
+evaluate in the loop position new frame
+
+ align:start position:0%
+evaluate in the loop position new frame
+ 
+
+ align:start position:0%
+evaluate in the loop position new frame
+since this carrier index in principle
+
+ align:start position:0%
+since this carrier index in principle
+ 
+
+ align:start position:0%
+since this carrier index in principle
+this can be a superposition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the uh you can mix them in the
+
+ align:start position:0%
+in the uh you can mix them in the
+ 
+
+ align:start position:0%
+in the uh you can mix them in the
+internal space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in principle we can have form like
+
+ align:start position:0%
+okay in principle we can have form like
+ 
+
+ align:start position:0%
+okay in principle we can have form like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+say for some
+
+ align:start position:0%
+say for some
+ 
+
+ align:start position:0%
+say for some
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+okay which depends on Lambda okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in principle
+
+ align:start position:0%
+so in principle
+ 
+
+ align:start position:0%
+so in principle
+you can have a transmission like this
+
+ align:start position:0%
+you can have a transmission like this
+ 
+
+ align:start position:0%
+you can have a transmission like this
+say say when you evaluate a new position
+
+ align:start position:0%
+say say when you evaluate a new position
+ 
+
+ align:start position:0%
+say say when you evaluate a new position
+it's given by the value at the old
+
+ align:start position:0%
+it's given by the value at the old
+ 
+
+ align:start position:0%
+it's given by the value at the old
+position but now you can make some
+
+ align:start position:0%
+position but now you can make some
+ 
+
+ align:start position:0%
+position but now you can make some
+rotations in the internal space
+
+ align:start position:0%
+rotations in the internal space
+ 
+
+ align:start position:0%
+rotations in the internal space
+just as here for the for the Maxwell
+
+ align:start position:0%
+just as here for the for the Maxwell
+ 
+
+ align:start position:0%
+just as here for the for the Maxwell
+field okay just as here for the max
+
+ align:start position:0%
+field okay just as here for the max
+ 
+
+ align:start position:0%
+field okay just as here for the max
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+so accept
+
+ align:start position:0%
+so accept
+ 
+
+ align:start position:0%
+so accept
+and so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose this as for this and then our
+
+ align:start position:0%
+suppose this as for this and then our
+ 
+
+ align:start position:0%
+suppose this as for this and then our
+range covariance would be the statement
+
+ align:start position:0%
+range covariance would be the statement
+ 
+
+ align:start position:0%
+range covariance would be the statement
+say for some yeah for some
+
+ align:start position:0%
+say for some yeah for some
+ 
+
+ align:start position:0%
+say for some yeah for some
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the Lorenz cover incident is a
+
+ align:start position:0%
+and then the Lorenz cover incident is a
+ 
+
+ align:start position:0%
+and then the Lorenz cover incident is a
+statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the statement starting from one
+
+ align:start position:0%
+is the statement starting from one
+ 
+
+ align:start position:0%
+is the statement starting from one
+from equation one
+
+ align:start position:0%
+from equation one
+ 
+
+ align:start position:0%
+from equation one
+you should be able to find go into the
+
+ align:start position:0%
+you should be able to find go into the
+ 
+
+ align:start position:0%
+you should be able to find go into the
+new frame
+
+ align:start position:0%
+new frame
+ 
+
+ align:start position:0%
+new frame
+you have a equation like this gamma mu
+
+ align:start position:0%
+you have a equation like this gamma mu
+ 
+
+ align:start position:0%
+you have a equation like this gamma mu
+partial mu Prime
+
+ align:start position:0%
+partial mu Prime
+ 
+
+ align:start position:0%
+partial mu Prime
+minus m
+
+ align:start position:0%
+minus m
+ 
+
+ align:start position:0%
+minus m
+PSI Prime
+
+ align:start position:0%
+PSI Prime
+ 
+
+ align:start position:0%
+PSI Prime
+X Prime equal to zero
+
+ align:start position:0%
+X Prime equal to zero
+ 
+
+ align:start position:0%
+X Prime equal to zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you should get a identical equation
+
+ align:start position:0%
+so you should get a identical equation
+ 
+
+ align:start position:0%
+so you should get a identical equation
+not an electrical equation two you
+
+ align:start position:0%
+not an electrical equation two you
+ 
+
+ align:start position:0%
+not an electrical equation two you
+should get the identical equation but
+
+ align:start position:0%
+should get the identical equation but
+ 
+
+ align:start position:0%
+should get the identical equation but
+now everything is in terms of prime
+
+ align:start position:0%
+now everything is in terms of prime
+ 
+
+ align:start position:0%
+now everything is in terms of prime
+okay everything in terms of prime
+
+ align:start position:0%
+okay everything in terms of prime
+ 
+
+ align:start position:0%
+okay everything in terms of prime
+so so why say emphasize the gamma mu
+
+ align:start position:0%
+so so why say emphasize the gamma mu
+ 
+
+ align:start position:0%
+so so why say emphasize the gamma mu
+does not change despite a carry index mu
+
+ align:start position:0%
+does not change despite a carry index mu
+ 
+
+ align:start position:0%
+does not change despite a carry index mu
+will gamma mu just some
+
+ align:start position:0%
+will gamma mu just some
+ 
+
+ align:start position:0%
+will gamma mu just some
+constant matrices okay to see it's a
+
+ align:start position:0%
+constant matrices okay to see it's a
+ 
+
+ align:start position:0%
+constant matrices okay to see it's a
+it's a it's just four matrices uh it
+
+ align:start position:0%
+it's a it's just four matrices uh it
+ 
+
+ align:start position:0%
+it's a it's just four matrices uh it
+does not transform under any space time
+
+ align:start position:0%
+does not transform under any space time
+ 
+
+ align:start position:0%
+does not transform under any space time
+chance it it's not dynamical variable it
+
+ align:start position:0%
+chance it it's not dynamical variable it
+ 
+
+ align:start position:0%
+chance it it's not dynamical variable it
+does not transform on the space-time
+
+ align:start position:0%
+does not transform on the space-time
+ 
+
+ align:start position:0%
+does not transform on the space-time
+transmission so so gamma mu does not
+
+ align:start position:0%
+transmission so so gamma mu does not
+ 
+
+ align:start position:0%
+transmission so so gamma mu does not
+change okay
+
+ align:start position:0%
+change okay
+ 
+
+ align:start position:0%
+change okay
+good so now the question
+
+ align:start position:0%
+good so now the question
+ 
+
+ align:start position:0%
+good so now the question
+of the Lorenz covariance where the drug
+
+ align:start position:0%
+of the Lorenz covariance where the drug
+ 
+
+ align:start position:0%
+of the Lorenz covariance where the drug
+equation is Lorenz coherent volume
+
+ align:start position:0%
+equation is Lorenz coherent volume
+ 
+
+ align:start position:0%
+equation is Lorenz coherent volume
+okay whether we can find the such s okay
+
+ align:start position:0%
+okay whether we can find the such s okay
+ 
+
+ align:start position:0%
+okay whether we can find the such s okay
+which the weather
+
+ align:start position:0%
+which the weather
+ 
+
+ align:start position:0%
+which the weather
+yeah the questions can we find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such an s
+
+ align:start position:0%
+such an s
+ 
+
+ align:start position:0%
+such an s
+okay so if you can find such a s
+
+ align:start position:0%
+okay so if you can find such a s
+ 
+
+ align:start position:0%
+okay so if you can find such a s
+which this is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we say the direct equation is
+
+ align:start position:0%
+then we say the direct equation is
+ 
+
+ align:start position:0%
+then we say the direct equation is
+Lorenz covarent
+
+ align:start position:0%
+Lorenz covarent
+ 
+
+ align:start position:0%
+Lorenz covarent
+and uh and this is how the Rock field
+
+ align:start position:0%
+and uh and this is how the Rock field
+ 
+
+ align:start position:0%
+and uh and this is how the Rock field
+should transform okay so this side is
+
+ align:start position:0%
+should transform okay so this side is
+ 
+
+ align:start position:0%
+should transform okay so this side is
+normally called the direct field okay
+
+ align:start position:0%
+normally called the direct field okay
+ 
+
+ align:start position:0%
+normally called the direct field okay
+and this is how the rock field should
+
+ align:start position:0%
+and this is how the rock field should
+ 
+
+ align:start position:0%
+and this is how the rock field should
+transform so so PSI is often called The
+
+ align:start position:0%
+transform so so PSI is often called The
+ 
+
+ align:start position:0%
+transform so so PSI is often called The
+Rock field it's also often called
+
+ align:start position:0%
+Rock field it's also often called
+ 
+
+ align:start position:0%
+Rock field it's also often called
+spinner field okay and uh it's often
+
+ align:start position:0%
+spinner field okay and uh it's often
+ 
+
+ align:start position:0%
+spinner field okay and uh it's often
+it's also often called The Rock spin the
+
+ align:start position:0%
+it's also often called The Rock spin the
+ 
+
+ align:start position:0%
+it's also often called The Rock spin the
+field and uh anyway and then that should
+
+ align:start position:0%
+field and uh anyway and then that should
+ 
+
+ align:start position:0%
+field and uh anyway and then that should
+be the way high is transformed okay
+
+ align:start position:0%
+be the way high is transformed okay
+ 
+
+ align:start position:0%
+be the way high is transformed okay
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah no no in this case
+
+ align:start position:0%
+yeah no no in this case
+ 
+
+ align:start position:0%
+yeah no no in this case
+so we will when you talk about transform
+
+ align:start position:0%
+so we will when you talk about transform
+ 
+
+ align:start position:0%
+so we will when you talk about transform
+over the scalar field itself of course
+
+ align:start position:0%
+over the scalar field itself of course
+ 
+
+ align:start position:0%
+over the scalar field itself of course
+it's just Phi go to Five Prime
+
+ align:start position:0%
+it's just Phi go to Five Prime
+ 
+
+ align:start position:0%
+it's just Phi go to Five Prime
+and uh because that function changes
+
+ align:start position:0%
+and uh because that function changes
+ 
+
+ align:start position:0%
+and uh because that function changes
+okay that function changes but here we
+
+ align:start position:0%
+okay that function changes but here we
+ 
+
+ align:start position:0%
+okay that function changes but here we
+are asking uh about the form of the
+
+ align:start position:0%
+are asking uh about the form of the
+ 
+
+ align:start position:0%
+are asking uh about the form of the
+equation in the new frame
+
+ align:start position:0%
+equation in the new frame
+ 
+
+ align:start position:0%
+equation in the new frame
+and so so when you go to the new frame
+
+ align:start position:0%
+and so so when you go to the new frame
+ 
+
+ align:start position:0%
+and so so when you go to the new frame
+your function form change but your
+
+ align:start position:0%
+your function form change but your
+ 
+
+ align:start position:0%
+your function form change but your
+coordinate also change so that's why you
+
+ align:start position:0%
+coordinate also change so that's why you
+ 
+
+ align:start position:0%
+coordinate also change so that's why you
+need to when we say the covariance you
+
+ align:start position:0%
+need to when we say the covariance you
+ 
+
+ align:start position:0%
+need to when we say the covariance you
+need to evaluate your new function in
+
+ align:start position:0%
+need to evaluate your new function in
+ 
+
+ align:start position:0%
+need to evaluate your new function in
+the new position yeah yeah yeah that
+
+ align:start position:0%
+the new position yeah yeah yeah that
+ 
+
+ align:start position:0%
+the new position yeah yeah yeah that
+means they look the same in different
+
+ align:start position:0%
+means they look the same in different
+ 
+
+ align:start position:0%
+means they look the same in different
+frame yeah
+
+ align:start position:0%
+frame yeah
+ 
+
+ align:start position:0%
+frame yeah
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah exactly good good exactly that's
+
+ align:start position:0%
+yeah exactly good good exactly that's
+ 
+
+ align:start position:0%
+yeah exactly good good exactly that's
+the that's exactly the right
+
+ align:start position:0%
+the that's exactly the right
+ 
+
+ align:start position:0%
+the that's exactly the right
+mathematical language uh to talk about
+
+ align:start position:0%
+mathematical language uh to talk about
+ 
+
+ align:start position:0%
+mathematical language uh to talk about
+this which we will mention later uh at
+
+ align:start position:0%
+this which we will mention later uh at
+ 
+
+ align:start position:0%
+this which we will mention later uh at
+the moment I didn't want to use
+
+ align:start position:0%
+the moment I didn't want to use
+ 
+
+ align:start position:0%
+the moment I didn't want to use
+mathematical language yeah yeah for
+
+ align:start position:0%
+mathematical language yeah yeah for
+ 
+
+ align:start position:0%
+mathematical language yeah yeah for
+those people who are familiar with group
+
+ align:start position:0%
+those people who are familiar with group
+ 
+
+ align:start position:0%
+those people who are familiar with group
+Theory indeed so this s would be the
+
+ align:start position:0%
+Theory indeed so this s would be the
+ 
+
+ align:start position:0%
+Theory indeed so this s would be the
+representation of the lorentz group in
+
+ align:start position:0%
+representation of the lorentz group in
+ 
+
+ align:start position:0%
+representation of the lorentz group in
+the uh in the spinner space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+okay so now let's try to find this s
+
+ align:start position:0%
+okay so now let's try to find this s
+ 
+
+ align:start position:0%
+okay so now let's try to find this s
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before do that let's first
+
+ align:start position:0%
+so before do that let's first
+ 
+
+ align:start position:0%
+so before do that let's first
+write what is a partial Prime X mu so
+
+ align:start position:0%
+write what is a partial Prime X mu so
+ 
+
+ align:start position:0%
+write what is a partial Prime X mu so
+recall
+
+ align:start position:0%
+recall
+ 
+
+ align:start position:0%
+recall
+partial Prime mu
+
+ align:start position:0%
+partial Prime mu
+ 
+
+ align:start position:0%
+partial Prime mu
+it should be partial partial X Prime mu
+
+ align:start position:0%
+it should be partial partial X Prime mu
+ 
+
+ align:start position:0%
+it should be partial partial X Prime mu
+this transform the new coordinates and
+
+ align:start position:0%
+this transform the new coordinates and
+ 
+
+ align:start position:0%
+this transform the new coordinates and
+from that transformation you can easily
+
+ align:start position:0%
+from that transformation you can easily
+ 
+
+ align:start position:0%
+from that transformation you can easily
+figure it out just chain rule so this is
+
+ align:start position:0%
+figure it out just chain rule so this is
+ 
+
+ align:start position:0%
+figure it out just chain rule so this is
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+partial
+
+ align:start position:0%
+partial
+ 
+
+ align:start position:0%
+partial
+partial X mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Lambda minus one
+
+ align:start position:0%
+and Lambda minus one
+ 
+
+ align:start position:0%
+and Lambda minus one
+new mu okay
+
+ align:start position:0%
+new mu okay
+ 
+
+ align:start position:0%
+new mu okay
+okay so this is very easy to figure it
+
+ align:start position:0%
+okay so this is very easy to figure it
+ 
+
+ align:start position:0%
+okay so this is very easy to figure it
+out because the uh because they have to
+
+ align:start position:0%
+out because the uh because they have to
+ 
+
+ align:start position:0%
+out because the uh because they have to
+be uh the X will multiply the X the
+
+ align:start position:0%
+be uh the X will multiply the X the
+ 
+
+ align:start position:0%
+be uh the X will multiply the X the
+pressure X will have to be a singlet so
+
+ align:start position:0%
+pressure X will have to be a singlet so
+ 
+
+ align:start position:0%
+pressure X will have to be a singlet so
+so this transform has an inverse Matrix
+
+ align:start position:0%
+so this transform has an inverse Matrix
+ 
+
+ align:start position:0%
+so this transform has an inverse Matrix
+so this implies
+
+ align:start position:0%
+so this implies
+ 
+
+ align:start position:0%
+so this implies
+that the gamma mu
+
+ align:start position:0%
+that the gamma mu
+ 
+
+ align:start position:0%
+that the gamma mu
+partial mu Prime should be equal to
+
+ align:start position:0%
+partial mu Prime should be equal to
+ 
+
+ align:start position:0%
+partial mu Prime should be equal to
+Lambda minus 1
+
+ align:start position:0%
+Lambda minus 1
+ 
+
+ align:start position:0%
+Lambda minus 1
+new mu
+
+ align:start position:0%
+new mu
+ 
+
+ align:start position:0%
+new mu
+comma
+
+ align:start position:0%
+comma
+ 
+
+ align:start position:0%
+comma
+mu pi to Nu okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so with this preparation then we can try
+
+ align:start position:0%
+so with this preparation then we can try
+ 
+
+ align:start position:0%
+so with this preparation then we can try
+to uh try to see whether we can find s
+
+ align:start position:0%
+to uh try to see whether we can find s
+ 
+
+ align:start position:0%
+to uh try to see whether we can find s
+from this equation okay
+
+ align:start position:0%
+from this equation okay
+ 
+
+ align:start position:0%
+from this equation okay
+no yeah I find this equation from what
+
+ align:start position:0%
+no yeah I find this equation from what
+ 
+
+ align:start position:0%
+no yeah I find this equation from what
+so what we can do is that let's multiply
+
+ align:start position:0%
+so what we can do is that let's multiply
+ 
+
+ align:start position:0%
+so what we can do is that let's multiply
+the equation one from the left by S okay
+
+ align:start position:0%
+the equation one from the left by S okay
+ 
+
+ align:start position:0%
+the equation one from the left by S okay
+so let's imagine we
+
+ align:start position:0%
+so let's imagine we
+ 
+
+ align:start position:0%
+so let's imagine we
+multiply s such a matrix again I always
+
+ align:start position:0%
+multiply s such a matrix again I always
+ 
+
+ align:start position:0%
+multiply s such a matrix again I always
+just suppress the spin the indices and
+
+ align:start position:0%
+just suppress the spin the indices and
+ 
+
+ align:start position:0%
+just suppress the spin the indices and
+just write in The Matrix form
+
+ align:start position:0%
+just write in The Matrix form
+ 
+
+ align:start position:0%
+just write in The Matrix form
+so let's just write gamma mu
+
+ align:start position:0%
+so let's just write gamma mu
+ 
+
+ align:start position:0%
+so let's just write gamma mu
+to take that equation 1
+
+ align:start position:0%
+to take that equation 1
+ 
+
+ align:start position:0%
+to take that equation 1
+we multiply by S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have two terms here so this is a
+
+ align:start position:0%
+so we have two terms here so this is a
+ 
+
+ align:start position:0%
+so we have two terms here so this is a
+matrix in the same space as s okay s act
+
+ align:start position:0%
+matrix in the same space as s okay s act
+ 
+
+ align:start position:0%
+matrix in the same space as s okay s act
+in the same space as gamma mu so so we
+
+ align:start position:0%
+in the same space as gamma mu so so we
+ 
+
+ align:start position:0%
+in the same space as gamma mu so so we
+cannot easily commute here okay uh they
+
+ align:start position:0%
+cannot easily commute here okay uh they
+ 
+
+ align:start position:0%
+cannot easily commute here okay uh they
+normally they don't compute
+
+ align:start position:0%
+normally they don't compute
+ 
+
+ align:start position:0%
+normally they don't compute
+but this but m is a constant so we can
+
+ align:start position:0%
+but this but m is a constant so we can
+ 
+
+ align:start position:0%
+but this but m is a constant so we can
+pass s through here okay we can pass
+
+ align:start position:0%
+pass s through here okay we can pass
+ 
+
+ align:start position:0%
+pass s through here okay we can pass
+through S here so we can rewrite this
+
+ align:start position:0%
+through S here so we can rewrite this
+ 
+
+ align:start position:0%
+through S here so we can rewrite this
+equation as follows
+
+ align:start position:0%
+equation as follows
+ 
+
+ align:start position:0%
+equation as follows
+we can write it as s gamma mu
+
+ align:start position:0%
+we can write it as s gamma mu
+ 
+
+ align:start position:0%
+we can write it as s gamma mu
+s minus 1
+
+ align:start position:0%
+s minus 1
+ 
+
+ align:start position:0%
+s minus 1
+mu minus m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s PSI zero okay
+
+ align:start position:0%
+s PSI zero okay
+ 
+
+ align:start position:0%
+s PSI zero okay
+so so for M
+
+ align:start position:0%
+so so for M
+ 
+
+ align:start position:0%
+so so for M
+I just passed s through through but for
+
+ align:start position:0%
+I just passed s through through but for
+ 
+
+ align:start position:0%
+I just passed s through through but for
+this term I just inserted s minus 1 and
+
+ align:start position:0%
+this term I just inserted s minus 1 and
+ 
+
+ align:start position:0%
+this term I just inserted s minus 1 and
+S and so yeah it's the same okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can use this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in here okay because s times PSI just
+
+ align:start position:0%
+in here okay because s times PSI just
+ 
+
+ align:start position:0%
+in here okay because s times PSI just
+equal to psi Prime
+
+ align:start position:0%
+equal to psi Prime
+ 
+
+ align:start position:0%
+equal to psi Prime
+X Prime okay so now we get
+
+ align:start position:0%
+X Prime okay so now we get
+ 
+
+ align:start position:0%
+X Prime okay so now we get
+s comma mu
+
+ align:start position:0%
+s comma mu
+ 
+
+ align:start position:0%
+s comma mu
+s minus one partial mu minus m
+
+ align:start position:0%
+s minus one partial mu minus m
+ 
+
+ align:start position:0%
+s minus one partial mu minus m
+PSI Prime X Prime
+
+ align:start position:0%
+PSI Prime X Prime
+ 
+
+ align:start position:0%
+PSI Prime X Prime
+equal to zero okay we just use that
+
+ align:start position:0%
+equal to zero okay we just use that
+ 
+
+ align:start position:0%
+equal to zero okay we just use that
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so that's the key I'm
+
+ align:start position:0%
+yeah yeah so that's the key I'm
+ 
+
+ align:start position:0%
+yeah yeah so that's the key I'm
+emphasized earlier so so X mu and PSI
+
+ align:start position:0%
+emphasized earlier so so X mu and PSI
+ 
+
+ align:start position:0%
+emphasized earlier so so X mu and PSI
+Alpha there in different space
+
+ align:start position:0%
+Alpha there in different space
+ 
+
+ align:start position:0%
+Alpha there in different space
+so so oh this s and the gamma they're
+
+ align:start position:0%
+so so oh this s and the gamma they're
+ 
+
+ align:start position:0%
+so so oh this s and the gamma they're
+all constant they don't depend on
+
+ align:start position:0%
+all constant they don't depend on
+ 
+
+ align:start position:0%
+all constant they don't depend on
+spatial location
+
+ align:start position:0%
+spatial location
+ 
+
+ align:start position:0%
+spatial location
+and so so partial mu does not act on S
+
+ align:start position:0%
+and so so partial mu does not act on S
+ 
+
+ align:start position:0%
+and so so partial mu does not act on S
+yeah for pi mu point B S is just a
+
+ align:start position:0%
+yeah for pi mu point B S is just a
+ 
+
+ align:start position:0%
+yeah for pi mu point B S is just a
+constant it's a space-time constant it
+
+ align:start position:0%
+constant it's a space-time constant it
+ 
+
+ align:start position:0%
+constant it's a space-time constant it
+only rotates it it only rotates say at
+
+ align:start position:0%
+only rotates it it only rotates say at
+ 
+
+ align:start position:0%
+only rotates it it only rotates say at
+the single point
+
+ align:start position:0%
+the single point
+ 
+
+ align:start position:0%
+the single point
+a different component of PSI at the
+
+ align:start position:0%
+a different component of PSI at the
+ 
+
+ align:start position:0%
+a different component of PSI at the
+single point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+okay so now we have this equation
+
+ align:start position:0%
+okay so now we have this equation
+ 
+
+ align:start position:0%
+okay so now we have this equation
+so now we can compare
+
+ align:start position:0%
+so now we can compare
+ 
+
+ align:start position:0%
+so now we can compare
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+object with this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah in particular this object is equal
+
+ align:start position:0%
+yeah in particular this object is equal
+ 
+
+ align:start position:0%
+yeah in particular this object is equal
+to that
+
+ align:start position:0%
+to that
+ 
+
+ align:start position:0%
+to that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we conclude that one goes to two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+s comma mu
+
+ align:start position:0%
+s comma mu
+ 
+
+ align:start position:0%
+s comma mu
+s minus 1 equal to
+
+ align:start position:0%
+s minus 1 equal to
+ 
+
+ align:start position:0%
+s minus 1 equal to
+this object
+
+ align:start position:0%
+this object
+ 
+
+ align:start position:0%
+this object
+Lambda minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new mu
+
+ align:start position:0%
+new mu
+ 
+
+ align:start position:0%
+new mu
+I think
+
+ align:start position:0%
+I think
+ 
+
+ align:start position:0%
+I think
+yeah I think I'm messing up a little bit
+
+ align:start position:0%
+yeah I think I'm messing up a little bit
+ 
+
+ align:start position:0%
+yeah I think I'm messing up a little bit
+notation here uh gamma mu
+
+ align:start position:0%
+notation here uh gamma mu
+ 
+
+ align:start position:0%
+notation here uh gamma mu
+I think my index is a little bit wrong
+
+ align:start position:0%
+I think my index is a little bit wrong
+ 
+
+ align:start position:0%
+I think my index is a little bit wrong
+let me just make sure
+
+ align:start position:0%
+let me just make sure
+ 
+
+ align:start position:0%
+let me just make sure
+oh yeah yeah here is a partial new sorry
+
+ align:start position:0%
+oh yeah yeah here is a partial new sorry
+ 
+
+ align:start position:0%
+oh yeah yeah here is a partial new sorry
+here is partial news I need to exchange
+
+ align:start position:0%
+here is partial news I need to exchange
+ 
+
+ align:start position:0%
+here is partial news I need to exchange
+the MU and the new index here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+comma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so so this has to be equal to that
+
+ align:start position:0%
+so so so this has to be equal to that
+ 
+
+ align:start position:0%
+so so so this has to be equal to that
+okay so this has to be equal to that and
+
+ align:start position:0%
+okay so this has to be equal to that and
+ 
+
+ align:start position:0%
+okay so this has to be equal to that and
+you need to uh to compare partial new
+
+ align:start position:0%
+you need to uh to compare partial new
+ 
+
+ align:start position:0%
+you need to uh to compare partial new
+with partial mu we have to exchange the
+
+ align:start position:0%
+with partial mu we have to exchange the
+ 
+
+ align:start position:0%
+with partial mu we have to exchange the
+new and new here anyway so so this is
+
+ align:start position:0%
+new and new here anyway so so this is
+ 
+
+ align:start position:0%
+new and new here anyway so so this is
+the equation we have to satisfy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we have to find a matrix as
+
+ align:start position:0%
+so we have to find a matrix as
+ 
+
+ align:start position:0%
+so we have to find a matrix as
+which act on gamma mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gamma mu is some function of H matrices
+
+ align:start position:0%
+gamma mu is some function of H matrices
+ 
+
+ align:start position:0%
+gamma mu is some function of H matrices
+and give you
+
+ align:start position:0%
+and give you
+ 
+
+ align:start position:0%
+and give you
+like this so as if the gamma mu actually
+
+ align:start position:0%
+like this so as if the gamma mu actually
+ 
+
+ align:start position:0%
+like this so as if the gamma mu actually
+when you ask about S as as if gamma mu
+
+ align:start position:0%
+when you ask about S as as if gamma mu
+ 
+
+ align:start position:0%
+when you ask about S as as if gamma mu
+transformed as some low range
+
+ align:start position:0%
+transformed as some low range
+ 
+
+ align:start position:0%
+transformed as some low range
+transformation okay yeah inverse romance
+
+ align:start position:0%
+transformation okay yeah inverse romance
+ 
+
+ align:start position:0%
+transformation okay yeah inverse romance
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so we need to now let's try to find
+
+ align:start position:0%
+so so we need to now let's try to find
+ 
+
+ align:start position:0%
+so so we need to now let's try to find
+this as
+
+ align:start position:0%
+this as
+ 
+
+ align:start position:0%
+this as
+so so to do this we again we use a trick
+
+ align:start position:0%
+so so to do this we again we use a trick
+ 
+
+ align:start position:0%
+so so to do this we again we use a trick
+which uh we have been using before
+
+ align:start position:0%
+which uh we have been using before
+ 
+
+ align:start position:0%
+which uh we have been using before
+so so how would you approach this
+
+ align:start position:0%
+so so how would you approach this
+ 
+
+ align:start position:0%
+so so how would you approach this
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good good yes yes just do a infinite
+
+ align:start position:0%
+good good yes yes just do a infinite
+ 
+
+ align:start position:0%
+good good yes yes just do a infinite
+test mode Transformations okay so once
+
+ align:start position:0%
+test mode Transformations okay so once
+ 
+
+ align:start position:0%
+test mode Transformations okay so once
+you learn how to do infinite test mode
+
+ align:start position:0%
+you learn how to do infinite test mode
+ 
+
+ align:start position:0%
+you learn how to do infinite test mode
+Transformations then you always know how
+
+ align:start position:0%
+Transformations then you always know how
+ 
+
+ align:start position:0%
+Transformations then you always know how
+to do finite once and if any decimal
+
+ align:start position:0%
+to do finite once and if any decimal
+ 
+
+ align:start position:0%
+to do finite once and if any decimal
+ones it's much much easier to do okay
+
+ align:start position:0%
+ones it's much much easier to do okay
+ 
+
+ align:start position:0%
+ones it's much much easier to do okay
+so now again we consider
+
+ align:start position:0%
+so now again we consider
+ 
+
+ align:start position:0%
+so now again we consider
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them the new new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close to Identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that means
+
+ align:start position:0%
+okay so that means
+ 
+
+ align:start position:0%
+okay so that means
+we write Lambda mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and stealtham mu Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the identity
+
+ align:start position:0%
+which is the identity
+ 
+
+ align:start position:0%
+which is the identity
+then plus
+
+ align:start position:0%
+then plus
+ 
+
+ align:start position:0%
+then plus
+Omega mu Nu
+
+ align:start position:0%
+Omega mu Nu
+ 
+
+ align:start position:0%
+Omega mu Nu
+and take the Omega to be small okay and
+
+ align:start position:0%
+and take the Omega to be small okay and
+ 
+
+ align:start position:0%
+and take the Omega to be small okay and
+also remember previously we discussed
+
+ align:start position:0%
+also remember previously we discussed
+ 
+
+ align:start position:0%
+also remember previously we discussed
+that Omega mu mu when you know the index
+
+ align:start position:0%
+that Omega mu mu when you know the index
+ 
+
+ align:start position:0%
+that Omega mu mu when you know the index
+is actually anti-symmetric
+
+ align:start position:0%
+is actually anti-symmetric
+ 
+
+ align:start position:0%
+is actually anti-symmetric
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so and this is infinitesimal so we
+
+ align:start position:0%
+so so and this is infinitesimal so we
+ 
+
+ align:start position:0%
+so so and this is infinitesimal so we
+take this to be infinitesimal and work
+
+ align:start position:0%
+take this to be infinitesimal and work
+ 
+
+ align:start position:0%
+take this to be infinitesimal and work
+everything to first order in Omega okay
+
+ align:start position:0%
+everything to first order in Omega okay
+ 
+
+ align:start position:0%
+everything to first order in Omega okay
+uh work everything uh the first order
+
+ align:start position:0%
+uh work everything uh the first order
+ 
+
+ align:start position:0%
+uh work everything uh the first order
+so similarly the Lambda minus
+
+ align:start position:0%
+so similarly the Lambda minus
+ 
+
+ align:start position:0%
+so similarly the Lambda minus
+we knew
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just equal to data menu
+
+ align:start position:0%
+just equal to data menu
+ 
+
+ align:start position:0%
+just equal to data menu
+just give you my minus Omega
+
+ align:start position:0%
+just give you my minus Omega
+ 
+
+ align:start position:0%
+just give you my minus Omega
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so yeah just to to Leading order in
+
+ align:start position:0%
+so so yeah just to to Leading order in
+ 
+
+ align:start position:0%
+so so yeah just to to Leading order in
+Omega expansion the inverse metric is
+
+ align:start position:0%
+Omega expansion the inverse metric is
+ 
+
+ align:start position:0%
+Omega expansion the inverse metric is
+just given by that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can try to so
+
+ align:start position:0%
+so now we can try to so
+ 
+
+ align:start position:0%
+so now we can try to so
+so since the s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so on the right hand side
+
+ align:start position:0%
+so on the right hand side
+ 
+
+ align:start position:0%
+so on the right hand side
+when when Lambda is close to the
+
+ align:start position:0%
+when when Lambda is close to the
+ 
+
+ align:start position:0%
+when when Lambda is close to the
+identity
+
+ align:start position:0%
+identity
+ 
+
+ align:start position:0%
+identity
+okay so uh uh uh so the right hand side
+
+ align:start position:0%
+okay so uh uh uh so the right hand side
+ 
+
+ align:start position:0%
+okay so uh uh uh so the right hand side
+is just the gamma mu okay just the
+
+ align:start position:0%
+is just the gamma mu okay just the
+ 
+
+ align:start position:0%
+is just the gamma mu okay just the
+identity does not do anything just
+
+ align:start position:0%
+identity does not do anything just
+ 
+
+ align:start position:0%
+identity does not do anything just
+common mu and then plus something
+
+ align:start position:0%
+common mu and then plus something
+ 
+
+ align:start position:0%
+common mu and then plus something
+proportion to Omega okay then that means
+
+ align:start position:0%
+proportion to Omega okay then that means
+ 
+
+ align:start position:0%
+proportion to Omega okay then that means
+that s
+
+ align:start position:0%
+that s
+ 
+
+ align:start position:0%
+that s
+must also have a a number is close to
+
+ align:start position:0%
+must also have a a number is close to
+ 
+
+ align:start position:0%
+must also have a a number is close to
+Identity means s must also have the
+
+ align:start position:0%
+Identity means s must also have the
+ 
+
+ align:start position:0%
+Identity means s must also have the
+structure to be identity and
+
+ align:start position:0%
+structure to be identity and
+ 
+
+ align:start position:0%
+structure to be identity and
+proportional to something linear in
+
+ align:start position:0%
+proportional to something linear in
+ 
+
+ align:start position:0%
+proportional to something linear in
+Omega okay so so the so the S must also
+
+ align:start position:0%
+Omega okay so so the so the S must also
+ 
+
+ align:start position:0%
+Omega okay so so the so the S must also
+have this structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me just don't write the index
+
+ align:start position:0%
+yeah let me just don't write the index
+ 
+
+ align:start position:0%
+yeah let me just don't write the index
+just a direction right as identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it should be something
+
+ align:start position:0%
+and then it should be something
+ 
+
+ align:start position:0%
+and then it should be something
+proportional to Omega okay
+
+ align:start position:0%
+proportional to Omega okay
+ 
+
+ align:start position:0%
+proportional to Omega okay
+so so from convention we write this way
+
+ align:start position:0%
+so so from convention we write this way
+ 
+
+ align:start position:0%
+so so from convention we write this way
+so it should be leading Omega mu and
+
+ align:start position:0%
+so it should be leading Omega mu and
+ 
+
+ align:start position:0%
+so it should be leading Omega mu and
+sigma
+
+ align:start position:0%
+sigma
+ 
+
+ align:start position:0%
+sigma
+so Sigma Mia are a bunch of matrices
+
+ align:start position:0%
+so Sigma Mia are a bunch of matrices
+ 
+
+ align:start position:0%
+so Sigma Mia are a bunch of matrices
+okay so remember s is a four by four
+
+ align:start position:0%
+okay so remember s is a four by four
+ 
+
+ align:start position:0%
+okay so remember s is a four by four
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+and so so Omega menu just some number
+
+ align:start position:0%
+and so so Omega menu just some number
+ 
+
+ align:start position:0%
+and so so Omega menu just some number
+okay just some number so so this will be
+
+ align:start position:0%
+okay just some number so so this will be
+ 
+
+ align:start position:0%
+okay just some number so so this will be
+a bunch of uh four by four matrices so
+
+ align:start position:0%
+a bunch of uh four by four matrices so
+ 
+
+ align:start position:0%
+a bunch of uh four by four matrices so
+from each Omega I can in principle uh
+
+ align:start position:0%
+from each Omega I can in principle uh
+ 
+
+ align:start position:0%
+from each Omega I can in principle uh
+independently uh uh uh multiplies on
+
+ align:start position:0%
+independently uh uh uh multiplies on
+ 
+
+ align:start position:0%
+independently uh uh uh multiplies on
+Matrix okay so this is the most General
+
+ align:start position:0%
+Matrix okay so this is the most General
+ 
+
+ align:start position:0%
+Matrix okay so this is the most General
+way to Pro to expand this linear order
+
+ align:start position:0%
+way to Pro to expand this linear order
+ 
+
+ align:start position:0%
+way to Pro to expand this linear order
+in Omega okay so so this Sigma
+
+ align:start position:0%
+in Omega okay so so this Sigma
+ 
+
+ align:start position:0%
+in Omega okay so so this Sigma
+essentially just the first derivative of
+
+ align:start position:0%
+essentially just the first derivative of
+ 
+
+ align:start position:0%
+essentially just the first derivative of
+s respect to each Omega okay
+
+ align:start position:0%
+s respect to each Omega okay
+ 
+
+ align:start position:0%
+s respect to each Omega okay
+and this I over 2 is just convention
+
+ align:start position:0%
+and this I over 2 is just convention
+ 
+
+ align:start position:0%
+and this I over 2 is just convention
+and similarly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the inverse is just corresponding you
+
+ align:start position:0%
+the inverse is just corresponding you
+ 
+
+ align:start position:0%
+the inverse is just corresponding you
+change the sign here to Leading mode in
+
+ align:start position:0%
+change the sign here to Leading mode in
+ 
+
+ align:start position:0%
+change the sign here to Leading mode in
+Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so okay so I emphasize each signal mu
+
+ align:start position:0%
+so okay so I emphasize each signal mu
+ 
+
+ align:start position:0%
+so okay so I emphasize each signal mu
+is a matrix okay it should be understood
+
+ align:start position:0%
+is a matrix okay it should be understood
+ 
+
+ align:start position:0%
+is a matrix okay it should be understood
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some Matrix
+
+ align:start position:0%
+some Matrix
+ 
+
+ align:start position:0%
+some Matrix
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in the in the spinner space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now you just need to plug in
+
+ align:start position:0%
+okay so now you just need to plug in
+ 
+
+ align:start position:0%
+okay so now you just need to plug in
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+plug in this s
+
+ align:start position:0%
+plug in this s
+ 
+
+ align:start position:0%
+plug in this s
+and S minus y into this equation yeah
+
+ align:start position:0%
+and S minus y into this equation yeah
+ 
+
+ align:start position:0%
+and S minus y into this equation yeah
+just expand the both sides to all the
+
+ align:start position:0%
+just expand the both sides to all the
+ 
+
+ align:start position:0%
+just expand the both sides to all the
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+okay and you equate the coefficient
+
+ align:start position:0%
+okay and you equate the coefficient
+ 
+
+ align:start position:0%
+okay and you equate the coefficient
+you create the coefficient from that way
+
+ align:start position:0%
+you create the coefficient from that way
+ 
+
+ align:start position:0%
+you create the coefficient from that way
+you determine the sigma okay
+
+ align:start position:0%
+you determine the sigma okay
+ 
+
+ align:start position:0%
+you determine the sigma okay
+so so let me call this equation star
+
+ align:start position:0%
+so so let me call this equation star
+ 
+
+ align:start position:0%
+so so let me call this equation star
+let me just call this question three
+
+ align:start position:0%
+let me just call this question three
+ 
+
+ align:start position:0%
+let me just call this question three
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um then Q order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega mu mu to linear order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then then equation three
+
+ align:start position:0%
+then then equation three
+ 
+
+ align:start position:0%
+then then equation three
+if when you expand on both sides to
+
+ align:start position:0%
+if when you expand on both sides to
+ 
+
+ align:start position:0%
+if when you expand on both sides to
+Omega to all the Omega and equate both
+
+ align:start position:0%
+Omega to all the Omega and equate both
+ 
+
+ align:start position:0%
+Omega to all the Omega and equate both
+sides then you find the following
+
+ align:start position:0%
+sides then you find the following
+ 
+
+ align:start position:0%
+sides then you find the following
+equation this is just a couple of lines
+
+ align:start position:0%
+equation this is just a couple of lines
+ 
+
+ align:start position:0%
+equation this is just a couple of lines
+algebra so I urge you to do it yourself
+
+ align:start position:0%
+algebra so I urge you to do it yourself
+ 
+
+ align:start position:0%
+algebra so I urge you to do it yourself
+so given by I
+
+ align:start position:0%
+so given by I
+ 
+
+ align:start position:0%
+so given by I
+commutator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+common view
+
+ align:start position:0%
+common view
+ 
+
+ align:start position:0%
+common view
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+ETA named the MU
+
+ align:start position:0%
+ETA named the MU
+ 
+
+ align:start position:0%
+ETA named the MU
+gamma rho
+
+ align:start position:0%
+gamma rho
+ 
+
+ align:start position:0%
+gamma rho
+Madness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you get this equation so the left
+
+ align:start position:0%
+so you get this equation so the left
+ 
+
+ align:start position:0%
+so you get this equation so the left
+hand side is very easy to understand
+
+ align:start position:0%
+hand side is very easy to understand
+ 
+
+ align:start position:0%
+hand side is very easy to understand
+so essentially you just
+
+ align:start position:0%
+so essentially you just
+ 
+
+ align:start position:0%
+so essentially you just
+whenever you have a commutator
+
+ align:start position:0%
+whenever you have a commutator
+ 
+
+ align:start position:0%
+whenever you have a commutator
+for people have done this a a baker
+
+ align:start position:0%
+for people have done this a a baker
+ 
+
+ align:start position:0%
+for people have done this a a baker
+house Stuff Etc the first of all the
+
+ align:start position:0%
+house Stuff Etc the first of all the
+ 
+
+ align:start position:0%
+house Stuff Etc the first of all the
+u.sk the commutator okay I always get
+
+ align:start position:0%
+u.sk the commutator okay I always get
+ 
+
+ align:start position:0%
+u.sk the commutator okay I always get
+the commented so that's where this
+
+ align:start position:0%
+the commented so that's where this
+ 
+
+ align:start position:0%
+the commented so that's where this
+commentator come from
+
+ align:start position:0%
+commentator come from
+ 
+
+ align:start position:0%
+commentator come from
+so the right hand side when you expand
+
+ align:start position:0%
+so the right hand side when you expand
+ 
+
+ align:start position:0%
+so the right hand side when you expand
+this it essentially just get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega mu mu because we have to lower the
+
+ align:start position:0%
+Omega mu mu because we have to lower the
+ 
+
+ align:start position:0%
+Omega mu mu because we have to lower the
+indices okay so so you have some ETA
+
+ align:start position:0%
+indices okay so so you have some ETA
+ 
+
+ align:start position:0%
+indices okay so so you have some ETA
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay you have ETA here and yeah yeah so
+
+ align:start position:0%
+okay you have ETA here and yeah yeah so
+ 
+
+ align:start position:0%
+okay you have ETA here and yeah yeah so
+that's how you get the right hand side
+
+ align:start position:0%
+that's how you get the right hand side
+ 
+
+ align:start position:0%
+that's how you get the right hand side
+okay and the reason you get two terms
+
+ align:start position:0%
+okay and the reason you get two terms
+ 
+
+ align:start position:0%
+okay and the reason you get two terms
+because it should be anti-symmetric uh
+
+ align:start position:0%
+because it should be anti-symmetric uh
+ 
+
+ align:start position:0%
+because it should be anti-symmetric uh
+in the uh uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so now just for your stand to solve
+
+ align:start position:0%
+good so now just for your stand to solve
+ 
+
+ align:start position:0%
+good so now just for your stand to solve
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+so if you can find Sigma
+
+ align:start position:0%
+so if you can find Sigma
+ 
+
+ align:start position:0%
+so if you can find Sigma
+satisfy this equation
+
+ align:start position:0%
+satisfy this equation
+ 
+
+ align:start position:0%
+satisfy this equation
+and and then then we are done
+
+ align:start position:0%
+and and then then we are done
+ 
+
+ align:start position:0%
+and and then then we are done
+okay and then we are done
+
+ align:start position:0%
+okay and then we are done
+ 
+
+ align:start position:0%
+okay and then we are done
+so so yeah of course this is a um
+
+ align:start position:0%
+so so yeah of course this is a um
+ 
+
+ align:start position:0%
+so so yeah of course this is a um
+and now you
+
+ align:start position:0%
+and now you
+ 
+
+ align:start position:0%
+and now you
+you do it by trial and arrow okay now
+
+ align:start position:0%
+you do it by trial and arrow okay now
+ 
+
+ align:start position:0%
+you do it by trial and arrow okay now
+you do by child narrow and uh um
+
+ align:start position:0%
+you do by child narrow and uh um
+ 
+
+ align:start position:0%
+you do by child narrow and uh um
+the bottom line is that there's a
+
+ align:start position:0%
+the bottom line is that there's a
+ 
+
+ align:start position:0%
+the bottom line is that there's a
+solution okay so let me just write down
+
+ align:start position:0%
+solution okay so let me just write down
+ 
+
+ align:start position:0%
+solution okay so let me just write down
+the solution and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the nice thing about the other people
+
+ align:start position:0%
+the nice thing about the other people
+ 
+
+ align:start position:0%
+the nice thing about the other people
+found the solution is that you can just
+
+ align:start position:0%
+found the solution is that you can just
+ 
+
+ align:start position:0%
+found the solution is that you can just
+check it okay so so so you can check
+
+ align:start position:0%
+check it okay so so so you can check
+ 
+
+ align:start position:0%
+check it okay so so so you can check
+this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this solves the equation
+
+ align:start position:0%
+this solves the equation
+ 
+
+ align:start position:0%
+this solves the equation
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so so just you can
+
+ align:start position:0%
+okay so so so just you can
+ 
+
+ align:start position:0%
+okay so so so just you can
+plug this
+
+ align:start position:0%
+plug this
+ 
+
+ align:start position:0%
+plug this
+so this is a commutative gamma Lambda
+
+ align:start position:0%
+so this is a commutative gamma Lambda
+ 
+
+ align:start position:0%
+so this is a commutative gamma Lambda
+and Gamma rho you plug into that then
+
+ align:start position:0%
+and Gamma rho you plug into that then
+ 
+
+ align:start position:0%
+and Gamma rho you plug into that then
+you just evaluate
+
+ align:start position:0%
+you just evaluate
+ 
+
+ align:start position:0%
+you just evaluate
+this gamma matrices okay
+
+ align:start position:0%
+this gamma matrices okay
+ 
+
+ align:start position:0%
+this gamma matrices okay
+and you uh use the um
+
+ align:start position:0%
+and you uh use the um
+ 
+
+ align:start position:0%
+and you uh use the um
+use this kind of equation over and over
+
+ align:start position:0%
+use this kind of equation over and over
+ 
+
+ align:start position:0%
+use this kind of equation over and over
+and you will find uh this is satisfied
+
+ align:start position:0%
+and you will find uh this is satisfied
+ 
+
+ align:start position:0%
+and you will find uh this is satisfied
+again I will leave it as exercise for
+
+ align:start position:0%
+again I will leave it as exercise for
+ 
+
+ align:start position:0%
+again I will leave it as exercise for
+yourself okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I exercise for yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's how you get this
+
+ align:start position:0%
+that's how you get this
+ 
+
+ align:start position:0%
+that's how you get this
+yeah yeah then the last thing is now
+
+ align:start position:0%
+yeah yeah then the last thing is now
+ 
+
+ align:start position:0%
+yeah yeah then the last thing is now
+actually is uh damage transformed
+
+ align:start position:0%
+actually is uh damage transformed
+ 
+
+ align:start position:0%
+actually is uh damage transformed
+and it's not partial details
+
+ align:start position:0%
+and it's not partial details
+ 
+
+ align:start position:0%
+and it's not partial details
+it seems like you're linking a
+
+ align:start position:0%
+it seems like you're linking a
+ 
+
+ align:start position:0%
+it seems like you're linking a
+transformation and partial view of the
+
+ align:start position:0%
+transformation and partial view of the
+ 
+
+ align:start position:0%
+transformation and partial view of the
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so here we we want to match one and
+
+ align:start position:0%
+so so here we we want to match one and
+ 
+
+ align:start position:0%
+so so here we we want to match one and
+two okay
+
+ align:start position:0%
+two okay
+ 
+
+ align:start position:0%
+two okay
+so so the step is we do or how each
+
+ align:start position:0%
+so so the step is we do or how each
+ 
+
+ align:start position:0%
+so so the step is we do or how each
+equation for from equation one
+
+ align:start position:0%
+equation for from equation one
+ 
+
+ align:start position:0%
+equation for from equation one
+we reach here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for me equation two
+
+ align:start position:0%
+for me equation two
+ 
+
+ align:start position:0%
+for me equation two
+we just plug this into there
+
+ align:start position:0%
+we just plug this into there
+ 
+
+ align:start position:0%
+we just plug this into there
+okay and so so each equation have done
+
+ align:start position:0%
+okay and so so each equation have done
+ 
+
+ align:start position:0%
+okay and so so each equation have done
+one step and then I equate them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh blend dangers and then in equation
+
+ align:start position:0%
+uh blend dangers and then in equation
+ 
+
+ align:start position:0%
+uh blend dangers and then in equation
+two you are transforming your gamma no
+
+ align:start position:0%
+two you are transforming your gamma no
+ 
+
+ align:start position:0%
+two you are transforming your gamma no
+no no no right no no no
+
+ align:start position:0%
+no no no right no no no
+ 
+
+ align:start position:0%
+no no no right no no no
+you want to show this you want to match
+
+ align:start position:0%
+you want to show this you want to match
+ 
+
+ align:start position:0%
+you want to show this you want to match
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+with this equation okay this equation is
+
+ align:start position:0%
+with this equation okay this equation is
+ 
+
+ align:start position:0%
+with this equation okay this equation is
+derived from one
+
+ align:start position:0%
+derived from one
+ 
+
+ align:start position:0%
+derived from one
+so we want to derive we want to find the
+
+ align:start position:0%
+so we want to derive we want to find the
+ 
+
+ align:start position:0%
+so we want to derive we want to find the
+two from one
+
+ align:start position:0%
+two from one
+ 
+
+ align:start position:0%
+two from one
+okay this equation one so I just
+
+ align:start position:0%
+okay this equation one so I just
+ 
+
+ align:start position:0%
+okay this equation one so I just
+slightly rewrite the equation two but by
+
+ align:start position:0%
+slightly rewrite the equation two but by
+ 
+
+ align:start position:0%
+slightly rewrite the equation two but by
+inserting this transformation here
+
+ align:start position:0%
+inserting this transformation here
+ 
+
+ align:start position:0%
+inserting this transformation here
+okay then I matched it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can just uh
+
+ align:start position:0%
+so now we can just uh
+ 
+
+ align:start position:0%
+so now we can just uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now we can just immediately so given
+
+ align:start position:0%
+now we can just immediately so given
+ 
+
+ align:start position:0%
+now we can just immediately so given
+this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we can immediately written the
+
+ align:start position:0%
+and now we can immediately written the
+ 
+
+ align:start position:0%
+and now we can immediately written the
+final transformation okay
+
+ align:start position:0%
+final transformation okay
+ 
+
+ align:start position:0%
+final transformation okay
+so we saw finite transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so for each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+each finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you can obtain the corresponding
+
+ align:start position:0%
+okay you can obtain the corresponding
+ 
+
+ align:start position:0%
+okay you can obtain the corresponding
+Omega mule
+
+ align:start position:0%
+Omega mule
+ 
+
+ align:start position:0%
+Omega mule
+okay and then this is also finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we can just obtain
+
+ align:start position:0%
+and now we can just obtain
+ 
+
+ align:start position:0%
+and now we can just obtain
+the S by exponentiate this okay and then
+
+ align:start position:0%
+the S by exponentiate this okay and then
+ 
+
+ align:start position:0%
+the S by exponentiate this okay and then
+then the corresponding s would be S
+
+ align:start position:0%
+then the corresponding s would be S
+ 
+
+ align:start position:0%
+then the corresponding s would be S
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+spatial
+
+ align:start position:0%
+spatial
+ 
+
+ align:start position:0%
+spatial
+minus I over Q
+
+ align:start position:0%
+minus I over Q
+ 
+
+ align:start position:0%
+minus I over Q
+or Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the signal maybe we just came
+
+ align:start position:0%
+okay and the signal maybe we just came
+ 
+
+ align:start position:0%
+okay and the signal maybe we just came
+back this one okay
+
+ align:start position:0%
+back this one okay
+ 
+
+ align:start position:0%
+back this one okay
+so and you can check yourself this
+
+ align:start position:0%
+so and you can check yourself this
+ 
+
+ align:start position:0%
+so and you can check yourself this
+satisfies
+
+ align:start position:0%
+satisfies
+ 
+
+ align:start position:0%
+satisfies
+you can check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this satisfies
+
+ align:start position:0%
+this satisfies
+ 
+
+ align:start position:0%
+this satisfies
+equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that finite equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now let me uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's make some remarks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so then this asks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it just generates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a range transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the only act on this uh off and
+
+ align:start position:0%
+because the only act on this uh off and
+ 
+
+ align:start position:0%
+because the only act on this uh off and
+beta okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Sigma and J
+
+ align:start position:0%
+so Sigma and J
+ 
+
+ align:start position:0%
+so Sigma and J
+or Sigma Sigma mu according to our
+
+ align:start position:0%
+or Sigma Sigma mu according to our
+ 
+
+ align:start position:0%
+or Sigma Sigma mu according to our
+standards
+
+ align:start position:0%
+standards
+ 
+
+ align:start position:0%
+standards
+uh terminology this is called the
+
+ align:start position:0%
+uh terminology this is called the
+ 
+
+ align:start position:0%
+uh terminology this is called the
+generator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the transformation Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when when
+
+ align:start position:0%
+when when
+ 
+
+ align:start position:0%
+when when
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+you knew when the new new you go to
+
+ align:start position:0%
+you knew when the new new you go to
+ 
+
+ align:start position:0%
+you knew when the new new you go to
+spatial directions
+
+ align:start position:0%
+spatial directions
+ 
+
+ align:start position:0%
+spatial directions
+and then that's corresponding to a
+
+ align:start position:0%
+and then that's corresponding to a
+ 
+
+ align:start position:0%
+and then that's corresponding to a
+space-time space spatial rotation okay
+
+ align:start position:0%
+space-time space spatial rotation okay
+ 
+
+ align:start position:0%
+space-time space spatial rotation okay
+and the zero I corresponding to a boost
+
+ align:start position:0%
+and the zero I corresponding to a boost
+ 
+
+ align:start position:0%
+and the zero I corresponding to a boost
+okay so remember so so that means
+
+ align:start position:0%
+okay so remember so so that means
+ 
+
+ align:start position:0%
+okay so remember so so that means
+for for Sigma AJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to I equal to 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comma a comma J
+
+ align:start position:0%
+comma a comma J
+ 
+
+ align:start position:0%
+comma a comma J
+this generates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of rotations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so also remember previously
+
+ align:start position:0%
+so also remember previously
+ 
+
+ align:start position:0%
+so also remember previously
+so if you remember how we do the long
+
+ align:start position:0%
+so if you remember how we do the long
+ 
+
+ align:start position:0%
+so if you remember how we do the long
+brain transformation
+
+ align:start position:0%
+brain transformation
+ 
+
+ align:start position:0%
+brain transformation
+the Omega i j
+
+ align:start position:0%
+the Omega i j
+ 
+
+ align:start position:0%
+the Omega i j
+would corresponding to the rotational
+
+ align:start position:0%
+would corresponding to the rotational
+ 
+
+ align:start position:0%
+would corresponding to the rotational
+angle
+
+ align:start position:0%
+angle
+ 
+
+ align:start position:0%
+angle
+in the IJ plane
+
+ align:start position:0%
+in the IJ plane
+ 
+
+ align:start position:0%
+in the IJ plane
+okay so you just rotate in the AJ plane
+
+ align:start position:0%
+okay so you just rotate in the AJ plane
+ 
+
+ align:start position:0%
+okay so you just rotate in the AJ plane
+by angle or or or yeah or
+
+ align:start position:0%
+by angle or or or yeah or
+ 
+
+ align:start position:0%
+by angle or or or yeah or
+Omega i j so then this then this just
+
+ align:start position:0%
+Omega i j so then this then this just
+ 
+
+ align:start position:0%
+Omega i j so then this then this just
+corresponding now because one into the
+
+ align:start position:0%
+corresponding now because one into the
+ 
+
+ align:start position:0%
+corresponding now because one into the
+generator of the rotations okay
+
+ align:start position:0%
+generator of the rotations okay
+ 
+
+ align:start position:0%
+generator of the rotations okay
+in IJ plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can because the gamma I and Gamma
+
+ align:start position:0%
+so you can because the gamma I and Gamma
+ 
+
+ align:start position:0%
+so you can because the gamma I and Gamma
+J are Commission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we call that the gamma I
+
+ align:start position:0%
+we call that the gamma I
+ 
+
+ align:start position:0%
+we call that the gamma I
+distribution and then the
+
+ align:start position:0%
+distribution and then the
+ 
+
+ align:start position:0%
+distribution and then the
+Sigma i j
+
+ align:start position:0%
+Sigma i j
+ 
+
+ align:start position:0%
+Sigma i j
+is also Commission
+
+ align:start position:0%
+is also Commission
+ 
+
+ align:start position:0%
+is also Commission
+okay because when you take the take the
+
+ align:start position:0%
+okay because when you take the take the
+ 
+
+ align:start position:0%
+okay because when you take the take the
+diagram of this I give you a minus sign
+
+ align:start position:0%
+diagram of this I give you a minus sign
+ 
+
+ align:start position:0%
+diagram of this I give you a minus sign
+but the commutator give you a minus sign
+
+ align:start position:0%
+but the commutator give you a minus sign
+ 
+
+ align:start position:0%
+but the commutator give you a minus sign
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the coming to the Q minus so this is
+
+ align:start position:0%
+the coming to the Q minus so this is
+ 
+
+ align:start position:0%
+the coming to the Q minus so this is
+Commission so that means that the s
+
+ align:start position:0%
+Commission so that means that the s
+ 
+
+ align:start position:0%
+Commission so that means that the s
+which corresponding to a rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is unitary okay so this is unitary
+
+ align:start position:0%
+is unitary okay so this is unitary
+ 
+
+ align:start position:0%
+is unitary okay so this is unitary
+so this is a unitary Matrix okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's consider the sigma 0i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which corresponding to the generator for
+
+ align:start position:0%
+which corresponding to the generator for
+ 
+
+ align:start position:0%
+which corresponding to the generator for
+Boost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this will have the form comma zero
+
+ align:start position:0%
+so this will have the form comma zero
+ 
+
+ align:start position:0%
+so this will have the form comma zero
+comma I
+
+ align:start position:0%
+comma I
+ 
+
+ align:start position:0%
+comma I
+so this is the generators for Boost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in ice Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in the in the in the spindle space
+
+ align:start position:0%
+okay in the in the in the spindle space
+ 
+
+ align:start position:0%
+okay in the in the in the spindle space
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now because the remember gamma zero
+
+ align:start position:0%
+and now because the remember gamma zero
+ 
+
+ align:start position:0%
+and now because the remember gamma zero
+when you take the dagger you get the
+
+ align:start position:0%
+when you take the dagger you get the
+ 
+
+ align:start position:0%
+when you take the dagger you get the
+minus sign
+
+ align:start position:0%
+minus sign
+ 
+
+ align:start position:0%
+minus sign
+so so the sigma zero I now if you take
+
+ align:start position:0%
+so so the sigma zero I now if you take
+ 
+
+ align:start position:0%
+so so the sigma zero I now if you take
+the dagger
+
+ align:start position:0%
+the dagger
+ 
+
+ align:start position:0%
+the dagger
+you actually also get the minus sign
+
+ align:start position:0%
+you actually also get the minus sign
+ 
+
+ align:start position:0%
+you actually also get the minus sign
+because the um yeah so now it's an
+
+ align:start position:0%
+because the um yeah so now it's an
+ 
+
+ align:start position:0%
+because the um yeah so now it's an
+anti-commission
+
+ align:start position:0%
+anti-commission
+ 
+
+ align:start position:0%
+anti-commission
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means the post matrices okay so
+
+ align:start position:0%
+so that means the post matrices okay so
+ 
+
+ align:start position:0%
+so that means the post matrices okay so
+so this is a boost transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is another unit region this is
+
+ align:start position:0%
+so this is another unit region this is
+ 
+
+ align:start position:0%
+so this is another unit region this is
+not unitary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is another unitary
+
+ align:start position:0%
+okay so this is another unitary
+ 
+
+ align:start position:0%
+okay so this is another unitary
+so so in general so normally as we said
+
+ align:start position:0%
+so so in general so normally as we said
+ 
+
+ align:start position:0%
+so so in general so normally as we said
+before normally when you do a symmetry
+
+ align:start position:0%
+before normally when you do a symmetry
+ 
+
+ align:start position:0%
+before normally when you do a symmetry
+transformation uh the transformation is
+
+ align:start position:0%
+transformation uh the transformation is
+ 
+
+ align:start position:0%
+transformation uh the transformation is
+unitary transformation but in this case
+
+ align:start position:0%
+unitary transformation but in this case
+ 
+
+ align:start position:0%
+unitary transformation but in this case
+actually uh yeah this is a classical
+
+ align:start position:0%
+actually uh yeah this is a classical
+ 
+
+ align:start position:0%
+actually uh yeah this is a classical
+transformation okay
+
+ align:start position:0%
+transformation okay
+ 
+
+ align:start position:0%
+transformation okay
+here uh it's actually another unitary
+
+ align:start position:0%
+here uh it's actually another unitary
+ 
+
+ align:start position:0%
+here uh it's actually another unitary
+Matrix okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a stagger in general
+
+ align:start position:0%
+that a stagger in general
+ 
+
+ align:start position:0%
+that a stagger in general
+for General Lauren transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say which including both say a rotation
+
+ align:start position:0%
+say which including both say a rotation
+ 
+
+ align:start position:0%
+say which including both say a rotation
+boost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so S and S cycle is not equal to one
+
+ align:start position:0%
+so S and S cycle is not equal to one
+ 
+
+ align:start position:0%
+so S and S cycle is not equal to one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yes it's not u21
+
+ align:start position:0%
+yes it's not u21
+ 
+
+ align:start position:0%
+yes it's not u21
+so this has very important consequences
+
+ align:start position:0%
+so this has very important consequences
+ 
+
+ align:start position:0%
+so this has very important consequences
+for for example for writing down an
+
+ align:start position:0%
+for for example for writing down an
+ 
+
+ align:start position:0%
+for for example for writing down an
+action for the rock equation
+
+ align:start position:0%
+action for the rock equation
+ 
+
+ align:start position:0%
+action for the rock equation
+so so far we only uh uh are writing
+
+ align:start position:0%
+so so far we only uh uh are writing
+ 
+
+ align:start position:0%
+so so far we only uh uh are writing
+wrote down the rock equation
+
+ align:start position:0%
+wrote down the rock equation
+ 
+
+ align:start position:0%
+wrote down the rock equation
+but we did remember previously we know
+
+ align:start position:0%
+but we did remember previously we know
+ 
+
+ align:start position:0%
+but we did remember previously we know
+we normally start with the action first
+
+ align:start position:0%
+we normally start with the action first
+ 
+
+ align:start position:0%
+we normally start with the action first
+and then from the action we derive
+
+ align:start position:0%
+and then from the action we derive
+ 
+
+ align:start position:0%
+and then from the action we derive
+equation motion but in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah since this spinder is a
+
+ align:start position:0%
+um yeah since this spinder is a
+ 
+
+ align:start position:0%
+um yeah since this spinder is a
+completely new concept we started with
+
+ align:start position:0%
+completely new concept we started with
+ 
+
+ align:start position:0%
+completely new concept we started with
+actually the equation okay but now if we
+
+ align:start position:0%
+actually the equation okay but now if we
+ 
+
+ align:start position:0%
+actually the equation okay but now if we
+want to write down our action
+
+ align:start position:0%
+want to write down our action
+ 
+
+ align:start position:0%
+want to write down our action
+which is by definition should be low
+
+ align:start position:0%
+which is by definition should be low
+ 
+
+ align:start position:0%
+which is by definition should be low
+renting warrant then we should
+
+ align:start position:0%
+renting warrant then we should
+ 
+
+ align:start position:0%
+renting warrant then we should
+construct quantities which are involved
+
+ align:start position:0%
+construct quantities which are involved
+ 
+
+ align:start position:0%
+construct quantities which are involved
+with non-lawrence Transformations okay
+
+ align:start position:0%
+with non-lawrence Transformations okay
+ 
+
+ align:start position:0%
+with non-lawrence Transformations okay
+and so and so this uh uh this poverty
+
+ align:start position:0%
+and so and so this uh uh this poverty
+ 
+
+ align:start position:0%
+and so and so this uh uh this poverty
+then become a key okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no here we are not talking about
+
+ align:start position:0%
+no no here we are not talking about
+ 
+
+ align:start position:0%
+no no here we are not talking about
+quantum mechanics here we're just
+
+ align:start position:0%
+quantum mechanics here we're just
+ 
+
+ align:start position:0%
+quantum mechanics here we're just
+talking about the equations classical
+
+ align:start position:0%
+talking about the equations classical
+ 
+
+ align:start position:0%
+talking about the equations classical
+equations we are just talking about
+
+ align:start position:0%
+equations we are just talking about
+ 
+
+ align:start position:0%
+equations we are just talking about
+their Matrix they're just Matrix
+
+ align:start position:0%
+their Matrix they're just Matrix
+ 
+
+ align:start position:0%
+their Matrix they're just Matrix
+we are talking about the uh whether they
+
+ align:start position:0%
+we are talking about the uh whether they
+ 
+
+ align:start position:0%
+we are talking about the uh whether they
+are unitary Matrix or their uh uh uh are
+
+ align:start position:0%
+are unitary Matrix or their uh uh uh are
+ 
+
+ align:start position:0%
+are unitary Matrix or their uh uh uh are
+not unitary Matrix they're just ordinary
+
+ align:start position:0%
+not unitary Matrix they're just ordinary
+ 
+
+ align:start position:0%
+not unitary Matrix they're just ordinary
+matrices four by four matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PSI
+
+ align:start position:0%
+PSI
+ 
+
+ align:start position:0%
+PSI
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+is a row vector and this is the column
+
+ align:start position:0%
+is a row vector and this is the column
+ 
+
+ align:start position:0%
+is a row vector and this is the column
+vector and all together this is a number
+
+ align:start position:0%
+vector and all together this is a number
+ 
+
+ align:start position:0%
+vector and all together this is a number
+so this means this is not a scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this transform under low range
+
+ align:start position:0%
+so so this transform under low range
+ 
+
+ align:start position:0%
+so so this transform under low range
+transformation as
+
+ align:start position:0%
+transformation as
+ 
+
+ align:start position:0%
+transformation as
+stagger
+
+ align:start position:0%
+stagger
+ 
+
+ align:start position:0%
+stagger
+s PSI
+
+ align:start position:0%
+s PSI
+ 
+
+ align:start position:0%
+s PSI
+so that means this is not since this is
+
+ align:start position:0%
+so that means this is not since this is
+ 
+
+ align:start position:0%
+so that means this is not since this is
+not equal to one then this is not
+
+ align:start position:0%
+not equal to one then this is not
+ 
+
+ align:start position:0%
+not equal to one then this is not
+scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the low range transformation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so uh so now we have to search a
+
+ align:start position:0%
+so so uh so now we have to search a
+ 
+
+ align:start position:0%
+so so uh so now we have to search a
+little bit harder
+
+ align:start position:0%
+little bit harder
+ 
+
+ align:start position:0%
+little bit harder
+to to uh
+
+ align:start position:0%
+to to uh
+ 
+
+ align:start position:0%
+to to uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh to find the scalar okay so yeah in
+
+ align:start position:0%
+uh to find the scalar okay so yeah in
+ 
+
+ align:start position:0%
+uh to find the scalar okay so yeah in
+order to write the action we need to
+
+ align:start position:0%
+order to write the action we need to
+ 
+
+ align:start position:0%
+order to write the action we need to
+find something which is environment
+
+ align:start position:0%
+find something which is environment
+ 
+
+ align:start position:0%
+find something which is environment
+transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the the easy thing to think about is
+
+ align:start position:0%
+so the the easy thing to think about is
+ 
+
+ align:start position:0%
+so the the easy thing to think about is
+this quantity okay because this
+
+ align:start position:0%
+this quantity okay because this
+ 
+
+ align:start position:0%
+this quantity okay because this
+automatically give you a number okay
+
+ align:start position:0%
+automatically give you a number okay
+ 
+
+ align:start position:0%
+automatically give you a number okay
+but this thing won't work okay so we
+
+ align:start position:0%
+but this thing won't work okay so we
+ 
+
+ align:start position:0%
+but this thing won't work okay so we
+have to search a little bit harder okay
+
+ align:start position:0%
+have to search a little bit harder okay
+ 
+
+ align:start position:0%
+have to search a little bit harder okay
+so to do that let's um we can get some
+
+ align:start position:0%
+so to do that let's um we can get some
+ 
+
+ align:start position:0%
+so to do that let's um we can get some
+hint
+
+ align:start position:0%
+hint
+ 
+
+ align:start position:0%
+hint
+from the following identity
+
+ align:start position:0%
+from the following identity
+ 
+
+ align:start position:0%
+from the following identity
+okay so let's look at what this s tag is
+
+ align:start position:0%
+okay so let's look at what this s tag is
+ 
+
+ align:start position:0%
+okay so let's look at what this s tag is
+really is okay
+
+ align:start position:0%
+really is okay
+ 
+
+ align:start position:0%
+really is okay
+so let's look at the property of s tag
+
+ align:start position:0%
+so let's look at the property of s tag
+ 
+
+ align:start position:0%
+so let's look at the property of s tag
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so recall that the uh I think I erased
+
+ align:start position:0%
+so recall that the uh I think I erased
+ 
+
+ align:start position:0%
+so recall that the uh I think I erased
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+yeah so so let me just write it again so
+
+ align:start position:0%
+yeah so so let me just write it again so
+ 
+
+ align:start position:0%
+yeah so so let me just write it again so
+gamma mu dagger
+
+ align:start position:0%
+gamma mu dagger
+ 
+
+ align:start position:0%
+gamma mu dagger
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+gamma zero
+
+ align:start position:0%
+gamma zero
+ 
+
+ align:start position:0%
+gamma zero
+comma mu
+
+ align:start position:0%
+comma mu
+ 
+
+ align:start position:0%
+comma mu
+comma zero okay so now let's try to find
+
+ align:start position:0%
+comma zero okay so now let's try to find
+ 
+
+ align:start position:0%
+comma zero okay so now let's try to find
+what's mu mu dagger
+
+ align:start position:0%
+what's mu mu dagger
+ 
+
+ align:start position:0%
+what's mu mu dagger
+so let's write music in the uniform so
+
+ align:start position:0%
+so let's write music in the uniform so
+ 
+
+ align:start position:0%
+so let's write music in the uniform so
+so even though we wrote it separately
+
+ align:start position:0%
+so even though we wrote it separately
+ 
+
+ align:start position:0%
+so even though we wrote it separately
+so you can easily check yourself because
+
+ align:start position:0%
+so you can easily check yourself because
+ 
+
+ align:start position:0%
+so you can easily check yourself because
+of this property
+
+ align:start position:0%
+of this property
+ 
+
+ align:start position:0%
+of this property
+so this is just given by minus gamma
+
+ align:start position:0%
+so this is just given by minus gamma
+ 
+
+ align:start position:0%
+so this is just given by minus gamma
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+Sigma mu
+
+ align:start position:0%
+Sigma mu
+ 
+
+ align:start position:0%
+Sigma mu
+comma zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because this is just a commutator so you
+
+ align:start position:0%
+because this is just a commutator so you
+ 
+
+ align:start position:0%
+because this is just a commutator so you
+can easily work it out that you just get
+
+ align:start position:0%
+can easily work it out that you just get
+ 
+
+ align:start position:0%
+can easily work it out that you just get
+this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can find the what uh what a
+
+ align:start position:0%
+so now we can find the what uh what a
+ 
+
+ align:start position:0%
+so now we can find the what uh what a
+stagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a stagger
+
+ align:start position:0%
+so a stagger
+ 
+
+ align:start position:0%
+so a stagger
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+the exponential one half I
+
+ align:start position:0%
+the exponential one half I
+ 
+
+ align:start position:0%
+the exponential one half I
+Omega mu mu
+
+ align:start position:0%
+Omega mu mu
+ 
+
+ align:start position:0%
+Omega mu mu
+then Sigma mu diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I over 2 Omega mu
+
+ align:start position:0%
+I over 2 Omega mu
+ 
+
+ align:start position:0%
+I over 2 Omega mu
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+comma zero
+
+ align:start position:0%
+comma zero
+ 
+
+ align:start position:0%
+comma zero
+Sigma mu comma zero
+
+ align:start position:0%
+Sigma mu comma zero
+ 
+
+ align:start position:0%
+Sigma mu comma zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if you remember gamma zero square
+
+ align:start position:0%
+so now if you remember gamma zero square
+ 
+
+ align:start position:0%
+so now if you remember gamma zero square
+is equal to minus one
+
+ align:start position:0%
+is equal to minus one
+ 
+
+ align:start position:0%
+is equal to minus one
+so whenever you have a such a situation
+
+ align:start position:0%
+so whenever you have a such a situation
+ 
+
+ align:start position:0%
+so whenever you have a such a situation
+and the uh and because gamma zero square
+
+ align:start position:0%
+and the uh and because gamma zero square
+ 
+
+ align:start position:0%
+and the uh and because gamma zero square
+is equal to -1
+
+ align:start position:0%
+is equal to -1
+ 
+
+ align:start position:0%
+is equal to -1
+then you can actually take the gamma
+
+ align:start position:0%
+then you can actually take the gamma
+ 
+
+ align:start position:0%
+then you can actually take the gamma
+zero outside of the exponential
+
+ align:start position:0%
+zero outside of the exponential
+ 
+
+ align:start position:0%
+zero outside of the exponential
+so this is actually equal to
+
+ align:start position:0%
+so this is actually equal to
+ 
+
+ align:start position:0%
+so this is actually equal to
+minus gamma zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+comma zero foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so if you just think you do a Taylor
+
+ align:start position:0%
+so so if you just think you do a Taylor
+ 
+
+ align:start position:0%
+so so if you just think you do a Taylor
+expansion of this expansion
+
+ align:start position:0%
+expansion of this expansion
+ 
+
+ align:start position:0%
+expansion of this expansion
+and then then when you take the uh
+
+ align:start position:0%
+and then then when you take the uh
+ 
+
+ align:start position:0%
+and then then when you take the uh
+the power of this
+
+ align:start position:0%
+the power of this
+ 
+
+ align:start position:0%
+the power of this
+then for each term the gamma zero at the
+
+ align:start position:0%
+then for each term the gamma zero at the
+ 
+
+ align:start position:0%
+then for each term the gamma zero at the
+end will
+
+ align:start position:0%
+end will
+ 
+
+ align:start position:0%
+end will
+pair with the gamma zero at the big
+
+ align:start position:0%
+pair with the gamma zero at the big
+ 
+
+ align:start position:0%
+pair with the gamma zero at the big
+beginning of the other term and then
+
+ align:start position:0%
+beginning of the other term and then
+ 
+
+ align:start position:0%
+beginning of the other term and then
+they give you minus one
+
+ align:start position:0%
+they give you minus one
+ 
+
+ align:start position:0%
+they give you minus one
+okay and then you have only the first
+
+ align:start position:0%
+okay and then you have only the first
+ 
+
+ align:start position:0%
+okay and then you have only the first
+gamma zero and the mass comma zero left
+
+ align:start position:0%
+gamma zero and the mass comma zero left
+ 
+
+ align:start position:0%
+gamma zero and the mass comma zero left
+and because that's given minus one they
+
+ align:start position:0%
+and because that's given minus one they
+ 
+
+ align:start position:0%
+and because that's given minus one they
+change this minus sign to a plus sign
+
+ align:start position:0%
+change this minus sign to a plus sign
+ 
+
+ align:start position:0%
+change this minus sign to a plus sign
+okay so you just do a Taylor expansion
+
+ align:start position:0%
+okay so you just do a Taylor expansion
+ 
+
+ align:start position:0%
+okay so you just do a Taylor expansion
+you will find here okay
+
+ align:start position:0%
+you will find here okay
+ 
+
+ align:start position:0%
+you will find here okay
+still explaining fine here
+
+ align:start position:0%
+still explaining fine here
+ 
+
+ align:start position:0%
+still explaining fine here
+and now we find the license relation
+
+ align:start position:0%
+and now we find the license relation
+ 
+
+ align:start position:0%
+and now we find the license relation
+so we find that this is just malice
+
+ align:start position:0%
+so we find that this is just malice
+ 
+
+ align:start position:0%
+so we find that this is just malice
+gamma zero and this is just equal to S
+
+ align:start position:0%
+gamma zero and this is just equal to S
+ 
+
+ align:start position:0%
+gamma zero and this is just equal to S
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+as a gamma zero
+
+ align:start position:0%
+as a gamma zero
+ 
+
+ align:start position:0%
+as a gamma zero
+ok
+
+ align:start position:0%
+ok
+ 
+
+ align:start position:0%
+ok
+so we find that the S tag is actually
+
+ align:start position:0%
+so we find that the S tag is actually
+ 
+
+ align:start position:0%
+so we find that the S tag is actually
+minus gamma zero s minus one uh
+
+ align:start position:0%
+minus gamma zero s minus one uh
+ 
+
+ align:start position:0%
+minus gamma zero s minus one uh
+then this tells us
+
+ align:start position:0%
+then this tells us
+ 
+
+ align:start position:0%
+then this tells us
+okay for from this property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+tells us that this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comma zero of PSI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should transform as a scalar okay so now
+
+ align:start position:0%
+should transform as a scalar okay so now
+ 
+
+ align:start position:0%
+should transform as a scalar okay so now
+let's take a look so this
+
+ align:start position:0%
+let's take a look so this
+ 
+
+ align:start position:0%
+let's take a look so this
+so this when you uh do a transformation
+
+ align:start position:0%
+so this when you uh do a transformation
+ 
+
+ align:start position:0%
+so this when you uh do a transformation
+so this gives you the side dagger
+
+ align:start position:0%
+so this gives you the side dagger
+ 
+
+ align:start position:0%
+so this gives you the side dagger
+a stagger
+
+ align:start position:0%
+a stagger
+ 
+
+ align:start position:0%
+a stagger
+and you have gamma zero
+
+ align:start position:0%
+and you have gamma zero
+ 
+
+ align:start position:0%
+and you have gamma zero
+then you have S PSI on the lower end
+
+ align:start position:0%
+then you have S PSI on the lower end
+ 
+
+ align:start position:0%
+then you have S PSI on the lower end
+transformation okay
+
+ align:start position:0%
+transformation okay
+ 
+
+ align:start position:0%
+transformation okay
+and now you're plugging this into a
+
+ align:start position:0%
+and now you're plugging this into a
+ 
+
+ align:start position:0%
+and now you're plugging this into a
+plugging a stack or equal to this into
+
+ align:start position:0%
+plugging a stack or equal to this into
+ 
+
+ align:start position:0%
+plugging a stack or equal to this into
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+yeah you just get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is comma zero and stack s minus
+
+ align:start position:0%
+so this is comma zero and stack s minus
+ 
+
+ align:start position:0%
+so this is comma zero and stack s minus
+one comma zero
+
+ align:start position:0%
+one comma zero
+ 
+
+ align:start position:0%
+one comma zero
+then gamma zero as PSI okay so this
+
+ align:start position:0%
+then gamma zero as PSI okay so this
+ 
+
+ align:start position:0%
+then gamma zero as PSI okay so this
+give you minus one cancel which is the
+
+ align:start position:0%
+give you minus one cancel which is the
+ 
+
+ align:start position:0%
+give you minus one cancel which is the
+one here and then S1 cancel with as s
+
+ align:start position:0%
+one here and then S1 cancel with as s
+ 
+
+ align:start position:0%
+one here and then S1 cancel with as s
+minus one cancels with s and then you
+
+ align:start position:0%
+minus one cancels with s and then you
+ 
+
+ align:start position:0%
+minus one cancels with s and then you
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this actually it's low renting
+
+ align:start position:0%
+okay so this actually it's low renting
+ 
+
+ align:start position:0%
+okay so this actually it's low renting
+warrant
+
+ align:start position:0%
+warrant
+ 
+
+ align:start position:0%
+warrant
+okay so this is laurentium art
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we find a nice low range
+
+ align:start position:0%
+so now we find a nice low range
+ 
+
+ align:start position:0%
+so now we find a nice low range
+environment quantity okay
+
+ align:start position:0%
+environment quantity okay
+ 
+
+ align:start position:0%
+environment quantity okay
+so since we use this all the time
+
+ align:start position:0%
+so since we use this all the time
+ 
+
+ align:start position:0%
+so since we use this all the time
+since we use this all the time so it's
+
+ align:start position:0%
+since we use this all the time so it's
+ 
+
+ align:start position:0%
+since we use this all the time so it's
+convenient to introduce a new notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now you introduce
+
+ align:start position:0%
+so so now you introduce
+ 
+
+ align:start position:0%
+so so now you introduce
+a minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we call PSI bar
+
+ align:start position:0%
+we call PSI bar
+ 
+
+ align:start position:0%
+we call PSI bar
+you're going to say that
+
+ align:start position:0%
+you're going to say that
+ 
+
+ align:start position:0%
+you're going to say that
+go to side dagger
+
+ align:start position:0%
+go to side dagger
+ 
+
+ align:start position:0%
+go to side dagger
+so here it's all just crossed this is
+
+ align:start position:0%
+so here it's all just crossed this is
+ 
+
+ align:start position:0%
+so here it's all just crossed this is
+stagger and it's all just matrix
+
+ align:start position:0%
+stagger and it's all just matrix
+ 
+
+ align:start position:0%
+stagger and it's all just matrix
+multiplication okay
+
+ align:start position:0%
+multiplication okay
+ 
+
+ align:start position:0%
+multiplication okay
+right now we are considering a classical
+
+ align:start position:0%
+right now we are considering a classical
+ 
+
+ align:start position:0%
+right now we are considering a classical
+Theory
+
+ align:start position:0%
+Theory
+ 
+
+ align:start position:0%
+Theory
+and so so it's convenient to introduce
+
+ align:start position:0%
+and so so it's convenient to introduce
+ 
+
+ align:start position:0%
+and so so it's convenient to introduce
+objects like this okay
+
+ align:start position:0%
+objects like this okay
+ 
+
+ align:start position:0%
+objects like this okay
+and then then we know that then PSI bar
+
+ align:start position:0%
+and then then we know that then PSI bar
+ 
+
+ align:start position:0%
+and then then we know that then PSI bar
+PSI is a scalar
+
+ align:start position:0%
+PSI is a scalar
+ 
+
+ align:start position:0%
+PSI is a scalar
+okay so so that thing just becomes a bar
+
+ align:start position:0%
+okay so so that thing just becomes a bar
+ 
+
+ align:start position:0%
+okay so so that thing just becomes a bar
+inside okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so it's convenient to work out
+
+ align:start position:0%
+so so it's convenient to work out
+ 
+
+ align:start position:0%
+so so it's convenient to work out
+the the help type bar transformed by
+
+ align:start position:0%
+the the help type bar transformed by
+ 
+
+ align:start position:0%
+the the help type bar transformed by
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+okay so so you just use this relation so
+
+ align:start position:0%
+okay so so you just use this relation so
+ 
+
+ align:start position:0%
+okay so so you just use this relation so
+you can check yourself okay so so
+
+ align:start position:0%
+you can check yourself okay so so
+ 
+
+ align:start position:0%
+you can check yourself okay so so
+exercise for you to check yourself
+
+ align:start position:0%
+exercise for you to check yourself
+ 
+
+ align:start position:0%
+exercise for you to check yourself
+under low range transformation we say
+
+ align:start position:0%
+under low range transformation we say
+ 
+
+ align:start position:0%
+under low range transformation we say
+bar
+
+ align:start position:0%
+bar
+ 
+
+ align:start position:0%
+bar
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+PSI bar Prime X Prime
+
+ align:start position:0%
+PSI bar Prime X Prime
+ 
+
+ align:start position:0%
+PSI bar Prime X Prime
+okay so if you go to the new episode bar
+
+ align:start position:0%
+okay so if you go to the new episode bar
+ 
+
+ align:start position:0%
+okay so if you go to the new episode bar
+Prime X Prime is equal to psi
+
+ align:start position:0%
+Prime X Prime is equal to psi
+ 
+
+ align:start position:0%
+Prime X Prime is equal to psi
+Phi X
+
+ align:start position:0%
+Phi X
+ 
+
+ align:start position:0%
+Phi X
+s minus one okay
+
+ align:start position:0%
+s minus one okay
+ 
+
+ align:start position:0%
+s minus one okay
+so you can easily check yourself this
+
+ align:start position:0%
+so you can easily check yourself this
+ 
+
+ align:start position:0%
+so you can easily check yourself this
+relation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarly using the using this
+
+ align:start position:0%
+similarly using the using this
+ 
+
+ align:start position:0%
+similarly using the using this
+transformation of gamma a partial mu you
+
+ align:start position:0%
+transformation of gamma a partial mu you
+ 
+
+ align:start position:0%
+transformation of gamma a partial mu you
+can also trans check
+
+ align:start position:0%
+can also trans check
+ 
+
+ align:start position:0%
+can also trans check
+that the gamma mu
+
+ align:start position:0%
+that the gamma mu
+ 
+
+ align:start position:0%
+that the gamma mu
+passion knew
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Prime PSI Prime X
+
+ align:start position:0%
+so Prime PSI Prime X
+ 
+
+ align:start position:0%
+so Prime PSI Prime X
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+equal to s
+
+ align:start position:0%
+equal to s
+ 
+
+ align:start position:0%
+equal to s
+gamma mu partial mu PSI
+
+ align:start position:0%
+gamma mu partial mu PSI
+ 
+
+ align:start position:0%
+gamma mu partial mu PSI
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can also check yourself or check
+
+ align:start position:0%
+so you can also check yourself or check
+ 
+
+ align:start position:0%
+so you can also check yourself or check
+this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah this is the just by using
+
+ align:start position:0%
+okay so yeah this is the just by using
+ 
+
+ align:start position:0%
+okay so yeah this is the just by using
+this properties of a stagger uh yeah
+
+ align:start position:0%
+this properties of a stagger uh yeah
+ 
+
+ align:start position:0%
+this properties of a stagger uh yeah
+just yeah this you don't use the you
+
+ align:start position:0%
+just yeah this you don't use the you
+ 
+
+ align:start position:0%
+just yeah this you don't use the you
+only use above the Stagger just use the
+
+ align:start position:0%
+only use above the Stagger just use the
+ 
+
+ align:start position:0%
+only use above the Stagger just use the
+how partial mu Prime transform and how
+
+ align:start position:0%
+how partial mu Prime transform and how
+ 
+
+ align:start position:0%
+how partial mu Prime transform and how
+PSI transform and then you can show this
+
+ align:start position:0%
+PSI transform and then you can show this
+ 
+
+ align:start position:0%
+PSI transform and then you can show this
+is true okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so so this also this gamma mu partial mu
+
+ align:start position:0%
+so so this also this gamma mu partial mu
+ 
+
+ align:start position:0%
+so so this also this gamma mu partial mu
+will appear a lot because this appears
+
+ align:start position:0%
+will appear a lot because this appears
+ 
+
+ align:start position:0%
+will appear a lot because this appears
+in the uh the rock equation so it's
+
+ align:start position:0%
+in the uh the rock equation so it's
+ 
+
+ align:start position:0%
+in the uh the rock equation so it's
+convenient to introduce a new rotation
+
+ align:start position:0%
+convenient to introduce a new rotation
+ 
+
+ align:start position:0%
+convenient to introduce a new rotation
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+comma mu partial mu
+
+ align:start position:0%
+comma mu partial mu
+ 
+
+ align:start position:0%
+comma mu partial mu
+we Define TB partial slash okay
+
+ align:start position:0%
+we Define TB partial slash okay
+ 
+
+ align:start position:0%
+we Define TB partial slash okay
+so so essentially
+
+ align:start position:0%
+so so essentially
+ 
+
+ align:start position:0%
+so so essentially
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+slash corresponding to that thing
+
+ align:start position:0%
+slash corresponding to that thing
+ 
+
+ align:start position:0%
+slash corresponding to that thing
+contracts with gamma mu okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and then this equation then can be
+
+ align:start position:0%
+so and then this equation then can be
+ 
+
+ align:start position:0%
+so and then this equation then can be
+written as
+
+ align:start position:0%
+written as
+ 
+
+ align:start position:0%
+written as
+the the partial
+
+ align:start position:0%
+the the partial
+ 
+
+ align:start position:0%
+the the partial
+Prime slash PSI Prime X Prime
+
+ align:start position:0%
+Prime slash PSI Prime X Prime
+ 
+
+ align:start position:0%
+Prime slash PSI Prime X Prime
+equal to s
+
+ align:start position:0%
+equal to s
+ 
+
+ align:start position:0%
+equal to s
+partial slash X
+
+ align:start position:0%
+partial slash X
+ 
+
+ align:start position:0%
+partial slash X
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so let me just mention one more since
+
+ align:start position:0%
+so so let me just mention one more since
+ 
+
+ align:start position:0%
+so so let me just mention one more since
+you can you can work out yourself okay
+
+ align:start position:0%
+you can you can work out yourself okay
+ 
+
+ align:start position:0%
+you can you can work out yourself okay
+so you can check
+
+ align:start position:0%
+so you can check
+ 
+
+ align:start position:0%
+so you can check
+so so so these are all things you can
+
+ align:start position:0%
+so so so these are all things you can
+ 
+
+ align:start position:0%
+so so so these are all things you can
+check yourself
+
+ align:start position:0%
+check yourself
+ 
+
+ align:start position:0%
+check yourself
+okay once you equip those
+
+ align:start position:0%
+okay once you equip those
+ 
+
+ align:start position:0%
+okay once you equip those
+transformations
+
+ align:start position:0%
+transformations
+ 
+
+ align:start position:0%
+transformations
+you can also check
+
+ align:start position:0%
+you can also check
+ 
+
+ align:start position:0%
+you can also check
+that come up
+
+ align:start position:0%
+that come up
+ 
+
+ align:start position:0%
+that come up
+sidebar
+
+ align:start position:0%
+sidebar
+ 
+
+ align:start position:0%
+sidebar
+comma mu
+
+ align:start position:0%
+comma mu
+ 
+
+ align:start position:0%
+comma mu
+PSI transforms as a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+PSI power Prime X Prime
+
+ align:start position:0%
+PSI power Prime X Prime
+ 
+
+ align:start position:0%
+PSI power Prime X Prime
+comma mu
+
+ align:start position:0%
+comma mu
+ 
+
+ align:start position:0%
+comma mu
+PSI Prime X Prime
+
+ align:start position:0%
+PSI Prime X Prime
+ 
+
+ align:start position:0%
+PSI Prime X Prime
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+Lambda mu Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PSI bar X plus I bar X
+
+ align:start position:0%
+PSI bar X plus I bar X
+ 
+
+ align:start position:0%
+PSI bar X plus I bar X
+comma Nu
+
+ align:start position:0%
+comma Nu
+ 
+
+ align:start position:0%
+comma Nu
+PSI X
+
+ align:start position:0%
+PSI X
+ 
+
+ align:start position:0%
+PSI X
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you view this whole thing as a
+
+ align:start position:0%
+so if you view this whole thing as a
+ 
+
+ align:start position:0%
+so if you view this whole thing as a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+and then you see the prime the quantity
+
+ align:start position:0%
+and then you see the prime the quantity
+ 
+
+ align:start position:0%
+and then you see the prime the quantity
+is equal to just a
+
+ align:start position:0%
+is equal to just a
+ 
+
+ align:start position:0%
+is equal to just a
+the low rents transformation Lambda on
+
+ align:start position:0%
+the low rents transformation Lambda on
+ 
+
+ align:start position:0%
+the low rents transformation Lambda on
+itself okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again this is something just based on
+
+ align:start position:0%
+so again this is something just based on
+ 
+
+ align:start position:0%
+so again this is something just based on
+the transformations of s and the
+
+ align:start position:0%
+the transformations of s and the
+ 
+
+ align:start position:0%
+the transformations of s and the
+relations between different comma
+
+ align:start position:0%
+relations between different comma
+ 
+
+ align:start position:0%
+relations between different comma
+matrices you can
+
+ align:start position:0%
+matrices you can
+ 
+
+ align:start position:0%
+matrices you can
+just show that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now with these preparations we can
+
+ align:start position:0%
+so now with these preparations we can
+ 
+
+ align:start position:0%
+so now with these preparations we can
+now write down the uh the action
+
+ align:start position:0%
+now write down the uh the action
+ 
+
+ align:start position:0%
+now write down the uh the action
+which give rise to the diracy equation
+
+ align:start position:0%
+which give rise to the diracy equation
+ 
+
+ align:start position:0%
+which give rise to the diracy equation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so the uh
+
+ align:start position:0%
+so so the uh
+ 
+
+ align:start position:0%
+so so the uh
+now we can write down the diracy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the action which gives you the
+
+ align:start position:0%
+and the action which gives you the
+ 
+
+ align:start position:0%
+and the action which gives you the
+question so I will just write down the
+
+ align:start position:0%
+question so I will just write down the
+ 
+
+ align:start position:0%
+question so I will just write down the
+answer it's very intuitive
+
+ align:start position:0%
+answer it's very intuitive
+ 
+
+ align:start position:0%
+answer it's very intuitive
+so you have just essentially s
+
+ align:start position:0%
+so you have just essentially s
+ 
+
+ align:start position:0%
+so you have just essentially s
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+minus I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d4x
+
+ align:start position:0%
+d4x
+ 
+
+ align:start position:0%
+d4x
+PSI bar
+
+ align:start position:0%
+PSI bar
+ 
+
+ align:start position:0%
+PSI bar
+gamma mu partial mu
+
+ align:start position:0%
+gamma mu partial mu
+ 
+
+ align:start position:0%
+gamma mu partial mu
+minus M PSI
+
+ align:start position:0%
+minus M PSI
+ 
+
+ align:start position:0%
+minus M PSI
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so so the the worry seems to
+
+ align:start position:0%
+so yeah so so the the worry seems to
+ 
+
+ align:start position:0%
+so yeah so so the the worry seems to
+uncompact here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so first just based on those
+
+ align:start position:0%
+so so first just based on those
+ 
+
+ align:start position:0%
+so so first just based on those
+relations
+
+ align:start position:0%
+relations
+ 
+
+ align:start position:0%
+relations
+based on this is a scalar
+
+ align:start position:0%
+based on this is a scalar
+ 
+
+ align:start position:0%
+based on this is a scalar
+this is a scalar
+
+ align:start position:0%
+this is a scalar
+ 
+
+ align:start position:0%
+this is a scalar
+and the transformation of this
+
+ align:start position:0%
+and the transformation of this
+ 
+
+ align:start position:0%
+and the transformation of this
+okay you can immediately see that this
+
+ align:start position:0%
+okay you can immediately see that this
+ 
+
+ align:start position:0%
+okay you can immediately see that this
+is a Lorenz scalar okay because you only
+
+ align:start position:0%
+is a Lorenz scalar okay because you only
+ 
+
+ align:start position:0%
+is a Lorenz scalar okay because you only
+move two variable one quantities PSI bar
+
+ align:start position:0%
+move two variable one quantities PSI bar
+ 
+
+ align:start position:0%
+move two variable one quantities PSI bar
+PSI with this m term and then PSI bar
+
+ align:start position:0%
+PSI with this m term and then PSI bar
+ 
+
+ align:start position:0%
+PSI with this m term and then PSI bar
+gamma mu function mule size and and that
+
+ align:start position:0%
+gamma mu function mule size and and that
+ 
+
+ align:start position:0%
+gamma mu function mule size and and that
+we already show here that the transform
+
+ align:start position:0%
+we already show here that the transform
+ 
+
+ align:start position:0%
+we already show here that the transform
+SS yeah uh so yeah you can easily check
+
+ align:start position:0%
+SS yeah uh so yeah you can easily check
+ 
+
+ align:start position:0%
+SS yeah uh so yeah you can easily check
+just based on those equations that this
+
+ align:start position:0%
+just based on those equations that this
+ 
+
+ align:start position:0%
+just based on those equations that this
+is a scale okay and this is the orange
+
+ align:start position:0%
+is a scale okay and this is the orange
+ 
+
+ align:start position:0%
+is a scale okay and this is the orange
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+uh so the second thing is that
+
+ align:start position:0%
+uh so the second thing is that
+ 
+
+ align:start position:0%
+uh so the second thing is that
+this I here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is for to make the action is real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you can show if you take the
+
+ align:start position:0%
+because you can show if you take the
+ 
+
+ align:start position:0%
+because you can show if you take the
+complex conjugate of these you actually
+
+ align:start position:0%
+complex conjugate of these you actually
+ 
+
+ align:start position:0%
+complex conjugate of these you actually
+get the minus num a minus sign and so
+
+ align:start position:0%
+get the minus num a minus sign and so
+ 
+
+ align:start position:0%
+get the minus num a minus sign and so
+you need the I to make it real okay
+
+ align:start position:0%
+you need the I to make it real okay
+ 
+
+ align:start position:0%
+you need the I to make it real okay
+and this minus sign
+
+ align:start position:0%
+and this minus sign
+ 
+
+ align:start position:0%
+and this minus sign
+which cannot be explained now which we
+
+ align:start position:0%
+which cannot be explained now which we
+ 
+
+ align:start position:0%
+which cannot be explained now which we
+will talk about it later uh when we
+
+ align:start position:0%
+will talk about it later uh when we
+ 
+
+ align:start position:0%
+will talk about it later uh when we
+quantize the theory and we see actually
+
+ align:start position:0%
+quantize the theory and we see actually
+ 
+
+ align:start position:0%
+quantize the theory and we see actually
+we need to put the minus sign here uh
+
+ align:start position:0%
+we need to put the minus sign here uh
+ 
+
+ align:start position:0%
+we need to put the minus sign here uh
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we are we are not really singling all
+
+ align:start position:0%
+we are we are not really singling all
+ 
+
+ align:start position:0%
+we are we are not really singling all
+the time direction we just
+
+ align:start position:0%
+the time direction we just
+ 
+
+ align:start position:0%
+the time direction we just
+just due to the property that gamma zero
+
+ align:start position:0%
+just due to the property that gamma zero
+ 
+
+ align:start position:0%
+just due to the property that gamma zero
+is not a hermitian
+
+ align:start position:0%
+is not a hermitian
+ 
+
+ align:start position:0%
+is not a hermitian
+yeah just so because if you look at all
+
+ align:start position:0%
+yeah just so because if you look at all
+ 
+
+ align:start position:0%
+yeah just so because if you look at all
+these all these complex complications
+
+ align:start position:0%
+these all these complex complications
+ 
+
+ align:start position:0%
+these all these complex complications
+just related to that this stagger is not
+
+ align:start position:0%
+just related to that this stagger is not
+ 
+
+ align:start position:0%
+just related to that this stagger is not
+yes it's not unitary and the reason is
+
+ align:start position:0%
+yes it's not unitary and the reason is
+ 
+
+ align:start position:0%
+yes it's not unitary and the reason is
+not utilities because gamma zero is not
+
+ align:start position:0%
+not utilities because gamma zero is not
+ 
+
+ align:start position:0%
+not utilities because gamma zero is not
+a commission yeah so you have to
+
+ align:start position:0%
+a commission yeah so you have to
+ 
+
+ align:start position:0%
+a commission yeah so you have to
+put in the gamma zero in various places
+
+ align:start position:0%
+put in the gamma zero in various places
+ 
+
+ align:start position:0%
+put in the gamma zero in various places
+to compensate for that
+
+ align:start position:0%
+to compensate for that
+ 
+
+ align:start position:0%
+to compensate for that
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+other questions yes so I guess the
+
+ align:start position:0%
+other questions yes so I guess the
+ 
+
+ align:start position:0%
+other questions yes so I guess the
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+if uh lorenzenber Lawrence Taylor you
+
+ align:start position:0%
+if uh lorenzenber Lawrence Taylor you
+ 
+
+ align:start position:0%
+if uh lorenzenber Lawrence Taylor you
+could have constructed like some product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so the sidebar gamma so that would
+
+ align:start position:0%
+yeah so the sidebar gamma so that would
+ 
+
+ align:start position:0%
+yeah so the sidebar gamma so that would
+be allowed
+
+ align:start position:0%
+be allowed
+ 
+
+ align:start position:0%
+be allowed
+I guess this gives the right answer but
+
+ align:start position:0%
+I guess this gives the right answer but
+ 
+
+ align:start position:0%
+I guess this gives the right answer but
+that could have appeared in the action
+
+ align:start position:0%
+that could have appeared in the action
+ 
+
+ align:start position:0%
+that could have appeared in the action
+which yeah disappeared in action yeah
+
+ align:start position:0%
+which yeah disappeared in action yeah
+ 
+
+ align:start position:0%
+which yeah disappeared in action yeah
+yeah so this is the so because this is a
+
+ align:start position:0%
+yeah so this is the so because this is a
+ 
+
+ align:start position:0%
+yeah so this is the so because this is a
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+so when this contracts with partial mule
+
+ align:start position:0%
+so when this contracts with partial mule
+ 
+
+ align:start position:0%
+so when this contracts with partial mule
+that give you the a scalar right
+
+ align:start position:0%
+that give you the a scalar right
+ 
+
+ align:start position:0%
+that give you the a scalar right
+yeah okay so that'll give you a scale
+
+ align:start position:0%
+yeah okay so that'll give you a scale
+ 
+
+ align:start position:0%
+yeah okay so that'll give you a scale
+uh so so yeah you can understand that
+
+ align:start position:0%
+uh so so yeah you can understand that
+ 
+
+ align:start position:0%
+uh so so yeah you can understand that
+this is uh in both ways this Transformer
+
+ align:start position:0%
+this is uh in both ways this Transformer
+ 
+
+ align:start position:0%
+this is uh in both ways this Transformer
+the Firebase Transformer Vector is also
+
+ align:start position:0%
+the Firebase Transformer Vector is also
+ 
+
+ align:start position:0%
+the Firebase Transformer Vector is also
+related to here yeah yeah just I mean
+
+ align:start position:0%
+related to here yeah yeah just I mean
+ 
+
+ align:start position:0%
+related to here yeah yeah just I mean
+just yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+so yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that we
+
+ align:start position:0%
+like that we
+ 
+
+ align:start position:0%
+like that we
+give like another children
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah yeah but then uh but but then you
+
+ align:start position:0%
+yeah yeah but then uh but but then you
+ 
+
+ align:start position:0%
+yeah yeah but then uh but but then you
+will have fourth size so four size will
+
+ align:start position:0%
+will have fourth size so four size will
+ 
+
+ align:start position:0%
+will have fourth size so four size will
+give you rise to an interacting CV yeah
+
+ align:start position:0%
+give you rise to an interacting CV yeah
+ 
+
+ align:start position:0%
+give you rise to an interacting CV yeah
+that's right here I'm writing down a a
+
+ align:start position:0%
+that's right here I'm writing down a a
+ 
+
+ align:start position:0%
+that's right here I'm writing down a a
+free Theory right now yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so you can also see that this
+
+ align:start position:0%
+so so you can also see that this
+ 
+
+ align:start position:0%
+so so you can also see that this
+equation or or give rise to the drug
+
+ align:start position:0%
+equation or or give rise to the drug
+ 
+
+ align:start position:0%
+equation or or give rise to the drug
+equation just imagine PSI bar is
+
+ align:start position:0%
+equation just imagine PSI bar is
+ 
+
+ align:start position:0%
+equation just imagine PSI bar is
+independent of PSI because this
+
+ align:start position:0%
+independent of PSI because this
+ 
+
+ align:start position:0%
+independent of PSI because this
+corresponding to side dagger so if you
+
+ align:start position:0%
+corresponding to side dagger so if you
+ 
+
+ align:start position:0%
+corresponding to side dagger so if you
+do the variation of this one you just
+
+ align:start position:0%
+do the variation of this one you just
+ 
+
+ align:start position:0%
+do the variation of this one you just
+multiplicate the drug equation okay then
+
+ align:start position:0%
+multiplicate the drug equation okay then
+ 
+
+ align:start position:0%
+multiplicate the drug equation okay then
+you can also use to be checked by
+
+ align:start position:0%
+you can also use to be checked by
+ 
+
+ align:start position:0%
+you can also use to be checked by
+integration by part and if you want to
+
+ align:start position:0%
+integration by part and if you want to
+ 
+
+ align:start position:0%
+integration by part and if you want to
+reply you get the the compressed
+
+ align:start position:0%
+reply you get the the compressed
+ 
+
+ align:start position:0%
+reply you get the the compressed
+conjugate version of the drug equation
+
+ align:start position:0%
+conjugate version of the drug equation
+ 
+
+ align:start position:0%
+conjugate version of the drug equation
+and acting on the opposite bar okay
+
+ align:start position:0%
+and acting on the opposite bar okay
+ 
+
+ align:start position:0%
+and acting on the opposite bar okay
+so so now let me just say a few words on
+
+ align:start position:0%
+so so now let me just say a few words on
+ 
+
+ align:start position:0%
+so so now let me just say a few words on
+why you need the I here so you can check
+
+ align:start position:0%
+why you need the I here so you can check
+ 
+
+ align:start position:0%
+why you need the I here so you can check
+so so here I'm missing some relations
+
+ align:start position:0%
+so so here I'm missing some relations
+ 
+
+ align:start position:0%
+so so here I'm missing some relations
+again each of them you need to
+
+ align:start position:0%
+again each of them you need to
+ 
+
+ align:start position:0%
+again each of them you need to
+really write down the paper yourself
+
+ align:start position:0%
+really write down the paper yourself
+ 
+
+ align:start position:0%
+really write down the paper yourself
+stare at it maybe do a little bit
+
+ align:start position:0%
+stare at it maybe do a little bit
+ 
+
+ align:start position:0%
+stare at it maybe do a little bit
+derivation to get intuition about
+
+ align:start position:0%
+derivation to get intuition about
+ 
+
+ align:start position:0%
+derivation to get intuition about
+yourself okay right now I'm just writing
+
+ align:start position:0%
+yourself okay right now I'm just writing
+ 
+
+ align:start position:0%
+yourself okay right now I'm just writing
+down those duration down okay so you can
+
+ align:start position:0%
+down those duration down okay so you can
+ 
+
+ align:start position:0%
+down those duration down okay so you can
+also check yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side dagger
+
+ align:start position:0%
+side dagger
+ 
+
+ align:start position:0%
+side dagger
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+again just go through all this scene
+
+ align:start position:0%
+again just go through all this scene
+ 
+
+ align:start position:0%
+again just go through all this scene
+you find it's equal to minus Side by
+
+ align:start position:0%
+you find it's equal to minus Side by
+ 
+
+ align:start position:0%
+you find it's equal to minus Side by
+upside
+
+ align:start position:0%
+upside
+ 
+
+ align:start position:0%
+upside
+okay so uh so this is just two lines
+
+ align:start position:0%
+okay so uh so this is just two lines
+ 
+
+ align:start position:0%
+okay so uh so this is just two lines
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+I will not write write them extricity to
+
+ align:start position:0%
+I will not write write them extricity to
+ 
+
+ align:start position:0%
+I will not write write them extricity to
+pull you
+
+ align:start position:0%
+pull you
+ 
+
+ align:start position:0%
+pull you
+and similarly you can check
+
+ align:start position:0%
+and similarly you can check
+ 
+
+ align:start position:0%
+and similarly you can check
+related to this the other term
+
+ align:start position:0%
+related to this the other term
+ 
+
+ align:start position:0%
+related to this the other term
+the gamma
+
+ align:start position:0%
+the gamma
+ 
+
+ align:start position:0%
+the gamma
+sidebar
+
+ align:start position:0%
+sidebar
+ 
+
+ align:start position:0%
+sidebar
+comma mu
+
+ align:start position:0%
+comma mu
+ 
+
+ align:start position:0%
+comma mu
+partial mu PSI
+
+ align:start position:0%
+partial mu PSI
+ 
+
+ align:start position:0%
+partial mu PSI
+if you take the dagger
+
+ align:start position:0%
+if you take the dagger
+ 
+
+ align:start position:0%
+if you take the dagger
+so here so this one is slightly more
+
+ align:start position:0%
+so here so this one is slightly more
+ 
+
+ align:start position:0%
+so here so this one is slightly more
+complicated okay uh but you can still
+
+ align:start position:0%
+complicated okay uh but you can still
+ 
+
+ align:start position:0%
+complicated okay uh but you can still
+just you can just walk it through you
+
+ align:start position:0%
+just you can just walk it through you
+ 
+
+ align:start position:0%
+just you can just walk it through you
+find it's just equal to negative of
+
+ align:start position:0%
+find it's just equal to negative of
+ 
+
+ align:start position:0%
+find it's just equal to negative of
+itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then plus total derivatives
+
+ align:start position:0%
+then plus total derivatives
+ 
+
+ align:start position:0%
+then plus total derivatives
+so this one is not you'd actually matter
+
+ align:start position:0%
+so this one is not you'd actually matter
+ 
+
+ align:start position:0%
+so this one is not you'd actually matter
+sign but you have to throw away some
+
+ align:start position:0%
+sign but you have to throw away some
+ 
+
+ align:start position:0%
+sign but you have to throw away some
+total derivatives so total derivatives
+
+ align:start position:0%
+total derivatives so total derivatives
+ 
+
+ align:start position:0%
+total derivatives so total derivatives
+which give you
+
+ align:start position:0%
+which give you
+ 
+
+ align:start position:0%
+which give you
+when you plug in the
+
+ align:start position:0%
+when you plug in the
+ 
+
+ align:start position:0%
+when you plug in the
+into the action they give rise user
+
+ align:start position:0%
+into the action they give rise user
+ 
+
+ align:start position:0%
+into the action they give rise user
+boundary terms and but they will always
+
+ align:start position:0%
+boundary terms and but they will always
+ 
+
+ align:start position:0%
+boundary terms and but they will always
+assume the field vanish at Infinity okay
+
+ align:start position:0%
+assume the field vanish at Infinity okay
+ 
+
+ align:start position:0%
+assume the field vanish at Infinity okay
+so so uh so so that explains why you
+
+ align:start position:0%
+so so uh so so that explains why you
+ 
+
+ align:start position:0%
+so so uh so so that explains why you
+leave this I because when you take the
+
+ align:start position:0%
+leave this I because when you take the
+ 
+
+ align:start position:0%
+leave this I because when you take the
+the complex conjugate of the the
+
+ align:start position:0%
+the complex conjugate of the the
+ 
+
+ align:start position:0%
+the complex conjugate of the the
+quantity here you always get the math
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good good okay so now it's getting a
+
+ align:start position:0%
+good good okay so now it's getting a
+ 
+
+ align:start position:0%
+good good okay so now it's getting a
+little bit awkward
+
+ align:start position:0%
+little bit awkward
+ 
+
+ align:start position:0%
+little bit awkward
+because our printer today broke
+
+ align:start position:0%
+because our printer today broke
+ 
+
+ align:start position:0%
+because our printer today broke
+so so I didn't spring enough of my notes
+
+ align:start position:0%
+so so I didn't spring enough of my notes
+ 
+
+ align:start position:0%
+so so I didn't spring enough of my notes
+so now I have to hide my computer to to
+
+ align:start position:0%
+so now I have to hide my computer to to
+ 
+
+ align:start position:0%
+so now I have to hide my computer to to
+remember my notes
+
+ align:start position:0%
+remember my notes
+ 
+
+ align:start position:0%
+remember my notes
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have to find the location
+
+ align:start position:0%
+you have to find the location
+ 
+
+ align:start position:0%
+you have to find the location
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so any questions on this
+
+ align:start position:0%
+so any questions on this
+ 
+
+ align:start position:0%
+so any questions on this
+Okay no Okay so now let's move to the
+
+ align:start position:0%
+Okay no Okay so now let's move to the
+ 
+
+ align:start position:0%
+Okay no Okay so now let's move to the
+last topic so now so this concludes our
+
+ align:start position:0%
+last topic so now so this concludes our
+ 
+
+ align:start position:0%
+last topic so now so this concludes our
+discussion of the Iraq equation
+
+ align:start position:0%
+discussion of the Iraq equation
+ 
+
+ align:start position:0%
+discussion of the Iraq equation
+so we have derived The Rock equation
+
+ align:start position:0%
+so we have derived The Rock equation
+ 
+
+ align:start position:0%
+so we have derived The Rock equation
+uh uh by uh and also we have discussed
+
+ align:start position:0%
+uh uh by uh and also we have discussed
+ 
+
+ align:start position:0%
+uh uh by uh and also we have discussed
+how what is quantities in the Rock
+
+ align:start position:0%
+how what is quantities in the Rock
+ 
+
+ align:start position:0%
+how what is quantities in the Rock
+equation should transform
+
+ align:start position:0%
+equation should transform
+ 
+
+ align:start position:0%
+equation should transform
+and and also the following the drug
+
+ align:start position:0%
+and and also the following the drug
+ 
+
+ align:start position:0%
+and and also the following the drug
+action okay
+
+ align:start position:0%
+action okay
+ 
+
+ align:start position:0%
+action okay
+so so that the next step
+
+ align:start position:0%
+so so that the next step
+ 
+
+ align:start position:0%
+so so that the next step
+the logic like step is to contact
+
+ align:start position:0%
+the logic like step is to contact
+ 
+
+ align:start position:0%
+the logic like step is to contact
+to go to the quantum field Series so
+
+ align:start position:0%
+to go to the quantum field Series so
+ 
+
+ align:start position:0%
+to go to the quantum field Series so
+right now so far everything is classical
+
+ align:start position:0%
+right now so far everything is classical
+ 
+
+ align:start position:0%
+right now so far everything is classical
+so so so so now the next step is that we
+
+ align:start position:0%
+so so so so now the next step is that we
+ 
+
+ align:start position:0%
+so so so so now the next step is that we
+want to quantize this Theory and when we
+
+ align:start position:0%
+want to quantize this Theory and when we
+ 
+
+ align:start position:0%
+want to quantize this Theory and when we
+contact this Theory we will see
+
+ align:start position:0%
+contact this Theory we will see
+ 
+
+ align:start position:0%
+contact this Theory we will see
+remarkable body formulas okay so we will
+
+ align:start position:0%
+remarkable body formulas okay so we will
+ 
+
+ align:start position:0%
+remarkable body formulas okay so we will
+see formula we will see probably
+
+ align:start position:0%
+see formula we will see probably
+ 
+
+ align:start position:0%
+see formula we will see probably
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+and uh but but before but but as we said
+
+ align:start position:0%
+and uh but but before but but as we said
+ 
+
+ align:start position:0%
+and uh but but before but but as we said
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+that when we quantize the theory
+
+ align:start position:0%
+that when we quantize the theory
+ 
+
+ align:start position:0%
+that when we quantize the theory
+we first leads to uh the simplest way is
+
+ align:start position:0%
+we first leads to uh the simplest way is
+ 
+
+ align:start position:0%
+we first leads to uh the simplest way is
+to First find this all its classical
+
+ align:start position:0%
+to First find this all its classical
+ 
+
+ align:start position:0%
+to First find this all its classical
+Solutions
+
+ align:start position:0%
+Solutions
+ 
+
+ align:start position:0%
+Solutions
+and then then the classical Solutions
+
+ align:start position:0%
+and then then the classical Solutions
+ 
+
+ align:start position:0%
+and then then the classical Solutions
+then become solutions to the operator
+
+ align:start position:0%
+then become solutions to the operator
+ 
+
+ align:start position:0%
+then become solutions to the operator
+equations and then we can automatically
+
+ align:start position:0%
+equations and then we can automatically
+ 
+
+ align:start position:0%
+equations and then we can automatically
+quantize it okay so so then before we
+
+ align:start position:0%
+quantize it okay so so then before we
+ 
+
+ align:start position:0%
+quantize it okay so so then before we
+actually do the quantization uh it's
+
+ align:start position:0%
+actually do the quantization uh it's
+ 
+
+ align:start position:0%
+actually do the quantization uh it's
+better we try to find the the all the
+
+ align:start position:0%
+better we try to find the the all the
+ 
+
+ align:start position:0%
+better we try to find the the all the
+classical Solutions of the rock equation
+
+ align:start position:0%
+classical Solutions of the rock equation
+ 
+
+ align:start position:0%
+classical Solutions of the rock equation
+and so it's not like a kind golden
+
+ align:start position:0%
+and so it's not like a kind golden
+ 
+
+ align:start position:0%
+and so it's not like a kind golden
+equation we can just immediately write
+
+ align:start position:0%
+equation we can just immediately write
+ 
+
+ align:start position:0%
+equation we can just immediately write
+down the solutions and the direct
+
+ align:start position:0%
+down the solutions and the direct
+ 
+
+ align:start position:0%
+down the solutions and the direct
+equation is a little bit more intricate
+
+ align:start position:0%
+equation is a little bit more intricate
+ 
+
+ align:start position:0%
+equation is a little bit more intricate
+so we need to spend a little bit effort
+
+ align:start position:0%
+so we need to spend a little bit effort
+ 
+
+ align:start position:0%
+so we need to spend a little bit effort
+to uh to write down the solution to find
+
+ align:start position:0%
+to uh to write down the solution to find
+ 
+
+ align:start position:0%
+to uh to write down the solution to find
+all the solutions of the Dera equation
+
+ align:start position:0%
+all the solutions of the Dera equation
+ 
+
+ align:start position:0%
+all the solutions of the Dera equation
+okay so that's what you need to do
+
+ align:start position:0%
+okay so that's what you need to do
+ 
+
+ align:start position:0%
+okay so that's what you need to do
+unfortunately
+
+ align:start position:0%
+unfortunately
+ 
+
+ align:start position:0%
+unfortunately
+we're not going to finish today
+
+ align:start position:0%
+we're not going to finish today
+ 
+
+ align:start position:0%
+we're not going to finish today
+and then we will have a long spring
+
+ align:start position:0%
+and then we will have a long spring
+ 
+
+ align:start position:0%
+and then we will have a long spring
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so I hope you still remember what we
+
+ align:start position:0%
+so I hope you still remember what we
+ 
+
+ align:start position:0%
+so I hope you still remember what we
+talked about today when you come back
+
+ align:start position:0%
+talked about today when you come back
+ 
+
+ align:start position:0%
+talked about today when you come back
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have
+
+ align:start position:0%
+okay so now we have
+ 
+
+ align:start position:0%
+okay so now we have
+classical Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so by construction the derived equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know must be propane to this ikx
+
+ align:start position:0%
+we know must be propane to this ikx
+ 
+
+ align:start position:0%
+we know must be propane to this ikx
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+K Square equal to minus M squared okay
+
+ align:start position:0%
+K Square equal to minus M squared okay
+ 
+
+ align:start position:0%
+K Square equal to minus M squared okay
+so this is by construction because we
+
+ align:start position:0%
+so this is by construction because we
+ 
+
+ align:start position:0%
+so this is by construction because we
+Square it
+
+ align:start position:0%
+Square it
+ 
+
+ align:start position:0%
+Square it
+we get the uh we get the uh crying
+
+ align:start position:0%
+we get the uh we get the uh crying
+ 
+
+ align:start position:0%
+we get the uh we get the uh crying
+golden equation so this K mu
+
+ align:start position:0%
+golden equation so this K mu
+ 
+
+ align:start position:0%
+golden equation so this K mu
+would be Omega k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but but this is not enough
+
+ align:start position:0%
+but but this is not enough
+ 
+
+ align:start position:0%
+but but this is not enough
+because of the rock equation uh because
+
+ align:start position:0%
+because of the rock equation uh because
+ 
+
+ align:start position:0%
+because of the rock equation uh because
+PSI have four components okay so so this
+
+ align:start position:0%
+PSI have four components okay so so this
+ 
+
+ align:start position:0%
+PSI have four components okay so so this
+just determines one factor of it and we
+
+ align:start position:0%
+just determines one factor of it and we
+ 
+
+ align:start position:0%
+just determines one factor of it and we
+also have to determine its uh the
+
+ align:start position:0%
+also have to determine its uh the
+ 
+
+ align:start position:0%
+also have to determine its uh the
+behavior of all its four components okay
+
+ align:start position:0%
+behavior of all its four components okay
+ 
+
+ align:start position:0%
+behavior of all its four components okay
+so and so now that's we're going to do
+
+ align:start position:0%
+so and so now that's we're going to do
+ 
+
+ align:start position:0%
+so and so now that's we're going to do
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we will separate the solutions into
+
+ align:start position:0%
+so we will separate the solutions into
+ 
+
+ align:start position:0%
+so we will separate the solutions into
+two type
+
+ align:start position:0%
+two type
+ 
+
+ align:start position:0%
+two type
+so one type is we could I Plus
+
+ align:start position:0%
+so one type is we could I Plus
+ 
+
+ align:start position:0%
+so one type is we could I Plus
+X which equals one into U
+
+ align:start position:0%
+X which equals one into U
+ 
+
+ align:start position:0%
+X which equals one into U
+k x
+
+ align:start position:0%
+k x
+ 
+
+ align:start position:0%
+k x
+say expression ikx
+
+ align:start position:0%
+say expression ikx
+ 
+
+ align:start position:0%
+say expression ikx
+and another we call the PSI minus X
+
+ align:start position:0%
+and another we call the PSI minus X
+ 
+
+ align:start position:0%
+and another we call the PSI minus X
+which corresponding to v k x
+
+ align:start position:0%
+which corresponding to v k x
+ 
+
+ align:start position:0%
+which corresponding to v k x
+V K yeah sorry no X
+
+ align:start position:0%
+V K yeah sorry no X
+ 
+
+ align:start position:0%
+V K yeah sorry no X
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so yeah so so UK VK they just they're
+
+ align:start position:0%
+so yeah so so UK VK they just they're
+ 
+
+ align:start position:0%
+so yeah so so UK VK they just they're
+all four components Spinners okay which
+
+ align:start position:0%
+all four components Spinners okay which
+ 
+
+ align:start position:0%
+all four components Spinners okay which
+have the same uh signal side because
+
+ align:start position:0%
+have the same uh signal side because
+ 
+
+ align:start position:0%
+have the same uh signal side because
+this is just some number
+
+ align:start position:0%
+this is just some number
+ 
+
+ align:start position:0%
+this is just some number
+so this because this is
+
+ align:start position:0%
+so this because this is
+ 
+
+ align:start position:0%
+so this because this is
+because K have the positive frequency
+
+ align:start position:0%
+because K have the positive frequency
+ 
+
+ align:start position:0%
+because K have the positive frequency
+okay so this is some kind of called the
+
+ align:start position:0%
+okay so this is some kind of called the
+ 
+
+ align:start position:0%
+okay so this is some kind of called the
+positive energy solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's the same thing as in the scalar
+
+ align:start position:0%
+but it's the same thing as in the scalar
+ 
+
+ align:start position:0%
+but it's the same thing as in the scalar
+case they don't really
+
+ align:start position:0%
+case they don't really
+ 
+
+ align:start position:0%
+case they don't really
+there's not really uh when we contact
+
+ align:start position:0%
+there's not really uh when we contact
+ 
+
+ align:start position:0%
+there's not really uh when we contact
+the series doesn't really know elective
+
+ align:start position:0%
+the series doesn't really know elective
+ 
+
+ align:start position:0%
+the series doesn't really know elective
+energy excitations okay uh uh it's just
+
+ align:start position:0%
+energy excitations okay uh uh it's just
+ 
+
+ align:start position:0%
+energy excitations okay uh uh it's just
+a name okay so uh so we call the
+
+ align:start position:0%
+a name okay so uh so we call the
+ 
+
+ align:start position:0%
+a name okay so uh so we call the
+positive energy and negative energy
+
+ align:start position:0%
+positive energy and negative energy
+ 
+
+ align:start position:0%
+positive energy and negative energy
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+so data physical excitations always have
+
+ align:start position:0%
+so data physical excitations always have
+ 
+
+ align:start position:0%
+so data physical excitations always have
+positive message okay
+
+ align:start position:0%
+positive message okay
+ 
+
+ align:start position:0%
+positive message okay
+so under this UK
+
+ align:start position:0%
+so under this UK
+ 
+
+ align:start position:0%
+so under this UK
+and v k
+
+ align:start position:0%
+and v k
+ 
+
+ align:start position:0%
+and v k
+they're all four components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah yeah right right yeah yeah uh
+
+ align:start position:0%
+uh yeah yeah right right yeah yeah uh
+ 
+
+ align:start position:0%
+uh yeah yeah right right yeah yeah uh
+yeah so this is just the basis of
+
+ align:start position:0%
+yeah so this is just the basis of
+ 
+
+ align:start position:0%
+yeah so this is just the basis of
+solutions indeed yeah we should label
+
+ align:start position:0%
+solutions indeed yeah we should label
+ 
+
+ align:start position:0%
+solutions indeed yeah we should label
+them back okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so so this the uh so essentially
+
+ align:start position:0%
+good so so this the uh so essentially
+ 
+
+ align:start position:0%
+good so so this the uh so essentially
+you just
+
+ align:start position:0%
+you just
+ 
+
+ align:start position:0%
+you just
+in the scalar case you just expand in
+
+ align:start position:0%
+in the scalar case you just expand in
+ 
+
+ align:start position:0%
+in the scalar case you just expand in
+terms of the plane wave and then just
+
+ align:start position:0%
+terms of the plane wave and then just
+ 
+
+ align:start position:0%
+terms of the plane wave and then just
+get some constants
+
+ align:start position:0%
+get some constants
+ 
+
+ align:start position:0%
+get some constants
+so here is exactly to indicates uh we
+
+ align:start position:0%
+so here is exactly to indicates uh we
+ 
+
+ align:start position:0%
+so here is exactly to indicates uh we
+have a vector now we need to solve these
+
+ align:start position:0%
+have a vector now we need to solve these
+ 
+
+ align:start position:0%
+have a vector now we need to solve these
+vectors okay so our goal is to solve
+
+ align:start position:0%
+vectors okay so our goal is to solve
+ 
+
+ align:start position:0%
+vectors okay so our goal is to solve
+these vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you just plug them into the
+
+ align:start position:0%
+and then you just plug them into the
+ 
+
+ align:start position:0%
+and then you just plug them into the
+direct equation okay just plug these two
+
+ align:start position:0%
+direct equation okay just plug these two
+ 
+
+ align:start position:0%
+direct equation okay just plug these two
+into the drug equation and then you get
+
+ align:start position:0%
+into the drug equation and then you get
+ 
+
+ align:start position:0%
+into the drug equation and then you get
+the equations for um
+
+ align:start position:0%
+the equations for um
+ 
+
+ align:start position:0%
+the equations for um
+for the UK and the and the v k okay
+
+ align:start position:0%
+for the UK and the and the v k okay
+ 
+
+ align:start position:0%
+for the UK and the and the v k okay
+I know I will also suppress the K in the
+
+ align:start position:0%
+I know I will also suppress the K in the
+ 
+
+ align:start position:0%
+I know I will also suppress the K in the
+in the U and the V so so just for
+
+ align:start position:0%
+in the U and the V so so just for
+ 
+
+ align:start position:0%
+in the U and the V so so just for
+rotational simplicities okay so when you
+
+ align:start position:0%
+rotational simplicities okay so when you
+ 
+
+ align:start position:0%
+rotational simplicities okay so when you
+have the gamma mu
+
+ align:start position:0%
+have the gamma mu
+ 
+
+ align:start position:0%
+have the gamma mu
+100 mu minus m
+
+ align:start position:0%
+100 mu minus m
+ 
+
+ align:start position:0%
+100 mu minus m
+PSI equal to zero you just plug the PSI
+
+ align:start position:0%
+PSI equal to zero you just plug the PSI
+ 
+
+ align:start position:0%
+PSI equal to zero you just plug the PSI
+plus Prime minus in and then you find
+
+ align:start position:0%
+plus Prime minus in and then you find
+ 
+
+ align:start position:0%
+plus Prime minus in and then you find
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+equations for U
+
+ align:start position:0%
+equations for U
+ 
+
+ align:start position:0%
+equations for U
+if you get i k slash minus m u equal to
+
+ align:start position:0%
+if you get i k slash minus m u equal to
+ 
+
+ align:start position:0%
+if you get i k slash minus m u equal to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+ik slash
+
+ align:start position:0%
+ik slash
+ 
+
+ align:start position:0%
+ik slash
+and minus
+
+ align:start position:0%
+and minus
+ 
+
+ align:start position:0%
+and minus
+yeah I think let me just double check
+
+ align:start position:0%
+yeah I think let me just double check
+ 
+
+ align:start position:0%
+yeah I think let me just double check
+the sign yeah indeed so you get okay
+
+ align:start position:0%
+the sign yeah indeed so you get okay
+ 
+
+ align:start position:0%
+the sign yeah indeed so you get okay
+slash plus and
+
+ align:start position:0%
+slash plus and
+ 
+
+ align:start position:0%
+slash plus and
+V equal to zero okay so you get these
+
+ align:start position:0%
+V equal to zero okay so you get these
+ 
+
+ align:start position:0%
+V equal to zero okay so you get these
+two increase
+
+ align:start position:0%
+two increase
+ 
+
+ align:start position:0%
+two increase
+so our goal is just to solve those
+
+ align:start position:0%
+so our goal is just to solve those
+ 
+
+ align:start position:0%
+so our goal is just to solve those
+equations okay and the case rise just as
+
+ align:start position:0%
+equations okay and the case rise just as
+ 
+
+ align:start position:0%
+equations okay and the case rise just as
+defined before
+
+ align:start position:0%
+defined before
+ 
+
+ align:start position:0%
+defined before
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh it just defined as in the partial
+
+ align:start position:0%
+uh it just defined as in the partial
+ 
+
+ align:start position:0%
+uh it just defined as in the partial
+slice okay slash
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so you can also work out their complex
+
+ align:start position:0%
+so you can also work out their complex
+ 
+
+ align:start position:0%
+so you can also work out their complex
+conjugates so let me just write down the
+
+ align:start position:0%
+conjugates so let me just write down the
+ 
+
+ align:start position:0%
+conjugates so let me just write down the
+uh uh the equations because sometimes
+
+ align:start position:0%
+uh uh the equations because sometimes
+ 
+
+ align:start position:0%
+uh uh the equations because sometimes
+they will be used later okay so the U
+
+ align:start position:0%
+they will be used later okay so the U
+ 
+
+ align:start position:0%
+they will be used later okay so the U
+Bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus m equal to zero the complex
+
+ align:start position:0%
+minus m equal to zero the complex
+ 
+
+ align:start position:0%
+minus m equal to zero the complex
+conjugate and V bar
+
+ align:start position:0%
+conjugate and V bar
+ 
+
+ align:start position:0%
+conjugate and V bar
+okay slash plus m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's try to work out the uh UK
+
+ align:start position:0%
+so now let's try to work out the uh UK
+ 
+
+ align:start position:0%
+so now let's try to work out the uh UK
+and the VK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by solving those equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we do this by
+
+ align:start position:0%
+so we do this by
+ 
+
+ align:start position:0%
+so we do this by
+you can in principle do it by Brute
+
+ align:start position:0%
+you can in principle do it by Brute
+ 
+
+ align:start position:0%
+you can in principle do it by Brute
+Force
+
+ align:start position:0%
+Force
+ 
+
+ align:start position:0%
+Force
+so after all they just
+
+ align:start position:0%
+so after all they just
+ 
+
+ align:start position:0%
+so after all they just
+these are just four by four equations
+
+ align:start position:0%
+these are just four by four equations
+ 
+
+ align:start position:0%
+these are just four by four equations
+okay 4x4 Matrix equations uh just linear
+
+ align:start position:0%
+okay 4x4 Matrix equations uh just linear
+ 
+
+ align:start position:0%
+okay 4x4 Matrix equations uh just linear
+algebra okay you can in principle become
+
+ align:start position:0%
+algebra okay you can in principle become
+ 
+
+ align:start position:0%
+algebra okay you can in principle become
+more solve it
+
+ align:start position:0%
+more solve it
+ 
+
+ align:start position:0%
+more solve it
+but the physics is often are lazy okay
+
+ align:start position:0%
+but the physics is often are lazy okay
+ 
+
+ align:start position:0%
+but the physics is often are lazy okay
+so we often still even for the problem
+
+ align:start position:0%
+so we often still even for the problem
+ 
+
+ align:start position:0%
+so we often still even for the problem
+you can you can solve we still look for
+
+ align:start position:0%
+you can you can solve we still look for
+ 
+
+ align:start position:0%
+you can you can solve we still look for
+shortcuts
+
+ align:start position:0%
+shortcuts
+ 
+
+ align:start position:0%
+shortcuts
+and so in this case there are two
+
+ align:start position:0%
+and so in this case there are two
+ 
+
+ align:start position:0%
+and so in this case there are two
+possible shortcuts there are two
+
+ align:start position:0%
+possible shortcuts there are two
+ 
+
+ align:start position:0%
+possible shortcuts there are two
+possible ways we can do okay and uh so
+
+ align:start position:0%
+possible ways we can do okay and uh so
+ 
+
+ align:start position:0%
+possible ways we can do okay and uh so
+so let me describe both ways
+
+ align:start position:0%
+so let me describe both ways
+ 
+
+ align:start position:0%
+so let me describe both ways
+uh actually I think we only have time to
+
+ align:start position:0%
+uh actually I think we only have time to
+ 
+
+ align:start position:0%
+uh actually I think we only have time to
+describe one way
+
+ align:start position:0%
+describe one way
+ 
+
+ align:start position:0%
+describe one way
+uh so
+
+ align:start position:0%
+uh so
+ 
+
+ align:start position:0%
+uh so
+so to find the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicit form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of u and v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so one simple thing to do is let's
+
+ align:start position:0%
+so so one simple thing to do is let's
+ 
+
+ align:start position:0%
+so so one simple thing to do is let's
+just consider in the simple case
+
+ align:start position:0%
+just consider in the simple case
+ 
+
+ align:start position:0%
+just consider in the simple case
+say consider the particle is at rest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when the particle is at rest then the
+
+ align:start position:0%
+when the particle is at rest then the
+ 
+
+ align:start position:0%
+when the particle is at rest then the
+Omega is just equal to m
+
+ align:start position:0%
+Omega is just equal to m
+ 
+
+ align:start position:0%
+Omega is just equal to m
+and then k equal to zero
+
+ align:start position:0%
+and then k equal to zero
+ 
+
+ align:start position:0%
+and then k equal to zero
+okay and then that equation just become
+
+ align:start position:0%
+okay and then that equation just become
+ 
+
+ align:start position:0%
+okay and then that equation just become
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+M comma zero
+
+ align:start position:0%
+M comma zero
+ 
+
+ align:start position:0%
+M comma zero
+minus m
+
+ align:start position:0%
+minus m
+ 
+
+ align:start position:0%
+minus m
+U equal to zero and I
+
+ align:start position:0%
+U equal to zero and I
+ 
+
+ align:start position:0%
+U equal to zero and I
+M comma zero plus m
+
+ align:start position:0%
+M comma zero plus m
+ 
+
+ align:start position:0%
+M comma zero plus m
+V equal to zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think
+
+ align:start position:0%
+I think
+ 
+
+ align:start position:0%
+I think
+do I
+
+ align:start position:0%
+do I
+ 
+
+ align:start position:0%
+do I
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah I think let me
+
+ align:start position:0%
+so yeah I think let me
+ 
+
+ align:start position:0%
+so yeah I think let me
+oh yeah yeah sorry I should have a minus
+
+ align:start position:0%
+oh yeah yeah sorry I should have a minus
+ 
+
+ align:start position:0%
+oh yeah yeah sorry I should have a minus
+sign here
+
+ align:start position:0%
+sign here
+ 
+
+ align:start position:0%
+sign here
+because of the uh because of the um is
+
+ align:start position:0%
+because of the uh because of the um is
+ 
+
+ align:start position:0%
+because of the uh because of the um is
+the K upper index
+
+ align:start position:0%
+the K upper index
+ 
+
+ align:start position:0%
+the K upper index
+so it's the K up index equal to Omega
+
+ align:start position:0%
+so it's the K up index equal to Omega
+ 
+
+ align:start position:0%
+so it's the K up index equal to Omega
+then called K low index equal to minus
+
+ align:start position:0%
+then called K low index equal to minus
+ 
+
+ align:start position:0%
+then called K low index equal to minus
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and here when we contract with gamma
+
+ align:start position:0%
+and here when we contract with gamma
+ 
+
+ align:start position:0%
+and here when we contract with gamma
+zero we use the low index so so we have
+
+ align:start position:0%
+zero we use the low index so so we have
+ 
+
+ align:start position:0%
+zero we use the low index so so we have
+a minus sign here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so essentially this just becomes
+
+ align:start position:0%
+okay so so essentially this just becomes
+ 
+
+ align:start position:0%
+okay so so essentially this just becomes
+so M can be canceled on both sides so
+
+ align:start position:0%
+so M can be canceled on both sides so
+ 
+
+ align:start position:0%
+so M can be canceled on both sides so
+essentially just become the
+
+ align:start position:0%
+essentially just become the
+ 
+
+ align:start position:0%
+essentially just become the
+um I comma zero U
+
+ align:start position:0%
+um I comma zero U
+ 
+
+ align:start position:0%
+um I comma zero U
+equal to manage U
+
+ align:start position:0%
+equal to manage U
+ 
+
+ align:start position:0%
+equal to manage U
+and I comma 0 V
+
+ align:start position:0%
+and I comma 0 V
+ 
+
+ align:start position:0%
+and I comma 0 V
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this tells you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this just tells you essentially gamma
+
+ align:start position:0%
+so this just tells you essentially gamma
+ 
+
+ align:start position:0%
+so this just tells you essentially gamma
+u u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going back to V and V they are just
+
+ align:start position:0%
+is going back to V and V they are just
+ 
+
+ align:start position:0%
+is going back to V and V they are just
+essentially diagonal Vector so comma
+
+ align:start position:0%
+essentially diagonal Vector so comma
+ 
+
+ align:start position:0%
+essentially diagonal Vector so comma
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay they just argument also comma zero
+
+ align:start position:0%
+okay they just argument also comma zero
+ 
+
+ align:start position:0%
+okay they just argument also comma zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so so let's just now to write the
+
+ align:start position:0%
+and so so let's just now to write the
+ 
+
+ align:start position:0%
+and so so let's just now to write the
+mix 3 c 3 so so now let's use the
+
+ align:start position:0%
+mix 3 c 3 so so now let's use the
+ 
+
+ align:start position:0%
+mix 3 c 3 so so now let's use the
+explicit representation of gamma
+
+ align:start position:0%
+explicit representation of gamma
+ 
+
+ align:start position:0%
+explicit representation of gamma
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+yeah let me just copy this
+
+ align:start position:0%
+yeah let me just copy this
+ 
+
+ align:start position:0%
+yeah let me just copy this
+so so now let's use this representation
+
+ align:start position:0%
+so so now let's use this representation
+ 
+
+ align:start position:0%
+so so now let's use this representation
+with the gamma zero
+
+ align:start position:0%
+with the gamma zero
+ 
+
+ align:start position:0%
+with the gamma zero
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+I zero zero I minus I and then gamma I
+
+ align:start position:0%
+I zero zero I minus I and then gamma I
+ 
+
+ align:start position:0%
+I zero zero I minus I and then gamma I
+is equal to zero I think on my I
+
+ align:start position:0%
+is equal to zero I think on my I
+ 
+
+ align:start position:0%
+is equal to zero I think on my I
+minus I Sigma I zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then now if you plug in this comma
+
+ align:start position:0%
+and then now if you plug in this comma
+ 
+
+ align:start position:0%
+and then now if you plug in this comma
+zero into those equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you find the equation for U and
+
+ align:start position:0%
+and then you find the equation for U and
+ 
+
+ align:start position:0%
+and then you find the equation for U and
+B become very simple
+
+ align:start position:0%
+B become very simple
+ 
+
+ align:start position:0%
+B become very simple
+for the U just become zero zero zero one
+
+ align:start position:0%
+for the U just become zero zero zero one
+ 
+
+ align:start position:0%
+for the U just become zero zero zero one
+U equal to zero so again this is two by
+
+ align:start position:0%
+U equal to zero so again this is two by
+ 
+
+ align:start position:0%
+U equal to zero so again this is two by
+two blocks okay because this here is two
+
+ align:start position:0%
+two blocks okay because this here is two
+ 
+
+ align:start position:0%
+two blocks okay because this here is two
+by two blocks
+
+ align:start position:0%
+by two blocks
+ 
+
+ align:start position:0%
+by two blocks
+and uh and for V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just the one zero zero
+
+ align:start position:0%
+just the one zero zero
+ 
+
+ align:start position:0%
+just the one zero zero
+V equal to zero
+
+ align:start position:0%
+V equal to zero
+ 
+
+ align:start position:0%
+V equal to zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that means
+
+ align:start position:0%
+so that means
+ 
+
+ align:start position:0%
+so that means
+you you can just take it to be the upper
+
+ align:start position:0%
+you you can just take it to be the upper
+ 
+
+ align:start position:0%
+you you can just take it to be the upper
+so that means the solution of this
+
+ align:start position:0%
+so that means the solution of this
+ 
+
+ align:start position:0%
+so that means the solution of this
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means that the solution of this
+
+ align:start position:0%
+so that means that the solution of this
+ 
+
+ align:start position:0%
+so that means that the solution of this
+equation for U
+
+ align:start position:0%
+equation for U
+ 
+
+ align:start position:0%
+equation for U
+so now let me write the upper index 0
+
+ align:start position:0%
+so now let me write the upper index 0
+ 
+
+ align:start position:0%
+so now let me write the upper index 0
+means that this is for the for the zero
+
+ align:start position:0%
+means that this is for the for the zero
+ 
+
+ align:start position:0%
+means that this is for the for the zero
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+so here we can just choose cubic PSI
+
+ align:start position:0%
+so here we can just choose cubic PSI
+ 
+
+ align:start position:0%
+so here we can just choose cubic PSI
+zero so PSI is some arbitrary two Vector
+
+ align:start position:0%
+zero so PSI is some arbitrary two Vector
+ 
+
+ align:start position:0%
+zero so PSI is some arbitrary two Vector
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+for V we can just choose the lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero ETA
+
+ align:start position:0%
+zero ETA
+ 
+
+ align:start position:0%
+zero ETA
+okay so PSI
+
+ align:start position:0%
+okay so PSI
+ 
+
+ align:start position:0%
+okay so PSI
+ETA arbitrary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two vectors two complex two complex
+
+ align:start position:0%
+two vectors two complex two complex
+ 
+
+ align:start position:0%
+two vectors two complex two complex
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+a two vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two component of vectors
+
+ align:start position:0%
+two component of vectors
+ 
+
+ align:start position:0%
+two component of vectors
+two components
+
+ align:start position:0%
+two components
+ 
+
+ align:start position:0%
+two components
+complex vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so once you have u0 and V 0 and we can
+
+ align:start position:0%
+so once you have u0 and V 0 and we can
+ 
+
+ align:start position:0%
+so once you have u0 and V 0 and we can
+choose the basis
+
+ align:start position:0%
+choose the basis
+ 
+
+ align:start position:0%
+choose the basis
+for example U zero
+
+ align:start position:0%
+for example U zero
+ 
+
+ align:start position:0%
+for example U zero
+one equal to zero one one zero zero zero
+
+ align:start position:0%
+one equal to zero one one zero zero zero
+ 
+
+ align:start position:0%
+one equal to zero one one zero zero zero
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+zero two equal to zero one zero zero and
+
+ align:start position:0%
+zero two equal to zero one zero zero and
+ 
+
+ align:start position:0%
+zero two equal to zero one zero zero and
+similarly for V zero
+
+ align:start position:0%
+similarly for V zero
+ 
+
+ align:start position:0%
+similarly for V zero
+one and V 0 2 okay so you can choose to
+
+ align:start position:0%
+one and V 0 2 okay so you can choose to
+ 
+
+ align:start position:0%
+one and V 0 2 okay so you can choose to
+be here one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you can just choose as a basis
+
+ align:start position:0%
+okay so you can just choose as a basis
+ 
+
+ align:start position:0%
+okay so you can just choose as a basis
+you can just choose the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now once you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so once you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so once you have the vector at k equal
+
+ align:start position:0%
+so once you have the vector at k equal
+ 
+
+ align:start position:0%
+so once you have the vector at k equal
+to zero for General K what do you do
+
+ align:start position:0%
+to zero for General K what do you do
+ 
+
+ align:start position:0%
+to zero for General K what do you do
+yes yes to a Lawrence post so we know
+
+ align:start position:0%
+yes yes to a Lawrence post so we know
+ 
+
+ align:start position:0%
+yes yes to a Lawrence post so we know
+the Matrix S
+
+ align:start position:0%
+the Matrix S
+ 
+
+ align:start position:0%
+the Matrix S
+and then you just for the general k
+
+ align:start position:0%
+and then you just for the general k
+ 
+
+ align:start position:0%
+and then you just for the general k
+you just s
+
+ align:start position:0%
+you just s
+ 
+
+ align:start position:0%
+you just s
+U zero
+
+ align:start position:0%
+U zero
+ 
+
+ align:start position:0%
+U zero
+and the v k
+
+ align:start position:0%
+and the v k
+ 
+
+ align:start position:0%
+and the v k
+s v0
+
+ align:start position:0%
+s v0
+ 
+
+ align:start position:0%
+s v0
+okay and then you can find the behavior
+
+ align:start position:0%
+okay and then you can find the behavior
+ 
+
+ align:start position:0%
+okay and then you can find the behavior
+as general k
+
+ align:start position:0%
+as general k
+ 
+
+ align:start position:0%
+as general k
+but this is work but this is easily said
+
+ align:start position:0%
+but this is work but this is easily said
+ 
+
+ align:start position:0%
+but this is work but this is easily said
+than two okay
+
+ align:start position:0%
+than two okay
+ 
+
+ align:start position:0%
+than two okay
+two this actually is not quite easy
+
+ align:start position:0%
+two this actually is not quite easy
+ 
+
+ align:start position:0%
+two this actually is not quite easy
+okay even though this sounds like a
+
+ align:start position:0%
+okay even though this sounds like a
+ 
+
+ align:start position:0%
+okay even though this sounds like a
+great idea okay let's find the zero
+
+ align:start position:0%
+great idea okay let's find the zero
+ 
+
+ align:start position:0%
+great idea okay let's find the zero
+momentum and then let's just do a boost
+
+ align:start position:0%
+momentum and then let's just do a boost
+ 
+
+ align:start position:0%
+momentum and then let's just do a boost
+but but this time it's still a little
+
+ align:start position:0%
+but but this time it's still a little
+ 
+
+ align:start position:0%
+but but this time it's still a little
+bit tedious
+
+ align:start position:0%
+bit tedious
+ 
+
+ align:start position:0%
+bit tedious
+but it's still uh
+
+ align:start position:0%
+but it's still uh
+ 
+
+ align:start position:0%
+but it's still uh
+it's doable and a little bit simpler
+
+ align:start position:0%
+it's doable and a little bit simpler
+ 
+
+ align:start position:0%
+it's doable and a little bit simpler
+than then solve the original equation by
+
+ align:start position:0%
+than then solve the original equation by
+ 
+
+ align:start position:0%
+than then solve the original equation by
+Brute Force okay and but it is again
+
+ align:start position:0%
+Brute Force okay and but it is again
+ 
+
+ align:start position:0%
+Brute Force okay and but it is again
+still another simpler methods
+
+ align:start position:0%
+still another simpler methods
+ 
+
+ align:start position:0%
+still another simpler methods
+which you can actually discuss the
+
+ align:start position:0%
+which you can actually discuss the
+ 
+
+ align:start position:0%
+which you can actually discuss the
+answer you don't have to do any
+
+ align:start position:0%
+answer you don't have to do any
+ 
+
+ align:start position:0%
+answer you don't have to do any
+calculation you can just guess the
+
+ align:start position:0%
+calculation you can just guess the
+ 
+
+ align:start position:0%
+calculation you can just guess the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+cast the solution for the full equation
+
+ align:start position:0%
+cast the solution for the full equation
+ 
+
+ align:start position:0%
+cast the solution for the full equation
+okay and I don't I think we don't have
+
+ align:start position:0%
+okay and I don't I think we don't have
+ 
+
+ align:start position:0%
+okay and I don't I think we don't have
+time to talk about it today and so we
+
+ align:start position:0%
+time to talk about it today and so we
+ 
+
+ align:start position:0%
+time to talk about it today and so we
+will talk about it next time
+
+ align:start position:0%
+will talk about it next time
+ 
+
+ align:start position:0%
+will talk about it next time
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+so so hopefully you still remember what
+
+ align:start position:0%
+so so hopefully you still remember what
+ 
+
+ align:start position:0%
+so so hopefully you still remember what
+we talked about today when we come back
+
+ align:start position:0%
+we talked about today when we come back
+ 
+
+ align:start position:0%
+we talked about today when we come back
+and uh hope you have a good spring break
\ No newline at end of file
diff --git a/ZPmBMd6OZeQ.txt b/ZPmBMd6OZeQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..350d455c7eb0705e6559cc7a91c6ce3b33f4ecb2
--- /dev/null
+++ b/ZPmBMd6OZeQ.txt
@@ -0,0 +1,7403 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay ready to go okay so uh
+
+ align:start position:0%
+ocw.mit.edu okay ready to go okay so uh
+ 
+
+ align:start position:0%
+ocw.mit.edu okay ready to go okay so uh
+first of all to say thank you to several
+
+ align:start position:0%
+first of all to say thank you to several
+ 
+
+ align:start position:0%
+first of all to say thank you to several
+people in the class who sent uh codes to
+
+ align:start position:0%
+people in the class who sent uh codes to
+ 
+
+ align:start position:0%
+people in the class who sent uh codes to
+find these um
+
+ align:start position:0%
+find these um
+ 
+
+ align:start position:0%
+find these um
+wavefronts when a shock a step function
+
+ align:start position:0%
+wavefronts when a shock a step function
+ 
+
+ align:start position:0%
+wavefronts when a shock a step function
+is moving along with velocity C uh I had
+
+ align:start position:0%
+is moving along with velocity C uh I had
+ 
+
+ align:start position:0%
+is moving along with velocity C uh I had
+roughly drawn uh what these three
+
+ align:start position:0%
+roughly drawn uh what these three
+ 
+
+ align:start position:0%
+roughly drawn uh what these three
+methods produce but it was much better
+
+ align:start position:0%
+methods produce but it was much better
+ 
+
+ align:start position:0%
+methods produce but it was much better
+to see it in Mr Sakura's movie that's on
+
+ align:start position:0%
+to see it in Mr Sakura's movie that's on
+ 
+
+ align:start position:0%
+to see it in Mr Sakura's movie that's on
+the 18086 site uh and sure enough behind
+
+ align:start position:0%
+the 18086 site uh and sure enough behind
+ 
+
+ align:start position:0%
+the 18086 site uh and sure enough behind
+the moving front is a is a
+
+ align:start position:0%
+the moving front is a is a
+ 
+
+ align:start position:0%
+the moving front is a is a
+overshoot that reminds us of the Gibbs
+
+ align:start position:0%
+overshoot that reminds us of the Gibbs
+ 
+
+ align:start position:0%
+overshoot that reminds us of the Gibbs
+phenomenon from LAX
+
+ align:start position:0%
+phenomenon from LAX
+ 
+
+ align:start position:0%
+phenomenon from LAX
+wend and I think it's sort of
+
+ align:start position:0%
+wend and I think it's sort of
+ 
+
+ align:start position:0%
+wend and I think it's sort of
+unavoidable if we have a negative if
+
+ align:start position:0%
+unavoidable if we have a negative if
+ 
+
+ align:start position:0%
+unavoidable if we have a negative if
+because one of the three coefficients at
+
+ align:start position:0%
+because one of the three coefficients at
+ 
+
+ align:start position:0%
+because one of the three coefficients at
+the previous time is negative for Lex
+
+ align:start position:0%
+the previous time is negative for Lex
+ 
+
+ align:start position:0%
+the previous time is negative for Lex
+wend that's how it gets its second order
+
+ align:start position:0%
+wend that's how it gets its second order
+ 
+
+ align:start position:0%
+wend that's how it gets its second order
+accuracy and we see that better accuracy
+
+ align:start position:0%
+accuracy and we see that better accuracy
+ 
+
+ align:start position:0%
+accuracy and we see that better accuracy
+in a much steeper much steeper profile
+
+ align:start position:0%
+in a much steeper much steeper profile
+ 
+
+ align:start position:0%
+in a much steeper much steeper profile
+and then LAX friedricks if you noticed
+
+ align:start position:0%
+and then LAX friedricks if you noticed
+ 
+
+ align:start position:0%
+and then LAX friedricks if you noticed
+has a sort of uh Jagged uh profile and I
+
+ align:start position:0%
+has a sort of uh Jagged uh profile and I
+ 
+
+ align:start position:0%
+has a sort of uh Jagged uh profile and I
+guess well maybe you realized why that
+
+ align:start position:0%
+guess well maybe you realized why that
+ 
+
+ align:start position:0%
+guess well maybe you realized why that
+would be somehow LAX
+
+ align:start position:0%
+would be somehow LAX
+ 
+
+ align:start position:0%
+would be somehow LAX
+friedrick uh is kind of operates on a
+
+ align:start position:0%
+friedrick uh is kind of operates on a
+ 
+
+ align:start position:0%
+friedrick uh is kind of operates on a
+staggered grid we'll see actually well
+
+ align:start position:0%
+staggered grid we'll see actually well
+ 
+
+ align:start position:0%
+staggered grid we'll see actually well
+I've I've drawn a staggered grid here so
+
+ align:start position:0%
+I've I've drawn a staggered grid here so
+ 
+
+ align:start position:0%
+I've I've drawn a staggered grid here so
+I can say what I mean LAX friedr
+
+ align:start position:0%
+I can say what I mean LAX friedr
+ 
+
+ align:start position:0%
+I can say what I mean LAX friedr
+computes this value from the two earlier
+
+ align:start position:0%
+computes this value from the two earlier
+ 
+
+ align:start position:0%
+computes this value from the two earlier
+values there and then at the next level
+
+ align:start position:0%
+values there and then at the next level
+ 
+
+ align:start position:0%
+values there and then at the next level
+again and so forth so that actually LAX
+
+ align:start position:0%
+again and so forth so that actually LAX
+ 
+
+ align:start position:0%
+again and so forth so that actually LAX
+LAX friedricks only
+
+ align:start position:0%
+LAX friedricks only
+ 
+
+ align:start position:0%
+LAX friedricks only
+uses is using two staggered grids
+
+ align:start position:0%
+uses is using two staggered grids
+ 
+
+ align:start position:0%
+uses is using two staggered grids
+separately and I think and normally we
+
+ align:start position:0%
+separately and I think and normally we
+ 
+
+ align:start position:0%
+separately and I think and normally we
+we with LA frieds we called that n plus
+
+ align:start position:0%
+we with LA frieds we called that n plus
+ 
+
+ align:start position:0%
+we with LA frieds we called that n plus
+one and n plus2 and n plus 3 but the
+
+ align:start position:0%
+one and n plus2 and n plus 3 but the
+ 
+
+ align:start position:0%
+one and n plus2 and n plus 3 but the
+picture is still right so I think that's
+
+ align:start position:0%
+picture is still right so I think that's
+ 
+
+ align:start position:0%
+picture is still right so I think that's
+probably responsible for what you see
+
+ align:start position:0%
+probably responsible for what you see
+ 
+
+ align:start position:0%
+probably responsible for what you see
+that that there's there there's two
+
+ align:start position:0%
+that that there's there there's two
+ 
+
+ align:start position:0%
+that that there's there there's two
+waves uh two fronts uh right one delt
+
+ align:start position:0%
+waves uh two fronts uh right one delt
+ 
+
+ align:start position:0%
+waves uh two fronts uh right one delt
+Delta X away from each other and finally
+
+ align:start position:0%
+Delta X away from each other and finally
+ 
+
+ align:start position:0%
+Delta X away from each other and finally
+upwind is also smeared out uh I I guess
+
+ align:start position:0%
+upwind is also smeared out uh I I guess
+ 
+
+ align:start position:0%
+upwind is also smeared out uh I I guess
+I I was so pleased to see these um
+
+ align:start position:0%
+I I was so pleased to see these um
+ 
+
+ align:start position:0%
+I I was so pleased to see these um
+actually showing on the website and that
+
+ align:start position:0%
+actually showing on the website and that
+ 
+
+ align:start position:0%
+actually showing on the website and that
+it makes me think of more questions and
+
+ align:start position:0%
+it makes me think of more questions and
+ 
+
+ align:start position:0%
+it makes me think of more questions and
+maybe you too um first of
+
+ align:start position:0%
+maybe you too um first of
+ 
+
+ align:start position:0%
+maybe you too um first of
+all um as time goes forward
+
+ align:start position:0%
+all um as time goes forward
+ 
+
+ align:start position:0%
+all um as time goes forward
+we see this bump beginning to appear so
+
+ align:start position:0%
+we see this bump beginning to appear so
+ 
+
+ align:start position:0%
+we see this bump beginning to appear so
+am I right in thinking that it reaches a
+
+ align:start position:0%
+am I right in thinking that it reaches a
+ 
+
+ align:start position:0%
+am I right in thinking that it reaches a
+certain height and and stays there so
+
+ align:start position:0%
+certain height and and stays there so
+ 
+
+ align:start position:0%
+certain height and and stays there so
+that I guess I'm thinking about sort of
+
+ align:start position:0%
+that I guess I'm thinking about sort of
+ 
+
+ align:start position:0%
+that I guess I'm thinking about sort of
+further questions because every time you
+
+ align:start position:0%
+further questions because every time you
+ 
+
+ align:start position:0%
+further questions because every time you
+do a numerical experiment good good
+
+ align:start position:0%
+do a numerical experiment good good
+ 
+
+ align:start position:0%
+do a numerical experiment good good
+additional questions show up and so I'm
+
+ align:start position:0%
+additional questions show up and so I'm
+ 
+
+ align:start position:0%
+additional questions show up and so I'm
+wondering as this wavefront forms is
+
+ align:start position:0%
+wondering as this wavefront forms is
+ 
+
+ align:start position:0%
+wondering as this wavefront forms is
+characteristic profile for these three
+
+ align:start position:0%
+characteristic profile for these three
+ 
+
+ align:start position:0%
+characteristic profile for these three
+methods um first of all do they does
+
+ align:start position:0%
+methods um first of all do they does
+ 
+
+ align:start position:0%
+methods um first of all do they does
+that profile settle down to a steady
+
+ align:start position:0%
+that profile settle down to a steady
+ 
+
+ align:start position:0%
+that profile settle down to a steady
+profile ultimately it'd be great to be
+
+ align:start position:0%
+profile ultimately it'd be great to be
+ 
+
+ align:start position:0%
+profile ultimately it'd be great to be
+able to predict what it would
+
+ align:start position:0%
+able to predict what it would
+ 
+
+ align:start position:0%
+able to predict what it would
+be uh and in particular does that bump
+
+ align:start position:0%
+be uh and in particular does that bump
+ 
+
+ align:start position:0%
+be uh and in particular does that bump
+reach a certain height because you can
+
+ align:start position:0%
+reach a certain height because you can
+ 
+
+ align:start position:0%
+reach a certain height because you can
+see it just barely forming and then you
+
+ align:start position:0%
+see it just barely forming and then you
+ 
+
+ align:start position:0%
+see it just barely forming and then you
+see it growing to a certain point and
+
+ align:start position:0%
+see it growing to a certain point and
+ 
+
+ align:start position:0%
+see it growing to a certain point and
+then when the movie
+
+ align:start position:0%
+then when the movie
+ 
+
+ align:start position:0%
+then when the movie
+ends fortunately it plots this picture
+
+ align:start position:0%
+ends fortunately it plots this picture
+ 
+
+ align:start position:0%
+ends fortunately it plots this picture
+and you really see the profile and you
+
+ align:start position:0%
+and you really see the profile and you
+ 
+
+ align:start position:0%
+and you really see the profile and you
+can actually see if you look closely
+
+ align:start position:0%
+can actually see if you look closely
+ 
+
+ align:start position:0%
+can actually see if you look closely
+that it goes above one again and
+
+ align:start position:0%
+that it goes above one again and
+ 
+
+ align:start position:0%
+that it goes above one again and
+probably more um
+
+ align:start position:0%
+probably more um
+ 
+
+ align:start position:0%
+probably more um
+so uh so that would be does it approach
+
+ align:start position:0%
+so uh so that would be does it approach
+ 
+
+ align:start position:0%
+so uh so that would be does it approach
+a steady
+
+ align:start position:0%
+a steady
+ 
+
+ align:start position:0%
+a steady
+profile does that height settle
+
+ align:start position:0%
+profile does that height settle
+ 
+
+ align:start position:0%
+profile does that height settle
+down well it' be fantastic to be able to
+
+ align:start position:0%
+down well it' be fantastic to be able to
+ 
+
+ align:start position:0%
+down well it' be fantastic to be able to
+predict that height and and for example
+
+ align:start position:0%
+predict that height and and for example
+ 
+
+ align:start position:0%
+predict that height and and for example
+you always want to know how do things
+
+ align:start position:0%
+you always want to know how do things
+ 
+
+ align:start position:0%
+you always want to know how do things
+depend on the parameter and the one
+
+ align:start position:0%
+depend on the parameter and the one
+ 
+
+ align:start position:0%
+depend on the parameter and the one
+parameter we have in this problem is r c
+
+ align:start position:0%
+parameter we have in this problem is r c
+ 
+
+ align:start position:0%
+parameter we have in this problem is r c
+delta T over Delta X if I change r I'm
+
+ align:start position:0%
+delta T over Delta X if I change r I'm
+ 
+
+ align:start position:0%
+delta T over Delta X if I change r I'm
+changing all the
+
+ align:start position:0%
+changing all the
+ 
+
+ align:start position:0%
+changing all the
+coefficients if I changed R to be
+
+ align:start position:0%
+coefficients if I changed R to be
+ 
+
+ align:start position:0%
+coefficients if I changed R to be
+exactly one then the profile would be
+
+ align:start position:0%
+exactly one then the profile would be
+ 
+
+ align:start position:0%
+exactly one then the profile would be
+perfect that right that's the golden
+
+ align:start position:0%
+perfect that right that's the golden
+ 
+
+ align:start position:0%
+perfect that right that's the golden
+ratio r equal 1 uh I would be
+
+ align:start position:0%
+ratio r equal 1 uh I would be
+ 
+
+ align:start position:0%
+ratio r equal 1 uh I would be
+Computing that value exactly from this
+
+ align:start position:0%
+Computing that value exactly from this
+ 
+
+ align:start position:0%
+Computing that value exactly from this
+value at exactly the right slope on the
+
+ align:start position:0%
+value at exactly the right slope on the
+ 
+
+ align:start position:0%
+value at exactly the right slope on the
+characteristic and uh
+
+ align:start position:0%
+characteristic and uh
+ 
+
+ align:start position:0%
+characteristic and uh
+Perfection but now as R goes away from
+
+ align:start position:0%
+Perfection but now as R goes away from
+ 
+
+ align:start position:0%
+Perfection but now as R goes away from
+one I presume it goes down below one of
+
+ align:start position:0%
+one I presume it goes down below one of
+ 
+
+ align:start position:0%
+one I presume it goes down below one of
+course if it goes above one catastrophe
+
+ align:start position:0%
+course if it goes above one catastrophe
+ 
+
+ align:start position:0%
+course if it goes above one catastrophe
+if it goes below one I presume the
+
+ align:start position:0%
+if it goes below one I presume the
+ 
+
+ align:start position:0%
+if it goes below one I presume the
+bump begins to appear goes higher I I
+
+ align:start position:0%
+bump begins to appear goes higher I I
+ 
+
+ align:start position:0%
+bump begins to appear goes higher I I
+don't know could could you see how the
+
+ align:start position:0%
+don't know could could you see how the
+ 
+
+ align:start position:0%
+don't know could could you see how the
+dependence on R appears and and then I
+
+ align:start position:0%
+dependence on R appears and and then I
+ 
+
+ align:start position:0%
+dependence on R appears and and then I
+can even suggest one more thing which is
+
+ align:start position:0%
+can even suggest one more thing which is
+ 
+
+ align:start position:0%
+can even suggest one more thing which is
+where what let's put a fourth guy onto
+
+ align:start position:0%
+where what let's put a fourth guy onto
+ 
+
+ align:start position:0%
+where what let's put a fourth guy onto
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um onto this um
+
+ align:start position:0%
+um onto this um
+ 
+
+ align:start position:0%
+um onto this um
+picture which would be Leap Frog Leap
+
+ align:start position:0%
+picture which would be Leap Frog Leap
+ 
+
+ align:start position:0%
+picture which would be Leap Frog Leap
+Frog for first order equation so let me
+
+ align:start position:0%
+Frog for first order equation so let me
+ 
+
+ align:start position:0%
+Frog for first order equation so let me
+just put down below what that would be
+
+ align:start position:0%
+just put down below what that would be
+ 
+
+ align:start position:0%
+just put down below what that would be
+so it would be on that kind of a
+
+ align:start position:0%
+so it would be on that kind of a
+ 
+
+ align:start position:0%
+so it would be on that kind of a
+staggered grid uh a new value at time n
+
+ align:start position:0%
+staggered grid uh a new value at time n
+ 
+
+ align:start position:0%
+staggered grid uh a new value at time n
++ one would come from these at time n
+
+ align:start position:0%
++ one would come from these at time n
+ 
+
+ align:start position:0%
++ one would come from these at time n
+really and this one at time n minus one
+
+ align:start position:0%
+really and this one at time n minus one
+ 
+
+ align:start position:0%
+really and this one at time n minus one
+so Lea frog would you you think of it
+
+ align:start position:0%
+so Lea frog would you you think of it
+ 
+
+ align:start position:0%
+so Lea frog would you you think of it
+right away I use a center
+
+ align:start position:0%
+right away I use a center
+ 
+
+ align:start position:0%
+right away I use a center
+difference in time u j n + 1 - UJ n -1 /
+
+ align:start position:0%
+difference in time u j n + 1 - UJ n -1 /
+ 
+
+ align:start position:0%
+difference in time u j n + 1 - UJ n -1 /
+2 Delta
+
+ align:start position:0%
+2 Delta
+ 
+
+ align:start position:0%
+2 Delta
+T's = C * a center difference in space u
+
+ align:start position:0%
+T's = C * a center difference in space u
+ 
+
+ align:start position:0%
+T's = C * a center difference in space u
+j + 1 nus u j -1 n over 2 Delta
+
+ align:start position:0%
+j + 1 nus u j -1 n over 2 Delta
+ 
+
+ align:start position:0%
+j + 1 nus u j -1 n over 2 Delta
+X so you see right away the twos
+
+ align:start position:0%
+X so you see right away the twos
+ 
+
+ align:start position:0%
+X so you see right away the twos
+cancel that Delta x * C delta T * C over
+
+ align:start position:0%
+cancel that Delta x * C delta T * C over
+ 
+
+ align:start position:0%
+cancel that Delta x * C delta T * C over
+Delta X is our old ratio R so this is
+
+ align:start position:0%
+Delta X is our old ratio R so this is
+ 
+
+ align:start position:0%
+Delta X is our old ratio R so this is
+this is easily easily written in terms
+
+ align:start position:0%
+this is easily easily written in terms
+ 
+
+ align:start position:0%
+this is easily easily written in terms
+of R again it does have this two
+
+ align:start position:0%
+of R again it does have this two
+ 
+
+ align:start position:0%
+of R again it does have this two
+EP uh
+
+ align:start position:0%
+EP uh
+ 
+
+ align:start position:0%
+EP uh
+issue uh and of course it has we have to
+
+ align:start position:0%
+issue uh and of course it has we have to
+ 
+
+ align:start position:0%
+issue uh and of course it has we have to
+think about stability I'm writing down a
+
+ align:start position:0%
+think about stability I'm writing down a
+ 
+
+ align:start position:0%
+think about stability I'm writing down a
+a a fourth candidate for the equation
+
+ align:start position:0%
+a a fourth candidate for the equation
+ 
+
+ align:start position:0%
+a a fourth candidate for the equation
+utal CX of
+
+ align:start position:0%
+utal CX of
+ 
+
+ align:start position:0%
+utal CX of
+course before I come back to the second
+
+ align:start position:0%
+course before I come back to the second
+ 
+
+ align:start position:0%
+course before I come back to the second
+order equations or systems let's I just
+
+ align:start position:0%
+order equations or systems let's I just
+ 
+
+ align:start position:0%
+order equations or systems let's I just
+wanted to put in these comments partly
+
+ align:start position:0%
+wanted to put in these comments partly
+ 
+
+ align:start position:0%
+wanted to put in these comments partly
+because I'm thinking about uh projects
+
+ align:start position:0%
+because I'm thinking about uh projects
+ 
+
+ align:start position:0%
+because I'm thinking about uh projects
+that are that and I hope you are that
+
+ align:start position:0%
+that are that and I hope you are that
+ 
+
+ align:start position:0%
+that are that and I hope you are that
+uh so some people will have uh like
+
+ align:start position:0%
+uh so some people will have uh like
+ 
+
+ align:start position:0%
+uh so some people will have uh like
+feces or or uh problems from other
+
+ align:start position:0%
+feces or or uh problems from other
+ 
+
+ align:start position:0%
+feces or or uh problems from other
+courses which involve solving pdes and
+
+ align:start position:0%
+courses which involve solving pdes and
+ 
+
+ align:start position:0%
+courses which involve solving pdes and
+that'd be perfect natural to to
+
+ align:start position:0%
+that'd be perfect natural to to
+ 
+
+ align:start position:0%
+that'd be perfect natural to to
+uh to uh base a project on uh but if you
+
+ align:start position:0%
+uh to uh base a project on uh but if you
+ 
+
+ align:start position:0%
+uh to uh base a project on uh but if you
+don't have some specific application
+
+ align:start position:0%
+don't have some specific application
+ 
+
+ align:start position:0%
+don't have some specific application
+then uh here are a whole lot of
+
+ align:start position:0%
+then uh here are a whole lot of
+ 
+
+ align:start position:0%
+then uh here are a whole lot of
+interesting questions uh to just go
+
+ align:start position:0%
+interesting questions uh to just go
+ 
+
+ align:start position:0%
+interesting questions uh to just go
+further with that so the the dependence
+
+ align:start position:0%
+further with that so the the dependence
+ 
+
+ align:start position:0%
+further with that so the the dependence
+on R would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a depend the
+
+ align:start position:0%
+a depend the
+ 
+
+ align:start position:0%
+a depend the
+profile the the
+
+ align:start position:0%
+profile the the
+ 
+
+ align:start position:0%
+profile the the
+profile
+
+ align:start position:0%
+profile
+ 
+
+ align:start position:0%
+profile
+dependence on
+
+ align:start position:0%
+dependence on
+ 
+
+ align:start position:0%
+dependence on
+r c delta T over Delta X would be a
+
+ align:start position:0%
+r c delta T over Delta X would be a
+ 
+
+ align:start position:0%
+r c delta T over Delta X would be a
+question and
+
+ align:start position:0%
+question and
+ 
+
+ align:start position:0%
+question and
+uh let me just emphasize what what's the
+
+ align:start position:0%
+uh let me just emphasize what what's the
+ 
+
+ align:start position:0%
+uh let me just emphasize what what's the
+goal when I say that this upwind one is
+
+ align:start position:0%
+goal when I say that this upwind one is
+ 
+
+ align:start position:0%
+goal when I say that this upwind one is
+smeared out I mean that it doesn't
+
+ align:start position:0%
+smeared out I mean that it doesn't
+ 
+
+ align:start position:0%
+smeared out I mean that it doesn't
+satisfy what you really hope for you you
+
+ align:start position:0%
+satisfy what you really hope for you you
+ 
+
+ align:start position:0%
+satisfy what you really hope for you you
+want to capture that shock that
+
+ align:start position:0%
+want to capture that shock that
+ 
+
+ align:start position:0%
+want to capture that shock that
+discontinuity well not perfectly you
+
+ align:start position:0%
+discontinuity well not perfectly you
+ 
+
+ align:start position:0%
+discontinuity well not perfectly you
+can't expect that but you want to
+
+ align:start position:0%
+can't expect that but you want to
+ 
+
+ align:start position:0%
+can't expect that but you want to
+capture it maybe in let's say 2 Delta x
+
+ align:start position:0%
+capture it maybe in let's say 2 Delta x
+ 
+
+ align:start position:0%
+capture it maybe in let's say 2 Delta x
+a good method captures the shock within
+
+ align:start position:0%
+a good method captures the shock within
+ 
+
+ align:start position:0%
+a good method captures the shock within
+2 Delta X and does it
+
+ align:start position:0%
+2 Delta X and does it
+ 
+
+ align:start position:0%
+2 Delta X and does it
+without much uh undesirable oscillation
+
+ align:start position:0%
+without much uh undesirable oscillation
+ 
+
+ align:start position:0%
+without much uh undesirable oscillation
+unphysical oscillation like that so
+
+ align:start position:0%
+unphysical oscillation like that so
+ 
+
+ align:start position:0%
+unphysical oscillation like that so
+these are methods where we we're trading
+
+ align:start position:0%
+these are methods where we we're trading
+ 
+
+ align:start position:0%
+these are methods where we we're trading
+off a good shock capture
+
+ align:start position:0%
+off a good shock capture
+ 
+
+ align:start position:0%
+off a good shock capture
+versus a smeared one which is not
+
+ align:start position:0%
+versus a smeared one which is not
+ 
+
+ align:start position:0%
+versus a smeared one which is not
+satisfactory really uh in in a lot of
+
+ align:start position:0%
+satisfactory really uh in in a lot of
+ 
+
+ align:start position:0%
+satisfactory really uh in in a lot of
+applications so capturing the shock
+
+ align:start position:0%
+applications so capturing the shock
+ 
+
+ align:start position:0%
+applications so capturing the shock
+within uh two Delta X roughly is uh
+
+ align:start position:0%
+within uh two Delta X roughly is uh
+ 
+
+ align:start position:0%
+within uh two Delta X roughly is uh
+highly desirable and and
+
+ align:start position:0%
+highly desirable and and
+ 
+
+ align:start position:0%
+highly desirable and and
+uh you might have to go to add a
+
+ align:start position:0%
+uh you might have to go to add a
+ 
+
+ align:start position:0%
+uh you might have to go to add a
+artificial viscosity that we'll discuss
+
+ align:start position:0%
+artificial viscosity that we'll discuss
+ 
+
+ align:start position:0%
+artificial viscosity that we'll discuss
+uh to get there okay so that's past
+
+ align:start position:0%
+uh to get there okay so that's past
+ 
+
+ align:start position:0%
+uh to get there okay so that's past
+things but still very much present if I
+
+ align:start position:0%
+things but still very much present if I
+ 
+
+ align:start position:0%
+things but still very much present if I
+can say and and here I've introduced a
+
+ align:start position:0%
+can say and and here I've introduced a
+ 
+
+ align:start position:0%
+can say and and here I've introduced a
+new a new Leap Frog a oneway oneway
+
+ align:start position:0%
+new a new Leap Frog a oneway oneway
+ 
+
+ align:start position:0%
+new a new Leap Frog a oneway oneway
+equation Leap Frog I I'll call
+
+ align:start position:0%
+equation Leap Frog I I'll call
+ 
+
+ align:start position:0%
+equation Leap Frog I I'll call
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the last lecture was about two-way
+
+ align:start position:0%
+where the last lecture was about two-way
+ 
+
+ align:start position:0%
+where the last lecture was about two-way
+Leap Frog Leap Frog for uttal c^2 uxx a
+
+ align:start position:0%
+Leap Frog Leap Frog for uttal c^2 uxx a
+ 
+
+ align:start position:0%
+Leap Frog Leap Frog for uttal c^2 uxx a
+two-way wave equation I I might just
+
+ align:start position:0%
+two-way wave equation I I might just
+ 
+
+ align:start position:0%
+two-way wave equation I I might just
+mentioned about this oneway Leap Frog
+
+ align:start position:0%
+mentioned about this oneway Leap Frog
+ 
+
+ align:start position:0%
+mentioned about this oneway Leap Frog
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+you put in e to the I KX as we always do
+
+ align:start position:0%
+you put in e to the I KX as we always do
+ 
+
+ align:start position:0%
+you put in e to the I KX as we always do
+or e to the
+
+ align:start position:0%
+or e to the
+ 
+
+ align:start position:0%
+or e to the
+i k j Delta X in the discret case so you
+
+ align:start position:0%
+i k j Delta X in the discret case so you
+ 
+
+ align:start position:0%
+i k j Delta X in the discret case so you
+would put in e to the i j j Delta
+
+ align:start position:0%
+would put in e to the i j j Delta
+ 
+
+ align:start position:0%
+would put in e to the i j j Delta
+X time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K and then find the G the growth factor
+
+ align:start position:0%
+K and then find the G the growth factor
+ 
+
+ align:start position:0%
+K and then find the G the growth factor
+in that'll depend on K and will tell us
+
+ align:start position:0%
+in that'll depend on K and will tell us
+ 
+
+ align:start position:0%
+in that'll depend on K and will tell us
+the time dependence it'll be a g to the
+
+ align:start position:0%
+the time dependence it'll be a g to the
+ 
+
+ align:start position:0%
+the time dependence it'll be a g to the
+N
+
+ align:start position:0%
+N
+ 
+
+ align:start position:0%
+N
+uh I think you'll
+
+ align:start position:0%
+uh I think you'll
+ 
+
+ align:start position:0%
+uh I think you'll
+find that for this guy the absolute
+
+ align:start position:0%
+find that for this guy the absolute
+ 
+
+ align:start position:0%
+find that for this guy the absolute
+value of G is exactly one while it's
+
+ align:start position:0%
+value of G is exactly one while it's
+ 
+
+ align:start position:0%
+value of G is exactly one while it's
+stable of course if the crun condition
+
+ align:start position:0%
+stable of course if the crun condition
+ 
+
+ align:start position:0%
+stable of course if the crun condition
+is violated then there's no way it could
+
+ align:start position:0%
+is violated then there's no way it could
+ 
+
+ align:start position:0%
+is violated then there's no way it could
+be stable and G's will grow be bigger
+
+ align:start position:0%
+be stable and G's will grow be bigger
+ 
+
+ align:start position:0%
+be stable and G's will grow be bigger
+than one
+
+ align:start position:0%
+than one
+ 
+
+ align:start position:0%
+than one
+but I think in the stable
+
+ align:start position:0%
+but I think in the stable
+ 
+
+ align:start position:0%
+but I think in the stable
+range you will have this G will have
+
+ align:start position:0%
+range you will have this G will have
+ 
+
+ align:start position:0%
+range you will have this G will have
+absolute value exactly
+
+ align:start position:0%
+absolute value exactly
+ 
+
+ align:start position:0%
+absolute value exactly
+one H and uh so it'll be on the unit
+
+ align:start position:0%
+one H and uh so it'll be on the unit
+ 
+
+ align:start position:0%
+one H and uh so it'll be on the unit
+circle and you don't have much leeway
+
+ align:start position:0%
+circle and you don't have much leeway
+ 
+
+ align:start position:0%
+circle and you don't have much leeway
+right we we found upwind was like well
+
+ align:start position:0%
+right we we found upwind was like well
+ 
+
+ align:start position:0%
+right we we found upwind was like well
+inside LAX friedricks was well inside
+
+ align:start position:0%
+inside LAX friedricks was well inside
+ 
+
+ align:start position:0%
+inside LAX friedricks was well inside
+LAX wend because it had higher accuracy
+
+ align:start position:0%
+LAX wend because it had higher accuracy
+ 
+
+ align:start position:0%
+LAX wend because it had higher accuracy
+near near for low
+
+ align:start position:0%
+near near for low
+ 
+
+ align:start position:0%
+near near for low
+frequencies was closer and I think this
+
+ align:start position:0%
+frequencies was closer and I think this
+ 
+
+ align:start position:0%
+frequencies was closer and I think this
+guy is right
+
+ align:start position:0%
+guy is right
+ 
+
+ align:start position:0%
+guy is right
+on so this is this is the first order
+
+ align:start position:0%
+on so this is this is the first order
+ 
+
+ align:start position:0%
+on so this is this is the first order
+methods this is LAX wend and this would
+
+ align:start position:0%
+methods this is LAX wend and this would
+ 
+
+ align:start position:0%
+methods this is LAX wend and this would
+be this second order method and so it's
+
+ align:start position:0%
+be this second order method and so it's
+ 
+
+ align:start position:0%
+be this second order method and so it's
+it's you're really playing with fire
+
+ align:start position:0%
+it's you're really playing with fire
+ 
+
+ align:start position:0%
+it's you're really playing with fire
+there and uh maybe this is not a
+
+ align:start position:0%
+there and uh maybe this is not a
+ 
+
+ align:start position:0%
+there and uh maybe this is not a
+favorite just because it's too close to
+
+ align:start position:0%
+favorite just because it's too close to
+ 
+
+ align:start position:0%
+favorite just because it's too close to
+the edge in fact right on the edge okay
+
+ align:start position:0%
+the edge in fact right on the edge okay
+ 
+
+ align:start position:0%
+the edge in fact right on the edge okay
+so those are some comments really
+
+ align:start position:0%
+so those are some comments really
+ 
+
+ align:start position:0%
+so those are some comments really
+generated by your uh your numerical
+
+ align:start position:0%
+generated by your uh your numerical
+ 
+
+ align:start position:0%
+generated by your uh your numerical
+experiments and and I think that's the
+
+ align:start position:0%
+experiments and and I think that's the
+ 
+
+ align:start position:0%
+experiments and and I think that's the
+way this course should uh homeworks and
+
+ align:start position:0%
+way this course should uh homeworks and
+ 
+
+ align:start position:0%
+way this course should uh homeworks and
+and projects should develop out of
+
+ align:start position:0%
+and projects should develop out of
+ 
+
+ align:start position:0%
+and projects should develop out of
+numerical experiments okay
+
+ align:start position:0%
+numerical experiments okay
+ 
+
+ align:start position:0%
+numerical experiments okay
+now I'll coming back for to complete my
+
+ align:start position:0%
+now I'll coming back for to complete my
+ 
+
+ align:start position:0%
+now I'll coming back for to complete my
+lecture on the second order wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation so we
+
+ align:start position:0%
+equation so we
+ 
+
+ align:start position:0%
+equation so we
+studied Leap Frog for
+
+ align:start position:0%
+studied Leap Frog for
+ 
+
+ align:start position:0%
+studied Leap Frog for
+that I won't repeat that but then with
+
+ align:start position:0%
+that I won't repeat that but then with
+ 
+
+ align:start position:0%
+that I won't repeat that but then with
+second order wave equation we have
+
+ align:start position:0%
+second order wave equation we have
+ 
+
+ align:start position:0%
+second order wave equation we have
+another option which is to
+
+ align:start position:0%
+another option which is to
+ 
+
+ align:start position:0%
+another option which is to
+reduce a sec a second order equation in
+
+ align:start position:0%
+reduce a sec a second order equation in
+ 
+
+ align:start position:0%
+reduce a sec a second order equation in
+with with a two time derivatives to a
+
+ align:start position:0%
+with with a two time derivatives to a
+ 
+
+ align:start position:0%
+with with a two time derivatives to a
+system of two equations with that are
+
+ align:start position:0%
+system of two equations with that are
+ 
+
+ align:start position:0%
+system of two equations with that are
+first order in time and
+
+ align:start position:0%
+first order in time and
+ 
+
+ align:start position:0%
+first order in time and
+space and I've chosen to use the letters
+
+ align:start position:0%
+space and I've chosen to use the letters
+ 
+
+ align:start position:0%
+space and I've chosen to use the letters
+H and e as a kind of
+
+ align:start position:0%
+H and e as a kind of
+ 
+
+ align:start position:0%
+H and e as a kind of
+a hint that that we're
+
+ align:start position:0%
+a hint that that we're
+ 
+
+ align:start position:0%
+a hint that that we're
+touching a really big application which
+
+ align:start position:0%
+touching a really big application which
+ 
+
+ align:start position:0%
+touching a really big application which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+electromagnetism so e for the electric
+
+ align:start position:0%
+electromagnetism so e for the electric
+ 
+
+ align:start position:0%
+electromagnetism so e for the electric
+field H for the magnetic field but here
+
+ align:start position:0%
+field H for the magnetic field but here
+ 
+
+ align:start position:0%
+field H for the magnetic field but here
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1D
+
+ align:start position:0%
+1D
+ 
+
+ align:start position:0%
+1D
+uh so it allows me just to mention
+
+ align:start position:0%
+uh so it allows me just to mention
+ 
+
+ align:start position:0%
+uh so it allows me just to mention
+that in 3D when e has three components H
+
+ align:start position:0%
+that in 3D when e has three components H
+ 
+
+ align:start position:0%
+that in 3D when e has three components H
+has three components this is really the
+
+ align:start position:0%
+has three components this is really the
+ 
+
+ align:start position:0%
+has three components this is really the
+curl and this is really minus the
+
+ align:start position:0%
+curl and this is really minus the
+ 
+
+ align:start position:0%
+curl and this is really minus the
+curl
+
+ align:start position:0%
+curl
+ 
+
+ align:start position:0%
+curl
+and the notes will show the
+
+ align:start position:0%
+and the notes will show the
+ 
+
+ align:start position:0%
+and the notes will show the
+beautiful
+
+ align:start position:0%
+beautiful
+ 
+
+ align:start position:0%
+beautiful
+uh Ye Ye uh
+
+ align:start position:0%
+uh Ye Ye uh
+ 
+
+ align:start position:0%
+uh Ye Ye uh
+mesh uh staggered mesh that that that
+
+ align:start position:0%
+mesh uh staggered mesh that that that
+ 
+
+ align:start position:0%
+mesh uh staggered mesh that that that
+copies for finite difference methods the
+
+ align:start position:0%
+copies for finite difference methods the
+ 
+
+ align:start position:0%
+copies for finite difference methods the
+uh uh the properties of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curl our our our interpretation of and
+
+ align:start position:0%
+curl our our our interpretation of and
+ 
+
+ align:start position:0%
+curl our our our interpretation of and
+the the properties of that Maxwell
+
+ align:start position:0%
+the the properties of that Maxwell
+ 
+
+ align:start position:0%
+the the properties of that Maxwell
+discovered the physics of you know
+
+ align:start position:0%
+discovered the physics of you know
+ 
+
+ align:start position:0%
+discovered the physics of you know
+current magnetic fields going around uh
+
+ align:start position:0%
+current magnetic fields going around uh
+ 
+
+ align:start position:0%
+current magnetic fields going around uh
+uh a wire that along which an electric
+
+ align:start position:0%
+uh a wire that along which an electric
+ 
+
+ align:start position:0%
+uh a wire that along which an electric
+field is going
+
+ align:start position:0%
+field is going
+ 
+
+ align:start position:0%
+field is going
+okay but I let me stay here with one
+
+ align:start position:0%
+okay but I let me stay here with one
+ 
+
+ align:start position:0%
+okay but I let me stay here with one
+dimension so first of all can we recover
+
+ align:start position:0%
+dimension so first of all can we recover
+ 
+
+ align:start position:0%
+dimension so first of all can we recover
+the wave equation from that let's just
+
+ align:start position:0%
+the wave equation from that let's just
+ 
+
+ align:start position:0%
+the wave equation from that let's just
+see that we haven't left behind the wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation okay so uh I just take the
+
+ align:start position:0%
+equation okay so uh I just take the
+ 
+
+ align:start position:0%
+equation okay so uh I just take the
+second derivative so the second
+
+ align:start position:0%
+second derivative so the second
+ 
+
+ align:start position:0%
+second derivative so the second
+derivative I I just want to recover the
+
+ align:start position:0%
+derivative I I just want to recover the
+ 
+
+ align:start position:0%
+derivative I I just want to recover the
+wave equation show that I haven't lost
+
+ align:start position:0%
+wave equation show that I haven't lost
+ 
+
+ align:start position:0%
+wave equation show that I haven't lost
+it here so this will be if I I'm taking
+
+ align:start position:0%
+it here so this will be if I I'm taking
+ 
+
+ align:start position:0%
+it here so this will be if I I'm taking
+the time derivative of the first first
+
+ align:start position:0%
+the time derivative of the first first
+ 
+
+ align:start position:0%
+the time derivative of the first first
+equation so I
+
+ align:start position:0%
+equation so I
+ 
+
+ align:start position:0%
+equation so I
+get DC H dtdx
+
+ align:start position:0%
+get DC H dtdx
+ 
+
+ align:start position:0%
+get DC H dtdx
+right but by the
+
+ align:start position:0%
+right but by the
+ 
+
+ align:start position:0%
+right but by the
+useful extremely useful fact that this
+
+ align:start position:0%
+useful extremely useful fact that this
+ 
+
+ align:start position:0%
+useful extremely useful fact that this
+is the same as taking the T derivative
+
+ align:start position:0%
+is the same as taking the T derivative
+ 
+
+ align:start position:0%
+is the same as taking the T derivative
+first and the X derivative
+
+ align:start position:0%
+first and the X derivative
+ 
+
+ align:start position:0%
+first and the X derivative
+second now I have the X derivative of
+
+ align:start position:0%
+second now I have the X derivative of
+ 
+
+ align:start position:0%
+second now I have the X derivative of
+this equation so this is
+
+ align:start position:0%
+this equation so this is
+ 
+
+ align:start position:0%
+this equation so this is
+C now I have the X
+
+ align:start position:0%
+C now I have the X
+ 
+
+ align:start position:0%
+C now I have the X
+derivative or c times it so now I'm up
+
+ align:start position:0%
+derivative or c times it so now I'm up
+ 
+
+ align:start position:0%
+derivative or c times it so now I'm up
+to c^2 the X derivative of the X
+
+ align:start position:0%
+to c^2 the X derivative of the X
+ 
+
+ align:start position:0%
+to c^2 the X derivative of the X
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+right okay so we eliminated
+
+ align:start position:0%
+right okay so we eliminated
+ 
+
+ align:start position:0%
+right okay so we eliminated
+H got back to one equation second order
+
+ align:start position:0%
+H got back to one equation second order
+ 
+
+ align:start position:0%
+H got back to one equation second order
+and it's the wave
+
+ align:start position:0%
+and it's the wave
+ 
+
+ align:start position:0%
+and it's the wave
+equation okay I I I want to show the
+
+ align:start position:0%
+equation okay I I I want to show the
+ 
+
+ align:start position:0%
+equation okay I I I want to show the
+same thing now for finite differences
+
+ align:start position:0%
+same thing now for finite differences
+ 
+
+ align:start position:0%
+same thing now for finite differences
+it's just it's it's such a simple and
+
+ align:start position:0%
+it's just it's it's such a simple and
+ 
+
+ align:start position:0%
+it's just it's it's such a simple and
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+device and our point will be that it
+
+ align:start position:0%
+device and our point will be that it
+ 
+
+ align:start position:0%
+device and our point will be that it
+works for just as well for differences
+
+ align:start position:0%
+works for just as well for differences
+ 
+
+ align:start position:0%
+works for just as well for differences
+and that allows us to do this staggered
+
+ align:start position:0%
+and that allows us to do this staggered
+ 
+
+ align:start position:0%
+and that allows us to do this staggered
+grid idea so so the staggered grid idea
+
+ align:start position:0%
+grid idea so so the staggered grid idea
+ 
+
+ align:start position:0%
+grid idea so so the staggered grid idea
+is I'll do
+
+ align:start position:0%
+is I'll do
+ 
+
+ align:start position:0%
+is I'll do
+e on this Grid at these grid points H at
+
+ align:start position:0%
+e on this Grid at these grid points H at
+ 
+
+ align:start position:0%
+e on this Grid at these grid points H at
+the half points e again at the integer
+
+ align:start position:0%
+the half points e again at the integer
+ 
+
+ align:start position:0%
+the half points e again at the integer
+point points H again at the half points
+
+ align:start position:0%
+point points H again at the half points
+ 
+
+ align:start position:0%
+point points H again at the half points
+and now so my my
+
+ align:start position:0%
+and now so my my
+ 
+
+ align:start position:0%
+and now so my my
+U difference method Leap Frog on the
+
+ align:start position:0%
+U difference method Leap Frog on the
+ 
+
+ align:start position:0%
+U difference method Leap Frog on the
+staggered mesh will copy so so the first
+
+ align:start position:0%
+staggered mesh will copy so so the first
+ 
+
+ align:start position:0%
+staggered mesh will copy so so the first
+equation will give e at the new
+
+ align:start position:0%
+equation will give e at the new
+ 
+
+ align:start position:0%
+equation will give e at the new
+time from the difference in h at this
+
+ align:start position:0%
+time from the difference in h at this
+ 
+
+ align:start position:0%
+time from the difference in h at this
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and so you see you see it D DT is going
+
+ align:start position:0%
+and so you see you see it D DT is going
+ 
+
+ align:start position:0%
+and so you see you see it D DT is going
+to be replaced
+
+ align:start position:0%
+to be replaced
+ 
+
+ align:start position:0%
+to be replaced
+by that that time difference dhdx is
+
+ align:start position:0%
+by that that time difference dhdx is
+ 
+
+ align:start position:0%
+by that that time difference dhdx is
+going to be replaced by this space
+
+ align:start position:0%
+going to be replaced by this space
+ 
+
+ align:start position:0%
+going to be replaced by this space
+difference and that will determine e at
+
+ align:start position:0%
+difference and that will determine e at
+ 
+
+ align:start position:0%
+difference and that will determine e at
+the new time so I need I need time zero
+
+ align:start position:0%
+the new time so I need I need time zero
+ 
+
+ align:start position:0%
+the new time so I need I need time zero
+and time 1/2 to get started maybe I put
+
+ align:start position:0%
+and time 1/2 to get started maybe I put
+ 
+
+ align:start position:0%
+and time 1/2 to get started maybe I put
+those down here somewhere I have to use
+
+ align:start position:0%
+those down here somewhere I have to use
+ 
+
+ align:start position:0%
+those down here somewhere I have to use
+the initial condition the initial
+
+ align:start position:0%
+the initial condition the initial
+ 
+
+ align:start position:0%
+the initial condition the initial
+velocity to get
+
+ align:start position:0%
+velocity to get
+ 
+
+ align:start position:0%
+velocity to get
+started on E and H and then I go onwards
+
+ align:start position:0%
+started on E and H and then I go onwards
+ 
+
+ align:start position:0%
+started on E and H and then I go onwards
+I've got to this point and this point
+
+ align:start position:0%
+I've got to this point and this point
+ 
+
+ align:start position:0%
+I've got to this point and this point
+then this guy comes from this one this
+
+ align:start position:0%
+then this guy comes from this one this
+ 
+
+ align:start position:0%
+then this guy comes from this one this
+one and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and of course that similarly comes
+
+ align:start position:0%
+one and of course that similarly comes
+ 
+
+ align:start position:0%
+one and of course that similarly comes
+from the same equation shifted over and
+
+ align:start position:0%
+from the same equation shifted over and
+ 
+
+ align:start position:0%
+from the same equation shifted over and
+then now I know these now I'm ready for
+
+ align:start position:0%
+then now I know these now I'm ready for
+ 
+
+ align:start position:0%
+then now I know these now I'm ready for
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+coming from now I'm what am I
+
+ align:start position:0%
+coming from now I'm what am I
+ 
+
+ align:start position:0%
+coming from now I'm what am I
+approximating now I'm on the the
+
+ align:start position:0%
+approximating now I'm on the the
+ 
+
+ align:start position:0%
+approximating now I'm on the the
+staggered part of the grid the the half
+
+ align:start position:0%
+staggered part of the grid the the half
+ 
+
+ align:start position:0%
+staggered part of the grid the the half
+steps I'm approximating this on the half
+
+ align:start position:0%
+steps I'm approximating this on the half
+ 
+
+ align:start position:0%
+steps I'm approximating this on the half
+steps where H is defined so that minus
+
+ align:start position:0%
+steps where H is defined so that minus
+ 
+
+ align:start position:0%
+steps where H is defined so that minus
+that is the time
+
+ align:start position:0%
+that is the time
+ 
+
+ align:start position:0%
+that is the time
+difference this minus this which I know
+
+ align:start position:0%
+difference this minus this which I know
+ 
+
+ align:start position:0%
+difference this minus this which I know
+these now is the space difference in
+
+ align:start position:0%
+these now is the space difference in
+ 
+
+ align:start position:0%
+these now is the space difference in
+this equation and that's what allows me
+
+ align:start position:0%
+this equation and that's what allows me
+ 
+
+ align:start position:0%
+this equation and that's what allows me
+to compute the new one you you see it's
+
+ align:start position:0%
+to compute the new one you you see it's
+ 
+
+ align:start position:0%
+to compute the new one you you see it's
+a simple
+
+ align:start position:0%
+a simple
+ 
+
+ align:start position:0%
+a simple
+idea it's very it's it's close but
+
+ align:start position:0%
+idea it's very it's it's close but
+ 
+
+ align:start position:0%
+idea it's very it's it's close but
+different from
+
+ align:start position:0%
+different from
+ 
+
+ align:start position:0%
+different from
+my uh from my uh scaler Leap Frog oneway
+
+ align:start position:0%
+my uh from my uh scaler Leap Frog oneway
+ 
+
+ align:start position:0%
+my uh from my uh scaler Leap Frog oneway
+Leap Frog here here it was the same U at
+
+ align:start position:0%
+Leap Frog here here it was the same U at
+ 
+
+ align:start position:0%
+Leap Frog here here it was the same U at
+all the points here it is e at the
+
+ align:start position:0%
+all the points here it is e at the
+ 
+
+ align:start position:0%
+all the points here it is e at the
+integer time time levels and H at the
+
+ align:start position:0%
+integer time time levels and H at the
+ 
+
+ align:start position:0%
+integer time time levels and H at the
+half integer time levels and and uh oh
+
+ align:start position:0%
+half integer time levels and and uh oh
+ 
+
+ align:start position:0%
+half integer time levels and and uh oh
+well it's natural to
+
+ align:start position:0%
+well it's natural to
+ 
+
+ align:start position:0%
+well it's natural to
+say I'm calling this Leap Frog could
+
+ align:start position:0%
+say I'm calling this Leap Frog could
+ 
+
+ align:start position:0%
+say I'm calling this Leap Frog could
+I could I do
+
+ align:start position:0%
+I could I do
+ 
+
+ align:start position:0%
+I could I do
+this for the difference
+
+ align:start position:0%
+this for the difference
+ 
+
+ align:start position:0%
+this for the difference
+equation I just want to see that if I
+
+ align:start position:0%
+equation I just want to see that if I
+ 
+
+ align:start position:0%
+equation I just want to see that if I
+eliminate H so you saw what happened
+
+ align:start position:0%
+eliminate H so you saw what happened
+ 
+
+ align:start position:0%
+eliminate H so you saw what happened
+there by using the identity that the
+
+ align:start position:0%
+there by using the identity that the
+ 
+
+ align:start position:0%
+there by using the identity that the
+second derivative in T and X is always
+
+ align:start position:0%
+second derivative in T and X is always
+ 
+
+ align:start position:0%
+second derivative in T and X is always
+the same as the second derivative in x
+
+ align:start position:0%
+the same as the second derivative in x
+ 
+
+ align:start position:0%
+the same as the second derivative in x
+and t I eliminated H and got an equation
+
+ align:start position:0%
+and t I eliminated H and got an equation
+ 
+
+ align:start position:0%
+and t I eliminated H and got an equation
+that involved e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only well what's going to be
+
+ align:start position:0%
+only well what's going to be
+ 
+
+ align:start position:0%
+only well what's going to be
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponding identity trivial but just
+
+ align:start position:0%
+corresponding identity trivial but just
+ 
+
+ align:start position:0%
+corresponding identity trivial but just
+trivial things are not bad things to
+
+ align:start position:0%
+trivial things are not bad things to
+ 
+
+ align:start position:0%
+trivial things are not bad things to
+notice uh for the difference
+
+ align:start position:0%
+notice uh for the difference
+ 
+
+ align:start position:0%
+notice uh for the difference
+method well here this is what I wanted
+
+ align:start position:0%
+method well here this is what I wanted
+ 
+
+ align:start position:0%
+method well here this is what I wanted
+to be sure of for for the h part this H
+
+ align:start position:0%
+to be sure of for for the h part this H
+ 
+
+ align:start position:0%
+to be sure of for for the h part this H
+and so the H were were now do you mind
+
+ align:start position:0%
+and so the H were were now do you mind
+ 
+
+ align:start position:0%
+and so the H were were now do you mind
+if I draw yet another symbol I I want to
+
+ align:start position:0%
+if I draw yet another symbol I I want to
+ 
+
+ align:start position:0%
+if I draw yet another symbol I I want to
+use this
+
+ align:start position:0%
+use this
+ 
+
+ align:start position:0%
+use this
+idea to eliminate H so let me put two h
+
+ align:start position:0%
+idea to eliminate H so let me put two h
+ 
+
+ align:start position:0%
+idea to eliminate H so let me put two h
+two h's there uh is that right yeah I I
+
+ align:start position:0%
+two h's there uh is that right yeah I I
+ 
+
+ align:start position:0%
+two h's there uh is that right yeah I I
+I think what I'd like to
+
+ align:start position:0%
+I think what I'd like to
+ 
+
+ align:start position:0%
+I think what I'd like to
+know well let me just say what what I
+
+ align:start position:0%
+know well let me just say what what I
+ 
+
+ align:start position:0%
+know well let me just say what what I
+believe I believe that
+
+ align:start position:0%
+believe I believe that
+ 
+
+ align:start position:0%
+believe I believe that
+the that the time difference of the
+
+ align:start position:0%
+the that the time difference of the
+ 
+
+ align:start position:0%
+the that the time difference of the
+space difference of H at mesh points is
+
+ align:start position:0%
+space difference of H at mesh points is
+ 
+
+ align:start position:0%
+space difference of H at mesh points is
+equal to the space difference of the
+
+ align:start position:0%
+equal to the space difference of the
+ 
+
+ align:start position:0%
+equal to the space difference of the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+difference of H at the same mesh points
+
+ align:start position:0%
+difference of H at the same mesh points
+ 
+
+ align:start position:0%
+difference of H at the same mesh points
+I meant to put these as subscripts
+
+ align:start position:0%
+I meant to put these as subscripts
+ 
+
+ align:start position:0%
+I meant to put these as subscripts
+that's not
+
+ align:start position:0%
+that's not
+ 
+
+ align:start position:0%
+that's not
+Delta it's not Delta X it's
+
+ align:start position:0%
+Delta it's not Delta X it's
+ 
+
+ align:start position:0%
+Delta it's not Delta X it's
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+subx difference in the time Direction
+
+ align:start position:0%
+subx difference in the time Direction
+ 
+
+ align:start position:0%
+subx difference in the time Direction
+difference in the space Direction let's
+
+ align:start position:0%
+difference in the space Direction let's
+ 
+
+ align:start position:0%
+difference in the space Direction let's
+just see what this means I have let me
+
+ align:start position:0%
+just see what this means I have let me
+ 
+
+ align:start position:0%
+just see what this means I have let me
+let me redraw these four points these
+
+ align:start position:0%
+let me redraw these four points these
+ 
+
+ align:start position:0%
+let me redraw these four points these
+are h h h at all those
+
+ align:start position:0%
+are h h h at all those
+ 
+
+ align:start position:0%
+are h h h at all those
+points so this
+
+ align:start position:0%
+points so this
+ 
+
+ align:start position:0%
+points so this
+says figure out the space differences so
+
+ align:start position:0%
+says figure out the space differences so
+ 
+
+ align:start position:0%
+says figure out the space differences so
+this this minus this and this minus
+
+ align:start position:0%
+this this minus this and this minus
+ 
+
+ align:start position:0%
+this this minus this and this minus
+this and then take the time difference
+
+ align:start position:0%
+this and then take the time difference
+ 
+
+ align:start position:0%
+this and then take the time difference
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+those can I see what I'll get if I do
+
+ align:start position:0%
+those can I see what I'll get if I do
+ 
+
+ align:start position:0%
+those can I see what I'll get if I do
+that so this means I take the space
+
+ align:start position:0%
+that so this means I take the space
+ 
+
+ align:start position:0%
+that so this means I take the space
+differences so I have 1 minus one and
+
+ align:start position:0%
+differences so I have 1 minus one and
+ 
+
+ align:start position:0%
+differences so I have 1 minus one and
+that would be 1 - one but now I'm going
+
+ align:start position:0%
+that would be 1 - one but now I'm going
+ 
+
+ align:start position:0%
+that would be 1 - one but now I'm going
+to take the time difference of those so
+
+ align:start position:0%
+to take the time difference of those so
+ 
+
+ align:start position:0%
+to take the time difference of those so
+that'll be this one minus this one and
+
+ align:start position:0%
+that'll be this one minus this one and
+ 
+
+ align:start position:0%
+that'll be this one minus this one and
+this one plus this
+
+ align:start position:0%
+this one plus this
+ 
+
+ align:start position:0%
+this one plus this
+one do you see
+
+ align:start position:0%
+one do you see
+ 
+
+ align:start position:0%
+one do you see
+that what we have here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is H at this point minus H at this point
+
+ align:start position:0%
+is H at this point minus H at this point
+ 
+
+ align:start position:0%
+is H at this point minus H at this point
+minus H at this point plus h at this
+
+ align:start position:0%
+minus H at this point plus h at this
+ 
+
+ align:start position:0%
+minus H at this point plus h at this
+point plus
+
+ align:start position:0%
+point plus
+ 
+
+ align:start position:0%
+point plus
+one and I claim that we have the same
+
+ align:start position:0%
+one and I claim that we have the same
+ 
+
+ align:start position:0%
+one and I claim that we have the same
+thing here that if I take the time
+
+ align:start position:0%
+thing here that if I take the time
+ 
+
+ align:start position:0%
+thing here that if I take the time
+differences first can I do that let me
+
+ align:start position:0%
+differences first can I do that let me
+ 
+
+ align:start position:0%
+differences first can I do that let me
+instead of taking the space differences
+
+ align:start position:0%
+instead of taking the space differences
+ 
+
+ align:start position:0%
+instead of taking the space differences
+first I'll take this one this this time
+
+ align:start position:0%
+first I'll take this one this this time
+ 
+
+ align:start position:0%
+first I'll take this one this this time
+difference this minus
+
+ align:start position:0%
+difference this minus
+ 
+
+ align:start position:0%
+difference this minus
+this and I'll subtract I'm taking now
+
+ align:start position:0%
+this and I'll subtract I'm taking now
+ 
+
+ align:start position:0%
+this and I'll subtract I'm taking now
+the space difference I'll subtract
+
+ align:start position:0%
+the space difference I'll subtract
+ 
+
+ align:start position:0%
+the space difference I'll subtract
+are you with
+
+ align:start position:0%
+are you with
+ 
+
+ align:start position:0%
+are you with
+me you see it's just the same
+
+ align:start position:0%
+me you see it's just the same
+ 
+
+ align:start position:0%
+me you see it's just the same
+four values two ones and two minus
+
+ align:start position:0%
+four values two ones and two minus
+ 
+
+ align:start position:0%
+four values two ones and two minus
+ones whether we go first in fact th this
+
+ align:start position:0%
+ones whether we go first in fact th this
+ 
+
+ align:start position:0%
+ones whether we go first in fact th this
+actually is a I think maybe throws a
+
+ align:start position:0%
+actually is a I think maybe throws a
+ 
+
+ align:start position:0%
+actually is a I think maybe throws a
+little light on the on the calculus uh
+
+ align:start position:0%
+little light on the on the calculus uh
+ 
+
+ align:start position:0%
+little light on the on the calculus uh
+identity that that that we
+
+ align:start position:0%
+identity that that that we
+ 
+
+ align:start position:0%
+identity that that that we
+can we can uh exchange the order of the
+
+ align:start position:0%
+can we can uh exchange the order of the
+ 
+
+ align:start position:0%
+can we can uh exchange the order of the
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+because we know we can exchange the
+
+ align:start position:0%
+because we know we can exchange the
+ 
+
+ align:start position:0%
+because we know we can exchange the
+order of the differences because we've
+
+ align:start position:0%
+order of the differences because we've
+ 
+
+ align:start position:0%
+order of the differences because we've
+just got numbers like 1 minus one minus
+
+ align:start position:0%
+just got numbers like 1 minus one minus
+ 
+
+ align:start position:0%
+just got numbers like 1 minus one minus
+one and plus
+
+ align:start position:0%
+one and plus
+ 
+
+ align:start position:0%
+one and plus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay so and if we let the
+
+ align:start position:0%
+okay so and if we let the
+ 
+
+ align:start position:0%
+okay so and if we let the
+spacing the mesh go to zero this I and
+
+ align:start position:0%
+spacing the mesh go to zero this I and
+ 
+
+ align:start position:0%
+spacing the mesh go to zero this I and
+divided by the Delta X and the delta T
+
+ align:start position:0%
+divided by the Delta X and the delta T
+ 
+
+ align:start position:0%
+divided by the Delta X and the delta T
+uh I I suppose we would prove the the uh
+
+ align:start position:0%
+uh I I suppose we would prove the the uh
+ 
+
+ align:start position:0%
+uh I I suppose we would prove the the uh
+continuous case so in a way this throws
+
+ align:start position:0%
+continuous case so in a way this throws
+ 
+
+ align:start position:0%
+continuous case so in a way this throws
+light on something that's probably
+
+ align:start position:0%
+light on something that's probably
+ 
+
+ align:start position:0%
+light on something that's probably
+something that we take for granted but
+
+ align:start position:0%
+something that we take for granted but
+ 
+
+ align:start position:0%
+something that we take for granted but
+we wouldn't want to be uh pressed on too
+
+ align:start position:0%
+we wouldn't want to be uh pressed on too
+ 
+
+ align:start position:0%
+we wouldn't want to be uh pressed on too
+closely okay
+
+ align:start position:0%
+closely okay
+ 
+
+ align:start position:0%
+closely okay
+so so having that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identity allows me to do exactly what I
+
+ align:start position:0%
+identity allows me to do exactly what I
+ 
+
+ align:start position:0%
+identity allows me to do exactly what I
+did with the continuous case there and
+
+ align:start position:0%
+did with the continuous case there and
+ 
+
+ align:start position:0%
+did with the continuous case there and
+show that
+
+ align:start position:0%
+show that
+ 
+
+ align:start position:0%
+show that
+this when I eliminate the half
+
+ align:start position:0%
+this when I eliminate the half
+ 
+
+ align:start position:0%
+this when I eliminate the half
+levels I've
+
+ align:start position:0%
+levels I've
+ 
+
+ align:start position:0%
+levels I've
+got ordinary Lea
+
+ align:start position:0%
+got ordinary Lea
+ 
+
+ align:start position:0%
+got ordinary Lea
+frog so when I eliminate half levels I
+
+ align:start position:0%
+frog so when I eliminate half levels I
+ 
+
+ align:start position:0%
+frog so when I eliminate half levels I
+will be when I eliminate this half level
+
+ align:start position:0%
+will be when I eliminate this half level
+ 
+
+ align:start position:0%
+will be when I eliminate this half level
+let's say then I'll be connecting well
+
+ align:start position:0%
+let's say then I'll be connecting well
+ 
+
+ align:start position:0%
+let's say then I'll be connecting well
+yep when I eliminate half levels I'm
+
+ align:start position:0%
+yep when I eliminate half levels I'm
+ 
+
+ align:start position:0%
+yep when I eliminate half levels I'm
+going to be connecting these at three
+
+ align:start position:0%
+going to be connecting these at three
+ 
+
+ align:start position:0%
+going to be connecting these at three
+levels one two three and the and the
+
+ align:start position:0%
+levels one two three and the and the
+ 
+
+ align:start position:0%
+levels one two three and the and the
+second different it'll be it'll be Lea
+
+ align:start position:0%
+second different it'll be it'll be Lea
+ 
+
+ align:start position:0%
+second different it'll be it'll be Lea
+frog it'll be so since it's been
+
+ align:start position:0%
+frog it'll be so since it's been
+ 
+
+ align:start position:0%
+frog it'll be so since it's been
+uh a few days since uh we wrote down
+
+ align:start position:0%
+uh a few days since uh we wrote down
+ 
+
+ align:start position:0%
+uh a few days since uh we wrote down
+two-way Leap
+
+ align:start position:0%
+two-way Leap
+ 
+
+ align:start position:0%
+two-way Leap
+Frog or second order equation Leap Frog
+
+ align:start position:0%
+Frog or second order equation Leap Frog
+ 
+
+ align:start position:0%
+Frog or second order equation Leap Frog
+let me just write it again and that's
+
+ align:start position:0%
+let me just write it again and that's
+ 
+
+ align:start position:0%
+let me just write it again and that's
+what we would get the time difference
+
+ align:start position:0%
+what we would get the time difference
+ 
+
+ align:start position:0%
+what we would get the time difference
+squared of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e is equal will be equal to c^ 2 time
+
+ align:start position:0%
+e is equal will be equal to c^ 2 time
+ 
+
+ align:start position:0%
+e is equal will be equal to c^ 2 time
+the space difference squar of e and of
+
+ align:start position:0%
+the space difference squar of e and of
+ 
+
+ align:start position:0%
+the space difference squar of e and of
+course here we have a Delta X squar and
+
+ align:start position:0%
+course here we have a Delta X squar and
+ 
+
+ align:start position:0%
+course here we have a Delta X squar and
+here a Delta
+
+ align:start position:0%
+here a Delta
+ 
+
+ align:start position:0%
+here a Delta
+t^2 so allog together an r s that's the
+
+ align:start position:0%
+t^2 so allog together an r s that's the
+ 
+
+ align:start position:0%
+t^2 so allog together an r s that's the
+that's the formula we know that's the
+
+ align:start position:0%
+that's the formula we know that's the
+ 
+
+ align:start position:0%
+that's the formula we know that's the
+formula we
+
+ align:start position:0%
+formula we
+ 
+
+ align:start position:0%
+formula we
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+okay so if I simplify this to make it
+
+ align:start position:0%
+okay so if I simplify this to make it
+ 
+
+ align:start position:0%
+okay so if I simplify this to make it
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+good uh put the Delta t^ squ up there
+
+ align:start position:0%
+good uh put the Delta t^ squ up there
+ 
+
+ align:start position:0%
+good uh put the Delta t^ squ up there
+you see that it's just R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SAR and maybe it's worth realizing that
+
+ align:start position:0%
+SAR and maybe it's worth realizing that
+ 
+
+ align:start position:0%
+SAR and maybe it's worth realizing that
+again the magic r equal one the magic so
+
+ align:start position:0%
+again the magic r equal one the magic so
+ 
+
+ align:start position:0%
+again the magic r equal one the magic so
+I'll the magic
+
+ align:start position:0%
+I'll the magic
+ 
+
+ align:start position:0%
+I'll the magic
+ratio r equal 1 gives the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exact you agreeing exactly with you yeah
+
+ align:start position:0%
+exact you agreeing exactly with you yeah
+ 
+
+ align:start position:0%
+exact you agreeing exactly with you yeah
+yeah this equation if R is one would be
+
+ align:start position:0%
+yeah this equation if R is one would be
+ 
+
+ align:start position:0%
+yeah this equation if R is one would be
+satisfied exactly by
+
+ align:start position:0%
+satisfied exactly by
+ 
+
+ align:start position:0%
+satisfied exactly by
+The Continuous solution and so it's the
+
+ align:start position:0%
+The Continuous solution and so it's the
+ 
+
+ align:start position:0%
+The Continuous solution and so it's the
+same as this
+
+ align:start position:0%
+same as this
+ 
+
+ align:start position:0%
+same as this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay so that's uh that's Leap Frog so so
+
+ align:start position:0%
+okay so that's uh that's Leap Frog so so
+ 
+
+ align:start position:0%
+okay so that's uh that's Leap Frog so so
+can I summarize Leap Frog Leap Frog was
+
+ align:start position:0%
+can I summarize Leap Frog Leap Frog was
+ 
+
+ align:start position:0%
+can I summarize Leap Frog Leap Frog was
+first of all that led us to these it it
+
+ align:start position:0%
+first of all that led us to these it it
+ 
+
+ align:start position:0%
+first of all that led us to these it it
+worked for second order
+
+ align:start position:0%
+worked for second order
+ 
+
+ align:start position:0%
+worked for second order
+equations it led us to the same
+
+ align:start position:0%
+equations it led us to the same
+ 
+
+ align:start position:0%
+equations it led us to the same
+stability
+
+ align:start position:0%
+stability
+ 
+
+ align:start position:0%
+stability
+condition that R had to be less or equal
+
+ align:start position:0%
+condition that R had to be less or equal
+ 
+
+ align:start position:0%
+condition that R had to be less or equal
+one but it
+
+ align:start position:0%
+one but it
+ 
+
+ align:start position:0%
+one but it
+took uh
+
+ align:start position:0%
+took uh
+ 
+
+ align:start position:0%
+took uh
+took uh um a quadratic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation for G remember we had g^ 2
+
+ align:start position:0%
+equation for G remember we had g^ 2
+ 
+
+ align:start position:0%
+equation for G remember we had g^ 2
+minus 2 G * some quantity a that
+
+ align:start position:0%
+minus 2 G * some quantity a that
+ 
+
+ align:start position:0%
+minus 2 G * some quantity a that
+involved RS and cosiness plus 1 equals z
+
+ align:start position:0%
+involved RS and cosiness plus 1 equals z
+ 
+
+ align:start position:0%
+involved RS and cosiness plus 1 equals z
+and the reason it was a quadratic was
+
+ align:start position:0%
+and the reason it was a quadratic was
+ 
+
+ align:start position:0%
+and the reason it was a quadratic was
+there were two time steps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involved but we handled that we got we
+
+ align:start position:0%
+involved but we handled that we got we
+ 
+
+ align:start position:0%
+involved but we handled that we got we
+got stability if R was less than or
+
+ align:start position:0%
+got stability if R was less than or
+ 
+
+ align:start position:0%
+got stability if R was less than or
+equal one that led us to a in magnitude
+
+ align:start position:0%
+equal one that led us to a in magnitude
+ 
+
+ align:start position:0%
+equal one that led us to a in magnitude
+less or equal one and that led us to G
+
+ align:start position:0%
+less or equal one and that led us to G
+ 
+
+ align:start position:0%
+less or equal one and that led us to G
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+I'll just remember those steps a less or
+
+ align:start position:0%
+I'll just remember those steps a less or
+ 
+
+ align:start position:0%
+I'll just remember those steps a less or
+equal 1 and that led us to G less or
+
+ align:start position:0%
+equal 1 and that led us to G less or
+ 
+
+ align:start position:0%
+equal 1 and that led us to G less or
+equal 1
+
+ align:start position:0%
+equal 1
+ 
+
+ align:start position:0%
+equal 1
+okay yeah the the notes
+
+ align:start position:0%
+okay yeah the the notes
+ 
+
+ align:start position:0%
+okay yeah the the notes
+um including
+
+ align:start position:0%
+um including
+ 
+
+ align:start position:0%
+um including
+uh more about Maxwell's equation and
+
+ align:start position:0%
+uh more about Maxwell's equation and
+ 
+
+ align:start position:0%
+uh more about Maxwell's equation and
+ye's beautiful method with a with a
+
+ align:start position:0%
+ye's beautiful method with a with a
+ 
+
+ align:start position:0%
+ye's beautiful method with a with a
+figure that shows his mesh uh will go up
+
+ align:start position:0%
+figure that shows his mesh uh will go up
+ 
+
+ align:start position:0%
+figure that shows his mesh uh will go up
+uh I mean every section is getting uh
+
+ align:start position:0%
+uh I mean every section is getting uh
+ 
+
+ align:start position:0%
+uh I mean every section is getting uh
+upgraded and this one will this is the
+
+ align:start position:0%
+upgraded and this one will this is the
+ 
+
+ align:start position:0%
+upgraded and this one will this is the
+next one to be upgraded probably by
+
+ align:start position:0%
+next one to be upgraded probably by
+ 
+
+ align:start position:0%
+next one to be upgraded probably by
+tomorrow uh you'll have a a good section
+
+ align:start position:0%
+tomorrow uh you'll have a a good section
+ 
+
+ align:start position:0%
+tomorrow uh you'll have a a good section
+on um second order
+
+ align:start position:0%
+on um second order
+ 
+
+ align:start position:0%
+on um second order
+equations anything so that for me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that's what I wanted to say about
+
+ align:start position:0%
+that that's what I wanted to say about
+ 
+
+ align:start position:0%
+that that's what I wanted to say about
+the wave
+
+ align:start position:0%
+the wave
+ 
+
+ align:start position:0%
+the wave
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+equation alone
+
+ align:start position:0%
+equation alone
+ 
+
+ align:start position:0%
+equation alone
+with no
+
+ align:start position:0%
+with no
+ 
+
+ align:start position:0%
+with no
+diffusion and now I'm ready to move to
+
+ align:start position:0%
+diffusion and now I'm ready to move to
+ 
+
+ align:start position:0%
+diffusion and now I'm ready to move to
+the heat
+
+ align:start position:0%
+the heat
+ 
+
+ align:start position:0%
+the heat
+equation so what do we have coming up so
+
+ align:start position:0%
+equation so what do we have coming up so
+ 
+
+ align:start position:0%
+equation so what do we have coming up so
+maybe maybe important to say what's
+
+ align:start position:0%
+maybe maybe important to say what's
+ 
+
+ align:start position:0%
+maybe maybe important to say what's
+coming up
+
+ align:start position:0%
+coming up
+ 
+
+ align:start position:0%
+coming up
+the so so we've done oneway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wave now we've done two-way
+
+ align:start position:0%
+wave now we've done two-way
+ 
+
+ align:start position:0%
+wave now we've done two-way
+waves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next comes the heat equation heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffusion and then will come a mixture
+
+ align:start position:0%
+diffusion and then will come a mixture
+ 
+
+ align:start position:0%
+diffusion and then will come a mixture
+of the two convection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffusion and by the way
+
+ align:start position:0%
+diffusion and by the way
+ 
+
+ align:start position:0%
+diffusion and by the way
+uh so I'll
+
+ align:start position:0%
+uh so I'll
+ 
+
+ align:start position:0%
+uh so I'll
+go straight toward to these uh in a
+
+ align:start position:0%
+go straight toward to these uh in a
+ 
+
+ align:start position:0%
+go straight toward to these uh in a
+couple of weeks uh we have our guest
+
+ align:start position:0%
+couple of weeks uh we have our guest
+ 
+
+ align:start position:0%
+couple of weeks uh we have our guest
+lecture who will do the applications to
+
+ align:start position:0%
+lecture who will do the applications to
+ 
+
+ align:start position:0%
+lecture who will do the applications to
+financial
+
+ align:start position:0%
+financial
+ 
+
+ align:start position:0%
+financial
+mathematics mathematical Finance in
+
+ align:start position:0%
+mathematics mathematical Finance in
+ 
+
+ align:start position:0%
+mathematics mathematical Finance in
+specifically the black skulls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation so you probably know that uh a
+
+ align:start position:0%
+equation so you probably know that uh a
+ 
+
+ align:start position:0%
+equation so you probably know that uh a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+effort and a lot of money are going
+
+ align:start position:0%
+effort and a lot of money are going
+ 
+
+ align:start position:0%
+effort and a lot of money are going
+into uh the valuation of options and
+
+ align:start position:0%
+into uh the valuation of options and
+ 
+
+ align:start position:0%
+into uh the valuation of options and
+other Financial
+
+ align:start position:0%
+other Financial
+ 
+
+ align:start position:0%
+other Financial
+derivatives and that this equation found
+
+ align:start position:0%
+derivatives and that this equation found
+ 
+
+ align:start position:0%
+derivatives and that this equation found
+this black skull's
+
+ align:start position:0%
+this black skull's
+ 
+
+ align:start position:0%
+this black skull's
+equation beautifully produced the heat
+
+ align:start position:0%
+equation beautifully produced the heat
+ 
+
+ align:start position:0%
+equation beautifully produced the heat
+equation and
+
+ align:start position:0%
+equation and
+ 
+
+ align:start position:0%
+equation and
+additional uh correction terms produce a
+
+ align:start position:0%
+additional uh correction terms produce a
+ 
+
+ align:start position:0%
+additional uh correction terms produce a
+will produce a convection diffusion
+
+ align:start position:0%
+will produce a convection diffusion
+ 
+
+ align:start position:0%
+will produce a convection diffusion
+equation so so this is a
+
+ align:start position:0%
+equation so so this is a
+ 
+
+ align:start position:0%
+equation so so this is a
+application that we wouldn't have made
+
+ align:start position:0%
+application that we wouldn't have made
+ 
+
+ align:start position:0%
+application that we wouldn't have made
+uh some years ago but now it's worth
+
+ align:start position:0%
+uh some years ago but now it's worth
+ 
+
+ align:start position:0%
+uh some years ago but now it's worth
+having uh focusing on that I think it's
+
+ align:start position:0%
+having uh focusing on that I think it's
+ 
+
+ align:start position:0%
+having uh focusing on that I think it's
+it's interesting itself and then so
+
+ align:start position:0%
+it's interesting itself and then so
+ 
+
+ align:start position:0%
+it's interesting itself and then so
+these this is what's coming and then uh
+
+ align:start position:0%
+these this is what's coming and then uh
+ 
+
+ align:start position:0%
+these this is what's coming and then uh
+you could say one-way wave equations but
+
+ align:start position:0%
+you could say one-way wave equations but
+ 
+
+ align:start position:0%
+you could say one-way wave equations but
+nonlinear so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonlinear wave equations and those are
+
+ align:start position:0%
+nonlinear wave equations and those are
+ 
+
+ align:start position:0%
+nonlinear wave equations and those are
+called conservation
+
+ align:start position:0%
+called conservation
+ 
+
+ align:start position:0%
+called conservation
+laws
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+that's that's after these linear cases
+
+ align:start position:0%
+that's that's after these linear cases
+ 
+
+ align:start position:0%
+that's that's after these linear cases
+all right so I'm ready to tackle the
+
+ align:start position:0%
+all right so I'm ready to tackle the
+ 
+
+ align:start position:0%
+all right so I'm ready to tackle the
+heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation starting then on to the next
+
+ align:start position:0%
+equation starting then on to the next
+ 
+
+ align:start position:0%
+equation starting then on to the next
+section of the notes okay so let me
+
+ align:start position:0%
+section of the notes okay so let me
+ 
+
+ align:start position:0%
+section of the notes okay so let me
+tackle it
+
+ align:start position:0%
+tackle it
+ 
+
+ align:start position:0%
+tackle it
+here so the heat equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me take it take the constant to be 1
+
+ align:start position:0%
+let me take it take the constant to be 1
+ 
+
+ align:start position:0%
+let me take it take the constant to be 1
+utal
+
+ align:start position:0%
+utal
+ 
+
+ align:start position:0%
+utal
+uxx okay because we already see the big
+
+ align:start position:0%
+uxx okay because we already see the big
+ 
+
+ align:start position:0%
+uxx okay because we already see the big
+difference now there's a second X
+
+ align:start position:0%
+difference now there's a second X
+ 
+
+ align:start position:0%
+difference now there's a second X
+derivative but only a first derivative
+
+ align:start position:0%
+derivative but only a first derivative
+ 
+
+ align:start position:0%
+derivative but only a first derivative
+in time the the the dimensions of T and
+
+ align:start position:0%
+in time the the the dimensions of T and
+ 
+
+ align:start position:0%
+in time the the the dimensions of T and
+X are not no longer the same we won't
+
+ align:start position:0%
+X are not no longer the same we won't
+ 
+
+ align:start position:0%
+X are not no longer the same we won't
+have delta T and Delta X comp
+
+ align:start position:0%
+have delta T and Delta X comp
+ 
+
+ align:start position:0%
+have delta T and Delta X comp
+comparable now it will be delta T
+
+ align:start position:0%
+comparable now it will be delta T
+ 
+
+ align:start position:0%
+comparable now it will be delta T
+comparable with Delta X SAR and that's a
+
+ align:start position:0%
+comparable with Delta X SAR and that's a
+ 
+
+ align:start position:0%
+comparable with Delta X SAR and that's a
+very significant difference because
+
+ align:start position:0%
+very significant difference because
+ 
+
+ align:start position:0%
+very significant difference because
+that's if Delta X is small Delta x^ s is
+
+ align:start position:0%
+that's if Delta X is small Delta x^ s is
+ 
+
+ align:start position:0%
+that's if Delta X is small Delta x^ s is
+extremely small so when delta T has to
+
+ align:start position:0%
+extremely small so when delta T has to
+ 
+
+ align:start position:0%
+extremely small so when delta T has to
+be is is constrained by Delta x^ squ
+
+ align:start position:0%
+be is is constrained by Delta x^ squ
+ 
+
+ align:start position:0%
+be is is constrained by Delta x^ squ
+we're we're looking at small time steps
+
+ align:start position:0%
+we're we're looking at small time steps
+ 
+
+ align:start position:0%
+we're we're looking at small time steps
+we're looking at stiff
+
+ align:start position:0%
+we're looking at stiff
+ 
+
+ align:start position:0%
+we're looking at stiff
+systems absolutely
+
+ align:start position:0%
+systems absolutely
+ 
+
+ align:start position:0%
+systems absolutely
+this is going to be a stiff problem
+
+ align:start position:0%
+this is going to be a stiff problem
+ 
+
+ align:start position:0%
+this is going to be a stiff problem
+because uh the low
+
+ align:start position:0%
+because uh the low
+ 
+
+ align:start position:0%
+because uh the low
+frequencies and the high frequencies
+
+ align:start position:0%
+frequencies and the high frequencies
+ 
+
+ align:start position:0%
+frequencies and the high frequencies
+differ enormously in the Decay rate in
+
+ align:start position:0%
+differ enormously in the Decay rate in
+ 
+
+ align:start position:0%
+differ enormously in the Decay rate in
+fact why don't we see it right away
+
+ align:start position:0%
+fact why don't we see it right away
+ 
+
+ align:start position:0%
+fact why don't we see it right away
+starting as always with exponentials so
+
+ align:start position:0%
+starting as always with exponentials so
+ 
+
+ align:start position:0%
+starting as always with exponentials so
+if I if I plug in U of x and t is some G
+
+ align:start position:0%
+if I if I plug in U of x and t is some G
+ 
+
+ align:start position:0%
+if I if I plug in U of x and t is some G
+of t e to the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX separating variable as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always look for a pure exponential
+
+ align:start position:0%
+always look for a pure exponential
+ 
+
+ align:start position:0%
+always look for a pure exponential
+solution plug that in we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dgdt time e to the I
+
+ align:start position:0%
+dgdt time e to the I
+ 
+
+ align:start position:0%
+dgdt time e to the I
+KX on the left and now I have to take
+
+ align:start position:0%
+KX on the left and now I have to take
+ 
+
+ align:start position:0%
+KX on the left and now I have to take
+two x derivatives so that brings ik K
+
+ align:start position:0%
+two x derivatives so that brings ik K
+ 
+
+ align:start position:0%
+two x derivatives so that brings ik K
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+twice so that's - k^ 2 i^ 2 giving the
+
+ align:start position:0%
+twice so that's - k^ 2 i^ 2 giving the
+ 
+
+ align:start position:0%
+twice so that's - k^ 2 i^ 2 giving the
+minus1 * G G * e to the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX and now of course I can cancel that
+
+ align:start position:0%
+KX and now of course I can cancel that
+ 
+
+ align:start position:0%
+KX and now of course I can cancel that
+which is never
+
+ align:start position:0%
+which is never
+ 
+
+ align:start position:0%
+which is never
+zero and I've separated out the time
+
+ align:start position:0%
+zero and I've separated out the time
+ 
+
+ align:start position:0%
+zero and I've separated out the time
+part the G part dgdt is minus k 2 G so G
+
+ align:start position:0%
+part the G part dgdt is minus k 2 G so G
+ 
+
+ align:start position:0%
+part the G part dgdt is minus k 2 G so G
+is e the minus k^ 2 T notice that it's k
+
+ align:start position:0%
+is e the minus k^ 2 T notice that it's k
+ 
+
+ align:start position:0%
+is e the minus k^ 2 T notice that it's k
+a squ that's the and notice that it's
+
+ align:start position:0%
+a squ that's the and notice that it's
+ 
+
+ align:start position:0%
+a squ that's the and notice that it's
+real and negative see that's a very big
+
+ align:start position:0%
+real and negative see that's a very big
+ 
+
+ align:start position:0%
+real and negative see that's a very big
+difference compare with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compare e to the ik e to the ik
+
+ align:start position:0%
+compare e to the ik e to the ik
+ 
+
+ align:start position:0%
+compare e to the ik e to the ik
+CT which it was for the one-way wave
+
+ align:start position:0%
+CT which it was for the one-way wave
+ 
+
+ align:start position:0%
+CT which it was for the one-way wave
+equation the difference is enormous here
+
+ align:start position:0%
+equation the difference is enormous here
+ 
+
+ align:start position:0%
+equation the difference is enormous here
+the the uh
+
+ align:start position:0%
+the the uh
+ 
+
+ align:start position:0%
+the the uh
+that's magnitude one energy
+
+ align:start position:0%
+that's magnitude one energy
+ 
+
+ align:start position:0%
+that's magnitude one energy
+conserved this is magnitude smaller than
+
+ align:start position:0%
+conserved this is magnitude smaller than
+ 
+
+ align:start position:0%
+conserved this is magnitude smaller than
+one energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dissipated this
+
+ align:start position:0%
+dissipated this
+ 
+
+ align:start position:0%
+dissipated this
+uh we
+
+ align:start position:0%
+uh we
+ 
+
+ align:start position:0%
+uh we
+had a ratio delta T over Delta X now
+
+ align:start position:0%
+had a ratio delta T over Delta X now
+ 
+
+ align:start position:0%
+had a ratio delta T over Delta X now
+we're going to see delta T over Delta X
+
+ align:start position:0%
+we're going to see delta T over Delta X
+ 
+
+ align:start position:0%
+we're going to see delta T over Delta X
+squ because
+
+ align:start position:0%
+squ because
+ 
+
+ align:start position:0%
+squ because
+somehow x and t are are are now have uh
+
+ align:start position:0%
+somehow x and t are are are now have uh
+ 
+
+ align:start position:0%
+somehow x and t are are are now have uh
+it's x s that matches T now okay so
+
+ align:start position:0%
+it's x s that matches T now okay so
+ 
+
+ align:start position:0%
+it's x s that matches T now okay so
+that's so now when I put that into here
+
+ align:start position:0%
+that's so now when I put that into here
+ 
+
+ align:start position:0%
+that's so now when I put that into here
+let me just do it g of T is eus k 2 T so
+
+ align:start position:0%
+let me just do it g of T is eus k 2 T so
+ 
+
+ align:start position:0%
+let me just do it g of T is eus k 2 T so
+there is the pure
+
+ align:start position:0%
+there is the pure
+ 
+
+ align:start position:0%
+there is the pure
+exponential simple as always because we
+
+ align:start position:0%
+exponential simple as always because we
+ 
+
+ align:start position:0%
+exponential simple as always because we
+have constant coefficients but highly
+
+ align:start position:0%
+have constant coefficients but highly
+ 
+
+ align:start position:0%
+have constant coefficients but highly
+informative I I guess another thing that
+
+ align:start position:0%
+informative I I guess another thing that
+ 
+
+ align:start position:0%
+informative I I guess another thing that
+I read off of that is what what
+
+ align:start position:0%
+I read off of that is what what
+ 
+
+ align:start position:0%
+I read off of that is what what
+frequencies are decaying fast high
+
+ align:start position:0%
+frequencies are decaying fast high
+ 
+
+ align:start position:0%
+frequencies are decaying fast high
+frequencies if k is
+
+ align:start position:0%
+frequencies if k is
+ 
+
+ align:start position:0%
+frequencies if k is
+large k^2 is very large and E Theus k^2
+
+ align:start position:0%
+large k^2 is very large and E Theus k^2
+ 
+
+ align:start position:0%
+large k^2 is very large and E Theus k^2
+T is decaying very quickly so oscill
+
+ align:start position:0%
+T is decaying very quickly so oscill
+ 
+
+ align:start position:0%
+T is decaying very quickly so oscill
+high frequency noise in the system
+
+ align:start position:0%
+high frequency noise in the system
+ 
+
+ align:start position:0%
+high frequency noise in the system
+roughness discontinuities are going to
+
+ align:start position:0%
+roughness discontinuities are going to
+ 
+
+ align:start position:0%
+roughness discontinuities are going to
+get smoothed
+
+ align:start position:0%
+get smoothed
+ 
+
+ align:start position:0%
+get smoothed
+out strongly by moving forward in time
+
+ align:start position:0%
+out strongly by moving forward in time
+ 
+
+ align:start position:0%
+out strongly by moving forward in time
+and physically what's happening is we
+
+ align:start position:0%
+and physically what's happening is we
+ 
+
+ align:start position:0%
+and physically what's happening is we
+have like our
+
+ align:start position:0%
+have like our
+ 
+
+ align:start position:0%
+have like our
+wavefront which stayed a
+
+ align:start position:0%
+wavefront which stayed a
+ 
+
+ align:start position:0%
+wavefront which stayed a
+perfect step function in the wave
+
+ align:start position:0%
+perfect step function in the wave
+ 
+
+ align:start position:0%
+perfect step function in the wave
+equation will
+
+ align:start position:0%
+equation will
+ 
+
+ align:start position:0%
+equation will
+instantly
+
+ align:start position:0%
+instantly
+ 
+
+ align:start position:0%
+instantly
+smear so diffusion smears
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discontinuities heat heat travels if we
+
+ align:start position:0%
+discontinuities heat heat travels if we
+ 
+
+ align:start position:0%
+discontinuities heat heat travels if we
+were back over
+
+ align:start position:0%
+were back over
+ 
+
+ align:start position:0%
+were back over
+here if the temperature starts out as
+
+ align:start position:0%
+here if the temperature starts out as
+ 
+
+ align:start position:0%
+here if the temperature starts out as
+one on this side and zero on this side
+
+ align:start position:0%
+one on this side and zero on this side
+ 
+
+ align:start position:0%
+one on this side and zero on this side
+then in an instant some
+
+ align:start position:0%
+then in an instant some
+ 
+
+ align:start position:0%
+then in an instant some
+heat flows from right to left in fact it
+
+ align:start position:0%
+heat flows from right to left in fact it
+ 
+
+ align:start position:0%
+heat flows from right to left in fact it
+flows at with infinite speed the in a in
+
+ align:start position:0%
+flows at with infinite speed the in a in
+ 
+
+ align:start position:0%
+flows at with infinite speed the in a in
+a short delta T there's a little heat
+
+ align:start position:0%
+a short delta T there's a little heat
+ 
+
+ align:start position:0%
+a short delta T there's a little heat
+all the way out there very little of
+
+ align:start position:0%
+all the way out there very little of
+ 
+
+ align:start position:0%
+all the way out there very little of
+course because it's uh well I guess we
+
+ align:start position:0%
+course because it's uh well I guess we
+ 
+
+ align:start position:0%
+course because it's uh well I guess we
+want to see how what that behavior
+
+ align:start position:0%
+want to see how what that behavior
+ 
+
+ align:start position:0%
+want to see how what that behavior
+is so and now want to write down staying
+
+ align:start position:0%
+is so and now want to write down staying
+ 
+
+ align:start position:0%
+is so and now want to write down staying
+with the differential
+
+ align:start position:0%
+with the differential
+ 
+
+ align:start position:0%
+with the differential
+equation what do we want to
+
+ align:start position:0%
+equation what do we want to
+ 
+
+ align:start position:0%
+equation what do we want to
+do we did the exponential
+
+ align:start position:0%
+do we did the exponential
+ 
+
+ align:start position:0%
+do we did the exponential
+case and learned a good bit from that
+
+ align:start position:0%
+case and learned a good bit from that
+ 
+
+ align:start position:0%
+case and learned a good bit from that
+the quick the fast decay of high
+
+ align:start position:0%
+the quick the fast decay of high
+ 
+
+ align:start position:0%
+the quick the fast decay of high
+frequencies but now comes the The Next
+
+ align:start position:0%
+frequencies but now comes the The Next
+ 
+
+ align:start position:0%
+frequencies but now comes the The Next
+Step would be to put different
+
+ align:start position:0%
+Step would be to put different
+ 
+
+ align:start position:0%
+Step would be to put different
+frequencies different KS
+
+ align:start position:0%
+frequencies different KS
+ 
+
+ align:start position:0%
+frequencies different KS
+together by linearity we can add these
+
+ align:start position:0%
+together by linearity we can add these
+ 
+
+ align:start position:0%
+together by linearity we can add these
+Solutions we can multiply by
+
+ align:start position:0%
+Solutions we can multiply by
+ 
+
+ align:start position:0%
+Solutions we can multiply by
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+any we can multiply that by any numbers
+
+ align:start position:0%
+any we can multiply that by any numbers
+ 
+
+ align:start position:0%
+any we can multiply that by any numbers
+we want depending on K we still have
+
+ align:start position:0%
+we want depending on K we still have
+ 
+
+ align:start position:0%
+we want depending on K we still have
+Solutions and we can integrate over K so
+
+ align:start position:0%
+Solutions and we can integrate over K so
+ 
+
+ align:start position:0%
+Solutions and we can integrate over K so
+we will actually that that will be the
+
+ align:start position:0%
+we will actually that that will be the
+ 
+
+ align:start position:0%
+we will actually that that will be the
+that will be the next step let me write
+
+ align:start position:0%
+that will be the next step let me write
+ 
+
+ align:start position:0%
+that will be the next step let me write
+down what that does I I'll I'm going to
+
+ align:start position:0%
+down what that does I I'll I'm going to
+ 
+
+ align:start position:0%
+down what that does I I'll I'm going to
+jump take a little jump
+
+ align:start position:0%
+jump take a little jump
+ 
+
+ align:start position:0%
+jump take a little jump
+here to put on the board what I just
+
+ align:start position:0%
+here to put on the board what I just
+ 
+
+ align:start position:0%
+here to put on the board what I just
+said in words I can multiply this e
+
+ align:start position:0%
+said in words I can multiply this e
+ 
+
+ align:start position:0%
+said in words I can multiply this e
+minus k^ 2 t e to the I
+
+ align:start position:0%
+minus k^ 2 t e to the I
+ 
+
+ align:start position:0%
+minus k^ 2 t e to the I
+KX that's what's happening to frequence
+
+ align:start position:0%
+KX that's what's happening to frequence
+ 
+
+ align:start position:0%
+KX that's what's happening to frequence
+to the pure frequency K If I multiply
+
+ align:start position:0%
+to the pure frequency K If I multiply
+ 
+
+ align:start position:0%
+to the pure frequency K If I multiply
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+by the
+
+ align:start position:0%
+by the
+ 
+
+ align:start position:0%
+by the
+amount of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency which is in the initial
+
+ align:start position:0%
+frequency which is in the initial
+ 
+
+ align:start position:0%
+frequency which is in the initial
+condition so here's the initial
+
+ align:start position:0%
+condition so here's the initial
+ 
+
+ align:start position:0%
+condition so here's the initial
+condition you
+
+ align:start position:0%
+condition you
+ 
+
+ align:start position:0%
+condition you
+Z and I've taken its 4A transform this
+
+ align:start position:0%
+Z and I've taken its 4A transform this
+ 
+
+ align:start position:0%
+Z and I've taken its 4A transform this
+tells me how much of frequency K is in
+
+ align:start position:0%
+tells me how much of frequency K is in
+ 
+
+ align:start position:0%
+tells me how much of frequency K is in
+the problem is in the initial
+
+ align:start position:0%
+the problem is in the initial
+ 
+
+ align:start position:0%
+the problem is in the initial
+problem this tells me how much of
+
+ align:start position:0%
+problem this tells me how much of
+ 
+
+ align:start position:0%
+problem this tells me how much of
+frequency K is in the initial
+
+ align:start position:0%
+frequency K is in the initial
+ 
+
+ align:start position:0%
+frequency K is in the initial
+problem that amount multiplies this with
+
+ align:start position:0%
+problem that amount multiplies this with
+ 
+
+ align:start position:0%
+problem that amount multiplies this with
+this rapid Decay as time goes forward
+
+ align:start position:0%
+this rapid Decay as time goes forward
+ 
+
+ align:start position:0%
+this rapid Decay as time goes forward
+but at any later time I'm just adding up
+
+ align:start position:0%
+but at any later time I'm just adding up
+ 
+
+ align:start position:0%
+but at any later time I'm just adding up
+and since K we're on the whole line K is
+
+ align:start position:0%
+and since K we're on the whole line K is
+ 
+
+ align:start position:0%
+and since K we're on the whole line K is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+continuous so there's we add up from K =
+
+ align:start position:0%
+continuous so there's we add up from K =
+ 
+
+ align:start position:0%
+continuous so there's we add up from K =
+minus infinity to infinity and I think
+
+ align:start position:0%
+minus infinity to infinity and I think
+ 
+
+ align:start position:0%
+minus infinity to infinity and I think
+we have to remember the 2 pi that
+
+ align:start position:0%
+we have to remember the 2 pi that
+ 
+
+ align:start position:0%
+we have to remember the 2 pi that
+depends on our particular definition of
+
+ align:start position:0%
+depends on our particular definition of
+ 
+
+ align:start position:0%
+depends on our particular definition of
+the transform but I I'm going to stay
+
+ align:start position:0%
+the transform but I I'm going to stay
+ 
+
+ align:start position:0%
+the transform but I I'm going to stay
+with this one that's the answer that's U
+
+ align:start position:0%
+with this one that's the answer that's U
+ 
+
+ align:start position:0%
+with this one that's the answer that's U
+of x and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've said that in words but actually
+
+ align:start position:0%
+so I've said that in words but actually
+ 
+
+ align:start position:0%
+so I've said that in words but actually
+we could just check
+
+ align:start position:0%
+we could just check
+ 
+
+ align:start position:0%
+we could just check
+it we would like to know that this left
+
+ align:start position:0%
+it we would like to know that this left
+ 
+
+ align:start position:0%
+it we would like to know that this left
+hand side solves the heat equation and
+
+ align:start position:0%
+hand side solves the heat equation and
+ 
+
+ align:start position:0%
+hand side solves the heat equation and
+we would like to know that it has the
+
+ align:start position:0%
+we would like to know that it has the
+ 
+
+ align:start position:0%
+we would like to know that it has the
+correct start the correct U of X and
+
+ align:start position:0%
+correct start the correct U of X and
+ 
+
+ align:start position:0%
+correct start the correct U of X and
+zero well let's check that at T equals z
+
+ align:start position:0%
+zero well let's check that at T equals z
+ 
+
+ align:start position:0%
+zero well let's check that at T equals z
+at the start this is
+
+ align:start position:0%
+at the start this is
+ 
+
+ align:start position:0%
+at the start this is
+one so at the
+
+ align:start position:0%
+one so at the
+ 
+
+ align:start position:0%
+one so at the
+start this formula without that thing
+
+ align:start position:0%
+start this formula without that thing
+ 
+
+ align:start position:0%
+start this formula without that thing
+there is just the inverse fora transform
+
+ align:start position:0%
+there is just the inverse fora transform
+ 
+
+ align:start position:0%
+there is just the inverse fora transform
+that takes the 4 a transform multiplies
+
+ align:start position:0%
+that takes the 4 a transform multiplies
+ 
+
+ align:start position:0%
+that takes the 4 a transform multiplies
+by this integrates to recover u
+
+ align:start position:0%
+by this integrates to recover u
+ 
+
+ align:start position:0%
+by this integrates to recover u
+u so it does start out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correctly should I say that again it
+
+ align:start position:0%
+correctly should I say that again it
+ 
+
+ align:start position:0%
+correctly should I say that again it
+starts correctly because at T equals 0
+
+ align:start position:0%
+starts correctly because at T equals 0
+ 
+
+ align:start position:0%
+starts correctly because at T equals 0
+this is just the inverse 4 a transform
+
+ align:start position:0%
+this is just the inverse 4 a transform
+ 
+
+ align:start position:0%
+this is just the inverse 4 a transform
+of u0 so it produces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U it inverts this transform that we
+
+ align:start position:0%
+U it inverts this transform that we
+ 
+
+ align:start position:0%
+U it inverts this transform that we
+took secondly does it solve the heat
+
+ align:start position:0%
+took secondly does it solve the heat
+ 
+
+ align:start position:0%
+took secondly does it solve the heat
+equation sure because for each
+
+ align:start position:0%
+equation sure because for each
+ 
+
+ align:start position:0%
+equation sure because for each
+K we've just found that that solves the
+
+ align:start position:0%
+K we've just found that that solves the
+ 
+
+ align:start position:0%
+K we've just found that that solves the
+heat equation and now we're just putting
+
+ align:start position:0%
+heat equation and now we're just putting
+ 
+
+ align:start position:0%
+heat equation and now we're just putting
+different KS
+
+ align:start position:0%
+different KS
+ 
+
+ align:start position:0%
+different KS
+together so that's the answer it's so
+
+ align:start position:0%
+together so that's the answer it's so
+ 
+
+ align:start position:0%
+together so that's the answer it's so
+you might say Okay
+
+ align:start position:0%
+you might say Okay
+ 
+
+ align:start position:0%
+you might say Okay
+Perfection
+
+ align:start position:0%
+Perfection
+ 
+
+ align:start position:0%
+Perfection
+we don't
+
+ align:start position:0%
+we don't
+ 
+
+ align:start position:0%
+we don't
+uh do do we need uh finite
+
+ align:start position:0%
+uh do do we need uh finite
+ 
+
+ align:start position:0%
+uh do do we need uh finite
+differences well I guess we do this is
+
+ align:start position:0%
+differences well I guess we do this is
+ 
+
+ align:start position:0%
+differences well I guess we do this is
+typical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of formulas that give the answer exactly
+
+ align:start position:0%
+of formulas that give the answer exactly
+ 
+
+ align:start position:0%
+of formulas that give the answer exactly
+but in terms that are not numerically
+
+ align:start position:0%
+but in terms that are not numerically
+ 
+
+ align:start position:0%
+but in terms that are not numerically
+convenient because look what we have to
+
+ align:start position:0%
+convenient because look what we have to
+ 
+
+ align:start position:0%
+convenient because look what we have to
+use this Formula First of all this this
+
+ align:start position:0%
+use this Formula First of all this this
+ 
+
+ align:start position:0%
+use this Formula First of all this this
+requires an integral an infinite
+
+ align:start position:0%
+requires an integral an infinite
+ 
+
+ align:start position:0%
+requires an integral an infinite
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to find integral to find for
+
+ align:start position:0%
+to find integral to find for
+ 
+
+ align:start position:0%
+to find integral to find for
+un you not U hat we would have
+
+ align:start position:0%
+un you not U hat we would have
+ 
+
+ align:start position:0%
+un you not U hat we would have
+to to use this formula we'd have to find
+
+ align:start position:0%
+to to use this formula we'd have to find
+ 
+
+ align:start position:0%
+to to use this formula we'd have to find
+this transform and then we have to do
+
+ align:start position:0%
+this transform and then we have to do
+ 
+
+ align:start position:0%
+this transform and then we have to do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+integral for the inverse
+
+ align:start position:0%
+integral for the inverse
+ 
+
+ align:start position:0%
+integral for the inverse
+transform this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+for the answer U
+
+ align:start position:0%
+for the answer U
+ 
+
+ align:start position:0%
+for the answer U
+two infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrals and not to mention the fact
+
+ align:start position:0%
+integrals and not to mention the fact
+ 
+
+ align:start position:0%
+integrals and not to mention the fact
+that on a finite
+
+ align:start position:0%
+that on a finite
+ 
+
+ align:start position:0%
+that on a finite
+interval when X doesn't go all the way
+
+ align:start position:0%
+interval when X doesn't go all the way
+ 
+
+ align:start position:0%
+interval when X doesn't go all the way
+from minus infinity to Infinity we've
+
+ align:start position:0%
+from minus infinity to Infinity we've
+ 
+
+ align:start position:0%
+from minus infinity to Infinity we've
+the formula we have to think all over
+
+ align:start position:0%
+the formula we have to think all over
+ 
+
+ align:start position:0%
+the formula we have to think all over
+again so we have a nice formula for the
+
+ align:start position:0%
+again so we have a nice formula for the
+ 
+
+ align:start position:0%
+again so we have a nice formula for the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+but it looks nice but it's not
+
+ align:start position:0%
+but it looks nice but it's not
+ 
+
+ align:start position:0%
+but it looks nice but it's not
+numerically
+
+ align:start position:0%
+numerically
+ 
+
+ align:start position:0%
+numerically
+terrific uh we can get a lot of
+
+ align:start position:0%
+terrific uh we can get a lot of
+ 
+
+ align:start position:0%
+terrific uh we can get a lot of
+information out of this and there's one
+
+ align:start position:0%
+information out of this and there's one
+ 
+
+ align:start position:0%
+information out of this and there's one
+other special solution that that's also
+
+ align:start position:0%
+other special solution that that's also
+ 
+
+ align:start position:0%
+other special solution that that's also
+extremely
+
+ align:start position:0%
+extremely
+ 
+
+ align:start position:0%
+extremely
+informative what
+
+ align:start position:0%
+informative what
+ 
+
+ align:start position:0%
+informative what
+if so I'm going to do a special case but
+
+ align:start position:0%
+if so I'm going to do a special case but
+ 
+
+ align:start position:0%
+if so I'm going to do a special case but
+it's the big case what if it's what if
+
+ align:start position:0%
+it's the big case what if it's what if
+ 
+
+ align:start position:0%
+it's the big case what if it's what if
+the initial condition is a Delta
+
+ align:start position:0%
+the initial condition is a Delta
+ 
+
+ align:start position:0%
+the initial condition is a Delta
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+what if the initial condition is a Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function an Impulse a Time
+
+ align:start position:0%
+function an Impulse a Time
+ 
+
+ align:start position:0%
+function an Impulse a Time
+Zero x equals z an an instant source of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heat at at a point a point source a
+
+ align:start position:0%
+heat at at a point a point source a
+ 
+
+ align:start position:0%
+heat at at a point a point source a
+point source with finite strength you
+
+ align:start position:0%
+point source with finite strength you
+ 
+
+ align:start position:0%
+point source with finite strength you
+could say an
+
+ align:start position:0%
+could say an
+ 
+
+ align:start position:0%
+could say an
+Impulse at Time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Zero
+
+ align:start position:0%
+Zero
+ 
+
+ align:start position:0%
+Zero
+for uh the wave equation what happened
+
+ align:start position:0%
+for uh the wave equation what happened
+ 
+
+ align:start position:0%
+for uh the wave equation what happened
+that was like turning on a flash of
+
+ align:start position:0%
+that was like turning on a flash of
+ 
+
+ align:start position:0%
+that was like turning on a flash of
+light and it went along the
+
+ align:start position:0%
+light and it went along the
+ 
+
+ align:start position:0%
+light and it went along the
+characteristics for the heat
+
+ align:start position:0%
+characteristics for the heat
+ 
+
+ align:start position:0%
+characteristics for the heat
+equation uh it'll be quite
+
+ align:start position:0%
+equation uh it'll be quite
+ 
+
+ align:start position:0%
+equation uh it'll be quite
+different there aren't characteristics
+
+ align:start position:0%
+different there aren't characteristics
+ 
+
+ align:start position:0%
+different there aren't characteristics
+here we but this is an extremely
+
+ align:start position:0%
+here we but this is an extremely
+ 
+
+ align:start position:0%
+here we but this is an extremely
+important solution and and I think you
+
+ align:start position:0%
+important solution and and I think you
+ 
+
+ align:start position:0%
+important solution and and I think you
+could call it the the fundamental
+
+ align:start position:0%
+could call it the the fundamental
+ 
+
+ align:start position:0%
+could call it the the fundamental
+solution to the heat equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you may know what it is you may have
+
+ align:start position:0%
+you may know what it is you may have
+ 
+
+ align:start position:0%
+you may know what it is you may have
+seen this
+
+ align:start position:0%
+seen this
+ 
+
+ align:start position:0%
+seen this
+formula it's fantastic that
+
+ align:start position:0%
+formula it's fantastic that
+ 
+
+ align:start position:0%
+formula it's fantastic that
+we get a formula for this one well you
+
+ align:start position:0%
+we get a formula for this one well you
+ 
+
+ align:start position:0%
+we get a formula for this one well you
+could say we've got a
+
+ align:start position:0%
+could say we've got a
+ 
+
+ align:start position:0%
+could say we've got a
+formula what's the 4A transform what's
+
+ align:start position:0%
+formula what's the 4A transform what's
+ 
+
+ align:start position:0%
+formula what's the 4A transform what's
+un not hat of K for the Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function one right the 4A transform
+
+ align:start position:0%
+function one right the 4A transform
+ 
+
+ align:start position:0%
+function one right the 4A transform
+of the Delta function is a constant one
+
+ align:start position:0%
+of the Delta function is a constant one
+ 
+
+ align:start position:0%
+of the Delta function is a constant one
+all frequencies are there in equal
+
+ align:start position:0%
+all frequencies are there in equal
+ 
+
+ align:start position:0%
+all frequencies are there in equal
+amounts this is a constant so I can
+
+ align:start position:0%
+amounts this is a constant so I can
+ 
+
+ align:start position:0%
+amounts this is a constant so I can
+remove it it's one and I'm left with a
+
+ align:start position:0%
+remove it it's one and I'm left with a
+ 
+
+ align:start position:0%
+remove it it's one and I'm left with a
+specific integral to
+
+ align:start position:0%
+specific integral to
+ 
+
+ align:start position:0%
+specific integral to
+do and the question is can I do
+
+ align:start position:0%
+do and the question is can I do
+ 
+
+ align:start position:0%
+do and the question is can I do
+it and the answer turns out to be yes
+
+ align:start position:0%
+it and the answer turns out to be yes
+ 
+
+ align:start position:0%
+it and the answer turns out to be yes
+you can do that integral with when this
+
+ align:start position:0%
+you can do that integral with when this
+ 
+
+ align:start position:0%
+you can do that integral with when this
+is a constant and that will give you the
+
+ align:start position:0%
+is a constant and that will give you the
+ 
+
+ align:start position:0%
+is a constant and that will give you the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+with that starting value and let me just
+
+ align:start position:0%
+with that starting value and let me just
+ 
+
+ align:start position:0%
+with that starting value and let me just
+say what that answer is U of x and t
+
+ align:start position:0%
+say what that answer is U of x and t
+ 
+
+ align:start position:0%
+say what that answer is U of x and t
+this is the fundamental solution U
+
+ align:start position:0%
+this is the fundamental solution U
+ 
+
+ align:start position:0%
+this is the fundamental solution U
+fundamental maybe I should
+
+ align:start position:0%
+fundamental maybe I should
+ 
+
+ align:start position:0%
+fundamental maybe I should
+say because it's such an important case
+
+ align:start position:0%
+say because it's such an important case
+ 
+
+ align:start position:0%
+say because it's such an important case
+is turns out to be well it's not obvious
+
+ align:start position:0%
+is turns out to be well it's not obvious
+ 
+
+ align:start position:0%
+is turns out to be well it's not obvious
+what that integral
+
+ align:start position:0%
+what that integral
+ 
+
+ align:start position:0%
+what that integral
+is and by the way
+
+ align:start position:0%
+is and by the way
+ 
+
+ align:start position:0%
+is and by the way
+normally
+
+ align:start position:0%
+normally
+ 
+
+ align:start position:0%
+normally
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but let's see yeah
+
+ align:start position:0%
+but let's see yeah
+ 
+
+ align:start position:0%
+but let's see yeah
+uh yeah Norm normally
+
+ align:start position:0%
+uh yeah Norm normally
+ 
+
+ align:start position:0%
+uh yeah Norm normally
+it's we take a kind of to to get the
+
+ align:start position:0%
+it's we take a kind of to to get the
+ 
+
+ align:start position:0%
+it's we take a kind of to to get the
+answer that I'm going to write down we
+
+ align:start position:0%
+answer that I'm going to write down we
+ 
+
+ align:start position:0%
+answer that I'm going to write down we
+take a kind of uh end run on the
+
+ align:start position:0%
+take a kind of uh end run on the
+ 
+
+ align:start position:0%
+take a kind of uh end run on the
+integral and I'm going to take a serious
+
+ align:start position:0%
+integral and I'm going to take a serious
+ 
+
+ align:start position:0%
+integral and I'm going to take a serious
+end run and write down the answer
+
+ align:start position:0%
+end run and write down the answer
+ 
+
+ align:start position:0%
+end run and write down the answer
+exactly uh
+
+ align:start position:0%
+exactly uh
+ 
+
+ align:start position:0%
+exactly uh
+there's here here's the key part of the
+
+ align:start position:0%
+there's here here's the key part of the
+ 
+
+ align:start position:0%
+there's here here's the key part of the
+answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer the solution which starts from a
+
+ align:start position:0%
+answer the solution which starts from a
+ 
+
+ align:start position:0%
+answer the solution which starts from a
+Delta function spreads of
+
+ align:start position:0%
+Delta function spreads of
+ 
+
+ align:start position:0%
+Delta function spreads of
+course and the shape as it spreads is a
+
+ align:start position:0%
+course and the shape as it spreads is a
+ 
+
+ align:start position:0%
+course and the shape as it spreads is a
+bell it's the famous bell-shaped
+
+ align:start position:0%
+bell it's the famous bell-shaped
+ 
+
+ align:start position:0%
+bell it's the famous bell-shaped
+gaussian
+
+ align:start position:0%
+gaussian
+ 
+
+ align:start position:0%
+gaussian
+distribution of e to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus so is it eus x^2 I
+
+ align:start position:0%
+minus so is it eus x^2 I
+ 
+
+ align:start position:0%
+minus so is it eus x^2 I
+guess and then always here comes the
+
+ align:start position:0%
+guess and then always here comes the
+ 
+
+ align:start position:0%
+guess and then always here comes the
+that scaler tells us the width of the
+
+ align:start position:0%
+that scaler tells us the width of the
+ 
+
+ align:start position:0%
+that scaler tells us the width of the
+Bell what how far has it spread at time
+
+ align:start position:0%
+Bell what how far has it spread at time
+ 
+
+ align:start position:0%
+Bell what how far has it spread at time
+T and what goes there is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4T that that's the key observation and
+
+ align:start position:0%
+4T that that's the key observation and
+ 
+
+ align:start position:0%
+4T that that's the key observation and
+notice how X2 and T are are coming in
+
+ align:start position:0%
+notice how X2 and T are are coming in
+ 
+
+ align:start position:0%
+notice how X2 and T are are coming in
+it's that ratio x^2 to T that's
+
+ align:start position:0%
+it's that ratio x^2 to T that's
+ 
+
+ align:start position:0%
+it's that ratio x^2 to T that's
+crucial that that's that's the the the
+
+ align:start position:0%
+crucial that that's that's the the the
+ 
+
+ align:start position:0%
+crucial that that's that's the the the
+parameter here and uh and we and of
+
+ align:start position:0%
+parameter here and uh and we and of
+ 
+
+ align:start position:0%
+parameter here and uh and we and of
+course we need to multiply by a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant and the why how do I know I
+
+ align:start position:0%
+constant and the why how do I know I
+ 
+
+ align:start position:0%
+constant and the why how do I know I
+need a constant because I because the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total the total heat is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conserved so the in other words the
+
+ align:start position:0%
+conserved so the in other words the
+ 
+
+ align:start position:0%
+conserved so the in other words the
+integral of the Delta function the
+
+ align:start position:0%
+integral of the Delta function the
+ 
+
+ align:start position:0%
+integral of the Delta function the
+original source of
+
+ align:start position:0%
+original source of
+ 
+
+ align:start position:0%
+original source of
+heat was one the integral from minus
+
+ align:start position:0%
+heat was one the integral from minus
+ 
+
+ align:start position:0%
+heat was one the integral from minus
+infinity to Infinity of the Delta
+
+ align:start position:0%
+infinity to Infinity of the Delta
+ 
+
+ align:start position:0%
+infinity to Infinity of the Delta
+function which is all totally
+
+ align:start position:0%
+function which is all totally
+ 
+
+ align:start position:0%
+function which is all totally
+concentrated at one point is one so I
+
+ align:start position:0%
+concentrated at one point is one so I
+ 
+
+ align:start position:0%
+concentrated at one point is one so I
+need to put on whatever constant it
+
+ align:start position:0%
+need to put on whatever constant it
+ 
+
+ align:start position:0%
+need to put on whatever constant it
+takes so that the integral of this thing
+
+ align:start position:0%
+takes so that the integral of this thing
+ 
+
+ align:start position:0%
+takes so that the integral of this thing
+shall stay one for later times so and it
+
+ align:start position:0%
+shall stay one for later times so and it
+ 
+
+ align:start position:0%
+shall stay one for later times so and it
+this is a this is one integral from
+
+ align:start position:0%
+this is a this is one integral from
+ 
+
+ align:start position:0%
+this is a this is one integral from
+minus infinity to Infinity that we can
+
+ align:start position:0%
+minus infinity to Infinity that we can
+ 
+
+ align:start position:0%
+minus infinity to Infinity that we can
+do and it turns out to need 1 over the <
+
+ align:start position:0%
+do and it turns out to need 1 over the <
+ 
+
+ align:start position:0%
+do and it turns out to need 1 over the <
+TK of 4 Pi
+
+ align:start position:0%
+TK of 4 Pi
+ 
+
+ align:start position:0%
+TK of 4 Pi
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+a that solves the heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation well it's not a lot of fun to
+
+ align:start position:0%
+equation well it's not a lot of fun to
+ 
+
+ align:start position:0%
+equation well it's not a lot of fun to
+plug that into the heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation but it's possible Right the X
+
+ align:start position:0%
+equation but it's possible Right the X
+ 
+
+ align:start position:0%
+equation but it's possible Right the X
+derivative the time derivative is going
+
+ align:start position:0%
+derivative the time derivative is going
+ 
+
+ align:start position:0%
+derivative the time derivative is going
+to be messy it'll have two terms the X
+
+ align:start position:0%
+to be messy it'll have two terms the X
+ 
+
+ align:start position:0%
+to be messy it'll have two terms the X
+derivative will have two terms and
+
+ align:start position:0%
+derivative will have two terms and
+ 
+
+ align:start position:0%
+derivative will have two terms and
+they'll agree yeah
+
+ align:start position:0%
+they'll agree yeah
+ 
+
+ align:start position:0%
+they'll agree yeah
+yeah and the notes will give one way to
+
+ align:start position:0%
+yeah and the notes will give one way to
+ 
+
+ align:start position:0%
+yeah and the notes will give one way to
+do the integral and get that answer
+
+ align:start position:0%
+do the integral and get that answer
+ 
+
+ align:start position:0%
+do the integral and get that answer
+right right you see that that integral
+
+ align:start position:0%
+right right you see that that integral
+ 
+
+ align:start position:0%
+right right you see that that integral
+it's integrals with e minus
+
+ align:start position:0%
+it's integrals with e minus
+ 
+
+ align:start position:0%
+it's integrals with e minus
+k^2 in them are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh are usually are are impossible on a
+
+ align:start position:0%
+uh are usually are are impossible on a
+ 
+
+ align:start position:0%
+uh are usually are are impossible on a
+finite
+
+ align:start position:0%
+finite
+ 
+
+ align:start position:0%
+finite
+interval but here we're going all the
+
+ align:start position:0%
+interval but here we're going all the
+ 
+
+ align:start position:0%
+interval but here we're going all the
+way from minus infinity to Infinity
+
+ align:start position:0%
+way from minus infinity to Infinity
+ 
+
+ align:start position:0%
+way from minus infinity to Infinity
+which you might think makes the problem
+
+ align:start position:0%
+which you might think makes the problem
+ 
+
+ align:start position:0%
+which you might think makes the problem
+harder but actually it makes it a great
+
+ align:start position:0%
+harder but actually it makes it a great
+ 
+
+ align:start position:0%
+harder but actually it makes it a great
+deal easier and and we get we can get an
+
+ align:start position:0%
+deal easier and and we get we can get an
+ 
+
+ align:start position:0%
+deal easier and and we get we can get an
+explicit answer a beautiful
+
+ align:start position:0%
+explicit answer a beautiful
+ 
+
+ align:start position:0%
+explicit answer a beautiful
+answer so we learn that the solution to
+
+ align:start position:0%
+answer so we learn that the solution to
+ 
+
+ align:start position:0%
+answer so we learn that the solution to
+the heat
+
+ align:start position:0%
+the heat
+ 
+
+ align:start position:0%
+the heat
+equation is coming from a point source
+
+ align:start position:0%
+equation is coming from a point source
+ 
+
+ align:start position:0%
+equation is coming from a point source
+is a bell-shaped gaussian curve that
+
+ align:start position:0%
+is a bell-shaped gaussian curve that
+ 
+
+ align:start position:0%
+is a bell-shaped gaussian curve that
+gets wider and wider as T increases
+
+ align:start position:0%
+gets wider and wider as T increases
+ 
+
+ align:start position:0%
+gets wider and wider as T increases
+and but I guess you would want to look
+
+ align:start position:0%
+and but I guess you would want to look
+ 
+
+ align:start position:0%
+and but I guess you would want to look
+to see well what happens if t comes down
+
+ align:start position:0%
+to see well what happens if t comes down
+ 
+
+ align:start position:0%
+to see well what happens if t comes down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+zero does that really
+
+ align:start position:0%
+zero does that really
+ 
+
+ align:start position:0%
+zero does that really
+approximate should I'm meant to say does
+
+ align:start position:0%
+approximate should I'm meant to say does
+ 
+
+ align:start position:0%
+approximate should I'm meant to say does
+it really converge
+
+ align:start position:0%
+it really converge
+ 
+
+ align:start position:0%
+it really converge
+to this should as T goes to zero this
+
+ align:start position:0%
+to this should as T goes to zero this
+ 
+
+ align:start position:0%
+to this should as T goes to zero this
+should go to the Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and in some way it does in some
+
+ align:start position:0%
+function and in some way it does in some
+ 
+
+ align:start position:0%
+function and in some way it does in some
+way it does it's a it's wonderful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Delta
+
+ align:start position:0%
+the Delta
+ 
+
+ align:start position:0%
+the Delta
+function of course is zero away from the
+
+ align:start position:0%
+function of course is zero away from the
+ 
+
+ align:start position:0%
+function of course is zero away from the
+origin so why does this approach zero
+
+ align:start position:0%
+origin so why does this approach zero
+ 
+
+ align:start position:0%
+origin so why does this approach zero
+away from the origin suppose X is one
+
+ align:start position:0%
+away from the origin suppose X is one
+ 
+
+ align:start position:0%
+away from the origin suppose X is one
+suppose X is one
+
+ align:start position:0%
+suppose X is one
+ 
+
+ align:start position:0%
+suppose X is one
+then do you see this thing going to zero
+
+ align:start position:0%
+then do you see this thing going to zero
+ 
+
+ align:start position:0%
+then do you see this thing going to zero
+as T goes to zero look look what's
+
+ align:start position:0%
+as T goes to zero look look what's
+ 
+
+ align:start position:0%
+as T goes to zero look look what's
+happening as T goes to zero this part is
+
+ align:start position:0%
+happening as T goes to zero this part is
+ 
+
+ align:start position:0%
+happening as T goes to zero this part is
+blowing up but kind of weakly that's not
+
+ align:start position:0%
+blowing up but kind of weakly that's not
+ 
+
+ align:start position:0%
+blowing up but kind of weakly that's not
+a disastrous
+
+ align:start position:0%
+a disastrous
+ 
+
+ align:start position:0%
+a disastrous
+blowup compared to this e to the minus
+
+ align:start position:0%
+blowup compared to this e to the minus
+ 
+
+ align:start position:0%
+blowup compared to this e to the minus
+let's say 1 over 4T as T goes to zero
+
+ align:start position:0%
+let's say 1 over 4T as T goes to zero
+ 
+
+ align:start position:0%
+let's say 1 over 4T as T goes to zero
+that's e to the to a very negative
+
+ align:start position:0%
+that's e to the to a very negative
+ 
+
+ align:start position:0%
+that's e to the to a very negative
+exponent that's going to zero very fast
+
+ align:start position:0%
+exponent that's going to zero very fast
+ 
+
+ align:start position:0%
+exponent that's going to zero very fast
+much faster than this is going to zero
+
+ align:start position:0%
+much faster than this is going to zero
+ 
+
+ align:start position:0%
+much faster than this is going to zero
+so if you like to think of lal's rule or
+
+ align:start position:0%
+so if you like to think of lal's rule or
+ 
+
+ align:start position:0%
+so if you like to think of lal's rule or
+Ratio or something this this quantity is
+
+ align:start position:0%
+Ratio or something this this quantity is
+ 
+
+ align:start position:0%
+Ratio or something this this quantity is
+going to zero way faster than this one
+
+ align:start position:0%
+going to zero way faster than this one
+ 
+
+ align:start position:0%
+going to zero way faster than this one
+is and the result is zero except at the
+
+ align:start position:0%
+is and the result is zero except at the
+ 
+
+ align:start position:0%
+is and the result is zero except at the
+one point x equals 0 where this is
+
+ align:start position:0%
+one point x equals 0 where this is
+ 
+
+ align:start position:0%
+one point x equals 0 where this is
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+the the fact that the total amount of
+
+ align:start position:0%
+the the fact that the total amount of
+ 
+
+ align:start position:0%
+the the fact that the total amount of
+heat stays at one tells us that the
+
+ align:start position:0%
+heat stays at one tells us that the
+ 
+
+ align:start position:0%
+heat stays at one tells us that the
+Delta function is the limit there okay
+
+ align:start position:0%
+Delta function is the limit there okay
+ 
+
+ align:start position:0%
+Delta function is the limit there okay
+so that's uh
+
+ align:start position:0%
+so that's uh
+ 
+
+ align:start position:0%
+so that's uh
+today was the heat
+
+ align:start position:0%
+today was the heat
+ 
+
+ align:start position:0%
+today was the heat
+equation ous
+
+ align:start position:0%
+equation ous
+ 
+
+ align:start position:0%
+equation ous
+case with these explicit answers and uh
+
+ align:start position:0%
+case with these explicit answers and uh
+ 
+
+ align:start position:0%
+case with these explicit answers and uh
+and then next next time is tomorrow I
+
+ align:start position:0%
+and then next next time is tomorrow I
+ 
+
+ align:start position:0%
+and then next next time is tomorrow I
+guess is the heat equation finite
+
+ align:start position:0%
+guess is the heat equation finite
+ 
+
+ align:start position:0%
+guess is the heat equation finite
+differences and again we'll have several
+
+ align:start position:0%
+differences and again we'll have several
+ 
+
+ align:start position:0%
+differences and again we'll have several
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+methods and to compare them would be
+
+ align:start position:0%
+methods and to compare them would be
+ 
+
+ align:start position:0%
+methods and to compare them would be
+terrific so maybe that please think
+
+ align:start position:0%
+terrific so maybe that please think
+ 
+
+ align:start position:0%
+terrific so maybe that please think
+about that comparison with the heat
+
+ align:start position:0%
+about that comparison with the heat
+ 
+
+ align:start position:0%
+about that comparison with the heat
+equation and or for what I was saying at
+
+ align:start position:0%
+equation and or for what I was saying at
+ 
+
+ align:start position:0%
+equation and or for what I was saying at
+the beginning of class the a deeper look
+
+ align:start position:0%
+the beginning of class the a deeper look
+ 
+
+ align:start position:0%
+the beginning of class the a deeper look
+at the comparison for the wave
+
+ align:start position:0%
+at the comparison for the wave
+ 
+
+ align:start position:0%
+at the comparison for the wave
+equation okay so see you tomorrow for
+
+ align:start position:0%
+equation okay so see you tomorrow for
+ 
+
+ align:start position:0%
+equation okay so see you tomorrow for
+difference equations for the for this
+
+ align:start position:0%
+difference equations for the for this
+ 
+
+ align:start position:0%
+difference equations for the for this
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks
\ No newline at end of file
diff --git a/ZaSMm2xvatw.txt b/ZaSMm2xvatw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2477b90f70359531980930ea61dea5598e5f3bb2
--- /dev/null
+++ b/ZaSMm2xvatw.txt
@@ -0,0 +1,14867 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right you guys ready for
+
+ align:start position:0%
+ocw.mit.edu all right you guys ready for
+ 
+
+ align:start position:0%
+ocw.mit.edu all right you guys ready for
+some more hardness
+
+ align:start position:0%
+some more hardness
+ 
+
+ align:start position:0%
+some more hardness
+proofs Let's Do It um so today we start
+
+ align:start position:0%
+proofs Let's Do It um so today we start
+ 
+
+ align:start position:0%
+proofs Let's Do It um so today we start
+uh the universe of three
+
+ align:start position:0%
+uh the universe of three
+ 
+
+ align:start position:0%
+uh the universe of three
+partition and in general we're going to
+
+ align:start position:0%
+partition and in general we're going to
+ 
+
+ align:start position:0%
+partition and in general we're going to
+see uh
+
+ align:start position:0%
+see uh
+ 
+
+ align:start position:0%
+see uh
+today two plus
+
+ align:start position:0%
+today two plus
+ 
+
+ align:start position:0%
+today two plus
+problems uh which are useful for dealing
+
+ align:start position:0%
+problems uh which are useful for dealing
+ 
+
+ align:start position:0%
+problems uh which are useful for dealing
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers uh
+
+ align:start position:0%
+numbers uh
+ 
+
+ align:start position:0%
+numbers uh
+for reducing
+
+ align:start position:0%
+for reducing
+ 
+
+ align:start position:0%
+for reducing
+to number problems numbers
+
+ align:start position:0%
+to number problems numbers
+ 
+
+ align:start position:0%
+to number problems numbers
+here um are going to be
+
+ align:start position:0%
+here um are going to be
+ 
+
+ align:start position:0%
+here um are going to be
+integers for the most
+
+ align:start position:0%
+integers for the most
+ 
+
+ align:start position:0%
+integers for the most
+part usually in complexity it's a lot
+
+ align:start position:0%
+part usually in complexity it's a lot
+ 
+
+ align:start position:0%
+part usually in complexity it's a lot
+easier to think of all your numbers
+
+ align:start position:0%
+easier to think of all your numbers
+ 
+
+ align:start position:0%
+easier to think of all your numbers
+being integers if they're not integers
+
+ align:start position:0%
+being integers if they're not integers
+ 
+
+ align:start position:0%
+being integers if they're not integers
+use fixed point or rationals and then
+
+ align:start position:0%
+use fixed point or rationals and then
+ 
+
+ align:start position:0%
+use fixed point or rationals and then
+they're basically integers um so we're
+
+ align:start position:0%
+they're basically integers um so we're
+ 
+
+ align:start position:0%
+they're basically integers um so we're
+going to talk my favorite is three
+
+ align:start position:0%
+going to talk my favorite is three
+ 
+
+ align:start position:0%
+going to talk my favorite is three
+partition and that will be pretty much
+
+ align:start position:0%
+partition and that will be pretty much
+ 
+
+ align:start position:0%
+partition and that will be pretty much
+all the proofs we'll do in the number
+
+ align:start position:0%
+all the proofs we'll do in the number
+ 
+
+ align:start position:0%
+all the proofs we'll do in the number
+context will be uh a reduction from
+
+ align:start position:0%
+context will be uh a reduction from
+ 
+
+ align:start position:0%
+context will be uh a reduction from
+three partition this is all about NP
+
+ align:start position:0%
+three partition this is all about NP
+ 
+
+ align:start position:0%
+three partition this is all about NP
+hardness I should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but before we get to three partition I'm
+
+ align:start position:0%
+but before we get to three partition I'm
+ 
+
+ align:start position:0%
+but before we get to three partition I'm
+going to talk about another problem
+
+ align:start position:0%
+going to talk about another problem
+ 
+
+ align:start position:0%
+going to talk about another problem
+which is called two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition so two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition first I'll just have to Define
+
+ align:start position:0%
+partition first I'll just have to Define
+ 
+
+ align:start position:0%
+partition first I'll just have to Define
+all these problems which will take a
+
+ align:start position:0%
+all these problems which will take a
+ 
+
+ align:start position:0%
+all these problems which will take a
+little while then we'll get to all the
+
+ align:start position:0%
+little while then we'll get to all the
+ 
+
+ align:start position:0%
+little while then we'll get to all the
+fun reductions so in two partition
+
+ align:start position:0%
+fun reductions so in two partition
+ 
+
+ align:start position:0%
+fun reductions so in two partition
+you're given n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers uh we'll call this set of them
+
+ align:start position:0%
+integers uh we'll call this set of them
+ 
+
+ align:start position:0%
+integers uh we'll call this set of them
+capital A and we'll call the integers
+
+ align:start position:0%
+capital A and we'll call the integers
+ 
+
+ align:start position:0%
+capital A and we'll call the integers
+themselves little a sub I I from 1 to n
+
+ align:start position:0%
+themselves little a sub I I from 1 to n
+ 
+
+ align:start position:0%
+themselves little a sub I I from 1 to n
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+say and what we'd like to do is
+
+ align:start position:0%
+say and what we'd like to do is
+ 
+
+ align:start position:0%
+say and what we'd like to do is
+partition them into two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+groups uh let's say A1 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A2 equals a uh of equal
+
+ align:start position:0%
+A2 equals a uh of equal
+ 
+
+ align:start position:0%
+A2 equals a uh of equal
+sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want the sum of the integers in A1 to
+
+ align:start position:0%
+we want the sum of the integers in A1 to
+ 
+
+ align:start position:0%
+we want the sum of the integers in A1 to
+equal the sum of the integers in A2 uh
+
+ align:start position:0%
+equal the sum of the integers in A2 uh
+ 
+
+ align:start position:0%
+equal the sum of the integers in A2 uh
+and therefore they will equal 12 the
+
+ align:start position:0%
+and therefore they will equal 12 the
+ 
+
+ align:start position:0%
+and therefore they will equal 12 the
+total sum okay so we just want to decide
+
+ align:start position:0%
+total sum okay so we just want to decide
+ 
+
+ align:start position:0%
+total sum okay so we just want to decide
+binary choice for each number should It
+
+ align:start position:0%
+binary choice for each number should It
+ 
+
+ align:start position:0%
+binary choice for each number should It
+Go in A1 or A2 so this problem is NP
+
+ align:start position:0%
+Go in A1 or A2 so this problem is NP
+ 
+
+ align:start position:0%
+Go in A1 or A2 so this problem is NP
+hard and it's one of the original uh
+
+ align:start position:0%
+hard and it's one of the original uh
+ 
+
+ align:start position:0%
+hard and it's one of the original uh
+carp problems there's this famous paper
+
+ align:start position:0%
+carp problems there's this famous paper
+ 
+
+ align:start position:0%
+carp problems there's this famous paper
+by karp in 1972 that had before that
+
+ align:start position:0%
+by karp in 1972 that had before that
+ 
+
+ align:start position:0%
+by karp in 1972 that had before that
+there was a paper by cook that proved
+
+ align:start position:0%
+there was a paper by cook that proved
+ 
+
+ align:start position:0%
+there was a paper by cook that proved
+sat is MP complete and then karp wrote a
+
+ align:start position:0%
+sat is MP complete and then karp wrote a
+ 
+
+ align:start position:0%
+sat is MP complete and then karp wrote a
+paper with a zillion uh not literally
+
+ align:start position:0%
+paper with a zillion uh not literally
+ 
+
+ align:start position:0%
+paper with a zillion uh not literally
+but dozens of MP hardness proofs from
+
+ align:start position:0%
+but dozens of MP hardness proofs from
+ 
+
+ align:start position:0%
+but dozens of MP hardness proofs from
+sat to things like two partition I will
+
+ align:start position:0%
+sat to things like two partition I will
+ 
+
+ align:start position:0%
+sat to things like two partition I will
+not cover the proof here if you're
+
+ align:start position:0%
+not cover the proof here if you're
+ 
+
+ align:start position:0%
+not cover the proof here if you're
+interested in it read Gary and Johnson
+
+ align:start position:0%
+interested in it read Gary and Johnson
+ 
+
+ align:start position:0%
+interested in it read Gary and Johnson
+there's a nice coverage of it of this
+
+ align:start position:0%
+there's a nice coverage of it of this
+ 
+
+ align:start position:0%
+there's a nice coverage of it of this
+problem and all the problems we'll be
+
+ align:start position:0%
+problem and all the problems we'll be
+ 
+
+ align:start position:0%
+problem and all the problems we'll be
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+today okay uh as a sideline I'll mention
+
+ align:start position:0%
+today okay uh as a sideline I'll mention
+ 
+
+ align:start position:0%
+today okay uh as a sideline I'll mention
+there's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generalization
+
+ align:start position:0%
+generalization
+ 
+
+ align:start position:0%
+generalization
+of this problem so it's also NP hard any
+
+ align:start position:0%
+of this problem so it's also NP hard any
+ 
+
+ align:start position:0%
+of this problem so it's also NP hard any
+generalization it's going to be even
+
+ align:start position:0%
+generalization it's going to be even
+ 
+
+ align:start position:0%
+generalization it's going to be even
+harder uh but it's useful to know about
+
+ align:start position:0%
+harder uh but it's useful to know about
+ 
+
+ align:start position:0%
+harder uh but it's useful to know about
+it's called subset sum occasionally it's
+
+ align:start position:0%
+it's called subset sum occasionally it's
+ 
+
+ align:start position:0%
+it's called subset sum occasionally it's
+easier to think about subset sum instead
+
+ align:start position:0%
+easier to think about subset sum instead
+ 
+
+ align:start position:0%
+easier to think about subset sum instead
+of partition although it's a
+
+ align:start position:0%
+of partition although it's a
+ 
+
+ align:start position:0%
+of partition although it's a
+generalization so if you can reduce from
+
+ align:start position:0%
+generalization so if you can reduce from
+ 
+
+ align:start position:0%
+generalization so if you can reduce from
+subset sum you can also reduce from
+
+ align:start position:0%
+subset sum you can also reduce from
+ 
+
+ align:start position:0%
+subset sum you can also reduce from
+partition um and here uh the setup is
+
+ align:start position:0%
+partition um and here uh the setup is
+ 
+
+ align:start position:0%
+partition um and here uh the setup is
+similar you're
+
+ align:start position:0%
+similar you're
+ 
+
+ align:start position:0%
+similar you're
+given uh and integers again just like
+
+ align:start position:0%
+given uh and integers again just like
+ 
+
+ align:start position:0%
+given uh and integers again just like
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+and you're given a Target sum this is
+
+ align:start position:0%
+and you're given a Target sum this is
+ 
+
+ align:start position:0%
+and you're given a Target sum this is
+one other integer we'll call the target
+
+ align:start position:0%
+one other integer we'll call the target
+ 
+
+ align:start position:0%
+one other integer we'll call the target
+sum T I'll also call this
+
+ align:start position:0%
+sum T I'll also call this
+ 
+
+ align:start position:0%
+sum T I'll also call this
+t uh and what we'd like to do is find a
+
+ align:start position:0%
+t uh and what we'd like to do is find a
+ 
+
+ align:start position:0%
+t uh and what we'd like to do is find a
+subset s of a uh whose sum is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T okay this is a strict generalization
+
+ align:start position:0%
+T okay this is a strict generalization
+ 
+
+ align:start position:0%
+T okay this is a strict generalization
+here you're not given a number T but
+
+ align:start position:0%
+here you're not given a number T but
+ 
+
+ align:start position:0%
+here you're not given a number T but
+you're essentially choosing a subset
+
+ align:start position:0%
+you're essentially choosing a subset
+ 
+
+ align:start position:0%
+you're essentially choosing a subset
+A1 uh whose sum equals the sum of a over
+
+ align:start position:0%
+A1 uh whose sum equals the sum of a over
+ 
+
+ align:start position:0%
+A1 uh whose sum equals the sum of a over
+two so this is really just a particular
+
+ align:start position:0%
+two so this is really just a particular
+ 
+
+ align:start position:0%
+two so this is really just a particular
+choice of T this is the general case
+
+ align:start position:0%
+choice of T this is the general case
+ 
+
+ align:start position:0%
+choice of T this is the general case
+where you're given T so this is harder
+
+ align:start position:0%
+where you're given T so this is harder
+ 
+
+ align:start position:0%
+where you're given T so this is harder
+than that uh but it's worth knowing
+
+ align:start position:0%
+than that uh but it's worth knowing
+ 
+
+ align:start position:0%
+than that uh but it's worth knowing
+about in particular there's a problem
+
+ align:start position:0%
+about in particular there's a problem
+ 
+
+ align:start position:0%
+about in particular there's a problem
+set problem uh the problem set will be
+
+ align:start position:0%
+set problem uh the problem set will be
+ 
+
+ align:start position:0%
+set problem uh the problem set will be
+out in a couple of hours and it's a
+
+ align:start position:0%
+out in a couple of hours and it's a
+ 
+
+ align:start position:0%
+out in a couple of hours and it's a
+little easier to think about subset sum
+
+ align:start position:0%
+little easier to think about subset sum
+ 
+
+ align:start position:0%
+little easier to think about subset sum
+we think you don't have to
+
+ align:start position:0%
+we think you don't have to
+ 
+
+ align:start position:0%
+we think you don't have to
+but uh all right so let's go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three partition my favorite NP complete
+
+ align:start position:0%
+three partition my favorite NP complete
+ 
+
+ align:start position:0%
+three partition my favorite NP complete
+problem um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so start is the
+
+ align:start position:0%
+so start is the
+ 
+
+ align:start position:0%
+so start is the
+same given integers A1 up to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n uh we're not given a Target sum what
+
+ align:start position:0%
+n uh we're not given a Target sum what
+ 
+
+ align:start position:0%
+n uh we're not given a Target sum what
+we'd like to do is partition
+
+ align:start position:0%
+we'd like to do is partition
+ 
+
+ align:start position:0%
+we'd like to do is partition
+them partition that set a
+
+ align:start position:0%
+them partition that set a
+ 
+
+ align:start position:0%
+them partition that set a
+into how many pieces three three nope n
+
+ align:start position:0%
+into how many pieces three three nope n
+ 
+
+ align:start position:0%
+into how many pieces three three nope n
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three uh it's kind of like
+
+ align:start position:0%
+three uh it's kind of like
+ 
+
+ align:start position:0%
+three uh it's kind of like
+three not quite uh let's say sets uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A1 a n over 3 equals a I'm using a union
+
+ align:start position:0%
+A1 a n over 3 equals a I'm using a union
+ 
+
+ align:start position:0%
+A1 a n over 3 equals a I'm using a union
+with a DOT to indicate it's disjoint
+
+ align:start position:0%
+with a DOT to indicate it's disjoint
+ 
+
+ align:start position:0%
+with a DOT to indicate it's disjoint
+Union so these it's that's what a
+
+ align:start position:0%
+Union so these it's that's what a
+ 
+
+ align:start position:0%
+Union so these it's that's what a
+partition means that's redundant this is
+
+ align:start position:0%
+partition means that's redundant this is
+ 
+
+ align:start position:0%
+partition means that's redundant this is
+oldfashioned notation you probably
+
+ align:start position:0%
+oldfashioned notation you probably
+ 
+
+ align:start position:0%
+oldfashioned notation you probably
+haven't seen it but when I was growing
+
+ align:start position:0%
+haven't seen it but when I was growing
+ 
+
+ align:start position:0%
+haven't seen it but when I was growing
+up that was the notation of the day uh
+
+ align:start position:0%
+up that was the notation of the day uh
+ 
+
+ align:start position:0%
+up that was the notation of the day uh
+then we
+
+ align:start position:0%
+then we
+ 
+
+ align:start position:0%
+then we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+right to n over three sets cool yeah
+
+ align:start position:0%
+right to n over three sets cool yeah
+ 
+
+ align:start position:0%
+right to n over three sets cool yeah
+assume n is divisible by three otherwise
+
+ align:start position:0%
+assume n is divisible by three otherwise
+ 
+
+ align:start position:0%
+assume n is divisible by three otherwise
+the answer is
+
+ align:start position:0%
+the answer is
+ 
+
+ align:start position:0%
+the answer is
+no okay and then which is the easy case
+
+ align:start position:0%
+no okay and then which is the easy case
+ 
+
+ align:start position:0%
+no okay and then which is the easy case
+uh of equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum so we want the sum of each AI to be
+
+ align:start position:0%
+sum so we want the sum of each AI to be
+ 
+
+ align:start position:0%
+sum so we want the sum of each AI to be
+equal to T which is to the same thing
+
+ align:start position:0%
+equal to T which is to the same thing
+ 
+
+ align:start position:0%
+equal to T which is to the same thing
+which is going to be the sum of the A's
+
+ align:start position:0%
+which is going to be the sum of the A's
+ 
+
+ align:start position:0%
+which is going to be the sum of the A's
+divided by n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over3 okay if this problem were about
+
+ align:start position:0%
+over3 okay if this problem were about
+ 
+
+ align:start position:0%
+over3 okay if this problem were about
+partitioning to three sets it would not
+
+ align:start position:0%
+partitioning to three sets it would not
+ 
+
+ align:start position:0%
+partitioning to three sets it would not
+be very interesting uh it would be
+
+ align:start position:0%
+be very interesting uh it would be
+ 
+
+ align:start position:0%
+be very interesting uh it would be
+basically identical to two partition
+
+ align:start position:0%
+basically identical to two partition
+ 
+
+ align:start position:0%
+basically identical to two partition
+with n over3 sets things are quite a bit
+
+ align:start position:0%
+with n over3 sets things are quite a bit
+ 
+
+ align:start position:0%
+with n over3 sets things are quite a bit
+different and we will get to that
+
+ align:start position:0%
+different and we will get to that
+ 
+
+ align:start position:0%
+different and we will get to that
+difference in a moment uh but first let
+
+ align:start position:0%
+difference in a moment uh but first let
+ 
+
+ align:start position:0%
+difference in a moment uh but first let
+me tell you about some fun facts about
+
+ align:start position:0%
+me tell you about some fun facts about
+ 
+
+ align:start position:0%
+me tell you about some fun facts about
+three part partion uh so we're
+
+ align:start position:0%
+three part partion uh so we're
+ 
+
+ align:start position:0%
+three part partion uh so we're
+partitioning into n over3 sets so you
+
+ align:start position:0%
+partitioning into n over3 sets so you
+ 
+
+ align:start position:0%
+partitioning into n over3 sets so you
+would expect on average most of the sets
+
+ align:start position:0%
+would expect on average most of the sets
+ 
+
+ align:start position:0%
+would expect on average most of the sets
+will have size three uh in fact you can
+
+ align:start position:0%
+will have size three uh in fact you can
+ 
+
+ align:start position:0%
+will have size three uh in fact you can
+make all of the sets have size exactly
+
+ align:start position:0%
+make all of the sets have size exactly
+ 
+
+ align:start position:0%
+make all of the sets have size exactly
+three because if you look at the
+
+ align:start position:0%
+three because if you look at the
+ 
+
+ align:start position:0%
+three because if you look at the
+reduction for this problem uh you
+
+ align:start position:0%
+reduction for this problem uh you
+ 
+
+ align:start position:0%
+reduction for this problem uh you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+assume that each
+
+ align:start position:0%
+assume that each
+ 
+
+ align:start position:0%
+assume that each
+AI is uh between uh T over4 strictly
+
+ align:start position:0%
+AI is uh between uh T over4 strictly
+ 
+
+ align:start position:0%
+AI is uh between uh T over4 strictly
+between T over4 and T over2
+
+ align:start position:0%
+between T over4 and T over2
+ 
+
+ align:start position:0%
+between T over4 and T over2
+okay if you have if you're going to have
+
+ align:start position:0%
+okay if you have if you're going to have
+ 
+
+ align:start position:0%
+okay if you have if you're going to have
+a set of numbers that sum to exactly
+
+ align:start position:0%
+a set of numbers that sum to exactly
+ 
+
+ align:start position:0%
+a set of numbers that sum to exactly
+T um and each of them is strictly bigger
+
+ align:start position:0%
+T um and each of them is strictly bigger
+ 
+
+ align:start position:0%
+T um and each of them is strictly bigger
+than T over4 then that means you can't
+
+ align:start position:0%
+than T over4 then that means you can't
+ 
+
+ align:start position:0%
+than T over4 then that means you can't
+have four of them because you would sum
+
+ align:start position:0%
+have four of them because you would sum
+ 
+
+ align:start position:0%
+have four of them because you would sum
+to too much and they're strictly less
+
+ align:start position:0%
+to too much and they're strictly less
+ 
+
+ align:start position:0%
+to too much and they're strictly less
+than T over2 then you can't just have
+
+ align:start position:0%
+than T over2 then you can't just have
+ 
+
+ align:start position:0%
+than T over2 then you can't just have
+two of them and hope to get to T so you
+
+ align:start position:0%
+two of them and hope to get to T so you
+ 
+
+ align:start position:0%
+two of them and hope to get to T so you
+have to have exactly three in every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set you don't have to assume that and in
+
+ align:start position:0%
+set you don't have to assume that and in
+ 
+
+ align:start position:0%
+set you don't have to assume that and in
+some situations it's useful to just say
+
+ align:start position:0%
+some situations it's useful to just say
+ 
+
+ align:start position:0%
+some situations it's useful to just say
+well the AIS are some sets that sum to
+
+ align:start position:0%
+well the AIS are some sets that sum to
+ 
+
+ align:start position:0%
+well the AIS are some sets that sum to
+the right thing sometimes it's useful to
+
+ align:start position:0%
+the right thing sometimes it's useful to
+ 
+
+ align:start position:0%
+the right thing sometimes it's useful to
+assume that they are triples uh it's up
+
+ align:start position:0%
+assume that they are triples uh it's up
+ 
+
+ align:start position:0%
+assume that they are triples uh it's up
+to you what you consider that part of
+
+ align:start position:0%
+to you what you consider that part of
+ 
+
+ align:start position:0%
+to you what you consider that part of
+the problem statement to ask for the AI
+
+ align:start position:0%
+the problem statement to ask for the AI
+ 
+
+ align:start position:0%
+the problem statement to ask for the AI
+to have size three or not and it's
+
+ align:start position:0%
+to have size three or not and it's
+ 
+
+ align:start position:0%
+to have size three or not and it's
+useful to have both um in fact you can
+
+ align:start position:0%
+useful to have both um in fact you can
+ 
+
+ align:start position:0%
+useful to have both um in fact you can
+uh once you have this you can make all
+
+ align:start position:0%
+uh once you have this you can make all
+ 
+
+ align:start position:0%
+uh once you have this you can make all
+the AIS very very close to t
+
+ align:start position:0%
+the AIS very very close to t
+ 
+
+ align:start position:0%
+the AIS very very close to t
+over3 uh using a trick which we'll see a
+
+ align:start position:0%
+over3 uh using a trick which we'll see a
+ 
+
+ align:start position:0%
+over3 uh using a trick which we'll see a
+bunch of times today uh so let's say you
+
+ align:start position:0%
+bunch of times today uh so let's say you
+ 
+
+ align:start position:0%
+bunch of times today uh so let's say you
+could add I'll call it
+
+ align:start position:0%
+could add I'll call it
+ 
+
+ align:start position:0%
+could add I'll call it
+Infinity uh to each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AI uh in that case of course any
+
+ align:start position:0%
+AI uh in that case of course any
+ 
+
+ align:start position:0%
+AI uh in that case of course any
+solution that you had before is still a
+
+ align:start position:0%
+solution that you had before is still a
+ 
+
+ align:start position:0%
+solution that you had before is still a
+solution uh just think of T is infinity
+
+ align:start position:0%
+solution uh just think of T is infinity
+ 
+
+ align:start position:0%
+solution uh just think of T is infinity
+is a really large number something like
+
+ align:start position:0%
+is a really large number something like
+ 
+
+ align:start position:0%
+is a really large number something like
+uh n^ the 100 times
+
+ align:start position:0%
+uh n^ the 100 times
+ 
+
+ align:start position:0%
+uh n^ the 100 times
+maximum uh item in a something like that
+
+ align:start position:0%
+maximum uh item in a something like that
+ 
+
+ align:start position:0%
+maximum uh item in a something like that
+that's a really maybe to the 100 power
+
+ align:start position:0%
+that's a really maybe to the 100 power
+ 
+
+ align:start position:0%
+that's a really maybe to the 100 power
+if you want but really big number uh
+
+ align:start position:0%
+if you want but really big number uh
+ 
+
+ align:start position:0%
+if you want but really big number uh
+this will Preserve of all solutions
+
+ align:start position:0%
+this will Preserve of all solutions
+ 
+
+ align:start position:0%
+this will Preserve of all solutions
+because all solutions every set has size
+
+ align:start position:0%
+because all solutions every set has size
+ 
+
+ align:start position:0%
+because all solutions every set has size
+exactly three so if you add three times
+
+ align:start position:0%
+exactly three so if you add three times
+ 
+
+ align:start position:0%
+exactly three so if you add three times
+infinity they'll still have the same
+
+ align:start position:0%
+infinity they'll still have the same
+ 
+
+ align:start position:0%
+infinity they'll still have the same
+sums and when you do that then most all
+
+ align:start position:0%
+sums and when you do that then most all
+ 
+
+ align:start position:0%
+sums and when you do that then most all
+the AIS are basically equal to each
+
+ align:start position:0%
+the AIS are basically equal to each
+ 
+
+ align:start position:0%
+the AIS are basically equal to each
+other which means they're roughly equal
+
+ align:start position:0%
+other which means they're roughly equal
+ 
+
+ align:start position:0%
+other which means they're roughly equal
+to T over3 um the the big the leading
+
+ align:start position:0%
+to T over3 um the the big the leading
+ 
+
+ align:start position:0%
+to T over3 um the the big the leading
+term is the same for everybody and then
+
+ align:start position:0%
+term is the same for everybody and then
+ 
+
+ align:start position:0%
+term is the same for everybody and then
+there's this little noise which was the
+
+ align:start position:0%
+there's this little noise which was the
+ 
+
+ align:start position:0%
+there's this little noise which was the
+original integer uh that you're adding
+
+ align:start position:0%
+original integer uh that you're adding
+ 
+
+ align:start position:0%
+original integer uh that you're adding
+on to uh that
+
+ align:start position:0%
+on to uh that
+ 
+
+ align:start position:0%
+on to uh that
+Infinity anyway so then all the ads are
+
+ align:start position:0%
+Infinity anyway so then all the ads are
+ 
+
+ align:start position:0%
+Infinity anyway so then all the ads are
+roughly T over3
+
+ align:start position:0%
+roughly T over3
+ 
+
+ align:start position:0%
+roughly T over3
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+let me tell you about a couple related
+
+ align:start position:0%
+let me tell you about a couple related
+ 
+
+ align:start position:0%
+let me tell you about a couple related
+problems to three partition and then
+
+ align:start position:0%
+problems to three partition and then
+ 
+
+ align:start position:0%
+problems to three partition and then
+I'll tell you why why we're talking even
+
+ align:start position:0%
+I'll tell you why why we're talking even
+ 
+
+ align:start position:0%
+I'll tell you why why we're talking even
+bothering to talk about two problems um
+
+ align:start position:0%
+bothering to talk about two problems um
+ 
+
+ align:start position:0%
+bothering to talk about two problems um
+instead of just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so uh next problem has a funny name
+
+ align:start position:0%
+one so uh next problem has a funny name
+ 
+
+ align:start position:0%
+one so uh next problem has a funny name
+especially when you don't know what
+
+ align:start position:0%
+especially when you don't know what
+ 
+
+ align:start position:0%
+especially when you don't know what
+three-dimensional matching is but we
+
+ align:start position:0%
+three-dimensional matching is but we
+ 
+
+ align:start position:0%
+three-dimensional matching is but we
+will get to that second don't worry
+
+ align:start position:0%
+will get to that second don't worry
+ 
+
+ align:start position:0%
+will get to that second don't worry
+about the name for the moment uh this is
+
+ align:start position:0%
+about the name for the moment uh this is
+ 
+
+ align:start position:0%
+about the name for the moment uh this is
+a closely related problem it's really uh
+
+ align:start position:0%
+a closely related problem it's really uh
+ 
+
+ align:start position:0%
+a closely related problem it's really uh
+a specialization of three
+
+ align:start position:0%
+a specialization of three
+ 
+
+ align:start position:0%
+a specialization of three
+partition uh but Okay so we've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got in this case we're going to be given
+
+ align:start position:0%
+got in this case we're going to be given
+ 
+
+ align:start position:0%
+got in this case we're going to be given
+three sets of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers and what we'd like to do is I
+
+ align:start position:0%
+integers and what we'd like to do is I
+ 
+
+ align:start position:0%
+integers and what we'd like to do is I
+mean it's basically the same problem
+
+ align:start position:0%
+mean it's basically the same problem
+ 
+
+ align:start position:0%
+mean it's basically the same problem
+just think of taking the union of those
+
+ align:start position:0%
+just think of taking the union of those
+ 
+
+ align:start position:0%
+just think of taking the union of those
+sets but uh each of these sets that
+
+ align:start position:0%
+sets but uh each of these sets that
+ 
+
+ align:start position:0%
+sets but uh each of these sets that
+we're choosing the AIS should consist of
+
+ align:start position:0%
+we're choosing the AIS should consist of
+ 
+
+ align:start position:0%
+we're choosing the AIS should consist of
+one element from a one element from B
+
+ align:start position:0%
+one element from a one element from B
+ 
+
+ align:start position:0%
+one element from a one element from B
+one element from C so how did I
+
+ align:start position:0%
+one element from C so how did I
+ 
+
+ align:start position:0%
+one element from C so how did I
+formalize that say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition uh the
+
+ align:start position:0%
+partition uh the
+ 
+
+ align:start position:0%
+partition uh the
+union guess this a disjoint Union uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triples
+
+ align:start position:0%
+triples
+ 
+
+ align:start position:0%
+triples
+si
+
+ align:start position:0%
+si
+ 
+
+ align:start position:0%
+si
+uh and cross product
+
+ align:start position:0%
+uh and cross product
+ 
+
+ align:start position:0%
+uh and cross product
+ABC so you're choosing one from each of
+
+ align:start position:0%
+ABC so you're choosing one from each of
+ 
+
+ align:start position:0%
+ABC so you're choosing one from each of
+these guys in each SI and they should be
+
+ align:start position:0%
+these guys in each SI and they should be
+ 
+
+ align:start position:0%
+these guys in each SI and they should be
+of equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum and so the sum will be sum of a plus
+
+ align:start position:0%
+sum and so the sum will be sum of a plus
+ 
+
+ align:start position:0%
+sum and so the sum will be sum of a plus
+the sum of B plus sum of C /
+
+ align:start position:0%
+the sum of B plus sum of C /
+ 
+
+ align:start position:0%
+the sum of B plus sum of C /
+by n
+
+ align:start position:0%
+by n
+ 
+
+ align:start position:0%
+by n
+I think because there's three of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them cool okay so almost the same
+
+ align:start position:0%
+them cool okay so almost the same
+ 
+
+ align:start position:0%
+them cool okay so almost the same
+problem I just changed what n was by a
+
+ align:start position:0%
+problem I just changed what n was by a
+ 
+
+ align:start position:0%
+problem I just changed what n was by a
+factor of three that's why there's n
+
+ align:start position:0%
+factor of three that's why there's n
+ 
+
+ align:start position:0%
+factor of three that's why there's n
+over three here and an N here um but
+
+ align:start position:0%
+over three here and an N here um but
+ 
+
+ align:start position:0%
+over three here and an N here um but
+here we're specializing in a sense to
+
+ align:start position:0%
+here we're specializing in a sense to
+ 
+
+ align:start position:0%
+here we're specializing in a sense to
+say that uh we we can we're giving
+
+ align:start position:0%
+say that uh we we can we're giving
+ 
+
+ align:start position:0%
+say that uh we we can we're giving
+different types of numbers the red
+
+ align:start position:0%
+different types of numbers the red
+ 
+
+ align:start position:0%
+different types of numbers the red
+integers the green integers and the blue
+
+ align:start position:0%
+integers the green integers and the blue
+ 
+
+ align:start position:0%
+integers the green integers and the blue
+integers you have to choose one of each
+
+ align:start position:0%
+integers you have to choose one of each
+ 
+
+ align:start position:0%
+integers you have to choose one of each
+color okay uh for fun
+
+ align:start position:0%
+color okay uh for fun
+ 
+
+ align:start position:0%
+color okay uh for fun
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+let me show you why this problem is uh
+
+ align:start position:0%
+let me show you why this problem is uh
+ 
+
+ align:start position:0%
+let me show you why this problem is uh
+in some sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simpler this also gives you a useful
+
+ align:start position:0%
+simpler this also gives you a useful
+ 
+
+ align:start position:0%
+simpler this also gives you a useful
+kind of technique for playing with these
+
+ align:start position:0%
+kind of technique for playing with these
+ 
+
+ align:start position:0%
+kind of technique for playing with these
+number problems uh so I want to reduce
+
+ align:start position:0%
+number problems uh so I want to reduce
+ 
+
+ align:start position:0%
+number problems uh so I want to reduce
+from this numerical threedimensional
+
+ align:start position:0%
+from this numerical threedimensional
+ 
+
+ align:start position:0%
+from this numerical threedimensional
+matching problem which you might also
+
+ align:start position:0%
+matching problem which you might also
+ 
+
+ align:start position:0%
+matching problem which you might also
+call the ABC version of three part I and
+
+ align:start position:0%
+call the ABC version of three part I and
+ 
+
+ align:start position:0%
+call the ABC version of three part I and
+we reduce it to three partition so I'm
+
+ align:start position:0%
+we reduce it to three partition so I'm
+ 
+
+ align:start position:0%
+we reduce it to three partition so I'm
+given an instance these numbers and I
+
+ align:start position:0%
+given an instance these numbers and I
+ 
+
+ align:start position:0%
+given an instance these numbers and I
+want to somehow
+
+ align:start position:0%
+want to somehow
+ 
+
+ align:start position:0%
+want to somehow
+Force so the basic idea is to take these
+
+ align:start position:0%
+Force so the basic idea is to take these
+ 
+
+ align:start position:0%
+Force so the basic idea is to take these
+numbers and just throw them into one big
+
+ align:start position:0%
+numbers and just throw them into one big
+ 
+
+ align:start position:0%
+numbers and just throw them into one big
+set a prime uh but I want to force uh
+
+ align:start position:0%
+set a prime uh but I want to force uh
+ 
+
+ align:start position:0%
+set a prime uh but I want to force uh
+this ABC property that I choose one from
+
+ align:start position:0%
+this ABC property that I choose one from
+ 
+
+ align:start position:0%
+this ABC property that I choose one from
+each uh maybe any suggestions how yeah
+
+ align:start position:0%
+each uh maybe any suggestions how yeah
+ 
+
+ align:start position:0%
+each uh maybe any suggestions how yeah
+well I just have a question we Define
+
+ align:start position:0%
+well I just have a question we Define
+ 
+
+ align:start position:0%
+well I just have a question we Define
+these all as sets you can't have
+
+ align:start position:0%
+these all as sets you can't have
+ 
+
+ align:start position:0%
+these all as sets you can't have
+duplicates uh I didn't say the word set
+
+ align:start position:0%
+duplicates uh I didn't say the word set
+ 
+
+ align:start position:0%
+duplicates uh I didn't say the word set
+I actually meant
+
+ align:start position:0%
+I actually meant
+ 
+
+ align:start position:0%
+I actually meant
+multiset yeah so
+
+ align:start position:0%
+multiset yeah so
+ 
+
+ align:start position:0%
+multiset yeah so
+this is a multiset good
+
+ align:start position:0%
+this is a multiset good
+ 
+
+ align:start position:0%
+this is a multiset good
+question all of them are multisets so it
+
+ align:start position:0%
+question all of them are multisets so it
+ 
+
+ align:start position:0%
+question all of them are multisets so it
+makes the notion of destroy a little bit
+
+ align:start position:0%
+makes the notion of destroy a little bit
+ 
+
+ align:start position:0%
+makes the notion of destroy a little bit
+weird but you know what I
+
+ align:start position:0%
+weird but you know what I
+ 
+
+ align:start position:0%
+weird but you know what I
+mean what yeah uh could you add a really
+
+ align:start position:0%
+mean what yeah uh could you add a really
+ 
+
+ align:start position:0%
+mean what yeah uh could you add a really
+big number to all the these and twice
+
+ align:start position:0%
+big number to all the these and twice
+ 
+
+ align:start position:0%
+big number to all the these and twice
+that really big number to all the C's
+
+ align:start position:0%
+that really big number to all the C's
+ 
+
+ align:start position:0%
+that really big number to all the C's
+Okay add a I hadn't thought about this
+
+ align:start position:0%
+Okay add a I hadn't thought about this
+ 
+
+ align:start position:0%
+Okay add a I hadn't thought about this
+so add a really big number to all the
+
+ align:start position:0%
+so add a really big number to all the
+ 
+
+ align:start position:0%
+so add a really big number to all the
+B's and then twice that big number to
+
+ align:start position:0%
+B's and then twice that big number to
+ 
+
+ align:start position:0%
+B's and then twice that big number to
+all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C's and then the target sum would be
+
+ align:start position:0%
+C's and then the target sum would be
+ 
+
+ align:start position:0%
+C's and then the target sum would be
+three times the big number
+
+ align:start position:0%
+three times the big number
+ 
+
+ align:start position:0%
+three times the big number
+plus sorry said make it like three
+
+ align:start position:0%
+plus sorry said make it like three
+ 
+
+ align:start position:0%
+plus sorry said make it like three
+instead so you can't do like three
+
+ align:start position:0%
+instead so you can't do like three
+ 
+
+ align:start position:0%
+instead so you can't do like three
+things from yeah right so you don't want
+
+ align:start position:0%
+things from yeah right so you don't want
+ 
+
+ align:start position:0%
+things from yeah right so you don't want
+you don't want to take two two B's and
+
+ align:start position:0%
+you don't want to take two two B's and
+ 
+
+ align:start position:0%
+you don't want to take two two B's and
+then that looks like a c uh so maybe you
+
+ align:start position:0%
+then that looks like a c uh so maybe you
+ 
+
+ align:start position:0%
+then that looks like a c uh so maybe you
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+uh three times a big number here and six
+
+ align:start position:0%
+uh three times a big number here and six
+ 
+
+ align:start position:0%
+uh three times a big number here and six
+times a big or nine times a big number
+
+ align:start position:0%
+times a big or nine times a big number
+ 
+
+ align:start position:0%
+times a big or nine times a big number
+here something like that I think
+
+ align:start position:0%
+here something like that I think
+ 
+
+ align:start position:0%
+here something like that I think
+actually one times a big number and
+
+ align:start position:0%
+actually one times a big number and
+ 
+
+ align:start position:0%
+actually one times a big number and
+three times a big number would do it
+
+ align:start position:0%
+three times a big number would do it
+ 
+
+ align:start position:0%
+three times a big number would do it
+yeah cool so uh the way I did it in the
+
+ align:start position:0%
+yeah cool so uh the way I did it in the
+ 
+
+ align:start position:0%
+yeah cool so uh the way I did it in the
+notes was adding a small number but
+
+ align:start position:0%
+notes was adding a small number but
+ 
+
+ align:start position:0%
+notes was adding a small number but
+either way works let's let's do it with
+
+ align:start position:0%
+either way works let's let's do it with
+ 
+
+ align:start position:0%
+either way works let's let's do it with
+the big number cuz that's fun uh so
+
+ align:start position:0%
+the big number cuz that's fun uh so
+ 
+
+ align:start position:0%
+the big number cuz that's fun uh so
+we're going to take
+
+ align:start position:0%
+we're going to take
+ 
+
+ align:start position:0%
+we're going to take
+um okay so we will construct I'll call
+
+ align:start position:0%
+um okay so we will construct I'll call
+ 
+
+ align:start position:0%
+um okay so we will construct I'll call
+it a
+
+ align:start position:0%
+it a
+ 
+
+ align:start position:0%
+it a
+prime to consist
+
+ align:start position:0%
+prime to consist
+ 
+
+ align:start position:0%
+prime to consist
+of uh a for all little a in big a and
+
+ align:start position:0%
+of uh a for all little a in big a and
+ 
+
+ align:start position:0%
+of uh a for all little a in big a and
+then we'll say a Plus usually big number
+
+ align:start position:0%
+then we'll say a Plus usually big number
+ 
+
+ align:start position:0%
+then we'll say a Plus usually big number
+I write with a capital B but that's not
+
+ align:start position:0%
+I write with a capital B but that's not
+ 
+
+ align:start position:0%
+I write with a capital B but that's not
+very good because we already have a
+
+ align:start position:0%
+very good because we already have a
+ 
+
+ align:start position:0%
+very good because we already have a
+couple B so call it X
+
+ align:start position:0%
+couple B so call it X
+ 
+
+ align:start position:0%
+couple B so call it X
+uh or I should call it Infinity for
+
+ align:start position:0%
+uh or I should call it Infinity for
+ 
+
+ align:start position:0%
+uh or I should call it Infinity for
+consistency right so for each B and B I
+
+ align:start position:0%
+consistency right so for each B and B I
+ 
+
+ align:start position:0%
+consistency right so for each B and B I
+will add infinity to it and then
+
+ align:start position:0%
+will add infinity to it and then
+ 
+
+ align:start position:0%
+will add infinity to it and then
+C um is going to be let say three times
+
+ align:start position:0%
+C um is going to be let say three times
+ 
+
+ align:start position:0%
+C um is going to be let say three times
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in let's do four times infinity it makes
+
+ align:start position:0%
+in let's do four times infinity it makes
+ 
+
+ align:start position:0%
+in let's do four times infinity it makes
+me feel a little safer somehow because
+
+ align:start position:0%
+me feel a little safer somehow because
+ 
+
+ align:start position:0%
+me feel a little safer somehow because
+but we're constructing a set of size
+
+ align:start position:0%
+but we're constructing a set of size
+ 
+
+ align:start position:0%
+but we're constructing a set of size
+three so if you take three of these I
+
+ align:start position:0%
+three so if you take three of these I
+ 
+
+ align:start position:0%
+three so if you take three of these I
+wor that looks like a c that's not
+
+ align:start position:0%
+wor that looks like a c that's not
+ 
+
+ align:start position:0%
+wor that looks like a c that's not
+enough but we'll be
+
+ align:start position:0%
+enough but we'll be
+ 
+
+ align:start position:0%
+enough but we'll be
+safe why not we can choose pretty big
+
+ align:start position:0%
+safe why not we can choose pretty big
+ 
+
+ align:start position:0%
+safe why not we can choose pretty big
+numbers here uh so
+
+ align:start position:0%
+numbers here uh so
+ 
+
+ align:start position:0%
+numbers here uh so
+happy
+
+ align:start position:0%
+happy
+ 
+
+ align:start position:0%
+happy
+no you might be able to do multiple A's
+
+ align:start position:0%
+no you might be able to do multiple A's
+ 
+
+ align:start position:0%
+no you might be able to do multiple A's
+in a single set um if they're
+
+ align:start position:0%
+in a single set um if they're
+ 
+
+ align:start position:0%
+in a single set um if they're
+sufficiently small because they're
+
+ align:start position:0%
+sufficiently small because they're
+ 
+
+ align:start position:0%
+sufficiently small because they're
+not yeah okay okay A's are a problem you
+
+ align:start position:0%
+not yeah okay okay A's are a problem you
+ 
+
+ align:start position:0%
+not yeah okay okay A's are a problem you
+could maybe do more than three total so
+
+ align:start position:0%
+could maybe do more than three total so
+ 
+
+ align:start position:0%
+could maybe do more than three total so
+let's do one
+
+ align:start position:0%
+let's do one
+ 
+
+ align:start position:0%
+let's do one
+Infinity then let me get a proper
+
+ align:start position:0%
+Infinity then let me get a proper
+ 
+
+ align:start position:0%
+Infinity then let me get a proper
+eraser good thing we have Sarah here to
+
+ align:start position:0%
+eraser good thing we have Sarah here to
+ 
+
+ align:start position:0%
+eraser good thing we have Sarah here to
+correct our
+
+ align:start position:0%
+correct our
+ 
+
+ align:start position:0%
+correct our
+proofs um 3
+
+ align:start position:0%
+proofs um 3
+ 
+
+ align:start position:0%
+proofs um 3
+Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9 six would be bad because then two of
+
+ align:start position:0%
+9 six would be bad because then two of
+ 
+
+ align:start position:0%
+9 six would be bad because then two of
+these would be one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those right so uh this means the new
+
+ align:start position:0%
+those right so uh this means the new
+ 
+
+ align:start position:0%
+those right so uh this means the new
+Target sum should be uh the old Target
+
+ align:start position:0%
+Target sum should be uh the old Target
+ 
+
+ align:start position:0%
+Target sum should be uh the old Target
+sum which was the sum of these divided
+
+ align:start position:0%
+sum which was the sum of these divided
+ 
+
+ align:start position:0%
+sum which was the sum of these divided
+by n Plus
+
+ align:start position:0%
+by n Plus
+ 
+
+ align:start position:0%
+by n Plus
+plus 13
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity infinity a function of NS uh
+
+ align:start position:0%
+infinity infinity a function of NS uh
+ 
+
+ align:start position:0%
+infinity infinity a function of NS uh
+infinity I should Define let's make it
+
+ align:start position:0%
+infinity I should Define let's make it
+ 
+
+ align:start position:0%
+infinity I should Define let's make it
+uh I think just like 10 times Max of a
+
+ align:start position:0%
+uh I think just like 10 times Max of a
+ 
+
+ align:start position:0%
+uh I think just like 10 times Max of a
+how to do
+
+ align:start position:0%
+how to do
+ 
+
+ align:start position:0%
+how to do
+it you you could be it as a function of
+
+ align:start position:0%
+it you you could be it as a function of
+ 
+
+ align:start position:0%
+it you you could be it as a function of
+N I don't think that's necessary here
+
+ align:start position:0%
+N I don't think that's necessary here
+ 
+
+ align:start position:0%
+N I don't think that's necessary here
+because all of our sets are of size
+
+ align:start position:0%
+because all of our sets are of size
+ 
+
+ align:start position:0%
+because all of our sets are of size
+three but if you're doing something like
+
+ align:start position:0%
+three but if you're doing something like
+ 
+
+ align:start position:0%
+three but if you're doing something like
+this for two partition you'd want to
+
+ align:start position:0%
+this for two partition you'd want to
+ 
+
+ align:start position:0%
+this for two partition you'd want to
+multiply by n or n squ this is a common
+
+ align:start position:0%
+multiply by n or n squ this is a common
+ 
+
+ align:start position:0%
+multiply by n or n squ this is a common
+trick uh to do this kind of scaling or
+
+ align:start position:0%
+trick uh to do this kind of scaling or
+ 
+
+ align:start position:0%
+trick uh to do this kind of scaling or
+offsets or things like that uh instead
+
+ align:start position:0%
+offsets or things like that uh instead
+ 
+
+ align:start position:0%
+offsets or things like that uh instead
+of infinity here you could write Epsilon
+
+ align:start position:0%
+of infinity here you could write Epsilon
+ 
+
+ align:start position:0%
+of infinity here you could write Epsilon
+where Epsilon is much smaller than one I
+
+ align:start position:0%
+where Epsilon is much smaller than one I
+ 
+
+ align:start position:0%
+where Epsilon is much smaller than one I
+think that would also work and that's
+
+ align:start position:0%
+think that would also work and that's
+ 
+
+ align:start position:0%
+think that would also work and that's
+what's done make it the max of the um a
+
+ align:start position:0%
+what's done make it the max of the um a
+ 
+
+ align:start position:0%
+what's done make it the max of the um a
+as opposed to a prime whoops uh this
+
+ align:start position:0%
+as opposed to a prime whoops uh this
+ 
+
+ align:start position:0%
+as opposed to a prime whoops uh this
+should probably be Max of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ABC uh yeah you can't make it Max of a
+
+ align:start position:0%
+ABC uh yeah you can't make it Max of a
+ 
+
+ align:start position:0%
+ABC uh yeah you can't make it Max of a
+prime that would be cyclic then Infinity
+
+ align:start position:0%
+prime that would be cyclic then Infinity
+ 
+
+ align:start position:0%
+prime that would be cyclic then Infinity
+would actually be infinite
+
+ align:start position:0%
+would actually be infinite
+ 
+
+ align:start position:0%
+would actually be infinite
+yeah good so I think that works there
+
+ align:start position:0%
+yeah good so I think that works there
+ 
+
+ align:start position:0%
+yeah good so I think that works there
+are things to check here obviously we
+
+ align:start position:0%
+are things to check here obviously we
+ 
+
+ align:start position:0%
+are things to check here obviously we
+need to check that uh whenever we have a
+
+ align:start position:0%
+need to check that uh whenever we have a
+ 
+
+ align:start position:0%
+need to check that uh whenever we have a
+solution to the original instance we
+
+ align:start position:0%
+solution to the original instance we
+ 
+
+ align:start position:0%
+solution to the original instance we
+have a solution to this instance that's
+
+ align:start position:0%
+have a solution to this instance that's
+ 
+
+ align:start position:0%
+have a solution to this instance that's
+pretty clear you just take the same
+
+ align:start position:0%
+pretty clear you just take the same
+ 
+
+ align:start position:0%
+pretty clear you just take the same
+choices of the AI bis and CIS uh and the
+
+ align:start position:0%
+choices of the AI bis and CIS uh and the
+ 
+
+ align:start position:0%
+choices of the AI bis and CIS uh and the
+Infinities will always add up to 13 uh
+
+ align:start position:0%
+Infinities will always add up to 13 uh
+ 
+
+ align:start position:0%
+Infinities will always add up to 13 uh
+the tricky part is to show that if you
+
+ align:start position:0%
+the tricky part is to show that if you
+ 
+
+ align:start position:0%
+the tricky part is to show that if you
+have a solution to this three partition
+
+ align:start position:0%
+have a solution to this three partition
+ 
+
+ align:start position:0%
+have a solution to this three partition
+instance you can convert that back into
+
+ align:start position:0%
+instance you can convert that back into
+ 
+
+ align:start position:0%
+instance you can convert that back into
+a solution to the numerical
+
+ align:start position:0%
+a solution to the numerical
+ 
+
+ align:start position:0%
+a solution to the numerical
+threedimensional matching instance and
+
+ align:start position:0%
+threedimensional matching instance and
+ 
+
+ align:start position:0%
+threedimensional matching instance and
+that's where you essentially want show
+
+ align:start position:0%
+that's where you essentially want show
+ 
+
+ align:start position:0%
+that's where you essentially want show
+that the Infinities can be treated
+
+ align:start position:0%
+that the Infinities can be treated
+ 
+
+ align:start position:0%
+that the Infinities can be treated
+algebraically because they're so huge
+
+ align:start position:0%
+algebraically because they're so huge
+ 
+
+ align:start position:0%
+algebraically because they're so huge
+you can never construct an Infinity in
+
+ align:start position:0%
+you can never construct an Infinity in
+ 
+
+ align:start position:0%
+you can never construct an Infinity in
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+way uh so but I'll leave that as an
+
+ align:start position:0%
+way uh so but I'll leave that as an
+ 
+
+ align:start position:0%
+way uh so but I'll leave that as an
+exercise to actually prove because we're
+
+ align:start position:0%
+exercise to actually prove because we're
+ 
+
+ align:start position:0%
+exercise to actually prove because we're
+not really going to use this problem too
+
+ align:start position:0%
+not really going to use this problem too
+ 
+
+ align:start position:0%
+not really going to use this problem too
+much you're welcome to maybe on problem
+
+ align:start position:0%
+much you're welcome to maybe on problem
+ 
+
+ align:start position:0%
+much you're welcome to maybe on problem
+sets maybe in open problems it would be
+
+ align:start position:0%
+sets maybe in open problems it would be
+ 
+
+ align:start position:0%
+sets maybe in open problems it would be
+good but uh most of the time I would say
+
+ align:start position:0%
+good but uh most of the time I would say
+ 
+
+ align:start position:0%
+good but uh most of the time I would say
+we use three partition I want you to
+
+ align:start position:0%
+we use three partition I want you to
+ 
+
+ align:start position:0%
+we use three partition I want you to
+know about this in particular because
+
+ align:start position:0%
+know about this in particular because
+ 
+
+ align:start position:0%
+know about this in particular because
+it's related to another problem which is
+
+ align:start position:0%
+it's related to another problem which is
+ 
+
+ align:start position:0%
+it's related to another problem which is
+called threedimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes is the assumption that the uh AI is
+
+ align:start position:0%
+yes is the assumption that the uh AI is
+ 
+
+ align:start position:0%
+yes is the assumption that the uh AI is
+all cardinality 3 built into the problem
+
+ align:start position:0%
+all cardinality 3 built into the problem
+ 
+
+ align:start position:0%
+all cardinality 3 built into the problem
+specification here you get a choice you
+
+ align:start position:0%
+specification here you get a choice you
+ 
+
+ align:start position:0%
+specification here you get a choice you
+can either make this part of the problem
+
+ align:start position:0%
+can either make this part of the problem
+ 
+
+ align:start position:0%
+can either make this part of the problem
+specification or not it won't matter
+
+ align:start position:0%
+specification or not it won't matter
+ 
+
+ align:start position:0%
+specification or not it won't matter
+okay well I think in this case if you
+
+ align:start position:0%
+okay well I think in this case if you
+ 
+
+ align:start position:0%
+okay well I think in this case if you
+don't build it into the problem spe can
+
+ align:start position:0%
+don't build it into the problem spe can
+ 
+
+ align:start position:0%
+don't build it into the problem spe can
+you take 12 A's or something uh and then
+
+ align:start position:0%
+you take 12 A's or something uh and then
+ 
+
+ align:start position:0%
+you take 12 A's or something uh and then
+you get 12 Infinities and then they add
+
+ align:start position:0%
+you get 12 Infinities and then they add
+ 
+
+ align:start position:0%
+you get 12 Infinities and then they add
+up to another Infinity yes we definitely
+
+ align:start position:0%
+up to another Infinity yes we definitely
+ 
+
+ align:start position:0%
+up to another Infinity yes we definitely
+want to take this as part of the
+
+ align:start position:0%
+want to take this as part of the
+ 
+
+ align:start position:0%
+want to take this as part of the
+specification for this reduction yeah
+
+ align:start position:0%
+specification for this reduction yeah
+ 
+
+ align:start position:0%
+specification for this reduction yeah
+good point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here's a problem uh you've probably
+
+ align:start position:0%
+so here's a problem uh you've probably
+ 
+
+ align:start position:0%
+so here's a problem uh you've probably
+heard of the matching problem matching
+
+ align:start position:0%
+heard of the matching problem matching
+ 
+
+ align:start position:0%
+heard of the matching problem matching
+problem let's say the perfect matching
+
+ align:start position:0%
+problem let's say the perfect matching
+ 
+
+ align:start position:0%
+problem let's say the perfect matching
+problem is you're given a graph and you
+
+ align:start position:0%
+problem is you're given a graph and you
+ 
+
+ align:start position:0%
+problem is you're given a graph and you
+want to find a set of edges which are
+
+ align:start position:0%
+want to find a set of edges which are
+ 
+
+ align:start position:0%
+want to find a set of edges which are
+disjoint meaning no two edges share a
+
+ align:start position:0%
+disjoint meaning no two edges share a
+ 
+
+ align:start position:0%
+disjoint meaning no two edges share a
+Vertex uh that covers all the vertices
+
+ align:start position:0%
+Vertex uh that covers all the vertices
+ 
+
+ align:start position:0%
+Vertex uh that covers all the vertices
+so if you have n vertices you'd like to
+
+ align:start position:0%
+so if you have n vertices you'd like to
+ 
+
+ align:start position:0%
+so if you have n vertices you'd like to
+find n over two edges that are disjoint
+
+ align:start position:0%
+find n over two edges that are disjoint
+ 
+
+ align:start position:0%
+find n over two edges that are disjoint
+from each other that's perfect matching
+
+ align:start position:0%
+from each other that's perfect matching
+ 
+
+ align:start position:0%
+from each other that's perfect matching
+you might call it two-dimensional
+
+ align:start position:0%
+you might call it two-dimensional
+ 
+
+ align:start position:0%
+you might call it two-dimensional
+matching because an edge has two ends
+
+ align:start position:0%
+matching because an edge has two ends
+ 
+
+ align:start position:0%
+matching because an edge has two ends
+three dimensional matching takes place
+
+ align:start position:0%
+three dimensional matching takes place
+ 
+
+ align:start position:0%
+three dimensional matching takes place
+in a hyper graph and in this case it's
+
+ align:start position:0%
+in a hyper graph and in this case it's
+ 
+
+ align:start position:0%
+in a hyper graph and in this case it's
+going to be a hyp
+
+ align:start position:0%
+going to be a hyp
+ 
+
+ align:start position:0%
+going to be a hyp
+um a tri partite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypergraph you may not have seen hyper
+
+ align:start position:0%
+hypergraph you may not have seen hyper
+ 
+
+ align:start position:0%
+hypergraph you may not have seen hyper
+graphs before they're just like graphs
+
+ align:start position:0%
+graphs before they're just like graphs
+ 
+
+ align:start position:0%
+graphs before they're just like graphs
+but edges can have more than two end
+
+ align:start position:0%
+but edges can have more than two end
+ 
+
+ align:start position:0%
+but edges can have more than two end
+points in this case they will have
+
+ align:start position:0%
+points in this case they will have
+ 
+
+ align:start position:0%
+points in this case they will have
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+three um so let's say the
+
+ align:start position:0%
+three um so let's say the
+ 
+
+ align:start position:0%
+three um so let's say the
+vertices are a distraint union B
+
+ align:start position:0%
+vertices are a distraint union B
+ 
+
+ align:start position:0%
+vertices are a distraint union B
+distraint Union
+
+ align:start position:0%
+distraint Union
+ 
+
+ align:start position:0%
+distraint Union
+C and let's say they all have size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and the hyper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e okay so this is uh maybe it's worth
+
+ align:start position:0%
+e okay so this is uh maybe it's worth
+ 
+
+ align:start position:0%
+e okay so this is uh maybe it's worth
+drawing a picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have uh the set a set B I guess
+
+ align:start position:0%
+so you have uh the set a set B I guess
+ 
+
+ align:start position:0%
+so you have uh the set a set B I guess
+they're all the same
+
+ align:start position:0%
+they're all the same
+ 
+
+ align:start position:0%
+they're all the same
+size set
+
+ align:start position:0%
+size set
+ 
+
+ align:start position:0%
+size set
+C and an edge might look like this or
+
+ align:start position:0%
+C and an edge might look like this or
+ 
+
+ align:start position:0%
+C and an edge might look like this or
+like this or so on okay those are you
+
+ align:start position:0%
+like this or so on okay those are you
+ 
+
+ align:start position:0%
+like this or so on okay those are you
+take one from each and then your goal is
+
+ align:start position:0%
+take one from each and then your goal is
+ 
+
+ align:start position:0%
+take one from each and then your goal is
+to find uh n
+
+ align:start position:0%
+to find uh n
+ 
+
+ align:start position:0%
+to find uh n
+over3 sorry n disjoint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges if you find that many and they're
+
+ align:start position:0%
+edges if you find that many and they're
+ 
+
+ align:start position:0%
+edges if you find that many and they're
+disjoint that means they will cover all
+
+ align:start position:0%
+disjoint that means they will cover all
+ 
+
+ align:start position:0%
+disjoint that means they will cover all
+of the vertices every vertex will be hit
+
+ align:start position:0%
+of the vertices every vertex will be hit
+ 
+
+ align:start position:0%
+of the vertices every vertex will be hit
+by exactly one Edge hyper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Edge okay so this is the
+
+ align:start position:0%
+Edge okay so this is the
+ 
+
+ align:start position:0%
+Edge okay so this is the
+three-dimensional version of bipartite
+
+ align:start position:0%
+three-dimensional version of bipartite
+ 
+
+ align:start position:0%
+three-dimensional version of bipartite
+matching I guess there's also a
+
+ align:start position:0%
+matching I guess there's also a
+ 
+
+ align:start position:0%
+matching I guess there's also a
+non-bipartite version for extra
+
+ align:start position:0%
+non-bipartite version for extra
+ 
+
+ align:start position:0%
+non-bipartite version for extra
+completeness there's something called
+
+ align:start position:0%
+completeness there's something called
+ 
+
+ align:start position:0%
+completeness there's something called
+exact cover by three sets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three meaning the cardinality this is
+
+ align:start position:0%
+three meaning the cardinality this is
+ 
+
+ align:start position:0%
+three meaning the cardinality this is
+called x3c you do see uh 3dm and x33
+
+ align:start position:0%
+called x3c you do see uh 3dm and x33
+ 
+
+ align:start position:0%
+called x3c you do see uh 3dm and x33
+frequently in the literature and
+
+ align:start position:0%
+frequently in the literature and
+ 
+
+ align:start position:0%
+frequently in the literature and
+especially in Gary and Johnson so
+
+ align:start position:0%
+especially in Gary and Johnson so
+ 
+
+ align:start position:0%
+especially in Gary and Johnson so
+they're good problems to know about uh
+
+ align:start position:0%
+they're good problems to know about uh
+ 
+
+ align:start position:0%
+they're good problems to know about uh
+here it's sort of the generalized
+
+ align:start position:0%
+here it's sort of the generalized
+ 
+
+ align:start position:0%
+here it's sort of the generalized
+version where you're given uh non
+
+ align:start position:0%
+version where you're given uh non
+ 
+
+ align:start position:0%
+version where you're given uh non
+tripartite just a uh three
+
+ align:start position:0%
+tripartite just a uh three
+ 
+
+ align:start position:0%
+tripartite just a uh three
+uniform hypergraph three uniform just
+
+ align:start position:0%
+uniform hypergraph three uniform just
+ 
+
+ align:start position:0%
+uniform hypergraph three uniform just
+means every Edge has cardinality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three and your goal is to
+
+ align:start position:0%
+three and your goal is to
+ 
+
+ align:start position:0%
+three and your goal is to
+find uh let's say it has n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices uh
+
+ align:start position:0%
+vertices uh
+ 
+
+ align:start position:0%
+vertices uh
+find uh n over3 disjoint hyperedges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay many times the almost same
+
+ align:start position:0%
+okay okay many times the almost same
+ 
+
+ align:start position:0%
+okay okay many times the almost same
+problem uh how do these relate well uh
+
+ align:start position:0%
+problem uh how do these relate well uh
+ 
+
+ align:start position:0%
+problem uh how do these relate well uh
+certainly if you take a numerical
+
+ align:start position:0%
+certainly if you take a numerical
+ 
+
+ align:start position:0%
+certainly if you take a numerical
+threedimensional matching problem that
+
+ align:start position:0%
+threedimensional matching problem that
+ 
+
+ align:start position:0%
+threedimensional matching problem that
+is a three-dimensional matching problem
+
+ align:start position:0%
+is a three-dimensional matching problem
+ 
+
+ align:start position:0%
+is a three-dimensional matching problem
+you can convert it into a graph like
+
+ align:start position:0%
+you can convert it into a graph like
+ 
+
+ align:start position:0%
+you can convert it into a graph like
+this uh you're just forgetting the fact
+
+ align:start position:0%
+this uh you're just forgetting the fact
+ 
+
+ align:start position:0%
+this uh you're just forgetting the fact
+that there's numbers but then when you
+
+ align:start position:0%
+that there's numbers but then when you
+ 
+
+ align:start position:0%
+that there's numbers but then when you
+draw the edge you draw one of these
+
+ align:start position:0%
+draw the edge you draw one of these
+ 
+
+ align:start position:0%
+draw the edge you draw one of these
+hyper edges exactly when uh AI plus bi
+
+ align:start position:0%
+hyper edges exactly when uh AI plus bi
+ 
+
+ align:start position:0%
+hyper edges exactly when uh AI plus bi
+plus c i equals the target sum okay so
+
+ align:start position:0%
+plus c i equals the target sum okay so
+ 
+
+ align:start position:0%
+plus c i equals the target sum okay so
+numerical threedimensional matching is a
+
+ align:start position:0%
+numerical threedimensional matching is a
+ 
+
+ align:start position:0%
+numerical threedimensional matching is a
+special case of threedimensional
+
+ align:start position:0%
+special case of threedimensional
+ 
+
+ align:start position:0%
+special case of threedimensional
+matching occasionally it's useful to
+
+ align:start position:0%
+matching occasionally it's useful to
+ 
+
+ align:start position:0%
+matching occasionally it's useful to
+start from threedimensional matching not
+
+ align:start position:0%
+start from threedimensional matching not
+ 
+
+ align:start position:0%
+start from threedimensional matching not
+for number problems though if you have a
+
+ align:start position:0%
+for number problems though if you have a
+ 
+
+ align:start position:0%
+for number problems though if you have a
+number problem you like the numerical
+
+ align:start position:0%
+number problem you like the numerical
+ 
+
+ align:start position:0%
+number problem you like the numerical
+version uh personally I prefer three
+
+ align:start position:0%
+version uh personally I prefer three
+ 
+
+ align:start position:0%
+version uh personally I prefer three
+partition but these two are pretty close
+
+ align:start position:0%
+partition but these two are pretty close
+ 
+
+ align:start position:0%
+partition but these two are pretty close
+uh we saw one connection between them
+
+ align:start position:0%
+uh we saw one connection between them
+ 
+
+ align:start position:0%
+uh we saw one connection between them
+hiac cover by three sets is in some
+
+ align:start position:0%
+hiac cover by three sets is in some
+ 
+
+ align:start position:0%
+hiac cover by three sets is in some
+sense even more General than
+
+ align:start position:0%
+sense even more General than
+ 
+
+ align:start position:0%
+sense even more General than
+three-dimensional
+
+ align:start position:0%
+three-dimensional
+ 
+
+ align:start position:0%
+three-dimensional
+matching
+
+ align:start position:0%
+matching
+ 
+
+ align:start position:0%
+matching
+uh yeah it is more
+
+ align:start position:0%
+uh yeah it is more
+ 
+
+ align:start position:0%
+uh yeah it is more
+General because tripartite hypergraph
+
+ align:start position:0%
+General because tripartite hypergraph
+ 
+
+ align:start position:0%
+General because tripartite hypergraph
+like this is uniform so this is a strict
+
+ align:start position:0%
+like this is uniform so this is a strict
+ 
+
+ align:start position:0%
+like this is uniform so this is a strict
+generalization of that but they all
+
+ align:start position:0%
+generalization of that but they all
+ 
+
+ align:start position:0%
+generalization of that but they all
+appear somewhat so that it would be good
+
+ align:start position:0%
+appear somewhat so that it would be good
+ 
+
+ align:start position:0%
+appear somewhat so that it would be good
+for you to know about them again three
+
+ align:start position:0%
+for you to know about them again three
+ 
+
+ align:start position:0%
+for you to know about them again three
+partition is where is where the action
+
+ align:start position:0%
+partition is where is where the action
+ 
+
+ align:start position:0%
+partition is where is where the action
+is all right let me go back to this
+
+ align:start position:0%
+is all right let me go back to this
+ 
+
+ align:start position:0%
+is all right let me go back to this
+issue of two
+
+ align:start position:0%
+issue of two
+ 
+
+ align:start position:0%
+issue of two
+partition versus three partition these
+
+ align:start position:0%
+partition versus three partition these
+ 
+
+ align:start position:0%
+partition versus three partition these
+are the two main problems I want to talk
+
+ align:start position:0%
+are the two main problems I want to talk
+ 
+
+ align:start position:0%
+are the two main problems I want to talk
+about um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they relate to an important distinction
+
+ align:start position:0%
+they relate to an important distinction
+ 
+
+ align:start position:0%
+they relate to an important distinction
+in NP hardness which is weak versus
+
+ align:start position:0%
+in NP hardness which is weak versus
+ 
+
+ align:start position:0%
+in NP hardness which is weak versus
+strong NP hardness so there are two
+
+ align:start position:0%
+strong NP hardness so there are two
+ 
+
+ align:start position:0%
+strong NP hardness so there are two
+types of NP
+
+ align:start position:0%
+types of NP
+ 
+
+ align:start position:0%
+types of NP
+hardness for number
+
+ align:start position:0%
+hardness for number
+ 
+
+ align:start position:0%
+hardness for number
+problems if your input is a graph these
+
+ align:start position:0%
+problems if your input is a graph these
+ 
+
+ align:start position:0%
+problems if your input is a graph these
+two Notions are the same so you don't
+
+ align:start position:0%
+two Notions are the same so you don't
+ 
+
+ align:start position:0%
+two Notions are the same so you don't
+need to worry about
+
+ align:start position:0%
+need to worry about
+ 
+
+ align:start position:0%
+need to worry about
+it but when your problem has integers as
+
+ align:start position:0%
+it but when your problem has integers as
+ 
+
+ align:start position:0%
+it but when your problem has integers as
+input uh then they're two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types uh weekly MP hard is in some sense
+
+ align:start position:0%
+types uh weekly MP hard is in some sense
+ 
+
+ align:start position:0%
+types uh weekly MP hard is in some sense
+the type you already know if you think
+
+ align:start position:0%
+the type you already know if you think
+ 
+
+ align:start position:0%
+the type you already know if you think
+about it in the right way in the
+
+ align:start position:0%
+about it in the right way in the
+ 
+
+ align:start position:0%
+about it in the right way in the
+intended way we haven't been super
+
+ align:start position:0%
+intended way we haven't been super
+ 
+
+ align:start position:0%
+intended way we haven't been super
+formal about how numbers get encoded but
+
+ align:start position:0%
+formal about how numbers get encoded but
+ 
+
+ align:start position:0%
+formal about how numbers get encoded but
+uh usually we think of NP hardness as
+
+ align:start position:0%
+uh usually we think of NP hardness as
+ 
+
+ align:start position:0%
+uh usually we think of NP hardness as
+uh uh in terms of the
+
+ align:start position:0%
+uh uh in terms of the
+ 
+
+ align:start position:0%
+uh uh in terms of the
+how how hard your problem is um in terms
+
+ align:start position:0%
+how how hard your problem is um in terms
+ 
+
+ align:start position:0%
+how how hard your problem is um in terms
+of the encoding size which we usually
+
+ align:start position:0%
+of the encoding size which we usually
+ 
+
+ align:start position:0%
+of the encoding size which we usually
+call n the encoding of your
+
+ align:start position:0%
+call n the encoding of your
+ 
+
+ align:start position:0%
+call n the encoding of your
+input okay so in the usual
+
+ align:start position:0%
+input okay so in the usual
+ 
+
+ align:start position:0%
+input okay so in the usual
+form uh what this means is that you
+
+ align:start position:0%
+form uh what this means is that you
+ 
+
+ align:start position:0%
+form uh what this means is that you
+allow
+
+ align:start position:0%
+allow
+ 
+
+ align:start position:0%
+allow
+numbers uh to have exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value because even when their value is
+
+ align:start position:0%
+value because even when their value is
+ 
+
+ align:start position:0%
+value because even when their value is
+exponential IAL the encoding of that
+
+ align:start position:0%
+exponential IAL the encoding of that
+ 
+
+ align:start position:0%
+exponential IAL the encoding of that
+value is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polom encoding length of such a number
+
+ align:start position:0%
+polom encoding length of such a number
+ 
+
+ align:start position:0%
+polom encoding length of such a number
+is uh you know if you write in binary
+
+ align:start position:0%
+is uh you know if you write in binary
+ 
+
+ align:start position:0%
+is uh you know if you write in binary
+that's log base 2 of the number if the
+
+ align:start position:0%
+that's log base 2 of the number if the
+ 
+
+ align:start position:0%
+that's log base 2 of the number if the
+number is 2 to the N to the C which is
+
+ align:start position:0%
+number is 2 to the N to the C which is
+ 
+
+ align:start position:0%
+number is 2 to the N to the C which is
+our definition of exponential that's
+
+ align:start position:0%
+our definition of exponential that's
+ 
+
+ align:start position:0%
+our definition of exponential that's
+going to be n the C uh and that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polinomial okay uh for here I'm going to
+
+ align:start position:0%
+polinomial okay uh for here I'm going to
+ 
+
+ align:start position:0%
+polinomial okay uh for here I'm going to
+let N be the number of numbers to avoid
+
+ align:start position:0%
+let N be the number of numbers to avoid
+ 
+
+ align:start position:0%
+let N be the number of numbers to avoid
+this to avoid uh circular uh definitions
+
+ align:start position:0%
+this to avoid uh circular uh definitions
+ 
+
+ align:start position:0%
+this to avoid uh circular uh definitions
+or something so I'm saying there are n
+
+ align:start position:0%
+or something so I'm saying there are n
+ 
+
+ align:start position:0%
+or something so I'm saying there are n
+different numbers if each of them is at
+
+ align:start position:0%
+different numbers if each of them is at
+ 
+
+ align:start position:0%
+different numbers if each of them is at
+most two to the N to the C in value and
+
+ align:start position:0%
+most two to the N to the C in value and
+ 
+
+ align:start position:0%
+most two to the N to the C in value and
+they're integers then I can encode them
+
+ align:start position:0%
+they're integers then I can encode them
+ 
+
+ align:start position:0%
+they're integers then I can encode them
+in this many bits and that's a
+
+ align:start position:0%
+in this many bits and that's a
+ 
+
+ align:start position:0%
+in this many bits and that's a
+polinomial number of bits so I consider
+
+ align:start position:0%
+polinomial number of bits so I consider
+ 
+
+ align:start position:0%
+polinomial number of bits so I consider
+that a reasonable in
+
+ align:start position:0%
+that a reasonable in
+ 
+
+ align:start position:0%
+that a reasonable in
+coding okay uh and sometimes that's just
+
+ align:start position:0%
+coding okay uh and sometimes that's just
+ 
+
+ align:start position:0%
+coding okay uh and sometimes that's just
+fine but there's a stronger notion which
+
+ align:start position:0%
+fine but there's a stronger notion which
+ 
+
+ align:start position:0%
+fine but there's a stronger notion which
+is really useful especially for a lot of
+
+ align:start position:0%
+is really useful especially for a lot of
+ 
+
+ align:start position:0%
+is really useful especially for a lot of
+problems we will see today and next
+
+ align:start position:0%
+problems we will see today and next
+ 
+
+ align:start position:0%
+problems we will see today and next
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+which is called strongly NP hard and
+
+ align:start position:0%
+which is called strongly NP hard and
+ 
+
+ align:start position:0%
+which is called strongly NP hard and
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is NP
+
+ align:start position:0%
+is NP
+ 
+
+ align:start position:0%
+is NP
+hard even
+
+ align:start position:0%
+hard even
+ 
+
+ align:start position:0%
+hard even
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+uh uh your problem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+restricted to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers of polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value so polinomial here is with respect
+
+ align:start position:0%
+value so polinomial here is with respect
+ 
+
+ align:start position:0%
+value so polinomial here is with respect
+to n n is the number of integers number
+
+ align:start position:0%
+to n n is the number of integers number
+ 
+
+ align:start position:0%
+to n n is the number of integers number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+numbers okay so uh strongly NP hard is
+
+ align:start position:0%
+numbers okay so uh strongly NP hard is
+ 
+
+ align:start position:0%
+numbers okay so uh strongly NP hard is
+stronger than weakly NP hard if you have
+
+ align:start position:0%
+stronger than weakly NP hard if you have
+ 
+
+ align:start position:0%
+stronger than weakly NP hard if you have
+if you're NP hard even when your numbers
+
+ align:start position:0%
+if you're NP hard even when your numbers
+ 
+
+ align:start position:0%
+if you're NP hard even when your numbers
+are only polinomial size then of course
+
+ align:start position:0%
+are only polinomial size then of course
+ 
+
+ align:start position:0%
+are only polinomial size then of course
+you're NP hard when you allow the
+
+ align:start position:0%
+you're NP hard when you allow the
+ 
+
+ align:start position:0%
+you're NP hard when you allow the
+numbers to be as large as exponential
+
+ align:start position:0%
+numbers to be as large as exponential
+ 
+
+ align:start position:0%
+numbers to be as large as exponential
+this is a weaker constraint on the
+
+ align:start position:0%
+this is a weaker constraint on the
+ 
+
+ align:start position:0%
+this is a weaker constraint on the
+problem so uh to cut to the chase two
+
+ align:start position:0%
+problem so uh to cut to the chase two
+ 
+
+ align:start position:0%
+problem so uh to cut to the chase two
+partition up here uh and subset sum are
+
+ align:start position:0%
+partition up here uh and subset sum are
+ 
+
+ align:start position:0%
+partition up here uh and subset sum are
+are weekly n beh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard and if you believe that the that P
+
+ align:start position:0%
+hard and if you believe that the that P
+ 
+
+ align:start position:0%
+hard and if you believe that the that P
+does not equal NP uh then it's not
+
+ align:start position:0%
+does not equal NP uh then it's not
+ 
+
+ align:start position:0%
+does not equal NP uh then it's not
+strongly MP hard that's the best you can
+
+ align:start position:0%
+strongly MP hard that's the best you can
+ 
+
+ align:start position:0%
+strongly MP hard that's the best you can
+hope for whereas three partition and
+
+ align:start position:0%
+hope for whereas three partition and
+ 
+
+ align:start position:0%
+hope for whereas three partition and
+every other problem we talked about is
+
+ align:start position:0%
+every other problem we talked about is
+ 
+
+ align:start position:0%
+every other problem we talked about is
+strongly NP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard I have a question what do you mean
+
+ align:start position:0%
+hard I have a question what do you mean
+ 
+
+ align:start position:0%
+hard I have a question what do you mean
+exactly by numbers having exponential
+
+ align:start position:0%
+exactly by numbers having exponential
+ 
+
+ align:start position:0%
+exactly by numbers having exponential
+value uh so again
+
+ align:start position:0%
+value uh so again
+ 
+
+ align:start position:0%
+value uh so again
+exponential like 2 the N the c n is the
+
+ align:start position:0%
+exponential like 2 the N the c n is the
+ 
+
+ align:start position:0%
+exponential like 2 the N the c n is the
+number of numbers in your input okay
+
+ align:start position:0%
+number of numbers in your input okay
+ 
+
+ align:start position:0%
+number of numbers in your input okay
+yeah so that's uh that's what I allow I
+
+ align:start position:0%
+yeah so that's uh that's what I allow I
+ 
+
+ align:start position:0%
+yeah so that's uh that's what I allow I
+mean this is what would be allowed if
+
+ align:start position:0%
+mean this is what would be allowed if
+ 
+
+ align:start position:0%
+mean this is what would be allowed if
+you didn't say anything if you interpret
+
+ align:start position:0%
+you didn't say anything if you interpret
+ 
+
+ align:start position:0%
+you didn't say anything if you interpret
+complexity theory in a way that I
+
+ align:start position:0%
+complexity theory in a way that I
+ 
+
+ align:start position:0%
+complexity theory in a way that I
+haven't necessarily told you but uh
+
+ align:start position:0%
+haven't necessarily told you but uh
+ 
+
+ align:start position:0%
+haven't necessarily told you but uh
+generally you want to assume that all
+
+ align:start position:0%
+generally you want to assume that all
+ 
+
+ align:start position:0%
+generally you want to assume that all
+your inputs are reasonably encoded in an
+
+ align:start position:0%
+your inputs are reasonably encoded in an
+ 
+
+ align:start position:0%
+your inputs are reasonably encoded in an
+efficient way that most possible input
+
+ align:start position:0%
+efficient way that most possible input
+ 
+
+ align:start position:0%
+efficient way that most possible input
+strings are valid inputs
+
+ align:start position:0%
+strings are valid inputs
+ 
+
+ align:start position:0%
+strings are valid inputs
+and so if you're encoding your then in
+
+ align:start position:0%
+and so if you're encoding your then in
+ 
+
+ align:start position:0%
+and so if you're encoding your then in
+particular you should encode your
+
+ align:start position:0%
+particular you should encode your
+ 
+
+ align:start position:0%
+particular you should encode your
+numbers in binary or Turner or coronary
+
+ align:start position:0%
+numbers in binary or Turner or coronary
+ 
+
+ align:start position:0%
+numbers in binary or Turner or coronary
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+hexadecimal anything bigger than one is
+
+ align:start position:0%
+hexadecimal anything bigger than one is
+ 
+
+ align:start position:0%
+hexadecimal anything bigger than one is
+good okay you should know if you're
+
+ align:start position:0%
+good okay you should know if you're
+ 
+
+ align:start position:0%
+good okay you should know if you're
+writing down a number don't use uny but
+
+ align:start position:0%
+writing down a number don't use uny but
+ 
+
+ align:start position:0%
+writing down a number don't use uny but
+today we're going to use un a lot so
+
+ align:start position:0%
+today we're going to use un a lot so
+ 
+
+ align:start position:0%
+today we're going to use un a lot so
+this is the same thing as saying uh en
+
+ align:start position:0%
+this is the same thing as saying uh en
+ 
+
+ align:start position:0%
+this is the same thing as saying uh en
+code in un strong NP
+
+ align:start position:0%
+code in un strong NP
+ 
+
+ align:start position:0%
+code in un strong NP
+hardness is like saying well my problem
+
+ align:start position:0%
+hardness is like saying well my problem
+ 
+
+ align:start position:0%
+hardness is like saying well my problem
+is so hard that even if I encode my
+
+ align:start position:0%
+is so hard that even if I encode my
+ 
+
+ align:start position:0%
+is so hard that even if I encode my
+numbers in un it's still hard in the
+
+ align:start position:0%
+numbers in un it's still hard in the
+ 
+
+ align:start position:0%
+numbers in un it's still hard in the
+resulting input size the input size
+
+ align:start position:0%
+resulting input size the input size
+ 
+
+ align:start position:0%
+resulting input size the input size
+would be if you write down every number
+
+ align:start position:0%
+would be if you write down every number
+ 
+
+ align:start position:0%
+would be if you write down every number
+uny add so add up all the numbers that's
+
+ align:start position:0%
+uny add so add up all the numbers that's
+ 
+
+ align:start position:0%
+uny add so add up all the numbers that's
+your input size three partition is that
+
+ align:start position:0%
+your input size three partition is that
+ 
+
+ align:start position:0%
+your input size three partition is that
+hard two partition is
+
+ align:start position:0%
+hard two partition is
+ 
+
+ align:start position:0%
+hard two partition is
+not okay so if you can prove strong
+
+ align:start position:0%
+not okay so if you can prove strong
+ 
+
+ align:start position:0%
+not okay so if you can prove strong
+empty hardness you should it's better if
+
+ align:start position:0%
+empty hardness you should it's better if
+ 
+
+ align:start position:0%
+empty hardness you should it's better if
+you can only prove weak mty hardness
+
+ align:start position:0%
+you can only prove weak mty hardness
+ 
+
+ align:start position:0%
+you can only prove weak mty hardness
+it's okay it's still
+
+ align:start position:0%
+it's okay it's still
+ 
+
+ align:start position:0%
+it's okay it's still
+hard uh now you should know there's
+
+ align:start position:0%
+hard uh now you should know there's
+ 
+
+ align:start position:0%
+hard uh now you should know there's
+corresponding Notions on the algorithm
+
+ align:start position:0%
+corresponding Notions on the algorithm
+ 
+
+ align:start position:0%
+corresponding Notions on the algorithm
+side so let's talk about that a little
+
+ align:start position:0%
+side so let's talk about that a little
+ 
+
+ align:start position:0%
+side so let's talk about that a little
+bit um so corresponding algorithmic
+
+ align:start position:0%
+bit um so corresponding algorithmic
+ 
+
+ align:start position:0%
+bit um so corresponding algorithmic
+Notions are there's actually three of
+
+ align:start position:0%
+Notions are there's actually three of
+ 
+
+ align:start position:0%
+Notions are there's actually three of
+them the main ones are pseudo polinomial
+
+ align:start position:0%
+them the main ones are pseudo polinomial
+ 
+
+ align:start position:0%
+them the main ones are pseudo polinomial
+and weekly polinomial sorry the weeklys
+
+ align:start position:0%
+and weekly polinomial sorry the weeklys
+ 
+
+ align:start position:0%
+and weekly polinomial sorry the weeklys
+are unrelated to each other but that's
+
+ align:start position:0%
+are unrelated to each other but that's
+ 
+
+ align:start position:0%
+are unrelated to each other but that's
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+life there's also a oce called strongly
+
+ align:start position:0%
+life there's also a oce called strongly
+ 
+
+ align:start position:0%
+life there's also a oce called strongly
+polinomial unrelated to strongly NP hard
+
+ align:start position:0%
+polinomial unrelated to strongly NP hard
+ 
+
+ align:start position:0%
+polinomial unrelated to strongly NP hard
+here you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go okay
+
+ align:start position:0%
+go okay
+ 
+
+ align:start position:0%
+go okay
+um so weekly polinomial is the usual
+
+ align:start position:0%
+um so weekly polinomial is the usual
+ 
+
+ align:start position:0%
+um so weekly polinomial is the usual
+notion of polinomial I should mention
+
+ align:start position:0%
+notion of polinomial I should mention
+ 
+
+ align:start position:0%
+notion of polinomial I should mention
+when I say I have a polinomial Time
+
+ align:start position:0%
+when I say I have a polinomial Time
+ 
+
+ align:start position:0%
+when I say I have a polinomial Time
+algorithm what you mean is weekly uh
+
+ align:start position:0%
+algorithm what you mean is weekly uh
+ 
+
+ align:start position:0%
+algorithm what you mean is weekly uh
+meaning that uh let's say I'll write it
+
+ align:start position:0%
+meaning that uh let's say I'll write it
+ 
+
+ align:start position:0%
+meaning that uh let's say I'll write it
+as polom in and the number of integers
+
+ align:start position:0%
+as polom in and the number of integers
+ 
+
+ align:start position:0%
+as polom in and the number of integers
+and uh let's say log of the largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integer largest number in the
+
+ align:start position:0%
+integer largest number in the
+ 
+
+ align:start position:0%
+integer largest number in the
+input okay that's a reasonable encoding
+
+ align:start position:0%
+input okay that's a reasonable encoding
+ 
+
+ align:start position:0%
+input okay that's a reasonable encoding
+size you write them in binary uh you add
+
+ align:start position:0%
+size you write them in binary uh you add
+ 
+
+ align:start position:0%
+size you write them in binary uh you add
+them all up so you multiply that by n or
+
+ align:start position:0%
+them all up so you multiply that by n or
+ 
+
+ align:start position:0%
+them all up so you multiply that by n or
+whatever the polinomial in that value is
+
+ align:start position:0%
+whatever the polinomial in that value is
+ 
+
+ align:start position:0%
+whatever the polinomial in that value is
+weekly polinomial uh pseudo polinomial
+
+ align:start position:0%
+weekly polinomial uh pseudo polinomial
+ 
+
+ align:start position:0%
+weekly polinomial uh pseudo polinomial
+you omit the
+
+ align:start position:0%
+you omit the
+ 
+
+ align:start position:0%
+you omit the
+log okay so I want Pol n and the largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number and strongly polinomial you emit
+
+ align:start position:0%
+number and strongly polinomial you emit
+ 
+
+ align:start position:0%
+number and strongly polinomial you emit
+that term Al together so you're just
+
+ align:start position:0%
+that term Al together so you're just
+ 
+
+ align:start position:0%
+that term Al together so you're just
+polinomial in the number of
+
+ align:start position:0%
+polinomial in the number of
+ 
+
+ align:start position:0%
+polinomial in the number of
+numbers okay so there's a different
+
+ align:start position:0%
+numbers okay so there's a different
+ 
+
+ align:start position:0%
+numbers okay so there's a different
+world of algorithms which we're not
+
+ align:start position:0%
+world of algorithms which we're not
+ 
+
+ align:start position:0%
+world of algorithms which we're not
+going to talk about here which is weakly
+
+ align:start position:0%
+going to talk about here which is weakly
+ 
+
+ align:start position:0%
+going to talk about here which is weakly
+polinomial algorithms versus strongly
+
+ align:start position:0%
+polinomial algorithms versus strongly
+ 
+
+ align:start position:0%
+polinomial algorithms versus strongly
+polinomial algorithms I'm not aware of
+
+ align:start position:0%
+polinomial algorithms I'm not aware of
+ 
+
+ align:start position:0%
+polinomial algorithms I'm not aware of
+any lower bounds about that but there's
+
+ align:start position:0%
+any lower bounds about that but there's
+ 
+
+ align:start position:0%
+any lower bounds about that but there's
+famous open questions like can you solve
+
+ align:start position:0%
+famous open questions like can you solve
+ 
+
+ align:start position:0%
+famous open questions like can you solve
+linear programming in strongl polinomial
+
+ align:start position:0%
+linear programming in strongl polinomial
+ 
+
+ align:start position:0%
+linear programming in strongl polinomial
+time we don't know there's no hardness
+
+ align:start position:0%
+time we don't know there's no hardness
+ 
+
+ align:start position:0%
+time we don't know there's no hardness
+notion there so we're not going to talk
+
+ align:start position:0%
+notion there so we're not going to talk
+ 
+
+ align:start position:0%
+notion there so we're not going to talk
+about it any more than that um what we
+
+ align:start position:0%
+about it any more than that um what we
+ 
+
+ align:start position:0%
+about it any more than that um what we
+care about more is this distinction
+
+ align:start position:0%
+care about more is this distinction
+ 
+
+ align:start position:0%
+care about more is this distinction
+between pseudo polinomial this is
+
+ align:start position:0%
+between pseudo polinomial this is
+ 
+
+ align:start position:0%
+between pseudo polinomial this is
+polinomial when the numbers are written
+
+ align:start position:0%
+polinomial when the numbers are written
+ 
+
+ align:start position:0%
+polinomial when the numbers are written
+in unary and this is polinomial when the
+
+ align:start position:0%
+in unary and this is polinomial when the
+ 
+
+ align:start position:0%
+in unary and this is polinomial when the
+numbers are written in binary so these
+
+ align:start position:0%
+numbers are written in binary so these
+ 
+
+ align:start position:0%
+numbers are written in binary so these
+two Notions correspond to these two
+
+ align:start position:0%
+two Notions correspond to these two
+ 
+
+ align:start position:0%
+two Notions correspond to these two
+Notions uh so in particular if you
+
+ align:start position:0%
+Notions uh so in particular if you
+ 
+
+ align:start position:0%
+Notions uh so in particular if you
+believe P does not equal NP then weekly
+
+ align:start position:0%
+believe P does not equal NP then weekly
+ 
+
+ align:start position:0%
+believe P does not equal NP then weekly
+NP hard means there is no weekly
+
+ align:start position:0%
+NP hard means there is no weekly
+ 
+
+ align:start position:0%
+NP hard means there is no weekly
+polinomial algorithm
+
+ align:start position:0%
+polinomial algorithm
+ 
+
+ align:start position:0%
+polinomial algorithm
+but there might be a pseudo polinomial
+
+ align:start position:0%
+but there might be a pseudo polinomial
+ 
+
+ align:start position:0%
+but there might be a pseudo polinomial
+algorithm strongly NP hard means there's
+
+ align:start position:0%
+algorithm strongly NP hard means there's
+ 
+
+ align:start position:0%
+algorithm strongly NP hard means there's
+no pseudo poomi algorithm and therefore
+
+ align:start position:0%
+no pseudo poomi algorithm and therefore
+ 
+
+ align:start position:0%
+no pseudo poomi algorithm and therefore
+there's no weakly polinomial algorithm
+
+ align:start position:0%
+there's no weakly polinomial algorithm
+ 
+
+ align:start position:0%
+there's no weakly polinomial algorithm
+Adam so the difference between weekly
+
+ align:start position:0%
+Adam so the difference between weekly
+ 
+
+ align:start position:0%
+Adam so the difference between weekly
+polinomial and strongly polinomial is
+
+ align:start position:0%
+polinomial and strongly polinomial is
+ 
+
+ align:start position:0%
+polinomial and strongly polinomial is
+that we don't even necessarily give
+
+ align:start position:0%
+that we don't even necessarily give
+ 
+
+ align:start position:0%
+that we don't even necessarily give
+ourselves time to read all the numbers
+
+ align:start position:0%
+ourselves time to read all the numbers
+ 
+
+ align:start position:0%
+ourselves time to read all the numbers
+uh okay I put it in binary uh I didn't
+
+ align:start position:0%
+uh okay I put it in binary uh I didn't
+ 
+
+ align:start position:0%
+uh okay I put it in binary uh I didn't
+want to get too much into models of
+
+ align:start position:0%
+want to get too much into models of
+ 
+
+ align:start position:0%
+want to get too much into models of
+computation but the model of computation
+
+ align:start position:0%
+computation but the model of computation
+ 
+
+ align:start position:0%
+computation but the model of computation
+here is that you're allowed to read an
+
+ align:start position:0%
+here is that you're allowed to read an
+ 
+
+ align:start position:0%
+here is that you're allowed to read an
+entire number in one time stamp so if
+
+ align:start position:0%
+entire number in one time stamp so if
+ 
+
+ align:start position:0%
+entire number in one time stamp so if
+you've taken 6851 Advanced data
+
+ align:start position:0%
+you've taken 6851 Advanced data
+ 
+
+ align:start position:0%
+you've taken 6851 Advanced data
+structure this is like uh word Ram so
+
+ align:start position:0%
+structure this is like uh word Ram so
+ 
+
+ align:start position:0%
+structure this is like uh word Ram so
+that's the only reason this would be
+
+ align:start position:0%
+that's the only reason this would be
+ 
+
+ align:start position:0%
+that's the only reason this would be
+reasonable otherwise you couldn't read
+
+ align:start position:0%
+reasonable otherwise you couldn't read
+ 
+
+ align:start position:0%
+reasonable otherwise you couldn't read
+the input that would be pretty hard so
+
+ align:start position:0%
+the input that would be pretty hard so
+ 
+
+ align:start position:0%
+the input that would be pretty hard so
+the the model is you can do you can take
+
+ align:start position:0%
+the the model is you can do you can take
+ 
+
+ align:start position:0%
+the the model is you can do you can take
+a constant number of your numbers do
+
+ align:start position:0%
+a constant number of your numbers do
+ 
+
+ align:start position:0%
+a constant number of your numbers do
+something with them output another
+
+ align:start position:0%
+something with them output another
+ 
+
+ align:start position:0%
+something with them output another
+number of the same type roughly in
+
+ align:start position:0%
+number of the same type roughly in
+ 
+
+ align:start position:0%
+number of the same type roughly in
+constant time and you want to do a
+
+ align:start position:0%
+constant time and you want to do a
+ 
+
+ align:start position:0%
+constant time and you want to do a
+polinomial number of such steps usually
+
+ align:start position:0%
+polinomial number of such steps usually
+ 
+
+ align:start position:0%
+polinomial number of such steps usually
+arithmetic
+
+ align:start position:0%
+arithmetic
+ 
+
+ align:start position:0%
+arithmetic
+operations uh here you don't have to be
+
+ align:start position:0%
+operations uh here you don't have to be
+ 
+
+ align:start position:0%
+operations uh here you don't have to be
+so careful about the model uh because
+
+ align:start position:0%
+so careful about the model uh because
+ 
+
+ align:start position:0%
+so careful about the model uh because
+any reasonable coding you can read it
+
+ align:start position:0%
+any reasonable coding you can read it
+ 
+
+ align:start position:0%
+any reasonable coding you can read it
+and do whatever you want with it if you
+
+ align:start position:0%
+and do whatever you want with it if you
+ 
+
+ align:start position:0%
+and do whatever you want with it if you
+don't care about the exponent the
+
+ align:start position:0%
+don't care about the exponent the
+ 
+
+ align:start position:0%
+don't care about the exponent the
+polinomial all models are equivalent if
+
+ align:start position:0%
+polinomial all models are equivalent if
+ 
+
+ align:start position:0%
+polinomial all models are equivalent if
+you believe the strong Church teing
+
+ align:start position:0%
+you believe the strong Church teing
+ 
+
+ align:start position:0%
+you believe the strong Church teing
+thesis
+
+ align:start position:0%
+thesis
+ 
+
+ align:start position:0%
+thesis
+anyway uh this one you have to be a
+
+ align:start position:0%
+anyway uh this one you have to be a
+ 
+
+ align:start position:0%
+anyway uh this one you have to be a
+little more careful what the model
+
+ align:start position:0%
+little more careful what the model
+ 
+
+ align:start position:0%
+little more careful what the model
+is good so let me draw my favorite
+
+ align:start position:0%
+is good so let me draw my favorite
+ 
+
+ align:start position:0%
+is good so let me draw my favorite
+diagram uh with the difficulty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis so but now instead of P I'm going
+
+ align:start position:0%
+axis so but now instead of P I'm going
+ 
+
+ align:start position:0%
+axis so but now instead of P I'm going
+to distinguish between weakly polinomial
+
+ align:start position:0%
+to distinguish between weakly polinomial
+ 
+
+ align:start position:0%
+to distinguish between weakly polinomial
+pseudo polinomial and strongly
+
+ align:start position:0%
+pseudo polinomial and strongly
+ 
+
+ align:start position:0%
+pseudo polinomial and strongly
+polinomial so uh these things are pseudo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+poly uh these things are weekly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+poly and these
+
+ align:start position:0%
+poly and these
+ 
+
+ align:start position:0%
+poly and these
+things are strongly poly this is on the
+
+ align:start position:0%
+things are strongly poly this is on the
+ 
+
+ align:start position:0%
+things are strongly poly this is on the
+algorithm side upper
+
+ align:start position:0%
+algorithm side upper
+ 
+
+ align:start position:0%
+algorithm side upper
+bounds being left of a particular
+
+ align:start position:0%
+bounds being left of a particular
+ 
+
+ align:start position:0%
+bounds being left of a particular
+position and then on the hardness side
+
+ align:start position:0%
+position and then on the hardness side
+ 
+
+ align:start position:0%
+position and then on the hardness side
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me use red it's more
+
+ align:start position:0%
+let me use red it's more
+ 
+
+ align:start position:0%
+let me use red it's more
+dramatic uh this thing is weekly NP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard this is if P does not equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NP then you're strictly to the right of
+
+ align:start position:0%
+NP then you're strictly to the right of
+ 
+
+ align:start position:0%
+NP then you're strictly to the right of
+pseudo so there's no pseudo problem
+
+ align:start position:0%
+pseudo so there's no pseudo problem
+ 
+
+ align:start position:0%
+pseudo so there's no pseudo problem
+there's also weakly EMP hard okay and
+
+ align:start position:0%
+there's also weakly EMP hard okay and
+ 
+
+ align:start position:0%
+there's also weakly EMP hard okay and
+then strong strongly empty hard excl
+
+ align:start position:0%
+then strong strongly empty hard excl
+ 
+
+ align:start position:0%
+then strong strongly empty hard excl
+includes even a weekly polinomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm okay so strictly to the right
+
+ align:start position:0%
+algorithm okay so strictly to the right
+ 
+
+ align:start position:0%
+algorithm okay so strictly to the right
+of that position so obviously strongly
+
+ align:start position:0%
+of that position so obviously strongly
+ 
+
+ align:start position:0%
+of that position so obviously strongly
+EMP hard is a better result because it's
+
+ align:start position:0%
+EMP hard is a better result because it's
+ 
+
+ align:start position:0%
+EMP hard is a better result because it's
+smaller than this
+
+ align:start position:0%
+smaller than this
+ 
+
+ align:start position:0%
+smaller than this
+class um but for example uh two
+
+ align:start position:0%
+class um but for example uh two
+ 
+
+ align:start position:0%
+class um but for example uh two
+partition which is only weekly NP hard
+
+ align:start position:0%
+partition which is only weekly NP hard
+ 
+
+ align:start position:0%
+partition which is only weekly NP hard
+has a pseudo polinomial algorithm you've
+
+ align:start position:0%
+has a pseudo polinomial algorithm you've
+ 
+
+ align:start position:0%
+has a pseudo polinomial algorithm you've
+probably even seen one in your
+
+ align:start position:0%
+probably even seen one in your
+ 
+
+ align:start position:0%
+probably even seen one in your
+algorithms class if you've ever done
+
+ align:start position:0%
+algorithms class if you've ever done
+ 
+
+ align:start position:0%
+algorithms class if you've ever done
+anything like
+
+ align:start position:0%
+anything like
+ 
+
+ align:start position:0%
+anything like
+napsack uh as a dynamic program that is
+
+ align:start position:0%
+napsack uh as a dynamic program that is
+ 
+
+ align:start position:0%
+napsack uh as a dynamic program that is
+a dynamic program probably originally
+
+ align:start position:0%
+a dynamic program probably originally
+ 
+
+ align:start position:0%
+a dynamic program probably originally
+done for two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition okay so that problem is
+
+ align:start position:0%
+partition okay so that problem is
+ 
+
+ align:start position:0%
+partition okay so that problem is
+somewhere in
+
+ align:start position:0%
+somewhere in
+ 
+
+ align:start position:0%
+somewhere in
+here weekly NP hard oops I think the
+
+ align:start position:0%
+here weekly NP hard oops I think the
+ 
+
+ align:start position:0%
+here weekly NP hard oops I think the
+diagram is backward problem if a problem
+
+ align:start position:0%
+diagram is backward problem if a problem
+ 
+
+ align:start position:0%
+diagram is backward problem if a problem
+is strongly polinomial then it's also
+
+ align:start position:0%
+is strongly polinomial then it's also
+ 
+
+ align:start position:0%
+is strongly polinomial then it's also
+weakly poal so the middle one's
+
+ align:start position:0%
+weakly poal so the middle one's
+ 
+
+ align:start position:0%
+weakly poal so the middle one's
+right thank you that seemed funny right
+
+ align:start position:0%
+right thank you that seemed funny right
+ 
+
+ align:start position:0%
+right thank you that seemed funny right
+strongly polinomial is the tightest
+
+ align:start position:0%
+strongly polinomial is the tightest
+ 
+
+ align:start position:0%
+strongly polinomial is the tightest
+class that's the best result and pseudo
+
+ align:start position:0%
+class that's the best result and pseudo
+ 
+
+ align:start position:0%
+class that's the best result and pseudo
+poly is the worst
+
+ align:start position:0%
+poly is the worst
+ 
+
+ align:start position:0%
+poly is the worst
+result did I get my arrows in the right
+
+ align:start position:0%
+result did I get my arrows in the right
+ 
+
+ align:start position:0%
+result did I get my arrows in the right
+place shift over shift over
+
+ align:start position:0%
+place shift over shift over
+ 
+
+ align:start position:0%
+place shift over shift over
+one right strongly NP
+
+ align:start position:0%
+one right strongly NP
+ 
+
+ align:start position:0%
+one right strongly NP
+hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops
+
+ align:start position:0%
+whoops
+ 
+
+ align:start position:0%
+whoops
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so weakly NP heart is here strongly NP
+
+ align:start position:0%
+so weakly NP heart is here strongly NP
+ 
+
+ align:start position:0%
+so weakly NP heart is here strongly NP
+heart is
+
+ align:start position:0%
+heart is
+ 
+
+ align:start position:0%
+heart is
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay cool so uh let's check so two
+
+ align:start position:0%
+okay cool so uh let's check so two
+ 
+
+ align:start position:0%
+okay cool so uh let's check so two
+partition should be pseudo so left of
+
+ align:start position:0%
+partition should be pseudo so left of
+ 
+
+ align:start position:0%
+partition should be pseudo so left of
+this line uh but weekly and be hard so
+
+ align:start position:0%
+this line uh but weekly and be hard so
+ 
+
+ align:start position:0%
+this line uh but weekly and be hard so
+right of that line that looks good so
+
+ align:start position:0%
+right of that line that looks good so
+ 
+
+ align:start position:0%
+right of that line that looks good so
+this is two
+
+ align:start position:0%
+this is two
+ 
+
+ align:start position:0%
+this is two
+partition three partition is out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I mean I draw this as a region but
+
+ align:start position:0%
+here I mean I draw this as a region but
+ 
+
+ align:start position:0%
+here I mean I draw this as a region but
+it's more like a point in my old diagram
+
+ align:start position:0%
+it's more like a point in my old diagram
+ 
+
+ align:start position:0%
+it's more like a point in my old diagram
+uh because three partition is actually
+
+ align:start position:0%
+uh because three partition is actually
+ 
+
+ align:start position:0%
+uh because three partition is actually
+in NP so it's strongly NP complete uh so
+
+ align:start position:0%
+in NP so it's strongly NP complete uh so
+ 
+
+ align:start position:0%
+in NP so it's strongly NP complete uh so
+it's like right at the edge there anyway
+
+ align:start position:0%
+it's like right at the edge there anyway
+ 
+
+ align:start position:0%
+it's like right at the edge there anyway
+there's no pseudo poomi algorithm for
+
+ align:start position:0%
+there's no pseudo poomi algorithm for
+ 
+
+ align:start position:0%
+there's no pseudo poomi algorithm for
+three partition unlike two partition the
+
+ align:start position:0%
+three partition unlike two partition the
+ 
+
+ align:start position:0%
+three partition unlike two partition the
+point of all
+
+ align:start position:0%
+point of all
+ 
+
+ align:start position:0%
+point of all
+that let's do some reduction shall we NP
+
+ align:start position:0%
+that let's do some reduction shall we NP
+ 
+
+ align:start position:0%
+that let's do some reduction shall we NP
+hardcore
+
+ align:start position:0%
+hardcore
+ 
+
+ align:start position:0%
+hardcore
+time uh
+
+ align:start position:0%
+time uh
+ 
+
+ align:start position:0%
+time uh
+so maybe over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the first reduction is going to be
+
+ align:start position:0%
+okay the first reduction is going to be
+ 
+
+ align:start position:0%
+okay the first reduction is going to be
+pretty can I ask a question go on so why
+
+ align:start position:0%
+pretty can I ask a question go on so why
+ 
+
+ align:start position:0%
+pretty can I ask a question go on so why
+is there no corresponding notion for
+
+ align:start position:0%
+is there no corresponding notion for
+ 
+
+ align:start position:0%
+is there no corresponding notion for
+problems that are not numeric like why
+
+ align:start position:0%
+problems that are not numeric like why
+ 
+
+ align:start position:0%
+problems that are not numeric like why
+isn't why can't for a graph problem we
+
+ align:start position:0%
+isn't why can't for a graph problem we
+ 
+
+ align:start position:0%
+isn't why can't for a graph problem we
+say well we're going to examine this
+
+ align:start position:0%
+say well we're going to examine this
+ 
+
+ align:start position:0%
+say well we're going to examine this
+graph problem assuming we're using an
+
+ align:start position:0%
+graph problem assuming we're using an
+ 
+
+ align:start position:0%
+graph problem assuming we're using an
+inefficient encoding of our graph to see
+
+ align:start position:0%
+inefficient encoding of our graph to see
+ 
+
+ align:start position:0%
+inefficient encoding of our graph to see
+how hard it is uh I guess you could try
+
+ align:start position:0%
+how hard it is uh I guess you could try
+ 
+
+ align:start position:0%
+how hard it is uh I guess you could try
+to Define this in terms for graphs but I
+
+ align:start position:0%
+to Define this in terms for graphs but I
+ 
+
+ align:start position:0%
+to Define this in terms for graphs but I
+don't think there's such an obvious
+
+ align:start position:0%
+don't think there's such an obvious
+ 
+
+ align:start position:0%
+don't think there's such an obvious
+inefficient notion of
+
+ align:start position:0%
+inefficient notion of
+ 
+
+ align:start position:0%
+inefficient notion of
+graphs uh I mean the obvious inefficient
+
+ align:start position:0%
+graphs uh I mean the obvious inefficient
+ 
+
+ align:start position:0%
+graphs uh I mean the obvious inefficient
+notion is like use a matrix instead of
+
+ align:start position:0%
+notion is like use a matrix instead of
+ 
+
+ align:start position:0%
+notion is like use a matrix instead of
+an uency list but that's polom
+
+ align:start position:0%
+an uency list but that's polom
+ 
+
+ align:start position:0%
+an uency list but that's polom
+equivalent so if I mean there certainly
+
+ align:start position:0%
+equivalent so if I mean there certainly
+ 
+
+ align:start position:0%
+equivalent so if I mean there certainly
+are other Notions you could imagine but
+
+ align:start position:0%
+are other Notions you could imagine but
+ 
+
+ align:start position:0%
+are other Notions you could imagine but
+uh but there aren't any in the
+
+ align:start position:0%
+uh but there aren't any in the
+ 
+
+ align:start position:0%
+uh but there aren't any in the
+literature all right so uh just to warn
+
+ align:start position:0%
+literature all right so uh just to warn
+ 
+
+ align:start position:0%
+literature all right so uh just to warn
+you the first reduction we do is going
+
+ align:start position:0%
+you the first reduction we do is going
+ 
+
+ align:start position:0%
+you the first reduction we do is going
+to be a little bit trivial so don't get
+
+ align:start position:0%
+to be a little bit trivial so don't get
+ 
+
+ align:start position:0%
+to be a little bit trivial so don't get
+too excited yet uh but this is where
+
+ align:start position:0%
+too excited yet uh but this is where
+ 
+
+ align:start position:0%
+too excited yet uh but this is where
+three partition comes from
+
+ align:start position:0%
+three partition comes from
+ 
+
+ align:start position:0%
+three partition comes from
+then we'll do lots of cool cool
+
+ align:start position:0%
+then we'll do lots of cool cool
+ 
+
+ align:start position:0%
+then we'll do lots of cool cool
+ones so multiprocessor
+
+ align:start position:0%
+ones so multiprocessor
+ 
+
+ align:start position:0%
+ones so multiprocessor
+scheduling let's say I have n
+
+ align:start position:0%
+scheduling let's say I have n
+ 
+
+ align:start position:0%
+scheduling let's say I have n
+jobs uh and they have uh completion
+
+ align:start position:0%
+jobs uh and they have uh completion
+ 
+
+ align:start position:0%
+jobs uh and they have uh completion
+times and that's it you can start them
+
+ align:start position:0%
+times and that's it you can start them
+ 
+
+ align:start position:0%
+times and that's it you can start them
+whenever you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want um and then on the other hand I
+
+ align:start position:0%
+want um and then on the other hand I
+ 
+
+ align:start position:0%
+want um and then on the other hand I
+have P processors to run those jobs each
+
+ align:start position:0%
+have P processors to run those jobs each
+ 
+
+ align:start position:0%
+have P processors to run those jobs each
+processor is sequential and I identical
+
+ align:start position:0%
+processor is sequential and I identical
+ 
+
+ align:start position:0%
+processor is sequential and I identical
+so the model is you assign jobs to
+
+ align:start position:0%
+so the model is you assign jobs to
+ 
+
+ align:start position:0%
+so the model is you assign jobs to
+processors job can only be on One
+
+ align:start position:0%
+processors job can only be on One
+ 
+
+ align:start position:0%
+processors job can only be on One
+processor and it runs to completion then
+
+ align:start position:0%
+processor and it runs to completion then
+ 
+
+ align:start position:0%
+processor and it runs to completion then
+it can run another job and so on my
+
+ align:start position:0%
+it can run another job and so on my
+ 
+
+ align:start position:0%
+it can run another job and so on my
+goal uh I'll State the decision version
+
+ align:start position:0%
+goal uh I'll State the decision version
+ 
+
+ align:start position:0%
+goal uh I'll State the decision version
+is to uh finish all
+
+ align:start position:0%
+is to uh finish all
+ 
+
+ align:start position:0%
+is to uh finish all
+jobs in
+
+ align:start position:0%
+jobs in
+ 
+
+ align:start position:0%
+jobs in
+time less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T okay so I claim this problem is NP
+
+ align:start position:0%
+T okay so I claim this problem is NP
+ 
+
+ align:start position:0%
+T okay so I claim this problem is NP
+some variety let's start with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduction from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition uh sorry um partition is a
+
+ align:start position:0%
+partition uh sorry um partition is a
+ 
+
+ align:start position:0%
+partition uh sorry um partition is a
+synonym for two partition usually we
+
+ align:start position:0%
+synonym for two partition usually we
+ 
+
+ align:start position:0%
+synonym for two partition usually we
+omit the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so reduction from
+
+ align:start position:0%
+two so reduction from
+ 
+
+ align:start position:0%
+two so reduction from
+partition this problem over here so I'm
+
+ align:start position:0%
+partition this problem over here so I'm
+ 
+
+ align:start position:0%
+partition this problem over here so I'm
+now I'm given some integers I want to
+
+ align:start position:0%
+now I'm given some integers I want to
+ 
+
+ align:start position:0%
+now I'm given some integers I want to
+split them in half
+
+ align:start position:0%
+split them in half
+ 
+
+ align:start position:0%
+split them in half
+basically uh any suggestions on what I
+
+ align:start position:0%
+basically uh any suggestions on what I
+ 
+
+ align:start position:0%
+basically uh any suggestions on what I
+could do to turn that into a
+
+ align:start position:0%
+could do to turn that into a
+ 
+
+ align:start position:0%
+could do to turn that into a
+multiprocessor scheduling
+
+ align:start position:0%
+multiprocessor scheduling
+ 
+
+ align:start position:0%
+multiprocessor scheduling
+problem two processor two processors
+
+ align:start position:0%
+problem two processor two processors
+ 
+
+ align:start position:0%
+problem two processor two processors
+yeah P equals 2 that is the reduction I
+
+ align:start position:0%
+yeah P equals 2 that is the reduction I
+ 
+
+ align:start position:0%
+yeah P equals 2 that is the reduction I
+guess technically I also have to specify
+
+ align:start position:0%
+guess technically I also have to specify
+ 
+
+ align:start position:0%
+guess technically I also have to specify
+what T is uh but it's over there so you
+
+ align:start position:0%
+what T is uh but it's over there so you
+ 
+
+ align:start position:0%
+what T is uh but it's over there so you
+set T to be the sum of the A's over two
+
+ align:start position:0%
+set T to be the sum of the A's over two
+ 
+
+ align:start position:0%
+set T to be the sum of the A's over two
+and you don't change a you just leave it
+
+ align:start position:0%
+and you don't change a you just leave it
+ 
+
+ align:start position:0%
+and you don't change a you just leave it
+alone so you just feed in the same AIS
+
+ align:start position:0%
+alone so you just feed in the same AIS
+ 
+
+ align:start position:0%
+alone so you just feed in the same AIS
+into this problem and that is two
+
+ align:start position:0%
+into this problem and that is two
+ 
+
+ align:start position:0%
+into this problem and that is two
+partition okay let's do a reduction from
+
+ align:start position:0%
+partition okay let's do a reduction from
+ 
+
+ align:start position:0%
+partition okay let's do a reduction from
+so now we know the problem is at least
+
+ align:start position:0%
+so now we know the problem is at least
+ 
+
+ align:start position:0%
+so now we know the problem is at least
+weakly NP hard but in fact it is
+
+ align:start position:0%
+weakly NP hard but in fact it is
+ 
+
+ align:start position:0%
+weakly NP hard but in fact it is
+strongly NP hard because we can reduce
+
+ align:start position:0%
+strongly NP hard because we can reduce
+ 
+
+ align:start position:0%
+strongly NP hard because we can reduce
+from three partition what do you
+
+ align:start position:0%
+from three partition what do you
+ 
+
+ align:start position:0%
+from three partition what do you
+do p n p equal n
+
+ align:start position:0%
+do p n p equal n
+ 
+
+ align:start position:0%
+do p n p equal n
+over3 that's it uh you set T accordingly
+
+ align:start position:0%
+over3 that's it uh you set T accordingly
+ 
+
+ align:start position:0%
+over3 that's it uh you set T accordingly
+some of the A's over
+
+ align:start position:0%
+some of the A's over
+ 
+
+ align:start position:0%
+some of the A's over
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+done okay uh so um this problem comes
+
+ align:start position:0%
+done okay uh so um this problem comes
+ 
+
+ align:start position:0%
+done okay uh so um this problem comes
+from the paper that introduces three
+
+ align:start position:0%
+from the paper that introduces three
+ 
+
+ align:start position:0%
+from the paper that introduces three
+part partition which is by Gary and
+
+ align:start position:0%
+part partition which is by Gary and
+ 
+
+ align:start position:0%
+part partition which is by Gary and
+Johnson same people who wrote the book
+
+ align:start position:0%
+Johnson same people who wrote the book
+ 
+
+ align:start position:0%
+Johnson same people who wrote the book
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so this is I mean this basically is
+
+ align:start position:0%
+so this is I mean this basically is
+ 
+
+ align:start position:0%
+so this is I mean this basically is
+three partition that's why they cared
+
+ align:start position:0%
+three partition that's why they cared
+ 
+
+ align:start position:0%
+three partition that's why they cared
+about it but here's a practical
+
+ align:start position:0%
+about it but here's a practical
+ 
+
+ align:start position:0%
+about it but here's a practical
+motivation for
+
+ align:start position:0%
+motivation for
+ 
+
+ align:start position:0%
+motivation for
+it uh cool let's do something more
+
+ align:start position:0%
+it uh cool let's do something more
+ 
+
+ align:start position:0%
+it uh cool let's do something more
+interesting and I got to want a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projector um any questions
+
+ align:start position:0%
+projector um any questions
+ 
+
+ align:start position:0%
+projector um any questions
+about uh I think youve had enough
+
+ align:start position:0%
+about uh I think youve had enough
+ 
+
+ align:start position:0%
+about uh I think youve had enough
+questions about pseudo poly weakly poly
+
+ align:start position:0%
+questions about pseudo poly weakly poly
+ 
+
+ align:start position:0%
+questions about pseudo poly weakly poly
+strongly poly as I erase them don't
+
+ align:start position:0%
+strongly poly as I erase them don't
+ 
+
+ align:start position:0%
+strongly poly as I erase them don't
+forget
+
+ align:start position:0%
+forget
+ 
+
+ align:start position:0%
+forget
+them uh but I think for the rest of
+
+ align:start position:0%
+them uh but I think for the rest of
+ 
+
+ align:start position:0%
+them uh but I think for the rest of
+today we're just going to be doing
+
+ align:start position:0%
+today we're just going to be doing
+ 
+
+ align:start position:0%
+today we're just going to be doing
+strong polinomial reductions uh from
+
+ align:start position:0%
+strong polinomial reductions uh from
+ 
+
+ align:start position:0%
+strong polinomial reductions uh from
+three partition I think next class we
+
+ align:start position:0%
+three partition I think next class we
+ 
+
+ align:start position:0%
+three partition I think next class we
+might do some weak ones but
+
+ align:start position:0%
+might do some weak ones but
+ 
+
+ align:start position:0%
+might do some weak ones but
+uh today we're going to really use the
+
+ align:start position:0%
+uh today we're going to really use the
+ 
+
+ align:start position:0%
+uh today we're going to really use the
+fact that it uh use the strongness and
+
+ align:start position:0%
+fact that it uh use the strongness and
+ 
+
+ align:start position:0%
+fact that it uh use the strongness and
+you'll see why because we really want to
+
+ align:start position:0%
+you'll see why because we really want to
+ 
+
+ align:start position:0%
+you'll see why because we really want to
+encode some numbers in
+
+ align:start position:0%
+encode some numbers in
+ 
+
+ align:start position:0%
+encode some numbers in
+un okay well let's start with what uh
+
+ align:start position:0%
+un okay well let's start with what uh
+ 
+
+ align:start position:0%
+un okay well let's start with what uh
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+problem rectangle packing this is going
+
+ align:start position:0%
+problem rectangle packing this is going
+ 
+
+ align:start position:0%
+problem rectangle packing this is going
+to lead us to a whole bunch of other
+
+ align:start position:0%
+to lead us to a whole bunch of other
+ 
+
+ align:start position:0%
+to lead us to a whole bunch of other
+types of packing problems so this is
+
+ align:start position:0%
+types of packing problems so this is
+ 
+
+ align:start position:0%
+types of packing problems so this is
+what you might call Packing rectangles
+
+ align:start position:0%
+what you might call Packing rectangles
+ 
+
+ align:start position:0%
+what you might call Packing rectangles
+into a rectangle so I'm given uh n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangles and I'm given a Target
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangle so when I say I'm given a
+
+ align:start position:0%
+rectangle so when I say I'm given a
+ 
+
+ align:start position:0%
+rectangle so when I say I'm given a
+rectangle what I really mean is I'm
+
+ align:start position:0%
+rectangle what I really mean is I'm
+ 
+
+ align:start position:0%
+rectangle what I really mean is I'm
+given the dimensions the width and the
+
+ align:start position:0%
+given the dimensions the width and the
+ 
+
+ align:start position:0%
+given the dimensions the width and the
+height as integers we're usually going
+
+ align:start position:0%
+height as integers we're usually going
+ 
+
+ align:start position:0%
+height as integers we're usually going
+to assume all our numbers of integers as
+
+ align:start position:0%
+to assume all our numbers of integers as
+ 
+
+ align:start position:0%
+to assume all our numbers of integers as
+I said
+
+ align:start position:0%
+I said
+ 
+
+ align:start position:0%
+I said
+uh do they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fit so what I'd like in a solution is to
+
+ align:start position:0%
+fit so what I'd like in a solution is to
+ 
+
+ align:start position:0%
+fit so what I'd like in a solution is to
+rotate and translate the the given
+
+ align:start position:0%
+rotate and translate the the given
+ 
+
+ align:start position:0%
+rotate and translate the the given
+rectangles so that they're disjoint from
+
+ align:start position:0%
+rectangles so that they're disjoint from
+ 
+
+ align:start position:0%
+rectangles so that they're disjoint from
+each other they can't overlap and they
+
+ align:start position:0%
+each other they can't overlap and they
+ 
+
+ align:start position:0%
+each other they can't overlap and they
+all fit inside the target rectangle
+
+ align:start position:0%
+all fit inside the target rectangle
+ 
+
+ align:start position:0%
+all fit inside the target rectangle
+right so this might be the target
+
+ align:start position:0%
+right so this might be the target
+ 
+
+ align:start position:0%
+right so this might be the target
+rectangle and then I don't know maybe
+
+ align:start position:0%
+rectangle and then I don't know maybe
+ 
+
+ align:start position:0%
+rectangle and then I don't know maybe
+this is is my set of rectangles
+
+ align:start position:0%
+this is is my set of rectangles
+ 
+
+ align:start position:0%
+this is is my set of rectangles
+appropriately
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packed uh so here maybe the answer is
+
+ align:start position:0%
+packed uh so here maybe the answer is
+ 
+
+ align:start position:0%
+packed uh so here maybe the answer is
+yes if they don't fit inside the target
+
+ align:start position:0%
+yes if they don't fit inside the target
+ 
+
+ align:start position:0%
+yes if they don't fit inside the target
+rectangle the answer is no this problem
+
+ align:start position:0%
+rectangle the answer is no this problem
+ 
+
+ align:start position:0%
+rectangle the answer is no this problem
+is strongly NP hard uh but I'm pretty
+
+ align:start position:0%
+is strongly NP hard uh but I'm pretty
+ 
+
+ align:start position:0%
+is strongly NP hard uh but I'm pretty
+sure we don't know whether it's in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NP so there are there are lots of open
+
+ align:start position:0%
+NP so there are there are lots of open
+ 
+
+ align:start position:0%
+NP so there are there are lots of open
+problems I don't mean to indicate
+
+ align:start position:0%
+problems I don't mean to indicate
+ 
+
+ align:start position:0%
+problems I don't mean to indicate
+everything's known uh this is a I should
+
+ align:start position:0%
+everything's known uh this is a I should
+ 
+
+ align:start position:0%
+everything's known uh this is a I should
+double check that this definitely not
+
+ align:start position:0%
+double check that this definitely not
+ 
+
+ align:start position:0%
+double check that this definitely not
+known but pretty sure it's open because
+
+ align:start position:0%
+known but pretty sure it's open because
+ 
+
+ align:start position:0%
+known but pretty sure it's open because
+of this rotation issue there's kind of a
+
+ align:start position:0%
+of this rotation issue there's kind of a
+ 
+
+ align:start position:0%
+of this rotation issue there's kind of a
+lot of things to worry about so it's not
+
+ align:start position:0%
+lot of things to worry about so it's not
+ 
+
+ align:start position:0%
+lot of things to worry about so it's not
+clear how efficiently you can encode a
+
+ align:start position:0%
+clear how efficiently you can encode a
+ 
+
+ align:start position:0%
+clear how efficiently you can encode a
+solution maybe you need a ton of bits of
+
+ align:start position:0%
+solution maybe you need a ton of bits of
+ 
+
+ align:start position:0%
+solution maybe you need a ton of bits of
+precision to say how things are rotated
+
+ align:start position:0%
+precision to say how things are rotated
+ 
+
+ align:start position:0%
+precision to say how things are rotated
+here they're all rotated at the same
+
+ align:start position:0%
+here they're all rotated at the same
+ 
+
+ align:start position:0%
+here they're all rotated at the same
+angle they may not be who knows uh so we
+
+ align:start position:0%
+angle they may not be who knows uh so we
+ 
+
+ align:start position:0%
+angle they may not be who knows uh so we
+will consider a a a special
+
+ align:start position:0%
+will consider a a a special
+ 
+
+ align:start position:0%
+will consider a a a special
+case which is
+
+ align:start position:0%
+case which is
+ 
+
+ align:start position:0%
+case which is
+um exact
+
+ align:start position:0%
+um exact
+ 
+
+ align:start position:0%
+um exact
+packing this also makes for a stronger
+
+ align:start position:0%
+packing this also makes for a stronger
+ 
+
+ align:start position:0%
+packing this also makes for a stronger
+hardness result so exact packing means
+
+ align:start position:0%
+hardness result so exact packing means
+ 
+
+ align:start position:0%
+hardness result so exact packing means
+uh there are no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gaps none of this
+
+ align:start position:0%
+gaps none of this
+ 
+
+ align:start position:0%
+gaps none of this
+stuff that's forbidden so if you have no
+
+ align:start position:0%
+stuff that's forbidden so if you have no
+ 
+
+ align:start position:0%
+stuff that's forbidden so if you have no
+gaps and you look at a corner of the
+
+ align:start position:0%
+gaps and you look at a corner of the
+ 
+
+ align:start position:0%
+gaps and you look at a corner of the
+rectangle that must mean there's a
+
+ align:start position:0%
+rectangle that must mean there's a
+ 
+
+ align:start position:0%
+rectangle that must mean there's a
+rectangle right there filling the corner
+
+ align:start position:0%
+rectangle right there filling the corner
+ 
+
+ align:start position:0%
+rectangle right there filling the corner
+which means there's no rotation well you
+
+ align:start position:0%
+which means there's no rotation well you
+ 
+
+ align:start position:0%
+which means there's no rotation well you
+could rotate by multiples of
+
+ align:start position:0%
+could rotate by multiples of
+ 
+
+ align:start position:0%
+could rotate by multiples of
+90 uh but so there's four rotations but
+
+ align:start position:0%
+90 uh but so there's four rotations but
+ 
+
+ align:start position:0%
+90 uh but so there's four rotations but
+I guess two for
+
+ align:start position:0%
+I guess two for
+ 
+
+ align:start position:0%
+I guess two for
+rectangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um into
+
+ align:start position:0%
+um into
+ 
+
+ align:start position:0%
+um into
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+90° so uh then the problem is in NP um
+
+ align:start position:0%
+90° so uh then the problem is in NP um
+ 
+
+ align:start position:0%
+90° so uh then the problem is in NP um
+because also you can show at that point
+
+ align:start position:0%
+because also you can show at that point
+ 
+
+ align:start position:0%
+because also you can show at that point
+because you have integer rectangles
+
+ align:start position:0%
+because you have integer rectangles
+ 
+
+ align:start position:0%
+because you have integer rectangles
+packing into an integer rectangle by
+
+ align:start position:0%
+packing into an integer rectangle by
+ 
+
+ align:start position:0%
+packing into an integer rectangle by
+induction uh the translations are
+
+ align:start position:0%
+induction uh the translations are
+ 
+
+ align:start position:0%
+induction uh the translations are
+integers therefore there are succinct
+
+ align:start position:0%
+integers therefore there are succinct
+ 
+
+ align:start position:0%
+integers therefore there are succinct
+codings of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them okay we don't have to do this but
+
+ align:start position:0%
+them okay we don't have to do this but
+ 
+
+ align:start position:0%
+them okay we don't have to do this but
+this is just to point out this is one
+
+ align:start position:0%
+this is just to point out this is one
+ 
+
+ align:start position:0%
+this is just to point out this is one
+way to make the problem in NP now there
+
+ align:start position:0%
+way to make the problem in NP now there
+ 
+
+ align:start position:0%
+way to make the problem in NP now there
+assing Solutions um so we're going to
+
+ align:start position:0%
+assing Solutions um so we're going to
+ 
+
+ align:start position:0%
+assing Solutions um so we're going to
+prove both of these problems are
+
+ align:start position:0%
+prove both of these problems are
+ 
+
+ align:start position:0%
+prove both of these problems are
+strongly n be
+
+ align:start position:0%
+strongly n be
+ 
+
+ align:start position:0%
+strongly n be
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+uh I think I'll I'll skip the we can't
+
+ align:start position:0%
+uh I think I'll I'll skip the we can't
+ 
+
+ align:start position:0%
+uh I think I'll I'll skip the we can't
+be hardness proof because it's not
+
+ align:start position:0%
+be hardness proof because it's not
+ 
+
+ align:start position:0%
+be hardness proof because it's not
+really any harder no pun intended um so
+
+ align:start position:0%
+really any harder no pun intended um so
+ 
+
+ align:start position:0%
+really any harder no pun intended um so
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh basic idea again we're reducing
+
+ align:start position:0%
+so uh basic idea again we're reducing
+ 
+
+ align:start position:0%
+so uh basic idea again we're reducing
+from three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partition so that means we're given an
+
+ align:start position:0%
+partition so that means we're given an
+ 
+
+ align:start position:0%
+partition so that means we're given an
+instance of three partition we're given
+
+ align:start position:0%
+instance of three partition we're given
+ 
+
+ align:start position:0%
+instance of three partition we're given
+an integers we want to represent those
+
+ align:start position:0%
+an integers we want to represent those
+ 
+
+ align:start position:0%
+an integers we want to represent those
+integers as rectangles so kind of the
+
+ align:start position:0%
+integers as rectangles so kind of the
+ 
+
+ align:start position:0%
+integers as rectangles so kind of the
+obvious way to do that is we take each
+
+ align:start position:0%
+obvious way to do that is we take each
+ 
+
+ align:start position:0%
+obvious way to do that is we take each
+Ai and we convert it into a rectangle
+
+ align:start position:0%
+Ai and we convert it into a rectangle
+ 
+
+ align:start position:0%
+Ai and we convert it into a rectangle
+let's say it's a AI by one that seems
+
+ align:start position:0%
+let's say it's a AI by one that seems
+ 
+
+ align:start position:0%
+let's say it's a AI by one that seems
+pretty obvious this is what you might
+
+ align:start position:0%
+pretty obvious this is what you might
+ 
+
+ align:start position:0%
+pretty obvious this is what you might
+call the AI Gadget this we're going to
+
+ align:start position:0%
+call the AI Gadget this we're going to
+ 
+
+ align:start position:0%
+call the AI Gadget this we're going to
+map this feature of our given instance
+
+ align:start position:0%
+map this feature of our given instance
+ 
+
+ align:start position:0%
+map this feature of our given instance
+to this feature of our constructed
+
+ align:start position:0%
+to this feature of our constructed
+ 
+
+ align:start position:0%
+to this feature of our constructed
+instance uh all that would be left at
+
+ align:start position:0%
+instance uh all that would be left at
+ 
+
+ align:start position:0%
+instance uh all that would be left at
+this point is what is the target
+
+ align:start position:0%
+this point is what is the target
+ 
+
+ align:start position:0%
+this point is what is the target
+rectangle um which I didn't give a
+
+ align:start position:0%
+rectangle um which I didn't give a
+ 
+
+ align:start position:0%
+rectangle um which I didn't give a
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+so let me call the target rectangle
+
+ align:start position:0%
+so let me call the target rectangle
+ 
+
+ align:start position:0%
+so let me call the target rectangle
+B that's what I use in my notes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh so let's say B is going to
+
+ align:start position:0%
+yeah uh so let's say B is going to
+ 
+
+ align:start position:0%
+yeah uh so let's say B is going to
+be it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangle uh what is the height of the
+
+ align:start position:0%
+rectangle uh what is the height of the
+ 
+
+ align:start position:0%
+rectangle uh what is the height of the
+rectangle n over
+
+ align:start position:0%
+rectangle n over
+ 
+
+ align:start position:0%
+rectangle n over
+three yes right and then the width the
+
+ align:start position:0%
+three yes right and then the width the
+ 
+
+ align:start position:0%
+three yes right and then the width the
+sum divid
+
+ align:start position:0%
+sum divid
+ 
+
+ align:start position:0%
+sum divid
+by the Target sum yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T cool so um the intent is uh if I that
+
+ align:start position:0%
+T cool so um the intent is uh if I that
+ 
+
+ align:start position:0%
+T cool so um the intent is uh if I that
+the rectangles will look something like
+
+ align:start position:0%
+the rectangles will look something like
+ 
+
+ align:start position:0%
+the rectangles will look something like
+this and always however uh if I fit
+
+ align:start position:0%
+this and always however uh if I fit
+ 
+
+ align:start position:0%
+this and always however uh if I fit
+three in here or maybe I could do more
+
+ align:start position:0%
+three in here or maybe I could do more
+ 
+
+ align:start position:0%
+three in here or maybe I could do more
+than three but uh we know that won't
+
+ align:start position:0%
+than three but uh we know that won't
+ 
+
+ align:start position:0%
+than three but uh we know that won't
+happen with the actual three partition
+
+ align:start position:0%
+happen with the actual three partition
+ 
+
+ align:start position:0%
+happen with the actual three partition
+instances we get uh because we can
+
+ align:start position:0%
+instances we get uh because we can
+ 
+
+ align:start position:0%
+instances we get uh because we can
+assume there's three of them but anyway
+
+ align:start position:0%
+assume there's three of them but anyway
+ 
+
+ align:start position:0%
+assume there's three of them but anyway
+uh we're not constraining there's only
+
+ align:start position:0%
+uh we're not constraining there's only
+ 
+
+ align:start position:0%
+uh we're not constraining there's only
+three you put in however many rectangles
+
+ align:start position:0%
+three you put in however many rectangles
+ 
+
+ align:start position:0%
+three you put in however many rectangles
+that add up to exactly the target sum
+
+ align:start position:0%
+that add up to exactly the target sum
+ 
+
+ align:start position:0%
+that add up to exactly the target sum
+boom you've got the target sum uh and
+
+ align:start position:0%
+boom you've got the target sum uh and
+ 
+
+ align:start position:0%
+boom you've got the target sum uh and
+there's just enough space for all of
+
+ align:start position:0%
+there's just enough space for all of
+ 
+
+ align:start position:0%
+there's just enough space for all of
+them if you pack them this way question
+
+ align:start position:0%
+them if you pack them this way question
+ 
+
+ align:start position:0%
+them if you pack them this way question
+uh shouldn't we specify that the AI
+
+ align:start position:0%
+uh shouldn't we specify that the AI
+ 
+
+ align:start position:0%
+uh shouldn't we specify that the AI
+rectangle is AI * n 3 + 1 to make sure
+
+ align:start position:0%
+rectangle is AI * n 3 + 1 to make sure
+ 
+
+ align:start position:0%
+rectangle is AI * n 3 + 1 to make sure
+that we can't accidentally rotate them
+
+ align:start position:0%
+that we can't accidentally rotate them
+ 
+
+ align:start position:0%
+that we can't accidentally rotate them
+yeah so uh part of my confusion in
+
+ align:start position:0%
+yeah so uh part of my confusion in
+ 
+
+ align:start position:0%
+yeah so uh part of my confusion in
+drawing this and a worry is you can take
+
+ align:start position:0%
+drawing this and a worry is you can take
+ 
+
+ align:start position:0%
+drawing this and a worry is you can take
+one of these rectangles and rotate it
+
+ align:start position:0%
+one of these rectangles and rotate it
+ 
+
+ align:start position:0%
+one of these rectangles and rotate it
+and then this reduction is wrong
+
+ align:start position:0%
+and then this reduction is wrong
+ 
+
+ align:start position:0%
+and then this reduction is wrong
+so this reduction is wrong uh so I will
+
+ align:start position:0%
+so this reduction is wrong uh so I will
+ 
+
+ align:start position:0%
+so this reduction is wrong uh so I will
+cheat and make this
+
+ align:start position:0%
+cheat and make this
+ 
+
+ align:start position:0%
+cheat and make this
+Epsilon and then multipli this by
+
+ align:start position:0%
+Epsilon and then multipli this by
+ 
+
+ align:start position:0%
+Epsilon and then multipli this by
+Epsilon this is one way to fix it of
+
+ align:start position:0%
+Epsilon this is one way to fix it of
+ 
+
+ align:start position:0%
+Epsilon this is one way to fix it of
+course now I have to scale everything up
+
+ align:start position:0%
+course now I have to scale everything up
+ 
+
+ align:start position:0%
+course now I have to scale everything up
+by one over Epsilon I have to tell you
+
+ align:start position:0%
+by one over Epsilon I have to tell you
+ 
+
+ align:start position:0%
+by one over Epsilon I have to tell you
+what Epsilon is uh you suggesting some
+
+ align:start position:0%
+what Epsilon is uh you suggesting some
+ 
+
+ align:start position:0%
+what Epsilon is uh you suggesting some
+multiple of N is a good good suggestion
+
+ align:start position:0%
+multiple of N is a good good suggestion
+ 
+
+ align:start position:0%
+multiple of N is a good good suggestion
+I think as long as we make this like
+
+ align:start position:0%
+I think as long as we make this like
+ 
+
+ align:start position:0%
+I think as long as we make this like
+much smaller than one then it's not
+
+ align:start position:0%
+much smaller than one then it's not
+ 
+
+ align:start position:0%
+much smaller than one then it's not
+possible to rotate because these guys
+
+ align:start position:0%
+possible to rotate because these guys
+ 
+
+ align:start position:0%
+possible to rotate because these guys
+are length at least one because they're
+
+ align:start position:0%
+are length at least one because they're
+ 
+
+ align:start position:0%
+are length at least one because they're
+integers so if I tried to rotate it has
+
+ align:start position:0%
+integers so if I tried to rotate it has
+ 
+
+ align:start position:0%
+integers so if I tried to rotate it has
+to be multiple 90° so I think as long as
+
+ align:start position:0%
+to be multiple 90° so I think as long as
+ 
+
+ align:start position:0%
+to be multiple 90° so I think as long as
+this is strictly less than one uh we are
+
+ align:start position:0%
+this is strictly less than one uh we are
+ 
+
+ align:start position:0%
+this is strictly less than one uh we are
+okay I didn't change the intended
+
+ align:start position:0%
+okay I didn't change the intended
+ 
+
+ align:start position:0%
+okay I didn't change the intended
+solution I just made everything
+
+ align:start position:0%
+solution I just made everything
+ 
+
+ align:start position:0%
+solution I just made everything
+narrower and so I just need to set
+
+ align:start position:0%
+narrower and so I just need to set
+ 
+
+ align:start position:0%
+narrower and so I just need to set
+Epsilon less than
+
+ align:start position:0%
+Epsilon less than
+ 
+
+ align:start position:0%
+Epsilon less than
+3n would be that
+
+ align:start position:0%
+3n would be that
+ 
+
+ align:start position:0%
+3n would be that
+inequality uh but I want integers so I
+
+ align:start position:0%
+inequality uh but I want integers so I
+ 
+
+ align:start position:0%
+inequality uh but I want integers so I
+should scale everything up by n over3 so
+
+ align:start position:0%
+should scale everything up by n over3 so
+ 
+
+ align:start position:0%
+should scale everything up by n over3 so
+just multiply all the numbers by n over
+
+ align:start position:0%
+just multiply all the numbers by n over
+ 
+
+ align:start position:0%
+just multiply all the numbers by n over
+three and you're
+
+ align:start position:0%
+three and you're
+ 
+
+ align:start position:0%
+three and you're
+done uh in fact you can be a little
+
+ align:start position:0%
+done uh in fact you can be a little
+ 
+
+ align:start position:0%
+done uh in fact you can be a little
+simpler and I drew this diagram long ago
+
+ align:start position:0%
+simpler and I drew this diagram long ago
+ 
+
+ align:start position:0%
+simpler and I drew this diagram long ago
+so I might as well show it to you uh you
+
+ align:start position:0%
+so I might as well show it to you uh you
+ 
+
+ align:start position:0%
+so I might as well show it to you uh you
+can just add N3 to all your integers
+
+ align:start position:0%
+can just add N3 to all your integers
+ 
+
+ align:start position:0%
+can just add N3 to all your integers
+that will also work um under the
+
+ align:start position:0%
+that will also work um under the
+ 
+
+ align:start position:0%
+that will also work um under the
+assumption that you only have you can
+
+ align:start position:0%
+assumption that you only have you can
+ 
+
+ align:start position:0%
+assumption that you only have you can
+only take three numbers and add them up
+
+ align:start position:0%
+only take three numbers and add them up
+ 
+
+ align:start position:0%
+only take three numbers and add them up
+then you'll always be adding three times
+
+ align:start position:0%
+then you'll always be adding three times
+ 
+
+ align:start position:0%
+then you'll always be adding three times
+n over3
+
+ align:start position:0%
+n over3
+ 
+
+ align:start position:0%
+n over3
+horizontally um and so so the AIS here
+
+ align:start position:0%
+horizontally um and so so the AIS here
+ 
+
+ align:start position:0%
+horizontally um and so so the AIS here
+are this the yellow part of these
+
+ align:start position:0%
+are this the yellow part of these
+ 
+
+ align:start position:0%
+are this the yellow part of these
+rectangles and then we're just adding
+
+ align:start position:0%
+rectangles and then we're just adding
+ 
+
+ align:start position:0%
+rectangles and then we're just adding
+this fixed n over three to all of them
+
+ align:start position:0%
+this fixed n over three to all of them
+ 
+
+ align:start position:0%
+this fixed n over three to all of them
+so is a four four four four five five
+
+ align:start position:0%
+so is a four four four four five five
+ 
+
+ align:start position:0%
+so is a four four four four five five
+five six 7
+
+ align:start position:0%
+five six 7
+ 
+
+ align:start position:0%
+five six 7
+um and that happens to be a positive
+
+ align:start position:0%
+um and that happens to be a positive
+ 
+
+ align:start position:0%
+um and that happens to be a positive
+instance of three partition there is a
+
+ align:start position:0%
+instance of three partition there is a
+ 
+
+ align:start position:0%
+instance of three partition there is a
+solution this is one way to do it so
+
+ align:start position:0%
+solution this is one way to do it so
+ 
+
+ align:start position:0%
+solution this is one way to do it so
+we're just adding n over all here
+
+ align:start position:0%
+we're just adding n over all here
+ 
+
+ align:start position:0%
+we're just adding n over all here
+because we have 3 * n over3 and that
+
+ align:start position:0%
+because we have 3 * n over3 and that
+ 
+
+ align:start position:0%
+because we have 3 * n over3 and that
+guarant and uh you know the length of
+
+ align:start position:0%
+guarant and uh you know the length of
+ 
+
+ align:start position:0%
+guarant and uh you know the length of
+these is always
+
+ align:start position:0%
+these is always
+ 
+
+ align:start position:0%
+these is always
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+smaller uh yeah rotation should not be
+
+ align:start position:0%
+smaller uh yeah rotation should not be
+ 
+
+ align:start position:0%
+smaller uh yeah rotation should not be
+possible right because each of these
+
+ align:start position:0%
+possible right because each of these
+ 
+
+ align:start position:0%
+possible right because each of these
+guys is going to be length strictly
+
+ align:start position:0%
+guys is going to be length strictly
+ 
+
+ align:start position:0%
+guys is going to be length strictly
+larger than n over3 because we add an
+
+ align:start position:0%
+larger than n over3 because we add an
+ 
+
+ align:start position:0%
+larger than n over3 because we add an
+integer to n a positive integer and the
+
+ align:start position:0%
+integer to n a positive integer and the
+ 
+
+ align:start position:0%
+integer to n a positive integer and the
+height here is N3 so that just barely
+
+ align:start position:0%
+height here is N3 so that just barely
+ 
+
+ align:start position:0%
+height here is N3 so that just barely
+works same thing more or less just this
+
+ align:start position:0%
+works same thing more or less just this
+ 
+
+ align:start position:0%
+works same thing more or less just this
+is scaling by a multiplicative Factor
+
+ align:start position:0%
+is scaling by a multiplicative Factor
+ 
+
+ align:start position:0%
+is scaling by a multiplicative Factor
+here we're doing an additive thing
+
+ align:start position:0%
+here we're doing an additive thing
+ 
+
+ align:start position:0%
+here we're doing an additive thing
+because we have this luxury of knowing
+
+ align:start position:0%
+because we have this luxury of knowing
+ 
+
+ align:start position:0%
+because we have this luxury of knowing
+there are three items in every
+
+ align:start position:0%
+there are three items in every
+ 
+
+ align:start position:0%
+there are three items in every
+triple cool rectangle packing question
+
+ align:start position:0%
+triple cool rectangle packing question
+ 
+
+ align:start position:0%
+triple cool rectangle packing question
+uh there's a question about three
+
+ align:start position:0%
+uh there's a question about three
+ 
+
+ align:start position:0%
+uh there's a question about three
+partition is it assumed that they're
+
+ align:start position:0%
+partition is it assumed that they're
+ 
+
+ align:start position:0%
+partition is it assumed that they're
+positive integers yes sorry all the
+
+ align:start position:0%
+positive integers yes sorry all the
+ 
+
+ align:start position:0%
+positive integers yes sorry all the
+integers are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive yeah I you don't have to but we
+
+ align:start position:0%
+positive yeah I you don't have to but we
+ 
+
+ align:start position:0%
+positive yeah I you don't have to but we
+can so we will
+
+ align:start position:0%
+can so we will
+ 
+
+ align:start position:0%
+can so we will
+makes our life a lot
+
+ align:start position:0%
+makes our life a lot
+ 
+
+ align:start position:0%
+makes our life a lot
+easier other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay
+
+ align:start position:0%
+questions okay
+ 
+
+ align:start position:0%
+questions okay
+uh time for some
+
+ align:start position:0%
+uh time for some
+ 
+
+ align:start position:0%
+uh time for some
+puzzles uh so I think I'll show you some
+
+ align:start position:0%
+puzzles uh so I think I'll show you some
+ 
+
+ align:start position:0%
+puzzles uh so I think I'll show you some
+real life puzzles first um there's this
+
+ align:start position:0%
+real life puzzles first um there's this
+ 
+
+ align:start position:0%
+real life puzzles first um there's this
+notion of an edge matching puzzle which
+
+ align:start position:0%
+notion of an edge matching puzzle which
+ 
+
+ align:start position:0%
+notion of an edge matching puzzle which
+goes back to the
+
+ align:start position:0%
+goes back to the
+ 
+
+ align:start position:0%
+goes back to the
+1890s I believe this one is from late
+
+ align:start position:0%
+1890s I believe this one is from late
+ 
+
+ align:start position:0%
+1890s I believe this one is from late
+1890s early 1900s so it's one of the
+
+ align:start position:0%
+1890s early 1900s so it's one of the
+ 
+
+ align:start position:0%
+1890s early 1900s so it's one of the
+older ones you prob at least when I was
+
+ align:start position:0%
+older ones you prob at least when I was
+ 
+
+ align:start position:0%
+older ones you prob at least when I was
+growing up we had these puzzles all over
+
+ align:start position:0%
+growing up we had these puzzles all over
+ 
+
+ align:start position:0%
+growing up we had these puzzles all over
+the place uh so what's going on here is
+
+ align:start position:0%
+the place uh so what's going on here is
+ 
+
+ align:start position:0%
+the place uh so what's going on here is
+you have physical triangles and these
+
+ align:start position:0%
+you have physical triangles and these
+ 
+
+ align:start position:0%
+you have physical triangles and these
+half frogs are drawn on the edges of the
+
+ align:start position:0%
+half frogs are drawn on the edges of the
+ 
+
+ align:start position:0%
+half frogs are drawn on the edges of the
+triangles and your goal is to pack all
+
+ align:start position:0%
+triangles and your goal is to pack all
+ 
+
+ align:start position:0%
+triangles and your goal is to pack all
+these triangles into the big triangle
+
+ align:start position:0%
+these triangles into the big triangle
+ 
+
+ align:start position:0%
+these triangles into the big triangle
+that's easy it's a regular triang uh uh
+
+ align:start position:0%
+that's easy it's a regular triang uh uh
+ 
+
+ align:start position:0%
+that's easy it's a regular triang uh uh
+triangulation but you need the half
+
+ align:start position:0%
+triangulation but you need the half
+ 
+
+ align:start position:0%
+triangulation but you need the half
+frogs to match up the B the the I don't
+
+ align:start position:0%
+frogs to match up the B the the I don't
+ 
+
+ align:start position:0%
+frogs to match up the B the the I don't
+know the the behind end of the white
+
+ align:start position:0%
+know the the behind end of the white
+ 
+
+ align:start position:0%
+know the the behind end of the white
+sorry yellow speckled frog matches the
+
+ align:start position:0%
+sorry yellow speckled frog matches the
+ 
+
+ align:start position:0%
+sorry yellow speckled frog matches the
+front end of the yellow black speckled
+
+ align:start position:0%
+front end of the yellow black speckled
+ 
+
+ align:start position:0%
+front end of the yellow black speckled
+frog as drawn here this is a valid
+
+ align:start position:0%
+frog as drawn here this is a valid
+ 
+
+ align:start position:0%
+frog as drawn here this is a valid
+solution but if I like rotated this tile
+
+ align:start position:0%
+solution but if I like rotated this tile
+ 
+
+ align:start position:0%
+solution but if I like rotated this tile
+120 degrees that's not a valid solution
+
+ align:start position:0%
+120 degrees that's not a valid solution
+ 
+
+ align:start position:0%
+120 degrees that's not a valid solution
+um even though it's all Hinds matching
+
+ align:start position:0%
+um even though it's all Hinds matching
+ 
+
+ align:start position:0%
+um even though it's all Hinds matching
+to fronts and so on okay rules clear uh
+
+ align:start position:0%
+to fronts and so on okay rules clear uh
+ 
+
+ align:start position:0%
+to fronts and so on okay rules clear uh
+so these are Edge matching puzzles this
+
+ align:start position:0%
+so these are Edge matching puzzles this
+ 
+
+ align:start position:0%
+so these are Edge matching puzzles this
+is formulated in a different way this is
+
+ align:start position:0%
+is formulated in a different way this is
+ 
+
+ align:start position:0%
+is formulated in a different way this is
+not a valid solution the goal is to get
+
+ align:start position:0%
+not a valid solution the goal is to get
+ 
+
+ align:start position:0%
+not a valid solution the goal is to get
+these colors to all match up so in
+
+ align:start position:0%
+these colors to all match up so in
+ 
+
+ align:start position:0%
+these colors to all match up so in
+general you can think of there being a
+
+ align:start position:0%
+general you can think of there being a
+ 
+
+ align:start position:0%
+general you can think of there being a
+color on an edge um and here it happens
+
+ align:start position:0%
+color on an edge um and here it happens
+ 
+
+ align:start position:0%
+color on an edge um and here it happens
+to be composed of these two colors and
+
+ align:start position:0%
+to be composed of these two colors and
+ 
+
+ align:start position:0%
+to be composed of these two colors and
+it have to match both of the colors on
+
+ align:start position:0%
+it have to match both of the colors on
+ 
+
+ align:start position:0%
+it have to match both of the colors on
+the other side so this essentially like
+
+ align:start position:0%
+the other side so this essentially like
+ 
+
+ align:start position:0%
+the other side so this essentially like
+having a color on each edge here we also
+
+ align:start position:0%
+having a color on each edge here we also
+ 
+
+ align:start position:0%
+having a color on each edge here we also
+have a color on each Edge but we also
+
+ align:start position:0%
+have a color on each Edge but we also
+ 
+
+ align:start position:0%
+have a color on each Edge but we also
+have a sign uh which is the front or the
+
+ align:start position:0%
+have a sign uh which is the front or the
+ 
+
+ align:start position:0%
+have a sign uh which is the front or the
+hind part of the Frog there you know the
+
+ align:start position:0%
+hind part of the Frog there you know the
+ 
+
+ align:start position:0%
+hind part of the Frog there you know the
+yellow frog the Red Frog the green frog
+
+ align:start position:0%
+yellow frog the Red Frog the green frog
+ 
+
+ align:start position:0%
+yellow frog the Red Frog the green frog
+the orange frog um so in general we're
+
+ align:start position:0%
+the orange frog um so in general we're
+ 
+
+ align:start position:0%
+the orange frog um so in general we're
+going to formulate this
+
+ align:start position:0%
+going to formulate this
+ 
+
+ align:start position:0%
+going to formulate this
+uh be over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there are many types of these
+
+ align:start position:0%
+okay there are many types of these
+ 
+
+ align:start position:0%
+okay there are many types of these
+puzzles um I'll try to
+
+ align:start position:0%
+puzzles um I'll try to
+ 
+
+ align:start position:0%
+puzzles um I'll try to
+capture that's not exactly either one of
+
+ align:start position:0%
+capture that's not exactly either one of
+ 
+
+ align:start position:0%
+capture that's not exactly either one of
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if you've ever studied something
+
+ align:start position:0%
+um if you've ever studied something
+ 
+
+ align:start position:0%
+um if you've ever studied something
+called Wang tiles uh this is exactly
+
+ align:start position:0%
+called Wang tiles uh this is exactly
+ 
+
+ align:start position:0%
+called Wang tiles uh this is exactly
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model just throw in the word there but
+
+ align:start position:0%
+model just throw in the word there but
+ 
+
+ align:start position:0%
+model just throw in the word there but
+uh what we have are n uh unit
+
+ align:start position:0%
+uh what we have are n uh unit
+ 
+
+ align:start position:0%
+uh what we have are n uh unit
+squares those are called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tiles each
+
+ align:start position:0%
+tiles each
+ 
+
+ align:start position:0%
+tiles each
+one has four colors uh a b c
+
+ align:start position:0%
+one has four colors uh a b c
+ 
+
+ align:start position:0%
+one has four colors uh a b c
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one color per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inedge
+
+ align:start position:0%
+inedge
+ 
+
+ align:start position:0%
+inedge
+and okay you're also given a Target
+
+ align:start position:0%
+and okay you're also given a Target
+ 
+
+ align:start position:0%
+and okay you're also given a Target
+rectangle it's going to be integer
+
+ align:start position:0%
+rectangle it's going to be integer
+ 
+
+ align:start position:0%
+rectangle it's going to be integer
+because these are unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squares and you want
+
+ align:start position:0%
+squares and you want
+ 
+
+ align:start position:0%
+squares and you want
+to pack probably exactly pack there's
+
+ align:start position:0%
+to pack probably exactly pack there's
+ 
+
+ align:start position:0%
+to pack probably exactly pack there's
+not going to be any gaps uh the squares
+
+ align:start position:0%
+not going to be any gaps uh the squares
+ 
+
+ align:start position:0%
+not going to be any gaps uh the squares
+into the
+
+ align:start position:0%
+into the
+ 
+
+ align:start position:0%
+into the
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+um with colors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matching so whenever I have two
+
+ align:start position:0%
+matching so whenever I have two
+ 
+
+ align:start position:0%
+matching so whenever I have two
+squares that share an edge the color
+
+ align:start position:0%
+squares that share an edge the color
+ 
+
+ align:start position:0%
+squares that share an edge the color
+that's written here better be the same
+
+ align:start position:0%
+that's written here better be the same
+ 
+
+ align:start position:0%
+that's written here better be the same
+color that's written there that's the
+
+ align:start position:0%
+color that's written there that's the
+ 
+
+ align:start position:0%
+color that's written there that's the
+rules if you're on the boundary no
+
+ align:start position:0%
+rules if you're on the boundary no
+ 
+
+ align:start position:0%
+rules if you're on the boundary no
+restriction but if you're an interior
+
+ align:start position:0%
+restriction but if you're an interior
+ 
+
+ align:start position:0%
+restriction but if you're an interior
+Edge you restrict in that way okay uh
+
+ align:start position:0%
+Edge you restrict in that way okay uh
+ 
+
+ align:start position:0%
+Edge you restrict in that way okay uh
+this actually closely matches what is
+
+ align:start position:0%
+this actually closely matches what is
+ 
+
+ align:start position:0%
+this actually closely matches what is
+currently maybe the most famous Edge
+
+ align:start position:0%
+currently maybe the most famous Edge
+ 
+
+ align:start position:0%
+currently maybe the most famous Edge
+matching puzzle called eternity 2 uh
+
+ align:start position:0%
+matching puzzle called eternity 2 uh
+ 
+
+ align:start position:0%
+matching puzzle called eternity 2 uh
+this one is still unsolved well the
+
+ align:start position:0%
+this one is still unsolved well the
+ 
+
+ align:start position:0%
+this one is still unsolved well the
+creator has a solution and if you ever
+
+ align:start position:0%
+creator has a solution and if you ever
+ 
+
+ align:start position:0%
+creator has a solution and if you ever
+find it or one of the many other
+
+ align:start position:0%
+find it or one of the many other
+ 
+
+ align:start position:0%
+find it or one of the many other
+Solutions who knows you will win $2
+
+ align:start position:0%
+Solutions who knows you will win $2
+ 
+
+ align:start position:0%
+Solutions who knows you will win $2
+million us so time to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rich well yeah I guess that's the way to
+
+ align:start position:0%
+rich well yeah I guess that's the way to
+ 
+
+ align:start position:0%
+rich well yeah I guess that's the way to
+make the most money is first solve P
+
+ align:start position:0%
+make the most money is first solve P
+ 
+
+ align:start position:0%
+make the most money is first solve P
+equals NP then solve eternity 2 I guess
+
+ align:start position:0%
+equals NP then solve eternity 2 I guess
+ 
+
+ align:start position:0%
+equals NP then solve eternity 2 I guess
+uh but you could easily solve this
+
+ align:start position:0%
+uh but you could easily solve this
+ 
+
+ align:start position:0%
+uh but you could easily solve this
+puzzle without uh P NP there actually a
+
+ align:start position:0%
+puzzle without uh P NP there actually a
+ 
+
+ align:start position:0%
+puzzle without uh P NP there actually a
+lot of almost Solutions out there uh I
+
+ align:start position:0%
+lot of almost Solutions out there uh I
+ 
+
+ align:start position:0%
+lot of almost Solutions out there uh I
+believe this is uh one of the leaders uh
+
+ align:start position:0%
+believe this is uh one of the leaders uh
+ 
+
+ align:start position:0%
+believe this is uh one of the leaders uh
+this guy leis verad um got so this is a
+
+ align:start position:0%
+this guy leis verad um got so this is a
+ 
+
+ align:start position:0%
+this guy leis verad um got so this is a
+complete solution with all the pieces uh
+
+ align:start position:0%
+complete solution with all the pieces uh
+ 
+
+ align:start position:0%
+complete solution with all the pieces uh
+but not all the edges match so it's hard
+
+ align:start position:0%
+but not all the edges match so it's hard
+ 
+
+ align:start position:0%
+but not all the edges match so it's hard
+to find them but here's one for example
+
+ align:start position:0%
+to find them but here's one for example
+ 
+
+ align:start position:0%
+to find them but here's one for example
+that mismatches so I didn't explain but
+
+ align:start position:0%
+that mismatches so I didn't explain but
+ 
+
+ align:start position:0%
+that mismatches so I didn't explain but
+there everything is a Square Tile here
+
+ align:start position:0%
+there everything is a Square Tile here
+ 
+
+ align:start position:0%
+there everything is a Square Tile here
+and there's a different shape and color
+
+ align:start position:0%
+and there's a different shape and color
+ 
+
+ align:start position:0%
+and there's a different shape and color
+but it's basically a color from
+
+ align:start position:0%
+but it's basically a color from
+ 
+
+ align:start position:0%
+but it's basically a color from
+mathematical perspective got a all up
+
+ align:start position:0%
+mathematical perspective got a all up
+ 
+
+ align:start position:0%
+mathematical perspective got a all up
+here he got 467 matches out of the 480
+
+ align:start position:0%
+here he got 467 matches out of the 480
+ 
+
+ align:start position:0%
+here he got 467 matches out of the 480
+edges and that won him already
+
+ align:start position:0%
+edges and that won him already
+ 
+
+ align:start position:0%
+edges and that won him already
+$10,000 and I believe it's found uh with
+
+ align:start position:0%
+$10,000 and I believe it's found uh with
+ 
+
+ align:start position:0%
+$10,000 and I believe it's found uh with
+computer a search uh got software that's
+
+ align:start position:0%
+computer a search uh got software that's
+ 
+
+ align:start position:0%
+computer a search uh got software that's
+not the person I I I don't know for sure
+
+ align:start position:0%
+not the person I I I don't know for sure
+ 
+
+ align:start position:0%
+not the person I I I don't know for sure
+uh I would guess that it's Louis's
+
+ align:start position:0%
+uh I would guess that it's Louis's
+ 
+
+ align:start position:0%
+uh I would guess that it's Louis's
+daughter um here's a different almost
+
+ align:start position:0%
+daughter um here's a different almost
+ 
+
+ align:start position:0%
+daughter um here's a different almost
+solution where there's some missing
+
+ align:start position:0%
+solution where there's some missing
+ 
+
+ align:start position:0%
+solution where there's some missing
+tiles but everything matches and then at
+
+ align:start position:0%
+tiles but everything matches and then at
+ 
+
+ align:start position:0%
+tiles but everything matches and then at
+the bottom of his web page you should
+
+ align:start position:0%
+the bottom of his web page you should
+ 
+
+ align:start position:0%
+the bottom of his web page you should
+check it out it's fun he says and here's
+
+ align:start position:0%
+check it out it's fun he says and here's
+ 
+
+ align:start position:0%
+check it out it's fun he says and here's
+a solution to Trinity 2 and I looked at
+
+ align:start position:0%
+a solution to Trinity 2 and I looked at
+ 
+
+ align:start position:0%
+a solution to Trinity 2 and I looked at
+this for a long time it's like I don't
+
+ align:start position:0%
+this for a long time it's like I don't
+ 
+
+ align:start position:0%
+this for a long time it's like I don't
+see any Edge matches uh but you guys are
+
+ align:start position:0%
+see any Edge matches uh but you guys are
+ 
+
+ align:start position:0%
+see any Edge matches uh but you guys are
+smart so you probably know uh there's
+
+ align:start position:0%
+smart so you probably know uh there's
+ 
+
+ align:start position:0%
+smart so you probably know uh there's
+one other cheat you could possibly do in
+
+ align:start position:0%
+one other cheat you could possibly do in
+ 
+
+ align:start position:0%
+one other cheat you could possibly do in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+puzzle maybe add a different add
+
+ align:start position:0%
+puzzle maybe add a different add
+ 
+
+ align:start position:0%
+puzzle maybe add a different add
+different tiles maybe although these are
+
+ align:start position:0%
+different tiles maybe although these are
+ 
+
+ align:start position:0%
+different tiles maybe although these are
+nicely printed tiles so I would guess he
+
+ align:start position:0%
+nicely printed tiles so I would guess he
+ 
+
+ align:start position:0%
+nicely printed tiles so I would guess he
+bought two
+
+ align:start position:0%
+bought two
+ 
+
+ align:start position:0%
+bought two
+sets uh and he's mixed some parts I
+
+ align:start position:0%
+sets uh and he's mixed some parts I
+ 
+
+ align:start position:0%
+sets uh and he's mixed some parts I
+wrote a program to check yes indeed some
+
+ align:start position:0%
+wrote a program to check yes indeed some
+ 
+
+ align:start position:0%
+wrote a program to check yes indeed some
+tiles are repeated here I forget exactly
+
+ align:start position:0%
+tiles are repeated here I forget exactly
+ 
+
+ align:start position:0%
+tiles are repeated here I forget exactly
+how many 10 or 20 or something it's
+
+ align:start position:0%
+how many 10 or 20 or something it's
+ 
+
+ align:start position:0%
+how many 10 or 20 or something it's
+still pretty cool it looks like it's
+
+ align:start position:0%
+still pretty cool it looks like it's
+ 
+
+ align:start position:0%
+still pretty cool it looks like it's
+done but there's no complete actual
+
+ align:start position:0%
+done but there's no complete actual
+ 
+
+ align:start position:0%
+done but there's no complete actual
+solution using each piece exactly once
+
+ align:start position:0%
+solution using each piece exactly once
+ 
+
+ align:start position:0%
+solution using each piece exactly once
+uh it's probably clear here but you only
+
+ align:start position:0%
+uh it's probably clear here but you only
+ 
+
+ align:start position:0%
+uh it's probably clear here but you only
+get one version of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square okay uh so there's your
+
+ align:start position:0%
+Square okay uh so there's your
+ 
+
+ align:start position:0%
+Square okay uh so there's your
+motivation for solving Edge matching so
+
+ align:start position:0%
+motivation for solving Edge matching so
+ 
+
+ align:start position:0%
+motivation for solving Edge matching so
+you might wonder oh can I solve it in
+
+ align:start position:0%
+you might wonder oh can I solve it in
+ 
+
+ align:start position:0%
+you might wonder oh can I solve it in
+polinomial time and the answer is no
+
+ align:start position:0%
+polinomial time and the answer is no
+ 
+
+ align:start position:0%
+polinomial time and the answer is no
+unless P equals NP um and here we're
+
+ align:start position:0%
+unless P equals NP um and here we're
+ 
+
+ align:start position:0%
+unless P equals NP um and here we're
+going to use essentially rectangle p
+
+ align:start position:0%
+going to use essentially rectangle p
+ 
+
+ align:start position:0%
+going to use essentially rectangle p
+packing and this
+
+ align:start position:0%
+packing and this
+ 
+
+ align:start position:0%
+packing and this
+reduction so how could I how could I
+
+ align:start position:0%
+reduction so how could I how could I
+ 
+
+ align:start position:0%
+reduction so how could I how could I
+again we're going to reduce from three
+
+ align:start position:0%
+again we're going to reduce from three
+ 
+
+ align:start position:0%
+again we're going to reduce from three
+partition how could I convert a number
+
+ align:start position:0%
+partition how could I convert a number
+ 
+
+ align:start position:0%
+partition how could I convert a number
+AI into something like a rectangle using
+
+ align:start position:0%
+AI into something like a rectangle using
+ 
+
+ align:start position:0%
+AI into something like a rectangle using
+Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matching uh I should probably copy over
+
+ align:start position:0%
+matching uh I should probably copy over
+ 
+
+ align:start position:0%
+matching uh I should probably copy over
+the one that we had in the end which was
+
+ align:start position:0%
+the one that we had in the end which was
+ 
+
+ align:start position:0%
+the one that we had in the end which was
+AI goes
+
+ align:start position:0%
+AI goes
+ 
+
+ align:start position:0%
+AI goes
+to uh n /3 + AI by 1 cuz we want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers yeah so um you make it so that
+
+ align:start position:0%
+integers yeah so um you make it so that
+ 
+
+ align:start position:0%
+integers yeah so um you make it so that
+there's sort of one color that's for
+
+ align:start position:0%
+there's sort of one color that's for
+ 
+
+ align:start position:0%
+there's sort of one color that's for
+joining most things and that that's
+
+ align:start position:0%
+joining most things and that that's
+ 
+
+ align:start position:0%
+joining most things and that that's
+going to go kind of on the outside of
+
+ align:start position:0%
+going to go kind of on the outside of
+ 
+
+ align:start position:0%
+going to go kind of on the outside of
+each rectangle we going to put together
+
+ align:start position:0%
+each rectangle we going to put together
+ 
+
+ align:start position:0%
+each rectangle we going to put together
+each rectangle if you need like if if
+
+ align:start position:0%
+each rectangle if you need like if if
+ 
+
+ align:start position:0%
+each rectangle if you need like if if
+the rectangle is like a I by 1 then
+
+ align:start position:0%
+the rectangle is like a I by 1 then
+ 
+
+ align:start position:0%
+the rectangle is like a I by 1 then
+you're going to need AI squares such
+
+ align:start position:0%
+you're going to need AI squares such
+ 
+
+ align:start position:0%
+you're going to need AI squares such
+that there's like one color for that
+
+ align:start position:0%
+that there's like one color for that
+ 
+
+ align:start position:0%
+that there's like one color for that
+rectangle that is only
+
+ align:start position:0%
+rectangle that is only
+ 
+
+ align:start position:0%
+rectangle that is only
+used to join together squ of that
+
+ align:start position:0%
+used to join together squ of that
+ 
+
+ align:start position:0%
+used to join together squ of that
+rectangle good so we're going to convert
+
+ align:start position:0%
+rectangle good so we're going to convert
+ 
+
+ align:start position:0%
+rectangle good so we're going to convert
+this something by one rectangle into
+
+ align:start position:0%
+this something by one rectangle into
+ 
+
+ align:start position:0%
+this something by one rectangle into
+that into something different squares
+
+ align:start position:0%
+that into something different squares
+ 
+
+ align:start position:0%
+that into something different squares
+that's and we're just going to subdivide
+
+ align:start position:0%
+that's and we're just going to subdivide
+ 
+
+ align:start position:0%
+that's and we're just going to subdivide
+like that and we're going to surround
+
+ align:start position:0%
+like that and we're going to surround
+ 
+
+ align:start position:0%
+like that and we're going to surround
+all these uh edges with the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color uh that will work and the interior
+
+ align:start position:0%
+color uh that will work and the interior
+ 
+
+ align:start position:0%
+color uh that will work and the interior
+edes the interior edges all right so
+
+ align:start position:0%
+edes the interior edges all right so
+ 
+
+ align:start position:0%
+edes the interior edges all right so
+we're going to take Ai and we're going
+
+ align:start position:0%
+we're going to take Ai and we're going
+ 
+
+ align:start position:0%
+we're going to take Ai and we're going
+to convert it
+
+ align:start position:0%
+to convert it
+ 
+
+ align:start position:0%
+to convert it
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay don't make me draw all of them
+
+ align:start position:0%
+uh okay don't make me draw all of them
+ 
+
+ align:start position:0%
+uh okay don't make me draw all of them
+um the width here let's say it'll be n
+
+ align:start position:0%
+um the width here let's say it'll be n
+ 
+
+ align:start position:0%
+um the width here let's say it'll be n
+over3 plus
+
+ align:start position:0%
+over3 plus
+ 
+
+ align:start position:0%
+over3 plus
+AI uh and we're going to use a special
+
+ align:start position:0%
+AI uh and we're going to use a special
+ 
+
+ align:start position:0%
+AI uh and we're going to use a special
+color I'll call it black on the outside
+
+ align:start position:0%
+color I'll call it black on the outside
+ 
+
+ align:start position:0%
+color I'll call it black on the outside
+and this color I'm going to call these
+
+ align:start position:0%
+and this color I'm going to call these
+ 
+
+ align:start position:0%
+and this color I'm going to call these
+red so it's slightly visible I'm gonna
+
+ align:start position:0%
+red so it's slightly visible I'm gonna
+ 
+
+ align:start position:0%
+red so it's slightly visible I'm gonna
+call I this is going to be a different
+
+ align:start position:0%
+call I this is going to be a different
+ 
+
+ align:start position:0%
+call I this is going to be a different
+color for
+
+ align:start position:0%
+color for
+ 
+
+ align:start position:0%
+color for
+um each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AI That's um this will require a little
+
+ align:start position:0%
+AI That's um this will require a little
+ 
+
+ align:start position:0%
+AI That's um this will require a little
+bit more work you could also use a
+
+ align:start position:0%
+bit more work you could also use a
+ 
+
+ align:start position:0%
+bit more work you could also use a
+different you could use i1 I2 I3 that
+
+ align:start position:0%
+different you could use i1 I2 I3 that
+ 
+
+ align:start position:0%
+different you could use i1 I2 I3 that
+would really Force this to go together
+
+ align:start position:0%
+would really Force this to go together
+ 
+
+ align:start position:0%
+would really Force this to go together
+in this way um if I'm a little if I'm
+
+ align:start position:0%
+in this way um if I'm a little if I'm
+ 
+
+ align:start position:0%
+in this way um if I'm a little if I'm
+trying to be conservative on colors I
+
+ align:start position:0%
+trying to be conservative on colors I
+ 
+
+ align:start position:0%
+trying to be conservative on colors I
+only use n of them um then I will put
+
+ align:start position:0%
+only use n of them um then I will put
+ 
+
+ align:start position:0%
+only use n of them um then I will put
+those all I and then is long as none of
+
+ align:start position:0%
+those all I and then is long as none of
+ 
+
+ align:start position:0%
+those all I and then is long as none of
+these match to the boundary I'm
+
+ align:start position:0%
+these match to the boundary I'm
+ 
+
+ align:start position:0%
+these match to the boundary I'm
+okay uh I guess even if I use the i1 I2
+
+ align:start position:0%
+okay uh I guess even if I use the i1 I2
+ 
+
+ align:start position:0%
+okay uh I guess even if I use the i1 I2
+I3 it's possible some of those match the
+
+ align:start position:0%
+I3 it's possible some of those match the
+ 
+
+ align:start position:0%
+I3 it's possible some of those match the
+boundary and then weird stuff could
+
+ align:start position:0%
+boundary and then weird stuff could
+ 
+
+ align:start position:0%
+boundary and then weird stuff could
+happen but as long as all these eye
+
+ align:start position:0%
+happen but as long as all these eye
+ 
+
+ align:start position:0%
+happen but as long as all these eye
+colors match up with each other you have
+
+ align:start position:0%
+colors match up with each other you have
+ 
+
+ align:start position:0%
+colors match up with each other you have
+to build this rectangle once and then we
+
+ align:start position:0%
+to build this rectangle once and then we
+ 
+
+ align:start position:0%
+to build this rectangle once and then we
+don't care about how the rectangles are
+
+ align:start position:0%
+don't care about how the rectangles are
+ 
+
+ align:start position:0%
+don't care about how the rectangles are
+assembled with respect to each other uh
+
+ align:start position:0%
+assembled with respect to each other uh
+ 
+
+ align:start position:0%
+assembled with respect to each other uh
+so we're basically simulating this
+
+ align:start position:0%
+so we're basically simulating this
+ 
+
+ align:start position:0%
+so we're basically simulating this
+reduction rectangle
+
+ align:start position:0%
+reduction rectangle
+ 
+
+ align:start position:0%
+reduction rectangle
+packing okay the one I have drawn here
+
+ align:start position:0%
+packing okay the one I have drawn here
+ 
+
+ align:start position:0%
+packing okay the one I have drawn here
+is slightly different um I don't
+
+ align:start position:0%
+is slightly different um I don't
+ 
+
+ align:start position:0%
+is slightly different um I don't
+remember why we did it this way this is
+
+ align:start position:0%
+remember why we did it this way this is
+ 
+
+ align:start position:0%
+remember why we did it this way this is
+Joint work with Marty domain the
+
+ align:start position:0%
+Joint work with Marty domain the
+ 
+
+ align:start position:0%
+Joint work with Marty domain the
+cameraman and and uh here uh we made the
+
+ align:start position:0%
+cameraman and and uh here uh we made the
+ 
+
+ align:start position:0%
+cameraman and and uh here uh we made the
+just I guess to be as simple as possible
+
+ align:start position:0%
+just I guess to be as simple as possible
+ 
+
+ align:start position:0%
+just I guess to be as simple as possible
+we made the width of each of the
+
+ align:start position:0%
+we made the width of each of the
+ 
+
+ align:start position:0%
+we made the width of each of the
+rectangles just
+
+ align:start position:0%
+rectangles just
+ 
+
+ align:start position:0%
+rectangles just
+AI that has the problem that you could
+
+ align:start position:0%
+AI that has the problem that you could
+ 
+
+ align:start position:0%
+AI that has the problem that you could
+rotate but to prevent rotation we use a
+
+ align:start position:0%
+rotate but to prevent rotation we use a
+ 
+
+ align:start position:0%
+rotate but to prevent rotation we use a
+different color horizontal and vertical
+
+ align:start position:0%
+different color horizontal and vertical
+ 
+
+ align:start position:0%
+different color horizontal and vertical
+so the top edges and the bottom edges
+
+ align:start position:0%
+so the top edges and the bottom edges
+ 
+
+ align:start position:0%
+so the top edges and the bottom edges
+all have the color percent sign uh I
+
+ align:start position:0%
+all have the color percent sign uh I
+ 
+
+ align:start position:0%
+all have the color percent sign uh I
+think this is a limitation of the
+
+ align:start position:0%
+think this is a limitation of the
+ 
+
+ align:start position:0%
+think this is a limitation of the
+drawing program I was using at the time
+
+ align:start position:0%
+drawing program I was using at the time
+ 
+
+ align:start position:0%
+drawing program I was using at the time
+xfig and dollar signs on the left and
+
+ align:start position:0%
+xfig and dollar signs on the left and
+ 
+
+ align:start position:0%
+xfig and dollar signs on the left and
+right side and then we're going to build
+
+ align:start position:0%
+right side and then we're going to build
+ 
+
+ align:start position:0%
+right side and then we're going to build
+frame this is what you might call
+
+ align:start position:0%
+frame this is what you might call
+ 
+
+ align:start position:0%
+frame this is what you might call
+infrastructure for the proof this is one
+
+ align:start position:0%
+infrastructure for the proof this is one
+ 
+
+ align:start position:0%
+infrastructure for the proof this is one
+Gadget happens you just execute it once
+
+ align:start position:0%
+Gadget happens you just execute it once
+ 
+
+ align:start position:0%
+Gadget happens you just execute it once
+this we execute for each of the AIS
+
+ align:start position:0%
+this we execute for each of the AIS
+ 
+
+ align:start position:0%
+this we execute for each of the AIS
+we're just going to have one copy of
+
+ align:start position:0%
+we're just going to have one copy of
+ 
+
+ align:start position:0%
+we're just going to have one copy of
+this big frame the goal of the frame is
+
+ align:start position:0%
+this big frame the goal of the frame is
+ 
+
+ align:start position:0%
+this big frame the goal of the frame is
+to hide the
+
+ align:start position:0%
+to hide the
+ 
+
+ align:start position:0%
+to hide the
+boundary uh so that none of these tiles
+
+ align:start position:0%
+boundary uh so that none of these tiles
+ 
+
+ align:start position:0%
+boundary uh so that none of these tiles
+could match with the boundary because
+
+ align:start position:0%
+could match with the boundary because
+ 
+
+ align:start position:0%
+could match with the boundary because
+when they match the boundary then you're
+
+ align:start position:0%
+when they match the boundary then you're
+ 
+
+ align:start position:0%
+when they match the boundary then you're
+breaking a rectangle in half and bad
+
+ align:start position:0%
+breaking a rectangle in half and bad
+ 
+
+ align:start position:0%
+breaking a rectangle in half and bad
+things could happen so instead uh what
+
+ align:start position:0%
+things could happen so instead uh what
+ 
+
+ align:start position:0%
+things could happen so instead uh what
+we're going to do all these capital
+
+ align:start position:0%
+we're going to do all these capital
+ 
+
+ align:start position:0%
+we're going to do all these capital
+letters on the outside and I ran out of
+
+ align:start position:0%
+letters on the outside and I ran out of
+ 
+
+ align:start position:0%
+letters on the outside and I ran out of
+letters I used a couple symbols those
+
+ align:start position:0%
+letters I used a couple symbols those
+ 
+
+ align:start position:0%
+letters I used a couple symbols those
+appear exactly once in the reduction so
+
+ align:start position:0%
+appear exactly once in the reduction so
+ 
+
+ align:start position:0%
+appear exactly once in the reduction so
+they can't match with anyone which means
+
+ align:start position:0%
+they can't match with anyone which means
+ 
+
+ align:start position:0%
+they can't match with anyone which means
+they have to be on the boundary
+
+ align:start position:0%
+they have to be on the boundary
+ 
+
+ align:start position:0%
+they have to be on the boundary
+okay so those guys have to be on the
+
+ align:start position:0%
+okay so those guys have to be on the
+ 
+
+ align:start position:0%
+okay so those guys have to be on the
+boundary um and then all these other
+
+ align:start position:0%
+boundary um and then all these other
+ 
+
+ align:start position:0%
+boundary um and then all these other
+colors are appear exactly twice so you
+
+ align:start position:0%
+colors are appear exactly twice so you
+ 
+
+ align:start position:0%
+colors are appear exactly twice so you
+have to join these tiles together in
+
+ align:start position:0%
+have to join these tiles together in
+ 
+
+ align:start position:0%
+have to join these tiles together in
+exactly this way uh and now the
+
+ align:start position:0%
+exactly this way uh and now the
+ 
+
+ align:start position:0%
+exactly this way uh and now the
+boundary's gone and we have set up
+
+ align:start position:0%
+boundary's gone and we have set up
+ 
+
+ align:start position:0%
+boundary's gone and we have set up
+dollar signs on the left side and the
+
+ align:start position:0%
+dollar signs on the left side and the
+ 
+
+ align:start position:0%
+dollar signs on the left side and the
+right side and percent signs on the top
+
+ align:start position:0%
+right side and percent signs on the top
+ 
+
+ align:start position:0%
+right side and percent signs on the top
+and the bottom sides uh in reality these
+
+ align:start position:0%
+and the bottom sides uh in reality these
+ 
+
+ align:start position:0%
+and the bottom sides uh in reality these
+would be uh whatever
+
+ align:start position:0%
+would be uh whatever
+ 
+
+ align:start position:0%
+would be uh whatever
+t uh wide and N over3 tall uh this is
+
+ align:start position:0%
+t uh wide and N over3 tall uh this is
+ 
+
+ align:start position:0%
+t uh wide and N over3 tall uh this is
+some different notation
+
+ align:start position:0%
+some different notation
+ 
+
+ align:start position:0%
+some different notation
+and uh that's it now you're simulating
+
+ align:start position:0%
+and uh that's it now you're simulating
+ 
+
+ align:start position:0%
+and uh that's it now you're simulating
+rectangle packing question why do you
+
+ align:start position:0%
+rectangle packing question why do you
+ 
+
+ align:start position:0%
+rectangle packing question why do you
+need two rows at the bottom ah so this
+
+ align:start position:0%
+need two rows at the bottom ah so this
+ 
+
+ align:start position:0%
+need two rows at the bottom ah so this
+two rows is to indicate uh for whatever
+
+ align:start position:0%
+two rows is to indicate uh for whatever
+ 
+
+ align:start position:0%
+two rows is to indicate uh for whatever
+reason because Edge matching puzzles
+
+ align:start position:0%
+reason because Edge matching puzzles
+ 
+
+ align:start position:0%
+reason because Edge matching puzzles
+usually the target shape is not a
+
+ align:start position:0%
+usually the target shape is not a
+ 
+
+ align:start position:0%
+usually the target shape is not a
+rectangle but a square and we wanted the
+
+ align:start position:0%
+rectangle but a square and we wanted the
+ 
+
+ align:start position:0%
+rectangle but a square and we wanted the
+stronger result that packing unit
+
+ align:start position:0%
+stronger result that packing unit
+ 
+
+ align:start position:0%
+stronger result that packing unit
+squares into a square with Edge matching
+
+ align:start position:0%
+squares into a square with Edge matching
+ 
+
+ align:start position:0%
+squares into a square with Edge matching
+results is NP hard uh so we just the
+
+ align:start position:0%
+results is NP hard uh so we just the
+ 
+
+ align:start position:0%
+results is NP hard uh so we just the
+point here is you just add however many
+
+ align:start position:0%
+point here is you just add however many
+ 
+
+ align:start position:0%
+point here is you just add however many
+rows or columns you need to make s y
+
+ align:start position:0%
+rows or columns you need to make s y
+ 
+
+ align:start position:0%
+rows or columns you need to make s y
+good question Jason so your different
+
+ align:start position:0%
+good question Jason so your different
+ 
+
+ align:start position:0%
+good question Jason so your different
+symbols I believe are also to let you
+
+ align:start position:0%
+symbols I believe are also to let you
+ 
+
+ align:start position:0%
+symbols I believe are also to let you
+build this in the rectangle later on
+
+ align:start position:0%
+build this in the rectangle later on
+ 
+
+ align:start position:0%
+build this in the rectangle later on
+otherwise we issues with rotating
+
+ align:start position:0%
+otherwise we issues with rotating
+ 
+
+ align:start position:0%
+otherwise we issues with rotating
+things we'll get there at this yeah so I
+
+ align:start position:0%
+things we'll get there at this yeah so I
+ 
+
+ align:start position:0%
+things we'll get there at this yeah so I
+have different symbols here and here in
+
+ align:start position:0%
+have different symbols here and here in
+ 
+
+ align:start position:0%
+have different symbols here and here in
+order to prevent rotation that's right
+
+ align:start position:0%
+order to prevent rotation that's right
+ 
+
+ align:start position:0%
+order to prevent rotation that's right
+instead of making them longer I could
+
+ align:start position:0%
+instead of making them longer I could
+ 
+
+ align:start position:0%
+instead of making them longer I could
+have instead made these longer like we
+
+ align:start position:0%
+have instead made these longer like we
+ 
+
+ align:start position:0%
+have instead made these longer like we
+had with the rectangle thing but uh I
+
+ align:start position:0%
+had with the rectangle thing but uh I
+ 
+
+ align:start position:0%
+had with the rectangle thing but uh I
+guess at the time I wasn't thinking of
+
+ align:start position:0%
+guess at the time I wasn't thinking of
+ 
+
+ align:start position:0%
+guess at the time I wasn't thinking of
+teaching in class about this so I didn't
+
+ align:start position:0%
+teaching in class about this so I didn't
+ 
+
+ align:start position:0%
+teaching in class about this so I didn't
+reuse my previous reduction for this one
+
+ align:start position:0%
+reuse my previous reduction for this one
+ 
+
+ align:start position:0%
+reuse my previous reduction for this one
+but oh well um
+
+ align:start position:0%
+but oh well um
+ 
+
+ align:start position:0%
+but oh well um
+yeah but uh yeah the the reason they
+
+ align:start position:0%
+yeah but uh yeah the the reason they
+ 
+
+ align:start position:0%
+yeah but uh yeah the the reason they
+dollar signs in that like
+
+ align:start position:0%
+dollar signs in that like
+ 
+
+ align:start position:0%
+dollar signs in that like
+red or some actual color is because uh
+
+ align:start position:0%
+red or some actual color is because uh
+ 
+
+ align:start position:0%
+red or some actual color is because uh
+yeah probably black and white printing
+
+ align:start position:0%
+yeah probably black and white printing
+ 
+
+ align:start position:0%
+yeah probably black and white printing
+was more common
+
+ align:start position:0%
+was more common
+ 
+
+ align:start position:0%
+was more common
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+okay cool that was one puzzle and now
+
+ align:start position:0%
+okay cool that was one puzzle and now
+ 
+
+ align:start position:0%
+okay cool that was one puzzle and now
+key Point what if we did this reduction
+
+ align:start position:0%
+key Point what if we did this reduction
+ 
+
+ align:start position:0%
+key Point what if we did this reduction
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+partition so with Partition instead of
+
+ align:start position:0%
+partition so with Partition instead of
+ 
+
+ align:start position:0%
+partition so with Partition instead of
+having n over3 groups here we just have
+
+ align:start position:0%
+having n over3 groups here we just have
+ 
+
+ align:start position:0%
+having n over3 groups here we just have
+two groups and same thing why not do
+
+ align:start position:0%
+two groups and same thing why not do
+ 
+
+ align:start position:0%
+two groups and same thing why not do
+that and it would be a
+
+ align:start position:0%
+that and it would be a
+ 
+
+ align:start position:0%
+that and it would be a
+week that would be a weekend be hard
+
+ align:start position:0%
+week that would be a weekend be hard
+ 
+
+ align:start position:0%
+week that would be a weekend be hard
+reduction now uh this problem here Edge
+
+ align:start position:0%
+reduction now uh this problem here Edge
+ 
+
+ align:start position:0%
+reduction now uh this problem here Edge
+matching puzzle n unit squares with four
+
+ align:start position:0%
+matching puzzle n unit squares with four
+ 
+
+ align:start position:0%
+matching puzzle n unit squares with four
+colors are there any numbers in this
+
+ align:start position:0%
+colors are there any numbers in this
+ 
+
+ align:start position:0%
+colors are there any numbers in this
+problem other than
+
+ align:start position:0%
+problem other than
+ 
+
+ align:start position:0%
+problem other than
+four and
+
+ align:start position:0%
+four and
+ 
+
+ align:start position:0%
+four and
+N are there any numbers that are inputs
+
+ align:start position:0%
+N are there any numbers that are inputs
+ 
+
+ align:start position:0%
+N are there any numbers that are inputs
+I guess the colors have to be
+
+ align:start position:0%
+I guess the colors have to be
+ 
+
+ align:start position:0%
+I guess the colors have to be
+represented as numbers the colors do
+
+ align:start position:0%
+represented as numbers the colors do
+ 
+
+ align:start position:0%
+represented as numbers the colors do
+have to be represented as numbers but um
+
+ align:start position:0%
+have to be represented as numbers but um
+ 
+
+ align:start position:0%
+have to be represented as numbers but um
+so this is sort of a Seline usually we
+
+ align:start position:0%
+so this is sort of a Seline usually we
+ 
+
+ align:start position:0%
+so this is sort of a Seline usually we
+when we're talking about colors all we
+
+ align:start position:0%
+when we're talking about colors all we
+ 
+
+ align:start position:0%
+when we're talking about colors all we
+care about is whether the colors are
+
+ align:start position:0%
+care about is whether the colors are
+ 
+
+ align:start position:0%
+care about is whether the colors are
+equal or not so
+
+ align:start position:0%
+equal or not so
+ 
+
+ align:start position:0%
+equal or not so
+you don't normally think of those as
+
+ align:start position:0%
+you don't normally think of those as
+ 
+
+ align:start position:0%
+you don't normally think of those as
+numbers you can think of them as
+
+ align:start position:0%
+numbers you can think of them as
+ 
+
+ align:start position:0%
+numbers you can think of them as
+vertices in a graph or something I mean
+
+ align:start position:0%
+vertices in a graph or something I mean
+ 
+
+ align:start position:0%
+vertices in a graph or something I mean
+they're more like combinatorial objects
+
+ align:start position:0%
+they're more like combinatorial objects
+ 
+
+ align:start position:0%
+they're more like combinatorial objects
+you're not you never adding two colors
+
+ align:start position:0%
+you're not you never adding two colors
+ 
+
+ align:start position:0%
+you're not you never adding two colors
+together yes um the other point is that
+
+ align:start position:0%
+together yes um the other point is that
+ 
+
+ align:start position:0%
+together yes um the other point is that
+the number of different colors you can
+
+ align:start position:0%
+the number of different colors you can
+ 
+
+ align:start position:0%
+the number of different colors you can
+get is at most four times n because
+
+ align:start position:0%
+get is at most four times n because
+ 
+
+ align:start position:0%
+get is at most four times n because
+number of colors is at most four * n
+
+ align:start position:0%
+number of colors is at most four * n
+ 
+
+ align:start position:0%
+number of colors is at most four * n
+yeah you could write down a color as two
+
+ align:start position:0%
+yeah you could write down a color as two
+ 
+
+ align:start position:0%
+yeah you could write down a color as two
+to the two to the N but why supposed to
+
+ align:start position:0%
+to the two to the N but why supposed to
+ 
+
+ align:start position:0%
+to the two to the N but why supposed to
+be an efficient encoding so there really
+
+ align:start position:0%
+be an efficient encoding so there really
+ 
+
+ align:start position:0%
+be an efficient encoding so there really
+no numbers here so it doesn't even make
+
+ align:start position:0%
+no numbers here so it doesn't even make
+ 
+
+ align:start position:0%
+no numbers here so it doesn't even make
+sense to say this problem is strongly NP
+
+ align:start position:0%
+sense to say this problem is strongly NP
+ 
+
+ align:start position:0%
+sense to say this problem is strongly NP
+hard but even worse if I started with
+
+ align:start position:0%
+hard but even worse if I started with
+ 
+
+ align:start position:0%
+hard but even worse if I started with
+two partition and I did this reduction
+
+ align:start position:0%
+two partition and I did this reduction
+ 
+
+ align:start position:0%
+two partition and I did this reduction
+exactly as drawn but not as tall I could
+
+ align:start position:0%
+exactly as drawn but not as tall I could
+ 
+
+ align:start position:0%
+exactly as drawn but not as tall I could
+still make it a square but uh everything
+
+ align:start position:0%
+still make it a square but uh everything
+ 
+
+ align:start position:0%
+still make it a square but uh everything
+would break because for two partition to
+
+ align:start position:0%
+would break because for two partition to
+ 
+
+ align:start position:0%
+would break because for two partition to
+be hard those numbers the AIS have to be
+
+ align:start position:0%
+be hard those numbers the AIS have to be
+ 
+
+ align:start position:0%
+be hard those numbers the AIS have to be
+exponential in value if I have an
+
+ align:start position:0%
+exponential in value if I have an
+ 
+
+ align:start position:0%
+exponential in value if I have an
+exponential value AI when I convert it
+
+ align:start position:0%
+exponential value AI when I convert it
+ 
+
+ align:start position:0%
+exponential value AI when I convert it
+into a rectangle or actually I convert
+
+ align:start position:0%
+into a rectangle or actually I convert
+ 
+
+ align:start position:0%
+into a rectangle or actually I convert
+it into a bunch of tiles I will have
+
+ align:start position:0%
+it into a bunch of tiles I will have
+ 
+
+ align:start position:0%
+it into a bunch of tiles I will have
+exponentially many tiles this
+
+ align:start position:0%
+exponentially many tiles this
+ 
+
+ align:start position:0%
+exponentially many tiles this
+construction will be of exponential size
+
+ align:start position:0%
+construction will be of exponential size
+ 
+
+ align:start position:0%
+construction will be of exponential size
+so I will get exponentially many
+
+ align:start position:0%
+so I will get exponentially many
+ 
+
+ align:start position:0%
+so I will get exponentially many
+different colors on the boundary so
+
+ align:start position:0%
+different colors on the boundary so
+ 
+
+ align:start position:0%
+different colors on the boundary so
+that's very bad even if you're clever
+
+ align:start position:0%
+that's very bad even if you're clever
+ 
+
+ align:start position:0%
+that's very bad even if you're clever
+and you say oh well all these tiles are
+
+ align:start position:0%
+and you say oh well all these tiles are
+ 
+
+ align:start position:0%
+and you say oh well all these tiles are
+all the same so maybe I'll encode them
+
+ align:start position:0%
+all the same so maybe I'll encode them
+ 
+
+ align:start position:0%
+all the same so maybe I'll encode them
+efficiently and say there's
+
+ align:start position:0%
+efficiently and say there's
+ 
+
+ align:start position:0%
+efficiently and say there's
+exponentially many of this one tile the
+
+ align:start position:0%
+exponentially many of this one tile the
+ 
+
+ align:start position:0%
+exponentially many of this one tile the
+ones in the boundary are all different
+
+ align:start position:0%
+ones in the boundary are all different
+ 
+
+ align:start position:0%
+ones in the boundary are all different
+so it's not a valid reduction you should
+
+ align:start position:0%
+so it's not a valid reduction you should
+ 
+
+ align:start position:0%
+so it's not a valid reduction you should
+always take a problem supposed to run in
+
+ align:start position:0%
+always take a problem supposed to run in
+ 
+
+ align:start position:0%
+always take a problem supposed to run in
+polinomial time and produce a result of
+
+ align:start position:0%
+polinomial time and produce a result of
+ 
+
+ align:start position:0%
+polinomial time and produce a result of
+polinomial size so if I start with
+
+ align:start position:0%
+polinomial size so if I start with
+ 
+
+ align:start position:0%
+polinomial size so if I start with
+something where the input is polinomial
+
+ align:start position:0%
+something where the input is polinomial
+ 
+
+ align:start position:0%
+something where the input is polinomial
+size but it has exponentially large AI I
+
+ align:start position:0%
+size but it has exponentially large AI I
+ 
+
+ align:start position:0%
+size but it has exponentially large AI I
+do this I get an exponential size
+
+ align:start position:0%
+do this I get an exponential size
+ 
+
+ align:start position:0%
+do this I get an exponential size
+uh puzzle which is tough to boring to
+
+ align:start position:0%
+uh puzzle which is tough to boring to
+ 
+
+ align:start position:0%
+uh puzzle which is tough to boring to
+solve I don't know uh it's not a valid
+
+ align:start position:0%
+solve I don't know uh it's not a valid
+ 
+
+ align:start position:0%
+solve I don't know uh it's not a valid
+NP hardness reduction this is why we
+
+ align:start position:0%
+NP hardness reduction this is why we
+ 
+
+ align:start position:0%
+NP hardness reduction this is why we
+want to start from three partition
+
+ align:start position:0%
+want to start from three partition
+ 
+
+ align:start position:0%
+want to start from three partition
+because then I know even if what I'm
+
+ align:start position:0%
+because then I know even if what I'm
+ 
+
+ align:start position:0%
+because then I know even if what I'm
+doing here is representing the AI in uny
+
+ align:start position:0%
+doing here is representing the AI in uny
+ 
+
+ align:start position:0%
+doing here is representing the AI in uny
+I take AI I say okay I'm going to have
+
+ align:start position:0%
+I take AI I say okay I'm going to have
+ 
+
+ align:start position:0%
+I take AI I say okay I'm going to have
+that many square tiles that is exactly
+
+ align:start position:0%
+that many square tiles that is exactly
+ 
+
+ align:start position:0%
+that many square tiles that is exactly
+unary representation and we know a three
+
+ align:start position:0%
+unary representation and we know a three
+ 
+
+ align:start position:0%
+unary representation and we know a three
+partition that will have polinomial size
+
+ align:start position:0%
+partition that will have polinomial size
+ 
+
+ align:start position:0%
+partition that will have polinomial size
+and so we're good this is why we care
+
+ align:start position:0%
+and so we're good this is why we care
+ 
+
+ align:start position:0%
+and so we're good this is why we care
+about strong andp hardness so much
+
+ align:start position:0%
+about strong andp hardness so much
+ 
+
+ align:start position:0%
+about strong andp hardness so much
+because a lot of puzzles you can only
+
+ align:start position:0%
+because a lot of puzzles you can only
+ 
+
+ align:start position:0%
+because a lot of puzzles you can only
+represent numbers uny then you you're
+
+ align:start position:0%
+represent numbers uny then you you're
+ 
+
+ align:start position:0%
+represent numbers uny then you you're
+forced to work with
+
+ align:start position:0%
+forced to work with
+ 
+
+ align:start position:0%
+forced to work with
+repartition Okay uh next
+
+ align:start position:0%
+repartition Okay uh next
+ 
+
+ align:start position:0%
+repartition Okay uh next
+puzzle is uh signed Edge matching
+
+ align:start position:0%
+puzzle is uh signed Edge matching
+ 
+
+ align:start position:0%
+puzzle is uh signed Edge matching
+puzzles like the lizards suppose same
+
+ align:start position:0%
+puzzles like the lizards suppose same
+ 
+
+ align:start position:0%
+puzzles like the lizards suppose same
+setup but now the colors aren't supposed
+
+ align:start position:0%
+setup but now the colors aren't supposed
+ 
+
+ align:start position:0%
+setup but now the colors aren't supposed
+to be equal they're supposed to be
+
+ align:start position:0%
+to be equal they're supposed to be
+ 
+
+ align:start position:0%
+to be equal they're supposed to be
+opposites uh so I'm just going to modify
+
+ align:start position:0%
+opposites uh so I'm just going to modify
+ 
+
+ align:start position:0%
+opposites uh so I'm just going to modify
+this diagram and I will use capital
+
+ align:start position:0%
+this diagram and I will use capital
+ 
+
+ align:start position:0%
+this diagram and I will use capital
+letters to denote tals of lizards and
+
+ align:start position:0%
+letters to denote tals of lizards and
+ 
+
+ align:start position:0%
+letters to denote tals of lizards and
+lowercase letters to represent heads of
+
+ align:start position:0%
+lowercase letters to represent heads of
+ 
+
+ align:start position:0%
+lowercase letters to represent heads of
+lizards and little B only matches
+
+ align:start position:0%
+lizards and little B only matches
+ 
+
+ align:start position:0%
+lizards and little B only matches
+capital B does not match little B you
+
+ align:start position:0%
+capital B does not match little B you
+ 
+
+ align:start position:0%
+capital B does not match little B you
+can't put two heads together two tails
+
+ align:start position:0%
+can't put two heads together two tails
+ 
+
+ align:start position:0%
+can't put two heads together two tails
+together uh well you can
+
+ align:start position:0%
+together uh well you can
+ 
+
+ align:start position:0%
+together uh well you can
+reduce uh these things which I'll call
+
+ align:start position:0%
+reduce uh these things which I'll call
+ 
+
+ align:start position:0%
+reduce uh these things which I'll call
+unsigned Edge matching puzzles to uh
+
+ align:start position:0%
+unsigned Edge matching puzzles to uh
+ 
+
+ align:start position:0%
+unsigned Edge matching puzzles to uh
+these things which I'll call signed Edge
+
+ align:start position:0%
+these things which I'll call signed Edge
+ 
+
+ align:start position:0%
+these things which I'll call signed Edge
+matching
+
+ align:start position:0%
+matching
+ 
+
+ align:start position:0%
+matching
+puzzles with this easy Gadget if you
+
+ align:start position:0%
+puzzles with this easy Gadget if you
+ 
+
+ align:start position:0%
+puzzles with this easy Gadget if you
+have a tile with let's just say colors
+
+ align:start position:0%
+have a tile with let's just say colors
+ 
+
+ align:start position:0%
+have a tile with let's just say colors
+AB B CD some of them might be equal I'm
+
+ align:start position:0%
+AB B CD some of them might be equal I'm
+ 
+
+ align:start position:0%
+AB B CD some of them might be equal I'm
+going to replace that one tile with
+
+ align:start position:0%
+going to replace that one tile with
+ 
+
+ align:start position:0%
+going to replace that one tile with
+these four tiles
+
+ align:start position:0%
+these four tiles
+ 
+
+ align:start position:0%
+these four tiles
+and scale everything up by a factor of
+
+ align:start position:0%
+and scale everything up by a factor of
+ 
+
+ align:start position:0%
+and scale everything up by a factor of
+two scale the target shape by a factor
+
+ align:start position:0%
+two scale the target shape by a factor
+ 
+
+ align:start position:0%
+two scale the target shape by a factor
+of two uh these colors appear
+
+ align:start position:0%
+of two uh these colors appear
+ 
+
+ align:start position:0%
+of two uh these colors appear
+exactly once with each sign and so
+
+ align:start position:0%
+exactly once with each sign and so
+ 
+
+ align:start position:0%
+exactly once with each sign and so
+you're forced again because there's a
+
+ align:start position:0%
+you're forced again because there's a
+ 
+
+ align:start position:0%
+you're forced again because there's a
+frame and all the boundary is eaten up
+
+ align:start position:0%
+frame and all the boundary is eaten up
+ 
+
+ align:start position:0%
+frame and all the boundary is eaten up
+you're forced uh to match these guys to
+
+ align:start position:0%
+you're forced uh to match these guys to
+ 
+
+ align:start position:0%
+you're forced uh to match these guys to
+each other therefore you're forced to
+
+ align:start position:0%
+each other therefore you're forced to
+ 
+
+ align:start position:0%
+each other therefore you're forced to
+make this 2x two
+
+ align:start position:0%
+make this 2x two
+ 
+
+ align:start position:0%
+make this 2x two
+tile and so uh that 2x two tile is
+
+ align:start position:0%
+tile and so uh that 2x two tile is
+ 
+
+ align:start position:0%
+tile and so uh that 2x two tile is
+supposed to represent this one by one
+
+ align:start position:0%
+supposed to represent this one by one
+ 
+
+ align:start position:0%
+supposed to represent this one by one
+tile and the claim is um signs no longer
+
+ align:start position:0%
+tile and the claim is um signs no longer
+ 
+
+ align:start position:0%
+tile and the claim is um signs no longer
+matter because we put little a big a
+
+ align:start position:0%
+matter because we put little a big a
+ 
+
+ align:start position:0%
+matter because we put little a big a
+little B Big B little c big c and so on
+
+ align:start position:0%
+little B Big B little c big c and so on
+ 
+
+ align:start position:0%
+little B Big B little c big c and so on
+so if I took another tile like over
+
+ align:start position:0%
+so if I took another tile like over
+ 
+
+ align:start position:0%
+so if I took another tile like over
+here um and it has something like
+
+ align:start position:0%
+here um and it has something like
+ 
+
+ align:start position:0%
+here um and it has something like
+capital D lowercase D that's going to
+
+ align:start position:0%
+capital D lowercase D that's going to
+ 
+
+ align:start position:0%
+capital D lowercase D that's going to
+match with this lowercase b lowercase b
+
+ align:start position:0%
+match with this lowercase b lowercase b
+ 
+
+ align:start position:0%
+match with this lowercase b lowercase b
+if and only if B equals D so if the
+
+ align:start position:0%
+if and only if B equals D so if the
+ 
+
+ align:start position:0%
+if and only if B equals D so if the
+original colors are equal the resulting
+
+ align:start position:0%
+original colors are equal the resulting
+ 
+
+ align:start position:0%
+original colors are equal the resulting
+colors will be equal and opposite so
+
+ align:start position:0%
+colors will be equal and opposite so
+ 
+
+ align:start position:0%
+colors will be equal and opposite so
+they'll be the same letter of the
+
+ align:start position:0%
+they'll be the same letter of the
+ 
+
+ align:start position:0%
+they'll be the same letter of the
+alphabet but with opposite signs and so
+
+ align:start position:0%
+alphabet but with opposite signs and so
+ 
+
+ align:start position:0%
+alphabet but with opposite signs and so
+everything will match up CU this capital
+
+ align:start position:0%
+everything will match up CU this capital
+ 
+
+ align:start position:0%
+everything will match up CU this capital
+letter will match here this lowercase
+
+ align:start position:0%
+letter will match here this lowercase
+ 
+
+ align:start position:0%
+letter will match here this lowercase
+letter will match there is that clear so
+
+ align:start position:0%
+letter will match there is that clear so
+ 
+
+ align:start position:0%
+letter will match there is that clear so
+it's really the becomes the same puzzle
+
+ align:start position:0%
+it's really the becomes the same puzzle
+ 
+
+ align:start position:0%
+it's really the becomes the same puzzle
+and you know this one's going to be
+
+ align:start position:0%
+and you know this one's going to be
+ 
+
+ align:start position:0%
+and you know this one's going to be
+solvable if only if this one is so we
+
+ align:start position:0%
+solvable if only if this one is so we
+ 
+
+ align:start position:0%
+solvable if only if this one is so we
+get strong NP well just NP hardness of
+
+ align:start position:0%
+get strong NP well just NP hardness of
+ 
+
+ align:start position:0%
+get strong NP well just NP hardness of
+signed Edge matching puzzles cool uh
+
+ align:start position:0%
+signed Edge matching puzzles cool uh
+ 
+
+ align:start position:0%
+signed Edge matching puzzles cool uh
+next puzzle these are all in the same
+
+ align:start position:0%
+next puzzle these are all in the same
+ 
+
+ align:start position:0%
+next puzzle these are all in the same
+paper it was a fun paper uh even older
+
+ align:start position:0%
+paper it was a fun paper uh even older
+ 
+
+ align:start position:0%
+paper it was a fun paper uh even older
+jigsaw puzzles this is not the oldest
+
+ align:start position:0%
+jigsaw puzzles this is not the oldest
+ 
+
+ align:start position:0%
+jigsaw puzzles this is not the oldest
+jigsaw puzzle it's one of the newest
+
+ align:start position:0%
+jigsaw puzzle it's one of the newest
+ 
+
+ align:start position:0%
+jigsaw puzzle it's one of the newest
+it's our course poster turned into a
+
+ align:start position:0%
+it's our course poster turned into a
+ 
+
+ align:start position:0%
+it's our course poster turned into a
+jigsa puzzle if you want to make your
+
+ align:start position:0%
+jigsa puzzle if you want to make your
+ 
+
+ align:start position:0%
+jigsa puzzle if you want to make your
+own jiga puzzles go there they go back
+
+ align:start position:0%
+own jiga puzzles go there they go back
+ 
+
+ align:start position:0%
+own jiga puzzles go there they go back
+to the 1760s when they were made with
+
+ align:start position:0%
+to the 1760s when they were made with
+ 
+
+ align:start position:0%
+to the 1760s when they were made with
+jigsaws hence the name uh but basically
+
+ align:start position:0%
+jigsaws hence the name uh but basically
+ 
+
+ align:start position:0%
+jigsaws hence the name uh but basically
+we have square pieces and each side of
+
+ align:start position:0%
+we have square pieces and each side of
+ 
+
+ align:start position:0%
+we have square pieces and each side of
+this I'll assume that's a special kind
+
+ align:start position:0%
+this I'll assume that's a special kind
+ 
+
+ align:start position:0%
+this I'll assume that's a special kind
+of jigsaw puzzle most common uh each
+
+ align:start position:0%
+of jigsaw puzzle most common uh each
+ 
+
+ align:start position:0%
+of jigsaw puzzle most common uh each
+Edge can either be straight that means
+
+ align:start position:0%
+Edge can either be straight that means
+ 
+
+ align:start position:0%
+Edge can either be straight that means
+it's on the boundary uh it can be uh a
+
+ align:start position:0%
+it's on the boundary uh it can be uh a
+ 
+
+ align:start position:0%
+it's on the boundary uh it can be uh a
+pocket or a tab and each pocket and tab
+
+ align:start position:0%
+pocket or a tab and each pocket and tab
+ 
+
+ align:start position:0%
+pocket or a tab and each pocket and tab
+is slightly differently shaped although
+
+ align:start position:0%
+is slightly differently shaped although
+ 
+
+ align:start position:0%
+is slightly differently shaped although
+maybe not in this picture usually they
+
+ align:start position:0%
+maybe not in this picture usually they
+ 
+
+ align:start position:0%
+maybe not in this picture usually they
+are um I'm going to allow that some of
+
+ align:start position:0%
+are um I'm going to allow that some of
+ 
+
+ align:start position:0%
+are um I'm going to allow that some of
+the pockets and the tabs have the same
+
+ align:start position:0%
+the pockets and the tabs have the same
+ 
+
+ align:start position:0%
+the pockets and the tabs have the same
+shape that's what you might call
+
+ align:start position:0%
+shape that's what you might call
+ 
+
+ align:start position:0%
+shape that's what you might call
+ambiguous mates most jigsaw puzzles sold
+
+ align:start position:0%
+ambiguous mates most jigsaw puzzles sold
+ 
+
+ align:start position:0%
+ambiguous mates most jigsaw puzzles sold
+in the world do not have ambiguous mates
+
+ align:start position:0%
+in the world do not have ambiguous mates
+ 
+
+ align:start position:0%
+in the world do not have ambiguous mates
+but let's say they do and to make it NP
+
+ align:start position:0%
+but let's say they do and to make it NP
+ 
+
+ align:start position:0%
+but let's say they do and to make it NP
+hardcore uh there's no image on the
+
+ align:start position:0%
+hardcore uh there's no image on the
+ 
+
+ align:start position:0%
+hardcore uh there's no image on the
+Pieces Just a white puzzle now those are
+
+ align:start position:0%
+Pieces Just a white puzzle now those are
+ 
+
+ align:start position:0%
+Pieces Just a white puzzle now those are
+sold you can buy white all wh or all
+
+ align:start position:0%
+sold you can buy white all wh or all
+ 
+
+ align:start position:0%
+sold you can buy white all wh or all
+single color uh puzzles and uh but
+
+ align:start position:0%
+single color uh puzzles and uh but
+ 
+
+ align:start position:0%
+single color uh puzzles and uh but
+usually they don't have ambiguous mates
+
+ align:start position:0%
+usually they don't have ambiguous mates
+ 
+
+ align:start position:0%
+usually they don't have ambiguous mates
+that's like the ultimate combo uh if you
+
+ align:start position:0%
+that's like the ultimate combo uh if you
+ 
+
+ align:start position:0%
+that's like the ultimate combo uh if you
+don't assume either of those things then
+
+ align:start position:0%
+don't assume either of those things then
+ 
+
+ align:start position:0%
+don't assume either of those things then
+the problem problem is easy so we don't
+
+ align:start position:0%
+the problem problem is easy so we don't
+ 
+
+ align:start position:0%
+the problem problem is easy so we don't
+care about that there are papers about
+
+ align:start position:0%
+care about that there are papers about
+ 
+
+ align:start position:0%
+care about that there are papers about
+how to solve jigsaw puzzles in the
+
+ align:start position:0%
+how to solve jigsaw puzzles in the
+ 
+
+ align:start position:0%
+how to solve jigsaw puzzles in the
+Practical case but um in our situation
+
+ align:start position:0%
+Practical case but um in our situation
+ 
+
+ align:start position:0%
+Practical case but um in our situation
+we can just I mean that's basically is
+
+ align:start position:0%
+we can just I mean that's basically is
+ 
+
+ align:start position:0%
+we can just I mean that's basically is
+Edge matching puzzles with signs this is
+
+ align:start position:0%
+Edge matching puzzles with signs this is
+ 
+
+ align:start position:0%
+Edge matching puzzles with signs this is
+actually probably why I care about
+
+ align:start position:0%
+actually probably why I care about
+ 
+
+ align:start position:0%
+actually probably why I care about
+signed puzzles the most uh I have
+
+ align:start position:0%
+signed puzzles the most uh I have
+ 
+
+ align:start position:0%
+signed puzzles the most uh I have
+lowercase letters those are going to
+
+ align:start position:0%
+lowercase letters those are going to
+ 
+
+ align:start position:0%
+lowercase letters those are going to
+correspond to Pockets I have uppercase
+
+ align:start position:0%
+correspond to Pockets I have uppercase
+ 
+
+ align:start position:0%
+correspond to Pockets I have uppercase
+letters those are going to correspond to
+
+ align:start position:0%
+letters those are going to correspond to
+ 
+
+ align:start position:0%
+letters those are going to correspond to
+tabs and of course a tab must meet a
+
+ align:start position:0%
+tabs and of course a tab must meet a
+ 
+
+ align:start position:0%
+tabs and of course a tab must meet a
+pocket same as a lowercase letter must
+
+ align:start position:0%
+pocket same as a lowercase letter must
+ 
+
+ align:start position:0%
+pocket same as a lowercase letter must
+meet an uppercase letter and so that is
+
+ align:start position:0%
+meet an uppercase letter and so that is
+ 
+
+ align:start position:0%
+meet an uppercase letter and so that is
+the same thing uh I would like my target
+
+ align:start position:0%
+the same thing uh I would like my target
+ 
+
+ align:start position:0%
+the same thing uh I would like my target
+shape to be a square cuz that's clean uh
+
+ align:start position:0%
+shape to be a square cuz that's clean uh
+ 
+
+ align:start position:0%
+shape to be a square cuz that's clean uh
+so whenever I have a unique color which
+
+ align:start position:0%
+so whenever I have a unique color which
+ 
+
+ align:start position:0%
+so whenever I have a unique color which
+is one that I know has to be on the
+
+ align:start position:0%
+is one that I know has to be on the
+ 
+
+ align:start position:0%
+is one that I know has to be on the
+boundary I'm going to make it a flat
+
+ align:start position:0%
+boundary I'm going to make it a flat
+ 
+
+ align:start position:0%
+boundary I'm going to make it a flat
+thing and then I know in this series of
+
+ align:start position:0%
+thing and then I know in this series of
+ 
+
+ align:start position:0%
+thing and then I know in this series of
+reductions I should draw the series of
+
+ align:start position:0%
+reductions I should draw the series of
+ 
+
+ align:start position:0%
+reductions I should draw the series of
+reductions because it's kind of fun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+far kind of started with rectangle
+
+ align:start position:0%
+far kind of started with rectangle
+ 
+
+ align:start position:0%
+far kind of started with rectangle
+packing I guess technically we started
+
+ align:start position:0%
+packing I guess technically we started
+ 
+
+ align:start position:0%
+packing I guess technically we started
+with three partition
+
+ align:start position:0%
+with three partition
+ 
+
+ align:start position:0%
+with three partition
+uh I'll draw it like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this we reduce that
+
+ align:start position:0%
+this we reduce that
+ 
+
+ align:start position:0%
+this we reduce that
+to uh Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matching
+
+ align:start position:0%
+matching
+ 
+
+ align:start position:0%
+matching
+puzzles then we reduce that
+
+ align:start position:0%
+puzzles then we reduce that
+ 
+
+ align:start position:0%
+puzzles then we reduce that
+to uh signed Edge matching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+puzzles then we reduce that to jigsaw
+
+ align:start position:0%
+puzzles then we reduce that to jigsaw
+ 
+
+ align:start position:0%
+puzzles then we reduce that to jigsaw
+puzzles
+
+ align:start position:0%
+puzzles
+ 
+
+ align:start position:0%
+puzzles
+and if you follow this series of
+
+ align:start position:0%
+and if you follow this series of
+ 
+
+ align:start position:0%
+and if you follow this series of
+reductions and see what you get we know
+
+ align:start position:0%
+reductions and see what you get we know
+ 
+
+ align:start position:0%
+reductions and see what you get we know
+that the boundary shape will be a square
+
+ align:start position:0%
+that the boundary shape will be a square
+ 
+
+ align:start position:0%
+that the boundary shape will be a square
+because that frame Gadget uh is a square
+
+ align:start position:0%
+because that frame Gadget uh is a square
+ 
+
+ align:start position:0%
+because that frame Gadget uh is a square
+and if we make all the unique things
+
+ align:start position:0%
+and if we make all the unique things
+ 
+
+ align:start position:0%
+and if we make all the unique things
+flat then the shape will actually be
+
+ align:start position:0%
+flat then the shape will actually be
+ 
+
+ align:start position:0%
+flat then the shape will actually be
+square there the reason I'm drawing it
+
+ align:start position:0%
+square there the reason I'm drawing it
+ 
+
+ align:start position:0%
+square there the reason I'm drawing it
+this way because we have another
+
+ align:start position:0%
+this way because we have another
+ 
+
+ align:start position:0%
+this way because we have another
+one um so next puzzle so you might ask
+
+ align:start position:0%
+one um so next puzzle so you might ask
+ 
+
+ align:start position:0%
+one um so next puzzle so you might ask
+well eternity 2 was an edge matching
+
+ align:start position:0%
+well eternity 2 was an edge matching
+ 
+
+ align:start position:0%
+well eternity 2 was an edge matching
+puzzle what was eternity one uh well
+
+ align:start position:0%
+puzzle what was eternity one uh well
+ 
+
+ align:start position:0%
+puzzle what was eternity one uh well
+it's something called a polyform packing
+
+ align:start position:0%
+it's something called a polyform packing
+ 
+
+ align:start position:0%
+it's something called a polyform packing
+puzzle uh these are um if you take an
+
+ align:start position:0%
+puzzle uh these are um if you take an
+ 
+
+ align:start position:0%
+puzzle uh these are um if you take an
+equilateral triangle and cut it in half
+
+ align:start position:0%
+equilateral triangle and cut it in half
+ 
+
+ align:start position:0%
+equilateral triangle and cut it in half
+like that um that's a shape and if you
+
+ align:start position:0%
+like that um that's a shape and if you
+ 
+
+ align:start position:0%
+like that um that's a shape and if you
+take uh K copies of that shape join them
+
+ align:start position:0%
+take uh K copies of that shape join them
+ 
+
+ align:start position:0%
+take uh K copies of that shape join them
+edge to edge along matching Edge lengths
+
+ align:start position:0%
+edge to edge along matching Edge lengths
+ 
+
+ align:start position:0%
+edge to edge along matching Edge lengths
+uh you get you can get all these shapes
+
+ align:start position:0%
+uh you get you can get all these shapes
+ 
+
+ align:start position:0%
+uh you get you can get all these shapes
+it's like Tetris but instead of with
+
+ align:start position:0%
+it's like Tetris but instead of with
+ 
+
+ align:start position:0%
+it's like Tetris but instead of with
+squares you start with that shape and
+
+ align:start position:0%
+squares you start with that shape and
+ 
+
+ align:start position:0%
+squares you start with that shape and
+you join a bunch more of them together I
+
+ align:start position:0%
+you join a bunch more of them together I
+ 
+
+ align:start position:0%
+you join a bunch more of them together I
+don't know exactly how many they may not
+
+ align:start position:0%
+don't know exactly how many they may not
+ 
+
+ align:start position:0%
+don't know exactly how many they may not
+even be all the same area and your goal
+
+ align:start position:0%
+even be all the same area and your goal
+ 
+
+ align:start position:0%
+even be all the same area and your goal
+is to fit inside this big uh decagon or
+
+ align:start position:0%
+is to fit inside this big uh decagon or
+ 
+
+ align:start position:0%
+is to fit inside this big uh decagon or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+uh this was solved million pounds were
+
+ align:start position:0%
+uh this was solved million pounds were
+ 
+
+ align:start position:0%
+uh this was solved million pounds were
+acquired uh by two people uh I think
+
+ align:start position:0%
+acquired uh by two people uh I think
+ 
+
+ align:start position:0%
+acquired uh by two people uh I think
+they were uh mathematicians Alex and
+
+ align:start position:0%
+they were uh mathematicians Alex and
+ 
+
+ align:start position:0%
+they were uh mathematicians Alex and
+Oliver in 2000 so actually quite soon
+
+ align:start position:0%
+Oliver in 2000 so actually quite soon
+ 
+
+ align:start position:0%
+Oliver in 2000 so actually quite soon
+after the puzzle was posed I think
+
+ align:start position:0%
+after the puzzle was posed I think
+ 
+
+ align:start position:0%
+after the puzzle was posed I think
+within a year less than a year uh so
+
+ align:start position:0%
+within a year less than a year uh so
+ 
+
+ align:start position:0%
+within a year less than a year uh so
+there was you know articles about uh how
+
+ align:start position:0%
+there was you know articles about uh how
+ 
+
+ align:start position:0%
+there was you know articles about uh how
+the insurance company was not happy but
+
+ align:start position:0%
+the insurance company was not happy but
+ 
+
+ align:start position:0%
+the insurance company was not happy but
+that's why you get insured against a
+
+ align:start position:0%
+that's why you get insured against a
+ 
+
+ align:start position:0%
+that's why you get insured against a
+puzzle being solved I guess but in
+
+ align:start position:0%
+puzzle being solved I guess but in
+ 
+
+ align:start position:0%
+puzzle being solved I guess but in
+eternity 2 a consequence is much harder
+
+ align:start position:0%
+eternity 2 a consequence is much harder
+ 
+
+ align:start position:0%
+eternity 2 a consequence is much harder
+and uh so no one has solved it yet but
+
+ align:start position:0%
+and uh so no one has solved it yet but
+ 
+
+ align:start position:0%
+and uh so no one has solved it yet but
+it will happen someday I'm sure uh so
+
+ align:start position:0%
+it will happen someday I'm sure uh so
+ 
+
+ align:start position:0%
+it will happen someday I'm sure uh so
+this gives you a clear sense of what the
+
+ align:start position:0%
+this gives you a clear sense of what the
+ 
+
+ align:start position:0%
+this gives you a clear sense of what the
+shapes look like uh so I want to prove
+
+ align:start position:0%
+shapes look like uh so I want to prove
+ 
+
+ align:start position:0%
+shapes look like uh so I want to prove
+these puzzles are NP hard
+
+ align:start position:0%
+these puzzles are NP hard
+ 
+
+ align:start position:0%
+these puzzles are NP hard
+also by reduction from jigsaw
+
+ align:start position:0%
+also by reduction from jigsaw
+ 
+
+ align:start position:0%
+also by reduction from jigsaw
+puzzles uh so let's just bring up the
+
+ align:start position:0%
+puzzles uh so let's just bring up the
+ 
+
+ align:start position:0%
+puzzles uh so let's just bring up the
+picture so we just we just did this
+
+ align:start position:0%
+picture so we just we just did this
+ 
+
+ align:start position:0%
+picture so we just we just did this
+reduction it actually works in both ways
+
+ align:start position:0%
+reduction it actually works in both ways
+ 
+
+ align:start position:0%
+reduction it actually works in both ways
+they're really the same puzzle this does
+
+ align:start position:0%
+they're really the same puzzle this does
+ 
+
+ align:start position:0%
+they're really the same puzzle this does
+not work so easily in both ways uh but
+
+ align:start position:0%
+not work so easily in both ways uh but
+ 
+
+ align:start position:0%
+not work so easily in both ways uh but
+I'm gonna take a jigsaw piece I'm going
+
+ align:start position:0%
+I'm gonna take a jigsaw piece I'm going
+ 
+
+ align:start position:0%
+I'm gonna take a jigsaw piece I'm going
+to turn it into roughly a square made up
+
+ align:start position:0%
+to turn it into roughly a square made up
+ 
+
+ align:start position:0%
+to turn it into roughly a square made up
+of little squares I'm not going to work
+
+ align:start position:0%
+of little squares I'm not going to work
+ 
+
+ align:start position:0%
+of little squares I'm not going to work
+on the the half triangles although I
+
+ align:start position:0%
+on the the half triangles although I
+ 
+
+ align:start position:0%
+on the the half triangles although I
+think it wouldn't be any harder it's a
+
+ align:start position:0%
+think it wouldn't be any harder it's a
+ 
+
+ align:start position:0%
+think it wouldn't be any harder it's a
+lot easier to think about Square puzzles
+
+ align:start position:0%
+lot easier to think about Square puzzles
+ 
+
+ align:start position:0%
+lot easier to think about Square puzzles
+more like Tetris these are polyomino so
+
+ align:start position:0%
+more like Tetris these are polyomino so
+ 
+
+ align:start position:0%
+more like Tetris these are polyomino so
+polyomino packing is this type of puzzle
+
+ align:start position:0%
+polyomino packing is this type of puzzle
+ 
+
+ align:start position:0%
+polyomino packing is this type of puzzle
+they also exist but that no one has won
+
+ align:start position:0%
+they also exist but that no one has won
+ 
+
+ align:start position:0%
+they also exist but that no one has won
+two million a million pounds from them
+
+ align:start position:0%
+two million a million pounds from them
+ 
+
+ align:start position:0%
+two million a million pounds from them
+so that's why I showed eternity um so
+
+ align:start position:0%
+so that's why I showed eternity um so
+ 
+
+ align:start position:0%
+so that's why I showed eternity um so
+almost a square but then in the middle
+
+ align:start position:0%
+almost a square but then in the middle
+ 
+
+ align:start position:0%
+almost a square but then in the middle
+of the edge we're going to write in
+
+ align:start position:0%
+of the edge we're going to write in
+ 
+
+ align:start position:0%
+of the edge we're going to write in
+binary uh what the shape was here I mean
+
+ align:start position:0%
+binary uh what the shape was here I mean
+ 
+
+ align:start position:0%
+binary uh what the shape was here I mean
+so there was you know a color over here
+
+ align:start position:0%
+so there was you know a color over here
+ 
+
+ align:start position:0%
+so there was you know a color over here
+and we can and a shape here uh all we
+
+ align:start position:0%
+and we can and a shape here uh all we
+ 
+
+ align:start position:0%
+and we can and a shape here uh all we
+care about is whether there're the same
+
+ align:start position:0%
+care about is whether there're the same
+ 
+
+ align:start position:0%
+care about is whether there're the same
+or different so there's only you know 4N
+
+ align:start position:0%
+or different so there's only you know 4N
+ 
+
+ align:start position:0%
+or different so there's only you know 4N
+different uh colors out there and so
+
+ align:start position:0%
+different uh colors out there and so
+ 
+
+ align:start position:0%
+different uh colors out there and so
+we're going to take log of 4N bits and
+
+ align:start position:0%
+we're going to take log of 4N bits and
+ 
+
+ align:start position:0%
+we're going to take log of 4N bits and
+write them in this way and if it was
+
+ align:start position:0%
+write them in this way and if it was
+ 
+
+ align:start position:0%
+write them in this way and if it was
+indented uh whenever we have a one we're
+
+ align:start position:0%
+indented uh whenever we have a one we're
+ 
+
+ align:start position:0%
+indented uh whenever we have a one we're
+going to indent here and if it's a a tab
+
+ align:start position:0%
+going to indent here and if it's a a tab
+ 
+
+ align:start position:0%
+going to indent here and if it's a a tab
+instead of a pocket wherever we have a
+
+ align:start position:0%
+instead of a pocket wherever we have a
+ 
+
+ align:start position:0%
+instead of a pocket wherever we have a
+one we're going to
+
+ align:start position:0%
+one we're going to
+ 
+
+ align:start position:0%
+one we're going to
+outdent okay so um these are all
+
+ align:start position:0%
+outdent okay so um these are all
+ 
+
+ align:start position:0%
+outdent okay so um these are all
+different codes and so none of them uh
+
+ align:start position:0%
+different codes and so none of them uh
+ 
+
+ align:start position:0%
+different codes and so none of them uh
+fit together for example uh
+
+ align:start position:0%
+fit together for example uh
+ 
+
+ align:start position:0%
+fit together for example uh
+and let's see anything match
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up this one matches with this one yeah
+
+ align:start position:0%
+up this one matches with this one yeah
+ 
+
+ align:start position:0%
+up this one matches with this one yeah
+because if I rotate it around stick it
+
+ align:start position:0%
+because if I rotate it around stick it
+ 
+
+ align:start position:0%
+because if I rotate it around stick it
+on it will match up so you have to make
+
+ align:start position:0%
+on it will match up so you have to make
+ 
+
+ align:start position:0%
+on it will match up so you have to make
+sure you get the orientations of the
+
+ align:start position:0%
+sure you get the orientations of the
+ 
+
+ align:start position:0%
+sure you get the orientations of the
+codes all right uh but you can do this
+
+ align:start position:0%
+codes all right uh but you can do this
+ 
+
+ align:start position:0%
+codes all right uh but you can do this
+and two things will fit together and
+
+ align:start position:0%
+and two things will fit together and
+ 
+
+ align:start position:0%
+and two things will fit together and
+make a nice clean seam if and only if
+
+ align:start position:0%
+make a nice clean seam if and only if
+ 
+
+ align:start position:0%
+make a nice clean seam if and only if
+the original colors matched and so this
+
+ align:start position:0%
+the original colors matched and so this
+ 
+
+ align:start position:0%
+the original colors matched and so this
+represents that puzzle where we've
+
+ align:start position:0%
+represents that puzzle where we've
+ 
+
+ align:start position:0%
+represents that puzzle where we've
+increased the we've blown everything up
+
+ align:start position:0%
+increased the we've blown everything up
+ 
+
+ align:start position:0%
+increased the we've blown everything up
+by like a logarithmic factor in each
+
+ align:start position:0%
+by like a logarithmic factor in each
+ 
+
+ align:start position:0%
+by like a logarithmic factor in each
+Dimension uh but the number of pieces is
+
+ align:start position:0%
+Dimension uh but the number of pieces is
+ 
+
+ align:start position:0%
+Dimension uh but the number of pieces is
+staying the same in a
+
+ align:start position:0%
+staying the same in a
+ 
+
+ align:start position:0%
+staying the same in a
+sense uh and then so that was this
+
+ align:start position:0%
+sense uh and then so that was this
+ 
+
+ align:start position:0%
+sense uh and then so that was this
+reduction to polyomino
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packing for fun we close the loop and
+
+ align:start position:0%
+packing for fun we close the loop and
+ 
+
+ align:start position:0%
+packing for fun we close the loop and
+reduce from polyomino packing to Edge
+
+ align:start position:0%
+reduce from polyomino packing to Edge
+ 
+
+ align:start position:0%
+reduce from polyomino packing to Edge
+matching uh in this way so we're going
+
+ align:start position:0%
+matching uh in this way so we're going
+ 
+
+ align:start position:0%
+matching uh in this way so we're going
+to take our polyomino carve it up into
+
+ align:start position:0%
+to take our polyomino carve it up into
+ 
+
+ align:start position:0%
+to take our polyomino carve it up into
+little squares turn them into Edge
+
+ align:start position:0%
+little squares turn them into Edge
+ 
+
+ align:start position:0%
+little squares turn them into Edge
+matching puzzle and here I actually want
+
+ align:start position:0%
+matching puzzle and here I actually want
+ 
+
+ align:start position:0%
+matching puzzle and here I actually want
+to allow rotation so I'm going to change
+
+ align:start position:0%
+to allow rotation so I'm going to change
+ 
+
+ align:start position:0%
+to allow rotation so I'm going to change
+these colors to all percent signs and
+
+ align:start position:0%
+these colors to all percent signs and
+ 
+
+ align:start position:0%
+these colors to all percent signs and
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh just the same puzzle yeah so we have
+
+ align:start position:0%
+uh just the same puzzle yeah so we have
+ 
+
+ align:start position:0%
+uh just the same puzzle yeah so we have
+to use the frame again and so if you
+
+ align:start position:0%
+to use the frame again and so if you
+ 
+
+ align:start position:0%
+to use the frame again and so if you
+want you can just keep following these
+
+ align:start position:0%
+want you can just keep following these
+ 
+
+ align:start position:0%
+want you can just keep following these
+reductions over and over and over uh I
+
+ align:start position:0%
+reductions over and over and over uh I
+ 
+
+ align:start position:0%
+reductions over and over and over uh I
+think every time you do it you increase
+
+ align:start position:0%
+think every time you do it you increase
+ 
+
+ align:start position:0%
+think every time you do it you increase
+the scale factor by like a log Factor uh
+
+ align:start position:0%
+the scale factor by like a log Factor uh
+ 
+
+ align:start position:0%
+the scale factor by like a log Factor uh
+but it's kind of fun I mean it really
+
+ align:start position:0%
+but it's kind of fun I mean it really
+ 
+
+ align:start position:0%
+but it's kind of fun I mean it really
+shows these puzzles are very close to
+
+ align:start position:0%
+shows these puzzles are very close to
+ 
+
+ align:start position:0%
+shows these puzzles are very close to
+identical uh in that we didn't have to
+
+ align:start position:0%
+identical uh in that we didn't have to
+ 
+
+ align:start position:0%
+identical uh in that we didn't have to
+blow up the puzzle size by very much to
+
+ align:start position:0%
+blow up the puzzle size by very much to
+ 
+
+ align:start position:0%
+blow up the puzzle size by very much to
+go from one puzzle to the next so
+
+ align:start position:0%
+go from one puzzle to the next so
+ 
+
+ align:start position:0%
+go from one puzzle to the next so
+usually we're just thinking about
+
+ align:start position:0%
+usually we're just thinking about
+ 
+
+ align:start position:0%
+usually we're just thinking about
+polinomial blowup here we have a very
+
+ align:start position:0%
+polinomial blowup here we have a very
+ 
+
+ align:start position:0%
+polinomial blowup here we have a very
+small notion of blowup which is some
+
+ align:start position:0%
+small notion of blowup which is some
+ 
+
+ align:start position:0%
+small notion of blowup which is some
+tight sense in which these puzzles are
+
+ align:start position:0%
+tight sense in which these puzzles are
+ 
+
+ align:start position:0%
+tight sense in which these puzzles are
+almost the
+
+ align:start position:0%
+almost the
+ 
+
+ align:start position:0%
+almost the
+same okay end of
+
+ align:start position:0%
+same okay end of
+ 
+
+ align:start position:0%
+same okay end of
+paper uh Fun open
+
+ align:start position:0%
+paper uh Fun open
+ 
+
+ align:start position:0%
+paper uh Fun open
+problem is uh this reduction Used Log n
+
+ align:start position:0%
+problem is uh this reduction Used Log n
+ 
+
+ align:start position:0%
+problem is uh this reduction Used Log n
+by log and Order log n by log n Pieces
+
+ align:start position:0%
+by log and Order log n by log n Pieces
+ 
+
+ align:start position:0%
+by log and Order log n by log n Pieces
+what if your pieces only have area log
+
+ align:start position:0%
+what if your pieces only have area log
+ 
+
+ align:start position:0%
+what if your pieces only have area log
+n so maybe they're root log n by root
+
+ align:start position:0%
+n so maybe they're root log n by root
+ 
+
+ align:start position:0%
+n so maybe they're root log n by root
+log n or something like that I'm sure it
+
+ align:start position:0%
+log n or something like that I'm sure it
+ 
+
+ align:start position:0%
+log n or something like that I'm sure it
+should still be NP hard but you never
+
+ align:start position:0%
+should still be NP hard but you never
+ 
+
+ align:start position:0%
+should still be NP hard but you never
+know uh if for example their constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size actually well let's say if they're
+
+ align:start position:0%
+size actually well let's say if they're
+ 
+
+ align:start position:0%
+size actually well let's say if they're
+size two it's easy leave it at that even
+
+ align:start position:0%
+size two it's easy leave it at that even
+ 
+
+ align:start position:0%
+size two it's easy leave it at that even
+if the shape is very messy uh but if
+
+ align:start position:0%
+if the shape is very messy uh but if
+ 
+
+ align:start position:0%
+if the shape is very messy uh but if
+they're also 2 by two blocks it's easy
+
+ align:start position:0%
+they're also 2 by two blocks it's easy
+ 
+
+ align:start position:0%
+they're also 2 by two blocks it's easy
+so they're clearly small shapes are too
+
+ align:start position:0%
+so they're clearly small shapes are too
+ 
+
+ align:start position:0%
+so they're clearly small shapes are too
+easy but probably logarithmic area is
+
+ align:start position:0%
+easy but probably logarithmic area is
+ 
+
+ align:start position:0%
+easy but probably logarithmic area is
+where it starts to get interesting I
+
+ align:start position:0%
+where it starts to get interesting I
+ 
+
+ align:start position:0%
+where it starts to get interesting I
+don't know what about log log area
+
+ align:start position:0%
+don't know what about log log area
+ 
+
+ align:start position:0%
+don't know what about log log area
+that's probably neither inp hard or
+
+ align:start position:0%
+that's probably neither inp hard or
+ 
+
+ align:start position:0%
+that's probably neither inp hard or
+polinomial but oh well um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool so um I want to talk about one more
+
+ align:start position:0%
+cool so um I want to talk about one more
+ 
+
+ align:start position:0%
+cool so um I want to talk about one more
+problem one more hardness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof in this similar vein it's about
+
+ align:start position:0%
+proof in this similar vein it's about
+ 
+
+ align:start position:0%
+proof in this similar vein it's about
+packing I already raed just packing
+
+ align:start position:0%
+packing I already raed just packing
+ 
+
+ align:start position:0%
+packing I already raed just packing
+rectangles into rectangles or rectangles
+
+ align:start position:0%
+rectangles into rectangles or rectangles
+ 
+
+ align:start position:0%
+rectangles into rectangles or rectangles
+into a square what about squares into a
+
+ align:start position:0%
+into a square what about squares into a
+ 
+
+ align:start position:0%
+into a square what about squares into a
+square if you can tell that's a square
+
+ align:start position:0%
+square if you can tell that's a square
+ 
+
+ align:start position:0%
+square if you can tell that's a square
+not a rectangle okay this is a nice
+
+ align:start position:0%
+not a rectangle okay this is a nice
+ 
+
+ align:start position:0%
+not a rectangle okay this is a nice
+paper uh we've used it for other
+
+ align:start position:0%
+paper uh we've used it for other
+ 
+
+ align:start position:0%
+paper uh we've used it for other
+hardness proofs uh which we probably
+
+ align:start position:0%
+hardness proofs uh which we probably
+ 
+
+ align:start position:0%
+hardness proofs uh which we probably
+talk about next class so I'm given a
+
+ align:start position:0%
+talk about next class so I'm given a
+ 
+
+ align:start position:0%
+talk about next class so I'm given a
+bunch of squares and I'm given a Target
+
+ align:start position:0%
+bunch of squares and I'm given a Target
+ 
+
+ align:start position:0%
+bunch of squares and I'm given a Target
+Square do these squares fit in there and
+
+ align:start position:0%
+Square do these squares fit in there and
+ 
+
+ align:start position:0%
+Square do these squares fit in there and
+again we we'll probably use exact um
+
+ align:start position:0%
+again we we'll probably use exact um
+ 
+
+ align:start position:0%
+again we we'll probably use exact um
+initially we won't be exact packing uh
+
+ align:start position:0%
+initially we won't be exact packing uh
+ 
+
+ align:start position:0%
+initially we won't be exact packing uh
+but let's say that the squares can't can
+
+ align:start position:0%
+but let's say that the squares can't can
+ 
+
+ align:start position:0%
+but let's say that the squares can't can
+only rotate by multiple of 90 in other
+
+ align:start position:0%
+only rotate by multiple of 90 in other
+ 
+
+ align:start position:0%
+only rotate by multiple of 90 in other
+words they can't
+
+ align:start position:0%
+words they can't
+ 
+
+ align:start position:0%
+words they can't
+rotate uh we will fix that by making
+
+ align:start position:0%
+rotate uh we will fix that by making
+ 
+
+ align:start position:0%
+rotate uh we will fix that by making
+exact packing but uh why don't I jump to
+
+ align:start position:0%
+exact packing but uh why don't I jump to
+ 
+
+ align:start position:0%
+exact packing but uh why don't I jump to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+reduction uh the heart of the reduction
+
+ align:start position:0%
+reduction uh the heart of the reduction
+ 
+
+ align:start position:0%
+reduction uh the heart of the reduction
+is this idea um we're just going to add
+
+ align:start position:0%
+is this idea um we're just going to add
+ 
+
+ align:start position:0%
+is this idea um we're just going to add
+a big number here I am going to use
+
+ align:start position:0%
+a big number here I am going to use
+ 
+
+ align:start position:0%
+a big number here I am going to use
+capital B for the big number this is
+
+ align:start position:0%
+capital B for the big number this is
+ 
+
+ align:start position:0%
+capital B for the big number this is
+what's in the paper this is a paper from
+
+ align:start position:0%
+what's in the paper this is a paper from
+ 
+
+ align:start position:0%
+what's in the paper this is a paper from
+1990 uh motivation here is you have a
+
+ align:start position:0%
+1990 uh motivation here is you have a
+ 
+
+ align:start position:0%
+1990 uh motivation here is you have a
+big grid supercomputer which were
+
+ align:start position:0%
+big grid supercomputer which were
+ 
+
+ align:start position:0%
+big grid supercomputer which were
+popular in the ' 80s and 90s um and you
+
+ align:start position:0%
+popular in the ' 80s and 90s um and you
+ 
+
+ align:start position:0%
+popular in the ' 80s and 90s um and you
+have a job which is a square grid of
+
+ align:start position:0%
+have a job which is a square grid of
+ 
+
+ align:start position:0%
+have a job which is a square grid of
+processors let's say and you want to
+
+ align:start position:0%
+processors let's say and you want to
+ 
+
+ align:start position:0%
+processors let's say and you want to
+execute them all in parallel but they're
+
+ align:start position:0%
+execute them all in parallel but they're
+ 
+
+ align:start position:0%
+execute them all in parallel but they're
+not allowed to overlap because that
+
+ align:start position:0%
+not allowed to overlap because that
+ 
+
+ align:start position:0%
+not allowed to overlap because that
+would slow your superc Computing down
+
+ align:start position:0%
+would slow your superc Computing down
+ 
+
+ align:start position:0%
+would slow your superc Computing down
+but you are allowed gaps let's
+
+ align:start position:0%
+but you are allowed gaps let's
+ 
+
+ align:start position:0%
+but you are allowed gaps let's
+say so uh I'm just going to take each of
+
+ align:start position:0%
+say so uh I'm just going to take each of
+ 
+
+ align:start position:0%
+say so uh I'm just going to take each of
+my AI numbers add this huge number to it
+
+ align:start position:0%
+my AI numbers add this huge number to it
+ 
+
+ align:start position:0%
+my AI numbers add this huge number to it
+so they're all roughly the same size
+
+ align:start position:0%
+so they're all roughly the same size
+ 
+
+ align:start position:0%
+so they're all roughly the same size
+this is the trick we did at the
+
+ align:start position:0%
+this is the trick we did at the
+ 
+
+ align:start position:0%
+this is the trick we did at the
+beginning of class with three partition
+
+ align:start position:0%
+beginning of class with three partition
+ 
+
+ align:start position:0%
+beginning of class with three partition
+right all these numbers all these sides
+
+ align:start position:0%
+right all these numbers all these sides
+ 
+
+ align:start position:0%
+right all these numbers all these sides
+are almost the same drawn them quite
+
+ align:start position:0%
+are almost the same drawn them quite
+ 
+
+ align:start position:0%
+are almost the same drawn them quite
+different but imagine they're just like
+
+ align:start position:0%
+different but imagine they're just like
+ 
+
+ align:start position:0%
+different but imagine they're just like
+tiny
+
+ align:start position:0%
+tiny
+ 
+
+ align:start position:0%
+tiny
+fluctuations and then uh I make the
+
+ align:start position:0%
+fluctuations and then uh I make the
+ 
+
+ align:start position:0%
+fluctuations and then uh I make the
+height of this rectangle for whatever
+
+ align:start position:0%
+height of this rectangle for whatever
+ 
+
+ align:start position:0%
+height of this rectangle for whatever
+reason I transpose my image uh that's
+
+ align:start position:0%
+reason I transpose my image uh that's
+ 
+
+ align:start position:0%
+reason I transpose my image uh that's
+probably why I was confused earlier um I
+
+ align:start position:0%
+probably why I was confused earlier um I
+ 
+
+ align:start position:0%
+probably why I was confused earlier um I
+just uh make the height three times the
+
+ align:start position:0%
+just uh make the height three times the
+ 
+
+ align:start position:0%
+just uh make the height three times the
+big number because I want three pieces
+
+ align:start position:0%
+big number because I want three pieces
+ 
+
+ align:start position:0%
+big number because I want three pieces
+to come together plus T my target sum of
+
+ align:start position:0%
+to come together plus T my target sum of
+ 
+
+ align:start position:0%
+to come together plus T my target sum of
+the AIS so this is a huge thing plus a
+
+ align:start position:0%
+the AIS so this is a huge thing plus a
+ 
+
+ align:start position:0%
+the AIS so this is a huge thing plus a
+super tiny thing uh but what it's saying
+
+ align:start position:0%
+super tiny thing uh but what it's saying
+ 
+
+ align:start position:0%
+super tiny thing uh but what it's saying
+is what you have slop they're all almost
+
+ align:start position:0%
+is what you have slop they're all almost
+ 
+
+ align:start position:0%
+is what you have slop they're all almost
+the same size there's that little bit of
+
+ align:start position:0%
+the same size there's that little bit of
+ 
+
+ align:start position:0%
+the same size there's that little bit of
+extra and that little bit extra has to
+
+ align:start position:0%
+extra and that little bit extra has to
+ 
+
+ align:start position:0%
+extra and that little bit extra has to
+add up to exactly T so this is one
+
+ align:start position:0%
+add up to exactly T so this is one
+ 
+
+ align:start position:0%
+add up to exactly T so this is one
+triple with the desired Target sum and
+
+ align:start position:0%
+triple with the desired Target sum and
+ 
+
+ align:start position:0%
+triple with the desired Target sum and
+then I want to get n over3 of them now
+
+ align:start position:0%
+then I want to get n over3 of them now
+ 
+
+ align:start position:0%
+then I want to get n over3 of them now
+here's where things get a little dicey
+
+ align:start position:0%
+here's where things get a little dicey
+ 
+
+ align:start position:0%
+here's where things get a little dicey
+you say okay let's just say I I take the
+
+ align:start position:0%
+you say okay let's just say I I take the
+ 
+
+ align:start position:0%
+you say okay let's just say I I take the
+largest one or actually I'll go all the
+
+ align:start position:0%
+largest one or actually I'll go all the
+ 
+
+ align:start position:0%
+largest one or actually I'll go all the
+way up to B plus T I know that every
+
+ align:start position:0%
+way up to B plus T I know that every
+ 
+
+ align:start position:0%
+way up to B plus T I know that every
+number I have is smaller than t uh
+
+ align:start position:0%
+number I have is smaller than t uh
+ 
+
+ align:start position:0%
+number I have is smaller than t uh
+because there sum of three of them is T
+
+ align:start position:0%
+because there sum of three of them is T
+ 
+
+ align:start position:0%
+because there sum of three of them is T
+so um I'm always going to have a gap
+
+ align:start position:0%
+so um I'm always going to have a gap
+ 
+
+ align:start position:0%
+so um I'm always going to have a gap
+here and let's say I just pack the next
+
+ align:start position:0%
+here and let's say I just pack the next
+ 
+
+ align:start position:0%
+here and let's say I just pack the next
+three there and then the next three
+
+ align:start position:0%
+three there and then the next three
+ 
+
+ align:start position:0%
+three there and then the next three
+there and so I'll leave enough room that
+
+ align:start position:0%
+there and so I'll leave enough room that
+ 
+
+ align:start position:0%
+there and so I'll leave enough room that
+even with this slop I can fit everything
+
+ align:start position:0%
+even with this slop I can fit everything
+ 
+
+ align:start position:0%
+even with this slop I can fit everything
+in so each one is B plus T and the
+
+ align:start position:0%
+in so each one is B plus T and the
+ 
+
+ align:start position:0%
+in so each one is B plus T and the
+number of them is n over3 so that will
+
+ align:start position:0%
+number of them is n over3 so that will
+ 
+
+ align:start position:0%
+number of them is n over3 so that will
+be the width of my rectangle looks like
+
+ align:start position:0%
+be the width of my rectangle looks like
+ 
+
+ align:start position:0%
+be the width of my rectangle looks like
+a lot of slop but that's because I drew
+
+ align:start position:0%
+a lot of slop but that's because I drew
+ 
+
+ align:start position:0%
+a lot of slop but that's because I drew
+this with the squares very different in
+
+ align:start position:0%
+this with the squares very different in
+ 
+
+ align:start position:0%
+this with the squares very different in
+size if we compute the amount of
+
+ align:start position:0%
+size if we compute the amount of
+ 
+
+ align:start position:0%
+size if we compute the amount of
+slop uh let's see the maximum like if
+
+ align:start position:0%
+slop uh let's see the maximum like if
+ 
+
+ align:start position:0%
+slop uh let's see the maximum like if
+you look at this distance um it's at
+
+ align:start position:0%
+you look at this distance um it's at
+ 
+
+ align:start position:0%
+you look at this distance um it's at
+most T certainly even if if AI were zero
+
+ align:start position:0%
+most T certainly even if if AI were zero
+ 
+
+ align:start position:0%
+most T certainly even if if AI were zero
+which is not allowed then this distance
+
+ align:start position:0%
+which is not allowed then this distance
+ 
+
+ align:start position:0%
+which is not allowed then this distance
+would be T so it's going to be even
+
+ align:start position:0%
+would be T so it's going to be even
+ 
+
+ align:start position:0%
+would be T so it's going to be even
+smaller than that but uh the gaps here
+
+ align:start position:0%
+smaller than that but uh the gaps here
+ 
+
+ align:start position:0%
+smaller than that but uh the gaps here
+are always at most T so we can take
+
+ align:start position:0%
+are always at most T so we can take
+ 
+
+ align:start position:0%
+are always at most T so we can take
+uh so this is a total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slop is
+
+ align:start position:0%
+slop is
+ 
+
+ align:start position:0%
+slop is
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+times uh the height so that was like the
+
+ align:start position:0%
+times uh the height so that was like the
+ 
+
+ align:start position:0%
+times uh the height so that was like the
+width of a of one sliver of slop and
+
+ align:start position:0%
+width of a of one sliver of slop and
+ 
+
+ align:start position:0%
+width of a of one sliver of slop and
+then the height is 3B plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+and then times n over3 because there's n
+
+ align:start position:0%
+and then times n over3 because there's n
+ 
+
+ align:start position:0%
+and then times n over3 because there's n
+over3 of those things and hopefully this
+
+ align:start position:0%
+over3 of those things and hopefully this
+ 
+
+ align:start position:0%
+over3 of those things and hopefully this
+works uh I want to say this is less than
+
+ align:start position:0%
+works uh I want to say this is less than
+ 
+
+ align:start position:0%
+works uh I want to say this is less than
+b^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if B is bigger than cool T * n thre's
+
+ align:start position:0%
+if B is bigger than cool T * n thre's
+ 
+
+ align:start position:0%
+if B is bigger than cool T * n thre's
+cancel so if B is I think this term
+
+ align:start position:0%
+cancel so if B is I think this term
+ 
+
+ align:start position:0%
+cancel so if B is I think this term
+won't matter because B is going to be
+
+ align:start position:0%
+won't matter because B is going to be
+ 
+
+ align:start position:0%
+won't matter because B is going to be
+bigger than T um so well yeah I maybe
+
+ align:start position:0%
+bigger than T um so well yeah I maybe
+ 
+
+ align:start position:0%
+bigger than T um so well yeah I maybe
+put a two there for extra safety then
+
+ align:start position:0%
+put a two there for extra safety then
+ 
+
+ align:start position:0%
+put a two there for extra safety then
+you're totally dwarfed uh so we're just
+
+ align:start position:0%
+you're totally dwarfed uh so we're just
+ 
+
+ align:start position:0%
+you're totally dwarfed uh so we're just
+dividing both sides by B we're getting 3
+
+ align:start position:0%
+dividing both sides by B we're getting 3
+ 
+
+ align:start position:0%
+dividing both sides by B we're getting 3
+* T * n over 3 that's T * n okay um cool
+
+ align:start position:0%
+* T * n over 3 that's T * n okay um cool
+ 
+
+ align:start position:0%
+* T * n over 3 that's T * n okay um cool
+so the point is the total area of slop
+
+ align:start position:0%
+so the point is the total area of slop
+ 
+
+ align:start position:0%
+so the point is the total area of slop
+that I have here is less than a single
+
+ align:start position:0%
+that I have here is less than a single
+ 
+
+ align:start position:0%
+that I have here is less than a single
+Square single square is even bigger than
+
+ align:start position:0%
+Square single square is even bigger than
+ 
+
+ align:start position:0%
+Square single square is even bigger than
+this uh so you're not going to be able
+
+ align:start position:0%
+this uh so you're not going to be able
+ 
+
+ align:start position:0%
+this uh so you're not going to be able
+to pack any more squares and uh that's a
+
+ align:start position:0%
+to pack any more squares and uh that's a
+ 
+
+ align:start position:0%
+to pack any more squares and uh that's a
+vague argument but enough hand waving
+
+ align:start position:0%
+vague argument but enough hand waving
+ 
+
+ align:start position:0%
+vague argument but enough hand waving
+later and you prove that in fact any
+
+ align:start position:0%
+later and you prove that in fact any
+ 
+
+ align:start position:0%
+later and you prove that in fact any
+packing of these squares will give you
+
+ align:start position:0%
+packing of these squares will give you
+ 
+
+ align:start position:0%
+packing of these squares will give you
+three partition that requires more work
+
+ align:start position:0%
+three partition that requires more work
+ 
+
+ align:start position:0%
+three partition that requires more work
+um but uh this is some intuition why it
+
+ align:start position:0%
+um but uh this is some intuition why it
+ 
+
+ align:start position:0%
+um but uh this is some intuition why it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+true um okay so this was actually
+
+ align:start position:0%
+true um okay so this was actually
+ 
+
+ align:start position:0%
+true um okay so this was actually
+packing squares into a rectangle but
+
+ align:start position:0%
+packing squares into a rectangle but
+ 
+
+ align:start position:0%
+packing squares into a rectangle but
+that wasn't the problem I started with I
+
+ align:start position:0%
+that wasn't the problem I started with I
+ 
+
+ align:start position:0%
+that wasn't the problem I started with I
+wanted to pack squares into a square uh
+
+ align:start position:0%
+wanted to pack squares into a square uh
+ 
+
+ align:start position:0%
+wanted to pack squares into a square uh
+so for that you need an infrastructure
+
+ align:start position:0%
+so for that you need an infrastructure
+ 
+
+ align:start position:0%
+so for that you need an infrastructure
+Gadget like the frame that we made
+
+ align:start position:0%
+Gadget like the frame that we made
+ 
+
+ align:start position:0%
+Gadget like the frame that we made
+before uh and this is kind of a cute
+
+ align:start position:0%
+before uh and this is kind of a cute
+ 
+
+ align:start position:0%
+before uh and this is kind of a cute
+number theory is Trick um I'm going to
+
+ align:start position:0%
+number theory is Trick um I'm going to
+ 
+
+ align:start position:0%
+number theory is Trick um I'm going to
+take some integer X we'll choose it
+
+ align:start position:0%
+take some integer X we'll choose it
+ 
+
+ align:start position:0%
+take some integer X we'll choose it
+later it's just going to be big enough
+
+ align:start position:0%
+later it's just going to be big enough
+ 
+
+ align:start position:0%
+later it's just going to be big enough
+something like n and we have one giant
+
+ align:start position:0%
+something like n and we have one giant
+ 
+
+ align:start position:0%
+something like n and we have one giant
+Square which is x * x + 1 minus one uh
+
+ align:start position:0%
+Square which is x * x + 1 minus one uh
+ 
+
+ align:start position:0%
+Square which is x * x + 1 minus one uh
+by they're all squares so by the same
+
+ align:start position:0%
+by they're all squares so by the same
+ 
+
+ align:start position:0%
+by they're all squares so by the same
+amount and then we're going to take
+
+ align:start position:0%
+amount and then we're going to take
+ 
+
+ align:start position:0%
+amount and then we're going to take
+these medium siiz squares of size X plus
+
+ align:start position:0%
+these medium siiz squares of size X plus
+ 
+
+ align:start position:0%
+these medium siiz squares of size X plus
+one and these small squares so much
+
+ align:start position:0%
+one and these small squares so much
+ 
+
+ align:start position:0%
+one and these small squares so much
+smaller of size X and because uh this is
+
+ align:start position:0%
+smaller of size X and because uh this is
+ 
+
+ align:start position:0%
+smaller of size X and because uh this is
+just one smaller uh than what it's
+
+ align:start position:0%
+just one smaller uh than what it's
+ 
+
+ align:start position:0%
+just one smaller uh than what it's
+supposed to be I mean if it was x * X+ 1
+
+ align:start position:0%
+supposed to be I mean if it was x * X+ 1
+ 
+
+ align:start position:0%
+supposed to be I mean if it was x * X+ 1
+it would come to here uh and so when you
+
+ align:start position:0%
+it would come to here uh and so when you
+ 
+
+ align:start position:0%
+it would come to here uh and so when you
+pack these guys up you go just one too
+
+ align:start position:0%
+pack these guys up you go just one too
+ 
+
+ align:start position:0%
+pack these guys up you go just one too
+far there but there's exactly enough
+
+ align:start position:0%
+far there but there's exactly enough
+ 
+
+ align:start position:0%
+far there but there's exactly enough
+room for one more if I put X plus one
+
+ align:start position:0%
+room for one more if I put X plus one
+ 
+
+ align:start position:0%
+room for one more if I put X plus one
+extra this is X that's the one and so on
+
+ align:start position:0%
+extra this is X that's the one and so on
+ 
+
+ align:start position:0%
+extra this is X that's the one and so on
+so uh this leaves as a Gap a
+
+ align:start position:0%
+so uh this leaves as a Gap a
+ 
+
+ align:start position:0%
+so uh this leaves as a Gap a
+rectangle now this is not the only
+
+ align:start position:0%
+rectangle now this is not the only
+ 
+
+ align:start position:0%
+rectangle now this is not the only
+solution these guys could slide down but
+
+ align:start position:0%
+solution these guys could slide down but
+ 
+
+ align:start position:0%
+solution these guys could slide down but
+you can show that will only make your
+
+ align:start position:0%
+you can show that will only make your
+ 
+
+ align:start position:0%
+you can show that will only make your
+life harder and the paper does that um
+
+ align:start position:0%
+life harder and the paper does that um
+ 
+
+ align:start position:0%
+life harder and the paper does that um
+that's sort of the easy part of the
+
+ align:start position:0%
+that's sort of the easy part of the
+ 
+
+ align:start position:0%
+that's sort of the easy part of the
+proof and so now you're left with a
+
+ align:start position:0%
+proof and so now you're left with a
+ 
+
+ align:start position:0%
+proof and so now you're left with a
+rectangle which is one by this thing uh
+
+ align:start position:0%
+rectangle which is one by this thing uh
+ 
+
+ align:start position:0%
+rectangle which is one by this thing uh
+you multiply everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by 3B plus T because that was what we
+
+ align:start position:0%
+by 3B plus T because that was what we
+ 
+
+ align:start position:0%
+by 3B plus T because that was what we
+wanted one of our Dimensions to be the
+
+ align:start position:0%
+wanted one of our Dimensions to be the
+ 
+
+ align:start position:0%
+wanted one of our Dimensions to be the
+smaller one uh so that scale up the
+
+ align:start position:0%
+smaller one uh so that scale up the
+ 
+
+ align:start position:0%
+smaller one uh so that scale up the
+rectangle and then the horizontal the
+
+ align:start position:0%
+rectangle and then the horizontal the
+ 
+
+ align:start position:0%
+rectangle and then the horizontal the
+widths may not match exactly uh but if
+
+ align:start position:0%
+widths may not match exactly uh but if
+ 
+
+ align:start position:0%
+widths may not match exactly uh but if
+if there's too much space here and we
+
+ align:start position:0%
+if there's too much space here and we
+ 
+
+ align:start position:0%
+if there's too much space here and we
+just set X to be large enough then
+
+ align:start position:0%
+just set X to be large enough then
+ 
+
+ align:start position:0%
+just set X to be large enough then
+there'll be extra space and just throw
+
+ align:start position:0%
+there'll be extra space and just throw
+ 
+
+ align:start position:0%
+there'll be extra space and just throw
+in a bunch of B byb blocks there to fill
+
+ align:start position:0%
+in a bunch of B byb blocks there to fill
+ 
+
+ align:start position:0%
+in a bunch of B byb blocks there to fill
+up the extra space you can figure out
+
+ align:start position:0%
+up the extra space you can figure out
+ 
+
+ align:start position:0%
+up the extra space you can figure out
+how much extra space there is and fill
+
+ align:start position:0%
+how much extra space there is and fill
+ 
+
+ align:start position:0%
+how much extra space there is and fill
+it in uh so there you go packing squares
+
+ align:start position:0%
+it in uh so there you go packing squares
+ 
+
+ align:start position:0%
+it in uh so there you go packing squares
+into a square and this is strong NP
+
+ align:start position:0%
+into a square and this is strong NP
+ 
+
+ align:start position:0%
+into a square and this is strong NP
+hardness so this even when the squares
+
+ align:start position:0%
+hardness so this even when the squares
+ 
+
+ align:start position:0%
+hardness so this even when the squares
+are only of polinomial area this problem
+
+ align:start position:0%
+are only of polinomial area this problem
+ 
+
+ align:start position:0%
+are only of polinomial area this problem
+is hard which is actually the case you
+
+ align:start position:0%
+is hard which is actually the case you
+ 
+
+ align:start position:0%
+is hard which is actually the case you
+care about when each of these one by one
+
+ align:start position:0%
+care about when each of these one by one
+ 
+
+ align:start position:0%
+care about when each of these one by one
+squares is a processor now this was not
+
+ align:start position:0%
+squares is a processor now this was not
+ 
+
+ align:start position:0%
+squares is a processor now this was not
+exact packing and so you might worry oh
+
+ align:start position:0%
+exact packing and so you might worry oh
+ 
+
+ align:start position:0%
+exact packing and so you might worry oh
+what if I rotate the squares and then
+
+ align:start position:0%
+what if I rotate the squares and then
+ 
+
+ align:start position:0%
+what if I rotate the squares and then
+crazy things can happen probably not but
+
+ align:start position:0%
+crazy things can happen probably not but
+ 
+
+ align:start position:0%
+crazy things can happen probably not but
+um you could also just compute how much
+
+ align:start position:0%
+um you could also just compute how much
+ 
+
+ align:start position:0%
+um you could also just compute how much
+extra slop there is because you know the
+
+ align:start position:0%
+extra slop there is because you know the
+ 
+
+ align:start position:0%
+extra slop there is because you know the
+area of the uh input squares and you
+
+ align:start position:0%
+area of the uh input squares and you
+ 
+
+ align:start position:0%
+area of the uh input squares and you
+know the area of the target square and
+
+ align:start position:0%
+know the area of the target square and
+ 
+
+ align:start position:0%
+know the area of the target square and
+just add a whole bunch of one by one uh
+
+ align:start position:0%
+just add a whole bunch of one by one uh
+ 
+
+ align:start position:0%
+just add a whole bunch of one by one uh
+little chips and that will fill in
+
+ align:start position:0%
+little chips and that will fill in
+ 
+
+ align:start position:0%
+little chips and that will fill in
+exactly the space then you have exact
+
+ align:start position:0%
+exactly the space then you have exact
+ 
+
+ align:start position:0%
+exactly the space then you have exact
+packing then you don't even have to
+
+ align:start position:0%
+packing then you don't even have to
+ 
+
+ align:start position:0%
+packing then you don't even have to
+worry about rotation so that makes proof
+
+ align:start position:0%
+worry about rotation so that makes proof
+ 
+
+ align:start position:0%
+worry about rotation so that makes proof
+even cleaner I think that wasn't in the
+
+ align:start position:0%
+even cleaner I think that wasn't in the
+ 
+
+ align:start position:0%
+even cleaner I think that wasn't in the
+original paper but it's a nice little
+
+ align:start position:0%
+original paper but it's a nice little
+ 
+
+ align:start position:0%
+original paper but it's a nice little
+addition and that is our packing through
+
+ align:start position:0%
+addition and that is our packing through
+ 
+
+ align:start position:0%
+addition and that is our packing through
+three partition next class we'll do more
+
+ align:start position:0%
+three partition next class we'll do more
+ 
+
+ align:start position:0%
+three partition next class we'll do more
+more three partition for different types
+
+ align:start position:0%
+more three partition for different types
+ 
+
+ align:start position:0%
+more three partition for different types
+of problems so in case you lose uh lots
+
+ align:start position:0%
+of problems so in case you lose uh lots
+ 
+
+ align:start position:0%
+of problems so in case you lose uh lots
+of pieces in your jig jiga puzzle we
+
+ align:start position:0%
+of pieces in your jig jiga puzzle we
+ 
+
+ align:start position:0%
+of pieces in your jig jiga puzzle we
+have the one piece jigsaw
+
+ align:start position:0%
+have the one piece jigsaw
+ 
+
+ align:start position:0%
+have the one piece jigsaw
+puzzle uh this is all the pieces are in
+
+ align:start position:0%
+puzzle uh this is all the pieces are in
+ 
+
+ align:start position:0%
+puzzle uh this is all the pieces are in
+one giant connected mess and still it is
+
+ align:start position:0%
+one giant connected mess and still it is
+ 
+
+ align:start position:0%
+one giant connected mess and still it is
+not so trivial to
+
+ align:start position:0%
+not so trivial to
+ 
+
+ align:start position:0%
+not so trivial to
+solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wow all right this is the one piece jiga
+
+ align:start position:0%
+wow all right this is the one piece jiga
+ 
+
+ align:start position:0%
+wow all right this is the one piece jiga
+puzzle in solve
+
+ align:start position:0%
+puzzle in solve
+ 
+
+ align:start position:0%
+puzzle in solve
+State it's a Simpsons Edition
+
+ align:start position:0%
+State it's a Simpsons Edition
+ 
+
+ align:start position:0%
+State it's a Simpsons Edition
+so you get it
+
+ align:start position:0%
+so you get it
+ 
+
+ align:start position:0%
+so you get it
+then you put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thater
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tada
\ No newline at end of file
diff --git a/_0PrwAbgoMA.txt b/_0PrwAbgoMA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07dc6358b56863ba80b979cf229a21cd10024b68
--- /dev/null
+++ b/_0PrwAbgoMA.txt
@@ -0,0 +1,547 @@
+align:start position:0%
+ 
+now let's consider the case where an
+
+ align:start position:0%
+now let's consider the case where an
+ 
+
+ align:start position:0%
+now let's consider the case where an
+object is undergoing circular motion but
+
+ align:start position:0%
+object is undergoing circular motion but
+ 
+
+ align:start position:0%
+object is undergoing circular motion but
+in this motion let's again introduce our
+
+ align:start position:0%
+in this motion let's again introduce our
+ 
+
+ align:start position:0%
+in this motion let's again introduce our
+polar coordinate system our hat and beta
+
+ align:start position:0%
+polar coordinate system our hat and beta
+ 
+
+ align:start position:0%
+polar coordinate system our hat and beta
+hat we now want to consider the case
+
+ align:start position:0%
+hat we now want to consider the case
+ 
+
+ align:start position:0%
+hat we now want to consider the case
+where d theta/dt is not constant and
+
+ align:start position:0%
+where d theta/dt is not constant and
+ 
+
+ align:start position:0%
+where d theta/dt is not constant and
+what does that mean
+
+ align:start position:0%
+what does that mean
+ 
+
+ align:start position:0%
+what does that mean
+that means that if d theta/dt is
+
+ align:start position:0%
+that means that if d theta/dt is
+ 
+
+ align:start position:0%
+that means that if d theta/dt is
+positive for instance the object is
+
+ align:start position:0%
+positive for instance the object is
+ 
+
+ align:start position:0%
+positive for instance the object is
+speeding up in this direction or if d
+
+ align:start position:0%
+speeding up in this direction or if d
+ 
+
+ align:start position:0%
+speeding up in this direction or if d
+theta/dt is negative the object is
+
+ align:start position:0%
+theta/dt is negative the object is
+ 
+
+ align:start position:0%
+theta/dt is negative the object is
+slowing down in this direction that's
+
+ align:start position:0%
+slowing down in this direction that's
+ 
+
+ align:start position:0%
+slowing down in this direction that's
+one type of case so in this instant we
+
+ align:start position:0%
+one type of case so in this instant we
+ 
+
+ align:start position:0%
+one type of case so in this instant we
+always know that there's a radial
+
+ align:start position:0%
+always know that there's a radial
+ 
+
+ align:start position:0%
+always know that there's a radial
+component at any instant given by minus
+
+ align:start position:0%
+component at any instant given by minus
+ 
+
+ align:start position:0%
+component at any instant given by minus
+R D theta DT squared but because it's
+
+ align:start position:0%
+R D theta DT squared but because it's
+ 
+
+ align:start position:0%
+R D theta DT squared but because it's
+speeding up and slowing down there is
+
+ align:start position:0%
+speeding up and slowing down there is
+ 
+
+ align:start position:0%
+speeding up and slowing down there is
+now a non zero tangential component to
+
+ align:start position:0%
+now a non zero tangential component to
+ 
+
+ align:start position:0%
+now a non zero tangential component to
+the acceleration and let's see where
+
+ align:start position:0%
+the acceleration and let's see where
+ 
+
+ align:start position:0%
+the acceleration and let's see where
+that comes from so again if we write our
+
+ align:start position:0%
+that comes from so again if we write our
+ 
+
+ align:start position:0%
+that comes from so again if we write our
+velocity vector as our D theta DT theta
+
+ align:start position:0%
+velocity vector as our D theta DT theta
+ 
+
+ align:start position:0%
+velocity vector as our D theta DT theta
+hat this is the product of two terms and
+
+ align:start position:0%
+hat this is the product of two terms and
+ 
+
+ align:start position:0%
+hat this is the product of two terms and
+because it's a product of two terms we
+
+ align:start position:0%
+because it's a product of two terms we
+ 
+
+ align:start position:0%
+because it's a product of two terms we
+need the product rule from calculus and
+
+ align:start position:0%
+need the product rule from calculus and
+ 
+
+ align:start position:0%
+need the product rule from calculus and
+when we take a derivative so the
+
+ align:start position:0%
+when we take a derivative so the
+ 
+
+ align:start position:0%
+when we take a derivative so the
+derivative will be the derivative of the
+
+ align:start position:0%
+derivative will be the derivative of the
+ 
+
+ align:start position:0%
+derivative will be the derivative of the
+first term times the second term plus
+
+ align:start position:0%
+first term times the second term plus
+ 
+
+ align:start position:0%
+first term times the second term plus
+the first term times the derivative of
+
+ align:start position:0%
+the first term times the derivative of
+ 
+
+ align:start position:0%
+the first term times the derivative of
+the second term
+
+ align:start position:0%
+the second term
+ 
+
+ align:start position:0%
+the second term
+now we've already analyzed this piece
+
+ align:start position:0%
+now we've already analyzed this piece
+ 
+
+ align:start position:0%
+now we've already analyzed this piece
+and this was precisely - our D theta DT
+
+ align:start position:0%
+and this was precisely - our D theta DT
+ 
+
+ align:start position:0%
+and this was precisely - our D theta DT
+quantity squared R hat that was the
+
+ align:start position:0%
+quantity squared R hat that was the
+ 
+
+ align:start position:0%
+quantity squared R hat that was the
+always the non zero ten radial
+
+ align:start position:0%
+always the non zero ten radial
+ 
+
+ align:start position:0%
+always the non zero ten radial
+acceleration but now let's analyze this
+
+ align:start position:0%
+acceleration but now let's analyze this
+ 
+
+ align:start position:0%
+acceleration but now let's analyze this
+piece separately R for our circular
+
+ align:start position:0%
+piece separately R for our circular
+ 
+
+ align:start position:0%
+piece separately R for our circular
+motion is a constant so it's only D
+
+ align:start position:0%
+motion is a constant so it's only D
+ 
+
+ align:start position:0%
+motion is a constant so it's only D
+theta DT that is no longer constant so
+
+ align:start position:0%
+theta DT that is no longer constant so
+ 
+
+ align:start position:0%
+theta DT that is no longer constant so
+we simply take a second derivative and
+
+ align:start position:0%
+we simply take a second derivative and
+ 
+
+ align:start position:0%
+we simply take a second derivative and
+so we get R times d squared theta DT
+
+ align:start position:0%
+so we get R times d squared theta DT
+ 
+
+ align:start position:0%
+so we get R times d squared theta DT
+squared theta hat
+
+ align:start position:0%
+squared theta hat
+ 
+
+ align:start position:0%
+squared theta hat
+and that is our acceleration notice that
+
+ align:start position:0%
+and that is our acceleration notice that
+ 
+
+ align:start position:0%
+and that is our acceleration notice that
+it has two components we'll write the
+
+ align:start position:0%
+it has two components we'll write the
+ 
+
+ align:start position:0%
+it has two components we'll write the
+first component a theta that's its
+
+ align:start position:0%
+first component a theta that's its
+ 
+
+ align:start position:0%
+first component a theta that's its
+tangential component theta hat plus the
+
+ align:start position:0%
+tangential component theta hat plus the
+ 
+
+ align:start position:0%
+tangential component theta hat plus the
+radial component a R that's again the
+
+ align:start position:0%
+radial component a R that's again the
+ 
+
+ align:start position:0%
+radial component a R that's again the
+component and because this is a vector R
+
+ align:start position:0%
+component and because this is a vector R
+ 
+
+ align:start position:0%
+component and because this is a vector R
+hat where the a theta is now the second
+
+ align:start position:0%
+hat where the a theta is now the second
+ 
+
+ align:start position:0%
+hat where the a theta is now the second
+derivative of D theta squared DT squared
+
+ align:start position:0%
+derivative of D theta squared DT squared
+ 
+
+ align:start position:0%
+derivative of D theta squared DT squared
+and just to remind you that a R is minus
+
+ align:start position:0%
+and just to remind you that a R is minus
+ 
+
+ align:start position:0%
+and just to remind you that a R is minus
+AR D theta DT squared so when d squared
+
+ align:start position:0%
+AR D theta DT squared so when d squared
+ 
+
+ align:start position:0%
+AR D theta DT squared so when d squared
+theta DT squared is positive it means D
+
+ align:start position:0%
+theta DT squared is positive it means D
+ 
+
+ align:start position:0%
+theta DT squared is positive it means D
+theta DT is increasing and so if this
+
+ align:start position:0%
+theta DT is increasing and so if this
+ 
+
+ align:start position:0%
+theta DT is increasing and so if this
+object is going in this clockwise
+
+ align:start position:0%
+object is going in this clockwise
+ 
+
+ align:start position:0%
+object is going in this clockwise
+direction we call that speeding up in a
+
+ align:start position:0%
+direction we call that speeding up in a
+ 
+
+ align:start position:0%
+direction we call that speeding up in a
+similar fashion it's easy to understand
+
+ align:start position:0%
+similar fashion it's easy to understand
+ 
+
+ align:start position:0%
+similar fashion it's easy to understand
+that when d squared theta DT squared is
+
+ align:start position:0%
+that when d squared theta DT squared is
+ 
+
+ align:start position:0%
+that when d squared theta DT squared is
+negative then D theta DT is decreasing
+
+ align:start position:0%
+negative then D theta DT is decreasing
+ 
+
+ align:start position:0%
+negative then D theta DT is decreasing
+and so it can be slowing down or if it
+
+ align:start position:0%
+and so it can be slowing down or if it
+ 
+
+ align:start position:0%
+and so it can be slowing down or if it
+slows down and stops you can start to
+
+ align:start position:0%
+slows down and stops you can start to
+ 
+
+ align:start position:0%
+slows down and stops you can start to
+move in the other direction so again the
+
+ align:start position:0%
+move in the other direction so again the
+ 
+
+ align:start position:0%
+move in the other direction so again the
+acceleration has two components a
+
+ align:start position:0%
+acceleration has two components a
+ 
+
+ align:start position:0%
+acceleration has two components a
+tangential component and that depends on
+
+ align:start position:0%
+tangential component and that depends on
+ 
+
+ align:start position:0%
+tangential component and that depends on
+the type of circular motion we're
+
+ align:start position:0%
+the type of circular motion we're
+ 
+
+ align:start position:0%
+the type of circular motion we're
+talking about whether d theta DT is
+
+ align:start position:0%
+talking about whether d theta DT is
+ 
+
+ align:start position:0%
+talking about whether d theta DT is
+constant or not it always has a nonzero
+
+ align:start position:0%
+constant or not it always has a nonzero
+ 
+
+ align:start position:0%
+constant or not it always has a nonzero
+inward radial component given by Muk the
+
+ align:start position:0%
+inward radial component given by Muk the
+ 
+
+ align:start position:0%
+inward radial component given by Muk the
+component minus R D theta T squared
+
+ align:start position:0%
+component minus R D theta T squared
+ 
+
+ align:start position:0%
+component minus R D theta T squared
+regardless of whether it's speeding up
+
+ align:start position:0%
+regardless of whether it's speeding up
+ 
+
+ align:start position:0%
+regardless of whether it's speeding up
+or slowing down
\ No newline at end of file
diff --git a/_GgdGtQME1I.txt b/_GgdGtQME1I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d2a0f78dde5a46ca009e9dd2b8853b8a2cb7a90d
--- /dev/null
+++ b/_GgdGtQME1I.txt
@@ -0,0 +1,16003 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so today I'm going to
+
+ align:start position:0%
+ocw.mit.edu okay so today I'm going to
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so today I'm going to
+sort of take a more empirical approach
+
+ align:start position:0%
+sort of take a more empirical approach
+ 
+
+ align:start position:0%
+sort of take a more empirical approach
+and I feel like I've done a lot of
+
+ align:start position:0%
+and I feel like I've done a lot of
+ 
+
+ align:start position:0%
+and I feel like I've done a lot of
+theory in this class so today I'm going
+
+ align:start position:0%
+theory in this class so today I'm going
+ 
+
+ align:start position:0%
+theory in this class so today I'm going
+to I'm going to play through the hands
+
+ align:start position:0%
+to I'm going to play through the hands
+ 
+
+ align:start position:0%
+to I'm going to play through the hands
+of an online tney so that I played and
+
+ align:start position:0%
+of an online tney so that I played and
+ 
+
+ align:start position:0%
+of an online tney so that I played and
+sort of show you the most interesting
+
+ align:start position:0%
+sort of show you the most interesting
+ 
+
+ align:start position:0%
+sort of show you the most interesting
+hands and show you exactly what I did I
+
+ align:start position:0%
+hands and show you exactly what I did I
+ 
+
+ align:start position:0%
+hands and show you exactly what I did I
+don't think I'm going to finish the
+
+ align:start position:0%
+don't think I'm going to finish the
+ 
+
+ align:start position:0%
+don't think I'm going to finish the
+whole T day but um I'm going to go
+
+ align:start position:0%
+whole T day but um I'm going to go
+ 
+
+ align:start position:0%
+whole T day but um I'm going to go
+through the first part and I'm only
+
+ align:start position:0%
+through the first part and I'm only
+ 
+
+ align:start position:0%
+through the first part and I'm only
+going to talk about a few theoretical
+
+ align:start position:0%
+going to talk about a few theoretical
+ 
+
+ align:start position:0%
+going to talk about a few theoretical
+Concepts but mostly just go through the
+
+ align:start position:0%
+Concepts but mostly just go through the
+ 
+
+ align:start position:0%
+Concepts but mostly just go through the
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+okay so it's it's a $55 buyin tournament
+
+ align:start position:0%
+okay so it's it's a $55 buyin tournament
+ 
+
+ align:start position:0%
+okay so it's it's a $55 buyin tournament
+on party poker and it's a fairly small
+
+ align:start position:0%
+on party poker and it's a fairly small
+ 
+
+ align:start position:0%
+on party poker and it's a fairly small
+field so this is a tournament I I played
+
+ align:start position:0%
+field so this is a tournament I I played
+ 
+
+ align:start position:0%
+field so this is a tournament I I played
+recently um
+
+ align:start position:0%
+recently um
+ 
+
+ align:start position:0%
+recently um
+um and okay so so let's just get into
+
+ align:start position:0%
+um and okay so so let's just get into
+ 
+
+ align:start position:0%
+um and okay so so let's just get into
+the hands I'm only going to show you the
+
+ align:start position:0%
+the hands I'm only going to show you the
+ 
+
+ align:start position:0%
+the hands I'm only going to show you the
+the hands where I did something at the
+
+ align:start position:0%
+the hands where I did something at the
+ 
+
+ align:start position:0%
+the hands where I did something at the
+start and we will start with a bit of
+
+ align:start position:0%
+start and we will start with a bit of
+ 
+
+ align:start position:0%
+start and we will start with a bit of
+theory okay so this is this is the
+
+ align:start position:0%
+theory okay so this is this is the
+ 
+
+ align:start position:0%
+theory okay so this is this is the
+situation it's folded to this player and
+
+ align:start position:0%
+situation it's folded to this player and
+ 
+
+ align:start position:0%
+situation it's folded to this player and
+so we have king queen here and it's a
+
+ align:start position:0%
+so we have king queen here and it's a
+ 
+
+ align:start position:0%
+so we have king queen here and it's a
+hand where we're in position and he
+
+ align:start position:0%
+hand where we're in position and he
+ 
+
+ align:start position:0%
+hand where we're in position and he
+raised from late enough position where I
+
+ align:start position:0%
+raised from late enough position where I
+ 
+
+ align:start position:0%
+raised from late enough position where I
+think our hand is too good to fold so if
+
+ align:start position:0%
+think our hand is too good to fold so if
+ 
+
+ align:start position:0%
+think our hand is too good to fold so if
+dream if dream crushed if if the guy who
+
+ align:start position:0%
+dream if dream crushed if if the guy who
+ 
+
+ align:start position:0%
+dream if dream crushed if if the guy who
+raised was from under the gun let's say
+
+ align:start position:0%
+raised was from under the gun let's say
+ 
+
+ align:start position:0%
+raised was from under the gun let's say
+then um then I might have I I probably
+
+ align:start position:0%
+then um then I might have I I probably
+ 
+
+ align:start position:0%
+then um then I might have I I probably
+would have folded because against an
+
+ align:start position:0%
+would have folded because against an
+ 
+
+ align:start position:0%
+would have folded because against an
+under the gun range king queen offly
+
+ align:start position:0%
+under the gun range king queen offly
+ 
+
+ align:start position:0%
+under the gun range king queen offly
+kind of gets crushed but against a range
+
+ align:start position:0%
+kind of gets crushed but against a range
+ 
+
+ align:start position:0%
+kind of gets crushed but against a range
+from High Jack minus one or low Jack I
+
+ align:start position:0%
+from High Jack minus one or low Jack I
+ 
+
+ align:start position:0%
+from High Jack minus one or low Jack I
+think king queen is good enough to play
+
+ align:start position:0%
+think king queen is good enough to play
+ 
+
+ align:start position:0%
+think king queen is good enough to play
+but the question is sort of what do we
+
+ align:start position:0%
+but the question is sort of what do we
+ 
+
+ align:start position:0%
+but the question is sort of what do we
+do do we raise do we call I don't think
+
+ align:start position:0%
+do do we raise do we call I don't think
+ 
+
+ align:start position:0%
+do do we raise do we call I don't think
+folding is the end of the world you know
+
+ align:start position:0%
+folding is the end of the world you know
+ 
+
+ align:start position:0%
+folding is the end of the world you know
+I think it's slightly profitable to play
+
+ align:start position:0%
+I think it's slightly profitable to play
+ 
+
+ align:start position:0%
+I think it's slightly profitable to play
+but it's not like you're giving up a ton
+
+ align:start position:0%
+but it's not like you're giving up a ton
+ 
+
+ align:start position:0%
+but it's not like you're giving up a ton
+of equity by folding this so what do we
+
+ align:start position:0%
+of equity by folding this so what do we
+ 
+
+ align:start position:0%
+of equity by folding this so what do we
+do okay so I'm going to start out with a
+
+ align:start position:0%
+do okay so I'm going to start out with a
+ 
+
+ align:start position:0%
+do okay so I'm going to start out with a
+bit of
+
+ align:start position:0%
+bit of
+ 
+
+ align:start position:0%
+bit of
+theory so I haven't really talked about
+
+ align:start position:0%
+theory so I haven't really talked about
+ 
+
+ align:start position:0%
+theory so I haven't really talked about
+this so this is so I want to talk a bit
+
+ align:start position:0%
+this so this is so I want to talk a bit
+ 
+
+ align:start position:0%
+this so this is so I want to talk a bit
+a bit about pre flop reising Theory so
+
+ align:start position:0%
+a bit about pre flop reising Theory so
+ 
+
+ align:start position:0%
+a bit about pre flop reising Theory so
+in this situation I don't want to just
+
+ align:start position:0%
+in this situation I don't want to just
+ 
+
+ align:start position:0%
+in this situation I don't want to just
+talk about what to do with this hand
+
+ align:start position:0%
+talk about what to do with this hand
+ 
+
+ align:start position:0%
+talk about what to do with this hand
+right this is how throughout this class
+
+ align:start position:0%
+right this is how throughout this class
+ 
+
+ align:start position:0%
+right this is how throughout this class
+I've been saying we shouldn't think
+
+ align:start position:0%
+I've been saying we shouldn't think
+ 
+
+ align:start position:0%
+I've been saying we shouldn't think
+about poker we should always think about
+
+ align:start position:0%
+about poker we should always think about
+ 
+
+ align:start position:0%
+about poker we should always think about
+the general situation what's the range
+
+ align:start position:0%
+the general situation what's the range
+ 
+
+ align:start position:0%
+the general situation what's the range
+of hands we could have what's the range
+
+ align:start position:0%
+of hands we could have what's the range
+ 
+
+ align:start position:0%
+of hands we could have what's the range
+of hands they could have and how do how
+
+ align:start position:0%
+of hands they could have and how do how
+ 
+
+ align:start position:0%
+of hands they could have and how do how
+should both players play their overall
+
+ align:start position:0%
+should both players play their overall
+ 
+
+ align:start position:0%
+should both players play their overall
+strategy with their entire range of
+
+ align:start position:0%
+strategy with their entire range of
+ 
+
+ align:start position:0%
+strategy with their entire range of
+hands so okay so there's a few
+
+ align:start position:0%
+hands so okay so there's a few
+ 
+
+ align:start position:0%
+hands so okay so there's a few
+interesting things to think about here
+
+ align:start position:0%
+interesting things to think about here
+ 
+
+ align:start position:0%
+interesting things to think about here
+um so there's sort of a dilemma so if we
+
+ align:start position:0%
+um so there's sort of a dilemma so if we
+ 
+
+ align:start position:0%
+um so there's sort of a dilemma so if we
+think about our overall strategy um okay
+
+ align:start position:0%
+think about our overall strategy um okay
+ 
+
+ align:start position:0%
+think about our overall strategy um okay
+so first first thing you notice is how
+
+ align:start position:0%
+so first first thing you notice is how
+ 
+
+ align:start position:0%
+so first first thing you notice is how
+many bets deep is it effective how many
+
+ align:start position:0%
+many bets deep is it effective how many
+ 
+
+ align:start position:0%
+many bets deep is it effective how many
+how what's the stack size effectively
+
+ align:start position:0%
+how what's the stack size effectively
+ 
+
+ align:start position:0%
+how what's the stack size effectively
+it's about it's about 28 right I think
+
+ align:start position:0%
+it's about it's about 28 right I think
+ 
+
+ align:start position:0%
+it's about it's about 28 right I think
+uh so yeah we have about the same amount
+
+ align:start position:0%
+uh so yeah we have about the same amount
+ 
+
+ align:start position:0%
+uh so yeah we have about the same amount
+of chips we have like 28 and a half big
+
+ align:start position:0%
+of chips we have like 28 and a half big
+ 
+
+ align:start position:0%
+of chips we have like 28 and a half big
+mines that's clear to everyone so it's
+
+ align:start position:0%
+mines that's clear to everyone so it's
+ 
+
+ align:start position:0%
+mines that's clear to everyone so it's
+important that it's fairly deep here so
+
+ align:start position:0%
+important that it's fairly deep here so
+ 
+
+ align:start position:0%
+important that it's fairly deep here so
+the the stack size the effective stack
+
+ align:start position:0%
+the the stack size the effective stack
+ 
+
+ align:start position:0%
+the the stack size the effective stack
+size is 282 big blinds
+
+ align:start position:0%
+size is 282 big blinds
+ 
+
+ align:start position:0%
+size is 282 big blinds
+and so what's the issue it's sometimes
+
+ align:start position:0%
+and so what's the issue it's sometimes
+ 
+
+ align:start position:0%
+and so what's the issue it's sometimes
+in this spot we have a hand that's good
+
+ align:start position:0%
+in this spot we have a hand that's good
+ 
+
+ align:start position:0%
+in this spot we have a hand that's good
+enough imp plied odds to play in
+
+ align:start position:0%
+enough imp plied odds to play in
+ 
+
+ align:start position:0%
+enough imp plied odds to play in
+position but it's not really like a good
+
+ align:start position:0%
+position but it's not really like a good
+ 
+
+ align:start position:0%
+position but it's not really like a good
+hand that we're trying to raise and make
+
+ align:start position:0%
+hand that we're trying to raise and make
+ 
+
+ align:start position:0%
+hand that we're trying to raise and make
+the pot bigger with like an example of
+
+ align:start position:0%
+the pot bigger with like an example of
+ 
+
+ align:start position:0%
+the pot bigger with like an example of
+this is like King Jack suited or like
+
+ align:start position:0%
+this is like King Jack suited or like
+ 
+
+ align:start position:0%
+this is like King Jack suited or like
+king queen off I think is a good example
+
+ align:start position:0%
+king queen off I think is a good example
+ 
+
+ align:start position:0%
+king queen off I think is a good example
+too it's a hand that's good enough to
+
+ align:start position:0%
+too it's a hand that's good enough to
+ 
+
+ align:start position:0%
+too it's a hand that's good enough to
+play but not a hand that's good enough
+
+ align:start position:0%
+play but not a hand that's good enough
+ 
+
+ align:start position:0%
+play but not a hand that's good enough
+that we necessarily want to raise and
+
+ align:start position:0%
+that we necessarily want to raise and
+ 
+
+ align:start position:0%
+that we necessarily want to raise and
+make the pot
+
+ align:start position:0%
+make the pot
+ 
+
+ align:start position:0%
+make the pot
+bigger on the other hand sometimes we
+
+ align:start position:0%
+bigger on the other hand sometimes we
+ 
+
+ align:start position:0%
+bigger on the other hand sometimes we
+have a hand that you want to raise and
+
+ align:start position:0%
+have a hand that you want to raise and
+ 
+
+ align:start position:0%
+have a hand that you want to raise and
+hope you get along with like Aces right
+
+ align:start position:0%
+hope you get along with like Aces right
+ 
+
+ align:start position:0%
+hope you get along with like Aces right
+so we do have the we have these sort of
+
+ align:start position:0%
+so we do have the we have these sort of
+ 
+
+ align:start position:0%
+so we do have the we have these sort of
+two types of hands that we want to play
+
+ align:start position:0%
+two types of hands that we want to play
+ 
+
+ align:start position:0%
+two types of hands that we want to play
+in the situation but if we play
+
+ align:start position:0%
+in the situation but if we play
+ 
+
+ align:start position:0%
+in the situation but if we play
+according to our hand it can become too
+
+ align:start position:0%
+according to our hand it can become too
+ 
+
+ align:start position:0%
+according to our hand it can become too
+predictable right so so this is like a
+
+ align:start position:0%
+predictable right so so this is like a
+ 
+
+ align:start position:0%
+predictable right so so this is like a
+somewhat intuitive strategy so you know
+
+ align:start position:0%
+somewhat intuitive strategy so you know
+ 
+
+ align:start position:0%
+somewhat intuitive strategy so you know
+let's suppose this was our strategy
+
+ align:start position:0%
+let's suppose this was our strategy
+ 
+
+ align:start position:0%
+let's suppose this was our strategy
+let's suppose our strategy was with the
+
+ align:start position:0%
+let's suppose our strategy was with the
+ 
+
+ align:start position:0%
+let's suppose our strategy was with the
+best hands that we're hoping to get it
+
+ align:start position:0%
+best hands that we're hoping to get it
+ 
+
+ align:start position:0%
+best hands that we're hoping to get it
+all in with let's say in this spot uh
+
+ align:start position:0%
+all in with let's say in this spot uh
+ 
+
+ align:start position:0%
+all in with let's say in this spot uh
+pocket 10 plus and Ace King I think
+
+ align:start position:0%
+pocket 10 plus and Ace King I think
+ 
+
+ align:start position:0%
+pocket 10 plus and Ace King I think
+that's reasonable as um as the set of
+
+ align:start position:0%
+that's reasonable as um as the set of
+ 
+
+ align:start position:0%
+that's reasonable as um as the set of
+hands were willing to and happy to go
+
+ align:start position:0%
+hands were willing to and happy to go
+ 
+
+ align:start position:0%
+hands were willing to and happy to go
+all in with so pocket TS plus a
+
+ align:start position:0%
+all in with so pocket TS plus a
+ 
+
+ align:start position:0%
+all in with so pocket TS plus a
+and then we call with uh pocket fives
+
+ align:start position:0%
+and then we call with uh pocket fives
+ 
+
+ align:start position:0%
+and then we call with uh pocket fives
+plus Ace jack off Ace 10 suited king
+
+ align:start position:0%
+plus Ace jack off Ace 10 suited king
+ 
+
+ align:start position:0%
+plus Ace jack off Ace 10 suited king
+queen off um it's so this I'd say this
+
+ align:start position:0%
+queen off um it's so this I'd say this
+ 
+
+ align:start position:0%
+queen off um it's so this I'd say this
+is a reasonable strategy to play but um
+
+ align:start position:0%
+is a reasonable strategy to play but um
+ 
+
+ align:start position:0%
+is a reasonable strategy to play but um
+what are some problems with this sort of
+
+ align:start position:0%
+what are some problems with this sort of
+ 
+
+ align:start position:0%
+what are some problems with this sort of
+intutive exploitative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy yeah people are just going to
+
+ align:start position:0%
+strategy yeah people are just going to
+ 
+
+ align:start position:0%
+strategy yeah people are just going to
+hold to your Aces and pick up money from
+
+ align:start position:0%
+hold to your Aces and pick up money from
+ 
+
+ align:start position:0%
+hold to your Aces and pick up money from
+you when you don't
+
+ align:start position:0%
+you when you don't
+ 
+
+ align:start position:0%
+you when you don't
+havep okay great yeah um good good so
+
+ align:start position:0%
+havep okay great yeah um good good so
+ 
+
+ align:start position:0%
+havep okay great yeah um good good so
+yeah so that's a yeah that's good point
+
+ align:start position:0%
+yeah so that's a yeah that's good point
+ 
+
+ align:start position:0%
+yeah so that's a yeah that's good point
+so basically right so people if we if we
+
+ align:start position:0%
+so basically right so people if we if we
+ 
+
+ align:start position:0%
+so basically right so people if we if we
+only raise with pocket 10 plus people
+
+ align:start position:0%
+only raise with pocket 10 plus people
+ 
+
+ align:start position:0%
+only raise with pocket 10 plus people
+can just fold pretty easily right
+
+ align:start position:0%
+can just fold pretty easily right
+ 
+
+ align:start position:0%
+can just fold pretty easily right
+because they know that we have a great
+
+ align:start position:0%
+because they know that we have a great
+ 
+
+ align:start position:0%
+because they know that we have a great
+hand whatever we raised good um okay
+
+ align:start position:0%
+hand whatever we raised good um okay
+ 
+
+ align:start position:0%
+hand whatever we raised good um okay
+what's another issue this one's a bit
+
+ align:start position:0%
+what's another issue this one's a bit
+ 
+
+ align:start position:0%
+what's another issue this one's a bit
+more subtle what's what's sort of
+
+ align:start position:0%
+more subtle what's what's sort of
+ 
+
+ align:start position:0%
+more subtle what's what's sort of
+another issue right so one issue is when
+
+ align:start position:0%
+another issue right so one issue is when
+ 
+
+ align:start position:0%
+another issue right so one issue is when
+we raise it's obviously we have a great
+
+ align:start position:0%
+we raise it's obviously we have a great
+ 
+
+ align:start position:0%
+we raise it's obviously we have a great
+hand and so on a similar line another
+
+ align:start position:0%
+hand and so on a similar line another
+ 
+
+ align:start position:0%
+hand and so on a similar line another
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+yeah oh sorry yeah if we call them they
+
+ align:start position:0%
+yeah oh sorry yeah if we call them they
+ 
+
+ align:start position:0%
+yeah oh sorry yeah if we call them they
+know we're weak right exactly okay good
+
+ align:start position:0%
+know we're weak right exactly okay good
+ 
+
+ align:start position:0%
+know we're weak right exactly okay good
+yeah so so the uh an almost bigger issue
+
+ align:start position:0%
+yeah so so the uh an almost bigger issue
+ 
+
+ align:start position:0%
+yeah so so the uh an almost bigger issue
+here is if we play like this when we
+
+ align:start position:0%
+here is if we play like this when we
+ 
+
+ align:start position:0%
+here is if we play like this when we
+call people know we can't have Aces so
+
+ align:start position:0%
+call people know we can't have Aces so
+ 
+
+ align:start position:0%
+call people know we can't have Aces so
+you know one of the guys behind like
+
+ align:start position:0%
+you know one of the guys behind like
+ 
+
+ align:start position:0%
+you know one of the guys behind like
+this guy all might just be able to raise
+
+ align:start position:0%
+this guy all might just be able to raise
+ 
+
+ align:start position:0%
+this guy all might just be able to raise
+and they they're going to know we're
+
+ align:start position:0%
+and they they're going to know we're
+ 
+
+ align:start position:0%
+and they they're going to know we're
+going to be fairly weak and we're going
+
+ align:start position:0%
+going to be fairly weak and we're going
+ 
+
+ align:start position:0%
+going to be fairly weak and we're going
+to have to fold most of the time right
+
+ align:start position:0%
+to have to fold most of the time right
+ 
+
+ align:start position:0%
+to have to fold most of the time right
+so basically this is not a really
+
+ align:start position:0%
+so basically this is not a really
+ 
+
+ align:start position:0%
+so basically this is not a really
+balanced strategy so what can we do well
+
+ align:start position:0%
+balanced strategy so what can we do well
+ 
+
+ align:start position:0%
+balanced strategy so what can we do well
+we could Raise Some assort of hands from
+
+ align:start position:0%
+we could Raise Some assort of hands from
+ 
+
+ align:start position:0%
+we could Raise Some assort of hands from
+the call category to balance it out we
+
+ align:start position:0%
+the call category to balance it out we
+ 
+
+ align:start position:0%
+the call category to balance it out we
+could call some hands from the raise
+
+ align:start position:0%
+could call some hands from the raise
+ 
+
+ align:start position:0%
+could call some hands from the raise
+category to small percent of the time
+
+ align:start position:0%
+category to small percent of the time
+ 
+
+ align:start position:0%
+category to small percent of the time
+like play a randomized strategy where
+
+ align:start position:0%
+like play a randomized strategy where
+ 
+
+ align:start position:0%
+like play a randomized strategy where
+you raise Aces 80% of the time and call
+
+ align:start position:0%
+you raise Aces 80% of the time and call
+ 
+
+ align:start position:0%
+you raise Aces 80% of the time and call
+Aces 20% of the time to balance it out
+
+ align:start position:0%
+Aces 20% of the time to balance it out
+ 
+
+ align:start position:0%
+Aces 20% of the time to balance it out
+um there's some other more extreme
+
+ align:start position:0%
+um there's some other more extreme
+ 
+
+ align:start position:0%
+um there's some other more extreme
+things you can do that I don't think are
+
+ align:start position:0%
+things you can do that I don't think are
+ 
+
+ align:start position:0%
+things you can do that I don't think are
+good in this situation but are
+
+ align:start position:0%
+good in this situation but are
+ 
+
+ align:start position:0%
+good in this situation but are
+reasonable when the stack size is
+
+ align:start position:0%
+reasonable when the stack size is
+ 
+
+ align:start position:0%
+reasonable when the stack size is
+different so I think if it's shallower
+
+ align:start position:0%
+different so I think if it's shallower
+ 
+
+ align:start position:0%
+different so I think if it's shallower
+let's say only 20 big blinds deep then
+
+ align:start position:0%
+let's say only 20 big blinds deep then
+ 
+
+ align:start position:0%
+let's say only 20 big blinds deep then
+just raising All Hands just raising the
+
+ align:start position:0%
+just raising All Hands just raising the
+ 
+
+ align:start position:0%
+just raising All Hands just raising the
+top x% of hands is a decent strategy
+
+ align:start position:0%
+top x% of hands is a decent strategy
+ 
+
+ align:start position:0%
+top x% of hands is a decent strategy
+because it 20 big blinds is sort of
+
+ align:start position:0%
+because it 20 big blinds is sort of
+ 
+
+ align:start position:0%
+because it 20 big blinds is sort of
+shallow enough where if you raise you
+
+ align:start position:0%
+shallow enough where if you raise you
+ 
+
+ align:start position:0%
+shallow enough where if you raise you
+you're kind of committing your whole
+
+ align:start position:0%
+you're kind of committing your whole
+ 
+
+ align:start position:0%
+you're kind of committing your whole
+stack anyway and if it's deeper then
+
+ align:start position:0%
+stack anyway and if it's deeper then
+ 
+
+ align:start position:0%
+stack anyway and if it's deeper then
+like if it's 100 big blinds deep some
+
+ align:start position:0%
+like if it's 100 big blinds deep some
+ 
+
+ align:start position:0%
+like if it's 100 big blinds deep some
+players will like to call 100% of the
+
+ align:start position:0%
+players will like to call 100% of the
+ 
+
+ align:start position:0%
+players will like to call 100% of the
+hands they'll just never raise um I
+
+ align:start position:0%
+hands they'll just never raise um I
+ 
+
+ align:start position:0%
+hands they'll just never raise um I
+don't think it's like the optimal
+
+ align:start position:0%
+don't think it's like the optimal
+ 
+
+ align:start position:0%
+don't think it's like the optimal
+strategy but it's not an unreasonable
+
+ align:start position:0%
+strategy but it's not an unreasonable
+ 
+
+ align:start position:0%
+strategy but it's not an unreasonable
+strategy when if you're 100 big blinds
+
+ align:start position:0%
+strategy when if you're 100 big blinds
+ 
+
+ align:start position:0%
+strategy when if you're 100 big blinds
+deep and you have position it's not
+
+ align:start position:0%
+deep and you have position it's not
+ 
+
+ align:start position:0%
+deep and you have position it's not
+terrible and then your range is
+
+ align:start position:0%
+terrible and then your range is
+ 
+
+ align:start position:0%
+terrible and then your range is
+completely disguised because you're
+
+ align:start position:0%
+completely disguised because you're
+ 
+
+ align:start position:0%
+completely disguised because you're
+playing all your hands the same pre flop
+
+ align:start position:0%
+playing all your hands the same pre flop
+ 
+
+ align:start position:0%
+playing all your hands the same pre flop
+so these are some reasonable solution
+
+ align:start position:0%
+so these are some reasonable solution
+ 
+
+ align:start position:0%
+so these are some reasonable solution
+ideas um so here's a sort of a better
+
+ align:start position:0%
+ideas um so here's a sort of a better
+ 
+
+ align:start position:0%
+ideas um so here's a sort of a better
+solution so so here's so this will sound
+
+ align:start position:0%
+solution so so here's so this will sound
+ 
+
+ align:start position:0%
+solution so so here's so this will sound
+really cool um compared to the previous
+
+ align:start position:0%
+really cool um compared to the previous
+ 
+
+ align:start position:0%
+really cool um compared to the previous
+slide which is instead of raising some
+
+ align:start position:0%
+slide which is instead of raising some
+ 
+
+ align:start position:0%
+slide which is instead of raising some
+of the call hands as as a bluff
+
+ align:start position:0%
+of the call hands as as a bluff
+ 
+
+ align:start position:0%
+of the call hands as as a bluff
+essentially to balance out the times we
+
+ align:start position:0%
+essentially to balance out the times we
+ 
+
+ align:start position:0%
+essentially to balance out the times we
+raise with a good hand what if we
+
+ align:start position:0%
+raise with a good hand what if we
+ 
+
+ align:start position:0%
+raise with a good hand what if we
+actually we Bluff rais the best hands
+
+ align:start position:0%
+actually we Bluff rais the best hands
+ 
+
+ align:start position:0%
+actually we Bluff rais the best hands
+that aren't good enough to call so let
+
+ align:start position:0%
+that aren't good enough to call so let
+ 
+
+ align:start position:0%
+that aren't good enough to call so let
+me just so we can look at this again
+
+ align:start position:0%
+me just so we can look at this again
+ 
+
+ align:start position:0%
+me just so we can look at this again
+right so our strategy was we're raising
+
+ align:start position:0%
+right so our strategy was we're raising
+ 
+
+ align:start position:0%
+right so our strategy was we're raising
+for Value AKA we're raising hoping to
+
+ align:start position:0%
+for Value AKA we're raising hoping to
+ 
+
+ align:start position:0%
+for Value AKA we're raising hoping to
+get called with t plus and Ace King
+
+ align:start position:0%
+get called with t plus and Ace King
+ 
+
+ align:start position:0%
+get called with t plus and Ace King
+we're we're calling with sort of the
+
+ align:start position:0%
+we're we're calling with sort of the
+ 
+
+ align:start position:0%
+we're we're calling with sort of the
+pretty good hands like pocket fives plus
+
+ align:start position:0%
+pretty good hands like pocket fives plus
+ 
+
+ align:start position:0%
+pretty good hands like pocket fives plus
+Ace Jack Ace 10 suited king queen off
+
+ align:start position:0%
+Ace Jack Ace 10 suited king queen off
+ 
+
+ align:start position:0%
+Ace Jack Ace 10 suited king queen off
+and then we're going to we're going to
+
+ align:start position:0%
+and then we're going to we're going to
+ 
+
+ align:start position:0%
+and then we're going to we're going to
+Bluff raise hands that aren't positive
+
+ align:start position:0%
+Bluff raise hands that aren't positive
+ 
+
+ align:start position:0%
+Bluff raise hands that aren't positive
+expectancy to call so like pocket fours
+
+ align:start position:0%
+expectancy to call so like pocket fours
+ 
+
+ align:start position:0%
+expectancy to call so like pocket fours
+Ace 10 off ace9 suited hands that are
+
+ align:start position:0%
+Ace 10 off ace9 suited hands that are
+ 
+
+ align:start position:0%
+Ace 10 off ace9 suited hands that are
+even weaker than the call hands but in
+
+ align:start position:0%
+even weaker than the call hands but in
+ 
+
+ align:start position:0%
+even weaker than the call hands but in
+some sense if we if we Bluff raise with
+
+ align:start position:0%
+some sense if we if we Bluff raise with
+ 
+
+ align:start position:0%
+some sense if we if we Bluff raise with
+these hands the benefit is we're sort of
+
+ align:start position:0%
+these hands the benefit is we're sort of
+ 
+
+ align:start position:0%
+these hands the benefit is we're sort of
+not wasting them right like let's say
+
+ align:start position:0%
+not wasting them right like let's say
+ 
+
+ align:start position:0%
+not wasting them right like let's say
+with these better hands like let's say
+
+ align:start position:0%
+with these better hands like let's say
+ 
+
+ align:start position:0%
+with these better hands like let's say
+with Ace jack off I and my opponent goes
+
+ align:start position:0%
+with Ace jack off I and my opponent goes
+ 
+
+ align:start position:0%
+with Ace jack off I and my opponent goes
+all in well I'm probably going to have
+
+ align:start position:0%
+all in well I'm probably going to have
+ 
+
+ align:start position:0%
+all in well I'm probably going to have
+to fold in this situation for 28 and a
+
+ align:start position:0%
+to fold in this situation for 28 and a
+ 
+
+ align:start position:0%
+to fold in this situation for 28 and a
+half big blinds so I've sort of like
+
+ align:start position:0%
+half big blinds so I've sort of like
+ 
+
+ align:start position:0%
+half big blinds so I've sort of like
+wasted my Ace Jack whereas you know if I
+
+ align:start position:0%
+wasted my Ace Jack whereas you know if I
+ 
+
+ align:start position:0%
+wasted my Ace Jack whereas you know if I
+did it with Ace 10 instead then I get to
+
+ align:start position:0%
+did it with Ace 10 instead then I get to
+ 
+
+ align:start position:0%
+did it with Ace 10 instead then I get to
+call with my Ace Jack which I know is
+
+ align:start position:0%
+call with my Ace Jack which I know is
+ 
+
+ align:start position:0%
+call with my Ace Jack which I know is
+plus EAS to call and not waste such a
+
+ align:start position:0%
+plus EAS to call and not waste such a
+ 
+
+ align:start position:0%
+plus EAS to call and not waste such a
+good hand Bluff raising so this is a
+
+ align:start position:0%
+good hand Bluff raising so this is a
+ 
+
+ align:start position:0%
+good hand Bluff raising so this is a
+very important Concept in poker it's
+
+ align:start position:0%
+very important Concept in poker it's
+ 
+
+ align:start position:0%
+very important Concept in poker it's
+called polarizing um and in general you
+
+ align:start position:0%
+called polarizing um and in general you
+ 
+
+ align:start position:0%
+called polarizing um and in general you
+know it's a sound strategy right by this
+
+ align:start position:0%
+know it's a sound strategy right by this
+ 
+
+ align:start position:0%
+know it's a sound strategy right by this
+like wasting argument I'm saying
+
+ align:start position:0%
+like wasting argument I'm saying
+ 
+
+ align:start position:0%
+like wasting argument I'm saying
+I'm talking about polarizing sounds like
+
+ align:start position:0%
+I'm talking about polarizing sounds like
+ 
+
+ align:start position:0%
+I'm talking about polarizing sounds like
+a pretty reasonable strategy right
+
+ align:start position:0%
+a pretty reasonable strategy right
+ 
+
+ align:start position:0%
+a pretty reasonable strategy right
+because it it ensures that you're not
+
+ align:start position:0%
+because it it ensures that you're not
+ 
+
+ align:start position:0%
+because it it ensures that you're not
+wasting your medium strength hands to to
+
+ align:start position:0%
+wasting your medium strength hands to to
+ 
+
+ align:start position:0%
+wasting your medium strength hands to to
+Bluff raids so so what's what's an issue
+
+ align:start position:0%
+Bluff raids so so what's what's an issue
+ 
+
+ align:start position:0%
+Bluff raids so so what's what's an issue
+with it so it can be exploited if your
+
+ align:start position:0%
+with it so it can be exploited if your
+ 
+
+ align:start position:0%
+with it so it can be exploited if your
+opponent um calls your three bit so uh
+
+ align:start position:0%
+opponent um calls your three bit so uh
+ 
+
+ align:start position:0%
+opponent um calls your three bit so uh
+so does anyone actually see does anyone
+
+ align:start position:0%
+so does anyone actually see does anyone
+ 
+
+ align:start position:0%
+so does anyone actually see does anyone
+actually see so let's say in this case
+
+ align:start position:0%
+actually see so let's say in this case
+ 
+
+ align:start position:0%
+actually see so let's say in this case
+suppose this was my strategy uh so I'm
+
+ align:start position:0%
+suppose this was my strategy uh so I'm
+ 
+
+ align:start position:0%
+suppose this was my strategy uh so I'm
+raising pocket 10 plus
+
+ align:start position:0%
+raising pocket 10 plus
+ 
+
+ align:start position:0%
+raising pocket 10 plus
+and uh and Ace King and I'm Bluff
+
+ align:start position:0%
+and uh and Ace King and I'm Bluff
+ 
+
+ align:start position:0%
+and uh and Ace King and I'm Bluff
+raising the hands I listed here against
+
+ align:start position:0%
+raising the hands I listed here against
+ 
+
+ align:start position:0%
+raising the hands I listed here against
+okay I'll give I'll give a $20 gift
+
+ align:start position:0%
+okay I'll give I'll give a $20 gift
+ 
+
+ align:start position:0%
+okay I'll give I'll give a $20 gift
+certificate to so like what's a specific
+
+ align:start position:0%
+certificate to so like what's a specific
+ 
+
+ align:start position:0%
+certificate to so like what's a specific
+board less say where someone can explain
+
+ align:start position:0%
+board less say where someone can explain
+ 
+
+ align:start position:0%
+board less say where someone can explain
+my strategy if this was my specific
+
+ align:start position:0%
+my strategy if this was my specific
+ 
+
+ align:start position:0%
+my strategy if this was my specific
+strategy um this is just for
+
+ align:start position:0%
+strategy um this is just for
+ 
+
+ align:start position:0%
+strategy um this is just for
+illustration but like so so look at my
+
+ align:start position:0%
+illustration but like so so look at my
+ 
+
+ align:start position:0%
+illustration but like so so look at my
+exact range and Can someone say sort of
+
+ align:start position:0%
+exact range and Can someone say sort of
+ 
+
+ align:start position:0%
+exact range and Can someone say sort of
+what's what's a very bad flop for my
+
+ align:start position:0%
+what's what's a very bad flop for my
+ 
+
+ align:start position:0%
+what's what's a very bad flop for my
+range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H yeah uh it flops High cards because
+
+ align:start position:0%
+H yeah uh it flops High cards because
+ 
+
+ align:start position:0%
+H yeah uh it flops High cards because
+they'll be thinking your range is
+
+ align:start position:0%
+they'll be thinking your range is
+ 
+
+ align:start position:0%
+they'll be thinking your range is
+generally High cards but those are bit
+
+ align:start position:0%
+generally High cards but those are bit
+ 
+
+ align:start position:0%
+generally High cards but those are bit
+lower uh right so so if there's High
+
+ align:start position:0%
+lower uh right so so if there's High
+ 
+
+ align:start position:0%
+lower uh right so so if there's High
+cards but we do have lots of Aces and
+
+ align:start position:0%
+cards but we do have lots of Aces and
+ 
+
+ align:start position:0%
+cards but we do have lots of Aces and
+Kings right like if the Flop comes like
+
+ align:start position:0%
+Kings right like if the Flop comes like
+ 
+
+ align:start position:0%
+Kings right like if the Flop comes like
+um like if there's an ace then it's it's
+
+ align:start position:0%
+um like if there's an ace then it's it's
+ 
+
+ align:start position:0%
+um like if there's an ace then it's it's
+pretty good for our range right um even
+
+ align:start position:0%
+pretty good for our range right um even
+ 
+
+ align:start position:0%
+pretty good for our range right um even
+though they might be able to fold easily
+
+ align:start position:0%
+though they might be able to fold easily
+ 
+
+ align:start position:0%
+though they might be able to fold easily
+but we're still going to win the pot but
+
+ align:start position:0%
+but we're still going to win the pot but
+ 
+
+ align:start position:0%
+but we're still going to win the pot but
+um but what is like a specific what's a
+
+ align:start position:0%
+um but what is like a specific what's a
+ 
+
+ align:start position:0%
+um but what is like a specific what's a
+specific is yeah like 567 somewhere in
+
+ align:start position:0%
+specific is yeah like 567 somewhere in
+ 
+
+ align:start position:0%
+specific is yeah like 567 somewhere in
+between okay good so 567 is kind of bad
+
+ align:start position:0%
+between okay good so 567 is kind of bad
+ 
+
+ align:start position:0%
+between okay good so 567 is kind of bad
+for us right because our range basically
+
+ align:start position:0%
+for us right because our range basically
+ 
+
+ align:start position:0%
+for us right because our range basically
+contains no fives no sixes no sevens um
+
+ align:start position:0%
+contains no fives no sixes no sevens um
+ 
+
+ align:start position:0%
+contains no fives no sixes no sevens um
+but even 5 six s we still have like a
+
+ align:start position:0%
+but even 5 six s we still have like a
+ 
+
+ align:start position:0%
+but even 5 six s we still have like a
+bigger pair quite often so what's like
+
+ align:start position:0%
+bigger pair quite often so what's like
+ 
+
+ align:start position:0%
+bigger pair quite often so what's like
+an even worst case I yeah High plus draw
+
+ align:start position:0%
+an even worst case I yeah High plus draw
+ 
+
+ align:start position:0%
+an even worst case I yeah High plus draw
+or a high straight draw straight draw uh
+
+ align:start position:0%
+or a high straight draw straight draw uh
+ 
+
+ align:start position:0%
+or a high straight draw straight draw uh
+yeah but we can have those right we have
+
+ align:start position:0%
+yeah but we can have those right we have
+ 
+
+ align:start position:0%
+yeah but we can have those right we have
+A9 suited in our range we have King 10
+
+ align:start position:0%
+A9 suited in our range we have King 10
+ 
+
+ align:start position:0%
+A9 suited in our range we have King 10
+suited in our range something like a low
+
+ align:start position:0%
+suited in our range something like a low
+ 
+
+ align:start position:0%
+suited in our range something like a low
+pair like 448
+
+ align:start position:0%
+pair like 448
+ 
+
+ align:start position:0%
+pair like 448
+um yeah we don't have fours or eights
+
+ align:start position:0%
+um yeah we don't have fours or eights
+ 
+
+ align:start position:0%
+um yeah we don't have fours or eights
+but you know on those boards like pocket
+
+ align:start position:0%
+but you know on those boards like pocket
+ 
+
+ align:start position:0%
+but you know on those boards like pocket
+Jacks even like Ace King high is a
+
+ align:start position:0%
+Jacks even like Ace King high is a
+ 
+
+ align:start position:0%
+Jacks even like Ace King high is a
+pretty good hand and pocket Jacks
+
+ align:start position:0%
+pretty good hand and pocket Jacks
+ 
+
+ align:start position:0%
+pretty good hand and pocket Jacks
+there's there's something very specific
+
+ align:start position:0%
+there's there's something very specific
+ 
+
+ align:start position:0%
+there's there's something very specific
+we're missing I mean this is just for
+
+ align:start position:0%
+we're missing I mean this is just for
+ 
+
+ align:start position:0%
+we're missing I mean this is just for
+this example but um yeah maybe if they
+
+ align:start position:0%
+this example but um yeah maybe if they
+ 
+
+ align:start position:0%
+this example but um yeah maybe if they
+have right okay good good yeah so that's
+
+ align:start position:0%
+have right okay good good yeah so that's
+ 
+
+ align:start position:0%
+have right okay good good yeah so that's
+sort of what I was looking for yeah you
+
+ align:start position:0%
+sort of what I was looking for yeah you
+ 
+
+ align:start position:0%
+sort of what I was looking for yeah you
+can come you can come get this now if
+
+ align:start position:0%
+can come you can come get this now if
+ 
+
+ align:start position:0%
+can come you can come get this now if
+you want um essentially like so suppose
+
+ align:start position:0%
+you want um essentially like so suppose
+ 
+
+ align:start position:0%
+you want um essentially like so suppose
+this was our exact strategy if the board
+
+ align:start position:0%
+this was our exact strategy if the board
+ 
+
+ align:start position:0%
+this was our exact strategy if the board
+comes Queen High then essentially they
+
+ align:start position:0%
+comes Queen High then essentially they
+ 
+
+ align:start position:0%
+comes Queen High then essentially they
+know that we are is pretty bad because
+
+ align:start position:0%
+know that we are is pretty bad because
+ 
+
+ align:start position:0%
+know that we are is pretty bad because
+we don't ever have a queen and we we I
+
+ align:start position:0%
+we don't ever have a queen and we we I
+ 
+
+ align:start position:0%
+we don't ever have a queen and we we I
+mean we could have Kings or Aces but all
+
+ align:start position:0%
+mean we could have Kings or Aces but all
+ 
+
+ align:start position:0%
+mean we could have Kings or Aces but all
+of our other pairs are going to be
+
+ align:start position:0%
+of our other pairs are going to be
+ 
+
+ align:start position:0%
+of our other pairs are going to be
+smaller than Queen so I mean this is
+
+ align:start position:0%
+smaller than Queen so I mean this is
+ 
+
+ align:start position:0%
+smaller than Queen so I mean this is
+just a specific example but I'm saying
+
+ align:start position:0%
+just a specific example but I'm saying
+ 
+
+ align:start position:0%
+just a specific example but I'm saying
+polarizing is in general a good concept
+
+ align:start position:0%
+polarizing is in general a good concept
+ 
+
+ align:start position:0%
+polarizing is in general a good concept
+by this argument that you're not wasting
+
+ align:start position:0%
+by this argument that you're not wasting
+ 
+
+ align:start position:0%
+by this argument that you're not wasting
+your good hands but it can be exploited
+
+ align:start position:0%
+your good hands but it can be exploited
+ 
+
+ align:start position:0%
+your good hands but it can be exploited
+if your opponent knows the specific way
+
+ align:start position:0%
+if your opponent knows the specific way
+ 
+
+ align:start position:0%
+if your opponent knows the specific way
+in which you're polarizing and they just
+
+ align:start position:0%
+in which you're polarizing and they just
+ 
+
+ align:start position:0%
+in which you're polarizing and they just
+call your rays and see the Flop and
+
+ align:start position:0%
+call your rays and see the Flop and
+ 
+
+ align:start position:0%
+call your rays and see the Flop and
+they'll be able to play very well on the
+
+ align:start position:0%
+they'll be able to play very well on the
+ 
+
+ align:start position:0%
+they'll be able to play very well on the
+flops still even if if you have some
+
+ align:start position:0%
+flops still even if if you have some
+ 
+
+ align:start position:0%
+flops still even if if you have some
+good hands and some Bluffs um it can
+
+ align:start position:0%
+good hands and some Bluffs um it can
+ 
+
+ align:start position:0%
+good hands and some Bluffs um it can
+also be bad against unpredictable
+
+ align:start position:0%
+also be bad against unpredictable
+ 
+
+ align:start position:0%
+also be bad against unpredictable
+opponents because um by the by the like
+
+ align:start position:0%
+opponents because um by the by the like
+ 
+
+ align:start position:0%
+opponents because um by the by the like
+Ace Jack Ace 10 argument again let's say
+
+ align:start position:0%
+Ace Jack Ace 10 argument again let's say
+ 
+
+ align:start position:0%
+Ace Jack Ace 10 argument again let's say
+you three bet with Ace 10 instead of Ace
+
+ align:start position:0%
+you three bet with Ace 10 instead of Ace
+ 
+
+ align:start position:0%
+you three bet with Ace 10 instead of Ace
+Jack as an attempt to polarize but let's
+
+ align:start position:0%
+Jack as an attempt to polarize but let's
+ 
+
+ align:start position:0%
+Jack as an attempt to polarize but let's
+say your opponent is kind of bad and
+
+ align:start position:0%
+say your opponent is kind of bad and
+ 
+
+ align:start position:0%
+say your opponent is kind of bad and
+they might make a loose call in the
+
+ align:start position:0%
+they might make a loose call in the
+ 
+
+ align:start position:0%
+they might make a loose call in the
+situation with Ace 10 then you you you
+
+ align:start position:0%
+situation with Ace 10 then you you you
+ 
+
+ align:start position:0%
+situation with Ace 10 then you you you
+would have really hoped to have Ace Jack
+
+ align:start position:0%
+would have really hoped to have Ace Jack
+ 
+
+ align:start position:0%
+would have really hoped to have Ace Jack
+instead of Ace 10 if they're going to
+
+ align:start position:0%
+instead of Ace 10 if they're going to
+ 
+
+ align:start position:0%
+instead of Ace 10 if they're going to
+call your raay with Ace 10 I mean if you
+
+ align:start position:0%
+call your raay with Ace 10 I mean if you
+ 
+
+ align:start position:0%
+call your raay with Ace 10 I mean if you
+so if you're polarizing you're sort of
+
+ align:start position:0%
+so if you're polarizing you're sort of
+ 
+
+ align:start position:0%
+so if you're polarizing you're sort of
+assuming your opponent is going to play
+
+ align:start position:0%
+assuming your opponent is going to play
+ 
+
+ align:start position:0%
+assuming your opponent is going to play
+reasonably right so the point is the
+
+ align:start position:0%
+reasonably right so the point is the
+ 
+
+ align:start position:0%
+reasonably right so the point is the
+reason why I don't want to sort of waste
+
+ align:start position:0%
+reason why I don't want to sort of waste
+ 
+
+ align:start position:0%
+reason why I don't want to sort of waste
+Ace Jack by raising is because my
+
+ align:start position:0%
+Ace Jack by raising is because my
+ 
+
+ align:start position:0%
+Ace Jack by raising is because my
+opponent's probably going to fold Ace 10
+
+ align:start position:0%
+opponent's probably going to fold Ace 10
+ 
+
+ align:start position:0%
+opponent's probably going to fold Ace 10
+but what if they might call ace10 then I
+
+ align:start position:0%
+but what if they might call ace10 then I
+ 
+
+ align:start position:0%
+but what if they might call ace10 then I
+really would have wished I I Rea a jack
+
+ align:start position:0%
+really would have wished I I Rea a jack
+ 
+
+ align:start position:0%
+really would have wished I I Rea a jack
+so okay the short answer is I'm not
+
+ align:start position:0%
+so okay the short answer is I'm not
+ 
+
+ align:start position:0%
+so okay the short answer is I'm not
+going to give a conclusive formula on
+
+ align:start position:0%
+going to give a conclusive formula on
+ 
+
+ align:start position:0%
+going to give a conclusive formula on
+how to play this situation because the
+
+ align:start position:0%
+how to play this situation because the
+ 
+
+ align:start position:0%
+how to play this situation because the
+short answer is it's complicated and I
+
+ align:start position:0%
+short answer is it's complicated and I
+ 
+
+ align:start position:0%
+short answer is it's complicated and I
+don't think anyone essentially knows
+
+ align:start position:0%
+don't think anyone essentially knows
+ 
+
+ align:start position:0%
+don't think anyone essentially knows
+what the optimal strategy is yet but um
+
+ align:start position:0%
+what the optimal strategy is yet but um
+ 
+
+ align:start position:0%
+what the optimal strategy is yet but um
+um in practice I think just raising a
+
+ align:start position:0%
+um in practice I think just raising a
+ 
+
+ align:start position:0%
+um in practice I think just raising a
+mix of hands from the call category
+
+ align:start position:0%
+mix of hands from the call category
+ 
+
+ align:start position:0%
+mix of hands from the call category
+mostly the offsuit hands which have
+
+ align:start position:0%
+mostly the offsuit hands which have
+ 
+
+ align:start position:0%
+mostly the offsuit hands which have
+worse imp ply dods is is pretty good as
+
+ align:start position:0%
+worse imp ply dods is is pretty good as
+ 
+
+ align:start position:0%
+worse imp ply dods is is pretty good as
+part of your like Bluff raising range
+
+ align:start position:0%
+part of your like Bluff raising range
+ 
+
+ align:start position:0%
+part of your like Bluff raising range
+and calling the best hands from the
+
+ align:start position:0%
+and calling the best hands from the
+ 
+
+ align:start position:0%
+and calling the best hands from the
+raise category like Aces like trapping a
+
+ align:start position:0%
+raise category like Aces like trapping a
+ 
+
+ align:start position:0%
+raise category like Aces like trapping a
+small percent of the time just calling
+
+ align:start position:0%
+small percent of the time just calling
+ 
+
+ align:start position:0%
+small percent of the time just calling
+Aces maybe a fifth of the time so that
+
+ align:start position:0%
+Aces maybe a fifth of the time so that
+ 
+
+ align:start position:0%
+Aces maybe a fifth of the time so that
+sometimes you have it when you call so
+
+ align:start position:0%
+sometimes you have it when you call so
+ 
+
+ align:start position:0%
+sometimes you have it when you call so
+that people can't just re ra when you
+
+ align:start position:0%
+that people can't just re ra when you
+ 
+
+ align:start position:0%
+that people can't just re ra when you
+call and also raise some of the best
+
+ align:start position:0%
+call and also raise some of the best
+ 
+
+ align:start position:0%
+call and also raise some of the best
+hands that aren't plus C to call so so
+
+ align:start position:0%
+hands that aren't plus C to call so so
+ 
+
+ align:start position:0%
+hands that aren't plus C to call so so
+polarize a bit essentially the short
+
+ align:start position:0%
+polarize a bit essentially the short
+ 
+
+ align:start position:0%
+polarize a bit essentially the short
+answer is it's complicated you need to
+
+ align:start position:0%
+answer is it's complicated you need to
+ 
+
+ align:start position:0%
+answer is it's complicated you need to
+do you need to do a bit of everything
+
+ align:start position:0%
+do you need to do a bit of everything
+ 
+
+ align:start position:0%
+do you need to do a bit of everything
+with all sorts of hands but um I just
+
+ align:start position:0%
+with all sorts of hands but um I just
+ 
+
+ align:start position:0%
+with all sorts of hands but um I just
+wanted to sort of talk about how
+
+ align:start position:0%
+wanted to sort of talk about how
+ 
+
+ align:start position:0%
+wanted to sort of talk about how
+complicated this situation can be all
+
+ align:start position:0%
+complicated this situation can be all
+ 
+
+ align:start position:0%
+complicated this situation can be all
+right uh so okay so let's get back to
+
+ align:start position:0%
+right uh so okay so let's get back to
+ 
+
+ align:start position:0%
+right uh so okay so let's get back to
+the hand so what I decided to do here
+
+ align:start position:0%
+the hand so what I decided to do here
+ 
+
+ align:start position:0%
+the hand so what I decided to do here
+was following the the thing I said about
+
+ align:start position:0%
+was following the the thing I said about
+ 
+
+ align:start position:0%
+was following the the thing I said about
+re raising with offit hands I decided to
+
+ align:start position:0%
+re raising with offit hands I decided to
+ 
+
+ align:start position:0%
+re raising with offit hands I decided to
+so I decided to raise here to 555 and so
+
+ align:start position:0%
+so I decided to raise here to 555 and so
+ 
+
+ align:start position:0%
+so I decided to raise here to 555 and so
+I think this is about the right sizing
+
+ align:start position:0%
+I think this is about the right sizing
+ 
+
+ align:start position:0%
+I think this is about the right sizing
+cuz we're making it about 2.5 times his
+
+ align:start position:0%
+cuz we're making it about 2.5 times his
+ 
+
+ align:start position:0%
+cuz we're making it about 2.5 times his
+raise and essentially we're bluffing
+
+ align:start position:0%
+raise and essentially we're bluffing
+ 
+
+ align:start position:0%
+raise and essentially we're bluffing
+here and our hand is good enough where
+
+ align:start position:0%
+here and our hand is good enough where
+ 
+
+ align:start position:0%
+here and our hand is good enough where
+it's not the end of the world if they
+
+ align:start position:0%
+it's not the end of the world if they
+ 
+
+ align:start position:0%
+it's not the end of the world if they
+call cuz we have a lot of chances to hit
+
+ align:start position:0%
+call cuz we have a lot of chances to hit
+ 
+
+ align:start position:0%
+call cuz we have a lot of chances to hit
+Top pair and if we do we're probably
+
+ align:start position:0%
+Top pair and if we do we're probably
+ 
+
+ align:start position:0%
+Top pair and if we do we're probably
+good because they're probably going on
+
+ align:start position:0%
+good because they're probably going on
+ 
+
+ align:start position:0%
+good because they're probably going on
+with Ace King or Ace Queen pre flop but
+
+ align:start position:0%
+with Ace King or Ace Queen pre flop but
+ 
+
+ align:start position:0%
+with Ace King or Ace Queen pre flop but
+essentially we're bluffing I'm
+
+ align:start position:0%
+essentially we're bluffing I'm
+ 
+
+ align:start position:0%
+essentially we're bluffing I'm
+definitely hoping he folds and and he
+
+ align:start position:0%
+definitely hoping he folds and and he
+ 
+
+ align:start position:0%
+definitely hoping he folds and and he
+does so okay we take down the pot
+
+ align:start position:0%
+does so okay we take down the pot
+ 
+
+ align:start position:0%
+does so okay we take down the pot
+uh okay so so the very next hand I
+
+ align:start position:0%
+uh okay so so the very next hand I
+ 
+
+ align:start position:0%
+uh okay so so the very next hand I
+actually just noticed this during uh
+
+ align:start position:0%
+actually just noticed this during uh
+ 
+
+ align:start position:0%
+actually just noticed this during uh
+when I was replaying through the hands
+
+ align:start position:0%
+when I was replaying through the hands
+ 
+
+ align:start position:0%
+when I was replaying through the hands
+so I didn't notice this I didn't notice
+
+ align:start position:0%
+so I didn't notice this I didn't notice
+ 
+
+ align:start position:0%
+so I didn't notice this I didn't notice
+this during the tournament actually but
+
+ align:start position:0%
+this during the tournament actually but
+ 
+
+ align:start position:0%
+this during the tournament actually but
+so what do you notice it's actually
+
+ align:start position:0%
+so what do you notice it's actually
+ 
+
+ align:start position:0%
+so what do you notice it's actually
+we're actually in the in the exact same
+
+ align:start position:0%
+we're actually in the in the exact same
+ 
+
+ align:start position:0%
+we're actually in the in the exact same
+situation together right but we have
+
+ align:start position:0%
+situation together right but we have
+ 
+
+ align:start position:0%
+situation together right but we have
+different cards so it's good that you
+
+ align:start position:0%
+different cards so it's good that you
+ 
+
+ align:start position:0%
+different cards so it's good that you
+know we thought about our overall
+
+ align:start position:0%
+know we thought about our overall
+ 
+
+ align:start position:0%
+know we thought about our overall
+strategy when we played that hand
+
+ align:start position:0%
+strategy when we played that hand
+ 
+
+ align:start position:0%
+strategy when we played that hand
+because you will end up in the same
+
+ align:start position:0%
+because you will end up in the same
+ 
+
+ align:start position:0%
+because you will end up in the same
+situation again with different cards so
+
+ align:start position:0%
+situation again with different cards so
+ 
+
+ align:start position:0%
+situation again with different cards so
+okay so along the same lines so you know
+
+ align:start position:0%
+okay so along the same lines so you know
+ 
+
+ align:start position:0%
+okay so along the same lines so you know
+but at the time you know I was probably
+
+ align:start position:0%
+but at the time you know I was probably
+ 
+
+ align:start position:0%
+but at the time you know I was probably
+playing like 15 tables or more so I
+
+ align:start position:0%
+playing like 15 tables or more so I
+ 
+
+ align:start position:0%
+playing like 15 tables or more so I
+wasn't really paying attention I
+
+ align:start position:0%
+wasn't really paying attention I
+ 
+
+ align:start position:0%
+wasn't really paying attention I
+probably didn't I probably didn't
+
+ align:start position:0%
+probably didn't I probably didn't
+ 
+
+ align:start position:0%
+probably didn't I probably didn't
+remember that I R raised my opponent the
+
+ align:start position:0%
+remember that I R raised my opponent the
+ 
+
+ align:start position:0%
+remember that I R raised my opponent the
+hand before but playing through this it
+
+ align:start position:0%
+hand before but playing through this it
+ 
+
+ align:start position:0%
+hand before but playing through this it
+actually yielded a really good result
+
+ align:start position:0%
+actually yielded a really good result
+ 
+
+ align:start position:0%
+actually yielded a really good result
+cuz what happened was they didn't
+
+ align:start position:0%
+cuz what happened was they didn't
+ 
+
+ align:start position:0%
+cuz what happened was they didn't
+believe my three bet the second time
+
+ align:start position:0%
+believe my three bet the second time
+ 
+
+ align:start position:0%
+believe my three bet the second time
+around and they went all in with you
+
+ align:start position:0%
+around and they went all in with you
+ 
+
+ align:start position:0%
+around and they went all in with you
+know pocket sevens is not a terrible
+
+ align:start position:0%
+know pocket sevens is not a terrible
+ 
+
+ align:start position:0%
+know pocket sevens is not a terrible
+hand but it's definitely I think a
+
+ align:start position:0%
+hand but it's definitely I think a
+ 
+
+ align:start position:0%
+hand but it's definitely I think a
+weaker hand than they would usually go
+
+ align:start position:0%
+weaker hand than they would usually go
+ 
+
+ align:start position:0%
+weaker hand than they would usually go
+on there with but I guess they didn't
+
+ align:start position:0%
+on there with but I guess they didn't
+ 
+
+ align:start position:0%
+on there with but I guess they didn't
+believe my Rays after the previous hand
+
+ align:start position:0%
+believe my Rays after the previous hand
+ 
+
+ align:start position:0%
+believe my Rays after the previous hand
+so this also sort of illustrates the
+
+ align:start position:0%
+so this also sort of illustrates the
+ 
+
+ align:start position:0%
+so this also sort of illustrates the
+importance of like you said of sometimes
+
+ align:start position:0%
+importance of like you said of sometimes
+ 
+
+ align:start position:0%
+importance of like you said of sometimes
+having a bad hand when you re ra so that
+
+ align:start position:0%
+having a bad hand when you re ra so that
+ 
+
+ align:start position:0%
+having a bad hand when you re ra so that
+people will give you action when you do
+
+ align:start position:0%
+people will give you action when you do
+ 
+
+ align:start position:0%
+people will give you action when you do
+have a good hand like P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jacks okay so okay so let's go on and so
+
+ align:start position:0%
+Jacks okay so okay so let's go on and so
+ 
+
+ align:start position:0%
+Jacks okay so okay so let's go on and so
+I'm only playing through the hands that
+
+ align:start position:0%
+I'm only playing through the hands that
+ 
+
+ align:start position:0%
+I'm only playing through the hands that
+I that I essentially played at the start
+
+ align:start position:0%
+I that I essentially played at the start
+ 
+
+ align:start position:0%
+I that I essentially played at the start
+of the tournament so so we doubled up
+
+ align:start position:0%
+of the tournament so so we doubled up
+ 
+
+ align:start position:0%
+of the tournament so so we doubled up
+the starting stack was 3,000 we've got
+
+ align:start position:0%
+the starting stack was 3,000 we've got
+ 
+
+ align:start position:0%
+the starting stack was 3,000 we've got
+6,000 now we get a queen we
+
+ align:start position:0%
+6,000 now we get a queen we
+ 
+
+ align:start position:0%
+6,000 now we get a queen we
+raise and we get Co here and here this
+
+ align:start position:0%
+raise and we get Co here and here this
+ 
+
+ align:start position:0%
+raise and we get Co here and here this
+guy makes it so this is a different
+
+ align:start position:0%
+guy makes it so this is a different
+ 
+
+ align:start position:0%
+guy makes it so this is a different
+player cuz we eliminated the guy who
+
+ align:start position:0%
+player cuz we eliminated the guy who
+ 
+
+ align:start position:0%
+player cuz we eliminated the guy who
+used to sit here and they make it
+
+ align:start position:0%
+used to sit here and they make it
+ 
+
+ align:start position:0%
+used to sit here and they make it
+755 and I decide to fold here I think
+
+ align:start position:0%
+755 and I decide to fold here I think
+ 
+
+ align:start position:0%
+755 and I decide to fold here I think
+Ace queen off suit is just a bit too
+
+ align:start position:0%
+Ace queen off suit is just a bit too
+ 
+
+ align:start position:0%
+Ace queen off suit is just a bit too
+weak I think going all in is it wouldn't
+
+ align:start position:0%
+weak I think going all in is it wouldn't
+ 
+
+ align:start position:0%
+weak I think going all in is it wouldn't
+be terrible but I think where when we
+
+ align:start position:0%
+be terrible but I think where when we
+ 
+
+ align:start position:0%
+be terrible but I think where when we
+raised from fairly early position under
+
+ align:start position:0%
+raised from fairly early position under
+ 
+
+ align:start position:0%
+raised from fairly early position under
+the gun plus one and this hijack called
+
+ align:start position:0%
+the gun plus one and this hijack called
+ 
+
+ align:start position:0%
+the gun plus one and this hijack called
+they're not going to be doing this as a
+
+ align:start position:0%
+they're not going to be doing this as a
+ 
+
+ align:start position:0%
+they're not going to be doing this as a
+bluff very often and they're re raised
+
+ align:start position:0%
+bluff very often and they're re raised
+ 
+
+ align:start position:0%
+bluff very often and they're re raised
+to 755 I think usually commits them it's
+
+ align:start position:0%
+to 755 I think usually commits them it's
+ 
+
+ align:start position:0%
+to 755 I think usually commits them it's
+not not guaranteed that they're going to
+
+ align:start position:0%
+not not guaranteed that they're going to
+ 
+
+ align:start position:0%
+not not guaranteed that they're going to
+they're going to go all in if we're
+
+ align:start position:0%
+they're going to go all in if we're
+ 
+
+ align:start position:0%
+they're going to go all in if we're
+they're going to call us if we go all in
+
+ align:start position:0%
+they're going to call us if we go all in
+ 
+
+ align:start position:0%
+they're going to call us if we go all in
+but I think most likely they will and
+
+ align:start position:0%
+but I think most likely they will and
+ 
+
+ align:start position:0%
+but I think most likely they will and
+they're going to be ahead of our range
+
+ align:start position:0%
+they're going to be ahead of our range
+ 
+
+ align:start position:0%
+they're going to be ahead of our range
+so I decided to fold it's a fairly tight
+
+ align:start position:0%
+so I decided to fold it's a fairly tight
+ 
+
+ align:start position:0%
+so I decided to fold it's a fairly tight
+fold so does a
+
+ align:start position:0%
+fold so does a
+ 
+
+ align:start position:0%
+fold so does a
+sky okay so yeah I'm just going to
+
+ align:start position:0%
+sky okay so yeah I'm just going to
+ 
+
+ align:start position:0%
+sky okay so yeah I'm just going to
+continue playing through my hands from
+
+ align:start position:0%
+continue playing through my hands from
+ 
+
+ align:start position:0%
+continue playing through my hands from
+the tournament if if you have any
+
+ align:start position:0%
+the tournament if if you have any
+ 
+
+ align:start position:0%
+the tournament if if you have any
+questions just stop me and
+
+ align:start position:0%
+questions just stop me and
+ 
+
+ align:start position:0%
+questions just stop me and
+ask okay so this is sort of a weird hand
+
+ align:start position:0%
+ask okay so this is sort of a weird hand
+ 
+
+ align:start position:0%
+ask okay so this is sort of a weird hand
+and I actually think I played this hand
+
+ align:start position:0%
+and I actually think I played this hand
+ 
+
+ align:start position:0%
+and I actually think I played this hand
+quite terribly so okay so this guy calls
+
+ align:start position:0%
+quite terribly so okay so this guy calls
+ 
+
+ align:start position:0%
+quite terribly so okay so this guy calls
+which I said we should never do but I
+
+ align:start position:0%
+which I said we should never do but I
+ 
+
+ align:start position:0%
+which I said we should never do but I
+guess he doesn't take my class um okay
+
+ align:start position:0%
+guess he doesn't take my class um okay
+ 
+
+ align:start position:0%
+guess he doesn't take my class um okay
+so we get Queen 10 here we check we see
+
+ align:start position:0%
+so we get Queen 10 here we check we see
+ 
+
+ align:start position:0%
+so we get Queen 10 here we check we see
+a flop uh so we flop a two over cards a
+
+ align:start position:0%
+a flop uh so we flop a two over cards a
+ 
+
+ align:start position:0%
+a flop uh so we flop a two over cards a
+back door flush draw and a gutter
+
+ align:start position:0%
+back door flush draw and a gutter
+ 
+
+ align:start position:0%
+back door flush draw and a gutter
+straight draw so I decided to lead into
+
+ align:start position:0%
+straight draw so I decided to lead into
+ 
+
+ align:start position:0%
+straight draw so I decided to lead into
+it and so lead lead my draws out hope he
+
+ align:start position:0%
+it and so lead lead my draws out hope he
+ 
+
+ align:start position:0%
+it and so lead lead my draws out hope he
+folds he calls and the turn is a three
+
+ align:start position:0%
+folds he calls and the turn is a three
+ 
+
+ align:start position:0%
+folds he calls and the turn is a three
+and then here so this is where I sort of
+
+ align:start position:0%
+and then here so this is where I sort of
+ 
+
+ align:start position:0%
+and then here so this is where I sort of
+he decided to suckered at me so I talked
+
+ align:start position:0%
+he decided to suckered at me so I talked
+ 
+
+ align:start position:0%
+he decided to suckered at me so I talked
+about how you know he should only be
+
+ align:start position:0%
+about how you know he should only be
+ 
+
+ align:start position:0%
+about how you know he should only be
+doing this if he doesn't respect me cuz
+
+ align:start position:0%
+doing this if he doesn't respect me cuz
+ 
+
+ align:start position:0%
+doing this if he doesn't respect me cuz
+I mean in this case it's you know it's
+
+ align:start position:0%
+I mean in this case it's you know it's
+ 
+
+ align:start position:0%
+I mean in this case it's you know it's
+not a completely insignificant fraction
+
+ align:start position:0%
+not a completely insignificant fraction
+ 
+
+ align:start position:0%
+not a completely insignificant fraction
+of the pot it's like 1 16 so he is
+
+ align:start position:0%
+of the pot it's like 1 16 so he is
+ 
+
+ align:start position:0%
+of the pot it's like 1 16 so he is
+actually getting some substantial
+
+ align:start position:0%
+actually getting some substantial
+ 
+
+ align:start position:0%
+actually getting some substantial
+payment into the pot but it's still
+
+ align:start position:0%
+payment into the pot but it's still
+ 
+
+ align:start position:0%
+payment into the pot but it's still
+fairly small and the main thing it does
+
+ align:start position:0%
+fairly small and the main thing it does
+ 
+
+ align:start position:0%
+fairly small and the main thing it does
+is it gives me an opportunity to check
+
+ align:start position:0%
+is it gives me an opportunity to check
+ 
+
+ align:start position:0%
+is it gives me an opportunity to check
+raay but I'm not going to I don't think
+
+ align:start position:0%
+raay but I'm not going to I don't think
+ 
+
+ align:start position:0%
+raay but I'm not going to I don't think
+I don't think they're going to fold
+
+ align:start position:0%
+I don't think they're going to fold
+ 
+
+ align:start position:0%
+I don't think they're going to fold
+often enough there's a lot of draws
+
+ align:start position:0%
+often enough there's a lot of draws
+ 
+
+ align:start position:0%
+often enough there's a lot of draws
+they're going to call me with and I'm
+
+ align:start position:0%
+they're going to call me with and I'm
+ 
+
+ align:start position:0%
+they're going to call me with and I'm
+going to have to Bluff again on the
+
+ align:start position:0%
+going to have to Bluff again on the
+ 
+
+ align:start position:0%
+going to have to Bluff again on the
+river so I decided to just call which is
+
+ align:start position:0%
+river so I decided to just call which is
+ 
+
+ align:start position:0%
+river so I decided to just call which is
+reasonable so this is where I think I
+
+ align:start position:0%
+reasonable so this is where I think I
+ 
+
+ align:start position:0%
+reasonable so this is where I think I
+played the hand poly so the river
+
+ align:start position:0%
+played the hand poly so the river
+ 
+
+ align:start position:0%
+played the hand poly so the river
+completes a lot of draws but doesn't
+
+ align:start position:0%
+completes a lot of draws but doesn't
+ 
+
+ align:start position:0%
+completes a lot of draws but doesn't
+complete my hand and I just check it
+
+ align:start position:0%
+complete my hand and I just check it
+ 
+
+ align:start position:0%
+complete my hand and I just check it
+down I just check it which the at the
+
+ align:start position:0%
+down I just check it which the at the
+ 
+
+ align:start position:0%
+down I just check it which the at the
+time I didn't lead out because I thought
+
+ align:start position:0%
+time I didn't lead out because I thought
+ 
+
+ align:start position:0%
+time I didn't lead out because I thought
+you know the fact that I only called the
+
+ align:start position:0%
+you know the fact that I only called the
+ 
+
+ align:start position:0%
+you know the fact that I only called the
+turn and suddenly decided to bet big on
+
+ align:start position:0%
+turn and suddenly decided to bet big on
+ 
+
+ align:start position:0%
+turn and suddenly decided to bet big on
+the river would probably get called but
+
+ align:start position:0%
+the river would probably get called but
+ 
+
+ align:start position:0%
+the river would probably get called but
+I think it's just not a balanced way to
+
+ align:start position:0%
+I think it's just not a balanced way to
+ 
+
+ align:start position:0%
+I think it's just not a balanced way to
+play the hand because plenty of times I
+
+ align:start position:0%
+play the hand because plenty of times I
+ 
+
+ align:start position:0%
+play the hand because plenty of times I
+will have clubs or you know or I'll have
+
+ align:start position:0%
+will have clubs or you know or I'll have
+ 
+
+ align:start position:0%
+will have clubs or you know or I'll have
+Jack 10 or something I'll have a Jack
+
+ align:start position:0%
+Jack 10 or something I'll have a Jack
+ 
+
+ align:start position:0%
+Jack 10 or something I'll have a Jack
+and I will want to bet for value and
+
+ align:start position:0%
+and I will want to bet for value and
+ 
+
+ align:start position:0%
+and I will want to bet for value and
+here when I have a hand that essentially
+
+ align:start position:0%
+here when I have a hand that essentially
+ 
+
+ align:start position:0%
+here when I have a hand that essentially
+has no chance of winning the winning the
+
+ align:start position:0%
+has no chance of winning the winning the
+ 
+
+ align:start position:0%
+has no chance of winning the winning the
+handed Showdown like essentially I'm
+
+ align:start position:0%
+handed Showdown like essentially I'm
+ 
+
+ align:start position:0%
+handed Showdown like essentially I'm
+giving up the pot for sure if I check
+
+ align:start position:0%
+giving up the pot for sure if I check
+ 
+
+ align:start position:0%
+giving up the pot for sure if I check
+cuz my queen high will never be good I
+
+ align:start position:0%
+cuz my queen high will never be good I
+ 
+
+ align:start position:0%
+cuz my queen high will never be good I
+should definitely be bluffing so I I
+
+ align:start position:0%
+should definitely be bluffing so I I
+ 
+
+ align:start position:0%
+should definitely be bluffing so I I
+didn't which I regret cuz I let him take
+
+ align:start position:0%
+didn't which I regret cuz I let him take
+ 
+
+ align:start position:0%
+didn't which I regret cuz I let him take
+down the pot with a pair of Threes um
+
+ align:start position:0%
+down the pot with a pair of Threes um
+ 
+
+ align:start position:0%
+down the pot with a pair of Threes um
+but yeah I guess he kind of played that
+
+ align:start position:0%
+but yeah I guess he kind of played that
+ 
+
+ align:start position:0%
+but yeah I guess he kind of played that
+hand well uh he called 83 suited and I
+
+ align:start position:0%
+hand well uh he called 83 suited and I
+ 
+
+ align:start position:0%
+hand well uh he called 83 suited and I
+guess he made money from me cuz I didn't
+
+ align:start position:0%
+guess he made money from me cuz I didn't
+ 
+
+ align:start position:0%
+guess he made money from me cuz I didn't
+play very well from the big
+
+ align:start position:0%
+play very well from the big
+ 
+
+ align:start position:0%
+play very well from the big
+blind uh okay so the next
+
+ align:start position:0%
+blind uh okay so the next
+ 
+
+ align:start position:0%
+blind uh okay so the next
+hand we get King jack off suit here we
+
+ align:start position:0%
+hand we get King jack off suit here we
+ 
+
+ align:start position:0%
+hand we get King jack off suit here we
+open probably one of the weakest hands
+
+ align:start position:0%
+open probably one of the weakest hands
+ 
+
+ align:start position:0%
+open probably one of the weakest hands
+I'm opening from this position I think
+
+ align:start position:0%
+I'm opening from this position I think
+ 
+
+ align:start position:0%
+I'm opening from this position I think
+probably in my recommendations this is
+
+ align:start position:0%
+probably in my recommendations this is
+ 
+
+ align:start position:0%
+probably in my recommendations this is
+not in the list you should open from uh
+
+ align:start position:0%
+not in the list you should open from uh
+ 
+
+ align:start position:0%
+not in the list you should open from uh
+hijack minus one but I decid to open
+
+ align:start position:0%
+hijack minus one but I decid to open
+ 
+
+ align:start position:0%
+hijack minus one but I decid to open
+because I'm bored I guess and we get
+
+ align:start position:0%
+because I'm bored I guess and we get
+ 
+
+ align:start position:0%
+because I'm bored I guess and we get
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+colors okay so the Flop is 4 64 with two
+
+ align:start position:0%
+colors okay so the Flop is 4 64 with two
+ 
+
+ align:start position:0%
+colors okay so the Flop is 4 64 with two
+hearts so I decide to continuation bet
+
+ align:start position:0%
+hearts so I decide to continuation bet
+ 
+
+ align:start position:0%
+hearts so I decide to continuation bet
+here I think it's a fairly marginal spot
+
+ align:start position:0%
+here I think it's a fairly marginal spot
+ 
+
+ align:start position:0%
+here I think it's a fairly marginal spot
+I think just giving up is okay I
+
+ align:start position:0%
+I think just giving up is okay I
+ 
+
+ align:start position:0%
+I think just giving up is okay I
+definitely wouldn't have stabbed at the
+
+ align:start position:0%
+definitely wouldn't have stabbed at the
+ 
+
+ align:start position:0%
+definitely wouldn't have stabbed at the
+pot if I didn't have the if I didn't
+
+ align:start position:0%
+pot if I didn't have the if I didn't
+ 
+
+ align:start position:0%
+pot if I didn't have the if I didn't
+have the King of Hearts but um the fact
+
+ align:start position:0%
+have the King of Hearts but um the fact
+ 
+
+ align:start position:0%
+have the King of Hearts but um the fact
+that I have a back door pretty good
+
+ align:start position:0%
+that I have a back door pretty good
+ 
+
+ align:start position:0%
+that I have a back door pretty good
+flush draw I decided to bet and just
+
+ align:start position:0%
+flush draw I decided to bet and just
+ 
+
+ align:start position:0%
+flush draw I decided to bet and just
+hope that everyone
+
+ align:start position:0%
+hope that everyone
+ 
+
+ align:start position:0%
+hope that everyone
+folds and we do get that which is which
+
+ align:start position:0%
+folds and we do get that which is which
+ 
+
+ align:start position:0%
+folds and we do get that which is which
+is pretty
+
+ align:start position:0%
+is pretty
+ 
+
+ align:start position:0%
+is pretty
+nice okay so so you know our stack is
+
+ align:start position:0%
+nice okay so so you know our stack is
+ 
+
+ align:start position:0%
+nice okay so so you know our stack is
+hovering around the same size we've won
+
+ align:start position:0%
+hovering around the same size we've won
+ 
+
+ align:start position:0%
+hovering around the same size we've won
+some hands lost some hands it's still
+
+ align:start position:0%
+some hands lost some hands it's still
+ 
+
+ align:start position:0%
+some hands lost some hands it's still
+early in the tournament the blinds have
+
+ align:start position:0%
+early in the tournament the blinds have
+ 
+
+ align:start position:0%
+early in the tournament the blinds have
+gone up a bit but it's still far away
+
+ align:start position:0%
+gone up a bit but it's still far away
+ 
+
+ align:start position:0%
+gone up a bit but it's still far away
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+payouts okay so we get Queen Jack on the
+
+ align:start position:0%
+payouts okay so we get Queen Jack on the
+ 
+
+ align:start position:0%
+payouts okay so we get Queen Jack on the
+button and and this guy just goes all in
+
+ align:start position:0%
+button and and this guy just goes all in
+ 
+
+ align:start position:0%
+button and and this guy just goes all in
+for a lot of vets um I mean it's I guess
+
+ align:start position:0%
+for a lot of vets um I mean it's I guess
+ 
+
+ align:start position:0%
+for a lot of vets um I mean it's I guess
+it's not that many it's like
+
+ align:start position:0%
+it's not that many it's like
+ 
+
+ align:start position:0%
+it's not that many it's like
+35 no sorry it's yeah it's about it's
+
+ align:start position:0%
+35 no sorry it's yeah it's about it's
+ 
+
+ align:start position:0%
+35 no sorry it's yeah it's about it's
+about 30 35 right uh so um so I mean I
+
+ align:start position:0%
+about 30 35 right uh so um so I mean I
+ 
+
+ align:start position:0%
+about 30 35 right uh so um so I mean I
+folded here obviously but I thought a
+
+ align:start position:0%
+folded here obviously but I thought a
+ 
+
+ align:start position:0%
+folded here obviously but I thought a
+bit about like his range and you know
+
+ align:start position:0%
+bit about like his range and you know
+ 
+
+ align:start position:0%
+bit about like his range and you know
+it's possible his range is like entirely
+
+ align:start position:0%
+it's possible his range is like entirely
+ 
+
+ align:start position:0%
+it's possible his range is like entirely
+so I talked about this in a previous
+
+ align:start position:0%
+so I talked about this in a previous
+ 
+
+ align:start position:0%
+so I talked about this in a previous
+class when do you want to be going all
+
+ align:start position:0%
+class when do you want to be going all
+ 
+
+ align:start position:0%
+class when do you want to be going all
+in for a huge size it's essentially with
+
+ align:start position:0%
+in for a huge size it's essentially with
+ 
+
+ align:start position:0%
+in for a huge size it's essentially with
+hands that are pretty good to get all in
+
+ align:start position:0%
+hands that are pretty good to get all in
+ 
+
+ align:start position:0%
+hands that are pretty good to get all in
+with pre flop but have terrible post
+
+ align:start position:0%
+with pre flop but have terrible post
+ 
+
+ align:start position:0%
+with pre flop but have terrible post
+flop implied odds in this situation and
+
+ align:start position:0%
+flop implied odds in this situation and
+ 
+
+ align:start position:0%
+flop implied odds in this situation and
+what were the hands that I listed there
+
+ align:start position:0%
+what were the hands that I listed there
+ 
+
+ align:start position:0%
+what were the hands that I listed there
+it's essentially small pairs right like
+
+ align:start position:0%
+it's essentially small pairs right like
+ 
+
+ align:start position:0%
+it's essentially small pairs right like
+pocket twos you really don't want to see
+
+ align:start position:0%
+pocket twos you really don't want to see
+ 
+
+ align:start position:0%
+pocket twos you really don't want to see
+a flop it's it's quite a good hand pre-
+
+ align:start position:0%
+a flop it's it's quite a good hand pre-
+ 
+
+ align:start position:0%
+a flop it's it's quite a good hand pre-
+flop but you really don't want to see a
+
+ align:start position:0%
+flop but you really don't want to see a
+ 
+
+ align:start position:0%
+flop but you really don't want to see a
+flop cuz it's pretty much always three
+
+ align:start position:0%
+flop cuz it's pretty much always three
+ 
+
+ align:start position:0%
+flop cuz it's pretty much always three
+higher cards are going to come and
+
+ align:start position:0%
+higher cards are going to come and
+ 
+
+ align:start position:0%
+higher cards are going to come and
+you're just going to be playing this
+
+ align:start position:0%
+you're just going to be playing this
+ 
+
+ align:start position:0%
+you're just going to be playing this
+guessing game trying to guess whether
+
+ align:start position:0%
+guessing game trying to guess whether
+ 
+
+ align:start position:0%
+guessing game trying to guess whether
+your opponent has a pair and the other
+
+ align:start position:0%
+your opponent has a pair and the other
+ 
+
+ align:start position:0%
+your opponent has a pair and the other
+type of hand is like Ace 2 offit where
+
+ align:start position:0%
+type of hand is like Ace 2 offit where
+ 
+
+ align:start position:0%
+type of hand is like Ace 2 offit where
+once again you you know you have an ace
+
+ align:start position:0%
+once again you you know you have an ace
+ 
+
+ align:start position:0%
+once again you you know you have an ace
+pre- flop which is decent but you're
+
+ align:start position:0%
+pre- flop which is decent but you're
+ 
+
+ align:start position:0%
+pre- flop which is decent but you're
+just going to be playing a guessing game
+
+ align:start position:0%
+just going to be playing a guessing game
+ 
+
+ align:start position:0%
+just going to be playing a guessing game
+on most flops so you know it probably if
+
+ align:start position:0%
+on most flops so you know it probably if
+ 
+
+ align:start position:0%
+on most flops so you know it probably if
+I had a very strong beat on him and I if
+
+ align:start position:0%
+I had a very strong beat on him and I if
+ 
+
+ align:start position:0%
+I had a very strong beat on him and I if
+I had like Jack 10 suited here calling
+
+ align:start position:0%
+I had like Jack 10 suited here calling
+ 
+
+ align:start position:0%
+I had like Jack 10 suited here calling
+is maybe not that bad because you're
+
+ align:start position:0%
+is maybe not that bad because you're
+ 
+
+ align:start position:0%
+is maybe not that bad because you're
+were like a coin flip against ace2 offit
+
+ align:start position:0%
+were like a coin flip against ace2 offit
+ 
+
+ align:start position:0%
+were like a coin flip against ace2 offit
+and you're like a 54% favorite against
+
+ align:start position:0%
+and you're like a 54% favorite against
+ 
+
+ align:start position:0%
+and you're like a 54% favorite against
+pocket 3s so I mean I F it here because
+
+ align:start position:0%
+pocket 3s so I mean I F it here because
+ 
+
+ align:start position:0%
+pocket 3s so I mean I F it here because
+my hand isn't suited and just because
+
+ align:start position:0%
+my hand isn't suited and just because
+ 
+
+ align:start position:0%
+my hand isn't suited and just because
+there's a small chance they're going to
+
+ align:start position:0%
+there's a small chance they're going to
+ 
+
+ align:start position:0%
+there's a small chance they're going to
+have Ace Queen and my read was nowhere
+
+ align:start position:0%
+have Ace Queen and my read was nowhere
+ 
+
+ align:start position:0%
+have Ace Queen and my read was nowhere
+near strong enough to to conclude that
+
+ align:start position:0%
+near strong enough to to conclude that
+ 
+
+ align:start position:0%
+near strong enough to to conclude that
+for sure their range was only small
+
+ align:start position:0%
+for sure their range was only small
+ 
+
+ align:start position:0%
+for sure their range was only small
+pairs in
+
+ align:start position:0%
+pairs in
+ 
+
+ align:start position:0%
+pairs in
+asex
+
+ align:start position:0%
+asex
+ 
+
+ align:start position:0%
+asex
+okay so we lose a bit of chips we're
+
+ align:start position:0%
+okay so we lose a bit of chips we're
+ 
+
+ align:start position:0%
+okay so we lose a bit of chips we're
+blinding down a bit here we got 102
+
+ align:start position:0%
+blinding down a bit here we got 102
+ 
+
+ align:start position:0%
+blinding down a bit here we got 102
+suited and so I call from the big blind
+
+ align:start position:0%
+suited and so I call from the big blind
+ 
+
+ align:start position:0%
+suited and so I call from the big blind
+with four and a half to one odds I think
+
+ align:start position:0%
+with four and a half to one odds I think
+ 
+
+ align:start position:0%
+with four and a half to one odds I think
+this is probably one of the weakest
+
+ align:start position:0%
+this is probably one of the weakest
+ 
+
+ align:start position:0%
+this is probably one of the weakest
+hands I call I might not call like 8 two
+
+ align:start position:0%
+hands I call I might not call like 8 two
+ 
+
+ align:start position:0%
+hands I call I might not call like 8 two
+suited although it's close I mean you
+
+ align:start position:0%
+suited although it's close I mean you
+ 
+
+ align:start position:0%
+suited although it's close I mean you
+can make a case for calling 8 two suited
+
+ align:start position:0%
+can make a case for calling 8 two suited
+ 
+
+ align:start position:0%
+can make a case for calling 8 two suited
+so once again my odds my odds are really
+
+ align:start position:0%
+so once again my odds my odds are really
+ 
+
+ align:start position:0%
+so once again my odds my odds are really
+good but the reverse implied odds do do
+
+ align:start position:0%
+good but the reverse implied odds do do
+ 
+
+ align:start position:0%
+good but the reverse implied odds do do
+sort of work against me quite a bit
+
+ align:start position:0%
+sort of work against me quite a bit
+ 
+
+ align:start position:0%
+sort of work against me quite a bit
+since I'm going to be out of position
+
+ align:start position:0%
+since I'm going to be out of position
+ 
+
+ align:start position:0%
+since I'm going to be out of position
+and I have small cards which will
+
+ align:start position:0%
+and I have small cards which will
+ 
+
+ align:start position:0%
+and I have small cards which will
+usually make a smaller pair than them
+
+ align:start position:0%
+usually make a smaller pair than them
+ 
+
+ align:start position:0%
+usually make a smaller pair than them
+but I decid to call and we FL a flush
+
+ align:start position:0%
+but I decid to call and we FL a flush
+ 
+
+ align:start position:0%
+but I decid to call and we FL a flush
+draw which is pretty good but I'm still
+
+ align:start position:0%
+draw which is pretty good but I'm still
+ 
+
+ align:start position:0%
+draw which is pretty good but I'm still
+going to check because this is a board
+
+ align:start position:0%
+going to check because this is a board
+ 
+
+ align:start position:0%
+going to check because this is a board
+where I'm just going to check to the
+
+ align:start position:0%
+where I'm just going to check to the
+ 
+
+ align:start position:0%
+where I'm just going to check to the
+pre- Flop raiser and let them
+
+ align:start position:0%
+pre- Flop raiser and let them
+ 
+
+ align:start position:0%
+pre- Flop raiser and let them
+continuation BET right so I talked about
+
+ align:start position:0%
+continuation BET right so I talked about
+ 
+
+ align:start position:0%
+continuation BET right so I talked about
+leading in an earlier class and I don't
+
+ align:start position:0%
+leading in an earlier class and I don't
+ 
+
+ align:start position:0%
+leading in an earlier class and I don't
+think this is a board where we should
+
+ align:start position:0%
+think this is a board where we should
+ 
+
+ align:start position:0%
+think this is a board where we should
+leading we should be leading and I think
+
+ align:start position:0%
+leading we should be leading and I think
+ 
+
+ align:start position:0%
+leading we should be leading and I think
+never leading is okay as well so I deci
+
+ align:start position:0%
+never leading is okay as well so I deci
+ 
+
+ align:start position:0%
+never leading is okay as well so I deci
+had to check and they check back so we
+
+ align:start position:0%
+had to check and they check back so we
+ 
+
+ align:start position:0%
+had to check and they check back so we
+turn the flush which is great and we bet
+
+ align:start position:0%
+turn the flush which is great and we bet
+ 
+
+ align:start position:0%
+turn the flush which is great and we bet
+600 into
+
+ align:start position:0%
+600 into
+ 
+
+ align:start position:0%
+600 into
+1080 so unfortunately we don't get any
+
+ align:start position:0%
+1080 so unfortunately we don't get any
+ 
+
+ align:start position:0%
+1080 so unfortunately we don't get any
+action so we take it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down okay uh so the next I think this is
+
+ align:start position:0%
+down okay uh so the next I think this is
+ 
+
+ align:start position:0%
+down okay uh so the next I think this is
+one Orbit
+
+ align:start position:0%
+one Orbit
+ 
+
+ align:start position:0%
+one Orbit
+later so under the gun raises small
+
+ align:start position:0%
+later so under the gun raises small
+ 
+
+ align:start position:0%
+later so under the gun raises small
+blind who is very very short who only
+
+ align:start position:0%
+blind who is very very short who only
+ 
+
+ align:start position:0%
+blind who is very very short who only
+has uh s and a half big blinds called
+
+ align:start position:0%
+has uh s and a half big blinds called
+ 
+
+ align:start position:0%
+has uh s and a half big blinds called
+calls and we decide to call with our
+
+ align:start position:0%
+calls and we decide to call with our
+ 
+
+ align:start position:0%
+calls and we decide to call with our
+seven with our six and a half to one
+
+ align:start position:0%
+seven with our six and a half to one
+ 
+
+ align:start position:0%
+seven with our six and a half to one
+odds
+
+ align:start position:0%
+odds
+ 
+
+ align:start position:0%
+odds
+here or 6 to1
+
+ align:start position:0%
+here or 6 to1
+ 
+
+ align:start position:0%
+here or 6 to1
+odds so we flop uh Queen Jack five so we
+
+ align:start position:0%
+odds so we flop uh Queen Jack five so we
+ 
+
+ align:start position:0%
+odds so we flop uh Queen Jack five so we
+have second pair with a backd door
+
+ align:start position:0%
+have second pair with a backd door
+ 
+
+ align:start position:0%
+have second pair with a backd door
+straight draw and a back door flush draw
+
+ align:start position:0%
+straight draw and a back door flush draw
+ 
+
+ align:start position:0%
+straight draw and a back door flush draw
+and the swamp line goes all in for 1054
+
+ align:start position:0%
+and the swamp line goes all in for 1054
+ 
+
+ align:start position:0%
+and the swamp line goes all in for 1054
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+1380 so this is sort of I think a pretty
+
+ align:start position:0%
+1380 so this is sort of I think a pretty
+ 
+
+ align:start position:0%
+1380 so this is sort of I think a pretty
+close spot I think if I knew for sure
+
+ align:start position:0%
+close spot I think if I knew for sure
+ 
+
+ align:start position:0%
+close spot I think if I knew for sure
+that ardom 1977 didn't have a hand here
+
+ align:start position:0%
+that ardom 1977 didn't have a hand here
+ 
+
+ align:start position:0%
+that ardom 1977 didn't have a hand here
+I think calling is definitely fine we're
+
+ align:start position:0%
+I think calling is definitely fine we're
+ 
+
+ align:start position:0%
+I think calling is definitely fine we're
+given about 2.3 to one odds and I think
+
+ align:start position:0%
+given about 2.3 to one odds and I think
+ 
+
+ align:start position:0%
+given about 2.3 to one odds and I think
+second pair with these back door draws
+
+ align:start position:0%
+second pair with these back door draws
+ 
+
+ align:start position:0%
+second pair with these back door draws
+is more than good enough against his
+
+ align:start position:0%
+is more than good enough against his
+ 
+
+ align:start position:0%
+is more than good enough against his
+range but um because I think his range
+
+ align:start position:0%
+range but um because I think his range
+ 
+
+ align:start position:0%
+range but um because I think his range
+will mostly be draws and top Pairs and
+
+ align:start position:0%
+will mostly be draws and top Pairs and
+ 
+
+ align:start position:0%
+will mostly be draws and top Pairs and
+second pairs probably not bottom pair
+
+ align:start position:0%
+second pairs probably not bottom pair
+ 
+
+ align:start position:0%
+second pairs probably not bottom pair
+that often because they did call Pre
+
+ align:start position:0%
+that often because they did call Pre
+ 
+
+ align:start position:0%
+that often because they did call Pre
+flop from the small blind which I don't
+
+ align:start position:0%
+flop from the small blind which I don't
+ 
+
+ align:start position:0%
+flop from the small blind which I don't
+expect most players would do with a hand
+
+ align:start position:0%
+expect most players would do with a hand
+ 
+
+ align:start position:0%
+expect most players would do with a hand
+like 75 suited so you know we're not
+
+ align:start position:0%
+like 75 suited so you know we're not
+ 
+
+ align:start position:0%
+like 75 suited so you know we're not
+even that happy to call him to be honest
+
+ align:start position:0%
+even that happy to call him to be honest
+ 
+
+ align:start position:0%
+even that happy to call him to be honest
+but I probably would call um but the
+
+ align:start position:0%
+but I probably would call um but the
+ 
+
+ align:start position:0%
+but I probably would call um but the
+fact that this guy here is behind and
+
+ align:start position:0%
+fact that this guy here is behind and
+ 
+
+ align:start position:0%
+fact that this guy here is behind and
+they could raise or they could call and
+
+ align:start position:0%
+they could raise or they could call and
+ 
+
+ align:start position:0%
+they could raise or they could call and
+we have to make more decisions on future
+
+ align:start position:0%
+we have to make more decisions on future
+ 
+
+ align:start position:0%
+we have to make more decisions on future
+streets I think really hurts us and I
+
+ align:start position:0%
+streets I think really hurts us and I
+ 
+
+ align:start position:0%
+streets I think really hurts us and I
+think we should have
+
+ align:start position:0%
+think we should have
+ 
+
+ align:start position:0%
+think we should have
+folded uh at the time I I decided to
+
+ align:start position:0%
+folded uh at the time I I decided to
+ 
+
+ align:start position:0%
+folded uh at the time I I decided to
+call so I I don't know why but I don't
+
+ align:start position:0%
+call so I I don't know why but I don't
+ 
+
+ align:start position:0%
+call so I I don't know why but I don't
+think this is a good play I think it's
+
+ align:start position:0%
+think this is a good play I think it's
+ 
+
+ align:start position:0%
+think this is a good play I think it's
+it's just too risky essentially you know
+
+ align:start position:0%
+it's just too risky essentially you know
+ 
+
+ align:start position:0%
+it's just too risky essentially you know
+it'll work most of the time and we and
+
+ align:start position:0%
+it'll work most of the time and we and
+ 
+
+ align:start position:0%
+it'll work most of the time and we and
+because most of the time Aram will fold
+
+ align:start position:0%
+because most of the time Aram will fold
+ 
+
+ align:start position:0%
+because most of the time Aram will fold
+because they're going to see two players
+
+ align:start position:0%
+because they're going to see two players
+ 
+
+ align:start position:0%
+because they're going to see two players
+putting money in but the times where
+
+ align:start position:0%
+putting money in but the times where
+ 
+
+ align:start position:0%
+putting money in but the times where
+they have something I'm going to have to
+
+ align:start position:0%
+they have something I'm going to have to
+ 
+
+ align:start position:0%
+they have something I'm going to have to
+fold and it's going to suck so so we do
+
+ align:start position:0%
+fold and it's going to suck so so we do
+ 
+
+ align:start position:0%
+fold and it's going to suck so so we do
+call um they actually had the same hand
+
+ align:start position:0%
+call um they actually had the same hand
+ 
+
+ align:start position:0%
+call um they actually had the same hand
+at us so it it worked out well I guess
+
+ align:start position:0%
+at us so it it worked out well I guess
+ 
+
+ align:start position:0%
+at us so it it worked out well I guess
+we sort of took a bad beat cuz we could
+
+ align:start position:0%
+we sort of took a bad beat cuz we could
+ 
+
+ align:start position:0%
+we sort of took a bad beat cuz we could
+have made a flush and they couldn't have
+
+ align:start position:0%
+have made a flush and they couldn't have
+ 
+
+ align:start position:0%
+have made a flush and they couldn't have
+so we were technically ahead but we get
+
+ align:start position:0%
+so we were technically ahead but we get
+ 
+
+ align:start position:0%
+so we were technically ahead but we get
+half to yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so yeah so I I'm not going through my
+
+ align:start position:0%
+um so yeah so I I'm not going through my
+ 
+
+ align:start position:0%
+um so yeah so I I'm not going through my
+tournament history from uh from maybe
+
+ align:start position:0%
+tournament history from uh from maybe
+ 
+
+ align:start position:0%
+tournament history from uh from maybe
+one month ago and saying I played every
+
+ align:start position:0%
+one month ago and saying I played every
+ 
+
+ align:start position:0%
+one month ago and saying I played every
+hand perfectly when I look through here
+
+ align:start position:0%
+hand perfectly when I look through here
+ 
+
+ align:start position:0%
+hand perfectly when I look through here
+I definitely there's a lot of there's a
+
+ align:start position:0%
+I definitely there's a lot of there's a
+ 
+
+ align:start position:0%
+I definitely there's a lot of there's a
+lot of mistakes there's a lot of hands I
+
+ align:start position:0%
+lot of mistakes there's a lot of hands I
+ 
+
+ align:start position:0%
+lot of mistakes there's a lot of hands I
+wish I could replay
+
+ align:start position:0%
+wish I could replay
+ 
+
+ align:start position:0%
+wish I could replay
+um so okay so this hand I guess is
+
+ align:start position:0%
+um so okay so this hand I guess is
+ 
+
+ align:start position:0%
+um so okay so this hand I guess is
+fairly simple so we have Ace King and I
+
+ align:start position:0%
+fairly simple so we have Ace King and I
+ 
+
+ align:start position:0%
+fairly simple so we have Ace King and I
+think it's definitely good enough to get
+
+ align:start position:0%
+think it's definitely good enough to get
+ 
+
+ align:start position:0%
+think it's definitely good enough to get
+it all in here with so as far as what my
+
+ align:start position:0%
+it all in here with so as far as what my
+ 
+
+ align:start position:0%
+it all in here with so as far as what my
+range is I
+
+ align:start position:0%
+range is I
+ 
+
+ align:start position:0%
+range is I
+think I think um sorry oh did you have
+
+ align:start position:0%
+think I think um sorry oh did you have
+ 
+
+ align:start position:0%
+think I think um sorry oh did you have
+suggestion on oh no no I I just saw this
+
+ align:start position:0%
+suggestion on oh no no I I just saw this
+ 
+
+ align:start position:0%
+suggestion on oh no no I I just saw this
+guy's uh handle and was
+
+ align:start position:0%
+guy's uh handle and was
+ 
+
+ align:start position:0%
+guy's uh handle and was
+I thought it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+funny um okay sorry you thought it was
+
+ align:start position:0%
+funny um okay sorry you thought it was
+ 
+
+ align:start position:0%
+funny um okay sorry you thought it was
+Who funny
+
+ align:start position:0%
+Who funny
+ 
+
+ align:start position:0%
+Who funny
+oh sorry s funny
+
+ align:start position:0%
+oh sorry s funny
+ 
+
+ align:start position:0%
+oh sorry s funny
+okay no yeah don't ask me what my handle
+
+ align:start position:0%
+okay no yeah don't ask me what my handle
+ 
+
+ align:start position:0%
+okay no yeah don't ask me what my handle
+means my handle is what does it
+
+ align:start position:0%
+means my handle is what does it
+ 
+
+ align:start position:0%
+means my handle is what does it
+mean I I can't even read it um okay
+
+ align:start position:0%
+mean I I can't even read it um okay
+ 
+
+ align:start position:0%
+mean I I can't even read it um okay
+so I think it stood for something I
+
+ align:start position:0%
+so I think it stood for something I
+ 
+
+ align:start position:0%
+so I think it stood for something I
+probably made it when I was like 17 and
+
+ align:start position:0%
+probably made it when I was like 17 and
+ 
+
+ align:start position:0%
+probably made it when I was like 17 and
+I think get stood for something and I I
+
+ align:start position:0%
+I think get stood for something and I I
+ 
+
+ align:start position:0%
+I think get stood for something and I I
+might I probably don't remember what it
+
+ align:start position:0%
+might I probably don't remember what it
+ 
+
+ align:start position:0%
+might I probably don't remember what it
+says Okay um so okay so we go all in
+
+ align:start position:0%
+says Okay um so okay so we go all in
+ 
+
+ align:start position:0%
+says Okay um so okay so we go all in
+here um so this is sort of a no-brainer
+
+ align:start position:0%
+here um so this is sort of a no-brainer
+ 
+
+ align:start position:0%
+here um so this is sort of a no-brainer
+hand but let's stop and think a bit
+
+ align:start position:0%
+hand but let's stop and think a bit
+ 
+
+ align:start position:0%
+hand but let's stop and think a bit
+about what our range should be so I
+
+ align:start position:0%
+about what our range should be so I
+ 
+
+ align:start position:0%
+about what our range should be so I
+think with Ace King Ace King in Pocket
+
+ align:start position:0%
+think with Ace King Ace King in Pocket
+ 
+
+ align:start position:0%
+think with Ace King Ace King in Pocket
+TS I think it's fairly easy to get it
+
+ align:start position:0%
+TS I think it's fairly easy to get it
+ 
+
+ align:start position:0%
+TS I think it's fairly easy to get it
+all in I think with Ace Queen suited I
+
+ align:start position:0%
+all in I think with Ace Queen suited I
+ 
+
+ align:start position:0%
+all in I think with Ace Queen suited I
+would get it in um I think if I had Ace
+
+ align:start position:0%
+would get it in um I think if I had Ace
+ 
+
+ align:start position:0%
+would get it in um I think if I had Ace
+queen off suit I would probably fold
+
+ align:start position:0%
+queen off suit I would probably fold
+ 
+
+ align:start position:0%
+queen off suit I would probably fold
+although um with Ace Queen suited
+
+ align:start position:0%
+although um with Ace Queen suited
+ 
+
+ align:start position:0%
+although um with Ace Queen suited
+actually if this jet ski fun guy had as
+
+ align:start position:0%
+actually if this jet ski fun guy had as
+ 
+
+ align:start position:0%
+actually if this jet ski fun guy had as
+many chips as us then maybe I would have
+
+ align:start position:0%
+many chips as us then maybe I would have
+ 
+
+ align:start position:0%
+many chips as us then maybe I would have
+folded but the fact that we're actually
+
+ align:start position:0%
+folded but the fact that we're actually
+ 
+
+ align:start position:0%
+folded but the fact that we're actually
+not risking our entire 6 6250 against
+
+ align:start position:0%
+not risking our entire 6 6250 against
+ 
+
+ align:start position:0%
+not risking our entire 6 6250 against
+the two players who are in the pot is
+
+ align:start position:0%
+the two players who are in the pot is
+ 
+
+ align:start position:0%
+the two players who are in the pot is
+very relevant cuz I mean ardam covers us
+
+ align:start position:0%
+very relevant cuz I mean ardam covers us
+ 
+
+ align:start position:0%
+very relevant cuz I mean ardam covers us
+and they could in theory pick up pocket
+
+ align:start position:0%
+and they could in theory pick up pocket
+ 
+
+ align:start position:0%
+and they could in theory pick up pocket
+aces but it's much less likely for them
+
+ align:start position:0%
+aces but it's much less likely for them
+ 
+
+ align:start position:0%
+aces but it's much less likely for them
+to pick up pocket aces than this jet ski
+
+ align:start position:0%
+to pick up pocket aces than this jet ski
+ 
+
+ align:start position:0%
+to pick up pocket aces than this jet ski
+fun guy who's already in the pot so the
+
+ align:start position:0%
+fun guy who's already in the pot so the
+ 
+
+ align:start position:0%
+fun guy who's already in the pot so the
+fact that they only have less than 20
+
+ align:start position:0%
+fact that they only have less than 20
+ 
+
+ align:start position:0%
+fact that they only have less than 20
+big blindes as well helps our case a lot
+
+ align:start position:0%
+big blindes as well helps our case a lot
+ 
+
+ align:start position:0%
+big blindes as well helps our case a lot
+so I would probably get it in with Ace
+
+ align:start position:0%
+so I would probably get it in with Ace
+ 
+
+ align:start position:0%
+so I would probably get it in with Ace
+Queen suited plus and then pocket pocket
+
+ align:start position:0%
+Queen suited plus and then pocket pocket
+ 
+
+ align:start position:0%
+Queen suited plus and then pocket pocket
+nines plus probably is what I'd get it
+
+ align:start position:0%
+nines plus probably is what I'd get it
+ 
+
+ align:start position:0%
+nines plus probably is what I'd get it
+in with here um so we go all in and we
+
+ align:start position:0%
+in with here um so we go all in and we
+ 
+
+ align:start position:0%
+in with here um so we go all in and we
+beat ace Jack which
+
+ align:start position:0%
+beat ace Jack which
+ 
+
+ align:start position:0%
+beat ace Jack which
+is which is good yeah so I think Ace
+
+ align:start position:0%
+is which is good yeah so I think Ace
+ 
+
+ align:start position:0%
+is which is good yeah so I think Ace
+Jack is slightly on the loose side I
+
+ align:start position:0%
+Jack is slightly on the loose side I
+ 
+
+ align:start position:0%
+Jack is slightly on the loose side I
+mean I think it's a fine play definitely
+
+ align:start position:0%
+mean I think it's a fine play definitely
+ 
+
+ align:start position:0%
+mean I think it's a fine play definitely
+to get it all in with Ace Jack but maybe
+
+ align:start position:0%
+to get it all in with Ace Jack but maybe
+ 
+
+ align:start position:0%
+to get it all in with Ace Jack but maybe
+they could have may like they because
+
+ align:start position:0%
+they could have may like they because
+ 
+
+ align:start position:0%
+they could have may like they because
+they do have more than 20 big blinds
+
+ align:start position:0%
+they do have more than 20 big blinds
+ 
+
+ align:start position:0%
+they do have more than 20 big blinds
+here so I think maybe they could have
+
+ align:start position:0%
+here so I think maybe they could have
+ 
+
+ align:start position:0%
+here so I think maybe they could have
+considered calling or raising small and
+
+ align:start position:0%
+considered calling or raising small and
+ 
+
+ align:start position:0%
+considered calling or raising small and
+folding if someone like us entered the
+
+ align:start position:0%
+folding if someone like us entered the
+ 
+
+ align:start position:0%
+folding if someone like us entered the
+pot but nonetheless I think they played
+
+ align:start position:0%
+pot but nonetheless I think they played
+ 
+
+ align:start position:0%
+pot but nonetheless I think they played
+their hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fine okay so the next thing we have
+
+ align:start position:0%
+fine okay so the next thing we have
+ 
+
+ align:start position:0%
+fine okay so the next thing we have
+pocket nines so many this guy raises we
+
+ align:start position:0%
+pocket nines so many this guy raises we
+ 
+
+ align:start position:0%
+pocket nines so many this guy raises we
+call so we're getting deeper now because
+
+ align:start position:0%
+call so we're getting deeper now because
+ 
+
+ align:start position:0%
+call so we're getting deeper now because
+we won the last hand so now we' got
+
+ align:start position:0%
+we won the last hand so now we' got
+ 
+
+ align:start position:0%
+we won the last hand so now we' got
+we've got 40 big blinds and we call this
+
+ align:start position:0%
+we've got 40 big blinds and we call this
+ 
+
+ align:start position:0%
+we've got 40 big blinds and we call this
+guy also calls and Liam kid goes all in
+
+ align:start position:0%
+guy also calls and Liam kid goes all in
+ 
+
+ align:start position:0%
+guy also calls and Liam kid goes all in
+for 30 big blinds and so they get out of
+
+ align:start position:0%
+for 30 big blinds and so they get out of
+ 
+
+ align:start position:0%
+for 30 big blinds and so they get out of
+the way I think this is actually a very
+
+ align:start position:0%
+the way I think this is actually a very
+ 
+
+ align:start position:0%
+the way I think this is actually a very
+close spot so um I do think one big uh
+
+ align:start position:0%
+close spot so um I do think one big uh
+ 
+
+ align:start position:0%
+close spot so um I do think one big uh
+incentive to get it all in is I think
+
+ align:start position:0%
+incentive to get it all in is I think
+ 
+
+ align:start position:0%
+incentive to get it all in is I think
+it's not that likely that Liam kid has
+
+ align:start position:0%
+it's not that likely that Liam kid has
+ 
+
+ align:start position:0%
+it's not that likely that Liam kid has
+like pocket kings or pocket aces because
+
+ align:start position:0%
+like pocket kings or pocket aces because
+ 
+
+ align:start position:0%
+like pocket kings or pocket aces because
+I think there's a good chance they would
+
+ align:start position:0%
+I think there's a good chance they would
+ 
+
+ align:start position:0%
+I think there's a good chance they would
+have just raised smaller maybe to try to
+
+ align:start position:0%
+have just raised smaller maybe to try to
+ 
+
+ align:start position:0%
+have just raised smaller maybe to try to
+sctor people in so I actually think I'm
+
+ align:start position:0%
+sctor people in so I actually think I'm
+ 
+
+ align:start position:0%
+sctor people in so I actually think I'm
+not losing to too muchu and same with
+
+ align:start position:0%
+not losing to too muchu and same with
+ 
+
+ align:start position:0%
+not losing to too muchu and same with
+ardam I think it's also very hard for
+
+ align:start position:0%
+ardam I think it's also very hard for
+ 
+
+ align:start position:0%
+ardam I think it's also very hard for
+ardam to have a good hand so even though
+
+ align:start position:0%
+ardam to have a good hand so even though
+ 
+
+ align:start position:0%
+ardam to have a good hand so even though
+in the first example we talked about how
+
+ align:start position:0%
+in the first example we talked about how
+ 
+
+ align:start position:0%
+in the first example we talked about how
+um sometimes you know calling with
+
+ align:start position:0%
+um sometimes you know calling with
+ 
+
+ align:start position:0%
+um sometimes you know calling with
+pocket Aces here is a good play but you
+
+ align:start position:0%
+pocket Aces here is a good play but you
+ 
+
+ align:start position:0%
+pocket Aces here is a good play but you
+know I said if one guy raised and you're
+
+ align:start position:0%
+know I said if one guy raised and you're
+ 
+
+ align:start position:0%
+know I said if one guy raised and you're
+the second guy you should maybe call
+
+ align:start position:0%
+the second guy you should maybe call
+ 
+
+ align:start position:0%
+the second guy you should maybe call
+with pocket aces like 20% of the time
+
+ align:start position:0%
+with pocket aces like 20% of the time
+ 
+
+ align:start position:0%
+with pocket aces like 20% of the time
+when it's two guys who have like when
+
+ align:start position:0%
+when it's two guys who have like when
+ 
+
+ align:start position:0%
+when it's two guys who have like when
+it's one guy who has raised me who has
+
+ align:start position:0%
+it's one guy who has raised me who has
+ 
+
+ align:start position:0%
+it's one guy who has raised me who has
+called and now you're deciding what to
+
+ align:start position:0%
+called and now you're deciding what to
+ 
+
+ align:start position:0%
+called and now you're deciding what to
+do with pocket aces you know instead of
+
+ align:start position:0%
+do with pocket aces you know instead of
+ 
+
+ align:start position:0%
+do with pocket aces you know instead of
+20% you should be calling it's literally
+
+ align:start position:0%
+20% you should be calling it's literally
+ 
+
+ align:start position:0%
+20% you should be calling it's literally
+like you know maybe like 2% or 1% you
+
+ align:start position:0%
+like you know maybe like 2% or 1% you
+ 
+
+ align:start position:0%
+like you know maybe like 2% or 1% you
+should be calling with pocket aces so
+
+ align:start position:0%
+should be calling with pocket aces so
+ 
+
+ align:start position:0%
+should be calling with pocket aces so
+you know if you combine multiply 1% by
+
+ align:start position:0%
+you know if you combine multiply 1% by
+ 
+
+ align:start position:0%
+you know if you combine multiply 1% by
+the probability of getting dealt pocket
+
+ align:start position:0%
+the probability of getting dealt pocket
+ 
+
+ align:start position:0%
+the probability of getting dealt pocket
+aces which is around like 1 and 200
+
+ align:start position:0%
+aces which is around like 1 and 200
+ 
+
+ align:start position:0%
+aces which is around like 1 and 200
+it's literally like one out of 20,000
+
+ align:start position:0%
+it's literally like one out of 20,000
+ 
+
+ align:start position:0%
+it's literally like one out of 20,000
+that PS pocket aces here so um so I'm
+
+ align:start position:0%
+that PS pocket aces here so um so I'm
+ 
+
+ align:start position:0%
+that PS pocket aces here so um so I'm
+not too afraid of him so I I really
+
+ align:start position:0%
+not too afraid of him so I I really
+ 
+
+ align:start position:0%
+not too afraid of him so I I really
+think getting it in is fine but at the
+
+ align:start position:0%
+think getting it in is fine but at the
+ 
+
+ align:start position:0%
+think getting it in is fine but at the
+same time you know I don't think I'm
+
+ align:start position:0%
+same time you know I don't think I'm
+ 
+
+ align:start position:0%
+same time you know I don't think I'm
+ever a favorite here I think their range
+
+ align:start position:0%
+ever a favorite here I think their range
+ 
+
+ align:start position:0%
+ever a favorite here I think their range
+is essentially like Ace King Ace Queen
+
+ align:start position:0%
+is essentially like Ace King Ace Queen
+ 
+
+ align:start position:0%
+is essentially like Ace King Ace Queen
+maybe Ace Jack suited and then
+
+ align:start position:0%
+maybe Ace Jack suited and then
+ 
+
+ align:start position:0%
+maybe Ace Jack suited and then
+essentially pocket 10s pocket NES pocket
+
+ align:start position:0%
+essentially pocket 10s pocket NES pocket
+ 
+
+ align:start position:0%
+essentially pocket 10s pocket NES pocket
+Jacks pocket Queens maybe occasionally
+
+ align:start position:0%
+Jacks pocket Queens maybe occasionally
+ 
+
+ align:start position:0%
+Jacks pocket Queens maybe occasionally
+pocket eights so I could have done an
+
+ align:start position:0%
+pocket eights so I could have done an
+ 
+
+ align:start position:0%
+pocket eights so I could have done an
+exact Equity calculation on poker stove
+
+ align:start position:0%
+exact Equity calculation on poker stove
+ 
+
+ align:start position:0%
+exact Equity calculation on poker stove
+and if I did it probably would have been
+
+ align:start position:0%
+and if I did it probably would have been
+ 
+
+ align:start position:0%
+and if I did it probably would have been
+very very close but I decided to fold
+
+ align:start position:0%
+very very close but I decided to fold
+ 
+
+ align:start position:0%
+very very close but I decided to fold
+and they take down the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P okay so the next hand we get Ace Jack
+
+ align:start position:0%
+P okay so the next hand we get Ace Jack
+ 
+
+ align:start position:0%
+P okay so the next hand we get Ace Jack
+we raise red the gun this uh this guy go
+
+ align:start position:0%
+we raise red the gun this uh this guy go
+ 
+
+ align:start position:0%
+we raise red the gun this uh this guy go
+this guy goes on in for six big blinds
+
+ align:start position:0%
+this guy goes on in for six big blinds
+ 
+
+ align:start position:0%
+this guy goes on in for six big blinds
+we're basically committed here even if
+
+ align:start position:0%
+we're basically committed here even if
+ 
+
+ align:start position:0%
+we're basically committed here even if
+we think he's crushing us so I call and
+
+ align:start position:0%
+we think he's crushing us so I call and
+ 
+
+ align:start position:0%
+we think he's crushing us so I call and
+we lose the Ace King not really too much
+
+ align:start position:0%
+we lose the Ace King not really too much
+ 
+
+ align:start position:0%
+we lose the Ace King not really too much
+we can do here um although this does
+
+ align:start position:0%
+we can do here um although this does
+ 
+
+ align:start position:0%
+we can do here um although this does
+illustrate one concept which is when
+
+ align:start position:0%
+illustrate one concept which is when
+ 
+
+ align:start position:0%
+illustrate one concept which is when
+there are Stacks behind like zarban who
+
+ align:start position:0%
+there are Stacks behind like zarban who
+ 
+
+ align:start position:0%
+there are Stacks behind like zarban who
+are short enough that they can commit
+
+ align:start position:0%
+are short enough that they can commit
+ 
+
+ align:start position:0%
+are short enough that they can commit
+You by going all in you should be
+
+ align:start position:0%
+You by going all in you should be
+ 
+
+ align:start position:0%
+You by going all in you should be
+slightly less incentivized to open
+
+ align:start position:0%
+slightly less incentivized to open
+ 
+
+ align:start position:0%
+slightly less incentivized to open
+speculative hands here like say I had
+
+ align:start position:0%
+speculative hands here like say I had
+ 
+
+ align:start position:0%
+speculative hands here like say I had
+109 suited I think while normally I
+
+ align:start position:0%
+109 suited I think while normally I
+ 
+
+ align:start position:0%
+109 suited I think while normally I
+would consider opening 109 suited here
+
+ align:start position:0%
+would consider opening 109 suited here
+ 
+
+ align:start position:0%
+would consider opening 109 suited here
+as a steal it's a huge disincentive to
+
+ align:start position:0%
+as a steal it's a huge disincentive to
+ 
+
+ align:start position:0%
+as a steal it's a huge disincentive to
+steal here with 10 n suited when someone
+
+ align:start position:0%
+steal here with 10 n suited when someone
+ 
+
+ align:start position:0%
+steal here with 10 n suited when someone
+like zarazan can just pick up you know
+
+ align:start position:0%
+like zarazan can just pick up you know
+ 
+
+ align:start position:0%
+like zarazan can just pick up you know
+even a hand as weak as like Ace Jack
+
+ align:start position:0%
+even a hand as weak as like Ace Jack
+ 
+
+ align:start position:0%
+even a hand as weak as like Ace Jack
+suited and or Ace jack off suit and go
+
+ align:start position:0%
+suited and or Ace jack off suit and go
+ 
+
+ align:start position:0%
+suited and or Ace jack off suit and go
+all in and beat our 109 suited so
+
+ align:start position:0%
+all in and beat our 109 suited so
+ 
+
+ align:start position:0%
+all in and beat our 109 suited so
+um but I mean Ace Jack is more than good
+
+ align:start position:0%
+um but I mean Ace Jack is more than good
+ 
+
+ align:start position:0%
+um but I mean Ace Jack is more than good
+enough to still raise here and we
+
+ align:start position:0%
+enough to still raise here and we
+ 
+
+ align:start position:0%
+enough to still raise here and we
+unfortunately run into Ace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+King okay so the next end we get e Jack
+
+ align:start position:0%
+King okay so the next end we get e Jack
+ 
+
+ align:start position:0%
+King okay so the next end we get e Jack
+again and uh the same guy who just
+
+ align:start position:0%
+again and uh the same guy who just
+ 
+
+ align:start position:0%
+again and uh the same guy who just
+doubled up through US goes all in and
+
+ align:start position:0%
+doubled up through US goes all in and
+ 
+
+ align:start position:0%
+doubled up through US goes all in and
+here I call him because here the even
+
+ align:start position:0%
+here I call him because here the even
+ 
+
+ align:start position:0%
+here I call him because here the even
+though there's more chips the positions
+
+ align:start position:0%
+though there's more chips the positions
+ 
+
+ align:start position:0%
+though there's more chips the positions
+are a lot later and specifically uh they
+
+ align:start position:0%
+are a lot later and specifically uh they
+ 
+
+ align:start position:0%
+are a lot later and specifically uh they
+went all in for 14 big blinds when no
+
+ align:start position:0%
+went all in for 14 big blinds when no
+ 
+
+ align:start position:0%
+went all in for 14 big blinds when no
+one else was in the pot so their range
+
+ align:start position:0%
+one else was in the pot so their range
+ 
+
+ align:start position:0%
+one else was in the pot so their range
+is you know their range isn't super
+
+ align:start position:0%
+is you know their range isn't super
+ 
+
+ align:start position:0%
+is you know their range isn't super
+duper wide but it's definitely wide
+
+ align:start position:0%
+duper wide but it's definitely wide
+ 
+
+ align:start position:0%
+duper wide but it's definitely wide
+enough that Ace Jack I'm happy to call
+
+ align:start position:0%
+enough that Ace Jack I'm happy to call
+ 
+
+ align:start position:0%
+enough that Ace Jack I'm happy to call
+here as far as what my range is I think
+
+ align:start position:0%
+here as far as what my range is I think
+ 
+
+ align:start position:0%
+here as far as what my range is I think
+um I think I wouldn't call with Ace 10
+
+ align:start position:0%
+um I think I wouldn't call with Ace 10
+ 
+
+ align:start position:0%
+um I think I wouldn't call with Ace 10
+off suit but I would call with Ace 10
+
+ align:start position:0%
+off suit but I would call with Ace 10
+ 
+
+ align:start position:0%
+off suit but I would call with Ace 10
+suited so probably Ace 10 suited and I
+
+ align:start position:0%
+suited so probably Ace 10 suited and I
+ 
+
+ align:start position:0%
+suited so probably Ace 10 suited and I
+think I'd call with king queen suited
+
+ align:start position:0%
+think I'd call with king queen suited
+ 
+
+ align:start position:0%
+think I'd call with king queen suited
+but not king queen off suit and the
+
+ align:start position:0%
+but not king queen off suit and the
+ 
+
+ align:start position:0%
+but not king queen off suit and the
+smallest pair I get it in with is
+
+ align:start position:0%
+smallest pair I get it in with is
+ 
+
+ align:start position:0%
+smallest pair I get it in with is
+probably pocket sixes I think um
+
+ align:start position:0%
+probably pocket sixes I think um
+ 
+
+ align:start position:0%
+probably pocket sixes I think um
+maybe pocket F
+
+ align:start position:0%
+maybe pocket F
+ 
+
+ align:start position:0%
+maybe pocket F
+okay yeah probably pocket FES is too
+
+ align:start position:0%
+okay yeah probably pocket FES is too
+ 
+
+ align:start position:0%
+okay yeah probably pocket FES is too
+loose yeah probably pocket
+
+ align:start position:0%
+loose yeah probably pocket
+ 
+
+ align:start position:0%
+loose yeah probably pocket
+sixes so we call so unfortunately we
+
+ align:start position:0%
+sixes so we call so unfortunately we
+ 
+
+ align:start position:0%
+sixes so we call so unfortunately we
+lose to King 10 suited so he doubles up
+
+ align:start position:0%
+lose to King 10 suited so he doubles up
+ 
+
+ align:start position:0%
+lose to King 10 suited so he doubles up
+through us again and we're kind of short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now a question yeah on that last hand
+
+ align:start position:0%
+now a question yeah on that last hand
+ 
+
+ align:start position:0%
+now a question yeah on that last hand
+why go all in yourself why not just call
+
+ align:start position:0%
+why go all in yourself why not just call
+ 
+
+ align:start position:0%
+why go all in yourself why not just call
+is all in oh okay good question yeah so
+
+ align:start position:0%
+is all in oh okay good question yeah so
+ 
+
+ align:start position:0%
+is all in oh okay good question yeah so
+yeah this is a good question so in this
+
+ align:start position:0%
+yeah this is a good question so in this
+ 
+
+ align:start position:0%
+yeah this is a good question so in this
+case the two plays I'd say are are
+
+ align:start position:0%
+case the two plays I'd say are are
+ 
+
+ align:start position:0%
+case the two plays I'd say are are
+fairly close to equiv um because okay so
+
+ align:start position:0%
+fairly close to equiv um because okay so
+ 
+
+ align:start position:0%
+fairly close to equiv um because okay so
+what's the difference right they they're
+
+ align:start position:0%
+what's the difference right they they're
+ 
+
+ align:start position:0%
+what's the difference right they they're
+going to be the same most of almost
+
+ align:start position:0%
+going to be the same most of almost
+ 
+
+ align:start position:0%
+going to be the same most of almost
+always because check raise is just going
+
+ align:start position:0%
+always because check raise is just going
+ 
+
+ align:start position:0%
+always because check raise is just going
+to fold yeah um but uh right but okay so
+
+ align:start position:0%
+to fold yeah um but uh right but okay so
+ 
+
+ align:start position:0%
+to fold yeah um but uh right but okay so
+what's the difference the difference is
+
+ align:start position:0%
+what's the difference the difference is
+ 
+
+ align:start position:0%
+what's the difference the difference is
+if we don't go all in then check Rays if
+
+ align:start position:0%
+if we don't go all in then check Rays if
+ 
+
+ align:start position:0%
+if we don't go all in then check Rays if
+let's say he picks up Aces right then he
+
+ align:start position:0%
+let's say he picks up Aces right then he
+ 
+
+ align:start position:0%
+let's say he picks up Aces right then he
+can just go all in and we're basically
+
+ align:start position:0%
+can just go all in and we're basically
+ 
+
+ align:start position:0%
+can just go all in and we're basically
+forced to call him cuz we can't if we if
+
+ align:start position:0%
+forced to call him cuz we can't if we if
+ 
+
+ align:start position:0%
+forced to call him cuz we can't if we if
+we put in four
+
+ align:start position:0%
+we put in four
+ 
+
+ align:start position:0%
+we put in four
+4,118 and they go all in we can't really
+
+ align:start position:0%
+4,118 and they go all in we can't really
+ 
+
+ align:start position:0%
+4,118 and they go all in we can't really
+fold for only 3,000 more we can't really
+
+ align:start position:0%
+fold for only 3,000 more we can't really
+ 
+
+ align:start position:0%
+fold for only 3,000 more we can't really
+fold pre flop with 41 odds would that
+
+ align:start position:0%
+fold pre flop with 41 odds would that
+ 
+
+ align:start position:0%
+fold pre flop with 41 odds would that
+change if you were the big stack if like
+
+ align:start position:0%
+change if you were the big stack if like
+ 
+
+ align:start position:0%
+change if you were the big stack if like
+you had check ra a stack and he had your
+
+ align:start position:0%
+you had check ra a stack and he had your
+ 
+
+ align:start position:0%
+you had check ra a stack and he had your
+stack oh yeah for sure yeah yeah that's
+
+ align:start position:0%
+stack oh yeah for sure yeah yeah that's
+ 
+
+ align:start position:0%
+stack oh yeah for sure yeah yeah that's
+a very good point yeah yeah for sure so
+
+ align:start position:0%
+a very good point yeah yeah for sure so
+ 
+
+ align:start position:0%
+a very good point yeah yeah for sure so
+if we had the same stack as check ra
+
+ align:start position:0%
+if we had the same stack as check ra
+ 
+
+ align:start position:0%
+if we had the same stack as check ra
+here I would just call and then if check
+
+ align:start position:0%
+here I would just call and then if check
+ 
+
+ align:start position:0%
+here I would just call and then if check
+raise goes all in I would probably fold
+
+ align:start position:0%
+raise goes all in I would probably fold
+ 
+
+ align:start position:0%
+raise goes all in I would probably fold
+okay but I I mean I'm also going to call
+
+ align:start position:0%
+okay but I I mean I'm also going to call
+ 
+
+ align:start position:0%
+okay but I I mean I'm also going to call
+here with pocket aces so they can't just
+
+ align:start position:0%
+here with pocket aces so they can't just
+ 
+
+ align:start position:0%
+here with pocket aces so they can't just
+look down at pocket twos and go all in
+
+ align:start position:0%
+look down at pocket twos and go all in
+ 
+
+ align:start position:0%
+look down at pocket twos and go all in
+and Bully me around okay yeah so so my
+
+ align:start position:0%
+and Bully me around okay yeah so so my
+ 
+
+ align:start position:0%
+and Bully me around okay yeah so so my
+strategy if we had their stack would be
+
+ align:start position:0%
+strategy if we had their stack would be
+ 
+
+ align:start position:0%
+strategy if we had their stack would be
+to um would be to call my entire range
+
+ align:start position:0%
+to um would be to call my entire range
+ 
+
+ align:start position:0%
+to um would be to call my entire range
+that I plan on playing but in this case
+
+ align:start position:0%
+that I plan on playing but in this case
+ 
+
+ align:start position:0%
+that I plan on playing but in this case
+the only thing calling does is it gives
+
+ align:start position:0%
+the only thing calling does is it gives
+ 
+
+ align:start position:0%
+the only thing calling does is it gives
+him more options like let's say they had
+
+ align:start position:0%
+him more options like let's say they had
+ 
+
+ align:start position:0%
+him more options like let's say they had
+a very marginal situation like let's say
+
+ align:start position:0%
+a very marginal situation like let's say
+ 
+
+ align:start position:0%
+a very marginal situation like let's say
+they had king queen suited I think if I
+
+ align:start position:0%
+they had king queen suited I think if I
+ 
+
+ align:start position:0%
+they had king queen suited I think if I
+if I only called they could maybe argue
+
+ align:start position:0%
+if I only called they could maybe argue
+ 
+
+ align:start position:0%
+if I only called they could maybe argue
+for callings with king queen suited and
+
+ align:start position:0%
+for callings with king queen suited and
+ 
+
+ align:start position:0%
+for callings with king queen suited and
+seeing a flop whereas if I go all in I
+
+ align:start position:0%
+seeing a flop whereas if I go all in I
+ 
+
+ align:start position:0%
+seeing a flop whereas if I go all in I
+think they're forced to fold king queen
+
+ align:start position:0%
+think they're forced to fold king queen
+ 
+
+ align:start position:0%
+think they're forced to fold king queen
+basically a better chance of making him
+
+ align:start position:0%
+basically a better chance of making him
+ 
+
+ align:start position:0%
+basically a better chance of making him
+exactly yeah I'm just giving him fewer
+
+ align:start position:0%
+exactly yeah I'm just giving him fewer
+ 
+
+ align:start position:0%
+exactly yeah I'm just giving him fewer
+options but it's very very marginal like
+
+ align:start position:0%
+options but it's very very marginal like
+ 
+
+ align:start position:0%
+options but it's very very marginal like
+it affects it affects it basically
+
+ align:start position:0%
+it affects it affects it basically
+ 
+
+ align:start position:0%
+it affects it affects it basically
+specifically for maybe king queen suited
+
+ align:start position:0%
+specifically for maybe king queen suited
+ 
+
+ align:start position:0%
+specifically for maybe king queen suited
+like it affects basically for one hand
+
+ align:start position:0%
+like it affects basically for one hand
+ 
+
+ align:start position:0%
+like it affects basically for one hand
+or I don't know maybe like two or three
+
+ align:start position:0%
+or I don't know maybe like two or three
+ 
+
+ align:start position:0%
+or I don't know maybe like two or three
+hands but yeah it's very rare but um but
+
+ align:start position:0%
+hands but yeah it's very rare but um but
+ 
+
+ align:start position:0%
+hands but yeah it's very rare but um but
+you might as well minimize the options
+
+ align:start position:0%
+you might as well minimize the options
+ 
+
+ align:start position:0%
+you might as well minimize the options
+you give your opponent
+
+ align:start position:0%
+you give your opponent
+ 
+
+ align:start position:0%
+you give your opponent
+so yeah like I'd say the the minimum
+
+ align:start position:0%
+so yeah like I'd say the the minimum
+ 
+
+ align:start position:0%
+so yeah like I'd say the the minimum
+stack size I would need before I call
+
+ align:start position:0%
+stack size I would need before I call
+ 
+
+ align:start position:0%
+stack size I would need before I call
+instead of go all in with is maybe um I
+
+ align:start position:0%
+instead of go all in with is maybe um I
+ 
+
+ align:start position:0%
+instead of go all in with is maybe um I
+think maybe like 13,000 yeah I think at
+
+ align:start position:0%
+think maybe like 13,000 yeah I think at
+ 
+
+ align:start position:0%
+think maybe like 13,000 yeah I think at
+13,000 it's sort of more than I I'd want
+
+ align:start position:0%
+13,000 it's sort of more than I I'd want
+ 
+
+ align:start position:0%
+13,000 it's sort of more than I I'd want
+to risk against this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so now we're kind of short so
+
+ align:start position:0%
+yeah okay so now we're kind of short so
+ 
+
+ align:start position:0%
+yeah okay so now we're kind of short so
+we blind down for a bit we don't get
+
+ align:start position:0%
+we blind down for a bit we don't get
+ 
+
+ align:start position:0%
+we blind down for a bit we don't get
+cards and when you don't get cards in a
+
+ align:start position:0%
+cards and when you don't get cards in a
+ 
+
+ align:start position:0%
+cards and when you don't get cards in a
+tournament there's not really much you
+
+ align:start position:0%
+tournament there's not really much you
+ 
+
+ align:start position:0%
+tournament there's not really much you
+can do other than blind down not like go
+
+ align:start position:0%
+can do other than blind down not like go
+ 
+
+ align:start position:0%
+can do other than blind down not like go
+all in with crap and just lose so we
+
+ align:start position:0%
+all in with crap and just lose so we
+ 
+
+ align:start position:0%
+all in with crap and just lose so we
+blind down for a bit but we're fortunate
+
+ align:start position:0%
+blind down for a bit but we're fortunate
+ 
+
+ align:start position:0%
+blind down for a bit but we're fortunate
+to pick up Kings so this is sort of a
+
+ align:start position:0%
+to pick up Kings so this is sort of a
+ 
+
+ align:start position:0%
+to pick up Kings so this is sort of a
+no-brainer we go all in there's no point
+
+ align:start position:0%
+no-brainer we go all in there's no point
+ 
+
+ align:start position:0%
+no-brainer we go all in there's no point
+trapping because they're guaranteed to
+
+ align:start position:0%
+trapping because they're guaranteed to
+ 
+
+ align:start position:0%
+trapping because they're guaranteed to
+call us and we get called by E5 and we
+
+ align:start position:0%
+call us and we get called by E5 and we
+ 
+
+ align:start position:0%
+call us and we get called by E5 and we
+win which is good
+
+ align:start position:0%
+win which is good
+ 
+
+ align:start position:0%
+win which is good
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+so the next hand we get 87 offit and
+
+ align:start position:0%
+so the next hand we get 87 offit and
+ 
+
+ align:start position:0%
+so the next hand we get 87 offit and
+against the button raids I think calling
+
+ align:start position:0%
+against the button raids I think calling
+ 
+
+ align:start position:0%
+against the button raids I think calling
+is fine I think their range is just
+
+ align:start position:0%
+is fine I think their range is just
+ 
+
+ align:start position:0%
+is fine I think their range is just
+going to be wide enough where even
+
+ align:start position:0%
+going to be wide enough where even
+ 
+
+ align:start position:0%
+going to be wide enough where even
+though the reverse implied odds once
+
+ align:start position:0%
+though the reverse implied odds once
+ 
+
+ align:start position:0%
+though the reverse implied odds once
+again really don't work in our favor we
+
+ align:start position:0%
+again really don't work in our favor we
+ 
+
+ align:start position:0%
+again really don't work in our favor we
+just have to sort of realize the equity
+
+ align:start position:0%
+just have to sort of realize the equity
+ 
+
+ align:start position:0%
+just have to sort of realize the equity
+from four and a half to one odds so I'm
+
+ align:start position:0%
+from four and a half to one odds so I'm
+ 
+
+ align:start position:0%
+from four and a half to one odds so I'm
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+call and so we flop nothing I'm planning
+
+ align:start position:0%
+call and so we flop nothing I'm planning
+ 
+
+ align:start position:0%
+call and so we flop nothing I'm planning
+to just check fold so I check they check
+
+ align:start position:0%
+to just check fold so I check they check
+ 
+
+ align:start position:0%
+to just check fold so I check they check
+back turn as a four once again we have
+
+ align:start position:0%
+back turn as a four once again we have
+ 
+
+ align:start position:0%
+back turn as a four once again we have
+nothing I could Bluff here but I figure
+
+ align:start position:0%
+nothing I could Bluff here but I figure
+ 
+
+ align:start position:0%
+nothing I could Bluff here but I figure
+you know I'm not really looking to make
+
+ align:start position:0%
+you know I'm not really looking to make
+ 
+
+ align:start position:0%
+you know I'm not really looking to make
+a big Bluff with this hand cuz I have no
+
+ align:start position:0%
+a big Bluff with this hand cuz I have no
+ 
+
+ align:start position:0%
+a big Bluff with this hand cuz I have no
+draw no pair there's no point um but I
+
+ align:start position:0%
+draw no pair there's no point um but I
+ 
+
+ align:start position:0%
+draw no pair there's no point um but I
+will probably look to make a bluff on
+
+ align:start position:0%
+will probably look to make a bluff on
+ 
+
+ align:start position:0%
+will probably look to make a bluff on
+the river if they also check just
+
+ align:start position:0%
+the river if they also check just
+ 
+
+ align:start position:0%
+the river if they also check just
+because whenever you have like no chance
+
+ align:start position:0%
+because whenever you have like no chance
+ 
+
+ align:start position:0%
+because whenever you have like no chance
+of winning the pot then and it's the
+
+ align:start position:0%
+of winning the pot then and it's the
+ 
+
+ align:start position:0%
+of winning the pot then and it's the
+river then making a bluff is not
+
+ align:start position:0%
+river then making a bluff is not
+ 
+
+ align:start position:0%
+river then making a bluff is not
+unreasonable but in this case bluffing
+
+ align:start position:0%
+unreasonable but in this case bluffing
+ 
+
+ align:start position:0%
+unreasonable but in this case bluffing
+is kind of bad because with any club
+
+ align:start position:0%
+is kind of bad because with any club
+ 
+
+ align:start position:0%
+is kind of bad because with any club
+they might just call me because any club
+
+ align:start position:0%
+they might just call me because any club
+ 
+
+ align:start position:0%
+they might just call me because any club
+is going to have some Equity
+
+ align:start position:0%
+is going to have some Equity
+ 
+
+ align:start position:0%
+is going to have some Equity
+so so I check they check back the r is a
+
+ align:start position:0%
+so so I check they check back the r is a
+ 
+
+ align:start position:0%
+so so I check they check back the r is a
+fourth club which is I think a pretty
+
+ align:start position:0%
+fourth club which is I think a pretty
+ 
+
+ align:start position:0%
+fourth club which is I think a pretty
+good card for me um because you know I
+
+ align:start position:0%
+good card for me um because you know I
+ 
+
+ align:start position:0%
+good card for me um because you know I
+can easily represent a small club and if
+
+ align:start position:0%
+can easily represent a small club and if
+ 
+
+ align:start position:0%
+can easily represent a small club and if
+I did have a small Club I am definitely
+
+ align:start position:0%
+I did have a small Club I am definitely
+ 
+
+ align:start position:0%
+I did have a small Club I am definitely
+value betting so you know it's a pretty
+
+ align:start position:0%
+value betting so you know it's a pretty
+ 
+
+ align:start position:0%
+value betting so you know it's a pretty
+good card for me to Bluff and they're
+
+ align:start position:0%
+good card for me to Bluff and they're
+ 
+
+ align:start position:0%
+good card for me to Bluff and they're
+probably going to have to fold King High
+
+ align:start position:0%
+probably going to have to fold King High
+ 
+
+ align:start position:0%
+probably going to have to fold King High
+so so I bet and I don't think I have to
+
+ align:start position:0%
+so so I bet and I don't think I have to
+ 
+
+ align:start position:0%
+so so I bet and I don't think I have to
+bet fairly big you know I I'm just
+
+ align:start position:0%
+bet fairly big you know I I'm just
+ 
+
+ align:start position:0%
+bet fairly big you know I I'm just
+looking for a size where they have to
+
+ align:start position:0%
+looking for a size where they have to
+ 
+
+ align:start position:0%
+looking for a size where they have to
+fold sometimes and they'll have to pay
+
+ align:start position:0%
+fold sometimes and they'll have to pay
+ 
+
+ align:start position:0%
+fold sometimes and they'll have to pay
+me off sometimes when I have to have a
+
+ align:start position:0%
+me off sometimes when I have to have a
+ 
+
+ align:start position:0%
+me off sometimes when I have to have a
+when I have a small club and so they
+
+ align:start position:0%
+when I have a small club and so they
+ 
+
+ align:start position:0%
+when I have a small club and so they
+raise me here which is which is pretty
+
+ align:start position:0%
+raise me here which is which is pretty
+ 
+
+ align:start position:0%
+raise me here which is which is pretty
+weird I don't really I still don't
+
+ align:start position:0%
+weird I don't really I still don't
+ 
+
+ align:start position:0%
+weird I don't really I still don't
+really have a good idea what I think he
+
+ align:start position:0%
+really have a good idea what I think he
+ 
+
+ align:start position:0%
+really have a good idea what I think he
+has um I mean I'm certain they have me
+
+ align:start position:0%
+has um I mean I'm certain they have me
+ 
+
+ align:start position:0%
+has um I mean I'm certain they have me
+beat you know so I I just folded like
+
+ align:start position:0%
+beat you know so I I just folded like
+ 
+
+ align:start position:0%
+beat you know so I I just folded like
+you know we could think a bit about
+
+ align:start position:0%
+you know we could think a bit about
+ 
+
+ align:start position:0%
+you know we could think a bit about
+doing something crazy like go all in but
+
+ align:start position:0%
+doing something crazy like go all in but
+ 
+
+ align:start position:0%
+doing something crazy like go all in but
+it would just be weird I I think it's
+
+ align:start position:0%
+it would just be weird I I think it's
+ 
+
+ align:start position:0%
+it would just be weird I I think it's
+unnecessary you know we've got nothing
+
+ align:start position:0%
+unnecessary you know we've got nothing
+ 
+
+ align:start position:0%
+unnecessary you know we've got nothing
+so I just folded yeah I don't really
+
+ align:start position:0%
+so I just folded yeah I don't really
+ 
+
+ align:start position:0%
+so I just folded yeah I don't really
+know maybe they just had like a slow
+
+ align:start position:0%
+know maybe they just had like a slow
+ 
+
+ align:start position:0%
+know maybe they just had like a slow
+played flush it's possible they have
+
+ align:start position:0%
+played flush it's possible they have
+ 
+
+ align:start position:0%
+played flush it's possible they have
+like a king High flush here and they
+
+ align:start position:0%
+like a king High flush here and they
+ 
+
+ align:start position:0%
+like a king High flush here and they
+slow played the Flop they decided to
+
+ align:start position:0%
+slow played the Flop they decided to
+ 
+
+ align:start position:0%
+slow played the Flop they decided to
+slow play the turn again because the
+
+ align:start position:0%
+slow play the turn again because the
+ 
+
+ align:start position:0%
+slow play the turn again because the
+turn sort of didn't hit anybody um yeah
+
+ align:start position:0%
+turn sort of didn't hit anybody um yeah
+ 
+
+ align:start position:0%
+turn sort of didn't hit anybody um yeah
+I'm not sure so i f here I mean it's
+
+ align:start position:0%
+I'm not sure so i f here I mean it's
+ 
+
+ align:start position:0%
+I'm not sure so i f here I mean it's
+possible they just had a high club but I
+
+ align:start position:0%
+possible they just had a high club but I
+ 
+
+ align:start position:0%
+possible they just had a high club but I
+feel like with a high club they should
+
+ align:start position:0%
+feel like with a high club they should
+ 
+
+ align:start position:0%
+feel like with a high club they should
+have bet at some point to sort of just
+
+ align:start position:0%
+have bet at some point to sort of just
+ 
+
+ align:start position:0%
+have bet at some point to sort of just
+because the a good flush straw is just
+
+ align:start position:0%
+because the a good flush straw is just
+ 
+
+ align:start position:0%
+because the a good flush straw is just
+has enough equity but nonetheless I
+
+ align:start position:0%
+has enough equity but nonetheless I
+ 
+
+ align:start position:0%
+has enough equity but nonetheless I
+guess we'll never know that's one
+
+ align:start position:0%
+guess we'll never know that's one
+ 
+
+ align:start position:0%
+guess we'll never know that's one
+benefit of calling you get to find out
+
+ align:start position:0%
+benefit of calling you get to find out
+ 
+
+ align:start position:0%
+benefit of calling you get to find out
+what your opponent had um okay so the
+
+ align:start position:0%
+what your opponent had um okay so the
+ 
+
+ align:start position:0%
+what your opponent had um okay so the
+next time we have Queen Jack we've got
+
+ align:start position:0%
+next time we have Queen Jack we've got
+ 
+
+ align:start position:0%
+next time we have Queen Jack we've got
+12 bets I just go all in 12 is around
+
+ align:start position:0%
+12 bets I just go all in 12 is around
+ 
+
+ align:start position:0%
+12 bets I just go all in 12 is around
+the cut off of right like I said 12 is
+
+ align:start position:0%
+the cut off of right like I said 12 is
+ 
+
+ align:start position:0%
+the cut off of right like I said 12 is
+sort of the cut off where if you have 12
+
+ align:start position:0%
+sort of the cut off where if you have 12
+ 
+
+ align:start position:0%
+sort of the cut off where if you have 12
+bets or less instead of raising just go
+
+ align:start position:0%
+bets or less instead of raising just go
+ 
+
+ align:start position:0%
+bets or less instead of raising just go
+all in
+
+ align:start position:0%
+all in
+ 
+
+ align:start position:0%
+all in
+and that's what we do so we get called
+
+ align:start position:0%
+and that's what we do so we get called
+ 
+
+ align:start position:0%
+and that's what we do so we get called
+but so this is actually a pretty sick
+
+ align:start position:0%
+but so this is actually a pretty sick
+ 
+
+ align:start position:0%
+but so this is actually a pretty sick
+board yeah so they cled a full house but
+
+ align:start position:0%
+board yeah so they cled a full house but
+ 
+
+ align:start position:0%
+board yeah so they cled a full house but
+we rered a higher Full
+
+ align:start position:0%
+we rered a higher Full
+ 
+
+ align:start position:0%
+we rered a higher Full
+House it was yeah it's sort of a waste
+
+ align:start position:0%
+House it was yeah it's sort of a waste
+ 
+
+ align:start position:0%
+House it was yeah it's sort of a waste
+because you know normally if this
+
+ align:start position:0%
+because you know normally if this
+ 
+
+ align:start position:0%
+because you know normally if this
+happens you could win like a 100 big
+
+ align:start position:0%
+happens you could win like a 100 big
+ 
+
+ align:start position:0%
+happens you could win like a 100 big
+blinds from them probably but instead we
+
+ align:start position:0%
+blinds from them probably but instead we
+ 
+
+ align:start position:0%
+blinds from them probably but instead we
+only want how many uh eight big blinds
+
+ align:start position:0%
+only want how many uh eight big blinds
+ 
+
+ align:start position:0%
+only want how many uh eight big blinds
+so it's sort of a waste but whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so the next hand I got pocket
+
+ align:start position:0%
+um okay so the next hand I got pocket
+ 
+
+ align:start position:0%
+um okay so the next hand I got pocket
+fives and we raised to we raised to a
+
+ align:start position:0%
+fives and we raised to we raised to a
+ 
+
+ align:start position:0%
+fives and we raised to we raised to a
+thousand and Liam kid goes on again and
+
+ align:start position:0%
+thousand and Liam kid goes on again and
+ 
+
+ align:start position:0%
+thousand and Liam kid goes on again and
+you know it's irritating but I think
+
+ align:start position:0%
+you know it's irritating but I think
+ 
+
+ align:start position:0%
+you know it's irritating but I think
+once again I have to fold it's I think
+
+ align:start position:0%
+once again I have to fold it's I think
+ 
+
+ align:start position:0%
+once again I have to fold it's I think
+I'm just I don't have enough equity to
+
+ align:start position:0%
+I'm just I don't have enough equity to
+ 
+
+ align:start position:0%
+I'm just I don't have enough equity to
+call like given his range um once again
+
+ align:start position:0%
+call like given his range um once again
+ 
+
+ align:start position:0%
+call like given his range um once again
+it's a situation where it's a fairly big
+
+ align:start position:0%
+it's a situation where it's a fairly big
+ 
+
+ align:start position:0%
+it's a situation where it's a fairly big
+all- in so you know I could maybe not
+
+ align:start position:0%
+all- in so you know I could maybe not
+ 
+
+ align:start position:0%
+all- in so you know I could maybe not
+put them on Aces although given that
+
+ align:start position:0%
+put them on Aces although given that
+ 
+
+ align:start position:0%
+put them on Aces although given that
+they've done this once they're more
+
+ align:start position:0%
+they've done this once they're more
+ 
+
+ align:start position:0%
+they've done this once they're more
+likely to just do this with their entire
+
+ align:start position:0%
+likely to just do this with their entire
+ 
+
+ align:start position:0%
+likely to just do this with their entire
+range and play a strategy where they're
+
+ align:start position:0%
+range and play a strategy where they're
+ 
+
+ align:start position:0%
+range and play a strategy where they're
+just going on pre- flop a lot so maybe
+
+ align:start position:0%
+just going on pre- flop a lot so maybe
+ 
+
+ align:start position:0%
+just going on pre- flop a lot so maybe
+they could have aces in their range but
+
+ align:start position:0%
+they could have aces in their range but
+ 
+
+ align:start position:0%
+they could have aces in their range but
+nonetheless regardless I think it's not
+
+ align:start position:0%
+nonetheless regardless I think it's not
+ 
+
+ align:start position:0%
+nonetheless regardless I think it's not
+even that close I just R um yeah we
+
+ align:start position:0%
+even that close I just R um yeah we
+ 
+
+ align:start position:0%
+even that close I just R um yeah we
+don't really want to call in frustration
+
+ align:start position:0%
+don't really want to call in frustration
+ 
+
+ align:start position:0%
+don't really want to call in frustration
+cuz you saw what happened to the guy
+
+ align:start position:0%
+cuz you saw what happened to the guy
+ 
+
+ align:start position:0%
+cuz you saw what happened to the guy
+with pocket sevens when they B into our
+
+ align:start position:0%
+with pocket sevens when they B into our
+ 
+
+ align:start position:0%
+with pocket sevens when they B into our
+pocket Jacks in the earlier
+
+ align:start position:0%
+pocket Jacks in the earlier
+ 
+
+ align:start position:0%
+pocket Jacks in the earlier
+hand uh okay so I'll take a short break
+
+ align:start position:0%
+hand uh okay so I'll take a short break
+ 
+
+ align:start position:0%
+hand uh okay so I'll take a short break
+there and then I'll finish up the rest
+
+ align:start position:0%
+there and then I'll finish up the rest
+ 
+
+ align:start position:0%
+there and then I'll finish up the rest
+of the hands in like two minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh okay so I'm going to get started
+
+ align:start position:0%
+yeah uh okay so I'm going to get started
+ 
+
+ align:start position:0%
+yeah uh okay so I'm going to get started
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay so so okay so the next hand we get
+
+ align:start position:0%
+okay so so okay so the next hand we get
+ 
+
+ align:start position:0%
+okay so so okay so the next hand we get
+we get King ad off suit and once again
+
+ align:start position:0%
+we get King ad off suit and once again
+ 
+
+ align:start position:0%
+we get King ad off suit and once again
+it's one of these situations where you
+
+ align:start position:0%
+it's one of these situations where you
+ 
+
+ align:start position:0%
+it's one of these situations where you
+know we're not thrilled to be calling
+
+ align:start position:0%
+know we're not thrilled to be calling
+ 
+
+ align:start position:0%
+know we're not thrilled to be calling
+especially now that our odds are even a
+
+ align:start position:0%
+especially now that our odds are even a
+ 
+
+ align:start position:0%
+especially now that our odds are even a
+bit worse cuz they actually made it
+
+ align:start position:0%
+bit worse cuz they actually made it
+ 
+
+ align:start position:0%
+bit worse cuz they actually made it
+2.25x actually a bit more like 2. 35x
+
+ align:start position:0%
+2.25x actually a bit more like 2. 35x
+ 
+
+ align:start position:0%
+2.25x actually a bit more like 2. 35x
+instead of uh 2x so against degenerated
+
+ align:start position:0%
+instead of uh 2x so against degenerated
+ 
+
+ align:start position:0%
+instead of uh 2x so against degenerated
+but I King a off suit two big cards I
+
+ align:start position:0%
+but I King a off suit two big cards I
+ 
+
+ align:start position:0%
+but I King a off suit two big cards I
+think with when we're sort of not that
+
+ align:start position:0%
+think with when we're sort of not that
+ 
+
+ align:start position:0%
+think with when we're sort of not that
+deep the rius and pli ODS don't work
+
+ align:start position:0%
+deep the rius and pli ODS don't work
+ 
+
+ align:start position:0%
+deep the rius and pli ODS don't work
+against us that much so so we
+
+ align:start position:0%
+against us that much so so we
+ 
+
+ align:start position:0%
+against us that much so so we
+call and we got a
+
+ align:start position:0%
+call and we got a
+ 
+
+ align:start position:0%
+call and we got a
+good so we check cuz once again I'm I'm
+
+ align:start position:0%
+good so we check cuz once again I'm I'm
+ 
+
+ align:start position:0%
+good so we check cuz once again I'm I'm
+checking my entire range that's how I
+
+ align:start position:0%
+checking my entire range that's how I
+ 
+
+ align:start position:0%
+checking my entire range that's how I
+choose to play my strategy and they bet
+
+ align:start position:0%
+choose to play my strategy and they bet
+ 
+
+ align:start position:0%
+choose to play my strategy and they bet
+and so this is sort of I think uh I
+
+ align:start position:0%
+and so this is sort of I think uh I
+ 
+
+ align:start position:0%
+and so this is sort of I think uh I
+think this is a somewhat close situation
+
+ align:start position:0%
+think this is a somewhat close situation
+ 
+
+ align:start position:0%
+think this is a somewhat close situation
+because I think um there are some draws
+
+ align:start position:0%
+because I think um there are some draws
+ 
+
+ align:start position:0%
+because I think um there are some draws
+right there is a flush draw and there
+
+ align:start position:0%
+right there is a flush draw and there
+ 
+
+ align:start position:0%
+right there is a flush draw and there
+are a bunch of straight draws if you if
+
+ align:start position:0%
+are a bunch of straight draws if you if
+ 
+
+ align:start position:0%
+are a bunch of straight draws if you if
+someone has Jack 10 or queen Jack or
+
+ align:start position:0%
+someone has Jack 10 or queen Jack or
+ 
+
+ align:start position:0%
+someone has Jack 10 or queen Jack or
+queen 10 so do think there is a decent
+
+ align:start position:0%
+queen 10 so do think there is a decent
+ 
+
+ align:start position:0%
+queen 10 so do think there is a decent
+amount of incentive to just check raise
+
+ align:start position:0%
+amount of incentive to just check raise
+ 
+
+ align:start position:0%
+amount of incentive to just check raise
+all in right so in the second lecture I
+
+ align:start position:0%
+all in right so in the second lecture I
+ 
+
+ align:start position:0%
+all in right so in the second lecture I
+showed you a bunch of examples where on
+
+ align:start position:0%
+showed you a bunch of examples where on
+ 
+
+ align:start position:0%
+showed you a bunch of examples where on
+boards like this you can check risol
+
+ align:start position:0%
+boards like this you can check risol
+ 
+
+ align:start position:0%
+boards like this you can check risol
+with your good hands and check risol
+
+ align:start position:0%
+with your good hands and check risol
+ 
+
+ align:start position:0%
+with your good hands and check risol
+with your draws and it's a pretty
+
+ align:start position:0%
+with your draws and it's a pretty
+ 
+
+ align:start position:0%
+with your draws and it's a pretty
+balanced strategy um because when you
+
+ align:start position:0%
+balanced strategy um because when you
+ 
+
+ align:start position:0%
+balanced strategy um because when you
+have a good hand you have a good hand
+
+ align:start position:0%
+have a good hand you have a good hand
+ 
+
+ align:start position:0%
+have a good hand you have a good hand
+and when you have a draw you have lots
+
+ align:start position:0%
+and when you have a draw you have lots
+ 
+
+ align:start position:0%
+and when you have a draw you have lots
+of outs when you get called um but in
+
+ align:start position:0%
+of outs when you get called um but in
+ 
+
+ align:start position:0%
+of outs when you get called um but in
+this and another advantage of going all
+
+ align:start position:0%
+this and another advantage of going all
+ 
+
+ align:start position:0%
+this and another advantage of going all
+in is let's say I had like let's say I
+
+ align:start position:0%
+in is let's say I had like let's say I
+ 
+
+ align:start position:0%
+in is let's say I had like let's say I
+had like 109 I would probably want to be
+
+ align:start position:0%
+had like 109 I would probably want to be
+ 
+
+ align:start position:0%
+had like 109 I would probably want to be
+raising because with 109 even though we
+
+ align:start position:0%
+raising because with 109 even though we
+ 
+
+ align:start position:0%
+raising because with 109 even though we
+have a pretty good hand we kind of sort
+
+ align:start position:0%
+have a pretty good hand we kind of sort
+ 
+
+ align:start position:0%
+have a pretty good hand we kind of sort
+of want to protect our hand right we
+
+ align:start position:0%
+of want to protect our hand right we
+ 
+
+ align:start position:0%
+of want to protect our hand right we
+don't really want a jack a queen or an
+
+ align:start position:0%
+don't really want a jack a queen or an
+ 
+
+ align:start position:0%
+don't really want a jack a queen or an
+ace to come that much so it's close but
+
+ align:start position:0%
+ace to come that much so it's close but
+ 
+
+ align:start position:0%
+ace to come that much so it's close but
+um but in the end I decided to call and
+
+ align:start position:0%
+um but in the end I decided to call and
+ 
+
+ align:start position:0%
+um but in the end I decided to call and
+I think I and I think I decided I'm just
+
+ align:start position:0%
+I think I and I think I decided I'm just
+ 
+
+ align:start position:0%
+I think I and I think I decided I'm just
+going to play pretty close pretty much
+
+ align:start position:0%
+going to play pretty close pretty much
+ 
+
+ align:start position:0%
+going to play pretty close pretty much
+my entire strategy I'm just going to
+
+ align:start position:0%
+my entire strategy I'm just going to
+ 
+
+ align:start position:0%
+my entire strategy I'm just going to
+call here um as tempting as it is like
+
+ align:start position:0%
+call here um as tempting as it is like
+ 
+
+ align:start position:0%
+call here um as tempting as it is like
+let's say I had I had uh Ace two of
+
+ align:start position:0%
+let's say I had I had uh Ace two of
+ 
+
+ align:start position:0%
+let's say I had I had uh Ace two of
+diamonds or let's say like Queen six of
+
+ align:start position:0%
+diamonds or let's say like Queen six of
+ 
+
+ align:start position:0%
+diamonds or let's say like Queen six of
+diamonds to check raise on I think it's
+
+ align:start position:0%
+diamonds to check raise on I think it's
+ 
+
+ align:start position:0%
+diamonds to check raise on I think it's
+a board where you know there it's
+
+ align:start position:0%
+a board where you know there it's
+ 
+
+ align:start position:0%
+a board where you know there it's
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+and if I have a flush draw I still have
+
+ align:start position:0%
+and if I have a flush draw I still have
+ 
+
+ align:start position:0%
+and if I have a flush draw I still have
+lots of opportunities to Bluff on the
+
+ align:start position:0%
+lots of opportunities to Bluff on the
+ 
+
+ align:start position:0%
+lots of opportunities to Bluff on the
+river and if I have a good hand there's
+
+ align:start position:0%
+river and if I have a good hand there's
+ 
+
+ align:start position:0%
+river and if I have a good hand there's
+not that many outs and especially when I
+
+ align:start position:0%
+not that many outs and especially when I
+ 
+
+ align:start position:0%
+not that many outs and especially when I
+have a king so I'm just going to call
+
+ align:start position:0%
+have a king so I'm just going to call
+ 
+
+ align:start position:0%
+have a king so I'm just going to call
+and hope that the board comes out well
+
+ align:start position:0%
+and hope that the board comes out well
+ 
+
+ align:start position:0%
+and hope that the board comes out well
+which I guess it
+
+ align:start position:0%
+which I guess it
+ 
+
+ align:start position:0%
+which I guess it
+does so so I check again because this is
+
+ align:start position:0%
+does so so I check again because this is
+ 
+
+ align:start position:0%
+does so so I check again because this is
+how I'm playing Jack 10 this is how I'm
+
+ align:start position:0%
+how I'm playing Jack 10 this is how I'm
+ 
+
+ align:start position:0%
+how I'm playing Jack 10 this is how I'm
+playing all my hands essentially so they
+
+ align:start position:0%
+playing all my hands essentially so they
+ 
+
+ align:start position:0%
+playing all my hands essentially so they
+check back the river is kind of bad for
+
+ align:start position:0%
+check back the river is kind of bad for
+ 
+
+ align:start position:0%
+check back the river is kind of bad for
+us but I think it's hard for them to
+
+ align:start position:0%
+us but I think it's hard for them to
+ 
+
+ align:start position:0%
+us but I think it's hard for them to
+have a king at this point so I just bet
+
+ align:start position:0%
+have a king at this point so I just bet
+ 
+
+ align:start position:0%
+have a king at this point so I just bet
+out uh about a bit more than half a pot
+
+ align:start position:0%
+out uh about a bit more than half a pot
+ 
+
+ align:start position:0%
+out uh about a bit more than half a pot
+maybe 60% of pot yeah 60% and and they
+
+ align:start position:0%
+maybe 60% of pot yeah 60% and and they
+ 
+
+ align:start position:0%
+maybe 60% of pot yeah 60% and and they
+oh so they actually call me with A7
+
+ align:start position:0%
+oh so they actually call me with A7
+ 
+
+ align:start position:0%
+oh so they actually call me with A7
+which I think is pretty reasonable like
+
+ align:start position:0%
+which I think is pretty reasonable like
+ 
+
+ align:start position:0%
+which I think is pretty reasonable like
+I think A7 is a fine call against my
+
+ align:start position:0%
+I think A7 is a fine call against my
+ 
+
+ align:start position:0%
+I think A7 is a fine call against my
+strategy um because I could have easily
+
+ align:start position:0%
+strategy um because I could have easily
+ 
+
+ align:start position:0%
+strategy um because I could have easily
+had Jack 10 or queen 10 or queen Jack
+
+ align:start position:0%
+had Jack 10 or queen 10 or queen Jack
+ 
+
+ align:start position:0%
+had Jack 10 or queen 10 or queen Jack
+here um although I probably also play a
+
+ align:start position:0%
+here um although I probably also play a
+ 
+
+ align:start position:0%
+here um although I probably also play a
+nine the same way so they are also
+
+ align:start position:0%
+nine the same way so they are also
+ 
+
+ align:start position:0%
+nine the same way so they are also
+paying off my
+
+ align:start position:0%
+paying off my
+ 
+
+ align:start position:0%
+paying off my
+nines and so one good thing actually so
+
+ align:start position:0%
+nines and so one good thing actually so
+ 
+
+ align:start position:0%
+nines and so one good thing actually so
+this is one uh interesting thing to
+
+ align:start position:0%
+this is one uh interesting thing to
+ 
+
+ align:start position:0%
+this is one uh interesting thing to
+think about that's sort of advanced but
+
+ align:start position:0%
+think about that's sort of advanced but
+ 
+
+ align:start position:0%
+think about that's sort of advanced but
+I think it's cool is the fact that they
+
+ align:start position:0%
+I think it's cool is the fact that they
+ 
+
+ align:start position:0%
+I think it's cool is the fact that they
+have A7 I think makes their call a lot
+
+ align:start position:0%
+have A7 I think makes their call a lot
+ 
+
+ align:start position:0%
+have A7 I think makes their call a lot
+better than if they had say ace 10 or
+
+ align:start position:0%
+better than if they had say ace 10 or
+ 
+
+ align:start position:0%
+better than if they had say ace 10 or
+Ace Jack and the reason for so even
+
+ align:start position:0%
+Ace Jack and the reason for so even
+ 
+
+ align:start position:0%
+Ace Jack and the reason for so even
+though ace7 is in some sense a worse
+
+ align:start position:0%
+though ace7 is in some sense a worse
+ 
+
+ align:start position:0%
+though ace7 is in some sense a worse
+hand than Ace 10 and Ace Jack they're
+
+ align:start position:0%
+hand than Ace 10 and Ace Jack they're
+ 
+
+ align:start position:0%
+hand than Ace 10 and Ace Jack they're
+they're the same on this board and I
+
+ align:start position:0%
+they're the same on this board and I
+ 
+
+ align:start position:0%
+they're the same on this board and I
+think it's a the the problem with Ace 10
+
+ align:start position:0%
+think it's a the the problem with Ace 10
+ 
+
+ align:start position:0%
+think it's a the the problem with Ace 10
+and Ace Jack is if they have a 10 or a
+
+ align:start position:0%
+and Ace Jack is if they have a 10 or a
+ 
+
+ align:start position:0%
+and Ace Jack is if they have a 10 or a
+Jack it's less likely I have a 10 or a
+
+ align:start position:0%
+Jack it's less likely I have a 10 or a
+ 
+
+ align:start position:0%
+Jack it's less likely I have a 10 or a
+Jack so you know cuz when they're
+
+ align:start position:0%
+Jack so you know cuz when they're
+ 
+
+ align:start position:0%
+Jack so you know cuz when they're
+calling with A7 essentially what they're
+
+ align:start position:0%
+calling with A7 essentially what they're
+ 
+
+ align:start position:0%
+calling with A7 essentially what they're
+hoping for is Hing for me to have Jack
+
+ align:start position:0%
+hoping for is Hing for me to have Jack
+ 
+
+ align:start position:0%
+hoping for is Hing for me to have Jack
+10 or queen 10 or queen Jack so if they
+
+ align:start position:0%
+10 or queen 10 or queen Jack so if they
+ 
+
+ align:start position:0%
+10 or queen 10 or queen Jack so if they
+have a ten or or Jack it just decreases
+
+ align:start position:0%
+have a ten or or Jack it just decreases
+ 
+
+ align:start position:0%
+have a ten or or Jack it just decreases
+that chance so it's almost like A7 is a
+
+ align:start position:0%
+that chance so it's almost like A7 is a
+ 
+
+ align:start position:0%
+that chance so it's almost like A7 is a
+better hand to call with an ace Jack so
+
+ align:start position:0%
+better hand to call with an ace Jack so
+ 
+
+ align:start position:0%
+better hand to call with an ace Jack so
+but nonetheless you know with any Ace I
+
+ align:start position:0%
+but nonetheless you know with any Ace I
+ 
+
+ align:start position:0%
+but nonetheless you know with any Ace I
+think calling here is reasonable cuz I
+
+ align:start position:0%
+think calling here is reasonable cuz I
+ 
+
+ align:start position:0%
+think calling here is reasonable cuz I
+do have plenty of Bluffs any Miss
+
+ align:start position:0%
+do have plenty of Bluffs any Miss
+ 
+
+ align:start position:0%
+do have plenty of Bluffs any Miss
+straight draw any Miss plus draw I will
+
+ align:start position:0%
+straight draw any Miss plus draw I will
+ 
+
+ align:start position:0%
+straight draw any Miss plus draw I will
+Bluff in the same way on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rer okay uh so the next hand so we yeah
+
+ align:start position:0%
+rer okay uh so the next hand so we yeah
+ 
+
+ align:start position:0%
+rer okay uh so the next hand so we yeah
+we won a bunch of pots which is nice so
+
+ align:start position:0%
+we won a bunch of pots which is nice so
+ 
+
+ align:start position:0%
+we won a bunch of pots which is nice so
+we we built our stack up so we got
+
+ align:start position:0%
+we we built our stack up so we got
+ 
+
+ align:start position:0%
+we we built our stack up so we got
+pocket Forest here and this guy raises
+
+ align:start position:0%
+pocket Forest here and this guy raises
+ 
+
+ align:start position:0%
+pocket Forest here and this guy raises
+it to 12200 pocket 4S is definitely a
+
+ align:start position:0%
+it to 12200 pocket 4S is definitely a
+ 
+
+ align:start position:0%
+it to 12200 pocket 4S is definitely a
+hand where I want to be Bluff re raising
+
+ align:start position:0%
+hand where I want to be Bluff re raising
+ 
+
+ align:start position:0%
+hand where I want to be Bluff re raising
+with so I'm not you know I'm not hoping
+
+ align:start position:0%
+with so I'm not you know I'm not hoping
+ 
+
+ align:start position:0%
+with so I'm not you know I'm not hoping
+to get called when I race here but it's
+
+ align:start position:0%
+to get called when I race here but it's
+ 
+
+ align:start position:0%
+to get called when I race here but it's
+a hand that does quite well against the
+
+ align:start position:0%
+a hand that does quite well against the
+ 
+
+ align:start position:0%
+a hand that does quite well against the
+range of hands I get called by because a
+
+ align:start position:0%
+range of hands I get called by because a
+ 
+
+ align:start position:0%
+range of hands I get called by because a
+lot of times it'll just be Ace King Ace
+
+ align:start position:0%
+lot of times it'll just be Ace King Ace
+ 
+
+ align:start position:0%
+lot of times it'll just be Ace King Ace
+Queen and and and they will fold quite a
+
+ align:start position:0%
+Queen and and and they will fold quite a
+ 
+
+ align:start position:0%
+Queen and and and they will fold quite a
+large percent of the time so I
+
+ align:start position:0%
+large percent of the time so I
+ 
+
+ align:start position:0%
+large percent of the time so I
+definitely want to raise the only
+
+ align:start position:0%
+definitely want to raise the only
+ 
+
+ align:start position:0%
+definitely want to raise the only
+question is how do I raise right I could
+
+ align:start position:0%
+question is how do I raise right I could
+ 
+
+ align:start position:0%
+question is how do I raise right I could
+just go all in which has the benefit
+
+ align:start position:0%
+just go all in which has the benefit
+ 
+
+ align:start position:0%
+just go all in which has the benefit
+that they can't call and try to hit a
+
+ align:start position:0%
+that they can't call and try to hit a
+ 
+
+ align:start position:0%
+that they can't call and try to hit a
+pair cuz that would actually be bad like
+
+ align:start position:0%
+pair cuz that would actually be bad like
+ 
+
+ align:start position:0%
+pair cuz that would actually be bad like
+let's say I made it let's say I only re
+
+ align:start position:0%
+let's say I made it let's say I only re
+ 
+
+ align:start position:0%
+let's say I made it let's say I only re
+raised to 3,000 here it's actually kind
+
+ align:start position:0%
+raised to 3,000 here it's actually kind
+ 
+
+ align:start position:0%
+raised to 3,000 here it's actually kind
+of bad if this guy calls with this queen
+
+ align:start position:0%
+of bad if this guy calls with this queen
+ 
+
+ align:start position:0%
+of bad if this guy calls with this queen
+Jack trying to hit a pair because that's
+
+ align:start position:0%
+Jack trying to hit a pair because that's
+ 
+
+ align:start position:0%
+Jack trying to hit a pair because that's
+actually the best strategy that their
+
+ align:start position:0%
+actually the best strategy that their
+ 
+
+ align:start position:0%
+actually the best strategy that their
+basically their obvious strategy is good
+
+ align:start position:0%
+basically their obvious strategy is good
+ 
+
+ align:start position:0%
+basically their obvious strategy is good
+against my hand so I want to either go
+
+ align:start position:0%
+against my hand so I want to either go
+ 
+
+ align:start position:0%
+against my hand so I want to either go
+all in which sort of denies them that
+
+ align:start position:0%
+all in which sort of denies them that
+ 
+
+ align:start position:0%
+all in which sort of denies them that
+opportunity or um or I could but the
+
+ align:start position:0%
+opportunity or um or I could but the
+ 
+
+ align:start position:0%
+opportunity or um or I could but the
+problem with going all in is let's
+
+ align:start position:0%
+problem with going all in is let's
+ 
+
+ align:start position:0%
+problem with going all in is let's
+suppose check raise picks up a hand
+
+ align:start position:0%
+suppose check raise picks up a hand
+ 
+
+ align:start position:0%
+suppose check raise picks up a hand
+right then I'm going to be losing with
+
+ align:start position:0%
+right then I'm going to be losing with
+ 
+
+ align:start position:0%
+right then I'm going to be losing with
+my pocket Force so you know there is
+
+ align:start position:0%
+my pocket Force so you know there is
+ 
+
+ align:start position:0%
+my pocket Force so you know there is
+this delicate balance here and this is
+
+ align:start position:0%
+this delicate balance here and this is
+ 
+
+ align:start position:0%
+this delicate balance here and this is
+why um in this is why I think
+
+ align:start position:0%
+why um in this is why I think
+ 
+
+ align:start position:0%
+why um in this is why I think
+tournaments are interesting because you
+
+ align:start position:0%
+tournaments are interesting because you
+ 
+
+ align:start position:0%
+tournaments are interesting because you
+know there's plays that are good against
+
+ align:start position:0%
+know there's plays that are good against
+ 
+
+ align:start position:0%
+know there's plays that are good against
+big stacks and plays that are good
+
+ align:start position:0%
+big stacks and plays that are good
+ 
+
+ align:start position:0%
+big stacks and plays that are good
+against small Stacks but in reality in a
+
+ align:start position:0%
+against small Stacks but in reality in a
+ 
+
+ align:start position:0%
+against small Stacks but in reality in a
+tournament there's going to be big
+
+ align:start position:0%
+tournament there's going to be big
+ 
+
+ align:start position:0%
+tournament there's going to be big
+stacks and small Stacks at the table and
+
+ align:start position:0%
+stacks and small Stacks at the table and
+ 
+
+ align:start position:0%
+stacks and small Stacks at the table and
+often you do have to compromise between
+
+ align:start position:0%
+often you do have to compromise between
+ 
+
+ align:start position:0%
+often you do have to compromise between
+the lesser of two evils and that's sort
+
+ align:start position:0%
+the lesser of two evils and that's sort
+ 
+
+ align:start position:0%
+the lesser of two evils and that's sort
+of what I do here so I decid to raise
+
+ align:start position:0%
+of what I do here so I decid to raise
+ 
+
+ align:start position:0%
+of what I do here so I decid to raise
+this 3600 which is bigger than I'd
+
+ align:start position:0%
+this 3600 which is bigger than I'd
+ 
+
+ align:start position:0%
+this 3600 which is bigger than I'd
+usually make it usually I'd make it
+
+ align:start position:0%
+usually make it usually I'd make it
+ 
+
+ align:start position:0%
+usually make it usually I'd make it
+maybe like 3,000 but when this guy is
+
+ align:start position:0%
+maybe like 3,000 but when this guy is
+ 
+
+ align:start position:0%
+maybe like 3,000 but when this guy is
+this short
+
+ align:start position:0%
+this short
+ 
+
+ align:start position:0%
+this short
+uh rawful L boom I um I don't really
+
+ align:start position:0%
+uh rawful L boom I um I don't really
+ 
+
+ align:start position:0%
+uh rawful L boom I um I don't really
+want to let them just call but uh on the
+
+ align:start position:0%
+want to let them just call but uh on the
+ 
+
+ align:start position:0%
+want to let them just call but uh on the
+other hand I want to be able to fold if
+
+ align:start position:0%
+other hand I want to be able to fold if
+ 
+
+ align:start position:0%
+other hand I want to be able to fold if
+one of these two guys cheze ra or vamson
+
+ align:start position:0%
+one of these two guys cheze ra or vamson
+ 
+
+ align:start position:0%
+one of these two guys cheze ra or vamson
+picks up a hand so I sort of compromise
+
+ align:start position:0%
+picks up a hand so I sort of compromise
+ 
+
+ align:start position:0%
+picks up a hand so I sort of compromise
+between making it 3600 they both fold
+
+ align:start position:0%
+between making it 3600 they both fold
+ 
+
+ align:start position:0%
+between making it 3600 they both fold
+and this guy also folds which is I guess
+
+ align:start position:0%
+and this guy also folds which is I guess
+ 
+
+ align:start position:0%
+and this guy also folds which is I guess
+an ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result okay the next hand we have a
+
+ align:start position:0%
+result okay the next hand we have a
+ 
+
+ align:start position:0%
+result okay the next hand we have a
+queen offit and we make it 1,600
+
+ align:start position:0%
+queen offit and we make it 1,600
+ 
+
+ align:start position:0%
+queen offit and we make it 1,600
+so I I I know I've said make it 2.25x
+
+ align:start position:0%
+so I I I know I've said make it 2.25x
+ 
+
+ align:start position:0%
+so I I I know I've said make it 2.25x
+and I I stand by that I think that's a
+
+ align:start position:0%
+and I I stand by that I think that's a
+ 
+
+ align:start position:0%
+and I I stand by that I think that's a
+good strategy I think at the time I'm
+
+ align:start position:0%
+good strategy I think at the time I'm
+ 
+
+ align:start position:0%
+good strategy I think at the time I'm
+just so once again I'm probably still
+
+ align:start position:0%
+just so once again I'm probably still
+ 
+
+ align:start position:0%
+just so once again I'm probably still
+playing a lot of tables and I'm kind of
+
+ align:start position:0%
+playing a lot of tables and I'm kind of
+ 
+
+ align:start position:0%
+playing a lot of tables and I'm kind of
+lazy so I'm too lazy to type in like
+
+ align:start position:0%
+lazy so I'm too lazy to type in like
+ 
+
+ align:start position:0%
+lazy so I'm too lazy to type in like
+1,00 manually whereas the software
+
+ align:start position:0%
+1,00 manually whereas the software
+ 
+
+ align:start position:0%
+1,00 manually whereas the software
+defaults to just 2x so I tend to just 2x
+
+ align:start position:0%
+defaults to just 2x so I tend to just 2x
+ 
+
+ align:start position:0%
+defaults to just 2x so I tend to just 2x
+but I think it's probably not the
+
+ align:start position:0%
+but I think it's probably not the
+ 
+
+ align:start position:0%
+but I think it's probably not the
+theoretical optimal strategy I would
+
+ align:start position:0%
+theoretical optimal strategy I would
+ 
+
+ align:start position:0%
+theoretical optimal strategy I would
+guess that the optimal thing to do is
+
+ align:start position:0%
+guess that the optimal thing to do is
+ 
+
+ align:start position:0%
+guess that the optimal thing to do is
+closer to
+
+ align:start position:0%
+closer to
+ 
+
+ align:start position:0%
+closer to
+2.25x uh so vamson calls us in position
+
+ align:start position:0%
+2.25x uh so vamson calls us in position
+ 
+
+ align:start position:0%
+2.25x uh so vamson calls us in position
+position and you know so so immediately
+
+ align:start position:0%
+position and you know so so immediately
+ 
+
+ align:start position:0%
+position and you know so so immediately
+I could think of it like what is their
+
+ align:start position:0%
+I could think of it like what is their
+ 
+
+ align:start position:0%
+I could think of it like what is their
+range cuz it's a spot where I expect
+
+ align:start position:0%
+range cuz it's a spot where I expect
+ 
+
+ align:start position:0%
+range cuz it's a spot where I expect
+them to go all in with most of their
+
+ align:start position:0%
+them to go all in with most of their
+ 
+
+ align:start position:0%
+them to go all in with most of their
+good hands so the question is you know
+
+ align:start position:0%
+good hands so the question is you know
+ 
+
+ align:start position:0%
+good hands so the question is you know
+are they trapping me or do they
+
+ align:start position:0%
+are they trapping me or do they
+ 
+
+ align:start position:0%
+are they trapping me or do they
+literally just always have a hand like
+
+ align:start position:0%
+literally just always have a hand like
+ 
+
+ align:start position:0%
+literally just always have a hand like
+Jack 10 suited king queen or something
+
+ align:start position:0%
+Jack 10 suited king queen or something
+ 
+
+ align:start position:0%
+Jack 10 suited king queen or something
+like that so so immediately it's it's
+
+ align:start position:0%
+like that so so immediately it's it's
+ 
+
+ align:start position:0%
+like that so so immediately it's it's
+sort of an interesting spot because I
+
+ align:start position:0%
+sort of an interesting spot because I
+ 
+
+ align:start position:0%
+sort of an interesting spot because I
+expect them to mostly be raising when
+
+ align:start position:0%
+expect them to mostly be raising when
+ 
+
+ align:start position:0%
+expect them to mostly be raising when
+they want to play their
+
+ align:start position:0%
+they want to play their
+ 
+
+ align:start position:0%
+they want to play their
+hand okay so we flop uh 4
+
+ align:start position:0%
+hand okay so we flop uh 4
+ 
+
+ align:start position:0%
+hand okay so we flop uh 4
+109 and it's definitely a pretty bad
+
+ align:start position:0%
+109 and it's definitely a pretty bad
+ 
+
+ align:start position:0%
+109 and it's definitely a pretty bad
+board for us overall like I think you
+
+ align:start position:0%
+board for us overall like I think you
+ 
+
+ align:start position:0%
+board for us overall like I think you
+know if like regardless of their
+
+ align:start position:0%
+know if like regardless of their
+ 
+
+ align:start position:0%
+know if like regardless of their
+strategy like if their strategy is to
+
+ align:start position:0%
+strategy like if their strategy is to
+ 
+
+ align:start position:0%
+strategy like if their strategy is to
+trap us sometimes then this this board
+
+ align:start position:0%
+trap us sometimes then this this board
+ 
+
+ align:start position:0%
+trap us sometimes then this this board
+is just terrible and even if their
+
+ align:start position:0%
+is just terrible and even if their
+ 
+
+ align:start position:0%
+is just terrible and even if their
+strategy isn't to trap us they've always
+
+ align:start position:0%
+strategy isn't to trap us they've always
+ 
+
+ align:start position:0%
+strategy isn't to trap us they've always
+got a straight draw on this board
+
+ align:start position:0%
+got a straight draw on this board
+ 
+
+ align:start position:0%
+got a straight draw on this board
+because they're going to have king queen
+
+ align:start position:0%
+because they're going to have king queen
+ 
+
+ align:start position:0%
+because they're going to have king queen
+or queen Jack or something so I think
+
+ align:start position:0%
+or queen Jack or something so I think
+ 
+
+ align:start position:0%
+or queen Jack or something so I think
+objectively it's a pretty bad board
+
+ align:start position:0%
+objectively it's a pretty bad board
+ 
+
+ align:start position:0%
+objectively it's a pretty bad board
+maybe they could have Ace Jack or Ace
+
+ align:start position:0%
+maybe they could have Ace Jack or Ace
+ 
+
+ align:start position:0%
+maybe they could have Ace Jack or Ace
+Queen thems although Ace Queen I think
+
+ align:start position:0%
+Queen thems although Ace Queen I think
+ 
+
+ align:start position:0%
+Queen thems although Ace Queen I think
+they're definitely raising pre flop so
+
+ align:start position:0%
+they're definitely raising pre flop so
+ 
+
+ align:start position:0%
+they're definitely raising pre flop so
+probably just ace Jack um so I do think
+
+ align:start position:0%
+probably just ace Jack um so I do think
+ 
+
+ align:start position:0%
+probably just ace Jack um so I do think
+we're not in great shape here but I
+
+ align:start position:0%
+we're not in great shape here but I
+ 
+
+ align:start position:0%
+we're not in great shape here but I
+decid to bet anyway essentially just
+
+ align:start position:0%
+decid to bet anyway essentially just
+ 
+
+ align:start position:0%
+decid to bet anyway essentially just
+banking on my as of clubs I I definitely
+
+ align:start position:0%
+banking on my as of clubs I I definitely
+ 
+
+ align:start position:0%
+banking on my as of clubs I I definitely
+wouldn't be betting this without the Ace
+
+ align:start position:0%
+wouldn't be betting this without the Ace
+ 
+
+ align:start position:0%
+wouldn't be betting this without the Ace
+of clubs but my strategy is to bet and
+
+ align:start position:0%
+of clubs but my strategy is to bet and
+ 
+
+ align:start position:0%
+of clubs but my strategy is to bet and
+if I get called I'm going to go all in
+
+ align:start position:0%
+if I get called I'm going to go all in
+ 
+
+ align:start position:0%
+if I get called I'm going to go all in
+on any club turn any Jack queen or east
+
+ align:start position:0%
+on any club turn any Jack queen or east
+ 
+
+ align:start position:0%
+on any club turn any Jack queen or east
+turn so essentially any club turn I have
+
+ align:start position:0%
+turn so essentially any club turn I have
+ 
+
+ align:start position:0%
+turn so essentially any club turn I have
+the nut flush draw any um Jack turn I
+
+ align:start position:0%
+the nut flush draw any um Jack turn I
+ 
+
+ align:start position:0%
+the nut flush draw any um Jack turn I
+have a good I have a good straight draw
+
+ align:start position:0%
+have a good I have a good straight draw
+ 
+
+ align:start position:0%
+have a good I have a good straight draw
+with two overcards and any queen or Ace
+
+ align:start position:0%
+with two overcards and any queen or Ace
+ 
+
+ align:start position:0%
+with two overcards and any queen or Ace
+turn uh gives pairs my hand so I just
+
+ align:start position:0%
+turn uh gives pairs my hand so I just
+ 
+
+ align:start position:0%
+turn uh gives pairs my hand so I just
+think there's enough turns where I can
+
+ align:start position:0%
+think there's enough turns where I can
+ 
+
+ align:start position:0%
+think there's enough turns where I can
+basically continue bluffing continue
+
+ align:start position:0%
+basically continue bluffing continue
+ 
+
+ align:start position:0%
+basically continue bluffing continue
+barreling on that one barrel has to be
+
+ align:start position:0%
+barreling on that one barrel has to be
+ 
+
+ align:start position:0%
+barreling on that one barrel has to be
+okay but I'm only making this play
+
+ align:start position:0%
+okay but I'm only making this play
+ 
+
+ align:start position:0%
+okay but I'm only making this play
+because I have the Ace of clubs like I
+
+ align:start position:0%
+because I have the Ace of clubs like I
+ 
+
+ align:start position:0%
+because I have the Ace of clubs like I
+think even with the Queen of Clubs I
+
+ align:start position:0%
+think even with the Queen of Clubs I
+ 
+
+ align:start position:0%
+think even with the Queen of Clubs I
+probably would have just given up this
+
+ align:start position:0%
+probably would have just given up this
+ 
+
+ align:start position:0%
+probably would have just given up this
+hand um but we do get a fold so I guess
+
+ align:start position:0%
+hand um but we do get a fold so I guess
+ 
+
+ align:start position:0%
+hand um but we do get a fold so I guess
+they probably had Ace Jack that's
+
+ align:start position:0%
+they probably had Ace Jack that's
+ 
+
+ align:start position:0%
+they probably had Ace Jack that's
+probably their most likely hand maybe
+
+ align:start position:0%
+probably their most likely hand maybe
+ 
+
+ align:start position:0%
+probably their most likely hand maybe
+something like pocket sevens they
+
+ align:start position:0%
+something like pocket sevens they
+ 
+
+ align:start position:0%
+something like pocket sevens they
+folded yeah so that sort of shows you
+
+ align:start position:0%
+folded yeah so that sort of shows you
+ 
+
+ align:start position:0%
+folded yeah so that sort of shows you
+the importance sometimes of back door
+
+ align:start position:0%
+the importance sometimes of back door
+ 
+
+ align:start position:0%
+the importance sometimes of back door
+draws because like let's say they had
+
+ align:start position:0%
+draws because like let's say they had
+ 
+
+ align:start position:0%
+draws because like let's say they had
+pocket sevens here like let's say they
+
+ align:start position:0%
+pocket sevens here like let's say they
+ 
+
+ align:start position:0%
+pocket sevens here like let's say they
+called with pocket sevens which I don't
+
+ align:start position:0%
+called with pocket sevens which I don't
+ 
+
+ align:start position:0%
+called with pocket sevens which I don't
+think is
+
+ align:start position:0%
+think is
+ 
+
+ align:start position:0%
+think is
+unreasonable if I didn't have the E of
+
+ align:start position:0%
+unreasonable if I didn't have the E of
+ 
+
+ align:start position:0%
+unreasonable if I didn't have the E of
+clubs I'm going to just have to end up
+
+ align:start position:0%
+clubs I'm going to just have to end up
+ 
+
+ align:start position:0%
+clubs I'm going to just have to end up
+giving up on a bunch of turns and they
+
+ align:start position:0%
+giving up on a bunch of turns and they
+ 
+
+ align:start position:0%
+giving up on a bunch of turns and they
+would take down the PO with their pocket
+
+ align:start position:0%
+would take down the PO with their pocket
+ 
+
+ align:start position:0%
+would take down the PO with their pocket
+sevens but because I have the Ace of
+
+ align:start position:0%
+sevens but because I have the Ace of
+ 
+
+ align:start position:0%
+sevens but because I have the Ace of
+clubs it's just very very unlikely they
+
+ align:start position:0%
+clubs it's just very very unlikely they
+ 
+
+ align:start position:0%
+clubs it's just very very unlikely they
+end up winning the hand with a pair of
+
+ align:start position:0%
+end up winning the hand with a pair of
+ 
+
+ align:start position:0%
+end up winning the hand with a pair of
+sevens cuz I'm going to shove a lot of
+
+ align:start position:0%
+sevens cuz I'm going to shove a lot of
+ 
+
+ align:start position:0%
+sevens cuz I'm going to shove a lot of
+turns and they're just going to have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fold okay so the next hand we get Queen
+
+ align:start position:0%
+fold okay so the next hand we get Queen
+ 
+
+ align:start position:0%
+fold okay so the next hand we get Queen
+Jack again and we raise here and so the
+
+ align:start position:0%
+Jack again and we raise here and so the
+ 
+
+ align:start position:0%
+Jack again and we raise here and so the
+same gu bamson they call and we get a
+
+ align:start position:0%
+same gu bamson they call and we get a
+ 
+
+ align:start position:0%
+same gu bamson they call and we get a
+good flop um so so I bet okay so I'm
+
+ align:start position:0%
+good flop um so so I bet okay so I'm
+ 
+
+ align:start position:0%
+good flop um so so I bet okay so I'm
+going to talk about this I so I bet,
+
+ align:start position:0%
+going to talk about this I so I bet,
+ 
+
+ align:start position:0%
+going to talk about this I so I bet,
+1600 here which is quite small it's like
+
+ align:start position:0%
+1600 here which is quite small it's like
+ 
+
+ align:start position:0%
+1600 here which is quite small it's like
+40% it's like less than 40% of pot I
+
+ align:start position:0%
+40% it's like less than 40% of pot I
+ 
+
+ align:start position:0%
+40% it's like less than 40% of pot I
+might have done it out of laziness but
+
+ align:start position:0%
+might have done it out of laziness but
+ 
+
+ align:start position:0%
+might have done it out of laziness but
+or I might have just done it because of
+
+ align:start position:0%
+or I might have just done it because of
+ 
+
+ align:start position:0%
+or I might have just done it because of
+my cards because I have two pair and I'm
+
+ align:start position:0%
+my cards because I have two pair and I'm
+ 
+
+ align:start position:0%
+my cards because I have two pair and I'm
+trying to separate him in and get him to
+
+ align:start position:0%
+trying to separate him in and get him to
+ 
+
+ align:start position:0%
+trying to separate him in and get him to
+put in all his money slowly but looking
+
+ align:start position:0%
+put in all his money slowly but looking
+ 
+
+ align:start position:0%
+put in all his money slowly but looking
+back I definitely don't think this is
+
+ align:start position:0%
+back I definitely don't think this is
+ 
+
+ align:start position:0%
+back I definitely don't think this is
+how I want to be playing my entire
+
+ align:start position:0%
+how I want to be playing my entire
+ 
+
+ align:start position:0%
+how I want to be playing my entire
+strategy on this spot like I think I
+
+ align:start position:0%
+strategy on this spot like I think I
+ 
+
+ align:start position:0%
+strategy on this spot like I think I
+want to be betting at least half the pot
+
+ align:start position:0%
+want to be betting at least half the pot
+ 
+
+ align:start position:0%
+want to be betting at least half the pot
+when there's a flush draw a straight
+
+ align:start position:0%
+when there's a flush draw a straight
+ 
+
+ align:start position:0%
+when there's a flush draw a straight
+draw like a bunch of straight draws I
+
+ align:start position:0%
+draw like a bunch of straight draws I
+ 
+
+ align:start position:0%
+draw like a bunch of straight draws I
+definitely think this bet is way too
+
+ align:start position:0%
+definitely think this bet is way too
+ 
+
+ align:start position:0%
+definitely think this bet is way too
+small it's just on average even even if
+
+ align:start position:0%
+small it's just on average even even if
+ 
+
+ align:start position:0%
+small it's just on average even even if
+I have a pretty good hand let's say like
+
+ align:start position:0%
+I have a pretty good hand let's say like
+ 
+
+ align:start position:0%
+I have a pretty good hand let's say like
+Queen n there's just a lot of bad cards
+
+ align:start position:0%
+Queen n there's just a lot of bad cards
+ 
+
+ align:start position:0%
+Queen n there's just a lot of bad cards
+for me that I don't want to be betting
+
+ align:start position:0%
+for me that I don't want to be betting
+ 
+
+ align:start position:0%
+for me that I don't want to be betting
+the small on this board so I don't know
+
+ align:start position:0%
+the small on this board so I don't know
+ 
+
+ align:start position:0%
+the small on this board so I don't know
+if at the time I just like misclicked
+
+ align:start position:0%
+if at the time I just like misclicked
+ 
+
+ align:start position:0%
+if at the time I just like misclicked
+and messed up or I was lazy and I just
+
+ align:start position:0%
+and messed up or I was lazy and I just
+ 
+
+ align:start position:0%
+and messed up or I was lazy and I just
+wanted to make it 2X or I spefic
+
+ align:start position:0%
+wanted to make it 2X or I spefic
+ 
+
+ align:start position:0%
+wanted to make it 2X or I spefic
+spefically had to read that I could
+
+ align:start position:0%
+spefically had to read that I could
+ 
+
+ align:start position:0%
+spefically had to read that I could
+exploit this player by betting small but
+
+ align:start position:0%
+exploit this player by betting small but
+ 
+
+ align:start position:0%
+exploit this player by betting small but
+this is not a balance this is not how I
+
+ align:start position:0%
+this is not a balance this is not how I
+ 
+
+ align:start position:0%
+this is not a balance this is not how I
+would like to balance my strategy and if
+
+ align:start position:0%
+would like to balance my strategy and if
+ 
+
+ align:start position:0%
+would like to balance my strategy and if
+you ever see me doing this most likely I
+
+ align:start position:0%
+you ever see me doing this most likely I
+ 
+
+ align:start position:0%
+you ever see me doing this most likely I
+have a really good hand as I do in this
+
+ align:start position:0%
+have a really good hand as I do in this
+ 
+
+ align:start position:0%
+have a really good hand as I do in this
+case um so unfortunately it doesn't work
+
+ align:start position:0%
+case um so unfortunately it doesn't work
+ 
+
+ align:start position:0%
+case um so unfortunately it doesn't work
+but so I'm going to talk about this a
+
+ align:start position:0%
+but so I'm going to talk about this a
+ 
+
+ align:start position:0%
+but so I'm going to talk about this a
+bit more so I'm going to jump back to
+
+ align:start position:0%
+bit more so I'm going to jump back to
+ 
+
+ align:start position:0%
+bit more so I'm going to jump back to
+Theory just for a bit um so I want to
+
+ align:start position:0%
+Theory just for a bit um so I want to
+ 
+
+ align:start position:0%
+Theory just for a bit um so I want to
+talk I don't think I've talked about
+
+ align:start position:0%
+talk I don't think I've talked about
+ 
+
+ align:start position:0%
+talk I don't think I've talked about
+this before but I want to say that bet
+
+ align:start position:0%
+this before but I want to say that bet
+ 
+
+ align:start position:0%
+this before but I want to say that bet
+sizing depends on board texture so let
+
+ align:start position:0%
+sizing depends on board texture so let
+ 
+
+ align:start position:0%
+sizing depends on board texture so let
+me explain what I mean here so
+
+ align:start position:0%
+me explain what I mean here so
+ 
+
+ align:start position:0%
+me explain what I mean here so
+essentially there's two types of boards
+
+ align:start position:0%
+essentially there's two types of boards
+ 
+
+ align:start position:0%
+essentially there's two types of boards
+there's dry boards and dry boards so I
+
+ align:start position:0%
+there's dry boards and dry boards so I
+ 
+
+ align:start position:0%
+there's dry boards and dry boards so I
+hate this terminology cuz these are two
+
+ align:start position:0%
+hate this terminology cuz these are two
+ 
+
+ align:start position:0%
+hate this terminology cuz these are two
+words that mean opposite things and they
+
+ align:start position:0%
+words that mean opposite things and they
+ 
+
+ align:start position:0%
+words that mean opposite things and they
+sound very similar especially if you
+
+ align:start position:0%
+sound very similar especially if you
+ 
+
+ align:start position:0%
+sound very similar especially if you
+don't runci it but it's dry and dry um
+
+ align:start position:0%
+don't runci it but it's dry and dry um
+ 
+
+ align:start position:0%
+don't runci it but it's dry and dry um
+maybe I can't pronounce them well but
+
+ align:start position:0%
+maybe I can't pronounce them well but
+ 
+
+ align:start position:0%
+maybe I can't pronounce them well but
+okay so dry boards is basically boards
+
+ align:start position:0%
+okay so dry boards is basically boards
+ 
+
+ align:start position:0%
+okay so dry boards is basically boards
+where the winner is mostly decided by
+
+ align:start position:0%
+where the winner is mostly decided by
+ 
+
+ align:start position:0%
+where the winner is mostly decided by
+before the river and you're either way
+
+ align:start position:0%
+before the river and you're either way
+ 
+
+ align:start position:0%
+before the river and you're either way
+ahead or way behind drawing boards is
+
+ align:start position:0%
+ahead or way behind drawing boards is
+ 
+
+ align:start position:0%
+ahead or way behind drawing boards is
+basically boards with lot of flush draws
+
+ align:start position:0%
+basically boards with lot of flush draws
+ 
+
+ align:start position:0%
+basically boards with lot of flush draws
+straight draws where every subsequent
+
+ align:start position:0%
+straight draws where every subsequent
+ 
+
+ align:start position:0%
+straight draws where every subsequent
+cards card can change the board a lot
+
+ align:start position:0%
+cards card can change the board a lot
+ 
+
+ align:start position:0%
+cards card can change the board a lot
+and it's hard to fold because all hands
+
+ align:start position:0%
+and it's hard to fold because all hands
+ 
+
+ align:start position:0%
+and it's hard to fold because all hands
+have Equity so in reality most boards
+
+ align:start position:0%
+have Equity so in reality most boards
+ 
+
+ align:start position:0%
+have Equity so in reality most boards
+you know they're somewhere in between
+
+ align:start position:0%
+you know they're somewhere in between
+ 
+
+ align:start position:0%
+you know they're somewhere in between
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+spectrum but okay so what are some
+
+ align:start position:0%
+spectrum but okay so what are some
+ 
+
+ align:start position:0%
+spectrum but okay so what are some
+characteristics of dry boards well a
+
+ align:start position:0%
+characteristics of dry boards well a
+ 
+
+ align:start position:0%
+characteristics of dry boards well a
+board tends to be dry if it's paired
+
+ align:start position:0%
+board tends to be dry if it's paired
+ 
+
+ align:start position:0%
+board tends to be dry if it's paired
+like 448 that tends to be pretty dry cuz
+
+ align:start position:0%
+like 448 that tends to be pretty dry cuz
+ 
+
+ align:start position:0%
+like 448 that tends to be pretty dry cuz
+not much is going in most people have
+
+ align:start position:0%
+not much is going in most people have
+ 
+
+ align:start position:0%
+not much is going in most people have
+missed that board um a board is dry if
+
+ align:start position:0%
+missed that board um a board is dry if
+ 
+
+ align:start position:0%
+missed that board um a board is dry if
+the highest card is big like if the
+
+ align:start position:0%
+the highest card is big like if the
+ 
+
+ align:start position:0%
+the highest card is big like if the
+highest card is an ace then against
+
+ align:start position:0%
+highest card is an ace then against
+ 
+
+ align:start position:0%
+highest card is an ace then against
+someone with an ace if you don't have a
+
+ align:start position:0%
+someone with an ace if you don't have a
+ 
+
+ align:start position:0%
+someone with an ace if you don't have a
+FL flush or straight draw you're already
+
+ align:start position:0%
+FL flush or straight draw you're already
+ 
+
+ align:start position:0%
+FL flush or straight draw you're already
+kind of drawing close to dead um whereas
+
+ align:start position:0%
+kind of drawing close to dead um whereas
+ 
+
+ align:start position:0%
+kind of drawing close to dead um whereas
+you know if the highest card is a 10
+
+ align:start position:0%
+you know if the highest card is a 10
+ 
+
+ align:start position:0%
+you know if the highest card is a 10
+then if you have a queen you always have
+
+ align:start position:0%
+then if you have a queen you always have
+ 
+
+ align:start position:0%
+then if you have a queen you always have
+an opportunity to turn a queen and beat
+
+ align:start position:0%
+an opportunity to turn a queen and beat
+ 
+
+ align:start position:0%
+an opportunity to turn a queen and beat
+them um it's dry if there's no middle
+
+ align:start position:0%
+them um it's dry if there's no middle
+ 
+
+ align:start position:0%
+them um it's dry if there's no middle
+cards for straight draws if there's no
+
+ align:start position:0%
+cards for straight draws if there's no
+ 
+
+ align:start position:0%
+cards for straight draws if there's no
+flush draws um or I'd say if there's
+
+ align:start position:0%
+flush draws um or I'd say if there's
+ 
+
+ align:start position:0%
+flush draws um or I'd say if there's
+already four to a flush or already four
+
+ align:start position:0%
+already four to a flush or already four
+ 
+
+ align:start position:0%
+already four to a flush or already four
+to a straight then it's also sort of dry
+
+ align:start position:0%
+to a straight then it's also sort of dry
+ 
+
+ align:start position:0%
+to a straight then it's also sort of dry
+because like if there's already four
+
+ align:start position:0%
+because like if there's already four
+ 
+
+ align:start position:0%
+because like if there's already four
+diamonds then it's also sort of decided
+
+ align:start position:0%
+diamonds then it's also sort of decided
+ 
+
+ align:start position:0%
+diamonds then it's also sort of decided
+who wins already like if you have a big
+
+ align:start position:0%
+who wins already like if you have a big
+ 
+
+ align:start position:0%
+who wins already like if you have a big
+diamond you're just pretty much
+
+ align:start position:0%
+diamond you're just pretty much
+ 
+
+ align:start position:0%
+diamond you're just pretty much
+guaranteed to win barring some fall
+
+ align:start position:0%
+guaranteed to win barring some fall
+ 
+
+ align:start position:0%
+guaranteed to win barring some fall
+house um same with four to a straight if
+
+ align:start position:0%
+house um same with four to a straight if
+ 
+
+ align:start position:0%
+house um same with four to a straight if
+it's like 9 10 Jack Queen if you have a
+
+ align:start position:0%
+it's like 9 10 Jack Queen if you have a
+ 
+
+ align:start position:0%
+it's like 9 10 Jack Queen if you have a
+king you're just pretty much guaranteed
+
+ align:start position:0%
+king you're just pretty much guaranteed
+ 
+
+ align:start position:0%
+king you're just pretty much guaranteed
+to win and so on the other hand what are
+
+ align:start position:0%
+to win and so on the other hand what are
+ 
+
+ align:start position:0%
+to win and so on the other hand what are
+dry boards it's sort of the opposite
+
+ align:start position:0%
+dry boards it's sort of the opposite
+ 
+
+ align:start position:0%
+dry boards it's sort of the opposite
+right small cards why small cards
+
+ align:start position:0%
+right small cards why small cards
+ 
+
+ align:start position:0%
+right small cards why small cards
+because everyone's going to have
+
+ align:start position:0%
+because everyone's going to have
+ 
+
+ align:start position:0%
+because everyone's going to have
+overcards which is 6 outs flush draws or
+
+ align:start position:0%
+overcards which is 6 outs flush draws or
+ 
+
+ align:start position:0%
+overcards which is 6 outs flush draws or
+three du a flush is also very dry
+
+ align:start position:0%
+three du a flush is also very dry
+ 
+
+ align:start position:0%
+three du a flush is also very dry
+because if there's three du a flush then
+
+ align:start position:0%
+because if there's three du a flush then
+ 
+
+ align:start position:0%
+because if there's three du a flush then
+someone with just an any card of that
+
+ align:start position:0%
+someone with just an any card of that
+ 
+
+ align:start position:0%
+someone with just an any card of that
+suit has a flush draw uh boards with
+
+ align:start position:0%
+suit has a flush draw uh boards with
+ 
+
+ align:start position:0%
+suit has a flush draw uh boards with
+straight draws so how should your Play
+
+ align:start position:0%
+straight draws so how should your Play
+ 
+
+ align:start position:0%
+straight draws so how should your Play
+Change on these two types of boards um
+
+ align:start position:0%
+Change on these two types of boards um
+ 
+
+ align:start position:0%
+Change on these two types of boards um
+well on dry boards you can bet pretty
+
+ align:start position:0%
+well on dry boards you can bet pretty
+ 
+
+ align:start position:0%
+well on dry boards you can bet pretty
+small fractions of the pot on the floppy
+
+ align:start position:0%
+small fractions of the pot on the floppy
+ 
+
+ align:start position:0%
+small fractions of the pot on the floppy
+turn and your opponent might not have
+
+ align:start position:0%
+turn and your opponent might not have
+ 
+
+ align:start position:0%
+turn and your opponent might not have
+the odds to call so like you know if the
+
+ align:start position:0%
+the odds to call so like you know if the
+ 
+
+ align:start position:0%
+the odds to call so like you know if the
+Flop is Ace ace2 or maybe Ace A7 with no
+
+ align:start position:0%
+Flop is Ace ace2 or maybe Ace A7 with no
+ 
+
+ align:start position:0%
+Flop is Ace ace2 or maybe Ace A7 with no
+flush draws you can bet like a fifth of
+
+ align:start position:0%
+flush draws you can bet like a fifth of
+ 
+
+ align:start position:0%
+flush draws you can bet like a fifth of
+the pot and your opponent is still going
+
+ align:start position:0%
+the pot and your opponent is still going
+ 
+
+ align:start position:0%
+the pot and your opponent is still going
+to have to fold a lot of their hands
+
+ align:start position:0%
+to have to fold a lot of their hands
+ 
+
+ align:start position:0%
+to have to fold a lot of their hands
+because if you've got an ace they're
+
+ align:start position:0%
+because if you've got an ace they're
+ 
+
+ align:start position:0%
+because if you've got an ace they're
+just way behind um what's another
+
+ align:start position:0%
+just way behind um what's another
+ 
+
+ align:start position:0%
+just way behind um what's another
+characteristic is any draw might be good
+
+ align:start position:0%
+characteristic is any draw might be good
+ 
+
+ align:start position:0%
+characteristic is any draw might be good
+enough to make a bluff so like if the
+
+ align:start position:0%
+enough to make a bluff so like if the
+ 
+
+ align:start position:0%
+enough to make a bluff so like if the
+board is a A7 with no flush draw and
+
+ align:start position:0%
+board is a A7 with no flush draw and
+ 
+
+ align:start position:0%
+board is a A7 with no flush draw and
+you've got like 89 with a back door
+
+ align:start position:0%
+you've got like 89 with a back door
+ 
+
+ align:start position:0%
+you've got like 89 with a back door
+flush draw that's a pretty good hand to
+
+ align:start position:0%
+flush draw that's a pretty good hand to
+ 
+
+ align:start position:0%
+flush draw that's a pretty good hand to
+make a bluff because you've got um
+
+ align:start position:0%
+make a bluff because you've got um
+ 
+
+ align:start position:0%
+make a bluff because you've got um
+you've got three to a straight and three
+
+ align:start position:0%
+you've got three to a straight and three
+ 
+
+ align:start position:0%
+you've got three to a straight and three
+do a flush which is sort of the most you
+
+ align:start position:0%
+do a flush which is sort of the most you
+ 
+
+ align:start position:0%
+do a flush which is sort of the most you
+could possibly ask for on that flop with
+
+ align:start position:0%
+could possibly ask for on that flop with
+ 
+
+ align:start position:0%
+could possibly ask for on that flop with
+respect to draws and another aspect of
+
+ align:start position:0%
+respect to draws and another aspect of
+ 
+
+ align:start position:0%
+respect to draws and another aspect of
+playing Drive boards is sort of slow
+
+ align:start position:0%
+playing Drive boards is sort of slow
+ 
+
+ align:start position:0%
+playing Drive boards is sort of slow
+playing tricky plays are good because
+
+ align:start position:0%
+playing tricky plays are good because
+ 
+
+ align:start position:0%
+playing tricky plays are good because
+the thing that matters isn't preventing
+
+ align:start position:0%
+the thing that matters isn't preventing
+ 
+
+ align:start position:0%
+the thing that matters isn't preventing
+your opponent from seeing the turn in
+
+ align:start position:0%
+your opponent from seeing the turn in
+ 
+
+ align:start position:0%
+your opponent from seeing the turn in
+river and not letting them see outs the
+
+ align:start position:0%
+river and not letting them see outs the
+ 
+
+ align:start position:0%
+river and not letting them see outs the
+thing that matters is sort of convincing
+
+ align:start position:0%
+thing that matters is sort of convincing
+ 
+
+ align:start position:0%
+thing that matters is sort of convincing
+your opponent
+
+ align:start position:0%
+your opponent
+ 
+
+ align:start position:0%
+your opponent
+that you have a good hand when you don't
+
+ align:start position:0%
+that you have a good hand when you don't
+ 
+
+ align:start position:0%
+that you have a good hand when you don't
+or like convincing them that you don't
+
+ align:start position:0%
+or like convincing them that you don't
+ 
+
+ align:start position:0%
+or like convincing them that you don't
+have a good hand when you do so it's all
+
+ align:start position:0%
+have a good hand when you do so it's all
+ 
+
+ align:start position:0%
+have a good hand when you do so it's all
+about tricking your opponent disguising
+
+ align:start position:0%
+about tricking your opponent disguising
+ 
+
+ align:start position:0%
+about tricking your opponent disguising
+these tricky I mean I shouldn't say that
+
+ align:start position:0%
+these tricky I mean I shouldn't say that
+ 
+
+ align:start position:0%
+these tricky I mean I shouldn't say that
+it's not all but like simple play can
+
+ align:start position:0%
+it's not all but like simple play can
+ 
+
+ align:start position:0%
+it's not all but like simple play can
+still be good on dry boards but in
+
+ align:start position:0%
+still be good on dry boards but in
+ 
+
+ align:start position:0%
+still be good on dry boards but in
+general slow playing is reasonable and
+
+ align:start position:0%
+general slow playing is reasonable and
+ 
+
+ align:start position:0%
+general slow playing is reasonable and
+and tricking trying to trick your
+
+ align:start position:0%
+and tricking trying to trick your
+ 
+
+ align:start position:0%
+and tricking trying to trick your
+opponent is is more important whereas on
+
+ align:start position:0%
+opponent is is more important whereas on
+ 
+
+ align:start position:0%
+opponent is is more important whereas on
+draw boards you know you just got to bet
+
+ align:start position:0%
+draw boards you know you just got to bet
+ 
+
+ align:start position:0%
+draw boards you know you just got to bet
+large fractions of the pot before the
+
+ align:start position:0%
+large fractions of the pot before the
+ 
+
+ align:start position:0%
+large fractions of the pot before the
+river because every hand has so many
+
+ align:start position:0%
+river because every hand has so many
+ 
+
+ align:start position:0%
+river because every hand has so many
+outs you really don't want to be giving
+
+ align:start position:0%
+outs you really don't want to be giving
+ 
+
+ align:start position:0%
+outs you really don't want to be giving
+them good odds to call and on the floing
+
+ align:start position:0%
+them good odds to call and on the floing
+ 
+
+ align:start position:0%
+them good odds to call and on the floing
+turn if you don't have anything then
+
+ align:start position:0%
+turn if you don't have anything then
+ 
+
+ align:start position:0%
+turn if you don't have anything then
+just don't put any money in because
+
+ align:start position:0%
+just don't put any money in because
+ 
+
+ align:start position:0%
+just don't put any money in because
+bluffing is pretty moot because so many
+
+ align:start position:0%
+bluffing is pretty moot because so many
+ 
+
+ align:start position:0%
+bluffing is pretty moot because so many
+hands aren't folding because they have
+
+ align:start position:0%
+hands aren't folding because they have
+ 
+
+ align:start position:0%
+hands aren't folding because they have
+oats um and yeah don't really slow play
+
+ align:start position:0%
+oats um and yeah don't really slow play
+ 
+
+ align:start position:0%
+oats um and yeah don't really slow play
+if you have a good hand similarly just
+
+ align:start position:0%
+if you have a good hand similarly just
+ 
+
+ align:start position:0%
+if you have a good hand similarly just
+put all the money in right away because
+
+ align:start position:0%
+put all the money in right away because
+ 
+
+ align:start position:0%
+put all the money in right away because
+they're going to call very often because
+
+ align:start position:0%
+they're going to call very often because
+ 
+
+ align:start position:0%
+they're going to call very often because
+they're always going to have some outs
+
+ align:start position:0%
+they're always going to have some outs
+ 
+
+ align:start position:0%
+they're always going to have some outs
+so that's roughly how uh how the Play
+
+ align:start position:0%
+so that's roughly how uh how the Play
+ 
+
+ align:start position:0%
+so that's roughly how uh how the Play
+Changes okay so uh okay so I'll come
+
+ align:start position:0%
+Changes okay so uh okay so I'll come
+ 
+
+ align:start position:0%
+Changes okay so uh okay so I'll come
+back to this we'll see these hands in a
+
+ align:start position:0%
+back to this we'll see these hands in a
+ 
+
+ align:start position:0%
+back to this we'll see these hands in a
+bit so coming back to this queen Jack
+
+ align:start position:0%
+bit so coming back to this queen Jack
+ 
+
+ align:start position:0%
+bit so coming back to this queen Jack
+Hand the reason why I think my beted is
+
+ align:start position:0%
+Hand the reason why I think my beted is
+ 
+
+ align:start position:0%
+Hand the reason why I think my beted is
+too small is because I would consider
+
+ align:start position:0%
+too small is because I would consider
+ 
+
+ align:start position:0%
+too small is because I would consider
+this queen Jack 3 with a flush draw to
+
+ align:start position:0%
+this queen Jack 3 with a flush draw to
+ 
+
+ align:start position:0%
+this queen Jack 3 with a flush draw to
+be a fairly dry board fairly close to
+
+ align:start position:0%
+be a fairly dry board fairly close to
+ 
+
+ align:start position:0%
+be a fairly dry board fairly close to
+the dry end of the spectrum and for that
+
+ align:start position:0%
+the dry end of the spectrum and for that
+ 
+
+ align:start position:0%
+the dry end of the spectrum and for that
+and I said you know you have to bet big
+
+ align:start position:0%
+and I said you know you have to bet big
+ 
+
+ align:start position:0%
+and I said you know you have to bet big
+fractions of the pot and here I am
+
+ align:start position:0%
+fractions of the pot and here I am
+ 
+
+ align:start position:0%
+fractions of the pot and here I am
+betting close to a third of the pot on
+
+ align:start position:0%
+betting close to a third of the pot on
+ 
+
+ align:start position:0%
+betting close to a third of the pot on
+the Flop so I think it's just not a good
+
+ align:start position:0%
+the Flop so I think it's just not a good
+ 
+
+ align:start position:0%
+the Flop so I think it's just not a good
+strategy but um I take the PT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down okay so the next
+
+ align:start position:0%
+down okay so the next
+ 
+
+ align:start position:0%
+down okay so the next
+hand we have Ace Queen offit and so this
+
+ align:start position:0%
+hand we have Ace Queen offit and so this
+ 
+
+ align:start position:0%
+hand we have Ace Queen offit and so this
+guy calls and so my rule was roughly you
+
+ align:start position:0%
+guy calls and so my rule was roughly you
+ 
+
+ align:start position:0%
+guy calls and so my rule was roughly you
+know raise it to 3x + 1 so three so you
+
+ align:start position:0%
+know raise it to 3x + 1 so three so you
+ 
+
+ align:start position:0%
+know raise it to 3x + 1 so three so you
+count how many limpers there are before
+
+ align:start position:0%
+count how many limpers there are before
+ 
+
+ align:start position:0%
+count how many limpers there are before
+you and you add three to that and you
+
+ align:start position:0%
+you and you add three to that and you
+ 
+
+ align:start position:0%
+you and you add three to that and you
+multiply that by the big blind is
+
+ align:start position:0%
+multiply that by the big blind is
+ 
+
+ align:start position:0%
+multiply that by the big blind is
+roughly what you raise it to so in this
+
+ align:start position:0%
+roughly what you raise it to so in this
+ 
+
+ align:start position:0%
+roughly what you raise it to so in this
+case 4,000 I make it
+
+ align:start position:0%
+case 4,000 I make it
+ 
+
+ align:start position:0%
+case 4,000 I make it
+4250 um if they decide to do some weird
+
+ align:start position:0%
+4250 um if they decide to do some weird
+ 
+
+ align:start position:0%
+4250 um if they decide to do some weird
+limp Rays by the way like if they go all
+
+ align:start position:0%
+limp Rays by the way like if they go all
+ 
+
+ align:start position:0%
+limp Rays by the way like if they go all
+in here I'm definitely calling I'm just
+
+ align:start position:0%
+in here I'm definitely calling I'm just
+ 
+
+ align:start position:0%
+in here I'm definitely calling I'm just
+not going to believe them and Ace Queen
+
+ align:start position:0%
+not going to believe them and Ace Queen
+ 
+
+ align:start position:0%
+not going to believe them and Ace Queen
+offsuit is definitely good enough so
+
+ align:start position:0%
+offsuit is definitely good enough so
+ 
+
+ align:start position:0%
+offsuit is definitely good enough so
+they decid to just call which is a bit
+
+ align:start position:0%
+they decid to just call which is a bit
+ 
+
+ align:start position:0%
+they decid to just call which is a bit
+bit weird considering their odds aren't
+
+ align:start position:0%
+bit weird considering their odds aren't
+ 
+
+ align:start position:0%
+bit weird considering their odds aren't
+that good and they're out of position
+
+ align:start position:0%
+that good and they're out of position
+ 
+
+ align:start position:0%
+that good and they're out of position
+but um we flop three hearts and we have
+
+ align:start position:0%
+but um we flop three hearts and we have
+ 
+
+ align:start position:0%
+but um we flop three hearts and we have
+the queen of hearts and in this
+
+ align:start position:0%
+the queen of hearts and in this
+ 
+
+ align:start position:0%
+the queen of hearts and in this
+situation I'm just betting uh I'm just
+
+ align:start position:0%
+situation I'm just betting uh I'm just
+ 
+
+ align:start position:0%
+situation I'm just betting uh I'm just
+betting pretty big into the pot so I
+
+ align:start position:0%
+betting pretty big into the pot so I
+ 
+
+ align:start position:0%
+betting pretty big into the pot so I
+consider this to be a fairly draw flop
+
+ align:start position:0%
+consider this to be a fairly draw flop
+ 
+
+ align:start position:0%
+consider this to be a fairly draw flop
+so I bet big um and so even though I'm
+
+ align:start position:0%
+so I bet big um and so even though I'm
+ 
+
+ align:start position:0%
+so I bet big um and so even though I'm
+in position so position is sort of an
+
+ align:start position:0%
+in position so position is sort of an
+ 
+
+ align:start position:0%
+in position so position is sort of an
+incentive to maybe bet smaller because
+
+ align:start position:0%
+incentive to maybe bet smaller because
+ 
+
+ align:start position:0%
+incentive to maybe bet smaller because
+you have position on later streets and
+
+ align:start position:0%
+you have position on later streets and
+ 
+
+ align:start position:0%
+you have position on later streets and
+you can control the betting better on
+
+ align:start position:0%
+you can control the betting better on
+ 
+
+ align:start position:0%
+you can control the betting better on
+later streets but so this is a fairly
+
+ align:start position:0%
+later streets but so this is a fairly
+ 
+
+ align:start position:0%
+later streets but so this is a fairly
+big bet considering I'm position but I'm
+
+ align:start position:0%
+big bet considering I'm position but I'm
+ 
+
+ align:start position:0%
+big bet considering I'm position but I'm
+just happy to get it in here um so
+
+ align:start position:0%
+just happy to get it in here um so
+ 
+
+ align:start position:0%
+just happy to get it in here um so
+contrast this with an earlier hand I
+
+ align:start position:0%
+contrast this with an earlier hand I
+ 
+
+ align:start position:0%
+contrast this with an earlier hand I
+think I also had Ace Queen um except uh
+
+ align:start position:0%
+think I also had Ace Queen um except uh
+ 
+
+ align:start position:0%
+think I also had Ace Queen um except uh
+it was only I only had three to a flush
+
+ align:start position:0%
+it was only I only had three to a flush
+ 
+
+ align:start position:0%
+it was only I only had three to a flush
+and I said it was very important that I
+
+ align:start position:0%
+and I said it was very important that I
+ 
+
+ align:start position:0%
+and I said it was very important that I
+had the ace of the suit but here it's
+
+ align:start position:0%
+had the ace of the suit but here it's
+ 
+
+ align:start position:0%
+had the ace of the suit but here it's
+just very hard for me to be in terrible
+
+ align:start position:0%
+just very hard for me to be in terrible
+ 
+
+ align:start position:0%
+just very hard for me to be in terrible
+shape you know like in theory they could
+
+ align:start position:0%
+shape you know like in theory they could
+ 
+
+ align:start position:0%
+shape you know like in theory they could
+have I suppose Ace 9 with the Ace of
+
+ align:start position:0%
+have I suppose Ace 9 with the Ace of
+ 
+
+ align:start position:0%
+have I suppose Ace 9 with the Ace of
+Hearts like that hand would be crushing
+
+ align:start position:0%
+Hearts like that hand would be crushing
+ 
+
+ align:start position:0%
+Hearts like that hand would be crushing
+me cuz I would be drawing to literally
+
+ align:start position:0%
+me cuz I would be drawing to literally
+ 
+
+ align:start position:0%
+me cuz I would be drawing to literally
+three outs to care my queen but it's
+
+ align:start position:0%
+three outs to care my queen but it's
+ 
+
+ align:start position:0%
+three outs to care my queen but it's
+just there's not that many combinations
+
+ align:start position:0%
+just there's not that many combinations
+ 
+
+ align:start position:0%
+just there's not that many combinations
+cuz it it would involve an offit hand
+
+ align:start position:0%
+cuz it it would involve an offit hand
+ 
+
+ align:start position:0%
+cuz it it would involve an offit hand
+which they're way less likely to have
+
+ align:start position:0%
+which they're way less likely to have
+ 
+
+ align:start position:0%
+which they're way less likely to have
+when they call me out of position or it
+
+ align:start position:0%
+when they call me out of position or it
+ 
+
+ align:start position:0%
+when they call me out of position or it
+would involve a hand like pocket kings
+
+ align:start position:0%
+would involve a hand like pocket kings
+ 
+
+ align:start position:0%
+would involve a hand like pocket kings
+with the king of hers which is also
+
+ align:start position:0%
+with the king of hers which is also
+ 
+
+ align:start position:0%
+with the king of hers which is also
+pretty unlikely because they probably
+
+ align:start position:0%
+pretty unlikely because they probably
+ 
+
+ align:start position:0%
+pretty unlikely because they probably
+would have done some raising pre flop so
+
+ align:start position:0%
+would have done some raising pre flop so
+ 
+
+ align:start position:0%
+would have done some raising pre flop so
+I just think no matter what they have
+
+ align:start position:0%
+I just think no matter what they have
+ 
+
+ align:start position:0%
+I just think no matter what they have
+I'm going to be in great shape here and
+
+ align:start position:0%
+I'm going to be in great shape here and
+ 
+
+ align:start position:0%
+I'm going to be in great shape here and
+I just have more than enough outs to
+
+ align:start position:0%
+I just have more than enough outs to
+ 
+
+ align:start position:0%
+I just have more than enough outs to
+just game W and so they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fold okay uh the next thing we have
+
+ align:start position:0%
+fold okay uh the next thing we have
+ 
+
+ align:start position:0%
+fold okay uh the next thing we have
+Queen 10 off so I open from under the
+
+ align:start position:0%
+Queen 10 off so I open from under the
+ 
+
+ align:start position:0%
+Queen 10 off so I open from under the
+gun um I think it's fine you know it
+
+ align:start position:0%
+gun um I think it's fine you know it
+ 
+
+ align:start position:0%
+gun um I think it's fine you know it
+looks a bit loose and it is but I think
+
+ align:start position:0%
+looks a bit loose and it is but I think
+ 
+
+ align:start position:0%
+looks a bit loose and it is but I think
+in terms of raising some smaller cards
+
+ align:start position:0%
+in terms of raising some smaller cards
+ 
+
+ align:start position:0%
+in terms of raising some smaller cards
+to balance it so that I will sometimes
+
+ align:start position:0%
+to balance it so that I will sometimes
+ 
+
+ align:start position:0%
+to balance it so that I will sometimes
+have smaller cards in my hand you know
+
+ align:start position:0%
+have smaller cards in my hand you know
+ 
+
+ align:start position:0%
+have smaller cards in my hand you know
+you can't really ask for more than a
+
+ align:start position:0%
+you can't really ask for more than a
+ 
+
+ align:start position:0%
+you can't really ask for more than a
+studed connector so Queen 10 suited I ra
+
+ align:start position:0%
+studed connector so Queen 10 suited I ra
+ 
+
+ align:start position:0%
+studed connector so Queen 10 suited I ra
+from under the gun and the big blind
+
+ align:start position:0%
+from under the gun and the big blind
+ 
+
+ align:start position:0%
+from under the gun and the big blind
+calls when they're they only start the
+
+ align:start position:0%
+calls when they're they only start the
+ 
+
+ align:start position:0%
+calls when they're they only start the
+hand being 18 bets
+
+ align:start position:0%
+hand being 18 bets
+ 
+
+ align:start position:0%
+hand being 18 bets
+deep so we Flop 2 to10 and I think so
+
+ align:start position:0%
+deep so we Flop 2 to10 and I think so
+ 
+
+ align:start position:0%
+deep so we Flop 2 to10 and I think so
+this is a good example of I think of
+
+ align:start position:0%
+this is a good example of I think of
+ 
+
+ align:start position:0%
+this is a good example of I think of
+very dry board where there's really not
+
+ align:start position:0%
+very dry board where there's really not
+ 
+
+ align:start position:0%
+very dry board where there's really not
+much going on um and it is possible they
+
+ align:start position:0%
+much going on um and it is possible they
+ 
+
+ align:start position:0%
+much going on um and it is possible they
+have a deuce but just in general there's
+
+ align:start position:0%
+have a deuce but just in general there's
+ 
+
+ align:start position:0%
+have a deuce but just in general there's
+no straight draws no flush draws I guess
+
+ align:start position:0%
+no straight draws no flush draws I guess
+ 
+
+ align:start position:0%
+no straight draws no flush draws I guess
+there are some overcards but still it's
+
+ align:start position:0%
+there are some overcards but still it's
+ 
+
+ align:start position:0%
+there are some overcards but still it's
+pretty close to as as dry as you can get
+
+ align:start position:0%
+pretty close to as as dry as you can get
+ 
+
+ align:start position:0%
+pretty close to as as dry as you can get
+get and they checked me and I bet 2,000
+
+ align:start position:0%
+get and they checked me and I bet 2,000
+ 
+
+ align:start position:0%
+get and they checked me and I bet 2,000
+which I think is actually too big here
+
+ align:start position:0%
+which I think is actually too big here
+ 
+
+ align:start position:0%
+which I think is actually too big here
+like to be honest I don't think I needed
+
+ align:start position:0%
+like to be honest I don't think I needed
+ 
+
+ align:start position:0%
+like to be honest I don't think I needed
+to risk this much I mean I have a good
+
+ align:start position:0%
+to risk this much I mean I have a good
+ 
+
+ align:start position:0%
+to risk this much I mean I have a good
+hand but you know if I had if I didn't
+
+ align:start position:0%
+hand but you know if I had if I didn't
+ 
+
+ align:start position:0%
+hand but you know if I had if I didn't
+have a pair I only want to be betting
+
+ align:start position:0%
+have a pair I only want to be betting
+ 
+
+ align:start position:0%
+have a pair I only want to be betting
+like 1, 1500 I think that's a fine size
+
+ align:start position:0%
+like 1, 1500 I think that's a fine size
+ 
+
+ align:start position:0%
+like 1, 1500 I think that's a fine size
+I think betting 1500 is more than enough
+
+ align:start position:0%
+I think betting 1500 is more than enough
+ 
+
+ align:start position:0%
+I think betting 1500 is more than enough
+on this board just because there's
+
+ align:start position:0%
+on this board just because there's
+ 
+
+ align:start position:0%
+on this board just because there's
+really nothing going on and um but I
+
+ align:start position:0%
+really nothing going on and um but I
+ 
+
+ align:start position:0%
+really nothing going on and um but I
+guess I was lazy I bet 2,000 and uh and
+
+ align:start position:0%
+guess I was lazy I bet 2,000 and uh and
+ 
+
+ align:start position:0%
+guess I was lazy I bet 2,000 and uh and
+they call so so yeah so this is the so
+
+ align:start position:0%
+they call so so yeah so this is the so
+ 
+
+ align:start position:0%
+they call so so yeah so this is the so
+as you can see there's a huge difference
+
+ align:start position:0%
+as you can see there's a huge difference
+ 
+
+ align:start position:0%
+as you can see there's a huge difference
+between my flop bet sizing depending on
+
+ align:start position:0%
+between my flop bet sizing depending on
+ 
+
+ align:start position:0%
+between my flop bet sizing depending on
+the texture of the board and that's sort
+
+ align:start position:0%
+the texture of the board and that's sort
+ 
+
+ align:start position:0%
+the texture of the board and that's sort
+of what I want to do drive that's the
+
+ align:start position:0%
+of what I want to do drive that's the
+ 
+
+ align:start position:0%
+of what I want to do drive that's the
+point I wanted to drive across through
+
+ align:start position:0%
+point I wanted to drive across through
+ 
+
+ align:start position:0%
+point I wanted to drive across through
+some of these examples so they call me
+
+ align:start position:0%
+some of these examples so they call me
+ 
+
+ align:start position:0%
+some of these examples so they call me
+so we turn a six and and they they check
+
+ align:start position:0%
+so we turn a six and and they they check
+ 
+
+ align:start position:0%
+so we turn a six and and they they check
+I'm just going to keep it simple and bet
+
+ align:start position:0%
+I'm just going to keep it simple and bet
+ 
+
+ align:start position:0%
+I'm just going to keep it simple and bet
+I'm not going to try anything tricky and
+
+ align:start position:0%
+I'm not going to try anything tricky and
+ 
+
+ align:start position:0%
+I'm not going to try anything tricky and
+obviously I'm not folding with top here
+
+ align:start position:0%
+obviously I'm not folding with top here
+ 
+
+ align:start position:0%
+obviously I'm not folding with top here
+and a flush
+
+ align:start position:0%
+and a flush
+ 
+
+ align:start position:0%
+and a flush
+drop so they go all in I call so we
+
+ align:start position:0%
+drop so they go all in I call so we
+ 
+
+ align:start position:0%
+drop so they go all in I call so we
+remember a flush and it turned out to
+
+ align:start position:0%
+remember a flush and it turned out to
+ 
+
+ align:start position:0%
+remember a flush and it turned out to
+actually be necessary cuz they had a
+
+ align:start position:0%
+actually be necessary cuz they had a
+ 
+
+ align:start position:0%
+actually be necessary cuz they had a
+deuce um so it is possible here I think
+
+ align:start position:0%
+deuce um so it is possible here I think
+ 
+
+ align:start position:0%
+deuce um so it is possible here I think
+for them you have a deuce you know I
+
+ align:start position:0%
+for them you have a deuce you know I
+ 
+
+ align:start position:0%
+for them you have a deuce you know I
+think their play preflop is is a bit
+
+ align:start position:0%
+think their play preflop is is a bit
+ 
+
+ align:start position:0%
+think their play preflop is is a bit
+loose with 29 suited but not completely
+
+ align:start position:0%
+loose with 29 suited but not completely
+ 
+
+ align:start position:0%
+loose with 29 suited but not completely
+terrible cuzz with four .5 to1 odds
+
+ align:start position:0%
+terrible cuzz with four .5 to1 odds
+ 
+
+ align:start position:0%
+terrible cuzz with four .5 to1 odds
+nothing is really that terrible but I
+
+ align:start position:0%
+nothing is really that terrible but I
+ 
+
+ align:start position:0%
+nothing is really that terrible but I
+guess yeah we get lucky but I do think
+
+ align:start position:0%
+guess yeah we get lucky but I do think
+ 
+
+ align:start position:0%
+guess yeah we get lucky but I do think
+their call is a bit marginal cuz we are
+
+ align:start position:0%
+their call is a bit marginal cuz we are
+ 
+
+ align:start position:0%
+their call is a bit marginal cuz we are
+under the gun so you know our range is
+
+ align:start position:0%
+under the gun so you know our range is
+ 
+
+ align:start position:0%
+under the gun so you know our range is
+fairly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strong so that's a nice pop to win so
+
+ align:start position:0%
+strong so that's a nice pop to win so
+ 
+
+ align:start position:0%
+strong so that's a nice pop to win so
+we're we're a fairly big stack now um I
+
+ align:start position:0%
+we're we're a fairly big stack now um I
+ 
+
+ align:start position:0%
+we're we're a fairly big stack now um I
+guess we're chip leader at the table and
+
+ align:start position:0%
+guess we're chip leader at the table and
+ 
+
+ align:start position:0%
+guess we're chip leader at the table and
+check raise Min raises from there and we
+
+ align:start position:0%
+check raise Min raises from there and we
+ 
+
+ align:start position:0%
+check raise Min raises from there and we
+have pocket Deuces I think definitely
+
+ align:start position:0%
+have pocket Deuces I think definitely
+ 
+
+ align:start position:0%
+have pocket Deuces I think definitely
+our hands too weak to go all in with as
+
+ align:start position:0%
+our hands too weak to go all in with as
+ 
+
+ align:start position:0%
+our hands too weak to go all in with as
+a bluff against an under the gun opening
+
+ align:start position:0%
+a bluff against an under the gun opening
+ 
+
+ align:start position:0%
+a bluff against an under the gun opening
+range so the only options really are
+
+ align:start position:0%
+range so the only options really are
+ 
+
+ align:start position:0%
+range so the only options really are
+call or fold uh basically our hand does
+
+ align:start position:0%
+call or fold uh basically our hand does
+ 
+
+ align:start position:0%
+call or fold uh basically our hand does
+have terrible reverse and ply dos post
+
+ align:start position:0%
+have terrible reverse and ply dos post
+ 
+
+ align:start position:0%
+have terrible reverse and ply dos post
+swap though so I think you know I think
+
+ align:start position:0%
+swap though so I think you know I think
+ 
+
+ align:start position:0%
+swap though so I think you know I think
+if you wanted to defold here it wouldn't
+
+ align:start position:0%
+if you wanted to defold here it wouldn't
+ 
+
+ align:start position:0%
+if you wanted to defold here it wouldn't
+be terrible but I guess I think calling
+
+ align:start position:0%
+be terrible but I guess I think calling
+ 
+
+ align:start position:0%
+be terrible but I guess I think calling
+is fine too with 4.5 to1 and also you
+
+ align:start position:0%
+is fine too with 4.5 to1 and also you
+ 
+
+ align:start position:0%
+is fine too with 4.5 to1 and also you
+know in some sense you do have odds to
+
+ align:start position:0%
+know in some sense you do have odds to
+ 
+
+ align:start position:0%
+know in some sense you do have odds to
+set mine here I think because uh because
+
+ align:start position:0%
+set mine here I think because uh because
+ 
+
+ align:start position:0%
+set mine here I think because uh because
+so the chances of hitting a third dece
+
+ align:start position:0%
+so the chances of hitting a third dece
+ 
+
+ align:start position:0%
+so the chances of hitting a third dece
+on the Flop is about one and eight so my
+
+ align:start position:0%
+on the Flop is about one and eight so my
+ 
+
+ align:start position:0%
+on the Flop is about one and eight so my
+odds are only 4.5 to one but there are
+
+ align:start position:0%
+odds are only 4.5 to one but there are
+ 
+
+ align:start position:0%
+odds are only 4.5 to one but there are
+implied odds in the case I do hit a set
+
+ align:start position:0%
+implied odds in the case I do hit a set
+ 
+
+ align:start position:0%
+implied odds in the case I do hit a set
+so like literally if my strategy is call
+
+ align:start position:0%
+so like literally if my strategy is call
+ 
+
+ align:start position:0%
+so like literally if my strategy is call
+and fold unless the pop has a two on it
+
+ align:start position:0%
+and fold unless the pop has a two on it
+ 
+
+ align:start position:0%
+and fold unless the pop has a two on it
+I don't think I'm losing a ton of money
+
+ align:start position:0%
+I don't think I'm losing a ton of money
+ 
+
+ align:start position:0%
+I don't think I'm losing a ton of money
+there and you know if there ever is a
+
+ align:start position:0%
+there and you know if there ever is a
+ 
+
+ align:start position:0%
+there and you know if there ever is a
+case where I where they check down and I
+
+ align:start position:0%
+case where I where they check down and I
+ 
+
+ align:start position:0%
+case where I where they check down and I
+get to take down the pot with just a
+
+ align:start position:0%
+get to take down the pot with just a
+ 
+
+ align:start position:0%
+get to take down the pot with just a
+pair of twos then I'm just printing
+
+ align:start position:0%
+pair of twos then I'm just printing
+ 
+
+ align:start position:0%
+pair of twos then I'm just printing
+money by calling so so I said call The
+
+ align:start position:0%
+money by calling so so I said call The
+ 
+
+ align:start position:0%
+money by calling so so I said call The
+Flop is the Flop doesn't have a two so
+
+ align:start position:0%
+Flop is the Flop doesn't have a two so
+ 
+
+ align:start position:0%
+Flop is the Flop doesn't have a two so
+it's bad but you know out of the flops I
+
+ align:start position:0%
+it's bad but you know out of the flops I
+ 
+
+ align:start position:0%
+it's bad but you know out of the flops I
+don't have a two it's probably not that
+
+ align:start position:0%
+don't have a two it's probably not that
+ 
+
+ align:start position:0%
+don't have a two it's probably not that
+bad considering the the three and seven
+
+ align:start position:0%
+bad considering the the three and seven
+ 
+
+ align:start position:0%
+bad considering the the three and seven
+is not that likely to PIR him when he's
+
+ align:start position:0%
+is not that likely to PIR him when he's
+ 
+
+ align:start position:0%
+is not that likely to PIR him when he's
+under the gun but nonetheless I fold you
+
+ align:start position:0%
+under the gun but nonetheless I fold you
+ 
+
+ align:start position:0%
+under the gun but nonetheless I fold you
+know like if I could do the cheat I
+
+ align:start position:0%
+know like if I could do the cheat I
+ 
+
+ align:start position:0%
+know like if I could do the cheat I
+talked about where I could disconnect
+
+ align:start position:0%
+talked about where I could disconnect
+ 
+
+ align:start position:0%
+talked about where I could disconnect
+and call and see the river I definitely
+
+ align:start position:0%
+and call and see the river I definitely
+ 
+
+ align:start position:0%
+and call and see the river I definitely
+would but you know if I call I have to
+
+ align:start position:0%
+would but you know if I call I have to
+ 
+
+ align:start position:0%
+would but you know if I call I have to
+decide again on the turn rther to call
+
+ align:start position:0%
+decide again on the turn rther to call
+ 
+
+ align:start position:0%
+decide again on the turn rther to call
+and decide again on the River weather to
+
+ align:start position:0%
+and decide again on the River weather to
+ 
+
+ align:start position:0%
+and decide again on the River weather to
+call and it's just not going to be a
+
+ align:start position:0%
+call and it's just not going to be a
+ 
+
+ align:start position:0%
+call and it's just not going to be a
+good situation even though for this
+
+ align:start position:0%
+good situation even though for this
+ 
+
+ align:start position:0%
+good situation even though for this
+immediate bet I think I definitely have
+
+ align:start position:0%
+immediate bet I think I definitely have
+ 
+
+ align:start position:0%
+immediate bet I think I definitely have
+odds to call uh with a back door flush
+
+ align:start position:0%
+odds to call uh with a back door flush
+ 
+
+ align:start position:0%
+odds to call uh with a back door flush
+draw and often they're just going to
+
+ align:start position:0%
+draw and often they're just going to
+ 
+
+ align:start position:0%
+draw and often they're just going to
+have Ace King but it's just impossible
+
+ align:start position:0%
+have Ace King but it's just impossible
+ 
+
+ align:start position:0%
+have Ace King but it's just impossible
+play the hand in this sort of just
+
+ align:start position:0%
+play the hand in this sort of just
+ 
+
+ align:start position:0%
+play the hand in this sort of just
+demonstrates you know why it's very
+
+ align:start position:0%
+demonstrates you know why it's very
+ 
+
+ align:start position:0%
+demonstrates you know why it's very
+risky when you decide to play hand like
+
+ align:start position:0%
+risky when you decide to play hand like
+ 
+
+ align:start position:0%
+risky when you decide to play hand like
+pocket Deuces out of position CU it's
+
+ align:start position:0%
+pocket Deuces out of position CU it's
+ 
+
+ align:start position:0%
+pocket Deuces out of position CU it's
+it's very easy to get roped in right
+
+ align:start position:0%
+it's very easy to get roped in right
+ 
+
+ align:start position:0%
+it's very easy to get roped in right
+like let's say I call here and then I
+
+ align:start position:0%
+like let's say I call here and then I
+ 
+
+ align:start position:0%
+like let's say I call here and then I
+call the Flop thinking they might have a
+
+ align:start position:0%
+call the Flop thinking they might have a
+ 
+
+ align:start position:0%
+call the Flop thinking they might have a
+king they bet small so I have good odds
+
+ align:start position:0%
+king they bet small so I have good odds
+ 
+
+ align:start position:0%
+king they bet small so I have good odds
+and I have a back door flash drop so
+
+ align:start position:0%
+and I have a back door flash drop so
+ 
+
+ align:start position:0%
+and I have a back door flash drop so
+let's say I call and then the turn is
+
+ align:start position:0%
+let's say I call and then the turn is
+ 
+
+ align:start position:0%
+let's say I call and then the turn is
+like the five of clubs or something and
+
+ align:start position:0%
+like the five of clubs or something and
+ 
+
+ align:start position:0%
+like the five of clubs or something and
+then they bet like 40% of pot well like
+
+ align:start position:0%
+then they bet like 40% of pot well like
+ 
+
+ align:start position:0%
+then they bet like 40% of pot well like
+am I going to talk talk myself into a
+
+ align:start position:0%
+am I going to talk talk myself into a
+ 
+
+ align:start position:0%
+am I going to talk talk myself into a
+call again maybe because now I hit a
+
+ align:start position:0%
+call again maybe because now I hit a
+ 
+
+ align:start position:0%
+call again maybe because now I hit a
+third Club but if I do then if the river
+
+ align:start position:0%
+third Club but if I do then if the river
+ 
+
+ align:start position:0%
+third Club but if I do then if the river
+something random I have to so it's just
+
+ align:start position:0%
+something random I have to so it's just
+ 
+
+ align:start position:0%
+something random I have to so it's just
+all these decisions that I'm not going
+
+ align:start position:0%
+all these decisions that I'm not going
+ 
+
+ align:start position:0%
+all these decisions that I'm not going
+to be able to make well whereas for my
+
+ align:start position:0%
+to be able to make well whereas for my
+ 
+
+ align:start position:0%
+to be able to make well whereas for my
+opponent it's going to be fairly easy
+
+ align:start position:0%
+opponent it's going to be fairly easy
+ 
+
+ align:start position:0%
+opponent it's going to be fairly easy
+they're going to just Bluff their bad
+
+ align:start position:0%
+they're going to just Bluff their bad
+ 
+
+ align:start position:0%
+they're going to just Bluff their bad
+hands value bet their good hands and
+
+ align:start position:0%
+hands value bet their good hands and
+ 
+
+ align:start position:0%
+hands value bet their good hands and
+check down the hands in the middle which
+
+ align:start position:0%
+check down the hands in the middle which
+ 
+
+ align:start position:0%
+check down the hands in the middle which
+beat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me okay so the next hand we get Ace King
+
+ align:start position:0%
+me okay so the next hand we get Ace King
+ 
+
+ align:start position:0%
+me okay so the next hand we get Ace King
+off suit and we raise and the big blind
+
+ align:start position:0%
+off suit and we raise and the big blind
+ 
+
+ align:start position:0%
+off suit and we raise and the big blind
+calls flop is 927 so note that the big
+
+ align:start position:0%
+calls flop is 927 so note that the big
+ 
+
+ align:start position:0%
+calls flop is 927 so note that the big
+blind just got moved to the table and
+
+ align:start position:0%
+blind just got moved to the table and
+ 
+
+ align:start position:0%
+blind just got moved to the table and
+they actually cover us so so they're
+
+ align:start position:0%
+they actually cover us so so they're
+ 
+
+ align:start position:0%
+they actually cover us so so they're
+they're probably one of the biggest
+
+ align:start position:0%
+they're probably one of the biggest
+ 
+
+ align:start position:0%
+they're probably one of the biggest
+Stacks in the tournament um so they
+
+ align:start position:0%
+Stacks in the tournament um so they
+ 
+
+ align:start position:0%
+Stacks in the tournament um so they
+checked to us I decided to check back
+
+ align:start position:0%
+checked to us I decided to check back
+ 
+
+ align:start position:0%
+checked to us I decided to check back
+here which I don't think is terrible but
+
+ align:start position:0%
+here which I don't think is terrible but
+ 
+
+ align:start position:0%
+here which I don't think is terrible but
+I think it's a bit of a scared play that
+
+ align:start position:0%
+I think it's a bit of a scared play that
+ 
+
+ align:start position:0%
+I think it's a bit of a scared play that
+I I think I would have rather saw myself
+
+ align:start position:0%
+I I think I would have rather saw myself
+ 
+
+ align:start position:0%
+I I think I would have rather saw myself
+bet um you know if it was shallower like
+
+ align:start position:0%
+bet um you know if it was shallower like
+ 
+
+ align:start position:0%
+bet um you know if it was shallower like
+let's say we only had 20,000 chips then
+
+ align:start position:0%
+let's say we only had 20,000 chips then
+ 
+
+ align:start position:0%
+let's say we only had 20,000 chips then
+I think just checking is good because if
+
+ align:start position:0%
+I think just checking is good because if
+ 
+
+ align:start position:0%
+I think just checking is good because if
+I bet they're probably going to be check
+
+ align:start position:0%
+I bet they're probably going to be check
+ 
+
+ align:start position:0%
+I bet they're probably going to be check
+raising with a lot of their flush draws
+
+ align:start position:0%
+raising with a lot of their flush draws
+ 
+
+ align:start position:0%
+raising with a lot of their flush draws
+straight draws and then like pairs of
+
+ align:start position:0%
+straight draws and then like pairs of
+ 
+
+ align:start position:0%
+straight draws and then like pairs of
+nines or pairs of sevens and I'm going
+
+ align:start position:0%
+nines or pairs of sevens and I'm going
+ 
+
+ align:start position:0%
+nines or pairs of sevens and I'm going
+to have to fold with a pretty good hand
+
+ align:start position:0%
+to have to fold with a pretty good hand
+ 
+
+ align:start position:0%
+to have to fold with a pretty good hand
+where I have two good overcards and a
+
+ align:start position:0%
+where I have two good overcards and a
+ 
+
+ align:start position:0%
+where I have two good overcards and a
+back door flash drop but when it's this
+
+ align:start position:0%
+back door flash drop but when it's this
+ 
+
+ align:start position:0%
+back door flash drop but when it's this
+deep you know they they really can't
+
+ align:start position:0%
+deep you know they they really can't
+ 
+
+ align:start position:0%
+deep you know they they really can't
+just check raise a nine CU they're going
+
+ align:start position:0%
+just check raise a nine CU they're going
+ 
+
+ align:start position:0%
+just check raise a nine CU they're going
+to have to be worried about pocket aces
+
+ align:start position:0%
+to have to be worried about pocket aces
+ 
+
+ align:start position:0%
+to have to be worried about pocket aces
+on our part so so I think it's we're not
+
+ align:start position:0%
+on our part so so I think it's we're not
+ 
+
+ align:start position:0%
+on our part so so I think it's we're not
+going to get check raised that often and
+
+ align:start position:0%
+going to get check raised that often and
+ 
+
+ align:start position:0%
+going to get check raised that often and
+by betting we just make the pot bigger
+
+ align:start position:0%
+by betting we just make the pot bigger
+ 
+
+ align:start position:0%
+by betting we just make the pot bigger
+when we do hit a king or an Ace and also
+
+ align:start position:0%
+when we do hit a king or an Ace and also
+ 
+
+ align:start position:0%
+when we do hit a king or an Ace and also
+make it more likely that we can Bluff
+
+ align:start position:0%
+make it more likely that we can Bluff
+ 
+
+ align:start position:0%
+make it more likely that we can Bluff
+them off a 9 or a seven by the river so
+
+ align:start position:0%
+them off a 9 or a seven by the river so
+ 
+
+ align:start position:0%
+them off a 9 or a seven by the river so
+I would have liked to see myself bet but
+
+ align:start position:0%
+I would have liked to see myself bet but
+ 
+
+ align:start position:0%
+I would have liked to see myself bet but
+I don't think checking is terrible by
+
+ align:start position:0%
+I don't think checking is terrible by
+ 
+
+ align:start position:0%
+I don't think checking is terrible by
+the argument that I will most of the
+
+ align:start position:0%
+the argument that I will most of the
+ 
+
+ align:start position:0%
+the argument that I will most of the
+time you know by betting I am folding
+
+ align:start position:0%
+time you know by betting I am folding
+ 
+
+ align:start position:0%
+time you know by betting I am folding
+out basically all the hands that I beat
+
+ align:start position:0%
+out basically all the hands that I beat
+ 
+
+ align:start position:0%
+out basically all the hands that I beat
+and keeping in all the hands that beat
+
+ align:start position:0%
+and keeping in all the hands that beat
+ 
+
+ align:start position:0%
+and keeping in all the hands that beat
+me so it's close but I would have lik to
+
+ align:start position:0%
+me so it's close but I would have lik to
+ 
+
+ align:start position:0%
+me so it's close but I would have lik to
+see myself that but as played you know
+
+ align:start position:0%
+see myself that but as played you know
+ 
+
+ align:start position:0%
+see myself that but as played you know
+if I'm going to check the Flop I'm not
+
+ align:start position:0%
+if I'm going to check the Flop I'm not
+ 
+
+ align:start position:0%
+if I'm going to check the Flop I'm not
+going to bet this turn cuz the whole
+
+ align:start position:0%
+going to bet this turn cuz the whole
+ 
+
+ align:start position:0%
+going to bet this turn cuz the whole
+point of betting the Flop is so that I
+
+ align:start position:0%
+point of betting the Flop is so that I
+ 
+
+ align:start position:0%
+point of betting the Flop is so that I
+could potentially bet the turn and bet
+
+ align:start position:0%
+could potentially bet the turn and bet
+ 
+
+ align:start position:0%
+could potentially bet the turn and bet
+the river and get him to fold a pair of
+
+ align:start position:0%
+the river and get him to fold a pair of
+ 
+
+ align:start position:0%
+the river and get him to fold a pair of
+nines or a pair of sevens but by now I'm
+
+ align:start position:0%
+nines or a pair of sevens but by now I'm
+ 
+
+ align:start position:0%
+nines or a pair of sevens but by now I'm
+not going to really have any hope of
+
+ align:start position:0%
+not going to really have any hope of
+ 
+
+ align:start position:0%
+not going to really have any hope of
+getting him to fold a nine and I'm just
+
+ align:start position:0%
+getting him to fold a nine and I'm just
+ 
+
+ align:start position:0%
+getting him to fold a nine and I'm just
+going to try to win the pot with my East
+
+ align:start position:0%
+going to try to win the pot with my East
+ 
+
+ align:start position:0%
+going to try to win the pot with my East
+King High and so I just check it down um
+
+ align:start position:0%
+King High and so I just check it down um
+ 
+
+ align:start position:0%
+King High and so I just check it down um
+the river check I think is very very
+
+ align:start position:0%
+the river check I think is very very
+ 
+
+ align:start position:0%
+the river check I think is very very
+obvious because I'm literally only
+
+ align:start position:0%
+obvious because I'm literally only
+ 
+
+ align:start position:0%
+obvious because I'm literally only
+getting called by better hands if I bet
+
+ align:start position:0%
+getting called by better hands if I bet
+ 
+
+ align:start position:0%
+getting called by better hands if I bet
+the river so they so they have Queen 10
+
+ align:start position:0%
+the river so they so they have Queen 10
+ 
+
+ align:start position:0%
+the river so they so they have Queen 10
+I think they probably should have
+
+ align:start position:0%
+I think they probably should have
+ 
+
+ align:start position:0%
+I think they probably should have
+bluffed the river I think Queen 10 is
+
+ align:start position:0%
+bluffed the river I think Queen 10 is
+ 
+
+ align:start position:0%
+bluffed the river I think Queen 10 is
+weak enough where they're just very
+
+ align:start position:0%
+weak enough where they're just very
+ 
+
+ align:start position:0%
+weak enough where they're just very
+rarely winning the pot with Queen 10
+
+ align:start position:0%
+rarely winning the pot with Queen 10
+ 
+
+ align:start position:0%
+rarely winning the pot with Queen 10
+high that they basically need to Bluff
+
+ align:start position:0%
+high that they basically need to Bluff
+ 
+
+ align:start position:0%
+high that they basically need to Bluff
+and then put me to a decision but nice
+
+ align:start position:0%
+and then put me to a decision but nice
+ 
+
+ align:start position:0%
+and then put me to a decision but nice
+to win
+
+ align:start position:0%
+to win
+ 
+
+ align:start position:0%
+to win
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay the next hand we have Jack 10 so
+
+ align:start position:0%
+okay the next hand we have Jack 10 so
+ 
+
+ align:start position:0%
+okay the next hand we have Jack 10 so
+not too exciting so this same guy who's
+
+ align:start position:0%
+not too exciting so this same guy who's
+ 
+
+ align:start position:0%
+not too exciting so this same guy who's
+now the button raises from the button
+
+ align:start position:0%
+now the button raises from the button
+ 
+
+ align:start position:0%
+now the button raises from the button
+and we call and we flop nothing so the
+
+ align:start position:0%
+and we call and we flop nothing so the
+ 
+
+ align:start position:0%
+and we call and we flop nothing so the
+best thing to do is Bluff off all your
+
+ align:start position:0%
+best thing to do is Bluff off all your
+ 
+
+ align:start position:0%
+best thing to do is Bluff off all your
+chips but no I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+juston okay so the next hand is also
+
+ align:start position:0%
+juston okay so the next hand is also
+ 
+
+ align:start position:0%
+juston okay so the next hand is also
+against this Garla edu so we're actually
+
+ align:start position:0%
+against this Garla edu so we're actually
+ 
+
+ align:start position:0%
+against this Garla edu so we're actually
+playing so the two big Stacks at the
+
+ align:start position:0%
+playing so the two big Stacks at the
+ 
+
+ align:start position:0%
+playing so the two big Stacks at the
+table are actually playing a lot of
+
+ align:start position:0%
+table are actually playing a lot of
+ 
+
+ align:start position:0%
+table are actually playing a lot of
+hands against each other um I just call
+
+ align:start position:0%
+hands against each other um I just call
+ 
+
+ align:start position:0%
+hands against each other um I just call
+here with Jacks I think I don't think it
+
+ align:start position:0%
+here with Jacks I think I don't think it
+ 
+
+ align:start position:0%
+here with Jacks I think I don't think it
+would be terrible to just raise and get
+
+ align:start position:0%
+would be terrible to just raise and get
+ 
+
+ align:start position:0%
+would be terrible to just raise and get
+it all in but I think it's it's it is
+
+ align:start position:0%
+it all in but I think it's it's it is
+ 
+
+ align:start position:0%
+it all in but I think it's it's it is
+sort of unnecessarily risky like I think
+
+ align:start position:0%
+sort of unnecessarily risky like I think
+ 
+
+ align:start position:0%
+sort of unnecessarily risky like I think
+um I think it wouldn't be it wouldn't be
+
+ align:start position:0%
+um I think it wouldn't be it wouldn't be
+ 
+
+ align:start position:0%
+um I think it wouldn't be it wouldn't be
+a terrible play to just raise and get it
+
+ align:start position:0%
+a terrible play to just raise and get it
+ 
+
+ align:start position:0%
+a terrible play to just raise and get it
+all in but it's definitely thin like
+
+ align:start position:0%
+all in but it's definitely thin like
+ 
+
+ align:start position:0%
+all in but it's definitely thin like
+you're not printing value by raising and
+
+ align:start position:0%
+you're not printing value by raising and
+ 
+
+ align:start position:0%
+you're not printing value by raising and
+getting it all in because if they rra
+
+ align:start position:0%
+getting it all in because if they rra
+ 
+
+ align:start position:0%
+getting it all in because if they rra
+all in their range is going to be pretty
+
+ align:start position:0%
+all in their range is going to be pretty
+ 
+
+ align:start position:0%
+all in their range is going to be pretty
+strong and pocket Jacks is not really
+
+ align:start position:0%
+strong and pocket Jacks is not really
+ 
+
+ align:start position:0%
+strong and pocket Jacks is not really
+crushing them so um I think you need to
+
+ align:start position:0%
+crushing them so um I think you need to
+ 
+
+ align:start position:0%
+crushing them so um I think you need to
+have queens or better to really be
+
+ align:start position:0%
+have queens or better to really be
+ 
+
+ align:start position:0%
+have queens or better to really be
+hoping to get it on against uh this guy
+
+ align:start position:0%
+hoping to get it on against uh this guy
+ 
+
+ align:start position:0%
+hoping to get it on against uh this guy
+here so with Jack I just call and also
+
+ align:start position:0%
+here so with Jack I just call and also
+ 
+
+ align:start position:0%
+here so with Jack I just call and also
+you know this protects my calling range
+
+ align:start position:0%
+you know this protects my calling range
+ 
+
+ align:start position:0%
+you know this protects my calling range
+of bit like let's say let's say like
+
+ align:start position:0%
+of bit like let's say let's say like
+ 
+
+ align:start position:0%
+of bit like let's say let's say like
+check Rays thinks I'm weak and decides
+
+ align:start position:0%
+check Rays thinks I'm weak and decides
+ 
+
+ align:start position:0%
+check Rays thinks I'm weak and decides
+to make a play here and they R ra to
+
+ align:start position:0%
+to make a play here and they R ra to
+ 
+
+ align:start position:0%
+to make a play here and they R ra to
+like 10,000 then if Gara Ed folds I can
+
+ align:start position:0%
+like 10,000 then if Gara Ed folds I can
+ 
+
+ align:start position:0%
+like 10,000 then if Gara Ed folds I can
+come back around and go all in and sort
+
+ align:start position:0%
+come back around and go all in and sort
+ 
+
+ align:start position:0%
+come back around and go all in and sort
+of surprise them so it does protect my
+
+ align:start position:0%
+of surprise them so it does protect my
+ 
+
+ align:start position:0%
+of surprise them so it does protect my
+calling range a bit as well I call we
+
+ align:start position:0%
+calling range a bit as well I call we
+ 
+
+ align:start position:0%
+calling range a bit as well I call we
+get a 965 flop um they check and I bet
+
+ align:start position:0%
+get a 965 flop um they check and I bet
+ 
+
+ align:start position:0%
+get a 965 flop um they check and I bet
+and I think betting is a fairly natural
+
+ align:start position:0%
+and I think betting is a fairly natural
+ 
+
+ align:start position:0%
+and I think betting is a fairly natural
+play you know I don't want to give Ace
+
+ align:start position:0%
+play you know I don't want to give Ace
+ 
+
+ align:start position:0%
+play you know I don't want to give Ace
+King outs and I just want to win the
+
+ align:start position:0%
+King outs and I just want to win the
+ 
+
+ align:start position:0%
+King outs and I just want to win the
+pawn right now but I was thinking to
+
+ align:start position:0%
+pawn right now but I was thinking to
+ 
+
+ align:start position:0%
+pawn right now but I was thinking to
+myself after that you know if they check
+
+ align:start position:0%
+myself after that you know if they check
+ 
+
+ align:start position:0%
+myself after that you know if they check
+raised here that's really a gross spot I
+
+ align:start position:0%
+raised here that's really a gross spot I
+ 
+
+ align:start position:0%
+raised here that's really a gross spot I
+I actually I I would hate my life if
+
+ align:start position:0%
+I actually I I would hate my life if
+ 
+
+ align:start position:0%
+I actually I I would hate my life if
+they check raised here because I I
+
+ align:start position:0%
+they check raised here because I I
+ 
+
+ align:start position:0%
+they check raised here because I I
+literally don't know what I should do
+
+ align:start position:0%
+literally don't know what I should do
+ 
+
+ align:start position:0%
+literally don't know what I should do
+it's at in one on one hand I would you
+
+ align:start position:0%
+it's at in one on one hand I would you
+ 
+
+ align:start position:0%
+it's at in one on one hand I would you
+know I would be inclined to fold because
+
+ align:start position:0%
+know I would be inclined to fold because
+ 
+
+ align:start position:0%
+know I would be inclined to fold because
+it's kind of weird for them to want to
+
+ align:start position:0%
+it's kind of weird for them to want to
+ 
+
+ align:start position:0%
+it's kind of weird for them to want to
+check raise me here I think without um
+
+ align:start position:0%
+check raise me here I think without um
+ 
+
+ align:start position:0%
+check raise me here I think without um
+having it without having like a big pair
+
+ align:start position:0%
+having it without having like a big pair
+ 
+
+ align:start position:0%
+having it without having like a big pair
+or flush draw with lots of outs but at
+
+ align:start position:0%
+or flush draw with lots of outs but at
+ 
+
+ align:start position:0%
+or flush draw with lots of outs but at
+the same time it's just you know why
+
+ align:start position:0%
+the same time it's just you know why
+ 
+
+ align:start position:0%
+the same time it's just you know why
+would they check pocket aces to me here
+
+ align:start position:0%
+would they check pocket aces to me here
+ 
+
+ align:start position:0%
+would they check pocket aces to me here
+maybe they try to trap me so um it would
+
+ align:start position:0%
+maybe they try to trap me so um it would
+ 
+
+ align:start position:0%
+maybe they try to trap me so um it would
+have been a really gross spot I think if
+
+ align:start position:0%
+have been a really gross spot I think if
+ 
+
+ align:start position:0%
+have been a really gross spot I think if
+I got check raised and by that argument
+
+ align:start position:0%
+I got check raised and by that argument
+ 
+
+ align:start position:0%
+I got check raised and by that argument
+I think against a very tricky player who
+
+ align:start position:0%
+I think against a very tricky player who
+ 
+
+ align:start position:0%
+I think against a very tricky player who
+could be check raising her as a trap and
+
+ align:start position:0%
+could be check raising her as a trap and
+ 
+
+ align:start position:0%
+could be check raising her as a trap and
+as a bluff with a Balan strategy maybe
+
+ align:start position:0%
+as a bluff with a Balan strategy maybe
+ 
+
+ align:start position:0%
+as a bluff with a Balan strategy maybe
+checking is better just to protect
+
+ align:start position:0%
+checking is better just to protect
+ 
+
+ align:start position:0%
+checking is better just to protect
+myself from that but I think against him
+
+ align:start position:0%
+myself from that but I think against him
+ 
+
+ align:start position:0%
+myself from that but I think against him
+I was reasonably confident nothing crazy
+
+ align:start position:0%
+I was reasonably confident nothing crazy
+ 
+
+ align:start position:0%
+I was reasonably confident nothing crazy
+was going to happen um and yeah so they
+
+ align:start position:0%
+was going to happen um and yeah so they
+ 
+
+ align:start position:0%
+was going to happen um and yeah so they
+just folded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's against this guy again I
+
+ align:start position:0%
+okay so it's against this guy again I
+ 
+
+ align:start position:0%
+okay so it's against this guy again I
+guess we're playing a lot of pots
+
+ align:start position:0%
+guess we're playing a lot of pots
+ 
+
+ align:start position:0%
+guess we're playing a lot of pots
+against the same player um I think it's
+
+ align:start position:0%
+against the same player um I think it's
+ 
+
+ align:start position:0%
+against the same player um I think it's
+getting fairly late into the tournament
+
+ align:start position:0%
+getting fairly late into the tournament
+ 
+
+ align:start position:0%
+getting fairly late into the tournament
+at this point it's not a huge tournament
+
+ align:start position:0%
+at this point it's not a huge tournament
+ 
+
+ align:start position:0%
+at this point it's not a huge tournament
+maybe like 80 90 players and it's
+
+ align:start position:0%
+maybe like 80 90 players and it's
+ 
+
+ align:start position:0%
+maybe like 80 90 players and it's
+probably down to like 2025 at this point
+
+ align:start position:0%
+probably down to like 2025 at this point
+ 
+
+ align:start position:0%
+probably down to like 2025 at this point
+so they raise we call with Queen eight
+
+ align:start position:0%
+so they raise we call with Queen eight
+ 
+
+ align:start position:0%
+so they raise we call with Queen eight
+off we're a bit deep here so our reverse
+
+ align:start position:0%
+off we're a bit deep here so our reverse
+ 
+
+ align:start position:0%
+off we're a bit deep here so our reverse
+implied odds are actually sort of bad
+
+ align:start position:0%
+implied odds are actually sort of bad
+ 
+
+ align:start position:0%
+implied odds are actually sort of bad
+but um but we decided to call and we
+
+ align:start position:0%
+but um but we decided to call and we
+ 
+
+ align:start position:0%
+but um but we decided to call and we
+flopped 235 so I'm just going to here
+
+ align:start position:0%
+flopped 235 so I'm just going to here
+ 
+
+ align:start position:0%
+flopped 235 so I'm just going to here
+but they decide to check and then we
+
+ align:start position:0%
+but they decide to check and then we
+ 
+
+ align:start position:0%
+but they decide to check and then we
+turn a flush draw but I'm still just
+
+ align:start position:0%
+turn a flush draw but I'm still just
+ 
+
+ align:start position:0%
+turn a flush draw but I'm still just
+going to check and basically bet bet
+
+ align:start position:0%
+going to check and basically bet bet
+ 
+
+ align:start position:0%
+going to check and basically bet bet
+pretty much every river um maybe not an
+
+ align:start position:0%
+pretty much every river um maybe not an
+ 
+
+ align:start position:0%
+pretty much every river um maybe not an
+eight River but so we River a six and I
+
+ align:start position:0%
+eight River but so we River a six and I
+ 
+
+ align:start position:0%
+eight River but so we River a six and I
+essentially bet is a bluff because our
+
+ align:start position:0%
+essentially bet is a bluff because our
+ 
+
+ align:start position:0%
+essentially bet is a bluff because our
+hand has no hope of winning if if it
+
+ align:start position:0%
+hand has no hope of winning if if it
+ 
+
+ align:start position:0%
+hand has no hope of winning if if it
+gets to Showdown and and it works this
+
+ align:start position:0%
+gets to Showdown and and it works this
+ 
+
+ align:start position:0%
+gets to Showdown and and it works this
+time so so yeah we played a lot of pots
+
+ align:start position:0%
+time so so yeah we played a lot of pots
+ 
+
+ align:start position:0%
+time so so yeah we played a lot of pots
+against them and it seems like they are
+
+ align:start position:0%
+against them and it seems like they are
+ 
+
+ align:start position:0%
+against them and it seems like they are
+fairly willing to just um check and fold
+
+ align:start position:0%
+fairly willing to just um check and fold
+ 
+
+ align:start position:0%
+fairly willing to just um check and fold
+their hands so not too aggressive so I I
+
+ align:start position:0%
+their hands so not too aggressive so I I
+ 
+
+ align:start position:0%
+their hands so not too aggressive so I I
+guess one thing to keep in mind is maybe
+
+ align:start position:0%
+guess one thing to keep in mind is maybe
+ 
+
+ align:start position:0%
+guess one thing to keep in mind is maybe
+we should get out of the way if we do
+
+ align:start position:0%
+we should get out of the way if we do
+ 
+
+ align:start position:0%
+we should get out of the way if we do
+see them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+raising um okay so this situation is
+
+ align:start position:0%
+raising um okay so this situation is
+ 
+
+ align:start position:0%
+raising um okay so this situation is
+similar to the situation the very
+
+ align:start position:0%
+similar to the situation the very
+ 
+
+ align:start position:0%
+similar to the situation the very
+firstand we discussed where we had king
+
+ align:start position:0%
+firstand we discussed where we had king
+ 
+
+ align:start position:0%
+firstand we discussed where we had king
+queen and we had roughly 30 big lines
+
+ align:start position:0%
+queen and we had roughly 30 big lines
+ 
+
+ align:start position:0%
+queen and we had roughly 30 big lines
+and I talked sort of about the benefits
+
+ align:start position:0%
+and I talked sort of about the benefits
+ 
+
+ align:start position:0%
+and I talked sort of about the benefits
+of raising versus calling it's pretty
+
+ align:start position:0%
+of raising versus calling it's pretty
+ 
+
+ align:start position:0%
+of raising versus calling it's pretty
+much the exact same situation and I
+
+ align:start position:0%
+much the exact same situation and I
+ 
+
+ align:start position:0%
+much the exact same situation and I
+decid to sort of raise essentially as a
+
+ align:start position:0%
+decid to sort of raise essentially as a
+ 
+
+ align:start position:0%
+decid to sort of raise essentially as a
+bluff but also king queen plays pretty
+
+ align:start position:0%
+bluff but also king queen plays pretty
+ 
+
+ align:start position:0%
+bluff but also king queen plays pretty
+well when they do call um I'm always
+
+ align:start position:0%
+well when they do call um I'm always
+ 
+
+ align:start position:0%
+well when they do call um I'm always
+good when I hit Top pair so we make it
+
+ align:start position:0%
+good when I hit Top pair so we make it
+ 
+
+ align:start position:0%
+good when I hit Top pair so we make it
+8,000 but unfortunately this time this
+
+ align:start position:0%
+8,000 but unfortunately this time this
+ 
+
+ align:start position:0%
+8,000 but unfortunately this time this
+Gerard dox goes all in so we basically
+
+ align:start position:0%
+Gerard dox goes all in so we basically
+ 
+
+ align:start position:0%
+Gerard dox goes all in so we basically
+just have to fold and um yeah
+
+ align:start position:0%
+just have to fold and um yeah
+ 
+
+ align:start position:0%
+just have to fold and um yeah
+unfortunately 8,000 is small enough
+
+ align:start position:0%
+unfortunately 8,000 is small enough
+ 
+
+ align:start position:0%
+unfortunately 8,000 is small enough
+where we can just happily get away here
+
+ align:start position:0%
+where we can just happily get away here
+ 
+
+ align:start position:0%
+where we can just happily get away here
+and it actually turns out this guy also
+
+ align:start position:0%
+and it actually turns out this guy also
+ 
+
+ align:start position:0%
+and it actually turns out this guy also
+goes on which makes the decision even
+
+ align:start position:0%
+goes on which makes the decision even
+ 
+
+ align:start position:0%
+goes on which makes the decision even
+easier so yeah it looks like we R do
+
+ align:start position:0%
+easier so yeah it looks like we R do
+ 
+
+ align:start position:0%
+easier so yeah it looks like we R do
+pocket aces and pocket kings that time
+
+ align:start position:0%
+pocket aces and pocket kings that time
+ 
+
+ align:start position:0%
+pocket aces and pocket kings that time
+so doesn't always work when you R raise
+
+ align:start position:0%
+so doesn't always work when you R raise
+ 
+
+ align:start position:0%
+so doesn't always work when you R raise
+with king queen um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so still at the same table we
+
+ align:start position:0%
+all right so still at the same table we
+ 
+
+ align:start position:0%
+all right so still at the same table we
+get Ace jack off suit under the gun We R
+
+ align:start position:0%
+get Ace jack off suit under the gun We R
+ 
+
+ align:start position:0%
+get Ace jack off suit under the gun We R
+and this uh jard do guy
+
+ align:start position:0%
+and this uh jard do guy
+ 
+
+ align:start position:0%
+and this uh jard do guy
+calls we flop King n Deuce with two
+
+ align:start position:0%
+calls we flop King n Deuce with two
+ 
+
+ align:start position:0%
+calls we flop King n Deuce with two
+hearts and I think this is sort of
+
+ align:start position:0%
+hearts and I think this is sort of
+ 
+
+ align:start position:0%
+hearts and I think this is sort of
+pretty much the worst swop I one of the
+
+ align:start position:0%
+pretty much the worst swop I one of the
+ 
+
+ align:start position:0%
+pretty much the worst swop I one of the
+worst swops I could get um you know if
+
+ align:start position:0%
+worst swops I could get um you know if
+ 
+
+ align:start position:0%
+worst swops I could get um you know if
+there if there was like two higher cards
+
+ align:start position:0%
+there if there was like two higher cards
+ 
+
+ align:start position:0%
+there if there was like two higher cards
+like a king and a queen I would have a
+
+ align:start position:0%
+like a king and a queen I would have a
+ 
+
+ align:start position:0%
+like a king and a queen I would have a
+gutshot straight draw and if it was all
+
+ align:start position:0%
+gutshot straight draw and if it was all
+ 
+
+ align:start position:0%
+gutshot straight draw and if it was all
+low cards I'd have two over cards but
+
+ align:start position:0%
+low cards I'd have two over cards but
+ 
+
+ align:start position:0%
+low cards I'd have two over cards but
+here there's a flush draw that I have no
+
+ align:start position:0%
+here there's a flush draw that I have no
+ 
+
+ align:start position:0%
+here there's a flush draw that I have no
+part of and also they're somewhat likely
+
+ align:start position:0%
+part of and also they're somewhat likely
+ 
+
+ align:start position:0%
+part of and also they're somewhat likely
+to have a king and if they do I only
+
+ align:start position:0%
+to have a king and if they do I only
+ 
+
+ align:start position:0%
+to have a king and if they do I only
+have three outs in my Aces so I'm just
+
+ align:start position:0%
+have three outs in my Aces so I'm just
+ 
+
+ align:start position:0%
+have three outs in my Aces so I'm just
+going to give this up you know so I
+
+ align:start position:0%
+going to give this up you know so I
+ 
+
+ align:start position:0%
+going to give this up you know so I
+talked about the power of continuation
+
+ align:start position:0%
+talked about the power of continuation
+ 
+
+ align:start position:0%
+talked about the power of continuation
+betting before where continuation
+
+ align:start position:0%
+betting before where continuation
+ 
+
+ align:start position:0%
+betting before where continuation
+betting is good because my range is
+
+ align:start position:0%
+betting is good because my range is
+ 
+
+ align:start position:0%
+betting is good because my range is
+stronger than theirs I can have Aces I
+
+ align:start position:0%
+stronger than theirs I can have Aces I
+ 
+
+ align:start position:0%
+stronger than theirs I can have Aces I
+can Bluff Etc and yeah in general
+
+ align:start position:0%
+can Bluff Etc and yeah in general
+ 
+
+ align:start position:0%
+can Bluff Etc and yeah in general
+continuation betting being aggressive
+
+ align:start position:0%
+continuation betting being aggressive
+ 
+
+ align:start position:0%
+continuation betting being aggressive
+especially when you're you're the pre-f
+
+ align:start position:0%
+especially when you're you're the pre-f
+ 
+
+ align:start position:0%
+especially when you're you're the pre-f
+Flop aggressor is very good but I think
+
+ align:start position:0%
+Flop aggressor is very good but I think
+ 
+
+ align:start position:0%
+Flop aggressor is very good but I think
+this is just one of the worst flops and
+
+ align:start position:0%
+this is just one of the worst flops and
+ 
+
+ align:start position:0%
+this is just one of the worst flops and
+I'm just going to give up um
+
+ align:start position:0%
+I'm just going to give up um
+ 
+
+ align:start position:0%
+I'm just going to give up um
+so I check they bet and I fold um I mean
+
+ align:start position:0%
+so I check they bet and I fold um I mean
+ 
+
+ align:start position:0%
+so I check they bet and I fold um I mean
+I think sometimes I will check a
+
+ align:start position:0%
+I think sometimes I will check a
+ 
+
+ align:start position:0%
+I think sometimes I will check a
+reasonably good hand here to protect the
+
+ align:start position:0%
+reasonably good hand here to protect the
+ 
+
+ align:start position:0%
+reasonably good hand here to protect the
+time so you know so so that they can't
+
+ align:start position:0%
+time so you know so so that they can't
+ 
+
+ align:start position:0%
+time so you know so so that they can't
+just bet here with any two cards and no
+
+ align:start position:0%
+just bet here with any two cards and no
+ 
+
+ align:start position:0%
+just bet here with any two cards and no
+for sure aold but most of the time when
+
+ align:start position:0%
+for sure aold but most of the time when
+ 
+
+ align:start position:0%
+for sure aold but most of the time when
+I'm checking here I'm going to be fairly
+
+ align:start position:0%
+I'm checking here I'm going to be fairly
+ 
+
+ align:start position:0%
+I'm checking here I'm going to be fairly
+weak which is maybe exploitable but I
+
+ align:start position:0%
+weak which is maybe exploitable but I
+ 
+
+ align:start position:0%
+weak which is maybe exploitable but I
+give up the
+
+ align:start position:0%
+give up the
+ 
+
+ align:start position:0%
+give up the
+hand so 85 suited I decided to call on
+
+ align:start position:0%
+hand so 85 suited I decided to call on
+ 
+
+ align:start position:0%
+hand so 85 suited I decided to call on
+the small blind um I know this goes
+
+ align:start position:0%
+the small blind um I know this goes
+ 
+
+ align:start position:0%
+the small blind um I know this goes
+against my recommendation from the first
+
+ align:start position:0%
+against my recommendation from the first
+ 
+
+ align:start position:0%
+against my recommendation from the first
+class I think calling from the small
+
+ align:start position:0%
+class I think calling from the small
+ 
+
+ align:start position:0%
+class I think calling from the small
+blind is actually both theoretically and
+
+ align:start position:0%
+blind is actually both theoretically and
+ 
+
+ align:start position:0%
+blind is actually both theoretically and
+practically a pretty good strategy for a
+
+ align:start position:0%
+practically a pretty good strategy for a
+ 
+
+ align:start position:0%
+practically a pretty good strategy for a
+lot of cases but it's a bit complicated
+
+ align:start position:0%
+lot of cases but it's a bit complicated
+ 
+
+ align:start position:0%
+lot of cases but it's a bit complicated
+because you have to sometimes like you
+
+ align:start position:0%
+because you have to sometimes like you
+ 
+
+ align:start position:0%
+because you have to sometimes like you
+have to sometimes limp Rays as a bluff
+
+ align:start position:0%
+have to sometimes limp Rays as a bluff
+ 
+
+ align:start position:0%
+have to sometimes limp Rays as a bluff
+you have to sometimes limp rays and trap
+
+ align:start position:0%
+you have to sometimes limp rays and trap
+ 
+
+ align:start position:0%
+you have to sometimes limp rays and trap
+with Aces so it's a bit complicated so I
+
+ align:start position:0%
+with Aces so it's a bit complicated so I
+ 
+
+ align:start position:0%
+with Aces so it's a bit complicated so I
+I just said for Simplicity you have to
+
+ align:start position:0%
+I just said for Simplicity you have to
+ 
+
+ align:start position:0%
+I just said for Simplicity you have to
+you should just raise or fold which is
+
+ align:start position:0%
+you should just raise or fold which is
+ 
+
+ align:start position:0%
+you should just raise or fold which is
+still reasonable I think but I decid to
+
+ align:start position:0%
+still reasonable I think but I decid to
+ 
+
+ align:start position:0%
+still reasonable I think but I decid to
+call here and it's
+
+ align:start position:0%
+call here and it's
+ 
+
+ align:start position:0%
+call here and it's
+checked we get a pretty good flop for
+
+ align:start position:0%
+checked we get a pretty good flop for
+ 
+
+ align:start position:0%
+checked we get a pretty good flop for
+our hand but probably a better flop for
+
+ align:start position:0%
+our hand but probably a better flop for
+ 
+
+ align:start position:0%
+our hand but probably a better flop for
+his range because when we call
+
+ align:start position:0%
+his range because when we call
+ 
+
+ align:start position:0%
+his range because when we call
+we're less likely to have really small
+
+ align:start position:0%
+we're less likely to have really small
+ 
+
+ align:start position:0%
+we're less likely to have really small
+cards than he does but I mean we have a
+
+ align:start position:0%
+cards than he does but I mean we have a
+ 
+
+ align:start position:0%
+cards than he does but I mean we have a
+good flop for our hand so I I'm still
+
+ align:start position:0%
+good flop for our hand so I I'm still
+ 
+
+ align:start position:0%
+good flop for our hand so I I'm still
+going to bet my good hands so I bet um I
+
+ align:start position:0%
+going to bet my good hands so I bet um I
+ 
+
+ align:start position:0%
+going to bet my good hands so I bet um I
+bet half pot which is maybe not big
+
+ align:start position:0%
+bet half pot which is maybe not big
+ 
+
+ align:start position:0%
+bet half pot which is maybe not big
+enough to be honest considering how dry
+
+ align:start position:0%
+enough to be honest considering how dry
+ 
+
+ align:start position:0%
+enough to be honest considering how dry
+the board is and we get a call we turn a
+
+ align:start position:0%
+the board is and we get a call we turn a
+ 
+
+ align:start position:0%
+the board is and we get a call we turn a
+nine which is a great
+
+ align:start position:0%
+nine which is a great
+ 
+
+ align:start position:0%
+nine which is a great
+card because um it's it gives not only
+
+ align:start position:0%
+card because um it's it gives not only
+ 
+
+ align:start position:0%
+card because um it's it gives not only
+does it complete our hand there's a lot
+
+ align:start position:0%
+does it complete our hand there's a lot
+ 
+
+ align:start position:0%
+does it complete our hand there's a lot
+of draws out there and I bet quite big
+
+ align:start position:0%
+of draws out there and I bet quite big
+ 
+
+ align:start position:0%
+of draws out there and I bet quite big
+here so this is where I was talking
+
+ align:start position:0%
+here so this is where I was talking
+ 
+
+ align:start position:0%
+here so this is where I was talking
+about if the board is dry you need to
+
+ align:start position:0%
+about if the board is dry you need to
+ 
+
+ align:start position:0%
+about if the board is dry you need to
+bet big and not give your opponent odds
+
+ align:start position:0%
+bet big and not give your opponent odds
+ 
+
+ align:start position:0%
+bet big and not give your opponent odds
+so I bet 688 into
+
+ align:start position:0%
+so I bet 688 into
+ 
+
+ align:start position:0%
+so I bet 688 into
+10800 um the reason for the eights is
+
+ align:start position:0%
+10800 um the reason for the eights is
+ 
+
+ align:start position:0%
+10800 um the reason for the eights is
+because it's easier to type like 6888
+
+ align:start position:0%
+because it's easier to type like 6888
+ 
+
+ align:start position:0%
+because it's easier to type like 6888
+than 6800 so you'll see that quite a lot
+
+ align:start position:0%
+than 6800 so you'll see that quite a lot
+ 
+
+ align:start position:0%
+than 6800 so you'll see that quite a lot
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+um and we get
+
+ align:start position:0%
+um and we get
+ 
+
+ align:start position:0%
+um and we get
+called yeah and another sometimes you
+
+ align:start position:0%
+called yeah and another sometimes you
+ 
+
+ align:start position:0%
+called yeah and another sometimes you
+can get more creative you can do like 1
+
+ align:start position:0%
+can get more creative you can do like 1
+ 
+
+ align:start position:0%
+can get more creative you can do like 1
+2 3 4 5 6 7 that's like a popular bet
+
+ align:start position:0%
+2 3 4 5 6 7 that's like a popular bet
+ 
+
+ align:start position:0%
+2 3 4 5 6 7 that's like a popular bet
+because you can just slide your finger
+
+ align:start position:0%
+because you can just slide your finger
+ 
+
+ align:start position:0%
+because you can just slide your finger
+across the keyboard um yeah there's a
+
+ align:start position:0%
+across the keyboard um yeah there's a
+ 
+
+ align:start position:0%
+across the keyboard um yeah there's a
+lot of weird idiots in Innes but okay so
+
+ align:start position:0%
+lot of weird idiots in Innes but okay so
+ 
+
+ align:start position:0%
+lot of weird idiots in Innes but okay so
+I bet
+
+ align:start position:0%
+I bet
+ 
+
+ align:start position:0%
+I bet
+15555 here and um he folds and yeah so I
+
+ align:start position:0%
+15555 here and um he folds and yeah so I
+ 
+
+ align:start position:0%
+15555 here and um he folds and yeah so I
+mean I'm playing I'm playing like this
+
+ align:start position:0%
+mean I'm playing I'm playing like this
+ 
+
+ align:start position:0%
+mean I'm playing I'm playing like this
+with my missed Spade draws my missed
+
+ align:start position:0%
+with my missed Spade draws my missed
+ 
+
+ align:start position:0%
+with my missed Spade draws my missed
+heart draws and unfortunately we don't
+
+ align:start position:0%
+heart draws and unfortunately we don't
+ 
+
+ align:start position:0%
+heart draws and unfortunately we don't
+get paid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off okay so Jack eight suited here the
+
+ align:start position:0%
+off okay so Jack eight suited here the
+ 
+
+ align:start position:0%
+off okay so Jack eight suited here the
+small blind raises definitely I'm going
+
+ align:start position:0%
+small blind raises definitely I'm going
+ 
+
+ align:start position:0%
+small blind raises definitely I'm going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+cough and we flop top pair they bet and
+
+ align:start position:0%
+cough and we flop top pair they bet and
+ 
+
+ align:start position:0%
+cough and we flop top pair they bet and
+so I think this is so this is spot where
+
+ align:start position:0%
+so I think this is so this is spot where
+ 
+
+ align:start position:0%
+so I think this is so this is spot where
+you know I think my hand is there's
+
+ align:start position:0%
+you know I think my hand is there's
+ 
+
+ align:start position:0%
+you know I think my hand is there's
+benefits of raising and benefits of
+
+ align:start position:0%
+benefits of raising and benefits of
+ 
+
+ align:start position:0%
+benefits of raising and benefits of
+calling and overall I decided the
+
+ align:start position:0%
+calling and overall I decided the
+ 
+
+ align:start position:0%
+calling and overall I decided the
+benefits of raising were higher so I
+
+ align:start position:0%
+benefits of raising were higher so I
+ 
+
+ align:start position:0%
+benefits of raising were higher so I
+decided to raise and just get it all in
+
+ align:start position:0%
+decided to raise and just get it all in
+ 
+
+ align:start position:0%
+decided to raise and just get it all in
+although I think calling is not
+
+ align:start position:0%
+although I think calling is not
+ 
+
+ align:start position:0%
+although I think calling is not
+unreasonable because your hand sort of
+
+ align:start position:0%
+unreasonable because your hand sort of
+ 
+
+ align:start position:0%
+unreasonable because your hand sort of
+isn't good enough where you're just like
+
+ align:start position:0%
+isn't good enough where you're just like
+ 
+
+ align:start position:0%
+isn't good enough where you're just like
+really really happy to get it all in I
+
+ align:start position:0%
+really really happy to get it all in I
+ 
+
+ align:start position:0%
+really really happy to get it all in I
+mean it's good enough where I'm going to
+
+ align:start position:0%
+mean it's good enough where I'm going to
+ 
+
+ align:start position:0%
+mean it's good enough where I'm going to
+get it all in but I'm not like thrilled
+
+ align:start position:0%
+get it all in but I'm not like thrilled
+ 
+
+ align:start position:0%
+get it all in but I'm not like thrilled
+if they go all in and I have to call so
+
+ align:start position:0%
+if they go all in and I have to call so
+ 
+
+ align:start position:0%
+if they go all in and I have to call so
+that's one disadvantage of getting it
+
+ align:start position:0%
+that's one disadvantage of getting it
+ 
+
+ align:start position:0%
+that's one disadvantage of getting it
+all in but I just think compared to the
+
+ align:start position:0%
+all in but I just think compared to the
+ 
+
+ align:start position:0%
+all in but I just think compared to the
+advantage of you know not giving them a
+
+ align:start position:0%
+advantage of you know not giving them a
+ 
+
+ align:start position:0%
+advantage of you know not giving them a
+chance to to suuck out on me and beat me
+
+ align:start position:0%
+chance to to suuck out on me and beat me
+ 
+
+ align:start position:0%
+chance to to suuck out on me and beat me
+in the hand is a pretty big Advantage
+
+ align:start position:0%
+in the hand is a pretty big Advantage
+ 
+
+ align:start position:0%
+in the hand is a pretty big Advantage
+you know not letting a queen king or Ace
+
+ align:start position:0%
+you know not letting a queen king or Ace
+ 
+
+ align:start position:0%
+you know not letting a queen king or Ace
+roll off um another advantage of calling
+
+ align:start position:0%
+roll off um another advantage of calling
+ 
+
+ align:start position:0%
+roll off um another advantage of calling
+is being would to pick off Bluffs but I
+
+ align:start position:0%
+is being would to pick off Bluffs but I
+ 
+
+ align:start position:0%
+is being would to pick off Bluffs but I
+just think in this flop I want to play a
+
+ align:start position:0%
+just think in this flop I want to play a
+ 
+
+ align:start position:0%
+just think in this flop I want to play a
+strategy where I'm going to raise to a
+
+ align:start position:0%
+strategy where I'm going to raise to a
+ 
+
+ align:start position:0%
+strategy where I'm going to raise to a
+small size and put him to the decision
+
+ align:start position:0%
+small size and put him to the decision
+ 
+
+ align:start position:0%
+small size and put him to the decision
+both with my top pairs like Jack and
+
+ align:start position:0%
+both with my top pairs like Jack and
+ 
+
+ align:start position:0%
+both with my top pairs like Jack and
+also my hands like 79 or whatever so I
+
+ align:start position:0%
+also my hands like 79 or whatever so I
+ 
+
+ align:start position:0%
+also my hands like 79 or whatever so I
+decided to raise but I think calling
+
+ align:start position:0%
+decided to raise but I think calling
+ 
+
+ align:start position:0%
+decided to raise but I think calling
+would have been fun and if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next hand we have Ace King all right
+
+ align:start position:0%
+the next hand we have Ace King all right
+ 
+
+ align:start position:0%
+the next hand we have Ace King all right
+so we got like seven more hands yeah so
+
+ align:start position:0%
+so we got like seven more hands yeah so
+ 
+
+ align:start position:0%
+so we got like seven more hands yeah so
+I'll I'll go a bit quickly near the end
+
+ align:start position:0%
+I'll I'll go a bit quickly near the end
+ 
+
+ align:start position:0%
+I'll I'll go a bit quickly near the end
+but I think we'll get through all the
+
+ align:start position:0%
+but I think we'll get through all the
+ 
+
+ align:start position:0%
+but I think we'll get through all the
+hands uh this hand is fairly easy they
+
+ align:start position:0%
+hands uh this hand is fairly easy they
+ 
+
+ align:start position:0%
+hands uh this hand is fairly easy they
+they make it 5,000 and we have Ace King
+
+ align:start position:0%
+they make it 5,000 and we have Ace King
+ 
+
+ align:start position:0%
+they make it 5,000 and we have Ace King
+and we just go all in there's no point
+
+ align:start position:0%
+and we just go all in there's no point
+ 
+
+ align:start position:0%
+and we just go all in there's no point
+slow playing essentially um especially
+
+ align:start position:0%
+slow playing essentially um especially
+ 
+
+ align:start position:0%
+slow playing essentially um especially
+when you know if they have Jack 10 they
+
+ align:start position:0%
+when you know if they have Jack 10 they
+ 
+
+ align:start position:0%
+when you know if they have Jack 10 they
+have lots of outs so we go on and they
+
+ align:start position:0%
+have lots of outs so we go on and they
+ 
+
+ align:start position:0%
+have lots of outs so we go on and they
+fold so it is a bit curious here because
+
+ align:start position:0%
+fold so it is a bit curious here because
+ 
+
+ align:start position:0%
+fold so it is a bit curious here because
+they actually only had 12 big blinds
+
+ align:start position:0%
+they actually only had 12 big blinds
+ 
+
+ align:start position:0%
+they actually only had 12 big blinds
+here so they could have just went all in
+
+ align:start position:0%
+here so they could have just went all in
+ 
+
+ align:start position:0%
+here so they could have just went all in
+self but they decided to raise small so
+
+ align:start position:0%
+self but they decided to raise small so
+ 
+
+ align:start position:0%
+self but they decided to raise small so
+that they could fold if someone behind
+
+ align:start position:0%
+that they could fold if someone behind
+ 
+
+ align:start position:0%
+that they could fold if someone behind
+picks up a monster and I guess they were
+
+ align:start position:0%
+picks up a monster and I guess they were
+ 
+
+ align:start position:0%
+picks up a monster and I guess they were
+paid off this time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but yeah like for this hand like one
+
+ align:start position:0%
+um but yeah like for this hand like one
+ 
+
+ align:start position:0%
+um but yeah like for this hand like one
+disadvantage of their play right like
+
+ align:start position:0%
+disadvantage of their play right like
+ 
+
+ align:start position:0%
+disadvantage of their play right like
+suppose we had King 2 suited we would
+
+ align:start position:0%
+suppose we had King 2 suited we would
+ 
+
+ align:start position:0%
+suppose we had King 2 suited we would
+have folded if they went all in but now
+
+ align:start position:0%
+have folded if they went all in but now
+ 
+
+ align:start position:0%
+have folded if they went all in but now
+we can call and see a flop so but but
+
+ align:start position:0%
+we can call and see a flop so but but
+ 
+
+ align:start position:0%
+we can call and see a flop so but but
+for because we had Ace King then I guess
+
+ align:start position:0%
+for because we had Ace King then I guess
+ 
+
+ align:start position:0%
+for because we had Ace King then I guess
+they profited from not committing their
+
+ align:start position:0%
+they profited from not committing their
+ 
+
+ align:start position:0%
+they profited from not committing their
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+stack okay we have King Jack offit we
+
+ align:start position:0%
+stack okay we have King Jack offit we
+ 
+
+ align:start position:0%
+stack okay we have King Jack offit we
+make it 6,000 and this guy goes all in I
+
+ align:start position:0%
+make it 6,000 and this guy goes all in I
+ 
+
+ align:start position:0%
+make it 6,000 and this guy goes all in I
+I fold here I think it's not that close
+
+ align:start position:0%
+I fold here I think it's not that close
+ 
+
+ align:start position:0%
+I fold here I think it's not that close
+I think with King Jack suited it's close
+
+ align:start position:0%
+I think with King Jack suited it's close
+ 
+
+ align:start position:0%
+I think with King Jack suited it's close
+but I'd still fold with King Jack suited
+
+ align:start position:0%
+but I'd still fold with King Jack suited
+ 
+
+ align:start position:0%
+but I'd still fold with King Jack suited
+I'd probably call with Ace jack off suit
+
+ align:start position:0%
+I'd probably call with Ace jack off suit
+ 
+
+ align:start position:0%
+I'd probably call with Ace jack off suit
+plus I would probably call with Ace 10
+
+ align:start position:0%
+plus I would probably call with Ace 10
+ 
+
+ align:start position:0%
+plus I would probably call with Ace 10
+suited and I'd call with king queen
+
+ align:start position:0%
+suited and I'd call with king queen
+ 
+
+ align:start position:0%
+suited and I'd call with king queen
+suited and probably king queen off suit
+
+ align:start position:0%
+suited and probably king queen off suit
+ 
+
+ align:start position:0%
+suited and probably king queen off suit
+as well um in this case so in the last
+
+ align:start position:0%
+as well um in this case so in the last
+ 
+
+ align:start position:0%
+as well um in this case so in the last
+class I said being suited is very
+
+ align:start position:0%
+class I said being suited is very
+ 
+
+ align:start position:0%
+class I said being suited is very
+important when you're behind but when
+
+ align:start position:0%
+important when you're behind but when
+ 
+
+ align:start position:0%
+important when you're behind but when
+you're potentially ahead just having a
+
+ align:start position:0%
+you're potentially ahead just having a
+ 
+
+ align:start position:0%
+you're potentially ahead just having a
+slightly better hand is very important
+
+ align:start position:0%
+slightly better hand is very important
+ 
+
+ align:start position:0%
+slightly better hand is very important
+so I think in this situation I would
+
+ align:start position:0%
+so I think in this situation I would
+ 
+
+ align:start position:0%
+so I think in this situation I would
+fold King Jack suited but call with king
+
+ align:start position:0%
+fold King Jack suited but call with king
+ 
+
+ align:start position:0%
+fold King Jack suited but call with king
+queen off suit because a decent part of
+
+ align:start position:0%
+queen off suit because a decent part of
+ 
+
+ align:start position:0%
+queen off suit because a decent part of
+his range is hands like King Jack and
+
+ align:start position:0%
+his range is hands like King Jack and
+ 
+
+ align:start position:0%
+his range is hands like King Jack and
+king queen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay here I have king queen and
+
+ align:start position:0%
+so okay here I have king queen and
+ 
+
+ align:start position:0%
+so okay here I have king queen and
+degenerated so I for some reason I love
+
+ align:start position:0%
+degenerated so I for some reason I love
+ 
+
+ align:start position:0%
+degenerated so I for some reason I love
+making this play with king queen um it's
+
+ align:start position:0%
+making this play with king queen um it's
+ 
+
+ align:start position:0%
+making this play with king queen um it's
+actually not that unfounded is just a
+
+ align:start position:0%
+actually not that unfounded is just a
+ 
+
+ align:start position:0%
+actually not that unfounded is just a
+good hand to Bluff with that at the same
+
+ align:start position:0%
+good hand to Bluff with that at the same
+ 
+
+ align:start position:0%
+good hand to Bluff with that at the same
+time sort of protects your range in the
+
+ align:start position:0%
+time sort of protects your range in the
+ 
+
+ align:start position:0%
+time sort of protects your range in the
+case that he calls and also your hand
+
+ align:start position:0%
+case that he calls and also your hand
+ 
+
+ align:start position:0%
+case that he calls and also your hand
+doesn't play that well if you just call
+
+ align:start position:0%
+doesn't play that well if you just call
+ 
+
+ align:start position:0%
+doesn't play that well if you just call
+because you're not suited so it's it it
+
+ align:start position:0%
+because you're not suited so it's it it
+ 
+
+ align:start position:0%
+because you're not suited so it's it it
+really is King I mean in this tournament
+
+ align:start position:0%
+really is King I mean in this tournament
+ 
+
+ align:start position:0%
+really is King I mean in this tournament
+we've happened to got we've happened to
+
+ align:start position:0%
+we've happened to got we've happened to
+ 
+
+ align:start position:0%
+we've happened to got we've happened to
+been dealt king queen a lot and gotone
+
+ align:start position:0%
+been dealt king queen a lot and gotone
+ 
+
+ align:start position:0%
+been dealt king queen a lot and gotone
+into situations where we can uh re ra
+
+ align:start position:0%
+into situations where we can uh re ra
+ 
+
+ align:start position:0%
+into situations where we can uh re ra
+Bluff people but it really is my
+
+ align:start position:0%
+Bluff people but it really is my
+ 
+
+ align:start position:0%
+Bluff people but it really is my
+favorite hand to do this with so it
+
+ align:start position:0%
+favorite hand to do this with so it
+ 
+
+ align:start position:0%
+favorite hand to do this with so it
+might be even be too predictable because
+
+ align:start position:0%
+might be even be too predictable because
+ 
+
+ align:start position:0%
+might be even be too predictable because
+I just always have king and queen
+
+ align:start position:0%
+I just always have king and queen
+ 
+
+ align:start position:0%
+I just always have king and queen
+whenever I do this um but we do take it
+
+ align:start position:0%
+whenever I do this um but we do take it
+ 
+
+ align:start position:0%
+whenever I do this um but we do take it
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay Ace jack off suit this guy so
+
+ align:start position:0%
+here okay Ace jack off suit this guy so
+ 
+
+ align:start position:0%
+here okay Ace jack off suit this guy so
+this degenerated guy who we just re at
+
+ align:start position:0%
+this degenerated guy who we just re at
+ 
+
+ align:start position:0%
+this degenerated guy who we just re at
+this point it's probably late enough in
+
+ align:start position:0%
+this point it's probably late enough in
+ 
+
+ align:start position:0%
+this point it's probably late enough in
+the tournament I am paying attention and
+
+ align:start position:0%
+the tournament I am paying attention and
+ 
+
+ align:start position:0%
+the tournament I am paying attention and
+I am aware that I just R raised this guy
+
+ align:start position:0%
+I am aware that I just R raised this guy
+ 
+
+ align:start position:0%
+I am aware that I just R raised this guy
+three hands earlier so they they make a
+
+ align:start position:0%
+three hands earlier so they they make a
+ 
+
+ align:start position:0%
+three hands earlier so they they make a
+big raise here to 9,000 and I call with
+
+ align:start position:0%
+big raise here to 9,000 and I call with
+ 
+
+ align:start position:0%
+big raise here to 9,000 and I call with
+a jack which I regret quite a bit I
+
+ align:start position:0%
+a jack which I regret quite a bit I
+ 
+
+ align:start position:0%
+a jack which I regret quite a bit I
+think it's just I think it's just too
+
+ align:start position:0%
+think it's just I think it's just too
+ 
+
+ align:start position:0%
+think it's just I think it's just too
+weak a hand to play and if I'm going to
+
+ align:start position:0%
+weak a hand to play and if I'm going to
+ 
+
+ align:start position:0%
+weak a hand to play and if I'm going to
+play it I think I should just go all in
+
+ align:start position:0%
+play it I think I should just go all in
+ 
+
+ align:start position:0%
+play it I think I should just go all in
+and try to win the hand pre flop this is
+
+ align:start position:0%
+and try to win the hand pre flop this is
+ 
+
+ align:start position:0%
+and try to win the hand pre flop this is
+even though I'm in position I think it's
+
+ align:start position:0%
+even though I'm in position I think it's
+ 
+
+ align:start position:0%
+even though I'm in position I think it's
+just going to be hard to play um you
+
+ align:start position:0%
+just going to be hard to play um you
+ 
+
+ align:start position:0%
+just going to be hard to play um you
+know even when I hit an ace or a Jack
+
+ align:start position:0%
+know even when I hit an ace or a Jack
+ 
+
+ align:start position:0%
+know even when I hit an ace or a Jack
+I'm still G to quite often be behind and
+
+ align:start position:0%
+I'm still G to quite often be behind and
+ 
+
+ align:start position:0%
+I'm still G to quite often be behind and
+if I don't hit an aceer a jack I'm
+
+ align:start position:0%
+if I don't hit an aceer a jack I'm
+ 
+
+ align:start position:0%
+if I don't hit an aceer a jack I'm
+pretty much always just going to have to
+
+ align:start position:0%
+pretty much always just going to have to
+ 
+
+ align:start position:0%
+pretty much always just going to have to
+fold and that's basically what happens
+
+ align:start position:0%
+fold and that's basically what happens
+ 
+
+ align:start position:0%
+fold and that's basically what happens
+so I don't know why I just gave away
+
+ align:start position:0%
+so I don't know why I just gave away
+ 
+
+ align:start position:0%
+so I don't know why I just gave away
+9,000 chips there
+
+ align:start position:0%
+9,000 chips there
+ 
+
+ align:start position:0%
+9,000 chips there
+but okay so Queen Jack
+
+ align:start position:0%
+but okay so Queen Jack
+ 
+
+ align:start position:0%
+but okay so Queen Jack
+suited I just go all in from the small
+
+ align:start position:0%
+suited I just go all in from the small
+ 
+
+ align:start position:0%
+suited I just go all in from the small
+blind because it's so even though we
+
+ align:start position:0%
+blind because it's so even though we
+ 
+
+ align:start position:0%
+blind because it's so even though we
+have 15 big blinds which is more than 12
+
+ align:start position:0%
+have 15 big blinds which is more than 12
+ 
+
+ align:start position:0%
+have 15 big blinds which is more than 12
+I said last class that from the small
+
+ align:start position:0%
+I said last class that from the small
+ 
+
+ align:start position:0%
+I said last class that from the small
+blind you're really really really
+
+ align:start position:0%
+blind you're really really really
+ 
+
+ align:start position:0%
+blind you're really really really
+incentivized to go all in because if you
+
+ align:start position:0%
+incentivized to go all in because if you
+ 
+
+ align:start position:0%
+incentivized to go all in because if you
+don't then the other guy has position
+
+ align:start position:0%
+don't then the other guy has position
+ 
+
+ align:start position:0%
+don't then the other guy has position
+whereas like from the button if you just
+
+ align:start position:0%
+whereas like from the button if you just
+ 
+
+ align:start position:0%
+whereas like from the button if you just
+raise the big blind calls you have
+
+ align:start position:0%
+raise the big blind calls you have
+ 
+
+ align:start position:0%
+raise the big blind calls you have
+position so I go all in Queen Jack
+
+ align:start position:0%
+position so I go all in Queen Jack
+ 
+
+ align:start position:0%
+position so I go all in Queen Jack
+suited is more than good enough and we
+
+ align:start position:0%
+suited is more than good enough and we
+ 
+
+ align:start position:0%
+suited is more than good enough and we
+get a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fold and the next hand okay so this is
+
+ align:start position:0%
+fold and the next hand okay so this is
+ 
+
+ align:start position:0%
+fold and the next hand okay so this is
+actually great illustration the very
+
+ align:start position:0%
+actually great illustration the very
+ 
+
+ align:start position:0%
+actually great illustration the very
+next hand we get Queen jack off and we
+
+ align:start position:0%
+next hand we get Queen jack off and we
+ 
+
+ align:start position:0%
+next hand we get Queen jack off and we
+just raise from this button and it's
+
+ align:start position:0%
+just raise from this button and it's
+ 
+
+ align:start position:0%
+just raise from this button and it's
+exactly the reason I said because we
+
+ align:start position:0%
+exactly the reason I said because we
+ 
+
+ align:start position:0%
+exactly the reason I said because we
+have position so we don't mind if the
+
+ align:start position:0%
+have position so we don't mind if the
+ 
+
+ align:start position:0%
+have position so we don't mind if the
+pot gets played post fly
+
+ align:start position:0%
+pot gets played post fly
+ 
+
+ align:start position:0%
+pot gets played post fly
+so the small blind goes all in and note
+
+ align:start position:0%
+so the small blind goes all in and note
+ 
+
+ align:start position:0%
+so the small blind goes all in and note
+note that they're actually fairly short
+
+ align:start position:0%
+note that they're actually fairly short
+ 
+
+ align:start position:0%
+note that they're actually fairly short
+here they only have 14 big blinds to
+
+ align:start position:0%
+here they only have 14 big blinds to
+ 
+
+ align:start position:0%
+here they only have 14 big blinds to
+start the hand so I I would have easily
+
+ align:start position:0%
+start the hand so I I would have easily
+ 
+
+ align:start position:0%
+start the hand so I I would have easily
+called with Queen Jack suited even with
+
+ align:start position:0%
+called with Queen Jack suited even with
+ 
+
+ align:start position:0%
+called with Queen Jack suited even with
+Queen jack off I'm not certain that
+
+ align:start position:0%
+Queen jack off I'm not certain that
+ 
+
+ align:start position:0%
+Queen jack off I'm not certain that
+folding is a better play than calling
+
+ align:start position:0%
+folding is a better play than calling
+ 
+
+ align:start position:0%
+folding is a better play than calling
+it's just your odds are basically good
+
+ align:start position:0%
+it's just your odds are basically good
+ 
+
+ align:start position:0%
+it's just your odds are basically good
+enough here and their range will be
+
+ align:start position:0%
+enough here and their range will be
+ 
+
+ align:start position:0%
+enough here and their range will be
+fairly loose when I raise from the
+
+ align:start position:0%
+fairly loose when I raise from the
+ 
+
+ align:start position:0%
+fairly loose when I raise from the
+button because they're going to think I
+
+ align:start position:0%
+button because they're going to think I
+ 
+
+ align:start position:0%
+button because they're going to think I
+don't have much when I raise from the
+
+ align:start position:0%
+don't have much when I raise from the
+ 
+
+ align:start position:0%
+don't have much when I raise from the
+button so it's quite possible calling
+
+ align:start position:0%
+button so it's quite possible calling
+ 
+
+ align:start position:0%
+button so it's quite possible calling
+here would have in the right play it's
+
+ align:start position:0%
+here would have in the right play it's
+ 
+
+ align:start position:0%
+here would have in the right play it's
+very close I think I would have
+
+ align:start position:0%
+very close I think I would have
+ 
+
+ align:start position:0%
+very close I think I would have
+definitely called with ECE 9 offit I
+
+ align:start position:0%
+definitely called with ECE 9 offit I
+ 
+
+ align:start position:0%
+definitely called with ECE 9 offit I
+would have definitely called with King
+
+ align:start position:0%
+would have definitely called with King
+ 
+
+ align:start position:0%
+would have definitely called with King
+10 offit um yeah it's pretty close I
+
+ align:start position:0%
+10 offit um yeah it's pretty close I
+ 
+
+ align:start position:0%
+10 offit um yeah it's pretty close I
+decided to fold maybe I also knew that
+
+ align:start position:0%
+decided to fold maybe I also knew that
+ 
+
+ align:start position:0%
+decided to fold maybe I also knew that
+they were kind of tight um normally when
+
+ align:start position:0%
+they were kind of tight um normally when
+ 
+
+ align:start position:0%
+they were kind of tight um normally when
+I play but I'm not showing here is I
+
+ align:start position:0%
+I play but I'm not showing here is I
+ 
+
+ align:start position:0%
+I play but I'm not showing here is I
+have like statistics on every player of
+
+ align:start position:0%
+have like statistics on every player of
+ 
+
+ align:start position:0%
+have like statistics on every player of
+like overall the hands what percent of
+
+ align:start position:0%
+like overall the hands what percent of
+ 
+
+ align:start position:0%
+like overall the hands what percent of
+the time they raise what percent they
+
+ align:start position:0%
+the time they raise what percent they
+ 
+
+ align:start position:0%
+the time they raise what percent they
+folded so I have a rough idea while I'm
+
+ align:start position:0%
+folded so I have a rough idea while I'm
+ 
+
+ align:start position:0%
+folded so I have a rough idea while I'm
+playing um of how tight everyone is and
+
+ align:start position:0%
+playing um of how tight everyone is and
+ 
+
+ align:start position:0%
+playing um of how tight everyone is and
+maybe I just knew he was tight actually
+
+ align:start position:0%
+maybe I just knew he was tight actually
+ 
+
+ align:start position:0%
+maybe I just knew he was tight actually
+let me see if I can turn it back on here
+
+ align:start position:0%
+let me see if I can turn it back on here
+ 
+
+ align:start position:0%
+let me see if I can turn it back on here
+yeah let me see that might be
+
+ align:start position:0%
+yeah let me see that might be
+ 
+
+ align:start position:0%
+yeah let me see that might be
+why uh so so at this okay so these
+
+ align:start position:0%
+why uh so so at this okay so these
+ 
+
+ align:start position:0%
+why uh so so at this okay so these
+numbers actually he's fairly loose yeah
+
+ align:start position:0%
+numbers actually he's fairly loose yeah
+ 
+
+ align:start position:0%
+numbers actually he's fairly loose yeah
+I actually I'm not sure why it folded so
+
+ align:start position:0%
+I actually I'm not sure why it folded so
+ 
+
+ align:start position:0%
+I actually I'm not sure why it folded so
+this 10.7 is his re ra percentage and
+
+ align:start position:0%
+this 10.7 is his re ra percentage and
+ 
+
+ align:start position:0%
+this 10.7 is his re ra percentage and
+what this says is 10.7% of the time he
+
+ align:start position:0%
+what this says is 10.7% of the time he
+ 
+
+ align:start position:0%
+what this says is 10.7% of the time he
+could have reraised he reraised it's
+
+ align:start position:0%
+could have reraised he reraised it's
+ 
+
+ align:start position:0%
+could have reraised he reraised it's
+only over a sample of 187 hands but it's
+
+ align:start position:0%
+only over a sample of 187 hands but it's
+ 
+
+ align:start position:0%
+only over a sample of 187 hands but it's
+it's all yeah I think it's definitely
+
+ align:start position:0%
+it's all yeah I think it's definitely
+ 
+
+ align:start position:0%
+it's all yeah I think it's definitely
+looser than average um although it's a
+
+ align:start position:0%
+looser than average um although it's a
+ 
+
+ align:start position:0%
+looser than average um although it's a
+bit biased because we're playing at a
+
+ align:start position:0%
+bit biased because we're playing at a
+ 
+
+ align:start position:0%
+bit biased because we're playing at a
+5-h handed table um nonetheless it's
+
+ align:start position:0%
+5-h handed table um nonetheless it's
+ 
+
+ align:start position:0%
+5-h handed table um nonetheless it's
+close I think calling probably would
+
+ align:start position:0%
+close I think calling probably would
+ 
+
+ align:start position:0%
+close I think calling probably would
+have been okay but I folded let me turn
+
+ align:start position:0%
+have been okay but I folded let me turn
+ 
+
+ align:start position:0%
+have been okay but I folded let me turn
+this off it's quite annoying
+
+ align:start position:0%
+this off it's quite annoying
+ 
+
+ align:start position:0%
+this off it's quite annoying
+um okay so so this is near the final
+
+ align:start position:0%
+um okay so so this is near the final
+ 
+
+ align:start position:0%
+um okay so so this is near the final
+table now this is I think the second
+
+ align:start position:0%
+table now this is I think the second
+ 
+
+ align:start position:0%
+table now this is I think the second
+Final Table there's maybe like 11 or 12
+
+ align:start position:0%
+Final Table there's maybe like 11 or 12
+ 
+
+ align:start position:0%
+Final Table there's maybe like 11 or 12
+left and I'm just going to show you the
+
+ align:start position:0%
+left and I'm just going to show you the
+ 
+
+ align:start position:0%
+left and I'm just going to show you the
+final hands before the final table so
+
+ align:start position:0%
+final hands before the final table so
+ 
+
+ align:start position:0%
+final hands before the final table so
+this hand is a no-brainer we go all in
+
+ align:start position:0%
+this hand is a no-brainer we go all in
+ 
+
+ align:start position:0%
+this hand is a no-brainer we go all in
+and fortunately we hold against pocket
+
+ align:start position:0%
+and fortunately we hold against pocket
+ 
+
+ align:start position:0%
+and fortunately we hold against pocket
+twos so um okay so the the very last
+
+ align:start position:0%
+twos so um okay so the the very last
+ 
+
+ align:start position:0%
+twos so um okay so the the very last
+hand uh
+
+ align:start position:0%
+hand uh
+ 
+
+ align:start position:0%
+hand uh
+also fairly no-brainer this guy goes all
+
+ align:start position:0%
+also fairly no-brainer this guy goes all
+ 
+
+ align:start position:0%
+also fairly no-brainer this guy goes all
+in so yeah poker is easy if you just get
+
+ align:start position:0%
+in so yeah poker is easy if you just get
+ 
+
+ align:start position:0%
+in so yeah poker is easy if you just get
+dealt pocket Jacks pocket pces all the
+
+ align:start position:0%
+dealt pocket Jacks pocket pces all the
+ 
+
+ align:start position:0%
+dealt pocket Jacks pocket pces all the
+time um so we win this one okay so this
+
+ align:start position:0%
+time um so we win this one okay so this
+ 
+
+ align:start position:0%
+time um so we win this one okay so this
+is the last hand before the final table
+
+ align:start position:0%
+is the last hand before the final table
+ 
+
+ align:start position:0%
+is the last hand before the final table
+so in a future class not the Friday
+
+ align:start position:0%
+so in a future class not the Friday
+ 
+
+ align:start position:0%
+so in a future class not the Friday
+class because Jennifer shahade is
+
+ align:start position:0%
+class because Jennifer shahade is
+ 
+
+ align:start position:0%
+class because Jennifer shahade is
+speaking but uh in a future class I'll
+
+ align:start position:0%
+speaking but uh in a future class I'll
+ 
+
+ align:start position:0%
+speaking but uh in a future class I'll
+go through the final table and I'll
+
+ align:start position:0%
+go through the final table and I'll
+ 
+
+ align:start position:0%
+go through the final table and I'll
+maybe also go through all the hands not
+
+ align:start position:0%
+maybe also go through all the hands not
+ 
+
+ align:start position:0%
+maybe also go through all the hands not
+just the hands where I got in a big pot
+
+ align:start position:0%
+just the hands where I got in a big pot
+ 
+
+ align:start position:0%
+just the hands where I got in a big pot
+so um let me just quickly go back to the
+
+ align:start position:0%
+so um let me just quickly go back to the
+ 
+
+ align:start position:0%
+so um let me just quickly go back to the
+slides
+
+ align:start position:0%
+slides
+ 
+
+ align:start position:0%
+slides
+right so so I really only talked about
+
+ align:start position:0%
+right so so I really only talked about
+ 
+
+ align:start position:0%
+right so so I really only talked about
+two concepts in this class it was this
+
+ align:start position:0%
+two concepts in this class it was this
+ 
+
+ align:start position:0%
+two concepts in this class it was this
+draw draw you versus dry boards so try
+
+ align:start position:0%
+draw draw you versus dry boards so try
+ 
+
+ align:start position:0%
+draw draw you versus dry boards so try
+to remember that while you guys are
+
+ align:start position:0%
+to remember that while you guys are
+ 
+
+ align:start position:0%
+to remember that while you guys are
+playing the changing your bet sizing
+
+ align:start position:0%
+playing the changing your bet sizing
+ 
+
+ align:start position:0%
+playing the changing your bet sizing
+depending on the board texture and also
+
+ align:start position:0%
+depending on the board texture and also
+ 
+
+ align:start position:0%
+depending on the board texture and also
+this pre flop re raising strategy even
+
+ align:start position:0%
+this pre flop re raising strategy even
+ 
+
+ align:start position:0%
+this pre flop re raising strategy even
+though I didn't give you a conclusion
+
+ align:start position:0%
+though I didn't give you a conclusion
+ 
+
+ align:start position:0%
+though I didn't give you a conclusion
+here on what to re ra with um I sort of
+
+ align:start position:0%
+here on what to re ra with um I sort of
+ 
+
+ align:start position:0%
+here on what to re ra with um I sort of
+gave you some rough guidelines and the
+
+ align:start position:0%
+gave you some rough guidelines and the
+ 
+
+ align:start position:0%
+gave you some rough guidelines and the
+advantages and disadvantages of each
+
+ align:start position:0%
+advantages and disadvantages of each
+ 
+
+ align:start position:0%
+advantages and disadvantages of each
+play and yeah Okay cool so that's it uh
+
+ align:start position:0%
+play and yeah Okay cool so that's it uh
+ 
+
+ align:start position:0%
+play and yeah Okay cool so that's it uh
+on Friday's class it should be should be
+
+ align:start position:0%
+on Friday's class it should be should be
+ 
+
+ align:start position:0%
+on Friday's class it should be should be
+really exciting Jennifer Shah she'll
+
+ align:start position:0%
+really exciting Jennifer Shah she'll
+ 
+
+ align:start position:0%
+really exciting Jennifer Shah she'll
+probably talk a bit about Chess as well
+
+ align:start position:0%
+probably talk a bit about Chess as well
+ 
+
+ align:start position:0%
+probably talk a bit about Chess as well
+but I'll convince her not to talk too
+
+ align:start position:0%
+but I'll convince her not to talk too
+ 
+
+ align:start position:0%
+but I'll convince her not to talk too
+much about Chess when it's a poker class
+
+ align:start position:0%
+much about Chess when it's a poker class
+ 
+
+ align:start position:0%
+much about Chess when it's a poker class
+but um thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys
\ No newline at end of file
diff --git a/_OZXEb8FxZQ.txt b/_OZXEb8FxZQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..196b4afc404b377487dc044bf9c229e720447f31
--- /dev/null
+++ b/_OZXEb8FxZQ.txt
@@ -0,0 +1,3219 @@
+align:start position:0%
+ 
+all right good morning and welcome to
+
+ align:start position:0%
+all right good morning and welcome to
+ 
+
+ align:start position:0%
+all right good morning and welcome to
+806 let's begin uh our subject in
+
+ align:start position:0%
+806 let's begin uh our subject in
+ 
+
+ align:start position:0%
+806 let's begin uh our subject in
+806 has to do with applications of
+
+ align:start position:0%
+806 has to do with applications of
+ 
+
+ align:start position:0%
+806 has to do with applications of
+quantum mechanics and using quantum
+
+ align:start position:0%
+quantum mechanics and using quantum
+ 
+
+ align:start position:0%
+quantum mechanics and using quantum
+mechanics to understand complex systems
+
+ align:start position:0%
+mechanics to understand complex systems
+ 
+
+ align:start position:0%
+mechanics to understand complex systems
+in in fact systems more complex than the
+
+ align:start position:0%
+in in fact systems more complex than the
+ 
+
+ align:start position:0%
+in in fact systems more complex than the
+ones you've understood before for
+
+ align:start position:0%
+ones you've understood before for
+ 
+
+ align:start position:0%
+ones you've understood before for
+example in the previous courses you've
+
+ align:start position:0%
+example in the previous courses you've
+ 
+
+ align:start position:0%
+example in the previous courses you've
+understood very well the simple harmonic
+
+ align:start position:0%
+understood very well the simple harmonic
+ 
+
+ align:start position:0%
+understood very well the simple harmonic
+oscillator you've solv for the
+
+ align:start position:0%
+oscillator you've solv for the
+ 
+
+ align:start position:0%
+oscillator you've solv for the
+hamiltonian you found all the aen states
+
+ align:start position:0%
+hamiltonian you found all the aen states
+ 
+
+ align:start position:0%
+hamiltonian you found all the aen states
+you found all the energies you know
+
+ align:start position:0%
+you found all the energies you know
+ 
+
+ align:start position:0%
+you found all the energies you know
+about the Spectrum you can do time
+
+ align:start position:0%
+about the Spectrum you can do time
+ 
+
+ align:start position:0%
+about the Spectrum you can do time
+evolution in the harmonic oscillator
+
+ align:start position:0%
+evolution in the harmonic oscillator
+ 
+
+ align:start position:0%
+evolution in the harmonic oscillator
+you've discussed even peculiar States
+
+ align:start position:0%
+you've discussed even peculiar States
+ 
+
+ align:start position:0%
+you've discussed even peculiar States
+like coherent States squeeze States you
+
+ align:start position:0%
+like coherent States squeeze States you
+ 
+
+ align:start position:0%
+like coherent States squeeze States you
+know a lot about this very simple
+
+ align:start position:0%
+know a lot about this very simple
+ 
+
+ align:start position:0%
+know a lot about this very simple
+hamiltonian you've also studied the
+
+ align:start position:0%
+hamiltonian you've also studied the
+ 
+
+ align:start position:0%
+hamiltonian you've also studied the
+hydrogen atom hamiltonian and you found
+
+ align:start position:0%
+hydrogen atom hamiltonian and you found
+ 
+
+ align:start position:0%
+hydrogen atom hamiltonian and you found
+the spectrum of the hydrogen atom with
+
+ align:start position:0%
+the spectrum of the hydrogen atom with
+ 
+
+ align:start position:0%
+the spectrum of the hydrogen atom with
+all the degeneracies that it has and
+
+ align:start position:0%
+all the degeneracies that it has and
+ 
+
+ align:start position:0%
+all the degeneracies that it has and
+understood some of those wave functions
+
+ align:start position:0%
+understood some of those wave functions
+ 
+
+ align:start position:0%
+understood some of those wave functions
+and the properties and those are exact
+
+ align:start position:0%
+and the properties and those are exact
+ 
+
+ align:start position:0%
+and the properties and those are exact
+systems but it turns out that in
+
+ align:start position:0%
+systems but it turns out that in
+ 
+
+ align:start position:0%
+systems but it turns out that in
+practice while those exact systems form
+
+ align:start position:0%
+practice while those exact systems form
+ 
+
+ align:start position:0%
+practice while those exact systems form
+the foundation of what you
+
+ align:start position:0%
+the foundation of what you
+ 
+
+ align:start position:0%
+the foundation of what you
+learn many systems and most of the
+
+ align:start position:0%
+learn many systems and most of the
+ 
+
+ align:start position:0%
+learn many systems and most of the
+systems you face in real life and in
+
+ align:start position:0%
+systems you face in real life and in
+ 
+
+ align:start position:0%
+systems you face in real life and in
+research are systems that are more
+
+ align:start position:0%
+research are systems that are more
+ 
+
+ align:start position:0%
+research are systems that are more
+complicated but at least a large
+
+ align:start position:0%
+complicated but at least a large
+ 
+
+ align:start position:0%
+complicated but at least a large
+fraction of them have a Saving Grace
+
+ align:start position:0%
+fraction of them have a Saving Grace
+ 
+
+ align:start position:0%
+fraction of them have a Saving Grace
+they can be thought as that simple
+
+ align:start position:0%
+they can be thought as that simple
+ 
+
+ align:start position:0%
+they can be thought as that simple
+hamiltonian that you understand very
+
+ align:start position:0%
+hamiltonian that you understand very
+ 
+
+ align:start position:0%
+hamiltonian that you understand very
+well plus an extra term or an extra
+
+ align:start position:0%
+well plus an extra term or an extra
+ 
+
+ align:start position:0%
+well plus an extra term or an extra
+effect some sort of a your total
+
+ align:start position:0%
+effect some sort of a your total
+ 
+
+ align:start position:0%
+effect some sort of a your total
+hamiltonian being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially the simple hamiltonian but
+
+ align:start position:0%
+essentially the simple hamiltonian but
+ 
+
+ align:start position:0%
+essentially the simple hamiltonian but
+differs from it by some
+
+ align:start position:0%
+differs from it by some
+ 
+
+ align:start position:0%
+differs from it by some
+amount that makes it a little different
+
+ align:start position:0%
+amount that makes it a little different
+ 
+
+ align:start position:0%
+amount that makes it a little different
+so your simple hamiltonian therefore can
+
+ align:start position:0%
+so your simple hamiltonian therefore can
+ 
+
+ align:start position:0%
+so your simple hamiltonian therefore can
+be the harmonic oscillator and in that
+
+ align:start position:0%
+be the harmonic oscillator and in that
+ 
+
+ align:start position:0%
+be the harmonic oscillator and in that
+case for example in general you may have
+
+ align:start position:0%
+case for example in general you may have
+ 
+
+ align:start position:0%
+case for example in general you may have
+a potential for a particle and you know
+
+ align:start position:0%
+a potential for a particle and you know
+ 
+
+ align:start position:0%
+a potential for a particle and you know
+near the minimum of the potential the
+
+ align:start position:0%
+near the minimum of the potential the
+ 
+
+ align:start position:0%
+near the minimum of the potential the
+potential is roughly quadratic in
+
+ align:start position:0%
+potential is roughly quadratic in
+ 
+
+ align:start position:0%
+potential is roughly quadratic in
+general but then as a tailor expansion
+
+ align:start position:0%
+general but then as a tailor expansion
+ 
+
+ align:start position:0%
+general but then as a tailor expansion
+around the minimum you'll find a
+
+ align:start position:0%
+around the minimum you'll find a
+ 
+
+ align:start position:0%
+around the minimum you'll find a
+quadratic term no linear term because
+
+ align:start position:0%
+quadratic term no linear term because
+ 
+
+ align:start position:0%
+quadratic term no linear term because
+it's a minimum a quadratic term and then
+
+ align:start position:0%
+it's a minimum a quadratic term and then
+ 
+
+ align:start position:0%
+it's a minimum a quadratic term and then
+you will find maybe a cubic or a quartic
+
+ align:start position:0%
+you will find maybe a cubic or a quartic
+ 
+
+ align:start position:0%
+you will find maybe a cubic or a quartic
+term and the oscillations are a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is studied by people that look at
+
+ align:start position:0%
+this is studied by people that look at
+ 
+
+ align:start position:0%
+this is studied by people that look at
+diatomic molecules the vibrations have
+
+ align:start position:0%
+diatomic molecules the vibrations have
+ 
+
+ align:start position:0%
+diatomic molecules the vibrations have
+this effect it's experimentally
+
+ align:start position:0%
+this effect it's experimentally
+ 
+
+ align:start position:0%
+this effect it's experimentally
+detectable you can have the hydrogen
+
+ align:start position:0%
+detectable you can have the hydrogen
+ 
+
+ align:start position:0%
+detectable you can have the hydrogen
+atom and if you want to study the
+
+ align:start position:0%
+atom and if you want to study the
+ 
+
+ align:start position:0%
+atom and if you want to study the
+hydrogen atom how does an
+
+ align:start position:0%
+hydrogen atom how does an
+ 
+
+ align:start position:0%
+hydrogen atom how does an
+experimentalist look at the hydrogen
+
+ align:start position:0%
+experimentalist look at the hydrogen
+ 
+
+ align:start position:0%
+experimentalist look at the hydrogen
+atom puts a hydrogen atom and inserts a
+
+ align:start position:0%
+atom puts a hydrogen atom and inserts a
+ 
+
+ align:start position:0%
+atom puts a hydrogen atom and inserts a
+magnetic field and sees what happens to
+
+ align:start position:0%
+magnetic field and sees what happens to
+ 
+
+ align:start position:0%
+magnetic field and sees what happens to
+the energy
+
+ align:start position:0%
+the energy
+ 
+
+ align:start position:0%
+the energy
+levels and then inserts an electric
+
+ align:start position:0%
+levels and then inserts an electric
+ 
+
+ align:start position:0%
+levels and then inserts an electric
+field this is what happens to the energy
+
+ align:start position:0%
+field this is what happens to the energy
+ 
+
+ align:start position:0%
+field this is what happens to the energy
+levels and those can be thought as
+
+ align:start position:0%
+levels and those can be thought as
+ 
+
+ align:start position:0%
+levels and those can be thought as
+slight variations of the original
+
+ align:start position:0%
+slight variations of the original
+ 
+
+ align:start position:0%
+slight variations of the original
+hamiltonian Vander Val's forces are you
+
+ align:start position:0%
+hamiltonian Vander Val's forces are you
+ 
+
+ align:start position:0%
+hamiltonian Vander Val's forces are you
+have two neutral atoms and they induce
+
+ align:start position:0%
+have two neutral atoms and they induce
+ 
+
+ align:start position:0%
+have two neutral atoms and they induce
+on each other diple moments and generate
+
+ align:start position:0%
+on each other diple moments and generate
+ 
+
+ align:start position:0%
+on each other diple moments and generate
+a force a very tiny effect on
+
+ align:start position:0%
+a force a very tiny effect on
+ 
+
+ align:start position:0%
+a force a very tiny effect on
+otherwise simple hydrogen atoms
+
+ align:start position:0%
+otherwise simple hydrogen atoms
+ 
+
+ align:start position:0%
+otherwise simple hydrogen atoms
+structure but a very important Force the
+
+ align:start position:0%
+structure but a very important Force the
+ 
+
+ align:start position:0%
+structure but a very important Force the
+vand deral force so what we're going to
+
+ align:start position:0%
+vand deral force so what we're going to
+ 
+
+ align:start position:0%
+vand deral force so what we're going to
+be doing is trying to understand these
+
+ align:start position:0%
+be doing is trying to understand these
+ 
+
+ align:start position:0%
+be doing is trying to understand these
+situations in which we
+
+ align:start position:0%
+situations in which we
+ 
+
+ align:start position:0%
+situations in which we
+have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hamiltonian that is
+
+ align:start position:0%
+hamiltonian that is
+ 
+
+ align:start position:0%
+hamiltonian that is
+equal to a wellknown hamiltonian this
+
+ align:start position:0%
+equal to a wellknown hamiltonian this
+ 
+
+ align:start position:0%
+equal to a wellknown hamiltonian this
+h0 zero meaning no perturbation no
+
+ align:start position:0%
+h0 zero meaning no perturbation no
+ 
+
+ align:start position:0%
+h0 zero meaning no perturbation no
+variation this is our wellknown
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+known
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system but then there's going to
+
+ align:start position:0%
+system but then there's going to
+ 
+
+ align:start position:0%
+system but then there's going to
+be an extra piece to that hamiltonian
+
+ align:start position:0%
+be an extra piece to that hamiltonian
+ 
+
+ align:start position:0%
+be an extra piece to that hamiltonian
+and we're going to call it Delta H Delta
+
+ align:start position:0%
+and we're going to call it Delta H Delta
+ 
+
+ align:start position:0%
+and we're going to call it Delta H Delta
+H is yet another
+
+ align:start position:0%
+H is yet another
+ 
+
+ align:start position:0%
+H is yet another
+hamiltonian it may be complicated may be
+
+ align:start position:0%
+hamiltonian it may be complicated may be
+ 
+
+ align:start position:0%
+hamiltonian it may be complicated may be
+simple uh
+
+ align:start position:0%
+simple uh
+ 
+
+ align:start position:0%
+simple uh
+but it's different from
+
+ align:start position:0%
+but it's different from
+ 
+
+ align:start position:0%
+but it's different from
+h0 now this will be the hamiltonian of
+
+ align:start position:0%
+h0 now this will be the hamiltonian of
+ 
+
+ align:start position:0%
+h0 now this will be the hamiltonian of
+the system that you're really trying to
+
+ align:start position:0%
+the system that you're really trying to
+ 
+
+ align:start position:0%
+the system that you're really trying to
+describe and therefore U you should
+
+ align:start position:0%
+describe and therefore U you should
+ 
+
+ align:start position:0%
+describe and therefore U you should
+demand of course that h0 Delta H and H
+
+ align:start position:0%
+demand of course that h0 Delta H and H
+ 
+
+ align:start position:0%
+demand of course that h0 Delta H and H
+are all her
+
+ align:start position:0%
+are all her
+ 
+
+ align:start position:0%
+are all her
+Mission all hamiltonians are supposed to
+
+ align:start position:0%
+Mission all hamiltonians are supposed to
+ 
+
+ align:start position:0%
+Mission all hamiltonians are supposed to
+be her
+
+ align:start position:0%
+be her
+ 
+
+ align:start position:0%
+be her
+Mission and this is uh the situation
+
+ align:start position:0%
+Mission and this is uh the situation
+ 
+
+ align:start position:0%
+Mission and this is uh the situation
+with want to understand in general this
+
+ align:start position:0%
+with want to understand in general this
+ 
+
+ align:start position:0%
+with want to understand in general this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+concrete mathematical description of the
+
+ align:start position:0%
+concrete mathematical description of the
+ 
+
+ align:start position:0%
+concrete mathematical description of the
+problem but we do a little more here we
+
+ align:start position:0%
+problem but we do a little more here we
+ 
+
+ align:start position:0%
+problem but we do a little more here we
+need a tool to help us deal with this
+
+ align:start position:0%
+need a tool to help us deal with this
+ 
+
+ align:start position:0%
+need a tool to help us deal with this
+and there's a wonderful nice tool
+
+ align:start position:0%
+and there's a wonderful nice tool
+ 
+
+ align:start position:0%
+and there's a wonderful nice tool
+provided by a parameter a parameter here
+
+ align:start position:0%
+provided by a parameter a parameter here
+ 
+
+ align:start position:0%
+provided by a parameter a parameter here
+makes all the
+
+ align:start position:0%
+makes all the
+ 
+
+ align:start position:0%
+makes all the
+difference what is this parameter it's a
+
+ align:start position:0%
+difference what is this parameter it's a
+ 
+
+ align:start position:0%
+difference what is this parameter it's a
+parameter we like to put here and we'll
+
+ align:start position:0%
+parameter we like to put here and we'll
+ 
+
+ align:start position:0%
+parameter we like to put here and we'll
+call it line
+
+ align:start position:0%
+call it line
+ 
+
+ align:start position:0%
+call it line
+Lambda you might have said no I don't
+
+ align:start position:0%
+Lambda you might have said no I don't
+ 
+
+ align:start position:0%
+Lambda you might have said no I don't
+have such thing U this is what I want to
+
+ align:start position:0%
+have such thing U this is what I want to
+ 
+
+ align:start position:0%
+have such thing U this is what I want to
+do but still it's better to put a Lambda
+
+ align:start position:0%
+do but still it's better to put a Lambda
+ 
+
+ align:start position:0%
+do but still it's better to put a Lambda
+there where Lambda is
+
+ align:start position:0%
+there where Lambda is
+ 
+
+ align:start position:0%
+there where Lambda is
+unitree no units and belongs to the
+
+ align:start position:0%
+unitree no units and belongs to the
+ 
+
+ align:start position:0%
+unitree no units and belongs to the
+interval 0 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one in that way you will have defined a
+
+ align:start position:0%
+one in that way you will have defined a
+ 
+
+ align:start position:0%
+one in that way you will have defined a
+family of hamiltonians that depend on
+
+ align:start position:0%
+family of hamiltonians that depend on
+ 
+
+ align:start position:0%
+family of hamiltonians that depend on
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+and Lambda is this quantity that you can
+
+ align:start position:0%
+and Lambda is this quantity that you can
+ 
+
+ align:start position:0%
+and Lambda is this quantity that you can
+vary from zero to one so you decide
+
+ align:start position:0%
+vary from zero to one so you decide
+ 
+
+ align:start position:0%
+vary from zero to one so you decide
+you're going to solve a more General
+
+ align:start position:0%
+you're going to solve a more General
+ 
+
+ align:start position:0%
+you're going to solve a more General
+problem perhaps you knew what is the
+
+ align:start position:0%
+problem perhaps you knew what is the
+ 
+
+ align:start position:0%
+problem perhaps you knew what is the
+extra term in the hamiltonian and you
+
+ align:start position:0%
+extra term in the hamiltonian and you
+ 
+
+ align:start position:0%
+extra term in the hamiltonian and you
+say why do I bother with Lambda the
+
+ align:start position:0%
+say why do I bother with Lambda the
+ 
+
+ align:start position:0%
+say why do I bother with Lambda the
+reason you bother with Lambda is that
+
+ align:start position:0%
+reason you bother with Lambda is that
+ 
+
+ align:start position:0%
+reason you bother with Lambda is that
+it's going to help us solve the
+
+ align:start position:0%
+it's going to help us solve the
+ 
+
+ align:start position:0%
+it's going to help us solve the
+equations clearly and second physically
+
+ align:start position:0%
+equations clearly and second physically
+ 
+
+ align:start position:0%
+equations clearly and second physically
+it's kind of interesting because you
+
+ align:start position:0%
+it's kind of interesting because you
+ 
+
+ align:start position:0%
+it's kind of interesting because you
+could think of Lambda as a extra
+
+ align:start position:0%
+could think of Lambda as a extra
+ 
+
+ align:start position:0%
+could think of Lambda as a extra
+parameter of the physics in which you
+
+ align:start position:0%
+parameter of the physics in which you
+ 
+
+ align:start position:0%
+parameter of the physics in which you
+maybe set it equal to zero and you
+
+ align:start position:0%
+maybe set it equal to zero and you
+ 
+
+ align:start position:0%
+maybe set it equal to zero and you
+recover the original
+
+ align:start position:0%
+recover the original
+ 
+
+ align:start position:0%
+recover the original
+hamiltonian or you vary it
+
+ align:start position:0%
+hamiltonian or you vary it
+ 
+
+ align:start position:0%
+hamiltonian or you vary it
+and when it reaches one it is the
+
+ align:start position:0%
+and when it reaches one it is the
+ 
+
+ align:start position:0%
+and when it reaches one it is the
+Hamilton and you're trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solve on the other hand this parameter
+
+ align:start position:0%
+solve on the other hand this parameter
+ 
+
+ align:start position:0%
+solve on the other hand this parameter
+allows you to do something very nice too
+
+ align:start position:0%
+allows you to do something very nice too
+ 
+
+ align:start position:0%
+allows you to do something very nice too
+one of the things we're going to try to
+
+ align:start position:0%
+one of the things we're going to try to
+ 
+
+ align:start position:0%
+one of the things we're going to try to
+clarify by the end of this lecture is
+
+ align:start position:0%
+clarify by the end of this lecture is
+ 
+
+ align:start position:0%
+clarify by the end of this lecture is
+shouldn't this thing be rather small
+
+ align:start position:0%
+shouldn't this thing be rather small
+ 
+
+ align:start position:0%
+shouldn't this thing be rather small
+compared to this one if we want to say
+
+ align:start position:0%
+compared to this one if we want to say
+ 
+
+ align:start position:0%
+compared to this one if we want to say
+it with deform the system slightly we
+
+ align:start position:0%
+it with deform the system slightly we
+ 
+
+ align:start position:0%
+it with deform the system slightly we
+want the correction to be small compared
+
+ align:start position:0%
+want the correction to be small compared
+ 
+
+ align:start position:0%
+want the correction to be small compared
+to the original
+
+ align:start position:0%
+to the original
+ 
+
+ align:start position:0%
+to the original
+hamiltonian so what does it mean for a
+
+ align:start position:0%
+hamiltonian so what does it mean for a
+ 
+
+ align:start position:0%
+hamiltonian so what does it mean for a
+hamiltonian to be small compared to
+
+ align:start position:0%
+hamiltonian to be small compared to
+ 
+
+ align:start position:0%
+hamiltonian to be small compared to
+another hamiltonian these are operator
+
+ align:start position:0%
+another hamiltonian these are operator
+ 
+
+ align:start position:0%
+another hamiltonian these are operator
+so what does it mean
+
+ align:start position:0%
+so what does it mean
+ 
+
+ align:start position:0%
+so what does it mean
+small you could say well
+
+ align:start position:0%
+small you could say well
+ 
+
+ align:start position:0%
+small you could say well
+I don't know precisely what it means
+
+ align:start position:0%
+I don't know precisely what it means
+ 
+
+ align:start position:0%
+I don't know precisely what it means
+small maybe it means that the Matrix
+
+ align:start position:0%
+small maybe it means that the Matrix
+ 
+
+ align:start position:0%
+small maybe it means that the Matrix
+elements of this Delta
+
+ align:start position:0%
+elements of this Delta
+ 
+
+ align:start position:0%
+elements of this Delta
+H are small compared to the Matrix
+
+ align:start position:0%
+H are small compared to the Matrix
+ 
+
+ align:start position:0%
+H are small compared to the Matrix
+elements of that and that is true
+
+ align:start position:0%
+elements of that and that is true
+ 
+
+ align:start position:0%
+elements of that and that is true
+surprisingly will not be
+
+ align:start position:0%
+surprisingly will not be
+ 
+
+ align:start position:0%
+surprisingly will not be
+enough on the other
+
+ align:start position:0%
+enough on the other
+ 
+
+ align:start position:0%
+enough on the other
+hand whatever is small we could all
+
+ align:start position:0%
+hand whatever is small we could all
+ 
+
+ align:start position:0%
+hand whatever is small we could all
+agree that if th if this is not small we
+
+ align:start position:0%
+agree that if th if this is not small we
+ 
+
+ align:start position:0%
+agree that if th if this is not small we
+could put Lambda equal
+
+ align:start position:0%
+could put Lambda equal
+ 
+
+ align:start position:0%
+could put Lambda equal
+0.01 maybe that's small but if that's
+
+ align:start position:0%
+0.01 maybe that's small but if that's
+ 
+
+ align:start position:0%
+0.01 maybe that's small but if that's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+small Lambda equal 10 the- 9 if that's
+
+ align:start position:0%
+small Lambda equal 10 the- 9 if that's
+ 
+
+ align:start position:0%
+small Lambda equal 10 the- 9 if that's
+not small 10 Theus 30 at some point this
+
+ align:start position:0%
+not small 10 Theus 30 at some point this
+ 
+
+ align:start position:0%
+not small 10 Theus 30 at some point this
+will be small enough and uh therefore we
+
+ align:start position:0%
+will be small enough and uh therefore we
+ 
+
+ align:start position:0%
+will be small enough and uh therefore we
+could try to make sense this allows you
+
+ align:start position:0%
+could try to make sense this allows you
+ 
+
+ align:start position:0%
+could try to make sense this allows you
+to really think of this as a
+
+ align:start position:0%
+to really think of this as a
+ 
+
+ align:start position:0%
+to really think of this as a
+perturbation for whatever Delta H is for
+
+ align:start position:0%
+perturbation for whatever Delta H is for
+ 
+
+ align:start position:0%
+perturbation for whatever Delta H is for
+sufficiently small Lambda this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small so uh this is what we're going to
+
+ align:start position:0%
+small so uh this is what we're going to
+ 
+
+ align:start position:0%
+small so uh this is what we're going to
+try to solve and let's try to imagine
+
+ align:start position:0%
+try to solve and let's try to imagine
+ 
+
+ align:start position:0%
+try to solve and let's try to imagine
+first um what can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen so I'm going to try to
+
+ align:start position:0%
+happen so I'm going to try to
+ 
+
+ align:start position:0%
+happen so I'm going to try to
+imagine what's going
+
+ align:start position:0%
+imagine what's going
+ 
+
+ align:start position:0%
+imagine what's going
+on a plot that's the best way to imagine
+
+ align:start position:0%
+on a plot that's the best way to imagine
+ 
+
+ align:start position:0%
+on a plot that's the best way to imagine
+thing so I'll do a
+
+ align:start position:0%
+thing so I'll do a
+ 
+
+ align:start position:0%
+thing so I'll do a
+plot here I put Lambda
+
+ align:start position:0%
+plot here I put Lambda
+ 
+
+ align:start position:0%
+plot here I put Lambda
+and here in the vertical axis I will
+
+ align:start position:0%
+and here in the vertical axis I will
+ 
+
+ align:start position:0%
+and here in the vertical axis I will
+indicate the spectrum of
+
+ align:start position:0%
+indicate the spectrum of
+ 
+
+ align:start position:0%
+indicate the spectrum of
+h0 the spectrum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of of h0 so this is going to be an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy so it may happen that the in our
+
+ align:start position:0%
+energy so it may happen that the in our
+ 
+
+ align:start position:0%
+energy so it may happen that the in our
+systems there's a ground state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this ground state is going to be a
+
+ align:start position:0%
+and this ground state is going to be a
+ 
+
+ align:start position:0%
+and this ground state is going to be a
+single state I will not put a name into
+
+ align:start position:0%
+single state I will not put a name into
+ 
+
+ align:start position:0%
+single state I will not put a name into
+it I will just say there is one state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here that means the ground state is non
+
+ align:start position:0%
+here that means the ground state is non
+ 
+
+ align:start position:0%
+here that means the ground state is non
+degenerate the generate states are
+
+ align:start position:0%
+degenerate the generate states are
+ 
+
+ align:start position:0%
+degenerate the generate states are
+states of the same energy and I say
+
+ align:start position:0%
+states of the same energy and I say
+ 
+
+ align:start position:0%
+states of the same energy and I say
+there's just one state so not
+
+ align:start position:0%
+there's just one state so not
+ 
+
+ align:start position:0%
+there's just one state so not
+degeneracy suppose you go here
+
+ align:start position:0%
+degeneracy suppose you go here
+ 
+
+ align:start position:0%
+degeneracy suppose you go here
+and now you find two states so I put two
+
+ align:start position:0%
+and now you find two states so I put two
+ 
+
+ align:start position:0%
+and now you find two states so I put two
+dots here to indicate that there are two
+
+ align:start position:0%
+dots here to indicate that there are two
+ 
+
+ align:start position:0%
+dots here to indicate that there are two
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+there finally let's go higher up and
+
+ align:start position:0%
+there finally let's go higher up and
+ 
+
+ align:start position:0%
+there finally let's go higher up and
+assume that this hamiltonian maybe has
+
+ align:start position:0%
+assume that this hamiltonian maybe has
+ 
+
+ align:start position:0%
+assume that this hamiltonian maybe has
+one state
+
+ align:start position:0%
+one state
+ 
+
+ align:start position:0%
+one state
+here but here it has four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states and these are the energies those
+
+ align:start position:0%
+states and these are the energies those
+ 
+
+ align:start position:0%
+states and these are the energies those
+are some numbers and this Spectrum must
+
+ align:start position:0%
+are some numbers and this Spectrum must
+ 
+
+ align:start position:0%
+are some numbers and this Spectrum must
+continue to exist so this is the
+
+ align:start position:0%
+continue to exist so this is the
+ 
+
+ align:start position:0%
+continue to exist so this is the
+spectrum of your
+
+ align:start position:0%
+spectrum of your
+ 
+
+ align:start position:0%
+spectrum of your
+h0 the hamiltonian you
+
+ align:start position:0%
+h0 the hamiltonian you
+ 
+
+ align:start position:0%
+h0 the hamiltonian you
+know certainly uh the hydrogen atom
+
+ align:start position:0%
+know certainly uh the hydrogen atom
+ 
+
+ align:start position:0%
+know certainly uh the hydrogen atom
+hamiltonian has the generate state so
+
+ align:start position:0%
+hamiltonian has the generate state so
+ 
+
+ align:start position:0%
+hamiltonian has the generate state so
+that's roughly what's happening
+
+ align:start position:0%
+that's roughly what's happening
+ 
+
+ align:start position:0%
+that's roughly what's happening
+there um the simple harmonic oscillator
+
+ align:start position:0%
+there um the simple harmonic oscillator
+ 
+
+ align:start position:0%
+there um the simple harmonic oscillator
+in one dimension doesn't have the
+
+ align:start position:0%
+in one dimension doesn't have the
+ 
+
+ align:start position:0%
+in one dimension doesn't have the
+generate States but the
+
+ align:start position:0%
+generate States but the
+ 
+
+ align:start position:0%
+generate States but the
+isotropic harmonic oscillator in two or
+
+ align:start position:0%
+isotropic harmonic oscillator in two or
+ 
+
+ align:start position:0%
+isotropic harmonic oscillator in two or
+three three dimensions does have lots of
+
+ align:start position:0%
+three three dimensions does have lots of
+ 
+
+ align:start position:0%
+three three dimensions does have lots of
+degeneracies you've seen those
+
+ align:start position:0%
+degeneracies you've seen those
+ 
+
+ align:start position:0%
+degeneracies you've seen those
+probably so that's typical so what are
+
+ align:start position:0%
+probably so that's typical so what are
+ 
+
+ align:start position:0%
+probably so that's typical so what are
+we aiming to understand we're aiming to
+
+ align:start position:0%
+we aiming to understand we're aiming to
+ 
+
+ align:start position:0%
+we aiming to understand we're aiming to
+understand what happens to the energy of
+
+ align:start position:0%
+understand what happens to the energy of
+ 
+
+ align:start position:0%
+understand what happens to the energy of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+States or what happens to the energy ion
+
+ align:start position:0%
+States or what happens to the energy ion
+ 
+
+ align:start position:0%
+States or what happens to the energy ion
+States as the perturbation is turned on
+
+ align:start position:0%
+States as the perturbation is turned on
+ 
+
+ align:start position:0%
+States as the perturbation is turned on
+so imagining Lambda going from 0er to
+
+ align:start position:0%
+so imagining Lambda going from 0er to
+ 
+
+ align:start position:0%
+so imagining Lambda going from 0er to
+one the process of turning on the
+
+ align:start position:0%
+one the process of turning on the
+ 
+
+ align:start position:0%
+one the process of turning on the
+perturbation
+
+ align:start position:0%
+perturbation
+ 
+
+ align:start position:0%
+perturbation
+and the igen states are going to change
+
+ align:start position:0%
+and the igen states are going to change
+ 
+
+ align:start position:0%
+and the igen states are going to change
+because whatever was an igen state of H
+
+ align:start position:0%
+because whatever was an igen state of H
+ 
+
+ align:start position:0%
+because whatever was an igen state of H
+zero is not going to be an Nan state of
+
+ align:start position:0%
+zero is not going to be an Nan state of
+ 
+
+ align:start position:0%
+zero is not going to be an Nan state of
+the new hamiltonian and the energies are
+
+ align:start position:0%
+the new hamiltonian and the energies are
+ 
+
+ align:start position:0%
+the new hamiltonian and the energies are
+going to change so everything is going
+
+ align:start position:0%
+going to change so everything is going
+ 
+
+ align:start position:0%
+going to change so everything is going
+to change but presumably it will happen
+
+ align:start position:0%
+to change but presumably it will happen
+ 
+
+ align:start position:0%
+to change but presumably it will happen
+continuously as you change Lambda
+
+ align:start position:0%
+continuously as you change Lambda
+ 
+
+ align:start position:0%
+continuously as you change Lambda
+continuously from zero to
+
+ align:start position:0%
+continuously from zero to
+ 
+
+ align:start position:0%
+continuously from zero to
+one so this first state for example exle
+
+ align:start position:0%
+one so this first state for example exle
+ 
+
+ align:start position:0%
+one so this first state for example exle
+may do
+
+ align:start position:0%
+may do
+ 
+
+ align:start position:0%
+may do
+this I don't know what it will do but it
+
+ align:start position:0%
+this I don't know what it will do but it
+ 
+
+ align:start position:0%
+this I don't know what it will do but it
+will vary as a function of Lambda the
+
+ align:start position:0%
+will vary as a function of Lambda the
+ 
+
+ align:start position:0%
+will vary as a function of Lambda the
+energy we'll do something maybe we can
+
+ align:start position:0%
+energy we'll do something maybe we can
+ 
+
+ align:start position:0%
+energy we'll do something maybe we can
+cut it here and say that Lambda is equal
+
+ align:start position:0%
+cut it here and say that Lambda is equal
+ 
+
+ align:start position:0%
+cut it here and say that Lambda is equal
+to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now we have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states so I can analyze this state with
+
+ align:start position:0%
+states so I can analyze this state with
+ 
+
+ align:start position:0%
+states so I can analyze this state with
+what's called n degenerate perturbation
+
+ align:start position:0%
+what's called n degenerate perturbation
+ 
+
+ align:start position:0%
+what's called n degenerate perturbation
+in theory which means you have a non
+
+ align:start position:0%
+in theory which means you have a non
+ 
+
+ align:start position:0%
+in theory which means you have a non
+degenerate State and there are
+
+ align:start position:0%
+degenerate State and there are
+ 
+
+ align:start position:0%
+degenerate State and there are
+techniques that we're going to do today
+
+ align:start position:0%
+techniques that we're going to do today
+ 
+
+ align:start position:0%
+techniques that we're going to do today
+to understand how this state varies but
+
+ align:start position:0%
+to understand how this state varies but
+ 
+
+ align:start position:0%
+to understand how this state varies but
+how about this one here you have two
+
+ align:start position:0%
+how about this one here you have two
+ 
+
+ align:start position:0%
+how about this one here you have two
+states what happens to them well two
+
+ align:start position:0%
+states what happens to them well two
+ 
+
+ align:start position:0%
+states what happens to them well two
+states should remain two states and
+
+ align:start position:0%
+states should remain two states and
+ 
+
+ align:start position:0%
+states should remain two states and
+their energies what will they do maybe
+
+ align:start position:0%
+their energies what will they do maybe
+ 
+
+ align:start position:0%
+their energies what will they do maybe
+they'll track each other but maybe the
+
+ align:start position:0%
+they'll track each other but maybe the
+ 
+
+ align:start position:0%
+they'll track each other but maybe the
+perturbation splits the degeneracy
+
+ align:start position:0%
+perturbation splits the degeneracy
+ 
+
+ align:start position:0%
+perturbation splits the degeneracy
+that's a very important phenomenon let's
+
+ align:start position:0%
+that's a very important phenomenon let's
+ 
+
+ align:start position:0%
+that's a very important phenomenon let's
+assume it does that so it may look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this like that for example the
+
+ align:start position:0%
+this like that for example the
+ 
+
+ align:start position:0%
+this like that for example the
+perturbation makes one state have more
+
+ align:start position:0%
+perturbation makes one state have more
+ 
+
+ align:start position:0%
+perturbation makes one state have more
+energy than the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other here is another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state now a phenomenon that might
+
+ align:start position:0%
+state now a phenomenon that might
+ 
+
+ align:start position:0%
+state now a phenomenon that might
+happen many things can happen this is a
+
+ align:start position:0%
+happen many things can happen this is a
+ 
+
+ align:start position:0%
+happen many things can happen this is a
+very rich subject because of all the
+
+ align:start position:0%
+very rich subject because of all the
+ 
+
+ align:start position:0%
+very rich subject because of all the
+things that can happen it may happen
+
+ align:start position:0%
+things that can happen it may happen
+ 
+
+ align:start position:0%
+things that can happen it may happen
+that this thing for
+
+ align:start position:0%
+that this thing for
+ 
+
+ align:start position:0%
+that this thing for
+example goes like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and like that but there are four
+
+ align:start position:0%
+this and like that but there are four
+ 
+
+ align:start position:0%
+this and like that but there are four
+states it may be that one state goes
+
+ align:start position:0%
+states it may be that one state goes
+ 
+
+ align:start position:0%
+states it may be that one state goes
+here and three states go here but then
+
+ align:start position:0%
+here and three states go here but then
+ 
+
+ align:start position:0%
+here and three states go here but then
+after a little while they'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depart how many did I want no I got too
+
+ align:start position:0%
+depart how many did I want no I got too
+ 
+
+ align:start position:0%
+depart how many did I want no I got too
+many well five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so it may happen something
+
+ align:start position:0%
+all right so it may happen something
+ 
+
+ align:start position:0%
+all right so it may happen something
+like that that they split and then to
+
+ align:start position:0%
+like that that they split and then to
+ 
+
+ align:start position:0%
+like that that they split and then to
+higher order they keep splitting
+
+ align:start position:0%
+higher order they keep splitting
+ 
+
+ align:start position:0%
+higher order they keep splitting
+um in fact they're splitting here
+
+ align:start position:0%
+um in fact they're splitting here
+ 
+
+ align:start position:0%
+um in fact they're splitting here
+already but you don't see it it's just
+
+ align:start position:0%
+already but you don't see it it's just
+ 
+
+ align:start position:0%
+already but you don't see it it's just
+coming is too close just the same way as
+
+ align:start position:0%
+coming is too close just the same way as
+ 
+
+ align:start position:0%
+coming is too close just the same way as
+X SAR and x to the 4th and x to the 8
+
+ align:start position:0%
+X SAR and x to the 4th and x to the 8
+ 
+
+ align:start position:0%
+X SAR and x to the 4th and x to the 8
+sort of at the origin they all look the
+
+ align:start position:0%
+sort of at the origin they all look the
+ 
+
+ align:start position:0%
+sort of at the origin they all look the
+same and then they eventually
+
+ align:start position:0%
+same and then they eventually
+ 
+
+ align:start position:0%
+same and then they eventually
+split so this is what we're going to to
+
+ align:start position:0%
+split so this is what we're going to to
+ 
+
+ align:start position:0%
+split so this is what we're going to to
+try to understand for
+
+ align:start position:0%
+try to understand for
+ 
+
+ align:start position:0%
+try to understand for
+this we need non degenerate perturbation
+
+ align:start position:0%
+this we need non degenerate perturbation
+ 
+
+ align:start position:0%
+this we need non degenerate perturbation
+theory for this degenerate perturbation
+
+ align:start position:0%
+theory for this degenerate perturbation
+ 
+
+ align:start position:0%
+theory for this degenerate perturbation
+theory for this we need sophisticated
+
+ align:start position:0%
+theory for this we need sophisticated
+ 
+
+ align:start position:0%
+theory for this we need sophisticated
+degenerate perturbation Theory very
+
+ align:start position:0%
+degenerate perturbation Theory very
+ 
+
+ align:start position:0%
+degenerate perturbation Theory very
+intricate phenomenon but still it
+
+ align:start position:0%
+intricate phenomenon but still it
+ 
+
+ align:start position:0%
+intricate phenomenon but still it
+happens and happens in many
+
+ align:start position:0%
+happens and happens in many
+ 
+
+ align:start position:0%
+happens and happens in many
+applications so we're going to start
+
+ align:start position:0%
+applications so we're going to start
+ 
+
+ align:start position:0%
+applications so we're going to start
+with a simpler one which is non
+
+ align:start position:0%
+with a simpler one which is non
+ 
+
+ align:start position:0%
+with a simpler one which is non
+degenerate perturbation Theory non
+
+ align:start position:0%
+degenerate perturbation Theory non
+ 
+
+ align:start position:0%
+degenerate perturbation Theory non
+degenerate perturbation Theory
+
+ align:start position:0%
+degenerate perturbation Theory
+ 
+
+ align:start position:0%
+degenerate perturbation Theory
+non the generate perturbation Theory and
+
+ align:start position:0%
+non the generate perturbation Theory and
+ 
+
+ align:start position:0%
+non the generate perturbation Theory and
+then we say well what does it mean that
+
+ align:start position:0%
+then we say well what does it mean that
+ 
+
+ align:start position:0%
+then we say well what does it mean that
+we understand
+
+ align:start position:0%
+we understand
+ 
+
+ align:start position:0%
+we understand
+h0 it means that we have
+
+ align:start position:0%
+h0 it means that we have
+ 
+
+ align:start position:0%
+h0 it means that we have
+found all the igen states with K one
+
+ align:start position:0%
+found all the igen states with K one
+ 
+
+ align:start position:0%
+found all the igen states with K one
+maybe up to Infinity I don't know K is
+
+ align:start position:0%
+maybe up to Infinity I don't know K is
+ 
+
+ align:start position:0%
+maybe up to Infinity I don't know K is
+not momentum these are the energy I
+
+ align:start position:0%
+not momentum these are the energy I
+ 
+
+ align:start position:0%
+not momentum these are the energy I
+states of h0 that we're supposed to know
+
+ align:start position:0%
+states of h0 that we're supposed to know
+ 
+
+ align:start position:0%
+states of h0 that we're supposed to know
+and there all
+
+ align:start position:0%
+and there all
+ 
+
+ align:start position:0%
+and there all
+orthonormal that can always be done when
+
+ align:start position:0%
+orthonormal that can always be done when
+ 
+
+ align:start position:0%
+orthonormal that can always be done when
+you have a Herm Mission hamiltonian you
+
+ align:start position:0%
+you have a Herm Mission hamiltonian you
+ 
+
+ align:start position:0%
+you have a Herm Mission hamiltonian you
+can find an orthonormal basis of states
+
+ align:start position:0%
+can find an orthonormal basis of states
+ 
+
+ align:start position:0%
+can find an orthonormal basis of states
+and being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal
+
+ align:start position:0%
+orthonormal
+ 
+
+ align:start position:0%
+orthonormal
+this orthogonality holds the states are
+
+ align:start position:0%
+this orthogonality holds the states are
+ 
+
+ align:start position:0%
+this orthogonality holds the states are
+igen states of
+
+ align:start position:0%
+igen states of
+ 
+
+ align:start position:0%
+igen states of
+the h0 so for
+
+ align:start position:0%
+the h0 so for
+ 
+
+ align:start position:0%
+the h0 so for
+this will will call this e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k0 the energy of this state k for the
+
+ align:start position:0%
+k0 the energy of this state k for the
+ 
+
+ align:start position:0%
+k0 the energy of this state k for the
+label of the state zero because we're
+
+ align:start position:0%
+label of the state zero because we're
+ 
+
+ align:start position:0%
+label of the state zero because we're
+not doing anything in perturbation yet
+
+ align:start position:0%
+not doing anything in perturbation yet
+ 
+
+ align:start position:0%
+not doing anything in perturbation yet
+we're dealing with the
+
+ align:start position:0%
+we're dealing with the
+ 
+
+ align:start position:0%
+we're dealing with the
+unperturbed zero or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system that defines the energies and
+
+ align:start position:0%
+system that defines the energies and
+ 
+
+ align:start position:0%
+system that defines the energies and
+this uh energies satisfy I say e 0 0 is
+
+ align:start position:0%
+this uh energies satisfy I say e 0 0 is
+ 
+
+ align:start position:0%
+this uh energies satisfy I say e 0 0 is
+less than or equal than E1
+
+ align:start position:0%
+less than or equal than E1
+ 
+
+ align:start position:0%
+less than or equal than E1
+0 less than or equal to
+
+ align:start position:0%
+0 less than or equal to
+ 
+
+ align:start position:0%
+0 less than or equal to
+E20 so all the energies are
+
+ align:start position:0%
+E20 so all the energies are
+ 
+
+ align:start position:0%
+E20 so all the energies are
+ordered um I need the equals because of
+
+ align:start position:0%
+ordered um I need the equals because of
+ 
+
+ align:start position:0%
+ordered um I need the equals because of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+degeneracy might be degenerate so you
+
+ align:start position:0%
+degeneracy might be degenerate so you
+ 
+
+ align:start position:0%
+degeneracy might be degenerate so you
+have this uh
+
+ align:start position:0%
+have this uh
+ 
+
+ align:start position:0%
+have this uh
+situation so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's
+
+ align:start position:0%
+um let's
+ 
+
+ align:start position:0%
+um let's
+consider this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state that is non degenerate and let's
+
+ align:start position:0%
+state that is non degenerate and let's
+ 
+
+ align:start position:0%
+state that is non degenerate and let's
+assume this is the state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n0 is the nth
+
+ align:start position:0%
+n0 is the nth
+ 
+
+ align:start position:0%
+n0 is the nth
+state if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n0 is non
+
+ align:start position:0%
+n0 is non
+ 
+
+ align:start position:0%
+n0 is non
+degenerate it means that e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n0 is really smaller than the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and it's really bigger the energy
+
+ align:start position:0%
+one and it's really bigger the energy
+ 
+
+ align:start position:0%
+one and it's really bigger the energy
+than the previous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one no equal signs there it really means
+
+ align:start position:0%
+one no equal signs there it really means
+ 
+
+ align:start position:0%
+one no equal signs there it really means
+those things are
+
+ align:start position:0%
+those things are
+ 
+
+ align:start position:0%
+those things are
+separate and that's the meaning of
+
+ align:start position:0%
+separate and that's the meaning of
+ 
+
+ align:start position:0%
+separate and that's the meaning of
+non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degeneracy and now what are we trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solve starting from this
+
+ align:start position:0%
+solve starting from this
+ 
+
+ align:start position:0%
+solve starting from this
+n0o we're trying to find how the energy
+
+ align:start position:0%
+n0o we're trying to find how the energy
+ 
+
+ align:start position:0%
+n0o we're trying to find how the energy
+changes and how the state changes both
+
+ align:start position:0%
+changes and how the state changes both
+ 
+
+ align:start position:0%
+changes and how the state changes both
+things are important so
+
+ align:start position:0%
+things are important so
+ 
+
+ align:start position:0%
+things are important so
+um we're going to try to solve therefore
+
+ align:start position:0%
+um we're going to try to solve therefore
+ 
+
+ align:start position:0%
+um we're going to try to solve therefore
+for for H of
+
+ align:start position:0%
+for for H of
+ 
+
+ align:start position:0%
+for for H of
+Lambda n Lambda the state n0 is going to
+
+ align:start position:0%
+Lambda n Lambda the state n0 is going to
+ 
+
+ align:start position:0%
+Lambda n Lambda the state n0 is going to
+change when Lambda turns on and it's
+
+ align:start position:0%
+change when Lambda turns on and it's
+ 
+
+ align:start position:0%
+change when Lambda turns on and it's
+going to become n of Lambda and this is
+
+ align:start position:0%
+going to become n of Lambda and this is
+ 
+
+ align:start position:0%
+going to become n of Lambda and this is
+going to have an energy e n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda instead of e
+
+ align:start position:0%
+Lambda instead of e
+ 
+
+ align:start position:0%
+Lambda instead of e
+n0 this has an energy e
+
+ align:start position:0%
+n0 this has an energy e
+ 
+
+ align:start position:0%
+n0 this has an energy e
+n zero with respect to the original
+
+ align:start position:0%
+n zero with respect to the original
+ 
+
+ align:start position:0%
+n zero with respect to the original
+hamiltonian now it's going to have an
+
+ align:start position:0%
+hamiltonian now it's going to have an
+ 
+
+ align:start position:0%
+hamiltonian now it's going to have an
+energy e n of
+
+ align:start position:0%
+energy e n of
+ 
+
+ align:start position:0%
+energy e n of
+Lambda n of Lambda so that's the
+
+ align:start position:0%
+Lambda n of Lambda so that's the
+ 
+
+ align:start position:0%
+Lambda n of Lambda so that's the
+equation we want to
+
+ align:start position:0%
+equation we want to
+ 
+
+ align:start position:0%
+equation we want to
+solve this
+
+ align:start position:0%
+solve this
+ 
+
+ align:start position:0%
+solve this
+is what the state n z becomes as you
+
+ align:start position:0%
+is what the state n z becomes as you
+ 
+
+ align:start position:0%
+is what the state n z becomes as you
+turn on Lambda and this is what the
+
+ align:start position:0%
+turn on Lambda and this is what the
+ 
+
+ align:start position:0%
+turn on Lambda and this is what the
+energy n0 becomes as you turn on Lambda
+
+ align:start position:0%
+energy n0 becomes as you turn on Lambda
+ 
+
+ align:start position:0%
+energy n0 becomes as you turn on Lambda
+so we note that n when Lambda equal to
+
+ align:start position:0%
+so we note that n when Lambda equal to
+ 
+
+ align:start position:0%
+so we note that n when Lambda equal to
+Z is what we call the state
+
+ align:start position:0%
+Z is what we call the state
+ 
+
+ align:start position:0%
+Z is what we call the state
+n0 and the energy e n at Lambda equal 0
+
+ align:start position:0%
+n0 and the energy e n at Lambda equal 0
+ 
+
+ align:start position:0%
+n0 and the energy e n at Lambda equal 0
+is what we called e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n0 so with this initial conditions at
+
+ align:start position:0%
+n0 so with this initial conditions at
+ 
+
+ align:start position:0%
+n0 so with this initial conditions at
+Lambda equals z we're trying to solve
+
+ align:start position:0%
+Lambda equals z we're trying to solve
+ 
+
+ align:start position:0%
+Lambda equals z we're trying to solve
+this system to see what the state
+
+ align:start position:0%
+this system to see what the state
+ 
+
+ align:start position:0%
+this system to see what the state
+becomes and now here comes a a key
+
+ align:start position:0%
+becomes and now here comes a a key
+ 
+
+ align:start position:0%
+becomes and now here comes a a key
+assumption that the way we're going to
+
+ align:start position:0%
+assumption that the way we're going to
+ 
+
+ align:start position:0%
+assumption that the way we're going to
+solve this allows us to write a
+
+ align:start position:0%
+solve this allows us to write a
+ 
+
+ align:start position:0%
+solve this allows us to write a
+perturbative serious expansion for this
+
+ align:start position:0%
+perturbative serious expansion for this
+ 
+
+ align:start position:0%
+perturbative serious expansion for this
+objects so in particular we'll write n
+
+ align:start position:0%
+objects so in particular we'll write n
+ 
+
+ align:start position:0%
+objects so in particular we'll write n
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Lambda is equal to
+
+ align:start position:0%
+Lambda is equal to
+ 
+
+ align:start position:0%
+Lambda is equal to
+n0 that's what n of Lambda should be
+
+ align:start position:0%
+n0 that's what n of Lambda should be
+ 
+
+ align:start position:0%
+n0 that's what n of Lambda should be
+when Lambda is equal to zero so then
+
+ align:start position:0%
+when Lambda is equal to zero so then
+ 
+
+ align:start position:0%
+when Lambda is equal to zero so then
+there will be a first order correction
+
+ align:start position:0%
+there will be a first order correction
+ 
+
+ align:start position:0%
+there will be a first order correction
+Lambda time the state
+
+ align:start position:0%
+Lambda time the state
+ 
+
+ align:start position:0%
+Lambda time the state
+N1 plus Lambda squar * the state
+
+ align:start position:0%
+N1 plus Lambda squar * the state
+ 
+
+ align:start position:0%
+N1 plus Lambda squar * the state
+N2 and it will go on and
+
+ align:start position:0%
+N2 and it will go on and
+ 
+
+ align:start position:0%
+N2 and it will go on and
+on moreover e n
+
+ align:start position:0%
+on moreover e n
+ 
+
+ align:start position:0%
+on moreover e n
+Lambda when Lambda is equal to zero
+
+ align:start position:0%
+Lambda when Lambda is equal to zero
+ 
+
+ align:start position:0%
+Lambda when Lambda is equal to zero
+you're back to the energy e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n0 but then there will be a Lambda corre
+
+ align:start position:0%
+n0 but then there will be a Lambda corre
+ 
+
+ align:start position:0%
+n0 but then there will be a Lambda corre
+ction time e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N1 that's a name for the first order
+
+ align:start position:0%
+N1 that's a name for the first order
+ 
+
+ align:start position:0%
+N1 that's a name for the first order
+correction plus a Lambda squared
+
+ align:start position:0%
+correction plus a Lambda squared
+ 
+
+ align:start position:0%
+correction plus a Lambda squared
+correction e n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so this is our
+
+ align:start position:0%
+2 so this is our
+ 
+
+ align:start position:0%
+2 so this is our
+hypothesis that there is a solution in a
+
+ align:start position:0%
+hypothesis that there is a solution in a
+ 
+
+ align:start position:0%
+hypothesis that there is a solution in a
+perative series expansion
+
+ align:start position:0%
+perative series expansion
+ 
+
+ align:start position:0%
+perative series expansion
+of this kind and what are our unknowns
+
+ align:start position:0%
+of this kind and what are our unknowns
+ 
+
+ align:start position:0%
+of this kind and what are our unknowns
+our unknowns are this object this one we
+
+ align:start position:0%
+our unknowns are this object this one we
+ 
+
+ align:start position:0%
+our unknowns are this object this one we
+know is the original state this object
+
+ align:start position:0%
+know is the original state this object
+ 
+
+ align:start position:0%
+know is the original state this object
+is unknown this is
+
+ align:start position:0%
+is unknown this is
+ 
+
+ align:start position:0%
+is unknown this is
+unknown this is
+
+ align:start position:0%
+unknown this is
+ 
+
+ align:start position:0%
+unknown this is
+unknown all these things are unknown and
+
+ align:start position:0%
+unknown all these things are unknown and
+ 
+
+ align:start position:0%
+unknown all these things are unknown and
+they go on like that most important all
+
+ align:start position:0%
+they go on like that most important all
+ 
+
+ align:start position:0%
+they go on like that most important all
+these objects don't depend on
+
+ align:start position:0%
+these objects don't depend on
+ 
+
+ align:start position:0%
+these objects don't depend on
+Lambda this the Lambda dependence is
+
+ align:start position:0%
+Lambda this the Lambda dependence is
+ 
+
+ align:start position:0%
+Lambda this the Lambda dependence is
+here Lambda Lambda squar Lambda on and
+
+ align:start position:0%
+here Lambda Lambda squar Lambda on and
+ 
+
+ align:start position:0%
+here Lambda Lambda squar Lambda on and
+these are things that don't depend on
+
+ align:start position:0%
+these are things that don't depend on
+ 
+
+ align:start position:0%
+these are things that don't depend on
+Lambda these are objects that have to be
+
+ align:start position:0%
+Lambda these are objects that have to be
+ 
+
+ align:start position:0%
+Lambda these are objects that have to be
+calculated they're all Lambda
+
+ align:start position:0%
+calculated they're all Lambda
+ 
+
+ align:start position:0%
+calculated they're all Lambda
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+so we are supposed to solve this
+
+ align:start position:0%
+so we are supposed to solve this
+ 
+
+ align:start position:0%
+so we are supposed to solve this
+equation under this conditions and
+
+ align:start position:0%
+equation under this conditions and
+ 
+
+ align:start position:0%
+equation under this conditions and
+that's what we're going to do next
\ No newline at end of file
diff --git a/_crDeSDpB20.txt b/_crDeSDpB20.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07aa85f06db0a952cf70901292ecfaa0fc2e99f5
--- /dev/null
+++ b/_crDeSDpB20.txt
@@ -0,0 +1,9147 @@
+align:start position:0%
+ 
+um okay so today uh despite my
+
+ align:start position:0%
+um okay so today uh despite my
+ 
+
+ align:start position:0%
+um okay so today uh despite my
+admonition doesn't look like a very good
+
+ align:start position:0%
+admonition doesn't look like a very good
+ 
+
+ align:start position:0%
+admonition doesn't look like a very good
+attendance so I'm going to give you all
+
+ align:start position:0%
+attendance so I'm going to give you all
+ 
+
+ align:start position:0%
+attendance so I'm going to give you all
+the answers to the midterm just to
+
+ align:start position:0%
+the answers to the midterm just to
+ 
+
+ align:start position:0%
+the answers to the midterm just to
+reward you for I'm I'm joking but uh I'm
+
+ align:start position:0%
+reward you for I'm I'm joking but uh I'm
+ 
+
+ align:start position:0%
+reward you for I'm I'm joking but uh I'm
+glad you decided to come because it's a
+
+ align:start position:0%
+glad you decided to come because it's a
+ 
+
+ align:start position:0%
+glad you decided to come because it's a
+fun lecture and it's very relevant to
+
+ align:start position:0%
+fun lecture and it's very relevant to
+ 
+
+ align:start position:0%
+fun lecture and it's very relevant to
+what is going to be what we're going to
+
+ align:start position:0%
+what is going to be what we're going to
+ 
+
+ align:start position:0%
+what is going to be what we're going to
+be learning really for the next few
+
+ align:start position:0%
+be learning really for the next few
+ 
+
+ align:start position:0%
+be learning really for the next few
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+which is thinking about models of
+
+ align:start position:0%
+which is thinking about models of
+ 
+
+ align:start position:0%
+which is thinking about models of
+oligopoly once again an awesome
+
+ align:start position:0%
+oligopoly once again an awesome
+ 
+
+ align:start position:0%
+oligopoly once again an awesome
+word which is really just a description
+
+ align:start position:0%
+word which is really just a description
+ 
+
+ align:start position:0%
+word which is really just a description
+of what most markets in America are so
+
+ align:start position:0%
+of what most markets in America are so
+ 
+
+ align:start position:0%
+of what most markets in America are so
+we've covered two extremes we've covered
+
+ align:start position:0%
+we've covered two extremes we've covered
+ 
+
+ align:start position:0%
+we've covered two extremes we've covered
+one extreme for markets which is perfect
+
+ align:start position:0%
+one extreme for markets which is perfect
+ 
+
+ align:start position:0%
+one extreme for markets which is perfect
+competition doesn't really exist we've
+
+ align:start position:0%
+competition doesn't really exist we've
+ 
+
+ align:start position:0%
+competition doesn't really exist we've
+covered another extreme which is
+
+ align:start position:0%
+covered another extreme which is
+ 
+
+ align:start position:0%
+covered another extreme which is
+Monopoly which is which does exist but
+
+ align:start position:0%
+Monopoly which is which does exist but
+ 
+
+ align:start position:0%
+Monopoly which is which does exist but
+it's still fairly rare the more common
+
+ align:start position:0%
+it's still fairly rare the more common
+ 
+
+ align:start position:0%
+it's still fairly rare the more common
+form of markets is what we call
+
+ align:start position:0%
+form of markets is what we call
+ 
+
+ align:start position:0%
+form of markets is what we call
+oligopoly which is when there's a small
+
+ align:start position:0%
+oligopoly which is when there's a small
+ 
+
+ align:start position:0%
+oligopoly which is when there's a small
+number of firms competing to provide the
+
+ align:start position:0%
+number of firms competing to provide the
+ 
+
+ align:start position:0%
+number of firms competing to provide the
+good so it's more than one firm so it's
+
+ align:start position:0%
+good so it's more than one firm so it's
+ 
+
+ align:start position:0%
+good so it's more than one firm so it's
+more than Monopoly but it's less than
+
+ align:start position:0%
+more than Monopoly but it's less than
+ 
+
+ align:start position:0%
+more than Monopoly but it's less than
+free entry it's less than a large number
+
+ align:start position:0%
+free entry it's less than a large number
+ 
+
+ align:start position:0%
+free entry it's less than a large number
+of firms driving profits to zero so
+
+ align:start position:0%
+of firms driving profits to zero so
+ 
+
+ align:start position:0%
+of firms driving profits to zero so
+let's see about the prototypical example
+
+ align:start position:0%
+let's see about the prototypical example
+ 
+
+ align:start position:0%
+let's see about the prototypical example
+of oligopolistic Industry the Auto
+
+ align:start position:0%
+of oligopolistic Industry the Auto
+ 
+
+ align:start position:0%
+of oligopolistic Industry the Auto
+industry most cars in America are sold
+
+ align:start position:0%
+industry most cars in America are sold
+ 
+
+ align:start position:0%
+industry most cars in America are sold
+by fewer than 20
+
+ align:start position:0%
+by fewer than 20
+ 
+
+ align:start position:0%
+by fewer than 20
+companies but they're sold by well more
+
+ align:start position:0%
+companies but they're sold by well more
+ 
+
+ align:start position:0%
+companies but they're sold by well more
+than than one so if you drive on the
+
+ align:start position:0%
+than than one so if you drive on the
+ 
+
+ align:start position:0%
+than than one so if you drive on the
+road you see cars from you know
+
+ align:start position:0%
+road you see cars from you know
+ 
+
+ align:start position:0%
+road you see cars from you know
+primarily 10 but maybe even up to 20
+
+ align:start position:0%
+primarily 10 but maybe even up to 20
+ 
+
+ align:start position:0%
+primarily 10 but maybe even up to 20
+different car
+
+ align:start position:0%
+different car
+ 
+
+ align:start position:0%
+different car
+companies so is that enough to drive us
+
+ align:start position:0%
+companies so is that enough to drive us
+ 
+
+ align:start position:0%
+companies so is that enough to drive us
+the perfectly competitive outcome that
+
+ align:start position:0%
+the perfectly competitive outcome that
+ 
+
+ align:start position:0%
+the perfectly competitive outcome that
+is those 10 to 20 car companies enough
+
+ align:start position:0%
+is those 10 to 20 car companies enough
+ 
+
+ align:start position:0%
+is those 10 to 20 car companies enough
+to drive us to zero
+
+ align:start position:0%
+to drive us to zero
+ 
+
+ align:start position:0%
+to drive us to zero
+profits probably not but is that enough
+
+ align:start position:0%
+profits probably not but is that enough
+ 
+
+ align:start position:0%
+profits probably not but is that enough
+that each company can simply set its
+
+ align:start position:0%
+that each company can simply set its
+ 
+
+ align:start position:0%
+that each company can simply set its
+price and pick its point on the demand
+
+ align:start position:0%
+price and pick its point on the demand
+ 
+
+ align:start position:0%
+price and pick its point on the demand
+curve probably not either so we're
+
+ align:start position:0%
+curve probably not either so we're
+ 
+
+ align:start position:0%
+curve probably not either so we're
+somewhere in between we're in an
+
+ align:start position:0%
+somewhere in between we're in an
+ 
+
+ align:start position:0%
+somewhere in between we're in an
+oligopolistic market now an
+
+ align:start position:0%
+oligopolistic market now an
+ 
+
+ align:start position:0%
+oligopolistic market now an
+oligopolistic Market firms can behave
+
+ align:start position:0%
+oligopolistic Market firms can behave
+ 
+
+ align:start position:0%
+oligopolistic Market firms can behave
+two ways they can behave cooperatively
+
+ align:start position:0%
+two ways they can behave cooperatively
+ 
+
+ align:start position:0%
+two ways they can behave cooperatively
+or non-cooperatively
+
+ align:start position:0%
+or non-cooperatively
+ 
+
+ align:start position:0%
+or non-cooperatively
+okay when there's one firm there's no
+
+ align:start position:0%
+okay when there's one firm there's no
+ 
+
+ align:start position:0%
+okay when there's one firm there's no
+issue just yourself when there's
+
+ align:start position:0%
+issue just yourself when there's
+ 
+
+ align:start position:0%
+issue just yourself when there's
+thousands of firms you can't figure out
+
+ align:start position:0%
+thousands of firms you can't figure out
+ 
+
+ align:start position:0%
+thousands of firms you can't figure out
+how to how to how to uh get together but
+
+ align:start position:0%
+how to how to how to uh get together but
+ 
+
+ align:start position:0%
+how to how to how to uh get together but
+when you have a small number of firms
+
+ align:start position:0%
+when you have a small number of firms
+ 
+
+ align:start position:0%
+when you have a small number of firms
+you can imagine behaving cooperatively
+
+ align:start position:0%
+you can imagine behaving cooperatively
+ 
+
+ align:start position:0%
+you can imagine behaving cooperatively
+non-cooperatively cooperatively would be
+
+ align:start position:0%
+non-cooperatively cooperatively would be
+ 
+
+ align:start position:0%
+non-cooperatively cooperatively would be
+to form a cartel so if you want to
+
+ align:start position:0%
+to form a cartel so if you want to
+ 
+
+ align:start position:0%
+to form a cartel so if you want to
+cooperate you form what's called a
+
+ align:start position:0%
+cooperate you form what's called a
+ 
+
+ align:start position:0%
+cooperate you form what's called a
+cartel which is a Cooperative
+
+ align:start position:0%
+cartel which is a Cooperative
+ 
+
+ align:start position:0%
+cartel which is a Cooperative
+organization of otherwise competing
+
+ align:start position:0%
+organization of otherwise competing
+ 
+
+ align:start position:0%
+organization of otherwise competing
+firms the classic example of this is
+
+ align:start position:0%
+firms the classic example of this is
+ 
+
+ align:start position:0%
+firms the classic example of this is
+OPEC the organization of petroleum
+
+ align:start position:0%
+OPEC the organization of petroleum
+ 
+
+ align:start position:0%
+OPEC the organization of petroleum
+exporting
+
+ align:start position:0%
+exporting
+ 
+
+ align:start position:0%
+exporting
+countries this organization formed in
+
+ align:start position:0%
+countries this organization formed in
+ 
+
+ align:start position:0%
+countries this organization formed in
+1970s of the Middle Eastern countries
+
+ align:start position:0%
+1970s of the Middle Eastern countries
+ 
+
+ align:start position:0%
+1970s of the Middle Eastern countries
+that responsible for about two-thirds of
+
+ align:start position:0%
+that responsible for about two-thirds of
+ 
+
+ align:start position:0%
+that responsible for about two-thirds of
+the world world's oil they got together
+
+ align:start position:0%
+the world world's oil they got together
+ 
+
+ align:start position:0%
+the world world's oil they got together
+and said let's produce
+
+ align:start position:0%
+and said let's produce
+ 
+
+ align:start position:0%
+and said let's produce
+cooperatively and we'll decide how much
+
+ align:start position:0%
+cooperatively and we'll decide how much
+ 
+
+ align:start position:0%
+cooperatively and we'll decide how much
+to produce and what price to set as if
+
+ align:start position:0%
+to produce and what price to set as if
+ 
+
+ align:start position:0%
+to produce and what price to set as if
+we were were sort of a collective
+
+ align:start position:0%
+we were were sort of a collective
+ 
+
+ align:start position:0%
+we were were sort of a collective
+Monopoly so in other words the idea of
+
+ align:start position:0%
+Monopoly so in other words the idea of
+ 
+
+ align:start position:0%
+Monopoly so in other words the idea of
+calization is you effectively turn
+
+ align:start position:0%
+calization is you effectively turn
+ 
+
+ align:start position:0%
+calization is you effectively turn
+yourself into a shared Monopoly with all
+
+ align:start position:0%
+yourself into a shared Monopoly with all
+ 
+
+ align:start position:0%
+yourself into a shared Monopoly with all
+the benefits we've talked about in terms
+
+ align:start position:0%
+the benefits we've talked about in terms
+ 
+
+ align:start position:0%
+the benefits we've talked about in terms
+of profits and
+
+ align:start position:0%
+of profits and
+ 
+
+ align:start position:0%
+of profits and
+things okay so basically the idea is
+
+ align:start position:0%
+things okay so basically the idea is
+ 
+
+ align:start position:0%
+things okay so basically the idea is
+look what do monopolies do they don't
+
+ align:start position:0%
+look what do monopolies do they don't
+ 
+
+ align:start position:0%
+look what do monopolies do they don't
+they get rid of competition they sort of
+
+ align:start position:0%
+they get rid of competition they sort of
+ 
+
+ align:start position:0%
+they get rid of competition they sort of
+maximize profits given the elasticity
+
+ align:start position:0%
+maximize profits given the elasticity
+ 
+
+ align:start position:0%
+maximize profits given the elasticity
+demand they face when you for a cartel
+
+ align:start position:0%
+demand they face when you for a cartel
+ 
+
+ align:start position:0%
+demand they face when you for a cartel
+you essentially say look let's do that
+
+ align:start position:0%
+you essentially say look let's do that
+ 
+
+ align:start position:0%
+you essentially say look let's do that
+let's get rid of competition let's just
+
+ align:start position:0%
+let's get rid of competition let's just
+ 
+
+ align:start position:0%
+let's get rid of competition let's just
+create a as big a piie as possible we'll
+
+ align:start position:0%
+create a as big a piie as possible we'll
+ 
+
+ align:start position:0%
+create a as big a piie as possible we'll
+figure out some way to split
+
+ align:start position:0%
+figure out some way to split
+ 
+
+ align:start position:0%
+figure out some way to split
+it okay now of course the Other Extreme
+
+ align:start position:0%
+it okay now of course the Other Extreme
+ 
+
+ align:start position:0%
+it okay now of course the Other Extreme
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+non-cooperative oligopolistic market
+
+ align:start position:0%
+non-cooperative oligopolistic market
+ 
+
+ align:start position:0%
+non-cooperative oligopolistic market
+where firms don't get together and
+
+ align:start position:0%
+where firms don't get together and
+ 
+
+ align:start position:0%
+where firms don't get together and
+compete where firms where firms I'm
+
+ align:start position:0%
+compete where firms where firms I'm
+ 
+
+ align:start position:0%
+compete where firms where firms I'm
+sorry don't get together and agree um uh
+
+ align:start position:0%
+sorry don't get together and agree um uh
+ 
+
+ align:start position:0%
+sorry don't get together and agree um uh
+on what to do and in fact that's more
+
+ align:start position:0%
+on what to do and in fact that's more
+ 
+
+ align:start position:0%
+on what to do and in fact that's more
+realistic and we'll talk about reasons
+
+ align:start position:0%
+realistic and we'll talk about reasons
+ 
+
+ align:start position:0%
+realistic and we'll talk about reasons
+why next lecture next lecture we'll talk
+
+ align:start position:0%
+why next lecture next lecture we'll talk
+ 
+
+ align:start position:0%
+why next lecture next lecture we'll talk
+about how cartels work and why they
+
+ align:start position:0%
+about how cartels work and why they
+ 
+
+ align:start position:0%
+about how cartels work and why they
+don't typically
+
+ align:start position:0%
+don't typically
+ 
+
+ align:start position:0%
+don't typically
+last so today we'll focus on the more
+
+ align:start position:0%
+last so today we'll focus on the more
+ 
+
+ align:start position:0%
+last so today we'll focus on the more
+realistic case of a nonco
+
+ align:start position:0%
+realistic case of a nonco
+ 
+
+ align:start position:0%
+realistic case of a nonco
+Cooperative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oligopoly which is when there's a small
+
+ align:start position:0%
+oligopoly which is when there's a small
+ 
+
+ align:start position:0%
+oligopoly which is when there's a small
+number of firms in an industry and they
+
+ align:start position:0%
+number of firms in an industry and they
+ 
+
+ align:start position:0%
+number of firms in an industry and they
+can't get together and and cooperate
+
+ align:start position:0%
+can't get together and and cooperate
+ 
+
+ align:start position:0%
+can't get together and and cooperate
+which makes sense I these are firms
+
+ align:start position:0%
+which makes sense I these are firms
+ 
+
+ align:start position:0%
+which makes sense I these are firms
+which grew up hating each other sort of
+
+ align:start position:0%
+which grew up hating each other sort of
+ 
+
+ align:start position:0%
+which grew up hating each other sort of
+makes sense it be hard to cooperate
+
+ align:start position:0%
+makes sense it be hard to cooperate
+ 
+
+ align:start position:0%
+makes sense it be hard to cooperate
+we'll talk about next time why that
+
+ align:start position:0%
+we'll talk about next time why that
+ 
+
+ align:start position:0%
+we'll talk about next time why that
+is so what do we
+
+ align:start position:0%
+is so what do we
+ 
+
+ align:start position:0%
+is so what do we
+do in that case well in that case things
+
+ align:start position:0%
+do in that case well in that case things
+ 
+
+ align:start position:0%
+do in that case well in that case things
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+hard the reason we start with perfect
+
+ align:start position:0%
+hard the reason we start with perfect
+ 
+
+ align:start position:0%
+hard the reason we start with perfect
+competition Monopoly is because they're
+
+ align:start position:0%
+competition Monopoly is because they're
+ 
+
+ align:start position:0%
+competition Monopoly is because they're
+relatively easy to think about oligopoly
+
+ align:start position:0%
+relatively easy to think about oligopoly
+ 
+
+ align:start position:0%
+relatively easy to think about oligopoly
+it gets super complicated and we have to
+
+ align:start position:0%
+it gets super complicated and we have to
+ 
+
+ align:start position:0%
+it gets super complicated and we have to
+turn to a new tool the tool of gain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory
+
+ align:start position:0%
+Theory
+ 
+
+ align:start position:0%
+Theory
+okay um basically the idea of game
+
+ align:start position:0%
+okay um basically the idea of game
+ 
+
+ align:start position:0%
+okay um basically the idea of game
+theory is to think of these firms
+
+ align:start position:0%
+theory is to think of these firms
+ 
+
+ align:start position:0%
+theory is to think of these firms
+interacting as if they're playing a
+
+ align:start position:0%
+interacting as if they're playing a
+ 
+
+ align:start position:0%
+interacting as if they're playing a
+game think of there's there's n firms in
+
+ align:start position:0%
+game think of there's there's n firms in
+ 
+
+ align:start position:0%
+game think of there's there's n firms in
+a market where n is
+
+ align:start position:0%
+a market where n is
+ 
+
+ align:start position:0%
+a market where n is
+small they're they're sort of playing a
+
+ align:start position:0%
+small they're they're sort of playing a
+ 
+
+ align:start position:0%
+small they're they're sort of playing a
+game against each
+
+ align:start position:0%
+game against each
+ 
+
+ align:start position:0%
+game against each
+other and so there's two key pieces of
+
+ align:start position:0%
+other and so there's two key pieces of
+ 
+
+ align:start position:0%
+other and so there's two key pieces of
+Game Theory to keep track of think about
+
+ align:start position:0%
+Game Theory to keep track of think about
+ 
+
+ align:start position:0%
+Game Theory to keep track of think about
+playing a game what are sort of two
+
+ align:start position:0%
+playing a game what are sort of two
+ 
+
+ align:start position:0%
+playing a game what are sort of two
+things you want to figure out the first
+
+ align:start position:0%
+things you want to figure out the first
+ 
+
+ align:start position:0%
+things you want to figure out the first
+thing is your
+
+ align:start position:0%
+thing is your
+ 
+
+ align:start position:0%
+thing is your
+strategy what is the right strategy to
+
+ align:start position:0%
+strategy what is the right strategy to
+ 
+
+ align:start position:0%
+strategy what is the right strategy to
+win this
+
+ align:start position:0%
+win this
+ 
+
+ align:start position:0%
+win this
+game the second point you want to figure
+
+ align:start position:0%
+game the second point you want to figure
+ 
+
+ align:start position:0%
+game the second point you want to figure
+out is
+
+ align:start position:0%
+out is
+ 
+
+ align:start position:0%
+out is
+equilibrium when is the game over when
+
+ align:start position:0%
+equilibrium when is the game over when
+ 
+
+ align:start position:0%
+equilibrium when is the game over when
+does the game settle into an answer that
+
+ align:start position:0%
+does the game settle into an answer that
+ 
+
+ align:start position:0%
+does the game settle into an answer that
+all parties agree on with Monopoly
+
+ align:start position:0%
+all parties agree on with Monopoly
+ 
+
+ align:start position:0%
+all parties agree on with Monopoly
+there's a set of rules once everybody
+
+ align:start position:0%
+there's a set of rules once everybody
+ 
+
+ align:start position:0%
+there's a set of rules once everybody
+else is bankrupt you win that's the
+
+ align:start position:0%
+else is bankrupt you win that's the
+ 
+
+ align:start position:0%
+else is bankrupt you win that's the
+equilibrium okay so basically any game
+
+ align:start position:0%
+equilibrium okay so basically any game
+ 
+
+ align:start position:0%
+equilibrium okay so basically any game
+has a strategy and an equilibrium
+
+ align:start position:0%
+has a strategy and an equilibrium
+ 
+
+ align:start position:0%
+has a strategy and an equilibrium
+rule it turns
+
+ align:start position:0%
+rule it turns
+ 
+
+ align:start position:0%
+rule it turns
+out defining equilibrium in a rule with
+
+ align:start position:0%
+out defining equilibrium in a rule with
+ 
+
+ align:start position:0%
+out defining equilibrium in a rule with
+in a game with explicit rules is easy
+
+ align:start position:0%
+in a game with explicit rules is easy
+ 
+
+ align:start position:0%
+in a game with explicit rules is easy
+defining in a game where firms are just
+
+ align:start position:0%
+defining in a game where firms are just
+ 
+
+ align:start position:0%
+defining in a game where firms are just
+competing in this blood in a potentially
+
+ align:start position:0%
+competing in this blood in a potentially
+ 
+
+ align:start position:0%
+competing in this blood in a potentially
+bloodthirsty manner is not so easy and
+
+ align:start position:0%
+bloodthirsty manner is not so easy and
+ 
+
+ align:start position:0%
+bloodthirsty manner is not so easy and
+it turns out there is an enormous field
+
+ align:start position:0%
+it turns out there is an enormous field
+ 
+
+ align:start position:0%
+it turns out there is an enormous field
+in economics all about how do you think
+
+ align:start position:0%
+in economics all about how do you think
+ 
+
+ align:start position:0%
+in economics all about how do you think
+about equilibrium in game theoretic
+
+ align:start position:0%
+about equilibrium in game theoretic
+ 
+
+ align:start position:0%
+about equilibrium in game theoretic
+markets how do you think about when
+
+ align:start position:0%
+markets how do you think about when
+ 
+
+ align:start position:0%
+markets how do you think about when
+things finally settle down and end up
+
+ align:start position:0%
+things finally settle down and end up
+ 
+
+ align:start position:0%
+things finally settle down and end up
+and the most famous of these ideas of
+
+ align:start position:0%
+and the most famous of these ideas of
+ 
+
+ align:start position:0%
+and the most famous of these ideas of
+how to find equilibrium is what we call
+
+ align:start position:0%
+how to find equilibrium is what we call
+ 
+
+ align:start position:0%
+how to find equilibrium is what we call
+the Nash equilibrium any you guys ever
+
+ align:start position:0%
+the Nash equilibrium any you guys ever
+ 
+
+ align:start position:0%
+the Nash equilibrium any you guys ever
+see or read a beautiful
+
+ align:start position:0%
+see or read a beautiful
+ 
+
+ align:start position:0%
+see or read a beautiful
+mind that movie a little bit raise your
+
+ align:start position:0%
+mind that movie a little bit raise your
+ 
+
+ align:start position:0%
+mind that movie a little bit raise your
+hands yeah okay so a bunch of you saw it
+
+ align:start position:0%
+hands yeah okay so a bunch of you saw it
+ 
+
+ align:start position:0%
+hands yeah okay so a bunch of you saw it
+so it's about John Nash fascinating
+
+ align:start position:0%
+so it's about John Nash fascinating
+ 
+
+ align:start position:0%
+so it's about John Nash fascinating
+character um he was a mathematician
+
+ align:start position:0%
+character um he was a mathematician
+ 
+
+ align:start position:0%
+character um he was a mathematician
+brilliant
+
+ align:start position:0%
+brilliant
+ 
+
+ align:start position:0%
+brilliant
+mathematician uh who whose fundamental
+
+ align:start position:0%
+mathematician uh who whose fundamental
+ 
+
+ align:start position:0%
+mathematician uh who whose fundamental
+insight and if you see the movie this is
+
+ align:start position:0%
+insight and if you see the movie this is
+ 
+
+ align:start position:0%
+insight and if you see the movie this is
+so Illustrated well in a bar with the
+
+ align:start position:0%
+so Illustrated well in a bar with the
+ 
+
+ align:start position:0%
+so Illustrated well in a bar with the
+group of men are trying to pick up a
+
+ align:start position:0%
+group of men are trying to pick up a
+ 
+
+ align:start position:0%
+group of men are trying to pick up a
+group of women and again with this
+
+ align:start position:0%
+group of women and again with this
+ 
+
+ align:start position:0%
+group of women and again with this
+fundamental Insight that competition can
+
+ align:start position:0%
+fundamental Insight that competition can
+ 
+
+ align:start position:0%
+fundamental Insight that competition can
+be bad now if you think about economics
+
+ align:start position:0%
+be bad now if you think about economics
+ 
+
+ align:start position:0%
+be bad now if you think about economics
+we've learned everything we learn about
+
+ align:start position:0%
+we've learned everything we learn about
+ 
+
+ align:start position:0%
+we've learned everything we learn about
+competition is good competition is good
+
+ align:start position:0%
+competition is good competition is good
+ 
+
+ align:start position:0%
+competition is good competition is good
+it delivers better outcomes for
+
+ align:start position:0%
+it delivers better outcomes for
+ 
+
+ align:start position:0%
+it delivers better outcomes for
+consumers it reduces deadweight loss but
+
+ align:start position:0%
+consumers it reduces deadweight loss but
+ 
+
+ align:start position:0%
+consumers it reduces deadweight loss but
+he he actually came up with a theory
+
+ align:start position:0%
+he he actually came up with a theory
+ 
+
+ align:start position:0%
+he he actually came up with a theory
+that where actually in certain
+
+ align:start position:0%
+that where actually in certain
+ 
+
+ align:start position:0%
+that where actually in certain
+situations competition can be bad and
+
+ align:start position:0%
+situations competition can be bad and
+ 
+
+ align:start position:0%
+situations competition can be bad and
+cooperation can be better and that was
+
+ align:start position:0%
+cooperation can be better and that was
+ 
+
+ align:start position:0%
+cooperation can be better and that was
+sort of his fundamental insight
+
+ align:start position:0%
+sort of his fundamental insight
+ 
+
+ align:start position:0%
+sort of his fundamental insight
+okay and then he went insane
+
+ align:start position:0%
+okay and then he went insane
+ 
+
+ align:start position:0%
+okay and then he went insane
+unfortunately as can sometimes happen
+
+ align:start position:0%
+unfortunately as can sometimes happen
+ 
+
+ align:start position:0%
+unfortunately as can sometimes happen
+and the movie is sort of all about that
+
+ align:start position:0%
+and the movie is sort of all about that
+ 
+
+ align:start position:0%
+and the movie is sort of all about that
+it's very interesting it's a very
+
+ align:start position:0%
+it's very interesting it's a very
+ 
+
+ align:start position:0%
+it's very interesting it's a very
+interesting movie well acted interesting
+
+ align:start position:0%
+interesting movie well acted interesting
+ 
+
+ align:start position:0%
+interesting movie well acted interesting
+story about this poor guy who uh had
+
+ align:start position:0%
+story about this poor guy who uh had
+ 
+
+ align:start position:0%
+story about this poor guy who uh had
+these B insights and then and then
+
+ align:start position:0%
+these B insights and then and then
+ 
+
+ align:start position:0%
+these B insights and then and then
+developed mental illness severe
+
+ align:start position:0%
+developed mental illness severe
+ 
+
+ align:start position:0%
+developed mental illness severe
+schizophrenia um so what John Nash
+
+ align:start position:0%
+schizophrenia um so what John Nash
+ 
+
+ align:start position:0%
+schizophrenia um so what John Nash
+defined is the Nash equilibrium and the
+
+ align:start position:0%
+defined is the Nash equilibrium and the
+ 
+
+ align:start position:0%
+defined is the Nash equilibrium and the
+Nash equilibrium is defined as follows
+
+ align:start position:0%
+Nash equilibrium is defined as follows
+ 
+
+ align:start position:0%
+Nash equilibrium is defined as follows
+precisely a Nash equilibrium is the
+
+ align:start position:0%
+precisely a Nash equilibrium is the
+ 
+
+ align:start position:0%
+precisely a Nash equilibrium is the
+equilibrium where no player wants to
+
+ align:start position:0%
+equilibrium where no player wants to
+ 
+
+ align:start position:0%
+equilibrium where no player wants to
+change their
+
+ align:start position:0%
+change their
+ 
+
+ align:start position:0%
+change their
+strategy given all the other players
+
+ align:start position:0%
+strategy given all the other players
+ 
+
+ align:start position:0%
+strategy given all the other players
+strategies so you're an equilibrium
+
+ align:start position:0%
+strategies so you're an equilibrium
+ 
+
+ align:start position:0%
+strategies so you're an equilibrium
+where no player wants to change their
+
+ align:start position:0%
+where no player wants to change their
+ 
+
+ align:start position:0%
+where no player wants to change their
+strategy given all the other player
+
+ align:start position:0%
+strategy given all the other player
+ 
+
+ align:start position:0%
+strategy given all the other player
+strategies that is a Nash equilibrium
+
+ align:start position:0%
+strategies that is a Nash equilibrium
+ 
+
+ align:start position:0%
+strategies that is a Nash equilibrium
+that is formally if you hold all other
+
+ align:start position:0%
+that is formally if you hold all other
+ 
+
+ align:start position:0%
+that is formally if you hold all other
+players Behavior
+
+ align:start position:0%
+players Behavior
+ 
+
+ align:start position:0%
+players Behavior
+constant I can't do any better when I've
+
+ align:start position:0%
+constant I can't do any better when I've
+ 
+
+ align:start position:0%
+constant I can't do any better when I've
+reached that point I'm in equilibrium we
+
+ align:start position:0%
+reached that point I'm in equilibrium we
+ 
+
+ align:start position:0%
+reached that point I'm in equilibrium we
+reach to a point where I can't do any
+
+ align:start position:0%
+reach to a point where I can't do any
+ 
+
+ align:start position:0%
+reach to a point where I can't do any
+better holding everybody's strategies
+
+ align:start position:0%
+better holding everybody's strategies
+ 
+
+ align:start position:0%
+better holding everybody's strategies
+constant than I'm an equilibrium and the
+
+ align:start position:0%
+constant than I'm an equilibrium and the
+ 
+
+ align:start position:0%
+constant than I'm an equilibrium and the
+best example of this is example some of
+
+ align:start position:0%
+best example of this is example some of
+ 
+
+ align:start position:0%
+best example of this is example some of
+you may have heard about and you've
+
+ align:start position:0%
+you may have heard about and you've
+ 
+
+ align:start position:0%
+you may have heard about and you've
+certainly seen in movies the example the
+
+ align:start position:0%
+certainly seen in movies the example the
+ 
+
+ align:start position:0%
+certainly seen in movies the example the
+prisoners dilemma okay the prisoners
+
+ align:start position:0%
+prisoners dilemma okay the prisoners
+ 
+
+ align:start position:0%
+prisoners dilemma okay the prisoners
+dilemma is a famous movie device but
+
+ align:start position:0%
+dilemma is a famous movie device but
+ 
+
+ align:start position:0%
+dilemma is a famous movie device but
+almost a f example which is two guys are
+
+ align:start position:0%
+almost a f example which is two guys are
+ 
+
+ align:start position:0%
+almost a f example which is two guys are
+arrested for a crime it's not airtight
+
+ align:start position:0%
+arrested for a crime it's not airtight
+ 
+
+ align:start position:0%
+arrested for a crime it's not airtight
+that they did it they think the two guys
+
+ align:start position:0%
+that they did it they think the two guys
+ 
+
+ align:start position:0%
+that they did it they think the two guys
+did it but they really to really make it
+
+ align:start position:0%
+did it but they really to really make it
+ 
+
+ align:start position:0%
+did it but they really to really make it
+airtight
+
+ align:start position:0%
+airtight
+ 
+
+ align:start position:0%
+airtight
+they'd need them to admit it so let's
+
+ align:start position:0%
+they'd need them to admit it so let's
+ 
+
+ align:start position:0%
+they'd need them to admit it so let's
+say in this example and we'll give you
+
+ align:start position:0%
+say in this example and we'll give you
+ 
+
+ align:start position:0%
+say in this example and we'll give you
+examples like this and you'll need to
+
+ align:start position:0%
+examples like this and you'll need to
+ 
+
+ align:start position:0%
+examples like this and you'll need to
+think out interpret them so the example
+
+ align:start position:0%
+think out interpret them so the example
+ 
+
+ align:start position:0%
+think out interpret them so the example
+is two guys get arrested right now today
+
+ align:start position:0%
+is two guys get arrested right now today
+ 
+
+ align:start position:0%
+is two guys get arrested right now today
+there is enough evidence to send each of
+
+ align:start position:0%
+there is enough evidence to send each of
+ 
+
+ align:start position:0%
+there is enough evidence to send each of
+them to jail for one
+
+ align:start position:0%
+them to jail for one
+ 
+
+ align:start position:0%
+them to jail for one
+year okay enough just one year but if
+
+ align:start position:0%
+year okay enough just one year but if
+ 
+
+ align:start position:0%
+year okay enough just one year but if
+one guy squeals and says no the other
+
+ align:start position:0%
+one guy squeals and says no the other
+ 
+
+ align:start position:0%
+one guy squeals and says no the other
+guy did it if he turned States evidence
+
+ align:start position:0%
+guy did it if he turned States evidence
+ 
+
+ align:start position:0%
+guy did it if he turned States evidence
+whove learned a lot about this in the
+
+ align:start position:0%
+whove learned a lot about this in the
+ 
+
+ align:start position:0%
+whove learned a lot about this in the
+FBF trial and the upcoming Trump's trial
+
+ align:start position:0%
+FBF trial and the upcoming Trump's trial
+ 
+
+ align:start position:0%
+FBF trial and the upcoming Trump's trial
+okay the idea is if one person turn
+
+ align:start position:0%
+okay the idea is if one person turn
+ 
+
+ align:start position:0%
+okay the idea is if one person turn
+States evidence or squeals then they get
+
+ align:start position:0%
+States evidence or squeals then they get
+ 
+
+ align:start position:0%
+States evidence or squeals then they get
+zero they walk away and the other guy
+
+ align:start position:0%
+zero they walk away and the other guy
+ 
+
+ align:start position:0%
+zero they walk away and the other guy
+gets five
+
+ align:start position:0%
+gets five
+ 
+
+ align:start position:0%
+gets five
+years okay now if they both squeal they
+
+ align:start position:0%
+years okay now if they both squeal they
+ 
+
+ align:start position:0%
+years okay now if they both squeal they
+both get five years okay so basic the
+
+ align:start position:0%
+both get five years okay so basic the
+ 
+
+ align:start position:0%
+both get five years okay so basic the
+situation is if nothing happens they
+
+ align:start position:0%
+situation is if nothing happens they
+ 
+
+ align:start position:0%
+situation is if nothing happens they
+each get one year if either tells on the
+
+ align:start position:0%
+each get one year if either tells on the
+ 
+
+ align:start position:0%
+each get one year if either tells on the
+other person then the person they told
+
+ align:start position:0%
+other person then the person they told
+ 
+
+ align:start position:0%
+other person then the person they told
+on gets five years so what the way we
+
+ align:start position:0%
+on gets five years so what the way we
+ 
+
+ align:start position:0%
+on gets five years so what the way we
+analyze game theoretic situations like
+
+ align:start position:0%
+analyze game theoretic situations like
+ 
+
+ align:start position:0%
+analyze game theoretic situations like
+this is we write down we call a payoff
+
+ align:start position:0%
+this is we write down we call a payoff
+ 
+
+ align:start position:0%
+this is we write down we call a payoff
+Matrix so write down a payoff Matrix so
+
+ align:start position:0%
+Matrix so write down a payoff Matrix so
+ 
+
+ align:start position:0%
+Matrix so write down a payoff Matrix so
+the payoff Matrix look as follow you got
+
+ align:start position:0%
+the payoff Matrix look as follow you got
+ 
+
+ align:start position:0%
+the payoff Matrix look as follow you got
+prisoner
+
+ align:start position:0%
+prisoner
+ 
+
+ align:start position:0%
+prisoner
+a on the Y AIS here and prisoner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B on the x- axis okay and you've got
+
+ align:start position:0%
+B on the x- axis okay and you've got
+ 
+
+ align:start position:0%
+B on the x- axis okay and you've got
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+situations okay in one case let's say
+
+ align:start position:0%
+situations okay in one case let's say
+ 
+
+ align:start position:0%
+situations okay in one case let's say
+prisoner
+
+ align:start position:0%
+prisoner
+ 
+
+ align:start position:0%
+prisoner
+a is
+
+ align:start position:0%
+a is
+ 
+
+ align:start position:0%
+a is
+silent he doesn't talk
+
+ align:start position:0%
+silent he doesn't talk
+ 
+
+ align:start position:0%
+silent he doesn't talk
+and prisoner B also stays silent they
+
+ align:start position:0%
+and prisoner B also stays silent they
+ 
+
+ align:start position:0%
+and prisoner B also stays silent they
+don't talk then in that case a gets one
+
+ align:start position:0%
+don't talk then in that case a gets one
+ 
+
+ align:start position:0%
+don't talk then in that case a gets one
+year and B gets one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year now let's say that prisoner a stays
+
+ align:start position:0%
+year now let's say that prisoner a stays
+ 
+
+ align:start position:0%
+year now let's say that prisoner a stays
+silent but prisoner B talks prisoner B
+
+ align:start position:0%
+silent but prisoner B talks prisoner B
+ 
+
+ align:start position:0%
+silent but prisoner B talks prisoner B
+squeals then prisoner a now gets five
+
+ align:start position:0%
+squeals then prisoner a now gets five
+ 
+
+ align:start position:0%
+squeals then prisoner a now gets five
+years and prisoner b gets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero over here we have what if prisoner
+
+ align:start position:0%
+zero over here we have what if prisoner
+ 
+
+ align:start position:0%
+zero over here we have what if prisoner
+a talks well if prisoner a talks and
+
+ align:start position:0%
+a talks well if prisoner a talks and
+ 
+
+ align:start position:0%
+a talks well if prisoner a talks and
+prisoner B remains silent then prisoner
+
+ align:start position:0%
+prisoner B remains silent then prisoner
+ 
+
+ align:start position:0%
+prisoner B remains silent then prisoner
+a gets zero and prisoner b gets
+
+ align:start position:0%
+a gets zero and prisoner b gets
+ 
+
+ align:start position:0%
+a gets zero and prisoner b gets
+five but if they both talk they both get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five okay questions about how I set up
+
+ align:start position:0%
+five okay questions about how I set up
+ 
+
+ align:start position:0%
+five okay questions about how I set up
+that Matrix given the words given the
+
+ align:start position:0%
+that Matrix given the words given the
+ 
+
+ align:start position:0%
+that Matrix given the words given the
+description of the problem you're going
+
+ align:start position:0%
+description of the problem you're going
+ 
+
+ align:start position:0%
+description of the problem you're going
+need to be able to take these descript
+
+ align:start position:0%
+need to be able to take these descript
+ 
+
+ align:start position:0%
+need to be able to take these descript
+set of matrices like this so any
+
+ align:start position:0%
+set of matrices like this so any
+ 
+
+ align:start position:0%
+set of matrices like this so any
+questions about how I did that
+
+ align:start position:0%
+questions about how I did that
+ 
+
+ align:start position:0%
+questions about how I did that
+okay now what we want to ask is what
+
+ align:start position:0%
+okay now what we want to ask is what
+ 
+
+ align:start position:0%
+okay now what we want to ask is what
+should each player do and the the sort
+
+ align:start position:0%
+should each player do and the the sort
+ 
+
+ align:start position:0%
+should each player do and the the sort
+of cheat in National equilibrium games
+
+ align:start position:0%
+of cheat in National equilibrium games
+ 
+
+ align:start position:0%
+of cheat in National equilibrium games
+the first step is to say look the
+
+ align:start position:0%
+the first step is to say look the
+ 
+
+ align:start position:0%
+the first step is to say look the
+easiest case would be if there is a
+
+ align:start position:0%
+easiest case would be if there is a
+ 
+
+ align:start position:0%
+easiest case would be if there is a
+dominant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy if there's a dominant strategy
+
+ align:start position:0%
+strategy if there's a dominant strategy
+ 
+
+ align:start position:0%
+strategy if there's a dominant strategy
+is there one strategy which no matter
+
+ align:start position:0%
+is there one strategy which no matter
+ 
+
+ align:start position:0%
+is there one strategy which no matter
+what the other guy does you want to do
+
+ align:start position:0%
+what the other guy does you want to do
+ 
+
+ align:start position:0%
+what the other guy does you want to do
+then that's the Nash equilibrium right
+
+ align:start position:0%
+then that's the Nash equilibrium right
+ 
+
+ align:start position:0%
+then that's the Nash equilibrium right
+that's that's the outcome that you're
+
+ align:start position:0%
+that's that's the outcome that you're
+ 
+
+ align:start position:0%
+that's that's the outcome that you're
+going to do if there a strategy that's
+
+ align:start position:0%
+going to do if there a strategy that's
+ 
+
+ align:start position:0%
+going to do if there a strategy that's
+dominant that's the strategy you're
+
+ align:start position:0%
+dominant that's the strategy you're
+ 
+
+ align:start position:0%
+dominant that's the strategy you're
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play okay the best thing to do no matter
+
+ align:start position:0%
+play okay the best thing to do no matter
+ 
+
+ align:start position:0%
+play okay the best thing to do no matter
+what the other person
+
+ align:start position:0%
+what the other person
+ 
+
+ align:start position:0%
+what the other person
+does okay now if they could agree to
+
+ align:start position:0%
+does okay now if they could agree to
+ 
+
+ align:start position:0%
+does okay now if they could agree to
+cooperate if the two of them got
+
+ align:start position:0%
+cooperate if the two of them got
+ 
+
+ align:start position:0%
+cooperate if the two of them got
+together in a room beforehand and they
+
+ align:start position:0%
+together in a room beforehand and they
+ 
+
+ align:start position:0%
+together in a room beforehand and they
+trusted each other they could Rec
+
+ align:start position:0%
+trusted each other they could Rec
+ 
+
+ align:start position:0%
+trusted each other they could Rec
+cooperate then clearly what is the
+
+ align:start position:0%
+cooperate then clearly what is the
+ 
+
+ align:start position:0%
+cooperate then clearly what is the
+dominant coop operative
+
+ align:start position:0%
+dominant coop operative
+ 
+
+ align:start position:0%
+dominant coop operative
+strategy yeah they both stay silent they
+
+ align:start position:0%
+strategy yeah they both stay silent they
+ 
+
+ align:start position:0%
+strategy yeah they both stay silent they
+both get a
+
+ align:start position:0%
+both get a
+ 
+
+ align:start position:0%
+both get a
+year but let's say they can't do that
+
+ align:start position:0%
+year but let's say they can't do that
+ 
+
+ align:start position:0%
+year but let's say they can't do that
+they can't get in room together they
+
+ align:start position:0%
+they can't get in room together they
+ 
+
+ align:start position:0%
+they can't get in room together they
+never put in room together in the movies
+
+ align:start position:0%
+never put in room together in the movies
+ 
+
+ align:start position:0%
+never put in room together in the movies
+right they keep them separate and
+
+ align:start position:0%
+right they keep them separate and
+ 
+
+ align:start position:0%
+right they keep them separate and
+they're scummy criminals they don't
+
+ align:start position:0%
+they're scummy criminals they don't
+ 
+
+ align:start position:0%
+they're scummy criminals they don't
+trust each other okay so basically what
+
+ align:start position:0%
+trust each other okay so basically what
+ 
+
+ align:start position:0%
+trust each other okay so basically what
+happens now if you're prisoner a and
+
+ align:start position:0%
+happens now if you're prisoner a and
+ 
+
+ align:start position:0%
+happens now if you're prisoner a and
+you're not sure what prisoner B is going
+
+ align:start position:0%
+you're not sure what prisoner B is going
+ 
+
+ align:start position:0%
+you're not sure what prisoner B is going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do what should you do if you think
+
+ align:start position:0%
+do what should you do if you think
+ 
+
+ align:start position:0%
+do what should you do if you think
+prisoner B is going to stay
+
+ align:start position:0%
+prisoner B is going to stay
+ 
+
+ align:start position:0%
+prisoner B is going to stay
+silent yeah
+
+ align:start position:0%
+silent yeah
+ 
+
+ align:start position:0%
+silent yeah
+talk because your
+
+ align:start position:0%
+talk because your
+ 
+
+ align:start position:0%
+talk because your
+payoff is better what should you do if
+
+ align:start position:0%
+payoff is better what should you do if
+ 
+
+ align:start position:0%
+payoff is better what should you do if
+you think prisoner B is going to
+
+ align:start position:0%
+you think prisoner B is going to
+ 
+
+ align:start position:0%
+you think prisoner B is going to
+talk yeah talk because your payoff if
+
+ align:start position:0%
+talk yeah talk because your payoff if
+ 
+
+ align:start position:0%
+talk yeah talk because your payoff if
+you think prisoner B is going to talk
+
+ align:start position:0%
+you think prisoner B is going to talk
+ 
+
+ align:start position:0%
+you think prisoner B is going to talk
+then you should
+
+ align:start position:0%
+then you should
+ 
+
+ align:start position:0%
+then you should
+talk okay so I'm sorry I wrote I wrote
+
+ align:start position:0%
+talk okay so I'm sorry I wrote I wrote
+ 
+
+ align:start position:0%
+talk okay so I'm sorry I wrote I wrote
+this uh did I do this right yep I did
+
+ align:start position:0%
+this uh did I do this right yep I did
+ 
+
+ align:start position:0%
+this uh did I do this right yep I did
+this wrong that's what I did wrong it's
+
+ align:start position:0%
+this wrong that's what I did wrong it's
+ 
+
+ align:start position:0%
+this wrong that's what I did wrong it's
+no better if they both talk I say they
+
+ align:start position:0%
+no better if they both talk I say they
+ 
+
+ align:start position:0%
+no better if they both talk I say they
+both get three that makes more sense I
+
+ align:start position:0%
+both get three that makes more sense I
+ 
+
+ align:start position:0%
+both get three that makes more sense I
+set the example up wrong if they both
+
+ align:start position:0%
+set the example up wrong if they both
+ 
+
+ align:start position:0%
+set the example up wrong if they both
+talk they both get three that makes your
+
+ align:start position:0%
+talk they both get three that makes your
+ 
+
+ align:start position:0%
+talk they both get three that makes your
+answer is still right but this makes it
+
+ align:start position:0%
+answer is still right but this makes it
+ 
+
+ align:start position:0%
+answer is still right but this makes it
+non-binding that that involves
+
+ align:start position:0%
+non-binding that that involves
+ 
+
+ align:start position:0%
+non-binding that that involves
+inequality this is this is non-binding
+
+ align:start position:0%
+inequality this is this is non-binding
+ 
+
+ align:start position:0%
+inequality this is this is non-binding
+so clearly prisoner
+
+ align:start position:0%
+so clearly prisoner
+ 
+
+ align:start position:0%
+so clearly prisoner
+a is better off talking no matter what
+
+ align:start position:0%
+a is better off talking no matter what
+ 
+
+ align:start position:0%
+a is better off talking no matter what
+prisoner B is going to do what about
+
+ align:start position:0%
+prisoner B is going to do what about
+ 
+
+ align:start position:0%
+prisoner B is going to do what about
+prisoner B what's their dominant
+
+ align:start position:0%
+prisoner B what's their dominant
+ 
+
+ align:start position:0%
+prisoner B what's their dominant
+strategy yeah same thing it's a
+
+ align:start position:0%
+strategy yeah same thing it's a
+ 
+
+ align:start position:0%
+strategy yeah same thing it's a
+symmetric problem these problems won't
+
+ align:start position:0%
+symmetric problem these problems won't
+ 
+
+ align:start position:0%
+symmetric problem these problems won't
+always be symmetric but it's a hell of a
+
+ align:start position:0%
+always be symmetric but it's a hell of a
+ 
+
+ align:start position:0%
+always be symmetric but it's a hell of a
+lot easier when they are so you only
+
+ align:start position:0%
+lot easier when they are so you only
+ 
+
+ align:start position:0%
+lot easier when they are so you only
+have to solve for one person you assume
+
+ align:start position:0%
+have to solve for one person you assume
+ 
+
+ align:start position:0%
+have to solve for one person you assume
+the other other person does the same
+
+ align:start position:0%
+the other other person does the same
+ 
+
+ align:start position:0%
+the other other person does the same
+thing so prisoner B's dominant strategy
+
+ align:start position:0%
+thing so prisoner B's dominant strategy
+ 
+
+ align:start position:0%
+thing so prisoner B's dominant strategy
+is to talk so we have a situation where
+
+ align:start position:0%
+is to talk so we have a situation where
+ 
+
+ align:start position:0%
+is to talk so we have a situation where
+both dominant strategies align therefore
+
+ align:start position:0%
+both dominant strategies align therefore
+ 
+
+ align:start position:0%
+both dominant strategies align therefore
+we have an
+
+ align:start position:0%
+we have an
+ 
+
+ align:start position:0%
+we have an
+equilibrium and that equilibrium is what
+
+ align:start position:0%
+equilibrium and that equilibrium is what
+ 
+
+ align:start position:0%
+equilibrium and that equilibrium is what
+it's they both
+
+ align:start position:0%
+it's they both
+ 
+
+ align:start position:0%
+it's they both
+talk and they both get three
+
+ align:start position:0%
+talk and they both get three
+ 
+
+ align:start position:0%
+talk and they both get three
+years here's what's fascinating they are
+
+ align:start position:0%
+years here's what's fascinating they are
+ 
+
+ align:start position:0%
+years here's what's fascinating they are
+worse off than if they both stayed
+
+ align:start position:0%
+worse off than if they both stayed
+ 
+
+ align:start position:0%
+worse off than if they both stayed
+silent competition has yielded a worse
+
+ align:start position:0%
+silent competition has yielded a worse
+ 
+
+ align:start position:0%
+silent competition has yielded a worse
+outcome we haven't seen that before in
+
+ align:start position:0%
+outcome we haven't seen that before in
+ 
+
+ align:start position:0%
+outcome we haven't seen that before in
+this class
+
+ align:start position:0%
+this class
+ 
+
+ align:start position:0%
+this class
+competition in the sense of trying to do
+
+ align:start position:0%
+competition in the sense of trying to do
+ 
+
+ align:start position:0%
+competition in the sense of trying to do
+what's best for you at the expense of
+
+ align:start position:0%
+what's best for you at the expense of
+ 
+
+ align:start position:0%
+what's best for you at the expense of
+the other guy has yielded the worse
+
+ align:start position:0%
+the other guy has yielded the worse
+ 
+
+ align:start position:0%
+the other guy has yielded the worse
+outcome than
+
+ align:start position:0%
+outcome than
+ 
+
+ align:start position:0%
+outcome than
+cooperation that's what's incredibly
+
+ align:start position:0%
+cooperation that's what's incredibly
+ 
+
+ align:start position:0%
+cooperation that's what's incredibly
+Innovative about that's what Nash Nash
+
+ align:start position:0%
+Innovative about that's what Nash Nash
+ 
+
+ align:start position:0%
+Innovative about that's what Nash Nash
+even though being a mathematician won
+
+ align:start position:0%
+even though being a mathematician won
+ 
+
+ align:start position:0%
+even though being a mathematician won
+the Nobel prize in economics in Game
+
+ align:start position:0%
+the Nobel prize in economics in Game
+ 
+
+ align:start position:0%
+the Nobel prize in economics in Game
+Theory went from something which was
+
+ align:start position:0%
+Theory went from something which was
+ 
+
+ align:start position:0%
+Theory went from something which was
+kind of relatively new when I was a grad
+
+ align:start position:0%
+kind of relatively new when I was a grad
+ 
+
+ align:start position:0%
+kind of relatively new when I was a grad
+student in the late 80s to now being a
+
+ align:start position:0%
+student in the late 80s to now being a
+ 
+
+ align:start position:0%
+student in the late 80s to now being a
+quarter of the
+
+ align:start position:0%
+quarter of the
+ 
+
+ align:start position:0%
+quarter of the
+introductory uh training that graduate
+
+ align:start position:0%
+introductory uh training that graduate
+ 
+
+ align:start position:0%
+introductory uh training that graduate
+students PhD students in economics get
+
+ align:start position:0%
+students PhD students in economics get
+ 
+
+ align:start position:0%
+students PhD students in economics get
+game theory has become a dominant so to
+
+ align:start position:0%
+game theory has become a dominant so to
+ 
+
+ align:start position:0%
+game theory has become a dominant so to
+speak uh element of all economics
+
+ align:start position:0%
+speak uh element of all economics
+ 
+
+ align:start position:0%
+speak uh element of all economics
+training because it provides such a
+
+ align:start position:0%
+training because it provides such a
+ 
+
+ align:start position:0%
+training because it provides such a
+valuable tool for thinking about this so
+
+ align:start position:0%
+valuable tool for thinking about this so
+ 
+
+ align:start position:0%
+valuable tool for thinking about this so
+basically you end up with What's called
+
+ align:start position:0%
+basically you end up with What's called
+ 
+
+ align:start position:0%
+basically you end up with What's called
+the prisoners
+
+ align:start position:0%
+the prisoners
+ 
+
+ align:start position:0%
+the prisoners
+dilemma which is prisoners are each
+
+ align:start position:0%
+dilemma which is prisoners are each
+ 
+
+ align:start position:0%
+dilemma which is prisoners are each
+better off by ratting on the other and
+
+ align:start position:0%
+better off by ratting on the other and
+ 
+
+ align:start position:0%
+better off by ratting on the other and
+it ends up they both end up worse off
+
+ align:start position:0%
+it ends up they both end up worse off
+ 
+
+ align:start position:0%
+it ends up they both end up worse off
+and this also shows us how to solve a
+
+ align:start position:0%
+and this also shows us how to solve a
+ 
+
+ align:start position:0%
+and this also shows us how to solve a
+nash game a game with a Nash equilibrium
+
+ align:start position:0%
+nash game a game with a Nash equilibrium
+ 
+
+ align:start position:0%
+nash game a game with a Nash equilibrium
+which is you look for each player's
+
+ align:start position:0%
+which is you look for each player's
+ 
+
+ align:start position:0%
+which is you look for each player's
+dominant strategy
+
+ align:start position:0%
+dominant strategy
+ 
+
+ align:start position:0%
+dominant strategy
+and you find the point where they
+
+ align:start position:0%
+and you find the point where they
+ 
+
+ align:start position:0%
+and you find the point where they
+align the point where the two dominant
+
+ align:start position:0%
+align the point where the two dominant
+ 
+
+ align:start position:0%
+align the point where the two dominant
+strategies align is by definition an as
+
+ align:start position:0%
+strategies align is by definition an as
+ 
+
+ align:start position:0%
+strategies align is by definition an as
+equilibrium why because they're both
+
+ align:start position:0%
+equilibrium why because they're both
+ 
+
+ align:start position:0%
+equilibrium why because they're both
+doing the best they can giveing the
+
+ align:start position:0%
+doing the best they can giveing the
+ 
+
+ align:start position:0%
+doing the best they can giveing the
+other person now if the two dominant
+
+ align:start position:0%
+other person now if the two dominant
+ 
+
+ align:start position:0%
+other person now if the two dominant
+strategies don't align there may not be
+
+ align:start position:0%
+strategies don't align there may not be
+ 
+
+ align:start position:0%
+strategies don't align there may not be
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+equilibrium you have situations where
+
+ align:start position:0%
+equilibrium you have situations where
+ 
+
+ align:start position:0%
+equilibrium you have situations where
+A's dominant strategy different than B's
+
+ align:start position:0%
+A's dominant strategy different than B's
+ 
+
+ align:start position:0%
+A's dominant strategy different than B's
+Domin strategy they don't align then you
+
+ align:start position:0%
+Domin strategy they don't align then you
+ 
+
+ align:start position:0%
+Domin strategy they don't align then you
+might not get an equilibrium but in this
+
+ align:start position:0%
+might not get an equilibrium but in this
+ 
+
+ align:start position:0%
+might not get an equilibrium but in this
+case they align and most cases will give
+
+ align:start position:0%
+case they align and most cases will give
+ 
+
+ align:start position:0%
+case they align and most cases will give
+you they align so you get a Nash
+
+ align:start position:0%
+you they align so you get a Nash
+ 
+
+ align:start position:0%
+you they align so you get a Nash
+equilibrium where they both
+
+ align:start position:0%
+equilibrium where they both
+ 
+
+ align:start position:0%
+equilibrium where they both
+align okay
+
+ align:start position:0%
+align okay
+ 
+
+ align:start position:0%
+align okay
+now this is all cute and stuff but like
+
+ align:start position:0%
+now this is all cute and stuff but like
+ 
+
+ align:start position:0%
+now this is all cute and stuff but like
+this is a class about economics not
+
+ align:start position:0%
+this is a class about economics not
+ 
+
+ align:start position:0%
+this is a class about economics not
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+crime but it turns out the same logic
+
+ align:start position:0%
+crime but it turns out the same logic
+ 
+
+ align:start position:0%
+crime but it turns out the same logic
+applies to playing economic games so
+
+ align:start position:0%
+applies to playing economic games so
+ 
+
+ align:start position:0%
+applies to playing economic games so
+imagine let's take the market for soda
+
+ align:start position:0%
+imagine let's take the market for soda
+ 
+
+ align:start position:0%
+imagine let's take the market for soda
+and imagine there's two big players
+
+ align:start position:0%
+and imagine there's two big players
+ 
+
+ align:start position:0%
+and imagine there's two big players
+Pepsi and
+
+ align:start position:0%
+Pepsi and
+ 
+
+ align:start position:0%
+Pepsi and
+Coke and let's imagine there's a $16
+
+ align:start position:0%
+Coke and let's imagine there's a $16
+ 
+
+ align:start position:0%
+Coke and let's imagine there's a $16
+billion soda
+
+ align:start position:0%
+billion soda
+ 
+
+ align:start position:0%
+billion soda
+Market let's further imagine that absent
+
+ align:start position:0%
+Market let's further imagine that absent
+ 
+
+ align:start position:0%
+Market let's further imagine that absent
+any advertising they would split it that
+
+ align:start position:0%
+any advertising they would split it that
+ 
+
+ align:start position:0%
+any advertising they would split it that
+with no advertising C and Pepsi would
+
+ align:start position:0%
+with no advertising C and Pepsi would
+ 
+
+ align:start position:0%
+with no advertising C and Pepsi would
+each get 8 billion
+
+ align:start position:0%
+each get 8 billion
+ 
+
+ align:start position:0%
+each get 8 billion
+out of the
+
+ align:start position:0%
+out of the
+ 
+
+ align:start position:0%
+out of the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+but they can
+
+ align:start position:0%
+but they can
+ 
+
+ align:start position:0%
+but they can
+advertise adverti advertising costs five
+
+ align:start position:0%
+advertise adverti advertising costs five
+ 
+
+ align:start position:0%
+advertise adverti advertising costs five
+billion so if they advertise they only
+
+ align:start position:0%
+billion so if they advertise they only
+ 
+
+ align:start position:0%
+billion so if they advertise they only
+take home three billion
+
+ align:start position:0%
+take home three billion
+ 
+
+ align:start position:0%
+take home three billion
+net however if they advertise they drive
+
+ align:start position:0%
+net however if they advertise they drive
+ 
+
+ align:start position:0%
+net however if they advertise they drive
+the other guy out of the
+
+ align:start position:0%
+the other guy out of the
+ 
+
+ align:start position:0%
+the other guy out of the
+market so the choices don't advertise
+
+ align:start position:0%
+market so the choices don't advertise
+ 
+
+ align:start position:0%
+market so the choices don't advertise
+and split the market advertise in which
+
+ align:start position:0%
+and split the market advertise in which
+ 
+
+ align:start position:0%
+and split the market advertise in which
+case um if you um
+
+ align:start position:0%
+case um if you um
+ 
+
+ align:start position:0%
+case um if you um
+in which case if you advertise and you
+
+ align:start position:0%
+in which case if you advertise and you
+ 
+
+ align:start position:0%
+in which case if you advertise and you
+win the other guy's
+
+ align:start position:0%
+win the other guy's
+ 
+
+ align:start position:0%
+win the other guy's
+gone okay and you get you get the whole
+
+ align:start position:0%
+gone okay and you get you get the whole
+ 
+
+ align:start position:0%
+gone okay and you get you get the whole
+Market but if you don't advertise and
+
+ align:start position:0%
+Market but if you don't advertise and
+ 
+
+ align:start position:0%
+Market but if you don't advertise and
+you don't win and the other guy
+
+ align:start position:0%
+you don't win and the other guy
+ 
+
+ align:start position:0%
+you don't win and the other guy
+advertises you're gone so what that
+
+ align:start position:0%
+advertises you're gone so what that
+ 
+
+ align:start position:0%
+advertises you're gone so what that
+payoff Matrix look like well let's write
+
+ align:start position:0%
+payoff Matrix look like well let's write
+ 
+
+ align:start position:0%
+payoff Matrix look like well let's write
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+down you've
+
+ align:start position:0%
+down you've
+ 
+
+ align:start position:0%
+down you've
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+Coke and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pepsi Coke and Pepsi Coke can not
+
+ align:start position:0%
+Pepsi Coke and Pepsi Coke can not
+ 
+
+ align:start position:0%
+Pepsi Coke and Pepsi Coke can not
+advertise or
+
+ align:start position:0%
+advertise or
+ 
+
+ align:start position:0%
+advertise or
+advertise okay Pepsi cannot advertise or
+
+ align:start position:0%
+advertise okay Pepsi cannot advertise or
+ 
+
+ align:start position:0%
+advertise okay Pepsi cannot advertise or
+advertise if Coke and Pepsi both don't
+
+ align:start position:0%
+advertise if Coke and Pepsi both don't
+ 
+
+ align:start position:0%
+advertise if Coke and Pepsi both don't
+advertise they each get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eight if Coke doesn't advertise and
+
+ align:start position:0%
+eight if Coke doesn't advertise and
+ 
+
+ align:start position:0%
+eight if Coke doesn't advertise and
+Pepsi does coke ends up with zero and
+
+ align:start position:0%
+Pepsi does coke ends up with zero and
+ 
+
+ align:start position:0%
+Pepsi does coke ends up with zero and
+Pepsi ends up with 11 which is the 16 is
+
+ align:start position:0%
+Pepsi ends up with 11 which is the 16 is
+ 
+
+ align:start position:0%
+Pepsi ends up with 11 which is the 16 is
+wrong in the notes by the way Andrew we
+
+ align:start position:0%
+wrong in the notes by the way Andrew we
+ 
+
+ align:start position:0%
+wrong in the notes by the way Andrew we
+should fix this um which is the 16 uh
+
+ align:start position:0%
+should fix this um which is the 16 uh
+ 
+
+ align:start position:0%
+should fix this um which is the 16 uh
+that they um the 16 that they got from
+
+ align:start position:0%
+that they um the 16 that they got from
+ 
+
+ align:start position:0%
+that they um the 16 that they got from
+having the market minus the five they
+
+ align:start position:0%
+having the market minus the five they
+ 
+
+ align:start position:0%
+having the market minus the five they
+spent in
+
+ align:start position:0%
+spent in
+ 
+
+ align:start position:0%
+spent in
+advertising on the other if Koke
+
+ align:start position:0%
+advertising on the other if Koke
+ 
+
+ align:start position:0%
+advertising on the other if Koke
+advertised and Pepsi doesn't then Koch
+
+ align:start position:0%
+advertised and Pepsi doesn't then Koch
+ 
+
+ align:start position:0%
+advertised and Pepsi doesn't then Koch
+gets 11 and Pepsi gets
+
+ align:start position:0%
+gets 11 and Pepsi gets
+ 
+
+ align:start position:0%
+gets 11 and Pepsi gets
+zero and if they both advertise Coke
+
+ align:start position:0%
+zero and if they both advertise Coke
+ 
+
+ align:start position:0%
+zero and if they both advertise Coke
+gets three and Pepsi gets
+
+ align:start position:0%
+gets three and Pepsi gets
+ 
+
+ align:start position:0%
+gets three and Pepsi gets
+three so once again the dominant
+
+ align:start position:0%
+three so once again the dominant
+ 
+
+ align:start position:0%
+three so once again the dominant
+cooperative strategy is they both don't
+
+ align:start position:0%
+cooperative strategy is they both don't
+ 
+
+ align:start position:0%
+cooperative strategy is they both don't
+advertise but the dominant
+
+ align:start position:0%
+advertise but the dominant
+ 
+
+ align:start position:0%
+advertise but the dominant
+non-cooperative strategy in each case is
+
+ align:start position:0%
+non-cooperative strategy in each case is
+ 
+
+ align:start position:0%
+non-cooperative strategy in each case is
+to advertise Koke is always better off
+
+ align:start position:0%
+to advertise Koke is always better off
+ 
+
+ align:start position:0%
+to advertise Koke is always better off
+if it
+
+ align:start position:0%
+if it
+ 
+
+ align:start position:0%
+if it
+advertises than if it doesn't Pepsi's
+
+ align:start position:0%
+advertises than if it doesn't Pepsi's
+ 
+
+ align:start position:0%
+advertises than if it doesn't Pepsi's
+always better off it advertises than it
+
+ align:start position:0%
+always better off it advertises than it
+ 
+
+ align:start position:0%
+always better off it advertises than it
+doesn't so they'll both advertise and
+
+ align:start position:0%
+doesn't so they'll both advertise and
+ 
+
+ align:start position:0%
+doesn't so they'll both advertise and
+you'll end up with both parties being
+
+ align:start position:0%
+you'll end up with both parties being
+ 
+
+ align:start position:0%
+you'll end up with both parties being
+worse off they just agreed not to
+
+ align:start position:0%
+worse off they just agreed not to
+ 
+
+ align:start position:0%
+worse off they just agreed not to
+advertise this is not an irrelevant
+
+ align:start position:0%
+advertise this is not an irrelevant
+ 
+
+ align:start position:0%
+advertise this is not an irrelevant
+example until about I don't know it's
+
+ align:start position:0%
+example until about I don't know it's
+ 
+
+ align:start position:0%
+example until about I don't know it's
+got to be about 10 years ago hard liquor
+
+ align:start position:0%
+got to be about 10 years ago hard liquor
+ 
+
+ align:start position:0%
+got to be about 10 years ago hard liquor
+you know whiskey vodka things like that
+
+ align:start position:0%
+you know whiskey vodka things like that
+ 
+
+ align:start position:0%
+you know whiskey vodka things like that
+never adverti on
+
+ align:start position:0%
+never adverti on
+ 
+
+ align:start position:0%
+never adverti on
+television now as a kid I thought that
+
+ align:start position:0%
+television now as a kid I thought that
+ 
+
+ align:start position:0%
+television now as a kid I thought that
+was a law but it turns out it wasn't it
+
+ align:start position:0%
+was a law but it turns out it wasn't it
+ 
+
+ align:start position:0%
+was a law but it turns out it wasn't it
+wasn't a law it was a Cooperative
+
+ align:start position:0%
+wasn't a law it was a Cooperative
+ 
+
+ align:start position:0%
+wasn't a law it was a Cooperative
+agreement among the manufacturer of hard
+
+ align:start position:0%
+agreement among the manufacturer of hard
+ 
+
+ align:start position:0%
+agreement among the manufacturer of hard
+liquor not to advertise on television
+
+ align:start position:0%
+liquor not to advertise on television
+ 
+
+ align:start position:0%
+liquor not to advertise on television
+they literally had reached the
+
+ align:start position:0%
+they literally had reached the
+ 
+
+ align:start position:0%
+they literally had reached the
+Cooperative equilibrium and then it
+
+ align:start position:0%
+Cooperative equilibrium and then it
+ 
+
+ align:start position:0%
+Cooperative equilibrium and then it
+broke down and now you see the ads on TV
+
+ align:start position:0%
+broke down and now you see the ads on TV
+ 
+
+ align:start position:0%
+broke down and now you see the ads on TV
+I don't know what be interesting I don't
+
+ align:start position:0%
+I don't know what be interesting I don't
+ 
+
+ align:start position:0%
+I don't know what be interesting I don't
+know what caused the broke down actually
+
+ align:start position:0%
+know what caused the broke down actually
+ 
+
+ align:start position:0%
+know what caused the broke down actually
+Andrew let's make a note I should do a
+
+ align:start position:0%
+Andrew let's make a note I should do a
+ 
+
+ align:start position:0%
+Andrew let's make a note I should do a
+case study on should add that that'd be
+
+ align:start position:0%
+case study on should add that that'd be
+ 
+
+ align:start position:0%
+case study on should add that that'd be
+good to add be be interesting to think
+
+ align:start position:0%
+good to add be be interesting to think
+ 
+
+ align:start position:0%
+good to add be be interesting to think
+about what caused that but they used to
+
+ align:start position:0%
+about what caused that but they used to
+ 
+
+ align:start position:0%
+about what caused that but they used to
+cooperate and they don't okay so B
+
+ align:start position:0%
+cooperate and they don't okay so B
+ 
+
+ align:start position:0%
+cooperate and they don't okay so B
+basically this an example of how the
+
+ align:start position:0%
+basically this an example of how the
+ 
+
+ align:start position:0%
+basically this an example of how the
+prisoner's dilemma can lead to a worse
+
+ align:start position:0%
+prisoner's dilemma can lead to a worse
+ 
+
+ align:start position:0%
+prisoner's dilemma can lead to a worse
+outcome questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay this doesn't just
+
+ align:start position:0%
+that okay this doesn't just
+ 
+
+ align:start position:0%
+that okay this doesn't just
+apply to Coke and Pepsi or prisoners
+
+ align:start position:0%
+apply to Coke and Pepsi or prisoners
+ 
+
+ align:start position:0%
+apply to Coke and Pepsi or prisoners
+think about Andrew here let's say Andrew
+
+ align:start position:0%
+think about Andrew here let's say Andrew
+ 
+
+ align:start position:0%
+think about Andrew here let's say Andrew
+is in a new relationship still try to
+
+ align:start position:0%
+is in a new relationship still try to
+ 
+
+ align:start position:0%
+is in a new relationship still try to
+feel out the his partner okay and they
+
+ align:start position:0%
+feel out the his partner okay and they
+ 
+
+ align:start position:0%
+feel out the his partner okay and they
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+fight and Andrew is thinking two things
+
+ align:start position:0%
+fight and Andrew is thinking two things
+ 
+
+ align:start position:0%
+fight and Andrew is thinking two things
+can happen I can go apolog oliz and I
+
+ align:start position:0%
+can happen I can go apolog oliz and I
+ 
+
+ align:start position:0%
+can happen I can go apolog oliz and I
+can go eat crow and say it's my fault
+
+ align:start position:0%
+can go eat crow and say it's my fault
+ 
+
+ align:start position:0%
+can go eat crow and say it's my fault
+let's say they're both at fault Andrew
+
+ align:start position:0%
+let's say they're both at fault Andrew
+ 
+
+ align:start position:0%
+let's say they're both at fault Andrew
+can say I can go eat crow and say it's
+
+ align:start position:0%
+can say I can go eat crow and say it's
+ 
+
+ align:start position:0%
+can say I can go eat crow and say it's
+my fault but then if my partners say
+
+ align:start position:0%
+my fault but then if my partners say
+ 
+
+ align:start position:0%
+my fault but then if my partners say
+it's their fault I'm GNA feel like
+
+ align:start position:0%
+it's their fault I'm GNA feel like
+ 
+
+ align:start position:0%
+it's their fault I'm GNA feel like
+ the partner's thinking the same
+
+ align:start position:0%
+ the partner's thinking the same
+ 
+
+ align:start position:0%
+ the partner's thinking the same
+thing they' both be better off if they
+
+ align:start position:0%
+thing they' both be better off if they
+ 
+
+ align:start position:0%
+thing they' both be better off if they
+just apologize because they're both at
+
+ align:start position:0%
+just apologize because they're both at
+ 
+
+ align:start position:0%
+just apologize because they're both at
+fault but they both don't apologize
+
+ align:start position:0%
+fault but they both don't apologize
+ 
+
+ align:start position:0%
+fault but they both don't apologize
+because they don't want to look like the
+
+ align:start position:0%
+because they don't want to look like the
+ 
+
+ align:start position:0%
+because they don't want to look like the
+loser and they break
+
+ align:start position:0%
+loser and they break
+ 
+
+ align:start position:0%
+loser and they break
+up okay prison is a lemon action in
+
+ align:start position:0%
+up okay prison is a lemon action in
+ 
+
+ align:start position:0%
+up okay prison is a lemon action in
+personal
+
+ align:start position:0%
+personal
+ 
+
+ align:start position:0%
+personal
+relationships okay basically it's hard
+
+ align:start position:0%
+relationships okay basically it's hard
+ 
+
+ align:start position:0%
+relationships okay basically it's hard
+to form Cooperative relationships
+
+ align:start position:0%
+to form Cooperative relationships
+ 
+
+ align:start position:0%
+to form Cooperative relationships
+and non-cooperative equilibria can lead
+
+ align:start position:0%
+and non-cooperative equilibria can lead
+ 
+
+ align:start position:0%
+and non-cooperative equilibria can lead
+to bad
+
+ align:start position:0%
+to bad
+ 
+
+ align:start position:0%
+to bad
+outcomes okay now this is the very very
+
+ align:start position:0%
+outcomes okay now this is the very very
+ 
+
+ align:start position:0%
+outcomes okay now this is the very very
+tip of the incredibly exciting field of
+
+ align:start position:0%
+tip of the incredibly exciting field of
+ 
+
+ align:start position:0%
+tip of the incredibly exciting field of
+Game Theory Game Theory is a wonderful
+
+ align:start position:0%
+Game Theory Game Theory is a wonderful
+ 
+
+ align:start position:0%
+Game Theory Game Theory is a wonderful
+exciting field we have a great course
+
+ align:start position:0%
+exciting field we have a great course
+ 
+
+ align:start position:0%
+exciting field we have a great course
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+1412 which is Game Theory which takes
+
+ align:start position:0%
+1412 which is Game Theory which takes
+ 
+
+ align:start position:0%
+1412 which is Game Theory which takes
+this little bit as its first lecture and
+
+ align:start position:0%
+this little bit as its first lecture and
+ 
+
+ align:start position:0%
+this little bit as its first lecture and
+from there develops a whole semester of
+
+ align:start position:0%
+from there develops a whole semester of
+ 
+
+ align:start position:0%
+from there develops a whole semester of
+Game Theory you might say well how you
+
+ align:start position:0%
+Game Theory you might say well how you
+ 
+
+ align:start position:0%
+Game Theory you might say well how you
+do a whole semester well let me give you
+
+ align:start position:0%
+do a whole semester well let me give you
+ 
+
+ align:start position:0%
+do a whole semester well let me give you
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+example let me give you one example of
+
+ align:start position:0%
+example let me give you one example of
+ 
+
+ align:start position:0%
+example let me give you one example of
+how you can solve
+
+ align:start position:0%
+how you can solve
+ 
+
+ align:start position:0%
+how you can solve
+the prisoners dilemma without explicit
+
+ align:start position:0%
+the prisoners dilemma without explicit
+ 
+
+ align:start position:0%
+the prisoners dilemma without explicit
+cooperation how do you solve pris
+
+ align:start position:0%
+cooperation how do you solve pris
+ 
+
+ align:start position:0%
+cooperation how do you solve pris
+without explicit cooperation you can do
+
+ align:start position:0%
+without explicit cooperation you can do
+ 
+
+ align:start position:0%
+without explicit cooperation you can do
+it through playing a repeated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game a repeated game so imagine the
+
+ align:start position:0%
+game a repeated game so imagine the
+ 
+
+ align:start position:0%
+game a repeated game so imagine the
+following imagine Coke and Pepsi play
+
+ align:start position:0%
+following imagine Coke and Pepsi play
+ 
+
+ align:start position:0%
+following imagine Coke and Pepsi play
+this game every year these is annual
+
+ align:start position:0%
+this game every year these is annual
+ 
+
+ align:start position:0%
+this game every year these is annual
+numbers play this game every year
+
+ align:start position:0%
+numbers play this game every year
+ 
+
+ align:start position:0%
+numbers play this game every year
+forever they play this game every year
+
+ align:start position:0%
+forever they play this game every year
+ 
+
+ align:start position:0%
+forever they play this game every year
+forever okay now imagine Coke says the
+
+ align:start position:0%
+forever okay now imagine Coke says the
+ 
+
+ align:start position:0%
+forever okay now imagine Coke says the
+following to Pepsi it's not it's not a
+
+ align:start position:0%
+following to Pepsi it's not it's not a
+ 
+
+ align:start position:0%
+following to Pepsi it's not it's not a
+cooperation it's it's a threat coch says
+
+ align:start position:0%
+cooperation it's it's a threat coch says
+ 
+
+ align:start position:0%
+cooperation it's it's a threat coch says
+to Pepsi I will not advertise as long as
+
+ align:start position:0%
+to Pepsi I will not advertise as long as
+ 
+
+ align:start position:0%
+to Pepsi I will not advertise as long as
+you don't
+
+ align:start position:0%
+you don't
+ 
+
+ align:start position:0%
+you don't
+advertise but the minute you advertise I
+
+ align:start position:0%
+advertise but the minute you advertise I
+ 
+
+ align:start position:0%
+advertise but the minute you advertise I
+will advertise
+
+ align:start position:0%
+will advertise
+ 
+
+ align:start position:0%
+will advertise
+forever so coke says to Pepsi I they
+
+ align:start position:0%
+forever so coke says to Pepsi I they
+ 
+
+ align:start position:0%
+forever so coke says to Pepsi I they
+start with no advertising Koke says I
+
+ align:start position:0%
+start with no advertising Koke says I
+ 
+
+ align:start position:0%
+start with no advertising Koke says I
+won't advertise you don't advertise but
+
+ align:start position:0%
+won't advertise you don't advertise but
+ 
+
+ align:start position:0%
+won't advertise you don't advertise but
+the minute you advertise I'll advertise
+
+ align:start position:0%
+the minute you advertise I'll advertise
+ 
+
+ align:start position:0%
+the minute you advertise I'll advertise
+forever now think about Pepsi's decision
+
+ align:start position:0%
+forever now think about Pepsi's decision
+ 
+
+ align:start position:0%
+forever now think about Pepsi's decision
+if Pepsi advertises in Period
+
+ align:start position:0%
+if Pepsi advertises in Period
+ 
+
+ align:start position:0%
+if Pepsi advertises in Period
+one in Period one they get the whole
+
+ align:start position:0%
+one in Period one they get the whole
+ 
+
+ align:start position:0%
+one in Period one they get the whole
+Market because kooch is committed to not
+
+ align:start position:0%
+Market because kooch is committed to not
+ 
+
+ align:start position:0%
+Market because kooch is committed to not
+advertise they get
+
+ align:start position:0%
+advertise they get
+ 
+
+ align:start position:0%
+advertise they get
+11 they get
+
+ align:start position:0%
+11 they get
+ 
+
+ align:start position:0%
+11 they get
+11 and then kooch says screw your
+
+ align:start position:0%
+11 and then kooch says screw your
+ 
+
+ align:start position:0%
+11 and then kooch says screw your
+advertising forever they get three plus
+
+ align:start position:0%
+advertising forever they get three plus
+ 
+
+ align:start position:0%
+advertising forever they get three plus
+three plus three plus dot do dot do
+
+ align:start position:0%
+three plus three plus dot do dot do
+ 
+
+ align:start position:0%
+three plus three plus dot do dot do
+dot what if Pepsi doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+advertise then they get eight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forever you don't to be a math genius to
+
+ align:start position:0%
+forever you don't to be a math genius to
+ 
+
+ align:start position:0%
+forever you don't to be a math genius to
+see this is a bigger
+
+ align:start position:0%
+see this is a bigger
+ 
+
+ align:start position:0%
+see this is a bigger
+number so it changes Pepsi's dominant
+
+ align:start position:0%
+number so it changes Pepsi's dominant
+ 
+
+ align:start position:0%
+number so it changes Pepsi's dominant
+strategy
+
+ align:start position:0%
+strategy
+ 
+
+ align:start position:0%
+strategy
+Koch simply issuing that threat changes
+
+ align:start position:0%
+Koch simply issuing that threat changes
+ 
+
+ align:start position:0%
+Koch simply issuing that threat changes
+the Domin strategy no cooperation here
+
+ align:start position:0%
+the Domin strategy no cooperation here
+ 
+
+ align:start position:0%
+the Domin strategy no cooperation here
+simply a threat and yet it enforces the
+
+ align:start position:0%
+simply a threat and yet it enforces the
+ 
+
+ align:start position:0%
+simply a threat and yet it enforces the
+Cooperative
+
+ align:start position:0%
+Cooperative
+ 
+
+ align:start position:0%
+Cooperative
+equilibrium but that doesn't work unless
+
+ align:start position:0%
+equilibrium but that doesn't work unless
+ 
+
+ align:start position:0%
+equilibrium but that doesn't work unless
+the game is
+
+ align:start position:0%
+the game is
+ 
+
+ align:start position:0%
+the game is
+infinite imagine that we know 100 years
+
+ align:start position:0%
+infinite imagine that we know 100 years
+ 
+
+ align:start position:0%
+infinite imagine that we know 100 years
+from now the US will ban soda and Coke
+
+ align:start position:0%
+from now the US will ban soda and Coke
+ 
+
+ align:start position:0%
+from now the US will ban soda and Coke
+and Pepsi know that they know at some
+
+ align:start position:0%
+and Pepsi know that they know at some
+ 
+
+ align:start position:0%
+and Pepsi know that they know at some
+point this game will end so do Market's
+
+ align:start position:0%
+point this game will end so do Market's
+ 
+
+ align:start position:0%
+point this game will end so do Market's
+going to go
+
+ align:start position:0%
+going to go
+ 
+
+ align:start position:0%
+going to go
+away what is Pepsi's optimal strategy in
+
+ align:start position:0%
+away what is Pepsi's optimal strategy in
+ 
+
+ align:start position:0%
+away what is Pepsi's optimal strategy in
+the 99th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year yeah because last year it's the
+
+ align:start position:0%
+year yeah because last year it's the
+ 
+
+ align:start position:0%
+year yeah because last year it's the
+last year Coke can't punish him it's
+
+ align:start position:0%
+last year Coke can't punish him it's
+ 
+
+ align:start position:0%
+last year Coke can't punish him it's
+over but kooch knows that so what's
+
+ align:start position:0%
+over but kooch knows that so what's
+ 
+
+ align:start position:0%
+over but kooch knows that so what's
+Coke's optimal strategy in the 998th
+
+ align:start position:0%
+Coke's optimal strategy in the 998th
+ 
+
+ align:start position:0%
+Coke's optimal strategy in the 998th
+year advertise because I know Pepsi's
+
+ align:start position:0%
+year advertise because I know Pepsi's
+ 
+
+ align:start position:0%
+year advertise because I know Pepsi's
+can advertise in the 99th year they
+
+ align:start position:0%
+can advertise in the 99th year they
+ 
+
+ align:start position:0%
+can advertise in the 99th year they
+might as well get ahead of the game and
+
+ align:start position:0%
+might as well get ahead of the game and
+ 
+
+ align:start position:0%
+might as well get ahead of the game and
+advertise 998th year you can work
+
+ align:start position:0%
+advertise 998th year you can work
+ 
+
+ align:start position:0%
+advertise 998th year you can work
+backwards to see the game
+
+ align:start position:0%
+backwards to see the game
+ 
+
+ align:start position:0%
+backwards to see the game
+collapses from year one no will
+
+ align:start position:0%
+collapses from year one no will
+ 
+
+ align:start position:0%
+collapses from year one no will
+play because they know working backwards
+
+ align:start position:0%
+play because they know working backwards
+ 
+
+ align:start position:0%
+play because they know working backwards
+that as soon as someone commits not to
+
+ align:start position:0%
+that as soon as someone commits not to
+ 
+
+ align:start position:0%
+that as soon as someone commits not to
+advertise they're going to advertise and
+
+ align:start position:0%
+advertise they're going to advertise and
+ 
+
+ align:start position:0%
+advertise they're going to advertise and
+then just going to advertise
+
+ align:start position:0%
+then just going to advertise
+ 
+
+ align:start position:0%
+then just going to advertise
+forever so here's a solution that works
+
+ align:start position:0%
+forever so here's a solution that works
+ 
+
+ align:start position:0%
+forever so here's a solution that works
+but only under particular conditions
+
+ align:start position:0%
+but only under particular conditions
+ 
+
+ align:start position:0%
+but only under particular conditions
+which is an infinite repeated
+
+ align:start position:0%
+which is an infinite repeated
+ 
+
+ align:start position:0%
+which is an infinite repeated
+game that's pretty
+
+ align:start position:0%
+game that's pretty
+ 
+
+ align:start position:0%
+game that's pretty
+cool okay and that is once again the
+
+ align:start position:0%
+cool okay and that is once again the
+ 
+
+ align:start position:0%
+cool okay and that is once again the
+kind of things you could think about
+
+ align:start position:0%
+kind of things you could think about
+ 
+
+ align:start position:0%
+kind of things you could think about
+with the tools of Game Theory what 1412
+
+ align:start position:0%
+with the tools of Game Theory what 1412
+ 
+
+ align:start position:0%
+with the tools of Game Theory what 1412
+does is show you how to mathematically
+
+ align:start position:0%
+does is show you how to mathematically
+ 
+
+ align:start position:0%
+does is show you how to mathematically
+to prove these things how think about
+
+ align:start position:0%
+to prove these things how think about
+ 
+
+ align:start position:0%
+to prove these things how think about
+all the cool games it depends on who has
+
+ align:start position:0%
+all the cool games it depends on who has
+ 
+
+ align:start position:0%
+all the cool games it depends on who has
+what information who has what bargaining
+
+ align:start position:0%
+what information who has what bargaining
+ 
+
+ align:start position:0%
+what information who has what bargaining
+strength there's all sorts of cool stuff
+
+ align:start position:0%
+strength there's all sorts of cool stuff
+ 
+
+ align:start position:0%
+strength there's all sorts of cool stuff
+that comes into play here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah don't know it's not but you don't
+
+ align:start position:0%
+yeah don't know it's not but you don't
+ 
+
+ align:start position:0%
+yeah don't know it's not but you don't
+know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stop you know I I think I think that's
+
+ align:start position:0%
+stop you know I I think I think that's
+ 
+
+ align:start position:0%
+stop you know I I think I think that's
+my I should have saved my whiskey
+
+ align:start position:0%
+my I should have saved my whiskey
+ 
+
+ align:start position:0%
+my I should have saved my whiskey
+example for this which is
+
+ align:start position:0%
+example for this which is
+ 
+
+ align:start position:0%
+example for this which is
+somehow the whiskey companies had
+
+ align:start position:0%
+somehow the whiskey companies had
+ 
+
+ align:start position:0%
+somehow the whiskey companies had
+decided they were playing this repeated
+
+ align:start position:0%
+decided they were playing this repeated
+ 
+
+ align:start position:0%
+decided they were playing this repeated
+equilibrium this this repeated game and
+
+ align:start position:0%
+equilibrium this this repeated game and
+ 
+
+ align:start position:0%
+equilibrium this this repeated game and
+somehow it broke down now I don't know
+
+ align:start position:0%
+somehow it broke down now I don't know
+ 
+
+ align:start position:0%
+somehow it broke down now I don't know
+what broke did they suddenly think G
+
+ align:start position:0%
+what broke did they suddenly think G
+ 
+
+ align:start position:0%
+what broke did they suddenly think G
+people losing their taste for hard
+
+ align:start position:0%
+people losing their taste for hard
+ 
+
+ align:start position:0%
+people losing their taste for hard
+liquor we better get you know get get it
+
+ align:start position:0%
+liquor we better get you know get get it
+ 
+
+ align:start position:0%
+liquor we better get you know get get it
+while it's good I don't know it's a good
+
+ align:start position:0%
+while it's good I don't know it's a good
+ 
+
+ align:start position:0%
+while it's good I don't know it's a good
+question but in reality sometimes it
+
+ align:start position:0%
+question but in reality sometimes it
+ 
+
+ align:start position:0%
+question but in reality sometimes it
+works sometimes it doesn't and that's
+
+ align:start position:0%
+works sometimes it doesn't and that's
+ 
+
+ align:start position:0%
+works sometimes it doesn't and that's
+what is exciting about game theory is to
+
+ align:start position:0%
+what is exciting about game theory is to
+ 
+
+ align:start position:0%
+what is exciting about game theory is to
+think about deriving the conditions
+
+ align:start position:0%
+think about deriving the conditions
+ 
+
+ align:start position:0%
+think about deriving the conditions
+under which it's likely to work and not
+
+ align:start position:0%
+under which it's likely to work and not
+ 
+
+ align:start position:0%
+under which it's likely to work and not
+likely to work good question other
+
+ align:start position:0%
+likely to work good question other
+ 
+
+ align:start position:0%
+likely to work good question other
+questions so that's game theory in a in
+
+ align:start position:0%
+questions so that's game theory in a in
+ 
+
+ align:start position:0%
+questions so that's game theory in a in
+a big uh sort of in a in in in in a
+
+ align:start position:0%
+a big uh sort of in a in in in in a
+ 
+
+ align:start position:0%
+a big uh sort of in a in in in in a
+nutshell okay what we're going to do now
+
+ align:start position:0%
+nutshell okay what we're going to do now
+ 
+
+ align:start position:0%
+nutshell okay what we're going to do now
+is move from this vague concept of Game
+
+ align:start position:0%
+is move from this vague concept of Game
+ 
+
+ align:start position:0%
+is move from this vague concept of Game
+Theory to a particular model a
+
+ align:start position:0%
+Theory to a particular model a
+ 
+
+ align:start position:0%
+Theory to a particular model a
+particular game theoretic model and
+
+ align:start position:0%
+particular game theoretic model and
+ 
+
+ align:start position:0%
+particular game theoretic model and
+that's the model we'll focus on in this
+
+ align:start position:0%
+that's the model we'll focus on in this
+ 
+
+ align:start position:0%
+that's the model we'll focus on in this
+class as the model of non-cooperative
+
+ align:start position:0%
+class as the model of non-cooperative
+ 
+
+ align:start position:0%
+class as the model of non-cooperative
+oligopoly but I'm going to tell you it's
+
+ align:start position:0%
+oligopoly but I'm going to tell you it's
+ 
+
+ align:start position:0%
+oligopoly but I'm going to tell you it's
+one model of an enormous class of models
+
+ align:start position:0%
+one model of an enormous class of models
+ 
+
+ align:start position:0%
+one model of an enormous class of models
+it's just a models particularly
+
+ align:start position:0%
+it's just a models particularly
+ 
+
+ align:start position:0%
+it's just a models particularly
+convenient to work with and it gives the
+
+ align:start position:0%
+convenient to work with and it gives the
+ 
+
+ align:start position:0%
+convenient to work with and it gives the
+intuition without the math being too
+
+ align:start position:0%
+intuition without the math being too
+ 
+
+ align:start position:0%
+intuition without the math being too
+hard okay so we're going to move to one
+
+ align:start position:0%
+hard okay so we're going to move to one
+ 
+
+ align:start position:0%
+hard okay so we're going to move to one
+particular model but recognize the model
+
+ align:start position:0%
+particular model but recognize the model
+ 
+
+ align:start position:0%
+particular model but recognize the model
+we're using is one of a class of models
+
+ align:start position:0%
+we're using is one of a class of models
+ 
+
+ align:start position:0%
+we're using is one of a class of models
+one could use to model non Cooperative
+
+ align:start position:0%
+one could use to model non Cooperative
+ 
+
+ align:start position:0%
+one could use to model non Cooperative
+oligopolistic equilibria that may be the
+
+ align:start position:0%
+oligopolistic equilibria that may be the
+ 
+
+ align:start position:0%
+oligopolistic equilibria that may be the
+most complicated three words I'll use
+
+ align:start position:0%
+most complicated three words I'll use
+ 
+
+ align:start position:0%
+most complicated three words I'll use
+together in this class non-cooperative
+
+ align:start position:0%
+together in this class non-cooperative
+ 
+
+ align:start position:0%
+together in this class non-cooperative
+oligopolistic equilibria okay so we're
+
+ align:start position:0%
+oligopolistic equilibria okay so we're
+ 
+
+ align:start position:0%
+oligopolistic equilibria okay so we're
+going to talk
+
+ align:start position:0%
+going to talk
+ 
+
+ align:start position:0%
+going to talk
+about the Corno
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model of non-cooperative equilibria this
+
+ align:start position:0%
+model of non-cooperative equilibria this
+ 
+
+ align:start position:0%
+model of non-cooperative equilibria this
+is basically a version of the Nash
+
+ align:start position:0%
+is basically a version of the Nash
+ 
+
+ align:start position:0%
+is basically a version of the Nash
+model okay so what we're going to do is
+
+ align:start position:0%
+model okay so what we're going to do is
+ 
+
+ align:start position:0%
+model okay so what we're going to do is
+we're going to take the general Nash
+
+ align:start position:0%
+we're going to take the general Nash
+ 
+
+ align:start position:0%
+we're going to take the general Nash
+model and we're going to enrich it
+
+ align:start position:0%
+model and we're going to enrich it
+ 
+
+ align:start position:0%
+model and we're going to enrich it
+saying beyond having two choices you
+
+ align:start position:0%
+saying beyond having two choices you
+ 
+
+ align:start position:0%
+saying beyond having two choices you
+have a whole schedule of choices your
+
+ align:start position:0%
+have a whole schedule of choices your
+ 
+
+ align:start position:0%
+have a whole schedule of choices your
+choice isn't just a versus B but there's
+
+ align:start position:0%
+choice isn't just a versus B but there's
+ 
+
+ align:start position:0%
+choice isn't just a versus B but there's
+a large set of choices you can make
+
+ align:start position:0%
+a large set of choices you can make
+ 
+
+ align:start position:0%
+a large set of choices you can make
+which is true in economic context
+
+ align:start position:0%
+which is true in economic context
+ 
+
+ align:start position:0%
+which is true in economic context
+usually not a versus B there's how much
+
+ align:start position:0%
+usually not a versus B there's how much
+ 
+
+ align:start position:0%
+usually not a versus B there's how much
+you're going to advertise Etc there's
+
+ align:start position:0%
+you're going to advertise Etc there's
+ 
+
+ align:start position:0%
+you're going to advertise Etc there's
+whole set of choices you can make and
+
+ align:start position:0%
+whole set of choices you can make and
+ 
+
+ align:start position:0%
+whole set of choices you can make and
+but we're still going to consider two
+
+ align:start position:0%
+but we're still going to consider two
+ 
+
+ align:start position:0%
+but we're still going to consider two
+firms playing because it gets really
+
+ align:start position:0%
+firms playing because it gets really
+ 
+
+ align:start position:0%
+firms playing because it gets really
+messy Beyond two firms although once
+
+ align:start position:0%
+messy Beyond two firms although once
+ 
+
+ align:start position:0%
+messy Beyond two firms although once
+they get 142 I'll teach you how to
+
+ align:start position:0%
+they get 142 I'll teach you how to
+ 
+
+ align:start position:0%
+they get 142 I'll teach you how to
+handle that so let's imagine the world
+
+ align:start position:0%
+handle that so let's imagine the world
+ 
+
+ align:start position:0%
+handle that so let's imagine the world
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+flights from New York to
+
+ align:start position:0%
+flights from New York to
+ 
+
+ align:start position:0%
+flights from New York to
+Chicago okay and let's imagine due to
+
+ align:start position:0%
+Chicago okay and let's imagine due to
+ 
+
+ align:start position:0%
+Chicago okay and let's imagine due to
+the hub and spoke problem we discussed
+
+ align:start position:0%
+the hub and spoke problem we discussed
+ 
+
+ align:start position:0%
+the hub and spoke problem we discussed
+last time there's only two firms that
+
+ align:start position:0%
+last time there's only two firms that
+ 
+
+ align:start position:0%
+last time there's only two firms that
+fly New York to Chicago United and
+
+ align:start position:0%
+fly New York to Chicago United and
+ 
+
+ align:start position:0%
+fly New York to Chicago United and
+American obviously there's more than
+
+ align:start position:0%
+American obviously there's more than
+ 
+
+ align:start position:0%
+American obviously there's more than
+that but just to make this example easy
+
+ align:start position:0%
+that but just to make this example easy
+ 
+
+ align:start position:0%
+that but just to make this example easy
+imagine only two firms that fly to these
+
+ align:start position:0%
+imagine only two firms that fly to these
+ 
+
+ align:start position:0%
+imagine only two firms that fly to these
+two firms do dominate the market to
+
+ align:start position:0%
+two firms do dominate the market to
+ 
+
+ align:start position:0%
+two firms do dominate the market to
+Chicago 90% of flight to Chicago one or
+
+ align:start position:0%
+Chicago 90% of flight to Chicago one or
+ 
+
+ align:start position:0%
+Chicago 90% of flight to Chicago one or
+the other of those so let's say that
+
+ align:start position:0%
+the other of those so let's say that
+ 
+
+ align:start position:0%
+the other of those so let's say that
+that these two firms the only firms in
+
+ align:start position:0%
+that these two firms the only firms in
+ 
+
+ align:start position:0%
+that these two firms the only firms in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+market and now we want to ask how does
+
+ align:start position:0%
+market and now we want to ask how does
+ 
+
+ align:start position:0%
+market and now we want to ask how does
+each firm KN the other firms out there
+
+ align:start position:0%
+each firm KN the other firms out there
+ 
+
+ align:start position:0%
+each firm KN the other firms out there
+how does each firm decide on what price
+
+ align:start position:0%
+how does each firm decide on what price
+ 
+
+ align:start position:0%
+how does each firm decide on what price
+to set and how many flights to run to do
+
+ align:start position:0%
+to set and how many flights to run to do
+ 
+
+ align:start position:0%
+to set and how many flights to run to do
+that we are going to set up the Coro
+
+ align:start position:0%
+that we are going to set up the Coro
+ 
+
+ align:start position:0%
+that we are going to set up the Coro
+model and the Coro model is going to say
+
+ align:start position:0%
+model and the Coro model is going to say
+ 
+
+ align:start position:0%
+model and the Coro model is going to say
+we're going to look for the Nash
+
+ align:start position:0%
+we're going to look for the Nash
+ 
+
+ align:start position:0%
+we're going to look for the Nash
+equilibrium but in terms of set of
+
+ align:start position:0%
+equilibrium but in terms of set of
+ 
+
+ align:start position:0%
+equilibrium but in terms of set of
+phrasing in a vague term like dominant
+
+ align:start position:0%
+phrasing in a vague term like dominant
+ 
+
+ align:start position:0%
+phrasing in a vague term like dominant
+strategy will phrase the Nash
+
+ align:start position:0%
+strategy will phrase the Nash
+ 
+
+ align:start position:0%
+strategy will phrase the Nash
+equilibrium as follows this is a long
+
+ align:start position:0%
+equilibrium as follows this is a long
+ 
+
+ align:start position:0%
+equilibrium as follows this is a long
+sentence so bear with me the keno
+
+ align:start position:0%
+sentence so bear with me the keno
+ 
+
+ align:start position:0%
+sentence so bear with me the keno
+equilibrium is the set of
+
+ align:start position:0%
+equilibrium is the set of
+ 
+
+ align:start position:0%
+equilibrium is the set of
+quantities for each firm so such that
+
+ align:start position:0%
+quantities for each firm so such that
+ 
+
+ align:start position:0%
+quantities for each firm so such that
+holding other firms quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant no firm can obtain a higher a
+
+ align:start position:0%
+constant no firm can obtain a higher a
+ 
+
+ align:start position:0%
+constant no firm can obtain a higher a
+higher profit by deviating say it again
+
+ align:start position:0%
+higher profit by deviating say it again
+ 
+
+ align:start position:0%
+higher profit by deviating say it again
+the set of quantities for each firm such
+
+ align:start position:0%
+the set of quantities for each firm such
+ 
+
+ align:start position:0%
+the set of quantities for each firm such
+that holding every other firm's quantity
+
+ align:start position:0%
+that holding every other firm's quantity
+ 
+
+ align:start position:0%
+that holding every other firm's quantity
+constant no firm can raise their profits
+
+ align:start position:0%
+constant no firm can raise their profits
+ 
+
+ align:start position:0%
+constant no firm can raise their profits
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+deviating so it's a schedule a set of
+
+ align:start position:0%
+deviating so it's a schedule a set of
+ 
+
+ align:start position:0%
+deviating so it's a schedule a set of
+quantities a schedule of quantities that
+
+ align:start position:0%
+quantities a schedule of quantities that
+ 
+
+ align:start position:0%
+quantities a schedule of quantities that
+sort of maps out your dominant strategy
+
+ align:start position:0%
+sort of maps out your dominant strategy
+ 
+
+ align:start position:0%
+sort of maps out your dominant strategy
+it's not like there's one dominant
+
+ align:start position:0%
+it's not like there's one dominant
+ 
+
+ align:start position:0%
+it's not like there's one dominant
+strategy there a dominant schedule of
+
+ align:start position:0%
+strategy there a dominant schedule of
+ 
+
+ align:start position:0%
+strategy there a dominant schedule of
+strategies to see that let's go to
+
+ align:start position:0%
+strategies to see that let's go to
+ 
+
+ align:start position:0%
+strategies to see that let's go to
+figure 131 this is an example of the
+
+ align:start position:0%
+figure 131 this is an example of the
+ 
+
+ align:start position:0%
+figure 131 this is an example of the
+kind of figure you're going to become
+
+ align:start position:0%
+kind of figure you're going to become
+ 
+
+ align:start position:0%
+kind of figure you're going to become
+familiar with over the next few
+
+ align:start position:0%
+familiar with over the next few
+ 
+
+ align:start position:0%
+familiar with over the next few
+lectures figure 131 shows the market for
+
+ align:start position:0%
+lectures figure 131 shows the market for
+ 
+
+ align:start position:0%
+lectures figure 131 shows the market for
+American Airlines as if it was a
+
+ align:start position:0%
+American Airlines as if it was a
+ 
+
+ align:start position:0%
+American Airlines as if it was a
+monopoly imagine American downside a
+
+ align:start position:0%
+monopoly imagine American downside a
+ 
+
+ align:start position:0%
+monopoly imagine American downside a
+monopoly and imagine we're going to
+
+ align:start position:0%
+monopoly and imagine we're going to
+ 
+
+ align:start position:0%
+monopoly and imagine we're going to
+write down arbitrarily that the demand
+
+ align:start position:0%
+write down arbitrarily that the demand
+ 
+
+ align:start position:0%
+write down arbitrarily that the demand
+curve for flights to Chicago
+
+ align:start position:0%
+curve for flights to Chicago
+ 
+
+ align:start position:0%
+curve for flights to Chicago
+is 339 minus Q where Q is the total
+
+ align:start position:0%
+is 339 minus Q where Q is the total
+ 
+
+ align:start position:0%
+is 339 minus Q where Q is the total
+number of flights that's the demand
+
+ align:start position:0%
+number of flights that's the demand
+ 
+
+ align:start position:0%
+number of flights that's the demand
+curve for flights to Chicago just arbitr
+
+ align:start position:0%
+curve for flights to Chicago just arbitr
+ 
+
+ align:start position:0%
+curve for flights to Chicago just arbitr
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+down and let's say further that
+
+ align:start position:0%
+down and let's say further that
+ 
+
+ align:start position:0%
+down and let's say further that
+arbitrarily that marginal cost equals
+
+ align:start position:0%
+arbitrarily that marginal cost equals
+ 
+
+ align:start position:0%
+arbitrarily that marginal cost equals
+$147 so it's 339 minus Q's demand
+
+ align:start position:0%
+$147 so it's 339 minus Q's demand
+ 
+
+ align:start position:0%
+$147 so it's 339 minus Q's demand
+marginal cost
+
+ align:start position:0%
+marginal cost
+ 
+
+ align:start position:0%
+marginal cost
+147 so what would a monopolis do well
+
+ align:start position:0%
+147 so what would a monopolis do well
+ 
+
+ align:start position:0%
+147 so what would a monopolis do well
+good practice for yall for tomorrow
+
+ align:start position:0%
+good practice for yall for tomorrow
+ 
+
+ align:start position:0%
+good practice for yall for tomorrow
+night what would a monopolis do
+
+ align:start position:0%
+night what would a monopolis do
+ 
+
+ align:start position:0%
+night what would a monopolis do
+monopolis would set marginal revenue to
+
+ align:start position:0%
+monopolis would set marginal revenue to
+ 
+
+ align:start position:0%
+monopolis would set marginal revenue to
+marginal cost well what's revenue
+
+ align:start position:0%
+marginal cost well what's revenue
+ 
+
+ align:start position:0%
+marginal cost well what's revenue
+revenue is
+
+ align:start position:0%
+revenue is
+ 
+
+ align:start position:0%
+revenue is
+339 Q - Q ^2 what's marginal revenue 339
+
+ align:start position:0%
+339 Q - Q ^2 what's marginal revenue 339
+ 
+
+ align:start position:0%
+339 Q - Q ^2 what's marginal revenue 339
+minus 2 Q so monopolis sets marginal
+
+ align:start position:0%
+minus 2 Q so monopolis sets marginal
+ 
+
+ align:start position:0%
+minus 2 Q so monopolis sets marginal
+revenue 339 - 2q equal to marginal cost
+
+ align:start position:0%
+revenue 339 - 2q equal to marginal cost
+ 
+
+ align:start position:0%
+revenue 339 - 2q equal to marginal cost
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+147 and you get that the alha Monopoly
+
+ align:start position:0%
+147 and you get that the alha Monopoly
+ 
+
+ align:start position:0%
+147 and you get that the alha Monopoly
+quantity
+
+ align:start position:0%
+quantity
+ 
+
+ align:start position:0%
+quantity
+qm is 90 is
+
+ align:start position:0%
+qm is 90 is
+ 
+
+ align:start position:0%
+qm is 90 is
+um qm is 96
+
+ align:start position:0%
+um qm is 96
+ 
+
+ align:start position:0%
+um qm is 96
+flights and the optimal price is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$243 we get the optimal quantity by
+
+ align:start position:0%
+$243 we get the optimal quantity by
+ 
+
+ align:start position:0%
+$243 we get the optimal quantity by
+solving this equation get the opal chice
+
+ align:start position:0%
+solving this equation get the opal chice
+ 
+
+ align:start position:0%
+solving this equation get the opal chice
+by plugging that back in the demand
+
+ align:start position:0%
+by plugging that back in the demand
+ 
+
+ align:start position:0%
+by plugging that back in the demand
+equation so if this is a monopoly this
+
+ align:start position:0%
+equation so if this is a monopoly this
+ 
+
+ align:start position:0%
+equation so if this is a monopoly this
+is what they're going to do note of
+
+ align:start position:0%
+is what they're going to do note of
+ 
+
+ align:start position:0%
+is what they're going to do note of
+course that price is well above marginal
+
+ align:start position:0%
+course that price is well above marginal
+ 
+
+ align:start position:0%
+course that price is well above marginal
+cost because it's a monopoly there's a
+
+ align:start position:0%
+cost because it's a monopoly there's a
+ 
+
+ align:start position:0%
+cost because it's a monopoly there's a
+markup okay so that's what they would
+
+ align:start position:0%
+markup okay so that's what they would
+ 
+
+ align:start position:0%
+markup okay so that's what they would
+and we could see that in figure 131 by
+
+ align:start position:0%
+and we could see that in figure 131 by
+ 
+
+ align:start position:0%
+and we could see that in figure 131 by
+drawing the monopolis problem you see
+
+ align:start position:0%
+drawing the monopolis problem you see
+ 
+
+ align:start position:0%
+drawing the monopolis problem you see
+the marginal cost is at
+
+ align:start position:0%
+the marginal cost is at
+ 
+
+ align:start position:0%
+the marginal cost is at
+147 you see the the main curve is the
+
+ align:start position:0%
+147 you see the the main curve is the
+ 
+
+ align:start position:0%
+147 you see the the main curve is the
+Blue
+
+ align:start position:0%
+Blue
+ 
+
+ align:start position:0%
+Blue
+Line the marginal revenue curve is the
+
+ align:start position:0%
+Line the marginal revenue curve is the
+ 
+
+ align:start position:0%
+Line the marginal revenue curve is the
+red downward sloping line the maroon
+
+ align:start position:0%
+red downward sloping line the maroon
+ 
+
+ align:start position:0%
+red downward sloping line the maroon
+line the darker red line we find the
+
+ align:start position:0%
+line the darker red line we find the
+ 
+
+ align:start position:0%
+line the darker red line we find the
+point where marginal revenue intersects
+
+ align:start position:0%
+point where marginal revenue intersects
+ 
+
+ align:start position:0%
+point where marginal revenue intersects
+marginal cost which is at 96 flights
+
+ align:start position:0%
+marginal cost which is at 96 flights
+ 
+
+ align:start position:0%
+marginal cost which is at 96 flights
+96,000
+
+ align:start position:0%
+96,000
+ 
+
+ align:start position:0%
+96,000
+whatever and then to find the price we
+
+ align:start position:0%
+whatever and then to find the price we
+ 
+
+ align:start position:0%
+whatever and then to find the price we
+read it off the demand curve which is
+
+ align:start position:0%
+read it off the demand curve which is
+ 
+
+ align:start position:0%
+read it off the demand curve which is
+the 96 flights the price is 243 and
+
+ align:start position:0%
+the 96 flights the price is 243 and
+ 
+
+ align:start position:0%
+the 96 flights the price is 243 and
+that's the Monopoly
+
+ align:start position:0%
+that's the Monopoly
+ 
+
+ align:start position:0%
+that's the Monopoly
+outcome okay questions about
+
+ align:start position:0%
+outcome okay questions about
+ 
+
+ align:start position:0%
+outcome okay questions about
+that now imagine and this is a weird
+
+ align:start position:0%
+that now imagine and this is a weird
+ 
+
+ align:start position:0%
+that now imagine and this is a weird
+weird case but just imagine for a minute
+
+ align:start position:0%
+weird case but just imagine for a minute
+ 
+
+ align:start position:0%
+weird case but just imagine for a minute
+somehow through the indust through
+
+ align:start position:0%
+somehow through the indust through
+ 
+
+ align:start position:0%
+somehow through the indust through
+industrial Espionage America knew that
+
+ align:start position:0%
+industrial Espionage America knew that
+ 
+
+ align:start position:0%
+industrial Espionage America knew that
+United imagine how United is in the
+
+ align:start position:0%
+United imagine how United is in the
+ 
+
+ align:start position:0%
+United imagine how United is in the
+market it's no longer Monopoly and
+
+ align:start position:0%
+market it's no longer Monopoly and
+ 
+
+ align:start position:0%
+market it's no longer Monopoly and
+imagine americ knows United's going to
+
+ align:start position:0%
+imagine americ knows United's going to
+ 
+
+ align:start position:0%
+imagine americ knows United's going to
+fly 64
+
+ align:start position:0%
+fly 64
+ 
+
+ align:start position:0%
+fly 64
+flights 64,000 is Thousands but doesn't
+
+ align:start position:0%
+flights 64,000 is Thousands but doesn't
+ 
+
+ align:start position:0%
+flights 64,000 is Thousands but doesn't
+matter Dr the unit I don't know somehow
+
+ align:start position:0%
+matter Dr the unit I don't know somehow
+ 
+
+ align:start position:0%
+matter Dr the unit I don't know somehow
+it knows they're going to do
+
+ align:start position:0%
+it knows they're going to do
+ 
+
+ align:start position:0%
+it knows they're going to do
+64 well what should American do given
+
+ align:start position:0%
+64 well what should American do given
+ 
+
+ align:start position:0%
+64 well what should American do given
+the knowledge that United's can do 64
+
+ align:start position:0%
+the knowledge that United's can do 64
+ 
+
+ align:start position:0%
+the knowledge that United's can do 64
+flights well what it should do is it
+
+ align:start position:0%
+flights well what it should do is it
+ 
+
+ align:start position:0%
+flights well what it should do is it
+should compute its residual
+
+ align:start position:0%
+should compute its residual
+ 
+
+ align:start position:0%
+should compute its residual
+demand what's its residual demand it's
+
+ align:start position:0%
+demand what's its residual demand it's
+ 
+
+ align:start position:0%
+demand what's its residual demand it's
+the demand that's left over after United
+
+ align:start position:0%
+the demand that's left over after United
+ 
+
+ align:start position:0%
+the demand that's left over after United
+does the 64 flights so what's its
+
+ align:start position:0%
+does the 64 flights so what's its
+ 
+
+ align:start position:0%
+does the 64 flights so what's its
+residual demand well it's its residual
+
+ align:start position:0%
+residual demand well it's its residual
+ 
+
+ align:start position:0%
+residual demand well it's its residual
+demand is 339
+
+ align:start position:0%
+demand is 339
+ 
+
+ align:start position:0%
+demand is 339
+minus what it's going to fly now it's
+
+ align:start position:0%
+minus what it's going to fly now it's
+ 
+
+ align:start position:0%
+minus what it's going to fly now it's
+little Q because there's two firms in
+
+ align:start position:0%
+little Q because there's two firms in
+ 
+
+ align:start position:0%
+little Q because there's two firms in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+market minus the 64 flights that
+
+ align:start position:0%
+market minus the 64 flights that
+ 
+
+ align:start position:0%
+market minus the 64 flights that
+America's going to
+
+ align:start position:0%
+America's going to
+ 
+
+ align:start position:0%
+America's going to
+provide so its residual demand is
+
+ align:start position:0%
+provide so its residual demand is
+ 
+
+ align:start position:0%
+provide so its residual demand is
+275 minus Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suba Q sub I'm sorry Q sub two yeah q75
+
+ align:start position:0%
+Suba Q sub I'm sorry Q sub two yeah q75
+ 
+
+ align:start position:0%
+Suba Q sub I'm sorry Q sub two yeah q75
+minus Q Suba that's its residual demand
+
+ align:start position:0%
+minus Q Suba that's its residual demand
+ 
+
+ align:start position:0%
+minus Q Suba that's its residual demand
+well arm with that residual demand we
+
+ align:start position:0%
+well arm with that residual demand we
+ 
+
+ align:start position:0%
+well arm with that residual demand we
+can go back and redo the Monopoly
+
+ align:start position:0%
+can go back and redo the Monopoly
+ 
+
+ align:start position:0%
+can go back and redo the Monopoly
+example so look at figure
+
+ align:start position:0%
+example so look at figure
+ 
+
+ align:start position:0%
+example so look at figure
+132 americ is originally the outer Blue
+
+ align:start position:0%
+132 americ is originally the outer Blue
+ 
+
+ align:start position:0%
+132 americ is originally the outer Blue
+Line D the fact that United is flying 64
+
+ align:start position:0%
+Line D the fact that United is flying 64
+ 
+
+ align:start position:0%
+Line D the fact that United is flying 64
+flights shifts it to the inner demand
+
+ align:start position:0%
+flights shifts it to the inner demand
+ 
+
+ align:start position:0%
+flights shifts it to the inner demand
+curve the residual demand curve D
+
+ align:start position:0%
+curve the residual demand curve D
+ 
+
+ align:start position:0%
+curve the residual demand curve D
+Prime but from there the magic is the
+
+ align:start position:0%
+Prime but from there the magic is the
+ 
+
+ align:start position:0%
+Prime but from there the magic is the
+same we compute marginal revenue which
+
+ align:start position:0%
+same we compute marginal revenue which
+ 
+
+ align:start position:0%
+same we compute marginal revenue which
+is Mr Prime we find where marginal
+
+ align:start position:0%
+is Mr Prime we find where marginal
+ 
+
+ align:start position:0%
+is Mr Prime we find where marginal
+revenue equals marginal
+
+ align:start position:0%
+revenue equals marginal
+ 
+
+ align:start position:0%
+revenue equals marginal
+cost okay so what what's marginal
+
+ align:start position:0%
+cost okay so what what's marginal
+ 
+
+ align:start position:0%
+cost okay so what what's marginal
+revenue marginal revenue here is going
+
+ align:start position:0%
+revenue marginal revenue here is going
+ 
+
+ align:start position:0%
+revenue marginal revenue here is going
+to be 275 minus 2 QA that's the marginal
+
+ align:start position:0%
+to be 275 minus 2 QA that's the marginal
+ 
+
+ align:start position:0%
+to be 275 minus 2 QA that's the marginal
+revenue I just multiplied that by q and
+
+ align:start position:0%
+revenue I just multiplied that by q and
+ 
+
+ align:start position:0%
+revenue I just multiplied that by q and
+then took the
+
+ align:start position:0%
+then took the
+ 
+
+ align:start position:0%
+then took the
+derivative marginal cost is
+
+ align:start position:0%
+derivative marginal cost is
+ 
+
+ align:start position:0%
+derivative marginal cost is
+147 so the new optimal Q subet is
+
+ align:start position:0%
+147 so the new optimal Q subet is
+ 
+
+ align:start position:0%
+147 so the new optimal Q subet is
+instead of 96 they're going to fly 64
+
+ align:start position:0%
+instead of 96 they're going to fly 64
+ 
+
+ align:start position:0%
+instead of 96 they're going to fly 64
+flights so the new optimal Q sub a
+
+ align:start position:0%
+flights so the new optimal Q sub a
+ 
+
+ align:start position:0%
+flights so the new optimal Q sub a
+remember now Q sub is the old big Q
+
+ align:start position:0%
+remember now Q sub is the old big Q
+ 
+
+ align:start position:0%
+remember now Q sub is the old big Q
+because there's now two firms not one
+
+ align:start position:0%
+because there's now two firms not one
+ 
+
+ align:start position:0%
+because there's now two firms not one
+firm the new optimal Q sub is 64 flights
+
+ align:start position:0%
+firm the new optimal Q sub is 64 flights
+ 
+
+ align:start position:0%
+firm the new optimal Q sub is 64 flights
+and the optimal price is
+
+ align:start position:0%
+and the optimal price is
+ 
+
+ align:start position:0%
+and the optimal price is
+211 the price has come
+
+ align:start position:0%
+211 the price has come
+ 
+
+ align:start position:0%
+211 the price has come
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+why because now part of the Market's
+
+ align:start position:0%
+why because now part of the Market's
+ 
+
+ align:start position:0%
+why because now part of the Market's
+been taken so if they want to sell at
+
+ align:start position:0%
+been taken so if they want to sell at
+ 
+
+ align:start position:0%
+been taken so if they want to sell at
+this Market they've got to have a lower
+
+ align:start position:0%
+this Market they've got to have a lower
+ 
+
+ align:start position:0%
+this Market they've got to have a lower
+price so you get the new equilibrium
+
+ align:start position:0%
+price so you get the new equilibrium
+ 
+
+ align:start position:0%
+price so you get the new equilibrium
+which is where the maroon line the MRP
+
+ align:start position:0%
+which is where the maroon line the MRP
+ 
+
+ align:start position:0%
+which is where the maroon line the MRP
+Prime hits the red line the
+
+ align:start position:0%
+Prime hits the red line the
+ 
+
+ align:start position:0%
+Prime hits the red line the
+MC that's a 64 flights and a price you
+
+ align:start position:0%
+MC that's a 64 flights and a price you
+ 
+
+ align:start position:0%
+MC that's a 64 flights and a price you
+read off the man curve of
+
+ align:start position:0%
+read off the man curve of
+ 
+
+ align:start position:0%
+read off the man curve of
+21 questions about
+
+ align:start position:0%
+21 questions about
+ 
+
+ align:start position:0%
+21 questions about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah no it the question is doesn't
+
+ align:start position:0%
+yeah no it the question is doesn't
+ 
+
+ align:start position:0%
+yeah no it the question is doesn't
+matter what price they're setting
+
+ align:start position:0%
+matter what price they're setting
+ 
+
+ align:start position:0%
+matter what price they're setting
+actually it doesn't because all you
+
+ align:start position:0%
+actually it doesn't because all you
+ 
+
+ align:start position:0%
+actually it doesn't because all you
+because your curve here is just depend
+
+ align:start position:0%
+because your curve here is just depend
+ 
+
+ align:start position:0%
+because your curve here is just depend
+on how many flights they're going to
+
+ align:start position:0%
+on how many flights they're going to
+ 
+
+ align:start position:0%
+on how many flights they're going to
+sell now in reality it would but in
+
+ align:start position:0%
+sell now in reality it would but in
+ 
+
+ align:start position:0%
+sell now in reality it would but in
+practice it doesn't because we're
+
+ align:start position:0%
+practice it doesn't because we're
+ 
+
+ align:start position:0%
+practice it doesn't because we're
+assuming that this we're basically as
+
+ align:start position:0%
+assuming that this we're basically as
+ 
+
+ align:start position:0%
+assuming that this we're basically as
+long long as we know the other firm's
+
+ align:start position:0%
+long long as we know the other firm's
+ 
+
+ align:start position:0%
+long long as we know the other firm's
+conditions in particular if we know
+
+ align:start position:0%
+conditions in particular if we know
+ 
+
+ align:start position:0%
+conditions in particular if we know
+their marginal costs and things we're
+
+ align:start position:0%
+their marginal costs and things we're
+ 
+
+ align:start position:0%
+their marginal costs and things we're
+good here we are going to assume that
+
+ align:start position:0%
+good here we are going to assume that
+ 
+
+ align:start position:0%
+good here we are going to assume that
+the marginal cost of American equals the
+
+ align:start position:0%
+the marginal cost of American equals the
+ 
+
+ align:start position:0%
+the marginal cost of American equals the
+marginal cost of United and that makes
+
+ align:start position:0%
+marginal cost of United and that makes
+ 
+
+ align:start position:0%
+marginal cost of United and that makes
+the problem easier in
+
+ align:start position:0%
+the problem easier in
+ 
+
+ align:start position:0%
+the problem easier in
+reality you would you know in in reality
+
+ align:start position:0%
+reality you would you know in in reality
+ 
+
+ align:start position:0%
+reality you would you know in in reality
+it'd be more complicated but as long as
+
+ align:start position:0%
+it'd be more complicated but as long as
+ 
+
+ align:start position:0%
+it'd be more complicated but as long as
+we assume the marginal cost the same I
+
+ align:start position:0%
+we assume the marginal cost the same I
+ 
+
+ align:start position:0%
+we assume the marginal cost the same I
+don't need to know what they're going to
+
+ align:start position:0%
+don't need to know what they're going to
+ 
+
+ align:start position:0%
+don't need to know what they're going to
+set the price at I know what they're
+
+ align:start position:0%
+set the price at I know what they're
+ 
+
+ align:start position:0%
+set the price at I know what they're
+going to set the price at because
+
+ align:start position:0%
+going to set the price at because
+ 
+
+ align:start position:0%
+going to set the price at because
+they're like me it makes the problem
+
+ align:start position:0%
+they're like me it makes the problem
+ 
+
+ align:start position:0%
+they're like me it makes the problem
+symmetric the marginal costs are
+
+ align:start position:0%
+symmetric the marginal costs are
+ 
+
+ align:start position:0%
+symmetric the marginal costs are
+different it's not symmetric it's more
+
+ align:start position:0%
+different it's not symmetric it's more
+ 
+
+ align:start position:0%
+different it's not symmetric it's more
+complicated okay good question
+
+ align:start position:0%
+complicated okay good question
+ 
+
+ align:start position:0%
+complicated okay good question
+okay so basically in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general in general of course American
+
+ align:start position:0%
+general in general of course American
+ 
+
+ align:start position:0%
+general in general of course American
+doesn't know how many flights United is
+
+ align:start position:0%
+doesn't know how many flights United is
+ 
+
+ align:start position:0%
+doesn't know how many flights United is
+going to fly so what American does is it
+
+ align:start position:0%
+going to fly so what American does is it
+ 
+
+ align:start position:0%
+going to fly so what American does is it
+asks for every quantity that United
+
+ align:start position:0%
+asks for every quantity that United
+ 
+
+ align:start position:0%
+asks for every quantity that United
+might fly how many do I want to fly it
+
+ align:start position:0%
+might fly how many do I want to fly it
+ 
+
+ align:start position:0%
+might fly how many do I want to fly it
+creates what we call its best response
+
+ align:start position:0%
+creates what we call its best response
+ 
+
+ align:start position:0%
+creates what we call its best response
+curve and that you can see as the Blue
+
+ align:start position:0%
+curve and that you can see as the Blue
+ 
+
+ align:start position:0%
+curve and that you can see as the Blue
+Line in figure
+
+ align:start position:0%
+Line in figure
+ 
+
+ align:start position:0%
+Line in figure
+133 figure 133 is the best response
+
+ align:start position:0%
+133 figure 133 is the best response
+ 
+
+ align:start position:0%
+133 figure 133 is the best response
+curve we know two points on this curve
+
+ align:start position:0%
+curve we know two points on this curve
+ 
+
+ align:start position:0%
+curve we know two points on this curve
+we know if you so what is this what let
+
+ align:start position:0%
+we know if you so what is this what let
+ 
+
+ align:start position:0%
+we know if you so what is this what let
+me back up what is this graph this graph
+
+ align:start position:0%
+me back up what is this graph this graph
+ 
+
+ align:start position:0%
+me back up what is this graph this graph
+has American this isn't price this isn't
+
+ align:start position:0%
+has American this isn't price this isn't
+ 
+
+ align:start position:0%
+has American this isn't price this isn't
+demand graph anymore this has the
+
+ align:start position:0%
+demand graph anymore this has the
+ 
+
+ align:start position:0%
+demand graph anymore this has the
+American quantity on the x axis and the
+
+ align:start position:0%
+American quantity on the x axis and the
+ 
+
+ align:start position:0%
+American quantity on the x axis and the
+United quantity on the y- axis so we're
+
+ align:start position:0%
+United quantity on the y- axis so we're
+ 
+
+ align:start position:0%
+United quantity on the y- axis so we're
+no longer doing a demand curve this is
+
+ align:start position:0%
+no longer doing a demand curve this is
+ 
+
+ align:start position:0%
+no longer doing a demand curve this is
+now a best response
+
+ align:start position:0%
+now a best response
+ 
+
+ align:start position:0%
+now a best response
+curve we know already I've already told
+
+ align:start position:0%
+curve we know already I've already told
+ 
+
+ align:start position:0%
+curve we know already I've already told
+you two points on this Blue Line I've
+
+ align:start position:0%
+you two points on this Blue Line I've
+ 
+
+ align:start position:0%
+you two points on this Blue Line I've
+told you that if United flies zero
+
+ align:start position:0%
+told you that if United flies zero
+ 
+
+ align:start position:0%
+told you that if United flies zero
+America flies 96 that's the x intercept
+
+ align:start position:0%
+America flies 96 that's the x intercept
+ 
+
+ align:start position:0%
+America flies 96 that's the x intercept
+of the Blue
+
+ align:start position:0%
+of the Blue
+ 
+
+ align:start position:0%
+of the Blue
+Line I've also told you that if United
+
+ align:start position:0%
+Line I've also told you that if United
+ 
+
+ align:start position:0%
+Line I've also told you that if United
+flies 64 American flyes 64 that's the
+
+ align:start position:0%
+flies 64 American flyes 64 that's the
+ 
+
+ align:start position:0%
+flies 64 American flyes 64 that's the
+6464 Point all this line is technically
+
+ align:start position:0%
+6464 Point all this line is technically
+ 
+
+ align:start position:0%
+6464 Point all this line is technically
+he going through this exercise over and
+
+ align:start position:0%
+he going through this exercise over and
+ 
+
+ align:start position:0%
+he going through this exercise over and
+over again for every possible qu
+
+ align:start position:0%
+over again for every possible qu
+ 
+
+ align:start position:0%
+over again for every possible qu
+quantity United could
+
+ align:start position:0%
+quantity United could
+ 
+
+ align:start position:0%
+quantity United could
+fly so this this exercise saying for
+
+ align:start position:0%
+fly so this this exercise saying for
+ 
+
+ align:start position:0%
+fly so this this exercise saying for
+every possible Quant United could fly
+
+ align:start position:0%
+every possible Quant United could fly
+ 
+
+ align:start position:0%
+every possible Quant United could fly
+what is my best response in other words
+
+ align:start position:0%
+what is my best response in other words
+ 
+
+ align:start position:0%
+what is my best response in other words
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+United is going to fly
+
+ align:start position:0%
+United is going to fly
+ 
+
+ align:start position:0%
+United is going to fly
+192 passengers in a quarter I should fly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+none now this problem is
+
+ align:start position:0%
+none now this problem is
+ 
+
+ align:start position:0%
+none now this problem is
+symmetric so United's best response
+
+ align:start position:0%
+symmetric so United's best response
+ 
+
+ align:start position:0%
+symmetric so United's best response
+curve is just the flip of American's
+
+ align:start position:0%
+curve is just the flip of American's
+ 
+
+ align:start position:0%
+curve is just the flip of American's
+best response curve they have the same
+
+ align:start position:0%
+best response curve they have the same
+ 
+
+ align:start position:0%
+best response curve they have the same
+cost structure marginal cost is the same
+
+ align:start position:0%
+cost structure marginal cost is the same
+ 
+
+ align:start position:0%
+cost structure marginal cost is the same
+and they face the same market conditions
+
+ align:start position:0%
+and they face the same market conditions
+ 
+
+ align:start position:0%
+and they face the same market conditions
+they're in the same demand market so
+
+ align:start position:0%
+they're in the same demand market so
+ 
+
+ align:start position:0%
+they're in the same demand market so
+it's a symmetric problem
+
+ align:start position:0%
+it's a symmetric problem
+ 
+
+ align:start position:0%
+it's a symmetric problem
+so United's best response curve is the
+
+ align:start position:0%
+so United's best response curve is the
+ 
+
+ align:start position:0%
+so United's best response curve is the
+flip if American flies
+
+ align:start position:0%
+flip if American flies
+ 
+
+ align:start position:0%
+flip if American flies
+nothing United should fly 96 which is
+
+ align:start position:0%
+nothing United should fly 96 which is
+ 
+
+ align:start position:0%
+nothing United should fly 96 which is
+the Y intercept of the red
+
+ align:start position:0%
+the Y intercept of the red
+ 
+
+ align:start position:0%
+the Y intercept of the red
+line if American flies 64 United should
+
+ align:start position:0%
+line if American flies 64 United should
+ 
+
+ align:start position:0%
+line if American flies 64 United should
+fly 64 and if America flies 192 United
+
+ align:start position:0%
+fly 64 and if America flies 192 United
+ 
+
+ align:start position:0%
+fly 64 and if America flies 192 United
+stat should fly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nothing these are the graphical
+
+ align:start position:0%
+nothing these are the graphical
+ 
+
+ align:start position:0%
+nothing these are the graphical
+illustration of each firm's dominant
+
+ align:start position:0%
+illustration of each firm's dominant
+ 
+
+ align:start position:0%
+illustration of each firm's dominant
+strategy
+
+ align:start position:0%
+strategy
+ 
+
+ align:start position:0%
+strategy
+their cor no strategy remember is asking
+
+ align:start position:0%
+their cor no strategy remember is asking
+ 
+
+ align:start position:0%
+their cor no strategy remember is asking
+what's the best thing I want to do given
+
+ align:start position:0%
+what's the best thing I want to do given
+ 
+
+ align:start position:0%
+what's the best thing I want to do given
+what the other person's doing well I
+
+ align:start position:0%
+what the other person's doing well I
+ 
+
+ align:start position:0%
+what the other person's doing well I
+told you what the person's doing so the
+
+ align:start position:0%
+told you what the person's doing so the
+ 
+
+ align:start position:0%
+told you what the person's doing so the
+dominant strategy for American is to
+
+ align:start position:0%
+dominant strategy for American is to
+ 
+
+ align:start position:0%
+dominant strategy for American is to
+plug in every possible thing United
+
+ align:start position:0%
+plug in every possible thing United
+ 
+
+ align:start position:0%
+plug in every possible thing United
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+do and then ask what's the best thing
+
+ align:start position:0%
+do and then ask what's the best thing
+ 
+
+ align:start position:0%
+do and then ask what's the best thing
+for me to
+
+ align:start position:0%
+for me to
+ 
+
+ align:start position:0%
+for me to
+do United does the same thing they plug
+
+ align:start position:0%
+do United does the same thing they plug
+ 
+
+ align:start position:0%
+do United does the same thing they plug
+in every possible thing American could
+
+ align:start position:0%
+in every possible thing American could
+ 
+
+ align:start position:0%
+in every possible thing American could
+do and ask what's the best thing for me
+
+ align:start position:0%
+do and ask what's the best thing for me
+ 
+
+ align:start position:0%
+do and ask what's the best thing for me
+to do if those two curves intersect
+
+ align:start position:0%
+to do if those two curves intersect
+ 
+
+ align:start position:0%
+to do if those two curves intersect
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+equilibrium the Koo equilibrium here is
+
+ align:start position:0%
+equilibrium the Koo equilibrium here is
+ 
+
+ align:start position:0%
+equilibrium the Koo equilibrium here is
+at the point
+
+ align:start position:0%
+at the point
+ 
+
+ align:start position:0%
+at the point
+6464 why because that is the one
+
+ align:start position:0%
+6464 why because that is the one
+ 
+
+ align:start position:0%
+6464 why because that is the one
+point where given what United's doing
+
+ align:start position:0%
+point where given what United's doing
+ 
+
+ align:start position:0%
+point where given what United's doing
+American doesn't want to change its
+
+ align:start position:0%
+American doesn't want to change its
+ 
+
+ align:start position:0%
+American doesn't want to change its
+strategy and given what Americans doing
+
+ align:start position:0%
+strategy and given what Americans doing
+ 
+
+ align:start position:0%
+strategy and given what Americans doing
+United doesn't want to change his
+
+ align:start position:0%
+United doesn't want to change his
+ 
+
+ align:start position:0%
+United doesn't want to change his
+strategy
+
+ align:start position:0%
+strategy
+ 
+
+ align:start position:0%
+strategy
+yeah what's that what
+
+ align:start position:0%
+yeah what's that what
+ 
+
+ align:start position:0%
+yeah what's that what
+there's uh once again that's why you
+
+ align:start position:0%
+there's uh once again that's why you
+ 
+
+ align:start position:0%
+there's uh once again that's why you
+take 1412 there's all sorts of fun
+
+ align:start position:0%
+take 1412 there's all sorts of fun
+ 
+
+ align:start position:0%
+take 1412 there's all sorts of fun
+things what if there's two intersections
+
+ align:start position:0%
+things what if there's two intersections
+ 
+
+ align:start position:0%
+things what if there's two intersections
+what if there's no inter intersection
+
+ align:start position:0%
+what if there's no inter intersection
+ 
+
+ align:start position:0%
+what if there's no inter intersection
+all sorts of fun examples take 1412
+
+ align:start position:0%
+all sorts of fun examples take 1412
+ 
+
+ align:start position:0%
+all sorts of fun examples take 1412
+we'll go through all of them we only
+
+ align:start position:0%
+we'll go through all of them we only
+ 
+
+ align:start position:0%
+we'll go through all of them we only
+have a couple lectures for Game Theory
+
+ align:start position:0%
+have a couple lectures for Game Theory
+ 
+
+ align:start position:0%
+have a couple lectures for Game Theory
+here so I can't go through all those but
+
+ align:start position:0%
+here so I can't go through all those but
+ 
+
+ align:start position:0%
+here so I can't go through all those but
+it gets complicated let me just say that
+
+ align:start position:0%
+it gets complicated let me just say that
+ 
+
+ align:start position:0%
+it gets complicated let me just say that
+you basically it's called a multiple
+
+ align:start position:0%
+you basically it's called a multiple
+ 
+
+ align:start position:0%
+you basically it's called a multiple
+equilibria and it basically then where
+
+ align:start position:0%
+equilibria and it basically then where
+ 
+
+ align:start position:0%
+equilibria and it basically then where
+you start determines where you finish in
+
+ align:start position:0%
+you start determines where you finish in
+ 
+
+ align:start position:0%
+you start determines where you finish in
+this model doesn't matter where you
+
+ align:start position:0%
+this model doesn't matter where you
+ 
+
+ align:start position:0%
+this model doesn't matter where you
+start there's one equilibria that's
+
+ align:start position:0%
+start there's one equilibria that's
+ 
+
+ align:start position:0%
+start there's one equilibria that's
+robust okay but um uh in a multiple
+
+ align:start position:0%
+robust okay but um uh in a multiple
+ 
+
+ align:start position:0%
+robust okay but um uh in a multiple
+equilibria uh where you start could
+
+ align:start position:0%
+equilibria uh where you start could
+ 
+
+ align:start position:0%
+equilibria uh where you start could
+could determine where you finish so in
+
+ align:start position:0%
+could determine where you finish so in
+ 
+
+ align:start position:0%
+could determine where you finish so in
+my example with Andrew okay in a single
+
+ align:start position:0%
+my example with Andrew okay in a single
+ 
+
+ align:start position:0%
+my example with Andrew okay in a single
+equilibrium model it doesn't matter sort
+
+ align:start position:0%
+equilibrium model it doesn't matter sort
+ 
+
+ align:start position:0%
+equilibrium model it doesn't matter sort
+of who started the fight okay but the
+
+ align:start position:0%
+of who started the fight okay but the
+ 
+
+ align:start position:0%
+of who started the fight okay but the
+multile model you might have very
+
+ align:start position:0%
+multile model you might have very
+ 
+
+ align:start position:0%
+multile model you might have very
+different outcomes based on who started
+
+ align:start position:0%
+different outcomes based on who started
+ 
+
+ align:start position:0%
+different outcomes based on who started
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+fight okay so basically that
+
+ align:start position:0%
+fight okay so basically that
+ 
+
+ align:start position:0%
+fight okay so basically that
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+intersection okay and you can't be
+
+ align:start position:0%
+intersection okay and you can't be
+ 
+
+ align:start position:0%
+intersection okay and you can't be
+here's the key
+
+ align:start position:0%
+here's the key
+ 
+
+ align:start position:0%
+here's the key
+Point American can't be can't say look
+
+ align:start position:0%
+Point American can't be can't say look
+ 
+
+ align:start position:0%
+Point American can't be can't say look
+gee but my profit I I I I liked it much
+
+ align:start position:0%
+gee but my profit I I I I liked it much
+ 
+
+ align:start position:0%
+gee but my profit I I I I liked it much
+better when I was doing this like I had
+
+ align:start position:0%
+better when I was doing this like I had
+ 
+
+ align:start position:0%
+better when I was doing this like I had
+96 lights at a higher price
+
+ align:start position:0%
+96 lights at a higher price
+ 
+
+ align:start position:0%
+96 lights at a higher price
+okay so I like that much better why
+
+ align:start position:0%
+okay so I like that much better why
+ 
+
+ align:start position:0%
+okay so I like that much better why
+can't I just do that well they can't
+
+ align:start position:0%
+can't I just do that well they can't
+ 
+
+ align:start position:0%
+can't I just do that well they can't
+because American because America won't
+
+ align:start position:0%
+because American because America won't
+ 
+
+ align:start position:0%
+because American because America won't
+let them or americ can't because United
+
+ align:start position:0%
+let them or americ can't because United
+ 
+
+ align:start position:0%
+let them or americ can't because United
+won't let them they have to account for
+
+ align:start position:0%
+won't let them they have to account for
+ 
+
+ align:start position:0%
+won't let them they have to account for
+the other firm's response and that's
+
+ align:start position:0%
+the other firm's response and that's
+ 
+
+ align:start position:0%
+the other firm's response and that's
+what's cool about oligopoly that's why
+
+ align:start position:0%
+what's cool about oligopoly that's why
+ 
+
+ align:start position:0%
+what's cool about oligopoly that's why
+the game theory because you have to
+
+ align:start position:0%
+the game theory because you have to
+ 
+
+ align:start position:0%
+the game theory because you have to
+account for the other firm's response
+
+ align:start position:0%
+account for the other firm's response
+ 
+
+ align:start position:0%
+account for the other firm's response
+okay that's the graphics let's go
+
+ align:start position:0%
+okay that's the graphics let's go
+ 
+
+ align:start position:0%
+okay that's the graphics let's go
+through the math okay let's do the Coro
+
+ align:start position:0%
+through the math okay let's do the Coro
+ 
+
+ align:start position:0%
+through the math okay let's do the Coro
+math to show you how this works
+
+ align:start position:0%
+math to show you how this works
+ 
+
+ align:start position:0%
+math to show you how this works
+mathematically
+
+ align:start position:0%
+mathematically
+ 
+
+ align:start position:0%
+mathematically
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+begin well that that's a great great
+
+ align:start position:0%
+begin well that that's a great great
+ 
+
+ align:start position:0%
+begin well that that's a great great
+question you're asking about sort of
+
+ align:start position:0%
+question you're asking about sort of
+ 
+
+ align:start position:0%
+question you're asking about sort of
+market dynamics we're calling this sort
+
+ align:start position:0%
+market dynamics we're calling this sort
+ 
+
+ align:start position:0%
+market dynamics we're calling this sort
+of a steady state equilibrium think of
+
+ align:start position:0%
+of a steady state equilibrium think of
+ 
+
+ align:start position:0%
+of a steady state equilibrium think of
+this as short run versus long run in the
+
+ align:start position:0%
+this as short run versus long run in the
+ 
+
+ align:start position:0%
+this as short run versus long run in the
+short run probably not right in the
+
+ align:start position:0%
+short run probably not right in the
+ 
+
+ align:start position:0%
+short run probably not right in the
+short run you'll buy a certain am planes
+
+ align:start position:0%
+short run you'll buy a certain am planes
+ 
+
+ align:start position:0%
+short run you'll buy a certain am planes
+they'll buy certain planes you'll you'll
+
+ align:start position:0%
+they'll buy certain planes you'll you'll
+ 
+
+ align:start position:0%
+they'll buy certain planes you'll you'll
+fck around for a while and then you'll
+
+ align:start position:0%
+fck around for a while and then you'll
+ 
+
+ align:start position:0%
+fck around for a while and then you'll
+say ah this is the point at which in the
+
+ align:start position:0%
+say ah this is the point at which in the
+ 
+
+ align:start position:0%
+say ah this is the point at which in the
+long run things are stable so let's kind
+
+ align:start position:0%
+long run things are stable so let's kind
+ 
+
+ align:start position:0%
+long run things are stable so let's kind
+of think of this more sort of a long run
+
+ align:start position:0%
+of think of this more sort of a long run
+ 
+
+ align:start position:0%
+of think of this more sort of a long run
+versus a short run
+
+ align:start position:0%
+versus a short run
+ 
+
+ align:start position:0%
+versus a short run
+okay other questions good question other
+
+ align:start position:0%
+okay other questions good question other
+ 
+
+ align:start position:0%
+okay other questions good question other
+questions okay so basically let's look
+
+ align:start position:0%
+questions okay so basically let's look
+ 
+
+ align:start position:0%
+questions okay so basically let's look
+at the math of the chono
+
+ align:start position:0%
+at the math of the chono
+ 
+
+ align:start position:0%
+at the math of the chono
+equilibrium okay
+
+ align:start position:0%
+equilibrium okay
+ 
+
+ align:start position:0%
+equilibrium okay
+so the first thing we do we don't do
+
+ align:start position:0%
+so the first thing we do we don't do
+ 
+
+ align:start position:0%
+so the first thing we do we don't do
+this whatever the hell that
+
+ align:start position:0%
+this whatever the hell that
+ 
+
+ align:start position:0%
+this whatever the hell that
+is the first thing we do is we solve for
+
+ align:start position:0%
+is the first thing we do is we solve for
+ 
+
+ align:start position:0%
+is the first thing we do is we solve for
+each firm's residual demand curve and
+
+ align:start position:0%
+each firm's residual demand curve and
+ 
+
+ align:start position:0%
+each firm's residual demand curve and
+it's a symmetric problem I could solve
+
+ align:start position:0%
+it's a symmetric problem I could solve
+ 
+
+ align:start position:0%
+it's a symmetric problem I could solve
+this for one
+
+ align:start position:0%
+this for one
+ 
+
+ align:start position:0%
+this for one
+firm and I know what I'll get for the
+
+ align:start position:0%
+firm and I know what I'll get for the
+ 
+
+ align:start position:0%
+firm and I know what I'll get for the
+other firm I have to solve for one firm
+
+ align:start position:0%
+other firm I have to solve for one firm
+ 
+
+ align:start position:0%
+other firm I have to solve for one firm
+so what is American's residual demand
+
+ align:start position:0%
+so what is American's residual demand
+ 
+
+ align:start position:0%
+so what is American's residual demand
+curve well it's
+
+ align:start position:0%
+curve well it's
+ 
+
+ align:start position:0%
+curve well it's
+339 minus QA minus qu I plugged in 64
+
+ align:start position:0%
+339 minus QA minus qu I plugged in 64
+ 
+
+ align:start position:0%
+339 minus QA minus qu I plugged in 64
+before because I had some industrial
+
+ align:start position:0%
+before because I had some industrial
+ 
+
+ align:start position:0%
+before because I had some industrial
+Espionage it was told me 64 but in
+
+ align:start position:0%
+Espionage it was told me 64 but in
+ 
+
+ align:start position:0%
+Espionage it was told me 64 but in
+general I don't know what United's going
+
+ align:start position:0%
+general I don't know what United's going
+ 
+
+ align:start position:0%
+general I don't know what United's going
+to do so I just put in this amount
+
+ align:start position:0%
+to do so I just put in this amount
+ 
+
+ align:start position:0%
+to do so I just put in this amount
+qu
+
+ align:start position:0%
+qu
+ 
+
+ align:start position:0%
+qu
+okay now what is revenue then revenue is
+
+ align:start position:0%
+okay now what is revenue then revenue is
+ 
+
+ align:start position:0%
+okay now what is revenue then revenue is
+339 QA this is American's calculation of
+
+ align:start position:0%
+339 QA this is American's calculation of
+ 
+
+ align:start position:0%
+339 QA this is American's calculation of
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+Revenue minus QA 2 minus qu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+QA what is marginal re Revenue well I
+
+ align:start position:0%
+QA what is marginal re Revenue well I
+ 
+
+ align:start position:0%
+QA what is marginal re Revenue well I
+differentiate with respect to QA this is
+
+ align:start position:0%
+differentiate with respect to QA this is
+ 
+
+ align:start position:0%
+differentiate with respect to QA this is
+American's decision so what it's his
+
+ align:start position:0%
+American's decision so what it's his
+ 
+
+ align:start position:0%
+American's decision so what it's his
+marginal revenue it's
+
+ align:start position:0%
+marginal revenue it's
+ 
+
+ align:start position:0%
+marginal revenue it's
+339 minus 2 QA minus
+
+ align:start position:0%
+339 minus 2 QA minus
+ 
+
+ align:start position:0%
+339 minus 2 QA minus
+qu so now I've got a a new term in my
+
+ align:start position:0%
+qu so now I've got a a new term in my
+ 
+
+ align:start position:0%
+qu so now I've got a a new term in my
+marginal revenue equation I didn't have
+
+ align:start position:0%
+marginal revenue equation I didn't have
+ 
+
+ align:start position:0%
+marginal revenue equation I didn't have
+before in other examples the other
+
+ align:start position:0%
+before in other examples the other
+ 
+
+ align:start position:0%
+before in other examples the other
+firm's quantity enters into my marginal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+revenue so we set this equal to marginal
+
+ align:start position:0%
+revenue so we set this equal to marginal
+ 
+
+ align:start position:0%
+revenue so we set this equal to marginal
+cost which is 147
+
+ align:start position:0%
+cost which is 147
+ 
+
+ align:start position:0%
+cost which is 147
+once again symmetrically I said marginal
+
+ align:start position:0%
+once again symmetrically I said marginal
+ 
+
+ align:start position:0%
+once again symmetrically I said marginal
+cost 147 for
+
+ align:start position:0%
+cost 147 for
+ 
+
+ align:start position:0%
+cost 147 for
+everybody set that equal the marginal
+
+ align:start position:0%
+everybody set that equal the marginal
+ 
+
+ align:start position:0%
+everybody set that equal the marginal
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+okay by the way let me go back one
+
+ align:start position:0%
+okay by the way let me go back one
+ 
+
+ align:start position:0%
+okay by the way let me go back one
+second go back to the figure go back to
+
+ align:start position:0%
+second go back to the figure go back to
+ 
+
+ align:start position:0%
+second go back to the figure go back to
+figure 131 and 132 one thing that's
+
+ align:start position:0%
+figure 131 and 132 one thing that's
+ 
+
+ align:start position:0%
+figure 131 and 132 one thing that's
+implicit I didn't say is an example
+
+ align:start position:0%
+implicit I didn't say is an example
+ 
+
+ align:start position:0%
+implicit I didn't say is an example
+average cost also equals marginal cost
+
+ align:start position:0%
+average cost also equals marginal cost
+ 
+
+ align:start position:0%
+average cost also equals marginal cost
+for the relevant range right because
+
+ align:start position:0%
+for the relevant range right because
+ 
+
+ align:start position:0%
+for the relevant range right because
+marginal cost is flat so the relevant
+
+ align:start position:0%
+marginal cost is flat so the relevant
+ 
+
+ align:start position:0%
+marginal cost is flat so the relevant
+range we're examining here average cost
+
+ align:start position:0%
+range we're examining here average cost
+ 
+
+ align:start position:0%
+range we're examining here average cost
+equals marginal cost it' be marginal
+
+ align:start position:0%
+equals marginal cost it' be marginal
+ 
+
+ align:start position:0%
+equals marginal cost it' be marginal
+cost could be the same and average cost
+
+ align:start position:0%
+cost could be the same and average cost
+ 
+
+ align:start position:0%
+cost could be the same and average cost
+could be structure be different and then
+
+ align:start position:0%
+could be structure be different and then
+ 
+
+ align:start position:0%
+could be structure be different and then
+it get complicated again so really what
+
+ align:start position:0%
+it get complicated again so really what
+ 
+
+ align:start position:0%
+it get complicated again so really what
+assuming is basically cost structure is
+
+ align:start position:0%
+assuming is basically cost structure is
+ 
+
+ align:start position:0%
+assuming is basically cost structure is
+the same across the companies at least a
+
+ align:start position:0%
+the same across the companies at least a
+ 
+
+ align:start position:0%
+the same across the companies at least a
+relevant range okay so you set that
+
+ align:start position:0%
+relevant range okay so you set that
+ 
+
+ align:start position:0%
+relevant range okay so you set that
+equal to marginal cost you solve and you
+
+ align:start position:0%
+equal to marginal cost you solve and you
+ 
+
+ align:start position:0%
+equal to marginal cost you solve and you
+get you solve that and you get the
+
+ align:start position:0%
+get you solve that and you get the
+ 
+
+ align:start position:0%
+get you solve that and you get the
+QA equal 96 minus 12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qu okay so now we don't get a
+
+ align:start position:0%
+qu okay so now we don't get a
+ 
+
+ align:start position:0%
+qu okay so now we don't get a
+deterministic answer we get that what I
+
+ align:start position:0%
+deterministic answer we get that what I
+ 
+
+ align:start position:0%
+deterministic answer we get that what I
+should fly is 96 -2 qu guess what that's
+
+ align:start position:0%
+should fly is 96 -2 qu guess what that's
+ 
+
+ align:start position:0%
+should fly is 96 -2 qu guess what that's
+the Blue Line in figure
+
+ align:start position:0%
+the Blue Line in figure
+ 
+
+ align:start position:0%
+the Blue Line in figure
+133 check it out it's 96 minus 1 12
+
+ align:start position:0%
+133 check it out it's 96 minus 1 12
+ 
+
+ align:start position:0%
+133 check it out it's 96 minus 1 12
+qu well it turns out the problem
+
+ align:start position:0%
+qu well it turns out the problem
+ 
+
+ align:start position:0%
+qu well it turns out the problem
+symmetric so United has the same best
+
+ align:start position:0%
+symmetric so United has the same best
+ 
+
+ align:start position:0%
+symmetric so United has the same best
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+function I could do the same math for
+
+ align:start position:0%
+function I could do the same math for
+ 
+
+ align:start position:0%
+function I could do the same math for
+United and i' get the qu equal 96 - 12
+
+ align:start position:0%
+United and i' get the qu equal 96 - 12
+ 
+
+ align:start position:0%
+United and i' get the qu equal 96 - 12
+QA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qu = 96 - 12 QA because it's symmetric
+
+ align:start position:0%
+qu = 96 - 12 QA because it's symmetric
+ 
+
+ align:start position:0%
+qu = 96 - 12 QA because it's symmetric
+so guess what I have two equations and
+
+ align:start position:0%
+so guess what I have two equations and
+ 
+
+ align:start position:0%
+so guess what I have two equations and
+two unknowns I have two best response
+
+ align:start position:0%
+two unknowns I have two best response
+ 
+
+ align:start position:0%
+two unknowns I have two best response
+functions intersecting or maybe not two
+
+ align:start position:0%
+functions intersecting or maybe not two
+ 
+
+ align:start position:0%
+functions intersecting or maybe not two
+equations two unknowns so I can solve
+
+ align:start position:0%
+equations two unknowns so I can solve
+ 
+
+ align:start position:0%
+equations two unknowns so I can solve
+this these two equations in two
+
+ align:start position:0%
+this these two equations in two
+ 
+
+ align:start position:0%
+this these two equations in two
+unknowns and I can get that QA equals 64
+
+ align:start position:0%
+unknowns and I can get that QA equals 64
+ 
+
+ align:start position:0%
+unknowns and I can get that QA equals 64
+and by
+
+ align:start position:0%
+and by
+ 
+
+ align:start position:0%
+and by
+symmetry qu equal 64
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that is how I just mathematically
+
+ align:start position:0%
+so that is how I just mathematically
+ 
+
+ align:start position:0%
+so that is how I just mathematically
+solved for that intersection now once
+
+ align:start position:0%
+solved for that intersection now once
+ 
+
+ align:start position:0%
+solved for that intersection now once
+again you might solve this if find no
+
+ align:start position:0%
+again you might solve this if find no
+ 
+
+ align:start position:0%
+again you might solve this if find no
+intersection two equations two unknowns
+
+ align:start position:0%
+intersection two equations two unknowns
+ 
+
+ align:start position:0%
+intersection two equations two unknowns
+you might get no rational answer and
+
+ align:start position:0%
+you might get no rational answer and
+ 
+
+ align:start position:0%
+you might get no rational answer and
+that would mean the market would just
+
+ align:start position:0%
+that would mean the market would just
+ 
+
+ align:start position:0%
+that would mean the market would just
+collapse okay or you get multiple
+
+ align:start position:0%
+collapse okay or you get multiple
+ 
+
+ align:start position:0%
+collapse okay or you get multiple
+answers and that's more
+
+ align:start position:0%
+answers and that's more
+ 
+
+ align:start position:0%
+answers and that's more
+complicated but generally you get one
+
+ align:start position:0%
+complicated but generally you get one
+ 
+
+ align:start position:0%
+complicated but generally you get one
+answer in this class at
+
+ align:start position:0%
+answer in this class at
+ 
+
+ align:start position:0%
+answer in this class at
+least okay and that with equilibrium
+
+ align:start position:0%
+least okay and that with equilibrium
+ 
+
+ align:start position:0%
+least okay and that with equilibrium
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great question does anyone know great
+
+ align:start position:0%
+great question does anyone know great
+ 
+
+ align:start position:0%
+great question does anyone know great
+question because what's big Q here big Q
+
+ align:start position:0%
+question because what's big Q here big Q
+ 
+
+ align:start position:0%
+question because what's big Q here big Q
+now in the market is 128 and what's the
+
+ align:start position:0%
+now in the market is 128 and what's the
+ 
+
+ align:start position:0%
+now in the market is 128 and what's the
+price well we know the demand curve the
+
+ align:start position:0%
+price well we know the demand curve the
+ 
+
+ align:start position:0%
+price well we know the demand curve the
+demand curve hasn't changed demand curve
+
+ align:start position:0%
+demand curve hasn't changed demand curve
+ 
+
+ align:start position:0%
+demand curve hasn't changed demand curve
+is 339 minus Q it's one market demand
+
+ align:start position:0%
+is 339 minus Q it's one market demand
+ 
+
+ align:start position:0%
+is 339 minus Q it's one market demand
+curve so the new price is uh 339 minus
+
+ align:start position:0%
+curve so the new price is uh 339 minus
+ 
+
+ align:start position:0%
+curve so the new price is uh 339 minus
+128 so 211
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but Q is 128 whereas when just
+
+ align:start position:0%
+okay but Q is 128 whereas when just
+ 
+
+ align:start position:0%
+okay but Q is 128 whereas when just
+America is 96 great question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+yeah like firm that controls everything
+
+ align:start position:0%
+yeah like firm that controls everything
+ 
+
+ align:start position:0%
+yeah like firm that controls everything
+PR PR well they're they're in between
+
+ align:start position:0%
+PR PR well they're they're in between
+ 
+
+ align:start position:0%
+PR PR well they're they're in between
+price takers and price makers but
+
+ align:start position:0%
+price takers and price makers but
+ 
+
+ align:start position:0%
+price takers and price makers but
+effectively the way we model it they're
+
+ align:start position:0%
+effectively the way we model it they're
+ 
+
+ align:start position:0%
+effectively the way we model it they're
+price takers but the intuition is when
+
+ align:start position:0%
+price takers but the intuition is when
+ 
+
+ align:start position:0%
+price takers but the intuition is when
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+monopolist I am maximizing the profits
+
+ align:start position:0%
+monopolist I am maximizing the profits
+ 
+
+ align:start position:0%
+monopolist I am maximizing the profits
+for me
+
+ align:start position:0%
+for me
+ 
+
+ align:start position:0%
+for me
+finding out what Max has my profits
+
+ align:start position:0%
+finding out what Max has my profits
+ 
+
+ align:start position:0%
+finding out what Max has my profits
+which is a high price and a low quantity
+
+ align:start position:0%
+which is a high price and a low quantity
+ 
+
+ align:start position:0%
+which is a high price and a low quantity
+once I'm sharing the market think about
+
+ align:start position:0%
+once I'm sharing the market think about
+ 
+
+ align:start position:0%
+once I'm sharing the market think about
+the Monopoly poison effect this is a
+
+ align:start position:0%
+the Monopoly poison effect this is a
+ 
+
+ align:start position:0%
+the Monopoly poison effect this is a
+great hint for what we'll cover next
+
+ align:start position:0%
+great hint for what we'll cover next
+ 
+
+ align:start position:0%
+great hint for what we'll cover next
+time think about what happens the
+
+ align:start position:0%
+time think about what happens the
+ 
+
+ align:start position:0%
+time think about what happens the
+Monopoly poisoning effect if I sell more
+
+ align:start position:0%
+Monopoly poisoning effect if I sell more
+ 
+
+ align:start position:0%
+Monopoly poisoning effect if I sell more
+in the market who bears that poisoning
+
+ align:start position:0%
+in the market who bears that poisoning
+ 
+
+ align:start position:0%
+in the market who bears that poisoning
+effect both of us because once Q goes up
+
+ align:start position:0%
+effect both of us because once Q goes up
+ 
+
+ align:start position:0%
+effect both of us because once Q goes up
+once big Q goes up the price Falls we
+
+ align:start position:0%
+once big Q goes up the price Falls we
+ 
+
+ align:start position:0%
+once big Q goes up the price Falls we
+both suffer from lower fall so it some
+
+ align:start position:0%
+both suffer from lower fall so it some
+ 
+
+ align:start position:0%
+both suffer from lower fall so it some
+says I'm offloading half of the
+
+ align:start position:0%
+says I'm offloading half of the
+ 
+
+ align:start position:0%
+says I'm offloading half of the
+poisoning effect when I'm monopolist
+
+ align:start position:0%
+poisoning effect when I'm monopolist
+ 
+
+ align:start position:0%
+poisoning effect when I'm monopolist
+every additional un price I want to
+
+ align:start position:0%
+every additional un price I want to
+ 
+
+ align:start position:0%
+every additional un price I want to
+sell low is my profit when I'm in this
+
+ align:start position:0%
+sell low is my profit when I'm in this
+ 
+
+ align:start position:0%
+sell low is my profit when I'm in this
+larger group there's sort of a sharing
+
+ align:start position:0%
+larger group there's sort of a sharing
+ 
+
+ align:start position:0%
+larger group there's sort of a sharing
+of the poisoning effect so each firm so
+
+ align:start position:0%
+of the poisoning effect so each firm so
+ 
+
+ align:start position:0%
+of the poisoning effect so each firm so
+you end up selling more what we'll show
+
+ align:start position:0%
+you end up selling more what we'll show
+ 
+
+ align:start position:0%
+you end up selling more what we'll show
+next time is why ex exactly this
+
+ align:start position:0%
+next time is why ex exactly this
+ 
+
+ align:start position:0%
+next time is why ex exactly this
+intuition will be clearer next time
+
+ align:start position:0%
+intuition will be clearer next time
+ 
+
+ align:start position:0%
+intuition will be clearer next time
+leads to cartels not to be
+
+ align:start position:0%
+leads to cartels not to be
+ 
+
+ align:start position:0%
+leads to cartels not to be
+functional and it's why we'll show next
+
+ align:start position:0%
+functional and it's why we'll show next
+ 
+
+ align:start position:0%
+functional and it's why we'll show next
+time the limit of oligopoly is perfect
+
+ align:start position:0%
+time the limit of oligopoly is perfect
+ 
+
+ align:start position:0%
+time the limit of oligopoly is perfect
+competition okay but the bottom line is
+
+ align:start position:0%
+competition okay but the bottom line is
+ 
+
+ align:start position:0%
+competition okay but the bottom line is
+when you get when you have a Coro
+
+ align:start position:0%
+when you get when you have a Coro
+ 
+
+ align:start position:0%
+when you get when you have a Coro
+equilibrium you end up with an answer
+
+ align:start position:0%
+equilibrium you end up with an answer
+ 
+
+ align:start position:0%
+equilibrium you end up with an answer
+that is not perfect competition remember
+
+ align:start position:0%
+that is not perfect competition remember
+ 
+
+ align:start position:0%
+that is not perfect competition remember
+what would perfect competition say the
+
+ align:start position:0%
+what would perfect competition say the
+ 
+
+ align:start position:0%
+what would perfect competition say the
+quantity would be can anyone tell me
+
+ align:start position:0%
+quantity would be can anyone tell me
+ 
+
+ align:start position:0%
+quantity would be can anyone tell me
+what would the quantity be under perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competition what would big Q be in this
+
+ align:start position:0%
+competition what would big Q be in this
+ 
+
+ align:start position:0%
+competition what would big Q be in this
+market with perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competition it involves one one equation
+
+ align:start position:0%
+competition it involves one one equation
+ 
+
+ align:start position:0%
+competition it involves one one equation
+solving one equation
+
+ align:start position:0%
+solving one equation
+ 
+
+ align:start position:0%
+solving one equation
+yeah it'd be n and how'd you get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh no perfect competition perfect that's
+
+ align:start position:0%
+uh no perfect competition perfect that's
+ 
+
+ align:start position:0%
+uh no perfect competition perfect that's
+exactly this question here if there's
+
+ align:start position:0%
+exactly this question here if there's
+ 
+
+ align:start position:0%
+exactly this question here if there's
+perfect competition what would yeah in
+
+ align:start position:0%
+perfect competition what would yeah in
+ 
+
+ align:start position:0%
+perfect competition what would yeah in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+back what 64 how'd you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that well well okay that's one way to do
+
+ align:start position:0%
+that well well okay that's one way to do
+ 
+
+ align:start position:0%
+that well well okay that's one way to do
+it what's another way to do it well if
+
+ align:start position:0%
+it what's another way to do it well if
+ 
+
+ align:start position:0%
+it what's another way to do it well if
+it's perfect competition what do we know
+
+ align:start position:0%
+it's perfect competition what do we know
+ 
+
+ align:start position:0%
+it's perfect competition what do we know
+come on guys got ready for tomorrow
+
+ align:start position:0%
+come on guys got ready for tomorrow
+ 
+
+ align:start position:0%
+come on guys got ready for tomorrow
+night what's the profit maximizing
+
+ align:start position:0%
+night what's the profit maximizing
+ 
+
+ align:start position:0%
+night what's the profit maximizing
+condition perfect competition price
+
+ align:start position:0%
+condition perfect competition price
+ 
+
+ align:start position:0%
+condition perfect competition price
+equals what marginal cost so we just say
+
+ align:start position:0%
+equals what marginal cost so we just say
+ 
+
+ align:start position:0%
+equals what marginal cost so we just say
+well look you want to competition price
+
+ align:start position:0%
+well look you want to competition price
+ 
+
+ align:start position:0%
+well look you want to competition price
+equals marginal cost so what's the price
+
+ align:start position:0%
+equals marginal cost so what's the price
+ 
+
+ align:start position:0%
+equals marginal cost so what's the price
+what's marginal cost 147 so you know
+
+ align:start position:0%
+what's marginal cost 147 so you know
+ 
+
+ align:start position:0%
+what's marginal cost 147 so you know
+price equals 147 and then you simply
+
+ align:start position:0%
+price equals 147 and then you simply
+ 
+
+ align:start position:0%
+price equals 147 and then you simply
+know that demand that the quantity is
+
+ align:start position:0%
+know that demand that the quantity is
+ 
+
+ align:start position:0%
+know that demand that the quantity is
+339 minus
+
+ align:start position:0%
+339 minus
+ 
+
+ align:start position:0%
+339 minus
+147 the quanti is going to be 3 339
+
+ align:start position:0%
+147 the quanti is going to be 3 339
+ 
+
+ align:start position:0%
+147 the quanti is going to be 3 339
+minus 147 which is going to be uh 192
+
+ align:start position:0%
+minus 147 which is going to be uh 192
+ 
+
+ align:start position:0%
+minus 147 which is going to be uh 192
+right is that right uh
+
+ align:start position:0%
+right is that right uh
+ 
+
+ align:start position:0%
+right is that right uh
+no uh no I got this wrong 33 9 - 147
+
+ align:start position:0%
+no uh no I got this wrong 33 9 - 147
+ 
+
+ align:start position:0%
+no uh no I got this wrong 33 9 - 147
+that's a hard math
+
+ align:start position:0%
+that's a hard math
+ 
+
+ align:start position:0%
+that's a hard math
+340 340 so
+
+ align:start position:0%
+340 340 so
+ 
+
+ align:start position:0%
+340 340 so
+200 200 yeah 192 right yeah 192 I don't
+
+ align:start position:0%
+200 200 yeah 192 right yeah 192 I don't
+ 
+
+ align:start position:0%
+200 200 yeah 192 right yeah 192 I don't
+have I'm really insecure about my math
+
+ align:start position:0%
+have I'm really insecure about my math
+ 
+
+ align:start position:0%
+have I'm really insecure about my math
+skills okay so 192
+
+ align:start position:0%
+skills okay so 192
+ 
+
+ align:start position:0%
+skills okay so 192
+192 is much bigger than Monopoly which
+
+ align:start position:0%
+192 is much bigger than Monopoly which
+ 
+
+ align:start position:0%
+192 is much bigger than Monopoly which
+was 96 it's also bigger than what we got
+
+ align:start position:0%
+was 96 it's also bigger than what we got
+ 
+
+ align:start position:0%
+was 96 it's also bigger than what we got
+in the oligopoly
+
+ align:start position:0%
+in the oligopoly
+ 
+
+ align:start position:0%
+in the oligopoly
+case so what we see is oligopoly leads
+
+ align:start position:0%
+case so what we see is oligopoly leads
+ 
+
+ align:start position:0%
+case so what we see is oligopoly leads
+us to be in between Monopoly and perfect
+
+ align:start position:0%
+us to be in between Monopoly and perfect
+ 
+
+ align:start position:0%
+us to be in between Monopoly and perfect
+competition and we'll come back next
+
+ align:start position:0%
+competition and we'll come back next
+ 
+
+ align:start position:0%
+competition and we'll come back next
+time review that and tell you why that
+
+ align:start position:0%
+time review that and tell you why that
+ 
+
+ align:start position:0%
+time review that and tell you why that
+is show you why that is all right okay
+
+ align:start position:0%
+is show you why that is all right okay
+ 
+
+ align:start position:0%
+is show you why that is all right okay
+let's stop there good luck tomorrow
+
+ align:start position:0%
+let's stop there good luck tomorrow
+ 
+
+ align:start position:0%
+let's stop there good luck tomorrow
+night I'll see yall bright and early on
+
+ align:start position:0%
+night I'll see yall bright and early on
+ 
+
+ align:start position:0%
+night I'll see yall bright and early on
+Wednesday and we'll continue this
+
+ align:start position:0%
+Wednesday and we'll continue this
+ 
+
+ align:start position:0%
+Wednesday and we'll continue this
+discussion
\ No newline at end of file
diff --git a/aAk1hYy7VuY.txt b/aAk1hYy7VuY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bef534a10c52f6740fc372d1d9a6a837f87fcff0
--- /dev/null
+++ b/aAk1hYy7VuY.txt
@@ -0,0 +1,8307 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so we were talking about
+
+ align:start position:0%
+ocw.mit.edu so we were talking about
+ 
+
+ align:start position:0%
+ocw.mit.edu so we were talking about
+factors affecting the rates of
+
+ align:start position:0%
+factors affecting the rates of
+ 
+
+ align:start position:0%
+factors affecting the rates of
+reaction and uh so we have gone through
+
+ align:start position:0%
+reaction and uh so we have gone through
+ 
+
+ align:start position:0%
+reaction and uh so we have gone through
+a number of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we talked last class about the effect
+
+ align:start position:0%
+so we talked last class about the effect
+ 
+
+ align:start position:0%
+so we talked last class about the effect
+of temperature we talked about mechanism
+
+ align:start position:0%
+of temperature we talked about mechanism
+ 
+
+ align:start position:0%
+of temperature we talked about mechanism
+last Wednesday we talked about nature of
+
+ align:start position:0%
+last Wednesday we talked about nature of
+ 
+
+ align:start position:0%
+last Wednesday we talked about nature of
+material and
+
+ align:start position:0%
+material and
+ 
+
+ align:start position:0%
+material and
+concentrations uh in the lectures
+
+ align:start position:0%
+concentrations uh in the lectures
+ 
+
+ align:start position:0%
+concentrations uh in the lectures
+preceding that and now we're up to the
+
+ align:start position:0%
+preceding that and now we're up to the
+ 
+
+ align:start position:0%
+preceding that and now we're up to the
+last thing that we had on our original
+
+ align:start position:0%
+last thing that we had on our original
+ 
+
+ align:start position:0%
+last thing that we had on our original
+list which are catalysts So today we're
+
+ align:start position:0%
+list which are catalysts So today we're
+ 
+
+ align:start position:0%
+list which are catalysts So today we're
+going to talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catalysis so this is on the lecture
+
+ align:start position:0%
+catalysis so this is on the lecture
+ 
+
+ align:start position:0%
+catalysis so this is on the lecture
+summaries that will arrive for you um
+
+ align:start position:0%
+summaries that will arrive for you um
+ 
+
+ align:start position:0%
+summaries that will arrive for you um
+so a catalyst is a substance that takes
+
+ align:start position:0%
+so a catalyst is a substance that takes
+ 
+
+ align:start position:0%
+so a catalyst is a substance that takes
+part in the reaction but isn't consumed
+
+ align:start position:0%
+part in the reaction but isn't consumed
+ 
+
+ align:start position:0%
+part in the reaction but isn't consumed
+in the reaction so it's it's a bystander
+
+ align:start position:0%
+in the reaction so it's it's a bystander
+ 
+
+ align:start position:0%
+in the reaction so it's it's a bystander
+of the reaction it'll speed it up but it
+
+ align:start position:0%
+of the reaction it'll speed it up but it
+ 
+
+ align:start position:0%
+of the reaction it'll speed it up but it
+doesn't undergo any permanent change
+
+ align:start position:0%
+doesn't undergo any permanent change
+ 
+
+ align:start position:0%
+doesn't undergo any permanent change
+itself so that's the definition of a
+
+ align:start position:0%
+itself so that's the definition of a
+ 
+
+ align:start position:0%
+itself so that's the definition of a
+catalyst so catalysts because they're
+
+ align:start position:0%
+catalyst so catalysts because they're
+ 
+
+ align:start position:0%
+catalyst so catalysts because they're
+not uh changing in their form are not
+
+ align:start position:0%
+not uh changing in their form are not
+ 
+
+ align:start position:0%
+not uh changing in their form are not
+part of an overall balanced equation so
+
+ align:start position:0%
+part of an overall balanced equation so
+ 
+
+ align:start position:0%
+part of an overall balanced equation so
+sometimes you'll see a balanced equation
+
+ align:start position:0%
+sometimes you'll see a balanced equation
+ 
+
+ align:start position:0%
+sometimes you'll see a balanced equation
+and a thing over the arrow which will
+
+ align:start position:0%
+and a thing over the arrow which will
+ 
+
+ align:start position:0%
+and a thing over the arrow which will
+indicate the conditions in which the
+
+ align:start position:0%
+indicate the conditions in which the
+ 
+
+ align:start position:0%
+indicate the conditions in which the
+reaction was done and often uh
+
+ align:start position:0%
+reaction was done and often uh
+ 
+
+ align:start position:0%
+reaction was done and often uh
+information about a catalyst that was
+
+ align:start position:0%
+information about a catalyst that was
+ 
+
+ align:start position:0%
+information about a catalyst that was
+used in the reaction uh will will take
+
+ align:start position:0%
+used in the reaction uh will will take
+ 
+
+ align:start position:0%
+used in the reaction uh will will take
+will be present there so what are
+
+ align:start position:0%
+will be present there so what are
+ 
+
+ align:start position:0%
+will be present there so what are
+catalysts actually
+
+ align:start position:0%
+catalysts actually
+ 
+
+ align:start position:0%
+catalysts actually
+doing so here is the uh potential uh
+
+ align:start position:0%
+doing so here is the uh potential uh
+ 
+
+ align:start position:0%
+doing so here is the uh potential uh
+energy diagram that we looked at last
+
+ align:start position:0%
+energy diagram that we looked at last
+ 
+
+ align:start position:0%
+energy diagram that we looked at last
+time and in this diagram you have uh
+
+ align:start position:0%
+time and in this diagram you have uh
+ 
+
+ align:start position:0%
+time and in this diagram you have uh
+some energy for reactants uh energy for
+
+ align:start position:0%
+some energy for reactants uh energy for
+ 
+
+ align:start position:0%
+some energy for reactants uh energy for
+products down here there's an overall
+
+ align:start position:0%
+products down here there's an overall
+ 
+
+ align:start position:0%
+products down here there's an overall
+change Delta e uh between the reactants
+
+ align:start position:0%
+change Delta e uh between the reactants
+ 
+
+ align:start position:0%
+change Delta e uh between the reactants
+and the products and again Delta e is
+
+ align:start position:0%
+and the products and again Delta e is
+ 
+
+ align:start position:0%
+and the products and again Delta e is
+very similar to Delta H um it's only one
+
+ align:start position:0%
+very similar to Delta H um it's only one
+ 
+
+ align:start position:0%
+very similar to Delta H um it's only one
+or two% off for gases and almost the
+
+ align:start position:0%
+or two% off for gases and almost the
+ 
+
+ align:start position:0%
+or two% off for gases and almost the
+same for liquids and solids um so that's
+
+ align:start position:0%
+same for liquids and solids um so that's
+ 
+
+ align:start position:0%
+same for liquids and solids um so that's
+uh information about the thermodynamics
+
+ align:start position:0%
+uh information about the thermodynamics
+ 
+
+ align:start position:0%
+uh information about the thermodynamics
+this is a calorimetry a thermodynamic
+
+ align:start position:0%
+this is a calorimetry a thermodynamic
+ 
+
+ align:start position:0%
+this is a calorimetry a thermodynamic
+measurement and then we saw that there's
+
+ align:start position:0%
+measurement and then we saw that there's
+ 
+
+ align:start position:0%
+measurement and then we saw that there's
+an activation energy and this is EA for
+
+ align:start position:0%
+an activation energy and this is EA for
+ 
+
+ align:start position:0%
+an activation energy and this is EA for
+the forward reaction uh that the
+
+ align:start position:0%
+the forward reaction uh that the
+ 
+
+ align:start position:0%
+the forward reaction uh that the
+molecules need to overcome critical
+
+ align:start position:0%
+molecules need to overcome critical
+ 
+
+ align:start position:0%
+molecules need to overcome critical
+energy that they need to overcome before
+
+ align:start position:0%
+energy that they need to overcome before
+ 
+
+ align:start position:0%
+energy that they need to overcome before
+they can go on and form products and
+
+ align:start position:0%
+they can go on and form products and
+ 
+
+ align:start position:0%
+they can go on and form products and
+that's uh that energy barrier is there
+
+ align:start position:0%
+that's uh that energy barrier is there
+ 
+
+ align:start position:0%
+that's uh that energy barrier is there
+because when molecules come together and
+
+ align:start position:0%
+because when molecules come together and
+ 
+
+ align:start position:0%
+because when molecules come together and
+attempt to react usually there's some
+
+ align:start position:0%
+attempt to react usually there's some
+ 
+
+ align:start position:0%
+attempt to react usually there's some
+amount of bond Distortion that has to
+
+ align:start position:0%
+amount of bond Distortion that has to
+ 
+
+ align:start position:0%
+amount of bond Distortion that has to
+occur things are
+
+ align:start position:0%
+occur things are
+ 
+
+ align:start position:0%
+occur things are
+rearranging and you form usually some
+
+ align:start position:0%
+rearranging and you form usually some
+ 
+
+ align:start position:0%
+rearranging and you form usually some
+kind of intermediate activated complex
+
+ align:start position:0%
+kind of intermediate activated complex
+ 
+
+ align:start position:0%
+kind of intermediate activated complex
+or transition state and when you get up
+
+ align:start position:0%
+or transition state and when you get up
+ 
+
+ align:start position:0%
+or transition state and when you get up
+there if the molecules have enough
+
+ align:start position:0%
+there if the molecules have enough
+ 
+
+ align:start position:0%
+there if the molecules have enough
+energy to react then they can go down to
+
+ align:start position:0%
+energy to react then they can go down to
+ 
+
+ align:start position:0%
+energy to react then they can go down to
+products if they don't have enough
+
+ align:start position:0%
+products if they don't have enough
+ 
+
+ align:start position:0%
+products if they don't have enough
+energy to react if there's not enough
+
+ align:start position:0%
+energy to react if there's not enough
+ 
+
+ align:start position:0%
+energy to react if there's not enough
+energy uh to distort those bonds and
+
+ align:start position:0%
+energy uh to distort those bonds and
+ 
+
+ align:start position:0%
+energy uh to distort those bonds and
+form this activated complex then they'll
+
+ align:start position:0%
+form this activated complex then they'll
+ 
+
+ align:start position:0%
+form this activated complex then they'll
+fall back apart to reactants so for an
+
+ align:start position:0%
+fall back apart to reactants so for an
+ 
+
+ align:start position:0%
+fall back apart to reactants so for an
+elementary reaction there's always some
+
+ align:start position:0%
+elementary reaction there's always some
+ 
+
+ align:start position:0%
+elementary reaction there's always some
+barrier to overcome and uh I I think
+
+ align:start position:0%
+barrier to overcome and uh I I think
+ 
+
+ align:start position:0%
+barrier to overcome and uh I I think
+about activation energy barriers in my
+
+ align:start position:0%
+about activation energy barriers in my
+ 
+
+ align:start position:0%
+about activation energy barriers in my
+own work all the time it seems like you
+
+ align:start position:0%
+own work all the time it seems like you
+ 
+
+ align:start position:0%
+own work all the time it seems like you
+know whenever I have to sit down and do
+
+ align:start position:0%
+know whenever I have to sit down and do
+ 
+
+ align:start position:0%
+know whenever I have to sit down and do
+something uh write a paper start writing
+
+ align:start position:0%
+something uh write a paper start writing
+ 
+
+ align:start position:0%
+something uh write a paper start writing
+a paper write a grant write the final
+
+ align:start position:0%
+a paper write a grant write the final
+ 
+
+ align:start position:0%
+a paper write a grant write the final
+exam there always seems to be some
+
+ align:start position:0%
+exam there always seems to be some
+ 
+
+ align:start position:0%
+exam there always seems to be some
+activation energy barrier to getting
+
+ align:start position:0%
+activation energy barrier to getting
+ 
+
+ align:start position:0%
+activation energy barrier to getting
+started and once you get started then
+
+ align:start position:0%
+started and once you get started then
+ 
+
+ align:start position:0%
+started and once you get started then
+then you uh if you get to this point uh
+
+ align:start position:0%
+then you uh if you get to this point uh
+ 
+
+ align:start position:0%
+then you uh if you get to this point uh
+then it's all downhill and things go
+
+ align:start position:0%
+then it's all downhill and things go
+ 
+
+ align:start position:0%
+then it's all downhill and things go
+much more smoothly but in the beginning
+
+ align:start position:0%
+much more smoothly but in the beginning
+ 
+
+ align:start position:0%
+much more smoothly but in the beginning
+it always seems like every reaction or
+
+ align:start position:0%
+it always seems like every reaction or
+ 
+
+ align:start position:0%
+it always seems like every reaction or
+every task has some kind of activation
+
+ align:start position:0%
+every task has some kind of activation
+ 
+
+ align:start position:0%
+every task has some kind of activation
+energy barrier so up at this top part
+
+ align:start position:0%
+energy barrier so up at this top part
+ 
+
+ align:start position:0%
+energy barrier so up at this top part
+there with this dash line then there's a
+
+ align:start position:0%
+there with this dash line then there's a
+ 
+
+ align:start position:0%
+there with this dash line then there's a
+transition state or an activated complex
+
+ align:start position:0%
+transition state or an activated complex
+ 
+
+ align:start position:0%
+transition state or an activated complex
+and here's the barrier without the
+
+ align:start position:0%
+and here's the barrier without the
+ 
+
+ align:start position:0%
+and here's the barrier without the
+Catalyst here's the energy barrier
+
+ align:start position:0%
+Catalyst here's the energy barrier
+ 
+
+ align:start position:0%
+Catalyst here's the energy barrier
+without the Catalyst and the line for
+
+ align:start position:0%
+without the Catalyst and the line for
+ 
+
+ align:start position:0%
+without the Catalyst and the line for
+the transition state and again if we go
+
+ align:start position:0%
+the transition state and again if we go
+ 
+
+ align:start position:0%
+the transition state and again if we go
+in the reverse direction of this there's
+
+ align:start position:0%
+in the reverse direction of this there's
+ 
+
+ align:start position:0%
+in the reverse direction of this there's
+an activation energy for the reverse
+
+ align:start position:0%
+an activation energy for the reverse
+ 
+
+ align:start position:0%
+an activation energy for the reverse
+reaction here and these will all sum up
+
+ align:start position:0%
+reaction here and these will all sum up
+ 
+
+ align:start position:0%
+reaction here and these will all sum up
+so Delta e is going to be equal to the
+
+ align:start position:0%
+so Delta e is going to be equal to the
+ 
+
+ align:start position:0%
+so Delta e is going to be equal to the
+activation energy for the forward
+
+ align:start position:0%
+activation energy for the forward
+ 
+
+ align:start position:0%
+activation energy for the forward
+reaction minus the activation energy for
+
+ align:start position:0%
+reaction minus the activation energy for
+ 
+
+ align:start position:0%
+reaction minus the activation energy for
+the reverse reaction so what does adding
+
+ align:start position:0%
+the reverse reaction so what does adding
+ 
+
+ align:start position:0%
+the reverse reaction so what does adding
+a catalyst do well adding a catalyst
+
+ align:start position:0%
+a catalyst do well adding a catalyst
+ 
+
+ align:start position:0%
+a catalyst do well adding a catalyst
+lowers that activation energy barrier so
+
+ align:start position:0%
+lowers that activation energy barrier so
+ 
+
+ align:start position:0%
+lowers that activation energy barrier so
+that's shown here in the blue line and
+
+ align:start position:0%
+that's shown here in the blue line and
+ 
+
+ align:start position:0%
+that's shown here in the blue line and
+this is also uh in the
+
+ align:start position:0%
+this is also uh in the
+ 
+
+ align:start position:0%
+this is also uh in the
+handout so this is the energy barrier um
+
+ align:start position:0%
+handout so this is the energy barrier um
+ 
+
+ align:start position:0%
+handout so this is the energy barrier um
+with a catalyst so it's lower and then
+
+ align:start position:0%
+with a catalyst so it's lower and then
+ 
+
+ align:start position:0%
+with a catalyst so it's lower and then
+the transition state with the Catalyst
+
+ align:start position:0%
+the transition state with the Catalyst
+ 
+
+ align:start position:0%
+the transition state with the Catalyst
+will also be slow be lower and so one
+
+ align:start position:0%
+will also be slow be lower and so one
+ 
+
+ align:start position:0%
+will also be slow be lower and so one
+way that you can think about this is
+
+ align:start position:0%
+way that you can think about this is
+ 
+
+ align:start position:0%
+way that you can think about this is
+that a catalyst lowers um or stabilizes
+
+ align:start position:0%
+that a catalyst lowers um or stabilizes
+ 
+
+ align:start position:0%
+that a catalyst lowers um or stabilizes
+the transition state
+
+ align:start position:0%
+the transition state
+ 
+
+ align:start position:0%
+the transition state
+all right so let's add a few more things
+
+ align:start position:0%
+all right so let's add a few more things
+ 
+
+ align:start position:0%
+all right so let's add a few more things
+to this diagram
+
+ align:start position:0%
+to this diagram
+ 
+
+ align:start position:0%
+to this diagram
+then so there'll be a new activation
+
+ align:start position:0%
+then so there'll be a new activation
+ 
+
+ align:start position:0%
+then so there'll be a new activation
+energy for the forward reaction shown in
+
+ align:start position:0%
+energy for the forward reaction shown in
+ 
+
+ align:start position:0%
+energy for the forward reaction shown in
+blue it's not as high a barrier now it's
+
+ align:start position:0%
+blue it's not as high a barrier now it's
+ 
+
+ align:start position:0%
+blue it's not as high a barrier now it's
+lowered down and there will be a new
+
+ align:start position:0%
+lowered down and there will be a new
+ 
+
+ align:start position:0%
+lowered down and there will be a new
+activation energy for the reverse
+
+ align:start position:0%
+activation energy for the reverse
+ 
+
+ align:start position:0%
+activation energy for the reverse
+reaction uh shown in blue so these are
+
+ align:start position:0%
+reaction uh shown in blue so these are
+ 
+
+ align:start position:0%
+reaction uh shown in blue so these are
+the values then with a catalyst so a
+
+ align:start position:0%
+the values then with a catalyst so a
+ 
+
+ align:start position:0%
+the values then with a catalyst so a
+catalyst is going to lower both the
+
+ align:start position:0%
+catalyst is going to lower both the
+ 
+
+ align:start position:0%
+catalyst is going to lower both the
+activation energy for the forward
+
+ align:start position:0%
+activation energy for the forward
+ 
+
+ align:start position:0%
+activation energy for the forward
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+and the activation energy for the
+
+ align:start position:0%
+and the activation energy for the
+ 
+
+ align:start position:0%
+and the activation energy for the
+reverse
+
+ align:start position:0%
+reverse
+ 
+
+ align:start position:0%
+reverse
+reaction and uh that's what said here so
+
+ align:start position:0%
+reaction and uh that's what said here so
+ 
+
+ align:start position:0%
+reaction and uh that's what said here so
+it lowers both both barriers forward and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reverse and another way to express this
+
+ align:start position:0%
+reverse and another way to express this
+ 
+
+ align:start position:0%
+reverse and another way to express this
+is that the Catal Catalyst stabilize
+
+ align:start position:0%
+is that the Catal Catalyst stabilize
+ 
+
+ align:start position:0%
+is that the Catal Catalyst stabilize
+this transition state or activated
+
+ align:start position:0%
+this transition state or activated
+ 
+
+ align:start position:0%
+this transition state or activated
+complex so they're going to lower the
+
+ align:start position:0%
+complex so they're going to lower the
+ 
+
+ align:start position:0%
+complex so they're going to lower the
+energy or stabilize that state and this
+
+ align:start position:0%
+energy or stabilize that state and this
+ 
+
+ align:start position:0%
+energy or stabilize that state and this
+way of thinking about this will come
+
+ align:start position:0%
+way of thinking about this will come
+ 
+
+ align:start position:0%
+way of thinking about this will come
+back to at the end of the lecture it's
+
+ align:start position:0%
+back to at the end of the lecture it's
+ 
+
+ align:start position:0%
+back to at the end of the lecture it's
+something that's used U by
+
+ align:start position:0%
+something that's used U by
+ 
+
+ align:start position:0%
+something that's used U by
+pharmaceutical companies in terms of
+
+ align:start position:0%
+pharmaceutical companies in terms of
+ 
+
+ align:start position:0%
+pharmaceutical companies in terms of
+Designing uh uh Inhibitors of enzymes to
+
+ align:start position:0%
+Designing uh uh Inhibitors of enzymes to
+ 
+
+ align:start position:0%
+Designing uh uh Inhibitors of enzymes to
+think about uh
+
+ align:start position:0%
+think about uh
+ 
+
+ align:start position:0%
+think about uh
+this so catalysts have no effect on the
+
+ align:start position:0%
+this so catalysts have no effect on the
+ 
+
+ align:start position:0%
+this so catalysts have no effect on the
+thermodynamics of the reaction so
+
+ align:start position:0%
+thermodynamics of the reaction so
+ 
+
+ align:start position:0%
+thermodynamics of the reaction so
+they're affecting the rate of the
+
+ align:start position:0%
+they're affecting the rate of the
+ 
+
+ align:start position:0%
+they're affecting the rate of the
+reaction but not the thermodynamics of
+
+ align:start position:0%
+reaction but not the thermodynamics of
+ 
+
+ align:start position:0%
+reaction but not the thermodynamics of
+the reaction you see that Delta e is not
+
+ align:start position:0%
+the reaction you see that Delta e is not
+ 
+
+ align:start position:0%
+the reaction you see that Delta e is not
+changing in this at all it's the same uh
+
+ align:start position:0%
+changing in this at all it's the same uh
+ 
+
+ align:start position:0%
+changing in this at all it's the same uh
+same energy difference between reactants
+
+ align:start position:0%
+same energy difference between reactants
+ 
+
+ align:start position:0%
+same energy difference between reactants
+and products so that term is is not
+
+ align:start position:0%
+and products so that term is is not
+ 
+
+ align:start position:0%
+and products so that term is is not
+changing and so uh also Delta Delta G uh
+
+ align:start position:0%
+changing and so uh also Delta Delta G uh
+ 
+
+ align:start position:0%
+changing and so uh also Delta Delta G uh
+would not change Delta G is a state
+
+ align:start position:0%
+would not change Delta G is a state
+ 
+
+ align:start position:0%
+would not change Delta G is a state
+function it's independent of the path so
+
+ align:start position:0%
+function it's independent of the path so
+ 
+
+ align:start position:0%
+function it's independent of the path so
+it is not going to change it doesn't
+
+ align:start position:0%
+it is not going to change it doesn't
+ 
+
+ align:start position:0%
+it is not going to change it doesn't
+care if it had to go over a higher
+
+ align:start position:0%
+care if it had to go over a higher
+ 
+
+ align:start position:0%
+care if it had to go over a higher
+barrier or a lower barrier it's
+
+ align:start position:0%
+barrier or a lower barrier it's
+ 
+
+ align:start position:0%
+barrier or a lower barrier it's
+independent of the path of the reaction
+
+ align:start position:0%
+independent of the path of the reaction
+ 
+
+ align:start position:0%
+independent of the path of the reaction
+it just uh cares about uh where it ends
+
+ align:start position:0%
+it just uh cares about uh where it ends
+ 
+
+ align:start position:0%
+it just uh cares about uh where it ends
+up so Delta G is not going to change
+
+ align:start position:0%
+up so Delta G is not going to change
+ 
+
+ align:start position:0%
+up so Delta G is not going to change
+with a catalyst uh therefore equilibrium
+
+ align:start position:0%
+with a catalyst uh therefore equilibrium
+ 
+
+ align:start position:0%
+with a catalyst uh therefore equilibrium
+constants not going to change with a
+
+ align:start position:0%
+constants not going to change with a
+ 
+
+ align:start position:0%
+constants not going to change with a
+catalyst so what you're changing is the
+
+ align:start position:0%
+catalyst so what you're changing is the
+ 
+
+ align:start position:0%
+catalyst so what you're changing is the
+activation energy barriers again in the
+
+ align:start position:0%
+activation energy barriers again in the
+ 
+
+ align:start position:0%
+activation energy barriers again in the
+Ford and the uh reverse reaction and
+
+ align:start position:0%
+Ford and the uh reverse reaction and
+ 
+
+ align:start position:0%
+Ford and the uh reverse reaction and
+you're speeding up then the
+
+ align:start position:0%
+you're speeding up then the
+ 
+
+ align:start position:0%
+you're speeding up then the
+reaction so um the uh the Chinese symbol
+
+ align:start position:0%
+reaction so um the uh the Chinese symbol
+ 
+
+ align:start position:0%
+reaction so um the uh the Chinese symbol
+for a catalyst is a marriage counselor
+
+ align:start position:0%
+for a catalyst is a marriage counselor
+ 
+
+ align:start position:0%
+for a catalyst is a marriage counselor
+so you can think about the catalyst as
+
+ align:start position:0%
+so you can think about the catalyst as
+ 
+
+ align:start position:0%
+so you can think about the catalyst as
+really facilitating those molecules
+
+ align:start position:0%
+really facilitating those molecules
+ 
+
+ align:start position:0%
+really facilitating those molecules
+coming together and having enough uh
+
+ align:start position:0%
+coming together and having enough uh
+ 
+
+ align:start position:0%
+coming together and having enough uh
+energy to react so say if they were at a
+
+ align:start position:0%
+energy to react so say if they were at a
+ 
+
+ align:start position:0%
+energy to react so say if they were at a
+lower temperature it would be harder to
+
+ align:start position:0%
+lower temperature it would be harder to
+ 
+
+ align:start position:0%
+lower temperature it would be harder to
+get over that activation energy barrier
+
+ align:start position:0%
+get over that activation energy barrier
+ 
+
+ align:start position:0%
+get over that activation energy barrier
+so a catalyst or or a molecule uh
+
+ align:start position:0%
+so a catalyst or or a molecule uh
+ 
+
+ align:start position:0%
+so a catalyst or or a molecule uh
+counselor will uh help lower that
+
+ align:start position:0%
+counselor will uh help lower that
+ 
+
+ align:start position:0%
+counselor will uh help lower that
+barrier and make it more more likely uh
+
+ align:start position:0%
+barrier and make it more more likely uh
+ 
+
+ align:start position:0%
+barrier and make it more more likely uh
+for these molecules to have that energy
+
+ align:start position:0%
+for these molecules to have that energy
+ 
+
+ align:start position:0%
+for these molecules to have that energy
+to react and go on to product and uh
+
+ align:start position:0%
+to react and go on to product and uh
+ 
+
+ align:start position:0%
+to react and go on to product and uh
+that'll uh speed up the reaction
+
+ align:start position:0%
+that'll uh speed up the reaction
+ 
+
+ align:start position:0%
+that'll uh speed up the reaction
+so we talked last time about if you're
+
+ align:start position:0%
+so we talked last time about if you're
+ 
+
+ align:start position:0%
+so we talked last time about if you're
+at high temperature or low temperature
+
+ align:start position:0%
+at high temperature or low temperature
+ 
+
+ align:start position:0%
+at high temperature or low temperature
+if you're at higher temperature more
+
+ align:start position:0%
+if you're at higher temperature more
+ 
+
+ align:start position:0%
+if you're at higher temperature more
+molecules can overcome the barrier lower
+
+ align:start position:0%
+molecules can overcome the barrier lower
+ 
+
+ align:start position:0%
+molecules can overcome the barrier lower
+molec lower uh temperature makes it
+
+ align:start position:0%
+molec lower uh temperature makes it
+ 
+
+ align:start position:0%
+molec lower uh temperature makes it
+harder to do that so a catalyst
+
+ align:start position:0%
+harder to do that so a catalyst
+ 
+
+ align:start position:0%
+harder to do that so a catalyst
+facilitates things by making the barrier
+
+ align:start position:0%
+facilitates things by making the barrier
+ 
+
+ align:start position:0%
+facilitates things by making the barrier
+lower so that's uh what a catalyst can
+
+ align:start position:0%
+lower so that's uh what a catalyst can
+ 
+
+ align:start position:0%
+lower so that's uh what a catalyst can
+do and in terms of your own thinking
+
+ align:start position:0%
+do and in terms of your own thinking
+ 
+
+ align:start position:0%
+do and in terms of your own thinking
+about things uh if you have big
+
+ align:start position:0%
+about things uh if you have big
+ 
+
+ align:start position:0%
+about things uh if you have big
+activation energy barriers for say
+
+ align:start position:0%
+activation energy barriers for say
+ 
+
+ align:start position:0%
+activation energy barriers for say
+studying for things or writing a final
+
+ align:start position:0%
+studying for things or writing a final
+ 
+
+ align:start position:0%
+studying for things or writing a final
+paper you can think of catalysts as
+
+ align:start position:0%
+paper you can think of catalysts as
+ 
+
+ align:start position:0%
+paper you can think of catalysts as
+being uh the due date being the next day
+
+ align:start position:0%
+being uh the due date being the next day
+ 
+
+ align:start position:0%
+being uh the due date being the next day
+uh so you've run out of time that can be
+
+ align:start position:0%
+uh so you've run out of time that can be
+ 
+
+ align:start position:0%
+uh so you've run out of time that can be
+a big Catalyst and lowering that barrier
+
+ align:start position:0%
+a big Catalyst and lowering that barrier
+ 
+
+ align:start position:0%
+a big Catalyst and lowering that barrier
+and helping you get started uh caffeine
+
+ align:start position:0%
+and helping you get started uh caffeine
+ 
+
+ align:start position:0%
+and helping you get started uh caffeine
+uh works for a lot of people in terms of
+
+ align:start position:0%
+uh works for a lot of people in terms of
+ 
+
+ align:start position:0%
+uh works for a lot of people in terms of
+uh getting over those activation energy
+
+ align:start position:0%
+uh getting over those activation energy
+ 
+
+ align:start position:0%
+uh getting over those activation energy
+barriers so you can think about in your
+
+ align:start position:0%
+barriers so you can think about in your
+ 
+
+ align:start position:0%
+barriers so you can think about in your
+own life what are good catalysts that uh
+
+ align:start position:0%
+own life what are good catalysts that uh
+ 
+
+ align:start position:0%
+own life what are good catalysts that uh
+that help you uh get over those
+
+ align:start position:0%
+that help you uh get over those
+ 
+
+ align:start position:0%
+that help you uh get over those
+barriers okay so an inhibitor then would
+
+ align:start position:0%
+barriers okay so an inhibitor then would
+ 
+
+ align:start position:0%
+barriers okay so an inhibitor then would
+be the opposite of a catalyst and uh it
+
+ align:start position:0%
+be the opposite of a catalyst and uh it
+ 
+
+ align:start position:0%
+be the opposite of a catalyst and uh it
+will it will slow the rate of a reaction
+
+ align:start position:0%
+will it will slow the rate of a reaction
+ 
+
+ align:start position:0%
+will it will slow the rate of a reaction
+and it can increase the activation
+
+ align:start position:0%
+and it can increase the activation
+ 
+
+ align:start position:0%
+and it can increase the activation
+energy barrier so an inhibitor is going
+
+ align:start position:0%
+energy barrier so an inhibitor is going
+ 
+
+ align:start position:0%
+energy barrier so an inhibitor is going
+to be the opposite and again uh we'll
+
+ align:start position:0%
+to be the opposite and again uh we'll
+ 
+
+ align:start position:0%
+to be the opposite and again uh we'll
+talk more about Inhibitors at the end of
+
+ align:start position:0%
+talk more about Inhibitors at the end of
+ 
+
+ align:start position:0%
+talk more about Inhibitors at the end of
+today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class so there are a couple types of
+
+ align:start position:0%
+class so there are a couple types of
+ 
+
+ align:start position:0%
+class so there are a couple types of
+catalysts so you can talk about a
+
+ align:start position:0%
+catalysts so you can talk about a
+ 
+
+ align:start position:0%
+catalysts so you can talk about a
+homogeneous catalyst and that is when
+
+ align:start position:0%
+homogeneous catalyst and that is when
+ 
+
+ align:start position:0%
+homogeneous catalyst and that is when
+the reactant and the catalyst are in the
+
+ align:start position:0%
+the reactant and the catalyst are in the
+ 
+
+ align:start position:0%
+the reactant and the catalyst are in the
+same phase so an example would be uh in
+
+ align:start position:0%
+same phase so an example would be uh in
+ 
+
+ align:start position:0%
+same phase so an example would be uh in
+the depletion of the ozone layer uh by
+
+ align:start position:0%
+the depletion of the ozone layer uh by
+ 
+
+ align:start position:0%
+the depletion of the ozone layer uh by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+chlorofluorocarbons those are all in the
+
+ align:start position:0%
+chlorofluorocarbons those are all in the
+ 
+
+ align:start position:0%
+chlorofluorocarbons those are all in the
+gas phase so uh this acts as a catalyst
+
+ align:start position:0%
+gas phase so uh this acts as a catalyst
+ 
+
+ align:start position:0%
+gas phase so uh this acts as a catalyst
+it catalyzes the depletion of ozone
+
+ align:start position:0%
+it catalyzes the depletion of ozone
+ 
+
+ align:start position:0%
+it catalyzes the depletion of ozone
+which is why people uh have been very
+
+ align:start position:0%
+which is why people uh have been very
+ 
+
+ align:start position:0%
+which is why people uh have been very
+concerned about uh uh spray cans and
+
+ align:start position:0%
+concerned about uh uh spray cans and
+ 
+
+ align:start position:0%
+concerned about uh uh spray cans and
+other things that release uh these uh
+
+ align:start position:0%
+other things that release uh these uh
+ 
+
+ align:start position:0%
+other things that release uh these uh
+these molecules into the environment you
+
+ align:start position:0%
+these molecules into the environment you
+ 
+
+ align:start position:0%
+these molecules into the environment you
+can also have heterogeneous catalyst so
+
+ align:start position:0%
+can also have heterogeneous catalyst so
+ 
+
+ align:start position:0%
+can also have heterogeneous catalyst so
+something that's in a different phase as
+
+ align:start position:0%
+something that's in a different phase as
+ 
+
+ align:start position:0%
+something that's in a different phase as
+the reacting
+
+ align:start position:0%
+the reacting
+ 
+
+ align:start position:0%
+the reacting
+molecules and we're all familiar with
+
+ align:start position:0%
+molecules and we're all familiar with
+ 
+
+ align:start position:0%
+molecules and we're all familiar with
+examples of this like a catalytic
+
+ align:start position:0%
+examples of this like a catalytic
+ 
+
+ align:start position:0%
+examples of this like a catalytic
+converter so uh in this case you might
+
+ align:start position:0%
+converter so uh in this case you might
+ 
+
+ align:start position:0%
+converter so uh in this case you might
+have your Catalyst would be solid Metals
+
+ align:start position:0%
+have your Catalyst would be solid Metals
+ 
+
+ align:start position:0%
+have your Catalyst would be solid Metals
+uh platinum plaum rodium and they will
+
+ align:start position:0%
+uh platinum plaum rodium and they will
+ 
+
+ align:start position:0%
+uh platinum plaum rodium and they will
+help uh catalyze oxidation of
+
+ align:start position:0%
+help uh catalyze oxidation of
+ 
+
+ align:start position:0%
+help uh catalyze oxidation of
+hydrocarbon Co gases um reduction of
+
+ align:start position:0%
+hydrocarbon Co gases um reduction of
+ 
+
+ align:start position:0%
+hydrocarbon Co gases um reduction of
+nitrogen oxides so to reduce pollution
+
+ align:start position:0%
+nitrogen oxides so to reduce pollution
+ 
+
+ align:start position:0%
+nitrogen oxides so to reduce pollution
+so the reactant molecules are gas passes
+
+ align:start position:0%
+so the reactant molecules are gas passes
+ 
+
+ align:start position:0%
+so the reactant molecules are gas passes
+but the catalyst is a metal so it's
+
+ align:start position:0%
+but the catalyst is a metal so it's
+ 
+
+ align:start position:0%
+but the catalyst is a metal so it's
+heterogeneous it's in a different phase
+
+ align:start position:0%
+heterogeneous it's in a different phase
+ 
+
+ align:start position:0%
+heterogeneous it's in a different phase
+uh so these two
+
+ align:start position:0%
+uh so these two
+ 
+
+ align:start position:0%
+uh so these two
+examples so I'll just show you a little
+
+ align:start position:0%
+examples so I'll just show you a little
+ 
+
+ align:start position:0%
+examples so I'll just show you a little
+movie of heterogeneous uh
+
+ align:start position:0%
+movie of heterogeneous uh
+ 
+
+ align:start position:0%
+movie of heterogeneous uh
+catalysis do you
+
+ align:start position:0%
+catalysis do you
+ 
+
+ align:start position:0%
+catalysis do you
+want yes could some of the Tas help the
+
+ align:start position:0%
+want yes could some of the Tas help the
+ 
+
+ align:start position:0%
+want yes could some of the Tas help the
+lecture notes are
+
+ align:start position:0%
+lecture notes are
+ 
+
+ align:start position:0%
+lecture notes are
+here so uh this movie is not in the
+
+ align:start position:0%
+here so uh this movie is not in the
+ 
+
+ align:start position:0%
+here so uh this movie is not in the
+lecture notes but um anyway so we have
+
+ align:start position:0%
+lecture notes but um anyway so we have
+ 
+
+ align:start position:0%
+lecture notes but um anyway so we have
+here a metal surface in blue
+
+ align:start position:0%
+here a metal surface in blue
+ 
+
+ align:start position:0%
+here a metal surface in blue
+and the metal is acting as a catalyst
+
+ align:start position:0%
+and the metal is acting as a catalyst
+ 
+
+ align:start position:0%
+and the metal is acting as a catalyst
+and uh in Gray we have these two dots
+
+ align:start position:0%
+and uh in Gray we have these two dots
+ 
+
+ align:start position:0%
+and uh in Gray we have these two dots
+those are hydrogens so what the metal
+
+ align:start position:0%
+those are hydrogens so what the metal
+ 
+
+ align:start position:0%
+those are hydrogens so what the metal
+did was helped to facilitate the
+
+ align:start position:0%
+did was helped to facilitate the
+ 
+
+ align:start position:0%
+did was helped to facilitate the
+dissociation of
+
+ align:start position:0%
+dissociation of
+ 
+
+ align:start position:0%
+dissociation of
+H2 so H2 which is not so reactive has
+
+ align:start position:0%
+H2 so H2 which is not so reactive has
+ 
+
+ align:start position:0%
+H2 so H2 which is not so reactive has
+been dissociated and you have uh broken
+
+ align:start position:0%
+been dissociated and you have uh broken
+ 
+
+ align:start position:0%
+been dissociated and you have uh broken
+into the two separate hydrogens and now
+
+ align:start position:0%
+into the two separate hydrogens and now
+ 
+
+ align:start position:0%
+into the two separate hydrogens and now
+if we bring in um a
+
+ align:start position:0%
+if we bring in um a
+ 
+
+ align:start position:0%
+if we bring in um a
+uh molecule of
+
+ align:start position:0%
+uh molecule of
+ 
+
+ align:start position:0%
+uh molecule of
+um of ethane then it will react with
+
+ align:start position:0%
+um of ethane then it will react with
+ 
+
+ align:start position:0%
+um of ethane then it will react with
+um react with this so you have a
+
+ align:start position:0%
+um react with this so you have a
+ 
+
+ align:start position:0%
+um react with this so you have a
+molecule come in in a different phase
+
+ align:start position:0%
+molecule come in in a different phase
+ 
+
+ align:start position:0%
+molecule come in in a different phase
+and see how the hydrogens just kind of
+
+ align:start position:0%
+and see how the hydrogens just kind of
+ 
+
+ align:start position:0%
+and see how the hydrogens just kind of
+Bop right on uh to the molecule so the
+
+ align:start position:0%
+Bop right on uh to the molecule so the
+ 
+
+ align:start position:0%
+Bop right on uh to the molecule so the
+metal surface was acting as a catalyst
+
+ align:start position:0%
+metal surface was acting as a catalyst
+ 
+
+ align:start position:0%
+metal surface was acting as a catalyst
+making the H2 gas I'll just do that one
+
+ align:start position:0%
+making the H2 gas I'll just do that one
+ 
+
+ align:start position:0%
+making the H2 gas I'll just do that one
+more time the H2 gas more reactive by
+
+ align:start position:0%
+more time the H2 gas more reactive by
+ 
+
+ align:start position:0%
+more time the H2 gas more reactive by
+having a dissociate first now they're
+
+ align:start position:0%
+having a dissociate first now they're
+ 
+
+ align:start position:0%
+having a dissociate first now they're
+sitting on the metal surface and the
+
+ align:start position:0%
+sitting on the metal surface and the
+ 
+
+ align:start position:0%
+sitting on the metal surface and the
+reaction uh is quite a bit faster
+
+ align:start position:0%
+reaction uh is quite a bit faster
+ 
+
+ align:start position:0%
+reaction uh is quite a bit faster
+so that would be an example of the
+
+ align:start position:0%
+so that would be an example of the
+ 
+
+ align:start position:0%
+so that would be an example of the
+heterogeneous uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catalysis all right so now I'm going to
+
+ align:start position:0%
+catalysis all right so now I'm going to
+ 
+
+ align:start position:0%
+catalysis all right so now I'm going to
+talk about my favorite kind of
+
+ align:start position:0%
+talk about my favorite kind of
+ 
+
+ align:start position:0%
+talk about my favorite kind of
+catalyst so catalysts of life or
+
+ align:start position:0%
+catalyst so catalysts of life or
+ 
+
+ align:start position:0%
+catalyst so catalysts of life or
+enzymes so enzymes are catalysts and if
+
+ align:start position:0%
+enzymes so enzymes are catalysts and if
+ 
+
+ align:start position:0%
+enzymes so enzymes are catalysts and if
+you're a biochemist enzymes are your
+
+ align:start position:0%
+you're a biochemist enzymes are your
+ 
+
+ align:start position:0%
+you're a biochemist enzymes are your
+favorite kind of
+
+ align:start position:0%
+favorite kind of
+ 
+
+ align:start position:0%
+favorite kind of
+catalyst so an enzyme uh is usually a
+
+ align:start position:0%
+catalyst so an enzyme uh is usually a
+ 
+
+ align:start position:0%
+catalyst so an enzyme uh is usually a
+protein there are some examples of uh
+
+ align:start position:0%
+protein there are some examples of uh
+ 
+
+ align:start position:0%
+protein there are some examples of uh
+RNA catalyzing reactions but most
+
+ align:start position:0%
+RNA catalyzing reactions but most
+ 
+
+ align:start position:0%
+RNA catalyzing reactions but most
+enzymes are made up of
+
+ align:start position:0%
+enzymes are made up of
+ 
+
+ align:start position:0%
+enzymes are made up of
+protein and uh they're usually fairly
+
+ align:start position:0%
+protein and uh they're usually fairly
+ 
+
+ align:start position:0%
+protein and uh they're usually fairly
+large so TP the sort of smallest
+
+ align:start position:0%
+large so TP the sort of smallest
+ 
+
+ align:start position:0%
+large so TP the sort of smallest
+molecular weight you might see would be
+
+ align:start position:0%
+molecular weight you might see would be
+ 
+
+ align:start position:0%
+molecular weight you might see would be
+about uh 20,000 uh grams per mole and
+
+ align:start position:0%
+about uh 20,000 uh grams per mole and
+ 
+
+ align:start position:0%
+about uh 20,000 uh grams per mole and
+again uh some people on exam 3 I'll just
+
+ align:start position:0%
+again uh some people on exam 3 I'll just
+ 
+
+ align:start position:0%
+again uh some people on exam 3 I'll just
+point this out when I asked for units of
+
+ align:start position:0%
+point this out when I asked for units of
+ 
+
+ align:start position:0%
+point this out when I asked for units of
+molecular weight um units of molecular
+
+ align:start position:0%
+molecular weight um units of molecular
+ 
+
+ align:start position:0%
+molecular weight um units of molecular
+weight grams per mole so uh some people
+
+ align:start position:0%
+weight grams per mole so uh some people
+ 
+
+ align:start position:0%
+weight grams per mole so uh some people
+uh didn't have the right units for that
+
+ align:start position:0%
+uh didn't have the right units for that
+ 
+
+ align:start position:0%
+uh didn't have the right units for that
+uh and that's you know the same uh
+
+ align:start position:0%
+uh and that's you know the same uh
+ 
+
+ align:start position:0%
+uh and that's you know the same uh
+molecular weight if you're talking about
+
+ align:start position:0%
+molecular weight if you're talking about
+ 
+
+ align:start position:0%
+molecular weight if you're talking about
+a weak acid or you're talking about an
+
+ align:start position:0%
+a weak acid or you're talking about an
+ 
+
+ align:start position:0%
+a weak acid or you're talking about an
+enzyme uh same units but different size
+
+ align:start position:0%
+enzyme uh same units but different size
+ 
+
+ align:start position:0%
+enzyme uh same units but different size
+so these enzymes are are capable of
+
+ align:start position:0%
+so these enzymes are are capable of
+ 
+
+ align:start position:0%
+so these enzymes are are capable of
+catalyzing a wide variety of different
+
+ align:start position:0%
+catalyzing a wide variety of different
+ 
+
+ align:start position:0%
+catalyzing a wide variety of different
+reactions in your
+
+ align:start position:0%
+reactions in your
+ 
+
+ align:start position:0%
+reactions in your
+body
+
+ align:start position:0%
+body
+ 
+
+ align:start position:0%
+body
+so uh proteins or enzymes are made up of
+
+ align:start position:0%
+so uh proteins or enzymes are made up of
+ 
+
+ align:start position:0%
+so uh proteins or enzymes are made up of
+amino acids and and amino acids have
+
+ align:start position:0%
+amino acids and and amino acids have
+ 
+
+ align:start position:0%
+amino acids and and amino acids have
+carbon nitrogen oxygen sulfur uh in
+
+ align:start position:0%
+carbon nitrogen oxygen sulfur uh in
+ 
+
+ align:start position:0%
+carbon nitrogen oxygen sulfur uh in
+them and uh I'll just um I'll I'll share
+
+ align:start position:0%
+them and uh I'll just um I'll I'll share
+ 
+
+ align:start position:0%
+them and uh I'll just um I'll I'll share
+with you a little recent story we have a
+
+ align:start position:0%
+with you a little recent story we have a
+ 
+
+ align:start position:0%
+with you a little recent story we have a
+collaborator who's in France and they
+
+ align:start position:0%
+collaborator who's in France and they
+ 
+
+ align:start position:0%
+collaborator who's in France and they
+tried to send us uh some protein uh to
+
+ align:start position:0%
+tried to send us uh some protein uh to
+ 
+
+ align:start position:0%
+tried to send us uh some protein uh to
+do uh crystallization
+
+ align:start position:0%
+do uh crystallization
+ 
+
+ align:start position:0%
+do uh crystallization
+experiments and so uh we got I got a
+
+ align:start position:0%
+experiments and so uh we got I got a
+ 
+
+ align:start position:0%
+experiments and so uh we got I got a
+call from um customs in uh the so there
+
+ align:start position:0%
+call from um customs in uh the so there
+ 
+
+ align:start position:0%
+call from um customs in uh the so there
+was a doer with this protein sitting in
+
+ align:start position:0%
+was a doer with this protein sitting in
+ 
+
+ align:start position:0%
+was a doer with this protein sitting in
+uh in newe Jersey and Customs was
+
+ align:start position:0%
+uh in newe Jersey and Customs was
+ 
+
+ align:start position:0%
+uh in newe Jersey and Customs was
+calling me and they said they couldn't
+
+ align:start position:0%
+calling me and they said they couldn't
+ 
+
+ align:start position:0%
+calling me and they said they couldn't
+release this material from from Customs
+
+ align:start position:0%
+release this material from from Customs
+ 
+
+ align:start position:0%
+release this material from from Customs
+uh without more information and they
+
+ align:start position:0%
+uh without more information and they
+ 
+
+ align:start position:0%
+uh without more information and they
+said it says that here the doer contains
+
+ align:start position:0%
+said it says that here the doer contains
+ 
+
+ align:start position:0%
+said it says that here the doer contains
+protein and we need to know what that
+
+ align:start position:0%
+protein and we need to know what that
+ 
+
+ align:start position:0%
+protein and we need to know what that
+protein is made of and we also needed to
+
+ align:start position:0%
+protein is made of and we also needed to
+ 
+
+ align:start position:0%
+protein is made of and we also needed to
+know who had manufactured the protein
+
+ align:start position:0%
+know who had manufactured the protein
+ 
+
+ align:start position:0%
+know who had manufactured the protein
+and uh so um now you can all answer the
+
+ align:start position:0%
+and uh so um now you can all answer the
+ 
+
+ align:start position:0%
+and uh so um now you can all answer the
+question if Customs call proteins are
+
+ align:start position:0%
+question if Customs call proteins are
+ 
+
+ align:start position:0%
+question if Customs call proteins are
+made up of amino acids I'm not really
+
+ align:start position:0%
+made up of amino acids I'm not really
+ 
+
+ align:start position:0%
+made up of amino acids I'm not really
+sure what they were getting at here
+
+ align:start position:0%
+sure what they were getting at here
+ 
+
+ align:start position:0%
+sure what they were getting at here
+um and uh in terms of who had
+
+ align:start position:0%
+um and uh in terms of who had
+ 
+
+ align:start position:0%
+um and uh in terms of who had
+manufactured it it was ecoli bacteria um
+
+ align:start position:0%
+manufactured it it was ecoli bacteria um
+ 
+
+ align:start position:0%
+manufactured it it was ecoli bacteria um
+we were actually afraid of saying that
+
+ align:start position:0%
+we were actually afraid of saying that
+ 
+
+ align:start position:0%
+we were actually afraid of saying that
+because there are strains of ecoli that
+
+ align:start position:0%
+because there are strains of ecoli that
+ 
+
+ align:start position:0%
+because there are strains of ecoli that
+seem to every once in a while uh make
+
+ align:start position:0%
+seem to every once in a while uh make
+ 
+
+ align:start position:0%
+seem to every once in a while uh make
+people very sick at McDonald's and White
+
+ align:start position:0%
+people very sick at McDonald's and White
+ 
+
+ align:start position:0%
+people very sick at McDonald's and White
+Castle and places like that so ecoli has
+
+ align:start position:0%
+Castle and places like that so ecoli has
+ 
+
+ align:start position:0%
+Castle and places like that so ecoli has
+now become a sort of a dangerous uh
+
+ align:start position:0%
+now become a sort of a dangerous uh
+ 
+
+ align:start position:0%
+now become a sort of a dangerous uh
+bacteria so uh we said that it was
+
+ align:start position:0%
+bacteria so uh we said that it was
+ 
+
+ align:start position:0%
+bacteria so uh we said that it was
+protein was made up of amino acids like
+
+ align:start position:0%
+protein was made up of amino acids like
+ 
+
+ align:start position:0%
+protein was made up of amino acids like
+you buy at the health food store and
+
+ align:start position:0%
+you buy at the health food store and
+ 
+
+ align:start position:0%
+you buy at the health food store and
+that the uh manuf ufacturer was quote
+
+ align:start position:0%
+that the uh manuf ufacturer was quote
+ 
+
+ align:start position:0%
+that the uh manuf ufacturer was quote
+natural sources so uh the protein was
+
+ align:start position:0%
+natural sources so uh the protein was
+ 
+
+ align:start position:0%
+natural sources so uh the protein was
+released to us but apparently uh the
+
+ align:start position:0%
+released to us but apparently uh the
+ 
+
+ align:start position:0%
+released to us but apparently uh the
+person at Customs had not had Much
+
+ align:start position:0%
+person at Customs had not had Much
+ 
+
+ align:start position:0%
+person at Customs had not had Much
+Chemistry or biochemistry in their
+
+ align:start position:0%
+Chemistry or biochemistry in their
+ 
+
+ align:start position:0%
+Chemistry or biochemistry in their
+background all right so proteins are
+
+ align:start position:0%
+background all right so proteins are
+ 
+
+ align:start position:0%
+background all right so proteins are
+made up of these amino acids and here's
+
+ align:start position:0%
+made up of these amino acids and here's
+ 
+
+ align:start position:0%
+made up of these amino acids and here's
+an amino acid and Professor Sarah talked
+
+ align:start position:0%
+an amino acid and Professor Sarah talked
+ 
+
+ align:start position:0%
+an amino acid and Professor Sarah talked
+about this before in terms of Bad Hair
+
+ align:start position:0%
+about this before in terms of Bad Hair
+ 
+
+ align:start position:0%
+about this before in terms of Bad Hair
+Days um so an amino acid uh here we have
+
+ align:start position:0%
+Days um so an amino acid uh here we have
+ 
+
+ align:start position:0%
+Days um so an amino acid uh here we have
+an amino group a carboxilic group and a
+
+ align:start position:0%
+an amino group a carboxilic group and a
+ 
+
+ align:start position:0%
+an amino group a carboxilic group and a
+car which is called the alpha carbon
+
+ align:start position:0%
+car which is called the alpha carbon
+ 
+
+ align:start position:0%
+car which is called the alpha carbon
+it's sitting in the middle and there's a
+
+ align:start position:0%
+it's sitting in the middle and there's a
+ 
+
+ align:start position:0%
+it's sitting in the middle and there's a
+group R and that can be 20 different
+
+ align:start position:0%
+group R and that can be 20 different
+ 
+
+ align:start position:0%
+group R and that can be 20 different
+kinds of side chains that make up the 20
+
+ align:start position:0%
+kinds of side chains that make up the 20
+ 
+
+ align:start position:0%
+kinds of side chains that make up the 20
+amino acids that are commonly found in
+
+ align:start position:0%
+amino acids that are commonly found in
+ 
+
+ align:start position:0%
+amino acids that are commonly found in
+proteins and so one amino acid gets
+
+ align:start position:0%
+proteins and so one amino acid gets
+ 
+
+ align:start position:0%
+proteins and so one amino acid gets
+linked to another amino acid uh by
+
+ align:start position:0%
+linked to another amino acid uh by
+ 
+
+ align:start position:0%
+linked to another amino acid uh by
+through What's called the peptide bond
+
+ align:start position:0%
+through What's called the peptide bond
+ 
+
+ align:start position:0%
+through What's called the peptide bond
+shown here and so here we have our first
+
+ align:start position:0%
+shown here and so here we have our first
+ 
+
+ align:start position:0%
+shown here and so here we have our first
+amino acid and our second and again you
+
+ align:start position:0%
+amino acid and our second and again you
+ 
+
+ align:start position:0%
+amino acid and our second and again you
+can have hundreds and hundreds of these
+
+ align:start position:0%
+can have hundreds and hundreds of these
+ 
+
+ align:start position:0%
+can have hundreds and hundreds of these
+amino acids connected to each other and
+
+ align:start position:0%
+amino acids connected to each other and
+ 
+
+ align:start position:0%
+amino acids connected to each other and
+then they fold up into into some kind of
+
+ align:start position:0%
+then they fold up into into some kind of
+ 
+
+ align:start position:0%
+then they fold up into into some kind of
+compact structure for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enzyme so in this particular case there
+
+ align:start position:0%
+enzyme so in this particular case there
+ 
+
+ align:start position:0%
+enzyme so in this particular case there
+are four different chains of peptides
+
+ align:start position:0%
+are four different chains of peptides
+ 
+
+ align:start position:0%
+are four different chains of peptides
+and each chain has 198 amino acids so
+
+ align:start position:0%
+and each chain has 198 amino acids so
+ 
+
+ align:start position:0%
+and each chain has 198 amino acids so
+each chain in this picture is shown in a
+
+ align:start position:0%
+each chain in this picture is shown in a
+ 
+
+ align:start position:0%
+each chain in this picture is shown in a
+different color uh yellow and green and
+
+ align:start position:0%
+different color uh yellow and green and
+ 
+
+ align:start position:0%
+different color uh yellow and green and
+red and blue and uh in these diagrams
+
+ align:start position:0%
+red and blue and uh in these diagrams
+ 
+
+ align:start position:0%
+red and blue and uh in these diagrams
+they can't they don't show all the atoms
+
+ align:start position:0%
+they can't they don't show all the atoms
+ 
+
+ align:start position:0%
+they can't they don't show all the atoms
+because that would just kind of be a big
+
+ align:start position:0%
+because that would just kind of be a big
+ 
+
+ align:start position:0%
+because that would just kind of be a big
+mess if you showed all the atoms but
+
+ align:start position:0%
+mess if you showed all the atoms but
+ 
+
+ align:start position:0%
+mess if you showed all the atoms but
+instead a ribbon is drawn through the
+
+ align:start position:0%
+instead a ribbon is drawn through the
+ 
+
+ align:start position:0%
+instead a ribbon is drawn through the
+positions of the Alpac carbons of every
+
+ align:start position:0%
+positions of the Alpac carbons of every
+ 
+
+ align:start position:0%
+positions of the Alpac carbons of every
+amino acid and so these uh kind of
+
+ align:start position:0%
+amino acid and so these uh kind of
+ 
+
+ align:start position:0%
+amino acid and so these uh kind of
+squirly things squiggly things here are
+
+ align:start position:0%
+squirly things squiggly things here are
+ 
+
+ align:start position:0%
+squirly things squiggly things here are
+alpha helices which is one type of a
+
+ align:start position:0%
+alpha helices which is one type of a
+ 
+
+ align:start position:0%
+alpha helices which is one type of a
+secondary structure and you'll learn
+
+ align:start position:0%
+secondary structure and you'll learn
+ 
+
+ align:start position:0%
+secondary structure and you'll learn
+about that in 507 or 705 and uh arrows
+
+ align:start position:0%
+about that in 507 or 705 and uh arrows
+ 
+
+ align:start position:0%
+about that in 507 or 705 and uh arrows
+are often indicated what's called beta
+
+ align:start position:0%
+are often indicated what's called beta
+ 
+
+ align:start position:0%
+are often indicated what's called beta
+sheets extended regions of the uh amino
+
+ align:start position:0%
+sheets extended regions of the uh amino
+ 
+
+ align:start position:0%
+sheets extended regions of the uh amino
+acids and so this kind of gives you a
+
+ align:start position:0%
+acids and so this kind of gives you a
+ 
+
+ align:start position:0%
+acids and so this kind of gives you a
+general sense of what we call the fold
+
+ align:start position:0%
+general sense of what we call the fold
+ 
+
+ align:start position:0%
+general sense of what we call the fold
+of the protein uh in these diagrams and
+
+ align:start position:0%
+of the protein uh in these diagrams and
+ 
+
+ align:start position:0%
+of the protein uh in these diagrams and
+so this gives you a sense of how big
+
+ align:start position:0%
+so this gives you a sense of how big
+ 
+
+ align:start position:0%
+so this gives you a sense of how big
+this molecule actually is and we report
+
+ align:start position:0%
+this molecule actually is and we report
+ 
+
+ align:start position:0%
+this molecule actually is and we report
+things in angstroms uh typically because
+
+ align:start position:0%
+things in angstroms uh typically because
+ 
+
+ align:start position:0%
+things in angstroms uh typically because
+that's a good a good unit of measure um
+
+ align:start position:0%
+that's a good a good unit of measure um
+ 
+
+ align:start position:0%
+that's a good a good unit of measure um
+that helps tell you about how far apart
+
+ align:start position:0%
+that helps tell you about how far apart
+ 
+
+ align:start position:0%
+that helps tell you about how far apart
+the atoms are in structures so what is
+
+ align:start position:0%
+the atoms are in structures so what is
+ 
+
+ align:start position:0%
+the atoms are in structures so what is
+this particular enzyme well this
+
+ align:start position:0%
+this particular enzyme well this
+ 
+
+ align:start position:0%
+this particular enzyme well this
+particular enzyme uh does uh is involved
+
+ align:start position:0%
+particular enzyme uh does uh is involved
+ 
+
+ align:start position:0%
+particular enzyme uh does uh is involved
+in catalyzing the last step in the
+
+ align:start position:0%
+in catalyzing the last step in the
+ 
+
+ align:start position:0%
+in catalyzing the last step in the
+biosynthesis of an antibiotic
+
+ align:start position:0%
+biosynthesis of an antibiotic
+ 
+
+ align:start position:0%
+biosynthesis of an antibiotic
+phosphomycin and so this is the uh
+
+ align:start position:0%
+phosphomycin and so this is the uh
+ 
+
+ align:start position:0%
+phosphomycin and so this is the uh
+reactant or uh substrate and this is the
+
+ align:start position:0%
+reactant or uh substrate and this is the
+ 
+
+ align:start position:0%
+reactant or uh substrate and this is the
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+phosphomycin so what phosphomycin does
+
+ align:start position:0%
+phosphomycin so what phosphomycin does
+ 
+
+ align:start position:0%
+phosphomycin so what phosphomycin does
+is it inhibits cell wall biosynthesis of
+
+ align:start position:0%
+is it inhibits cell wall biosynthesis of
+ 
+
+ align:start position:0%
+is it inhibits cell wall biosynthesis of
+bacteria and it forms a calent adduct
+
+ align:start position:0%
+bacteria and it forms a calent adduct
+ 
+
+ align:start position:0%
+bacteria and it forms a calent adduct
+with amino acid in the active site of uh
+
+ align:start position:0%
+with amino acid in the active site of uh
+ 
+
+ align:start position:0%
+with amino acid in the active site of uh
+one of the important enzymes in cell
+
+ align:start position:0%
+one of the important enzymes in cell
+ 
+
+ align:start position:0%
+one of the important enzymes in cell
+wall biosynthesis and so a lot of
+
+ align:start position:0%
+wall biosynthesis and so a lot of
+ 
+
+ align:start position:0%
+wall biosynthesis and so a lot of
+antibiotics Target cell wall
+
+ align:start position:0%
+antibiotics Target cell wall
+ 
+
+ align:start position:0%
+antibiotics Target cell wall
+biosynthesis so recently I mean it was
+
+ align:start position:0%
+biosynthesis so recently I mean it was
+ 
+
+ align:start position:0%
+biosynthesis so recently I mean it was
+first approved to treat um mostly like
+
+ align:start position:0%
+first approved to treat um mostly like
+ 
+
+ align:start position:0%
+first approved to treat um mostly like
+bladder infections and sort of more
+
+ align:start position:0%
+bladder infections and sort of more
+ 
+
+ align:start position:0%
+bladder infections and sort of more
+minor type of infections but recently
+
+ align:start position:0%
+minor type of infections but recently
+ 
+
+ align:start position:0%
+minor type of infections but recently
+they found that it works against um
+
+ align:start position:0%
+they found that it works against um
+ 
+
+ align:start position:0%
+they found that it works against um
+strains of of staff orus infection which
+
+ align:start position:0%
+strains of of staff orus infection which
+ 
+
+ align:start position:0%
+strains of of staff orus infection which
+is pretty serious um there's several
+
+ align:start position:0%
+is pretty serious um there's several
+ 
+
+ align:start position:0%
+is pretty serious um there's several
+strains of of staff infections now that
+
+ align:start position:0%
+strains of of staff infections now that
+ 
+
+ align:start position:0%
+strains of of staff infections now that
+are resistant to some of the powerful
+
+ align:start position:0%
+are resistant to some of the powerful
+ 
+
+ align:start position:0%
+are resistant to some of the powerful
+kinds of antibiotics that have been used
+
+ align:start position:0%
+kinds of antibiotics that have been used
+ 
+
+ align:start position:0%
+kinds of antibiotics that have been used
+before and so they're looking for new
+
+ align:start position:0%
+before and so they're looking for new
+ 
+
+ align:start position:0%
+before and so they're looking for new
+antibiotics that might that might be
+
+ align:start position:0%
+antibiotics that might that might be
+ 
+
+ align:start position:0%
+antibiotics that might that might be
+successful in treating those infections
+
+ align:start position:0%
+successful in treating those infections
+ 
+
+ align:start position:0%
+successful in treating those infections
+so antibiotic resistance of certain
+
+ align:start position:0%
+so antibiotic resistance of certain
+ 
+
+ align:start position:0%
+so antibiotic resistance of certain
+kinds of uh of uh bacteria has become
+
+ align:start position:0%
+kinds of uh of uh bacteria has become
+ 
+
+ align:start position:0%
+kinds of uh of uh bacteria has become
+really enormous problem and it's just
+
+ align:start position:0%
+really enormous problem and it's just
+ 
+
+ align:start position:0%
+really enormous problem and it's just
+getting worse I always like to ask a
+
+ align:start position:0%
+getting worse I always like to ask a
+ 
+
+ align:start position:0%
+getting worse I always like to ask a
+crowd like this um how many have taken
+
+ align:start position:0%
+crowd like this um how many have taken
+ 
+
+ align:start position:0%
+crowd like this um how many have taken
+antibiotics just zero times in their
+
+ align:start position:0%
+antibiotics just zero times in their
+ 
+
+ align:start position:0%
+antibiotics just zero times in their
+life first never taking
+
+ align:start position:0%
+life first never taking
+ 
+
+ align:start position:0%
+life first never taking
+antibiotics okay I don't see anybody how
+
+ align:start position:0%
+antibiotics okay I don't see anybody how
+ 
+
+ align:start position:0%
+antibiotics okay I don't see anybody how
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+once like three people
+
+ align:start position:0%
+once like three people
+ 
+
+ align:start position:0%
+once like three people
+twice a few more three times
+
+ align:start position:0%
+twice a few more three times
+ 
+
+ align:start position:0%
+twice a few more three times
+you probably don't remember uh say you
+
+ align:start position:0%
+you probably don't remember uh say you
+ 
+
+ align:start position:0%
+you probably don't remember uh say you
+know around maybe five or more or
+
+ align:start position:0%
+know around maybe five or more or
+ 
+
+ align:start position:0%
+know around maybe five or more or
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+that okay so uh you can see from looking
+
+ align:start position:0%
+that okay so uh you can see from looking
+ 
+
+ align:start position:0%
+that okay so uh you can see from looking
+around why this is a problem so uh
+
+ align:start position:0%
+around why this is a problem so uh
+ 
+
+ align:start position:0%
+around why this is a problem so uh
+bacteria they're they're they're clever
+
+ align:start position:0%
+bacteria they're they're they're clever
+ 
+
+ align:start position:0%
+bacteria they're they're they're clever
+uh they figure out try to get around
+
+ align:start position:0%
+uh they figure out try to get around
+ 
+
+ align:start position:0%
+uh they figure out try to get around
+ways if they can they want to survive so
+
+ align:start position:0%
+ways if they can they want to survive so
+ 
+
+ align:start position:0%
+ways if they can they want to survive so
+there's some nice natural selection
+
+ align:start position:0%
+there's some nice natural selection
+ 
+
+ align:start position:0%
+there's some nice natural selection
+going on and they're actually resistant
+
+ align:start position:0%
+going on and they're actually resistant
+ 
+
+ align:start position:0%
+going on and they're actually resistant
+strains to phosph mey as well as well
+
+ align:start position:0%
+strains to phosph mey as well as well
+ 
+
+ align:start position:0%
+strains to phosph mey as well as well
+and what happens in that case is I said
+
+ align:start position:0%
+and what happens in that case is I said
+ 
+
+ align:start position:0%
+and what happens in that case is I said
+that it works by becoming attached to
+
+ align:start position:0%
+that it works by becoming attached to
+ 
+
+ align:start position:0%
+that it works by becoming attached to
+amino acid and then the enzyme is dead
+
+ align:start position:0%
+amino acid and then the enzyme is dead
+ 
+
+ align:start position:0%
+amino acid and then the enzyme is dead
+but if that amino acid is mutated it's a
+
+ align:start position:0%
+but if that amino acid is mutated it's a
+ 
+
+ align:start position:0%
+but if that amino acid is mutated it's a
+cysteine if it mutates to an aspartic
+
+ align:start position:0%
+cysteine if it mutates to an aspartic
+ 
+
+ align:start position:0%
+cysteine if it mutates to an aspartic
+acid then it can no longer be inhibited
+
+ align:start position:0%
+acid then it can no longer be inhibited
+ 
+
+ align:start position:0%
+acid then it can no longer be inhibited
+by this and it still works it's not as
+
+ align:start position:0%
+by this and it still works it's not as
+ 
+
+ align:start position:0%
+by this and it still works it's not as
+good an enzyme but it still works so if
+
+ align:start position:0%
+good an enzyme but it still works so if
+ 
+
+ align:start position:0%
+good an enzyme but it still works so if
+there's pressure applied natural
+
+ align:start position:0%
+there's pressure applied natural
+ 
+
+ align:start position:0%
+there's pressure applied natural
+selection die or mutate uh a lot of
+
+ align:start position:0%
+selection die or mutate uh a lot of
+ 
+
+ align:start position:0%
+selection die or mutate uh a lot of
+things will be very happy to mutate if
+
+ align:start position:0%
+things will be very happy to mutate if
+ 
+
+ align:start position:0%
+things will be very happy to mutate if
+they can and some of the antibiotics if
+
+ align:start position:0%
+they can and some of the antibiotics if
+ 
+
+ align:start position:0%
+they can and some of the antibiotics if
+it mutates it only just one amino acid
+
+ align:start position:0%
+it mutates it only just one amino acid
+ 
+
+ align:start position:0%
+it mutates it only just one amino acid
+changes all of a sudden uh there's a
+
+ align:start position:0%
+changes all of a sudden uh there's a
+ 
+
+ align:start position:0%
+changes all of a sudden uh there's a
+resistance going on so the more times
+
+ align:start position:0%
+resistance going on so the more times
+ 
+
+ align:start position:0%
+resistance going on so the more times
+that uh bacteria are exposed to
+
+ align:start position:0%
+that uh bacteria are exposed to
+ 
+
+ align:start position:0%
+that uh bacteria are exposed to
+antibiotics the more likely it is
+
+ align:start position:0%
+antibiotics the more likely it is
+ 
+
+ align:start position:0%
+antibiotics the more likely it is
+they'll mutate in such a way that uh
+
+ align:start position:0%
+they'll mutate in such a way that uh
+ 
+
+ align:start position:0%
+they'll mutate in such a way that uh
+they'll be resistant in the future so
+
+ align:start position:0%
+they'll be resistant in the future so
+ 
+
+ align:start position:0%
+they'll be resistant in the future so
+this is a really huge problem so if
+
+ align:start position:0%
+this is a really huge problem so if
+ 
+
+ align:start position:0%
+this is a really huge problem so if
+you're thinking about you know you're
+
+ align:start position:0%
+you're thinking about you know you're
+ 
+
+ align:start position:0%
+you're thinking about you know you're
+interested in science what should I do
+
+ align:start position:0%
+interested in science what should I do
+ 
+
+ align:start position:0%
+interested in science what should I do
+with my life this is uh one one thing
+
+ align:start position:0%
+with my life this is uh one one thing
+ 
+
+ align:start position:0%
+with my life this is uh one one thing
+that uh you might want to think about a
+
+ align:start position:0%
+that uh you might want to think about a
+ 
+
+ align:start position:0%
+that uh you might want to think about a
+lot of what we take antibiotics for used
+
+ align:start position:0%
+lot of what we take antibiotics for used
+ 
+
+ align:start position:0%
+lot of what we take antibiotics for used
+to be conditions that um were deadly so
+
+ align:start position:0%
+to be conditions that um were deadly so
+ 
+
+ align:start position:0%
+to be conditions that um were deadly so
+if we don't have antibiotics then um
+
+ align:start position:0%
+if we don't have antibiotics then um
+ 
+
+ align:start position:0%
+if we don't have antibiotics then um
+life expectancy is quite a bit different
+
+ align:start position:0%
+life expectancy is quite a bit different
+ 
+
+ align:start position:0%
+life expectancy is quite a bit different
+anyway so this is one of the projects in
+
+ align:start position:0%
+anyway so this is one of the projects in
+ 
+
+ align:start position:0%
+anyway so this is one of the projects in
+my lab we're looking at a number of uh
+
+ align:start position:0%
+my lab we're looking at a number of uh
+ 
+
+ align:start position:0%
+my lab we're looking at a number of uh
+different enzymes that are involved in
+
+ align:start position:0%
+different enzymes that are involved in
+ 
+
+ align:start position:0%
+different enzymes that are involved in
+antibiotic
+
+ align:start position:0%
+antibiotic
+ 
+
+ align:start position:0%
+antibiotic
+biosynthesis all right so enzyme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catalysis so uh we're gonna I'm going to
+
+ align:start position:0%
+catalysis so uh we're gonna I'm going to
+ 
+
+ align:start position:0%
+catalysis so uh we're gonna I'm going to
+introduce you to a few terms and then
+
+ align:start position:0%
+introduce you to a few terms and then
+ 
+
+ align:start position:0%
+introduce you to a few terms and then
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+use the things that you learned mostly
+
+ align:start position:0%
+use the things that you learned mostly
+ 
+
+ align:start position:0%
+use the things that you learned mostly
+last Wednesday on mechanism of reactions
+
+ align:start position:0%
+last Wednesday on mechanism of reactions
+ 
+
+ align:start position:0%
+last Wednesday on mechanism of reactions
+and we're going to derive uh the michaus
+
+ align:start position:0%
+and we're going to derive uh the michaus
+ 
+
+ align:start position:0%
+and we're going to derive uh the michaus
+Menan equations for enzyme kinetics so
+
+ align:start position:0%
+Menan equations for enzyme kinetics so
+ 
+
+ align:start position:0%
+Menan equations for enzyme kinetics so
+you didn't you might not have realized
+
+ align:start position:0%
+you didn't you might not have realized
+ 
+
+ align:start position:0%
+you didn't you might not have realized
+that on Wednesday you were learning all
+
+ align:start position:0%
+that on Wednesday you were learning all
+ 
+
+ align:start position:0%
+that on Wednesday you were learning all
+the sort of tools you need in
+
+ align:start position:0%
+the sort of tools you need in
+ 
+
+ align:start position:0%
+the sort of tools you need in
+Biochemistry you were actually learning
+
+ align:start position:0%
+Biochemistry you were actually learning
+ 
+
+ align:start position:0%
+Biochemistry you were actually learning
+biochemistry but you were and I think
+
+ align:start position:0%
+biochemistry but you were and I think
+ 
+
+ align:start position:0%
+biochemistry but you were and I think
+you'll see that uh see that now so first
+
+ align:start position:0%
+you'll see that uh see that now so first
+ 
+
+ align:start position:0%
+you'll see that uh see that now so first
+a couple of new terms I already
+
+ align:start position:0%
+a couple of new terms I already
+ 
+
+ align:start position:0%
+a couple of new terms I already
+introduced this a little bit but
+
+ align:start position:0%
+introduced this a little bit but
+ 
+
+ align:start position:0%
+introduced this a little bit but
+reactant molecules we're always talking
+
+ align:start position:0%
+reactant molecules we're always talking
+ 
+
+ align:start position:0%
+reactant molecules we're always talking
+about reactants when you're talking
+
+ align:start position:0%
+about reactants when you're talking
+ 
+
+ align:start position:0%
+about reactants when you're talking
+about enzymes you're talking about
+
+ align:start position:0%
+about enzymes you're talking about
+ 
+
+ align:start position:0%
+about enzymes you're talking about
+substrates so we no longer call them
+
+ align:start position:0%
+substrates so we no longer call them
+ 
+
+ align:start position:0%
+substrates so we no longer call them
+reactants We Now call them
+
+ align:start position:0%
+reactants We Now call them
+ 
+
+ align:start position:0%
+reactants We Now call them
+substrates and substrates bind to what's
+
+ align:start position:0%
+substrates and substrates bind to what's
+ 
+
+ align:start position:0%
+substrates and substrates bind to what's
+known as the active site of the enzyme
+
+ align:start position:0%
+known as the active site of the enzyme
+ 
+
+ align:start position:0%
+known as the active site of the enzyme
+uh that's the site where catalysis
+
+ align:start position:0%
+uh that's the site where catalysis
+ 
+
+ align:start position:0%
+uh that's the site where catalysis
+occurs so it's active and that's pretty
+
+ align:start position:0%
+occurs so it's active and that's pretty
+ 
+
+ align:start position:0%
+occurs so it's active and that's pretty
+easy to
+
+ align:start position:0%
+easy to
+ 
+
+ align:start position:0%
+easy to
+remember so here is a very very simple
+
+ align:start position:0%
+remember so here is a very very simple
+ 
+
+ align:start position:0%
+remember so here is a very very simple
+enzyme reaction and a lot of enzyme
+
+ align:start position:0%
+enzyme reaction and a lot of enzyme
+ 
+
+ align:start position:0%
+enzyme reaction and a lot of enzyme
+reactions actually are fairly simple so
+
+ align:start position:0%
+reactions actually are fairly simple so
+ 
+
+ align:start position:0%
+reactions actually are fairly simple so
+here uh you'd have an enzyme binding to
+
+ align:start position:0%
+here uh you'd have an enzyme binding to
+ 
+
+ align:start position:0%
+here uh you'd have an enzyme binding to
+your substrate enzyme called e substrate
+
+ align:start position:0%
+your substrate enzyme called e substrate
+ 
+
+ align:start position:0%
+your substrate enzyme called e substrate
+called s when the substrate binds to the
+
+ align:start position:0%
+called s when the substrate binds to the
+ 
+
+ align:start position:0%
+called s when the substrate binds to the
+enzyme it forms an enzyme substrate
+
+ align:start position:0%
+enzyme it forms an enzyme substrate
+ 
+
+ align:start position:0%
+enzyme it forms an enzyme substrate
+complex which is known as an es
+
+ align:start position:0%
+complex which is known as an es
+ 
+
+ align:start position:0%
+complex which is known as an es
+complex that enzyme substrate complex or
+
+ align:start position:0%
+complex that enzyme substrate complex or
+ 
+
+ align:start position:0%
+complex that enzyme substrate complex or
+ES complex will go on and form enzyme e
+
+ align:start position:0%
+ES complex will go on and form enzyme e
+ 
+
+ align:start position:0%
+ES complex will go on and form enzyme e
+and product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P so just to show that in cartoon form
+
+ align:start position:0%
+P so just to show that in cartoon form
+ 
+
+ align:start position:0%
+P so just to show that in cartoon form
+and it pains me to do this to draw the
+
+ align:start position:0%
+and it pains me to do this to draw the
+ 
+
+ align:start position:0%
+and it pains me to do this to draw the
+enzyme like this because as you saw in
+
+ align:start position:0%
+enzyme like this because as you saw in
+ 
+
+ align:start position:0%
+enzyme like this because as you saw in
+the last slide enzymes are really quite
+
+ align:start position:0%
+the last slide enzymes are really quite
+ 
+
+ align:start position:0%
+the last slide enzymes are really quite
+beautiful and uh this is a very sad uh
+
+ align:start position:0%
+beautiful and uh this is a very sad uh
+ 
+
+ align:start position:0%
+beautiful and uh this is a very sad uh
+description of what an enzyme looks like
+
+ align:start position:0%
+description of what an enzyme looks like
+ 
+
+ align:start position:0%
+description of what an enzyme looks like
+and also here are the substrates about
+
+ align:start position:0%
+and also here are the substrates about
+ 
+
+ align:start position:0%
+and also here are the substrates about
+the size of the enzyme which is also all
+
+ align:start position:0%
+the size of the enzyme which is also all
+ 
+
+ align:start position:0%
+the size of the enzyme which is also all
+uh off but uh here is the substrate
+
+ align:start position:0%
+uh off but uh here is the substrate
+ 
+
+ align:start position:0%
+uh off but uh here is the substrate
+binding to the enzy this would be the
+
+ align:start position:0%
+binding to the enzy this would be the
+ 
+
+ align:start position:0%
+binding to the enzy this would be the
+active site and uh would be designed
+
+ align:start position:0%
+active site and uh would be designed
+ 
+
+ align:start position:0%
+active site and uh would be designed
+just to uh fit the substrate in there
+
+ align:start position:0%
+just to uh fit the substrate in there
+ 
+
+ align:start position:0%
+just to uh fit the substrate in there
+quite
+
+ align:start position:0%
+quite
+ 
+
+ align:start position:0%
+quite
+nicely when substrate binds to the
+
+ align:start position:0%
+nicely when substrate binds to the
+ 
+
+ align:start position:0%
+nicely when substrate binds to the
+enzyme you form what's known as the es
+
+ align:start position:0%
+enzyme you form what's known as the es
+ 
+
+ align:start position:0%
+enzyme you form what's known as the es
+complex and usually this binding is
+
+ align:start position:0%
+complex and usually this binding is
+ 
+
+ align:start position:0%
+complex and usually this binding is
+reversible so uh not all substrate that
+
+ align:start position:0%
+reversible so uh not all substrate that
+ 
+
+ align:start position:0%
+reversible so uh not all substrate that
+binds to the enzyme will go on to form
+
+ align:start position:0%
+binds to the enzyme will go on to form
+ 
+
+ align:start position:0%
+binds to the enzyme will go on to form
+product some will go back and form free
+
+ align:start position:0%
+product some will go back and form free
+ 
+
+ align:start position:0%
+product some will go back and form free
+substrate and
+
+ align:start position:0%
+substrate and
+ 
+
+ align:start position:0%
+substrate and
+enzyme and in this uh drawing then when
+
+ align:start position:0%
+enzyme and in this uh drawing then when
+ 
+
+ align:start position:0%
+enzyme and in this uh drawing then when
+the enzyme reacts on the substrate it'll
+
+ align:start position:0%
+the enzyme reacts on the substrate it'll
+ 
+
+ align:start position:0%
+the enzyme reacts on the substrate it'll
+form product and free enzyme again and
+
+ align:start position:0%
+form product and free enzyme again and
+ 
+
+ align:start position:0%
+form product and free enzyme again and
+this is drawn with a single line uh as
+
+ align:start position:0%
+this is drawn with a single line uh as
+ 
+
+ align:start position:0%
+this is drawn with a single line uh as
+not being a a reversible uh step in the
+
+ align:start position:0%
+not being a a reversible uh step in the
+ 
+
+ align:start position:0%
+not being a a reversible uh step in the
+reaction so here you see substrate and
+
+ align:start position:0%
+reaction so here you see substrate and
+ 
+
+ align:start position:0%
+reaction so here you see substrate and
+what the enzyme this enzyme did is sort
+
+ align:start position:0%
+what the enzyme this enzyme did is sort
+ 
+
+ align:start position:0%
+what the enzyme this enzyme did is sort
+of make the substrate look a little more
+
+ align:start position:0%
+of make the substrate look a little more
+ 
+
+ align:start position:0%
+of make the substrate look a little more
+like a Mickey Mouse so there's our
+
+ align:start position:0%
+like a Mickey Mouse so there's our
+ 
+
+ align:start position:0%
+like a Mickey Mouse so there's our
+product coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off so now we can
+
+ align:start position:0%
+off so now we can
+ 
+
+ align:start position:0%
+off so now we can
+drive uh we can drive equations to
+
+ align:start position:0%
+drive uh we can drive equations to
+ 
+
+ align:start position:0%
+drive uh we can drive equations to
+represent that reaction that I just
+
+ align:start position:0%
+represent that reaction that I just
+ 
+
+ align:start position:0%
+represent that reaction that I just
+showed you and we can use all the same
+
+ align:start position:0%
+showed you and we can use all the same
+ 
+
+ align:start position:0%
+showed you and we can use all the same
+ideas that we had when we were driving
+
+ align:start position:0%
+ideas that we had when we were driving
+ 
+
+ align:start position:0%
+ideas that we had when we were driving
+mechanisms in class last Wednesday and
+
+ align:start position:0%
+mechanisms in class last Wednesday and
+ 
+
+ align:start position:0%
+mechanisms in class last Wednesday and
+on problem set
+
+ align:start position:0%
+on problem set
+ 
+
+ align:start position:0%
+on problem set
+10 so again the reaction is enzyme plus
+
+ align:start position:0%
+10 so again the reaction is enzyme plus
+ 
+
+ align:start position:0%
+10 so again the reaction is enzyme plus
+substrate e plus s going in a reversible
+
+ align:start position:0%
+substrate e plus s going in a reversible
+ 
+
+ align:start position:0%
+substrate e plus s going in a reversible
+step to uh the enzyme strstr complex es
+
+ align:start position:0%
+step to uh the enzyme strstr complex es
+ 
+
+ align:start position:0%
+step to uh the enzyme strstr complex es
+and then going with a single uh
+
+ align:start position:0%
+and then going with a single uh
+ 
+
+ align:start position:0%
+and then going with a single uh
+non-reversible step to enzyme and
+
+ align:start position:0%
+non-reversible step to enzyme and
+ 
+
+ align:start position:0%
+non-reversible step to enzyme and
+product so we can put this in Two Steps
+
+ align:start position:0%
+product so we can put this in Two Steps
+ 
+
+ align:start position:0%
+product so we can put this in Two Steps
+step one uh is the reversible step of
+
+ align:start position:0%
+step one uh is the reversible step of
+ 
+
+ align:start position:0%
+step one uh is the reversible step of
+enzyme and substrate going to the enzyme
+
+ align:start position:0%
+enzyme and substrate going to the enzyme
+ 
+
+ align:start position:0%
+enzyme and substrate going to the enzyme
+substrate complex with Ray constants K1
+
+ align:start position:0%
+substrate complex with Ray constants K1
+ 
+
+ align:start position:0%
+substrate complex with Ray constants K1
+for forward step and K minus one for the
+
+ align:start position:0%
+for forward step and K minus one for the
+ 
+
+ align:start position:0%
+for forward step and K minus one for the
+reverse step in step two we have the
+
+ align:start position:0%
+reverse step in step two we have the
+ 
+
+ align:start position:0%
+reverse step in step two we have the
+enzyme substrate complex going to enzyme
+
+ align:start position:0%
+enzyme substrate complex going to enzyme
+ 
+
+ align:start position:0%
+enzyme substrate complex going to enzyme
+and product with rate constant K2 so
+
+ align:start position:0%
+and product with rate constant K2 so
+ 
+
+ align:start position:0%
+and product with rate constant K2 so
+these then are Elementary reactions and
+
+ align:start position:0%
+these then are Elementary reactions and
+ 
+
+ align:start position:0%
+these then are Elementary reactions and
+so we can write the rate law for each
+
+ align:start position:0%
+so we can write the rate law for each
+ 
+
+ align:start position:0%
+so we can write the rate law for each
+step uh just based as how the reaction
+
+ align:start position:0%
+step uh just based as how the reaction
+ 
+
+ align:start position:0%
+step uh just based as how the reaction
+is written so what would be the uh rate
+
+ align:start position:0%
+is written so what would be the uh rate
+ 
+
+ align:start position:0%
+is written so what would be the uh rate
+for the forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction K1
+
+ align:start position:0%
+reaction K1
+ 
+
+ align:start position:0%
+reaction K1
+* e *
+
+ align:start position:0%
+* e *
+ 
+
+ align:start position:0%
+* e *
+s all right so there's the rate for the
+
+ align:start position:0%
+s all right so there's the rate for the
+ 
+
+ align:start position:0%
+s all right so there's the rate for the
+forward reaction again just based on
+
+ align:start position:0%
+forward reaction again just based on
+ 
+
+ align:start position:0%
+forward reaction again just based on
+rate constant times the two things that
+
+ align:start position:0%
+rate constant times the two things that
+ 
+
+ align:start position:0%
+rate constant times the two things that
+are reacting what about for the reverse
+
+ align:start position:0%
+are reacting what about for the reverse
+ 
+
+ align:start position:0%
+are reacting what about for the reverse
+reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we
+
+ align:start position:0%
+so we
+ 
+
+ align:start position:0%
+so we
+have what's the rate
+
+ align:start position:0%
+have what's the rate
+ 
+
+ align:start position:0%
+have what's the rate
+constant K minus1 time es right so that
+
+ align:start position:0%
+constant K minus1 time es right so that
+ 
+
+ align:start position:0%
+constant K minus1 time es right so that
+would be for the reverse reaction and
+
+ align:start position:0%
+would be for the reverse reaction and
+ 
+
+ align:start position:0%
+would be for the reverse reaction and
+what about the rate for step
+
+ align:start position:0%
+what about the rate for step
+ 
+
+ align:start position:0%
+what about the rate for step
+two K2
+
+ align:start position:0%
+two K2
+ 
+
+ align:start position:0%
+two K2
+times times es right okay so now we can
+
+ align:start position:0%
+times times es right okay so now we can
+ 
+
+ align:start position:0%
+times times es right okay so now we can
+look at the rate of formation of product
+
+ align:start position:0%
+look at the rate of formation of product
+ 
+
+ align:start position:0%
+look at the rate of formation of product
+the overall reaction so the rate of
+
+ align:start position:0%
+the overall reaction so the rate of
+ 
+
+ align:start position:0%
+the overall reaction so the rate of
+product formation
+
+ align:start position:0%
+product formation
+ 
+
+ align:start position:0%
+product formation
+can be expressed as the uh change DP DT
+
+ align:start position:0%
+can be expressed as the uh change DP DT
+ 
+
+ align:start position:0%
+can be expressed as the uh change DP DT
+with time uh for product and also we can
+
+ align:start position:0%
+with time uh for product and also we can
+ 
+
+ align:start position:0%
+with time uh for product and also we can
+just write it from the from the second
+
+ align:start position:0%
+just write it from the from the second
+ 
+
+ align:start position:0%
+just write it from the from the second
+step in terms of K2 times es s so that's
+
+ align:start position:0%
+step in terms of K2 times es s so that's
+ 
+
+ align:start position:0%
+step in terms of K2 times es s so that's
+the rate of formation of
+
+ align:start position:0%
+the rate of formation of
+ 
+
+ align:start position:0%
+the rate of formation of
+product are we
+
+ align:start position:0%
+product are we
+ 
+
+ align:start position:0%
+product are we
+done no because
+
+ align:start position:0%
+done no because
+ 
+
+ align:start position:0%
+done no because
+why there's an
+
+ align:start position:0%
+why there's an
+ 
+
+ align:start position:0%
+why there's an
+intermediate so we have to solve for the
+
+ align:start position:0%
+intermediate so we have to solve for the
+ 
+
+ align:start position:0%
+intermediate so we have to solve for the
+intermediate again this should seem
+
+ align:start position:0%
+intermediate again this should seem
+ 
+
+ align:start position:0%
+intermediate again this should seem
+familiar it's all the same stuff we were
+
+ align:start position:0%
+familiar it's all the same stuff we were
+ 
+
+ align:start position:0%
+familiar it's all the same stuff we were
+talking about last
+
+ align:start position:0%
+talking about last
+ 
+
+ align:start position:0%
+talking about last
+week so we need to solve for the
+
+ align:start position:0%
+week so we need to solve for the
+ 
+
+ align:start position:0%
+week so we need to solve for the
+intermediate we're not given anything
+
+ align:start position:0%
+intermediate we're not given anything
+ 
+
+ align:start position:0%
+intermediate we're not given anything
+about fast and slow steps so we're going
+
+ align:start position:0%
+about fast and slow steps so we're going
+ 
+
+ align:start position:0%
+about fast and slow steps so we're going
+to use the steady state
+
+ align:start position:0%
+to use the steady state
+ 
+
+ align:start position:0%
+to use the steady state
+approximation uh which is going to tell
+
+ align:start position:0%
+approximation uh which is going to tell
+ 
+
+ align:start position:0%
+approximation uh which is going to tell
+you that the net formation of
+
+ align:start position:0%
+you that the net formation of
+ 
+
+ align:start position:0%
+you that the net formation of
+intermediates is pretty much constant
+
+ align:start position:0%
+intermediates is pretty much constant
+ 
+
+ align:start position:0%
+intermediates is pretty much constant
+it's in the steady state another way to
+
+ align:start position:0%
+it's in the steady state another way to
+ 
+
+ align:start position:0%
+it's in the steady state another way to
+express that is that the uh all the
+
+ align:start position:0%
+express that is that the uh all the
+ 
+
+ align:start position:0%
+express that is that the uh all the
+steps that form uh the intermediate are
+
+ align:start position:0%
+steps that form uh the intermediate are
+ 
+
+ align:start position:0%
+steps that form uh the intermediate are
+equal in rate to all the steps that get
+
+ align:start position:0%
+equal in rate to all the steps that get
+ 
+
+ align:start position:0%
+equal in rate to all the steps that get
+rid of that intermediate either consume
+
+ align:start position:0%
+rid of that intermediate either consume
+ 
+
+ align:start position:0%
+rid of that intermediate either consume
+it or decompose it so first we need to
+
+ align:start position:0%
+it or decompose it so first we need to
+ 
+
+ align:start position:0%
+it or decompose it so first we need to
+uh look at what all the steps are that
+
+ align:start position:0%
+uh look at what all the steps are that
+ 
+
+ align:start position:0%
+uh look at what all the steps are that
+have to do with the
+
+ align:start position:0%
+have to do with the
+ 
+
+ align:start position:0%
+have to do with the
+intermediate so here is the uh rate of
+
+ align:start position:0%
+intermediate so here is the uh rate of
+ 
+
+ align:start position:0%
+intermediate so here is the uh rate of
+uh the formation of that intermediate
+
+ align:start position:0%
+uh the formation of that intermediate
+ 
+
+ align:start position:0%
+uh the formation of that intermediate
+and so that's going to be equal to the
+
+ align:start position:0%
+and so that's going to be equal to the
+ 
+
+ align:start position:0%
+and so that's going to be equal to the
+steps involved in forming the
+
+ align:start position:0%
+steps involved in forming the
+ 
+
+ align:start position:0%
+steps involved in forming the
+intermediate and it's only formed in
+
+ align:start position:0%
+intermediate and it's only formed in
+ 
+
+ align:start position:0%
+intermediate and it's only formed in
+that first step for direction of the
+
+ align:start position:0%
+that first step for direction of the
+ 
+
+ align:start position:0%
+that first step for direction of the
+first step
+
+ align:start position:0%
+first step
+ 
+
+ align:start position:0%
+first step
+so it's rate K1 time the concentration
+
+ align:start position:0%
+so it's rate K1 time the concentration
+ 
+
+ align:start position:0%
+so it's rate K1 time the concentration
+of etimes the concentration of s so
+
+ align:start position:0%
+of etimes the concentration of s so
+ 
+
+ align:start position:0%
+of etimes the concentration of s so
+that's the rate of
+
+ align:start position:0%
+that's the rate of
+ 
+
+ align:start position:0%
+that's the rate of
+formation and then we're going to
+
+ align:start position:0%
+formation and then we're going to
+ 
+
+ align:start position:0%
+formation and then we're going to
+subtract from that steps that are
+
+ align:start position:0%
+subtract from that steps that are
+ 
+
+ align:start position:0%
+subtract from that steps that are
+involved in the decomposition or in the
+
+ align:start position:0%
+involved in the decomposition or in the
+ 
+
+ align:start position:0%
+involved in the decomposition or in the
+consumption of the intermediate the
+
+ align:start position:0%
+consumption of the intermediate the
+ 
+
+ align:start position:0%
+consumption of the intermediate the
+intermediate decomposes in the reverse
+
+ align:start position:0%
+intermediate decomposes in the reverse
+ 
+
+ align:start position:0%
+intermediate decomposes in the reverse
+direction of step one so that's this
+
+ align:start position:0%
+direction of step one so that's this
+ 
+
+ align:start position:0%
+direction of step one so that's this
+rate K minus1 * e s
+
+ align:start position:0%
+rate K minus1 * e s
+ 
+
+ align:start position:0%
+rate K minus1 * e s
+and it's also consumed in this second
+
+ align:start position:0%
+and it's also consumed in this second
+ 
+
+ align:start position:0%
+and it's also consumed in this second
+step so it's consumed um by the rate K2
+
+ align:start position:0%
+step so it's consumed um by the rate K2
+ 
+
+ align:start position:0%
+step so it's consumed um by the rate K2
+times es again this is exactly the same
+
+ align:start position:0%
+times es again this is exactly the same
+ 
+
+ align:start position:0%
+times es again this is exactly the same
+as what we looked at last week and now
+
+ align:start position:0%
+as what we looked at last week and now
+ 
+
+ align:start position:0%
+as what we looked at last week and now
+we can consider the steady state
+
+ align:start position:0%
+we can consider the steady state
+ 
+
+ align:start position:0%
+we can consider the steady state
+approximation and we can set that whole
+
+ align:start position:0%
+approximation and we can set that whole
+ 
+
+ align:start position:0%
+approximation and we can set that whole
+term equal to zero so steady state again
+
+ align:start position:0%
+term equal to zero so steady state again
+ 
+
+ align:start position:0%
+term equal to zero so steady state again
+the net rate of formation of the
+
+ align:start position:0%
+the net rate of formation of the
+ 
+
+ align:start position:0%
+the net rate of formation of the
+intermediate is equal to the net rate at
+
+ align:start position:0%
+intermediate is equal to the net rate at
+ 
+
+ align:start position:0%
+intermediate is equal to the net rate at
+which it goes away so so so it's it's uh
+
+ align:start position:0%
+which it goes away so so so it's it's uh
+ 
+
+ align:start position:0%
+which it goes away so so so it's it's uh
+the whole equation can be set equal to
+
+ align:start position:0%
+the whole equation can be set equal to
+ 
+
+ align:start position:0%
+the whole equation can be set equal to
+zero so we can do that here set this
+
+ align:start position:0%
+zero so we can do that here set this
+ 
+
+ align:start position:0%
+zero so we can do that here set this
+term equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero now there's a slight change so it's
+
+ align:start position:0%
+zero now there's a slight change so it's
+ 
+
+ align:start position:0%
+zero now there's a slight change so it's
+not 100% what we did before uh there is
+
+ align:start position:0%
+not 100% what we did before uh there is
+ 
+
+ align:start position:0%
+not 100% what we did before uh there is
+a slight change and that comes out of a
+
+ align:start position:0%
+a slight change and that comes out of a
+ 
+
+ align:start position:0%
+a slight change and that comes out of a
+practical
+
+ align:start position:0%
+practical
+ 
+
+ align:start position:0%
+practical
+consideration so when you're doing these
+
+ align:start position:0%
+consideration so when you're doing these
+ 
+
+ align:start position:0%
+consideration so when you're doing these
+experiments in the term that we had you
+
+ align:start position:0%
+experiments in the term that we had you
+ 
+
+ align:start position:0%
+experiments in the term that we had you
+usually don't know how much enzyme is
+
+ align:start position:0%
+usually don't know how much enzyme is
+ 
+
+ align:start position:0%
+usually don't know how much enzyme is
+free and it's hard to figure that out at
+
+ align:start position:0%
+free and it's hard to figure that out at
+ 
+
+ align:start position:0%
+free and it's hard to figure that out at
+any one time how much enzyme is not
+
+ align:start position:0%
+any one time how much enzyme is not
+ 
+
+ align:start position:0%
+any one time how much enzyme is not
+reacting with the substrate it's much
+
+ align:start position:0%
+reacting with the substrate it's much
+ 
+
+ align:start position:0%
+reacting with the substrate it's much
+easier to know how much enzyme you added
+
+ align:start position:0%
+easier to know how much enzyme you added
+ 
+
+ align:start position:0%
+easier to know how much enzyme you added
+to the reaction to begin with that's a
+
+ align:start position:0%
+to the reaction to begin with that's a
+ 
+
+ align:start position:0%
+to the reaction to begin with that's a
+number that you should know you should
+
+ align:start position:0%
+number that you should know you should
+ 
+
+ align:start position:0%
+number that you should know you should
+have carefully figured out how much
+
+ align:start position:0%
+have carefully figured out how much
+ 
+
+ align:start position:0%
+have carefully figured out how much
+enzyme that you were going to use in
+
+ align:start position:0%
+enzyme that you were going to use in
+ 
+
+ align:start position:0%
+enzyme that you were going to use in
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+experiment so instead of solving for the
+
+ align:start position:0%
+experiment so instead of solving for the
+ 
+
+ align:start position:0%
+experiment so instead of solving for the
+intermediate in terms of the free enzyme
+
+ align:start position:0%
+intermediate in terms of the free enzyme
+ 
+
+ align:start position:0%
+intermediate in terms of the free enzyme
+it's easier to solve for it in terms of
+
+ align:start position:0%
+it's easier to solve for it in terms of
+ 
+
+ align:start position:0%
+it's easier to solve for it in terms of
+um the total enzyme which we're going to
+
+ align:start position:0%
+um the total enzyme which we're going to
+ 
+
+ align:start position:0%
+um the total enzyme which we're going to
+call E not how much enzyme you put into
+
+ align:start position:0%
+call E not how much enzyme you put into
+ 
+
+ align:start position:0%
+call E not how much enzyme you put into
+the equation so the total enzyme that's
+
+ align:start position:0%
+the equation so the total enzyme that's
+ 
+
+ align:start position:0%
+the equation so the total enzyme that's
+going that's that's reacting with
+
+ align:start position:0%
+going that's that's reacting with
+ 
+
+ align:start position:0%
+going that's that's reacting with
+substrate uh that you put into the
+
+ align:start position:0%
+substrate uh that you put into the
+ 
+
+ align:start position:0%
+substrate uh that you put into the
+experiment would equal the amount that's
+
+ align:start position:0%
+experiment would equal the amount that's
+ 
+
+ align:start position:0%
+experiment would equal the amount that's
+free the amount that's not reacting at
+
+ align:start position:0%
+free the amount that's not reacting at
+ 
+
+ align:start position:0%
+free the amount that's not reacting at
+any given time or that just finished
+
+ align:start position:0%
+any given time or that just finished
+ 
+
+ align:start position:0%
+any given time or that just finished
+reacting and the amount of the enzyme
+
+ align:start position:0%
+reacting and the amount of the enzyme
+ 
+
+ align:start position:0%
+reacting and the amount of the enzyme
+that's bound it's only going to be free
+
+ align:start position:0%
+that's bound it's only going to be free
+ 
+
+ align:start position:0%
+that's bound it's only going to be free
+or bound so the total enzyme equals
+
+ align:start position:0%
+or bound so the total enzyme equals
+ 
+
+ align:start position:0%
+or bound so the total enzyme equals
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+and so you can go back to your other
+
+ align:start position:0%
+and so you can go back to your other
+ 
+
+ align:start position:0%
+and so you can go back to your other
+equation right now and wherever you had
+
+ align:start position:0%
+equation right now and wherever you had
+ 
+
+ align:start position:0%
+equation right now and wherever you had
+free enzyme you can substitute in terms
+
+ align:start position:0%
+free enzyme you can substitute in terms
+ 
+
+ align:start position:0%
+free enzyme you can substitute in terms
+for total enzyme minus bound because
+
+ align:start position:0%
+for total enzyme minus bound because
+ 
+
+ align:start position:0%
+for total enzyme minus bound because
+that's going to be equal to free and
+
+ align:start position:0%
+that's going to be equal to free and
+ 
+
+ align:start position:0%
+that's going to be equal to free and
+again this is just a practical
+
+ align:start position:0%
+again this is just a practical
+ 
+
+ align:start position:0%
+again this is just a practical
+consideration that it's easier if you're
+
+ align:start position:0%
+consideration that it's easier if you're
+ 
+
+ align:start position:0%
+consideration that it's easier if you're
+doing these experiments and again
+
+ align:start position:0%
+doing these experiments and again
+ 
+
+ align:start position:0%
+doing these experiments and again
+biochemistry is and experimental science
+
+ align:start position:0%
+biochemistry is and experimental science
+ 
+
+ align:start position:0%
+biochemistry is and experimental science
+to know how much enzyme you started with
+
+ align:start position:0%
+to know how much enzyme you started with
+ 
+
+ align:start position:0%
+to know how much enzyme you started with
+than to know how much is non-reacting at
+
+ align:start position:0%
+than to know how much is non-reacting at
+ 
+
+ align:start position:0%
+than to know how much is non-reacting at
+any given time so this is just a
+
+ align:start position:0%
+any given time so this is just a
+ 
+
+ align:start position:0%
+any given time so this is just a
+practical thing and for all the other
+
+ align:start position:0%
+practical thing and for all the other
+ 
+
+ align:start position:0%
+practical thing and for all the other
+things we worked on you're always
+
+ align:start position:0%
+things we worked on you're always
+ 
+
+ align:start position:0%
+things we worked on you're always
+wanting to solve for the intermediate
+
+ align:start position:0%
+wanting to solve for the intermediate
+ 
+
+ align:start position:0%
+wanting to solve for the intermediate
+and things in terms of things you could
+
+ align:start position:0%
+and things in terms of things you could
+ 
+
+ align:start position:0%
+and things in terms of things you could
+measure like rate constants and
+
+ align:start position:0%
+measure like rate constants and
+ 
+
+ align:start position:0%
+measure like rate constants and
+concentration of reactants or products
+
+ align:start position:0%
+concentration of reactants or products
+ 
+
+ align:start position:0%
+concentration of reactants or products
+it's a similar kind of idea you want to
+
+ align:start position:0%
+it's a similar kind of idea you want to
+ 
+
+ align:start position:0%
+it's a similar kind of idea you want to
+be able to solve for things in terms of
+
+ align:start position:0%
+be able to solve for things in terms of
+ 
+
+ align:start position:0%
+be able to solve for things in terms of
+stuff that you can actually
+
+ align:start position:0%
+stuff that you can actually
+ 
+
+ align:start position:0%
+stuff that you can actually
+measure so now we can go back again we
+
+ align:start position:0%
+measure so now we can go back again we
+ 
+
+ align:start position:0%
+measure so now we can go back again we
+had this is the equation that we were
+
+ align:start position:0%
+had this is the equation that we were
+ 
+
+ align:start position:0%
+had this is the equation that we were
+solving for our intermediate if you use
+
+ align:start position:0%
+solving for our intermediate if you use
+ 
+
+ align:start position:0%
+solving for our intermediate if you use
+a steady state approximation you set the
+
+ align:start position:0%
+a steady state approximation you set the
+ 
+
+ align:start position:0%
+a steady state approximation you set the
+whole term equal to zero and now we can
+
+ align:start position:0%
+whole term equal to zero and now we can
+ 
+
+ align:start position:0%
+whole term equal to zero and now we can
+take this term and substitute so we're
+
+ align:start position:0%
+take this term and substitute so we're
+ 
+
+ align:start position:0%
+take this term and substitute so we're
+going to replace this e and that's the
+
+ align:start position:0%
+going to replace this e and that's the
+ 
+
+ align:start position:0%
+going to replace this e and that's the
+only free enzyme that we had in in in
+
+ align:start position:0%
+only free enzyme that we had in in in
+ 
+
+ align:start position:0%
+only free enzyme that we had in in in
+this whole expression so we're going to
+
+ align:start position:0%
+this whole expression so we're going to
+ 
+
+ align:start position:0%
+this whole expression so we're going to
+replace this now with total enzyme minus
+
+ align:start position:0%
+replace this now with total enzyme minus
+ 
+
+ align:start position:0%
+replace this now with total enzyme minus
+the bound enzyme so we're going to put
+
+ align:start position:0%
+the bound enzyme so we're going to put
+ 
+
+ align:start position:0%
+the bound enzyme so we're going to put
+that term in here and that gives us the
+
+ align:start position:0%
+that term in here and that gives us the
+ 
+
+ align:start position:0%
+that term in here and that gives us the
+following so now we have k1s times in
+
+ align:start position:0%
+following so now we have k1s times in
+ 
+
+ align:start position:0%
+following so now we have k1s times in
+parentheses this term which equals free
+
+ align:start position:0%
+parentheses this term which equals free
+ 
+
+ align:start position:0%
+parentheses this term which equals free
+enzyme total minus bound and now now we
+
+ align:start position:0%
+enzyme total minus bound and now now we
+ 
+
+ align:start position:0%
+enzyme total minus bound and now now we
+can multiply that out so K1 s times a
+
+ align:start position:0%
+can multiply that out so K1 s times a
+ 
+
+ align:start position:0%
+can multiply that out so K1 s times a
+total enzyme here and then there's a
+
+ align:start position:0%
+total enzyme here and then there's a
+ 
+
+ align:start position:0%
+total enzyme here and then there's a
+minus here so uh we have K1 es uh times
+
+ align:start position:0%
+minus here so uh we have K1 es uh times
+ 
+
+ align:start position:0%
+minus here so uh we have K1 es uh times
+substrate over here and these parts are
+
+ align:start position:0%
+substrate over here and these parts are
+ 
+
+ align:start position:0%
+substrate over here and these parts are
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unchanged so now we can uh solve for
+
+ align:start position:0%
+unchanged so now we can uh solve for
+ 
+
+ align:start position:0%
+unchanged so now we can uh solve for
+ES so here is our expression from the
+
+ align:start position:0%
+ES so here is our expression from the
+ 
+
+ align:start position:0%
+ES so here is our expression from the
+last sheet and now we can rearrange to
+
+ align:start position:0%
+last sheet and now we can rearrange to
+ 
+
+ align:start position:0%
+last sheet and now we can rearrange to
+solve for ES
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to put all the es terms
+
+ align:start position:0%
+so we're going to put all the es terms
+ 
+
+ align:start position:0%
+so we're going to put all the es terms
+onto one side so here's an es term here
+
+ align:start position:0%
+onto one side so here's an es term here
+ 
+
+ align:start position:0%
+onto one side so here's an es term here
+was an es term here was an es term so we
+
+ align:start position:0%
+was an es term here was an es term so we
+ 
+
+ align:start position:0%
+was an es term here was an es term so we
+moved those down to the other side of
+
+ align:start position:0%
+moved those down to the other side of
+ 
+
+ align:start position:0%
+moved those down to the other side of
+the equation gets rid of the negative
+
+ align:start position:0%
+the equation gets rid of the negative
+ 
+
+ align:start position:0%
+the equation gets rid of the negative
+bring that over bring that over and the
+
+ align:start position:0%
+bring that over bring that over and the
+ 
+
+ align:start position:0%
+bring that over bring that over and the
+only thing on the other side of the
+
+ align:start position:0%
+only thing on the other side of the
+ 
+
+ align:start position:0%
+only thing on the other side of the
+equation is this term here K1 * total
+
+ align:start position:0%
+equation is this term here K1 * total
+ 
+
+ align:start position:0%
+equation is this term here K1 * total
+enzyme time substrate now we can go
+
+ align:start position:0%
+enzyme time substrate now we can go
+ 
+
+ align:start position:0%
+enzyme time substrate now we can go
+ahead and as we did before pull out all
+
+ align:start position:0%
+ahead and as we did before pull out all
+ 
+
+ align:start position:0%
+ahead and as we did before pull out all
+of these es terms and come up with an
+
+ align:start position:0%
+of these es terms and come up with an
+ 
+
+ align:start position:0%
+of these es terms and come up with an
+expression that solves for it so we're
+
+ align:start position:0%
+expression that solves for it so we're
+ 
+
+ align:start position:0%
+expression that solves for it so we're
+going to solve for
+
+ align:start position:0%
+going to solve for
+ 
+
+ align:start position:0%
+going to solve for
+ES so we've pulled out es here we have
+
+ align:start position:0%
+ES so we've pulled out es here we have
+ 
+
+ align:start position:0%
+ES so we've pulled out es here we have
+k1s we have K2 K minus one and we have
+
+ align:start position:0%
+k1s we have K2 K minus one and we have
+ 
+
+ align:start position:0%
+k1s we have K2 K minus one and we have
+K2 and we have this expression over here
+
+ align:start position:0%
+K2 and we have this expression over here
+ 
+
+ align:start position:0%
+K2 and we have this expression over here
+and now we can take this expression and
+
+ align:start position:0%
+and now we can take this expression and
+ 
+
+ align:start position:0%
+and now we can take this expression and
+divide by that
+
+ align:start position:0%
+divide by that
+ 
+
+ align:start position:0%
+divide by that
+term and so this gives us an expression
+
+ align:start position:0%
+term and so this gives us an expression
+ 
+
+ align:start position:0%
+term and so this gives us an expression
+then for the concentration of our
+
+ align:start position:0%
+then for the concentration of our
+ 
+
+ align:start position:0%
+then for the concentration of our
+intermediate and now we're going to do
+
+ align:start position:0%
+intermediate and now we're going to do
+ 
+
+ align:start position:0%
+intermediate and now we're going to do
+one other thing that's a bit different
+
+ align:start position:0%
+one other thing that's a bit different
+ 
+
+ align:start position:0%
+one other thing that's a bit different
+this term has a lot of ks in it and so
+
+ align:start position:0%
+this term has a lot of ks in it and so
+ 
+
+ align:start position:0%
+this term has a lot of ks in it and so
+we're going to uh substitute these KS
+
+ align:start position:0%
+we're going to uh substitute these KS
+ 
+
+ align:start position:0%
+we're going to uh substitute these KS
+for another term that is more convenient
+
+ align:start position:0%
+for another term that is more convenient
+ 
+
+ align:start position:0%
+for another term that is more convenient
+to measure than any of these are by
+
+ align:start position:0%
+to measure than any of these are by
+ 
+
+ align:start position:0%
+to measure than any of these are by
+themselves so again this is a practical
+
+ align:start position:0%
+themselves so again this is a practical
+ 
+
+ align:start position:0%
+themselves so again this is a practical
+consideration you want to be able to use
+
+ align:start position:0%
+consideration you want to be able to use
+ 
+
+ align:start position:0%
+consideration you want to be able to use
+these equations to get information about
+
+ align:start position:0%
+these equations to get information about
+ 
+
+ align:start position:0%
+these equations to get information about
+enzyme
+
+ align:start position:0%
+enzyme
+ 
+
+ align:start position:0%
+enzyme
+kinetics and so the term that we're
+
+ align:start position:0%
+kinetics and so the term that we're
+ 
+
+ align:start position:0%
+kinetics and so the term that we're
+going to introduce is called Big K
+
+ align:start position:0%
+going to introduce is called Big K
+ 
+
+ align:start position:0%
+going to introduce is called Big K
+to the Little M the Michaelis Menton
+
+ align:start position:0%
+to the Little M the Michaelis Menton
+ 
+
+ align:start position:0%
+to the Little M the Michaelis Menton
+constant and so the Michaelis Menton
+
+ align:start position:0%
+constant and so the Michaelis Menton
+ 
+
+ align:start position:0%
+constant and so the Michaelis Menton
+constant and we'll talk about what this
+
+ align:start position:0%
+constant and we'll talk about what this
+ 
+
+ align:start position:0%
+constant and we'll talk about what this
+really means what this constant means in
+
+ align:start position:0%
+really means what this constant means in
+ 
+
+ align:start position:0%
+really means what this constant means in
+Practical terms in in a couple minutes
+
+ align:start position:0%
+Practical terms in in a couple minutes
+ 
+
+ align:start position:0%
+Practical terms in in a couple minutes
+um km equals kus1 + K2 ided
+
+ align:start position:0%
+um km equals kus1 + K2 ided
+ 
+
+ align:start position:0%
+um km equals kus1 + K2 ided
+K1 so now we somehow want to get this
+
+ align:start position:0%
+K1 so now we somehow want to get this
+ 
+
+ align:start position:0%
+K1 so now we somehow want to get this
+term into this expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's the expression again we want
+
+ align:start position:0%
+so here's the expression again we want
+ 
+
+ align:start position:0%
+so here's the expression again we want
+this term in here so if you notice at
+
+ align:start position:0%
+this term in here so if you notice at
+ 
+
+ align:start position:0%
+this term in here so if you notice at
+the bottom here there's a k minus one
+
+ align:start position:0%
+the bottom here there's a k minus one
+ 
+
+ align:start position:0%
+the bottom here there's a k minus one
+and a K2 just like there is here so if
+
+ align:start position:0%
+and a K2 just like there is here so if
+ 
+
+ align:start position:0%
+and a K2 just like there is here so if
+we divided these two by K1 we would have
+
+ align:start position:0%
+we divided these two by K1 we would have
+ 
+
+ align:start position:0%
+we divided these two by K1 we would have
+km over here but if we do that we have
+
+ align:start position:0%
+km over here but if we do that we have
+ 
+
+ align:start position:0%
+km over here but if we do that we have
+to divide everything by
+
+ align:start position:0%
+to divide everything by
+ 
+
+ align:start position:0%
+to divide everything by
+K1 so let's divide everything by K1 and
+
+ align:start position:0%
+K1 so let's divide everything by K1 and
+ 
+
+ align:start position:0%
+K1 so let's divide everything by K1 and
+turn this part of the expression into a
+
+ align:start position:0%
+turn this part of the expression into a
+ 
+
+ align:start position:0%
+turn this part of the expression into a
+km so if we do that we divide the top
+
+ align:start position:0%
+km so if we do that we divide the top
+ 
+
+ align:start position:0%
+km so if we do that we divide the top
+term by K1 we divide this term here k1s
+
+ align:start position:0%
+term by K1 we divide this term here k1s
+ 
+
+ align:start position:0%
+term by K1 we divide this term here k1s
+by K1 and we divide these two by
+
+ align:start position:0%
+by K1 and we divide these two by
+ 
+
+ align:start position:0%
+by K1 and we divide these two by
+K1 and we do that because now this is
+
+ align:start position:0%
+K1 and we do that because now this is
+ 
+
+ align:start position:0%
+K1 and we do that because now this is
+going to be equal to km all right so we
+
+ align:start position:0%
+going to be equal to km all right so we
+ 
+
+ align:start position:0%
+going to be equal to km all right so we
+can simplify this expression uh we have
+
+ align:start position:0%
+can simplify this expression uh we have
+ 
+
+ align:start position:0%
+can simplify this expression uh we have
+uh various things that we can cross out
+
+ align:start position:0%
+uh various things that we can cross out
+ 
+
+ align:start position:0%
+uh various things that we can cross out
+so if we do that see you can cross these
+
+ align:start position:0%
+so if we do that see you can cross these
+ 
+
+ align:start position:0%
+so if we do that see you can cross these
+two out up here can also cross these two
+
+ align:start position:0%
+two out up here can also cross these two
+ 
+
+ align:start position:0%
+two out up here can also cross these two
+out down here and what is that leave us
+
+ align:start position:0%
+out down here and what is that leave us
+ 
+
+ align:start position:0%
+out down here and what is that leave us
+with that leaves us with this so the top
+
+ align:start position:0%
+with that leaves us with this so the top
+ 
+
+ align:start position:0%
+with that leaves us with this so the top
+term we have total enzyme concentration
+
+ align:start position:0%
+term we have total enzyme concentration
+ 
+
+ align:start position:0%
+term we have total enzyme concentration
+times substrate
+
+ align:start position:0%
+times substrate
+ 
+
+ align:start position:0%
+times substrate
+concentration over substrate
+
+ align:start position:0%
+concentration over substrate
+ 
+
+ align:start position:0%
+concentration over substrate
+concentration plus this term here which
+
+ align:start position:0%
+concentration plus this term here which
+ 
+
+ align:start position:0%
+concentration plus this term here which
+is KNM so we've taken something that was
+
+ align:start position:0%
+is KNM so we've taken something that was
+ 
+
+ align:start position:0%
+is KNM so we've taken something that was
+a little bit more clunky and uh turned
+
+ align:start position:0%
+a little bit more clunky and uh turned
+ 
+
+ align:start position:0%
+a little bit more clunky and uh turned
+it into an expression that has a few
+
+ align:start position:0%
+it into an expression that has a few
+ 
+
+ align:start position:0%
+it into an expression that has a few
+fewer terms including uh this new term
+
+ align:start position:0%
+fewer terms including uh this new term
+ 
+
+ align:start position:0%
+fewer terms including uh this new term
+that's used for enzyme kinetics this KNM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term now we can finally go back and take
+
+ align:start position:0%
+term now we can finally go back and take
+ 
+
+ align:start position:0%
+term now we can finally go back and take
+our term for uh the concentration of the
+
+ align:start position:0%
+our term for uh the concentration of the
+ 
+
+ align:start position:0%
+our term for uh the concentration of the
+intermediate and plug it into our rate
+
+ align:start position:0%
+intermediate and plug it into our rate
+ 
+
+ align:start position:0%
+intermediate and plug it into our rate
+law for formation of product so again
+
+ align:start position:0%
+law for formation of product so again
+ 
+
+ align:start position:0%
+law for formation of product so again
+this was our uh expression for the rate
+
+ align:start position:0%
+this was our uh expression for the rate
+ 
+
+ align:start position:0%
+this was our uh expression for the rate
+of product formation K2 times the
+
+ align:start position:0%
+of product formation K2 times the
+ 
+
+ align:start position:0%
+of product formation K2 times the
+concentration of es and and we can take
+
+ align:start position:0%
+concentration of es and and we can take
+ 
+
+ align:start position:0%
+concentration of es and and we can take
+this and plug that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and that gives us this term K2 *
+
+ align:start position:0%
+here and that gives us this term K2 *
+ 
+
+ align:start position:0%
+here and that gives us this term K2 *
+total enzyme time substrate over
+
+ align:start position:0%
+total enzyme time substrate over
+ 
+
+ align:start position:0%
+total enzyme time substrate over
+substrate plus KNM and this is the
+
+ align:start position:0%
+substrate plus KNM and this is the
+ 
+
+ align:start position:0%
+substrate plus KNM and this is the
+Michaela me an equation so we used a lot
+
+ align:start position:0%
+Michaela me an equation so we used a lot
+ 
+
+ align:start position:0%
+Michaela me an equation so we used a lot
+of the use a steady state approximation
+
+ align:start position:0%
+of the use a steady state approximation
+ 
+
+ align:start position:0%
+of the use a steady state approximation
+we solved for an intermediate we did two
+
+ align:start position:0%
+we solved for an intermediate we did two
+ 
+
+ align:start position:0%
+we solved for an intermediate we did two
+things differently we didn't solve for
+
+ align:start position:0%
+things differently we didn't solve for
+ 
+
+ align:start position:0%
+things differently we didn't solve for
+free enzyme we solve for total enzyme
+
+ align:start position:0%
+free enzyme we solve for total enzyme
+ 
+
+ align:start position:0%
+free enzyme we solve for total enzyme
+and we also introduced this term km and
+
+ align:start position:0%
+and we also introduced this term km and
+ 
+
+ align:start position:0%
+and we also introduced this term km and
+and uh took out some of the individual
+
+ align:start position:0%
+and uh took out some of the individual
+ 
+
+ align:start position:0%
+and uh took out some of the individual
+rate constants and expressed them in
+
+ align:start position:0%
+rate constants and expressed them in
+ 
+
+ align:start position:0%
+rate constants and expressed them in
+terms of this uh of this constant so
+
+ align:start position:0%
+terms of this uh of this constant so
+ 
+
+ align:start position:0%
+terms of this uh of this constant so
+here is our rate equation for formation
+
+ align:start position:0%
+here is our rate equation for formation
+ 
+
+ align:start position:0%
+here is our rate equation for formation
+of product now let's think about what
+
+ align:start position:0%
+of product now let's think about what
+ 
+
+ align:start position:0%
+of product now let's think about what
+this equation can do what what it means
+
+ align:start position:0%
+this equation can do what what it means
+ 
+
+ align:start position:0%
+this equation can do what what it means
+what happens when enzyme is making
+
+ align:start position:0%
+what happens when enzyme is making
+ 
+
+ align:start position:0%
+what happens when enzyme is making
+product is acting as the Catalyst and
+
+ align:start position:0%
+product is acting as the Catalyst and
+ 
+
+ align:start position:0%
+product is acting as the Catalyst and
+turning our substrate into
+
+ align:start position:0%
+turning our substrate into
+ 
+
+ align:start position:0%
+turning our substrate into
+product so here would be a graph of uh
+
+ align:start position:0%
+product so here would be a graph of uh
+ 
+
+ align:start position:0%
+product so here would be a graph of uh
+what it might look look like you have
+
+ align:start position:0%
+what it might look look like you have
+ 
+
+ align:start position:0%
+what it might look look like you have
+here the rate of formation of product
+
+ align:start position:0%
+here the rate of formation of product
+ 
+
+ align:start position:0%
+here the rate of formation of product
+expressed as dpdt so that's just rate of
+
+ align:start position:0%
+expressed as dpdt so that's just rate of
+ 
+
+ align:start position:0%
+expressed as dpdt so that's just rate of
+product formation versus substrate
+
+ align:start position:0%
+product formation versus substrate
+ 
+
+ align:start position:0%
+product formation versus substrate
+concentration and you see that the curve
+
+ align:start position:0%
+concentration and you see that the curve
+ 
+
+ align:start position:0%
+concentration and you see that the curve
+goes up and then levels off so so what's
+
+ align:start position:0%
+goes up and then levels off so so what's
+ 
+
+ align:start position:0%
+goes up and then levels off so so what's
+happening in this
+
+ align:start position:0%
+happening in this
+ 
+
+ align:start position:0%
+happening in this
+case well at low substrate concentration
+
+ align:start position:0%
+case well at low substrate concentration
+ 
+
+ align:start position:0%
+case well at low substrate concentration
+and down here so this this is low
+
+ align:start position:0%
+and down here so this this is low
+ 
+
+ align:start position:0%
+and down here so this this is low
+substrate concentration at low substrate
+
+ align:start position:0%
+substrate concentration at low substrate
+ 
+
+ align:start position:0%
+substrate concentration at low substrate
+concentration when you add more
+
+ align:start position:0%
+concentration when you add more
+ 
+
+ align:start position:0%
+concentration when you add more
+substrate
+
+ align:start position:0%
+substrate
+ 
+
+ align:start position:0%
+substrate
+uh the rate goes up quite quickly and
+
+ align:start position:0%
+uh the rate goes up quite quickly and
+ 
+
+ align:start position:0%
+uh the rate goes up quite quickly and
+then starts to level off and at low
+
+ align:start position:0%
+then starts to level off and at low
+ 
+
+ align:start position:0%
+then starts to level off and at low
+substrate concentration incre adding
+
+ align:start position:0%
+substrate concentration incre adding
+ 
+
+ align:start position:0%
+substrate concentration incre adding
+more substrate increases the rate a lot
+
+ align:start position:0%
+more substrate increases the rate a lot
+ 
+
+ align:start position:0%
+more substrate increases the rate a lot
+because there's a bunch of enzyme that's
+
+ align:start position:0%
+because there's a bunch of enzyme that's
+ 
+
+ align:start position:0%
+because there's a bunch of enzyme that's
+free that's just hanging out and it's
+
+ align:start position:0%
+free that's just hanging out and it's
+ 
+
+ align:start position:0%
+free that's just hanging out and it's
+not making product because it doesn't
+
+ align:start position:0%
+not making product because it doesn't
+ 
+
+ align:start position:0%
+not making product because it doesn't
+have any substrate but you give it
+
+ align:start position:0%
+have any substrate but you give it
+ 
+
+ align:start position:0%
+have any substrate but you give it
+substrate and it'll quickly make product
+
+ align:start position:0%
+substrate and it'll quickly make product
+ 
+
+ align:start position:0%
+substrate and it'll quickly make product
+so that's what's happening you have lots
+
+ align:start position:0%
+so that's what's happening you have lots
+ 
+
+ align:start position:0%
+so that's what's happening you have lots
+of free enzyme around it's ready for
+
+ align:start position:0%
+of free enzyme around it's ready for
+ 
+
+ align:start position:0%
+of free enzyme around it's ready for
+substrate when you add substrate it
+
+ align:start position:0%
+substrate when you add substrate it
+ 
+
+ align:start position:0%
+substrate when you add substrate it
+reacts lots of pro is formed so why
+
+ align:start position:0%
+reacts lots of pro is formed so why
+ 
+
+ align:start position:0%
+reacts lots of pro is formed so why
+would it level off well it will level
+
+ align:start position:0%
+would it level off well it will level
+ 
+
+ align:start position:0%
+would it level off well it will level
+off at higher substrate
+
+ align:start position:0%
+off at higher substrate
+ 
+
+ align:start position:0%
+off at higher substrate
+concentrations because the en at higher
+
+ align:start position:0%
+concentrations because the en at higher
+ 
+
+ align:start position:0%
+concentrations because the en at higher
+substrate concentrations there really
+
+ align:start position:0%
+substrate concentrations there really
+ 
+
+ align:start position:0%
+substrate concentrations there really
+isn't any free enzyme around anymore so
+
+ align:start position:0%
+isn't any free enzyme around anymore so
+ 
+
+ align:start position:0%
+isn't any free enzyme around anymore so
+adding more substrate when the enzyme
+
+ align:start position:0%
+adding more substrate when the enzyme
+ 
+
+ align:start position:0%
+adding more substrate when the enzyme
+already has substrate bound is not going
+
+ align:start position:0%
+already has substrate bound is not going
+ 
+
+ align:start position:0%
+already has substrate bound is not going
+to increase the rate at which the
+
+ align:start position:0%
+to increase the rate at which the
+ 
+
+ align:start position:0%
+to increase the rate at which the
+products being formed when we say that
+
+ align:start position:0%
+products being formed when we say that
+ 
+
+ align:start position:0%
+products being formed when we say that
+the enzyme is saturated the enzyme
+
+ align:start position:0%
+the enzyme is saturated the enzyme
+ 
+
+ align:start position:0%
+the enzyme is saturated the enzyme
+already has as much substrate as it can
+
+ align:start position:0%
+already has as much substrate as it can
+ 
+
+ align:start position:0%
+already has as much substrate as it can
+use and you just have to wait until it
+
+ align:start position:0%
+use and you just have to wait until it
+ 
+
+ align:start position:0%
+use and you just have to wait until it
+finishes the uh reaction to product
+
+ align:start position:0%
+finishes the uh reaction to product
+ 
+
+ align:start position:0%
+finishes the uh reaction to product
+before a new substrate uh can be bound
+
+ align:start position:0%
+before a new substrate uh can be bound
+ 
+
+ align:start position:0%
+before a new substrate uh can be bound
+so the rate is going to level off at
+
+ align:start position:0%
+so the rate is going to level off at
+ 
+
+ align:start position:0%
+so the rate is going to level off at
+some point because there's no free
+
+ align:start position:0%
+some point because there's no free
+ 
+
+ align:start position:0%
+some point because there's no free
+enzyme around you've saturated with
+
+ align:start position:0%
+enzyme around you've saturated with
+ 
+
+ align:start position:0%
+enzyme around you've saturated with
+substrate adding more doesn't help your
+
+ align:start position:0%
+substrate adding more doesn't help your
+ 
+
+ align:start position:0%
+substrate adding more doesn't help your
+raid so we can think about this in terms
+
+ align:start position:0%
+raid so we can think about this in terms
+ 
+
+ align:start position:0%
+raid so we can think about this in terms
+of the Michaelis Menton
+
+ align:start position:0%
+of the Michaelis Menton
+ 
+
+ align:start position:0%
+of the Michaelis Menton
+equation so we can think about when
+
+ align:start position:0%
+equation so we can think about when
+ 
+
+ align:start position:0%
+equation so we can think about when
+substrate concentrations are really high
+
+ align:start position:0%
+substrate concentrations are really high
+ 
+
+ align:start position:0%
+substrate concentrations are really high
+when you have lots of substrates and we
+
+ align:start position:0%
+when you have lots of substrates and we
+ 
+
+ align:start position:0%
+when you have lots of substrates and we
+can think about that in terms of this
+
+ align:start position:0%
+can think about that in terms of this
+ 
+
+ align:start position:0%
+can think about that in terms of this
+value for km so again we're looking here
+
+ align:start position:0%
+value for km so again we're looking here
+ 
+
+ align:start position:0%
+value for km so again we're looking here
+at the bottom of this equation and we're
+
+ align:start position:0%
+at the bottom of this equation and we're
+ 
+
+ align:start position:0%
+at the bottom of this equation and we're
+thinking about how big is this term
+
+ align:start position:0%
+thinking about how big is this term
+ 
+
+ align:start position:0%
+thinking about how big is this term
+compared to that term so under
+
+ align:start position:0%
+compared to that term so under
+ 
+
+ align:start position:0%
+compared to that term so under
+conditions of the experiment where
+
+ align:start position:0%
+conditions of the experiment where
+ 
+
+ align:start position:0%
+conditions of the experiment where
+substrate concentration is a much bigger
+
+ align:start position:0%
+substrate concentration is a much bigger
+ 
+
+ align:start position:0%
+substrate concentration is a much bigger
+number than
+
+ align:start position:0%
+number than
+ 
+
+ align:start position:0%
+number than
+km we can get rid of the km term so we
+
+ align:start position:0%
+km we can get rid of the km term so we
+ 
+
+ align:start position:0%
+km we can get rid of the km term so we
+can cross this out again if you a really
+
+ align:start position:0%
+can cross this out again if you a really
+ 
+
+ align:start position:0%
+can cross this out again if you a really
+big number in the denominator added to a
+
+ align:start position:0%
+big number in the denominator added to a
+ 
+
+ align:start position:0%
+big number in the denominator added to a
+much smaller number the much smaller
+
+ align:start position:0%
+much smaller number the much smaller
+ 
+
+ align:start position:0%
+much smaller number the much smaller
+number isn't really contributing much
+
+ align:start position:0%
+number isn't really contributing much
+ 
+
+ align:start position:0%
+number isn't really contributing much
+and you can just get rid of it now we
+
+ align:start position:0%
+and you can just get rid of it now we
+ 
+
+ align:start position:0%
+and you can just get rid of it now we
+can simplify this equation then if we
+
+ align:start position:0%
+can simplify this equation then if we
+ 
+
+ align:start position:0%
+can simplify this equation then if we
+did that what else could we cancel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out we can cancel out s can get rid of
+
+ align:start position:0%
+out we can cancel out s can get rid of
+ 
+
+ align:start position:0%
+out we can cancel out s can get rid of
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+substrate and that leaves us with this
+
+ align:start position:0%
+substrate and that leaves us with this
+ 
+
+ align:start position:0%
+substrate and that leaves us with this
+expression that the rate of formation of
+
+ align:start position:0%
+expression that the rate of formation of
+ 
+
+ align:start position:0%
+expression that the rate of formation of
+product under these conditions when
+
+ align:start position:0%
+product under these conditions when
+ 
+
+ align:start position:0%
+product under these conditions when
+substrate is is a much bigger number
+
+ align:start position:0%
+substrate is is a much bigger number
+ 
+
+ align:start position:0%
+substrate is is a much bigger number
+than this km term then we get this
+
+ align:start position:0%
+than this km term then we get this
+ 
+
+ align:start position:0%
+than this km term then we get this
+expression that the rate is just equal
+
+ align:start position:0%
+expression that the rate is just equal
+ 
+
+ align:start position:0%
+expression that the rate is just equal
+to K2 times the total enzyme that we had
+
+ align:start position:0%
+to K2 times the total enzyme that we had
+ 
+
+ align:start position:0%
+to K2 times the total enzyme that we had
+in our reaction and this has a
+
+ align:start position:0%
+in our reaction and this has a
+ 
+
+ align:start position:0%
+in our reaction and this has a
+name and it's called
+
+ align:start position:0%
+name and it's called
+ 
+
+ align:start position:0%
+name and it's called
+Vmax so Vmax equals K2 * total enzyme
+
+ align:start position:0%
+Vmax so Vmax equals K2 * total enzyme
+ 
+
+ align:start position:0%
+Vmax so Vmax equals K2 * total enzyme
+and Vmax is the maximum rate of the of
+
+ align:start position:0%
+and Vmax is the maximum rate of the of
+ 
+
+ align:start position:0%
+and Vmax is the maximum rate of the of
+the reaction and so when you have lots
+
+ align:start position:0%
+the reaction and so when you have lots
+ 
+
+ align:start position:0%
+the reaction and so when you have lots
+and lots of substrates you're under
+
+ align:start position:0%
+and lots of substrates you're under
+ 
+
+ align:start position:0%
+and lots of substrates you're under
+under these conditions where you can
+
+ align:start position:0%
+under these conditions where you can
+ 
+
+ align:start position:0%
+under these conditions where you can
+determine the maximum rate of the enzyme
+
+ align:start position:0%
+determine the maximum rate of the enzyme
+ 
+
+ align:start position:0%
+determine the maximum rate of the enzyme
+the Vmax of the enzyme and it's only
+
+ align:start position:0%
+the Vmax of the enzyme and it's only
+ 
+
+ align:start position:0%
+the Vmax of the enzyme and it's only
+equal to this K2 times how much ever
+
+ align:start position:0%
+equal to this K2 times how much ever
+ 
+
+ align:start position:0%
+equal to this K2 times how much ever
+enzyme you had in that particular
+
+ align:start position:0%
+enzyme you had in that particular
+ 
+
+ align:start position:0%
+enzyme you had in that particular
+experiment again the maximum rate of the
+
+ align:start position:0%
+experiment again the maximum rate of the
+ 
+
+ align:start position:0%
+experiment again the maximum rate of the
+enzyme under these
+
+ align:start position:0%
+enzyme under these
+ 
+
+ align:start position:0%
+enzyme under these
+conditions so again that would be up
+
+ align:start position:0%
+conditions so again that would be up
+ 
+
+ align:start position:0%
+conditions so again that would be up
+here the rate levels off when you have
+
+ align:start position:0%
+here the rate levels off when you have
+ 
+
+ align:start position:0%
+here the rate levels off when you have
+high substrate concentration then you're
+
+ align:start position:0%
+high substrate concentration then you're
+ 
+
+ align:start position:0%
+high substrate concentration then you're
+at the maximum rate the enzyme can't go
+
+ align:start position:0%
+at the maximum rate the enzyme can't go
+ 
+
+ align:start position:0%
+at the maximum rate the enzyme can't go
+any faster at that point uh it just
+
+ align:start position:0%
+any faster at that point uh it just
+ 
+
+ align:start position:0%
+any faster at that point uh it just
+depends on how the rate depends on how
+
+ align:start position:0%
+depends on how the rate depends on how
+ 
+
+ align:start position:0%
+depends on how the rate depends on how
+much enzyme you have and the K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term so now let's consider uh this
+
+ align:start position:0%
+term so now let's consider uh this
+ 
+
+ align:start position:0%
+term so now let's consider uh this
+scenario where these two terms at the
+
+ align:start position:0%
+scenario where these two terms at the
+ 
+
+ align:start position:0%
+scenario where these two terms at the
+bottom of the expression are equal to
+
+ align:start position:0%
+bottom of the expression are equal to
+ 
+
+ align:start position:0%
+bottom of the expression are equal to
+each other when substrate equals km the
+
+ align:start position:0%
+each other when substrate equals km the
+ 
+
+ align:start position:0%
+each other when substrate equals km the
+concentration of substrate equals km so
+
+ align:start position:0%
+concentration of substrate equals km so
+ 
+
+ align:start position:0%
+concentration of substrate equals km so
+if those are equal we can get rid of the
+
+ align:start position:0%
+if those are equal we can get rid of the
+ 
+
+ align:start position:0%
+if those are equal we can get rid of the
+knen term and put in another substrate
+
+ align:start position:0%
+knen term and put in another substrate
+ 
+
+ align:start position:0%
+knen term and put in another substrate
+term because they're equal
+
+ align:start position:0%
+term because they're equal
+ 
+
+ align:start position:0%
+term because they're equal
+so we'll just put in uh another
+
+ align:start position:0%
+so we'll just put in uh another
+ 
+
+ align:start position:0%
+so we'll just put in uh another
+substrate term and uh then we can
+
+ align:start position:0%
+substrate term and uh then we can
+ 
+
+ align:start position:0%
+substrate term and uh then we can
+simplify
+
+ align:start position:0%
+simplify
+ 
+
+ align:start position:0%
+simplify
+again so two two substrates are down
+
+ align:start position:0%
+again so two two substrates are down
+ 
+
+ align:start position:0%
+again so two two substrates are down
+here one is up here we can cancel one of
+
+ align:start position:0%
+here one is up here we can cancel one of
+ 
+
+ align:start position:0%
+here one is up here we can cancel one of
+them and get the following so we cancel
+
+ align:start position:0%
+them and get the following so we cancel
+ 
+
+ align:start position:0%
+them and get the following so we cancel
+one we have 12 K2 times the total enzyme
+
+ align:start position:0%
+one we have 12 K2 times the total enzyme
+ 
+
+ align:start position:0%
+one we have 12 K2 times the total enzyme
+concentration and this would be
+
+ align:start position:0%
+concentration and this would be
+ 
+
+ align:start position:0%
+concentration and this would be
+then the half maximal rate
+
+ align:start position:0%
+then the half maximal rate
+ 
+
+ align:start position:0%
+then the half maximal rate
+so the maximal rate was K2 times the
+
+ align:start position:0%
+so the maximal rate was K2 times the
+ 
+
+ align:start position:0%
+so the maximal rate was K2 times the
+enzyme concent total enzyme
+
+ align:start position:0%
+enzyme concent total enzyme
+ 
+
+ align:start position:0%
+enzyme concent total enzyme
+concentration half maximal is half that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate and now we can finally Define
+
+ align:start position:0%
+rate and now we can finally Define
+ 
+
+ align:start position:0%
+rate and now we can finally Define
+km we can Define km as the concentration
+
+ align:start position:0%
+km we can Define km as the concentration
+ 
+
+ align:start position:0%
+km we can Define km as the concentration
+of substrate for which the rate is half
+
+ align:start position:0%
+of substrate for which the rate is half
+ 
+
+ align:start position:0%
+of substrate for which the rate is half
+maximum so uh the concentration of
+
+ align:start position:0%
+maximum so uh the concentration of
+ 
+
+ align:start position:0%
+maximum so uh the concentration of
+substrate when you have this this half
+
+ align:start position:0%
+substrate when you have this this half
+ 
+
+ align:start position:0%
+substrate when you have this this half
+maximal rate that's what km is and so
+
+ align:start position:0%
+maximal rate that's what km is and so
+ 
+
+ align:start position:0%
+maximal rate that's what km is and so
+this is a term that's easy to measure
+
+ align:start position:0%
+this is a term that's easy to measure
+ 
+
+ align:start position:0%
+this is a term that's easy to measure
+then and that's why we did some
+
+ align:start position:0%
+then and that's why we did some
+ 
+
+ align:start position:0%
+then and that's why we did some
+manipulations to get it into our
+
+ align:start position:0%
+manipulations to get it into our
+ 
+
+ align:start position:0%
+manipulations to get it into our
+equation because it's a term where you
+
+ align:start position:0%
+equation because it's a term where you
+ 
+
+ align:start position:0%
+equation because it's a term where you
+can find the answer the km value so if
+
+ align:start position:0%
+can find the answer the km value so if
+ 
+
+ align:start position:0%
+can find the answer the km value so if
+you know the maximal rate you can find
+
+ align:start position:0%
+you know the maximal rate you can find
+ 
+
+ align:start position:0%
+you know the maximal rate you can find
+the half maximal rate and figure out
+
+ align:start position:0%
+the half maximal rate and figure out
+ 
+
+ align:start position:0%
+the half maximal rate and figure out
+what substrate concentration gives you
+
+ align:start position:0%
+what substrate concentration gives you
+ 
+
+ align:start position:0%
+what substrate concentration gives you
+that half maximal rate and that's just
+
+ align:start position:0%
+that half maximal rate and that's just
+ 
+
+ align:start position:0%
+that half maximal rate and that's just
+going to be your km so in some problems
+
+ align:start position:0%
+going to be your km so in some problems
+ 
+
+ align:start position:0%
+going to be your km so in some problems
+that you're going to have in the extra
+
+ align:start position:0%
+that you're going to have in the extra
+ 
+
+ align:start position:0%
+that you're going to have in the extra
+problems that are posted it may tell you
+
+ align:start position:0%
+problems that are posted it may tell you
+ 
+
+ align:start position:0%
+problems that are posted it may tell you
+the maximal rate and uh then tell you
+
+ align:start position:0%
+the maximal rate and uh then tell you
+ 
+
+ align:start position:0%
+the maximal rate and uh then tell you
+the substrate concentration that gives
+
+ align:start position:0%
+the substrate concentration that gives
+ 
+
+ align:start position:0%
+the substrate concentration that gives
+you the half maximal rate and you have
+
+ align:start position:0%
+you the half maximal rate and you have
+ 
+
+ align:start position:0%
+you the half maximal rate and you have
+to find the km well that's not a hard
+
+ align:start position:0%
+to find the km well that's not a hard
+ 
+
+ align:start position:0%
+to find the km well that's not a hard
+problem if you're told the substrate
+
+ align:start position:0%
+problem if you're told the substrate
+ 
+
+ align:start position:0%
+problem if you're told the substrate
+concentration that gives you the half
+
+ align:start position:0%
+concentration that gives you the half
+ 
+
+ align:start position:0%
+concentration that gives you the half
+maximal rate that is the km so it's just
+
+ align:start position:0%
+maximal rate that is the km so it's just
+ 
+
+ align:start position:0%
+maximal rate that is the km so it's just
+a matter of knowing the definition so
+
+ align:start position:0%
+a matter of knowing the definition so
+ 
+
+ align:start position:0%
+a matter of knowing the definition so
+the levels of problems that you have in
+
+ align:start position:0%
+the levels of problems that you have in
+ 
+
+ align:start position:0%
+the levels of problems that you have in
+your chapter on enzyme kinetics are
+
+ align:start position:0%
+your chapter on enzyme kinetics are
+ 
+
+ align:start position:0%
+your chapter on enzyme kinetics are
+really pretty simple if you know if you
+
+ align:start position:0%
+really pretty simple if you know if you
+ 
+
+ align:start position:0%
+really pretty simple if you know if you
+know some of the definitions you're all
+
+ align:start position:0%
+know some of the definitions you're all
+ 
+
+ align:start position:0%
+know some of the definitions you're all
+set so finally let's just look at
+
+ align:start position:0%
+set so finally let's just look at
+ 
+
+ align:start position:0%
+set so finally let's just look at
+Inhibitors in the last uh few
+
+ align:start position:0%
+Inhibitors in the last uh few
+ 
+
+ align:start position:0%
+Inhibitors in the last uh few
+minutes so um this is a very simplistic
+
+ align:start position:0%
+minutes so um this is a very simplistic
+ 
+
+ align:start position:0%
+minutes so um this is a very simplistic
+view of uh of an inhibitor situation so
+
+ align:start position:0%
+view of uh of an inhibitor situation so
+ 
+
+ align:start position:0%
+view of uh of an inhibitor situation so
+if your inhibitor is I it may bind to
+
+ align:start position:0%
+if your inhibitor is I it may bind to
+ 
+
+ align:start position:0%
+if your inhibitor is I it may bind to
+your free enzyme to give you an EI
+
+ align:start position:0%
+your free enzyme to give you an EI
+ 
+
+ align:start position:0%
+your free enzyme to give you an EI
+complex an inhibitor bound complex and
+
+ align:start position:0%
+complex an inhibitor bound complex and
+ 
+
+ align:start position:0%
+complex an inhibitor bound complex and
+if the inhibitor is bound in the active
+
+ align:start position:0%
+if the inhibitor is bound in the active
+ 
+
+ align:start position:0%
+if the inhibitor is bound in the active
+site and it's bound pretty well
+
+ align:start position:0%
+site and it's bound pretty well
+ 
+
+ align:start position:0%
+site and it's bound pretty well
+substrate's going to come along but it
+
+ align:start position:0%
+substrate's going to come along but it
+ 
+
+ align:start position:0%
+substrate's going to come along but it
+can't bind so you can't make any product
+
+ align:start position:0%
+can't bind so you can't make any product
+ 
+
+ align:start position:0%
+can't bind so you can't make any product
+so uh the inhibitor has stopped the
+
+ align:start position:0%
+so uh the inhibitor has stopped the
+ 
+
+ align:start position:0%
+so uh the inhibitor has stopped the
+activity so that's just a very
+
+ align:start position:0%
+activity so that's just a very
+ 
+
+ align:start position:0%
+activity so that's just a very
+simplistic scheme of what can be going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on so many Pharmaceuticals work are are
+
+ align:start position:0%
+on so many Pharmaceuticals work are are
+ 
+
+ align:start position:0%
+on so many Pharmaceuticals work are are
+enzyme Inhibitors that's that's what
+
+ align:start position:0%
+enzyme Inhibitors that's that's what
+ 
+
+ align:start position:0%
+enzyme Inhibitors that's that's what
+they do uh so they stop uh enzymes
+
+ align:start position:0%
+they do uh so they stop uh enzymes
+ 
+
+ align:start position:0%
+they do uh so they stop uh enzymes
+biological catalysts and the way in
+
+ align:start position:0%
+biological catalysts and the way in
+ 
+
+ align:start position:0%
+biological catalysts and the way in
+which they work often is that they're
+
+ align:start position:0%
+which they work often is that they're
+ 
+
+ align:start position:0%
+which they work often is that they're
+designed the inhibitor is designed to
+
+ align:start position:0%
+designed the inhibitor is designed to
+ 
+
+ align:start position:0%
+designed the inhibitor is designed to
+mimic the transition state of of the uh
+
+ align:start position:0%
+mimic the transition state of of the uh
+ 
+
+ align:start position:0%
+mimic the transition state of of the uh
+reaction so if you have things coming
+
+ align:start position:0%
+reaction so if you have things coming
+ 
+
+ align:start position:0%
+reaction so if you have things coming
+together and they form a activated
+
+ align:start position:0%
+together and they form a activated
+ 
+
+ align:start position:0%
+together and they form a activated
+complex or transition state before they
+
+ align:start position:0%
+complex or transition state before they
+ 
+
+ align:start position:0%
+complex or transition state before they
+go on to say form products often the
+
+ align:start position:0%
+go on to say form products often the
+ 
+
+ align:start position:0%
+go on to say form products often the
+inhibitor is designed to look like that
+
+ align:start position:0%
+inhibitor is designed to look like that
+ 
+
+ align:start position:0%
+inhibitor is designed to look like that
+transition state that's formed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the reason why it would do this is
+
+ align:start position:0%
+so the reason why it would do this is
+ 
+
+ align:start position:0%
+so the reason why it would do this is
+because molecules that resemble the
+
+ align:start position:0%
+because molecules that resemble the
+ 
+
+ align:start position:0%
+because molecules that resemble the
+transition state should bind more
+
+ align:start position:0%
+transition state should bind more
+ 
+
+ align:start position:0%
+transition state should bind more
+tightly uh to the enzyme than either the
+
+ align:start position:0%
+tightly uh to the enzyme than either the
+ 
+
+ align:start position:0%
+tightly uh to the enzyme than either the
+reactants or the products and so
+
+ align:start position:0%
+reactants or the products and so
+ 
+
+ align:start position:0%
+reactants or the products and so
+therefore they can serve as effective
+
+ align:start position:0%
+therefore they can serve as effective
+ 
+
+ align:start position:0%
+therefore they can serve as effective
+Inhibitors so if you just recall what we
+
+ align:start position:0%
+Inhibitors so if you just recall what we
+ 
+
+ align:start position:0%
+Inhibitors so if you just recall what we
+showed at the beginning of the talk uh
+
+ align:start position:0%
+showed at the beginning of the talk uh
+ 
+
+ align:start position:0%
+showed at the beginning of the talk uh
+catalysts work by lowering this barrier
+
+ align:start position:0%
+catalysts work by lowering this barrier
+ 
+
+ align:start position:0%
+catalysts work by lowering this barrier
+or by stabilizing the transition state
+
+ align:start position:0%
+or by stabilizing the transition state
+ 
+
+ align:start position:0%
+or by stabilizing the transition state
+bringing the transition state to a lower
+
+ align:start position:0%
+bringing the transition state to a lower
+ 
+
+ align:start position:0%
+bringing the transition state to a lower
+energy and so often uh Inhibitors that
+
+ align:start position:0%
+energy and so often uh Inhibitors that
+ 
+
+ align:start position:0%
+energy and so often uh Inhibitors that
+look like a transition state will bind
+
+ align:start position:0%
+look like a transition state will bind
+ 
+
+ align:start position:0%
+look like a transition state will bind
+to the enzyme quite tightly and you want
+
+ align:start position:0%
+to the enzyme quite tightly and you want
+ 
+
+ align:start position:0%
+to the enzyme quite tightly and you want
+the inhibitor to bind tightly because
+
+ align:start position:0%
+the inhibitor to bind tightly because
+ 
+
+ align:start position:0%
+the inhibitor to bind tightly because
+you don't want substrate to be able to
+
+ align:start position:0%
+you don't want substrate to be able to
+ 
+
+ align:start position:0%
+you don't want substrate to be able to
+come along and displace the inhibitor if
+
+ align:start position:0%
+come along and displace the inhibitor if
+ 
+
+ align:start position:0%
+come along and displace the inhibitor if
+you're trying to stop the enzyme from
+
+ align:start position:0%
+you're trying to stop the enzyme from
+ 
+
+ align:start position:0%
+you're trying to stop the enzyme from
+working you want a tightly bound
+
+ align:start position:0%
+working you want a tightly bound
+ 
+
+ align:start position:0%
+working you want a tightly bound
+inhibitor so they often look to the
+
+ align:start position:0%
+inhibitor so they often look to the
+ 
+
+ align:start position:0%
+inhibitor so they often look to the
+transition state and let me just give
+
+ align:start position:0%
+transition state and let me just give
+ 
+
+ align:start position:0%
+transition state and let me just give
+you one example that's been uh pretty
+
+ align:start position:0%
+you one example that's been uh pretty
+ 
+
+ align:start position:0%
+you one example that's been uh pretty
+successful
+
+ align:start position:0%
+successful
+ 
+
+ align:start position:0%
+successful
+uh and that is with protas Inhibitors uh
+
+ align:start position:0%
+uh and that is with protas Inhibitors uh
+ 
+
+ align:start position:0%
+uh and that is with protas Inhibitors uh
+so protas Inhibitors are used in the
+
+ align:start position:0%
+so protas Inhibitors are used in the
+ 
+
+ align:start position:0%
+so protas Inhibitors are used in the
+treatment of
+
+ align:start position:0%
+treatment of
+ 
+
+ align:start position:0%
+treatment of
+HIV and um the uh proteases are enzymes
+
+ align:start position:0%
+HIV and um the uh proteases are enzymes
+ 
+
+ align:start position:0%
+HIV and um the uh proteases are enzymes
+which cleave peptide bonds and so we
+
+ align:start position:0%
+which cleave peptide bonds and so we
+ 
+
+ align:start position:0%
+which cleave peptide bonds and so we
+talked about the formation of a peptide
+
+ align:start position:0%
+talked about the formation of a peptide
+ 
+
+ align:start position:0%
+talked about the formation of a peptide
+bond so this is a reaction that
+
+ align:start position:0%
+bond so this is a reaction that
+ 
+
+ align:start position:0%
+bond so this is a reaction that
+catalyzes the reverse process breaking
+
+ align:start position:0%
+catalyzes the reverse process breaking
+ 
+
+ align:start position:0%
+catalyzes the reverse process breaking
+down the peptide bond and so here might
+
+ align:start position:0%
+down the peptide bond and so here might
+ 
+
+ align:start position:0%
+down the peptide bond and so here might
+be a Rea simplified reaction mechanism
+
+ align:start position:0%
+be a Rea simplified reaction mechanism
+ 
+
+ align:start position:0%
+be a Rea simplified reaction mechanism
+uh you have something coming in a
+
+ align:start position:0%
+uh you have something coming in a
+ 
+
+ align:start position:0%
+uh you have something coming in a
+attacking here's your peptide bond
+
+ align:start position:0%
+attacking here's your peptide bond
+ 
+
+ align:start position:0%
+attacking here's your peptide bond
+you're forming a tetrahedral
+
+ align:start position:0%
+you're forming a tetrahedral
+ 
+
+ align:start position:0%
+you're forming a tetrahedral
+intermediate here and what would be the
+
+ align:start position:0%
+intermediate here and what would be the
+ 
+
+ align:start position:0%
+intermediate here and what would be the
+angles of a tetrahedral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermediate
+
+ align:start position:0%
+intermediate
+ 
+
+ align:start position:0%
+intermediate
+109.5 and then this would break down and
+
+ align:start position:0%
+109.5 and then this would break down and
+ 
+
+ align:start position:0%
+109.5 and then this would break down and
+you would form these two products so the
+
+ align:start position:0%
+you would form these two products so the
+ 
+
+ align:start position:0%
+you would form these two products so the
+peptide bond then gets cleaved and so uh
+
+ align:start position:0%
+peptide bond then gets cleaved and so uh
+ 
+
+ align:start position:0%
+peptide bond then gets cleaved and so uh
+designers of Inhibitors or
+
+ align:start position:0%
+designers of Inhibitors or
+ 
+
+ align:start position:0%
+designers of Inhibitors or
+pharmaceutical drugs have tried to mimic
+
+ align:start position:0%
+pharmaceutical drugs have tried to mimic
+ 
+
+ align:start position:0%
+pharmaceutical drugs have tried to mimic
+this tetrahedral inter immediate to try
+
+ align:start position:0%
+this tetrahedral inter immediate to try
+ 
+
+ align:start position:0%
+this tetrahedral inter immediate to try
+to get tight binding so you have the
+
+ align:start position:0%
+to get tight binding so you have the
+ 
+
+ align:start position:0%
+to get tight binding so you have the
+idea that uh molecules with this uh
+
+ align:start position:0%
+idea that uh molecules with this uh
+ 
+
+ align:start position:0%
+idea that uh molecules with this uh
+stabal tetrahedral site that can't be
+
+ align:start position:0%
+stabal tetrahedral site that can't be
+ 
+
+ align:start position:0%
+stabal tetrahedral site that can't be
+cleaved uh could bind to the enzyme uh
+
+ align:start position:0%
+cleaved uh could bind to the enzyme uh
+ 
+
+ align:start position:0%
+cleaved uh could bind to the enzyme uh
+more tightly than than uh substrate and
+
+ align:start position:0%
+more tightly than than uh substrate and
+ 
+
+ align:start position:0%
+more tightly than than uh substrate and
+this is just one example of a drug that
+
+ align:start position:0%
+this is just one example of a drug that
+ 
+
+ align:start position:0%
+this is just one example of a drug that
+inhibits HIV protease that has that
+
+ align:start position:0%
+inhibits HIV protease that has that
+ 
+
+ align:start position:0%
+inhibits HIV protease that has that
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+tetrahedral uh site where that cannot be
+
+ align:start position:0%
+tetrahedral uh site where that cannot be
+ 
+
+ align:start position:0%
+tetrahedral uh site where that cannot be
+cleaved I'm almost done so here's a
+
+ align:start position:0%
+cleaved I'm almost done so here's a
+ 
+
+ align:start position:0%
+cleaved I'm almost done so here's a
+picture of it bound uh to the enzyme so
+
+ align:start position:0%
+picture of it bound uh to the enzyme so
+ 
+
+ align:start position:0%
+picture of it bound uh to the enzyme so
+here's the inhibitor bound to the active
+
+ align:start position:0%
+here's the inhibitor bound to the active
+ 
+
+ align:start position:0%
+here's the inhibitor bound to the active
+site so it fits quite well in there um
+
+ align:start position:0%
+site so it fits quite well in there um
+ 
+
+ align:start position:0%
+site so it fits quite well in there um
+and let me just mention finally that one
+
+ align:start position:0%
+and let me just mention finally that one
+ 
+
+ align:start position:0%
+and let me just mention finally that one
+problem with designing Inhibitors toward
+
+ align:start position:0%
+problem with designing Inhibitors toward
+ 
+
+ align:start position:0%
+problem with designing Inhibitors toward
+enzymes there's many in this case many
+
+ align:start position:0%
+enzymes there's many in this case many
+ 
+
+ align:start position:0%
+enzymes there's many in this case many
+proteases so you might not want to stop
+
+ align:start position:0%
+proteases so you might not want to stop
+ 
+
+ align:start position:0%
+proteases so you might not want to stop
+all proteases from working you only want
+
+ align:start position:0%
+all proteases from working you only want
+ 
+
+ align:start position:0%
+all proteases from working you only want
+to stop the HIV protease from working so
+
+ align:start position:0%
+to stop the HIV protease from working so
+ 
+
+ align:start position:0%
+to stop the HIV protease from working so
+there's a lot of issues of specificity
+
+ align:start position:0%
+there's a lot of issues of specificity
+ 
+
+ align:start position:0%
+there's a lot of issues of specificity
+so that's one of the complication of
+
+ align:start position:0%
+so that's one of the complication of
+ 
+
+ align:start position:0%
+so that's one of the complication of
+drug design design and that again is
+
+ align:start position:0%
+drug design design and that again is
+ 
+
+ align:start position:0%
+drug design design and that again is
+another important uh area for you to
+
+ align:start position:0%
+another important uh area for you to
+ 
+
+ align:start position:0%
+another important uh area for you to
+think about doing uh there's still a
+
+ align:start position:0%
+think about doing uh there's still a
+ 
+
+ align:start position:0%
+think about doing uh there's still a
+huge problem with HIV uh not so as much
+
+ align:start position:0%
+huge problem with HIV uh not so as much
+ 
+
+ align:start position:0%
+huge problem with HIV uh not so as much
+in the US but in other countries so it's
+
+ align:start position:0%
+in the US but in other countries so it's
+ 
+
+ align:start position:0%
+in the US but in other countries so it's
+something else you can think about doing
+
+ align:start position:0%
+something else you can think about doing
+ 
+
+ align:start position:0%
+something else you can think about doing
+all right see you Wednesday
\ No newline at end of file
diff --git a/aBEZyrqUV28.txt b/aBEZyrqUV28.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ed29ba4d3614884b591cedda7ee54d586d2e38b
--- /dev/null
+++ b/aBEZyrqUV28.txt
@@ -0,0 +1,2763 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrostatic precipitation demonstrates
+
+ align:start position:0%
+electrostatic precipitation demonstrates
+ 
+
+ align:start position:0%
+electrostatic precipitation demonstrates
+how air ions generated by a Corona
+
+ align:start position:0%
+how air ions generated by a Corona
+ 
+
+ align:start position:0%
+how air ions generated by a Corona
+discharge can be used to charge
+
+ align:start position:0%
+discharge can be used to charge
+ 
+
+ align:start position:0%
+discharge can be used to charge
+macroscopic
+
+ align:start position:0%
+macroscopic
+ 
+
+ align:start position:0%
+macroscopic
+particles and how those particles can
+
+ align:start position:0%
+particles and how those particles can
+ 
+
+ align:start position:0%
+particles and how those particles can
+then be removed from the air by the
+
+ align:start position:0%
+then be removed from the air by the
+ 
+
+ align:start position:0%
+then be removed from the air by the
+applied electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field in an electric field e a particle
+
+ align:start position:0%
+field in an electric field e a particle
+ 
+
+ align:start position:0%
+field in an electric field e a particle
+having the charge Q is subject to the
+
+ align:start position:0%
+having the charge Q is subject to the
+ 
+
+ align:start position:0%
+having the charge Q is subject to the
+Loren Force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for particles such as dust and smoke in
+
+ align:start position:0%
+for particles such as dust and smoke in
+ 
+
+ align:start position:0%
+for particles such as dust and smoke in
+air their velocity is so low that even
+
+ align:start position:0%
+air their velocity is so low that even
+ 
+
+ align:start position:0%
+air their velocity is so low that even
+if there were much of an applied
+
+ align:start position:0%
+if there were much of an applied
+ 
+
+ align:start position:0%
+if there were much of an applied
+magnetic field its contribution would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible in air the inertia of fine
+
+ align:start position:0%
+negligible in air the inertia of fine
+ 
+
+ align:start position:0%
+negligible in air the inertia of fine
+particles is often
+
+ align:start position:0%
+particles is often
+ 
+
+ align:start position:0%
+particles is often
+negligible the electrical force is
+
+ align:start position:0%
+negligible the electrical force is
+ 
+
+ align:start position:0%
+negligible the electrical force is
+balanced by a drag
+
+ align:start position:0%
+balanced by a drag
+ 
+
+ align:start position:0%
+balanced by a drag
+Force this drag force is proportional to
+
+ align:start position:0%
+Force this drag force is proportional to
+ 
+
+ align:start position:0%
+Force this drag force is proportional to
+the particles velocity V relative to the
+
+ align:start position:0%
+the particles velocity V relative to the
+ 
+
+ align:start position:0%
+the particles velocity V relative to the
+air for example if such particles were
+
+ align:start position:0%
+air for example if such particles were
+ 
+
+ align:start position:0%
+air for example if such particles were
+spherical with a radius
+
+ align:start position:0%
+spherical with a radius
+ 
+
+ align:start position:0%
+spherical with a radius
+R this force would be the Stokes drag
+
+ align:start position:0%
+R this force would be the Stokes drag
+ 
+
+ align:start position:0%
+R this force would be the Stokes drag
+where Ada is the viscosity of
+
+ align:start position:0%
+where Ada is the viscosity of
+ 
+
+ align:start position:0%
+where Ada is the viscosity of
+air the particle velocity is then
+
+ align:start position:0%
+air the particle velocity is then
+ 
+
+ align:start position:0%
+air the particle velocity is then
+proportional to the applied electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field the particle velocity is
+
+ align:start position:0%
+field the particle velocity is
+ 
+
+ align:start position:0%
+field the particle velocity is
+proportional to the applied electric
+
+ align:start position:0%
+proportional to the applied electric
+ 
+
+ align:start position:0%
+proportional to the applied electric
+field the coefficient relating the
+
+ align:start position:0%
+field the coefficient relating the
+ 
+
+ align:start position:0%
+field the coefficient relating the
+particle velocity to the electric field
+
+ align:start position:0%
+particle velocity to the electric field
+ 
+
+ align:start position:0%
+particle velocity to the electric field
+intensity mu is defined as the
+
+ align:start position:0%
+intensity mu is defined as the
+ 
+
+ align:start position:0%
+intensity mu is defined as the
+mobility it is generally proportional to
+
+ align:start position:0%
+mobility it is generally proportional to
+ 
+
+ align:start position:0%
+mobility it is generally proportional to
+the particle charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q if these particles are the only ones
+
+ align:start position:0%
+Q if these particles are the only ones
+ 
+
+ align:start position:0%
+Q if these particles are the only ones
+that are charged and moving the current
+
+ align:start position:0%
+that are charged and moving the current
+ 
+
+ align:start position:0%
+that are charged and moving the current
+density is the product of their
+
+ align:start position:0%
+density is the product of their
+ 
+
+ align:start position:0%
+density is the product of their
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+and the charge density
+
+ align:start position:0%
+and the charge density
+ 
+
+ align:start position:0%
+and the charge density
+Row the product of mu and row is an
+
+ align:start position:0%
+Row the product of mu and row is an
+ 
+
+ align:start position:0%
+Row the product of mu and row is an
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+conductivity unlike the conductivity
+
+ align:start position:0%
+conductivity unlike the conductivity
+ 
+
+ align:start position:0%
+conductivity unlike the conductivity
+associated with an omic model this
+
+ align:start position:0%
+associated with an omic model this
+ 
+
+ align:start position:0%
+associated with an omic model this
+conductivity is a function of a variable
+
+ align:start position:0%
+conductivity is a function of a variable
+ 
+
+ align:start position:0%
+conductivity is a function of a variable
+that is itself as much a function of
+
+ align:start position:0%
+that is itself as much a function of
+ 
+
+ align:start position:0%
+that is itself as much a function of
+space as the
+
+ align:start position:0%
+space as the
+ 
+
+ align:start position:0%
+space as the
+potential although the mobility formula
+
+ align:start position:0%
+potential although the mobility formula
+ 
+
+ align:start position:0%
+potential although the mobility formula
+is strictly only applicable to
+
+ align:start position:0%
+is strictly only applicable to
+ 
+
+ align:start position:0%
+is strictly only applicable to
+macroscopic spherical particles more
+
+ align:start position:0%
+macroscopic spherical particles more
+ 
+
+ align:start position:0%
+macroscopic spherical particles more
+than about5 micrometer in diameter and
+
+ align:start position:0%
+than about5 micrometer in diameter and
+ 
+
+ align:start position:0%
+than about5 micrometer in diameter and
+yet small enough that their inertia is
+
+ align:start position:0%
+yet small enough that their inertia is
+ 
+
+ align:start position:0%
+yet small enough that their inertia is
+negligible the expressions for the
+
+ align:start position:0%
+negligible the expressions for the
+ 
+
+ align:start position:0%
+negligible the expressions for the
+velocity and current density are useful
+
+ align:start position:0%
+velocity and current density are useful
+ 
+
+ align:start position:0%
+velocity and current density are useful
+for describing both the macroscopic
+
+ align:start position:0%
+for describing both the macroscopic
+ 
+
+ align:start position:0%
+for describing both the macroscopic
+particles and the ions that now account
+
+ align:start position:0%
+particles and the ions that now account
+ 
+
+ align:start position:0%
+particles and the ions that now account
+for what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observe the apparatus consists of these
+
+ align:start position:0%
+observe the apparatus consists of these
+ 
+
+ align:start position:0%
+observe the apparatus consists of these
+coaxial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductors the outer one is essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grounded
+
+ align:start position:0%
+grounded
+ 
+
+ align:start position:0%
+grounded
+the inner one this fine
+
+ align:start position:0%
+the inner one this fine
+ 
+
+ align:start position:0%
+the inner one this fine
+wire is connected to the high voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generator although it's made of glass so
+
+ align:start position:0%
+generator although it's made of glass so
+ 
+
+ align:start position:0%
+generator although it's made of glass so
+that we can see through it this cylinder
+
+ align:start position:0%
+that we can see through it this cylinder
+ 
+
+ align:start position:0%
+that we can see through it this cylinder
+is coated on the inside by tin oxide so
+
+ align:start position:0%
+is coated on the inside by tin oxide so
+ 
+
+ align:start position:0%
+is coated on the inside by tin oxide so
+that it is
+
+ align:start position:0%
+that it is
+ 
+
+ align:start position:0%
+that it is
+conducting for the present purposes it
+
+ align:start position:0%
+conducting for the present purposes it
+ 
+
+ align:start position:0%
+conducting for the present purposes it
+can be regarded as a perfect
+
+ align:start position:0%
+can be regarded as a perfect
+ 
+
+ align:start position:0%
+can be regarded as a perfect
+conductor it's grounded
+
+ align:start position:0%
+conductor it's grounded
+ 
+
+ align:start position:0%
+conductor it's grounded
+through this micro am
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meter this fine wire is stretched along
+
+ align:start position:0%
+meter this fine wire is stretched along
+ 
+
+ align:start position:0%
+meter this fine wire is stretched along
+the axis of the
+
+ align:start position:0%
+the axis of the
+ 
+
+ align:start position:0%
+the axis of the
+cylinder it's connected to a positive
+
+ align:start position:0%
+cylinder it's connected to a positive
+ 
+
+ align:start position:0%
+cylinder it's connected to a positive
+source of high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage because we only require modest
+
+ align:start position:0%
+voltage because we only require modest
+ 
+
+ align:start position:0%
+voltage because we only require modest
+currents we can protect ourselves by
+
+ align:start position:0%
+currents we can protect ourselves by
+ 
+
+ align:start position:0%
+currents we can protect ourselves by
+having a series
+
+ align:start position:0%
+having a series
+ 
+
+ align:start position:0%
+having a series
+resistance to limit the short circuit
+
+ align:start position:0%
+resistance to limit the short circuit
+ 
+
+ align:start position:0%
+resistance to limit the short circuit
+current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the voltage is indicated by this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meter because the wire is so fine
+
+ align:start position:0%
+meter because the wire is so fine
+ 
+
+ align:start position:0%
+meter because the wire is so fine
+raising its voltage results in
+
+ align:start position:0%
+raising its voltage results in
+ 
+
+ align:start position:0%
+raising its voltage results in
+ionization of the air in a hissing
+
+ align:start position:0%
+ionization of the air in a hissing
+ 
+
+ align:start position:0%
+ionization of the air in a hissing
+electrical
+
+ align:start position:0%
+electrical
+ 
+
+ align:start position:0%
+electrical
+breakdown this discharge is confined to
+
+ align:start position:0%
+breakdown this discharge is confined to
+ 
+
+ align:start position:0%
+breakdown this discharge is confined to
+the immediate vicinity of the
+
+ align:start position:0%
+the immediate vicinity of the
+ 
+
+ align:start position:0%
+the immediate vicinity of the
+wire with the help of this microphone we
+
+ align:start position:0%
+wire with the help of this microphone we
+ 
+
+ align:start position:0%
+wire with the help of this microphone we
+can hear this Corona
+
+ align:start position:0%
+can hear this Corona
+ 
+
+ align:start position:0%
+can hear this Corona
+discharge as it starts as the voltage is
+
+ align:start position:0%
+discharge as it starts as the voltage is
+ 
+
+ align:start position:0%
+discharge as it starts as the voltage is
+raised
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it starts at just a little more than 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kilts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs of ions generated by the corona
+
+ align:start position:0%
+pairs of ions generated by the corona
+ 
+
+ align:start position:0%
+pairs of ions generated by the corona
+discharge are separated by the electric
+
+ align:start position:0%
+discharge are separated by the electric
+ 
+
+ align:start position:0%
+discharge are separated by the electric
+field some of the positive ones follow
+
+ align:start position:0%
+field some of the positive ones follow
+ 
+
+ align:start position:0%
+field some of the positive ones follow
+the field lines to the outer
+
+ align:start position:0%
+the field lines to the outer
+ 
+
+ align:start position:0%
+the field lines to the outer
+cylinder
+
+ align:start position:0%
+cylinder
+ 
+
+ align:start position:0%
+cylinder
+thus as we raise the voltage and he the
+
+ align:start position:0%
+thus as we raise the voltage and he the
+ 
+
+ align:start position:0%
+thus as we raise the voltage and he the
+discharge start there should be an onset
+
+ align:start position:0%
+discharge start there should be an onset
+ 
+
+ align:start position:0%
+discharge start there should be an onset
+of current passing from the inner wire
+
+ align:start position:0%
+of current passing from the inner wire
+ 
+
+ align:start position:0%
+of current passing from the inner wire
+to the outer
+
+ align:start position:0%
+to the outer
+ 
+
+ align:start position:0%
+to the outer
+cylinder we can measure that current
+
+ align:start position:0%
+cylinder we can measure that current
+ 
+
+ align:start position:0%
+cylinder we can measure that current
+with this micro am
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meter here's the microamp meter 10
+
+ align:start position:0%
+meter here's the microamp meter 10
+ 
+
+ align:start position:0%
+meter here's the microamp meter 10
+microamps full
+
+ align:start position:0%
+microamps full
+ 
+
+ align:start position:0%
+microamps full
+scale here's the
+
+ align:start position:0%
+scale here's the
+ 
+
+ align:start position:0%
+scale here's the
+voltmeter let's watch the current as we
+
+ align:start position:0%
+voltmeter let's watch the current as we
+ 
+
+ align:start position:0%
+voltmeter let's watch the current as we
+again raise the voltage
+
+ align:start position:0%
+again raise the voltage
+ 
+
+ align:start position:0%
+again raise the voltage
+and listen to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discharge we have two other evidences of
+
+ align:start position:0%
+discharge we have two other evidences of
+ 
+
+ align:start position:0%
+discharge we have two other evidences of
+the corona discharge one is the smell of
+
+ align:start position:0%
+the corona discharge one is the smell of
+ 
+
+ align:start position:0%
+the corona discharge one is the smell of
+ozone generated by the
+
+ align:start position:0%
+ozone generated by the
+ 
+
+ align:start position:0%
+ozone generated by the
+discharge the odor is deceivingly like
+
+ align:start position:0%
+discharge the odor is deceivingly like
+ 
+
+ align:start position:0%
+discharge the odor is deceivingly like
+that associated with fresh
+
+ align:start position:0%
+that associated with fresh
+ 
+
+ align:start position:0%
+that associated with fresh
+air you can't appreciate that but if we
+
+ align:start position:0%
+air you can't appreciate that but if we
+ 
+
+ align:start position:0%
+air you can't appreciate that but if we
+turn the lights out and make the camera
+
+ align:start position:0%
+turn the lights out and make the camera
+ 
+
+ align:start position:0%
+turn the lights out and make the camera
+as sensitive as possible we might be
+
+ align:start position:0%
+as sensitive as possible we might be
+ 
+
+ align:start position:0%
+as sensitive as possible we might be
+able to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it perhaps you can see the slight bluish
+
+ align:start position:0%
+it perhaps you can see the slight bluish
+ 
+
+ align:start position:0%
+it perhaps you can see the slight bluish
+discharge that is uniform typical of a
+
+ align:start position:0%
+discharge that is uniform typical of a
+ 
+
+ align:start position:0%
+discharge that is uniform typical of a
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discharge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the current and voltage provide enough
+
+ align:start position:0%
+the current and voltage provide enough
+ 
+
+ align:start position:0%
+the current and voltage provide enough
+information to estimate the effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductivity at 12 kilovolts the current
+
+ align:start position:0%
+conductivity at 12 kilovolts the current
+ 
+
+ align:start position:0%
+conductivity at 12 kilovolts the current
+is 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microamp this total current is the
+
+ align:start position:0%
+microamp this total current is the
+ 
+
+ align:start position:0%
+microamp this total current is the
+current density at the outer wall
+
+ align:start position:0%
+current density at the outer wall
+ 
+
+ align:start position:0%
+current density at the outer wall
+multiplied by its area
+
+ align:start position:0%
+multiplied by its area
+ 
+
+ align:start position:0%
+multiplied by its area
+a the current density is in turn the
+
+ align:start position:0%
+a the current density is in turn the
+ 
+
+ align:start position:0%
+a the current density is in turn the
+product of the mobility the charge
+
+ align:start position:0%
+product of the mobility the charge
+ 
+
+ align:start position:0%
+product of the mobility the charge
+density and the field intensity at the
+
+ align:start position:0%
+density and the field intensity at the
+ 
+
+ align:start position:0%
+density and the field intensity at the
+outer
+
+ align:start position:0%
+outer
+ 
+
+ align:start position:0%
+outer
+wall so the effective conductivity is
+
+ align:start position:0%
+wall so the effective conductivity is
+ 
+
+ align:start position:0%
+wall so the effective conductivity is
+the total current divided by the product
+
+ align:start position:0%
+the total current divided by the product
+ 
+
+ align:start position:0%
+the total current divided by the product
+of the field in density and the
+
+ align:start position:0%
+of the field in density and the
+ 
+
+ align:start position:0%
+of the field in density and the
+area the electric field in this coaxial
+
+ align:start position:0%
+area the electric field in this coaxial
+ 
+
+ align:start position:0%
+area the electric field in this coaxial
+geometry is not uniform so if we take e
+
+ align:start position:0%
+geometry is not uniform so if we take e
+ 
+
+ align:start position:0%
+geometry is not uniform so if we take e
+to B the voltage divided by the spacing
+
+ align:start position:0%
+to B the voltage divided by the spacing
+ 
+
+ align:start position:0%
+to B the voltage divided by the spacing
+between the wire and the outer cylinder
+
+ align:start position:0%
+between the wire and the outer cylinder
+ 
+
+ align:start position:0%
+between the wire and the outer cylinder
+it would seem to be a very crude
+
+ align:start position:0%
+it would seem to be a very crude
+ 
+
+ align:start position:0%
+it would seem to be a very crude
+approximation however the space charge
+
+ align:start position:0%
+approximation however the space charge
+ 
+
+ align:start position:0%
+approximation however the space charge
+due to the ions tends to make the field
+
+ align:start position:0%
+due to the ions tends to make the field
+ 
+
+ align:start position:0%
+due to the ions tends to make the field
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+uniform so we take e as being
+
+ align:start position:0%
+uniform so we take e as being
+ 
+
+ align:start position:0%
+uniform so we take e as being
+approximately 12 Kilts divided by 6 cm
+
+ align:start position:0%
+approximately 12 Kilts divided by 6 cm
+ 
+
+ align:start position:0%
+approximately 12 Kilts divided by 6 cm
+about 2 * 10 5th volts per
+
+ align:start position:0%
+about 2 * 10 5th volts per
+ 
+
+ align:start position:0%
+about 2 * 10 5th volts per
+meter the cylinder area is 2 pi * the
+
+ align:start position:0%
+meter the cylinder area is 2 pi * the
+ 
+
+ align:start position:0%
+meter the cylinder area is 2 pi * the
+radius times a height of4
+
+ align:start position:0%
+radius times a height of4
+ 
+
+ align:start position:0%
+radius times a height of4
+M the effective conductivity is
+
+ align:start position:0%
+M the effective conductivity is
+ 
+
+ align:start position:0%
+M the effective conductivity is
+therefore about 3.3 * 10us 10 semans per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meter the electric field is 2 * 10 5
+
+ align:start position:0%
+meter the electric field is 2 * 10 5
+ 
+
+ align:start position:0%
+meter the electric field is 2 * 10 5
+Vols per
+
+ align:start position:0%
+Vols per
+ 
+
+ align:start position:0%
+Vols per
+meter the mobility of air ions is about
+
+ align:start position:0%
+meter the mobility of air ions is about
+ 
+
+ align:start position:0%
+meter the mobility of air ions is about
+1 * 10 - 4 m/s per volt per
+
+ align:start position:0%
+1 * 10 - 4 m/s per volt per
+ 
+
+ align:start position:0%
+1 * 10 - 4 m/s per volt per
+meter the velocity of an ion with a
+
+ align:start position:0%
+meter the velocity of an ion with a
+ 
+
+ align:start position:0%
+meter the velocity of an ion with a
+voltage at 12 KT is therefore about 20
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m/s the time required for an ion to
+
+ align:start position:0%
+m/s the time required for an ion to
+ 
+
+ align:start position:0%
+m/s the time required for an ion to
+cross from the wire to the cylinder to
+
+ align:start position:0%
+cross from the wire to the cylinder to
+ 
+
+ align:start position:0%
+cross from the wire to the cylinder to
+travel the radius R of 6
+
+ align:start position:0%
+travel the radius R of 6
+ 
+
+ align:start position:0%
+travel the radius R of 6
+cm is about 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+milliseconds common smoke alarms depend
+
+ align:start position:0%
+milliseconds common smoke alarms depend
+ 
+
+ align:start position:0%
+milliseconds common smoke alarms depend
+on the tendency of fine particles to
+
+ align:start position:0%
+on the tendency of fine particles to
+ 
+
+ align:start position:0%
+on the tendency of fine particles to
+collect these ions
+
+ align:start position:0%
+collect these ions
+ 
+
+ align:start position:0%
+collect these ions
+here we have a source of
+
+ align:start position:0%
+here we have a source of
+ 
+
+ align:start position:0%
+here we have a source of
+smoke watch what happens to the current
+
+ align:start position:0%
+smoke watch what happens to the current
+ 
+
+ align:start position:0%
+smoke watch what happens to the current
+as the smoke is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+introduced as the smoke enters the
+
+ align:start position:0%
+introduced as the smoke enters the
+ 
+
+ align:start position:0%
+introduced as the smoke enters the
+region of ionic conduction the curent is
+
+ align:start position:0%
+region of ionic conduction the curent is
+ 
+
+ align:start position:0%
+region of ionic conduction the curent is
+reduced let's see if we can explain
+
+ align:start position:0%
+reduced let's see if we can explain
+ 
+
+ align:start position:0%
+reduced let's see if we can explain
+this here greatly enlarged is a
+
+ align:start position:0%
+this here greatly enlarged is a
+ 
+
+ align:start position:0%
+this here greatly enlarged is a
+macroscopic particle such as comprises
+
+ align:start position:0%
+macroscopic particle such as comprises
+ 
+
+ align:start position:0%
+macroscopic particle such as comprises
+smoke under these circumstances it does
+
+ align:start position:0%
+smoke under these circumstances it does
+ 
+
+ align:start position:0%
+smoke under these circumstances it does
+not have to conduct much to behave as an
+
+ align:start position:0%
+not have to conduct much to behave as an
+ 
+
+ align:start position:0%
+not have to conduct much to behave as an
+essentially perfect
+
+ align:start position:0%
+essentially perfect
+ 
+
+ align:start position:0%
+essentially perfect
+conductor thus in the vicinity of the
+
+ align:start position:0%
+conductor thus in the vicinity of the
+ 
+
+ align:start position:0%
+conductor thus in the vicinity of the
+particle field lines tend to terminate
+
+ align:start position:0%
+particle field lines tend to terminate
+ 
+
+ align:start position:0%
+particle field lines tend to terminate
+on its South Pole and emanate from its
+
+ align:start position:0%
+on its South Pole and emanate from its
+ 
+
+ align:start position:0%
+on its South Pole and emanate from its
+North
+
+ align:start position:0%
+North
+ 
+
+ align:start position:0%
+North
+Pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ions migrating along these lines
+
+ align:start position:0%
+ions migrating along these lines
+ 
+
+ align:start position:0%
+ions migrating along these lines
+terminating on the South Pole impact the
+
+ align:start position:0%
+terminating on the South Pole impact the
+ 
+
+ align:start position:0%
+terminating on the South Pole impact the
+surface of the
+
+ align:start position:0%
+surface of the
+ 
+
+ align:start position:0%
+surface of the
+particle as the ions accumulate so does
+
+ align:start position:0%
+particle as the ions accumulate so does
+ 
+
+ align:start position:0%
+particle as the ions accumulate so does
+the net charge Q of the macroscopic
+
+ align:start position:0%
+the net charge Q of the macroscopic
+ 
+
+ align:start position:0%
+the net charge Q of the macroscopic
+particle as the particle charges more
+
+ align:start position:0%
+particle as the particle charges more
+ 
+
+ align:start position:0%
+particle as the particle charges more
+and more of its surface sustains outward
+
+ align:start position:0%
+and more of its surface sustains outward
+ 
+
+ align:start position:0%
+and more of its surface sustains outward
+directed field
+
+ align:start position:0%
+directed field
+ 
+
+ align:start position:0%
+directed field
+lines as it charges the southern window
+
+ align:start position:0%
+lines as it charges the southern window
+ 
+
+ align:start position:0%
+lines as it charges the southern window
+over which ions can impact the particle
+
+ align:start position:0%
+over which ions can impact the particle
+ 
+
+ align:start position:0%
+over which ions can impact the particle
+closes so there's a maximum charge that
+
+ align:start position:0%
+closes so there's a maximum charge that
+ 
+
+ align:start position:0%
+closes so there's a maximum charge that
+can accumulate on the
+
+ align:start position:0%
+can accumulate on the
+ 
+
+ align:start position:0%
+can accumulate on the
+particle this maximum charge is reached
+
+ align:start position:0%
+particle this maximum charge is reached
+ 
+
+ align:start position:0%
+particle this maximum charge is reached
+when the radial electric field is
+
+ align:start position:0%
+when the radial electric field is
+ 
+
+ align:start position:0%
+when the radial electric field is
+everywhere outward on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface here's the time
+
+ align:start position:0%
+surface here's the time
+ 
+
+ align:start position:0%
+surface here's the time
+dependence of the charge on a particle
+
+ align:start position:0%
+dependence of the charge on a particle
+ 
+
+ align:start position:0%
+dependence of the charge on a particle
+having no initial
+
+ align:start position:0%
+having no initial
+ 
+
+ align:start position:0%
+having no initial
+charge the charge saturates at a
+
+ align:start position:0%
+charge the charge saturates at a
+ 
+
+ align:start position:0%
+charge the charge saturates at a
+critical charge Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subc This critical charge is is
+
+ align:start position:0%
+subc This critical charge is is
+ 
+
+ align:start position:0%
+subc This critical charge is is
+independent of the mobility or ion
+
+ align:start position:0%
+independent of the mobility or ion
+ 
+
+ align:start position:0%
+independent of the mobility or ion
+density and is proportional to esay the
+
+ align:start position:0%
+density and is proportional to esay the
+ 
+
+ align:start position:0%
+density and is proportional to esay the
+field intensity in the neighborhood of
+
+ align:start position:0%
+field intensity in the neighborhood of
+ 
+
+ align:start position:0%
+field intensity in the neighborhood of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+particle and proportional to the
+
+ align:start position:0%
+particle and proportional to the
+ 
+
+ align:start position:0%
+particle and proportional to the
+particle surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+to is the rate with which the particle
+
+ align:start position:0%
+to is the rate with which the particle
+ 
+
+ align:start position:0%
+to is the rate with which the particle
+charges it depends on the effective
+
+ align:start position:0%
+charges it depends on the effective
+ 
+
+ align:start position:0%
+charges it depends on the effective
+conductivity mu row in a similar way as
+
+ align:start position:0%
+conductivity mu row in a similar way as
+ 
+
+ align:start position:0%
+conductivity mu row in a similar way as
+for the charge relaxation time of an
+
+ align:start position:0%
+for the charge relaxation time of an
+ 
+
+ align:start position:0%
+for the charge relaxation time of an
+omic
+
+ align:start position:0%
+omic
+ 
+
+ align:start position:0%
+omic
+conductor
+
+ align:start position:0%
+conductor
+ 
+
+ align:start position:0%
+conductor
+at 12 Kilts we found an effective
+
+ align:start position:0%
+at 12 Kilts we found an effective
+ 
+
+ align:start position:0%
+at 12 Kilts we found an effective
+conductivity to be 3.3 * 10us 10 C per
+
+ align:start position:0%
+conductivity to be 3.3 * 10us 10 C per
+ 
+
+ align:start position:0%
+conductivity to be 3.3 * 10us 10 C per
+meter so our ions can give an
+
+ align:start position:0%
+meter so our ions can give an
+ 
+
+ align:start position:0%
+meter so our ions can give an
+appreciable charge to a smoke particle
+
+ align:start position:0%
+appreciable charge to a smoke particle
+ 
+
+ align:start position:0%
+appreciable charge to a smoke particle
+within about 1/10th of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second once charged the smoke particles
+
+ align:start position:0%
+second once charged the smoke particles
+ 
+
+ align:start position:0%
+second once charged the smoke particles
+are themselves pulled toward the outer
+
+ align:start position:0%
+are themselves pulled toward the outer
+ 
+
+ align:start position:0%
+are themselves pulled toward the outer
+electrode by the electric
+
+ align:start position:0%
+electrode by the electric
+ 
+
+ align:start position:0%
+electrode by the electric
+field let's see this
+
+ align:start position:0%
+field let's see this
+ 
+
+ align:start position:0%
+field let's see this
+happen with the voltage off and the
+
+ align:start position:0%
+happen with the voltage off and the
+ 
+
+ align:start position:0%
+happen with the voltage off and the
+upper end of the cylinder closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off we'll fill it with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smoke watch the smoke as the voltage is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applied the particles are presumably
+
+ align:start position:0%
+applied the particles are presumably
+ 
+
+ align:start position:0%
+applied the particles are presumably
+charged in less than a tenth of a second
+
+ align:start position:0%
+charged in less than a tenth of a second
+ 
+
+ align:start position:0%
+charged in less than a tenth of a second
+so the charging time cannot account for
+
+ align:start position:0%
+so the charging time cannot account for
+ 
+
+ align:start position:0%
+so the charging time cannot account for
+the few seconds it takes to precipitate
+
+ align:start position:0%
+the few seconds it takes to precipitate
+ 
+
+ align:start position:0%
+the few seconds it takes to precipitate
+the Smoke On The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wall apparently these smoke particles do
+
+ align:start position:0%
+Wall apparently these smoke particles do
+ 
+
+ align:start position:0%
+Wall apparently these smoke particles do
+not move through the air with nearly the
+
+ align:start position:0%
+not move through the air with nearly the
+ 
+
+ align:start position:0%
+not move through the air with nearly the
+velocity of the ions which we estimated
+
+ align:start position:0%
+velocity of the ions which we estimated
+ 
+
+ align:start position:0%
+velocity of the ions which we estimated
+to be on the order of 20 m/s or
+
+ align:start position:0%
+to be on the order of 20 m/s or
+ 
+
+ align:start position:0%
+to be on the order of 20 m/s or
+more we can see that this is so by
+
+ align:start position:0%
+more we can see that this is so by
+ 
+
+ align:start position:0%
+more we can see that this is so by
+calculating the velocity of a smoke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle first we approximate the
+
+ align:start position:0%
+particle first we approximate the
+ 
+
+ align:start position:0%
+particle first we approximate the
+largest charge that can accumulate on a
+
+ align:start position:0%
+largest charge that can accumulate on a
+ 
+
+ align:start position:0%
+largest charge that can accumulate on a
+smoke particle we guess that the
+
+ align:start position:0%
+smoke particle we guess that the
+ 
+
+ align:start position:0%
+smoke particle we guess that the
+particle has a radius of half a
+
+ align:start position:0%
+particle has a radius of half a
+ 
+
+ align:start position:0%
+particle has a radius of half a
+micrometer and use the same average
+
+ align:start position:0%
+micrometer and use the same average
+ 
+
+ align:start position:0%
+micrometer and use the same average
+field as
+
+ align:start position:0%
+field as
+ 
+
+ align:start position:0%
+field as
+before then the charge per particle is
+
+ align:start position:0%
+before then the charge per particle is
+ 
+
+ align:start position:0%
+before then the charge per particle is
+about 1.7 * 10-7
+
+ align:start position:0%
+about 1.7 * 10-7
+ 
+
+ align:start position:0%
+about 1.7 * 10-7
+K that's about 100 electronic
+
+ align:start position:0%
+K that's about 100 electronic
+ 
+
+ align:start position:0%
+K that's about 100 electronic
+charges it follows that the mobility of
+
+ align:start position:0%
+charges it follows that the mobility of
+ 
+
+ align:start position:0%
+charges it follows that the mobility of
+the smoke is this charge divided by 6 pi
+
+ align:start position:0%
+the smoke is this charge divided by 6 pi
+ 
+
+ align:start position:0%
+the smoke is this charge divided by 6 pi
+times the viscosity of
+
+ align:start position:0%
+times the viscosity of
+ 
+
+ align:start position:0%
+times the viscosity of
+air and the particle
+
+ align:start position:0%
+air and the particle
+ 
+
+ align:start position:0%
+air and the particle
+radius the mobility of the smoke is
+
+ align:start position:0%
+radius the mobility of the smoke is
+ 
+
+ align:start position:0%
+radius the mobility of the smoke is
+about 10- 7 m/s per volt per
+
+ align:start position:0%
+about 10- 7 m/s per volt per
+ 
+
+ align:start position:0%
+about 10- 7 m/s per volt per
+meter about 1,000 times less than for
+
+ align:start position:0%
+meter about 1,000 times less than for
+ 
+
+ align:start position:0%
+meter about 1,000 times less than for
+the ions
+
+ align:start position:0%
+the ions
+ 
+
+ align:start position:0%
+the ions
+so in our field 2 * 10 5th Vols per
+
+ align:start position:0%
+so in our field 2 * 10 5th Vols per
+ 
+
+ align:start position:0%
+so in our field 2 * 10 5th Vols per
+meter the smoke particle moves with a
+
+ align:start position:0%
+meter the smoke particle moves with a
+ 
+
+ align:start position:0%
+meter the smoke particle moves with a
+velocity of 2 cm/ second about a
+
+ align:start position:0%
+velocity of 2 cm/ second about a
+ 
+
+ align:start position:0%
+velocity of 2 cm/ second about a
+thousand times slower than the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ions what we see at relatively large
+
+ align:start position:0%
+ions what we see at relatively large
+ 
+
+ align:start position:0%
+ions what we see at relatively large
+particle densities is particle motions
+
+ align:start position:0%
+particle densities is particle motions
+ 
+
+ align:start position:0%
+particle densities is particle motions
+that are Complicated by the motion of
+
+ align:start position:0%
+that are Complicated by the motion of
+ 
+
+ align:start position:0%
+that are Complicated by the motion of
+the air
+
+ align:start position:0%
+the air
+ 
+
+ align:start position:0%
+the air
+itself induced by both the ions and the
+
+ align:start position:0%
+itself induced by both the ions and the
+ 
+
+ align:start position:0%
+itself induced by both the ions and the
+particles this is typical of practical
+
+ align:start position:0%
+particles this is typical of practical
+ 
+
+ align:start position:0%
+particles this is typical of practical
+precipitators which are used for air
+
+ align:start position:0%
+precipitators which are used for air
+ 
+
+ align:start position:0%
+precipitators which are used for air
+pollution control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+purposes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the macroscopic particle motions can be
+
+ align:start position:0%
+the macroscopic particle motions can be
+ 
+
+ align:start position:0%
+the macroscopic particle motions can be
+made more evident by using styrofoam
+
+ align:start position:0%
+made more evident by using styrofoam
+ 
+
+ align:start position:0%
+made more evident by using styrofoam
+particles rather than the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smoke Watch What Happens as they
+
+ align:start position:0%
+smoke Watch What Happens as they
+ 
+
+ align:start position:0%
+smoke Watch What Happens as they
+encounter the combination of radially
+
+ align:start position:0%
+encounter the combination of radially
+ 
+
+ align:start position:0%
+encounter the combination of radially
+migrating ions and Radial electric
+
+ align:start position:0%
+migrating ions and Radial electric
+ 
+
+ align:start position:0%
+migrating ions and Radial electric
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as long as the field is on the particles
+
+ align:start position:0%
+as long as the field is on the particles
+ 
+
+ align:start position:0%
+as long as the field is on the particles
+are electrically pinned to the
+
+ align:start position:0%
+are electrically pinned to the
+ 
+
+ align:start position:0%
+are electrically pinned to the
+wall but when the field is
+
+ align:start position:0%
+wall but when the field is
+ 
+
+ align:start position:0%
+wall but when the field is
+removed so is the pinning
+
+ align:start position:0%
+removed so is the pinning
+ 
+
+ align:start position:0%
+removed so is the pinning
+Force as purchased these particles are
+
+ align:start position:0%
+Force as purchased these particles are
+ 
+
+ align:start position:0%
+Force as purchased these particles are
+good insulators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're naturally sufficiently
+
+ align:start position:0%
+they're naturally sufficiently
+ 
+
+ align:start position:0%
+they're naturally sufficiently
+insulating that they can contact a
+
+ align:start position:0%
+insulating that they can contact a
+ 
+
+ align:start position:0%
+insulating that they can contact a
+conducting surface like the cylinder
+
+ align:start position:0%
+conducting surface like the cylinder
+ 
+
+ align:start position:0%
+conducting surface like the cylinder
+wall and still retain most of their
+
+ align:start position:0%
+wall and still retain most of their
+ 
+
+ align:start position:0%
+wall and still retain most of their
+charge if the charge were retained on
+
+ align:start position:0%
+charge if the charge were retained on
+ 
+
+ align:start position:0%
+charge if the charge were retained on
+the particles we would expect that they
+
+ align:start position:0%
+the particles we would expect that they
+ 
+
+ align:start position:0%
+the particles we would expect that they
+would stick to the wall after the field
+
+ align:start position:0%
+would stick to the wall after the field
+ 
+
+ align:start position:0%
+would stick to the wall after the field
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+removed to understand what we've seen we
+
+ align:start position:0%
+removed to understand what we've seen we
+ 
+
+ align:start position:0%
+removed to understand what we've seen we
+need to explain that these particles
+
+ align:start position:0%
+need to explain that these particles
+ 
+
+ align:start position:0%
+need to explain that these particles
+have been sprayed with antistatic agent
+
+ align:start position:0%
+have been sprayed with antistatic agent
+ 
+
+ align:start position:0%
+have been sprayed with antistatic agent
+much is used to prevent electrification
+
+ align:start position:0%
+much is used to prevent electrification
+ 
+
+ align:start position:0%
+much is used to prevent electrification
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+laundry so they charge leaks away after
+
+ align:start position:0%
+laundry so they charge leaks away after
+ 
+
+ align:start position:0%
+laundry so they charge leaks away after
+the field is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+removed our experiment illustrates the
+
+ align:start position:0%
+removed our experiment illustrates the
+ 
+
+ align:start position:0%
+removed our experiment illustrates the
+nature of two types of charged particles
+
+ align:start position:0%
+nature of two types of charged particles
+ 
+
+ align:start position:0%
+nature of two types of charged particles
+that are described by unipolar
+
+ align:start position:0%
+that are described by unipolar
+ 
+
+ align:start position:0%
+that are described by unipolar
+conduction of molecular Dimensions were
+
+ align:start position:0%
+conduction of molecular Dimensions were
+ 
+
+ align:start position:0%
+conduction of molecular Dimensions were
+the ions generated by a Corona
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discharge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with mobilities of 10us 4 m/s per volt
+
+ align:start position:0%
+with mobilities of 10us 4 m/s per volt
+ 
+
+ align:start position:0%
+with mobilities of 10us 4 m/s per volt
+per meter they crossed through the air
+
+ align:start position:0%
+per meter they crossed through the air
+ 
+
+ align:start position:0%
+per meter they crossed through the air
+between the wire and the wall with a
+
+ align:start position:0%
+between the wire and the wall with a
+ 
+
+ align:start position:0%
+between the wire and the wall with a
+velocity of 20
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m/s macroscopic particles of smoke
+
+ align:start position:0%
+m/s macroscopic particles of smoke
+ 
+
+ align:start position:0%
+m/s macroscopic particles of smoke
+passing through the ion flux were
+
+ align:start position:0%
+passing through the ion flux were
+ 
+
+ align:start position:0%
+passing through the ion flux were
+quickly charged to much higher levels
+
+ align:start position:0%
+quickly charged to much higher levels
+ 
+
+ align:start position:0%
+quickly charged to much higher levels
+than the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ions because of their larger size they
+
+ align:start position:0%
+ions because of their larger size they
+ 
+
+ align:start position:0%
+ions because of their larger size they
+still had mobilities a thousand times
+
+ align:start position:0%
+still had mobilities a thousand times
+ 
+
+ align:start position:0%
+still had mobilities a thousand times
+less than the ions their velocities
+
+ align:start position:0%
+less than the ions their velocities
+ 
+
+ align:start position:0%
+less than the ions their velocities
+relative to the air were 1,000 times
+
+ align:start position:0%
+relative to the air were 1,000 times
+ 
+
+ align:start position:0%
+relative to the air were 1,000 times
+less than the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ions ion impact charging of particles
+
+ align:start position:0%
+ions ion impact charging of particles
+ 
+
+ align:start position:0%
+ions ion impact charging of particles
+and the resulting electrical force
+
+ align:start position:0%
+and the resulting electrical force
+ 
+
+ align:start position:0%
+and the resulting electrical force
+explained what we saw using the
+
+ align:start position:0%
+explained what we saw using the
+ 
+
+ align:start position:0%
+explained what we saw using the
+styrofoam beads
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these particles have not been sprayed
+
+ align:start position:0%
+these particles have not been sprayed
+ 
+
+ align:start position:0%
+these particles have not been sprayed
+with antistatic
+
+ align:start position:0%
+with antistatic
+ 
+
+ align:start position:0%
+with antistatic
+agent they too are precipitated to the
+
+ align:start position:0%
+agent they too are precipitated to the
+ 
+
+ align:start position:0%
+agent they too are precipitated to the
+walls although in a somewhat different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pattern however now when the power is
+
+ align:start position:0%
+pattern however now when the power is
+ 
+
+ align:start position:0%
+pattern however now when the power is
+turned
+
+ align:start position:0%
+turned
+ 
+
+ align:start position:0%
+turned
+off they tend to stick to the wall
+
+ align:start position:0%
+off they tend to stick to the wall
+ 
+
+ align:start position:0%
+off they tend to stick to the wall
+they're so highly insulating that they
+
+ align:start position:0%
+they're so highly insulating that they
+ 
+
+ align:start position:0%
+they're so highly insulating that they
+retain their
+
+ align:start position:0%
+retain their
+ 
+
+ align:start position:0%
+retain their
+charge we can either think of their
+
+ align:start position:0%
+charge we can either think of their
+ 
+
+ align:start position:0%
+charge we can either think of their
+being mutually repelled to the walls or
+
+ align:start position:0%
+being mutually repelled to the walls or
+ 
+
+ align:start position:0%
+being mutually repelled to the walls or
+of they're being attracted to the image
+
+ align:start position:0%
+of they're being attracted to the image
+ 
+
+ align:start position:0%
+of they're being attracted to the image
+charges on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+walls the mutual repulsion of light
+
+ align:start position:0%
+walls the mutual repulsion of light
+ 
+
+ align:start position:0%
+walls the mutual repulsion of light
+charged particles is more evident when
+
+ align:start position:0%
+charged particles is more evident when
+ 
+
+ align:start position:0%
+charged particles is more evident when
+the cylinder is turned on its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side once charged by ion impact and
+
+ align:start position:0%
+side once charged by ion impact and
+ 
+
+ align:start position:0%
+side once charged by ion impact and
+precipitated on the wall these particles
+
+ align:start position:0%
+precipitated on the wall these particles
+ 
+
+ align:start position:0%
+precipitated on the wall these particles
+retain their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge
\ No newline at end of file
diff --git a/aQAhRAn6ewc.txt b/aQAhRAn6ewc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6ad4974e926fa454b51d963388dd30e868531c32
--- /dev/null
+++ b/aQAhRAn6ewc.txt
@@ -0,0 +1,819 @@
+align:start position:0%
+ 
+welcome back to
+
+ align:start position:0%
+welcome back to
+ 
+
+ align:start position:0%
+welcome back to
+820 special relativity
+
+ align:start position:0%
+820 special relativity
+ 
+
+ align:start position:0%
+820 special relativity
+so in this section we want to look again
+
+ align:start position:0%
+so in this section we want to look again
+ 
+
+ align:start position:0%
+so in this section we want to look again
+at collisions
+
+ align:start position:0%
+at collisions
+ 
+
+ align:start position:0%
+at collisions
+and study momentum conservation
+
+ align:start position:0%
+and study momentum conservation
+ 
+
+ align:start position:0%
+and study momentum conservation
+and so we have this scenario here in
+
+ align:start position:0%
+and so we have this scenario here in
+ 
+
+ align:start position:0%
+and so we have this scenario here in
+which we have you know two balls
+
+ align:start position:0%
+which we have you know two balls
+ 
+
+ align:start position:0%
+which we have you know two balls
+colliding with velocities u a and u b
+
+ align:start position:0%
+colliding with velocities u a and u b
+ 
+
+ align:start position:0%
+colliding with velocities u a and u b
+masses m a and m
+
+ align:start position:0%
+masses m a and m
+ 
+
+ align:start position:0%
+masses m a and m
+and after the collisions there the
+
+ align:start position:0%
+and after the collisions there the
+ 
+
+ align:start position:0%
+and after the collisions there the
+masses change to m c and m d and the
+
+ align:start position:0%
+masses change to m c and m d and the
+ 
+
+ align:start position:0%
+masses change to m c and m d and the
+velocities are u c and u d
+
+ align:start position:0%
+velocities are u c and u d
+ 
+
+ align:start position:0%
+velocities are u c and u d
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+random conservation tells you that the
+
+ align:start position:0%
+random conservation tells you that the
+ 
+
+ align:start position:0%
+random conservation tells you that the
+product of the mars and velocities
+
+ align:start position:0%
+product of the mars and velocities
+ 
+
+ align:start position:0%
+product of the mars and velocities
+and the sum of the two particles before
+
+ align:start position:0%
+and the sum of the two particles before
+ 
+
+ align:start position:0%
+and the sum of the two particles before
+and after the collisions is the same
+
+ align:start position:0%
+and after the collisions is the same
+ 
+
+ align:start position:0%
+and after the collisions is the same
+but now what happens if we boost the
+
+ align:start position:0%
+but now what happens if we boost the
+ 
+
+ align:start position:0%
+but now what happens if we boost the
+system if we
+
+ align:start position:0%
+system if we
+ 
+
+ align:start position:0%
+system if we
+look at the very same system with a
+
+ align:start position:0%
+look at the very same system with a
+ 
+
+ align:start position:0%
+look at the very same system with a
+boosted reference frame
+
+ align:start position:0%
+boosted reference frame
+ 
+
+ align:start position:0%
+boosted reference frame
+um you know and we can just
+
+ align:start position:0%
+um you know and we can just
+ 
+
+ align:start position:0%
+um you know and we can just
+you know simplify the case here by just
+
+ align:start position:0%
+you know simplify the case here by just
+ 
+
+ align:start position:0%
+you know simplify the case here by just
+considering the x direction
+
+ align:start position:0%
+considering the x direction
+ 
+
+ align:start position:0%
+considering the x direction
+so the question is if momentum is
+
+ align:start position:0%
+so the question is if momentum is
+ 
+
+ align:start position:0%
+so the question is if momentum is
+conserved in a frame s
+
+ align:start position:0%
+conserved in a frame s
+ 
+
+ align:start position:0%
+conserved in a frame s
+like the one we are looking here in this
+
+ align:start position:0%
+like the one we are looking here in this
+ 
+
+ align:start position:0%
+like the one we are looking here in this
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+is the momentum also conserved in a
+
+ align:start position:0%
+is the momentum also conserved in a
+ 
+
+ align:start position:0%
+is the momentum also conserved in a
+moving reference frame
+
+ align:start position:0%
+moving reference frame
+ 
+
+ align:start position:0%
+moving reference frame
+with the relative velocity uh uh v
+
+ align:start position:0%
+with the relative velocity uh uh v
+ 
+
+ align:start position:0%
+with the relative velocity uh uh v
+and so you can show this quite easily
+
+ align:start position:0%
+and so you can show this quite easily
+ 
+
+ align:start position:0%
+and so you can show this quite easily
+that this is actually not the case right
+
+ align:start position:0%
+that this is actually not the case right
+ 
+
+ align:start position:0%
+that this is actually not the case right
+so you write down the velocities
+
+ align:start position:0%
+so you write down the velocities
+ 
+
+ align:start position:0%
+so you write down the velocities
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the momentum equation the same equation
+
+ align:start position:0%
+the momentum equation the same equation
+ 
+
+ align:start position:0%
+the momentum equation the same equation
+as before with boosted velocities and
+
+ align:start position:0%
+as before with boosted velocities and
+ 
+
+ align:start position:0%
+as before with boosted velocities and
+you find that this is not the case you
+
+ align:start position:0%
+you find that this is not the case you
+ 
+
+ align:start position:0%
+you find that this is not the case you
+can easily show this by for example you
+
+ align:start position:0%
+can easily show this by for example you
+ 
+
+ align:start position:0%
+can easily show this by for example you
+know setting the right part of this
+
+ align:start position:0%
+know setting the right part of this
+ 
+
+ align:start position:0%
+know setting the right part of this
+equation to zero
+
+ align:start position:0%
+equation to zero
+ 
+
+ align:start position:0%
+equation to zero
+and see
+
+ align:start position:0%
+and see
+ 
+
+ align:start position:0%
+and see
+whether or not this this equation will
+
+ align:start position:0%
+whether or not this this equation will
+ 
+
+ align:start position:0%
+whether or not this this equation will
+hold true in general and it doesn't
+
+ align:start position:0%
+hold true in general and it doesn't
+ 
+
+ align:start position:0%
+hold true in general and it doesn't
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+in the last section we introduced the
+
+ align:start position:0%
+in the last section we introduced the
+ 
+
+ align:start position:0%
+in the last section we introduced the
+new concept of proper velocity
+
+ align:start position:0%
+new concept of proper velocity
+ 
+
+ align:start position:0%
+new concept of proper velocity
+so how about
+
+ align:start position:0%
+so how about
+ 
+
+ align:start position:0%
+so how about
+redefining momentum through proper
+
+ align:start position:0%
+redefining momentum through proper
+ 
+
+ align:start position:0%
+redefining momentum through proper
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+and just saying
+
+ align:start position:0%
+and just saying
+ 
+
+ align:start position:0%
+and just saying
+m a times proper velocity a plus m b
+
+ align:start position:0%
+m a times proper velocity a plus m b
+ 
+
+ align:start position:0%
+m a times proper velocity a plus m b
+times proper velocity b
+
+ align:start position:0%
+times proper velocity b
+ 
+
+ align:start position:0%
+times proper velocity b
+is equal to m c
+
+ align:start position:0%
+is equal to m c
+ 
+
+ align:start position:0%
+is equal to m c
+times over velocity c and so on
+
+ align:start position:0%
+times over velocity c and so on
+ 
+
+ align:start position:0%
+times over velocity c and so on
+and see whether or not we can learn
+
+ align:start position:0%
+and see whether or not we can learn
+ 
+
+ align:start position:0%
+and see whether or not we can learn
+something from this equation
+
+ align:start position:0%
+something from this equation
+ 
+
+ align:start position:0%
+something from this equation
+so why don't we write down this very
+
+ align:start position:0%
+so why don't we write down this very
+ 
+
+ align:start position:0%
+so why don't we write down this very
+same equation and with proper velocity
+
+ align:start position:0%
+same equation and with proper velocity
+ 
+
+ align:start position:0%
+same equation and with proper velocity
+and see whether or not it's invariant in
+
+ align:start position:0%
+and see whether or not it's invariant in
+ 
+
+ align:start position:0%
+and see whether or not it's invariant in
+the lawrence transformation
+
+ align:start position:0%
+the lawrence transformation
+ 
+
+ align:start position:0%
+the lawrence transformation
+okay again a good moment to stop the
+
+ align:start position:0%
+okay again a good moment to stop the
+ 
+
+ align:start position:0%
+okay again a good moment to stop the
+video and just work out the mass by
+
+ align:start position:0%
+video and just work out the mass by
+ 
+
+ align:start position:0%
+video and just work out the mass by
+yourself on your own
+
+ align:start position:0%
+yourself on your own
+ 
+
+ align:start position:0%
+yourself on your own
+so i did this here
+
+ align:start position:0%
+so i did this here
+ 
+
+ align:start position:0%
+so i did this here
+and i'm just doing this for the x
+
+ align:start position:0%
+and i'm just doing this for the x
+ 
+
+ align:start position:0%
+and i'm just doing this for the x
+component so we have our proper velocity
+
+ align:start position:0%
+component so we have our proper velocity
+ 
+
+ align:start position:0%
+component so we have our proper velocity
+vector which is gamma times z
+
+ align:start position:0%
+vector which is gamma times z
+ 
+
+ align:start position:0%
+vector which is gamma times z
+gamma times ux gamma times u y and gamma
+
+ align:start position:0%
+gamma times ux gamma times u y and gamma
+ 
+
+ align:start position:0%
+gamma times ux gamma times u y and gamma
+times uz
+
+ align:start position:0%
+times uz
+ 
+
+ align:start position:0%
+times uz
+so the x component is the first
+
+ align:start position:0%
+so the x component is the first
+ 
+
+ align:start position:0%
+so the x component is the first
+component
+
+ align:start position:0%
+component
+ 
+
+ align:start position:0%
+component
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in the boosted reference frame
+
+ align:start position:0%
+in the boosted reference frame
+ 
+
+ align:start position:0%
+in the boosted reference frame
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+proper velocity of the x component in
+
+ align:start position:0%
+proper velocity of the x component in
+ 
+
+ align:start position:0%
+proper velocity of the x component in
+our boosters frame is gamma times
+
+ align:start position:0%
+our boosters frame is gamma times
+ 
+
+ align:start position:0%
+our boosters frame is gamma times
+the proper velocity of the particle a
+
+ align:start position:0%
+the proper velocity of the particle a
+ 
+
+ align:start position:0%
+the proper velocity of the particle a
+first component minus beta proper
+
+ align:start position:0%
+first component minus beta proper
+ 
+
+ align:start position:0%
+first component minus beta proper
+velocity of a zeroth component
+
+ align:start position:0%
+velocity of a zeroth component
+ 
+
+ align:start position:0%
+velocity of a zeroth component
+and so then you can write your equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this should be our momentum energy
+
+ align:start position:0%
+and this should be our momentum energy
+ 
+
+ align:start position:0%
+and this should be our momentum energy
+momentum conservation equation
+
+ align:start position:0%
+momentum conservation equation
+ 
+
+ align:start position:0%
+momentum conservation equation
+okay and the loans transformation we
+
+ align:start position:0%
+okay and the loans transformation we
+ 
+
+ align:start position:0%
+okay and the loans transformation we
+find this one here
+
+ align:start position:0%
+find this one here
+ 
+
+ align:start position:0%
+find this one here
+and so all we need to do now in order to
+
+ align:start position:0%
+and so all we need to do now in order to
+ 
+
+ align:start position:0%
+and so all we need to do now in order to
+show that this is always true or true in
+
+ align:start position:0%
+show that this is always true or true in
+ 
+
+ align:start position:0%
+show that this is always true or true in
+general is to
+
+ align:start position:0%
+general is to
+ 
+
+ align:start position:0%
+general is to
+re-assign relabel
+
+ align:start position:0%
+re-assign relabel
+ 
+
+ align:start position:0%
+re-assign relabel
+the reorder the individual terms and i
+
+ align:start position:0%
+the reorder the individual terms and i
+ 
+
+ align:start position:0%
+the reorder the individual terms and i
+did this here um to make this visible
+
+ align:start position:0%
+did this here um to make this visible
+ 
+
+ align:start position:0%
+did this here um to make this visible
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+everything behind in this bracket behind
+
+ align:start position:0%
+everything behind in this bracket behind
+ 
+
+ align:start position:0%
+everything behind in this bracket behind
+the better is equal to the equation we
+
+ align:start position:0%
+the better is equal to the equation we
+ 
+
+ align:start position:0%
+the better is equal to the equation we
+had before there's a minus sign in
+
+ align:start position:0%
+had before there's a minus sign in
+ 
+
+ align:start position:0%
+had before there's a minus sign in
+between which means it's zero and
+
+ align:start position:0%
+between which means it's zero and
+ 
+
+ align:start position:0%
+between which means it's zero and
+everything we see on the top for the
+
+ align:start position:0%
+everything we see on the top for the
+ 
+
+ align:start position:0%
+everything we see on the top for the
+first component
+
+ align:start position:0%
+first component
+ 
+
+ align:start position:0%
+first component
+is also b0 that's for the boosted
+
+ align:start position:0%
+is also b0 that's for the boosted
+ 
+
+ align:start position:0%
+is also b0 that's for the boosted
+reference right so we see here and i
+
+ align:start position:0%
+reference right so we see here and i
+ 
+
+ align:start position:0%
+reference right so we see here and i
+just showed this for the x component you
+
+ align:start position:0%
+just showed this for the x component you
+ 
+
+ align:start position:0%
+just showed this for the x component you
+can show the for all component that
+
+ align:start position:0%
+can show the for all component that
+ 
+
+ align:start position:0%
+can show the for all component that
+momentum is conserved
\ No newline at end of file
diff --git a/an5E940fqZQ.txt b/an5E940fqZQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c93cc3b19ae8d086c1f72abdb23de83ad04abe80
--- /dev/null
+++ b/an5E940fqZQ.txt
@@ -0,0 +1,6683 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ 
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today we're going to conclude our
+
+ align:start position:0%
+hi today we're going to conclude our
+ 
+
+ align:start position:0%
+hi today we're going to conclude our
+study of linear differential equations
+
+ align:start position:0%
+study of linear differential equations
+ 
+
+ align:start position:0%
+study of linear differential equations
+and we're going to use the occasion to
+
+ align:start position:0%
+and we're going to use the occasion to
+ 
+
+ align:start position:0%
+and we're going to use the occasion to
+introduce the concept of AAS transform I
+
+ align:start position:0%
+introduce the concept of AAS transform I
+ 
+
+ align:start position:0%
+introduce the concept of AAS transform I
+should point out that the llas transform
+
+ align:start position:0%
+should point out that the llas transform
+ 
+
+ align:start position:0%
+should point out that the llas transform
+has much greater application than just
+
+ align:start position:0%
+has much greater application than just
+ 
+
+ align:start position:0%
+has much greater application than just
+to linear differential equations it's
+
+ align:start position:0%
+to linear differential equations it's
+ 
+
+ align:start position:0%
+to linear differential equations it's
+related to the Fier transform it has
+
+ align:start position:0%
+related to the Fier transform it has
+ 
+
+ align:start position:0%
+related to the Fier transform it has
+applications in the subject known as the
+
+ align:start position:0%
+applications in the subject known as the
+ 
+
+ align:start position:0%
+applications in the subject known as the
+convolution integral many applications
+
+ align:start position:0%
+convolution integral many applications
+ 
+
+ align:start position:0%
+convolution integral many applications
+which we'll talk about during the during
+
+ align:start position:0%
+which we'll talk about during the during
+ 
+
+ align:start position:0%
+which we'll talk about during the during
+the learning exercises in this unit but
+
+ align:start position:0%
+the learning exercises in this unit but
+ 
+
+ align:start position:0%
+the learning exercises in this unit but
+within the framework of linear
+
+ align:start position:0%
+within the framework of linear
+ 
+
+ align:start position:0%
+within the framework of linear
+differential equations I thought this
+
+ align:start position:0%
+differential equations I thought this
+ 
+
+ align:start position:0%
+differential equations I thought this
+would be a good time to introduce this
+
+ align:start position:0%
+would be a good time to introduce this
+ 
+
+ align:start position:0%
+would be a good time to introduce this
+rather important concept consequently
+
+ align:start position:0%
+rather important concept consequently
+ 
+
+ align:start position:0%
+rather important concept consequently
+our topic for today is called quite
+
+ align:start position:0%
+our topic for today is called quite
+ 
+
+ align:start position:0%
+our topic for today is called quite
+simply the llast transform and it hinges
+
+ align:start position:0%
+simply the llast transform and it hinges
+ 
+
+ align:start position:0%
+simply the llast transform and it hinges
+on the fact that e to the T goes to
+
+ align:start position:0%
+on the fact that e to the T goes to
+ 
+
+ align:start position:0%
+on the fact that e to the T goes to
+Infinity for as T approaches Infinity
+
+ align:start position:0%
+Infinity for as T approaches Infinity
+ 
+
+ align:start position:0%
+Infinity for as T approaches Infinity
+you see much more rapidly than most
+
+ align:start position:0%
+you see much more rapidly than most
+ 
+
+ align:start position:0%
+you see much more rapidly than most
+functions of T and by the way I say t
+
+ align:start position:0%
+functions of T and by the way I say t
+ 
+
+ align:start position:0%
+functions of T and by the way I say t
+here instead of X because theast
+
+ align:start position:0%
+here instead of X because theast
+ 
+
+ align:start position:0%
+here instead of X because theast
+transform was introduced primarily for
+
+ align:start position:0%
+transform was introduced primarily for
+ 
+
+ align:start position:0%
+transform was introduced primarily for
+differential equations in which the
+
+ align:start position:0%
+differential equations in which the
+ 
+
+ align:start position:0%
+differential equations in which the
+independent variable was time so
+
+ align:start position:0%
+independent variable was time so
+ 
+
+ align:start position:0%
+independent variable was time so
+traditionally one usually talks about F
+
+ align:start position:0%
+traditionally one usually talks about F
+ 
+
+ align:start position:0%
+traditionally one usually talks about F
+of T when one is talking about the
+
+ align:start position:0%
+of T when one is talking about the
+ 
+
+ align:start position:0%
+of T when one is talking about the
+transform uh Concepts but the entire
+
+ align:start position:0%
+transform uh Concepts but the entire
+ 
+
+ align:start position:0%
+transform uh Concepts but the entire
+idea is this remember as we saw in part
+
+ align:start position:0%
+idea is this remember as we saw in part
+ 
+
+ align:start position:0%
+idea is this remember as we saw in part
+one of our course that e to the T goes
+
+ align:start position:0%
+one of our course that e to the T goes
+ 
+
+ align:start position:0%
+one of our course that e to the T goes
+to Infinity much faster than t to the N
+
+ align:start position:0%
+to Infinity much faster than t to the N
+ 
+
+ align:start position:0%
+to Infinity much faster than t to the N
+for any integer n
+
+ align:start position:0%
+for any integer n
+ 
+
+ align:start position:0%
+for any integer n
+consequently what this means is since
+
+ align:start position:0%
+consequently what this means is since
+ 
+
+ align:start position:0%
+consequently what this means is since
+most functions can be represented in the
+
+ align:start position:0%
+most functions can be represented in the
+ 
+
+ align:start position:0%
+most functions can be represented in the
+power series one would expect that if
+
+ align:start position:0%
+power series one would expect that if
+ 
+
+ align:start position:0%
+power series one would expect that if
+one were to take a function like f of T
+
+ align:start position:0%
+one were to take a function like f of T
+ 
+
+ align:start position:0%
+one were to take a function like f of T
+and multiply it by e to the minus St
+
+ align:start position:0%
+and multiply it by e to the minus St
+ 
+
+ align:start position:0%
+and multiply it by e to the minus St
+where s was a constant greater than zero
+
+ align:start position:0%
+where s was a constant greater than zero
+ 
+
+ align:start position:0%
+where s was a constant greater than zero
+one would expect that e to Theus St F of
+
+ align:start position:0%
+one would expect that e to Theus St F of
+ 
+
+ align:start position:0%
+one would expect that e to Theus St F of
+T would approach zero rapidly as T
+
+ align:start position:0%
+T would approach zero rapidly as T
+ 
+
+ align:start position:0%
+T would approach zero rapidly as T
+approaches Infinity okay now this may
+
+ align:start position:0%
+approaches Infinity okay now this may
+ 
+
+ align:start position:0%
+approaches Infinity okay now this may
+not happen we'll talk about that in more
+
+ align:start position:0%
+not happen we'll talk about that in more
+ 
+
+ align:start position:0%
+not happen we'll talk about that in more
+detail later but at any rate let's
+
+ align:start position:0%
+detail later but at any rate let's
+ 
+
+ align:start position:0%
+detail later but at any rate let's
+assume that we're dealing with a
+
+ align:start position:0%
+assume that we're dealing with a
+ 
+
+ align:start position:0%
+assume that we're dealing with a
+particular function f of T where not
+
+ align:start position:0%
+particular function f of T where not
+ 
+
+ align:start position:0%
+particular function f of T where not
+only does e to Theus s of Ft F of T go
+
+ align:start position:0%
+only does e to Theus s of Ft F of T go
+ 
+
+ align:start position:0%
+only does e to Theus s of Ft F of T go
+to zero rapidly for some value of s as T
+
+ align:start position:0%
+to zero rapidly for some value of s as T
+ 
+
+ align:start position:0%
+to zero rapidly for some value of s as T
+approaches Infinity but so rapidly that
+
+ align:start position:0%
+approaches Infinity but so rapidly that
+ 
+
+ align:start position:0%
+approaches Infinity but so rapidly that
+the integral of e to Theus St F of T DT
+
+ align:start position:0%
+the integral of e to Theus St F of T DT
+ 
+
+ align:start position:0%
+the integral of e to Theus St F of T DT
+from 0er to Infinity converges let's
+
+ align:start position:0%
+from 0er to Infinity converges let's
+ 
+
+ align:start position:0%
+from 0er to Infinity converges let's
+just keep that in mind for the time
+
+ align:start position:0%
+just keep that in mind for the time
+ 
+
+ align:start position:0%
+just keep that in mind for the time
+being and with this in mind one defines
+
+ align:start position:0%
+being and with this in mind one defines
+ 
+
+ align:start position:0%
+being and with this in mind one defines
+the llast transform of a function f of T
+
+ align:start position:0%
+the llast transform of a function f of T
+ 
+
+ align:start position:0%
+the llast transform of a function f of T
+namely given F of t the llast transform
+
+ align:start position:0%
+namely given F of t the llast transform
+ 
+
+ align:start position:0%
+namely given F of t the llast transform
+of f of T written L of f of T is defined
+
+ align:start position:0%
+of f of T written L of f of T is defined
+ 
+
+ align:start position:0%
+of f of T written L of f of T is defined
+to be the integral from 0 to Infinity e
+
+ align:start position:0%
+to be the integral from 0 to Infinity e
+ 
+
+ align:start position:0%
+to be the integral from 0 to Infinity e
+the minus St F of T DT provided that
+
+ align:start position:0%
+the minus St F of T DT provided that
+ 
+
+ align:start position:0%
+the minus St F of T DT provided that
+this integral converges notice by the
+
+ align:start position:0%
+this integral converges notice by the
+ 
+
+ align:start position:0%
+this integral converges notice by the
+way that since T is the variable of
+
+ align:start position:0%
+way that since T is the variable of
+ 
+
+ align:start position:0%
+way that since T is the variable of
+integration when we evaluate this
+
+ align:start position:0%
+integration when we evaluate this
+ 
+
+ align:start position:0%
+integration when we evaluate this
+integral at tal 0 and tal
+
+ align:start position:0%
+integral at tal 0 and tal
+ 
+
+ align:start position:0%
+integral at tal 0 and tal
+Infinity the resulting function becomes
+
+ align:start position:0%
+Infinity the resulting function becomes
+ 
+
+ align:start position:0%
+Infinity the resulting function becomes
+a function of s alone in other words we
+
+ align:start position:0%
+a function of s alone in other words we
+ 
+
+ align:start position:0%
+a function of s alone in other words we
+evaluate this as T goes from 0 to
+
+ align:start position:0%
+evaluate this as T goes from 0 to
+ 
+
+ align:start position:0%
+evaluate this as T goes from 0 to
+Infinity the resulting integral is a
+
+ align:start position:0%
+Infinity the resulting integral is a
+ 
+
+ align:start position:0%
+Infinity the resulting integral is a
+function of s alone consequently one
+
+ align:start position:0%
+function of s alone consequently one
+ 
+
+ align:start position:0%
+function of s alone consequently one
+often to identify the function with its
+
+ align:start position:0%
+often to identify the function with its
+ 
+
+ align:start position:0%
+often to identify the function with its
+llast transform indicates that if the
+
+ align:start position:0%
+llast transform indicates that if the
+ 
+
+ align:start position:0%
+llast transform indicates that if the
+function was F of T the llast transform
+
+ align:start position:0%
+function was F of T the llast transform
+ 
+
+ align:start position:0%
+function was F of T the llast transform
+IS F Bar of s and notice by the way what
+
+ align:start position:0%
+IS F Bar of s and notice by the way what
+ 
+
+ align:start position:0%
+IS F Bar of s and notice by the way what
+this thing means pictorially this is an
+
+ align:start position:0%
+this thing means pictorially this is an
+ 
+
+ align:start position:0%
+this thing means pictorially this is an
+area under a curve and what you're
+
+ align:start position:0%
+area under a curve and what you're
+ 
+
+ align:start position:0%
+area under a curve and what you're
+really saying if the llast transform of
+
+ align:start position:0%
+really saying if the llast transform of
+ 
+
+ align:start position:0%
+really saying if the llast transform of
+a function exists is that this area
+
+ align:start position:0%
+a function exists is that this area
+ 
+
+ align:start position:0%
+a function exists is that this area
+under the curve as T goes from zero to
+
+ align:start position:0%
+under the curve as T goes from zero to
+ 
+
+ align:start position:0%
+under the curve as T goes from zero to
+Infinity is indeed finite by the way
+
+ align:start position:0%
+Infinity is indeed finite by the way
+ 
+
+ align:start position:0%
+Infinity is indeed finite by the way
+this should also lead you to believe
+
+ align:start position:0%
+this should also lead you to believe
+ 
+
+ align:start position:0%
+this should also lead you to believe
+that if this is finite for one value of
+
+ align:start position:0%
+that if this is finite for one value of
+ 
+
+ align:start position:0%
+that if this is finite for one value of
+s if s becomes is replaced by something
+
+ align:start position:0%
+s if s becomes is replaced by something
+ 
+
+ align:start position:0%
+s if s becomes is replaced by something
+larger this goes to zero even faster and
+
+ align:start position:0%
+larger this goes to zero even faster and
+ 
+
+ align:start position:0%
+larger this goes to zero even faster and
+consequently the uh area under the Curve
+
+ align:start position:0%
+consequently the uh area under the Curve
+ 
+
+ align:start position:0%
+consequently the uh area under the Curve
+will exist for all values of s Beyond a
+
+ align:start position:0%
+will exist for all values of s Beyond a
+ 
+
+ align:start position:0%
+will exist for all values of s Beyond a
+certain value once the area exists for
+
+ align:start position:0%
+certain value once the area exists for
+ 
+
+ align:start position:0%
+certain value once the area exists for
+that one value maybe the easiest way to
+
+ align:start position:0%
+that one value maybe the easiest way to
+ 
+
+ align:start position:0%
+that one value maybe the easiest way to
+say that is in terms of a picture here
+
+ align:start position:0%
+say that is in terms of a picture here
+ 
+
+ align:start position:0%
+say that is in terms of a picture here
+I've drawn two representative functions
+
+ align:start position:0%
+I've drawn two representative functions
+ 
+
+ align:start position:0%
+I've drawn two representative functions
+yal F of t one case being uh a pulsation
+
+ align:start position:0%
+yal F of t one case being uh a pulsation
+ 
+
+ align:start position:0%
+yal F of t one case being uh a pulsation
+type of thing where you have a an
+
+ align:start position:0%
+type of thing where you have a an
+ 
+
+ align:start position:0%
+type of thing where you have a an
+irregular pulse repeated here the other
+
+ align:start position:0%
+irregular pulse repeated here the other
+ 
+
+ align:start position:0%
+irregular pulse repeated here the other
+being a polinomial yal t ^2 what we're
+
+ align:start position:0%
+being a polinomial yal t ^2 what we're
+ 
+
+ align:start position:0%
+being a polinomial yal t ^2 what we're
+saying is that if I multiply F of T by e
+
+ align:start position:0%
+saying is that if I multiply F of T by e
+ 
+
+ align:start position:0%
+saying is that if I multiply F of T by e
+to the minus St remember e to the minus
+
+ align:start position:0%
+to the minus St remember e to the minus
+ 
+
+ align:start position:0%
+to the minus St remember e to the minus
+St for positive values of s is a curve
+
+ align:start position:0%
+St for positive values of s is a curve
+ 
+
+ align:start position:0%
+St for positive values of s is a curve
+that goes to zero very rapidly and what
+
+ align:start position:0%
+that goes to zero very rapidly and what
+ 
+
+ align:start position:0%
+that goes to zero very rapidly and what
+this tends to do is to pull this thing
+
+ align:start position:0%
+this tends to do is to pull this thing
+ 
+
+ align:start position:0%
+this tends to do is to pull this thing
+down so that you go to zero very rapidly
+
+ align:start position:0%
+down so that you go to zero very rapidly
+ 
+
+ align:start position:0%
+down so that you go to zero very rapidly
+and the fact that the integral exists
+
+ align:start position:0%
+and the fact that the integral exists
+ 
+
+ align:start position:0%
+and the fact that the integral exists
+says not only does this go to zero very
+
+ align:start position:0%
+says not only does this go to zero very
+ 
+
+ align:start position:0%
+says not only does this go to zero very
+rapidly but it goes to zero so fast that
+
+ align:start position:0%
+rapidly but it goes to zero so fast that
+ 
+
+ align:start position:0%
+rapidly but it goes to zero so fast that
+the area under the curve stays finite
+
+ align:start position:0%
+the area under the curve stays finite
+ 
+
+ align:start position:0%
+the area under the curve stays finite
+remember that was our version of
+
+ align:start position:0%
+remember that was our version of
+ 
+
+ align:start position:0%
+remember that was our version of
+infinity time Z it's not enough that
+
+ align:start position:0%
+infinity time Z it's not enough that
+ 
+
+ align:start position:0%
+infinity time Z it's not enough that
+this goes to zero that this approaches
+
+ align:start position:0%
+this goes to zero that this approaches
+ 
+
+ align:start position:0%
+this goes to zero that this approaches
+the T axis it has to approach fast
+
+ align:start position:0%
+the T axis it has to approach fast
+ 
+
+ align:start position:0%
+the T axis it has to approach fast
+enough so that the area under the curve
+
+ align:start position:0%
+enough so that the area under the curve
+ 
+
+ align:start position:0%
+enough so that the area under the curve
+is finite and all we're saying is that
+
+ align:start position:0%
+is finite and all we're saying is that
+ 
+
+ align:start position:0%
+is finite and all we're saying is that
+if you can find one value of s that
+
+ align:start position:0%
+if you can find one value of s that
+ 
+
+ align:start position:0%
+if you can find one value of s that
+makes the area under the Curve finite
+
+ align:start position:0%
+makes the area under the Curve finite
+ 
+
+ align:start position:0%
+makes the area under the Curve finite
+any larger value of s will certainly
+
+ align:start position:0%
+any larger value of s will certainly
+ 
+
+ align:start position:0%
+any larger value of s will certainly
+make the area under the curve finite
+
+ align:start position:0%
+make the area under the curve finite
+ 
+
+ align:start position:0%
+make the area under the curve finite
+because this will be pulled down even
+
+ align:start position:0%
+because this will be pulled down even
+ 
+
+ align:start position:0%
+because this will be pulled down even
+faster and perhaps you can begin to see
+
+ align:start position:0%
+faster and perhaps you can begin to see
+ 
+
+ align:start position:0%
+faster and perhaps you can begin to see
+intuitively that as I let s get larger
+
+ align:start position:0%
+intuitively that as I let s get larger
+ 
+
+ align:start position:0%
+intuitively that as I let s get larger
+and larger not only does the area under
+
+ align:start position:0%
+and larger not only does the area under
+ 
+
+ align:start position:0%
+and larger not only does the area under
+the curve stay finite but one would
+
+ align:start position:0%
+the curve stay finite but one would
+ 
+
+ align:start position:0%
+the curve stay finite but one would
+expect that it would also approach zero
+
+ align:start position:0%
+expect that it would also approach zero
+ 
+
+ align:start position:0%
+expect that it would also approach zero
+because for large values of s e to the
+
+ align:start position:0%
+because for large values of s e to the
+ 
+
+ align:start position:0%
+because for large values of s e to the
+minus St goes to zero so rapidly that
+
+ align:start position:0%
+minus St goes to zero so rapidly that
+ 
+
+ align:start position:0%
+minus St goes to zero so rapidly that
+even large values up here would be
+
+ align:start position:0%
+even large values up here would be
+ 
+
+ align:start position:0%
+even large values up here would be
+pulled down very rapidly at any rate let
+
+ align:start position:0%
+pulled down very rapidly at any rate let
+ 
+
+ align:start position:0%
+pulled down very rapidly at any rate let
+me illustrate this by means of an
+
+ align:start position:0%
+me illustrate this by means of an
+ 
+
+ align:start position:0%
+me illustrate this by means of an
+example suppose I pick for f of T
+
+ align:start position:0%
+example suppose I pick for f of T
+ 
+
+ align:start position:0%
+example suppose I pick for f of T
+something as simple as e to the a t
+
+ align:start position:0%
+something as simple as e to the a t
+ 
+
+ align:start position:0%
+something as simple as e to the a t
+where a is a given constant what I mean
+
+ align:start position:0%
+where a is a given constant what I mean
+ 
+
+ align:start position:0%
+where a is a given constant what I mean
+by simple here is recalling that that
+
+ align:start position:0%
+by simple here is recalling that that
+ 
+
+ align:start position:0%
+by simple here is recalling that that
+the llas transform involves multiplying
+
+ align:start position:0%
+the llas transform involves multiplying
+ 
+
+ align:start position:0%
+the llas transform involves multiplying
+F of T by e to the minus St this will
+
+ align:start position:0%
+F of T by e to the minus St this will
+ 
+
+ align:start position:0%
+F of T by e to the minus St this will
+give me a simple algebraic manipulation
+
+ align:start position:0%
+give me a simple algebraic manipulation
+ 
+
+ align:start position:0%
+give me a simple algebraic manipulation
+to perform by definition how do I form
+
+ align:start position:0%
+to perform by definition how do I form
+ 
+
+ align:start position:0%
+to perform by definition how do I form
+the llast transform of e to the a t what
+
+ align:start position:0%
+the llast transform of e to the a t what
+ 
+
+ align:start position:0%
+the llast transform of e to the a t what
+I do is I multiply e to the a t by e to
+
+ align:start position:0%
+I do is I multiply e to the a t by e to
+ 
+
+ align:start position:0%
+I do is I multiply e to the a t by e to
+the minus St and integrate that from 0
+
+ align:start position:0%
+the minus St and integrate that from 0
+ 
+
+ align:start position:0%
+the minus St and integrate that from 0
+to infinity and if that integral exists
+
+ align:start position:0%
+to infinity and if that integral exists
+ 
+
+ align:start position:0%
+to infinity and if that integral exists
+meaning if the integral converges if
+
+ align:start position:0%
+meaning if the integral converges if
+ 
+
+ align:start position:0%
+meaning if the integral converges if
+this limit is finite I call that the
+
+ align:start position:0%
+this limit is finite I call that the
+ 
+
+ align:start position:0%
+this limit is finite I call that the
+llast transform at any rate just
+
+ align:start position:0%
+llast transform at any rate just
+ 
+
+ align:start position:0%
+llast transform at any rate just
+substituting in here then F of T becomes
+
+ align:start position:0%
+substituting in here then F of T becomes
+ 
+
+ align:start position:0%
+substituting in here then F of T becomes
+e to the a t this says integral from 0
+
+ align:start position:0%
+e to the a t this says integral from 0
+ 
+
+ align:start position:0%
+e to the a t this says integral from 0
+to Infinity e to the a - s * T power DT
+
+ align:start position:0%
+to Infinity e to the a - s * T power DT
+ 
+
+ align:start position:0%
+to Infinity e to the a - s * T power DT
+since A and S are constants the integral
+
+ align:start position:0%
+since A and S are constants the integral
+ 
+
+ align:start position:0%
+since A and S are constants the integral
+e to the A- s t comes out to be 1 / A- s
+
+ align:start position:0%
+e to the A- s t comes out to be 1 / A- s
+ 
+
+ align:start position:0%
+e to the A- s t comes out to be 1 / A- s
+e to the a minus St evaluated as T goes
+
+ align:start position:0%
+e to the a minus St evaluated as T goes
+ 
+
+ align:start position:0%
+e to the a minus St evaluated as T goes
+from 0 to Infinity now the key point to
+
+ align:start position:0%
+from 0 to Infinity now the key point to
+ 
+
+ align:start position:0%
+from 0 to Infinity now the key point to
+notice here is that as soon as s is
+
+ align:start position:0%
+notice here is that as soon as s is
+ 
+
+ align:start position:0%
+notice here is that as soon as s is
+greater than a this gives me a negative
+
+ align:start position:0%
+greater than a this gives me a negative
+ 
+
+ align:start position:0%
+greater than a this gives me a negative
+exponent as soon as s is greater than a
+
+ align:start position:0%
+exponent as soon as s is greater than a
+ 
+
+ align:start position:0%
+exponent as soon as s is greater than a
+consequently as T goes to Infinity this
+
+ align:start position:0%
+consequently as T goes to Infinity this
+ 
+
+ align:start position:0%
+consequently as T goes to Infinity this
+essentially behaves like 1 over e to the
+
+ align:start position:0%
+essentially behaves like 1 over e to the
+ 
+
+ align:start position:0%
+essentially behaves like 1 over e to the
+infinity which is zero in other words
+
+ align:start position:0%
+infinity which is zero in other words
+ 
+
+ align:start position:0%
+infinity which is zero in other words
+once s is greater than a the upper limit
+
+ align:start position:0%
+once s is greater than a the upper limit
+ 
+
+ align:start position:0%
+once s is greater than a the upper limit
+drops out my lower limit would just be e
+
+ align:start position:0%
+drops out my lower limit would just be e
+ 
+
+ align:start position:0%
+drops out my lower limit would just be e
+to the 0 you see and I'm subtracting
+
+ align:start position:0%
+to the 0 you see and I'm subtracting
+ 
+
+ align:start position:0%
+to the 0 you see and I'm subtracting
+that at any rate to make a long story
+
+ align:start position:0%
+that at any rate to make a long story
+ 
+
+ align:start position:0%
+that at any rate to make a long story
+short and to summarize what we're saying
+
+ align:start position:0%
+short and to summarize what we're saying
+ 
+
+ align:start position:0%
+short and to summarize what we're saying
+simply observe that if s is greater than
+
+ align:start position:0%
+simply observe that if s is greater than
+ 
+
+ align:start position:0%
+simply observe that if s is greater than
+zero the limit as T approaches Infinity
+
+ align:start position:0%
+zero the limit as T approaches Infinity
+ 
+
+ align:start position:0%
+zero the limit as T approaches Infinity
+e to the a minus St T is zero and that
+
+ align:start position:0%
+e to the a minus St T is zero and that
+ 
+
+ align:start position:0%
+e to the a minus St T is zero and that
+therefore the llast transform of e to
+
+ align:start position:0%
+therefore the llast transform of e to
+ 
+
+ align:start position:0%
+therefore the llast transform of e to
+the a t is simply 1 / s minus a provided
+
+ align:start position:0%
+the a t is simply 1 / s minus a provided
+ 
+
+ align:start position:0%
+the a t is simply 1 / s minus a provided
+s is greater than a in other words again
+
+ align:start position:0%
+s is greater than a in other words again
+ 
+
+ align:start position:0%
+s is greater than a in other words again
+just looking back here see I subtract
+
+ align:start position:0%
+just looking back here see I subtract
+ 
+
+ align:start position:0%
+just looking back here see I subtract
+the lower limit when T is zero this is
+
+ align:start position:0%
+the lower limit when T is zero this is
+ 
+
+ align:start position:0%
+the lower limit when T is zero this is
+one but I'm subtracting it makes it
+
+ align:start position:0%
+one but I'm subtracting it makes it
+ 
+
+ align:start position:0%
+one but I'm subtracting it makes it
+minus one and - 1 / a - s is the same as
+
+ align:start position:0%
+minus one and - 1 / a - s is the same as
+ 
+
+ align:start position:0%
+minus one and - 1 / a - s is the same as
+1 / s - A to State this then in other
+
+ align:start position:0%
+1 / s - A to State this then in other
+ 
+
+ align:start position:0%
+1 / s - A to State this then in other
+words if F of T is e to the a t f bar of
+
+ align:start position:0%
+words if F of T is e to the a t f bar of
+ 
+
+ align:start position:0%
+words if F of T is e to the a t f bar of
+s is 1 / s minus a where the domain of f
+
+ align:start position:0%
+s is 1 / s minus a where the domain of f
+ 
+
+ align:start position:0%
+s is 1 / s minus a where the domain of f
+is a set of all s such that s is greater
+
+ align:start position:0%
+is a set of all s such that s is greater
+ 
+
+ align:start position:0%
+is a set of all s such that s is greater
+than a and what does this mean
+
+ align:start position:0%
+than a and what does this mean
+ 
+
+ align:start position:0%
+than a and what does this mean
+geometrically this is the area under the
+
+ align:start position:0%
+geometrically this is the area under the
+ 
+
+ align:start position:0%
+geometrically this is the area under the
+curve e to the minus st e to the a t as
+
+ align:start position:0%
+curve e to the minus st e to the a t as
+ 
+
+ align:start position:0%
+curve e to the minus st e to the a t as
+T goes from 0 to Infinity that that area
+
+ align:start position:0%
+T goes from 0 to Infinity that that area
+ 
+
+ align:start position:0%
+T goes from 0 to Infinity that that area
+will be finite as soon as s is greater
+
+ align:start position:0%
+will be finite as soon as s is greater
+ 
+
+ align:start position:0%
+will be finite as soon as s is greater
+than a by way of illustration if I
+
+ align:start position:0%
+than a by way of illustration if I
+ 
+
+ align:start position:0%
+than a by way of illustration if I
+replace a by two what we're saying is
+
+ align:start position:0%
+replace a by two what we're saying is
+ 
+
+ align:start position:0%
+replace a by two what we're saying is
+that the llast transform of e 2T is 1 /
+
+ align:start position:0%
+that the llast transform of e 2T is 1 /
+ 
+
+ align:start position:0%
+that the llast transform of e 2T is 1 /
+s minus 2 notice that nice polinomial
+
+ align:start position:0%
+s minus 2 notice that nice polinomial
+ 
+
+ align:start position:0%
+s minus 2 notice that nice polinomial
+quotient idea the rather simple
+
+ align:start position:0%
+quotient idea the rather simple
+ 
+
+ align:start position:0%
+quotient idea the rather simple
+expression 1 / s - 2 if s is greater
+
+ align:start position:0%
+expression 1 / s - 2 if s is greater
+ 
+
+ align:start position:0%
+expression 1 / s - 2 if s is greater
+than two if we replace a by minus 3 and
+
+ align:start position:0%
+than two if we replace a by minus 3 and
+ 
+
+ align:start position:0%
+than two if we replace a by minus 3 and
+use this recipe we have that the llas
+
+ align:start position:0%
+use this recipe we have that the llas
+ 
+
+ align:start position:0%
+use this recipe we have that the llas
+transform of eus 3T is 1 / s - -3 1 / s
+
+ align:start position:0%
+transform of eus 3T is 1 / s - -3 1 / s
+ 
+
+ align:start position:0%
+transform of eus 3T is 1 / s - -3 1 / s
++ 3 where s must be greater than -3
+
+ align:start position:0%
++ 3 where s must be greater than -3
+ 
+
+ align:start position:0%
++ 3 where s must be greater than -3
+notice also here that by the comparison
+
+ align:start position:0%
+notice also here that by the comparison
+ 
+
+ align:start position:0%
+notice also here that by the comparison
+test so to speak remember the same
+
+ align:start position:0%
+test so to speak remember the same
+ 
+
+ align:start position:0%
+test so to speak remember the same
+comparison test that we use for infinite
+
+ align:start position:0%
+comparison test that we use for infinite
+ 
+
+ align:start position:0%
+comparison test that we use for infinite
+series if the magnitude of f of T is
+
+ align:start position:0%
+series if the magnitude of f of T is
+ 
+
+ align:start position:0%
+series if the magnitude of f of T is
+less than some constant C * e to the a t
+
+ align:start position:0%
+less than some constant C * e to the a t
+ 
+
+ align:start position:0%
+less than some constant C * e to the a t
+power for all values of T then the
+
+ align:start position:0%
+power for all values of T then the
+ 
+
+ align:start position:0%
+power for all values of T then the
+integral from 0 to Infinity e to Theus
+
+ align:start position:0%
+integral from 0 to Infinity e to Theus
+ 
+
+ align:start position:0%
+integral from 0 to Infinity e to Theus
+St F of T DT must also converge in other
+
+ align:start position:0%
+St F of T DT must also converge in other
+ 
+
+ align:start position:0%
+St F of T DT must also converge in other
+words we are already know that this
+
+ align:start position:0%
+words we are already know that this
+ 
+
+ align:start position:0%
+words we are already know that this
+integral converges shall we say if the
+
+ align:start position:0%
+integral converges shall we say if the
+ 
+
+ align:start position:0%
+integral converges shall we say if the
+integran were e to the a t right
+
+ align:start position:0%
+integran were e to the a t right
+ 
+
+ align:start position:0%
+integran were e to the a t right
+therefore we're saying it'll converge if
+
+ align:start position:0%
+therefore we're saying it'll converge if
+ 
+
+ align:start position:0%
+therefore we're saying it'll converge if
+you multiply that by a constant because
+
+ align:start position:0%
+you multiply that by a constant because
+ 
+
+ align:start position:0%
+you multiply that by a constant because
+convergence isn't affected by
+
+ align:start position:0%
+convergence isn't affected by
+ 
+
+ align:start position:0%
+convergence isn't affected by
+multiplying by a constant consequently
+
+ align:start position:0%
+multiplying by a constant consequently
+ 
+
+ align:start position:0%
+multiplying by a constant consequently
+if in magnitude the integrant that we're
+
+ align:start position:0%
+if in magnitude the integrant that we're
+ 
+
+ align:start position:0%
+if in magnitude the integrant that we're
+investigating is smaller than this in
+
+ align:start position:0%
+investigating is smaller than this in
+ 
+
+ align:start position:0%
+investigating is smaller than this in
+magnitude it must also have a the plus
+
+ align:start position:0%
+magnitude it must also have a the plus
+ 
+
+ align:start position:0%
+magnitude it must also have a the plus
+transform that this thing here must
+
+ align:start position:0%
+transform that this thing here must
+ 
+
+ align:start position:0%
+transform that this thing here must
+converge now because this is so obvious
+
+ align:start position:0%
+converge now because this is so obvious
+ 
+
+ align:start position:0%
+converge now because this is so obvious
+and so important one defines a function
+
+ align:start position:0%
+and so important one defines a function
+ 
+
+ align:start position:0%
+and so important one defines a function
+with this property to have a very
+
+ align:start position:0%
+with this property to have a very
+ 
+
+ align:start position:0%
+with this property to have a very
+special name namely the function f of T
+
+ align:start position:0%
+special name namely the function f of T
+ 
+
+ align:start position:0%
+special name namely the function f of T
+is set to have exponential order if and
+
+ align:start position:0%
+is set to have exponential order if and
+ 
+
+ align:start position:0%
+is set to have exponential order if and
+only if there exists constant c and a
+
+ align:start position:0%
+only if there exists constant c and a
+ 
+
+ align:start position:0%
+only if there exists constant c and a
+such that the magnitude of f of T is
+
+ align:start position:0%
+such that the magnitude of f of T is
+ 
+
+ align:start position:0%
+such that the magnitude of f of T is
+less than c e to the a t for T all T
+
+ align:start position:0%
+less than c e to the a t for T all T
+ 
+
+ align:start position:0%
+less than c e to the a t for T all T
+greater than zero what we are saying in
+
+ align:start position:0%
+greater than zero what we are saying in
+ 
+
+ align:start position:0%
+greater than zero what we are saying in
+summary is that by this definition of
+
+ align:start position:0%
+summary is that by this definition of
+ 
+
+ align:start position:0%
+summary is that by this definition of
+exponential order and the comparison
+
+ align:start position:0%
+exponential order and the comparison
+ 
+
+ align:start position:0%
+exponential order and the comparison
+test all functions of exponential order
+
+ align:start position:0%
+test all functions of exponential order
+ 
+
+ align:start position:0%
+test all functions of exponential order
+have llast transforms because that
+
+ align:start position:0%
+have llast transforms because that
+ 
+
+ align:start position:0%
+have llast transforms because that
+integral from 0 to Infinity e to the
+
+ align:start position:0%
+integral from 0 to Infinity e to the
+ 
+
+ align:start position:0%
+integral from 0 to Infinity e to the
+minus St F of T DT will converge by
+
+ align:start position:0%
+minus St F of T DT will converge by
+ 
+
+ align:start position:0%
+minus St F of T DT will converge by
+comparison with the integral 0 to
+
+ align:start position:0%
+comparison with the integral 0 to
+ 
+
+ align:start position:0%
+comparison with the integral 0 to
+Infinity e to the minus st e the a tdt
+
+ align:start position:0%
+Infinity e to the minus st e the a tdt
+ 
+
+ align:start position:0%
+Infinity e to the minus st e the a tdt
+for S greater than in other words this
+
+ align:start position:0%
+for S greater than in other words this
+ 
+
+ align:start position:0%
+for S greater than in other words this
+will all converge where the value of s
+
+ align:start position:0%
+will all converge where the value of s
+ 
+
+ align:start position:0%
+will all converge where the value of s
+has to be greater than a now the idea is
+
+ align:start position:0%
+has to be greater than a now the idea is
+ 
+
+ align:start position:0%
+has to be greater than a now the idea is
+what's so important about functions of
+
+ align:start position:0%
+what's so important about functions of
+ 
+
+ align:start position:0%
+what's so important about functions of
+exponential order why do I stress these
+
+ align:start position:0%
+exponential order why do I stress these
+ 
+
+ align:start position:0%
+exponential order why do I stress these
+and the answer is that in terms of
+
+ align:start position:0%
+and the answer is that in terms of
+ 
+
+ align:start position:0%
+and the answer is that in terms of
+linear differential equations with
+
+ align:start position:0%
+linear differential equations with
+ 
+
+ align:start position:0%
+linear differential equations with
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+coefficients the functions that we tend
+
+ align:start position:0%
+coefficients the functions that we tend
+ 
+
+ align:start position:0%
+coefficients the functions that we tend
+to deal with all have exponential order
+
+ align:start position:0%
+to deal with all have exponential order
+ 
+
+ align:start position:0%
+to deal with all have exponential order
+in other words they will all have llast
+
+ align:start position:0%
+in other words they will all have llast
+ 
+
+ align:start position:0%
+in other words they will all have llast
+transforms for example e to the a t
+
+ align:start position:0%
+transforms for example e to the a t
+ 
+
+ align:start position:0%
+transforms for example e to the a t
+trivially is a function uh that has
+
+ align:start position:0%
+trivially is a function uh that has
+ 
+
+ align:start position:0%
+trivially is a function uh that has
+exponential order that was our model for
+
+ align:start position:0%
+exponential order that was our model for
+ 
+
+ align:start position:0%
+exponential order that was our model for
+the definition in fact e to the a t is 1
+
+ align:start position:0%
+the definition in fact e to the a t is 1
+ 
+
+ align:start position:0%
+the definition in fact e to the a t is 1
+e to the a t simply take a to be a and C
+
+ align:start position:0%
+e to the a t simply take a to be a and C
+ 
+
+ align:start position:0%
+e to the a t simply take a to be a and C
+to be one and we have the Criterion for
+
+ align:start position:0%
+to be one and we have the Criterion for
+ 
+
+ align:start position:0%
+to be one and we have the Criterion for
+exponential order being obeyed the sign
+
+ align:start position:0%
+exponential order being obeyed the sign
+ 
+
+ align:start position:0%
+exponential order being obeyed the sign
+of a t where a is any constant has
+
+ align:start position:0%
+of a t where a is any constant has
+ 
+
+ align:start position:0%
+of a t where a is any constant has
+exponential order why because the
+
+ align:start position:0%
+exponential order why because the
+ 
+
+ align:start position:0%
+exponential order why because the
+magnitude of sin a t is certainly no
+
+ align:start position:0%
+magnitude of sin a t is certainly no
+ 
+
+ align:start position:0%
+magnitude of sin a t is certainly no
+greater than one and one is certainly no
+
+ align:start position:0%
+greater than one and one is certainly no
+ 
+
+ align:start position:0%
+greater than one and one is certainly no
+greater than e to the T for any positive
+
+ align:start position:0%
+greater than e to the T for any positive
+ 
+
+ align:start position:0%
+greater than e to the T for any positive
+value of T see e to the 0 is already one
+
+ align:start position:0%
+value of T see e to the 0 is already one
+ 
+
+ align:start position:0%
+value of T see e to the 0 is already one
+therefore sin a t is less than 1 e to
+
+ align:start position:0%
+therefore sin a t is less than 1 e to
+ 
+
+ align:start position:0%
+therefore sin a t is less than 1 e to
+the 1 T if T is greater than zero so sin
+
+ align:start position:0%
+the 1 T if T is greater than zero so sin
+ 
+
+ align:start position:0%
+the 1 T if T is greater than zero so sin
+a t has exponential order finally we
+
+ align:start position:0%
+a t has exponential order finally we
+ 
+
+ align:start position:0%
+a t has exponential order finally we
+dealt with polinomial t to the N where n
+
+ align:start position:0%
+dealt with polinomial t to the N where n
+ 
+
+ align:start position:0%
+dealt with polinomial t to the N where n
+was a positive integer and in part one
+
+ align:start position:0%
+was a positive integer and in part one
+ 
+
+ align:start position:0%
+was a positive integer and in part one
+of our course either using lopital rule
+
+ align:start position:0%
+of our course either using lopital rule
+ 
+
+ align:start position:0%
+of our course either using lopital rule
+or power series or what have you we
+
+ align:start position:0%
+or power series or what have you we
+ 
+
+ align:start position:0%
+or power series or what have you we
+showed that for any fixed positive
+
+ align:start position:0%
+showed that for any fixed positive
+ 
+
+ align:start position:0%
+showed that for any fixed positive
+integer n t the n * eus T went to zero
+
+ align:start position:0%
+integer n t the n * eus T went to zero
+ 
+
+ align:start position:0%
+integer n t the n * eus T went to zero
+in the limit as T went to Infinity
+
+ align:start position:0%
+in the limit as T went to Infinity
+ 
+
+ align:start position:0%
+in the limit as T went to Infinity
+consequently for large values of T the
+
+ align:start position:0%
+consequently for large values of T the
+ 
+
+ align:start position:0%
+consequently for large values of T the
+magnitude of t to the N is less than e
+
+ align:start position:0%
+magnitude of t to the N is less than e
+ 
+
+ align:start position:0%
+magnitude of t to the N is less than e
+to the T I'll leave the details out here
+
+ align:start position:0%
+to the T I'll leave the details out here
+ 
+
+ align:start position:0%
+to the T I'll leave the details out here
+I'm just trying to illustrate what's
+
+ align:start position:0%
+I'm just trying to illustrate what's
+ 
+
+ align:start position:0%
+I'm just trying to illustrate what's
+going on the important point is that the
+
+ align:start position:0%
+going on the important point is that the
+ 
+
+ align:start position:0%
+going on the important point is that the
+usual functions in counted in linear
+
+ align:start position:0%
+usual functions in counted in linear
+ 
+
+ align:start position:0%
+usual functions in counted in linear
+differential equations with coefficients
+
+ align:start position:0%
+differential equations with coefficients
+ 
+
+ align:start position:0%
+differential equations with coefficients
+have the
+
+ align:start position:0%
+have the
+ 
+
+ align:start position:0%
+have the
+transforms and I would like to make a
+
+ align:start position:0%
+transforms and I would like to make a
+ 
+
+ align:start position:0%
+transforms and I would like to make a
+couple of notes about this thing one
+
+ align:start position:0%
+couple of notes about this thing one
+ 
+
+ align:start position:0%
+couple of notes about this thing one
+I've already said but I'd like to
+
+ align:start position:0%
+I've already said but I'd like to
+ 
+
+ align:start position:0%
+I've already said but I'd like to
+reinforce
+
+ align:start position:0%
+reinforce
+ 
+
+ align:start position:0%
+reinforce
+it the what we've already seen is is
+
+ align:start position:0%
+it the what we've already seen is is
+ 
+
+ align:start position:0%
+it the what we've already seen is is
+that if F has exponential order F Bar of
+
+ align:start position:0%
+that if F has exponential order F Bar of
+ 
+
+ align:start position:0%
+that if F has exponential order F Bar of
+s the llast transform of s must be less
+
+ align:start position:0%
+s the llast transform of s must be less
+ 
+
+ align:start position:0%
+s the llast transform of s must be less
+than or equal to the llast transform of
+
+ align:start position:0%
+than or equal to the llast transform of
+ 
+
+ align:start position:0%
+than or equal to the llast transform of
+e to the well a constant times e to the
+
+ align:start position:0%
+e to the well a constant times e to the
+ 
+
+ align:start position:0%
+e to the well a constant times e to the
+a t but that the llast transform of e to
+
+ align:start position:0%
+a t but that the llast transform of e to
+ 
+
+ align:start position:0%
+a t but that the llast transform of e to
+the a t is 1 / s minus a so the class
+
+ align:start position:0%
+the a t is 1 / s minus a so the class
+ 
+
+ align:start position:0%
+the a t is 1 / s minus a so the class
+transform of f of f of f of T if F has
+
+ align:start position:0%
+transform of f of f of f of T if F has
+ 
+
+ align:start position:0%
+transform of f of f of f of T if F has
+exponential order can be no bigger than
+
+ align:start position:0%
+exponential order can be no bigger than
+ 
+
+ align:start position:0%
+exponential order can be no bigger than
+c/ S minus a since C is a constant and a
+
+ align:start position:0%
+c/ S minus a since C is a constant and a
+ 
+
+ align:start position:0%
+c/ S minus a since C is a constant and a
+is a constant as s goes to Infinity fbar
+
+ align:start position:0%
+is a constant as s goes to Infinity fbar
+ 
+
+ align:start position:0%
+is a constant as s goes to Infinity fbar
+of s goes to zero in other words for
+
+ align:start position:0%
+of s goes to zero in other words for
+ 
+
+ align:start position:0%
+of s goes to zero in other words for
+sufficiently large values of s the llast
+
+ align:start position:0%
+sufficiently large values of s the llast
+ 
+
+ align:start position:0%
+sufficiently large values of s the llast
+transform which names an area under a
+
+ align:start position:0%
+transform which names an area under a
+ 
+
+ align:start position:0%
+transform which names an area under a
+curve goes to zero meaning as we would
+
+ align:start position:0%
+curve goes to zero meaning as we would
+ 
+
+ align:start position:0%
+curve goes to zero meaning as we would
+expect the area under the curve does go
+
+ align:start position:0%
+expect the area under the curve does go
+ 
+
+ align:start position:0%
+expect the area under the curve does go
+to zero as s increases without bound
+
+ align:start position:0%
+to zero as s increases without bound
+ 
+
+ align:start position:0%
+to zero as s increases without bound
+what that means in particular you see is
+
+ align:start position:0%
+what that means in particular you see is
+ 
+
+ align:start position:0%
+what that means in particular you see is
+that not any function can be a llast
+
+ align:start position:0%
+that not any function can be a llast
+ 
+
+ align:start position:0%
+that not any function can be a llast
+transform of something you see in
+
+ align:start position:0%
+transform of something you see in
+ 
+
+ align:start position:0%
+transform of something you see in
+particular this says that for F Bar to
+
+ align:start position:0%
+particular this says that for F Bar to
+ 
+
+ align:start position:0%
+particular this says that for F Bar to
+be the llast transform of something F
+
+ align:start position:0%
+be the llast transform of something F
+ 
+
+ align:start position:0%
+be the llast transform of something F
+Bar of s must go to zero as s goes to
+
+ align:start position:0%
+Bar of s must go to zero as s goes to
+ 
+
+ align:start position:0%
+Bar of s must go to zero as s goes to
+Infinity for example if I were to write
+
+ align:start position:0%
+Infinity for example if I were to write
+ 
+
+ align:start position:0%
+Infinity for example if I were to write
+down F Bar of s to be S over s minus one
+
+ align:start position:0%
+down F Bar of s to be S over s minus one
+ 
+
+ align:start position:0%
+down F Bar of s to be S over s minus one
+or s+ one even F Bar of s is s over s +
+
+ align:start position:0%
+or s+ one even F Bar of s is s over s +
+ 
+
+ align:start position:0%
+or s+ one even F Bar of s is s over s +
+one notice that the limit of F Bar of s
+
+ align:start position:0%
+one notice that the limit of F Bar of s
+ 
+
+ align:start position:0%
+one notice that the limit of F Bar of s
+as s goes to Infinity is one con
+
+ align:start position:0%
+as s goes to Infinity is one con
+ 
+
+ align:start position:0%
+as s goes to Infinity is one con
+consequently this F Bar cannot be the
+
+ align:start position:0%
+consequently this F Bar cannot be the
+ 
+
+ align:start position:0%
+consequently this F Bar cannot be the
+llas transform of any function at least
+
+ align:start position:0%
+llas transform of any function at least
+ 
+
+ align:start position:0%
+llas transform of any function at least
+of exponential order because we've
+
+ align:start position:0%
+of exponential order because we've
+ 
+
+ align:start position:0%
+of exponential order because we've
+already seen that the llast transform of
+
+ align:start position:0%
+already seen that the llast transform of
+ 
+
+ align:start position:0%
+already seen that the llast transform of
+a function uh at least of exponential
+
+ align:start position:0%
+a function uh at least of exponential
+ 
+
+ align:start position:0%
+a function uh at least of exponential
+order must go to zero as s goes to
+
+ align:start position:0%
+order must go to zero as s goes to
+ 
+
+ align:start position:0%
+order must go to zero as s goes to
+Infinity okay so not every function can
+
+ align:start position:0%
+Infinity okay so not every function can
+ 
+
+ align:start position:0%
+Infinity okay so not every function can
+be a lli transform of something and
+
+ align:start position:0%
+be a lli transform of something and
+ 
+
+ align:start position:0%
+be a lli transform of something and
+secondly not every function has
+
+ align:start position:0%
+secondly not every function has
+ 
+
+ align:start position:0%
+secondly not every function has
+exponential order it may be true as we
+
+ align:start position:0%
+exponential order it may be true as we
+ 
+
+ align:start position:0%
+exponential order it may be true as we
+just showed that every function that
+
+ align:start position:0%
+just showed that every function that
+ 
+
+ align:start position:0%
+just showed that every function that
+we're dealing with when we're dealing
+
+ align:start position:0%
+we're dealing with when we're dealing
+ 
+
+ align:start position:0%
+we're dealing with when we're dealing
+with linear differ equations with
+
+ align:start position:0%
+with linear differ equations with
+ 
+
+ align:start position:0%
+with linear differ equations with
+constant coefficients or most functions
+
+ align:start position:0%
+constant coefficients or most functions
+ 
+
+ align:start position:0%
+constant coefficients or most functions
+that we're dealing with with linear
+
+ align:start position:0%
+that we're dealing with with linear
+ 
+
+ align:start position:0%
+that we're dealing with with linear
+differential equations with constant
+
+ align:start position:0%
+differential equations with constant
+ 
+
+ align:start position:0%
+differential equations with constant
+coefficients has our functions of
+
+ align:start position:0%
+coefficients has our functions of
+ 
+
+ align:start position:0%
+coefficients has our functions of
+exponential order not all functions have
+
+ align:start position:0%
+exponential order not all functions have
+ 
+
+ align:start position:0%
+exponential order not all functions have
+exponential order for example e to the
+
+ align:start position:0%
+exponential order for example e to the
+ 
+
+ align:start position:0%
+exponential order for example e to the
+t^2 does not have exponential order not
+
+ align:start position:0%
+t^2 does not have exponential order not
+ 
+
+ align:start position:0%
+t^2 does not have exponential order not
+order order
+
+ align:start position:0%
+order order
+ 
+
+ align:start position:0%
+order order
+order since notice that e to the t^2
+
+ align:start position:0%
+order since notice that e to the t^2
+ 
+
+ align:start position:0%
+order since notice that e to the t^2
+divided by c e to the a t would be 1 / c
+
+ align:start position:0%
+divided by c e to the a t would be 1 / c
+ 
+
+ align:start position:0%
+divided by c e to the a t would be 1 / c
+e to the T ^2 minus a t which is T * T
+
+ align:start position:0%
+e to the T ^2 minus a t which is T * T
+ 
+
+ align:start position:0%
+e to the T ^2 minus a t which is T * T
+minus a and notice now that if T is
+
+ align:start position:0%
+minus a and notice now that if T is
+ 
+
+ align:start position:0%
+minus a and notice now that if T is
+greater than a this exponent will be
+
+ align:start position:0%
+greater than a this exponent will be
+ 
+
+ align:start position:0%
+greater than a this exponent will be
+positive and as T goes to Infinity you
+
+ align:start position:0%
+positive and as T goes to Infinity you
+ 
+
+ align:start position:0%
+positive and as T goes to Infinity you
+see once T is greater than a this thing
+
+ align:start position:0%
+see once T is greater than a this thing
+ 
+
+ align:start position:0%
+see once T is greater than a this thing
+increases without bound and consequently
+
+ align:start position:0%
+increases without bound and consequently
+ 
+
+ align:start position:0%
+increases without bound and consequently
+since C is a constant you essentially
+
+ align:start position:0%
+since C is a constant you essentially
+ 
+
+ align:start position:0%
+since C is a constant you essentially
+have Infinity divided by a non-zero
+
+ align:start position:0%
+have Infinity divided by a non-zero
+ 
+
+ align:start position:0%
+have Infinity divided by a non-zero
+constant so you have what that e to the
+
+ align:start position:0%
+constant so you have what that e to the
+ 
+
+ align:start position:0%
+constant so you have what that e to the
+t^2 over C to the a t goes to Infinity
+
+ align:start position:0%
+t^2 over C to the a t goes to Infinity
+ 
+
+ align:start position:0%
+t^2 over C to the a t goes to Infinity
+as T approaches Infinity in particular
+
+ align:start position:0%
+as T approaches Infinity in particular
+ 
+
+ align:start position:0%
+as T approaches Infinity in particular
+this says that e to the t^ 2 dwarfs c e
+
+ align:start position:0%
+this says that e to the t^ 2 dwarfs c e
+ 
+
+ align:start position:0%
+this says that e to the t^ 2 dwarfs c e
+to the a t for large values of T other
+
+ align:start position:0%
+to the a t for large values of T other
+ 
+
+ align:start position:0%
+to the a t for large values of T other
+in particular you cannot have that uh e
+
+ align:start position:0%
+in particular you cannot have that uh e
+ 
+
+ align:start position:0%
+in particular you cannot have that uh e
+to the T ^ 2 is less than some constant
+
+ align:start position:0%
+to the T ^ 2 is less than some constant
+ 
+
+ align:start position:0%
+to the T ^ 2 is less than some constant
+time e to the a t now the question that
+
+ align:start position:0%
+time e to the a t now the question that
+ 
+
+ align:start position:0%
+time e to the a t now the question that
+comes up is what's so important now
+
+ align:start position:0%
+comes up is what's so important now
+ 
+
+ align:start position:0%
+comes up is what's so important now
+about the llast transform in terms of
+
+ align:start position:0%
+about the llast transform in terms of
+ 
+
+ align:start position:0%
+about the llast transform in terms of
+linear differential equations
+
+ align:start position:0%
+linear differential equations
+ 
+
+ align:start position:0%
+linear differential equations
+and the the answer is that the llast
+
+ align:start position:0%
+and the the answer is that the llast
+ 
+
+ align:start position:0%
+and the the answer is that the llast
+transform amazing enough has properties
+
+ align:start position:0%
+transform amazing enough has properties
+ 
+
+ align:start position:0%
+transform amazing enough has properties
+of linearity what do you mean by
+
+ align:start position:0%
+of linearity what do you mean by
+ 
+
+ align:start position:0%
+of linearity what do you mean by
+properties of linearity you mean what
+
+ align:start position:0%
+properties of linearity you mean what
+ 
+
+ align:start position:0%
+properties of linearity you mean what
+that for a function to be
+
+ align:start position:0%
+that for a function to be
+ 
+
+ align:start position:0%
+that for a function to be
+linear L of a sum must be the sum of the
+
+ align:start position:0%
+linear L of a sum must be the sum of the
+ 
+
+ align:start position:0%
+linear L of a sum must be the sum of the
+L's and L of a constant time something
+
+ align:start position:0%
+L's and L of a constant time something
+ 
+
+ align:start position:0%
+L's and L of a constant time something
+must be the constant times L of
+
+ align:start position:0%
+must be the constant times L of
+ 
+
+ align:start position:0%
+must be the constant times L of
+something well look at when you're
+
+ align:start position:0%
+something well look at when you're
+ 
+
+ align:start position:0%
+something well look at when you're
+dealing with
+
+ align:start position:0%
+dealing with
+ 
+
+ align:start position:0%
+dealing with
+integrals the given two definite
+
+ align:start position:0%
+integrals the given two definite
+ 
+
+ align:start position:0%
+integrals the given two definite
+integrals which exist the sum of the
+
+ align:start position:0%
+integrals which exist the sum of the
+ 
+
+ align:start position:0%
+integrals which exist the sum of the
+integrals is the integral of the sum the
+
+ align:start position:0%
+integrals is the integral of the sum the
+ 
+
+ align:start position:0%
+integrals is the integral of the sum the
+integral of a constant times an
+
+ align:start position:0%
+integral of a constant times an
+ 
+
+ align:start position:0%
+integral of a constant times an
+integrand is a constant times the
+
+ align:start position:0%
+integrand is a constant times the
+ 
+
+ align:start position:0%
+integrand is a constant times the
+integral of the integrand itself in
+
+ align:start position:0%
+integral of the integrand itself in
+ 
+
+ align:start position:0%
+integral of the integrand itself in
+other words sparing you the details
+
+ align:start position:0%
+other words sparing you the details
+ 
+
+ align:start position:0%
+other words sparing you the details
+because they follow right from the
+
+ align:start position:0%
+because they follow right from the
+ 
+
+ align:start position:0%
+because they follow right from the
+definition and that is assuming that f
+
+ align:start position:0%
+definition and that is assuming that f
+ 
+
+ align:start position:0%
+definition and that is assuming that f
+and g have llas transforms in other
+
+ align:start position:0%
+and g have llas transforms in other
+ 
+
+ align:start position:0%
+and g have llas transforms in other
+words that that improper integral from
+
+ align:start position:0%
+words that that improper integral from
+ 
+
+ align:start position:0%
+words that that improper integral from
+zero to Infinity e to the minus St F of
+
+ align:start position:0%
+zero to Infinity e to the minus St F of
+ 
+
+ align:start position:0%
+zero to Infinity e to the minus St F of
+T DT converges then what's true is that
+
+ align:start position:0%
+T DT converges then what's true is that
+ 
+
+ align:start position:0%
+T DT converges then what's true is that
+L of f+ G is L of f plus L of G and L of
+
+ align:start position:0%
+L of f+ G is L of f plus L of G and L of
+ 
+
+ align:start position:0%
+L of f+ G is L of f plus L of G and L of
+C * f is C * L of f see the linearity
+
+ align:start position:0%
+C * f is C * L of f see the linearity
+ 
+
+ align:start position:0%
+C * f is C * L of f see the linearity
+properties now how does that help us and
+
+ align:start position:0%
+properties now how does that help us and
+ 
+
+ align:start position:0%
+properties now how does that help us and
+why does that give us a hint that there
+
+ align:start position:0%
+why does that give us a hint that there
+ 
+
+ align:start position:0%
+why does that give us a hint that there
+will be some usage of the llast
+
+ align:start position:0%
+will be some usage of the llast
+ 
+
+ align:start position:0%
+will be some usage of the llast
+transform in solving linear differential
+
+ align:start position:0%
+transform in solving linear differential
+ 
+
+ align:start position:0%
+transform in solving linear differential
+equations with constant coefficients
+
+ align:start position:0%
+equations with constant coefficients
+ 
+
+ align:start position:0%
+equations with constant coefficients
+well perhaps the best way to see this is
+
+ align:start position:0%
+well perhaps the best way to see this is
+ 
+
+ align:start position:0%
+well perhaps the best way to see this is
+by means of an illustration let's assume
+
+ align:start position:0%
+by means of an illustration let's assume
+ 
+
+ align:start position:0%
+by means of an illustration let's assume
+that we're given that Y is a twice
+
+ align:start position:0%
+that we're given that Y is a twice
+ 
+
+ align:start position:0%
+that we're given that Y is a twice
+differentiable function of T and that y
+
+ align:start position:0%
+differentiable function of T and that y
+ 
+
+ align:start position:0%
+differentiable function of T and that y
+prime plus 2 a y prime plus b y where A
+
+ align:start position:0%
+prime plus 2 a y prime plus b y where A
+ 
+
+ align:start position:0%
+prime plus 2 a y prime plus b y where A
+and B are constants is some function f
+
+ align:start position:0%
+and B are constants is some function f
+ 
+
+ align:start position:0%
+and B are constants is some function f
+of t
+
+ align:start position:0%
+of t
+ 
+
+ align:start position:0%
+of t
+the idea is this I simply take the llast
+
+ align:start position:0%
+the idea is this I simply take the llast
+ 
+
+ align:start position:0%
+the idea is this I simply take the llast
+transform of both
+
+ align:start position:0%
+transform of both
+ 
+
+ align:start position:0%
+transform of both
+sides
+
+ align:start position:0%
+sides
+ 
+
+ align:start position:0%
+sides
+see by linearity since the laast
+
+ align:start position:0%
+see by linearity since the laast
+ 
+
+ align:start position:0%
+see by linearity since the laast
+transform is a linear function a linear
+
+ align:start position:0%
+transform is a linear function a linear
+ 
+
+ align:start position:0%
+transform is a linear function a linear
+operator L of Y Prime + 2 a y prime plus
+
+ align:start position:0%
+operator L of Y Prime + 2 a y prime plus
+ 
+
+ align:start position:0%
+operator L of Y Prime + 2 a y prime plus
+b y is simply L of Y prime plus 2 a l of
+
+ align:start position:0%
+b y is simply L of Y prime plus 2 a l of
+ 
+
+ align:start position:0%
+b y is simply L of Y prime plus 2 a l of
+Y prime plus b l of Y and the llast
+
+ align:start position:0%
+Y prime plus b l of Y and the llast
+ 
+
+ align:start position:0%
+Y prime plus b l of Y and the llast
+transform of f of T assuming that F of T
+
+ align:start position:0%
+transform of f of T assuming that F of T
+ 
+
+ align:start position:0%
+transform of f of T assuming that F of T
+has a llast transform and in particular
+
+ align:start position:0%
+has a llast transform and in particular
+ 
+
+ align:start position:0%
+has a llast transform and in particular
+if f F of T happens to be a function of
+
+ align:start position:0%
+if f F of T happens to be a function of
+ 
+
+ align:start position:0%
+if f F of T happens to be a function of
+exponential order we've already seen it
+
+ align:start position:0%
+exponential order we've already seen it
+ 
+
+ align:start position:0%
+exponential order we've already seen it
+it will have a llast transform all we're
+
+ align:start position:0%
+it will have a llast transform all we're
+ 
+
+ align:start position:0%
+it will have a llast transform all we're
+saying is let's call the llast transform
+
+ align:start position:0%
+saying is let's call the llast transform
+ 
+
+ align:start position:0%
+saying is let's call the llast transform
+of f of t as usual fbar of s and now
+
+ align:start position:0%
+of f of t as usual fbar of s and now
+ 
+
+ align:start position:0%
+of f of t as usual fbar of s and now
+what we have is an equation involving
+
+ align:start position:0%
+what we have is an equation involving
+ 
+
+ align:start position:0%
+what we have is an equation involving
+theast transform of Y the llast
+
+ align:start position:0%
+theast transform of Y the llast
+ 
+
+ align:start position:0%
+theast transform of Y the llast
+transform of Y Prime the llast transform
+
+ align:start position:0%
+transform of Y Prime the llast transform
+ 
+
+ align:start position:0%
+transform of Y Prime the llast transform
+of Y dble Prime in terms of F Bar of s
+
+ align:start position:0%
+of Y dble Prime in terms of F Bar of s
+ 
+
+ align:start position:0%
+of Y dble Prime in terms of F Bar of s
+if somehow we could manipulate this to
+
+ align:start position:0%
+if somehow we could manipulate this to
+ 
+
+ align:start position:0%
+if somehow we could manipulate this to
+solve for L of Y in other words if we
+
+ align:start position:0%
+solve for L of Y in other words if we
+ 
+
+ align:start position:0%
+solve for L of Y in other words if we
+could find what theast transform of Y
+
+ align:start position:0%
+could find what theast transform of Y
+ 
+
+ align:start position:0%
+could find what theast transform of Y
+was in terms of s maybe we could then
+
+ align:start position:0%
+was in terms of s maybe we could then
+ 
+
+ align:start position:0%
+was in terms of s maybe we could then
+invert so to speak and find out what the
+
+ align:start position:0%
+invert so to speak and find out what the
+ 
+
+ align:start position:0%
+invert so to speak and find out what the
+function itself must have been in other
+
+ align:start position:0%
+function itself must have been in other
+ 
+
+ align:start position:0%
+function itself must have been in other
+words the the idea of inverse functions
+
+ align:start position:0%
+words the the idea of inverse functions
+ 
+
+ align:start position:0%
+words the the idea of inverse functions
+comes up the same way here as it comes
+
+ align:start position:0%
+comes up the same way here as it comes
+ 
+
+ align:start position:0%
+comes up the same way here as it comes
+up every place namely starting with a
+
+ align:start position:0%
+up every place namely starting with a
+ 
+
+ align:start position:0%
+up every place namely starting with a
+function that Maps X into y one often
+
+ align:start position:0%
+function that Maps X into y one often
+ 
+
+ align:start position:0%
+function that Maps X into y one often
+says if I know what Y is can I determine
+
+ align:start position:0%
+says if I know what Y is can I determine
+ 
+
+ align:start position:0%
+says if I know what Y is can I determine
+what x must have been and that's why one
+
+ align:start position:0%
+what x must have been and that's why one
+ 
+
+ align:start position:0%
+what x must have been and that's why one
+to Oneness is so important in other
+
+ align:start position:0%
+to Oneness is so important in other
+ 
+
+ align:start position:0%
+to Oneness is so important in other
+words if it turns out that the llast
+
+ align:start position:0%
+words if it turns out that the llast
+ 
+
+ align:start position:0%
+words if it turns out that the llast
+transform is one: one
+
+ align:start position:0%
+transform is one: one
+ 
+
+ align:start position:0%
+transform is one: one
+once I know theast transform I
+
+ align:start position:0%
+once I know theast transform I
+ 
+
+ align:start position:0%
+once I know theast transform I
+essentially know the function because if
+
+ align:start position:0%
+essentially know the function because if
+ 
+
+ align:start position:0%
+essentially know the function because if
+two different functions can't have the
+
+ align:start position:0%
+two different functions can't have the
+ 
+
+ align:start position:0%
+two different functions can't have the
+same replast transform and by the way as
+
+ align:start position:0%
+same replast transform and by the way as
+ 
+
+ align:start position:0%
+same replast transform and by the way as
+a finale for today's lecture we will
+
+ align:start position:0%
+a finale for today's lecture we will
+ 
+
+ align:start position:0%
+a finale for today's lecture we will
+show that this is essentially the case
+
+ align:start position:0%
+show that this is essentially the case
+ 
+
+ align:start position:0%
+show that this is essentially the case
+that the llast transform is one to one
+
+ align:start position:0%
+that the llast transform is one to one
+ 
+
+ align:start position:0%
+that the llast transform is one to one
+and what I mean by essentially will be
+
+ align:start position:0%
+and what I mean by essentially will be
+ 
+
+ align:start position:0%
+and what I mean by essentially will be
+pointed out in the learning exercises
+
+ align:start position:0%
+pointed out in the learning exercises
+ 
+
+ align:start position:0%
+pointed out in the learning exercises
+but don't worry about that now the idea
+
+ align:start position:0%
+but don't worry about that now the idea
+ 
+
+ align:start position:0%
+but don't worry about that now the idea
+is simply this Suppose there was some
+
+ align:start position:0%
+is simply this Suppose there was some
+ 
+
+ align:start position:0%
+is simply this Suppose there was some
+way of expressing L of Y Prime and L of
+
+ align:start position:0%
+way of expressing L of Y Prime and L of
+ 
+
+ align:start position:0%
+way of expressing L of Y Prime and L of
+Y double Prime in terms of L of Y I
+
+ align:start position:0%
+Y double Prime in terms of L of Y I
+ 
+
+ align:start position:0%
+Y double Prime in terms of L of Y I
+could then solve the resulting equation
+
+ align:start position:0%
+could then solve the resulting equation
+ 
+
+ align:start position:0%
+could then solve the resulting equation
+for L of Y in terms of s having a table
+
+ align:start position:0%
+for L of Y in terms of s having a table
+ 
+
+ align:start position:0%
+for L of Y in terms of s having a table
+of llast transforms I could then locate
+
+ align:start position:0%
+of llast transforms I could then locate
+ 
+
+ align:start position:0%
+of llast transforms I could then locate
+what that function of s is the llast
+
+ align:start position:0%
+what that function of s is the llast
+ 
+
+ align:start position:0%
+what that function of s is the llast
+transform of and then invert this to
+
+ align:start position:0%
+transform of and then invert this to
+ 
+
+ align:start position:0%
+transform of and then invert this to
+find what my y must have been the
+
+ align:start position:0%
+find what my y must have been the
+ 
+
+ align:start position:0%
+find what my y must have been the
+problem is how do I know that I can
+
+ align:start position:0%
+problem is how do I know that I can
+ 
+
+ align:start position:0%
+problem is how do I know that I can
+express L of Y Prime L of Y Prime L of
+
+ align:start position:0%
+express L of Y Prime L of Y Prime L of
+ 
+
+ align:start position:0%
+express L of Y Prime L of Y Prime L of
+yle prime I'm only going up to the
+
+ align:start position:0%
+yle prime I'm only going up to the
+ 
+
+ align:start position:0%
+yle prime I'm only going up to the
+second derivative in terms of our usual
+
+ align:start position:0%
+second derivative in terms of our usual
+ 
+
+ align:start position:0%
+second derivative in terms of our usual
+Convention of illustrating everything by
+
+ align:start position:0%
+Convention of illustrating everything by
+ 
+
+ align:start position:0%
+Convention of illustrating everything by
+second order equations even though the
+
+ align:start position:0%
+second order equations even though the
+ 
+
+ align:start position:0%
+second order equations even though the
+results hold for higher orders the
+
+ align:start position:0%
+results hold for higher orders the
+ 
+
+ align:start position:0%
+results hold for higher orders the
+question though is how do we know that
+
+ align:start position:0%
+question though is how do we know that
+ 
+
+ align:start position:0%
+question though is how do we know that
+we can express these llast transforms in
+
+ align:start position:0%
+we can express these llast transforms in
+ 
+
+ align:start position:0%
+we can express these llast transforms in
+terms of the llast transform of Y itself
+
+ align:start position:0%
+terms of the llast transform of Y itself
+ 
+
+ align:start position:0%
+terms of the llast transform of Y itself
+and this brings up the second reason why
+
+ align:start position:0%
+and this brings up the second reason why
+ 
+
+ align:start position:0%
+and this brings up the second reason why
+that factor e to the minus St as a
+
+ align:start position:0%
+that factor e to the minus St as a
+ 
+
+ align:start position:0%
+that factor e to the minus St as a
+multiplying factor is so important you
+
+ align:start position:0%
+multiplying factor is so important you
+ 
+
+ align:start position:0%
+multiplying factor is so important you
+see aside from the fact that for most
+
+ align:start position:0%
+see aside from the fact that for most
+ 
+
+ align:start position:0%
+see aside from the fact that for most
+functions that e to the minus St makes
+
+ align:start position:0%
+functions that e to the minus St makes
+ 
+
+ align:start position:0%
+functions that e to the minus St makes
+sure that the resulting integral will
+
+ align:start position:0%
+sure that the resulting integral will
+ 
+
+ align:start position:0%
+sure that the resulting integral will
+converge the other ke property is that
+
+ align:start position:0%
+converge the other ke property is that
+ 
+
+ align:start position:0%
+converge the other ke property is that
+when you integrate or differentiate e to
+
+ align:start position:0%
+when you integrate or differentiate e to
+ 
+
+ align:start position:0%
+when you integrate or differentiate e to
+Theus St because s is a parameter
+
+ align:start position:0%
+Theus St because s is a parameter
+ 
+
+ align:start position:0%
+Theus St because s is a parameter
+meaning it's being treated as a constant
+
+ align:start position:0%
+meaning it's being treated as a constant
+ 
+
+ align:start position:0%
+meaning it's being treated as a constant
+for a given for at a given time what
+
+ align:start position:0%
+for a given for at a given time what
+ 
+
+ align:start position:0%
+for a given for at a given time what
+this thing means is that the integral or
+
+ align:start position:0%
+this thing means is that the integral or
+ 
+
+ align:start position:0%
+this thing means is that the integral or
+the derivative of e to Theus St is
+
+ align:start position:0%
+the derivative of e to Theus St is
+ 
+
+ align:start position:0%
+the derivative of e to Theus St is
+simply a constant times eus St well let
+
+ align:start position:0%
+simply a constant times eus St well let
+ 
+
+ align:start position:0%
+simply a constant times eus St well let
+me show you how this is used let's
+
+ align:start position:0%
+me show you how this is used let's
+ 
+
+ align:start position:0%
+me show you how this is used let's
+suppose for example that I wanted to
+
+ align:start position:0%
+suppose for example that I wanted to
+ 
+
+ align:start position:0%
+suppose for example that I wanted to
+find the laast transform of frime of T
+
+ align:start position:0%
+find the laast transform of frime of T
+ 
+
+ align:start position:0%
+find the laast transform of frime of T
+and I didn't know any tricks and by the
+
+ align:start position:0%
+and I didn't know any tricks and by the
+ 
+
+ align:start position:0%
+and I didn't know any tricks and by the
+way I hope that this is one of The
+
+ align:start position:0%
+way I hope that this is one of The
+ 
+
+ align:start position:0%
+way I hope that this is one of The
+Fringe benefit benefits that this course
+
+ align:start position:0%
+Fringe benefit benefits that this course
+ 
+
+ align:start position:0%
+Fringe benefit benefits that this course
+is teaching you that we do not have to
+
+ align:start position:0%
+is teaching you that we do not have to
+ 
+
+ align:start position:0%
+is teaching you that we do not have to
+be tricky in mathematics all we have to
+
+ align:start position:0%
+be tricky in mathematics all we have to
+ 
+
+ align:start position:0%
+be tricky in mathematics all we have to
+know is the basic definitions and how to
+
+ align:start position:0%
+know is the basic definitions and how to
+ 
+
+ align:start position:0%
+know is the basic definitions and how to
+manipulate them I do admit that it is a
+
+ align:start position:0%
+manipulate them I do admit that it is a
+ 
+
+ align:start position:0%
+manipulate them I do admit that it is a
+stroke of Genius sometimes in inventing
+
+ align:start position:0%
+stroke of Genius sometimes in inventing
+ 
+
+ align:start position:0%
+stroke of Genius sometimes in inventing
+the basic definition that we're going to
+
+ align:start position:0%
+the basic definition that we're going to
+ 
+
+ align:start position:0%
+the basic definition that we're going to
+use for example it's my own belief that
+
+ align:start position:0%
+use for example it's my own belief that
+ 
+
+ align:start position:0%
+use for example it's my own belief that
+it's a lot easier to use the llast
+
+ align:start position:0%
+it's a lot easier to use the llast
+ 
+
+ align:start position:0%
+it's a lot easier to use the llast
+transform than it was to have invented
+
+ align:start position:0%
+transform than it was to have invented
+ 
+
+ align:start position:0%
+transform than it was to have invented
+the concept in the first place but once
+
+ align:start position:0%
+the concept in the first place but once
+ 
+
+ align:start position:0%
+the concept in the first place but once
+I've defined what the llast transform is
+
+ align:start position:0%
+I've defined what the llast transform is
+ 
+
+ align:start position:0%
+I've defined what the llast transform is
+what happens here is very simple namely
+
+ align:start position:0%
+what happens here is very simple namely
+ 
+
+ align:start position:0%
+what happens here is very simple namely
+by definition what is the llast
+
+ align:start position:0%
+by definition what is the llast
+ 
+
+ align:start position:0%
+by definition what is the llast
+transform of frime of T I simply
+
+ align:start position:0%
+transform of frime of T I simply
+ 
+
+ align:start position:0%
+transform of frime of T I simply
+multiply frime of T by E Theus St and
+
+ align:start position:0%
+multiply frime of T by E Theus St and
+ 
+
+ align:start position:0%
+multiply frime of T by E Theus St and
+integrate that from Z to infinity and if
+
+ align:start position:0%
+integrate that from Z to infinity and if
+ 
+
+ align:start position:0%
+integrate that from Z to infinity and if
+that integral converges then the llast
+
+ align:start position:0%
+that integral converges then the llast
+ 
+
+ align:start position:0%
+that integral converges then the llast
+transform exists Let Me Assume for the
+
+ align:start position:0%
+transform exists Let Me Assume for the
+ 
+
+ align:start position:0%
+transform exists Let Me Assume for the
+sake of argument now that the llast
+
+ align:start position:0%
+sake of argument now that the llast
+ 
+
+ align:start position:0%
+sake of argument now that the llast
+transform of f of T exists and by the
+
+ align:start position:0%
+transform of f of T exists and by the
+ 
+
+ align:start position:0%
+transform of f of T exists and by the
+way again remember I'm not really
+
+ align:start position:0%
+way again remember I'm not really
+ 
+
+ align:start position:0%
+way again remember I'm not really
+assuming anything when I'm dealing with
+
+ align:start position:0%
+assuming anything when I'm dealing with
+ 
+
+ align:start position:0%
+assuming anything when I'm dealing with
+linear differential equations with
+
+ align:start position:0%
+linear differential equations with
+ 
+
+ align:start position:0%
+linear differential equations with
+constant coefficients because the
+
+ align:start position:0%
+constant coefficients because the
+ 
+
+ align:start position:0%
+constant coefficients because the
+functions that come up as possible
+
+ align:start position:0%
+functions that come up as possible
+ 
+
+ align:start position:0%
+functions that come up as possible
+solutions there are of exponential order
+
+ align:start position:0%
+solutions there are of exponential order
+ 
+
+ align:start position:0%
+solutions there are of exponential order
+and we have already seen that for
+
+ align:start position:0%
+and we have already seen that for
+ 
+
+ align:start position:0%
+and we have already seen that for
+functions of exponential order the llast
+
+ align:start position:0%
+functions of exponential order the llast
+ 
+
+ align:start position:0%
+functions of exponential order the llast
+transform does indeed exist but at any
+
+ align:start position:0%
+transform does indeed exist but at any
+ 
+
+ align:start position:0%
+transform does indeed exist but at any
+rate the idea is this by definition this
+
+ align:start position:0%
+rate the idea is this by definition this
+ 
+
+ align:start position:0%
+rate the idea is this by definition this
+is the llast transform of frime of T I
+
+ align:start position:0%
+is the llast transform of frime of T I
+ 
+
+ align:start position:0%
+is the llast transform of frime of T I
+would like to be able to integrate this
+
+ align:start position:0%
+would like to be able to integrate this
+ 
+
+ align:start position:0%
+would like to be able to integrate this
+well the idea is that the integral of
+
+ align:start position:0%
+well the idea is that the integral of
+ 
+
+ align:start position:0%
+well the idea is that the integral of
+fime of T is certainly F of T and if I
+
+ align:start position:0%
+fime of T is certainly F of T and if I
+ 
+
+ align:start position:0%
+fime of T is certainly F of T and if I
+up to a constant but that's not
+
+ align:start position:0%
+up to a constant but that's not
+ 
+
+ align:start position:0%
+up to a constant but that's not
+important what I'm thinking of is an
+
+ align:start position:0%
+important what I'm thinking of is an
+ 
+
+ align:start position:0%
+important what I'm thinking of is an
+integrating by Parts notice that if I
+
+ align:start position:0%
+integrating by Parts notice that if I
+ 
+
+ align:start position:0%
+integrating by Parts notice that if I
+let U equal eus St and DV be frime of T
+
+ align:start position:0%
+let U equal eus St and DV be frime of T
+ 
+
+ align:start position:0%
+let U equal eus St and DV be frime of T
+DT then du is minus s e to the minus St
+
+ align:start position:0%
+DT then du is minus s e to the minus St
+ 
+
+ align:start position:0%
+DT then du is minus s e to the minus St
+V would just be F of T remembering the
+
+ align:start position:0%
+V would just be F of T remembering the
+ 
+
+ align:start position:0%
+V would just be F of T remembering the
+recipe for integration by pots remember
+
+ align:start position:0%
+recipe for integration by pots remember
+ 
+
+ align:start position:0%
+recipe for integration by pots remember
+just by way of quick review integral UV
+
+ align:start position:0%
+just by way of quick review integral UV
+ 
+
+ align:start position:0%
+just by way of quick review integral UV
+is equal to UV minus the integral vdu
+
+ align:start position:0%
+is equal to UV minus the integral vdu
+ 
+
+ align:start position:0%
+is equal to UV minus the integral vdu
+what we're saying here is that to
+
+ align:start position:0%
+what we're saying here is that to
+ 
+
+ align:start position:0%
+what we're saying here is that to
+evaluate this integral we simply take
+
+ align:start position:0%
+evaluate this integral we simply take
+ 
+
+ align:start position:0%
+evaluate this integral we simply take
+What U * v e to Us St F of T evaluate
+
+ align:start position:0%
+What U * v e to Us St F of T evaluate
+ 
+
+ align:start position:0%
+What U * v e to Us St F of T evaluate
+that as T goes from 0 to Infinity minus
+
+ align:start position:0%
+that as T goes from 0 to Infinity minus
+ 
+
+ align:start position:0%
+that as T goes from 0 to Infinity minus
+the integral VD du is already negative s
+
+ align:start position:0%
+the integral VD du is already negative s
+ 
+
+ align:start position:0%
+the integral VD du is already negative s
+is a constant so minus integral VD is
+
+ align:start position:0%
+is a constant so minus integral VD is
+ 
+
+ align:start position:0%
+is a constant so minus integral VD is
+just plus s integral 0 to Infinity e to
+
+ align:start position:0%
+just plus s integral 0 to Infinity e to
+ 
+
+ align:start position:0%
+just plus s integral 0 to Infinity e to
+the minus St F of T DT and lo and behold
+
+ align:start position:0%
+the minus St F of T DT and lo and behold
+ 
+
+ align:start position:0%
+the minus St F of T DT and lo and behold
+you see that's that beautiful property
+
+ align:start position:0%
+you see that's that beautiful property
+ 
+
+ align:start position:0%
+you see that's that beautiful property
+of e to the minus
+
+ align:start position:0%
+of e to the minus
+ 
+
+ align:start position:0%
+of e to the minus
+St it's still in here the integral is
+
+ align:start position:0%
+St it's still in here the integral is
+ 
+
+ align:start position:0%
+St it's still in here the integral is
+precisely what we mean by what L of f of
+
+ align:start position:0%
+precisely what we mean by what L of f of
+ 
+
+ align:start position:0%
+precisely what we mean by what L of f of
+T in other words theast transform of f
+
+ align:start position:0%
+T in other words theast transform of f
+ 
+
+ align:start position:0%
+T in other words theast transform of f
+Prime of T is this thing plus stimes the
+
+ align:start position:0%
+Prime of T is this thing plus stimes the
+ 
+
+ align:start position:0%
+Prime of T is this thing plus stimes the
+llast transform of f of T but let me not
+
+ align:start position:0%
+llast transform of f of T but let me not
+ 
+
+ align:start position:0%
+llast transform of f of T but let me not
+be so informal let me not refer to this
+
+ align:start position:0%
+be so informal let me not refer to this
+ 
+
+ align:start position:0%
+be so informal let me not refer to this
+as this thing let's see what this thing
+
+ align:start position:0%
+as this thing let's see what this thing
+ 
+
+ align:start position:0%
+as this thing let's see what this thing
+really is notice that because the llast
+
+ align:start position:0%
+really is notice that because the llast
+ 
+
+ align:start position:0%
+really is notice that because the llast
+transform of f of T is assumed to exist
+
+ align:start position:0%
+transform of f of T is assumed to exist
+ 
+
+ align:start position:0%
+transform of f of T is assumed to exist
+the fact that the integral of this from
+
+ align:start position:0%
+the fact that the integral of this from
+ 
+
+ align:start position:0%
+the fact that the integral of this from
+0 to Infinity is finite means in
+
+ align:start position:0%
+0 to Infinity is finite means in
+ 
+
+ align:start position:0%
+0 to Infinity is finite means in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+that at Infinity the integr must be zero
+
+ align:start position:0%
+that at Infinity the integr must be zero
+ 
+
+ align:start position:0%
+that at Infinity the integr must be zero
+you see that otherwi how could the area
+
+ align:start position:0%
+you see that otherwi how could the area
+ 
+
+ align:start position:0%
+you see that otherwi how could the area
+under the curve be finite if the curve
+
+ align:start position:0%
+under the curve be finite if the curve
+ 
+
+ align:start position:0%
+under the curve be finite if the curve
+didn't at least ASM totically approach
+
+ align:start position:0%
+didn't at least ASM totically approach
+ 
+
+ align:start position:0%
+didn't at least ASM totically approach
+the T axis so in other words the
+
+ align:start position:0%
+the T axis so in other words the
+ 
+
+ align:start position:0%
+the T axis so in other words the
+assumption that F has a llast transform
+
+ align:start position:0%
+assumption that F has a llast transform
+ 
+
+ align:start position:0%
+assumption that F has a llast transform
+means that the upper limit gives me zero
+
+ align:start position:0%
+means that the upper limit gives me zero
+ 
+
+ align:start position:0%
+means that the upper limit gives me zero
+the lower limit gives me what when I
+
+ align:start position:0%
+the lower limit gives me what when I
+ 
+
+ align:start position:0%
+the lower limit gives me what when I
+plug in t equals z this is e Theus s0
+
+ align:start position:0%
+plug in t equals z this is e Theus s0
+ 
+
+ align:start position:0%
+plug in t equals z this is e Theus s0
+which is one this is f of 0 so the lower
+
+ align:start position:0%
+which is one this is f of 0 so the lower
+ 
+
+ align:start position:0%
+which is one this is f of 0 so the lower
+limit is f of0 and since I'm subtracting
+
+ align:start position:0%
+limit is f of0 and since I'm subtracting
+ 
+
+ align:start position:0%
+limit is f of0 and since I'm subtracting
+the lower limit I have what that the
+
+ align:start position:0%
+the lower limit I have what that the
+ 
+
+ align:start position:0%
+the lower limit I have what that the
+that the thing that I called this thing
+
+ align:start position:0%
+that the thing that I called this thing
+ 
+
+ align:start position:0%
+that the thing that I called this thing
+is more precisely minus F of0 in other
+
+ align:start position:0%
+is more precisely minus F of0 in other
+ 
+
+ align:start position:0%
+is more precisely minus F of0 in other
+words to find the llast transform of
+
+ align:start position:0%
+words to find the llast transform of
+ 
+
+ align:start position:0%
+words to find the llast transform of
+frime of T it's simply minus F of 0 plus
+
+ align:start position:0%
+frime of T it's simply minus F of 0 plus
+ 
+
+ align:start position:0%
+frime of T it's simply minus F of 0 plus
+stimes the llast transform of f of T
+
+ align:start position:0%
+stimes the llast transform of f of T
+ 
+
+ align:start position:0%
+stimes the llast transform of f of T
+well look at if I happen to know what f
+
+ align:start position:0%
+well look at if I happen to know what f
+ 
+
+ align:start position:0%
+well look at if I happen to know what f
+of0 is in other words if I pick a
+
+ align:start position:0%
+of0 is in other words if I pick a
+ 
+
+ align:start position:0%
+of0 is in other words if I pick a
+particular member of the family F of t
+
+ align:start position:0%
+particular member of the family F of t
+ 
+
+ align:start position:0%
+particular member of the family F of t
+uh given the curve yal F of t I
+
+ align:start position:0%
+uh given the curve yal F of t I
+ 
+
+ align:start position:0%
+uh given the curve yal F of t I
+certainly know what f of0 is this says
+
+ align:start position:0%
+certainly know what f of0 is this says
+ 
+
+ align:start position:0%
+certainly know what f of0 is this says
+what the llast transform of frime of T
+
+ align:start position:0%
+what the llast transform of frime of T
+ 
+
+ align:start position:0%
+what the llast transform of frime of T
+is some constant plus s times the llast
+
+ align:start position:0%
+is some constant plus s times the llast
+ 
+
+ align:start position:0%
+is some constant plus s times the llast
+transform of f of T itself in other
+
+ align:start position:0%
+transform of f of T itself in other
+ 
+
+ align:start position:0%
+transform of f of T itself in other
+words somehow or other I have now
+
+ align:start position:0%
+words somehow or other I have now
+ 
+
+ align:start position:0%
+words somehow or other I have now
+managed to express the llast transform
+
+ align:start position:0%
+managed to express the llast transform
+ 
+
+ align:start position:0%
+managed to express the llast transform
+of frime of T in terms of a polinomial
+
+ align:start position:0%
+of frime of T in terms of a polinomial
+ 
+
+ align:start position:0%
+of frime of T in terms of a polinomial
+involving s and the last and the llast
+
+ align:start position:0%
+involving s and the last and the llast
+ 
+
+ align:start position:0%
+involving s and the last and the llast
+transform of f of T Itself by the way
+
+ align:start position:0%
+transform of f of T Itself by the way
+ 
+
+ align:start position:0%
+transform of f of T Itself by the way
+notice that generically here there is
+
+ align:start position:0%
+notice that generically here there is
+ 
+
+ align:start position:0%
+notice that generically here there is
+nothing sacred about F of zero uh or F
+
+ align:start position:0%
+nothing sacred about F of zero uh or F
+ 
+
+ align:start position:0%
+nothing sacred about F of zero uh or F
+think of f as being any function and F
+
+ align:start position:0%
+think of f as being any function and F
+ 
+
+ align:start position:0%
+think of f as being any function and F
+Prime as being its derivative in
+
+ align:start position:0%
+Prime as being its derivative in
+ 
+
+ align:start position:0%
+Prime as being its derivative in
+particular I could allow F Prime to play
+
+ align:start position:0%
+particular I could allow F Prime to play
+ 
+
+ align:start position:0%
+particular I could allow F Prime to play
+the role of f see this says what the
+
+ align:start position:0%
+the role of f see this says what the
+ 
+
+ align:start position:0%
+the role of f see this says what the
+llast transform of the of the derivative
+
+ align:start position:0%
+llast transform of the of the derivative
+ 
+
+ align:start position:0%
+llast transform of the of the derivative
+is minus the function evaluated at zero
+
+ align:start position:0%
+is minus the function evaluated at zero
+ 
+
+ align:start position:0%
+is minus the function evaluated at zero
+plus s times the llast transform of that
+
+ align:start position:0%
+plus s times the llast transform of that
+ 
+
+ align:start position:0%
+plus s times the llast transform of that
+function all right so if I now take my
+
+ align:start position:0%
+function all right so if I now take my
+ 
+
+ align:start position:0%
+function all right so if I now take my
+function to be fpre its derivative is f
+
+ align:start position:0%
+function to be fpre its derivative is f
+ 
+
+ align:start position:0%
+function to be fpre its derivative is f
+Prime the function is itself fpre so all
+
+ align:start position:0%
+Prime the function is itself fpre so all
+ 
+
+ align:start position:0%
+Prime the function is itself fpre so all
+I really do is what go into this recipe
+
+ align:start position:0%
+I really do is what go into this recipe
+ 
+
+ align:start position:0%
+I really do is what go into this recipe
+here every place I see a prime replace
+
+ align:start position:0%
+here every place I see a prime replace
+ 
+
+ align:start position:0%
+here every place I see a prime replace
+it by a double Prime every place I see
+
+ align:start position:0%
+it by a double Prime every place I see
+ 
+
+ align:start position:0%
+it by a double Prime every place I see
+no Prime put a prime in and I have that
+
+ align:start position:0%
+no Prime put a prime in and I have that
+ 
+
+ align:start position:0%
+no Prime put a prime in and I have that
+the llast transform of FP Prime of T is
+
+ align:start position:0%
+the llast transform of FP Prime of T is
+ 
+
+ align:start position:0%
+the llast transform of FP Prime of T is
+minus frime of 0 plus s time the llast
+
+ align:start position:0%
+minus frime of 0 plus s time the llast
+ 
+
+ align:start position:0%
+minus frime of 0 plus s time the llast
+transform of frime of T by the way to
+
+ align:start position:0%
+transform of frime of T by the way to
+ 
+
+ align:start position:0%
+transform of frime of T by the way to
+make sure you see this notice what would
+
+ align:start position:0%
+make sure you see this notice what would
+ 
+
+ align:start position:0%
+make sure you see this notice what would
+the llast transform of fle prime be the
+
+ align:start position:0%
+the llast transform of fle prime be the
+ 
+
+ align:start position:0%
+the llast transform of fle prime be the
+llast transform of fle prime of T would
+
+ align:start position:0%
+llast transform of fle prime of T would
+ 
+
+ align:start position:0%
+llast transform of fle prime of T would
+be minus f Prime of 0 plus s * the lass
+
+ align:start position:0%
+be minus f Prime of 0 plus s * the lass
+ 
+
+ align:start position:0%
+be minus f Prime of 0 plus s * the lass
+transform of f Prime of T so assuming
+
+ align:start position:0%
+transform of f Prime of T so assuming
+ 
+
+ align:start position:0%
+transform of f Prime of T so assuming
+that the that F Prime also has a llast
+
+ align:start position:0%
+that the that F Prime also has a llast
+ 
+
+ align:start position:0%
+that the that F Prime also has a llast
+transform we see what the llast
+
+ align:start position:0%
+transform we see what the llast
+ 
+
+ align:start position:0%
+transform we see what the llast
+transform of FP Prime of T looks like in
+
+ align:start position:0%
+transform of FP Prime of T looks like in
+ 
+
+ align:start position:0%
+transform of FP Prime of T looks like in
+terms of frime of T the llast transform
+
+ align:start position:0%
+terms of frime of T the llast transform
+ 
+
+ align:start position:0%
+terms of frime of T the llast transform
+of frime of T we know what the llast
+
+ align:start position:0%
+of frime of T we know what the llast
+ 
+
+ align:start position:0%
+of frime of T we know what the llast
+transform of frime of T looks like in
+
+ align:start position:0%
+transform of frime of T looks like in
+ 
+
+ align:start position:0%
+transform of frime of T looks like in
+terms of the llast transform of T in
+
+ align:start position:0%
+terms of the llast transform of T in
+ 
+
+ align:start position:0%
+terms of the llast transform of T in
+other words from here I simply replace L
+
+ align:start position:0%
+other words from here I simply replace L
+ 
+
+ align:start position:0%
+other words from here I simply replace L
+of fime of T by its value in this
+
+ align:start position:0%
+of fime of T by its value in this
+ 
+
+ align:start position:0%
+of fime of T by its value in this
+equation and I want up with that the
+
+ align:start position:0%
+equation and I want up with that the
+ 
+
+ align:start position:0%
+equation and I want up with that the
+llast transform of f Prime of T is
+
+ align:start position:0%
+llast transform of f Prime of T is
+ 
+
+ align:start position:0%
+llast transform of f Prime of T is
+nothing more than minus frime of 0 - s *
+
+ align:start position:0%
+nothing more than minus frime of 0 - s *
+ 
+
+ align:start position:0%
+nothing more than minus frime of 0 - s *
+F of 0 plus S2 L of f of T and now you
+
+ align:start position:0%
+F of 0 plus S2 L of f of T and now you
+ 
+
+ align:start position:0%
+F of 0 plus S2 L of f of T and now you
+see I've solved the problem that I was
+
+ align:start position:0%
+see I've solved the problem that I was
+ 
+
+ align:start position:0%
+see I've solved the problem that I was
+discussing over here namely once I know
+
+ align:start position:0%
+discussing over here namely once I know
+ 
+
+ align:start position:0%
+discussing over here namely once I know
+what y of zero is I'm using by the way
+
+ align:start position:0%
+what y of zero is I'm using by the way
+ 
+
+ align:start position:0%
+what y of zero is I'm using by the way
+don't confuse the F here with the F here
+
+ align:start position:0%
+don't confuse the F here with the F here
+ 
+
+ align:start position:0%
+don't confuse the F here with the F here
+that's an unfortunate Choice which I've
+
+ align:start position:0%
+that's an unfortunate Choice which I've
+ 
+
+ align:start position:0%
+that's an unfortunate Choice which I've
+just notice the F that I'm referring to
+
+ align:start position:0%
+just notice the F that I'm referring to
+ 
+
+ align:start position:0%
+just notice the F that I'm referring to
+here names the function whose llas
+
+ align:start position:0%
+here names the function whose llas
+ 
+
+ align:start position:0%
+here names the function whose llas
+transform I'm trying to find notice that
+
+ align:start position:0%
+transform I'm trying to find notice that
+ 
+
+ align:start position:0%
+transform I'm trying to find notice that
+the fime and FP Prime are served by y
+
+ align:start position:0%
+the fime and FP Prime are served by y
+ 
+
+ align:start position:0%
+the fime and FP Prime are served by y
+Prime and Y Prime here what we're saying
+
+ align:start position:0%
+Prime and Y Prime here what we're saying
+ 
+
+ align:start position:0%
+Prime and Y Prime here what we're saying
+in terms of this notation is that I can
+
+ align:start position:0%
+in terms of this notation is that I can
+ 
+
+ align:start position:0%
+in terms of this notation is that I can
+express L of YP Prime and L of Y Prime
+
+ align:start position:0%
+express L of YP Prime and L of Y Prime
+ 
+
+ align:start position:0%
+express L of YP Prime and L of Y Prime
+in terms of the llast transform of L of
+
+ align:start position:0%
+in terms of the llast transform of L of
+ 
+
+ align:start position:0%
+in terms of the llast transform of L of
+Y plus powers of s provided I know only
+
+ align:start position:0%
+Y plus powers of s provided I know only
+ 
+
+ align:start position:0%
+Y plus powers of s provided I know only
+what Y of0 is and what y Prime of0 is
+
+ align:start position:0%
+what Y of0 is and what y Prime of0 is
+ 
+
+ align:start position:0%
+what Y of0 is and what y Prime of0 is
+and by the way again notice that in a
+
+ align:start position:0%
+and by the way again notice that in a
+ 
+
+ align:start position:0%
+and by the way again notice that in a
+physical problem it is very natural to
+
+ align:start position:0%
+physical problem it is very natural to
+ 
+
+ align:start position:0%
+physical problem it is very natural to
+look at Y and Y Prime when T equals z
+
+ align:start position:0%
+look at Y and Y Prime when T equals z
+ 
+
+ align:start position:0%
+look at Y and Y Prime when T equals z
+because in many instances T equals 0
+
+ align:start position:0%
+because in many instances T equals 0
+ 
+
+ align:start position:0%
+because in many instances T equals 0
+represents the time at which we've
+
+ align:start position:0%
+represents the time at which we've
+ 
+
+ align:start position:0%
+represents the time at which we've
+started the measurement at our
+
+ align:start position:0%
+started the measurement at our
+ 
+
+ align:start position:0%
+started the measurement at our
+experiment and this becomes a very
+
+ align:start position:0%
+experiment and this becomes a very
+ 
+
+ align:start position:0%
+experiment and this becomes a very
+natural interpretation for what you mean
+
+ align:start position:0%
+natural interpretation for what you mean
+ 
+
+ align:start position:0%
+natural interpretation for what you mean
+by the initial conditions namely what's
+
+ align:start position:0%
+by the initial conditions namely what's
+ 
+
+ align:start position:0%
+by the initial conditions namely what's
+going on when T equals z any rate we are
+
+ align:start position:0%
+going on when T equals z any rate we are
+ 
+
+ align:start position:0%
+going on when T equals z any rate we are
+now in a position to apply our results
+
+ align:start position:0%
+now in a position to apply our results
+ 
+
+ align:start position:0%
+now in a position to apply our results
+to an actual linear differential
+
+ align:start position:0%
+to an actual linear differential
+ 
+
+ align:start position:0%
+to an actual linear differential
+equation with constant coefficients
+
+ align:start position:0%
+equation with constant coefficients
+ 
+
+ align:start position:0%
+equation with constant coefficients
+given initial conditions as to what's
+
+ align:start position:0%
+given initial conditions as to what's
+ 
+
+ align:start position:0%
+given initial conditions as to what's
+happening at zero in terms of the Y
+
+ align:start position:0%
+happening at zero in terms of the Y
+ 
+
+ align:start position:0%
+happening at zero in terms of the Y
+coordinate and the Y Prime coordinate
+
+ align:start position:0%
+coordinate and the Y Prime coordinate
+ 
+
+ align:start position:0%
+coordinate and the Y Prime coordinate
+Etc in other words as an application to
+
+ align:start position:0%
+Etc in other words as an application to
+ 
+
+ align:start position:0%
+Etc in other words as an application to
+linear differential equations with
+
+ align:start position:0%
+linear differential equations with
+ 
+
+ align:start position:0%
+linear differential equations with
+constant coefficients suppose we want to
+
+ align:start position:0%
+constant coefficients suppose we want to
+ 
+
+ align:start position:0%
+constant coefficients suppose we want to
+solve meaning what find what function y
+
+ align:start position:0%
+solve meaning what find what function y
+ 
+
+ align:start position:0%
+solve meaning what find what function y
+is of T if y Prime - 4 y Prime + 3 yal e
+
+ align:start position:0%
+is of T if y Prime - 4 y Prime + 3 yal e
+ 
+
+ align:start position:0%
+is of T if y Prime - 4 y Prime + 3 yal e
+2 T given that my initial conditions
+
+ align:start position:0%
+2 T given that my initial conditions
+ 
+
+ align:start position:0%
+2 T given that my initial conditions
+namely when T is zero Y is going to be
+
+ align:start position:0%
+namely when T is zero Y is going to be
+ 
+
+ align:start position:0%
+namely when T is zero Y is going to be
+zero and Y Prime is going to be one I
+
+ align:start position:0%
+zero and Y Prime is going to be one I
+ 
+
+ align:start position:0%
+zero and Y Prime is going to be one I
+these could be any conditions I want
+
+ align:start position:0%
+these could be any conditions I want
+ 
+
+ align:start position:0%
+these could be any conditions I want
+over here I just chose these to give me
+
+ align:start position:0%
+over here I just chose these to give me
+ 
+
+ align:start position:0%
+over here I just chose these to give me
+a a simple algebraic uh example and I'll
+
+ align:start position:0%
+a a simple algebraic uh example and I'll
+ 
+
+ align:start position:0%
+a a simple algebraic uh example and I'll
+pick more complicated things in the
+
+ align:start position:0%
+pick more complicated things in the
+ 
+
+ align:start position:0%
+pick more complicated things in the
+exercises but the idea is this we have
+
+ align:start position:0%
+exercises but the idea is this we have
+ 
+
+ align:start position:0%
+exercises but the idea is this we have
+already seen by linearity that if I take
+
+ align:start position:0%
+already seen by linearity that if I take
+ 
+
+ align:start position:0%
+already seen by linearity that if I take
+theast transform of both sides here I
+
+ align:start position:0%
+theast transform of both sides here I
+ 
+
+ align:start position:0%
+theast transform of both sides here I
+have that L of Y Prime minus 4 L of Y
+
+ align:start position:0%
+have that L of Y Prime minus 4 L of Y
+ 
+
+ align:start position:0%
+have that L of Y Prime minus 4 L of Y
+prime plus 3 l of Y is the llast
+
+ align:start position:0%
+prime plus 3 l of Y is the llast
+ 
+
+ align:start position:0%
+prime plus 3 l of Y is the llast
+transform of e to 2T now we just saw on
+
+ align:start position:0%
+transform of e to 2T now we just saw on
+ 
+
+ align:start position:0%
+transform of e to 2T now we just saw on
+right over here that the llast transform
+
+ align:start position:0%
+right over here that the llast transform
+ 
+
+ align:start position:0%
+right over here that the llast transform
+of Y Prime is minus y Prime evaluated 0
+
+ align:start position:0%
+of Y Prime is minus y Prime evaluated 0
+ 
+
+ align:start position:0%
+of Y Prime is minus y Prime evaluated 0
+- s y of 0 + s^2 L of Y the llast
+
+ align:start position:0%
+- s y of 0 + s^2 L of Y the llast
+ 
+
+ align:start position:0%
+- s y of 0 + s^2 L of Y the llast
+transform of Y Prime was minus you see y
+
+ align:start position:0%
+transform of Y Prime was minus you see y
+ 
+
+ align:start position:0%
+transform of Y Prime was minus you see y
+of0 plus s l y you see so minus 4 * that
+
+ align:start position:0%
+of0 plus s l y you see so minus 4 * that
+ 
+
+ align:start position:0%
+of0 plus s l y you see so minus 4 * that
+is just 4 * y of 0 - 4 S L of y + 3 l of
+
+ align:start position:0%
+is just 4 * y of 0 - 4 S L of y + 3 l of
+ 
+
+ align:start position:0%
+is just 4 * y of 0 - 4 S L of y + 3 l of
+Y and we saw earlier that the llast
+
+ align:start position:0%
+Y and we saw earlier that the llast
+ 
+
+ align:start position:0%
+Y and we saw earlier that the llast
+transform of e to the a t is 1 / s- a
+
+ align:start position:0%
+transform of e to the a t is 1 / s- a
+ 
+
+ align:start position:0%
+transform of e to the a t is 1 / s- a
+where s is is any number greater than
+
+ align:start position:0%
+where s is is any number greater than
+ 
+
+ align:start position:0%
+where s is is any number greater than
+two in particular this is that formula
+
+ align:start position:0%
+two in particular this is that formula
+ 
+
+ align:start position:0%
+two in particular this is that formula
+with a equal s is any number greater
+
+ align:start position:0%
+with a equal s is any number greater
+ 
+
+ align:start position:0%
+with a equal s is any number greater
+than a in particular this is that
+
+ align:start position:0%
+than a in particular this is that
+ 
+
+ align:start position:0%
+than a in particular this is that
+formula with a equal to 2 so the
+
+ align:start position:0%
+formula with a equal to 2 so the
+ 
+
+ align:start position:0%
+formula with a equal to 2 so the
+transform of e 2 T is 1 / s- 2 provided
+
+ align:start position:0%
+transform of e 2 T is 1 / s- 2 provided
+ 
+
+ align:start position:0%
+transform of e 2 T is 1 / s- 2 provided
+s is greater than two by the way notice
+
+ align:start position:0%
+s is greater than two by the way notice
+ 
+
+ align:start position:0%
+s is greater than two by the way notice
+up to this point I have not used the
+
+ align:start position:0%
+up to this point I have not used the
+ 
+
+ align:start position:0%
+up to this point I have not used the
+initial conditions I have not used the
+
+ align:start position:0%
+initial conditions I have not used the
+ 
+
+ align:start position:0%
+initial conditions I have not used the
+fact that y of 0 is 0 and that y Prime
+
+ align:start position:0%
+fact that y of 0 is 0 and that y Prime
+ 
+
+ align:start position:0%
+fact that y of 0 is 0 and that y Prime
+of 0 is 1 notice that even without this
+
+ align:start position:0%
+of 0 is 1 notice that even without this
+ 
+
+ align:start position:0%
+of 0 is 1 notice that even without this
+the L of Y is here by itself it's going
+
+ align:start position:0%
+the L of Y is here by itself it's going
+ 
+
+ align:start position:0%
+the L of Y is here by itself it's going
+to be multiplied by s^2 - 4 S + 3 these
+
+ align:start position:0%
+to be multiplied by s^2 - 4 S + 3 these
+ 
+
+ align:start position:0%
+to be multiplied by s^2 - 4 S + 3 these
+terms can go over onto the other side of
+
+ align:start position:0%
+terms can go over onto the other side of
+ 
+
+ align:start position:0%
+terms can go over onto the other side of
+the equation I will get a function of s
+
+ align:start position:0%
+the equation I will get a function of s
+ 
+
+ align:start position:0%
+the equation I will get a function of s
+alone I then divide through by s^2 - 4 S
+
+ align:start position:0%
+alone I then divide through by s^2 - 4 S
+ 
+
+ align:start position:0%
+alone I then divide through by s^2 - 4 S
++ 3 that will give me L of Y as a
+
+ align:start position:0%
++ 3 that will give me L of Y as a
+ 
+
+ align:start position:0%
++ 3 that will give me L of Y as a
+function of s and if I can then find one
+
+ align:start position:0%
+function of s and if I can then find one
+ 
+
+ align:start position:0%
+function of s and if I can then find one
+function which has that function of s as
+
+ align:start position:0%
+function which has that function of s as
+ 
+
+ align:start position:0%
+function which has that function of s as
+its theast transform I can conclude that
+
+ align:start position:0%
+its theast transform I can conclude that
+ 
+
+ align:start position:0%
+its theast transform I can conclude that
+that function is the one I'm looking for
+
+ align:start position:0%
+that function is the one I'm looking for
+ 
+
+ align:start position:0%
+that function is the one I'm looking for
+provided only that L is a one:1 operator
+
+ align:start position:0%
+provided only that L is a one:1 operator
+ 
+
+ align:start position:0%
+provided only that L is a one:1 operator
+that the llas transform is a one to one
+
+ align:start position:0%
+that the llas transform is a one to one
+ 
+
+ align:start position:0%
+that the llas transform is a one to one
+function at any rate all I did in our
+
+ align:start position:0%
+function at any rate all I did in our
+ 
+
+ align:start position:0%
+function at any rate all I did in our
+problem was to simplify this by
+
+ align:start position:0%
+problem was to simplify this by
+ 
+
+ align:start position:0%
+problem was to simplify this by
+specifying that y of 0 was 0 and that y
+
+ align:start position:0%
+specifying that y of 0 was 0 and that y
+ 
+
+ align:start position:0%
+specifying that y of 0 was 0 and that y
+Prime of 0 was one these two terms drop
+
+ align:start position:0%
+Prime of 0 was one these two terms drop
+ 
+
+ align:start position:0%
+Prime of 0 was one these two terms drop
+out this is minus one it comes over onto
+
+ align:start position:0%
+out this is minus one it comes over onto
+ 
+
+ align:start position:0%
+out this is minus one it comes over onto
+the other side as + one and so I wind up
+
+ align:start position:0%
+the other side as + one and so I wind up
+ 
+
+ align:start position:0%
+the other side as + one and so I wind up
+with this particular equation okay and
+
+ align:start position:0%
+with this particular equation okay and
+ 
+
+ align:start position:0%
+with this particular equation okay and
+by the way notice that this simply says
+
+ align:start position:0%
+by the way notice that this simply says
+ 
+
+ align:start position:0%
+by the way notice that this simply says
+what s - 2 + 1/ S - 2 in other words
+
+ align:start position:0%
+what s - 2 + 1/ S - 2 in other words
+ 
+
+ align:start position:0%
+what s - 2 + 1/ S - 2 in other words
+this is s -1 / s - 2 this factors into s
+
+ align:start position:0%
+this is s -1 / s - 2 this factors into s
+ 
+
+ align:start position:0%
+this is s -1 / s - 2 this factors into s
+-1 * s - 3 so in other words what I'm
+
+ align:start position:0%
+-1 * s - 3 so in other words what I'm
+ 
+
+ align:start position:0%
+-1 * s - 3 so in other words what I'm
+now faced with is that s -1 * s - 3 * L
+
+ align:start position:0%
+now faced with is that s -1 * s - 3 * L
+ 
+
+ align:start position:0%
+now faced with is that s -1 * s - 3 * L
+of Y is equal to S -1 / s - 2 I have to
+
+ align:start position:0%
+of Y is equal to S -1 / s - 2 I have to
+ 
+
+ align:start position:0%
+of Y is equal to S -1 / s - 2 I have to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+careful you see I want to divide see I
+
+ align:start position:0%
+careful you see I want to divide see I
+ 
+
+ align:start position:0%
+careful you see I want to divide see I
+want to be able to cancel out the S
+
+ align:start position:0%
+want to be able to cancel out the S
+ 
+
+ align:start position:0%
+want to be able to cancel out the S
+minus 1's here I want to be able to
+
+ align:start position:0%
+minus 1's here I want to be able to
+ 
+
+ align:start position:0%
+minus 1's here I want to be able to
+divide through by s - 3 I have to be
+
+ align:start position:0%
+divide through by s - 3 I have to be
+ 
+
+ align:start position:0%
+divide through by s - 3 I have to be
+careful of zero denominators and the
+
+ align:start position:0%
+careful of zero denominators and the
+ 
+
+ align:start position:0%
+careful of zero denominators and the
+safest way to take care of everything is
+
+ align:start position:0%
+safest way to take care of everything is
+ 
+
+ align:start position:0%
+safest way to take care of everything is
+that all I really care about is whether
+
+ align:start position:0%
+that all I really care about is whether
+ 
+
+ align:start position:0%
+that all I really care about is whether
+the llast transform exists for
+
+ align:start position:0%
+the llast transform exists for
+ 
+
+ align:start position:0%
+the llast transform exists for
+sufficiently large values of s to get
+
+ align:start position:0%
+sufficiently large values of s to get
+ 
+
+ align:start position:0%
+sufficiently large values of s to get
+rid of my headache I'll simply assume
+
+ align:start position:0%
+rid of my headache I'll simply assume
+ 
+
+ align:start position:0%
+rid of my headache I'll simply assume
+that I'm not even looking at the laas
+
+ align:start position:0%
+that I'm not even looking at the laas
+ 
+
+ align:start position:0%
+that I'm not even looking at the laas
+transform until shall we say f s is
+
+ align:start position:0%
+transform until shall we say f s is
+ 
+
+ align:start position:0%
+transform until shall we say f s is
+greater than three you see once s is
+
+ align:start position:0%
+greater than three you see once s is
+ 
+
+ align:start position:0%
+greater than three you see once s is
+greater than three this Factor can't be
+
+ align:start position:0%
+greater than three this Factor can't be
+ 
+
+ align:start position:0%
+greater than three this Factor can't be
+zero this Factor can't be zero
+
+ align:start position:0%
+zero this Factor can't be zero
+ 
+
+ align:start position:0%
+zero this Factor can't be zero
+consequently I can solve for L of Y and
+
+ align:start position:0%
+consequently I can solve for L of Y and
+ 
+
+ align:start position:0%
+consequently I can solve for L of Y and
+conclude that L of Y is 1 / s - 3 * s -
+
+ align:start position:0%
+conclude that L of Y is 1 / s - 3 * s -
+ 
+
+ align:start position:0%
+conclude that L of Y is 1 / s - 3 * s -
+2 provided that s is greater than 3 now
+
+ align:start position:0%
+2 provided that s is greater than 3 now
+ 
+
+ align:start position:0%
+2 provided that s is greater than 3 now
+I resort to that same method
+
+ align:start position:0%
+I resort to that same method
+ 
+
+ align:start position:0%
+I resort to that same method
+of partial fractions that we used when
+
+ align:start position:0%
+of partial fractions that we used when
+ 
+
+ align:start position:0%
+of partial fractions that we used when
+we integrated back in part one using
+
+ align:start position:0%
+we integrated back in part one using
+ 
+
+ align:start position:0%
+we integrated back in part one using
+partial fractions I simply try to find
+
+ align:start position:0%
+partial fractions I simply try to find
+ 
+
+ align:start position:0%
+partial fractions I simply try to find
+constants A and B such that I can write
+
+ align:start position:0%
+constants A and B such that I can write
+ 
+
+ align:start position:0%
+constants A and B such that I can write
+this as a/ s- 3 + b/ s-2 in other words
+
+ align:start position:0%
+this as a/ s- 3 + b/ s-2 in other words
+ 
+
+ align:start position:0%
+this as a/ s- 3 + b/ s-2 in other words
+break this down into simpler Parts
+
+ align:start position:0%
+break this down into simpler Parts
+ 
+
+ align:start position:0%
+break this down into simpler Parts
+sparing you the details it follows very
+
+ align:start position:0%
+sparing you the details it follows very
+ 
+
+ align:start position:0%
+sparing you the details it follows very
+simply in this case that this expression
+
+ align:start position:0%
+simply in this case that this expression
+ 
+
+ align:start position:0%
+simply in this case that this expression
+is simply 1 / s - 3 - 1 / s -2 in other
+
+ align:start position:0%
+is simply 1 / s - 3 - 1 / s -2 in other
+ 
+
+ align:start position:0%
+is simply 1 / s - 3 - 1 / s -2 in other
+words that if I put this over common
+
+ align:start position:0%
+words that if I put this over common
+ 
+
+ align:start position:0%
+words that if I put this over common
+denominator I get 1 / s - 3 * s - 2 now
+
+ align:start position:0%
+denominator I get 1 / s - 3 * s - 2 now
+ 
+
+ align:start position:0%
+denominator I get 1 / s - 3 * s - 2 now
+here's where the kicker comes in
+
+ align:start position:0%
+here's where the kicker comes in
+ 
+
+ align:start position:0%
+here's where the kicker comes in
+remember we have already seen that 1 / s
+
+ align:start position:0%
+remember we have already seen that 1 / s
+ 
+
+ align:start position:0%
+remember we have already seen that 1 / s
+minus a is the laast transform of e to
+
+ align:start position:0%
+minus a is the laast transform of e to
+ 
+
+ align:start position:0%
+minus a is the laast transform of e to
+the a t provided s is greater than a in
+
+ align:start position:0%
+the a t provided s is greater than a in
+ 
+
+ align:start position:0%
+the a t provided s is greater than a in
+particular the llast transform of e to
+
+ align:start position:0%
+particular the llast transform of e to
+ 
+
+ align:start position:0%
+particular the llast transform of e to
+3T would 1 / s- 3 provided s was greater
+
+ align:start position:0%
+3T would 1 / s- 3 provided s was greater
+ 
+
+ align:start position:0%
+3T would 1 / s- 3 provided s was greater
+than 3 similarly the llast transform of
+
+ align:start position:0%
+than 3 similarly the llast transform of
+ 
+
+ align:start position:0%
+than 3 similarly the llast transform of
+e 2T would be 1 / s- 2 provided s was
+
+ align:start position:0%
+e 2T would be 1 / s- 2 provided s was
+ 
+
+ align:start position:0%
+e 2T would be 1 / s- 2 provided s was
+greater than two by the way notice that
+
+ align:start position:0%
+greater than two by the way notice that
+ 
+
+ align:start position:0%
+greater than two by the way notice that
+both of these conditions are obeyed as
+
+ align:start position:0%
+both of these conditions are obeyed as
+ 
+
+ align:start position:0%
+both of these conditions are obeyed as
+soon as s is greater than three
+
+ align:start position:0%
+soon as s is greater than three
+ 
+
+ align:start position:0%
+soon as s is greater than three
+obviously if s is greater than three it
+
+ align:start position:0%
+obviously if s is greater than three it
+ 
+
+ align:start position:0%
+obviously if s is greater than three it
+must be greater than two so I'm sure
+
+ align:start position:0%
+must be greater than two so I'm sure
+ 
+
+ align:start position:0%
+must be greater than two so I'm sure
+that both of these results are true once
+
+ align:start position:0%
+that both of these results are true once
+ 
+
+ align:start position:0%
+that both of these results are true once
+s is greater than three you see the same
+
+ align:start position:0%
+s is greater than three you see the same
+ 
+
+ align:start position:0%
+s is greater than three you see the same
+three I have up here now by arity I know
+
+ align:start position:0%
+three I have up here now by arity I know
+ 
+
+ align:start position:0%
+three I have up here now by arity I know
+that the llast transform of a difference
+
+ align:start position:0%
+that the llast transform of a difference
+ 
+
+ align:start position:0%
+that the llast transform of a difference
+is the difference of the llast
+
+ align:start position:0%
+is the difference of the llast
+ 
+
+ align:start position:0%
+is the difference of the llast
+transforms you see by equals added to
+
+ align:start position:0%
+transforms you see by equals added to
+ 
+
+ align:start position:0%
+transforms you see by equals added to
+equals this tells me that L of e 3T
+
+ align:start position:0%
+equals this tells me that L of e 3T
+ 
+
+ align:start position:0%
+equals this tells me that L of e 3T
+minus L of e 2T is 1 / s - 3 - 1 / s- 2
+
+ align:start position:0%
+minus L of e 2T is 1 / s - 3 - 1 / s- 2
+ 
+
+ align:start position:0%
+minus L of e 2T is 1 / s - 3 - 1 / s- 2
+but by linearity e l of e to 3T minus L
+
+ align:start position:0%
+but by linearity e l of e to 3T minus L
+ 
+
+ align:start position:0%
+but by linearity e l of e to 3T minus L
+of e to 2T is L of the quantity e to 3T
+
+ align:start position:0%
+of e to 2T is L of the quantity e to 3T
+ 
+
+ align:start position:0%
+of e to 2T is L of the quantity e to 3T
+minus E 2T in particular then do I know
+
+ align:start position:0%
+minus E 2T in particular then do I know
+ 
+
+ align:start position:0%
+minus E 2T in particular then do I know
+one function whose llast transform is 1
+
+ align:start position:0%
+one function whose llast transform is 1
+ 
+
+ align:start position:0%
+one function whose llast transform is 1
+/ s - 3 - 1 / s -2 and the answer is yes
+
+ align:start position:0%
+/ s - 3 - 1 / s -2 and the answer is yes
+ 
+
+ align:start position:0%
+/ s - 3 - 1 / s -2 and the answer is yes
+we've just constructed it namely the
+
+ align:start position:0%
+we've just constructed it namely the
+ 
+
+ align:start position:0%
+we've just constructed it namely the
+function y = e 3 T minus E 2 T in other
+
+ align:start position:0%
+function y = e 3 T minus E 2 T in other
+ 
+
+ align:start position:0%
+function y = e 3 T minus E 2 T in other
+words what we do know is that in any
+
+ align:start position:0%
+words what we do know is that in any
+ 
+
+ align:start position:0%
+words what we do know is that in any
+event whether Y is the given function or
+
+ align:start position:0%
+event whether Y is the given function or
+ 
+
+ align:start position:0%
+event whether Y is the given function or
+not whatever L of Y is it's l of e 3 T
+
+ align:start position:0%
+not whatever L of Y is it's l of e 3 T
+ 
+
+ align:start position:0%
+not whatever L of Y is it's l of e 3 T
+minus E 2T and therefore we could
+
+ align:start position:0%
+minus E 2T and therefore we could
+ 
+
+ align:start position:0%
+minus E 2T and therefore we could
+conclude that Y Must equal e 3 T minus E
+
+ align:start position:0%
+conclude that Y Must equal e 3 T minus E
+ 
+
+ align:start position:0%
+conclude that Y Must equal e 3 T minus E
+2 T provided that L is 1 to one provided
+
+ align:start position:0%
+2 T provided that L is 1 to one provided
+ 
+
+ align:start position:0%
+2 T provided that L is 1 to one provided
+that there is only one function that can
+
+ align:start position:0%
+that there is only one function that can
+ 
+
+ align:start position:0%
+that there is only one function that can
+have a given Li transform you see you
+
+ align:start position:0%
+have a given Li transform you see you
+ 
+
+ align:start position:0%
+have a given Li transform you see you
+cannot automatically conclude that
+
+ align:start position:0%
+cannot automatically conclude that
+ 
+
+ align:start position:0%
+cannot automatically conclude that
+because these two things are equal the
+
+ align:start position:0%
+because these two things are equal the
+ 
+
+ align:start position:0%
+because these two things are equal the
+that L of with the whole expression is
+
+ align:start position:0%
+that L of with the whole expression is
+ 
+
+ align:start position:0%
+that L of with the whole expression is
+equal that the inputs must be equal for
+
+ align:start position:0%
+equal that the inputs must be equal for
+ 
+
+ align:start position:0%
+equal that the inputs must be equal for
+example you cannot conclude that xal < /
+
+ align:start position:0%
+example you cannot conclude that xal < /
+ 
+
+ align:start position:0%
+example you cannot conclude that xal < /
+6 simply because you know that Sin xal
+
+ align:start position:0%
+6 simply because you know that Sin xal
+ 
+
+ align:start position:0%
+6 simply because you know that Sin xal
+Sin pi/ 6 you see the sign function is
+
+ align:start position:0%
+Sin pi/ 6 you see the sign function is
+ 
+
+ align:start position:0%
+Sin pi/ 6 you see the sign function is
+not 1: one well at any rate I think you
+
+ align:start position:0%
+not 1: one well at any rate I think you
+ 
+
+ align:start position:0%
+not 1: one well at any rate I think you
+can sense intuitively
+
+ align:start position:0%
+can sense intuitively
+ 
+
+ align:start position:0%
+can sense intuitively
+that because we already know that for
+
+ align:start position:0%
+that because we already know that for
+ 
+
+ align:start position:0%
+that because we already know that for
+linear differential equations with
+
+ align:start position:0%
+linear differential equations with
+ 
+
+ align:start position:0%
+linear differential equations with
+constant coefficients there are no
+
+ align:start position:0%
+constant coefficients there are no
+ 
+
+ align:start position:0%
+constant coefficients there are no
+singular Solutions and once you found
+
+ align:start position:0%
+singular Solutions and once you found
+ 
+
+ align:start position:0%
+singular Solutions and once you found
+one solution subject to given initial
+
+ align:start position:0%
+one solution subject to given initial
+ 
+
+ align:start position:0%
+one solution subject to given initial
+conditions you found them all I think
+
+ align:start position:0%
+conditions you found them all I think
+ 
+
+ align:start position:0%
+conditions you found them all I think
+you can guess that at least for
+
+ align:start position:0%
+you can guess that at least for
+ 
+
+ align:start position:0%
+you can guess that at least for
+functions of exponential order this
+
+ align:start position:0%
+functions of exponential order this
+ 
+
+ align:start position:0%
+functions of exponential order this
+should be a True Result and the fact
+
+ align:start position:0%
+should be a True Result and the fact
+ 
+
+ align:start position:0%
+should be a True Result and the fact
+that it is true is known in the
+
+ align:start position:0%
+that it is true is known in the
+ 
+
+ align:start position:0%
+that it is true is known in the
+literature under the name of lures
+
+ align:start position:0%
+literature under the name of lures
+ 
+
+ align:start position:0%
+literature under the name of lures
+theorem luch not lur CH but ler CH it's
+
+ align:start position:0%
+theorem luch not lur CH but ler CH it's
+ 
+
+ align:start position:0%
+theorem luch not lur CH but ler CH it's
+known under the name of luches theorem
+
+ align:start position:0%
+known under the name of luches theorem
+ 
+
+ align:start position:0%
+known under the name of luches theorem
+and by but and I have taken the liberty
+
+ align:start position:0%
+and by but and I have taken the liberty
+ 
+
+ align:start position:0%
+and by but and I have taken the liberty
+of stating it in a less controversial
+
+ align:start position:0%
+of stating it in a less controversial
+ 
+
+ align:start position:0%
+of stating it in a less controversial
+form saving the generalization for the
+
+ align:start position:0%
+form saving the generalization for the
+ 
+
+ align:start position:0%
+form saving the generalization for the
+learning exercises but essentially all
+
+ align:start position:0%
+learning exercises but essentially all
+ 
+
+ align:start position:0%
+learning exercises but essentially all
+luches theorem says is this if f and g
+
+ align:start position:0%
+luches theorem says is this if f and g
+ 
+
+ align:start position:0%
+luches theorem says is this if f and g
+are continuous and of exponential order
+
+ align:start position:0%
+are continuous and of exponential order
+ 
+
+ align:start position:0%
+are continuous and of exponential order
+Okay then if the llast transform of f
+
+ align:start position:0%
+Okay then if the llast transform of f
+ 
+
+ align:start position:0%
+Okay then if the llast transform of f
+equals the llast transform of G for all
+
+ align:start position:0%
+equals the llast transform of G for all
+ 
+
+ align:start position:0%
+equals the llast transform of G for all
+sufficiently large values of s in other
+
+ align:start position:0%
+sufficiently large values of s in other
+ 
+
+ align:start position:0%
+sufficiently large values of s in other
+words if Beyond a certain S F Bar of s
+
+ align:start position:0%
+words if Beyond a certain S F Bar of s
+ 
+
+ align:start position:0%
+words if Beyond a certain S F Bar of s
+equals g bar of s in other words f and g
+
+ align:start position:0%
+equals g bar of s in other words f and g
+ 
+
+ align:start position:0%
+equals g bar of s in other words f and g
+have the same llas transform then f and
+
+ align:start position:0%
+have the same llas transform then f and
+ 
+
+ align:start position:0%
+have the same llas transform then f and
+g must be identical and there is a
+
+ align:start position:0%
+g must be identical and there is a
+ 
+
+ align:start position:0%
+g must be identical and there is a
+slight modification of this that comes
+
+ align:start position:0%
+slight modification of this that comes
+ 
+
+ align:start position:0%
+slight modification of this that comes
+up if you leave out the word continuous
+
+ align:start position:0%
+up if you leave out the word continuous
+ 
+
+ align:start position:0%
+up if you leave out the word continuous
+here L's theorem is stated only in terms
+
+ align:start position:0%
+here L's theorem is stated only in terms
+ 
+
+ align:start position:0%
+here L's theorem is stated only in terms
+of f and g being peace wise continuous
+
+ align:start position:0%
+of f and g being peace wise continuous
+ 
+
+ align:start position:0%
+of f and g being peace wise continuous
+in other words there could be jump
+
+ align:start position:0%
+in other words there could be jump
+ 
+
+ align:start position:0%
+in other words there could be jump
+discontinuities in the curves and things
+
+ align:start position:0%
+discontinuities in the curves and things
+ 
+
+ align:start position:0%
+discontinuities in the curves and things
+like this at which case this would hold
+
+ align:start position:0%
+like this at which case this would hold
+ 
+
+ align:start position:0%
+like this at which case this would hold
+except possibly at the points at which
+
+ align:start position:0%
+except possibly at the points at which
+ 
+
+ align:start position:0%
+except possibly at the points at which
+you had jump uh discontinuities I prefer
+
+ align:start position:0%
+you had jump uh discontinuities I prefer
+ 
+
+ align:start position:0%
+you had jump uh discontinuities I prefer
+not to get into this at this particular
+
+ align:start position:0%
+not to get into this at this particular
+ 
+
+ align:start position:0%
+not to get into this at this particular
+time but rather to wrap up our lecture
+
+ align:start position:0%
+time but rather to wrap up our lecture
+ 
+
+ align:start position:0%
+time but rather to wrap up our lecture
+at this particular point and to Simply
+
+ align:start position:0%
+at this particular point and to Simply
+ 
+
+ align:start position:0%
+at this particular point and to Simply
+say that we have done what now we have
+
+ align:start position:0%
+say that we have done what now we have
+ 
+
+ align:start position:0%
+say that we have done what now we have
+studied linear differential equations we
+
+ align:start position:0%
+studied linear differential equations we
+ 
+
+ align:start position:0%
+studied linear differential equations we
+have used this last lecture to introduce
+
+ align:start position:0%
+have used this last lecture to introduce
+ 
+
+ align:start position:0%
+have used this last lecture to introduce
+the concept of the lass
+
+ align:start position:0%
+the concept of the lass
+ 
+
+ align:start position:0%
+the concept of the lass
+transform which has secondary value in
+
+ align:start position:0%
+transform which has secondary value in
+ 
+
+ align:start position:0%
+transform which has secondary value in
+terms of solving differential equations
+
+ align:start position:0%
+terms of solving differential equations
+ 
+
+ align:start position:0%
+terms of solving differential equations
+but which has other applications that go
+
+ align:start position:0%
+but which has other applications that go
+ 
+
+ align:start position:0%
+but which has other applications that go
+far beyond the scope of this particular
+
+ align:start position:0%
+far beyond the scope of this particular
+ 
+
+ align:start position:0%
+far beyond the scope of this particular
+course and what I'm hoping is that this
+
+ align:start position:0%
+course and what I'm hoping is that this
+ 
+
+ align:start position:0%
+course and what I'm hoping is that this
+rather introductory lecture coupled with
+
+ align:start position:0%
+rather introductory lecture coupled with
+ 
+
+ align:start position:0%
+rather introductory lecture coupled with
+well-chosen
+
+ align:start position:0%
+well-chosen
+ 
+
+ align:start position:0%
+well-chosen
+exercises will give you enough insight
+
+ align:start position:0%
+exercises will give you enough insight
+ 
+
+ align:start position:0%
+exercises will give you enough insight
+to theast transform so that you will be
+
+ align:start position:0%
+to theast transform so that you will be
+ 
+
+ align:start position:0%
+to theast transform so that you will be
+able to handle it not only in terms of
+
+ align:start position:0%
+able to handle it not only in terms of
+ 
+
+ align:start position:0%
+able to handle it not only in terms of
+solving linear differential equations
+
+ align:start position:0%
+solving linear differential equations
+ 
+
+ align:start position:0%
+solving linear differential equations
+with constant coefficients but in other
+
+ align:start position:0%
+with constant coefficients but in other
+ 
+
+ align:start position:0%
+with constant coefficients but in other
+contexts where they might occur in the
+
+ align:start position:0%
+contexts where they might occur in the
+ 
+
+ align:start position:0%
+contexts where they might occur in the
+particular line of work and research
+
+ align:start position:0%
+particular line of work and research
+ 
+
+ align:start position:0%
+particular line of work and research
+that you're doing at any rate this
+
+ align:start position:0%
+that you're doing at any rate this
+ 
+
+ align:start position:0%
+that you're doing at any rate this
+completes our work on block seven and in
+
+ align:start position:0%
+completes our work on block seven and in
+ 
+
+ align:start position:0%
+completes our work on block seven and in
+our next lecture what we shall do is
+
+ align:start position:0%
+our next lecture what we shall do is
+ 
+
+ align:start position:0%
+our next lecture what we shall do is
+start the final block of our course and
+
+ align:start position:0%
+start the final block of our course and
+ 
+
+ align:start position:0%
+start the final block of our course and
+revisit the concept of vector spaces
+
+ align:start position:0%
+revisit the concept of vector spaces
+ 
+
+ align:start position:0%
+revisit the concept of vector spaces
+from hopefully a more productive point
+
+ align:start position:0%
+from hopefully a more productive point
+ 
+
+ align:start position:0%
+from hopefully a more productive point
+of view than what we've had before but
+
+ align:start position:0%
+of view than what we've had before but
+ 
+
+ align:start position:0%
+of view than what we've had before but
+more about that next time until next
+
+ align:start position:0%
+more about that next time until next
+ 
+
+ align:start position:0%
+more about that next time until next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/b1eKhyC9TTo.txt b/b1eKhyC9TTo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8708d90379d35da86cfaff4cb4fdd7f65bd9c20a
--- /dev/null
+++ b/b1eKhyC9TTo.txt
@@ -0,0 +1,9736 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm back
+
+ align:start position:0%
+so I'm back
+ 
+
+ align:start position:0%
+so I'm back
+welcome back also to al-suri so today
+
+ align:start position:0%
+welcome back also to al-suri so today
+ 
+
+ align:start position:0%
+welcome back also to al-suri so today
+what we are going to do is to is
+
+ align:start position:0%
+what we are going to do is to is
+ 
+
+ align:start position:0%
+what we are going to do is to is
+something really interesting so it's to
+
+ align:start position:0%
+something really interesting so it's to
+ 
+
+ align:start position:0%
+something really interesting so it's to
+understand how we use symmetry to help
+
+ align:start position:0%
+understand how we use symmetry to help
+ 
+
+ align:start position:0%
+understand how we use symmetry to help
+us with prediction of physical
+
+ align:start position:0%
+us with prediction of physical
+ 
+
+ align:start position:0%
+us with prediction of physical
+situations so so first I will go through
+
+ align:start position:0%
+situations so so first I will go through
+ 
+
+ align:start position:0%
+situations so so first I will go through
+two concrete examples of symmetry and
+
+ align:start position:0%
+two concrete examples of symmetry and
+ 
+
+ align:start position:0%
+two concrete examples of symmetry and
+see what we can learn from there and
+
+ align:start position:0%
+see what we can learn from there and
+ 
+
+ align:start position:0%
+see what we can learn from there and
+also today we are going to go to
+
+ align:start position:0%
+also today we are going to go to
+ 
+
+ align:start position:0%
+also today we are going to go to
+infinite number of coupled oscillators
+
+ align:start position:0%
+infinite number of coupled oscillators
+ 
+
+ align:start position:0%
+infinite number of coupled oscillators
+okay okay I think we are done with
+
+ align:start position:0%
+okay okay I think we are done with
+ 
+
+ align:start position:0%
+okay okay I think we are done with
+finite numbers okay all right so what we
+
+ align:start position:0%
+finite numbers okay all right so what we
+ 
+
+ align:start position:0%
+finite numbers okay all right so what we
+have learned last time when Pollock was
+
+ align:start position:0%
+have learned last time when Pollock was
+ 
+
+ align:start position:0%
+have learned last time when Pollock was
+giving the lecture I hope we have
+
+ align:start position:0%
+giving the lecture I hope we have
+ 
+
+ align:start position:0%
+giving the lecture I hope we have
+learned a driving force can excite a
+
+ align:start position:0%
+learned a driving force can excite a
+ 
+
+ align:start position:0%
+learned a driving force can excite a
+specific normal mode right so if you
+
+ align:start position:0%
+specific normal mode right so if you
+ 
+
+ align:start position:0%
+specific normal mode right so if you
+type the system at the frequency
+
+ align:start position:0%
+type the system at the frequency
+ 
+
+ align:start position:0%
+type the system at the frequency
+persistent like then the system will
+
+ align:start position:0%
+persistent like then the system will
+ 
+
+ align:start position:0%
+persistent like then the system will
+respond and the other day at driving
+
+ align:start position:0%
+respond and the other day at driving
+ 
+
+ align:start position:0%
+respond and the other day at driving
+frequency with large amplitude okay and
+
+ align:start position:0%
+frequency with large amplitude okay and
+ 
+
+ align:start position:0%
+frequency with large amplitude okay and
+also we have learned that the full
+
+ align:start position:0%
+also we have learned that the full
+ 
+
+ align:start position:0%
+also we have learned that the full
+solution of a coupled oscillator is
+
+ align:start position:0%
+solution of a coupled oscillator is
+ 
+
+ align:start position:0%
+solution of a coupled oscillator is
+actually pretty similar to the situation
+
+ align:start position:0%
+actually pretty similar to the situation
+ 
+
+ align:start position:0%
+actually pretty similar to the situation
+we got from single oscillator so you
+
+ align:start position:0%
+we got from single oscillator so you
+ 
+
+ align:start position:0%
+we got from single oscillator so you
+have particular solution and homogeneous
+
+ align:start position:0%
+have particular solution and homogeneous
+ 
+
+ align:start position:0%
+have particular solution and homogeneous
+solution and the full solution will be a
+
+ align:start position:0%
+solution and the full solution will be a
+ 
+
+ align:start position:0%
+solution and the full solution will be a
+superposition of the two country
+
+ align:start position:0%
+superposition of the two country
+ 
+
+ align:start position:0%
+superposition of the two country
+component and all the unknown
+
+ align:start position:0%
+component and all the unknown
+ 
+
+ align:start position:0%
+component and all the unknown
+coefficients are in the homogenous part
+
+ align:start position:0%
+coefficients are in the homogenous part
+ 
+
+ align:start position:0%
+coefficients are in the homogenous part
+of the solution
+
+ align:start position:0%
+of the solution
+ 
+
+ align:start position:0%
+of the solution
+okay and today I hope I can help you and
+
+ align:start position:0%
+okay and today I hope I can help you and
+ 
+
+ align:start position:0%
+okay and today I hope I can help you and
+convince you that symmetry actually can
+
+ align:start position:0%
+convince you that symmetry actually can
+ 
+
+ align:start position:0%
+convince you that symmetry actually can
+help us to solve the normal modes
+
+ align:start position:0%
+help us to solve the normal modes
+ 
+
+ align:start position:0%
+help us to solve the normal modes
+without knowing the detail or a nice one
+
+ align:start position:0%
+without knowing the detail or a nice one
+ 
+
+ align:start position:0%
+without knowing the detail or a nice one
+make a matrix actually so that is
+
+ align:start position:0%
+make a matrix actually so that is
+ 
+
+ align:start position:0%
+make a matrix actually so that is
+actually something really cool and I
+
+ align:start position:0%
+actually something really cool and I
+ 
+
+ align:start position:0%
+actually something really cool and I
+would like to talk about that in this
+
+ align:start position:0%
+would like to talk about that in this
+ 
+
+ align:start position:0%
+would like to talk about that in this
+lecture today so this is actually what
+
+ align:start position:0%
+lecture today so this is actually what
+ 
+
+ align:start position:0%
+lecture today so this is actually what
+we have been doing so far right so we
+
+ align:start position:0%
+we have been doing so far right so we
+ 
+
+ align:start position:0%
+we have been doing so far right so we
+write everything in terms of matrix so
+
+ align:start position:0%
+write everything in terms of matrix so
+ 
+
+ align:start position:0%
+write everything in terms of matrix so
+we start from the equation of motion and
+
+ align:start position:0%
+we start from the equation of motion and
+ 
+
+ align:start position:0%
+we start from the equation of motion and
+X double dot equal to minus KX and then
+
+ align:start position:0%
+X double dot equal to minus KX and then
+ 
+
+ align:start position:0%
+X double dot equal to minus KX and then
+we write everything in a complex
+
+ align:start position:0%
+we write everything in a complex
+ 
+
+ align:start position:0%
+we write everything in a complex
+notation exponential I Omega T plus Phi
+
+ align:start position:0%
+notation exponential I Omega T plus Phi
+ 
+
+ align:start position:0%
+notation exponential I Omega T plus Phi
+times a a they should be back to right
+
+ align:start position:0%
+times a a they should be back to right
+ 
+
+ align:start position:0%
+times a a they should be back to right
+so it's actually a 1 a 2 a series it
+
+ align:start position:0%
+so it's actually a 1 a 2 a series it
+ 
+
+ align:start position:0%
+so it's actually a 1 a 2 a series it
+says with the amplitude of the
+
+ align:start position:0%
+says with the amplitude of the
+ 
+
+ align:start position:0%
+says with the amplitude of the
+oscillation of the first second and
+
+ align:start position:0%
+oscillation of the first second and
+ 
+
+ align:start position:0%
+oscillation of the first second and
+third etcetera I said to a component of
+
+ align:start position:0%
+third etcetera I said to a component of
+ 
+
+ align:start position:0%
+third etcetera I said to a component of
+the system right then we actually found
+
+ align:start position:0%
+the system right then we actually found
+ 
+
+ align:start position:0%
+the system right then we actually found
+that in the end of the day we are
+
+ align:start position:0%
+that in the end of the day we are
+ 
+
+ align:start position:0%
+that in the end of the day we are
+actually solving this problem like
+
+ align:start position:0%
+actually solving this problem like
+ 
+
+ align:start position:0%
+actually solving this problem like
+eigenvalue problem right so basically we
+
+ align:start position:0%
+eigenvalue problem right so basically we
+ 
+
+ align:start position:0%
+eigenvalue problem right so basically we
+have M minus 1 K matrix describe how
+
+ align:start position:0%
+have M minus 1 K matrix describe how
+ 
+
+ align:start position:0%
+have M minus 1 K matrix describe how
+each component in the system interact
+
+ align:start position:0%
+each component in the system interact
+ 
+
+ align:start position:0%
+each component in the system interact
+with each other okay then what is this
+
+ align:start position:0%
+with each other okay then what is this
+ 
+
+ align:start position:0%
+with each other okay then what is this
+with the angular frequency of the normal
+
+ align:start position:0%
+with the angular frequency of the normal
+ 
+
+ align:start position:0%
+with the angular frequency of the normal
+modes essentially coming from this
+
+ align:start position:0%
+modes essentially coming from this
+ 
+
+ align:start position:0%
+modes essentially coming from this
+eigenvalue problem M minus 1 K a equal
+
+ align:start position:0%
+eigenvalue problem M minus 1 K a equal
+ 
+
+ align:start position:0%
+eigenvalue problem M minus 1 K a equal
+to Omega square a then you just go ahead
+
+ align:start position:0%
+to Omega square a then you just go ahead
+ 
+
+ align:start position:0%
+to Omega square a then you just go ahead
+and solve the eigenvalue problem then
+
+ align:start position:0%
+and solve the eigenvalue problem then
+ 
+
+ align:start position:0%
+and solve the eigenvalue problem then
+you will be able to figure out what are
+
+ align:start position:0%
+you will be able to figure out what are
+ 
+
+ align:start position:0%
+you will be able to figure out what are
+the normal mode frequencies and
+
+ align:start position:0%
+the normal mode frequencies and
+ 
+
+ align:start position:0%
+the normal mode frequencies and
+therefore what are the relative the
+
+ align:start position:0%
+therefore what are the relative the
+ 
+
+ align:start position:0%
+therefore what are the relative the
+ratio of the amplitude in the normal
+
+ align:start position:0%
+ratio of the amplitude in the normal
+ 
+
+ align:start position:0%
+ratio of the amplitude in the normal
+mode which is actually a vector okay the
+
+ align:start position:0%
+mode which is actually a vector okay the
+ 
+
+ align:start position:0%
+mode which is actually a vector okay the
+eye contact okay so that's issue what we
+
+ align:start position:0%
+eye contact okay so that's issue what we
+ 
+
+ align:start position:0%
+eye contact okay so that's issue what we
+have been doing okay and today what I am
+
+ align:start position:0%
+have been doing okay and today what I am
+ 
+
+ align:start position:0%
+have been doing okay and today what I am
+going to do is to introduce you a very
+
+ align:start position:0%
+going to do is to introduce you a very
+ 
+
+ align:start position:0%
+going to do is to introduce you a very
+important concept in physics not only in
+
+ align:start position:0%
+important concept in physics not only in
+ 
+
+ align:start position:0%
+important concept in physics not only in
+physics but also in mathematics and also
+
+ align:start position:0%
+physics but also in mathematics and also
+ 
+
+ align:start position:0%
+physics but also in mathematics and also
+art right so you see symmetry in the art
+
+ align:start position:0%
+art right so you see symmetry in the art
+ 
+
+ align:start position:0%
+art right so you see symmetry in the art
+you can see here there are several
+
+ align:start position:0%
+you can see here there are several
+ 
+
+ align:start position:0%
+you can see here there are several
+graphs here and you can see that there
+
+ align:start position:0%
+graphs here and you can see that there
+ 
+
+ align:start position:0%
+graphs here and you can see that there
+the parent symmetry you have rotational
+
+ align:start position:0%
+the parent symmetry you have rotational
+ 
+
+ align:start position:0%
+the parent symmetry you have rotational
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they are your fracturing symmetry and
+
+ align:start position:0%
+they are your fracturing symmetry and
+ 
+
+ align:start position:0%
+they are your fracturing symmetry and
+you can see that when we build the
+
+ align:start position:0%
+you can see that when we build the
+ 
+
+ align:start position:0%
+you can see that when we build the
+particle detector visible lower-right
+
+ align:start position:0%
+particle detector visible lower-right
+ 
+
+ align:start position:0%
+particle detector visible lower-right
+bra is a cns detector camera so noise in
+
+ align:start position:0%
+bra is a cns detector camera so noise in
+ 
+
+ align:start position:0%
+bra is a cns detector camera so noise in
+the Large Hadron Collider we also try to
+
+ align:start position:0%
+the Large Hadron Collider we also try to
+ 
+
+ align:start position:0%
+the Large Hadron Collider we also try to
+build this detector symmetric right
+
+ align:start position:0%
+build this detector symmetric right
+ 
+
+ align:start position:0%
+build this detector symmetric right
+because otherwise if I get a very
+
+ align:start position:0%
+because otherwise if I get a very
+ 
+
+ align:start position:0%
+because otherwise if I get a very
+complicated shape of the data then the
+
+ align:start position:0%
+complicated shape of the data then the
+ 
+
+ align:start position:0%
+complicated shape of the data then the
+analysis of the data will be really
+
+ align:start position:0%
+analysis of the data will be really
+ 
+
+ align:start position:0%
+analysis of the data will be really
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+so therefore everybody like symmetry and
+
+ align:start position:0%
+so therefore everybody like symmetry and
+ 
+
+ align:start position:0%
+so therefore everybody like symmetry and
+everybody don't like really chaos right
+
+ align:start position:0%
+everybody don't like really chaos right
+ 
+
+ align:start position:0%
+everybody don't like really chaos right
+okay so that's really nice
+
+ align:start position:0%
+okay so that's really nice
+ 
+
+ align:start position:0%
+okay so that's really nice
+the question is how do we speak the
+
+ align:start position:0%
+the question is how do we speak the
+ 
+
+ align:start position:0%
+the question is how do we speak the
+language not let the natural speak how
+
+ align:start position:0%
+language not let the natural speak how
+ 
+
+ align:start position:0%
+language not let the natural speak how
+do we actually describe symmetry that's
+
+ align:start position:0%
+do we actually describe symmetry that's
+ 
+
+ align:start position:0%
+do we actually describe symmetry that's
+actually the question I'm asking and I'm
+
+ align:start position:0%
+actually the question I'm asking and I'm
+ 
+
+ align:start position:0%
+actually the question I'm asking and I'm
+going to show you that okay we can issue
+
+ align:start position:0%
+going to show you that okay we can issue
+ 
+
+ align:start position:0%
+going to show you that okay we can issue
+use mathematics to describe a symmetry
+
+ align:start position:0%
+use mathematics to describe a symmetry
+ 
+
+ align:start position:0%
+use mathematics to describe a symmetry
+so before we go to infinite number of
+
+ align:start position:0%
+so before we go to infinite number of
+ 
+
+ align:start position:0%
+so before we go to infinite number of
+oscillator that me give you a concrete
+
+ align:start position:0%
+oscillator that me give you a concrete
+ 
+
+ align:start position:0%
+oscillator that me give you a concrete
+example of symmetry and then see if we
+
+ align:start position:0%
+example of symmetry and then see if we
+ 
+
+ align:start position:0%
+example of symmetry and then see if we
+can understand how to use the math to
+
+ align:start position:0%
+can understand how to use the math to
+ 
+
+ align:start position:0%
+can understand how to use the math to
+describe symmetry okay so there's a two
+
+ align:start position:0%
+describe symmetry okay so there's a two
+ 
+
+ align:start position:0%
+describe symmetry okay so there's a two
+component system two pendulums which we
+
+ align:start position:0%
+component system two pendulums which we
+ 
+
+ align:start position:0%
+component system two pendulums which we
+work together in the last few lectures
+
+ align:start position:0%
+work together in the last few lectures
+ 
+
+ align:start position:0%
+work together in the last few lectures
+that they are coupled to each other
+
+ align:start position:0%
+that they are coupled to each other
+ 
+
+ align:start position:0%
+that they are coupled to each other
+and there is a parent symmetry of this
+
+ align:start position:0%
+and there is a parent symmetry of this
+ 
+
+ align:start position:0%
+and there is a parent symmetry of this
+system can somebody tell me what is the
+
+ align:start position:0%
+system can somebody tell me what is the
+ 
+
+ align:start position:0%
+system can somebody tell me what is the
+same symmetry you can see from this
+
+ align:start position:0%
+same symmetry you can see from this
+ 
+
+ align:start position:0%
+same symmetry you can see from this
+system somebody anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you refract this system as I show
+
+ align:start position:0%
+so if you refract this system as I show
+ 
+
+ align:start position:0%
+so if you refract this system as I show
+you in the leg in that slide you can see
+
+ align:start position:0%
+you in the leg in that slide you can see
+ 
+
+ align:start position:0%
+you in the leg in that slide you can see
+that if you reflect this picture it
+
+ align:start position:0%
+that if you reflect this picture it
+ 
+
+ align:start position:0%
+that if you reflect this picture it
+looks identical right so that is
+
+ align:start position:0%
+looks identical right so that is
+ 
+
+ align:start position:0%
+looks identical right so that is
+actually really good news
+
+ align:start position:0%
+actually really good news
+ 
+
+ align:start position:0%
+actually really good news
+that means if I do this in refraction x1
+
+ align:start position:0%
+that means if I do this in refraction x1
+ 
+
+ align:start position:0%
+that means if I do this in refraction x1
+go to minus x2 you have a minus sign
+
+ align:start position:0%
+go to minus x2 you have a minus sign
+ 
+
+ align:start position:0%
+go to minus x2 you have a minus sign
+because you can see that you have the
+
+ align:start position:0%
+because you can see that you have the
+ 
+
+ align:start position:0%
+because you can see that you have the
+refraction the amplitude change sign
+
+ align:start position:0%
+refraction the amplitude change sign
+ 
+
+ align:start position:0%
+refraction the amplitude change sign
+right x2 co 2 minus x1 the system looks
+
+ align:start position:0%
+right x2 co 2 minus x1 the system looks
+ 
+
+ align:start position:0%
+right x2 co 2 minus x1 the system looks
+identical and the physics should not
+
+ align:start position:0%
+identical and the physics should not
+ 
+
+ align:start position:0%
+identical and the physics should not
+change okay so that's actually what we
+
+ align:start position:0%
+change okay so that's actually what we
+ 
+
+ align:start position:0%
+change okay so that's actually what we
+can learn from but there so that means
+
+ align:start position:0%
+can learn from but there so that means
+ 
+
+ align:start position:0%
+can learn from but there so that means
+if I have I to this refraction then I
+
+ align:start position:0%
+if I have I to this refraction then I
+ 
+
+ align:start position:0%
+if I have I to this refraction then I
+can have actually defined X tilde P this
+
+ align:start position:0%
+can have actually defined X tilde P this
+ 
+
+ align:start position:0%
+can have actually defined X tilde P this
+is equal to minus x2 minus x1 okay to be
+
+ align:start position:0%
+is equal to minus x2 minus x1 okay to be
+ 
+
+ align:start position:0%
+is equal to minus x2 minus x1 okay to be
+with eggs okay and this is also going to
+
+ align:start position:0%
+with eggs okay and this is also going to
+ 
+
+ align:start position:0%
+with eggs okay and this is also going to
+be the solution of the equation of
+
+ align:start position:0%
+be the solution of the equation of
+ 
+
+ align:start position:0%
+be the solution of the equation of
+motion if the original X is already a
+
+ align:start position:0%
+motion if the original X is already a
+ 
+
+ align:start position:0%
+motion if the original X is already a
+solution okay so that's the power of the
+
+ align:start position:0%
+solution okay so that's the power of the
+ 
+
+ align:start position:0%
+solution okay so that's the power of the
+refraction symmetry okay if X is a
+
+ align:start position:0%
+refraction symmetry okay if X is a
+ 
+
+ align:start position:0%
+refraction symmetry okay if X is a
+solution then I do this refraction and I
+
+ align:start position:0%
+solution then I do this refraction and I
+ 
+
+ align:start position:0%
+solution then I do this refraction and I
+can figure out that X tilde is also a
+
+ align:start position:0%
+can figure out that X tilde is also a
+ 
+
+ align:start position:0%
+can figure out that X tilde is also a
+solution okay so how do I actually how
+
+ align:start position:0%
+solution okay so how do I actually how
+ 
+
+ align:start position:0%
+solution okay so how do I actually how
+do I actually describe the symmetry in
+
+ align:start position:0%
+do I actually describe the symmetry in
+ 
+
+ align:start position:0%
+do I actually describe the symmetry in
+the form of mathematics what we actually
+
+ align:start position:0%
+the form of mathematics what we actually
+ 
+
+ align:start position:0%
+the form of mathematics what we actually
+do is to define s-matrix symmetry matrix
+
+ align:start position:0%
+do is to define s-matrix symmetry matrix
+ 
+
+ align:start position:0%
+do is to define s-matrix symmetry matrix
+and in this case when we talk about
+
+ align:start position:0%
+and in this case when we talk about
+ 
+
+ align:start position:0%
+and in this case when we talk about
+reflection symmetry is actually defined
+
+ align:start position:0%
+reflection symmetry is actually defined
+ 
+
+ align:start position:0%
+reflection symmetry is actually defined
+as 0 minus 1 minus 1 0 this is actually
+
+ align:start position:0%
+as 0 minus 1 minus 1 0 this is actually
+ 
+
+ align:start position:0%
+as 0 minus 1 minus 1 0 this is actually
+a 2 by 2 matrix and if I do this
+
+ align:start position:0%
+a 2 by 2 matrix and if I do this
+ 
+
+ align:start position:0%
+a 2 by 2 matrix and if I do this
+operation s operation this X matrix then
+
+ align:start position:0%
+operation s operation this X matrix then
+ 
+
+ align:start position:0%
+operation s operation this X matrix then
+that especially going to give you the X
+
+ align:start position:0%
+that especially going to give you the X
+ 
+
+ align:start position:0%
+that especially going to give you the X
+tilde okay so that's the issue the the
+
+ align:start position:0%
+tilde okay so that's the issue the the
+ 
+
+ align:start position:0%
+tilde okay so that's the issue the the
+row of the symmetry matrix ok any
+
+ align:start position:0%
+row of the symmetry matrix ok any
+ 
+
+ align:start position:0%
+row of the symmetry matrix ok any
+questions ok so now we have defined a
+
+ align:start position:0%
+questions ok so now we have defined a
+ 
+
+ align:start position:0%
+questions ok so now we have defined a
+symmetry matrix and though then you can
+
+ align:start position:0%
+symmetry matrix and though then you can
+ 
+
+ align:start position:0%
+symmetry matrix and though then you can
+ask why do we as you care and why do we
+
+ align:start position:0%
+ask why do we as you care and why do we
+ 
+
+ align:start position:0%
+ask why do we as you care and why do we
+actually introduce symmetry matrix right
+
+ align:start position:0%
+actually introduce symmetry matrix right
+ 
+
+ align:start position:0%
+actually introduce symmetry matrix right
+because I can always write down the X
+
+ align:start position:0%
+because I can always write down the X
+ 
+
+ align:start position:0%
+because I can always write down the X
+tilde in that way that is because I
+
+ align:start position:0%
+tilde in that way that is because I
+ 
+
+ align:start position:0%
+tilde in that way that is because I
+think by the end of this lecture you
+
+ align:start position:0%
+think by the end of this lecture you
+ 
+
+ align:start position:0%
+think by the end of this lecture you
+you'll find that if s matrix describe
+
+ align:start position:0%
+you'll find that if s matrix describe
+ 
+
+ align:start position:0%
+you'll find that if s matrix describe
+the symmetry of the system ok
+
+ align:start position:0%
+the symmetry of the system ok
+ 
+
+ align:start position:0%
+the symmetry of the system ok
+that will mean as matrix will come mute
+
+ align:start position:0%
+that will mean as matrix will come mute
+ 
+
+ align:start position:0%
+that will mean as matrix will come mute
+with ms1 key metrics which you don't
+
+ align:start position:0%
+with ms1 key metrics which you don't
+ 
+
+ align:start position:0%
+with ms1 key metrics which you don't
+know commute yet but I will introduce
+
+ align:start position:0%
+know commute yet but I will introduce
+ 
+
+ align:start position:0%
+know commute yet but I will introduce
+you that means n minus 1 K metric and s
+
+ align:start position:0%
+you that means n minus 1 K metric and s
+ 
+
+ align:start position:0%
+you that means n minus 1 K metric and s
+can actually swap Freedy okay if that
+
+ align:start position:0%
+can actually swap Freedy okay if that
+ 
+
+ align:start position:0%
+can actually swap Freedy okay if that
+happens then s matrix will share the
+
+ align:start position:0%
+happens then s matrix will share the
+ 
+
+ align:start position:0%
+happens then s matrix will share the
+same sets of eigenvectors
+
+ align:start position:0%
+same sets of eigenvectors
+ 
+
+ align:start position:0%
+same sets of eigenvectors
+as the N minus 1 K metrics what does
+
+ align:start position:0%
+as the N minus 1 K metrics what does
+ 
+
+ align:start position:0%
+as the N minus 1 K metrics what does
+that mean that means okay before we're
+
+ align:start position:0%
+that mean that means okay before we're
+ 
+
+ align:start position:0%
+that mean that means okay before we're
+doing this solution right we are solving
+
+ align:start position:0%
+doing this solution right we are solving
+ 
+
+ align:start position:0%
+doing this solution right we are solving
+n minus 1 K matrix eigen value problem
+
+ align:start position:0%
+n minus 1 K matrix eigen value problem
+ 
+
+ align:start position:0%
+n minus 1 K matrix eigen value problem
+right and then we get an eigen vector
+
+ align:start position:0%
+right and then we get an eigen vector
+ 
+
+ align:start position:0%
+right and then we get an eigen vector
+which is the amplitude ratio of normal
+
+ align:start position:0%
+which is the amplitude ratio of normal
+ 
+
+ align:start position:0%
+which is the amplitude ratio of normal
+modes and that means you have an
+
+ align:start position:0%
+modes and that means you have an
+ 
+
+ align:start position:0%
+modes and that means you have an
+alternative way to get the normal mode
+
+ align:start position:0%
+alternative way to get the normal mode
+ 
+
+ align:start position:0%
+alternative way to get the normal mode
+you can solve the eigen value problem of
+
+ align:start position:0%
+you can solve the eigen value problem of
+ 
+
+ align:start position:0%
+you can solve the eigen value problem of
+asthmatics
+
+ align:start position:0%
+asthmatics
+ 
+
+ align:start position:0%
+asthmatics
+then you can get the same set of
+
+ align:start position:0%
+then you can get the same set of
+ 
+
+ align:start position:0%
+then you can get the same set of
+amplitude ratios as M minus 1 made ok
+
+ align:start position:0%
+amplitude ratios as M minus 1 made ok
+ 
+
+ align:start position:0%
+amplitude ratios as M minus 1 made ok
+matrix eigenvalue problem okay and that
+
+ align:start position:0%
+matrix eigenvalue problem okay and that
+ 
+
+ align:start position:0%
+matrix eigenvalue problem okay and that
+usually the eigenvalue problem of s
+
+ align:start position:0%
+usually the eigenvalue problem of s
+ 
+
+ align:start position:0%
+usually the eigenvalue problem of s
+matrix it's far much easier than n minus
+
+ align:start position:0%
+matrix it's far much easier than n minus
+ 
+
+ align:start position:0%
+matrix it's far much easier than n minus
+1 K matrix ok so that's actually why we
+
+ align:start position:0%
+1 K matrix ok so that's actually why we
+ 
+
+ align:start position:0%
+1 K matrix ok so that's actually why we
+are doing this ok so now I would like to
+
+ align:start position:0%
+are doing this ok so now I would like to
+ 
+
+ align:start position:0%
+are doing this ok so now I would like to
+convince you that s matrix and M minus 1
+
+ align:start position:0%
+convince you that s matrix and M minus 1
+ 
+
+ align:start position:0%
+convince you that s matrix and M minus 1
+K matrix will share I come back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's go ahead and prove this or
+
+ align:start position:0%
+okay so let's go ahead and prove this or
+ 
+
+ align:start position:0%
+okay so let's go ahead and prove this or
+demonstrate this idea okay so the
+
+ align:start position:0%
+demonstrate this idea okay so the
+ 
+
+ align:start position:0%
+demonstrate this idea okay so the
+original equation motion looks like this
+
+ align:start position:0%
+original equation motion looks like this
+ 
+
+ align:start position:0%
+original equation motion looks like this
+X double dot okay equal to n minus 1 K X
+
+ align:start position:0%
+X double dot okay equal to n minus 1 K X
+ 
+
+ align:start position:0%
+X double dot okay equal to n minus 1 K X
+right so that is actually the original
+
+ align:start position:0%
+right so that is actually the original
+ 
+
+ align:start position:0%
+right so that is actually the original
+equation of motion okay and if this
+
+ align:start position:0%
+equation of motion okay and if this
+ 
+
+ align:start position:0%
+equation of motion okay and if this
+system satisfy the refraction symmetry
+
+ align:start position:0%
+system satisfy the refraction symmetry
+ 
+
+ align:start position:0%
+system satisfy the refraction symmetry
+that means X tilde is also a solution
+
+ align:start position:0%
+that means X tilde is also a solution
+ 
+
+ align:start position:0%
+that means X tilde is also a solution
+right therefore what does that mean that
+
+ align:start position:0%
+right therefore what does that mean that
+ 
+
+ align:start position:0%
+right therefore what does that mean that
+means X tilde power dot will be also
+
+ align:start position:0%
+means X tilde power dot will be also
+ 
+
+ align:start position:0%
+means X tilde power dot will be also
+equal to M s 1 K X because it's also a
+
+ align:start position:0%
+equal to M s 1 K X because it's also a
+ 
+
+ align:start position:0%
+equal to M s 1 K X because it's also a
+solution to the equation of motion right
+
+ align:start position:0%
+solution to the equation of motion right
+ 
+
+ align:start position:0%
+solution to the equation of motion right
+that's a pretty nature okay now I can
+
+ align:start position:0%
+that's a pretty nature okay now I can
+ 
+
+ align:start position:0%
+that's a pretty nature okay now I can
+actually use this expression X tilde is
+
+ align:start position:0%
+actually use this expression X tilde is
+ 
+
+ align:start position:0%
+actually use this expression X tilde is
+equal to s times X right those things
+
+ align:start position:0%
+equal to s times X right those things
+ 
+
+ align:start position:0%
+equal to s times X right those things
+are metrics okay just to be careful okay
+
+ align:start position:0%
+are metrics okay just to be careful okay
+ 
+
+ align:start position:0%
+are metrics okay just to be careful okay
+that means I can write this like this s
+
+ align:start position:0%
+that means I can write this like this s
+ 
+
+ align:start position:0%
+that means I can write this like this s
+X double dot equal to n minus 1 K s ok
+
+ align:start position:0%
+X double dot equal to n minus 1 K s ok
+ 
+
+ align:start position:0%
+X double dot equal to n minus 1 K s ok
+there's no matrix I can also replace I'm
+
+ align:start position:0%
+there's no matrix I can also replace I'm
+ 
+
+ align:start position:0%
+there's no matrix I can also replace I'm
+just replacing X tilde by SX ok
+
+ align:start position:0%
+just replacing X tilde by SX ok
+ 
+
+ align:start position:0%
+just replacing X tilde by SX ok
+and also I call this su one I call this
+
+ align:start position:0%
+and also I call this su one I call this
+ 
+
+ align:start position:0%
+and also I call this su one I call this
+as u - ok I can multiply X from the left
+
+ align:start position:0%
+as u - ok I can multiply X from the left
+ 
+
+ align:start position:0%
+as u - ok I can multiply X from the left
+hand side of one okay and see what will
+
+ align:start position:0%
+hand side of one okay and see what will
+ 
+
+ align:start position:0%
+hand side of one okay and see what will
+happen so if I do that then what I am
+
+ align:start position:0%
+happen so if I do that then what I am
+ 
+
+ align:start position:0%
+happen so if I do that then what I am
+going to get is s X double dot ok that
+
+ align:start position:0%
+going to get is s X double dot ok that
+ 
+
+ align:start position:0%
+going to get is s X double dot ok that
+would be equal to s n minus 1 K X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay if you compare this equation and
+
+ align:start position:0%
+okay if you compare this equation and
+ 
+
+ align:start position:0%
+okay if you compare this equation and
+the equation number three this two
+
+ align:start position:0%
+the equation number three this two
+ 
+
+ align:start position:0%
+the equation number three this two
+equation you will see that lap inside is
+
+ align:start position:0%
+equation you will see that lap inside is
+ 
+
+ align:start position:0%
+equation you will see that lap inside is
+the same right right hand side huh
+
+ align:start position:0%
+the same right right hand side huh
+ 
+
+ align:start position:0%
+the same right right hand side huh
+something interesting is happening
+
+ align:start position:0%
+something interesting is happening
+ 
+
+ align:start position:0%
+something interesting is happening
+Emmons 1k s must be equal to s and minus
+
+ align:start position:0%
+Emmons 1k s must be equal to s and minus
+ 
+
+ align:start position:0%
+Emmons 1k s must be equal to s and minus
+one tape right what does that mean this
+
+ align:start position:0%
+one tape right what does that mean this
+ 
+
+ align:start position:0%
+one tape right what does that mean this
+means that they understand a minus 1 K s
+
+ align:start position:0%
+means that they understand a minus 1 K s
+ 
+
+ align:start position:0%
+means that they understand a minus 1 K s
+is equal to s M minus 1 K so if I say
+
+ align:start position:0%
+is equal to s M minus 1 K so if I say
+ 
+
+ align:start position:0%
+is equal to s M minus 1 K so if I say
+this system satisfies a symmetry it is
+
+ align:start position:0%
+this system satisfies a symmetry it is
+ 
+
+ align:start position:0%
+this system satisfies a symmetry it is
+quite 5s metrics that means X tilde
+
+ align:start position:0%
+quite 5s metrics that means X tilde
+ 
+
+ align:start position:0%
+quite 5s metrics that means X tilde
+which essentially the transformed
+
+ align:start position:0%
+which essentially the transformed
+ 
+
+ align:start position:0%
+which essentially the transformed
+amplitude will be also a solution to the
+
+ align:start position:0%
+amplitude will be also a solution to the
+ 
+
+ align:start position:0%
+amplitude will be also a solution to the
+equation of motion and therefore an
+
+ align:start position:0%
+equation of motion and therefore an
+ 
+
+ align:start position:0%
+equation of motion and therefore an
+inevitable consequence is that M minus 1
+
+ align:start position:0%
+inevitable consequence is that M minus 1
+ 
+
+ align:start position:0%
+inevitable consequence is that M minus 1
+K s will be equal to s ms 1k usually
+
+ align:start position:0%
+K s will be equal to s ms 1k usually
+ 
+
+ align:start position:0%
+K s will be equal to s ms 1k usually
+when you start the physics we write this
+
+ align:start position:0%
+when you start the physics we write this
+ 
+
+ align:start position:0%
+when you start the physics we write this
+in terms of communicator okay so we call
+
+ align:start position:0%
+in terms of communicator okay so we call
+ 
+
+ align:start position:0%
+in terms of communicator okay so we call
+this as these two things as you commute
+
+ align:start position:0%
+this as these two things as you commute
+ 
+
+ align:start position:0%
+this as these two things as you commute
+okay so communicator is actually defined
+
+ align:start position:0%
+okay so communicator is actually defined
+ 
+
+ align:start position:0%
+okay so communicator is actually defined
+as a bracket of a and B this is a should
+
+ align:start position:0%
+as a bracket of a and B this is a should
+ 
+
+ align:start position:0%
+as a bracket of a and B this is a should
+equal defined us ap minus VA okay if if
+
+ align:start position:0%
+equal defined us ap minus VA okay if if
+ 
+
+ align:start position:0%
+equal defined us ap minus VA okay if if
+a and the P commute okay it's just new
+
+ align:start position:0%
+a and the P commute okay it's just new
+ 
+
+ align:start position:0%
+a and the P commute okay it's just new
+word probably for most of you if they
+
+ align:start position:0%
+word probably for most of you if they
+ 
+
+ align:start position:0%
+word probably for most of you if they
+can mute that means a see in the bracket
+
+ align:start position:0%
+can mute that means a see in the bracket
+ 
+
+ align:start position:0%
+can mute that means a see in the bracket
+is equal to 0 okay so this expression I
+
+ align:start position:0%
+is equal to 0 okay so this expression I
+ 
+
+ align:start position:0%
+is equal to 0 okay so this expression I
+can actually write it down like this
+
+ align:start position:0%
+can actually write it down like this
+ 
+
+ align:start position:0%
+can actually write it down like this
+commutator of s M minus 1 K that is
+
+ align:start position:0%
+commutator of s M minus 1 K that is
+ 
+
+ align:start position:0%
+commutator of s M minus 1 K that is
+equal to 0 and you will see this really
+
+ align:start position:0%
+equal to 0 and you will see this really
+ 
+
+ align:start position:0%
+equal to 0 and you will see this really
+a lot when you study quantum physics
+
+ align:start position:0%
+a lot when you study quantum physics
+ 
+
+ align:start position:0%
+a lot when you study quantum physics
+okay so I hope this I should give you
+
+ align:start position:0%
+okay so I hope this I should give you
+ 
+
+ align:start position:0%
+okay so I hope this I should give you
+some flavor about commutator okay so now
+
+ align:start position:0%
+some flavor about commutator okay so now
+ 
+
+ align:start position:0%
+some flavor about commutator okay so now
+that's actually pretty nice
+
+ align:start position:0%
+that's actually pretty nice
+ 
+
+ align:start position:0%
+that's actually pretty nice
+this means that like commute okay if I
+
+ align:start position:0%
+this means that like commute okay if I
+ 
+
+ align:start position:0%
+this means that like commute okay if I
+take X of T this is equal to a 1 cosine
+
+ align:start position:0%
+take X of T this is equal to a 1 cosine
+ 
+
+ align:start position:0%
+take X of T this is equal to a 1 cosine
+Omega 1 okay so this means that a is
+
+ align:start position:0%
+Omega 1 okay so this means that a is
+ 
+
+ align:start position:0%
+Omega 1 okay so this means that a is
+actually in sorry X is actually a
+
+ align:start position:0%
+actually in sorry X is actually a
+ 
+
+ align:start position:0%
+actually in sorry X is actually a
+solution which is a normal mode a
+
+ align:start position:0%
+solution which is a normal mode a
+ 
+
+ align:start position:0%
+solution which is a normal mode a
+solution right and a is actually
+
+ align:start position:0%
+solution right and a is actually
+ 
+
+ align:start position:0%
+solution right and a is actually
+amplitude the vector the the amplitude
+
+ align:start position:0%
+amplitude the vector the the amplitude
+ 
+
+ align:start position:0%
+amplitude the vector the the amplitude
+factor over the first normal mode and
+
+ align:start position:0%
+factor over the first normal mode and
+ 
+
+ align:start position:0%
+factor over the first normal mode and
+Omega 1 is actually the first normal
+
+ align:start position:0%
+Omega 1 is actually the first normal
+ 
+
+ align:start position:0%
+Omega 1 is actually the first normal
+frequency okay if this is the case okay
+
+ align:start position:0%
+frequency okay if this is the case okay
+ 
+
+ align:start position:0%
+frequency okay if this is the case okay
+then I will have X tilde of T will be
+
+ align:start position:0%
+then I will have X tilde of T will be
+ 
+
+ align:start position:0%
+then I will have X tilde of T will be
+also proportional to a 1 cosine Omega 1t
+
+ align:start position:0%
+also proportional to a 1 cosine Omega 1t
+ 
+
+ align:start position:0%
+also proportional to a 1 cosine Omega 1t
+right because if I actually exchange x1
+
+ align:start position:0%
+right because if I actually exchange x1
+ 
+
+ align:start position:0%
+right because if I actually exchange x1
+x2 their answer that same frequency is
+
+ align:start position:0%
+x2 their answer that same frequency is
+ 
+
+ align:start position:0%
+x2 their answer that same frequency is
+not going to change right therefore
+
+ align:start position:0%
+not going to change right therefore
+ 
+
+ align:start position:0%
+not going to change right therefore
+since this system is in the same normal
+
+ align:start position:0%
+since this system is in the same normal
+ 
+
+ align:start position:0%
+since this system is in the same normal
+mode with angular frequency Omega 1
+
+ align:start position:0%
+mode with angular frequency Omega 1
+ 
+
+ align:start position:0%
+mode with angular frequency Omega 1
+therefore the amplitude ratio of the
+
+ align:start position:0%
+therefore the amplitude ratio of the
+ 
+
+ align:start position:0%
+therefore the amplitude ratio of the
+first and second oscillator will stay
+
+ align:start position:0%
+first and second oscillator will stay
+ 
+
+ align:start position:0%
+first and second oscillator will stay
+constant right because you are in one of
+
+ align:start position:0%
+constant right because you are in one of
+ 
+
+ align:start position:0%
+constant right because you are in one of
+the normal mode right therefore I can
+
+ align:start position:0%
+the normal mode right therefore I can
+ 
+
+ align:start position:0%
+the normal mode right therefore I can
+conclude that X tilde it's going to be
+
+ align:start position:0%
+conclude that X tilde it's going to be
+ 
+
+ align:start position:0%
+conclude that X tilde it's going to be
+proportional to this expression because
+
+ align:start position:0%
+proportional to this expression because
+ 
+
+ align:start position:0%
+proportional to this expression because
+they are innocent normal mode
+
+ align:start position:0%
+they are innocent normal mode
+ 
+
+ align:start position:0%
+they are innocent normal mode
+oscillating at the same frequency okay
+
+ align:start position:0%
+oscillating at the same frequency okay
+ 
+
+ align:start position:0%
+oscillating at the same frequency okay
+is that too fast everybody is following
+
+ align:start position:0%
+is that too fast everybody is following
+ 
+
+ align:start position:0%
+is that too fast everybody is following
+ok so that's nice
+
+ align:start position:0%
+ok so that's nice
+ 
+
+ align:start position:0%
+ok so that's nice
+so this means that SX
+
+ align:start position:0%
+so this means that SX
+ 
+
+ align:start position:0%
+so this means that SX
+teehee okay will be equal to s a1 cosine
+
+ align:start position:0%
+teehee okay will be equal to s a1 cosine
+ 
+
+ align:start position:0%
+teehee okay will be equal to s a1 cosine
+Omega 1 P okay so this is actually
+
+ align:start position:0%
+Omega 1 P okay so this is actually
+ 
+
+ align:start position:0%
+Omega 1 P okay so this is actually
+coming from here right I am repressing
+
+ align:start position:0%
+coming from here right I am repressing
+ 
+
+ align:start position:0%
+coming from here right I am repressing
+so I am decreasing X tilde is X based on
+
+ align:start position:0%
+so I am decreasing X tilde is X based on
+ 
+
+ align:start position:0%
+so I am decreasing X tilde is X based on
+this definition okay
+
+ align:start position:0%
+this definition okay
+ 
+
+ align:start position:0%
+this definition okay
+then again I'd replace I write X
+
+ align:start position:0%
+then again I'd replace I write X
+ 
+
+ align:start position:0%
+then again I'd replace I write X
+explicitly which is 1/8 cosine Omega 1t
+
+ align:start position:0%
+explicitly which is 1/8 cosine Omega 1t
+ 
+
+ align:start position:0%
+explicitly which is 1/8 cosine Omega 1t
+okay then you get this expression and
+
+ align:start position:0%
+okay then you get this expression and
+ 
+
+ align:start position:0%
+okay then you get this expression and
+from this above the expression above you
+
+ align:start position:0%
+from this above the expression above you
+ 
+
+ align:start position:0%
+from this above the expression above you
+see that we will conclude that this is
+
+ align:start position:0%
+see that we will conclude that this is
+ 
+
+ align:start position:0%
+see that we will conclude that this is
+proportional to a1 cosine Omega 1t
+
+ align:start position:0%
+proportional to a1 cosine Omega 1t
+ 
+
+ align:start position:0%
+proportional to a1 cosine Omega 1t
+that's very nice that means s a cosine
+
+ align:start position:0%
+that's very nice that means s a cosine
+ 
+
+ align:start position:0%
+that's very nice that means s a cosine
+Omega 1 T is proportional to a1 cosine
+
+ align:start position:0%
+Omega 1 T is proportional to a1 cosine
+ 
+
+ align:start position:0%
+Omega 1 T is proportional to a1 cosine
+Omega P and you can actually I cancel
+
+ align:start position:0%
+Omega P and you can actually I cancel
+ 
+
+ align:start position:0%
+Omega P and you can actually I cancel
+this now you see that as a 1 is
+
+ align:start position:0%
+this now you see that as a 1 is
+ 
+
+ align:start position:0%
+this now you see that as a 1 is
+proportional to a 1 or I can write it as
+
+ align:start position:0%
+proportional to a 1 or I can write it as
+ 
+
+ align:start position:0%
+proportional to a 1 or I can write it as
+as a 1 is equal to theta what does that
+
+ align:start position:0%
+as a 1 is equal to theta what does that
+ 
+
+ align:start position:0%
+as a 1 is equal to theta what does that
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+this means that a 1 okay originally what
+
+ align:start position:0%
+this means that a 1 okay originally what
+ 
+
+ align:start position:0%
+this means that a 1 okay originally what
+with a one coming from a 1 is the
+
+ align:start position:0%
+with a one coming from a 1 is the
+ 
+
+ align:start position:0%
+with a one coming from a 1 is the
+amplitude of all the components in the
+
+ align:start position:0%
+amplitude of all the components in the
+ 
+
+ align:start position:0%
+amplitude of all the components in the
+first normal mode right that's coming
+
+ align:start position:0%
+first normal mode right that's coming
+ 
+
+ align:start position:0%
+first normal mode right that's coming
+from the eigenvalue problem which we
+
+ align:start position:0%
+from the eigenvalue problem which we
+ 
+
+ align:start position:0%
+from the eigenvalue problem which we
+actually does in this slide I can value
+
+ align:start position:0%
+actually does in this slide I can value
+ 
+
+ align:start position:0%
+actually does in this slide I can value
+problem MS 1 ka equal to Omega square a
+
+ align:start position:0%
+problem MS 1 ka equal to Omega square a
+ 
+
+ align:start position:0%
+problem MS 1 ka equal to Omega square a
+will give you the solution of normal
+
+ align:start position:0%
+will give you the solution of normal
+ 
+
+ align:start position:0%
+will give you the solution of normal
+mode and there are vectors which is an
+
+ align:start position:0%
+mode and there are vectors which is an
+ 
+
+ align:start position:0%
+mode and there are vectors which is an
+amplitude ratios of all the components
+
+ align:start position:0%
+amplitude ratios of all the components
+ 
+
+ align:start position:0%
+amplitude ratios of all the components
+in the system right so that means a1 is
+
+ align:start position:0%
+in the system right so that means a1 is
+ 
+
+ align:start position:0%
+in the system right so that means a1 is
+not only n minus 1 K matrix eigen
+
+ align:start position:0%
+not only n minus 1 K matrix eigen
+ 
+
+ align:start position:0%
+not only n minus 1 K matrix eigen
+vectors it's also eigen vector of s
+
+ align:start position:0%
+vectors it's also eigen vector of s
+ 
+
+ align:start position:0%
+vectors it's also eigen vector of s
+matrix ok
+
+ align:start position:0%
+matrix ok
+ 
+
+ align:start position:0%
+matrix ok
+so that is actually a very good news and
+
+ align:start position:0%
+so that is actually a very good news and
+ 
+
+ align:start position:0%
+so that is actually a very good news and
+I can also do the same thing for a tool
+
+ align:start position:0%
+I can also do the same thing for a tool
+ 
+
+ align:start position:0%
+I can also do the same thing for a tool
+to prove that it also worked for a to
+
+ align:start position:0%
+to prove that it also worked for a to
+ 
+
+ align:start position:0%
+to prove that it also worked for a to
+activation is identical so I am NOT
+
+ align:start position:0%
+activation is identical so I am NOT
+ 
+
+ align:start position:0%
+activation is identical so I am NOT
+going to do that again so that means
+
+ align:start position:0%
+going to do that again so that means
+ 
+
+ align:start position:0%
+going to do that again so that means
+actually starting from starting from
+
+ align:start position:0%
+actually starting from starting from
+ 
+
+ align:start position:0%
+actually starting from starting from
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+if X and X tilde oppose solution to the
+
+ align:start position:0%
+if X and X tilde oppose solution to the
+ 
+
+ align:start position:0%
+if X and X tilde oppose solution to the
+equation motion okay I will conclude
+
+ align:start position:0%
+equation motion okay I will conclude
+ 
+
+ align:start position:0%
+equation motion okay I will conclude
+that as matrix and the N minus 1 K
+
+ align:start position:0%
+that as matrix and the N minus 1 K
+ 
+
+ align:start position:0%
+that as matrix and the N minus 1 K
+matrix they commute
+
+ align:start position:0%
+matrix they commute
+ 
+
+ align:start position:0%
+matrix they commute
+okay to how to tell if assistance
+
+ align:start position:0%
+okay to how to tell if assistance
+ 
+
+ align:start position:0%
+okay to how to tell if assistance
+satisfy a specific symmetry defined by
+
+ align:start position:0%
+satisfy a specific symmetry defined by
+ 
+
+ align:start position:0%
+satisfy a specific symmetry defined by
+my symmetry metrics in spite this way
+
+ align:start position:0%
+my symmetry metrics in spite this way
+ 
+
+ align:start position:0%
+my symmetry metrics in spite this way
+you can check if M is 1 K and the S
+
+ align:start position:0%
+you can check if M is 1 K and the S
+ 
+
+ align:start position:0%
+you can check if M is 1 K and the S
+commute if they commute that means this
+
+ align:start position:0%
+commute if they commute that means this
+ 
+
+ align:start position:0%
+commute if they commute that means this
+system actually satisfy this symmetry
+
+ align:start position:0%
+system actually satisfy this symmetry
+ 
+
+ align:start position:0%
+system actually satisfy this symmetry
+and also the consequence is that from
+
+ align:start position:0%
+and also the consequence is that from
+ 
+
+ align:start position:0%
+and also the consequence is that from
+there you can clue that if you have so
+
+ align:start position:0%
+there you can clue that if you have so
+ 
+
+ align:start position:0%
+there you can clue that if you have so
+will have a set of eigen vectors from M
+
+ align:start position:0%
+will have a set of eigen vectors from M
+ 
+
+ align:start position:0%
+will have a set of eigen vectors from M
+s 1 K matrix eigen value problem and
+
+ align:start position:0%
+s 1 K matrix eigen value problem and
+ 
+
+ align:start position:0%
+s 1 K matrix eigen value problem and
+that is going to be also the eigenvector
+
+ align:start position:0%
+that is going to be also the eigenvector
+ 
+
+ align:start position:0%
+that is going to be also the eigenvector
+of s okay any questions okay so M minus
+
+ align:start position:0%
+of s okay any questions okay so M minus
+ 
+
+ align:start position:0%
+of s okay any questions okay so M minus
+1 K eigen vectors ah also s I come back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's actually what we have
+
+ align:start position:0%
+okay that's actually what we have
+ 
+
+ align:start position:0%
+okay that's actually what we have
+learned from this small exercise now you
+
+ align:start position:0%
+learned from this small exercise now you
+ 
+
+ align:start position:0%
+learned from this small exercise now you
+can say wait wait this is actually now
+
+ align:start position:0%
+can say wait wait this is actually now
+ 
+
+ align:start position:0%
+can say wait wait this is actually now
+we would need right
+
+ align:start position:0%
+we would need right
+ 
+
+ align:start position:0%
+we would need right
+I would like we would like to argue that
+
+ align:start position:0%
+I would like we would like to argue that
+ 
+
+ align:start position:0%
+I would like we would like to argue that
+s matrix I can stop s matrix eigenvalue
+
+ align:start position:0%
+s matrix I can stop s matrix eigenvalue
+ 
+
+ align:start position:0%
+s matrix I can stop s matrix eigenvalue
+problem then I can learn about a
+
+ align:start position:0%
+problem then I can learn about a
+ 
+
+ align:start position:0%
+problem then I can learn about a
+solution of n minus 1 K matrix by this
+
+ align:start position:0%
+solution of n minus 1 K matrix by this
+ 
+
+ align:start position:0%
+solution of n minus 1 K matrix by this
+logic essentially in the opposite
+
+ align:start position:0%
+logic essentially in the opposite
+ 
+
+ align:start position:0%
+logic essentially in the opposite
+direction right you said okay you solve
+
+ align:start position:0%
+direction right you said okay you solve
+ 
+
+ align:start position:0%
+direction right you said okay you solve
+things already then actually is also s
+
+ align:start position:0%
+things already then actually is also s
+ 
+
+ align:start position:0%
+things already then actually is also s
+matrix eigenvalue problem so now what
+
+ align:start position:0%
+matrix eigenvalue problem so now what
+ 
+
+ align:start position:0%
+matrix eigenvalue problem so now what
+I'm going to do is to reverse the logic
+
+ align:start position:0%
+I'm going to do is to reverse the logic
+ 
+
+ align:start position:0%
+I'm going to do is to reverse the logic
+and see if it works okay again to see
+
+ align:start position:0%
+and see if it works okay again to see
+ 
+
+ align:start position:0%
+and see if it works okay again to see
+what will happen
+
+ align:start position:0%
+what will happen
+ 
+
+ align:start position:0%
+what will happen
+okay so now I would like to prove that
+
+ align:start position:0%
+okay so now I would like to prove that
+ 
+
+ align:start position:0%
+okay so now I would like to prove that
+if I saw s matrix eigenvalue problem
+
+ align:start position:0%
+if I saw s matrix eigenvalue problem
+ 
+
+ align:start position:0%
+if I saw s matrix eigenvalue problem
+i have also solved the eigenvectors for
+
+ align:start position:0%
+i have also solved the eigenvectors for
+ 
+
+ align:start position:0%
+i have also solved the eigenvectors for
+msy Hemet run the logic in the opposite
+
+ align:start position:0%
+msy Hemet run the logic in the opposite
+ 
+
+ align:start position:0%
+msy Hemet run the logic in the opposite
+direction okay so if i really v'n two
+
+ align:start position:0%
+direction okay so if i really v'n two
+ 
+
+ align:start position:0%
+direction okay so if i really v'n two
+things one s a is equal to beta a number
+
+ align:start position:0%
+things one s a is equal to beta a number
+ 
+
+ align:start position:0%
+things one s a is equal to beta a number
+two s matrix and the M minus 1 K matrix
+
+ align:start position:0%
+two s matrix and the M minus 1 K matrix
+ 
+
+ align:start position:0%
+two s matrix and the M minus 1 K matrix
+commute okay if those are like even
+
+ align:start position:0%
+commute okay if those are like even
+ 
+
+ align:start position:0%
+commute okay if those are like even
+conditions okay then I can as we
+
+ align:start position:0%
+conditions okay then I can as we
+ 
+
+ align:start position:0%
+conditions okay then I can as we
+conclude that s M minus 1 K hey okay I
+
+ align:start position:0%
+conclude that s M minus 1 K hey okay I
+ 
+
+ align:start position:0%
+conclude that s M minus 1 K hey okay I
+can as you construct this expression I
+
+ align:start position:0%
+can as you construct this expression I
+ 
+
+ align:start position:0%
+can as you construct this expression I
+write down s n minus 1 K a ok because
+
+ align:start position:0%
+write down s n minus 1 K a ok because
+ 
+
+ align:start position:0%
+write down s n minus 1 K a ok because
+they commute right they can expect in a
+
+ align:start position:0%
+they commute right they can expect in a
+ 
+
+ align:start position:0%
+they commute right they can expect in a
+to swap em s 1 K and as safely without
+
+ align:start position:0%
+to swap em s 1 K and as safely without
+ 
+
+ align:start position:0%
+to swap em s 1 K and as safely without
+actually introducing any more turns and
+
+ align:start position:0%
+actually introducing any more turns and
+ 
+
+ align:start position:0%
+actually introducing any more turns and
+this will be equal to n minus 1 K s a ok
+
+ align:start position:0%
+this will be equal to n minus 1 K s a ok
+ 
+
+ align:start position:0%
+this will be equal to n minus 1 K s a ok
+and s a from the first expression as n
+
+ align:start position:0%
+and s a from the first expression as n
+ 
+
+ align:start position:0%
+and s a from the first expression as n
+is equal to Beta Beta is a number okay
+
+ align:start position:0%
+is equal to Beta Beta is a number okay
+ 
+
+ align:start position:0%
+is equal to Beta Beta is a number okay
+therefore this expression will become
+
+ align:start position:0%
+therefore this expression will become
+ 
+
+ align:start position:0%
+therefore this expression will become
+beta n minus 1 K a so beta can penetrate
+
+ align:start position:0%
+beta n minus 1 K a so beta can penetrate
+ 
+
+ align:start position:0%
+beta n minus 1 K a so beta can penetrate
+su matrix because beta is just a number
+
+ align:start position:0%
+su matrix because beta is just a number
+ 
+
+ align:start position:0%
+su matrix because beta is just a number
+is the eigenvalue it's an eigenvalue or
+
+ align:start position:0%
+is the eigenvalue it's an eigenvalue or
+ 
+
+ align:start position:0%
+is the eigenvalue it's an eigenvalue or
+s matrix okay so what does this mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so so what does it mean
+
+ align:start position:0%
+okay so so so what does it mean
+ 
+
+ align:start position:0%
+okay so so so what does it mean
+so this means that if you look at this
+
+ align:start position:0%
+so this means that if you look at this
+ 
+
+ align:start position:0%
+so this means that if you look at this
+this part and that part you look at the
+
+ align:start position:0%
+this part and that part you look at the
+ 
+
+ align:start position:0%
+this part and that part you look at the
+beginning and at the end of the
+
+ align:start position:0%
+beginning and at the end of the
+ 
+
+ align:start position:0%
+beginning and at the end of the
+expression you immediately conclude that
+
+ align:start position:0%
+expression you immediately conclude that
+ 
+
+ align:start position:0%
+expression you immediately conclude that
+n minus 1 K a ok this expression is also
+
+ align:start position:0%
+n minus 1 K a ok this expression is also
+ 
+
+ align:start position:0%
+n minus 1 K a ok this expression is also
+an eigenvector of s matrix right so you
+
+ align:start position:0%
+an eigenvector of s matrix right so you
+ 
+
+ align:start position:0%
+an eigenvector of s matrix right so you
+have s matrix acting n minus 1 T a and
+
+ align:start position:0%
+have s matrix acting n minus 1 T a and
+ 
+
+ align:start position:0%
+have s matrix acting n minus 1 T a and
+that will give you something
+
+ align:start position:0%
+that will give you something
+ 
+
+ align:start position:0%
+that will give you something
+proportional to n minus 1 K a you see
+
+ align:start position:0%
+proportional to n minus 1 K a you see
+ 
+
+ align:start position:0%
+proportional to n minus 1 K a you see
+it's a metric right it's actually not
+
+ align:start position:0%
+it's a metric right it's actually not
+ 
+
+ align:start position:0%
+it's a metric right it's actually not
+magic but it says she's just you know
+
+ align:start position:0%
+magic but it says she's just you know
+ 
+
+ align:start position:0%
+magic but it says she's just you know
+already a logical extension right okay
+
+ align:start position:0%
+already a logical extension right okay
+ 
+
+ align:start position:0%
+already a logical extension right okay
+well cool so that means this is also an
+
+ align:start position:0%
+well cool so that means this is also an
+ 
+
+ align:start position:0%
+well cool so that means this is also an
+eigenvector OS right and also another
+
+ align:start position:0%
+eigenvector OS right and also another
+ 
+
+ align:start position:0%
+eigenvector OS right and also another
+thing which is interesting is that they
+
+ align:start position:0%
+thing which is interesting is that they
+ 
+
+ align:start position:0%
+thing which is interesting is that they
+share the same I come back I can value
+
+ align:start position:0%
+share the same I come back I can value
+ 
+
+ align:start position:0%
+share the same I come back I can value
+beta right listen I can value right okay
+
+ align:start position:0%
+beta right listen I can value right okay
+ 
+
+ align:start position:0%
+beta right listen I can value right okay
+so if I can values of s so you can get
+
+ align:start position:0%
+so if I can values of s so you can get
+ 
+
+ align:start position:0%
+so if I can values of s so you can get
+several I can value right in this case
+
+ align:start position:0%
+several I can value right in this case
+ 
+
+ align:start position:0%
+several I can value right in this case
+two by two matrix you will get how many
+
+ align:start position:0%
+two by two matrix you will get how many
+ 
+
+ align:start position:0%
+two by two matrix you will get how many
+to write to eigen values if those two
+
+ align:start position:0%
+to write to eigen values if those two
+ 
+
+ align:start position:0%
+to write to eigen values if those two
+eigen values are different then I can
+
+ align:start position:0%
+eigen values are different then I can
+ 
+
+ align:start position:0%
+eigen values are different then I can
+conclude that n minus 1 K a okay must be
+
+ align:start position:0%
+conclude that n minus 1 K a okay must be
+ 
+
+ align:start position:0%
+conclude that n minus 1 K a okay must be
+proportional to a right because though
+
+ align:start position:0%
+proportional to a right because though
+ 
+
+ align:start position:0%
+proportional to a right because though
+because this is actually the same eigen
+
+ align:start position:0%
+because this is actually the same eigen
+ 
+
+ align:start position:0%
+because this is actually the same eigen
+value problem and listen I can well do
+
+ align:start position:0%
+value problem and listen I can well do
+ 
+
+ align:start position:0%
+value problem and listen I can well do
+beta since all the eigen values from the
+
+ align:start position:0%
+beta since all the eigen values from the
+ 
+
+ align:start position:0%
+beta since all the eigen values from the
+solution of eigen value problem of as a
+
+ align:start position:0%
+solution of eigen value problem of as a
+ 
+
+ align:start position:0%
+solution of eigen value problem of as a
+equal to beta a those eigen values are
+
+ align:start position:0%
+equal to beta a those eigen values are
+ 
+
+ align:start position:0%
+equal to beta a those eigen values are
+all different therefore I can argue that
+
+ align:start position:0%
+all different therefore I can argue that
+ 
+
+ align:start position:0%
+all different therefore I can argue that
+n minus 1 ka is proportional to a ok
+
+ align:start position:0%
+n minus 1 ka is proportional to a ok
+ 
+
+ align:start position:0%
+n minus 1 ka is proportional to a ok
+therefore M minus 1 K a is equal to
+
+ align:start position:0%
+therefore M minus 1 K a is equal to
+ 
+
+ align:start position:0%
+therefore M minus 1 K a is equal to
+Omega square Omega square is actually
+
+ align:start position:0%
+Omega square Omega square is actually
+ 
+
+ align:start position:0%
+Omega square Omega square is actually
+some constant ok this is really amazing
+
+ align:start position:0%
+some constant ok this is really amazing
+ 
+
+ align:start position:0%
+some constant ok this is really amazing
+because that means even the two
+
+ align:start position:0%
+because that means even the two
+ 
+
+ align:start position:0%
+because that means even the two
+condition the first one I can figure out
+
+ align:start position:0%
+condition the first one I can figure out
+ 
+
+ align:start position:0%
+condition the first one I can figure out
+that I can value and eigen vectors of s
+
+ align:start position:0%
+that I can value and eigen vectors of s
+ 
+
+ align:start position:0%
+that I can value and eigen vectors of s
+matrix second if s matrix and then n
+
+ align:start position:0%
+matrix second if s matrix and then n
+ 
+
+ align:start position:0%
+matrix second if s matrix and then n
+minus 1 K matrix interaction matrix they
+
+ align:start position:0%
+minus 1 K matrix interaction matrix they
+ 
+
+ align:start position:0%
+minus 1 K matrix interaction matrix they
+commute then I can actually already
+
+ align:start position:0%
+commute then I can actually already
+ 
+
+ align:start position:0%
+commute then I can actually already
+figure out what are the eigen vectors of
+
+ align:start position:0%
+figure out what are the eigen vectors of
+ 
+
+ align:start position:0%
+figure out what are the eigen vectors of
+n minus 1 K matrix ok and another thing
+
+ align:start position:0%
+n minus 1 K matrix ok and another thing
+ 
+
+ align:start position:0%
+n minus 1 K matrix ok and another thing
+which we learn from here is that wow
+
+ align:start position:0%
+which we learn from here is that wow
+ 
+
+ align:start position:0%
+which we learn from here is that wow
+that's good because the eigenvectors are
+
+ align:start position:0%
+that's good because the eigenvectors are
+ 
+
+ align:start position:0%
+that's good because the eigenvectors are
+already saw therefore i just have to
+
+ align:start position:0%
+already saw therefore i just have to
+ 
+
+ align:start position:0%
+already saw therefore i just have to
+calculate this i just it's just a normal
+
+ align:start position:0%
+calculate this i just it's just a normal
+ 
+
+ align:start position:0%
+calculate this i just it's just a normal
+operation it's not the eigenvalue
+
+ align:start position:0%
+operation it's not the eigenvalue
+ 
+
+ align:start position:0%
+operation it's not the eigenvalue
+problem anymore i just multiply MS 1 k
+
+ align:start position:0%
+problem anymore i just multiply MS 1 k
+ 
+
+ align:start position:0%
+problem anymore i just multiply MS 1 k
+times a then i can actually get the
+
+ align:start position:0%
+times a then i can actually get the
+ 
+
+ align:start position:0%
+times a then i can actually get the
+value Omega square you see that's
+
+ align:start position:0%
+value Omega square you see that's
+ 
+
+ align:start position:0%
+value Omega square you see that's
+actually much easier than solving like
+
+ align:start position:0%
+actually much easier than solving like
+ 
+
+ align:start position:0%
+actually much easier than solving like
+um where the problem of M minus 1 K
+
+ align:start position:0%
+um where the problem of M minus 1 K
+ 
+
+ align:start position:0%
+um where the problem of M minus 1 K
+matrix ok that says very good news
+
+ align:start position:0%
+matrix ok that says very good news
+ 
+
+ align:start position:0%
+matrix ok that says very good news
+finally I think the most important
+
+ align:start position:0%
+finally I think the most important
+ 
+
+ align:start position:0%
+finally I think the most important
+consequence is that sorry for this the
+
+ align:start position:0%
+consequence is that sorry for this the
+ 
+
+ align:start position:0%
+consequence is that sorry for this the
+most important consequence is that once
+
+ align:start position:0%
+most important consequence is that once
+ 
+
+ align:start position:0%
+most important consequence is that once
+we solve this system which satisfy the
+
+ align:start position:0%
+we solve this system which satisfy the
+ 
+
+ align:start position:0%
+we solve this system which satisfy the
+symmetry described by this s matrix we
+
+ align:start position:0%
+symmetry described by this s matrix we
+ 
+
+ align:start position:0%
+symmetry described by this s matrix we
+have solved all the possible systems
+
+ align:start position:0%
+have solved all the possible systems
+ 
+
+ align:start position:0%
+have solved all the possible systems
+which satisfy the same symmetry for
+
+ align:start position:0%
+which satisfy the same symmetry for
+ 
+
+ align:start position:0%
+which satisfy the same symmetry for
+example in this case I solve a type of
+
+ align:start position:0%
+example in this case I solve a type of
+ 
+
+ align:start position:0%
+example in this case I solve a type of
+pendulum problem ok they look symmetric
+
+ align:start position:0%
+pendulum problem ok they look symmetric
+ 
+
+ align:start position:0%
+pendulum problem ok they look symmetric
+right and I can of course I can draw
+
+ align:start position:0%
+right and I can of course I can draw
+ 
+
+ align:start position:0%
+right and I can of course I can draw
+another one which is like this
+
+ align:start position:0%
+another one which is like this
+ 
+
+ align:start position:0%
+another one which is like this
+it's my circular and there are two wars
+
+ align:start position:0%
+it's my circular and there are two wars
+ 
+
+ align:start position:0%
+it's my circular and there are two wars
+which essentially there are three
+
+ align:start position:0%
+which essentially there are three
+ 
+
+ align:start position:0%
+which essentially there are three
+Springs connected to the wall this
+
+ align:start position:0%
+Springs connected to the wall this
+ 
+
+ align:start position:0%
+Springs connected to the wall this
+problem is already also solved right
+
+ align:start position:0%
+problem is already also solved right
+ 
+
+ align:start position:0%
+problem is already also solved right
+because it also satisfies the same
+
+ align:start position:0%
+because it also satisfies the same
+ 
+
+ align:start position:0%
+because it also satisfies the same
+symmetry and of course I can add more
+
+ align:start position:0%
+symmetry and of course I can add more
+ 
+
+ align:start position:0%
+symmetry and of course I can add more
+like like this called crazy more this is
+
+ align:start position:0%
+like like this called crazy more this is
+ 
+
+ align:start position:0%
+like like this called crazy more this is
+also solved right because this is also
+
+ align:start position:0%
+also solved right because this is also
+ 
+
+ align:start position:0%
+also solved right because this is also
+symmetric right I can add more okay
+
+ align:start position:0%
+symmetric right I can add more okay
+ 
+
+ align:start position:0%
+symmetric right I can add more okay
+right that is right it's also symmetric
+
+ align:start position:0%
+right that is right it's also symmetric
+ 
+
+ align:start position:0%
+right that is right it's also symmetric
+right and this let's see the eigenvector
+
+ align:start position:0%
+right and this let's see the eigenvector
+ 
+
+ align:start position:0%
+right and this let's see the eigenvector
+of this n minus 1 k matrix eigenvalue
+
+ align:start position:0%
+of this n minus 1 k matrix eigenvalue
+ 
+
+ align:start position:0%
+of this n minus 1 k matrix eigenvalue
+problem will be identical to what we
+
+ align:start position:0%
+problem will be identical to what we
+ 
+
+ align:start position:0%
+problem will be identical to what we
+have already saw here okay so that
+
+ align:start position:0%
+have already saw here okay so that
+ 
+
+ align:start position:0%
+have already saw here okay so that
+essentially is really amazing if you
+
+ align:start position:0%
+essentially is really amazing if you
+ 
+
+ align:start position:0%
+essentially is really amazing if you
+speak the right language and the cut
+
+ align:start position:0%
+speak the right language and the cut
+ 
+
+ align:start position:0%
+speak the right language and the cut
+into the pattern in the right angle you
+
+ align:start position:0%
+into the pattern in the right angle you
+ 
+
+ align:start position:0%
+into the pattern in the right angle you
+actually found out AG you can solve a
+
+ align:start position:0%
+actually found out AG you can solve a
+ 
+
+ align:start position:0%
+actually found out AG you can solve a
+multiple problem at one time okay any
+
+ align:start position:0%
+multiple problem at one time okay any
+ 
+
+ align:start position:0%
+multiple problem at one time okay any
+questions okay
+
+ align:start position:0%
+questions okay
+ 
+
+ align:start position:0%
+questions okay
+so so that is actually very nice and
+
+ align:start position:0%
+so so that is actually very nice and
+ 
+
+ align:start position:0%
+so so that is actually very nice and
+this is actually a very important
+
+ align:start position:0%
+this is actually a very important
+ 
+
+ align:start position:0%
+this is actually a very important
+preparation to the the next step
+
+ align:start position:0%
+preparation to the the next step
+ 
+
+ align:start position:0%
+preparation to the the next step
+actually so now we have understood
+
+ align:start position:0%
+actually so now we have understood
+ 
+
+ align:start position:0%
+actually so now we have understood
+coupled oscillator and we have learned a
+
+ align:start position:0%
+coupled oscillator and we have learned a
+ 
+
+ align:start position:0%
+coupled oscillator and we have learned a
+little bit about symmetry right
+
+ align:start position:0%
+little bit about symmetry right
+ 
+
+ align:start position:0%
+little bit about symmetry right
+therefore I would like to go to Infini
+
+ align:start position:0%
+therefore I would like to go to Infini
+ 
+
+ align:start position:0%
+therefore I would like to go to Infini
+number of coupled oscillators okay
+
+ align:start position:0%
+number of coupled oscillators okay
+ 
+
+ align:start position:0%
+number of coupled oscillators okay
+so that is actually the next step which
+
+ align:start position:0%
+so that is actually the next step which
+ 
+
+ align:start position:0%
+so that is actually the next step which
+we are going to move on in the three so
+
+ align:start position:0%
+we are going to move on in the three so
+ 
+
+ align:start position:0%
+we are going to move on in the three so
+this is actually why example infinite
+
+ align:start position:0%
+this is actually why example infinite
+ 
+
+ align:start position:0%
+this is actually why example infinite
+system okay
+
+ align:start position:0%
+system okay
+ 
+
+ align:start position:0%
+system okay
+and I cannot write the whole universe
+
+ align:start position:0%
+and I cannot write the whole universe
+ 
+
+ align:start position:0%
+and I cannot write the whole universe
+right because it is infinite so I
+
+ align:start position:0%
+right because it is infinite so I
+ 
+
+ align:start position:0%
+right because it is infinite so I
+couldn't include everything in the in
+
+ align:start position:0%
+couldn't include everything in the in
+ 
+
+ align:start position:0%
+couldn't include everything in the in
+the slide but this is your example
+
+ align:start position:0%
+the slide but this is your example
+ 
+
+ align:start position:0%
+the slide but this is your example
+system okay looks hopeful is right in
+
+ align:start position:0%
+system okay looks hopeful is right in
+ 
+
+ align:start position:0%
+system okay looks hopeful is right in
+general we don't know how to solve
+
+ align:start position:0%
+general we don't know how to solve
+ 
+
+ align:start position:0%
+general we don't know how to solve
+infinite system because if you have
+
+ align:start position:0%
+infinite system because if you have
+ 
+
+ align:start position:0%
+infinite system because if you have
+symphony number of things they are
+
+ align:start position:0%
+symphony number of things they are
+ 
+
+ align:start position:0%
+symphony number of things they are
+connected to each other in random ways
+
+ align:start position:0%
+connected to each other in random ways
+ 
+
+ align:start position:0%
+connected to each other in random ways
+then the see the problem become really
+
+ align:start position:0%
+then the see the problem become really
+ 
+
+ align:start position:0%
+then the see the problem become really
+pree Katie okay in general I don't know
+
+ align:start position:0%
+pree Katie okay in general I don't know
+ 
+
+ align:start position:0%
+pree Katie okay in general I don't know
+how to solve this problem
+
+ align:start position:0%
+how to solve this problem
+ 
+
+ align:start position:0%
+how to solve this problem
+okay and if you are at a Bui major the
+
+ align:start position:0%
+okay and if you are at a Bui major the
+ 
+
+ align:start position:0%
+okay and if you are at a Bui major the
+first thing maybe you would like to do
+
+ align:start position:0%
+first thing maybe you would like to do
+ 
+
+ align:start position:0%
+first thing maybe you would like to do
+is now I have this picture and I can put
+
+ align:start position:0%
+is now I have this picture and I can put
+ 
+
+ align:start position:0%
+is now I have this picture and I can put
+everything in my computer and see how
+
+ align:start position:0%
+everything in my computer and see how
+ 
+
+ align:start position:0%
+everything in my computer and see how
+things evolve as a function of time
+
+ align:start position:0%
+things evolve as a function of time
+ 
+
+ align:start position:0%
+things evolve as a function of time
+right of course we can rely on the
+
+ align:start position:0%
+right of course we can rely on the
+ 
+
+ align:start position:0%
+right of course we can rely on the
+computers and see what we can learn from
+
+ align:start position:0%
+computers and see what we can learn from
+ 
+
+ align:start position:0%
+computers and see what we can learn from
+it and if you met you are a major of
+
+ align:start position:0%
+it and if you met you are a major of
+ 
+
+ align:start position:0%
+it and if you met you are a major of
+mathematics you say no this is not the
+
+ align:start position:0%
+mathematics you say no this is not the
+ 
+
+ align:start position:0%
+mathematics you say no this is not the
+problem I am going to work on okay I
+
+ align:start position:0%
+problem I am going to work on okay I
+ 
+
+ align:start position:0%
+problem I am going to work on okay I
+don't care but as a physicist what we
+
+ align:start position:0%
+don't care but as a physicist what we
+ 
+
+ align:start position:0%
+don't care but as a physicist what we
+are going to do is that how we look at
+
+ align:start position:0%
+are going to do is that how we look at
+ 
+
+ align:start position:0%
+are going to do is that how we look at
+these infinities then okay interesting
+
+ align:start position:0%
+these infinities then okay interesting
+ 
+
+ align:start position:0%
+these infinities then okay interesting
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+there's a lot of things a lot of small
+
+ align:start position:0%
+there's a lot of things a lot of small
+ 
+
+ align:start position:0%
+there's a lot of things a lot of small
+balls connected to big balls right super
+
+ align:start position:0%
+balls connected to big balls right super
+ 
+
+ align:start position:0%
+balls connected to big balls right super
+big one and protein since in log scale
+
+ align:start position:0%
+big one and protein since in log scale
+ 
+
+ align:start position:0%
+big one and protein since in log scale
+so those poles are really really large
+
+ align:start position:0%
+so those poles are really really large
+ 
+
+ align:start position:0%
+so those poles are really really large
+compared to the all the other ports
+
+ align:start position:0%
+compared to the all the other ports
+ 
+
+ align:start position:0%
+compared to the all the other ports
+connected to this system therefore as a
+
+ align:start position:0%
+connected to this system therefore as a
+ 
+
+ align:start position:0%
+connected to this system therefore as a
+physicist I'm going to ignore all the
+
+ align:start position:0%
+physicist I'm going to ignore all the
+ 
+
+ align:start position:0%
+physicist I'm going to ignore all the
+other boys oh if I do that then it began
+
+ align:start position:0%
+other boys oh if I do that then it began
+ 
+
+ align:start position:0%
+other boys oh if I do that then it began
+this is some kind of symmetry you can
+
+ align:start position:0%
+this is some kind of symmetry you can
+ 
+
+ align:start position:0%
+this is some kind of symmetry you can
+let you see from here right what I did I
+
+ align:start position:0%
+let you see from here right what I did I
+ 
+
+ align:start position:0%
+let you see from here right what I did I
+see the symmetry you see there are three
+
+ align:start position:0%
+see the symmetry you see there are three
+ 
+
+ align:start position:0%
+see the symmetry you see there are three
+poles
+
+ align:start position:0%
+poles
+ 
+
+ align:start position:0%
+poles
+they're connected to each other they are
+
+ align:start position:0%
+they're connected to each other they are
+ 
+
+ align:start position:0%
+they're connected to each other they are
+equally spaced we have a translation
+
+ align:start position:0%
+equally spaced we have a translation
+ 
+
+ align:start position:0%
+equally spaced we have a translation
+symmetry you see so you can see that
+
+ align:start position:0%
+symmetry you see so you can see that
+ 
+
+ align:start position:0%
+symmetry you see so you can see that
+actually that's actually how we actually
+
+ align:start position:0%
+actually that's actually how we actually
+ 
+
+ align:start position:0%
+actually that's actually how we actually
+think about a problem of course
+
+ align:start position:0%
+think about a problem of course
+ 
+
+ align:start position:0%
+think about a problem of course
+different few have different kind of
+
+ align:start position:0%
+different few have different kind of
+ 
+
+ align:start position:0%
+different few have different kind of
+thinking and a different kind of problem
+
+ align:start position:0%
+thinking and a different kind of problem
+ 
+
+ align:start position:0%
+thinking and a different kind of problem
+they would like to focus on but as a
+
+ align:start position:0%
+they would like to focus on but as a
+ 
+
+ align:start position:0%
+they would like to focus on but as a
+position I would like to know how this
+
+ align:start position:0%
+position I would like to know how this
+ 
+
+ align:start position:0%
+position I would like to know how this
+system will work and that is actually
+
+ align:start position:0%
+system will work and that is actually
+ 
+
+ align:start position:0%
+system will work and that is actually
+what I'm going to do okay so that's very
+
+ align:start position:0%
+what I'm going to do okay so that's very
+ 
+
+ align:start position:0%
+what I'm going to do okay so that's very
+nice we are going to discuss infinite
+
+ align:start position:0%
+nice we are going to discuss infinite
+ 
+
+ align:start position:0%
+nice we are going to discuss infinite
+system so what is actually the infinite
+
+ align:start position:0%
+system so what is actually the infinite
+ 
+
+ align:start position:0%
+system so what is actually the infinite
+system I am going to talk about
+
+ align:start position:0%
+system I am going to talk about
+ 
+
+ align:start position:0%
+system I am going to talk about
+essentially there's infinite system with
+
+ align:start position:0%
+essentially there's infinite system with
+ 
+
+ align:start position:0%
+essentially there's infinite system with
+space translation symmetry
+
+ align:start position:0%
+space translation symmetry
+ 
+
+ align:start position:0%
+space translation symmetry
+so to save some time I have already
+
+ align:start position:0%
+so to save some time I have already
+ 
+
+ align:start position:0%
+so to save some time I have already
+written right I have already written
+
+ align:start position:0%
+written right I have already written
+ 
+
+ align:start position:0%
+written right I have already written
+founded the matrix involving this system
+
+ align:start position:0%
+founded the matrix involving this system
+ 
+
+ align:start position:0%
+founded the matrix involving this system
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+what I'm interested is mass-spring
+
+ align:start position:0%
+what I'm interested is mass-spring
+ 
+
+ align:start position:0%
+what I'm interested is mass-spring
+system okay infinite number of mass and
+
+ align:start position:0%
+system okay infinite number of mass and
+ 
+
+ align:start position:0%
+system okay infinite number of mass and
+spring and they actually satisfy space
+
+ align:start position:0%
+spring and they actually satisfy space
+ 
+
+ align:start position:0%
+spring and they actually satisfy space
+translation symmetry okay they are
+
+ align:start position:0%
+translation symmetry okay they are
+ 
+
+ align:start position:0%
+translation symmetry okay they are
+connected to each other by Springs with
+
+ align:start position:0%
+connected to each other by Springs with
+ 
+
+ align:start position:0%
+connected to each other by Springs with
+natural ends a and spring constant K
+
+ align:start position:0%
+natural ends a and spring constant K
+ 
+
+ align:start position:0%
+natural ends a and spring constant K
+okay and there are infinite number of
+
+ align:start position:0%
+okay and there are infinite number of
+ 
+
+ align:start position:0%
+okay and there are infinite number of
+them actually line up from the left-hand
+
+ align:start position:0%
+them actually line up from the left-hand
+ 
+
+ align:start position:0%
+them actually line up from the left-hand
+side of the edge of the universe to the
+
+ align:start position:0%
+side of the edge of the universe to the
+ 
+
+ align:start position:0%
+side of the edge of the universe to the
+right-hand side edge of the universe
+
+ align:start position:0%
+right-hand side edge of the universe
+ 
+
+ align:start position:0%
+right-hand side edge of the universe
+okay I prepared this system ok took me a
+
+ align:start position:0%
+okay I prepared this system ok took me a
+ 
+
+ align:start position:0%
+okay I prepared this system ok took me a
+long time okay all right it's very
+
+ align:start position:0%
+long time okay all right it's very
+ 
+
+ align:start position:0%
+long time okay all right it's very
+difficult to describe this kind of
+
+ align:start position:0%
+difficult to describe this kind of
+ 
+
+ align:start position:0%
+difficult to describe this kind of
+system right so the first thing we have
+
+ align:start position:0%
+system right so the first thing we have
+ 
+
+ align:start position:0%
+system right so the first thing we have
+done from ao3 is that in order to
+
+ align:start position:0%
+done from ao3 is that in order to
+ 
+
+ align:start position:0%
+done from ao3 is that in order to
+describe this system I need to define a
+
+ align:start position:0%
+describe this system I need to define a
+ 
+
+ align:start position:0%
+describe this system I need to define a
+coordinate system right and also help
+
+ align:start position:0%
+coordinate system right and also help
+ 
+
+ align:start position:0%
+coordinate system right and also help
+everything properly labeled so I
+
+ align:start position:0%
+everything properly labeled so I
+ 
+
+ align:start position:0%
+everything properly labeled so I
+introduce a label say minus 1 j j plus 1
+
+ align:start position:0%
+introduce a label say minus 1 j j plus 1
+ 
+
+ align:start position:0%
+introduce a label say minus 1 j j plus 1
+j plus 2 just to name each little math I
+
+ align:start position:0%
+j plus 2 just to name each little math I
+ 
+
+ align:start position:0%
+j plus 2 just to name each little math I
+am talking about okay no other purpose
+
+ align:start position:0%
+am talking about okay no other purpose
+ 
+
+ align:start position:0%
+am talking about okay no other purpose
+then once I have the label I can
+
+ align:start position:0%
+then once I have the label I can
+ 
+
+ align:start position:0%
+then once I have the label I can
+actually write everything Express the
+
+ align:start position:0%
+actually write everything Express the
+ 
+
+ align:start position:0%
+actually write everything Express the
+displacement or total mass as XT minus 1
+
+ align:start position:0%
+displacement or total mass as XT minus 1
+ 
+
+ align:start position:0%
+displacement or total mass as XT minus 1
+X a X a + 1 XA plus 2 that's just a
+
+ align:start position:0%
+X a X a + 1 XA plus 2 that's just a
+ 
+
+ align:start position:0%
+X a X a + 1 XA plus 2 that's just a
+displacement from the equilibrium
+
+ align:start position:0%
+displacement from the equilibrium
+ 
+
+ align:start position:0%
+displacement from the equilibrium
+position of the mass okay and this
+
+ align:start position:0%
+position of the mass okay and this
+ 
+
+ align:start position:0%
+position of the mass okay and this
+system will have an equation of motion
+
+ align:start position:0%
+system will have an equation of motion
+ 
+
+ align:start position:0%
+system will have an equation of motion
+looks like this so if now I focus the
+
+ align:start position:0%
+looks like this so if now I focus the
+ 
+
+ align:start position:0%
+looks like this so if now I focus the
+detailed mass check ok then I can I
+
+ align:start position:0%
+detailed mass check ok then I can I
+ 
+
+ align:start position:0%
+detailed mass check ok then I can I
+should write down the equation of motion
+
+ align:start position:0%
+should write down the equation of motion
+ 
+
+ align:start position:0%
+should write down the equation of motion
+there are two Springs there are there
+
+ align:start position:0%
+there are two Springs there are there
+ 
+
+ align:start position:0%
+there are two Springs there are there
+are two Springs connected to this mass
+
+ align:start position:0%
+are two Springs connected to this mass
+ 
+
+ align:start position:0%
+are two Springs connected to this mass
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+therefore you are
+
+ align:start position:0%
+therefore you are
+ 
+
+ align:start position:0%
+therefore you are
+to have tools spring force right since
+
+ align:start position:0%
+to have tools spring force right since
+ 
+
+ align:start position:0%
+to have tools spring force right since
+this is usually idealized the Springs
+
+ align:start position:0%
+this is usually idealized the Springs
+ 
+
+ align:start position:0%
+this is usually idealized the Springs
+with spring constant capital K therefore
+
+ align:start position:0%
+with spring constant capital K therefore
+ 
+
+ align:start position:0%
+with spring constant capital K therefore
+I can write down immediately the
+
+ align:start position:0%
+I can write down immediately the
+ 
+
+ align:start position:0%
+I can write down immediately the
+equation of motion is actually equal to
+
+ align:start position:0%
+equation of motion is actually equal to
+ 
+
+ align:start position:0%
+equation of motion is actually equal to
+MX double dot J is equal to minus k XA
+
+ align:start position:0%
+MX double dot J is equal to minus k XA
+ 
+
+ align:start position:0%
+MX double dot J is equal to minus k XA
+minus XA minus 1 minus this disaster
+
+ align:start position:0%
+minus XA minus 1 minus this disaster
+ 
+
+ align:start position:0%
+minus XA minus 1 minus this disaster
+that the right hand side spring force
+
+ align:start position:0%
+that the right hand side spring force
+ 
+
+ align:start position:0%
+that the right hand side spring force
+minus k xj minus XA plus 1 we have done
+
+ align:start position:0%
+minus k xj minus XA plus 1 we have done
+ 
+
+ align:start position:0%
+minus k xj minus XA plus 1 we have done
+this exercise before I with a simpler
+
+ align:start position:0%
+this exercise before I with a simpler
+ 
+
+ align:start position:0%
+this exercise before I with a simpler
+problem ok as you Joe I can collect all
+
+ align:start position:0%
+problem ok as you Joe I can collect all
+ 
+
+ align:start position:0%
+problem ok as you Joe I can collect all
+the terms associated with XA minus 1 XA
+
+ align:start position:0%
+the terms associated with XA minus 1 XA
+ 
+
+ align:start position:0%
+the terms associated with XA minus 1 XA
+and the XA plus 1 together then I get
+
+ align:start position:0%
+and the XA plus 1 together then I get
+ 
+
+ align:start position:0%
+and the XA plus 1 together then I get
+this expression which is really looks
+
+ align:start position:0%
+this expression which is really looks
+ 
+
+ align:start position:0%
+this expression which is really looks
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+okay and I assume that this system is
+
+ align:start position:0%
+okay and I assume that this system is
+ 
+
+ align:start position:0%
+okay and I assume that this system is
+actually undergoing some kind of
+
+ align:start position:0%
+actually undergoing some kind of
+ 
+
+ align:start position:0%
+actually undergoing some kind of
+oscillation okay therefore I assume that
+
+ align:start position:0%
+oscillation okay therefore I assume that
+ 
+
+ align:start position:0%
+oscillation okay therefore I assume that
+this is a solution X J will be equal to
+
+ align:start position:0%
+this is a solution X J will be equal to
+ 
+
+ align:start position:0%
+this is a solution X J will be equal to
+AJ is the amplitude of J's mass okay
+
+ align:start position:0%
+AJ is the amplitude of J's mass okay
+ 
+
+ align:start position:0%
+AJ is the amplitude of J's mass okay
+cosine Omega T plus Phi Omega is a
+
+ align:start position:0%
+cosine Omega T plus Phi Omega is a
+ 
+
+ align:start position:0%
+cosine Omega T plus Phi Omega is a
+should the oscillation frequency and
+
+ align:start position:0%
+should the oscillation frequency and
+ 
+
+ align:start position:0%
+should the oscillation frequency and
+finally the face and I don't know what
+
+ align:start position:0%
+finally the face and I don't know what
+ 
+
+ align:start position:0%
+finally the face and I don't know what
+is actually Omega and AJ yet okay we
+
+ align:start position:0%
+is actually Omega and AJ yet okay we
+ 
+
+ align:start position:0%
+is actually Omega and AJ yet okay we
+would like to figure that out and let's
+
+ align:start position:0%
+would like to figure that out and let's
+ 
+
+ align:start position:0%
+would like to figure that out and let's
+do job okay you can issued it right down
+
+ align:start position:0%
+do job okay you can issued it right down
+ 
+
+ align:start position:0%
+do job okay you can issued it right down
+the n matrix okay and matrix is actually
+
+ align:start position:0%
+the n matrix okay and matrix is actually
+ 
+
+ align:start position:0%
+the n matrix okay and matrix is actually
+really simple
+
+ align:start position:0%
+really simple
+ 
+
+ align:start position:0%
+really simple
+in the diagonal turns ago no turns out o
+
+ align:start position:0%
+in the diagonal turns ago no turns out o
+ 
+
+ align:start position:0%
+in the diagonal turns ago no turns out o
+N and the off diagonal terms are all 0
+
+ align:start position:0%
+N and the off diagonal terms are all 0
+ 
+
+ align:start position:0%
+N and the off diagonal terms are all 0
+right and you don't really need to copy
+
+ align:start position:0%
+right and you don't really need to copy
+ 
+
+ align:start position:0%
+right and you don't really need to copy
+them because we are organizing the
+
+ align:start position:0%
+them because we are organizing the
+ 
+
+ align:start position:0%
+them because we are organizing the
+lecture note n minus 1 K matrix hi I
+
+ align:start position:0%
+lecture note n minus 1 K matrix hi I
+ 
+
+ align:start position:0%
+lecture note n minus 1 K matrix hi I
+have already arranged my turns here
+
+ align:start position:0%
+have already arranged my turns here
+ 
+
+ align:start position:0%
+have already arranged my turns here
+therefore it looks like this you have a
+
+ align:start position:0%
+therefore it looks like this you have a
+ 
+
+ align:start position:0%
+therefore it looks like this you have a
+strange structure you have three turns
+
+ align:start position:0%
+strange structure you have three turns
+ 
+
+ align:start position:0%
+strange structure you have three turns
+kind of in the diagonal turns and this
+
+ align:start position:0%
+kind of in the diagonal turns and this
+ 
+
+ align:start position:0%
+kind of in the diagonal turns and this
+issue is shifting as a function of
+
+ align:start position:0%
+issue is shifting as a function of
+ 
+
+ align:start position:0%
+issue is shifting as a function of
+number of rows and the OD other part of
+
+ align:start position:0%
+number of rows and the OD other part of
+ 
+
+ align:start position:0%
+number of rows and the OD other part of
+the metrics actually zero okay it's an
+
+ align:start position:0%
+the metrics actually zero okay it's an
+ 
+
+ align:start position:0%
+the metrics actually zero okay it's an
+infinite as Infini dimension matrix
+
+ align:start position:0%
+infinite as Infini dimension matrix
+ 
+
+ align:start position:0%
+infinite as Infini dimension matrix
+finally I would like to also write my a
+
+ align:start position:0%
+finally I would like to also write my a
+ 
+
+ align:start position:0%
+finally I would like to also write my a
+matrix is the vector of M produced right
+
+ align:start position:0%
+matrix is the vector of M produced right
+ 
+
+ align:start position:0%
+matrix is the vector of M produced right
+so you have many many numbers AJ AJ plus
+
+ align:start position:0%
+so you have many many numbers AJ AJ plus
+ 
+
+ align:start position:0%
+so you have many many numbers AJ AJ plus
+one eight eight plus two okay etcetera
+
+ align:start position:0%
+one eight eight plus two okay etcetera
+ 
+
+ align:start position:0%
+one eight eight plus two okay etcetera
+etcetera okay now very easy right
+
+ align:start position:0%
+etcetera okay now very easy right
+ 
+
+ align:start position:0%
+etcetera okay now very easy right
+the question is actually can be solved
+
+ align:start position:0%
+the question is actually can be solved
+ 
+
+ align:start position:0%
+the question is actually can be solved
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+you just have to solve the n minus 1 K
+
+ align:start position:0%
+you just have to solve the n minus 1 K
+ 
+
+ align:start position:0%
+you just have to solve the n minus 1 K
+matrix right that's easy right it is an
+
+ align:start position:0%
+matrix right that's easy right it is an
+ 
+
+ align:start position:0%
+matrix right that's easy right it is an
+infinite number times infinite number of
+
+ align:start position:0%
+infinite number times infinite number of
+ 
+
+ align:start position:0%
+infinite number times infinite number of
+metrics right super easy no actually not
+
+ align:start position:0%
+metrics right super easy no actually not
+ 
+
+ align:start position:0%
+metrics right super easy no actually not
+right so we are in trouble I don't know
+
+ align:start position:0%
+right so we are in trouble I don't know
+ 
+
+ align:start position:0%
+right so we are in trouble I don't know
+how to solve this problem okay what can
+
+ align:start position:0%
+how to solve this problem okay what can
+ 
+
+ align:start position:0%
+how to solve this problem okay what can
+we do anybody have any suggestion to me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah math department is coming in to
+
+ align:start position:0%
+yeah math department is coming in to
+ 
+
+ align:start position:0%
+yeah math department is coming in to
+help yes but they're actually people
+
+ align:start position:0%
+help yes but they're actually people
+ 
+
+ align:start position:0%
+help yes but they're actually people
+asking that we learn some concept which
+
+ align:start position:0%
+asking that we learn some concept which
+ 
+
+ align:start position:0%
+asking that we learn some concept which
+we just learned like there's a what what
+
+ align:start position:0%
+we just learned like there's a what what
+ 
+
+ align:start position:0%
+we just learned like there's a what what
+kind of property of this sister symmetry
+
+ align:start position:0%
+kind of property of this sister symmetry
+ 
+
+ align:start position:0%
+kind of property of this sister symmetry
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+we have symmetry okay so this n minus 1
+
+ align:start position:0%
+we have symmetry okay so this n minus 1
+ 
+
+ align:start position:0%
+we have symmetry okay so this n minus 1
+K matrix looks horrible right but if I'd
+
+ align:start position:0%
+K matrix looks horrible right but if I'd
+ 
+
+ align:start position:0%
+K matrix looks horrible right but if I'd
+write down the symmetric matrix actually
+
+ align:start position:0%
+write down the symmetric matrix actually
+ 
+
+ align:start position:0%
+write down the symmetric matrix actually
+it looks slightly better okay so what is
+
+ align:start position:0%
+it looks slightly better okay so what is
+ 
+
+ align:start position:0%
+it looks slightly better okay so what is
+actually the symmetry matrix okay so one
+
+ align:start position:0%
+actually the symmetry matrix okay so one
+ 
+
+ align:start position:0%
+actually the symmetry matrix okay so one
+observation we can make from this system
+
+ align:start position:0%
+observation we can make from this system
+ 
+
+ align:start position:0%
+observation we can make from this system
+is that if I shipped this system a to
+
+ align:start position:0%
+is that if I shipped this system a to
+ 
+
+ align:start position:0%
+is that if I shipped this system a to
+the left okay I shipped this these two
+
+ align:start position:0%
+the left okay I shipped this these two
+ 
+
+ align:start position:0%
+the left okay I shipped this these two
+masts to laughing I should all the math
+
+ align:start position:0%
+masts to laughing I should all the math
+ 
+
+ align:start position:0%
+masts to laughing I should all the math
+I have to hire many many students to
+
+ align:start position:0%
+I have to hire many many students to
+ 
+
+ align:start position:0%
+I have to hire many many students to
+smooth all the mess from lapin side of
+
+ align:start position:0%
+smooth all the mess from lapin side of
+ 
+
+ align:start position:0%
+smooth all the mess from lapin side of
+the universe to right hand side of the
+
+ align:start position:0%
+the universe to right hand side of the
+ 
+
+ align:start position:0%
+the universe to right hand side of the
+universe okay and after they have done
+
+ align:start position:0%
+universe okay and after they have done
+ 
+
+ align:start position:0%
+universe okay and after they have done
+that the system looks the same right
+
+ align:start position:0%
+that the system looks the same right
+ 
+
+ align:start position:0%
+that the system looks the same right
+that's very good okay after all the hard
+
+ align:start position:0%
+that's very good okay after all the hard
+ 
+
+ align:start position:0%
+that's very good okay after all the hard
+work right
+
+ align:start position:0%
+work right
+ 
+
+ align:start position:0%
+work right
+so what is issue going to be the
+
+ align:start position:0%
+so what is issue going to be the
+ 
+
+ align:start position:0%
+so what is issue going to be the
+symmetry matrix okay now I would like to
+
+ align:start position:0%
+symmetry matrix okay now I would like to
+ 
+
+ align:start position:0%
+symmetry matrix okay now I would like to
+achieve something which is a prong equal
+
+ align:start position:0%
+achieve something which is a prong equal
+ 
+
+ align:start position:0%
+achieve something which is a prong equal
+to s and that this s actually shipped
+
+ align:start position:0%
+to s and that this s actually shipped
+ 
+
+ align:start position:0%
+to s and that this s actually shipped
+the mass by a distance of a right so
+
+ align:start position:0%
+the mass by a distance of a right so
+ 
+
+ align:start position:0%
+the mass by a distance of a right so
+what would be the function of phony over
+
+ align:start position:0%
+what would be the function of phony over
+ 
+
+ align:start position:0%
+what would be the function of phony over
+this s matrix we were looks like this
+
+ align:start position:0%
+this s matrix we were looks like this
+ 
+
+ align:start position:0%
+this s matrix we were looks like this
+it's going to be 0 1 0 0 0 0 0 1 0 0 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+ok so the next two diagonal turn is all
+
+ align:start position:0%
+ok so the next two diagonal turn is all
+ 
+
+ align:start position:0%
+ok so the next two diagonal turn is all
+one all the rest of the component is 0
+
+ align:start position:0%
+one all the rest of the component is 0
+ 
+
+ align:start position:0%
+one all the rest of the component is 0
+ok and this looks a lot more friendly
+
+ align:start position:0%
+ok and this looks a lot more friendly
+ 
+
+ align:start position:0%
+ok and this looks a lot more friendly
+compared to a mess 1 K matrix right see
+
+ align:start position:0%
+compared to a mess 1 K matrix right see
+ 
+
+ align:start position:0%
+compared to a mess 1 K matrix right see
+oh this is is this horrible thing to do
+
+ align:start position:0%
+oh this is is this horrible thing to do
+ 
+
+ align:start position:0%
+oh this is is this horrible thing to do
+because this is an infinite number of
+
+ align:start position:0%
+because this is an infinite number of
+ 
+
+ align:start position:0%
+because this is an infinite number of
+times in terminal number dimension
+
+ align:start position:0%
+times in terminal number dimension
+ 
+
+ align:start position:0%
+times in terminal number dimension
+matrix ok so we would like to find the
+
+ align:start position:0%
+matrix ok so we would like to find the
+ 
+
+ align:start position:0%
+matrix ok so we would like to find the
+eigen vectors of s matrix ok so this
+
+ align:start position:0%
+eigen vectors of s matrix ok so this
+ 
+
+ align:start position:0%
+eigen vectors of s matrix ok so this
+means that if I manage you to solve the
+
+ align:start position:0%
+means that if I manage you to solve the
+ 
+
+ align:start position:0%
+means that if I manage you to solve the
+eigenvalue problem assuming that ok I
+
+ align:start position:0%
+eigenvalue problem assuming that ok I
+ 
+
+ align:start position:0%
+eigenvalue problem assuming that ok I
+haven't solve it but I assuming that I
+
+ align:start position:0%
+haven't solve it but I assuming that I
+ 
+
+ align:start position:0%
+haven't solve it but I assuming that I
+can solve it
+
+ align:start position:0%
+can solve it
+ 
+
+ align:start position:0%
+can solve it
+ok then what I'm going to do is going to
+
+ align:start position:0%
+ok then what I'm going to do is going to
+ 
+
+ align:start position:0%
+ok then what I'm going to do is going to
+get this essay will be equal to theta
+
+ align:start position:0%
+get this essay will be equal to theta
+ 
+
+ align:start position:0%
+get this essay will be equal to theta
+where a is actually eigen vector of s
+
+ align:start position:0%
+where a is actually eigen vector of s
+ 
+
+ align:start position:0%
+where a is actually eigen vector of s
+matrix ok and and then si we just learn
+
+ align:start position:0%
+matrix ok and and then si we just learn
+ 
+
+ align:start position:0%
+matrix ok and and then si we just learn
+from here right it's actually equal to a
+
+ align:start position:0%
+from here right it's actually equal to a
+ 
+
+ align:start position:0%
+from here right it's actually equal to a
+prime so beta is the eigen value and a
+
+ align:start position:0%
+prime so beta is the eigen value and a
+ 
+
+ align:start position:0%
+prime so beta is the eigen value and a
+is actually the eigenvector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means originally I have a which
+
+ align:start position:0%
+so that means originally I have a which
+ 
+
+ align:start position:0%
+so that means originally I have a which
+is something sensing a say it a plus one
+
+ align:start position:0%
+is something sensing a say it a plus one
+ 
+
+ align:start position:0%
+is something sensing a say it a plus one
+it's a plus two proper bra okay and the
+
+ align:start position:0%
+it's a plus two proper bra okay and the
+ 
+
+ align:start position:0%
+it's a plus two proper bra okay and the
+apron after I actually multiply a by s
+
+ align:start position:0%
+apron after I actually multiply a by s
+ 
+
+ align:start position:0%
+apron after I actually multiply a by s
+matrix I get a prompt which looks like
+
+ align:start position:0%
+matrix I get a prompt which looks like
+ 
+
+ align:start position:0%
+matrix I get a prompt which looks like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+hey J plus 1 J plus 2 J plus 3 okay so
+
+ align:start position:0%
+hey J plus 1 J plus 2 J plus 3 okay so
+ 
+
+ align:start position:0%
+hey J plus 1 J plus 2 J plus 3 okay so
+what I'm going to do is what actually
+
+ align:start position:0%
+what I'm going to do is what actually
+ 
+
+ align:start position:0%
+what I'm going to do is what actually
+this S matrix does is to shift the a
+
+ align:start position:0%
+this S matrix does is to shift the a
+ 
+
+ align:start position:0%
+this S matrix does is to shift the a
+component by one one row right okay so
+
+ align:start position:0%
+component by one one row right okay so
+ 
+
+ align:start position:0%
+component by one one row right okay so
+then we basically get this expression
+
+ align:start position:0%
+then we basically get this expression
+ 
+
+ align:start position:0%
+then we basically get this expression
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and of course a1 is equal to beta which
+
+ align:start position:0%
+and of course a1 is equal to beta which
+ 
+
+ align:start position:0%
+and of course a1 is equal to beta which
+is a constant I say right so if you
+
+ align:start position:0%
+is a constant I say right so if you
+ 
+
+ align:start position:0%
+is a constant I say right so if you
+compare for example here okay you can
+
+ align:start position:0%
+compare for example here okay you can
+ 
+
+ align:start position:0%
+compare for example here okay you can
+get that AJ prime will be equal to beta
+
+ align:start position:0%
+get that AJ prime will be equal to beta
+ 
+
+ align:start position:0%
+get that AJ prime will be equal to beta
+AJ which is actually equal to AJ plus
+
+ align:start position:0%
+AJ which is actually equal to AJ plus
+ 
+
+ align:start position:0%
+AJ which is actually equal to AJ plus
+one by AJ prime is actually equal to AJ
+
+ align:start position:0%
+one by AJ prime is actually equal to AJ
+ 
+
+ align:start position:0%
+one by AJ prime is actually equal to AJ
+plus one maybe it's just what shifting
+
+ align:start position:0%
+plus one maybe it's just what shifting
+ 
+
+ align:start position:0%
+plus one maybe it's just what shifting
+one you need you know label right okay
+
+ align:start position:0%
+one you need you know label right okay
+ 
+
+ align:start position:0%
+one you need you know label right okay
+so so this is the expression I am
+
+ align:start position:0%
+so so this is the expression I am
+ 
+
+ align:start position:0%
+so so this is the expression I am
+looking for okay we don't know yet what
+
+ align:start position:0%
+looking for okay we don't know yet what
+ 
+
+ align:start position:0%
+looking for okay we don't know yet what
+is H beta
+
+ align:start position:0%
+is H beta
+ 
+
+ align:start position:0%
+is H beta
+okay beta I sound number assuming that I
+
+ align:start position:0%
+okay beta I sound number assuming that I
+ 
+
+ align:start position:0%
+okay beta I sound number assuming that I
+can solve the eigenvalue problem okay
+
+ align:start position:0%
+can solve the eigenvalue problem okay
+ 
+
+ align:start position:0%
+can solve the eigenvalue problem okay
+but I do now if I have 8 0 if a 0 is
+
+ align:start position:0%
+but I do now if I have 8 0 if a 0 is
+ 
+
+ align:start position:0%
+but I do now if I have 8 0 if a 0 is
+equal to 0
+
+ align:start position:0%
+equal to 0
+ 
+
+ align:start position:0%
+equal to 0
+okay from this this expression okay that
+
+ align:start position:0%
+okay from this this expression okay that
+ 
+
+ align:start position:0%
+okay from this this expression okay that
+means a 1 will be a 0 is equal to 1 if a
+
+ align:start position:0%
+means a 1 will be a 0 is equal to 1 if a
+ 
+
+ align:start position:0%
+means a 1 will be a 0 is equal to 1 if a
+0 is 0 then everything is 0 right and
+
+ align:start position:0%
+0 is 0 then everything is 0 right and
+ 
+
+ align:start position:0%
+0 is 0 then everything is 0 right and
+it's not right
+
+ align:start position:0%
+it's not right
+ 
+
+ align:start position:0%
+it's not right
+ok n 0 is equal to 1 then something will
+
+ align:start position:0%
+ok n 0 is equal to 1 then something will
+ 
+
+ align:start position:0%
+ok n 0 is equal to 1 then something will
+happen a 1 will be equal to beta right
+
+ align:start position:0%
+happen a 1 will be equal to beta right
+ 
+
+ align:start position:0%
+happen a 1 will be equal to beta right
+from this expression right because beta
+
+ align:start position:0%
+from this expression right because beta
+ 
+
+ align:start position:0%
+from this expression right because beta
+IJ is equal to 8 a plus 1
+
+ align:start position:0%
+IJ is equal to 8 a plus 1
+ 
+
+ align:start position:0%
+IJ is equal to 8 a plus 1
+a two will be equal to beta square etc
+
+ align:start position:0%
+a two will be equal to beta square etc
+ 
+
+ align:start position:0%
+a two will be equal to beta square etc
+etc and I can say that
+
+ align:start position:0%
+etc and I can say that
+ 
+
+ align:start position:0%
+etc and I can say that
+AJ if I assume a 0 if 0 is equal to 1
+
+ align:start position:0%
+AJ if I assume a 0 if 0 is equal to 1
+ 
+
+ align:start position:0%
+AJ if I assume a 0 if 0 is equal to 1
+then AJ will be equal to beta 2 details
+
+ align:start position:0%
+then AJ will be equal to beta 2 details
+ 
+
+ align:start position:0%
+then AJ will be equal to beta 2 details
+ok I going too fast here everybody is
+
+ align:start position:0%
+ok I going too fast here everybody is
+ 
+
+ align:start position:0%
+ok I going too fast here everybody is
+following your question no good and
+
+ align:start position:0%
+following your question no good and
+ 
+
+ align:start position:0%
+following your question no good and
+study we found that we have already
+
+ align:start position:0%
+study we found that we have already
+ 
+
+ align:start position:0%
+study we found that we have already
+solved that I can build your problem
+
+ align:start position:0%
+solved that I can build your problem
+ 
+
+ align:start position:0%
+solved that I can build your problem
+right because I have already the
+
+ align:start position:0%
+right because I have already the
+ 
+
+ align:start position:0%
+right because I have already the
+expression for the AJ which is actually
+
+ align:start position:0%
+expression for the AJ which is actually
+ 
+
+ align:start position:0%
+expression for the AJ which is actually
+in the form of beta to the tail right so
+
+ align:start position:0%
+in the form of beta to the tail right so
+ 
+
+ align:start position:0%
+in the form of beta to the tail right so
+beta is son I should some kind of number
+
+ align:start position:0%
+beta is son I should some kind of number
+ 
+
+ align:start position:0%
+beta is son I should some kind of number
+okay and the infinite number of beta
+
+ align:start position:0%
+okay and the infinite number of beta
+ 
+
+ align:start position:0%
+okay and the infinite number of beta
+actually can satisfy this eigenvalue
+
+ align:start position:0%
+actually can satisfy this eigenvalue
+ 
+
+ align:start position:0%
+actually can satisfy this eigenvalue
+problem no matter what kind of weight I
+
+ align:start position:0%
+problem no matter what kind of weight I
+ 
+
+ align:start position:0%
+problem no matter what kind of weight I
+choose it can be wine can be to 3.14 can
+
+ align:start position:0%
+choose it can be wine can be to 3.14 can
+ 
+
+ align:start position:0%
+choose it can be wine can be to 3.14 can
+be PI okay
+
+ align:start position:0%
+be PI okay
+ 
+
+ align:start position:0%
+be PI okay
+and what I'm going to get is the
+
+ align:start position:0%
+and what I'm going to get is the
+ 
+
+ align:start position:0%
+and what I'm going to get is the
+corresponding AJ corresponding a vector
+
+ align:start position:0%
+corresponding AJ corresponding a vector
+ 
+
+ align:start position:0%
+corresponding AJ corresponding a vector
+which will satisfy this expression okay
+
+ align:start position:0%
+which will satisfy this expression okay
+ 
+
+ align:start position:0%
+which will satisfy this expression okay
+so that means some magic happen we have
+
+ align:start position:0%
+so that means some magic happen we have
+ 
+
+ align:start position:0%
+so that means some magic happen we have
+already solved the eigenvalue poppin
+
+ align:start position:0%
+already solved the eigenvalue poppin
+ 
+
+ align:start position:0%
+already solved the eigenvalue poppin
+without really deriving you know a lot
+
+ align:start position:0%
+without really deriving you know a lot
+ 
+
+ align:start position:0%
+without really deriving you know a lot
+of deviation right a second e another
+
+ align:start position:0%
+of deviation right a second e another
+ 
+
+ align:start position:0%
+of deviation right a second e another
+thing which we learn is that they are
+
+ align:start position:0%
+thing which we learn is that they are
+ 
+
+ align:start position:0%
+thing which we learn is that they are
+infinite number of eigen value which
+
+ align:start position:0%
+infinite number of eigen value which
+ 
+
+ align:start position:0%
+infinite number of eigen value which
+satisfy the this item value problem the
+
+ align:start position:0%
+satisfy the this item value problem the
+ 
+
+ align:start position:0%
+satisfy the this item value problem the
+question is does that make sense or not
+
+ align:start position:0%
+question is does that make sense or not
+ 
+
+ align:start position:0%
+question is does that make sense or not
+infinite number of eigen values can
+
+ align:start position:0%
+infinite number of eigen values can
+ 
+
+ align:start position:0%
+infinite number of eigen values can
+actually satisfy this infinitely long
+
+ align:start position:0%
+actually satisfy this infinitely long
+ 
+
+ align:start position:0%
+actually satisfy this infinitely long
+system it's kind of making sense right
+
+ align:start position:0%
+system it's kind of making sense right
+ 
+
+ align:start position:0%
+system it's kind of making sense right
+because we have work on one oscillator
+
+ align:start position:0%
+because we have work on one oscillator
+ 
+
+ align:start position:0%
+because we have work on one oscillator
+you have one no more more - oscillator
+
+ align:start position:0%
+you have one no more more - oscillator
+ 
+
+ align:start position:0%
+you have one no more more - oscillator
+you have to know more more
+
+ align:start position:0%
+you have to know more more
+ 
+
+ align:start position:0%
+you have to know more more
+three oscillator you have seen no more
+
+ align:start position:0%
+three oscillator you have seen no more
+ 
+
+ align:start position:0%
+three oscillator you have seen no more
+more infinite number of oscillators
+
+ align:start position:0%
+more infinite number of oscillators
+ 
+
+ align:start position:0%
+more infinite number of oscillators
+you should have infinite number no more
+
+ align:start position:0%
+you should have infinite number no more
+ 
+
+ align:start position:0%
+you should have infinite number no more
+mode right
+
+ align:start position:0%
+mode right
+ 
+
+ align:start position:0%
+mode right
+okay so that is actually a very very
+
+ align:start position:0%
+okay so that is actually a very very
+ 
+
+ align:start position:0%
+okay so that is actually a very very
+good news because we have already saw
+
+ align:start position:0%
+good news because we have already saw
+ 
+
+ align:start position:0%
+good news because we have already saw
+the problem and we also know the
+
+ align:start position:0%
+the problem and we also know the
+ 
+
+ align:start position:0%
+the problem and we also know the
+functional form of eigenvectors okay so
+
+ align:start position:0%
+functional form of eigenvectors okay so
+ 
+
+ align:start position:0%
+functional form of eigenvectors okay so
+let's take a look at those example
+
+ align:start position:0%
+let's take a look at those example
+ 
+
+ align:start position:0%
+let's take a look at those example
+system which are actually close to
+
+ align:start position:0%
+system which are actually close to
+ 
+
+ align:start position:0%
+system which are actually close to
+infinitely long so here you have
+
+ align:start position:0%
+infinitely long so here you have
+ 
+
+ align:start position:0%
+infinitely long so here you have
+pelipper machine which usually app can
+
+ align:start position:0%
+pelipper machine which usually app can
+ 
+
+ align:start position:0%
+pelipper machine which usually app can
+have have actually multiple coupled
+
+ align:start position:0%
+have have actually multiple coupled
+ 
+
+ align:start position:0%
+have have actually multiple coupled
+oscillators each of each one of them can
+
+ align:start position:0%
+oscillators each of each one of them can
+ 
+
+ align:start position:0%
+oscillators each of each one of them can
+also they up and down and you can see
+
+ align:start position:0%
+also they up and down and you can see
+ 
+
+ align:start position:0%
+also they up and down and you can see
+that huh if I actually try to move them
+
+ align:start position:0%
+that huh if I actually try to move them
+ 
+
+ align:start position:0%
+that huh if I actually try to move them
+up and down they're complicated kind of
+
+ align:start position:0%
+up and down they're complicated kind of
+ 
+
+ align:start position:0%
+up and down they're complicated kind of
+motion can occur from this system
+
+ align:start position:0%
+motion can occur from this system
+ 
+
+ align:start position:0%
+motion can occur from this system
+actually if I do this and you see the
+
+ align:start position:0%
+actually if I do this and you see the
+ 
+
+ align:start position:0%
+actually if I do this and you see the
+idea something similar to wave is
+
+ align:start position:0%
+idea something similar to wave is
+ 
+
+ align:start position:0%
+idea something similar to wave is
+happening and if I do this continuously
+
+ align:start position:0%
+happening and if I do this continuously
+ 
+
+ align:start position:0%
+happening and if I do this continuously
+oh some kind of kind of like a standing
+
+ align:start position:0%
+oh some kind of kind of like a standing
+ 
+
+ align:start position:0%
+oh some kind of kind of like a standing
+wave is produced right and this system
+
+ align:start position:0%
+wave is produced right and this system
+ 
+
+ align:start position:0%
+wave is produced right and this system
+is actually really really hard to
+
+ align:start position:0%
+is actually really really hard to
+ 
+
+ align:start position:0%
+is actually really really hard to
+describe right if if I if I look at how
+
+ align:start position:0%
+describe right if if I if I look at how
+ 
+
+ align:start position:0%
+describe right if if I if I look at how
+how many since this system can actually
+
+ align:start position:0%
+how many since this system can actually
+ 
+
+ align:start position:0%
+how many since this system can actually
+do okay
+
+ align:start position:0%
+do okay
+ 
+
+ align:start position:0%
+do okay
+another example is actually okay so you
+
+ align:start position:0%
+another example is actually okay so you
+ 
+
+ align:start position:0%
+another example is actually okay so you
+can say come on this is actually not
+
+ align:start position:0%
+can say come on this is actually not
+ 
+
+ align:start position:0%
+can say come on this is actually not
+infinitely long sister right you have to
+
+ align:start position:0%
+infinitely long sister right you have to
+ 
+
+ align:start position:0%
+infinitely long sister right you have to
+find a number right so how about I use
+
+ align:start position:0%
+find a number right so how about I use
+ 
+
+ align:start position:0%
+find a number right so how about I use
+this system as a demonstration this is
+
+ align:start position:0%
+this system as a demonstration this is
+ 
+
+ align:start position:0%
+this system as a demonstration this is
+actually a much nicer or much better
+
+ align:start position:0%
+actually a much nicer or much better
+ 
+
+ align:start position:0%
+actually a much nicer or much better
+approximation okay to to an infinitely
+
+ align:start position:0%
+approximation okay to to an infinitely
+ 
+
+ align:start position:0%
+approximation okay to to an infinitely
+long system you can see that okay each
+
+ align:start position:0%
+long system you can see that okay each
+ 
+
+ align:start position:0%
+long system you can see that okay each
+mass each okay I can say for example
+
+ align:start position:0%
+mass each okay I can say for example
+ 
+
+ align:start position:0%
+mass each okay I can say for example
+each small component of the spring it's
+
+ align:start position:0%
+each small component of the spring it's
+ 
+
+ align:start position:0%
+each small component of the spring it's
+actually can be considered as a small
+
+ align:start position:0%
+actually can be considered as a small
+ 
+
+ align:start position:0%
+actually can be considered as a small
+and in my in my right and the issue act
+
+ align:start position:0%
+and in my in my right and the issue act
+ 
+
+ align:start position:0%
+and in my in my right and the issue act
+now I can actually instead of
+
+ align:start position:0%
+now I can actually instead of
+ 
+
+ align:start position:0%
+now I can actually instead of
+oscillating then pactum force I
+
+ align:start position:0%
+oscillating then pactum force I
+ 
+
+ align:start position:0%
+oscillating then pactum force I
+oscillate an upside down okay you can
+
+ align:start position:0%
+oscillate an upside down okay you can
+ 
+
+ align:start position:0%
+oscillate an upside down okay you can
+see that hand they are interesting kind
+
+ align:start position:0%
+see that hand they are interesting kind
+ 
+
+ align:start position:0%
+see that hand they are interesting kind
+of motion I can have okay
+
+ align:start position:0%
+of motion I can have okay
+ 
+
+ align:start position:0%
+of motion I can have okay
+this which is like a standing wave I can
+
+ align:start position:0%
+this which is like a standing wave I can
+ 
+
+ align:start position:0%
+this which is like a standing wave I can
+I can do this I can stop this system and
+
+ align:start position:0%
+I can do this I can stop this system and
+ 
+
+ align:start position:0%
+I can do this I can stop this system and
+like produce whoo I can produce a wave
+
+ align:start position:0%
+like produce whoo I can produce a wave
+ 
+
+ align:start position:0%
+like produce whoo I can produce a wave
+and it goes back and forth and I can do
+
+ align:start position:0%
+and it goes back and forth and I can do
+ 
+
+ align:start position:0%
+and it goes back and forth and I can do
+this like crazy then you see that
+
+ align:start position:0%
+this like crazy then you see that
+ 
+
+ align:start position:0%
+this like crazy then you see that
+exciting a much higher frequency normal
+
+ align:start position:0%
+exciting a much higher frequency normal
+ 
+
+ align:start position:0%
+exciting a much higher frequency normal
+mode right and that's really complicated
+
+ align:start position:0%
+mode right and that's really complicated
+ 
+
+ align:start position:0%
+mode right and that's really complicated
+and I the question is how can we
+
+ align:start position:0%
+and I the question is how can we
+ 
+
+ align:start position:0%
+and I the question is how can we
+actually understand this kind of system
+
+ align:start position:0%
+actually understand this kind of system
+ 
+
+ align:start position:0%
+actually understand this kind of system
+it seems that this system is so much so
+
+ align:start position:0%
+it seems that this system is so much so
+ 
+
+ align:start position:0%
+it seems that this system is so much so
+complicated and have infinite amount of
+
+ align:start position:0%
+complicated and have infinite amount of
+ 
+
+ align:start position:0%
+complicated and have infinite amount of
+possibilities right so how are we going
+
+ align:start position:0%
+possibilities right so how are we going
+ 
+
+ align:start position:0%
+possibilities right so how are we going
+to understand this very good news is
+
+ align:start position:0%
+to understand this very good news is
+ 
+
+ align:start position:0%
+to understand this very good news is
+that we have solved the normal mode of
+
+ align:start position:0%
+that we have solved the normal mode of
+ 
+
+ align:start position:0%
+that we have solved the normal mode of
+this kind of system right so the normal
+
+ align:start position:0%
+this kind of system right so the normal
+ 
+
+ align:start position:0%
+this kind of system right so the normal
+mode looks like this AJ equal to beta J
+
+ align:start position:0%
+mode looks like this AJ equal to beta J
+ 
+
+ align:start position:0%
+mode looks like this AJ equal to beta J
+ok and the following lecture the rest of
+
+ align:start position:0%
+ok and the following lecture the rest of
+ 
+
+ align:start position:0%
+ok and the following lecture the rest of
+the lecture is to understand what does
+
+ align:start position:0%
+the lecture is to understand what does
+ 
+
+ align:start position:0%
+the lecture is to understand what does
+that mean and also make petitions ok so
+
+ align:start position:0%
+that mean and also make petitions ok so
+ 
+
+ align:start position:0%
+that mean and also make petitions ok so
+so now we have actually the eigen
+
+ align:start position:0%
+so now we have actually the eigen
+ 
+
+ align:start position:0%
+so now we have actually the eigen
+vectors ok that's really nice so from
+
+ align:start position:0%
+vectors ok that's really nice so from
+ 
+
+ align:start position:0%
+vectors ok that's really nice so from
+our previous discussion if this system
+
+ align:start position:0%
+our previous discussion if this system
+ 
+
+ align:start position:0%
+our previous discussion if this system
+actually satisfy the symmetry have the
+
+ align:start position:0%
+actually satisfy the symmetry have the
+ 
+
+ align:start position:0%
+actually satisfy the symmetry have the
+symmetry it is quite by the S matrix
+
+ align:start position:0%
+symmetry it is quite by the S matrix
+ 
+
+ align:start position:0%
+symmetry it is quite by the S matrix
+which I have here that means n minus 1 K
+
+ align:start position:0%
+which I have here that means n minus 1 K
+ 
+
+ align:start position:0%
+which I have here that means n minus 1 K
+matrix where share the same sets of
+
+ align:start position:0%
+matrix where share the same sets of
+ 
+
+ align:start position:0%
+matrix where share the same sets of
+eigenvectors as matrix right so what
+
+ align:start position:0%
+eigenvectors as matrix right so what
+ 
+
+ align:start position:0%
+eigenvectors as matrix right so what
+this actually the rest part of the work
+
+ align:start position:0%
+this actually the rest part of the work
+ 
+
+ align:start position:0%
+this actually the rest part of the work
+is to evaluate this n minus 1 K
+
+ align:start position:0%
+is to evaluate this n minus 1 K
+ 
+
+ align:start position:0%
+is to evaluate this n minus 1 K
+multiplied by a and that will give you
+
+ align:start position:0%
+multiplied by a and that will give you
+ 
+
+ align:start position:0%
+multiplied by a and that will give you
+Omega square H ok so I just need to
+
+ align:start position:0%
+Omega square H ok so I just need to
+ 
+
+ align:start position:0%
+Omega square H ok so I just need to
+multiply M minus 1 K matrix by a what is
+
+ align:start position:0%
+multiply M minus 1 K matrix by a what is
+ 
+
+ align:start position:0%
+multiply M minus 1 K matrix by a what is
+a is here right now what decision M
+
+ align:start position:0%
+a is here right now what decision M
+ 
+
+ align:start position:0%
+a is here right now what decision M
+minus 1 K matrix and when M minus 1 K
+
+ align:start position:0%
+minus 1 K matrix and when M minus 1 K
+ 
+
+ align:start position:0%
+minus 1 K matrix and when M minus 1 K
+matrix is here have a kind of
+
+ align:start position:0%
+matrix is here have a kind of
+ 
+
+ align:start position:0%
+matrix is here have a kind of
+complicated structure
+
+ align:start position:0%
+complicated structure
+ 
+
+ align:start position:0%
+complicated structure
+okay on the other hand if I only focus
+
+ align:start position:0%
+okay on the other hand if I only focus
+ 
+
+ align:start position:0%
+okay on the other hand if I only focus
+on the taste object okay the object
+
+ align:start position:0%
+on the taste object okay the object
+ 
+
+ align:start position:0%
+on the taste object okay the object
+which is named they have the label say
+
+ align:start position:0%
+which is named they have the label say
+ 
+
+ align:start position:0%
+which is named they have the label say
+okay then
+
+ align:start position:0%
+okay then
+ 
+
+ align:start position:0%
+okay then
+actually I can write down okay the right
+
+ align:start position:0%
+actually I can write down okay the right
+ 
+
+ align:start position:0%
+actually I can write down okay the right
+hand side is a she's just Omega square a
+
+ align:start position:0%
+hand side is a she's just Omega square a
+ 
+
+ align:start position:0%
+hand side is a she's just Omega square a
+say alright because this is actually
+
+ align:start position:0%
+say alright because this is actually
+ 
+
+ align:start position:0%
+say alright because this is actually
+just if I only focus on that there's a
+
+ align:start position:0%
+just if I only focus on that there's a
+ 
+
+ align:start position:0%
+just if I only focus on that there's a
+component okay
+
+ align:start position:0%
+component okay
+ 
+
+ align:start position:0%
+component okay
+lamp inside essentially just ms 1k a x a
+
+ align:start position:0%
+lamp inside essentially just ms 1k a x a
+ 
+
+ align:start position:0%
+lamp inside essentially just ms 1k a x a
+right okay so basically only there are
+
+ align:start position:0%
+right okay so basically only there are
+ 
+
+ align:start position:0%
+right okay so basically only there are
+only three turns coming to pray right if
+
+ align:start position:0%
+only three turns coming to pray right if
+ 
+
+ align:start position:0%
+only three turns coming to pray right if
+this is a 2-1 so 18 minus one will
+
+ align:start position:0%
+this is a 2-1 so 18 minus one will
+ 
+
+ align:start position:0%
+this is a 2-1 so 18 minus one will
+multiply 5 minus K over N AJ work
+
+ align:start position:0%
+multiply 5 minus K over N AJ work
+ 
+
+ align:start position:0%
+multiply 5 minus K over N AJ work
+multiplied by 2 K over N and AJ past one
+
+ align:start position:0%
+multiplied by 2 K over N and AJ past one
+ 
+
+ align:start position:0%
+multiplied by 2 K over N and AJ past one
+will multiply by minus K over N right
+
+ align:start position:0%
+will multiply by minus K over N right
+ 
+
+ align:start position:0%
+will multiply by minus K over N right
+the rest of the turns are all 0
+
+ align:start position:0%
+the rest of the turns are all 0
+ 
+
+ align:start position:0%
+the rest of the turns are all 0
+okay it's actually not as complicated as
+
+ align:start position:0%
+okay it's actually not as complicated as
+ 
+
+ align:start position:0%
+okay it's actually not as complicated as
+we sought ok so if I write it down
+
+ align:start position:0%
+we sought ok so if I write it down
+ 
+
+ align:start position:0%
+we sought ok so if I write it down
+explicitly the left hand side part then
+
+ align:start position:0%
+explicitly the left hand side part then
+ 
+
+ align:start position:0%
+explicitly the left hand side part then
+what I'm going to get is minus K over N
+
+ align:start position:0%
+what I'm going to get is minus K over N
+ 
+
+ align:start position:0%
+what I'm going to get is minus K over N
+capital K over N AJ minus one price to
+
+ align:start position:0%
+capital K over N AJ minus one price to
+ 
+
+ align:start position:0%
+capital K over N AJ minus one price to
+capital K over N AJ minus capital K over
+
+ align:start position:0%
+capital K over N AJ minus capital K over
+ 
+
+ align:start position:0%
+capital K over N AJ minus capital K over
+N it's a plus 1 okay so this is actually
+
+ align:start position:0%
+N it's a plus 1 okay so this is actually
+ 
+
+ align:start position:0%
+N it's a plus 1 okay so this is actually
+the day's time okay now I can define
+
+ align:start position:0%
+the day's time okay now I can define
+ 
+
+ align:start position:0%
+the day's time okay now I can define
+Omega 0 square equal it's defined as
+
+ align:start position:0%
+Omega 0 square equal it's defined as
+ 
+
+ align:start position:0%
+Omega 0 square equal it's defined as
+capital K over N if I do that then
+
+ align:start position:0%
+capital K over N if I do that then
+ 
+
+ align:start position:0%
+capital K over N if I do that then
+basically I can I can see that Omega
+
+ align:start position:0%
+basically I can I can see that Omega
+ 
+
+ align:start position:0%
+basically I can I can see that Omega
+square AJ would be equal to Omega 0
+
+ align:start position:0%
+square AJ would be equal to Omega 0
+ 
+
+ align:start position:0%
+square AJ would be equal to Omega 0
+square okay I'm taking all the way over
+
+ align:start position:0%
+square okay I'm taking all the way over
+ 
+
+ align:start position:0%
+square okay I'm taking all the way over
+and out of the game and the lighted tag
+
+ align:start position:0%
+and out of the game and the lighted tag
+ 
+
+ align:start position:0%
+and out of the game and the lighted tag
+is Omega 0 square okay
+
+ align:start position:0%
+is Omega 0 square okay
+ 
+
+ align:start position:0%
+is Omega 0 square okay
+- 8a minus 1 plus 2 AJ - AJ possible
+
+ align:start position:0%
+- 8a minus 1 plus 2 AJ - AJ possible
+ 
+
+ align:start position:0%
+- 8a minus 1 plus 2 AJ - AJ possible
+okay and also we know from the previous
+
+ align:start position:0%
+okay and also we know from the previous
+ 
+
+ align:start position:0%
+okay and also we know from the previous
+discussion s matrix and the N minus 1 K
+
+ align:start position:0%
+discussion s matrix and the N minus 1 K
+ 
+
+ align:start position:0%
+discussion s matrix and the N minus 1 K
+matrix should share the same sets of
+
+ align:start position:0%
+matrix should share the same sets of
+ 
+
+ align:start position:0%
+matrix should share the same sets of
+eigenvectors therefore I can actually
+
+ align:start position:0%
+eigenvectors therefore I can actually
+ 
+
+ align:start position:0%
+eigenvectors therefore I can actually
+try to proc in one of the eigenvector
+
+ align:start position:0%
+try to proc in one of the eigenvector
+ 
+
+ align:start position:0%
+try to proc in one of the eigenvector
+from s matrix right AJ equal to beta J
+
+ align:start position:0%
+from s matrix right AJ equal to beta J
+ 
+
+ align:start position:0%
+from s matrix right AJ equal to beta J
+okay I can Proctor then basically I get
+
+ align:start position:0%
+okay I can Proctor then basically I get
+ 
+
+ align:start position:0%
+okay I can Proctor then basically I get
+Omega 0 square minus P minus beta J
+
+ align:start position:0%
+Omega 0 square minus P minus beta J
+ 
+
+ align:start position:0%
+Omega 0 square minus P minus beta J
+minus 1 plus 2 beta 2 DJ minus beta J
+
+ align:start position:0%
+minus 1 plus 2 beta 2 DJ minus beta J
+ 
+
+ align:start position:0%
+minus 1 plus 2 beta 2 DJ minus beta J
+plus 1 and the left hand side will be
+
+ align:start position:0%
+plus 1 and the left hand side will be
+ 
+
+ align:start position:0%
+plus 1 and the left hand side will be
+knitting like Omega square beta to the
+
+ align:start position:0%
+knitting like Omega square beta to the
+ 
+
+ align:start position:0%
+knitting like Omega square beta to the
+chain okay questions okay
+
+ align:start position:0%
+chain okay questions okay
+ 
+
+ align:start position:0%
+chain okay questions okay
+so now I can cancel I can actually
+
+ align:start position:0%
+so now I can cancel I can actually
+ 
+
+ align:start position:0%
+so now I can cancel I can actually
+divide everything by beta to each a
+
+ align:start position:0%
+divide everything by beta to each a
+ 
+
+ align:start position:0%
+divide everything by beta to each a
+right I can get rid of a tattoo it's a
+
+ align:start position:0%
+right I can get rid of a tattoo it's a
+ 
+
+ align:start position:0%
+right I can get rid of a tattoo it's a
+then basically I get omega squared equal
+
+ align:start position:0%
+then basically I get omega squared equal
+ 
+
+ align:start position:0%
+then basically I get omega squared equal
+to Omega 0 square minus 1 over beta plus
+
+ align:start position:0%
+to Omega 0 square minus 1 over beta plus
+ 
+
+ align:start position:0%
+to Omega 0 square minus 1 over beta plus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+- okay and as we discussed before beta
+
+ align:start position:0%
+- okay and as we discussed before beta
+ 
+
+ align:start position:0%
+- okay and as we discussed before beta
+can have any value okay and also you can
+
+ align:start position:0%
+can have any value okay and also you can
+ 
+
+ align:start position:0%
+can have any value okay and also you can
+see from here that huh once I know the
+
+ align:start position:0%
+see from here that huh once I know the
+ 
+
+ align:start position:0%
+see from here that huh once I know the
+icon value of s matrix and eigen vector
+
+ align:start position:0%
+icon value of s matrix and eigen vector
+ 
+
+ align:start position:0%
+icon value of s matrix and eigen vector
+or matrix I also know what this entry
+
+ align:start position:0%
+or matrix I also know what this entry
+ 
+
+ align:start position:0%
+or matrix I also know what this entry
+the corresponding angular frequency of
+
+ align:start position:0%
+the corresponding angular frequency of
+ 
+
+ align:start position:0%
+the corresponding angular frequency of
+the normal model right by using n minus
+
+ align:start position:0%
+the normal model right by using n minus
+ 
+
+ align:start position:0%
+the normal model right by using n minus
+1 K times a you can figure out what is
+
+ align:start position:0%
+1 K times a you can figure out what is
+ 
+
+ align:start position:0%
+1 K times a you can figure out what is
+actually the corresponding Omega the
+
+ align:start position:0%
+actually the corresponding Omega the
+ 
+
+ align:start position:0%
+actually the corresponding Omega the
+normal mode frequency okay so that is
+
+ align:start position:0%
+normal mode frequency okay so that is
+ 
+
+ align:start position:0%
+normal mode frequency okay so that is
+actually pretty nice but on the other
+
+ align:start position:0%
+actually pretty nice but on the other
+ 
+
+ align:start position:0%
+actually pretty nice but on the other
+hand if you step back and the sync about
+
+ align:start position:0%
+hand if you step back and the sync about
+ 
+
+ align:start position:0%
+hand if you step back and the sync about
+what we have been doing okay so very
+
+ align:start position:0%
+what we have been doing okay so very
+ 
+
+ align:start position:0%
+what we have been doing okay so very
+good you have a beta which is a random
+
+ align:start position:0%
+good you have a beta which is a random
+ 
+
+ align:start position:0%
+good you have a beta which is a random
+value you can evaluate this is C then
+
+ align:start position:0%
+value you can evaluate this is C then
+ 
+
+ align:start position:0%
+value you can evaluate this is C then
+you can get the corresponding Omega with
+
+ align:start position:0%
+you can get the corresponding Omega with
+ 
+
+ align:start position:0%
+you can get the corresponding Omega with
+that but this something doesn't feel
+
+ align:start position:0%
+that but this something doesn't feel
+ 
+
+ align:start position:0%
+that but this something doesn't feel
+right right for example if you have beta
+
+ align:start position:0%
+right right for example if you have beta
+ 
+
+ align:start position:0%
+right right for example if you have beta
+equal to 2 what is going to happen if
+
+ align:start position:0%
+equal to 2 what is going to happen if
+ 
+
+ align:start position:0%
+equal to 2 what is going to happen if
+you have beta equal to 2 what does that
+
+ align:start position:0%
+you have beta equal to 2 what does that
+ 
+
+ align:start position:0%
+you have beta equal to 2 what does that
+mean that means a day will be equal to 2
+
+ align:start position:0%
+mean that means a day will be equal to 2
+ 
+
+ align:start position:0%
+mean that means a day will be equal to 2
+to DJ okay that's very dangerous
+
+ align:start position:0%
+to DJ okay that's very dangerous
+ 
+
+ align:start position:0%
+to DJ okay that's very dangerous
+hey that means okay so I am I deployed
+
+ align:start position:0%
+hey that means okay so I am I deployed
+ 
+
+ align:start position:0%
+hey that means okay so I am I deployed
+the whole system okay from the lapin
+
+ align:start position:0%
+the whole system okay from the lapin
+ 
+
+ align:start position:0%
+the whole system okay from the lapin
+side of the new universe to the
+
+ align:start position:0%
+side of the new universe to the
+ 
+
+ align:start position:0%
+side of the new universe to the
+right-hand side of the universe okay so
+
+ align:start position:0%
+right-hand side of the universe okay so
+ 
+
+ align:start position:0%
+right-hand side of the universe okay so
+now means if I go to the the
+
+ align:start position:0%
+now means if I go to the the
+ 
+
+ align:start position:0%
+now means if I go to the the
+your right-hand side of the universe
+
+ align:start position:0%
+your right-hand side of the universe
+ 
+
+ align:start position:0%
+your right-hand side of the universe
+okay the amplitude explode right it's
+
+ align:start position:0%
+okay the amplitude explode right it's
+ 
+
+ align:start position:0%
+okay the amplitude explode right it's
+actually two to the infini number right
+
+ align:start position:0%
+actually two to the infini number right
+ 
+
+ align:start position:0%
+actually two to the infini number right
+okay it's now physics doesn't sound like
+
+ align:start position:0%
+okay it's now physics doesn't sound like
+ 
+
+ align:start position:0%
+okay it's now physics doesn't sound like
+a physical system to me right if
+
+ align:start position:0%
+a physical system to me right if
+ 
+
+ align:start position:0%
+a physical system to me right if
+actually beta is greater than one then
+
+ align:start position:0%
+actually beta is greater than one then
+ 
+
+ align:start position:0%
+actually beta is greater than one then
+the right-hand side edge of the universe
+
+ align:start position:0%
+the right-hand side edge of the universe
+ 
+
+ align:start position:0%
+the right-hand side edge of the universe
+the Emperor to there will explode okay
+
+ align:start position:0%
+the Emperor to there will explode okay
+ 
+
+ align:start position:0%
+the Emperor to there will explode okay
+doesn't sound right right so I don't
+
+ align:start position:0%
+doesn't sound right right so I don't
+ 
+
+ align:start position:0%
+doesn't sound right right so I don't
+like that okay maybe you like it but I I
+
+ align:start position:0%
+like that okay maybe you like it but I I
+ 
+
+ align:start position:0%
+like that okay maybe you like it but I I
+don't like it for the moment on the
+
+ align:start position:0%
+don't like it for the moment on the
+ 
+
+ align:start position:0%
+don't like it for the moment on the
+other hand if the beta okay again it's
+
+ align:start position:0%
+other hand if the beta okay again it's
+ 
+
+ align:start position:0%
+other hand if the beta okay again it's
+not one but some other than one what is
+
+ align:start position:0%
+not one but some other than one what is
+ 
+
+ align:start position:0%
+not one but some other than one what is
+going to happen if the beta is smoother
+
+ align:start position:0%
+going to happen if the beta is smoother
+ 
+
+ align:start position:0%
+going to happen if the beta is smoother
+than one what is going to happen is that
+
+ align:start position:0%
+than one what is going to happen is that
+ 
+
+ align:start position:0%
+than one what is going to happen is that
+huh okay
+
+ align:start position:0%
+huh okay
+ 
+
+ align:start position:0%
+huh okay
+the right-hand side universe is fine is
+
+ align:start position:0%
+the right-hand side universe is fine is
+ 
+
+ align:start position:0%
+the right-hand side universe is fine is
+finite because the amplitudes become
+
+ align:start position:0%
+finite because the amplitudes become
+ 
+
+ align:start position:0%
+finite because the amplitudes become
+smaller and smaller but the Lavin's are
+
+ align:start position:0%
+smaller and smaller but the Lavin's are
+ 
+
+ align:start position:0%
+smaller and smaller but the Lavin's are
+part of the universe the amplitude still
+
+ align:start position:0%
+part of the universe the amplitude still
+ 
+
+ align:start position:0%
+part of the universe the amplitude still
+explode right so what does that mean
+
+ align:start position:0%
+explode right so what does that mean
+ 
+
+ align:start position:0%
+explode right so what does that mean
+this means that if beta if the absolute
+
+ align:start position:0%
+this means that if beta if the absolute
+ 
+
+ align:start position:0%
+this means that if beta if the absolute
+value of beta is not equal to one the
+
+ align:start position:0%
+value of beta is not equal to one the
+ 
+
+ align:start position:0%
+value of beta is not equal to one the
+amplitude at some point goes to infinity
+
+ align:start position:0%
+amplitude at some point goes to infinity
+ 
+
+ align:start position:0%
+amplitude at some point goes to infinity
+okay so that's actually not very nice
+
+ align:start position:0%
+okay so that's actually not very nice
+ 
+
+ align:start position:0%
+okay so that's actually not very nice
+that's because AJ is actually
+
+ align:start position:0%
+that's because AJ is actually
+ 
+
+ align:start position:0%
+that's because AJ is actually
+proportional to beta to you take okay so
+
+ align:start position:0%
+proportional to beta to you take okay so
+ 
+
+ align:start position:0%
+proportional to beta to you take okay so
+in the discussion we have here we
+
+ align:start position:0%
+in the discussion we have here we
+ 
+
+ align:start position:0%
+in the discussion we have here we
+consider beta equal to one case
+
+ align:start position:0%
+consider beta equal to one case
+ 
+
+ align:start position:0%
+consider beta equal to one case
+okay otherwise this actually things will
+
+ align:start position:0%
+okay otherwise this actually things will
+ 
+
+ align:start position:0%
+okay otherwise this actually things will
+explode
+
+ align:start position:0%
+explode
+ 
+
+ align:start position:0%
+explode
+okay so if the absolute value of beta is
+
+ align:start position:0%
+okay so if the absolute value of beta is
+ 
+
+ align:start position:0%
+okay so if the absolute value of beta is
+equal to one in general beta can be
+
+ align:start position:0%
+equal to one in general beta can be
+ 
+
+ align:start position:0%
+equal to one in general beta can be
+exponential I smoke a a right then
+
+ align:start position:0%
+exponential I smoke a a right then
+ 
+
+ align:start position:0%
+exponential I smoke a a right then
+usually you can edges get absolute value
+
+ align:start position:0%
+usually you can edges get absolute value
+ 
+
+ align:start position:0%
+usually you can edges get absolute value
+of one okay if beta is equal to one that
+
+ align:start position:0%
+of one okay if beta is equal to one that
+ 
+
+ align:start position:0%
+of one okay if beta is equal to one that
+means the amplitude of all the
+
+ align:start position:0%
+means the amplitude of all the
+ 
+
+ align:start position:0%
+means the amplitude of all the
+oscillators are the same okay
+
+ align:start position:0%
+oscillators are the same okay
+ 
+
+ align:start position:0%
+oscillators are the same okay
+all right so now if if we accept this we
+
+ align:start position:0%
+all right so now if if we accept this we
+ 
+
+ align:start position:0%
+all right so now if if we accept this we
+only limit ourselves to the discussion
+
+ align:start position:0%
+only limit ourselves to the discussion
+ 
+
+ align:start position:0%
+only limit ourselves to the discussion
+of beta absolute beta value of beta
+
+ align:start position:0%
+of beta absolute beta value of beta
+ 
+
+ align:start position:0%
+of beta absolute beta value of beta
+equal to 1 then beta can be written as
+
+ align:start position:0%
+equal to 1 then beta can be written as
+ 
+
+ align:start position:0%
+equal to 1 then beta can be written as
+exponential I K a that if I practice
+
+ align:start position:0%
+exponential I K a that if I practice
+ 
+
+ align:start position:0%
+exponential I K a that if I practice
+back into this basically what you are
+
+ align:start position:0%
+back into this basically what you are
+ 
+
+ align:start position:0%
+back into this basically what you are
+going to get is Omega square is equal to
+
+ align:start position:0%
+going to get is Omega square is equal to
+ 
+
+ align:start position:0%
+going to get is Omega square is equal to
+Omega 0 square 2 minus exponential I K a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus exponential minus I K right because
+
+ align:start position:0%
+plus exponential minus I K right because
+ 
+
+ align:start position:0%
+plus exponential minus I K right because
+you have minus 1 over beta the beta
+
+ align:start position:0%
+you have minus 1 over beta the beta
+ 
+
+ align:start position:0%
+you have minus 1 over beta the beta
+therefore you have exponential I K a and
+
+ align:start position:0%
+therefore you have exponential I K a and
+ 
+
+ align:start position:0%
+therefore you have exponential I K a and
+the exponential minus I theta ok it's a
+
+ align:start position:0%
+the exponential minus I theta ok it's a
+ 
+
+ align:start position:0%
+the exponential minus I theta ok it's a
+lot of math in this the this lecture but
+
+ align:start position:0%
+lot of math in this the this lecture but
+ 
+
+ align:start position:0%
+lot of math in this the this lecture but
+I we are getting all over to it ok all
+
+ align:start position:0%
+I we are getting all over to it ok all
+ 
+
+ align:start position:0%
+I we are getting all over to it ok all
+right so that essentially we actually
+
+ align:start position:0%
+right so that essentially we actually
+ 
+
+ align:start position:0%
+right so that essentially we actually
+can identify this and this issue can be
+
+ align:start position:0%
+can identify this and this issue can be
+ 
+
+ align:start position:0%
+can identify this and this issue can be
+written as 2 Omega 0 Square 1 minus
+
+ align:start position:0%
+written as 2 Omega 0 Square 1 minus
+ 
+
+ align:start position:0%
+written as 2 Omega 0 Square 1 minus
+cosine K ok we have arrived a
+
+ align:start position:0%
+cosine K ok we have arrived a
+ 
+
+ align:start position:0%
+cosine K ok we have arrived a
+surprisingly simple expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take a look at this expression
+
+ align:start position:0%
+so let's take a look at this expression
+ 
+
+ align:start position:0%
+so let's take a look at this expression
+carefully so that means for each given K
+
+ align:start position:0%
+carefully so that means for each given K
+ 
+
+ align:start position:0%
+carefully so that means for each given K
+small K okay then we have a
+
+ align:start position:0%
+small K okay then we have a
+ 
+
+ align:start position:0%
+small K okay then we have a
+corresponding angular frequency Omega
+
+ align:start position:0%
+corresponding angular frequency Omega
+ 
+
+ align:start position:0%
+corresponding angular frequency Omega
+square okay so still there are infinite
+
+ align:start position:0%
+square okay so still there are infinite
+ 
+
+ align:start position:0%
+square okay so still there are infinite
+number of we are infinite number of
+
+ align:start position:0%
+number of we are infinite number of
+ 
+
+ align:start position:0%
+number of we are infinite number of
+possible normal modes okay from this so
+
+ align:start position:0%
+possible normal modes okay from this so
+ 
+
+ align:start position:0%
+possible normal modes okay from this so
+if I take a look at the amplitude okay
+
+ align:start position:0%
+if I take a look at the amplitude okay
+ 
+
+ align:start position:0%
+if I take a look at the amplitude okay
+so if I I select a K value okay
+
+ align:start position:0%
+so if I I select a K value okay
+ 
+
+ align:start position:0%
+so if I I select a K value okay
+small K value if I if K is given I can
+
+ align:start position:0%
+small K value if I if K is given I can
+ 
+
+ align:start position:0%
+small K value if I if K is given I can
+actually calculate that K is found in a
+
+ align:start position:0%
+actually calculate that K is found in a
+ 
+
+ align:start position:0%
+actually calculate that K is found in a
+day so that a day I can actually define
+
+ align:start position:0%
+day so that a day I can actually define
+ 
+
+ align:start position:0%
+day so that a day I can actually define
+as a superposition of exponential I take
+
+ align:start position:0%
+as a superposition of exponential I take
+ 
+
+ align:start position:0%
+as a superposition of exponential I take
+K a and minus exponential I J okay
+
+ align:start position:0%
+K a and minus exponential I J okay
+ 
+
+ align:start position:0%
+K a and minus exponential I J okay
+and now will give you a sinusoidal shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I give you the K okay basically
+
+ align:start position:0%
+so if I give you the K okay basically
+ 
+
+ align:start position:0%
+so if I give you the K okay basically
+you will see that if I give you it okay
+
+ align:start position:0%
+you will see that if I give you it okay
+ 
+
+ align:start position:0%
+you will see that if I give you it okay
+then you you get a corresponding beta
+
+ align:start position:0%
+then you you get a corresponding beta
+ 
+
+ align:start position:0%
+then you you get a corresponding beta
+right and the you get you are going to
+
+ align:start position:0%
+right and the you get you are going to
+ 
+
+ align:start position:0%
+right and the you get you are going to
+get Omega the corresponding Omega square
+
+ align:start position:0%
+get Omega the corresponding Omega square
+ 
+
+ align:start position:0%
+get Omega the corresponding Omega square
+but one interesting C of this expression
+
+ align:start position:0%
+but one interesting C of this expression
+ 
+
+ align:start position:0%
+but one interesting C of this expression
+is that if you keep beta or keep you
+
+ align:start position:0%
+is that if you keep beta or keep you
+ 
+
+ align:start position:0%
+is that if you keep beta or keep you
+keep one over beta you are going to get
+
+ align:start position:0%
+keep one over beta you are going to get
+ 
+
+ align:start position:0%
+keep one over beta you are going to get
+the same Omega therefore I can now use
+
+ align:start position:0%
+the same Omega therefore I can now use
+ 
+
+ align:start position:0%
+the same Omega therefore I can now use
+superposition principle basically I can
+
+ align:start position:0%
+superposition principle basically I can
+ 
+
+ align:start position:0%
+superposition principle basically I can
+actually add this to solution together
+
+ align:start position:0%
+actually add this to solution together
+ 
+
+ align:start position:0%
+actually add this to solution together
+since they are going to be oscillating
+
+ align:start position:0%
+since they are going to be oscillating
+ 
+
+ align:start position:0%
+since they are going to be oscillating
+at the same frequency then what I am
+
+ align:start position:0%
+at the same frequency then what I am
+ 
+
+ align:start position:0%
+at the same frequency then what I am
+going to get is that huh interesting
+
+ align:start position:0%
+going to get is that huh interesting
+ 
+
+ align:start position:0%
+going to get is that huh interesting
+thing happen the AJ the amplitude as a
+
+ align:start position:0%
+thing happen the AJ the amplitude as a
+ 
+
+ align:start position:0%
+thing happen the AJ the amplitude as a
+function of J is like a sinusoidal
+
+ align:start position:0%
+function of J is like a sinusoidal
+ 
+
+ align:start position:0%
+function of J is like a sinusoidal
+function okay so that is essentially
+
+ align:start position:0%
+function okay so that is essentially
+ 
+
+ align:start position:0%
+function okay so that is essentially
+what is a really predicted to infinite
+
+ align:start position:0%
+what is a really predicted to infinite
+ 
+
+ align:start position:0%
+what is a really predicted to infinite
+long system for example if I do this you
+
+ align:start position:0%
+long system for example if I do this you
+ 
+
+ align:start position:0%
+long system for example if I do this you
+can see that hi indeed I can see
+
+ align:start position:0%
+can see that hi indeed I can see
+ 
+
+ align:start position:0%
+can see that hi indeed I can see
+sinusoidal shape okay and and you can
+
+ align:start position:0%
+sinusoidal shape okay and and you can
+ 
+
+ align:start position:0%
+sinusoidal shape okay and and you can
+see that this sinusoidal shape is
+
+ align:start position:0%
+see that this sinusoidal shape is
+ 
+
+ align:start position:0%
+see that this sinusoidal shape is
+actually oscillating up and down like a
+
+ align:start position:0%
+actually oscillating up and down like a
+ 
+
+ align:start position:0%
+actually oscillating up and down like a
+know like a standing wave and that is
+
+ align:start position:0%
+know like a standing wave and that is
+ 
+
+ align:start position:0%
+know like a standing wave and that is
+actually exactly this expression so that
+
+ align:start position:0%
+actually exactly this expression so that
+ 
+
+ align:start position:0%
+actually exactly this expression so that
+tells you something really interesting
+
+ align:start position:0%
+tells you something really interesting
+ 
+
+ align:start position:0%
+tells you something really interesting
+that means this sign so little shape is
+
+ align:start position:0%
+that means this sign so little shape is
+ 
+
+ align:start position:0%
+that means this sign so little shape is
+associated with what associated with
+
+ align:start position:0%
+associated with what associated with
+ 
+
+ align:start position:0%
+associated with what associated with
+translation symmetry right all I have
+
+ align:start position:0%
+translation symmetry right all I have
+ 
+
+ align:start position:0%
+translation symmetry right all I have
+been doing is to require this
+
+ align:start position:0%
+been doing is to require this
+ 
+
+ align:start position:0%
+been doing is to require this
+translation symmetry then you already
+
+ align:start position:0%
+translation symmetry then you already
+ 
+
+ align:start position:0%
+translation symmetry then you already
+get the amplitude AJ and if you choose
+
+ align:start position:0%
+get the amplitude AJ and if you choose
+ 
+
+ align:start position:0%
+get the amplitude AJ and if you choose
+the physical beta value then you already
+
+ align:start position:0%
+the physical beta value then you already
+ 
+
+ align:start position:0%
+the physical beta value then you already
+immediately arrive a solution which is
+
+ align:start position:0%
+immediately arrive a solution which is
+ 
+
+ align:start position:0%
+immediately arrive a solution which is
+actually like sinusoidal shape that
+
+ align:start position:0%
+actually like sinusoidal shape that
+ 
+
+ align:start position:0%
+actually like sinusoidal shape that
+sounds really amazing to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I think it's time to good to
+
+ align:start position:0%
+okay so I think it's time to good to
+ 
+
+ align:start position:0%
+okay so I think it's time to good to
+take a five-minute break because I can
+
+ align:start position:0%
+take a five-minute break because I can
+ 
+
+ align:start position:0%
+take a five-minute break because I can
+see that you are overwhelmed by the mess
+
+ align:start position:0%
+see that you are overwhelmed by the mess
+ 
+
+ align:start position:0%
+see that you are overwhelmed by the mess
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+and of course let's come back in five
+
+ align:start position:0%
+and of course let's come back in five
+ 
+
+ align:start position:0%
+and of course let's come back in five
+minutes then we can discuss some more
+
+ align:start position:0%
+minutes then we can discuss some more
+ 
+
+ align:start position:0%
+minutes then we can discuss some more
+about what we have learned from this
+
+ align:start position:0%
+about what we have learned from this
+ 
+
+ align:start position:0%
+about what we have learned from this
+mathematics and if you have any
+
+ align:start position:0%
+mathematics and if you have any
+ 
+
+ align:start position:0%
+mathematics and if you have any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+everybody of course you are welcome to
+
+ align:start position:0%
+everybody of course you are welcome to
+ 
+
+ align:start position:0%
+everybody of course you are welcome to
+come back here and the prayer with the
+
+ align:start position:0%
+come back here and the prayer with the
+ 
+
+ align:start position:0%
+come back here and the prayer with the
+demonstration okay so so very good so
+
+ align:start position:0%
+demonstration okay so so very good so
+ 
+
+ align:start position:0%
+demonstration okay so so very good so
+during the break there are several
+
+ align:start position:0%
+during the break there are several
+ 
+
+ align:start position:0%
+during the break there are several
+questions asked which i think is no
+
+ align:start position:0%
+questions asked which i think is no
+ 
+
+ align:start position:0%
+questions asked which i think is no
+those are very good questions and that's
+
+ align:start position:0%
+those are very good questions and that's
+ 
+
+ align:start position:0%
+those are very good questions and that's
+actually the purpose of this break so
+
+ align:start position:0%
+actually the purpose of this break so
+ 
+
+ align:start position:0%
+actually the purpose of this break so
+it's a long day already right a lot of
+
+ align:start position:0%
+it's a long day already right a lot of
+ 
+
+ align:start position:0%
+it's a long day already right a lot of
+mathematics and I hope everybody
+
+ align:start position:0%
+mathematics and I hope everybody
+ 
+
+ align:start position:0%
+mathematics and I hope everybody
+survived
+
+ align:start position:0%
+survived
+ 
+
+ align:start position:0%
+survived
+okay no dead body yet okay you can see
+
+ align:start position:0%
+okay no dead body yet okay you can see
+ 
+
+ align:start position:0%
+okay no dead body yet okay you can see
+that here I'm doing something really
+
+ align:start position:0%
+that here I'm doing something really
+ 
+
+ align:start position:0%
+that here I'm doing something really
+crazy here so okay consider okay I think
+
+ align:start position:0%
+crazy here so okay consider okay I think
+ 
+
+ align:start position:0%
+crazy here so okay consider okay I think
+most of you cut this point beta naught
+
+ align:start position:0%
+most of you cut this point beta naught
+ 
+
+ align:start position:0%
+most of you cut this point beta naught
+equal to Y is now nice something is pro
+
+ align:start position:0%
+equal to Y is now nice something is pro
+ 
+
+ align:start position:0%
+equal to Y is now nice something is pro
+at the edge of the universe so I don't
+
+ align:start position:0%
+at the edge of the universe so I don't
+ 
+
+ align:start position:0%
+at the edge of the universe so I don't
+like that therefore I consider only the
+
+ align:start position:0%
+like that therefore I consider only the
+ 
+
+ align:start position:0%
+like that therefore I consider only the
+case which you have absolute value beta
+
+ align:start position:0%
+case which you have absolute value beta
+ 
+
+ align:start position:0%
+case which you have absolute value beta
+equal to 1 and then we say okay you can
+
+ align:start position:0%
+equal to 1 and then we say okay you can
+ 
+
+ align:start position:0%
+equal to 1 and then we say okay you can
+be plus 1 and minus 1 but that's
+
+ align:start position:0%
+be plus 1 and minus 1 but that's
+ 
+
+ align:start position:0%
+be plus 1 and minus 1 but that's
+actually not the whole story right you
+
+ align:start position:0%
+actually not the whole story right you
+ 
+
+ align:start position:0%
+actually not the whole story right you
+can have in general beta equal to
+
+ align:start position:0%
+can have in general beta equal to
+ 
+
+ align:start position:0%
+can have in general beta equal to
+exponential I some number all right
+
+ align:start position:0%
+exponential I some number all right
+ 
+
+ align:start position:0%
+exponential I some number all right
+sounds real number okay and and I write
+
+ align:start position:0%
+sounds real number okay and and I write
+ 
+
+ align:start position:0%
+sounds real number okay and and I write
+here a very fancy expression beta equal
+
+ align:start position:0%
+here a very fancy expression beta equal
+ 
+
+ align:start position:0%
+here a very fancy expression beta equal
+to exponential I K a why i ka it's a
+
+ align:start position:0%
+to exponential I K a why i ka it's a
+ 
+
+ align:start position:0%
+to exponential I K a why i ka it's a
+very good question right what is a I
+
+ align:start position:0%
+very good question right what is a I
+ 
+
+ align:start position:0%
+very good question right what is a I
+think most of us you already forgot what
+
+ align:start position:0%
+think most of us you already forgot what
+ 
+
+ align:start position:0%
+think most of us you already forgot what
+is a a is actually the natural length of
+
+ align:start position:0%
+is a a is actually the natural length of
+ 
+
+ align:start position:0%
+is a a is actually the natural length of
+the spring okay so I was going to pass
+
+ align:start position:0%
+the spring okay so I was going to pass
+ 
+
+ align:start position:0%
+the spring okay so I was going to pass
+because I would like to get to a break
+
+ align:start position:0%
+because I would like to get to a break
+ 
+
+ align:start position:0%
+because I would like to get to a break
+to hear your questions so what is a is
+
+ align:start position:0%
+to hear your questions so what is a is
+ 
+
+ align:start position:0%
+to hear your questions so what is a is
+the natural length okay and the K what
+
+ align:start position:0%
+the natural length okay and the K what
+ 
+
+ align:start position:0%
+the natural length okay and the K what
+is K later you will figure that out
+
+ align:start position:0%
+is K later you will figure that out
+ 
+
+ align:start position:0%
+is K later you will figure that out
+you'll find that HK is wave number okay
+
+ align:start position:0%
+you'll find that HK is wave number okay
+ 
+
+ align:start position:0%
+you'll find that HK is wave number okay
+so that is actually much more meaningful
+
+ align:start position:0%
+so that is actually much more meaningful
+ 
+
+ align:start position:0%
+so that is actually much more meaningful
+now right after the explanation so you
+
+ align:start position:0%
+now right after the explanation so you
+ 
+
+ align:start position:0%
+now right after the explanation so you
+can see that beta is equal to
+
+ align:start position:0%
+can see that beta is equal to
+ 
+
+ align:start position:0%
+can see that beta is equal to
+exponential ice on number and I call it
+
+ align:start position:0%
+exponential ice on number and I call it
+ 
+
+ align:start position:0%
+exponential ice on number and I call it
+ka a pencil name of this number and it
+
+ align:start position:0%
+ka a pencil name of this number and it
+ 
+
+ align:start position:0%
+ka a pencil name of this number and it
+has some physical meaning okay another
+
+ align:start position:0%
+has some physical meaning okay another
+ 
+
+ align:start position:0%
+has some physical meaning okay another
+thing which is interesting is that
+
+ align:start position:0%
+thing which is interesting is that
+ 
+
+ align:start position:0%
+thing which is interesting is that
+if I plug in beta equal to a poor beta
+
+ align:start position:0%
+if I plug in beta equal to a poor beta
+ 
+
+ align:start position:0%
+if I plug in beta equal to a poor beta
+equal to 1 over a ok into the same
+
+ align:start position:0%
+equal to 1 over a ok into the same
+ 
+
+ align:start position:0%
+equal to 1 over a ok into the same
+expression ok if I practice either beta
+
+ align:start position:0%
+expression ok if I practice either beta
+ 
+
+ align:start position:0%
+expression ok if I practice either beta
+a or equal over beta equal to 1 moreover
+
+ align:start position:0%
+a or equal over beta equal to 1 moreover
+ 
+
+ align:start position:0%
+a or equal over beta equal to 1 moreover
+a to this expression I'm going to get
+
+ align:start position:0%
+a to this expression I'm going to get
+ 
+
+ align:start position:0%
+a to this expression I'm going to get
+exactly the same Omega so that means ok
+
+ align:start position:0%
+exactly the same Omega so that means ok
+ 
+
+ align:start position:0%
+exactly the same Omega so that means ok
+both of them will be both value will be
+
+ align:start position:0%
+both of them will be both value will be
+ 
+
+ align:start position:0%
+both of them will be both value will be
+oscillating at the same frequency okay
+
+ align:start position:0%
+oscillating at the same frequency okay
+ 
+
+ align:start position:0%
+oscillating at the same frequency okay
+so if you choose beta equal to a choose
+
+ align:start position:0%
+so if you choose beta equal to a choose
+ 
+
+ align:start position:0%
+so if you choose beta equal to a choose
+a beta equal to mine 1 minus ay they are
+
+ align:start position:0%
+a beta equal to mine 1 minus ay they are
+ 
+
+ align:start position:0%
+a beta equal to mine 1 minus ay they are
+oscillating at the same frequency what
+
+ align:start position:0%
+oscillating at the same frequency what
+ 
+
+ align:start position:0%
+oscillating at the same frequency what
+does that mean that means linear
+
+ align:start position:0%
+does that mean that means linear
+ 
+
+ align:start position:0%
+does that mean that means linear
+combination of eigenvector coming from
+
+ align:start position:0%
+combination of eigenvector coming from
+ 
+
+ align:start position:0%
+combination of eigenvector coming from
+beta equal to a and eigenvector coming
+
+ align:start position:0%
+beta equal to a and eigenvector coming
+ 
+
+ align:start position:0%
+beta equal to a and eigenvector coming
+from beta equal to 1 over a linear
+
+ align:start position:0%
+from beta equal to 1 over a linear
+ 
+
+ align:start position:0%
+from beta equal to 1 over a linear
+combination of those eigenvectors are
+
+ align:start position:0%
+combination of those eigenvectors are
+ 
+
+ align:start position:0%
+combination of those eigenvectors are
+also eigen vectors the of the n minus 1
+
+ align:start position:0%
+also eigen vectors the of the n minus 1
+ 
+
+ align:start position:0%
+also eigen vectors the of the n minus 1
+K matrix okay and that's actually where
+
+ align:start position:0%
+K matrix okay and that's actually where
+ 
+
+ align:start position:0%
+K matrix okay and that's actually where
+okay those are different eigen vectors
+
+ align:start position:0%
+okay those are different eigen vectors
+ 
+
+ align:start position:0%
+okay those are different eigen vectors
+for s but the linear combination of
+
+ align:start position:0%
+for s but the linear combination of
+ 
+
+ align:start position:0%
+for s but the linear combination of
+these vectors the same are all the eigen
+
+ align:start position:0%
+these vectors the same are all the eigen
+ 
+
+ align:start position:0%
+these vectors the same are all the eigen
+vector of n minus 1 K matrix and the
+
+ align:start position:0%
+vector of n minus 1 K matrix and the
+ 
+
+ align:start position:0%
+vector of n minus 1 K matrix and the
+with the same eigen value Omega square
+
+ align:start position:0%
+with the same eigen value Omega square
+ 
+
+ align:start position:0%
+with the same eigen value Omega square
+okay so that's another thing which is
+
+ align:start position:0%
+okay so that's another thing which is
+ 
+
+ align:start position:0%
+okay so that's another thing which is
+important and finally I said that there
+
+ align:start position:0%
+important and finally I said that there
+ 
+
+ align:start position:0%
+important and finally I said that there
+are infinite number of choice oh tape
+
+ align:start position:0%
+are infinite number of choice oh tape
+ 
+
+ align:start position:0%
+are infinite number of choice oh tape
+that's bad right because you can choose
+
+ align:start position:0%
+that's bad right because you can choose
+ 
+
+ align:start position:0%
+that's bad right because you can choose
+our little number then you get a
+
+ align:start position:0%
+our little number then you get a
+ 
+
+ align:start position:0%
+our little number then you get a
+corresponding beta then you get a
+
+ align:start position:0%
+corresponding beta then you get a
+ 
+
+ align:start position:0%
+corresponding beta then you get a
+corresponding Omega so you have infinite
+
+ align:start position:0%
+corresponding Omega so you have infinite
+ 
+
+ align:start position:0%
+corresponding Omega so you have infinite
+number of normal modes secondly if I
+
+ align:start position:0%
+number of normal modes secondly if I
+ 
+
+ align:start position:0%
+number of normal modes secondly if I
+give you okay okay if I give you a K or
+
+ align:start position:0%
+give you okay okay if I give you a K or
+ 
+
+ align:start position:0%
+give you okay okay if I give you a K or
+I can give you another value which is
+
+ align:start position:0%
+I can give you another value which is
+ 
+
+ align:start position:0%
+I can give you another value which is
+minus K okay then I will that means you
+
+ align:start position:0%
+minus K okay then I will that means you
+ 
+
+ align:start position:0%
+minus K okay then I will that means you
+will get beta and 1 over beta right
+
+ align:start position:0%
+will get beta and 1 over beta right
+ 
+
+ align:start position:0%
+will get beta and 1 over beta right
+minus K will give you 1 over beta right
+
+ align:start position:0%
+minus K will give you 1 over beta right
+ 
+
+ align:start position:0%
+minus K will give you 1 over beta right
+and the answer I mentioned before big
+
+ align:start position:0%
+and the answer I mentioned before big
+ 
+
+ align:start position:0%
+and the answer I mentioned before big
+high equal to a and beta equal to
+
+ align:start position:0%
+high equal to a and beta equal to
+ 
+
+ align:start position:0%
+high equal to a and beta equal to
+I will give you the same Omega therefore
+
+ align:start position:0%
+I will give you the same Omega therefore
+ 
+
+ align:start position:0%
+I will give you the same Omega therefore
+a linear combination of the vectors are
+
+ align:start position:0%
+a linear combination of the vectors are
+ 
+
+ align:start position:0%
+a linear combination of the vectors are
+also eigen vector of ms1 kinetics
+
+ align:start position:0%
+also eigen vector of ms1 kinetics
+ 
+
+ align:start position:0%
+also eigen vector of ms1 kinetics
+nothing to what I am doing here right so
+
+ align:start position:0%
+nothing to what I am doing here right so
+ 
+
+ align:start position:0%
+nothing to what I am doing here right so
+in order to show you a real amplitude
+
+ align:start position:0%
+in order to show you a real amplitude
+ 
+
+ align:start position:0%
+in order to show you a real amplitude
+and doing a linear combination of
+
+ align:start position:0%
+and doing a linear combination of
+ 
+
+ align:start position:0%
+and doing a linear combination of
+explanation I take a a and the
+
+ align:start position:0%
+explanation I take a a and the
+ 
+
+ align:start position:0%
+explanation I take a a and the
+explanation - I take it's just a choice
+
+ align:start position:0%
+explanation - I take it's just a choice
+ 
+
+ align:start position:0%
+explanation - I take it's just a choice
+okay of course you can say okay I choose
+
+ align:start position:0%
+okay of course you can say okay I choose
+ 
+
+ align:start position:0%
+okay of course you can say okay I choose
+price and / - then you get the cosine
+
+ align:start position:0%
+price and / - then you get the cosine
+ 
+
+ align:start position:0%
+price and / - then you get the cosine
+right but if I choose this expression
+
+ align:start position:0%
+right but if I choose this expression
+ 
+
+ align:start position:0%
+right but if I choose this expression
+then what I'm going to get is that huh
+
+ align:start position:0%
+then what I'm going to get is that huh
+ 
+
+ align:start position:0%
+then what I'm going to get is that huh
+since both of them post vectors are
+
+ align:start position:0%
+since both of them post vectors are
+ 
+
+ align:start position:0%
+since both of them post vectors are
+corresponding to the same eigenvalue
+
+ align:start position:0%
+corresponding to the same eigenvalue
+ 
+
+ align:start position:0%
+corresponding to the same eigenvalue
+Omega square therefore linear
+
+ align:start position:0%
+Omega square therefore linear
+ 
+
+ align:start position:0%
+Omega square therefore linear
+combination of them also oscillate at
+
+ align:start position:0%
+combination of them also oscillate at
+ 
+
+ align:start position:0%
+combination of them also oscillate at
+the angular frequency of Omega therefore
+
+ align:start position:0%
+the angular frequency of Omega therefore
+ 
+
+ align:start position:0%
+the angular frequency of Omega therefore
+if I calculate this and make it real
+
+ align:start position:0%
+if I calculate this and make it real
+ 
+
+ align:start position:0%
+if I calculate this and make it real
+then I found out the amplitude as a
+
+ align:start position:0%
+then I found out the amplitude as a
+ 
+
+ align:start position:0%
+then I found out the amplitude as a
+function would say essentially a
+
+ align:start position:0%
+function would say essentially a
+ 
+
+ align:start position:0%
+function would say essentially a
+sinusoidal function which is sine say K
+
+ align:start position:0%
+sinusoidal function which is sine say K
+ 
+
+ align:start position:0%
+sinusoidal function which is sine say K
+okay so what does that mean this means
+
+ align:start position:0%
+okay so what does that mean this means
+ 
+
+ align:start position:0%
+okay so what does that mean this means
+that if I plot the eight if I prod AJ as
+
+ align:start position:0%
+that if I plot the eight if I prod AJ as
+ 
+
+ align:start position:0%
+that if I plot the eight if I prod AJ as
+a function of J this is actually what I
+
+ align:start position:0%
+a function of J this is actually what I
+ 
+
+ align:start position:0%
+a function of J this is actually what I
+am going to get this is a sign so dito
+
+ align:start position:0%
+am going to get this is a sign so dito
+ 
+
+ align:start position:0%
+am going to get this is a sign so dito
+shape okay and we know that XJ is
+
+ align:start position:0%
+shape okay and we know that XJ is
+ 
+
+ align:start position:0%
+shape okay and we know that XJ is
+actually equal to eight a cosine Omega T
+
+ align:start position:0%
+actually equal to eight a cosine Omega T
+ 
+
+ align:start position:0%
+actually equal to eight a cosine Omega T
+plus Phi right Omega I can actually
+
+ align:start position:0%
+plus Phi right Omega I can actually
+ 
+
+ align:start position:0%
+plus Phi right Omega I can actually
+evaluate that right from here right just
+
+ align:start position:0%
+evaluate that right from here right just
+ 
+
+ align:start position:0%
+evaluate that right from here right just
+a reminder
+
+ align:start position:0%
+a reminder
+ 
+
+ align:start position:0%
+a reminder
+and what we are going to get is when
+
+ align:start position:0%
+and what we are going to get is when
+ 
+
+ align:start position:0%
+and what we are going to get is when
+this system is in normal mode okay
+
+ align:start position:0%
+this system is in normal mode okay
+ 
+
+ align:start position:0%
+this system is in normal mode okay
+actually this is this system is still a
+
+ align:start position:0%
+actually this is this system is still a
+ 
+
+ align:start position:0%
+actually this is this system is still a
+discrete system so I actually would like
+
+ align:start position:0%
+discrete system so I actually would like
+ 
+
+ align:start position:0%
+discrete system so I actually would like
+to point out that as a function of H as
+
+ align:start position:0%
+to point out that as a function of H as
+ 
+
+ align:start position:0%
+to point out that as a function of H as
+a function say only discrete location
+
+ align:start position:0%
+a function say only discrete location
+ 
+
+ align:start position:0%
+a function say only discrete location
+have have mass right so you
+
+ align:start position:0%
+have have mass right so you
+ 
+
+ align:start position:0%
+have have mass right so you
+see that those are individual mess they
+
+ align:start position:0%
+see that those are individual mess they
+ 
+
+ align:start position:0%
+see that those are individual mess they
+are oscillating up and down okay and
+
+ align:start position:0%
+are oscillating up and down okay and
+ 
+
+ align:start position:0%
+are oscillating up and down okay and
+there you can see that okay since they
+
+ align:start position:0%
+there you can see that okay since they
+ 
+
+ align:start position:0%
+there you can see that okay since they
+are oscillating up and down there for
+
+ align:start position:0%
+are oscillating up and down there for
+ 
+
+ align:start position:0%
+are oscillating up and down there for
+the oscillation essentially going up and
+
+ align:start position:0%
+the oscillation essentially going up and
+ 
+
+ align:start position:0%
+the oscillation essentially going up and
+down therefore what is the what is
+
+ align:start position:0%
+down therefore what is the what is
+ 
+
+ align:start position:0%
+down therefore what is the what is
+situated normal more of this liquid in
+
+ align:start position:0%
+situated normal more of this liquid in
+ 
+
+ align:start position:0%
+situated normal more of this liquid in
+the long system the normal more are
+
+ align:start position:0%
+the long system the normal more are
+ 
+
+ align:start position:0%
+the long system the normal more are
+issued the standing waves but I actually
+
+ align:start position:0%
+issued the standing waves but I actually
+ 
+
+ align:start position:0%
+issued the standing waves but I actually
+only appear in the discrete value of T
+
+ align:start position:0%
+only appear in the discrete value of T
+ 
+
+ align:start position:0%
+only appear in the discrete value of T
+and it has a functional form of
+
+ align:start position:0%
+and it has a functional form of
+ 
+
+ align:start position:0%
+and it has a functional form of
+something like a sinusoidal shape or
+
+ align:start position:0%
+something like a sinusoidal shape or
+ 
+
+ align:start position:0%
+something like a sinusoidal shape or
+cosine okay so that's actually what we
+
+ align:start position:0%
+cosine okay so that's actually what we
+ 
+
+ align:start position:0%
+cosine okay so that's actually what we
+we learned unless you can you can see
+
+ align:start position:0%
+we learned unless you can you can see
+ 
+
+ align:start position:0%
+we learned unless you can you can see
+that from here so if I isolate is it
+
+ align:start position:0%
+that from here so if I isolate is it
+ 
+
+ align:start position:0%
+that from here so if I isolate is it
+it's unselected and pre - okay not quite
+
+ align:start position:0%
+it's unselected and pre - okay not quite
+ 
+
+ align:start position:0%
+it's unselected and pre - okay not quite
+get it yeah so you see that okay it's
+
+ align:start position:0%
+get it yeah so you see that okay it's
+ 
+
+ align:start position:0%
+get it yeah so you see that okay it's
+roughly like a standing wave with a
+
+ align:start position:0%
+roughly like a standing wave with a
+ 
+
+ align:start position:0%
+roughly like a standing wave with a
+fixed frequency okay I would like to
+
+ align:start position:0%
+fixed frequency okay I would like to
+ 
+
+ align:start position:0%
+fixed frequency okay I would like to
+discuss with you as really interesting
+
+ align:start position:0%
+discuss with you as really interesting
+ 
+
+ align:start position:0%
+discuss with you as really interesting
+selection so if I now take a look at so
+
+ align:start position:0%
+selection so if I now take a look at so
+ 
+
+ align:start position:0%
+selection so if I now take a look at so
+we have went through a lot of mess right
+
+ align:start position:0%
+we have went through a lot of mess right
+ 
+
+ align:start position:0%
+we have went through a lot of mess right
+so now it's the time to enjoy what we
+
+ align:start position:0%
+so now it's the time to enjoy what we
+ 
+
+ align:start position:0%
+so now it's the time to enjoy what we
+have learned right so if I now take an
+
+ align:start position:0%
+have learned right so if I now take an
+ 
+
+ align:start position:0%
+have learned right so if I now take an
+extreme value consign ka okay equal to
+
+ align:start position:0%
+extreme value consign ka okay equal to
+ 
+
+ align:start position:0%
+extreme value consign ka okay equal to
+minus one okay then I am reaching the
+
+ align:start position:0%
+minus one okay then I am reaching the
+ 
+
+ align:start position:0%
+minus one okay then I am reaching the
+Maxima oscillation frequency right so if
+
+ align:start position:0%
+Maxima oscillation frequency right so if
+ 
+
+ align:start position:0%
+Maxima oscillation frequency right so if
+I choose cosine K small K a equal to
+
+ align:start position:0%
+I choose cosine K small K a equal to
+ 
+
+ align:start position:0%
+I choose cosine K small K a equal to
+minus one okay what is going to happen
+
+ align:start position:0%
+minus one okay what is going to happen
+ 
+
+ align:start position:0%
+minus one okay what is going to happen
+is like this this is as a function
+
+ align:start position:0%
+is like this this is as a function
+ 
+
+ align:start position:0%
+is like this this is as a function
+though say byproduct AJ as a function
+
+ align:start position:0%
+though say byproduct AJ as a function
+ 
+
+ align:start position:0%
+though say byproduct AJ as a function
+say what you are going to get is 19 like
+
+ align:start position:0%
+say what you are going to get is 19 like
+ 
+
+ align:start position:0%
+say what you are going to get is 19 like
+this those are actually the amplitude of
+
+ align:start position:0%
+this those are actually the amplitude of
+ 
+
+ align:start position:0%
+this those are actually the amplitude of
+individual mass so you can see that if
+
+ align:start position:0%
+individual mass so you can see that if
+ 
+
+ align:start position:0%
+individual mass so you can see that if
+cosine ka is equal to minus 1 Omega
+
+ align:start position:0%
+cosine ka is equal to minus 1 Omega
+ 
+
+ align:start position:0%
+cosine ka is equal to minus 1 Omega
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+based on that expression 1 minus minus 1
+
+ align:start position:0%
+based on that expression 1 minus minus 1
+ 
+
+ align:start position:0%
+based on that expression 1 minus minus 1
+you get 2 therefore you get Omega square
+
+ align:start position:0%
+you get 2 therefore you get Omega square
+ 
+
+ align:start position:0%
+you get 2 therefore you get Omega square
+equal to 4 Omega 0 square ok and if you
+
+ align:start position:0%
+equal to 4 Omega 0 square ok and if you
+ 
+
+ align:start position:0%
+equal to 4 Omega 0 square ok and if you
+prat the AJ as a functional J that is
+
+ align:start position:0%
+prat the AJ as a functional J that is
+ 
+
+ align:start position:0%
+prat the AJ as a functional J that is
+actually what going you are going to get
+
+ align:start position:0%
+actually what going you are going to get
+ 
+
+ align:start position:0%
+actually what going you are going to get
+you actually have Maxima stretch to the
+
+ align:start position:0%
+you actually have Maxima stretch to the
+ 
+
+ align:start position:0%
+you actually have Maxima stretch to the
+system right you can see that it's
+
+ align:start position:0%
+system right you can see that it's
+ 
+
+ align:start position:0%
+system right you can see that it's
+actually positive negative positive
+
+ align:start position:0%
+actually positive negative positive
+ 
+
+ align:start position:0%
+actually positive negative positive
+negative positive negative that will
+
+ align:start position:0%
+negative positive negative that will
+ 
+
+ align:start position:0%
+negative positive negative that will
+reach the maximum speed of the
+
+ align:start position:0%
+reach the maximum speed of the
+ 
+
+ align:start position:0%
+reach the maximum speed of the
+oscillation and of course we cannot demo
+
+ align:start position:0%
+oscillation and of course we cannot demo
+ 
+
+ align:start position:0%
+oscillation and of course we cannot demo
+we cannot demo maximum Pony number
+
+ align:start position:0%
+we cannot demo maximum Pony number
+ 
+
+ align:start position:0%
+we cannot demo maximum Pony number
+oscillator but of course I can't demo a
+
+ align:start position:0%
+oscillator but of course I can't demo a
+ 
+
+ align:start position:0%
+oscillator but of course I can't demo a
+system with ten oscillators so you can
+
+ align:start position:0%
+system with ten oscillators so you can
+ 
+
+ align:start position:0%
+system with ten oscillators so you can
+see that now I maximize the amplitude of
+
+ align:start position:0%
+see that now I maximize the amplitude of
+ 
+
+ align:start position:0%
+see that now I maximize the amplitude of
+the highest frequency normal more and
+
+ align:start position:0%
+the highest frequency normal more and
+ 
+
+ align:start position:0%
+the highest frequency normal more and
+then I let go and you see that this is
+
+ align:start position:0%
+then I let go and you see that this is
+ 
+
+ align:start position:0%
+then I let go and you see that this is
+actually exactly what is going to happen
+
+ align:start position:0%
+actually exactly what is going to happen
+ 
+
+ align:start position:0%
+actually exactly what is going to happen
+when I have cosine ka equal to minus 1
+
+ align:start position:0%
+when I have cosine ka equal to minus 1
+ 
+
+ align:start position:0%
+when I have cosine ka equal to minus 1
+then the the the wetlands is very small
+
+ align:start position:0%
+then the the the wetlands is very small
+ 
+
+ align:start position:0%
+then the the the wetlands is very small
+and you actually reach the maximum speed
+
+ align:start position:0%
+and you actually reach the maximum speed
+ 
+
+ align:start position:0%
+and you actually reach the maximum speed
+makes my speed is actually to be
+
+ align:start position:0%
+makes my speed is actually to be
+ 
+
+ align:start position:0%
+makes my speed is actually to be
+compared with for example a lower
+
+ align:start position:0%
+compared with for example a lower
+ 
+
+ align:start position:0%
+compared with for example a lower
+frequency mode like this one right this
+
+ align:start position:0%
+frequency mode like this one right this
+ 
+
+ align:start position:0%
+frequency mode like this one right this
+is actually oscillating at much lower
+
+ align:start position:0%
+is actually oscillating at much lower
+ 
+
+ align:start position:0%
+is actually oscillating at much lower
+frequency and there you can ask okay
+
+ align:start position:0%
+frequency and there you can ask okay
+ 
+
+ align:start position:0%
+frequency and there you can ask okay
+does that make sense if I have this
+
+ align:start position:0%
+does that make sense if I have this
+ 
+
+ align:start position:0%
+does that make sense if I have this
+really really zigzag shape why this
+
+ align:start position:0%
+really really zigzag shape why this
+ 
+
+ align:start position:0%
+really really zigzag shape why this
+system should be oscillating at the
+
+ align:start position:0%
+system should be oscillating at the
+ 
+
+ align:start position:0%
+system should be oscillating at the
+highest possible frequency why is that
+
+ align:start position:0%
+highest possible frequency why is that
+ 
+
+ align:start position:0%
+highest possible frequency why is that
+you also make sense right if you have
+
+ align:start position:0%
+you also make sense right if you have
+ 
+
+ align:start position:0%
+you also make sense right if you have
+that set up then you are stretching this
+
+ align:start position:0%
+that set up then you are stretching this
+ 
+
+ align:start position:0%
+that set up then you are stretching this
+system to the maximum possible amount
+
+ align:start position:0%
+system to the maximum possible amount
+ 
+
+ align:start position:0%
+system to the maximum possible amount
+right so so actually now the louder the
+
+ align:start position:0%
+right so so actually now the louder the
+ 
+
+ align:start position:0%
+right so so actually now the louder the
+spring looks like this stretching is
+
+ align:start position:0%
+spring looks like this stretching is
+ 
+
+ align:start position:0%
+spring looks like this stretching is
+really hard
+
+ align:start position:0%
+really hard
+ 
+
+ align:start position:0%
+really hard
+and therefore the restoring force is
+
+ align:start position:0%
+and therefore the restoring force is
+ 
+
+ align:start position:0%
+and therefore the restoring force is
+going to be large therefore you get high
+
+ align:start position:0%
+going to be large therefore you get high
+ 
+
+ align:start position:0%
+going to be large therefore you get high
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+okay okay so I hope you actually enjoy
+
+ align:start position:0%
+okay okay so I hope you actually enjoy
+ 
+
+ align:start position:0%
+okay okay so I hope you actually enjoy
+the lecture today is a lot of
+
+ align:start position:0%
+the lecture today is a lot of
+ 
+
+ align:start position:0%
+the lecture today is a lot of
+mathematics but what we have learned is
+
+ align:start position:0%
+mathematics but what we have learned is
+ 
+
+ align:start position:0%
+mathematics but what we have learned is
+really a lot we learned how to issue the
+
+ align:start position:0%
+really a lot we learned how to issue the
+ 
+
+ align:start position:0%
+really a lot we learned how to issue the
+described system how to actually solve a
+
+ align:start position:0%
+described system how to actually solve a
+ 
+
+ align:start position:0%
+described system how to actually solve a
+system without HD touching the MS 1k
+
+ align:start position:0%
+system without HD touching the MS 1k
+ 
+
+ align:start position:0%
+system without HD touching the MS 1k
+metrics we can actually already get the
+
+ align:start position:0%
+metrics we can actually already get the
+ 
+
+ align:start position:0%
+metrics we can actually already get the
+eigenvectors and using n minus 1 k
+
+ align:start position:0%
+eigenvectors and using n minus 1 k
+ 
+
+ align:start position:0%
+eigenvectors and using n minus 1 k
+matrix we can actually evaluate Omega as
+
+ align:start position:0%
+matrix we can actually evaluate Omega as
+ 
+
+ align:start position:0%
+matrix we can actually evaluate Omega as
+a function of the input parameter from s
+
+ align:start position:0%
+a function of the input parameter from s
+ 
+
+ align:start position:0%
+a function of the input parameter from s
+I can value and the next lectures we are
+
+ align:start position:0%
+I can value and the next lectures we are
+ 
+
+ align:start position:0%
+I can value and the next lectures we are
+going to discuss more examples and make
+
+ align:start position:0%
+going to discuss more examples and make
+ 
+
+ align:start position:0%
+going to discuss more examples and make
+the whole system continues thank you
+
+ align:start position:0%
+the whole system continues thank you
+ 
+
+ align:start position:0%
+the whole system continues thank you
+very much if you have any more questions
+
+ align:start position:0%
+very much if you have any more questions
+ 
+
+ align:start position:0%
+very much if you have any more questions
+I'll be very happy to answer your
+
+ align:start position:0%
+I'll be very happy to answer your
+ 
+
+ align:start position:0%
+I'll be very happy to answer your
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/b9X0osuciZI.txt b/b9X0osuciZI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..379061035739bbf594e7cb96c75c52bf9eb3bf59
--- /dev/null
+++ b/b9X0osuciZI.txt
@@ -0,0 +1,9997 @@
+align:start position:0%
+ 
+so we're we're very privileged to have
+
+ align:start position:0%
+so we're we're very privileged to have
+ 
+
+ align:start position:0%
+so we're we're very privileged to have
+people who flown from as far away in the
+
+ align:start position:0%
+people who flown from as far away in the
+ 
+
+ align:start position:0%
+people who flown from as far away in the
+world as you can get from here to here
+
+ align:start position:0%
+world as you can get from here to here
+ 
+
+ align:start position:0%
+world as you can get from here to here
+to be with us
+
+ align:start position:0%
+to be with us
+ 
+
+ align:start position:0%
+to be with us
+today and uh I'm going to load the the
+
+ align:start position:0%
+today and uh I'm going to load the the
+ 
+
+ align:start position:0%
+today and uh I'm going to load the the
+latest version of the
+
+ align:start position:0%
+latest version of the
+ 
+
+ align:start position:0%
+latest version of the
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+um Dr Dr Zang will be our first Speaker
+
+ align:start position:0%
+um Dr Dr Zang will be our first Speaker
+ 
+
+ align:start position:0%
+um Dr Dr Zang will be our first Speaker
+he is professor and director of the
+
+ align:start position:0%
+he is professor and director of the
+ 
+
+ align:start position:0%
+he is professor and director of the
+Department of high technology
+
+ align:start position:0%
+Department of high technology
+ 
+
+ align:start position:0%
+Department of high technology
+development and industrialization at the
+
+ align:start position:0%
+development and industrialization at the
+ 
+
+ align:start position:0%
+development and industrialization at the
+ministry of Science and Technology in uh
+
+ align:start position:0%
+ministry of Science and Technology in uh
+ 
+
+ align:start position:0%
+ministry of Science and Technology in uh
+in in China
+
+ align:start position:0%
+in in China
+ 
+
+ align:start position:0%
+in in China
+uh and is one of the lead Regulators for
+
+ align:start position:0%
+uh and is one of the lead Regulators for
+ 
+
+ align:start position:0%
+uh and is one of the lead Regulators for
+RFID who we've heard here throughout two
+
+ align:start position:0%
+RFID who we've heard here throughout two
+ 
+
+ align:start position:0%
+RFID who we've heard here throughout two
+days from in many cases from companies
+
+ align:start position:0%
+days from in many cases from companies
+ 
+
+ align:start position:0%
+days from in many cases from companies
+looking at how do we how do we integrate
+
+ align:start position:0%
+looking at how do we how do we integrate
+ 
+
+ align:start position:0%
+looking at how do we how do we integrate
+RFID what do we want to do with RFID and
+
+ align:start position:0%
+RFID what do we want to do with RFID and
+ 
+
+ align:start position:0%
+RFID what do we want to do with RFID and
+our companies and so he's he's got an
+
+ align:start position:0%
+our companies and so he's he's got an
+ 
+
+ align:start position:0%
+our companies and so he's he's got an
+even larger Beast to to wrestle with so
+
+ align:start position:0%
+even larger Beast to to wrestle with so
+ 
+
+ align:start position:0%
+even larger Beast to to wrestle with so
+we're very privileged to have him with
+
+ align:start position:0%
+we're very privileged to have him with
+ 
+
+ align:start position:0%
+we're very privileged to have him with
+us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anybody know the password on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+machine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+password thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+presentation in MIT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes this is New Vision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you yeah I would like to take take this
+
+ align:start position:0%
+you yeah I would like to take take this
+ 
+
+ align:start position:0%
+you yeah I would like to take take this
+opportunity to say several words for for
+
+ align:start position:0%
+opportunity to say several words for for
+ 
+
+ align:start position:0%
+opportunity to say several words for for
+IID in China so I think a lot of people
+
+ align:start position:0%
+IID in China so I think a lot of people
+ 
+
+ align:start position:0%
+IID in China so I think a lot of people
+um pay more attention to um our our
+
+ align:start position:0%
+um pay more attention to um our our
+ 
+
+ align:start position:0%
+um pay more attention to um our our
+country how to use
+
+ align:start position:0%
+country how to use
+ 
+
+ align:start position:0%
+country how to use
+RFID so I think this is uh several
+
+ align:start position:0%
+RFID so I think this is uh several
+ 
+
+ align:start position:0%
+RFID so I think this is uh several
+reasion the one is the uh the China is
+
+ align:start position:0%
+reasion the one is the uh the China is
+ 
+
+ align:start position:0%
+reasion the one is the uh the China is
+the largest population in the world
+
+ align:start position:0%
+the largest population in the world
+ 
+
+ align:start position:0%
+the largest population in the world
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+also y
+
+ align:start position:0%
+also y
+ 
+
+ align:start position:0%
+also y
+maybe this is an old
+
+ align:start position:0%
+maybe this is an old
+ 
+
+ align:start position:0%
+maybe this is an old
+Vision this old Vision not not
+
+ align:start position:0%
+Vision this old Vision not not
+ 
+
+ align:start position:0%
+Vision this old Vision not not
+new oh this is the old version okay we
+
+ align:start position:0%
+new oh this is the old version okay we
+ 
+
+ align:start position:0%
+new oh this is the old version okay we
+have a new
+
+ align:start position:0%
+have a new
+ 
+
+ align:start position:0%
+have a new
+version so I
+
+ align:start position:0%
+version so I
+ 
+
+ align:start position:0%
+version so I
+think okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just open it just open
+
+ align:start position:0%
+just open it just open
+ 
+
+ align:start position:0%
+just open it just open
+it just open
+
+ align:start position:0%
+it just open
+ 
+
+ align:start position:0%
+it just open
+it yeah just use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this yeah I at first I want to to
+
+ align:start position:0%
+this yeah I at first I want to to
+ 
+
+ align:start position:0%
+this yeah I at first I want to to
+introduce some the uh so sever words for
+
+ align:start position:0%
+introduce some the uh so sever words for
+ 
+
+ align:start position:0%
+introduce some the uh so sever words for
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+ministry our ministry is science and
+
+ align:start position:0%
+ministry our ministry is science and
+ 
+
+ align:start position:0%
+ministry our ministry is science and
+technology Ministry and they focus on
+
+ align:start position:0%
+technology Ministry and they focus on
+ 
+
+ align:start position:0%
+technology Ministry and they focus on
+the research and uh set forth and the
+
+ align:start position:0%
+the research and uh set forth and the
+ 
+
+ align:start position:0%
+the research and uh set forth and the
+micro strategic for Science and
+
+ align:start position:0%
+micro strategic for Science and
+ 
+
+ align:start position:0%
+micro strategic for Science and
+Technology development as well as the uh
+
+ align:start position:0%
+Technology development as well as the uh
+ 
+
+ align:start position:0%
+Technology development as well as the uh
+Gathering uh policies and uh uh
+
+ align:start position:0%
+Gathering uh policies and uh uh
+ 
+
+ align:start position:0%
+Gathering uh policies and uh uh
+regulations for Science and Technology
+
+ align:start position:0%
+regulations for Science and Technology
+ 
+
+ align:start position:0%
+regulations for Science and Technology
+and also to the uh conduct research on
+
+ align:start position:0%
+and also to the uh conduct research on
+ 
+
+ align:start position:0%
+and also to the uh conduct research on
+key issue Rel related to the uh um
+
+ align:start position:0%
+key issue Rel related to the uh um
+ 
+
+ align:start position:0%
+key issue Rel related to the uh um
+promotion of Economic and Society
+
+ align:start position:0%
+promotion of Economic and Society
+ 
+
+ align:start position:0%
+promotion of Economic and Society
+development of by science and
+
+ align:start position:0%
+development of by science and
+ 
+
+ align:start position:0%
+development of by science and
+technology also to research and
+
+ align:start position:0%
+technology also to research and
+ 
+
+ align:start position:0%
+technology also to research and
+uh determined to major development and
+
+ align:start position:0%
+uh determined to major development and
+ 
+
+ align:start position:0%
+uh determined to major development and
+uh PR priority areas for Science and
+
+ align:start position:0%
+uh PR priority areas for Science and
+ 
+
+ align:start position:0%
+uh PR priority areas for Science and
+Technology development and also to
+
+ align:start position:0%
+Technology development and also to
+ 
+
+ align:start position:0%
+Technology development and also to
+promote the uh build
+
+ align:start position:0%
+promote the uh build
+ 
+
+ align:start position:0%
+promote the uh build
+of the uh National Sense Technology
+
+ align:start position:0%
+of the uh National Sense Technology
+ 
+
+ align:start position:0%
+of the uh National Sense Technology
+Innovation System and uh improve the
+
+ align:start position:0%
+Innovation System and uh improve the
+ 
+
+ align:start position:0%
+Innovation System and uh improve the
+national sense and Technology Innovation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacity so I think uh lot of people um
+
+ align:start position:0%
+capacity so I think uh lot of people um
+ 
+
+ align:start position:0%
+capacity so I think uh lot of people um
+look at the uh China how to develop RFID
+
+ align:start position:0%
+look at the uh China how to develop RFID
+ 
+
+ align:start position:0%
+look at the uh China how to develop RFID
+the application because this is the
+
+ align:start position:0%
+the application because this is the
+ 
+
+ align:start position:0%
+the application because this is the
+several region the first reason is the
+
+ align:start position:0%
+several region the first reason is the
+ 
+
+ align:start position:0%
+several region the first reason is the
+the largest population and the
+
+ align:start position:0%
+the largest population and the
+ 
+
+ align:start position:0%
+the largest population and the
+larg
+
+ align:start position:0%
+larg
+ 
+
+ align:start position:0%
+larg
+um consumer Market in the in the world
+
+ align:start position:0%
+um consumer Market in the in the world
+ 
+
+ align:start position:0%
+um consumer Market in the in the world
+so the second reason is the
+
+ align:start position:0%
+so the second reason is the
+ 
+
+ align:start position:0%
+so the second reason is the
+manufacturing center of the world and uh
+
+ align:start position:0%
+manufacturing center of the world and uh
+ 
+
+ align:start position:0%
+manufacturing center of the world and uh
+also related for the uh
+
+ align:start position:0%
+also related for the uh
+ 
+
+ align:start position:0%
+also related for the uh
+big the company in the world
+
+ align:start position:0%
+big the company in the world
+ 
+
+ align:start position:0%
+big the company in the world
+so um how to use the RFID also not only
+
+ align:start position:0%
+so um how to use the RFID also not only
+ 
+
+ align:start position:0%
+so um how to use the RFID also not only
+um related with the Chinese company also
+
+ align:start position:0%
+um related with the Chinese company also
+ 
+
+ align:start position:0%
+um related with the Chinese company also
+for the uh uh foreign big company and
+
+ align:start position:0%
+for the uh uh foreign big company and
+ 
+
+ align:start position:0%
+for the uh uh foreign big company and
+also it applications is just at the
+
+ align:start position:0%
+also it applications is just at the
+ 
+
+ align:start position:0%
+also it applications is just at the
+beginning with much more um potential to
+
+ align:start position:0%
+beginning with much more um potential to
+ 
+
+ align:start position:0%
+beginning with much more um potential to
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explored and this picture is the rid
+
+ align:start position:0%
+explored and this picture is the rid
+ 
+
+ align:start position:0%
+explored and this picture is the rid
+Market in
+
+ align:start position:0%
+Market in
+ 
+
+ align:start position:0%
+Market in
+2004 and uh rid technology and
+
+ align:start position:0%
+2004 and uh rid technology and
+ 
+
+ align:start position:0%
+2004 and uh rid technology and
+applications have got the promot
+
+ align:start position:0%
+applications have got the promot
+ 
+
+ align:start position:0%
+applications have got the promot
+development in the last two years in
+
+ align:start position:0%
+development in the last two years in
+ 
+
+ align:start position:0%
+development in the last two years in
+China and uh recently all all of the uh
+
+ align:start position:0%
+China and uh recently all all of the uh
+ 
+
+ align:start position:0%
+China and uh recently all all of the uh
+everybody have a new ID use the r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ID so this total the market is about uh
+
+ align:start position:0%
+ID so this total the market is about uh
+ 
+
+ align:start position:0%
+ID so this total the market is about uh
+uh$ 150 million
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us and the potential application in
+
+ align:start position:0%
+us and the potential application in
+ 
+
+ align:start position:0%
+us and the potential application in
+China Market uh I think maybe in the
+
+ align:start position:0%
+China Market uh I think maybe in the
+ 
+
+ align:start position:0%
+China Market uh I think maybe in the
+this several area the one is the uh
+
+ align:start position:0%
+this several area the one is the uh
+ 
+
+ align:start position:0%
+this several area the one is the uh
+security and the safety
+
+ align:start position:0%
+security and the safety
+ 
+
+ align:start position:0%
+security and the safety
+and also it's very important area is
+
+ align:start position:0%
+and also it's very important area is
+ 
+
+ align:start position:0%
+and also it's very important area is
+uh uh Artic uh counterfeit for example
+
+ align:start position:0%
+uh uh Artic uh counterfeit for example
+ 
+
+ align:start position:0%
+uh uh Artic uh counterfeit for example
+some the uh health and Health Care
+
+ align:start position:0%
+some the uh health and Health Care
+ 
+
+ align:start position:0%
+some the uh health and Health Care
+tobacco and the
+
+ align:start position:0%
+tobacco and the
+ 
+
+ align:start position:0%
+tobacco and the
+liak and also we application the RFID
+
+ align:start position:0%
+liak and also we application the RFID
+ 
+
+ align:start position:0%
+liak and also we application the RFID
+maybe in their
+
+ align:start position:0%
+maybe in their
+ 
+
+ align:start position:0%
+maybe in their
+Logistics and also for the manufact uh
+
+ align:start position:0%
+Logistics and also for the manufact uh
+ 
+
+ align:start position:0%
+Logistics and also for the manufact uh
+manufacturing Process Management
+
+ align:start position:0%
+manufacturing Process Management
+ 
+
+ align:start position:0%
+manufacturing Process Management
+and also for the E tiet
+
+ align:start position:0%
+and also for the E tiet
+ 
+
+ align:start position:0%
+and also for the E tiet
+system and such as the uh Subway ticket
+
+ align:start position:0%
+system and such as the uh Subway ticket
+ 
+
+ align:start position:0%
+system and such as the uh Subway ticket
+we already use it in Shanghai and also
+
+ align:start position:0%
+we already use it in Shanghai and also
+ 
+
+ align:start position:0%
+we already use it in Shanghai and also
+we want use it in olypic games in the
+
+ align:start position:0%
+we want use it in olypic games in the
+ 
+
+ align:start position:0%
+we want use it in olypic games in the
+2008 and uh shangai W the uh
+
+ align:start position:0%
+2008 and uh shangai W the uh
+ 
+
+ align:start position:0%
+2008 and uh shangai W the uh
+Exposition and in
+
+ align:start position:0%
+Exposition and in
+ 
+
+ align:start position:0%
+Exposition and in
+2010 and also we developed this uh rid
+
+ align:start position:0%
+2010 and also we developed this uh rid
+ 
+
+ align:start position:0%
+2010 and also we developed this uh rid
+using the vehicle man uh management
+
+ align:start position:0%
+using the vehicle man uh management
+ 
+
+ align:start position:0%
+using the vehicle man uh management
+system when the uh vehicle pass the gate
+
+ align:start position:0%
+system when the uh vehicle pass the gate
+ 
+
+ align:start position:0%
+system when the uh vehicle pass the gate
+they can show you the picture and the
+
+ align:start position:0%
+they can show you the picture and the
+ 
+
+ align:start position:0%
+they can show you the picture and the
+color and you can find it and also um we
+
+ align:start position:0%
+color and you can find it and also um we
+ 
+
+ align:start position:0%
+color and you can find it and also um we
+use it in the supply chair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+management and this is the
+
+ align:start position:0%
+management and this is the
+ 
+
+ align:start position:0%
+management and this is the
+uh um har use the uh
+
+ align:start position:0%
+uh um har use the uh
+ 
+
+ align:start position:0%
+uh um har use the uh
+RFID so this is uh um container tricking
+
+ align:start position:0%
+RFID so this is uh um container tricking
+ 
+
+ align:start position:0%
+RFID so this is uh um container tricking
+this is located in
+
+ align:start position:0%
+this is located in
+ 
+
+ align:start position:0%
+this is located in
+Shanghai and uh recently we we used the
+
+ align:start position:0%
+Shanghai and uh recently we we used the
+ 
+
+ align:start position:0%
+Shanghai and uh recently we we used the
+RFID the tag in Shanghai International
+
+ align:start position:0%
+RFID the tag in Shanghai International
+ 
+
+ align:start position:0%
+RFID the tag in Shanghai International
+Port Harbor and uh they connect with the
+
+ align:start position:0%
+Port Harbor and uh they connect with the
+ 
+
+ align:start position:0%
+Port Harbor and uh they connect with the
+uh another very important Harbor in y s
+
+ align:start position:0%
+uh another very important Harbor in y s
+ 
+
+ align:start position:0%
+uh another very important Harbor in y s
+Province after now they already shipped
+
+ align:start position:0%
+Province after now they already shipped
+ 
+
+ align:start position:0%
+Province after now they already shipped
+more than 7,000 containers just still to
+
+ align:start position:0%
+more than 7,000 containers just still to
+ 
+
+ align:start position:0%
+more than 7,000 containers just still to
+the demo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also we are we already use it in the uh
+
+ align:start position:0%
+also we are we already use it in the uh
+ 
+
+ align:start position:0%
+also we are we already use it in the uh
+fairworks
+
+ align:start position:0%
+fairworks
+ 
+
+ align:start position:0%
+fairworks
+management because it's dangerous always
+
+ align:start position:0%
+management because it's dangerous always
+ 
+
+ align:start position:0%
+management because it's dangerous always
+take place from the
+
+ align:start position:0%
+take place from the
+ 
+
+ align:start position:0%
+take place from the
+accident and also we used the rid in the
+
+ align:start position:0%
+accident and also we used the rid in the
+ 
+
+ align:start position:0%
+accident and also we used the rid in the
+dangerous case
+
+ align:start position:0%
+dangerous case
+ 
+
+ align:start position:0%
+dangerous case
+managements so we put the uh tag in the
+
+ align:start position:0%
+managements so we put the uh tag in the
+ 
+
+ align:start position:0%
+managements so we put the uh tag in the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+tanks and also we we used our
+
+ align:start position:0%
+tanks and also we we used our
+ 
+
+ align:start position:0%
+tanks and also we we used our
+to management animal and the
+
+ align:start position:0%
+to management animal and the
+ 
+
+ align:start position:0%
+to management animal and the
+foods and also in sh we have put the tag
+
+ align:start position:0%
+foods and also in sh we have put the tag
+ 
+
+ align:start position:0%
+foods and also in sh we have put the tag
+in in the air of the dog so we can find
+
+ align:start position:0%
+in in the air of the dog so we can find
+ 
+
+ align:start position:0%
+in in the air of the dog so we can find
+it and they put some um illegal or only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ille and also we use it in the co Manor
+
+ align:start position:0%
+ille and also we use it in the co Manor
+ 
+
+ align:start position:0%
+ille and also we use it in the co Manor
+location and the
+
+ align:start position:0%
+location and the
+ 
+
+ align:start position:0%
+location and the
+tricking so also in China and frequency
+
+ align:start position:0%
+tricking so also in China and frequency
+ 
+
+ align:start position:0%
+tricking so also in China and frequency
+to take a place some the accident in a
+
+ align:start position:0%
+to take a place some the accident in a
+ 
+
+ align:start position:0%
+to take a place some the accident in a
+manner so how to catch time to save the
+
+ align:start position:0%
+manner so how to catch time to save the
+ 
+
+ align:start position:0%
+manner so how to catch time to save the
+life this is very
+
+ align:start position:0%
+life this is very
+ 
+
+ align:start position:0%
+life this is very
+important so I think in the I just uh
+
+ align:start position:0%
+important so I think in the I just uh
+ 
+
+ align:start position:0%
+important so I think in the I just uh
+look at the TV North Kina also take
+
+ align:start position:0%
+look at the TV North Kina also take
+ 
+
+ align:start position:0%
+look at the TV North Kina also take
+place some the accident so I think this
+
+ align:start position:0%
+place some the accident so I think this
+ 
+
+ align:start position:0%
+place some the accident so I think this
+is uh very popular in the near future
+
+ align:start position:0%
+is uh very popular in the near future
+ 
+
+ align:start position:0%
+is uh very popular in the near future
+how to c application this uh technology
+
+ align:start position:0%
+how to c application this uh technology
+ 
+
+ align:start position:0%
+how to c application this uh technology
+to save the SE life
+
+ align:start position:0%
+to save the SE life
+ 
+
+ align:start position:0%
+to save the SE life
+and we already give them the pilot
+
+ align:start position:0%
+and we already give them the pilot
+ 
+
+ align:start position:0%
+and we already give them the pilot
+project for the post office this a China
+
+ align:start position:0%
+project for the post office this a China
+ 
+
+ align:start position:0%
+project for the post office this a China
+p and post office use the uh the tag put
+
+ align:start position:0%
+p and post office use the uh the tag put
+ 
+
+ align:start position:0%
+p and post office use the uh the tag put
+it into the uh mirr bags in uh for the
+
+ align:start position:0%
+it into the uh mirr bags in uh for the
+ 
+
+ align:start position:0%
+it into the uh mirr bags in uh for the
+EMS
+
+ align:start position:0%
+EMS
+ 
+
+ align:start position:0%
+EMS
+the this is a Shanghai use the uh the PO
+
+ align:start position:0%
+the this is a Shanghai use the uh the PO
+ 
+
+ align:start position:0%
+the this is a Shanghai use the uh the PO
+post office use the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RFID and this is a Manufacturing Process
+
+ align:start position:0%
+RFID and this is a Manufacturing Process
+ 
+
+ align:start position:0%
+RFID and this is a Manufacturing Process
+Management and for
+
+ align:start position:0%
+Management and for
+ 
+
+ align:start position:0%
+Management and for
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the products land to manage the
+
+ align:start position:0%
+the products land to manage the
+ 
+
+ align:start position:0%
+the products land to manage the
+uh each and products
+
+ align:start position:0%
+uh each and products
+ 
+
+ align:start position:0%
+uh each and products
+Point can control the the product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quality this is a China the FID industry
+
+ align:start position:0%
+quality this is a China the FID industry
+ 
+
+ align:start position:0%
+quality this is a China the FID industry
+policy well of the most important area
+
+ align:start position:0%
+policy well of the most important area
+ 
+
+ align:start position:0%
+policy well of the most important area
+in China the national development
+
+ align:start position:0%
+in China the national development
+ 
+
+ align:start position:0%
+in China the national development
+planning and on the high tech area for
+
+ align:start position:0%
+planning and on the high tech area for
+ 
+
+ align:start position:0%
+planning and on the high tech area for
+the coming F
+
+ align:start position:0%
+the coming F
+ 
+
+ align:start position:0%
+the coming F
+years so this is a a big program program
+
+ align:start position:0%
+years so this is a a big program program
+ 
+
+ align:start position:0%
+years so this is a a big program program
+and also make China RFID technology
+
+ align:start position:0%
+and also make China RFID technology
+ 
+
+ align:start position:0%
+and also make China RFID technology
+strategy and policy funding RFID
+
+ align:start position:0%
+strategy and policy funding RFID
+ 
+
+ align:start position:0%
+strategy and policy funding RFID
+application to promote promote the RFID
+
+ align:start position:0%
+application to promote promote the RFID
+ 
+
+ align:start position:0%
+application to promote promote the RFID
+technology and Industry development
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh our ministry and also con uh
+
+ align:start position:0%
+uh our ministry and also con uh
+ 
+
+ align:start position:0%
+uh our ministry and also con uh
+constitute constitute the China IID
+
+ align:start position:0%
+constitute constitute the China IID
+ 
+
+ align:start position:0%
+constitute constitute the China IID
+technology with paper work together with
+
+ align:start position:0%
+technology with paper work together with
+ 
+
+ align:start position:0%
+technology with paper work together with
+the other 14 Ministry or departments
+
+ align:start position:0%
+the other 14 Ministry or departments
+ 
+
+ align:start position:0%
+the other 14 Ministry or departments
+because you know this kind of
+
+ align:start position:0%
+because you know this kind of
+ 
+
+ align:start position:0%
+because you know this kind of
+application related with the different
+
+ align:start position:0%
+application related with the different
+ 
+
+ align:start position:0%
+application related with the different
+Ministry or different department so we
+
+ align:start position:0%
+Ministry or different department so we
+ 
+
+ align:start position:0%
+Ministry or different department so we
+must work with them together to make the
+
+ align:start position:0%
+must work with them together to make the
+ 
+
+ align:start position:0%
+must work with them together to make the
+policy and make some
+
+ align:start position:0%
+policy and make some
+ 
+
+ align:start position:0%
+policy and make some
+standard also research and establish the
+
+ align:start position:0%
+standard also research and establish the
+ 
+
+ align:start position:0%
+standard also research and establish the
+architecture for the China RFID uh
+
+ align:start position:0%
+architecture for the China RFID uh
+ 
+
+ align:start position:0%
+architecture for the China RFID uh
+standard which connect with the
+
+ align:start position:0%
+standard which connect with the
+ 
+
+ align:start position:0%
+standard which connect with the
+international standard and the
+
+ align:start position:0%
+international standard and the
+ 
+
+ align:start position:0%
+international standard and the
+accommodate the China um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surrounding and the state a spe uh
+
+ align:start position:0%
+surrounding and the state a spe uh
+ 
+
+ align:start position:0%
+surrounding and the state a spe uh
+specific rid program in National hch R&D
+
+ align:start position:0%
+specific rid program in National hch R&D
+ 
+
+ align:start position:0%
+specific rid program in National hch R&D
+program this 836 program established in
+
+ align:start position:0%
+program this 836 program established in
+ 
+
+ align:start position:0%
+program this 836 program established in
+March
+
+ align:start position:0%
+March
+ 
+
+ align:start position:0%
+March
+1986 this reviewed by the very famous
+
+ align:start position:0%
+1986 this reviewed by the very famous
+ 
+
+ align:start position:0%
+1986 this reviewed by the very famous
+leader Dana
+
+ align:start position:0%
+leader Dana
+ 
+
+ align:start position:0%
+leader Dana
+ping so to speed up the progress of RFID
+
+ align:start position:0%
+ping so to speed up the progress of RFID
+ 
+
+ align:start position:0%
+ping so to speed up the progress of RFID
+research application and
+
+ align:start position:0%
+research application and
+ 
+
+ align:start position:0%
+research application and
+industrialization and set up a RFID
+
+ align:start position:0%
+industrialization and set up a RFID
+ 
+
+ align:start position:0%
+industrialization and set up a RFID
+committee to make the national RFID
+
+ align:start position:0%
+committee to make the national RFID
+ 
+
+ align:start position:0%
+committee to make the national RFID
+research plan and the F RFID research
+
+ align:start position:0%
+research plan and the F RFID research
+ 
+
+ align:start position:0%
+research plan and the F RFID research
+and the found the rid application and
+
+ align:start position:0%
+and the found the rid application and
+ 
+
+ align:start position:0%
+and the found the rid application and
+help local government to set up IID
+
+ align:start position:0%
+help local government to set up IID
+ 
+
+ align:start position:0%
+help local government to set up IID
+research technology and Industry
+
+ align:start position:0%
+research technology and Industry
+ 
+
+ align:start position:0%
+research technology and Industry
+industrial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Zone also um we are pay more attention
+
+ align:start position:0%
+Zone also um we are pay more attention
+ 
+
+ align:start position:0%
+Zone also um we are pay more attention
+research on
+
+ align:start position:0%
+research on
+ 
+
+ align:start position:0%
+research on
+standard I think the standard and
+
+ align:start position:0%
+standard I think the standard and
+ 
+
+ align:start position:0%
+standard I think the standard and
+can research for the
+
+ align:start position:0%
+can research for the
+ 
+
+ align:start position:0%
+can research for the
+several uh Direction the one is the
+
+ align:start position:0%
+several uh Direction the one is the
+ 
+
+ align:start position:0%
+several uh Direction the one is the
+products code coding standard and also
+
+ align:start position:0%
+products code coding standard and also
+ 
+
+ align:start position:0%
+products code coding standard and also
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+RFID uh
+
+ align:start position:0%
+RFID uh
+ 
+
+ align:start position:0%
+RFID uh
+communication and pro protocol and also
+
+ align:start position:0%
+communication and pro protocol and also
+ 
+
+ align:start position:0%
+communication and pro protocol and also
+rid product standard and Equipment
+
+ align:start position:0%
+rid product standard and Equipment
+ 
+
+ align:start position:0%
+rid product standard and Equipment
+standard and also for the application
+
+ align:start position:0%
+standard and also for the application
+ 
+
+ align:start position:0%
+standard and also for the application
+standard for example if we want to use
+
+ align:start position:0%
+standard for example if we want to use
+ 
+
+ align:start position:0%
+standard for example if we want to use
+in the post office we must uh make sure
+
+ align:start position:0%
+in the post office we must uh make sure
+ 
+
+ align:start position:0%
+in the post office we must uh make sure
+and what kind of uh the in
+
+ align:start position:0%
+and what kind of uh the in
+ 
+
+ align:start position:0%
+and what kind of uh the in
+the and which the position you can put
+
+ align:start position:0%
+the and which the position you can put
+ 
+
+ align:start position:0%
+the and which the position you can put
+it put it put on and uh what the
+
+ align:start position:0%
+it put it put on and uh what the
+ 
+
+ align:start position:0%
+it put it put on and uh what the
+frequency you want to use it and also
+
+ align:start position:0%
+frequency you want to use it and also
+ 
+
+ align:start position:0%
+frequency you want to use it and also
+for the different industry area we must
+
+ align:start position:0%
+for the different industry area we must
+ 
+
+ align:start position:0%
+for the different industry area we must
+make decision what kind of frequency you
+
+ align:start position:0%
+make decision what kind of frequency you
+ 
+
+ align:start position:0%
+make decision what kind of frequency you
+can use it so for example for The Med
+
+ align:start position:0%
+can use it so for example for The Med
+ 
+
+ align:start position:0%
+can use it so for example for The Med
+pills so where you can put it in the in
+
+ align:start position:0%
+pills so where you can put it in the in
+ 
+
+ align:start position:0%
+pills so where you can put it in the in
+the the bottle
+
+ align:start position:0%
+the the bottle
+ 
+
+ align:start position:0%
+the the bottle
+so we must make a lot of applications
+
+ align:start position:0%
+so we must make a lot of applications
+ 
+
+ align:start position:0%
+so we must make a lot of applications
+Stander this is very important I think
+
+ align:start position:0%
+Stander this is very important I think
+ 
+
+ align:start position:0%
+Stander this is very important I think
+and also we establish some the testing
+
+ align:start position:0%
+and also we establish some the testing
+ 
+
+ align:start position:0%
+and also we establish some the testing
+and certification Center we are set up
+
+ align:start position:0%
+and certification Center we are set up
+ 
+
+ align:start position:0%
+and certification Center we are set up
+the national testing center on FID
+
+ align:start position:0%
+the national testing center on FID
+ 
+
+ align:start position:0%
+the national testing center on FID
+technology so one of them they will test
+
+ align:start position:0%
+technology so one of them they will test
+ 
+
+ align:start position:0%
+technology so one of them they will test
+the products performance and also we uh
+
+ align:start position:0%
+the products performance and also we uh
+ 
+
+ align:start position:0%
+the products performance and also we uh
+evaluate the RFID products and uh
+
+ align:start position:0%
+evaluate the RFID products and uh
+ 
+
+ align:start position:0%
+evaluate the RFID products and uh
+simulate application environments and
+
+ align:start position:0%
+simulate application environments and
+ 
+
+ align:start position:0%
+simulate application environments and
+uh as is the
+
+ align:start position:0%
+uh as is the
+ 
+
+ align:start position:0%
+uh as is the
+applications for example I say say that
+
+ align:start position:0%
+applications for example I say say that
+ 
+
+ align:start position:0%
+applications for example I say say that
+we useing the uh Co Manor the tricking
+
+ align:start position:0%
+we useing the uh Co Manor the tricking
+ 
+
+ align:start position:0%
+we useing the uh Co Manor the tricking
+system we may maybe we want to use the
+
+ align:start position:0%
+system we may maybe we want to use the
+ 
+
+ align:start position:0%
+system we may maybe we want to use the
+uh active
+
+ align:start position:0%
+uh active
+ 
+
+ align:start position:0%
+uh active
+Tech in the in the normal surrounding
+
+ align:start position:0%
+Tech in the in the normal surrounding
+ 
+
+ align:start position:0%
+Tech in the in the normal surrounding
+maybe they can transfer the information
+
+ align:start position:0%
+maybe they can transfer the information
+ 
+
+ align:start position:0%
+maybe they can transfer the information
+more than 100 meter but when take place
+
+ align:start position:0%
+more than 100 meter but when take place
+ 
+
+ align:start position:0%
+more than 100 meter but when take place
+the AC accident the code will fall down
+
+ align:start position:0%
+the AC accident the code will fall down
+ 
+
+ align:start position:0%
+the AC accident the code will fall down
+so in this kind of situation how long
+
+ align:start position:0%
+so in this kind of situation how long
+ 
+
+ align:start position:0%
+so in this kind of situation how long
+they can transfer the information so
+
+ align:start position:0%
+they can transfer the information so
+ 
+
+ align:start position:0%
+they can transfer the information so
+this is must the simulate in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+labor also um there we are pay more
+
+ align:start position:0%
+labor also um there we are pay more
+ 
+
+ align:start position:0%
+labor also um there we are pay more
+attention to the
+
+ align:start position:0%
+attention to the
+ 
+
+ align:start position:0%
+attention to the
+TX we are set up the some research proog
+
+ align:start position:0%
+TX we are set up the some research proog
+ 
+
+ align:start position:0%
+TX we are set up the some research proog
+and project for example we are research
+
+ align:start position:0%
+and project for example we are research
+ 
+
+ align:start position:0%
+and project for example we are research
+the UHF chips and the
+
+ align:start position:0%
+the UHF chips and the
+ 
+
+ align:start position:0%
+the UHF chips and the
+UHF antenna design and also Tech
+
+ align:start position:0%
+UHF antenna design and also Tech
+ 
+
+ align:start position:0%
+UHF antenna design and also Tech
+integrate with the other sensor
+
+ align:start position:0%
+integrate with the other sensor
+ 
+
+ align:start position:0%
+integrate with the other sensor
+technology and also and pay more
+
+ align:start position:0%
+technology and also and pay more
+ 
+
+ align:start position:0%
+technology and also and pay more
+attention to
+
+ align:start position:0%
+attention to
+ 
+
+ align:start position:0%
+attention to
+packaging and uh in the reader we are
+
+ align:start position:0%
+packaging and uh in the reader we are
+ 
+
+ align:start position:0%
+packaging and uh in the reader we are
+also research some UHF reader and the
+
+ align:start position:0%
+also research some UHF reader and the
+ 
+
+ align:start position:0%
+also research some UHF reader and the
+UHF reader antenna design and also
+
+ align:start position:0%
+UHF reader antenna design and also
+ 
+
+ align:start position:0%
+UHF reader antenna design and also
+active IID
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technology and for the research network
+
+ align:start position:0%
+technology and for the research network
+ 
+
+ align:start position:0%
+technology and for the research network
+uh architecture and
+
+ align:start position:0%
+uh architecture and
+ 
+
+ align:start position:0%
+uh architecture and
+uh product name service system for
+
+ align:start position:0%
+uh product name service system for
+ 
+
+ align:start position:0%
+uh product name service system for
+Supply Chain
+
+ align:start position:0%
+Supply Chain
+ 
+
+ align:start position:0%
+Supply Chain
+management and also we support the uh
+
+ align:start position:0%
+management and also we support the uh
+ 
+
+ align:start position:0%
+management and also we support the uh
+planning to set up local products name
+
+ align:start position:0%
+planning to set up local products name
+ 
+
+ align:start position:0%
+planning to set up local products name
+service system on the China domestic
+
+ align:start position:0%
+service system on the China domestic
+ 
+
+ align:start position:0%
+service system on the China domestic
+supply chain
+
+ align:start position:0%
+supply chain
+ 
+
+ align:start position:0%
+supply chain
+environment which could
+
+ align:start position:0%
+environment which could
+ 
+
+ align:start position:0%
+environment which could
+map the um the
+
+ align:start position:0%
+map the um the
+ 
+
+ align:start position:0%
+map the um the
+secon the data with the other name
+
+ align:start position:0%
+secon the data with the other name
+ 
+
+ align:start position:0%
+secon the data with the other name
+system for example the O system
+
+ align:start position:0%
+system for example the O system
+ 
+
+ align:start position:0%
+system for example the O system
+so carry out the international uh
+
+ align:start position:0%
+so carry out the international uh
+ 
+
+ align:start position:0%
+so carry out the international uh
+collaboration with the all kind of the
+
+ align:start position:0%
+collaboration with the all kind of the
+ 
+
+ align:start position:0%
+collaboration with the all kind of the
+organizations such as the standard
+
+ align:start position:0%
+organizations such as the standard
+ 
+
+ align:start position:0%
+organizations such as the standard
+committee and the research and Academy
+
+ align:start position:0%
+committee and the research and Academy
+ 
+
+ align:start position:0%
+committee and the research and Academy
+also for the some big company or some
+
+ align:start position:0%
+also for the some big company or some
+ 
+
+ align:start position:0%
+also for the some big company or some
+foreign uh government so I think this we
+
+ align:start position:0%
+foreign uh government so I think this we
+ 
+
+ align:start position:0%
+foreign uh government so I think this we
+open the door to want to cooperation
+
+ align:start position:0%
+open the door to want to cooperation
+ 
+
+ align:start position:0%
+open the door to want to cooperation
+with the different partner um based
+
+ align:start position:0%
+with the different partner um based
+ 
+
+ align:start position:0%
+with the different partner um based
+their women cooperation so I think this
+
+ align:start position:0%
+their women cooperation so I think this
+ 
+
+ align:start position:0%
+their women cooperation so I think this
+is a big issue not only useful for China
+
+ align:start position:0%
+is a big issue not only useful for China
+ 
+
+ align:start position:0%
+is a big issue not only useful for China
+to develop their technology and also I
+
+ align:start position:0%
+to develop their technology and also I
+ 
+
+ align:start position:0%
+to develop their technology and also I
+think must cooperation uh with the every
+
+ align:start position:0%
+think must cooperation uh with the every
+ 
+
+ align:start position:0%
+think must cooperation uh with the every
+every organization or every country they
+
+ align:start position:0%
+every organization or every country they
+ 
+
+ align:start position:0%
+every organization or every country they
+can do more best to reduce the cost and
+
+ align:start position:0%
+can do more best to reduce the cost and
+ 
+
+ align:start position:0%
+can do more best to reduce the cost and
+also develop the Next Generation the
+
+ align:start position:0%
+also develop the Next Generation the
+ 
+
+ align:start position:0%
+also develop the Next Generation the
+technology make the the chips more cheap
+
+ align:start position:0%
+technology make the the chips more cheap
+ 
+
+ align:start position:0%
+technology make the the chips more cheap
+and also for the tax the uh also redu
+
+ align:start position:0%
+and also for the tax the uh also redu
+ 
+
+ align:start position:0%
+and also for the tax the uh also redu
+the cost so I think this is a big issue
+
+ align:start position:0%
+the cost so I think this is a big issue
+ 
+
+ align:start position:0%
+the cost so I think this is a big issue
+so we must cooperation each
+
+ align:start position:0%
+so we must cooperation each
+ 
+
+ align:start position:0%
+so we must cooperation each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks thank you very much Dr Zang and
+
+ align:start position:0%
+thanks thank you very much Dr Zang and
+ 
+
+ align:start position:0%
+thanks thank you very much Dr Zang and
+now for a different perspective from
+
+ align:start position:0%
+now for a different perspective from
+ 
+
+ align:start position:0%
+now for a different perspective from
+Europe uh we're very privileged to have
+
+ align:start position:0%
+Europe uh we're very privileged to have
+ 
+
+ align:start position:0%
+Europe uh we're very privileged to have
+uh Peter F who is the DG Information
+
+ align:start position:0%
+uh Peter F who is the DG Information
+ 
+
+ align:start position:0%
+uh Peter F who is the DG Information
+Society and media Network and
+
+ align:start position:0%
+Society and media Network and
+ 
+
+ align:start position:0%
+Society and media Network and
+Communications Technologies ICT for
+
+ align:start position:0%
+Communications Technologies ICT for
+ 
+
+ align:start position:0%
+Communications Technologies ICT for
+Enterprise networking director for
+
+ align:start position:0%
+Enterprise networking director for
+ 
+
+ align:start position:0%
+Enterprise networking director for
+Europe and and is actually one of the
+
+ align:start position:0%
+Europe and and is actually one of the
+ 
+
+ align:start position:0%
+Europe and and is actually one of the
+principal funders of uh some programs
+
+ align:start position:0%
+principal funders of uh some programs
+ 
+
+ align:start position:0%
+principal funders of uh some programs
+that you've already heard about
+
+ align:start position:0%
+that you've already heard about
+ 
+
+ align:start position:0%
+that you've already heard about
+including the uh promise program that
+
+ align:start position:0%
+including the uh promise program that
+ 
+
+ align:start position:0%
+including the uh promise program that
+that was introduced yesterday thank you
+
+ align:start position:0%
+that was introduced yesterday thank you
+ 
+
+ align:start position:0%
+that was introduced yesterday thank you
+I put it
+
+ align:start position:0%
+I put it
+ 
+
+ align:start position:0%
+I put it
+here fine
+
+ align:start position:0%
+here fine
+ 
+
+ align:start position:0%
+here fine
+okay so let's find this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just take my papers thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much well perfect thank you very much
+
+ align:start position:0%
+much well perfect thank you very much
+ 
+
+ align:start position:0%
+much well perfect thank you very much
+good afternoon ladies and gentlemen
+
+ align:start position:0%
+good afternoon ladies and gentlemen
+ 
+
+ align:start position:0%
+good afternoon ladies and gentlemen
+thanks a lot to Steve and and John to
+
+ align:start position:0%
+thanks a lot to Steve and and John to
+ 
+
+ align:start position:0%
+thanks a lot to Steve and and John to
+have to opportunity to talk today on
+
+ align:start position:0%
+have to opportunity to talk today on
+ 
+
+ align:start position:0%
+have to opportunity to talk today on
+behalf of the European commission it was
+
+ align:start position:0%
+behalf of the European commission it was
+ 
+
+ align:start position:0%
+behalf of the European commission it was
+quite a long journey anyhow to come over
+
+ align:start position:0%
+quite a long journey anyhow to come over
+ 
+
+ align:start position:0%
+quite a long journey anyhow to come over
+and it was for me the last the last time
+
+ align:start position:0%
+and it was for me the last the last time
+ 
+
+ align:start position:0%
+and it was for me the last the last time
+I've been States was is 26 years ago
+
+ align:start position:0%
+I've been States was is 26 years ago
+ 
+
+ align:start position:0%
+I've been States was is 26 years ago
+so and then I have been to California so
+
+ align:start position:0%
+so and then I have been to California so
+ 
+
+ align:start position:0%
+so and then I have been to California so
+it's first time to be the New England
+
+ align:start position:0%
+it's first time to be the New England
+ 
+
+ align:start position:0%
+it's first time to be the New England
+states well I would like to present you
+
+ align:start position:0%
+states well I would like to present you
+ 
+
+ align:start position:0%
+states well I would like to present you
+briefly the P European perspective from
+
+ align:start position:0%
+briefly the P European perspective from
+ 
+
+ align:start position:0%
+briefly the P European perspective from
+RFID I'm working in um public
+
+ align:start position:0%
+RFID I'm working in um public
+ 
+
+ align:start position:0%
+RFID I'm working in um public
+administration at the European
+
+ align:start position:0%
+administration at the European
+ 
+
+ align:start position:0%
+administration at the European
+commission I'm sure that you're familiar
+
+ align:start position:0%
+commission I'm sure that you're familiar
+ 
+
+ align:start position:0%
+commission I'm sure that you're familiar
+how the commission works we are
+
+ align:start position:0%
+how the commission works we are
+ 
+
+ align:start position:0%
+how the commission works we are
+supernational
+
+ align:start position:0%
+supernational
+ 
+
+ align:start position:0%
+supernational
+body and we have no Ministeries but we
+
+ align:start position:0%
+body and we have no Ministeries but we
+ 
+
+ align:start position:0%
+body and we have no Ministeries but we
+have a lot of director generals and each
+
+ align:start position:0%
+have a lot of director generals and each
+ 
+
+ align:start position:0%
+have a lot of director generals and each
+director General has a commissioner and
+
+ align:start position:0%
+director General has a commissioner and
+ 
+
+ align:start position:0%
+director General has a commissioner and
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+yesterday told about the 30 models on
+
+ align:start position:0%
+yesterday told about the 30 models on
+ 
+
+ align:start position:0%
+yesterday told about the 30 models on
+pedigree this reminded me quite well of
+
+ align:start position:0%
+pedigree this reminded me quite well of
+ 
+
+ align:start position:0%
+pedigree this reminded me quite well of
+our work because we have always 25
+
+ align:start position:0%
+our work because we have always 25
+ 
+
+ align:start position:0%
+our work because we have always 25
+member states and depending on the
+
+ align:start position:0%
+member states and depending on the
+ 
+
+ align:start position:0%
+member states and depending on the
+subject we have a very let me say um
+
+ align:start position:0%
+subject we have a very let me say um
+ 
+
+ align:start position:0%
+subject we have a very let me say um
+good direct power or we are more working
+
+ align:start position:0%
+good direct power or we are more working
+ 
+
+ align:start position:0%
+good direct power or we are more working
+on a basis of of being a facilitator so
+
+ align:start position:0%
+on a basis of of being a facilitator so
+ 
+
+ align:start position:0%
+on a basis of of being a facilitator so
+and for our ID I think it's uh between
+
+ align:start position:0%
+and for our ID I think it's uh between
+ 
+
+ align:start position:0%
+and for our ID I think it's uh between
+both um I'm working on Research
+
+ align:start position:0%
+both um I'm working on Research
+ 
+
+ align:start position:0%
+both um I'm working on Research
+Administration which means that
+
+ align:start position:0%
+Administration which means that
+ 
+
+ align:start position:0%
+Administration which means that
+basically Europe the European commission
+
+ align:start position:0%
+basically Europe the European commission
+ 
+
+ align:start position:0%
+basically Europe the European commission
+is not um executing aearch on its own
+
+ align:start position:0%
+is not um executing aearch on its own
+ 
+
+ align:start position:0%
+is not um executing aearch on its own
+apart from some specialized Institutes
+
+ align:start position:0%
+apart from some specialized Institutes
+ 
+
+ align:start position:0%
+apart from some specialized Institutes
+um we are always commissioning in the
+
+ align:start position:0%
+um we are always commissioning in the
+ 
+
+ align:start position:0%
+um we are always commissioning in the
+work or in the frame of some framework
+
+ align:start position:0%
+work or in the frame of some framework
+ 
+
+ align:start position:0%
+work or in the frame of some framework
+programs uh
+
+ align:start position:0%
+programs uh
+ 
+
+ align:start position:0%
+programs uh
+research and um what we try always is of
+
+ align:start position:0%
+research and um what we try always is of
+ 
+
+ align:start position:0%
+research and um what we try always is of
+course in terms of speeding up Europeans
+
+ align:start position:0%
+course in terms of speeding up Europeans
+ 
+
+ align:start position:0%
+course in terms of speeding up Europeans
+uh Europe's competence and
+
+ align:start position:0%
+uh Europe's competence and
+ 
+
+ align:start position:0%
+uh Europe's competence and
+competitiveness to facilitate the right
+
+ align:start position:0%
+competitiveness to facilitate the right
+ 
+
+ align:start position:0%
+competitiveness to facilitate the right
+research issues in the same time to
+
+ align:start position:0%
+research issues in the same time to
+ 
+
+ align:start position:0%
+research issues in the same time to
+ensure that um the the results of the
+
+ align:start position:0%
+ensure that um the the results of the
+ 
+
+ align:start position:0%
+ensure that um the the results of the
+research are going to be taken up
+
+ align:start position:0%
+research are going to be taken up
+ 
+
+ align:start position:0%
+research are going to be taken up
+afterwards and there are quite often
+
+ align:start position:0%
+afterwards and there are quite often
+ 
+
+ align:start position:0%
+afterwards and there are quite often
+Europe has some
+
+ align:start position:0%
+Europe has some
+ 
+
+ align:start position:0%
+Europe has some
+weaknesses so basically what we try to
+
+ align:start position:0%
+weaknesses so basically what we try to
+ 
+
+ align:start position:0%
+weaknesses so basically what we try to
+do as I do did yesterday and to today is
+
+ align:start position:0%
+do as I do did yesterday and to today is
+ 
+
+ align:start position:0%
+do as I do did yesterday and to today is
+to learn and to see what should we uh
+
+ align:start position:0%
+to learn and to see what should we uh
+ 
+
+ align:start position:0%
+to learn and to see what should we uh
+where should we proceed in terms of the
+
+ align:start position:0%
+where should we proceed in terms of the
+ 
+
+ align:start position:0%
+where should we proceed in terms of the
+future R RFID um
+
+ align:start position:0%
+future R RFID um
+ 
+
+ align:start position:0%
+future R RFID um
+research um so I'm Ching around about uh
+
+ align:start position:0%
+research um so I'm Ching around about uh
+ 
+
+ align:start position:0%
+research um so I'm Ching around about uh
+inter service working group we
+
+ align:start position:0%
+inter service working group we
+ 
+
+ align:start position:0%
+inter service working group we
+established last year on RFID on
+
+ align:start position:0%
+established last year on RFID on
+ 
+
+ align:start position:0%
+established last year on RFID on
+International collaboration European
+
+ align:start position:0%
+International collaboration European
+ 
+
+ align:start position:0%
+International collaboration European
+research and RFID topics of RFID
+
+ align:start position:0%
+research and RFID topics of RFID
+ 
+
+ align:start position:0%
+research and RFID topics of RFID
+discussion in Europe today and next
+
+ align:start position:0%
+discussion in Europe today and next
+ 
+
+ align:start position:0%
+discussion in Europe today and next
+steps what what happens quite quite
+
+ align:start position:0%
+steps what what happens quite quite
+ 
+
+ align:start position:0%
+steps what what happens quite quite
+often it's in public administration that
+
+ align:start position:0%
+often it's in public administration that
+ 
+
+ align:start position:0%
+often it's in public administration that
+depending on the application cases a
+
+ align:start position:0%
+depending on the application cases a
+ 
+
+ align:start position:0%
+depending on the application cases a
+topic pops up in different um different
+
+ align:start position:0%
+topic pops up in different um different
+ 
+
+ align:start position:0%
+topic pops up in different um different
+uh administrations and for example there
+
+ align:start position:0%
+uh administrations and for example there
+ 
+
+ align:start position:0%
+uh administrations and for example there
+is the topic on standardization RFID in
+
+ align:start position:0%
+is the topic on standardization RFID in
+ 
+
+ align:start position:0%
+is the topic on standardization RFID in
+frequency it's about um Customs issu
+
+ align:start position:0%
+frequency it's about um Customs issu
+ 
+
+ align:start position:0%
+frequency it's about um Customs issu
+it's about Enterprise cor Corporation
+
+ align:start position:0%
+it's about Enterprise cor Corporation
+ 
+
+ align:start position:0%
+it's about Enterprise cor Corporation
+Supply Chain management and then we
+
+ align:start position:0%
+Supply Chain management and then we
+ 
+
+ align:start position:0%
+Supply Chain management and then we
+discovered actually last year that we
+
+ align:start position:0%
+discovered actually last year that we
+ 
+
+ align:start position:0%
+discovered actually last year that we
+should um realign our forces and should
+
+ align:start position:0%
+should um realign our forces and should
+ 
+
+ align:start position:0%
+should um realign our forces and should
+go for a coherent approach so actually
+
+ align:start position:0%
+go for a coherent approach so actually
+ 
+
+ align:start position:0%
+go for a coherent approach so actually
+12 director General
+
+ align:start position:0%
+12 director General
+ 
+
+ align:start position:0%
+12 director General
+um then since then try to work together
+
+ align:start position:0%
+um then since then try to work together
+ 
+
+ align:start position:0%
+um then since then try to work together
+and actually my head of unit is um the
+
+ align:start position:0%
+and actually my head of unit is um the
+ 
+
+ align:start position:0%
+and actually my head of unit is um the
+coordinator and my colleague from from
+
+ align:start position:0%
+coordinator and my colleague from from
+ 
+
+ align:start position:0%
+coordinator and my colleague from from
+and myself we are managing this um inter
+
+ align:start position:0%
+and myself we are managing this um inter
+ 
+
+ align:start position:0%
+and myself we are managing this um inter
+service working group which is quite
+
+ align:start position:0%
+service working group which is quite
+ 
+
+ align:start position:0%
+service working group which is quite
+promising and seems to be a good um
+
+ align:start position:0%
+promising and seems to be a good um
+ 
+
+ align:start position:0%
+promising and seems to be a good um
+opportunity a good um action for Europe
+
+ align:start position:0%
+opportunity a good um action for Europe
+ 
+
+ align:start position:0%
+opportunity a good um action for Europe
+actually what we want to do is of course
+
+ align:start position:0%
+actually what we want to do is of course
+ 
+
+ align:start position:0%
+actually what we want to do is of course
+go for a horizontal coordination of
+
+ align:start position:0%
+go for a horizontal coordination of
+ 
+
+ align:start position:0%
+go for a horizontal coordination of
+activities in RFID in
+
+ align:start position:0%
+activities in RFID in
+ 
+
+ align:start position:0%
+activities in RFID in
+Europe try to cooperate with national
+
+ align:start position:0%
+Europe try to cooperate with national
+ 
+
+ align:start position:0%
+Europe try to cooperate with national
+authorities and solarization bodies as
+
+ align:start position:0%
+authorities and solarization bodies as
+ 
+
+ align:start position:0%
+authorities and solarization bodies as
+it has to do a lot with aligning I would
+
+ align:start position:0%
+it has to do a lot with aligning I would
+ 
+
+ align:start position:0%
+it has to do a lot with aligning I would
+say efforts and standards and provision
+
+ align:start position:0%
+say efforts and standards and provision
+ 
+
+ align:start position:0%
+say efforts and standards and provision
+of ground for international cooporation
+
+ align:start position:0%
+of ground for international cooporation
+ 
+
+ align:start position:0%
+of ground for international cooporation
+of course we see that um Europe as all
+
+ align:start position:0%
+of course we see that um Europe as all
+ 
+
+ align:start position:0%
+of course we see that um Europe as all
+the big economic zones tries to be one
+
+ align:start position:0%
+the big economic zones tries to be one
+ 
+
+ align:start position:0%
+the big economic zones tries to be one
+of the leading ones but still as RFID is
+
+ align:start position:0%
+of the leading ones but still as RFID is
+ 
+
+ align:start position:0%
+of the leading ones but still as RFID is
+a global issue we have to always go for
+
+ align:start position:0%
+a global issue we have to always go for
+ 
+
+ align:start position:0%
+a global issue we have to always go for
+a global cooporation and I give you some
+
+ align:start position:0%
+a global cooporation and I give you some
+ 
+
+ align:start position:0%
+a global cooporation and I give you some
+examples we had quite some contact with
+
+ align:start position:0%
+examples we had quite some contact with
+ 
+
+ align:start position:0%
+examples we had quite some contact with
+Dan capio from the Department of
+
+ align:start position:0%
+Dan capio from the Department of
+ 
+
+ align:start position:0%
+Dan capio from the Department of
+Commerce
+
+ align:start position:0%
+Commerce
+ 
+
+ align:start position:0%
+Commerce
+there was recently the US Information
+
+ align:start position:0%
+there was recently the US Information
+ 
+
+ align:start position:0%
+there was recently the US Information
+Society dialogue and one major issue was
+
+ align:start position:0%
+Society dialogue and one major issue was
+ 
+
+ align:start position:0%
+Society dialogue and one major issue was
+RFID there are informal discussions
+
+ align:start position:0%
+RFID there are informal discussions
+ 
+
+ align:start position:0%
+RFID there are informal discussions
+since uh last year and there was
+
+ align:start position:0%
+since uh last year and there was
+ 
+
+ align:start position:0%
+since uh last year and there was
+attendance for us on a um Department of
+
+ align:start position:0%
+attendance for us on a um Department of
+ 
+
+ align:start position:0%
+attendance for us on a um Department of
+Commerce
+
+ align:start position:0%
+Commerce
+ 
+
+ align:start position:0%
+Commerce
+workshop last week our commissioner
+
+ align:start position:0%
+workshop last week our commissioner
+ 
+
+ align:start position:0%
+workshop last week our commissioner
+reading uh visited China so there was a
+
+ align:start position:0%
+reading uh visited China so there was a
+ 
+
+ align:start position:0%
+reading uh visited China so there was a
+contact with the European Ministry of
+
+ align:start position:0%
+contact with the European Ministry of
+ 
+
+ align:start position:0%
+contact with the European Ministry of
+sorry with the China Ministry of Science
+
+ align:start position:0%
+sorry with the China Ministry of Science
+ 
+
+ align:start position:0%
+sorry with the China Ministry of Science
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Technology we cooperate uh with the oecd
+
+ align:start position:0%
+Technology we cooperate uh with the oecd
+ 
+
+ align:start position:0%
+Technology we cooperate uh with the oecd
+and we have as well a transatlantic uh
+
+ align:start position:0%
+and we have as well a transatlantic uh
+ 
+
+ align:start position:0%
+and we have as well a transatlantic uh
+consumer Di
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um what we normally do in Europe is
+
+ align:start position:0%
+um what we normally do in Europe is
+ 
+
+ align:start position:0%
+um what we normally do in Europe is
+apart from National research programs
+
+ align:start position:0%
+apart from National research programs
+ 
+
+ align:start position:0%
+apart from National research programs
+that we have so-called M multianal
+
+ align:start position:0%
+that we have so-called M multianal
+ 
+
+ align:start position:0%
+that we have so-called M multianal
+framework programs which are like some
+
+ align:start position:0%
+framework programs which are like some
+ 
+
+ align:start position:0%
+framework programs which are like some
+sort of some big machineries that based
+
+ align:start position:0%
+sort of some big machineries that based
+ 
+
+ align:start position:0%
+sort of some big machineries that based
+on extensive stakeholder discussion
+
+ align:start position:0%
+on extensive stakeholder discussion
+ 
+
+ align:start position:0%
+on extensive stakeholder discussion
+consultation we're going to develop
+
+ align:start position:0%
+consultation we're going to develop
+ 
+
+ align:start position:0%
+consultation we're going to develop
+specific uh research subjects which then
+
+ align:start position:0%
+specific uh research subjects which then
+ 
+
+ align:start position:0%
+specific uh research subjects which then
+are updated each um two
+
+ align:start position:0%
+are updated each um two
+ 
+
+ align:start position:0%
+are updated each um two
+years and as you can see that we do
+
+ align:start position:0%
+years and as you can see that we do
+ 
+
+ align:start position:0%
+years and as you can see that we do
+quite a lot on Al research since 10
+
+ align:start position:0%
+quite a lot on Al research since 10
+ 
+
+ align:start position:0%
+quite a lot on Al research since 10
+years difference between project and
+
+ align:start position:0%
+years difference between project and
+ 
+
+ align:start position:0%
+years difference between project and
+funding is that this is always a
+
+ align:start position:0%
+funding is that this is always a
+ 
+
+ align:start position:0%
+funding is that this is always a
+collaborative funding so we normally ask
+
+ align:start position:0%
+collaborative funding so we normally ask
+ 
+
+ align:start position:0%
+collaborative funding so we normally ask
+the participants which means um research
+
+ align:start position:0%
+the participants which means um research
+ 
+
+ align:start position:0%
+the participants which means um research
+institutes and um companies to
+
+ align:start position:0%
+institutes and um companies to
+ 
+
+ align:start position:0%
+institutes and um companies to
+contribute uh up to 50% of um of the
+
+ align:start position:0%
+contribute uh up to 50% of um of the
+ 
+
+ align:start position:0%
+contribute uh up to 50% of um of the
+project budget to to carry out the work
+
+ align:start position:0%
+project budget to to carry out the work
+ 
+
+ align:start position:0%
+project budget to to carry out the work
+um this figure gives you only idea on
+
+ align:start position:0%
+um this figure gives you only idea on
+ 
+
+ align:start position:0%
+um this figure gives you only idea on
+European level and a part of this I
+
+ align:start position:0%
+European level and a part of this I
+ 
+
+ align:start position:0%
+European level and a part of this I
+think you can easily double this is we
+
+ align:start position:0%
+think you can easily double this is we
+ 
+
+ align:start position:0%
+think you can easily double this is we
+have all of of course in different
+
+ align:start position:0%
+have all of of course in different
+ 
+
+ align:start position:0%
+have all of of course in different
+member states national um research and
+
+ align:start position:0%
+member states national um research and
+ 
+
+ align:start position:0%
+member states national um research and
+what we try since some years is to go
+
+ align:start position:0%
+what we try since some years is to go
+ 
+
+ align:start position:0%
+what we try since some years is to go
+for so-called European research area
+
+ align:start position:0%
+for so-called European research area
+ 
+
+ align:start position:0%
+for so-called European research area
+which means that we try to coordinate
+
+ align:start position:0%
+which means that we try to coordinate
+ 
+
+ align:start position:0%
+which means that we try to coordinate
+better European and um Nationwide
+
+ align:start position:0%
+better European and um Nationwide
+ 
+
+ align:start position:0%
+better European and um Nationwide
+research and I think it starts to
+
+ align:start position:0%
+research and I think it starts to
+ 
+
+ align:start position:0%
+research and I think it starts to
+work just to give a glance on the topics
+
+ align:start position:0%
+work just to give a glance on the topics
+ 
+
+ align:start position:0%
+work just to give a glance on the topics
+we cover it's a very colorful pile and
+
+ align:start position:0%
+we cover it's a very colorful pile and
+ 
+
+ align:start position:0%
+we cover it's a very colorful pile and
+it shows actually that it goes really
+
+ align:start position:0%
+it shows actually that it goes really
+ 
+
+ align:start position:0%
+it shows actually that it goes really
+from Supply Chain management e
+
+ align:start position:0%
+from Supply Chain management e
+ 
+
+ align:start position:0%
+from Supply Chain management e
+government Justice Liberty and freedom
+
+ align:start position:0%
+government Justice Liberty and freedom
+ 
+
+ align:start position:0%
+government Justice Liberty and freedom
+I'm just picking up some smart devices
+
+ align:start position:0%
+I'm just picking up some smart devices
+ 
+
+ align:start position:0%
+I'm just picking up some smart devices
+goes into nanot technology so there
+
+ align:start position:0%
+goes into nanot technology so there
+ 
+
+ align:start position:0%
+goes into nanot technology so there
+really a big uh bundle and a bunch of a
+
+ align:start position:0%
+really a big uh bundle and a bunch of a
+ 
+
+ align:start position:0%
+really a big uh bundle and a bunch of a
+um diverse subjects all dealing around
+
+ align:start position:0%
+um diverse subjects all dealing around
+ 
+
+ align:start position:0%
+um diverse subjects all dealing around
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RFID what we see today on as typical
+
+ align:start position:0%
+RFID what we see today on as typical
+ 
+
+ align:start position:0%
+RFID what we see today on as typical
+topics in
+
+ align:start position:0%
+topics in
+ 
+
+ align:start position:0%
+topics in
+Europe is in terms of the application
+
+ align:start position:0%
+Europe is in terms of the application
+ 
+
+ align:start position:0%
+Europe is in terms of the application
+areas is the supply chain Logistics uh
+
+ align:start position:0%
+areas is the supply chain Logistics uh
+ 
+
+ align:start position:0%
+areas is the supply chain Logistics uh
+on the Forefront we see product life
+
+ align:start position:0%
+on the Forefront we see product life
+ 
+
+ align:start position:0%
+on the Forefront we see product life
+cycle after sales service intelligent
+
+ align:start position:0%
+cycle after sales service intelligent
+ 
+
+ align:start position:0%
+cycle after sales service intelligent
+maintainance M for you see uh health is
+
+ align:start position:0%
+maintainance M for you see uh health is
+ 
+
+ align:start position:0%
+maintainance M for you see uh health is
+a very important issue and to some
+
+ align:start position:0%
+a very important issue and to some
+ 
+
+ align:start position:0%
+a very important issue and to some
+extent as well inclusion which means how
+
+ align:start position:0%
+extent as well inclusion which means how
+ 
+
+ align:start position:0%
+extent as well inclusion which means how
+can we help um Elder and disabled people
+
+ align:start position:0%
+can we help um Elder and disabled people
+ 
+
+ align:start position:0%
+can we help um Elder and disabled people
+people's additional needs to participate
+
+ align:start position:0%
+people's additional needs to participate
+ 
+
+ align:start position:0%
+people's additional needs to participate
+in a modern society in particular as you
+
+ align:start position:0%
+in a modern society in particular as you
+ 
+
+ align:start position:0%
+in a modern society in particular as you
+notice that Europe always try or has
+
+ align:start position:0%
+notice that Europe always try or has
+ 
+
+ align:start position:0%
+notice that Europe always try or has
+give a gives a special emphasis on
+
+ align:start position:0%
+give a gives a special emphasis on
+ 
+
+ align:start position:0%
+give a gives a special emphasis on
+so-called social coherence and and
+
+ align:start position:0%
+so-called social coherence and and
+ 
+
+ align:start position:0%
+so-called social coherence and and
+inclusion in terms of research and
+
+ align:start position:0%
+inclusion in terms of research and
+ 
+
+ align:start position:0%
+inclusion in terms of research and
+development it's basically about te R
+
+ align:start position:0%
+development it's basically about te R
+ 
+
+ align:start position:0%
+development it's basically about te R
+Hardware it's about smart sensors it's
+
+ align:start position:0%
+Hardware it's about smart sensors it's
+ 
+
+ align:start position:0%
+Hardware it's about smart sensors it's
+about software application it's about
+
+ align:start position:0%
+about software application it's about
+ 
+
+ align:start position:0%
+about software application it's about
+nanomaterials interoperability and
+
+ align:start position:0%
+nanomaterials interoperability and
+ 
+
+ align:start position:0%
+nanomaterials interoperability and
+standards uh basically frequencies data
+
+ align:start position:0%
+standards uh basically frequencies data
+ 
+
+ align:start position:0%
+standards uh basically frequencies data
+structures and tag
+
+ align:start position:0%
+structures and tag
+ 
+
+ align:start position:0%
+structures and tag
+interrogation and particularly on this
+
+ align:start position:0%
+interrogation and particularly on this
+ 
+
+ align:start position:0%
+interrogation and particularly on this
+in terms of frequency of course we have
+
+ align:start position:0%
+in terms of frequency of course we have
+ 
+
+ align:start position:0%
+in terms of frequency of course we have
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+harmonize uh frequency spectrums for
+
+ align:start position:0%
+harmonize uh frequency spectrums for
+ 
+
+ align:start position:0%
+harmonize uh frequency spectrums for
+RFID usage in 25 member states and um
+
+ align:start position:0%
+RFID usage in 25 member states and um
+ 
+
+ align:start position:0%
+RFID usage in 25 member states and um
+there we are on good track we gave as
+
+ align:start position:0%
+there we are on good track we gave as
+ 
+
+ align:start position:0%
+there we are on good track we gave as
+well a particular emphasis on RFID
+
+ align:start position:0%
+well a particular emphasis on RFID
+ 
+
+ align:start position:0%
+well a particular emphasis on RFID
+governance which means rules and
+
+ align:start position:0%
+governance which means rules and
+ 
+
+ align:start position:0%
+governance which means rules and
+procedures competition robot Ness in
+
+ align:start position:0%
+procedures competition robot Ness in
+ 
+
+ align:start position:0%
+procedures competition robot Ness in
+terms of um object naming services and
+
+ align:start position:0%
+terms of um object naming services and
+ 
+
+ align:start position:0%
+terms of um object naming services and
+Discovery Services as we see this is um
+
+ align:start position:0%
+Discovery Services as we see this is um
+ 
+
+ align:start position:0%
+Discovery Services as we see this is um
+a very important issue and want of
+
+ align:start position:0%
+a very important issue and want of
+ 
+
+ align:start position:0%
+a very important issue and want of
+course to have um no let me say
+
+ align:start position:0%
+course to have um no let me say
+ 
+
+ align:start position:0%
+course to have um no let me say
+incumbent power so really would like to
+
+ align:start position:0%
+incumbent power so really would like to
+ 
+
+ align:start position:0%
+incumbent power so really would like to
+go there for some mixture between a open
+
+ align:start position:0%
+go there for some mixture between a open
+ 
+
+ align:start position:0%
+go there for some mixture between a open
+and competitive
+
+ align:start position:0%
+and competitive
+ 
+
+ align:start position:0%
+and competitive
+approach privacy and data protection is
+
+ align:start position:0%
+approach privacy and data protection is
+ 
+
+ align:start position:0%
+approach privacy and data protection is
+of course high on the political agenda
+
+ align:start position:0%
+of course high on the political agenda
+ 
+
+ align:start position:0%
+of course high on the political agenda
+and as well all security issues around
+
+ align:start position:0%
+and as well all security issues around
+ 
+
+ align:start position:0%
+and as well all security issues around
+RFID what we see as well is and our RPI
+
+ align:start position:0%
+RFID what we see as well is and our RPI
+ 
+
+ align:start position:0%
+RFID what we see as well is and our RPI
+free standards intellectual property
+
+ align:start position:0%
+free standards intellectual property
+ 
+
+ align:start position:0%
+free standards intellectual property
+rights International Trade Health
+
+ align:start position:0%
+rights International Trade Health
+ 
+
+ align:start position:0%
+rights International Trade Health
+environment identity left ethical
+
+ align:start position:0%
+environment identity left ethical
+ 
+
+ align:start position:0%
+environment identity left ethical
+aspects I think are going to become very
+
+ align:start position:0%
+aspects I think are going to become very
+ 
+
+ align:start position:0%
+aspects I think are going to become very
+important and what we see as well as
+
+ align:start position:0%
+important and what we see as well as
+ 
+
+ align:start position:0%
+important and what we see as well as
+labor practices so we try to have a look
+
+ align:start position:0%
+labor practices so we try to have a look
+ 
+
+ align:start position:0%
+labor practices so we try to have a look
+that um usage of RFID might have some
+
+ align:start position:0%
+that um usage of RFID might have some
+ 
+
+ align:start position:0%
+that um usage of RFID might have some
+impact on not only negative but might
+
+ align:start position:0%
+impact on not only negative but might
+ 
+
+ align:start position:0%
+impact on not only negative but might
+have impact of course on labor forces
+
+ align:start position:0%
+have impact of course on labor forces
+ 
+
+ align:start position:0%
+have impact of course on labor forces
+and perhaps you do have to to act as
+
+ align:start position:0%
+and perhaps you do have to to act as
+ 
+
+ align:start position:0%
+and perhaps you do have to to act as
+well besides some technical
+
+ align:start position:0%
+well besides some technical
+ 
+
+ align:start position:0%
+well besides some technical
+technological development um to provide
+
+ align:start position:0%
+technological development um to provide
+ 
+
+ align:start position:0%
+technological development um to provide
+some measures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I give you here some typical examples uh
+
+ align:start position:0%
+I give you here some typical examples uh
+ 
+
+ align:start position:0%
+I give you here some typical examples uh
+what we try to do in European research
+
+ align:start position:0%
+what we try to do in European research
+ 
+
+ align:start position:0%
+what we try to do in European research
+and RFID and I'm proud that in two
+
+ align:start position:0%
+and RFID and I'm proud that in two
+ 
+
+ align:start position:0%
+and RFID and I'm proud that in two
+projects we have outdoor daps included
+
+ align:start position:0%
+projects we have outdoor daps included
+ 
+
+ align:start position:0%
+projects we have outdoor daps included
+for example Professor fish's
+
+ align:start position:0%
+for example Professor fish's
+ 
+
+ align:start position:0%
+for example Professor fish's
+participating as well I think it's even
+
+ align:start position:0%
+participating as well I think it's even
+ 
+
+ align:start position:0%
+participating as well I think it's even
+the the MIT and as part of the Bridge
+
+ align:start position:0%
+the the MIT and as part of the Bridge
+ 
+
+ align:start position:0%
+the the MIT and as part of the Bridge
+Project in which EPC Global and gs1
+
+ align:start position:0%
+Project in which EPC Global and gs1
+ 
+
+ align:start position:0%
+Project in which EPC Global and gs1
+organizations are going to participate
+
+ align:start position:0%
+organizations are going to participate
+ 
+
+ align:start position:0%
+organizations are going to participate
+so what you see for example apart from
+
+ align:start position:0%
+so what you see for example apart from
+ 
+
+ align:start position:0%
+so what you see for example apart from
+Supply Chain management it's really
+
+ align:start position:0%
+Supply Chain management it's really
+ 
+
+ align:start position:0%
+Supply Chain management it's really
+about um
+
+ align:start position:0%
+about um
+ 
+
+ align:start position:0%
+about um
+using RFID to go for a let me say a
+
+ align:start position:0%
+using RFID to go for a let me say a
+ 
+
+ align:start position:0%
+using RFID to go for a let me say a
+better customer service apart from just
+
+ align:start position:0%
+better customer service apart from just
+ 
+
+ align:start position:0%
+better customer service apart from just
+providing the right product the right
+
+ align:start position:0%
+providing the right product the right
+ 
+
+ align:start position:0%
+providing the right product the right
+time and the right um shelf or display
+
+ align:start position:0%
+time and the right um shelf or display
+ 
+
+ align:start position:0%
+time and the right um shelf or display
+it's really to say how could we use um
+
+ align:start position:0%
+it's really to say how could we use um
+ 
+
+ align:start position:0%
+it's really to say how could we use um
+data to um save resources and improve
+
+ align:start position:0%
+data to um save resources and improve
+ 
+
+ align:start position:0%
+data to um save resources and improve
+customer
+
+ align:start position:0%
+customer
+ 
+
+ align:start position:0%
+customer
+service I think uh RFID solution for
+
+ align:start position:0%
+service I think uh RFID solution for
+ 
+
+ align:start position:0%
+service I think uh RFID solution for
+global environment bridge is 3 to say
+
+ align:start position:0%
+global environment bridge is 3 to say
+ 
+
+ align:start position:0%
+global environment bridge is 3 to say
+that in seven application sectors from
+
+ align:start position:0%
+that in seven application sectors from
+ 
+
+ align:start position:0%
+that in seven application sectors from
+some sort of European perspective in a
+
+ align:start position:0%
+some sort of European perspective in a
+ 
+
+ align:start position:0%
+some sort of European perspective in a
+globalwide um frame um the gs1
+
+ align:start position:0%
+globalwide um frame um the gs1
+ 
+
+ align:start position:0%
+globalwide um frame um the gs1
+organizations would like to to drive um
+
+ align:start position:0%
+organizations would like to to drive um
+ 
+
+ align:start position:0%
+organizations would like to to drive um
+the roll out of um APC
+
+ align:start position:0%
+the roll out of um APC
+ 
+
+ align:start position:0%
+the roll out of um APC
+Global yesterday we talked as well about
+
+ align:start position:0%
+Global yesterday we talked as well about
+ 
+
+ align:start position:0%
+Global yesterday we talked as well about
+on um anti-c counter fighting Solutions
+
+ align:start position:0%
+on um anti-c counter fighting Solutions
+ 
+
+ align:start position:0%
+on um anti-c counter fighting Solutions
+it's very important and for example
+
+ align:start position:0%
+it's very important and for example
+ 
+
+ align:start position:0%
+it's very important and for example
+another ex um important issue is the uh
+
+ align:start position:0%
+another ex um important issue is the uh
+ 
+
+ align:start position:0%
+another ex um important issue is the uh
+quality of food to traceability of of
+
+ align:start position:0%
+quality of food to traceability of of
+ 
+
+ align:start position:0%
+quality of food to traceability of of
+Liv look there was um some Scandal on on
+
+ align:start position:0%
+Liv look there was um some Scandal on on
+ 
+
+ align:start position:0%
+Liv look there was um some Scandal on on
+on um on meat some years ago so there's
+
+ align:start position:0%
+on um on meat some years ago so there's
+ 
+
+ align:start position:0%
+on um on meat some years ago so there's
+some sort of uh sensibility and
+
+ align:start position:0%
+some sort of uh sensibility and
+ 
+
+ align:start position:0%
+some sort of uh sensibility and
+awareness in Europe to have good food
+
+ align:start position:0%
+awareness in Europe to have good food
+ 
+
+ align:start position:0%
+awareness in Europe to have good food
+and life
+
+ align:start position:0%
+and life
+ 
+
+ align:start position:0%
+and life
+quality
+
+ align:start position:0%
+quality
+ 
+
+ align:start position:0%
+quality
+perhaps what we see as well it's not
+
+ align:start position:0%
+perhaps what we see as well it's not
+ 
+
+ align:start position:0%
+perhaps what we see as well it's not
+only that we see
+
+ align:start position:0%
+only that we see
+ 
+
+ align:start position:0%
+only that we see
+RFID and itself we try to see it in in a
+
+ align:start position:0%
+RFID and itself we try to see it in in a
+ 
+
+ align:start position:0%
+RFID and itself we try to see it in in a
+broader context which is apart from
+
+ align:start position:0%
+broader context which is apart from
+ 
+
+ align:start position:0%
+broader context which is apart from
+saying it's the internet of things that
+
+ align:start position:0%
+saying it's the internet of things that
+ 
+
+ align:start position:0%
+saying it's the internet of things that
+we say uh tomorrow the world will
+
+ align:start position:0%
+we say uh tomorrow the world will
+ 
+
+ align:start position:0%
+we say uh tomorrow the world will
+networked and and consisting of a lot of
+
+ align:start position:0%
+networked and and consisting of a lot of
+ 
+
+ align:start position:0%
+networked and and consisting of a lot of
+intelligent products and uh objectives
+
+ align:start position:0%
+intelligent products and uh objectives
+ 
+
+ align:start position:0%
+intelligent products and uh objectives
+in this case of course you have to go
+
+ align:start position:0%
+in this case of course you have to go
+ 
+
+ align:start position:0%
+in this case of course you have to go
+for different um business models
+
+ align:start position:0%
+for different um business models
+ 
+
+ align:start position:0%
+for different um business models
+different development processes new um
+
+ align:start position:0%
+different development processes new um
+ 
+
+ align:start position:0%
+different development processes new um
+ways of Corporation of suppliers and
+
+ align:start position:0%
+ways of Corporation of suppliers and
+ 
+
+ align:start position:0%
+ways of Corporation of suppliers and
+after service sorry after sales service
+
+ align:start position:0%
+after service sorry after sales service
+ 
+
+ align:start position:0%
+after service sorry after sales service
+providers I think it's about um a very
+
+ align:start position:0%
+providers I think it's about um a very
+ 
+
+ align:start position:0%
+providers I think it's about um a very
+robust robust and safe it and network
+
+ align:start position:0%
+robust robust and safe it and network
+ 
+
+ align:start position:0%
+robust robust and safe it and network
+infrastructure as the network will the
+
+ align:start position:0%
+infrastructure as the network will the
+ 
+
+ align:start position:0%
+infrastructure as the network will the
+major backbone uh to facilitate the the
+
+ align:start position:0%
+major backbone uh to facilitate the the
+ 
+
+ align:start position:0%
+major backbone uh to facilitate the the
+existence of all this intelligent
+
+ align:start position:0%
+existence of all this intelligent
+ 
+
+ align:start position:0%
+existence of all this intelligent
+objectives and I think of of course it's
+
+ align:start position:0%
+objectives and I think of of course it's
+ 
+
+ align:start position:0%
+objectives and I think of of course it's
+how in a world of increasing complexity
+
+ align:start position:0%
+how in a world of increasing complexity
+ 
+
+ align:start position:0%
+how in a world of increasing complexity
+which where and how we should use
+
+ align:start position:0%
+which where and how we should use
+ 
+
+ align:start position:0%
+which where and how we should use
+intelligent machines to handle um to
+
+ align:start position:0%
+intelligent machines to handle um to
+ 
+
+ align:start position:0%
+intelligent machines to handle um to
+handle all datas and information which I
+
+ align:start position:0%
+handle all datas and information which I
+ 
+
+ align:start position:0%
+handle all datas and information which I
+think it would be more and more
+
+ align:start position:0%
+think it would be more and more
+ 
+
+ align:start position:0%
+think it would be more and more
+difficult for human beings to cope with
+
+ align:start position:0%
+difficult for human beings to cope with
+ 
+
+ align:start position:0%
+difficult for human beings to cope with
+the increasing amount of data and
+
+ align:start position:0%
+the increasing amount of data and
+ 
+
+ align:start position:0%
+the increasing amount of data and
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+what we see this year is um very
+
+ align:start position:0%
+what we see this year is um very
+ 
+
+ align:start position:0%
+what we see this year is um very
+important from European perspective as
+
+ align:start position:0%
+important from European perspective as
+ 
+
+ align:start position:0%
+important from European perspective as
+far as Rd is concerned you're going to
+
+ align:start position:0%
+far as Rd is concerned you're going to
+ 
+
+ align:start position:0%
+far as Rd is concerned you're going to
+shape the next uh framework program it's
+
+ align:start position:0%
+shape the next uh framework program it's
+ 
+
+ align:start position:0%
+shape the next uh framework program it's
+the fp7 which is going to start in
+
+ align:start position:0%
+the fp7 which is going to start in
+ 
+
+ align:start position:0%
+the fp7 which is going to start in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+furthermore we try to provide
+
+ align:start position:0%
+furthermore we try to provide
+ 
+
+ align:start position:0%
+furthermore we try to provide
+orientation for stakeholders we talked a
+
+ align:start position:0%
+orientation for stakeholders we talked a
+ 
+
+ align:start position:0%
+orientation for stakeholders we talked a
+lot to Intel APC Global VAR sign
+
+ align:start position:0%
+lot to Intel APC Global VAR sign
+ 
+
+ align:start position:0%
+lot to Intel APC Global VAR sign
+consumer organizations and apart from
+
+ align:start position:0%
+consumer organizations and apart from
+ 
+
+ align:start position:0%
+consumer organizations and apart from
+the idea that there is or is not uh the
+
+ align:start position:0%
+the idea that there is or is not uh the
+ 
+
+ align:start position:0%
+the idea that there is or is not uh the
+need for some regulations regulation we
+
+ align:start position:0%
+need for some regulations regulation we
+ 
+
+ align:start position:0%
+need for some regulations regulation we
+see that um quite often it's a question
+
+ align:start position:0%
+see that um quite often it's a question
+ 
+
+ align:start position:0%
+see that um quite often it's a question
+of orientation saying what would be a
+
+ align:start position:0%
+of orientation saying what would be a
+ 
+
+ align:start position:0%
+of orientation saying what would be a
+good practice or on on on what should we
+
+ align:start position:0%
+good practice or on on on what should we
+ 
+
+ align:start position:0%
+good practice or on on on what should we
+conclude to go to go ahead and for this
+
+ align:start position:0%
+conclude to go to go ahead and for this
+ 
+
+ align:start position:0%
+conclude to go to go ahead and for this
+we try to carry out as part of a public
+
+ align:start position:0%
+we try to carry out as part of a public
+ 
+
+ align:start position:0%
+we try to carry out as part of a public
+consultation five important workshops
+
+ align:start position:0%
+consultation five important workshops
+ 
+
+ align:start position:0%
+consultation five important workshops
+where we try to invite relevant
+
+ align:start position:0%
+where we try to invite relevant
+ 
+
+ align:start position:0%
+where we try to invite relevant
+stakeholders to come up with ideas how
+
+ align:start position:0%
+stakeholders to come up with ideas how
+ 
+
+ align:start position:0%
+stakeholders to come up with ideas how
+we should go on what should be in terms
+
+ align:start position:0%
+we should go on what should be in terms
+ 
+
+ align:start position:0%
+we should go on what should be in terms
+of Regulation but and as well in terms
+
+ align:start position:0%
+of Regulation but and as well in terms
+ 
+
+ align:start position:0%
+of Regulation but and as well in terms
+of um let me say Solutions um
+
+ align:start position:0%
+of um let me say Solutions um
+ 
+
+ align:start position:0%
+of um let me say Solutions um
+definitions what should be a good way
+
+ align:start position:0%
+definitions what should be a good way
+ 
+
+ align:start position:0%
+definitions what should be a good way
+for Europe to go forward in the balance
+
+ align:start position:0%
+for Europe to go forward in the balance
+ 
+
+ align:start position:0%
+for Europe to go forward in the balance
+between uh being competitive and at the
+
+ align:start position:0%
+between uh being competitive and at the
+ 
+
+ align:start position:0%
+between uh being competitive and at the
+same time try to um to stick to European
+
+ align:start position:0%
+same time try to um to stick to European
+ 
+
+ align:start position:0%
+same time try to um to stick to European
+values as we try always to to carry them
+
+ align:start position:0%
+values as we try always to to carry them
+ 
+
+ align:start position:0%
+values as we try always to to carry them
+on um as I said as well um I think that
+
+ align:start position:0%
+on um as I said as well um I think that
+ 
+
+ align:start position:0%
+on um as I said as well um I think that
+we at the end of the year we could have
+
+ align:start position:0%
+we at the end of the year we could have
+ 
+
+ align:start position:0%
+we at the end of the year we could have
+some ideas about political action in
+
+ align:start position:0%
+some ideas about political action in
+ 
+
+ align:start position:0%
+some ideas about political action in
+order to to drive uh the usage of
+
+ align:start position:0%
+order to to drive uh the usage of
+ 
+
+ align:start position:0%
+order to to drive uh the usage of
+RFID um
+
+ align:start position:0%
+RFID um
+ 
+
+ align:start position:0%
+RFID um
+I would like to invite you if you anyhow
+
+ align:start position:0%
+I would like to invite you if you anyhow
+ 
+
+ align:start position:0%
+I would like to invite you if you anyhow
+in Europe or try to come over we're
+
+ align:start position:0%
+in Europe or try to come over we're
+ 
+
+ align:start position:0%
+in Europe or try to come over we're
+going to have two important workshops
+
+ align:start position:0%
+going to have two important workshops
+ 
+
+ align:start position:0%
+going to have two important workshops
+soon one is called from RF The Internet
+
+ align:start position:0%
+soon one is called from RF The Internet
+ 
+
+ align:start position:0%
+soon one is called from RF The Internet
+of Things it's more about sensor
+
+ align:start position:0%
+of Things it's more about sensor
+ 
+
+ align:start position:0%
+of Things it's more about sensor
+networks and ideas they discussed
+
+ align:start position:0%
+networks and ideas they discussed
+ 
+
+ align:start position:0%
+networks and ideas they discussed
+yesterday so I would invite you to come
+
+ align:start position:0%
+yesterday so I would invite you to come
+ 
+
+ align:start position:0%
+yesterday so I would invite you to come
+over to participant in this Workshop or
+
+ align:start position:0%
+over to participant in this Workshop or
+ 
+
+ align:start position:0%
+over to participant in this Workshop or
+one week earlier is uh the slightly
+
+ align:start position:0%
+one week earlier is uh the slightly
+ 
+
+ align:start position:0%
+one week earlier is uh the slightly
+enhanced perspective it's about ambient
+
+ align:start position:0%
+enhanced perspective it's about ambient
+ 
+
+ align:start position:0%
+enhanced perspective it's about ambient
+intelligent Technologies to enhance the
+
+ align:start position:0%
+intelligent Technologies to enhance the
+ 
+
+ align:start position:0%
+intelligent Technologies to enhance the
+product life cycle which goes more
+
+ align:start position:0%
+product life cycle which goes more
+ 
+
+ align:start position:0%
+product life cycle which goes more
+towards the idea um of networked and
+
+ align:start position:0%
+towards the idea um of networked and
+ 
+
+ align:start position:0%
+towards the idea um of networked and
+intelligent um objectives and further
+
+ align:start position:0%
+intelligent um objectives and further
+ 
+
+ align:start position:0%
+intelligent um objectives and further
+research needs and of course we try to
+
+ align:start position:0%
+research needs and of course we try to
+ 
+
+ align:start position:0%
+research needs and of course we try to
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+this to um get the ideas and to fill up
+
+ align:start position:0%
+this to um get the ideas and to fill up
+ 
+
+ align:start position:0%
+this to um get the ideas and to fill up
+the next uh work programs which then of
+
+ align:start position:0%
+the next uh work programs which then of
+ 
+
+ align:start position:0%
+the next uh work programs which then of
+course later on will lead to call for
+
+ align:start position:0%
+course later on will lead to call for
+ 
+
+ align:start position:0%
+course later on will lead to call for
+tenders and um then of course we would
+
+ align:start position:0%
+tenders and um then of course we would
+ 
+
+ align:start position:0%
+tenders and um then of course we would
+like to invite you to participate and
+
+ align:start position:0%
+like to invite you to participate and
+ 
+
+ align:start position:0%
+like to invite you to participate and
+last word to say it's basically European
+
+ align:start position:0%
+last word to say it's basically European
+ 
+
+ align:start position:0%
+last word to say it's basically European
+research but there are lot of mechanisms
+
+ align:start position:0%
+research but there are lot of mechanisms
+ 
+
+ align:start position:0%
+research but there are lot of mechanisms
+to going for international corporation
+
+ align:start position:0%
+to going for international corporation
+ 
+
+ align:start position:0%
+to going for international corporation
+which Asia China and us okay thank you
+
+ align:start position:0%
+which Asia China and us okay thank you
+ 
+
+ align:start position:0%
+which Asia China and us okay thank you
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much thank you very much our our next
+
+ align:start position:0%
+much thank you very much our our next
+ 
+
+ align:start position:0%
+much thank you very much our our next
+speaker is a colleague from the Auto ID
+
+ align:start position:0%
+speaker is a colleague from the Auto ID
+ 
+
+ align:start position:0%
+speaker is a colleague from the Auto ID
+Labs at ICU in SE Korea his name is dong
+
+ align:start position:0%
+Labs at ICU in SE Korea his name is dong
+ 
+
+ align:start position:0%
+Labs at ICU in SE Korea his name is dong
+Kim and he is uh uh his talk is on the
+
+ align:start position:0%
+Kim and he is uh uh his talk is on the
+ 
+
+ align:start position:0%
+Kim and he is uh uh his talk is on the
+evolvable network of tiny sensors
+
+ align:start position:0%
+evolvable network of tiny sensors
+ 
+
+ align:start position:0%
+evolvable network of tiny sensors
+otherwise known as ants and the hanra
+
+ align:start position:0%
+otherwise known as ants and the hanra
+ 
+
+ align:start position:0%
+otherwise known as ants and the hanra
+mountain disaster Management program
+
+ align:start position:0%
+mountain disaster Management program
+ 
+
+ align:start position:0%
+mountain disaster Management program
+which We Gather is one of the flagship
+
+ align:start position:0%
+which We Gather is one of the flagship
+ 
+
+ align:start position:0%
+which We Gather is one of the flagship
+programs in Korea thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks uh good
+
+ align:start position:0%
+thanks uh good
+ 
+
+ align:start position:0%
+thanks uh good
+afternoon uh yeah first of all I'd like
+
+ align:start position:0%
+afternoon uh yeah first of all I'd like
+ 
+
+ align:start position:0%
+afternoon uh yeah first of all I'd like
+to thank you also Boston you know the
+
+ align:start position:0%
+to thank you also Boston you know the
+ 
+
+ align:start position:0%
+to thank you also Boston you know the
+poon gave me a gift you know yesterday
+
+ align:start position:0%
+poon gave me a gift you know yesterday
+ 
+
+ align:start position:0%
+poon gave me a gift you know yesterday
+it's called you know I just called the
+
+ align:start position:0%
+it's called you know I just called the
+ 
+
+ align:start position:0%
+it's called you know I just called the
+call so without call you know the my my
+
+ align:start position:0%
+call so without call you know the my my
+ 
+
+ align:start position:0%
+call so without call you know the my my
+actually my original voice is much worse
+
+ align:start position:0%
+actually my original voice is much worse
+ 
+
+ align:start position:0%
+actually my original voice is much worse
+than this you know thank thank you
+
+ align:start position:0%
+than this you know thank thank you
+ 
+
+ align:start position:0%
+than this you know thank thank you
+both uh my you know the talk topic is a
+
+ align:start position:0%
+both uh my you know the talk topic is a
+ 
+
+ align:start position:0%
+both uh my you know the talk topic is a
+little different you know from original
+
+ align:start position:0%
+little different you know from original
+ 
+
+ align:start position:0%
+little different you know from original
+RF id you know I'm more interested in
+
+ align:start position:0%
+RF id you know I'm more interested in
+ 
+
+ align:start position:0%
+RF id you know I'm more interested in
+you know the sensor Network and um so uh
+
+ align:start position:0%
+you know the sensor Network and um so uh
+ 
+
+ align:start position:0%
+you know the sensor Network and um so uh
+actually the ANS is the project you know
+
+ align:start position:0%
+actually the ANS is the project you know
+ 
+
+ align:start position:0%
+actually the ANS is the project you know
+I have carried out lot of for years and
+
+ align:start position:0%
+I have carried out lot of for years and
+ 
+
+ align:start position:0%
+I have carried out lot of for years and
+the ends aimed for you know some uh
+
+ align:start position:0%
+the ends aimed for you know some uh
+ 
+
+ align:start position:0%
+the ends aimed for you know some uh
+public sense Network you know we would
+
+ align:start position:0%
+public sense Network you know we would
+ 
+
+ align:start position:0%
+public sense Network you know we would
+like in Korea we would like to deploy
+
+ align:start position:0%
+like in Korea we would like to deploy
+ 
+
+ align:start position:0%
+like in Korea we would like to deploy
+sense Network in you know in the nation
+
+ align:start position:0%
+sense Network in you know in the nation
+ 
+
+ align:start position:0%
+sense Network in you know in the nation
+like uh internet internet is you know
+
+ align:start position:0%
+like uh internet internet is you know
+ 
+
+ align:start position:0%
+like uh internet internet is you know
+the now worldwide right so uh that's a
+
+ align:start position:0%
+the now worldwide right so uh that's a
+ 
+
+ align:start position:0%
+the now worldwide right so uh that's a
+public sense net without public sense
+
+ align:start position:0%
+public sense net without public sense
+ 
+
+ align:start position:0%
+public sense net without public sense
+Network you know we we we cannot the
+
+ align:start position:0%
+Network you know we we we cannot the
+ 
+
+ align:start position:0%
+Network you know we we we cannot the
+companies and government you know the uh
+
+ align:start position:0%
+companies and government you know the uh
+ 
+
+ align:start position:0%
+companies and government you know the uh
+organization cannot you know the share
+
+ align:start position:0%
+organization cannot you know the share
+ 
+
+ align:start position:0%
+organization cannot you know the share
+the you know the sense information so we
+
+ align:start position:0%
+the you know the sense information so we
+ 
+
+ align:start position:0%
+the you know the sense information so we
+need some you know standardization of a
+
+ align:start position:0%
+need some you know standardization of a
+ 
+
+ align:start position:0%
+need some you know standardization of a
+sense Network that's a public sense
+
+ align:start position:0%
+sense Network that's a public sense
+ 
+
+ align:start position:0%
+sense Network that's a public sense
+Network also uh there are another
+
+ align:start position:0%
+Network also uh there are another
+ 
+
+ align:start position:0%
+Network also uh there are another
+research topic you know that's EPC sense
+
+ align:start position:0%
+research topic you know that's EPC sense
+ 
+
+ align:start position:0%
+research topic you know that's EPC sense
+Network you know the uh actually you
+
+ align:start position:0%
+Network you know the uh actually you
+ 
+
+ align:start position:0%
+Network you know the uh actually you
+already know that you know the EPC you
+
+ align:start position:0%
+already know that you know the EPC you
+ 
+
+ align:start position:0%
+already know that you know the EPC you
+know Auto lefts already planned you know
+
+ align:start position:0%
+know Auto lefts already planned you know
+ 
+
+ align:start position:0%
+know Auto lefts already planned you know
+to develop EPC class two three four and
+
+ align:start position:0%
+to develop EPC class two three four and
+ 
+
+ align:start position:0%
+to develop EPC class two three four and
+five you know actually class four Tech
+
+ align:start position:0%
+five you know actually class four Tech
+ 
+
+ align:start position:0%
+five you know actually class four Tech
+is Ador active uh Tech that's very
+
+ align:start position:0%
+is Ador active uh Tech that's very
+ 
+
+ align:start position:0%
+is Ador active uh Tech that's very
+similar to the you know the sense
+
+ align:start position:0%
+similar to the you know the sense
+ 
+
+ align:start position:0%
+similar to the you know the sense
+Network so uh actually this is not a new
+
+ align:start position:0%
+Network so uh actually this is not a new
+ 
+
+ align:start position:0%
+Network so uh actually this is not a new
+topic so this is a Reserva topic so I'd
+
+ align:start position:0%
+topic so this is a Reserva topic so I'd
+ 
+
+ align:start position:0%
+topic so this is a Reserva topic so I'd
+like to propose you know to uh research
+
+ align:start position:0%
+like to propose you know to uh research
+ 
+
+ align:start position:0%
+like to propose you know to uh research
+more on EP sensor
+
+ align:start position:0%
+more on EP sensor
+ 
+
+ align:start position:0%
+more on EP sensor
+network uh this is the contents you know
+
+ align:start position:0%
+network uh this is the contents you know
+ 
+
+ align:start position:0%
+network uh this is the contents you know
+I'd like to talk today the first one is
+
+ align:start position:0%
+I'd like to talk today the first one is
+ 
+
+ align:start position:0%
+I'd like to talk today the first one is
+the ubiquitous sens Network you know the
+
+ align:start position:0%
+the ubiquitous sens Network you know the
+ 
+
+ align:start position:0%
+the ubiquitous sens Network you know the
+uh that's some uh new terminologies uh
+
+ align:start position:0%
+uh that's some uh new terminologies uh
+ 
+
+ align:start position:0%
+uh that's some uh new terminologies uh
+uh actually this was named by the
+
+ align:start position:0%
+uh actually this was named by the
+ 
+
+ align:start position:0%
+uh actually this was named by the
+minister Minister Ministry of
+
+ align:start position:0%
+minister Minister Ministry of
+ 
+
+ align:start position:0%
+minister Minister Ministry of
+information and communication in Korea
+
+ align:start position:0%
+information and communication in Korea
+ 
+
+ align:start position:0%
+information and communication in Korea
+he is Dr Zen he's a pharmacy of Samsung
+
+ align:start position:0%
+he is Dr Zen he's a pharmacy of Samsung
+ 
+
+ align:start position:0%
+he is Dr Zen he's a pharmacy of Samsung
+Electronics i' would like to you know
+
+ align:start position:0%
+Electronics i' would like to you know
+ 
+
+ align:start position:0%
+Electronics i' would like to you know
+the uh Define u sense first and then
+
+ align:start position:0%
+the uh Define u sense first and then
+ 
+
+ align:start position:0%
+the uh Define u sense first and then
+ends and also if is sense net will be
+
+ align:start position:0%
+ends and also if is sense net will be
+ 
+
+ align:start position:0%
+ends and also if is sense net will be
+described Uh u sense Network actually
+
+ align:start position:0%
+described Uh u sense Network actually
+ 
+
+ align:start position:0%
+described Uh u sense Network actually
+you know includes passive AR text and
+
+ align:start position:0%
+you know includes passive AR text and
+ 
+
+ align:start position:0%
+you know includes passive AR text and
+active text and also some sensor text
+
+ align:start position:0%
+active text and also some sensor text
+ 
+
+ align:start position:0%
+active text and also some sensor text
+and the sensor Network so uh actually at
+
+ align:start position:0%
+and the sensor Network so uh actually at
+ 
+
+ align:start position:0%
+and the sensor Network so uh actually at
+you know the we con four different types
+
+ align:start position:0%
+you know the we con four different types
+ 
+
+ align:start position:0%
+you know the we con four different types
+of text the first one is uh EPC you know
+
+ align:start position:0%
+of text the first one is uh EPC you know
+ 
+
+ align:start position:0%
+of text the first one is uh EPC you know
+the passive AR Network as you know text
+
+ align:start position:0%
+the passive AR Network as you know text
+ 
+
+ align:start position:0%
+the passive AR Network as you know text
+readers and all bunches of you know this
+
+ align:start position:0%
+readers and all bunches of you know this
+ 
+
+ align:start position:0%
+readers and all bunches of you know this
+U EP Network middle Wheels uh are for
+
+ align:start position:0%
+U EP Network middle Wheels uh are for
+ 
+
+ align:start position:0%
+U EP Network middle Wheels uh are for
+the EP R Network architect and the
+
+ align:start position:0%
+the EP R Network architect and the
+ 
+
+ align:start position:0%
+the EP R Network architect and the
+second one is active tax we use a
+
+ align:start position:0%
+second one is active tax we use a
+ 
+
+ align:start position:0%
+second one is active tax we use a
+battery to lengthen the radio ranges uh
+
+ align:start position:0%
+battery to lengthen the radio ranges uh
+ 
+
+ align:start position:0%
+battery to lengthen the radio ranges uh
+this is some examples from the company
+
+ align:start position:0%
+this is some examples from the company
+ 
+
+ align:start position:0%
+this is some examples from the company
+Sai you know the using uh app we can uh
+
+ align:start position:0%
+Sai you know the using uh app we can uh
+ 
+
+ align:start position:0%
+Sai you know the using uh app we can uh
+achieve you know the more than 100 m of
+
+ align:start position:0%
+achieve you know the more than 100 m of
+ 
+
+ align:start position:0%
+achieve you know the more than 100 m of
+radio range that's active tax and third
+
+ align:start position:0%
+radio range that's active tax and third
+ 
+
+ align:start position:0%
+radio range that's active tax and third
+one is smart active Rael or a sens tech
+
+ align:start position:0%
+one is smart active Rael or a sens tech
+ 
+
+ align:start position:0%
+one is smart active Rael or a sens tech
+here you know we put uh some batteries
+
+ align:start position:0%
+here you know we put uh some batteries
+ 
+
+ align:start position:0%
+here you know we put uh some batteries
+and also sensors in very you know se you
+
+ align:start position:0%
+and also sensors in very you know se you
+ 
+
+ align:start position:0%
+and also sensors in very you know se you
+know tag so that's a smart active labels
+
+ align:start position:0%
+know tag so that's a smart active labels
+ 
+
+ align:start position:0%
+know tag so that's a smart active labels
+you know there are also semi uh uh smart
+
+ align:start position:0%
+you know there are also semi uh uh smart
+ 
+
+ align:start position:0%
+you know there are also semi uh uh smart
+active labels and smart active ra labels
+
+ align:start position:0%
+active labels and smart active ra labels
+ 
+
+ align:start position:0%
+active labels and smart active ra labels
+in this type and the final one is you
+
+ align:start position:0%
+in this type and the final one is you
+ 
+
+ align:start position:0%
+in this type and the final one is you
+know the sensor uh Network you know the
+
+ align:start position:0%
+know the sensor uh Network you know the
+ 
+
+ align:start position:0%
+know the sensor uh Network you know the
+sensor network is what what network of
+
+ align:start position:0%
+sensor network is what what network of
+ 
+
+ align:start position:0%
+sensor network is what what network of
+sensor no and each sensor no has a
+
+ align:start position:0%
+sensor no and each sensor no has a
+ 
+
+ align:start position:0%
+sensor no and each sensor no has a
+microc contr so it has uh computation uh
+
+ align:start position:0%
+microc contr so it has uh computation uh
+ 
+
+ align:start position:0%
+microc contr so it has uh computation uh
+capabil capabilities and also active wi
+
+ align:start position:0%
+capabil capabilities and also active wi
+ 
+
+ align:start position:0%
+capabil capabilities and also active wi
+risk communication capability and lots
+
+ align:start position:0%
+risk communication capability and lots
+ 
+
+ align:start position:0%
+risk communication capability and lots
+of you know different types of sensors
+
+ align:start position:0%
+of you know different types of sensors
+ 
+
+ align:start position:0%
+of you know different types of sensors
+if they are deployed then they you know
+
+ align:start position:0%
+if they are deployed then they you know
+ 
+
+ align:start position:0%
+if they are deployed then they you know
+the self configure they form adoc
+
+ align:start position:0%
+the self configure they form adoc
+ 
+
+ align:start position:0%
+the self configure they form adoc
+Network right so we can cover some larg
+
+ align:start position:0%
+Network right so we can cover some larg
+ 
+
+ align:start position:0%
+Network right so we can cover some larg
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+
+ align:start position:0%
+area larg areas with the sensor
+ 
+
+ align:start position:0%
+area larg areas with the sensor
+Network so uh you know so so far you
+
+ align:start position:0%
+Network so uh you know so so far you
+ 
+
+ align:start position:0%
+Network so uh you know so so far you
+know the there were you know RFI
+
+ align:start position:0%
+know the there were you know RFI
+ 
+
+ align:start position:0%
+know the there were you know RFI
+research Community Development community
+
+ align:start position:0%
+research Community Development community
+ 
+
+ align:start position:0%
+research Community Development community
+and also there are many people are
+
+ align:start position:0%
+and also there are many people are
+ 
+
+ align:start position:0%
+and also there are many people are
+working in sensor Network areas very you
+
+ align:start position:0%
+working in sensor Network areas very you
+ 
+
+ align:start position:0%
+working in sensor Network areas very you
+know hard topics so I think wishing you
+
+ align:start position:0%
+know hard topics so I think wishing you
+ 
+
+ align:start position:0%
+know hard topics so I think wishing you
+know the arip people and sense netor
+
+ align:start position:0%
+know the arip people and sense netor
+ 
+
+ align:start position:0%
+know the arip people and sense netor
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+
+ align:start position:0%
+people should meet together and then
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+
+ align:start position:0%
+people should meet together and then
+find you know the more you know the
+
+ align:start position:0%
+find you know the more you know the
+ 
+
+ align:start position:0%
+find you know the more you know the
+different or Advanced you know types of
+
+ align:start position:0%
+different or Advanced you know types of
+ 
+
+ align:start position:0%
+different or Advanced you know types of
+business model so you we could just
+
+ align:start position:0%
+business model so you we could just
+ 
+
+ align:start position:0%
+business model so you we could just
+stand n we Define you know
+
+ align:start position:0%
+stand n we Define you know
+ 
+
+ align:start position:0%
+stand n we Define you know
+the uh actually you can see uh uh in the
+
+ align:start position:0%
+the uh actually you can see uh uh in the
+ 
+
+ align:start position:0%
+the uh actually you can see uh uh in the
+uh right hand side uh we call it uh bcn
+
+ align:start position:0%
+uh right hand side uh we call it uh bcn
+ 
+
+ align:start position:0%
+uh right hand side uh we call it uh bcn
+Broadband converence Network that's just
+
+ align:start position:0%
+Broadband converence Network that's just
+ 
+
+ align:start position:0%
+Broadband converence Network that's just
+some you know highspeed uh internet uh
+
+ align:start position:0%
+some you know highspeed uh internet uh
+ 
+
+ align:start position:0%
+some you know highspeed uh internet uh
+it also include some you know the
+
+ align:start position:0%
+it also include some you know the
+ 
+
+ align:start position:0%
+it also include some you know the
+cellone networks and dmbs network that's
+
+ align:start position:0%
+cellone networks and dmbs network that's
+ 
+
+ align:start position:0%
+cellone networks and dmbs network that's
+some kind of leg network uh we would
+
+ align:start position:0%
+some kind of leg network uh we would
+ 
+
+ align:start position:0%
+some kind of leg network uh we would
+like should you know the include u pive
+
+ align:start position:0%
+like should you know the include u pive
+ 
+
+ align:start position:0%
+like should you know the include u pive
+p active tax and all sensor tax and
+
+ align:start position:0%
+p active tax and all sensor tax and
+ 
+
+ align:start position:0%
+p active tax and all sensor tax and
+sensor Network and then you would like
+
+ align:start position:0%
+sensor Network and then you would like
+ 
+
+ align:start position:0%
+sensor Network and then you would like
+uh make it as some public infrastructure
+
+ align:start position:0%
+uh make it as some public infrastructure
+ 
+
+ align:start position:0%
+uh make it as some public infrastructure
+that's a ous uh
+
+ align:start position:0%
+that's a ous uh
+ 
+
+ align:start position:0%
+that's a ous uh
+netor so uh as s told yesterday you know
+
+ align:start position:0%
+netor so uh as s told yesterday you know
+ 
+
+ align:start position:0%
+netor so uh as s told yesterday you know
+the uh Korean government has some Vision
+
+ align:start position:0%
+the uh Korean government has some Vision
+ 
+
+ align:start position:0%
+the uh Korean government has some Vision
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+it8 39 actually you know the The
+
+ align:start position:0%
+it8 39 actually you know the The
+ 
+
+ align:start position:0%
+it8 39 actually you know the The
+Minister's Cate number is a390 you know
+
+ align:start position:0%
+Minister's Cate number is a390 you know
+ 
+
+ align:start position:0%
+Minister's Cate number is a390 you know
+okay and the vice Minister K is a391
+
+ align:start position:0%
+okay and the vice Minister K is a391
+ 
+
+ align:start position:0%
+okay and the vice Minister K is a391
+something like that you know so the
+
+ align:start position:0%
+something like that you know so the
+ 
+
+ align:start position:0%
+something like that you know so the
+government you know the emphasize you
+
+ align:start position:0%
+government you know the emphasize you
+ 
+
+ align:start position:0%
+government you know the emphasize you
+know the all you know this it39
+
+ align:start position:0%
+know the all you know this it39
+ 
+
+ align:start position:0%
+know the all you know this it39
+strategy and uh we said you know three
+
+ align:start position:0%
+strategy and uh we said you know three
+ 
+
+ align:start position:0%
+strategy and uh we said you know three
+public infrastructure that's a one is a
+
+ align:start position:0%
+public infrastructure that's a one is a
+ 
+
+ align:start position:0%
+public infrastructure that's a one is a
+a Broadband convergence Network and
+
+ align:start position:0%
+a Broadband convergence Network and
+ 
+
+ align:start position:0%
+a Broadband convergence Network and
+second one is this u sense Network
+
+ align:start position:0%
+second one is this u sense Network
+ 
+
+ align:start position:0%
+second one is this u sense Network
+including both passive RFI active Tech
+
+ align:start position:0%
+including both passive RFI active Tech
+ 
+
+ align:start position:0%
+including both passive RFI active Tech
+sense Tech and sense Network and then
+
+ align:start position:0%
+sense Tech and sense Network and then
+ 
+
+ align:start position:0%
+sense Tech and sense Network and then
+the last one is IP version six so that's
+
+ align:start position:0%
+the last one is IP version six so that's
+ 
+
+ align:start position:0%
+the last one is IP version six so that's
+you know the some public infrastructure
+
+ align:start position:0%
+you know the some public infrastructure
+ 
+
+ align:start position:0%
+you know the some public infrastructure
+we would like to build in
+
+ align:start position:0%
+we would like to build in
+ 
+
+ align:start position:0%
+we would like to build in
+career uh I'd like to you know the
+
+ align:start position:0%
+career uh I'd like to you know the
+ 
+
+ align:start position:0%
+career uh I'd like to you know the
+person introduce uh uh my uh current
+
+ align:start position:0%
+person introduce uh uh my uh current
+ 
+
+ align:start position:0%
+person introduce uh uh my uh current
+project that's a that's for public
+
+ align:start position:0%
+project that's a that's for public
+ 
+
+ align:start position:0%
+project that's a that's for public
+sensor networks you know uh sensor
+
+ align:start position:0%
+sensor networks you know uh sensor
+ 
+
+ align:start position:0%
+sensor networks you know uh sensor
+network is as I said very you know the
+
+ align:start position:0%
+network is as I said very you know the
+ 
+
+ align:start position:0%
+network is as I said very you know the
+popular you know the uh uh areas and
+
+ align:start position:0%
+popular you know the uh uh areas and
+ 
+
+ align:start position:0%
+popular you know the uh uh areas and
+there are many people are working on it
+
+ align:start position:0%
+there are many people are working on it
+ 
+
+ align:start position:0%
+there are many people are working on it
+uh when I started this project for years
+
+ align:start position:0%
+uh when I started this project for years
+ 
+
+ align:start position:0%
+uh when I started this project for years
+ago you know I set some uh theme you
+
+ align:start position:0%
+ago you know I set some uh theme you
+ 
+
+ align:start position:0%
+ago you know I set some uh theme you
+know that's a evolvability you know uh I
+
+ align:start position:0%
+know that's a evolvability you know uh I
+ 
+
+ align:start position:0%
+know that's a evolvability you know uh I
+IV Vision that you know the uh in the
+
+ align:start position:0%
+IV Vision that you know the uh in the
+ 
+
+ align:start position:0%
+IV Vision that you know the uh in the
+future sense network uh we also you know
+
+ align:start position:0%
+future sense network uh we also you know
+ 
+
+ align:start position:0%
+future sense network uh we also you know
+the populate the globe you know like uh
+
+ align:start position:0%
+the populate the globe you know like uh
+ 
+
+ align:start position:0%
+the populate the globe you know like uh
+currently internet does today so so the
+
+ align:start position:0%
+currently internet does today so so the
+ 
+
+ align:start position:0%
+currently internet does today so so the
+sense Network there there will be many
+
+ align:start position:0%
+sense Network there there will be many
+ 
+
+ align:start position:0%
+sense Network there there will be many
+you know the sense notes like there will
+
+ align:start position:0%
+you know the sense notes like there will
+ 
+
+ align:start position:0%
+you know the sense notes like there will
+be many ADI text in the world so uh the
+
+ align:start position:0%
+be many ADI text in the world so uh the
+ 
+
+ align:start position:0%
+be many ADI text in the world so uh the
+lifetime of a sense netor will be also
+
+ align:start position:0%
+lifetime of a sense netor will be also
+ 
+
+ align:start position:0%
+lifetime of a sense netor will be also
+very long 5 years 10 years 20 years who
+
+ align:start position:0%
+very long 5 years 10 years 20 years who
+ 
+
+ align:start position:0%
+very long 5 years 10 years 20 years who
+knows right so uh uh after they are
+
+ align:start position:0%
+knows right so uh uh after they are
+ 
+
+ align:start position:0%
+knows right so uh uh after they are
+deployed then uh they will evolve you
+
+ align:start position:0%
+deployed then uh they will evolve you
+ 
+
+ align:start position:0%
+deployed then uh they will evolve you
+know sometimes for example the mission
+
+ align:start position:0%
+know sometimes for example the mission
+ 
+
+ align:start position:0%
+know sometimes for example the mission
+is changed so we have to uh update the
+
+ align:start position:0%
+is changed so we have to uh update the
+ 
+
+ align:start position:0%
+is changed so we have to uh update the
+mission or some Network even you know
+
+ align:start position:0%
+mission or some Network even you know
+ 
+
+ align:start position:0%
+mission or some Network even you know
+the network protocols and some you know
+
+ align:start position:0%
+the network protocols and some you know
+ 
+
+ align:start position:0%
+the network protocols and some you know
+the key components also can be changed
+
+ align:start position:0%
+the key components also can be changed
+ 
+
+ align:start position:0%
+the key components also can be changed
+so so uh so all the components of sensor
+
+ align:start position:0%
+so so uh so all the components of sensor
+ 
+
+ align:start position:0%
+so so uh so all the components of sensor
+network from Hardware operating system
+
+ align:start position:0%
+network from Hardware operating system
+ 
+
+ align:start position:0%
+network from Hardware operating system
+and network protocols even you know the
+
+ align:start position:0%
+and network protocols even you know the
+ 
+
+ align:start position:0%
+and network protocols even you know the
+some location sensing protocol should
+
+ align:start position:0%
+some location sensing protocol should
+ 
+
+ align:start position:0%
+some location sensing protocol should
+have a capability of some Evol ability
+
+ align:start position:0%
+have a capability of some Evol ability
+ 
+
+ align:start position:0%
+have a capability of some Evol ability
+so to do that uh we have developed uh
+
+ align:start position:0%
+so to do that uh we have developed uh
+ 
+
+ align:start position:0%
+so to do that uh we have developed uh
+and you know the hardware and software
+
+ align:start position:0%
+and you know the hardware and software
+ 
+
+ align:start position:0%
+and you know the hardware and software
+platform you know those are Hardwares
+
+ align:start position:0%
+platform you know those are Hardwares
+ 
+
+ align:start position:0%
+platform you know those are Hardwares
+and softwares maybe you know the
+
+ align:start position:0%
+and softwares maybe you know the
+ 
+
+ align:start position:0%
+and softwares maybe you know the
+similarly EPC class 4 Tech may have you
+
+ align:start position:0%
+similarly EPC class 4 Tech may have you
+ 
+
+ align:start position:0%
+similarly EPC class 4 Tech may have you
+know this kind of a software inside from
+
+ align:start position:0%
+know this kind of a software inside from
+ 
+
+ align:start position:0%
+know this kind of a software inside from
+the bottom actually we have four types
+
+ align:start position:0%
+the bottom actually we have four types
+ 
+
+ align:start position:0%
+the bottom actually we have four types
+of Hardwares the H1 is a very small sens
+
+ align:start position:0%
+of Hardwares the H1 is a very small sens
+ 
+
+ align:start position:0%
+of Hardwares the H1 is a very small sens
+no it can be attached to the switches or
+
+ align:start position:0%
+no it can be attached to the switches or
+ 
+
+ align:start position:0%
+no it can be attached to the switches or
+some uh light you know and H2 is a more
+
+ align:start position:0%
+some uh light you know and H2 is a more
+ 
+
+ align:start position:0%
+some uh light you know and H2 is a more
+advanced you know the Sens no it's it's
+
+ align:start position:0%
+advanced you know the Sens no it's it's
+ 
+
+ align:start position:0%
+advanced you know the Sens no it's it's
+very similar to you know the bual is on
+
+ align:start position:0%
+very similar to you know the bual is on
+ 
+
+ align:start position:0%
+very similar to you know the bual is on
+mic 3 Moto 3 and H3 is a uh actually
+
+ align:start position:0%
+mic 3 Moto 3 and H3 is a uh actually
+ 
+
+ align:start position:0%
+mic 3 Moto 3 and H3 is a uh actually
+more advanced you know the sensor node
+
+ align:start position:0%
+more advanced you know the sensor node
+ 
+
+ align:start position:0%
+more advanced you know the sensor node
+it has sensors like CCD cameras and
+
+ align:start position:0%
+it has sensors like CCD cameras and
+ 
+
+ align:start position:0%
+it has sensors like CCD cameras and
+something like that and also it can have
+
+ align:start position:0%
+something like that and also it can have
+ 
+
+ align:start position:0%
+something like that and also it can have
+some image processing capability inside
+
+ align:start position:0%
+some image processing capability inside
+ 
+
+ align:start position:0%
+some image processing capability inside
+and H4 is a uh some Bas station and
+
+ align:start position:0%
+and H4 is a uh some Bas station and
+ 
+
+ align:start position:0%
+and H4 is a uh some Bas station and
+gateway to the Legacy Network it can be
+
+ align:start position:0%
+gateway to the Legacy Network it can be
+ 
+
+ align:start position:0%
+gateway to the Legacy Network it can be
+uh compared to the AR leader in our EPC
+
+ align:start position:0%
+uh compared to the AR leader in our EPC
+ 
+
+ align:start position:0%
+uh compared to the AR leader in our EPC
+Network above the hard layers so we have
+
+ align:start position:0%
+Network above the hard layers so we have
+ 
+
+ align:start position:0%
+Network above the hard layers so we have
+operating systems and uh several
+
+ align:start position:0%
+operating systems and uh several
+ 
+
+ align:start position:0%
+operating systems and uh several
+different types of you know nwork stack
+
+ align:start position:0%
+different types of you know nwork stack
+ 
+
+ align:start position:0%
+different types of you know nwork stack
+including Max and net Rayas and also
+
+ align:start position:0%
+including Max and net Rayas and also
+ 
+
+ align:start position:0%
+including Max and net Rayas and also
+Securities and the time synchronization
+
+ align:start position:0%
+Securities and the time synchronization
+ 
+
+ align:start position:0%
+Securities and the time synchronization
+protols and also location sensing
+
+ align:start position:0%
+protols and also location sensing
+ 
+
+ align:start position:0%
+protols and also location sensing
+algorithms and power management and also
+
+ align:start position:0%
+algorithms and power management and also
+ 
+
+ align:start position:0%
+algorithms and power management and also
+some uh middle Wheels that's the
+
+ align:start position:0%
+some uh middle Wheels that's the
+ 
+
+ align:start position:0%
+some uh middle Wheels that's the
+platform we have using uh this platform
+
+ align:start position:0%
+platform we have using uh this platform
+ 
+
+ align:start position:0%
+platform we have using uh this platform
+uh uh we have uh prototyped some systems
+
+ align:start position:0%
+uh uh we have uh prototyped some systems
+ 
+
+ align:start position:0%
+uh uh we have uh prototyped some systems
+like some military reconnaissance system
+
+ align:start position:0%
+like some military reconnaissance system
+ 
+
+ align:start position:0%
+like some military reconnaissance system
+using aanda helicopters and also you use
+
+ align:start position:0%
+using aanda helicopters and also you use
+ 
+
+ align:start position:0%
+using aanda helicopters and also you use
+you know sens n in the greenhouse
+
+ align:start position:0%
+you know sens n in the greenhouse
+ 
+
+ align:start position:0%
+you know sens n in the greenhouse
+something like that this is a the uh
+
+ align:start position:0%
+something like that this is a the uh
+ 
+
+ align:start position:0%
+something like that this is a the uh
+current you know project what I'm
+
+ align:start position:0%
+current you know project what I'm
+ 
+
+ align:start position:0%
+current you know project what I'm
+carrying out in
+
+ align:start position:0%
+carrying out in
+ 
+
+ align:start position:0%
+carrying out in
+Korea uh uh if you you know the P Korea
+
+ align:start position:0%
+Korea uh uh if you you know the P Korea
+ 
+
+ align:start position:0%
+Korea uh uh if you you know the P Korea
+uh actually this is the South Korea and
+
+ align:start position:0%
+uh actually this is the South Korea and
+ 
+
+ align:start position:0%
+uh actually this is the South Korea and
+then uh in southernmost area we have
+
+ align:start position:0%
+then uh in southernmost area we have
+ 
+
+ align:start position:0%
+then uh in southernmost area we have
+some big you know the Fantastic Island
+
+ align:start position:0%
+some big you know the Fantastic Island
+ 
+
+ align:start position:0%
+some big you know the Fantastic Island
+uh it is called jzu Island uh we have a
+
+ align:start position:0%
+uh it is called jzu Island uh we have a
+ 
+
+ align:start position:0%
+uh it is called jzu Island uh we have a
+you know the the highest mountain in JZ
+
+ align:start position:0%
+you know the the highest mountain in JZ
+ 
+
+ align:start position:0%
+you know the the highest mountain in JZ
+Island in Korea is almost 2 kilometers
+
+ align:start position:0%
+Island in Korea is almost 2 kilometers
+ 
+
+ align:start position:0%
+Island in Korea is almost 2 kilometers
+high now we are deploying you know
+
+ align:start position:0%
+high now we are deploying you know
+ 
+
+ align:start position:0%
+high now we are deploying you know
+sensor networks in the trail of you know
+
+ align:start position:0%
+sensor networks in the trail of you know
+ 
+
+ align:start position:0%
+sensor networks in the trail of you know
+this mountain Hala Mountain uh actually
+
+ align:start position:0%
+this mountain Hala Mountain uh actually
+ 
+
+ align:start position:0%
+this mountain Hala Mountain uh actually
+it has four trads among four we choose
+
+ align:start position:0%
+it has four trads among four we choose
+ 
+
+ align:start position:0%
+it has four trads among four we choose
+two one is 4.7 kilm long the other one
+
+ align:start position:0%
+two one is 4.7 kilm long the other one
+ 
+
+ align:start position:0%
+two one is 4.7 kilm long the other one
+is 3.1 kilm long so we deploy sensors
+
+ align:start position:0%
+is 3.1 kilm long so we deploy sensors
+ 
+
+ align:start position:0%
+is 3.1 kilm long so we deploy sensors
+every 100 m in some areas every 250 M
+
+ align:start position:0%
+every 100 m in some areas every 250 M
+ 
+
+ align:start position:0%
+every 100 m in some areas every 250 M
+and then we collected uh the you know
+
+ align:start position:0%
+and then we collected uh the you know
+ 
+
+ align:start position:0%
+and then we collected uh the you know
+the weather information in in real time
+
+ align:start position:0%
+the weather information in in real time
+ 
+
+ align:start position:0%
+the weather information in in real time
+and then we uh actually that collected
+
+ align:start position:0%
+and then we uh actually that collected
+ 
+
+ align:start position:0%
+and then we uh actually that collected
+information will be forwarded to the my
+
+ align:start position:0%
+information will be forwarded to the my
+ 
+
+ align:start position:0%
+information will be forwarded to the my
+University actually it's a 500
+
+ align:start position:0%
+University actually it's a 500
+ 
+
+ align:start position:0%
+University actually it's a 500
+kilometers away from you know the this
+
+ align:start position:0%
+kilometers away from you know the this
+ 
+
+ align:start position:0%
+kilometers away from you know the this
+mountain and then this collected
+
+ align:start position:0%
+mountain and then this collected
+ 
+
+ align:start position:0%
+mountain and then this collected
+information uh uh is going to be
+
+ align:start position:0%
+information uh uh is going to be
+ 
+
+ align:start position:0%
+information uh uh is going to be
+delivered to the uh some climbers you
+
+ align:start position:0%
+delivered to the uh some climbers you
+ 
+
+ align:start position:0%
+delivered to the uh some climbers you
+know climber who carries cellone okay so
+
+ align:start position:0%
+know climber who carries cellone okay so
+ 
+
+ align:start position:0%
+know climber who carries cellone okay so
+uh they can browse the weather
+
+ align:start position:0%
+uh they can browse the weather
+ 
+
+ align:start position:0%
+uh they can browse the weather
+information uh in the trail you know
+
+ align:start position:0%
+information uh in the trail you know
+ 
+
+ align:start position:0%
+information uh in the trail you know
+actually you know the because this is
+
+ align:start position:0%
+actually you know the because this is
+ 
+
+ align:start position:0%
+actually you know the because this is
+two Kil two k high mountain you know the
+
+ align:start position:0%
+two Kil two k high mountain you know the
+ 
+
+ align:start position:0%
+two Kil two k high mountain you know the
+weather varies a lot you know when we go
+
+ align:start position:0%
+weather varies a lot you know when we go
+ 
+
+ align:start position:0%
+weather varies a lot you know when we go
+to the mountain to test uh in the in the
+
+ align:start position:0%
+to the mountain to test uh in the in the
+ 
+
+ align:start position:0%
+to the mountain to test uh in the in the
+you know the circle uh we see the
+
+ align:start position:0%
+you know the circle uh we see the
+ 
+
+ align:start position:0%
+you know the circle uh we see the
+mountain then it looks like a Lany okay
+
+ align:start position:0%
+mountain then it looks like a Lany okay
+ 
+
+ align:start position:0%
+mountain then it looks like a Lany okay
+and then uh I ask a student to buy Lane
+
+ align:start position:0%
+and then uh I ask a student to buy Lane
+ 
+
+ align:start position:0%
+and then uh I ask a student to buy Lane
+cat and I climbed then you know at that
+
+ align:start position:0%
+cat and I climbed then you know at that
+ 
+
+ align:start position:0%
+cat and I climbed then you know at that
+time you know uh actually my pace and
+
+ align:start position:0%
+time you know uh actually my pace and
+ 
+
+ align:start position:0%
+time you know uh actually my pace and
+arm are all burned you know so you know
+
+ align:start position:0%
+arm are all burned you know so you know
+ 
+
+ align:start position:0%
+arm are all burned you know so you know
+the weather is you know
+
+ align:start position:0%
+the weather is you know
+ 
+
+ align:start position:0%
+the weather is you know
+verying and even you know I uh arrived
+
+ align:start position:0%
+verying and even you know I uh arrived
+ 
+
+ align:start position:0%
+verying and even you know I uh arrived
+at p and then I saw people wept you know
+
+ align:start position:0%
+at p and then I saw people wept you know
+ 
+
+ align:start position:0%
+at p and then I saw people wept you know
+they took another you know the trail so
+
+ align:start position:0%
+they took another you know the trail so
+ 
+
+ align:start position:0%
+they took another you know the trail so
+this is very important for the climat so
+
+ align:start position:0%
+this is very important for the climat so
+ 
+
+ align:start position:0%
+this is very important for the climat so
+this is a one of our you know sensor n
+
+ align:start position:0%
+this is a one of our you know sensor n
+ 
+
+ align:start position:0%
+this is a one of our you know sensor n
+products so uh this is some you know the
+
+ align:start position:0%
+products so uh this is some you know the
+ 
+
+ align:start position:0%
+products so uh this is some you know the
+pictures I have taken in the trial and
+
+ align:start position:0%
+pictures I have taken in the trial and
+ 
+
+ align:start position:0%
+pictures I have taken in the trial and
+uh this is currently installed in the uh
+
+ align:start position:0%
+uh this is currently installed in the uh
+ 
+
+ align:start position:0%
+uh this is currently installed in the uh
+Mountain actually still we are in the
+
+ align:start position:0%
+Mountain actually still we are in the
+ 
+
+ align:start position:0%
+Mountain actually still we are in the
+development and the
+
+ align:start position:0%
+development and the
+ 
+
+ align:start position:0%
+development and the
+test and uh so that's that's that's for
+
+ align:start position:0%
+test and uh so that's that's that's for
+ 
+
+ align:start position:0%
+test and uh so that's that's that's for
+the you know the public U sens Network
+
+ align:start position:0%
+the you know the public U sens Network
+ 
+
+ align:start position:0%
+the you know the public U sens Network
+actually uh I'm I'm the chair of uh
+
+ align:start position:0%
+actually uh I'm I'm the chair of uh
+ 
+
+ align:start position:0%
+actually uh I'm I'm the chair of uh
+Korean national standards committee for
+
+ align:start position:0%
+Korean national standards committee for
+ 
+
+ align:start position:0%
+Korean national standards committee for
+the public U sensor Network you know so
+
+ align:start position:0%
+the public U sensor Network you know so
+ 
+
+ align:start position:0%
+the public U sensor Network you know so
+we are trying to you know the
+
+ align:start position:0%
+we are trying to you know the
+ 
+
+ align:start position:0%
+we are trying to you know the
+standardize networ protocols uh and also
+
+ align:start position:0%
+standardize networ protocols uh and also
+ 
+
+ align:start position:0%
+standardize networ protocols uh and also
+Network management protocol and
+
+ align:start position:0%
+Network management protocol and
+ 
+
+ align:start position:0%
+Network management protocol and
+something like that and then uh actually
+
+ align:start position:0%
+something like that and then uh actually
+ 
+
+ align:start position:0%
+something like that and then uh actually
+uh we joined auts you know the last
+
+ align:start position:0%
+uh we joined auts you know the last
+ 
+
+ align:start position:0%
+uh we joined auts you know the last
+April and then we Lear you know the
+
+ align:start position:0%
+April and then we Lear you know the
+ 
+
+ align:start position:0%
+April and then we Lear you know the
+other part stops and then there are also
+
+ align:start position:0%
+other part stops and then there are also
+ 
+
+ align:start position:0%
+other part stops and then there are also
+very interesting topics here you know uh
+
+ align:start position:0%
+very interesting topics here you know uh
+ 
+
+ align:start position:0%
+very interesting topics here you know uh
+actually this is maybe drawn by Elga you
+
+ align:start position:0%
+actually this is maybe drawn by Elga you
+ 
+
+ align:start position:0%
+actually this is maybe drawn by Elga you
+know the uh so uh Auto IDs have you know
+
+ align:start position:0%
+know the uh so uh Auto IDs have you know
+ 
+
+ align:start position:0%
+know the uh so uh Auto IDs have you know
+the three different uh research you know
+
+ align:start position:0%
+the three different uh research you know
+ 
+
+ align:start position:0%
+the three different uh research you know
+the categories from bottom RF and Chip
+
+ align:start position:0%
+the categories from bottom RF and Chip
+ 
+
+ align:start position:0%
+the categories from bottom RF and Chip
+design including uh EP class 1 2 3 4 and
+
+ align:start position:0%
+design including uh EP class 1 2 3 4 and
+ 
+
+ align:start position:0%
+design including uh EP class 1 2 3 4 and
+five and networking and software and uh
+
+ align:start position:0%
+five and networking and software and uh
+ 
+
+ align:start position:0%
+five and networking and software and uh
+business and application also you know
+
+ align:start position:0%
+business and application also you know
+ 
+
+ align:start position:0%
+business and application also you know
+the privacy and security actually we
+
+ align:start position:0%
+the privacy and security actually we
+ 
+
+ align:start position:0%
+the privacy and security actually we
+have interested in
+
+ align:start position:0%
+have interested in
+ 
+
+ align:start position:0%
+have interested in
+uh EPC uh class four okay so maybe EPC
+
+ align:start position:0%
+uh EPC uh class four okay so maybe EPC
+ 
+
+ align:start position:0%
+uh EPC uh class four okay so maybe EPC
+class one in G to a interface three may
+
+ align:start position:0%
+class one in G to a interface three may
+ 
+
+ align:start position:0%
+class one in G to a interface three may
+use the you know the same interface
+
+ align:start position:0%
+use the you know the same interface
+ 
+
+ align:start position:0%
+use the you know the same interface
+interface three actually I don't know
+
+ align:start position:0%
+interface three actually I don't know
+ 
+
+ align:start position:0%
+interface three actually I don't know
+maybe four four the interace should be
+
+ align:start position:0%
+maybe four four the interace should be
+ 
+
+ align:start position:0%
+maybe four four the interace should be
+changed you know we need a Mac protocol
+
+ align:start position:0%
+changed you know we need a Mac protocol
+ 
+
+ align:start position:0%
+changed you know we need a Mac protocol
+and also we need you know addon net
+
+ align:start position:0%
+and also we need you know addon net
+ 
+
+ align:start position:0%
+and also we need you know addon net
+protocol so we have interested in and we
+
+ align:start position:0%
+protocol so we have interested in and we
+ 
+
+ align:start position:0%
+protocol so we have interested in and we
+also you know the analyzed the you know
+
+ align:start position:0%
+also you know the analyzed the you know
+ 
+
+ align:start position:0%
+also you know the analyzed the you know
+sens that EP netork middle you
+
+ align:start position:0%
+sens that EP netork middle you
+ 
+
+ align:start position:0%
+sens that EP netork middle you
+know uh to include okay sorry to include
+
+ align:start position:0%
+know uh to include okay sorry to include
+ 
+
+ align:start position:0%
+know uh to include okay sorry to include
+you know sensor text and the sensor
+
+ align:start position:0%
+you know sensor text and the sensor
+ 
+
+ align:start position:0%
+you know sensor text and the sensor
+Network you know the also the middleware
+
+ align:start position:0%
+Network you know the also the middleware
+ 
+
+ align:start position:0%
+Network you know the also the middleware
+maybe should be you know the change it
+
+ align:start position:0%
+maybe should be you know the change it
+ 
+
+ align:start position:0%
+maybe should be you know the change it
+mod modified and added and something
+
+ align:start position:0%
+mod modified and added and something
+ 
+
+ align:start position:0%
+mod modified and added and something
+like that for example uh uh a uh and the
+
+ align:start position:0%
+like that for example uh uh a uh and the
+ 
+
+ align:start position:0%
+like that for example uh uh a uh and the
+Le protocol it has some filtering
+
+ align:start position:0%
+Le protocol it has some filtering
+ 
+
+ align:start position:0%
+Le protocol it has some filtering
+capabilities right so it can filter out
+
+ align:start position:0%
+capabilities right so it can filter out
+ 
+
+ align:start position:0%
+capabilities right so it can filter out
+some specific uh EP
+
+ align:start position:0%
+some specific uh EP
+ 
+
+ align:start position:0%
+some specific uh EP
+uh same you know the for example if we
+
+ align:start position:0%
+uh same you know the for example if we
+ 
+
+ align:start position:0%
+uh same you know the for example if we
+include sensors then we can also
+
+ align:start position:0%
+include sensors then we can also
+ 
+
+ align:start position:0%
+include sensors then we can also
+filtering out some uh data which has you
+
+ align:start position:0%
+filtering out some uh data which has you
+ 
+
+ align:start position:0%
+filtering out some uh data which has you
+know sense value within some range
+
+ align:start position:0%
+know sense value within some range
+ 
+
+ align:start position:0%
+know sense value within some range
+something like that so filtering uh also
+
+ align:start position:0%
+something like that so filtering uh also
+ 
+
+ align:start position:0%
+something like that so filtering uh also
+epis repository to we have to
+
+ align:start position:0%
+epis repository to we have to
+ 
+
+ align:start position:0%
+epis repository to we have to
+accommodate you know sensor information
+
+ align:start position:0%
+accommodate you know sensor information
+ 
+
+ align:start position:0%
+accommodate you know sensor information
+and epis Discovery you also have to use
+
+ align:start position:0%
+and epis Discovery you also have to use
+ 
+
+ align:start position:0%
+and epis Discovery you also have to use
+you know the sensor value you know for
+
+ align:start position:0%
+you know the sensor value you know for
+ 
+
+ align:start position:0%
+you know the sensor value you know for
+the discovery something like that so uh
+
+ align:start position:0%
+the discovery something like that so uh
+ 
+
+ align:start position:0%
+the discovery something like that so uh
+I think this is also very uh great
+
+ align:start position:0%
+I think this is also very uh great
+ 
+
+ align:start position:0%
+I think this is also very uh great
+challenge you know so uh this is the
+
+ align:start position:0%
+challenge you know so uh this is the
+ 
+
+ align:start position:0%
+challenge you know so uh this is the
+proposal you know I'd like to propose in
+
+ align:start position:0%
+proposal you know I'd like to propose in
+ 
+
+ align:start position:0%
+proposal you know I'd like to propose in
+uh this iFish Global Community okay
+
+ align:start position:0%
+uh this iFish Global Community okay
+ 
+
+ align:start position:0%
+uh this iFish Global Community okay
+thank you very
+
+ align:start position:0%
+thank you very
+ 
+
+ align:start position:0%
+thank you very
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+much so so by the way the the the title
+
+ align:start position:0%
+much so so by the way the the the title
+ 
+
+ align:start position:0%
+much so so by the way the the the title
+of this session is is beyond the supply
+
+ align:start position:0%
+of this session is is beyond the supply
+ 
+
+ align:start position:0%
+of this session is is beyond the supply
+chain right so we talked about some of
+
+ align:start position:0%
+chain right so we talked about some of
+ 
+
+ align:start position:0%
+chain right so we talked about some of
+the range of applications down into the
+
+ align:start position:0%
+the range of applications down into the
+ 
+
+ align:start position:0%
+the range of applications down into the
+coal mines in China and then and then in
+
+ align:start position:0%
+coal mines in China and then and then in
+ 
+
+ align:start position:0%
+coal mines in China and then and then in
+Europe uh and uh up in the mountains of
+
+ align:start position:0%
+Europe uh and uh up in the mountains of
+ 
+
+ align:start position:0%
+Europe uh and uh up in the mountains of
+hanaro uh and and now we're privileged
+
+ align:start position:0%
+hanaro uh and and now we're privileged
+ 
+
+ align:start position:0%
+hanaro uh and and now we're privileged
+to have
+
+ align:start position:0%
+to have
+ 
+
+ align:start position:0%
+to have
+um J Yong who is the emerging business
+
+ align:start position:0%
+um J Yong who is the emerging business
+ 
+
+ align:start position:0%
+um J Yong who is the emerging business
+incubation manager of the technology
+
+ align:start position:0%
+incubation manager of the technology
+ 
+
+ align:start position:0%
+incubation manager of the technology
+strategy office of SK Telecom uh in in
+
+ align:start position:0%
+strategy office of SK Telecom uh in in
+ 
+
+ align:start position:0%
+strategy office of SK Telecom uh in in
+Korea uh who will share with us how how
+
+ align:start position:0%
+Korea uh who will share with us how how
+ 
+
+ align:start position:0%
+Korea uh who will share with us how how
+they're extending RFID into the network
+
+ align:start position:0%
+they're extending RFID into the network
+ 
+
+ align:start position:0%
+they're extending RFID into the network
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh good afternoon uh gentlemen uh I am
+
+ align:start position:0%
+uh good afternoon uh gentlemen uh I am
+ 
+
+ align:start position:0%
+uh good afternoon uh gentlemen uh I am
+Jun from SK Telecom which has about 18
+
+ align:start position:0%
+Jun from SK Telecom which has about 18
+ 
+
+ align:start position:0%
+Jun from SK Telecom which has about 18
+million mobile subscribers in Korea
+
+ align:start position:0%
+million mobile subscribers in Korea
+ 
+
+ align:start position:0%
+million mobile subscribers in Korea
+today I would like to introduced the
+
+ align:start position:0%
+today I would like to introduced the
+ 
+
+ align:start position:0%
+today I would like to introduced the
+mobile applications for RFID technology
+
+ align:start position:0%
+mobile applications for RFID technology
+ 
+
+ align:start position:0%
+mobile applications for RFID technology
+currently planned by SK
+
+ align:start position:0%
+currently planned by SK
+ 
+
+ align:start position:0%
+currently planned by SK
+Telecom first of all let me briefly
+
+ align:start position:0%
+Telecom first of all let me briefly
+ 
+
+ align:start position:0%
+Telecom first of all let me briefly
+introduce SK Telcom to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you es Telecom uh since its foundation
+
+ align:start position:0%
+you es Telecom uh since its foundation
+ 
+
+ align:start position:0%
+you es Telecom uh since its foundation
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1984 has been providing mobile
+
+ align:start position:0%
+1984 has been providing mobile
+ 
+
+ align:start position:0%
+1984 has been providing mobile
+Communication Service in Korea over 20
+
+ align:start position:0%
+Communication Service in Korea over 20
+ 
+
+ align:start position:0%
+Communication Service in Korea over 20
+years we commercialize the CDMA network
+
+ align:start position:0%
+years we commercialize the CDMA network
+ 
+
+ align:start position:0%
+years we commercialize the CDMA network
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1996 for the first time in the
+
+ align:start position:0%
+1996 for the first time in the
+ 
+
+ align:start position:0%
+1996 for the first time in the
+world uh skel wireless internet services
+
+ align:start position:0%
+world uh skel wireless internet services
+ 
+
+ align:start position:0%
+world uh skel wireless internet services
+are oped in two Brands Nate and
+
+ align:start position:0%
+are oped in two Brands Nate and
+ 
+
+ align:start position:0%
+are oped in two Brands Nate and
+June Nate is General wireless internet
+
+ align:start position:0%
+June Nate is General wireless internet
+ 
+
+ align:start position:0%
+June Nate is General wireless internet
+service whereas June is a multimedia
+
+ align:start position:0%
+service whereas June is a multimedia
+ 
+
+ align:start position:0%
+service whereas June is a multimedia
+service based on CDMA EV video Network
+
+ align:start position:0%
+service based on CDMA EV video Network
+ 
+
+ align:start position:0%
+service based on CDMA EV video Network
+Technology s telecom's wireless internet
+
+ align:start position:0%
+Technology s telecom's wireless internet
+ 
+
+ align:start position:0%
+Technology s telecom's wireless internet
+services loed on approximate
+
+ align:start position:0%
+services loed on approximate
+ 
+
+ align:start position:0%
+services loed on approximate
+record of 1.7 billion US
+
+ align:start position:0%
+record of 1.7 billion US
+ 
+
+ align:start position:0%
+record of 1.7 billion US
+dollar the wireless internet service
+
+ align:start position:0%
+dollar the wireless internet service
+ 
+
+ align:start position:0%
+dollar the wireless internet service
+took up
+
+ align:start position:0%
+took up
+ 
+
+ align:start position:0%
+took up
+20.6% of SK telecoms entire Revenue
+
+ align:start position:0%
+20.6% of SK telecoms entire Revenue
+ 
+
+ align:start position:0%
+20.6% of SK telecoms entire Revenue
+which increased by threefold in the last
+
+ align:start position:0%
+which increased by threefold in the last
+ 
+
+ align:start position:0%
+which increased by threefold in the last
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+years the current growth momentum is
+
+ align:start position:0%
+years the current growth momentum is
+ 
+
+ align:start position:0%
+years the current growth momentum is
+expected to continue but Korean mobile
+
+ align:start position:0%
+expected to continue but Korean mobile
+ 
+
+ align:start position:0%
+expected to continue but Korean mobile
+market is fast getting
+
+ align:start position:0%
+market is fast getting
+ 
+
+ align:start position:0%
+market is fast getting
+saturated we must develop new grow
+
+ align:start position:0%
+saturated we must develop new grow
+ 
+
+ align:start position:0%
+saturated we must develop new grow
+opportunity now and we think the mobile
+
+ align:start position:0%
+opportunity now and we think the mobile
+ 
+
+ align:start position:0%
+opportunity now and we think the mobile
+RFID application will be one of gross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+engine we think we have found one
+
+ align:start position:0%
+engine we think we have found one
+ 
+
+ align:start position:0%
+engine we think we have found one
+solution that is U quter service based
+
+ align:start position:0%
+solution that is U quter service based
+ 
+
+ align:start position:0%
+solution that is U quter service based
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+convergence our customers desire
+
+ align:start position:0%
+convergence our customers desire
+ 
+
+ align:start position:0%
+convergence our customers desire
+personalized customized services and
+
+ align:start position:0%
+personalized customized services and
+ 
+
+ align:start position:0%
+personalized customized services and
+more userfriendly devices
+
+ align:start position:0%
+more userfriendly devices
+ 
+
+ align:start position:0%
+more userfriendly devices
+such customer needs will spell an
+
+ align:start position:0%
+such customer needs will spell an
+ 
+
+ align:start position:0%
+such customer needs will spell an
+opportunity for operators to use as a
+
+ align:start position:0%
+opportunity for operators to use as a
+ 
+
+ align:start position:0%
+opportunity for operators to use as a
+new gross
+
+ align:start position:0%
+new gross
+ 
+
+ align:start position:0%
+new gross
+engine this trend will be further
+
+ align:start position:0%
+engine this trend will be further
+ 
+
+ align:start position:0%
+engine this trend will be further
+accelerated by the interactions between
+
+ align:start position:0%
+accelerated by the interactions between
+ 
+
+ align:start position:0%
+accelerated by the interactions between
+drivers of
+
+ align:start position:0%
+drivers of
+ 
+
+ align:start position:0%
+drivers of
+convergence while the convergence Trend
+
+ align:start position:0%
+convergence while the convergence Trend
+ 
+
+ align:start position:0%
+convergence while the convergence Trend
+will present both opportunities and
+
+ align:start position:0%
+will present both opportunities and
+ 
+
+ align:start position:0%
+will present both opportunities and
+treats to Telecom operators it will
+
+ align:start position:0%
+treats to Telecom operators it will
+ 
+
+ align:start position:0%
+treats to Telecom operators it will
+undoubtedly bring about much enhanced
+
+ align:start position:0%
+undoubtedly bring about much enhanced
+ 
+
+ align:start position:0%
+undoubtedly bring about much enhanced
+value values to our customer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will explain the bus strategy of es
+
+ align:start position:0%
+I will explain the bus strategy of es
+ 
+
+ align:start position:0%
+I will explain the bus strategy of es
+Telecom as you can see in the chart on
+
+ align:start position:0%
+Telecom as you can see in the chart on
+ 
+
+ align:start position:0%
+Telecom as you can see in the chart on
+the left es Telecom has recognized the
+
+ align:start position:0%
+the left es Telecom has recognized the
+ 
+
+ align:start position:0%
+the left es Telecom has recognized the
+convergence business as a new grow
+
+ align:start position:0%
+convergence business as a new grow
+ 
+
+ align:start position:0%
+convergence business as a new grow
+opportunity and is now stepping up its
+
+ align:start position:0%
+opportunity and is now stepping up its
+ 
+
+ align:start position:0%
+opportunity and is now stepping up its
+effort to find new business
+
+ align:start position:0%
+effort to find new business
+ 
+
+ align:start position:0%
+effort to find new business
+models so far we have presence in
+
+ align:start position:0%
+models so far we have presence in
+ 
+
+ align:start position:0%
+models so far we have presence in
+broadcasting Finance and commerce
+
+ align:start position:0%
+broadcasting Finance and commerce
+ 
+
+ align:start position:0%
+broadcasting Finance and commerce
+content distribution fixed line services
+
+ align:start position:0%
+content distribution fixed line services
+ 
+
+ align:start position:0%
+content distribution fixed line services
+and hands and Manufacturing
+
+ align:start position:0%
+and hands and Manufacturing
+ 
+
+ align:start position:0%
+and hands and Manufacturing
+businesses in the future we plan to
+
+ align:start position:0%
+businesses in the future we plan to
+ 
+
+ align:start position:0%
+businesses in the future we plan to
+expand our business into telematics and
+
+ align:start position:0%
+expand our business into telematics and
+ 
+
+ align:start position:0%
+expand our business into telematics and
+RFID terminals equipped with our DMB
+
+ align:start position:0%
+RFID terminals equipped with our DMB
+ 
+
+ align:start position:0%
+RFID terminals equipped with our DMB
+finance and buil-in cameras are sold on
+
+ align:start position:0%
+finance and buil-in cameras are sold on
+ 
+
+ align:start position:0%
+finance and buil-in cameras are sold on
+the market today and the terminal
+
+ align:start position:0%
+the market today and the terminal
+ 
+
+ align:start position:0%
+the market today and the terminal
+equiped RFI leer will be introduced by
+
+ align:start position:0%
+equiped RFI leer will be introduced by
+ 
+
+ align:start position:0%
+equiped RFI leer will be introduced by
+this year
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next I will explain the ucg scenario of
+
+ align:start position:0%
+next I will explain the ucg scenario of
+ 
+
+ align:start position:0%
+next I will explain the ucg scenario of
+physical mobile RI
+
+ align:start position:0%
+physical mobile RI
+ 
+
+ align:start position:0%
+physical mobile RI
+application first the user scans the ri
+
+ align:start position:0%
+application first the user scans the ri
+ 
+
+ align:start position:0%
+application first the user scans the ri
+tag with the mobile terminal this result
+
+ align:start position:0%
+tag with the mobile terminal this result
+ 
+
+ align:start position:0%
+tag with the mobile terminal this result
+in the RFI
+
+ align:start position:0%
+in the RFI
+ 
+
+ align:start position:0%
+in the RFI
+code being transform transferred from
+
+ align:start position:0%
+code being transform transferred from
+ 
+
+ align:start position:0%
+code being transform transferred from
+the tag to the mobile terminal the
+
+ align:start position:0%
+the tag to the mobile terminal the
+ 
+
+ align:start position:0%
+the tag to the mobile terminal the
+mobile terminal access the mobile
+
+ align:start position:0%
+mobile terminal access the mobile
+ 
+
+ align:start position:0%
+mobile terminal access the mobile
+network and ask the user to select the
+
+ align:start position:0%
+network and ask the user to select the
+ 
+
+ align:start position:0%
+network and ask the user to select the
+RFI service RFI service then directs
+
+ align:start position:0%
+RFI service RFI service then directs
+ 
+
+ align:start position:0%
+RFI service RFI service then directs
+request for information to the RFID
+
+ align:start position:0%
+request for information to the RFID
+ 
+
+ align:start position:0%
+request for information to the RFID
+service platform consisting of object
+
+ align:start position:0%
+service platform consisting of object
+ 
+
+ align:start position:0%
+service platform consisting of object
+directory server object tability server
+
+ align:start position:0%
+directory server object tability server
+ 
+
+ align:start position:0%
+directory server object tability server
+and object information
+
+ align:start position:0%
+and object information
+ 
+
+ align:start position:0%
+and object information
+server these servers contain the
+
+ align:start position:0%
+server these servers contain the
+ 
+
+ align:start position:0%
+server these servers contain the
+necessary information about tagged
+
+ align:start position:0%
+necessary information about tagged
+ 
+
+ align:start position:0%
+necessary information about tagged
+object from Simple Text information to
+
+ align:start position:0%
+object from Simple Text information to
+ 
+
+ align:start position:0%
+object from Simple Text information to
+audio video content
+
+ align:start position:0%
+audio video content
+ 
+
+ align:start position:0%
+audio video content
+this information is sent back to the
+
+ align:start position:0%
+this information is sent back to the
+ 
+
+ align:start position:0%
+this information is sent back to the
+mobile terminal the user consumes this
+
+ align:start position:0%
+mobile terminal the user consumes this
+ 
+
+ align:start position:0%
+mobile terminal the user consumes this
+information and then the mobile terminal
+
+ align:start position:0%
+information and then the mobile terminal
+ 
+
+ align:start position:0%
+information and then the mobile terminal
+will send building information to the
+
+ align:start position:0%
+will send building information to the
+ 
+
+ align:start position:0%
+will send building information to the
+mobile network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator future many kind senses will be
+
+ align:start position:0%
+operator future many kind senses will be
+ 
+
+ align:start position:0%
+operator future many kind senses will be
+applied to various plac to sensing the
+
+ align:start position:0%
+applied to various plac to sensing the
+ 
+
+ align:start position:0%
+applied to various plac to sensing the
+environment condition which information
+
+ align:start position:0%
+environment condition which information
+ 
+
+ align:start position:0%
+environment condition which information
+transmit and to data managing equipment
+
+ align:start position:0%
+transmit and to data managing equipment
+ 
+
+ align:start position:0%
+transmit and to data managing equipment
+through mobile l Network infra we call
+
+ align:start position:0%
+through mobile l Network infra we call
+ 
+
+ align:start position:0%
+through mobile l Network infra we call
+it us environment which has the
+
+ align:start position:0%
+it us environment which has the
+ 
+
+ align:start position:0%
+it us environment which has the
+tremendous mobile business chance now we
+
+ align:start position:0%
+tremendous mobile business chance now we
+ 
+
+ align:start position:0%
+tremendous mobile business chance now we
+are trying to make new kind service with
+
+ align:start position:0%
+are trying to make new kind service with
+ 
+
+ align:start position:0%
+are trying to make new kind service with
+a mobile phone with has RI leader chip
+
+ align:start position:0%
+a mobile phone with has RI leader chip
+ 
+
+ align:start position:0%
+a mobile phone with has RI leader chip
+inside this is the main concept of
+
+ align:start position:0%
+inside this is the main concept of
+ 
+
+ align:start position:0%
+inside this is the main concept of
+mobile I service or technology with
+
+ align:start position:0%
+mobile I service or technology with
+ 
+
+ align:start position:0%
+mobile I service or technology with
+convergence between mobile phone and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RFID mobile II technology is a wireless
+
+ align:start position:0%
+RFID mobile II technology is a wireless
+ 
+
+ align:start position:0%
+RFID mobile II technology is a wireless
+technology that provides new valuable
+
+ align:start position:0%
+technology that provides new valuable
+ 
+
+ align:start position:0%
+technology that provides new valuable
+service to customers by integrating RFID
+
+ align:start position:0%
+service to customers by integrating RFID
+ 
+
+ align:start position:0%
+service to customers by integrating RFID
+infrastructure with mobile communication
+
+ align:start position:0%
+infrastructure with mobile communication
+ 
+
+ align:start position:0%
+infrastructure with mobile communication
+and wireless internet we hope mobile
+
+ align:start position:0%
+and wireless internet we hope mobile
+ 
+
+ align:start position:0%
+and wireless internet we hope mobile
+RFID technology and the service would
+
+ align:start position:0%
+RFID technology and the service would
+ 
+
+ align:start position:0%
+RFID technology and the service would
+bring these four conditions first one is
+
+ align:start position:0%
+bring these four conditions first one is
+ 
+
+ align:start position:0%
+bring these four conditions first one is
+creating new value for mobile phone
+
+ align:start position:0%
+creating new value for mobile phone
+ 
+
+ align:start position:0%
+creating new value for mobile phone
+users second one is building new markets
+
+ align:start position:0%
+users second one is building new markets
+ 
+
+ align:start position:0%
+users second one is building new markets
+third one is improving quality of uus
+
+ align:start position:0%
+third one is improving quality of uus
+ 
+
+ align:start position:0%
+third one is improving quality of uus
+life and the last one is developing and
+
+ align:start position:0%
+life and the last one is developing and
+ 
+
+ align:start position:0%
+life and the last one is developing and
+leading technology and standards with
+
+ align:start position:0%
+leading technology and standards with
+ 
+
+ align:start position:0%
+leading technology and standards with
+mobile ad services using 900 MHz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RFID I would like to introduce some
+
+ align:start position:0%
+RFID I would like to introduce some
+ 
+
+ align:start position:0%
+RFID I would like to introduce some
+examples of mobile ad services in this
+
+ align:start position:0%
+examples of mobile ad services in this
+ 
+
+ align:start position:0%
+examples of mobile ad services in this
+slide you can see the information
+
+ align:start position:0%
+slide you can see the information
+ 
+
+ align:start position:0%
+slide you can see the information
+providing service IDI tag is attached on
+
+ align:start position:0%
+providing service IDI tag is attached on
+ 
+
+ align:start position:0%
+providing service IDI tag is attached on
+PS or cases of medicine cover page of
+
+ align:start position:0%
+PS or cases of medicine cover page of
+ 
+
+ align:start position:0%
+PS or cases of medicine cover page of
+books vide tapes Etc using mobile phone
+
+ align:start position:0%
+books vide tapes Etc using mobile phone
+ 
+
+ align:start position:0%
+books vide tapes Etc using mobile phone
+which has artifi leadership inside Le
+
+ align:start position:0%
+which has artifi leadership inside Le
+ 
+
+ align:start position:0%
+which has artifi leadership inside Le
+this ad teag in the network there is
+
+ align:start position:0%
+this ad teag in the network there is
+ 
+
+ align:start position:0%
+this ad teag in the network there is
+some kind of server which provide
+
+ align:start position:0%
+some kind of server which provide
+ 
+
+ align:start position:0%
+some kind of server which provide
+content address mobile phone sends IDE
+
+ align:start position:0%
+content address mobile phone sends IDE
+ 
+
+ align:start position:0%
+content address mobile phone sends IDE
+tag ID or users Tex user data to This
+
+ align:start position:0%
+tag ID or users Tex user data to This
+ 
+
+ align:start position:0%
+tag ID or users Tex user data to This
+Server then the server returns address
+
+ align:start position:0%
+Server then the server returns address
+ 
+
+ align:start position:0%
+Server then the server returns address
+of contents in response to RI teag ID to
+
+ align:start position:0%
+of contents in response to RI teag ID to
+ 
+
+ align:start position:0%
+of contents in response to RI teag ID to
+mobile phone with this address mobile
+
+ align:start position:0%
+mobile phone with this address mobile
+ 
+
+ align:start position:0%
+mobile phone with this address mobile
+phone can access contents server which
+
+ align:start position:0%
+phone can access contents server which
+ 
+
+ align:start position:0%
+phone can access contents server which
+has contents for medicine books Etc
+
+ align:start position:0%
+has contents for medicine books Etc
+ 
+
+ align:start position:0%
+has contents for medicine books Etc
+these contents could be just a simple W
+
+ align:start position:0%
+these contents could be just a simple W
+ 
+
+ align:start position:0%
+these contents could be just a simple W
+that is a wireless application protocol
+
+ align:start position:0%
+that is a wireless application protocol
+ 
+
+ align:start position:0%
+that is a wireless application protocol
+page or multimedia data such as the
+
+ align:start position:0%
+page or multimedia data such as the
+ 
+
+ align:start position:0%
+page or multimedia data such as the
+preview of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+movie a product authentication is very
+
+ align:start position:0%
+movie a product authentication is very
+ 
+
+ align:start position:0%
+movie a product authentication is very
+good example of RF application there is
+
+ align:start position:0%
+good example of RF application there is
+ 
+
+ align:start position:0%
+good example of RF application there is
+a strong demand for product
+
+ align:start position:0%
+a strong demand for product
+ 
+
+ align:start position:0%
+a strong demand for product
+authentication in used car market food
+
+ align:start position:0%
+authentication in used car market food
+ 
+
+ align:start position:0%
+authentication in used car market food
+at drug industry medical user such as
+
+ align:start position:0%
+at drug industry medical user such as
+ 
+
+ align:start position:0%
+at drug industry medical user such as
+tracking broad supplies and almost all
+
+ align:start position:0%
+tracking broad supplies and almost all
+ 
+
+ align:start position:0%
+tracking broad supplies and almost all
+secondhand product markets so at first
+
+ align:start position:0%
+secondhand product markets so at first
+ 
+
+ align:start position:0%
+secondhand product markets so at first
+we developed the jinen authentication
+
+ align:start position:0%
+we developed the jinen authentication
+ 
+
+ align:start position:0%
+we developed the jinen authentication
+Service to detect the counterfeit
+
+ align:start position:0%
+Service to detect the counterfeit
+ 
+
+ align:start position:0%
+Service to detect the counterfeit
+product in
+
+ align:start position:0%
+product in
+ 
+
+ align:start position:0%
+product in
+domestic excuse me and the international
+
+ align:start position:0%
+domestic excuse me and the international
+ 
+
+ align:start position:0%
+domestic excuse me and the international
+market usion s Global loing function now
+
+ align:start position:0%
+market usion s Global loing function now
+ 
+
+ align:start position:0%
+market usion s Global loing function now
+these Services started three shops and
+
+ align:start position:0%
+these Services started three shops and
+ 
+
+ align:start position:0%
+these Services started three shops and
+the one department store as a trial
+
+ align:start position:0%
+the one department store as a trial
+ 
+
+ align:start position:0%
+the one department store as a trial
+business we use the handheld terminal
+
+ align:start position:0%
+business we use the handheld terminal
+ 
+
+ align:start position:0%
+business we use the handheld terminal
+combining with the CDM module and other
+
+ align:start position:0%
+combining with the CDM module and other
+ 
+
+ align:start position:0%
+combining with the CDM module and other
+by leader these services will launch
+
+ align:start position:0%
+by leader these services will launch
+ 
+
+ align:start position:0%
+by leader these services will launch
+commercially after verifying the
+
+ align:start position:0%
+commercially after verifying the
+ 
+
+ align:start position:0%
+commercially after verifying the
+performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mobile Ari technology can be applied for
+
+ align:start position:0%
+mobile Ari technology can be applied for
+ 
+
+ align:start position:0%
+mobile Ari technology can be applied for
+route guidance such as public
+
+ align:start position:0%
+route guidance such as public
+ 
+
+ align:start position:0%
+route guidance such as public
+transportation route and Road guidance
+
+ align:start position:0%
+transportation route and Road guidance
+ 
+
+ align:start position:0%
+transportation route and Road guidance
+in Leisure and lifestyle area it can be
+
+ align:start position:0%
+in Leisure and lifestyle area it can be
+ 
+
+ align:start position:0%
+in Leisure and lifestyle area it can be
+used for root guidance natural
+
+ align:start position:0%
+used for root guidance natural
+ 
+
+ align:start position:0%
+used for root guidance natural
+experience promotional events and for
+
+ align:start position:0%
+experience promotional events and for
+ 
+
+ align:start position:0%
+experience promotional events and for
+shopping banking applications and so on
+
+ align:start position:0%
+shopping banking applications and so on
+ 
+
+ align:start position:0%
+shopping banking applications and so on
+as Tel will start trial experience for
+
+ align:start position:0%
+as Tel will start trial experience for
+ 
+
+ align:start position:0%
+as Tel will start trial experience for
+these businesses within this year and
+
+ align:start position:0%
+these businesses within this year and
+ 
+
+ align:start position:0%
+these businesses within this year and
+plan do more business case for
+
+ align:start position:0%
+plan do more business case for
+ 
+
+ align:start position:0%
+plan do more business case for
+commercial after
+
+ align:start position:0%
+commercial after
+ 
+
+ align:start position:0%
+commercial after
+trial actually we draw PR about 200
+
+ align:start position:0%
+trial actually we draw PR about 200
+ 
+
+ align:start position:0%
+trial actually we draw PR about 200
+different service models that will be
+
+ align:start position:0%
+different service models that will be
+ 
+
+ align:start position:0%
+different service models that will be
+Commercial Business targeting for our
+
+ align:start position:0%
+Commercial Business targeting for our
+ 
+
+ align:start position:0%
+Commercial Business targeting for our
+mobile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+customers after the major area of RFI
+
+ align:start position:0%
+customers after the major area of RFI
+ 
+
+ align:start position:0%
+customers after the major area of RFI
+technology is in information downloading
+
+ align:start position:0%
+technology is in information downloading
+ 
+
+ align:start position:0%
+technology is in information downloading
+applications the flower sales show is
+
+ align:start position:0%
+applications the flower sales show is
+ 
+
+ align:start position:0%
+applications the flower sales show is
+very good showcase for such a
+
+ align:start position:0%
+very good showcase for such a
+ 
+
+ align:start position:0%
+very good showcase for such a
+purpose uh scanning IDI text on prints
+
+ align:start position:0%
+purpose uh scanning IDI text on prints
+ 
+
+ align:start position:0%
+purpose uh scanning IDI text on prints
+and flowers we can get information of
+
+ align:start position:0%
+and flowers we can get information of
+ 
+
+ align:start position:0%
+and flowers we can get information of
+flowers like name place and the history
+
+ align:start position:0%
+flowers like name place and the history
+ 
+
+ align:start position:0%
+flowers like name place and the history
+of origin brooming time medical
+
+ align:start position:0%
+of origin brooming time medical
+ 
+
+ align:start position:0%
+of origin brooming time medical
+treatment as well as download of related
+
+ align:start position:0%
+treatment as well as download of related
+ 
+
+ align:start position:0%
+treatment as well as download of related
+pictures and the songs to mobile handset
+
+ align:start position:0%
+pictures and the songs to mobile handset
+ 
+
+ align:start position:0%
+pictures and the songs to mobile handset
+and combine with promotion events each
+
+ align:start position:0%
+and combine with promotion events each
+ 
+
+ align:start position:0%
+and combine with promotion events each
+customer request delivery of items for
+
+ align:start position:0%
+customer request delivery of items for
+ 
+
+ align:start position:0%
+customer request delivery of items for
+sale with mobile phone with a as a gift
+
+ align:start position:0%
+sale with mobile phone with a as a gift
+ 
+
+ align:start position:0%
+sale with mobile phone with a as a gift
+we can send the favorite song and the
+
+ align:start position:0%
+we can send the favorite song and the
+ 
+
+ align:start position:0%
+we can send the favorite song and the
+message with it by reading AR tag on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flowers shops and restaurants are also
+
+ align:start position:0%
+flowers shops and restaurants are also
+ 
+
+ align:start position:0%
+flowers shops and restaurants are also
+perfectly well suit suited for deploying
+
+ align:start position:0%
+perfectly well suit suited for deploying
+ 
+
+ align:start position:0%
+perfectly well suit suited for deploying
+adap technology to enhance value for
+
+ align:start position:0%
+adap technology to enhance value for
+ 
+
+ align:start position:0%
+adap technology to enhance value for
+customers tags attached to the entrance
+
+ align:start position:0%
+customers tags attached to the entrance
+ 
+
+ align:start position:0%
+customers tags attached to the entrance
+and or table scan ofi tag with a mobile
+
+ align:start position:0%
+and or table scan ofi tag with a mobile
+ 
+
+ align:start position:0%
+and or table scan ofi tag with a mobile
+phone and then mobile phone display the
+
+ align:start position:0%
+phone and then mobile phone display the
+ 
+
+ align:start position:0%
+phone and then mobile phone display the
+contents users can access the contents
+
+ align:start position:0%
+contents users can access the contents
+ 
+
+ align:start position:0%
+contents users can access the contents
+very easily then download information
+
+ align:start position:0%
+very easily then download information
+ 
+
+ align:start position:0%
+very easily then download information
+about restaurant record their
+
+ align:start position:0%
+about restaurant record their
+ 
+
+ align:start position:0%
+about restaurant record their
+favorite page at their own site a
+
+ align:start position:0%
+favorite page at their own site a
+ 
+
+ align:start position:0%
+favorite page at their own site a
+businessman of sh needs to promote their
+
+ align:start position:0%
+businessman of sh needs to promote their
+ 
+
+ align:start position:0%
+businessman of sh needs to promote their
+product and record their information on
+
+ align:start position:0%
+product and record their information on
+ 
+
+ align:start position:0%
+product and record their information on
+mobile upon also customer can needs to
+
+ align:start position:0%
+mobile upon also customer can needs to
+ 
+
+ align:start position:0%
+mobile upon also customer can needs to
+decide the menu for lunch or dinner for
+
+ align:start position:0%
+decide the menu for lunch or dinner for
+ 
+
+ align:start position:0%
+decide the menu for lunch or dinner for
+especially this service is good mobile
+
+ align:start position:0%
+especially this service is good mobile
+ 
+
+ align:start position:0%
+especially this service is good mobile
+business because our customer desire
+
+ align:start position:0%
+business because our customer desire
+ 
+
+ align:start position:0%
+business because our customer desire
+personalized and customized services and
+
+ align:start position:0%
+personalized and customized services and
+ 
+
+ align:start position:0%
+personalized and customized services and
+more userfriendly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+access II based Road information service
+
+ align:start position:0%
+access II based Road information service
+ 
+
+ align:start position:0%
+access II based Road information service
+can be made into whole platform for
+
+ align:start position:0%
+can be made into whole platform for
+ 
+
+ align:start position:0%
+can be made into whole platform for
+providing all types of root information
+
+ align:start position:0%
+providing all types of root information
+ 
+
+ align:start position:0%
+providing all types of root information
+service aied technology can use location
+
+ align:start position:0%
+service aied technology can use location
+ 
+
+ align:start position:0%
+service aied technology can use location
+determination where cannot fulfilled by
+
+ align:start position:0%
+determination where cannot fulfilled by
+ 
+
+ align:start position:0%
+determination where cannot fulfilled by
+GPS technology such as inside of
+
+ align:start position:0%
+GPS technology such as inside of
+ 
+
+ align:start position:0%
+GPS technology such as inside of
+buildings and could ultimately be
+
+ align:start position:0%
+buildings and could ultimately be
+ 
+
+ align:start position:0%
+buildings and could ultimately be
+cheaper once Tech prices
+
+ align:start position:0%
+cheaper once Tech prices
+ 
+
+ align:start position:0%
+cheaper once Tech prices
+decline customers can get the root
+
+ align:start position:0%
+decline customers can get the root
+ 
+
+ align:start position:0%
+decline customers can get the root
+Guidance the is a store location
+
+ align:start position:0%
+Guidance the is a store location
+ 
+
+ align:start position:0%
+Guidance the is a store location
+location maps and the building
+
+ align:start position:0%
+location maps and the building
+ 
+
+ align:start position:0%
+location maps and the building
+information very easily and simply we
+
+ align:start position:0%
+information very easily and simply we
+ 
+
+ align:start position:0%
+information very easily and simply we
+expect these Services can increase the
+
+ align:start position:0%
+expect these Services can increase the
+ 
+
+ align:start position:0%
+expect these Services can increase the
+mobile data access
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traffic PO is sometimes very Troublesome
+
+ align:start position:0%
+traffic PO is sometimes very Troublesome
+ 
+
+ align:start position:0%
+traffic PO is sometimes very Troublesome
+work if the poll company can send the
+
+ align:start position:0%
+work if the poll company can send the
+ 
+
+ align:start position:0%
+work if the poll company can send the
+reward like free mobile phone bell sound
+
+ align:start position:0%
+reward like free mobile phone bell sound
+ 
+
+ align:start position:0%
+reward like free mobile phone bell sound
+download purchasing coupons so then
+
+ align:start position:0%
+download purchasing coupons so then
+ 
+
+ align:start position:0%
+download purchasing coupons so then
+customers can do it willingly users
+
+ align:start position:0%
+customers can do it willingly users
+ 
+
+ align:start position:0%
+customers can do it willingly users
+touch the aride tag attached on the bus
+
+ align:start position:0%
+touch the aride tag attached on the bus
+ 
+
+ align:start position:0%
+touch the aride tag attached on the bus
+stops Subway advertisement board and the
+
+ align:start position:0%
+stops Subway advertisement board and the
+ 
+
+ align:start position:0%
+stops Subway advertisement board and the
+download poll information on their
+
+ align:start position:0%
+download poll information on their
+ 
+
+ align:start position:0%
+download poll information on their
+mobile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terminals our taxi is not always a safe
+
+ align:start position:0%
+terminals our taxi is not always a safe
+ 
+
+ align:start position:0%
+terminals our taxi is not always a safe
+place for woman and night saf Home
+
+ align:start position:0%
+place for woman and night saf Home
+ 
+
+ align:start position:0%
+place for woman and night saf Home
+Service uses adate technology to track
+
+ align:start position:0%
+Service uses adate technology to track
+ 
+
+ align:start position:0%
+Service uses adate technology to track
+taxes in case of theft and any other
+
+ align:start position:0%
+taxes in case of theft and any other
+ 
+
+ align:start position:0%
+taxes in case of theft and any other
+unpr experience a passenger may
+
+ align:start position:0%
+unpr experience a passenger may
+ 
+
+ align:start position:0%
+unpr experience a passenger may
+experience a passenger can lead the tag
+
+ align:start position:0%
+experience a passenger can lead the tag
+ 
+
+ align:start position:0%
+experience a passenger can lead the tag
+in installed in the taxi on the ceiling
+
+ align:start position:0%
+in installed in the taxi on the ceiling
+ 
+
+ align:start position:0%
+in installed in the taxi on the ceiling
+under the seat or under the driver
+
+ align:start position:0%
+under the seat or under the driver
+ 
+
+ align:start position:0%
+under the seat or under the driver
+registration card then taxi company send
+
+ align:start position:0%
+registration card then taxi company send
+ 
+
+ align:start position:0%
+registration card then taxi company send
+the information about the taxi to the
+
+ align:start position:0%
+the information about the taxi to the
+ 
+
+ align:start position:0%
+the information about the taxi to the
+passenger passenger can send those
+
+ align:start position:0%
+passenger passenger can send those
+ 
+
+ align:start position:0%
+passenger passenger can send those
+information to their parents or friends
+
+ align:start position:0%
+information to their parents or friends
+ 
+
+ align:start position:0%
+information to their parents or friends
+using the mobile sh message service
+
+ align:start position:0%
+using the mobile sh message service
+ 
+
+ align:start position:0%
+using the mobile sh message service
+pressing just the send button on mobile
+
+ align:start position:0%
+pressing just the send button on mobile
+ 
+
+ align:start position:0%
+pressing just the send button on mobile
+phone finally I think customers are
+
+ align:start position:0%
+phone finally I think customers are
+ 
+
+ align:start position:0%
+phone finally I think customers are
+always the most critical element in our
+
+ align:start position:0%
+always the most critical element in our
+ 
+
+ align:start position:0%
+always the most critical element in our
+business I believe that RFID can delive
+
+ align:start position:0%
+business I believe that RFID can delive
+ 
+
+ align:start position:0%
+business I believe that RFID can delive
+the success factors and get insight to
+
+ align:start position:0%
+the success factors and get insight to
+ 
+
+ align:start position:0%
+the success factors and get insight to
+the Future Direction operators must take
+
+ align:start position:0%
+the Future Direction operators must take
+ 
+
+ align:start position:0%
+the Future Direction operators must take
+if we study these issues from the
+
+ align:start position:0%
+if we study these issues from the
+ 
+
+ align:start position:0%
+if we study these issues from the
+customers perspective which enhance
+
+ align:start position:0%
+customers perspective which enhance
+ 
+
+ align:start position:0%
+customers perspective which enhance
+customer values and improve user
+
+ align:start position:0%
+customer values and improve user
+ 
+
+ align:start position:0%
+customer values and improve user
+friendliness we will SE continuous
+
+ align:start position:0%
+friendliness we will SE continuous
+ 
+
+ align:start position:0%
+friendliness we will SE continuous
+Technology Innovation to get the most
+
+ align:start position:0%
+Technology Innovation to get the most
+ 
+
+ align:start position:0%
+Technology Innovation to get the most
+optimal service
+
+ align:start position:0%
+optimal service
+ 
+
+ align:start position:0%
+optimal service
+environment thank you very much for your
+
+ align:start position:0%
+environment thank you very much for your
+ 
+
+ align:start position:0%
+environment thank you very much for your
+attention
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you very much are there any
+
+ align:start position:0%
+thank you very much are there any
+ 
+
+ align:start position:0%
+thank you very much are there any
+questions if there are if you could come
+
+ align:start position:0%
+questions if there are if you could come
+ 
+
+ align:start position:0%
+questions if there are if you could come
+down to the mic please and once again
+
+ align:start position:0%
+down to the mic please and once again
+ 
+
+ align:start position:0%
+down to the mic please and once again
+thanks very much to our our uh speakers
+
+ align:start position:0%
+thanks very much to our our uh speakers
+ 
+
+ align:start position:0%
+thanks very much to our our uh speakers
+who have come from halfway around the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world if there if there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh hi I'm Matthew dorin from MIT and I
+
+ align:start position:0%
+oh hi I'm Matthew dorin from MIT and I
+ 
+
+ align:start position:0%
+oh hi I'm Matthew dorin from MIT and I
+have two questions for Mr Yun
+
+ align:start position:0%
+have two questions for Mr Yun
+ 
+
+ align:start position:0%
+have two questions for Mr Yun
+um first there are several different
+
+ align:start position:0%
+um first there are several different
+ 
+
+ align:start position:0%
+um first there are several different
+protocols that have been discussed for
+
+ align:start position:0%
+protocols that have been discussed for
+ 
+
+ align:start position:0%
+protocols that have been discussed for
+mobile RFID applications NFC is probably
+
+ align:start position:0%
+mobile RFID applications NFC is probably
+ 
+
+ align:start position:0%
+mobile RFID applications NFC is probably
+the most wellknown but there's also
+
+ align:start position:0%
+the most wellknown but there's also
+ 
+
+ align:start position:0%
+the most wellknown but there's also
+something called rch R and I think there
+
+ align:start position:0%
+something called rch R and I think there
+ 
+
+ align:start position:0%
+something called rch R and I think there
+are a few others so my first question is
+
+ align:start position:0%
+are a few others so my first question is
+ 
+
+ align:start position:0%
+are a few others so my first question is
+which of those do you see being the
+
+ align:start position:0%
+which of those do you see being the
+ 
+
+ align:start position:0%
+which of those do you see being the
+choice of SK Telecom or is it too soon
+
+ align:start position:0%
+choice of SK Telecom or is it too soon
+ 
+
+ align:start position:0%
+choice of SK Telecom or is it too soon
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+tell uh yes as Telecom consider the
+
+ align:start position:0%
+tell uh yes as Telecom consider the
+ 
+
+ align:start position:0%
+tell uh yes as Telecom consider the
+several technology like NFC RFID or CHP
+
+ align:start position:0%
+several technology like NFC RFID or CHP
+ 
+
+ align:start position:0%
+several technology like NFC RFID or CHP
+and many things when we compare the NFC
+
+ align:start position:0%
+and many things when we compare the NFC
+ 
+
+ align:start position:0%
+and many things when we compare the NFC
+and RFID 9 900 MH
+
+ align:start position:0%
+and RFID 9 900 MH
+ 
+
+ align:start position:0%
+and RFID 9 900 MH
+jfid uh NFC has the many uh dedicated
+
+ align:start position:0%
+jfid uh NFC has the many uh dedicated
+ 
+
+ align:start position:0%
+jfid uh NFC has the many uh dedicated
+functions like the security and the or
+
+ align:start position:0%
+functions like the security and the or
+ 
+
+ align:start position:0%
+functions like the security and the or
+many uh safe safe functions so that uh
+
+ align:start position:0%
+many uh safe safe functions so that uh
+ 
+
+ align:start position:0%
+many uh safe safe functions so that uh
+CH that tag is the more expensive than
+
+ align:start position:0%
+CH that tag is the more expensive than
+ 
+
+ align:start position:0%
+CH that tag is the more expensive than
+the 900 MHz tag
+
+ align:start position:0%
+the 900 MHz tag
+ 
+
+ align:start position:0%
+the 900 MHz tag
+tags also NFC needs the very short
+
+ align:start position:0%
+tags also NFC needs the very short
+ 
+
+ align:start position:0%
+tags also NFC needs the very short
+distance leading distance but R the tag
+
+ align:start position:0%
+distance leading distance but R the tag
+ 
+
+ align:start position:0%
+distance leading distance but R the tag
+is the uh longer distance so we selected
+
+ align:start position:0%
+is the uh longer distance so we selected
+ 
+
+ align:start position:0%
+is the uh longer distance so we selected
+the 900
+
+ align:start position:0%
+the 900
+ 
+
+ align:start position:0%
+the 900
+MHz uh RFID for useful things and also
+
+ align:start position:0%
+MHz uh RFID for useful things and also
+ 
+
+ align:start position:0%
+MHz uh RFID for useful things and also
+we will study the NFC service as the pay
+
+ align:start position:0%
+we will study the NFC service as the pay
+ 
+
+ align:start position:0%
+we will study the NFC service as the pay
+or uh tickets okay so you would use the
+
+ align:start position:0%
+or uh tickets okay so you would use the
+ 
+
+ align:start position:0%
+or uh tickets okay so you would use the
+NFC service for payment for tickets we
+
+ align:start position:0%
+NFC service for payment for tickets we
+ 
+
+ align:start position:0%
+NFC service for payment for tickets we
+prepared now
+
+ align:start position:0%
+prepared now
+ 
+
+ align:start position:0%
+prepared now
+okay so this would sort of replace the
+
+ align:start position:0%
+okay so this would sort of replace the
+ 
+
+ align:start position:0%
+okay so this would sort of replace the
+Monita program that you have had or
+
+ align:start position:0%
+Monita program that you have had or
+ 
+
+ align:start position:0%
+Monita program that you have had or
+would it just be an extension of the
+
+ align:start position:0%
+would it just be an extension of the
+ 
+
+ align:start position:0%
+would it just be an extension of the
+Monita program yes okay okay thank
+
+ align:start position:0%
+Monita program yes okay okay thank
+ 
+
+ align:start position:0%
+Monita program yes okay okay thank
+you so thank you very much to the panel
+
+ align:start position:0%
+you so thank you very much to the panel
+ 
+
+ align:start position:0%
+you so thank you very much to the panel
+[Applause]
\ No newline at end of file
diff --git a/bFi8yxWZhR4.txt b/bFi8yxWZhR4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3ea2803e3818319f82f6a514360de3800e64a6f9
--- /dev/null
+++ b/bFi8yxWZhR4.txt
@@ -0,0 +1,363 @@
+align:start position:0%
+ 
+Team 15 is up Team 15 keeps going up and
+
+ align:start position:0%
+Team 15 is up Team 15 keeps going up and
+ 
+
+ align:start position:0%
+Team 15 is up Team 15 keeps going up and
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great effort by uh Team 15 with a
+
+ align:start position:0%
+great effort by uh Team 15 with a
+ 
+
+ align:start position:0%
+great effort by uh Team 15 with a
+beautiful
+
+ align:start position:0%
+beautiful
+ 
+
+ align:start position:0%
+beautiful
+Landing by English
+
+ align:start position:0%
+Landing by English
+ 
+
+ align:start position:0%
+Landing by English
+Bob
+
+ align:start position:0%
+Bob
+ 
+
+ align:start position:0%
+Bob
+beautiful I thought my life was
+
+ align:start position:0%
+beautiful I thought my life was
+ 
+
+ align:start position:0%
+beautiful I thought my life was
+uh was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we have uh te 15 um they seem
+
+ align:start position:0%
+all right we have uh te 15 um they seem
+ 
+
+ align:start position:0%
+all right we have uh te 15 um they seem
+to have
+
+ align:start position:0%
+to have
+ 
+
+ align:start position:0%
+to have
+a placing the eggs inverted on the belly
+
+ align:start position:0%
+a placing the eggs inverted on the belly
+ 
+
+ align:start position:0%
+a placing the eggs inverted on the belly
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+aircraft being very careful here
+
+ align:start position:0%
+aircraft being very careful here
+ 
+
+ align:start position:0%
+aircraft being very careful here
+we didn't see a whole lot of running on
+
+ align:start position:0%
+we didn't see a whole lot of running on
+ 
+
+ align:start position:0%
+we didn't see a whole lot of running on
+the charmac like we saw in
+
+ align:start position:0%
+the charmac like we saw in
+ 
+
+ align:start position:0%
+the charmac like we saw in
+um previous we have almost the whole
+
+ align:start position:0%
+um previous we have almost the whole
+ 
+
+ align:start position:0%
+um previous we have almost the whole
+crew working with the aircraft right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now detailed
+
+ align:start position:0%
+now detailed
+ 
+
+ align:start position:0%
+now detailed
+operation's being rather serious about
+
+ align:start position:0%
+operation's being rather serious about
+ 
+
+ align:start position:0%
+operation's being rather serious about
+uh their work
+
+ align:start position:0%
+uh their work
+ 
+
+ align:start position:0%
+uh their work
+here find the detailed
+
+ align:start position:0%
+here find the detailed
+ 
+
+ align:start position:0%
+here find the detailed
+work careful and meticulous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too they have two minutes without any
+
+ align:start position:0%
+too they have two minutes without any
+ 
+
+ align:start position:0%
+too they have two minutes without any
+sort of penalty
+
+ align:start position:0%
+sort of penalty
+ 
+
+ align:start position:0%
+sort of penalty
+which is an innovation that Colonel
+
+ align:start position:0%
+which is an innovation that Colonel
+ 
+
+ align:start position:0%
+which is an innovation that Colonel
+young brought to the competition sort of
+
+ align:start position:0%
+young brought to the competition sort of
+ 
+
+ align:start position:0%
+young brought to the competition sort of
+Ensure students didn't rush and um
+
+ align:start position:0%
+Ensure students didn't rush and um
+ 
+
+ align:start position:0%
+Ensure students didn't rush and um
+potentially damage their airplanes so
+
+ align:start position:0%
+potentially damage their airplanes so
+ 
+
+ align:start position:0%
+potentially damage their airplanes so
+going to give them 2 minutes no penalty
+
+ align:start position:0%
+going to give them 2 minutes no penalty
+ 
+
+ align:start position:0%
+going to give them 2 minutes no penalty
+to get it all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that first place
+
+ align:start position:0%
+and that first place
+ 
+
+ align:start position:0%
+and that first place
+team
+
+ align:start position:0%
+team
+ 
+
+ align:start position:0%
+team
+good all right we have the resident
+
+ align:start position:0%
+good all right we have the resident
+ 
+
+ align:start position:0%
+good all right we have the resident
+Argentinian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now English
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bob but I think everybody else is just
+
+ align:start position:0%
+Bob but I think everybody else is just
+ 
+
+ align:start position:0%
+Bob but I think everybody else is just
+boring playing All
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+American flying a little
+
+ align:start position:0%
+American flying a little
+ 
+
+ align:start position:0%
+American flying a little
+high this team has a teail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configuration and uh
+
+ align:start position:0%
+configuration and uh
+ 
+
+ align:start position:0%
+configuration and uh
+English Bob is doing
+
+ align:start position:0%
+English Bob is doing
+ 
+
+ align:start position:0%
+English Bob is doing
+his best 35 seconds all right 35 seconds
+
+ align:start position:0%
+his best 35 seconds all right 35 seconds
+ 
+
+ align:start position:0%
+his best 35 seconds all right 35 seconds
+[Applause]
\ No newline at end of file
diff --git a/bHdzkFrgRcA.txt b/bHdzkFrgRcA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07a609f7e805790d53d75c9e671690fe29b8e723
--- /dev/null
+++ b/bHdzkFrgRcA.txt
@@ -0,0 +1,7736 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so okay so remember last
+
+ align:start position:0%
+ocw.mit.edu so okay so remember last
+ 
+
+ align:start position:0%
+ocw.mit.edu so okay so remember last
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we learned about the cross product of
+
+ align:start position:0%
+we learned about the cross product of
+ 
+
+ align:start position:0%
+we learned about the cross product of
+vectors in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+so remember the definition of cross
+
+ align:start position:0%
+so remember the definition of cross
+ 
+
+ align:start position:0%
+so remember the definition of cross
+product is in terms of this
+
+ align:start position:0%
+product is in terms of this
+ 
+
+ align:start position:0%
+product is in terms of this
+determinant I hat J hat K hat and then
+
+ align:start position:0%
+determinant I hat J hat K hat and then
+ 
+
+ align:start position:0%
+determinant I hat J hat K hat and then
+the components of a A1 A2 A3 and then
+
+ align:start position:0%
+the components of a A1 A2 A3 and then
+ 
+
+ align:start position:0%
+the components of a A1 A2 A3 and then
+the components of
+
+ align:start position:0%
+the components of
+ 
+
+ align:start position:0%
+the components of
+B and
+
+ align:start position:0%
+B and
+ 
+
+ align:start position:0%
+B and
+this is not an actual determinant
+
+ align:start position:0%
+this is not an actual determinant
+ 
+
+ align:start position:0%
+this is not an actual determinant
+because these are not numbers but it's a
+
+ align:start position:0%
+because these are not numbers but it's a
+ 
+
+ align:start position:0%
+because these are not numbers but it's a
+symbolic notation to remember what the
+
+ align:start position:0%
+symbolic notation to remember what the
+ 
+
+ align:start position:0%
+symbolic notation to remember what the
+actual formula is and the actual formula
+
+ align:start position:0%
+actual formula is and the actual formula
+ 
+
+ align:start position:0%
+actual formula is and the actual formula
+is obtained by
+
+ align:start position:0%
+is obtained by
+ 
+
+ align:start position:0%
+is obtained by
+expanding the determinant so we have
+
+ align:start position:0%
+expanding the determinant so we have
+ 
+
+ align:start position:0%
+expanding the determinant so we have
+actually this smaller determinant A2 A3
+
+ align:start position:0%
+actually this smaller determinant A2 A3
+ 
+
+ align:start position:0%
+actually this smaller determinant A2 A3
+B2 B3 * I
+
+ align:start position:0%
+B2 B3 * I
+ 
+
+ align:start position:0%
+B2 B3 * I
+hat minus determinant of A1 A3 B1 B3 * J
+
+ align:start position:0%
+hat minus determinant of A1 A3 B1 B3 * J
+ 
+
+ align:start position:0%
+hat minus determinant of A1 A3 B1 B3 * J
+hat
+
+ align:start position:0%
+hat
+ 
+
+ align:start position:0%
+hat
+plus determinant of A1 A2 B1 B2 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K and we also saw a more geometric
+
+ align:start position:0%
+K and we also saw a more geometric
+ 
+
+ align:start position:0%
+K and we also saw a more geometric
+definition of a cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+product so we've learned
+
+ align:start position:0%
+product so we've learned
+ 
+
+ align:start position:0%
+product so we've learned
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the length of the cross product is equal
+
+ align:start position:0%
+the length of the cross product is equal
+ 
+
+ align:start position:0%
+the length of the cross product is equal
+to the area of the parallelogram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with sides A and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B we've also learned that the
+
+ align:start position:0%
+B we've also learned that the
+ 
+
+ align:start position:0%
+B we've also learned that the
+direction of the cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+product is given by taking the direction
+
+ align:start position:0%
+product is given by taking the direction
+ 
+
+ align:start position:0%
+product is given by taking the direction
+that's perpendicular
+
+ align:start position:0%
+that's perpendicular
+ 
+
+ align:start position:0%
+that's perpendicular
+to A and
+
+ align:start position:0%
+to A and
+ 
+
+ align:start position:0%
+to A and
+B so in
+
+ align:start position:0%
+B so in
+ 
+
+ align:start position:0%
+B so in
+fact if I draw a and b in a
+
+ align:start position:0%
+fact if I draw a and b in a
+ 
+
+ align:start position:0%
+fact if I draw a and b in a
+plane they determine a plane together
+
+ align:start position:0%
+plane they determine a plane together
+ 
+
+ align:start position:0%
+plane they determine a plane together
+then the cross product should go in a
+
+ align:start position:0%
+then the cross product should go in a
+ 
+
+ align:start position:0%
+then the cross product should go in a
+Direction that's perpendicular to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane now there's two different possible
+
+ align:start position:0%
+plane now there's two different possible
+ 
+
+ align:start position:0%
+plane now there's two different possible
+directions that are perpendicular to a
+
+ align:start position:0%
+directions that are perpendicular to a
+ 
+
+ align:start position:0%
+directions that are perpendicular to a
+plane and to decide which one it is we
+
+ align:start position:0%
+plane and to decide which one it is we
+ 
+
+ align:start position:0%
+plane and to decide which one it is we
+use the right hand rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which says if you extend your right hand
+
+ align:start position:0%
+which says if you extend your right hand
+ 
+
+ align:start position:0%
+which says if you extend your right hand
+in the direction of vector a then curve
+
+ align:start position:0%
+in the direction of vector a then curve
+ 
+
+ align:start position:0%
+in the direction of vector a then curve
+your fingers in the direction of B then
+
+ align:start position:0%
+your fingers in the direction of B then
+ 
+
+ align:start position:0%
+your fingers in the direction of B then
+your thumb will go in the direction of
+
+ align:start position:0%
+your thumb will go in the direction of
+ 
+
+ align:start position:0%
+your thumb will go in the direction of
+the cross
+
+ align:start position:0%
+the cross
+ 
+
+ align:start position:0%
+the cross
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so one thing I didn't quite get to say
+
+ align:start position:0%
+so one thing I didn't quite get to say
+ 
+
+ align:start position:0%
+so one thing I didn't quite get to say
+last time is that there are some funny
+
+ align:start position:0%
+last time is that there are some funny
+ 
+
+ align:start position:0%
+last time is that there are some funny
+manipulation rules um what are we
+
+ align:start position:0%
+manipulation rules um what are we
+ 
+
+ align:start position:0%
+manipulation rules um what are we
+allowed to do or not do with cross
+
+ align:start position:0%
+allowed to do or not do with cross
+ 
+
+ align:start position:0%
+allowed to do or not do with cross
+products so let me tell you right away
+
+ align:start position:0%
+products so let me tell you right away
+ 
+
+ align:start position:0%
+products so let me tell you right away
+the most surprising one maybe if you've
+
+ align:start position:0%
+the most surprising one maybe if you've
+ 
+
+ align:start position:0%
+the most surprising one maybe if you've
+never seen it before it's that A cross B
+
+ align:start position:0%
+never seen it before it's that A cross B
+ 
+
+ align:start position:0%
+never seen it before it's that A cross B
+and B cross a are not the same
+
+ align:start position:0%
+and B cross a are not the same
+ 
+
+ align:start position:0%
+and B cross a are not the same
+thing okay why are they not the same
+
+ align:start position:0%
+thing okay why are they not the same
+ 
+
+ align:start position:0%
+thing okay why are they not the same
+thing well when way to see it is to
+
+ align:start position:0%
+thing well when way to see it is to
+ 
+
+ align:start position:0%
+thing well when way to see it is to
+think geometrically sure the
+
+ align:start position:0%
+think geometrically sure the
+ 
+
+ align:start position:0%
+think geometrically sure the
+parallelogram still has the same area
+
+ align:start position:0%
+parallelogram still has the same area
+ 
+
+ align:start position:0%
+parallelogram still has the same area
+and it's still in the same plane so
+
+ align:start position:0%
+and it's still in the same plane so
+ 
+
+ align:start position:0%
+and it's still in the same plane so
+still perpendicular to the same plane
+
+ align:start position:0%
+still perpendicular to the same plane
+ 
+
+ align:start position:0%
+still perpendicular to the same plane
+but what happens is if you try to apply
+
+ align:start position:0%
+but what happens is if you try to apply
+ 
+
+ align:start position:0%
+but what happens is if you try to apply
+the right hand rle but exchanging the
+
+ align:start position:0%
+the right hand rle but exchanging the
+ 
+
+ align:start position:0%
+the right hand rle but exchanging the
+roles of A and B then you will either
+
+ align:start position:0%
+roles of A and B then you will either
+ 
+
+ align:start position:0%
+roles of A and B then you will either
+injure yourself or you will end up
+
+ align:start position:0%
+injure yourself or you will end up
+ 
+
+ align:start position:0%
+injure yourself or you will end up
+pointing in the opposite direction okay
+
+ align:start position:0%
+pointing in the opposite direction okay
+ 
+
+ align:start position:0%
+pointing in the opposite direction okay
+so in
+
+ align:start position:0%
+so in
+ 
+
+ align:start position:0%
+so in
+fact B cross A and A cross B are
+
+ align:start position:0%
+fact B cross A and A cross B are
+ 
+
+ align:start position:0%
+fact B cross A and A cross B are
+opposite of each other and you can check
+
+ align:start position:0%
+opposite of each other and you can check
+ 
+
+ align:start position:0%
+opposite of each other and you can check
+that in the formula because see for
+
+ align:start position:0%
+that in the formula because see for
+ 
+
+ align:start position:0%
+that in the formula because see for
+example the I component is A2 B3 minus
+
+ align:start position:0%
+example the I component is A2 B3 minus
+ 
+
+ align:start position:0%
+example the I component is A2 B3 minus
+A3 B2 if you swap the roles of A and B
+
+ align:start position:0%
+A3 B2 if you swap the roles of A and B
+ 
+
+ align:start position:0%
+A3 B2 if you swap the roles of A and B
+you will also have to change the
+
+ align:start position:0%
+you will also have to change the
+ 
+
+ align:start position:0%
+you will also have to change the
+signs okay so that's a slightly
+
+ align:start position:0%
+signs okay so that's a slightly
+ 
+
+ align:start position:0%
+signs okay so that's a slightly
+surprising think but you'll see one
+
+ align:start position:0%
+surprising think but you'll see one
+ 
+
+ align:start position:0%
+surprising think but you'll see one
+easily adjust to it it just means resist
+
+ align:start position:0%
+easily adjust to it it just means resist
+ 
+
+ align:start position:0%
+easily adjust to it it just means resist
+the temptation to write you know a
+
+ align:start position:0%
+the temptation to write you know a
+ 
+
+ align:start position:0%
+the temptation to write you know a
+equals ba whenever you do that put a
+
+ align:start position:0%
+equals ba whenever you do that put a
+ 
+
+ align:start position:0%
+equals ba whenever you do that put a
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign now in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular well what happens if I do a
+
+ align:start position:0%
+particular well what happens if I do a
+ 
+
+ align:start position:0%
+particular well what happens if I do a
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+a well I will get zero and you know
+
+ align:start position:0%
+a well I will get zero and you know
+ 
+
+ align:start position:0%
+a well I will get zero and you know
+there's many ways to see that when is to
+
+ align:start position:0%
+there's many ways to see that when is to
+ 
+
+ align:start position:0%
+there's many ways to see that when is to
+use the formula uh also you can say just
+
+ align:start position:0%
+use the formula uh also you can say just
+ 
+
+ align:start position:0%
+use the formula uh also you can say just
+that you know the parallelogram formed
+
+ align:start position:0%
+that you know the parallelogram formed
+ 
+
+ align:start position:0%
+that you know the parallelogram formed
+by a and a is completely flat and it has
+
+ align:start position:0%
+by a and a is completely flat and it has
+ 
+
+ align:start position:0%
+by a and a is completely flat and it has
+area zero so that's the zero
+
+ align:start position:0%
+area zero so that's the zero
+ 
+
+ align:start position:0%
+area zero so that's the zero
+Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so hopefully you got practice with
+
+ align:start position:0%
+okay so hopefully you got practice with
+ 
+
+ align:start position:0%
+okay so hopefully you got practice with
+cross products and Computing them in
+
+ align:start position:0%
+cross products and Computing them in
+ 
+
+ align:start position:0%
+cross products and Computing them in
+recitation
+
+ align:start position:0%
+recitation
+ 
+
+ align:start position:0%
+recitation
+yesterday uh let me just point out one
+
+ align:start position:0%
+yesterday uh let me just point out one
+ 
+
+ align:start position:0%
+yesterday uh let me just point out one
+important application of cross product
+
+ align:start position:0%
+important application of cross product
+ 
+
+ align:start position:0%
+important application of cross product
+that maybe you haven't seen yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say that I'm given three points
+
+ align:start position:0%
+so let's say that I'm given three points
+ 
+
+ align:start position:0%
+so let's say that I'm given three points
+in space and I want to find the equation
+
+ align:start position:0%
+in space and I want to find the equation
+ 
+
+ align:start position:0%
+in space and I want to find the equation
+of a plane that contains them so say I
+
+ align:start position:0%
+of a plane that contains them so say I
+ 
+
+ align:start position:0%
+of a plane that contains them so say I
+have P1 P2 P3 three points in
+
+ align:start position:0%
+have P1 P2 P3 three points in
+ 
+
+ align:start position:0%
+have P1 P2 P3 three points in
+space well they determine a plane I mean
+
+ align:start position:0%
+space well they determine a plane I mean
+ 
+
+ align:start position:0%
+space well they determine a plane I mean
+at least if they not aligned and we
+
+ align:start position:0%
+at least if they not aligned and we
+ 
+
+ align:start position:0%
+at least if they not aligned and we
+would like to find the equation of the
+
+ align:start position:0%
+would like to find the equation of the
+ 
+
+ align:start position:0%
+would like to find the equation of the
+plane that we determine so that means
+
+ align:start position:0%
+plane that we determine so that means
+ 
+
+ align:start position:0%
+plane that we determine so that means
+let's say that we have a point p in
+
+ align:start position:0%
+let's say that we have a point p in
+ 
+
+ align:start position:0%
+let's say that we have a point p in
+space with coordinates x y z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the equation of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane let's say the plane containing P1
+
+ align:start position:0%
+plane let's say the plane containing P1
+ 
+
+ align:start position:0%
+plane let's say the plane containing P1
+P2 and
+
+ align:start position:0%
+P2 and
+ 
+
+ align:start position:0%
+P2 and
+P3 that so that means find a
+
+ align:start position:0%
+P3 that so that means find a
+ 
+
+ align:start position:0%
+P3 that so that means find a
+condition we need to find a condition on
+
+ align:start position:0%
+condition we need to find a condition on
+ 
+
+ align:start position:0%
+condition we need to find a condition on
+the coordinates
+
+ align:start position:0%
+the coordinates
+ 
+
+ align:start position:0%
+the coordinates
+XYZ telling us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whether p is in the plane or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not okay so we have several ways of
+
+ align:start position:0%
+not okay so we have several ways of
+ 
+
+ align:start position:0%
+not okay so we have several ways of
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+that for example one thing we could do
+
+ align:start position:0%
+that for example one thing we could do
+ 
+
+ align:start position:0%
+that for example one thing we could do
+let me just backtrack to determinants
+
+ align:start position:0%
+let me just backtrack to determinants
+ 
+
+ align:start position:0%
+let me just backtrack to determinants
+that we saw last time so one way to
+
+ align:start position:0%
+that we saw last time so one way to
+ 
+
+ align:start position:0%
+that we saw last time so one way to
+think about it is to
+
+ align:start position:0%
+think about it is to
+ 
+
+ align:start position:0%
+think about it is to
+consider these vectors P1 P2 P1 P3 and
+
+ align:start position:0%
+consider these vectors P1 P2 P1 P3 and
+ 
+
+ align:start position:0%
+consider these vectors P1 P2 P1 P3 and
+P1
+
+ align:start position:0%
+P1
+ 
+
+ align:start position:0%
+P1
+P okay so the question of whether
+
+ align:start position:0%
+P okay so the question of whether
+ 
+
+ align:start position:0%
+P okay so the question of whether
+they're all in the same plane is the
+
+ align:start position:0%
+they're all in the same plane is the
+ 
+
+ align:start position:0%
+they're all in the same plane is the
+same as asking ourselves whether the
+
+ align:start position:0%
+same as asking ourselves whether the
+ 
+
+ align:start position:0%
+same as asking ourselves whether the
+parallelepiped that they form is
+
+ align:start position:0%
+parallelepiped that they form is
+ 
+
+ align:start position:0%
+parallelepiped that they form is
+actually completely
+
+ align:start position:0%
+actually completely
+ 
+
+ align:start position:0%
+actually completely
+flattened right if I try to form a
+
+ align:start position:0%
+flattened right if I try to form a
+ 
+
+ align:start position:0%
+flattened right if I try to form a
+parallelepiped with these three sides
+
+ align:start position:0%
+parallelepiped with these three sides
+ 
+
+ align:start position:0%
+parallelepiped with these three sides
+well if p is not in the plane then it
+
+ align:start position:0%
+well if p is not in the plane then it
+ 
+
+ align:start position:0%
+well if p is not in the plane then it
+will have some volume but if p is in the
+
+ align:start position:0%
+will have some volume but if p is in the
+ 
+
+ align:start position:0%
+will have some volume but if p is in the
+plane that means that it's actually
+
+ align:start position:0%
+plane that means that it's actually
+ 
+
+ align:start position:0%
+plane that means that it's actually
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+squished so one possible answer
+
+ align:start position:0%
+squished so one possible answer
+ 
+
+ align:start position:0%
+squished so one possible answer
+one way to think of the equation of a
+
+ align:start position:0%
+one way to think of the equation of a
+ 
+
+ align:start position:0%
+one way to think of the equation of a
+plane should be that the determinant of
+
+ align:start position:0%
+plane should be that the determinant of
+ 
+
+ align:start position:0%
+plane should be that the determinant of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+vectors should be
+
+ align:start position:0%
+vectors should be
+ 
+
+ align:start position:0%
+vectors should be
+zero determinant of P1
+
+ align:start position:0%
+zero determinant of P1
+ 
+
+ align:start position:0%
+zero determinant of P1
+P2 P1 P3 and actually let me do it in a
+
+ align:start position:0%
+P2 P1 P3 and actually let me do it in a
+ 
+
+ align:start position:0%
+P2 P1 P3 and actually let me do it in a
+different order it doesn't really matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but so one possible way to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+express the condition that P is in the
+
+ align:start position:0%
+express the condition that P is in the
+ 
+
+ align:start position:0%
+express the condition that P is in the
+plane is to say that the determinant of
+
+ align:start position:0%
+plane is to say that the determinant of
+ 
+
+ align:start position:0%
+plane is to say that the determinant of
+these three vectors has to be zero and
+
+ align:start position:0%
+these three vectors has to be zero and
+ 
+
+ align:start position:0%
+these three vectors has to be zero and
+if I'm given coordinates for these
+
+ align:start position:0%
+if I'm given coordinates for these
+ 
+
+ align:start position:0%
+if I'm given coordinates for these
+points I mean I'm not giving you numbers
+
+ align:start position:0%
+points I mean I'm not giving you numbers
+ 
+
+ align:start position:0%
+points I mean I'm not giving you numbers
+but if I gave you numbers then you would
+
+ align:start position:0%
+but if I gave you numbers then you would
+ 
+
+ align:start position:0%
+but if I gave you numbers then you would
+be able to plug these numbers in so you
+
+ align:start position:0%
+be able to plug these numbers in so you
+ 
+
+ align:start position:0%
+be able to plug these numbers in so you
+could compute these two vectors
+
+ align:start position:0%
+could compute these two vectors
+ 
+
+ align:start position:0%
+could compute these two vectors
+explicitly you would have numbers here
+
+ align:start position:0%
+explicitly you would have numbers here
+ 
+
+ align:start position:0%
+explicitly you would have numbers here
+but here of course this would depend on
+
+ align:start position:0%
+but here of course this would depend on
+ 
+
+ align:start position:0%
+but here of course this would depend on
+X Y and Z so when you compute the
+
+ align:start position:0%
+X Y and Z so when you compute the
+ 
+
+ align:start position:0%
+X Y and Z so when you compute the
+determinant you get a formula that
+
+ align:start position:0%
+determinant you get a formula that
+ 
+
+ align:start position:0%
+determinant you get a formula that
+involves X Y and Z and you will find
+
+ align:start position:0%
+involves X Y and Z and you will find
+ 
+
+ align:start position:0%
+involves X Y and Z and you will find
+that this condition in XYZ that's the
+
+ align:start position:0%
+that this condition in XYZ that's the
+ 
+
+ align:start position:0%
+that this condition in XYZ that's the
+equation of a plane okay so we're going
+
+ align:start position:0%
+equation of a plane okay so we're going
+ 
+
+ align:start position:0%
+equation of a plane okay so we're going
+to see more about that pretty soon now
+
+ align:start position:0%
+to see more about that pretty soon now
+ 
+
+ align:start position:0%
+to see more about that pretty soon now
+let me tell you about a slightly faster
+
+ align:start position:0%
+let me tell you about a slightly faster
+ 
+
+ align:start position:0%
+let me tell you about a slightly faster
+way of doing
+
+ align:start position:0%
+way of doing
+ 
+
+ align:start position:0%
+way of doing
+it actually it's not much faster it's
+
+ align:start position:0%
+it actually it's not much faster it's
+ 
+
+ align:start position:0%
+it actually it's not much faster it's
+pretty much the same calculation but
+
+ align:start position:0%
+pretty much the same calculation but
+ 
+
+ align:start position:0%
+pretty much the same calculation but
+it's maybe more
+
+ align:start position:0%
+it's maybe more
+ 
+
+ align:start position:0%
+it's maybe more
+enlightening oh let me actually show you
+
+ align:start position:0%
+enlightening oh let me actually show you
+ 
+
+ align:start position:0%
+enlightening oh let me actually show you
+the nice color picture that I prepared
+
+ align:start position:0%
+the nice color picture that I prepared
+ 
+
+ align:start position:0%
+the nice color picture that I prepared
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all right so one thing that's on this
+
+ align:start position:0%
+so all right so one thing that's on this
+ 
+
+ align:start position:0%
+so all right so one thing that's on this
+picture that I haven't thrown there is
+
+ align:start position:0%
+picture that I haven't thrown there is
+ 
+
+ align:start position:0%
+picture that I haven't thrown there is
+the normal Vector to the plane so why is
+
+ align:start position:0%
+the normal Vector to the plane so why is
+ 
+
+ align:start position:0%
+the normal Vector to the plane so why is
+that well let's say that we know how to
+
+ align:start position:0%
+that well let's say that we know how to
+ 
+
+ align:start position:0%
+that well let's say that we know how to
+find a vector that's perpendicular to
+
+ align:start position:0%
+find a vector that's perpendicular to
+ 
+
+ align:start position:0%
+find a vector that's perpendicular to
+our plane then what does it mean for the
+
+ align:start position:0%
+our plane then what does it mean for the
+ 
+
+ align:start position:0%
+our plane then what does it mean for the
+point P to be in the plane well it means
+
+ align:start position:0%
+point P to be in the plane well it means
+ 
+
+ align:start position:0%
+point P to be in the plane well it means
+that the direction say from P1 to P has
+
+ align:start position:0%
+that the direction say from P1 to P has
+ 
+
+ align:start position:0%
+that the direction say from P1 to P has
+to be perpendicular to this Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay so here's another solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so p is in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane only when well exactly
+
+ align:start position:0%
+plane only when well exactly
+ 
+
+ align:start position:0%
+plane only when well exactly
+when the vector P1 p is perpendicular to
+
+ align:start position:0%
+when the vector P1 p is perpendicular to
+ 
+
+ align:start position:0%
+when the vector P1 p is perpendicular to
+n where n is some
+
+ align:start position:0%
+n where n is some
+ 
+
+ align:start position:0%
+n where n is some
+Vector that's perpendicular to the plane
+
+ align:start position:0%
+Vector that's perpendicular to the plane
+ 
+
+ align:start position:0%
+Vector that's perpendicular to the plane
+so that's called a normal
+
+ align:start position:0%
+so that's called a normal
+ 
+
+ align:start position:0%
+so that's called a normal
+Vector not that the other are abnormal
+
+ align:start position:0%
+Vector not that the other are abnormal
+ 
+
+ align:start position:0%
+Vector not that the other are abnormal
+but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how do we rephrase this
+
+ align:start position:0%
+so how do we rephrase this
+ 
+
+ align:start position:0%
+so how do we rephrase this
+condition well we've learned how to
+
+ align:start position:0%
+condition well we've learned how to
+ 
+
+ align:start position:0%
+condition well we've learned how to
+detect whether two vectors are
+
+ align:start position:0%
+detect whether two vectors are
+ 
+
+ align:start position:0%
+detect whether two vectors are
+perpendicular to each other using dot
+
+ align:start position:0%
+perpendicular to each other using dot
+ 
+
+ align:start position:0%
+perpendicular to each other using dot
+product okay dot product that's the
+
+ align:start position:0%
+product okay dot product that's the
+ 
+
+ align:start position:0%
+product okay dot product that's the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+lecture so these two vectors are
+
+ align:start position:0%
+lecture so these two vectors are
+ 
+
+ align:start position:0%
+lecture so these two vectors are
+perpendicular exactly when their dot
+
+ align:start position:0%
+perpendicular exactly when their dot
+ 
+
+ align:start position:0%
+perpendicular exactly when their dot
+product is
+
+ align:start position:0%
+product is
+ 
+
+ align:start position:0%
+product is
+zero okay and so now concretely well if
+
+ align:start position:0%
+zero okay and so now concretely well if
+ 
+
+ align:start position:0%
+zero okay and so now concretely well if
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+we have a point P1 given to us and say
+
+ align:start position:0%
+we have a point P1 given to us and say
+ 
+
+ align:start position:0%
+we have a point P1 given to us and say
+we have been able to compute the vector
+
+ align:start position:0%
+we have been able to compute the vector
+ 
+
+ align:start position:0%
+we have been able to compute the vector
+n then well when we actually compute
+
+ align:start position:0%
+n then well when we actually compute
+ 
+
+ align:start position:0%
+n then well when we actually compute
+what happens here we will have the
+
+ align:start position:0%
+what happens here we will have the
+ 
+
+ align:start position:0%
+what happens here we will have the
+coordinates XYZ of a point p and we'll
+
+ align:start position:0%
+coordinates XYZ of a point p and we'll
+ 
+
+ align:start position:0%
+coordinates XYZ of a point p and we'll
+get some condition on XYZ that will be
+
+ align:start position:0%
+get some condition on XYZ that will be
+ 
+
+ align:start position:0%
+get some condition on XYZ that will be
+the equation of a plane
+
+ align:start position:0%
+the equation of a plane
+ 
+
+ align:start position:0%
+the equation of a plane
+again now why are these things the
+
+ align:start position:0%
+again now why are these things the
+ 
+
+ align:start position:0%
+again now why are these things the
+same well before I can tell you that I
+
+ align:start position:0%
+same well before I can tell you that I
+ 
+
+ align:start position:0%
+same well before I can tell you that I
+should tell you how can we find a normal
+
+ align:start position:0%
+should tell you how can we find a normal
+ 
+
+ align:start position:0%
+should tell you how can we find a normal
+Vector but maybe you are already
+
+ align:start position:0%
+Vector but maybe you are already
+ 
+
+ align:start position:0%
+Vector but maybe you are already
+starting to see what the method should
+
+ align:start position:0%
+starting to see what the method should
+ 
+
+ align:start position:0%
+starting to see what the method should
+be because we know how to find vectors
+
+ align:start position:0%
+be because we know how to find vectors
+ 
+
+ align:start position:0%
+be because we know how to find vectors
+perpendicular to two given
+
+ align:start position:0%
+perpendicular to two given
+ 
+
+ align:start position:0%
+perpendicular to two given
+vectors right so we know two vectors in
+
+ align:start position:0%
+vectors right so we know two vectors in
+ 
+
+ align:start position:0%
+vectors right so we know two vectors in
+that plane for example P1 P2 and P1 P3
+
+ align:start position:0%
+that plane for example P1 P2 and P1 P3
+ 
+
+ align:start position:0%
+that plane for example P1 P2 and P1 P3
+actually I could have used you know
+
+ align:start position:0%
+actually I could have used you know
+ 
+
+ align:start position:0%
+actually I could have used you know
+another permutation of the points but
+
+ align:start position:0%
+another permutation of the points but
+ 
+
+ align:start position:0%
+another permutation of the points but
+let's use these so if I want to find a
+
+ align:start position:0%
+let's use these so if I want to find a
+ 
+
+ align:start position:0%
+let's use these so if I want to find a
+vector that's perpendicular to both P1
+
+ align:start position:0%
+vector that's perpendicular to both P1
+ 
+
+ align:start position:0%
+vector that's perpendicular to both P1
+P2 and P1 P3 at the same time all I have
+
+ align:start position:0%
+P2 and P1 P3 at the same time all I have
+ 
+
+ align:start position:0%
+P2 and P1 P3 at the same time all I have
+to do is take the cross
+
+ align:start position:0%
+to do is take the cross
+ 
+
+ align:start position:0%
+to do is take the cross
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+so how do we
+
+ align:start position:0%
+so how do we
+ 
+
+ align:start position:0%
+so how do we
+find this Vector that's perpendicular to
+
+ align:start position:0%
+find this Vector that's perpendicular to
+ 
+
+ align:start position:0%
+find this Vector that's perpendicular to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+plane well the answer
+
+ align:start position:0%
+plane well the answer
+ 
+
+ align:start position:0%
+plane well the answer
+is we can just take the cross product P1
+
+ align:start position:0%
+is we can just take the cross product P1
+ 
+
+ align:start position:0%
+is we can just take the cross product P1
+P2 cross P1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P3 I should say well you know say that
+
+ align:start position:0%
+P3 I should say well you know say that
+ 
+
+ align:start position:0%
+P3 I should say well you know say that
+actually you took the point in a
+
+ align:start position:0%
+actually you took the point in a
+ 
+
+ align:start position:0%
+actually you took the point in a
+different order you did P1 P3 cross P1
+
+ align:start position:0%
+different order you did P1 P3 cross P1
+ 
+
+ align:start position:0%
+different order you did P1 P3 cross P1
+P2 you would get of course the opposite
+
+ align:start position:0%
+P2 you would get of course the opposite
+ 
+
+ align:start position:0%
+P2 you would get of course the opposite
+Vector but it's fine any plane has
+
+ align:start position:0%
+Vector but it's fine any plane has
+ 
+
+ align:start position:0%
+Vector but it's fine any plane has
+actually infinitely many normal vectors
+
+ align:start position:0%
+actually infinitely many normal vectors
+ 
+
+ align:start position:0%
+actually infinitely many normal vectors
+you can just you know multiply the
+
+ align:start position:0%
+you can just you know multiply the
+ 
+
+ align:start position:0%
+you can just you know multiply the
+normal vector by any constant you will
+
+ align:start position:0%
+normal vector by any constant you will
+ 
+
+ align:start position:0%
+normal vector by any constant you will
+still get a normal Vector that's
+
+ align:start position:0%
+still get a normal Vector that's
+ 
+
+ align:start position:0%
+still get a normal Vector that's
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+so that's going to be one of the main
+
+ align:start position:0%
+so that's going to be one of the main
+ 
+
+ align:start position:0%
+so that's going to be one of the main
+uses of dot product see when we know two
+
+ align:start position:0%
+uses of dot product see when we know two
+ 
+
+ align:start position:0%
+uses of dot product see when we know two
+vectors in a plane it lets us find the
+
+ align:start position:0%
+vectors in a plane it lets us find the
+ 
+
+ align:start position:0%
+vectors in a plane it lets us find the
+normal Vector to the plane and that is
+
+ align:start position:0%
+normal Vector to the plane and that is
+ 
+
+ align:start position:0%
+normal Vector to the plane and that is
+what we need to find the
+
+ align:start position:0%
+what we need to find the
+ 
+
+ align:start position:0%
+what we need to find the
+equation now why is that the same as the
+
+ align:start position:0%
+equation now why is that the same as the
+ 
+
+ align:start position:0%
+equation now why is that the same as the
+answer over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there well
+
+ align:start position:0%
+there well
+ 
+
+ align:start position:0%
+there well
+the condition that we have is that P1 P
+
+ align:start position:0%
+the condition that we have is that P1 P
+ 
+
+ align:start position:0%
+the condition that we have is that P1 P
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+n should be zero and we said n is
+
+ align:start position:0%
+n should be zero and we said n is
+ 
+
+ align:start position:0%
+n should be zero and we said n is
+actually P1
+
+ align:start position:0%
+actually P1
+ 
+
+ align:start position:0%
+actually P1
+P2 cross P1
+
+ align:start position:0%
+P2 cross P1
+ 
+
+ align:start position:0%
+P2 cross P1
+P3 so this is what we want to be zero
+
+ align:start position:0%
+P3 so this is what we want to be zero
+ 
+
+ align:start position:0%
+P3 so this is what we want to be zero
+now if you remember stuff from a long
+
+ align:start position:0%
+now if you remember stuff from a long
+ 
+
+ align:start position:0%
+now if you remember stuff from a long
+time ago I mean that was Friday um then
+
+ align:start position:0%
+time ago I mean that was Friday um then
+ 
+
+ align:start position:0%
+time ago I mean that was Friday um then
+we've introduced this thing and called
+
+ align:start position:0%
+we've introduced this thing and called
+ 
+
+ align:start position:0%
+we've introduced this thing and called
+it the triple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+product okay and what we've seen is that
+
+ align:start position:0%
+product okay and what we've seen is that
+ 
+
+ align:start position:0%
+product okay and what we've seen is that
+the triple product is the same thing as
+
+ align:start position:0%
+the triple product is the same thing as
+ 
+
+ align:start position:0%
+the triple product is the same thing as
+the determinant so in fact these two
+
+ align:start position:0%
+the determinant so in fact these two
+ 
+
+ align:start position:0%
+the determinant so in fact these two
+ways of thinking one saying that the Box
+
+ align:start position:0%
+ways of thinking one saying that the Box
+ 
+
+ align:start position:0%
+ways of thinking one saying that the Box
+formed by these three vectors should be
+
+ align:start position:0%
+formed by these three vectors should be
+ 
+
+ align:start position:0%
+formed by these three vectors should be
+flat and have volume zero and the other
+
+ align:start position:0%
+flat and have volume zero and the other
+ 
+
+ align:start position:0%
+flat and have volume zero and the other
+one saying that we can find a normal
+
+ align:start position:0%
+one saying that we can find a normal
+ 
+
+ align:start position:0%
+one saying that we can find a normal
+vector and then Express the condition
+
+ align:start position:0%
+vector and then Express the condition
+ 
+
+ align:start position:0%
+vector and then Express the condition
+that a vector is in the plane if it's
+
+ align:start position:0%
+that a vector is in the plane if it's
+ 
+
+ align:start position:0%
+that a vector is in the plane if it's
+perpendicular to the normal Vector
+
+ align:start position:0%
+perpendicular to the normal Vector
+ 
+
+ align:start position:0%
+perpendicular to the normal Vector
+they're actually giving us the same
+
+ align:start position:0%
+they're actually giving us the same
+ 
+
+ align:start position:0%
+they're actually giving us the same
+formula in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+okay any quick questions before we move
+
+ align:start position:0%
+okay any quick questions before we move
+ 
+
+ align:start position:0%
+okay any quick questions before we move
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so these two quantities P1 P do uh
+
+ align:start position:0%
+yes so these two quantities P1 P do uh
+ 
+
+ align:start position:0%
+yes so these two quantities P1 P do uh
+cross product of the determinant of the
+
+ align:start position:0%
+cross product of the determinant of the
+ 
+
+ align:start position:0%
+cross product of the determinant of the
+three vectors they're always equal to
+
+ align:start position:0%
+three vectors they're always equal to
+ 
+
+ align:start position:0%
+three vectors they're always equal to
+each other okay they're always the same
+
+ align:start position:0%
+each other okay they're always the same
+ 
+
+ align:start position:0%
+each other okay they're always the same
+and now if the point is not in the plane
+
+ align:start position:0%
+and now if the point is not in the plane
+ 
+
+ align:start position:0%
+and now if the point is not in the plane
+then the numerical value will be non
+
+ align:start position:0%
+then the numerical value will be non
+ 
+
+ align:start position:0%
+then the numerical value will be non
+zero if p is in the plane it will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay let's move on and talk a bit
+
+ align:start position:0%
+zero okay let's move on and talk a bit
+ 
+
+ align:start position:0%
+zero okay let's move on and talk a bit
+about matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so probably some of you have seen about
+
+ align:start position:0%
+so probably some of you have seen about
+ 
+
+ align:start position:0%
+so probably some of you have seen about
+matrices a little bit in high school uh
+
+ align:start position:0%
+matrices a little bit in high school uh
+ 
+
+ align:start position:0%
+matrices a little bit in high school uh
+but certainly not all of you and so
+
+ align:start position:0%
+but certainly not all of you and so
+ 
+
+ align:start position:0%
+but certainly not all of you and so
+anyway let me just introduce you to a
+
+ align:start position:0%
+anyway let me just introduce you to a
+ 
+
+ align:start position:0%
+anyway let me just introduce you to a
+little bit about matrices just enough
+
+ align:start position:0%
+little bit about matrices just enough
+ 
+
+ align:start position:0%
+little bit about matrices just enough
+for what we'll need later in this class
+
+ align:start position:0%
+for what we'll need later in this class
+ 
+
+ align:start position:0%
+for what we'll need later in this class
+uh I should say if you want to know
+
+ align:start position:0%
+uh I should say if you want to know
+ 
+
+ align:start position:0%
+uh I should say if you want to know
+everything about the secret life of
+
+ align:start position:0%
+everything about the secret life of
+ 
+
+ align:start position:0%
+everything about the secret life of
+matrices when you should take 1806
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+someday so okay so what's going to be
+
+ align:start position:0%
+someday so okay so what's going to be
+ 
+
+ align:start position:0%
+someday so okay so what's going to be
+our motivation for matrices well in life
+
+ align:start position:0%
+our motivation for matrices well in life
+ 
+
+ align:start position:0%
+our motivation for matrices well in life
+a lot of things are related by linear
+
+ align:start position:0%
+a lot of things are related by linear
+ 
+
+ align:start position:0%
+a lot of things are related by linear
+formulas and even if they are not some
+
+ align:start position:0%
+formulas and even if they are not some
+ 
+
+ align:start position:0%
+formulas and even if they are not some
+maybe sometimes you can approximate them
+
+ align:start position:0%
+maybe sometimes you can approximate them
+ 
+
+ align:start position:0%
+maybe sometimes you can approximate them
+by linear formulas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so often we have linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relations between variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example well if we if we do a change of
+
+ align:start position:0%
+example well if we if we do a change of
+ 
+
+ align:start position:0%
+example well if we if we do a change of
+coordinate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems so for example you know say
+
+ align:start position:0%
+systems so for example you know say
+ 
+
+ align:start position:0%
+systems so for example you know say
+that we're in
+
+ align:start position:0%
+that we're in
+ 
+
+ align:start position:0%
+that we're in
+space well and we have a point so its
+
+ align:start position:0%
+space well and we have a point so its
+ 
+
+ align:start position:0%
+space well and we have a point so its
+coordinates might be let me call them X1
+
+ align:start position:0%
+coordinates might be let me call them X1
+ 
+
+ align:start position:0%
+coordinates might be let me call them X1
+X 2 X3 in my initial coordinate system
+
+ align:start position:0%
+X 2 X3 in my initial coordinate system
+ 
+
+ align:start position:0%
+X 2 X3 in my initial coordinate system
+but then maybe I need to actually switch
+
+ align:start position:0%
+but then maybe I need to actually switch
+ 
+
+ align:start position:0%
+but then maybe I need to actually switch
+to different coordinates to better solve
+
+ align:start position:0%
+to different coordinates to better solve
+ 
+
+ align:start position:0%
+to different coordinates to better solve
+my problem because it's more adapted to
+
+ align:start position:0%
+my problem because it's more adapted to
+ 
+
+ align:start position:0%
+my problem because it's more adapted to
+other things I will do in my problem and
+
+ align:start position:0%
+other things I will do in my problem and
+ 
+
+ align:start position:0%
+other things I will do in my problem and
+so I have other coordinate
+
+ align:start position:0%
+so I have other coordinate
+ 
+
+ align:start position:0%
+so I have other coordinate
+AES and then in these new
+
+ align:start position:0%
+AES and then in these new
+ 
+
+ align:start position:0%
+AES and then in these new
+coordinates well it will have actually
+
+ align:start position:0%
+coordinates well it will have actually
+ 
+
+ align:start position:0%
+coordinates well it will have actually
+different coordinates let me call them
+
+ align:start position:0%
+different coordinates let me call them
+ 
+
+ align:start position:0%
+different coordinates let me call them
+say U1 U2
+
+ align:start position:0%
+say U1 U2
+ 
+
+ align:start position:0%
+say U1 U2
+u3 and then the relation between the old
+
+ align:start position:0%
+u3 and then the relation between the old
+ 
+
+ align:start position:0%
+u3 and then the relation between the old
+and the new coordinates is going to be
+
+ align:start position:0%
+and the new coordinates is going to be
+ 
+
+ align:start position:0%
+and the new coordinates is going to be
+by linear formulas
+
+ align:start position:0%
+by linear formulas
+ 
+
+ align:start position:0%
+by linear formulas
+I mean especially if I choose the same
+
+ align:start position:0%
+I mean especially if I choose the same
+ 
+
+ align:start position:0%
+I mean especially if I choose the same
+origin otherwise there might be constant
+
+ align:start position:0%
+origin otherwise there might be constant
+ 
+
+ align:start position:0%
+origin otherwise there might be constant
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+which I will not insist
+
+ align:start position:0%
+which I will not insist
+ 
+
+ align:start position:0%
+which I will not insist
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+so let me just give an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example for example maybe I don't
+
+ align:start position:0%
+example for example maybe I don't
+ 
+
+ align:start position:0%
+example for example maybe I don't
+know let's say for example U1 could be
+
+ align:start position:0%
+know let's say for example U1 could be
+ 
+
+ align:start position:0%
+know let's say for example U1 could be
+twice X1 + 3 * X2 Plus 3 *
+
+ align:start position:0%
+twice X1 + 3 * X2 Plus 3 *
+ 
+
+ align:start position:0%
+twice X1 + 3 * X2 Plus 3 *
+X3 U2 might be 2 * X1 + 4 * X2 + 5 * X3
+
+ align:start position:0%
+X3 U2 might be 2 * X1 + 4 * X2 + 5 * X3
+ 
+
+ align:start position:0%
+X3 U2 might be 2 * X1 + 4 * X2 + 5 * X3
+u3 might be X1 + X2 + tce X3 do not ask
+
+ align:start position:0%
+u3 might be X1 + X2 + tce X3 do not ask
+ 
+
+ align:start position:0%
+u3 might be X1 + X2 + tce X3 do not ask
+me where these numbers come from I just
+
+ align:start position:0%
+me where these numbers come from I just
+ 
+
+ align:start position:0%
+me where these numbers come from I just
+made them up okay that's just an example
+
+ align:start position:0%
+made them up okay that's just an example
+ 
+
+ align:start position:0%
+made them up okay that's just an example
+of what might
+
+ align:start position:0%
+of what might
+ 
+
+ align:start position:0%
+of what might
+happen um so plug you know put here your
+
+ align:start position:0%
+happen um so plug you know put here your
+ 
+
+ align:start position:0%
+happen um so plug you know put here your
+favorite numbers if you
+
+ align:start position:0%
+favorite numbers if you
+ 
+
+ align:start position:0%
+favorite numbers if you
+want okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in order to express this kind of
+
+ align:start position:0%
+now in order to express this kind of
+ 
+
+ align:start position:0%
+now in order to express this kind of
+linear relation we can use matrices so a
+
+ align:start position:0%
+linear relation we can use matrices so a
+ 
+
+ align:start position:0%
+linear relation we can use matrices so a
+matrix is just a table with numbers in
+
+ align:start position:0%
+matrix is just a table with numbers in
+ 
+
+ align:start position:0%
+matrix is just a table with numbers in
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and so we can reformulate
+
+ align:start position:0%
+and so we can reformulate
+ 
+
+ align:start position:0%
+and so we can reformulate
+this in terms of matrix
+
+ align:start position:0%
+this in terms of matrix
+ 
+
+ align:start position:0%
+this in terms of matrix
+multiplication or matrix
+
+ align:start position:0%
+multiplication or matrix
+ 
+
+ align:start position:0%
+multiplication or matrix
+product okay
+
+ align:start position:0%
+product okay
+ 
+
+ align:start position:0%
+product okay
+so instead of writing this I will write
+
+ align:start position:0%
+so instead of writing this I will write
+ 
+
+ align:start position:0%
+so instead of writing this I will write
+that The Matrix 2 3 3 2 4
+
+ align:start position:0%
+that The Matrix 2 3 3 2 4
+ 
+
+ align:start position:0%
+that The Matrix 2 3 3 2 4
+5 1 1
+
+ align:start position:0%
+5 1 1
+ 
+
+ align:start position:0%
+5 1 1
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+times the vector X1 X2
+
+ align:start position:0%
+times the vector X1 X2
+ 
+
+ align:start position:0%
+times the vector X1 X2
+X3 is equal to U1 U2
+
+ align:start position:0%
+X3 is equal to U1 U2
+ 
+
+ align:start position:0%
+X3 is equal to U1 U2
+u3 okay so hopefully you see that
+
+ align:start position:0%
+u3 okay so hopefully you see that
+ 
+
+ align:start position:0%
+u3 okay so hopefully you see that
+there's the same information content on
+
+ align:start position:0%
+there's the same information content on
+ 
+
+ align:start position:0%
+there's the same information content on
+both sides I just need to explain to you
+
+ align:start position:0%
+both sides I just need to explain to you
+ 
+
+ align:start position:0%
+both sides I just need to explain to you
+what this
+
+ align:start position:0%
+what this
+ 
+
+ align:start position:0%
+what this
+way of multiplying tables of numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means well what it means is really that
+
+ align:start position:0%
+means well what it means is really that
+ 
+
+ align:start position:0%
+means well what it means is really that
+you know we take exactly these
+
+ align:start position:0%
+you know we take exactly these
+ 
+
+ align:start position:0%
+you know we take exactly these
+quantities
+
+ align:start position:0%
+quantities
+ 
+
+ align:start position:0%
+quantities
+but uh let me just say that more
+
+ align:start position:0%
+but uh let me just say that more
+ 
+
+ align:start position:0%
+but uh let me just say that more
+symbolically so maybe this Matrix we
+
+ align:start position:0%
+symbolically so maybe this Matrix we
+ 
+
+ align:start position:0%
+symbolically so maybe this Matrix we
+could call a you
+
+ align:start position:0%
+could call a you
+ 
+
+ align:start position:0%
+could call a you
+know and this we could call X and this
+
+ align:start position:0%
+know and this we could call X and this
+ 
+
+ align:start position:0%
+know and this we could call X and this
+we could call Capital U capital x then
+
+ align:start position:0%
+we could call Capital U capital x then
+ 
+
+ align:start position:0%
+we could call Capital U capital x then
+we'll say a * xal U which is is a lot
+
+ align:start position:0%
+we'll say a * xal U which is is a lot
+ 
+
+ align:start position:0%
+we'll say a * xal U which is is a lot
+shorter than that of course I need to
+
+ align:start position:0%
+shorter than that of course I need to
+ 
+
+ align:start position:0%
+shorter than that of course I need to
+tell you what a x and U are in terms of
+
+ align:start position:0%
+tell you what a x and U are in terms of
+ 
+
+ align:start position:0%
+tell you what a x and U are in terms of
+their entries for you to get the
+
+ align:start position:0%
+their entries for you to get the
+ 
+
+ align:start position:0%
+their entries for you to get the
+formula but it's convenient
+
+ align:start position:0%
+formula but it's convenient
+ 
+
+ align:start position:0%
+formula but it's convenient
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+so what does it mean to do a matrix
+
+ align:start position:0%
+so what does it mean to do a matrix
+ 
+
+ align:start position:0%
+so what does it mean to do a matrix
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+entries in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+product so you should say so in the
+
+ align:start position:0%
+product so you should say so in the
+ 
+
+ align:start position:0%
+product so you should say so in the
+matrix product
+
+ align:start position:0%
+matrix product
+ 
+
+ align:start position:0%
+matrix product
+are obtained by doing the dot
+
+ align:start position:0%
+are obtained by doing the dot
+ 
+
+ align:start position:0%
+are obtained by doing the dot
+product so let's say we're doing the
+
+ align:start position:0%
+product so let's say we're doing the
+ 
+
+ align:start position:0%
+product so let's say we're doing the
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+ax so we do a DOT product
+
+ align:start position:0%
+ax so we do a DOT product
+ 
+
+ align:start position:0%
+ax so we do a DOT product
+between the rows dot products between
+
+ align:start position:0%
+between the rows dot products between
+ 
+
+ align:start position:0%
+between the rows dot products between
+the rows of
+
+ align:start position:0%
+the rows of
+ 
+
+ align:start position:0%
+the rows of
+a and The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Columns of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X so
+
+ align:start position:0%
+X so
+ 
+
+ align:start position:0%
+X so
+maybe I should say here a is a 3X3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix that just means there's you know
+
+ align:start position:0%
+Matrix that just means there's you know
+ 
+
+ align:start position:0%
+Matrix that just means there's you know
+three rows and three columns and X is a
+
+ align:start position:0%
+three rows and three columns and X is a
+ 
+
+ align:start position:0%
+three rows and three columns and X is a
+column
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector which we can think of as a 3X one
+
+ align:start position:0%
+Vector which we can think of as a 3X one
+ 
+
+ align:start position:0%
+Vector which we can think of as a 3X one
+Matrix it has three rows and only one
+
+ align:start position:0%
+Matrix it has three rows and only one
+ 
+
+ align:start position:0%
+Matrix it has three rows and only one
+column okay so now what can we do well I
+
+ align:start position:0%
+column okay so now what can we do well I
+ 
+
+ align:start position:0%
+column okay so now what can we do well I
+said we're going to do the dot product
+
+ align:start position:0%
+said we're going to do the dot product
+ 
+
+ align:start position:0%
+said we're going to do the dot product
+between a row of a 2 3 3 and a column of
+
+ align:start position:0%
+between a row of a 2 3 3 and a column of
+ 
+
+ align:start position:0%
+between a row of a 2 3 3 and a column of
+X X1 X2 X3 well that dot product will be
+
+ align:start position:0%
+X X1 X2 X3 well that dot product will be
+ 
+
+ align:start position:0%
+X X1 X2 X3 well that dot product will be
+2 * X1 + 3 * X2 + 3 * X3 it's exactly
+
+ align:start position:0%
+2 * X1 + 3 * X2 + 3 * X3 it's exactly
+ 
+
+ align:start position:0%
+2 * X1 + 3 * X2 + 3 * X3 it's exactly
+what we want to set U Want equal to
+
+ align:start position:0%
+what we want to set U Want equal to
+ 
+
+ align:start position:0%
+what we want to set U Want equal to
+let's do the second one I take the
+
+ align:start position:0%
+let's do the second one I take the
+ 
+
+ align:start position:0%
+let's do the second one I take the
+second row of a 2 45 and I do the dot
+
+ align:start position:0%
+second row of a 2 45 and I do the dot
+ 
+
+ align:start position:0%
+second row of a 2 45 and I do the dot
+product with X1 X2 X3 I will get 2 * x1+
+
+ align:start position:0%
+product with X1 X2 X3 I will get 2 * x1+
+ 
+
+ align:start position:0%
+product with X1 X2 X3 I will get 2 * x1+
+4 4 * X2 + 5 * X3 okay which is this
+
+ align:start position:0%
+4 4 * X2 + 5 * X3 okay which is this
+ 
+
+ align:start position:0%
+4 4 * X2 + 5 * X3 okay which is this
+thing and same with the third one 1 * X1
+
+ align:start position:0%
+thing and same with the third one 1 * X1
+ 
+
+ align:start position:0%
+thing and same with the third one 1 * X1
++ 1 * X2 + 2 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X3 okay so that's matrix
+
+ align:start position:0%
+X3 okay so that's matrix
+ 
+
+ align:start position:0%
+X3 okay so that's matrix
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+so again I mean Let Me
+
+ align:start position:0%
+so again I mean Let Me
+ 
+
+ align:start position:0%
+so again I mean Let Me
+Maybe restate that more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generally
+
+ align:start position:0%
+generally
+ 
+
+ align:start position:0%
+generally
+so if I want to find the
+
+ align:start position:0%
+so if I want to find the
+ 
+
+ align:start position:0%
+so if I want to find the
+entries of a product of two matrices A
+
+ align:start position:0%
+entries of a product of two matrices A
+ 
+
+ align:start position:0%
+entries of a product of two matrices A
+and B so I'm saying matrices but they
+
+ align:start position:0%
+and B so I'm saying matrices but they
+ 
+
+ align:start position:0%
+and B so I'm saying matrices but they
+could be of course vectors are now a
+
+ align:start position:0%
+could be of course vectors are now a
+ 
+
+ align:start position:0%
+could be of course vectors are now a
+special case of matrices just by taking
+
+ align:start position:0%
+special case of matrices just by taking
+ 
+
+ align:start position:0%
+special case of matrices just by taking
+a matrix of width
+
+ align:start position:0%
+a matrix of width
+ 
+
+ align:start position:0%
+a matrix of width
+one okay
+
+ align:start position:0%
+one okay
+ 
+
+ align:start position:0%
+one okay
+so if I have my Matrix
+
+ align:start position:0%
+so if I have my Matrix
+ 
+
+ align:start position:0%
+so if I have my Matrix
+a and I have my Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B and then I will get the product
+
+ align:start position:0%
+B and then I will get the product
+ 
+
+ align:start position:0%
+B and then I will get the product
+AB well let's say for example that a you
+
+ align:start position:0%
+AB well let's say for example that a you
+ 
+
+ align:start position:0%
+AB well let's say for example that a you
+know this works in any sizes so let's
+
+ align:start position:0%
+know this works in any sizes so let's
+ 
+
+ align:start position:0%
+know this works in any sizes so let's
+say that a is a four sorry a 3x4 matrix
+
+ align:start position:0%
+say that a is a four sorry a 3x4 matrix
+ 
+
+ align:start position:0%
+say that a is a four sorry a 3x4 matrix
+so it has three rows four columns and
+
+ align:start position:0%
+so it has three rows four columns and
+ 
+
+ align:start position:0%
+so it has three rows four columns and
+here I'm not going to give you the
+
+ align:start position:0%
+here I'm not going to give you the
+ 
+
+ align:start position:0%
+here I'm not going to give you the
+values because I'm not going to compute
+
+ align:start position:0%
+values because I'm not going to compute
+ 
+
+ align:start position:0%
+values because I'm not going to compute
+everything it would take you know the
+
+ align:start position:0%
+everything it would take you know the
+ 
+
+ align:start position:0%
+everything it would take you know the
+rest of the lecture so and let's say
+
+ align:start position:0%
+rest of the lecture so and let's say
+ 
+
+ align:start position:0%
+rest of the lecture so and let's say
+that b is maybe size 4X two so it has
+
+ align:start position:0%
+that b is maybe size 4X two so it has
+ 
+
+ align:start position:0%
+that b is maybe size 4X two so it has
+two columns and four rows and let's say
+
+ align:start position:0%
+two columns and four rows and let's say
+ 
+
+ align:start position:0%
+two columns and four rows and let's say
+for example that we have the second
+
+ align:start position:0%
+for example that we have the second
+ 
+
+ align:start position:0%
+for example that we have the second
+column is 03
+
+ align:start position:0%
+column is 03
+ 
+
+ align:start position:0%
+column is 03
+02 so a * B I claim will have well the
+
+ align:start position:0%
+02 so a * B I claim will have well the
+ 
+
+ align:start position:0%
+02 so a * B I claim will have well the
+entries should be the dot products
+
+ align:start position:0%
+entries should be the dot products
+ 
+
+ align:start position:0%
+entries should be the dot products
+between these rows and these columns
+
+ align:start position:0%
+between these rows and these columns
+ 
+
+ align:start position:0%
+between these rows and these columns
+here we have two columns here we have
+
+ align:start position:0%
+here we have two columns here we have
+ 
+
+ align:start position:0%
+here we have two columns here we have
+three rows so we should get you know
+
+ align:start position:0%
+three rows so we should get you know
+ 
+
+ align:start position:0%
+three rows so we should get you know
+three times two different possibilities
+
+ align:start position:0%
+three times two different possibilities
+ 
+
+ align:start position:0%
+three times two different possibilities
+and so the answer will have size 3x
+
+ align:start position:0%
+and so the answer will have size 3x
+ 
+
+ align:start position:0%
+and so the answer will have size 3x
+two okay and well we cannot compute most
+
+ align:start position:0%
+two okay and well we cannot compute most
+ 
+
+ align:start position:0%
+two okay and well we cannot compute most
+of them because I didn't give you
+
+ align:start position:0%
+of them because I didn't give you
+ 
+
+ align:start position:0%
+of them because I didn't give you
+numbers but one of them we can compute
+
+ align:start position:0%
+numbers but one of them we can compute
+ 
+
+ align:start position:0%
+numbers but one of them we can compute
+we can compute the one that goes here
+
+ align:start position:0%
+we can compute the one that goes here
+ 
+
+ align:start position:0%
+we can compute the one that goes here
+namely this one in the second column so
+
+ align:start position:0%
+namely this one in the second column so
+ 
+
+ align:start position:0%
+namely this one in the second column so
+I select the second column of B and in
+
+ align:start position:0%
+I select the second column of B and in
+ 
+
+ align:start position:0%
+I select the second column of B and in
+the first row so I take the first row of
+
+ align:start position:0%
+the first row so I take the first row of
+ 
+
+ align:start position:0%
+the first row so I take the first row of
+a and I find well 1 * 0 0 2 * 3 6 + 0 +
+
+ align:start position:0%
+a and I find well 1 * 0 0 2 * 3 6 + 0 +
+ 
+
+ align:start position:0%
+a and I find well 1 * 0 0 2 * 3 6 + 0 +
+8 should make 14 so this entry here is
+
+ align:start position:0%
+8 should make 14 so this entry here is
+ 
+
+ align:start position:0%
+8 should make 14 so this entry here is
+14 okay
+
+ align:start position:0%
+14 okay
+ 
+
+ align:start position:0%
+14 okay
+so in fact let me tell you about another
+
+ align:start position:0%
+so in fact let me tell you about another
+ 
+
+ align:start position:0%
+so in fact let me tell you about another
+way to set it up so that you remember
+
+ align:start position:0%
+way to set it up so that you remember
+ 
+
+ align:start position:0%
+way to set it up so that you remember
+more easily how you know what goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where so one way that you can set it up
+
+ align:start position:0%
+where so one way that you can set it up
+ 
+
+ align:start position:0%
+where so one way that you can set it up
+is you can put a
+
+ align:start position:0%
+is you can put a
+ 
+
+ align:start position:0%
+is you can put a
+here you can put B up here and then you
+
+ align:start position:0%
+here you can put B up here and then you
+ 
+
+ align:start position:0%
+here you can put B up here and then you
+will get the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and if you want to find what goes
+
+ align:start position:0%
+here and if you want to find what goes
+ 
+
+ align:start position:0%
+here and if you want to find what goes
+in a given slot here then you just look
+
+ align:start position:0%
+in a given slot here then you just look
+ 
+
+ align:start position:0%
+in a given slot here then you just look
+to its left and you look above it and
+
+ align:start position:0%
+to its left and you look above it and
+ 
+
+ align:start position:0%
+to its left and you look above it and
+you do the dot product between these
+
+ align:start position:0%
+you do the dot product between these
+ 
+
+ align:start position:0%
+you do the dot product between these
+guys okay so that's I think an easy way
+
+ align:start position:0%
+guys okay so that's I think an easy way
+ 
+
+ align:start position:0%
+guys okay so that's I think an easy way
+to remember you know first of all it
+
+ align:start position:0%
+to remember you know first of all it
+ 
+
+ align:start position:0%
+to remember you know first of all it
+tells you what the size of the answer
+
+ align:start position:0%
+tells you what the size of the answer
+ 
+
+ align:start position:0%
+tells you what the size of the answer
+will be the size will be well what fits
+
+ align:start position:0%
+will be the size will be well what fits
+ 
+
+ align:start position:0%
+will be the size will be well what fits
+nicely in this box should have the same
+
+ align:start position:0%
+nicely in this box should have the same
+ 
+
+ align:start position:0%
+nicely in this box should have the same
+width as B and the same height as a and
+
+ align:start position:0%
+width as B and the same height as a and
+ 
+
+ align:start position:0%
+width as B and the same height as a and
+second it tells you which product to
+
+ align:start position:0%
+second it tells you which product to
+ 
+
+ align:start position:0%
+second it tells you which product to
+compute for each
+
+ align:start position:0%
+compute for each
+ 
+
+ align:start position:0%
+compute for each
+position okay so you just look at what's
+
+ align:start position:0%
+position okay so you just look at what's
+ 
+
+ align:start position:0%
+position okay so you just look at what's
+to the left and what's above the given
+
+ align:start position:0%
+to the left and what's above the given
+ 
+
+ align:start position:0%
+to the left and what's above the given
+position now now there's a catch can we
+
+ align:start position:0%
+position now now there's a catch can we
+ 
+
+ align:start position:0%
+position now now there's a catch can we
+multiply anything by anything well no
+
+ align:start position:0%
+multiply anything by anything well no
+ 
+
+ align:start position:0%
+multiply anything by anything well no
+okay I mean I wouldn't ask the question
+
+ align:start position:0%
+okay I mean I wouldn't ask the question
+ 
+
+ align:start position:0%
+okay I mean I wouldn't ask the question
+otherwise but but anyway uh see to be
+
+ align:start position:0%
+otherwise but but anyway uh see to be
+ 
+
+ align:start position:0%
+otherwise but but anyway uh see to be
+able to do this dot product we need to
+
+ align:start position:0%
+able to do this dot product we need to
+ 
+
+ align:start position:0%
+able to do this dot product we need to
+have the same number of entries here and
+
+ align:start position:0%
+have the same number of entries here and
+ 
+
+ align:start position:0%
+have the same number of entries here and
+here otherwise we can't say take this
+
+ align:start position:0%
+here otherwise we can't say take this
+ 
+
+ align:start position:0%
+here otherwise we can't say take this
+time that plus this time that and so on
+
+ align:start position:0%
+time that plus this time that and so on
+ 
+
+ align:start position:0%
+time that plus this time that and so on
+if we run out of space on one of them
+
+ align:start position:0%
+if we run out of space on one of them
+ 
+
+ align:start position:0%
+if we run out of space on one of them
+before the
+
+ align:start position:0%
+before the
+ 
+
+ align:start position:0%
+before the
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the condition and it's kind of
+
+ align:start position:0%
+so the condition and it's kind of
+ 
+
+ align:start position:0%
+so the condition and it's kind of
+important so let me write it in right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that the width of
+
+ align:start position:0%
+is that the width of
+ 
+
+ align:start position:0%
+is that the width of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+must
+
+ align:start position:0%
+must
+ 
+
+ align:start position:0%
+must
+equal the height of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay sorry it's a bit cluttered but
+
+ align:start position:0%
+B okay sorry it's a bit cluttered but
+ 
+
+ align:start position:0%
+B okay sorry it's a bit cluttered but
+hopefully you can still see what I'm
+
+ align:start position:0%
+hopefully you can still see what I'm
+ 
+
+ align:start position:0%
+hopefully you can still see what I'm
+fighting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay okay but now we know how to
+
+ align:start position:0%
+so okay okay but now we know how to
+ 
+
+ align:start position:0%
+so okay okay but now we know how to
+multiply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices so what does it mean to
+
+ align:start position:0%
+matrices so what does it mean to
+ 
+
+ align:start position:0%
+matrices so what does it mean to
+multiply matrices I mean of
+
+ align:start position:0%
+multiply matrices I mean of
+ 
+
+ align:start position:0%
+multiply matrices I mean of
+course we've seen uh you know on this
+
+ align:start position:0%
+course we've seen uh you know on this
+ 
+
+ align:start position:0%
+course we've seen uh you know on this
+example that we can use the Matrix to
+
+ align:start position:0%
+example that we can use the Matrix to
+ 
+
+ align:start position:0%
+example that we can use the Matrix to
+tell us how to transform from X's to
+
+ align:start position:0%
+tell us how to transform from X's to
+ 
+
+ align:start position:0%
+tell us how to transform from X's to
+use and that's an example of
+
+ align:start position:0%
+use and that's an example of
+ 
+
+ align:start position:0%
+use and that's an example of
+multiplication but now let's say that we
+
+ align:start position:0%
+multiplication but now let's say that we
+ 
+
+ align:start position:0%
+multiplication but now let's say that we
+have two matrices like that telling us
+
+ align:start position:0%
+have two matrices like that telling us
+ 
+
+ align:start position:0%
+have two matrices like that telling us
+how to transform from something to
+
+ align:start position:0%
+how to transform from something to
+ 
+
+ align:start position:0%
+how to transform from something to
+something else what does it mean to
+
+ align:start position:0%
+something else what does it mean to
+ 
+
+ align:start position:0%
+something else what does it mean to
+multiply
+
+ align:start position:0%
+multiply
+ 
+
+ align:start position:0%
+multiply
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I
+
+ align:start position:0%
+so I
+ 
+
+ align:start position:0%
+so I
+claim is that so I claim that the
+
+ align:start position:0%
+claim is that so I claim that the
+ 
+
+ align:start position:0%
+claim is that so I claim that the
+product AB
+
+ align:start position:0%
+product AB
+ 
+
+ align:start position:0%
+product AB
+represents doing first the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation B
+
+ align:start position:0%
+transformation B
+ 
+
+ align:start position:0%
+transformation B
+then trans formation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so that's a slightly counterintuitive
+
+ align:start position:0%
+a so that's a slightly counterintuitive
+ 
+
+ align:start position:0%
+a so that's a slightly counterintuitive
+thing because we're used to writing
+
+ align:start position:0%
+thing because we're used to writing
+ 
+
+ align:start position:0%
+thing because we're used to writing
+things from left to right uh
+
+ align:start position:0%
+things from left to right uh
+ 
+
+ align:start position:0%
+things from left to right uh
+unfortunately with matrices the way
+
+ align:start position:0%
+unfortunately with matrices the way
+ 
+
+ align:start position:0%
+unfortunately with matrices the way
+they're done you multipy I mean you
+
+ align:start position:0%
+they're done you multipy I mean you
+ 
+
+ align:start position:0%
+they're done you multipy I mean you
+multiply things from right to left if
+
+ align:start position:0%
+multiply things from right to left if
+ 
+
+ align:start position:0%
+multiply things from right to left if
+you think about it you know when you
+
+ align:start position:0%
+you think about it you know when you
+ 
+
+ align:start position:0%
+you think about it you know when you
+write say you have two functions f and g
+
+ align:start position:0%
+write say you have two functions f and g
+ 
+
+ align:start position:0%
+write say you have two functions f and g
+you write F of G of X it really means
+
+ align:start position:0%
+you write F of G of X it really means
+ 
+
+ align:start position:0%
+you write F of G of X it really means
+you apply first G then F so it works the
+
+ align:start position:0%
+you apply first G then F so it works the
+ 
+
+ align:start position:0%
+you apply first G then F so it works the
+same way as that
+
+ align:start position:0%
+same way as that
+ 
+
+ align:start position:0%
+same way as that
+okay so why why is this well if I write
+
+ align:start position:0%
+okay so why why is this well if I write
+ 
+
+ align:start position:0%
+okay so why why is this well if I write
+AB * X where X is some Vector that I
+
+ align:start position:0%
+AB * X where X is some Vector that I
+ 
+
+ align:start position:0%
+AB * X where X is some Vector that I
+want to transform it's the same as a *
+
+ align:start position:0%
+want to transform it's the same as a *
+ 
+
+ align:start position:0%
+want to transform it's the same as a *
+BX okay so this property is called
+
+ align:start position:0%
+BX okay so this property is called
+ 
+
+ align:start position:0%
+BX okay so this property is called
+associativity and it's a good property
+
+ align:start position:0%
+associativity and it's a good property
+ 
+
+ align:start position:0%
+associativity and it's a good property
+of well behaved products uh not of cross
+
+ align:start position:0%
+of well behaved products uh not of cross
+ 
+
+ align:start position:0%
+of well behaved products uh not of cross
+product by the way but so matrix product
+
+ align:start position:0%
+product by the way but so matrix product
+ 
+
+ align:start position:0%
+product by the way but so matrix product
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+associative that means we can actually
+
+ align:start position:0%
+associative that means we can actually
+ 
+
+ align:start position:0%
+associative that means we can actually
+think of a product ax and multiply them
+
+ align:start position:0%
+think of a product ax and multiply them
+ 
+
+ align:start position:0%
+think of a product ax and multiply them
+in whichever order we want we can start
+
+ align:start position:0%
+in whichever order we want we can start
+ 
+
+ align:start position:0%
+in whichever order we want we can start
+with BX or we can start with
+
+ align:start position:0%
+with BX or we can start with
+ 
+
+ align:start position:0%
+with BX or we can start with
+a so
+
+ align:start position:0%
+a so
+ 
+
+ align:start position:0%
+a so
+now BX means we apply the transformation
+
+ align:start position:0%
+now BX means we apply the transformation
+ 
+
+ align:start position:0%
+now BX means we apply the transformation
+B to X and then multiplying by a means
+
+ align:start position:0%
+B to X and then multiplying by a means
+ 
+
+ align:start position:0%
+B to X and then multiplying by a means
+we apply the transformation
+
+ align:start position:0%
+we apply the transformation
+ 
+
+ align:start position:0%
+we apply the transformation
+a so we first apply B then we apply a
+
+ align:start position:0%
+a so we first apply B then we apply a
+ 
+
+ align:start position:0%
+a so we first apply B then we apply a
+that's the same as applying a all at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another note of warning is that ab and
+
+ align:start position:0%
+another note of warning is that ab and
+ 
+
+ align:start position:0%
+another note of warning is that ab and
+ba are not the same thing at all well I
+
+ align:start position:0%
+ba are not the same thing at all well I
+ 
+
+ align:start position:0%
+ba are not the same thing at all well I
+mean you probably see that already from
+
+ align:start position:0%
+mean you probably see that already from
+ 
+
+ align:start position:0%
+mean you probably see that already from
+this interpretation it's not the same
+
+ align:start position:0%
+this interpretation it's not the same
+ 
+
+ align:start position:0%
+this interpretation it's not the same
+thing to you know convert oranges to
+
+ align:start position:0%
+thing to you know convert oranges to
+ 
+
+ align:start position:0%
+thing to you know convert oranges to
+bananas then to carrots or vice versa
+
+ align:start position:0%
+bananas then to carrots or vice versa
+ 
+
+ align:start position:0%
+bananas then to carrots or vice versa
+um uh on the other
+
+ align:start position:0%
+um uh on the other
+ 
+
+ align:start position:0%
+um uh on the other
+hand well I mean actually even worse
+
+ align:start position:0%
+hand well I mean actually even worse
+ 
+
+ align:start position:0%
+hand well I mean actually even worse
+this thing might not can be well defined
+
+ align:start position:0%
+this thing might not can be well defined
+ 
+
+ align:start position:0%
+this thing might not can be well defined
+because you know if the
+
+ align:start position:0%
+because you know if the
+ 
+
+ align:start position:0%
+because you know if the
+height of sorry the width of a equals
+
+ align:start position:0%
+height of sorry the width of a equals
+ 
+
+ align:start position:0%
+height of sorry the width of a equals
+the height of B we can do this product
+
+ align:start position:0%
+the height of B we can do this product
+ 
+
+ align:start position:0%
+the height of B we can do this product
+but we we don't necessarily I mean it's
+
+ align:start position:0%
+but we we don't necessarily I mean it's
+ 
+
+ align:start position:0%
+but we we don't necessarily I mean it's
+not clear that the width of B will equal
+
+ align:start position:0%
+not clear that the width of B will equal
+ 
+
+ align:start position:0%
+not clear that the width of B will equal
+the height of of a which is what we
+
+ align:start position:0%
+the height of of a which is what we
+ 
+
+ align:start position:0%
+the height of of a which is what we
+would need for that
+
+ align:start position:0%
+would need for that
+ 
+
+ align:start position:0%
+would need for that
+one okay so you know the size condition
+
+ align:start position:0%
+one okay so you know the size condition
+ 
+
+ align:start position:0%
+one okay so you know the size condition
+to be able to do the product might not
+
+ align:start position:0%
+to be able to do the product might not
+ 
+
+ align:start position:0%
+to be able to do the product might not
+make sense actually maybe one of them
+
+ align:start position:0%
+make sense actually maybe one of them
+ 
+
+ align:start position:0%
+make sense actually maybe one of them
+doesn't even make sense even if they
+
+ align:start position:0%
+doesn't even make sense even if they
+ 
+
+ align:start position:0%
+doesn't even make sense even if they
+both make sense they're usually complet
+
+ align:start position:0%
+both make sense they're usually complet
+ 
+
+ align:start position:0%
+both make sense they're usually complet
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things okay the next thing I need to
+
+ align:start position:0%
+things okay the next thing I need to
+ 
+
+ align:start position:0%
+things okay the next thing I need to
+tell you is something called the
+
+ align:start position:0%
+tell you is something called the
+ 
+
+ align:start position:0%
+tell you is something called the
+identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix well the identity Matrix is the
+
+ align:start position:0%
+Matrix well the identity Matrix is the
+ 
+
+ align:start position:0%
+Matrix well the identity Matrix is the
+Matrix that does nothing okay so what
+
+ align:start position:0%
+Matrix that does nothing okay so what
+ 
+
+ align:start position:0%
+Matrix that does nothing okay so what
+does it mean to do nothing I don't mean
+
+ align:start position:0%
+does it mean to do nothing I don't mean
+ 
+
+ align:start position:0%
+does it mean to do nothing I don't mean
+the Matrix Zero The Matrix zero would
+
+ align:start position:0%
+the Matrix Zero The Matrix zero would
+ 
+
+ align:start position:0%
+the Matrix Zero The Matrix zero would
+take X and would always give you back
+
+ align:start position:0%
+take X and would always give you back
+ 
+
+ align:start position:0%
+take X and would always give you back
+zero that's not very interesting
+
+ align:start position:0%
+zero that's not very interesting
+ 
+
+ align:start position:0%
+zero that's not very interesting
+transformation um what I mean is the guy
+
+ align:start position:0%
+transformation um what I mean is the guy
+ 
+
+ align:start position:0%
+transformation um what I mean is the guy
+that takes X and gives you X again so it
+
+ align:start position:0%
+that takes X and gives you X again so it
+ 
+
+ align:start position:0%
+that takes X and gives you X again so it
+satisfies you know property I so it's
+
+ align:start position:0%
+satisfies you know property I so it's
+ 
+
+ align:start position:0%
+satisfies you know property I so it's
+called I and it has a property that IX
+
+ align:start position:0%
+called I and it has a property that IX
+ 
+
+ align:start position:0%
+called I and it has a property that IX
+equals X for all X so it's the
+
+ align:start position:0%
+equals X for all X so it's the
+ 
+
+ align:start position:0%
+equals X for all X so it's the
+transformation from something to itself
+
+ align:start position:0%
+transformation from something to itself
+ 
+
+ align:start position:0%
+transformation from something to itself
+it's the obvious transformation called
+
+ align:start position:0%
+it's the obvious transformation called
+ 
+
+ align:start position:0%
+it's the obvious transformation called
+the identity
+
+ align:start position:0%
+the identity
+ 
+
+ align:start position:0%
+the identity
+transformation so how do we write that
+
+ align:start position:0%
+transformation so how do we write that
+ 
+
+ align:start position:0%
+transformation so how do we write that
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+matrix well so actually there's an
+
+ align:start position:0%
+matrix well so actually there's an
+ 
+
+ align:start position:0%
+matrix well so actually there's an
+identity for each size you know because
+
+ align:start position:0%
+identity for each size you know because
+ 
+
+ align:start position:0%
+identity for each size you know because
+of course depending on whether X has two
+
+ align:start position:0%
+of course depending on whether X has two
+ 
+
+ align:start position:0%
+of course depending on whether X has two
+entries or 10 entries uh The Matrix I
+
+ align:start position:0%
+entries or 10 entries uh The Matrix I
+ 
+
+ align:start position:0%
+entries or 10 entries uh The Matrix I
+needs to have a different
+
+ align:start position:0%
+needs to have a different
+ 
+
+ align:start position:0%
+needs to have a different
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+so for example the identity Matrix of
+
+ align:start position:0%
+so for example the identity Matrix of
+ 
+
+ align:start position:0%
+so for example the identity Matrix of
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+3x3 has entries one one one on the
+
+ align:start position:0%
+3x3 has entries one one one on the
+ 
+
+ align:start position:0%
+3x3 has entries one one one on the
+diagonal and Zer everywhere
+
+ align:start position:0%
+diagonal and Zer everywhere
+ 
+
+ align:start position:0%
+diagonal and Zer everywhere
+else okay let's check if we multiply
+
+ align:start position:0%
+else okay let's check if we multiply
+ 
+
+ align:start position:0%
+else okay let's check if we multiply
+this with a vector well okay maybe I
+
+ align:start position:0%
+this with a vector well okay maybe I
+ 
+
+ align:start position:0%
+this with a vector well okay maybe I
+should do that on a separate board
+
+ align:start position:0%
+should do that on a separate board
+ 
+
+ align:start position:0%
+should do that on a separate board
+but so start thinking about it what
+
+ align:start position:0%
+but so start thinking about it what
+ 
+
+ align:start position:0%
+but so start thinking about it what
+happens when I multiply this with a
+
+ align:start position:0%
+happens when I multiply this with a
+ 
+
+ align:start position:0%
+happens when I multiply this with a
+vector X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's say I
+
+ align:start position:0%
+okay so let's say I
+ 
+
+ align:start position:0%
+okay so let's say I
+multiply The
+
+ align:start position:0%
+multiply The
+ 
+
+ align:start position:0%
+multiply The
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I with a vector X1 X2
+
+ align:start position:0%
+I with a vector X1 X2
+ 
+
+ align:start position:0%
+I with a vector X1 X2
+X3 well what will be the first
+
+ align:start position:0%
+X3 well what will be the first
+ 
+
+ align:start position:0%
+X3 well what will be the first
+entry it will be the dot product between
+
+ align:start position:0%
+entry it will be the dot product between
+ 
+
+ align:start position:0%
+entry it will be the dot product between
+1 0 0 and X1 X2 X3 if you want this
+
+ align:start position:0%
+1 0 0 and X1 X2 X3 if you want this
+ 
+
+ align:start position:0%
+1 0 0 and X1 X2 X3 if you want this
+Vector is I hat okay so if you do the
+
+ align:start position:0%
+Vector is I hat okay so if you do the
+ 
+
+ align:start position:0%
+Vector is I hat okay so if you do the
+dot product with IH hat you will get the
+
+ align:start position:0%
+dot product with IH hat you will get the
+ 
+
+ align:start position:0%
+dot product with IH hat you will get the
+X component you will get the first
+
+ align:start position:0%
+X component you will get the first
+ 
+
+ align:start position:0%
+X component you will get the first
+component that will be X1 1 * X1 + 0 0
+
+ align:start position:0%
+component that will be X1 1 * X1 + 0 0
+ 
+
+ align:start position:0%
+component that will be X1 1 * X1 + 0 0
+similarly here if I do the dot product I
+
+ align:start position:0%
+similarly here if I do the dot product I
+ 
+
+ align:start position:0%
+similarly here if I do the dot product I
+get 0 + X2 + z i get x2 and here I get
+
+ align:start position:0%
+get 0 + X2 + z i get x2 and here I get
+ 
+
+ align:start position:0%
+get 0 + X2 + z i get x2 and here I get
+X3 okay it
+
+ align:start position:0%
+X3 okay it
+ 
+
+ align:start position:0%
+X3 okay it
+works same thing if I put here a matrix
+
+ align:start position:0%
+works same thing if I put here a matrix
+ 
+
+ align:start position:0%
+works same thing if I put here a matrix
+I will get back the same
+
+ align:start position:0%
+I will get back the same
+ 
+
+ align:start position:0%
+I will get back the same
+Matrix now of
+
+ align:start position:0%
+Matrix now of
+ 
+
+ align:start position:0%
+Matrix now of
+course okay so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general the identity Matrix in size n
+
+ align:start position:0%
+general the identity Matrix in size n
+ 
+
+ align:start position:0%
+general the identity Matrix in size n
+byn
+
+ align:start position:0%
+byn
+ 
+
+ align:start position:0%
+byn
+so it's an N byn thing with ones on the
+
+ align:start position:0%
+so it's an N byn thing with ones on the
+ 
+
+ align:start position:0%
+so it's an N byn thing with ones on the
+diagonal and Zer everywhere
+
+ align:start position:0%
+diagonal and Zer everywhere
+ 
+
+ align:start position:0%
+diagonal and Zer everywhere
+else okay you just put one at every
+
+ align:start position:0%
+else okay you just put one at every
+ 
+
+ align:start position:0%
+else okay you just put one at every
+diagonal position and zero elsewhere and
+
+ align:start position:0%
+diagonal position and zero elsewhere and
+ 
+
+ align:start position:0%
+diagonal position and zero elsewhere and
+then you can see if you multiply that by
+
+ align:start position:0%
+then you can see if you multiply that by
+ 
+
+ align:start position:0%
+then you can see if you multiply that by
+a vector you will get the same Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh let me give you another example
+
+ align:start position:0%
+okay uh let me give you another example
+ 
+
+ align:start position:0%
+okay uh let me give you another example
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix let's say that in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane we look at the transformation that
+
+ align:start position:0%
+plane we look at the transformation that
+ 
+
+ align:start position:0%
+plane we look at the transformation that
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+Rotation by
+
+ align:start position:0%
+Rotation by
+ 
+
+ align:start position:0%
+Rotation by
+90° uh let's
+
+ align:start position:0%
+90° uh let's
+ 
+
+ align:start position:0%
+90° uh let's
+say counterclockwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I claim that this is given by The
+
+ align:start position:0%
+so I claim that this is given by The
+ 
+
+ align:start position:0%
+so I claim that this is given by The
+Matrix 0 1 - 1 0 so let's try to see why
+
+ align:start position:0%
+Matrix 0 1 - 1 0 so let's try to see why
+ 
+
+ align:start position:0%
+Matrix 0 1 - 1 0 so let's try to see why
+that is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case well if I do R * I hat so if I
+
+ align:start position:0%
+case well if I do R * I hat so if I
+ 
+
+ align:start position:0%
+case well if I do R * I hat so if I
+apply that to the first vector
+
+ align:start position:0%
+apply that to the first vector
+ 
+
+ align:start position:0%
+apply that to the first vector
+IH hat so that means
+
+ align:start position:0%
+IH hat so that means
+ 
+
+ align:start position:0%
+IH hat so that means
+okay IH hat will be one
+
+ align:start position:0%
+okay IH hat will be one
+ 
+
+ align:start position:0%
+okay IH hat will be one
+Z this product well here you will get
+
+ align:start position:0%
+Z this product well here you will get
+ 
+
+ align:start position:0%
+Z this product well here you will get
+zero and then you will get
+
+ align:start position:0%
+zero and then you will get
+ 
+
+ align:start position:0%
+zero and then you will get
+one you get J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hat okay so this thing
+
+ align:start position:0%
+hat okay so this thing
+ 
+
+ align:start position:0%
+hat okay so this thing
+sends IH hat to
+
+ align:start position:0%
+sends IH hat to
+ 
+
+ align:start position:0%
+sends IH hat to
+jut what about Jad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you
+
+ align:start position:0%
+well you
+ 
+
+ align:start position:0%
+well you
+get1 and then you get zero so that's
+
+ align:start position:0%
+get1 and then you get zero so that's
+ 
+
+ align:start position:0%
+get1 and then you get zero so that's
+minus I so J is sent towards here and in
+
+ align:start position:0%
+minus I so J is sent towards here and in
+ 
+
+ align:start position:0%
+minus I so J is sent towards here and in
+general if you apply it to a vector with
+
+ align:start position:0%
+general if you apply it to a vector with
+ 
+
+ align:start position:0%
+general if you apply it to a vector with
+coordinates XY with components XY then
+
+ align:start position:0%
+coordinates XY with components XY then
+ 
+
+ align:start position:0%
+coordinates XY with components XY then
+you will get back uh minus YX which is
+
+ align:start position:0%
+you will get back uh minus YX which is
+ 
+
+ align:start position:0%
+you will get back uh minus YX which is
+the formula we've seen for rotating a
+
+ align:start position:0%
+the formula we've seen for rotating a
+ 
+
+ align:start position:0%
+the formula we've seen for rotating a
+vector by 90°
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it seems to do what we
+
+ align:start position:0%
+so it seems to do what we
+ 
+
+ align:start position:0%
+so it seems to do what we
+want uh by the way I should point out so
+
+ align:start position:0%
+want uh by the way I should point out so
+ 
+
+ align:start position:0%
+want uh by the way I should point out so
+the columns in this Matrix represent
+
+ align:start position:0%
+the columns in this Matrix represent
+ 
+
+ align:start position:0%
+the columns in this Matrix represent
+what happens to each basis Vector to the
+
+ align:start position:0%
+what happens to each basis Vector to the
+ 
+
+ align:start position:0%
+what happens to each basis Vector to the
+vectors I and J see what I mean this guy
+
+ align:start position:0%
+vectors I and J see what I mean this guy
+ 
+
+ align:start position:0%
+vectors I and J see what I mean this guy
+here is exactly what we get when we
+
+ align:start position:0%
+here is exactly what we get when we
+ 
+
+ align:start position:0%
+here is exactly what we get when we
+multiply R by I and when when we
+
+ align:start position:0%
+multiply R by I and when when we
+ 
+
+ align:start position:0%
+multiply R by I and when when we
+multiply R by J we get this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so what's interesting about this
+
+ align:start position:0%
+here so what's interesting about this
+ 
+
+ align:start position:0%
+here so what's interesting about this
+Matrix well we can do computations with
+
+ align:start position:0%
+Matrix well we can do computations with
+ 
+
+ align:start position:0%
+Matrix well we can do computations with
+matrices in ways that are easier than
+
+ align:start position:0%
+matrices in ways that are easier than
+ 
+
+ align:start position:0%
+matrices in ways that are easier than
+writing coordinate change formulas for
+
+ align:start position:0%
+writing coordinate change formulas for
+ 
+
+ align:start position:0%
+writing coordinate change formulas for
+example if you compute R squ so if you
+
+ align:start position:0%
+example if you compute R squ so if you
+ 
+
+ align:start position:0%
+example if you compute R squ so if you
+multiply r with
+
+ align:start position:0%
+multiply r with
+ 
+
+ align:start position:0%
+multiply r with
+itself well I let you do it as an
+
+ align:start position:0%
+itself well I let you do it as an
+ 
+
+ align:start position:0%
+itself well I let you do it as an
+exercise but you will find that you get
+
+ align:start position:0%
+exercise but you will find that you get
+ 
+
+ align:start position:0%
+exercise but you will find that you get
+minus1 - 1 0 0 so that's minus the
+
+ align:start position:0%
+minus1 - 1 0 0 so that's minus the
+ 
+
+ align:start position:0%
+minus1 - 1 0 0 so that's minus the
+identity
+
+ align:start position:0%
+identity
+ 
+
+ align:start position:0%
+identity
+Matrix why is that well if I rotate
+
+ align:start position:0%
+Matrix why is that well if I rotate
+ 
+
+ align:start position:0%
+Matrix why is that well if I rotate
+something by 90° and then I rotate by
+
+ align:start position:0%
+something by 90° and then I rotate by
+ 
+
+ align:start position:0%
+something by 90° and then I rotate by
+90° again then I will rotate by 180°
+
+ align:start position:0%
+90° again then I will rotate by 180°
+ 
+
+ align:start position:0%
+90° again then I will rotate by 180°
+that means I will actually just go to
+
+ align:start position:0%
+that means I will actually just go to
+ 
+
+ align:start position:0%
+that means I will actually just go to
+the opposite Point around the origin so
+
+ align:start position:0%
+the opposite Point around the origin so
+ 
+
+ align:start position:0%
+the opposite Point around the origin so
+I will take X Y to - xus
+
+ align:start position:0%
+I will take X Y to - xus
+ 
+
+ align:start position:0%
+I will take X Y to - xus
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+okay and if I applied r four * R to 4
+
+ align:start position:0%
+okay and if I applied r four * R to 4
+ 
+
+ align:start position:0%
+okay and if I applied r four * R to 4
+would be identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um questions yes came for matx is
+
+ align:start position:0%
+okay um questions yes came for matx is
+ 
+
+ align:start position:0%
+okay um questions yes came for matx is
+that r
+
+ align:start position:0%
+that r
+ 
+
+ align:start position:0%
+that r
+or Ah that's a very good question so how
+
+ align:start position:0%
+or Ah that's a very good question so how
+ 
+
+ align:start position:0%
+or Ah that's a very good question so how
+did I come up with this R well secretly
+
+ align:start position:0%
+did I come up with this R well secretly
+ 
+
+ align:start position:0%
+did I come up with this R well secretly
+I worked pretty hard to find what are
+
+ align:start position:0%
+I worked pretty hard to find what are
+ 
+
+ align:start position:0%
+I worked pretty hard to find what are
+the entries that would tell me how to
+
+ align:start position:0%
+the entries that would tell me how to
+ 
+
+ align:start position:0%
+the entries that would tell me how to
+rotate something by 90 degrees
+
+ align:start position:0%
+rotate something by 90 degrees
+ 
+
+ align:start position:0%
+rotate something by 90 degrees
+counterclockwise so remember I mean I
+
+ align:start position:0%
+counterclockwise so remember I mean I
+ 
+
+ align:start position:0%
+counterclockwise so remember I mean I
+should have said um what we saw I think
+
+ align:start position:0%
+should have said um what we saw I think
+ 
+
+ align:start position:0%
+should have said um what we saw I think
+last time or the first lecture is that
+
+ align:start position:0%
+last time or the first lecture is that
+ 
+
+ align:start position:0%
+last time or the first lecture is that
+to rotate a vector by
+
+ align:start position:0%
+to rotate a vector by
+ 
+
+ align:start position:0%
+to rotate a vector by
+90° we should change XY
+
+ align:start position:0%
+90° we should change XY
+ 
+
+ align:start position:0%
+90° we should change XY
+to minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+YX okay and so now I'm trying to express
+
+ align:start position:0%
+YX okay and so now I'm trying to express
+ 
+
+ align:start position:0%
+YX okay and so now I'm trying to express
+the this transformation as a matrix and
+
+ align:start position:0%
+the this transformation as a matrix and
+ 
+
+ align:start position:0%
+the this transformation as a matrix and
+if you work out you know how these guys
+
+ align:start position:0%
+if you work out you know how these guys
+ 
+
+ align:start position:0%
+if you work out you know how these guys
+so maybe you want to call these guys u
+
+ align:start position:0%
+so maybe you want to call these guys u
+ 
+
+ align:start position:0%
+so maybe you want to call these guys u
+and v and if you write U equals 0x - 1 y
+
+ align:start position:0%
+and v and if you write U equals 0x - 1 y
+ 
+
+ align:start position:0%
+and v and if you write U equals 0x - 1 y
+0x - 1 Y and then V = 1x + 0 y 1 x + 0 y
+
+ align:start position:0%
+0x - 1 Y and then V = 1x + 0 y 1 x + 0 y
+ 
+
+ align:start position:0%
+0x - 1 Y and then V = 1x + 0 y 1 x + 0 y
+okay so that's how I would find it uh
+
+ align:start position:0%
+okay so that's how I would find it uh
+ 
+
+ align:start position:0%
+okay so that's how I would find it uh
+here actually I just gave it to you you
+
+ align:start position:0%
+here actually I just gave it to you you
+ 
+
+ align:start position:0%
+here actually I just gave it to you you
+know ready made so you didn't really see
+
+ align:start position:0%
+know ready made so you didn't really see
+ 
+
+ align:start position:0%
+know ready made so you didn't really see
+how I how I found
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it uh you will see more about rotations
+
+ align:start position:0%
+it uh you will see more about rotations
+ 
+
+ align:start position:0%
+it uh you will see more about rotations
+on the problem on the problem set
+
+ align:start position:0%
+on the problem on the problem set
+ 
+
+ align:start position:0%
+on the problem on the problem set
+there so you're going to see more about
+
+ align:start position:0%
+there so you're going to see more about
+ 
+
+ align:start position:0%
+there so you're going to see more about
+these things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh so next I need to tell you how
+
+ align:start position:0%
+okay uh so next I need to tell you how
+ 
+
+ align:start position:0%
+okay uh so next I need to tell you how
+to invert matrices so what's the point
+
+ align:start position:0%
+to invert matrices so what's the point
+ 
+
+ align:start position:0%
+to invert matrices so what's the point
+of matrices it's that it gives us a nice
+
+ align:start position:0%
+of matrices it's that it gives us a nice
+ 
+
+ align:start position:0%
+of matrices it's that it gives us a nice
+way to think about these changes of
+
+ align:start position:0%
+way to think about these changes of
+ 
+
+ align:start position:0%
+way to think about these changes of
+variables and in particular if we know
+
+ align:start position:0%
+variables and in particular if we know
+ 
+
+ align:start position:0%
+variables and in particular if we know
+how to express u in terms of X maybe
+
+ align:start position:0%
+how to express u in terms of X maybe
+ 
+
+ align:start position:0%
+how to express u in terms of X maybe
+we'd like to know how to express X in
+
+ align:start position:0%
+we'd like to know how to express X in
+ 
+
+ align:start position:0%
+we'd like to know how to express X in
+terms of U well we can do that because
+
+ align:start position:0%
+terms of U well we can do that because
+ 
+
+ align:start position:0%
+terms of U well we can do that because
+we've learned how to solve linear
+
+ align:start position:0%
+we've learned how to solve linear
+ 
+
+ align:start position:0%
+we've learned how to solve linear
+systems like this okay so in principle
+
+ align:start position:0%
+systems like this okay so in principle
+ 
+
+ align:start position:0%
+systems like this okay so in principle
+we could start working substituting and
+
+ align:start position:0%
+we could start working substituting and
+ 
+
+ align:start position:0%
+we could start working substituting and
+so on to find formulas for the X1 X2 X3
+
+ align:start position:0%
+so on to find formulas for the X1 X2 X3
+ 
+
+ align:start position:0%
+so on to find formulas for the X1 X2 X3
+as functions of U1 U2
+
+ align:start position:0%
+as functions of U1 U2
+ 
+
+ align:start position:0%
+as functions of U1 U2
+u3 and the relation will be again a
+
+ align:start position:0%
+u3 and the relation will be again a
+ 
+
+ align:start position:0%
+u3 and the relation will be again a
+linear relation it will again be given
+
+ align:start position:0%
+linear relation it will again be given
+ 
+
+ align:start position:0%
+linear relation it will again be given
+by a matrix well what's that matrix it's
+
+ align:start position:0%
+by a matrix well what's that matrix it's
+ 
+
+ align:start position:0%
+by a matrix well what's that matrix it's
+the inverse transformation so it's the
+
+ align:start position:0%
+the inverse transformation so it's the
+ 
+
+ align:start position:0%
+the inverse transformation so it's the
+inverse of the Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so we're going to learn how to find
+
+ align:start position:0%
+a so we're going to learn how to find
+ 
+
+ align:start position:0%
+a so we're going to learn how to find
+the inverse of a matrix directly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse of a by definition it's a
+
+ align:start position:0%
+inverse of a by definition it's a
+ 
+
+ align:start position:0%
+inverse of a by definition it's a
+matrix M with a
+
+ align:start position:0%
+matrix M with a
+ 
+
+ align:start position:0%
+matrix M with a
+property that
+
+ align:start position:0%
+property that
+ 
+
+ align:start position:0%
+property that
+If I multiply a by m then I get identity
+
+ align:start position:0%
+If I multiply a by m then I get identity
+ 
+
+ align:start position:0%
+If I multiply a by m then I get identity
+and If I multiply M by a I also get
+
+ align:start position:0%
+and If I multiply M by a I also get
+ 
+
+ align:start position:0%
+and If I multiply M by a I also get
+identity the two properties are
+
+ align:start position:0%
+identity the two properties are
+ 
+
+ align:start position:0%
+identity the two properties are
+equivalent um so that means you know if
+
+ align:start position:0%
+equivalent um so that means you know if
+ 
+
+ align:start position:0%
+equivalent um so that means you know if
+I apply first the transformation a then
+
+ align:start position:0%
+I apply first the transformation a then
+ 
+
+ align:start position:0%
+I apply first the transformation a then
+the transformation M I actually I undo
+
+ align:start position:0%
+the transformation M I actually I undo
+ 
+
+ align:start position:0%
+the transformation M I actually I undo
+the transformation a and vice versa
+
+ align:start position:0%
+the transformation a and vice versa
+ 
+
+ align:start position:0%
+the transformation a and vice versa
+these two Transformations are the
+
+ align:start position:0%
+these two Transformations are the
+ 
+
+ align:start position:0%
+these two Transformations are the
+opposite of each other well I should say
+
+ align:start position:0%
+opposite of each other well I should say
+ 
+
+ align:start position:0%
+opposite of each other well I should say
+the inverse of each
+
+ align:start position:0%
+the inverse of each
+ 
+
+ align:start position:0%
+the inverse of each
+other okay so
+
+ align:start position:0%
+other okay so
+ 
+
+ align:start position:0%
+other okay so
+for this to make sense we
+
+ align:start position:0%
+for this to make sense we
+ 
+
+ align:start position:0%
+for this to make sense we
+need a must be a square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix okay so it must have size n by n
+
+ align:start position:0%
+Matrix okay so it must have size n by n
+ 
+
+ align:start position:0%
+Matrix okay so it must have size n by n
+can be any size but it must be the same
+
+ align:start position:0%
+can be any size but it must be the same
+ 
+
+ align:start position:0%
+can be any size but it must be the same
+number of rows as
+
+ align:start position:0%
+number of rows as
+ 
+
+ align:start position:0%
+number of rows as
+columns and um it's a general fact that
+
+ align:start position:0%
+columns and um it's a general fact that
+ 
+
+ align:start position:0%
+columns and um it's a general fact that
+I mean you will see more in detail in
+
+ align:start position:0%
+I mean you will see more in detail in
+ 
+
+ align:start position:0%
+I mean you will see more in detail in
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+algebra if you take
+
+ align:start position:0%
+algebra if you take
+ 
+
+ align:start position:0%
+algebra if you take
+it um so let's just admit that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the Matrix M we will denote by a
+
+ align:start position:0%
+so so the Matrix M we will denote by a
+ 
+
+ align:start position:0%
+so so the Matrix M we will denote by a
+inverse like this
+
+ align:start position:0%
+inverse like this
+ 
+
+ align:start position:0%
+inverse like this
+okay and then what is it good for well
+
+ align:start position:0%
+okay and then what is it good for well
+ 
+
+ align:start position:0%
+okay and then what is it good for well
+for example the
+
+ align:start position:0%
+for example the
+ 
+
+ align:start position:0%
+for example the
+solution to a linear
+
+ align:start position:0%
+solution to a linear
+ 
+
+ align:start position:0%
+solution to a linear
+system so what's a linear system in our
+
+ align:start position:0%
+system so what's a linear system in our
+ 
+
+ align:start position:0%
+system so what's a linear system in our
+new language it's a matrix times some
+
+ align:start position:0%
+new language it's a matrix times some
+ 
+
+ align:start position:0%
+new language it's a matrix times some
+unknown Vector x equals some known
+
+ align:start position:0%
+unknown Vector x equals some known
+ 
+
+ align:start position:0%
+unknown Vector x equals some known
+Vector B
+
+ align:start position:0%
+Vector B
+ 
+
+ align:start position:0%
+Vector B
+well how do we solve
+
+ align:start position:0%
+well how do we solve
+ 
+
+ align:start position:0%
+well how do we solve
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+just compute xals a inverse B why does
+
+ align:start position:0%
+just compute xals a inverse B why does
+ 
+
+ align:start position:0%
+just compute xals a inverse B why does
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+work how do I get from here to here
+
+ align:start position:0%
+work how do I get from here to here
+ 
+
+ align:start position:0%
+work how do I get from here to here
+let's be
+
+ align:start position:0%
+let's be
+ 
+
+ align:start position:0%
+let's be
+careful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay well I'm going to reuse this
+
+ align:start position:0%
+oh okay well I'm going to reuse this
+ 
+
+ align:start position:0%
+oh okay well I'm going to reuse this
+Matrix but I'm going to erase it
+
+ align:start position:0%
+Matrix but I'm going to erase it
+ 
+
+ align:start position:0%
+Matrix but I'm going to erase it
+nonetheless I'll just rewrite it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm saying if ax equals
+
+ align:start position:0%
+so I'm saying if ax equals
+ 
+
+ align:start position:0%
+so I'm saying if ax equals
+B then
+
+ align:start position:0%
+B then
+ 
+
+ align:start position:0%
+B then
+let's multiply both sides by a inverse a
+
+ align:start position:0%
+let's multiply both sides by a inverse a
+ 
+
+ align:start position:0%
+let's multiply both sides by a inverse a
+inverse * a x is a inverse B and then
+
+ align:start position:0%
+inverse * a x is a inverse B and then
+ 
+
+ align:start position:0%
+inverse * a x is a inverse B and then
+well a inverse * a is identity so I get
+
+ align:start position:0%
+well a inverse * a is identity so I get
+ 
+
+ align:start position:0%
+well a inverse * a is identity so I get
+x equals a inverse B that's how I solved
+
+ align:start position:0%
+x equals a inverse B that's how I solved
+ 
+
+ align:start position:0%
+x equals a inverse B that's how I solved
+my system of
+
+ align:start position:0%
+my system of
+ 
+
+ align:start position:0%
+my system of
+equations so if you have a calculator
+
+ align:start position:0%
+equations so if you have a calculator
+ 
+
+ align:start position:0%
+equations so if you have a calculator
+that can invert matrices then you can
+
+ align:start position:0%
+that can invert matrices then you can
+ 
+
+ align:start position:0%
+that can invert matrices then you can
+solve linear systems very
+
+ align:start position:0%
+solve linear systems very
+ 
+
+ align:start position:0%
+solve linear systems very
+quickly now we should still learn how to
+
+ align:start position:0%
+quickly now we should still learn how to
+ 
+
+ align:start position:0%
+quickly now we should still learn how to
+compute these things yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do I know that a inverse will be on
+
+ align:start position:0%
+how do I know that a inverse will be on
+ 
+
+ align:start position:0%
+how do I know that a inverse will be on
+the left of B and not after it well it's
+
+ align:start position:0%
+the left of B and not after it well it's
+ 
+
+ align:start position:0%
+the left of B and not after it well it's
+exactly in this derivation so if you're
+
+ align:start position:0%
+exactly in this derivation so if you're
+ 
+
+ align:start position:0%
+exactly in this derivation so if you're
+ever not sure then just reproduce this
+
+ align:start position:0%
+ever not sure then just reproduce this
+ 
+
+ align:start position:0%
+ever not sure then just reproduce this
+calculation see I mean to get from here
+
+ align:start position:0%
+calculation see I mean to get from here
+ 
+
+ align:start position:0%
+calculation see I mean to get from here
+to here what I did is I multiplied
+
+ align:start position:0%
+to here what I did is I multiplied
+ 
+
+ align:start position:0%
+to here what I did is I multiplied
+things on the left by a inverse and then
+
+ align:start position:0%
+things on the left by a inverse and then
+ 
+
+ align:start position:0%
+things on the left by a inverse and then
+this gu simplify if I had put a inverse
+
+ align:start position:0%
+this gu simplify if I had put a inverse
+ 
+
+ align:start position:0%
+this gu simplify if I had put a inverse
+on the right I would have a x a inverse
+
+ align:start position:0%
+on the right I would have a x a inverse
+ 
+
+ align:start position:0%
+on the right I would have a x a inverse
+which might not make sense and even if
+
+ align:start position:0%
+which might not make sense and even if
+ 
+
+ align:start position:0%
+which might not make sense and even if
+it makes sense it doesn't
+
+ align:start position:0%
+it makes sense it doesn't
+ 
+
+ align:start position:0%
+it makes sense it doesn't
+simplify so I me the basic rle is you
+
+ align:start position:0%
+simplify so I me the basic rle is you
+ 
+
+ align:start position:0%
+simplify so I me the basic rle is you
+know you have to multiply by inverse on
+
+ align:start position:0%
+know you have to multiply by inverse on
+ 
+
+ align:start position:0%
+know you have to multiply by inverse on
+the left so that it cancels with this a
+
+ align:start position:0%
+the left so that it cancels with this a
+ 
+
+ align:start position:0%
+the left so that it cancels with this a
+that's on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left that's correct so and you know in
+
+ align:start position:0%
+left that's correct so and you know in
+ 
+
+ align:start position:0%
+left that's correct so and you know in
+our usual way of dealing with matrices
+
+ align:start position:0%
+our usual way of dealing with matrices
+ 
+
+ align:start position:0%
+our usual way of dealing with matrices
+where the vectors are column vectors I
+
+ align:start position:0%
+where the vectors are column vectors I
+ 
+
+ align:start position:0%
+where the vectors are column vectors I
+mean it's just something to remember
+
+ align:start position:0%
+mean it's just something to remember
+ 
+
+ align:start position:0%
+mean it's just something to remember
+that if you have a square Matrix times a
+
+ align:start position:0%
+that if you have a square Matrix times a
+ 
+
+ align:start position:0%
+that if you have a square Matrix times a
+column Vector I mean the product that
+
+ align:start position:0%
+column Vector I mean the product that
+ 
+
+ align:start position:0%
+column Vector I mean the product that
+makes sense is with the Matrix on the
+
+ align:start position:0%
+makes sense is with the Matrix on the
+ 
+
+ align:start position:0%
+makes sense is with the Matrix on the
+left the vect on the right the other one
+
+ align:start position:0%
+left the vect on the right the other one
+ 
+
+ align:start position:0%
+left the vect on the right the other one
+just doesn't work it's not sized you
+
+ align:start position:0%
+just doesn't work it's not sized you
+ 
+
+ align:start position:0%
+just doesn't work it's not sized you
+cannot take x * a if a and
+
+ align:start position:0%
+cannot take x * a if a and
+ 
+
+ align:start position:0%
+cannot take x * a if a and
+X you know if a is a square Matrix and X
+
+ align:start position:0%
+X you know if a is a square Matrix and X
+ 
+
+ align:start position:0%
+X you know if a is a square Matrix and X
+is a column Vector this product makes
+
+ align:start position:0%
+is a column Vector this product makes
+ 
+
+ align:start position:0%
+is a column Vector this product makes
+sense the other one doesn't make sense
+
+ align:start position:0%
+sense the other one doesn't make sense
+ 
+
+ align:start position:0%
+sense the other one doesn't make sense
+it's not the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+okay so what we need to do is to learn
+
+ align:start position:0%
+okay so what we need to do is to learn
+ 
+
+ align:start position:0%
+okay so what we need to do is to learn
+how to invert a matrix and it's useful
+
+ align:start position:0%
+how to invert a matrix and it's useful
+ 
+
+ align:start position:0%
+how to invert a matrix and it's useful
+to know first for your general knowledge
+
+ align:start position:0%
+to know first for your general knowledge
+ 
+
+ align:start position:0%
+to know first for your general knowledge
+and second because uh actually
+
+ align:start position:0%
+and second because uh actually
+ 
+
+ align:start position:0%
+and second because uh actually
+it's uh it's actually useful later for
+
+ align:start position:0%
+it's uh it's actually useful later for
+ 
+
+ align:start position:0%
+it's uh it's actually useful later for
+things we'll see in this class so in
+
+ align:start position:0%
+things we'll see in this class so in
+ 
+
+ align:start position:0%
+things we'll see in this class so in
+particular on the exam you will need to
+
+ align:start position:0%
+particular on the exam you will need to
+ 
+
+ align:start position:0%
+particular on the exam you will need to
+know how to invert a matrix by
+
+ align:start position:0%
+know how to invert a matrix by
+ 
+
+ align:start position:0%
+know how to invert a matrix by
+hand so I should say this formula is
+
+ align:start position:0%
+hand so I should say this formula is
+ 
+
+ align:start position:0%
+hand so I should say this formula is
+actually good for small matrices you
+
+ align:start position:0%
+actually good for small matrices you
+ 
+
+ align:start position:0%
+actually good for small matrices you
+know 3x3
+
+ align:start position:0%
+know 3x3
+ 
+
+ align:start position:0%
+know 3x3
+4x4 it's not good at all if you have a
+
+ align:start position:0%
+4x4 it's not good at all if you have a
+ 
+
+ align:start position:0%
+4x4 it's not good at all if you have a
+matrix of size a thousand by a thousand
+
+ align:start position:0%
+matrix of size a thousand by a thousand
+ 
+
+ align:start position:0%
+matrix of size a thousand by a thousand
+so in computer software actually for
+
+ align:start position:0%
+so in computer software actually for
+ 
+
+ align:start position:0%
+so in computer software actually for
+small matrices they do this for larger
+
+ align:start position:0%
+small matrices they do this for larger
+ 
+
+ align:start position:0%
+small matrices they do this for larger
+matrices they use other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithms but let's just see how we do
+
+ align:start position:0%
+algorithms but let's just see how we do
+ 
+
+ align:start position:0%
+algorithms but let's just see how we do
+it so I'm going to do it okay so first
+
+ align:start position:0%
+it so I'm going to do it okay so first
+ 
+
+ align:start position:0%
+it so I'm going to do it okay so first
+of all I will give you the final
+
+ align:start position:0%
+of all I will give you the final
+ 
+
+ align:start position:0%
+of all I will give you the final
+answer and of course for that I will
+
+ align:start position:0%
+answer and of course for that I will
+ 
+
+ align:start position:0%
+answer and of course for that I will
+need to explain what the answer
+
+ align:start position:0%
+need to explain what the answer
+ 
+
+ align:start position:0%
+need to explain what the answer
+means so we'll have to compute something
+
+ align:start position:0%
+means so we'll have to compute something
+ 
+
+ align:start position:0%
+means so we'll have to compute something
+called The adjoint Matrix and I will
+
+ align:start position:0%
+called The adjoint Matrix and I will
+ 
+
+ align:start position:0%
+called The adjoint Matrix and I will
+tell you how to do that and then we'll
+
+ align:start position:0%
+tell you how to do that and then we'll
+ 
+
+ align:start position:0%
+tell you how to do that and then we'll
+divide by the determinant of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do we get to the adjoint Matrix
+
+ align:start position:0%
+so how do we get to the adjoint Matrix
+ 
+
+ align:start position:0%
+so how do we get to the adjoint Matrix
+so let's go through the
+
+ align:start position:0%
+so let's go through the
+ 
+
+ align:start position:0%
+so let's go through the
+steps on a 3X3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example the steps are the same no matter
+
+ align:start position:0%
+example the steps are the same no matter
+ 
+
+ align:start position:0%
+example the steps are the same no matter
+what the size is but let's do 3 by
+
+ align:start position:0%
+what the size is but let's do 3 by
+ 
+
+ align:start position:0%
+what the size is but let's do 3 by
+three so let's say that I'm giving you
+
+ align:start position:0%
+three so let's say that I'm giving you
+ 
+
+ align:start position:0%
+three so let's say that I'm giving you
+the Matrix a well let's say it's the
+
+ align:start position:0%
+the Matrix a well let's say it's the
+ 
+
+ align:start position:0%
+the Matrix a well let's say it's the
+same as earlier the one I erased so that
+
+ align:start position:0%
+same as earlier the one I erased so that
+ 
+
+ align:start position:0%
+same as earlier the one I erased so that
+was the one relating
+
+ align:start position:0%
+was the one relating
+ 
+
+ align:start position:0%
+was the one relating
+our xes and our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use so the first thing I want to
+
+ align:start position:0%
+use so the first thing I want to
+ 
+
+ align:start position:0%
+use so the first thing I want to
+do is find What's called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minors so what's a
+
+ align:start position:0%
+minors so what's a
+ 
+
+ align:start position:0%
+minors so what's a
+minor well it's a slightly smaller
+
+ align:start position:0%
+minor well it's a slightly smaller
+ 
+
+ align:start position:0%
+minor well it's a slightly smaller
+determinant we've already seen them
+
+ align:start position:0%
+determinant we've already seen them
+ 
+
+ align:start position:0%
+determinant we've already seen them
+without calling them that way
+
+ align:start position:0%
+without calling them that way
+ 
+
+ align:start position:0%
+without calling them that way
+so for example so the Matrix of miners
+
+ align:start position:0%
+so for example so the Matrix of miners
+ 
+
+ align:start position:0%
+so for example so the Matrix of miners
+will have again the same size okay let's
+
+ align:start position:0%
+will have again the same size okay let's
+ 
+
+ align:start position:0%
+will have again the same size okay let's
+say we want this entry then we just
+
+ align:start position:0%
+say we want this entry then we just
+ 
+
+ align:start position:0%
+say we want this entry then we just
+delete this row and this column sorry
+
+ align:start position:0%
+delete this row and this column sorry
+ 
+
+ align:start position:0%
+delete this row and this column sorry
+this row and this column and we're left
+
+ align:start position:0%
+this row and this column and we're left
+ 
+
+ align:start position:0%
+this row and this column and we're left
+with a 2X two determinant okay so here
+
+ align:start position:0%
+with a 2X two determinant okay so here
+ 
+
+ align:start position:0%
+with a 2X two determinant okay so here
+we'll put the determinant 4 51 2 which
+
+ align:start position:0%
+we'll put the determinant 4 51 2 which
+ 
+
+ align:start position:0%
+we'll put the determinant 4 51 2 which
+is 4 * 2 8 - 5
+
+ align:start position:0%
+is 4 * 2 8 - 5
+ 
+
+ align:start position:0%
+is 4 * 2 8 - 5
+3 let's do the next one so for this
+
+ align:start position:0%
+3 let's do the next one so for this
+ 
+
+ align:start position:0%
+3 let's do the next one so for this
+entry I delete this row and this column
+
+ align:start position:0%
+entry I delete this row and this column
+ 
+
+ align:start position:0%
+entry I delete this row and this column
+I'm left with 2 5 1 2 determinant will
+
+ align:start position:0%
+I'm left with 2 5 1 2 determinant will
+ 
+
+ align:start position:0%
+I'm left with 2 5 1 2 determinant will
+be 2 * 2 - 5
+
+ align:start position:0%
+be 2 * 2 - 5
+ 
+
+ align:start position:0%
+be 2 * 2 - 5
+is1
+
+ align:start position:0%
+is1
+ 
+
+ align:start position:0%
+is1
+then minus two then I get to the second
+
+ align:start position:0%
+then minus two then I get to the second
+ 
+
+ align:start position:0%
+then minus two then I get to the second
+row so I get to this entry well to find
+
+ align:start position:0%
+row so I get to this entry well to find
+ 
+
+ align:start position:0%
+row so I get to this entry well to find
+the minor here I will delete this row
+
+ align:start position:0%
+the minor here I will delete this row
+ 
+
+ align:start position:0%
+the minor here I will delete this row
+and this column and I'm left with 3 3 1
+
+ align:start position:0%
+and this column and I'm left with 3 3 1
+ 
+
+ align:start position:0%
+and this column and I'm left with 3 3 1
+2 3 * 2us 3 is
+
+ align:start position:0%
+2 3 * 2us 3 is
+ 
+
+ align:start position:0%
+2 3 * 2us 3 is
+3 and let me just cheat and give you the
+
+ align:start position:0%
+3 and let me just cheat and give you the
+ 
+
+ align:start position:0%
+3 and let me just cheat and give you the
+others I mean I think I've shown you
+
+ align:start position:0%
+others I mean I think I've shown you
+ 
+
+ align:start position:0%
+others I mean I think I've shown you
+that I can do them
+
+ align:start position:0%
+that I can do them
+ 
+
+ align:start position:0%
+that I can do them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so okay so let's just explain the last
+
+ align:start position:0%
+so okay so let's just explain the last
+ 
+
+ align:start position:0%
+so okay so let's just explain the last
+one again the last one this two um so to
+
+ align:start position:0%
+one again the last one this two um so to
+ 
+
+ align:start position:0%
+one again the last one this two um so to
+find the minor here I delete this column
+
+ align:start position:0%
+find the minor here I delete this column
+ 
+
+ align:start position:0%
+find the minor here I delete this column
+and this row and I take this determinant
+
+ align:start position:0%
+and this row and I take this determinant
+ 
+
+ align:start position:0%
+and this row and I take this determinant
+2 * 4 minus 2 *
+
+ align:start position:0%
+2 * 4 minus 2 *
+ 
+
+ align:start position:0%
+2 * 4 minus 2 *
+3 okay so it's the same kind of
+
+ align:start position:0%
+3 okay so it's the same kind of
+ 
+
+ align:start position:0%
+3 okay so it's the same kind of
+manipulation that we've seen when we've
+
+ align:start position:0%
+manipulation that we've seen when we've
+ 
+
+ align:start position:0%
+manipulation that we've seen when we've
+taken determinants and cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products okay step
+
+ align:start position:0%
+products okay step
+ 
+
+ align:start position:0%
+products okay step
+two we go to another Matrix that's
+
+ align:start position:0%
+two we go to another Matrix that's
+ 
+
+ align:start position:0%
+two we go to another Matrix that's
+called co-actors so the co-actors are
+
+ align:start position:0%
+called co-actors so the co-actors are
+ 
+
+ align:start position:0%
+called co-actors so the co-actors are
+pretty much the same thing as the minus
+
+ align:start position:0%
+pretty much the same thing as the minus
+ 
+
+ align:start position:0%
+pretty much the same thing as the minus
+except the signs are slightly
+
+ align:start position:0%
+except the signs are slightly
+ 
+
+ align:start position:0%
+except the signs are slightly
+different okay so what we do is we flip
+
+ align:start position:0%
+different okay so what we do is we flip
+ 
+
+ align:start position:0%
+different okay so what we do is we flip
+signs according to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+checkerboard diagram
+
+ align:start position:0%
+checkerboard diagram
+ 
+
+ align:start position:0%
+checkerboard diagram
+so you start with a plus in the upper
+
+ align:start position:0%
+so you start with a plus in the upper
+ 
+
+ align:start position:0%
+so you start with a plus in the upper
+left corner and you alternate pluses and
+
+ align:start position:0%
+left corner and you alternate pluses and
+ 
+
+ align:start position:0%
+left corner and you alternate pluses and
+minuses Okay so
+
+ align:start position:0%
+minuses Okay so
+ 
+
+ align:start position:0%
+minuses Okay so
+the rule is if there's a plus somewhere
+
+ align:start position:0%
+the rule is if there's a plus somewhere
+ 
+
+ align:start position:0%
+the rule is if there's a plus somewhere
+then there's a minus next to it and
+
+ align:start position:0%
+then there's a minus next to it and
+ 
+
+ align:start position:0%
+then there's a minus next to it and
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+it and then below a minus or to the
+
+ align:start position:0%
+it and then below a minus or to the
+ 
+
+ align:start position:0%
+it and then below a minus or to the
+right of a minus there's a plus okay so
+
+ align:start position:0%
+right of a minus there's a plus okay so
+ 
+
+ align:start position:0%
+right of a minus there's a plus okay so
+that's what it looks in size
+
+ align:start position:0%
+that's what it looks in size
+ 
+
+ align:start position:0%
+that's what it looks in size
+3x3 um so what do I mean by that so I
+
+ align:start position:0%
+3x3 um so what do I mean by that so I
+ 
+
+ align:start position:0%
+3x3 um so what do I mean by that so I
+don't mean you know make this positive
+
+ align:start position:0%
+don't mean you know make this positive
+ 
+
+ align:start position:0%
+don't mean you know make this positive
+make this negative and so on that's not
+
+ align:start position:0%
+make this negative and so on that's not
+ 
+
+ align:start position:0%
+make this negative and so on that's not
+what I mean what I mean is if there's a
+
+ align:start position:0%
+what I mean what I mean is if there's a
+ 
+
+ align:start position:0%
+what I mean what I mean is if there's a
+plus that means leave it alone okay we
+
+ align:start position:0%
+plus that means leave it alone okay we
+ 
+
+ align:start position:0%
+plus that means leave it alone okay we
+don't do anything to it if there's a
+
+ align:start position:0%
+don't do anything to it if there's a
+ 
+
+ align:start position:0%
+don't do anything to it if there's a
+minus that means we flip the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign okay so here we get well three
+
+ align:start position:0%
+sign okay so here we get well three
+ 
+
+ align:start position:0%
+sign okay so here we get well three
+then 1 minus
+
+ align:start position:0%
+then 1 minus
+ 
+
+ align:start position:0%
+then 1 minus
+2us 3 1 +
+
+ align:start position:0%
+2us 3 1 +
+ 
+
+ align:start position:0%
+2us 3 1 +
+1be I'll put pluses just to emphasize 3
+
+ align:start position:0%
+1be I'll put pluses just to emphasize 3
+ 
+
+ align:start position:0%
+1be I'll put pluses just to emphasize 3
+- 4 and
+
+ align:start position:0%
+- 4 and
+ 
+
+ align:start position:0%
+- 4 and
+two okay let's St is pretty easy I mean
+
+ align:start position:0%
+two okay let's St is pretty easy I mean
+ 
+
+ align:start position:0%
+two okay let's St is pretty easy I mean
+the only hard step in terms of
+
+ align:start position:0%
+the only hard step in terms of
+ 
+
+ align:start position:0%
+the only hard step in terms of
+calculations is this one because you
+
+ align:start position:0%
+calculations is this one because you
+ 
+
+ align:start position:0%
+calculations is this one because you
+have to compute all of these 2x two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinants by the way I mean this
+
+ align:start position:0%
+determinants by the way I mean this
+ 
+
+ align:start position:0%
+determinants by the way I mean this
+minus sign here see it's actually very
+
+ align:start position:0%
+minus sign here see it's actually very
+ 
+
+ align:start position:0%
+minus sign here see it's actually very
+related to the way in which when we do a
+
+ align:start position:0%
+related to the way in which when we do a
+ 
+
+ align:start position:0%
+related to the way in which when we do a
+cross product we have a minus sign for
+
+ align:start position:0%
+cross product we have a minus sign for
+ 
+
+ align:start position:0%
+cross product we have a minus sign for
+the second
+
+ align:start position:0%
+the second
+ 
+
+ align:start position:0%
+the second
+entry okay we
+
+ align:start position:0%
+entry okay we
+ 
+
+ align:start position:0%
+entry okay we
+are almost done third step is to
+
+ align:start position:0%
+are almost done third step is to
+ 
+
+ align:start position:0%
+are almost done third step is to
+transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what does it mean to transpose it
+
+ align:start position:0%
+so what does it mean to transpose it
+ 
+
+ align:start position:0%
+so what does it mean to transpose it
+means you read the rows of your Matrix
+
+ align:start position:0%
+means you read the rows of your Matrix
+ 
+
+ align:start position:0%
+means you read the rows of your Matrix
+and you write that as columns or vice
+
+ align:start position:0%
+and you write that as columns or vice
+ 
+
+ align:start position:0%
+and you write that as columns or vice
+versa okay so let me just say we
+
+ align:start position:0%
+versa okay so let me just say we
+ 
+
+ align:start position:0%
+versa okay so let me just say we
+switch rows and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+columns so what do we get well let's
+
+ align:start position:0%
+columns so what do we get well let's
+ 
+
+ align:start position:0%
+columns so what do we get well let's
+just read it horizontally and write it
+
+ align:start position:0%
+just read it horizontally and write it
+ 
+
+ align:start position:0%
+just read it horizontally and write it
+vertically we read 3 1 - 2 3 1 - 2 then
+
+ align:start position:0%
+vertically we read 3 1 - 2 3 1 - 2 then
+ 
+
+ align:start position:0%
+vertically we read 3 1 - 2 3 1 - 2 then
+we read - 3 1 1
+
+ align:start position:0%
+we read - 3 1 1
+ 
+
+ align:start position:0%
+we read - 3 1 1
+- 3 1 1 then 3 - 4 2 3 - 4
+
+ align:start position:0%
+- 3 1 1 then 3 - 4 2 3 - 4
+ 
+
+ align:start position:0%
+- 3 1 1 then 3 - 4 2 3 - 4
+2 okay that's pretty
+
+ align:start position:0%
+2 okay that's pretty
+ 
+
+ align:start position:0%
+2 okay that's pretty
+easy and we're almost done the last step
+
+ align:start position:0%
+easy and we're almost done the last step
+ 
+
+ align:start position:0%
+easy and we're almost done the last step
+so what we get here is this is the
+
+ align:start position:0%
+so what we get here is this is the
+ 
+
+ align:start position:0%
+so what we get here is this is the
+adjoint
+
+ align:start position:0%
+adjoint
+ 
+
+ align:start position:0%
+adjoint
+Matrix so the fourth and last step is to
+
+ align:start position:0%
+Matrix so the fourth and last step is to
+ 
+
+ align:start position:0%
+Matrix so the fourth and last step is to
+divide by the determinant of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here we have to compute the
+
+ align:start position:0%
+okay so here we have to compute the
+ 
+
+ align:start position:0%
+okay so here we have to compute the
+determinant 2 3 three so we should say
+
+ align:start position:0%
+determinant 2 3 three so we should say
+ 
+
+ align:start position:0%
+determinant 2 3 three so we should say
+determinant of a okay not the
+
+ align:start position:0%
+determinant of a okay not the
+ 
+
+ align:start position:0%
+determinant of a okay not the
+determinant of this
+
+ align:start position:0%
+determinant of this
+ 
+
+ align:start position:0%
+determinant of this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+so 2 3 3 2 4 5 112 well I let you check
+
+ align:start position:0%
+so 2 3 3 2 4 5 112 well I let you check
+ 
+
+ align:start position:0%
+so 2 3 3 2 4 5 112 well I let you check
+my computation I found that it's equal
+
+ align:start position:0%
+my computation I found that it's equal
+ 
+
+ align:start position:0%
+my computation I found that it's equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+three okay so the final answer is that a
+
+ align:start position:0%
+three okay so the final answer is that a
+ 
+
+ align:start position:0%
+three okay so the final answer is that a
+inverse is 1/3 of The Matrix we got
+
+ align:start position:0%
+inverse is 1/3 of The Matrix we got
+ 
+
+ align:start position:0%
+inverse is 1/3 of The Matrix we got
+there 3 - 3 3 1 1 - 4 - 2 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay and now so that tells us
+
+ align:start position:0%
+two okay and now so that tells us
+ 
+
+ align:start position:0%
+two okay and now so that tells us
+remember a told us how to find the use
+
+ align:start position:0%
+remember a told us how to find the use
+ 
+
+ align:start position:0%
+remember a told us how to find the use
+in terms of the X's this one tells us
+
+ align:start position:0%
+in terms of the X's this one tells us
+ 
+
+ align:start position:0%
+in terms of the X's this one tells us
+now how to find the x's in terms of the
+
+ align:start position:0%
+now how to find the x's in terms of the
+ 
+
+ align:start position:0%
+now how to find the x's in terms of the
+use if you multiply U1 U2 u3 by this you
+
+ align:start position:0%
+use if you multiply U1 U2 u3 by this you
+ 
+
+ align:start position:0%
+use if you multiply U1 U2 u3 by this you
+get back X1 X2
+
+ align:start position:0%
+get back X1 X2
+ 
+
+ align:start position:0%
+get back X1 X2
+X3 it also tells you how to solve the
+
+ align:start position:0%
+X3 it also tells you how to solve the
+ 
+
+ align:start position:0%
+X3 it also tells you how to solve the
+linear system a * xal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something okay that's the end for today
\ No newline at end of file
diff --git a/c15RtHXBVuQ.txt b/c15RtHXBVuQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f3fd121dc4159e13cb5d5a6f8f5752a0da0668d
--- /dev/null
+++ b/c15RtHXBVuQ.txt
@@ -0,0 +1,1027 @@
+align:start position:0%
+ 
+let's consider examples of our principle
+
+ align:start position:0%
+let's consider examples of our principle
+ 
+
+ align:start position:0%
+let's consider examples of our principle
+that the external torque about a point
+
+ align:start position:0%
+that the external torque about a point
+ 
+
+ align:start position:0%
+that the external torque about a point
+as causes the angular momentum of a
+
+ align:start position:0%
+as causes the angular momentum of a
+ 
+
+ align:start position:0%
+as causes the angular momentum of a
+system to change about s we've examined
+
+ align:start position:0%
+system to change about s we've examined
+ 
+
+ align:start position:0%
+system to change about s we've examined
+central force problems in which we chose
+
+ align:start position:0%
+central force problems in which we chose
+ 
+
+ align:start position:0%
+central force problems in which we chose
+the point s to be the central point in
+
+ align:start position:0%
+the point s to be the central point in
+ 
+
+ align:start position:0%
+the point s to be the central point in
+which there was no torque now as
+
+ align:start position:0%
+which there was no torque now as
+ 
+
+ align:start position:0%
+which there was no torque now as
+examples let's look at a case where we
+
+ align:start position:0%
+examples let's look at a case where we
+ 
+
+ align:start position:0%
+examples let's look at a case where we
+have a pivoted object so I could take an
+
+ align:start position:0%
+have a pivoted object so I could take an
+ 
+
+ align:start position:0%
+have a pivoted object so I could take an
+example of a object let's see this will
+
+ align:start position:0%
+example of a object let's see this will
+ 
+
+ align:start position:0%
+example of a object let's see this will
+be an overhead view of a ring of radius
+
+ align:start position:0%
+be an overhead view of a ring of radius
+ 
+
+ align:start position:0%
+be an overhead view of a ring of radius
+R and I'm going to have a mass coming in
+
+ align:start position:0%
+R and I'm going to have a mass coming in
+ 
+
+ align:start position:0%
+R and I'm going to have a mass coming in
+I'll call this ring mass M 1 this object
+
+ align:start position:0%
+I'll call this ring mass M 1 this object
+ 
+
+ align:start position:0%
+I'll call this ring mass M 1 this object
+and to this object is coming in with an
+
+ align:start position:0%
+and to this object is coming in with an
+ 
+
+ align:start position:0%
+and to this object is coming in with an
+initial velocity and this is my pivot
+
+ align:start position:0%
+initial velocity and this is my pivot
+ 
+
+ align:start position:0%
+initial velocity and this is my pivot
+point now when the object m2 is hitting
+
+ align:start position:0%
+point now when the object m2 is hitting
+ 
+
+ align:start position:0%
+point now when the object m2 is hitting
+the ring we have a force f2 on one this
+
+ align:start position:0%
+the ring we have a force f2 on one this
+ 
+
+ align:start position:0%
+the ring we have a force f2 on one this
+is the collision here's our pivot point
+
+ align:start position:0%
+is the collision here's our pivot point
+ 
+
+ align:start position:0%
+is the collision here's our pivot point
+and when this hits the ring we'll have
+
+ align:start position:0%
+and when this hits the ring we'll have
+ 
+
+ align:start position:0%
+and when this hits the ring we'll have
+some type of pivot force I'm just going
+
+ align:start position:0%
+some type of pivot force I'm just going
+ 
+
+ align:start position:0%
+some type of pivot force I'm just going
+to denote the pivot force we're not
+
+ align:start position:0%
+to denote the pivot force we're not
+ 
+
+ align:start position:0%
+to denote the pivot force we're not
+quite sure what it will point out but
+
+ align:start position:0%
+quite sure what it will point out but
+ 
+
+ align:start position:0%
+quite sure what it will point out but
+I'll just say F pivot for the moment is
+
+ align:start position:0%
+I'll just say F pivot for the moment is
+ 
+
+ align:start position:0%
+I'll just say F pivot for the moment is
+holding this point in place at the same
+
+ align:start position:0%
+holding this point in place at the same
+ 
+
+ align:start position:0%
+holding this point in place at the same
+time the object will have a force f1 -
+
+ align:start position:0%
+time the object will have a force f1 -
+ 
+
+ align:start position:0%
+time the object will have a force f1 -
+acting on the object here's our pivot
+
+ align:start position:0%
+acting on the object here's our pivot
+ 
+
+ align:start position:0%
+acting on the object here's our pivot
+point P and now what point should we if
+
+ align:start position:0%
+point P and now what point should we if
+ 
+
+ align:start position:0%
+point P and now what point should we if
+we should we choose to see if there's no
+
+ align:start position:0%
+we should we choose to see if there's no
+ 
+
+ align:start position:0%
+we should we choose to see if there's no
+torque about suppose we choose
+
+ align:start position:0%
+torque about suppose we choose
+ 
+
+ align:start position:0%
+torque about suppose we choose
+the pivot point well Pete well clearly
+
+ align:start position:0%
+the pivot point well Pete well clearly
+ 
+
+ align:start position:0%
+the pivot point well Pete well clearly
+the pivot force has no torque about the
+
+ align:start position:0%
+the pivot force has no torque about the
+ 
+
+ align:start position:0%
+the pivot force has no torque about the
+pivot because the vector from the pivot
+
+ align:start position:0%
+pivot because the vector from the pivot
+ 
+
+ align:start position:0%
+pivot because the vector from the pivot
+point to where the pivot force is acting
+
+ align:start position:0%
+point to where the pivot force is acting
+ 
+
+ align:start position:0%
+point to where the pivot force is acting
+is zero
+
+ align:start position:0%
+is zero
+ 
+
+ align:start position:0%
+is zero
+remember pivot forces have no torque
+
+ align:start position:0%
+remember pivot forces have no torque
+ 
+
+ align:start position:0%
+remember pivot forces have no torque
+about the pivot point however this
+
+ align:start position:0%
+about the pivot point however this
+ 
+
+ align:start position:0%
+about the pivot point however this
+collision force will produce a torque
+
+ align:start position:0%
+collision force will produce a torque
+ 
+
+ align:start position:0%
+collision force will produce a torque
+about the pivot and that's the angular
+
+ align:start position:0%
+about the pivot and that's the angular
+ 
+
+ align:start position:0%
+about the pivot and that's the angular
+momentum of the Ring is not constant
+
+ align:start position:0%
+momentum of the Ring is not constant
+ 
+
+ align:start position:0%
+momentum of the Ring is not constant
+because the ring will start to rotate
+
+ align:start position:0%
+because the ring will start to rotate
+ 
+
+ align:start position:0%
+because the ring will start to rotate
+similarly this object is reversing to
+
+ align:start position:0%
+similarly this object is reversing to
+ 
+
+ align:start position:0%
+similarly this object is reversing to
+will reverse directions or will do
+
+ align:start position:0%
+will reverse directions or will do
+ 
+
+ align:start position:0%
+will reverse directions or will do
+something due to the collision and again
+
+ align:start position:0%
+something due to the collision and again
+ 
+
+ align:start position:0%
+something due to the collision and again
+this force will produce a torque that's
+
+ align:start position:0%
+this force will produce a torque that's
+ 
+
+ align:start position:0%
+this force will produce a torque that's
+equal and opposite to the torque on the
+
+ align:start position:0%
+equal and opposite to the torque on the
+ 
+
+ align:start position:0%
+equal and opposite to the torque on the
+ring this is the torque on the particle
+
+ align:start position:0%
+ring this is the torque on the particle
+ 
+
+ align:start position:0%
+ring this is the torque on the particle
+but if we make our system equal to the
+
+ align:start position:0%
+but if we make our system equal to the
+ 
+
+ align:start position:0%
+but if we make our system equal to the
+particle and the ring so we'll call this
+
+ align:start position:0%
+particle and the ring so we'll call this
+ 
+
+ align:start position:0%
+particle and the ring so we'll call this
+our system is now both the particle and
+
+ align:start position:0%
+our system is now both the particle and
+ 
+
+ align:start position:0%
+our system is now both the particle and
+the ring then these torques are internal
+
+ align:start position:0%
+the ring then these torques are internal
+ 
+
+ align:start position:0%
+the ring then these torques are internal
+and because they're equal and opposite
+
+ align:start position:0%
+and because they're equal and opposite
+ 
+
+ align:start position:0%
+and because they're equal and opposite
+forces the RS vector is exactly the same
+
+ align:start position:0%
+forces the RS vector is exactly the same
+ 
+
+ align:start position:0%
+forces the RS vector is exactly the same
+RS vector the internal torques cancel in
+
+ align:start position:0%
+RS vector the internal torques cancel in
+ 
+
+ align:start position:0%
+RS vector the internal torques cancel in
+pairs the pivot force produces no torque
+
+ align:start position:0%
+pairs the pivot force produces no torque
+ 
+
+ align:start position:0%
+pairs the pivot force produces no torque
+so the torque on the system about the
+
+ align:start position:0%
+so the torque on the system about the
+ 
+
+ align:start position:0%
+so the torque on the system about the
+pivot is zero and that tells us that the
+
+ align:start position:0%
+pivot is zero and that tells us that the
+ 
+
+ align:start position:0%
+pivot is zero and that tells us that the
+angular momentum of the system about
+
+ align:start position:0%
+angular momentum of the system about
+ 
+
+ align:start position:0%
+angular momentum of the system about
+that pivot point initially will be equal
+
+ align:start position:0%
+that pivot point initially will be equal
+ 
+
+ align:start position:0%
+that pivot point initially will be equal
+to the angular momentum about that pivot
+
+ align:start position:0%
+to the angular momentum about that pivot
+ 
+
+ align:start position:0%
+to the angular momentum about that pivot
+point finally if we take two initial and
+
+ align:start position:0%
+point finally if we take two initial and
+ 
+
+ align:start position:0%
+point finally if we take two initial and
+final States in particular suppose our
+
+ align:start position:0%
+final States in particular suppose our
+ 
+
+ align:start position:0%
+final States in particular suppose our
+initial state is here's the pivot our
+
+ align:start position:0%
+initial state is here's the pivot our
+ 
+
+ align:start position:0%
+initial state is here's the pivot our
+object is coming in that was M to be I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the moment arm is our and our vector
+
+ align:start position:0%
+the moment arm is our and our vector
+ 
+
+ align:start position:0%
+the moment arm is our and our vector
+from here to the object RS initial has a
+
+ align:start position:0%
+from here to the object RS initial has a
+ 
+
+ align:start position:0%
+from here to the object RS initial has a
+moment component that way if we put
+
+ align:start position:0%
+moment component that way if we put
+ 
+
+ align:start position:0%
+moment component that way if we put
+these vectors tail the tail and figure
+
+ align:start position:0%
+these vectors tail the tail and figure
+ 
+
+ align:start position:0%
+these vectors tail the tail and figure
+out that the angular momentum is
+
+ align:start position:0%
+out that the angular momentum is
+ 
+
+ align:start position:0%
+out that the angular momentum is
+pointing in this direction L initial I
+
+ align:start position:0%
+pointing in this direction L initial I
+ 
+
+ align:start position:0%
+pointing in this direction L initial I
+and the moment arm is R then the initial
+
+ align:start position:0%
+and the moment arm is R then the initial
+ 
+
+ align:start position:0%
+and the moment arm is R then the initial
+angular momentum about this pivot point
+
+ align:start position:0%
+angular momentum about this pivot point
+ 
+
+ align:start position:0%
+angular momentum about this pivot point
+is just due to this moving object so
+
+ align:start position:0%
+is just due to this moving object so
+ 
+
+ align:start position:0%
+is just due to this moving object so
+that's M to the I and the moment arm is
+
+ align:start position:0%
+that's M to the I and the moment arm is
+ 
+
+ align:start position:0%
+that's M to the I and the moment arm is
+R and we'll denote its direction that
+
+ align:start position:0%
+R and we'll denote its direction that
+ 
+
+ align:start position:0%
+R and we'll denote its direction that
+way now the final angular Mountain let's
+
+ align:start position:0%
+way now the final angular Mountain let's
+ 
+
+ align:start position:0%
+way now the final angular Mountain let's
+imagine that it sticks so we have M 2
+
+ align:start position:0%
+imagine that it sticks so we have M 2
+ 
+
+ align:start position:0%
+imagine that it sticks so we have M 2
+pivot and now our ring is going to be
+
+ align:start position:0%
+pivot and now our ring is going to be
+ 
+
+ align:start position:0%
+pivot and now our ring is going to be
+rotating with some Omega final because
+
+ align:start position:0%
+rotating with some Omega final because
+ 
+
+ align:start position:0%
+rotating with some Omega final because
+this object hits it and notice that this
+
+ align:start position:0%
+this object hits it and notice that this
+ 
+
+ align:start position:0%
+this object hits it and notice that this
+object is a distance root 2 R from the
+
+ align:start position:0%
+object is a distance root 2 R from the
+ 
+
+ align:start position:0%
+object is a distance root 2 R from the
+pivot point so the final angular
+
+ align:start position:0%
+pivot point so the final angular
+ 
+
+ align:start position:0%
+pivot point so the final angular
+momentum can be two different pieces you
+
+ align:start position:0%
+momentum can be two different pieces you
+ 
+
+ align:start position:0%
+momentum can be two different pieces you
+can think of this as a system where we
+
+ align:start position:0%
+can think of this as a system where we
+ 
+
+ align:start position:0%
+can think of this as a system where we
+have I of the system about P times Omega
+
+ align:start position:0%
+have I of the system about P times Omega
+ 
+
+ align:start position:0%
+have I of the system about P times Omega
+final because now it's just a rigid body
+
+ align:start position:0%
+final because now it's just a rigid body
+ 
+
+ align:start position:0%
+final because now it's just a rigid body
+and the angular momentum of the system
+
+ align:start position:0%
+and the angular momentum of the system
+ 
+
+ align:start position:0%
+and the angular momentum of the system
+is consisting of two pieces its the
+
+ align:start position:0%
+is consisting of two pieces its the
+ 
+
+ align:start position:0%
+is consisting of two pieces its the
+angular momentum of the ring about the
+
+ align:start position:0%
+angular momentum of the ring about the
+ 
+
+ align:start position:0%
+angular momentum of the ring about the
+pivot plus the angular momentum of the
+
+ align:start position:0%
+pivot plus the angular momentum of the
+ 
+
+ align:start position:0%
+pivot plus the angular momentum of the
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the pivot times Omega final now
+
+ align:start position:0%
+about the pivot times Omega final now
+ 
+
+ align:start position:0%
+about the pivot times Omega final now
+this is a center of mass this is the
+
+ align:start position:0%
+this is a center of mass this is the
+ 
+
+ align:start position:0%
+this is a center of mass this is the
+pivot point P the angular momentum of
+
+ align:start position:0%
+pivot point P the angular momentum of
+ 
+
+ align:start position:0%
+pivot point P the angular momentum of
+the Ring is the angular momentum about
+
+ align:start position:0%
+the Ring is the angular momentum about
+ 
+
+ align:start position:0%
+the Ring is the angular momentum about
+the center we'll use the parallel axis
+
+ align:start position:0%
+the center we'll use the parallel axis
+ 
+
+ align:start position:0%
+the center we'll use the parallel axis
+theorem angular momentum about the
+
+ align:start position:0%
+theorem angular momentum about the
+ 
+
+ align:start position:0%
+theorem angular momentum about the
+center of mass plus the distance from
+
+ align:start position:0%
+center of mass plus the distance from
+ 
+
+ align:start position:0%
+center of mass plus the distance from
+the center of mass to the parallel axis
+
+ align:start position:0%
+the center of mass to the parallel axis
+ 
+
+ align:start position:0%
+the center of mass to the parallel axis
+which is a distance R so the first piece
+
+ align:start position:0%
+which is a distance R so the first piece
+ 
+
+ align:start position:0%
+which is a distance R so the first piece
+is ICM ring plus M R squared and the
+
+ align:start position:0%
+is ICM ring plus M R squared and the
+ 
+
+ align:start position:0%
+is ICM ring plus M R squared and the
+angular mentioned about the particle
+
+ align:start position:0%
+angular mentioned about the particle
+ 
+
+ align:start position:0%
+angular mentioned about the particle
+this is going in a circle of radius R 2
+
+ align:start position:0%
+this is going in a circle of radius R 2
+ 
+
+ align:start position:0%
+this is going in a circle of radius R 2
+root 2 R so when we square that by the
+
+ align:start position:0%
+root 2 R so when we square that by the
+ 
+
+ align:start position:0%
+root 2 R so when we square that by the
+way this was mass of the ring was one
+
+ align:start position:0%
+way this was mass of the ring was one
+ 
+
+ align:start position:0%
+way this was mass of the ring was one
+mass of the particle was m2 times R
+
+ align:start position:0%
+mass of the particle was m2 times R
+ 
+
+ align:start position:0%
+mass of the particle was m2 times R
+squared which is this distance squared
+
+ align:start position:0%
+squared which is this distance squared
+ 
+
+ align:start position:0%
+squared which is this distance squared
+which is 2 R squared times will make a
+
+ align:start position:0%
+which is 2 R squared times will make a
+ 
+
+ align:start position:0%
+which is 2 R squared times will make a
+final the moment of inertia of the ring
+
+ align:start position:0%
+final the moment of inertia of the ring
+ 
+
+ align:start position:0%
+final the moment of inertia of the ring
+is M 1 R squared about the center of
+
+ align:start position:0%
+is M 1 R squared about the center of
+ 
+
+ align:start position:0%
+is M 1 R squared about the center of
+mass we have a factor 2 we have another
+
+ align:start position:0%
+mass we have a factor 2 we have another
+ 
+
+ align:start position:0%
+mass we have a factor 2 we have another
+factor of 2 and so we get M 1 plus M 2
+
+ align:start position:0%
+factor of 2 and so we get M 1 plus M 2
+ 
+
+ align:start position:0%
+factor of 2 and so we get M 1 plus M 2
+times a factor 2 R squared Omega final
+
+ align:start position:0%
+times a factor 2 R squared Omega final
+ 
+
+ align:start position:0%
+times a factor 2 R squared Omega final
+which we can call Omega F pointing out
+
+ align:start position:0%
+which we can call Omega F pointing out
+ 
+
+ align:start position:0%
+which we can call Omega F pointing out
+of the board and so now we have a
+
+ align:start position:0%
+of the board and so now we have a
+ 
+
+ align:start position:0%
+of the board and so now we have a
+angular momentum condition which is that
+
+ align:start position:0%
+angular momentum condition which is that
+ 
+
+ align:start position:0%
+angular momentum condition which is that
+M 2 VI R equals to M 1 plus M 2 R
+
+ align:start position:0%
+M 2 VI R equals to M 1 plus M 2 R
+ 
+
+ align:start position:0%
+M 2 VI R equals to M 1 plus M 2 R
+squared will make a final and that is a
+
+ align:start position:0%
+squared will make a final and that is a
+ 
+
+ align:start position:0%
+squared will make a final and that is a
+statement that the initial angular
+
+ align:start position:0%
+statement that the initial angular
+ 
+
+ align:start position:0%
+statement that the initial angular
+momentum of our system the ring is at
+
+ align:start position:0%
+momentum of our system the ring is at
+ 
+
+ align:start position:0%
+momentum of our system the ring is at
+rest here is equal to the final angular
+
+ align:start position:0%
+rest here is equal to the final angular
+ 
+
+ align:start position:0%
+rest here is equal to the final angular
+momentum of the system where M 2 is
+
+ align:start position:0%
+momentum of the system where M 2 is
+ 
+
+ align:start position:0%
+momentum of the system where M 2 is
+stuck to the ring and they're all
+
+ align:start position:0%
+stuck to the ring and they're all
+ 
+
+ align:start position:0%
+stuck to the ring and they're all
+rotating about this pivot point with
+
+ align:start position:0%
+rotating about this pivot point with
+ 
+
+ align:start position:0%
+rotating about this pivot point with
+omega final that's the angular momentum
+
+ align:start position:0%
+omega final that's the angular momentum
+ 
+
+ align:start position:0%
+omega final that's the angular momentum
+of the system about P will make a final
+
+ align:start position:0%
+of the system about P will make a final
+ 
+
+ align:start position:0%
+of the system about P will make a final
+this is the initial angular momentum and
+
+ align:start position:0%
+this is the initial angular momentum and
+ 
+
+ align:start position:0%
+this is the initial angular momentum and
+so I can conclude that Omega final is M
+
+ align:start position:0%
+so I can conclude that Omega final is M
+ 
+
+ align:start position:0%
+so I can conclude that Omega final is M
+2 VI over 2 m 1 plus M 2 times R
+
+ align:start position:0%
+2 VI over 2 m 1 plus M 2 times R
+ 
+
+ align:start position:0%
+2 VI over 2 m 1 plus M 2 times R
+you
\ No newline at end of file
diff --git a/cbSkFpO2jgQ.txt b/cbSkFpO2jgQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..40c4aa026ba16bcd48028226a01172e95039e6d1
--- /dev/null
+++ b/cbSkFpO2jgQ.txt
@@ -0,0 +1,2611 @@
+align:start position:0%
+ 
+hi welcome back to
+
+ align:start position:0%
+hi welcome back to
+ 
+
+ align:start position:0%
+hi welcome back to
+tation in lecture you've been learning
+
+ align:start position:0%
+tation in lecture you've been learning
+ 
+
+ align:start position:0%
+tation in lecture you've been learning
+about trip
+
+ align:start position:0%
+about trip
+ 
+
+ align:start position:0%
+about trip
+I have a nice average value problem for
+
+ align:start position:0%
+I have a nice average value problem for
+ 
+
+ align:start position:0%
+I have a nice average value problem for
+you using triple integration here so
+
+ align:start position:0%
+you using triple integration here so
+ 
+
+ align:start position:0%
+you using triple integration here so
+what I'd like you to do is to consider
+
+ align:start position:0%
+what I'd like you to do is to consider
+ 
+
+ align:start position:0%
+what I'd like you to do is to consider
+the tetrahedron that has vertices at the
+
+ align:start position:0%
+the tetrahedron that has vertices at the
+ 
+
+ align:start position:0%
+the tetrahedron that has vertices at the
+origin and at the points 1 0 0 0 1 0 and
+
+ align:start position:0%
+origin and at the points 1 0 0 0 1 0 and
+ 
+
+ align:start position:0%
+origin and at the points 1 0 0 0 1 0 and
+0 0 1 so that's one point on each of the
+
+ align:start position:0%
+0 0 1 so that's one point on each of the
+ 
+
+ align:start position:0%
+0 0 1 so that's one point on each of the
+positive axes at distance 1 from the
+
+ align:start position:0%
+positive axes at distance 1 from the
+ 
+
+ align:start position:0%
+positive axes at distance 1 from the
+origin so it's taking the liberty of
+
+ align:start position:0%
+origin so it's taking the liberty of
+ 
+
+ align:start position:0%
+origin so it's taking the liberty of
+drawing it here for you so consider that
+
+ align:start position:0%
+drawing it here for you so consider that
+ 
+
+ align:start position:0%
+drawing it here for you so consider that
+tetrahedron the solid tetrahedron and
+
+ align:start position:0%
+tetrahedron the solid tetrahedron and
+ 
+
+ align:start position:0%
+tetrahedron the solid tetrahedron and
+what I'd like you to do is find the
+
+ align:start position:0%
+what I'd like you to do is find the
+ 
+
+ align:start position:0%
+what I'd like you to do is find the
+average distance of the points in that
+
+ align:start position:0%
+average distance of the points in that
+ 
+
+ align:start position:0%
+average distance of the points in that
+tetrahedron from the XY plane all right
+
+ align:start position:0%
+tetrahedron from the XY plane all right
+ 
+
+ align:start position:0%
+tetrahedron from the XY plane all right
+so I'd like you to compute that the
+
+ align:start position:0%
+so I'd like you to compute that the
+ 
+
+ align:start position:0%
+so I'd like you to compute that the
+average value of the distance as the
+
+ align:start position:0%
+average value of the distance as the
+ 
+
+ align:start position:0%
+average value of the distance as the
+point ranges over the whole tetrahedron
+
+ align:start position:0%
+point ranges over the whole tetrahedron
+ 
+
+ align:start position:0%
+point ranges over the whole tetrahedron
+of of its of its distance from the XY
+
+ align:start position:0%
+of of its of its distance from the XY
+ 
+
+ align:start position:0%
+of of its of its distance from the XY
+plane so why don't you pause the video
+
+ align:start position:0%
+plane so why don't you pause the video
+ 
+
+ align:start position:0%
+plane so why don't you pause the video
+spend some time working that out come
+
+ align:start position:0%
+spend some time working that out come
+ 
+
+ align:start position:0%
+spend some time working that out come
+back and we can work it out together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully you had some luck with this
+
+ align:start position:0%
+hopefully you had some luck with this
+ 
+
+ align:start position:0%
+hopefully you had some luck with this
+problem let's get started so you know
+
+ align:start position:0%
+problem let's get started so you know
+ 
+
+ align:start position:0%
+problem let's get started so you know
+for an average value problem that that
+
+ align:start position:0%
+for an average value problem that that
+ 
+
+ align:start position:0%
+for an average value problem that that
+if you have a function f so the average
+
+ align:start position:0%
+if you have a function f so the average
+ 
+
+ align:start position:0%
+if you have a function f so the average
+value of a function f over a region R is
+
+ align:start position:0%
+value of a function f over a region R is
+ 
+
+ align:start position:0%
+value of a function f over a region R is
+going to be it's 1 over the volume of
+
+ align:start position:0%
+going to be it's 1 over the volume of
+ 
+
+ align:start position:0%
+going to be it's 1 over the volume of
+the region times the triple integral
+
+ align:start position:0%
+the region times the triple integral
+ 
+
+ align:start position:0%
+the region times the triple integral
+over your whole region R of the function
+
+ align:start position:0%
+over your whole region R of the function
+ 
+
+ align:start position:0%
+over your whole region R of the function
+value f of X Y C with respect to volume
+
+ align:start position:0%
+value f of X Y C with respect to volume
+ 
+
+ align:start position:0%
+value f of X Y C with respect to volume
+so you know in any order you want so I
+
+ align:start position:0%
+so you know in any order you want so I
+ 
+
+ align:start position:0%
+so you know in any order you want so I
+guess I'll write DV here and then you
+
+ align:start position:0%
+guess I'll write DV here and then you
+ 
+
+ align:start position:0%
+guess I'll write DV here and then you
+know to evaluate this you set it up as
+
+ align:start position:0%
+know to evaluate this you set it up as
+ 
+
+ align:start position:0%
+know to evaluate this you set it up as
+an iterated integral so in our case the
+
+ align:start position:0%
+an iterated integral so in our case the
+ 
+
+ align:start position:0%
+an iterated integral so in our case the
+function we're trying to find the
+
+ align:start position:0%
+function we're trying to find the
+ 
+
+ align:start position:0%
+function we're trying to find the
+average value of is the distance between
+
+ align:start position:0%
+average value of is the distance between
+ 
+
+ align:start position:0%
+average value of is the distance between
+a point and the XY plane but that's
+
+ align:start position:0%
+a point and the XY plane but that's
+ 
+
+ align:start position:0%
+a point and the XY plane but that's
+that's an easy function right that's
+
+ align:start position:0%
+that's an easy function right that's
+ 
+
+ align:start position:0%
+that's an easy function right that's
+just Z for any for any point in space
+
+ align:start position:0%
+just Z for any for any point in space
+ 
+
+ align:start position:0%
+just Z for any for any point in space
+it's its distance from the XY plane is
+
+ align:start position:0%
+it's its distance from the XY plane is
+ 
+
+ align:start position:0%
+it's its distance from the XY plane is
+just its height it's its Z value so the
+
+ align:start position:0%
+just its height it's its Z value so the
+ 
+
+ align:start position:0%
+just its height it's its Z value so the
+function that we're seeking to find the
+
+ align:start position:0%
+function that we're seeking to find the
+ 
+
+ align:start position:0%
+function that we're seeking to find the
+average value of is Z and so most of the
+
+ align:start position:0%
+average value of is Z and so most of the
+ 
+
+ align:start position:0%
+average value of is Z and so most of the
+work of this problem then is gonna be in
+
+ align:start position:0%
+work of this problem then is gonna be in
+ 
+
+ align:start position:0%
+work of this problem then is gonna be in
+figuring out what the bounds are and
+
+ align:start position:0%
+figuring out what the bounds are and
+ 
+
+ align:start position:0%
+figuring out what the bounds are and
+then doing the actual integral after
+
+ align:start position:0%
+then doing the actual integral after
+ 
+
+ align:start position:0%
+then doing the actual integral after
+that so ok so let's so let's think about
+
+ align:start position:0%
+that so ok so let's so let's think about
+ 
+
+ align:start position:0%
+that so ok so let's so let's think about
+the bounce now you can integrate this
+
+ align:start position:0%
+the bounce now you can integrate this
+ 
+
+ align:start position:0%
+the bounce now you can integrate this
+tetrahedron is a nice reasonably simple
+
+ align:start position:0%
+tetrahedron is a nice reasonably simple
+ 
+
+ align:start position:0%
+tetrahedron is a nice reasonably simple
+geometric thing object so in fact it
+
+ align:start position:0%
+geometric thing object so in fact it
+ 
+
+ align:start position:0%
+geometric thing object so in fact it
+doesn't matter too much which which
+
+ align:start position:0%
+doesn't matter too much which which
+ 
+
+ align:start position:0%
+doesn't matter too much which which
+order you take your bounds in so I think
+
+ align:start position:0%
+order you take your bounds in so I think
+ 
+
+ align:start position:0%
+order you take your bounds in so I think
+I'm gonna do it in the order DZ dy DX
+
+ align:start position:0%
+I'm gonna do it in the order DZ dy DX
+ 
+
+ align:start position:0%
+I'm gonna do it in the order DZ dy DX
+you know I'll do Z first and then Y in
+
+ align:start position:0%
+you know I'll do Z first and then Y in
+ 
+
+ align:start position:0%
+you know I'll do Z first and then Y in
+the next but it doesn't matter if you
+
+ align:start position:0%
+the next but it doesn't matter if you
+ 
+
+ align:start position:0%
+the next but it doesn't matter if you
+did a different way it'll probably work
+
+ align:start position:0%
+did a different way it'll probably work
+ 
+
+ align:start position:0%
+did a different way it'll probably work
+out very similar overall and and you'll
+
+ align:start position:0%
+out very similar overall and and you'll
+ 
+
+ align:start position:0%
+out very similar overall and and you'll
+you'll still be able to compare the
+
+ align:start position:0%
+you'll still be able to compare the
+ 
+
+ align:start position:0%
+you'll still be able to compare the
+overall process so let's so let's think
+
+ align:start position:0%
+overall process so let's so let's think
+ 
+
+ align:start position:0%
+overall process so let's so let's think
+about Z yeah so in this tetrahedron as
+
+ align:start position:0%
+about Z yeah so in this tetrahedron as
+ 
+
+ align:start position:0%
+about Z yeah so in this tetrahedron as
+as the so we want Z we want to integrate
+
+ align:start position:0%
+as the so we want Z we want to integrate
+ 
+
+ align:start position:0%
+as the so we want Z we want to integrate
+with respect to Z first so we look at
+
+ align:start position:0%
+with respect to Z first so we look at
+ 
+
+ align:start position:0%
+with respect to Z first so we look at
+this tetrahedron when we say ok at a
+
+ align:start position:0%
+this tetrahedron when we say ok at a
+ 
+
+ align:start position:0%
+this tetrahedron when we say ok at a
+point x and y you know when we choose
+
+ align:start position:0%
+point x and y you know when we choose
+ 
+
+ align:start position:0%
+point x and y you know when we choose
+the x and y values what's the sort of
+
+ align:start position:0%
+the x and y values what's the sort of
+ 
+
+ align:start position:0%
+the x and y values what's the sort of
+lowest surface what's the smallest value
+
+ align:start position:0%
+lowest surface what's the smallest value
+ 
+
+ align:start position:0%
+lowest surface what's the smallest value
+Z can take and what's the upper surface
+
+ align:start position:0%
+Z can take and what's the upper surface
+ 
+
+ align:start position:0%
+Z can take and what's the upper surface
+what's the largest value Z can take so
+
+ align:start position:0%
+what's the largest value Z can take so
+ 
+
+ align:start position:0%
+what's the largest value Z can take so
+the lowest surface here is the xy-plane
+
+ align:start position:0%
+the lowest surface here is the xy-plane
+ 
+
+ align:start position:0%
+the lowest surface here is the xy-plane
+that's the bottom face of this
+
+ align:start position:0%
+that's the bottom face of this
+ 
+
+ align:start position:0%
+that's the bottom face of this
+tetrahedron and for any point for any
+
+ align:start position:0%
+tetrahedron and for any point for any
+ 
+
+ align:start position:0%
+tetrahedron and for any point for any
+choice x and y the lowest values you can
+
+ align:start position:0%
+choice x and y the lowest values you can
+ 
+
+ align:start position:0%
+choice x and y the lowest values you can
+take is when it's when it's in the
+
+ align:start position:0%
+take is when it's when it's in the
+ 
+
+ align:start position:0%
+take is when it's when it's in the
+xy-plane so when it's equal to zero so
+
+ align:start position:0%
+xy-plane so when it's equal to zero so
+ 
+
+ align:start position:0%
+xy-plane so when it's equal to zero so
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+boundaries so this is gonna be equal so
+
+ align:start position:0%
+boundaries so this is gonna be equal so
+ 
+
+ align:start position:0%
+boundaries so this is gonna be equal so
+in our case so let's set this up it's
+
+ align:start position:0%
+in our case so let's set this up it's
+ 
+
+ align:start position:0%
+in our case so let's set this up it's
+gonna be an iterated integral the
+
+ align:start position:0%
+gonna be an iterated integral the
+ 
+
+ align:start position:0%
+gonna be an iterated integral the
+function we're integrating is Z and I
+
+ align:start position:0%
+function we're integrating is Z and I
+ 
+
+ align:start position:0%
+function we're integrating is Z and I
+said we'll do DZ dy DX and we just said
+
+ align:start position:0%
+said we'll do DZ dy DX and we just said
+ 
+
+ align:start position:0%
+said we'll do DZ dy DX and we just said
+that okay so the lowest value that Z
+
+ align:start position:0%
+that okay so the lowest value that Z
+ 
+
+ align:start position:0%
+that okay so the lowest value that Z
+takes the DZ is 0 so the up highest
+
+ align:start position:0%
+takes the DZ is 0 so the up highest
+ 
+
+ align:start position:0%
+takes the DZ is 0 so the up highest
+value that Z takes is when it hits this
+
+ align:start position:0%
+value that Z takes is when it hits this
+ 
+
+ align:start position:0%
+value that Z takes is when it hits this
+this top surface this plane that passes
+
+ align:start position:0%
+this top surface this plane that passes
+ 
+
+ align:start position:0%
+this top surface this plane that passes
+through the point 1 0 0 0 1 0 and 0 0 1
+
+ align:start position:0%
+through the point 1 0 0 0 1 0 and 0 0 1
+ 
+
+ align:start position:0%
+through the point 1 0 0 0 1 0 and 0 0 1
+all right so we need to know the
+
+ align:start position:0%
+all right so we need to know the
+ 
+
+ align:start position:0%
+all right so we need to know the
+equation of that plane luckily that's a
+
+ align:start position:0%
+equation of that plane luckily that's a
+ 
+
+ align:start position:0%
+equation of that plane luckily that's a
+pretty easy plane to write down the
+
+ align:start position:0%
+pretty easy plane to write down the
+ 
+
+ align:start position:0%
+pretty easy plane to write down the
+equation for so this slanted surface so
+
+ align:start position:0%
+equation for so this slanted surface so
+ 
+
+ align:start position:0%
+equation for so this slanted surface so
+this slanted plane passing through the
+
+ align:start position:0%
+this slanted plane passing through the
+ 
+
+ align:start position:0%
+this slanted plane passing through the
+the 3 vertices other than the origin is
+
+ align:start position:0%
+the 3 vertices other than the origin is
+ 
+
+ align:start position:0%
+the 3 vertices other than the origin is
+the plane X plus y plus Z equals 1 all
+
+ align:start position:0%
+the plane X plus y plus Z equals 1 all
+ 
+
+ align:start position:0%
+the plane X plus y plus Z equals 1 all
+right so it's a it's a nice easy plane
+
+ align:start position:0%
+right so it's a it's a nice easy plane
+ 
+
+ align:start position:0%
+right so it's a it's a nice easy plane
+to work with and so what we want to know
+
+ align:start position:0%
+to work with and so what we want to know
+ 
+
+ align:start position:0%
+to work with and so what we want to know
+is what's the value of Z on that plane
+
+ align:start position:0%
+is what's the value of Z on that plane
+ 
+
+ align:start position:0%
+is what's the value of Z on that plane
+and so okay so we we isolate Z on one
+
+ align:start position:0%
+and so okay so we we isolate Z on one
+ 
+
+ align:start position:0%
+and so okay so we we isolate Z on one
+side and we bring everything else over
+
+ align:start position:0%
+side and we bring everything else over
+ 
+
+ align:start position:0%
+side and we bring everything else over
+so we we have that that that top value
+
+ align:start position:0%
+so we we have that that that top value
+ 
+
+ align:start position:0%
+so we we have that that that top value
+of Z the largest value of Z that Z can
+
+ align:start position:0%
+of Z the largest value of Z that Z can
+ 
+
+ align:start position:0%
+of Z the largest value of Z that Z can
+take when x and y are fixed is 1 minus X
+
+ align:start position:0%
+take when x and y are fixed is 1 minus X
+ 
+
+ align:start position:0%
+take when x and y are fixed is 1 minus X
+minus y so that's what goes up here 1
+
+ align:start position:0%
+minus y so that's what goes up here 1
+ 
+
+ align:start position:0%
+minus y so that's what goes up here 1
+minus s minus y so that's the biggest
+
+ align:start position:0%
+minus s minus y so that's the biggest
+ 
+
+ align:start position:0%
+minus s minus y so that's the biggest
+values you can take ok good so now we
+
+ align:start position:0%
+values you can take ok good so now we
+ 
+
+ align:start position:0%
+values you can take ok good so now we
+need to figure out what the bounds on Y
+
+ align:start position:0%
+need to figure out what the bounds on Y
+ 
+
+ align:start position:0%
+need to figure out what the bounds on Y
+are in terms of X so what I like to do
+
+ align:start position:0%
+are in terms of X so what I like to do
+ 
+
+ align:start position:0%
+are in terms of X so what I like to do
+in this case is I like to draw a
+
+ align:start position:0%
+in this case is I like to draw a
+ 
+
+ align:start position:0%
+in this case is I like to draw a
+projection of your of your surface so
+
+ align:start position:0%
+projection of your of your surface so
+ 
+
+ align:start position:0%
+projection of your of your surface so
+then your in in a sort of
+
+ align:start position:0%
+then your in in a sort of
+ 
+
+ align:start position:0%
+then your in in a sort of
+two-dimensional world and then you can
+
+ align:start position:0%
+two-dimensional world and then you can
+ 
+
+ align:start position:0%
+two-dimensional world and then you can
+look at that image more easily so so
+
+ align:start position:0%
+look at that image more easily so so
+ 
+
+ align:start position:0%
+look at that image more easily so so
+what we're gonna do is we're gonna look
+
+ align:start position:0%
+what we're gonna do is we're gonna look
+ 
+
+ align:start position:0%
+what we're gonna do is we're gonna look
+at this tetrahedron and we're gonna
+
+ align:start position:0%
+at this tetrahedron and we're gonna
+ 
+
+ align:start position:0%
+at this tetrahedron and we're gonna
+imagine projecting it down into the XY
+
+ align:start position:0%
+imagine projecting it down into the XY
+ 
+
+ align:start position:0%
+imagine projecting it down into the XY
+plane so for every point in the
+
+ align:start position:0%
+plane so for every point in the
+ 
+
+ align:start position:0%
+plane so for every point in the
+tetrahedron we're gonna draw a dot below
+
+ align:start position:0%
+tetrahedron we're gonna draw a dot below
+ 
+
+ align:start position:0%
+tetrahedron we're gonna draw a dot below
+it in the XY plane we're gonna look at
+
+ align:start position:0%
+it in the XY plane we're gonna look at
+ 
+
+ align:start position:0%
+it in the XY plane we're gonna look at
+that set of dots so that what that's
+
+ align:start position:0%
+that set of dots so that what that's
+ 
+
+ align:start position:0%
+that set of dots so that what that's
+going to give us is this this in this
+
+ align:start position:0%
+going to give us is this this in this
+ 
+
+ align:start position:0%
+going to give us is this this in this
+case it's gonna give us this bottom face
+
+ align:start position:0%
+case it's gonna give us this bottom face
+ 
+
+ align:start position:0%
+case it's gonna give us this bottom face
+of the tetrahedron every point of the
+
+ align:start position:0%
+of the tetrahedron every point of the
+ 
+
+ align:start position:0%
+of the tetrahedron every point of the
+tetrahedron is above its bottom face
+
+ align:start position:0%
+tetrahedron is above its bottom face
+ 
+
+ align:start position:0%
+tetrahedron is above its bottom face
+that's not true for every tetrahedron
+
+ align:start position:0%
+that's not true for every tetrahedron
+ 
+
+ align:start position:0%
+that's not true for every tetrahedron
+but it's true for this one so the region
+
+ align:start position:0%
+but it's true for this one so the region
+ 
+
+ align:start position:0%
+but it's true for this one so the region
+that we're interested in is that bottom
+
+ align:start position:0%
+that we're interested in is that bottom
+ 
+
+ align:start position:0%
+that we're interested in is that bottom
+face so I'm gonna draw another picture
+
+ align:start position:0%
+face so I'm gonna draw another picture
+ 
+
+ align:start position:0%
+face so I'm gonna draw another picture
+of it over over on my left here so that
+
+ align:start position:0%
+of it over over on my left here so that
+ 
+
+ align:start position:0%
+of it over over on my left here so that
+region is the region that has vertices 0
+
+ align:start position:0%
+region is the region that has vertices 0
+ 
+
+ align:start position:0%
+region is the region that has vertices 0
+0 & 1 0 0
+
+ align:start position:0%
+0 & 1 0 0
+ 
+
+ align:start position:0%
+0 & 1 0 0
+and sorry 0 0 1 0 & 0 1 so it's this
+
+ align:start position:0%
+and sorry 0 0 1 0 & 0 1 so it's this
+ 
+
+ align:start position:0%
+and sorry 0 0 1 0 & 0 1 so it's this
+triangle and this bottom edge of the
+
+ align:start position:0%
+triangle and this bottom edge of the
+ 
+
+ align:start position:0%
+triangle and this bottom edge of the
+triangle is the line y equals 0 this
+
+ align:start position:0%
+triangle is the line y equals 0 this
+ 
+
+ align:start position:0%
+triangle is the line y equals 0 this
+left edge is the line x equals 0 and
+
+ align:start position:0%
+left edge is the line x equals 0 and
+ 
+
+ align:start position:0%
+left edge is the line x equals 0 and
+this slanted line is the line x plus y
+
+ align:start position:0%
+this slanted line is the line x plus y
+ 
+
+ align:start position:0%
+this slanted line is the line x plus y
+equals 1 ok so this is that this is that
+
+ align:start position:0%
+equals 1 ok so this is that this is that
+ 
+
+ align:start position:0%
+equals 1 ok so this is that this is that
+same bottom face that we just drew but
+
+ align:start position:0%
+same bottom face that we just drew but
+ 
+
+ align:start position:0%
+same bottom face that we just drew but
+now I've you know I've changed my axes
+
+ align:start position:0%
+now I've you know I've changed my axes
+ 
+
+ align:start position:0%
+now I've you know I've changed my axes
+to our usual 2-dimensional Direction xn
+
+ align:start position:0%
+to our usual 2-dimensional Direction xn
+ 
+
+ align:start position:0%
+to our usual 2-dimensional Direction xn
+with X to the right and Y up okay so we
+
+ align:start position:0%
+with X to the right and Y up okay so we
+ 
+
+ align:start position:0%
+with X to the right and Y up okay so we
+need to figure out now so we're doing dy
+
+ align:start position:0%
+need to figure out now so we're doing dy
+ 
+
+ align:start position:0%
+need to figure out now so we're doing dy
+next so we need to figure out for a
+
+ align:start position:0%
+next so we need to figure out for a
+ 
+
+ align:start position:0%
+next so we need to figure out for a
+fixed value of x what are the bounds on
+
+ align:start position:0%
+fixed value of x what are the bounds on
+ 
+
+ align:start position:0%
+fixed value of x what are the bounds on
+Y and so okay so we see from this
+
+ align:start position:0%
+Y and so okay so we see from this
+ 
+
+ align:start position:0%
+Y and so okay so we see from this
+picture that for any for any fixed value
+
+ align:start position:0%
+picture that for any for any fixed value
+ 
+
+ align:start position:0%
+picture that for any for any fixed value
+of x Y goes from 0 this the x-axis up to
+
+ align:start position:0%
+of x Y goes from 0 this the x-axis up to
+ 
+
+ align:start position:0%
+of x Y goes from 0 this the x-axis up to
+this line okay so on the x-axis Y takes
+
+ align:start position:0%
+this line okay so on the x-axis Y takes
+ 
+
+ align:start position:0%
+this line okay so on the x-axis Y takes
+the value 0 and on this line Y takes the
+
+ align:start position:0%
+the value 0 and on this line Y takes the
+ 
+
+ align:start position:0%
+the value 0 and on this line Y takes the
+value 1 minus X finally our our
+
+ align:start position:0%
+value 1 minus X finally our our
+ 
+
+ align:start position:0%
+value 1 minus X finally our our
+outermost variable of integration is X
+
+ align:start position:0%
+outermost variable of integration is X
+ 
+
+ align:start position:0%
+outermost variable of integration is X
+and so we need to know what are the
+
+ align:start position:0%
+and so we need to know what are the
+ 
+
+ align:start position:0%
+and so we need to know what are the
+absolute largest and smallest values
+
+ align:start position:0%
+absolute largest and smallest values
+ 
+
+ align:start position:0%
+absolute largest and smallest values
+that X take that X takes so we okay so
+
+ align:start position:0%
+that X take that X takes so we okay so
+ 
+
+ align:start position:0%
+that X take that X takes so we okay so
+we can do that looking either at this
+
+ align:start position:0%
+we can do that looking either at this
+ 
+
+ align:start position:0%
+we can do that looking either at this
+picture or looking at our original
+
+ align:start position:0%
+picture or looking at our original
+ 
+
+ align:start position:0%
+picture or looking at our original
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+either way it's it's not hard to see
+
+ align:start position:0%
+either way it's it's not hard to see
+ 
+
+ align:start position:0%
+either way it's it's not hard to see
+that X just goes between 0 & 1 the
+
+ align:start position:0%
+that X just goes between 0 & 1 the
+ 
+
+ align:start position:0%
+that X just goes between 0 & 1 the
+smallest value that X takes in this
+
+ align:start position:0%
+smallest value that X takes in this
+ 
+
+ align:start position:0%
+smallest value that X takes in this
+tetrahedron is 0 the largest value it
+
+ align:start position:0%
+tetrahedron is 0 the largest value it
+ 
+
+ align:start position:0%
+tetrahedron is 0 the largest value it
+takes is 1 so that's our integral that
+
+ align:start position:0%
+takes is 1 so that's our integral that
+ 
+
+ align:start position:0%
+takes is 1 so that's our integral that
+we have to compute so that's not that
+
+ align:start position:0%
+we have to compute so that's not that
+ 
+
+ align:start position:0%
+we have to compute so that's not that
+bad at all so now you have to go through
+
+ align:start position:0%
+bad at all so now you have to go through
+ 
+
+ align:start position:0%
+bad at all so now you have to go through
+and you have to actually integrate this
+
+ align:start position:0%
+and you have to actually integrate this
+ 
+
+ align:start position:0%
+and you have to actually integrate this
+yeah and so I'm gonna you know look at
+
+ align:start position:0%
+yeah and so I'm gonna you know look at
+ 
+
+ align:start position:0%
+yeah and so I'm gonna you know look at
+my notes just to make sure I don't make
+
+ align:start position:0%
+my notes just to make sure I don't make
+ 
+
+ align:start position:0%
+my notes just to make sure I don't make
+any big arithmetic mistakes so let's see
+
+ align:start position:0%
+any big arithmetic mistakes so let's see
+ 
+
+ align:start position:0%
+any big arithmetic mistakes so let's see
+so we've got so we now we do these one
+
+ align:start position:0%
+so we've got so we now we do these one
+ 
+
+ align:start position:0%
+so we've got so we now we do these one
+at a time so this innermost integral is
+
+ align:start position:0%
+at a time so this innermost integral is
+ 
+
+ align:start position:0%
+at a time so this innermost integral is
+an integral of zdz ok well that's easy
+
+ align:start position:0%
+an integral of zdz ok well that's easy
+ 
+
+ align:start position:0%
+an integral of zdz ok well that's easy
+that's Z squared over 2 and then we're
+
+ align:start position:0%
+that's Z squared over 2 and then we're
+ 
+
+ align:start position:0%
+that's Z squared over 2 and then we're
+taking Z squared over 2 between 0 & 1
+
+ align:start position:0%
+taking Z squared over 2 between 0 & 1
+ 
+
+ align:start position:0%
+taking Z squared over 2 between 0 & 1
+minus X minus y so this innermost
+
+ align:start position:0%
+minus X minus y so this innermost
+ 
+
+ align:start position:0%
+minus X minus y so this innermost
+integral is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z squared over 2 between 0 & 1 minus X
+
+ align:start position:0%
+Z squared over 2 between 0 & 1 minus X
+ 
+
+ align:start position:0%
+Z squared over 2 between 0 & 1 minus X
+minus y so that's equal to so the
+
+ align:start position:0%
+minus y so that's equal to so the
+ 
+
+ align:start position:0%
+minus y so that's equal to so the
+innermost integral gives us 1 minus X
+
+ align:start position:0%
+innermost integral gives us 1 minus X
+ 
+
+ align:start position:0%
+innermost integral gives us 1 minus X
+minus y squared over 2 so that's what we
+
+ align:start position:0%
+minus y squared over 2 so that's what we
+ 
+
+ align:start position:0%
+minus y squared over 2 so that's what we
+get for the innermost integral so our
+
+ align:start position:0%
+get for the innermost integral so our
+ 
+
+ align:start position:0%
+get for the innermost integral so our
+integral that we're looking at then is
+
+ align:start position:0%
+integral that we're looking at then is
+ 
+
+ align:start position:0%
+integral that we're looking at then is
+equal to well it's the integral as X
+
+ align:start position:0%
+equal to well it's the integral as X
+ 
+
+ align:start position:0%
+equal to well it's the integral as X
+goes from 0 to 1 of the integral as Y
+
+ align:start position:0%
+goes from 0 to 1 of the integral as Y
+ 
+
+ align:start position:0%
+goes from 0 to 1 of the integral as Y
+goes from 0 to 1 minus X of this
+
+ align:start position:0%
+goes from 0 to 1 minus X of this
+ 
+
+ align:start position:0%
+goes from 0 to 1 minus X of this
+integrand so this was the inner one let
+
+ align:start position:0%
+integrand so this was the inner one let
+ 
+
+ align:start position:0%
+integrand so this was the inner one let
+me write that inner that's what I've got
+
+ align:start position:0%
+me write that inner that's what I've got
+ 
+
+ align:start position:0%
+me write that inner that's what I've got
+here just integrating Z with respect to
+
+ align:start position:0%
+here just integrating Z with respect to
+ 
+
+ align:start position:0%
+here just integrating Z with respect to
+Z gives me Z squared over 2 and then I
+
+ align:start position:0%
+Z gives me Z squared over 2 and then I
+ 
+
+ align:start position:0%
+Z gives me Z squared over 2 and then I
+evaluated at the bounds of the integral
+
+ align:start position:0%
+evaluated at the bounds of the integral
+ 
+
+ align:start position:0%
+evaluated at the bounds of the integral
+ok so now I need to do the middle one so
+
+ align:start position:0%
+ok so now I need to do the middle one so
+ 
+
+ align:start position:0%
+ok so now I need to do the middle one so
+let's do that up here so I need to
+
+ align:start position:0%
+let's do that up here so I need to
+ 
+
+ align:start position:0%
+let's do that up here so I need to
+compute so this is the middle integral
+
+ align:start position:0%
+compute so this is the middle integral
+ 
+
+ align:start position:0%
+compute so this is the middle integral
+so I need to compute the integral so now
+
+ align:start position:0%
+so I need to compute the integral so now
+ 
+
+ align:start position:0%
+so I need to compute the integral so now
+I take the bounds so the middle one is y
+
+ align:start position:0%
+I take the bounds so the middle one is y
+ 
+
+ align:start position:0%
+I take the bounds so the middle one is y
+and the bounds are from 0 to 1 minus x 0
+
+ align:start position:0%
+and the bounds are from 0 to 1 minus x 0
+ 
+
+ align:start position:0%
+and the bounds are from 0 to 1 minus x 0
+to 1 minus x of the inner integrand so
+
+ align:start position:0%
+to 1 minus x of the inner integrand so
+ 
+
+ align:start position:0%
+to 1 minus x of the inner integrand so
+this thing that I just the inner
+
+ align:start position:0%
+this thing that I just the inner
+ 
+
+ align:start position:0%
+this thing that I just the inner
+integral this thing that I just computed
+
+ align:start position:0%
+integral this thing that I just computed
+ 
+
+ align:start position:0%
+integral this thing that I just computed
+so that's of 1 minus X minus y squared
+
+ align:start position:0%
+so that's of 1 minus X minus y squared
+ 
+
+ align:start position:0%
+so that's of 1 minus X minus y squared
+over 2 dy okay
+
+ align:start position:0%
+over 2 dy okay
+ 
+
+ align:start position:0%
+over 2 dy okay
+so all right so this isn't that bad this
+
+ align:start position:0%
+so all right so this isn't that bad this
+ 
+
+ align:start position:0%
+so all right so this isn't that bad this
+is a quadratic polynomial in Y and so
+
+ align:start position:0%
+is a quadratic polynomial in Y and so
+ 
+
+ align:start position:0%
+is a quadratic polynomial in Y and so
+it's not terribly hard to see I'm sort
+
+ align:start position:0%
+it's not terribly hard to see I'm sort
+ 
+
+ align:start position:0%
+it's not terribly hard to see I'm sort
+of running out a little bit out of board
+
+ align:start position:0%
+of running out a little bit out of board
+ 
+
+ align:start position:0%
+of running out a little bit out of board
+space so I'm not gonna you know give you
+
+ align:start position:0%
+space so I'm not gonna you know give you
+ 
+
+ align:start position:0%
+space so I'm not gonna you know give you
+a full detailed explanation but it's not
+
+ align:start position:0%
+a full detailed explanation but it's not
+ 
+
+ align:start position:0%
+a full detailed explanation but it's not
+hard to see I think that that this
+
+ align:start position:0%
+hard to see I think that that this
+ 
+
+ align:start position:0%
+hard to see I think that that this
+integral is that the integral of 1 minus
+
+ align:start position:0%
+integral is that the integral of 1 minus
+ 
+
+ align:start position:0%
+integral is that the integral of 1 minus
+X minus y squared over 2 is 1 minus X
+
+ align:start position:0%
+X minus y squared over 2 is 1 minus X
+ 
+
+ align:start position:0%
+X minus y squared over 2 is 1 minus X
+minus y with respect to Y of course of
+
+ align:start position:0%
+minus y with respect to Y of course of
+ 
+
+ align:start position:0%
+minus y with respect to Y of course of
+is 1 minus X minus y cubed over 3 but
+
+ align:start position:0%
+is 1 minus X minus y cubed over 3 but
+ 
+
+ align:start position:0%
+is 1 minus X minus y cubed over 3 but
+it's negative because the sign here is
+
+ align:start position:0%
+it's negative because the sign here is
+ 
+
+ align:start position:0%
+it's negative because the sign here is
+negative and you could check by
+
+ align:start position:0%
+negative and you could check by
+ 
+
+ align:start position:0%
+negative and you could check by
+differentiating this and seeing that you
+
+ align:start position:0%
+differentiating this and seeing that you
+ 
+
+ align:start position:0%
+differentiating this and seeing that you
+get that and okay so we have to evaluate
+
+ align:start position:0%
+get that and okay so we have to evaluate
+ 
+
+ align:start position:0%
+get that and okay so we have to evaluate
+that as Y goes from 0 to 1 minus X so
+
+ align:start position:0%
+that as Y goes from 0 to 1 minus X so
+ 
+
+ align:start position:0%
+that as Y goes from 0 to 1 minus X so
+what do we get
+
+ align:start position:0%
+what do we get
+ 
+
+ align:start position:0%
+what do we get
+well when Y is equal to 1 minus X this
+
+ align:start position:0%
+well when Y is equal to 1 minus X this
+ 
+
+ align:start position:0%
+well when Y is equal to 1 minus X this
+is 0
+
+ align:start position:0%
+is 0
+ 
+
+ align:start position:0%
+is 0
+so we get zero minus and when Y is equal
+
+ align:start position:0%
+so we get zero minus and when Y is equal
+ 
+
+ align:start position:0%
+so we get zero minus and when Y is equal
+to zero this is minus 1 minus X quantity
+
+ align:start position:0%
+to zero this is minus 1 minus X quantity
+ 
+
+ align:start position:0%
+to zero this is minus 1 minus X quantity
+cubed over 6 so this is so it's minus -1
+
+ align:start position:0%
+cubed over 6 so this is so it's minus -1
+ 
+
+ align:start position:0%
+cubed over 6 so this is so it's minus -1
+minus X cubed over 6 so that's just 1
+
+ align:start position:0%
+minus X cubed over 6 so that's just 1
+ 
+
+ align:start position:0%
+minus X cubed over 6 so that's just 1
+minus X cubed over 6 and so finally the
+
+ align:start position:0%
+minus X cubed over 6 and so finally the
+ 
+
+ align:start position:0%
+minus X cubed over 6 and so finally the
+outer integral outermost integral is we
+
+ align:start position:0%
+outer integral outermost integral is we
+ 
+
+ align:start position:0%
+outer integral outermost integral is we
+you know take the inner two integrals
+
+ align:start position:0%
+you know take the inner two integrals
+ 
+
+ align:start position:0%
+you know take the inner two integrals
+and we integrate them with respect to X
+
+ align:start position:0%
+and we integrate them with respect to X
+ 
+
+ align:start position:0%
+and we integrate them with respect to X
+as X goes from zero to one so it's the
+
+ align:start position:0%
+as X goes from zero to one so it's the
+ 
+
+ align:start position:0%
+as X goes from zero to one so it's the
+integral from 0 to 1 of 1 minus X cubed
+
+ align:start position:0%
+integral from 0 to 1 of 1 minus X cubed
+ 
+
+ align:start position:0%
+integral from 0 to 1 of 1 minus X cubed
+over 6 DX and that's gonna equal alright
+
+ align:start position:0%
+over 6 DX and that's gonna equal alright
+ 
+
+ align:start position:0%
+over 6 DX and that's gonna equal alright
+I've run out of space so that integral
+
+ align:start position:0%
+I've run out of space so that integral
+ 
+
+ align:start position:0%
+I've run out of space so that integral
+is 1 over 24 all right except I've done
+
+ align:start position:0%
+is 1 over 24 all right except I've done
+ 
+
+ align:start position:0%
+is 1 over 24 all right except I've done
+something wrong right at the beginning I
+
+ align:start position:0%
+something wrong right at the beginning I
+ 
+
+ align:start position:0%
+something wrong right at the beginning I
+hope you all caught me right I had this
+
+ align:start position:0%
+hope you all caught me right I had this
+ 
+
+ align:start position:0%
+hope you all caught me right I had this
+one over V factor here and it
+
+ align:start position:0%
+one over V factor here and it
+ 
+
+ align:start position:0%
+one over V factor here and it
+disappeared right I forgot about this 1
+
+ align:start position:0%
+disappeared right I forgot about this 1
+ 
+
+ align:start position:0%
+disappeared right I forgot about this 1
+over V so over here I should have
+
+ align:start position:0%
+over V so over here I should have
+ 
+
+ align:start position:0%
+over V so over here I should have
+written a 1 over V right in front of
+
+ align:start position:0%
+written a 1 over V right in front of
+ 
+
+ align:start position:0%
+written a 1 over V right in front of
+that integral and so what that means is
+
+ align:start position:0%
+that integral and so what that means is
+ 
+
+ align:start position:0%
+that integral and so what that means is
+that 1 over 24 so okay so I've computed
+
+ align:start position:0%
+that 1 over 24 so okay so I've computed
+ 
+
+ align:start position:0%
+that 1 over 24 so okay so I've computed
+correctly computed 1 over 24 as the
+
+ align:start position:0%
+correctly computed 1 over 24 as the
+ 
+
+ align:start position:0%
+correctly computed 1 over 24 as the
+value of my triple integral but the
+
+ align:start position:0%
+value of my triple integral but the
+ 
+
+ align:start position:0%
+value of my triple integral but the
+average height here isn't 1 over 24 it's
+
+ align:start position:0%
+average height here isn't 1 over 24 it's
+ 
+
+ align:start position:0%
+average height here isn't 1 over 24 it's
+1 over 24 V alright so so the average
+
+ align:start position:0%
+1 over 24 V alright so so the average
+ 
+
+ align:start position:0%
+1 over 24 V alright so so the average
+height is 1 over 24 V so we need to go
+
+ align:start position:0%
+height is 1 over 24 V so we need to go
+ 
+
+ align:start position:0%
+height is 1 over 24 V so we need to go
+and we need to look at our tetrahedron
+
+ align:start position:0%
+and we need to look at our tetrahedron
+ 
+
+ align:start position:0%
+and we need to look at our tetrahedron
+and figure out what its volume is so if
+
+ align:start position:0%
+and figure out what its volume is so if
+ 
+
+ align:start position:0%
+and figure out what its volume is so if
+we come over here see our tetrahedron
+
+ align:start position:0%
+we come over here see our tetrahedron
+ 
+
+ align:start position:0%
+we come over here see our tetrahedron
+now this is a nice simple tetrahedron
+
+ align:start position:0%
+now this is a nice simple tetrahedron
+ 
+
+ align:start position:0%
+now this is a nice simple tetrahedron
+volume of a tetrahedron is 1/2 know 1/3
+
+ align:start position:0%
+volume of a tetrahedron is 1/2 know 1/3
+ 
+
+ align:start position:0%
+volume of a tetrahedron is 1/2 know 1/3
+the area of the base times the height
+
+ align:start position:0%
+the area of the base times the height
+ 
+
+ align:start position:0%
+the area of the base times the height
+right so this is a nice easy tetrahedron
+
+ align:start position:0%
+right so this is a nice easy tetrahedron
+ 
+
+ align:start position:0%
+right so this is a nice easy tetrahedron
+its height is 1 its base is a right
+
+ align:start position:0%
+its height is 1 its base is a right
+ 
+
+ align:start position:0%
+its height is 1 its base is a right
+triangle whose legs are both 1 so the
+
+ align:start position:0%
+triangle whose legs are both 1 so the
+ 
+
+ align:start position:0%
+triangle whose legs are both 1 so the
+base area is 1/2 so the volume is 1/6
+
+ align:start position:0%
+base area is 1/2 so the volume is 1/6
+ 
+
+ align:start position:0%
+base area is 1/2 so the volume is 1/6
+all right so if the volume is 1/6 we
+
+ align:start position:0%
+all right so if the volume is 1/6 we
+ 
+
+ align:start position:0%
+all right so if the volume is 1/6 we
+said the average value is 1 over 24 V so
+
+ align:start position:0%
+said the average value is 1 over 24 V so
+ 
+
+ align:start position:0%
+said the average value is 1 over 24 V so
+that works out to 1 over 4 so let me
+
+ align:start position:0%
+that works out to 1 over 4 so let me
+ 
+
+ align:start position:0%
+that works out to 1 over 4 so let me
+write that just in this space so the
+
+ align:start position:0%
+write that just in this space so the
+ 
+
+ align:start position:0%
+write that just in this space so the
+average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi then is one over four so that's gonna
+
+ align:start position:0%
+hi then is one over four so that's gonna
+ 
+
+ align:start position:0%
+hi then is one over four so that's gonna
+be our final answer okay so let's just
+
+ align:start position:0%
+be our final answer okay so let's just
+ 
+
+ align:start position:0%
+be our final answer okay so let's just
+recap briefly what we did we had an
+
+ align:start position:0%
+recap briefly what we did we had an
+ 
+
+ align:start position:0%
+recap briefly what we did we had an
+average value problem that we started
+
+ align:start position:0%
+average value problem that we started
+ 
+
+ align:start position:0%
+average value problem that we started
+with so we use this general formula for
+
+ align:start position:0%
+with so we use this general formula for
+ 
+
+ align:start position:0%
+with so we use this general formula for
+average value problems when you have a
+
+ align:start position:0%
+average value problems when you have a
+ 
+
+ align:start position:0%
+average value problems when you have a
+function f that you want to take its
+
+ align:start position:0%
+function f that you want to take its
+ 
+
+ align:start position:0%
+function f that you want to take its
+average value of over over a region R
+
+ align:start position:0%
+average value of over over a region R
+ 
+
+ align:start position:0%
+average value of over over a region R
+what do you do will you take one over
+
+ align:start position:0%
+what do you do will you take one over
+ 
+
+ align:start position:0%
+what do you do will you take one over
+the volume of the region times the
+
+ align:start position:0%
+the volume of the region times the
+ 
+
+ align:start position:0%
+the volume of the region times the
+triple integral of your function f with
+
+ align:start position:0%
+triple integral of your function f with
+ 
+
+ align:start position:0%
+triple integral of your function f with
+respect to volume over that region okay
+
+ align:start position:0%
+respect to volume over that region okay
+ 
+
+ align:start position:0%
+respect to volume over that region okay
+so this is this is the average value in
+
+ align:start position:0%
+so this is this is the average value in
+ 
+
+ align:start position:0%
+so this is this is the average value in
+general in our particular case the the
+
+ align:start position:0%
+general in our particular case the the
+ 
+
+ align:start position:0%
+general in our particular case the the
+function was the height it was Z and
+
+ align:start position:0%
+function was the height it was Z and
+ 
+
+ align:start position:0%
+function was the height it was Z and
+then you have to set about choosing the
+
+ align:start position:0%
+then you have to set about choosing the
+ 
+
+ align:start position:0%
+then you have to set about choosing the
+proper balance for your integrals so in
+
+ align:start position:0%
+proper balance for your integrals so in
+ 
+
+ align:start position:0%
+proper balance for your integrals so in
+this case you know you so you choose
+
+ align:start position:0%
+this case you know you so you choose
+ 
+
+ align:start position:0%
+this case you know you so you choose
+some order of integration based on the
+
+ align:start position:0%
+some order of integration based on the
+ 
+
+ align:start position:0%
+some order of integration based on the
+region in this particular case it's a
+
+ align:start position:0%
+region in this particular case it's a
+ 
+
+ align:start position:0%
+region in this particular case it's a
+nice simple region it doesn't matter too
+
+ align:start position:0%
+nice simple region it doesn't matter too
+ 
+
+ align:start position:0%
+nice simple region it doesn't matter too
+much what order you choose so you have
+
+ align:start position:0%
+much what order you choose so you have
+ 
+
+ align:start position:0%
+much what order you choose so you have
+you know so I chose GZ dy/dx and then
+
+ align:start position:0%
+you know so I chose GZ dy/dx and then
+ 
+
+ align:start position:0%
+you know so I chose GZ dy/dx and then
+what does that mean so for the innermost
+
+ align:start position:0%
+what does that mean so for the innermost
+ 
+
+ align:start position:0%
+what does that mean so for the innermost
+one you look at your original solid so
+
+ align:start position:0%
+one you look at your original solid so
+ 
+
+ align:start position:0%
+one you look at your original solid so
+I'm gonna go back and look at this
+
+ align:start position:0%
+I'm gonna go back and look at this
+ 
+
+ align:start position:0%
+I'm gonna go back and look at this
+picture again so for your innermost
+
+ align:start position:0%
+picture again so for your innermost
+ 
+
+ align:start position:0%
+picture again so for your innermost
+variable you say so if it's Z you say
+
+ align:start position:0%
+variable you say so if it's Z you say
+ 
+
+ align:start position:0%
+variable you say so if it's Z you say
+okay so when i fix X&Y what's the bottom
+
+ align:start position:0%
+okay so when i fix X&Y what's the bottom
+ 
+
+ align:start position:0%
+okay so when i fix X&Y what's the bottom
+surface and what's the top surface for z
+
+ align:start position:0%
+surface and what's the top surface for z
+ 
+
+ align:start position:0%
+surface and what's the top surface for z
+you know when i solve that for Z in
+
+ align:start position:0%
+you know when i solve that for Z in
+ 
+
+ align:start position:0%
+you know when i solve that for Z in
+terms of x and y so here that was that
+
+ align:start position:0%
+terms of x and y so here that was that
+ 
+
+ align:start position:0%
+terms of x and y so here that was that
+the plane Z equals zero and the plane Z
+
+ align:start position:0%
+the plane Z equals zero and the plane Z
+ 
+
+ align:start position:0%
+the plane Z equals zero and the plane Z
+equals one minus X minus y so that
+
+ align:start position:0%
+equals one minus X minus y so that
+ 
+
+ align:start position:0%
+equals one minus X minus y so that
+explains my bounds over here why they
+
+ align:start position:0%
+explains my bounds over here why they
+ 
+
+ align:start position:0%
+explains my bounds over here why they
+were 0 and 1 minus X minus y then when
+
+ align:start position:0%
+were 0 and 1 minus X minus y then when
+ 
+
+ align:start position:0%
+were 0 and 1 minus X minus y then when
+you go to your next variable in this
+
+ align:start position:0%
+you go to your next variable in this
+ 
+
+ align:start position:0%
+you go to your next variable in this
+case it was y what do you do well you
+
+ align:start position:0%
+case it was y what do you do well you
+ 
+
+ align:start position:0%
+case it was y what do you do well you
+you first you project to eliminate this
+
+ align:start position:0%
+you first you project to eliminate this
+ 
+
+ align:start position:0%
+you first you project to eliminate this
+first variable so you project your
+
+ align:start position:0%
+first variable so you project your
+ 
+
+ align:start position:0%
+first variable so you project your
+region down well down in this case
+
+ align:start position:0%
+region down well down in this case
+ 
+
+ align:start position:0%
+region down well down in this case
+because it's Z so you project in the Z
+
+ align:start position:0%
+because it's Z so you project in the Z
+ 
+
+ align:start position:0%
+because it's Z so you project in the Z
+direction and you draw the sort of
+
+ align:start position:0%
+direction and you draw the sort of
+ 
+
+ align:start position:0%
+direction and you draw the sort of
+shadow of your region so this was what I
+
+ align:start position:0%
+shadow of your region so this was what I
+ 
+
+ align:start position:0%
+shadow of your region so this was what I
+drew here this is the shadow of my
+
+ align:start position:0%
+drew here this is the shadow of my
+ 
+
+ align:start position:0%
+drew here this is the shadow of my
+region in the XY plane after I projected
+
+ align:start position:0%
+region in the XY plane after I projected
+ 
+
+ align:start position:0%
+region in the XY plane after I projected
+it and then you do the same thing so now
+
+ align:start position:0%
+it and then you do the same thing so now
+ 
+
+ align:start position:0%
+it and then you do the same thing so now
+this is back and just like what you did
+
+ align:start position:0%
+this is back and just like what you did
+ 
+
+ align:start position:0%
+this is back and just like what you did
+when you had to find bounds for double
+
+ align:start position:0%
+when you had to find bounds for double
+ 
+
+ align:start position:0%
+when you had to find bounds for double
+integrals when you wrote them as
+
+ align:start position:0%
+integrals when you wrote them as
+ 
+
+ align:start position:0%
+integrals when you wrote them as
+iterated integrals a few a few lectures
+
+ align:start position:0%
+iterated integrals a few a few lectures
+ 
+
+ align:start position:0%
+iterated integrals a few a few lectures
+ago
+
+ align:start position:0%
+ago
+ 
+
+ align:start position:0%
+ago
+so okay and so then you do the same
+
+ align:start position:0%
+so okay and so then you do the same
+ 
+
+ align:start position:0%
+so okay and so then you do the same
+thing so then
+
+ align:start position:0%
+thing so then
+ 
+
+ align:start position:0%
+thing so then
+in this case I was next integrating with
+
+ align:start position:0%
+in this case I was next integrating with
+ 
+
+ align:start position:0%
+in this case I was next integrating with
+respect to Y so I needed to find the
+
+ align:start position:0%
+respect to Y so I needed to find the
+ 
+
+ align:start position:0%
+respect to Y so I needed to find the
+bounds on Y with respect to X so I
+
+ align:start position:0%
+bounds on Y with respect to X so I
+ 
+
+ align:start position:0%
+bounds on Y with respect to X so I
+needed to look in this picture at the
+
+ align:start position:0%
+needed to look in this picture at the
+ 
+
+ align:start position:0%
+needed to look in this picture at the
+bottom edge and the top edge of this
+
+ align:start position:0%
+bottom edge and the top edge of this
+ 
+
+ align:start position:0%
+bottom edge and the top edge of this
+region and okay and then your outermost
+
+ align:start position:0%
+region and okay and then your outermost
+ 
+
+ align:start position:0%
+region and okay and then your outermost
+variable you look at its absolute bounce
+
+ align:start position:0%
+variable you look at its absolute bounce
+ 
+
+ align:start position:0%
+variable you look at its absolute bounce
+so the largest and smallest value it
+
+ align:start position:0%
+so the largest and smallest value it
+ 
+
+ align:start position:0%
+so the largest and smallest value it
+takes on the region so then okay then
+
+ align:start position:0%
+takes on the region so then okay then
+ 
+
+ align:start position:0%
+takes on the region so then okay then
+you have an iterated integral and you
+
+ align:start position:0%
+you have an iterated integral and you
+ 
+
+ align:start position:0%
+you have an iterated integral and you
+evaluate it by successive integrations
+
+ align:start position:0%
+evaluate it by successive integrations
+ 
+
+ align:start position:0%
+evaluate it by successive integrations
+okay so that was what we did we just did
+
+ align:start position:0%
+okay so that was what we did we just did
+ 
+
+ align:start position:0%
+okay so that was what we did we just did
+the the three integrals starting from
+
+ align:start position:0%
+the the three integrals starting from
+ 
+
+ align:start position:0%
+the the three integrals starting from
+the inside and working our way out
\ No newline at end of file
diff --git a/cyQZP23YbCY.txt b/cyQZP23YbCY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a8264b7bfc097c84103db4eab5015b7663fc0e66
--- /dev/null
+++ b/cyQZP23YbCY.txt
@@ -0,0 +1,11371 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going through sounds good this was
+
+ align:start position:0%
+I'm going through sounds good this was
+ 
+
+ align:start position:0%
+I'm going through sounds good this was
+going to be a couple of hours plus of
+
+ align:start position:0%
+going to be a couple of hours plus of
+ 
+
+ align:start position:0%
+going to be a couple of hours plus of
+basic machine learning ok and I want to
+
+ align:start position:0%
+basic machine learning ok and I want to
+ 
+
+ align:start position:0%
+basic machine learning ok and I want to
+emphasize a bit the word basic because
+
+ align:start position:0%
+emphasize a bit the word basic because
+ 
+
+ align:start position:0%
+emphasize a bit the word basic because
+really I tried to just stick to the
+
+ align:start position:0%
+really I tried to just stick to the
+ 
+
+ align:start position:0%
+really I tried to just stick to the
+essentials or things that I would think
+
+ align:start position:0%
+essentials or things that I would think
+ 
+
+ align:start position:0%
+essentials or things that I would think
+of essentials to just start suppose that
+
+ align:start position:0%
+of essentials to just start suppose that
+ 
+
+ align:start position:0%
+of essentials to just start suppose that
+you have zero knowledge of machine
+
+ align:start position:0%
+you have zero knowledge of machine
+ 
+
+ align:start position:0%
+you have zero knowledge of machine
+learning and you just want to start from
+
+ align:start position:0%
+learning and you just want to start from
+ 
+
+ align:start position:0%
+learning and you just want to start from
+zero okay so if you already had classes
+
+ align:start position:0%
+zero okay so if you already had classes
+ 
+
+ align:start position:0%
+zero okay so if you already had classes
+in machine learning you might just find
+
+ align:start position:0%
+in machine learning you might just find
+ 
+
+ align:start position:0%
+in machine learning you might just find
+this little bit boring or at least kind
+
+ align:start position:0%
+this little bit boring or at least kind
+ 
+
+ align:start position:0%
+this little bit boring or at least kind
+of rehearsing things that you already
+
+ align:start position:0%
+of rehearsing things that you already
+ 
+
+ align:start position:0%
+of rehearsing things that you already
+know the idea of looking at machine
+
+ align:start position:0%
+know the idea of looking at machine
+ 
+
+ align:start position:0%
+know the idea of looking at machine
+learning these days is come from at
+
+ align:start position:0%
+learning these days is come from at
+ 
+
+ align:start position:0%
+learning these days is come from at
+least two different perspective the
+
+ align:start position:0%
+least two different perspective the
+ 
+
+ align:start position:0%
+least two different perspective the
+first one is for you for those of you
+
+ align:start position:0%
+first one is for you for those of you
+ 
+
+ align:start position:0%
+first one is for you for those of you
+probably most of you there interest to
+
+ align:start position:0%
+probably most of you there interest to
+ 
+
+ align:start position:0%
+probably most of you there interest to
+develop intelligent systems in a very
+
+ align:start position:0%
+develop intelligent systems in a very
+ 
+
+ align:start position:0%
+develop intelligent systems in a very
+broad sense what happened in the last
+
+ align:start position:0%
+broad sense what happened in the last
+ 
+
+ align:start position:0%
+broad sense what happened in the last
+few years that there's been a kind of
+
+ align:start position:0%
+few years that there's been a kind of
+ 
+
+ align:start position:0%
+few years that there's been a kind of
+data driven revolution where system that
+
+ align:start position:0%
+data driven revolution where system that
+ 
+
+ align:start position:0%
+data driven revolution where system that
+are trained rather that programmed start
+
+ align:start position:0%
+are trained rather that programmed start
+ 
+
+ align:start position:0%
+are trained rather that programmed start
+to be the key engines to solve tasks and
+
+ align:start position:0%
+to be the key engines to solve tasks and
+ 
+
+ align:start position:0%
+to be the key engines to solve tasks and
+here there is just some pictures that
+
+ align:start position:0%
+here there is just some pictures that
+ 
+
+ align:start position:0%
+here there is just some pictures that
+are probably outdated like robotics you
+
+ align:start position:0%
+are probably outdated like robotics you
+ 
+
+ align:start position:0%
+are probably outdated like robotics you
+know we have Siri on our phone we hear
+
+ align:start position:0%
+know we have Siri on our phone we hear
+ 
+
+ align:start position:0%
+know we have Siri on our phone we hear
+about self-driving cars in all this
+
+ align:start position:0%
+about self-driving cars in all this
+ 
+
+ align:start position:0%
+about self-driving cars in all this
+systems one key engine is providing data
+
+ align:start position:0%
+systems one key engine is providing data
+ 
+
+ align:start position:0%
+systems one key engine is providing data
+to the system to essentially try to
+
+ align:start position:0%
+to the system to essentially try to
+ 
+
+ align:start position:0%
+to the system to essentially try to
+learn how to solve a task and so one
+
+ align:start position:0%
+learn how to solve a task and so one
+ 
+
+ align:start position:0%
+learn how to solve a task and so one
+idea of this class is try to see what
+
+ align:start position:0%
+idea of this class is try to see what
+ 
+
+ align:start position:0%
+idea of this class is try to see what
+does it mean to learn and this the
+
+ align:start position:0%
+does it mean to learn and this the
+ 
+
+ align:start position:0%
+does it mean to learn and this the
+moment that you know you start to use
+
+ align:start position:0%
+moment that you know you start to use
+ 
+
+ align:start position:0%
+moment that you know you start to use
+data to solve complex tasks then there
+
+ align:start position:0%
+data to solve complex tasks then there
+ 
+
+ align:start position:0%
+data to solve complex tasks then there
+is a natural connection with what today
+
+ align:start position:0%
+is a natural connection with what today
+ 
+
+ align:start position:0%
+is a natural connection with what today
+is called data science which is somewhat
+
+ align:start position:0%
+is called data science which is somewhat
+ 
+
+ align:start position:0%
+is called data science which is somewhat
+a Paris want you know renovated version
+
+ align:start position:0%
+a Paris want you know renovated version
+ 
+
+ align:start position:0%
+a Paris want you know renovated version
+of the word that you used to call what
+
+ align:start position:0%
+of the word that you used to call what
+ 
+
+ align:start position:0%
+of the word that you used to call what
+we used to call just statistics so
+
+ align:start position:0%
+we used to call just statistics so
+ 
+
+ align:start position:0%
+we used to call just statistics so
+basically we start to have tons of data
+
+ align:start position:0%
+basically we start to have tons of data
+ 
+
+ align:start position:0%
+basically we start to have tons of data
+of all kinds there are very easy to
+
+ align:start position:0%
+of all kinds there are very easy to
+ 
+
+ align:start position:0%
+of all kinds there are very easy to
+collect and we are starving for
+
+ align:start position:0%
+collect and we are starving for
+ 
+
+ align:start position:0%
+collect and we are starving for
+knowledge and try to extract information
+
+ align:start position:0%
+knowledge and try to extract information
+ 
+
+ align:start position:0%
+knowledge and try to extract information
+from these data and as it turns out many
+
+ align:start position:0%
+from these data and as it turns out many
+ 
+
+ align:start position:0%
+from these data and as it turns out many
+of the techniques that are used to
+
+ align:start position:0%
+of the techniques that are used to
+ 
+
+ align:start position:0%
+of the techniques that are used to
+develop intelligent system are the same
+
+ align:start position:0%
+develop intelligent system are the same
+ 
+
+ align:start position:0%
+develop intelligent system are the same
+very taken
+
+ align:start position:0%
+very taken
+ 
+
+ align:start position:0%
+very taken
+that you can use to try to extract
+
+ align:start position:0%
+that you can use to try to extract
+ 
+
+ align:start position:0%
+that you can use to try to extract
+relevant information patterns data from
+
+ align:start position:0%
+relevant information patterns data from
+ 
+
+ align:start position:0%
+relevant information patterns data from
+your data so what we want to do today is
+
+ align:start position:0%
+your data so what we want to do today is
+ 
+
+ align:start position:0%
+your data so what we want to do today is
+try to see a bit what's in the middle
+
+ align:start position:0%
+try to see a bit what's in the middle
+ 
+
+ align:start position:0%
+try to see a bit what's in the middle
+what is the set of techniques that
+
+ align:start position:0%
+what is the set of techniques that
+ 
+
+ align:start position:0%
+what is the set of techniques that
+allows you indeed to go from data to
+
+ align:start position:0%
+allows you indeed to go from data to
+ 
+
+ align:start position:0%
+allows you indeed to go from data to
+knowledge or to acquiring ability to
+
+ align:start position:0%
+knowledge or to acquiring ability to
+ 
+
+ align:start position:0%
+knowledge or to acquiring ability to
+solve tasks machine learning is used
+
+ align:start position:0%
+solve tasks machine learning is used
+ 
+
+ align:start position:0%
+solve tasks machine learning is used
+these days and there are tons of
+
+ align:start position:0%
+these days and there are tons of
+ 
+
+ align:start position:0%
+these days and there are tons of
+possible application there has been
+
+ align:start position:0%
+possible application there has been
+ 
+
+ align:start position:0%
+possible application there has been
+Theory developed in the last 20-30 years
+
+ align:start position:0%
+Theory developed in the last 20-30 years
+ 
+
+ align:start position:0%
+Theory developed in the last 20-30 years
+that brought the field to a certain
+
+ align:start position:0%
+that brought the field to a certain
+ 
+
+ align:start position:0%
+that brought the field to a certain
+level of maturity from a mathematical
+
+ align:start position:0%
+level of maturity from a mathematical
+ 
+
+ align:start position:0%
+level of maturity from a mathematical
+point of view they're having tons and
+
+ align:start position:0%
+point of view they're having tons and
+ 
+
+ align:start position:0%
+point of view they're having tons and
+tons and tons of algorithms developed ok
+
+ align:start position:0%
+tons and tons of algorithms developed ok
+ 
+
+ align:start position:0%
+tons and tons of algorithms developed ok
+so in three hours there's no way I could
+
+ align:start position:0%
+so in three hours there's no way I could
+ 
+
+ align:start position:0%
+so in three hours there's no way I could
+give you an even just little view of
+
+ align:start position:0%
+give you an even just little view of
+ 
+
+ align:start position:0%
+give you an even just little view of
+what machine learning is these days so
+
+ align:start position:0%
+what machine learning is these days so
+ 
+
+ align:start position:0%
+what machine learning is these days so
+what I did is pretty much this so now
+
+ align:start position:0%
+what I did is pretty much this so now
+ 
+
+ align:start position:0%
+what I did is pretty much this so now
+when you do it I don't know if you ever
+
+ align:start position:0%
+when you do it I don't know if you ever
+ 
+
+ align:start position:0%
+when you do it I don't know if you ever
+done this but you know used a mixtape
+
+ align:start position:0%
+done this but you know used a mixtape
+ 
+
+ align:start position:0%
+done this but you know used a mixtape
+and you try to pick the songs that you
+
+ align:start position:0%
+and you try to pick the songs that you
+ 
+
+ align:start position:0%
+and you try to pick the songs that you
+would bring with yourself on a desert
+
+ align:start position:0%
+would bring with yourself on a desert
+ 
+
+ align:start position:0%
+would bring with yourself on a desert
+island that's kind of the way I thought
+
+ align:start position:0%
+island that's kind of the way I thought
+ 
+
+ align:start position:0%
+island that's kind of the way I thought
+about what to put in this cookie in this
+
+ align:start position:0%
+about what to put in this cookie in this
+ 
+
+ align:start position:0%
+about what to put in this cookie in this
+one feels little life that you're going
+
+ align:start position:0%
+one feels little life that you're going
+ 
+
+ align:start position:0%
+one feels little life that you're going
+to show in a minute so basically I
+
+ align:start position:0%
+to show in a minute so basically I
+ 
+
+ align:start position:0%
+to show in a minute so basically I
+thought you know what what are those
+
+ align:start position:0%
+thought you know what what are those
+ 
+
+ align:start position:0%
+thought you know what what are those
+three four five learning algorithm that
+
+ align:start position:0%
+three four five learning algorithm that
+ 
+
+ align:start position:0%
+three four five learning algorithm that
+you should know okay if you know nothing
+
+ align:start position:0%
+you should know okay if you know nothing
+ 
+
+ align:start position:0%
+you should know okay if you know nothing
+about machine learning and this is more
+
+ align:start position:0%
+about machine learning and this is more
+ 
+
+ align:start position:0%
+about machine learning and this is more
+or less at least one part of course
+
+ align:start position:0%
+or less at least one part of course
+ 
+
+ align:start position:0%
+or less at least one part of course
+there are few songs that stayed out of
+
+ align:start position:0%
+there are few songs that stayed out of
+ 
+
+ align:start position:0%
+there are few songs that stayed out of
+the compilation but this is like one
+
+ align:start position:0%
+the compilation but this is like one
+ 
+
+ align:start position:0%
+the compilation but this is like one
+selection okay so we're gonna such we're
+
+ align:start position:0%
+selection okay so we're gonna such we're
+ 
+
+ align:start position:0%
+selection okay so we're gonna such we're
+gonna start as I said simple and the
+
+ align:start position:0%
+gonna start as I said simple and the
+ 
+
+ align:start position:0%
+gonna start as I said simple and the
+idea is that this morning you're gonna
+
+ align:start position:0%
+idea is that this morning you're gonna
+ 
+
+ align:start position:0%
+idea is that this morning you're gonna
+see a few algorithms and we're gonna I
+
+ align:start position:0%
+see a few algorithms and we're gonna I
+ 
+
+ align:start position:0%
+see a few algorithms and we're gonna I
+picked algorithm that are relatively
+
+ align:start position:0%
+picked algorithm that are relatively
+ 
+
+ align:start position:0%
+picked algorithm that are relatively
+simple from a computational point of
+
+ align:start position:0%
+simple from a computational point of
+ 
+
+ align:start position:0%
+simple from a computational point of
+view so the math level is gonna be
+
+ align:start position:0%
+view so the math level is gonna be
+ 
+
+ align:start position:0%
+view so the math level is gonna be
+pretty basic okay I think I'm gonna use
+
+ align:start position:0%
+pretty basic okay I think I'm gonna use
+ 
+
+ align:start position:0%
+pretty basic okay I think I'm gonna use
+some linear algebra at some point and
+
+ align:start position:0%
+some linear algebra at some point and
+ 
+
+ align:start position:0%
+some linear algebra at some point and
+maybe some calculus but that's about it
+
+ align:start position:0%
+maybe some calculus but that's about it
+ 
+
+ align:start position:0%
+maybe some calculus but that's about it
+so mostly the idea here is to emphasize
+
+ align:start position:0%
+so mostly the idea here is to emphasize
+ 
+
+ align:start position:0%
+so mostly the idea here is to emphasize
+conceptual ideas okay the concepts and
+
+ align:start position:0%
+conceptual ideas okay the concepts and
+ 
+
+ align:start position:0%
+conceptual ideas okay the concepts and
+then today afternoon there's gonna be
+
+ align:start position:0%
+then today afternoon there's gonna be
+ 
+
+ align:start position:0%
+then today afternoon there's gonna be
+basically labs where you sit and you
+
+ align:start position:0%
+basically labs where you sit and you
+ 
+
+ align:start position:0%
+basically labs where you sit and you
+just pick this kind of algorithm and use
+
+ align:start position:0%
+just pick this kind of algorithm and use
+ 
+
+ align:start position:0%
+just pick this kind of algorithm and use
+them so you immediately see what does it
+
+ align:start position:0%
+them so you immediately see what does it
+ 
+
+ align:start position:0%
+them so you immediately see what does it
+mean okay so at the end of the day you
+
+ align:start position:0%
+mean okay so at the end of the day you
+ 
+
+ align:start position:0%
+mean okay so at the end of the day you
+should have a reasonable knowledge about
+
+ align:start position:0%
+should have a reasonable knowledge about
+ 
+
+ align:start position:0%
+should have a reasonable knowledge about
+whatever you've seen this morning so
+
+ align:start position:0%
+whatever you've seen this morning so
+ 
+
+ align:start position:0%
+whatever you've seen this morning so
+this is how the class is structured it's
+
+ align:start position:0%
+this is how the class is structured it's
+ 
+
+ align:start position:0%
+this is how the class is structured it's
+dividing three parts plus the lab
+
+ align:start position:0%
+dividing three parts plus the lab
+ 
+
+ align:start position:0%
+dividing three parts plus the lab
+so in the first part what we want to do
+
+ align:start position:0%
+so in the first part what we want to do
+ 
+
+ align:start position:0%
+so in the first part what we want to do
+is start from the probably the simplest
+
+ align:start position:0%
+is start from the probably the simplest
+ 
+
+ align:start position:0%
+is start from the probably the simplest
+learning algorithm you can think of to
+
+ align:start position:0%
+learning algorithm you can think of to
+ 
+
+ align:start position:0%
+learning algorithm you can think of to
+try to emphasize and use that as an
+
+ align:start position:0%
+try to emphasize and use that as an
+ 
+
+ align:start position:0%
+try to emphasize and use that as an
+excuse to introduce the idea of
+
+ align:start position:0%
+excuse to introduce the idea of
+ 
+
+ align:start position:0%
+excuse to introduce the idea of
+bias-variance tradeoff which to me is
+
+ align:start position:0%
+bias-variance tradeoff which to me is
+ 
+
+ align:start position:0%
+bias-variance tradeoff which to me is
+probably either the or one of the most
+
+ align:start position:0%
+probably either the or one of the most
+ 
+
+ align:start position:0%
+probably either the or one of the most
+fundamental concept in statistics and
+
+ align:start position:0%
+fundamental concept in statistics and
+ 
+
+ align:start position:0%
+fundamental concept in statistics and
+machine learning which is this idea that
+
+ align:start position:0%
+machine learning which is this idea that
+ 
+
+ align:start position:0%
+machine learning which is this idea that
+you're gonna see in a few minutes in
+
+ align:start position:0%
+you're gonna see in a few minutes in
+ 
+
+ align:start position:0%
+you're gonna see in a few minutes in
+more detail but it's essentially that is
+
+ align:start position:0%
+more detail but it's essentially that is
+ 
+
+ align:start position:0%
+more detail but it's essentially that is
+that you never have enough data okay and
+
+ align:start position:0%
+that you never have enough data okay and
+ 
+
+ align:start position:0%
+that you never have enough data okay and
+the game here is not about describing
+
+ align:start position:0%
+the game here is not about describing
+ 
+
+ align:start position:0%
+the game here is not about describing
+the data that you have today as much as
+
+ align:start position:0%
+the data that you have today as much as
+ 
+
+ align:start position:0%
+the data that you have today as much as
+using the data you have today as the
+
+ align:start position:0%
+using the data you have today as the
+ 
+
+ align:start position:0%
+using the data you have today as the
+basis of a knowledge to distract it that
+
+ align:start position:0%
+basis of a knowledge to distract it that
+ 
+
+ align:start position:0%
+basis of a knowledge to distract it that
+you're gonna get tomorrow so there is
+
+ align:start position:0%
+you're gonna get tomorrow so there is
+ 
+
+ align:start position:0%
+you're gonna get tomorrow so there is
+this Niren trade-off between what you
+
+ align:start position:0%
+this Niren trade-off between what you
+ 
+
+ align:start position:0%
+this Niren trade-off between what you
+have a disposal and what would you like
+
+ align:start position:0%
+have a disposal and what would you like
+ 
+
+ align:start position:0%
+have a disposal and what would you like
+to predict and then you have to
+
+ align:start position:0%
+to predict and then you have to
+ 
+
+ align:start position:0%
+to predict and then you have to
+essentially turns out that you have to
+
+ align:start position:0%
+essentially turns out that you have to
+ 
+
+ align:start position:0%
+essentially turns out that you have to
+somewhat decide how much you want to
+
+ align:start position:0%
+somewhat decide how much you want to
+ 
+
+ align:start position:0%
+somewhat decide how much you want to
+trust the data and how much you want
+
+ align:start position:0%
+trust the data and how much you want
+ 
+
+ align:start position:0%
+trust the data and how much you want
+instead somewhat throw away or you know
+
+ align:start position:0%
+instead somewhat throw away or you know
+ 
+
+ align:start position:0%
+instead somewhat throw away or you know
+regularize as they say smooth out the
+
+ align:start position:0%
+regularize as they say smooth out the
+ 
+
+ align:start position:0%
+regularize as they say smooth out the
+information in your data because you
+
+ align:start position:0%
+information in your data because you
+ 
+
+ align:start position:0%
+information in your data because you
+think that it's actually an accident is
+
+ align:start position:0%
+think that it's actually an accident is
+ 
+
+ align:start position:0%
+think that it's actually an accident is
+just because you're so data with aspects
+
+ align:start position:0%
+just because you're so data with aspects
+ 
+
+ align:start position:0%
+just because you're so data with aspects
+today they are not really reflective of
+
+ align:start position:0%
+today they are not really reflective of
+ 
+
+ align:start position:0%
+today they are not really reflective of
+the phenomenon they produce them but
+
+ align:start position:0%
+the phenomenon they produce them but
+ 
+
+ align:start position:0%
+the phenomenon they produce them but
+it's just because I saw 10 points rather
+
+ align:start position:0%
+it's just because I saw 10 points rather
+ 
+
+ align:start position:0%
+it's just because I saw 10 points rather
+than 100 the basic idea here is this
+
+ align:start position:0%
+than 100 the basic idea here is this
+ 
+
+ align:start position:0%
+than 100 the basic idea here is this
+essentially the law of large numbers or
+
+ align:start position:0%
+essentially the law of large numbers or
+ 
+
+ align:start position:0%
+essentially the law of large numbers or
+you know toss a coin you might find out
+
+ align:start position:0%
+you know toss a coin you might find out
+ 
+
+ align:start position:0%
+you know toss a coin you might find out
+that if it was it just ten times it
+
+ align:start position:0%
+that if it was it just ten times it
+ 
+
+ align:start position:0%
+that if it was it just ten times it
+looks like it's not the fair coin but if
+
+ align:start position:0%
+looks like it's not the fair coin but if
+ 
+
+ align:start position:0%
+looks like it's not the fair coin but if
+you go for a hundred or Taj and you
+
+ align:start position:0%
+you go for a hundred or Taj and you
+ 
+
+ align:start position:0%
+you go for a hundred or Taj and you
+start to see that it converts to 5050
+
+ align:start position:0%
+start to see that it converts to 5050
+ 
+
+ align:start position:0%
+start to see that it converts to 5050
+okay so that's kind of what's going on
+
+ align:start position:0%
+okay so that's kind of what's going on
+ 
+
+ align:start position:0%
+okay so that's kind of what's going on
+here so the idea that you want to use
+
+ align:start position:0%
+here so the idea that you want to use
+ 
+
+ align:start position:0%
+here so the idea that you want to use
+some kind of induction principle that
+
+ align:start position:0%
+some kind of induction principle that
+ 
+
+ align:start position:0%
+some kind of induction principle that
+tells you how much you can trust the
+
+ align:start position:0%
+tells you how much you can trust the
+ 
+
+ align:start position:0%
+tells you how much you can trust the
+data moving on from this basic class of
+
+ align:start position:0%
+data moving on from this basic class of
+ 
+
+ align:start position:0%
+data moving on from this basic class of
+algorithm we're going to consider so
+
+ align:start position:0%
+algorithm we're going to consider so
+ 
+
+ align:start position:0%
+algorithm we're going to consider so
+called regularization techniques this is
+
+ align:start position:0%
+called regularization techniques this is
+ 
+
+ align:start position:0%
+called regularization techniques this is
+a very I use regularization a very broad
+
+ align:start position:0%
+a very I use regularization a very broad
+ 
+
+ align:start position:0%
+a very I use regularization a very broad
+sense and here we're gonna concentrate
+
+ align:start position:0%
+sense and here we're gonna concentrate
+ 
+
+ align:start position:0%
+sense and here we're gonna concentrate
+on lean least squares essentially
+
+ align:start position:0%
+on lean least squares essentially
+ 
+
+ align:start position:0%
+on lean least squares essentially
+because a it's simple and it just
+
+ align:start position:0%
+because a it's simple and it just
+ 
+
+ align:start position:0%
+because a it's simple and it just
+reduces to linear algebra and so you
+
+ align:start position:0%
+reduces to linear algebra and so you
+ 
+
+ align:start position:0%
+reduces to linear algebra and so you
+have no you don't have to know anything
+
+ align:start position:0%
+have no you don't have to know anything
+ 
+
+ align:start position:0%
+have no you don't have to know anything
+about convex optimization or any other
+
+ align:start position:0%
+about convex optimization or any other
+ 
+
+ align:start position:0%
+about convex optimization or any other
+kind of fancy optimization techniques
+
+ align:start position:0%
+kind of fancy optimization techniques
+ 
+
+ align:start position:0%
+kind of fancy optimization techniques
+and B because it's relatively simple to
+
+ align:start position:0%
+and B because it's relatively simple to
+ 
+
+ align:start position:0%
+and B because it's relatively simple to
+move from linear models to nonparametric
+
+ align:start position:0%
+move from linear models to nonparametric
+ 
+
+ align:start position:0%
+move from linear models to nonparametric
+nonlinear models using kernels okay and
+
+ align:start position:0%
+nonlinear models using kernels okay and
+ 
+
+ align:start position:0%
+nonlinear models using kernels okay and
+kernels are a big field but we you know
+
+ align:start position:0%
+kernels are a big field but we you know
+ 
+
+ align:start position:0%
+kernels are a big field but we you know
+with a lot of math but you're just gonna
+
+ align:start position:0%
+with a lot of math but you're just gonna
+ 
+
+ align:start position:0%
+with a lot of math but you're just gonna
+more at the recipe to move from simple
+
+ align:start position:0%
+more at the recipe to move from simple
+ 
+
+ align:start position:0%
+more at the recipe to move from simple
+models to complicated models so finally
+
+ align:start position:0%
+models to complicated models so finally
+ 
+
+ align:start position:0%
+models to complicated models so finally
+the last part we're going to move a bit
+
+ align:start position:0%
+the last part we're going to move a bit
+ 
+
+ align:start position:0%
+the last part we're going to move a bit
+away from pure prediction so the
+
+ align:start position:0%
+away from pure prediction so the
+ 
+
+ align:start position:0%
+away from pure prediction so the
+basically these first two parts are
+
+ align:start position:0%
+basically these first two parts are
+ 
+
+ align:start position:0%
+basically these first two parts are
+about prediction or what is called
+
+ align:start position:0%
+about prediction or what is called
+ 
+
+ align:start position:0%
+about prediction or what is called
+supervised learning and here we're going
+
+ align:start position:0%
+supervised learning and here we're going
+ 
+
+ align:start position:0%
+supervised learning and here we're going
+to move a bit away from prediction and
+
+ align:start position:0%
+to move a bit away from prediction and
+ 
+
+ align:start position:0%
+to move a bit away from prediction and
+we're going to ask question more related
+
+ align:start position:0%
+we're going to ask question more related
+ 
+
+ align:start position:0%
+we're going to ask question more related
+to you have data and you want to know
+
+ align:start position:0%
+to you have data and you want to know
+ 
+
+ align:start position:0%
+to you have data and you want to know
+what are the important sectors in your
+
+ align:start position:0%
+what are the important sectors in your
+ 
+
+ align:start position:0%
+what are the important sectors in your
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+okay so you've the one key word here is
+
+ align:start position:0%
+okay so you've the one key word here is
+ 
+
+ align:start position:0%
+okay so you've the one key word here is
+the interpretability you want to have
+
+ align:start position:0%
+the interpretability you want to have
+ 
+
+ align:start position:0%
+the interpretability you want to have
+some form of interpret ability of the
+
+ align:start position:0%
+some form of interpret ability of the
+ 
+
+ align:start position:0%
+some form of interpret ability of the
+data at hand you would like to know not
+
+ align:start position:0%
+data at hand you would like to know not
+ 
+
+ align:start position:0%
+data at hand you would like to know not
+only how you can make good predictions
+
+ align:start position:0%
+only how you can make good predictions
+ 
+
+ align:start position:0%
+only how you can make good predictions
+but what are the important sectors so
+
+ align:start position:0%
+but what are the important sectors so
+ 
+
+ align:start position:0%
+but what are the important sectors so
+you not only want to do good prediction
+
+ align:start position:0%
+you not only want to do good prediction
+ 
+
+ align:start position:0%
+you not only want to do good prediction
+but you want to know how you make good
+
+ align:start position:0%
+but you want to know how you make good
+ 
+
+ align:start position:0%
+but you want to know how you make good
+prediction what are the important
+
+ align:start position:0%
+prediction what are the important
+ 
+
+ align:start position:0%
+prediction what are the important
+information to actually get good
+
+ align:start position:0%
+information to actually get good
+ 
+
+ align:start position:0%
+information to actually get good
+prediction and so in this last part
+
+ align:start position:0%
+prediction and so in this last part
+ 
+
+ align:start position:0%
+prediction and so in this last part
+we're gonna take a peek into this and as
+
+ align:start position:0%
+we're gonna take a peek into this and as
+ 
+
+ align:start position:0%
+we're gonna take a peek into this and as
+I said the afternoon is basically going
+
+ align:start position:0%
+I said the afternoon is basically going
+ 
+
+ align:start position:0%
+I said the afternoon is basically going
+to be practical session if it's all
+
+ align:start position:0%
+to be practical session if it's all
+ 
+
+ align:start position:0%
+to be practical session if it's all
+MATLAB I think there is some quick if
+
+ align:start position:0%
+MATLAB I think there is some quick if
+ 
+
+ align:start position:0%
+MATLAB I think there is some quick if
+you've never seen MATLAB before you can
+
+ align:start position:0%
+you've never seen MATLAB before you can
+ 
+
+ align:start position:0%
+you've never seen MATLAB before you can
+play around with a little bit just a
+
+ align:start position:0%
+play around with a little bit just a
+ 
+
+ align:start position:0%
+play around with a little bit just a
+little bit but it's very easy and then
+
+ align:start position:0%
+little bit but it's very easy and then
+ 
+
+ align:start position:0%
+little bit but it's very easy and then
+you've got a few different proposals I
+
+ align:start position:0%
+you've got a few different proposals I
+ 
+
+ align:start position:0%
+you've got a few different proposals I
+think of things you can do and you can
+
+ align:start position:0%
+think of things you can do and you can
+ 
+
+ align:start position:0%
+think of things you can do and you can
+pick depending on what you already know
+
+ align:start position:0%
+pick depending on what you already know
+ 
+
+ align:start position:0%
+pick depending on what you already know
+what you can try you can start from that
+
+ align:start position:0%
+what you can try you can start from that
+ 
+
+ align:start position:0%
+what you can try you can start from that
+and be more or less fancy okay so those
+
+ align:start position:0%
+and be more or less fancy okay so those
+ 
+
+ align:start position:0%
+and be more or less fancy okay so those
+without saying stop me it's the more we
+
+ align:start position:0%
+without saying stop me it's the more we
+ 
+
+ align:start position:0%
+without saying stop me it's the more we
+interact the better it is so the first
+
+ align:start position:0%
+interact the better it is so the first
+ 
+
+ align:start position:0%
+interact the better it is so the first
+part is I said the idea is to use
+
+ align:start position:0%
+part is I said the idea is to use
+ 
+
+ align:start position:0%
+part is I said the idea is to use
+so-called local methods as an excuse to
+
+ align:start position:0%
+so-called local methods as an excuse to
+ 
+
+ align:start position:0%
+so-called local methods as an excuse to
+understand by experience ok so we're
+
+ align:start position:0%
+understand by experience ok so we're
+ 
+
+ align:start position:0%
+understand by experience ok so we're
+going to introduce the simplest
+
+ align:start position:0%
+going to introduce the simplest
+ 
+
+ align:start position:0%
+going to introduce the simplest
+algorithm you can think of and we're
+
+ align:start position:0%
+algorithm you can think of and we're
+ 
+
+ align:start position:0%
+algorithm you can think of and we're
+gonna use it to understand a much deeper
+
+ align:start position:0%
+gonna use it to understand a much deeper
+ 
+
+ align:start position:0%
+gonna use it to understand a much deeper
+concept so first of all let's just put
+
+ align:start position:0%
+concept so first of all let's just put
+ 
+
+ align:start position:0%
+concept so first of all let's just put
+our set up ok put down our set up the
+
+ align:start position:0%
+our set up ok put down our set up the
+ 
+
+ align:start position:0%
+our set up ok put down our set up the
+idea is that we're so how many of you
+
+ align:start position:0%
+idea is that we're so how many of you
+ 
+
+ align:start position:0%
+idea is that we're so how many of you
+had a machine learning cost before
+
+ align:start position:0%
+had a machine learning cost before
+ 
+
+ align:start position:0%
+had a machine learning cost before
+alright so don't be too bored the idea
+
+ align:start position:0%
+alright so don't be too bored the idea
+ 
+
+ align:start position:0%
+alright so don't be too bored the idea
+is - we want to do supervised learning
+
+ align:start position:0%
+is - we want to do supervised learning
+ 
+
+ align:start position:0%
+is - we want to do supervised learning
+so in supervised learning there is an
+
+ align:start position:0%
+so in supervised learning there is an
+ 
+
+ align:start position:0%
+so in supervised learning there is an
+input and an output and these input and
+
+ align:start position:0%
+input and an output and these input and
+ 
+
+ align:start position:0%
+input and an output and these input and
+output are somewhat related and I'll be
+
+ align:start position:0%
+output are somewhat related and I'll be
+ 
+
+ align:start position:0%
+output are somewhat related and I'll be
+more precise efficient but the idea is
+
+ align:start position:0%
+more precise efficient but the idea is
+ 
+
+ align:start position:0%
+more precise efficient but the idea is
+that you want to learn this input-output
+
+ align:start position:0%
+that you want to learn this input-output
+ 
+
+ align:start position:0%
+that you want to learn this input-output
+relationship and all you have at
+
+ align:start position:0%
+relationship and all you have at
+ 
+
+ align:start position:0%
+relationship and all you have at
+disposal are sets of inputs and outputs
+
+ align:start position:0%
+disposal are sets of inputs and outputs
+ 
+
+ align:start position:0%
+disposal are sets of inputs and outputs
+ok so X here is an input and Y is the
+
+ align:start position:0%
+ok so X here is an input and Y is the
+ 
+
+ align:start position:0%
+ok so X here is an input and Y is the
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+F is a functional relation between the
+
+ align:start position:0%
+F is a functional relation between the
+ 
+
+ align:start position:0%
+F is a functional relation between the
+input and the output all you have this
+
+ align:start position:0%
+input and the output all you have this
+ 
+
+ align:start position:0%
+input and the output all you have this
+puzzle are these couples okay so I give
+
+ align:start position:0%
+puzzle are these couples okay so I give
+ 
+
+ align:start position:0%
+puzzle are these couples okay so I give
+you an input and I know what's the
+
+ align:start position:0%
+you an input and I know what's the
+ 
+
+ align:start position:0%
+you an input and I know what's the
+corresponding output I give another
+
+ align:start position:0%
+corresponding output I give another
+ 
+
+ align:start position:0%
+corresponding output I give another
+input and I know what's the
+
+ align:start position:0%
+input and I know what's the
+ 
+
+ align:start position:0%
+input and I know what's the
+corresponding output but they don't give
+
+ align:start position:0%
+corresponding output but they don't give
+ 
+
+ align:start position:0%
+corresponding output but they don't give
+you all of them
+
+ align:start position:0%
+you all of them
+ 
+
+ align:start position:0%
+you all of them
+you just have n okay is n is the number
+
+ align:start position:0%
+you just have n okay is n is the number
+ 
+
+ align:start position:0%
+you just have n okay is n is the number
+of points and you call this a training
+
+ align:start position:0%
+of points and you call this a training
+ 
+
+ align:start position:0%
+of points and you call this a training
+set because there will be the basis of
+
+ align:start position:0%
+set because there will be the basis of
+ 
+
+ align:start position:0%
+set because there will be the basis of
+knowledge in which you can try to train
+
+ align:start position:0%
+knowledge in which you can try to train
+ 
+
+ align:start position:0%
+knowledge in which you can try to train
+a machine to estimate this functional
+
+ align:start position:0%
+a machine to estimate this functional
+ 
+
+ align:start position:0%
+a machine to estimate this functional
+relationship okay and the key point here
+
+ align:start position:0%
+relationship okay and the key point here
+ 
+
+ align:start position:0%
+relationship okay and the key point here
+is that on the one hand you want to
+
+ align:start position:0%
+is that on the one hand you want to
+ 
+
+ align:start position:0%
+is that on the one hand you want to
+describe well this data so you want to
+
+ align:start position:0%
+describe well this data so you want to
+ 
+
+ align:start position:0%
+describe well this data so you want to
+get a function relationship that works
+
+ align:start position:0%
+get a function relationship that works
+ 
+
+ align:start position:0%
+get a function relationship that works
+well in you know if you get the next one
+
+ align:start position:0%
+well in you know if you get the next one
+ 
+
+ align:start position:0%
+well in you know if you get the next one
+to give you an F x1 which is close to y1
+
+ align:start position:0%
+to give you an F x1 which is close to y1
+ 
+
+ align:start position:0%
+to give you an F x1 which is close to y1
+and so on and F x2 which is close to y2
+
+ align:start position:0%
+and so on and F x2 which is close to y2
+ 
+
+ align:start position:0%
+and so on and F x2 which is close to y2
+but more importantly you want an F that
+
+ align:start position:0%
+but more importantly you want an F that
+ 
+
+ align:start position:0%
+but more importantly you want an F that
+given a new point that was not here will
+
+ align:start position:0%
+given a new point that was not here will
+ 
+
+ align:start position:0%
+given a new point that was not here will
+give you an output which is a good
+
+ align:start position:0%
+give you an output which is a good
+ 
+
+ align:start position:0%
+give you an output which is a good
+estimate of the true output to respond
+
+ align:start position:0%
+estimate of the true output to respond
+ 
+
+ align:start position:0%
+estimate of the true output to respond
+to that input okay this is the the most
+
+ align:start position:0%
+to that input okay this is the the most
+ 
+
+ align:start position:0%
+to that input okay this is the the most
+important thing of the set up okay the
+
+ align:start position:0%
+important thing of the set up okay the
+ 
+
+ align:start position:0%
+important thing of the set up okay the
+idea of so called generalization if you
+
+ align:start position:0%
+idea of so called generalization if you
+ 
+
+ align:start position:0%
+idea of so called generalization if you
+want prediction you want to really do
+
+ align:start position:0%
+want prediction you want to really do
+ 
+
+ align:start position:0%
+want prediction you want to really do
+inference you don't want to do
+
+ align:start position:0%
+inference you don't want to do
+ 
+
+ align:start position:0%
+inference you don't want to do
+descriptive statistics you really want
+
+ align:start position:0%
+descriptive statistics you really want
+ 
+
+ align:start position:0%
+descriptive statistics you really want
+to do inferential statistics so this is
+
+ align:start position:0%
+to do inferential statistics so this is
+ 
+
+ align:start position:0%
+to do inferential statistics so this is
+just a very very simple example but just
+
+ align:start position:0%
+just a very very simple example but just
+ 
+
+ align:start position:0%
+just a very very simple example but just
+to start to have something in mind
+
+ align:start position:0%
+to start to have something in mind
+ 
+
+ align:start position:0%
+to start to have something in mind
+suppose that you have well the it it's
+
+ align:start position:0%
+suppose that you have well the it it's
+ 
+
+ align:start position:0%
+suppose that you have well the it it's
+just a like a toy version of the face
+
+ align:start position:0%
+just a like a toy version of the face
+ 
+
+ align:start position:0%
+just a like a toy version of the face
+recognition system we have on our phones
+
+ align:start position:0%
+recognition system we have on our phones
+ 
+
+ align:start position:0%
+recognition system we have on our phones
+you know that when you take a picture
+
+ align:start position:0%
+you know that when you take a picture
+ 
+
+ align:start position:0%
+you know that when you take a picture
+you start they really want to talk to
+
+ align:start position:0%
+you start they really want to talk to
+ 
+
+ align:start position:0%
+you start they really want to talk to
+you you you have something like these
+
+ align:start position:0%
+you you you have something like these
+ 
+
+ align:start position:0%
+you you you have something like these
+you have a legal square appearing around
+
+ align:start position:0%
+you have a legal square appearing around
+ 
+
+ align:start position:0%
+you have a legal square appearing around
+a face sometimes it means that basically
+
+ align:start position:0%
+a face sometimes it means that basically
+ 
+
+ align:start position:0%
+a face sometimes it means that basically
+the system is actually going inside the
+
+ align:start position:0%
+the system is actually going inside the
+ 
+
+ align:start position:0%
+the system is actually going inside the
+image and recognizing faces okay so the
+
+ align:start position:0%
+image and recognizing faces okay so the
+ 
+
+ align:start position:0%
+image and recognizing faces okay so the
+idea is that it's a bit more complicated
+
+ align:start position:0%
+idea is that it's a bit more complicated
+ 
+
+ align:start position:0%
+idea is that it's a bit more complicated
+in this but a toy version of this
+
+ align:start position:0%
+in this but a toy version of this
+ 
+
+ align:start position:0%
+in this but a toy version of this
+algorithm is you have an image like this
+
+ align:start position:0%
+algorithm is you have an image like this
+ 
+
+ align:start position:0%
+algorithm is you have an image like this
+okay the image you can think of as an
+
+ align:start position:0%
+okay the image you can think of as an
+ 
+
+ align:start position:0%
+okay the image you can think of as an
+hour like matrix of numbers each number
+
+ align:start position:0%
+hour like matrix of numbers each number
+ 
+
+ align:start position:0%
+hour like matrix of numbers each number
+is going now this is just this is color
+
+ align:start position:0%
+is going now this is just this is color
+ 
+
+ align:start position:0%
+is going now this is just this is color
+but imagine it's black and white okay
+
+ align:start position:0%
+but imagine it's black and white okay
+ 
+
+ align:start position:0%
+but imagine it's black and white okay
+then it will just contain a number which
+
+ align:start position:0%
+then it will just contain a number which
+ 
+
+ align:start position:0%
+then it will just contain a number which
+is the pixel value with the color with
+
+ align:start position:0%
+is the pixel value with the color with
+ 
+
+ align:start position:0%
+is the pixel value with the color with
+the light intensity of that pixel and it
+
+ align:start position:0%
+the light intensity of that pixel and it
+ 
+
+ align:start position:0%
+the light intensity of that pixel and it
+does that these array
+
+ align:start position:0%
+does that these array
+ 
+
+ align:start position:0%
+does that these array
+and then if you want you can brutalize
+
+ align:start position:0%
+and then if you want you can brutalize
+ 
+
+ align:start position:0%
+and then if you want you can brutalize
+it with this and just unroll the matrix
+
+ align:start position:0%
+it with this and just unroll the matrix
+ 
+
+ align:start position:0%
+it with this and just unroll the matrix
+into a long vector okay let's take this
+
+ align:start position:0%
+into a long vector okay let's take this
+ 
+
+ align:start position:0%
+into a long vector okay let's take this
+one vector so P here would be what the
+
+ align:start position:0%
+one vector so P here would be what the
+ 
+
+ align:start position:0%
+one vector so P here would be what the
+number of just a number of pixels okay
+
+ align:start position:0%
+number of just a number of pixels okay
+ 
+
+ align:start position:0%
+number of just a number of pixels okay
+so I take this image and I unroll it I
+
+ align:start position:0%
+so I take this image and I unroll it I
+ 
+
+ align:start position:0%
+so I take this image and I unroll it I
+take another image and I unroll it and I
+
+ align:start position:0%
+take another image and I unroll it and I
+ 
+
+ align:start position:0%
+take another image and I unroll it and I
+take images and you see some images here
+
+ align:start position:0%
+take images and you see some images here
+ 
+
+ align:start position:0%
+take images and you see some images here
+do contain faces some other images do
+
+ align:start position:0%
+do contain faces some other images do
+ 
+
+ align:start position:0%
+do contain faces some other images do
+not contain faces okay and I here use
+
+ align:start position:0%
+not contain faces okay and I here use
+ 
+
+ align:start position:0%
+not contain faces okay and I here use
+color to code them and now what I have
+
+ align:start position:0%
+color to code them and now what I have
+ 
+
+ align:start position:0%
+color to code them and now what I have
+is that images are my input okay are the
+
+ align:start position:0%
+is that images are my input okay are the
+ 
+
+ align:start position:0%
+is that images are my input okay are the
+X's so here full disclosure I sometimes
+
+ align:start position:0%
+X's so here full disclosure I sometimes
+ 
+
+ align:start position:0%
+X's so here full disclosure I sometimes
+I don't I never use the little arrow
+
+ align:start position:0%
+I don't I never use the little arrow
+ 
+
+ align:start position:0%
+I don't I never use the little arrow
+above letters to denote vectors so
+
+ align:start position:0%
+above letters to denote vectors so
+ 
+
+ align:start position:0%
+above letters to denote vectors so
+hopefully will be clear from the context
+
+ align:start position:0%
+hopefully will be clear from the context
+ 
+
+ align:start position:0%
+hopefully will be clear from the context
+when it's really useful I use like upper
+
+ align:start position:0%
+when it's really useful I use like upper
+ 
+
+ align:start position:0%
+when it's really useful I use like upper
+or lower indices anyway so this is the
+
+ align:start position:0%
+or lower indices anyway so this is the
+ 
+
+ align:start position:0%
+or lower indices anyway so this is the
+data matrix rows are inputs and columns
+
+ align:start position:0%
+data matrix rows are inputs and columns
+ 
+
+ align:start position:0%
+data matrix rows are inputs and columns
+are so-called features or variables are
+
+ align:start position:0%
+are so-called features or variables are
+ 
+
+ align:start position:0%
+are so-called features or variables are
+the entries of each vector okay and I
+
+ align:start position:0%
+the entries of each vector okay and I
+ 
+
+ align:start position:0%
+the entries of each vector okay and I
+have n rows and P columns associated to
+
+ align:start position:0%
+have n rows and P columns associated to
+ 
+
+ align:start position:0%
+have n rows and P columns associated to
+this I have my output vector and what is
+
+ align:start position:0%
+this I have my output vector and what is
+ 
+
+ align:start position:0%
+this I have my output vector and what is
+the output vector well in this case it
+
+ align:start position:0%
+the output vector well in this case it
+ 
+
+ align:start position:0%
+the output vector well in this case it
+is just a simple binary vector and the
+
+ align:start position:0%
+is just a simple binary vector and the
+ 
+
+ align:start position:0%
+is just a simple binary vector and the
+idea here is if there is a face I put
+
+ align:start position:0%
+idea here is if there is a face I put
+ 
+
+ align:start position:0%
+idea here is if there is a face I put
+one if there is not a face I put minus
+
+ align:start position:0%
+one if there is not a face I put minus
+ 
+
+ align:start position:0%
+one if there is not a face I put minus
+one okay so this is the way I turn like
+
+ align:start position:0%
+one okay so this is the way I turn like
+ 
+
+ align:start position:0%
+one okay so this is the way I turn like
+an abstract question recognize faces in
+
+ align:start position:0%
+an abstract question recognize faces in
+ 
+
+ align:start position:0%
+an abstract question recognize faces in
+images into some data structure that in
+
+ align:start position:0%
+images into some data structure that in
+ 
+
+ align:start position:0%
+images into some data structure that in
+a minute we're going to elaborate to try
+
+ align:start position:0%
+a minute we're going to elaborate to try
+ 
+
+ align:start position:0%
+a minute we're going to elaborate to try
+to actually answer the question whether
+
+ align:start position:0%
+to actually answer the question whether
+ 
+
+ align:start position:0%
+to actually answer the question whether
+there is a face in an image or not okay
+
+ align:start position:0%
+there is a face in an image or not okay
+ 
+
+ align:start position:0%
+there is a face in an image or not okay
+so this first step it's kind of obvious
+
+ align:start position:0%
+so this first step it's kind of obvious
+ 
+
+ align:start position:0%
+so this first step it's kind of obvious
+in this case but it's actually a tricky
+
+ align:start position:0%
+in this case but it's actually a tricky
+ 
+
+ align:start position:0%
+in this case but it's actually a tricky
+step okay is the part where I'm not that
+
+ align:start position:0%
+step okay is the part where I'm not that
+ 
+
+ align:start position:0%
+step okay is the part where I'm not that
+I'm not gonna give you any hint about
+
+ align:start position:0%
+I'm not gonna give you any hint about
+ 
+
+ align:start position:0%
+I'm not gonna give you any hint about
+it's kind of an art you have data and
+
+ align:start position:0%
+it's kind of an art you have data and
+ 
+
+ align:start position:0%
+it's kind of an art you have data and
+you have at the very beginning you have
+
+ align:start position:0%
+you have at the very beginning you have
+ 
+
+ align:start position:0%
+you have at the very beginning you have
+to turn them into some kind of
+
+ align:start position:0%
+to turn them into some kind of
+ 
+
+ align:start position:0%
+to turn them into some kind of
+manageable data structure okay then you
+
+ align:start position:0%
+manageable data structure okay then you
+ 
+
+ align:start position:0%
+manageable data structure okay then you
+can elaborate in multiple ways but the
+
+ align:start position:0%
+can elaborate in multiple ways but the
+ 
+
+ align:start position:0%
+can elaborate in multiple ways but the
+very first step is you deciding for
+
+ align:start position:0%
+very first step is you deciding for
+ 
+
+ align:start position:0%
+very first step is you deciding for
+example here we decided to unroll all
+
+ align:start position:0%
+example here we decided to unroll all
+ 
+
+ align:start position:0%
+example here we decided to unroll all
+these number into vectors this sounds
+
+ align:start position:0%
+these number into vectors this sounds
+ 
+
+ align:start position:0%
+these number into vectors this sounds
+like a good idea or a bad idea
+
+ align:start position:0%
+like a good idea or a bad idea
+ 
+
+ align:start position:0%
+like a good idea or a bad idea
+one thing that you're doing is that the
+
+ align:start position:0%
+one thing that you're doing is that the
+ 
+
+ align:start position:0%
+one thing that you're doing is that the
+pixel here and the pixel here are
+
+ align:start position:0%
+pixel here and the pixel here are
+ 
+
+ align:start position:0%
+pixel here and the pixel here are
+probably related right and in this case
+
+ align:start position:0%
+probably related right and in this case
+ 
+
+ align:start position:0%
+probably related right and in this case
+there are some structure in the image
+
+ align:start position:0%
+there are some structure in the image
+ 
+
+ align:start position:0%
+there are some structure in the image
+and so when you take the expected one
+
+ align:start position:0%
+and so when you take the expected one
+ 
+
+ align:start position:0%
+and so when you take the expected one
+three six and you unroll it it comes
+
+ align:start position:0%
+three six and you unroll it it comes
+ 
+
+ align:start position:0%
+three six and you unroll it it comes
+here so they're not close okay now here
+
+ align:start position:0%
+here so they're not close okay now here
+ 
+
+ align:start position:0%
+here so they're not close okay now here
+it turns out that if you think about it
+
+ align:start position:0%
+it turns out that if you think about it
+ 
+
+ align:start position:0%
+it turns out that if you think about it
+you'll see in a minute for those of you
+
+ align:start position:0%
+you'll see in a minute for those of you
+ 
+
+ align:start position:0%
+you'll see in a minute for those of you
+remember if you just took Euclidean
+
+ align:start position:0%
+remember if you just took Euclidean
+ 
+
+ align:start position:0%
+remember if you just took Euclidean
+distance you take product of numbers and
+
+ align:start position:0%
+distance you take product of numbers and
+ 
+
+ align:start position:0%
+distance you take product of numbers and
+you sum them up that's invariant to the
+
+ align:start position:0%
+you sum them up that's invariant to the
+ 
+
+ align:start position:0%
+you sum them up that's invariant to the
+position of the individual pixels so
+
+ align:start position:0%
+position of the individual pixels so
+ 
+
+ align:start position:0%
+position of the individual pixels so
+that's okay okay but yet again there is
+
+ align:start position:0%
+that's okay okay but yet again there is
+ 
+
+ align:start position:0%
+that's okay okay but yet again there is
+this intuition that well maybe here I'm
+
+ align:start position:0%
+this intuition that well maybe here I'm
+ 
+
+ align:start position:0%
+this intuition that well maybe here I'm
+losing too much geometric information
+
+ align:start position:0%
+losing too much geometric information
+ 
+
+ align:start position:0%
+losing too much geometric information
+about the contact of the image and
+
+ align:start position:0%
+about the contact of the image and
+ 
+
+ align:start position:0%
+about the contact of the image and
+indeed well this kind of work in
+
+ align:start position:0%
+indeed well this kind of work in
+ 
+
+ align:start position:0%
+indeed well this kind of work in
+practice but if you want to get better
+
+ align:start position:0%
+practice but if you want to get better
+ 
+
+ align:start position:0%
+practice but if you want to get better
+results you have to do the fancy stuff
+
+ align:start position:0%
+results you have to do the fancy stuff
+ 
+
+ align:start position:0%
+results you have to do the fancy stuff
+that Andrei was talking about today
+
+ align:start position:0%
+that Andrei was talking about today
+ 
+
+ align:start position:0%
+that Andrei was talking about today
+looking locally and try to look a
+
+ align:start position:0%
+looking locally and try to look a
+ 
+
+ align:start position:0%
+looking locally and try to look a
+collection try to keep more geometric
+
+ align:start position:0%
+collection try to keep more geometric
+ 
+
+ align:start position:0%
+collection try to keep more geometric
+information okay so I'm not going to
+
+ align:start position:0%
+information okay so I'm not going to
+ 
+
+ align:start position:0%
+information okay so I'm not going to
+talk about that kind of stuff this up
+
+ align:start position:0%
+talk about that kind of stuff this up
+ 
+
+ align:start position:0%
+talk about that kind of stuff this up
+today it's a lot of engineering and some
+
+ align:start position:0%
+today it's a lot of engineering and some
+ 
+
+ align:start position:0%
+today it's a lot of engineering and some
+good way to learn it but we're gonna try
+
+ align:start position:0%
+good way to learn it but we're gonna try
+ 
+
+ align:start position:0%
+good way to learn it but we're gonna try
+to just stick to simple representations
+
+ align:start position:0%
+to just stick to simple representations
+ 
+
+ align:start position:0%
+to just stick to simple representations
+okay so how do you build representation
+
+ align:start position:0%
+okay so how do you build representation
+ 
+
+ align:start position:0%
+okay so how do you build representation
+is now gonna be part of the what I'm
+
+ align:start position:0%
+is now gonna be part of the what I'm
+ 
+
+ align:start position:0%
+is now gonna be part of the what I'm
+gonna talk about so imagine that either
+
+ align:start position:0%
+gonna talk about so imagine that either
+ 
+
+ align:start position:0%
+gonna talk about so imagine that either
+you stick to this super simple
+
+ align:start position:0%
+you stick to this super simple
+ 
+
+ align:start position:0%
+you stick to this super simple
+representation or some friends of yours
+
+ align:start position:0%
+representation or some friends of yours
+ 
+
+ align:start position:0%
+representation or some friends of yours
+come in and put a box here in the middle
+
+ align:start position:0%
+come in and put a box here in the middle
+ 
+
+ align:start position:0%
+come in and put a box here in the middle
+where you put this array of numbers and
+
+ align:start position:0%
+where you put this array of numbers and
+ 
+
+ align:start position:0%
+where you put this array of numbers and
+you extract another vector much fancier
+
+ align:start position:0%
+you extract another vector much fancier
+ 
+
+ align:start position:0%
+you extract another vector much fancier
+than this that contains some better
+
+ align:start position:0%
+than this that contains some better
+ 
+
+ align:start position:0%
+than this that contains some better
+representation of an image okay but then
+
+ align:start position:0%
+representation of an image okay but then
+ 
+
+ align:start position:0%
+representation of an image okay but then
+in the end of the day my job starts when
+
+ align:start position:0%
+in the end of the day my job starts when
+ 
+
+ align:start position:0%
+in the end of the day my job starts when
+you give me a vector representation that
+
+ align:start position:0%
+you give me a vector representation that
+ 
+
+ align:start position:0%
+you give me a vector representation that
+I can trust and I can basically say that
+
+ align:start position:0%
+I can trust and I can basically say that
+ 
+
+ align:start position:0%
+I can trust and I can basically say that
+if two vectors seems similar they should
+
+ align:start position:0%
+if two vectors seems similar they should
+ 
+
+ align:start position:0%
+if two vectors seems similar they should
+have the same label and that's the basic
+
+ align:start position:0%
+have the same label and that's the basic
+ 
+
+ align:start position:0%
+have the same label and that's the basic
+idea okay all right so the little game
+
+ align:start position:0%
+idea okay all right so the little game
+ 
+
+ align:start position:0%
+idea okay all right so the little game
+here is okay imagine that these are just
+
+ align:start position:0%
+here is okay imagine that these are just
+ 
+
+ align:start position:0%
+here is okay imagine that these are just
+the two pixel version of the images I
+
+ align:start position:0%
+the two pixel version of the images I
+ 
+
+ align:start position:0%
+the two pixel version of the images I
+show you before you have some boxes some
+
+ align:start position:0%
+show you before you have some boxes some
+ 
+
+ align:start position:0%
+show you before you have some boxes some
+some circles and then I give you this
+
+ align:start position:0%
+some circles and then I give you this
+ 
+
+ align:start position:0%
+some circles and then I give you this
+one triangle very original and very show
+
+ align:start position:0%
+one triangle very original and very show
+ 
+
+ align:start position:0%
+one triangle very original and very show
+you this yesterday and the question is
+
+ align:start position:0%
+you this yesterday and the question is
+ 
+
+ align:start position:0%
+you this yesterday and the question is
+what's the color of that okay and unless
+
+ align:start position:0%
+what's the color of that okay and unless
+ 
+
+ align:start position:0%
+what's the color of that okay and unless
+you are you haven't slept a minute
+
+ align:start position:0%
+you are you haven't slept a minute
+ 
+
+ align:start position:0%
+you are you haven't slept a minute
+you're gonna say it's orange but the
+
+ align:start position:0%
+you're gonna say it's orange but the
+ 
+
+ align:start position:0%
+you're gonna say it's orange but the
+question is how do you why you think
+
+ align:start position:0%
+question is how do you why you think
+ 
+
+ align:start position:0%
+question is how do you why you think
+it's orange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry on it surrounded by oranges okay
+
+ align:start position:0%
+sorry on it surrounded by oranges okay
+ 
+
+ align:start position:0%
+sorry on it surrounded by oranges okay
+and she said it's close to oranges so it
+
+ align:start position:0%
+and she said it's close to oranges so it
+ 
+
+ align:start position:0%
+and she said it's close to oranges so it
+turns out that this is actually the
+
+ align:start position:0%
+turns out that this is actually the
+ 
+
+ align:start position:0%
+turns out that this is actually the
+simplest algorithm you can think of okay
+
+ align:start position:0%
+simplest algorithm you can think of okay
+ 
+
+ align:start position:0%
+simplest algorithm you can think of okay
+you check who you have close to you and
+
+ align:start position:0%
+you check who you have close to you and
+ 
+
+ align:start position:0%
+you check who you have close to you and
+if it's orange you say orange and if
+
+ align:start position:0%
+if it's orange you say orange and if
+ 
+
+ align:start position:0%
+if it's orange you say orange and if
+it's blue you say blue okay but we
+
+ align:start position:0%
+it's blue you say blue okay but we
+ 
+
+ align:start position:0%
+it's blue you say blue okay but we
+already made an assumption here which
+
+ align:start position:0%
+already made an assumption here which
+ 
+
+ align:start position:0%
+already made an assumption here which
+was green question which is that nearby
+
+ align:start position:0%
+was green question which is that nearby
+ 
+
+ align:start position:0%
+was green question which is that nearby
+things so we are basically saying that
+
+ align:start position:0%
+things so we are basically saying that
+ 
+
+ align:start position:0%
+things so we are basically saying that
+our victorial representation is such
+
+ align:start position:0%
+our victorial representation is such
+ 
+
+ align:start position:0%
+our victorial representation is such
+that if two things are close so I do
+
+ align:start position:0%
+that if two things are close so I do
+ 
+
+ align:start position:0%
+that if two things are close so I do
+have a distance and if two things are
+
+ align:start position:0%
+have a distance and if two things are
+ 
+
+ align:start position:0%
+have a distance and if two things are
+close then they might have the same
+
+ align:start position:0%
+close then they might have the same
+ 
+
+ align:start position:0%
+close then they might have the same
+semantic content okay which might be
+
+ align:start position:0%
+semantic content okay which might be
+ 
+
+ align:start position:0%
+semantic content okay which might be
+true or not for example if you take this
+
+ align:start position:0%
+true or not for example if you take this
+ 
+
+ align:start position:0%
+true or not for example if you take this
+inter you know this thing I show you
+
+ align:start position:0%
+inter you know this thing I show you
+ 
+
+ align:start position:0%
+inter you know this thing I show you
+here well we cannot just draw it right
+
+ align:start position:0%
+here well we cannot just draw it right
+ 
+
+ align:start position:0%
+here well we cannot just draw it right
+we cannot just take you know 200 times
+
+ align:start position:0%
+we cannot just take you know 200 times
+ 
+
+ align:start position:0%
+we cannot just take you know 200 times
+200 vectors and just look at them and
+
+ align:start position:0%
+200 vectors and just look at them and
+ 
+
+ align:start position:0%
+200 vectors and just look at them and
+say you know visual inspection you have
+
+ align:start position:0%
+say you know visual inspection you have
+ 
+
+ align:start position:0%
+say you know visual inspection you have
+to believe that this distance will be
+
+ align:start position:0%
+to believe that this distance will be
+ 
+
+ align:start position:0%
+to believe that this distance will be
+fine and so the discussion that we just
+
+ align:start position:0%
+fine and so the discussion that we just
+ 
+
+ align:start position:0%
+fine and so the discussion that we just
+tell about what is a good representation
+
+ align:start position:0%
+tell about what is a good representation
+ 
+
+ align:start position:0%
+tell about what is a good representation
+is gonna kick in okay
+
+ align:start position:0%
+is gonna kick in okay
+ 
+
+ align:start position:0%
+is gonna kick in okay
+but the assumption you make in this case
+
+ align:start position:0%
+but the assumption you make in this case
+ 
+
+ align:start position:0%
+but the assumption you make in this case
+visually it's very easy it's low
+
+ align:start position:0%
+visually it's very easy it's low
+ 
+
+ align:start position:0%
+visually it's very easy it's low
+dimension is that nearby things have
+
+ align:start position:0%
+dimension is that nearby things have
+ 
+
+ align:start position:0%
+dimension is that nearby things have
+similar labels one thing that I forgot
+
+ align:start position:0%
+similar labels one thing that I forgot
+ 
+
+ align:start position:0%
+similar labels one thing that I forgot
+to tell you in the previous slides but
+
+ align:start position:0%
+to tell you in the previous slides but
+ 
+
+ align:start position:0%
+to tell you in the previous slides but
+it's key is exactly this observation
+
+ align:start position:0%
+it's key is exactly this observation
+ 
+
+ align:start position:0%
+it's key is exactly this observation
+that we move away in machine learning we
+
+ align:start position:0%
+that we move away in machine learning we
+ 
+
+ align:start position:0%
+that we move away in machine learning we
+typically move away from situation like
+
+ align:start position:0%
+typically move away from situation like
+ 
+
+ align:start position:0%
+typically move away from situation like
+this one where you can do visual
+
+ align:start position:0%
+this one where you can do visual
+ 
+
+ align:start position:0%
+this one where you can do visual
+inspection and you have low
+
+ align:start position:0%
+inspection and you have low
+ 
+
+ align:start position:0%
+inspection and you have low
+dimensionality to kind of situation like
+
+ align:start position:0%
+dimensionality to kind of situation like
+ 
+
+ align:start position:0%
+dimensionality to kind of situation like
+the one I just show you in a minute
+
+ align:start position:0%
+the one I just show you in a minute
+ 
+
+ align:start position:0%
+the one I just show you in a minute
+before where you have images and if you
+
+ align:start position:0%
+before where you have images and if you
+ 
+
+ align:start position:0%
+before where you have images and if you
+have to think of each of these circles
+
+ align:start position:0%
+have to think of each of these circles
+ 
+
+ align:start position:0%
+have to think of each of these circles
+as an image you won't be able to draw it
+
+ align:start position:0%
+as an image you won't be able to draw it
+ 
+
+ align:start position:0%
+as an image you won't be able to draw it
+because it's gonna be a several hundreds
+
+ align:start position:0%
+because it's gonna be a several hundreds
+ 
+
+ align:start position:0%
+because it's gonna be a several hundreds
+typical or tens dimensional vector okay
+
+ align:start position:0%
+typical or tens dimensional vector okay
+ 
+
+ align:start position:0%
+typical or tens dimensional vector okay
+so the game is kind of different you
+
+ align:start position:0%
+so the game is kind of different you
+ 
+
+ align:start position:0%
+so the game is kind of different you
+know how many of the things that you
+
+ align:start position:0%
+know how many of the things that you
+ 
+
+ align:start position:0%
+know how many of the things that you
+know can we still do this kind of stuff
+
+ align:start position:0%
+know can we still do this kind of stuff
+ 
+
+ align:start position:0%
+know can we still do this kind of stuff
+can we just say that close things or
+
+ align:start position:0%
+can we just say that close things or
+ 
+
+ align:start position:0%
+can we just say that close things or
+should have the same semantic content
+
+ align:start position:0%
+should have the same semantic content
+ 
+
+ align:start position:0%
+should have the same semantic content
+that's another question we try to answer
+
+ align:start position:0%
+that's another question we try to answer
+ 
+
+ align:start position:0%
+that's another question we try to answer
+okay but so I just want to do a bit of
+
+ align:start position:0%
+okay but so I just want to do a bit of
+ 
+
+ align:start position:0%
+okay but so I just want to do a bit of
+an exception this is a big deal okay
+
+ align:start position:0%
+an exception this is a big deal okay
+ 
+
+ align:start position:0%
+an exception this is a big deal okay
+going from low dimension to very high
+
+ align:start position:0%
+going from low dimension to very high
+ 
+
+ align:start position:0%
+going from low dimension to very high
+dimensions alright but let's stick for a
+
+ align:start position:0%
+dimensions alright but let's stick for a
+ 
+
+ align:start position:0%
+dimensions alright but let's stick for a
+minute to the idea that nearby things
+
+ align:start position:0%
+minute to the idea that nearby things
+ 
+
+ align:start position:0%
+minute to the idea that nearby things
+should have the same label and just just
+
+ align:start position:0%
+should have the same label and just just
+ 
+
+ align:start position:0%
+should have the same label and just just
+write the one line that write down the
+
+ align:start position:0%
+write the one line that write down the
+ 
+
+ align:start position:0%
+write the one line that write down the
+algorithm it's the kind of cases where
+
+ align:start position:0%
+algorithm it's the kind of cases where
+ 
+
+ align:start position:0%
+algorithm it's the kind of cases where
+it's harder to write it down than to
+
+ align:start position:0%
+it's harder to write it down than to
+ 
+
+ align:start position:0%
+it's harder to write it down than to
+code it up we'll just explain what it is
+
+ align:start position:0%
+code it up we'll just explain what it is
+ 
+
+ align:start position:0%
+code it up we'll just explain what it is
+it's super simple what you
+
+ align:start position:0%
+it's super simple what you
+ 
+
+ align:start position:0%
+it's super simple what you
+is you have data points X I so X I is
+
+ align:start position:0%
+is you have data points X I so X I is
+ 
+
+ align:start position:0%
+is you have data points X I so X I is
+the training set the input data in the
+
+ align:start position:0%
+the training set the input data in the
+ 
+
+ align:start position:0%
+the training set the input data in the
+training set X bar is what I call X new
+
+ align:start position:0%
+training set X bar is what I call X new
+ 
+
+ align:start position:0%
+training set X bar is what I call X new
+before it's a new point what you do is
+
+ align:start position:0%
+before it's a new point what you do is
+ 
+
+ align:start position:0%
+before it's a new point what you do is
+that you search this just says look for
+
+ align:start position:0%
+that you search this just says look for
+ 
+
+ align:start position:0%
+that you search this just says look for
+the index of the closest point that's
+
+ align:start position:0%
+the index of the closest point that's
+ 
+
+ align:start position:0%
+the index of the closest point that's
+what you did before okay so here I prime
+
+ align:start position:0%
+what you did before okay so here I prime
+ 
+
+ align:start position:0%
+what you did before okay so here I prime
+is the index of the point X I closes to
+
+ align:start position:0%
+is the index of the point X I closes to
+ 
+
+ align:start position:0%
+is the index of the point X I closes to
+X bar once you find it go in your data
+
+ align:start position:0%
+X bar once you find it go in your data
+ 
+
+ align:start position:0%
+X bar once you find it go in your data
+set and find the label of that point and
+
+ align:start position:0%
+set and find the label of that point and
+ 
+
+ align:start position:0%
+set and find the label of that point and
+then assign that label to the new point
+
+ align:start position:0%
+then assign that label to the new point
+ 
+
+ align:start position:0%
+then assign that label to the new point
+that make sense everybody's happy
+
+ align:start position:0%
+that make sense everybody's happy
+ 
+
+ align:start position:0%
+that make sense everybody's happy
+not super complicated fair enough
+
+ align:start position:0%
+not super complicated fair enough
+ 
+
+ align:start position:0%
+not super complicated fair enough
+how does it work so let me see if I can
+
+ align:start position:0%
+how does it work so let me see if I can
+ 
+
+ align:start position:0%
+how does it work so let me see if I can
+do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is extremely fancy code let's see
+
+ align:start position:0%
+this is extremely fancy code let's see
+ 
+
+ align:start position:0%
+this is extremely fancy code let's see
+all right so what I do let me do it it'd
+
+ align:start position:0%
+all right so what I do let me do it it'd
+ 
+
+ align:start position:0%
+all right so what I do let me do it it'd
+be smaller so this is just a simple two
+
+ align:start position:0%
+be smaller so this is just a simple two
+ 
+
+ align:start position:0%
+be smaller so this is just a simple two
+dimensional data sets I take 40 points
+
+ align:start position:0%
+dimensional data sets I take 40 points
+ 
+
+ align:start position:0%
+dimensional data sets I take 40 points
+this is just to the data set look like
+
+ align:start position:0%
+this is just to the data set look like
+ 
+
+ align:start position:0%
+this is just to the data set look like
+this the data set is the one on the left
+
+ align:start position:0%
+this the data set is the one on the left
+ 
+
+ align:start position:0%
+this the data set is the one on the left
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and what I do I take 40 points and to
+
+ align:start position:0%
+and what I do I take 40 points and to
+ 
+
+ align:start position:0%
+and what I do I take 40 points and to
+make it a bit more complex
+
+ align:start position:0%
+make it a bit more complex
+ 
+
+ align:start position:0%
+make it a bit more complex
+I flip some of the labels okay so you
+
+ align:start position:0%
+I flip some of the labels okay so you
+ 
+
+ align:start position:0%
+I flip some of the labels okay so you
+basically see that the two data sets are
+
+ align:start position:0%
+basically see that the two data sets are
+ 
+
+ align:start position:0%
+basically see that the two data sets are
+this is called the two moons data set or
+
+ align:start position:0%
+this is called the two moons data set or
+ 
+
+ align:start position:0%
+this is called the two moons data set or
+something like this and what I did is
+
+ align:start position:0%
+something like this and what I did is
+ 
+
+ align:start position:0%
+something like this and what I did is
+that some of the labels in this see I
+
+ align:start position:0%
+that some of the labels in this see I
+ 
+
+ align:start position:0%
+that some of the labels in this see I
+change color I change label okay so that
+
+ align:start position:0%
+change color I change label okay so that
+ 
+
+ align:start position:0%
+change color I change label okay so that
+I make the problem a bit harder and here
+
+ align:start position:0%
+I make the problem a bit harder and here
+ 
+
+ align:start position:0%
+I make the problem a bit harder and here
+it's what you will fortunately you don't
+
+ align:start position:0%
+it's what you will fortunately you don't
+ 
+
+ align:start position:0%
+it's what you will fortunately you don't
+have in practice okay here we're
+
+ align:start position:0%
+have in practice okay here we're
+ 
+
+ align:start position:0%
+have in practice okay here we're
+cheating we're doing just the
+
+ align:start position:0%
+cheating we're doing just the
+ 
+
+ align:start position:0%
+cheating we're doing just the
+simulations we're looking at the future
+
+ align:start position:0%
+simulations we're looking at the future
+ 
+
+ align:start position:0%
+simulations we're looking at the future
+we assumed that because we can generate
+
+ align:start position:0%
+we assumed that because we can generate
+ 
+
+ align:start position:0%
+we assumed that because we can generate
+this data we can look at the future and
+
+ align:start position:0%
+this data we can look at the future and
+ 
+
+ align:start position:0%
+this data we can look at the future and
+check how we're going to do and future
+
+ align:start position:0%
+check how we're going to do and future
+ 
+
+ align:start position:0%
+check how we're going to do and future
+data so you can think of these as future
+
+ align:start position:0%
+data so you can think of these as future
+ 
+
+ align:start position:0%
+data so you can think of these as future
+data that typically you don't have so
+
+ align:start position:0%
+data that typically you don't have so
+ 
+
+ align:start position:0%
+data that typically you don't have so
+here you're a normal human being here
+
+ align:start position:0%
+here you're a normal human being here
+ 
+
+ align:start position:0%
+here you're a normal human being here
+you're playing God and looking at the
+
+ align:start position:0%
+you're playing God and looking at the
+ 
+
+ align:start position:0%
+you're playing God and looking at the
+future okay because we just want to do a
+
+ align:start position:0%
+future okay because we just want to do a
+ 
+
+ align:start position:0%
+future okay because we just want to do a
+little simulation so based on that we
+
+ align:start position:0%
+little simulation so based on that we
+ 
+
+ align:start position:0%
+little simulation so based on that we
+can just go here put one string and then
+
+ align:start position:0%
+can just go here put one string and then
+ 
+
+ align:start position:0%
+can just go here put one string and then
+test and plot so what you see here is
+
+ align:start position:0%
+test and plot so what you see here is
+ 
+
+ align:start position:0%
+test and plot so what you see here is
+the so-called decision boundary okay
+
+ align:start position:0%
+the so-called decision boundary okay
+ 
+
+ align:start position:0%
+the so-called decision boundary okay
+what I did is what we it's the cook is
+
+ align:start position:0%
+what I did is what we it's the cook is
+ 
+
+ align:start position:0%
+what I did is what we it's the cook is
+exactly that one line of code you saw
+
+ align:start position:0%
+exactly that one line of code you saw
+ 
+
+ align:start position:0%
+exactly that one line of code you saw
+before okay and what I did is this case
+
+ align:start position:0%
+before okay and what I did is this case
+ 
+
+ align:start position:0%
+before okay and what I did is this case
+I can draw it because it's low dimension
+
+ align:start position:0%
+I can draw it because it's low dimension
+ 
+
+ align:start position:0%
+I can draw it because it's low dimension
+and basically what they do is that I
+
+ align:start position:0%
+and basically what they do is that I
+ 
+
+ align:start position:0%
+and basically what they do is that I
+just put in the regions where I think I
+
+ align:start position:0%
+just put in the regions where I think I
+ 
+
+ align:start position:0%
+just put in the regions where I think I
+should put orange and the region where I
+
+ align:start position:0%
+should put orange and the region where I
+ 
+
+ align:start position:0%
+should put orange and the region where I
+think I should put blue okay and here
+
+ align:start position:0%
+think I should put blue okay and here
+ 
+
+ align:start position:0%
+think I should put blue okay and here
+you can kind of see what's going on this
+
+ align:start position:0%
+you can kind of see what's going on this
+ 
+
+ align:start position:0%
+you can kind of see what's going on this
+is actually very good on the data right
+
+ align:start position:0%
+is actually very good on the data right
+ 
+
+ align:start position:0%
+is actually very good on the data right
+how many mistakes do you make on the new
+
+ align:start position:0%
+how many mistakes do you make on the new
+ 
+
+ align:start position:0%
+how many mistakes do you make on the new
+data set oh sorry on the on the training
+
+ align:start position:0%
+data set oh sorry on the on the training
+ 
+
+ align:start position:0%
+data set oh sorry on the on the training
+set zero it's perfect okay is that a
+
+ align:start position:0%
+set zero it's perfect okay is that a
+ 
+
+ align:start position:0%
+set zero it's perfect okay is that a
+good idea well when you look at it here
+
+ align:start position:0%
+good idea well when you look at it here
+ 
+
+ align:start position:0%
+good idea well when you look at it here
+it doesn't look that good okay there is
+
+ align:start position:0%
+it doesn't look that good okay there is
+ 
+
+ align:start position:0%
+it doesn't look that good okay there is
+this whole region of point for example
+
+ align:start position:0%
+this whole region of point for example
+ 
+
+ align:start position:0%
+this whole region of point for example
+there are going to be
+
+ align:start position:0%
+there are going to be
+ 
+
+ align:start position:0%
+there are going to be
+predicted to be orange but they're
+
+ align:start position:0%
+predicted to be orange but they're
+ 
+
+ align:start position:0%
+predicted to be orange but they're
+actually blue of course if you want to
+
+ align:start position:0%
+actually blue of course if you want to
+ 
+
+ align:start position:0%
+actually blue of course if you want to
+have zero air on the training set
+
+ align:start position:0%
+have zero air on the training set
+ 
+
+ align:start position:0%
+have zero air on the training set
+there's nothing else you can do right
+
+ align:start position:0%
+there's nothing else you can do right
+ 
+
+ align:start position:0%
+there's nothing else you can do right
+because you see you have this orange
+
+ align:start position:0%
+because you see you have this orange
+ 
+
+ align:start position:0%
+because you see you have this orange
+point here you have these two orange
+
+ align:start position:0%
+point here you have these two orange
+ 
+
+ align:start position:0%
+point here you have these two orange
+points here and you want to go and
+
+ align:start position:0%
+points here and you want to go and
+ 
+
+ align:start position:0%
+points here and you want to go and
+follow them so there's nothing you can
+
+ align:start position:0%
+follow them so there's nothing you can
+ 
+
+ align:start position:0%
+follow them so there's nothing you can
+do so this is the first observation the
+
+ align:start position:0%
+do so this is the first observation the
+ 
+
+ align:start position:0%
+do so this is the first observation the
+second observation is the curve if you
+
+ align:start position:0%
+second observation is the curve if you
+ 
+
+ align:start position:0%
+second observation is the curve if you
+look close enough it's piecewise linear
+
+ align:start position:0%
+look close enough it's piecewise linear
+ 
+
+ align:start position:0%
+look close enough it's piecewise linear
+it's like a sequence of piece linear
+
+ align:start position:0%
+it's like a sequence of piece linear
+ 
+
+ align:start position:0%
+it's like a sequence of piece linear
+pieces stuck together if we just try to
+
+ align:start position:0%
+pieces stuck together if we just try to
+ 
+
+ align:start position:0%
+pieces stuck together if we just try to
+do a little game and generate some new
+
+ align:start position:0%
+do a little game and generate some new
+ 
+
+ align:start position:0%
+do a little game and generate some new
+data okay so imagine again I'm playing
+
+ align:start position:0%
+data okay so imagine again I'm playing
+ 
+
+ align:start position:0%
+data okay so imagine again I'm playing
+God now I judge enervate a new data set
+
+ align:start position:0%
+God now I judge enervate a new data set
+ 
+
+ align:start position:0%
+God now I judge enervate a new data set
+that should look like so take another
+
+ align:start position:0%
+that should look like so take another
+ 
+
+ align:start position:0%
+that should look like so take another
+peek at this okay so now I generate them
+
+ align:start position:0%
+peek at this okay so now I generate them
+ 
+
+ align:start position:0%
+peek at this okay so now I generate them
+I plot them I train
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now let's test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you remember that decision
+
+ align:start position:0%
+okay if you remember that decision
+ 
+
+ align:start position:0%
+okay if you remember that decision
+curves you've seen before what do you
+
+ align:start position:0%
+curves you've seen before what do you
+ 
+
+ align:start position:0%
+curves you've seen before what do you
+notice here they're very different
+
+ align:start position:0%
+notice here they're very different
+ 
+
+ align:start position:0%
+notice here they're very different
+okay for example that one before if you
+
+ align:start position:0%
+okay for example that one before if you
+ 
+
+ align:start position:0%
+okay for example that one before if you
+remember we notice it was going all the
+
+ align:start position:0%
+remember we notice it was going all the
+ 
+
+ align:start position:0%
+remember we notice it was going all the
+way down here to follow those couple of
+
+ align:start position:0%
+way down here to follow those couple of
+ 
+
+ align:start position:0%
+way down here to follow those couple of
+points but here you don't have those
+
+ align:start position:0%
+points but here you don't have those
+ 
+
+ align:start position:0%
+points but here you don't have those
+couple of points okay so now is that a
+
+ align:start position:0%
+couple of points okay so now is that a
+ 
+
+ align:start position:0%
+couple of points okay so now is that a
+good thing or a bad thing well the point
+
+ align:start position:0%
+good thing or a bad thing well the point
+ 
+
+ align:start position:0%
+good thing or a bad thing well the point
+here is that because you have so few
+
+ align:start position:0%
+here is that because you have so few
+ 
+
+ align:start position:0%
+here is that because you have so few
+points the moment you start to just fit
+
+ align:start position:0%
+points the moment you start to just fit
+ 
+
+ align:start position:0%
+points the moment you start to just fit
+the date that this will happen okay you
+
+ align:start position:0%
+the date that this will happen okay you
+ 
+
+ align:start position:0%
+the date that this will happen okay you
+have something that changes all the time
+
+ align:start position:0%
+have something that changes all the time
+ 
+
+ align:start position:0%
+have something that changes all the time
+it's very unstable that's a key word
+
+ align:start position:0%
+it's very unstable that's a key word
+ 
+
+ align:start position:0%
+it's very unstable that's a key word
+okay you have something that you change
+
+ align:start position:0%
+okay you have something that you change
+ 
+
+ align:start position:0%
+okay you have something that you change
+the data just a little bit and changes
+
+ align:start position:0%
+the data just a little bit and changes
+ 
+
+ align:start position:0%
+the data just a little bit and changes
+completely that sounds like a bad idea
+
+ align:start position:0%
+completely that sounds like a bad idea
+ 
+
+ align:start position:0%
+completely that sounds like a bad idea
+okay if I want to make prediction if I
+
+ align:start position:0%
+okay if I want to make prediction if I
+ 
+
+ align:start position:0%
+okay if I want to make prediction if I
+keep on getting little data you know
+
+ align:start position:0%
+keep on getting little data you know
+ 
+
+ align:start position:0%
+keep on getting little data you know
+slightly different data and I change my
+
+ align:start position:0%
+slightly different data and I change my
+ 
+
+ align:start position:0%
+slightly different data and I change my
+mind completely that's probably not a
+
+ align:start position:0%
+mind completely that's probably not a
+ 
+
+ align:start position:0%
+mind completely that's probably not a
+good way to make prediction about
+
+ align:start position:0%
+good way to make prediction about
+ 
+
+ align:start position:0%
+good way to make prediction about
+anything okay and this is happening all
+
+ align:start position:0%
+anything okay and this is happening all
+ 
+
+ align:start position:0%
+anything okay and this is happening all
+the time here and it's exactly because
+
+ align:start position:0%
+the time here and it's exactly because
+ 
+
+ align:start position:0%
+the time here and it's exactly because
+our algorithm means in some sense is
+
+ align:start position:0%
+our algorithm means in some sense is
+ 
+
+ align:start position:0%
+our algorithm means in some sense is
+greedy you just try to get perfect
+
+ align:start position:0%
+greedy you just try to get perfect
+ 
+
+ align:start position:0%
+greedy you just try to get perfect
+performance on the training set without
+
+ align:start position:0%
+performance on the training set without
+ 
+
+ align:start position:0%
+performance on the training set without
+much of worrying much about the future
+
+ align:start position:0%
+much of worrying much about the future
+ 
+
+ align:start position:0%
+much of worrying much about the future
+let's do it just once more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we keeping keep on going okay
+
+ align:start position:0%
+okay and we keeping keep on going okay
+ 
+
+ align:start position:0%
+okay and we keeping keep on going okay
+is gonna change all the time all the
+
+ align:start position:0%
+is gonna change all the time all the
+ 
+
+ align:start position:0%
+is gonna change all the time all the
+time of course no I don't know how much
+
+ align:start position:0%
+time of course no I don't know how much
+ 
+
+ align:start position:0%
+time of course no I don't know how much
+I can push this because it's not super
+
+ align:start position:0%
+I can push this because it's not super
+ 
+
+ align:start position:0%
+I can push this because it's not super
+duper fast but let's try 30
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I did now is just that I hope
+
+ align:start position:0%
+so what I did now is just that I hope
+ 
+
+ align:start position:0%
+so what I did now is just that I hope
+mented the number of points in my
+
+ align:start position:0%
+mented the number of points in my
+ 
+
+ align:start position:0%
+mented the number of points in my
+training set it was a twenty or thirty I
+
+ align:start position:0%
+training set it was a twenty or thirty I
+ 
+
+ align:start position:0%
+training set it was a twenty or thirty I
+remember now I make it a hundred
+
+ align:start position:0%
+remember now I make it a hundred
+ 
+
+ align:start position:0%
+remember now I make it a hundred
+so now you should see okay so this is
+
+ align:start position:0%
+so now you should see okay so this is
+ 
+
+ align:start position:0%
+so now you should see okay so this is
+one solution we want to play the same
+
+ align:start position:0%
+one solution we want to play the same
+ 
+
+ align:start position:0%
+one solution we want to play the same
+game just want to generate in other data
+
+ align:start position:0%
+game just want to generate in other data
+ 
+
+ align:start position:0%
+game just want to generate in other data
+sets of the same so maybe now we're
+
+ align:start position:0%
+sets of the same so maybe now we're
+ 
+
+ align:start position:0%
+sets of the same so maybe now we're
+gonna it might be that I took them all
+
+ align:start position:0%
+gonna it might be that I took them all
+ 
+
+ align:start position:0%
+gonna it might be that I took them all
+and I remember how many they are no I
+
+ align:start position:0%
+and I remember how many they are no I
+ 
+
+ align:start position:0%
+and I remember how many they are no I
+didn't take them all so what do you see
+
+ align:start position:0%
+didn't take them all so what do you see
+ 
+
+ align:start position:0%
+didn't take them all so what do you see
+now we are doing exactly the same thing
+
+ align:start position:0%
+now we are doing exactly the same thing
+ 
+
+ align:start position:0%
+now we are doing exactly the same thing
+okay and this is something that you can
+
+ align:start position:0%
+okay and this is something that you can
+ 
+
+ align:start position:0%
+okay and this is something that you can
+absolutely not do in practice because
+
+ align:start position:0%
+absolutely not do in practice because
+ 
+
+ align:start position:0%
+absolutely not do in practice because
+you cannot just generate data sets but
+
+ align:start position:0%
+you cannot just generate data sets but
+ 
+
+ align:start position:0%
+you cannot just generate data sets but
+here what you see is that I just
+
+ align:start position:0%
+here what you see is that I just
+ 
+
+ align:start position:0%
+here what you see is that I just
+augmented the number of training set
+
+ align:start position:0%
+augmented the number of training set
+ 
+
+ align:start position:0%
+augmented the number of training set
+points and what you see that now the
+
+ align:start position:0%
+points and what you see that now the
+ 
+
+ align:start position:0%
+points and what you see that now the
+solution does change but not as much
+
+ align:start position:0%
+solution does change but not as much
+ 
+
+ align:start position:0%
+solution does change but not as much
+okay and you can kind of start to see
+
+ align:start position:0%
+okay and you can kind of start to see
+ 
+
+ align:start position:0%
+okay and you can kind of start to see
+that there is something going on a bit
+
+ align:start position:0%
+that there is something going on a bit
+ 
+
+ align:start position:0%
+that there is something going on a bit
+like this here okay so this one actually
+
+ align:start position:0%
+like this here okay so this one actually
+ 
+
+ align:start position:0%
+like this here okay so this one actually
+looks pretty bad let's try to do one
+
+ align:start position:0%
+looks pretty bad let's try to do one
+ 
+
+ align:start position:0%
+looks pretty bad let's try to do one
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again it does change a lot but
+
+ align:start position:0%
+okay so again it does change a lot but
+ 
+
+ align:start position:0%
+okay so again it does change a lot but
+not as much as before and you roughly
+
+ align:start position:0%
+not as much as before and you roughly
+ 
+
+ align:start position:0%
+not as much as before and you roughly
+see that this guy says that here it
+
+ align:start position:0%
+see that this guy says that here it
+ 
+
+ align:start position:0%
+see that this guy says that here it
+should be orange and here should be blue
+
+ align:start position:0%
+should be orange and here should be blue
+ 
+
+ align:start position:0%
+should be orange and here should be blue
+okay so that's kind of what you expect
+
+ align:start position:0%
+okay so that's kind of what you expect
+ 
+
+ align:start position:0%
+okay so that's kind of what you expect
+the number of the more points you get
+
+ align:start position:0%
+the number of the more points you get
+ 
+
+ align:start position:0%
+the number of the more points you get
+the better your solution would get and
+
+ align:start position:0%
+the better your solution would get and
+ 
+
+ align:start position:0%
+the better your solution would get and
+if I put here all the possible points
+
+ align:start position:0%
+if I put here all the possible points
+ 
+
+ align:start position:0%
+if I put here all the possible points
+what you will start to see is that the
+
+ align:start position:0%
+what you will start to see is that the
+ 
+
+ align:start position:0%
+what you will start to see is that the
+closest point to any point here will be
+
+ align:start position:0%
+closest point to any point here will be
+ 
+
+ align:start position:0%
+closest point to any point here will be
+a blue point okay so will be perfect so
+
+ align:start position:0%
+a blue point okay so will be perfect so
+ 
+
+ align:start position:0%
+a blue point okay so will be perfect so
+if I ask you if this is a good alga
+
+ align:start position:0%
+if I ask you if this is a good alga
+ 
+
+ align:start position:0%
+if I ask you if this is a good alga
+rhythm or not
+
+ align:start position:0%
+rhythm or not
+ 
+
+ align:start position:0%
+rhythm or not
+what would you say it's kind of over
+
+ align:start position:0%
+what would you say it's kind of over
+ 
+
+ align:start position:0%
+what would you say it's kind of over
+fitting the data but it's not always
+
+ align:start position:0%
+fitting the data but it's not always
+ 
+
+ align:start position:0%
+fitting the data but it's not always
+overfitting the date if they did are
+
+ align:start position:0%
+overfitting the date if they did are
+ 
+
+ align:start position:0%
+overfitting the date if they did are
+good oh it's a good idea to feed them
+
+ align:start position:0%
+good oh it's a good idea to feed them
+ 
+
+ align:start position:0%
+good oh it's a good idea to feed them
+okay but so in some sense these
+
+ align:start position:0%
+okay but so in some sense these
+ 
+
+ align:start position:0%
+okay but so in some sense these
+algorithm doesn't have a way to prevent
+
+ align:start position:0%
+algorithm doesn't have a way to prevent
+ 
+
+ align:start position:0%
+algorithm doesn't have a way to prevent
+itself to fall in love with the data
+
+ align:start position:0%
+itself to fall in love with the data
+ 
+
+ align:start position:0%
+itself to fall in love with the data
+when they're very few and if you have
+
+ align:start position:0%
+when they're very few and if you have
+ 
+
+ align:start position:0%
+when they're very few and if you have
+very few data points you start to just
+
+ align:start position:0%
+very few data points you start to just
+ 
+
+ align:start position:0%
+very few data points you start to just
+wiggle around become extremely unstable
+
+ align:start position:0%
+wiggle around become extremely unstable
+ 
+
+ align:start position:0%
+wiggle around become extremely unstable
+change your mind all the time
+
+ align:start position:0%
+change your mind all the time
+ 
+
+ align:start position:0%
+change your mind all the time
+if the data are enough it stabilizes and
+
+ align:start position:0%
+if the data are enough it stabilizes and
+ 
+
+ align:start position:0%
+if the data are enough it stabilizes and
+in some sense is the setting we're
+
+ align:start position:0%
+in some sense is the setting we're
+ 
+
+ align:start position:0%
+in some sense is the setting we're
+fitting the data or as she sang
+
+ align:start position:0%
+fitting the data or as she sang
+ 
+
+ align:start position:0%
+fitting the data or as she sang
+overfitting the data is actually not a
+
+ align:start position:0%
+overfitting the data is actually not a
+ 
+
+ align:start position:0%
+overfitting the data is actually not a
+bad thing okay so this is what's going
+
+ align:start position:0%
+bad thing okay so this is what's going
+ 
+
+ align:start position:0%
+bad thing okay so this is what's going
+on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fitting a bit too much so if you look
+
+ align:start position:0%
+fitting a bit too much so if you look
+ 
+
+ align:start position:0%
+fitting a bit too much so if you look
+here so here if you look what you're
+
+ align:start position:0%
+here so here if you look what you're
+ 
+
+ align:start position:0%
+here so here if you look what you're
+doing here you're always fitting the
+
+ align:start position:0%
+doing here you're always fitting the
+ 
+
+ align:start position:0%
+doing here you're always fitting the
+data okay but here you didn't doing
+
+ align:start position:0%
+data okay but here you didn't doing
+ 
+
+ align:start position:0%
+data okay but here you didn't doing
+nothing else and so if you have a few
+
+ align:start position:0%
+nothing else and so if you have a few
+ 
+
+ align:start position:0%
+nothing else and so if you have a few
+data points fit in the data is fine if
+
+ align:start position:0%
+data points fit in the data is fine if
+ 
+
+ align:start position:0%
+data points fit in the data is fine if
+you have sorry if you have many data
+
+ align:start position:0%
+you have sorry if you have many data
+ 
+
+ align:start position:0%
+you have sorry if you have many data
+points fitting data is just fine if you
+
+ align:start position:0%
+points fitting data is just fine if you
+ 
+
+ align:start position:0%
+points fitting data is just fine if you
+have few data points by fitting them you
+
+ align:start position:0%
+have few data points by fitting them you
+ 
+
+ align:start position:0%
+have few data points by fitting them you
+in some sense over fit in the sense that
+
+ align:start position:0%
+in some sense over fit in the sense that
+ 
+
+ align:start position:0%
+in some sense over fit in the sense that
+when you look at new data points you
+
+ align:start position:0%
+when you look at new data points you
+ 
+
+ align:start position:0%
+when you look at new data points you
+have done a bit too much okay what you
+
+ align:start position:0%
+have done a bit too much okay what you
+ 
+
+ align:start position:0%
+have done a bit too much okay what you
+saw before that you get this thinking
+
+ align:start position:0%
+saw before that you get this thinking
+ 
+
+ align:start position:0%
+saw before that you get this thinking
+that it's very good because it perfectly
+
+ align:start position:0%
+that it's very good because it perfectly
+ 
+
+ align:start position:0%
+that it's very good because it perfectly
+fits that but it's overfitting with
+
+ align:start position:0%
+fits that but it's overfitting with
+ 
+
+ align:start position:0%
+fits that but it's overfitting with
+respect to the future whereas here the
+
+ align:start position:0%
+respect to the future whereas here the
+ 
+
+ align:start position:0%
+respect to the future whereas here the
+fitting on the left-hand side kind of
+
+ align:start position:0%
+fitting on the left-hand side kind of
+ 
+
+ align:start position:0%
+fitting on the left-hand side kind of
+reflect not too badly the fitting on the
+
+ align:start position:0%
+reflect not too badly the fitting on the
+ 
+
+ align:start position:0%
+reflect not too badly the fitting on the
+right-hand side okay so this this the
+
+ align:start position:0%
+right-hand side okay so this this the
+ 
+
+ align:start position:0%
+right-hand side okay so this this the
+idea of overfitting and stability that
+
+ align:start position:0%
+idea of overfitting and stability that
+ 
+
+ align:start position:0%
+idea of overfitting and stability that
+came out in this discussion are key okay
+
+ align:start position:0%
+came out in this discussion are key okay
+ 
+
+ align:start position:0%
+came out in this discussion are key okay
+if you want everything we're going to do
+
+ align:start position:0%
+if you want everything we're going to do
+ 
+
+ align:start position:0%
+if you want everything we're going to do
+in the next three hours is understand
+
+ align:start position:0%
+in the next three hours is understand
+ 
+
+ align:start position:0%
+in the next three hours is understand
+how you can prevent overfitting and
+
+ align:start position:0%
+how you can prevent overfitting and
+ 
+
+ align:start position:0%
+how you can prevent overfitting and
+build good way to stabilize your
+
+ align:start position:0%
+build good way to stabilize your
+ 
+
+ align:start position:0%
+build good way to stabilize your
+algorithms okay so let's go back here
+
+ align:start position:0%
+algorithms okay so let's go back here
+ 
+
+ align:start position:0%
+algorithms okay so let's go back here
+and it's gonna be quick because if I ask
+
+ align:start position:0%
+and it's gonna be quick because if I ask
+ 
+
+ align:start position:0%
+and it's gonna be quick because if I ask
+you what is this
+
+ align:start position:0%
+you what is this
+ 
+
+ align:start position:0%
+you what is this
+what would you say so the idea is that
+
+ align:start position:0%
+what would you say so the idea is that
+ 
+
+ align:start position:0%
+what would you say so the idea is that
+when you have a situation like this
+
+ align:start position:0%
+when you have a situation like this
+ 
+
+ align:start position:0%
+when you have a situation like this
+you're still pretty much able to say
+
+ align:start position:0%
+you're still pretty much able to say
+ 
+
+ align:start position:0%
+you're still pretty much able to say
+what's the right answer and what you're
+
+ align:start position:0%
+what's the right answer and what you're
+ 
+
+ align:start position:0%
+what's the right answer and what you're
+gonna do is that you're gonna move away
+
+ align:start position:0%
+gonna do is that you're gonna move away
+ 
+
+ align:start position:0%
+gonna do is that you're gonna move away
+from just saying what's the closest
+
+ align:start position:0%
+from just saying what's the closest
+ 
+
+ align:start position:0%
+from just saying what's the closest
+point and you just look at a few more
+
+ align:start position:0%
+point and you just look at a few more
+ 
+
+ align:start position:0%
+point and you just look at a few more
+points you just don't look at one okay
+
+ align:start position:0%
+points you just don't look at one okay
+ 
+
+ align:start position:0%
+points you just don't look at one okay
+you look at how many boo-boo is a very
+
+ align:start position:0%
+you look at how many boo-boo is a very
+ 
+
+ align:start position:0%
+you look at how many boo-boo is a very
+useful Italian word it means I don't
+
+ align:start position:0%
+useful Italian word it means I don't
+ 
+
+ align:start position:0%
+useful Italian word it means I don't
+know so this algorithm it's called the K
+
+ align:start position:0%
+know so this algorithm it's called the K
+ 
+
+ align:start position:0%
+know so this algorithm it's called the K
+nearest neighbor algorithm it's probably
+
+ align:start position:0%
+nearest neighbor algorithm it's probably
+ 
+
+ align:start position:0%
+nearest neighbor algorithm it's probably
+the second simplest algorithm you can
+
+ align:start position:0%
+the second simplest algorithm you can
+ 
+
+ align:start position:0%
+the second simplest algorithm you can
+think of it's kind of the same as before
+
+ align:start position:0%
+think of it's kind of the same as before
+ 
+
+ align:start position:0%
+think of it's kind of the same as before
+the notation here is a bit boring but
+
+ align:start position:0%
+the notation here is a bit boring but
+ 
+
+ align:start position:0%
+the notation here is a bit boring but
+it's basically saying take the points
+
+ align:start position:0%
+it's basically saying take the points
+ 
+
+ align:start position:0%
+it's basically saying take the points
+given a new points check the distance
+
+ align:start position:0%
+given a new points check the distance
+ 
+
+ align:start position:0%
+given a new points check the distance
+with everybody sort it and take the
+
+ align:start position:0%
+with everybody sort it and take the
+ 
+
+ align:start position:0%
+with everybody sort it and take the
+first K okay if it's a classification
+
+ align:start position:0%
+first K okay if it's a classification
+ 
+
+ align:start position:0%
+first K okay if it's a classification
+probably probably good idea to take a
+
+ align:start position:0%
+probably probably good idea to take a
+ 
+
+ align:start position:0%
+probably probably good idea to take a
+odd number for K so that you can then
+
+ align:start position:0%
+odd number for K so that you can then
+ 
+
+ align:start position:0%
+odd number for K so that you can then
+just have a voting and basically
+
+ align:start position:0%
+just have a voting and basically
+ 
+
+ align:start position:0%
+just have a voting and basically
+everybody votes H vote counts one and
+
+ align:start position:0%
+everybody votes H vote counts one and
+ 
+
+ align:start position:0%
+everybody votes H vote counts one and
+somebody says blue somebody says orange
+
+ align:start position:0%
+somebody says blue somebody says orange
+ 
+
+ align:start position:0%
+somebody says blue somebody says orange
+and any and you make a decision okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fair enough
+
+ align:start position:0%
+fair enough
+ 
+
+ align:start position:0%
+fair enough
+well how does this work you can kind of
+
+ align:start position:0%
+well how does this work you can kind of
+ 
+
+ align:start position:0%
+well how does this work you can kind of
+imagine so so we have to do so for
+
+ align:start position:0%
+imagine so so we have to do so for
+ 
+
+ align:start position:0%
+imagine so so we have to do so for
+example here we had this guy okay now
+
+ align:start position:0%
+example here we had this guy okay now
+ 
+
+ align:start position:0%
+example here we had this guy okay now
+let's just put K well let's make this a
+
+ align:start position:0%
+let's just put K well let's make this a
+ 
+
+ align:start position:0%
+let's just put K well let's make this a
+bit smaller so we do forty generate plot
+
+ align:start position:0%
+bit smaller so we do forty generate plot
+ 
+
+ align:start position:0%
+bit smaller so we do forty generate plot
+train boring yes okay
+
+ align:start position:0%
+train boring yes okay
+ 
+
+ align:start position:0%
+train boring yes okay
+well we got a bit lucky okay this is
+
+ align:start position:0%
+well we got a bit lucky okay this is
+ 
+
+ align:start position:0%
+well we got a bit lucky okay this is
+actually a good dataset because in some
+
+ align:start position:0%
+actually a good dataset because in some
+ 
+
+ align:start position:0%
+actually a good dataset because in some
+sense there are no what you might call
+
+ align:start position:0%
+sense there are no what you might call
+ 
+
+ align:start position:0%
+sense there are no what you might call
+outliers there are not orange point that
+
+ align:start position:0%
+outliers there are not orange point that
+ 
+
+ align:start position:0%
+outliers there are not orange point that
+really go and sit in the blue so I just
+
+ align:start position:0%
+really go and sit in the blue so I just
+ 
+
+ align:start position:0%
+really go and sit in the blue so I just
+want to show you a bit of a dramatic
+
+ align:start position:0%
+want to show you a bit of a dramatic
+ 
+
+ align:start position:0%
+want to show you a bit of a dramatic
+effect of this so let me just try to
+
+ align:start position:0%
+effect of this so let me just try to
+ 
+
+ align:start position:0%
+effect of this so let me just try to
+redo this one so that we get the more
+
+ align:start position:0%
+redo this one so that we get the more
+ 
+
+ align:start position:0%
+redo this one so that we get the more
+yes and you should do okay so this is
+
+ align:start position:0%
+yes and you should do okay so this is
+ 
+
+ align:start position:0%
+yes and you should do okay so this is
+nearest neighbor is the solution you get
+
+ align:start position:0%
+nearest neighbor is the solution you get
+ 
+
+ align:start position:0%
+nearest neighbor is the solution you get
+it's not too horrible but for example
+
+ align:start position:0%
+it's not too horrible but for example
+ 
+
+ align:start position:0%
+it's not too horrible but for example
+you see that the start follows this guy
+
+ align:start position:0%
+you see that the start follows this guy
+ 
+
+ align:start position:0%
+you see that the start follows this guy
+okay now what you can do is that just
+
+ align:start position:0%
+okay now what you can do is that just
+ 
+
+ align:start position:0%
+okay now what you can do is that just
+can just go in and say for well for is a
+
+ align:start position:0%
+can just go in and say for well for is a
+ 
+
+ align:start position:0%
+can just go in and say for well for is a
+bad idea five you retrain on the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and all of a sudden it does ignore this
+
+ align:start position:0%
+and all of a sudden it does ignore this
+ 
+
+ align:start position:0%
+and all of a sudden it does ignore this
+guy because the moment that you put more
+
+ align:start position:0%
+guy because the moment that you put more
+ 
+
+ align:start position:0%
+guy because the moment that you put more
+in well I just realized that he's
+
+ align:start position:0%
+in well I just realized that he's
+ 
+
+ align:start position:0%
+in well I just realized that he's
+surrounded by blue guys so it's probably
+
+ align:start position:0%
+surrounded by blue guys so it's probably
+ 
+
+ align:start position:0%
+surrounded by blue guys so it's probably
+just his vote discount one against four
+
+ align:start position:0%
+just his vote discount one against four
+ 
+
+ align:start position:0%
+just his vote discount one against four
+okay and you can keep on going and the
+
+ align:start position:0%
+okay and you can keep on going and the
+ 
+
+ align:start position:0%
+okay and you can keep on going and the
+idea here is that the more you make this
+
+ align:start position:0%
+idea here is that the more you make this
+ 
+
+ align:start position:0%
+idea here is that the more you make this
+big the more your solution is going to
+
+ align:start position:0%
+big the more your solution is going to
+ 
+
+ align:start position:0%
+big the more your solution is going to
+be what well you can say it's gonna be
+
+ align:start position:0%
+be what well you can say it's gonna be
+ 
+
+ align:start position:0%
+be what well you can say it's gonna be
+good but it's actually not true because
+
+ align:start position:0%
+good but it's actually not true because
+ 
+
+ align:start position:0%
+good but it's actually not true because
+if you start to put cake too big at some
+
+ align:start position:0%
+if you start to put cake too big at some
+ 
+
+ align:start position:0%
+if you start to put cake too big at some
+point all you're doing is counting how
+
+ align:start position:0%
+point all you're doing is counting how
+ 
+
+ align:start position:0%
+point all you're doing is counting how
+many points you have in class one
+
+ align:start position:0%
+many points you have in class one
+ 
+
+ align:start position:0%
+many points you have in class one
+counting how many points you have in
+
+ align:start position:0%
+counting how many points you have in
+ 
+
+ align:start position:0%
+counting how many points you have in
+class two and always say the same thing
+
+ align:start position:0%
+class two and always say the same thing
+ 
+
+ align:start position:0%
+class two and always say the same thing
+okay so how many we have put here twenty
+
+ align:start position:0%
+okay so how many we have put here twenty
+ 
+
+ align:start position:0%
+okay so how many we have put here twenty
+what you start to see is that you start
+
+ align:start position:0%
+what you start to see is that you start
+ 
+
+ align:start position:0%
+what you start to see is that you start
+to obtain a decision boundary which is
+
+ align:start position:0%
+to obtain a decision boundary which is
+ 
+
+ align:start position:0%
+to obtain a decision boundary which is
+simpler and simpler and simpler okay it
+
+ align:start position:0%
+simpler and simpler and simpler okay it
+ 
+
+ align:start position:0%
+simpler and simpler and simpler okay it
+looks kind of linear here what you will
+
+ align:start position:0%
+looks kind of linear here what you will
+ 
+
+ align:start position:0%
+looks kind of linear here what you will
+see is that suppose that now I
+
+ align:start position:0%
+see is that suppose that now I
+ 
+
+ align:start position:0%
+see is that suppose that now I
+regenerate the data and you remember how
+
+ align:start position:0%
+regenerate the data and you remember how
+ 
+
+ align:start position:0%
+regenerate the data and you remember how
+much it changed before when I was using
+
+ align:start position:0%
+much it changed before when I was using
+ 
+
+ align:start position:0%
+much it changed before when I was using
+nearest neighbor with just k equal to 1
+
+ align:start position:0%
+nearest neighbor with just k equal to 1
+ 
+
+ align:start position:0%
+nearest neighbor with just k equal to 1
+okay so of course here you know it it's
+
+ align:start position:0%
+okay so of course here you know it it's
+ 
+
+ align:start position:0%
+okay so of course here you know it it's
+probabilistic okay so of course I'm
+
+ align:start position:0%
+probabilistic okay so of course I'm
+ 
+
+ align:start position:0%
+probabilistic okay so of course I'm
+gonna get it data that's like the one I
+
+ align:start position:0%
+gonna get it data that's like the one I
+ 
+
+ align:start position:0%
+gonna get it data that's like the one I
+just show you a minute ago and ahead it
+
+ align:start position:0%
+just show you a minute ago and ahead it
+ 
+
+ align:start position:0%
+just show you a minute ago and ahead it
+as fast as possible
+
+ align:start position:0%
+as fast as possible
+ 
+
+ align:start position:0%
+as fast as possible
+because if I pick ten one is gonna look
+
+ align:start position:0%
+because if I pick ten one is gonna look
+ 
+
+ align:start position:0%
+because if I pick ten one is gonna look
+like data and nine are gonna look like
+
+ align:start position:0%
+like data and nine are gonna look like
+ 
+
+ align:start position:0%
+like data and nine are gonna look like
+this okay then when I look like this you
+
+ align:start position:0%
+this okay then when I look like this you
+ 
+
+ align:start position:0%
+this okay then when I look like this you
+see they kind of start to have this kind
+
+ align:start position:0%
+see they kind of start to have this kind
+ 
+
+ align:start position:0%
+see they kind of start to have this kind
+of line like decision boundary
+
+ align:start position:0%
+of line like decision boundary
+ 
+
+ align:start position:0%
+of line like decision boundary
+some twist but it's very simple okay and
+
+ align:start position:0%
+some twist but it's very simple okay and
+ 
+
+ align:start position:0%
+some twist but it's very simple okay and
+at some point if I put K big enough that
+
+ align:start position:0%
+at some point if I put K big enough that
+ 
+
+ align:start position:0%
+at some point if I put K big enough that
+is the number of old points you won't
+
+ align:start position:0%
+is the number of old points you won't
+ 
+
+ align:start position:0%
+is the number of old points you won't
+change any more okay it will just be
+
+ align:start position:0%
+change any more okay it will just be
+ 
+
+ align:start position:0%
+change any more okay it will just be
+exactly dividing the deserts into equal
+
+ align:start position:0%
+exactly dividing the deserts into equal
+ 
+
+ align:start position:0%
+exactly dividing the deserts into equal
+part so they make sense so would it make
+
+ align:start position:0%
+part so they make sense so would it make
+ 
+
+ align:start position:0%
+part so they make sense so would it make
+sense to vote to make different votes
+
+ align:start position:0%
+sense to vote to make different votes
+ 
+
+ align:start position:0%
+sense to vote to make different votes
+essentially the idea is if the point is
+
+ align:start position:0%
+essentially the idea is if the point is
+ 
+
+ align:start position:0%
+essentially the idea is if the point is
+closest this vote should count more than
+
+ align:start position:0%
+closest this vote should count more than
+ 
+
+ align:start position:0%
+closest this vote should count more than
+if a point is more far away yes
+
+ align:start position:0%
+if a point is more far away yes
+ 
+
+ align:start position:0%
+if a point is more far away yes
+absolutely is this you know let's say
+
+ align:start position:0%
+absolutely is this you know let's say
+ 
+
+ align:start position:0%
+absolutely is this you know let's say
+here we're making the simplest thing in
+
+ align:start position:0%
+here we're making the simplest thing in
+ 
+
+ align:start position:0%
+here we're making the simplest thing in
+the world the second simple thing about
+
+ align:start position:0%
+the world the second simple thing about
+ 
+
+ align:start position:0%
+the world the second simple thing about
+this third interesting in the world is
+
+ align:start position:0%
+this third interesting in the world is
+ 
+
+ align:start position:0%
+this third interesting in the world is
+doing that okay and you can see that you
+
+ align:start position:0%
+doing that okay and you can see that you
+ 
+
+ align:start position:0%
+doing that okay and you can see that you
+can go pretty far with this they mean
+
+ align:start position:0%
+can go pretty far with this they mean
+ 
+
+ align:start position:0%
+can go pretty far with this they mean
+it's simple but these are actual
+
+ align:start position:0%
+it's simple but these are actual
+ 
+
+ align:start position:0%
+it's simple but these are actual
+algorithm that are used sometimes and
+
+ align:start position:0%
+algorithm that are used sometimes and
+ 
+
+ align:start position:0%
+algorithm that are used sometimes and
+what you do is that if you just look at
+
+ align:start position:0%
+what you do is that if you just look at
+ 
+
+ align:start position:0%
+what you do is that if you just look at
+this again these are 1 1 explained too
+
+ align:start position:0%
+this again these are 1 1 explained too
+ 
+
+ align:start position:0%
+this again these are 1 1 explained too
+much if you've seen it before it's
+
+ align:start position:0%
+much if you've seen it before it's
+ 
+
+ align:start position:0%
+much if you've seen it before it's
+simple otherwise it doesn't really
+
+ align:start position:0%
+simple otherwise it doesn't really
+ 
+
+ align:start position:0%
+simple otherwise it doesn't really
+matter but the basic idea here is that
+
+ align:start position:0%
+matter but the basic idea here is that
+ 
+
+ align:start position:0%
+matter but the basic idea here is that
+each vote is going to between between 0
+
+ align:start position:0%
+each vote is going to between between 0
+ 
+
+ align:start position:0%
+each vote is going to between between 0
+so you see here I put the distance
+
+ align:start position:0%
+so you see here I put the distance
+ 
+
+ align:start position:0%
+so you see here I put the distance
+between every the new point and all the
+
+ align:start position:0%
+between every the new point and all the
+ 
+
+ align:start position:0%
+between every the new point and all the
+other points on top of an exponential so
+
+ align:start position:0%
+other points on top of an exponential so
+ 
+
+ align:start position:0%
+other points on top of an exponential so
+the number I get is not 1 but is between
+
+ align:start position:0%
+the number I get is not 1 but is between
+ 
+
+ align:start position:0%
+the number I get is not 1 but is between
+0 & 1 if the two points are close in the
+
+ align:start position:0%
+0 & 1 if the two points are close in the
+ 
+
+ align:start position:0%
+0 & 1 if the two points are close in the
+limit suppose that they are the same it
+
+ align:start position:0%
+limit suppose that they are the same it
+ 
+
+ align:start position:0%
+limit suppose that they are the same it
+becomes a 0 and it counts exactly 1 if
+
+ align:start position:0%
+becomes a 0 and it counts exactly 1 if
+ 
+
+ align:start position:0%
+becomes a 0 and it counts exactly 1 if
+they're very far away okay it will be
+
+ align:start position:0%
+they're very far away okay it will be
+ 
+
+ align:start position:0%
+they're very far away okay it will be
+Fei infinity and then it will be close
+
+ align:start position:0%
+Fei infinity and then it will be close
+ 
+
+ align:start position:0%
+Fei infinity and then it will be close
+to 0 so the closest you are the more you
+
+ align:start position:0%
+to 0 so the closest you are the more you
+ 
+
+ align:start position:0%
+to 0 so the closest you are the more you
+count if you want you can read like this
+
+ align:start position:0%
+count if you want you can read like this
+ 
+
+ align:start position:0%
+count if you want you can read like this
+you're sitting on a new point and you
+
+ align:start position:0%
+you're sitting on a new point and you
+ 
+
+ align:start position:0%
+you're sitting on a new point and you
+put like a zooming window a like yeah
+
+ align:start position:0%
+put like a zooming window a like yeah
+ 
+
+ align:start position:0%
+put like a zooming window a like yeah
+like a zooming window of a certain size
+
+ align:start position:0%
+like a zooming window of a certain size
+ 
+
+ align:start position:0%
+like a zooming window of a certain size
+and you basically check that everything
+
+ align:start position:0%
+and you basically check that everything
+ 
+
+ align:start position:0%
+and you basically check that everything
+which is inside this window will be
+
+ align:start position:0%
+which is inside this window will be
+ 
+
+ align:start position:0%
+which is inside this window will be
+close and the more you go far away so
+
+ align:start position:0%
+close and the more you go far away so
+ 
+
+ align:start position:0%
+close and the more you go far away so
+the window is like this okay and you
+
+ align:start position:0%
+the window is like this okay and you
+ 
+
+ align:start position:0%
+the window is like this okay and you
+deform the space so that basically what
+
+ align:start position:0%
+deform the space so that basically what
+ 
+
+ align:start position:0%
+deform the space so that basically what
+you say is things are far away they're
+
+ align:start position:0%
+you say is things are far away they're
+ 
+
+ align:start position:0%
+you say is things are far away they're
+gonna count less and if I move Sigma
+
+ align:start position:0%
+gonna count less and if I move Sigma
+ 
+
+ align:start position:0%
+gonna count less and if I move Sigma
+here I'm somewhat making my visual field
+
+ align:start position:0%
+here I'm somewhat making my visual field
+ 
+
+ align:start position:0%
+here I'm somewhat making my visual field
+if you want larger or smaller okay
+
+ align:start position:0%
+if you want larger or smaller okay
+ 
+
+ align:start position:0%
+if you want larger or smaller okay
+around this one new point there's just a
+
+ align:start position:0%
+around this one new point there's just a
+ 
+
+ align:start position:0%
+around this one new point there's just a
+physical interpretation of what this is
+
+ align:start position:0%
+physical interpretation of what this is
+ 
+
+ align:start position:0%
+physical interpretation of what this is
+doing there 15 other ways of looking at
+
+ align:start position:0%
+doing there 15 other ways of looking at
+ 
+
+ align:start position:0%
+doing there 15 other ways of looking at
+what discussion is doing voting you know
+
+ align:start position:0%
+what discussion is doing voting you know
+ 
+
+ align:start position:0%
+what discussion is doing voting you know
+changing the weight of the vote is
+
+ align:start position:0%
+changing the weight of the vote is
+ 
+
+ align:start position:0%
+changing the weight of the vote is
+another one okay white the Gaussian here
+
+ align:start position:0%
+another one okay white the Gaussian here
+ 
+
+ align:start position:0%
+another one okay white the Gaussian here
+well because just because you can use
+
+ align:start position:0%
+well because just because you can use
+ 
+
+ align:start position:0%
+well because just because you can use
+many many others you can use for example
+
+ align:start position:0%
+many many others you can use for example
+ 
+
+ align:start position:0%
+many many others you can use for example
+window and this is part of your prior
+
+ align:start position:0%
+window and this is part of your prior
+ 
+
+ align:start position:0%
+window and this is part of your prior
+knowledge how much you wanna wait if you
+
+ align:start position:0%
+knowledge how much you wanna wait if you
+ 
+
+ align:start position:0%
+knowledge how much you wanna wait if you
+are in this kind of low dimensional
+
+ align:start position:0%
+are in this kind of low dimensional
+ 
+
+ align:start position:0%
+are in this kind of low dimensional
+situation you might have good ways to
+
+ align:start position:0%
+situation you might have good ways to
+ 
+
+ align:start position:0%
+situation you might have good ways to
+just look inside the data and decide and
+
+ align:start position:0%
+just look inside the data and decide and
+ 
+
+ align:start position:0%
+just look inside the data and decide and
+almost like doing by visual inspection
+
+ align:start position:0%
+almost like doing by visual inspection
+ 
+
+ align:start position:0%
+almost like doing by visual inspection
+otherwise you have to trust some more
+
+ align:start position:0%
+otherwise you have to trust some more
+ 
+
+ align:start position:0%
+otherwise you have to trust some more
+broad principle and it's again back to
+
+ align:start position:0%
+broad principle and it's again back to
+ 
+
+ align:start position:0%
+broad principle and it's again back to
+the problem of learning the
+
+ align:start position:0%
+the problem of learning the
+ 
+
+ align:start position:0%
+the problem of learning the
+representation and deciding how you to
+
+ align:start position:0%
+representation and deciding how you to
+ 
+
+ align:start position:0%
+representation and deciding how you to
+measure distance which are two faces of
+
+ align:start position:0%
+measure distance which are two faces of
+ 
+
+ align:start position:0%
+measure distance which are two faces of
+the same story okay and the other thing
+
+ align:start position:0%
+the same story okay and the other thing
+ 
+
+ align:start position:0%
+the same story okay and the other thing
+you see is that if you start to do these
+
+ align:start position:0%
+you see is that if you start to do these
+ 
+
+ align:start position:0%
+you see is that if you start to do these
+games you might actually add more
+
+ align:start position:0%
+games you might actually add more
+ 
+
+ align:start position:0%
+games you might actually add more
+parameters okay because we start for
+
+ align:start position:0%
+parameters okay because we start for
+ 
+
+ align:start position:0%
+parameters okay because we start for
+nearest-neighbor which was completed
+
+ align:start position:0%
+nearest-neighbor which was completed
+ 
+
+ align:start position:0%
+nearest-neighbor which was completed
+parameter free but it was very unstable
+
+ align:start position:0%
+parameter free but it was very unstable
+ 
+
+ align:start position:0%
+parameter free but it was very unstable
+we are that k we allow ourself to go
+
+ align:start position:0%
+we are that k we allow ourself to go
+ 
+
+ align:start position:0%
+we are that k we allow ourself to go
+from simple to complex from stability to
+
+ align:start position:0%
+from simple to complex from stability to
+ 
+
+ align:start position:0%
+from simple to complex from stability to
+overfitting but we introduced a new
+
+ align:start position:0%
+overfitting but we introduced a new
+ 
+
+ align:start position:0%
+overfitting but we introduced a new
+parameter and so that's not an algorithm
+
+ align:start position:0%
+parameter and so that's not an algorithm
+ 
+
+ align:start position:0%
+parameter and so that's not an algorithm
+anymore it's a half algorithm throughout
+
+ align:start position:0%
+anymore it's a half algorithm throughout
+ 
+
+ align:start position:0%
+anymore it's a half algorithm throughout
+the reason is a parameter free algorithm
+
+ align:start position:0%
+the reason is a parameter free algorithm
+ 
+
+ align:start position:0%
+the reason is a parameter free algorithm
+where I tell you how you choose
+
+ align:start position:0%
+where I tell you how you choose
+ 
+
+ align:start position:0%
+where I tell you how you choose
+everything okay so if you just give you
+
+ align:start position:0%
+everything okay so if you just give you
+ 
+
+ align:start position:0%
+everything okay so if you just give you
+something say there's K yeah well how do
+
+ align:start position:0%
+something say there's K yeah well how do
+ 
+
+ align:start position:0%
+something say there's K yeah well how do
+you choose it okay it's not it's not
+
+ align:start position:0%
+you choose it okay it's not it's not
+ 
+
+ align:start position:0%
+you choose it okay it's not it's not
+something you can use and here I'm
+
+ align:start position:0%
+something you can use and here I'm
+ 
+
+ align:start position:0%
+something you can use and here I'm
+adding Sigma and again you have to
+
+ align:start position:0%
+adding Sigma and again you have to
+ 
+
+ align:start position:0%
+adding Sigma and again you have to
+decide how you use it okay so that's
+
+ align:start position:0%
+decide how you use it okay so that's
+ 
+
+ align:start position:0%
+decide how you use it okay so that's
+what we want to ask in a minute so
+
+ align:start position:0%
+what we want to ask in a minute so
+ 
+
+ align:start position:0%
+what we want to ask in a minute so
+before doing that just a side remark is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've been looking at vector data okay
+
+ align:start position:0%
+we've been looking at vector data okay
+ 
+
+ align:start position:0%
+we've been looking at vector data okay
+we were basically measuring distance to
+
+ align:start position:0%
+we were basically measuring distance to
+ 
+
+ align:start position:0%
+we were basically measuring distance to
+just the Euclidean norm okay just the
+
+ align:start position:0%
+just the Euclidean norm okay just the
+ 
+
+ align:start position:0%
+just the Euclidean norm okay just the
+usual one or this version like the
+
+ align:start position:0%
+usual one or this version like the
+ 
+
+ align:start position:0%
+usual one or this version like the
+Gaussian kernel that somewhat amplify
+
+ align:start position:0%
+Gaussian kernel that somewhat amplify
+ 
+
+ align:start position:0%
+Gaussian kernel that somewhat amplify
+distances what if you have strings for
+
+ align:start position:0%
+distances what if you have strings for
+ 
+
+ align:start position:0%
+distances what if you have strings for
+example or graphs okay your data turns
+
+ align:start position:0%
+example or graphs okay your data turns
+ 
+
+ align:start position:0%
+example or graphs okay your data turns
+out to be strings and you want to
+
+ align:start position:0%
+out to be strings and you want to
+ 
+
+ align:start position:0%
+out to be strings and you want to
+compare them those are no there isn't
+
+ align:start position:0%
+compare them those are no there isn't
+ 
+
+ align:start position:0%
+compare them those are no there isn't
+you can see even if they're binary
+
+ align:start position:0%
+you can see even if they're binary
+ 
+
+ align:start position:0%
+you can see even if they're binary
+strings there is no linear structure you
+
+ align:start position:0%
+strings there is no linear structure you
+ 
+
+ align:start position:0%
+strings there is no linear structure you
+cannot just sum them up that Euclidean
+
+ align:start position:0%
+cannot just sum them up that Euclidean
+ 
+
+ align:start position:0%
+cannot just sum them up that Euclidean
+distant really make a lot of sense but
+
+ align:start position:0%
+distant really make a lot of sense but
+ 
+
+ align:start position:0%
+distant really make a lot of sense but
+what you can do is that as long as you
+
+ align:start position:0%
+what you can do is that as long as you
+ 
+
+ align:start position:0%
+what you can do is that as long as you
+can define a distance and say this one
+
+ align:start position:0%
+can define a distance and say this one
+ 
+
+ align:start position:0%
+can define a distance and say this one
+would be the simplest one just the
+
+ align:start position:0%
+would be the simplest one just the
+ 
+
+ align:start position:0%
+would be the simplest one just the
+hamming distance just check entries and
+
+ align:start position:0%
+hamming distance just check entries and
+ 
+
+ align:start position:0%
+hamming distance just check entries and
+if they're the same you count one if
+
+ align:start position:0%
+if they're the same you count one if
+ 
+
+ align:start position:0%
+if they're the same you count one if
+they're different you count zero okay
+
+ align:start position:0%
+they're different you count zero okay
+ 
+
+ align:start position:0%
+they're different you count zero okay
+the moment you can define a distance or
+
+ align:start position:0%
+the moment you can define a distance or
+ 
+
+ align:start position:0%
+the moment you can define a distance or
+your data then you can use this kind of
+
+ align:start position:0%
+your data then you can use this kind of
+ 
+
+ align:start position:0%
+your data then you can use this kind of
+techniques and so this technique is
+
+ align:start position:0%
+techniques and so this technique is
+ 
+
+ align:start position:0%
+techniques and so this technique is
+pretty flexible in that cell in that
+
+ align:start position:0%
+pretty flexible in that cell in that
+ 
+
+ align:start position:0%
+pretty flexible in that cell in that
+sense that whenever you can
+
+ align:start position:0%
+sense that whenever you can
+ 
+
+ align:start position:0%
+sense that whenever you can
+if you don't need a vectorial
+
+ align:start position:0%
+if you don't need a vectorial
+ 
+
+ align:start position:0%
+if you don't need a vectorial
+representation you just need a way to
+
+ align:start position:0%
+representation you just need a way to
+ 
+
+ align:start position:0%
+representation you just need a way to
+measure say similarity or distances
+
+ align:start position:0%
+measure say similarity or distances
+ 
+
+ align:start position:0%
+measure say similarity or distances
+between things and then you can use this
+
+ align:start position:0%
+between things and then you can use this
+ 
+
+ align:start position:0%
+between things and then you can use this
+method okay so here I just mentioned it
+
+ align:start position:0%
+method okay so here I just mentioned it
+ 
+
+ align:start position:0%
+method okay so here I just mentioned it
+and that's really most of these classes
+
+ align:start position:0%
+and that's really most of these classes
+ 
+
+ align:start position:0%
+and that's really most of these classes
+going to be about vector data but this
+
+ align:start position:0%
+going to be about vector data but this
+ 
+
+ align:start position:0%
+going to be about vector data but this
+is one point where the moment you have K
+
+ align:start position:0%
+is one point where the moment you have K
+ 
+
+ align:start position:0%
+is one point where the moment you have K
+you can think of this case and ten is
+
+ align:start position:0%
+you can think of this case and ten is
+ 
+
+ align:start position:0%
+you can think of this case and ten is
+the similarity okay similarity is kind
+
+ align:start position:0%
+the similarity okay similarity is kind
+ 
+
+ align:start position:0%
+the similarity okay similarity is kind
+of a constitutes do all two distances so
+
+ align:start position:0%
+of a constitutes do all two distances so
+ 
+
+ align:start position:0%
+of a constitutes do all two distances so
+if it's similarities big is good
+
+ align:start position:0%
+if it's similarities big is good
+ 
+
+ align:start position:0%
+if it's similarities big is good
+distance small is good okay and so here
+
+ align:start position:0%
+distance small is good okay and so here
+ 
+
+ align:start position:0%
+distance small is good okay and so here
+if you have a way to build the K or a
+
+ align:start position:0%
+if you have a way to build the K or a
+ 
+
+ align:start position:0%
+if you have a way to build the K or a
+distance then you're good to go
+
+ align:start position:0%
+distance then you're good to go
+ 
+
+ align:start position:0%
+distance then you're good to go
+and there you we're not going to really
+
+ align:start position:0%
+and there you we're not going to really
+ 
+
+ align:start position:0%
+and there you we're not going to really
+talk about but there's a whole industry
+
+ align:start position:0%
+talk about but there's a whole industry
+ 
+
+ align:start position:0%
+talk about but there's a whole industry
+about how you build this kind of stuff
+
+ align:start position:0%
+about how you build this kind of stuff
+ 
+
+ align:start position:0%
+about how you build this kind of stuff
+so if they give you strings maybe I want
+
+ align:start position:0%
+so if they give you strings maybe I want
+ 
+
+ align:start position:0%
+so if they give you strings maybe I want
+to say that I should not only look at
+
+ align:start position:0%
+to say that I should not only look at
+ 
+
+ align:start position:0%
+to say that I should not only look at
+the entry of a string but also the
+
+ align:start position:0%
+the entry of a string but also the
+ 
+
+ align:start position:0%
+the entry of a string but also the
+nearby entry when I make the score for
+
+ align:start position:0%
+nearby entry when I make the score for
+ 
+
+ align:start position:0%
+nearby entry when I make the score for
+that specific so maybe you know I
+
+ align:start position:0%
+that specific so maybe you know I
+ 
+
+ align:start position:0%
+that specific so maybe you know I
+shifted a value of the string a little
+
+ align:start position:0%
+shifted a value of the string a little
+ 
+
+ align:start position:0%
+shifted a value of the string a little
+bit is not right here is in the next
+
+ align:start position:0%
+bit is not right here is in the next
+ 
+
+ align:start position:0%
+bit is not right here is in the next
+position over so that should count a bit
+
+ align:start position:0%
+position over so that should count a bit
+ 
+
+ align:start position:0%
+position over so that should count a bit
+so I want to do a soft version of this
+
+ align:start position:0%
+so I want to do a soft version of this
+ 
+
+ align:start position:0%
+so I want to do a soft version of this
+okay or maybe have graphs and I want to
+
+ align:start position:0%
+okay or maybe have graphs and I want to
+ 
+
+ align:start position:0%
+okay or maybe have graphs and I want to
+compare graphs and I want to say that if
+
+ align:start position:0%
+compare graphs and I want to say that if
+ 
+
+ align:start position:0%
+compare graphs and I want to say that if
+two graphs are close then I want them to
+
+ align:start position:0%
+two graphs are close then I want them to
+ 
+
+ align:start position:0%
+two graphs are close then I want them to
+have the same label okay how do you do
+
+ align:start position:0%
+have the same label okay how do you do
+ 
+
+ align:start position:0%
+have the same label okay how do you do
+that the next big question is we
+
+ align:start position:0%
+that the next big question is we
+ 
+
+ align:start position:0%
+that the next big question is we
+introduced three parameters they look
+
+ align:start position:0%
+introduced three parameters they look
+ 
+
+ align:start position:0%
+introduced three parameters they look
+really nice because they kind of allowed
+
+ align:start position:0%
+really nice because they kind of allowed
+ 
+
+ align:start position:0%
+really nice because they kind of allowed
+us to get more flexible solutions to the
+
+ align:start position:0%
+us to get more flexible solutions to the
+ 
+
+ align:start position:0%
+us to get more flexible solutions to the
+problem by choosing for example K or the
+
+ align:start position:0%
+problem by choosing for example K or the
+ 
+
+ align:start position:0%
+problem by choosing for example K or the
+Sigma in the Gaussian we can go from
+
+ align:start position:0%
+Sigma in the Gaussian we can go from
+ 
+
+ align:start position:0%
+Sigma in the Gaussian we can go from
+over fittings to stability but then of
+
+ align:start position:0%
+over fittings to stability but then of
+ 
+
+ align:start position:0%
+over fittings to stability but then of
+course we have to choose the parameter
+
+ align:start position:0%
+course we have to choose the parameter
+ 
+
+ align:start position:0%
+course we have to choose the parameter
+and we have to find good ways to choose
+
+ align:start position:0%
+and we have to find good ways to choose
+ 
+
+ align:start position:0%
+and we have to find good ways to choose
+them and so there are a bunch of
+
+ align:start position:0%
+them and so there are a bunch of
+ 
+
+ align:start position:0%
+them and so there are a bunch of
+questions so the first one is well is
+
+ align:start position:0%
+questions so the first one is well is
+ 
+
+ align:start position:0%
+questions so the first one is well is
+there an optimal value at all okay there
+
+ align:start position:0%
+there an optimal value at all okay there
+ 
+
+ align:start position:0%
+there an optimal value at all okay there
+does it exist
+
+ align:start position:0%
+does it exist
+ 
+
+ align:start position:0%
+does it exist
+but if you do exist I can go try to
+
+ align:start position:0%
+but if you do exist I can go try to
+ 
+
+ align:start position:0%
+but if you do exist I can go try to
+estimate it in some way if it doesn't
+
+ align:start position:0%
+estimate it in some way if it doesn't
+ 
+
+ align:start position:0%
+estimate it in some way if it doesn't
+well there's no even make sense edges
+
+ align:start position:0%
+well there's no even make sense edges
+ 
+
+ align:start position:0%
+well there's no even make sense edges
+there's throw a random number I should
+
+ align:start position:0%
+there's throw a random number I should
+ 
+
+ align:start position:0%
+there's throw a random number I should
+take k equal 4 why just because okay so
+
+ align:start position:0%
+take k equal 4 why just because okay so
+ 
+
+ align:start position:0%
+take k equal 4 why just because okay so
+what do you think it exists or not
+
+ align:start position:0%
+what do you think it exists or not
+ 
+
+ align:start position:0%
+what do you think it exists or not
+what is it depends on because that's the
+
+ align:start position:0%
+what is it depends on because that's the
+ 
+
+ align:start position:0%
+what is it depends on because that's the
+next question what is it depends on can
+
+ align:start position:0%
+next question what is it depends on can
+ 
+
+ align:start position:0%
+next question what is it depends on can
+we compute it ok so let's try to guess
+
+ align:start position:0%
+we compute it ok so let's try to guess
+ 
+
+ align:start position:0%
+we compute it ok so let's try to guess
+one minute before we go and check how we
+
+ align:start position:0%
+one minute before we go and check how we
+ 
+
+ align:start position:0%
+one minute before we go and check how we
+do this ok ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have to choose it how do I choose it
+
+ align:start position:0%
+I have to choose it how do I choose it
+ 
+
+ align:start position:0%
+I have to choose it how do I choose it
+what does it depend on one thing is the
+
+ align:start position:0%
+what does it depend on one thing is the
+ 
+
+ align:start position:0%
+what does it depend on one thing is the
+size of the data set because what we saw
+
+ align:start position:0%
+size of the data set because what we saw
+ 
+
+ align:start position:0%
+size of the data set because what we saw
+is that as small K seems a good idea
+
+ align:start position:0%
+is that as small K seems a good idea
+ 
+
+ align:start position:0%
+is that as small K seems a good idea
+when you have a lot of data but it seems
+
+ align:start position:0%
+when you have a lot of data but it seems
+ 
+
+ align:start position:0%
+when you have a lot of data but it seems
+like a bad idea when you have a few okay
+
+ align:start position:0%
+like a bad idea when you have a few okay
+ 
+
+ align:start position:0%
+like a bad idea when you have a few okay
+so it should depends it should be
+
+ align:start position:0%
+so it should depends it should be
+ 
+
+ align:start position:0%
+so it should depends it should be
+something that scale with n the number
+
+ align:start position:0%
+something that scale with n the number
+ 
+
+ align:start position:0%
+something that scale with n the number
+of points and probably also the training
+
+ align:start position:0%
+of points and probably also the training
+ 
+
+ align:start position:0%
+of points and probably also the training
+set itself but we want something that
+
+ align:start position:0%
+set itself but we want something that
+ 
+
+ align:start position:0%
+set itself but we want something that
+works for all data set say in
+
+ align:start position:0%
+works for all data set say in
+ 
+
+ align:start position:0%
+works for all data set say in
+expectation so cardinality of the
+
+ align:start position:0%
+expectation so cardinality of the
+ 
+
+ align:start position:0%
+expectation so cardinality of the
+training set is going to be a main
+
+ align:start position:0%
+training set is going to be a main
+ 
+
+ align:start position:0%
+training set is going to be a main
+factor what else the what the smoothness
+
+ align:start position:0%
+factor what else the what the smoothness
+ 
+
+ align:start position:0%
+factor what else the what the smoothness
+of the boundary yeah so what he's saying
+
+ align:start position:0%
+of the boundary yeah so what he's saying
+ 
+
+ align:start position:0%
+of the boundary yeah so what he's saying
+is if my problem looks like this or if
+
+ align:start position:0%
+is if my problem looks like this or if
+ 
+
+ align:start position:0%
+is if my problem looks like this or if
+my problem looks like this it looks like
+
+ align:start position:0%
+my problem looks like this it looks like
+ 
+
+ align:start position:0%
+my problem looks like this it looks like
+K should be different in this case I can
+
+ align:start position:0%
+K should be different in this case I can
+ 
+
+ align:start position:0%
+K should be different in this case I can
+take any arbitrary high K and sorry yeah
+
+ align:start position:0%
+take any arbitrary high K and sorry yeah
+ 
+
+ align:start position:0%
+take any arbitrary high K and sorry yeah
+small K I guess or I it doesn't matter
+
+ align:start position:0%
+small K I guess or I it doesn't matter
+ 
+
+ align:start position:0%
+small K I guess or I it doesn't matter
+because whatever you do you pretty much
+
+ align:start position:0%
+because whatever you do you pretty much
+ 
+
+ align:start position:0%
+because whatever you do you pretty much
+get the good thing but if you start to
+
+ align:start position:0%
+get the good thing but if you start to
+ 
+
+ align:start position:0%
+get the good thing but if you start to
+something like this okay then you want K
+
+ align:start position:0%
+something like this okay then you want K
+ 
+
+ align:start position:0%
+something like this okay then you want K
+is small enough because otherwise you
+
+ align:start position:0%
+is small enough because otherwise you
+ 
+
+ align:start position:0%
+is small enough because otherwise you
+start to blur everything and this is
+
+ align:start position:0%
+start to blur everything and this is
+ 
+
+ align:start position:0%
+start to blur everything and this is
+exactly what he's saying if your problem
+
+ align:start position:0%
+exactly what he's saying if your problem
+ 
+
+ align:start position:0%
+exactly what he's saying if your problem
+is complicated or it's easy okay and at
+
+ align:start position:0%
+is complicated or it's easy okay and at
+ 
+
+ align:start position:0%
+is complicated or it's easy okay and at
+the same time this is related to the
+
+ align:start position:0%
+the same time this is related to the
+ 
+
+ align:start position:0%
+the same time this is related to the
+fact of how much noise you might have in
+
+ align:start position:0%
+fact of how much noise you might have in
+ 
+
+ align:start position:0%
+fact of how much noise you might have in
+the data okay how much you know how much
+
+ align:start position:0%
+the data okay how much you know how much
+ 
+
+ align:start position:0%
+the data okay how much you know how much
+flipping you might have in your data if
+
+ align:start position:0%
+flipping you might have in your data if
+ 
+
+ align:start position:0%
+flipping you might have in your data if
+the problem is hard then you expect to
+
+ align:start position:0%
+the problem is hard then you expect to
+ 
+
+ align:start position:0%
+the problem is hard then you expect to
+need a different K okay so it depends on
+
+ align:start position:0%
+need a different K okay so it depends on
+ 
+
+ align:start position:0%
+need a different K okay so it depends on
+the cardinality of the data and how
+
+ align:start position:0%
+the cardinality of the data and how
+ 
+
+ align:start position:0%
+the cardinality of the data and how
+complicated is the problem how
+
+ align:start position:0%
+complicated is the problem how
+ 
+
+ align:start position:0%
+complicated is the problem how
+complicated is the boundary or much
+
+ align:start position:0%
+complicated is the boundary or much
+ 
+
+ align:start position:0%
+complicated is the boundary or much
+noise I have okay so it turns out that
+
+ align:start position:0%
+noise I have okay so it turns out that
+ 
+
+ align:start position:0%
+noise I have okay so it turns out that
+one thing you can ask is can we prove it
+
+ align:start position:0%
+one thing you can ask is can we prove it
+ 
+
+ align:start position:0%
+one thing you can ask is can we prove it
+okay can we prove a theorem that says
+
+ align:start position:0%
+okay can we prove a theorem that says
+ 
+
+ align:start position:0%
+okay can we prove a theorem that says
+that there is an optimal K and it really
+
+ align:start position:0%
+that there is an optimal K and it really
+ 
+
+ align:start position:0%
+that there is an optimal K and it really
+does depends on this okay
+
+ align:start position:0%
+does depends on this okay
+ 
+
+ align:start position:0%
+does depends on this okay
+on these quantities and it turns out
+
+ align:start position:0%
+on these quantities and it turns out
+ 
+
+ align:start position:0%
+on these quantities and it turns out
+that you can okay of course as always to
+
+ align:start position:0%
+that you can okay of course as always to
+ 
+
+ align:start position:0%
+that you can okay of course as always to
+make a theory to make assumptions and
+
+ align:start position:0%
+make a theory to make assumptions and
+ 
+
+ align:start position:0%
+make a theory to make assumptions and
+you have to work within a model and the
+
+ align:start position:0%
+you have to work within a model and the
+ 
+
+ align:start position:0%
+you have to work within a model and the
+model you wanna work on is the following
+
+ align:start position:0%
+model you wanna work on is the following
+ 
+
+ align:start position:0%
+model you wanna work on is the following
+you're basically saying this is the K
+
+ align:start position:0%
+you're basically saying this is the K
+ 
+
+ align:start position:0%
+you're basically saying this is the K
+nearest neighbors solution so big K here
+
+ align:start position:0%
+nearest neighbors solution so big K here
+ 
+
+ align:start position:0%
+nearest neighbors solution so big K here
+is the number of neighbor and this is
+
+ align:start position:0%
+is the number of neighbor and this is
+ 
+
+ align:start position:0%
+is the number of neighbor and this is
+hat because it depends on the data and
+
+ align:start position:0%
+hat because it depends on the data and
+ 
+
+ align:start position:0%
+hat because it depends on the data and
+what I say here is that I'm just gonna
+
+ align:start position:0%
+what I say here is that I'm just gonna
+ 
+
+ align:start position:0%
+what I say here is that I'm just gonna
+look at square loss error just because
+
+ align:start position:0%
+look at square loss error just because
+ 
+
+ align:start position:0%
+look at square loss error just because
+it's easy and I'm gonna look at the
+
+ align:start position:0%
+it's easy and I'm gonna look at the
+ 
+
+ align:start position:0%
+it's easy and I'm gonna look at the
+regression problem not just this
+
+ align:start position:0%
+regression problem not just this
+ 
+
+ align:start position:0%
+regression problem not just this
+classification and what you do here is
+
+ align:start position:0%
+classification and what you do here is
+ 
+
+ align:start position:0%
+classification and what you do here is
+that you take expectation over all
+
+ align:start position:0%
+that you take expectation over all
+ 
+
+ align:start position:0%
+that you take expectation over all
+possible input output pairs so basically
+
+ align:start position:0%
+possible input output pairs so basically
+ 
+
+ align:start position:0%
+possible input output pairs so basically
+you say when I when I
+
+ align:start position:0%
+you say when I when I
+ 
+
+ align:start position:0%
+you say when I when I
+try to do math I want to see what's
+
+ align:start position:0%
+try to do math I want to see what's
+ 
+
+ align:start position:0%
+try to do math I want to see what's
+ideal and ideally I want the solution
+
+ align:start position:0%
+ideal and ideally I want the solution
+ 
+
+ align:start position:0%
+ideal and ideally I want the solution
+that as well on future points okay so
+
+ align:start position:0%
+that as well on future points okay so
+ 
+
+ align:start position:0%
+that as well on future points okay so
+how do I do that I take the average air
+
+ align:start position:0%
+how do I do that I take the average air
+ 
+
+ align:start position:0%
+how do I do that I take the average air
+over all possible points in the future x
+
+ align:start position:0%
+over all possible points in the future x
+ 
+
+ align:start position:0%
+over all possible points in the future x
+and y so this is the meaning of this
+
+ align:start position:0%
+and y so this is the meaning of this
+ 
+
+ align:start position:0%
+and y so this is the meaning of this
+first expectation that makes sense yes
+
+ align:start position:0%
+first expectation that makes sense yes
+ 
+
+ align:start position:0%
+first expectation that makes sense yes
+No
+
+ align:start position:0%
+No
+ 
+
+ align:start position:0%
+No
+so if I fix Y and X this is the error on
+
+ align:start position:0%
+so if I fix Y and X this is the error on
+ 
+
+ align:start position:0%
+so if I fix Y and X this is the error on
+a specific couple input and output I
+
+ align:start position:0%
+a specific couple input and output I
+ 
+
+ align:start position:0%
+a specific couple input and output I
+give you the input I do FK X and then I
+
+ align:start position:0%
+give you the input I do FK X and then I
+ 
+
+ align:start position:0%
+give you the input I do FK X and then I
+check if it's close or not to why but
+
+ align:start position:0%
+check if it's close or not to why but
+ 
+
+ align:start position:0%
+check if it's close or not to why but
+what I want to do if I want to be
+
+ align:start position:0%
+what I want to do if I want to be
+ 
+
+ align:start position:0%
+what I want to do if I want to be
+theoretically to say okay what I would
+
+ align:start position:0%
+theoretically to say okay what I would
+ 
+
+ align:start position:0%
+theoretically to say okay what I would
+really like to be small is this error
+
+ align:start position:0%
+really like to be small is this error
+ 
+
+ align:start position:0%
+really like to be small is this error
+over all possible points so I take the
+
+ align:start position:0%
+over all possible points so I take the
+ 
+
+ align:start position:0%
+over all possible points so I take the
+expectation not the one on the training
+
+ align:start position:0%
+expectation not the one on the training
+ 
+
+ align:start position:0%
+expectation not the one on the training
+set the one in the future and I take
+
+ align:start position:0%
+set the one in the future and I take
+ 
+
+ align:start position:0%
+set the one in the future and I take
+expectation so that if points are more
+
+ align:start position:0%
+expectation so that if points are more
+ 
+
+ align:start position:0%
+expectation so that if points are more
+likely to be sampled they will count
+
+ align:start position:0%
+likely to be sampled they will count
+ 
+
+ align:start position:0%
+likely to be sampled they will count
+more that points are less likely to be
+
+ align:start position:0%
+more that points are less likely to be
+ 
+
+ align:start position:0%
+more that points are less likely to be
+sampled okay that we haven't got to that
+
+ align:start position:0%
+sampled okay that we haven't got to that
+ 
+
+ align:start position:0%
+sampled okay that we haven't got to that
+one yet okay so e XY is what I just said
+
+ align:start position:0%
+one yet okay so e XY is what I just said
+ 
+
+ align:start position:0%
+one yet okay so e XY is what I just said
+what is yes with the expectation over
+
+ align:start position:0%
+what is yes with the expectation over
+ 
+
+ align:start position:0%
+what is yes with the expectation over
+the training set why do we need that
+
+ align:start position:0%
+the training set why do we need that
+ 
+
+ align:start position:0%
+the training set why do we need that
+well because if you don't put that
+
+ align:start position:0%
+well because if you don't put that
+ 
+
+ align:start position:0%
+well because if you don't put that
+expectation I basically tell you what's
+
+ align:start position:0%
+expectation I basically tell you what's
+ 
+
+ align:start position:0%
+expectation I basically tell you what's
+the good K for this one training set
+
+ align:start position:0%
+the good K for this one training set
+ 
+
+ align:start position:0%
+the good K for this one training set
+here then I give you another training
+
+ align:start position:0%
+here then I give you another training
+ 
+
+ align:start position:0%
+here then I give you another training
+set and I get another one which is in
+
+ align:start position:0%
+set and I get another one which is in
+ 
+
+ align:start position:0%
+set and I get another one which is in
+some sense it's good but it's also bad
+
+ align:start position:0%
+some sense it's good but it's also bad
+ 
+
+ align:start position:0%
+some sense it's good but it's also bad
+because you would like to have like a
+
+ align:start position:0%
+because you would like to have like a
+ 
+
+ align:start position:0%
+because you would like to have like a
+take-home message that we hold for all
+
+ align:start position:0%
+take-home message that we hold for all
+ 
+
+ align:start position:0%
+take-home message that we hold for all
+training set and this is the simplest
+
+ align:start position:0%
+training set and this is the simplest
+ 
+
+ align:start position:0%
+training set and this is the simplest
+you say for the average training set
+
+ align:start position:0%
+you say for the average training set
+ 
+
+ align:start position:0%
+you say for the average training set
+this is how I should choose K that's
+
+ align:start position:0%
+this is how I should choose K that's
+ 
+
+ align:start position:0%
+this is how I should choose K that's
+what we want to do okay so the first
+
+ align:start position:0%
+what we want to do okay so the first
+ 
+
+ align:start position:0%
+what we want to do okay so the first
+expectation is to measure error with
+
+ align:start position:0%
+expectation is to measure error with
+ 
+
+ align:start position:0%
+expectation is to measure error with
+respect to future the second expectation
+
+ align:start position:0%
+respect to future the second expectation
+ 
+
+ align:start position:0%
+respect to future the second expectation
+is to say how I wanna deal with the fact
+
+ align:start position:0%
+is to say how I wanna deal with the fact
+ 
+
+ align:start position:0%
+is to say how I wanna deal with the fact
+that I have just several potential
+
+ align:start position:0%
+that I have just several potential
+ 
+
+ align:start position:0%
+that I have just several potential
+training set appearing
+
+ align:start position:0%
+training set appearing
+ 
+
+ align:start position:0%
+training set appearing
+okay so the next couple of slide this
+
+ align:start position:0%
+okay so the next couple of slide this
+ 
+
+ align:start position:0%
+okay so the next couple of slide this
+red dot means that there are
+
+ align:start position:0%
+red dot means that there are
+ 
+
+ align:start position:0%
+red dot means that there are
+computations okay and so I want to do
+
+ align:start position:0%
+computations okay and so I want to do
+ 
+
+ align:start position:0%
+computations okay and so I want to do
+them quickly and the important thing of
+
+ align:start position:0%
+them quickly and the important thing of
+ 
+
+ align:start position:0%
+them quickly and the important thing of
+this bit is it's an exercise okay so
+
+ align:start position:0%
+this bit is it's an exercise okay so
+ 
+
+ align:start position:0%
+this bit is it's an exercise okay so
+this is an exercise of stats zero okay
+
+ align:start position:0%
+this is an exercise of stats zero okay
+ 
+
+ align:start position:0%
+this is an exercise of stats zero okay
+so I don't we don't want to spend time
+
+ align:start position:0%
+so I don't we don't want to spend time
+ 
+
+ align:start position:0%
+so I don't we don't want to spend time
+doing that the important thing is gonna
+
+ align:start position:0%
+doing that the important thing is gonna
+ 
+
+ align:start position:0%
+doing that the important thing is gonna
+be the concept of price so I'm gonna be
+
+ align:start position:0%
+be the concept of price so I'm gonna be
+ 
+
+ align:start position:0%
+be the concept of price so I'm gonna be
+go ab it quickly through it so you start
+
+ align:start position:0%
+go ab it quickly through it so you start
+ 
+
+ align:start position:0%
+go ab it quickly through it so you start
+from this and you would like to
+
+ align:start position:0%
+from this and you would like to
+ 
+
+ align:start position:0%
+from this and you would like to
+understand that if there exists so this
+
+ align:start position:0%
+understand that if there exists so this
+ 
+
+ align:start position:0%
+understand that if there exists so this
+is the quantity you would like to make
+
+ align:start position:0%
+is the quantity you would like to make
+ 
+
+ align:start position:0%
+is the quantity you would like to make
+small ideally okay you all never x-axis
+
+ align:start position:0%
+small ideally okay you all never x-axis
+ 
+
+ align:start position:0%
+small ideally okay you all never x-axis
+to this but ideally
+
+ align:start position:0%
+to this but ideally
+ 
+
+ align:start position:0%
+to this but ideally
+in the optimal scenario you want K to
+
+ align:start position:0%
+in the optimal scenario you want K to
+ 
+
+ align:start position:0%
+in the optimal scenario you want K to
+make this small okay now the problem is
+
+ align:start position:0%
+make this small okay now the problem is
+ 
+
+ align:start position:0%
+make this small okay now the problem is
+that you you want to stand too much
+
+ align:start position:0%
+that you you want to stand too much
+ 
+
+ align:start position:0%
+that you you want to stand too much
+matically study this minimization
+
+ align:start position:0%
+matically study this minimization
+ 
+
+ align:start position:0%
+matically study this minimization
+problem but it's not easy because how do
+
+ align:start position:0%
+problem but it's not easy because how do
+ 
+
+ align:start position:0%
+problem but it's not easy because how do
+you do this okay
+
+ align:start position:0%
+you do this okay
+ 
+
+ align:start position:0%
+you do this okay
+the dependence of this function on K is
+
+ align:start position:0%
+the dependence of this function on K is
+ 
+
+ align:start position:0%
+the dependence of this function on K is
+complicated is that equation we had
+
+ align:start position:0%
+complicated is that equation we had
+ 
+
+ align:start position:0%
+complicated is that equation we had
+before right so you cannot just take the
+
+ align:start position:0%
+before right so you cannot just take the
+ 
+
+ align:start position:0%
+before right so you cannot just take the
+Rif didn't set it equal to zero let's
+
+ align:start position:0%
+Rif didn't set it equal to zero let's
+ 
+
+ align:start position:0%
+Rif didn't set it equal to zero let's
+keep on going a bit to this so what we
+
+ align:start position:0%
+keep on going a bit to this so what we
+ 
+
+ align:start position:0%
+keep on going a bit to this so what we
+were at is this is the quantity we like
+
+ align:start position:0%
+were at is this is the quantity we like
+ 
+
+ align:start position:0%
+were at is this is the quantity we like
+to make small I would like to choose K
+
+ align:start position:0%
+to make small I would like to choose K
+ 
+
+ align:start position:0%
+to make small I would like to choose K
+so that they can make this small I want
+
+ align:start position:0%
+so that they can make this small I want
+ 
+
+ align:start position:0%
+so that they can make this small I want
+to study this from a mathematical point
+
+ align:start position:0%
+to study this from a mathematical point
+ 
+
+ align:start position:0%
+to study this from a mathematical point
+of view but I cannot just use what you
+
+ align:start position:0%
+of view but I cannot just use what you
+ 
+
+ align:start position:0%
+of view but I cannot just use what you
+do in calculus which is taking the
+
+ align:start position:0%
+do in calculus which is taking the
+ 
+
+ align:start position:0%
+do in calculus which is taking the
+derivative and set it equal to zero
+
+ align:start position:0%
+derivative and set it equal to zero
+ 
+
+ align:start position:0%
+derivative and set it equal to zero
+because the dependence of these two K
+
+ align:start position:0%
+because the dependence of these two K
+ 
+
+ align:start position:0%
+because the dependence of these two K
+which is my variable it's complicated
+
+ align:start position:0%
+which is my variable it's complicated
+ 
+
+ align:start position:0%
+which is my variable it's complicated
+okay so we go a bit of a round weight
+
+ align:start position:0%
+okay so we go a bit of a round weight
+ 
+
+ align:start position:0%
+okay so we go a bit of a round weight
+would turn out to be pretty Universal
+
+ align:start position:0%
+would turn out to be pretty Universal
+ 
+
+ align:start position:0%
+would turn out to be pretty Universal
+and this is what we're going to do first
+
+ align:start position:0%
+and this is what we're going to do first
+ 
+
+ align:start position:0%
+and this is what we're going to do first
+of all we assume a model for our data
+
+ align:start position:0%
+of all we assume a model for our data
+ 
+
+ align:start position:0%
+of all we assume a model for our data
+and this is just for the sake of
+
+ align:start position:0%
+and this is just for the sake of
+ 
+
+ align:start position:0%
+and this is just for the sake of
+simplicity okay I can use this much more
+
+ align:start position:0%
+simplicity okay I can use this much more
+ 
+
+ align:start position:0%
+simplicity okay I can use this much more
+general model but this is the model I'm
+
+ align:start position:0%
+general model but this is the model I'm
+ 
+
+ align:start position:0%
+general model but this is the model I'm
+gonna say that my Y are just some fixed
+
+ align:start position:0%
+gonna say that my Y are just some fixed
+ 
+
+ align:start position:0%
+gonna say that my Y are just some fixed
+function X star plus some noise okay and
+
+ align:start position:0%
+function X star plus some noise okay and
+ 
+
+ align:start position:0%
+function X star plus some noise okay and
+the noise is zero mean and variance
+
+ align:start position:0%
+the noise is zero mean and variance
+ 
+
+ align:start position:0%
+the noise is zero mean and variance
+Sigma square for all entries okay this
+
+ align:start position:0%
+Sigma square for all entries okay this
+ 
+
+ align:start position:0%
+Sigma square for all entries okay this
+is the simplest model okay is a Gaussian
+
+ align:start position:0%
+is the simplest model okay is a Gaussian
+ 
+
+ align:start position:0%
+is the simplest model okay is a Gaussian
+regression model then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so one thing I'm doing but this is
+
+ align:start position:0%
+okay so one thing I'm doing but this is
+ 
+
+ align:start position:0%
+okay so one thing I'm doing but this is
+like a trick and you can really forget
+
+ align:start position:0%
+like a trick and you can really forget
+ 
+
+ align:start position:0%
+like a trick and you can really forget
+it but you just make life much easier is
+
+ align:start position:0%
+it but you just make life much easier is
+ 
+
+ align:start position:0%
+it but you just make life much easier is
+that I take this petition over X Y and I
+
+ align:start position:0%
+that I take this petition over X Y and I
+ 
+
+ align:start position:0%
+that I take this petition over X Y and I
+condition here okay the reason why you
+
+ align:start position:0%
+condition here okay the reason why you
+ 
+
+ align:start position:0%
+condition here okay the reason why you
+do this is just to make the math a bit
+
+ align:start position:0%
+do this is just to make the math a bit
+ 
+
+ align:start position:0%
+do this is just to make the math a bit
+easier because basically now if you put
+
+ align:start position:0%
+easier because basically now if you put
+ 
+
+ align:start position:0%
+easier because basically now if you put
+this expectation out and you look just
+
+ align:start position:0%
+this expectation out and you look just
+ 
+
+ align:start position:0%
+this expectation out and you look just
+at this quantity you're looking at
+
+ align:start position:0%
+at this quantity you're looking at
+ 
+
+ align:start position:0%
+at this quantity you're looking at
+everything for fixed X and this just
+
+ align:start position:0%
+everything for fixed X and this just
+ 
+
+ align:start position:0%
+everything for fixed X and this just
+become a real number okay not the
+
+ align:start position:0%
+become a real number okay not the
+ 
+
+ align:start position:0%
+become a real number okay not the
+function anymore
+
+ align:start position:0%
+function anymore
+ 
+
+ align:start position:0%
+function anymore
+so you can use normal calculus you have
+
+ align:start position:0%
+so you can use normal calculus you have
+ 
+
+ align:start position:0%
+so you can use normal calculus you have
+a functional a real valued function I
+
+ align:start position:0%
+a functional a real valued function I
+ 
+
+ align:start position:0%
+a functional a real valued function I
+can just use the usual stuff okay again
+
+ align:start position:0%
+can just use the usual stuff okay again
+ 
+
+ align:start position:0%
+can just use the usual stuff okay again
+I'm going to be quickly over this
+
+ align:start position:0%
+I'm going to be quickly over this
+ 
+
+ align:start position:0%
+I'm going to be quickly over this
+because it doesn't really mean that so
+
+ align:start position:0%
+because it doesn't really mean that so
+ 
+
+ align:start position:0%
+because it doesn't really mean that so
+this is ingredient one this is
+
+ align:start position:0%
+this is ingredient one this is
+ 
+
+ align:start position:0%
+this is ingredient one this is
+observation - was there bacon three is
+
+ align:start position:0%
+observation - was there bacon three is
+ 
+
+ align:start position:0%
+observation - was there bacon three is
+that you need to introduce a object
+
+ align:start position:0%
+that you need to introduce a object
+ 
+
+ align:start position:0%
+that you need to introduce a object
+between the solution you get in practice
+
+ align:start position:0%
+between the solution you get in practice
+ 
+
+ align:start position:0%
+between the solution you get in practice
+and this ideal function what is this is
+
+ align:start position:0%
+and this ideal function what is this is
+ 
+
+ align:start position:0%
+and this ideal function what is this is
+this kind of what is called is the
+
+ align:start position:0%
+this kind of what is called is the
+ 
+
+ align:start position:0%
+this kind of what is called is the
+expectation of my algorithm what you do
+
+ align:start position:0%
+expectation of my algorithm what you do
+ 
+
+ align:start position:0%
+expectation of my algorithm what you do
+is that in my algorithm what I do here
+
+ align:start position:0%
+is that in my algorithm what I do here
+ 
+
+ align:start position:0%
+is that in my algorithm what I do here
+is that I put Y I okay just the label of
+
+ align:start position:0%
+is that I put Y I okay just the label of
+ 
+
+ align:start position:0%
+is that I put Y I okay just the label of
+my training set and the label are noisy
+
+ align:start position:0%
+my training set and the label are noisy
+ 
+
+ align:start position:0%
+my training set and the label are noisy
+but this is an ideal object where you
+
+ align:start position:0%
+but this is an ideal object where you
+ 
+
+ align:start position:0%
+but this is an ideal object where you
+put the true function itself and you
+
+ align:start position:0%
+put the true function itself and you
+ 
+
+ align:start position:0%
+put the true function itself and you
+just average the value of the true
+
+ align:start position:0%
+just average the value of the true
+ 
+
+ align:start position:0%
+just average the value of the true
+function if you why do I use this
+
+ align:start position:0%
+function if you why do I use this
+ 
+
+ align:start position:0%
+function if you why do I use this
+because I want to get something which is
+
+ align:start position:0%
+because I want to get something which is
+ 
+
+ align:start position:0%
+because I want to get something which is
+in between this F star and this as hell
+
+ align:start position:0%
+in between this F star and this as hell
+ 
+
+ align:start position:0%
+in between this F star and this as hell
+so if you put K big enough so if you
+
+ align:start position:0%
+so if you put K big enough so if you
+ 
+
+ align:start position:0%
+so if you put K big enough so if you
+have enough point this is gonna be sorry
+
+ align:start position:0%
+have enough point this is gonna be sorry
+ 
+
+ align:start position:0%
+have enough point this is gonna be sorry
+if you take K small enough so this is
+
+ align:start position:0%
+if you take K small enough so this is
+ 
+
+ align:start position:0%
+if you take K small enough so this is
+closer to F star than my asset okay
+
+ align:start position:0%
+closer to F star than my asset okay
+ 
+
+ align:start position:0%
+closer to F star than my asset okay
+because you get the non noisy data and
+
+ align:start position:0%
+because you get the non noisy data and
+ 
+
+ align:start position:0%
+because you get the non noisy data and
+what they want to do what I want to do
+
+ align:start position:0%
+what they want to do what I want to do
+ 
+
+ align:start position:0%
+what they want to do what I want to do
+is that I want to plug it in the middle
+
+ align:start position:0%
+is that I want to plug it in the middle
+ 
+
+ align:start position:0%
+is that I want to plug it in the middle
+and split this error in two and this is
+
+ align:start position:0%
+and split this error in two and this is
+ 
+
+ align:start position:0%
+and split this error in two and this is
+what I do okay if you do this you can
+
+ align:start position:0%
+what I do okay if you do this you can
+ 
+
+ align:start position:0%
+what I do okay if you do this you can
+check that you have a square here you
+
+ align:start position:0%
+check that you have a square here you
+ 
+
+ align:start position:0%
+check that you have a square here you
+get two terms one simplifies because of
+
+ align:start position:0%
+get two terms one simplifies because of
+ 
+
+ align:start position:0%
+get two terms one simplifies because of
+this assumption on the noise and you get
+
+ align:start position:0%
+this assumption on the noise and you get
+ 
+
+ align:start position:0%
+this assumption on the noise and you get
+these two terms okay and the important
+
+ align:start position:0%
+these two terms okay and the important
+ 
+
+ align:start position:0%
+these two terms okay and the important
+thing is these two terms are one is the
+
+ align:start position:0%
+thing is these two terms are one is the
+ 
+
+ align:start position:0%
+thing is these two terms are one is the
+comparison between my algorithm and its
+
+ align:start position:0%
+comparison between my algorithm and its
+ 
+
+ align:start position:0%
+comparison between my algorithm and its
+expectation so that's is that what we
+
+ align:start position:0%
+expectation so that's is that what we
+ 
+
+ align:start position:0%
+expectation so that's is that what we
+called a variance okay and one is the
+
+ align:start position:0%
+called a variance okay and one is the
+ 
+
+ align:start position:0%
+called a variance okay and one is the
+comparison between the value of the true
+
+ align:start position:0%
+comparison between the value of the true
+ 
+
+ align:start position:0%
+comparison between the value of the true
+function here and the value of this
+
+ align:start position:0%
+function here and the value of this
+ 
+
+ align:start position:0%
+function here and the value of this
+other function sorry this should
+
+ align:start position:0%
+other function sorry this should
+ 
+
+ align:start position:0%
+other function sorry this should
+oh yeah this is the expectation which is
+
+ align:start position:0%
+oh yeah this is the expectation which is
+ 
+
+ align:start position:0%
+oh yeah this is the expectation which is
+my ideal version of my algorithm the one
+
+ align:start position:0%
+my ideal version of my algorithm the one
+ 
+
+ align:start position:0%
+my ideal version of my algorithm the one
+that has access to the noiseless labels
+
+ align:start position:0%
+that has access to the noiseless labels
+ 
+
+ align:start position:0%
+that has access to the noiseless labels
+okay it's what you call a bias it's
+
+ align:start position:0%
+okay it's what you call a bias it's
+ 
+
+ align:start position:0%
+okay it's what you call a bias it's
+basically because instead of using the
+
+ align:start position:0%
+basically because instead of using the
+ 
+
+ align:start position:0%
+basically because instead of using the
+exact value of the function you blur it
+
+ align:start position:0%
+exact value of the function you blur it
+ 
+
+ align:start position:0%
+exact value of the function you blur it
+a bit by averaging out okay you see here
+
+ align:start position:0%
+a bit by averaging out okay you see here
+ 
+
+ align:start position:0%
+a bit by averaging out okay you see here
+instead of using the value of the
+
+ align:start position:0%
+instead of using the value of the
+ 
+
+ align:start position:0%
+instead of using the value of the
+function u average out a few nearby
+
+ align:start position:0%
+function u average out a few nearby
+ 
+
+ align:start position:0%
+function u average out a few nearby
+value so you're you're making it a bit
+
+ align:start position:0%
+value so you're you're making it a bit
+ 
+
+ align:start position:0%
+value so you're you're making it a bit
+dirtier the question now is how would
+
+ align:start position:0%
+dirtier the question now is how would
+ 
+
+ align:start position:0%
+dirtier the question now is how would
+these two quantities depend on K how
+
+ align:start position:0%
+these two quantities depend on K how
+ 
+
+ align:start position:0%
+these two quantities depend on K how
+this quantity depends on K and how this
+
+ align:start position:0%
+this quantity depends on K and how this
+ 
+
+ align:start position:0%
+this quantity depends on K and how this
+quantity depends on K okay and then by
+
+ align:start position:0%
+quantity depends on K okay and then by
+ 
+
+ align:start position:0%
+quantity depends on K okay and then by
+putting this together we'll see that we
+
+ align:start position:0%
+putting this together we'll see that we
+ 
+
+ align:start position:0%
+putting this together we'll see that we
+have a certain behavior of this and a
+
+ align:start position:0%
+have a certain behavior of this and a
+ 
+
+ align:start position:0%
+have a certain behavior of this and a
+certain behavior of this and then we
+
+ align:start position:0%
+certain behavior of this and then we
+ 
+
+ align:start position:0%
+certain behavior of this and then we
+balancing this out will get what the
+
+ align:start position:0%
+balancing this out will get what the
+ 
+
+ align:start position:0%
+balancing this out will get what the
+optimal value looked like and this is
+
+ align:start position:0%
+optimal value looked like and this is
+ 
+
+ align:start position:0%
+optimal value looked like and this is
+going to be all useless from so this is
+
+ align:start position:0%
+going to be all useless from so this is
+ 
+
+ align:start position:0%
+going to be all useless from so this is
+going to be interesting from a
+
+ align:start position:0%
+going to be interesting from a
+ 
+
+ align:start position:0%
+going to be interesting from a
+conceptual perspective we're going to
+
+ align:start position:0%
+conceptual perspective we're going to
+ 
+
+ align:start position:0%
+conceptual perspective we're going to
+learn something but we'll still have to
+
+ align:start position:0%
+learn something but we'll still have to
+ 
+
+ align:start position:0%
+learn something but we'll still have to
+do something practical because nothing
+
+ align:start position:0%
+do something practical because nothing
+ 
+
+ align:start position:0%
+do something practical because nothing
+of these you can measure in practice
+
+ align:start position:0%
+of these you can measure in practice
+ 
+
+ align:start position:0%
+of these you can measure in practice
+okay so you the next question will be
+
+ align:start position:0%
+okay so you the next question will be
+ 
+
+ align:start position:0%
+okay so you the next question will be
+holding now that we know that it exists
+
+ align:start position:0%
+holding now that we know that it exists
+ 
+
+ align:start position:0%
+holding now that we know that it exists
+and it depends on this stuff how can we
+
+ align:start position:0%
+and it depends on this stuff how can we
+ 
+
+ align:start position:0%
+and it depends on this stuff how can we
+actually approximate it in practice and
+
+ align:start position:0%
+actually approximate it in practice and
+ 
+
+ align:start position:0%
+actually approximate it in practice and
+cross-validation is going to pop out at
+
+ align:start position:0%
+cross-validation is going to pop out at
+ 
+
+ align:start position:0%
+cross-validation is going to pop out at
+the window okay but is it about the
+
+ align:start position:0%
+the window okay but is it about the
+ 
+
+ align:start position:0%
+the window okay but is it about the
+theory that shows you that this would
+
+ align:start position:0%
+theory that shows you that this would
+ 
+
+ align:start position:0%
+theory that shows you that this would
+help proving a theory that shows that
+
+ align:start position:0%
+help proving a theory that shows that
+ 
+
+ align:start position:0%
+help proving a theory that shows that
+cross-validation is a good idea
+
+ align:start position:0%
+cross-validation is a good idea
+ 
+
+ align:start position:0%
+cross-validation is a good idea
+in a precise sense take-home messages by
+
+ align:start position:0%
+in a precise sense take-home messages by
+ 
+
+ align:start position:0%
+in a precise sense take-home messages by
+making this model and using this as an
+
+ align:start position:0%
+making this model and using this as an
+ 
+
+ align:start position:0%
+making this model and using this as an
+intermediate object you split the error
+
+ align:start position:0%
+intermediate object you split the error
+ 
+
+ align:start position:0%
+intermediate object you split the error
+in two and you start to be able to study
+
+ align:start position:0%
+in two and you start to be able to study
+ 
+
+ align:start position:0%
+in two and you start to be able to study
+and what you get is basically the
+
+ align:start position:0%
+and what you get is basically the
+ 
+
+ align:start position:0%
+and what you get is basically the
+following this term by basically using
+
+ align:start position:0%
+following this term by basically using
+ 
+
+ align:start position:0%
+following this term by basically using
+independence of what we assume that the
+
+ align:start position:0%
+independence of what we assume that the
+ 
+
+ align:start position:0%
+independence of what we assume that the
+data I didn't say that but that's
+
+ align:start position:0%
+data I didn't say that but that's
+ 
+
+ align:start position:0%
+data I didn't say that but that's
+important we assume that the data are
+
+ align:start position:0%
+important we assume that the data are
+ 
+
+ align:start position:0%
+important we assume that the data are
+independent with each other okay and by
+
+ align:start position:0%
+independent with each other okay and by
+ 
+
+ align:start position:0%
+independent with each other okay and by
+using that you get these results right
+
+ align:start position:0%
+using that you get these results right
+ 
+
+ align:start position:0%
+using that you get these results right
+away essentially using the fact that the
+
+ align:start position:0%
+away essentially using the fact that the
+ 
+
+ align:start position:0%
+away essentially using the fact that the
+variance of sum of independent variables
+
+ align:start position:0%
+variance of sum of independent variables
+ 
+
+ align:start position:0%
+variance of sum of independent variables
+the sum of the variances you get these
+
+ align:start position:0%
+the sum of the variances you get these
+ 
+
+ align:start position:0%
+the sum of the variances you get these
+results in one line okay and basically
+
+ align:start position:0%
+results in one line okay and basically
+ 
+
+ align:start position:0%
+results in one line okay and basically
+what this shows is that if K gets big so
+
+ align:start position:0%
+what this shows is that if K gets big so
+ 
+
+ align:start position:0%
+what this shows is that if K gets big so
+variance is another word for the
+
+ align:start position:0%
+variance is another word for the
+ 
+
+ align:start position:0%
+variance is another word for the
+stability okay so if if you have a big
+
+ align:start position:0%
+stability okay so if if you have a big
+ 
+
+ align:start position:0%
+stability okay so if if you have a big
+variance things will vary a lot it will
+
+ align:start position:0%
+variance things will vary a lot it will
+ 
+
+ align:start position:0%
+variance things will vary a lot it will
+be unstable so what you see here is
+
+ align:start position:0%
+be unstable so what you see here is
+ 
+
+ align:start position:0%
+be unstable so what you see here is
+exactly what we observe in the in the
+
+ align:start position:0%
+exactly what we observe in the in the
+ 
+
+ align:start position:0%
+exactly what we observe in the in the
+plots before if K was big things were
+
+ align:start position:0%
+plots before if K was big things were
+ 
+
+ align:start position:0%
+plots before if K was big things were
+not changing as much if K was more
+
+ align:start position:0%
+not changing as much if K was more
+ 
+
+ align:start position:0%
+not changing as much if K was more
+things were changing a lot okay and this
+
+ align:start position:0%
+things were changing a lot okay and this
+ 
+
+ align:start position:0%
+things were changing a lot okay and this
+is the one equation that shows you that
+
+ align:start position:0%
+is the one equation that shows you that
+ 
+
+ align:start position:0%
+is the one equation that shows you that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and if you just look at that you would
+
+ align:start position:0%
+and if you just look at that you would
+ 
+
+ align:start position:0%
+and if you just look at that you would
+just tell you the biggest the better big
+
+ align:start position:0%
+just tell you the biggest the better big
+ 
+
+ align:start position:0%
+just tell you the biggest the better big
+respect to what to the noise okay
+
+ align:start position:0%
+respect to what to the noise okay
+ 
+
+ align:start position:0%
+respect to what to the noise okay
+there's a lot of noise I should make it
+
+ align:start position:0%
+there's a lot of noise I should make it
+ 
+
+ align:start position:0%
+there's a lot of noise I should make it
+bigger should a small noise I can make
+
+ align:start position:0%
+bigger should a small noise I can make
+ 
+
+ align:start position:0%
+bigger should a small noise I can make
+it smaller but the point is that we saw
+
+ align:start position:0%
+it smaller but the point is that we saw
+ 
+
+ align:start position:0%
+it smaller but the point is that we saw
+before is that the problem putting K
+
+ align:start position:0%
+before is that the problem putting K
+ 
+
+ align:start position:0%
+before is that the problem putting K
+large was that we were forgetting about
+
+ align:start position:0%
+large was that we were forgetting about
+ 
+
+ align:start position:0%
+large was that we were forgetting about
+the problem we're just getting with
+
+ align:start position:0%
+the problem we're just getting with
+ 
+
+ align:start position:0%
+the problem we're just getting with
+something were very stable but could be
+
+ align:start position:0%
+something were very stable but could be
+ 
+
+ align:start position:0%
+something were very stable but could be
+potentially very bad if my function was
+
+ align:start position:0%
+potentially very bad if my function was
+ 
+
+ align:start position:0%
+potentially very bad if my function was
+not that simple okay this is a bit
+
+ align:start position:0%
+not that simple okay this is a bit
+ 
+
+ align:start position:0%
+not that simple okay this is a bit
+harder to study mathematically okay this
+
+ align:start position:0%
+harder to study mathematically okay this
+ 
+
+ align:start position:0%
+harder to study mathematically okay this
+is the calculation that I show you
+
+ align:start position:0%
+is the calculation that I show you
+ 
+
+ align:start position:0%
+is the calculation that I show you
+because you can do it yourself in like
+
+ align:start position:0%
+because you can do it yourself in like
+ 
+
+ align:start position:0%
+because you can do it yourself in like
+20 minutes
+
+ align:start position:0%
+20 minutes
+ 
+
+ align:start position:0%
+20 minutes
+okay or less this one it takes a bit
+
+ align:start position:0%
+okay or less this one it takes a bit
+ 
+
+ align:start position:0%
+okay or less this one it takes a bit
+more but we can get the hunch on how it
+
+ align:start position:0%
+more but we can get the hunch on how it
+ 
+
+ align:start position:0%
+more but we can get the hunch on how it
+looks like and the basic idea is what we
+
+ align:start position:0%
+looks like and the basic idea is what we
+ 
+
+ align:start position:0%
+looks like and the basic idea is what we
+already said if K is small in some sense
+
+ align:start position:0%
+already said if K is small in some sense
+ 
+
+ align:start position:0%
+already said if K is small in some sense
+weird and the points are close enough
+
+ align:start position:0%
+weird and the points are close enough
+ 
+
+ align:start position:0%
+weird and the points are close enough
+instead of F star X we are taking an F
+
+ align:start position:0%
+instead of F star X we are taking an F
+ 
+
+ align:start position:0%
+instead of F star X we are taking an F
+star X K X I and the I is close enough
+
+ align:start position:0%
+star X K X I and the I is close enough
+ 
+
+ align:start position:0%
+star X K X I and the I is close enough
+okay now if we start to put K bigger we
+
+ align:start position:0%
+okay now if we start to put K bigger we
+ 
+
+ align:start position:0%
+okay now if we start to put K bigger we
+start to blur that prediction by looking
+
+ align:start position:0%
+start to blur that prediction by looking
+ 
+
+ align:start position:0%
+start to blur that prediction by looking
+at many nearby points and but here there
+
+ align:start position:0%
+at many nearby points and but here there
+ 
+
+ align:start position:0%
+at many nearby points and but here there
+is no noise okay so that sounds like a
+
+ align:start position:0%
+is no noise okay so that sounds like a
+ 
+
+ align:start position:0%
+is no noise okay so that sounds like a
+bad idea so they we expect that error in
+
+ align:start position:0%
+bad idea so they we expect that error in
+ 
+
+ align:start position:0%
+bad idea so they we expect that error in
+that case to be either increasing or at
+
+ align:start position:0%
+that case to be either increasing or at
+ 
+
+ align:start position:0%
+that case to be either increasing or at
+least flat with respect to K so when we
+
+ align:start position:0%
+least flat with respect to K so when we
+ 
+
+ align:start position:0%
+least flat with respect to K so when we
+take K larger we're blurring this
+
+ align:start position:0%
+take K larger we're blurring this
+ 
+
+ align:start position:0%
+take K larger we're blurring this
+prediction and potentially make it far
+
+ align:start position:0%
+prediction and potentially make it far
+ 
+
+ align:start position:0%
+prediction and potentially make it far
+away from the true one okay and you can
+
+ align:start position:0%
+away from the true one okay and you can
+ 
+
+ align:start position:0%
+away from the true one okay and you can
+make this statement precise you can do
+
+ align:start position:0%
+make this statement precise you can do
+ 
+
+ align:start position:0%
+make this statement precise you can do
+you can prove it okay and what you if
+
+ align:start position:0%
+you can prove it okay and what you if
+ 
+
+ align:start position:0%
+you can prove it okay and what you if
+you will prove is basically that you
+
+ align:start position:0%
+you will prove is basically that you
+ 
+
+ align:start position:0%
+you will prove is basically that you
+have you have linear dependence so the
+
+ align:start position:0%
+have you have linear dependence so the
+ 
+
+ align:start position:0%
+have you have linear dependence so the
+error here is linearly increasing or
+
+ align:start position:0%
+error here is linearly increasing or
+ 
+
+ align:start position:0%
+error here is linearly increasing or
+polynomial increase in fact I don't
+
+ align:start position:0%
+polynomial increase in fact I don't
+ 
+
+ align:start position:0%
+polynomial increase in fact I don't
+remember with respect to K okay so the
+
+ align:start position:0%
+remember with respect to K okay so the
+ 
+
+ align:start position:0%
+remember with respect to K okay so the
+reason why I'm showing you this is
+
+ align:start position:0%
+reason why I'm showing you this is
+ 
+
+ align:start position:0%
+reason why I'm showing you this is
+skipping all these details just gave you
+
+ align:start position:0%
+skipping all these details just gave you
+ 
+
+ align:start position:0%
+skipping all these details just gave you
+a feeling of the kind of competition
+
+ align:start position:0%
+a feeling of the kind of competition
+ 
+
+ align:start position:0%
+a feeling of the kind of competition
+that answer the question is there is if
+
+ align:start position:0%
+that answer the question is there is if
+ 
+
+ align:start position:0%
+that answer the question is there is if
+there is an optimal value and what does
+
+ align:start position:0%
+there is an optimal value and what does
+ 
+
+ align:start position:0%
+there is an optimal value and what does
+it depends on and then at these points
+
+ align:start position:0%
+it depends on and then at these points
+ 
+
+ align:start position:0%
+it depends on and then at these points
+once you get these you start to see this
+
+ align:start position:0%
+once you get these you start to see this
+ 
+
+ align:start position:0%
+once you get these you start to see this
+kind of plot and typically here I put
+
+ align:start position:0%
+kind of plot and typically here I put
+ 
+
+ align:start position:0%
+kind of plot and typically here I put
+them the wrong way but here you
+
+ align:start position:0%
+them the wrong way but here you
+ 
+
+ align:start position:0%
+them the wrong way but here you
+basically say I have this one function I
+
+ align:start position:0%
+basically say I have this one function I
+ 
+
+ align:start position:0%
+basically say I have this one function I
+wanted to study which is the sum of two
+
+ align:start position:0%
+wanted to study which is the sum of two
+ 
+
+ align:start position:0%
+wanted to study which is the sum of two
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+I have this and have this okay
+
+ align:start position:0%
+I have this and have this okay
+ 
+
+ align:start position:0%
+I have this and have this okay
+and now to study the minimum I'm
+
+ align:start position:0%
+and now to study the minimum I'm
+ 
+
+ align:start position:0%
+and now to study the minimum I'm
+basically gonna sum them up and see
+
+ align:start position:0%
+basically gonna sum them up and see
+ 
+
+ align:start position:0%
+basically gonna sum them up and see
+what's the optimal value to optimize
+
+ align:start position:0%
+what's the optimal value to optimize
+ 
+
+ align:start position:0%
+what's the optimal value to optimize
+these two and the K that optimize this
+
+ align:start position:0%
+these two and the K that optimize this
+ 
+
+ align:start position:0%
+these two and the K that optimize this
+is exactly the optimal K and you see
+
+ align:start position:0%
+is exactly the optimal K and you see
+ 
+
+ align:start position:0%
+is exactly the optimal K and you see
+that the optimal K will behave as you
+
+ align:start position:0%
+that the optimal K will behave as you
+ 
+
+ align:start position:0%
+that the optimal K will behave as you
+expected okay be forced so here one
+
+ align:start position:0%
+expected okay be forced so here one
+ 
+
+ align:start position:0%
+expected okay be forced so here one
+ingredient is missing and it's just
+
+ align:start position:0%
+ingredient is missing and it's just
+ 
+
+ align:start position:0%
+ingredient is missing and it's just
+missing because I didn't put it in which
+
+ align:start position:0%
+missing because I didn't put it in which
+ 
+
+ align:start position:0%
+missing because I didn't put it in which
+is the number of points okay it's just
+
+ align:start position:0%
+is the number of points okay it's just
+ 
+
+ align:start position:0%
+is the number of points okay it's just
+because I didn't realize things okay it
+
+ align:start position:0%
+because I didn't realize things okay it
+ 
+
+ align:start position:0%
+because I didn't realize things okay it
+should be a 1 over n here is the after I
+
+ align:start position:0%
+should be a 1 over n here is the after I
+ 
+
+ align:start position:0%
+should be a 1 over n here is the after I
+didn't realize okay so but you announced
+
+ align:start position:0%
+didn't realize okay so but you announced
+ 
+
+ align:start position:0%
+didn't realize okay so but you announced
+it and it's good because it's true there
+
+ align:start position:0%
+it and it's good because it's true there
+ 
+
+ align:start position:0%
+it and it's good because it's true there
+should be one other end there but the
+
+ align:start position:0%
+should be one other end there but the
+ 
+
+ align:start position:0%
+should be one other end there but the
+rest is what we expected okay in some
+
+ align:start position:0%
+rest is what we expected okay in some
+ 
+
+ align:start position:0%
+rest is what we expected okay in some
+sense what we expect is that if my
+
+ align:start position:0%
+sense what we expect is that if my
+ 
+
+ align:start position:0%
+sense what we expect is that if my
+problem is complicated
+
+ align:start position:0%
+problem is complicated
+ 
+
+ align:start position:0%
+problem is complicated
+I need the smaller K if there is a lot
+
+ align:start position:0%
+I need the smaller K if there is a lot
+ 
+
+ align:start position:0%
+I need the smaller K if there is a lot
+of noise and in smaller I need a bigger
+
+ align:start position:0%
+of noise and in smaller I need a bigger
+ 
+
+ align:start position:0%
+of noise and in smaller I need a bigger
+K and depending on the number of points
+
+ align:start position:0%
+K and depending on the number of points
+ 
+
+ align:start position:0%
+K and depending on the number of points
+which would be in denominator here I can
+
+ align:start position:0%
+which would be in denominator here I can
+ 
+
+ align:start position:0%
+which would be in denominator here I can
+make them more or bigger or larger okay
+
+ align:start position:0%
+make them more or bigger or larger okay
+ 
+
+ align:start position:0%
+make them more or bigger or larger okay
+okay this plot is fundamental because it
+
+ align:start position:0%
+okay this plot is fundamental because it
+ 
+
+ align:start position:0%
+okay this plot is fundamental because it
+shows some property which is inheriting
+
+ align:start position:0%
+shows some property which is inheriting
+ 
+
+ align:start position:0%
+shows some property which is inheriting
+the problem and is like the theorem that
+
+ align:start position:0%
+the problem and is like the theorem that
+ 
+
+ align:start position:0%
+the problem and is like the theorem that
+some what is behind the intuition I've
+
+ align:start position:0%
+some what is behind the intuition I've
+ 
+
+ align:start position:0%
+some what is behind the intuition I've
+been saying you know repeating over and
+
+ align:start position:0%
+been saying you know repeating over and
+ 
+
+ align:start position:0%
+been saying you know repeating over and
+over which is this intuition that you
+
+ align:start position:0%
+over which is this intuition that you
+ 
+
+ align:start position:0%
+over which is this intuition that you
+cannot trust the data too much and there
+
+ align:start position:0%
+cannot trust the data too much and there
+ 
+
+ align:start position:0%
+cannot trust the data too much and there
+is the optimal amount of trust you can
+
+ align:start position:0%
+is the optimal amount of trust you can
+ 
+
+ align:start position:0%
+is the optimal amount of trust you can
+offer your data based on certain
+
+ align:start position:0%
+offer your data based on certain
+ 
+
+ align:start position:0%
+offer your data based on certain
+assumption okay and in our case the
+
+ align:start position:0%
+assumption okay and in our case the
+ 
+
+ align:start position:0%
+assumption okay and in our case the
+assumption where this kind of model so
+
+ align:start position:0%
+assumption where this kind of model so
+ 
+
+ align:start position:0%
+assumption where this kind of model so
+these grounds this little calculation I
+
+ align:start position:0%
+these grounds this little calculation I
+ 
+
+ align:start position:0%
+these grounds this little calculation I
+show you quickly grounds this intuition
+
+ align:start position:0%
+show you quickly grounds this intuition
+ 
+
+ align:start position:0%
+show you quickly grounds this intuition
+into a mathematical argument okay all
+
+ align:start position:0%
+into a mathematical argument okay all
+ 
+
+ align:start position:0%
+into a mathematical argument okay all
+right so we spent quite a bit of time on
+
+ align:start position:0%
+right so we spent quite a bit of time on
+ 
+
+ align:start position:0%
+right so we spent quite a bit of time on
+this in some sense this is a create from
+
+ align:start position:0%
+this in some sense this is a create from
+ 
+
+ align:start position:0%
+this in some sense this is a create from
+a conceptual point of view this is a
+
+ align:start position:0%
+a conceptual point of view this is a
+ 
+
+ align:start position:0%
+a conceptual point of view this is a
+critical idea okay because it's behind
+
+ align:start position:0%
+critical idea okay because it's behind
+ 
+
+ align:start position:0%
+critical idea okay because it's behind
+pretty much everything this idea of how
+
+ align:start position:0%
+pretty much everything this idea of how
+ 
+
+ align:start position:0%
+pretty much everything this idea of how
+much you can trust or not the data of
+
+ align:start position:0%
+much you can trust or not the data of
+ 
+
+ align:start position:0%
+much you can trust or not the data of
+course here as we said this is
+
+ align:start position:0%
+course here as we said this is
+ 
+
+ align:start position:0%
+course here as we said this is
+informative hopefully but you don't
+
+ align:start position:0%
+informative hopefully but you don't
+ 
+
+ align:start position:0%
+informative hopefully but you don't
+cannot really choose this K because you
+
+ align:start position:0%
+cannot really choose this K because you
+ 
+
+ align:start position:0%
+cannot really choose this K because you
+would need to know the noise but
+
+ align:start position:0%
+would need to know the noise but
+ 
+
+ align:start position:0%
+would need to know the noise but
+especially to know how to estimate this
+
+ align:start position:0%
+especially to know how to estimate this
+ 
+
+ align:start position:0%
+especially to know how to estimate this
+in order to minimize this quantity so in
+
+ align:start position:0%
+in order to minimize this quantity so in
+ 
+
+ align:start position:0%
+in order to minimize this quantity so in
+practice what you can show is you can
+
+ align:start position:0%
+practice what you can show is you can
+ 
+
+ align:start position:0%
+practice what you can show is you can
+use what is called cross-validation and
+
+ align:start position:0%
+use what is called cross-validation and
+ 
+
+ align:start position:0%
+use what is called cross-validation and
+in fact correlation is one one of a few
+
+ align:start position:0%
+in fact correlation is one one of a few
+ 
+
+ align:start position:0%
+in fact correlation is one one of a few
+other techniques you can use and the
+
+ align:start position:0%
+other techniques you can use and the
+ 
+
+ align:start position:0%
+other techniques you can use and the
+idea is that you don't have access but
+
+ align:start position:0%
+idea is that you don't have access but
+ 
+
+ align:start position:0%
+idea is that you don't have access but
+you can show that if you take a bunch of
+
+ align:start position:0%
+you can show that if you take a bunch of
+ 
+
+ align:start position:0%
+you can show that if you take a bunch of
+data points okay you split them in to
+
+ align:start position:0%
+data points okay you split them in to
+ 
+
+ align:start position:0%
+data points okay you split them in to
+use half for the training as usual is
+
+ align:start position:0%
+use half for the training as usual is
+ 
+
+ align:start position:0%
+use half for the training as usual is
+done and use the other half as a proxy
+
+ align:start position:0%
+done and use the other half as a proxy
+ 
+
+ align:start position:0%
+done and use the other half as a proxy
+for this future data then by minimizing
+
+ align:start position:0%
+for this future data then by minimizing
+ 
+
+ align:start position:0%
+for this future data then by minimizing
+the K taking the kid that minimize the
+
+ align:start position:0%
+the K taking the kid that minimize the
+ 
+
+ align:start position:0%
+the K taking the kid that minimize the
+error on this so-called holdout set then
+
+ align:start position:0%
+error on this so-called holdout set then
+ 
+
+ align:start position:0%
+error on this so-called holdout set then
+you can prove as good as if you could
+
+ align:start position:0%
+you can prove as good as if you could
+ 
+
+ align:start position:0%
+you can prove as good as if you could
+have access to this okay and it's
+
+ align:start position:0%
+have access to this okay and it's
+ 
+
+ align:start position:0%
+have access to this okay and it's
+actually very easy to prove you can show
+
+ align:start position:0%
+actually very easy to prove you can show
+ 
+
+ align:start position:0%
+actually very easy to prove you can show
+that if you just split in two okay and
+
+ align:start position:0%
+that if you just split in two okay and
+ 
+
+ align:start position:0%
+that if you just split in two okay and
+you minimize the urn the second half
+
+ align:start position:0%
+you minimize the urn the second half
+ 
+
+ align:start position:0%
+you minimize the urn the second half
+will you do what is called the holdout
+
+ align:start position:0%
+will you do what is called the holdout
+ 
+
+ align:start position:0%
+will you do what is called the holdout
+cross-validation is as good as if you
+
+ align:start position:0%
+cross-validation is as good as if you
+ 
+
+ align:start position:0%
+cross-validation is as good as if you
+had access to this okay so it's
+
+ align:start position:0%
+had access to this okay so it's
+ 
+
+ align:start position:0%
+had access to this okay so it's
+subdermal in a way now the problem with
+
+ align:start position:0%
+subdermal in a way now the problem with
+ 
+
+ align:start position:0%
+subdermal in a way now the problem with
+this is that we are only looking at say
+
+ align:start position:0%
+this is that we are only looking at say
+ 
+
+ align:start position:0%
+this is that we are only looking at say
+the error in expectation and what you
+
+ align:start position:0%
+the error in expectation and what you
+ 
+
+ align:start position:0%
+the error in expectation and what you
+can check is that if you look at higher
+
+ align:start position:0%
+can check is that if you look at higher
+ 
+
+ align:start position:0%
+can check is that if you look at higher
+order statistics say the variance of
+
+ align:start position:0%
+order statistics say the variance of
+ 
+
+ align:start position:0%
+order statistics say the variance of
+your estimators and so on and so forth
+
+ align:start position:0%
+your estimators and so on and so forth
+ 
+
+ align:start position:0%
+your estimators and so on and so forth
+what you might get is that by splitting
+
+ align:start position:0%
+what you might get is that by splitting
+ 
+
+ align:start position:0%
+what you might get is that by splitting
+in two if this big is fine in practice
+
+ align:start position:0%
+in two if this big is fine in practice
+ 
+
+ align:start position:0%
+in two if this big is fine in practice
+the data set is small you may get that
+
+ align:start position:0%
+the data set is small you may get that
+ 
+
+ align:start position:0%
+the data set is small you may get that
+the way you spray it might matter you
+
+ align:start position:0%
+the way you spray it might matter you
+ 
+
+ align:start position:0%
+the way you spray it might matter you
+might have bad luck and just fit in a
+
+ align:start position:0%
+might have bad luck and just fit in a
+ 
+
+ align:start position:0%
+might have bad luck and just fit in a
+certain way and so there is a whole
+
+ align:start position:0%
+certain way and so there is a whole
+ 
+
+ align:start position:0%
+certain way and so there is a whole
+zoology of ways of splitting and the
+
+ align:start position:0%
+zoology of ways of splitting and the
+ 
+
+ align:start position:0%
+zoology of ways of splitting and the
+basic one is a split say for this is for
+
+ align:start position:0%
+basic one is a split say for this is for
+ 
+
+ align:start position:0%
+basic one is a split say for this is for
+example the simplest okay split in a
+
+ align:start position:0%
+example the simplest okay split in a
+ 
+
+ align:start position:0%
+example the simplest okay split in a
+bunch of groups okay k fold or v-fold
+
+ align:start position:0%
+bunch of groups okay k fold or v-fold
+ 
+
+ align:start position:0%
+bunch of groups okay k fold or v-fold
+cross-validation take one group out of
+
+ align:start position:0%
+cross-validation take one group out of
+ 
+
+ align:start position:0%
+cross-validation take one group out of
+the time okay and do the same trim you
+
+ align:start position:0%
+the time okay and do the same trim you
+ 
+
+ align:start position:0%
+the time okay and do the same trim you
+know you train here and calculate the
+
+ align:start position:0%
+know you train here and calculate the
+ 
+
+ align:start position:0%
+know you train here and calculate the
+error here for different case then you
+
+ align:start position:0%
+error here for different case then you
+ 
+
+ align:start position:0%
+error here for different case then you
+do the same here do the same here do the
+
+ align:start position:0%
+do the same here do the same here do the
+ 
+
+ align:start position:0%
+do the same here do the same here do the
+same here some day errors up
+
+ align:start position:0%
+same here some day errors up
+ 
+
+ align:start position:0%
+same here some day errors up
+renormalizing and then just choose the K
+
+ align:start position:0%
+renormalizing and then just choose the K
+ 
+
+ align:start position:0%
+renormalizing and then just choose the K
+that minimize this new form of error
+
+ align:start position:0%
+that minimize this new form of error
+ 
+
+ align:start position:0%
+that minimize this new form of error
+and if the business there are small
+
+ align:start position:0%
+and if the business there are small
+ 
+
+ align:start position:0%
+and if the business there are small
+small small then typically this set will
+
+ align:start position:0%
+small small then typically this set will
+ 
+
+ align:start position:0%
+small small then typically this set will
+become very small and in the limit it
+
+ align:start position:0%
+become very small and in the limit it
+ 
+
+ align:start position:0%
+become very small and in the limit it
+becomes one they leave one out error
+
+ align:start position:0%
+becomes one they leave one out error
+ 
+
+ align:start position:0%
+becomes one they leave one out error
+okay what you do is that you literally
+
+ align:start position:0%
+okay what you do is that you literally
+ 
+
+ align:start position:0%
+okay what you do is that you literally
+leave one out train on the rest get
+
+ align:start position:0%
+leave one out train on the rest get
+ 
+
+ align:start position:0%
+leave one out train on the rest get
+there for all the values of K in this
+
+ align:start position:0%
+there for all the values of K in this
+ 
+
+ align:start position:0%
+there for all the values of K in this
+case put it back in take another one out
+
+ align:start position:0%
+case put it back in take another one out
+ 
+
+ align:start position:0%
+case put it back in take another one out
+and repeat the procedure now the
+
+ align:start position:0%
+and repeat the procedure now the
+ 
+
+ align:start position:0%
+and repeat the procedure now the
+question that I had 10-15 minutes ago
+
+ align:start position:0%
+question that I had 10-15 minutes ago
+ 
+
+ align:start position:0%
+question that I had 10-15 minutes ago
+was how do you choose V okay shall I
+
+ align:start position:0%
+was how do you choose V okay shall I
+ 
+
+ align:start position:0%
+was how do you choose V okay shall I
+make this two so I just do one split
+
+ align:start position:0%
+make this two so I just do one split
+ 
+
+ align:start position:0%
+make this two so I just do one split
+like this or shall I make it any so they
+
+ align:start position:0%
+like this or shall I make it any so they
+ 
+
+ align:start position:0%
+like this or shall I make it any so they
+do leave one out and that's right I know
+
+ align:start position:0%
+do leave one out and that's right I know
+ 
+
+ align:start position:0%
+do leave one out and that's right I know
+there is not a lot of theory that would
+
+ align:start position:0%
+there is not a lot of theory that would
+ 
+
+ align:start position:0%
+there is not a lot of theory that would
+support this you know an answer to this
+
+ align:start position:0%
+support this you know an answer to this
+ 
+
+ align:start position:0%
+support this you know an answer to this
+question and what I know is mostly you
+
+ align:start position:0%
+question and what I know is mostly you
+ 
+
+ align:start position:0%
+question and what I know is mostly you
+know what you can expect intuitively
+
+ align:start position:0%
+know what you can expect intuitively
+ 
+
+ align:start position:0%
+know what you can expect intuitively
+which is if you have a lot of data
+
+ align:start position:0%
+which is if you have a lot of data
+ 
+
+ align:start position:0%
+which is if you have a lot of data
+points what does it mean a lot I don't
+
+ align:start position:0%
+points what does it mean a lot I don't
+ 
+
+ align:start position:0%
+points what does it mean a lot I don't
+know if you have to millions ten
+
+ align:start position:0%
+know if you have to millions ten
+ 
+
+ align:start position:0%
+know if you have to millions ten
+thousand I don't know if you have a big
+
+ align:start position:0%
+thousand I don't know if you have a big
+ 
+
+ align:start position:0%
+thousand I don't know if you have a big
+data set
+
+ align:start position:0%
+data set
+ 
+
+ align:start position:0%
+data set
+typically splitting in two or maybe
+
+ align:start position:0%
+typically splitting in two or maybe
+ 
+
+ align:start position:0%
+typically splitting in two or maybe
+doing just random splits is stable
+
+ align:start position:0%
+doing just random splits is stable
+ 
+
+ align:start position:0%
+doing just random splits is stable
+enough what does it mean that you try
+
+ align:start position:0%
+enough what does it mean that you try
+ 
+
+ align:start position:0%
+enough what does it mean that you try
+okay and you look how much it moves
+
+ align:start position:0%
+okay and you look how much it moves
+ 
+
+ align:start position:0%
+okay and you look how much it moves
+whereas if you have say you know I don't
+
+ align:start position:0%
+whereas if you have say you know I don't
+ 
+
+ align:start position:0%
+whereas if you have say you know I don't
+know if it even exists application like
+
+ align:start position:0%
+know if it even exists application like
+ 
+
+ align:start position:0%
+know if it even exists application like
+you know if you were micro replication
+
+ align:start position:0%
+you know if you were micro replication
+ 
+
+ align:start position:0%
+you know if you were micro replication
+where we would have 20 30 inputs
+
+ align:start position:0%
+where we would have 20 30 inputs
+ 
+
+ align:start position:0%
+where we would have 20 30 inputs
+anywhere 20 mentions and then in that
+
+ align:start position:0%
+anywhere 20 mentions and then in that
+ 
+
+ align:start position:0%
+anywhere 20 mentions and then in that
+case you really don't do much splitting
+
+ align:start position:0%
+case you really don't do much splitting
+ 
+
+ align:start position:0%
+case you really don't do much splitting
+okay if you have 20 example you try to
+
+ align:start position:0%
+okay if you have 20 example you try to
+ 
+
+ align:start position:0%
+okay if you have 20 example you try to
+leave one out and it's the best you can
+
+ align:start position:0%
+leave one out and it's the best you can
+ 
+
+ align:start position:0%
+leave one out and it's the best you can
+do and it's really very unstable and
+
+ align:start position:0%
+do and it's really very unstable and
+ 
+
+ align:start position:0%
+do and it's really very unstable and
+sucks okay so in this case there is work
+
+ align:start position:0%
+sucks okay so in this case there is work
+ 
+
+ align:start position:0%
+sucks okay so in this case there is work
+to be done I mean there is as far as I
+
+ align:start position:0%
+to be done I mean there is as far as I
+ 
+
+ align:start position:0%
+to be done I mean there is as far as I
+know that's the state of things okay so
+
+ align:start position:0%
+know that's the state of things okay so
+ 
+
+ align:start position:0%
+know that's the state of things okay so
+we introduced the class of very simple
+
+ align:start position:0%
+we introduced the class of very simple
+ 
+
+ align:start position:0%
+we introduced the class of very simple
+algorithms they seem to be pretty
+
+ align:start position:0%
+algorithms they seem to be pretty
+ 
+
+ align:start position:0%
+algorithms they seem to be pretty
+reasonable they seem to allow us
+
+ align:start position:0%
+reasonable they seem to allow us
+ 
+
+ align:start position:0%
+reasonable they seem to allow us
+provided that we have a way to measure
+
+ align:start position:0%
+provided that we have a way to measure
+ 
+
+ align:start position:0%
+provided that we have a way to measure
+distances or similarity to go from
+
+ align:start position:0%
+distances or similarity to go from
+ 
+
+ align:start position:0%
+distances or similarity to go from
+simple to complex but and we have some
+
+ align:start position:0%
+simple to complex but and we have some
+ 
+
+ align:start position:0%
+simple to complex but and we have some
+kind of theory that tells us how what is
+
+ align:start position:0%
+kind of theory that tells us how what is
+ 
+
+ align:start position:0%
+kind of theory that tells us how what is
+the optimal value of time kind of
+
+ align:start position:0%
+the optimal value of time kind of
+ 
+
+ align:start position:0%
+the optimal value of time kind of
+practical procedure to actually choose
+
+ align:start position:0%
+practical procedure to actually choose
+ 
+
+ align:start position:0%
+practical procedure to actually choose
+it in practice okay are we done it is
+
+ align:start position:0%
+it in practice okay are we done it is
+ 
+
+ align:start position:0%
+it in practice okay are we done it is
+that all okay do we need to do anything
+
+ align:start position:0%
+that all okay do we need to do anything
+ 
+
+ align:start position:0%
+that all okay do we need to do anything
+else what's missing here one thing that
+
+ align:start position:0%
+else what's missing here one thing that
+ 
+
+ align:start position:0%
+else what's missing here one thing that
+is missing here is that most of the
+
+ align:start position:0%
+is missing here is that most of the
+ 
+
+ align:start position:0%
+is missing here is that most of the
+intuition we develop so far are really
+
+ align:start position:0%
+intuition we develop so far are really
+ 
+
+ align:start position:0%
+intuition we develop so far are really
+related to low dimension okay and here
+
+ align:start position:0%
+related to low dimension okay and here
+ 
+
+ align:start position:0%
+related to low dimension okay and here
+very quickly if you just do a little
+
+ align:start position:0%
+very quickly if you just do a little
+ 
+
+ align:start position:0%
+very quickly if you just do a little
+exercise where you try to say how
+
+ align:start position:0%
+exercise where you try to say how
+ 
+
+ align:start position:0%
+exercise where you try to say how
+is a cube that covers 1% of the bigger
+
+ align:start position:0%
+is a cube that covers 1% of the bigger
+ 
+
+ align:start position:0%
+is a cube that covers 1% of the bigger
+cube of unit length okay so the big cube
+
+ align:start position:0%
+cube of unit length okay so the big cube
+ 
+
+ align:start position:0%
+cube of unit length okay so the big cube
+is volume 1 length of Diaz use 1 and ask
+
+ align:start position:0%
+is volume 1 length of Diaz use 1 and ask
+ 
+
+ align:start position:0%
+is volume 1 length of Diaz use 1 and ask
+you how big is this if it has to cover 1
+
+ align:start position:0%
+you how big is this if it has to cover 1
+ 
+
+ align:start position:0%
+you how big is this if it has to cover 1
+percent of the volume it's ready to
+
+ align:start position:0%
+percent of the volume it's ready to
+ 
+
+ align:start position:0%
+percent of the volume it's ready to
+check that you just dis is just going to
+
+ align:start position:0%
+check that you just dis is just going to
+ 
+
+ align:start position:0%
+check that you just dis is just going to
+be a D roof where D is the dimension of
+
+ align:start position:0%
+be a D roof where D is the dimension of
+ 
+
+ align:start position:0%
+be a D roof where D is the dimension of
+the cube and this is the shape of the
+
+ align:start position:0%
+the cube and this is the shape of the
+ 
+
+ align:start position:0%
+the cube and this is the shape of the
+eros okay so if you're in low dimension
+
+ align:start position:0%
+eros okay so if you're in low dimension
+ 
+
+ align:start position:0%
+eros okay so if you're in low dimension
+basically for 1% is intuitively small
+
+ align:start position:0%
+basically for 1% is intuitively small
+ 
+
+ align:start position:0%
+basically for 1% is intuitively small
+within the big cube but as soon as you
+
+ align:start position:0%
+within the big cube but as soon as you
+ 
+
+ align:start position:0%
+within the big cube but as soon as you
+go in harder dimension what you see is
+
+ align:start position:0%
+go in harder dimension what you see is
+ 
+
+ align:start position:0%
+go in harder dimension what you see is
+that the length of the edge of the
+
+ align:start position:0%
+that the length of the edge of the
+ 
+
+ align:start position:0%
+that the length of the edge of the
+little cube that has to cover one
+
+ align:start position:0%
+little cube that has to cover one
+ 
+
+ align:start position:0%
+little cube that has to cover one
+percent of the volume becomes very close
+
+ align:start position:0%
+percent of the volume becomes very close
+ 
+
+ align:start position:0%
+percent of the volume becomes very close
+to one almost immediately is this curve
+
+ align:start position:0%
+to one almost immediately is this curve
+ 
+
+ align:start position:0%
+to one almost immediately is this curve
+going up okay what does it mean that we
+
+ align:start position:0%
+going up okay what does it mean that we
+ 
+
+ align:start position:0%
+going up okay what does it mean that we
+feel call if you say I won't think you
+
+ align:start position:0%
+feel call if you say I won't think you
+ 
+
+ align:start position:0%
+feel call if you say I won't think you
+know our intuition is well one percent
+
+ align:start position:0%
+know our intuition is well one percent
+ 
+
+ align:start position:0%
+know our intuition is well one percent
+is a pretty small volume if I just took
+
+ align:start position:0%
+is a pretty small volume if I just took
+ 
+
+ align:start position:0%
+is a pretty small volume if I just took
+the neighbors in one percent they're
+
+ align:start position:0%
+the neighbors in one percent they're
+ 
+
+ align:start position:0%
+the neighbors in one percent they're
+pretty close so they should have the
+
+ align:start position:0%
+pretty close so they should have the
+ 
+
+ align:start position:0%
+pretty close so they should have the
+same label well in dimension 10 it's
+
+ align:start position:0%
+same label well in dimension 10 it's
+ 
+
+ align:start position:0%
+same label well in dimension 10 it's
+everything ok so our intuition no agency
+
+ align:start position:0%
+everything ok so our intuition no agency
+ 
+
+ align:start position:0%
+everything ok so our intuition no agency
+probably there is something wrong with
+
+ align:start position:0%
+probably there is something wrong with
+ 
+
+ align:start position:0%
+probably there is something wrong with
+my way of thinking of volume sure but
+
+ align:start position:0%
+my way of thinking of volume sure but
+ 
+
+ align:start position:0%
+my way of thinking of volume sure but
+the problem is that we have to rethink a
+
+ align:start position:0%
+the problem is that we have to rethink a
+ 
+
+ align:start position:0%
+the problem is that we have to rethink a
+bit how you think of dimensions and
+
+ align:start position:0%
+bit how you think of dimensions and
+ 
+
+ align:start position:0%
+bit how you think of dimensions and
+similarity and high dimension because
+
+ align:start position:0%
+similarity and high dimension because
+ 
+
+ align:start position:0%
+similarity and high dimension because
+things that are obviously low
+
+ align:start position:0%
+things that are obviously low
+ 
+
+ align:start position:0%
+things that are obviously low
+dimensional start to be very complicated
+
+ align:start position:0%
+dimensional start to be very complicated
+ 
+
+ align:start position:0%
+dimensional start to be very complicated
+okay and the basic idea is that this
+
+ align:start position:0%
+okay and the basic idea is that this
+ 
+
+ align:start position:0%
+okay and the basic idea is that this
+neighbor techniques just look at what's
+
+ align:start position:0%
+neighbor techniques just look at what's
+ 
+
+ align:start position:0%
+neighbor techniques just look at what's
+happening in one regions but hope to do
+
+ align:start position:0%
+happening in one regions but hope to do
+ 
+
+ align:start position:0%
+happening in one regions but hope to do
+is that if your function actually have
+
+ align:start position:0%
+is that if your function actually have
+ 
+
+ align:start position:0%
+is that if your function actually have
+some kind of global properties okay so
+
+ align:start position:0%
+some kind of global properties okay so
+ 
+
+ align:start position:0%
+some kind of global properties okay so
+say for example a sign is the simplest
+
+ align:start position:0%
+say for example a sign is the simplest
+ 
+
+ align:start position:0%
+say for example a sign is the simplest
+example of something which is global
+
+ align:start position:0%
+example of something which is global
+ 
+
+ align:start position:0%
+example of something which is global
+because the value here and the value
+
+ align:start position:0%
+because the value here and the value
+ 
+
+ align:start position:0%
+because the value here and the value
+here are very much related and then I go
+
+ align:start position:0%
+here are very much related and then I go
+ 
+
+ align:start position:0%
+here are very much related and then I go
+up and it's the same then it goes down
+
+ align:start position:0%
+up and it's the same then it goes down
+ 
+
+ align:start position:0%
+up and it's the same then it goes down
+so if you know something like this that
+
+ align:start position:0%
+so if you know something like this that
+ 
+
+ align:start position:0%
+so if you know something like this that
+is that you can borrow a strength from
+
+ align:start position:0%
+is that you can borrow a strength from
+ 
+
+ align:start position:0%
+is that you can borrow a strength from
+points which are far away in some sense
+
+ align:start position:0%
+points which are far away in some sense
+ 
+
+ align:start position:0%
+points which are far away in some sense
+the function has some similar properties
+
+ align:start position:0%
+the function has some similar properties
+ 
+
+ align:start position:0%
+the function has some similar properties
+and so you want to go from a local
+
+ align:start position:0%
+and so you want to go from a local
+ 
+
+ align:start position:0%
+and so you want to go from a local
+estimation to some form of global
+
+ align:start position:0%
+estimation to some form of global
+ 
+
+ align:start position:0%
+estimation to some form of global
+estimation okay and instead of making a
+
+ align:start position:0%
+estimation okay and instead of making a
+ 
+
+ align:start position:0%
+estimation okay and instead of making a
+decision based only on the neighbors of
+
+ align:start position:0%
+decision based only on the neighbors of
+ 
+
+ align:start position:0%
+decision based only on the neighbors of
+the point you might want to use points
+
+ align:start position:0%
+the point you might want to use points
+ 
+
+ align:start position:0%
+the point you might want to use points
+which are potentially far away okay and
+
+ align:start position:0%
+which are potentially far away okay and
+ 
+
+ align:start position:0%
+which are potentially far away okay and
+this seems to be like a good idea in
+
+ align:start position:0%
+this seems to be like a good idea in
+ 
+
+ align:start position:0%
+this seems to be like a good idea in
+high dimensions where you have that
+
+ align:start position:0%
+high dimensions where you have that
+ 
+
+ align:start position:0%
+high dimensions where you have that
+neighboring points might not be enough
+
+ align:start position:0%
+neighboring points might not be enough
+ 
+
+ align:start position:0%
+neighboring points might not be enough
+information and that's kind of what's
+
+ align:start position:0%
+information and that's kind of what's
+ 
+
+ align:start position:0%
+information and that's kind of what's
+called curse of dimensionality okay so
+
+ align:start position:0%
+called curse of dimensionality okay so
+ 
+
+ align:start position:0%
+called curse of dimensionality okay so
+what I want to do next but we can take a
+
+ align:start position:0%
+what I want to do next but we can take a
+ 
+
+ align:start position:0%
+what I want to do next but we can take a
+break here is discussing least squares
+
+ align:start position:0%
+break here is discussing least squares
+ 
+
+ align:start position:0%
+break here is discussing least squares
+and currently squares okay well what
+
+ align:start position:0%
+and currently squares okay well what
+ 
+
+ align:start position:0%
+and currently squares okay well what
+we're gonna do is that we're gonna take
+
+ align:start position:0%
+we're gonna do is that we're gonna take
+ 
+
+ align:start position:0%
+we're gonna do is that we're gonna take
+a linear model of our data and then
+
+ align:start position:0%
+a linear model of our data and then
+ 
+
+ align:start position:0%
+a linear model of our data and then
+we're gonna try to see how you can
+
+ align:start position:0%
+we're gonna try to see how you can
+ 
+
+ align:start position:0%
+we're gonna try to see how you can
+estimate and learn and we're gonna look
+
+ align:start position:0%
+estimate and learn and we're gonna look
+ 
+
+ align:start position:0%
+estimate and learn and we're gonna look
+at bit of the computation a bit of the
+
+ align:start position:0%
+at bit of the computation a bit of the
+ 
+
+ align:start position:0%
+at bit of the computation a bit of the
+statistical idea underlying this model
+
+ align:start position:0%
+statistical idea underlying this model
+ 
+
+ align:start position:0%
+statistical idea underlying this model
+and then we're going to play around in a
+
+ align:start position:0%
+and then we're going to play around in a
+ 
+
+ align:start position:0%
+and then we're going to play around in a
+very simple way to the way to extend
+
+ align:start position:0%
+very simple way to the way to extend
+ 
+
+ align:start position:0%
+very simple way to the way to extend
+from a linear model to a nonlinear model
+
+ align:start position:0%
+from a linear model to a nonlinear model
+ 
+
+ align:start position:0%
+from a linear model to a nonlinear model
+and actually make it nonparametric tell
+
+ align:start position:0%
+and actually make it nonparametric tell
+ 
+
+ align:start position:0%
+and actually make it nonparametric tell
+you what nonparametric means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
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+
+PROFESSOR: OK, we're ready for
+the second lecture today.
+
+We will start to get into a
+little technical material,
+
+which doesn't mean necessarily
+that it's more important.
+
+It just means that it's easier
+because it deals with
+
+mathematics.
+
+I'm going to spend a little
+bit more time reviewing
+
+probability, as you
+learned it before.
+
+I want to review it at a
+slightly more fundamental
+
+level than what you're
+used to seeing it as.
+
+You will understand why as we go
+on because when we get into
+
+stochastic processes, we will
+find that there are lots of
+
+very peculiar things
+that happen.
+
+And when peculiar things happen,
+the only thing you can
+
+do is go back to basics ideas.
+
+And if you don't understand what
+those basic ideas are,
+
+then you're in real trouble.
+
+So we'll start out by talking
+about expectations just a
+
+little bit.
+
+Distribution function of a
+random variable often says
+
+more than you're really
+interested in.
+
+In other words, a distribution
+function is a function from
+
+the whole sample space into
+the real numbers.
+
+And that's a very complicated
+thing in general.
+
+And the expectation is just
+one simple number.
+
+And with that one simple number,
+you get an idea of
+
+what that random variable is all
+about, whether it's big or
+
+it's little or what have you.
+
+They're a bunch of formulas that
+you're familiar with for
+
+finding the expectation.
+
+If you have a discrete random
+variable, the usual formula is
+
+you take all of the possible
+sample values, multiply each
+
+of them by the probability
+of that sample value,
+
+and you sum it up.
+
+This is what you learned right
+at the beginning of taking
+
+probability.
+
+If you've never taken
+probability, you learned it in
+
+statistic classes just as
+something you don't know where
+
+it comes from.
+
+But it's there.
+
+If you have a continuous random
+variable, a continuous
+
+random variable is one
+that has a density.
+
+You can find the expectation
+there.
+
+If you have an arbitrary random
+variable and it's not
+
+negative, then there's this
+peculiar formula here, which I
+
+will point to.
+
+I think I'll point to it.
+
+Ah yes, I will point to it.
+
+This formula down here, you
+might or might not have seen.
+
+And I hope by the end of this
+course, you'll realize that
+
+it's one, more fundamental and
+two, probably more useful than
+
+either of these two.
+
+And then there's a final one,
+which this final formula, I'll
+
+tell you a little bit about
+that when we get to it.
+
+OK, the formula for the expected
+value in terms of the
+
+integral of the complimentary
+distribution function.
+
+There's a picture here which
+shows you how it corresponds
+
+to the usual thing you're
+used to for a
+
+discrete random variable.
+
+Namely what you're doing is
+you're integrating this
+
+complimentary distribution
+function, which is the
+
+probability that the random
+variable x is greater than any
+
+particular x along
+the axis here.
+
+So you integrate this
+function along here.
+
+And according to what I'm trying
+to convince you of,
+
+just integrating that function
+gives you the expected value.
+
+And the reason is that this top
+little square here is a1
+
+times the probability that
+x is equal to a1.
+
+Next one is a2 times the
+probability it's equal to a2
+
+and so forth down.
+
+And you can obviously generalize
+this to any
+
+discrete random variable,
+which is non-negative.
+
+And I'm just talking about
+non-negative random variables
+
+for the moment.
+
+If x has a density, the same
+argument applies to any
+
+Riemann sum for that integral.
+
+You can take integrals.
+
+You can break them up
+into little slices.
+
+If you break them up into
+little slices, you can
+
+represent it in this way.
+
+And presto, again, you get that
+this integral is equal to
+
+the expectation.
+
+And if you have any other thing
+at all, you can always
+
+represent it in terms
+of this Riemann sum.
+
+Now why is it even more
+powerful then that?
+
+Well, it's more powerful then
+that because if you took
+
+measure theory--
+
+which most of you presumably
+have not taken yet, and many
+
+of you might never take it--
+
+you will find out that this
+is really the fundamental
+
+definition after all.
+
+And integration, when you look
+and measure theoretic terms,
+
+instead of taking little slices
+that go this way, you
+
+wind up taking little slices
+that go that way.
+
+So that any way this is the
+fundamental definition of
+
+expectation.
+
+If you're worried about whether
+expectations exist or
+
+not, why is this much nicer?
+
+Because what you're integrating
+here is simply a
+
+function, which is monotonic
+decreasing with x.
+
+In other words, if you try to
+integrate it by integrating
+
+this function out to some
+largest value and then
+
+chopping if off there, what
+you get is some number.
+
+If you extend this chopping off
+point out, what you get is
+
+a number which keeps
+increasing.
+
+What can happen?
+
+As you take a number which is
+increasing, you either get to
+
+infinity or you get to
+some finite limit.
+
+Nothing else can happen.
+
+So there aren't any limiting
+problems here.
+
+And when you take expectations
+in other ways, there are
+
+always questions that
+you have to ask.
+
+And they're often serious.
+
+So this is just a much nicer
+way of doing it.
+
+Anyway, that's the way
+we're going to do it.
+
+And so now we go on.
+
+Oh, I should mention where the
+other formula comes from.
+
+This formula back here.
+
+You get that by representing x
+as both the positive part of x
+
+plus the negative part of x.
+
+And if you want to see how to
+do that exactly, it's in the
+
+notes where it talks about
+first this and then this.
+
+So you just put the
+two together.
+
+And then you get an
+expected value.
+
+A word about notation here, and
+there's nothing I can do
+
+about this.
+
+It's an unfortunate thing.
+
+When somebody says that the
+expected value of a random
+
+variable exists, what
+do they mean?
+
+Any engineer would try to
+integrate it and would either
+
+get something which was
+undefined, because it was
+
+infinite going this way.
+
+It's minus infinity
+going that way.
+
+And there's no way to put
+the two together.
+
+If you get infinity going this
+way, something finite going
+
+that way, like with a
+non-negative random variable,
+
+it's kind of silly to say the
+expectation doesn't exist.
+
+Because really what's happening
+is the expectation
+
+is infinite.
+
+Now mathematicians and everybody
+who writes books,
+
+everybody who writes
+papers, everybody--
+
+I think--
+
+defines expected value as
+existing only if it's finite.
+
+In other words, what you're
+doing is taking this integral
+
+over the set of real values.
+
+And you don't allow plus
+infinity or minus infinity.
+
+So you say that the expectation
+does not exist if
+
+in fact it's infinite or it's
+minus infinity or it is
+
+undefined completely.
+
+And you say it's undefined
+in all of those cases.
+
+And that's just a convention
+that everybody lives by.
+
+So the other way of saying this
+is if the expected value
+
+of the magnitude of the random
+variable is infinite, then the
+
+expectation doesn't exist.
+
+So we will try to say it
+that way sometimes
+
+when it's really important.
+
+OK, let's go on to indicator
+random variables.
+
+You're probably familiar
+with these.
+
+For every event you can think
+of, an event is something
+
+which is true, which occurs when
+some set of the sample
+
+points occur and is not
+true otherwise.
+
+So the definition of an
+indicator random variable is
+
+that the indicator
+for an event a--
+
+as a function of the
+sample space--
+
+is equal to 1, if omega is in
+the event a, and 0 otherwise.
+
+So if you draw the distribution
+function of it,
+
+the distribution function of the
+indicator function is 0 up
+
+until the point 0.
+
+Then it jumps up to 1 minus
+the probability of a.
+
+At 1, it jumps all
+the way up to 1.
+
+So it's simply a binary
+random variable.
+
+So every event has an indicator
+random variable.
+
+Every indicator random
+variable has a
+
+binary random variable.
+
+So indicator random variables
+are very simple.
+
+Events are very simple because
+you can map any event into an
+
+indicator random variable
+[INAUDIBLE].
+
+And this also says that since
+we want to talk about events
+
+very often, binary random
+variables are particularly
+
+important in this field.
+
+OK, but what this really says
+now is that any theorem about
+
+random variables can be
+applied to events.
+
+This is one of the few examples
+I know where it's
+
+much harder to find the
+expectation by taking the
+
+complimentary distribution
+function and integrating it.
+
+It's not hard.
+
+But it's far easier to take
+the probability that the
+
+indicator random variable
+is 0, which is 1 minus
+
+probability of a.
+
+The probability is equal to 1,
+which is probability of a, and
+
+take the expectation, which is
+the probability of a, and the
+
+standard deviation, which
+is the square root the
+
+probability of a times 1 minus
+the probability of a.
+
+So random variables are sort
+of trivial things in a way.
+
+OK, let's go on to multiple
+random variables.
+
+Now here's something that's
+a trick question in a way.
+
+But it's a very important
+trick question.
+
+Is a random variable specified
+by its distribution function?
+
+We've already seen that it's
+not really specified by its
+
+density or by its probability
+mass function.
+
+But we've said a distribution
+function is a more general
+
+thing so that every random
+variable has a
+
+distribution function.
+
+Does the distribution function
+specify the random variable?
+
+No, that's the whole
+reason for what
+
+Kolmogorov did back in 1933.
+
+Or at least it was one
+of the main reasons
+
+for what he was doing.
+
+He wanted to straighten out
+this ambiguity which runs
+
+through the field about
+confusing random variables
+
+with their distribution
+function.
+
+Random variables are functions
+from the sample space to the
+
+real numbers.
+
+And they're not anything else.
+
+So if you want to really define
+a random variable, you
+
+not only have to know what that
+random variable is but
+
+you also have to know what
+its relationships are.
+
+It's like if you're trying
+to understand the person.
+
+You can't understand the person
+without understanding
+
+something about who they know,
+how they know them, all those
+
+other things.
+
+All those relationships
+are important.
+
+And it's the same with
+random variables.
+
+You got to know about all
+the relationships.
+
+Many problems you can solve
+just in terms of
+
+distribution function.
+
+But ultimately you have to--
+
+or ultimately in many cases,
+you have to deal with these
+
+joint distribution functions.
+
+And random variables
+are independent.
+
+If the joint distribution
+function is equal to the
+
+product of the distribution
+functions for all x1 to xn,
+
+and that same form carries over
+for density functions and
+
+for probability mass
+functions.
+
+OK, if you have discrete random
+variables, the idea of
+
+independence is a whole lot more
+intuitive if you express
+
+it in terms of conditional
+probabilities.
+
+The conditional probability
+that the random variable x
+
+takes on some sample value x
+given that the random variable
+
+y takes on a sample value y.
+
+Just as one side comment here,
+when you're doing problems,
+
+you will very often want to
+leave out the subscripts here
+
+saying what random variables
+you're dealing with.
+
+And you will use either capital
+or small letters here
+
+mixing up the argument and the
+function itself, which
+
+everybody does.
+
+And it's perfectly all right.
+
+I suggest that you try not to do
+it for a while because you
+
+get so confused doing this,
+not being able to sort out
+
+what's a random variable and
+what's a real number.
+
+A lot of wags say random
+variables are neither random,
+
+because they're functions
+of the sample space,
+
+nor are they variables.
+
+And both of those are true.
+
+That's immaterial here.
+
+It's just that when you start
+getting confused about a
+
+problem, it's important to
+sort out which things are
+
+random variables and which
+things are arguments.
+
+Now this conditional probability
+is something
+
+you're all familiar with.
+
+But x and y are independent then
+if the probability of x
+
+conditional on y is the same
+as the probability of x not
+
+conditional on y.
+
+In other words, if observing
+what y is doesn't tell you
+
+anything about what x is, that's
+really your intuitive
+
+definition of independence.
+
+It's what you use if
+you're dealing with
+
+some real world situation.
+
+And you're asking what does
+this have to do with that?
+
+And if this has nothing to
+do with that, the random
+
+variables over here have nothing
+to do with the random
+
+variables over there, you would
+say in the real world
+
+that these things are
+independent of each other.
+
+When you have a probability
+model, you say they're
+
+statistically independent
+of each other.
+
+OK, so that's the relationship
+between the real world and the
+
+models that we're dealing
+with all the time.
+
+We call it independence
+in both cases.
+
+But it means somewhat different
+things in the two
+
+situations.
+
+OK, next about IID
+random variables.
+
+What are they?
+
+Well, the joint distribution
+function has to be equal to
+
+the product of the individual
+distribution functions.
+
+You notice I've done something
+funny here, which is a
+
+convention I always use.
+
+A lot of people use it.
+
+If you have a bunch of
+independent random variables,
+
+they all have the same
+distribution function.
+
+If they all have the same
+distribution function, it gets
+
+confusing to refer to their
+distribution functions as a
+
+distribution function of
+the random variable x1,
+
+distribution function of
+the random variable x2.
+
+It's nicer to just take a
+generic random variable x,
+
+which has the same distribution
+as all of these,
+
+and express this numerically
+in this way.
+
+You have the same product form
+for probability mass functions
+
+and for density functions.
+
+So this works throughout.
+
+OK next, think about a
+probability model in which r,
+
+the set of real numbers,
+is a sample space.
+
+And x is some random variable
+on that sample space.
+
+Namely x then is a function from
+the real numbers on to
+
+the real numbers.
+
+The interesting thing
+here, and what I'm
+
+saying here is obvious.
+
+It's something that
+you all know.
+
+It's something that you've all
+been using even before you
+
+started to learn about
+probability theory.
+
+But at the same time, you
+probably never thought about
+
+it in a serious enough way that
+you would really make
+
+sense out of it.
+
+You can always create an
+extended probability model in
+
+which the Cartesian space r to
+the n-- in other words, the
+
+space of n real numbers--
+
+is the sample space.
+
+And x1 to xn are independent
+identity
+
+distributed random variables.
+
+This is not obvious.
+
+And that's something
+you have to prove.
+
+But it's not hard to prove.
+
+And all you have to do is start
+out with a probability
+
+model for one random variable.
+
+And then just define all
+products to be what they're
+
+supposed to be and go from the
+products to all unions and all
+
+intersections.
+
+We're just going to assume that
+that's true because we
+
+have to assume it's true if we
+don't want to use any measure
+
+theory here.
+
+This is one of the easier
+things to show
+
+using measure theory.
+
+But it's something you
+are always used to.
+
+When you think of a random
+experiment, when you think of
+
+playing dice with somebody
+or playing cards with
+
+someone, you are--
+
+from the very beginning when you
+started to talk about odds
+
+or anything of that sort, you
+have always had the idea that
+
+this is a game which you
+can play repeatedly.
+
+And each time you play it,
+it's the same game.
+
+But the outcome is different.
+
+But all the probabilities
+are exactly the same.
+
+What this says is you can always
+make a probability
+
+model that way.
+
+You can always make a
+probability model which
+
+corresponds to what you've
+always believed deep in your
+
+hearts all your lives.
+
+And fortunately, that's true.
+
+Otherwise, you wouldn't
+use probability.
+
+OK, so let's move
+on from that.
+
+The page of philosophy, I will
+stop doing that pretty soon.
+
+But I have to get across what
+the relationship is between
+
+the real world and
+these models that
+
+we're dealing with.
+
+Because otherwise, you as
+engineers or business people
+
+or financial analysts or
+whatever the heck you're going
+
+to become will start believing
+in your probability models.
+
+And you will cause untold damage
+by losing track of the
+
+fact that these are supposedly
+models of something.
+
+And you better think of
+what they're supposed
+
+to be models of.
+
+OK, in order to do that, we're
+going to study the sample
+
+average, namely the sum of n
+random variables divided by n.
+
+That's the way you take
+sample averages.
+
+You add them all up.
+
+You divide by n.
+
+The law of large numbers, which
+we're going to talk
+
+about very soon, says that s
+sub n over n essentially
+
+becomes deterministic as
+n becomes very large.
+
+What we mean by that-- and most
+of you have seen that in
+
+various ways.
+
+We will review it later today.
+
+Well, we'll do it today
+and on Wednesday.
+
+And there's a big question
+of about what becoming
+
+deterministic means.
+
+But there is an essential
+idea there.
+
+The extended model, namely
+when you have one random
+
+variable, you create a very
+large number of them.
+
+If it corresponds to repeated
+experiments in the real world,
+
+then s sub n over n corresponds
+to the arithmetic
+
+average in the real world.
+
+In the real world, you do take
+arithmetic averages.
+
+Whenever you open up a
+newspaper, somebody is taking
+
+an arithmetic average of
+something and says, gee, this
+
+is significant.
+
+This shows what's going
+on someplace.
+
+Models can have two types
+of difficulties.
+
+This paragraph is a little
+different than what I wrote in
+
+the handout because I realized
+what I wrote in the handout
+
+didn't make a whole
+lot of sense.
+
+OK, the two types of
+difficulties you have with
+
+models, especially when you're
+trying to model things by IID
+
+random variables.
+
+In one, a sequence of real
+world experiments is not
+
+sufficiently similar and
+isolated to each other to
+
+correspond to the IID
+extended model.
+
+In other words, you want to
+model things so that each
+
+time, each trial of this
+experiment, you do the same
+
+thing but get a potentially
+different answer.
+
+Sometimes you rig things without
+trying to do so in
+
+such a way that these
+experiments are not
+
+independent of each other
+and in fact are very,
+
+very heavily biased.
+
+You find people taking risk
+models in the financial world
+
+where they take all sorts
+of these things.
+
+And they say, oh, all right,
+these things are all
+
+independent of each other.
+
+They look independent.
+
+And then suddenly a
+scare comes along.
+
+And everybody sells
+simultaneously.
+
+And you find out that all these
+random variables were
+
+not independent at all.
+
+They were very closely related
+to each other but in a way you
+
+never saw before.
+
+OK, the other way that these
+models are not true or not
+
+valid is that the IID
+extension is OK.
+
+But the basic model
+is not right.
+
+OK, in other words,
+you model a coin.
+
+It's coming out heads with
+probability 1/2.
+
+And somebody has put
+a loaded coin in.
+
+And the probability that it
+comes up heads is 0.45.
+
+And the probability that it
+comes up tails is 0.55.
+
+And you might guess that this
+person always bets on tails
+
+and tries to get you
+to bet on heads.
+
+So in that case, the basic
+model that you're
+
+using is not OK.
+
+So you have both of these
+kinds of problems.
+
+You should try to keep
+them straight.
+
+But we'll learn about these
+problems through
+
+study of the models.
+
+Namely, we're not going to go
+through an enormous amount of
+
+study on how you can bias a coin
+or things of this sort.
+
+OK, science, symmetry,
+analogies, earlier models, all
+
+of these are used to model
+real world situations.
+
+Let me again talk about an
+example I talked about a
+
+little bit last time because the
+model was so trivial that
+
+you probably understood
+everything about the model in
+
+the situation.
+
+But you didn't understand what
+it was illustrating.
+
+You have two dice.
+
+One of them is red.
+
+And one of them is white.
+
+You roll them.
+
+By symmetry, each one comes up
+to be 1, 2, 3, up to 6, each
+
+with equal probability.
+
+If you roll them with two hands
+or something, they're
+
+going to be independent
+of each other.
+
+And therefore, the probability
+of each pair of outcomes--
+
+red is equal to i.
+
+White is equal to j.
+
+Probability of each one of
+those is going to be 136
+
+because that's the size
+of the sample space.
+
+Now you take two white dice.
+
+And you roll them.
+
+What's the sample space?
+
+Well, as far as the real world
+is concerned, you can't
+
+distinguish a red 1 from
+a white 1 and a white
+
+2 from a red 2.
+
+In other words, those two
+possibilities can't be
+
+distinguished.
+
+So you might say I want to
+use a sample space which
+
+corresponds to the--
+
+what's the word I used here?--
+finest grain possible outcome
+
+that you can observe.
+
+And who would do that?
+
+You'd be crazy to do that.
+
+I mean, you have a nice model
+of rolling dice where each
+
+outcome has probability 136.
+
+And you would replace that
+with something where the
+
+probability of a 1, 1 is 136.
+
+But the probability of a 1, 2 is
+1/18 because you can get a
+
+2 in two different ways.
+
+You get a 2 in two different
+ways, which says you're really
+
+thinking about a red die
+and a white die.
+
+Otherwise, you wouldn't
+be able to say that.
+
+So the appropriate model here is
+certainly to think in terms
+
+of a red die and a white die.
+
+It's what everybody does.
+
+They just don't talk about it.
+
+OK, so the point that I'm trying
+to make here is that
+
+what you call a finest grain
+model is not at all clear.
+
+And if it's not at all clear in
+the case of dice, it sure
+
+as hell is not clear in most of
+the kinds of problems you
+
+want to deal with.
+
+So you need something
+considerably more than that.
+
+OK, so neither the axioms
+nor experimentation
+
+motivate this model.
+
+In other words, you really
+have to use common sense.
+
+You have to use judgment.
+
+And all of you have that.
+
+It's just that by learning
+all this mathematics, you
+
+eventually start to think that
+maybe you shouldn't use your
+
+common sense.
+
+So I have to keep saying that
+no, you keep on using your
+
+common sense.
+
+You want to learn what these
+models are about.
+
+You want to use your
+common sense also.
+
+And you've got to go back and
+forth between the two of them.
+
+OK, that's almost the end
+of our philosophy.
+
+I guess one more slide.
+
+I'm getting tired
+of this stuff.
+
+Comparing models for similar
+situations and analyzing
+
+limited and effective
+models helps a lot
+
+in clarifying fuzziness.
+
+But ultimately, as in
+all of science, some
+
+experimentation is needed.
+
+This is like any other
+branch of science.
+
+You need experimentation
+sometimes.
+
+You don't want to do too much of
+it because you'd always be
+
+doing experiments.
+
+But the important thing is
+that the outcome of an
+
+experiment is a sample point.
+
+It's not a probability.
+
+You do an experiment.
+
+You get an outcome.
+
+And all you find is one sample
+point, if you do the
+
+experiment once.
+
+And there's nothing that
+lets you draw a
+
+probability from that.
+
+The only way you can get things
+that you would call
+
+probabilities is to use an
+extended model, hope the
+
+extended model corresponds to
+the physical situation, and
+
+deal with these law of large
+numbers kind of things.
+
+You don't necessarily need
+IID random variables.
+
+But you need something that you
+know about between a large
+
+number of random variables
+to get from an outcome to
+
+something you could reasonably
+call a probability.
+
+OK, so that's enough.
+
+Let's go on to the law
+of large numbers.
+
+Let's do it in pictures first.
+
+So you can lie back and relax
+for a minute or stop being
+
+bored by all this stuff.
+
+What I've done here is to take
+the simplest random variable I
+
+can think of, which as
+you might guess is a
+
+binary random variable.
+
+It's either 0 or 1.
+
+Here it's 1 with probability
+1/4 and 0
+
+with probability 3/4.
+
+I have actually calculated
+these things.
+
+The distribution function of
+x1 plus x2 plus x3 plus x4,
+
+this point down here,
+is the probability
+
+of all 0's, I guess.
+
+And then you get the probability
+of all 0's plus 1,
+
+1 and so forth.
+
+Here's where you take the sum
+of 20 random variables.
+
+And you're looking at the
+distribution function of the
+
+number of 1's that you get.
+
+And it comes out like this.
+
+Here you're looking at s50.
+
+You're adding up 50
+random variables.
+
+And what's happening as far
+as the gross picture
+
+is concerned here?
+
+Well, the mean value of s sub
+n is the mean of a sum of
+
+random variables.
+
+And that's equal to n times
+a mean of a single random
+
+variable when you have
+identically distributed random
+
+variables or random variables
+that have the same mean.
+
+The variance is equal to
+n times sigma squared.
+
+Namely, when you take the
+expected value of this
+
+quantity squared, all these
+cross terms are going to
+
+balance out with the
+mean when you do.
+
+I mean, all of you know how to
+find the variance of s sub n.
+
+I hope you know how
+to find that.
+
+And when you do that,
+it increases with n.
+
+And the mean increases with n.
+
+The standard deviation, which
+gives you a picture of how
+
+wide the distribution is,
+only goes up as the
+
+square root of n.
+
+This is really the essence of
+the weak law of large numbers.
+
+I mean, everything else is
+mathematical detail.
+
+And then if you go on beyond
+this and you talk about the
+
+sample average, namely the sum
+of these n random variables--
+
+assume them IID again.
+
+In fact, assume for this picture
+that they're the same
+
+binary random variables.
+
+You look at the sample
+average.
+
+You find the mean of
+the sample average.
+
+And it's the mean of a single
+random variable.
+
+You find the variance of it.
+
+Because of this n here and the
+squaring that you're doing,
+
+the variance of the sum divided
+by n, the sigma
+
+squared divided by n, what
+happens as n gets large?
+
+This variance goes to 0.
+
+What happens when you have a
+random variable, a sequence of
+
+random variables, all of which
+have the same mean and whose
+
+standard deviation
+is going to 0?
+
+Well, you might play around with
+a lot of funny kinds of
+
+things that you might think
+of as happening.
+
+But essentially what's going
+on here is the nice feature
+
+that when you add all these
+things up, the distribution
+
+function gets scrunched
+down into a unit step.
+
+In other words, since the
+standard deviation is going to
+
+0, the sequence of random
+variables--
+
+since they all have
+the same mean--
+
+they all have smaller and
+smaller standard deviations.
+
+The only way you can do that is
+to scrunch them down into a
+
+limiting random variable,
+which is deterministic.
+
+And you can see that
+happening here.
+
+Namely the largest value is
+the black thing, which is
+
+getting smaller and smaller.
+
+And the left side is
+going that way.
+
+On the right side, it's
+going that way.
+
+So it looks like it's
+approaching a unit step.
+
+That has to be proven.
+
+And there's a simple
+proof of it.
+
+And we'll see that.
+
+And you've all seen
+that before.
+
+And you've all probably
+said, ho-hum.
+
+But that's the way it is.
+
+Now the next thing to look at
+for this same set of random
+
+variables, the same sum, is
+you look at the normalized
+
+sum, namely sn minus
+n times the mean.
+
+And you divide that by the
+square root of n times sigma.
+
+And what do you get?
+
+Well, every one of these
+random variables--
+
+for every n has mean 0, has mean
+0 because the mean of sn
+
+is n times x bar.
+
+So you're subtracting off
+of the mean essentially.
+
+And every one of them
+has variance 1.
+
+So you've got a whole sequence
+of random variables, which are
+
+just sticking there at
+the same mean, 0,
+
+and at the same variance.
+
+What's extraordinary when you
+do that, and you can sort of
+
+see this happening a little
+bit, this curve looks like
+
+it's going into a fixed
+curve, which starts
+
+out sticking to 0.
+
+And then it gradually
+comes up.
+
+And it looks fairly smooth.
+
+It goes off this way.
+
+And if you read a lot about this
+or if you think that all
+
+respectable random variables are
+Gaussian random variables,
+
+and I hope at the end of this
+course you will realize that
+
+only most respectable
+random variables are
+
+Gaussian random variables.
+
+There are many very interesting
+random variables
+
+that aren't.
+
+But what the central limit
+theorem says is that as you
+
+add up more and more random
+variables and you look at this
+
+normalized sum here, what you
+get is in fact the normal
+
+distribution, which is this
+strange integral here, that e
+
+to the minus x squared
+over 2 times the x.
+
+Now what I want to do with the
+rest of our time is to show
+
+you why in fact that happens.
+
+I've never seen this proof
+of the central
+
+limit theorem before.
+
+I'm sure that some people
+have done it.
+
+I'm only going to do it for
+the case of a binomial
+
+distribution, which is the only
+place where this works.
+
+But I think in doing this you
+will see why in fact that
+
+strange e to the minus x squared
+over 2 comes up.
+
+It sure is not obvious by
+looking at this problem.
+
+OK, so that's what we're
+going to do.
+
+And I'm hoping that after you
+see this, you will in fact
+
+understand why the central limit
+theorem is true as well
+
+as knowing that it's true.
+
+OK, so let's look at the
+Bernoulli process.
+
+You have a sequence of binary
+random variables, each of them
+
+is IID, each of them is
+1 with probability p.
+
+And a 0 with probability
+q equals 1 minus p.
+
+You add them all up.
+
+They're IID.
+
+And the question is, what
+does the distribution of
+
+the sum look like?
+
+Well, it has a nice
+formula to it.
+
+It's that formula down there.
+
+You've probably seen that
+formula before.
+
+Let's get some idea
+of where it comes
+
+from and what it means.
+
+Each n tuple that starts with
+k1's and then ends with n
+
+minus k0's, each one of those
+has the same probability.
+
+And it's p to the k times
+q to the n minus k.
+
+In other words, the probability
+you get a 1 on the
+
+first toss is p.
+
+The probability you get a 1 on
+the second toss also, since
+
+those are independent,
+probability you get two 1's in
+
+a row is p squared.
+
+Probably you get three 1's
+in a row is p cubed and
+
+so forth up to k.
+
+Because we're looking at the
+probability that the first k
+
+outputs are 1, so the
+probability of
+
+that is p to the k.
+
+That's this term.
+
+And the probability that the
+rest of them are all 0's is q
+
+to the n minus k.
+
+And this is sometimes confusing
+to you because you
+
+often think that this is going
+to be maximized when k is
+
+equal to p over n.
+
+You have some strange view of
+the law of large numbers.
+
+Well no, this quantity--
+
+if p is less than 1/2, it's
+going to be largest at k
+
+equals zero.
+
+The most probable single outcome
+from n tosses of a
+
+coin, and it's a biased
+coin, it comes out 1's
+
+more often than 0's.
+
+0's are more probable
+than 1's.
+
+The most probable output
+is all 0's.
+
+Very improbable, but that's the
+most probable of all these
+
+improbable things.
+
+But as you probably know
+already, there are n choose k
+
+different n tuples, all of which
+have k1's in them and n
+
+minus k0's.
+
+If you don't know that,
+I didn't even
+
+put that in the text.
+
+I put most things there.
+
+This is one of those basic
+combinatorial facts.
+
+Look it up in Wikipedia.
+
+You'll probably get a cleaner
+explanation of it there than
+
+anywhere else.
+
+But look it up in any elementary
+probability book or
+
+in any elementary combinatorics
+book.
+
+I'm sure that all of you
+have seen this stuff.
+
+So when you put this together,
+the probability that the sum
+
+of a n random variables, all
+of which are binary, the
+
+probability of getting k1's is
+n choose k times p to the k
+
+times q to the n minus k.
+
+Now you look at that.
+
+And if k is 1,000 and if n is
+1,000, I mean, your eyes
+
+boggle because you can't
+imagine what that
+
+number looks like.
+
+So we want to find out
+what it looks like.
+
+And here's a tricky
+way of doing it.
+
+What we want to do is to see
+how this varies with k.
+
+And in particular, we want to
+see how it varies with k when
+
+n is very large and when k is
+relatively close to p times n.
+
+So what we're going to do
+is take the ratio of the
+
+probability of k plus 1 1's
+to the ratio of k1's.
+
+And what is that?
+
+I've written it out.
+
+n choose k, n choose
+k plus 1--
+
+which is this term here--
+
+is n factorial divided by k plus
+1 factorial times n minus
+
+k minus 1 factorial.
+
+This term here--
+
+you put the n factorial down
+on the bottom, k factorial
+
+times n minus k quantity
+factorial.
+
+And then you take the
+p's and the q's.
+
+For this term here you have p
+to the k plus 1 q to the n
+
+minus k minus 1.
+
+And for this one here you
+have p to the k times p
+
+to the n minus k.
+
+All that stuff cancels out,
+which is really cute.
+
+When you look at this term you
+have p to the k plus 1
+
+over p to the k.
+
+That's just p.
+
+And here you have q to the
+n minus k minus 1 over q
+
+to the n minus k.
+
+That's just q in the
+denominator.
+
+So this goes into p over q.
+
+This quantity here is almost
+a simple n factorial over n
+
+factorial is 1.
+
+k plus 1 factorial divided by
+k factorial is k plus 1.
+
+That's this term here.
+
+And the n minus k over n minus
+k minus 1 is n minus k.
+
+So this ratio here
+is just that very
+
+simple expression there.
+
+Now this ratio is strictly
+decreasing in k.
+
+How do I see that?
+
+Well, as k gets bigger and
+bigger, what happens?
+
+As k gets bigger, the numerator
+gets larger.
+
+The denominator--
+
+excuse me, as k gets larger,
+the numerator gets smaller.
+
+The denominator gets larger.
+
+So the ratio of the
+two gets smaller.
+
+So this whole quantity here,
+as k gets larger and larger
+
+for fixed n, is just decreasing
+and decreasing and
+
+decreasing.
+
+Now let's look a little bit at
+where this crosses 1, if it
+
+does cross 1.
+
+And what I claim here is that
+when k plus 1 is less than or
+
+equal to pn, what
+happens here?
+
+Well if I can do this--
+
+I usually get confused
+doing these things.
+
+But if k plus 1 is less than
+or equal to pn, this is the
+
+last of these choices here, then
+k is also less than or
+
+equal to pn.
+
+And therefore, n minus
+k is greater than--
+
+in fact, k is strictly
+less than pn.
+
+And n minus k is strictly
+greater than n minus pn.
+
+And since q is 1 minus
+p, this is n times q.
+
+OK, so you take this
+divided by this.
+
+And you take this
+divided by this.
+
+And sure enough, this ratio
+here is greater than 1 any
+
+time you have a k which is
+smaller than what you think k
+
+ought to be, which
+is p over n.
+
+OK, so you have these three
+quantities here.
+
+Let me go on to the
+next slide.
+
+Since these ratios are less
+than 1 when k is large,
+
+approximately equal to 1 when k
+is close to pn, and greater
+
+than 1 when it's smaller than
+1, if I plot these things,
+
+what I find is that as k is
+increasing, getting closer and
+
+closer to pn, it's getting
+larger and larger.
+
+As k is increasing further,
+getting larger than pn, this
+
+ratio says that these
+things have to be
+
+getting smaller and smaller.
+
+So just from looking at this, we
+know that these terms have
+
+to be increasing for terms less
+than pn and have to be
+
+decreasing for terms
+greater than pn.
+
+So this is a bell-shaped
+curve.
+
+We've already seen that.
+
+It might not be quite clear that
+it's bell-shaped in the
+
+sense that it kind of tapers
+off as you get smaller.
+
+Because these ratios are getting
+bigger and bigger, as
+
+k gets bigger and bigger, the
+ratio of this term to this
+
+term gets bigger and bigger.
+
+So what's happening there?
+
+As this ratio gets bigger and
+bigger, these terms get
+
+smaller and smaller.
+
+But as these terms get smaller
+and smaller, they're getting
+
+closer and closer to 0.
+
+So even though they're going to
+0 like a bat out of hell,
+
+they still can't get
+any smaller than 0.
+
+So they just taper down and
+start to get close to 0.
+
+So that is roughly how
+this sum of binary
+
+random variables behave.
+
+OK, so let's go on and show that
+the central limit theorem
+
+holds for the Bernoulli
+process.
+
+And that's just as
+easy really.
+
+There's nothing more difficult
+about it that we
+
+have to deal with.
+
+This ratio, as we've said, is
+equal to n minus k over k plus
+
+1 times p over k.
+
+What we're interested
+in here--
+
+I mean, we've already seen from
+the last slide that the
+
+interesting thing here
+is the big terms.
+
+And the big terms are the terms
+which are close to pn.
+
+So what we'd like to do is look
+at values of k which are
+
+close to pn.
+
+What I've done here is to plot
+this as k minus the integer
+
+value of pn.
+
+So we get integers.
+
+What I'm going to assume now,
+because this gets a little
+
+hairy if I don't do that, I'm
+going to assume that pn is
+
+equal to an integer.
+
+It doesn't make a whole lot of
+difference to the argument.
+
+It just leaves out a lot
+of terms that you don't
+
+have to play with.
+
+So we'll assume that
+pn is an integer.
+
+With this example, we're
+looking at where
+
+p is equal to 1/4.
+
+Pn is going to be an integer
+whenever n is a multiple of 4.
+
+So things are fine then.
+
+If I try to make p equal to 1
+over pi, then that doesn't
+
+work so well.
+
+But after all, no reason to
+chose p in such a strange way.
+
+OK, so I'm going to look at this
+for a fixed value of n.
+
+I'm going to look at it as k
+increases for k less than pn.
+
+I'm going to look at it
+as it decreases for k
+
+greater than pn.
+
+And I'm going to define k to
+be equal to the i plus pn.
+
+So I'm going to put the whole
+thing in terms of
+
+i instead of k.
+
+OK, so when I substitute i
+equals k minus pn for k here,
+
+what I'm going to get
+is this term.
+
+It's going to be the probability
+of pn plus i plus
+
+1 over p of--
+
+fortunately when you're using
+textures, you can distinguish
+
+different kinds of p's.
+
+I have too many p's
+in this equation.
+
+This is the probability
+mass function.
+
+This is just my probability
+of a 1.
+
+And p's are things that you
+like to use a lot in
+
+probability.
+
+So it's nice to have that
+separation there.
+
+OK, when I take this and I
+substitute it into that with k
+
+equal to i, what I get is
+n minus pn minus i.
+
+That's n minus k over pn plus
+i plus 1 times p over q.
+
+Fair enough, OK, all I'm doing
+is replacing k with pn plus i
+
+because I want i to be very
+close to 0 in this argument.
+
+Because I've already seen that
+these terms are only
+
+significant when i is relatively
+close to 0.
+
+Because when I get away from 0,
+these terms are going down
+
+very, very fast.
+
+So when I do that,
+what do I get?
+
+I get n minus pn
+is equal to qn.
+
+That's nice.
+
+So I have an nq here.
+
+I have a q here.
+
+I have a pn here.
+
+I have a p here.
+
+I'm going to multiply
+this p by n.
+
+I'm going to multiply
+this q by n.
+
+And I'm going to take a ratio
+of this pair of things.
+
+So when I take this ratio,
+I'm going to get nq over
+
+nq, which is 1.
+
+And the other terms there
+become minus i over nq.
+
+In the denominator, I'm going to
+divide pn plus i plus 1 by
+
+p, by pn, which gives me 1 plus
+i plus 1 divided by np.
+
+So I get two terms, ratio of
+two terms, which are both
+
+close to 1 at this point and
+which are getting closer and
+
+closer to 1 as n gets
+larger and larger.
+
+Now let's take the logarithm
+of this.
+
+Let me justify taking the
+logarithm of it in two
+
+different ways.
+
+One of them is that what
+we're trying to prove--
+
+and I'm playing the game
+that all of you
+
+always play in quizzes.
+
+When you're trying to prove
+something, what do you do?
+
+You start at the beginning.
+
+You work this way.
+
+You start at the end.
+
+You work back this way.
+
+And you hope, at some point, the
+two things come together.
+
+If they don't come together,
+you get to this point.
+
+And you say, obviously.
+
+And then you go to that point
+which leads to-- yeah.
+
+[LAUGHTER]
+
+PROFESSOR: OK, so I'm doing
+the same thing here.
+
+This probability that we're
+trying to calculate--
+
+well, I've listed it
+here in terms of--
+
+I have put it here in terms of
+a distribution function.
+
+I will do just as well if I can
+do it in terms of an PMF.
+
+And what I'd like to show is
+that the PMF of sn minus nX
+
+bar over square root of n
+times sigma is somehow
+
+proportional to e to the
+minus x squared over 2.
+
+Now if I want to do that, it
+will be all right if I can
+
+take the logarithm of this
+term and show that
+
+it's a square nX.
+
+And if I want to show that this
+logarithm is a square nX,
+
+and I'm looking at the
+differentials at each time,
+
+what are the differentials going
+to be if the sum of the
+
+differentials is quadratic?
+
+If the sum of these
+differentials is quadratic,
+
+then the individual terms
+have to be linear.
+
+If I take a bunch of linear
+terms, if I add up 1 plus 2
+
+plus 3 plus 4 plus 5, you've
+all done this I'm sure.
+
+And down here you write n plus
+n minus 1 plus, plus 1.
+
+And what do you get?
+
+You get n times n
+plus 1 over 2.
+
+You can also approximate
+that by integrating.
+
+Whenever you add up a sum
+of linear terms, you
+
+get a square term.
+
+And I'm just curious.
+
+How many of you have
+seen that?
+
+Good, OK.
+
+Well, it's only about 1/2.
+
+So it's something you've
+probably seen in high school.
+
+Or your haven't seen
+it at all.
+
+So let's go on with
+this argument.
+
+OK, so I'm going to take
+the logarithm of
+
+this expression here.
+
+I'm going to take
+the logarithm.
+
+I'm going to have the logarithm
+of 1 minus i over nq
+
+minus the logarithm of 1
+plus i plus 1 over np.
+
+And I'm going to use what I
+think of as one of the most
+
+useful inequalities that you
+will ever see, which is the
+
+natural log of 1 plus x.
+
+If we use a power expansion, we
+get x minus x squared over
+
+2 plus x cubed over 3 minus--
+
+it's an alternating series.
+
+If x is negative, this
+term is negative.
+
+This term is negative.
+
+This term is negative.
+
+And all this makes sense
+because if I draw this
+
+function here, logarithm of
+1 plus x at x equals 0.
+
+This is equal to 0.
+
+It comes up with a slope of 1.
+
+And it levels off.
+
+And here it's going
+down very fast.
+
+So these terms, you get
+these negative terms.
+
+And on the positive side, you
+get these alternating terms.
+
+So this goes up slowly,
+down fast.
+
+The slope here is x, which
+is this term here.
+
+The curvature here gives you
+the minus x squared over 2.
+
+And the approximation, which is
+very useful here, is that
+
+the logarithm of 1 plus x, when
+x is small, is equal to x
+
+plus what we call
+little l of x.
+
+Namely something which goes
+to 0 faster than x
+
+as x goes to 0.
+
+OK, all of you know
+that, right?
+
+Well, if you don't know
+it, now you know it.
+
+It's useful.
+
+You will use it again
+and again.
+
+OK, so what we're
+going to do is--
+
+well, that's pretty good.
+
+Where did I get to that point?
+
+I skipped something.
+
+What I have shown is that this
+increment in the probability,
+
+in the PMF for s sub n, namely
+the increment as you increase
+
+i by 1, is linear in i.
+
+And in fact, the logarithm of
+this increment is linear in i.
+
+So therefore, by what I was
+saying before, the logarithm
+
+of the actual terms should be
+rather than linear in i, they
+
+should be quadratic in i.
+
+So that's what I'm trying
+to do here.
+
+I just missed this
+whole term here.
+
+What I'm interested in now is
+getting a handle on pn plus
+
+some larger value,
+j, divided by the
+
+probability of sn for pn.
+
+What am I trying to do here?
+
+I should've said what
+I was trying to do.
+
+This term is just one term.
+
+It's fixed.
+
+Be nice if we knew what it was,
+we don't at the moment.
+
+But I'm trying to express
+everything else in terms of
+
+that one unknown term.
+
+And what I'm trying to do is to
+show that the logarithm of
+
+this everything else is going
+to be quadratic in j.
+
+And if I can do that, then I
+only have one undetermined
+
+factor in this whole sum.
+
+And I can use the fact that PMF
+summed to 1 to solve the
+
+whole problem.
+
+So I'm going to express the
+probability that we get pn
+
+plus j1's divided by the
+probability that we get pn1's.
+
+It's the sum of the probability
+pn plus i plus 1
+
+over pn plus i.
+
+And we increase i.
+
+We start out at i equals 0.
+
+And then the denominator is
+probability of pn plus 0,
+
+which is this term.
+
+And each time we increase i by
+1, this term cancels out with
+
+the previous or the next
+value of this term.
+
+And when I get all done, all I
+have is this expression here.
+
+Everybody see that?
+
+OK, I see a lot of--
+
+if you don't see it,
+just look at it.
+
+And you'll see that this--
+
+I think you'll see
+that this works.
+
+OK, so now I take this
+expression here.
+
+This logarithm is this
+linear term here.
+
+What do I want to do?
+
+I want to sum i from
+0 up to j minus 1.
+
+What do I get when I sum
+i from 0 to j minus 1?
+
+I get this expression here.
+
+I get j times j minus
+1 divided by 2n.
+
+Oh, I was--
+
+I skipped something.
+
+Let's go back a little bit.
+
+Because it'll look like
+it was a typo.
+
+When I took this logarithm and
+I applied this approximation
+
+to it, I got minus i over nq
+minus i over np minus 1 over
+
+np plus square terms in n.
+
+When I take i over nq minus i
+over np, I can combine those
+
+two things together.
+
+I can take ip over npq
+minus iq times npq.
+
+And q plus p is equal to 1.
+
+So the numerator
+all goes away.
+
+And these two terms combine to
+be minus i over n times p
+
+times p times q.
+
+And I just has this one last
+little term left here.
+
+Don't know what to
+do with that.
+
+But then I add up
+all these terms.
+
+This one is the one that
+leads to j times j
+
+minus 1 over 2 npq.
+
+This one is the one that
+leads to j over np.
+
+And I just neglect this term,
+which is negligible compared
+
+to j squared.
+
+I get minus j squared
+over 2 npq.
+
+Let me come back later to say
+why I'm so eager to neglect
+
+this term except that that's
+what I have to do if I want to
+
+get the right answer.
+
+OK, so we'll see why that has
+to be negligible in just a
+
+little bit.
+
+But now this logarithm is coming
+out to be exactly the
+
+term that I want it to be.
+
+So finally, the logarithm of
+the sum of these random
+
+variables pn plus j, namely j
+off the mean, divided by that
+
+if pn is equal to minus j
+squared over 2 npq plus some
+
+negligible terms.
+
+And this says when I
+exponentiate things, that the
+
+probability that sn is j off
+the mean is approximately
+
+equal to this term, the
+probability that it's right at
+
+the mean, times e to the minus
+j squared over 2 npq.
+
+What that is saying is that this
+sum of terms that I was
+
+looking at before--
+
+this term here, this term, this
+term, this term, this
+
+term, and so forth down--
+
+these terms here are actually
+going as minus j squared over
+
+2 npq, which is what they should
+be going as if you have
+
+a Gaussian curve here.
+
+OK, now there's one other thing
+we have to do, which is
+
+figure out what this term is.
+
+And if you look at this as an
+undetermined coefficient on
+
+these Gaussian-type terms and
+you think of what happens if I
+
+sum this over all i, well, if
+I sum it over all i what I'm
+
+going to get is the sum of all
+of these terms here, which are
+
+negligible except where j
+squared is proportional to n.
+
+So I don't have to sum them
+beyond the point where this
+
+approximation makes sense.
+
+So I want to sum all
+these terms.
+
+In summing these terms, when n
+gets very, very large, these
+
+things are dropping off
+very, very slowly.
+
+The curve is getting
+very, very wide.
+
+If i scrunch the curve back in
+again, what I get is a Riemann
+
+approximation to a normal
+density curve.
+
+Therefore, I can integrate it.
+
+And believe me.
+
+If you don't believe me,
+I'll go through it.
+
+And you won't like that.
+
+When you go through this, what
+you get is in fact this
+
+expression right here, which
+says that when n gets very,
+
+very large and j is the offset
+from the mean and is
+
+proportional to--
+
+well, it's proportional to
+the square root of n.
+
+Then what I get is this PMF
+here, which is in fact what
+
+the central limit
+theorem says.
+
+And now if you go back and try
+to think of exactly what we've
+
+done, what we've done is to
+show that the logarithm of
+
+these differences here is
+in fact linear in i.
+
+Therefore, when you sum them,
+you get something which is
+
+quadratic in j.
+
+And because of that, all you
+have to do is normalize with a
+
+center term.
+
+And you get this.
+
+The central limit theorem,
+especially for the binary
+
+case, is almost always done
+by using a Stirling
+
+approximation.
+
+And a Stirling approximation is
+one of these things which
+
+is black magic.
+
+I don't know any place except in
+William Feller's book where
+
+anyone talks about where this
+formula comes from.
+
+If you now go back and look
+very carefully at this
+
+derivation, this tells
+you what the Stirling
+
+approximation is.
+
+Because if you do this for p
+equals q, what you're doing is
+
+actually evaluating n choose
+k where k is very
+
+close to and over 2.
+
+And that will tell you exactly
+what Stirling's
+
+approximation has to be.
+
+In other words, that's a way
+of deriving Stirling's
+
+approximation.
+
+The very backward way of
+doing things it seems.
+
+But often backward ways
+are the best ways
+
+of doing these things.
+
+OK, so I told you I
+would stop at some
+
+point and ask for questions.
+
+Yes?
+
+AUDIENCE: Can you please go
+back one slide before this
+
+slide where can you neglect
+a term, which [INAUDIBLE],
+
+minus j over np.
+
+PROFESSOR: Why did I neglect
+the j over np?
+
+OK, that's a good question.
+
+If you look at this curve here,
+and I put the j in.
+
+I can put the j in by just
+making this expression here
+
+look at one smaller value of
+j or one larger value of j.
+
+And you get something different
+whether you're
+
+looking at the minus side
+or the plus side.
+
+In fact, if p is equal to q,
+this term cancels out.
+
+If p is not equal to q, what
+happens is that the central
+
+limit theorem is approximately
+symmetric.
+
+But in this first ordered term,
+
+it's not quite symmetric.
+
+It can't be symmetric because
+this is p times n.
+
+And you have all these
+terms out to 1.
+
+And you have many, many
+fewer terms back to 0.
+
+So it has to be slightly
+asymmetric.
+
+But it's only asymmetric over at
+most a unit of value here,
+
+which is not significant.
+
+Because as n gets bigger,
+these terms--
+
+well, as I've done
+it, the terms do
+
+not get close together.
+
+But if I want to think of it
+as a normalized Gaussian
+
+curve, I have to make the
+terms close together.
+
+So that extra term is
+not significant.
+
+I wish I had a nicer way of
+taking care of all the
+
+approximations here.
+
+I haven't put this in the notes
+because I still haven't
+
+figured out how to do that.
+
+But I still think you get more
+insight from doing it this way
+
+than you do by going through
+Stirling's approximation, all
+
+those pages and pages
+of algebra.
+
+Anything else?
+
+OK, well, see you
+Wednesday then.
\ No newline at end of file
diff --git a/dBMtJEt6aO8.txt b/dBMtJEt6aO8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9ffb195d039cad235479416d4ff691651b693c3d
--- /dev/null
+++ b/dBMtJEt6aO8.txt
@@ -0,0 +1,1107 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu this demonstration is for
+
+ align:start position:0%
+ocw.mit.edu this demonstration is for
+ 
+
+ align:start position:0%
+ocw.mit.edu this demonstration is for
+those of you who would like to dig a
+
+ align:start position:0%
+those of you who would like to dig a
+ 
+
+ align:start position:0%
+those of you who would like to dig a
+little more deeply into laser behavior
+
+ align:start position:0%
+little more deeply into laser behavior
+ 
+
+ align:start position:0%
+little more deeply into laser behavior
+as we know a laser like this one here
+
+ align:start position:0%
+as we know a laser like this one here
+ 
+
+ align:start position:0%
+as we know a laser like this one here
+consists of two mirrors and an amplifier
+
+ align:start position:0%
+consists of two mirrors and an amplifier
+ 
+
+ align:start position:0%
+consists of two mirrors and an amplifier
+and if the gain of the amplifier is
+
+ align:start position:0%
+and if the gain of the amplifier is
+ 
+
+ align:start position:0%
+and if the gain of the amplifier is
+bigger than the losses in the cavity
+
+ align:start position:0%
+bigger than the losses in the cavity
+ 
+
+ align:start position:0%
+bigger than the losses in the cavity
+then we can get laser action and if
+
+ align:start position:0%
+then we can get laser action and if
+ 
+
+ align:start position:0%
+then we can get laser action and if
+let's say this mirror has a little bit
+
+ align:start position:0%
+let's say this mirror has a little bit
+ 
+
+ align:start position:0%
+let's say this mirror has a little bit
+of transmission then we can get laser
+
+ align:start position:0%
+of transmission then we can get laser
+ 
+
+ align:start position:0%
+of transmission then we can get laser
+light coming out that we can use so let
+
+ align:start position:0%
+light coming out that we can use so let
+ 
+
+ align:start position:0%
+light coming out that we can use so let
+me turn then this laser on and show you
+
+ align:start position:0%
+me turn then this laser on and show you
+ 
+
+ align:start position:0%
+me turn then this laser on and show you
+here on this card the the output of the
+
+ align:start position:0%
+here on this card the the output of the
+ 
+
+ align:start position:0%
+here on this card the the output of the
+laser now in this demonstration we'd
+
+ align:start position:0%
+laser now in this demonstration we'd
+ 
+
+ align:start position:0%
+laser now in this demonstration we'd
+like to show that the light inside the
+
+ align:start position:0%
+like to show that the light inside the
+ 
+
+ align:start position:0%
+like to show that the light inside the
+laser cavity that's going backwards and
+
+ align:start position:0%
+laser cavity that's going backwards and
+ 
+
+ align:start position:0%
+laser cavity that's going backwards and
+forwards between the two mirrors inside
+
+ align:start position:0%
+forwards between the two mirrors inside
+ 
+
+ align:start position:0%
+forwards between the two mirrors inside
+the laser cavity is much bigger than
+
+ align:start position:0%
+the laser cavity is much bigger than
+ 
+
+ align:start position:0%
+the laser cavity is much bigger than
+then the light that's coming outside
+
+ align:start position:0%
+then the light that's coming outside
+ 
+
+ align:start position:0%
+then the light that's coming outside
+question is how do we how do we do this
+
+ align:start position:0%
+question is how do we how do we do this
+ 
+
+ align:start position:0%
+question is how do we how do we do this
+because if we try to place a detector
+
+ align:start position:0%
+because if we try to place a detector
+ 
+
+ align:start position:0%
+because if we try to place a detector
+inside the laser cavity like here we
+
+ align:start position:0%
+inside the laser cavity like here we
+ 
+
+ align:start position:0%
+inside the laser cavity like here we
+would interrupt the laser action the
+
+ align:start position:0%
+would interrupt the laser action the
+ 
+
+ align:start position:0%
+would interrupt the laser action the
+laser quits so obviously that's not a
+
+ align:start position:0%
+laser quits so obviously that's not a
+ 
+
+ align:start position:0%
+laser quits so obviously that's not a
+smart way of doing this so what are we
+
+ align:start position:0%
+smart way of doing this so what are we
+ 
+
+ align:start position:0%
+smart way of doing this so what are we
+going to do I'm going to use a simple
+
+ align:start position:0%
+going to do I'm going to use a simple
+ 
+
+ align:start position:0%
+going to do I'm going to use a simple
+method like this we're going to take a
+
+ align:start position:0%
+method like this we're going to take a
+ 
+
+ align:start position:0%
+method like this we're going to take a
+piece of glass and depending on the
+
+ align:start position:0%
+piece of glass and depending on the
+ 
+
+ align:start position:0%
+piece of glass and depending on the
+orientation of the piece of glass we're
+
+ align:start position:0%
+orientation of the piece of glass we're
+ 
+
+ align:start position:0%
+orientation of the piece of glass we're
+going to sample the light both outside
+
+ align:start position:0%
+going to sample the light both outside
+ 
+
+ align:start position:0%
+going to sample the light both outside
+the cavity and inside the cavity and
+
+ align:start position:0%
+the cavity and inside the cavity and
+ 
+
+ align:start position:0%
+the cavity and inside the cavity and
+hopefully that the the the loss that we
+
+ align:start position:0%
+hopefully that the the the loss that we
+ 
+
+ align:start position:0%
+hopefully that the the the loss that we
+will place inside the cavity laser
+
+ align:start position:0%
+will place inside the cavity laser
+ 
+
+ align:start position:0%
+will place inside the cavity laser
+cavity is so small that we will not
+
+ align:start position:0%
+cavity is so small that we will not
+ 
+
+ align:start position:0%
+cavity is so small that we will not
+interrupt the laser action at least by
+
+ align:start position:0%
+interrupt the laser action at least by
+ 
+
+ align:start position:0%
+interrupt the laser action at least by
+by too much alright so here we go so
+
+ align:start position:0%
+by too much alright so here we go so
+ 
+
+ align:start position:0%
+by too much alright so here we go so
+first we have to show that
+
+ align:start position:0%
+first we have to show that
+ 
+
+ align:start position:0%
+first we have to show that
+ah that we can sample some of the light
+
+ align:start position:0%
+ah that we can sample some of the light
+ 
+
+ align:start position:0%
+ah that we can sample some of the light
+with with this piece of glass so here we
+
+ align:start position:0%
+with with this piece of glass so here we
+ 
+
+ align:start position:0%
+with with this piece of glass so here we
+are is this piece of glass now let me
+
+ align:start position:0%
+are is this piece of glass now let me
+ 
+
+ align:start position:0%
+are is this piece of glass now let me
+tell you what's what's happening this
+
+ align:start position:0%
+tell you what's what's happening this
+ 
+
+ align:start position:0%
+tell you what's what's happening this
+piece of glass is is placed in this
+
+ align:start position:0%
+piece of glass is is placed in this
+ 
+
+ align:start position:0%
+piece of glass is is placed in this
+orientation and then I can rotate it
+
+ align:start position:0%
+orientation and then I can rotate it
+ 
+
+ align:start position:0%
+orientation and then I can rotate it
+like so this using this rotation stage
+
+ align:start position:0%
+like so this using this rotation stage
+ 
+
+ align:start position:0%
+like so this using this rotation stage
+now if you look at the reflection from
+
+ align:start position:0%
+now if you look at the reflection from
+ 
+
+ align:start position:0%
+now if you look at the reflection from
+piece of glass on this little screen you
+
+ align:start position:0%
+piece of glass on this little screen you
+ 
+
+ align:start position:0%
+piece of glass on this little screen you
+can see that the light gets the
+
+ align:start position:0%
+can see that the light gets the
+ 
+
+ align:start position:0%
+can see that the light gets the
+extinguished when I am at at the
+
+ align:start position:0%
+extinguished when I am at at the
+ 
+
+ align:start position:0%
+extinguished when I am at at the
+Brewster angle remember the the
+
+ align:start position:0%
+Brewster angle remember the the
+ 
+
+ align:start position:0%
+Brewster angle remember the the
+polarization of this laser in the
+
+ align:start position:0%
+polarization of this laser in the
+ 
+
+ align:start position:0%
+polarization of this laser in the
+vertical plane so that I can I can
+
+ align:start position:0%
+vertical plane so that I can I can
+ 
+
+ align:start position:0%
+vertical plane so that I can I can
+achieve Brewster angle condition using
+
+ align:start position:0%
+achieve Brewster angle condition using
+ 
+
+ align:start position:0%
+achieve Brewster angle condition using
+this orientation of the glass so so now
+
+ align:start position:0%
+this orientation of the glass so so now
+ 
+
+ align:start position:0%
+this orientation of the glass so so now
+when I have brewster boosters angle it's
+
+ align:start position:0%
+when I have brewster boosters angle it's
+ 
+
+ align:start position:0%
+when I have brewster boosters angle it's
+when these two markers one on the on the
+
+ align:start position:0%
+when these two markers one on the on the
+ 
+
+ align:start position:0%
+when these two markers one on the on the
+rotating part of the stage and the other
+
+ align:start position:0%
+rotating part of the stage and the other
+ 
+
+ align:start position:0%
+rotating part of the stage and the other
+one on the fixed part of the rotation
+
+ align:start position:0%
+one on the fixed part of the rotation
+ 
+
+ align:start position:0%
+one on the fixed part of the rotation
+state when they line up we're at
+
+ align:start position:0%
+state when they line up we're at
+ 
+
+ align:start position:0%
+state when they line up we're at
+Brewster's angle and when I move away
+
+ align:start position:0%
+Brewster's angle and when I move away
+ 
+
+ align:start position:0%
+Brewster's angle and when I move away
+from Brewster's angle like so I can
+
+ align:start position:0%
+from Brewster's angle like so I can
+ 
+
+ align:start position:0%
+from Brewster's angle like so I can
+increase the amount of light sampled by
+
+ align:start position:0%
+increase the amount of light sampled by
+ 
+
+ align:start position:0%
+increase the amount of light sampled by
+the piece of glass so let's say if i set
+
+ align:start position:0%
+the piece of glass so let's say if i set
+ 
+
+ align:start position:0%
+the piece of glass so let's say if i set
+it this position here then i have a
+
+ align:start position:0%
+it this position here then i have a
+ 
+
+ align:start position:0%
+it this position here then i have a
+small percentage of light that's
+
+ align:start position:0%
+small percentage of light that's
+ 
+
+ align:start position:0%
+small percentage of light that's
+reflected by the piece of glass onto
+
+ align:start position:0%
+reflected by the piece of glass onto
+ 
+
+ align:start position:0%
+reflected by the piece of glass onto
+onto the screen now what i'm going to do
+
+ align:start position:0%
+onto the screen now what i'm going to do
+ 
+
+ align:start position:0%
+onto the screen now what i'm going to do
+is take a similar piece of glass and put
+
+ align:start position:0%
+is take a similar piece of glass and put
+ 
+
+ align:start position:0%
+is take a similar piece of glass and put
+it again in the in the beam like so and
+
+ align:start position:0%
+it again in the in the beam like so and
+ 
+
+ align:start position:0%
+it again in the in the beam like so and
+again the markers are the same as in the
+
+ align:start position:0%
+again the markers are the same as in the
+ 
+
+ align:start position:0%
+again the markers are the same as in the
+is in the other stage so when the when
+
+ align:start position:0%
+is in the other stage so when the when
+ 
+
+ align:start position:0%
+is in the other stage so when the when
+the markers are lined up then I get no
+
+ align:start position:0%
+the markers are lined up then I get no
+ 
+
+ align:start position:0%
+the markers are lined up then I get no
+light reflected this means Bruce's
+
+ align:start position:0%
+light reflected this means Bruce's
+ 
+
+ align:start position:0%
+light reflected this means Bruce's
+condition and when I'm over here I get
+
+ align:start position:0%
+condition and when I'm over here I get
+ 
+
+ align:start position:0%
+condition and when I'm over here I get
+pretty much the same amount of light as
+
+ align:start position:0%
+pretty much the same amount of light as
+ 
+
+ align:start position:0%
+pretty much the same amount of light as
+as in as in this case all right so now I
+
+ align:start position:0%
+as in as in this case all right so now I
+ 
+
+ align:start position:0%
+as in as in this case all right so now I
+have calibrated these two pieces of
+
+ align:start position:0%
+have calibrated these two pieces of
+ 
+
+ align:start position:0%
+have calibrated these two pieces of
+glass in terms of in terms of angle now
+
+ align:start position:0%
+glass in terms of in terms of angle now
+ 
+
+ align:start position:0%
+glass in terms of in terms of angle now
+what I'm going to do I'm going to take
+
+ align:start position:0%
+what I'm going to do I'm going to take
+ 
+
+ align:start position:0%
+what I'm going to do I'm going to take
+one of them
+
+ align:start position:0%
+one of them
+ 
+
+ align:start position:0%
+one of them
+and without changing the angle place it
+
+ align:start position:0%
+and without changing the angle place it
+ 
+
+ align:start position:0%
+and without changing the angle place it
+inside the laser cavity and hopefully
+
+ align:start position:0%
+inside the laser cavity and hopefully
+ 
+
+ align:start position:0%
+inside the laser cavity and hopefully
+the laser won't go out on me so as I put
+
+ align:start position:0%
+the laser won't go out on me so as I put
+ 
+
+ align:start position:0%
+the laser won't go out on me so as I put
+it in here without changing the angle
+
+ align:start position:0%
+it in here without changing the angle
+ 
+
+ align:start position:0%
+it in here without changing the angle
+you can see I'm going to sample some of
+
+ align:start position:0%
+you can see I'm going to sample some of
+ 
+
+ align:start position:0%
+you can see I'm going to sample some of
+the light and you'll see it on on this
+
+ align:start position:0%
+the light and you'll see it on on this
+ 
+
+ align:start position:0%
+the light and you'll see it on on this
+on this screen and note that the word
+
+ align:start position:0%
+on this screen and note that the word
+ 
+
+ align:start position:0%
+on this screen and note that the word
+inside here that means that this piece
+
+ align:start position:0%
+inside here that means that this piece
+ 
+
+ align:start position:0%
+inside here that means that this piece
+of glass is inside the laser cavity and
+
+ align:start position:0%
+of glass is inside the laser cavity and
+ 
+
+ align:start position:0%
+of glass is inside the laser cavity and
+then one outside the laser cavity is
+
+ align:start position:0%
+then one outside the laser cavity is
+ 
+
+ align:start position:0%
+then one outside the laser cavity is
+labeled again by the word outside and
+
+ align:start position:0%
+labeled again by the word outside and
+ 
+
+ align:start position:0%
+labeled again by the word outside and
+now I want I would like you to look at
+
+ align:start position:0%
+now I want I would like you to look at
+ 
+
+ align:start position:0%
+now I want I would like you to look at
+at the spot reflected by the piece of
+
+ align:start position:0%
+at the spot reflected by the piece of
+ 
+
+ align:start position:0%
+at the spot reflected by the piece of
+glass outside the cavity and the spot
+
+ align:start position:0%
+glass outside the cavity and the spot
+ 
+
+ align:start position:0%
+glass outside the cavity and the spot
+reflected by the piece of glass inside
+
+ align:start position:0%
+reflected by the piece of glass inside
+ 
+
+ align:start position:0%
+reflected by the piece of glass inside
+the cavity so if we have now the split
+
+ align:start position:0%
+the cavity so if we have now the split
+ 
+
+ align:start position:0%
+the cavity so if we have now the split
+screen in position you can see that the
+
+ align:start position:0%
+screen in position you can see that the
+ 
+
+ align:start position:0%
+screen in position you can see that the
+one inside is much brighter than than
+
+ align:start position:0%
+one inside is much brighter than than
+ 
+
+ align:start position:0%
+one inside is much brighter than than
+the one outside in fact it's brighter in
+
+ align:start position:0%
+the one outside in fact it's brighter in
+ 
+
+ align:start position:0%
+the one outside in fact it's brighter in
+this case by about a factor of 50 or so
+
+ align:start position:0%
+this case by about a factor of 50 or so
+ 
+
+ align:start position:0%
+this case by about a factor of 50 or so
+the question I want to leave with you is
+
+ align:start position:0%
+the question I want to leave with you is
+ 
+
+ align:start position:0%
+the question I want to leave with you is
+it why the light coming out of the laser
+
+ align:start position:0%
+it why the light coming out of the laser
+ 
+
+ align:start position:0%
+it why the light coming out of the laser
+is much weaker than the light inside the
+
+ align:start position:0%
+is much weaker than the light inside the
+ 
+
+ align:start position:0%
+is much weaker than the light inside the
+laser and what determines that ratio so
+
+ align:start position:0%
+laser and what determines that ratio so
+ 
+
+ align:start position:0%
+laser and what determines that ratio so
+that's a nice little puzzle for you now
+
+ align:start position:0%
+that's a nice little puzzle for you now
+ 
+
+ align:start position:0%
+that's a nice little puzzle for you now
+sometimes one would like to increase the
+
+ align:start position:0%
+sometimes one would like to increase the
+ 
+
+ align:start position:0%
+sometimes one would like to increase the
+light coming out of the laser now how
+
+ align:start position:0%
+light coming out of the laser now how
+ 
+
+ align:start position:0%
+light coming out of the laser now how
+can you do it well you notice that since
+
+ align:start position:0%
+can you do it well you notice that since
+ 
+
+ align:start position:0%
+can you do it well you notice that since
+there's a lot of light inside the cavity
+
+ align:start position:0%
+there's a lot of light inside the cavity
+ 
+
+ align:start position:0%
+there's a lot of light inside the cavity
+one way of quickly increasing the laser
+
+ align:start position:0%
+one way of quickly increasing the laser
+ 
+
+ align:start position:0%
+one way of quickly increasing the laser
+intensity even though for a very short
+
+ align:start position:0%
+intensity even though for a very short
+ 
+
+ align:start position:0%
+intensity even though for a very short
+time is by removing one of the mirrors
+
+ align:start position:0%
+time is by removing one of the mirrors
+ 
+
+ align:start position:0%
+time is by removing one of the mirrors
+and like for example if I take this
+
+ align:start position:0%
+and like for example if I take this
+ 
+
+ align:start position:0%
+and like for example if I take this
+mirror out from the laser very quickly
+
+ align:start position:0%
+mirror out from the laser very quickly
+ 
+
+ align:start position:0%
+mirror out from the laser very quickly
+then I can essentially dump out all the
+
+ align:start position:0%
+then I can essentially dump out all the
+ 
+
+ align:start position:0%
+then I can essentially dump out all the
+photons that are stored in the laser
+
+ align:start position:0%
+photons that are stored in the laser
+ 
+
+ align:start position:0%
+photons that are stored in the laser
+cavity in fact this is called cavity
+
+ align:start position:0%
+cavity in fact this is called cavity
+ 
+
+ align:start position:0%
+cavity in fact this is called cavity
+dumping and what this gives you this
+
+ align:start position:0%
+dumping and what this gives you this
+ 
+
+ align:start position:0%
+dumping and what this gives you this
+gives you a huge increase in the
+
+ align:start position:0%
+gives you a huge increase in the
+ 
+
+ align:start position:0%
+gives you a huge increase in the
+number of photons coming out from the
+
+ align:start position:0%
+number of photons coming out from the
+ 
+
+ align:start position:0%
+number of photons coming out from the
+laser but only for a very short time in
+
+ align:start position:0%
+laser but only for a very short time in
+ 
+
+ align:start position:0%
+laser but only for a very short time in
+fact it just takes all the photon the
+
+ align:start position:0%
+fact it just takes all the photon the
+ 
+
+ align:start position:0%
+fact it just takes all the photon the
+stored in the laser cavity and just
+
+ align:start position:0%
+stored in the laser cavity and just
+ 
+
+ align:start position:0%
+stored in the laser cavity and just
+dumps them out and for of course for
+
+ align:start position:0%
+dumps them out and for of course for
+ 
+
+ align:start position:0%
+dumps them out and for of course for
+very short time in fact the time is just
+
+ align:start position:0%
+very short time in fact the time is just
+ 
+
+ align:start position:0%
+very short time in fact the time is just
+the twice the time that you go the
+
+ align:start position:0%
+the twice the time that you go the
+ 
+
+ align:start position:0%
+the twice the time that you go the
+transit time of the of the cabot so the
+
+ align:start position:0%
+transit time of the of the cabot so the
+ 
+
+ align:start position:0%
+transit time of the of the cabot so the
+fact that one knows something about the
+
+ align:start position:0%
+fact that one knows something about the
+ 
+
+ align:start position:0%
+fact that one knows something about the
+light inside the laser is big in the
+
+ align:start position:0%
+light inside the laser is big in the
+ 
+
+ align:start position:0%
+light inside the laser is big in the
+light outside the laser then one can
+
+ align:start position:0%
+light outside the laser then one can
+ 
+
+ align:start position:0%
+light outside the laser then one can
+come up with this concept of cavity
+
+ align:start position:0%
+come up with this concept of cavity
+ 
+
+ align:start position:0%
+come up with this concept of cavity
+dumping which which can be useful for
+
+ align:start position:0%
+dumping which which can be useful for
+ 
+
+ align:start position:0%
+dumping which which can be useful for
+some applications
\ No newline at end of file
diff --git a/eBkhAL-0l50.txt b/eBkhAL-0l50.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42b221427d0459444539cdcbcb7f36170ebbfcc7
--- /dev/null
+++ b/eBkhAL-0l50.txt
@@ -0,0 +1,13051 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu like to do today is continue
+
+ align:start position:0%
+ocw.mit.edu like to do today is continue
+ 
+
+ align:start position:0%
+ocw.mit.edu like to do today is continue
+a bit with a survey of third order uh
+
+ align:start position:0%
+a bit with a survey of third order uh
+ 
+
+ align:start position:0%
+a bit with a survey of third order uh
+spectroscopies um little little bit uh
+
+ align:start position:0%
+spectroscopies um little little bit uh
+ 
+
+ align:start position:0%
+spectroscopies um little little bit uh
+faster little fewer equations um just to
+
+ align:start position:0%
+faster little fewer equations um just to
+ 
+
+ align:start position:0%
+faster little fewer equations um just to
+give you a feeling for what uh we do
+
+ align:start position:0%
+give you a feeling for what uh we do
+ 
+
+ align:start position:0%
+give you a feeling for what uh we do
+with them but so third order just uh
+
+ align:start position:0%
+with them but so third order just uh
+ 
+
+ align:start position:0%
+with them but so third order just uh
+from last time remember if you do a
+
+ align:start position:0%
+from last time remember if you do a
+ 
+
+ align:start position:0%
+from last time remember if you do a
+nonlinear spectroscopy or you're not
+
+ align:start position:0%
+nonlinear spectroscopy or you're not
+ 
+
+ align:start position:0%
+nonlinear spectroscopy or you're not
+sure but you think you
+
+ align:start position:0%
+sure but you think you
+ 
+
+ align:start position:0%
+sure but you think you
+do chances are you're doing a third
+
+ align:start position:0%
+do chances are you're doing a third
+ 
+
+ align:start position:0%
+do chances are you're doing a third
+order nonlinear experiment so it
+
+ align:start position:0%
+order nonlinear experiment so it
+ 
+
+ align:start position:0%
+order nonlinear experiment so it
+um also known as four-wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing it's um basically all of the
+
+ align:start position:0%
+mixing it's um basically all of the
+ 
+
+ align:start position:0%
+mixing it's um basically all of the
+coherent Ultra fast spectroscopies you
+
+ align:start position:0%
+coherent Ultra fast spectroscopies you
+ 
+
+ align:start position:0%
+coherent Ultra fast spectroscopies you
+know 90% of them fall into this class um
+
+ align:start position:0%
+know 90% of them fall into this class um
+ 
+
+ align:start position:0%
+know 90% of them fall into this class um
+so we're talking
+
+ align:start position:0%
+so we're talking
+ 
+
+ align:start position:0%
+so we're talking
+about things
+
+ align:start position:0%
+about things
+ 
+
+ align:start position:0%
+about things
+like Photon
+
+ align:start position:0%
+like Photon
+ 
+
+ align:start position:0%
+like Photon
+Echoes transient grade
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradings
+
+ align:start position:0%
+gradings
+ 
+
+ align:start position:0%
+gradings
+um all of the standard uh pump probe or
+
+ align:start position:0%
+um all of the standard uh pump probe or
+ 
+
+ align:start position:0%
+um all of the standard uh pump probe or
+transient absorption experim
+
+ align:start position:0%
+transient absorption experim
+ 
+
+ align:start position:0%
+transient absorption experim
+experiments whether you do that with
+
+ align:start position:0%
+experiments whether you do that with
+ 
+
+ align:start position:0%
+experiments whether you do that with
+coherent detection or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+incoherent
+
+ align:start position:0%
+incoherent
+ 
+
+ align:start position:0%
+incoherent
+um basically 90% of all of the uh
+
+ align:start position:0%
+um basically 90% of all of the uh
+ 
+
+ align:start position:0%
+um basically 90% of all of the uh
+two-dimensional spectroscopies that are
+
+ align:start position:0%
+two-dimensional spectroscopies that are
+ 
+
+ align:start position:0%
+two-dimensional spectroscopies that are
+being used these
+
+ align:start position:0%
+being used these
+ 
+
+ align:start position:0%
+being used these
+days
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CR can't write and talk at the same time
+
+ align:start position:0%
+CR can't write and talk at the same time
+ 
+
+ align:start position:0%
+CR can't write and talk at the same time
+um and there there's a few other example
+
+ align:start position:0%
+um and there there's a few other example
+ 
+
+ align:start position:0%
+um and there there's a few other example
+so I I want to go through some of these
+
+ align:start position:0%
+so I I want to go through some of these
+ 
+
+ align:start position:0%
+so I I want to go through some of these
+just to kind of give you a feeling for
+
+ align:start position:0%
+just to kind of give you a feeling for
+ 
+
+ align:start position:0%
+just to kind of give you a feeling for
+how they're all held together and
+
+ align:start position:0%
+how they're all held together and
+ 
+
+ align:start position:0%
+how they're all held together and
+they're all related to one another
+
+ align:start position:0%
+they're all related to one another
+ 
+
+ align:start position:0%
+they're all related to one another
+through these third order nonlinear
+
+ align:start position:0%
+through these third order nonlinear
+ 
+
+ align:start position:0%
+through these third order nonlinear
+response function yeah does anyone do
+
+ align:start position:0%
+response function yeah does anyone do
+ 
+
+ align:start position:0%
+response function yeah does anyone do
+second order stuff on nonent
+
+ align:start position:0%
+second order stuff on nonent
+ 
+
+ align:start position:0%
+second order stuff on nonent
+symmetric so
+
+ align:start position:0%
+symmetric so
+ 
+
+ align:start position:0%
+symmetric so
+that uh well the the classic example is
+
+ align:start position:0%
+that uh well the the classic example is
+ 
+
+ align:start position:0%
+that uh well the the classic example is
+uh surface selective experiments where
+
+ align:start position:0%
+uh surface selective experiments where
+ 
+
+ align:start position:0%
+uh surface selective experiments where
+you're making use of the surface to
+
+ align:start position:0%
+you're making use of the surface to
+ 
+
+ align:start position:0%
+you're making use of the surface to
+break the Symmetry um and and look for
+
+ align:start position:0%
+break the Symmetry um and and look for
+ 
+
+ align:start position:0%
+break the Symmetry um and and look for
+surface selective things um but it it is
+
+ align:start position:0%
+surface selective things um but it it is
+ 
+
+ align:start position:0%
+surface selective things um but it it is
+true you could absolutely do nonlinear
+
+ align:start position:0%
+true you could absolutely do nonlinear
+ 
+
+ align:start position:0%
+true you could absolutely do nonlinear
+stuff at at second order in a non-
+
+ align:start position:0%
+stuff at at second order in a non-
+ 
+
+ align:start position:0%
+stuff at at second order in a non-
+Centro symmetric
+
+ align:start position:0%
+Centro symmetric
+ 
+
+ align:start position:0%
+Centro symmetric
+medium but uh just because that's
+
+ align:start position:0%
+medium but uh just because that's
+ 
+
+ align:start position:0%
+medium but uh just because that's
+relatively rare and also bloody hard to
+
+ align:start position:0%
+relatively rare and also bloody hard to
+ 
+
+ align:start position:0%
+relatively rare and also bloody hard to
+do um most people don't do
+
+ align:start position:0%
+do um most people don't do
+ 
+
+ align:start position:0%
+do um most people don't do
+it oh
+
+ align:start position:0%
+it oh
+ 
+
+ align:start position:0%
+it oh
+um okay so last time we talked a bit
+
+ align:start position:0%
+um okay so last time we talked a bit
+ 
+
+ align:start position:0%
+um okay so last time we talked a bit
+about uh Photon Echoes um but sort of
+
+ align:start position:0%
+about uh Photon Echoes um but sort of
+ 
+
+ align:start position:0%
+about uh Photon Echoes um but sort of
+what I'm hoping oh yeah and the other
+
+ align:start position:0%
+what I'm hoping oh yeah and the other
+ 
+
+ align:start position:0%
+what I'm hoping oh yeah and the other
+big
+
+ align:start position:0%
+big
+ 
+
+ align:start position:0%
+big
+class are coherent Ramen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectroscopies and that refers to many
+
+ align:start position:0%
+spectroscopies and that refers to many
+ 
+
+ align:start position:0%
+spectroscopies and that refers to many
+different sorts of
+
+ align:start position:0%
+different sorts of
+ 
+
+ align:start position:0%
+different sorts of
+things um okay so I I'd like to keep
+
+ align:start position:0%
+things um okay so I I'd like to keep
+ 
+
+ align:start position:0%
+things um okay so I I'd like to keep
+going through this list a little bit and
+
+ align:start position:0%
+going through this list a little bit and
+ 
+
+ align:start position:0%
+going through this list a little bit and
+try and tie them all together we talked
+
+ align:start position:0%
+try and tie them all together we talked
+ 
+
+ align:start position:0%
+try and tie them all together we talked
+about Photon Echoes and the ability
+
+ align:start position:0%
+about Photon Echoes and the ability
+ 
+
+ align:start position:0%
+about Photon Echoes and the ability
+there to um talk about heterogene in a
+
+ align:start position:0%
+there to um talk about heterogene in a
+ 
+
+ align:start position:0%
+there to um talk about heterogene in a
+sample um using the rephasing
+
+ align:start position:0%
+sample um using the rephasing
+ 
+
+ align:start position:0%
+sample um using the rephasing
+characteristics of some of the
+
+ align:start position:0%
+characteristics of some of the
+ 
+
+ align:start position:0%
+characteristics of some of the
+correlation functions that contribute to
+
+ align:start position:0%
+correlation functions that contribute to
+ 
+
+ align:start position:0%
+correlation functions that contribute to
+the third order response let's um pick
+
+ align:start position:0%
+the third order response let's um pick
+ 
+
+ align:start position:0%
+the third order response let's um pick
+it up now with transient gradings um
+
+ align:start position:0%
+it up now with transient gradings um
+ 
+
+ align:start position:0%
+it up now with transient gradings um
+transient gradings that are great
+
+ align:start position:0%
+transient gradings that are great
+ 
+
+ align:start position:0%
+transient gradings that are great
+experiments because they have a very
+
+ align:start position:0%
+experiments because they have a very
+ 
+
+ align:start position:0%
+experiments because they have a very
+nice physical picture um that goes along
+
+ align:start position:0%
+nice physical picture um that goes along
+ 
+
+ align:start position:0%
+nice physical picture um that goes along
+with them so just to review for a second
+
+ align:start position:0%
+with them so just to review for a second
+ 
+
+ align:start position:0%
+with them so just to review for a second
+um we're talking about
+
+ align:start position:0%
+um we're talking about
+ 
+
+ align:start position:0%
+um we're talking about
+degenerate uh four-wave mixing at the
+
+ align:start position:0%
+degenerate uh four-wave mixing at the
+ 
+
+ align:start position:0%
+degenerate uh four-wave mixing at the
+moment um all the colors are the same
+
+ align:start position:0%
+moment um all the colors are the same
+ 
+
+ align:start position:0%
+moment um all the colors are the same
+it's very commonly performed in this box
+
+ align:start position:0%
+it's very commonly performed in this box
+ 
+
+ align:start position:0%
+it's very commonly performed in this box
+geometry
+
+ align:start position:0%
+geometry
+ 
+
+ align:start position:0%
+geometry
+we generate a signal in the fourth
+
+ align:start position:0%
+we generate a signal in the fourth
+ 
+
+ align:start position:0%
+we generate a signal in the fourth
+corner of a box that dictates a
+
+ align:start position:0%
+corner of a box that dictates a
+ 
+
+ align:start position:0%
+corner of a box that dictates a
+particular phase matching condition and
+
+ align:start position:0%
+particular phase matching condition and
+ 
+
+ align:start position:0%
+particular phase matching condition and
+we then can control the timing to sort
+
+ align:start position:0%
+we then can control the timing to sort
+ 
+
+ align:start position:0%
+we then can control the timing to sort
+of Select uh different
+
+ align:start position:0%
+of Select uh different
+ 
+
+ align:start position:0%
+of Select uh different
+contributions okay so the transient
+
+ align:start position:0%
+contributions okay so the transient
+ 
+
+ align:start position:0%
+contributions okay so the transient
+grading refers to the specific case
+
+ align:start position:0%
+grading refers to the specific case
+ 
+
+ align:start position:0%
+grading refers to the specific case
+where the first two fields are time
+
+ align:start position:0%
+where the first two fields are time
+ 
+
+ align:start position:0%
+where the first two fields are time
+coincident and they um they act as a
+
+ align:start position:0%
+coincident and they um they act as a
+ 
+
+ align:start position:0%
+coincident and they um they act as a
+pulse pair that is a pump field and
+
+ align:start position:0%
+pulse pair that is a pump field and
+ 
+
+ align:start position:0%
+pulse pair that is a pump field and
+there's a time delayed uh probe field
+
+ align:start position:0%
+there's a time delayed uh probe field
+ 
+
+ align:start position:0%
+there's a time delayed uh probe field
+okay um so what we're talking about is
+
+ align:start position:0%
+okay um so what we're talking about is
+ 
+
+ align:start position:0%
+okay um so what we're talking about is
+um we're going to generate a signal in
+
+ align:start position:0%
+um we're going to generate a signal in
+ 
+
+ align:start position:0%
+um we're going to generate a signal in
+one corner of the box and uh any
+
+ align:start position:0%
+one corner of the box and uh any
+ 
+
+ align:start position:0%
+one corner of the box and uh any
+adjacent pair of these beams are going
+
+ align:start position:0%
+adjacent pair of these beams are going
+ 
+
+ align:start position:0%
+adjacent pair of these beams are going
+to be timed up with one another um we'll
+
+ align:start position:0%
+to be timed up with one another um we'll
+ 
+
+ align:start position:0%
+to be timed up with one another um we'll
+call them one and two but in practice
+
+ align:start position:0%
+call them one and two but in practice
+ 
+
+ align:start position:0%
+call them one and two but in practice
+because they're time coincident you
+
+ align:start position:0%
+because they're time coincident you
+ 
+
+ align:start position:0%
+because they're time coincident you
+can't distinguish which is first and
+
+ align:start position:0%
+can't distinguish which is first and
+ 
+
+ align:start position:0%
+can't distinguish which is first and
+which is second we'll just call those uh
+
+ align:start position:0%
+which is second we'll just call those uh
+ 
+
+ align:start position:0%
+which is second we'll just call those uh
+I guess we could call them pump
+
+ align:start position:0%
+I guess we could call them pump
+ 
+
+ align:start position:0%
+I guess we could call them pump
+um and then there's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probe and if you now work through all of
+
+ align:start position:0%
+probe and if you now work through all of
+ 
+
+ align:start position:0%
+probe and if you now work through all of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh processes that will contribute to
+
+ align:start position:0%
+uh processes that will contribute to
+ 
+
+ align:start position:0%
+uh processes that will contribute to
+this you well the first thing you
+
+ align:start position:0%
+this you well the first thing you
+ 
+
+ align:start position:0%
+this you well the first thing you
+realize is the time variable that you
+
+ align:start position:0%
+realize is the time variable that you
+ 
+
+ align:start position:0%
+realize is the time variable that you
+have control over is after the second
+
+ align:start position:0%
+have control over is after the second
+ 
+
+ align:start position:0%
+have control over is after the second
+interaction with the light and of the
+
+ align:start position:0%
+interaction with the light and of the
+ 
+
+ align:start position:0%
+interaction with the light and of the
+light with the matter and so in your
+
+ align:start position:0%
+light with the matter and so in your
+ 
+
+ align:start position:0%
+light with the matter and so in your
+response functions you're looking at the
+
+ align:start position:0%
+response functions you're looking at the
+ 
+
+ align:start position:0%
+response functions you're looking at the
+t2 variable and that typic has many
+
+ align:start position:0%
+t2 variable and that typic has many
+ 
+
+ align:start position:0%
+t2 variable and that typic has many
+contributions we'll talk about those but
+
+ align:start position:0%
+contributions we'll talk about those but
+ 
+
+ align:start position:0%
+contributions we'll talk about those but
+um what you're doing is looking at
+
+ align:start position:0%
+um what you're doing is looking at
+ 
+
+ align:start position:0%
+um what you're doing is looking at
+relaxation of whatever um
+
+ align:start position:0%
+relaxation of whatever um
+ 
+
+ align:start position:0%
+relaxation of whatever um
+happens uh upon you exitation with that
+
+ align:start position:0%
+happens uh upon you exitation with that
+ 
+
+ align:start position:0%
+happens uh upon you exitation with that
+pulse pair okay so the the nice thing
+
+ align:start position:0%
+pulse pair okay so the the nice thing
+ 
+
+ align:start position:0%
+pulse pair okay so the the nice thing
+about transient gradings is that uh you
+
+ align:start position:0%
+about transient gradings is that uh you
+ 
+
+ align:start position:0%
+about transient gradings is that uh you
+should recognize that when you have two
+
+ align:start position:0%
+should recognize that when you have two
+ 
+
+ align:start position:0%
+should recognize that when you have two
+Fields where the wave fronts you know
+
+ align:start position:0%
+Fields where the wave fronts you know
+ 
+
+ align:start position:0%
+Fields where the wave fronts you know
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+perpendicular to the direction of
+
+ align:start position:0%
+perpendicular to the direction of
+ 
+
+ align:start position:0%
+perpendicular to the direction of
+propagation and you cross these
+
+ align:start position:0%
+propagation and you cross these
+ 
+
+ align:start position:0%
+propagation and you cross these
+simultaneously in a sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one has
+
+ align:start position:0%
+that one has
+ 
+
+ align:start position:0%
+that one has
+um constructive and destructive
+
+ align:start position:0%
+um constructive and destructive
+ 
+
+ align:start position:0%
+um constructive and destructive
+interference in the crossing area and
+
+ align:start position:0%
+interference in the crossing area and
+ 
+
+ align:start position:0%
+interference in the crossing area and
+you can think about this by sort of
+
+ align:start position:0%
+you can think about this by sort of
+ 
+
+ align:start position:0%
+you can think about this by sort of
+writing out the product of those fields
+
+ align:start position:0%
+writing out the product of those fields
+ 
+
+ align:start position:0%
+writing out the product of those fields
+and it'll look sort of like a magnitude
+
+ align:start position:0%
+and it'll look sort of like a magnitude
+ 
+
+ align:start position:0%
+and it'll look sort of like a magnitude
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um something like
+
+ align:start position:0%
+um something like
+ 
+
+ align:start position:0%
+um something like
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+cosine Omega 1 - Omega
+
+ align:start position:0%
+cosine Omega 1 - Omega
+ 
+
+ align:start position:0%
+cosine Omega 1 - Omega
+2 t
+
+ align:start position:0%
+2 t
+ 
+
+ align:start position:0%
+2 t
+-
+
+ align:start position:0%
+-
+ 
+
+ align:start position:0%
+-
+k um K1 -
+
+ align:start position:0%
+k um K1 -
+ 
+
+ align:start position:0%
+k um K1 -
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+R hope I got that right let me see but
+
+ align:start position:0%
+R hope I got that right let me see but
+ 
+
+ align:start position:0%
+R hope I got that right let me see but
+in any case what you have is yeah let me
+
+ align:start position:0%
+in any case what you have is yeah let me
+ 
+
+ align:start position:0%
+in any case what you have is yeah let me
+just write
+
+ align:start position:0%
+just write
+ 
+
+ align:start position:0%
+just write
+it just to make sure I don't screw
+
+ align:start position:0%
+it just to make sure I don't screw
+ 
+
+ align:start position:0%
+it just to make sure I don't screw
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xpi the what you have is both a you have
+
+ align:start position:0%
+xpi the what you have is both a you have
+ 
+
+ align:start position:0%
+xpi the what you have is both a you have
+a spa variation of the intensity and
+
+ align:start position:0%
+a spa variation of the intensity and
+ 
+
+ align:start position:0%
+a spa variation of the intensity and
+phase pattern in the sample over here
+
+ align:start position:0%
+phase pattern in the sample over here
+ 
+
+ align:start position:0%
+phase pattern in the sample over here
+okay that's encoded over here so K1
+
+ align:start position:0%
+okay that's encoded over here so K1
+ 
+
+ align:start position:0%
+okay that's encoded over here so K1
+minus K2 the difference in the wave
+
+ align:start position:0%
+minus K2 the difference in the wave
+ 
+
+ align:start position:0%
+minus K2 the difference in the wave
+vectors for the two incident
+
+ align:start position:0%
+vectors for the two incident
+ 
+
+ align:start position:0%
+vectors for the two incident
+pumps uh lies uh perpendicular to this
+
+ align:start position:0%
+pumps uh lies uh perpendicular to this
+ 
+
+ align:start position:0%
+pumps uh lies uh perpendicular to this
+direction which you're cross you know
+
+ align:start position:0%
+direction which you're cross you know
+ 
+
+ align:start position:0%
+direction which you're cross you know
+propagating the beams and it's an
+
+ align:start position:0%
+propagating the beams and it's an
+ 
+
+ align:start position:0%
+propagating the beams and it's an
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+pattern which if you think about it as
+
+ align:start position:0%
+pattern which if you think about it as
+ 
+
+ align:start position:0%
+pattern which if you think about it as
+intensity would be sort of a light dark
+
+ align:start position:0%
+intensity would be sort of a light dark
+ 
+
+ align:start position:0%
+intensity would be sort of a light dark
+light dark pattern um but at the same
+
+ align:start position:0%
+light dark pattern um but at the same
+ 
+
+ align:start position:0%
+light dark pattern um but at the same
+time it's also a phase variation at the
+
+ align:start position:0%
+time it's also a phase variation at the
+ 
+
+ align:start position:0%
+time it's also a phase variation at the
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+level and uh this is the pattern that
+
+ align:start position:0%
+level and uh this is the pattern that
+ 
+
+ align:start position:0%
+level and uh this is the pattern that
+gets imaged into your sample through the
+
+ align:start position:0%
+gets imaged into your sample through the
+ 
+
+ align:start position:0%
+gets imaged into your sample through the
+light matter interaction so if we're
+
+ align:start position:0%
+light matter interaction so if we're
+ 
+
+ align:start position:0%
+light matter interaction so if we're
+talking just about exciting population
+
+ align:start position:0%
+talking just about exciting population
+ 
+
+ align:start position:0%
+talking just about exciting population
+we're saying that we're going to create
+
+ align:start position:0%
+we're saying that we're going to create
+ 
+
+ align:start position:0%
+we're saying that we're going to create
+a spatial variation of
+
+ align:start position:0%
+a spatial variation of
+ 
+
+ align:start position:0%
+a spatial variation of
+populations uh that are excited and so
+
+ align:start position:0%
+populations uh that are excited and so
+ 
+
+ align:start position:0%
+populations uh that are excited and so
+by Imaging that Optical p pattern into
+
+ align:start position:0%
+by Imaging that Optical p pattern into
+ 
+
+ align:start position:0%
+by Imaging that Optical p pattern into
+the sample what you've done is uh
+
+ align:start position:0%
+the sample what you've done is uh
+ 
+
+ align:start position:0%
+the sample what you've done is uh
+created a grading right it's a spatial
+
+ align:start position:0%
+created a grading right it's a spatial
+ 
+
+ align:start position:0%
+created a grading right it's a spatial
+variation of the complex index of
+
+ align:start position:0%
+variation of the complex index of
+ 
+
+ align:start position:0%
+variation of the complex index of
+refraction so they're both the
+
+ align:start position:0%
+refraction so they're both the
+ 
+
+ align:start position:0%
+refraction so they're both the
+absorptive and the dispersive parts okay
+
+ align:start position:0%
+absorptive and the dispersive parts okay
+ 
+
+ align:start position:0%
+absorptive and the dispersive parts okay
+um the nice thing you have is uh you've
+
+ align:start position:0%
+um the nice thing you have is uh you've
+ 
+
+ align:start position:0%
+um the nice thing you have is uh you've
+have control over the grading wave
+
+ align:start position:0%
+have control over the grading wave
+ 
+
+ align:start position:0%
+have control over the grading wave
+Vector because that's really just
+
+ align:start position:0%
+Vector because that's really just
+ 
+
+ align:start position:0%
+Vector because that's really just
+dictated by The Crossing angle so as
+
+ align:start position:0%
+dictated by The Crossing angle so as
+ 
+
+ align:start position:0%
+dictated by The Crossing angle so as
+I've pointed out here if you um Cross by
+
+ align:start position:0%
+I've pointed out here if you um Cross by
+ 
+
+ align:start position:0%
+I've pointed out here if you um Cross by
+an angle to Theta then the um grading
+
+ align:start position:0%
+an angle to Theta then the um grading
+ 
+
+ align:start position:0%
+an angle to Theta then the um grading
+Fringe spacing is uh you know dictated
+
+ align:start position:0%
+Fringe spacing is uh you know dictated
+ 
+
+ align:start position:0%
+Fringe spacing is uh you know dictated
+by the wavelength of the light and the
+
+ align:start position:0%
+by the wavelength of the light and the
+ 
+
+ align:start position:0%
+by the wavelength of the light and the
+sign of the crossing angles of written
+
+ align:start position:0%
+sign of the crossing angles of written
+ 
+
+ align:start position:0%
+sign of the crossing angles of written
+up there okay um so this turns out to be
+
+ align:start position:0%
+up there okay um so this turns out to be
+ 
+
+ align:start position:0%
+up there okay um so this turns out to be
+very effective uh particularly if you're
+
+ align:start position:0%
+very effective uh particularly if you're
+ 
+
+ align:start position:0%
+very effective uh particularly if you're
+interested in watching um relaxation
+
+ align:start position:0%
+interested in watching um relaxation
+ 
+
+ align:start position:0%
+interested in watching um relaxation
+processes on spatial scales you
+
+ align:start position:0%
+processes on spatial scales you
+ 
+
+ align:start position:0%
+processes on spatial scales you
+know uh of optical you know the optical
+
+ align:start position:0%
+know uh of optical you know the optical
+ 
+
+ align:start position:0%
+know uh of optical you know the optical
+wavelength range okay so um y
+
+ align:start position:0%
+wavelength range okay so um y
+ 
+
+ align:start position:0%
+wavelength range okay so um y
+does anyone able to do microscopy on
+
+ align:start position:0%
+does anyone able to do microscopy on
+ 
+
+ align:start position:0%
+does anyone able to do microscopy on
+that like image that y uh I think a good
+
+ align:start position:0%
+that like image that y uh I think a good
+ 
+
+ align:start position:0%
+that like image that y uh I think a good
+great example is what Andy Marcus does
+
+ align:start position:0%
+great example is what Andy Marcus does
+ 
+
+ align:start position:0%
+great example is what Andy Marcus does
+at Oregon he there he's really trying to
+
+ align:start position:0%
+at Oregon he there he's really trying to
+ 
+
+ align:start position:0%
+at Oregon he there he's really trying to
+look at anisotropic diffusion um you
+
+ align:start position:0%
+look at anisotropic diffusion um you
+ 
+
+ align:start position:0%
+look at anisotropic diffusion um you
+know perpendicular and parallel to
+
+ align:start position:0%
+know perpendicular and parallel to
+ 
+
+ align:start position:0%
+know perpendicular and parallel to
+fringes in an you know Optical uh
+
+ align:start position:0%
+fringes in an you know Optical uh
+ 
+
+ align:start position:0%
+fringes in an you know Optical uh
+grading
+
+ align:start position:0%
+grading
+ 
+
+ align:start position:0%
+grading
+yeah it's uh sort of the trans um you
+
+ align:start position:0%
+yeah it's uh sort of the trans um you
+ 
+
+ align:start position:0%
+yeah it's uh sort of the trans um you
+transient gradings
+
+ align:start position:0%
+transient gradings
+ 
+
+ align:start position:0%
+transient gradings
+are pretty much analogous to pump probe
+
+ align:start position:0%
+are pretty much analogous to pump probe
+ 
+
+ align:start position:0%
+are pretty much analogous to pump probe
+experiments they are sort of the limit
+
+ align:start position:0%
+experiments they are sort of the limit
+ 
+
+ align:start position:0%
+experiments they are sort of the limit
+that the crossing angle goes to zero and
+
+ align:start position:0%
+that the crossing angle goes to zero and
+ 
+
+ align:start position:0%
+that the crossing angle goes to zero and
+uh the fix experiments that Andy does
+
+ align:start position:0%
+uh the fix experiments that Andy does
+ 
+
+ align:start position:0%
+uh the fix experiments that Andy does
+are functionally the transient grading
+
+ align:start position:0%
+are functionally the transient grading
+ 
+
+ align:start position:0%
+are functionally the transient grading
+version of what uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it fix is to fluoresence correlation
+
+ align:start position:0%
+it fix is to fluoresence correlation
+ 
+
+ align:start position:0%
+it fix is to fluoresence correlation
+spectroscopy what transient gradings are
+
+ align:start position:0%
+spectroscopy what transient gradings are
+ 
+
+ align:start position:0%
+spectroscopy what transient gradings are
+to pump probe experiments if that makes
+
+ align:start position:0%
+to pump probe experiments if that makes
+ 
+
+ align:start position:0%
+to pump probe experiments if that makes
+sense it's the same kind of technique
+
+ align:start position:0%
+sense it's the same kind of technique
+ 
+
+ align:start position:0%
+sense it's the same kind of technique
+but you're making use of this spatial
+
+ align:start position:0%
+but you're making use of this spatial
+ 
+
+ align:start position:0%
+but you're making use of this spatial
+variation to tell you about anisotropic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Behavior okay so but uh now as you can
+
+ align:start position:0%
+Behavior okay so but uh now as you can
+ 
+
+ align:start position:0%
+Behavior okay so but uh now as you can
+imagine there's all sorts of ways in
+
+ align:start position:0%
+imagine there's all sorts of ways in
+ 
+
+ align:start position:0%
+imagine there's all sorts of ways in
+which this grading can relax you know
+
+ align:start position:0%
+which this grading can relax you know
+ 
+
+ align:start position:0%
+which this grading can relax you know
+what I failed to point out is okay
+
+ align:start position:0%
+what I failed to point out is okay
+ 
+
+ align:start position:0%
+what I failed to point out is okay
+you've imaged a grading into the sample
+
+ align:start position:0%
+you've imaged a grading into the sample
+ 
+
+ align:start position:0%
+you've imaged a grading into the sample
+and now what you can think of is that
+
+ align:start position:0%
+and now what you can think of is that
+ 
+
+ align:start position:0%
+and now what you can think of is that
+the probe pulse is something that um
+
+ align:start position:0%
+the probe pulse is something that um
+ 
+
+ align:start position:0%
+the probe pulse is something that um
+defract off of that grading that the
+
+ align:start position:0%
+defract off of that grading that the
+ 
+
+ align:start position:0%
+defract off of that grading that the
+efficiency of light scattered off of
+
+ align:start position:0%
+efficiency of light scattered off of
+ 
+
+ align:start position:0%
+efficiency of light scattered off of
+that grading is what you were measuring
+
+ align:start position:0%
+that grading is what you were measuring
+ 
+
+ align:start position:0%
+that grading is what you were measuring
+measuring in a transient grading
+
+ align:start position:0%
+measuring in a transient grading
+ 
+
+ align:start position:0%
+measuring in a transient grading
+experiment so that um that's sort of the
+
+ align:start position:0%
+experiment so that um that's sort of the
+ 
+
+ align:start position:0%
+experiment so that um that's sort of the
+physical picture that goes with it and
+
+ align:start position:0%
+physical picture that goes with it and
+ 
+
+ align:start position:0%
+physical picture that goes with it and
+you can imagine a bunch of different
+
+ align:start position:0%
+you can imagine a bunch of different
+ 
+
+ align:start position:0%
+you can imagine a bunch of different
+types of relaxation processes if you're
+
+ align:start position:0%
+types of relaxation processes if you're
+ 
+
+ align:start position:0%
+types of relaxation processes if you're
+just looking at relaxation of uh excited
+
+ align:start position:0%
+just looking at relaxation of uh excited
+ 
+
+ align:start position:0%
+just looking at relaxation of uh excited
+States this is the amplitude of that
+
+ align:start position:0%
+States this is the amplitude of that
+ 
+
+ align:start position:0%
+States this is the amplitude of that
+grading gradually washing out with time
+
+ align:start position:0%
+grading gradually washing out with time
+ 
+
+ align:start position:0%
+grading gradually washing out with time
+and you know you can imagine that that
+
+ align:start position:0%
+and you know you can imagine that that
+ 
+
+ align:start position:0%
+and you know you can imagine that that
+would lead to a um signal where the
+
+ align:start position:0%
+would lead to a um signal where the
+ 
+
+ align:start position:0%
+would lead to a um signal where the
+scattering efficiency just uh decreases
+
+ align:start position:0%
+scattering efficiency just uh decreases
+ 
+
+ align:start position:0%
+scattering efficiency just uh decreases
+with the relaxation processes
+
+ align:start position:0%
+with the relaxation processes
+ 
+
+ align:start position:0%
+with the relaxation processes
+it's also possible that um if this
+
+ align:start position:0%
+it's also possible that um if this
+ 
+
+ align:start position:0%
+it's also possible that um if this
+grading is imaged rapidly that you can
+
+ align:start position:0%
+grading is imaged rapidly that you can
+ 
+
+ align:start position:0%
+grading is imaged rapidly that you can
+jump
+
+ align:start position:0%
+jump
+ 
+
+ align:start position:0%
+jump
+the index in you know functionally
+
+ align:start position:0%
+the index in you know functionally
+ 
+
+ align:start position:0%
+the index in you know functionally
+heating or expanding the material in the
+
+ align:start position:0%
+heating or expanding the material in the
+ 
+
+ align:start position:0%
+heating or expanding the material in the
+high-intensity regions and you can
+
+ align:start position:0%
+high-intensity regions and you can
+ 
+
+ align:start position:0%
+high-intensity regions and you can
+launch acoustic waves that propagate
+
+ align:start position:0%
+launch acoustic waves that propagate
+ 
+
+ align:start position:0%
+launch acoustic waves that propagate
+counter propagate actually through the
+
+ align:start position:0%
+counter propagate actually through the
+ 
+
+ align:start position:0%
+counter propagate actually through the
+sample um and as you might imagine that
+
+ align:start position:0%
+sample um and as you might imagine that
+ 
+
+ align:start position:0%
+sample um and as you might imagine that
+will modulate the defraction efficiency
+
+ align:start position:0%
+will modulate the defraction efficiency
+ 
+
+ align:start position:0%
+will modulate the defraction efficiency
+as they move across and so that would uh
+
+ align:start position:0%
+as they move across and so that would uh
+ 
+
+ align:start position:0%
+as they move across and so that would uh
+typically you know show up as a
+
+ align:start position:0%
+typically you know show up as a
+ 
+
+ align:start position:0%
+typically you know show up as a
+modulation on you know on top of a
+
+ align:start position:0%
+modulation on you know on top of a
+ 
+
+ align:start position:0%
+modulation on you know on top of a
+relaxation
+
+ align:start position:0%
+relaxation
+ 
+
+ align:start position:0%
+relaxation
+process um time scale of course there is
+
+ align:start position:0%
+process um time scale of course there is
+ 
+
+ align:start position:0%
+process um time scale of course there is
+dictated by you know acoustic
+
+ align:start position:0%
+dictated by you know acoustic
+ 
+
+ align:start position:0%
+dictated by you know acoustic
+propagation so you're you know soft me
+
+ align:start position:0%
+propagation so you're you know soft me
+ 
+
+ align:start position:0%
+propagation so you're you know soft me
+to you're talking sort of nanc behavior
+
+ align:start position:0%
+to you're talking sort of nanc behavior
+ 
+
+ align:start position:0%
+to you're talking sort of nanc behavior
+usually um and then as you might imagine
+
+ align:start position:0%
+usually um and then as you might imagine
+ 
+
+ align:start position:0%
+usually um and then as you might imagine
+you can get look at very long um thermal
+
+ align:start position:0%
+you can get look at very long um thermal
+ 
+
+ align:start position:0%
+you can get look at very long um thermal
+relaxation processes you if you're
+
+ align:start position:0%
+relaxation processes you if you're
+ 
+
+ align:start position:0%
+relaxation processes you if you're
+really heating the system in these light
+
+ align:start position:0%
+really heating the system in these light
+ 
+
+ align:start position:0%
+really heating the system in these light
+spots then you've created a modulation
+
+ align:start position:0%
+spots then you've created a modulation
+ 
+
+ align:start position:0%
+spots then you've created a modulation
+in the index of refraction that because
+
+ align:start position:0%
+in the index of refraction that because
+ 
+
+ align:start position:0%
+in the index of refraction that because
+of the temperature dependence to that
+
+ align:start position:0%
+of the temperature dependence to that
+ 
+
+ align:start position:0%
+of the temperature dependence to that
+index and as that uh
+
+ align:start position:0%
+index and as that uh
+ 
+
+ align:start position:0%
+index and as that uh
+grading starts well defined and
+
+ align:start position:0%
+grading starts well defined and
+ 
+
+ align:start position:0%
+grading starts well defined and
+gradually washes
+
+ align:start position:0%
+gradually washes
+ 
+
+ align:start position:0%
+gradually washes
+out due to Thermal diffusion from Peaks
+
+ align:start position:0%
+out due to Thermal diffusion from Peaks
+ 
+
+ align:start position:0%
+out due to Thermal diffusion from Peaks
+into nulls that also contributes and so
+
+ align:start position:0%
+into nulls that also contributes and so
+ 
+
+ align:start position:0%
+into nulls that also contributes and so
+basically at the end of the day any sort
+
+ align:start position:0%
+basically at the end of the day any sort
+ 
+
+ align:start position:0%
+basically at the end of the day any sort
+of Transport process that has a um
+
+ align:start position:0%
+of Transport process that has a um
+ 
+
+ align:start position:0%
+of Transport process that has a um
+wavelength dependence to it or or a or a
+
+ align:start position:0%
+wavelength dependence to it or or a or a
+ 
+
+ align:start position:0%
+wavelength dependence to it or or a or a
+um intensity dependence to it uh that
+
+ align:start position:0%
+um intensity dependence to it uh that
+ 
+
+ align:start position:0%
+um intensity dependence to it uh that
+can be and that that it'll work on this
+
+ align:start position:0%
+can be and that that it'll work on this
+ 
+
+ align:start position:0%
+can be and that that it'll work on this
+distance scale of the optical wavelength
+
+ align:start position:0%
+distance scale of the optical wavelength
+ 
+
+ align:start position:0%
+distance scale of the optical wavelength
+you can probe that with transient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradings okay any questions on that
+
+ align:start position:0%
+gradings okay any questions on that
+ 
+
+ align:start position:0%
+gradings okay any questions on that
+one you ever do experiments where either
+
+ align:start position:0%
+one you ever do experiments where either
+ 
+
+ align:start position:0%
+one you ever do experiments where either
+the pump or probe in a transient gring
+
+ align:start position:0%
+the pump or probe in a transient gring
+ 
+
+ align:start position:0%
+the pump or probe in a transient gring
+is actually not so transient as the C A
+
+ align:start position:0%
+is actually not so transient as the C A
+ 
+
+ align:start position:0%
+is actually not so transient as the C A
+CW beam so you either have like a
+
+ align:start position:0%
+CW beam so you either have like a
+ 
+
+ align:start position:0%
+CW beam so you either have like a
+optical grading there and you image it
+
+ align:start position:0%
+optical grading there and you image it
+ 
+
+ align:start position:0%
+optical grading there and you image it
+with some transing probe or uh of
+
+ align:start position:0%
+with some transing probe or uh of
+ 
+
+ align:start position:0%
+with some transing probe or uh of
+actually Imaging the the grading
+
+ align:start position:0%
+actually Imaging the the grading
+ 
+
+ align:start position:0%
+actually Imaging the the grading
+itself I don't know I think we got to
+
+ align:start position:0%
+itself I don't know I think we got to
+ 
+
+ align:start position:0%
+itself I don't know I think we got to
+ask that to the Nelson folks I think you
+
+ align:start position:0%
+ask that to the Nelson folks I think you
+ 
+
+ align:start position:0%
+ask that to the Nelson folks I think you
+guys were doing something like that in
+
+ align:start position:0%
+guys were doing something like that in
+ 
+
+ align:start position:0%
+guys were doing something like that in
+that but it's not a CW no but not CW
+
+ align:start position:0%
+that but it's not a CW no but not CW
+ 
+
+ align:start position:0%
+that but it's not a CW no but not CW
+right yeah no it uh but this this is
+
+ align:start position:0%
+right yeah no it uh but this this is
+ 
+
+ align:start position:0%
+right yeah no it uh but this this is
+getting back a little bit to what Paul
+
+ align:start position:0%
+getting back a little bit to what Paul
+ 
+
+ align:start position:0%
+getting back a little bit to what Paul
+was asking earlier there you know you
+
+ align:start position:0%
+was asking earlier there you know you
+ 
+
+ align:start position:0%
+was asking earlier there you know you
+know there there are some microscopies
+
+ align:start position:0%
+know there there are some microscopies
+ 
+
+ align:start position:0%
+know there there are some microscopies
+in which you can really image the
+
+ align:start position:0%
+in which you can really image the
+ 
+
+ align:start position:0%
+in which you can really image the
+grading directly and um try and use it
+
+ align:start position:0%
+grading directly and um try and use it
+ 
+
+ align:start position:0%
+grading directly and um try and use it
+to distinguish diffusion of particles
+
+ align:start position:0%
+to distinguish diffusion of particles
+ 
+
+ align:start position:0%
+to distinguish diffusion of particles
+you know along the direction of The
+
+ align:start position:0%
+you know along the direction of The
+ 
+
+ align:start position:0%
+you know along the direction of The
+Fringe the the gring wave
+
+ align:start position:0%
+Fringe the the gring wave
+ 
+
+ align:start position:0%
+Fringe the the gring wave
+Vector U but no it's I mean the way you
+
+ align:start position:0%
+Vector U but no it's I mean the way you
+ 
+
+ align:start position:0%
+Vector U but no it's I mean the way you
+described it that's very
+
+ align:start position:0%
+described it that's very
+ 
+
+ align:start position:0%
+described it that's very
+uncommon but it's true you can just as
+
+ align:start position:0%
+uncommon but it's true you can just as
+ 
+
+ align:start position:0%
+uncommon but it's true you can just as
+well do this with uh CW beams but you at
+
+ align:start position:0%
+well do this with uh CW beams but you at
+ 
+
+ align:start position:0%
+well do this with uh CW beams but you at
+that moment you also want to recognize
+
+ align:start position:0%
+that moment you also want to recognize
+ 
+
+ align:start position:0%
+that moment you also want to recognize
+that there you can't enforce the kind of
+
+ align:start position:0%
+that there you can't enforce the kind of
+ 
+
+ align:start position:0%
+that there you can't enforce the kind of
+time ordering that we have here there's
+
+ align:start position:0%
+time ordering that we have here there's
+ 
+
+ align:start position:0%
+time ordering that we have here there's
+addition in addition to what I've
+
+ align:start position:0%
+addition in addition to what I've
+ 
+
+ align:start position:0%
+addition in addition to what I've
+described there will be additional
+
+ align:start position:0%
+described there will be additional
+ 
+
+ align:start position:0%
+described there will be additional
+relaxation processes that you know
+
+ align:start position:0%
+relaxation processes that you know
+ 
+
+ align:start position:0%
+relaxation processes that you know
+depend on um uh you know coherence that
+
+ align:start position:0%
+depend on um uh you know coherence that
+ 
+
+ align:start position:0%
+depend on um uh you know coherence that
+different here I've described it really
+
+ align:start position:0%
+different here I've described it really
+ 
+
+ align:start position:0%
+different here I've described it really
+all as incoherent relaxation processes
+
+ align:start position:0%
+all as incoherent relaxation processes
+ 
+
+ align:start position:0%
+all as incoherent relaxation processes
+right that now that's not uh like you
+
+ align:start position:0%
+right that now that's not uh like you
+ 
+
+ align:start position:0%
+right that now that's not uh like you
+know that's not entirely the case um and
+
+ align:start position:0%
+know that's not entirely the case um and
+ 
+
+ align:start position:0%
+know that's not entirely the case um and
+this is sort of getting uh toward
+
+ align:start position:0%
+this is sort of getting uh toward
+ 
+
+ align:start position:0%
+this is sort of getting uh toward
+coherent Ramen methods the other way to
+
+ align:start position:0%
+coherent Ramen methods the other way to
+ 
+
+ align:start position:0%
+coherent Ramen methods the other way to
+look at this is just because um The Wave
+
+ align:start position:0%
+look at this is just because um The Wave
+ 
+
+ align:start position:0%
+look at this is just because um The Wave
+Vector matching and the time
+
+ align:start position:0%
+Vector matching and the time
+ 
+
+ align:start position:0%
+Vector matching and the time
+ordering
+
+ align:start position:0%
+ordering
+ 
+
+ align:start position:0%
+ordering
+um says that there's a difference in
+
+ align:start position:0%
+um says that there's a difference in
+ 
+
+ align:start position:0%
+um says that there's a difference in
+wave Vector between the um difference in
+
+ align:start position:0%
+wave Vector between the um difference in
+ 
+
+ align:start position:0%
+wave Vector between the um difference in
+momentum between the first two
+
+ align:start position:0%
+momentum between the first two
+ 
+
+ align:start position:0%
+momentum between the first two
+interactions that also means that
+
+ align:start position:0%
+interactions that also means that
+ 
+
+ align:start position:0%
+interactions that also means that
+there's a difference in frequency um so
+
+ align:start position:0%
+there's a difference in frequency um so
+ 
+
+ align:start position:0%
+there's a difference in frequency um so
+for degenerate cases you know this uh
+
+ align:start position:0%
+for degenerate cases you know this uh
+ 
+
+ align:start position:0%
+for degenerate cases you know this uh
+disappears um if these are slightly
+
+ align:start position:0%
+disappears um if these are slightly
+ 
+
+ align:start position:0%
+disappears um if these are slightly
+different frequencies you have a you
+
+ align:start position:0%
+different frequencies you have a you
+ 
+
+ align:start position:0%
+different frequencies you have a you
+know um you can now imagine this
+
+ align:start position:0%
+know um you can now imagine this
+ 
+
+ align:start position:0%
+know um you can now imagine this
+experiment as a Ramen experiment where
+
+ align:start position:0%
+experiment as a Ramen experiment where
+ 
+
+ align:start position:0%
+experiment as a Ramen experiment where
+you're driving coherences at the
+
+ align:start position:0%
+you're driving coherences at the
+ 
+
+ align:start position:0%
+you're driving coherences at the
+difference frequency between the two
+
+ align:start position:0%
+difference frequency between the two
+ 
+
+ align:start position:0%
+difference frequency between the two
+incident fields that that creates a
+
+ align:start position:0%
+incident fields that that creates a
+ 
+
+ align:start position:0%
+incident fields that that creates a
+moving rating right it now moves in TI
+
+ align:start position:0%
+moving rating right it now moves in TI
+ 
+
+ align:start position:0%
+moving rating right it now moves in TI
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space um yeah so we'll get to coherent
+
+ align:start position:0%
+space um yeah so we'll get to coherent
+ 
+
+ align:start position:0%
+space um yeah so we'll get to coherent
+romen a little bit but the the grading
+
+ align:start position:0%
+romen a little bit but the the grading
+ 
+
+ align:start position:0%
+romen a little bit but the the grading
+the um just one question
+
+ align:start position:0%
+the um just one question
+ 
+
+ align:start position:0%
+the um just one question
+so what if you make your grading out of
+
+ align:start position:0%
+so what if you make your grading out of
+ 
+
+ align:start position:0%
+so what if you make your grading out of
+more than two beans in particular if you
+
+ align:start position:0%
+more than two beans in particular if you
+ 
+
+ align:start position:0%
+more than two beans in particular if you
+want to make not a 1D grading but a
+
+ align:start position:0%
+want to make not a 1D grading but a
+ 
+
+ align:start position:0%
+want to make not a 1D grading but a
+m sure people is that something like
+
+ align:start position:0%
+m sure people is that something like
+ 
+
+ align:start position:0%
+m sure people is that something like
+it's actually
+
+ align:start position:0%
+it's actually
+ 
+
+ align:start position:0%
+it's actually
+possible um boy yes I mean people there
+
+ align:start position:0%
+possible um boy yes I mean people there
+ 
+
+ align:start position:0%
+possible um boy yes I mean people there
+there was a there was a time where
+
+ align:start position:0%
+there was a there was a time where
+ 
+
+ align:start position:0%
+there was a there was a time where
+people really talked a lot about
+
+ align:start position:0%
+people really talked a lot about
+ 
+
+ align:start position:0%
+people really talked a lot about
+holographic data storage you know with
+
+ align:start position:0%
+holographic data storage you know with
+ 
+
+ align:start position:0%
+holographic data storage you know with
+um many beams right and I don't know a
+
+ align:start position:0%
+um many beams right and I don't know a
+ 
+
+ align:start position:0%
+um many beams right and I don't know a
+heck of a lot about that but um that of
+
+ align:start position:0%
+heck of a lot about that but um that of
+ 
+
+ align:start position:0%
+heck of a lot about that but um that of
+course that would fall into a you know
+
+ align:start position:0%
+course that would fall into a you know
+ 
+
+ align:start position:0%
+course that would fall into a you know
+sort of another class light matter
+
+ align:start position:0%
+sort of another class light matter
+ 
+
+ align:start position:0%
+sort of another class light matter
+interactions you're going to need
+
+ align:start position:0%
+interactions you're going to need
+ 
+
+ align:start position:0%
+interactions you're going to need
+additional Fields but but it's right
+
+ align:start position:0%
+additional Fields but but it's right
+ 
+
+ align:start position:0%
+additional Fields but but it's right
+that's analogous it seemed like those
+
+ align:start position:0%
+that's analogous it seemed like those
+ 
+
+ align:start position:0%
+that's analogous it seemed like those
+things never actually got experimentally
+
+ align:start position:0%
+things never actually got experimentally
+ 
+
+ align:start position:0%
+things never actually got experimentally
+realized
+
+ align:start position:0%
+realized
+ 
+
+ align:start position:0%
+realized
+yeah experimentally is this really
+
+ align:start position:0%
+yeah experimentally is this really
+ 
+
+ align:start position:0%
+yeah experimentally is this really
+hard no that's no problem at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so now let me turn to
+
+ align:start position:0%
+yeah okay so now let me turn to
+ 
+
+ align:start position:0%
+yeah okay so now let me turn to
+transient absorption I um I wanted to
+
+ align:start position:0%
+transient absorption I um I wanted to
+ 
+
+ align:start position:0%
+transient absorption I um I wanted to
+save this a little bit just to put a a
+
+ align:start position:0%
+save this a little bit just to put a a
+ 
+
+ align:start position:0%
+save this a little bit just to put a a
+slightly different spin on it what we're
+
+ align:start position:0%
+slightly different spin on it what we're
+ 
+
+ align:start position:0%
+slightly different spin on it what we're
+talking about now is really
+
+ align:start position:0%
+talking about now is really
+ 
+
+ align:start position:0%
+talking about now is really
+um any sort of an experiment where
+
+ align:start position:0%
+um any sort of an experiment where
+ 
+
+ align:start position:0%
+um any sort of an experiment where
+you're using two
+
+ align:start position:0%
+you're using two
+ 
+
+ align:start position:0%
+you're using two
+Fields driving the system waiting a
+
+ align:start position:0%
+Fields driving the system waiting a
+ 
+
+ align:start position:0%
+Fields driving the system waiting a
+period of time and then just watching
+
+ align:start position:0%
+period of time and then just watching
+ 
+
+ align:start position:0%
+period of time and then just watching
+the response so this is probably the
+
+ align:start position:0%
+the response so this is probably the
+ 
+
+ align:start position:0%
+the response so this is probably the
+most common type of an experiment and
+
+ align:start position:0%
+most common type of an experiment and
+ 
+
+ align:start position:0%
+most common type of an experiment and
+and I'm going to specifically talk about
+
+ align:start position:0%
+and I'm going to specifically talk about
+ 
+
+ align:start position:0%
+and I'm going to specifically talk about
+the case where you know I just crossed
+
+ align:start position:0%
+the case where you know I just crossed
+ 
+
+ align:start position:0%
+the case where you know I just crossed
+two beams I've got one that precedes the
+
+ align:start position:0%
+two beams I've got one that precedes the
+ 
+
+ align:start position:0%
+two beams I've got one that precedes the
+other I call the first pump and the
+
+ align:start position:0%
+other I call the first pump and the
+ 
+
+ align:start position:0%
+other I call the first pump and the
+second the probe there's one time delay
+
+ align:start position:0%
+second the probe there's one time delay
+ 
+
+ align:start position:0%
+second the probe there's one time delay
+between these two um and what I'm going
+
+ align:start position:0%
+between these two um and what I'm going
+ 
+
+ align:start position:0%
+between these two um and what I'm going
+to do is put a
+
+ align:start position:0%
+to do is put a
+ 
+
+ align:start position:0%
+to do is put a
+detector on the uh transmitted probe
+
+ align:start position:0%
+detector on the uh transmitted probe
+ 
+
+ align:start position:0%
+detector on the uh transmitted probe
+beam and I'm just interested in looking
+
+ align:start position:0%
+beam and I'm just interested in looking
+ 
+
+ align:start position:0%
+beam and I'm just interested in looking
+at the change in
+
+ align:start position:0%
+at the change in
+ 
+
+ align:start position:0%
+at the change in
+intensity that I see with and without
+
+ align:start position:0%
+intensity that I see with and without
+ 
+
+ align:start position:0%
+intensity that I see with and without
+the pump beam there
+
+ align:start position:0%
+the pump beam there
+ 
+
+ align:start position:0%
+the pump beam there
+okay um so this is is transient
+
+ align:start position:0%
+okay um so this is is transient
+ 
+
+ align:start position:0%
+okay um so this is is transient
+absorption um and what I'm talking about
+
+ align:start position:0%
+absorption um and what I'm talking about
+ 
+
+ align:start position:0%
+absorption um and what I'm talking about
+applies pretty much also to the other
+
+ align:start position:0%
+applies pretty much also to the other
+ 
+
+ align:start position:0%
+applies pretty much also to the other
+common case which is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you're looking at spontaneous
+
+ align:start position:0%
+um you're looking at spontaneous
+ 
+
+ align:start position:0%
+um you're looking at spontaneous
+emission or or some sort of an
+
+ align:start position:0%
+emission or or some sort of an
+ 
+
+ align:start position:0%
+emission or or some sort of an
+incoherent
+
+ align:start position:0%
+incoherent
+ 
+
+ align:start position:0%
+incoherent
+process um from the sample and you're
+
+ align:start position:0%
+process um from the sample and you're
+ 
+
+ align:start position:0%
+process um from the sample and you're
+looking at the change of that scattered
+
+ align:start position:0%
+looking at the change of that scattered
+ 
+
+ align:start position:0%
+looking at the change of that scattered
+intensity as a result of these two
+
+ align:start position:0%
+intensity as a result of these two
+ 
+
+ align:start position:0%
+intensity as a result of these two
+interactions okay uh as we talked about
+
+ align:start position:0%
+interactions okay uh as we talked about
+ 
+
+ align:start position:0%
+interactions okay uh as we talked about
+last time this the formulation for this
+
+ align:start position:0%
+last time this the formulation for this
+ 
+
+ align:start position:0%
+last time this the formulation for this
+is a little bit different you got to
+
+ align:start position:0%
+is a little bit different you got to
+ 
+
+ align:start position:0%
+is a little bit different you got to
+tweak it a bit um but uh it's follows
+
+ align:start position:0%
+tweak it a bit um but uh it's follows
+ 
+
+ align:start position:0%
+tweak it a bit um but uh it's follows
+the ideas we're going to talk about so
+
+ align:start position:0%
+the ideas we're going to talk about so
+ 
+
+ align:start position:0%
+the ideas we're going to talk about so
+what we are talking about here is any
+
+ align:start position:0%
+what we are talking about here is any
+ 
+
+ align:start position:0%
+what we are talking about here is any
+experiment in which you've got three
+
+ align:start position:0%
+experiment in which you've got three
+ 
+
+ align:start position:0%
+experiment in which you've got three
+independent variables okay up here I
+
+ align:start position:0%
+independent variables okay up here I
+ 
+
+ align:start position:0%
+independent variables okay up here I
+just want to point out remember in our
+
+ align:start position:0%
+just want to point out remember in our
+ 
+
+ align:start position:0%
+just want to point out remember in our
+third order response function this
+
+ align:start position:0%
+third order response function this
+ 
+
+ align:start position:0%
+third order response function this
+involves three independent uh time
+
+ align:start position:0%
+involves three independent uh time
+ 
+
+ align:start position:0%
+involves three independent uh time
+variables the time delays between it
+
+ align:start position:0%
+variables the time delays between it
+ 
+
+ align:start position:0%
+variables the time delays between it
+different fields those are the ones we
+
+ align:start position:0%
+different fields those are the ones we
+ 
+
+ align:start position:0%
+different fields those are the ones we
+like or um three independent input
+
+ align:start position:0%
+like or um three independent input
+ 
+
+ align:start position:0%
+like or um three independent input
+frequencies or some combination thereof
+
+ align:start position:0%
+frequencies or some combination thereof
+ 
+
+ align:start position:0%
+frequencies or some combination thereof
+okay and in the case of pump probe
+
+ align:start position:0%
+okay and in the case of pump probe
+ 
+
+ align:start position:0%
+okay and in the case of pump probe
+experiments the way we think of this is
+
+ align:start position:0%
+experiments the way we think of this is
+ 
+
+ align:start position:0%
+experiments the way we think of this is
+that this is uh the three variables that
+
+ align:start position:0%
+that this is uh the three variables that
+ 
+
+ align:start position:0%
+that this is uh the three variables that
+we have control over are you know the
+
+ align:start position:0%
+we have control over are you know the
+ 
+
+ align:start position:0%
+we have control over are you know the
+frequency of the pump the frequency of
+
+ align:start position:0%
+frequency of the pump the frequency of
+ 
+
+ align:start position:0%
+frequency of the pump the frequency of
+the probe and probably the time delay
+
+ align:start position:0%
+the probe and probably the time delay
+ 
+
+ align:start position:0%
+the probe and probably the time delay
+between the two
+
+ align:start position:0%
+between the two
+ 
+
+ align:start position:0%
+between the two
+okay so that's that's the first clue
+
+ align:start position:0%
+okay so that's that's the first clue
+ 
+
+ align:start position:0%
+okay so that's that's the first clue
+that you've got a third order
+
+ align:start position:0%
+that you've got a third order
+ 
+
+ align:start position:0%
+that you've got a third order
+experiment okay
+
+ align:start position:0%
+experiment okay
+ 
+
+ align:start position:0%
+experiment okay
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so the the first thing to
+
+ align:start position:0%
+yeah okay so the the first thing to
+ 
+
+ align:start position:0%
+yeah okay so the the first thing to
+recognize is that uh this two beam
+
+ align:start position:0%
+recognize is that uh this two beam
+ 
+
+ align:start position:0%
+recognize is that uh this two beam
+experiment and the change and intensity
+
+ align:start position:0%
+experiment and the change and intensity
+ 
+
+ align:start position:0%
+experiment and the change and intensity
+on that signal detector really can just
+
+ align:start position:0%
+on that signal detector really can just
+ 
+
+ align:start position:0%
+on that signal detector really can just
+be thought of as a coherent third order
+
+ align:start position:0%
+be thought of as a coherent third order
+ 
+
+ align:start position:0%
+be thought of as a coherent third order
+experiment if we go back to
+
+ align:start position:0%
+experiment if we go back to
+ 
+
+ align:start position:0%
+experiment if we go back to
+um you know a standard box geometry here
+
+ align:start position:0%
+um you know a standard box geometry here
+ 
+
+ align:start position:0%
+um you know a standard box geometry here
+and we you know remember we thought of
+
+ align:start position:0%
+and we you know remember we thought of
+ 
+
+ align:start position:0%
+and we you know remember we thought of
+the transient grading as being this pump
+
+ align:start position:0%
+the transient grading as being this pump
+ 
+
+ align:start position:0%
+the transient grading as being this pump
+pair spatially separated and crossed in
+
+ align:start position:0%
+pair spatially separated and crossed in
+ 
+
+ align:start position:0%
+pair spatially separated and crossed in
+the sample and then a probe if you take
+
+ align:start position:0%
+the sample and then a probe if you take
+ 
+
+ align:start position:0%
+the sample and then a probe if you take
+the limit that pulse one and two overlap
+
+ align:start position:0%
+the limit that pulse one and two overlap
+ 
+
+ align:start position:0%
+the limit that pulse one and two overlap
+and that they in fact come from the same
+
+ align:start position:0%
+and that they in fact come from the same
+ 
+
+ align:start position:0%
+and that they in fact come from the same
+field that's just a pump probe
+
+ align:start position:0%
+field that's just a pump probe
+ 
+
+ align:start position:0%
+field that's just a pump probe
+experiment that also means that as
+
+ align:start position:0%
+experiment that also means that as
+ 
+
+ align:start position:0%
+experiment that also means that as
+you're gradually approaching colinearity
+
+ align:start position:0%
+you're gradually approaching colinearity
+ 
+
+ align:start position:0%
+you're gradually approaching colinearity
+here it means that the signal is
+
+ align:start position:0%
+here it means that the signal is
+ 
+
+ align:start position:0%
+here it means that the signal is
+gradually uh becoming colinear with the
+
+ align:start position:0%
+gradually uh becoming colinear with the
+ 
+
+ align:start position:0%
+gradually uh becoming colinear with the
+transmitted probe and so what she really
+
+ align:start position:0%
+transmitted probe and so what she really
+ 
+
+ align:start position:0%
+transmitted probe and so what she really
+observing when you look at the intensity
+
+ align:start position:0%
+observing when you look at the intensity
+ 
+
+ align:start position:0%
+observing when you look at the intensity
+of the transmitted probe is a sum of two
+
+ align:start position:0%
+of the transmitted probe is a sum of two
+ 
+
+ align:start position:0%
+of the transmitted probe is a sum of two
+Fields the transmitted field and the
+
+ align:start position:0%
+Fields the transmitted field and the
+ 
+
+ align:start position:0%
+Fields the transmitted field and the
+generated signal okay and so that um
+
+ align:start position:0%
+generated signal okay and so that um
+ 
+
+ align:start position:0%
+generated signal okay and so that um
+that's sort of the coherent description
+
+ align:start position:0%
+that's sort of the coherent description
+ 
+
+ align:start position:0%
+that's sort of the coherent description
+of a pump probe experiment and so then
+
+ align:start position:0%
+of a pump probe experiment and so then
+ 
+
+ align:start position:0%
+of a pump probe experiment and so then
+you know you can start talking about
+
+ align:start position:0%
+you know you can start talking about
+ 
+
+ align:start position:0%
+you know you can start talking about
+okay what is the change of intensity
+
+ align:start position:0%
+okay what is the change of intensity
+ 
+
+ align:start position:0%
+okay what is the change of intensity
+that I see when I add the pump
+
+ align:start position:0%
+that I see when I add the pump
+ 
+
+ align:start position:0%
+that I see when I add the pump
+beam
+
+ align:start position:0%
+beam
+ 
+
+ align:start position:0%
+beam
+um as a function of this delay and it uh
+
+ align:start position:0%
+um as a function of this delay and it uh
+ 
+
+ align:start position:0%
+um as a function of this delay and it uh
+is basically going to involve you know
+
+ align:start position:0%
+is basically going to involve you know
+ 
+
+ align:start position:0%
+is basically going to involve you know
+what is the
+
+ align:start position:0%
+what is the
+ 
+
+ align:start position:0%
+what is the
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+um with the pump there why it's the
+
+ align:start position:0%
+um with the pump there why it's the
+ 
+
+ align:start position:0%
+um with the pump there why it's the
+intensity without the pump there okay do
+
+ align:start position:0%
+intensity without the pump there okay do
+ 
+
+ align:start position:0%
+intensity without the pump there okay do
+you had a
+
+ align:start position:0%
+you had a
+ 
+
+ align:start position:0%
+you had a
+question I just want to clarify some
+
+ align:start position:0%
+question I just want to clarify some
+ 
+
+ align:start position:0%
+question I just want to clarify some
+language in mind what you just described
+
+ align:start position:0%
+language in mind what you just described
+ 
+
+ align:start position:0%
+language in mind what you just described
+is this the same as saying that pump
+
+ align:start position:0%
+is this the same as saying that pump
+ 
+
+ align:start position:0%
+is this the same as saying that pump
+probe is always heter just yes exactly
+
+ align:start position:0%
+probe is always heter just yes exactly
+ 
+
+ align:start position:0%
+probe is always heter just yes exactly
+it's intrinsically heterodon that's the
+
+ align:start position:0%
+it's intrinsically heterodon that's the
+ 
+
+ align:start position:0%
+it's intrinsically heterodon that's the
+word we use for yeah so that that's sort
+
+ align:start position:0%
+word we use for yeah so that that's sort
+ 
+
+ align:start position:0%
+word we use for yeah so that that's sort
+of what I want to show here is that that
+
+ align:start position:0%
+of what I want to show here is that that
+ 
+
+ align:start position:0%
+of what I want to show here is that that
+um that it is uh you're not actually
+
+ align:start position:0%
+um that it is uh you're not actually
+ 
+
+ align:start position:0%
+um that it is uh you're not actually
+measuring a technique you're you're not
+
+ align:start position:0%
+measuring a technique you're you're not
+ 
+
+ align:start position:0%
+measuring a technique you're you're not
+measuring an intensity actually but
+
+ align:start position:0%
+measuring an intensity actually but
+ 
+
+ align:start position:0%
+measuring an intensity actually but
+you're really measuring something
+
+ align:start position:0%
+you're really measuring something
+ 
+
+ align:start position:0%
+you're really measuring something
+directly proportional to the
+
+ align:start position:0%
+directly proportional to the
+ 
+
+ align:start position:0%
+directly proportional to the
+polarization in the response okay so if
+
+ align:start position:0%
+polarization in the response okay so if
+ 
+
+ align:start position:0%
+polarization in the response okay so if
+you think about this a little bit the
+
+ align:start position:0%
+you think about this a little bit the
+ 
+
+ align:start position:0%
+you think about this a little bit the
+intensity with the pump there is going
+
+ align:start position:0%
+intensity with the pump there is going
+ 
+
+ align:start position:0%
+intensity with the pump there is going
+to look something like the um intensity
+
+ align:start position:0%
+to look something like the um intensity
+ 
+
+ align:start position:0%
+to look something like the um intensity
+of the transmitted pump light and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry the the the field of the pump
+
+ align:start position:0%
+I'm sorry the the the field of the pump
+ 
+
+ align:start position:0%
+I'm sorry the the the field of the pump
+plus the signal and of course the
+
+ align:start position:0%
+plus the signal and of course the
+ 
+
+ align:start position:0%
+plus the signal and of course the
+intensity is going to go as a modulus
+
+ align:start position:0%
+intensity is going to go as a modulus
+ 
+
+ align:start position:0%
+intensity is going to go as a modulus
+squared and then you're going to
+
+ align:start position:0%
+squared and then you're going to
+ 
+
+ align:start position:0%
+squared and then you're going to
+subtract away just
+
+ align:start position:0%
+subtract away just
+ 
+
+ align:start position:0%
+subtract away just
+the um intensity of the probe beam
+
+ align:start position:0%
+the um intensity of the probe beam
+ 
+
+ align:start position:0%
+the um intensity of the probe beam
+itself without the pump so this
+
+ align:start position:0%
+itself without the pump so this
+ 
+
+ align:start position:0%
+itself without the pump so this
+is oh I'm sorry I'm getting this wrong
+
+ align:start position:0%
+is oh I'm sorry I'm getting this wrong
+ 
+
+ align:start position:0%
+is oh I'm sorry I'm getting this wrong
+intensity of the probe beam
+
+ align:start position:0%
+intensity of the probe beam
+ 
+
+ align:start position:0%
+intensity of the probe beam
+transmitted subtract that okay so
+
+ align:start position:0%
+transmitted subtract that okay so
+ 
+
+ align:start position:0%
+transmitted subtract that okay so
+technically this is what your measure
+
+ align:start position:0%
+technically this is what your measure
+ 
+
+ align:start position:0%
+technically this is what your measure
+meur in okay and so you're typically
+
+ align:start position:0%
+meur in okay and so you're typically
+ 
+
+ align:start position:0%
+meur in okay and so you're typically
+working in a regime where this change of
+
+ align:start position:0%
+working in a regime where this change of
+ 
+
+ align:start position:0%
+working in a regime where this change of
+intensity is small compared to the uh
+
+ align:start position:0%
+intensity is small compared to the uh
+ 
+
+ align:start position:0%
+intensity is small compared to the uh
+intensity of the pump probe itself and
+
+ align:start position:0%
+intensity of the pump probe itself and
+ 
+
+ align:start position:0%
+intensity of the pump probe itself and
+so what you're saying by that is that
+
+ align:start position:0%
+so what you're saying by that is that
+ 
+
+ align:start position:0%
+so what you're saying by that is that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+magnitude of the probe uh the field is
+
+ align:start position:0%
+magnitude of the probe uh the field is
+ 
+
+ align:start position:0%
+magnitude of the probe uh the field is
+going to be much
+
+ align:start position:0%
+going to be much
+ 
+
+ align:start position:0%
+going to be much
+greater and that of the
+
+ align:start position:0%
+greater and that of the
+ 
+
+ align:start position:0%
+greater and that of the
+signal okay oops and confusing things
+
+ align:start position:0%
+signal okay oops and confusing things
+ 
+
+ align:start position:0%
+signal okay oops and confusing things
+here and So based on that we can expand
+
+ align:start position:0%
+here and So based on that we can expand
+ 
+
+ align:start position:0%
+here and So based on that we can expand
+this out you can see what happens is
+
+ align:start position:0%
+this out you can see what happens is
+ 
+
+ align:start position:0%
+this out you can see what happens is
+sort of the biggest term the leading
+
+ align:start position:0%
+sort of the biggest term the leading
+ 
+
+ align:start position:0%
+sort of the biggest term the leading
+term which is uh the intensity of the
+
+ align:start position:0%
+term which is uh the intensity of the
+ 
+
+ align:start position:0%
+term which is uh the intensity of the
+probe here and here those subtract away
+
+ align:start position:0%
+probe here and here those subtract away
+ 
+
+ align:start position:0%
+probe here and here those subtract away
+um the square signal term we're going to
+
+ align:start position:0%
+um the square signal term we're going to
+ 
+
+ align:start position:0%
+um the square signal term we're going to
+ignore that just because it's small
+
+ align:start position:0%
+ignore that just because it's small
+ 
+
+ align:start position:0%
+ignore that just because it's small
+compared to the Cross term and the cross
+
+ align:start position:0%
+compared to the Cross term and the cross
+ 
+
+ align:start position:0%
+compared to the Cross term and the cross
+term um you know looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so this is just the real part I
+
+ align:start position:0%
+okay and so this is just the real part I
+ 
+
+ align:start position:0%
+okay and so this is just the real part I
+by the way I've left out all the
+
+ align:start position:0%
+by the way I've left out all the
+ 
+
+ align:start position:0%
+by the way I've left out all the
+proportionality factors here this is
+
+ align:start position:0%
+proportionality factors here this is
+ 
+
+ align:start position:0%
+proportionality factors here this is
+just the real part of
+
+ align:start position:0%
+just the real part of
+ 
+
+ align:start position:0%
+just the real part of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um probe times the
+
+ align:start position:0%
+um probe times the
+ 
+
+ align:start position:0%
+um probe times the
+signal okay and now if you look at which
+
+ align:start position:0%
+signal okay and now if you look at which
+ 
+
+ align:start position:0%
+signal okay and now if you look at which
+of those quantities are dependent on
+
+ align:start position:0%
+of those quantities are dependent on
+ 
+
+ align:start position:0%
+of those quantities are dependent on
+this time delay over here here well this
+
+ align:start position:0%
+this time delay over here here well this
+ 
+
+ align:start position:0%
+this time delay over here here well this
+this is just a constant and so you
+
+ align:start position:0%
+this is just a constant and so you
+ 
+
+ align:start position:0%
+this is just a constant and so you
+really have something linearly
+
+ align:start position:0%
+really have something linearly
+ 
+
+ align:start position:0%
+really have something linearly
+proportional this is the function of the
+
+ align:start position:0%
+proportional this is the function of the
+ 
+
+ align:start position:0%
+proportional this is the function of the
+time delay you really have a that the
+
+ align:start position:0%
+time delay you really have a that the
+ 
+
+ align:start position:0%
+time delay you really have a that the
+change in intensity is linearly
+
+ align:start position:0%
+change in intensity is linearly
+ 
+
+ align:start position:0%
+change in intensity is linearly
+proportional to the nonlinear signal
+
+ align:start position:0%
+proportional to the nonlinear signal
+ 
+
+ align:start position:0%
+proportional to the nonlinear signal
+okay and uh just remembering
+
+ align:start position:0%
+okay and uh just remembering
+ 
+
+ align:start position:0%
+okay and uh just remembering
+that the uh signal had a pi over 2 phase
+
+ align:start position:0%
+that the uh signal had a pi over 2 phase
+ 
+
+ align:start position:0%
+that the uh signal had a pi over 2 phase
+shift relative to the nonlinear
+
+ align:start position:0%
+shift relative to the nonlinear
+ 
+
+ align:start position:0%
+shift relative to the nonlinear
+polarization
+
+ align:start position:0%
+polarization
+ 
+
+ align:start position:0%
+polarization
+and also remembering that for our
+
+ align:start position:0%
+and also remembering that for our
+ 
+
+ align:start position:0%
+and also remembering that for our
+purposes that the nonlinear polarization
+
+ align:start position:0%
+purposes that the nonlinear polarization
+ 
+
+ align:start position:0%
+purposes that the nonlinear polarization
+is proportional to the response function
+
+ align:start position:0%
+is proportional to the response function
+ 
+
+ align:start position:0%
+is proportional to the response function
+what we are really measuring is um the
+
+ align:start position:0%
+what we are really measuring is um the
+ 
+
+ align:start position:0%
+what we are really measuring is um the
+imaginary part of the product of the
+
+ align:start position:0%
+imaginary part of the product of the
+ 
+
+ align:start position:0%
+imaginary part of the product of the
+probe and Signal um probe field and uh
+
+ align:start position:0%
+probe and Signal um probe field and uh
+ 
+
+ align:start position:0%
+probe and Signal um probe field and uh
+signal polarization or or nonlinear
+
+ align:start position:0%
+signal polarization or or nonlinear
+ 
+
+ align:start position:0%
+signal polarization or or nonlinear
+response
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay which um which is sort of what we
+
+ align:start position:0%
+okay which um which is sort of what we
+ 
+
+ align:start position:0%
+okay which um which is sort of what we
+expected right uh you would think of
+
+ align:start position:0%
+expected right uh you would think of
+ 
+
+ align:start position:0%
+expected right uh you would think of
+this experiment as transient absorption
+
+ align:start position:0%
+this experiment as transient absorption
+ 
+
+ align:start position:0%
+this experiment as transient absorption
+how does the you know how is the
+
+ align:start position:0%
+how does the you know how is the
+ 
+
+ align:start position:0%
+how does the you know how is the
+absorption of the sample modulated by
+
+ align:start position:0%
+absorption of the sample modulated by
+ 
+
+ align:start position:0%
+absorption of the sample modulated by
+the pump beam right and that's just what
+
+ align:start position:0%
+the pump beam right and that's just what
+ 
+
+ align:start position:0%
+the pump beam right and that's just what
+we're looking at here the imaginary part
+
+ align:start position:0%
+we're looking at here the imaginary part
+ 
+
+ align:start position:0%
+we're looking at here the imaginary part
+of the polarization the absorptive
+
+ align:start position:0%
+of the polarization the absorptive
+ 
+
+ align:start position:0%
+of the polarization the absorptive
+part okay so it's just like you said
+
+ align:start position:0%
+part okay so it's just like you said
+ 
+
+ align:start position:0%
+part okay so it's just like you said
+that you can think of this as the
+
+ align:start position:0%
+that you can think of this as the
+ 
+
+ align:start position:0%
+that you can think of this as the
+transmitted field being aerodine a phase
+
+ align:start position:0%
+transmitted field being aerodine a phase
+ 
+
+ align:start position:0%
+transmitted field being aerodine a phase
+locked heterodon field that's that
+
+ align:start position:0%
+locked heterodon field that's that
+ 
+
+ align:start position:0%
+locked heterodon field that's that
+you're beating against the system and
+
+ align:start position:0%
+you're beating against the system and
+ 
+
+ align:start position:0%
+you're beating against the system and
+uh you know for an incoherent experiment
+
+ align:start position:0%
+uh you know for an incoherent experiment
+ 
+
+ align:start position:0%
+uh you know for an incoherent experiment
+you're going through an awful lot of
+
+ align:start position:0%
+you're going through an awful lot of
+ 
+
+ align:start position:0%
+you're going through an awful lot of
+math to describe that but it makes a lot
+
+ align:start position:0%
+math to describe that but it makes a lot
+ 
+
+ align:start position:0%
+math to describe that but it makes a lot
+of sense when you start to look at wave
+
+ align:start position:0%
+of sense when you start to look at wave
+ 
+
+ align:start position:0%
+of sense when you start to look at wave
+packet Dynamics on on pump probe
+
+ align:start position:0%
+packet Dynamics on on pump probe
+ 
+
+ align:start position:0%
+packet Dynamics on on pump probe
+experiments okay any any questions on
+
+ align:start position:0%
+experiments okay any any questions on
+ 
+
+ align:start position:0%
+experiments okay any any questions on
+that okay um
+
+ align:start position:0%
+that okay um
+ 
+
+ align:start position:0%
+that okay um
+so so just uh let's
+
+ align:start position:0%
+so so just uh let's
+ 
+
+ align:start position:0%
+so so just uh let's
+see um so as you might imagine let me
+
+ align:start position:0%
+see um so as you might imagine let me
+ 
+
+ align:start position:0%
+see um so as you might imagine let me
+just go just for purposes of making this
+
+ align:start position:0%
+just go just for purposes of making this
+ 
+
+ align:start position:0%
+just go just for purposes of making this
+easy let's see
+
+ align:start position:0%
+easy let's see
+ 
+
+ align:start position:0%
+easy let's see
+um as you might imagine any sort of
+
+ align:start position:0%
+um as you might imagine any sort of
+ 
+
+ align:start position:0%
+um as you might imagine any sort of
+relaxation process that contributes to
+
+ align:start position:0%
+relaxation process that contributes to
+ 
+
+ align:start position:0%
+relaxation process that contributes to
+the absorptive the imaginary part of the
+
+ align:start position:0%
+the absorptive the imaginary part of the
+ 
+
+ align:start position:0%
+the absorptive the imaginary part of the
+polarization the absorption change in
+
+ align:start position:0%
+polarization the absorption change in
+ 
+
+ align:start position:0%
+polarization the absorption change in
+the sample as a function at time delay
+
+ align:start position:0%
+the sample as a function at time delay
+ 
+
+ align:start position:0%
+the sample as a function at time delay
+you're going to see it and um now one
+
+ align:start position:0%
+you're going to see it and um now one
+ 
+
+ align:start position:0%
+you're going to see it and um now one
+other thing to point out is you know
+
+ align:start position:0%
+other thing to point out is you know
+ 
+
+ align:start position:0%
+other thing to point out is you know
+when you write out all of the possible
+
+ align:start position:0%
+when you write out all of the possible
+ 
+
+ align:start position:0%
+when you write out all of the possible
+dipole interaction processes that can
+
+ align:start position:0%
+dipole interaction processes that can
+ 
+
+ align:start position:0%
+dipole interaction processes that can
+contribute in that signal Direction it's
+
+ align:start position:0%
+contribute in that signal Direction it's
+ 
+
+ align:start position:0%
+contribute in that signal Direction it's
+all four of the possible correlation
+
+ align:start position:0%
+all four of the possible correlation
+ 
+
+ align:start position:0%
+all four of the possible correlation
+functions in that nonlinear
+
+ align:start position:0%
+functions in that nonlinear
+ 
+
+ align:start position:0%
+functions in that nonlinear
+response and so what uh you
+
+ align:start position:0%
+response and so what uh you
+ 
+
+ align:start position:0%
+response and so what uh you
+will um see is a number of different
+
+ align:start position:0%
+will um see is a number of different
+ 
+
+ align:start position:0%
+will um see is a number of different
+contributions probably the one that
+
+ align:start position:0%
+contributions probably the one that
+ 
+
+ align:start position:0%
+contributions probably the one that
+contributes to you know everyone that
+
+ align:start position:0%
+contributes to you know everyone that
+ 
+
+ align:start position:0%
+contributes to you know everyone that
+does this experiment is that Delta I
+
+ align:start position:0%
+does this experiment is that Delta I
+ 
+
+ align:start position:0%
+does this experiment is that Delta I
+will look at the um population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relaxation um in in the uh ground and
+
+ align:start position:0%
+relaxation um in in the uh ground and
+ 
+
+ align:start position:0%
+relaxation um in in the uh ground and
+the excited States that you are coupling
+
+ align:start position:0%
+the excited States that you are coupling
+ 
+
+ align:start position:0%
+the excited States that you are coupling
+together so if you imagine you do these
+
+ align:start position:0%
+together so if you imagine you do these
+ 
+
+ align:start position:0%
+together so if you imagine you do these
+all with this um with the same color
+
+ align:start position:0%
+all with this um with the same color
+ 
+
+ align:start position:0%
+all with this um with the same color
+experiment now what you're doing is um
+
+ align:start position:0%
+experiment now what you're doing is um
+ 
+
+ align:start position:0%
+experiment now what you're doing is um
+call this one a and this one B you will
+
+ align:start position:0%
+call this one a and this one B you will
+ 
+
+ align:start position:0%
+call this one a and this one B you will
+find that there are processes that tell
+
+ align:start position:0%
+find that there are processes that tell
+ 
+
+ align:start position:0%
+find that there are processes that tell
+you about how fast does population relax
+
+ align:start position:0%
+you about how fast does population relax
+ 
+
+ align:start position:0%
+you about how fast does population relax
+out of the excited state and furthermore
+
+ align:start position:0%
+out of the excited state and furthermore
+ 
+
+ align:start position:0%
+out of the excited state and furthermore
+how does population return to the ground
+
+ align:start position:0%
+how does population return to the ground
+ 
+
+ align:start position:0%
+how does population return to the ground
+state you can think of that as the pump
+
+ align:start position:0%
+state you can think of that as the pump
+ 
+
+ align:start position:0%
+state you can think of that as the pump
+field not only creates an excited state
+
+ align:start position:0%
+field not only creates an excited state
+ 
+
+ align:start position:0%
+field not only creates an excited state
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+but it also creates a bleach a hole in
+
+ align:start position:0%
+but it also creates a bleach a hole in
+ 
+
+ align:start position:0%
+but it also creates a bleach a hole in
+the ground state and you watch both of
+
+ align:start position:0%
+the ground state and you watch both of
+ 
+
+ align:start position:0%
+the ground state and you watch both of
+those things in the limit that you
+
+ align:start position:0%
+those things in the limit that you
+ 
+
+ align:start position:0%
+those things in the limit that you
+return from the excited state to the
+
+ align:start position:0%
+return from the excited state to the
+ 
+
+ align:start position:0%
+return from the excited state to the
+ground state this becomes a simple simp
+
+ align:start position:0%
+ground state this becomes a simple simp
+ 
+
+ align:start position:0%
+ground state this becomes a simple simp
+exponential but um could be more
+
+ align:start position:0%
+exponential but um could be more
+ 
+
+ align:start position:0%
+exponential but um could be more
+complicated than that
+
+ align:start position:0%
+complicated than that
+ 
+
+ align:start position:0%
+complicated than that
+okay it's coupling through the fat
+
+ align:start position:0%
+okay it's coupling through the fat
+ 
+
+ align:start position:0%
+okay it's coupling through the fat
+States well you can imagine yeah right
+
+ align:start position:0%
+States well you can imagine yeah right
+ 
+
+ align:start position:0%
+States well you can imagine yeah right
+if you mean by dark States here right so
+
+ align:start position:0%
+if you mean by dark States here right so
+ 
+
+ align:start position:0%
+if you mean by dark States here right so
+you can imagine say you have an
+
+ align:start position:0%
+you can imagine say you have an
+ 
+
+ align:start position:0%
+you can imagine say you have an
+intermediate state that you're relax
+
+ align:start position:0%
+intermediate state that you're relax
+ 
+
+ align:start position:0%
+intermediate state that you're relax
+through on your way down you know then
+
+ align:start position:0%
+through on your way down you know then
+ 
+
+ align:start position:0%
+through on your way down you know then
+the rate of leaving this state and the
+
+ align:start position:0%
+the rate of leaving this state and the
+ 
+
+ align:start position:0%
+the rate of leaving this state and the
+rate of arriving here is going to be
+
+ align:start position:0%
+rate of arriving here is going to be
+ 
+
+ align:start position:0%
+rate of arriving here is going to be
+different so seeing by exponential
+
+ align:start position:0%
+different so seeing by exponential
+ 
+
+ align:start position:0%
+different so seeing by exponential
+Behavior shouldn't be a surprise
+
+ align:start position:0%
+Behavior shouldn't be a surprise
+ 
+
+ align:start position:0%
+Behavior shouldn't be a surprise
+right okay so uh now this way of
+
+ align:start position:0%
+right okay so uh now this way of
+ 
+
+ align:start position:0%
+right okay so uh now this way of
+thinking about it really applies to
+
+ align:start position:0%
+thinking about it really applies to
+ 
+
+ align:start position:0%
+thinking about it really applies to
+experiments that look at wave packet
+
+ align:start position:0%
+experiments that look at wave packet
+ 
+
+ align:start position:0%
+experiments that look at wave packet
+propagation whether you're talking about
+
+ align:start position:0%
+propagation whether you're talking about
+ 
+
+ align:start position:0%
+propagation whether you're talking about
+you know electronic or vibrational
+
+ align:start position:0%
+you know electronic or vibrational
+ 
+
+ align:start position:0%
+you know electronic or vibrational
+spectroscopies um basic idea is you know
+
+ align:start position:0%
+spectroscopies um basic idea is you know
+ 
+
+ align:start position:0%
+spectroscopies um basic idea is you know
+it's pretty common that you see
+
+ align:start position:0%
+it's pretty common that you see
+ 
+
+ align:start position:0%
+it's pretty common that you see
+experiments that describe starting in
+
+ align:start position:0%
+experiments that describe starting in
+ 
+
+ align:start position:0%
+experiments that describe starting in
+some you know electronic
+
+ align:start position:0%
+some you know electronic
+ 
+
+ align:start position:0%
+some you know electronic
+State uh
+
+ align:start position:0%
+State uh
+ 
+
+ align:start position:0%
+State uh
+propagating the system then on an
+
+ align:start position:0%
+propagating the system then on an
+ 
+
+ align:start position:0%
+propagating the system then on an
+excited electronic surface and you know
+
+ align:start position:0%
+excited electronic surface and you know
+ 
+
+ align:start position:0%
+excited electronic surface and you know
+people probe this all over if if you you
+
+ align:start position:0%
+people probe this all over if if you you
+ 
+
+ align:start position:0%
+people probe this all over if if you you
+know really are interested in it
+
+ align:start position:0%
+know really are interested in it
+ 
+
+ align:start position:0%
+know really are interested in it
+studying the system as a function of you
+
+ align:start position:0%
+studying the system as a function of you
+ 
+
+ align:start position:0%
+studying the system as a function of you
+know sort of the nuclear coordinates of
+
+ align:start position:0%
+know sort of the nuclear coordinates of
+ 
+
+ align:start position:0%
+know sort of the nuclear coordinates of
+the uh system say in a reactive one you
+
+ align:start position:0%
+the uh system say in a reactive one you
+ 
+
+ align:start position:0%
+the uh system say in a reactive one you
+know you might imagine choosing the
+
+ align:start position:0%
+know you might imagine choosing the
+ 
+
+ align:start position:0%
+know you might imagine choosing the
+probe
+
+ align:start position:0%
+probe
+ 
+
+ align:start position:0%
+probe
+uh the pump and the probe frequency
+
+ align:start position:0%
+uh the pump and the probe frequency
+ 
+
+ align:start position:0%
+uh the pump and the probe frequency
+don't have to be the same at all
+
+ align:start position:0%
+don't have to be the same at all
+ 
+
+ align:start position:0%
+don't have to be the same at all
+right um they are chosen to match
+
+ align:start position:0%
+right um they are chosen to match
+ 
+
+ align:start position:0%
+right um they are chosen to match
+certain energy gaps in the uh um you
+
+ align:start position:0%
+certain energy gaps in the uh um you
+ 
+
+ align:start position:0%
+certain energy gaps in the uh um you
+know along this potential and You by
+
+ align:start position:0%
+know along this potential and You by
+ 
+
+ align:start position:0%
+know along this potential and You by
+tuning your prob beam you can imagine uh
+
+ align:start position:0%
+tuning your prob beam you can imagine uh
+ 
+
+ align:start position:0%
+tuning your prob beam you can imagine uh
+pulling out um the you know wave packet
+
+ align:start position:0%
+pulling out um the you know wave packet
+ 
+
+ align:start position:0%
+pulling out um the you know wave packet
+Dynamics um as a function of this
+
+ align:start position:0%
+Dynamics um as a function of this
+ 
+
+ align:start position:0%
+Dynamics um as a function of this
+coordinate Q okay so the pump and the
+
+ align:start position:0%
+coordinate Q okay so the pump and the
+ 
+
+ align:start position:0%
+coordinate Q okay so the pump and the
+probe are just independent variables and
+
+ align:start position:0%
+probe are just independent variables and
+ 
+
+ align:start position:0%
+probe are just independent variables and
+you'll notice going back to the wave
+
+ align:start position:0%
+you'll notice going back to the wave
+ 
+
+ align:start position:0%
+you'll notice going back to the wave
+Vector matching that that's the beauty
+
+ align:start position:0%
+Vector matching that that's the beauty
+ 
+
+ align:start position:0%
+Vector matching that that's the beauty
+of a pump probe in our language is that
+
+ align:start position:0%
+of a pump probe in our language is that
+ 
+
+ align:start position:0%
+of a pump probe in our language is that
+it's always wave Vector matched just by
+
+ align:start position:0%
+it's always wave Vector matched just by
+ 
+
+ align:start position:0%
+it's always wave Vector matched just by
+by definition how how it's set up okay
+
+ align:start position:0%
+by definition how how it's set up okay
+ 
+
+ align:start position:0%
+by definition how how it's set up okay
+so um in the diagrammatic perturbation
+
+ align:start position:0%
+so um in the diagrammatic perturbation
+ 
+
+ align:start position:0%
+so um in the diagrammatic perturbation
+Theory language what we're talking about
+
+ align:start position:0%
+Theory language what we're talking about
+ 
+
+ align:start position:0%
+Theory language what we're talking about
+is uh these sorts of diagrams so let me
+
+ align:start position:0%
+is uh these sorts of diagrams so let me
+ 
+
+ align:start position:0%
+is uh these sorts of diagrams so let me
+go back for a
+
+ align:start position:0%
+go back for a
+ 
+
+ align:start position:0%
+go back for a
+moment I I showed you that these are
+
+ align:start position:0%
+moment I I showed you that these are
+ 
+
+ align:start position:0%
+moment I I showed you that these are
+sort of the fundamental
+
+ align:start position:0%
+sort of the fundamental
+ 
+
+ align:start position:0%
+sort of the fundamental
+um four fundamental interaction
+
+ align:start position:0%
+um four fundamental interaction
+ 
+
+ align:start position:0%
+um four fundamental interaction
+processes for light coupling um to a
+
+ align:start position:0%
+processes for light coupling um to a
+ 
+
+ align:start position:0%
+processes for light coupling um to a
+twole uh system um but in you know in
+
+ align:start position:0%
+twole uh system um but in you know in
+ 
+
+ align:start position:0%
+twole uh system um but in you know in
+general you can have up to four levels
+
+ align:start position:0%
+general you can have up to four levels
+ 
+
+ align:start position:0%
+general you can have up to four levels
+that are coupled in a third
+
+ align:start position:0%
+that are coupled in a third
+ 
+
+ align:start position:0%
+that are coupled in a third
+order um experiment and this is just
+
+ align:start position:0%
+order um experiment and this is just
+ 
+
+ align:start position:0%
+order um experiment and this is just
+sort of generalizing those diagrams to
+
+ align:start position:0%
+sort of generalizing those diagrams to
+ 
+
+ align:start position:0%
+sort of generalizing those diagrams to
+four levels that I've arranged in a
+
+ align:start position:0%
+four levels that I've arranged in a
+ 
+
+ align:start position:0%
+four levels that I've arranged in a
+particular way just because they
+
+ align:start position:0%
+particular way just because they
+ 
+
+ align:start position:0%
+particular way just because they
+correspond to this wave packet type of
+
+ align:start position:0%
+correspond to this wave packet type of
+ 
+
+ align:start position:0%
+correspond to this wave packet type of
+process we have some
+
+ align:start position:0%
+process we have some
+ 
+
+ align:start position:0%
+process we have some
+uh processes that create wave packets in
+
+ align:start position:0%
+uh processes that create wave packets in
+ 
+
+ align:start position:0%
+uh processes that create wave packets in
+the you can see here is a difference
+
+ align:start position:0%
+the you can see here is a difference
+ 
+
+ align:start position:0%
+the you can see here is a difference
+frequency creates a coherence a wave
+
+ align:start position:0%
+frequency creates a coherence a wave
+ 
+
+ align:start position:0%
+frequency creates a coherence a wave
+packet in the ground electronic state
+
+ align:start position:0%
+packet in the ground electronic state
+ 
+
+ align:start position:0%
+packet in the ground electronic state
+where you whereas you've got others that
+
+ align:start position:0%
+where you whereas you've got others that
+ 
+
+ align:start position:0%
+where you whereas you've got others that
+create Co a wave packet on the excited
+
+ align:start position:0%
+create Co a wave packet on the excited
+ 
+
+ align:start position:0%
+create Co a wave packet on the excited
+state both of these then propagate
+
+ align:start position:0%
+state both of these then propagate
+ 
+
+ align:start position:0%
+state both of these then propagate
+freely during the second T2 the second
+
+ align:start position:0%
+freely during the second T2 the second
+ 
+
+ align:start position:0%
+freely during the second T2 the second
+time variable one on the excited state
+
+ align:start position:0%
+time variable one on the excited state
+ 
+
+ align:start position:0%
+time variable one on the excited state
+one on the ground state and then you
+
+ align:start position:0%
+one on the ground state and then you
+ 
+
+ align:start position:0%
+one on the ground state and then you
+probe it and of course you know you can
+
+ align:start position:0%
+probe it and of course you know you can
+ 
+
+ align:start position:0%
+probe it and of course you know you can
+choose where you probe it and how you
+
+ align:start position:0%
+choose where you probe it and how you
+ 
+
+ align:start position:0%
+choose where you probe it and how you
+probe it okay so th um
+
+ align:start position:0%
+probe it okay so th um
+ 
+
+ align:start position:0%
+probe it okay so th um
+so those
+
+ align:start position:0%
+so those
+ 
+
+ align:start position:0%
+so those
+are uh the processes that you know I was
+
+ align:start position:0%
+are uh the processes that you know I was
+ 
+
+ align:start position:0%
+are uh the processes that you know I was
+uh picturing here that
+
+ align:start position:0%
+uh picturing here that
+ 
+
+ align:start position:0%
+uh picturing here that
+um those uh sorts of diagrams are sort
+
+ align:start position:0%
+um those uh sorts of diagrams are sort
+ 
+
+ align:start position:0%
+um those uh sorts of diagrams are sort
+of the mathematical way of describing
+
+ align:start position:0%
+of the mathematical way of describing
+ 
+
+ align:start position:0%
+of the mathematical way of describing
+why one would see Quantum beats for
+
+ align:start position:0%
+why one would see Quantum beats for
+ 
+
+ align:start position:0%
+why one would see Quantum beats for
+instance in a
+
+ align:start position:0%
+instance in a
+ 
+
+ align:start position:0%
+instance in a
+um either a transient absorption or even
+
+ align:start position:0%
+um either a transient absorption or even
+ 
+
+ align:start position:0%
+um either a transient absorption or even
+an incoherent uh fluoresence experiment
+
+ align:start position:0%
+an incoherent uh fluoresence experiment
+ 
+
+ align:start position:0%
+an incoherent uh fluoresence experiment
+with two you know with two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields by
+
+ align:start position:0%
+Fields by
+ 
+
+ align:start position:0%
+Fields by
+by the way one one important thing I
+
+ align:start position:0%
+by the way one one important thing I
+ 
+
+ align:start position:0%
+by the way one one important thing I
+don't want you to carry away from this
+
+ align:start position:0%
+don't want you to carry away from this
+ 
+
+ align:start position:0%
+don't want you to carry away from this
+is that there there is no simple
+
+ align:start position:0%
+is that there there is no simple
+ 
+
+ align:start position:0%
+is that there there is no simple
+connection between these types
+
+ align:start position:0%
+connection between these types
+ 
+
+ align:start position:0%
+connection between these types
+of diagrams that are really commonly
+
+ align:start position:0%
+of diagrams that are really commonly
+ 
+
+ align:start position:0%
+of diagrams that are really commonly
+drawn and the fan diagrams these are not
+
+ align:start position:0%
+drawn and the fan diagrams these are not
+ 
+
+ align:start position:0%
+drawn and the fan diagrams these are not
+the same thing it is true that there
+
+ align:start position:0%
+the same thing it is true that there
+ 
+
+ align:start position:0%
+the same thing it is true that there
+happens to be know mapping onto the
+
+ align:start position:0%
+happens to be know mapping onto the
+ 
+
+ align:start position:0%
+happens to be know mapping onto the
+same uh energy axis if you're drawing
+
+ align:start position:0%
+same uh energy axis if you're drawing
+ 
+
+ align:start position:0%
+same uh energy axis if you're drawing
+lad diagrams but uh find and lad
+
+ align:start position:0%
+lad diagrams but uh find and lad
+ 
+
+ align:start position:0%
+lad diagrams but uh find and lad
+diagrams propagate the density Matrix
+
+ align:start position:0%
+diagrams propagate the density Matrix
+ 
+
+ align:start position:0%
+diagrams propagate the density Matrix
+and this is energies is a function of
+
+ align:start position:0%
+and this is energies is a function of
+ 
+
+ align:start position:0%
+and this is energies is a function of
+nuclear coordinate
+
+ align:start position:0%
+nuclear coordinate
+ 
+
+ align:start position:0%
+nuclear coordinate
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so that what I'm implying by that is
+
+ align:start position:0%
+so so that what I'm implying by that is
+ 
+
+ align:start position:0%
+so so that what I'm implying by that is
+that when you draw one of these types of
+
+ align:start position:0%
+that when you draw one of these types of
+ 
+
+ align:start position:0%
+that when you draw one of these types of
+processes and and say that you create a
+
+ align:start position:0%
+processes and and say that you create a
+ 
+
+ align:start position:0%
+processes and and say that you create a
+wave packet in a density Matrix language
+
+ align:start position:0%
+wave packet in a density Matrix language
+ 
+
+ align:start position:0%
+wave packet in a density Matrix language
+that is equivalent
+
+ align:start position:0%
+that is equivalent
+ 
+
+ align:start position:0%
+that is equivalent
+to creating a coherent superposition of
+
+ align:start position:0%
+to creating a coherent superposition of
+ 
+
+ align:start position:0%
+to creating a coherent superposition of
+two igen states of the electronic ided
+
+ align:start position:0%
+two igen states of the electronic ided
+ 
+
+ align:start position:0%
+two igen states of the electronic ided
+surface that then propagate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right any any questions on pump
+
+ align:start position:0%
+okay all right any any questions on pump
+ 
+
+ align:start position:0%
+okay all right any any questions on pump
+probes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um sort of in our in our list of things
+
+ align:start position:0%
+um sort of in our in our list of things
+ 
+
+ align:start position:0%
+um sort of in our in our list of things
+let me what I'm hoping to do at some
+
+ align:start position:0%
+let me what I'm hoping to do at some
+ 
+
+ align:start position:0%
+let me what I'm hoping to do at some
+point is actually spend some real time
+
+ align:start position:0%
+point is actually spend some real time
+ 
+
+ align:start position:0%
+point is actually spend some real time
+on Ramen spectroscopies but just uh so
+
+ align:start position:0%
+on Ramen spectroscopies but just uh so
+ 
+
+ align:start position:0%
+on Ramen spectroscopies but just uh so
+that we see it I want to talk a bit
+
+ align:start position:0%
+that we see it I want to talk a bit
+ 
+
+ align:start position:0%
+that we see it I want to talk a bit
+about um car spectroscopy just as an
+
+ align:start position:0%
+about um car spectroscopy just as an
+ 
+
+ align:start position:0%
+about um car spectroscopy just as an
+example of coherent Ramen techniques
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see yeah I have to say I think there's
+
+ align:start position:0%
+see yeah I have to say I think there's
+ 
+
+ align:start position:0%
+see yeah I have to say I think there's
+nothing quite as stunning as going into
+
+ align:start position:0%
+nothing quite as stunning as going into
+ 
+
+ align:start position:0%
+nothing quite as stunning as going into
+a lab that does cars in the visible
+
+ align:start position:0%
+a lab that does cars in the visible
+ 
+
+ align:start position:0%
+a lab that does cars in the visible
+because this is one of these experiments
+
+ align:start position:0%
+because this is one of these experiments
+ 
+
+ align:start position:0%
+because this is one of these experiments
+now which is not a degenerate experiment
+
+ align:start position:0%
+now which is not a degenerate experiment
+ 
+
+ align:start position:0%
+now which is not a degenerate experiment
+where you have multiple colors and
+
+ align:start position:0%
+where you have multiple colors and
+ 
+
+ align:start position:0%
+where you have multiple colors and
+you're specifically trying to take
+
+ align:start position:0%
+you're specifically trying to take
+ 
+
+ align:start position:0%
+you're specifically trying to take
+advantage of difference frequencies in
+
+ align:start position:0%
+advantage of difference frequencies in
+ 
+
+ align:start position:0%
+advantage of difference frequencies in
+the optical range to drive vibrational
+
+ align:start position:0%
+the optical range to drive vibrational
+ 
+
+ align:start position:0%
+the optical range to drive vibrational
+Transitions and you know it it is pretty
+
+ align:start position:0%
+Transitions and you know it it is pretty
+ 
+
+ align:start position:0%
+Transitions and you know it it is pretty
+stunning with people that do three color
+
+ align:start position:0%
+stunning with people that do three color
+ 
+
+ align:start position:0%
+stunning with people that do three color
+cars where really have three tunable
+
+ align:start position:0%
+cars where really have three tunable
+ 
+
+ align:start position:0%
+cars where really have three tunable
+colors incident on the sample Crossing
+
+ align:start position:0%
+colors incident on the sample Crossing
+ 
+
+ align:start position:0%
+colors incident on the sample Crossing
+and you get an enormous array of spots
+
+ align:start position:0%
+and you get an enormous array of spots
+ 
+
+ align:start position:0%
+and you get an enormous array of spots
+in every color you can imagine that
+
+ align:start position:0%
+in every color you can imagine that
+ 
+
+ align:start position:0%
+in every color you can imagine that
+comes out the back of the sample and
+
+ align:start position:0%
+comes out the back of the sample and
+ 
+
+ align:start position:0%
+comes out the back of the sample and
+each one of these encodes some sort of a
+
+ align:start position:0%
+each one of these encodes some sort of a
+ 
+
+ align:start position:0%
+each one of these encodes some sort of a
+different uh coherent vibrational
+
+ align:start position:0%
+different uh coherent vibrational
+ 
+
+ align:start position:0%
+different uh coherent vibrational
+dynamics of the system and cars is
+
+ align:start position:0%
+dynamics of the system and cars is
+ 
+
+ align:start position:0%
+dynamics of the system and cars is
+probably the the one that uh has been
+
+ align:start position:0%
+probably the the one that uh has been
+ 
+
+ align:start position:0%
+probably the the one that uh has been
+around the longest and still is really
+
+ align:start position:0%
+around the longest and still is really
+ 
+
+ align:start position:0%
+around the longest and still is really
+important um so the idea here
+
+ align:start position:0%
+important um so the idea here
+ 
+
+ align:start position:0%
+important um so the idea here
+is you can think of this as a Ramen
+
+ align:start position:0%
+is you can think of this as a Ramen
+ 
+
+ align:start position:0%
+is you can think of this as a Ramen
+transition
+
+ align:start position:0%
+transition
+ 
+
+ align:start position:0%
+transition
+um and now this sort of emphasizes the
+
+ align:start position:0%
+um and now this sort of emphasizes the
+ 
+
+ align:start position:0%
+um and now this sort of emphasizes the
+fact that if you look at our nonlinear
+
+ align:start position:0%
+fact that if you look at our nonlinear
+ 
+
+ align:start position:0%
+fact that if you look at our nonlinear
+response functions um as long as say for
+
+ align:start position:0%
+response functions um as long as say for
+ 
+
+ align:start position:0%
+response functions um as long as say for
+instance your first two fields our time
+
+ align:start position:0%
+instance your first two fields our time
+ 
+
+ align:start position:0%
+instance your first two fields our time
+coincident um you don't actually have to
+
+ align:start position:0%
+coincident um you don't actually have to
+ 
+
+ align:start position:0%
+coincident um you don't actually have to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+resonant with a state um during the time
+
+ align:start position:0%
+resonant with a state um during the time
+ 
+
+ align:start position:0%
+resonant with a state um during the time
+period between the first and second
+
+ align:start position:0%
+period between the first and second
+ 
+
+ align:start position:0%
+period between the first and second
+interaction that uh just by the 4A
+
+ align:start position:0%
+interaction that uh just by the 4A
+ 
+
+ align:start position:0%
+interaction that uh just by the 4A
+transform principle if you remember
+
+ align:start position:0%
+transform principle if you remember
+ 
+
+ align:start position:0%
+transform principle if you remember
+those uh lovely sync functions from 574
+
+ align:start position:0%
+those uh lovely sync functions from 574
+ 
+
+ align:start position:0%
+those uh lovely sync functions from 574
+that uh when time is very short you can
+
+ align:start position:0%
+that uh when time is very short you can
+ 
+
+ align:start position:0%
+that uh when time is very short you can
+be resonant at any frequency you want
+
+ align:start position:0%
+be resonant at any frequency you want
+ 
+
+ align:start position:0%
+be resonant at any frequency you want
+and it's resonance is only a condition
+
+ align:start position:0%
+and it's resonance is only a condition
+ 
+
+ align:start position:0%
+and it's resonance is only a condition
+that happens after several cycles of the
+
+ align:start position:0%
+that happens after several cycles of the
+ 
+
+ align:start position:0%
+that happens after several cycles of the
+field and so this is the language for
+
+ align:start position:0%
+field and so this is the language for
+ 
+
+ align:start position:0%
+field and so this is the language for
+this is virtual States and so what it
+
+ align:start position:0%
+this is virtual States and so what it
+ 
+
+ align:start position:0%
+this is virtual States and so what it
+means is if we take two fields and we
+
+ align:start position:0%
+means is if we take two fields and we
+ 
+
+ align:start position:0%
+means is if we take two fields and we
+are time
+
+ align:start position:0%
+are time
+ 
+
+ align:start position:0%
+are time
+coincident we can um generate
+
+ align:start position:0%
+coincident we can um generate
+ 
+
+ align:start position:0%
+coincident we can um generate
+excitations at difference frequencies so
+
+ align:start position:0%
+excitations at difference frequencies so
+ 
+
+ align:start position:0%
+excitations at difference frequencies so
+we choose two Fields um and in the cars
+
+ align:start position:0%
+we choose two Fields um and in the cars
+ 
+
+ align:start position:0%
+we choose two Fields um and in the cars
+language this would be the pump
+
+ align:start position:0%
+language this would be the pump
+ 
+
+ align:start position:0%
+language this would be the pump
+beam and the Stokes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam and what you do is then we'll call
+
+ align:start position:0%
+beam and what you do is then we'll call
+ 
+
+ align:start position:0%
+beam and what you do is then we'll call
+these say the or what did I call them up
+
+ align:start position:0%
+these say the or what did I call them up
+ 
+
+ align:start position:0%
+these say the or what did I call them up
+here g& e the ground and excited
+
+ align:start position:0%
+here g& e the ground and excited
+ 
+
+ align:start position:0%
+here g& e the ground and excited
+vibrational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State um and it goes through sort of a
+
+ align:start position:0%
+State um and it goes through sort of a
+ 
+
+ align:start position:0%
+State um and it goes through sort of a
+virtual State and so um this is involves
+
+ align:start position:0%
+virtual State and so um this is involves
+ 
+
+ align:start position:0%
+virtual State and so um this is involves
+two transition dipole interactions the F
+
+ align:start position:0%
+two transition dipole interactions the F
+ 
+
+ align:start position:0%
+two transition dipole interactions the F
+so let's see what do we do
+
+ align:start position:0%
+so let's see what do we do
+ 
+
+ align:start position:0%
+so let's see what do we do
+e mu VG mu EG e
+
+ align:start position:0%
+e mu VG mu EG e
+ 
+
+ align:start position:0%
+e mu VG mu EG e
+v I'm okay they occur simultaneously and
+
+ align:start position:0%
+v I'm okay they occur simultaneously and
+ 
+
+ align:start position:0%
+v I'm okay they occur simultaneously and
+now the system is in a coherence and it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propagates
+
+ align:start position:0%
+propagates
+ 
+
+ align:start position:0%
+propagates
+um oscillating with uh time this is to
+
+ align:start position:0%
+um oscillating with uh time this is to
+ 
+
+ align:start position:0%
+um oscillating with uh time this is to
+two um and we can say put some damping
+
+ align:start position:0%
+two um and we can say put some damping
+ 
+
+ align:start position:0%
+two um and we can say put some damping
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+this this vibrational wave package this
+
+ align:start position:0%
+this this vibrational wave package this
+ 
+
+ align:start position:0%
+this this vibrational wave package this
+vibrational coherence propagates with
+
+ align:start position:0%
+vibrational coherence propagates with
+ 
+
+ align:start position:0%
+vibrational coherence propagates with
+time and then we can probe it now in
+
+ align:start position:0%
+time and then we can probe it now in
+ 
+
+ align:start position:0%
+time and then we can probe it now in
+practice people use the same pump beam
+
+ align:start position:0%
+practice people use the same pump beam
+ 
+
+ align:start position:0%
+practice people use the same pump beam
+as also the probing field okay and this
+
+ align:start position:0%
+as also the probing field okay and this
+ 
+
+ align:start position:0%
+as also the probing field okay and this
+leads to an anti- Stoke signal
+
+ align:start position:0%
+leads to an anti- Stoke signal
+ 
+
+ align:start position:0%
+leads to an anti- Stoke signal
+emission um which is at a completely
+
+ align:start position:0%
+emission um which is at a completely
+ 
+
+ align:start position:0%
+emission um which is at a completely
+unique color so now just looking at this
+
+ align:start position:0%
+unique color so now just looking at this
+ 
+
+ align:start position:0%
+unique color so now just looking at this
+process this is Omega pump we can see
+
+ align:start position:0%
+process this is Omega pump we can see
+ 
+
+ align:start position:0%
+process this is Omega pump we can see
+that the signal is going to be plus
+
+ align:start position:0%
+that the signal is going to be plus
+ 
+
+ align:start position:0%
+that the signal is going to be plus
+Omega pump for the first one minus Omega
+
+ align:start position:0%
+Omega pump for the first one minus Omega
+ 
+
+ align:start position:0%
+Omega pump for the first one minus Omega
+Stokes for the second one plus Omega
+
+ align:start position:0%
+Stokes for the second one plus Omega
+ 
+
+ align:start position:0%
+Stokes for the second one plus Omega
+pump for the third one okay that's 2
+
+ align:start position:0%
+pump for the third one okay that's 2
+ 
+
+ align:start position:0%
+pump for the third one okay that's 2
+Omega P minus Omega s so uh typically
+
+ align:start position:0%
+Omega P minus Omega s so uh typically
+ 
+
+ align:start position:0%
+Omega P minus Omega s so uh typically
+you know you might imagine a green beam
+
+ align:start position:0%
+you know you might imagine a green beam
+ 
+
+ align:start position:0%
+you know you might imagine a green beam
+going in for the pump and a red one for
+
+ align:start position:0%
+going in for the pump and a red one for
+ 
+
+ align:start position:0%
+going in for the pump and a red one for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Stokes um and what you see where is that
+
+ align:start position:0%
+Stokes um and what you see where is that
+ 
+
+ align:start position:0%
+Stokes um and what you see where is that
+uh you know you might have a green pump
+
+ align:start position:0%
+uh you know you might have a green pump
+ 
+
+ align:start position:0%
+uh you know you might have a green pump
+and a red Stokes and you'll see sort of
+
+ align:start position:0%
+and a red Stokes and you'll see sort of
+ 
+
+ align:start position:0%
+and a red Stokes and you'll see sort of
+a blue spot out to the side um and you
+
+ align:start position:0%
+a blue spot out to the side um and you
+ 
+
+ align:start position:0%
+a blue spot out to the side um and you
+can understand that then immediately
+
+ align:start position:0%
+can understand that then immediately
+ 
+
+ align:start position:0%
+can understand that then immediately
+from this because it also immediately
+
+ align:start position:0%
+from this because it also immediately
+ 
+
+ align:start position:0%
+from this because it also immediately
+says that the wave Vector matching for
+
+ align:start position:0%
+says that the wave Vector matching for
+ 
+
+ align:start position:0%
+says that the wave Vector matching for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+experiment is um two two momenta units
+
+ align:start position:0%
+experiment is um two two momenta units
+ 
+
+ align:start position:0%
+experiment is um two two momenta units
+of momenta coming from the pump minus
+
+ align:start position:0%
+of momenta coming from the pump minus
+ 
+
+ align:start position:0%
+of momenta coming from the pump minus
+one of the Stokes and that leads to the
+
+ align:start position:0%
+one of the Stokes and that leads to the
+ 
+
+ align:start position:0%
+one of the Stokes and that leads to the
+wave Vector matching condition that I've
+
+ align:start position:0%
+wave Vector matching condition that I've
+ 
+
+ align:start position:0%
+wave Vector matching condition that I've
+drawn up there right that um we're going
+
+ align:start position:0%
+drawn up there right that um we're going
+ 
+
+ align:start position:0%
+drawn up there right that um we're going
+in the forward Direction and we bring in
+
+ align:start position:0%
+in the forward Direction and we bring in
+ 
+
+ align:start position:0%
+in the forward Direction and we bring in
+the Stokes at an angle the signal field
+
+ align:start position:0%
+the Stokes at an angle the signal field
+ 
+
+ align:start position:0%
+the Stokes at an angle the signal field
+um will come out at a particular
+
+ align:start position:0%
+um will come out at a particular
+ 
+
+ align:start position:0%
+um will come out at a particular
+Direction dictated by the frequency and
+
+ align:start position:0%
+Direction dictated by the frequency and
+ 
+
+ align:start position:0%
+Direction dictated by the frequency and
+wave Vector matching in One Direction
+
+ align:start position:0%
+wave Vector matching in One Direction
+ 
+
+ align:start position:0%
+wave Vector matching in One Direction
+and when you're doing this with
+
+ align:start position:0%
+and when you're doing this with
+ 
+
+ align:start position:0%
+and when you're doing this with
+well-defined frequencies then the wave
+
+ align:start position:0%
+well-defined frequencies then the wave
+ 
+
+ align:start position:0%
+well-defined frequencies then the wave
+Vector issues that we talked about
+
+ align:start position:0%
+Vector issues that we talked about
+ 
+
+ align:start position:0%
+Vector issues that we talked about
+yesterday come into play and the angle
+
+ align:start position:0%
+yesterday come into play and the angle
+ 
+
+ align:start position:0%
+yesterday come into play and the angle
+between the pump and the Stokes become
+
+ align:start position:0%
+between the pump and the Stokes become
+ 
+
+ align:start position:0%
+between the pump and the Stokes become
+really critical to get an efficient uh
+
+ align:start position:0%
+really critical to get an efficient uh
+ 
+
+ align:start position:0%
+really critical to get an efficient uh
+signal generation okay but uh so you can
+
+ align:start position:0%
+signal generation okay but uh so you can
+ 
+
+ align:start position:0%
+signal generation okay but uh so you can
+see here if you now do this with um time
+
+ align:start position:0%
+see here if you now do this with um time
+ 
+
+ align:start position:0%
+see here if you now do this with um time
+resolved pulses that you can move the
+
+ align:start position:0%
+resolved pulses that you can move the
+ 
+
+ align:start position:0%
+resolved pulses that you can move the
+time delay between these pump and probe
+
+ align:start position:0%
+time delay between these pump and probe
+ 
+
+ align:start position:0%
+time delay between these pump and probe
+and that just gives you the vibrational
+
+ align:start position:0%
+and that just gives you the vibrational
+ 
+
+ align:start position:0%
+and that just gives you the vibrational
+Dynamics in the system and that is the
+
+ align:start position:0%
+Dynamics in the system and that is the
+ 
+
+ align:start position:0%
+Dynamics in the system and that is the
+time domain version of a Ramen Spectrum
+
+ align:start position:0%
+time domain version of a Ramen Spectrum
+ 
+
+ align:start position:0%
+time domain version of a Ramen Spectrum
+right in the limit that you go to very
+
+ align:start position:0%
+right in the limit that you go to very
+ 
+
+ align:start position:0%
+right in the limit that you go to very
+short pulses um with the same color you
+
+ align:start position:0%
+short pulses um with the same color you
+ 
+
+ align:start position:0%
+short pulses um with the same color you
+should recognize that the transient
+
+ align:start position:0%
+should recognize that the transient
+ 
+
+ align:start position:0%
+should recognize that the transient
+grading experiments we did correspond to
+
+ align:start position:0%
+grading experiments we did correspond to
+ 
+
+ align:start position:0%
+grading experiments we did correspond to
+this process also where this difference
+
+ align:start position:0%
+this process also where this difference
+ 
+
+ align:start position:0%
+this process also where this difference
+in colors these are colors that both lie
+
+ align:start position:0%
+in colors these are colors that both lie
+ 
+
+ align:start position:0%
+in colors these are colors that both lie
+within the bandwidth of the exitation
+
+ align:start position:0%
+within the bandwidth of the exitation
+ 
+
+ align:start position:0%
+within the bandwidth of the exitation
+fields okay so you can imagine that
+
+ align:start position:0%
+fields okay so you can imagine that
+ 
+
+ align:start position:0%
+fields okay so you can imagine that
+you're there's enough colors in your
+
+ align:start position:0%
+you're there's enough colors in your
+ 
+
+ align:start position:0%
+you're there's enough colors in your
+short pulses that they span this whole
+
+ align:start position:0%
+short pulses that they span this whole
+ 
+
+ align:start position:0%
+short pulses that they span this whole
+the bandwidth spans this whole region so
+
+ align:start position:0%
+the bandwidth spans this whole region so
+ 
+
+ align:start position:0%
+the bandwidth spans this whole region so
+okay so they they they can't they don't
+
+ align:start position:0%
+okay so they they they can't they don't
+ 
+
+ align:start position:0%
+okay so they they they can't they don't
+need to be different colors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right any yep when people do
+
+ align:start position:0%
+okay all right any yep when people do
+ 
+
+ align:start position:0%
+okay all right any yep when people do
+these cars experiments do they bring in
+
+ align:start position:0%
+these cars experiments do they bring in
+ 
+
+ align:start position:0%
+these cars experiments do they bring in
+a local oscillator at some point to
+
+ align:start position:0%
+a local oscillator at some point to
+ 
+
+ align:start position:0%
+a local oscillator at some point to
+heter Signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh yes and no there's uh you you know
+
+ align:start position:0%
+so uh yes and no there's uh you you know
+ 
+
+ align:start position:0%
+so uh yes and no there's uh you you know
+in terms of people doing coherent Ramen
+
+ align:start position:0%
+in terms of people doing coherent Ramen
+ 
+
+ align:start position:0%
+in terms of people doing coherent Ramen
+with heterodon detection I think there's
+
+ align:start position:0%
+with heterodon detection I think there's
+ 
+
+ align:start position:0%
+with heterodon detection I think there's
+not many people that are going a whole
+
+ align:start position:0%
+not many people that are going a whole
+ 
+
+ align:start position:0%
+not many people that are going a whole
+lot further than the Nelson group does
+
+ align:start position:0%
+lot further than the Nelson group does
+ 
+
+ align:start position:0%
+lot further than the Nelson group does
+right um although you know with multiple
+
+ align:start position:0%
+right um although you know with multiple
+ 
+
+ align:start position:0%
+right um although you know with multiple
+colors now that
+
+ align:start position:0%
+colors now that
+ 
+
+ align:start position:0%
+colors now that
+happens there are a handful of coherent
+
+ align:start position:0%
+happens there are a handful of coherent
+ 
+
+ align:start position:0%
+happens there are a handful of coherent
+Ramen experiments that do this
+
+ align:start position:0%
+Ramen experiments that do this
+ 
+
+ align:start position:0%
+Ramen experiments that do this
+um shall we say unintentionally and I
+
+ align:start position:0%
+um shall we say unintentionally and I
+ 
+
+ align:start position:0%
+um shall we say unintentionally and I
+think the F to Second you know the
+
+ align:start position:0%
+think the F to Second you know the
+ 
+
+ align:start position:0%
+think the F to Second you know the
+stimulated Ramen spectroscopy that rich
+
+ align:start position:0%
+stimulated Ramen spectroscopy that rich
+ 
+
+ align:start position:0%
+stimulated Ramen spectroscopy that rich
+Matthews does is an example of this
+
+ align:start position:0%
+Matthews does is an example of this
+ 
+
+ align:start position:0%
+Matthews does is an example of this
+where it's uh sort of intrinsically
+
+ align:start position:0%
+where it's uh sort of intrinsically
+ 
+
+ align:start position:0%
+where it's uh sort of intrinsically
+heter roded sort of like um the pump
+
+ align:start position:0%
+heter roded sort of like um the pump
+ 
+
+ align:start position:0%
+heter roded sort of like um the pump
+probe experiment um I'm actually hoping
+
+ align:start position:0%
+probe experiment um I'm actually hoping
+ 
+
+ align:start position:0%
+probe experiment um I'm actually hoping
+I can spend a whole you know a whole
+
+ align:start position:0%
+I can spend a whole you know a whole
+ 
+
+ align:start position:0%
+I can spend a whole you know a whole
+chunk of time on coherent Ramen because
+
+ align:start position:0%
+chunk of time on coherent Ramen because
+ 
+
+ align:start position:0%
+chunk of time on coherent Ramen because
+there's a whole slug of interesting you
+
+ align:start position:0%
+there's a whole slug of interesting you
+ 
+
+ align:start position:0%
+there's a whole slug of interesting you
+know techniques and you do them with and
+
+ align:start position:0%
+know techniques and you do them with and
+ 
+
+ align:start position:0%
+know techniques and you do them with and
+without header dining and um lot lots of
+
+ align:start position:0%
+without header dining and um lot lots of
+ 
+
+ align:start position:0%
+without header dining and um lot lots of
+interesting information to get out of
+
+ align:start position:0%
+interesting information to get out of
+ 
+
+ align:start position:0%
+interesting information to get out of
+that but
+
+ align:start position:0%
+that but
+ 
+
+ align:start position:0%
+that but
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh it's the header dining idea has even
+
+ align:start position:0%
+uh it's the header dining idea has even
+ 
+
+ align:start position:0%
+uh it's the header dining idea has even
+been used header dining cars has also
+
+ align:start position:0%
+been used header dining cars has also
+ 
+
+ align:start position:0%
+been used header dining cars has also
+been used for Imaging um that sunish
+
+ align:start position:0%
+been used for Imaging um that sunish
+ 
+
+ align:start position:0%
+been used for Imaging um that sunish
+she's been doing some of that although
+
+ align:start position:0%
+she's been doing some of that although
+ 
+
+ align:start position:0%
+she's been doing some of that although
+I'm not sure if he's real fond of doing
+
+ align:start position:0%
+I'm not sure if he's real fond of doing
+ 
+
+ align:start position:0%
+I'm not sure if he's real fond of doing
+that really tough
+
+ align:start position:0%
+that really tough
+ 
+
+ align:start position:0%
+that really tough
+experiment he's fond of tough
+
+ align:start position:0%
+experiment he's fond of tough
+ 
+
+ align:start position:0%
+experiment he's fond of tough
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+yeah another point is that so most
+
+ align:start position:0%
+yeah another point is that so most
+ 
+
+ align:start position:0%
+yeah another point is that so most
+people do this in the in the frequency
+
+ align:start position:0%
+people do this in the in the frequency
+ 
+
+ align:start position:0%
+people do this in the in the frequency
+domain in the frequency domain it's
+
+ align:start position:0%
+domain in the frequency domain it's
+ 
+
+ align:start position:0%
+domain in the frequency domain it's
+important that you
+
+ align:start position:0%
+important that you
+ 
+
+ align:start position:0%
+important that you
+little okay people usually have two
+
+ align:start position:0%
+little okay people usually have two
+ 
+
+ align:start position:0%
+little okay people usually have two
+green like the two Mega pumps the same
+
+ align:start position:0%
+green like the two Mega pumps the same
+ 
+
+ align:start position:0%
+green like the two Mega pumps the same
+beam right in principle they don't have
+
+ align:start position:0%
+beam right in principle they don't have
+ 
+
+ align:start position:0%
+beam right in principle they don't have
+to be so what's important if you do this
+
+ align:start position:0%
+to be so what's important if you do this
+ 
+
+ align:start position:0%
+to be so what's important if you do this
+in the frequency domain is that your
+
+ align:start position:0%
+in the frequency domain is that your
+ 
+
+ align:start position:0%
+in the frequency domain is that your
+last beam your last Mega pump is narrow
+
+ align:start position:0%
+last beam your last Mega pump is narrow
+ 
+
+ align:start position:0%
+last beam your last Mega pump is narrow
+P so if not you can wash out
+
+ align:start position:0%
+P so if not you can wash out
+ 
+
+ align:start position:0%
+P so if not you can wash out
+your your your frequency resolution is
+
+ align:start position:0%
+your your your frequency resolution is
+ 
+
+ align:start position:0%
+your your your frequency resolution is
+it's it's depending on your last so you
+
+ align:start position:0%
+it's it's depending on your last so you
+ 
+
+ align:start position:0%
+it's it's depending on your last so you
+need to have a narrow Pand mhm right
+
+ align:start position:0%
+need to have a narrow Pand mhm right
+ 
+
+ align:start position:0%
+need to have a narrow Pand mhm right
+there yeah yeah thanks thanks for
+
+ align:start position:0%
+there yeah yeah thanks thanks for
+ 
+
+ align:start position:0%
+there yeah yeah thanks thanks for
+pointing that out there's so what I
+
+ align:start position:0%
+pointing that out there's so what I
+ 
+
+ align:start position:0%
+pointing that out there's so what I
+described was sort of the time domain
+
+ align:start position:0%
+described was sort of the time domain
+ 
+
+ align:start position:0%
+described was sort of the time domain
+limit um thinking about this as a Time
+
+ align:start position:0%
+limit um thinking about this as a Time
+ 
+
+ align:start position:0%
+limit um thinking about this as a Time
+domain experiment in which you use a you
+
+ align:start position:0%
+domain experiment in which you use a you
+ 
+
+ align:start position:0%
+domain experiment in which you use a you
+know short pair of pulses to create a
+
+ align:start position:0%
+know short pair of pulses to create a
+ 
+
+ align:start position:0%
+know short pair of pulses to create a
+vibration you listen to it and and
+
+ align:start position:0%
+vibration you listen to it and and
+ 
+
+ align:start position:0%
+vibration you listen to it and and
+you're controlling that time variable
+
+ align:start position:0%
+you're controlling that time variable
+ 
+
+ align:start position:0%
+you're controlling that time variable
+the other approach is like Paul was
+
+ align:start position:0%
+the other approach is like Paul was
+ 
+
+ align:start position:0%
+the other approach is like Paul was
+saying is treated it as a frequency
+
+ align:start position:0%
+saying is treated it as a frequency
+ 
+
+ align:start position:0%
+saying is treated it as a frequency
+domain experiment you I mean you you
+
+ align:start position:0%
+domain experiment you I mean you you
+ 
+
+ align:start position:0%
+domain experiment you I mean you you
+still in principle have this you know
+
+ align:start position:0%
+still in principle have this you know
+ 
+
+ align:start position:0%
+still in principle have this you know
+control over um this time delay but uh
+
+ align:start position:0%
+control over um this time delay but uh
+ 
+
+ align:start position:0%
+control over um this time delay but uh
+it's very often that you might actually
+
+ align:start position:0%
+it's very often that you might actually
+ 
+
+ align:start position:0%
+it's very often that you might actually
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+to excite a range of Transitions and
+
+ align:start position:0%
+to excite a range of Transitions and
+ 
+
+ align:start position:0%
+to excite a range of Transitions and
+look at the frequency dependent changes
+
+ align:start position:0%
+look at the frequency dependent changes
+ 
+
+ align:start position:0%
+look at the frequency dependent changes
+and um by spectrally dispersing you know
+
+ align:start position:0%
+and um by spectrally dispersing you know
+ 
+
+ align:start position:0%
+and um by spectrally dispersing you know
+what comes out as a signal and then
+
+ align:start position:0%
+what comes out as a signal and then
+ 
+
+ align:start position:0%
+what comes out as a signal and then
+Paul's right is because the virtual
+
+ align:start position:0%
+Paul's right is because the virtual
+ 
+
+ align:start position:0%
+Paul's right is because the virtual
+state is at any frequency you want you
+
+ align:start position:0%
+state is at any frequency you want you
+ 
+
+ align:start position:0%
+state is at any frequency you want you
+want to use a uh combination of short
+
+ align:start position:0%
+want to use a uh combination of short
+ 
+
+ align:start position:0%
+want to use a uh combination of short
+exitation and narrow band probing to uh
+
+ align:start position:0%
+exitation and narrow band probing to uh
+ 
+
+ align:start position:0%
+exitation and narrow band probing to uh
+give you the both the time and the
+
+ align:start position:0%
+give you the both the time and the
+ 
+
+ align:start position:0%
+give you the both the time and the
+frequency resolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions so I think now is a
+
+ align:start position:0%
+okay any questions so I think now is a
+ 
+
+ align:start position:0%
+okay any questions so I think now is a
+good time to take a
+
+ align:start position:0%
+good time to take a
+ 
+
+ align:start position:0%
+good time to take a
+break all right folks um what I'd like
+
+ align:start position:0%
+break all right folks um what I'd like
+ 
+
+ align:start position:0%
+break all right folks um what I'd like
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+is sort of get into an introduction to
+
+ align:start position:0%
+is sort of get into an introduction to
+ 
+
+ align:start position:0%
+is sort of get into an introduction to
+two-dimensional spectroscopy a little
+
+ align:start position:0%
+two-dimensional spectroscopy a little
+ 
+
+ align:start position:0%
+two-dimensional spectroscopy a little
+bit of motivating why you do it and sort
+
+ align:start position:0%
+bit of motivating why you do it and sort
+ 
+
+ align:start position:0%
+bit of motivating why you do it and sort
+of the general ideas behind
+
+ align:start position:0%
+of the general ideas behind
+ 
+
+ align:start position:0%
+of the general ideas behind
+it and but I want to motivated by the
+
+ align:start position:0%
+it and but I want to motivated by the
+ 
+
+ align:start position:0%
+it and but I want to motivated by the
+couple of the examples I gave at the
+
+ align:start position:0%
+couple of the examples I gave at the
+ 
+
+ align:start position:0%
+couple of the examples I gave at the
+beginning you know why you do nonlinear
+
+ align:start position:0%
+beginning you know why you do nonlinear
+ 
+
+ align:start position:0%
+beginning you know why you do nonlinear
+spectroscopy you know it's if I have a
+
+ align:start position:0%
+spectroscopy you know it's if I have a
+ 
+
+ align:start position:0%
+spectroscopy you know it's if I have a
+linear experiment I see two peaks you
+
+ align:start position:0%
+linear experiment I see two peaks you
+ 
+
+ align:start position:0%
+linear experiment I see two peaks you
+know what uh do I use to interpret what
+
+ align:start position:0%
+know what uh do I use to interpret what
+ 
+
+ align:start position:0%
+know what uh do I use to interpret what
+the origin of those Peaks are I could
+
+ align:start position:0%
+the origin of those Peaks are I could
+ 
+
+ align:start position:0%
+the origin of those Peaks are I could
+imagine there are two two entirely
+
+ align:start position:0%
+imagine there are two two entirely
+ 
+
+ align:start position:0%
+imagine there are two two entirely
+different molecules spatially separated
+
+ align:start position:0%
+different molecules spatially separated
+ 
+
+ align:start position:0%
+different molecules spatially separated
+don't know about each other and they
+
+ align:start position:0%
+don't know about each other and they
+ 
+
+ align:start position:0%
+don't know about each other and they
+give rise to these Peaks I can also
+
+ align:start position:0%
+give rise to these Peaks I can also
+ 
+
+ align:start position:0%
+give rise to these Peaks I can also
+imagine that um these arise from igen
+
+ align:start position:0%
+imagine that um these arise from igen
+ 
+
+ align:start position:0%
+imagine that um these arise from igen
+states that reflect the coupling between
+
+ align:start position:0%
+states that reflect the coupling between
+ 
+
+ align:start position:0%
+states that reflect the coupling between
+different um electronic or vibrational
+
+ align:start position:0%
+different um electronic or vibrational
+ 
+
+ align:start position:0%
+different um electronic or vibrational
+States how do you distinguish
+
+ align:start position:0%
+States how do you distinguish
+ 
+
+ align:start position:0%
+States how do you distinguish
+them the other example which is sort of
+
+ align:start position:0%
+them the other example which is sort of
+ 
+
+ align:start position:0%
+them the other example which is sort of
+analogous is you know if you have a very
+
+ align:start position:0%
+analogous is you know if you have a very
+ 
+
+ align:start position:0%
+analogous is you know if you have a very
+broad line do you think of that is that
+
+ align:start position:0%
+broad line do you think of that is that
+ 
+
+ align:start position:0%
+broad line do you think of that is that
+an inhomogeneous line or not how would
+
+ align:start position:0%
+an inhomogeneous line or not how would
+ 
+
+ align:start position:0%
+an inhomogeneous line or not how would
+you go about tackling these problems
+
+ align:start position:0%
+you go about tackling these problems
+ 
+
+ align:start position:0%
+you go about tackling these problems
+um so uh you know I think the there's a
+
+ align:start position:0%
+um so uh you know I think the there's a
+ 
+
+ align:start position:0%
+um so uh you know I think the there's a
+real simple exercise that tells you that
+
+ align:start position:0%
+real simple exercise that tells you that
+ 
+
+ align:start position:0%
+real simple exercise that tells you that
+you should be able to solve these
+
+ align:start position:0%
+you should be able to solve these
+ 
+
+ align:start position:0%
+you should be able to solve these
+problems if you do on probe experiments
+
+ align:start position:0%
+problems if you do on probe experiments
+ 
+
+ align:start position:0%
+problems if you do on probe experiments
+um of the kind that we just discussed
+
+ align:start position:0%
+um of the kind that we just discussed
+ 
+
+ align:start position:0%
+um of the kind that we just discussed
+and what um we talked about is that with
+
+ align:start position:0%
+and what um we talked about is that with
+ 
+
+ align:start position:0%
+and what um we talked about is that with
+um pum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probes that we have three independent
+
+ align:start position:0%
+probes that we have three independent
+ 
+
+ align:start position:0%
+probes that we have three independent
+variables and we tend to think of these
+
+ align:start position:0%
+variables and we tend to think of these
+ 
+
+ align:start position:0%
+variables and we tend to think of these
+I mean when we write out response
+
+ align:start position:0%
+I mean when we write out response
+ 
+
+ align:start position:0%
+I mean when we write out response
+functions we have three independent time
+
+ align:start position:0%
+functions we have three independent time
+ 
+
+ align:start position:0%
+functions we have three independent time
+variables but for pump probes you can
+
+ align:start position:0%
+variables but for pump probes you can
+ 
+
+ align:start position:0%
+variables but for pump probes you can
+think of these as sort of being
+
+ align:start position:0%
+think of these as sort of being
+ 
+
+ align:start position:0%
+think of these as sort of being
+the frequency of the pump
+
+ align:start position:0%
+the frequency of the pump
+ 
+
+ align:start position:0%
+the frequency of the pump
+field uh time delay between the pump and
+
+ align:start position:0%
+field uh time delay between the pump and
+ 
+
+ align:start position:0%
+field uh time delay between the pump and
+the prob and frequency
+
+ align:start position:0%
+the prob and frequency
+ 
+
+ align:start position:0%
+the prob and frequency
+Pro and um now let's just actually sort
+
+ align:start position:0%
+Pro and um now let's just actually sort
+ 
+
+ align:start position:0%
+Pro and um now let's just actually sort
+of consider the case where this is
+
+ align:start position:0%
+of consider the case where this is
+ 
+
+ align:start position:0%
+of consider the case where this is
+really a frequency domain experiment
+
+ align:start position:0%
+really a frequency domain experiment
+ 
+
+ align:start position:0%
+really a frequency domain experiment
+just a double resonance experiment in
+
+ align:start position:0%
+just a double resonance experiment in
+ 
+
+ align:start position:0%
+just a double resonance experiment in
+which we independently control the
+
+ align:start position:0%
+which we independently control the
+ 
+
+ align:start position:0%
+which we independently control the
+frequency of the pump and the problem so
+
+ align:start position:0%
+frequency of the pump and the problem so
+ 
+
+ align:start position:0%
+frequency of the pump and the problem so
+this is sort of what I refer to as
+
+ align:start position:0%
+this is sort of what I refer to as
+ 
+
+ align:start position:0%
+this is sort of what I refer to as
+double resonance to
+
+ align:start position:0%
+double resonance to
+ 
+
+ align:start position:0%
+double resonance to
+the yeah by the way he said ideas have
+
+ align:start position:0%
+the yeah by the way he said ideas have
+ 
+
+ align:start position:0%
+the yeah by the way he said ideas have
+been around forever the only things that
+
+ align:start position:0%
+been around forever the only things that
+ 
+
+ align:start position:0%
+been around forever the only things that
+are new these days is the ways of doing
+
+ align:start position:0%
+are new these days is the ways of doing
+ 
+
+ align:start position:0%
+are new these days is the ways of doing
+them and think about the nonlinear
+
+ align:start position:0%
+them and think about the nonlinear
+ 
+
+ align:start position:0%
+them and think about the nonlinear
+response in terms of a huge two or three
+
+ align:start position:0%
+response in terms of a huge two or three
+ 
+
+ align:start position:0%
+response in terms of a huge two or three
+dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface okay so let's do that and apply
+
+ align:start position:0%
+surface okay so let's do that and apply
+ 
+
+ align:start position:0%
+surface okay so let's do that and apply
+it to these two problems okay and so
+
+ align:start position:0%
+it to these two problems okay and so
+ 
+
+ align:start position:0%
+it to these two problems okay and so
+here's how we're going to do this
+
+ align:start position:0%
+here's how we're going to do this
+ 
+
+ align:start position:0%
+here's how we're going to do this
+um as before cross two beams in a sample
+
+ align:start position:0%
+um as before cross two beams in a sample
+ 
+
+ align:start position:0%
+um as before cross two beams in a sample
+um here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my probe here's my FR I'm going to put
+
+ align:start position:0%
+my probe here's my FR I'm going to put
+ 
+
+ align:start position:0%
+my probe here's my FR I'm going to put
+it detector on here and measure the
+
+ align:start position:0%
+it detector on here and measure the
+ 
+
+ align:start position:0%
+it detector on here and measure the
+change of intensity on there as a result
+
+ align:start position:0%
+change of intensity on there as a result
+ 
+
+ align:start position:0%
+change of intensity on there as a result
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+field and I'm going to start with the
+
+ align:start position:0%
+field and I'm going to start with the
+ 
+
+ align:start position:0%
+field and I'm going to start with the
+Spectrum and I measure that with
+
+ align:start position:0%
+Spectrum and I measure that with
+ 
+
+ align:start position:0%
+Spectrum and I measure that with
+my probe field so called this Mega probe
+
+ align:start position:0%
+my probe field so called this Mega probe
+ 
+
+ align:start position:0%
+my probe field so called this Mega probe
+and now imagine that I T my pump
+
+ align:start position:0%
+and now imagine that I T my pump
+ 
+
+ align:start position:0%
+and now imagine that I T my pump
+beam to be on resonance with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state um so what could happen well
+
+ align:start position:0%
+state um so what could happen well
+ 
+
+ align:start position:0%
+state um so what could happen well
+actually just uh to make it more
+
+ align:start position:0%
+actually just uh to make it more
+ 
+
+ align:start position:0%
+actually just uh to make it more
+interesting let's put a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+third so one way of thinking what might
+
+ align:start position:0%
+third so one way of thinking what might
+ 
+
+ align:start position:0%
+third so one way of thinking what might
+happen just uh take the extremely
+
+ align:start position:0%
+happen just uh take the extremely
+ 
+
+ align:start position:0%
+happen just uh take the extremely
+intense limit there is a poor molecule
+
+ align:start position:0%
+intense limit there is a poor molecule
+ 
+
+ align:start position:0%
+intense limit there is a poor molecule
+that's sitting under that frequency that
+
+ align:start position:0%
+that's sitting under that frequency that
+ 
+
+ align:start position:0%
+that's sitting under that frequency that
+is just going to get obliterated we're
+
+ align:start position:0%
+is just going to get obliterated we're
+ 
+
+ align:start position:0%
+is just going to get obliterated we're
+just going to destroy it
+
+ align:start position:0%
+just going to destroy it
+ 
+
+ align:start position:0%
+just going to destroy it
+photochemically bang it's gone what
+
+ align:start position:0%
+photochemically bang it's gone what
+ 
+
+ align:start position:0%
+photochemically bang it's gone what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+if you know if you sort of somehow
+
+ align:start position:0%
+if you know if you sort of somehow
+ 
+
+ align:start position:0%
+if you know if you sort of somehow
+remove that set of
+
+ align:start position:0%
+remove that set of
+ 
+
+ align:start position:0%
+remove that set of
+molecules um means you've really removed
+
+ align:start position:0%
+molecules um means you've really removed
+ 
+
+ align:start position:0%
+molecules um means you've really removed
+the possibility to make absorption of
+
+ align:start position:0%
+the possibility to make absorption of
+ 
+
+ align:start position:0%
+the possibility to make absorption of
+any of those frequencies so really any
+
+ align:start position:0%
+any of those frequencies so really any
+ 
+
+ align:start position:0%
+any of those frequencies so really any
+sort of uh other transition that
+
+ align:start position:0%
+sort of uh other transition that
+ 
+
+ align:start position:0%
+sort of uh other transition that
+originated from that same molecule will
+
+ align:start position:0%
+originated from that same molecule will
+ 
+
+ align:start position:0%
+originated from that same molecule will
+also be
+
+ align:start position:0%
+also be
+ 
+
+ align:start position:0%
+also be
+done okay so you know imagine we go
+
+ align:start position:0%
+done okay so you know imagine we go
+ 
+
+ align:start position:0%
+done okay so you know imagine we go
+through now and we add the pump and we
+
+ align:start position:0%
+through now and we add the pump and we
+ 
+
+ align:start position:0%
+through now and we add the pump and we
+see that oh this intensity drops this
+
+ align:start position:0%
+see that oh this intensity drops this
+ 
+
+ align:start position:0%
+see that oh this intensity drops this
+one doesn't this one does says point you
+
+ align:start position:0%
+one doesn't this one does says point you
+ 
+
+ align:start position:0%
+one doesn't this one does says point you
+know you know immediately know that
+
+ align:start position:0%
+know you know immediately know that
+ 
+
+ align:start position:0%
+know you know immediately know that
+there's a spectal correlation between
+
+ align:start position:0%
+there's a spectal correlation between
+ 
+
+ align:start position:0%
+there's a spectal correlation between
+that Peak and this peak and it's the
+
+ align:start position:0%
+that Peak and this peak and it's the
+ 
+
+ align:start position:0%
+that Peak and this peak and it's the
+same molecule you destroyed it so what
+
+ align:start position:0%
+same molecule you destroyed it so what
+ 
+
+ align:start position:0%
+same molecule you destroyed it so what
+we are talking about in a you know in a
+
+ align:start position:0%
+we are talking about in a you know in a
+ 
+
+ align:start position:0%
+we are talking about in a you know in a
+more General two-dimensional experiment
+
+ align:start position:0%
+more General two-dimensional experiment
+ 
+
+ align:start position:0%
+more General two-dimensional experiment
+is that we're looking at the same sorts
+
+ align:start position:0%
+is that we're looking at the same sorts
+ 
+
+ align:start position:0%
+is that we're looking at the same sorts
+of molecular couplings that transfer
+
+ align:start position:0%
+of molecular couplings that transfer
+ 
+
+ align:start position:0%
+of molecular couplings that transfer
+energy from one state to another and
+
+ align:start position:0%
+energy from one state to another and
+ 
+
+ align:start position:0%
+energy from one state to another and
+that means that bleaching one transition
+
+ align:start position:0%
+that means that bleaching one transition
+ 
+
+ align:start position:0%
+that means that bleaching one transition
+will lead to bleaches in other couple of
+
+ align:start position:0%
+will lead to bleaches in other couple of
+ 
+
+ align:start position:0%
+will lead to bleaches in other couple of
+transitions so um what this means is now
+
+ align:start position:0%
+transitions so um what this means is now
+ 
+
+ align:start position:0%
+transitions so um what this means is now
+your change of intensity as a function
+
+ align:start position:0%
+your change of intensity as a function
+ 
+
+ align:start position:0%
+your change of intensity as a function
+of the prob is going to be positive and
+
+ align:start position:0%
+of the prob is going to be positive and
+ 
+
+ align:start position:0%
+of the prob is going to be positive and
+positive here no change in between and
+
+ align:start position:0%
+positive here no change in between and
+ 
+
+ align:start position:0%
+positive here no change in between and
+now think of this as one slice through a
+
+ align:start position:0%
+now think of this as one slice through a
+ 
+
+ align:start position:0%
+now think of this as one slice through a
+two-dimensional surface right now repeat
+
+ align:start position:0%
+two-dimensional surface right now repeat
+ 
+
+ align:start position:0%
+two-dimensional surface right now repeat
+that experiment for all possible pump
+
+ align:start position:0%
+that experiment for all possible pump
+ 
+
+ align:start position:0%
+that experiment for all possible pump
+frequencies and now make up a map of
+
+ align:start position:0%
+frequencies and now make up a map of
+ 
+
+ align:start position:0%
+frequencies and now make up a map of
+this Delta I as
+
+ align:start position:0%
+this Delta I as
+ 
+
+ align:start position:0%
+this Delta I as
+pumping the
+
+ align:start position:0%
+pumping the
+ 
+
+ align:start position:0%
+pumping the
+pump and the probe frequency so this is
+
+ align:start position:0%
+pump and the probe frequency so this is
+ 
+
+ align:start position:0%
+pump and the probe frequency so this is
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slice vertically through
+
+ align:start position:0%
+slice vertically through
+ 
+
+ align:start position:0%
+slice vertically through
+here and it happens to be at on
+
+ align:start position:0%
+here and it happens to be at on
+ 
+
+ align:start position:0%
+here and it happens to be at on
+resonance with that be you map this all
+
+ align:start position:0%
+resonance with that be you map this all
+ 
+
+ align:start position:0%
+resonance with that be you map this all
+out and you would expect to see a
+
+ align:start position:0%
+out and you would expect to see a
+ 
+
+ align:start position:0%
+out and you would expect to see a
+spectrum that
+
+ align:start position:0%
+spectrum that
+ 
+
+ align:start position:0%
+spectrum that
+looks about like
+
+ align:start position:0%
+looks about like
+ 
+
+ align:start position:0%
+looks about like
+this this is sort of the diagonal
+
+ align:start position:0%
+this this is sort of the diagonal
+ 
+
+ align:start position:0%
+this this is sort of the diagonal
+frequency AIS so what is the Spectrum
+
+ align:start position:0%
+frequency AIS so what is the Spectrum
+ 
+
+ align:start position:0%
+frequency AIS so what is the Spectrum
+report to you it says these uh cross
+
+ align:start position:0%
+report to you it says these uh cross
+ 
+
+ align:start position:0%
+report to you it says these uh cross
+Peaks that is um changes in intensity at
+
+ align:start position:0%
+Peaks that is um changes in intensity at
+ 
+
+ align:start position:0%
+Peaks that is um changes in intensity at
+frequencies different than where you
+
+ align:start position:0%
+frequencies different than where you
+ 
+
+ align:start position:0%
+frequencies different than where you
+pumped is telling you about uh the
+
+ align:start position:0%
+pumped is telling you about uh the
+ 
+
+ align:start position:0%
+pumped is telling you about uh the
+correlation between spectral features it
+
+ align:start position:0%
+correlation between spectral features it
+ 
+
+ align:start position:0%
+correlation between spectral features it
+tells you about you know microscopic
+
+ align:start position:0%
+tells you about you know microscopic
+ 
+
+ align:start position:0%
+tells you about you know microscopic
+interactions this tells you this peak is
+
+ align:start position:0%
+interactions this tells you this peak is
+ 
+
+ align:start position:0%
+interactions this tells you this peak is
+not correlated with other ones whereas
+
+ align:start position:0%
+not correlated with other ones whereas
+ 
+
+ align:start position:0%
+not correlated with other ones whereas
+this one is or you can take the other
+
+ align:start position:0%
+this one is or you can take the other
+ 
+
+ align:start position:0%
+this one is or you can take the other
+limit you know the intensity of those
+
+ align:start position:0%
+limit you know the intensity of those
+ 
+
+ align:start position:0%
+limit you know the intensity of those
+Peaks will tell you how strongly they
+
+ align:start position:0%
+Peaks will tell you how strongly they
+ 
+
+ align:start position:0%
+Peaks will tell you how strongly they
+interact so that's one way of um ironing
+
+ align:start position:0%
+interact so that's one way of um ironing
+ 
+
+ align:start position:0%
+interact so that's one way of um ironing
+it out I'll take the same approach and
+
+ align:start position:0%
+it out I'll take the same approach and
+ 
+
+ align:start position:0%
+it out I'll take the same approach and
+yeah as a practical question is there
+
+ align:start position:0%
+yeah as a practical question is there
+ 
+
+ align:start position:0%
+yeah as a practical question is there
+ever any utility in placing your Omega
+
+ align:start position:0%
+ever any utility in placing your Omega
+ 
+
+ align:start position:0%
+ever any utility in placing your Omega
+pump where you don't have a peak in
+
+ align:start position:0%
+pump where you don't have a peak in
+ 
+
+ align:start position:0%
+pump where you don't have a peak in
+theeg Pro Spectrum where you just
+
+ align:start position:0%
+theeg Pro Spectrum where you just
+ 
+
+ align:start position:0%
+theeg Pro Spectrum where you just
+wasting time by okay uh I'm just uh so
+
+ align:start position:0%
+wasting time by okay uh I'm just uh so
+ 
+
+ align:start position:0%
+wasting time by okay uh I'm just uh so
+when it comes to practical stuff then
+
+ align:start position:0%
+when it comes to practical stuff then
+ 
+
+ align:start position:0%
+when it comes to practical stuff then
+how you do it is going to be different
+
+ align:start position:0%
+how you do it is going to be different
+ 
+
+ align:start position:0%
+how you do it is going to be different
+but so I'm just saying this sort from a
+
+ align:start position:0%
+but so I'm just saying this sort from a
+ 
+
+ align:start position:0%
+but so I'm just saying this sort from a
+conceptual point of view um if you it is
+
+ align:start position:0%
+conceptual point of view um if you it is
+ 
+
+ align:start position:0%
+conceptual point of view um if you it is
+true you know if you know the linear
+
+ align:start position:0%
+true you know if you know the linear
+ 
+
+ align:start position:0%
+true you know if you know the linear
+experiment and you know the pump
+
+ align:start position:0%
+experiment and you know the pump
+ 
+
+ align:start position:0%
+experiment and you know the pump
+interaction then you at least know in
+
+ align:start position:0%
+interaction then you at least know in
+ 
+
+ align:start position:0%
+interaction then you at least know in
+one dimension where to go
+
+ align:start position:0%
+one dimension where to go
+ 
+
+ align:start position:0%
+one dimension where to go
+scan and it doesn't count for the other
+
+ align:start position:0%
+scan and it doesn't count for the other
+ 
+
+ align:start position:0%
+scan and it doesn't count for the other
+dimension um but uh because you can open
+
+ align:start position:0%
+dimension um but uh because you can open
+ 
+
+ align:start position:0%
+dimension um but uh because you can open
+up new transitions with the first
+
+ align:start position:0%
+up new transitions with the first
+ 
+
+ align:start position:0%
+up new transitions with the first
+interaction that you didn't know about
+
+ align:start position:0%
+interaction that you didn't know about
+ 
+
+ align:start position:0%
+interaction that you didn't know about
+but it is true
+
+ align:start position:0%
+but it is true
+ 
+
+ align:start position:0%
+but it is true
+absolutely if you've got a sparse
+
+ align:start position:0%
+absolutely if you've got a sparse
+ 
+
+ align:start position:0%
+absolutely if you've got a sparse
+Spectrum then you know you have a
+
+ align:start position:0%
+Spectrum then you know you have a
+ 
+
+ align:start position:0%
+Spectrum then you know you have a
+limited set of areas to
+
+ align:start position:0%
+limited set of areas to
+ 
+
+ align:start position:0%
+limited set of areas to
+go this is the whole reason why I think
+
+ align:start position:0%
+go this is the whole reason why I think
+ 
+
+ align:start position:0%
+go this is the whole reason why I think
+you know the large fraction of high
+
+ align:start position:0%
+you know the large fraction of high
+ 
+
+ align:start position:0%
+you know the large fraction of high
+quality gas space spectroscopy really
+
+ align:start position:0%
+quality gas space spectroscopy really
+ 
+
+ align:start position:0%
+quality gas space spectroscopy really
+falls into this class of it's it's two
+
+ align:start position:0%
+falls into this class of it's it's two
+ 
+
+ align:start position:0%
+falls into this class of it's it's two
+dimensional spectroscopy it's just it's
+
+ align:start position:0%
+dimensional spectroscopy it's just it's
+ 
+
+ align:start position:0%
+dimensional spectroscopy it's just it's
+presented as slices through you know a
+
+ align:start position:0%
+presented as slices through you know a
+ 
+
+ align:start position:0%
+presented as slices through you know a
+surface well because they're they're not
+
+ align:start position:0%
+surface well because they're they're not
+ 
+
+ align:start position:0%
+surface well because they're they're not
+they're not part so it's very hard to
+
+ align:start position:0%
+they're not part so it's very hard to
+ 
+
+ align:start position:0%
+they're not part so it's very hard to
+visualizing there right so then we start
+
+ align:start position:0%
+visualizing there right so then we start
+ 
+
+ align:start position:0%
+visualizing there right so then we start
+getting into of the Practical issues
+
+ align:start position:0%
+getting into of the Practical issues
+ 
+
+ align:start position:0%
+getting into of the Practical issues
+about why would you do an experiment one
+
+ align:start position:0%
+about why would you do an experiment one
+ 
+
+ align:start position:0%
+about why would you do an experiment one
+way or another and imagine mix time you
+
+ align:start position:0%
+way or another and imagine mix time you
+ 
+
+ align:start position:0%
+way or another and imagine mix time you
+can imagine this is talked about this is
+
+ align:start position:0%
+can imagine this is talked about this is
+ 
+
+ align:start position:0%
+can imagine this is talked about this is
+a frequency domain experiment talk about
+
+ align:start position:0%
+a frequency domain experiment talk about
+ 
+
+ align:start position:0%
+a frequency domain experiment talk about
+time domain and there's practical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isues okay so um but but one thing that
+
+ align:start position:0%
+isues okay so um but but one thing that
+ 
+
+ align:start position:0%
+isues okay so um but but one thing that
+you know is great about 2D is that there
+
+ align:start position:0%
+you know is great about 2D is that there
+ 
+
+ align:start position:0%
+you know is great about 2D is that there
+is a great power of visualizing all of
+
+ align:start position:0%
+is a great power of visualizing all of
+ 
+
+ align:start position:0%
+is a great power of visualizing all of
+the interactions in one certain spect
+
+ align:start position:0%
+the interactions in one certain spect
+ 
+
+ align:start position:0%
+the interactions in one certain spect
+there there's a lot to that in
+
+ align:start position:0%
+there there's a lot to that in
+ 
+
+ align:start position:0%
+there there's a lot to that in
+mind this gets back to the issue of a
+
+ align:start position:0%
+mind this gets back to the issue of a
+ 
+
+ align:start position:0%
+mind this gets back to the issue of a
+spectroscop is only as good as it can
+
+ align:start position:0%
+spectroscop is only as good as it can
+ 
+
+ align:start position:0%
+spectroscop is only as good as it can
+distinguish different models and and
+
+ align:start position:0%
+distinguish different models and and
+ 
+
+ align:start position:0%
+distinguish different models and and
+it's I mean it may just be me being a
+
+ align:start position:0%
+it's I mean it may just be me being a
+ 
+
+ align:start position:0%
+it's I mean it may just be me being a
+visual learner but when you sort of see
+
+ align:start position:0%
+visual learner but when you sort of see
+ 
+
+ align:start position:0%
+visual learner but when you sort of see
+the interaction system is mapped out in
+
+ align:start position:0%
+the interaction system is mapped out in
+ 
+
+ align:start position:0%
+the interaction system is mapped out in
+front of you it really gives you this
+
+ align:start position:0%
+front of you it really gives you this
+ 
+
+ align:start position:0%
+front of you it really gives you this
+Insight okay so let's let's apply the
+
+ align:start position:0%
+Insight okay so let's let's apply the
+ 
+
+ align:start position:0%
+Insight okay so let's let's apply the
+same example then to this inhomogeneous
+
+ align:start position:0%
+same example then to this inhomogeneous
+ 
+
+ align:start position:0%
+same example then to this inhomogeneous
+line shape so now these are both CW yeah
+
+ align:start position:0%
+line shape so now these are both CW yeah
+ 
+
+ align:start position:0%
+line shape so now these are both CW yeah
+just think of them well um well defined
+
+ align:start position:0%
+just think of them well um well defined
+ 
+
+ align:start position:0%
+just think of them well um well defined
+frequencies
+
+ align:start position:0%
+frequencies
+ 
+
+ align:start position:0%
+frequencies
+narrow okay um now now imagine say we
+
+ align:start position:0%
+narrow okay um now now imagine say we
+ 
+
+ align:start position:0%
+narrow okay um now now imagine say we
+have an
+
+ align:start position:0%
+have an
+ 
+
+ align:start position:0%
+have an
+inhome okay we'll do the same thing this
+
+ align:start position:0%
+inhome okay we'll do the same thing this
+ 
+
+ align:start position:0%
+inhome okay we'll do the same thing this
+is our uh probe beam we're going to come
+
+ align:start position:0%
+is our uh probe beam we're going to come
+ 
+
+ align:start position:0%
+is our uh probe beam we're going to come
+in with the narrow band pump and now
+
+ align:start position:0%
+in with the narrow band pump and now
+ 
+
+ align:start position:0%
+in with the narrow band pump and now
+what happens is we'll sort of bleach a
+
+ align:start position:0%
+what happens is we'll sort of bleach a
+ 
+
+ align:start position:0%
+what happens is we'll sort of bleach a
+hole into this
+
+ align:start position:0%
+hole into this
+ 
+
+ align:start position:0%
+hole into this
+line we're looking specifically at the
+
+ align:start position:0%
+line we're looking specifically at the
+ 
+
+ align:start position:0%
+line we're looking specifically at the
+case of an inhomogeneous Lune so now the
+
+ align:start position:0%
+case of an inhomogeneous Lune so now the
+ 
+
+ align:start position:0%
+case of an inhomogeneous Lune so now the
+change in intensity actually looks quite
+
+ align:start position:0%
+change in intensity actually looks quite
+ 
+
+ align:start position:0%
+change in intensity actually looks quite
+narrow along the prob and this also is
+
+ align:start position:0%
+narrow along the prob and this also is
+ 
+
+ align:start position:0%
+narrow along the prob and this also is
+one slice through a two dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface if we look along the diagonal
+
+ align:start position:0%
+surface if we look along the diagonal
+ 
+
+ align:start position:0%
+surface if we look along the diagonal
+axis this uh this is the slice we took
+
+ align:start position:0%
+axis this uh this is the slice we took
+ 
+
+ align:start position:0%
+axis this uh this is the slice we took
+and it's really quite narrow now if you
+
+ align:start position:0%
+and it's really quite narrow now if you
+ 
+
+ align:start position:0%
+and it's really quite narrow now if you
+map out the whole surface you imagine
+
+ align:start position:0%
+map out the whole surface you imagine
+ 
+
+ align:start position:0%
+map out the whole surface you imagine
+seeing something that looks it's
+
+ align:start position:0%
+seeing something that looks it's
+ 
+
+ align:start position:0%
+seeing something that looks it's
+diagonally elongated like
+
+ align:start position:0%
+diagonally elongated like
+ 
+
+ align:start position:0%
+diagonally elongated like
+this okay I'm drawing just sort of
+
+ align:start position:0%
+this okay I'm drawing just sort of
+ 
+
+ align:start position:0%
+this okay I'm drawing just sort of
+Contours for what you might expect to
+
+ align:start position:0%
+Contours for what you might expect to
+ 
+
+ align:start position:0%
+Contours for what you might expect to
+see um so what is this telling us
+
+ align:start position:0%
+see um so what is this telling us
+ 
+
+ align:start position:0%
+see um so what is this telling us
+well clearly you can see that I take a
+
+ align:start position:0%
+well clearly you can see that I take a
+ 
+
+ align:start position:0%
+well clearly you can see that I take a
+slice along this diagonal axis I'm
+
+ align:start position:0%
+slice along this diagonal axis I'm
+ 
+
+ align:start position:0%
+slice along this diagonal axis I'm
+really just going to be mapping
+
+ align:start position:0%
+really just going to be mapping
+ 
+
+ align:start position:0%
+really just going to be mapping
+out the large broad profile that I saw
+
+ align:start position:0%
+out the large broad profile that I saw
+ 
+
+ align:start position:0%
+out the large broad profile that I saw
+in the absorption
+
+ align:start position:0%
+in the absorption
+ 
+
+ align:start position:0%
+in the absorption
+spect but um this whole burning
+
+ align:start position:0%
+spect but um this whole burning
+ 
+
+ align:start position:0%
+spect but um this whole burning
+experiment is clearly doing some sort of
+
+ align:start position:0%
+experiment is clearly doing some sort of
+ 
+
+ align:start position:0%
+experiment is clearly doing some sort of
+a line narrowing and in fact if you look
+
+ align:start position:0%
+a line narrowing and in fact if you look
+ 
+
+ align:start position:0%
+a line narrowing and in fact if you look
+at a little bit more carefully you can
+
+ align:start position:0%
+at a little bit more carefully you can
+ 
+
+ align:start position:0%
+at a little bit more carefully you can
+convince yourself that slice along this
+
+ align:start position:0%
+convince yourself that slice along this
+ 
+
+ align:start position:0%
+convince yourself that slice along this
+anti- diagonal but that actually gives
+
+ align:start position:0%
+anti- diagonal but that actually gives
+ 
+
+ align:start position:0%
+anti- diagonal but that actually gives
+you the homogeneous
+
+ align:start position:0%
+you the homogeneous
+ 
+
+ align:start position:0%
+you the homogeneous
+line so the idea is this is sort of the
+
+ align:start position:0%
+line so the idea is this is sort of the
+ 
+
+ align:start position:0%
+line so the idea is this is sort of the
+idea of a line shape that a line shape
+
+ align:start position:0%
+idea of a line shape that a line shape
+ 
+
+ align:start position:0%
+idea of a line shape that a line shape
+and analyzing a line shape can give you
+
+ align:start position:0%
+and analyzing a line shape can give you
+ 
+
+ align:start position:0%
+and analyzing a line shape can give you
+some sort of an information about how
+
+ align:start position:0%
+some sort of an information about how
+ 
+
+ align:start position:0%
+some sort of an information about how
+the ensembles meet
+
+ align:start position:0%
+the ensembles meet
+ 
+
+ align:start position:0%
+the ensembles meet
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+and and this is sort of much more than
+
+ align:start position:0%
+and and this is sort of much more than
+ 
+
+ align:start position:0%
+and and this is sort of much more than
+just doing say a photon Ono experiment
+
+ align:start position:0%
+just doing say a photon Ono experiment
+ 
+
+ align:start position:0%
+just doing say a photon Ono experiment
+which gives you an average measurement
+
+ align:start position:0%
+which gives you an average measurement
+ 
+
+ align:start position:0%
+which gives you an average measurement
+you can imagine that this line shape is
+
+ align:start position:0%
+you can imagine that this line shape is
+ 
+
+ align:start position:0%
+you can imagine that this line shape is
+composed of slightly different
+
+ align:start position:0%
+composed of slightly different
+ 
+
+ align:start position:0%
+composed of slightly different
+environments and it vary with frequency
+
+ align:start position:0%
+environments and it vary with frequency
+ 
+
+ align:start position:0%
+environments and it vary with frequency
+and that would show up as you know
+
+ align:start position:0%
+and that would show up as you know
+ 
+
+ align:start position:0%
+and that would show up as you know
+subtle details what this line shape
+
+ align:start position:0%
+subtle details what this line shape
+ 
+
+ align:start position:0%
+subtle details what this line shape
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+like so there's a a lot in then
+
+ align:start position:0%
+like so there's a a lot in then
+ 
+
+ align:start position:0%
+like so there's a a lot in then
+analyzing those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Contour so that that's um that's sort of
+
+ align:start position:0%
+Contour so that that's um that's sort of
+ 
+
+ align:start position:0%
+Contour so that that's um that's sort of
+the motivation for doing uh 2D
+
+ align:start position:0%
+the motivation for doing uh 2D
+ 
+
+ align:start position:0%
+the motivation for doing uh 2D
+these sorts of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um for the moment what I'd like to talk
+
+ align:start position:0%
+um for the moment what I'd like to talk
+ 
+
+ align:start position:0%
+um for the moment what I'd like to talk
+a little bit about is is this case here
+
+ align:start position:0%
+a little bit about is is this case here
+ 
+
+ align:start position:0%
+a little bit about is is this case here
+couple
+
+ align:start position:0%
+couple
+ 
+
+ align:start position:0%
+couple
+systems um because that that's one of
+
+ align:start position:0%
+systems um because that that's one of
+ 
+
+ align:start position:0%
+systems um because that that's one of
+the big uh reasons to do yeah actually
+
+ align:start position:0%
+the big uh reasons to do yeah actually
+ 
+
+ align:start position:0%
+the big uh reasons to do yeah actually
+there is one further example I didn't
+
+ align:start position:0%
+there is one further example I didn't
+ 
+
+ align:start position:0%
+there is one further example I didn't
+think about before but
+
+ align:start position:0%
+think about before but
+ 
+
+ align:start position:0%
+think about before but
+um you can also use this to tell you
+
+ align:start position:0%
+um you can also use this to tell you
+ 
+
+ align:start position:0%
+um you can also use this to tell you
+about reaction kinetics right you can
+
+ align:start position:0%
+about reaction kinetics right you can
+ 
+
+ align:start position:0%
+about reaction kinetics right you can
+imagine that uh you can pump if you have
+
+ align:start position:0%
+imagine that uh you can pump if you have
+ 
+
+ align:start position:0%
+imagine that uh you can pump if you have
+a sort of a chemical equilibrium you can
+
+ align:start position:0%
+a sort of a chemical equilibrium you can
+ 
+
+ align:start position:0%
+a sort of a chemical equilibrium you can
+pump one and probe the other and then
+
+ align:start position:0%
+pump one and probe the other and then
+ 
+
+ align:start position:0%
+pump one and probe the other and then
+time the time rate of change of Heats in
+
+ align:start position:0%
+time the time rate of change of Heats in
+ 
+
+ align:start position:0%
+time the time rate of change of Heats in
+that Sur tell you
+
+ align:start position:0%
+that Sur tell you
+ 
+
+ align:start position:0%
+that Sur tell you
+about but you know once you once you
+
+ align:start position:0%
+about but you know once you once you
+ 
+
+ align:start position:0%
+about but you know once you once you
+think about all the ways and people use
+
+ align:start position:0%
+think about all the ways and people use
+ 
+
+ align:start position:0%
+think about all the ways and people use
+a pump probe experiment that have been
+
+ align:start position:0%
+a pump probe experiment that have been
+ 
+
+ align:start position:0%
+a pump probe experiment that have been
+done for
+
+ align:start position:0%
+done for
+ 
+
+ align:start position:0%
+done for
+decades um you can see that there
+
+ align:start position:0%
+decades um you can see that there
+ 
+
+ align:start position:0%
+decades um you can see that there
+there's a mapping of the two
+
+ align:start position:0%
+there's a mapping of the two
+ 
+
+ align:start position:0%
+there's a mapping of the two
+dimensionals okay
+
+ align:start position:0%
+dimensionals okay
+ 
+
+ align:start position:0%
+dimensionals okay
+anyway um so one of the big applications
+
+ align:start position:0%
+anyway um so one of the big applications
+ 
+
+ align:start position:0%
+anyway um so one of the big applications
+is to understand uh molecular couplings
+
+ align:start position:0%
+is to understand uh molecular couplings
+ 
+
+ align:start position:0%
+is to understand uh molecular couplings
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+interactions right it's trying
+
+ align:start position:0%
+interactions right it's trying
+ 
+
+ align:start position:0%
+interactions right it's trying
+to boil down you know the essence of
+
+ align:start position:0%
+to boil down you know the essence of
+ 
+
+ align:start position:0%
+to boil down you know the essence of
+what's Happening molecularly that gives
+
+ align:start position:0%
+what's Happening molecularly that gives
+ 
+
+ align:start position:0%
+what's Happening molecularly that gives
+rise to a particular spectr and perhaps
+
+ align:start position:0%
+rise to a particular spectr and perhaps
+ 
+
+ align:start position:0%
+rise to a particular spectr and perhaps
+even trying to do things like invert a
+
+ align:start position:0%
+even trying to do things like invert a
+ 
+
+ align:start position:0%
+even trying to do things like invert a
+structure from
+
+ align:start position:0%
+structure from
+ 
+
+ align:start position:0%
+structure from
+it and so to start with that I just
+
+ align:start position:0%
+it and so to start with that I just
+ 
+
+ align:start position:0%
+it and so to start with that I just
+wanted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as I've said
+
+ align:start position:0%
+as I've said
+ 
+
+ align:start position:0%
+as I've said
+before spectroscopy modeling is all one
+
+ align:start position:0%
+before spectroscopy modeling is all one
+ 
+
+ align:start position:0%
+before spectroscopy modeling is all one
+and the same we can't separate the two
+
+ align:start position:0%
+and the same we can't separate the two
+ 
+
+ align:start position:0%
+and the same we can't separate the two
+and so you know in terms of trying to
+
+ align:start position:0%
+and so you know in terms of trying to
+ 
+
+ align:start position:0%
+and so you know in terms of trying to
+describe what gives rise to cross PS in
+
+ align:start position:0%
+describe what gives rise to cross PS in
+ 
+
+ align:start position:0%
+describe what gives rise to cross PS in
+that reflect molecular interactions in
+
+ align:start position:0%
+that reflect molecular interactions in
+ 
+
+ align:start position:0%
+that reflect molecular interactions in
+the Spectra you really have to think
+
+ align:start position:0%
+the Spectra you really have to think
+ 
+
+ align:start position:0%
+the Spectra you really have to think
+about it in terms of a hamiltonian that
+
+ align:start position:0%
+about it in terms of a hamiltonian that
+ 
+
+ align:start position:0%
+about it in terms of a hamiltonian that
+includes these sorts of comps so I just
+
+ align:start position:0%
+includes these sorts of comps so I just
+ 
+
+ align:start position:0%
+includes these sorts of comps so I just
+wanted to write down some of the popular
+
+ align:start position:0%
+wanted to write down some of the popular
+ 
+
+ align:start position:0%
+wanted to write down some of the popular
+ones
+
+ align:start position:0%
+ones
+ 
+
+ align:start position:0%
+ones
+which you will see everywhere and in one
+
+ align:start position:0%
+which you will see everywhere and in one
+ 
+
+ align:start position:0%
+which you will see everywhere and in one
+form or another these are all the same
+
+ align:start position:0%
+form or another these are all the same
+ 
+
+ align:start position:0%
+form or another these are all the same
+thing with very subtle tweaks
+
+ align:start position:0%
+thing with very subtle tweaks
+ 
+
+ align:start position:0%
+thing with very subtle tweaks
+um for people that look at electronic
+
+ align:start position:0%
+um for people that look at electronic
+ 
+
+ align:start position:0%
+um for people that look at electronic
+couplings um in molecular systems it's
+
+ align:start position:0%
+couplings um in molecular systems it's
+ 
+
+ align:start position:0%
+couplings um in molecular systems it's
+called a Frankle aeton panel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T sometimes uh it's known as a couple
+
+ align:start position:0%
+T sometimes uh it's known as a couple
+ 
+
+ align:start position:0%
+T sometimes uh it's known as a couple
+three Lev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system for people
+
+ align:start position:0%
+system for people
+ 
+
+ align:start position:0%
+system for people
+doing vibrational work
+
+ align:start position:0%
+doing vibrational work
+ 
+
+ align:start position:0%
+doing vibrational work
+um might talk about couple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillators and all you know in in
+
+ align:start position:0%
+oscillators and all you know in in
+ 
+
+ align:start position:0%
+oscillators and all you know in in
+essence what you're trying to do derive
+
+ align:start position:0%
+essence what you're trying to do derive
+ 
+
+ align:start position:0%
+essence what you're trying to do derive
+is the minimum hamiltonian that
+
+ align:start position:0%
+is the minimum hamiltonian that
+ 
+
+ align:start position:0%
+is the minimum hamiltonian that
+describes the interaction between two
+
+ align:start position:0%
+describes the interaction between two
+ 
+
+ align:start position:0%
+describes the interaction between two
+molecular
+
+ align:start position:0%
+molecular
+ 
+
+ align:start position:0%
+molecular
+States so um these uh at the simplest
+
+ align:start position:0%
+States so um these uh at the simplest
+ 
+
+ align:start position:0%
+States so um these uh at the simplest
+level these can boil this down to a 2x2
+
+ align:start position:0%
+level these can boil this down to a 2x2
+ 
+
+ align:start position:0%
+level these can boil this down to a 2x2
+Hamilton Quantum States and in a coup
+
+ align:start position:0%
+Hamilton Quantum States and in a coup
+ 
+
+ align:start position:0%
+Hamilton Quantum States and in a coup
+but um so the basic idea behind all of
+
+ align:start position:0%
+but um so the basic idea behind all of
+ 
+
+ align:start position:0%
+but um so the basic idea behind all of
+these is that you know you imagine that
+
+ align:start position:0%
+these is that you know you imagine that
+ 
+
+ align:start position:0%
+these is that you know you imagine that
+I've got
+
+ align:start position:0%
+I've got
+ 
+
+ align:start position:0%
+I've got
+um two different Quantum states that may
+
+ align:start position:0%
+um two different Quantum states that may
+ 
+
+ align:start position:0%
+um two different Quantum states that may
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+on and uh that I'm going to introduce an
+
+ align:start position:0%
+on and uh that I'm going to introduce an
+ 
+
+ align:start position:0%
+on and uh that I'm going to introduce an
+interaction between these two um so of
+
+ align:start position:0%
+interaction between these two um so of
+ 
+
+ align:start position:0%
+interaction between these two um so of
+coupling these two states together with
+
+ align:start position:0%
+coupling these two states together with
+ 
+
+ align:start position:0%
+coupling these two states together with
+an interaction be we know that that sort
+
+ align:start position:0%
+an interaction be we know that that sort
+ 
+
+ align:start position:0%
+an interaction be we know that that sort
+of creates a common ground state and a
+
+ align:start position:0%
+of creates a common ground state and a
+ 
+
+ align:start position:0%
+of creates a common ground state and a
+split
+
+ align:start position:0%
+split
+ 
+
+ align:start position:0%
+split
+now the I if this was um call
+
+ align:start position:0%
+now the I if this was um call
+ 
+
+ align:start position:0%
+now the I if this was um call
+it and um but that this leads to a set
+
+ align:start position:0%
+it and um but that this leads to a set
+ 
+
+ align:start position:0%
+it and um but that this leads to a set
+of iding States let's say I mean in 574
+
+ align:start position:0%
+of iding States let's say I mean in 574
+ 
+
+ align:start position:0%
+of iding States let's say I mean in 574
+we called them plus and minus but I
+
+ align:start position:0%
+we called them plus and minus but I
+ 
+
+ align:start position:0%
+we called them plus and minus but I
+think I'll call them a they call this
+
+ align:start position:0%
+think I'll call them a they call this
+ 
+
+ align:start position:0%
+think I'll call them a they call this
+one a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c and now these are I states of the
+
+ align:start position:0%
+c and now these are I states of the
+ 
+
+ align:start position:0%
+c and now these are I states of the
+material Anon we've been writing down so
+
+ align:start position:0%
+material Anon we've been writing down so
+ 
+
+ align:start position:0%
+material Anon we've been writing down so
+far and these now would be the states
+
+ align:start position:0%
+far and these now would be the states
+ 
+
+ align:start position:0%
+far and these now would be the states
+that one would think about creating
+
+ align:start position:0%
+that one would think about creating
+ 
+
+ align:start position:0%
+that one would think about creating
+resonances with
+
+ align:start position:0%
+resonances with
+ 
+
+ align:start position:0%
+resonances with
+in the the hamiltonian we've been
+
+ align:start position:0%
+in the the hamiltonian we've been
+ 
+
+ align:start position:0%
+in the the hamiltonian we've been
+describing the finding diagrams and the
+
+ align:start position:0%
+describing the finding diagrams and the
+ 
+
+ align:start position:0%
+describing the finding diagrams and the
+lad diagrams we've been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+describing so in in any case usually the
+
+ align:start position:0%
+describing so in in any case usually the
+ 
+
+ align:start position:0%
+describing so in in any case usually the
+information you want is back here so all
+
+ align:start position:0%
+information you want is back here so all
+ 
+
+ align:start position:0%
+information you want is back here so all
+of this is constructed in this local or
+
+ align:start position:0%
+of this is constructed in this local or
+ 
+
+ align:start position:0%
+of this is constructed in this local or
+site molecular
+
+ align:start position:0%
+site molecular
+ 
+
+ align:start position:0%
+site molecular
+basis so this Frankle xon amilon well
+
+ align:start position:0%
+basis so this Frankle xon amilon well
+ 
+
+ align:start position:0%
+basis so this Frankle xon amilon well
+let me just start with something that
+
+ align:start position:0%
+let me just start with something that
+ 
+
+ align:start position:0%
+let me just start with something that
+look familiar like a couple do you
+
+ align:start position:0%
+look familiar like a couple do you
+ 
+
+ align:start position:0%
+look familiar like a couple do you
+imagine two
+
+ align:start position:0%
+imagine two
+ 
+
+ align:start position:0%
+imagine two
+vibrations something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like okay there's one VI one vibration
+
+ align:start position:0%
+like okay there's one VI one vibration
+ 
+
+ align:start position:0%
+like okay there's one VI one vibration
+and there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another was too now you have to couple
+
+ align:start position:0%
+another was too now you have to couple
+ 
+
+ align:start position:0%
+another was too now you have to couple
+them together in some and that involves
+
+ align:start position:0%
+them together in some and that involves
+ 
+
+ align:start position:0%
+them together in some and that involves
+in some way a coordinate or the moment
+
+ align:start position:0%
+in some way a coordinate or the moment
+ 
+
+ align:start position:0%
+in some way a coordinate or the moment
+of of the um these two oscillators so at
+
+ align:start position:0%
+of of the um these two oscillators so at
+ 
+
+ align:start position:0%
+of of the um these two oscillators so at
+the simplest level you might imagine um
+
+ align:start position:0%
+the simplest level you might imagine um
+ 
+
+ align:start position:0%
+the simplest level you might imagine um
+a linear compx it's called
+
+ align:start position:0%
+a linear compx it's called
+ 
+
+ align:start position:0%
+a linear compx it's called
+V or some more complicated combination
+
+ align:start position:0%
+V or some more complicated combination
+ 
+
+ align:start position:0%
+V or some more complicated combination
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+things um the frankal exaton anorm and
+
+ align:start position:0%
+things um the frankal exaton anorm and
+ 
+
+ align:start position:0%
+things um the frankal exaton anorm and
+it's usually Written In terms of raising
+
+ align:start position:0%
+it's usually Written In terms of raising
+ 
+
+ align:start position:0%
+it's usually Written In terms of raising
+and lowering operators in the
+
+ align:start position:0%
+and lowering operators in the
+ 
+
+ align:start position:0%
+and lowering operators in the
+electronics stes and by the way this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it might be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um two diagonal terms and a cent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I just want you to realize that all that
+
+ align:start position:0%
+I just want you to realize that all that
+ 
+
+ align:start position:0%
+I just want you to realize that all that
+is is shorthand for the 2x two Matrix
+
+ align:start position:0%
+is is shorthand for the 2x two Matrix
+ 
+
+ align:start position:0%
+is is shorthand for the 2x two Matrix
+that we know and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+love now just so the thing I want you to
+
+ align:start position:0%
+love now just so the thing I want you to
+ 
+
+ align:start position:0%
+love now just so the thing I want you to
+see is that uh these are really
+
+ align:start position:0%
+see is that uh these are really
+ 
+
+ align:start position:0%
+see is that uh these are really
+functionally the same hamiltoni right if
+
+ align:start position:0%
+functionally the same hamiltoni right if
+ 
+
+ align:start position:0%
+functionally the same hamiltoni right if
+you go now express your operational
+
+ align:start position:0%
+you go now express your operational
+ 
+
+ align:start position:0%
+you go now express your operational
+states of raising and lowering operators
+
+ align:start position:0%
+states of raising and lowering operators
+ 
+
+ align:start position:0%
+states of raising and lowering operators
+and just sort of take the leading
+
+ align:start position:0%
+and just sort of take the leading
+ 
+
+ align:start position:0%
+and just sort of take the leading
+harmonic term in these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrations and this term here is going
+
+ align:start position:0%
+vibrations and this term here is going
+ 
+
+ align:start position:0%
+vibrations and this term here is going
+to have all sorts of um cross cross term
+
+ align:start position:0%
+to have all sorts of um cross cross term
+ 
+
+ align:start position:0%
+to have all sorts of um cross cross term
+and interactions right some of which
+
+ align:start position:0%
+and interactions right some of which
+ 
+
+ align:start position:0%
+and interactions right some of which
+will take the form wrot up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there and extra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Stu so what are these things telling you
+
+ align:start position:0%
+Stu so what are these things telling you
+ 
+
+ align:start position:0%
+Stu so what are these things telling you
+you're saying I've got two two
+
+ align:start position:0%
+you're saying I've got two two
+ 
+
+ align:start position:0%
+you're saying I've got two two
+vibrations two electronic States there's
+
+ align:start position:0%
+vibrations two electronic States there's
+ 
+
+ align:start position:0%
+vibrations two electronic States there's
+a coupling and that coupling um leads to
+
+ align:start position:0%
+a coupling and that coupling um leads to
+ 
+
+ align:start position:0%
+a coupling and that coupling um leads to
+will lead to in talking in this
+
+ align:start position:0%
+will lead to in talking in this
+ 
+
+ align:start position:0%
+will lead to in talking in this
+molecular base it's going to lead to
+
+ align:start position:0%
+molecular base it's going to lead to
+ 
+
+ align:start position:0%
+molecular base it's going to lead to
+energy being transferred from one state
+
+ align:start position:0%
+energy being transferred from one state
+ 
+
+ align:start position:0%
+energy being transferred from one state
+to another in an igen State
+
+ align:start position:0%
+to another in an igen State
+ 
+
+ align:start position:0%
+to another in an igen State
+picture translate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this this uh creates a you know a new
+
+ align:start position:0%
+this this uh creates a you know a new
+ 
+
+ align:start position:0%
+this this uh creates a you know a new
+set of split I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States okay so there is
+
+ align:start position:0%
+States okay so there is
+ 
+
+ align:start position:0%
+States okay so there is
+a now for the purposes of 2D
+
+ align:start position:0%
+a now for the purposes of 2D
+ 
+
+ align:start position:0%
+a now for the purposes of 2D
+spectroscopy we have to worry about a
+
+ align:start position:0%
+spectroscopy we have to worry about a
+ 
+
+ align:start position:0%
+spectroscopy we have to worry about a
+little bit extra um and that is you
+
+ align:start position:0%
+little bit extra um and that is you
+ 
+
+ align:start position:0%
+little bit extra um and that is you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+for electronic systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have to worry about the fact that
+
+ align:start position:0%
+we have to worry about the fact that
+ 
+
+ align:start position:0%
+we have to worry about the fact that
+there may be a in the IG State Pi there
+
+ align:start position:0%
+there may be a in the IG State Pi there
+ 
+
+ align:start position:0%
+there may be a in the IG State Pi there
+is a common ground state and then there
+
+ align:start position:0%
+is a common ground state and then there
+ 
+
+ align:start position:0%
+is a common ground state and then there
+are two um sly excited States also known
+
+ align:start position:0%
+are two um sly excited States also known
+ 
+
+ align:start position:0%
+are two um sly excited States also known
+as the one exiton States and we can call
+
+ align:start position:0%
+as the one exiton States and we can call
+ 
+
+ align:start position:0%
+as the one exiton States and we can call
+those plus or minus but for for my
+
+ align:start position:0%
+those plus or minus but for for my
+ 
+
+ align:start position:0%
+those plus or minus but for for my
+purposes I'd like to call them
+
+ align:start position:0%
+purposes I'd like to call them
+ 
+
+ align:start position:0%
+purposes I'd like to call them
+use my vibrational
+
+ align:start position:0%
+use my vibrational
+ 
+
+ align:start position:0%
+use my vibrational
+language it's yeah no that's not quite
+
+ align:start position:0%
+language it's yeah no that's not quite
+ 
+
+ align:start position:0%
+language it's yeah no that's not quite
+right basically I have um two possible
+
+ align:start position:0%
+right basically I have um two possible
+ 
+
+ align:start position:0%
+right basically I have um two possible
+States and I can put one Quantum of
+
+ align:start position:0%
+States and I can put one Quantum of
+ 
+
+ align:start position:0%
+States and I can put one Quantum of
+exitation into one State or the other we
+
+ align:start position:0%
+exitation into one State or the other we
+ 
+
+ align:start position:0%
+exitation into one State or the other we
+have to recognize there's also the
+
+ align:start position:0%
+have to recognize there's also the
+ 
+
+ align:start position:0%
+have to recognize there's also the
+possibility when you start talking about
+
+ align:start position:0%
+possibility when you start talking about
+ 
+
+ align:start position:0%
+possibility when you start talking about
+multiple interactions that there's a two
+
+ align:start position:0%
+multiple interactions that there's a two
+ 
+
+ align:start position:0%
+multiple interactions that there's a two
+exiton state where you've got one
+
+ align:start position:0%
+exiton state where you've got one
+ 
+
+ align:start position:0%
+exiton state where you've got one
+exitation um in each state
+
+ align:start position:0%
+exitation um in each state
+ 
+
+ align:start position:0%
+exitation um in each state
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um we in a coupled electronic system
+
+ align:start position:0%
+um we in a coupled electronic system
+ 
+
+ align:start position:0%
+um we in a coupled electronic system
+we're really four levels you have to
+
+ align:start position:0%
+we're really four levels you have to
+ 
+
+ align:start position:0%
+we're really four levels you have to
+worry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about um in a vibrational system it's
+
+ align:start position:0%
+about um in a vibrational system it's
+ 
+
+ align:start position:0%
+about um in a vibrational system it's
+basically the same except that you know
+
+ align:start position:0%
+basically the same except that you know
+ 
+
+ align:start position:0%
+basically the same except that you know
+with um bons you can uh unlike the
+
+ align:start position:0%
+with um bons you can uh unlike the
+ 
+
+ align:start position:0%
+with um bons you can uh unlike the
+firion you can put multiple excitations
+
+ align:start position:0%
+firion you can put multiple excitations
+ 
+
+ align:start position:0%
+firion you can put multiple excitations
+into the same vibration so there's an
+
+ align:start position:0%
+into the same vibration so there's an
+ 
+
+ align:start position:0%
+into the same vibration so there's an
+additional
+
+ align:start position:0%
+additional
+ 
+
+ align:start position:0%
+additional
+process you think of the I of a coupled
+
+ align:start position:0%
+process you think of the I of a coupled
+ 
+
+ align:start position:0%
+process you think of the I of a coupled
+vibration system not only do you have
+
+ align:start position:0%
+vibration system not only do you have
+ 
+
+ align:start position:0%
+vibration system not only do you have
+the ground
+
+ align:start position:0%
+the ground
+ 
+
+ align:start position:0%
+the ground
+state the U singly excited ion States
+
+ align:start position:0%
+state the U singly excited ion States
+ 
+
+ align:start position:0%
+state the U singly excited ion States
+but you also
+
+ align:start position:0%
+but you also
+ 
+
+ align:start position:0%
+but you also
+have three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states two Quantum in either of the hi
+
+ align:start position:0%
+states two Quantum in either of the hi
+ 
+
+ align:start position:0%
+states two Quantum in either of the hi
+States and also you know what we like to
+
+ align:start position:0%
+States and also you know what we like to
+ 
+
+ align:start position:0%
+States and also you know what we like to
+call the combination it's where youve
+
+ align:start position:0%
+call the combination it's where youve
+ 
+
+ align:start position:0%
+call the combination it's where youve
+got one in each
+
+ align:start position:0%
+got one in each
+ 
+
+ align:start position:0%
+got one in each
+and so it's these four level and six
+
+ align:start position:0%
+and so it's these four level and six
+ 
+
+ align:start position:0%
+and so it's these four level and six
+level systems that um that are important
+
+ align:start position:0%
+level systems that um that are important
+ 
+
+ align:start position:0%
+level systems that um that are important
+to your sort of understanding the origin
+
+ align:start position:0%
+to your sort of understanding the origin
+ 
+
+ align:start position:0%
+to your sort of understanding the origin
+of all the peaks in the 2D
+
+ align:start position:0%
+of all the peaks in the 2D
+ 
+
+ align:start position:0%
+of all the peaks in the 2D
+spect
+
+ align:start position:0%
+spect
+ 
+
+ align:start position:0%
+spect
+so okay now when you go and uh apply the
+
+ align:start position:0%
+so okay now when you go and uh apply the
+ 
+
+ align:start position:0%
+so okay now when you go and uh apply the
+pump probe wave thinking that let's take
+
+ align:start position:0%
+pump probe wave thinking that let's take
+ 
+
+ align:start position:0%
+pump probe wave thinking that let's take
+this double resonance approach um and
+
+ align:start position:0%
+this double resonance approach um and
+ 
+
+ align:start position:0%
+this double resonance approach um and
+assume that the system always begins in
+
+ align:start position:0%
+assume that the system always begins in
+ 
+
+ align:start position:0%
+assume that the system always begins in
+this lowest lying State and you can of
+
+ align:start position:0%
+this lowest lying State and you can of
+ 
+
+ align:start position:0%
+this lowest lying State and you can of
+immediately map out a set of interaction
+
+ align:start position:0%
+immediately map out a set of interaction
+ 
+
+ align:start position:0%
+immediately map out a set of interaction
+processes that will give rise to a set
+
+ align:start position:0%
+processes that will give rise to a set
+ 
+
+ align:start position:0%
+processes that will give rise to a set
+of peaks in this spectrum so taking
+
+ align:start position:0%
+of peaks in this spectrum so taking
+ 
+
+ align:start position:0%
+of peaks in this spectrum so taking
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+so so for the electronic case
+
+ align:start position:0%
+so so for the electronic case
+ 
+
+ align:start position:0%
+so so for the electronic case
+um you can see any initial interaction
+
+ align:start position:0%
+um you can see any initial interaction
+ 
+
+ align:start position:0%
+um you can see any initial interaction
+um with the electronic system is going
+
+ align:start position:0%
+um with the electronic system is going
+ 
+
+ align:start position:0%
+um with the electronic system is going
+to drive one of these one Quantum state
+
+ align:start position:0%
+to drive one of these one Quantum state
+ 
+
+ align:start position:0%
+to drive one of these one Quantum state
+so you um along the pump
+
+ align:start position:0%
+so you um along the pump
+ 
+
+ align:start position:0%
+so you um along the pump
+axis you know that you're only going to
+
+ align:start position:0%
+axis you know that you're only going to
+ 
+
+ align:start position:0%
+axis you know that you're only going to
+have resonances at let's see what should
+
+ align:start position:0%
+have resonances at let's see what should
+ 
+
+ align:start position:0%
+have resonances at let's see what should
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call let's call this
+
+ align:start position:0%
+call let's call this
+ 
+
+ align:start position:0%
+call let's call this
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c make a b make a
+
+ align:start position:0%
+c make a b make a
+ 
+
+ align:start position:0%
+c make a b make a
+CA you know that this is uh all of the
+
+ align:start position:0%
+CA you know that this is uh all of the
+ 
+
+ align:start position:0%
+CA you know that this is uh all of the
+pains that we observe we going going to
+
+ align:start position:0%
+pains that we observe we going going to
+ 
+
+ align:start position:0%
+pains that we observe we going going to
+have to be along these two directions
+
+ align:start position:0%
+have to be along these two directions
+ 
+
+ align:start position:0%
+have to be along these two directions
+and that in fact you know exactly what
+
+ align:start position:0%
+and that in fact you know exactly what
+ 
+
+ align:start position:0%
+and that in fact you know exactly what
+your linear spectrum is going to look
+
+ align:start position:0%
+your linear spectrum is going to look
+ 
+
+ align:start position:0%
+your linear spectrum is going to look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that two peaks that correspond to those
+
+ align:start position:0%
+that two peaks that correspond to those
+ 
+
+ align:start position:0%
+that two peaks that correspond to those
+ion stes the sly
+
+ align:start position:0%
+ion stes the sly
+ 
+
+ align:start position:0%
+ion stes the sly
+excited now you look at the possible
+
+ align:start position:0%
+excited now you look at the possible
+ 
+
+ align:start position:0%
+excited now you look at the possible
+permutations of how the system can
+
+ align:start position:0%
+permutations of how the system can
+ 
+
+ align:start position:0%
+permutations of how the system can
+evolve upwards and the
+
+ align:start position:0%
+evolve upwards and the
+ 
+
+ align:start position:0%
+evolve upwards and the
+possibilities involve well let's let me
+
+ align:start position:0%
+possibilities involve well let's let me
+ 
+
+ align:start position:0%
+possibilities involve well let's let me
+draw some
+
+ align:start position:0%
+draw some
+ 
+
+ align:start position:0%
+draw some
+possible what you'll find is that
+
+ align:start position:0%
+possible what you'll find is that
+ 
+
+ align:start position:0%
+possible what you'll find is that
+there's six Poss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes and uh actually I'm offsetting
+
+ align:start position:0%
+processes and uh actually I'm offsetting
+ 
+
+ align:start position:0%
+processes and uh actually I'm offsetting
+these two but uh the way I wrote the
+
+ align:start position:0%
+these two but uh the way I wrote the
+ 
+
+ align:start position:0%
+these two but uh the way I wrote the
+hamiltonian these are going to be
+
+ align:start position:0%
+hamiltonian these are going to be
+ 
+
+ align:start position:0%
+hamiltonian these are going to be
+sitting on top of one
+
+ align:start position:0%
+sitting on top of one
+ 
+
+ align:start position:0%
+sitting on top of one
+another um you'll see that these
+
+ align:start position:0%
+another um you'll see that these
+ 
+
+ align:start position:0%
+another um you'll see that these
+diagonal Peaks and one of these cross
+
+ align:start position:0%
+diagonal Peaks and one of these cross
+ 
+
+ align:start position:0%
+diagonal Peaks and one of these cross
+Peaks will all positive
+
+ align:start position:0%
+Peaks will all positive
+ 
+
+ align:start position:0%
+Peaks will all positive
+sign and the other cross a negative sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is okay what gives rise to these things
+
+ align:start position:0%
+is okay what gives rise to these things
+ 
+
+ align:start position:0%
+is okay what gives rise to these things
+well first of all the diagonal stuff
+
+ align:start position:0%
+well first of all the diagonal stuff
+ 
+
+ align:start position:0%
+well first of all the diagonal stuff
+that should be obvious this is just all
+
+ align:start position:0%
+that should be obvious this is just all
+ 
+
+ align:start position:0%
+that should be obvious this is just all
+the pump probe stuff we've already
+
+ align:start position:0%
+the pump probe stuff we've already
+ 
+
+ align:start position:0%
+the pump probe stuff we've already
+written before that's a single
+
+ align:start position:0%
+written before that's a single
+ 
+
+ align:start position:0%
+written before that's a single
+transition where you drive the system
+
+ align:start position:0%
+transition where you drive the system
+ 
+
+ align:start position:0%
+transition where you drive the system
+upward create a population in that
+
+ align:start position:0%
+upward create a population in that
+ 
+
+ align:start position:0%
+upward create a population in that
+state um and
+
+ align:start position:0%
+state um and
+ 
+
+ align:start position:0%
+state um and
+then uh probe that
+
+ align:start position:0%
+then uh probe that
+ 
+
+ align:start position:0%
+then uh probe that
+state these cross p speaks you know uh
+
+ align:start position:0%
+state these cross p speaks you know uh
+ 
+
+ align:start position:0%
+state these cross p speaks you know uh
+to first order that is um the process I
+
+ align:start position:0%
+to first order that is um the process I
+ 
+
+ align:start position:0%
+to first order that is um the process I
+described up there cartoon ver that
+
+ align:start position:0%
+described up there cartoon ver that
+ 
+
+ align:start position:0%
+described up there cartoon ver that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+driving population into one
+
+ align:start position:0%
+driving population into one
+ 
+
+ align:start position:0%
+driving population into one
+state and then probing the other
+
+ align:start position:0%
+state and then probing the other
+ 
+
+ align:start position:0%
+state and then probing the other
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+okay now this uh what's important is
+
+ align:start position:0%
+okay now this uh what's important is
+ 
+
+ align:start position:0%
+okay now this uh what's important is
+this other negative diagram and that
+
+ align:start position:0%
+this other negative diagram and that
+ 
+
+ align:start position:0%
+this other negative diagram and that
+that's where these two Exon or two
+
+ align:start position:0%
+that's where these two Exon or two
+ 
+
+ align:start position:0%
+that's where these two Exon or two
+quantum States come in those have
+
+ align:start position:0%
+quantum States come in those have
+ 
+
+ align:start position:0%
+quantum States come in those have
+opposite signs this going back to our
+
+ align:start position:0%
+opposite signs this going back to our
+ 
+
+ align:start position:0%
+opposite signs this going back to our
+how many times do you act on the bra
+
+ align:start position:0%
+how many times do you act on the bra
+ 
+
+ align:start position:0%
+how many times do you act on the bra
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+process and they involve um processes in
+
+ align:start position:0%
+process and they involve um processes in
+ 
+
+ align:start position:0%
+process and they involve um processes in
+which you excite one vibration and then
+
+ align:start position:0%
+which you excite one vibration and then
+ 
+
+ align:start position:0%
+which you excite one vibration and then
+add in another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantum uh onto the other mode so let's
+
+ align:start position:0%
+quantum uh onto the other mode so let's
+ 
+
+ align:start position:0%
+quantum uh onto the other mode so let's
+say This
+
+ align:start position:0%
+say This
+ 
+
+ align:start position:0%
+say This
+Means A to B means we are putting let's
+
+ align:start position:0%
+Means A to B means we are putting let's
+ 
+
+ align:start position:0%
+Means A to B means we are putting let's
+start in the ground state put one
+
+ align:start position:0%
+start in the ground state put one
+ 
+
+ align:start position:0%
+start in the ground state put one
+Quantum into
+
+ align:start position:0%
+Quantum into
+ 
+
+ align:start position:0%
+Quantum into
+State B and then I'm going to add a
+
+ align:start position:0%
+State B and then I'm going to add a
+ 
+
+ align:start position:0%
+State B and then I'm going to add a
+Quantum in the state
+
+ align:start position:0%
+Quantum in the state
+ 
+
+ align:start position:0%
+Quantum in the state
+a and then I'll
+
+ align:start position:0%
+a and then I'll
+ 
+
+ align:start position:0%
+a and then I'll
+uh prob that state okay so now
+
+ align:start position:0%
+uh prob that state okay so now
+ 
+
+ align:start position:0%
+uh prob that state okay so now
+technically this
+
+ align:start position:0%
+technically this
+ 
+
+ align:start position:0%
+technically this
+transition comes out at a
+
+ align:start position:0%
+transition comes out at a
+ 
+
+ align:start position:0%
+transition comes out at a
+frequency call this guy
+
+ align:start position:0%
+frequency call this guy
+ 
+
+ align:start position:0%
+frequency call this guy
+D um we started at Omega VA and then
+
+ align:start position:0%
+D um we started at Omega VA and then
+ 
+
+ align:start position:0%
+D um we started at Omega VA and then
+we're going to observe the system at
+
+ align:start position:0%
+we're going to observe the system at
+ 
+
+ align:start position:0%
+we're going to observe the system at
+Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DB
+
+ align:start position:0%
+DB
+ 
+
+ align:start position:0%
+DB
+so actually I'm really doing it wrong
+
+ align:start position:0%
+so actually I'm really doing it wrong
+ 
+
+ align:start position:0%
+so actually I'm really doing it wrong
+now this negative Peak is going to be at
+
+ align:start position:0%
+now this negative Peak is going to be at
+ 
+
+ align:start position:0%
+now this negative Peak is going to be at
+a slightly different
+
+ align:start position:0%
+a slightly different
+ 
+
+ align:start position:0%
+a slightly different
+frequency now in this one thing you'll
+
+ align:start position:0%
+frequency now in this one thing you'll
+ 
+
+ align:start position:0%
+frequency now in this one thing you'll
+notice is in this very commonly written
+
+ align:start position:0%
+notice is in this very commonly written
+ 
+
+ align:start position:0%
+notice is in this very commonly written
+hamiltonian in which you just have
+
+ align:start position:0%
+hamiltonian in which you just have
+ 
+
+ align:start position:0%
+hamiltonian in which you just have
+simple linear
+
+ align:start position:0%
+simple linear
+ 
+
+ align:start position:0%
+simple linear
+couplings simple AAG terms
+
+ align:start position:0%
+couplings simple AAG terms
+ 
+
+ align:start position:0%
+couplings simple AAG terms
+simple linear q1 Q2 types of terms and
+
+ align:start position:0%
+simple linear q1 Q2 types of terms and
+ 
+
+ align:start position:0%
+simple linear q1 Q2 types of terms and
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+systems coincidentally it
+
+ align:start position:0%
+systems coincidentally it
+ 
+
+ align:start position:0%
+systems coincidentally it
+happens not coincidentally quite on
+
+ align:start position:0%
+happens not coincidentally quite on
+ 
+
+ align:start position:0%
+happens not coincidentally quite on
+purpose that um
+
+ align:start position:0%
+purpose that um
+ 
+
+ align:start position:0%
+purpose that um
+Omega VA
+
+ align:start position:0%
+Omega VA
+ 
+
+ align:start position:0%
+Omega VA
+a and Omega DC are
+
+ align:start position:0%
+a and Omega DC are
+ 
+
+ align:start position:0%
+a and Omega DC are
+identical not only that but um
+
+ align:start position:0%
+identical not only that but um
+ 
+
+ align:start position:0%
+identical not only that but um
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+CA and Omega DB they're identical also
+
+ align:start position:0%
+CA and Omega DB they're identical also
+ 
+
+ align:start position:0%
+CA and Omega DB they're identical also
+and what that means is you're going to
+
+ align:start position:0%
+and what that means is you're going to
+ 
+
+ align:start position:0%
+and what that means is you're going to
+have two terms with opposite sign that
+
+ align:start position:0%
+have two terms with opposite sign that
+ 
+
+ align:start position:0%
+have two terms with opposite sign that
+show up right on top of each other
+
+ align:start position:0%
+show up right on top of each other
+ 
+
+ align:start position:0%
+show up right on top of each other
+disappears so for this kind of a simple
+
+ align:start position:0%
+disappears so for this kind of a simple
+ 
+
+ align:start position:0%
+disappears so for this kind of a simple
+system and that same goes for a coupled
+
+ align:start position:0%
+system and that same goes for a coupled
+ 
+
+ align:start position:0%
+system and that same goes for a coupled
+harmonic oscillator system um see these
+
+ align:start position:0%
+harmonic oscillator system um see these
+ 
+
+ align:start position:0%
+harmonic oscillator system um see these
+cross PS actually vanish and this is a
+
+ align:start position:0%
+cross PS actually vanish and this is a
+ 
+
+ align:start position:0%
+cross PS actually vanish and this is a
+manifestation of the fact that there is
+
+ align:start position:0%
+manifestation of the fact that there is
+ 
+
+ align:start position:0%
+manifestation of the fact that there is
+no nonlinear response from a harmonic
+
+ align:start position:0%
+no nonlinear response from a harmonic
+ 
+
+ align:start position:0%
+no nonlinear response from a harmonic
+system you need some sort of uh more
+
+ align:start position:0%
+system you need some sort of uh more
+ 
+
+ align:start position:0%
+system you need some sort of uh more
+complex coupling and harmonicity and
+
+ align:start position:0%
+complex coupling and harmonicity and
+ 
+
+ align:start position:0%
+complex coupling and harmonicity and
+harmonicity in a vibration system that's
+
+ align:start position:0%
+harmonicity in a vibration system that's
+ 
+
+ align:start position:0%
+harmonicity in a vibration system that's
+the word we use there or this may mean
+
+ align:start position:0%
+the word we use there or this may mean
+ 
+
+ align:start position:0%
+the word we use there or this may mean
+um other types of electron electron
+
+ align:start position:0%
+um other types of electron electron
+ 
+
+ align:start position:0%
+um other types of electron electron
+interactions to give you a measurable um
+
+ align:start position:0%
+interactions to give you a measurable um
+ 
+
+ align:start position:0%
+interactions to give you a measurable um
+type of inter uh coupling or interaction
+
+ align:start position:0%
+type of inter uh coupling or interaction
+ 
+
+ align:start position:0%
+type of inter uh coupling or interaction
+that one sees in a 2d Spectrum what do I
+
+ align:start position:0%
+that one sees in a 2d Spectrum what do I
+ 
+
+ align:start position:0%
+that one sees in a 2d Spectrum what do I
+mean by
+
+ align:start position:0%
+mean by
+ 
+
+ align:start position:0%
+mean by
+that what I mean is in a physical just
+
+ align:start position:0%
+that what I mean is in a physical just
+ 
+
+ align:start position:0%
+that what I mean is in a physical just
+sort of from a physical picture
+
+ align:start position:0%
+sort of from a physical picture
+ 
+
+ align:start position:0%
+sort of from a physical picture
+sense I need an effect where there is a
+
+ align:start position:0%
+sense I need an effect where there is a
+ 
+
+ align:start position:0%
+sense I need an effect where there is a
+difference where if I put one Quantum of
+
+ align:start position:0%
+difference where if I put one Quantum of
+ 
+
+ align:start position:0%
+difference where if I put one Quantum of
+exaltation into one state and then
+
+ align:start position:0%
+exaltation into one state and then
+ 
+
+ align:start position:0%
+exaltation into one state and then
+another quantum into the other state
+
+ align:start position:0%
+another quantum into the other state
+ 
+
+ align:start position:0%
+another quantum into the other state
+that that is not merely just the sum of
+
+ align:start position:0%
+that that is not merely just the sum of
+ 
+
+ align:start position:0%
+that that is not merely just the sum of
+the two energies the I need some
+
+ align:start position:0%
+the two energies the I need some
+ 
+
+ align:start position:0%
+the two energies the I need some
+physical effect where if I put energy
+
+ align:start position:0%
+physical effect where if I put energy
+ 
+
+ align:start position:0%
+physical effect where if I put energy
+into one state they communicate with
+
+ align:start position:0%
+into one state they communicate with
+ 
+
+ align:start position:0%
+into one state they communicate with
+each other and so by definition I will
+
+ align:start position:0%
+each other and so by definition I will
+ 
+
+ align:start position:0%
+each other and so by definition I will
+need to put a little less or a little
+
+ align:start position:0%
+need to put a little less or a little
+ 
+
+ align:start position:0%
+need to put a little less or a little
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+energy uh into the system for that
+
+ align:start position:0%
+energy uh into the system for that
+ 
+
+ align:start position:0%
+energy uh into the system for that
+second quum just because of the initial
+
+ align:start position:0%
+second quum just because of the initial
+ 
+
+ align:start position:0%
+second quum just because of the initial
+interaction uh and so uh how do you
+
+ align:start position:0%
+interaction uh and so uh how do you
+ 
+
+ align:start position:0%
+interaction uh and so uh how do you
+write those sorts of things in the case
+
+ align:start position:0%
+write those sorts of things in the case
+ 
+
+ align:start position:0%
+write those sorts of things in the case
+of um vibrational systems it comes about
+
+ align:start position:0%
+of um vibrational systems it comes about
+ 
+
+ align:start position:0%
+of um vibrational systems it comes about
+from anharmonicities it might be the
+
+ align:start position:0%
+from anharmonicities it might be the
+ 
+
+ align:start position:0%
+from anharmonicities it might be the
+higher order terms and the anharmonic
+
+ align:start position:0%
+higher order terms and the anharmonic
+ 
+
+ align:start position:0%
+higher order terms and the anharmonic
+potential it may be nonlinear
+
+ align:start position:0%
+potential it may be nonlinear
+ 
+
+ align:start position:0%
+potential it may be nonlinear
+couplings over in the case of the exaton
+
+ align:start position:0%
+couplings over in the case of the exaton
+ 
+
+ align:start position:0%
+couplings over in the case of the exaton
+hamiltonian we're saying things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like imagine you have a coupling
+
+ align:start position:0%
+like imagine you have a coupling
+ 
+
+ align:start position:0%
+like imagine you have a coupling
+constant that goes as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ability to put an exitation into n
+
+ align:start position:0%
+the ability to put an exitation into n
+ 
+
+ align:start position:0%
+the ability to put an exitation into n
+depends on whether I have populated M
+
+ align:start position:0%
+depends on whether I have populated M
+ 
+
+ align:start position:0%
+depends on whether I have populated M
+there and the magnitude of that effect
+
+ align:start position:0%
+there and the magnitude of that effect
+ 
+
+ align:start position:0%
+there and the magnitude of that effect
+depends on data so you need um a term
+
+ align:start position:0%
+depends on data so you need um a term
+ 
+
+ align:start position:0%
+depends on data so you need um a term
+that goes higher order than just simple
+
+ align:start position:0%
+that goes higher order than just simple
+ 
+
+ align:start position:0%
+that goes higher order than just simple
+AA diagr types of terms what that leads
+
+ align:start position:0%
+AA diagr types of terms what that leads
+ 
+
+ align:start position:0%
+AA diagr types of terms what that leads
+to is a shift of this um exaton
+
+ align:start position:0%
+to is a shift of this um exaton
+ 
+
+ align:start position:0%
+to is a shift of this um exaton
+State um typically an harmonicity look
+
+ align:start position:0%
+State um typically an harmonicity look
+ 
+
+ align:start position:0%
+State um typically an harmonicity look
+in vibrational systems will shift down
+
+ align:start position:0%
+in vibrational systems will shift down
+ 
+
+ align:start position:0%
+in vibrational systems will shift down
+all of these levels in the electronic
+
+ align:start position:0%
+all of these levels in the electronic
+ 
+
+ align:start position:0%
+all of these levels in the electronic
+case you can imagine shifts both up and
+
+ align:start position:0%
+case you can imagine shifts both up and
+ 
+
+ align:start position:0%
+case you can imagine shifts both up and
+down and it really just depends on the
+
+ align:start position:0%
+down and it really just depends on the
+ 
+
+ align:start position:0%
+down and it really just depends on the
+electron electron interactions if you
+
+ align:start position:0%
+electron electron interactions if you
+ 
+
+ align:start position:0%
+electron electron interactions if you
+have positive or negative coupl see yeah
+
+ align:start position:0%
+have positive or negative coupl see yeah
+ 
+
+ align:start position:0%
+have positive or negative coupl see yeah
+right positive and negative couplings
+
+ align:start position:0%
+right positive and negative couplings
+ 
+
+ align:start position:0%
+right positive and negative couplings
+can take this up or down and that will
+
+ align:start position:0%
+can take this up or down and that will
+ 
+
+ align:start position:0%
+can take this up or down and that will
+dictate which way this peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shifts and then what we do is go sort of
+
+ align:start position:0%
+shifts and then what we do is go sort of
+ 
+
+ align:start position:0%
+shifts and then what we do is go sort of
+analyze the splittings between these
+
+ align:start position:0%
+analyze the splittings between these
+ 
+
+ align:start position:0%
+analyze the splittings between these
+cross Peaks and and that gives rise to
+
+ align:start position:0%
+cross Peaks and and that gives rise to
+ 
+
+ align:start position:0%
+cross Peaks and and that gives rise to
+sort of information about what the
+
+ align:start position:0%
+sort of information about what the
+ 
+
+ align:start position:0%
+sort of information about what the
+coupling
+
+ align:start position:0%
+coupling
+ 
+
+ align:start position:0%
+coupling
+is these will be related to electron
+
+ align:start position:0%
+is these will be related to electron
+ 
+
+ align:start position:0%
+is these will be related to electron
+electron equ okay so the vibrational
+
+ align:start position:0%
+electron equ okay so the vibrational
+ 
+
+ align:start position:0%
+electron equ okay so the vibrational
+system is exactly the same I mean at
+
+ align:start position:0%
+system is exactly the same I mean at
+ 
+
+ align:start position:0%
+system is exactly the same I mean at
+first level you're going to end up
+
+ align:start position:0%
+first level you're going to end up
+ 
+
+ align:start position:0%
+first level you're going to end up
+with you know two diagonal PS these are
+
+ align:start position:0%
+with you know two diagonal PS these are
+ 
+
+ align:start position:0%
+with you know two diagonal PS these are
+now going to have a doublet shape and
+
+ align:start position:0%
+now going to have a doublet shape and
+ 
+
+ align:start position:0%
+now going to have a doublet shape and
+that just reflects the fact that you
+
+ align:start position:0%
+that just reflects the fact that you
+ 
+
+ align:start position:0%
+that just reflects the fact that you
+have these two one States
+
+ align:start position:0%
+have these two one States
+ 
+
+ align:start position:0%
+have these two one States
+also and proc speaks between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them and in this case it's similar but
+
+ align:start position:0%
+them and in this case it's similar but
+ 
+
+ align:start position:0%
+them and in this case it's similar but
+um the way I've written that hamiltonian
+
+ align:start position:0%
+um the way I've written that hamiltonian
+ 
+
+ align:start position:0%
+um the way I've written that hamiltonian
+over there splitting between these PES
+
+ align:start position:0%
+over there splitting between these PES
+ 
+
+ align:start position:0%
+over there splitting between these PES
+um in the case that you have two
+
+ align:start position:0%
+um in the case that you have two
+ 
+
+ align:start position:0%
+um in the case that you have two
+degenerate oscillators this is going to
+
+ align:start position:0%
+degenerate oscillators this is going to
+ 
+
+ align:start position:0%
+degenerate oscillators this is going to
+be twice the
+
+ align:start position:0%
+be twice the
+ 
+
+ align:start position:0%
+be twice the
+comp and that just reflects the fact
+
+ align:start position:0%
+comp and that just reflects the fact
+ 
+
+ align:start position:0%
+comp and that just reflects the fact
+that um the
+
+ align:start position:0%
+that um the
+ 
+
+ align:start position:0%
+that um the
+energy of the combination band in a
+
+ align:start position:0%
+energy of the combination band in a
+ 
+
+ align:start position:0%
+energy of the combination band in a
+coupled system is to L written it's
+
+ align:start position:0%
+coupled system is to L written it's
+ 
+
+ align:start position:0%
+coupled system is to L written it's
+Omega 1 it's the sum of the two energies
+
+ align:start position:0%
+Omega 1 it's the sum of the two energies
+ 
+
+ align:start position:0%
+Omega 1 it's the sum of the two energies
+minus twice coupling Between the
+
+ align:start position:0%
+minus twice coupling Between the
+ 
+
+ align:start position:0%
+minus twice coupling Between the
+States you had a question so would the
+
+ align:start position:0%
+States you had a question so would the
+ 
+
+ align:start position:0%
+States you had a question so would the
+same whether you have inter cpls you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+so in so in this vibrational case as do
+
+ align:start position:0%
+so in so in this vibrational case as do
+ 
+
+ align:start position:0%
+so in so in this vibrational case as do
+it turns out if you just do a simple
+
+ align:start position:0%
+it turns out if you just do a simple
+ 
+
+ align:start position:0%
+it turns out if you just do a simple
+linear coupling between anharmonic
+
+ align:start position:0%
+linear coupling between anharmonic
+ 
+
+ align:start position:0%
+linear coupling between anharmonic
+oscillators you will um get
+
+ align:start position:0%
+oscillators you will um get
+ 
+
+ align:start position:0%
+oscillators you will um get
+anharmonically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shifted what if you don't have just have
+
+ align:start position:0%
+shifted what if you don't have just have
+ 
+
+ align:start position:0%
+shifted what if you don't have just have
+two an no then you won't u i mean then
+
+ align:start position:0%
+two an no then you won't u i mean then
+ 
+
+ align:start position:0%
+two an no then you won't u i mean then
+you really have two independent
+
+ align:start position:0%
+you really have two independent
+ 
+
+ align:start position:0%
+you really have two independent
+oscillators you need something that you
+
+ align:start position:0%
+oscillators you need something that you
+ 
+
+ align:start position:0%
+oscillators you need something that you
+mean you need some sort of a term that
+
+ align:start position:0%
+mean you need some sort of a term that
+ 
+
+ align:start position:0%
+mean you need some sort of a term that
+laws the
+
+ align:start position:0%
+laws the
+ 
+
+ align:start position:0%
+laws the
+two you do need something in one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coord and and what this is saying is
+
+ align:start position:0%
+coord and and what this is saying is
+ 
+
+ align:start position:0%
+coord and and what this is saying is
+that um for simple harmonic system are
+
+ align:start position:0%
+that um for simple harmonic system are
+ 
+
+ align:start position:0%
+that um for simple harmonic system are
+simple two Lev systems with the linear
+
+ align:start position:0%
+simple two Lev systems with the linear
+ 
+
+ align:start position:0%
+simple two Lev systems with the linear
+couplings and harmonic Behavior are sort
+
+ align:start position:0%
+couplings and harmonic Behavior are sort
+ 
+
+ align:start position:0%
+couplings and harmonic Behavior are sort
+of synonymous with one another and if
+
+ align:start position:0%
+of synonymous with one another and if
+ 
+
+ align:start position:0%
+of synonymous with one another and if
+you have linear cup cup LS and harmonic
+
+ align:start position:0%
+you have linear cup cup LS and harmonic
+ 
+
+ align:start position:0%
+you have linear cup cup LS and harmonic
+Behavior there is no nonlinear response
+
+ align:start position:0%
+Behavior there is no nonlinear response
+ 
+
+ align:start position:0%
+Behavior there is no nonlinear response
+when you really work
+
+ align:start position:0%
+when you really work
+ 
+
+ align:start position:0%
+when you really work
+through there you will always find terms
+
+ align:start position:0%
+through there you will always find terms
+ 
+
+ align:start position:0%
+through there you will always find terms
+that have opposite sign that destructive
+
+ align:start position:0%
+that have opposite sign that destructive
+ 
+
+ align:start position:0%
+that have opposite sign that destructive
+they interfere
+
+ align:start position:0%
+they interfere
+ 
+
+ align:start position:0%
+they interfere
+with other so but if you had diagonales
+
+ align:start position:0%
+with other so but if you had diagonales
+ 
+
+ align:start position:0%
+with other so but if you had diagonales
+would get her that frequency matching
+
+ align:start position:0%
+would get her that frequency matching
+ 
+
+ align:start position:0%
+would get her that frequency matching
+between the two qu of levels one one
+
+ align:start position:0%
+between the two qu of levels one one
+ 
+
+ align:start position:0%
+between the two qu of levels one one
+yeah exactly so that
+
+ align:start position:0%
+yeah exactly so that
+ 
+
+ align:start position:0%
+yeah exactly so that
+would that get rid of the cancellation
+
+ align:start position:0%
+would that get rid of the cancellation
+ 
+
+ align:start position:0%
+would that get rid of the cancellation
+between the cross yeah exactly so you
+
+ align:start position:0%
+between the cross yeah exactly so you
+ 
+
+ align:start position:0%
+between the cross yeah exactly so you
+can take anharmonic oscillators with
+
+ align:start position:0%
+can take anharmonic oscillators with
+ 
+
+ align:start position:0%
+can take anharmonic oscillators with
+linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coupling okay
+
+ align:start position:0%
+coupling okay
+ 
+
+ align:start position:0%
+coupling okay
+um what the why the pie on the diagonal
+
+ align:start position:0%
+um what the why the pie on the diagonal
+ 
+
+ align:start position:0%
+um what the why the pie on the diagonal
+have two loes again um so that that
+
+ align:start position:0%
+have two loes again um so that that
+ 
+
+ align:start position:0%
+have two loes again um so that that
+reflects the overtone we put two P into
+
+ align:start position:0%
+reflects the overtone we put two P into
+ 
+
+ align:start position:0%
+reflects the overtone we put two P into
+the same vition so this feet reflects
+
+ align:start position:0%
+the same vition so this feet reflects
+ 
+
+ align:start position:0%
+the same vition so this feet reflects
+the fact that you can go
+
+ align:start position:0%
+the fact that you can go
+ 
+
+ align:start position:0%
+the fact that you can go
+0 0 1 0 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 you can pump the fundamental
+
+ align:start position:0%
+0 you can pump the fundamental
+ 
+
+ align:start position:0%
+0 you can pump the fundamental
+transition and probe the overtone
+
+ align:start position:0%
+transition and probe the overtone
+ 
+
+ align:start position:0%
+transition and probe the overtone
+transition and that typically is
+
+ align:start position:0%
+transition and that typically is
+ 
+
+ align:start position:0%
+transition and that typically is
+anharmonically shifted by a little bit
+
+ align:start position:0%
+anharmonically shifted by a little bit
+ 
+
+ align:start position:0%
+anharmonically shifted by a little bit
+if it's a harmonic oscillator they're
+
+ align:start position:0%
+if it's a harmonic oscillator they're
+ 
+
+ align:start position:0%
+if it's a harmonic oscillator they're
+the same and that that's going to vanish
+
+ align:start position:0%
+the same and that that's going to vanish
+ 
+
+ align:start position:0%
+the same and that that's going to vanish
+so again for harmonic Behavior the
+
+ align:start position:0%
+so again for harmonic Behavior the
+ 
+
+ align:start position:0%
+so again for harmonic Behavior the
+nonlinear response management so another
+
+ align:start position:0%
+nonlinear response management so another
+ 
+
+ align:start position:0%
+nonlinear response management so another
+way of thinking about this which might
+
+ align:start position:0%
+way of thinking about this which might
+ 
+
+ align:start position:0%
+way of thinking about this which might
+be more useful is really just think of
+
+ align:start position:0%
+be more useful is really just think of
+ 
+
+ align:start position:0%
+be more useful is really just think of
+this as the sum of two very close Peaks
+
+ align:start position:0%
+this as the sum of two very close Peaks
+ 
+
+ align:start position:0%
+this as the sum of two very close Peaks
+and that you just are going to have Net
+
+ align:start position:0%
+and that you just are going to have Net
+ 
+
+ align:start position:0%
+and that you just are going to have Net
+One Peak whose
+
+ align:start position:0%
+One Peak whose
+ 
+
+ align:start position:0%
+One Peak whose
+amplitude is going to reflect the
+
+ align:start position:0%
+amplitude is going to reflect the
+ 
+
+ align:start position:0%
+amplitude is going to reflect the
+magnitude of the C and you've got two
+
+ align:start position:0%
+magnitude of the C and you've got two
+ 
+
+ align:start position:0%
+magnitude of the C and you've got two
+overlapping Peaks that are just moving a
+
+ align:start position:0%
+overlapping Peaks that are just moving a
+ 
+
+ align:start position:0%
+overlapping Peaks that are just moving a
+little bit you can show that the
+
+ align:start position:0%
+little bit you can show that the
+ 
+
+ align:start position:0%
+little bit you can show that the
+amplitude of that sum is going to scale
+
+ align:start position:0%
+amplitude of that sum is going to scale
+ 
+
+ align:start position:0%
+amplitude of that sum is going to scale
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+comp in practice can you usually resolve
+
+ align:start position:0%
+comp in practice can you usually resolve
+ 
+
+ align:start position:0%
+comp in practice can you usually resolve
+them as two separate P so um C you know
+
+ align:start position:0%
+them as two separate P so um C you know
+ 
+
+ align:start position:0%
+them as two separate P so um C you know
+C there's many times that we see it um
+
+ align:start position:0%
+C there's many times that we see it um
+ 
+
+ align:start position:0%
+C there's many times that we see it um
+in the vibrational systems but you know
+
+ align:start position:0%
+in the vibrational systems but you know
+ 
+
+ align:start position:0%
+in the vibrational systems but you know
+if I kind of do a survey in my head of
+
+ align:start position:0%
+if I kind of do a survey in my head of
+ 
+
+ align:start position:0%
+if I kind of do a survey in my head of
+things I've seen i' see on average it's
+
+ align:start position:0%
+things I've seen i' see on average it's
+ 
+
+ align:start position:0%
+things I've seen i' see on average it's
+more like this that you're looking at
+
+ align:start position:0%
+more like this that you're looking at
+ 
+
+ align:start position:0%
+more like this that you're looking at
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+effects that it's hard to distinguish
+
+ align:start position:0%
+effects that it's hard to distinguish
+ 
+
+ align:start position:0%
+effects that it's hard to distinguish
+discrete resonances but but certainly in
+
+ align:start position:0%
+discrete resonances but but certainly in
+ 
+
+ align:start position:0%
+discrete resonances but but certainly in
+strongly coupled systems there's many
+
+ align:start position:0%
+strongly coupled systems there's many
+ 
+
+ align:start position:0%
+strongly coupled systems there's many
+examples of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this doesn't that get complicated though
+
+ align:start position:0%
+this doesn't that get complicated though
+ 
+
+ align:start position:0%
+this doesn't that get complicated though
+because your your di moments will change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two right so it is true what I I haven't
+
+ align:start position:0%
+two right so it is true what I I haven't
+ 
+
+ align:start position:0%
+two right so it is true what I I haven't
+talked about you do have to worry about
+
+ align:start position:0%
+talked about you do have to worry about
+ 
+
+ align:start position:0%
+talked about you do have to worry about
+the selection rules um and so the way
+
+ align:start position:0%
+the selection rules um and so the way
+ 
+
+ align:start position:0%
+the selection rules um and so the way
+I've drawn this is using harmonic
+
+ align:start position:0%
+I've drawn this is using harmonic
+ 
+
+ align:start position:0%
+I've drawn this is using harmonic
+oscillator selection rules and in that
+
+ align:start position:0%
+oscillator selection rules and in that
+ 
+
+ align:start position:0%
+oscillator selection rules and in that
+case you're not you're going to allow
+
+ align:start position:0%
+case you're not you're going to allow
+ 
+
+ align:start position:0%
+case you're not you're going to allow
+transitions between the ground and
+
+ align:start position:0%
+transitions between the ground and
+ 
+
+ align:start position:0%
+transitions between the ground and
+either of the first excited States and
+
+ align:start position:0%
+either of the first excited States and
+ 
+
+ align:start position:0%
+either of the first excited States and
+then also between either of the first
+
+ align:start position:0%
+then also between either of the first
+ 
+
+ align:start position:0%
+then also between either of the first
+excited States and any of the upper Ling
+
+ align:start position:0%
+excited States and any of the upper Ling
+ 
+
+ align:start position:0%
+excited States and any of the upper Ling
+states that are single Quantum
+
+ align:start position:0%
+states that are single Quantum
+ 
+
+ align:start position:0%
+states that are single Quantum
+transitions di you know harmonic
+
+ align:start position:0%
+transitions di you know harmonic
+ 
+
+ align:start position:0%
+transitions di you know harmonic
+oscillator selection goes so in this
+
+ align:start position:0%
+oscillator selection goes so in this
+ 
+
+ align:start position:0%
+oscillator selection goes so in this
+case there's two in this case it's the
+
+ align:start position:0%
+case there's two in this case it's the
+ 
+
+ align:start position:0%
+case there's two in this case it's the
+same you can connect the one exitation
+
+ align:start position:0%
+same you can connect the one exitation
+ 
+
+ align:start position:0%
+same you can connect the one exitation
+states to the
+
+ align:start position:0%
+states to the
+ 
+
+ align:start position:0%
+states to the
+overtone um but the
+
+ align:start position:0%
+overtone um but the
+ 
+
+ align:start position:0%
+overtone um but the
+um I'm sorry to the combination band but
+
+ align:start position:0%
+um I'm sorry to the combination band but
+ 
+
+ align:start position:0%
+um I'm sorry to the combination band but
+the overtone states can only be
+
+ align:start position:0%
+the overtone states can only be
+ 
+
+ align:start position:0%
+the overtone states can only be
+connected to their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ini there there are examples where you
+
+ align:start position:0%
+ini there there are examples where you
+ 
+
+ align:start position:0%
+ini there there are examples where you
+can start to pick out extra Peaks that
+
+ align:start position:0%
+can start to pick out extra Peaks that
+ 
+
+ align:start position:0%
+can start to pick out extra Peaks that
+arise from them harmonically this
+
+ align:start position:0%
+arise from them harmonically this
+ 
+
+ align:start position:0%
+arise from them harmonically this
+allowed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transitions okay any any questions on
+
+ align:start position:0%
+Transitions okay any any questions on
+ 
+
+ align:start position:0%
+Transitions okay any any questions on
+that on
+
+ align:start position:0%
+that on
+ 
+
+ align:start position:0%
+that on
+that okay um so I could uh get now into
+
+ align:start position:0%
+that okay um so I could uh get now into
+ 
+
+ align:start position:0%
+that okay um so I could uh get now into
+sort of the other example of you know of
+
+ align:start position:0%
+sort of the other example of you know of
+ 
+
+ align:start position:0%
+sort of the other example of you know of
+looking at line shapes but I mean I
+
+ align:start position:0%
+looking at line shapes but I mean I
+ 
+
+ align:start position:0%
+looking at line shapes but I mean I
+think it's better we just call it a day
+
+ align:start position:0%
+think it's better we just call it a day
+ 
+
+ align:start position:0%
+think it's better we just call it a day
+here
\ No newline at end of file
diff --git a/eG_aRPy1KVE.txt b/eG_aRPy1KVE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3a534f81cfd118e917953c8a665fa2bfe159dd5e
--- /dev/null
+++ b/eG_aRPy1KVE.txt
@@ -0,0 +1,14643 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right okay let's get uh
+
+ align:start position:0%
+ocw.mit.edu all right okay let's get uh
+ 
+
+ align:start position:0%
+ocw.mit.edu all right okay let's get uh
+started um so before I make an
+
+ align:start position:0%
+started um so before I make an
+ 
+
+ align:start position:0%
+started um so before I make an
+introduction let me just make a few uh
+
+ align:start position:0%
+introduction let me just make a few uh
+ 
+
+ align:start position:0%
+introduction let me just make a few uh
+announcement
+
+ align:start position:0%
+announcement
+ 
+
+ align:start position:0%
+announcement
+a few of you came to us asking about the
+
+ align:start position:0%
+a few of you came to us asking about the
+ 
+
+ align:start position:0%
+a few of you came to us asking about the
+the grading uh for the term and some
+
+ align:start position:0%
+the grading uh for the term and some
+ 
+
+ align:start position:0%
+the grading uh for the term and some
+youi the problem sets may be on the
+
+ align:start position:0%
+youi the problem sets may be on the
+ 
+
+ align:start position:0%
+youi the problem sets may be on the
+difficult side and uh some of you
+
+ align:start position:0%
+difficult side and uh some of you
+ 
+
+ align:start position:0%
+difficult side and uh some of you
+haven't done all of them and some of you
+
+ align:start position:0%
+haven't done all of them and some of you
+ 
+
+ align:start position:0%
+haven't done all of them and some of you
+done more so we just want to let you
+
+ align:start position:0%
+done more so we just want to let you
+ 
+
+ align:start position:0%
+done more so we just want to let you
+know that uh the most important thing uh
+
+ align:start position:0%
+know that uh the most important thing uh
+ 
+
+ align:start position:0%
+know that uh the most important thing uh
+to us in grading is really you know you
+
+ align:start position:0%
+to us in grading is really you know you
+ 
+
+ align:start position:0%
+to us in grading is really you know you
+show your effort in terms of learning
+
+ align:start position:0%
+show your effort in terms of learning
+ 
+
+ align:start position:0%
+show your effort in terms of learning
+and we purposely made the problem sets
+
+ align:start position:0%
+and we purposely made the problem sets
+ 
+
+ align:start position:0%
+and we purposely made the problem sets
+more difficult than the lecture so you
+
+ align:start position:0%
+more difficult than the lecture so you
+ 
+
+ align:start position:0%
+more difficult than the lecture so you
+can if you want to dig into uh deeper so
+
+ align:start position:0%
+can if you want to dig into uh deeper so
+ 
+
+ align:start position:0%
+can if you want to dig into uh deeper so
+you have the opportunity to learn more
+
+ align:start position:0%
+you have the opportunity to learn more
+ 
+
+ align:start position:0%
+you have the opportunity to learn more
+but by no means uh we expect you to
+
+ align:start position:0%
+but by no means uh we expect you to
+ 
+
+ align:start position:0%
+but by no means uh we expect you to
+finish or feel easy in solving all the
+
+ align:start position:0%
+finish or feel easy in solving all the
+ 
+
+ align:start position:0%
+finish or feel easy in solving all the
+problem um uh do the other the problem
+
+ align:start position:0%
+problem um uh do the other the problem
+ 
+
+ align:start position:0%
+problem um uh do the other the problem
+sets so I just want to put you at ease
+
+ align:start position:0%
+sets so I just want to put you at ease
+ 
+
+ align:start position:0%
+sets so I just want to put you at ease
+that uh if that's your concern that's
+
+ align:start position:0%
+that uh if that's your concern that's
+ 
+
+ align:start position:0%
+that uh if that's your concern that's
+definitely you don't need to worry about
+
+ align:start position:0%
+definitely you don't need to worry about
+ 
+
+ align:start position:0%
+definitely you don't need to worry about
+it and uh we will be um uh really just
+
+ align:start position:0%
+it and uh we will be um uh really just
+ 
+
+ align:start position:0%
+it and uh we will be um uh really just
+evaluating
+
+ align:start position:0%
+evaluating
+ 
+
+ align:start position:0%
+evaluating
+uh your effort and based on what we
+
+ align:start position:0%
+uh your effort and based on what we
+ 
+
+ align:start position:0%
+uh your effort and based on what we
+observed so far we actually believe
+
+ align:start position:0%
+observed so far we actually believe
+ 
+
+ align:start position:0%
+observed so far we actually believe
+every single one of you is doing quite
+
+ align:start position:0%
+every single one of you is doing quite
+ 
+
+ align:start position:0%
+every single one of you is doing quite
+well so you shouldn't uh worry about uh
+
+ align:start position:0%
+well so you shouldn't uh worry about uh
+ 
+
+ align:start position:0%
+well so you shouldn't uh worry about uh
+your performance at the class so
+
+ align:start position:0%
+your performance at the class so
+ 
+
+ align:start position:0%
+your performance at the class so
+continue to uh do a good job on your uh
+
+ align:start position:0%
+continue to uh do a good job on your uh
+ 
+
+ align:start position:0%
+continue to uh do a good job on your uh
+class participation and uh do some of
+
+ align:start position:0%
+class participation and uh do some of
+ 
+
+ align:start position:0%
+class participation and uh do some of
+the problem sets and then will you'll be
+
+ align:start position:0%
+the problem sets and then will you'll be
+ 
+
+ align:start position:0%
+the problem sets and then will you'll be
+in fine shape for your grade so that
+
+ align:start position:0%
+in fine shape for your grade so that
+ 
+
+ align:start position:0%
+in fine shape for your grade so that
+that's all of that so without any
+
+ align:start position:0%
+that's all of that so without any
+ 
+
+ align:start position:0%
+that's all of that so without any
+further delay let me uh introduce my
+
+ align:start position:0%
+further delay let me uh introduce my
+ 
+
+ align:start position:0%
+further delay let me uh introduce my
+colleague Dr Steven BL I'll be very
+
+ align:start position:0%
+colleague Dr Steven BL I'll be very
+ 
+
+ align:start position:0%
+colleague Dr Steven BL I'll be very
+brief and he's uh Steven is um doing two
+
+ align:start position:0%
+brief and he's uh Steven is um doing two
+ 
+
+ align:start position:0%
+brief and he's uh Steven is um doing two
+jobs at the same time he's um
+
+ align:start position:0%
+jobs at the same time he's um
+ 
+
+ align:start position:0%
+jobs at the same time he's um
+responsible for the all the public
+
+ align:start position:0%
+responsible for the all the public
+ 
+
+ align:start position:0%
+responsible for the all the public
+markets at the Harvard management uh as
+
+ align:start position:0%
+markets at the Harvard management uh as
+ 
+
+ align:start position:0%
+markets at the Harvard management uh as
+well as being a professor of practice at
+
+ align:start position:0%
+well as being a professor of practice at
+ 
+
+ align:start position:0%
+well as being a professor of practice at
+Harvard so with that I turn to Stephen
+
+ align:start position:0%
+Harvard so with that I turn to Stephen
+ 
+
+ align:start position:0%
+Harvard so with that I turn to Stephen
+okay well thank you Jake and thank you
+
+ align:start position:0%
+okay well thank you Jake and thank you
+ 
+
+ align:start position:0%
+okay well thank you Jake and thank you
+for having me to to speak this afternoon
+
+ align:start position:0%
+for having me to to speak this afternoon
+ 
+
+ align:start position:0%
+for having me to to speak this afternoon
+uh before I um before I begin I wanted
+
+ align:start position:0%
+uh before I um before I begin I wanted
+ 
+
+ align:start position:0%
+uh before I um before I begin I wanted
+to ask you a question um so I'm speaking
+
+ align:start position:0%
+to ask you a question um so I'm speaking
+ 
+
+ align:start position:0%
+to ask you a question um so I'm speaking
+actually at uh almost exactly the 20th
+
+ align:start position:0%
+actually at uh almost exactly the 20th
+ 
+
+ align:start position:0%
+actually at uh almost exactly the 20th
+anniversary is something very important
+
+ align:start position:0%
+anniversary is something very important
+ 
+
+ align:start position:0%
+anniversary is something very important
+so um on the 19th of October
+
+ align:start position:0%
+so um on the 19th of October
+ 
+
+ align:start position:0%
+so um on the 19th of October
+1993 which I guess might be the birthday
+
+ align:start position:0%
+1993 which I guess might be the birthday
+ 
+
+ align:start position:0%
+1993 which I guess might be the birthday
+of uh some of you but any almost exactly
+
+ align:start position:0%
+of uh some of you but any almost exactly
+ 
+
+ align:start position:0%
+of uh some of you but any almost exactly
+20 years
+
+ align:start position:0%
+20 years
+ 
+
+ align:start position:0%
+20 years
+ago uh
+
+ align:start position:0%
+ago uh
+ 
+
+ align:start position:0%
+ago uh
+Congress voted 264 to 159 I actually
+
+ align:start position:0%
+Congress voted 264 to 159 I actually
+ 
+
+ align:start position:0%
+Congress voted 264 to 159 I actually
+remember the count of the vote uh to do
+
+ align:start position:0%
+remember the count of the vote uh to do
+ 
+
+ align:start position:0%
+remember the count of the vote uh to do
+something so anybody uh like to guess
+
+ align:start position:0%
+something so anybody uh like to guess
+ 
+
+ align:start position:0%
+something so anybody uh like to guess
+what they voted to do on the 19th of
+
+ align:start position:0%
+what they voted to do on the 19th of
+ 
+
+ align:start position:0%
+what they voted to do on the 19th of
+October 1993 that might be tangentially
+
+ align:start position:0%
+October 1993 that might be tangentially
+ 
+
+ align:start position:0%
+October 1993 that might be tangentially
+relevant to uh Finance in quantitative
+
+ align:start position:0%
+relevant to uh Finance in quantitative
+ 
+
+ align:start position:0%
+relevant to uh Finance in quantitative
+Finance anyone here from HMC is not
+
+ align:start position:0%
+Finance anyone here from HMC is not
+ 
+
+ align:start position:0%
+Finance anyone here from HMC is not
+allowed to answer anybody any
+
+ align:start position:0%
+allowed to answer anybody any
+ 
+
+ align:start position:0%
+allowed to answer anybody any
+guesses any ideas at all coming into
+
+ align:start position:0%
+guesses any ideas at all coming into
+ 
+
+ align:start position:0%
+guesses any ideas at all coming into
+people's minds was it Le Bailey no
+
+ align:start position:0%
+people's minds was it Le Bailey no
+ 
+
+ align:start position:0%
+people's minds was it Le Bailey no
+these good good uh good guess but
+
+ align:start position:0%
+these good good uh good guess but
+ 
+
+ align:start position:0%
+these good good uh good guess but
+actually that is actually too related to
+
+ align:start position:0%
+actually that is actually too related to
+ 
+
+ align:start position:0%
+actually that is actually too related to
+finance actually this is actually um
+
+ align:start position:0%
+finance actually this is actually um
+ 
+
+ align:start position:0%
+finance actually this is actually um
+wasn't directly financially related so
+
+ align:start position:0%
+wasn't directly financially related so
+ 
+
+ align:start position:0%
+wasn't directly financially related so
+that was related the fut anybody else
+
+ align:start position:0%
+that was related the fut anybody else
+ 
+
+ align:start position:0%
+that was related the fut anybody else
+think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about what does Congress usually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do no no ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatsoever what do you think Congress
+
+ align:start position:0%
+whatsoever what do you think Congress
+ 
+
+ align:start position:0%
+whatsoever what do you think Congress
+did 20 years ago they voted to do
+
+ align:start position:0%
+did 20 years ago they voted to do
+ 
+
+ align:start position:0%
+did 20 years ago they voted to do
+something okay well what Congress do
+
+ align:start position:0%
+something okay well what Congress do
+ 
+
+ align:start position:0%
+something okay well what Congress do
+usually they cut money to something so
+
+ align:start position:0%
+usually they cut money to something so
+ 
+
+ align:start position:0%
+usually they cut money to something so
+they voted to cut financing to
+
+ align:start position:0%
+they voted to cut financing to
+ 
+
+ align:start position:0%
+they voted to cut financing to
+something what do they cut financing to
+
+ align:start position:0%
+something what do they cut financing to
+ 
+
+ align:start position:0%
+something what do they cut financing to
+anybody anybody
+
+ align:start position:0%
+anybody anybody
+ 
+
+ align:start position:0%
+anybody anybody
+guess I know this isn't business school
+
+ align:start position:0%
+guess I know this isn't business school
+ 
+
+ align:start position:0%
+guess I know this isn't business school
+in business school it'd be like right
+
+ align:start position:0%
+in business school it'd be like right
+ 
+
+ align:start position:0%
+in business school it'd be like right
+you're failed no past class
+
+ align:start position:0%
+you're failed no past class
+ 
+
+ align:start position:0%
+you're failed no past class
+participation you're failed you're got
+
+ align:start position:0%
+participation you're failed you're got
+ 
+
+ align:start position:0%
+participation you're failed you're got
+to say something in business school so I
+
+ align:start position:0%
+to say something in business school so I
+ 
+
+ align:start position:0%
+to say something in business school so I
+know it's not business school but anyway
+
+ align:start position:0%
+know it's not business school but anyway
+ 
+
+ align:start position:0%
+know it's not business school but anyway
+it's and I don't teach in business
+
+ align:start position:0%
+it's and I don't teach in business
+ 
+
+ align:start position:0%
+it's and I don't teach in business
+school either but this is actually these
+
+ align:start position:0%
+school either but this is actually these
+ 
+
+ align:start position:0%
+school either but this is actually these
+round desks make me think of business
+
+ align:start position:0%
+round desks make me think of business
+ 
+
+ align:start position:0%
+round desks make me think of business
+school and uh striding into the middle
+
+ align:start position:0%
+school and uh striding into the middle
+ 
+
+ align:start position:0%
+school and uh striding into the middle
+of the the room and saying okay come on
+
+ align:start position:0%
+of the the room and saying okay come on
+ 
+
+ align:start position:0%
+of the the room and saying okay come on
+fortunately you don't have names
+
+ align:start position:0%
+fortunately you don't have names
+ 
+
+ align:start position:0%
+fortunately you don't have names
+otherwise I'd pick on you no no
+
+ align:start position:0%
+otherwise I'd pick on you no no
+ 
+
+ align:start position:0%
+otherwise I'd pick on you no no
+guesses no guesses whatsoever this is
+
+ align:start position:0%
+guesses no guesses whatsoever this is
+ 
+
+ align:start position:0%
+guesses no guesses whatsoever this is
+I'm going to take this up the road to
+
+ align:start position:0%
+I'm going to take this up the road to
+ 
+
+ align:start position:0%
+I'm going to take this up the road to
+Harvard Square and say when I taught at
+
+ align:start position:0%
+Harvard Square and say when I taught at
+ 
+
+ align:start position:0%
+Harvard Square and say when I taught at
+MIT no one had any guesses for this
+
+ align:start position:0%
+MIT no one had any guesses for this
+ 
+
+ align:start position:0%
+MIT no one had any guesses for this
+question one guess actually the
+
+ align:start position:0%
+question one guess actually the
+ 
+
+ align:start position:0%
+question one guess actually the
+gentleman here what do they cancel
+
+ align:start position:0%
+gentleman here what do they cancel
+ 
+
+ align:start position:0%
+gentleman here what do they cancel
+cancel uh what did they cancel their
+
+ align:start position:0%
+cancel uh what did they cancel their
+ 
+
+ align:start position:0%
+cancel uh what did they cancel their
+financing for in 1993
+
+ align:start position:0%
+financing for in 1993
+ 
+
+ align:start position:0%
+financing for in 1993
+so all right well let's say it was the
+
+ align:start position:0%
+so all right well let's say it was the
+ 
+
+ align:start position:0%
+so all right well let's say it was the
+Super conducting super
+
+ align:start position:0%
+Super conducting super
+ 
+
+ align:start position:0%
+Super conducting super
+collider uh underneath Texas just south
+
+ align:start position:0%
+collider uh underneath Texas just south
+ 
+
+ align:start position:0%
+collider uh underneath Texas just south
+of Dallas so um $2 billion had been
+
+ align:start position:0%
+of Dallas so um $2 billion had been
+ 
+
+ align:start position:0%
+of Dallas so um $2 billion had been
+spent on the super collider and the
+
+ align:start position:0%
+spent on the super collider and the
+ 
+
+ align:start position:0%
+spent on the super collider and the
+budget had expanded from I think six
+
+ align:start position:0%
+budget had expanded from I think six
+ 
+
+ align:start position:0%
+budget had expanded from I think six
+billion to 11 billion so they by
+
+ align:start position:0%
+billion to 11 billion so they by
+ 
+
+ align:start position:0%
+billion to 11 billion so they by
+canceling they had a $9 billion saving
+
+ align:start position:0%
+canceling they had a $9 billion saving
+ 
+
+ align:start position:0%
+canceling they had a $9 billion saving
+this was 20 years ago ex almost exactly
+
+ align:start position:0%
+this was 20 years ago ex almost exactly
+ 
+
+ align:start position:0%
+this was 20 years ago ex almost exactly
+um and as a result of that one result of
+
+ align:start position:0%
+um and as a result of that one result of
+ 
+
+ align:start position:0%
+um and as a result of that one result of
+that was of course the academic job
+
+ align:start position:0%
+that was of course the academic job
+ 
+
+ align:start position:0%
+that was of course the academic job
+market for
+
+ align:start position:0%
+market for
+ 
+
+ align:start position:0%
+market for
+physicists collapsed
+
+ align:start position:0%
+physicists collapsed
+ 
+
+ align:start position:0%
+physicists collapsed
+overnight and two of my roommates were
+
+ align:start position:0%
+overnight and two of my roommates were
+ 
+
+ align:start position:0%
+overnight and two of my roommates were
+theoretical physicists at Harvard and
+
+ align:start position:0%
+theoretical physicists at Harvard and
+ 
+
+ align:start position:0%
+theoretical physicists at Harvard and
+they basically realized their job
+
+ align:start position:0%
+they basically realized their job
+ 
+
+ align:start position:0%
+they basically realized their job
+prospects in Academia had vaporized
+
+ align:start position:0%
+prospects in Academia had vaporized
+ 
+
+ align:start position:0%
+prospects in Academia had vaporized
+instantaneously that day and both of
+
+ align:start position:0%
+instantaneously that day and both of
+ 
+
+ align:start position:0%
+instantaneously that day and both of
+them within six months had found jobs
+
+ align:start position:0%
+them within six months had found jobs
+ 
+
+ align:start position:0%
+them within six months had found jobs
+with Goldman Sachs in New
+
+ align:start position:0%
+with Goldman Sachs in New
+ 
+
+ align:start position:0%
+with Goldman Sachs in New
+York and they catalyzed they I mean they
+
+ align:start position:0%
+York and they catalyzed they I mean they
+ 
+
+ align:start position:0%
+York and they catalyzed they I mean they
+and the cohort I've call the super
+
+ align:start position:0%
+and the cohort I've call the super
+ 
+
+ align:start position:0%
+and the cohort I've call the super
+superc conducting super collider
+
+ align:start position:0%
+superc conducting super collider
+ 
+
+ align:start position:0%
+superc conducting super collider
+generation if you ever wondered why
+
+ align:start position:0%
+generation if you ever wondered why
+ 
+
+ align:start position:0%
+generation if you ever wondered why
+people like myself and like Jake who got
+
+ align:start position:0%
+people like myself and like Jake who got
+ 
+
+ align:start position:0%
+people like myself and like Jake who got
+phds in quantitative subjects around the
+
+ align:start position:0%
+phds in quantitative subjects around the
+ 
+
+ align:start position:0%
+phds in quantitative subjects around the
+turn of around 1992 1993 all ended up in
+
+ align:start position:0%
+turn of around 1992 1993 all ended up in
+ 
+
+ align:start position:0%
+turn of around 1992 1993 all ended up in
+a financial path part of it is due to
+
+ align:start position:0%
+a financial path part of it is due to
+ 
+
+ align:start position:0%
+a financial path part of it is due to
+Congress cancelling the super superc
+
+ align:start position:0%
+Congress cancelling the super superc
+ 
+
+ align:start position:0%
+Congress cancelling the super superc
+conducting super collider because this
+
+ align:start position:0%
+conducting super collider because this
+ 
+
+ align:start position:0%
+conducting super collider because this
+cohort catalyzed this growth in
+
+ align:start position:0%
+cohort catalyzed this growth in
+ 
+
+ align:start position:0%
+cohort catalyzed this growth in
+quantitative Finance so actually they
+
+ align:start position:0%
+quantitative Finance so actually they
+ 
+
+ align:start position:0%
+quantitative Finance so actually they
+created a field Financial engineering
+
+ align:start position:0%
+created a field Financial engineering
+ 
+
+ align:start position:0%
+created a field Financial engineering
+which you are all somewhat interested in
+
+ align:start position:0%
+which you are all somewhat interested in
+ 
+
+ align:start position:0%
+which you are all somewhat interested in
+by taking this class okay and they also
+
+ align:start position:0%
+by taking this class okay and they also
+ 
+
+ align:start position:0%
+by taking this class okay and they also
+created a career path quantitative
+
+ align:start position:0%
+created a career path quantitative
+ 
+
+ align:start position:0%
+created a career path quantitative
+analyst or Quant right which really did
+
+ align:start position:0%
+analyst or Quant right which really did
+ 
+
+ align:start position:0%
+analyst or Quant right which really did
+not exist before 1993 okay and that
+
+ align:start position:0%
+not exist before 1993 okay and that
+ 
+
+ align:start position:0%
+not exist before 1993 okay and that
+growth
+
+ align:start position:0%
+growth
+ 
+
+ align:start position:0%
+growth
+of mathematical Finance Financial
+
+ align:start position:0%
+of mathematical Finance Financial
+ 
+
+ align:start position:0%
+of mathematical Finance Financial
+engineering quantitative Finance however
+
+ align:start position:0%
+engineering quantitative Finance however
+ 
+
+ align:start position:0%
+engineering quantitative Finance however
+you want to look at it was basically
+
+ align:start position:0%
+you want to look at it was basically
+ 
+
+ align:start position:0%
+you want to look at it was basically
+exponential from 1993 up until actually
+
+ align:start position:0%
+exponential from 1993 up until actually
+ 
+
+ align:start position:0%
+exponential from 1993 up until actually
+2008 in the financial crisis exactly
+
+ align:start position:0%
+2008 in the financial crisis exactly
+ 
+
+ align:start position:0%
+2008 in the financial crisis exactly
+five years ago funly enough and uh since
+
+ align:start position:0%
+five years ago funly enough and uh since
+ 
+
+ align:start position:0%
+five years ago funly enough and uh since
+then it's been a little bit rockier so
+
+ align:start position:0%
+then it's been a little bit rockier so
+ 
+
+ align:start position:0%
+then it's been a little bit rockier so
+if you're actually interested in this
+
+ align:start position:0%
+if you're actually interested in this
+ 
+
+ align:start position:0%
+if you're actually interested in this
+aftermath of the physics funding what's
+
+ align:start position:0%
+aftermath of the physics funding what's
+ 
+
+ align:start position:0%
+aftermath of the physics funding what's
+interesting is the Large Hadron Collider
+
+ align:start position:0%
+interesting is the Large Hadron Collider
+ 
+
+ align:start position:0%
+interesting is the Large Hadron Collider
+which you might know was up and running
+
+ align:start position:0%
+which you might know was up and running
+ 
+
+ align:start position:0%
+which you might know was up and running
+in Geneva and we just found the higs
+
+ align:start position:0%
+in Geneva and we just found the higs
+ 
+
+ align:start position:0%
+in Geneva and we just found the higs
+boson has sort of reversed the trend
+
+ align:start position:0%
+boson has sort of reversed the trend
+ 
+
+ align:start position:0%
+boson has sort of reversed the trend
+somewhat so if there's there used to be
+
+ align:start position:0%
+somewhat so if there's there used to be
+ 
+
+ align:start position:0%
+somewhat so if there's there used to be
+a whole cohort of people going into
+
+ align:start position:0%
+a whole cohort of people going into
+ 
+
+ align:start position:0%
+a whole cohort of people going into
+Finance instead of physics now because
+
+ align:start position:0%
+Finance instead of physics now because
+ 
+
+ align:start position:0%
+Finance instead of physics now because
+Finance has this somewhat a orative
+
+ align:start position:0%
+Finance has this somewhat a orative
+ 
+
+ align:start position:0%
+Finance has this somewhat a orative
+nature to it you know people don't like
+
+ align:start position:0%
+nature to it you know people don't like
+ 
+
+ align:start position:0%
+nature to it you know people don't like
+Bankers generally and they kind of like
+
+ align:start position:0%
+Bankers generally and they kind of like
+ 
+
+ align:start position:0%
+Bankers generally and they kind of like
+physicist to find the higb on and get a
+
+ align:start position:0%
+physicist to find the higb on and get a
+ 
+
+ align:start position:0%
+physicist to find the higb on and get a
+Nobel Prize maybe we're getting a
+
+ align:start position:0%
+Nobel Prize maybe we're getting a
+ 
+
+ align:start position:0%
+Nobel Prize maybe we're getting a
+reversal but anyway we're still in
+
+ align:start position:0%
+reversal but anyway we're still in
+ 
+
+ align:start position:0%
+reversal but anyway we're still in
+finance I I've um as as Jake mentioned
+
+ align:start position:0%
+finance I I've um as as Jake mentioned
+ 
+
+ align:start position:0%
+finance I I've um as as Jake mentioned
+um well I didn't mention I I I was
+
+ align:start position:0%
+um well I didn't mention I I I was
+ 
+
+ align:start position:0%
+um well I didn't mention I I I was
+originally an academic so I was actually
+
+ align:start position:0%
+originally an academic so I was actually
+ 
+
+ align:start position:0%
+originally an academic so I was actually
+a mathematics uh faculty member in
+
+ align:start position:0%
+a mathematics uh faculty member in
+ 
+
+ align:start position:0%
+a mathematics uh faculty member in
+London when I got my PhD I got my PhD
+
+ align:start position:0%
+London when I got my PhD I got my PhD
+ 
+
+ align:start position:0%
+London when I got my PhD I got my PhD
+from Harvard and in 1993 I was an
+
+ align:start position:0%
+from Harvard and in 1993 I was an
+ 
+
+ align:start position:0%
+from Harvard and in 1993 I was an
+academic and then all my friends I saw
+
+ align:start position:0%
+academic and then all my friends I saw
+ 
+
+ align:start position:0%
+academic and then all my friends I saw
+them go to finance so I followed them uh
+
+ align:start position:0%
+them go to finance so I followed them uh
+ 
+
+ align:start position:0%
+them go to finance so I followed them uh
+spent a career in New York and then came
+
+ align:start position:0%
+spent a career in New York and then came
+ 
+
+ align:start position:0%
+spent a career in New York and then came
+back to Harvard in 2006 to run a part of
+
+ align:start position:0%
+back to Harvard in 2006 to run a part of
+ 
+
+ align:start position:0%
+back to Harvard in 2006 to run a part of
+the endowment and I've also started
+
+ align:start position:0%
+the endowment and I've also started
+ 
+
+ align:start position:0%
+the endowment and I've also started
+teaching so um just as a plug uh for
+
+ align:start position:0%
+teaching so um just as a plug uh for
+ 
+
+ align:start position:0%
+teaching so um just as a plug uh for
+those of you interested in mathematical
+
+ align:start position:0%
+those of you interested in mathematical
+ 
+
+ align:start position:0%
+those of you interested in mathematical
+finance and applications of mathematical
+
+ align:start position:0%
+finance and applications of mathematical
+ 
+
+ align:start position:0%
+finance and applications of mathematical
+Finance I teach a course at at Harvard
+
+ align:start position:0%
+Finance I teach a course at at Harvard
+ 
+
+ align:start position:0%
+Finance I teach a course at at Harvard
+it's an upper level undergraduate course
+
+ align:start position:0%
+it's an upper level undergraduate course
+ 
+
+ align:start position:0%
+it's an upper level undergraduate course
+called applied quantitative Finance
+
+ align:start position:0%
+called applied quantitative Finance
+ 
+
+ align:start position:0%
+called applied quantitative Finance
+which of course you can cross-register
+
+ align:start position:0%
+which of course you can cross-register
+ 
+
+ align:start position:0%
+which of course you can cross-register
+for um and today is also the one week
+
+ align:start position:0%
+for um and today is also the one week
+ 
+
+ align:start position:0%
+for um and today is also the one week
+anniversary of the publication of my
+
+ align:start position:0%
+anniversary of the publication of my
+ 
+
+ align:start position:0%
+anniversary of the publication of my
+book so um if you're interested in what
+
+ align:start position:0%
+book so um if you're interested in what
+ 
+
+ align:start position:0%
+book so um if you're interested in what
+my course is about you can just buy my
+
+ align:start position:0%
+my course is about you can just buy my
+ 
+
+ align:start position:0%
+my course is about you can just buy my
+book it's only 30 bucks so it's and I'll
+
+ align:start position:0%
+book it's only 30 bucks so it's and I'll
+ 
+
+ align:start position:0%
+book it's only 30 bucks so it's and I'll
+sign it first first edition first
+
+ align:start position:0%
+sign it first first edition first
+ 
+
+ align:start position:0%
+sign it first first edition first
+printing first impression book
+
+ align:start position:0%
+printing first impression book
+ 
+
+ align:start position:0%
+printing first impression book
+introduction to quantative Finance um
+
+ align:start position:0%
+introduction to quantative Finance um
+ 
+
+ align:start position:0%
+introduction to quantative Finance um
+and that is that's what that's what the
+
+ align:start position:0%
+and that is that's what that's what the
+ 
+
+ align:start position:0%
+and that is that's what that's what the
+course it's quite distilled when this
+
+ align:start position:0%
+course it's quite distilled when this
+ 
+
+ align:start position:0%
+course it's quite distilled when this
+book came out I thought that's really
+
+ align:start position:0%
+book came out I thought that's really
+ 
+
+ align:start position:0%
+book came out I thought that's really
+thin this is like three years of my work
+
+ align:start position:0%
+thin this is like three years of my work
+ 
+
+ align:start position:0%
+thin this is like three years of my work
+of my life's work it's come out it's
+
+ align:start position:0%
+of my life's work it's come out it's
+ 
+
+ align:start position:0%
+of my life's work it's come out it's
+very thin but I like to think it's like
+
+ align:start position:0%
+very thin but I like to think it's like
+ 
+
+ align:start position:0%
+very thin but I like to think it's like
+whiskey it's very it's well well
+
+ align:start position:0%
+whiskey it's very it's well well
+ 
+
+ align:start position:0%
+whiskey it's very it's well well
+distilled and highly potent and you have
+
+ align:start position:0%
+distilled and highly potent and you have
+ 
+
+ align:start position:0%
+distilled and highly potent and you have
+to sip it and take it take it bit by bit
+
+ align:start position:0%
+to sip it and take it take it bit by bit
+ 
+
+ align:start position:0%
+to sip it and take it take it bit by bit
+anyway that is that is the book of my my
+
+ align:start position:0%
+anyway that is that is the book of my my
+ 
+
+ align:start position:0%
+anyway that is that is the book of my my
+class and um the the Genesis of the
+
+ align:start position:0%
+class and um the the Genesis of the
+ 
+
+ align:start position:0%
+class and um the the Genesis of the
+class um was really that when I'd been
+
+ align:start position:0%
+class um was really that when I'd been
+ 
+
+ align:start position:0%
+class um was really that when I'd been
+on Wall Street and I was a colleague of
+
+ align:start position:0%
+on Wall Street and I was a colleague of
+ 
+
+ align:start position:0%
+on Wall Street and I was a colleague of
+Jake morg Stanley uh in this rapidly
+
+ align:start position:0%
+Jake morg Stanley uh in this rapidly
+ 
+
+ align:start position:0%
+Jake morg Stanley uh in this rapidly
+growing
+
+ align:start position:0%
+growing
+ 
+
+ align:start position:0%
+growing
+quantitative Finance field uh we
+
+ align:start position:0%
+quantitative Finance field uh we
+ 
+
+ align:start position:0%
+quantitative Finance field uh we
+encountered on the trading desk in the
+
+ align:start position:0%
+encountered on the trading desk in the
+ 
+
+ align:start position:0%
+encountered on the trading desk in the
+late 1990s in the early
+
+ align:start position:0%
+late 1990s in the early
+ 
+
+ align:start position:0%
+late 1990s in the early
+2000s uh problems from real the real
+
+ align:start position:0%
+2000s uh problems from real the real
+ 
+
+ align:start position:0%
+2000s uh problems from real the real
+economy things that we had to trade we
+
+ align:start position:0%
+economy things that we had to trade we
+ 
+
+ align:start position:0%
+economy things that we had to trade we
+were things that were coming to us on
+
+ align:start position:0%
+were things that were coming to us on
+ 
+
+ align:start position:0%
+were things that were coming to us on
+the trading desk that required
+
+ align:start position:0%
+the trading desk that required
+ 
+
+ align:start position:0%
+the trading desk that required
+um subtle understanding of the
+
+ align:start position:0%
+um subtle understanding of the
+ 
+
+ align:start position:0%
+um subtle understanding of the
+underlying Theory so that
+
+ align:start position:0%
+underlying Theory so that
+ 
+
+ align:start position:0%
+underlying Theory so that
+we in essence we built theoretical
+
+ align:start position:0%
+we in essence we built theoretical
+ 
+
+ align:start position:0%
+we in essence we built theoretical
+framework to solve the problems that
+
+ align:start position:0%
+framework to solve the problems that
+ 
+
+ align:start position:0%
+framework to solve the problems that
+were given to us by the financial
+
+ align:start position:0%
+were given to us by the financial
+ 
+
+ align:start position:0%
+were given to us by the financial
+markets so that period especially around
+
+ align:start position:0%
+markets so that period especially around
+ 
+
+ align:start position:0%
+markets so that period especially around
+the turn of uh 10 of the century um
+
+ align:start position:0%
+the turn of uh 10 of the century um
+ 
+
+ align:start position:0%
+the turn of uh 10 of the century um
+there's a big growth in derivatives
+
+ align:start position:0%
+there's a big growth in derivatives
+ 
+
+ align:start position:0%
+there's a big growth in derivatives
+markets which
+
+ align:start position:0%
+markets which
+ 
+
+ align:start position:0%
+markets which
+options Futures forwards Etc swaps um
+
+ align:start position:0%
+options Futures forwards Etc swaps um
+ 
+
+ align:start position:0%
+options Futures forwards Etc swaps um
+and we needed to build theoretical tools
+
+ align:start position:0%
+and we needed to build theoretical tools
+ 
+
+ align:start position:0%
+and we needed to build theoretical tools
+to tackle them and that's really what
+
+ align:start position:0%
+to tackle them and that's really what
+ 
+
+ align:start position:0%
+to tackle them and that's really what
+the the course was uh evolved out of to
+
+ align:start position:0%
+the the course was uh evolved out of to
+ 
+
+ align:start position:0%
+the the course was uh evolved out of to
+build the appropriate theoretical
+
+ align:start position:0%
+build the appropriate theoretical
+ 
+
+ align:start position:0%
+build the appropriate theoretical
+framework motivated by the problems we
+
+ align:start position:0%
+framework motivated by the problems we
+ 
+
+ align:start position:0%
+framework motivated by the problems we
+encountered um why I enthus about the
+
+ align:start position:0%
+encountered um why I enthus about the
+ 
+
+ align:start position:0%
+encountered um why I enthus about the
+subject um and I really like teaching
+
+ align:start position:0%
+subject um and I really like teaching
+ 
+
+ align:start position:0%
+subject um and I really like teaching
+the subject is that there is a an
+
+ align:start position:0%
+the subject is that there is a an
+ 
+
+ align:start position:0%
+the subject is that there is a an
+impression that quantative Finance is a
+
+ align:start position:0%
+impression that quantative Finance is a
+ 
+
+ align:start position:0%
+impression that quantative Finance is a
+very Arcane and
+
+ align:start position:0%
+very Arcane and
+ 
+
+ align:start position:0%
+very Arcane and
+contrived subject just a whole bunch of
+
+ align:start position:0%
+contrived subject just a whole bunch of
+ 
+
+ align:start position:0%
+contrived subject just a whole bunch of
+phds on Wall Street coming up with crazy
+
+ align:start position:0%
+phds on Wall Street coming up with crazy
+ 
+
+ align:start position:0%
+phds on Wall Street coming up with crazy
+ideas and they need complicated
+
+ align:start position:0%
+ideas and they need complicated
+ 
+
+ align:start position:0%
+ideas and they need complicated
+mathematics it's just complicated for
+
+ align:start position:0%
+mathematics it's just complicated for
+ 
+
+ align:start position:0%
+mathematics it's just complicated for
+the sake of complexity and the theory is
+
+ align:start position:0%
+the sake of complexity and the theory is
+ 
+
+ align:start position:0%
+the sake of complexity and the theory is
+just sort of a contrived Theory but in
+
+ align:start position:0%
+just sort of a contrived Theory but in
+ 
+
+ align:start position:0%
+just sort of a contrived Theory but in
+fact at the heart of Wall Street is that
+
+ align:start position:0%
+fact at the heart of Wall Street is that
+ 
+
+ align:start position:0%
+fact at the heart of Wall Street is that
+the real economy demands some of these
+
+ align:start position:0%
+the real economy demands some of these
+ 
+
+ align:start position:0%
+the real economy demands some of these
+products by supply and demand they're
+
+ align:start position:0%
+products by supply and demand they're
+ 
+
+ align:start position:0%
+products by supply and demand they're
+actual real participants in the
+
+ align:start position:0%
+actual real participants in the
+ 
+
+ align:start position:0%
+actual real participants in the
+financial markets who want to trade
+
+ align:start position:0%
+financial markets who want to trade
+ 
+
+ align:start position:0%
+financial markets who want to trade
+derivatives and therefore in order to
+
+ align:start position:0%
+derivatives and therefore in order to
+ 
+
+ align:start position:0%
+derivatives and therefore in order to
+understand them you need to develop a
+
+ align:start position:0%
+understand them you need to develop a
+ 
+
+ align:start position:0%
+understand them you need to develop a
+theory so it's actually driven by real
+
+ align:start position:0%
+theory so it's actually driven by real
+ 
+
+ align:start position:0%
+theory so it's actually driven by real
+examples that's one part the other part
+
+ align:start position:0%
+examples that's one part the other part
+ 
+
+ align:start position:0%
+examples that's one part the other part
+is that the theory that comes out of it
+
+ align:start position:0%
+is that the theory that comes out of it
+ 
+
+ align:start position:0%
+is that the theory that comes out of it
+and in particular the the approach I
+
+ align:start position:0%
+and in particular the the approach I
+ 
+
+ align:start position:0%
+and in particular the the approach I
+take here I think is just very elegant
+
+ align:start position:0%
+take here I think is just very elegant
+ 
+
+ align:start position:0%
+take here I think is just very elegant
+okay so there's some subtlety and
+
+ align:start position:0%
+okay so there's some subtlety and
+ 
+
+ align:start position:0%
+okay so there's some subtlety and
+elegance and Beauty to the underlying
+
+ align:start position:0%
+elegance and Beauty to the underlying
+ 
+
+ align:start position:0%
+elegance and Beauty to the underlying
+Theory you need to um that comes out of
+
+ align:start position:0%
+Theory you need to um that comes out of
+ 
+
+ align:start position:0%
+Theory you need to um that comes out of
+addressing real problems this course in
+
+ align:start position:0%
+addressing real problems this course in
+ 
+
+ align:start position:0%
+addressing real problems this course in
+the way that I I teach Finance um is
+
+ align:start position:0%
+the way that I I teach Finance um is
+ 
+
+ align:start position:0%
+the way that I I teach Finance um is
+very probability Centric you probably
+
+ align:start position:0%
+very probability Centric you probably
+ 
+
+ align:start position:0%
+very probability Centric you probably
+realized from the lectures you've seen
+
+ align:start position:0%
+realized from the lectures you've seen
+ 
+
+ align:start position:0%
+realized from the lectures you've seen
+already in this class there are many
+
+ align:start position:0%
+already in this class there are many
+ 
+
+ align:start position:0%
+already in this class there are many
+different approaches many different
+
+ align:start position:0%
+different approaches many different
+ 
+
+ align:start position:0%
+different approaches many different
+methods that are used in finance
+
+ align:start position:0%
+methods that are used in finance
+ 
+
+ align:start position:0%
+methods that are used in finance
+stochastic calculus partial differential
+
+ align:start position:0%
+stochastic calculus partial differential
+ 
+
+ align:start position:0%
+stochastic calculus partial differential
+equations simulation and so on okay the
+
+ align:start position:0%
+equations simulation and so on okay the
+ 
+
+ align:start position:0%
+equations simulation and so on okay the
+classical derivation of black schs is
+
+ align:start position:0%
+classical derivation of black schs is
+ 
+
+ align:start position:0%
+classical derivation of black schs is
+well but it's a solution of a
+
+ align:start position:0%
+well but it's a solution of a
+ 
+
+ align:start position:0%
+well but it's a solution of a
+pde okay that has appeal to people in
+
+ align:start position:0%
+pde okay that has appeal to people in
+ 
+
+ align:start position:0%
+pde okay that has appeal to people in
+fact this is why in some ways quantative
+
+ align:start position:0%
+fact this is why in some ways quantative
+ 
+
+ align:start position:0%
+fact this is why in some ways quantative
+Finance is a broad church because
+
+ align:start position:0%
+Finance is a broad church because
+ 
+
+ align:start position:0%
+Finance is a broad church because
+whether you're a physicist or a
+
+ align:start position:0%
+whether you're a physicist or a
+ 
+
+ align:start position:0%
+whether you're a physicist or a
+probabilist or a chemical engineer all
+
+ align:start position:0%
+probabilist or a chemical engineer all
+ 
+
+ align:start position:0%
+probabilist or a chemical engineer all
+the the techniques you learn can be
+
+ align:start position:0%
+the the techniques you learn can be
+ 
+
+ align:start position:0%
+the the techniques you learn can be
+applied you you know stochastic calculus
+
+ align:start position:0%
+applied you you know stochastic calculus
+ 
+
+ align:start position:0%
+applied you you know stochastic calculus
+or you know differential equations they
+
+ align:start position:0%
+or you know differential equations they
+ 
+
+ align:start position:0%
+or you know differential equations they
+can be applied but the path that I take
+
+ align:start position:0%
+can be applied but the path that I take
+ 
+
+ align:start position:0%
+can be applied but the path that I take
+in this class is very much through the
+
+ align:start position:0%
+in this class is very much through the
+ 
+
+ align:start position:0%
+in this class is very much through the
+probabilistic route okay which is my
+
+ align:start position:0%
+probabilistic route okay which is my
+ 
+
+ align:start position:0%
+probabilistic route okay which is my
+background as a as a probabilist as a as
+
+ align:start position:0%
+background as a as a probabilist as a as
+ 
+
+ align:start position:0%
+background as a as a probabilist as a as
+an academic or statistician as an
+
+ align:start position:0%
+an academic or statistician as an
+ 
+
+ align:start position:0%
+an academic or statistician as an
+academic and this is in particular I
+
+ align:start position:0%
+academic and this is in particular I
+ 
+
+ align:start position:0%
+academic and this is in particular I
+think a very elegant path to understand
+
+ align:start position:0%
+think a very elegant path to understand
+ 
+
+ align:start position:0%
+think a very elegant path to understand
+finance and the linkage between
+
+ align:start position:0%
+finance and the linkage between
+ 
+
+ align:start position:0%
+finance and the linkage between
+derivative products which might seem
+
+ align:start position:0%
+derivative products which might seem
+ 
+
+ align:start position:0%
+derivative products which might seem
+contrived and probability distributions
+
+ align:start position:0%
+contrived and probability distributions
+ 
+
+ align:start position:0%
+contrived and probability distributions
+which are sort of natural things for
+
+ align:start position:0%
+which are sort of natural things for
+ 
+
+ align:start position:0%
+which are sort of natural things for
+probabilists so this what I'm going to
+
+ align:start position:0%
+probabilists so this what I'm going to
+ 
+
+ align:start position:0%
+probabilists so this what I'm going to
+talk about today is really this link
+
+ align:start position:0%
+talk about today is really this link
+ 
+
+ align:start position:0%
+talk about today is really this link
+um which I call
+
+ align:start position:0%
+um which I call
+ 
+
+ align:start position:0%
+um which I call
+option
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+Duality
+
+ align:start position:0%
+Duality
+ 
+
+ align:start position:0%
+Duality
+which in um in essence in the simplest
+
+ align:start position:0%
+which in um in essence in the simplest
+ 
+
+ align:start position:0%
+which in um in essence in the simplest
+form is just saying option prices is
+
+ align:start position:0%
+form is just saying option prices is
+ 
+
+ align:start position:0%
+form is just saying option prices is
+they're just probability distributions
+
+ align:start position:0%
+they're just probability distributions
+ 
+
+ align:start position:0%
+they're just probability distributions
+therefore these complicated derivatives
+
+ align:start position:0%
+therefore these complicated derivatives
+ 
+
+ align:start position:0%
+therefore these complicated derivatives
+that people talk about all these options
+
+ align:start position:0%
+that people talk about all these options
+ 
+
+ align:start position:0%
+that people talk about all these options
+these Financial Engineers these quants
+
+ align:start position:0%
+these Financial Engineers these quants
+ 
+
+ align:start position:0%
+these Financial Engineers these quants
+these Exotics we're really just talking
+
+ align:start position:0%
+these Exotics we're really just talking
+ 
+
+ align:start position:0%
+these Exotics we're really just talking
+about probability distributions and we
+
+ align:start position:0%
+about probability distributions and we
+ 
+
+ align:start position:0%
+about probability distributions and we
+can go between them option prices
+
+ align:start position:0%
+can go between them option prices
+ 
+
+ align:start position:0%
+can go between them option prices
+probability distributions and back and
+
+ align:start position:0%
+probability distributions and back and
+ 
+
+ align:start position:0%
+probability distributions and back and
+forth in a very elegant way and what I
+
+ align:start position:0%
+forth in a very elegant way and what I
+ 
+
+ align:start position:0%
+forth in a very elegant way and what I
+love about this subject in particular is
+
+ align:start position:0%
+love about this subject in particular is
+ 
+
+ align:start position:0%
+love about this subject in particular is
+that to get to that point where we see
+
+ align:start position:0%
+that to get to that point where we see
+ 
+
+ align:start position:0%
+that to get to that point where we see
+this Duality does not
+
+ align:start position:0%
+this Duality does not
+ 
+
+ align:start position:0%
+this Duality does not
+need a whole framework and
+
+ align:start position:0%
+need a whole framework and
+ 
+
+ align:start position:0%
+need a whole framework and
+infrastructure of comp complicated
+
+ align:start position:0%
+infrastructure of comp complicated
+ 
+
+ align:start position:0%
+infrastructure of comp complicated
+definitions or formula or option pricing
+
+ align:start position:0%
+definitions or formula or option pricing
+ 
+
+ align:start position:0%
+definitions or formula or option pricing
+formula or so on so that's what I'm
+
+ align:start position:0%
+formula or so on so that's what I'm
+ 
+
+ align:start position:0%
+formula or so on so that's what I'm
+going to try and do in this hour or so
+
+ align:start position:0%
+going to try and do in this hour or so
+ 
+
+ align:start position:0%
+going to try and do in this hour or so
+is introduce this concept of option
+
+ align:start position:0%
+is introduce this concept of option
+ 
+
+ align:start position:0%
+is introduce this concept of option
+price probability Duality and show how
+
+ align:start position:0%
+price probability Duality and show how
+ 
+
+ align:start position:0%
+price probability Duality and show how
+it's sort of a natural so there's a
+
+ align:start position:0%
+it's sort of a natural so there's a
+ 
+
+ align:start position:0%
+it's sort of a natural so there's a
+natural Duality it can be seen in a
+
+ align:start position:0%
+natural Duality it can be seen in a
+ 
+
+ align:start position:0%
+natural Duality it can be seen in a
+number of different ways okay so we're
+
+ align:start position:0%
+number of different ways okay so we're
+ 
+
+ align:start position:0%
+number of different ways okay so we're
+going to um need a few a few definitions
+
+ align:start position:0%
+going to um need a few a few definitions
+ 
+
+ align:start position:0%
+going to um need a few a few definitions
+that should be familiar uh to you we're
+
+ align:start position:0%
+that should be familiar uh to you we're
+ 
+
+ align:start position:0%
+that should be familiar uh to you we're
+going to Define three
+
+ align:start position:0%
+going to Define three
+ 
+
+ align:start position:0%
+going to Define three
+assets um I have a call
+
+ align:start position:0%
+assets um I have a call
+ 
+
+ align:start position:0%
+assets um I have a call
+option you know about out um a zero
+
+ align:start position:0%
+option you know about out um a zero
+ 
+
+ align:start position:0%
+option you know about out um a zero
+coupon
+
+ align:start position:0%
+coupon
+ 
+
+ align:start position:0%
+coupon
+Bond call a
+
+ align:start position:0%
+Bond call a
+ 
+
+ align:start position:0%
+Bond call a
+zcb this is the one thing I haven't
+
+ align:start position:0%
+zcb this is the one thing I haven't
+ 
+
+ align:start position:0%
+zcb this is the one thing I haven't
+become American is on I still call this
+
+ align:start position:0%
+become American is on I still call this
+ 
+
+ align:start position:0%
+become American is on I still call this
+Zed it's a other things I've become um
+
+ align:start position:0%
+Zed it's a other things I've become um
+ 
+
+ align:start position:0%
+Zed it's a other things I've become um
+and then a digital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+option okay all right so what are they
+
+ align:start position:0%
+option okay all right so what are they
+ 
+
+ align:start position:0%
+option okay all right so what are they
+well they're all going to be defined by
+
+ align:start position:0%
+well they're all going to be defined by
+ 
+
+ align:start position:0%
+well they're all going to be defined by
+their payout at maturity okay so we're
+
+ align:start position:0%
+their payout at maturity okay so we're
+ 
+
+ align:start position:0%
+their payout at maturity okay so we're
+going to have some maturity capital T um
+
+ align:start position:0%
+going to have some maturity capital T um
+ 
+
+ align:start position:0%
+going to have some maturity capital T um
+and some underlying asset s the stock
+
+ align:start position:0%
+and some underlying asset s the stock
+ 
+
+ align:start position:0%
+and some underlying asset s the stock
+with some price St okay so we know that
+
+ align:start position:0%
+with some price St okay so we know that
+ 
+
+ align:start position:0%
+with some price St okay so we know that
+the call option has payout at T so let's
+
+ align:start position:0%
+the call option has payout at T so let's
+ 
+
+ align:start position:0%
+the call option has payout at T so let's
+called pay out at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T So T is some fixed time in the future
+
+ align:start position:0%
+T So T is some fixed time in the future
+ 
+
+ align:start position:0%
+T So T is some fixed time in the future
+we can we'll change it in future but
+
+ align:start position:0%
+we can we'll change it in future but
+ 
+
+ align:start position:0%
+we can we'll change it in future but
+some fixed time this is simply the max
+
+ align:start position:0%
+some fixed time this is simply the max
+ 
+
+ align:start position:0%
+some fixed time this is simply the max
+of St minus K and
+
+ align:start position:0%
+of St minus K and
+ 
+
+ align:start position:0%
+of St minus K and
+zero okay that's the call option um you
+
+ align:start position:0%
+zero okay that's the call option um you
+ 
+
+ align:start position:0%
+zero okay that's the call option um you
+know you can go
+
+ align:start position:0%
+know you can go
+ 
+
+ align:start position:0%
+know you can go
+through the right to buy etc etc but
+
+ align:start position:0%
+through the right to buy etc etc but
+ 
+
+ align:start position:0%
+through the right to buy etc etc but
+clearly it's just value at maturity is
+
+ align:start position:0%
+clearly it's just value at maturity is
+ 
+
+ align:start position:0%
+clearly it's just value at maturity is
+just the max of stus K and Z um the zero
+
+ align:start position:0%
+just the max of stus K and Z um the zero
+ 
+
+ align:start position:0%
+just the max of stus K and Z um the zero
+coupon bond with maturity T is just
+
+ align:start position:0%
+coupon bond with maturity T is just
+ 
+
+ align:start position:0%
+coupon bond with maturity T is just
+something that's worth one at time T so
+
+ align:start position:0%
+something that's worth one at time T so
+ 
+
+ align:start position:0%
+something that's worth one at time T so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+just pay one that's definition so you
+
+ align:start position:0%
+just pay one that's definition so you
+ 
+
+ align:start position:0%
+just pay one that's definition so you
+can think of these all as definitions um
+
+ align:start position:0%
+can think of these all as definitions um
+ 
+
+ align:start position:0%
+can think of these all as definitions um
+and then the digital option is just the
+
+ align:start position:0%
+and then the digital option is just the
+ 
+
+ align:start position:0%
+and then the digital option is just the
+indicator function of St being greater
+
+ align:start position:0%
+indicator function of St being greater
+ 
+
+ align:start position:0%
+indicator function of St being greater
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+K okay okay so here
+
+ align:start position:0%
+K okay okay so here
+ 
+
+ align:start position:0%
+K okay okay so here
+um T is the maturity K is the strike
+
+ align:start position:0%
+um T is the maturity K is the strike
+ 
+
+ align:start position:0%
+um T is the maturity K is the strike
+okay so T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maturity okay is
+
+ align:start position:0%
+maturity okay is
+ 
+
+ align:start position:0%
+maturity okay is
+Strike okay and these are three three
+
+ align:start position:0%
+Strike okay and these are three three
+ 
+
+ align:start position:0%
+Strike okay and these are three three
+assets so this is in some sense the
+
+ align:start position:0%
+assets so this is in some sense the
+ 
+
+ align:start position:0%
+assets so this is in some sense the
+payout function okay all derivative
+
+ align:start position:0%
+payout function okay all derivative
+ 
+
+ align:start position:0%
+payout function okay all derivative
+products can be defined in terms of a
+
+ align:start position:0%
+products can be defined in terms of a
+ 
+
+ align:start position:0%
+products can be defined in terms of a
+function not all of them many derivative
+
+ align:start position:0%
+function not all of them many derivative
+ 
+
+ align:start position:0%
+function not all of them many derivative
+products can be defined just simp a
+
+ align:start position:0%
+products can be defined just simp a
+ 
+
+ align:start position:0%
+products can be defined just simp a
+function of St and here are three
+
+ align:start position:0%
+function of St and here are three
+ 
+
+ align:start position:0%
+function of St and here are three
+functions of St is the identity one okay
+
+ align:start position:0%
+functions of St is the identity one okay
+ 
+
+ align:start position:0%
+functions of St is the identity one okay
+and then I'm just going to um get
+
+ align:start position:0%
+and then I'm just going to um get
+ 
+
+ align:start position:0%
+and then I'm just going to um get
+notation for their price at T less than
+
+ align:start position:0%
+notation for their price at T less than
+ 
+
+ align:start position:0%
+notation for their price at T less than
+equal to T we can think about Little T
+
+ align:start position:0%
+equal to T we can think about Little T
+ 
+
+ align:start position:0%
+equal to T we can think about Little T
+as current time today or we can think of
+
+ align:start position:0%
+as current time today or we can think of
+ 
+
+ align:start position:0%
+as current time today or we can think of
+some future time between now and capital
+
+ align:start position:0%
+some future time between now and capital
+ 
+
+ align:start position:0%
+some future time between now and capital
+T um and I'm just going to introduce
+
+ align:start position:0%
+T um and I'm just going to introduce
+ 
+
+ align:start position:0%
+T um and I'm just going to introduce
+notation every different Finance book
+
+ align:start position:0%
+notation every different Finance book
+ 
+
+ align:start position:0%
+notation every different Finance book
+uses different notations so just um um
+
+ align:start position:0%
+uses different notations so just um um
+ 
+
+ align:start position:0%
+uses different notations so just um um
+let's just C for call Price with strike
+
+ align:start position:0%
+let's just C for call Price with strike
+ 
+
+ align:start position:0%
+let's just C for call Price with strike
+K uh at Little T with maturity Big T
+
+ align:start position:0%
+K uh at Little T with maturity Big T
+ 
+
+ align:start position:0%
+K uh at Little T with maturity Big T
+okay just that notation the zero coupon
+
+ align:start position:0%
+okay just that notation the zero coupon
+ 
+
+ align:start position:0%
+okay just that notation the zero coupon
+Bond the price at Little T we's call
+
+ align:start position:0%
+Bond the price at Little T we's call
+ 
+
+ align:start position:0%
+Bond the price at Little T we's call
+that Zed okay that's the price of little
+
+ align:start position:0%
+that Zed okay that's the price of little
+ 
+
+ align:start position:0%
+that Zed okay that's the price of little
+T and the digital we'll just call that
+
+ align:start position:0%
+T and the digital we'll just call that
+ 
+
+ align:start position:0%
+T and the digital we'll just call that
+D okay so this is what we're going to
+
+ align:start position:0%
+D okay so this is what we're going to
+ 
+
+ align:start position:0%
+D okay so this is what we're going to
+we're going to set this up U the not
+
+ align:start position:0%
+we're going to set this up U the not
+ 
+
+ align:start position:0%
+we're going to set this up U the not
+actually you could help you could have a
+
+ align:start position:0%
+actually you could help you could have a
+ 
+
+ align:start position:0%
+actually you could help you could have a
+whole lecture on why notation different
+
+ align:start position:0%
+whole lecture on why notation different
+ 
+
+ align:start position:0%
+whole lecture on why notation different
+notation K and capital T are actually
+
+ align:start position:0%
+notation K and capital T are actually
+ 
+
+ align:start position:0%
+notation K and capital T are actually
+embedded in the terms of the contract
+
+ align:start position:0%
+embedded in the terms of the contract
+ 
+
+ align:start position:0%
+embedded in the terms of the contract
+Little T is of my calendar time so you
+
+ align:start position:0%
+Little T is of my calendar time so you
+ 
+
+ align:start position:0%
+Little T is of my calendar time so you
+might think why don't you put K in
+
+ align:start position:0%
+might think why don't you put K in
+ 
+
+ align:start position:0%
+might think why don't you put K in
+capital D somewhere else well when you
+
+ align:start position:0%
+capital D somewhere else well when you
+ 
+
+ align:start position:0%
+capital D somewhere else well when you
+get actually to modeling derivatives you
+
+ align:start position:0%
+get actually to modeling derivatives you
+ 
+
+ align:start position:0%
+get actually to modeling derivatives you
+like to be moving both maturity and a
+
+ align:start position:0%
+like to be moving both maturity and a
+ 
+
+ align:start position:0%
+like to be moving both maturity and a
+forward time and calendar time that's
+
+ align:start position:0%
+forward time and calendar time that's
+ 
+
+ align:start position:0%
+forward time and calendar time that's
+why I just write it like that but
+
+ align:start position:0%
+why I just write it like that but
+ 
+
+ align:start position:0%
+why I just write it like that but
+there's no okay so C subk Little T Big T
+
+ align:start position:0%
+there's no okay so C subk Little T Big T
+ 
+
+ align:start position:0%
+there's no okay so C subk Little T Big T
+is the price at time Little T of a call
+
+ align:start position:0%
+is the price at time Little T of a call
+ 
+
+ align:start position:0%
+is the price at time Little T of a call
+with maturity capital T and strike K
+
+ align:start position:0%
+with maturity capital T and strike K
+ 
+
+ align:start position:0%
+with maturity capital T and strike K
+okay right black shs and other option
+
+ align:start position:0%
+okay right black shs and other option
+ 
+
+ align:start position:0%
+okay right black shs and other option
+pricing formula are all about
+
+ align:start position:0%
+pricing formula are all about
+ 
+
+ align:start position:0%
+pricing formula are all about
+determining
+
+ align:start position:0%
+determining
+ 
+
+ align:start position:0%
+determining
+this right for T less than T okay cuz
+
+ align:start position:0%
+this right for T less than T okay cuz
+ 
+
+ align:start position:0%
+this right for T less than T okay cuz
+clearly
+
+ align:start position:0%
+clearly
+ 
+
+ align:start position:0%
+clearly
+we know that the price at maturity is
+
+ align:start position:0%
+we know that the price at maturity is
+ 
+
+ align:start position:0%
+we know that the price at maturity is
+simply the payout right I mean that's
+
+ align:start position:0%
+simply the payout right I mean that's
+ 
+
+ align:start position:0%
+simply the payout right I mean that's
+again just the
+
+ align:start position:0%
+again just the
+ 
+
+ align:start position:0%
+again just the
+definition okay so that's that's trivial
+
+ align:start position:0%
+definition okay so that's that's trivial
+ 
+
+ align:start position:0%
+definition okay so that's that's trivial
+but we want to find out what the price
+
+ align:start position:0%
+but we want to find out what the price
+ 
+
+ align:start position:0%
+but we want to find out what the price
+is at Little T okay so that's a whole
+
+ align:start position:0%
+is at Little T okay so that's a whole
+ 
+
+ align:start position:0%
+is at Little T okay so that's a whole
+path of Finance black shs and other
+
+ align:start position:0%
+path of Finance black shs and other
+ 
+
+ align:start position:0%
+path of Finance black shs and other
+price option pricing methodology is
+
+ align:start position:0%
+price option pricing methodology is
+ 
+
+ align:start position:0%
+price option pricing methodology is
+working out this but we're actually
+
+ align:start position:0%
+working out this but we're actually
+ 
+
+ align:start position:0%
+working out this but we're actually
+going to go down a a different route
+
+ align:start position:0%
+going to go down a a different route
+ 
+
+ align:start position:0%
+going to go down a a different route
+okay right so what we're going to do we
+
+ align:start position:0%
+okay right so what we're going to do we
+ 
+
+ align:start position:0%
+okay right so what we're going to do we
+are going to construct a uh portfolio
+
+ align:start position:0%
+are going to construct a uh portfolio
+ 
+
+ align:start position:0%
+are going to construct a uh portfolio
+so we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider as a
+
+ align:start position:0%
+consider as a
+ 
+
+ align:start position:0%
+consider as a
+portfolio of what we're going to consist
+
+ align:start position:0%
+portfolio of what we're going to consist
+ 
+
+ align:start position:0%
+portfolio of what we're going to consist
+of two calls okay we're going to have
+
+ align:start position:0%
+of two calls okay we're going to have
+ 
+
+ align:start position:0%
+of two calls okay we're going to have
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+calls with strike
+
+ align:start position:0%
+calls with strike
+ 
+
+ align:start position:0%
+calls with strike
+K okay so I just this the mount holding
+
+ align:start position:0%
+K okay so I just this the mount holding
+ 
+
+ align:start position:0%
+K okay so I just this the mount holding
+of and everything is going to be with
+
+ align:start position:0%
+of and everything is going to be with
+ 
+
+ align:start position:0%
+of and everything is going to be with
+maturity capital T So Lambda calls with
+
+ align:start position:0%
+maturity capital T So Lambda calls with
+ 
+
+ align:start position:0%
+maturity capital T So Lambda calls with
+strike K and maturity T and minus Lambda
+
+ align:start position:0%
+strike K and maturity T and minus Lambda
+ 
+
+ align:start position:0%
+strike K and maturity T and minus Lambda
+calls with
+
+ align:start position:0%
+calls with
+ 
+
+ align:start position:0%
+calls with
+strike k + 1 /
+
+ align:start position:0%
+strike k + 1 /
+ 
+
+ align:start position:0%
+strike k + 1 /
+Lambda okay we just consider that
+
+ align:start position:0%
+Lambda okay we just consider that
+ 
+
+ align:start position:0%
+Lambda okay we just consider that
+portfolio consists of two
+
+ align:start position:0%
+portfolio consists of two
+ 
+
+ align:start position:0%
+portfolio consists of two
+options all right well it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price at T well that's easy we just
+
+ align:start position:0%
+price at T well that's easy we just
+ 
+
+ align:start position:0%
+price at T well that's easy we just
+let's just write it in terms of what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda times the price of the call with
+
+ align:start position:0%
+Lambda times the price of the call with
+ 
+
+ align:start position:0%
+Lambda times the price of the call with
+strike
+
+ align:start position:0%
+strike
+ 
+
+ align:start position:0%
+strike
+K minus Lambda
+
+ align:start position:0%
+K minus Lambda
+ 
+
+ align:start position:0%
+K minus Lambda
+call with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strike k + one over Lambda okay it's
+
+ align:start position:0%
+strike k + one over Lambda okay it's
+ 
+
+ align:start position:0%
+strike k + one over Lambda okay it's
+just by definition that's its price at
+
+ align:start position:0%
+just by definition that's its price at
+ 
+
+ align:start position:0%
+just by definition that's its price at
+T okay well let's look at its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+payout time capital T
+
+ align:start position:0%
+payout time capital T
+ 
+
+ align:start position:0%
+payout time capital T
+graphically right okay so you know about
+
+ align:start position:0%
+graphically right okay so you know about
+ 
+
+ align:start position:0%
+graphically right okay so you know about
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+options right the payout function is
+
+ align:start position:0%
+options right the payout function is
+ 
+
+ align:start position:0%
+options right the payout function is
+just the hockey stick shape clearly
+
+ align:start position:0%
+just the hockey stick shape clearly
+ 
+
+ align:start position:0%
+just the hockey stick shape clearly
+that's confusing to people from the UK
+
+ align:start position:0%
+that's confusing to people from the UK
+ 
+
+ align:start position:0%
+that's confusing to people from the UK
+cu in in UK hockey means field hockey
+
+ align:start position:0%
+cu in in UK hockey means field hockey
+ 
+
+ align:start position:0%
+cu in in UK hockey means field hockey
+not ice hockey and of course hockey sck
+
+ align:start position:0%
+not ice hockey and of course hockey sck
+ 
+
+ align:start position:0%
+not ice hockey and of course hockey sck
+shape and field hockey looks very
+
+ align:start position:0%
+shape and field hockey looks very
+ 
+
+ align:start position:0%
+shape and field hockey looks very
+different anyway that's uh you
+
+ align:start position:0%
+different anyway that's uh you
+ 
+
+ align:start position:0%
+different anyway that's uh you
+understand what the payout of a call is
+
+ align:start position:0%
+understand what the payout of a call is
+ 
+
+ align:start position:0%
+understand what the payout of a call is
+clearly this payout function of a call
+
+ align:start position:0%
+clearly this payout function of a call
+ 
+
+ align:start position:0%
+clearly this payout function of a call
+looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay well putting
+
+ align:start position:0%
+right okay well putting
+ 
+
+ align:start position:0%
+right okay well putting
+this P of Lambda C strike K minus Lambda
+
+ align:start position:0%
+this P of Lambda C strike K minus Lambda
+ 
+
+ align:start position:0%
+this P of Lambda C strike K minus Lambda
+C strike K plus one over Lambda let's
+
+ align:start position:0%
+C strike K plus one over Lambda let's
+ 
+
+ align:start position:0%
+C strike K plus one over Lambda let's
+assume Lambda is positive for the time
+
+ align:start position:0%
+assume Lambda is positive for the time
+ 
+
+ align:start position:0%
+assume Lambda is positive for the time
+being what does it look like well it's
+
+ align:start position:0%
+being what does it look like well it's
+ 
+
+ align:start position:0%
+being what does it look like well it's
+zero below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K it's flat above k + 1/ Lambda it has
+
+ align:start position:0%
+K it's flat above k + 1/ Lambda it has
+ 
+
+ align:start position:0%
+K it's flat above k + 1/ Lambda it has
+slope
+
+ align:start position:0%
+slope
+ 
+
+ align:start position:0%
+slope
+Lambda okay and has value one here
+
+ align:start position:0%
+Lambda okay and has value one here
+ 
+
+ align:start position:0%
+Lambda okay and has value one here
+okay right you should be able to see
+
+ align:start position:0%
+okay right you should be able to see
+ 
+
+ align:start position:0%
+okay right you should be able to see
+that just
+
+ align:start position:0%
+that just
+ 
+
+ align:start position:0%
+that just
+easily okay so that's the the pay this
+
+ align:start position:0%
+easily okay so that's the the pay this
+ 
+
+ align:start position:0%
+easily okay so that's the the pay this
+is called call spread just the spread
+
+ align:start position:0%
+is called call spread just the spread
+ 
+
+ align:start position:0%
+is called call spread just the spread
+between two calls okay it has this
+
+ align:start position:0%
+between two calls okay it has this
+ 
+
+ align:start position:0%
+between two calls okay it has this
+payout function Okay so natural thing to
+
+ align:start position:0%
+payout function Okay so natural thing to
+ 
+
+ align:start position:0%
+payout function Okay so natural thing to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+here being a mathematics class let's
+
+ align:start position:0%
+here being a mathematics class let's
+ 
+
+ align:start position:0%
+here being a mathematics class let's
+take limits just let let Lambda tend to
+
+ align:start position:0%
+take limits just let let Lambda tend to
+ 
+
+ align:start position:0%
+take limits just let let Lambda tend to
+Infinity okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay well then this becomes the
+
+ align:start position:0%
+so okay well then this becomes the
+ 
+
+ align:start position:0%
+so okay well then this becomes the
+partial derivative of the core price
+
+ align:start position:0%
+partial derivative of the core price
+ 
+
+ align:start position:0%
+partial derivative of the core price
+with respect to K or the negative of it
+
+ align:start position:0%
+with respect to K or the negative of it
+ 
+
+ align:start position:0%
+with respect to K or the negative of it
+so this tends to
+
+ align:start position:0%
+so this tends to
+ 
+
+ align:start position:0%
+so this tends to
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+okay right let's
+
+ align:start position:0%
+okay right let's
+ 
+
+ align:start position:0%
+okay right let's
+just okay so that's that and then this
+
+ align:start position:0%
+just okay so that's that and then this
+ 
+
+ align:start position:0%
+just okay so that's that and then this
+of course as Lambda goes to Infinity
+
+ align:start position:0%
+of course as Lambda goes to Infinity
+ 
+
+ align:start position:0%
+of course as Lambda goes to Infinity
+this stays at one so this tends
+
+ align:start position:0%
+this stays at one so this tends
+ 
+
+ align:start position:0%
+this stays at one so this tends
+to a payout
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function that looks like that
+
+ align:start position:0%
+function that looks like that
+ 
+
+ align:start position:0%
+function that looks like that
+okay right okay so this is easy calculus
+
+ align:start position:0%
+okay right okay so this is easy calculus
+ 
+
+ align:start position:0%
+okay right okay so this is easy calculus
+this is just by
+
+ align:start position:0%
+this is just by
+ 
+
+ align:start position:0%
+this is just by
+inspection right okay so this clearly is
+
+ align:start position:0%
+inspection right okay so this clearly is
+ 
+
+ align:start position:0%
+inspection right okay so this clearly is
+the payout of the digital
+
+ align:start position:0%
+the payout of the digital
+ 
+
+ align:start position:0%
+the payout of the digital
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so right of the strictly digital call
+
+ align:start position:0%
+so right of the strictly digital call
+ 
+
+ align:start position:0%
+so right of the strictly digital call
+but that's called the digital digital
+
+ align:start position:0%
+but that's called the digital digital
+ 
+
+ align:start position:0%
+but that's called the digital digital
+option okay um just as a note here's
+
+ align:start position:0%
+option okay um just as a note here's
+ 
+
+ align:start position:0%
+option okay um just as a note here's
+just greater than you might think okay
+
+ align:start position:0%
+just greater than you might think okay
+ 
+
+ align:start position:0%
+just greater than you might think okay
+should does doesn't matter if this is
+
+ align:start position:0%
+should does doesn't matter if this is
+ 
+
+ align:start position:0%
+should does doesn't matter if this is
+greater than or equal to well in
+
+ align:start position:0%
+greater than or equal to well in
+ 
+
+ align:start position:0%
+greater than or equal to well in
+practice you know the chance of
+
+ align:start position:0%
+practice you know the chance of
+ 
+
+ align:start position:0%
+practice you know the chance of
+something equaling a number exactly you
+
+ align:start position:0%
+something equaling a number exactly you
+ 
+
+ align:start position:0%
+something equaling a number exactly you
+can is is zero I mean if it's a
+
+ align:start position:0%
+can is is zero I mean if it's a
+ 
+
+ align:start position:0%
+can is is zero I mean if it's a
+continuous distribution well in theory
+
+ align:start position:0%
+continuous distribution well in theory
+ 
+
+ align:start position:0%
+continuous distribution well in theory
+so I should say the chance of something
+
+ align:start position:0%
+so I should say the chance of something
+ 
+
+ align:start position:0%
+so I should say the chance of something
+actually nailing the strike actually
+
+ align:start position:0%
+actually nailing the strike actually
+ 
+
+ align:start position:0%
+actually nailing the strike actually
+being equal to K is zero so it doesn't
+
+ align:start position:0%
+being equal to K is zero so it doesn't
+ 
+
+ align:start position:0%
+being equal to K is zero so it doesn't
+really matter whether def Finance is
+
+ align:start position:0%
+really matter whether def Finance is
+ 
+
+ align:start position:0%
+really matter whether def Finance is
+greater than or greater than or equal to
+
+ align:start position:0%
+greater than or greater than or equal to
+ 
+
+ align:start position:0%
+greater than or greater than or equal to
+but in practice of course Finance is in
+
+ align:start position:0%
+but in practice of course Finance is in
+ 
+
+ align:start position:0%
+but in practice of course Finance is in
+discrete time because you don't quote
+
+ align:start position:0%
+discrete time because you don't quote
+ 
+
+ align:start position:0%
+discrete time because you don't quote
+things to a million decimal places right
+
+ align:start position:0%
+things to a million decimal places right
+ 
+
+ align:start position:0%
+things to a million decimal places right
+so certain assets actually which are
+
+ align:start position:0%
+so certain assets actually which are
+ 
+
+ align:start position:0%
+so certain assets actually which are
+quoted only in e or 16th or 302s or 64s
+
+ align:start position:0%
+quoted only in e or 16th or 302s or 64s
+ 
+
+ align:start position:0%
+quoted only in e or 16th or 302s or 64s
+this matters actually with you def find
+
+ align:start position:0%
+this matters actually with you def find
+ 
+
+ align:start position:0%
+this matters actually with you def find
+it's greater than greater or equal to
+
+ align:start position:0%
+it's greater than greater or equal to
+ 
+
+ align:start position:0%
+it's greater than greater or equal to
+but theoretically it doesn't make any
+
+ align:start position:0%
+but theoretically it doesn't make any
+ 
+
+ align:start position:0%
+but theoretically it doesn't make any
+difference Okay so we've got the call
+
+ align:start position:0%
+difference Okay so we've got the call
+ 
+
+ align:start position:0%
+difference Okay so we've got the call
+spread tending
+
+ align:start position:0%
+spread tending
+ 
+
+ align:start position:0%
+spread tending
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+digital okay all right
+
+ align:start position:0%
+digital okay all right
+ 
+
+ align:start position:0%
+digital okay all right
+so this tends to um so the limit of this
+
+ align:start position:0%
+so this tends to um so the limit of this
+ 
+
+ align:start position:0%
+so this tends to um so the limit of this
+cor
+
+ align:start position:0%
+cor
+ 
+
+ align:start position:0%
+cor
+spread of this price of the cor spread
+
+ align:start position:0%
+spread of this price of the cor spread
+ 
+
+ align:start position:0%
+spread of this price of the cor spread
+is the digital and
+
+ align:start position:0%
+is the digital and
+ 
+
+ align:start position:0%
+is the digital and
+so we know that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay see this is the price at T this is
+
+ align:start position:0%
+okay see this is the price at T this is
+ 
+
+ align:start position:0%
+okay see this is the price at T this is
+the pay of capital T okay the price of
+
+ align:start position:0%
+the pay of capital T okay the price of
+ 
+
+ align:start position:0%
+the pay of capital T okay the price of
+the digital must equal just the partial
+
+ align:start position:0%
+the digital must equal just the partial
+ 
+
+ align:start position:0%
+the digital must equal just the partial
+derivative with respect to strike of the
+
+ align:start position:0%
+derivative with respect to strike of the
+ 
+
+ align:start position:0%
+derivative with respect to strike of the
+call Price
+
+ align:start position:0%
+call Price
+ 
+
+ align:start position:0%
+call Price
+okay all right so that's just
+
+ align:start position:0%
+okay all right so that's just
+ 
+
+ align:start position:0%
+okay all right so that's just
+a um nice little result uh where does
+
+ align:start position:0%
+a um nice little result uh where does
+ 
+
+ align:start position:0%
+a um nice little result uh where does
+this bring in probability okay so this
+
+ align:start position:0%
+this bring in probability okay so this
+ 
+
+ align:start position:0%
+this bring in probability okay so this
+is the next
+
+ align:start position:0%
+is the next
+ 
+
+ align:start position:0%
+is the next
+um Okay so this is where we'll make
+
+ align:start position:0%
+um Okay so this is where we'll make
+ 
+
+ align:start position:0%
+um Okay so this is where we'll make
+one um
+
+ align:start position:0%
+one um
+ 
+
+ align:start position:0%
+one um
+assumption um and it's actually a very
+
+ align:start position:0%
+assumption um and it's actually a very
+ 
+
+ align:start position:0%
+assumption um and it's actually a very
+important and fundamental assumption um
+
+ align:start position:0%
+important and fundamental assumption um
+ 
+
+ align:start position:0%
+important and fundamental assumption um
+and it's fundamental because it's called
+
+ align:start position:0%
+and it's fundamental because it's called
+ 
+
+ align:start position:0%
+and it's fundamental because it's called
+the fundamental theorem of Finance or
+
+ align:start position:0%
+the fundamental theorem of Finance or
+ 
+
+ align:start position:0%
+the fundamental theorem of Finance or
+the fundamental theorem of asset prices
+
+ align:start position:0%
+the fundamental theorem of asset prices
+ 
+
+ align:start position:0%
+the fundamental theorem of asset prices
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so so I call this
+
+ align:start position:0%
+so so I call this
+ 
+
+ align:start position:0%
+so so I call this
+ftap fundamental theorem of asset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pricing by this theorem which we're
+
+ align:start position:0%
+pricing by this theorem which we're
+ 
+
+ align:start position:0%
+pricing by this theorem which we're
+going to here the
+
+ align:start position:0%
+going to here the
+ 
+
+ align:start position:0%
+going to here the
+intuitive answer is correct meaning that
+
+ align:start position:0%
+intuitive answer is correct meaning that
+ 
+
+ align:start position:0%
+intuitive answer is correct meaning that
+prices today our expected values is the
+
+ align:start position:0%
+prices today our expected values is the
+ 
+
+ align:start position:0%
+prices today our expected values is the
+expectation of the future payout okay so
+
+ align:start position:0%
+expectation of the future payout okay so
+ 
+
+ align:start position:0%
+expectation of the future payout okay so
+by ftap the
+
+ align:start position:0%
+by ftap the
+ 
+
+ align:start position:0%
+by ftap the
+price at T is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+payout at time capital P suit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discounted
+
+ align:start position:0%
+discounted
+ 
+
+ align:start position:0%
+discounted
+so there's both something very
+
+ align:start position:0%
+so there's both something very
+ 
+
+ align:start position:0%
+so there's both something very
+straightforward here and something very
+
+ align:start position:0%
+straightforward here and something very
+ 
+
+ align:start position:0%
+straightforward here and something very
+deep right if you would think about what
+
+ align:start position:0%
+deep right if you would think about what
+ 
+
+ align:start position:0%
+deep right if you would think about what
+how much would you pay for a contract
+
+ align:start position:0%
+how much would you pay for a contract
+ 
+
+ align:start position:0%
+how much would you pay for a contract
+that gives you a dollar if an event
+
+ align:start position:0%
+that gives you a dollar if an event
+ 
+
+ align:start position:0%
+that gives you a dollar if an event
+happens in this case the event being
+
+ align:start position:0%
+happens in this case the event being
+ 
+
+ align:start position:0%
+happens in this case the event being
+stock being greater than k at maturity
+
+ align:start position:0%
+stock being greater than k at maturity
+ 
+
+ align:start position:0%
+stock being greater than k at maturity
+you would intuitively think that's
+
+ align:start position:0%
+you would intuitively think that's
+ 
+
+ align:start position:0%
+you would intuitively think that's
+related to the probability of of the
+
+ align:start position:0%
+related to the probability of of the
+ 
+
+ align:start position:0%
+related to the probability of of the
+event happening right how much would you
+
+ align:start position:0%
+event happening right how much would you
+ 
+
+ align:start position:0%
+event happening right how much would you
+pay to receive a dollar if a coin comes
+
+ align:start position:0%
+pay to receive a dollar if a coin comes
+ 
+
+ align:start position:0%
+pay to receive a dollar if a coin comes
+up ahead you'd pay a
+
+ align:start position:0%
+up ahead you'd pay a
+ 
+
+ align:start position:0%
+up ahead you'd pay a
+half probably okay it's very very
+
+ align:start position:0%
+half probably okay it's very very
+ 
+
+ align:start position:0%
+half probably okay it's very very
+intuitive
+
+ align:start position:0%
+intuitive
+ 
+
+ align:start position:0%
+intuitive
+but the deepness is that this is
+
+ align:start position:0%
+but the deepness is that this is
+ 
+
+ align:start position:0%
+but the deepness is that this is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+holds under a particular probability
+
+ align:start position:0%
+holds under a particular probability
+ 
+
+ align:start position:0%
+holds under a particular probability
+distribution I'm not going to go go into
+
+ align:start position:0%
+distribution I'm not going to go go into
+ 
+
+ align:start position:0%
+distribution I'm not going to go go into
+that here but the by the fundamental
+
+ align:start position:0%
+that here but the by the fundamental
+ 
+
+ align:start position:0%
+that here but the by the fundamental
+theorem this is this is true okay so I
+
+ align:start position:0%
+theorem this is this is true okay so I
+ 
+
+ align:start position:0%
+theorem this is this is true okay so I
+can write in the case of the
+
+ align:start position:0%
+can write in the case of the
+ 
+
+ align:start position:0%
+can write in the case of the
+digital the digital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+equals the
+
+ align:start position:0%
+equals the
+ 
+
+ align:start position:0%
+equals the
+discounted and we'll explain why we want
+
+ align:start position:0%
+discounted and we'll explain why we want
+ 
+
+ align:start position:0%
+discounted and we'll explain why we want
+to put the zero coupon bond price here
+
+ align:start position:0%
+to put the zero coupon bond price here
+ 
+
+ align:start position:0%
+to put the zero coupon bond price here
+that's the present value of a dollar at
+
+ align:start position:0%
+that's the present value of a dollar at
+ 
+
+ align:start position:0%
+that's the present value of a dollar at
+time T right okay that's just a discount
+
+ align:start position:0%
+time T right okay that's just a discount
+ 
+
+ align:start position:0%
+time T right okay that's just a discount
+factor it's very trivial but that's
+
+ align:start position:0%
+factor it's very trivial but that's
+ 
+
+ align:start position:0%
+factor it's very trivial but that's
+written in terms of an asset price times
+
+ align:start position:0%
+written in terms of an asset price times
+ 
+
+ align:start position:0%
+written in terms of an asset price times
+the expected value of the payout
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so either you can take this as
+
+ align:start position:0%
+so okay so either you can take this as
+ 
+
+ align:start position:0%
+so okay so either you can take this as
+this makes a lot of sense the discounted
+
+ align:start position:0%
+this makes a lot of sense the discounted
+ 
+
+ align:start position:0%
+this makes a lot of sense the discounted
+expected
+
+ align:start position:0%
+expected
+ 
+
+ align:start position:0%
+expected
+payout or you can say I don't understand
+
+ align:start position:0%
+payout or you can say I don't understand
+ 
+
+ align:start position:0%
+payout or you can say I don't understand
+this I want to find out about the
+
+ align:start position:0%
+this I want to find out about the
+ 
+
+ align:start position:0%
+this I want to find out about the
+fundamental theorem of asset pricing
+
+ align:start position:0%
+fundamental theorem of asset pricing
+ 
+
+ align:start position:0%
+fundamental theorem of asset pricing
+which we will prove in my in my class
+
+ align:start position:0%
+which we will prove in my in my class
+ 
+
+ align:start position:0%
+which we will prove in my in my class
+but this is s of intuitively makes sense
+
+ align:start position:0%
+but this is s of intuitively makes sense
+ 
+
+ align:start position:0%
+but this is s of intuitively makes sense
+the key here okay is that the expected
+
+ align:start position:0%
+the key here okay is that the expected
+ 
+
+ align:start position:0%
+the key here okay is that the expected
+value actually has to be taken out under
+
+ align:start position:0%
+value actually has to be taken out under
+ 
+
+ align:start position:0%
+value actually has to be taken out under
+the appropriate distribution called the
+
+ align:start position:0%
+the appropriate distribution called the
+ 
+
+ align:start position:0%
+the appropriate distribution called the
+risk neutral distribution okay but this
+
+ align:start position:0%
+risk neutral distribution okay but this
+ 
+
+ align:start position:0%
+risk neutral distribution okay but this
+formula holds in fact
+
+ align:start position:0%
+formula holds in fact
+ 
+
+ align:start position:0%
+formula holds in fact
+strictly I write this here just
+
+ align:start position:0%
+strictly I write this here just
+ 
+
+ align:start position:0%
+strictly I write this here just
+for what holds is that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price at time Little T divided by the
+
+ align:start position:0%
+price at time Little T divided by the
+ 
+
+ align:start position:0%
+price at time Little T divided by the
+zero coupon
+
+ align:start position:0%
+zero coupon
+ 
+
+ align:start position:0%
+zero coupon
+Bond okay is a marting gale for those of
+
+ align:start position:0%
+Bond okay is a marting gale for those of
+ 
+
+ align:start position:0%
+Bond okay is a marting gale for those of
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+into probability
+
+ align:start position:0%
+into probability
+ 
+
+ align:start position:0%
+into probability
+Theory and this gets probabilists very
+
+ align:start position:0%
+Theory and this gets probabilists very
+ 
+
+ align:start position:0%
+Theory and this gets probabilists very
+excited of course because they love
+
+ align:start position:0%
+excited of course because they love
+ 
+
+ align:start position:0%
+excited of course because they love
+martingales everyone in probability
+
+ align:start position:0%
+martingales everyone in probability
+ 
+
+ align:start position:0%
+martingales everyone in probability
+Theory loves martingales a lot of lot of
+
+ align:start position:0%
+Theory loves martingales a lot of lot of
+ 
+
+ align:start position:0%
+Theory loves martingales a lot of lot of
+theorems about martingales and you'll
+
+ align:start position:0%
+theorems about martingales and you'll
+ 
+
+ align:start position:0%
+theorems about martingales and you'll
+see of course that this is actually a
+
+ align:start position:0%
+see of course that this is actually a
+ 
+
+ align:start position:0%
+see of course that this is actually a
+restatement of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this um assertion okay because Zed
+
+ align:start position:0%
+this um assertion okay because Zed
+ 
+
+ align:start position:0%
+this um assertion okay because Zed
+capital D capital t is one right okay so
+
+ align:start position:0%
+capital D capital t is one right okay so
+ 
+
+ align:start position:0%
+capital D capital t is one right okay so
+this statement here is a is simply a
+
+ align:start position:0%
+this statement here is a is simply a
+ 
+
+ align:start position:0%
+this statement here is a is simply a
+reexpression of this Martingale
+
+ align:start position:0%
+reexpression of this Martingale
+ 
+
+ align:start position:0%
+reexpression of this Martingale
+condition okay so I just pause here just
+
+ align:start position:0%
+condition okay so I just pause here just
+ 
+
+ align:start position:0%
+condition okay so I just pause here just
+from a probability point of view when I
+
+ align:start position:0%
+from a probability point of view when I
+ 
+
+ align:start position:0%
+from a probability point of view when I
+Lear probability it was under David
+
+ align:start position:0%
+Lear probability it was under David
+ 
+
+ align:start position:0%
+Lear probability it was under David
+Williams who wrote the book
+
+ align:start position:0%
+Williams who wrote the book
+ 
+
+ align:start position:0%
+Williams who wrote the book
+probabilities in probability with Martin
+
+ align:start position:0%
+probabilities in probability with Martin
+ 
+
+ align:start position:0%
+probabilities in probability with Martin
+GS which is is a wonderful book and I
+
+ align:start position:0%
+GS which is is a wonderful book and I
+ 
+
+ align:start position:0%
+GS which is is a wonderful book and I
+thought Martin gals is a great thing so
+
+ align:start position:0%
+thought Martin gals is a great thing so
+ 
+
+ align:start position:0%
+thought Martin gals is a great thing so
+I sort of happy it took me about seven
+
+ align:start position:0%
+I sort of happy it took me about seven
+ 
+
+ align:start position:0%
+I sort of happy it took me about seven
+or eight years of being in finance to
+
+ align:start position:0%
+or eight years of being in finance to
+ 
+
+ align:start position:0%
+or eight years of being in finance to
+realize there a whole lot of marting
+
+ align:start position:0%
+realize there a whole lot of marting
+ 
+
+ align:start position:0%
+realize there a whole lot of marting
+girls floating around because this
+
+ align:start position:0%
+girls floating around because this
+ 
+
+ align:start position:0%
+girls floating around because this
+actual approach is formalization
+
+ align:start position:0%
+actual approach is formalization
+ 
+
+ align:start position:0%
+actual approach is formalization
+of uh asset pricing really only became
+
+ align:start position:0%
+of uh asset pricing really only became
+ 
+
+ align:start position:0%
+of uh asset pricing really only became
+embraced on the trade floor around the
+
+ align:start position:0%
+embraced on the trade floor around the
+ 
+
+ align:start position:0%
+embraced on the trade floor around the
+early 2000s even though the kind of
+
+ align:start position:0%
+early 2000s even though the kind of
+ 
+
+ align:start position:0%
+early 2000s even though the kind of
+underlying theory was always there this
+
+ align:start position:0%
+underlying theory was always there this
+ 
+
+ align:start position:0%
+underlying theory was always there this
+idea of this marting girls anyway so
+
+ align:start position:0%
+idea of this marting girls anyway so
+ 
+
+ align:start position:0%
+idea of this marting girls anyway so
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+um um and this of course
+
+ align:start position:0%
+um um and this of course
+ 
+
+ align:start position:0%
+um um and this of course
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simply okay the expected value of the
+
+ align:start position:0%
+simply okay the expected value of the
+ 
+
+ align:start position:0%
+simply okay the expected value of the
+indicator function is just the
+
+ align:start position:0%
+indicator function is just the
+ 
+
+ align:start position:0%
+indicator function is just the
+probability of the event okay all right
+
+ align:start position:0%
+probability of the event okay all right
+ 
+
+ align:start position:0%
+probability of the event okay all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+I've one by intuition just here's the
+
+ align:start position:0%
+I've one by intuition just here's the
+ 
+
+ align:start position:0%
+I've one by intuition just here's the
+probability of the payout occurring of
+
+ align:start position:0%
+probability of the payout occurring of
+ 
+
+ align:start position:0%
+probability of the payout occurring of
+price a digital I've Al price of digital
+
+ align:start position:0%
+price a digital I've Al price of digital
+ 
+
+ align:start position:0%
+price a digital I've Al price of digital
+by taking the limit of Co spreads so now
+
+ align:start position:0%
+by taking the limit of Co spreads so now
+ 
+
+ align:start position:0%
+by taking the limit of Co spreads so now
+we just going to equate
+
+ align:start position:0%
+we just going to equate
+ 
+
+ align:start position:0%
+we just going to equate
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay right
+
+ align:start position:0%
+okay right
+ 
+
+ align:start position:0%
+okay right
+so by equating these two prices for the
+
+ align:start position:0%
+so by equating these two prices for the
+ 
+
+ align:start position:0%
+so by equating these two prices for the
+digital I simply get that the second
+
+ align:start position:0%
+digital I simply get that the second
+ 
+
+ align:start position:0%
+digital I simply get that the second
+sorry the derivative of the call Price
+
+ align:start position:0%
+sorry the derivative of the call Price
+ 
+
+ align:start position:0%
+sorry the derivative of the call Price
+with respect to strike equals the
+
+ align:start position:0%
+with respect to strike equals the
+ 
+
+ align:start position:0%
+with respect to strike equals the
+discounted
+
+ align:start position:0%
+discounted
+ 
+
+ align:start position:0%
+discounted
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the stock being above k
+
+ align:start position:0%
+the stock being above k
+ 
+
+ align:start position:0%
+the stock being above k
+okay I'll just reorganize a little bit
+
+ align:start position:0%
+okay I'll just reorganize a little bit
+ 
+
+ align:start position:0%
+okay I'll just reorganize a little bit
+take one minus and so I've get the
+
+ align:start position:0%
+take one minus and so I've get the
+ 
+
+ align:start position:0%
+take one minus and so I've get the
+probability that
+
+ align:start position:0%
+probability that
+ 
+
+ align:start position:0%
+probability that
+uh well I can clearly reorganize I'm
+
+ align:start position:0%
+uh well I can clearly reorganize I'm
+ 
+
+ align:start position:0%
+uh well I can clearly reorganize I'm
+going to get um all right so if I want
+
+ align:start position:0%
+going to get um all right so if I want
+ 
+
+ align:start position:0%
+going to get um all right so if I want
+to Simply get the cumulative
+
+ align:start position:0%
+to Simply get the cumulative
+ 
+
+ align:start position:0%
+to Simply get the cumulative
+distribution function it's just one
+
+ align:start position:0%
+distribution function it's just one
+ 
+
+ align:start position:0%
+distribution function it's just one
+minus this so divide here take one minus
+
+ align:start position:0%
+minus this so divide here take one minus
+ 
+
+ align:start position:0%
+minus this so divide here take one minus
+okay so I get the the cumulative
+
+ align:start position:0%
+okay so I get the the cumulative
+ 
+
+ align:start position:0%
+okay so I get the the cumulative
+distribution function for the stock
+
+ align:start position:0%
+distribution function for the stock
+ 
+
+ align:start position:0%
+distribution function for the stock
+price at T is equal to 1 plus the d c by
+
+ align:start position:0%
+price at T is equal to 1 plus the d c by
+ 
+
+ align:start position:0%
+price at T is equal to 1 plus the d c by
+DK * 1 /
+
+ align:start position:0%
+DK * 1 /
+ 
+
+ align:start position:0%
+DK * 1 /
+Z right just rearranging so here now is
+
+ align:start position:0%
+Z right just rearranging so here now is
+ 
+
+ align:start position:0%
+Z right just rearranging so here now is
+the cumulative distribution function
+
+ align:start position:0%
+the cumulative distribution function
+ 
+
+ align:start position:0%
+the cumulative distribution function
+clearly I just need to differentiate
+
+ align:start position:0%
+clearly I just need to differentiate
+ 
+
+ align:start position:0%
+clearly I just need to differentiate
+again to get the probability density
+
+ align:start position:0%
+again to get the probability density
+ 
+
+ align:start position:0%
+again to get the probability density
+function right
+
+ align:start position:0%
+function right
+ 
+
+ align:start position:0%
+function right
+so um now here's where the little
+
+ align:start position:0%
+so um now here's where the little
+ 
+
+ align:start position:0%
+so um now here's where the little
+notation gets gets kind of messy but
+
+ align:start position:0%
+notation gets gets kind of messy but
+ 
+
+ align:start position:0%
+notation gets gets kind of messy but
+clearly the probability density function
+
+ align:start position:0%
+clearly the probability density function
+ 
+
+ align:start position:0%
+clearly the probability density function
+of so
+
+ align:start position:0%
+of so
+ 
+
+ align:start position:0%
+of so
+F okay for
+
+ align:start position:0%
+F okay for
+ 
+
+ align:start position:0%
+F okay for
+my um random variable f subt right the
+
+ align:start position:0%
+my um random variable f subt right the
+ 
+
+ align:start position:0%
+my um random variable f subt right the
+density of Express that is I always
+
+ align:start position:0%
+density of Express that is I always
+ 
+
+ align:start position:0%
+density of Express that is I always
+funny problem when you talk about
+
+ align:start position:0%
+funny problem when you talk about
+ 
+
+ align:start position:0%
+funny problem when you talk about
+densities they always got want to say f
+
+ align:start position:0%
+densities they always got want to say f
+ 
+
+ align:start position:0%
+densities they always got want to say f
+ofx and it's the same with me as f of x
+
+ align:start position:0%
+ofx and it's the same with me as f of x
+ 
+
+ align:start position:0%
+ofx and it's the same with me as f of x
+is the density is simply just the next
+
+ align:start position:0%
+is the density is simply just the next
+ 
+
+ align:start position:0%
+is the density is simply just the next
+the second derivative we take the
+
+ align:start position:0%
+the second derivative we take the
+ 
+
+ align:start position:0%
+the second derivative we take the
+derivative of this is the second
+
+ align:start position:0%
+derivative of this is the second
+ 
+
+ align:start position:0%
+derivative of this is the second
+derivative of the core price with
+
+ align:start position:0%
+derivative of the core price with
+ 
+
+ align:start position:0%
+derivative of the core price with
+respect to strike evaluated at Little X
+
+ align:start position:0%
+respect to strike evaluated at Little X
+ 
+
+ align:start position:0%
+respect to strike evaluated at Little X
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so all right so what we've done here is
+
+ align:start position:0%
+so all right so what we've done here is
+ 
+
+ align:start position:0%
+so all right so what we've done here is
+start off with simple definition of
+
+ align:start position:0%
+start off with simple definition of
+ 
+
+ align:start position:0%
+start off with simple definition of
+three assets priced the digital in two
+
+ align:start position:0%
+three assets priced the digital in two
+ 
+
+ align:start position:0%
+three assets priced the digital in two
+different ways and now we have a rather
+
+ align:start position:0%
+different ways and now we have a rather
+ 
+
+ align:start position:0%
+different ways and now we have a rather
+elegant linkage between call
+
+ align:start position:0%
+elegant linkage between call
+ 
+
+ align:start position:0%
+elegant linkage between call
+prices Okay C and the
+
+ align:start position:0%
+prices Okay C and the
+ 
+
+ align:start position:0%
+prices Okay C and the
+density uh of the random variable that
+
+ align:start position:0%
+density uh of the random variable that
+ 
+
+ align:start position:0%
+density uh of the random variable that
+is the underlying stock price at capital
+
+ align:start position:0%
+is the underlying stock price at capital
+ 
+
+ align:start position:0%
+is the underlying stock price at capital
+t Okay so we've established one side of
+
+ align:start position:0%
+t Okay so we've established one side of
+ 
+
+ align:start position:0%
+t Okay so we've established one side of
+The Duality which is given the set set
+
+ align:start position:0%
+The Duality which is given the set set
+ 
+
+ align:start position:0%
+The Duality which is given the set set
+of call
+
+ align:start position:0%
+of call
+ 
+
+ align:start position:0%
+of call
+prices for all
+
+ align:start position:0%
+prices for all
+ 
+
+ align:start position:0%
+prices for all
+K okay I can then uniquely determine the
+
+ align:start position:0%
+K okay I can then uniquely determine the
+ 
+
+ align:start position:0%
+K okay I can then uniquely determine the
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+of of the underlying asset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so that might think okay this
+
+ align:start position:0%
+okay okay so that might think okay this
+ 
+
+ align:start position:0%
+okay okay so that might think okay this
+is um this kind of nice how does this
+
+ align:start position:0%
+is um this kind of nice how does this
+ 
+
+ align:start position:0%
+is um this kind of nice how does this
+actually work in practice
+
+ align:start position:0%
+actually work in practice
+ 
+
+ align:start position:0%
+actually work in practice
+um do we actually think in terms of
+
+ align:start position:0%
+um do we actually think in terms of
+ 
+
+ align:start position:0%
+um do we actually think in terms of
+probability trading right we just said
+
+ align:start position:0%
+probability trading right we just said
+ 
+
+ align:start position:0%
+probability trading right we just said
+that call options are equivalent to
+
+ align:start position:0%
+that call options are equivalent to
+ 
+
+ align:start position:0%
+that call options are equivalent to
+probability density functions well
+
+ align:start position:0%
+probability density functions well
+ 
+
+ align:start position:0%
+probability density functions well
+actually there's a very neat way of
+
+ align:start position:0%
+actually there's a very neat way of
+ 
+
+ align:start position:0%
+actually there's a very neat way of
+accessing this density function through
+
+ align:start position:0%
+accessing this density function through
+ 
+
+ align:start position:0%
+accessing this density function through
+another portfolio of options okay so
+
+ align:start position:0%
+another portfolio of options okay so
+ 
+
+ align:start position:0%
+another portfolio of options okay so
+this is actually where we get to me sort
+
+ align:start position:0%
+this is actually where we get to me sort
+ 
+
+ align:start position:0%
+this is actually where we get to me sort
+of practical relevance of some of this
+
+ align:start position:0%
+of practical relevance of some of this
+ 
+
+ align:start position:0%
+of practical relevance of some of this
+Theory so let me just um show you that
+
+ align:start position:0%
+Theory so let me just um show you that
+ 
+
+ align:start position:0%
+Theory so let me just um show you that
+okay so we're going to consider another
+
+ align:start position:0%
+okay so we're going to consider another
+ 
+
+ align:start position:0%
+okay so we're going to consider another
+portfol
+
+ align:start position:0%
+portfol
+ 
+
+ align:start position:0%
+portfol
+okay so here we
+
+ align:start position:0%
+okay so here we
+ 
+
+ align:start position:0%
+okay so here we
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+portfolio as
+
+ align:start position:0%
+portfolio as
+ 
+
+ align:start position:0%
+portfolio as
+follows okay it's actually going to be
+
+ align:start position:0%
+follows okay it's actually going to be
+ 
+
+ align:start position:0%
+follows okay it's actually going to be
+the difference between two call spreads
+
+ align:start position:0%
+the difference between two call spreads
+ 
+
+ align:start position:0%
+the difference between two call spreads
+so Lambda
+
+ align:start position:0%
+so Lambda
+ 
+
+ align:start position:0%
+so Lambda
+calls with
+
+ align:start position:0%
+calls with
+ 
+
+ align:start position:0%
+calls with
+strike K minus 1/
+
+ align:start position:0%
+strike K minus 1/
+ 
+
+ align:start position:0%
+strike K minus 1/
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+okay uh minus two Lambda
+
+ align:start position:0%
+okay uh minus two Lambda
+ 
+
+ align:start position:0%
+okay uh minus two Lambda
+calls with strike
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K and Lambda
+
+ align:start position:0%
+K and Lambda
+ 
+
+ align:start position:0%
+K and Lambda
+calls with strike K plus one over Lambda
+
+ align:start position:0%
+calls with strike K plus one over Lambda
+ 
+
+ align:start position:0%
+calls with strike K plus one over Lambda
+again Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive okay all right why are we doing
+
+ align:start position:0%
+positive okay all right why are we doing
+ 
+
+ align:start position:0%
+positive okay all right why are we doing
+this let's just stop for a bit of
+
+ align:start position:0%
+this let's just stop for a bit of
+ 
+
+ align:start position:0%
+this let's just stop for a bit of
+intuition here we've seen that the cor
+
+ align:start position:0%
+intuition here we've seen that the cor
+ 
+
+ align:start position:0%
+intuition here we've seen that the cor
+spread so obviously the discrete
+
+ align:start position:0%
+spread so obviously the discrete
+ 
+
+ align:start position:0%
+spread so obviously the discrete
+approximation to the first
+
+ align:start position:0%
+approximation to the first
+ 
+
+ align:start position:0%
+approximation to the first
+derivative of cor price with respect to
+
+ align:start position:0%
+derivative of cor price with respect to
+ 
+
+ align:start position:0%
+derivative of cor price with respect to
+strike so clearly if I want to
+
+ align:start position:0%
+strike so clearly if I want to
+ 
+
+ align:start position:0%
+strike so clearly if I want to
+approximate the second derivative I'm
+
+ align:start position:0%
+approximate the second derivative I'm
+ 
+
+ align:start position:0%
+approximate the second derivative I'm
+going to take the difference between two
+
+ align:start position:0%
+going to take the difference between two
+ 
+
+ align:start position:0%
+going to take the difference between two
+Co spreads appropriately scaled okay you
+
+ align:start position:0%
+Co spreads appropriately scaled okay you
+ 
+
+ align:start position:0%
+Co spreads appropriately scaled okay you
+know I'm going to have to have a do
+
+ align:start position:0%
+know I'm going to have to have a do
+ 
+
+ align:start position:0%
+know I'm going to have to have a do
+there's going to have to be another
+
+ align:start position:0%
+there's going to have to be another
+ 
+
+ align:start position:0%
+there's going to have to be another
+Lambda coming in here at some point this
+
+ align:start position:0%
+Lambda coming in here at some point this
+ 
+
+ align:start position:0%
+Lambda coming in here at some point this
+is just a difference between two Co
+
+ align:start position:0%
+is just a difference between two Co
+ 
+
+ align:start position:0%
+is just a difference between two Co
+spreads so that's the difference between
+
+ align:start position:0%
+spreads so that's the difference between
+ 
+
+ align:start position:0%
+spreads so that's the difference between
+two approximations of the first
+
+ align:start position:0%
+two approximations of the first
+ 
+
+ align:start position:0%
+two approximations of the first
+derivative so I'm going to have to scale
+
+ align:start position:0%
+derivative so I'm going to have to scale
+ 
+
+ align:start position:0%
+derivative so I'm going to have to scale
+by Lambda in order to approximate the
+
+ align:start position:0%
+by Lambda in order to approximate the
+ 
+
+ align:start position:0%
+by Lambda in order to approximate the
+second derivative okay so this is
+
+ align:start position:0%
+second derivative okay so this is
+ 
+
+ align:start position:0%
+second derivative okay so this is
+actually called a CO butterfly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a beautiful thing for two
+
+ align:start position:0%
+and this is a beautiful thing for two
+ 
+
+ align:start position:0%
+and this is a beautiful thing for two
+reasons one is they actually trade a lot
+
+ align:start position:0%
+reasons one is they actually trade a lot
+ 
+
+ align:start position:0%
+reasons one is they actually trade a lot
+surprisingly this is not a contrived
+
+ align:start position:0%
+surprisingly this is not a contrived
+ 
+
+ align:start position:0%
+surprisingly this is not a contrived
+thing that I just made up a it trades a
+
+ align:start position:0%
+thing that I just made up a it trades a
+ 
+
+ align:start position:0%
+thing that I just made up a it trades a
+lot so you can actually trade this thing
+
+ align:start position:0%
+lot so you can actually trade this thing
+ 
+
+ align:start position:0%
+lot so you can actually trade this thing
+and the second is as you can kind of
+
+ align:start position:0%
+and the second is as you can kind of
+ 
+
+ align:start position:0%
+and the second is as you can kind of
+imagine the right scaling of this core
+
+ align:start position:0%
+imagine the right scaling of this core
+ 
+
+ align:start position:0%
+imagine the right scaling of this core
+butterfly is going to approximate this
+
+ align:start position:0%
+butterfly is going to approximate this
+ 
+
+ align:start position:0%
+butterfly is going to approximate this
+second derivative and that's
+
+ align:start position:0%
+second derivative and that's
+ 
+
+ align:start position:0%
+second derivative and that's
+approximating the density function so
+
+ align:start position:0%
+approximating the density function so
+ 
+
+ align:start position:0%
+approximating the density function so
+this is a traded
+
+ align:start position:0%
+this is a traded
+ 
+
+ align:start position:0%
+this is a traded
+object kind of approximate the the
+
+ align:start position:0%
+object kind of approximate the the
+ 
+
+ align:start position:0%
+object kind of approximate the the
+density function
+
+ align:start position:0%
+density function
+ 
+
+ align:start position:0%
+density function
+yeah but in real world you can
+
+ align:start position:0%
+yeah but in real world you can
+ 
+
+ align:start position:0%
+yeah but in real world you can
+distance like small so they have some
+
+ align:start position:0%
+distance like small so they have some
+ 
+
+ align:start position:0%
+distance like small so they have some
+way how can approximate that yeah so
+
+ align:start position:0%
+way how can approximate that yeah so
+ 
+
+ align:start position:0%
+way how can approximate that yeah so
+it's a good point we're not going to be
+
+ align:start position:0%
+it's a good point we're not going to be
+ 
+
+ align:start position:0%
+it's a good point we're not going to be
+yeah so the question is how in practice
+
+ align:start position:0%
+yeah so the question is how in practice
+ 
+
+ align:start position:0%
+yeah so the question is how in practice
+we can't go infinitely small which is
+
+ align:start position:0%
+we can't go infinitely small which is
+ 
+
+ align:start position:0%
+we can't go infinitely small which is
+true but in we can go pretty small so in
+
+ align:start position:0%
+true but in we can go pretty small so in
+ 
+
+ align:start position:0%
+true but in we can go pretty small so in
+interest rates we might be able to trade
+
+ align:start position:0%
+interest rates we might be able to trade
+ 
+
+ align:start position:0%
+interest rates we might be able to trade
+a you know one 50 160
+
+ align:start position:0%
+a you know one 50 160
+ 
+
+ align:start position:0%
+a you know one 50 160
+170 call butterfly or equivalent 10
+
+ align:start position:0%
+170 call butterfly or equivalent 10
+ 
+
+ align:start position:0%
+170 call butterfly or equivalent 10
+basis points wide that's a re I mean
+
+ align:start position:0%
+basis points wide that's a re I mean
+ 
+
+ align:start position:0%
+basis points wide that's a re I mean
+it's a reasonable approximation to the
+
+ align:start position:0%
+it's a reasonable approximation to the
+ 
+
+ align:start position:0%
+it's a reasonable approximation to the
+probability of being in that interval
+
+ align:start position:0%
+probability of being in that interval
+ 
+
+ align:start position:0%
+probability of being in that interval
+okay so so these are all I mean you make
+
+ align:start position:0%
+okay so so these are all I mean you make
+ 
+
+ align:start position:0%
+okay so so these are all I mean you make
+a good point that I mean in fact all of
+
+ align:start position:0%
+a good point that I mean in fact all of
+ 
+
+ align:start position:0%
+a good point that I mean in fact all of
+Finance is discreet in my view so
+
+ align:start position:0%
+Finance is discreet in my view so
+ 
+
+ align:start position:0%
+Finance is discreet in my view so
+continuous Time Finance is done in
+
+ align:start position:0%
+continuous Time Finance is done in
+ 
+
+ align:start position:0%
+continuous Time Finance is done in
+continuous time because the theory is
+
+ align:start position:0%
+continuous time because the theory is
+ 
+
+ align:start position:0%
+continuous time because the theory is
+much more
+
+ align:start position:0%
+much more
+ 
+
+ align:start position:0%
+much more
+elegant but in practice it's all
+
+ align:start position:0%
+elegant but in practice it's all
+ 
+
+ align:start position:0%
+elegant but in practice it's all
+discreete in time and space okay right
+
+ align:start position:0%
+discreete in time and space okay right
+ 
+
+ align:start position:0%
+discreete in time and space okay right
+you can only trade finally off in a day
+
+ align:start position:0%
+you can only trade finally off in a day
+ 
+
+ align:start position:0%
+you can only trade finally off in a day
+and so on okay um I'm going go into the
+
+ align:start position:0%
+and so on okay um I'm going go into the
+ 
+
+ align:start position:0%
+and so on okay um I'm going go into the
+the detail but you can see the price let
+
+ align:start position:0%
+the detail but you can see the price let
+ 
+
+ align:start position:0%
+the detail but you can see the price let
+me just write down the first the price
+
+ align:start position:0%
+me just write down the first the price
+ 
+
+ align:start position:0%
+me just write down the first the price
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this right I just Express as the
+
+ align:start position:0%
+this right I just Express as the
+ 
+
+ align:start position:0%
+this right I just Express as the
+difference between two cor
+
+ align:start position:0%
+difference between two cor
+ 
+
+ align:start position:0%
+difference between two cor
+spreads so it's Lambda
+
+ align:start position:0%
+spreads so it's Lambda
+ 
+
+ align:start position:0%
+spreads so it's Lambda
+times the co spread from 1us Lambda to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um to K so K1 minus Lambda to to K minus
+
+ align:start position:0%
+um to K so K1 minus Lambda to to K minus
+ 
+
+ align:start position:0%
+um to K so K1 minus Lambda to to K minus
+the call spread
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from K to k+ 1/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda okay so difference between two
+
+ align:start position:0%
+Lambda okay so difference between two
+ 
+
+ align:start position:0%
+Lambda okay so difference between two
+cor spreads
+
+ align:start position:0%
+cor spreads
+ 
+
+ align:start position:0%
+cor spreads
+um we'll call this this is the butterfly
+
+ align:start position:0%
+um we'll call this this is the butterfly
+ 
+
+ align:start position:0%
+um we'll call this this is the butterfly
+we're just going to use temporary
+
+ align:start position:0%
+we're just going to use temporary
+ 
+
+ align:start position:0%
+we're just going to use temporary
+notation call that b b for butterfly um
+
+ align:start position:0%
+notation call that b b for butterfly um
+ 
+
+ align:start position:0%
+notation call that b b for butterfly um
+so the price B and then you get confused
+
+ align:start position:0%
+so the price B and then you get confused
+ 
+
+ align:start position:0%
+so the price B and then you get confused
+it's B centered at K with width Lambda
+
+ align:start position:0%
+it's B centered at K with width Lambda
+ 
+
+ align:start position:0%
+it's B centered at K with width Lambda
+no one ever uses notation outside this
+
+ align:start position:0%
+no one ever uses notation outside this
+ 
+
+ align:start position:0%
+no one ever uses notation outside this
+one section of my class so that's a
+
+ align:start position:0%
+one section of my class so that's a
+ 
+
+ align:start position:0%
+one section of my class so that's a
+that's why but it's just handy for this
+
+ align:start position:0%
+that's why but it's just handy for this
+ 
+
+ align:start position:0%
+that's why but it's just handy for this
+so that is the butterfly price is equal
+
+ align:start position:0%
+so that is the butterfly price is equal
+ 
+
+ align:start position:0%
+so that is the butterfly price is equal
+to the difference between these two call
+
+ align:start position:0%
+to the difference between these two call
+ 
+
+ align:start position:0%
+to the difference between these two call
+spreads what I want to do is I want to
+
+ align:start position:0%
+spreads what I want to do is I want to
+ 
+
+ align:start position:0%
+spreads what I want to do is I want to
+take limits of this suitably scal to get
+
+ align:start position:0%
+take limits of this suitably scal to get
+ 
+
+ align:start position:0%
+take limits of this suitably scal to get
+the second derivative and the if you
+
+ align:start position:0%
+the second derivative and the if you
+ 
+
+ align:start position:0%
+the second derivative and the if you
+uh do you just need to take Lambda time
+
+ align:start position:0%
+uh do you just need to take Lambda time
+ 
+
+ align:start position:0%
+uh do you just need to take Lambda time
+BK of
+
+ align:start position:0%
+BK of
+ 
+
+ align:start position:0%
+BK of
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+TT is indeed approximately if I take
+
+ align:start position:0%
+TT is indeed approximately if I take
+ 
+
+ align:start position:0%
+TT is indeed approximately if I take
+limits is is exactly the second
+
+ align:start position:0%
+limits is is exactly the second
+ 
+
+ align:start position:0%
+limits is is exactly the second
+derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the core
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price okay so right here's here here's
+
+ align:start position:0%
+price okay so right here's here here's
+ 
+
+ align:start position:0%
+price okay so right here's here here's
+how I'm accessing the second derivative
+
+ align:start position:0%
+how I'm accessing the second derivative
+ 
+
+ align:start position:0%
+how I'm accessing the second derivative
+through a portfolio of traded options
+
+ align:start position:0%
+through a portfolio of traded options
+ 
+
+ align:start position:0%
+through a portfolio of traded options
+all right and
+
+ align:start position:0%
+all right and
+ 
+
+ align:start position:0%
+all right and
+so the price of this butterfly B if I
+
+ align:start position:0%
+so the price of this butterfly B if I
+ 
+
+ align:start position:0%
+so the price of this butterfly B if I
+just reorganize and
+
+ align:start position:0%
+just reorganize and
+ 
+
+ align:start position:0%
+just reorganize and
+substitute okay so um I get
+
+ align:start position:0%
+substitute okay so um I get
+ 
+
+ align:start position:0%
+substitute okay so um I get
+BK for small lamb sorry for large Lambda
+
+ align:start position:0%
+BK for small lamb sorry for large Lambda
+ 
+
+ align:start position:0%
+BK for small lamb sorry for large Lambda
+I a small
+
+ align:start position:0%
+I a small
+ 
+
+ align:start position:0%
+I a small
+interval okay is approximately 1/ Lambda
+
+ align:start position:0%
+interval okay is approximately 1/ Lambda
+ 
+
+ align:start position:0%
+interval okay is approximately 1/ Lambda
+times the density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function okay actually evaluated at
+
+ align:start position:0%
+function okay actually evaluated at
+ 
+
+ align:start position:0%
+function okay actually evaluated at
+K right so I
+
+ align:start position:0%
+K right so I
+ 
+
+ align:start position:0%
+K right so I
+have obtained this density
+
+ align:start position:0%
+have obtained this density
+ 
+
+ align:start position:0%
+have obtained this density
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+um by this traded portfolio and to your
+
+ align:start position:0%
+um by this traded portfolio and to your
+ 
+
+ align:start position:0%
+um by this traded portfolio and to your
+to your point about we haven't we're not
+
+ align:start position:0%
+to your point about we haven't we're not
+ 
+
+ align:start position:0%
+to your point about we haven't we're not
+we're not getting infinitely small
+
+ align:start position:0%
+we're not getting infinitely small
+ 
+
+ align:start position:0%
+we're not getting infinitely small
+that's absolutely right but if if you
+
+ align:start position:0%
+that's absolutely right but if if you
+ 
+
+ align:start position:0%
+that's absolutely right but if if you
+think about what the density you know
+
+ align:start position:0%
+think about what the density you know
+ 
+
+ align:start position:0%
+think about what the density you know
+when you learn about density functions
+
+ align:start position:0%
+when you learn about density functions
+ 
+
+ align:start position:0%
+when you learn about density functions
+for the for the first time you say the
+
+ align:start position:0%
+for the for the first time you say the
+ 
+
+ align:start position:0%
+for the for the first time you say the
+density function at x times a small
+
+ align:start position:0%
+density function at x times a small
+ 
+
+ align:start position:0%
+density function at x times a small
+interval is the probability of being in
+
+ align:start position:0%
+interval is the probability of being in
+ 
+
+ align:start position:0%
+interval is the probability of being in
+that small interval right so you know
+
+ align:start position:0%
+that small interval right so you know
+ 
+
+ align:start position:0%
+that small interval right so you know
+when we think about the density
+
+ align:start position:0%
+when we think about the density
+ 
+
+ align:start position:0%
+when we think about the density
+function f ofx if we have a small
+
+ align:start position:0%
+function f ofx if we have a small
+ 
+
+ align:start position:0%
+function f ofx if we have a small
+interval of width Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X okay then clearly the probability of
+
+ align:start position:0%
+X okay then clearly the probability of
+ 
+
+ align:start position:0%
+X okay then clearly the probability of
+being in this interval is approximately
+
+ align:start position:0%
+being in this interval is approximately
+ 
+
+ align:start position:0%
+being in this interval is approximately
+F ofx Delta X
+
+ align:start position:0%
+F ofx Delta X
+ 
+
+ align:start position:0%
+F ofx Delta X
+right okay liit that is true so what
+
+ align:start position:0%
+right okay liit that is true so what
+ 
+
+ align:start position:0%
+right okay liit that is true so what
+we're showing here if you actually think
+
+ align:start position:0%
+we're showing here if you actually think
+ 
+
+ align:start position:0%
+we're showing here if you actually think
+about what interval we're looking at
+
+ align:start position:0%
+about what interval we're looking at
+ 
+
+ align:start position:0%
+about what interval we're looking at
+we're actually looking at in this cor
+
+ align:start position:0%
+we're actually looking at in this cor
+ 
+
+ align:start position:0%
+we're actually looking at in this cor
+butterfly if you actually to draw it out
+
+ align:start position:0%
+butterfly if you actually to draw it out
+ 
+
+ align:start position:0%
+butterfly if you actually to draw it out
+this cor
+
+ align:start position:0%
+this cor
+ 
+
+ align:start position:0%
+this cor
+butterfly this is looks like
+
+ align:start position:0%
+butterfly this is looks like
+ 
+
+ align:start position:0%
+butterfly this is looks like
+that around
+
+ align:start position:0%
+that around
+ 
+
+ align:start position:0%
+that around
+K it actually so it's a little triangle
+
+ align:start position:0%
+K it actually so it's a little triangle
+ 
+
+ align:start position:0%
+K it actually so it's a little triangle
+it's not actually a rectangle but it's a
+
+ align:start position:0%
+it's not actually a rectangle but it's a
+ 
+
+ align:start position:0%
+it's not actually a rectangle but it's a
+little triangle of width 2 over Lambda
+
+ align:start position:0%
+little triangle of width 2 over Lambda
+ 
+
+ align:start position:0%
+little triangle of width 2 over Lambda
+okay so it is actually this is the
+
+ align:start position:0%
+okay so it is actually this is the
+ 
+
+ align:start position:0%
+okay so it is actually this is the
+area right of the of this triangle right
+
+ align:start position:0%
+area right of the of this triangle right
+ 
+
+ align:start position:0%
+area right of the of this triangle right
+it's 2 Lambda time half time f x and
+
+ align:start position:0%
+it's 2 Lambda time half time f x and
+ 
+
+ align:start position:0%
+it's 2 Lambda time half time f x and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+actually this right so this is this is
+
+ align:start position:0%
+actually this right so this is this is
+ 
+
+ align:start position:0%
+actually this right so this is this is
+this has width two over
+
+ align:start position:0%
+this has width two over
+ 
+
+ align:start position:0%
+this has width two over
+Lambda okay so in fact we've got here
+
+ align:start position:0%
+Lambda okay so in fact we've got here
+ 
+
+ align:start position:0%
+Lambda okay so in fact we've got here
+exactly an approxim exactly exactly
+
+ align:start position:0%
+exactly an approxim exactly exactly
+ 
+
+ align:start position:0%
+exactly an approxim exactly exactly
+approximation that doesn't sound right
+
+ align:start position:0%
+approximation that doesn't sound right
+ 
+
+ align:start position:0%
+approximation that doesn't sound right
+but is entirely analogous to the
+
+ align:start position:0%
+but is entirely analogous to the
+ 
+
+ align:start position:0%
+but is entirely analogous to the
+approximation of the probability of
+
+ align:start position:0%
+approximation of the probability of
+ 
+
+ align:start position:0%
+approximation of the probability of
+being in a small interval here is the
+
+ align:start position:0%
+being in a small interval here is the
+ 
+
+ align:start position:0%
+being in a small interval here is the
+the probability of being in this this
+
+ align:start position:0%
+the probability of being in this this
+ 
+
+ align:start position:0%
+the probability of being in this this
+inter
+
+ align:start position:0%
+inter
+ 
+
+ align:start position:0%
+inter
+here okay just the area under that is
+
+ align:start position:0%
+here okay just the area under that is
+ 
+
+ align:start position:0%
+here okay just the area under that is
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+um one over lamb F ofx okay so here is
+
+ align:start position:0%
+um one over lamb F ofx okay so here is
+ 
+
+ align:start position:0%
+um one over lamb F ofx okay so here is
+actually something that people do do is
+
+ align:start position:0%
+actually something that people do do is
+ 
+
+ align:start position:0%
+actually something that people do do is
+they say okay I will look
+
+ align:start position:0%
+they say okay I will look
+ 
+
+ align:start position:0%
+they say okay I will look
+at the price of this
+
+ align:start position:0%
+at the price of this
+ 
+
+ align:start position:0%
+at the price of this
+butterfly okay which gives me the
+
+ align:start position:0%
+butterfly okay which gives me the
+ 
+
+ align:start position:0%
+butterfly okay which gives me the
+probability of this underlying random
+
+ align:start position:0%
+probability of this underlying random
+ 
+
+ align:start position:0%
+probability of this underlying random
+variable ending up around
+
+ align:start position:0%
+variable ending up around
+ 
+
+ align:start position:0%
+variable ending up around
+K and I'll make a judgment whether I
+
+ align:start position:0%
+K and I'll make a judgment whether I
+ 
+
+ align:start position:0%
+K and I'll make a judgment whether I
+agree with that probability or not
+
+ align:start position:0%
+agree with that probability or not
+ 
+
+ align:start position:0%
+agree with that probability or not
+and if I think that
+
+ align:start position:0%
+and if I think that
+ 
+
+ align:start position:0%
+and if I think that
+probability is higher
+
+ align:start position:0%
+probability is higher
+ 
+
+ align:start position:0%
+probability is higher
+than this price
+
+ align:start position:0%
+than this price
+ 
+
+ align:start position:0%
+than this price
+implies then I'll do a trade I'll buy it
+
+ align:start position:0%
+implies then I'll do a trade I'll buy it
+ 
+
+ align:start position:0%
+implies then I'll do a trade I'll buy it
+I'll buy that
+
+ align:start position:0%
+I'll buy that
+ 
+
+ align:start position:0%
+I'll buy that
+butterfly so there is actually a an
+
+ align:start position:0%
+butterfly so there is actually a an
+ 
+
+ align:start position:0%
+butterfly so there is actually a an
+active Market in butterflies and so I
+
+ align:start position:0%
+active Market in butterflies and so I
+ 
+
+ align:start position:0%
+active Market in butterflies and so I
+like to think an active trading in
+
+ align:start position:0%
+like to think an active trading in
+ 
+
+ align:start position:0%
+like to think an active trading in
+probabilities right probabilities of the
+
+ align:start position:0%
+probabilities right probabilities of the
+ 
+
+ align:start position:0%
+probabilities right probabilities of the
+underlying variable being um at K at
+
+ align:start position:0%
+underlying variable being um at K at
+ 
+
+ align:start position:0%
+underlying variable being um at K at
+maturity
+
+ align:start position:0%
+maturity
+ 
+
+ align:start position:0%
+maturity
+okay right so um okay so that's the
+
+ align:start position:0%
+okay right so um okay so that's the
+ 
+
+ align:start position:0%
+okay right so um okay so that's the
+first the first linkage here both the
+
+ align:start position:0%
+first the first linkage here both the
+ 
+
+ align:start position:0%
+first the first linkage here both the
+density is the second derivative and the
+
+ align:start position:0%
+density is the second derivative and the
+ 
+
+ align:start position:0%
+density is the second derivative and the
+second derivative is essentially a
+
+ align:start position:0%
+second derivative is essentially a
+ 
+
+ align:start position:0%
+second derivative is essentially a
+portfolio of traded options and none of
+
+ align:start position:0%
+portfolio of traded options and none of
+ 
+
+ align:start position:0%
+portfolio of traded options and none of
+this is dependent on the actual price of
+
+ align:start position:0%
+this is dependent on the actual price of
+ 
+
+ align:start position:0%
+this is dependent on the actual price of
+the call option in the sense that this
+
+ align:start position:0%
+the call option in the sense that this
+ 
+
+ align:start position:0%
+the call option in the sense that this
+holds regardless clearly this is a
+
+ align:start position:0%
+holds regardless clearly this is a
+ 
+
+ align:start position:0%
+holds regardless clearly this is a
+function of the price of the call option
+
+ align:start position:0%
+function of the price of the call option
+ 
+
+ align:start position:0%
+function of the price of the call option
+but I don't need any model for the
+
+ align:start position:0%
+but I don't need any model for the
+ 
+
+ align:start position:0%
+but I don't need any model for the
+option price to hold in order for the
+
+ align:start position:0%
+option price to hold in order for the
+ 
+
+ align:start position:0%
+option price to hold in order for the
+these relationships to hold right so
+
+ align:start position:0%
+these relationships to hold right so
+ 
+
+ align:start position:0%
+these relationships to hold right so
+this is model independent relationships
+
+ align:start position:0%
+this is model independent relationships
+ 
+
+ align:start position:0%
+this is model independent relationships
+clearly if you were
+
+ align:start position:0%
+clearly if you were
+ 
+
+ align:start position:0%
+clearly if you were
+to put the black shs formula into
+
+ align:start position:0%
+to put the black shs formula into
+ 
+
+ align:start position:0%
+to put the black shs formula into
+C okay black sh formula of the call
+
+ align:start position:0%
+C okay black sh formula of the call
+ 
+
+ align:start position:0%
+C okay black sh formula of the call
+Price and take the second derivative
+
+ align:start position:0%
+Price and take the second derivative
+ 
+
+ align:start position:0%
+Price and take the second derivative
+with respect to K which would be a mess
+
+ align:start position:0%
+with respect to K which would be a mess
+ 
+
+ align:start position:0%
+with respect to K which would be a mess
+you'll end up with a log normal
+
+ align:start position:0%
+you'll end up with a log normal
+ 
+
+ align:start position:0%
+you'll end up with a log normal
+distribution right because that's what
+
+ align:start position:0%
+distribution right because that's what
+ 
+
+ align:start position:0%
+distribution right because that's what
+actually the black shs formula is is
+
+ align:start position:0%
+actually the black shs formula is is
+ 
+
+ align:start position:0%
+actually the black shs formula is is
+expected value of the payout under a log
+
+ align:start position:0%
+expected value of the payout under a log
+ 
+
+ align:start position:0%
+expected value of the payout under a log
+normal distribution and that will hold
+
+ align:start position:0%
+normal distribution and that will hold
+ 
+
+ align:start position:0%
+normal distribution and that will hold
+okay so this will hold for
+
+ align:start position:0%
+okay so this will hold for
+ 
+
+ align:start position:0%
+okay so this will hold for
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deps yes it does but right does not
+
+ align:start position:0%
+deps yes it does but right does not
+ 
+
+ align:start position:0%
+deps yes it does but right does not
+what's what's the role of that yeah so
+
+ align:start position:0%
+what's what's the role of that yeah so
+ 
+
+ align:start position:0%
+what's what's the role of that yeah so
+it's a really good point and I've been
+
+ align:start position:0%
+it's a really good point and I've been
+ 
+
+ align:start position:0%
+it's a really good point and I've been
+loose in my notation so here what is it
+
+ align:start position:0%
+loose in my notation so here what is it
+ 
+
+ align:start position:0%
+loose in my notation so here what is it
+it's actually the conditional
+
+ align:start position:0%
+it's actually the conditional
+ 
+
+ align:start position:0%
+it's actually the conditional
+distribution of S capital T given s
+
+ align:start position:0%
+distribution of S capital T given s
+ 
+
+ align:start position:0%
+distribution of S capital T given s
+Little T so this is the conditional
+
+ align:start position:0%
+Little T so this is the conditional
+ 
+
+ align:start position:0%
+Little T so this is the conditional
+distribution given that we're currently
+
+ align:start position:0%
+distribution given that we're currently
+ 
+
+ align:start position:0%
+distribution given that we're currently
+at time Little T with price s Little T
+
+ align:start position:0%
+at time Little T with price s Little T
+ 
+
+ align:start position:0%
+at time Little T with price s Little T
+or for the distribution at time capital
+
+ align:start position:0%
+or for the distribution at time capital
+ 
+
+ align:start position:0%
+or for the distribution at time capital
+T so that's where that's where it comes
+
+ align:start position:0%
+T so that's where that's where it comes
+ 
+
+ align:start position:0%
+T so that's where that's where it comes
+in it's absolutely right so in fact a
+
+ align:start position:0%
+in it's absolutely right so in fact a
+ 
+
+ align:start position:0%
+in it's absolutely right so in fact a
+lot of um this expected value right
+
+ align:start position:0%
+lot of um this expected value right
+ 
+
+ align:start position:0%
+lot of um this expected value right
+strictly should be conditional on
+
+ align:start position:0%
+strictly should be conditional on
+ 
+
+ align:start position:0%
+strictly should be conditional on
+St okay this probability is a
+
+ align:start position:0%
+St okay this probability is a
+ 
+
+ align:start position:0%
+St okay this probability is a
+probability conditional on St absolutely
+
+ align:start position:0%
+probability conditional on St absolutely
+ 
+
+ align:start position:0%
+probability conditional on St absolutely
+okay and in fact this Martingale
+
+ align:start position:0%
+okay and in fact this Martingale
+ 
+
+ align:start position:0%
+okay and in fact this Martingale
+condition is the marting GS with respect
+
+ align:start position:0%
+condition is the marting GS with respect
+ 
+
+ align:start position:0%
+condition is the marting GS with respect
+to s t Okay well may okay so that where
+
+ align:start position:0%
+to s t Okay well may okay so that where
+ 
+
+ align:start position:0%
+to s t Okay well may okay so that where
+the little t comes comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in here yes sorry there's one over
+
+ align:start position:0%
+in here yes sorry there's one over
+ 
+
+ align:start position:0%
+in here yes sorry there's one over
+Z that's right this just a constant here
+
+ align:start position:0%
+Z that's right this just a constant here
+ 
+
+ align:start position:0%
+Z that's right this just a constant here
+this is this number especially s
+
+ align:start position:0%
+this is this number especially s
+ 
+
+ align:start position:0%
+this is this number especially s
+especially because interest rates are so
+
+ align:start position:0%
+especially because interest rates are so
+ 
+
+ align:start position:0%
+especially because interest rates are so
+low in the US so this number is so close
+
+ align:start position:0%
+low in the US so this number is so close
+ 
+
+ align:start position:0%
+low in the US so this number is so close
+to one that you always forget about that
+
+ align:start position:0%
+to one that you always forget about that
+ 
+
+ align:start position:0%
+to one that you always forget about that
+I mean not when we're trading but when
+
+ align:start position:0%
+I mean not when we're trading but when
+ 
+
+ align:start position:0%
+I mean not when we're trading but when
+you sort of oh well that's just a you
+
+ align:start position:0%
+you sort of oh well that's just a you
+ 
+
+ align:start position:0%
+you sort of oh well that's just a you
+just think about which one is um this is
+
+ align:start position:0%
+just think about which one is um this is
+ 
+
+ align:start position:0%
+just think about which one is um this is
+a quantity that's in the future right
+
+ align:start position:0%
+a quantity that's in the future right
+ 
+
+ align:start position:0%
+a quantity that's in the future right
+because it's C prices okay any say
+
+ align:start position:0%
+because it's C prices okay any say
+ 
+
+ align:start position:0%
+because it's C prices okay any say
+that's how we going
+
+ align:start position:0%
+that's how we going
+ 
+
+ align:start position:0%
+that's how we going
+to so all right so that's that's the
+
+ align:start position:0%
+to so all right so that's that's the
+ 
+
+ align:start position:0%
+to so all right so that's that's the
+first the first bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so um when I when I was uh an
+
+ align:start position:0%
+um so um when I when I was uh an
+ 
+
+ align:start position:0%
+um so um when I when I was uh an
+undergraduate actually learning
+
+ align:start position:0%
+undergraduate actually learning
+ 
+
+ align:start position:0%
+undergraduate actually learning
+probability one thing I learned about
+
+ align:start position:0%
+probability one thing I learned about
+ 
+
+ align:start position:0%
+probability one thing I learned about
+probability was from my probability
+
+ align:start position:0%
+probability was from my probability
+ 
+
+ align:start position:0%
+probability was from my probability
+lecturer who said the attention span of
+
+ align:start position:0%
+lecturer who said the attention span of
+ 
+
+ align:start position:0%
+lecturer who said the attention span of
+students is no more than about 40
+
+ align:start position:0%
+students is no more than about 40
+ 
+
+ align:start position:0%
+students is no more than about 40
+minutes so there's no point lecturing
+
+ align:start position:0%
+minutes so there's no point lecturing
+ 
+
+ align:start position:0%
+minutes so there's no point lecturing
+continuously for 40 minutes because
+
+ align:start position:0%
+continuously for 40 minutes because
+ 
+
+ align:start position:0%
+continuously for 40 minutes because
+people will start you know they'll just
+
+ align:start position:0%
+people will start you know they'll just
+ 
+
+ align:start position:0%
+people will start you know they'll just
+start switching off after 40 minutes so
+
+ align:start position:0%
+start switching off after 40 minutes so
+ 
+
+ align:start position:0%
+start switching off after 40 minutes so
+rather than wait just have a break and
+
+ align:start position:0%
+rather than wait just have a break and
+ 
+
+ align:start position:0%
+rather than wait just have a break and
+waste of time the lecturer said I'm just
+
+ align:start position:0%
+waste of time the lecturer said I'm just
+ 
+
+ align:start position:0%
+waste of time the lecturer said I'm just
+going to give you some random
+
+ align:start position:0%
+going to give you some random
+ 
+
+ align:start position:0%
+going to give you some random
+information in a break and then we'll go
+
+ align:start position:0%
+information in a break and then we'll go
+ 
+
+ align:start position:0%
+information in a break and then we'll go
+back to probability so I learned that
+
+ align:start position:0%
+back to probability so I learned that
+ 
+
+ align:start position:0%
+back to probability so I learned that
+from 25 years ago I can't remember you
+
+ align:start position:0%
+from 25 years ago I can't remember you
+ 
+
+ align:start position:0%
+from 25 years ago I can't remember you
+know I actually remember the material I
+
+ align:start position:0%
+know I actually remember the material I
+ 
+
+ align:start position:0%
+know I actually remember the material I
+can't remember any of the random
+
+ align:start position:0%
+can't remember any of the random
+ 
+
+ align:start position:0%
+can't remember any of the random
+material so that's what I do in my
+
+ align:start position:0%
+material so that's what I do in my
+ 
+
+ align:start position:0%
+material so that's what I do in my
+lectures is I break them up and and talk
+
+ align:start position:0%
+lectures is I break them up and and talk
+ 
+
+ align:start position:0%
+lectures is I break them up and and talk
+about something something random so I
+
+ align:start position:0%
+about something something random so I
+ 
+
+ align:start position:0%
+about something something random so I
+thought I'd do that here as well with
+
+ align:start position:0%
+thought I'd do that here as well with
+ 
+
+ align:start position:0%
+thought I'd do that here as well with
+with some not completely random so this
+
+ align:start position:0%
+with some not completely random so this
+ 
+
+ align:start position:0%
+with some not completely random so this
+is somewhat applicable this being a math
+
+ align:start position:0%
+is somewhat applicable this being a math
+ 
+
+ align:start position:0%
+is somewhat applicable this being a math
+class so um so uh how many of you are
+
+ align:start position:0%
+class so um so uh how many of you are
+ 
+
+ align:start position:0%
+class so um so uh how many of you are
+math concentrators or applied math
+
+ align:start position:0%
+math concentrators or applied math
+ 
+
+ align:start position:0%
+math concentrators or applied math
+concentrators one okay a lot okay
+
+ align:start position:0%
+concentrators one okay a lot okay
+ 
+
+ align:start position:0%
+concentrators one okay a lot okay
+applied math concentrators okay
+
+ align:start position:0%
+applied math concentrators okay
+ 
+
+ align:start position:0%
+applied math concentrators okay
+especially for the applied math
+
+ align:start position:0%
+especially for the applied math
+ 
+
+ align:start position:0%
+especially for the applied math
+concentrators
+
+ align:start position:0%
+concentrators
+ 
+
+ align:start position:0%
+concentrators
+um going going straight to the
+
+ align:start position:0%
+um going going straight to the
+ 
+
+ align:start position:0%
+um going going straight to the
+conclusion your entire syllabus was
+
+ align:start position:0%
+conclusion your entire syllabus was
+ 
+
+ align:start position:0%
+conclusion your entire syllabus was
+generated at Cambridge University that's
+
+ align:start position:0%
+generated at Cambridge University that's
+ 
+
+ align:start position:0%
+generated at Cambridge University that's
+the conclusion so anyway here's the uh
+
+ align:start position:0%
+the conclusion so anyway here's the uh
+ 
+
+ align:start position:0%
+the conclusion so anyway here's the uh
+here's the story so um back in the 19th
+
+ align:start position:0%
+here's the story so um back in the 19th
+ 
+
+ align:start position:0%
+here's the story so um back in the 19th
+century the um the Cambridge Mathematics
+
+ align:start position:0%
+century the um the Cambridge Mathematics
+ 
+
+ align:start position:0%
+century the um the Cambridge Mathematics
+degree the undergraduate mathematics
+
+ align:start position:0%
+degree the undergraduate mathematics
+ 
+
+ align:start position:0%
+degree the undergraduate mathematics
+degree uh was the most um prestigious
+
+ align:start position:0%
+degree uh was the most um prestigious
+ 
+
+ align:start position:0%
+degree uh was the most um prestigious
+degree in the world in fact it was
+
+ align:start position:0%
+degree in the world in fact it was
+ 
+
+ align:start position:0%
+degree in the world in fact it was
+actually the the first
+
+ align:start position:0%
+actually the the first
+ 
+
+ align:start position:0%
+actually the the first
+it was the first undergraduate degree
+
+ align:start position:0%
+it was the first undergraduate degree
+ 
+
+ align:start position:0%
+it was the first undergraduate degree
+with the written
+
+ align:start position:0%
+with the written
+ 
+
+ align:start position:0%
+with the written
+examination it was Cambridge Mathematics
+
+ align:start position:0%
+examination it was Cambridge Mathematics
+ 
+
+ align:start position:0%
+examination it was Cambridge Mathematics
+so they have a lot to you know lot to be
+
+ align:start position:0%
+so they have a lot to you know lot to be
+ 
+
+ align:start position:0%
+so they have a lot to you know lot to be
+responsible for um and each year people
+
+ align:start position:0%
+responsible for um and each year people
+ 
+
+ align:start position:0%
+responsible for um and each year people
+took the exam and they were ranked and
+
+ align:start position:0%
+took the exam and they were ranked and
+ 
+
+ align:start position:0%
+took the exam and they were ranked and
+that ranking was published in the times
+
+ align:start position:0%
+that ranking was published in the times
+ 
+
+ align:start position:0%
+that ranking was published in the times
+of London so in the National newspaper
+
+ align:start position:0%
+of London so in the National newspaper
+ 
+
+ align:start position:0%
+of London so in the National newspaper
+um and the people who got first class
+
+ align:start position:0%
+um and the people who got first class
+ 
+
+ align:start position:0%
+um and the people who got first class
+degrees so summer degrees in Cambridge
+
+ align:start position:0%
+degrees so summer degrees in Cambridge
+ 
+
+ align:start position:0%
+degrees so summer degrees in Cambridge
+Mathematics were called Wranglers and
+
+ align:start position:0%
+Mathematics were called Wranglers and
+ 
+
+ align:start position:0%
+Mathematics were called Wranglers and
+still are called Wranglers actually and
+
+ align:start position:0%
+still are called Wranglers actually and
+ 
+
+ align:start position:0%
+still are called Wranglers actually and
+the reason they're called Wranglers was
+
+ align:start position:0%
+the reason they're called Wranglers was
+ 
+
+ align:start position:0%
+the reason they're called Wranglers was
+from way back in the 17th century where
+
+ align:start position:0%
+from way back in the 17th century where
+ 
+
+ align:start position:0%
+from way back in the 17th century where
+before they had exams or the 18th
+
+ align:start position:0%
+before they had exams or the 18th
+ 
+
+ align:start position:0%
+before they had exams or the 18th
+century I should say before they had
+
+ align:start position:0%
+century I should say before they had
+ 
+
+ align:start position:0%
+century I should say before they had
+exams instead of writing down exam you'd
+
+ align:start position:0%
+exams instead of writing down exam you'd
+ 
+
+ align:start position:0%
+exams instead of writing down exam you'd
+have to argue or dispute or Wrangle with
+
+ align:start position:0%
+have to argue or dispute or Wrangle with
+ 
+
+ align:start position:0%
+have to argue or dispute or Wrangle with
+your professor to get to pass the the
+
+ align:start position:0%
+your professor to get to pass the the
+ 
+
+ align:start position:0%
+your professor to get to pass the the
+class so that that's where Wrangle comes
+
+ align:start position:0%
+class so that that's where Wrangle comes
+ 
+
+ align:start position:0%
+class so that that's where Wrangle comes
+from so these these um uh people who got
+
+ align:start position:0%
+from so these these um uh people who got
+ 
+
+ align:start position:0%
+from so these these um uh people who got
+the first class degree called Wranglers
+
+ align:start position:0%
+the first class degree called Wranglers
+ 
+
+ align:start position:0%
+the first class degree called Wranglers
+and they are ranked and basically the
+
+ align:start position:0%
+and they are ranked and basically the
+ 
+
+ align:start position:0%
+and they are ranked and basically the
+the senior Wrangler was um a very famous
+
+ align:start position:0%
+the senior Wrangler was um a very famous
+ 
+
+ align:start position:0%
+the senior Wrangler was um a very famous
+person in the UK in the 19th century and
+
+ align:start position:0%
+person in the UK in the 19th century and
+ 
+
+ align:start position:0%
+person in the UK in the 19th century and
+a lot of them turned out to be quite
+
+ align:start position:0%
+a lot of them turned out to be quite
+ 
+
+ align:start position:0%
+a lot of them turned out to be quite
+successful so here are here are a few
+
+ align:start position:0%
+successful so here are here are a few
+ 
+
+ align:start position:0%
+successful so here are here are a few
+few wrangles I just U got this
+
+ align:start position:0%
+few wrangles I just U got this
+ 
+
+ align:start position:0%
+few wrangles I just U got this
+one I can't reach that there can I so
+
+ align:start position:0%
+one I can't reach that there can I so
+ 
+
+ align:start position:0%
+one I can't reach that there can I so
+some of them you might you might
+
+ align:start position:0%
+some of them you might you might
+ 
+
+ align:start position:0%
+some of them you might you might
+recognize and then I just wanted to tell
+
+ align:start position:0%
+recognize and then I just wanted to tell
+ 
+
+ align:start position:0%
+recognize and then I just wanted to tell
+you a quick story about the uh one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them okay so um let's start so
+
+ align:start position:0%
+them okay so um let's start so
+ 
+
+ align:start position:0%
+them okay so um let's start so
+1841 senior angler was uh George Stokes
+
+ align:start position:0%
+1841 senior angler was uh George Stokes
+ 
+
+ align:start position:0%
+1841 senior angler was uh George Stokes
+so basically fluid dynamics the whole
+
+ align:start position:0%
+so basically fluid dynamics the whole
+ 
+
+ align:start position:0%
+so basically fluid dynamics the whole
+the fluid dynamics that's George Stokes
+
+ align:start position:0%
+the fluid dynamics that's George Stokes
+ 
+
+ align:start position:0%
+the fluid dynamics that's George Stokes
+um 18
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+54 uh second Wrangler this is this is
+
+ align:start position:0%
+54 uh second Wrangler this is this is
+ 
+
+ align:start position:0%
+54 uh second Wrangler this is this is
+who was the first Wrangler second
+
+ align:start position:0%
+who was the first Wrangler second
+ 
+
+ align:start position:0%
+who was the first Wrangler second
+Wrangler was James Maxwell so
+
+ align:start position:0%
+Wrangler was James Maxwell so
+ 
+
+ align:start position:0%
+Wrangler was James Maxwell so
+electrodynamics Maxwell equations he was
+
+ align:start position:0%
+electrodynamics Maxwell equations he was
+ 
+
+ align:start position:0%
+electrodynamics Maxwell equations he was
+the second I mean I can't I can't quite
+
+ align:start position:0%
+the second I mean I can't I can't quite
+ 
+
+ align:start position:0%
+the second I mean I can't I can't quite
+work out who was who was the first um
+
+ align:start position:0%
+work out who was who was the first um
+ 
+
+ align:start position:0%
+work out who was who was the first um
+1880 the second Wrangler was uh JJ
+
+ align:start position:0%
+1880 the second Wrangler was uh JJ
+ 
+
+ align:start position:0%
+1880 the second Wrangler was uh JJ
+Thompson so electrons Atomic physics
+
+ align:start position:0%
+Thompson so electrons Atomic physics
+ 
+
+ align:start position:0%
+Thompson so electrons Atomic physics
+that comes out of he was only
+
+ align:start position:0%
+that comes out of he was only
+ 
+
+ align:start position:0%
+that comes out of he was only
+second um 1865 senior r Lord Raley so he
+
+ align:start position:0%
+second um 1865 senior r Lord Raley so he
+ 
+
+ align:start position:0%
+second um 1865 senior r Lord Raley so he
+was the uh you know the sky is
+
+ align:start position:0%
+was the uh you know the sky is
+ 
+
+ align:start position:0%
+was the uh you know the sky is
+blue
+
+ align:start position:0%
+blue
+ 
+
+ align:start position:0%
+blue
+um he was first okay so they're pretty
+
+ align:start position:0%
+um he was first okay so they're pretty
+ 
+
+ align:start position:0%
+um he was first okay so they're pretty
+they're a pretty pretty good Bunch um so
+
+ align:start position:0%
+they're a pretty pretty good Bunch um so
+ 
+
+ align:start position:0%
+they're a pretty pretty good Bunch um so
+the best the best the story the best
+
+ align:start position:0%
+the best the best the story the best
+ 
+
+ align:start position:0%
+the best the best the story the best
+story 1845 and going back uh the the
+
+ align:start position:0%
+story 1845 and going back uh the the
+ 
+
+ align:start position:0%
+story 1845 and going back uh the the
+second Wrangler was Lord
+
+ align:start position:0%
+second Wrangler was Lord
+ 
+
+ align:start position:0%
+second Wrangler was Lord
+Kelvin so absolute zero amongst other
+
+ align:start position:0%
+Kelvin so absolute zero amongst other
+ 
+
+ align:start position:0%
+Kelvin so absolute zero amongst other
+things of course but yeah absolute zero
+
+ align:start position:0%
+things of course but yeah absolute zero
+ 
+
+ align:start position:0%
+things of course but yeah absolute zero
+he was second Wrangler and the great
+
+ align:start position:0%
+he was second Wrangler and the great
+ 
+
+ align:start position:0%
+he was second Wrangler and the great
+story about him he was he was the most
+
+ align:start position:0%
+story about him he was he was the most
+ 
+
+ align:start position:0%
+story about him he was he was the most
+talented mathematician of his of the
+
+ align:start position:0%
+talented mathematician of his of the
+ 
+
+ align:start position:0%
+talented mathematician of his of the
+decade
+
+ align:start position:0%
+decade
+ 
+
+ align:start position:0%
+decade
+and it was such a lock for senior angler
+
+ align:start position:0%
+and it was such a lock for senior angler
+ 
+
+ align:start position:0%
+and it was such a lock for senior angler
+that and I actually read the biography
+
+ align:start position:0%
+that and I actually read the biography
+ 
+
+ align:start position:0%
+that and I actually read the biography
+so this is a sort of true statement that
+
+ align:start position:0%
+so this is a sort of true statement that
+ 
+
+ align:start position:0%
+so this is a sort of true statement that
+he sent his servant to the Senate house
+
+ align:start position:0%
+he sent his servant to the Senate house
+ 
+
+ align:start position:0%
+he sent his servant to the Senate house
+where these things are being read out
+
+ align:start position:0%
+where these things are being read out
+ 
+
+ align:start position:0%
+where these things are being read out
+and with a request tell me who is second
+
+ align:start position:0%
+and with a request tell me who is second
+ 
+
+ align:start position:0%
+and with a request tell me who is second
+Wrangler and the servant came back and
+
+ align:start position:0%
+Wrangler and the servant came back and
+ 
+
+ align:start position:0%
+Wrangler and the servant came back and
+said you sir and uh because he was he he
+
+ align:start position:0%
+said you sir and uh because he was he he
+ 
+
+ align:start position:0%
+said you sir and uh because he was he he
+was such a lock to be uh first Wrangler
+
+ align:start position:0%
+was such a lock to be uh first Wrangler
+ 
+
+ align:start position:0%
+was such a lock to be uh first Wrangler
+and in fact what happened was the
+
+ align:start position:0%
+and in fact what happened was the
+ 
+
+ align:start position:0%
+and in fact what happened was the
+question on the mathematical
+
+ align:start position:0%
+question on the mathematical
+ 
+
+ align:start position:0%
+question on the mathematical
+exam was a theorem that he had proved
+
+ align:start position:0%
+exam was a theorem that he had proved
+ 
+
+ align:start position:0%
+exam was a theorem that he had proved
+two years before in the Cambridge
+
+ align:start position:0%
+two years before in the Cambridge
+ 
+
+ align:start position:0%
+two years before in the Cambridge
+mathematical Jour mathematical Journal
+
+ align:start position:0%
+mathematical Jour mathematical Journal
+ 
+
+ align:start position:0%
+mathematical Jour mathematical Journal
+so it's his theorem was set on the exam
+
+ align:start position:0%
+so it's his theorem was set on the exam
+ 
+
+ align:start position:0%
+so it's his theorem was set on the exam
+but of course he had not memorized it so
+
+ align:start position:0%
+but of course he had not memorized it so
+ 
+
+ align:start position:0%
+but of course he had not memorized it so
+he had to reprove it whereas the person
+
+ align:start position:0%
+he had to reprove it whereas the person
+ 
+
+ align:start position:0%
+he had to reprove it whereas the person
+who became senior Wrangler had memorized
+
+ align:start position:0%
+who became senior Wrangler had memorized
+ 
+
+ align:start position:0%
+who became senior Wrangler had memorized
+the proof and was able to regenerate it
+
+ align:start position:0%
+the proof and was able to regenerate it
+ 
+
+ align:start position:0%
+the proof and was able to regenerate it
+and in those days there was a lot of
+
+ align:start position:0%
+and in those days there was a lot of
+ 
+
+ align:start position:0%
+and in those days there was a lot of
+cramming to be done in these exams so
+
+ align:start position:0%
+cramming to be done in these exams so
+ 
+
+ align:start position:0%
+cramming to be done in these exams so
+the guy who um Steven Parkinson was
+
+ align:start position:0%
+the guy who um Steven Parkinson was
+ 
+
+ align:start position:0%
+the guy who um Steven Parkinson was
+senior Wrangler he went on to be F FRS
+
+ align:start position:0%
+senior Wrangler he went on to be F FRS
+ 
+
+ align:start position:0%
+senior Wrangler he went on to be F FRS
+and eminent but so he wasn't uh so
+
+ align:start position:0%
+and eminent but so he wasn't uh so
+ 
+
+ align:start position:0%
+and eminent but so he wasn't uh so
+anyway so these are so here you go
+
+ align:start position:0%
+anyway so these are so here you go
+ 
+
+ align:start position:0%
+anyway so these are so here you go
+here's the applied math syllabus um
+
+ align:start position:0%
+here's the applied math syllabus um
+ 
+
+ align:start position:0%
+here's the applied math syllabus um
+here's a couple of other ones which I
+
+ align:start position:0%
+here's a couple of other ones which I
+ 
+
+ align:start position:0%
+here's a couple of other ones which I
+really like so in
+
+ align:start position:0%
+really like so in
+ 
+
+ align:start position:0%
+really like so in
+1904 John Mayar
+
+ align:start position:0%
+1904 John Mayar
+ 
+
+ align:start position:0%
+1904 John Mayar
+KES was a 12th Wrangler now I can tell
+
+ align:start position:0%
+KES was a 12th Wrangler now I can tell
+ 
+
+ align:start position:0%
+KES was a 12th Wrangler now I can tell
+the story either way depending on
+
+ align:start position:0%
+the story either way depending on
+ 
+
+ align:start position:0%
+the story either way depending on
+whether I'm in an audience of economists
+
+ align:start position:0%
+whether I'm in an audience of economists
+ 
+
+ align:start position:0%
+whether I'm in an audience of economists
+or audience of mathematicians it since
+
+ align:start position:0%
+or audience of mathematicians it since
+ 
+
+ align:start position:0%
+or audience of mathematicians it since
+I'm in an audience of mathematicians I
+
+ align:start position:0%
+I'm in an audience of mathematicians I
+ 
+
+ align:start position:0%
+I'm in an audience of mathematicians I
+like to say look the greatest Economist
+
+ align:start position:0%
+like to say look the greatest Economist
+ 
+
+ align:start position:0%
+like to say look the greatest Economist
+he was so poor at mathematics he only
+
+ align:start position:0%
+he was so poor at mathematics he only
+ 
+
+ align:start position:0%
+he was so poor at mathematics he only
+managed to be 12th Wrangler they're 11th
+
+ align:start position:0%
+managed to be 12th Wrangler they're 11th
+ 
+
+ align:start position:0%
+managed to be 12th Wrangler they're 11th
+better mathematicians in the UK in that
+
+ align:start position:0%
+better mathematicians in the UK in that
+ 
+
+ align:start position:0%
+better mathematicians in the UK in that
+year so he was obviously not not not
+
+ align:start position:0%
+year so he was obviously not not not
+ 
+
+ align:start position:0%
+year so he was obviously not not not
+that great if I was talking to Economist
+
+ align:start position:0%
+that great if I was talking to Economist
+ 
+
+ align:start position:0%
+that great if I was talking to Economist
+would say this guy was so brilliant that
+
+ align:start position:0%
+would say this guy was so brilliant that
+ 
+
+ align:start position:0%
+would say this guy was so brilliant that
+his main field was economics and yet as
+
+ align:start position:0%
+his main field was economics and yet as
+ 
+
+ align:start position:0%
+his main field was economics and yet as
+part-time he was able to be the 12th
+
+ align:start position:0%
+part-time he was able to be the 12th
+ 
+
+ align:start position:0%
+part-time he was able to be the 12th
+best mathematician in the UK so um
+
+ align:start position:0%
+best mathematician in the UK so um
+ 
+
+ align:start position:0%
+best mathematician in the UK so um
+anyway all right so the last one I
+
+ align:start position:0%
+anyway all right so the last one I
+ 
+
+ align:start position:0%
+anyway all right so the last one I
+wanted to talk about
+
+ align:start position:0%
+wanted to talk about
+ 
+
+ align:start position:0%
+wanted to talk about
+1879 all right here's a here's a um
+
+ align:start position:0%
+1879 all right here's a here's a um
+ 
+
+ align:start position:0%
+1879 all right here's a here's a um
+here's a quiz this one you have to have
+
+ align:start position:0%
+here's a quiz this one you have to have
+ 
+
+ align:start position:0%
+here's a quiz this one you have to have
+some answers for okay so um
+
+ align:start position:0%
+some answers for okay so um
+ 
+
+ align:start position:0%
+some answers for okay so um
+198 something I can't remember what it
+
+ align:start position:0%
+198 something I can't remember what it
+ 
+
+ align:start position:0%
+198 something I can't remember what it
+is okay so here's one here's two here's
+
+ align:start position:0%
+is okay so here's one here's two here's
+ 
+
+ align:start position:0%
+is okay so here's one here's two here's
+three right I'm going to give you one
+
+ align:start position:0%
+three right I'm going to give you one
+ 
+
+ align:start position:0%
+three right I'm going to give you one
+and two you got to in three right you're
+
+ align:start position:0%
+and two you got to in three right you're
+ 
+
+ align:start position:0%
+and two you got to in three right you're
+probably not going to be able to get
+
+ align:start position:0%
+probably not going to be able to get
+ 
+
+ align:start position:0%
+probably not going to be able to get
+this one yet but anyway so this is uh uh
+
+ align:start position:0%
+this one yet but anyway so this is uh uh
+ 
+
+ align:start position:0%
+this one yet but anyway so this is uh uh
+Andrew
+
+ align:start position:0%
+Andrew
+ 
+
+ align:start position:0%
+Andrew
+Allen senior Wrangler uh George Walker
+
+ align:start position:0%
+Allen senior Wrangler uh George Walker
+ 
+
+ align:start position:0%
+Allen senior Wrangler uh George Walker
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+Wrangler and number three the question
+
+ align:start position:0%
+Wrangler and number three the question
+ 
+
+ align:start position:0%
+Wrangler and number three the question
+okay so that's that's a question uh 1980
+
+ align:start position:0%
+okay so that's that's a question uh 1980
+ 
+
+ align:start position:0%
+okay so that's that's a question uh 1980
+uh uh hakeim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alan uh s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Boe question mark okay who's question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mark do we know which sport these people
+
+ align:start position:0%
+mark do we know which sport these people
+ 
+
+ align:start position:0%
+mark do we know which sport these people
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+play that yes right there you go that's
+
+ align:start position:0%
+play that yes right there you go that's
+ 
+
+ align:start position:0%
+play that yes right there you go that's
+Michael Jordan exactly I think you know
+
+ align:start position:0%
+Michael Jordan exactly I think you know
+ 
+
+ align:start position:0%
+Michael Jordan exactly I think you know
+this is this a question could go on
+
+ align:start position:0%
+this is this a question could go on
+ 
+
+ align:start position:0%
+this is this a question could go on
+forever in the UK because they does so
+
+ align:start position:0%
+forever in the UK because they does so
+ 
+
+ align:start position:0%
+forever in the UK because they does so
+Michael Jordan famously was only picked
+
+ align:start position:0%
+Michael Jordan famously was only picked
+ 
+
+ align:start position:0%
+Michael Jordan famously was only picked
+third in the NBA draft in
+
+ align:start position:0%
+third in the NBA draft in
+ 
+
+ align:start position:0%
+third in the NBA draft in
+1984 was it four five something like
+
+ align:start position:0%
+1984 was it four five something like
+ 
+
+ align:start position:0%
+1984 was it four five something like
+that so now hakeim Al was actually
+
+ align:start position:0%
+that so now hakeim Al was actually
+ 
+
+ align:start position:0%
+that so now hakeim Al was actually
+pretty good but is a total bust so
+
+ align:start position:0%
+pretty good but is a total bust so
+ 
+
+ align:start position:0%
+pretty good but is a total bust so
+but he was third so in 1879 and the came
+
+ align:start position:0%
+but he was third so in 1879 and the came
+ 
+
+ align:start position:0%
+but he was third so in 1879 and the came
+mathematics tripos these two people
+
+ align:start position:0%
+mathematics tripos these two people
+ 
+
+ align:start position:0%
+mathematics tripos these two people
+you've never heard of were first and
+
+ align:start position:0%
+you've never heard of were first and
+ 
+
+ align:start position:0%
+you've never heard of were first and
+second and the person who came third
+
+ align:start position:0%
+second and the person who came third
+ 
+
+ align:start position:0%
+second and the person who came third
+you've probably heard of I this is more
+
+ align:start position:0%
+you've probably heard of I this is more
+ 
+
+ align:start position:0%
+you've probably heard of I this is more
+of a statistics thing um people know
+
+ align:start position:0%
+of a statistics thing um people know
+ 
+
+ align:start position:0%
+of a statistics thing um people know
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+correlation what's the correlation who's
+
+ align:start position:0%
+correlation what's the correlation who's
+ 
+
+ align:start position:0%
+correlation what's the correlation who's
+correlation coefficient named
+
+ align:start position:0%
+correlation coefficient named
+ 
+
+ align:start position:0%
+correlation coefficient named
+after Pearson very good k k Pearson so
+
+ align:start position:0%
+after Pearson very good k k Pearson so
+ 
+
+ align:start position:0%
+after Pearson very good k k Pearson so
+so K
+
+ align:start position:0%
+so K
+ 
+
+ align:start position:0%
+so K
+Pearson was the third Wrangler in 1879
+
+ align:start position:0%
+Pearson was the third Wrangler in 1879
+ 
+
+ align:start position:0%
+Pearson was the third Wrangler in 1879
+and the founder of Statistics he founded
+
+ align:start position:0%
+and the founder of Statistics he founded
+ 
+
+ align:start position:0%
+and the founder of Statistics he founded
+the first ever statistics Department and
+
+ align:start position:0%
+the first ever statistics Department and
+ 
+
+ align:start position:0%
+the first ever statistics Department and
+um obviously invented correlation with
+
+ align:start position:0%
+um obviously invented correlation with
+ 
+
+ align:start position:0%
+um obviously invented correlation with
+golden golden Pearson so anyway it's
+
+ align:start position:0%
+golden golden Pearson so anyway it's
+ 
+
+ align:start position:0%
+golden golden Pearson so anyway it's
+only the third Wrangler and
+
+ align:start position:0%
+only the third Wrangler and
+ 
+
+ align:start position:0%
+only the third Wrangler and
+unfortunately these people have very
+
+ align:start position:0%
+unfortunately these people have very
+ 
+
+ align:start position:0%
+unfortunately these people have very
+common name so I have no idea what they
+
+ align:start position:0%
+common name so I have no idea what they
+ 
+
+ align:start position:0%
+common name so I have no idea what they
+went on to do right Google these people
+
+ align:start position:0%
+went on to do right Google these people
+ 
+
+ align:start position:0%
+went on to do right Google these people
+is not not not very effective anyway so
+
+ align:start position:0%
+is not not not very effective anyway so
+ 
+
+ align:start position:0%
+is not not not very effective anyway so
+that's the uh that's the story of uh
+
+ align:start position:0%
+that's the uh that's the story of uh
+ 
+
+ align:start position:0%
+that's the uh that's the story of uh
+Cambridge Cambridge Mathematics lot of
+
+ align:start position:0%
+Cambridge Cambridge Mathematics lot of
+ 
+
+ align:start position:0%
+Cambridge Cambridge Mathematics lot of
+uh lots of good good stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so um last half hour I just
+
+ align:start position:0%
+all right so um last half hour I just
+ 
+
+ align:start position:0%
+all right so um last half hour I just
+want to go the other
+
+ align:start position:0%
+want to go the other
+ 
+
+ align:start position:0%
+want to go the other
+way um
+
+ align:start position:0%
+way um
+ 
+
+ align:start position:0%
+way um
+from where's my page three okay so the
+
+ align:start position:0%
+from where's my page three okay so the
+ 
+
+ align:start position:0%
+from where's my page three okay so the
+other way we went from option prices to
+
+ align:start position:0%
+other way we went from option prices to
+ 
+
+ align:start position:0%
+other way we went from option prices to
+probability let's go from probability to
+
+ align:start position:0%
+probability let's go from probability to
+ 
+
+ align:start position:0%
+probability let's go from probability to
+option price we sort of already have
+
+ align:start position:0%
+option price we sort of already have
+ 
+
+ align:start position:0%
+option price we sort of already have
+actually this is what the fundamental
+
+ align:start position:0%
+actually this is what the fundamental
+ 
+
+ align:start position:0%
+actually this is what the fundamental
+theorem does if we're thinking if we
+
+ align:start position:0%
+theorem does if we're thinking if we
+ 
+
+ align:start position:0%
+theorem does if we're thinking if we
+let's take on trust that the fundamental
+
+ align:start position:0%
+let's take on trust that the fundamental
+ 
+
+ align:start position:0%
+let's take on trust that the fundamental
+theorem holds namely option prices today
+
+ align:start position:0%
+theorem holds namely option prices today
+ 
+
+ align:start position:0%
+theorem holds namely option prices today
+are the discounted expected
+
+ align:start position:0%
+are the discounted expected
+ 
+
+ align:start position:0%
+are the discounted expected
+payout at maturity okay let take that on
+
+ align:start position:0%
+payout at maturity okay let take that on
+ 
+
+ align:start position:0%
+payout at maturity okay let take that on
+on trust then we're going from
+
+ align:start position:0%
+on trust then we're going from
+ 
+
+ align:start position:0%
+on trust then we're going from
+probability distribution to option price
+
+ align:start position:0%
+probability distribution to option price
+ 
+
+ align:start position:0%
+probability distribution to option price
+in the following way so let's actually
+
+ align:start position:0%
+in the following way so let's actually
+ 
+
+ align:start position:0%
+in the following way so let's actually
+State the the fundamental
+
+ align:start position:0%
+State the the fundamental
+ 
+
+ align:start position:0%
+State the the fundamental
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ft okay so
+
+ align:start position:0%
+ft okay so
+ 
+
+ align:start position:0%
+ft okay so
+um so I'm going to General derivative D
+
+ align:start position:0%
+um so I'm going to General derivative D
+ 
+
+ align:start position:0%
+um so I'm going to General derivative D
+it's D digital D derivative it's um so a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative with pay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at T So this could be the digital payout
+
+ align:start position:0%
+at T So this could be the digital payout
+ 
+
+ align:start position:0%
+at T So this could be the digital payout
+it could be the call option payout it
+
+ align:start position:0%
+it could be the call option payout it
+ 
+
+ align:start position:0%
+it could be the call option payout it
+could be one um and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+right okay so often we we actually think
+
+ align:start position:0%
+right okay so often we we actually think
+ 
+
+ align:start position:0%
+right okay so often we we actually think
+about the payout function is just a
+
+ align:start position:0%
+about the payout function is just a
+ 
+
+ align:start position:0%
+about the payout function is just a
+simple function of the the stock price
+
+ align:start position:0%
+simple function of the the stock price
+ 
+
+ align:start position:0%
+simple function of the the stock price
+um but this notation is useful when we
+
+ align:start position:0%
+um but this notation is useful when we
+ 
+
+ align:start position:0%
+um but this notation is useful when we
+think about the prices being marting
+
+ align:start position:0%
+think about the prices being marting
+ 
+
+ align:start position:0%
+think about the prices being marting
+Gales okay
+
+ align:start position:0%
+Gales okay
+ 
+
+ align:start position:0%
+Gales okay
+then what is ftap um
+
+ align:start position:0%
+then what is ftap um
+ 
+
+ align:start position:0%
+then what is ftap um
+D the ratio of the price to the zero
+
+ align:start position:0%
+D the ratio of the price to the zero
+ 
+
+ align:start position:0%
+D the ratio of the price to the zero
+coupon
+
+ align:start position:0%
+coupon
+ 
+
+ align:start position:0%
+coupon
+bond is equal to is a Martingale in
+
+ align:start position:0%
+bond is equal to is a Martingale in
+ 
+
+ align:start position:0%
+bond is equal to is a Martingale in
+other words there expected value under
+
+ align:start position:0%
+other words there expected value under
+ 
+
+ align:start position:0%
+other words there expected value under
+the special distribution risk neutral
+
+ align:start position:0%
+the special distribution risk neutral
+ 
+
+ align:start position:0%
+the special distribution risk neutral
+distribution of the payout at maturity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to your point it's conditional on St
+
+ align:start position:0%
+and to your point it's conditional on St
+ 
+
+ align:start position:0%
+and to your point it's conditional on St
+so this is the proper statement so this
+
+ align:start position:0%
+so this is the proper statement so this
+ 
+
+ align:start position:0%
+so this is the proper statement so this
+is the fundamental theorem of asset
+
+ align:start position:0%
+is the fundamental theorem of asset
+ 
+
+ align:start position:0%
+is the fundamental theorem of asset
+prices in words it's saying this ratio
+
+ align:start position:0%
+prices in words it's saying this ratio
+ 
+
+ align:start position:0%
+prices in words it's saying this ratio
+is a Martingale with respect to the
+
+ align:start position:0%
+is a Martingale with respect to the
+ 
+
+ align:start position:0%
+is a Martingale with respect to the
+stock price under the risk neutral
+
+ align:start position:0%
+stock price under the risk neutral
+ 
+
+ align:start position:0%
+stock price under the risk neutral
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+okay okay that's the statement of the
+
+ align:start position:0%
+okay okay that's the statement of the
+ 
+
+ align:start position:0%
+okay okay that's the statement of the
+fundamental theorem this is actually
+
+ align:start position:0%
+fundamental theorem this is actually
+ 
+
+ align:start position:0%
+fundamental theorem this is actually
+rather neat to prove in the binomial
+
+ align:start position:0%
+rather neat to prove in the binomial
+ 
+
+ align:start position:0%
+rather neat to prove in the binomial
+tree twostep two- State world is very
+
+ align:start position:0%
+tree twostep two- State world is very
+ 
+
+ align:start position:0%
+tree twostep two- State world is very
+very difficult to prove in continuous
+
+ align:start position:0%
+very difficult to prove in continuous
+ 
+
+ align:start position:0%
+very difficult to prove in continuous
+time this is uh Harrison and creps in
+
+ align:start position:0%
+time this is uh Harrison and creps in
+ 
+
+ align:start position:0%
+time this is uh Harrison and creps in
+1979 it's a proof that you know however
+
+ align:start position:0%
+1979 it's a proof that you know however
+ 
+
+ align:start position:0%
+1979 it's a proof that you know however
+many times you look at it you're only
+
+ align:start position:0%
+many times you look at it you're only
+ 
+
+ align:start position:0%
+many times you look at it you're only
+probably going to get through the two or
+
+ align:start position:0%
+probably going to get through the two or
+ 
+
+ align:start position:0%
+probably going to get through the two or
+three pages before thinking okay that's
+
+ align:start position:0%
+three pages before thinking okay that's
+ 
+
+ align:start position:0%
+three pages before thinking okay that's
+hard but it's it was done sorry okay so
+
+ align:start position:0%
+hard but it's it was done sorry okay so
+ 
+
+ align:start position:0%
+hard but it's it was done sorry okay so
+this is um you can imagine continuous
+
+ align:start position:0%
+this is um you can imagine continuous
+ 
+
+ align:start position:0%
+this is um you can imagine continuous
+time infinite amount of trading
+
+ align:start position:0%
+time infinite amount of trading
+ 
+
+ align:start position:0%
+time infinite amount of trading
+different states of the world it's very
+
+ align:start position:0%
+different states of the world it's very
+ 
+
+ align:start position:0%
+different states of the world it's very
+okay so now this of course is
+
+ align:start position:0%
+okay so now this of course is
+ 
+
+ align:start position:0%
+okay so now this of course is
+one okay um and this can come up this is
+
+ align:start position:0%
+one okay um and this can come up this is
+ 
+
+ align:start position:0%
+one okay um and this can come up this is
+these are known at time Little T so if
+
+ align:start position:0%
+these are known at time Little T so if
+ 
+
+ align:start position:0%
+these are known at time Little T so if
+I'm thinking at if I'm at current time
+
+ align:start position:0%
+I'm thinking at if I'm at current time
+ 
+
+ align:start position:0%
+I'm thinking at if I'm at current time
+Little T therefore the derivative
+
+ align:start position:0%
+Little T therefore the derivative
+ 
+
+ align:start position:0%
+Little T therefore the derivative
+price is what we had
+
+ align:start position:0%
+price is what we had
+ 
+
+ align:start position:0%
+price is what we had
+before the expected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+payout okay so this is rather nice nice
+
+ align:start position:0%
+payout okay so this is rather nice nice
+ 
+
+ align:start position:0%
+payout okay so this is rather nice nice
+expression and now we can actually just
+
+ align:start position:0%
+expression and now we can actually just
+ 
+
+ align:start position:0%
+expression and now we can actually just
+write down what this is this is the
+
+ align:start position:0%
+write down what this is this is the
+ 
+
+ align:start position:0%
+write down what this is this is the
+expected value of a function of a random
+
+ align:start position:0%
+expected value of a function of a random
+ 
+
+ align:start position:0%
+expected value of a function of a random
+variable okay so this is
+
+ align:start position:0%
+variable okay so this is
+ 
+
+ align:start position:0%
+variable okay so this is
+just the
+
+ align:start position:0%
+just the
+ 
+
+ align:start position:0%
+just the
+integral of G of x
+
+ align:start position:0%
+integral of G of x
+ 
+
+ align:start position:0%
+integral of G of x
+f of
+
+ align:start position:0%
+f of
+ 
+
+ align:start position:0%
+f of
+x DX where this is the density of the
+
+ align:start position:0%
+x DX where this is the density of the
+ 
+
+ align:start position:0%
+x DX where this is the density of the
+random variable at time capital D
+
+ align:start position:0%
+random variable at time capital D
+ 
+
+ align:start position:0%
+random variable at time capital D
+condition one being at St so this
+
+ align:start position:0%
+condition one being at St so this
+ 
+
+ align:start position:0%
+condition one being at St so this
+conditional density okay so this is a
+
+ align:start position:0%
+conditional density okay so this is a
+ 
+
+ align:start position:0%
+conditional density okay so this is a
+restatement of um the fundamental
+
+ align:start position:0%
+restatement of um the fundamental
+ 
+
+ align:start position:0%
+restatement of um the fundamental
+theorem so this is essentially the
+
+ align:start position:0%
+theorem so this is essentially the
+ 
+
+ align:start position:0%
+theorem so this is essentially the
+fundamental theorem and this is a
+
+ align:start position:0%
+fundamental theorem and this is a
+ 
+
+ align:start position:0%
+fundamental theorem and this is a
+intuition made good or intuition made
+
+ align:start position:0%
+intuition made good or intuition made
+ 
+
+ align:start position:0%
+intuition made good or intuition made
+real expected
+
+ align:start position:0%
+real expected
+ 
+
+ align:start position:0%
+real expected
+payouts okay this is um sometimes called
+
+ align:start position:0%
+payouts okay this is um sometimes called
+ 
+
+ align:start position:0%
+payouts okay this is um sometimes called
+Lotus the of the unconscious statistici
+
+ align:start position:0%
+Lotus the of the unconscious statistici
+ 
+
+ align:start position:0%
+Lotus the of the unconscious statistici
+it's just that the expected value of G
+
+ align:start position:0%
+it's just that the expected value of G
+ 
+
+ align:start position:0%
+it's just that the expected value of G
+ofx is integral G of x f ofx that's not
+
+ align:start position:0%
+ofx is integral G of x f ofx that's not
+ 
+
+ align:start position:0%
+ofx is integral G of x f ofx that's not
+immediate from the definition of
+
+ align:start position:0%
+immediate from the definition of
+ 
+
+ align:start position:0%
+immediate from the definition of
+expected value you should really work
+
+ align:start position:0%
+expected value you should really work
+ 
+
+ align:start position:0%
+expected value you should really work
+out the density of G of X right and then
+
+ align:start position:0%
+out the density of G of X right and then
+ 
+
+ align:start position:0%
+out the density of G of X right and then
+integral of x the density of G of X DX
+
+ align:start position:0%
+integral of x the density of G of X DX
+ 
+
+ align:start position:0%
+integral of x the density of G of X DX
+but it turns out to be this okay so
+
+ align:start position:0%
+but it turns out to be this okay so
+ 
+
+ align:start position:0%
+but it turns out to be this okay so
+that's a really nice nice result okay so
+
+ align:start position:0%
+that's a really nice nice result okay so
+ 
+
+ align:start position:0%
+that's a really nice nice result okay so
+here is now
+
+ align:start position:0%
+here is now
+ 
+
+ align:start position:0%
+here is now
+our way of going from density to price
+
+ align:start position:0%
+our way of going from density to price
+ 
+
+ align:start position:0%
+our way of going from density to price
+if I put in the call
+
+ align:start position:0%
+if I put in the call
+ 
+
+ align:start position:0%
+if I put in the call
+option payout for G and I have the
+
+ align:start position:0%
+option payout for G and I have the
+ 
+
+ align:start position:0%
+option payout for G and I have the
+density I can then derive the price C
+
+ align:start position:0%
+density I can then derive the price C
+ 
+
+ align:start position:0%
+density I can then derive the price C
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you like the way I go from density
+
+ align:start position:0%
+so if you like the way I go from density
+ 
+
+ align:start position:0%
+so if you like the way I go from density
+to or probability distribution to option
+
+ align:start position:0%
+to or probability distribution to option
+ 
+
+ align:start position:0%
+to or probability distribution to option
+price is exactly the fundamental theorem
+
+ align:start position:0%
+price is exactly the fundamental theorem
+ 
+
+ align:start position:0%
+price is exactly the fundamental theorem
+or the root I take is a fundamental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem okay so ftap fundamental theorem
+
+ align:start position:0%
+theorem okay so ftap fundamental theorem
+ 
+
+ align:start position:0%
+theorem okay so ftap fundamental theorem
+of asset pricing means I can go from the
+
+ align:start position:0%
+of asset pricing means I can go from the
+ 
+
+ align:start position:0%
+of asset pricing means I can go from the
+probability density to the price of the
+
+ align:start position:0%
+probability density to the price of the
+ 
+
+ align:start position:0%
+probability density to the price of the
+derivative for any derivative
+
+ align:start position:0%
+derivative for any derivative
+ 
+
+ align:start position:0%
+derivative for any derivative
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+right okay so now we can go either way
+
+ align:start position:0%
+right okay so now we can go either way
+ 
+
+ align:start position:0%
+right okay so now we can go either way
+density to derivative or call Price to
+
+ align:start position:0%
+density to derivative or call Price to
+ 
+
+ align:start position:0%
+density to derivative or call Price to
+density you might say well hang on a sec
+
+ align:start position:0%
+density you might say well hang on a sec
+ 
+
+ align:start position:0%
+density you might say well hang on a sec
+we've only gone from we need the core
+
+ align:start position:0%
+we've only gone from we need the core
+ 
+
+ align:start position:0%
+we've only gone from we need the core
+prices to get the density well of course
+
+ align:start position:0%
+prices to get the density well of course
+ 
+
+ align:start position:0%
+prices to get the density well of course
+you know we can
+
+ align:start position:0%
+you know we can
+ 
+
+ align:start position:0%
+you know we can
+go via an intermediate step right so to
+
+ align:start position:0%
+go via an intermediate step right so to
+ 
+
+ align:start position:0%
+go via an intermediate step right so to
+get from the core price to these an
+
+ align:start position:0%
+get from the core price to these an
+ 
+
+ align:start position:0%
+get from the core price to these an
+arbitrary derivative price I just go via
+
+ align:start position:0%
+arbitrary derivative price I just go via
+ 
+
+ align:start position:0%
+arbitrary derivative price I just go via
+the density right so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular this is reating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowledge of all the C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prices okay for all
+
+ align:start position:0%
+prices okay for all
+ 
+
+ align:start position:0%
+prices okay for all
+K okay determines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this derivative pair for any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay so if I know all calls I know the
+
+ align:start position:0%
+G okay so if I know all calls I know the
+ 
+
+ align:start position:0%
+G okay so if I know all calls I know the
+density and then if I know the density I
+
+ align:start position:0%
+density and then if I know the density I
+ 
+
+ align:start position:0%
+density and then if I know the density I
+know an arbitary derivative price okay
+
+ align:start position:0%
+know an arbitary derivative price okay
+ 
+
+ align:start position:0%
+know an arbitary derivative price okay
+it's obvious as we state it here but
+
+ align:start position:0%
+it's obvious as we state it here but
+ 
+
+ align:start position:0%
+it's obvious as we state it here but
+what this is saying is the call options
+
+ align:start position:0%
+what this is saying is the call options
+ 
+
+ align:start position:0%
+what this is saying is the call options
+often introduces this why are they
+
+ align:start position:0%
+often introduces this why are they
+ 
+
+ align:start position:0%
+often introduces this why are they
+important are the spanning set right of
+
+ align:start position:0%
+important are the spanning set right of
+ 
+
+ align:start position:0%
+important are the spanning set right of
+all derivative prices so calls
+
+ align:start position:0%
+all derivative prices so calls
+ 
+
+ align:start position:0%
+all derivative prices so calls
+span call prices
+
+ align:start position:0%
+span call prices
+ 
+
+ align:start position:0%
+span call prices
+span span
+
+ align:start position:0%
+span span
+ 
+
+ align:start position:0%
+span span
+all all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative prices and they're a
+
+ align:start position:0%
+derivative prices and they're a
+ 
+
+ align:start position:0%
+derivative prices and they're a
+particular type of derivative the ones
+
+ align:start position:0%
+particular type of derivative the ones
+ 
+
+ align:start position:0%
+particular type of derivative the ones
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+determined um exactly by their payout at
+
+ align:start position:0%
+determined um exactly by their payout at
+ 
+
+ align:start position:0%
+determined um exactly by their payout at
+maturity right one can imagine other
+
+ align:start position:0%
+maturity right one can imagine other
+ 
+
+ align:start position:0%
+maturity right one can imagine other
+things that are function of the path or
+
+ align:start position:0%
+things that are function of the path or
+ 
+
+ align:start position:0%
+things that are function of the path or
+whatever but this is particular
+
+ align:start position:0%
+whatever but this is particular
+ 
+
+ align:start position:0%
+whatever but this is particular
+derivative price European derivative
+
+ align:start position:0%
+derivative price European derivative
+ 
+
+ align:start position:0%
+derivative price European derivative
+prices are
+
+ align:start position:0%
+prices are
+ 
+
+ align:start position:0%
+prices are
+determined by calls okay so that's kind
+
+ align:start position:0%
+determined by calls okay so that's kind
+ 
+
+ align:start position:0%
+determined by calls okay so that's kind
+of nice sort of obvious well well it's
+
+ align:start position:0%
+of nice sort of obvious well well it's
+ 
+
+ align:start position:0%
+of nice sort of obvious well well it's
+elegant there's are two ways there are
+
+ align:start position:0%
+elegant there's are two ways there are
+ 
+
+ align:start position:0%
+elegant there's are two ways there are
+two other ways of
+
+ align:start position:0%
+two other ways of
+ 
+
+ align:start position:0%
+two other ways of
+of looking at this though right if I
+
+ align:start position:0%
+of looking at this though right if I
+ 
+
+ align:start position:0%
+of looking at this though right if I
+think about my function
+
+ align:start position:0%
+think about my function
+ 
+
+ align:start position:0%
+think about my function
+G right so think about consider
+
+ align:start position:0%
+G right so think about consider
+ 
+
+ align:start position:0%
+G right so think about consider
+um function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay so that that that determines my
+
+ align:start position:0%
+G okay so that that that determines my
+ 
+
+ align:start position:0%
+G okay so that that that determines my
+um derivative so it determines defines
+
+ align:start position:0%
+um derivative so it determines defines
+ 
+
+ align:start position:0%
+um derivative so it determines defines
+the derivative by its payout at maturity
+
+ align:start position:0%
+the derivative by its payout at maturity
+ 
+
+ align:start position:0%
+the derivative by its payout at maturity
+let's just graph it okay okay so it
+
+ align:start position:0%
+let's just graph it okay okay so it
+ 
+
+ align:start position:0%
+let's just graph it okay okay so it
+might look let's let's assume first it's
+
+ align:start position:0%
+might look let's let's assume first it's
+ 
+
+ align:start position:0%
+might look let's let's assume first it's
+piecewise linear right so it looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like right suppose this is this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay well you can kind of see I can
+
+ align:start position:0%
+G okay well you can kind of see I can
+ 
+
+ align:start position:0%
+G okay well you can kind of see I can
+replicate this portfolio or this option
+
+ align:start position:0%
+replicate this portfolio or this option
+ 
+
+ align:start position:0%
+replicate this portfolio or this option
+by a portfolio of calls in fact a linear
+
+ align:start position:0%
+by a portfolio of calls in fact a linear
+ 
+
+ align:start position:0%
+by a portfolio of calls in fact a linear
+combination of calls right I have no
+
+ align:start position:0%
+combination of calls right I have no
+ 
+
+ align:start position:0%
+combination of calls right I have no
+calls but if this is say
+
+ align:start position:0%
+calls but if this is say
+ 
+
+ align:start position:0%
+calls but if this is say
+K1 this is
+
+ align:start position:0%
+K1 this is
+ 
+
+ align:start position:0%
+K1 this is
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+K3
+
+ align:start position:0%
+K3
+ 
+
+ align:start position:0%
+K3
+K4 K5
+
+ align:start position:0%
+K4 K5
+ 
+
+ align:start position:0%
+K4 K5
+Etc okay you can see what the portfolio
+
+ align:start position:0%
+Etc okay you can see what the portfolio
+ 
+
+ align:start position:0%
+Etc okay you can see what the portfolio
+of calls will be in order to replicate
+
+ align:start position:0%
+of calls will be in order to replicate
+ 
+
+ align:start position:0%
+of calls will be in order to replicate
+this payout at maturity right it'll be a
+
+ align:start position:0%
+this payout at maturity right it'll be a
+ 
+
+ align:start position:0%
+this payout at maturity right it'll be a
+certain amount of calls with strike K1
+
+ align:start position:0%
+certain amount of calls with strike K1
+ 
+
+ align:start position:0%
+certain amount of calls with strike K1
+so that the slope is Right minus a
+
+ align:start position:0%
+so that the slope is Right minus a
+ 
+
+ align:start position:0%
+so that the slope is Right minus a
+certain amount of K2 to get this slope
+
+ align:start position:0%
+certain amount of K2 to get this slope
+ 
+
+ align:start position:0%
+certain amount of K2 to get this slope
+plus a certain amount of K3 minus K4
+
+ align:start position:0%
+plus a certain amount of K3 minus K4
+ 
+
+ align:start position:0%
+plus a certain amount of K3 minus K4
+minus K5 plus k6 Etc so in this case so
+
+ align:start position:0%
+minus K5 plus k6 Etc so in this case so
+ 
+
+ align:start position:0%
+minus K5 plus k6 Etc so in this case so
+a pie wise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear linear
+
+ align:start position:0%
+linear linear
+ 
+
+ align:start position:0%
+linear linear
+G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+replicating
+
+ align:start position:0%
+replicating
+ 
+
+ align:start position:0%
+replicating
+portfolio of
+
+ align:start position:0%
+portfolio of
+ 
+
+ align:start position:0%
+portfolio of
+calls is
+
+ align:start position:0%
+calls is
+ 
+
+ align:start position:0%
+calls is
+obvious
+
+ align:start position:0%
+obvious
+ 
+
+ align:start position:0%
+obvious
+okay all right so if I can replicate the
+
+ align:start position:0%
+okay all right so if I can replicate the
+ 
+
+ align:start position:0%
+okay all right so if I can replicate the
+payout exactly at maturity the price at
+
+ align:start position:0%
+payout exactly at maturity the price at
+ 
+
+ align:start position:0%
+payout exactly at maturity the price at
+time Little T of this derivative
+
+ align:start position:0%
+time Little T of this derivative
+ 
+
+ align:start position:0%
+time Little T of this derivative
+must be the price at Little T of the
+
+ align:start position:0%
+must be the price at Little T of the
+ 
+
+ align:start position:0%
+must be the price at Little T of the
+replicating
+
+ align:start position:0%
+replicating
+ 
+
+ align:start position:0%
+replicating
+portfolio that's actually
+
+ align:start position:0%
+portfolio that's actually
+ 
+
+ align:start position:0%
+portfolio that's actually
+a I do that early on in my class and of
+
+ align:start position:0%
+a I do that early on in my class and of
+ 
+
+ align:start position:0%
+a I do that early on in my class and of
+the 100 people Everyone say okay that's
+
+ align:start position:0%
+the 100 people Everyone say okay that's
+ 
+
+ align:start position:0%
+the 100 people Everyone say okay that's
+that makes sense and someone says does
+
+ align:start position:0%
+that makes sense and someone says does
+ 
+
+ align:start position:0%
+that makes sense and someone says does
+that always have to be the case and it's
+
+ align:start position:0%
+that always have to be the case and it's
+ 
+
+ align:start position:0%
+that always have to be the case and it's
+actually a really really good question
+
+ align:start position:0%
+actually a really really good question
+ 
+
+ align:start position:0%
+actually a really really good question
+now here I was about to just handwave
+
+ align:start position:0%
+now here I was about to just handwave
+ 
+
+ align:start position:0%
+now here I was about to just handwave
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+it is it the case that if I have one
+
+ align:start position:0%
+it is it the case that if I have one
+ 
+
+ align:start position:0%
+it is it the case that if I have one
+derivative contract with this payout at
+
+ align:start position:0%
+derivative contract with this payout at
+ 
+
+ align:start position:0%
+derivative contract with this payout at
+maturity okay and I have a linear
+
+ align:start position:0%
+maturity okay and I have a linear
+ 
+
+ align:start position:0%
+maturity okay and I have a linear
+combination of
+
+ align:start position:0%
+combination of
+ 
+
+ align:start position:0%
+combination of
+calls with the identical payout at
+
+ align:start position:0%
+calls with the identical payout at
+ 
+
+ align:start position:0%
+calls with the identical payout at
+maturity capital T must these two
+
+ align:start position:0%
+maturity capital T must these two
+ 
+
+ align:start position:0%
+maturity capital T must these two
+portfolios have the same value at Little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T well one think so because it's right
+
+ align:start position:0%
+T well one think so because it's right
+ 
+
+ align:start position:0%
+T well one think so because it's right
+they're both the same at maturity so
+
+ align:start position:0%
+they're both the same at maturity so
+ 
+
+ align:start position:0%
+they're both the same at maturity so
+they must both be the same thing they're
+
+ align:start position:0%
+they must both be the same thing they're
+ 
+
+ align:start position:0%
+they must both be the same thing they're
+just constructed differently and the
+
+ align:start position:0%
+just constructed differently and the
+ 
+
+ align:start position:0%
+just constructed differently and the
+Assumption of no Arbitrage which is
+
+ align:start position:0%
+Assumption of no Arbitrage which is
+ 
+
+ align:start position:0%
+Assumption of no Arbitrage which is
+underpins everything in some sense what
+
+ align:start position:0%
+underpins everything in some sense what
+ 
+
+ align:start position:0%
+underpins everything in some sense what
+what we're doing would allow you to say
+
+ align:start position:0%
+what we're doing would allow you to say
+ 
+
+ align:start position:0%
+what we're doing would allow you to say
+yes indeed that is true right in fact
+
+ align:start position:0%
+yes indeed that is true right in fact
+ 
+
+ align:start position:0%
+yes indeed that is true right in fact
+it's actually the fundamental of Finance
+
+ align:start position:0%
+it's actually the fundamental of Finance
+ 
+
+ align:start position:0%
+it's actually the fundamental of Finance
+right if if two things are worth a
+
+ align:start position:0%
+right if if two things are worth a
+ 
+
+ align:start position:0%
+right if if two things are worth a
+dollar in a year's time they got to be
+
+ align:start position:0%
+dollar in a year's time they got to be
+ 
+
+ align:start position:0%
+dollar in a year's time they got to be
+worth the same today
+
+ align:start position:0%
+worth the same today
+ 
+
+ align:start position:0%
+worth the same today
+right that's what we're saying if they
+
+ align:start position:0%
+right that's what we're saying if they
+ 
+
+ align:start position:0%
+right that's what we're saying if they
+you can match the portfolio at T that is
+
+ align:start position:0%
+you can match the portfolio at T that is
+ 
+
+ align:start position:0%
+you can match the portfolio at T that is
+actually the definition
+
+ align:start position:0%
+actually the definition
+ 
+
+ align:start position:0%
+actually the definition
+of it follows immediately from no
+
+ align:start position:0%
+of it follows immediately from no
+ 
+
+ align:start position:0%
+of it follows immediately from no
+Arbitrage what has been
+
+ align:start position:0%
+Arbitrage what has been
+ 
+
+ align:start position:0%
+Arbitrage what has been
+interesting in finance especially since
+
+ align:start position:0%
+interesting in finance especially since
+ 
+
+ align:start position:0%
+interesting in finance especially since
+2008 is that that no arbit this
+
+ align:start position:0%
+2008 is that that no arbit this
+ 
+
+ align:start position:0%
+2008 is that that no arbit this
+assumption has broken down
+
+ align:start position:0%
+assumption has broken down
+ 
+
+ align:start position:0%
+assumption has broken down
+in other words I've hold I can hold a
+
+ align:start position:0%
+in other words I've hold I can hold a
+ 
+
+ align:start position:0%
+in other words I've hold I can hold a
+portfolio of things when aggregated have
+
+ align:start position:0%
+portfolio of things when aggregated have
+ 
+
+ align:start position:0%
+portfolio of things when aggregated have
+exactly this
+
+ align:start position:0%
+exactly this
+ 
+
+ align:start position:0%
+exactly this
+payout against an option with exactly
+
+ align:start position:0%
+payout against an option with exactly
+ 
+
+ align:start position:0%
+payout against an option with exactly
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+payout and be paid for
+
+ align:start position:0%
+payout and be paid for
+ 
+
+ align:start position:0%
+payout and be paid for
+that and this is actually really it's a
+
+ align:start position:0%
+that and this is actually really it's a
+ 
+
+ align:start position:0%
+that and this is actually really it's a
+very it's a very fascinating thing to
+
+ align:start position:0%
+very it's a very fascinating thing to
+ 
+
+ align:start position:0%
+very it's a very fascinating thing to
+think about actually the Dynamics of
+
+ align:start position:0%
+think about actually the Dynamics of
+ 
+
+ align:start position:0%
+think about actually the Dynamics of
+financial markets when Arbitrage can
+
+ align:start position:0%
+financial markets when Arbitrage can
+ 
+
+ align:start position:0%
+financial markets when Arbitrage can
+break down what is the main theme Here
+
+ align:start position:0%
+break down what is the main theme Here
+ 
+
+ align:start position:0%
+break down what is the main theme Here
+is that when capital t is a long way in
+
+ align:start position:0%
+is that when capital t is a long way in
+ 
+
+ align:start position:0%
+is that when capital t is a long way in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+future 10 years 20
+
+ align:start position:0%
+future 10 years 20
+ 
+
+ align:start position:0%
+future 10 years 20
+years there's nothing to stop the price
+
+ align:start position:0%
+years there's nothing to stop the price
+ 
+
+ align:start position:0%
+years there's nothing to stop the price
+of the option in the replicating
+
+ align:start position:0%
+of the option in the replicating
+ 
+
+ align:start position:0%
+of the option in the replicating
+portfolio going arbitrarily wide other
+
+ align:start position:0%
+portfolio going arbitrarily wide other
+ 
+
+ align:start position:0%
+portfolio going arbitrarily wide other
+than people believing that there has to
+
+ align:start position:0%
+than people believing that there has to
+ 
+
+ align:start position:0%
+than people believing that there has to
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal the only way that you can
+
+ align:start position:0%
+equal the only way that you can
+ 
+
+ align:start position:0%
+equal the only way that you can
+guarantee the two things to be equal is
+
+ align:start position:0%
+guarantee the two things to be equal is
+ 
+
+ align:start position:0%
+guarantee the two things to be equal is
+by holding it until capital T right for
+
+ align:start position:0%
+by holding it until capital T right for
+ 
+
+ align:start position:0%
+by holding it until capital T right for
+10 years for 20 years in the
+
+ align:start position:0%
+10 years for 20 years in the
+ 
+
+ align:start position:0%
+10 years for 20 years in the
+meantime those prices can move
+
+ align:start position:0%
+meantime those prices can move
+ 
+
+ align:start position:0%
+meantime those prices can move
+empirically they've been shown to move
+
+ align:start position:0%
+empirically they've been shown to move
+ 
+
+ align:start position:0%
+empirically they've been shown to move
+away from each other right so it's
+
+ align:start position:0%
+away from each other right so it's
+ 
+
+ align:start position:0%
+away from each other right so it's
+actually a of a deep economic question
+
+ align:start position:0%
+actually a of a deep economic question
+ 
+
+ align:start position:0%
+actually a of a deep economic question
+here it's like
+
+ align:start position:0%
+here it's like
+ 
+
+ align:start position:0%
+here it's like
+if if there is the presence of Arbitrage
+
+ align:start position:0%
+if if there is the presence of Arbitrage
+ 
+
+ align:start position:0%
+if if there is the presence of Arbitrage
+in the markets then that Arbitrage can
+
+ align:start position:0%
+in the markets then that Arbitrage can
+ 
+
+ align:start position:0%
+in the markets then that Arbitrage can
+be arbitrarily big I mean if because
+
+ align:start position:0%
+be arbitrarily big I mean if because
+ 
+
+ align:start position:0%
+be arbitrarily big I mean if because
+you're saying there aren't enough
+
+ align:start position:0%
+you're saying there aren't enough
+ 
+
+ align:start position:0%
+you're saying there aren't enough
+there's not enough capital or there's
+
+ align:start position:0%
+there's not enough capital or there's
+ 
+
+ align:start position:0%
+there's not enough capital or there's
+not enough risk capital for people to
+
+ align:start position:0%
+not enough risk capital for people to
+ 
+
+ align:start position:0%
+not enough risk capital for people to
+come in and say okay these two things
+
+ align:start position:0%
+come in and say okay these two things
+ 
+
+ align:start position:0%
+come in and say okay these two things
+have to be worth the same in 10 years
+
+ align:start position:0%
+have to be worth the same in 10 years
+ 
+
+ align:start position:0%
+have to be worth the same in 10 years
+time therefore I'm prepared to
+
+ align:start position:0%
+time therefore I'm prepared to
+ 
+
+ align:start position:0%
+time therefore I'm prepared to
+buy one a dollar cheaper than the other
+
+ align:start position:0%
+buy one a dollar cheaper than the other
+ 
+
+ align:start position:0%
+buy one a dollar cheaper than the other
+it's actually a question really of
+
+ align:start position:0%
+it's actually a question really of
+ 
+
+ align:start position:0%
+it's actually a question really of
+relevance to the Harvard endowment we're
+
+ align:start position:0%
+relevance to the Harvard endowment we're
+ 
+
+ align:start position:0%
+relevance to the Harvard endowment we're
+a long-term investor you say why doesn't
+
+ align:start position:0%
+a long-term investor you say why doesn't
+ 
+
+ align:start position:0%
+a long-term investor you say why doesn't
+the Harvard endowment if these two
+
+ align:start position:0%
+the Harvard endowment if these two
+ 
+
+ align:start position:0%
+the Harvard endowment if these two
+things are a dollar
+
+ align:start position:0%
+things are a dollar
+ 
+
+ align:start position:0%
+things are a dollar
+apart buy the thing that's dollar
+
+ align:start position:0%
+apart buy the thing that's dollar
+ 
+
+ align:start position:0%
+apart buy the thing that's dollar
+cheaper and just hold them for 10 years
+
+ align:start position:0%
+cheaper and just hold them for 10 years
+ 
+
+ align:start position:0%
+cheaper and just hold them for 10 years
+make the dollar Well we'd like to but if
+
+ align:start position:0%
+make the dollar Well we'd like to but if
+ 
+
+ align:start position:0%
+make the dollar Well we'd like to but if
+if we think that they're going to be a
+
+ align:start position:0%
+if we think that they're going to be a
+ 
+
+ align:start position:0%
+if we think that they're going to be a
+dollar apart and they're going to go to
+
+ align:start position:0%
+dollar apart and they're going to go to
+ 
+
+ align:start position:0%
+dollar apart and they're going to go to
+$10 apart we don't want to buy them at a
+
+ align:start position:0%
+$10 apart we don't want to buy them at a
+ 
+
+ align:start position:0%
+$10 apart we don't want to buy them at a
+dollar apart we want to buy them at $10
+
+ align:start position:0%
+dollar apart we want to buy them at $10
+ 
+
+ align:start position:0%
+dollar apart we want to buy them at $10
+apart I mean you know yes we're a
+
+ align:start position:0%
+apart I mean you know yes we're a
+ 
+
+ align:start position:0%
+apart I mean you know yes we're a
+long-term investor but we care about our
+
+ align:start position:0%
+long-term investor but we care about our
+ 
+
+ align:start position:0%
+long-term investor but we care about our
+annual returns or 5year returns suppose
+
+ align:start position:0%
+annual returns or 5year returns suppose
+ 
+
+ align:start position:0%
+annual returns or 5year returns suppose
+this is a 20-year trade this is very
+
+ align:start position:0%
+this is a 20-year trade this is very
+ 
+
+ align:start position:0%
+this is a 20-year trade this is very
+prevalent when these things are 20 years
+
+ align:start position:0%
+prevalent when these things are 20 years
+ 
+
+ align:start position:0%
+prevalent when these things are 20 years
+out anyway it's a whole this is um it's
+
+ align:start position:0%
+out anyway it's a whole this is um it's
+ 
+
+ align:start position:0%
+out anyway it's a whole this is um it's
+a little bit it's a
+
+ align:start position:0%
+a little bit it's a
+ 
+
+ align:start position:0%
+a little bit it's a
+foundational issue it's a thing where I
+
+ align:start position:0%
+foundational issue it's a thing where I
+ 
+
+ align:start position:0%
+foundational issue it's a thing where I
+could shake the foundational
+
+ align:start position:0%
+could shake the foundational
+ 
+
+ align:start position:0%
+could shake the foundational
+underpinnings of quantitative Finance if
+
+ align:start position:0%
+underpinnings of quantitative Finance if
+ 
+
+ align:start position:0%
+underpinnings of quantitative Finance if
+you don't allow this replicating
+
+ align:start position:0%
+you don't allow this replicating
+ 
+
+ align:start position:0%
+you don't allow this replicating
+portfolio to have the same price as the
+
+ align:start position:0%
+portfolio to have the same price as the
+ 
+
+ align:start position:0%
+portfolio to have the same price as the
+actual option but mathematically you can
+
+ align:start position:0%
+actual option but mathematically you can
+ 
+
+ align:start position:0%
+actual option but mathematically you can
+see that we can replicate it certainly
+
+ align:start position:0%
+see that we can replicate it certainly
+ 
+
+ align:start position:0%
+see that we can replicate it certainly
+capital T and therefore the price at
+
+ align:start position:0%
+capital T and therefore the price at
+ 
+
+ align:start position:0%
+capital T and therefore the price at
+time Little T is just the linear
+
+ align:start position:0%
+time Little T is just the linear
+ 
+
+ align:start position:0%
+time Little T is just the linear
+combination of core prices okay so let's
+
+ align:start position:0%
+combination of core prices okay so let's
+ 
+
+ align:start position:0%
+combination of core prices okay so let's
+assume that and then obviously
+
+ align:start position:0%
+assume that and then obviously
+ 
+
+ align:start position:0%
+assume that and then obviously
+continuous function can be arbitrarily
+
+ align:start position:0%
+continuous function can be arbitrarily
+ 
+
+ align:start position:0%
+continuous function can be arbitrarily
+well approximated by piecewise linear
+
+ align:start position:0%
+well approximated by piecewise linear
+ 
+
+ align:start position:0%
+well approximated by piecewise linear
+function function therefore any
+
+ align:start position:0%
+function function therefore any
+ 
+
+ align:start position:0%
+function function therefore any
+function um at
+
+ align:start position:0%
+function um at
+ 
+
+ align:start position:0%
+function um at
+time any function with this of this
+
+ align:start position:0%
+time any function with this of this
+ 
+
+ align:start position:0%
+time any function with this of this
+form uh a derivative with a pair of that
+
+ align:start position:0%
+form uh a derivative with a pair of that
+ 
+
+ align:start position:0%
+form uh a derivative with a pair of that
+form can
+
+ align:start position:0%
+form can
+ 
+
+ align:start position:0%
+form can
+be uh replicated by a portfolio of call
+
+ align:start position:0%
+be uh replicated by a portfolio of call
+ 
+
+ align:start position:0%
+be uh replicated by a portfolio of call
+options so we can sort of handwave to
+
+ align:start position:0%
+options so we can sort of handwave to
+ 
+
+ align:start position:0%
+options so we can sort of handwave to
+kind of say this must be this must be
+
+ align:start position:0%
+kind of say this must be this must be
+ 
+
+ align:start position:0%
+kind of say this must be this must be
+true that calls are spanding set okay
+
+ align:start position:0%
+true that calls are spanding set okay
+ 
+
+ align:start position:0%
+true that calls are spanding set okay
+there's another way to look at it which
+
+ align:start position:0%
+there's another way to look at it which
+ 
+
+ align:start position:0%
+there's another way to look at it which
+is I just like from calculus where we
+
+ align:start position:0%
+is I just like from calculus where we
+ 
+
+ align:start position:0%
+is I just like from calculus where we
+can actually make explicit it what this
+
+ align:start position:0%
+can actually make explicit it what this
+ 
+
+ align:start position:0%
+can actually make explicit it what this
+spanning what this portfolio of C looks
+
+ align:start position:0%
+spanning what this portfolio of C looks
+ 
+
+ align:start position:0%
+spanning what this portfolio of C looks
+like in the arbitrary case okay so let
+
+ align:start position:0%
+like in the arbitrary case okay so let
+ 
+
+ align:start position:0%
+like in the arbitrary case okay so let
+me just uh do that
+
+ align:start position:0%
+me just uh do that
+ 
+
+ align:start position:0%
+me just uh do that
+um so you can sort of see okay there
+
+ align:start position:0%
+um so you can sort of see okay there
+ 
+
+ align:start position:0%
+um so you can sort of see okay there
+must be a linear combination uh by this
+
+ align:start position:0%
+must be a linear combination uh by this
+ 
+
+ align:start position:0%
+must be a linear combination uh by this
+for a piecewise linear therefore in the
+
+ align:start position:0%
+for a piecewise linear therefore in the
+ 
+
+ align:start position:0%
+for a piecewise linear therefore in the
+limit any continuous function must be
+
+ align:start position:0%
+limit any continuous function must be
+ 
+
+ align:start position:0%
+limit any continuous function must be
+able to be replicated by calls how many
+
+ align:start position:0%
+able to be replicated by calls how many
+ 
+
+ align:start position:0%
+able to be replicated by calls how many
+of each well it's actually a very very
+
+ align:start position:0%
+of each well it's actually a very very
+ 
+
+ align:start position:0%
+of each well it's actually a very very
+simple um very very simple result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is as follows and um well let's
+
+ align:start position:0%
+that is as follows and um well let's
+ 
+
+ align:start position:0%
+that is as follows and um well let's
+just write down an exact Taylor series
+
+ align:start position:0%
+just write down an exact Taylor series
+ 
+
+ align:start position:0%
+just write down an exact Taylor series
+okay to the second order so this is um
+
+ align:start position:0%
+okay to the second order so this is um
+ 
+
+ align:start position:0%
+okay to the second order so this is um
+so for any
+
+ align:start position:0%
+so for any
+ 
+
+ align:start position:0%
+so for any
+function with second derivative we let's
+
+ align:start position:0%
+function with second derivative we let's
+ 
+
+ align:start position:0%
+function with second derivative we let's
+just write down the Taylor
+
+ align:start position:0%
+just write down the Taylor
+ 
+
+ align:start position:0%
+just write down the Taylor
+series okay the first two terms and
+
+ align:start position:0%
+series okay the first two terms and
+ 
+
+ align:start position:0%
+series okay the first two terms and
+let's put the second term we just do an
+
+ align:start position:0%
+let's put the second term we just do an
+ 
+
+ align:start position:0%
+let's put the second term we just do an
+exact exact second order term so 0 To
+
+ align:start position:0%
+exact exact second order term so 0 To
+ 
+
+ align:start position:0%
+exact exact second order term so 0 To
+infinity x - c
+
+ align:start position:0%
+infinity x - c
+ 
+
+ align:start position:0%
+infinity x - c
+plus G Prime of C DC C is my dummy
+
+ align:start position:0%
+plus G Prime of C DC C is my dummy
+ 
+
+ align:start position:0%
+plus G Prime of C DC C is my dummy
+variable um actually I've gone to gone
+
+ align:start position:0%
+variable um actually I've gone to gone
+ 
+
+ align:start position:0%
+variable um actually I've gone to gone
+to plus notation here's the max of this
+
+ align:start position:0%
+to plus notation here's the max of this
+ 
+
+ align:start position:0%
+to plus notation here's the max of this
+and zero okay
+
+ align:start position:0%
+and zero okay
+ 
+
+ align:start position:0%
+and zero okay
+so so okay that's a that's an exact
+
+ align:start position:0%
+so so okay that's a that's an exact
+ 
+
+ align:start position:0%
+so so okay that's a that's an exact
+Taylor series true for any it's not an
+
+ align:start position:0%
+Taylor series true for any it's not an
+ 
+
+ align:start position:0%
+Taylor series true for any it's not an
+approximation that's exact you just
+
+ align:start position:0%
+approximation that's exact you just
+ 
+
+ align:start position:0%
+approximation that's exact you just
+integrate the right hand side by Parts
+
+ align:start position:0%
+integrate the right hand side by Parts
+ 
+
+ align:start position:0%
+integrate the right hand side by Parts
+if you want to verify maybe it's obvious
+
+ align:start position:0%
+if you want to verify maybe it's obvious
+ 
+
+ align:start position:0%
+if you want to verify maybe it's obvious
+to you but you know I'm so used to just
+
+ align:start position:0%
+to you but you know I'm so used to just
+ 
+
+ align:start position:0%
+to you but you know I'm so used to just
+doing non-exact tayor theories anyway so
+
+ align:start position:0%
+doing non-exact tayor theories anyway so
+ 
+
+ align:start position:0%
+doing non-exact tayor theories anyway so
+this is the second order so this holds
+
+ align:start position:0%
+this is the second order so this holds
+ 
+
+ align:start position:0%
+this is the second order so this holds
+for any any G exactly um and now I'm
+
+ align:start position:0%
+for any any G exactly um and now I'm
+ 
+
+ align:start position:0%
+for any any G exactly um and now I'm
+just going to make one little change
+
+ align:start position:0%
+just going to make one little change
+ 
+
+ align:start position:0%
+just going to make one little change
+which sort of might make obvious what
+
+ align:start position:0%
+which sort of might make obvious what
+ 
+
+ align:start position:0%
+which sort of might make obvious what
+we're trying to do I'm just going to
+
+ align:start position:0%
+we're trying to do I'm just going to
+ 
+
+ align:start position:0%
+we're trying to do I'm just going to
+take this dummy variable C which we're
+
+ align:start position:0%
+take this dummy variable C which we're
+ 
+
+ align:start position:0%
+take this dummy variable C which we're
+integrating over from Zer to infinity
+
+ align:start position:0%
+integrating over from Zer to infinity
+ 
+
+ align:start position:0%
+integrating over from Zer to infinity
+and just call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K okay certainly do
+
+ align:start position:0%
+K okay certainly do
+ 
+
+ align:start position:0%
+K okay certainly do
+that all right this now looks like the
+
+ align:start position:0%
+that all right this now looks like the
+ 
+
+ align:start position:0%
+that all right this now looks like the
+payout of a
+
+ align:start position:0%
+payout of a
+ 
+
+ align:start position:0%
+payout of a
+call right okay it's payout of the call
+
+ align:start position:0%
+call right okay it's payout of the call
+ 
+
+ align:start position:0%
+call right okay it's payout of the call
+Price now I don't want to be integrating
+
+ align:start position:0%
+Price now I don't want to be integrating
+ 
+
+ align:start position:0%
+Price now I don't want to be integrating
+remember if I want to actually get the
+
+ align:start position:0%
+remember if I want to actually get the
+ 
+
+ align:start position:0%
+remember if I want to actually get the
+call Price I take the expected value of
+
+ align:start position:0%
+call Price I take the expected value of
+ 
+
+ align:start position:0%
+call Price I take the expected value of
+this I integrate x over x with respect
+
+ align:start position:0%
+this I integrate x over x with respect
+ 
+
+ align:start position:0%
+this I integrate x over x with respect
+to its density right this is this is G
+
+ align:start position:0%
+to its density right this is this is G
+ 
+
+ align:start position:0%
+to its density right this is this is G
+of my payout function of X here here I'm
+
+ align:start position:0%
+of my payout function of X here here I'm
+ 
+
+ align:start position:0%
+of my payout function of X here here I'm
+integrating over K so I'm doing
+
+ align:start position:0%
+integrating over K so I'm doing
+ 
+
+ align:start position:0%
+integrating over K so I'm doing
+something a bit different but this is
+
+ align:start position:0%
+something a bit different but this is
+ 
+
+ align:start position:0%
+something a bit different but this is
+the call option payout right so this
+
+ align:start position:0%
+the call option payout right so this
+ 
+
+ align:start position:0%
+the call option payout right so this
+holds it's a
+
+ align:start position:0%
+holds it's a
+ 
+
+ align:start position:0%
+holds it's a
+linear linear equation obviously and of
+
+ align:start position:0%
+linear linear equation obviously and of
+ 
+
+ align:start position:0%
+linear linear equation obviously and of
+course expected expectation is a linear
+
+ align:start position:0%
+course expected expectation is a linear
+ 
+
+ align:start position:0%
+course expected expectation is a linear
+operator so I'm just going to
+
+ align:start position:0%
+operator so I'm just going to
+ 
+
+ align:start position:0%
+operator so I'm just going to
+take well I'm going to do two steps
+
+ align:start position:0%
+take well I'm going to do two steps
+ 
+
+ align:start position:0%
+take well I'm going to do two steps
+first of all I'm just going to replace x
+
+ align:start position:0%
+first of all I'm just going to replace x
+ 
+
+ align:start position:0%
+first of all I'm just going to replace x
+with my random variable s subt okay so
+
+ align:start position:0%
+with my random variable s subt okay so
+ 
+
+ align:start position:0%
+with my random variable s subt okay so
+that's can that I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do this also
+
+ align:start position:0%
+do this also
+ 
+
+ align:start position:0%
+do this also
+holds and formally of course s sub2 is a
+
+ align:start position:0%
+holds and formally of course s sub2 is a
+ 
+
+ align:start position:0%
+holds and formally of course s sub2 is a
+random variable so it's a function from
+
+ align:start position:0%
+random variable so it's a function from
+ 
+
+ align:start position:0%
+random variable so it's a function from
+the sample space of the real line but if
+
+ align:start position:0%
+the sample space of the real line but if
+ 
+
+ align:start position:0%
+the sample space of the real line but if
+this holds for every point on the sample
+
+ align:start position:0%
+this holds for every point on the sample
+ 
+
+ align:start position:0%
+this holds for every point on the sample
+space space right so I can write down
+
+ align:start position:0%
+space space right so I can write down
+ 
+
+ align:start position:0%
+space space right so I can write down
+this this equation between random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables okay here's just the integral
+
+ align:start position:0%
+variables okay here's just the integral
+ 
+
+ align:start position:0%
+variables okay here's just the integral
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+DK right so that's that holds now I'm
+
+ align:start position:0%
+DK right so that's that holds now I'm
+ 
+
+ align:start position:0%
+DK right so that's that holds now I'm
+going to take um the expectation
+
+ align:start position:0%
+going to take um the expectation
+ 
+
+ align:start position:0%
+going to take um the expectation
+operator so take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discounted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expected value
+
+ align:start position:0%
+expected value
+ 
+
+ align:start position:0%
+expected value
+okay so of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side so in other words what is my
+
+ align:start position:0%
+side so in other words what is my
+ 
+
+ align:start position:0%
+side so in other words what is my
+operator de side it looks like Zed
+
+ align:start position:0%
+operator de side it looks like Zed
+ 
+
+ align:start position:0%
+operator de side it looks like Zed
+TT expected value of given
+
+ align:start position:0%
+TT expected value of given
+ 
+
+ align:start position:0%
+TT expected value of given
+St
+
+ align:start position:0%
+St
+ 
+
+ align:start position:0%
+St
+right okay so this one is a discounted
+
+ align:start position:0%
+right okay so this one is a discounted
+ 
+
+ align:start position:0%
+right okay so this one is a discounted
+expected value that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price so this
+
+ align:start position:0%
+price so this
+ 
+
+ align:start position:0%
+price so this
+becomes price of the
+
+ align:start position:0%
+becomes price of the
+ 
+
+ align:start position:0%
+becomes price of the
+derivative with payout at maturity
+
+ align:start position:0%
+derivative with payout at maturity
+ 
+
+ align:start position:0%
+derivative with payout at maturity
+G all right what do we have here well
+
+ align:start position:0%
+G all right what do we have here well
+ 
+
+ align:start position:0%
+G all right what do we have here well
+first we' got a
+
+ align:start position:0%
+first we' got a
+ 
+
+ align:start position:0%
+first we' got a
+constant right so we've got a constant
+
+ align:start position:0%
+constant right so we've got a constant
+ 
+
+ align:start position:0%
+constant right so we've got a constant
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant okay now we got the discounted
+
+ align:start position:0%
+constant okay now we got the discounted
+ 
+
+ align:start position:0%
+constant okay now we got the discounted
+expected stock price okay little bit of
+
+ align:start position:0%
+expected stock price okay little bit of
+ 
+
+ align:start position:0%
+expected stock price okay little bit of
+thought on the terms of the fundamental
+
+ align:start position:0%
+thought on the terms of the fundamental
+ 
+
+ align:start position:0%
+thought on the terms of the fundamental
+theorem will show you that the
+
+ align:start position:0%
+theorem will show you that the
+ 
+
+ align:start position:0%
+theorem will show you that the
+discounted expected stock price under
+
+ align:start position:0%
+discounted expected stock price under
+ 
+
+ align:start position:0%
+discounted expected stock price under
+this operator is the current stock price
+
+ align:start position:0%
+this operator is the current stock price
+ 
+
+ align:start position:0%
+this operator is the current stock price
+it's actually non I hand wa here not
+
+ align:start position:0%
+it's actually non I hand wa here not
+ 
+
+ align:start position:0%
+it's actually non I hand wa here not
+non-trivial but just think of the stock
+
+ align:start position:0%
+non-trivial but just think of the stock
+ 
+
+ align:start position:0%
+non-trivial but just think of the stock
+itself as a derivative right with payout
+
+ align:start position:0%
+itself as a derivative right with payout
+ 
+
+ align:start position:0%
+itself as a derivative right with payout
+s and apply the fundamental theorem okay
+
+ align:start position:0%
+s and apply the fundamental theorem okay
+ 
+
+ align:start position:0%
+s and apply the fundamental theorem okay
+this has to be has to be the case
+
+ align:start position:0%
+this has to be has to be the case
+ 
+
+ align:start position:0%
+this has to be has to be the case
+because the replicating portfolio of the
+
+ align:start position:0%
+because the replicating portfolio of the
+ 
+
+ align:start position:0%
+because the replicating portfolio of the
+stock is just a holding of the
+
+ align:start position:0%
+stock is just a holding of the
+ 
+
+ align:start position:0%
+stock is just a holding of the
+stock okay plus and then we just the
+
+ align:start position:0%
+stock okay plus and then we just the
+ 
+
+ align:start position:0%
+stock okay plus and then we just the
+take the integral so the expectation
+
+ align:start position:0%
+take the integral so the expectation
+ 
+
+ align:start position:0%
+take the integral so the expectation
+inside the
+
+ align:start position:0%
+inside the
+ 
+
+ align:start position:0%
+inside the
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so now I've got discounted
+
+ align:start position:0%
+um okay so now I've got discounted
+ 
+
+ align:start position:0%
+um okay so now I've got discounted
+expected payout of this and the
+
+ align:start position:0%
+expected payout of this and the
+ 
+
+ align:start position:0%
+expected payout of this and the
+discounted expected payout of this is
+
+ align:start position:0%
+discounted expected payout of this is
+ 
+
+ align:start position:0%
+discounted expected payout of this is
+just the call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Price with stri K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so I really like this this
+
+ align:start position:0%
+right okay so I really like this this
+ 
+
+ align:start position:0%
+right okay so I really like this this
+formula I mean in some sense it's it's a
+
+ align:start position:0%
+formula I mean in some sense it's it's a
+ 
+
+ align:start position:0%
+formula I mean in some sense it's it's a
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+nothing tooo complicated about how to
+
+ align:start position:0%
+nothing tooo complicated about how to
+ 
+
+ align:start position:0%
+nothing tooo complicated about how to
+derive it but it says explicitly now how
+
+ align:start position:0%
+derive it but it says explicitly now how
+ 
+
+ align:start position:0%
+derive it but it says explicitly now how
+do I replicate an
+
+ align:start position:0%
+do I replicate an
+ 
+
+ align:start position:0%
+do I replicate an
+arbitrary derivative product with payout
+
+ align:start position:0%
+arbitrary derivative product with payout
+ 
+
+ align:start position:0%
+arbitrary derivative product with payout
+G of X or G of s at maturity well as
+
+ align:start position:0%
+G of X or G of s at maturity well as
+ 
+
+ align:start position:0%
+G of X or G of s at maturity well as
+clear I replicate it by g0 zero coupon
+
+ align:start position:0%
+clear I replicate it by g0 zero coupon
+ 
+
+ align:start position:0%
+clear I replicate it by g0 zero coupon
+bonds okay so I have g0 of zero coupon
+
+ align:start position:0%
+bonds okay so I have g0 of zero coupon
+ 
+
+ align:start position:0%
+bonds okay so I have g0 of zero coupon
+bonds that's this I have G Prime Z Z of
+
+ align:start position:0%
+bonds that's this I have G Prime Z Z of
+ 
+
+ align:start position:0%
+bonds that's this I have G Prime Z Z of
+stock that's this and I have this linear
+
+ align:start position:0%
+stock that's this and I have this linear
+ 
+
+ align:start position:0%
+stock that's this and I have this linear
+combination of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calls okay all right so there is you
+
+ align:start position:0%
+calls okay all right so there is you
+ 
+
+ align:start position:0%
+calls okay all right so there is you
+it's kind of kind of makes sense right
+
+ align:start position:0%
+it's kind of kind of makes sense right
+ 
+
+ align:start position:0%
+it's kind of kind of makes sense right
+you want the zero coupon bond amount is
+
+ align:start position:0%
+you want the zero coupon bond amount is
+ 
+
+ align:start position:0%
+you want the zero coupon bond amount is
+just the intercept of G the number of
+
+ align:start position:0%
+just the intercept of G the number of
+ 
+
+ align:start position:0%
+just the intercept of G the number of
+stocks is just the slope of g at zero
+
+ align:start position:0%
+stocks is just the slope of g at zero
+ 
+
+ align:start position:0%
+stocks is just the slope of g at zero
+and then I have this linear combination
+
+ align:start position:0%
+and then I have this linear combination
+ 
+
+ align:start position:0%
+and then I have this linear combination
+of core prices okay I've just proved
+
+ align:start position:0%
+of core prices okay I've just proved
+ 
+
+ align:start position:0%
+of core prices okay I've just proved
+that by taking this and taking expected
+
+ align:start position:0%
+that by taking this and taking expected
+ 
+
+ align:start position:0%
+that by taking this and taking expected
+values all right
+
+ align:start position:0%
+values all right
+ 
+
+ align:start position:0%
+values all right
+so this is sort of a looking at the uh
+
+ align:start position:0%
+so this is sort of a looking at the uh
+ 
+
+ align:start position:0%
+so this is sort of a looking at the uh
+duality of call option option prices and
+
+ align:start position:0%
+duality of call option option prices and
+ 
+
+ align:start position:0%
+duality of call option option prices and
+probabilities in different ways but then
+
+ align:start position:0%
+probabilities in different ways but then
+ 
+
+ align:start position:0%
+probabilities in different ways but then
+also how calls span everything so the
+
+ align:start position:0%
+also how calls span everything so the
+ 
+
+ align:start position:0%
+also how calls span everything so the
+calls in some sense are the Primitive
+
+ align:start position:0%
+calls in some sense are the Primitive
+ 
+
+ align:start position:0%
+calls in some sense are the Primitive
+primitive information once I know all
+
+ align:start position:0%
+primitive information once I know all
+ 
+
+ align:start position:0%
+primitive information once I know all
+call option prices is I know the
+
+ align:start position:0%
+call option prices is I know the
+ 
+
+ align:start position:0%
+call option prices is I know the
+probability distribution exactly okay so
+
+ align:start position:0%
+probability distribution exactly okay so
+ 
+
+ align:start position:0%
+probability distribution exactly okay so
+there are a couple of um sort of
+
+ align:start position:0%
+there are a couple of um sort of
+ 
+
+ align:start position:0%
+there are a couple of um sort of
+interesting further questions you might
+
+ align:start position:0%
+interesting further questions you might
+ 
+
+ align:start position:0%
+interesting further questions you might
+might want to want to pose we seem to
+
+ align:start position:0%
+might want to want to pose we seem to
+ 
+
+ align:start position:0%
+might want to want to pose we seem to
+have done everything
+
+ align:start position:0%
+have done everything
+ 
+
+ align:start position:0%
+have done everything
+here with regard
+
+ align:start position:0%
+here with regard
+ 
+
+ align:start position:0%
+here with regard
+to uh the distribution at time capital T
+
+ align:start position:0%
+to uh the distribution at time capital T
+ 
+
+ align:start position:0%
+to uh the distribution at time capital T
+and that's true I know all the calls I
+
+ align:start position:0%
+and that's true I know all the calls I
+ 
+
+ align:start position:0%
+and that's true I know all the calls I
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+the distribution at time capital T I
+
+ align:start position:0%
+the distribution at time capital T I
+ 
+
+ align:start position:0%
+the distribution at time capital T I
+know all the calls I know the price of
+
+ align:start position:0%
+know all the calls I know the price of
+ 
+
+ align:start position:0%
+know all the calls I know the price of
+any option with a payout defined slow
+
+ align:start position:0%
+any option with a payout defined slow
+ 
+
+ align:start position:0%
+any option with a payout defined slow
+solely by a function at capital T but I
+
+ align:start position:0%
+solely by a function at capital T but I
+ 
+
+ align:start position:0%
+solely by a function at capital T but I
+said nothing about the path that takes
+
+ align:start position:0%
+said nothing about the path that takes
+ 
+
+ align:start position:0%
+said nothing about the path that takes
+the stock from today until capital T so
+
+ align:start position:0%
+the stock from today until capital T so
+ 
+
+ align:start position:0%
+the stock from today until capital T so
+I just going to leave you with two two
+
+ align:start position:0%
+I just going to leave you with two two
+ 
+
+ align:start position:0%
+I just going to leave you with two two
+things to to think about
+
+ align:start position:0%
+things to to think about
+ 
+
+ align:start position:0%
+things to to think about
+um actually it's one thing to think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about two people thought about it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lot okay it's the following it's the
+
+ align:start position:0%
+lot okay it's the following it's the
+ 
+
+ align:start position:0%
+lot okay it's the following it's the
+following question which now we'll start
+
+ align:start position:0%
+following question which now we'll start
+ 
+
+ align:start position:0%
+following question which now we'll start
+transitioning into stochastic calculus
+
+ align:start position:0%
+transitioning into stochastic calculus
+ 
+
+ align:start position:0%
+transitioning into stochastic calculus
+and stochastic processes a little bit
+
+ align:start position:0%
+and stochastic processes a little bit
+ 
+
+ align:start position:0%
+and stochastic processes a little bit
+okay so we know let's just
+
+ align:start position:0%
+okay so we know let's just
+ 
+
+ align:start position:0%
+okay so we know let's just
+imagine two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times all right so suppose we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know so we know the set of
+
+ align:start position:0%
+know so we know the set of
+ 
+
+ align:start position:0%
+know so we know the set of
+all Co prices with maturity T1
+
+ align:start position:0%
+all Co prices with maturity T1
+ 
+
+ align:start position:0%
+all Co prices with maturity T1
+okay 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K and the set of all Coral prices with
+
+ align:start position:0%
+K and the set of all Coral prices with
+ 
+
+ align:start position:0%
+K and the set of all Coral prices with
+maturity
+
+ align:start position:0%
+maturity
+ 
+
+ align:start position:0%
+maturity
+T2 for
+
+ align:start position:0%
+T2 for
+ 
+
+ align:start position:0%
+T2 for
+K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so then we know the
+
+ align:start position:0%
+okay okay so then we know the
+ 
+
+ align:start position:0%
+okay okay so then we know the
+distribution well there two
+
+ align:start position:0%
+distribution well there two
+ 
+
+ align:start position:0%
+distribution well there two
+distributions we know the distribution
+
+ align:start position:0%
+distributions we know the distribution
+ 
+
+ align:start position:0%
+distributions we know the distribution
+of T1 given us
+
+ align:start position:0%
+of T1 given us
+ 
+
+ align:start position:0%
+of T1 given us
+T and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but do we know the distribution of
+
+ align:start position:0%
+okay but do we know the distribution of
+ 
+
+ align:start position:0%
+okay but do we know the distribution of
+the stock at s at T2 given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T1 right more of a general Point suppose
+
+ align:start position:0%
+T1 right more of a general Point suppose
+ 
+
+ align:start position:0%
+T1 right more of a general Point suppose
+I know this for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T let's put t z here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I know all option prices of all
+
+ align:start position:0%
+okay I know all option prices of all
+ 
+
+ align:start position:0%
+okay I know all option prices of all
+maturities and all strikes
+
+ align:start position:0%
+maturities and all strikes
+ 
+
+ align:start position:0%
+maturities and all strikes
+okay can I
+
+ align:start position:0%
+okay can I
+ 
+
+ align:start position:0%
+okay can I
+determine the stochastic process for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+St I over this time is the underlying
+
+ align:start position:0%
+St I over this time is the underlying
+ 
+
+ align:start position:0%
+St I over this time is the underlying
+stochastic process for the stock price
+
+ align:start position:0%
+stochastic process for the stock price
+ 
+
+ align:start position:0%
+stochastic process for the stock price
+fully determined by knowing all call
+
+ align:start position:0%
+fully determined by knowing all call
+ 
+
+ align:start position:0%
+fully determined by knowing all call
+option prices for all strikes and all
+
+ align:start position:0%
+option prices for all strikes and all
+ 
+
+ align:start position:0%
+option prices for all strikes and all
+maturities okay the marginal
+
+ align:start position:0%
+maturities okay the marginal
+ 
+
+ align:start position:0%
+maturities okay the marginal
+distributions or the conditional
+
+ align:start position:0%
+distributions or the conditional
+ 
+
+ align:start position:0%
+distributions or the conditional
+distributions for all maturities are
+
+ align:start position:0%
+distributions for all maturities are
+ 
+
+ align:start position:0%
+distributions for all maturities are
+determined because we know that
+
+ align:start position:0%
+determined because we know that
+ 
+
+ align:start position:0%
+determined because we know that
+here well you probably see this is a
+
+ align:start position:0%
+here well you probably see this is a
+ 
+
+ align:start position:0%
+here well you probably see this is a
+rephrasing of sort of a finite
+
+ align:start position:0%
+rephrasing of sort of a finite
+ 
+
+ align:start position:0%
+rephrasing of sort of a finite
+dimensional problem from from
+
+ align:start position:0%
+dimensional problem from from
+ 
+
+ align:start position:0%
+dimensional problem from from
+probability the answer is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no and the reason to think about is if I
+
+ align:start position:0%
+no and the reason to think about is if I
+ 
+
+ align:start position:0%
+no and the reason to think about is if I
+know all the I me my my intuition for
+
+ align:start position:0%
+know all the I me my my intuition for
+ 
+
+ align:start position:0%
+know all the I me my my intuition for
+this is if I know all the distributions
+
+ align:start position:0%
+this is if I know all the distributions
+ 
+
+ align:start position:0%
+this is if I know all the distributions
+that yeah think about just a denser and
+
+ align:start position:0%
+that yeah think about just a denser and
+ 
+
+ align:start position:0%
+that yeah think about just a denser and
+denser grid of times that I know the
+
+ align:start position:0%
+denser grid of times that I know the
+ 
+
+ align:start position:0%
+denser grid of times that I know the
+distribution well getting closer and
+
+ align:start position:0%
+distribution well getting closer and
+ 
+
+ align:start position:0%
+distribution well getting closer and
+closer I can still allow the stock to
+
+ align:start position:0%
+closer I can still allow the stock to
+ 
+
+ align:start position:0%
+closer I can still allow the stock to
+flip instantaneously quickly imagine
+
+ align:start position:0%
+flip instantaneously quickly imagine
+ 
+
+ align:start position:0%
+flip instantaneously quickly imagine
+they're all essentially symmetric
+
+ align:start position:0%
+they're all essentially symmetric
+ 
+
+ align:start position:0%
+they're all essentially symmetric
+distributions and they're all roughly
+
+ align:start position:0%
+distributions and they're all roughly
+ 
+
+ align:start position:0%
+distributions and they're all roughly
+the same expanding out I can imagine
+
+ align:start position:0%
+the same expanding out I can imagine
+ 
+
+ align:start position:0%
+the same expanding out I can imagine
+this the stock flipping
+
+ align:start position:0%
+this the stock flipping
+ 
+
+ align:start position:0%
+this the stock flipping
+discontinuously right over an
+
+ align:start position:0%
+discontinuously right over an
+ 
+
+ align:start position:0%
+discontinuously right over an
+arbitrarily small time interval so
+
+ align:start position:0%
+arbitrarily small time interval so
+ 
+
+ align:start position:0%
+arbitrarily small time interval so
+without a constraint on the continuity
+
+ align:start position:0%
+without a constraint on the continuity
+ 
+
+ align:start position:0%
+without a constraint on the continuity
+of this process or mathematical
+
+ align:start position:0%
+of this process or mathematical
+ 
+
+ align:start position:0%
+of this process or mathematical
+constraints on this process you can't
+
+ align:start position:0%
+constraints on this process you can't
+ 
+
+ align:start position:0%
+constraints on this process you can't
+determine the actual process for the
+
+ align:start position:0%
+determine the actual process for the
+ 
+
+ align:start position:0%
+determine the actual process for the
+stock even given all the option prices
+
+ align:start position:0%
+stock even given all the option prices
+ 
+
+ align:start position:0%
+stock even given all the option prices
+called option prices kind of a okay so
+
+ align:start position:0%
+called option prices kind of a okay so
+ 
+
+ align:start position:0%
+called option prices kind of a okay so
+there are two um so Ty Emanuel
+
+ align:start position:0%
+there are two um so Ty Emanuel
+ 
+
+ align:start position:0%
+there are two um so Ty Emanuel
+durman who was at Goldman Sachs now at
+
+ align:start position:0%
+durman who was at Goldman Sachs now at
+ 
+
+ align:start position:0%
+durman who was at Goldman Sachs now at
+Columbia and Bruno dupier who's I think
+
+ align:start position:0%
+Columbia and Bruno dupier who's I think
+ 
+
+ align:start position:0%
+Columbia and Bruno dupier who's I think
+still at Bloomberg this is this is the
+
+ align:start position:0%
+still at Bloomberg this is this is the
+ 
+
+ align:start position:0%
+still at Bloomberg this is this is the
+early 90s basically determine the
+
+ align:start position:0%
+early 90s basically determine the
+ 
+
+ align:start position:0%
+early 90s basically determine the
+conditions that you need and basically
+
+ align:start position:0%
+conditions that you need and basically
+ 
+
+ align:start position:0%
+conditions that you need and basically
+the conditions are this just a stock has
+
+ align:start position:0%
+the conditions are this just a stock has
+ 
+
+ align:start position:0%
+the conditions are this just a stock has
+to be a diffusion process if it is a
+
+ align:start position:0%
+to be a diffusion process if it is a
+ 
+
+ align:start position:0%
+to be a diffusion process if it is a
+diffusion process I as a brown the
+
+ align:start position:0%
+diffusion process I as a brown the
+ 
+
+ align:start position:0%
+diffusion process I as a brown the
+random term as a brownie motion then it
+
+ align:start position:0%
+random term as a brownie motion then it
+ 
+
+ align:start position:0%
+random term as a brownie motion then it
+is actually fully determined okay and
+
+ align:start position:0%
+is actually fully determined okay and
+ 
+
+ align:start position:0%
+is actually fully determined okay and
+there's a really nice elegant elegant
+
+ align:start position:0%
+there's a really nice elegant elegant
+ 
+
+ align:start position:0%
+there's a really nice elegant elegant
+result so this is this is what gets
+
+ align:start position:0%
+result so this is this is what gets
+ 
+
+ align:start position:0%
+result so this is this is what gets
+mathematically quite nice and and a
+
+ align:start position:0%
+mathematically quite nice and and a
+ 
+
+ align:start position:0%
+mathematically quite nice and and a
+little tricky um but there's a
+
+ align:start position:0%
+little tricky um but there's a
+ 
+
+ align:start position:0%
+little tricky um but there's a
+practical um implication of this as well
+
+ align:start position:0%
+practical um implication of this as well
+ 
+
+ align:start position:0%
+practical um implication of this as well
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is in practice ice I will know a finite
+
+ align:start position:0%
+is in practice ice I will know a finite
+ 
+
+ align:start position:0%
+is in practice ice I will know a finite
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+of call options those prices will be
+
+ align:start position:0%
+of call options those prices will be
+ 
+
+ align:start position:0%
+of call options those prices will be
+available to me in the market okay so
+
+ align:start position:0%
+available to me in the market okay so
+ 
+
+ align:start position:0%
+available to me in the market okay so
+they will be given okay so one thing I
+
+ align:start position:0%
+they will be given okay so one thing I
+ 
+
+ align:start position:0%
+they will be given okay so one thing I
+know for sure is that even with a very
+
+ align:start position:0%
+know for sure is that even with a very
+ 
+
+ align:start position:0%
+know for sure is that even with a very
+densely set of call option prices there
+
+ align:start position:0%
+densely set of call option prices there
+ 
+
+ align:start position:0%
+densely set of call option prices there
+will be some other derivative prices
+
+ align:start position:0%
+will be some other derivative prices
+ 
+
+ align:start position:0%
+will be some other derivative prices
+whose price is not exactly determined by
+
+ align:start position:0%
+whose price is not exactly determined by
+ 
+
+ align:start position:0%
+whose price is not exactly determined by
+that set of calls because in particular
+
+ align:start position:0%
+that set of calls because in particular
+ 
+
+ align:start position:0%
+that set of calls because in particular
+I know that the set of R does not
+
+ align:start position:0%
+I know that the set of R does not
+ 
+
+ align:start position:0%
+I know that the set of R does not
+determine the underlying stochastic
+
+ align:start position:0%
+determine the underlying stochastic
+ 
+
+ align:start position:0%
+determine the underlying stochastic
+process even if I knew all of them right
+
+ align:start position:0%
+process even if I knew all of them right
+ 
+
+ align:start position:0%
+process even if I knew all of them right
+so that's a very important thing for
+
+ align:start position:0%
+so that's a very important thing for
+ 
+
+ align:start position:0%
+so that's a very important thing for
+Traders to understand is that even if I
+
+ align:start position:0%
+Traders to understand is that even if I
+ 
+
+ align:start position:0%
+Traders to understand is that even if I
+know a lot of Market information someone
+
+ align:start position:0%
+know a lot of Market information someone
+ 
+
+ align:start position:0%
+know a lot of Market information someone
+gives me here are the prices of a number
+
+ align:start position:0%
+gives me here are the prices of a number
+ 
+
+ align:start position:0%
+gives me here are the prices of a number
+of a large number of European options
+
+ align:start position:0%
+of a large number of European options
+ 
+
+ align:start position:0%
+of a large number of European options
+European call options I can
+
+ align:start position:0%
+European call options I can
+ 
+
+ align:start position:0%
+European call options I can
+trade there may be a complicate a
+
+ align:start position:0%
+trade there may be a complicate a
+ 
+
+ align:start position:0%
+trade there may be a complicate a
+complex or non-standard derivative
+
+ align:start position:0%
+complex or non-standard derivative
+ 
+
+ align:start position:0%
+complex or non-standard derivative
+product whose price is not determined
+
+ align:start position:0%
+product whose price is not determined
+ 
+
+ align:start position:0%
+product whose price is not determined
+uniquely simply by knowing those options
+
+ align:start position:0%
+uniquely simply by knowing those options
+ 
+
+ align:start position:0%
+uniquely simply by knowing those options
+and and that's is one of the challenges
+
+ align:start position:0%
+and and that's is one of the challenges
+ 
+
+ align:start position:0%
+and and that's is one of the challenges
+for some of the the Quant groups
+
+ align:start position:0%
+for some of the the Quant groups
+ 
+
+ align:start position:0%
+for some of the the Quant groups
+so anyway with that that is all I wanted
+
+ align:start position:0%
+so anyway with that that is all I wanted
+ 
+
+ align:start position:0%
+so anyway with that that is all I wanted
+to convey I'm happy to take some
+
+ align:start position:0%
+to convey I'm happy to take some
+ 
+
+ align:start position:0%
+to convey I'm happy to take some
+questions and uh um thank you for um
+
+ align:start position:0%
+questions and uh um thank you for um
+ 
+
+ align:start position:0%
+questions and uh um thank you for um
+thank you for your time and for having
+
+ align:start position:0%
+thank you for your time and for having
+ 
+
+ align:start position:0%
+thank you for your time and for having
+me appreciate
+
+ align:start position:0%
+me appreciate
+ 
+
+ align:start position:0%
+me appreciate
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+it um yeah I had questions about I was
+
+ align:start position:0%
+it um yeah I had questions about I was
+ 
+
+ align:start position:0%
+it um yeah I had questions about I was
+just wondering so you said the call Al
+
+ align:start position:0%
+just wondering so you said the call Al
+ 
+
+ align:start position:0%
+just wondering so you said the call Al
+set of all calls basically spans space
+
+ align:start position:0%
+set of all calls basically spans space
+ 
+
+ align:start position:0%
+set of all calls basically spans space
+of all possible uh payouts right yes so
+
+ align:start position:0%
+of all possible uh payouts right yes so
+ 
+
+ align:start position:0%
+of all possible uh payouts right yes so
+I was just wondering maybe if we could
+
+ align:start position:0%
+I was just wondering maybe if we could
+ 
+
+ align:start position:0%
+I was just wondering maybe if we could
+change and select some other such bases
+
+ align:start position:0%
+change and select some other such bases
+ 
+
+ align:start position:0%
+change and select some other such bases
+for for for spanning it you know instead
+
+ align:start position:0%
+for for for spanning it you know instead
+ 
+
+ align:start position:0%
+for for for spanning it you know instead
+of call maybe some other kind
+
+ align:start position:0%
+of call maybe some other kind
+ 
+
+ align:start position:0%
+of call maybe some other kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+basic payoff that could still spend the
+
+ align:start position:0%
+basic payoff that could still spend the
+ 
+
+ align:start position:0%
+basic payoff that could still spend the
+same thing and maybe it's more easily
+
+ align:start position:0%
+same thing and maybe it's more easily
+ 
+
+ align:start position:0%
+same thing and maybe it's more easily
+tradable or something yeah that's a
+
+ align:start position:0%
+tradable or something yeah that's a
+ 
+
+ align:start position:0%
+tradable or something yeah that's a
+that's a good I mean there must be be
+
+ align:start position:0%
+that's a good I mean there must be be
+ 
+
+ align:start position:0%
+that's a good I mean there must be be
+many if I can uh I mean but this given
+
+ align:start position:0%
+many if I can uh I mean but this given
+ 
+
+ align:start position:0%
+many if I can uh I mean but this given
+that this is the the simplest expansion
+
+ align:start position:0%
+that this is the the simplest expansion
+ 
+
+ align:start position:0%
+that this is the the simplest expansion
+of a the function G an arbitrary
+
+ align:start position:0%
+of a the function G an arbitrary
+ 
+
+ align:start position:0%
+of a the function G an arbitrary
+function G and the second term comes in
+
+ align:start position:0%
+function G and the second term comes in
+ 
+
+ align:start position:0%
+function G and the second term comes in
+with this call
+
+ align:start position:0%
+with this call
+ 
+
+ align:start position:0%
+with this call
+payout right gives us its Elegance right
+
+ align:start position:0%
+payout right gives us its Elegance right
+ 
+
+ align:start position:0%
+payout right gives us its Elegance right
+now of course if I know all the
+
+ align:start position:0%
+now of course if I know all the
+ 
+
+ align:start position:0%
+now of course if I know all the
+digitals I know the cumulative
+
+ align:start position:0%
+digitals I know the cumulative
+ 
+
+ align:start position:0%
+digitals I know the cumulative
+distribution function and therefore I
+
+ align:start position:0%
+distribution function and therefore I
+ 
+
+ align:start position:0%
+distribution function and therefore I
+know the density so I mean digitals do
+
+ align:start position:0%
+know the density so I mean digitals do
+ 
+
+ align:start position:0%
+know the density so I mean digitals do
+the same and in fact you arod de Bru
+
+ align:start position:0%
+the same and in fact you arod de Bru
+ 
+
+ align:start position:0%
+the same and in fact you arod de Bru
+Securities which are sort of building
+
+ align:start position:0%
+Securities which are sort of building
+ 
+
+ align:start position:0%
+Securities which are sort of building
+blocks which is something that pays off
+
+ align:start position:0%
+blocks which is something that pays off
+ 
+
+ align:start position:0%
+blocks which is something that pays off
+one in a particular State sample State
+
+ align:start position:0%
+one in a particular State sample State
+ 
+
+ align:start position:0%
+one in a particular State sample State
+also are building blocks
+
+ align:start position:0%
+also are building blocks
+ 
+
+ align:start position:0%
+also are building blocks
+so yeah yeah I mean some could be you
+
+ align:start position:0%
+so yeah yeah I mean some could be you
+ 
+
+ align:start position:0%
+so yeah yeah I mean some could be you
+can think about an arbitary basis that
+
+ align:start position:0%
+can think about an arbitary basis that
+ 
+
+ align:start position:0%
+can think about an arbitary basis that
+will span an arbitary basis of of
+
+ align:start position:0%
+will span an arbitary basis of of
+ 
+
+ align:start position:0%
+will span an arbitary basis of of
+functions that will span any continuous
+
+ align:start position:0%
+functions that will span any continuous
+ 
+
+ align:start position:0%
+functions that will span any continuous
+function I mean some you could do it in
+
+ align:start position:0%
+function I mean some you could do it in
+ 
+
+ align:start position:0%
+function I mean some you could do it in
+any any polinomial expansion if you have
+
+ align:start position:0%
+any any polinomial expansion if you have
+ 
+
+ align:start position:0%
+any any polinomial expansion if you have
+a price of any of those payouts and I've
+
+ align:start position:0%
+a price of any of those payouts and I've
+ 
+
+ align:start position:0%
+a price of any of those payouts and I've
+got my my spanning set right but this is
+
+ align:start position:0%
+got my my spanning set right but this is
+ 
+
+ align:start position:0%
+got my my spanning set right but this is
+the most elegant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question well because Market is
+
+ align:start position:0%
+question well because Market is
+ 
+
+ align:start position:0%
+question well because Market is
+incomplete so you cannot sort of use
+
+ align:start position:0%
+incomplete so you cannot sort of use
+ 
+
+ align:start position:0%
+incomplete so you cannot sort of use
+core option to rep replicate the stock
+
+ align:start position:0%
+core option to rep replicate the stock
+ 
+
+ align:start position:0%
+core option to rep replicate the stock
+itself um you can use the call option to
+
+ align:start position:0%
+itself um you can use the call option to
+ 
+
+ align:start position:0%
+itself um you can use the call option to
+replicate the
+
+ align:start position:0%
+replicate the
+ 
+
+ align:start position:0%
+replicate the
+stock yeah is it like and as long as you
+
+ align:start position:0%
+stock yeah is it like and as long as you
+ 
+
+ align:start position:0%
+stock yeah is it like and as long as you
+have zero c as you can see from here I
+
+ align:start position:0%
+have zero c as you can see from here I
+ 
+
+ align:start position:0%
+have zero c as you can see from here I
+can just re reorganize anything here to
+
+ align:start position:0%
+can just re reorganize anything here to
+ 
+
+ align:start position:0%
+can just re reorganize anything here to
+zero coupon Bond stock and a set of
+
+ align:start position:0%
+zero coupon Bond stock and a set of
+ 
+
+ align:start position:0%
+zero coupon Bond stock and a set of
+calls will span anything at with
+
+ align:start position:0%
+calls will span anything at with
+ 
+
+ align:start position:0%
+calls will span anything at with
+maturity T what they sort of saying is
+
+ align:start position:0%
+maturity T what they sort of saying is
+ 
+
+ align:start position:0%
+maturity T what they sort of saying is
+if I have this strange process with
+
+ align:start position:0%
+if I have this strange process with
+ 
+
+ align:start position:0%
+if I have this strange process with
+jumps right and flips and
+
+ align:start position:0%
+jumps right and flips and
+ 
+
+ align:start position:0%
+jumps right and flips and
+discontinuities then the market is
+
+ align:start position:0%
+discontinuities then the market is
+ 
+
+ align:start position:0%
+discontinuities then the market is
+incomplete I guess is what what this is
+
+ align:start position:0%
+incomplete I guess is what what this is
+ 
+
+ align:start position:0%
+incomplete I guess is what what this is
+saying okay Alo in is due to that
+
+ align:start position:0%
+saying okay Alo in is due to that
+ 
+
+ align:start position:0%
+saying okay Alo in is due to that
+inconvenience yeah I mean the sense of
+
+ align:start position:0%
+inconvenience yeah I mean the sense of
+ 
+
+ align:start position:0%
+inconvenience yeah I mean the sense of
+most Finance in fact all continuous Time
+
+ align:start position:0%
+most Finance in fact all continuous Time
+ 
+
+ align:start position:0%
+most Finance in fact all continuous Time
+Finance will assume there's some
+
+ align:start position:0%
+Finance will assume there's some
+ 
+
+ align:start position:0%
+Finance will assume there's some
+diffusion process for some process for
+
+ align:start position:0%
+diffusion process for some process for
+ 
+
+ align:start position:0%
+diffusion process for some process for
+the stock which has
+
+ align:start position:0%
+the stock which has
+ 
+
+ align:start position:0%
+the stock which has
+some BR New Motion there's some function
+
+ align:start position:0%
+some BR New Motion there's some function
+ 
+
+ align:start position:0%
+some BR New Motion there's some function
+here and some function for the drift
+
+ align:start position:0%
+here and some function for the drift
+ 
+
+ align:start position:0%
+here and some function for the drift
+term right in that case then all the
+
+ align:start position:0%
+term right in that case then all the
+ 
+
+ align:start position:0%
+term right in that case then all the
+core prices do
+
+ align:start position:0%
+core prices do
+ 
+
+ align:start position:0%
+core prices do
+determine right if you think there's
+
+ align:start position:0%
+determine right if you think there's
+ 
+
+ align:start position:0%
+determine right if you think there's
+some exogenous flipping parameter right
+
+ align:start position:0%
+some exogenous flipping parameter right
+ 
+
+ align:start position:0%
+some exogenous flipping parameter right
+it's that's my intuition for it so there
+
+ align:start position:0%
+it's that's my intuition for it so there
+ 
+
+ align:start position:0%
+it's that's my intuition for it so there
+some that's why this is incomplete so
+
+ align:start position:0%
+some that's why this is incomplete so
+ 
+
+ align:start position:0%
+some that's why this is incomplete so
+this will not determine so in particular
+
+ align:start position:0%
+this will not determine so in particular
+ 
+
+ align:start position:0%
+this will not determine so in particular
+I could know all these core prices then
+
+ align:start position:0%
+I could know all these core prices then
+ 
+
+ align:start position:0%
+I could know all these core prices then
+I could determine a particular
+
+ align:start position:0%
+I could determine a particular
+ 
+
+ align:start position:0%
+I could determine a particular
+derivative product it could be the
+
+ align:start position:0%
+derivative product it could be the
+ 
+
+ align:start position:0%
+derivative product it could be the
+number of times that in an arbitrarily
+
+ align:start position:0%
+number of times that in an arbitrarily
+ 
+
+ align:start position:0%
+number of times that in an arbitrarily
+small interval the stock is you flips
+
+ align:start position:0%
+small interval the stock is you flips
+ 
+
+ align:start position:0%
+small interval the stock is you flips
+this many times I mean there something
+
+ align:start position:0%
+this many times I mean there something
+ 
+
+ align:start position:0%
+this many times I mean there something
+you can create whatever you like for a
+
+ align:start position:0%
+you can create whatever you like for a
+ 
+
+ align:start position:0%
+you can create whatever you like for a
+derivative then it would be incomplete
+
+ align:start position:0%
+derivative then it would be incomplete
+ 
+
+ align:start position:0%
+derivative then it would be incomplete
+with these calls yeah so so in this case
+
+ align:start position:0%
+with these calls yeah so so in this case
+ 
+
+ align:start position:0%
+with these calls yeah so so in this case
+go back to previous question as we just
+
+ align:start position:0%
+go back to previous question as we just
+ 
+
+ align:start position:0%
+go back to previous question as we just
+mentioned the second order derivative of
+
+ align:start position:0%
+mentioned the second order derivative of
+ 
+
+ align:start position:0%
+mentioned the second order derivative of
+call option with respect to strike is ke
+
+ align:start position:0%
+call option with respect to strike is ke
+ 
+
+ align:start position:0%
+call option with respect to strike is ke
+neutral density so in this case it was
+
+ align:start position:0%
+neutral density so in this case it was
+ 
+
+ align:start position:0%
+neutral density so in this case it was
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+that risk neutral density is a
+
+ align:start position:0%
+that risk neutral density is a
+ 
+
+ align:start position:0%
+that risk neutral density is a
+particular instance of that rather it's
+
+ align:start position:0%
+particular instance of that rather it's
+ 
+
+ align:start position:0%
+particular instance of that rather it's
+not uniquely determined right no the
+
+ align:start position:0%
+not uniquely determined right no the
+ 
+
+ align:start position:0%
+not uniquely determined right no the
+risk neutral density is uniquely
+
+ align:start position:0%
+risk neutral density is uniquely
+ 
+
+ align:start position:0%
+risk neutral density is uniquely
+determined the stochastic process for SD
+
+ align:start position:0%
+determined the stochastic process for SD
+ 
+
+ align:start position:0%
+determined the stochastic process for SD
+overall time is not stochastic is not
+
+ align:start position:0%
+overall time is not stochastic is not
+ 
+
+ align:start position:0%
+overall time is not stochastic is not
+uniquely determined so this is uniquely
+
+ align:start position:0%
+uniquely determined so this is uniquely
+ 
+
+ align:start position:0%
+uniquely determined so this is uniquely
+determined oops by by call option
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prices that is uniquely
+
+ align:start position:0%
+prices that is uniquely
+ 
+
+ align:start position:0%
+prices that is uniquely
+determined okay but knowing the
+
+ align:start position:0%
+determined okay but knowing the
+ 
+
+ align:start position:0%
+determined okay but knowing the
+conditional distribution of S capital T
+
+ align:start position:0%
+conditional distribution of S capital T
+ 
+
+ align:start position:0%
+conditional distribution of S capital T
+given s Little T doesn't determine
+
+ align:start position:0%
+given s Little T doesn't determine
+ 
+
+ align:start position:0%
+given s Little T doesn't determine
+the process of the stock price to get
+
+ align:start position:0%
+the process of the stock price to get
+ 
+
+ align:start position:0%
+the process of the stock price to get
+there I can think of infinitely many
+
+ align:start position:0%
+there I can think of infinitely many
+ 
+
+ align:start position:0%
+there I can think of infinitely many
+processes of the stock price that give
+
+ align:start position:0%
+processes of the stock price that give
+ 
+
+ align:start position:0%
+processes of the stock price that give
+rise to this
+
+ align:start position:0%
+rise to this
+ 
+
+ align:start position:0%
+rise to this
+distribution okay that's what's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determined the ter the terminal
+
+ align:start position:0%
+determined the ter the terminal
+ 
+
+ align:start position:0%
+determined the ter the terminal
+distribution is is is uniquely
+
+ align:start position:0%
+distribution is is is uniquely
+ 
+
+ align:start position:0%
+distribution is is is uniquely
+determined by the call option prices
+
+ align:start position:0%
+determined by the call option prices
+ 
+
+ align:start position:0%
+determined by the call option prices
+nothing else so in this case if we take
+
+ align:start position:0%
+nothing else so in this case if we take
+ 
+
+ align:start position:0%
+nothing else so in this case if we take
+real data so we will get a particular
+
+ align:start position:0%
+real data so we will get a particular
+ 
+
+ align:start position:0%
+real data so we will get a particular
+rity for each particular stock that's
+
+ align:start position:0%
+rity for each particular stock that's
+ 
+
+ align:start position:0%
+rity for each particular stock that's
+correct okay that's correct
+
+ align:start position:0%
+correct okay that's correct
+ 
+
+ align:start position:0%
+correct okay that's correct
+all right thank you very much appreciate
+
+ align:start position:0%
+all right thank you very much appreciate
+ 
+
+ align:start position:0%
+all right thank you very much appreciate
+it
\ No newline at end of file
diff --git a/eXUFm8lA5yE.txt b/eXUFm8lA5yE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1362fee573fa18c5541f48945b51724832e95bb
--- /dev/null
+++ b/eXUFm8lA5yE.txt
@@ -0,0 +1,1937 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: And today I'll
+continue with both ideal and
+
+non-ideal, or real,
+liquid mixtures.
+
+And let me just say the reason
+we're in some sense lavishing
+
+so much attention on this topic
+is because, after all,
+
+there's just an enormous amount
+of chemistry that
+
+happens in liquid mixtures.
+
+Awful lot of biology.
+
+Awful lot of just processing
+of stuff.
+
+Distillation and everything
+else.
+
+So there's so much chemistry
+that takes place in liquid
+
+mixtures that it is really
+important to have a sense of
+
+what the free energy and
+chemical potential of each of
+
+the species is doing in there.
+
+Because of course this is what
+directly guides the chemistry
+
+that happens.
+
+So I just want to start by
+finishing up something, a
+
+couple of things, from the
+topics from the last lecture.
+
+One of them is, I derived an
+expression for the lever rule.
+
+And I just wanted to
+make a little more
+
+explicit the result.
+
+It may not have been
+completely clear.
+
+So, I just want to
+go back to that.
+
+We had looked at what happens
+if you start at some
+
+particular point, labeled one,
+and work your way up.
+
+So we're raising the pressure.
+
+So we're in the all gas
+region to start.
+
+All gas region of the
+phase diagram.
+
+This is xB and yB.
+
+The liquid and gas mole
+fractions of B. And the idea
+
+is that here is our
+initial value.
+
+Now we're only in
+the gas phase.
+
+There is no liquid.
+
+So this is yB of one.
+
+There is no xB at this point.
+
+We raise the pressure.
+
+And at some point, depending on
+where we end, we then look
+
+to both coexistence curves to
+determine the compositions of
+
+both the liquid and
+the gas phases.
+
+So when we look out here,
+at the liquid phase.
+
+That gives us xB.
+
+At where I labeled point two, so
+there's two after we raise
+
+the pressure.
+
+We started at one.
+
+And then over here, we look at
+the gas phase coexistence
+
+curve. so there's our yB
+value at two, right?
+
+And I derived an expression for
+the ratio of the number of
+
+moles in the gas and
+liquid phases.
+
+Because the idea here is, let's
+say you're working your
+
+way up on the curve.
+
+If you just barely get to the
+coexistence curve, of course
+
+then you could see how
+much material you've
+
+got in the two phases.
+
+But there's very little
+material still.
+
+You've still got almost
+everything in the gas phase
+
+when you first reach here.
+
+And as you work your way up in
+pressure, you'd have more and
+
+more liquid.
+
+Of course, if you were to just
+keep going, you'd get into the
+
+pure liquid phase.
+
+Typically, though, you might
+stop somewhere in the middle
+
+and have some reasonable amount
+of material in both
+
+phases, and you want
+to find out the
+
+composition in each phase.
+
+And also, want to know
+how much material
+
+there is in each phase.
+
+So the result that I derived
+was n gas at two
+
+over n liquid at two.
+
+The ratio of total moles in
+the gas to the liquid.
+
+What I derived was xA of
+two minus yA of one.
+
+Over yA of one.
+
+Minus yA of two, and I just want
+to, in some sense, finish
+
+up by making the obvious
+substitution, which is, of
+
+course these are
+mole fractions.
+
+So I can just write xA
+is one minus xB.
+
+And yA is one minus yB.
+
+And I just want to put this in
+the terms that are written
+
+here in the phase diagram.
+
+When I got to this result I
+pointed out that therefore you
+
+can use the lever rule.
+
+And I just want to make that
+a little bit more explicit.
+
+So using that relation, then we
+can see that ng of two over
+
+nl of two, total number of moles
+in the gas to the liquid
+
+is, now I'm going to substitute
+in to get yB of one
+
+minus xB of two over yB of
+two minus yB of one.
+
+So all I've done here is
+substitute in these
+
+expressions.
+
+And now I'm going to just
+switch both of these.
+
+And so I'm going to multiply
+both sides by negative one.
+
+So I can write xB of two minus
+yB of one over yB of
+
+one minus yB of two.
+
+So that's the result
+that I want.
+
+Because if I look at the two
+segments of this line, on
+
+either side of the pressure
+value I've reached, then what
+
+I see, of course, is that
+over here I've got xB of
+
+two minus yB of one.
+
+That's this.
+
+And this part is yB of
+one minus yB of two.
+
+That is, it's this part.
+
+And that's here.
+
+And so that's the point, is that
+the ratio of moles in the
+
+gas and liquid phases is just
+given by the two segments of
+
+this on either side.
+
+And so what this allows us to
+see very simply is alright,
+
+I'm going to raise the pressure
+at some point.
+
+And depending on how much
+material I feel like I need to
+
+collect in the new phase, I
+can always determine that
+
+simply by reading off the phase
+diagram what the ratio
+
+of these two segment
+lengths is.
+
+Now what I want to do.
+
+What what we've done mostly is
+just go through these phase
+
+diagrams, see how
+to read them.
+
+How to follow events on them
+as you change pressure in a
+
+diagram like this.
+
+Or change temperature
+in diagrams like I
+
+also showed last time.
+
+Now what I'd like to do is go a
+little bit further and just
+
+look at expressions for the
+chemical potential and the
+
+free energies.
+
+So that we can, a little more
+quantitatively, see
+
+what's going on.
+
+So let's just see what's
+happening.
+
+So let's look at the chemical
+potentials.
+
+In ideal liquid mixtures.
+
+So everything is derived from
+the fact that when we have any
+
+of the constituents in both
+phases, the chemical potential
+
+must be equal in both phases.
+
+Right?
+
+So, we can write for A, mu
+A of the liquid at some
+
+temperature and pressure must
+equal chemical potential of A
+
+for the gas.
+
+That's the partial pressure.
+
+So if we have an ideal gas, and
+certainly if we're going
+
+to assume an ideal liquid
+mixture, we can safely assume
+
+that it's an ideal
+gas above it.
+
+Then we can write
+mu A in the gas.
+
+Is just mu A naught.
+
+That's a function of the
+temperature plus RT
+
+log of pA over p0.
+
+Nothing new here, this is just
+our expression for the
+
+chemical potential in the
+gas, with reference
+
+to a standard potential.
+
+Usually one bar.
+
+At whatever the temperature
+is.
+
+And, of course, this is how it
+varies as the partial pressure
+
+of A in the gas phase varies.
+
+So then we can just write our
+expression for the liquid.
+
+At our temperature and pressure,
+it's given by mu
+
+naught in the gas phase.
+
+Plus RT log pA over p0.
+
+So it's the same thing.
+
+Because I'm just taking
+advantage of this equality.
+
+But of course, this is
+an obvious step,
+
+having written this.
+
+But is a super important step.
+
+That's what allows us to do
+this treatment in such a
+
+straightforward way.
+
+We know a lot about the
+chemical potential of
+
+something in the gas phase.
+
+Since the gas and liquid are in
+equilibrium, therefore we
+
+know the chemical potential
+in the liquid phase too.
+
+So we can rewrite this by
+recognizing that if we just go
+
+to the limit where we only have
+pure liquid A, so pure
+
+liquid A. Well, in that case, mu
+A naught or sorry, mu A in
+
+the liquid phase, mu A star is
+mu A naught in the gas phase.
+
+Plus RT log pA over p0.
+
+And so for the mixture, now all
+I'm going to do is just
+
+add and subtract terms.
+
+So we can write mu A in the
+liquid at T and p, right?
+
+So this is in the case of the
+limit of the pure liquid.
+
+Now we're going to
+the mixture.
+
+So it's just mu A naught plus
+RT log pA star over p0 minus
+
+RT log of pA star over p0.
+
+Wait a minute, lost a term.
+
+Plus RT log pA over p0.
+
+And all I want to do now
+is combine terms.
+
+To write mu A star liquid
+temperature and pressure.
+
+Plus RT log of pA
+over pA star.
+
+So this is a very convenient
+form for it.
+
+And then, of course, we have an
+expression for pA, right?
+
+From Raoult's law. pA
+is just the mole
+
+fraction xA times pA star.
+
+That's just true for
+the ideal mixture.
+
+So now, finally, we can write
+that mu A in the liquid at T
+
+and p is just given
+by mu A star.
+
+So that's for the pure
+liquid at that
+
+temperature and pressure.
+
+Plus RT log of the mole fraction
+of A. So that's a
+
+very simple expression for the
+chemical potential of A. And
+
+of course the analogous
+expression will hold for any
+
+of the constituents.
+
+In an ideal liquid mixture.
+
+By the way, it's convenient
+because it looks just like the
+
+chemical potential in a mixture
+of ideal gases.
+
+Except that we have liquid
+instead of gases, right?
+
+Now, of course, since this is
+a mole fraction, it's always
+
+between zero and one.
+
+That means this is always
+a negative number.
+
+So what that means is that the
+chemical potential in the
+
+solution is always lower than
+the chemical potential of the
+
+pure liquid.
+
+Very important result.
+
+So it has all sorts of
+implications that we'll see.
+
+One of them is osmotic
+pressure.
+
+It means that if I have a
+biological cell, or some
+
+container with a membrane
+through which one of the
+
+constituents might pass.
+
+So in other words, the let's
+say, component A, maybe it's
+
+just water.
+
+It can pass freely, let's say,
+from the outside to the inside
+
+of the cell, or from one side
+to another of a membrane.
+
+And on one side I've just
+got pure water.
+
+And on the other I've got saline
+solution or whatever is
+
+in the cells, right?
+
+What's the water going to
+do in that situation?
+
+What's going to happen?
+
+Anybody know?
+
+So I've got, I just take fresh
+cells and plunk them into pure
+
+water solution.
+
+What happens?
+
+Yeah.
+
+They burst.
+
+Water rushes in.
+
+Because the chemical potential
+is lower inside.
+
+It's always lower in solution
+than outside.
+
+So water rushes in, and
+the membrane expands.
+
+Now, if the membrane is
+strong enough, at some
+
+point it may not burst.
+
+And the pressure might
+start to go up.
+
+Let's say the membrane
+is strong enough to
+
+resist and not burst.
+
+Eventually, the water won't keep
+going in indefinitely.
+
+That's because it won't be at
+the same temperature and
+
+pressure any more.
+
+In particular, the pressure
+will have changed.
+
+So you can build up some high
+pressure, what's called
+
+osmotic pressure.
+
+Because of the fact that at the
+same pressure the chemical
+
+potential of the water's lower
+inside the cell or inside the
+
+enclosure with the membrane.
+
+So water will keep filling.
+
+And at some point the chemical
+potentials will equalize
+
+because of the change
+in pressure.
+
+And at that point there'll be
+an equilibrium established.
+
+We'll see that quantitatively
+a little bit later.
+
+OK.
+
+The other thing to notice is,
+this is familiar from the
+
+expression for a gas mixture.
+
+What drives the gas mixture?
+
+Remember back when we discussed
+mixing of gases and
+
+the fact that they
+would mix at all.
+
+What makes that happen?
+
+What's driving it?
+
+Yeah, it's entropy, right?
+
+And that's what's happening
+here too.
+
+Of course, in the case of the
+ideal liquid mixture, there's
+
+no energetic interaction.
+
+The molecules are
+non-interacting in this case.
+
+But of course, entropy is going
+to want them to mix.
+
+And that's what's
+resulting in the
+
+decrease in chemical potential.
+
+Let's see that a little more
+explicitly by just calculating
+
+out the free energy
+change of mixing.
+
+So, delta G of mixing.
+
+So we're going to start with
+two separated liquids.
+
+And then we'll remove
+the barrier.
+
+And we'll have the two
+mixed together.
+
+So of course, the free energy in
+either case is just the sum
+
+of the number of moles of
+each times the chemical
+
+potential of each.
+
+We have expressions for that.
+
+So starting G1 in this case.
+
+It's n of A, number of
+moles of A. Times
+
+the chemical potential.
+
+So it's xA mu A star
+in the liquid.
+
+Plus nB xB B mu B star
+of the liquid.
+
+Here, G of two.
+
+After we let them mix.
+
+Then it's n -- wait a minute.
+
+It's just n.
+
+I think I've got that wrong
+in the notes also.
+
+Right, it's just a number of
+moles times the chemical
+
+potential in each case.
+
+So it's the number of
+moles times xA.
+
+Times mu A in the mixture.
+
+Plus n xB mu B in the mixture.
+
+But we've just figured it out
+our expressions for mu A and
+
+mu B, our chemical potentials
+of each constituent in the
+
+ideal liquid mixture.
+
+So this is just n xA.
+
+And here's our expression.
+
+And of course these are
+going to cancel.
+
+Let's write it out.
+
+So it's mu A star
+plus RT log xA.
+
+And then, mu B star
+plus RT log xB.
+
+So our delta G of mixing
+is just the difference
+
+between these two.
+
+So it's n RT xA log
+xA plus xB log xB.
+
+Where have you seen
+that before?
+
+Yeah.
+
+The same thing that you had for
+the delta G of mixing for
+
+an ideal gas mixture.
+
+Why?
+
+Because we're not accounting for
+any interactions between
+
+the molecules in either
+of the phases.
+
+And if the molecules aren't
+interacting, it's all entropy.
+
+And the entropy term has the
+same form in either case.
+
+In microscopic terms, it's just
+measuring the fact that
+
+there's more disorder
+in the mixture
+
+than in the pure liquids.
+
+Just the same it was
+in the gas phase.
+
+OK.
+
+We can see this even more
+explicitly if we just recall
+
+that G is V dp minus S dT.
+
+So we can just explicitly
+calculate
+
+the entropy of mixing.
+
+Delta S of mixing is just the
+partial of delta G of mixing.
+
+Negative partial.
+
+With respect to temperature.
+
+At constant pressure.
+
+So it's just minus n R xA
+log xA plus xB log xB.
+
+So that's our entropy
+of mixing.
+
+We can calculate our
+enthalpy of mixing.
+
+Just delta G of mixing.
+
+Plus T delta S of mixing.
+
+But it's immediately apparent
+that these are just going to
+
+cancel when we multiply
+this by T. So there's
+
+no enthalpy of mixing.
+
+Just as we expect when
+there are no
+
+energetic terms involved.
+
+It's all entropy that's
+driving the mixture.
+
+One more detail, it's
+straightforward to see that
+
+there's no volume change.
+
+That is, if we take the
+derivative of delta G of
+
+mixing the partial derivative
+with respect to pressure, at
+
+constant temperature, of course,
+there's no explicit
+
+pressure dependence.
+
+This is zero.
+
+So again, in the ideal liquid
+mixture case, their molecules
+
+aren't interacting.
+
+So there's no reason, when I
+open that barrier, that the
+
+amount of volume they occupy
+altogether is going to change.
+
+Any questions, so far?
+
+OK.
+
+Then, let's move on to
+non-ideal solutions.
+
+By the way, just to return
+briefly to this topic of
+
+osmotic pressure, I just want
+to emphasize that result
+
+didn't need any kind of energy
+of mixing, either, right?
+
+Just from the entropy
+term you would burst
+
+the cell or do whatever.
+
+You end up with a
+larger pressure.
+
+So in other words, if you have
+a situation where, here is A,
+
+pure liquid.
+
+And here is A plus B liquid, so
+mu A star is greater than
+
+mu A. We know that in all cases
+at the same pressure,
+
+the chemical potential of the
+mixture is lower than the
+
+chemical potential of
+the pure liquid.
+
+What's going to happen?
+
+Well, A is going to, oh,
+sorry, A over here is
+
+going to rush in.
+
+It's going to get through
+this, if I've got a
+
+semi-permeable membrane, it's
+permeable to A but not to B.
+
+Common situation, of course.
+
+That's certainly the case
+for the cell membrane.
+
+Water may flow easily in through
+the membrane, but all
+
+of the stuff, all the salt and
+everything else that's inside
+
+the cell generally won't.
+
+So of course A then flows
+through this, what's called a
+
+semi-permeable membrane.
+
+And you'll wind up with either a
+burst membrane, or something
+
+that looks like this.
+
+Where now there is additional
+pressure here.
+
+And you'll have some different
+mole fraction than you started
+
+with before.
+
+Now let's go over to non-ideal
+solutions.
+
+So let's just think
+microscopically for a moment
+
+about how this is
+going to work.
+
+You know, normally, always,
+there are interactions between
+
+the molecules and the liquid.
+
+The liquid is a condensed
+phase.
+
+The molecules are in immediate
+proximity to each other.
+
+So it's very different from the
+gas phase, where it can be
+
+a pretty realistic approximation
+to say, well,
+
+the molecules are essentially
+non-interacting.
+
+The ideal gas law may turn
+out to be a very good
+
+approximation.
+
+In the liquid, really, it's
+never the case that you don't
+
+have interactions.
+
+So if we just sketch that.
+
+If we start with a bunch of
+molecules in A, they're
+
+interacting.
+
+So there's some interaction
+energy.
+
+I'll call it AA, it's the
+interaction between two
+
+molecules of A. In most cases
+it'll be less than zero.
+
+That is, there'd be
+a weak attraction.
+
+Same thing between
+molecules of B.
+
+So that's my situation in
+the separated liquids.
+
+I've got molecules in
+each container.
+
+They're interacting.
+
+There's some energy associated
+with that.
+
+So here's the pure separated
+liquids.
+
+And now, I'll open up
+the barrier and
+
+let the liquids mix.
+
+And now suddenly, of course, A
+and B are going to interact
+
+with each other as well
+as other molecules
+
+of their own kind.
+
+So now, suddenly, there's going
+to be some interaction
+
+energy. uAB.
+
+And very simplistically, we can
+envision that for some of
+
+the molecules, essentially,
+there would be
+
+exchange of this sort.
+
+So, one neighbor of this
+molecule and one neighbor of
+
+this molecule will wind up
+exchanged for some pairs of
+
+molecules with the
+unlike species.
+
+And essentially, likes
+interactions will be replaced
+
+by unlike interactions.
+
+So there's some now change
+in energy involved.
+
+There's a delta u.
+
+And as outlined in this simple
+picture, it's just 2 uAB minus
+
+uAA plus uBB.
+
+Real liquids are very
+complicated.
+
+For liquids with relatively
+simple non-directional
+
+interactions, things like
+organic liquids that might
+
+interact van der Waal's
+interactions.
+
+This might be a reasonable
+starting point.
+
+And in general, if we're going
+to deal with relatively small
+
+deviations from the ideal liquid
+mixture, the ideal
+
+solution, then we can start
+with a model like this.
+
+And this difference is what's
+going to determine how far the
+
+liquid mixture will deviate from
+the ideal solution case.
+
+Of course, we could always just
+write a term like this.
+
+It may or may not be easily
+expressed in this sort of way.
+
+So let's just think about what
+the possibilities are.
+
+Of course, simply,
+there are two.
+
+The sign could be positive
+or negative.
+
+And what that means is, you
+could have situations where
+
+it's positive because basically
+there's an energy of
+
+mixing now in these cases.
+
+If that's not zero, unlike the
+ideal case, now unlike before,
+
+where we just had entropy
+driving the mixture, now
+
+there's an energy of mixing.
+
+Could be positive or negative.
+
+If it's positive, that means
+energetically speaking, the
+
+mixture is unfavorable.
+
+In other words, the
+intermolecular interactions
+
+between like molecules are
+more favorable then the
+
+interactions between the unlike
+
+molecules, in that case.
+
+So, delta u is greater
+than zero.
+
+And our delta H of mixing
+is going to be close
+
+to delta u of mixing.
+
+That is, we're going to figure
+that delta pV is not going to
+
+be something large.
+
+And in that case, we can say
+delta G of mixing is 1/4 n.
+
+And that's only because there
+are 4 species involved here.
+
+Times delta u.
+
+In other words, I'm
+multiplying this
+
+molecular delta u.
+
+This is the change in
+energy for this
+
+collection of four molecules.
+
+Or of four molecular pairs.
+
+Plus the other stuff that we've
+seen for the ideal case.
+
+That is, the entropy term, of
+course, is still there. xA log
+
+xA plus xB log xB.
+
+And because we're treating the
+case where this is positive,
+
+that means this is bigger than
+in the ideal solution case.
+
+So of course there are lots of
+examples of each of these.
+
+In fact, this is the more
+common deviation.
+
+So, and lots of examples.
+
+An easy one is acetone.
+
+And carbon disulfide.
+
+So, if we look at that, and
+just see what the phase
+
+diagram is going to look like,
+it's the following.
+
+So let's start with
+the ideal case.
+
+So I'm going to make B the
+more volatile component.
+
+That is, B is going to be CS2.
+
+So here's p star CS2, which
+I'll call p star B. And
+
+somewhere down here will be p
+star for A, that is, p star
+
+for acetone.
+
+And this is going to be the
+mole fraction of CS2.
+
+Or xB.
+
+So let's start with
+the ideal case.
+
+Not steep enough.
+
+Pretty good.
+
+OK.
+
+And now let's look at
+what's going to
+
+happen in the real mixture.
+
+Well, because we've got a
+positive deviation, what's
+
+going to happen is the mixing
+is unfavorable.
+
+The molecules aren't
+that happy any more
+
+about being in solution.
+
+So what that means is,
+relative to the ideal
+
+solution, they'd rather go
+up into the gas phase.
+
+They don't like being
+in the mixture.
+
+Compared to what they would feel
+in the ideal solution,
+
+where there are no
+interactions.
+
+Because the interactions between
+unlike molecules are
+
+unfavorable.
+
+So what's going to
+happen, then, is
+
+the pressure is higher.
+
+You have deviations from
+the ideal case,
+
+in the total pressure.
+
+And in each of the individual
+partial pressures.
+
+That's the total pressure.
+pA plus pB.
+
+In the ideal case it's
+this straight line.
+
+In the non-ideal case, though,
+it's bigger than
+
+the straight line.
+
+Because more stuff wants to
+get up into the gas phase.
+
+And it's the same for each
+individual component.
+
+So here's pA.
+
+And there's pB.
+
+Any questions?
+
+OK, so it's obvious just from
+looking at this that each of
+
+the partial pressures
+is bigger than it is
+
+in the ideal case.
+
+And so, so is the
+total pressure.
+
+So in other words, if I say
+what's the partial pressure of
+
+CS2, well, since it's not the
+simple ideal case, actually I
+
+don't know what it
+is in general.
+
+It's not easy to calculate a
+priori what it's going to do
+
+all the way across the phase
+diagram for any mole fraction.
+
+What I do know, though, is it's
+bigger than it would be
+
+for the ideal solution case.
+
+In other words, it's bigger than
+x CS2 times p star CS2,
+
+the pressure over the
+pure liquid CS2.
+
+Same for acetone.
+
+It's bigger than x acetone
+p star acetone.
+
+And since both partial pressures
+are bigger, the
+
+total pressure has
+to be bigger.
+
+And of course, that's something
+you can read right
+
+off the diagram as well.
+
+In other words, the total
+pressure is bigger than in the
+
+ideal solution case.
+
+Any questions?
+
+OK.
+
+So the negative case,
+of course,
+
+is exactly the opposite.
+
+So I'll just go through
+it quickly.
+
+So, remember positive deviations
+came, let's put
+
+this back up there.
+
+That came from the case where
+the unlike intermolecular
+
+interactions are not
+as favorable.
+
+There's less attraction, more
+repulsion than in this case.
+
+Of course, there are plenty of
+cases of the opposite sort.
+
+Where the unlike intermolecular
+interactions
+
+are attractive.
+
+More than the interactions
+between like molecules.
+
+And in that case, you have
+the opposite result.
+
+So you can have negative
+deviations.
+
+In other words, delta
+u is less than zero.
+
+Lots of examples.
+
+I've got one in the notes,
+it's just acetone and
+
+chloroform.
+
+So if we get rid of the carbon
+disulfide and put CHCl3 in
+
+there, that's more favorable.
+
+Because there's weak
+hydrogen bonding
+
+between the unlike species.
+
+And not between the
+like species.
+
+So what happens is, you have
+acetone, it's this.
+
+And you have chloroform.
+
+And there's weak hydrogen
+bonding between them.
+
+There's an attraction there.
+
+That doesn't exist
+between either
+
+case of the like molecules.
+
+So now there's stronger
+attraction between them than
+
+there is between molecules
+in either of
+
+the pure liquid cases.
+
+So, of course, you know
+that the opposite
+
+result is going to happen.
+
+In this case, now you mix them
+together, relative to the
+
+ideal solution where there are
+no interactions, now they want
+
+to be together.
+
+They're clinging to each other
+through these hydrogen bonds.
+
+What's that mean for the
+pressure up in the gas phase,
+
+in the solution?
+
+They don't want to go
+there any more.
+
+Stuff in the gas phase now wants
+to condense down into
+
+the liquid.
+
+Because there they have
+favorable interactions.
+
+So that's, of course,
+what'll happen.
+
+And so then you just see the
+opposite sort of deviation
+
+from what I just illustrated
+before.
+
+So then if we look at
+p star CHCl3, where
+
+are these lines going?
+
+Well, may have been
+more artistic.
+
+But I'm afraid I'm going to
+have to go with reality.
+
+p star for acetone.
+
+There's chloroform.
+
+And now our deviation
+is going to be in
+
+the opposite direction.
+
+So all the, both of the partial
+pressures and the
+
+total pressure are going to go
+lower than indicated here.
+
+So p total is now less than,
+for the real case, is less
+
+than p total for
+the ideal case.
+
+In the situation where you have
+attractive interactions
+
+between the unlike molecules.
+
+Any questions?
+
+OK.
+
+Now, in general, this
+is complicated.
+
+To describe quantitatively
+throughout the
+
+entire phase diagram.
+
+The interactions are
+complicated.
+
+Lots of times, molecules
+interact with
+
+more than one neighbor.
+
+So in general, we don't have a
+simple analytical expression
+
+for what the pressure is going
+to do as a function of mole
+
+fraction all the way
+from zero to one.
+
+Of course, we have it
+in very simple form
+
+for the ideal solution.
+
+Because everything's linear.
+
+So it's very simple.
+
+These are replaced by equalities
+and we know
+
+everything.
+
+Now we don't.
+
+But we can at least make some
+progress by looking at the
+
+limiting cases.
+
+Where you have just very
+dilute solutions.
+
+So in that case, you
+can anticipate
+
+what's going to happen.
+
+So let's say we mix A and B.
+And one of them is in very
+
+dilute concentration.
+
+For the other one, for B, most
+molecules of B are just going
+
+to see themselves.
+
+They hardly know that
+you've mixed any
+
+molecules of A in there.
+
+For them, it's pretty much
+an ideal solution.
+
+They think they're in
+an ideal solution.
+
+Which is to say there's an
+entropy change in mixing.
+
+But hardly any of them
+experience interactions with
+
+the unlike molecules.
+
+For the dilute molecules,
+there is a change.
+
+You can't use Raoult's
+law any more.
+
+But at least we can look of
+the slope of the curve and
+
+say, OK, at least in the dilute
+solution case for a
+
+little while it's going
+to be linear.
+
+We can understand it.
+
+We can tabulate it.
+
+So let's look at
+how that works.
+
+Alright.
+
+That limit is something that has
+a name, that's called the
+
+ideal dilute solution.
+
+Not to be confused with
+the ideal solution.
+
+Where both constituents
+follow Raoult's law,
+
+as we've seen before.
+
+So ideal dilute solution.
+
+We're going to just look
+at these limits.
+
+So, if we start with the ideal
+case, so let's imagine we're
+
+going to look at carbon
+disulfide again.
+
+Here's p star CS2, which
+is our pB star.
+
+And this is x CS2, or xB.
+
+OK, well, what happens
+if we've got
+
+almost pure carbon disulfide.
+
+Well, what's going to happen is
+in this limit, like I was
+
+mentioning, up here the CS2
+pretty much sees other CS2.
+
+It thinks it's in an
+ideal solution.
+
+It's going to look like that.
+
+Now, let's go to the
+other limit.
+
+So this is the limit x CS2
+equals xB approaches one.
+
+Raoult's law.
+
+Two, the other limit. x
+CS2 approaches zero.
+
+We're down here.
+
+So it's definitely not
+going to be the same.
+
+Because now, every molecule,
+every CS2 molecule, is
+
+completely surrounded
+by acetone.
+
+So they all feel the
+energy of mixing.
+
+Because there are hardly
+any of them there.
+
+So every one of them is, it's
+very rare for one to find a
+
+neighbor of its own kind.
+
+And this is a case where there's
+a positive deviation
+
+from ideality.
+
+That is, the interactions
+are less favorable
+
+between unlike species.
+
+So, it's up here.
+
+Doesn't like that.
+
+It says, get me out here, I'd
+much rather be in the gas
+
+phase, compared to the ideal
+case, then surrounded by all
+
+these acetone molecules,
+right?
+
+So that's what'll happen.
+
+And now it's up to the artist.
+
+But in some way there's
+going to be a set
+
+of values in between.
+
+And the ideal dilute solution by
+itself isn't going to tell
+
+us about that.
+
+It's telling us about
+the two limits.
+
+Now, if we follow this,
+and I can see I'm
+
+going to be in trouble.
+
+But I can do a little creative
+bending of the line here.
+
+If I follow this slope
+up to here,
+
+it'll intercept somewhere.
+
+That has a name.
+
+It's called the Henry's
+law constant.
+
+I can write it as
+K CS2, or KB.
+
+So the point is, that at
+least for some range of
+
+concentrations, the variation
+is linear.
+
+And what that means is, if
+I know this Henry's law
+
+constant, for CS2 mixed with
+acetone specifically, it would
+
+be different.
+
+If it's mixed with something
+else, right?
+
+Other kinds of interactions with
+different energies will
+
+have a different slope.
+
+But if I know that number,
+it's still useful.
+
+Because at least for that pair
+of constituents, I know the
+
+dependents for some range
+of concentrations.
+
+So this is Henry's
+law. p CS --
+
+Oops, CS2 is x CS2
+times K CS2.
+
+Not quite as convenient
+as Raoult's law.
+
+That number, I don't need
+to know what the other
+
+constituent is.
+
+It's just a property of CS2.
+
+It depends on the temperature,
+but not the other member of
+
+the mixture.
+
+This one does, but still there's
+at least a substantial
+
+number of these things
+tabulated.
+
+Especially for important
+mixtures.
+
+So it becomes useful for
+dilute solutions.
+
+And there's an awful
+lot of chemistry.
+
+There's an awful lot of biology
+that happens in
+
+relatively dilute solutions.
+
+OK.
+
+I'll leave it at this point.
+
+Next time we'll look at the
+total phase diagram, just like
+
+we did last time looking at
+both the liquid and gas
+
+coexistence curves, and seeing
+what the behavior is as a
+
+function of mole fractions.
+
+And we'll talk about
+distillation and so forth in
+
+non-ideal liquids.
\ No newline at end of file
diff --git a/fQcJNoe-q-s.txt b/fQcJNoe-q-s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d5a7b9d398f546608695745fbce2408fe463fa58
--- /dev/null
+++ b/fQcJNoe-q-s.txt
@@ -0,0 +1,8123 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi my name is Harry balakrishnan I'm
+
+ align:start position:0%
+hi my name is Harry balakrishnan I'm
+ 
+
+ align:start position:0%
+hi my name is Harry balakrishnan I'm
+your replacement professor you guys know
+
+ align:start position:0%
+your replacement professor you guys know
+ 
+
+ align:start position:0%
+your replacement professor you guys know
+what replacement referees so on the
+
+ align:start position:0%
+what replacement referees so on the
+ 
+
+ align:start position:0%
+what replacement referees so on the
+other professor in the class and I
+
+ align:start position:0%
+other professor in the class and I
+ 
+
+ align:start position:0%
+other professor in the class and I
+generally not with materials that's a
+
+ align:start position:0%
+generally not with materials that's a
+ 
+
+ align:start position:0%
+generally not with materials that's a
+little bit later but what we thought
+
+ align:start position:0%
+little bit later but what we thought
+ 
+
+ align:start position:0%
+little bit later but what we thought
+we'd do today is to talk about this
+
+ align:start position:0%
+we'd do today is to talk about this
+ 
+
+ align:start position:0%
+we'd do today is to talk about this
+audio com library so before I get
+
+ align:start position:0%
+audio com library so before I get
+ 
+
+ align:start position:0%
+audio com library so before I get
+started and show you how to use this and
+
+ align:start position:0%
+started and show you how to use this and
+ 
+
+ align:start position:0%
+started and show you how to use this and
+all the different ways in which things
+
+ align:start position:0%
+all the different ways in which things
+ 
+
+ align:start position:0%
+all the different ways in which things
+will break because it's something in the
+
+ align:start position:0%
+will break because it's something in the
+ 
+
+ align:start position:0%
+will break because it's something in the
+real world let me see a show of hands
+
+ align:start position:0%
+real world let me see a show of hands
+ 
+
+ align:start position:0%
+real world let me see a show of hands
+how many people have tried to install or
+
+ align:start position:0%
+how many people have tried to install or
+ 
+
+ align:start position:0%
+how many people have tried to install or
+run or do something with it okay how
+
+ align:start position:0%
+run or do something with it okay how
+ 
+
+ align:start position:0%
+run or do something with it okay how
+many people have sort of don't have any
+
+ align:start position:0%
+many people have sort of don't have any
+ 
+
+ align:start position:0%
+many people have sort of don't have any
+idea what I'm talking about okay and how
+
+ align:start position:0%
+idea what I'm talking about okay and how
+ 
+
+ align:start position:0%
+idea what I'm talking about okay and how
+many people have managed to get
+
+ align:start position:0%
+many people have managed to get
+ 
+
+ align:start position:0%
+many people have managed to get
+something to work by work it's if you
+
+ align:start position:0%
+something to work by work it's if you
+ 
+
+ align:start position:0%
+something to work by work it's if you
+got the preamble to decode it means
+
+ align:start position:0%
+got the preamble to decode it means
+ 
+
+ align:start position:0%
+got the preamble to decode it means
+something is working alright how many
+
+ align:start position:0%
+something is working alright how many
+ 
+
+ align:start position:0%
+something is working alright how many
+people would got nothing okay well it'll
+
+ align:start position:0%
+people would got nothing okay well it'll
+ 
+
+ align:start position:0%
+people would got nothing okay well it'll
+all work it's just a question of
+
+ align:start position:0%
+all work it's just a question of
+ 
+
+ align:start position:0%
+all work it's just a question of
+figuring out how to get it to work okay
+
+ align:start position:0%
+figuring out how to get it to work okay
+ 
+
+ align:start position:0%
+figuring out how to get it to work okay
+so here's the story in order to do
+
+ align:start position:0%
+so here's the story in order to do
+ 
+
+ align:start position:0%
+so here's the story in order to do
+something practical with all the theory
+
+ align:start position:0%
+something practical with all the theory
+ 
+
+ align:start position:0%
+something practical with all the theory
+that you're learning it's important to
+
+ align:start position:0%
+that you're learning it's important to
+ 
+
+ align:start position:0%
+that you're learning it's important to
+try to implement something now the
+
+ align:start position:0%
+try to implement something now the
+ 
+
+ align:start position:0%
+try to implement something now the
+theory we're learning applies to a wide
+
+ align:start position:0%
+theory we're learning applies to a wide
+ 
+
+ align:start position:0%
+theory we're learning applies to a wide
+range of communication channels it
+
+ align:start position:0%
+range of communication channels it
+ 
+
+ align:start position:0%
+range of communication channels it
+applies to radio it applies to wired
+
+ align:start position:0%
+applies to radio it applies to wired
+ 
+
+ align:start position:0%
+applies to radio it applies to wired
+links you know ethernet or cables it
+
+ align:start position:0%
+links you know ethernet or cables it
+ 
+
+ align:start position:0%
+links you know ethernet or cables it
+applies to optical links like infrared
+
+ align:start position:0%
+applies to optical links like infrared
+ 
+
+ align:start position:0%
+applies to optical links like infrared
+or you know free space optical links and
+
+ align:start position:0%
+or you know free space optical links and
+ 
+
+ align:start position:0%
+or you know free space optical links and
+it also applies to audio
+
+ align:start position:0%
+it also applies to audio
+ 
+
+ align:start position:0%
+it also applies to audio
+and we've decided to use audio as the
+
+ align:start position:0%
+and we've decided to use audio as the
+ 
+
+ align:start position:0%
+and we've decided to use audio as the
+vehicle to bring these ideas into the
+
+ align:start position:0%
+vehicle to bring these ideas into the
+ 
+
+ align:start position:0%
+vehicle to bring these ideas into the
+lab for two reasons the first and most
+
+ align:start position:0%
+lab for two reasons the first and most
+ 
+
+ align:start position:0%
+lab for two reasons the first and most
+important reason is that it turns out
+
+ align:start position:0%
+important reason is that it turns out
+ 
+
+ align:start position:0%
+important reason is that it turns out
+it's the easiest piece of hardware it's
+
+ align:start position:0%
+it's the easiest piece of hardware it's
+ 
+
+ align:start position:0%
+it's the easiest piece of hardware it's
+the most convenient piece of hardware
+
+ align:start position:0%
+the most convenient piece of hardware
+ 
+
+ align:start position:0%
+the most convenient piece of hardware
+that everybody has access to all you
+
+ align:start position:0%
+that everybody has access to all you
+ 
+
+ align:start position:0%
+that everybody has access to all you
+actually need is a computer with a
+
+ align:start position:0%
+actually need is a computer with a
+ 
+
+ align:start position:0%
+actually need is a computer with a
+microphone and speaker and in fact I
+
+ align:start position:0%
+microphone and speaker and in fact I
+ 
+
+ align:start position:0%
+microphone and speaker and in fact I
+would imagine that in the next couple of
+
+ align:start position:0%
+would imagine that in the next couple of
+ 
+
+ align:start position:0%
+would imagine that in the next couple of
+years it will run on this thing too so
+
+ align:start position:0%
+years it will run on this thing too so
+ 
+
+ align:start position:0%
+years it will run on this thing too so
+you could write apps on this that will
+
+ align:start position:0%
+you could write apps on this that will
+ 
+
+ align:start position:0%
+you could write apps on this that will
+make this work already we have stopped
+
+ align:start position:0%
+make this work already we have stopped
+ 
+
+ align:start position:0%
+make this work already we have stopped
+working on on an Android and iPhone to
+
+ align:start position:0%
+working on on an Android and iPhone to
+ 
+
+ align:start position:0%
+working on on an Android and iPhone to
+do much of the stuff so the first one is
+
+ align:start position:0%
+do much of the stuff so the first one is
+ 
+
+ align:start position:0%
+do much of the stuff so the first one is
+just it's everywhere everybody has it
+
+ align:start position:0%
+just it's everywhere everybody has it
+ 
+
+ align:start position:0%
+just it's everywhere everybody has it
+you don't have to do anything special to
+
+ align:start position:0%
+you don't have to do anything special to
+ 
+
+ align:start position:0%
+you don't have to do anything special to
+get it the second is that it turns out
+
+ align:start position:0%
+get it the second is that it turns out
+ 
+
+ align:start position:0%
+get it the second is that it turns out
+it actually illustrates many of the
+
+ align:start position:0%
+it actually illustrates many of the
+ 
+
+ align:start position:0%
+it actually illustrates many of the
+problems that we're talking about noise
+
+ align:start position:0%
+problems that we're talking about noise
+ 
+
+ align:start position:0%
+problems that we're talking about noise
+and this idea of how linear
+
+ align:start position:0%
+and this idea of how linear
+ 
+
+ align:start position:0%
+and this idea of how linear
+time-invariant systems an understanding
+
+ align:start position:0%
+time-invariant systems an understanding
+ 
+
+ align:start position:0%
+time-invariant systems an understanding
+of linear time-invariant systems applies
+
+ align:start position:0%
+of linear time-invariant systems applies
+ 
+
+ align:start position:0%
+of linear time-invariant systems applies
+to what we're trying to be billed to
+
+ align:start position:0%
+to what we're trying to be billed to
+ 
+
+ align:start position:0%
+to what we're trying to be billed to
+communication channels and how you use
+
+ align:start position:0%
+communication channels and how you use
+ 
+
+ align:start position:0%
+communication channels and how you use
+the ideas you've learned about LTI
+
+ align:start position:0%
+the ideas you've learned about LTI
+ 
+
+ align:start position:0%
+the ideas you've learned about LTI
+systems to improve the performance of
+
+ align:start position:0%
+systems to improve the performance of
+ 
+
+ align:start position:0%
+systems to improve the performance of
+whatever you implement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to restrict myself to this
+
+ align:start position:0%
+I'm going to restrict myself to this
+ 
+
+ align:start position:0%
+I'm going to restrict myself to this
+audio comm system but it you know these
+
+ align:start position:0%
+audio comm system but it you know these
+ 
+
+ align:start position:0%
+audio comm system but it you know these
+ideas apply across the board so let me
+
+ align:start position:0%
+ideas apply across the board so let me
+ 
+
+ align:start position:0%
+ideas apply across the board so let me
+tell you how this system does its job
+
+ align:start position:0%
+tell you how this system does its job
+ 
+
+ align:start position:0%
+tell you how this system does its job
+and this goes back to what Professor
+
+ align:start position:0%
+and this goes back to what Professor
+ 
+
+ align:start position:0%
+and this goes back to what Professor
+Fergie's was telling you before
+
+ align:start position:0%
+Fergie's was telling you before
+ 
+
+ align:start position:0%
+Fergie's was telling you before
+ultimately all of the information is
+
+ align:start position:0%
+ultimately all of the information is
+ 
+
+ align:start position:0%
+ultimately all of the information is
+modulated on top of a carrier and a
+
+ align:start position:0%
+modulated on top of a carrier and a
+ 
+
+ align:start position:0%
+modulated on top of a carrier and a
+carriers as you as you know a sinusoid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so time goes this way and this is the
+
+ align:start position:0%
+so time goes this way and this is the
+ 
+
+ align:start position:0%
+so time goes this way and this is the
+amplitude or which we also call the
+
+ align:start position:0%
+amplitude or which we also call the
+ 
+
+ align:start position:0%
+amplitude or which we also call the
+voltage such a time varying waveform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what your receiver is capable so the
+
+ align:start position:0%
+what your receiver is capable so the
+ 
+
+ align:start position:0%
+what your receiver is capable so the
+transmitter is capable of generating
+
+ align:start position:0%
+transmitter is capable of generating
+ 
+
+ align:start position:0%
+transmitter is capable of generating
+these kinds of waveforms at different
+
+ align:start position:0%
+these kinds of waveforms at different
+ 
+
+ align:start position:0%
+these kinds of waveforms at different
+frequencies so this might be for example
+
+ align:start position:0%
+frequencies so this might be for example
+ 
+
+ align:start position:0%
+frequencies so this might be for example
+1 kilohertz a 1000 Hertz we can go up to
+
+ align:start position:0%
+1 kilohertz a 1000 Hertz we can go up to
+ 
+
+ align:start position:0%
+1 kilohertz a 1000 Hertz we can go up to
+you know I've got mine to work up to 20
+
+ align:start position:0%
+you know I've got mine to work up to 20
+ 
+
+ align:start position:0%
+you know I've got mine to work up to 20
+kilohertz which is fortunate because I
+
+ align:start position:0%
+kilohertz which is fortunate because I
+ 
+
+ align:start position:0%
+kilohertz which is fortunate because I
+can't hear it and you know it does a
+
+ align:start position:0%
+can't hear it and you know it does a
+ 
+
+ align:start position:0%
+can't hear it and you know it does a
+wide range of frequencies this could
+
+ align:start position:0%
+wide range of frequencies this could
+ 
+
+ align:start position:0%
+wide range of frequencies this could
+work in in the lab I found that things
+
+ align:start position:0%
+work in in the lab I found that things
+ 
+
+ align:start position:0%
+work in in the lab I found that things
+tend to work between 1 kilohertz and
+
+ align:start position:0%
+tend to work between 1 kilohertz and
+ 
+
+ align:start position:0%
+tend to work between 1 kilohertz and
+only about three or four kilos so that's
+
+ align:start position:0%
+only about three or four kilos so that's
+ 
+
+ align:start position:0%
+only about three or four kilos so that's
+the range when talking about so you pick
+
+ align:start position:0%
+the range when talking about so you pick
+ 
+
+ align:start position:0%
+the range when talking about so you pick
+a carrier wave form for your
+
+ align:start position:0%
+a carrier wave form for your
+ 
+
+ align:start position:0%
+a carrier wave form for your
+transmission what the receivers capable
+
+ align:start position:0%
+transmission what the receivers capable
+ 
+
+ align:start position:0%
+transmission what the receivers capable
+of doing is it's a digital receiver so
+
+ align:start position:0%
+of doing is it's a digital receiver so
+ 
+
+ align:start position:0%
+of doing is it's a digital receiver so
+what it's capable of doing is receiving
+
+ align:start position:0%
+what it's capable of doing is receiving
+ 
+
+ align:start position:0%
+what it's capable of doing is receiving
+data receiving signals from the sound
+
+ align:start position:0%
+data receiving signals from the sound
+ 
+
+ align:start position:0%
+data receiving signals from the sound
+card at a certain number of samples per
+
+ align:start position:0%
+card at a certain number of samples per
+ 
+
+ align:start position:0%
+card at a certain number of samples per
+second we're going to call that the
+
+ align:start position:0%
+second we're going to call that the
+ 
+
+ align:start position:0%
+second we're going to call that the
+sampling rate we've used the term we've
+
+ align:start position:0%
+sampling rate we've used the term we've
+ 
+
+ align:start position:0%
+sampling rate we've used the term we've
+used the storm before the sampling rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be anything by default in the system
+
+ align:start position:0%
+can be anything by default in the system
+ 
+
+ align:start position:0%
+can be anything by default in the system
+we pick the highest possible sampling
+
+ align:start position:0%
+we pick the highest possible sampling
+ 
+
+ align:start position:0%
+we pick the highest possible sampling
+rate of 48 kilohertz in some cases you
+
+ align:start position:0%
+rate of 48 kilohertz in some cases you
+ 
+
+ align:start position:0%
+rate of 48 kilohertz in some cases you
+might have to yank it down you might
+
+ align:start position:0%
+might have to yank it down you might
+ 
+
+ align:start position:0%
+might have to yank it down you might
+have to go as low as 8 kilohertz but 48
+
+ align:start position:0%
+have to go as low as 8 kilohertz but 48
+ 
+
+ align:start position:0%
+have to go as low as 8 kilohertz but 48
+kilohertz seems to work in the lab it
+
+ align:start position:0%
+kilohertz seems to work in the lab it
+ 
+
+ align:start position:0%
+kilohertz seems to work in the lab it
+works on a bunch of machines that I've
+
+ align:start position:0%
+works on a bunch of machines that I've
+ 
+
+ align:start position:0%
+works on a bunch of machines that I've
+looked at so we have tokens we have the
+
+ align:start position:0%
+looked at so we have tokens we have the
+ 
+
+ align:start position:0%
+looked at so we have tokens we have the
+1 kilohertz which is the carrier wave
+
+ align:start position:0%
+1 kilohertz which is the carrier wave
+ 
+
+ align:start position:0%
+1 kilohertz which is the carrier wave
+form will use the notation MC and we can
+
+ align:start position:0%
+form will use the notation MC and we can
+ 
+
+ align:start position:0%
+form will use the notation MC and we can
+receive samples at 48 kilohertz and
+
+ align:start position:0%
+receive samples at 48 kilohertz and
+ 
+
+ align:start position:0%
+receive samples at 48 kilohertz and
+that's how the transmitter also when it
+
+ align:start position:0%
+that's how the transmitter also when it
+ 
+
+ align:start position:0%
+that's how the transmitter also when it
+wants to send stuff only on the air it
+
+ align:start position:0%
+wants to send stuff only on the air it
+ 
+
+ align:start position:0%
+wants to send stuff only on the air it
+picks a sampling rate it's going to pick
+
+ align:start position:0%
+picks a sampling rate it's going to pick
+ 
+
+ align:start position:0%
+picks a sampling rate it's going to pick
+48 kilohertz the receiver and sender
+
+ align:start position:0%
+48 kilohertz the receiver and sender
+ 
+
+ align:start position:0%
+48 kilohertz the receiver and sender
+need to agree on the sampling rate what
+
+ align:start position:0%
+need to agree on the sampling rate what
+ 
+
+ align:start position:0%
+need to agree on the sampling rate what
+happens then is very straightforward if
+
+ align:start position:0%
+happens then is very straightforward if
+ 
+
+ align:start position:0%
+happens then is very straightforward if
+you have a carrier wave form that looks
+
+ align:start position:0%
+you have a carrier wave form that looks
+ 
+
+ align:start position:0%
+you have a carrier wave form that looks
+like this what 1 kilohertz means is that
+
+ align:start position:0%
+like this what 1 kilohertz means is that
+ 
+
+ align:start position:0%
+like this what 1 kilohertz means is that
+we do this cycle a thousand times a
+
+ align:start position:0%
+we do this cycle a thousand times a
+ 
+
+ align:start position:0%
+we do this cycle a thousand times a
+second which means that one period of
+
+ align:start position:0%
+second which means that one period of
+ 
+
+ align:start position:0%
+second which means that one period of
+the cycle is one thousandth of a second
+
+ align:start position:0%
+the cycle is one thousandth of a second
+ 
+
+ align:start position:0%
+the cycle is one thousandth of a second
+or one millisecond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if I sample this at 48,000 or 48
+
+ align:start position:0%
+now if I sample this at 48,000 or 48
+ 
+
+ align:start position:0%
+now if I sample this at 48,000 or 48
+kilohertz or 48,000 times a second in
+
+ align:start position:0%
+kilohertz or 48,000 times a second in
+ 
+
+ align:start position:0%
+kilohertz or 48,000 times a second in
+one of these periods how many samples do
+
+ align:start position:0%
+one of these periods how many samples do
+ 
+
+ align:start position:0%
+one of these periods how many samples do
+I get this is where you have to tell me
+
+ align:start position:0%
+I get this is where you have to tell me
+ 
+
+ align:start position:0%
+I get this is where you have to tell me
+something shoot sorry 48 great so I
+
+ align:start position:0%
+something shoot sorry 48 great so I
+ 
+
+ align:start position:0%
+something shoot sorry 48 great so I
+sample it forty thousand times a second
+
+ align:start position:0%
+sample it forty thousand times a second
+ 
+
+ align:start position:0%
+sample it forty thousand times a second
+each of these things as one thousandth
+
+ align:start position:0%
+each of these things as one thousandth
+ 
+
+ align:start position:0%
+each of these things as one thousandth
+of a second so i get 48 what that means
+
+ align:start position:0%
+of a second so i get 48 what that means
+ 
+
+ align:start position:0%
+of a second so i get 48 what that means
+is that we pick a sample here we pick a
+
+ align:start position:0%
+is that we pick a sample here we pick a
+ 
+
+ align:start position:0%
+is that we pick a sample here we pick a
+sample here we pick a sample here 1 2 3
+
+ align:start position:0%
+sample here we pick a sample here 1 2 3
+ 
+
+ align:start position:0%
+sample here we pick a sample here 1 2 3
+4 5 6 7 8 10 12 and we keep going 12 12
+
+ align:start position:0%
+4 5 6 7 8 10 12 and we keep going 12 12
+ 
+
+ align:start position:0%
+4 5 6 7 8 10 12 and we keep going 12 12
+etc so we get 48 okay so if I were to
+
+ align:start position:0%
+etc so we get 48 okay so if I were to
+ 
+
+ align:start position:0%
+etc so we get 48 okay so if I were to
+send a pure sinusoid at the receiver and
+
+ align:start position:0%
+send a pure sinusoid at the receiver and
+ 
+
+ align:start position:0%
+send a pure sinusoid at the receiver and
+this and the way the sinusoid is
+
+ align:start position:0%
+this and the way the sinusoid is
+ 
+
+ align:start position:0%
+this and the way the sinusoid is
+transmitted is by providing these
+
+ align:start position:0%
+transmitted is by providing these
+ 
+
+ align:start position:0%
+transmitted is by providing these
+samples each sample being equal to this
+
+ align:start position:0%
+samples each sample being equal to this
+ 
+
+ align:start position:0%
+samples each sample being equal to this
+voltage value picked from this curve and
+
+ align:start position:0%
+voltage value picked from this curve and
+ 
+
+ align:start position:0%
+voltage value picked from this curve and
+I send each of those samples and each of
+
+ align:start position:0%
+I send each of those samples and each of
+ 
+
+ align:start position:0%
+I send each of those samples and each of
+those in our implementation is a
+
+ align:start position:0%
+those in our implementation is a
+ 
+
+ align:start position:0%
+those in our implementation is a
+floating point number okay like a 32-bit
+
+ align:start position:0%
+floating point number okay like a 32-bit
+ 
+
+ align:start position:0%
+floating point number okay like a 32-bit
+floating point number I pick a number
+
+ align:start position:0%
+floating point number I pick a number
+ 
+
+ align:start position:0%
+floating point number I pick a number
+here 0 and then I pick something here
+
+ align:start position:0%
+here 0 and then I pick something here
+ 
+
+ align:start position:0%
+here 0 and then I pick something here
+which is the sign the value of the
+
+ align:start position:0%
+which is the sign the value of the
+ 
+
+ align:start position:0%
+which is the sign the value of the
+sinusoid at this point in time and this
+
+ align:start position:0%
+sinusoid at this point in time and this
+ 
+
+ align:start position:0%
+sinusoid at this point in time and this
+and this and this and all the way down
+
+ align:start position:0%
+and this and this and all the way down
+ 
+
+ align:start position:0%
+and this and this and all the way down
+and I send those samples the receiver is
+
+ align:start position:0%
+and I send those samples the receiver is
+ 
+
+ align:start position:0%
+and I send those samples the receiver is
+going to be listening at 48 kilohertz
+
+ align:start position:0%
+going to be listening at 48 kilohertz
+ 
+
+ align:start position:0%
+going to be listening at 48 kilohertz
+and picking up whatever it's getting on
+
+ align:start position:0%
+and picking up whatever it's getting on
+ 
+
+ align:start position:0%
+and picking up whatever it's getting on
+the audio channel and that's what it's
+
+ align:start position:0%
+the audio channel and that's what it's
+ 
+
+ align:start position:0%
+the audio channel and that's what it's
+going to be are assuming that's what
+
+ align:start position:0%
+going to be are assuming that's what
+ 
+
+ align:start position:0%
+going to be are assuming that's what
+it's going to assume was sent of course
+
+ align:start position:0%
+it's going to assume was sent of course
+ 
+
+ align:start position:0%
+it's going to assume was sent of course
+in the real world if I stand at one vote
+
+ align:start position:0%
+in the real world if I stand at one vote
+ 
+
+ align:start position:0%
+in the real world if I stand at one vote
+what might be received is point 01 volt
+
+ align:start position:0%
+what might be received is point 01 volt
+ 
+
+ align:start position:0%
+what might be received is point 01 volt
+so point two words or whatever because
+
+ align:start position:0%
+so point two words or whatever because
+ 
+
+ align:start position:0%
+so point two words or whatever because
+signals may in fact lose amplitude as
+
+ align:start position:0%
+signals may in fact lose amplitude as
+ 
+
+ align:start position:0%
+signals may in fact lose amplitude as
+you transmit them over the air so that's
+
+ align:start position:0%
+you transmit them over the air so that's
+ 
+
+ align:start position:0%
+you transmit them over the air so that's
+the overall context so I'm going to
+
+ align:start position:0%
+the overall context so I'm going to
+ 
+
+ align:start position:0%
+the overall context so I'm going to
+start by showing you a few things here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first thing I'll show is this graph
+
+ align:start position:0%
+the first thing I'll show is this graph
+ 
+
+ align:start position:0%
+the first thing I'll show is this graph
+or program that actually is part of the
+
+ align:start position:0%
+or program that actually is part of the
+ 
+
+ align:start position:0%
+or program that actually is part of the
+package but you need some gtk toolkit
+
+ align:start position:0%
+package but you need some gtk toolkit
+ 
+
+ align:start position:0%
+package but you need some gtk toolkit
+for this to work so we're not record we
+
+ align:start position:0%
+for this to work so we're not record we
+ 
+
+ align:start position:0%
+for this to work so we're not record we
+don't you don't need this for the lab
+
+ align:start position:0%
+don't you don't need this for the lab
+ 
+
+ align:start position:0%
+don't you don't need this for the lab
+but this is just a useful test if I
+
+ align:start position:0%
+but this is just a useful test if I
+ 
+
+ align:start position:0%
+but this is just a useful test if I
+transmit a waveform this program assumes
+
+ align:start position:0%
+transmit a waveform this program assumes
+ 
+
+ align:start position:0%
+transmit a waveform this program assumes
+that I'm transmitting data at 1
+
+ align:start position:0%
+that I'm transmitting data at 1
+ 
+
+ align:start position:0%
+that I'm transmitting data at 1
+kilohertz if I send data at 1 kilohertz
+
+ align:start position:0%
+kilohertz if I send data at 1 kilohertz
+ 
+
+ align:start position:0%
+kilohertz if I send data at 1 kilohertz
+and this is a pure sinusoid let me do
+
+ align:start position:0%
+and this is a pure sinusoid let me do
+ 
+
+ align:start position:0%
+and this is a pure sinusoid let me do
+that I'll explain these parameters in a
+
+ align:start position:0%
+that I'll explain these parameters in a
+ 
+
+ align:start position:0%
+that I'll explain these parameters in a
+big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that what's going on here is
+
+ align:start position:0%
+you can see that what's going on here is
+ 
+
+ align:start position:0%
+you can see that what's going on here is
+if I'm silent
+
+ align:start position:0%
+if I'm silent
+ 
+
+ align:start position:0%
+if I'm silent
+the points get demodulated at plus 1 and
+
+ align:start position:0%
+the points get demodulated at plus 1 and
+ 
+
+ align:start position:0%
+the points get demodulated at plus 1 and
+minus 1 that correspond to the top and
+
+ align:start position:0%
+minus 1 that correspond to the top and
+ 
+
+ align:start position:0%
+minus 1 that correspond to the top and
+the bottom of the waveform and if I make
+
+ align:start position:0%
+the bottom of the waveform and if I make
+ 
+
+ align:start position:0%
+the bottom of the waveform and if I make
+a noise the effects of noise get visible
+
+ align:start position:0%
+a noise the effects of noise get visible
+ 
+
+ align:start position:0%
+a noise the effects of noise get visible
+and in fact you can see that sometimes
+
+ align:start position:0%
+and in fact you can see that sometimes
+ 
+
+ align:start position:0%
+and in fact you can see that sometimes
+the guy on the left goes to the right
+
+ align:start position:0%
+the guy on the left goes to the right
+ 
+
+ align:start position:0%
+the guy on the left goes to the right
+and vice versa okay so that's actually a
+
+ align:start position:0%
+and vice versa okay so that's actually a
+ 
+
+ align:start position:0%
+and vice versa okay so that's actually a
+very visual effect of what noise does to
+
+ align:start position:0%
+very visual effect of what noise does to
+ 
+
+ align:start position:0%
+very visual effect of what noise does to
+your transmission i'm going to show this
+
+ align:start position:0%
+your transmission i'm going to show this
+ 
+
+ align:start position:0%
+your transmission i'm going to show this
+again i'm going to do this again so you
+
+ align:start position:0%
+again i'm going to do this again so you
+ 
+
+ align:start position:0%
+again i'm going to do this again so you
+can see what's going on as the amount of
+
+ align:start position:0%
+can see what's going on as the amount of
+ 
+
+ align:start position:0%
+can see what's going on as the amount of
+noise increases you can see that you can
+
+ align:start position:0%
+noise increases you can see that you can
+ 
+
+ align:start position:0%
+noise increases you can see that you can
+imagine that what's going on here in the
+
+ align:start position:0%
+imagine that what's going on here in the
+ 
+
+ align:start position:0%
+imagine that what's going on here in the
+signaling this is called bipolar
+
+ align:start position:0%
+signaling this is called bipolar
+ 
+
+ align:start position:0%
+signaling this is called bipolar
+signaling where you might send a bit 0
+
+ align:start position:0%
+signaling where you might send a bit 0
+ 
+
+ align:start position:0%
+signaling where you might send a bit 0
+ad as a particular kind of sinusoid and
+
+ align:start position:0%
+ad as a particular kind of sinusoid and
+ 
+
+ align:start position:0%
+ad as a particular kind of sinusoid and
+a bit one at the other way as the other
+
+ align:start position:0%
+a bit one at the other way as the other
+ 
+
+ align:start position:0%
+a bit one at the other way as the other
+kind so the idea would be that the zeros
+
+ align:start position:0%
+kind so the idea would be that the zeros
+ 
+
+ align:start position:0%
+kind so the idea would be that the zeros
+get mapped to the left the ones get
+
+ align:start position:0%
+get mapped to the left the ones get
+ 
+
+ align:start position:0%
+get mapped to the left the ones get
+mapped to the right and as we increase
+
+ align:start position:0%
+mapped to the right and as we increase
+ 
+
+ align:start position:0%
+mapped to the right and as we increase
+the amount of noise you can start to see
+
+ align:start position:0%
+the amount of noise you can start to see
+ 
+
+ align:start position:0%
+the amount of noise you can start to see
+that they cross over and we'll be making
+
+ align:start position:0%
+that they cross over and we'll be making
+ 
+
+ align:start position:0%
+that they cross over and we'll be making
+errors in our estimation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so things are working fine now but as I
+
+ align:start position:0%
+so things are working fine now but as I
+ 
+
+ align:start position:0%
+so things are working fine now but as I
+make noise or as you start talking and
+
+ align:start position:0%
+make noise or as you start talking and
+ 
+
+ align:start position:0%
+make noise or as you start talking and
+you create additional noise we're gonna
+
+ align:start position:0%
+you create additional noise we're gonna
+ 
+
+ align:start position:0%
+you create additional noise we're gonna
+start to see the effects of the noise
+
+ align:start position:0%
+start to see the effects of the noise
+ 
+
+ align:start position:0%
+start to see the effects of the noise
+and this is annoying so I'm going to
+
+ align:start position:0%
+and this is annoying so I'm going to
+ 
+
+ align:start position:0%
+and this is annoying so I'm going to
+turn it off okay so um that's the first
+
+ align:start position:0%
+turn it off okay so um that's the first
+ 
+
+ align:start position:0%
+turn it off okay so um that's the first
+order way in which you determine that
+
+ align:start position:0%
+order way in which you determine that
+ 
+
+ align:start position:0%
+order way in which you determine that
+things are working you don't need to use
+
+ align:start position:0%
+things are working you don't need to use
+ 
+
+ align:start position:0%
+things are working you don't need to use
+the graphing program to do that and this
+
+ align:start position:0%
+the graphing program to do that and this
+ 
+
+ align:start position:0%
+the graphing program to do that and this
+is actually annoying to the eye so let
+
+ align:start position:0%
+is actually annoying to the eye so let
+ 
+
+ align:start position:0%
+is actually annoying to the eye so let
+me turn that off too so you run and and
+
+ align:start position:0%
+me turn that off too so you run and and
+ 
+
+ align:start position:0%
+me turn that off too so you run and and
+the documentation we've given you tells
+
+ align:start position:0%
+the documentation we've given you tells
+ 
+
+ align:start position:0%
+the documentation we've given you tells
+you how you go about step by step
+
+ align:start position:0%
+you how you go about step by step
+ 
+
+ align:start position:0%
+you how you go about step by step
+drawing it about this so let me tell you
+
+ align:start position:0%
+drawing it about this so let me tell you
+ 
+
+ align:start position:0%
+drawing it about this so let me tell you
+what these options mean it's all written
+
+ align:start position:0%
+what these options mean it's all written
+ 
+
+ align:start position:0%
+what these options mean it's all written
+up so you don't have to listen you don't
+
+ align:start position:0%
+up so you don't have to listen you don't
+ 
+
+ align:start position:0%
+up so you don't have to listen you don't
+have to take notes right now everything
+
+ align:start position:0%
+have to take notes right now everything
+ 
+
+ align:start position:0%
+have to take notes right now everything
+is there in that command line the dash
+
+ align:start position:0%
+is there in that command line the dash
+ 
+
+ align:start position:0%
+is there in that command line the dash
+little s 256 refers to the number of
+
+ align:start position:0%
+little s 256 refers to the number of
+ 
+
+ align:start position:0%
+little s 256 refers to the number of
+samples per bit i'll get to that point
+
+ align:start position:0%
+samples per bit i'll get to that point
+ 
+
+ align:start position:0%
+samples per bit i'll get to that point
+in a second the dash capital s 1 means
+
+ align:start position:0%
+in a second the dash capital s 1 means
+ 
+
+ align:start position:0%
+in a second the dash capital s 1 means
+that we send capital S is that kind of
+
+ align:start position:0%
+that we send capital S is that kind of
+ 
+
+ align:start position:0%
+that we send capital S is that kind of
+source you know it's it's it's something
+
+ align:start position:0%
+source you know it's it's it's something
+ 
+
+ align:start position:0%
+source you know it's it's it's something
+about the nature of the source capital S
+
+ align:start position:0%
+about the nature of the source capital S
+ 
+
+ align:start position:0%
+about the nature of the source capital S
+one means that my entire information is
+
+ align:start position:0%
+one means that my entire information is
+ 
+
+ align:start position:0%
+one means that my entire information is
+sent as ones which means i'm selling a
+
+ align:start position:0%
+sent as ones which means i'm selling a
+ 
+
+ align:start position:0%
+sent as ones which means i'm selling a
+pure sinusoidal carrier all i'm doing is
+
+ align:start position:0%
+pure sinusoidal carrier all i'm doing is
+ 
+
+ align:start position:0%
+pure sinusoidal carrier all i'm doing is
+sending the sinusoidal carrier dash g
+
+ align:start position:0%
+sending the sinusoidal carrier dash g
+ 
+
+ align:start position:0%
+sending the sinusoidal carrier dash g
+just means show me some graphs and n
+
+ align:start position:0%
+just means show me some graphs and n
+ 
+
+ align:start position:0%
+just means show me some graphs and n
+refers to the number of bits i wish to
+
+ align:start position:0%
+refers to the number of bits i wish to
+ 
+
+ align:start position:0%
+refers to the number of bits i wish to
+send ok so these are all documented in
+
+ align:start position:0%
+send ok so these are all documented in
+ 
+
+ align:start position:0%
+send ok so these are all documented in
+different to worry about so what we're
+
+ align:start position:0%
+different to worry about so what we're
+ 
+
+ align:start position:0%
+different to worry about so what we're
+going to do now is actually to show you
+
+ align:start position:0%
+going to do now is actually to show you
+ 
+
+ align:start position:0%
+going to do now is actually to show you
+what happens when we transmit some data
+
+ align:start position:0%
+what happens when we transmit some data
+ 
+
+ align:start position:0%
+what happens when we transmit some data
+this is actually the very first task in
+
+ align:start position:0%
+this is actually the very first task in
+ 
+
+ align:start position:0%
+this is actually the very first task in
+the lab you transmit some data and you
+
+ align:start position:0%
+the lab you transmit some data and you
+ 
+
+ align:start position:0%
+the lab you transmit some data and you
+plot what the noise histogram looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we did was we sent a couple
+
+ align:start position:0%
+so what we did was we sent a couple
+ 
+
+ align:start position:0%
+so what we did was we sent a couple
+hundred bits at some appropriate number
+
+ align:start position:0%
+hundred bits at some appropriate number
+ 
+
+ align:start position:0%
+hundred bits at some appropriate number
+of samples per bit you know the way you
+
+ align:start position:0%
+of samples per bit you know the way you
+ 
+
+ align:start position:0%
+of samples per bit you know the way you
+tell if stops working is that line there
+
+ align:start position:0%
+tell if stops working is that line there
+ 
+
+ align:start position:0%
+tell if stops working is that line there
+if it receives the preamble and there's
+
+ align:start position:0%
+if it receives the preamble and there's
+ 
+
+ align:start position:0%
+if it receives the preamble and there's
+this long preamble I'll explain what
+
+ align:start position:0%
+this long preamble I'll explain what
+ 
+
+ align:start position:0%
+this long preamble I'll explain what
+that word means but if you receive the
+
+ align:start position:0%
+that word means but if you receive the
+ 
+
+ align:start position:0%
+that word means but if you receive the
+preamble it means that stops working if
+
+ align:start position:0%
+preamble it means that stops working if
+ 
+
+ align:start position:0%
+preamble it means that stops working if
+you didn't get the preamble it means
+
+ align:start position:0%
+you didn't get the preamble it means
+ 
+
+ align:start position:0%
+you didn't get the preamble it means
+that it doesn't mean that things are
+
+ align:start position:0%
+that it doesn't mean that things are
+ 
+
+ align:start position:0%
+that it doesn't mean that things are
+completely broken it just means you got
+
+ align:start position:0%
+completely broken it just means you got
+ 
+
+ align:start position:0%
+completely broken it just means you got
+it a little bit more work now we also
+
+ align:start position:0%
+it a little bit more work now we also
+ 
+
+ align:start position:0%
+it a little bit more work now we also
+plot out the signal-to-noise ratio of
+
+ align:start position:0%
+plot out the signal-to-noise ratio of
+ 
+
+ align:start position:0%
+plot out the signal-to-noise ratio of
+the transmission and that shows up there
+
+ align:start position:0%
+the transmission and that shows up there
+ 
+
+ align:start position:0%
+the transmission and that shows up there
+if that signal to noise ratio is
+
+ align:start position:0%
+if that signal to noise ratio is
+ 
+
+ align:start position:0%
+if that signal to noise ratio is
+something like 20 DB or 15 DB things are
+
+ align:start position:0%
+something like 20 DB or 15 DB things are
+ 
+
+ align:start position:0%
+something like 20 DB or 15 DB things are
+fine this system doesn't really work
+
+ align:start position:0%
+fine this system doesn't really work
+ 
+
+ align:start position:0%
+fine this system doesn't really work
+below 15 or 10 decibels it means that
+
+ align:start position:0%
+below 15 or 10 decibels it means that
+ 
+
+ align:start position:0%
+below 15 or 10 decibels it means that
+the signal-to-noise ratio is too low
+
+ align:start position:0%
+the signal-to-noise ratio is too low
+ 
+
+ align:start position:0%
+the signal-to-noise ratio is too low
+which means you either have to yank up
+
+ align:start position:0%
+which means you either have to yank up
+ 
+
+ align:start position:0%
+which means you either have to yank up
+the volume or you have to go to a
+
+ align:start position:0%
+the volume or you have to go to a
+ 
+
+ align:start position:0%
+the volume or you have to go to a
+quieter location or and I'll explain
+
+ align:start position:0%
+quieter location or and I'll explain
+ 
+
+ align:start position:0%
+quieter location or and I'll explain
+this you have to change some of the
+
+ align:start position:0%
+this you have to change some of the
+ 
+
+ align:start position:0%
+this you have to change some of the
+parameters in the program now what is
+
+ align:start position:0%
+parameters in the program now what is
+ 
+
+ align:start position:0%
+parameters in the program now what is
+this graph look like will they know this
+
+ align:start position:0%
+this graph look like will they know this
+ 
+
+ align:start position:0%
+this graph look like will they know this
+for a second for this number of samples
+
+ align:start position:0%
+for a second for this number of samples
+ 
+
+ align:start position:0%
+for a second for this number of samples
+that was the noise distribution at point
+
+ align:start position:0%
+that was the noise distribution at point
+ 
+
+ align:start position:0%
+that was the noise distribution at point
+four four you know you could look at it
+
+ align:start position:0%
+four four you know you could look at it
+ 
+
+ align:start position:0%
+four four you know you could look at it
+and it sort of looks Gaussian it's not
+
+ align:start position:0%
+and it sort of looks Gaussian it's not
+ 
+
+ align:start position:0%
+and it sort of looks Gaussian it's not
+quite a Gaussian explain why in a little
+
+ align:start position:0%
+quite a Gaussian explain why in a little
+ 
+
+ align:start position:0%
+quite a Gaussian explain why in a little
+bit what these pictures show is this is
+
+ align:start position:0%
+bit what these pictures show is this is
+ 
+
+ align:start position:0%
+bit what these pictures show is this is
+what the noise this is what the received
+
+ align:start position:0%
+what the noise this is what the received
+ 
+
+ align:start position:0%
+what the noise this is what the received
+samples look like and it's it has a
+
+ align:start position:0%
+samples look like and it's it has a
+ 
+
+ align:start position:0%
+samples look like and it's it has a
+median a mean value that's in the center
+
+ align:start position:0%
+median a mean value that's in the center
+ 
+
+ align:start position:0%
+median a mean value that's in the center
+and then it's kind of got a shape on
+
+ align:start position:0%
+and then it's kind of got a shape on
+ 
+
+ align:start position:0%
+and then it's kind of got a shape on
+both sides
+
+ align:start position:0%
+both sides
+ 
+
+ align:start position:0%
+both sides
+this picture in the middle are the
+
+ align:start position:0%
+this picture in the middle are the
+ 
+
+ align:start position:0%
+this picture in the middle are the
+samples post demodulation it's actually
+
+ align:start position:0%
+samples post demodulation it's actually
+ 
+
+ align:start position:0%
+samples post demodulation it's actually
+what you received at the receiver after
+
+ align:start position:0%
+what you received at the receiver after
+ 
+
+ align:start position:0%
+what you received at the receiver after
+we ran the demodulation step and the
+
+ align:start position:0%
+we ran the demodulation step and the
+ 
+
+ align:start position:0%
+we ran the demodulation step and the
+stuff on top the blue refers to what was
+
+ align:start position:0%
+stuff on top the blue refers to what was
+ 
+
+ align:start position:0%
+stuff on top the blue refers to what was
+transmitted which in this case was
+
+ align:start position:0%
+transmitted which in this case was
+ 
+
+ align:start position:0%
+transmitted which in this case was
+appealed carrier the green shows what
+
+ align:start position:0%
+appealed carrier the green shows what
+ 
+
+ align:start position:0%
+appealed carrier the green shows what
+was received which was some noisy
+
+ align:start position:0%
+was received which was some noisy
+ 
+
+ align:start position:0%
+was received which was some noisy
+version of the carrier because we didn't
+
+ align:start position:0%
+version of the carrier because we didn't
+ 
+
+ align:start position:0%
+version of the carrier because we didn't
+send information other than just the
+
+ align:start position:0%
+send information other than just the
+ 
+
+ align:start position:0%
+send information other than just the
+carrier this is effectively the first
+
+ align:start position:0%
+carrier this is effectively the first
+ 
+
+ align:start position:0%
+carrier this is effectively the first
+lab we have to do nothing more than
+
+ align:start position:0%
+lab we have to do nothing more than
+ 
+
+ align:start position:0%
+lab we have to do nothing more than
+round us a few times and you know the
+
+ align:start position:0%
+round us a few times and you know the
+ 
+
+ align:start position:0%
+round us a few times and you know the
+essence most of the first task in the
+
+ align:start position:0%
+essence most of the first task in the
+ 
+
+ align:start position:0%
+essence most of the first task in the
+lab first two tasks in the lab is just
+
+ align:start position:0%
+lab first two tasks in the lab is just
+ 
+
+ align:start position:0%
+lab first two tasks in the lab is just
+making sure that the stuff works now
+
+ align:start position:0%
+making sure that the stuff works now
+ 
+
+ align:start position:0%
+making sure that the stuff works now
+this entire system you know everything
+
+ align:start position:0%
+this entire system you know everything
+ 
+
+ align:start position:0%
+this entire system you know everything
+works if this thing called the preamble
+
+ align:start position:0%
+works if this thing called the preamble
+ 
+
+ align:start position:0%
+works if this thing called the preamble
+is decoded so what is this preamble and
+
+ align:start position:0%
+is decoded so what is this preamble and
+ 
+
+ align:start position:0%
+is decoded so what is this preamble and
+why do we need it the problem is that as
+
+ align:start position:0%
+why do we need it the problem is that as
+ 
+
+ align:start position:0%
+why do we need it the problem is that as
+you saw in this graphing receiver when I
+
+ align:start position:0%
+you saw in this graphing receiver when I
+ 
+
+ align:start position:0%
+you saw in this graphing receiver when I
+showed this to you the audio hardware is
+
+ align:start position:0%
+showed this to you the audio hardware is
+ 
+
+ align:start position:0%
+showed this to you the audio hardware is
+going to be a you know what it's doing
+
+ align:start position:0%
+going to be a you know what it's doing
+ 
+
+ align:start position:0%
+going to be a you know what it's doing
+is it's always listening when you run
+
+ align:start position:0%
+is it's always listening when you run
+ 
+
+ align:start position:0%
+is it's always listening when you run
+the program it's always listening on the
+
+ align:start position:0%
+the program it's always listening on the
+ 
+
+ align:start position:0%
+the program it's always listening on the
+channel so it's getting data even when
+
+ align:start position:0%
+channel so it's getting data even when
+ 
+
+ align:start position:0%
+channel so it's getting data even when
+I'm not sending anything it's getting
+
+ align:start position:0%
+I'm not sending anything it's getting
+ 
+
+ align:start position:0%
+I'm not sending anything it's getting
+something there's always something on
+
+ align:start position:0%
+something there's always something on
+ 
+
+ align:start position:0%
+something there's always something on
+the audio channel so the question is how
+
+ align:start position:0%
+the audio channel so the question is how
+ 
+
+ align:start position:0%
+the audio channel so the question is how
+do you know how does this they will know
+
+ align:start position:0%
+do you know how does this they will know
+ 
+
+ align:start position:0%
+do you know how does this they will know
+that what it's receiving as part of the
+
+ align:start position:0%
+that what it's receiving as part of the
+ 
+
+ align:start position:0%
+that what it's receiving as part of the
+legitimate transmission all
+
+ align:start position:0%
+legitimate transmission all
+ 
+
+ align:start position:0%
+legitimate transmission all
+communication systems need to solve this
+
+ align:start position:0%
+communication systems need to solve this
+ 
+
+ align:start position:0%
+communication systems need to solve this
+problem of synchronizing between the
+
+ align:start position:0%
+problem of synchronizing between the
+ 
+
+ align:start position:0%
+problem of synchronizing between the
+sender and receiver and that's done
+
+ align:start position:0%
+sender and receiver and that's done
+ 
+
+ align:start position:0%
+sender and receiver and that's done
+using a preamble the preamble is nothing
+
+ align:start position:0%
+using a preamble the preamble is nothing
+ 
+
+ align:start position:0%
+using a preamble the preamble is nothing
+more than a well known which sequence
+
+ align:start position:0%
+more than a well known which sequence
+ 
+
+ align:start position:0%
+more than a well known which sequence
+sequence of bits that the sender and
+
+ align:start position:0%
+sequence of bits that the sender and
+ 
+
+ align:start position:0%
+sequence of bits that the sender and
+receiver both agree on so in this case
+
+ align:start position:0%
+receiver both agree on so in this case
+ 
+
+ align:start position:0%
+receiver both agree on so in this case
+our preamble is that long sequence there
+
+ align:start position:0%
+our preamble is that long sequence there
+ 
+
+ align:start position:0%
+our preamble is that long sequence there
+1 0 1 1 0 1 1 1 etc and there's some
+
+ align:start position:0%
+1 0 1 1 0 1 1 1 etc and there's some
+ 
+
+ align:start position:0%
+1 0 1 1 0 1 1 1 etc and there's some
+guidelines and rules of thumb that go
+
+ align:start position:0%
+guidelines and rules of thumb that go
+ 
+
+ align:start position:0%
+guidelines and rules of thumb that go
+into how what I'm what makes the
+
+ align:start position:0%
+into how what I'm what makes the
+ 
+
+ align:start position:0%
+into how what I'm what makes the
+preamble good and what makes it not so
+
+ align:start position:0%
+preamble good and what makes it not so
+ 
+
+ align:start position:0%
+preamble good and what makes it not so
+good we're not going to worry about that
+
+ align:start position:0%
+good we're not going to worry about that
+ 
+
+ align:start position:0%
+good we're not going to worry about that
+here I'm just telling you that's the
+
+ align:start position:0%
+here I'm just telling you that's the
+ 
+
+ align:start position:0%
+here I'm just telling you that's the
+preamble so as long as the receiver is
+
+ align:start position:0%
+preamble so as long as the receiver is
+ 
+
+ align:start position:0%
+preamble so as long as the receiver is
+successfully able to decode the preamble
+
+ align:start position:0%
+successfully able to decode the preamble
+ 
+
+ align:start position:0%
+successfully able to decode the preamble
+it means that it knows that there's a
+
+ align:start position:0%
+it means that it knows that there's a
+ 
+
+ align:start position:0%
+it means that it knows that there's a
+legitimate transmission over the air and
+
+ align:start position:0%
+legitimate transmission over the air and
+ 
+
+ align:start position:0%
+legitimate transmission over the air and
+it can start listening to it so if you
+
+ align:start position:0%
+it can start listening to it so if you
+ 
+
+ align:start position:0%
+it can start listening to it so if you
+don't get the preamble we can all bets
+
+ align:start position:0%
+don't get the preamble we can all bets
+ 
+
+ align:start position:0%
+don't get the preamble we can all bets
+are off as to what the heck is going on
+
+ align:start position:0%
+are off as to what the heck is going on
+ 
+
+ align:start position:0%
+are off as to what the heck is going on
+on the channel and sometimes you may not
+
+ align:start position:0%
+on the channel and sometimes you may not
+ 
+
+ align:start position:0%
+on the channel and sometimes you may not
+give the preamble now one of the things
+
+ align:start position:0%
+give the preamble now one of the things
+ 
+
+ align:start position:0%
+give the preamble now one of the things
+you would have to do you would want to
+
+ align:start position:0%
+you would have to do you would want to
+ 
+
+ align:start position:0%
+you would have to do you would want to
+do is when you don't get a preamble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usually it's a sign that the either some
+
+ align:start position:0%
+usually it's a sign that the either some
+ 
+
+ align:start position:0%
+usually it's a sign that the either some
+samples are being lost because the audio
+
+ align:start position:0%
+samples are being lost because the audio
+ 
+
+ align:start position:0%
+samples are being lost because the audio
+hardware isn't able to cope with it and
+
+ align:start position:0%
+hardware isn't able to cope with it and
+ 
+
+ align:start position:0%
+hardware isn't able to cope with it and
+the documentation describes how you deal
+
+ align:start position:0%
+the documentation describes how you deal
+ 
+
+ align:start position:0%
+the documentation describes how you deal
+with that problem or it means that the
+
+ align:start position:0%
+with that problem or it means that the
+ 
+
+ align:start position:0%
+with that problem or it means that the
+sampling rate is too high and maybe
+
+ align:start position:0%
+sampling rate is too high and maybe
+ 
+
+ align:start position:0%
+sampling rate is too high and maybe
+something's running on your computer
+
+ align:start position:0%
+something's running on your computer
+ 
+
+ align:start position:0%
+something's running on your computer
+that's you know I don't know you have
+
+ align:start position:0%
+that's you know I don't know you have
+ 
+
+ align:start position:0%
+that's you know I don't know you have
+some video going on in the background
+
+ align:start position:0%
+some video going on in the background
+ 
+
+ align:start position:0%
+some video going on in the background
+and it's not keeping up to read at forty
+
+ align:start position:0%
+and it's not keeping up to read at forty
+ 
+
+ align:start position:0%
+and it's not keeping up to read at forty
+eight thousand Hertz or at the sign that
+
+ align:start position:0%
+eight thousand Hertz or at the sign that
+ 
+
+ align:start position:0%
+eight thousand Hertz or at the sign that
+the signal-to-noise ratio is too low
+
+ align:start position:0%
+the signal-to-noise ratio is too low
+ 
+
+ align:start position:0%
+the signal-to-noise ratio is too low
+maybe you're in a very crowded location
+
+ align:start position:0%
+maybe you're in a very crowded location
+ 
+
+ align:start position:0%
+maybe you're in a very crowded location
+or maybe the volume is too low so those
+
+ align:start position:0%
+or maybe the volume is too low so those
+ 
+
+ align:start position:0%
+or maybe the volume is too low so those
+are usually the ways in which you go
+
+ align:start position:0%
+are usually the ways in which you go
+ 
+
+ align:start position:0%
+are usually the ways in which you go
+about fixing this problem with the
+
+ align:start position:0%
+about fixing this problem with the
+ 
+
+ align:start position:0%
+about fixing this problem with the
+preamble now I want to show you one more
+
+ align:start position:0%
+preamble now I want to show you one more
+ 
+
+ align:start position:0%
+preamble now I want to show you one more
+noise graph what I'd like you to do now
+
+ align:start position:0%
+noise graph what I'd like you to do now
+ 
+
+ align:start position:0%
+noise graph what I'd like you to do now
+is actually make you know we're going to
+
+ align:start position:0%
+is actually make you know we're going to
+ 
+
+ align:start position:0%
+is actually make you know we're going to
+try to do this with some music on the
+
+ align:start position:0%
+try to do this with some music on the
+ 
+
+ align:start position:0%
+try to do this with some music on the
+side what I want to show you is that as
+
+ align:start position:0%
+side what I want to show you is that as
+ 
+
+ align:start position:0%
+side what I want to show you is that as
+you increase the amount of noise the
+
+ align:start position:0%
+you increase the amount of noise the
+ 
+
+ align:start position:0%
+you increase the amount of noise the
+noise is captured in the variance of the
+
+ align:start position:0%
+noise is captured in the variance of the
+ 
+
+ align:start position:0%
+noise is captured in the variance of the
+Gaussian distribution with more the
+
+ align:start position:0%
+Gaussian distribution with more the
+ 
+
+ align:start position:0%
+Gaussian distribution with more the
+noise the bigger the variance of the
+
+ align:start position:0%
+noise the bigger the variance of the
+ 
+
+ align:start position:0%
+noise the bigger the variance of the
+distribution so I'm going to try to do
+
+ align:start position:0%
+distribution so I'm going to try to do
+ 
+
+ align:start position:0%
+distribution so I'm going to try to do
+this by sending a thousand bits that
+
+ align:start position:0%
+this by sending a thousand bits that
+ 
+
+ align:start position:0%
+this by sending a thousand bits that
+this will take a little bit of time so
+
+ align:start position:0%
+this will take a little bit of time so
+ 
+
+ align:start position:0%
+this will take a little bit of time so
+let's first send it without
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll send this without a huge amount
+
+ align:start position:0%
+so we'll send this without a huge amount
+ 
+
+ align:start position:0%
+so we'll send this without a huge amount
+of noise I mean there's some ambient
+
+ align:start position:0%
+of noise I mean there's some ambient
+ 
+
+ align:start position:0%
+of noise I mean there's some ambient
+noise in the room and this will take a
+
+ align:start position:0%
+noise in the room and this will take a
+ 
+
+ align:start position:0%
+noise in the room and this will take a
+little bit of time to demodulate and get
+
+ align:start position:0%
+little bit of time to demodulate and get
+ 
+
+ align:start position:0%
+little bit of time to demodulate and get
+working there's a little couple of
+
+ align:start position:0%
+working there's a little couple of
+ 
+
+ align:start position:0%
+working there's a little couple of
+errors bit error rate was point over to
+
+ align:start position:0%
+errors bit error rate was point over to
+ 
+
+ align:start position:0%
+errors bit error rate was point over to
+two bits were an error here and we saw
+
+ align:start position:0%
+two bits were an error here and we saw
+ 
+
+ align:start position:0%
+two bits were an error here and we saw
+something like this it isn't quite a
+
+ align:start position:0%
+something like this it isn't quite a
+ 
+
+ align:start position:0%
+something like this it isn't quite a
+Gaussian in this case but we saw
+
+ align:start position:0%
+Gaussian in this case but we saw
+ 
+
+ align:start position:0%
+Gaussian in this case but we saw
+something like that now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'd like you to do is kind of start
+
+ align:start position:0%
+what I'd like you to do is kind of start
+ 
+
+ align:start position:0%
+what I'd like you to do is kind of start
+when I say yes just start making some
+
+ align:start position:0%
+when I say yes just start making some
+ 
+
+ align:start position:0%
+when I say yes just start making some
+noise just trap or just talk or whatever
+
+ align:start position:0%
+noise just trap or just talk or whatever
+ 
+
+ align:start position:0%
+noise just trap or just talk or whatever
+just you know turn on your phones do
+
+ align:start position:0%
+just you know turn on your phones do
+ 
+
+ align:start position:0%
+just you know turn on your phones do
+something yeah all right all right I was
+
+ align:start position:0%
+something yeah all right all right I was
+ 
+
+ align:start position:0%
+something yeah all right all right I was
+actually going to play I found some nice
+
+ align:start position:0%
+actually going to play I found some nice
+ 
+
+ align:start position:0%
+actually going to play I found some nice
+youtube clips of a music group one of
+
+ align:start position:0%
+youtube clips of a music group one of
+ 
+
+ align:start position:0%
+youtube clips of a music group one of
+the MIT acapella music groups okay we
+
+ align:start position:0%
+the MIT acapella music groups okay we
+ 
+
+ align:start position:0%
+the MIT acapella music groups okay we
+really got toasted here because you guys
+
+ align:start position:0%
+really got toasted here because you guys
+ 
+
+ align:start position:0%
+really got toasted here because you guys
+started talking and we couldn't recover
+
+ align:start position:0%
+started talking and we couldn't recover
+ 
+
+ align:start position:0%
+started talking and we couldn't recover
+the preamble but we probably got that
+
+ align:start position:0%
+the preamble but we probably got that
+ 
+
+ align:start position:0%
+the preamble but we probably got that
+was the noise distribution that we saw
+
+ align:start position:0%
+was the noise distribution that we saw
+ 
+
+ align:start position:0%
+was the noise distribution that we saw
+and you can see that it's actually kind
+
+ align:start position:0%
+and you can see that it's actually kind
+ 
+
+ align:start position:0%
+and you can see that it's actually kind
+of a fat redistribution I'll show you
+
+ align:start position:0%
+of a fat redistribution I'll show you
+ 
+
+ align:start position:0%
+of a fat redistribution I'll show you
+what this picture is this is a picture
+
+ align:start position:0%
+what this picture is this is a picture
+ 
+
+ align:start position:0%
+what this picture is this is a picture
+that essentially you will become your
+
+ align:start position:0%
+that essentially you will become your
+ 
+
+ align:start position:0%
+that essentially you will become your
+best friend or maybe your worst enemy
+
+ align:start position:0%
+best friend or maybe your worst enemy
+ 
+
+ align:start position:0%
+best friend or maybe your worst enemy
+this is called an eye diagram and it
+
+ align:start position:0%
+this is called an eye diagram and it
+ 
+
+ align:start position:0%
+this is called an eye diagram and it
+looks completely messed up so i'm going
+
+ align:start position:0%
+looks completely messed up so i'm going
+ 
+
+ align:start position:0%
+looks completely messed up so i'm going
+to show you what that is and we don't
+
+ align:start position:0%
+to show you what that is and we don't
+ 
+
+ align:start position:0%
+to show you what that is and we don't
+talk about um so let me explain to you
+
+ align:start position:0%
+talk about um so let me explain to you
+ 
+
+ align:start position:0%
+talk about um so let me explain to you
+noise was too high on and the point here
+
+ align:start position:0%
+noise was too high on and the point here
+ 
+
+ align:start position:0%
+noise was too high on and the point here
+is that that's shown in this picture
+
+ align:start position:0%
+is that that's shown in this picture
+ 
+
+ align:start position:0%
+is that that's shown in this picture
+here where we ended up with enough of a
+
+ align:start position:0%
+here where we ended up with enough of a
+ 
+
+ align:start position:0%
+here where we ended up with enough of a
+variation that we couldn't distinguish
+
+ align:start position:0%
+variation that we couldn't distinguish
+ 
+
+ align:start position:0%
+variation that we couldn't distinguish
+between zeros and ones we sent something
+
+ align:start position:0%
+between zeros and ones we sent something
+ 
+
+ align:start position:0%
+between zeros and ones we sent something
+which had a little bit of zeros in the
+
+ align:start position:0%
+which had a little bit of zeros in the
+ 
+
+ align:start position:0%
+which had a little bit of zeros in the
+beginning and then the entire one
+
+ align:start position:0%
+beginning and then the entire one
+ 
+
+ align:start position:0%
+beginning and then the entire one
+distribution was spread between you know
+
+ align:start position:0%
+distribution was spread between you know
+ 
+
+ align:start position:0%
+distribution was spread between you know
+point one volts two point nine volts the
+
+ align:start position:0%
+point one volts two point nine volts the
+ 
+
+ align:start position:0%
+point one volts two point nine volts the
+variance is extremely high now let's do
+
+ align:start position:0%
+variance is extremely high now let's do
+ 
+
+ align:start position:0%
+variance is extremely high now let's do
+one thing i'm going to change this to
+
+ align:start position:0%
+one thing i'm going to change this to
+ 
+
+ align:start position:0%
+one thing i'm going to change this to
+just transmit random pieces of
+
+ align:start position:0%
+just transmit random pieces of
+ 
+
+ align:start position:0%
+just transmit random pieces of
+information here when I don't give
+
+ align:start position:0%
+information here when I don't give
+ 
+
+ align:start position:0%
+information here when I don't give
+anything it means that dama the data
+
+ align:start position:0%
+anything it means that dama the data
+ 
+
+ align:start position:0%
+anything it means that dama the data
+that's being sent is just a random
+
+ align:start position:0%
+that's being sent is just a random
+ 
+
+ align:start position:0%
+that's being sent is just a random
+sequence of zeros and ones let me change
+
+ align:start position:0%
+sequence of zeros and ones let me change
+ 
+
+ align:start position:0%
+sequence of zeros and ones let me change
+this to 200 beds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright so we got those bits through and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a beautiful I diagram I'll
+
+ align:start position:0%
+that's a beautiful I diagram I'll
+ 
+
+ align:start position:0%
+that's a beautiful I diagram I'll
+explain what this means but the point is
+
+ align:start position:0%
+explain what this means but the point is
+ 
+
+ align:start position:0%
+explain what this means but the point is
+that when you see the separation and you
+
+ align:start position:0%
+that when you see the separation and you
+ 
+
+ align:start position:0%
+that when you see the separation and you
+see a point in the middle here with a
+
+ align:start position:0%
+see a point in the middle here with a
+ 
+
+ align:start position:0%
+see a point in the middle here with a
+big gap on this I diagram graph and then
+
+ align:start position:0%
+big gap on this I diagram graph and then
+ 
+
+ align:start position:0%
+big gap on this I diagram graph and then
+you see a separation between these were
+
+ align:start position:0%
+you see a separation between these were
+ 
+
+ align:start position:0%
+you see a separation between these were
+the zeros and those were the ones which
+
+ align:start position:0%
+the zeros and those were the ones which
+ 
+
+ align:start position:0%
+the zeros and those were the ones which
+means you could threshold somewhere in
+
+ align:start position:0%
+means you could threshold somewhere in
+ 
+
+ align:start position:0%
+means you could threshold somewhere in
+the middle and separate out which bits
+
+ align:start position:0%
+the middle and separate out which bits
+ 
+
+ align:start position:0%
+the middle and separate out which bits
+with zeros in which bits were one it
+
+ align:start position:0%
+with zeros in which bits were one it
+ 
+
+ align:start position:0%
+with zeros in which bits were one it
+means you're cooking things are great
+
+ align:start position:0%
+means you're cooking things are great
+ 
+
+ align:start position:0%
+means you're cooking things are great
+okay so you can see that there's some
+
+ align:start position:0%
+okay so you can see that there's some
+ 
+
+ align:start position:0%
+okay so you can see that there's some
+distribution here of what the ones look
+
+ align:start position:0%
+distribution here of what the ones look
+ 
+
+ align:start position:0%
+distribution here of what the ones look
+like in the empirical data there's a
+
+ align:start position:0%
+like in the empirical data there's a
+ 
+
+ align:start position:0%
+like in the empirical data there's a
+distribution hear what the zeros are
+
+ align:start position:0%
+distribution hear what the zeros are
+ 
+
+ align:start position:0%
+distribution hear what the zeros are
+look like this is not going to be a
+
+ align:start position:0%
+look like this is not going to be a
+ 
+
+ align:start position:0%
+look like this is not going to be a
+Gaussian at all I'll explain why that is
+
+ align:start position:0%
+Gaussian at all I'll explain why that is
+ 
+
+ align:start position:0%
+Gaussian at all I'll explain why that is
+in a moment okay so I have to do two
+
+ align:start position:0%
+in a moment okay so I have to do two
+ 
+
+ align:start position:0%
+in a moment okay so I have to do two
+more things today and then I'll turn it
+
+ align:start position:0%
+more things today and then I'll turn it
+ 
+
+ align:start position:0%
+more things today and then I'll turn it
+over to Professor for gays the first one
+
+ align:start position:0%
+over to Professor for gays the first one
+ 
+
+ align:start position:0%
+over to Professor for gays the first one
+I want to explain to you is what this
+
+ align:start position:0%
+I want to explain to you is what this
+ 
+
+ align:start position:0%
+I want to explain to you is what this
+eye diagram is and why it's kind of
+
+ align:start position:0%
+eye diagram is and why it's kind of
+ 
+
+ align:start position:0%
+eye diagram is and why it's kind of
+useful and why as you add more noise
+
+ align:start position:0%
+useful and why as you add more noise
+ 
+
+ align:start position:0%
+useful and why as you add more noise
+into the system the combination of
+
+ align:start position:0%
+into the system the combination of
+ 
+
+ align:start position:0%
+into the system the combination of
+something called inter symbol
+
+ align:start position:0%
+something called inter symbol
+ 
+
+ align:start position:0%
+something called inter symbol
+interference and noise getting way
+
+ align:start position:0%
+interference and noise getting way
+ 
+
+ align:start position:0%
+interference and noise getting way
+recording the base now on this channel
+
+ align:start position:0%
+recording the base now on this channel
+ 
+
+ align:start position:0%
+recording the base now on this channel
+there are two things that distort the
+
+ align:start position:0%
+there are two things that distort the
+ 
+
+ align:start position:0%
+there are two things that distort the
+quality of communication the first is
+
+ align:start position:0%
+quality of communication the first is
+ 
+
+ align:start position:0%
+quality of communication the first is
+novice and you kind of saw the effect of
+
+ align:start position:0%
+novice and you kind of saw the effect of
+ 
+
+ align:start position:0%
+novice and you kind of saw the effect of
+that the second is this thing that we've
+
+ align:start position:0%
+that the second is this thing that we've
+ 
+
+ align:start position:0%
+that the second is this thing that we've
+been studying with by modeling it as a
+
+ align:start position:0%
+been studying with by modeling it as a
+ 
+
+ align:start position:0%
+been studying with by modeling it as a
+linear time-invariant system the idea is
+
+ align:start position:0%
+linear time-invariant system the idea is
+ 
+
+ align:start position:0%
+linear time-invariant system the idea is
+that when you have a sequence of zeros
+
+ align:start position:0%
+that when you have a sequence of zeros
+ 
+
+ align:start position:0%
+that when you have a sequence of zeros
+on the input and then you go into a
+
+ align:start position:0%
+on the input and then you go into a
+ 
+
+ align:start position:0%
+on the input and then you go into a
+sequence of one samples that sudden
+
+ align:start position:0%
+sequence of one samples that sudden
+ 
+
+ align:start position:0%
+sequence of one samples that sudden
+sharp input transition does not
+
+ align:start position:0%
+sharp input transition does not
+ 
+
+ align:start position:0%
+sharp input transition does not
+immediately get captured the receiver it
+
+ align:start position:0%
+immediately get captured the receiver it
+ 
+
+ align:start position:0%
+immediately get captured the receiver it
+takes time for the zero to settle into a
+
+ align:start position:0%
+takes time for the zero to settle into a
+ 
+
+ align:start position:0%
+takes time for the zero to settle into a
+one and one to settle in 20 and you can
+
+ align:start position:0%
+one and one to settle in 20 and you can
+ 
+
+ align:start position:0%
+one and one to settle in 20 and you can
+see that in this picture here now let's
+
+ align:start position:0%
+see that in this picture here now let's
+ 
+
+ align:start position:0%
+see that in this picture here now let's
+focus in in this picture here and look
+
+ align:start position:0%
+focus in in this picture here and look
+ 
+
+ align:start position:0%
+focus in in this picture here and look
+carefully at this place here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's do this again I learned
+
+ align:start position:0%
+all right let's do this again I learned
+ 
+
+ align:start position:0%
+all right let's do this again I learned
+about this like 15 minutes ago so bear
+
+ align:start position:0%
+about this like 15 minutes ago so bear
+ 
+
+ align:start position:0%
+about this like 15 minutes ago so bear
+with me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright so there was zeros at the bottom
+
+ align:start position:0%
+alright so there was zeros at the bottom
+ 
+
+ align:start position:0%
+alright so there was zeros at the bottom
+and then we bumped up to a one on the
+
+ align:start position:0%
+and then we bumped up to a one on the
+ 
+
+ align:start position:0%
+and then we bumped up to a one on the
+input the input bumped from a zero to a
+
+ align:start position:0%
+input the input bumped from a zero to a
+ 
+
+ align:start position:0%
+input the input bumped from a zero to a
+one this is after we'd be modulated so
+
+ align:start position:0%
+one this is after we'd be modulated so
+ 
+
+ align:start position:0%
+one this is after we'd be modulated so
+if things work perfectly you would see
+
+ align:start position:0%
+if things work perfectly you would see
+ 
+
+ align:start position:0%
+if things work perfectly you would see
+at the output the zero immediately goes
+
+ align:start position:0%
+at the output the zero immediately goes
+ 
+
+ align:start position:0%
+at the output the zero immediately goes
+to one but what do you actually see you
+
+ align:start position:0%
+to one but what do you actually see you
+ 
+
+ align:start position:0%
+to one but what do you actually see you
+see that it takes a while for the one to
+
+ align:start position:0%
+see that it takes a while for the one to
+ 
+
+ align:start position:0%
+see that it takes a while for the one to
+settle down right it goes from a zero to
+
+ align:start position:0%
+settle down right it goes from a zero to
+ 
+
+ align:start position:0%
+settle down right it goes from a zero to
+one sharply on the input but it takes a
+
+ align:start position:0%
+one sharply on the input but it takes a
+ 
+
+ align:start position:0%
+one sharply on the input but it takes a
+while to go from 0 to 1 and then I go up
+
+ align:start position:0%
+while to go from 0 to 1 and then I go up
+ 
+
+ align:start position:0%
+while to go from 0 to 1 and then I go up
+like that and then I want to go from one
+
+ align:start position:0%
+like that and then I want to go from one
+ 
+
+ align:start position:0%
+like that and then I want to go from one
+to zero and you can see that as it comes
+
+ align:start position:0%
+to zero and you can see that as it comes
+ 
+
+ align:start position:0%
+to zero and you can see that as it comes
+down to zero it takes a while to settle
+
+ align:start position:0%
+down to zero it takes a while to settle
+ 
+
+ align:start position:0%
+down to zero it takes a while to settle
+down do you guys all understand why that
+
+ align:start position:0%
+down do you guys all understand why that
+ 
+
+ align:start position:0%
+down do you guys all understand why that
+happens I don't mean the physics of why
+
+ align:start position:0%
+happens I don't mean the physics of why
+ 
+
+ align:start position:0%
+happens I don't mean the physics of why
+it happens but what I mean is how that
+
+ align:start position:0%
+it happens but what I mean is how that
+ 
+
+ align:start position:0%
+it happens but what I mean is how that
+idea relates to this idea of the unit
+
+ align:start position:0%
+idea relates to this idea of the unit
+ 
+
+ align:start position:0%
+idea relates to this idea of the unit
+step response from the unit sample
+
+ align:start position:0%
+step response from the unit sample
+ 
+
+ align:start position:0%
+step response from the unit sample
+response this is nothing more than the
+
+ align:start position:0%
+response this is nothing more than the
+ 
+
+ align:start position:0%
+response this is nothing more than the
+unit step response of this channel right
+
+ align:start position:0%
+unit step response of this channel right
+ 
+
+ align:start position:0%
+unit step response of this channel right
+I have a zero and I've assumed among 0
+
+ align:start position:0%
+I have a zero and I've assumed among 0
+ 
+
+ align:start position:0%
+I have a zero and I've assumed among 0
+for a while I bump up to a one and it
+
+ align:start position:0%
+for a while I bump up to a one and it
+ 
+
+ align:start position:0%
+for a while I bump up to a one and it
+takes a while for it to go from 0 to 1
+
+ align:start position:0%
+takes a while for it to go from 0 to 1
+ 
+
+ align:start position:0%
+takes a while for it to go from 0 to 1
+and similarly takes a while for it to go
+
+ align:start position:0%
+and similarly takes a while for it to go
+ 
+
+ align:start position:0%
+and similarly takes a while for it to go
+from one back to zero now suppose I end
+
+ align:start position:0%
+from one back to zero now suppose I end
+ 
+
+ align:start position:0%
+from one back to zero now suppose I end
+up switching 0 1 1 0 0 1 0 1 0 1 very
+
+ align:start position:0%
+up switching 0 1 1 0 0 1 0 1 0 1 very
+ 
+
+ align:start position:0%
+up switching 0 1 1 0 0 1 0 1 0 1 very
+very quickly and I don't give enough
+
+ align:start position:0%
+very quickly and I don't give enough
+ 
+
+ align:start position:0%
+very quickly and I don't give enough
+time for the whole thing to settle down
+
+ align:start position:0%
+time for the whole thing to settle down
+ 
+
+ align:start position:0%
+time for the whole thing to settle down
+in other words as I go from a zero to
+
+ align:start position:0%
+in other words as I go from a zero to
+ 
+
+ align:start position:0%
+in other words as I go from a zero to
+LaVon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before it settles down into one if the
+
+ align:start position:0%
+before it settles down into one if the
+ 
+
+ align:start position:0%
+before it settles down into one if the
+next bit is a zero and then I start
+
+ align:start position:0%
+next bit is a zero and then I start
+ 
+
+ align:start position:0%
+next bit is a zero and then I start
+coming down and before it the next bit
+
+ align:start position:0%
+coming down and before it the next bit
+ 
+
+ align:start position:0%
+coming down and before it the next bit
+settles down to 0 I get to a 1 and
+
+ align:start position:0%
+settles down to 0 I get to a 1 and
+ 
+
+ align:start position:0%
+settles down to 0 I get to a 1 and
+before it comes back to zero you know I
+
+ align:start position:0%
+before it comes back to zero you know I
+ 
+
+ align:start position:0%
+before it comes back to zero you know I
+keep doing that what I'm going to end up
+
+ align:start position:0%
+keep doing that what I'm going to end up
+ 
+
+ align:start position:0%
+keep doing that what I'm going to end up
+with is this combination of zeros and
+
+ align:start position:0%
+with is this combination of zeros and
+ 
+
+ align:start position:0%
+with is this combination of zeros and
+ones that are sort of random start
+
+ align:start position:0%
+ones that are sort of random start
+ 
+
+ align:start position:0%
+ones that are sort of random start
+confusing the receiver because we're not
+
+ align:start position:0%
+confusing the receiver because we're not
+ 
+
+ align:start position:0%
+confusing the receiver because we're not
+giving enough time for the zero to
+
+ align:start position:0%
+giving enough time for the zero to
+ 
+
+ align:start position:0%
+giving enough time for the zero to
+settle down and similarly when we go
+
+ align:start position:0%
+settle down and similarly when we go
+ 
+
+ align:start position:0%
+settle down and similarly when we go
+from a zero to one we're not giving
+
+ align:start position:0%
+from a zero to one we're not giving
+ 
+
+ align:start position:0%
+from a zero to one we're not giving
+enough time for the one to settle down
+
+ align:start position:0%
+enough time for the one to settle down
+ 
+
+ align:start position:0%
+enough time for the one to settle down
+that's what this I diagram was referring
+
+ align:start position:0%
+that's what this I diagram was referring
+ 
+
+ align:start position:0%
+that's what this I diagram was referring
+to where we found in this confused case
+
+ align:start position:0%
+to where we found in this confused case
+ 
+
+ align:start position:0%
+to where we found in this confused case
+and then when you have noise some of the
+
+ align:start position:0%
+and then when you have noise some of the
+ 
+
+ align:start position:0%
+and then when you have noise some of the
+zeros get moved to one anyway and ones
+
+ align:start position:0%
+zeros get moved to one anyway and ones
+ 
+
+ align:start position:0%
+zeros get moved to one anyway and ones
+get moved to zero and we end up with
+
+ align:start position:0%
+get moved to zero and we end up with
+ 
+
+ align:start position:0%
+get moved to zero and we end up with
+this very crowded picture the way you
+
+ align:start position:0%
+this very crowded picture the way you
+ 
+
+ align:start position:0%
+this very crowded picture the way you
+tackle this problem is it all has to do
+
+ align:start position:0%
+tackle this problem is it all has to do
+ 
+
+ align:start position:0%
+tackle this problem is it all has to do
+with the number of samples that you
+
+ align:start position:0%
+with the number of samples that you
+ 
+
+ align:start position:0%
+with the number of samples that you
+decide to use within one pit so coming
+
+ align:start position:0%
+decide to use within one pit so coming
+ 
+
+ align:start position:0%
+decide to use within one pit so coming
+back to this picture if I do this at
+
+ align:start position:0%
+back to this picture if I do this at
+ 
+
+ align:start position:0%
+back to this picture if I do this at
+forty eight thousand samples per second
+
+ align:start position:0%
+forty eight thousand samples per second
+ 
+
+ align:start position:0%
+forty eight thousand samples per second
+in any one of these carriers I have 48
+
+ align:start position:0%
+in any one of these carriers I have 48
+ 
+
+ align:start position:0%
+in any one of these carriers I have 48
+samples that I use but now I get to
+
+ align:start position:0%
+samples that I use but now I get to
+ 
+
+ align:start position:0%
+samples that I use but now I get to
+decide how many samples corresponds to
+
+ align:start position:0%
+decide how many samples corresponds to
+ 
+
+ align:start position:0%
+decide how many samples corresponds to
+one bit of information when I have a bit
+
+ align:start position:0%
+one bit of information when I have a bit
+ 
+
+ align:start position:0%
+one bit of information when I have a bit
+that I want to transmit let's say a 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many arm sounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what that effectively means is to
+
+ align:start position:0%
+what that effectively means is to
+ 
+
+ align:start position:0%
+what that effectively means is to
+transmit a one how many of these periods
+
+ align:start position:0%
+transmit a one how many of these periods
+ 
+
+ align:start position:0%
+transmit a one how many of these periods
+of this waveform do I want to use to
+
+ align:start position:0%
+of this waveform do I want to use to
+ 
+
+ align:start position:0%
+of this waveform do I want to use to
+transmit a one so for example if I pick
+
+ align:start position:0%
+transmit a one so for example if I pick
+ 
+
+ align:start position:0%
+transmit a one so for example if I pick
+um if I decide I want to send a one as
+
+ align:start position:0%
+um if I decide I want to send a one as
+ 
+
+ align:start position:0%
+um if I decide I want to send a one as
+three carriers of the waveform then in
+
+ align:start position:0%
+three carriers of the waveform then in
+ 
+
+ align:start position:0%
+three carriers of the waveform then in
+any one of these carriers I have 48
+
+ align:start position:0%
+any one of these carriers I have 48
+ 
+
+ align:start position:0%
+any one of these carriers I have 48
+samples therefore I represent a one as
+
+ align:start position:0%
+samples therefore I represent a one as
+ 
+
+ align:start position:0%
+samples therefore I represent a one as
+48 x 3 which is 144 samples probate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now to transmit a zero I could do a
+
+ align:start position:0%
+now to transmit a zero I could do a
+ 
+
+ align:start position:0%
+now to transmit a zero I could do a
+bunch of different things I could decide
+
+ align:start position:0%
+bunch of different things I could decide
+ 
+
+ align:start position:0%
+bunch of different things I could decide
+to keep the channel silent if I do that
+
+ align:start position:0%
+to keep the channel silent if I do that
+ 
+
+ align:start position:0%
+to keep the channel silent if I do that
+it's about on-off keying and that's what
+
+ align:start position:0%
+it's about on-off keying and that's what
+ 
+
+ align:start position:0%
+it's about on-off keying and that's what
+we're using here so we're sending one as
+
+ align:start position:0%
+we're using here so we're sending one as
+ 
+
+ align:start position:0%
+we're using here so we're sending one as
+if we decide to use 144 samples per bit
+
+ align:start position:0%
+if we decide to use 144 samples per bit
+ 
+
+ align:start position:0%
+if we decide to use 144 samples per bit
+then it means we represent a one as 144
+
+ align:start position:0%
+then it means we represent a one as 144
+ 
+
+ align:start position:0%
+then it means we represent a one as 144
+samples which corresponds to three of
+
+ align:start position:0%
+samples which corresponds to three of
+ 
+
+ align:start position:0%
+samples which corresponds to three of
+these and then we represent a zero as
+
+ align:start position:0%
+these and then we represent a zero as
+ 
+
+ align:start position:0%
+these and then we represent a zero as
+nothing so we don't say anything if we
+
+ align:start position:0%
+nothing so we don't say anything if we
+ 
+
+ align:start position:0%
+nothing so we don't say anything if we
+do that this is called on-off keying
+
+ align:start position:0%
+do that this is called on-off keying
+ 
+
+ align:start position:0%
+do that this is called on-off keying
+because we send on for one where we send
+
+ align:start position:0%
+because we send on for one where we send
+ 
+
+ align:start position:0%
+because we send on for one where we send
+a sinusoid and for sending a zero bit we
+
+ align:start position:0%
+a sinusoid and for sending a zero bit we
+ 
+
+ align:start position:0%
+a sinusoid and for sending a zero bit we
+send nothing now if the number of
+
+ align:start position:0%
+send nothing now if the number of
+ 
+
+ align:start position:0%
+send nothing now if the number of
+samples i select / bit is too small you
+
+ align:start position:0%
+samples i select / bit is too small you
+ 
+
+ align:start position:0%
+samples i select / bit is too small you
+end up with this effect that I don't
+
+ align:start position:0%
+end up with this effect that I don't
+ 
+
+ align:start position:0%
+end up with this effect that I don't
+give enough time for the 0 to settle
+
+ align:start position:0%
+give enough time for the 0 to settle
+ 
+
+ align:start position:0%
+give enough time for the 0 to settle
+down to better when I make the
+
+ align:start position:0%
+down to better when I make the
+ 
+
+ align:start position:0%
+down to better when I make the
+transition from a 0 to a 1 if I pick two
+
+ align:start position:0%
+transition from a 0 to a 1 if I pick two
+ 
+
+ align:start position:0%
+transition from a 0 to a 1 if I pick two
+small samples per bit before we settle
+
+ align:start position:0%
+small samples per bit before we settle
+ 
+
+ align:start position:0%
+small samples per bit before we settle
+into a 1 the next bit may show up as a 0
+
+ align:start position:0%
+into a 1 the next bit may show up as a 0
+ 
+
+ align:start position:0%
+into a 1 the next bit may show up as a 0
+and then before we settle down in 20 the
+
+ align:start position:0%
+and then before we settle down in 20 the
+ 
+
+ align:start position:0%
+and then before we settle down in 20 the
+next bit shows up perhaps as a 1 and we
+
+ align:start position:0%
+next bit shows up perhaps as a 1 and we
+ 
+
+ align:start position:0%
+next bit shows up perhaps as a 1 and we
+end up coming lling the zeros and the
+
+ align:start position:0%
+end up coming lling the zeros and the
+ 
+
+ align:start position:0%
+end up coming lling the zeros and the
+ones and we're not able at the receiver
+
+ align:start position:0%
+ones and we're not able at the receiver
+ 
+
+ align:start position:0%
+ones and we're not able at the receiver
+to tell the difference between these
+
+ align:start position:0%
+to tell the difference between these
+ 
+
+ align:start position:0%
+to tell the difference between these
+different voltage samples after we
+
+ align:start position:0%
+different voltage samples after we
+ 
+
+ align:start position:0%
+different voltage samples after we
+demodulate so we don't know what
+
+ align:start position:0%
+demodulate so we don't know what
+ 
+
+ align:start position:0%
+demodulate so we don't know what
+happened so if the eye diagram is a way
+
+ align:start position:0%
+happened so if the eye diagram is a way
+ 
+
+ align:start position:0%
+happened so if the eye diagram is a way
+to capture that what the eye diagram
+
+ align:start position:0%
+to capture that what the eye diagram
+ 
+
+ align:start position:0%
+to capture that what the eye diagram
+does is it's a kind of a clever hack
+
+ align:start position:0%
+does is it's a kind of a clever hack
+ 
+
+ align:start position:0%
+does is it's a kind of a clever hack
+what it does is thought I had it
+
+ align:start position:0%
+what it does is thought I had it
+ 
+
+ align:start position:0%
+what it does is thought I had it
+somewhere else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way you generate an eye diagram you
+
+ align:start position:0%
+the way you generate an eye diagram you
+ 
+
+ align:start position:0%
+the way you generate an eye diagram you
+don't have to worry about the writing
+
+ align:start position:0%
+don't have to worry about the writing
+ 
+
+ align:start position:0%
+don't have to worry about the writing
+the software for it but you will look at
+
+ align:start position:0%
+the software for it but you will look at
+ 
+
+ align:start position:0%
+the software for it but you will look at
+a lot of these kinds of pictures in lab
+
+ align:start position:0%
+a lot of these kinds of pictures in lab
+ 
+
+ align:start position:0%
+a lot of these kinds of pictures in lab
+5 you transmit a random sequence of bits
+
+ align:start position:0%
+5 you transmit a random sequence of bits
+ 
+
+ align:start position:0%
+5 you transmit a random sequence of bits
+and then you look at the samples that
+
+ align:start position:0%
+and then you look at the samples that
+ 
+
+ align:start position:0%
+and then you look at the samples that
+were received at the receiver after the
+
+ align:start position:0%
+were received at the receiver after the
+ 
+
+ align:start position:0%
+were received at the receiver after the
+demodulation was done those the output
+
+ align:start position:0%
+demodulation was done those the output
+ 
+
+ align:start position:0%
+demodulation was done those the output
+of the demodulation is a set of voltage
+
+ align:start position:0%
+of the demodulation is a set of voltage
+ 
+
+ align:start position:0%
+of the demodulation is a set of voltage
+values what you do is you look at three
+
+ align:start position:0%
+values what you do is you look at three
+ 
+
+ align:start position:0%
+values what you do is you look at three
+bit periods in other words you look at a
+
+ align:start position:0%
+bit periods in other words you look at a
+ 
+
+ align:start position:0%
+bit periods in other words you look at a
+sequence of time a number of samples
+
+ align:start position:0%
+sequence of time a number of samples
+ 
+
+ align:start position:0%
+sequence of time a number of samples
+that corresponds to three big period so
+
+ align:start position:0%
+that corresponds to three big period so
+ 
+
+ align:start position:0%
+that corresponds to three big period so
+for example if i pick 144 samples per
+
+ align:start position:0%
+for example if i pick 144 samples per
+ 
+
+ align:start position:0%
+for example if i pick 144 samples per
+big what I do is I take 144 and multiply
+
+ align:start position:0%
+big what I do is I take 144 and multiply
+ 
+
+ align:start position:0%
+big what I do is I take 144 and multiply
+that by three a bit periods and I look
+
+ align:start position:0%
+that by three a bit periods and I look
+ 
+
+ align:start position:0%
+that by three a bit periods and I look
+at that many samples so for every three
+
+ align:start position:0%
+at that many samples so for every three
+ 
+
+ align:start position:0%
+at that many samples so for every three
+big periods I take all the samples and I
+
+ align:start position:0%
+big periods I take all the samples and I
+ 
+
+ align:start position:0%
+big periods I take all the samples and I
+plot them okay so a particular sequence
+
+ align:start position:0%
+plot them okay so a particular sequence
+ 
+
+ align:start position:0%
+plot them okay so a particular sequence
+of bits in this case it might be a0 and
+
+ align:start position:0%
+of bits in this case it might be a0 and
+ 
+
+ align:start position:0%
+of bits in this case it might be a0 and
+a1 and a0 this is a zero followed by a
+
+ align:start position:0%
+a1 and a0 this is a zero followed by a
+ 
+
+ align:start position:0%
+a1 and a0 this is a zero followed by a
+one followed by zero a different
+
+ align:start position:0%
+one followed by zero a different
+ 
+
+ align:start position:0%
+one followed by zero a different
+sequence of bits could be a one followed
+
+ align:start position:0%
+sequence of bits could be a one followed
+ 
+
+ align:start position:0%
+sequence of bits could be a one followed
+by one followed by one a different
+
+ align:start position:0%
+by one followed by one a different
+ 
+
+ align:start position:0%
+by one followed by one a different
+sequence of bits could be a zero
+
+ align:start position:0%
+sequence of bits could be a zero
+ 
+
+ align:start position:0%
+sequence of bits could be a zero
+followed by zero followed by zero so
+
+ align:start position:0%
+followed by zero followed by zero so
+ 
+
+ align:start position:0%
+followed by zero followed by zero so
+there are you know eight combinations of
+
+ align:start position:0%
+there are you know eight combinations of
+ 
+
+ align:start position:0%
+there are you know eight combinations of
+sequences of three bits each so there
+
+ align:start position:0%
+sequences of three bits each so there
+ 
+
+ align:start position:0%
+sequences of three bits each so there
+are eight you know you have a clean
+
+ align:start position:0%
+are eight you know you have a clean
+ 
+
+ align:start position:0%
+are eight you know you have a clean
+system clean I diagram like this you're
+
+ align:start position:0%
+system clean I diagram like this you're
+ 
+
+ align:start position:0%
+system clean I diagram like this you're
+going to see a variety of different
+
+ align:start position:0%
+going to see a variety of different
+ 
+
+ align:start position:0%
+going to see a variety of different
+lines corresponding to all the places
+
+ align:start position:0%
+lines corresponding to all the places
+ 
+
+ align:start position:0%
+lines corresponding to all the places
+where different three bit sequences
+
+ align:start position:0%
+where different three bit sequences
+ 
+
+ align:start position:0%
+where different three bit sequences
+appeared in your input so for any given
+
+ align:start position:0%
+appeared in your input so for any given
+ 
+
+ align:start position:0%
+appeared in your input so for any given
+3-bit sequence at the input there's a
+
+ align:start position:0%
+3-bit sequence at the input there's a
+ 
+
+ align:start position:0%
+3-bit sequence at the input there's a
+3-bit sample sequence at the output that
+
+ align:start position:0%
+3-bit sample sequence at the output that
+ 
+
+ align:start position:0%
+3-bit sample sequence at the output that
+corresponds to a number of samples equal
+
+ align:start position:0%
+corresponds to a number of samples equal
+ 
+
+ align:start position:0%
+corresponds to a number of samples equal
+to the samples per bit x three
+
+ align:start position:0%
+to the samples per bit x three
+ 
+
+ align:start position:0%
+to the samples per bit x three
+and each of those generates one of those
+
+ align:start position:0%
+and each of those generates one of those
+ 
+
+ align:start position:0%
+and each of those generates one of those
+trajectories through this picture if you
+
+ align:start position:0%
+trajectories through this picture if you
+ 
+
+ align:start position:0%
+trajectories through this picture if you
+generate that picture and you find that
+
+ align:start position:0%
+generate that picture and you find that
+ 
+
+ align:start position:0%
+generate that picture and you find that
+there's a very clean gap between all
+
+ align:start position:0%
+there's a very clean gap between all
+ 
+
+ align:start position:0%
+there's a very clean gap between all
+possible combinations of these bit
+
+ align:start position:0%
+possible combinations of these bit
+ 
+
+ align:start position:0%
+possible combinations of these bit
+sequences as is in this case here then
+
+ align:start position:0%
+sequences as is in this case here then
+ 
+
+ align:start position:0%
+sequences as is in this case here then
+it means that you've been able to decode
+
+ align:start position:0%
+it means that you've been able to decode
+ 
+
+ align:start position:0%
+it means that you've been able to decode
+you're very likely to be able to decode
+
+ align:start position:0%
+you're very likely to be able to decode
+ 
+
+ align:start position:0%
+you're very likely to be able to decode
+because what you can do is essentially
+
+ align:start position:0%
+because what you can do is essentially
+ 
+
+ align:start position:0%
+because what you can do is essentially
+the receiver can decide that you know
+
+ align:start position:0%
+the receiver can decide that you know
+ 
+
+ align:start position:0%
+the receiver can decide that you know
+when one's happen it corresponds to
+
+ align:start position:0%
+when one's happen it corresponds to
+ 
+
+ align:start position:0%
+when one's happen it corresponds to
+something over here at point three five
+
+ align:start position:0%
+something over here at point three five
+ 
+
+ align:start position:0%
+something over here at point three five
+or point 4 volts when a zero happens it
+
+ align:start position:0%
+or point 4 volts when a zero happens it
+ 
+
+ align:start position:0%
+or point 4 volts when a zero happens it
+may not be a zero but it'd make a
+
+ align:start position:0%
+may not be a zero but it'd make a
+ 
+
+ align:start position:0%
+may not be a zero but it'd make a
+respond to something like a point 1 volt
+
+ align:start position:0%
+respond to something like a point 1 volt
+ 
+
+ align:start position:0%
+respond to something like a point 1 volt
+here which means i can pick the middle
+
+ align:start position:0%
+here which means i can pick the middle
+ 
+
+ align:start position:0%
+here which means i can pick the middle
+point and slice it at that middle point
+
+ align:start position:0%
+point and slice it at that middle point
+ 
+
+ align:start position:0%
+point and slice it at that middle point
+to determine whether the receive bits
+
+ align:start position:0%
+to determine whether the receive bits
+ 
+
+ align:start position:0%
+to determine whether the receive bits
+were a 0 or a 1 now if we would run this
+
+ align:start position:0%
+were a 0 or a 1 now if we would run this
+ 
+
+ align:start position:0%
+were a 0 or a 1 now if we would run this
+experiment again and make a lot of noise
+
+ align:start position:0%
+experiment again and make a lot of noise
+ 
+
+ align:start position:0%
+experiment again and make a lot of noise
+let's try that what could happen is we
+
+ align:start position:0%
+let's try that what could happen is we
+ 
+
+ align:start position:0%
+let's try that what could happen is we
+may not be able to decode at all so I'm
+
+ align:start position:0%
+may not be able to decode at all so I'm
+ 
+
+ align:start position:0%
+may not be able to decode at all so I'm
+going to request you guys to make a
+
+ align:start position:0%
+going to request you guys to make a
+ 
+
+ align:start position:0%
+going to request you guys to make a
+little bit of noise so after I start and
+
+ align:start position:0%
+little bit of noise so after I start and
+ 
+
+ align:start position:0%
+little bit of noise so after I start and
+then we'll see how it goes alright start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know what it wasn't loud enough it
+
+ align:start position:0%
+you know what it wasn't loud enough it
+ 
+
+ align:start position:0%
+you know what it wasn't loud enough it
+work great but let's look at what the
+
+ align:start position:0%
+work great but let's look at what the
+ 
+
+ align:start position:0%
+work great but let's look at what the
+eye diagram looks like well that's a
+
+ align:start position:0%
+eye diagram looks like well that's a
+ 
+
+ align:start position:0%
+eye diagram looks like well that's a
+little worse than the other one but i
+
+ align:start position:0%
+little worse than the other one but i
+ 
+
+ align:start position:0%
+little worse than the other one but i
+think the energy is down in this room so
+
+ align:start position:0%
+think the energy is down in this room so
+ 
+
+ align:start position:0%
+think the energy is down in this room so
+let's do it one more time oh I want to
+
+ align:start position:0%
+let's do it one more time oh I want to
+ 
+
+ align:start position:0%
+let's do it one more time oh I want to
+be in a position where nothing decodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well fifteen percent bit errors in fact
+
+ align:start position:0%
+well fifteen percent bit errors in fact
+ 
+
+ align:start position:0%
+well fifteen percent bit errors in fact
+my preamble decoded which is amazing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what it looked like ok this is a
+
+ align:start position:0%
+that's what it looked like ok this is a
+ 
+
+ align:start position:0%
+that's what it looked like ok this is a
+an eye diagram even a mother wouldn't
+
+ align:start position:0%
+an eye diagram even a mother wouldn't
+ 
+
+ align:start position:0%
+an eye diagram even a mother wouldn't
+like all right so I'm going to stop here
+
+ align:start position:0%
+like all right so I'm going to stop here
+ 
+
+ align:start position:0%
+like all right so I'm going to stop here
+before I turn it over to Professor with
+
+ align:start position:0%
+before I turn it over to Professor with
+ 
+
+ align:start position:0%
+before I turn it over to Professor with
+these are there any questions anything
+
+ align:start position:0%
+these are there any questions anything
+ 
+
+ align:start position:0%
+these are there any questions anything
+at all I know some of you have had
+
+ align:start position:0%
+at all I know some of you have had
+ 
+
+ align:start position:0%
+at all I know some of you have had
+issues and I met want to talk you this
+
+ align:start position:0%
+issues and I met want to talk you this
+ 
+
+ align:start position:0%
+issues and I met want to talk you this
+morning to fix your computers and I'm
+
+ align:start position:0%
+morning to fix your computers and I'm
+ 
+
+ align:start position:0%
+morning to fix your computers and I'm
+happy to do that I'll be in the lab from
+
+ align:start position:0%
+happy to do that I'll be in the lab from
+ 
+
+ align:start position:0%
+happy to do that I'll be in the lab from
+four o'clock we'll get it working on
+
+ align:start position:0%
+four o'clock we'll get it working on
+ 
+
+ align:start position:0%
+four o'clock we'll get it working on
+your computer's if it doesn't work then
+
+ align:start position:0%
+your computer's if it doesn't work then
+ 
+
+ align:start position:0%
+your computer's if it doesn't work then
+you're going to have to use the lab
+
+ align:start position:0%
+you're going to have to use the lab
+ 
+
+ align:start position:0%
+you're going to have to use the lab
+machines let's take some questions or
+
+ align:start position:0%
+machines let's take some questions or
+ 
+
+ align:start position:0%
+machines let's take some questions or
+comments any if people have any
+
+ align:start position:0%
+comments any if people have any
+ 
+
+ align:start position:0%
+comments any if people have any
+questions about this stuff so people get
+
+ align:start position:0%
+questions about this stuff so people get
+ 
+
+ align:start position:0%
+questions about this stuff so people get
+an idea of what's going on and what you
+
+ align:start position:0%
+an idea of what's going on and what you
+ 
+
+ align:start position:0%
+an idea of what's going on and what you
+need to do once you get this working the
+
+ align:start position:0%
+need to do once you get this working the
+ 
+
+ align:start position:0%
+need to do once you get this working the
+labs sort of you know they'll write
+
+ align:start position:0%
+labs sort of you know they'll write
+ 
+
+ align:start position:0%
+labs sort of you know they'll write
+themselves you just have to a little bit
+
+ align:start position:0%
+themselves you just have to a little bit
+ 
+
+ align:start position:0%
+themselves you just have to a little bit
+of work
+
+ align:start position:0%
+of work
+ 
+
+ align:start position:0%
+of work
+questions this can go up to higher
+
+ align:start position:0%
+questions this can go up to higher
+ 
+
+ align:start position:0%
+questions this can go up to higher
+frequencies to so the sounds annoying
+
+ align:start position:0%
+frequencies to so the sounds annoying
+ 
+
+ align:start position:0%
+frequencies to so the sounds annoying
+your ears you can actually get it to
+
+ align:start position:0%
+your ears you can actually get it to
+ 
+
+ align:start position:0%
+your ears you can actually get it to
+work I know one of you guys is trying to
+
+ align:start position:0%
+work I know one of you guys is trying to
+ 
+
+ align:start position:0%
+work I know one of you guys is trying to
+get this to work with ultrasonic
+
+ align:start position:0%
+get this to work with ultrasonic
+ 
+
+ align:start position:0%
+get this to work with ultrasonic
+reception that's challenging but we can
+
+ align:start position:0%
+reception that's challenging but we can
+ 
+
+ align:start position:0%
+reception that's challenging but we can
+probably help you off yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform noise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you mean if you were to make
+
+ align:start position:0%
+yeah you mean if you were to make
+ 
+
+ align:start position:0%
+yeah you mean if you were to make
+another transmission are exactly the
+
+ align:start position:0%
+another transmission are exactly the
+ 
+
+ align:start position:0%
+another transmission are exactly the
+same frequency the beauty of this is
+
+ align:start position:0%
+same frequency the beauty of this is
+ 
+
+ align:start position:0%
+same frequency the beauty of this is
+that there's there's different
+
+ align:start position:0%
+that there's there's different
+ 
+
+ align:start position:0%
+that there's there's different
+demodulation schemes right now we're
+
+ align:start position:0%
+demodulation schemes right now we're
+ 
+
+ align:start position:0%
+demodulation schemes right now we're
+using something called the envelope
+
+ align:start position:0%
+using something called the envelope
+ 
+
+ align:start position:0%
+using something called the envelope
+demodulation which are several gives
+
+ align:start position:0%
+demodulation which are several gives
+ 
+
+ align:start position:0%
+demodulation which are several gives
+talked about before all that's doing is
+
+ align:start position:0%
+talked about before all that's doing is
+ 
+
+ align:start position:0%
+talked about before all that's doing is
+it's taking the absolute value of every
+
+ align:start position:0%
+it's taking the absolute value of every
+ 
+
+ align:start position:0%
+it's taking the absolute value of every
+received sample and then running a
+
+ align:start position:0%
+received sample and then running a
+ 
+
+ align:start position:0%
+received sample and then running a
+simple averaging filter and that's what
+
+ align:start position:0%
+simple averaging filter and that's what
+ 
+
+ align:start position:0%
+simple averaging filter and that's what
+you write in the lab it's a very very
+
+ align:start position:0%
+you write in the lab it's a very very
+ 
+
+ align:start position:0%
+you write in the lab it's a very very
+simple demodulation will study something
+
+ align:start position:0%
+simple demodulation will study something
+ 
+
+ align:start position:0%
+simple demodulation will study something
+called quadrature demodulation in a
+
+ align:start position:0%
+called quadrature demodulation in a
+ 
+
+ align:start position:0%
+called quadrature demodulation in a
+probably next lecture or the one after
+
+ align:start position:0%
+probably next lecture or the one after
+ 
+
+ align:start position:0%
+probably next lecture or the one after
+that which means that we'll have the
+
+ align:start position:0%
+that which means that we'll have the
+ 
+
+ align:start position:0%
+that which means that we'll have the
+property that if you transmit at a
+
+ align:start position:0%
+property that if you transmit at a
+ 
+
+ align:start position:0%
+property that if you transmit at a
+certain frequency and somebody else
+
+ align:start position:0%
+certain frequency and somebody else
+ 
+
+ align:start position:0%
+certain frequency and somebody else
+interferes and transmits at a different
+
+ align:start position:0%
+interferes and transmits at a different
+ 
+
+ align:start position:0%
+interferes and transmits at a different
+carrier frequency you're still going to
+
+ align:start position:0%
+carrier frequency you're still going to
+ 
+
+ align:start position:0%
+carrier frequency you're still going to
+be able to recover your transmission but
+
+ align:start position:0%
+be able to recover your transmission but
+ 
+
+ align:start position:0%
+be able to recover your transmission but
+if it if the other transmitter has
+
+ align:start position:0%
+if it if the other transmitter has
+ 
+
+ align:start position:0%
+if it if the other transmitter has
+significant strength signal strength in
+
+ align:start position:0%
+significant strength signal strength in
+ 
+
+ align:start position:0%
+significant strength signal strength in
+the same frequencies that you're
+
+ align:start position:0%
+the same frequencies that you're
+ 
+
+ align:start position:0%
+the same frequencies that you're
+transmitting in then he's going to start
+
+ align:start position:0%
+transmitting in then he's going to start
+ 
+
+ align:start position:0%
+transmitting in then he's going to start
+to look like noise to you and that's
+
+ align:start position:0%
+to look like noise to you and that's
+ 
+
+ align:start position:0%
+to look like noise to you and that's
+going to not work so what happened here
+
+ align:start position:0%
+going to not work so what happened here
+ 
+
+ align:start position:0%
+going to not work so what happened here
+is when you guys were all whistling and
+
+ align:start position:0%
+is when you guys were all whistling and
+ 
+
+ align:start position:0%
+is when you guys were all whistling and
+were clapping and so on you know there
+
+ align:start position:0%
+were clapping and so on you know there
+ 
+
+ align:start position:0%
+were clapping and so on you know there
+was there were signal generated across
+
+ align:start position:0%
+was there were signal generated across
+ 
+
+ align:start position:0%
+was there were signal generated across
+all frequencies including the frequency
+
+ align:start position:0%
+all frequencies including the frequency
+ 
+
+ align:start position:0%
+all frequencies including the frequency
+at which I was transmitting and that's
+
+ align:start position:0%
+at which I was transmitting and that's
+ 
+
+ align:start position:0%
+at which I was transmitting and that's
+what caused the signal to have noise
+
+ align:start position:0%
+what caused the signal to have noise
+ 
+
+ align:start position:0%
+what caused the signal to have noise
+it's not like you know you were all
+
+ align:start position:0%
+it's not like you know you were all
+ 
+
+ align:start position:0%
+it's not like you know you were all
+transmitting at a thousand Hertz it just
+
+ align:start position:0%
+transmitting at a thousand Hertz it just
+ 
+
+ align:start position:0%
+transmitting at a thousand Hertz it just
+so happens that you know that
+
+ align:start position:0%
+so happens that you know that
+ 
+
+ align:start position:0%
+so happens that you know that
+combination of noise you were making had
+
+ align:start position:0%
+combination of noise you were making had
+ 
+
+ align:start position:0%
+combination of noise you were making had
+a component a thousand Hertz that answer
+
+ align:start position:0%
+a component a thousand Hertz that answer
+ 
+
+ align:start position:0%
+a component a thousand Hertz that answer
+your question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other questions comments or marks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah we've been talking about
+
+ align:start position:0%
+okay yeah we've been talking about
+ 
+
+ align:start position:0%
+okay yeah we've been talking about
+modeling the baseband channel and we've
+
+ align:start position:0%
+modeling the baseband channel and we've
+ 
+
+ align:start position:0%
+modeling the baseband channel and we've
+said we'll focus on LTI channels so I
+
+ align:start position:0%
+said we'll focus on LTI channels so I
+ 
+
+ align:start position:0%
+said we'll focus on LTI channels so I
+just wanted to take advantage of this
+
+ align:start position:0%
+just wanted to take advantage of this
+ 
+
+ align:start position:0%
+just wanted to take advantage of this
+being up here to have you think about
+
+ align:start position:0%
+being up here to have you think about
+ 
+
+ align:start position:0%
+being up here to have you think about
+what this tells you about how close to
+
+ align:start position:0%
+what this tells you about how close to
+ 
+
+ align:start position:0%
+what this tells you about how close to
+linear this channel is and how close to
+
+ align:start position:0%
+linear this channel is and how close to
+ 
+
+ align:start position:0%
+linear this channel is and how close to
+time invariant it is what do you think
+
+ align:start position:0%
+time invariant it is what do you think
+ 
+
+ align:start position:0%
+time invariant it is what do you think
+what we're seeing here is for instance a
+
+ align:start position:0%
+what we're seeing here is for instance a
+ 
+
+ align:start position:0%
+what we're seeing here is for instance a
+step response to something that's at
+
+ align:start position:0%
+step response to something that's at
+ 
+
+ align:start position:0%
+step response to something that's at
+zero and then goes up to one and stays
+
+ align:start position:0%
+zero and then goes up to one and stays
+ 
+
+ align:start position:0%
+zero and then goes up to one and stays
+at one we're seeing a superposition of
+
+ align:start position:0%
+at one we're seeing a superposition of
+ 
+
+ align:start position:0%
+at one we're seeing a superposition of
+many such 021 transitions some 120
+
+ align:start position:0%
+many such 021 transitions some 120
+ 
+
+ align:start position:0%
+many such 021 transitions some 120
+transitions later 120 transitions and so
+
+ align:start position:0%
+transitions later 120 transitions and so
+ 
+
+ align:start position:0%
+transitions later 120 transitions and so
+on right so we're really looking at a
+
+ align:start position:0%
+on right so we're really looking at a
+ 
+
+ align:start position:0%
+on right so we're really looking at a
+superposition of step responses
+
+ align:start position:0%
+superposition of step responses
+ 
+
+ align:start position:0%
+superposition of step responses
+staggered in time and going from 0 to
+
+ align:start position:0%
+staggered in time and going from 0 to
+ 
+
+ align:start position:0%
+staggered in time and going from 0 to
+100 120 do you think time and variances
+
+ align:start position:0%
+100 120 do you think time and variances
+ 
+
+ align:start position:0%
+100 120 do you think time and variances
+may be a good assumption for this
+
+ align:start position:0%
+may be a good assumption for this
+ 
+
+ align:start position:0%
+may be a good assumption for this
+channel plausible right because the step
+
+ align:start position:0%
+channel plausible right because the step
+ 
+
+ align:start position:0%
+channel plausible right because the step
+that we get here looks a lot like the
+
+ align:start position:0%
+that we get here looks a lot like the
+ 
+
+ align:start position:0%
+that we get here looks a lot like the
+step we're getting here the deviations
+
+ align:start position:0%
+step we're getting here the deviations
+ 
+
+ align:start position:0%
+step we're getting here the deviations
+might be noise but the more structured
+
+ align:start position:0%
+might be noise but the more structured
+ 
+
+ align:start position:0%
+might be noise but the more structured
+parts of the waveform here match the
+
+ align:start position:0%
+parts of the waveform here match the
+ 
+
+ align:start position:0%
+parts of the waveform here match the
+structured part of the waveform here and
+
+ align:start position:0%
+structured part of the waveform here and
+ 
+
+ align:start position:0%
+structured part of the waveform here and
+what you're really seeing is the the
+
+ align:start position:0%
+what you're really seeing is the the
+ 
+
+ align:start position:0%
+what you're really seeing is the the
+loudspeaker here reverberating through
+
+ align:start position:0%
+loudspeaker here reverberating through
+ 
+
+ align:start position:0%
+loudspeaker here reverberating through
+the room their eggs you're all staying
+
+ align:start position:0%
+the room their eggs you're all staying
+ 
+
+ align:start position:0%
+the room their eggs you're all staying
+fixed so the echoes are from fixed
+
+ align:start position:0%
+fixed so the echoes are from fixed
+ 
+
+ align:start position:0%
+fixed so the echoes are from fixed
+locations the walls are fixed and so
+
+ align:start position:0%
+locations the walls are fixed and so
+ 
+
+ align:start position:0%
+locations the walls are fixed and so
+what we're seeing is the step response
+
+ align:start position:0%
+what we're seeing is the step response
+ 
+
+ align:start position:0%
+what we're seeing is the step response
+of the room in effect and if you hit the
+
+ align:start position:0%
+of the room in effect and if you hit the
+ 
+
+ align:start position:0%
+of the room in effect and if you hit the
+room a little bit later while you get
+
+ align:start position:0%
+room a little bit later while you get
+ 
+
+ align:start position:0%
+room a little bit later while you get
+the same response but a little later
+
+ align:start position:0%
+the same response but a little later
+ 
+
+ align:start position:0%
+the same response but a little later
+does this look like it's very linear it
+
+ align:start position:0%
+does this look like it's very linear it
+ 
+
+ align:start position:0%
+does this look like it's very linear it
+would linearity the good assumption for
+
+ align:start position:0%
+would linearity the good assumption for
+ 
+
+ align:start position:0%
+would linearity the good assumption for
+this channel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean this is very partial information
+
+ align:start position:0%
+I mean this is very partial information
+ 
+
+ align:start position:0%
+I mean this is very partial information
+but does it give you enough to to judge
+
+ align:start position:0%
+but does it give you enough to to judge
+ 
+
+ align:start position:0%
+but does it give you enough to to judge
+so why do you think it linearity might
+
+ align:start position:0%
+so why do you think it linearity might
+ 
+
+ align:start position:0%
+so why do you think it linearity might
+be good here were you saying yes it's a
+
+ align:start position:0%
+be good here were you saying yes it's a
+ 
+
+ align:start position:0%
+be good here were you saying yes it's a
+good assumption because what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that's the time invariance argument
+
+ align:start position:0%
+but that's the time invariance argument
+ 
+
+ align:start position:0%
+but that's the time invariance argument
+that you're giving me what's a linearity
+
+ align:start position:0%
+that you're giving me what's a linearity
+ 
+
+ align:start position:0%
+that you're giving me what's a linearity
+argument yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so when you scale so we're not
+
+ align:start position:0%
+okay so when you scale so we're not
+ 
+
+ align:start position:0%
+okay so when you scale so we're not
+really seeing too much while we are
+
+ align:start position:0%
+really seeing too much while we are
+ 
+
+ align:start position:0%
+really seeing too much while we are
+seeing scaling what kind of scaling are
+
+ align:start position:0%
+seeing scaling what kind of scaling are
+ 
+
+ align:start position:0%
+seeing scaling what kind of scaling are
+you seeing here we have zero to one
+
+ align:start position:0%
+you seeing here we have zero to one
+ 
+
+ align:start position:0%
+you seeing here we have zero to one
+transitions but we also have 120 kinds
+
+ align:start position:0%
+transitions but we also have 120 kinds
+ 
+
+ align:start position:0%
+transitions but we also have 120 kinds
+of transitions right what would you want
+
+ align:start position:0%
+of transitions right what would you want
+ 
+
+ align:start position:0%
+of transitions right what would you want
+to see for a linear channel for how the
+
+ align:start position:0%
+to see for a linear channel for how the
+ 
+
+ align:start position:0%
+to see for a linear channel for how the
+120 transition behaves relative to the
+
+ align:start position:0%
+120 transition behaves relative to the
+ 
+
+ align:start position:0%
+120 transition behaves relative to the
+zero to one transition what would you
+
+ align:start position:0%
+zero to one transition what would you
+ 
+
+ align:start position:0%
+zero to one transition what would you
+expect on the linear channel yeah so
+
+ align:start position:0%
+expect on the linear channel yeah so
+ 
+
+ align:start position:0%
+expect on the linear channel yeah so
+from superposition you would really
+
+ align:start position:0%
+from superposition you would really
+ 
+
+ align:start position:0%
+from superposition you would really
+expect to see the same shape on the
+
+ align:start position:0%
+expect to see the same shape on the
+ 
+
+ align:start position:0%
+expect to see the same shape on the
+downslope that you see on the upslope
+
+ align:start position:0%
+downslope that you see on the upslope
+ 
+
+ align:start position:0%
+downslope that you see on the upslope
+right so when you look at the upward
+
+ align:start position:0%
+right so when you look at the upward
+ 
+
+ align:start position:0%
+right so when you look at the upward
+transition here you see a certain shape
+
+ align:start position:0%
+transition here you see a certain shape
+ 
+
+ align:start position:0%
+transition here you see a certain shape
+well it's not quite matched on the
+
+ align:start position:0%
+well it's not quite matched on the
+ 
+
+ align:start position:0%
+well it's not quite matched on the
+downward slope here and the reason is
+
+ align:start position:0%
+downward slope here and the reason is
+ 
+
+ align:start position:0%
+downward slope here and the reason is
+that the particular simple demodulation
+
+ align:start position:0%
+that the particular simple demodulation
+ 
+
+ align:start position:0%
+that the particular simple demodulation
+we're using here for this on/off scheme
+
+ align:start position:0%
+we're using here for this on/off scheme
+ 
+
+ align:start position:0%
+we're using here for this on/off scheme
+actually makes that not look very linear
+
+ align:start position:0%
+actually makes that not look very linear
+ 
+
+ align:start position:0%
+actually makes that not look very linear
+for signals that are four channels that
+
+ align:start position:0%
+for signals that are four channels that
+ 
+
+ align:start position:0%
+for signals that are four channels that
+have this kind of an overshoot to them
+
+ align:start position:0%
+have this kind of an overshoot to them
+ 
+
+ align:start position:0%
+have this kind of an overshoot to them
+but the other scheme that Hari mentioned
+
+ align:start position:0%
+but the other scheme that Hari mentioned
+ 
+
+ align:start position:0%
+but the other scheme that Hari mentioned
+the quadrature demodulation will
+
+ align:start position:0%
+the quadrature demodulation will
+ 
+
+ align:start position:0%
+the quadrature demodulation will
+actually do a lot better we in fact saw
+
+ align:start position:0%
+actually do a lot better we in fact saw
+ 
+
+ align:start position:0%
+actually do a lot better we in fact saw
+that right we saw that there was
+
+ align:start position:0%
+that right we saw that there was
+ 
+
+ align:start position:0%
+that right we saw that there was
+modulation that essentially pulled out
+
+ align:start position:0%
+modulation that essentially pulled out
+ 
+
+ align:start position:0%
+modulation that essentially pulled out
+essentially pulled out the absolute
+
+ align:start position:0%
+essentially pulled out the absolute
+ 
+
+ align:start position:0%
+essentially pulled out the absolute
+value of what you were sending and then
+
+ align:start position:0%
+value of what you were sending and then
+ 
+
+ align:start position:0%
+value of what you were sending and then
+there was another modulation scheme that
+
+ align:start position:0%
+there was another modulation scheme that
+ 
+
+ align:start position:0%
+there was another modulation scheme that
+actually pulled out the signal itself
+
+ align:start position:0%
+actually pulled out the signal itself
+ 
+
+ align:start position:0%
+actually pulled out the signal itself
+and so if you if you're doing things
+
+ align:start position:0%
+and so if you if you're doing things
+ 
+
+ align:start position:0%
+and so if you if you're doing things
+like taking absolute value somewhere in
+
+ align:start position:0%
+like taking absolute value somewhere in
+ 
+
+ align:start position:0%
+like taking absolute value somewhere in
+the middle there then you're going to
+
+ align:start position:0%
+the middle there then you're going to
+ 
+
+ align:start position:0%
+the middle there then you're going to
+start losing the ability to model it as
+
+ align:start position:0%
+start losing the ability to model it as
+ 
+
+ align:start position:0%
+start losing the ability to model it as
+linear okay so linear time-invariant
+
+ align:start position:0%
+linear okay so linear time-invariant
+ 
+
+ align:start position:0%
+linear okay so linear time-invariant
+models are not necessarily good for all
+
+ align:start position:0%
+models are not necessarily good for all
+ 
+
+ align:start position:0%
+models are not necessarily good for all
+channels it's something that you've got
+
+ align:start position:0%
+channels it's something that you've got
+ 
+
+ align:start position:0%
+channels it's something that you've got
+to look for their good reasons to try
+
+ align:start position:0%
+to look for their good reasons to try
+ 
+
+ align:start position:0%
+to look for their good reasons to try
+and structure a channel so that it's
+
+ align:start position:0%
+and structure a channel so that it's
+ 
+
+ align:start position:0%
+and structure a channel so that it's
+close to linear and time invariant
+
+ align:start position:0%
+close to linear and time invariant
+ 
+
+ align:start position:0%
+close to linear and time invariant
+because then you can do a lot of
+
+ align:start position:0%
+because then you can do a lot of
+ 
+
+ align:start position:0%
+because then you can do a lot of
+analysis and design for it okay so I
+
+ align:start position:0%
+analysis and design for it okay so I
+ 
+
+ align:start position:0%
+analysis and design for it okay so I
+want to continue talking about our
+
+ align:start position:0%
+want to continue talking about our
+ 
+
+ align:start position:0%
+want to continue talking about our
+models for LTI channels
+
+ align:start position:0%
+models for LTI channels
+ 
+
+ align:start position:0%
+models for LTI channels
+and still in the time domain next time
+
+ align:start position:0%
+and still in the time domain next time
+ 
+
+ align:start position:0%
+and still in the time domain next time
+we'll start to look at this in the
+
+ align:start position:0%
+we'll start to look at this in the
+ 
+
+ align:start position:0%
+we'll start to look at this in the
+frequency domain Hari mentioned
+
+ align:start position:0%
+frequency domain Hari mentioned
+ 
+
+ align:start position:0%
+frequency domain Hari mentioned
+frequency several times here so we're
+
+ align:start position:0%
+frequency several times here so we're
+ 
+
+ align:start position:0%
+frequency several times here so we're
+talking about an LTI channel linear
+
+ align:start position:0%
+talking about an LTI channel linear
+ 
+
+ align:start position:0%
+talking about an LTI channel linear
+time-invariant we talked about
+
+ align:start position:0%
+time-invariant we talked about
+ 
+
+ align:start position:0%
+time-invariant we talked about
+characterizing it by its unit sample
+
+ align:start position:0%
+characterizing it by its unit sample
+ 
+
+ align:start position:0%
+characterizing it by its unit sample
+response and so let's see unit sample
+
+ align:start position:0%
+response and so let's see unit sample
+ 
+
+ align:start position:0%
+response and so let's see unit sample
+response means put in a unit sample
+
+ align:start position:0%
+response means put in a unit sample
+ 
+
+ align:start position:0%
+response means put in a unit sample
+function you get out an output that
+
+ align:start position:0%
+function you get out an output that
+ 
+
+ align:start position:0%
+function you get out an output that
+you're going to call the unit sample
+
+ align:start position:0%
+you're going to call the unit sample
+ 
+
+ align:start position:0%
+you're going to call the unit sample
+response put in an input X n that is the
+
+ align:start position:0%
+response put in an input X n that is the
+ 
+
+ align:start position:0%
+response put in an input X n that is the
+summation of such things let's say x k
+
+ align:start position:0%
+summation of such things let's say x k
+ 
+
+ align:start position:0%
+summation of such things let's say x k
+delta of n minus k summed over all K
+
+ align:start position:0%
+delta of n minus k summed over all K
+ 
+
+ align:start position:0%
+delta of n minus k summed over all K
+right that's a general input represented
+
+ align:start position:0%
+right that's a general input represented
+ 
+
+ align:start position:0%
+right that's a general input represented
+as a weighted combination of unit
+
+ align:start position:0%
+as a weighted combination of unit
+ 
+
+ align:start position:0%
+as a weighted combination of unit
+samples well what comes out in that case
+
+ align:start position:0%
+samples well what comes out in that case
+ 
+
+ align:start position:0%
+samples well what comes out in that case
+what is y of n if we're talking about a
+
+ align:start position:0%
+what is y of n if we're talking about a
+ 
+
+ align:start position:0%
+what is y of n if we're talking about a
+linear time invariant systems and it's
+
+ align:start position:0%
+linear time invariant systems and it's
+ 
+
+ align:start position:0%
+linear time invariant systems and it's
+the same weighted combination of the
+
+ align:start position:0%
+the same weighted combination of the
+ 
+
+ align:start position:0%
+the same weighted combination of the
+responses to these unit samples so we're
+
+ align:start position:0%
+responses to these unit samples so we're
+ 
+
+ align:start position:0%
+responses to these unit samples so we're
+going to get summation XK H of n minus K
+
+ align:start position:0%
+going to get summation XK H of n minus K
+ 
+
+ align:start position:0%
+going to get summation XK H of n minus K
+right so this is the convolution
+
+ align:start position:0%
+right so this is the convolution
+ 
+
+ align:start position:0%
+right so this is the convolution
+expression that we talked about last
+
+ align:start position:0%
+expression that we talked about last
+ 
+
+ align:start position:0%
+expression that we talked about last
+time so what I want to do in the rest of
+
+ align:start position:0%
+time so what I want to do in the rest of
+ 
+
+ align:start position:0%
+time so what I want to do in the rest of
+how the lecturers give you some other
+
+ align:start position:0%
+how the lecturers give you some other
+ 
+
+ align:start position:0%
+how the lecturers give you some other
+ways to think about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our notation for this was y of n equals
+
+ align:start position:0%
+our notation for this was y of n equals
+ 
+
+ align:start position:0%
+our notation for this was y of n equals
+x convolved with H evaluated a time n
+
+ align:start position:0%
+x convolved with H evaluated a time n
+ 
+
+ align:start position:0%
+x convolved with H evaluated a time n
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another way to think about this let's
+
+ align:start position:0%
+another way to think about this let's
+ 
+
+ align:start position:0%
+another way to think about this let's
+see let me actually first do an example
+
+ align:start position:0%
+see let me actually first do an example
+ 
+
+ align:start position:0%
+see let me actually first do an example
+and then give you another way to think
+
+ align:start position:0%
+and then give you another way to think
+ 
+
+ align:start position:0%
+and then give you another way to think
+about this suppose I have a system whose
+
+ align:start position:0%
+about this suppose I have a system whose
+ 
+
+ align:start position:0%
+about this suppose I have a system whose
+effect is to multiply the input by a
+
+ align:start position:0%
+effect is to multiply the input by a
+ 
+
+ align:start position:0%
+effect is to multiply the input by a
+some number a and delay by some number D
+
+ align:start position:0%
+some number a and delay by some number D
+ 
+
+ align:start position:0%
+some number a and delay by some number D
+and I tell you that this is Lt I
+
+ align:start position:0%
+and I tell you that this is Lt I
+ 
+
+ align:start position:0%
+and I tell you that this is Lt I
+actually I don't have to tell you that
+
+ align:start position:0%
+actually I don't have to tell you that
+ 
+
+ align:start position:0%
+actually I don't have to tell you that
+it's LTI you can prove that it's LTI if
+
+ align:start position:0%
+it's LTI you can prove that it's LTI if
+ 
+
+ align:start position:0%
+it's LTI you can prove that it's LTI if
+I tell you have a system there's only
+
+ align:start position:0%
+I tell you have a system there's only
+ 
+
+ align:start position:0%
+I tell you have a system there's only
+action on the input is to delay the
+
+ align:start position:0%
+action on the input is to delay the
+ 
+
+ align:start position:0%
+action on the input is to delay the
+input by capital d and multiply the end
+
+ align:start position:0%
+input by capital d and multiply the end
+ 
+
+ align:start position:0%
+input by capital d and multiply the end
+scale the input by capital A you can
+
+ align:start position:0%
+scale the input by capital A you can
+ 
+
+ align:start position:0%
+scale the input by capital A you can
+actually prove that it satisfies time
+
+ align:start position:0%
+actually prove that it satisfies time
+ 
+
+ align:start position:0%
+actually prove that it satisfies time
+and variance and that it that you can
+
+ align:start position:0%
+and variance and that it that you can
+ 
+
+ align:start position:0%
+and variance and that it that you can
+superpose okay so this is Lt I so what's
+
+ align:start position:0%
+superpose okay so this is Lt I so what's
+ 
+
+ align:start position:0%
+superpose okay so this is Lt I so what's
+the unit sample response if i put in
+
+ align:start position:0%
+the unit sample response if i put in
+ 
+
+ align:start position:0%
+the unit sample response if i put in
+unit sample function of the input what's
+
+ align:start position:0%
+unit sample function of the input what's
+ 
+
+ align:start position:0%
+unit sample function of the input what's
+the output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah a dolt of n minus T right and if I
+
+ align:start position:0%
+yeah a dolt of n minus T right and if I
+ 
+
+ align:start position:0%
+yeah a dolt of n minus T right and if I
+put some general input function in here
+
+ align:start position:0%
+put some general input function in here
+ 
+
+ align:start position:0%
+put some general input function in here
+what's the output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+without telling me about convolution
+
+ align:start position:0%
+without telling me about convolution
+ 
+
+ align:start position:0%
+without telling me about convolution
+somebody I heard a voice here yeah right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we didn't have to do any convolution to
+
+ align:start position:0%
+we didn't have to do any convolution to
+ 
+
+ align:start position:0%
+we didn't have to do any convolution to
+figure this out right because I describe
+
+ align:start position:0%
+figure this out right because I describe
+ 
+
+ align:start position:0%
+figure this out right because I describe
+the system to you in a simple way you
+
+ align:start position:0%
+the system to you in a simple way you
+ 
+
+ align:start position:0%
+the system to you in a simple way you
+could tell me what it does to the output
+
+ align:start position:0%
+could tell me what it does to the output
+ 
+
+ align:start position:0%
+could tell me what it does to the output
+all right so I want to give you another
+
+ align:start position:0%
+all right so I want to give you another
+ 
+
+ align:start position:0%
+all right so I want to give you another
+way to think about a system with the
+
+ align:start position:0%
+way to think about a system with the
+ 
+
+ align:start position:0%
+way to think about a system with the
+unit sample response of H of n so I'm
+
+ align:start position:0%
+unit sample response of H of n so I'm
+ 
+
+ align:start position:0%
+unit sample response of H of n so I'm
+talking about a youth system with the
+
+ align:start position:0%
+talking about a youth system with the
+ 
+
+ align:start position:0%
+talking about a youth system with the
+unit sample response to H of n so what
+
+ align:start position:0%
+unit sample response to H of n so what
+ 
+
+ align:start position:0%
+unit sample response to H of n so what
+does that mean that means at a time 0 I
+
+ align:start position:0%
+does that mean that means at a time 0 I
+ 
+
+ align:start position:0%
+does that mean that means at a time 0 I
+get evaluate 0 when I put out and put in
+
+ align:start position:0%
+get evaluate 0 when I put out and put in
+ 
+
+ align:start position:0%
+get evaluate 0 when I put out and put in
+a unit sample at time 1 I get some h1 a
+
+ align:start position:0%
+a unit sample at time 1 I get some h1 a
+ 
+
+ align:start position:0%
+a unit sample at time 1 I get some h1 a
+time to I get some h 2 and so on this is
+
+ align:start position:0%
+time to I get some h 2 and so on this is
+ 
+
+ align:start position:0%
+time to I get some h 2 and so on this is
+HN ok so if I give you a system and tell
+
+ align:start position:0%
+HN ok so if I give you a system and tell
+ 
+
+ align:start position:0%
+HN ok so if I give you a system and tell
+you that the unit sample response is
+
+ align:start position:0%
+you that the unit sample response is
+ 
+
+ align:start position:0%
+you that the unit sample response is
+this function H here's a way to think of
+
+ align:start position:0%
+this function H here's a way to think of
+ 
+
+ align:start position:0%
+this function H here's a way to think of
+what it is inside there here's what my
+
+ align:start position:0%
+what it is inside there here's what my
+ 
+
+ align:start position:0%
+what it is inside there here's what my
+system can be thought of as doing inside
+
+ align:start position:0%
+system can be thought of as doing inside
+ 
+
+ align:start position:0%
+system can be thought of as doing inside
+here I've got many parallel paths of God
+
+ align:start position:0%
+here I've got many parallel paths of God
+ 
+
+ align:start position:0%
+here I've got many parallel paths of God
+a system that scales by 80
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delays by zero and in parallel with the
+
+ align:start position:0%
+delays by zero and in parallel with the
+ 
+
+ align:start position:0%
+delays by zero and in parallel with the
+system that scales by you put it up here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scales by h1 delay by one and so on okay
+
+ align:start position:0%
+scales by h1 delay by one and so on okay
+ 
+
+ align:start position:0%
+scales by h1 delay by one and so on okay
+so all of these in parallel each one is
+
+ align:start position:0%
+so all of these in parallel each one is
+ 
+
+ align:start position:0%
+so all of these in parallel each one is
+very simple each one is as simple as the
+
+ align:start position:0%
+very simple each one is as simple as the
+ 
+
+ align:start position:0%
+very simple each one is as simple as the
+example I showed you okay I've got a
+
+ align:start position:0%
+example I showed you okay I've got a
+ 
+
+ align:start position:0%
+example I showed you okay I've got a
+whole bunch of these parallel systems
+
+ align:start position:0%
+whole bunch of these parallel systems
+ 
+
+ align:start position:0%
+whole bunch of these parallel systems
+each one as simple as this if I put a
+
+ align:start position:0%
+each one as simple as this if I put a
+ 
+
+ align:start position:0%
+each one as simple as this if I put a
+unit sample in here what comes out it's
+
+ align:start position:0%
+unit sample in here what comes out it's
+ 
+
+ align:start position:0%
+unit sample in here what comes out it's
+going to be exactly that right because
+
+ align:start position:0%
+going to be exactly that right because
+ 
+
+ align:start position:0%
+going to be exactly that right because
+the unit sample would get scaled by zero
+
+ align:start position:0%
+the unit sample would get scaled by zero
+ 
+
+ align:start position:0%
+the unit sample would get scaled by zero
+delayed by nothing will come out there
+
+ align:start position:0%
+delayed by nothing will come out there
+ 
+
+ align:start position:0%
+delayed by nothing will come out there
+the unit sample get through this path
+
+ align:start position:0%
+the unit sample get through this path
+ 
+
+ align:start position:0%
+the unit sample get through this path
+scaled by h1 delayed by one come out
+
+ align:start position:0%
+scaled by h1 delayed by one come out
+ 
+
+ align:start position:0%
+scaled by h1 delayed by one come out
+there when you assemble all of these
+
+ align:start position:0%
+there when you assemble all of these
+ 
+
+ align:start position:0%
+there when you assemble all of these
+with this summer here you're going to
+
+ align:start position:0%
+with this summer here you're going to
+ 
+
+ align:start position:0%
+with this summer here you're going to
+get exactly that response so here's
+
+ align:start position:0%
+get exactly that response so here's
+ 
+
+ align:start position:0%
+get exactly that response so here's
+another way to think about what's
+
+ align:start position:0%
+another way to think about what's
+ 
+
+ align:start position:0%
+another way to think about what's
+sitting inside a system an LTI system
+
+ align:start position:0%
+sitting inside a system an LTI system
+ 
+
+ align:start position:0%
+sitting inside a system an LTI system
+whose unit sample response is given to
+
+ align:start position:0%
+whose unit sample response is given to
+ 
+
+ align:start position:0%
+whose unit sample response is given to
+be that ok so if i put x an in what is
+
+ align:start position:0%
+be that ok so if i put x an in what is
+ 
+
+ align:start position:0%
+be that ok so if i put x an in what is
+it that's going to come out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i put x n in what comes out well
+
+ align:start position:0%
+if i put x n in what comes out well
+ 
+
+ align:start position:0%
+if i put x n in what comes out well
+through this path i get XM scale by zero
+
+ align:start position:0%
+through this path i get XM scale by zero
+ 
+
+ align:start position:0%
+through this path i get XM scale by zero
+and delayed by nothing through this path
+
+ align:start position:0%
+and delayed by nothing through this path
+ 
+
+ align:start position:0%
+and delayed by nothing through this path
+i get x n scale by h1 and delayed by one
+
+ align:start position:0%
+i get x n scale by h1 and delayed by one
+ 
+
+ align:start position:0%
+i get x n scale by h1 and delayed by one
+and so on so what comes out y of n is
+
+ align:start position:0%
+and so on so what comes out y of n is
+ 
+
+ align:start position:0%
+and so on so what comes out y of n is
+equal to hm x of n minus n overall an ok
+
+ align:start position:0%
+equal to hm x of n minus n overall an ok
+ 
+
+ align:start position:0%
+equal to hm x of n minus n overall an ok
+so i take x n i shifted by nothing i
+
+ align:start position:0%
+so i take x n i shifted by nothing i
+ 
+
+ align:start position:0%
+so i take x n i shifted by nothing i
+scale by zero that's one of these terms
+
+ align:start position:0%
+scale by zero that's one of these terms
+ 
+
+ align:start position:0%
+scale by zero that's one of these terms
+the term corresponding to M equals zero
+
+ align:start position:0%
+the term corresponding to M equals zero
+ 
+
+ align:start position:0%
+the term corresponding to M equals zero
+i take x n scale it by h1 delay by one
+
+ align:start position:0%
+i take x n scale it by h1 delay by one
+ 
+
+ align:start position:0%
+i take x n scale it by h1 delay by one
+that gives me the term with M equals one
+
+ align:start position:0%
+that gives me the term with M equals one
+ 
+
+ align:start position:0%
+that gives me the term with M equals one
+so here's another way to write it ok
+
+ align:start position:0%
+so here's another way to write it ok
+ 
+
+ align:start position:0%
+so here's another way to write it ok
+last time I said that actually you can
+
+ align:start position:0%
+last time I said that actually you can
+ 
+
+ align:start position:0%
+last time I said that actually you can
+write convolution in this form or with
+
+ align:start position:0%
+write convolution in this form or with
+ 
+
+ align:start position:0%
+write convolution in this form or with
+the operation reversed so it actually
+
+ align:start position:0%
+the operation reversed so it actually
+ 
+
+ align:start position:0%
+the operation reversed so it actually
+doesn't matter which order you write
+
+ align:start position:0%
+doesn't matter which order you write
+ 
+
+ align:start position:0%
+doesn't matter which order you write
+things in this would be something you
+
+ align:start position:0%
+things in this would be something you
+ 
+
+ align:start position:0%
+things in this would be something you
+might write as h convolved with X at
+
+ align:start position:0%
+might write as h convolved with X at
+ 
+
+ align:start position:0%
+might write as h convolved with X at
+time n so two different ways of writing
+
+ align:start position:0%
+time n so two different ways of writing
+ 
+
+ align:start position:0%
+time n so two different ways of writing
+the convolution and two different ways
+
+ align:start position:0%
+the convolution and two different ways
+ 
+
+ align:start position:0%
+the convolution and two different ways
+of thinking about how the output gets
+
+ align:start position:0%
+of thinking about how the output gets
+ 
+
+ align:start position:0%
+of thinking about how the output gets
+represented that way you can easily get
+
+ align:start position:0%
+represented that way you can easily get
+ 
+
+ align:start position:0%
+represented that way you can easily get
+from one representation to the other by
+
+ align:start position:0%
+from one representation to the other by
+ 
+
+ align:start position:0%
+from one representation to the other by
+just making a change of variables like
+
+ align:start position:0%
+just making a change of variables like
+ 
+
+ align:start position:0%
+just making a change of variables like
+let n minus K equals M and you get from
+
+ align:start position:0%
+let n minus K equals M and you get from
+ 
+
+ align:start position:0%
+let n minus K equals M and you get from
+this representation to the other this is
+
+ align:start position:0%
+this representation to the other this is
+ 
+
+ align:start position:0%
+this representation to the other this is
+a more mechanistic way of thinking about
+
+ align:start position:0%
+a more mechanistic way of thinking about
+ 
+
+ align:start position:0%
+a more mechanistic way of thinking about
+why these two representations work ok so
+
+ align:start position:0%
+why these two representations work ok so
+ 
+
+ align:start position:0%
+why these two representations work ok so
+what that is a given let me show you how
+
+ align:start position:0%
+what that is a given let me show you how
+ 
+
+ align:start position:0%
+what that is a given let me show you how
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+actually carry out these operations
+
+ align:start position:0%
+actually carry out these operations
+ 
+
+ align:start position:0%
+actually carry out these operations
+graphically in either form here's a
+
+ align:start position:0%
+graphically in either form here's a
+ 
+
+ align:start position:0%
+graphically in either form here's a
+simple graphical way to think about
+
+ align:start position:0%
+simple graphical way to think about
+ 
+
+ align:start position:0%
+simple graphical way to think about
+what's going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to determine why a time n this is the
+
+ align:start position:0%
+so to determine why a time n this is the
+ 
+
+ align:start position:0%
+so to determine why a time n this is the
+operation that I have to carry out all
+
+ align:start position:0%
+operation that I have to carry out all
+ 
+
+ align:start position:0%
+operation that I have to carry out all
+right so defined why at time n the
+
+ align:start position:0%
+right so defined why at time n the
+ 
+
+ align:start position:0%
+right so defined why at time n the
+output at time and I've got to find a
+
+ align:start position:0%
+output at time and I've got to find a
+ 
+
+ align:start position:0%
+output at time and I've got to find a
+way to implement this operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how are we going to think of this
+
+ align:start position:0%
+so how are we going to think of this
+ 
+
+ align:start position:0%
+so how are we going to think of this
+graphically I want to sketch the signal
+
+ align:start position:0%
+graphically I want to sketch the signal
+ 
+
+ align:start position:0%
+graphically I want to sketch the signal
+X I want to sketch the signal h and then
+
+ align:start position:0%
+X I want to sketch the signal h and then
+ 
+
+ align:start position:0%
+X I want to sketch the signal h and then
+do something with these two signals to
+
+ align:start position:0%
+do something with these two signals to
+ 
+
+ align:start position:0%
+do something with these two signals to
+construct this okay so when I plot x and
+
+ align:start position:0%
+construct this okay so when I plot x and
+ 
+
+ align:start position:0%
+construct this okay so when I plot x and
+i plot h to implement this operation
+
+ align:start position:0%
+i plot h to implement this operation
+ 
+
+ align:start position:0%
+i plot h to implement this operation
+what's my what's the name of my time
+
+ align:start position:0%
+what's my what's the name of my time
+ 
+
+ align:start position:0%
+what's my what's the name of my time
+axis is it and that i'm going to stick
+
+ align:start position:0%
+axis is it and that i'm going to stick
+ 
+
+ align:start position:0%
+axis is it and that i'm going to stick
+here or k or what I want to implement
+
+ align:start position:0%
+here or k or what I want to implement
+ 
+
+ align:start position:0%
+here or k or what I want to implement
+this i want to draw these two time
+
+ align:start position:0%
+this i want to draw these two time
+ 
+
+ align:start position:0%
+this i want to draw these two time
+functions their functions of k right and
+
+ align:start position:0%
+functions their functions of k right and
+ 
+
+ align:start position:0%
+functions their functions of k right and
+it's just the number that i'm specifying
+
+ align:start position:0%
+it's just the number that i'm specifying
+ 
+
+ align:start position:0%
+it's just the number that i'm specifying
+here okay so on the k axis I'm going to
+
+ align:start position:0%
+here okay so on the k axis I'm going to
+ 
+
+ align:start position:0%
+here okay so on the k axis I'm going to
+take X and plot it so X is some time
+
+ align:start position:0%
+take X and plot it so X is some time
+ 
+
+ align:start position:0%
+take X and plot it so X is some time
+function here's my ex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to label them all because I get
+
+ align:start position:0%
+I want to label them all because I get
+ 
+
+ align:start position:0%
+I want to label them all because I get
+crowded and just to keep things clean
+
+ align:start position:0%
+crowded and just to keep things clean
+ 
+
+ align:start position:0%
+crowded and just to keep things clean
+let's change colors here how am I going
+
+ align:start position:0%
+let's change colors here how am I going
+ 
+
+ align:start position:0%
+let's change colors here how am I going
+to plot H of n minus K well let's start
+
+ align:start position:0%
+to plot H of n minus K well let's start
+ 
+
+ align:start position:0%
+to plot H of n minus K well let's start
+thinking about the N equals 0 case so
+
+ align:start position:0%
+thinking about the N equals 0 case so
+ 
+
+ align:start position:0%
+thinking about the N equals 0 case so
+for n equals 0 I've got to plot H of
+
+ align:start position:0%
+for n equals 0 I've got to plot H of
+ 
+
+ align:start position:0%
+for n equals 0 I've got to plot H of
+minus K so how does H of minus K relate
+
+ align:start position:0%
+minus K so how does H of minus K relate
+ 
+
+ align:start position:0%
+minus K so how does H of minus K relate
+to the unit sample response H of K or
+
+ align:start position:0%
+to the unit sample response H of K or
+ 
+
+ align:start position:0%
+to the unit sample response H of K or
+hmm if I tell you that out of that I
+
+ align:start position:0%
+hmm if I tell you that out of that I
+ 
+
+ align:start position:0%
+hmm if I tell you that out of that I
+have a system we had an example up here
+
+ align:start position:0%
+have a system we had an example up here
+ 
+
+ align:start position:0%
+have a system we had an example up here
+didn't we I lost it if i tell you that i
+
+ align:start position:0%
+didn't we I lost it if i tell you that i
+ 
+
+ align:start position:0%
+didn't we I lost it if i tell you that i
+have a system with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this unit sample response let's do
+
+ align:start position:0%
+this unit sample response let's do
+ 
+
+ align:start position:0%
+this unit sample response let's do
+something simple let's say that this is
+
+ align:start position:0%
+something simple let's say that this is
+ 
+
+ align:start position:0%
+something simple let's say that this is
+one half to the end okay four times u of
+
+ align:start position:0%
+one half to the end okay four times u of
+ 
+
+ align:start position:0%
+one half to the end okay four times u of
+n so for positive time it's kind of a
+
+ align:start position:0%
+n so for positive time it's kind of a
+ 
+
+ align:start position:0%
+n so for positive time it's kind of a
+decaying geometric series and for- time
+
+ align:start position:0%
+decaying geometric series and for- time
+ 
+
+ align:start position:0%
+decaying geometric series and for- time
+at zero okay so that's an example of an
+
+ align:start position:0%
+at zero okay so that's an example of an
+ 
+
+ align:start position:0%
+at zero okay so that's an example of an
+unit sample response of a system so if
+
+ align:start position:0%
+unit sample response of a system so if
+ 
+
+ align:start position:0%
+unit sample response of a system so if
+that's H of n what does age of minus K
+
+ align:start position:0%
+that's H of n what does age of minus K
+ 
+
+ align:start position:0%
+that's H of n what does age of minus K
+look like yeah anyone sorry it's the
+
+ align:start position:0%
+look like yeah anyone sorry it's the
+ 
+
+ align:start position:0%
+look like yeah anyone sorry it's the
+reflection okay so if i want for N
+
+ align:start position:0%
+reflection okay so if i want for N
+ 
+
+ align:start position:0%
+reflection okay so if i want for N
+equals zero to plot just the age of
+
+ align:start position:0%
+equals zero to plot just the age of
+ 
+
+ align:start position:0%
+equals zero to plot just the age of
+minus K that I need here it's that
+
+ align:start position:0%
+minus K that I need here it's that
+ 
+
+ align:start position:0%
+minus K that I need here it's that
+reversed okay and plotted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is h of minus K here what
+
+ align:start position:0%
+okay so this is h of minus K here what
+ 
+
+ align:start position:0%
+okay so this is h of minus K here what
+about H of minus k sorry what about H of
+
+ align:start position:0%
+about H of minus k sorry what about H of
+ 
+
+ align:start position:0%
+about H of minus k sorry what about H of
+n minus K suppose I had an equals 3 now
+
+ align:start position:0%
+n minus K suppose I had an equals 3 now
+ 
+
+ align:start position:0%
+n minus K suppose I had an equals 3 now
+how do I get h of 3 minus k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to get h of three minus K so
+
+ align:start position:0%
+so I want to get h of three minus K so
+ 
+
+ align:start position:0%
+so I want to get h of three minus K so
+that corresponds to sliding this over do
+
+ align:start position:0%
+that corresponds to sliding this over do
+ 
+
+ align:start position:0%
+that corresponds to sliding this over do
+I slide it to the right by three to the
+
+ align:start position:0%
+I slide it to the right by three to the
+ 
+
+ align:start position:0%
+I slide it to the right by three to the
+left by three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can tell by looking at the argument
+
+ align:start position:0%
+you can tell by looking at the argument
+ 
+
+ align:start position:0%
+you can tell by looking at the argument
+here whatever used to happen at zero has
+
+ align:start position:0%
+here whatever used to happen at zero has
+ 
+
+ align:start position:0%
+here whatever used to happen at zero has
+now got to happen at K equals 3 so that
+
+ align:start position:0%
+now got to happen at K equals 3 so that
+ 
+
+ align:start position:0%
+now got to happen at K equals 3 so that
+means the rightward shift ok so you flip
+
+ align:start position:0%
+means the rightward shift ok so you flip
+ 
+
+ align:start position:0%
+means the rightward shift ok so you flip
+this over and then you slide it by n
+
+ align:start position:0%
+this over and then you slide it by n
+ 
+
+ align:start position:0%
+this over and then you slide it by n
+steps ok so you take the h of k flip it
+
+ align:start position:0%
+steps ok so you take the h of k flip it
+ 
+
+ align:start position:0%
+steps ok so you take the h of k flip it
+around to get h of minus k slide it by n
+
+ align:start position:0%
+around to get h of minus k slide it by n
+ 
+
+ align:start position:0%
+around to get h of minus k slide it by n
+steps so if n is positive you're sliding
+
+ align:start position:0%
+steps so if n is positive you're sliding
+ 
+
+ align:start position:0%
+steps so if n is positive you're sliding
+it to the right if n is negative you're
+
+ align:start position:0%
+it to the right if n is negative you're
+ 
+
+ align:start position:0%
+it to the right if n is negative you're
+sliding it to the left so now you've on
+
+ align:start position:0%
+sliding it to the left so now you've on
+ 
+
+ align:start position:0%
+sliding it to the left so now you've on
+a single figure you've managed to plot
+
+ align:start position:0%
+a single figure you've managed to plot
+ 
+
+ align:start position:0%
+a single figure you've managed to plot
+these two what's the remaining operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which you've got to do is the point by
+
+ align:start position:0%
+which you've got to do is the point by
+ 
+
+ align:start position:0%
+which you've got to do is the point by
+point product of these two waveforms and
+
+ align:start position:0%
+point product of these two waveforms and
+ 
+
+ align:start position:0%
+point product of these two waveforms and
+some over the entire time axis it's like
+
+ align:start position:0%
+some over the entire time axis it's like
+ 
+
+ align:start position:0%
+some over the entire time axis it's like
+taking a dot product right so you're
+
+ align:start position:0%
+taking a dot product right so you're
+ 
+
+ align:start position:0%
+taking a dot product right so you're
+going to take this value of the red
+
+ align:start position:0%
+going to take this value of the red
+ 
+
+ align:start position:0%
+going to take this value of the red
+curve well actually let me slide it over
+
+ align:start position:0%
+curve well actually let me slide it over
+ 
+
+ align:start position:0%
+curve well actually let me slide it over
+let's let's do this case this is the
+
+ align:start position:0%
+let's let's do this case this is the
+ 
+
+ align:start position:0%
+let's let's do this case this is the
+slid over case right you're going to
+
+ align:start position:0%
+slid over case right you're going to
+ 
+
+ align:start position:0%
+slid over case right you're going to
+take every one of the purple values
+
+ align:start position:0%
+take every one of the purple values
+ 
+
+ align:start position:0%
+take every one of the purple values
+multiplied by the white and some over
+
+ align:start position:0%
+multiplied by the white and some over
+ 
+
+ align:start position:0%
+multiplied by the white and some over
+the entire time axis that's an
+
+ align:start position:0%
+the entire time axis that's an
+ 
+
+ align:start position:0%
+the entire time axis that's an
+implementation of this right so in
+
+ align:start position:0%
+implementation of this right so in
+ 
+
+ align:start position:0%
+implementation of this right so in
+recitation tomorrow you'll get practice
+
+ align:start position:0%
+recitation tomorrow you'll get practice
+ 
+
+ align:start position:0%
+recitation tomorrow you'll get practice
+on this that what you want to think of
+
+ align:start position:0%
+on this that what you want to think of
+ 
+
+ align:start position:0%
+on this that what you want to think of
+sort of the mantra for graphical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implementation of convolution is you've
+
+ align:start position:0%
+implementation of convolution is you've
+ 
+
+ align:start position:0%
+implementation of convolution is you've
+got to do the flip of one of the time
+
+ align:start position:0%
+got to do the flip of one of the time
+ 
+
+ align:start position:0%
+got to do the flip of one of the time
+functions slide by n
+
+ align:start position:0%
+functions slide by n
+ 
+
+ align:start position:0%
+functions slide by n
+and then the dot product okay so you do
+
+ align:start position:0%
+and then the dot product okay so you do
+ 
+
+ align:start position:0%
+and then the dot product okay so you do
+you slide it to get one particular value
+
+ align:start position:0%
+you slide it to get one particular value
+ 
+
+ align:start position:0%
+you slide it to get one particular value
+of n if you want the next value of n you
+
+ align:start position:0%
+of n if you want the next value of n you
+ 
+
+ align:start position:0%
+of n if you want the next value of n you
+slide it one over and go through this
+
+ align:start position:0%
+slide it one over and go through this
+ 
+
+ align:start position:0%
+slide it one over and go through this
+whole thing so it's flipping sliding by
+
+ align:start position:0%
+whole thing so it's flipping sliding by
+ 
+
+ align:start position:0%
+whole thing so it's flipping sliding by
+the right number of spots doing the
+
+ align:start position:0%
+the right number of spots doing the
+ 
+
+ align:start position:0%
+the right number of spots doing the
+inner product that gives you one value
+
+ align:start position:0%
+inner product that gives you one value
+ 
+
+ align:start position:0%
+inner product that gives you one value
+of the answer and then you repeat all
+
+ align:start position:0%
+of the answer and then you repeat all
+ 
+
+ align:start position:0%
+of the answer and then you repeat all
+right you'll get more practice in
+
+ align:start position:0%
+right you'll get more practice in
+ 
+
+ align:start position:0%
+right you'll get more practice in
+recitation
\ No newline at end of file
diff --git a/fWOGfzC3IeY.txt b/fWOGfzC3IeY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..092f9b6255a1be4aefb2aced9fc8fdac99513e0b
--- /dev/null
+++ b/fWOGfzC3IeY.txt
@@ -0,0 +1,1787 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I want to show how we can use change of
+
+ align:start position:0%
+I want to show how we can use change of
+ 
+
+ align:start position:0%
+I want to show how we can use change of
+variables to Polar coordinates in
+
+ align:start position:0%
+variables to Polar coordinates in
+ 
+
+ align:start position:0%
+variables to Polar coordinates in
+particular to evaluate an integral that
+
+ align:start position:0%
+particular to evaluate an integral that
+ 
+
+ align:start position:0%
+particular to evaluate an integral that
+without the change in variables we we
+
+ align:start position:0%
+without the change in variables we we
+ 
+
+ align:start position:0%
+without the change in variables we we
+don't have the techniques to do so I'm
+
+ align:start position:0%
+don't have the techniques to do so I'm
+ 
+
+ align:start position:0%
+don't have the techniques to do so I'm
+going to show us how to evaluate the
+
+ align:start position:0%
+going to show us how to evaluate the
+ 
+
+ align:start position:0%
+going to show us how to evaluate the
+integral from minus infinity to Infinity
+
+ align:start position:0%
+integral from minus infinity to Infinity
+ 
+
+ align:start position:0%
+integral from minus infinity to Infinity
+of eus x^2 DX and I'll just point out
+
+ align:start position:0%
+of eus x^2 DX and I'll just point out
+ 
+
+ align:start position:0%
+of eus x^2 DX and I'll just point out
+that if you do anything in probability
+
+ align:start position:0%
+that if you do anything in probability
+ 
+
+ align:start position:0%
+that if you do anything in probability
+you will see
+
+ align:start position:0%
+you will see
+ 
+
+ align:start position:0%
+you will see
+uh this integral a great deal so this
+
+ align:start position:0%
+uh this integral a great deal so this
+ 
+
+ align:start position:0%
+uh this integral a great deal so this
+this is a distribution and you'll see it
+
+ align:start position:0%
+this is a distribution and you'll see it
+ 
+
+ align:start position:0%
+this is a distribution and you'll see it
+a great deal if you ever do anything in
+
+ align:start position:0%
+a great deal if you ever do anything in
+ 
+
+ align:start position:0%
+a great deal if you ever do anything in
+probability Theory but how are we going
+
+ align:start position:0%
+probability Theory but how are we going
+ 
+
+ align:start position:0%
+probability Theory but how are we going
+to use how are we going to use polar
+
+ align:start position:0%
+to use how are we going to use polar
+ 
+
+ align:start position:0%
+to use how are we going to use polar
+coordinates to evaluate this well the
+
+ align:start position:0%
+coordinates to evaluate this well the
+ 
+
+ align:start position:0%
+coordinates to evaluate this well the
+object is going to be to introduce uh a
+
+ align:start position:0%
+object is going to be to introduce uh a
+ 
+
+ align:start position:0%
+object is going to be to introduce uh a
+little bit more um into this integral so
+
+ align:start position:0%
+little bit more um into this integral so
+ 
+
+ align:start position:0%
+little bit more um into this integral so
+that when I when I actually introduce
+
+ align:start position:0%
+that when I when I actually introduce
+ 
+
+ align:start position:0%
+that when I when I actually introduce
+that in I'm going to have an R squ term
+
+ align:start position:0%
+that in I'm going to have an R squ term
+ 
+
+ align:start position:0%
+that in I'm going to have an R squ term
+in the exponent and I'm going to have of
+
+ align:start position:0%
+in the exponent and I'm going to have of
+ 
+
+ align:start position:0%
+in the exponent and I'm going to have of
+course by the change of variables in the
+
+ align:start position:0%
+course by the change of variables in the
+ 
+
+ align:start position:0%
+course by the change of variables in the
+Jacobian and multiplied by R and that's
+
+ align:start position:0%
+Jacobian and multiplied by R and that's
+ 
+
+ align:start position:0%
+Jacobian and multiplied by R and that's
+what's going to save us so let me
+
+ align:start position:0%
+what's going to save us so let me
+ 
+
+ align:start position:0%
+what's going to save us so let me
+actually just get right to it so I um
+
+ align:start position:0%
+actually just get right to it so I um
+ 
+
+ align:start position:0%
+actually just get right to it so I um
+I'm going to call this integral this
+
+ align:start position:0%
+I'm going to call this integral this
+ 
+
+ align:start position:0%
+I'm going to call this integral this
+quantity capital I we'll just call this
+
+ align:start position:0%
+quantity capital I we'll just call this
+ 
+
+ align:start position:0%
+quantity capital I we'll just call this
+quantity capital I and then what I'm
+
+ align:start position:0%
+quantity capital I and then what I'm
+ 
+
+ align:start position:0%
+quantity capital I and then what I'm
+going to do is introduce a couple more
+
+ align:start position:0%
+going to do is introduce a couple more
+ 
+
+ align:start position:0%
+going to do is introduce a couple more
+things so let me write it down and then
+
+ align:start position:0%
+things so let me write it down and then
+ 
+
+ align:start position:0%
+things so let me write it down and then
+I will justify that it's reasonable to
+
+ align:start position:0%
+I will justify that it's reasonable to
+ 
+
+ align:start position:0%
+I will justify that it's reasonable to
+even look at this thing and that it will
+
+ align:start position:0%
+even look at this thing and that it will
+ 
+
+ align:start position:0%
+even look at this thing and that it will
+give us something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful okay okay so I just took this
+
+ align:start position:0%
+useful okay okay so I just took this
+ 
+
+ align:start position:0%
+useful okay okay so I just took this
+integral and what I've done is I've now
+
+ align:start position:0%
+integral and what I've done is I've now
+ 
+
+ align:start position:0%
+integral and what I've done is I've now
+taken this quantity and I've and I've uh
+
+ align:start position:0%
+taken this quantity and I've and I've uh
+ 
+
+ align:start position:0%
+taken this quantity and I've and I've uh
+multiplied by an eus y^ 2 and then I'm
+
+ align:start position:0%
+multiplied by an eus y^ 2 and then I'm
+ 
+
+ align:start position:0%
+multiplied by an eus y^ 2 and then I'm
+now integrating from minus infinity to
+
+ align:start position:0%
+now integrating from minus infinity to
+ 
+
+ align:start position:0%
+now integrating from minus infinity to
+infinity and Dy also and what I want to
+
+ align:start position:0%
+infinity and Dy also and what I want to
+ 
+
+ align:start position:0%
+infinity and Dy also and what I want to
+point out that maybe isn't immediately
+
+ align:start position:0%
+point out that maybe isn't immediately
+ 
+
+ align:start position:0%
+point out that maybe isn't immediately
+obvious from the way it's written here
+
+ align:start position:0%
+obvious from the way it's written here
+ 
+
+ align:start position:0%
+obvious from the way it's written here
+but will be immediately obvious when I
+
+ align:start position:0%
+but will be immediately obvious when I
+ 
+
+ align:start position:0%
+but will be immediately obvious when I
+write it a different way is that this
+
+ align:start position:0%
+write it a different way is that this
+ 
+
+ align:start position:0%
+write it a different way is that this
+quantity is actually just the square of
+
+ align:start position:0%
+quantity is actually just the square of
+ 
+
+ align:start position:0%
+quantity is actually just the square of
+this quantity so it's actually just two
+
+ align:start position:0%
+this quantity so it's actually just two
+ 
+
+ align:start position:0%
+this quantity so it's actually just two
+of these multiplied together and let me
+
+ align:start position:0%
+of these multiplied together and let me
+ 
+
+ align:start position:0%
+of these multiplied together and let me
+point out why that is because this term
+
+ align:start position:0%
+point out why that is because this term
+ 
+
+ align:start position:0%
+point out why that is because this term
+right here can be Rewritten as e- x^2
+
+ align:start position:0%
+right here can be Rewritten as e- x^2
+ 
+
+ align:start position:0%
+right here can be Rewritten as e- x^2
+eus
+
+ align:start position:0%
+eus
+ 
+
+ align:start position:0%
+eus
+y^2 and then I have two
+
+ align:start position:0%
+y^2 and then I have two
+ 
+
+ align:start position:0%
+y^2 and then I have two
+integrals which are from minus infinity
+
+ align:start position:0%
+integrals which are from minus infinity
+ 
+
+ align:start position:0%
+integrals which are from minus infinity
+to Infinity both sorry that one looks a
+
+ align:start position:0%
+to Infinity both sorry that one looks a
+ 
+
+ align:start position:0%
+to Infinity both sorry that one looks a
+little off kilter but those two
+
+ align:start position:0%
+little off kilter but those two
+ 
+
+ align:start position:0%
+little off kilter but those two
+integrals which I the the bounds are
+
+ align:start position:0%
+integrals which I the the bounds are
+ 
+
+ align:start position:0%
+integrals which I the the bounds are
+minus infinity to Infinity for both and
+
+ align:start position:0%
+minus infinity to Infinity for both and
+ 
+
+ align:start position:0%
+minus infinity to Infinity for both and
+then I have a DX and a
+
+ align:start position:0%
+then I have a DX and a
+ 
+
+ align:start position:0%
+then I have a DX and a
+Dy now the reason that it is just i s
+
+ align:start position:0%
+Dy now the reason that it is just i s
+ 
+
+ align:start position:0%
+Dy now the reason that it is just i s
+this quantity is just I squ is because
+
+ align:start position:0%
+this quantity is just I squ is because
+ 
+
+ align:start position:0%
+this quantity is just I squ is because
+because if you notice this first
+
+ align:start position:0%
+because if you notice this first
+ 
+
+ align:start position:0%
+because if you notice this first
+integral the inside integral this is
+
+ align:start position:0%
+integral the inside integral this is
+ 
+
+ align:start position:0%
+integral the inside integral this is
+independent of X so I can move it out so
+
+ align:start position:0%
+independent of X so I can move it out so
+ 
+
+ align:start position:0%
+independent of X so I can move it out so
+let me actually come up here and write
+
+ align:start position:0%
+let me actually come up here and write
+ 
+
+ align:start position:0%
+let me actually come up here and write
+that down so I can move it out and I can
+
+ align:start position:0%
+that down so I can move it out and I can
+ 
+
+ align:start position:0%
+that down so I can move it out and I can
+actually rewrite the integral and I'll
+
+ align:start position:0%
+actually rewrite the integral and I'll
+ 
+
+ align:start position:0%
+actually rewrite the integral and I'll
+put the bounds here because it's high up
+
+ align:start position:0%
+put the bounds here because it's high up
+ 
+
+ align:start position:0%
+put the bounds here because it's high up
+enough that I can actually write it eus
+
+ align:start position:0%
+enough that I can actually write it eus
+ 
+
+ align:start position:0%
+enough that I can actually write it eus
+y^ 2 and then integral from minus
+
+ align:start position:0%
+y^ 2 and then integral from minus
+ 
+
+ align:start position:0%
+y^ 2 and then integral from minus
+infinity to Infinity e to -
+
+ align:start position:0%
+infinity to Infinity e to -
+ 
+
+ align:start position:0%
+infinity to Infinity e to -
+x^2 DX Dy right so let's point out again
+
+ align:start position:0%
+x^2 DX Dy right so let's point out again
+ 
+
+ align:start position:0%
+x^2 DX Dy right so let's point out again
+what I did this quantity I circled was
+
+ align:start position:0%
+what I did this quantity I circled was
+ 
+
+ align:start position:0%
+what I did this quantity I circled was
+was a constant when I when I consider X
+
+ align:start position:0%
+was a constant when I when I consider X
+ 
+
+ align:start position:0%
+was a constant when I when I consider X
+the variable right in terms of X this is
+
+ align:start position:0%
+the variable right in terms of X this is
+ 
+
+ align:start position:0%
+the variable right in terms of X this is
+a constant so I can move it in front of
+
+ align:start position:0%
+a constant so I can move it in front of
+ 
+
+ align:start position:0%
+a constant so I can move it in front of
+that integral which is the DX integral
+
+ align:start position:0%
+that integral which is the DX integral
+ 
+
+ align:start position:0%
+that integral which is the DX integral
+and so now what do I see well this
+
+ align:start position:0%
+and so now what do I see well this
+ 
+
+ align:start position:0%
+and so now what do I see well this
+quantity is what I've called I and so
+
+ align:start position:0%
+quantity is what I've called I and so
+ 
+
+ align:start position:0%
+quantity is what I've called I and so
+now that's a constant so I can move that
+
+ align:start position:0%
+now that's a constant so I can move that
+ 
+
+ align:start position:0%
+now that's a constant so I can move that
+out to the front that's a constant
+
+ align:start position:0%
+out to the front that's a constant
+ 
+
+ align:start position:0%
+out to the front that's a constant
+that's I as designated and so now I have
+
+ align:start position:0%
+that's I as designated and so now I have
+ 
+
+ align:start position:0%
+that's I as designated and so now I have
+the integral from minus infinity to
+
+ align:start position:0%
+the integral from minus infinity to
+ 
+
+ align:start position:0%
+the integral from minus infinity to
+Infinity of eus y^2
+
+ align:start position:0%
+Infinity of eus y^2
+ 
+
+ align:start position:0%
+Infinity of eus y^2
+Y and then that again is another I
+
+ align:start position:0%
+Y and then that again is another I
+ 
+
+ align:start position:0%
+Y and then that again is another I
+because if you notice I mean this was e-
+
+ align:start position:0%
+because if you notice I mean this was e-
+ 
+
+ align:start position:0%
+because if you notice I mean this was e-
+x^2 DX and so if I keep this as eus y^2
+
+ align:start position:0%
+x^2 DX and so if I keep this as eus y^2
+ 
+
+ align:start position:0%
+x^2 DX and so if I keep this as eus y^2
+Dy it's going to be exactly the same
+
+ align:start position:0%
+Dy it's going to be exactly the same
+ 
+
+ align:start position:0%
+Dy it's going to be exactly the same
+value so this is actually equal to
+
+ align:start position:0%
+value so this is actually equal to
+ 
+
+ align:start position:0%
+value so this is actually equal to
+i^2 so the point I want to make if you
+
+ align:start position:0%
+i^2 so the point I want to make if you
+ 
+
+ align:start position:0%
+i^2 so the point I want to make if you
+come back over here to this to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral is is that this quantity I'm
+
+ align:start position:0%
+integral is is that this quantity I'm
+ 
+
+ align:start position:0%
+integral is is that this quantity I'm
+going to be able to integrate very
+
+ align:start position:0%
+going to be able to integrate very
+ 
+
+ align:start position:0%
+going to be able to integrate very
+easily and when I do that if I take the
+
+ align:start position:0%
+easily and when I do that if I take the
+ 
+
+ align:start position:0%
+easily and when I do that if I take the
+square root I'm going to get this
+
+ align:start position:0%
+square root I'm going to get this
+ 
+
+ align:start position:0%
+square root I'm going to get this
+value because I just showed this thing
+
+ align:start position:0%
+value because I just showed this thing
+ 
+
+ align:start position:0%
+value because I just showed this thing
+in the Box was equal to i s all right so
+
+ align:start position:0%
+in the Box was equal to i s all right so
+ 
+
+ align:start position:0%
+in the Box was equal to i s all right so
+let me write it down uh on this last
+
+ align:start position:0%
+let me write it down uh on this last
+ 
+
+ align:start position:0%
+let me write it down uh on this last
+part of the board I will write down that
+
+ align:start position:0%
+part of the board I will write down that
+ 
+
+ align:start position:0%
+part of the board I will write down that
+thing again and then we'll actually
+
+ align:start position:0%
+thing again and then we'll actually
+ 
+
+ align:start position:0%
+thing again and then we'll actually
+evaluate it and we'll see what we
+
+ align:start position:0%
+evaluate it and we'll see what we
+ 
+
+ align:start position:0%
+evaluate it and we'll see what we
+get so let me rewrite this is the thing
+
+ align:start position:0%
+get so let me rewrite this is the thing
+ 
+
+ align:start position:0%
+get so let me rewrite this is the thing
+we want to evaluate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to remind myself that
+
+ align:start position:0%
+and I'm going to remind myself that
+ 
+
+ align:start position:0%
+and I'm going to remind myself that
+that's equal to i^2 i^2 is equal to this
+
+ align:start position:0%
+that's equal to i^2 i^2 is equal to this
+ 
+
+ align:start position:0%
+that's equal to i^2 i^2 is equal to this
+quantity and I mentioned at the
+
+ align:start position:0%
+quantity and I mentioned at the
+ 
+
+ align:start position:0%
+quantity and I mentioned at the
+beginning that we're going to use a
+
+ align:start position:0%
+beginning that we're going to use a
+ 
+
+ align:start position:0%
+beginning that we're going to use a
+trick we're going to change variables
+
+ align:start position:0%
+trick we're going to change variables
+ 
+
+ align:start position:0%
+trick we're going to change variables
+into Polar coordinates and so notice
+
+ align:start position:0%
+into Polar coordinates and so notice
+ 
+
+ align:start position:0%
+into Polar coordinates and so notice
+that the region we're integrating over
+
+ align:start position:0%
+that the region we're integrating over
+ 
+
+ align:start position:0%
+that the region we're integrating over
+is the entire XY plane and in polar
+
+ align:start position:0%
+is the entire XY plane and in polar
+ 
+
+ align:start position:0%
+is the entire XY plane and in polar
+coordinates what's that going to be
+
+ align:start position:0%
+coordinates what's that going to be
+ 
+
+ align:start position:0%
+coordinates what's that going to be
+Theta is going to run from zero all the
+
+ align:start position:0%
+Theta is going to run from zero all the
+ 
+
+ align:start position:0%
+Theta is going to run from zero all the
+way around to 2 pi and R is going to run
+
+ align:start position:0%
+way around to 2 pi and R is going to run
+ 
+
+ align:start position:0%
+way around to 2 pi and R is going to run
+from zero to infinity and so those will
+
+ align:start position:0%
+from zero to infinity and so those will
+ 
+
+ align:start position:0%
+from zero to infinity and so those will
+be our bounds for R and Theta because if
+
+ align:start position:0%
+be our bounds for R and Theta because if
+ 
+
+ align:start position:0%
+be our bounds for R and Theta because if
+you want to get the entire XY plane in
+
+ align:start position:0%
+you want to get the entire XY plane in
+ 
+
+ align:start position:0%
+you want to get the entire XY plane in
+terms of R and Theta that is what you
+
+ align:start position:0%
+terms of R and Theta that is what you
+ 
+
+ align:start position:0%
+terms of R and Theta that is what you
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+do and I want to mention also what is
+
+ align:start position:0%
+do and I want to mention also what is
+ 
+
+ align:start position:0%
+do and I want to mention also what is
+this quantity going to become in terms
+
+ align:start position:0%
+this quantity going to become in terms
+ 
+
+ align:start position:0%
+this quantity going to become in terms
+of R and Theta well notice that this is
+
+ align:start position:0%
+of R and Theta well notice that this is
+ 
+
+ align:start position:0%
+of R and Theta well notice that this is
+e- x^2 - y^2 it's just really e to the
+
+ align:start position:0%
+e- x^2 - y^2 it's just really e to the
+ 
+
+ align:start position:0%
+e- x^2 - y^2 it's just really e to the
+minus quantity x^2 + y^2 it's really e
+
+ align:start position:0%
+minus quantity x^2 + y^2 it's really e
+ 
+
+ align:start position:0%
+minus quantity x^2 + y^2 it's really e
+to Theus R 2 so what we get when we do a
+
+ align:start position:0%
+to Theus R 2 so what we get when we do a
+ 
+
+ align:start position:0%
+to Theus R 2 so what we get when we do a
+change of change of variables as we do
+
+ align:start position:0%
+change of change of variables as we do
+ 
+
+ align:start position:0%
+change of change of variables as we do
+uh I'll put the Theta on the I'll put
+
+ align:start position:0%
+uh I'll put the Theta on the I'll put
+ 
+
+ align:start position:0%
+uh I'll put the Theta on the I'll put
+the Theta on the inside actually because
+
+ align:start position:0%
+the Theta on the inside actually because
+ 
+
+ align:start position:0%
+the Theta on the inside actually because
+that'll be easy to do first so the r is
+
+ align:start position:0%
+that'll be easy to do first so the r is
+ 
+
+ align:start position:0%
+that'll be easy to do first so the r is
+going to be on the outside the Theta is
+
+ align:start position:0%
+going to be on the outside the Theta is
+ 
+
+ align:start position:0%
+going to be on the outside the Theta is
+going to be on the inside and then e
+
+ align:start position:0%
+going to be on the inside and then e
+ 
+
+ align:start position:0%
+going to be on the inside and then e
+Theus R 2 that's a direct substitution
+
+ align:start position:0%
+Theus R 2 that's a direct substitution
+ 
+
+ align:start position:0%
+Theus R 2 that's a direct substitution
+x^2 + y^2 = r^2 and then I get r d Theta
+
+ align:start position:0%
+x^2 + y^2 = r^2 and then I get r d Theta
+ 
+
+ align:start position:0%
+x^2 + y^2 = r^2 and then I get r d Theta
+Dr and this comes from the Jacobian that
+
+ align:start position:0%
+Dr and this comes from the Jacobian that
+ 
+
+ align:start position:0%
+Dr and this comes from the Jacobian that
+you computed I believe in in lecture
+
+ align:start position:0%
+you computed I believe in in lecture
+ 
+
+ align:start position:0%
+you computed I believe in in lecture
+even uh to show how you change from XY
+
+ align:start position:0%
+even uh to show how you change from XY
+ 
+
+ align:start position:0%
+even uh to show how you change from XY
+variables to R Theta variables and I put
+
+ align:start position:0%
+variables to R Theta variables and I put
+ 
+
+ align:start position:0%
+variables to R Theta variables and I put
+the D Theta first here because I wanted
+
+ align:start position:0%
+the D Theta first here because I wanted
+ 
+
+ align:start position:0%
+the D Theta first here because I wanted
+to integrate in Theta first and the
+
+ align:start position:0%
+to integrate in Theta first and the
+ 
+
+ align:start position:0%
+to integrate in Theta first and the
+reason I want to integrate in Theta
+
+ align:start position:0%
+reason I want to integrate in Theta
+ 
+
+ align:start position:0%
+reason I want to integrate in Theta
+first is notice that because nothing
+
+ align:start position:0%
+first is notice that because nothing
+ 
+
+ align:start position:0%
+first is notice that because nothing
+here depends on Theta all I pick up is a
+
+ align:start position:0%
+here depends on Theta all I pick up is a
+ 
+
+ align:start position:0%
+here depends on Theta all I pick up is a
+2 pi I just pick up when I integrate I
+
+ align:start position:0%
+2 pi I just pick up when I integrate I
+ 
+
+ align:start position:0%
+2 pi I just pick up when I integrate I
+get a Theta I evaluate it at 2 pi and
+
+ align:start position:0%
+get a Theta I evaluate it at 2 pi and
+ 
+
+ align:start position:0%
+get a Theta I evaluate it at 2 pi and
+then I evaluate it at zero and I take
+
+ align:start position:0%
+then I evaluate it at zero and I take
+ 
+
+ align:start position:0%
+then I evaluate it at zero and I take
+the difference and so if I do that line
+
+ align:start position:0%
+the difference and so if I do that line
+ 
+
+ align:start position:0%
+the difference and so if I do that line
+all I get is well I should probably
+
+ align:start position:0%
+all I get is well I should probably
+ 
+
+ align:start position:0%
+all I get is well I should probably
+write it in front all I get is 2 pi from
+
+ align:start position:0%
+write it in front all I get is 2 pi from
+ 
+
+ align:start position:0%
+write it in front all I get is 2 pi from
+the Theta and then the integral from
+
+ align:start position:0%
+the Theta and then the integral from
+ 
+
+ align:start position:0%
+the Theta and then the integral from
+zero to
+
+ align:start position:0%
+zero to
+ 
+
+ align:start position:0%
+zero to
+Infinity eus r^ 2 * r d r now this isn't
+
+ align:start position:0%
+Infinity eus r^ 2 * r d r now this isn't
+ 
+
+ align:start position:0%
+Infinity eus r^ 2 * r d r now this isn't
+much easier quantity to evaluate than
+
+ align:start position:0%
+much easier quantity to evaluate than
+ 
+
+ align:start position:0%
+much easier quantity to evaluate than
+eus x^2 DX if because now we have an R
+
+ align:start position:0%
+eus x^2 DX if because now we have an R
+ 
+
+ align:start position:0%
+eus x^2 DX if because now we have an R
+here so now it's a natural substitution
+
+ align:start position:0%
+here so now it's a natural substitution
+ 
+
+ align:start position:0%
+here so now it's a natural substitution
+type of problem and we can do it right
+
+ align:start position:0%
+type of problem and we can do it right
+ 
+
+ align:start position:0%
+type of problem and we can do it right
+away I'm going to write it down and then
+
+ align:start position:0%
+away I'm going to write it down and then
+ 
+
+ align:start position:0%
+away I'm going to write it down and then
+we'll check and make sure I didn't make
+
+ align:start position:0%
+we'll check and make sure I didn't make
+ 
+
+ align:start position:0%
+we'll check and make sure I didn't make
+a mistake we should get something like
+
+ align:start position:0%
+a mistake we should get something like
+ 
+
+ align:start position:0%
+a mistake we should get something like
+eus r^
+
+ align:start position:0%
+eus r^
+ 
+
+ align:start position:0%
+eus r^
+2 over 2 with a negative sign in front
+
+ align:start position:0%
+2 over 2 with a negative sign in front
+ 
+
+ align:start position:0%
+2 over 2 with a negative sign in front
+so let me make sure when I take this
+
+ align:start position:0%
+so let me make sure when I take this
+ 
+
+ align:start position:0%
+so let me make sure when I take this
+derivative you could just do a
+
+ align:start position:0%
+derivative you could just do a
+ 
+
+ align:start position:0%
+derivative you could just do a
+substitution to check but you should get
+
+ align:start position:0%
+substitution to check but you should get
+ 
+
+ align:start position:0%
+substitution to check but you should get
+exactly this kind of thing I take the
+
+ align:start position:0%
+exactly this kind of thing I take the
+ 
+
+ align:start position:0%
+exactly this kind of thing I take the
+derivative of eus r^ 2 I get a
+
+ align:start position:0%
+derivative of eus r^ 2 I get a
+ 
+
+ align:start position:0%
+derivative of eus r^ 2 I get a
+-2r and then uh did I do something wrong
+
+ align:start position:0%
+-2r and then uh did I do something wrong
+ 
+
+ align:start position:0%
+-2r and then uh did I do something wrong
+here oh yeah I'm good I get a
+
+ align:start position:0%
+here oh yeah I'm good I get a
+ 
+
+ align:start position:0%
+here oh yeah I'm good I get a
+-2r and so the negatives kill off the
+
+ align:start position:0%
+-2r and so the negatives kill off the
+ 
+
+ align:start position:0%
+-2r and so the negatives kill off the
+twos divide out and I get my e to the
+
+ align:start position:0%
+twos divide out and I get my e to the
+ 
+
+ align:start position:0%
+twos divide out and I get my e to the
+minus r^ 2 * R so that's good and now I
+
+ align:start position:0%
+minus r^ 2 * R so that's good and now I
+ 
+
+ align:start position:0%
+minus r^ 2 * R so that's good and now I
+have to evaluate it at the
+
+ align:start position:0%
+have to evaluate it at the
+ 
+
+ align:start position:0%
+have to evaluate it at the
+bounds so again this was much easier to
+
+ align:start position:0%
+bounds so again this was much easier to
+ 
+
+ align:start position:0%
+bounds so again this was much easier to
+evaluate if I if I let uh if I do a
+
+ align:start position:0%
+evaluate if I if I let uh if I do a
+ 
+
+ align:start position:0%
+evaluate if I if I let uh if I do a
+substitution and I let uh
+
+ align:start position:0%
+substitution and I let uh
+ 
+
+ align:start position:0%
+substitution and I let uh
+R I think I want to let R2 equal U or
+
+ align:start position:0%
+R I think I want to let R2 equal U or
+ 
+
+ align:start position:0%
+R I think I want to let R2 equal U or
+something like this I don't even know I
+
+ align:start position:0%
+something like this I don't even know I
+ 
+
+ align:start position:0%
+something like this I don't even know I
+just did the substitution without
+
+ align:start position:0%
+just did the substitution without
+ 
+
+ align:start position:0%
+just did the substitution without
+thinking about it so you can figure out
+
+ align:start position:0%
+thinking about it so you can figure out
+ 
+
+ align:start position:0%
+thinking about it so you can figure out
+what you need to substitute but this is
+
+ align:start position:0%
+what you need to substitute but this is
+ 
+
+ align:start position:0%
+what you need to substitute but this is
+what you get and so let me actually just
+
+ align:start position:0%
+what you get and so let me actually just
+ 
+
+ align:start position:0%
+what you get and so let me actually just
+evaluate at the bounds and see what
+
+ align:start position:0%
+evaluate at the bounds and see what
+ 
+
+ align:start position:0%
+evaluate at the bounds and see what
+happens so as R goes to Infinity I get e
+
+ align:start position:0%
+happens so as R goes to Infinity I get e
+ 
+
+ align:start position:0%
+happens so as R goes to Infinity I get e
+to the minus r 2 as R goes to Infinity
+
+ align:start position:0%
+to the minus r 2 as R goes to Infinity
+ 
+
+ align:start position:0%
+to the minus r 2 as R goes to Infinity
+uh e to the minus r squ goes to zero and
+
+ align:start position:0%
+uh e to the minus r squ goes to zero and
+ 
+
+ align:start position:0%
+uh e to the minus r squ goes to zero and
+so the first term is zero when I
+
+ align:start position:0%
+so the first term is zero when I
+ 
+
+ align:start position:0%
+so the first term is zero when I
+evaluate and then so the second term I
+
+ align:start position:0%
+evaluate and then so the second term I
+ 
+
+ align:start position:0%
+evaluate and then so the second term I
+get is I do 0 minus 2 pi times if I
+
+ align:start position:0%
+get is I do 0 minus 2 pi times if I
+ 
+
+ align:start position:0%
+get is I do 0 minus 2 pi times if I
+evaluate at e to the 0o I get 1 so I
+
+ align:start position:0%
+evaluate at e to the 0o I get 1 so I
+ 
+
+ align:start position:0%
+evaluate at e to the 0o I get 1 so I
+get1 / 2 right the negative one comes
+
+ align:start position:0%
+get1 / 2 right the negative one comes
+ 
+
+ align:start position:0%
+get1 / 2 right the negative one comes
+from e to the zero right and then I
+
+ align:start position:0%
+from e to the zero right and then I
+ 
+
+ align:start position:0%
+from e to the zero right and then I
+divide by two so I get my two there so a
+
+ align:start position:0%
+divide by two so I get my two there so a
+ 
+
+ align:start position:0%
+divide by two so I get my two there so a
+negative and a negative gives me a
+
+ align:start position:0%
+negative and a negative gives me a
+ 
+
+ align:start position:0%
+negative and a negative gives me a
+positive two divided two and so the
+
+ align:start position:0%
+positive two divided two and so the
+ 
+
+ align:start position:0%
+positive two divided two and so the
+whole thing equals
+
+ align:start position:0%
+whole thing equals
+ 
+
+ align:start position:0%
+whole thing equals
+Pi just enough room and so I just want
+
+ align:start position:0%
+Pi just enough room and so I just want
+ 
+
+ align:start position:0%
+Pi just enough room and so I just want
+to remind us where we came from we came
+
+ align:start position:0%
+to remind us where we came from we came
+ 
+
+ align:start position:0%
+to remind us where we came from we came
+from PI we we wanted to uh show was
+
+ align:start position:0%
+from PI we we wanted to uh show was
+ 
+
+ align:start position:0%
+from PI we we wanted to uh show was
+equal we well the pi where did it come
+
+ align:start position:0%
+equal we well the pi where did it come
+ 
+
+ align:start position:0%
+equal we well the pi where did it come
+from it's equal if we go all the way
+
+ align:start position:0%
+from it's equal if we go all the way
+ 
+
+ align:start position:0%
+from it's equal if we go all the way
+back up to i^
+
+ align:start position:0%
+back up to i^
+ 
+
+ align:start position:0%
+back up to i^
+S and so we wanted to show what I was
+
+ align:start position:0%
+S and so we wanted to show what I was
+ 
+
+ align:start position:0%
+S and so we wanted to show what I was
+equal to I then is equal to just the
+
+ align:start position:0%
+equal to I then is equal to just the
+ 
+
+ align:start position:0%
+equal to I then is equal to just the
+square root of Pi so I can come back
+
+ align:start position:0%
+square root of Pi so I can come back
+ 
+
+ align:start position:0%
+square root of Pi so I can come back
+over to where I started which is over
+
+ align:start position:0%
+over to where I started which is over
+ 
+
+ align:start position:0%
+over to where I started which is over
+here and I can say this is equal to the
+
+ align:start position:0%
+here and I can say this is equal to the
+ 
+
+ align:start position:0%
+here and I can say this is equal to the
+square root of
+
+ align:start position:0%
+square root of
+ 
+
+ align:start position:0%
+square root of
+Pi and again I just want to mention what
+
+ align:start position:0%
+Pi and again I just want to mention what
+ 
+
+ align:start position:0%
+Pi and again I just want to mention what
+it came down to came down to introducing
+
+ align:start position:0%
+it came down to came down to introducing
+ 
+
+ align:start position:0%
+it came down to came down to introducing
+a little bit more essentially we we took
+
+ align:start position:0%
+a little bit more essentially we we took
+ 
+
+ align:start position:0%
+a little bit more essentially we we took
+something that was a single variable
+
+ align:start position:0%
+something that was a single variable
+ 
+
+ align:start position:0%
+something that was a single variable
+problem we made it a multivariable
+
+ align:start position:0%
+problem we made it a multivariable
+ 
+
+ align:start position:0%
+problem we made it a multivariable
+problem but what that allowed us to do
+
+ align:start position:0%
+problem but what that allowed us to do
+ 
+
+ align:start position:0%
+problem but what that allowed us to do
+is to do a change of coordinates from XY
+
+ align:start position:0%
+is to do a change of coordinates from XY
+ 
+
+ align:start position:0%
+is to do a change of coordinates from XY
+into the polar coordinate system and the
+
+ align:start position:0%
+into the polar coordinate system and the
+ 
+
+ align:start position:0%
+into the polar coordinate system and the
+trick here as you come through the trick
+
+ align:start position:0%
+trick here as you come through the trick
+ 
+
+ align:start position:0%
+trick here as you come through the trick
+where it actually happens is right here
+
+ align:start position:0%
+where it actually happens is right here
+ 
+
+ align:start position:0%
+where it actually happens is right here
+is because this is easy to integrate now
+
+ align:start position:0%
+is because this is easy to integrate now
+ 
+
+ align:start position:0%
+is because this is easy to integrate now
+that I have an R here okay if I didn't
+
+ align:start position:0%
+that I have an R here okay if I didn't
+ 
+
+ align:start position:0%
+that I have an R here okay if I didn't
+have my problem initially was I didn't
+
+ align:start position:0%
+have my problem initially was I didn't
+ 
+
+ align:start position:0%
+have my problem initially was I didn't
+have an X when I was trying to find an
+
+ align:start position:0%
+have an X when I was trying to find an
+ 
+
+ align:start position:0%
+have an X when I was trying to find an
+anti-derivative but when I do the change
+
+ align:start position:0%
+anti-derivative but when I do the change
+ 
+
+ align:start position:0%
+anti-derivative but when I do the change
+of variables I get an eus R 2 and then
+
+ align:start position:0%
+of variables I get an eus R 2 and then
+ 
+
+ align:start position:0%
+of variables I get an eus R 2 and then
+with an R here that's much easier to
+
+ align:start position:0%
+with an R here that's much easier to
+ 
+
+ align:start position:0%
+with an R here that's much easier to
+find an anti-derivative
+
+ align:start position:0%
+find an anti-derivative
+ 
+
+ align:start position:0%
+find an anti-derivative
+okay so I think that is where I will
+
+ align:start position:0%
+okay so I think that is where I will
+ 
+
+ align:start position:0%
+okay so I think that is where I will
+stop
\ No newline at end of file
diff --git a/fdbeCmYRVzA.txt b/fdbeCmYRVzA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4b4a9cfc72e5307e2f570edcc7c3b853447d5ebf
--- /dev/null
+++ b/fdbeCmYRVzA.txt
@@ -0,0 +1,1003 @@
+align:start position:0%
+ 
+so as an aside for those of you who have
+
+ align:start position:0%
+so as an aside for those of you who have
+ 
+
+ align:start position:0%
+so as an aside for those of you who have
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+understanding of probability theory and
+
+ align:start position:0%
+understanding of probability theory and
+ 
+
+ align:start position:0%
+understanding of probability theory and
+stochastic processes
+
+ align:start position:0%
+stochastic processes
+ 
+
+ align:start position:0%
+stochastic processes
+let me just explain why it is valid to
+
+ align:start position:0%
+let me just explain why it is valid to
+ 
+
+ align:start position:0%
+let me just explain why it is valid to
+bound
+
+ align:start position:0%
+bound
+ 
+
+ align:start position:0%
+bound
+the mean transmission rate in defining
+
+ align:start position:0%
+the mean transmission rate in defining
+ 
+
+ align:start position:0%
+the mean transmission rate in defining
+the indoor reproductive number
+
+ align:start position:0%
+the indoor reproductive number
+ 
+
+ align:start position:0%
+the indoor reproductive number
+when we might be more concerned about
+
+ align:start position:0%
+when we might be more concerned about
+ 
+
+ align:start position:0%
+when we might be more concerned about
+bounding the probability of a
+
+ align:start position:0%
+bounding the probability of a
+ 
+
+ align:start position:0%
+bounding the probability of a
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+so let's let a capital t
+
+ align:start position:0%
+so let's let a capital t
+ 
+
+ align:start position:0%
+so let's let a capital t
+be a random variable which describes the
+
+ align:start position:0%
+be a random variable which describes the
+ 
+
+ align:start position:0%
+be a random variable which describes the
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+number of transmissions that occur in
+
+ align:start position:0%
+number of transmissions that occur in
+ 
+
+ align:start position:0%
+number of transmissions that occur in
+the room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and this is specifically for the
+
+ align:start position:0%
+and and this is specifically for the
+ 
+
+ align:start position:0%
+and and this is specifically for the
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+for one infector
+
+ align:start position:0%
+for one infector
+ 
+
+ align:start position:0%
+for one infector
+or infected person and
+
+ align:start position:0%
+or infected person and
+ 
+
+ align:start position:0%
+or infected person and
+n minus 1 susceptible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again the situation of the
+
+ align:start position:0%
+so again the situation of the
+ 
+
+ align:start position:0%
+so again the situation of the
+reproductive number where for every
+
+ align:start position:0%
+reproductive number where for every
+ 
+
+ align:start position:0%
+reproductive number where for every
+person that comes in we want to know is
+
+ align:start position:0%
+person that comes in we want to know is
+ 
+
+ align:start position:0%
+person that comes in we want to know is
+there going to be a transmission and
+
+ align:start position:0%
+there going to be a transmission and
+ 
+
+ align:start position:0%
+there going to be a transmission and
+typically only one affected person would
+
+ align:start position:0%
+typically only one affected person would
+ 
+
+ align:start position:0%
+typically only one affected person would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+would be seen so this is a random
+
+ align:start position:0%
+would be seen so this is a random
+ 
+
+ align:start position:0%
+would be seen so this is a random
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+and let's let f
+
+ align:start position:0%
+and let's let f
+ 
+
+ align:start position:0%
+and let's let f
+f t of n be the probability density
+
+ align:start position:0%
+f t of n be the probability density
+ 
+
+ align:start position:0%
+f t of n be the probability density
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+that gives the probability of little n
+
+ align:start position:0%
+that gives the probability of little n
+ 
+
+ align:start position:0%
+that gives the probability of little n
+transmissions
+
+ align:start position:0%
+transmissions
+ 
+
+ align:start position:0%
+transmissions
+and then we can define the
+
+ align:start position:0%
+and then we can define the
+ 
+
+ align:start position:0%
+and then we can define the
+risk of a transmission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the risk of at least one transmission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the probability that this random
+
+ align:start position:0%
+as the probability that this random
+ 
+
+ align:start position:0%
+as the probability that this random
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+takes on a value which is greater than
+
+ align:start position:0%
+takes on a value which is greater than
+ 
+
+ align:start position:0%
+takes on a value which is greater than
+or equal to one
+
+ align:start position:0%
+or equal to one
+ 
+
+ align:start position:0%
+or equal to one
+okay well in terms of the probability
+
+ align:start position:0%
+okay well in terms of the probability
+ 
+
+ align:start position:0%
+okay well in terms of the probability
+density function then
+
+ align:start position:0%
+density function then
+ 
+
+ align:start position:0%
+density function then
+that would be a sum
+
+ align:start position:0%
+that would be a sum
+ 
+
+ align:start position:0%
+that would be a sum
+from one to infinity of the
+
+ align:start position:0%
+from one to infinity of the
+ 
+
+ align:start position:0%
+from one to infinity of the
+uh ft of n basically so
+
+ align:start position:0%
+uh ft of n basically so
+ 
+
+ align:start position:0%
+uh ft of n basically so
+we're just adding the probabilities that
+
+ align:start position:0%
+we're just adding the probabilities that
+ 
+
+ align:start position:0%
+we're just adding the probabilities that
+each we're not uh
+
+ align:start position:0%
+each we're not uh
+ 
+
+ align:start position:0%
+each we're not uh
+seeing a transmission uh to those uh
+
+ align:start position:0%
+seeing a transmission uh to those uh
+ 
+
+ align:start position:0%
+seeing a transmission uh to those uh
+or possibly a transition to those
+
+ align:start position:0%
+or possibly a transition to those
+ 
+
+ align:start position:0%
+or possibly a transition to those
+different numbers of people
+
+ align:start position:0%
+different numbers of people
+ 
+
+ align:start position:0%
+different numbers of people
+now i'd like to do a little calculation
+
+ align:start position:0%
+now i'd like to do a little calculation
+ 
+
+ align:start position:0%
+now i'd like to do a little calculation
+to get an upper bound on this quantity
+
+ align:start position:0%
+to get an upper bound on this quantity
+ 
+
+ align:start position:0%
+to get an upper bound on this quantity
+so we can say that this is less than or
+
+ align:start position:0%
+so we can say that this is less than or
+ 
+
+ align:start position:0%
+so we can say that this is less than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+the sum from n equals 1 to infinity of n
+
+ align:start position:0%
+the sum from n equals 1 to infinity of n
+ 
+
+ align:start position:0%
+the sum from n equals 1 to infinity of n
+f t of n now this
+
+ align:start position:0%
+f t of n now this
+ 
+
+ align:start position:0%
+f t of n now this
+is just a mathematical trick here so n
+
+ align:start position:0%
+is just a mathematical trick here so n
+ 
+
+ align:start position:0%
+is just a mathematical trick here so n
+refers to the natural numbers 1 2
+
+ align:start position:0%
+refers to the natural numbers 1 2
+ 
+
+ align:start position:0%
+refers to the natural numbers 1 2
+3 4 etc those are all positive numbers
+
+ align:start position:0%
+3 4 etc those are all positive numbers
+ 
+
+ align:start position:0%
+3 4 etc those are all positive numbers
+and they're all greater than or equal to
+
+ align:start position:0%
+and they're all greater than or equal to
+ 
+
+ align:start position:0%
+and they're all greater than or equal to
+1. so if i take
+
+ align:start position:0%
+1. so if i take
+ 
+
+ align:start position:0%
+1. so if i take
+1 in this expression over here or
+
+ align:start position:0%
+1 in this expression over here or
+ 
+
+ align:start position:0%
+1 in this expression over here or
+replace it with little n i'm only
+
+ align:start position:0%
+replace it with little n i'm only
+ 
+
+ align:start position:0%
+replace it with little n i'm only
+increasing the value of that sum
+
+ align:start position:0%
+increasing the value of that sum
+ 
+
+ align:start position:0%
+increasing the value of that sum
+because also this ft is a probability
+
+ align:start position:0%
+because also this ft is a probability
+ 
+
+ align:start position:0%
+because also this ft is a probability
+density that has to be positive
+
+ align:start position:0%
+density that has to be positive
+ 
+
+ align:start position:0%
+density that has to be positive
+and then now i can also say that this is
+
+ align:start position:0%
+and then now i can also say that this is
+ 
+
+ align:start position:0%
+and then now i can also say that this is
+actually equal to
+
+ align:start position:0%
+actually equal to
+ 
+
+ align:start position:0%
+actually equal to
+throwing in n equals 0 because that is a
+
+ align:start position:0%
+throwing in n equals 0 because that is a
+ 
+
+ align:start position:0%
+throwing in n equals 0 because that is a
+term that
+
+ align:start position:0%
+term that
+ 
+
+ align:start position:0%
+term that
+is actually identically zero so i can
+
+ align:start position:0%
+is actually identically zero so i can
+ 
+
+ align:start position:0%
+is actually identically zero so i can
+change the summation
+
+ align:start position:0%
+change the summation
+ 
+
+ align:start position:0%
+change the summation
+and then by definition here this thing
+
+ align:start position:0%
+and then by definition here this thing
+ 
+
+ align:start position:0%
+and then by definition here this thing
+is the expected value of the number of
+
+ align:start position:0%
+is the expected value of the number of
+ 
+
+ align:start position:0%
+is the expected value of the number of
+transmissions because i'm
+
+ align:start position:0%
+transmissions because i'm
+ 
+
+ align:start position:0%
+transmissions because i'm
+summing the number of transmissions
+
+ align:start position:0%
+summing the number of transmissions
+ 
+
+ align:start position:0%
+summing the number of transmissions
+little n times the probability of that
+
+ align:start position:0%
+little n times the probability of that
+ 
+
+ align:start position:0%
+little n times the probability of that
+event occurring so that is the
+
+ align:start position:0%
+event occurring so that is the
+ 
+
+ align:start position:0%
+event occurring so that is the
+definition of the average
+
+ align:start position:0%
+definition of the average
+ 
+
+ align:start position:0%
+definition of the average
+so what we're seeing here is that
+
+ align:start position:0%
+so what we're seeing here is that
+ 
+
+ align:start position:0%
+so what we're seeing here is that
+the risk of a transmission
+
+ align:start position:0%
+the risk of a transmission
+ 
+
+ align:start position:0%
+the risk of a transmission
+is rigorously bounded above by the
+
+ align:start position:0%
+is rigorously bounded above by the
+ 
+
+ align:start position:0%
+is rigorously bounded above by the
+expected number of transmissions and so
+
+ align:start position:0%
+expected number of transmissions and so
+ 
+
+ align:start position:0%
+expected number of transmissions and so
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+if we require that this is less than
+
+ align:start position:0%
+if we require that this is less than
+ 
+
+ align:start position:0%
+if we require that this is less than
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+our risk tolerance that we've just
+
+ align:start position:0%
+our risk tolerance that we've just
+ 
+
+ align:start position:0%
+our risk tolerance that we've just
+introduced
+
+ align:start position:0%
+introduced
+ 
+
+ align:start position:0%
+introduced
+this is a conservative bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the true risk
+
+ align:start position:0%
+on the true risk
+ 
+
+ align:start position:0%
+on the true risk
+which let's say here is defined by rt so
+
+ align:start position:0%
+which let's say here is defined by rt so
+ 
+
+ align:start position:0%
+which let's say here is defined by rt so
+if your goal
+
+ align:start position:0%
+if your goal
+ 
+
+ align:start position:0%
+if your goal
+is to control the probability of having
+
+ align:start position:0%
+is to control the probability of having
+ 
+
+ align:start position:0%
+is to control the probability of having
+at least one transmission so basically
+
+ align:start position:0%
+at least one transmission so basically
+ 
+
+ align:start position:0%
+at least one transmission so basically
+to ensure that no transmissions occur
+
+ align:start position:0%
+to ensure that no transmissions occur
+ 
+
+ align:start position:0%
+to ensure that no transmissions occur
+then you would do well to bound the
+
+ align:start position:0%
+then you would do well to bound the
+ 
+
+ align:start position:0%
+then you would do well to bound the
+expected number of transmissions because
+
+ align:start position:0%
+expected number of transmissions because
+ 
+
+ align:start position:0%
+expected number of transmissions because
+that's an upper bound
+
+ align:start position:0%
+that's an upper bound
+ 
+
+ align:start position:0%
+that's an upper bound
+it can also be shown that as
+
+ align:start position:0%
+it can also be shown that as
+ 
+
+ align:start position:0%
+it can also be shown that as
+epsilon goes to zero so we're talking
+
+ align:start position:0%
+epsilon goes to zero so we're talking
+ 
+
+ align:start position:0%
+epsilon goes to zero so we're talking
+about very low probabilities of
+
+ align:start position:0%
+about very low probabilities of
+ 
+
+ align:start position:0%
+about very low probabilities of
+transmission and often times that is the
+
+ align:start position:0%
+transmission and often times that is the
+ 
+
+ align:start position:0%
+transmission and often times that is the
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+then rt is asymptotically the same
+
+ align:start position:0%
+then rt is asymptotically the same
+ 
+
+ align:start position:0%
+then rt is asymptotically the same
+as the expected number of transmissions
+
+ align:start position:0%
+as the expected number of transmissions
+ 
+
+ align:start position:0%
+as the expected number of transmissions
+so this so this overall risk
+
+ align:start position:0%
+so this so this overall risk
+ 
+
+ align:start position:0%
+so this so this overall risk
+of a transmission and the expected
+
+ align:start position:0%
+of a transmission and the expected
+ 
+
+ align:start position:0%
+of a transmission and the expected
+number are the same
+
+ align:start position:0%
+number are the same
+ 
+
+ align:start position:0%
+number are the same
+and in fact that's one way you can
+
+ align:start position:0%
+and in fact that's one way you can
+ 
+
+ align:start position:0%
+and in fact that's one way you can
+understand sort of even the definition
+
+ align:start position:0%
+understand sort of even the definition
+ 
+
+ align:start position:0%
+understand sort of even the definition
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+of a probability in terms of an expected
+
+ align:start position:0%
+of a probability in terms of an expected
+ 
+
+ align:start position:0%
+of a probability in terms of an expected
+number of events and we are typically
+
+ align:start position:0%
+number of events and we are typically
+ 
+
+ align:start position:0%
+number of events and we are typically
+thinking of cases where epsilon is much
+
+ align:start position:0%
+thinking of cases where epsilon is much
+ 
+
+ align:start position:0%
+thinking of cases where epsilon is much
+less than one
+
+ align:start position:0%
+less than one
+ 
+
+ align:start position:0%
+less than one
+so uh for those of you that have some
+
+ align:start position:0%
+so uh for those of you that have some
+ 
+
+ align:start position:0%
+so uh for those of you that have some
+background and probability you may
+
+ align:start position:0%
+background and probability you may
+ 
+
+ align:start position:0%
+background and probability you may
+recognize that what i've just done here
+
+ align:start position:0%
+recognize that what i've just done here
+ 
+
+ align:start position:0%
+recognize that what i've just done here
+is an example of a much more general
+
+ align:start position:0%
+is an example of a much more general
+ 
+
+ align:start position:0%
+is an example of a much more general
+result which is called markov's
+
+ align:start position:0%
+result which is called markov's
+ 
+
+ align:start position:0%
+result which is called markov's
+inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can safely proceed by
+
+ align:start position:0%
+so now we can safely proceed by
+ 
+
+ align:start position:0%
+so now we can safely proceed by
+continuing to work with average values
+
+ align:start position:0%
+continuing to work with average values
+ 
+
+ align:start position:0%
+continuing to work with average values
+of all the quantities of interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/fh1bvrJN4Fc.txt b/fh1bvrJN4Fc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..80e2d0c0334ba06b3e19318a7923a057b02955bf
--- /dev/null
+++ b/fh1bvrJN4Fc.txt
@@ -0,0 +1,243 @@
+align:start position:0%
+ 
+so so I start the class the only way
+
+ align:start position:0%
+so so I start the class the only way
+ 
+
+ align:start position:0%
+so so I start the class the only way
+first day while they are still fresh and
+
+ align:start position:0%
+first day while they are still fresh and
+ 
+
+ align:start position:0%
+first day while they are still fresh and
+unsuspecting of the class contents of my
+
+ align:start position:0%
+unsuspecting of the class contents of my
+ 
+
+ align:start position:0%
+unsuspecting of the class contents of my
+own ideology I give them a survey where
+
+ align:start position:0%
+own ideology I give them a survey where
+ 
+
+ align:start position:0%
+own ideology I give them a survey where
+ask me simple questions you know the
+
+ align:start position:0%
+ask me simple questions you know the
+ 
+
+ align:start position:0%
+ask me simple questions you know the
+major the year but also ask them
+
+ align:start position:0%
+major the year but also ask them
+ 
+
+ align:start position:0%
+major the year but also ask them
+personal questions where were they born
+
+ align:start position:0%
+personal questions where were they born
+ 
+
+ align:start position:0%
+personal questions where were they born
+where they travel during what years they
+
+ align:start position:0%
+where they travel during what years they
+ 
+
+ align:start position:0%
+where they travel during what years they
+were in which parts of the country of
+
+ align:start position:0%
+were in which parts of the country of
+ 
+
+ align:start position:0%
+were in which parts of the country of
+the world and I ask them about some of
+
+ align:start position:0%
+the world and I ask them about some of
+ 
+
+ align:start position:0%
+the world and I ask them about some of
+the course contents you know what do
+
+ align:start position:0%
+the course contents you know what do
+ 
+
+ align:start position:0%
+the course contents you know what do
+they know about cruel languages how they
+
+ align:start position:0%
+they know about cruel languages how they
+ 
+
+ align:start position:0%
+they know about cruel languages how they
+define identity what is the word
+
+ align:start position:0%
+define identity what is the word
+ 
+
+ align:start position:0%
+define identity what is the word
+identity mean what kind of images does
+
+ align:start position:0%
+identity mean what kind of images does
+ 
+
+ align:start position:0%
+identity mean what kind of images does
+the word Caribbean sugar in the mind so
+
+ align:start position:0%
+the word Caribbean sugar in the mind so
+ 
+
+ align:start position:0%
+the word Caribbean sugar in the mind so
+very easy questions to answer but
+
+ align:start position:0%
+very easy questions to answer but
+ 
+
+ align:start position:0%
+very easy questions to answer but
+through these questions what I'm about
+
+ align:start position:0%
+through these questions what I'm about
+ 
+
+ align:start position:0%
+through these questions what I'm about
+to see and go to get a sense of both the
+
+ align:start position:0%
+to see and go to get a sense of both the
+ 
+
+ align:start position:0%
+to see and go to get a sense of both the
+personal background but also what kind
+
+ align:start position:0%
+personal background but also what kind
+ 
+
+ align:start position:0%
+personal background but also what kind
+of what kind of assumptions they bring
+
+ align:start position:0%
+of what kind of assumptions they bring
+ 
+
+ align:start position:0%
+of what kind of assumptions they bring
+to the course and and then I can use
+
+ align:start position:0%
+to the course and and then I can use
+ 
+
+ align:start position:0%
+to the course and and then I can use
+that to kind of have a beginning where I
+
+ align:start position:0%
+that to kind of have a beginning where I
+ 
+
+ align:start position:0%
+that to kind of have a beginning where I
+can address these fundamental assumption
+
+ align:start position:0%
+can address these fundamental assumption
+ 
+
+ align:start position:0%
+can address these fundamental assumption
+that we do bring in the course and also
+
+ align:start position:0%
+that we do bring in the course and also
+ 
+
+ align:start position:0%
+that we do bring in the course and also
+to connect the discussion to the
+
+ align:start position:0%
+to connect the discussion to the
+ 
+
+ align:start position:0%
+to connect the discussion to the
+personal profiles and then that and then
+
+ align:start position:0%
+personal profiles and then that and then
+ 
+
+ align:start position:0%
+personal profiles and then that and then
+as we progress I can from time to time
+
+ align:start position:0%
+as we progress I can from time to time
+ 
+
+ align:start position:0%
+as we progress I can from time to time
+check to see how some of the ideas might
+
+ align:start position:0%
+check to see how some of the ideas might
+ 
+
+ align:start position:0%
+check to see how some of the ideas might
+have mutated merav evolve through our
+
+ align:start position:0%
+have mutated merav evolve through our
+ 
+
+ align:start position:0%
+have mutated merav evolve through our
+discussions so it's a nice benchmark to
+
+ align:start position:0%
+discussions so it's a nice benchmark to
+ 
+
+ align:start position:0%
+discussions so it's a nice benchmark to
+start with
\ No newline at end of file
diff --git a/fuo2j6f8yok.txt b/fuo2j6f8yok.txt
new file mode 100644
index 0000000000000000000000000000000000000000..12a6e5996455fc617e45152edd933ba04e541b2a
--- /dev/null
+++ b/fuo2j6f8yok.txt
@@ -0,0 +1,883 @@
+align:start position:0%
+ 
+okay why does this matter well this is
+
+ align:start position:0%
+okay why does this matter well this is
+ 
+
+ align:start position:0%
+okay why does this matter well this is
+one reason
+
+ align:start position:0%
+one reason
+ 
+
+ align:start position:0%
+one reason
+if you don't plan your cold work
+
+ align:start position:0%
+if you don't plan your cold work
+ 
+
+ align:start position:0%
+if you don't plan your cold work
+carefully
+
+ align:start position:0%
+carefully
+ 
+
+ align:start position:0%
+carefully
+you might make the material too brittle
+
+ align:start position:0%
+you might make the material too brittle
+ 
+
+ align:start position:0%
+you might make the material too brittle
+you wanted it to be so hard because this
+
+ align:start position:0%
+you wanted it to be so hard because this
+ 
+
+ align:start position:0%
+you wanted it to be so hard because this
+was such an important ship
+
+ align:start position:0%
+was such an important ship
+ 
+
+ align:start position:0%
+was such an important ship
+and it was going to be a big deal and
+
+ align:start position:0%
+and it was going to be a big deal and
+ 
+
+ align:start position:0%
+and it was going to be a big deal and
+the launch was really exciting and then
+
+ align:start position:0%
+the launch was really exciting and then
+ 
+
+ align:start position:0%
+the launch was really exciting and then
+it cracks in half
+
+ align:start position:0%
+it cracks in half
+ 
+
+ align:start position:0%
+it cracks in half
+the entire ship why because you didn't
+
+ align:start position:0%
+the entire ship why because you didn't
+ 
+
+ align:start position:0%
+the entire ship why because you didn't
+look up
+
+ align:start position:0%
+look up
+ 
+
+ align:start position:0%
+look up
+what dislocations mean you didn't take
+
+ align:start position:0%
+what dislocations mean you didn't take
+ 
+
+ align:start position:0%
+what dislocations mean you didn't take
+309 one
+
+ align:start position:0%
+309 one
+ 
+
+ align:start position:0%
+309 one
+that's why that's a pretty big crack
+
+ align:start position:0%
+that's why that's a pretty big crack
+ 
+
+ align:start position:0%
+that's why that's a pretty big crack
+but the the main why this matters oh i
+
+ align:start position:0%
+but the the main why this matters oh i
+ 
+
+ align:start position:0%
+but the the main why this matters oh i
+couldn't help it
+
+ align:start position:0%
+couldn't help it
+ 
+
+ align:start position:0%
+couldn't help it
+i am a big fan of wind wind energy is
+
+ align:start position:0%
+i am a big fan of wind wind energy is
+ 
+
+ align:start position:0%
+i am a big fan of wind wind energy is
+growing and growing and it's it's
+
+ align:start position:0%
+growing and growing and it's it's
+ 
+
+ align:start position:0%
+growing and growing and it's it's
+it's such a great resource it's such a
+
+ align:start position:0%
+it's such a great resource it's such a
+ 
+
+ align:start position:0%
+it's such a great resource it's such a
+great national resource
+
+ align:start position:0%
+great national resource
+ 
+
+ align:start position:0%
+great national resource
+here's the global uh capacity and
+
+ align:start position:0%
+here's the global uh capacity and
+ 
+
+ align:start position:0%
+here's the global uh capacity and
+this is install capacity for wind
+
+ align:start position:0%
+this is install capacity for wind
+ 
+
+ align:start position:0%
+this is install capacity for wind
+turbines
+
+ align:start position:0%
+turbines
+ 
+
+ align:start position:0%
+turbines
+um but see this is a mechanical
+
+ align:start position:0%
+um but see this is a mechanical
+ 
+
+ align:start position:0%
+um but see this is a mechanical
+materials problem that you are now
+
+ align:start position:0%
+materials problem that you are now
+ 
+
+ align:start position:0%
+materials problem that you are now
+equipped to think about more deeply
+
+ align:start position:0%
+equipped to think about more deeply
+ 
+
+ align:start position:0%
+equipped to think about more deeply
+right um because you see you can
+
+ align:start position:0%
+right um because you see you can
+ 
+
+ align:start position:0%
+right um because you see you can
+you can do a lot of different
+
+ align:start position:0%
+you can do a lot of different
+ 
+
+ align:start position:0%
+you can do a lot of different
+experiments on those turbines so the
+
+ align:start position:0%
+experiments on those turbines so the
+ 
+
+ align:start position:0%
+experiments on those turbines so the
+turbine
+
+ align:start position:0%
+turbine
+ 
+
+ align:start position:0%
+turbine
+so the blades here are critical you can
+
+ align:start position:0%
+so the blades here are critical you can
+ 
+
+ align:start position:0%
+so the blades here are critical you can
+imagine that
+
+ align:start position:0%
+imagine that
+ 
+
+ align:start position:0%
+imagine that
+you want them to be light but but if
+
+ align:start position:0%
+you want them to be light but but if
+ 
+
+ align:start position:0%
+you want them to be light but but if
+they're too light there may not be
+
+ align:start position:0%
+they're too light there may not be
+ 
+
+ align:start position:0%
+they're too light there may not be
+strong enough and then how do they need
+
+ align:start position:0%
+strong enough and then how do they need
+ 
+
+ align:start position:0%
+strong enough and then how do they need
+to be strong because you've got
+
+ align:start position:0%
+to be strong because you've got
+ 
+
+ align:start position:0%
+to be strong because you've got
+huge amounts of wind coming at them
+
+ align:start position:0%
+huge amounts of wind coming at them
+ 
+
+ align:start position:0%
+huge amounts of wind coming at them
+and it turns out you need to hit just
+
+ align:start position:0%
+and it turns out you need to hit just
+ 
+
+ align:start position:0%
+and it turns out you need to hit just
+the right balance
+
+ align:start position:0%
+the right balance
+ 
+
+ align:start position:0%
+the right balance
+of elastic deformation
+
+ align:start position:0%
+of elastic deformation
+ 
+
+ align:start position:0%
+of elastic deformation
+before it goes into some plastic regime
+
+ align:start position:0%
+before it goes into some plastic regime
+ 
+
+ align:start position:0%
+before it goes into some plastic regime
+you need to hit just the right balance
+
+ align:start position:0%
+you need to hit just the right balance
+ 
+
+ align:start position:0%
+you need to hit just the right balance
+of ductility
+
+ align:start position:0%
+of ductility
+ 
+
+ align:start position:0%
+of ductility
+so here's for example uh these are some
+
+ align:start position:0%
+so here's for example uh these are some
+ 
+
+ align:start position:0%
+so here's for example uh these are some
+simulations here are some experiments on
+
+ align:start position:0%
+simulations here are some experiments on
+ 
+
+ align:start position:0%
+simulations here are some experiments on
+a new
+
+ align:start position:0%
+a new
+ 
+
+ align:start position:0%
+a new
+material for a wind turbine blade and
+
+ align:start position:0%
+material for a wind turbine blade and
+ 
+
+ align:start position:0%
+material for a wind turbine blade and
+then you put it out there
+
+ align:start position:0%
+then you put it out there
+ 
+
+ align:start position:0%
+then you put it out there
+and and look at what happens ice by the
+
+ align:start position:0%
+and and look at what happens ice by the
+ 
+
+ align:start position:0%
+and and look at what happens ice by the
+way this ice
+
+ align:start position:0%
+way this ice
+ 
+
+ align:start position:0%
+way this ice
+comes off at hundreds of miles an hour
+
+ align:start position:0%
+comes off at hundreds of miles an hour
+ 
+
+ align:start position:0%
+comes off at hundreds of miles an hour
+in chunks
+
+ align:start position:0%
+in chunks
+ 
+
+ align:start position:0%
+in chunks
+these farmers are not happy about that
+
+ align:start position:0%
+these farmers are not happy about that
+ 
+
+ align:start position:0%
+these farmers are not happy about that
+seriously but those are bugs
+
+ align:start position:0%
+seriously but those are bugs
+ 
+
+ align:start position:0%
+seriously but those are bugs
+those are bugs so actually bugs in
+
+ align:start position:0%
+those are bugs so actually bugs in
+ 
+
+ align:start position:0%
+those are bugs so actually bugs in
+wind turbine blades is a serious problem
+
+ align:start position:0%
+wind turbine blades is a serious problem
+ 
+
+ align:start position:0%
+wind turbine blades is a serious problem
+how do you clean
+
+ align:start position:0%
+how do you clean
+ 
+
+ align:start position:0%
+how do you clean
+bugs off of it because it dramatically
+
+ align:start position:0%
+bugs off of it because it dramatically
+ 
+
+ align:start position:0%
+bugs off of it because it dramatically
+changes the aerodynamics and the
+
+ align:start position:0%
+changes the aerodynamics and the
+ 
+
+ align:start position:0%
+changes the aerodynamics and the
+efficiency
+
+ align:start position:0%
+efficiency
+ 
+
+ align:start position:0%
+efficiency
+it also can damage the blade itself
+
+ align:start position:0%
+it also can damage the blade itself
+ 
+
+ align:start position:0%
+it also can damage the blade itself
+so there's all sorts of work going on
+
+ align:start position:0%
+so there's all sorts of work going on
+ 
+
+ align:start position:0%
+so there's all sorts of work going on
+how do you make bug proof
+
+ align:start position:0%
+how do you make bug proof
+ 
+
+ align:start position:0%
+how do you make bug proof
+wind turbine blades okay well now just
+
+ align:start position:0%
+wind turbine blades okay well now just
+ 
+
+ align:start position:0%
+wind turbine blades okay well now just
+spray it with something ah but then does
+
+ align:start position:0%
+spray it with something ah but then does
+ 
+
+ align:start position:0%
+spray it with something ah but then does
+it have the right
+
+ align:start position:0%
+it have the right
+ 
+
+ align:start position:0%
+it have the right
+plastic different what does it have the
+
+ align:start position:0%
+plastic different what does it have the
+ 
+
+ align:start position:0%
+plastic different what does it have the
+right yield point or is it just going to
+
+ align:start position:0%
+right yield point or is it just going to
+ 
+
+ align:start position:0%
+right yield point or is it just going to
+crack
+
+ align:start position:0%
+crack
+ 
+
+ align:start position:0%
+crack
+right and by the way it's got to have uh
+
+ align:start position:0%
+right and by the way it's got to have uh
+ 
+
+ align:start position:0%
+right and by the way it's got to have uh
+five times ten to the ninth cycles
+
+ align:start position:0%
+five times ten to the ninth cycles
+ 
+
+ align:start position:0%
+five times ten to the ninth cycles
+before it can fail
+
+ align:start position:0%
+before it can fail
+ 
+
+ align:start position:0%
+before it can fail
+that's like the metric so that's a
+
+ align:start position:0%
+that's like the metric so that's a
+ 
+
+ align:start position:0%
+that's like the metric so that's a
+pretty big ask of a material
+
+ align:start position:0%
+pretty big ask of a material
+ 
+
+ align:start position:0%
+pretty big ask of a material
+it all comes down to understanding this
+
+ align:start position:0%
+it all comes down to understanding this
+ 
+
+ align:start position:0%
+it all comes down to understanding this
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+and and in the broader sense of
+
+ align:start position:0%
+and and in the broader sense of
+ 
+
+ align:start position:0%
+and and in the broader sense of
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+this to me is a very exciting ask
+
+ align:start position:0%
+this to me is a very exciting ask
+ 
+
+ align:start position:0%
+this to me is a very exciting ask
+why because if you look at a plot
+
+ align:start position:0%
+why because if you look at a plot
+ 
+
+ align:start position:0%
+why because if you look at a plot
+of the density of materials okay heavy
+
+ align:start position:0%
+of the density of materials okay heavy
+ 
+
+ align:start position:0%
+of the density of materials okay heavy
+light good kilograms per meter cubed and
+
+ align:start position:0%
+light good kilograms per meter cubed and
+ 
+
+ align:start position:0%
+light good kilograms per meter cubed and
+and the young's modulus now this is a
+
+ align:start position:0%
+and the young's modulus now this is a
+ 
+
+ align:start position:0%
+and the young's modulus now this is a
+measure of
+
+ align:start position:0%
+measure of
+ 
+
+ align:start position:0%
+measure of
+of the strength of the material right
+
+ align:start position:0%
+of the strength of the material right
+ 
+
+ align:start position:0%
+of the strength of the material right
+it's a measure of how much
+
+ align:start position:0%
+it's a measure of how much
+ 
+
+ align:start position:0%
+it's a measure of how much
+strain you could put on the material
+
+ align:start position:0%
+strain you could put on the material
+ 
+
+ align:start position:0%
+strain you could put on the material
+before it breaks or
+
+ align:start position:0%
+before it breaks or
+ 
+
+ align:start position:0%
+before it breaks or
+it goes through deformation but look at
+
+ align:start position:0%
+it goes through deformation but look at
+ 
+
+ align:start position:0%
+it goes through deformation but look at
+this different materials are here
+
+ align:start position:0%
+this different materials are here
+ 
+
+ align:start position:0%
+this different materials are here
+rubbers foams okay foams have
+
+ align:start position:0%
+rubbers foams okay foams have
+ 
+
+ align:start position:0%
+rubbers foams okay foams have
+relatively low young's modulus but
+
+ align:start position:0%
+relatively low young's modulus but
+ 
+
+ align:start position:0%
+relatively low young's modulus but
+they're really light that could be good
+
+ align:start position:0%
+they're really light that could be good
+ 
+
+ align:start position:0%
+they're really light that could be good
+up here you've got metals and alloys
+
+ align:start position:0%
+up here you've got metals and alloys
+ 
+
+ align:start position:0%
+up here you've got metals and alloys
+ceramics
+
+ align:start position:0%
+ceramics
+ 
+
+ align:start position:0%
+ceramics
+you've got polymers in here but but
+
+ align:start position:0%
+you've got polymers in here but but
+ 
+
+ align:start position:0%
+you've got polymers in here but but
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+i've got so many different applications
+
+ align:start position:0%
+i've got so many different applications
+ 
+
+ align:start position:0%
+i've got so many different applications
+and needs in the applications
+
+ align:start position:0%
+and needs in the applications
+ 
+
+ align:start position:0%
+and needs in the applications
+and i've got this plot where i've got
+
+ align:start position:0%
+and i've got this plot where i've got
+ 
+
+ align:start position:0%
+and i've got this plot where i've got
+nothing here and nothing
+
+ align:start position:0%
+nothing here and nothing
+ 
+
+ align:start position:0%
+nothing here and nothing
+here even though if i could fill this
+
+ align:start position:0%
+here even though if i could fill this
+ 
+
+ align:start position:0%
+here even though if i could fill this
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+and dial up any stress strain curve
+
+ align:start position:0%
+and dial up any stress strain curve
+ 
+
+ align:start position:0%
+and dial up any stress strain curve
+for any density or young's modulus you
+
+ align:start position:0%
+for any density or young's modulus you
+ 
+
+ align:start position:0%
+for any density or young's modulus you
+can make a big difference in a lot of
+
+ align:start position:0%
+can make a big difference in a lot of
+ 
+
+ align:start position:0%
+can make a big difference in a lot of
+different applications
+
+ align:start position:0%
+different applications
+ 
+
+ align:start position:0%
+different applications
+so i think this is a great a great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+challenge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/gQ1YPzcHZqo.txt b/gQ1YPzcHZqo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..44b0c1883912a8978538de35163a2969d055b439
--- /dev/null
+++ b/gQ1YPzcHZqo.txt
@@ -0,0 +1,14099 @@
+align:start position:0%
+ 
+so what we'll do today is really um
+
+ align:start position:0%
+so what we'll do today is really um
+ 
+
+ align:start position:0%
+so what we'll do today is really um
+switching to sort of the computational
+
+ align:start position:0%
+switching to sort of the computational
+ 
+
+ align:start position:0%
+switching to sort of the computational
+description and characterization of
+
+ align:start position:0%
+description and characterization of
+ 
+
+ align:start position:0%
+description and characterization of
+thermodynamical properties uh as we have
+
+ align:start position:0%
+thermodynamical properties uh as we have
+ 
+
+ align:start position:0%
+thermodynamical properties uh as we have
+seen sort of in a lot of the previous
+
+ align:start position:0%
+seen sort of in a lot of the previous
+ 
+
+ align:start position:0%
+seen sort of in a lot of the previous
+lectures we have been focusing on
+
+ align:start position:0%
+lectures we have been focusing on
+ 
+
+ align:start position:0%
+lectures we have been focusing on
+finding out good energy models that is
+
+ align:start position:0%
+finding out good energy models that is
+ 
+
+ align:start position:0%
+finding out good energy models that is
+being able to calculate what is the
+
+ align:start position:0%
+being able to calculate what is the
+ 
+
+ align:start position:0%
+being able to calculate what is the
+energy of a system giving the coordinate
+
+ align:start position:0%
+energy of a system giving the coordinate
+ 
+
+ align:start position:0%
+energy of a system giving the coordinate
+of its ions and now what we want to
+
+ align:start position:0%
+of its ions and now what we want to
+ 
+
+ align:start position:0%
+of its ions and now what we want to
+understand really is what is the
+
+ align:start position:0%
+understand really is what is the
+ 
+
+ align:start position:0%
+understand really is what is the
+evolution of this system in the the
+
+ align:start position:0%
+evolution of this system in the the
+ 
+
+ align:start position:0%
+evolution of this system in the the
+presence of a fin at temperature
+
+ align:start position:0%
+presence of a fin at temperature
+ 
+
+ align:start position:0%
+presence of a fin at temperature
+temperature really means that there is
+
+ align:start position:0%
+temperature really means that there is
+ 
+
+ align:start position:0%
+temperature really means that there is
+an average kinetic energy available for
+
+ align:start position:0%
+an average kinetic energy available for
+ 
+
+ align:start position:0%
+an average kinetic energy available for
+all the atoms and the molecules in your
+
+ align:start position:0%
+all the atoms and the molecules in your
+ 
+
+ align:start position:0%
+all the atoms and the molecules in your
+system that means that there is really a
+
+ align:start position:0%
+system that means that there is really a
+ 
+
+ align:start position:0%
+system that means that there is really a
+microscopic Dynamics and we want to
+
+ align:start position:0%
+microscopic Dynamics and we want to
+ 
+
+ align:start position:0%
+microscopic Dynamics and we want to
+follow that uh one of the most important
+
+ align:start position:0%
+follow that uh one of the most important
+ 
+
+ align:start position:0%
+follow that uh one of the most important
+things and this sort of goes back to
+
+ align:start position:0%
+things and this sort of goes back to
+ 
+
+ align:start position:0%
+things and this sort of goes back to
+really the first lecture that you have
+
+ align:start position:0%
+really the first lecture that you have
+ 
+
+ align:start position:0%
+really the first lecture that you have
+seen in this sort of class for the
+
+ align:start position:0%
+seen in this sort of class for the
+ 
+
+ align:start position:0%
+seen in this sort of class for the
+quantum part is that there is the sort
+
+ align:start position:0%
+quantum part is that there is the sort
+ 
+
+ align:start position:0%
+quantum part is that there is the sort
+of fundamental de BR relation uh that
+
+ align:start position:0%
+of fundamental de BR relation uh that
+ 
+
+ align:start position:0%
+of fundamental de BR relation uh that
+sort of gives us an estimate of what is
+
+ align:start position:0%
+sort of gives us an estimate of what is
+ 
+
+ align:start position:0%
+sort of gives us an estimate of what is
+the Quantum wavelength of any kind of
+
+ align:start position:0%
+the Quantum wavelength of any kind of
+ 
+
+ align:start position:0%
+the Quantum wavelength of any kind of
+object remember we said that sort of the
+
+ align:start position:0%
+object remember we said that sort of the
+ 
+
+ align:start position:0%
+object remember we said that sort of the
+wavelength times the momentum should
+
+ align:start position:0%
+wavelength times the momentum should
+ 
+
+ align:start position:0%
+wavelength times the momentum should
+sort of be equal to the plank constant
+
+ align:start position:0%
+sort of be equal to the plank constant
+ 
+
+ align:start position:0%
+sort of be equal to the plank constant
+and that really means that for an object
+
+ align:start position:0%
+and that really means that for an object
+ 
+
+ align:start position:0%
+and that really means that for an object
+like an electron the de wavelength that
+
+ align:start position:0%
+like an electron the de wavelength that
+ 
+
+ align:start position:0%
+like an electron the de wavelength that
+comes out from that relation is
+
+ align:start position:0%
+comes out from that relation is
+ 
+
+ align:start position:0%
+comes out from that relation is
+comparable to the distance between the
+
+ align:start position:0%
+comparable to the distance between the
+ 
+
+ align:start position:0%
+comparable to the distance between the
+atoms so if the wavelength of an
+
+ align:start position:0%
+atoms so if the wavelength of an
+ 
+
+ align:start position:0%
+atoms so if the wavelength of an
+electron is of the order of the anstrom
+
+ align:start position:0%
+electron is of the order of the anstrom
+ 
+
+ align:start position:0%
+electron is of the order of the anstrom
+10 Theus 10 m it means means that the
+
+ align:start position:0%
+10 Theus 10 m it means means that the
+ 
+
+ align:start position:0%
+10 Theus 10 m it means means that the
+wav like properties of the electrons
+
+ align:start position:0%
+wav like properties of the electrons
+ 
+
+ align:start position:0%
+wav like properties of the electrons
+needs to be studied and the electron
+
+ align:start position:0%
+needs to be studied and the electron
+ 
+
+ align:start position:0%
+needs to be studied and the electron
+will be behave as a wave and that's why
+
+ align:start position:0%
+will be behave as a wave and that's why
+ 
+
+ align:start position:0%
+will be behave as a wave and that's why
+we sort of use the shedding equation to
+
+ align:start position:0%
+we sort of use the shedding equation to
+ 
+
+ align:start position:0%
+we sort of use the shedding equation to
+describe electrons um the wavelength of
+
+ align:start position:0%
+describe electrons um the wavelength of
+ 
+
+ align:start position:0%
+describe electrons um the wavelength of
+the nucle is much much smaller that
+
+ align:start position:0%
+the nucle is much much smaller that
+ 
+
+ align:start position:0%
+the nucle is much much smaller that
+means that nuclei really didn't we don't
+
+ align:start position:0%
+means that nuclei really didn't we don't
+ 
+
+ align:start position:0%
+means that nuclei really didn't we don't
+really need to sort of take into account
+
+ align:start position:0%
+really need to sort of take into account
+ 
+
+ align:start position:0%
+really need to sort of take into account
+to a good approximation the quantum
+
+ align:start position:0%
+to a good approximation the quantum
+ 
+
+ align:start position:0%
+to a good approximation the quantum
+nature of the nuclei their wavelength is
+
+ align:start position:0%
+nature of the nuclei their wavelength is
+ 
+
+ align:start position:0%
+nature of the nuclei their wavelength is
+so small that they can be treated U
+
+ align:start position:0%
+so small that they can be treated U
+ 
+
+ align:start position:0%
+so small that they can be treated U
+practically correctly as classical
+
+ align:start position:0%
+practically correctly as classical
+ 
+
+ align:start position:0%
+practically correctly as classical
+particles and that's why actually nuclei
+
+ align:start position:0%
+particles and that's why actually nuclei
+ 
+
+ align:start position:0%
+particles and that's why actually nuclei
+in a way still follow the rules of
+
+ align:start position:0%
+in a way still follow the rules of
+ 
+
+ align:start position:0%
+in a way still follow the rules of
+classical dynamics that is they evolve
+
+ align:start position:0%
+classical dynamics that is they evolve
+ 
+
+ align:start position:0%
+classical dynamics that is they evolve
+in time following Newton equation of
+
+ align:start position:0%
+in time following Newton equation of
+ 
+
+ align:start position:0%
+in time following Newton equation of
+motion again this is an approximation
+
+ align:start position:0%
+motion again this is an approximation
+ 
+
+ align:start position:0%
+motion again this is an approximation
+that involves treating the nuclear as
+
+ align:start position:0%
+that involves treating the nuclear as
+ 
+
+ align:start position:0%
+that involves treating the nuclear as
+classical particles and not as Quantum
+
+ align:start position:0%
+classical particles and not as Quantum
+ 
+
+ align:start position:0%
+classical particles and not as Quantum
+particles but especially at high
+
+ align:start position:0%
+particles but especially at high
+ 
+
+ align:start position:0%
+particles but especially at high
+temperature this is a very good
+
+ align:start position:0%
+temperature this is a very good
+ 
+
+ align:start position:0%
+temperature this is a very good
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+and so a lot of uh approaches in
+
+ align:start position:0%
+and so a lot of uh approaches in
+ 
+
+ align:start position:0%
+and so a lot of uh approaches in
+computational Material Science have to
+
+ align:start position:0%
+computational Material Science have to
+ 
+
+ align:start position:0%
+computational Material Science have to
+do with solving a Newton equation of
+
+ align:start position:0%
+do with solving a Newton equation of
+ 
+
+ align:start position:0%
+do with solving a Newton equation of
+motions for a system of interacting
+
+ align:start position:0%
+motions for a system of interacting
+ 
+
+ align:start position:0%
+motions for a system of interacting
+nuclei and evolving those nucle in time
+
+ align:start position:0%
+nuclei and evolving those nucle in time
+ 
+
+ align:start position:0%
+nuclei and evolving those nucle in time
+to study the thermodynamical properties
+
+ align:start position:0%
+to study the thermodynamical properties
+ 
+
+ align:start position:0%
+to study the thermodynamical properties
+of the system and so that's why I
+
+ align:start position:0%
+of the system and so that's why I
+ 
+
+ align:start position:0%
+of the system and so that's why I
+actually sort of started with a reminder
+
+ align:start position:0%
+actually sort of started with a reminder
+ 
+
+ align:start position:0%
+actually sort of started with a reminder
+of Newton equation of motion that is
+
+ align:start position:0%
+of Newton equation of motion that is
+ 
+
+ align:start position:0%
+of Newton equation of motion that is
+really a Ordinary second order
+
+ align:start position:0%
+really a Ordinary second order
+ 
+
+ align:start position:0%
+really a Ordinary second order
+differential equation that is when you
+
+ align:start position:0%
+differential equation that is when you
+ 
+
+ align:start position:0%
+differential equation that is when you
+have a particle of mass m in a force
+
+ align:start position:0%
+have a particle of mass m in a force
+ 
+
+ align:start position:0%
+have a particle of mass m in a force
+field that is this F ofr Well we can
+
+ align:start position:0%
+field that is this F ofr Well we can
+ 
+
+ align:start position:0%
+field that is this F ofr Well we can
+calculate its trajectory that is its
+
+ align:start position:0%
+calculate its trajectory that is its
+ 
+
+ align:start position:0%
+calculate its trajectory that is its
+position as a function of time and its
+
+ align:start position:0%
+position as a function of time and its
+ 
+
+ align:start position:0%
+position as a function of time and its
+velocity as a function of time uh by
+
+ align:start position:0%
+velocity as a function of time uh by
+ 
+
+ align:start position:0%
+velocity as a function of time uh by
+integrating this differential equation
+
+ align:start position:0%
+integrating this differential equation
+ 
+
+ align:start position:0%
+integrating this differential equation
+and you know sort of the classical case
+
+ align:start position:0%
+and you know sort of the classical case
+ 
+
+ align:start position:0%
+and you know sort of the classical case
+that sort of you know is always
+
+ align:start position:0%
+that sort of you know is always
+ 
+
+ align:start position:0%
+that sort of you know is always
+presented say is the evolution of a
+
+ align:start position:0%
+presented say is the evolution of a
+ 
+
+ align:start position:0%
+presented say is the evolution of a
+particle say in a constant force field
+
+ align:start position:0%
+particle say in a constant force field
+ 
+
+ align:start position:0%
+particle say in a constant force field
+like a particle you know under the
+
+ align:start position:0%
+like a particle you know under the
+ 
+
+ align:start position:0%
+like a particle you know under the
+gravitational law that's of to a large
+
+ align:start position:0%
+gravitational law that's of to a large
+ 
+
+ align:start position:0%
+gravitational law that's of to a large
+extent is constant if you don't move
+
+ align:start position:0%
+extent is constant if you don't move
+ 
+
+ align:start position:0%
+extent is constant if you don't move
+very much and because in that case the
+
+ align:start position:0%
+very much and because in that case the
+ 
+
+ align:start position:0%
+very much and because in that case the
+force is really a constant the
+
+ align:start position:0%
+force is really a constant the
+ 
+
+ align:start position:0%
+force is really a constant the
+integration of this becomes trivial it's
+
+ align:start position:0%
+integration of this becomes trivial it's
+ 
+
+ align:start position:0%
+integration of this becomes trivial it's
+really a sort of you know second
+
+ align:start position:0%
+really a sort of you know second
+ 
+
+ align:start position:0%
+really a sort of you know second
+derivative that needs to be equal a
+
+ align:start position:0%
+derivative that needs to be equal a
+ 
+
+ align:start position:0%
+derivative that needs to be equal a
+constant and integrating that gives us a
+
+ align:start position:0%
+constant and integrating that gives us a
+ 
+
+ align:start position:0%
+constant and integrating that gives us a
+parabola but the reason why I'm sort of
+
+ align:start position:0%
+parabola but the reason why I'm sort of
+ 
+
+ align:start position:0%
+parabola but the reason why I'm sort of
+you know focusing on this is to sort of
+
+ align:start position:0%
+you know focusing on this is to sort of
+ 
+
+ align:start position:0%
+you know focusing on this is to sort of
+remind you of the initial conditions in
+
+ align:start position:0%
+remind you of the initial conditions in
+ 
+
+ align:start position:0%
+remind you of the initial conditions in
+a differential equations that is if we
+
+ align:start position:0%
+a differential equations that is if we
+ 
+
+ align:start position:0%
+a differential equations that is if we
+have a second order differential
+
+ align:start position:0%
+have a second order differential
+ 
+
+ align:start position:0%
+have a second order differential
+equation um the general solution let's
+
+ align:start position:0%
+equation um the general solution let's
+ 
+
+ align:start position:0%
+equation um the general solution let's
+say in this case for this force field
+
+ align:start position:0%
+say in this case for this force field
+ 
+
+ align:start position:0%
+say in this case for this force field
+would be a parabola is uniquely
+
+ align:start position:0%
+would be a parabola is uniquely
+ 
+
+ align:start position:0%
+would be a parabola is uniquely
+identified once we specify the position
+
+ align:start position:0%
+identified once we specify the position
+ 
+
+ align:start position:0%
+identified once we specify the position
+at a certain instant and the velocity as
+
+ align:start position:0%
+at a certain instant and the velocity as
+ 
+
+ align:start position:0%
+at a certain instant and the velocity as
+a certain instant that is among all the
+
+ align:start position:0%
+a certain instant that is among all the
+ 
+
+ align:start position:0%
+a certain instant that is among all the
+possible parabolas in the world you
+
+ align:start position:0%
+possible parabolas in the world you
+ 
+
+ align:start position:0%
+possible parabolas in the world you
+select the one that your projectile is
+
+ align:start position:0%
+select the one that your projectile is
+ 
+
+ align:start position:0%
+select the one that your projectile is
+going to follow once you have the
+
+ align:start position:0%
+going to follow once you have the
+ 
+
+ align:start position:0%
+going to follow once you have the
+position and the velocity at a certain
+
+ align:start position:0%
+position and the velocity at a certain
+ 
+
+ align:start position:0%
+position and the velocity at a certain
+instant and that's why actually Dynamics
+
+ align:start position:0%
+instant and that's why actually Dynamics
+ 
+
+ align:start position:0%
+instant and that's why actually Dynamics
+and molecular Dynamics and a lot of
+
+ align:start position:0%
+and molecular Dynamics and a lot of
+ 
+
+ align:start position:0%
+and molecular Dynamics and a lot of
+physical properties basically depend
+
+ align:start position:0%
+physical properties basically depend
+ 
+
+ align:start position:0%
+physical properties basically depend
+essentially on the position of the
+
+ align:start position:0%
+essentially on the position of the
+ 
+
+ align:start position:0%
+essentially on the position of the
+particle in your system and the Velocity
+
+ align:start position:0%
+particle in your system and the Velocity
+ 
+
+ align:start position:0%
+particle in your system and the Velocity
+in the of the particle in your system
+
+ align:start position:0%
+in the of the particle in your system
+ 
+
+ align:start position:0%
+in the of the particle in your system
+that's why there is sort of you know no
+
+ align:start position:0%
+that's why there is sort of you know no
+ 
+
+ align:start position:0%
+that's why there is sort of you know no
+physical observable that depends say on
+
+ align:start position:0%
+physical observable that depends say on
+ 
+
+ align:start position:0%
+physical observable that depends say on
+the fifth derivative with respect to
+
+ align:start position:0%
+the fifth derivative with respect to
+ 
+
+ align:start position:0%
+the fifth derivative with respect to
+time it's really because the Dynamics of
+
+ align:start position:0%
+time it's really because the Dynamics of
+ 
+
+ align:start position:0%
+time it's really because the Dynamics of
+that system follows Newton's equation of
+
+ align:start position:0%
+that system follows Newton's equation of
+ 
+
+ align:start position:0%
+that system follows Newton's equation of
+motion okay with this what we really
+
+ align:start position:0%
+motion okay with this what we really
+ 
+
+ align:start position:0%
+motion okay with this what we really
+need to deal in general is with you know
+
+ align:start position:0%
+need to deal in general is with you know
+ 
+
+ align:start position:0%
+need to deal in general is with you know
+a system of interacting particles and
+
+ align:start position:0%
+a system of interacting particles and
+ 
+
+ align:start position:0%
+a system of interacting particles and
+you know for a moment you could actually
+
+ align:start position:0%
+you know for a moment you could actually
+ 
+
+ align:start position:0%
+you know for a moment you could actually
+think that you know this uh I
+
+ align:start position:0%
+think that you know this uh I
+ 
+
+ align:start position:0%
+think that you know this uh I
+interacting particles could be the
+
+ align:start position:0%
+interacting particles could be the
+ 
+
+ align:start position:0%
+interacting particles could be the
+planets orbiting around the Sun so each
+
+ align:start position:0%
+planets orbiting around the Sun so each
+ 
+
+ align:start position:0%
+planets orbiting around the Sun so each
+of the planet I will have its own
+
+ align:start position:0%
+of the planet I will have its own
+ 
+
+ align:start position:0%
+of the planet I will have its own
+trajectory R oft will have its own mass
+
+ align:start position:0%
+trajectory R oft will have its own mass
+ 
+
+ align:start position:0%
+trajectory R oft will have its own mass
+and they all live in a force field
+
+ align:start position:0%
+and they all live in a force field
+ 
+
+ align:start position:0%
+and they all live in a force field
+that's really where the many body
+
+ align:start position:0%
+that's really where the many body
+ 
+
+ align:start position:0%
+that's really where the many body
+complexity again comes out it's a many
+
+ align:start position:0%
+complexity again comes out it's a many
+ 
+
+ align:start position:0%
+complexity again comes out it's a many
+body complexity that is much easier to
+
+ align:start position:0%
+body complexity that is much easier to
+ 
+
+ align:start position:0%
+body complexity that is much easier to
+deal with than the many body complex of
+
+ align:start position:0%
+deal with than the many body complex of
+ 
+
+ align:start position:0%
+deal with than the many body complex of
+the electron problem because again now
+
+ align:start position:0%
+the electron problem because again now
+ 
+
+ align:start position:0%
+the electron problem because again now
+we describe each object just with a set
+
+ align:start position:0%
+we describe each object just with a set
+ 
+
+ align:start position:0%
+we describe each object just with a set
+of six variables it's three space
+
+ align:start position:0%
+of six variables it's three space
+ 
+
+ align:start position:0%
+of six variables it's three space
+coordinate and it's three momentum
+
+ align:start position:0%
+coordinate and it's three momentum
+ 
+
+ align:start position:0%
+coordinate and it's three momentum
+coordinate but still each and every
+
+ align:start position:0%
+coordinate but still each and every
+ 
+
+ align:start position:0%
+coordinate but still each and every
+object interact with each other when you
+
+ align:start position:0%
+object interact with each other when you
+ 
+
+ align:start position:0%
+object interact with each other when you
+look at the planets orbiting around the
+
+ align:start position:0%
+look at the planets orbiting around the
+ 
+
+ align:start position:0%
+look at the planets orbiting around the
+Sun you sort of you know to First
+
+ align:start position:0%
+Sun you sort of you know to First
+ 
+
+ align:start position:0%
+Sun you sort of you know to First
+approximation could only consider the
+
+ align:start position:0%
+approximation could only consider the
+ 
+
+ align:start position:0%
+approximation could only consider the
+gravitational attraction to the Sun but
+
+ align:start position:0%
+gravitational attraction to the Sun but
+ 
+
+ align:start position:0%
+gravitational attraction to the Sun but
+in reality also the planets interact
+
+ align:start position:0%
+in reality also the planets interact
+ 
+
+ align:start position:0%
+in reality also the planets interact
+with each other and so again even if
+
+ align:start position:0%
+with each other and so again even if
+ 
+
+ align:start position:0%
+with each other and so again even if
+sort of you know this is much simpler
+
+ align:start position:0%
+sort of you know this is much simpler
+ 
+
+ align:start position:0%
+sort of you know this is much simpler
+than the shadinger equation as soon as
+
+ align:start position:0%
+than the shadinger equation as soon as
+ 
+
+ align:start position:0%
+than the shadinger equation as soon as
+you start have more than two body
+
+ align:start position:0%
+you start have more than two body
+ 
+
+ align:start position:0%
+you start have more than two body
+interacting it really becomes too
+
+ align:start position:0%
+interacting it really becomes too
+ 
+
+ align:start position:0%
+interacting it really becomes too
+complex to solve analytically and so all
+
+ align:start position:0%
+complex to solve analytically and so all
+ 
+
+ align:start position:0%
+complex to solve analytically and so all
+the molecular Dynamic techniques have as
+
+ align:start position:0%
+the molecular Dynamic techniques have as
+ 
+
+ align:start position:0%
+the molecular Dynamic techniques have as
+their only object basically the
+
+ align:start position:0%
+their only object basically the
+ 
+
+ align:start position:0%
+their only object basically the
+integration in time of this equation of
+
+ align:start position:0%
+integration in time of this equation of
+ 
+
+ align:start position:0%
+integration in time of this equation of
+motion in an efficient in an efficient
+
+ align:start position:0%
+motion in an efficient in an efficient
+ 
+
+ align:start position:0%
+motion in an efficient in an efficient
+form uh there are sort of a couple of
+
+ align:start position:0%
+form uh there are sort of a couple of
+ 
+
+ align:start position:0%
+form uh there are sort of a couple of
+comments that sort of one wants to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in general we deal with a
+
+ align:start position:0%
+uh in general we deal with a
+ 
+
+ align:start position:0%
+uh in general we deal with a
+conservative fields that is uh the force
+
+ align:start position:0%
+conservative fields that is uh the force
+ 
+
+ align:start position:0%
+conservative fields that is uh the force
+depends on position only that also means
+
+ align:start position:0%
+depends on position only that also means
+ 
+
+ align:start position:0%
+depends on position only that also means
+that the work that you making going from
+
+ align:start position:0%
+that the work that you making going from
+ 
+
+ align:start position:0%
+that the work that you making going from
+one point to another point the integral
+
+ align:start position:0%
+one point to another point the integral
+ 
+
+ align:start position:0%
+one point to another point the integral
+of the force times um the displacement
+
+ align:start position:0%
+of the force times um the displacement
+ 
+
+ align:start position:0%
+of the force times um the displacement
+is going to be independent from the
+
+ align:start position:0%
+is going to be independent from the
+ 
+
+ align:start position:0%
+is going to be independent from the
+trajectory so the energy if you want is
+
+ align:start position:0%
+trajectory so the energy if you want is
+ 
+
+ align:start position:0%
+trajectory so the energy if you want is
+just a function of the position uh the
+
+ align:start position:0%
+just a function of the position uh the
+ 
+
+ align:start position:0%
+just a function of the position uh the
+other thing that sort of descends
+
+ align:start position:0%
+other thing that sort of descends
+ 
+
+ align:start position:0%
+other thing that sort of descends
+immediately
+
+ align:start position:0%
+immediately
+ 
+
+ align:start position:0%
+immediately
+from this equation of motion is that the
+
+ align:start position:0%
+from this equation of motion is that the
+ 
+
+ align:start position:0%
+from this equation of motion is that the
+total energy of the system is conserved
+
+ align:start position:0%
+total energy of the system is conserved
+ 
+
+ align:start position:0%
+total energy of the system is conserved
+and that's easy very easy to prove and
+
+ align:start position:0%
+and that's easy very easy to prove and
+ 
+
+ align:start position:0%
+and that's easy very easy to prove and
+I'll do it in a moment and that's what's
+
+ align:start position:0%
+I'll do it in a moment and that's what's
+ 
+
+ align:start position:0%
+I'll do it in a moment and that's what's
+often called a microcanonical Evolution
+
+ align:start position:0%
+often called a microcanonical Evolution
+ 
+
+ align:start position:0%
+often called a microcanonical Evolution
+when you sort of read about
+
+ align:start position:0%
+when you sort of read about
+ 
+
+ align:start position:0%
+when you sort of read about
+microcanonical ensembles uh it means
+
+ align:start position:0%
+microcanonical ensembles uh it means
+ 
+
+ align:start position:0%
+microcanonical ensembles uh it means
+that you're actually under the condition
+
+ align:start position:0%
+that you're actually under the condition
+ 
+
+ align:start position:0%
+that you're actually under the condition
+in which the total energy of your system
+
+ align:start position:0%
+in which the total energy of your system
+ 
+
+ align:start position:0%
+in which the total energy of your system
+is conserved and again what is the total
+
+ align:start position:0%
+is conserved and again what is the total
+ 
+
+ align:start position:0%
+is conserved and again what is the total
+energy of your system well if you have
+
+ align:start position:0%
+energy of your system well if you have
+ 
+
+ align:start position:0%
+energy of your system well if you have
+one particle is just trivially the
+
+ align:start position:0%
+one particle is just trivially the
+ 
+
+ align:start position:0%
+one particle is just trivially the
+kinetic energy 12 M
+
+ align:start position:0%
+kinetic energy 12 M
+ 
+
+ align:start position:0%
+kinetic energy 12 M
+v² plus the potential
+
+ align:start position:0%
+v² plus the potential
+ 
+
+ align:start position:0%
+v² plus the potential
+energy V of R of that particle I'm just
+
+ align:start position:0%
+energy V of R of that particle I'm just
+ 
+
+ align:start position:0%
+energy V of R of that particle I'm just
+doing everything in one dimension and
+
+ align:start position:0%
+doing everything in one dimension and
+ 
+
+ align:start position:0%
+doing everything in one dimension and
+you ask why is this going to be
+
+ align:start position:0%
+you ask why is this going to be
+ 
+
+ align:start position:0%
+you ask why is this going to be
+conserved well you can just prove it by
+
+ align:start position:0%
+conserved well you can just prove it by
+ 
+
+ align:start position:0%
+conserved well you can just prove it by
+taking the time derivative of this
+
+ align:start position:0%
+taking the time derivative of this
+ 
+
+ align:start position:0%
+taking the time derivative of this
+quantity okay so we have taken kinetic
+
+ align:start position:0%
+quantity okay so we have taken kinetic
+ 
+
+ align:start position:0%
+quantity okay so we have taken kinetic
+energy plus potential energy we look at
+
+ align:start position:0%
+energy plus potential energy we look at
+ 
+
+ align:start position:0%
+energy plus potential energy we look at
+the time derivative and this is sort of
+
+ align:start position:0%
+the time derivative and this is sort of
+ 
+
+ align:start position:0%
+the time derivative and this is sort of
+you know just simple simple algebra what
+
+ align:start position:0%
+you know just simple simple algebra what
+ 
+
+ align:start position:0%
+you know just simple simple algebra what
+you get is 12 M * 2 * V time the
+
+ align:start position:0%
+you get is 12 M * 2 * V time the
+ 
+
+ align:start position:0%
+you get is 12 M * 2 * V time the
+derivative of we with respect to time
+
+ align:start position:0%
+derivative of we with respect to time
+ 
+
+ align:start position:0%
+derivative of we with respect to time
+that is the
+
+ align:start position:0%
+that is the
+ 
+
+ align:start position:0%
+that is the
+acceleration plus um the derivative of
+
+ align:start position:0%
+acceleration plus um the derivative of
+ 
+
+ align:start position:0%
+acceleration plus um the derivative of
+the potential with respect to time and
+
+ align:start position:0%
+the potential with respect to time and
+ 
+
+ align:start position:0%
+the potential with respect to time and
+this can just be written as um mass time
+
+ align:start position:0%
+this can just be written as um mass time
+ 
+
+ align:start position:0%
+this can just be written as um mass time
+velocity time acceleration plus and we
+
+ align:start position:0%
+velocity time acceleration plus and we
+ 
+
+ align:start position:0%
+velocity time acceleration plus and we
+can rewrite the derivative of the
+
+ align:start position:0%
+can rewrite the derivative of the
+ 
+
+ align:start position:0%
+can rewrite the derivative of the
+potential with time as the derivative of
+
+ align:start position:0%
+potential with time as the derivative of
+ 
+
+ align:start position:0%
+potential with time as the derivative of
+the potential with respect to position
+
+ align:start position:0%
+the potential with respect to position
+ 
+
+ align:start position:0%
+the potential with respect to position
+time the derivative of the position with
+
+ align:start position:0%
+time the derivative of the position with
+ 
+
+ align:start position:0%
+time the derivative of the position with
+respect to time and now you see where we
+
+ align:start position:0%
+respect to time and now you see where we
+ 
+
+ align:start position:0%
+respect to time and now you see where we
+are getting to because uh uh this term
+
+ align:start position:0%
+are getting to because uh uh this term
+ 
+
+ align:start position:0%
+are getting to because uh uh this term
+here is equal to minus the force while
+
+ align:start position:0%
+here is equal to minus the force while
+ 
+
+ align:start position:0%
+here is equal to minus the force while
+these terms here is equal to the
+
+ align:start position:0%
+these terms here is equal to the
+ 
+
+ align:start position:0%
+these terms here is equal to the
+velocity and so it goes away with here
+
+ align:start position:0%
+velocity and so it goes away with here
+ 
+
+ align:start position:0%
+velocity and so it goes away with here
+and so what we have is that um the
+
+ align:start position:0%
+and so what we have is that um the
+ 
+
+ align:start position:0%
+and so what we have is that um the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+of the total energy with respect to time
+
+ align:start position:0%
+of the total energy with respect to time
+ 
+
+ align:start position:0%
+of the total energy with respect to time
+is equal to the mass time the
+
+ align:start position:0%
+is equal to the mass time the
+ 
+
+ align:start position:0%
+is equal to the mass time the
+acceleration minus the force that is
+
+ align:start position:0%
+acceleration minus the force that is
+ 
+
+ align:start position:0%
+acceleration minus the force that is
+zero because the particle follows Newton
+
+ align:start position:0%
+zero because the particle follows Newton
+ 
+
+ align:start position:0%
+zero because the particle follows Newton
+equation of motion so because of Newton
+
+ align:start position:0%
+equation of motion so because of Newton
+ 
+
+ align:start position:0%
+equation of motion so because of Newton
+equation of motion and because the
+
+ align:start position:0%
+equation of motion and because the
+ 
+
+ align:start position:0%
+equation of motion and because the
+particle follows exactly that Evolution
+
+ align:start position:0%
+particle follows exactly that Evolution
+ 
+
+ align:start position:0%
+particle follows exactly that Evolution
+we have that the sum of the kinetic
+
+ align:start position:0%
+we have that the sum of the kinetic
+ 
+
+ align:start position:0%
+we have that the sum of the kinetic
+energy plus the potential energy needs
+
+ align:start position:0%
+energy plus the potential energy needs
+ 
+
+ align:start position:0%
+energy plus the potential energy needs
+to be conserved um during the evolution
+
+ align:start position:0%
+to be conserved um during the evolution
+ 
+
+ align:start position:0%
+to be conserved um during the evolution
+and that's actually sort of the um
+
+ align:start position:0%
+and that's actually sort of the um
+ 
+
+ align:start position:0%
+and that's actually sort of the um
+fundamental sanity check that you will
+
+ align:start position:0%
+fundamental sanity check that you will
+ 
+
+ align:start position:0%
+fundamental sanity check that you will
+always have and you can always do during
+
+ align:start position:0%
+always have and you can always do during
+ 
+
+ align:start position:0%
+always have and you can always do during
+a molecular Dynamic simulation that is
+
+ align:start position:0%
+a molecular Dynamic simulation that is
+ 
+
+ align:start position:0%
+a molecular Dynamic simulation that is
+you can check that your integration is
+
+ align:start position:0%
+you can check that your integration is
+ 
+
+ align:start position:0%
+you can check that your integration is
+correct by making sure that the total
+
+ align:start position:0%
+correct by making sure that the total
+ 
+
+ align:start position:0%
+correct by making sure that the total
+energy of your system is
+
+ align:start position:0%
+energy of your system is
+ 
+
+ align:start position:0%
+energy of your system is
+conserved okay so what do we do in a
+
+ align:start position:0%
+conserved okay so what do we do in a
+ 
+
+ align:start position:0%
+conserved okay so what do we do in a
+sort of practical molecular Dynamic
+
+ align:start position:0%
+sort of practical molecular Dynamic
+ 
+
+ align:start position:0%
+sort of practical molecular Dynamic
+simulation well the idea is that as in
+
+ align:start position:0%
+simulation well the idea is that as in
+ 
+
+ align:start position:0%
+simulation well the idea is that as in
+the motion of the planets we want to
+
+ align:start position:0%
+the motion of the planets we want to
+ 
+
+ align:start position:0%
+the motion of the planets we want to
+integrate the equation of motions uh
+
+ align:start position:0%
+integrate the equation of motions uh
+ 
+
+ align:start position:0%
+integrate the equation of motions uh
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+that again each particle interacts with
+
+ align:start position:0%
+that again each particle interacts with
+ 
+
+ align:start position:0%
+that again each particle interacts with
+each other each other particle and so
+
+ align:start position:0%
+each other each other particle and so
+ 
+
+ align:start position:0%
+each other each other particle and so
+it's really a many body problem even if
+
+ align:start position:0%
+it's really a many body problem even if
+ 
+
+ align:start position:0%
+it's really a many body problem even if
+it is a classical many body problem and
+
+ align:start position:0%
+it is a classical many body problem and
+ 
+
+ align:start position:0%
+it is a classical many body problem and
+so it's really easier to integrate than
+
+ align:start position:0%
+so it's really easier to integrate than
+ 
+
+ align:start position:0%
+so it's really easier to integrate than
+uh the sort of many body shadinger um um
+
+ align:start position:0%
+uh the sort of many body shadinger um um
+ 
+
+ align:start position:0%
+uh the sort of many body shadinger um um
+equation and in general sort of the way
+
+ align:start position:0%
+equation and in general sort of the way
+ 
+
+ align:start position:0%
+equation and in general sort of the way
+particle interact with each other can be
+
+ align:start position:0%
+particle interact with each other can be
+ 
+
+ align:start position:0%
+particle interact with each other can be
+described by empirical force fields or
+
+ align:start position:0%
+described by empirical force fields or
+ 
+
+ align:start position:0%
+described by empirical force fields or
+in sort of you know the best case
+
+ align:start position:0%
+in sort of you know the best case
+ 
+
+ align:start position:0%
+in sort of you know the best case
+scenario um can be described using uh
+
+ align:start position:0%
+scenario um can be described using uh
+ 
+
+ align:start position:0%
+scenario um can be described using uh
+quantum mechanics density functional
+
+ align:start position:0%
+quantum mechanics density functional
+ 
+
+ align:start position:0%
+quantum mechanics density functional
+Theory Arch F and so what you will have
+
+ align:start position:0%
+Theory Arch F and so what you will have
+ 
+
+ align:start position:0%
+Theory Arch F and so what you will have
+to do in that case is that for every
+
+ align:start position:0%
+to do in that case is that for every
+ 
+
+ align:start position:0%
+to do in that case is that for every
+configuration of your ionic system you
+
+ align:start position:0%
+configuration of your ionic system you
+ 
+
+ align:start position:0%
+configuration of your ionic system you
+need to solve an entire um total energy
+
+ align:start position:0%
+need to solve an entire um total energy
+ 
+
+ align:start position:0%
+need to solve an entire um total energy
+self-consistent problem and that's why
+
+ align:start position:0%
+self-consistent problem and that's why
+ 
+
+ align:start position:0%
+self-consistent problem and that's why
+actually first principle molecular
+
+ align:start position:0%
+actually first principle molecular
+ 
+
+ align:start position:0%
+actually first principle molecular
+Dynamics becomes a very very expensive
+
+ align:start position:0%
+Dynamics becomes a very very expensive
+ 
+
+ align:start position:0%
+Dynamics becomes a very very expensive
+Challenge and we'll see sort of in uh
+
+ align:start position:0%
+Challenge and we'll see sort of in uh
+ 
+
+ align:start position:0%
+Challenge and we'll see sort of in uh
+one of the later classes how this is how
+
+ align:start position:0%
+one of the later classes how this is how
+ 
+
+ align:start position:0%
+one of the later classes how this is how
+this is solved uh there are a lot of
+
+ align:start position:0%
+this is solved uh there are a lot of
+ 
+
+ align:start position:0%
+this is solved uh there are a lot of
+system that can be described accurately
+
+ align:start position:0%
+system that can be described accurately
+ 
+
+ align:start position:0%
+system that can be described accurately
+even with very simple potential um even
+
+ align:start position:0%
+even with very simple potential um even
+ 
+
+ align:start position:0%
+even with very simple potential um even
+more than in the case of the total
+
+ align:start position:0%
+more than in the case of the total
+ 
+
+ align:start position:0%
+more than in the case of the total
+energy certain thermodynamic transitions
+
+ align:start position:0%
+energy certain thermodynamic transitions
+ 
+
+ align:start position:0%
+energy certain thermodynamic transitions
+like the transition from a solid to a
+
+ align:start position:0%
+like the transition from a solid to a
+ 
+
+ align:start position:0%
+like the transition from a solid to a
+liquid can be thought sort of broadly
+
+ align:start position:0%
+liquid can be thought sort of broadly
+ 
+
+ align:start position:0%
+liquid can be thought sort of broadly
+independent of the details of the
+
+ align:start position:0%
+independent of the details of the
+ 
+
+ align:start position:0%
+independent of the details of the
+interacting potentials so even studying
+
+ align:start position:0%
+interacting potentials so even studying
+ 
+
+ align:start position:0%
+interacting potentials so even studying
+a system you know with a Jon potential
+
+ align:start position:0%
+a system you know with a Jon potential
+ 
+
+ align:start position:0%
+a system you know with a Jon potential
+that's after all sort of you know was
+
+ align:start position:0%
+that's after all sort of you know was
+ 
+
+ align:start position:0%
+that's after all sort of you know was
+developed especially to do molecular
+
+ align:start position:0%
+developed especially to do molecular
+ 
+
+ align:start position:0%
+developed especially to do molecular
+Dynamic simulation of rare gas atoms or
+
+ align:start position:0%
+Dynamic simulation of rare gas atoms or
+ 
+
+ align:start position:0%
+Dynamic simulation of rare gas atoms or
+even just studying A system that is made
+
+ align:start position:0%
+even just studying A system that is made
+ 
+
+ align:start position:0%
+even just studying A system that is made
+by hard spheres that don't really
+
+ align:start position:0%
+by hard spheres that don't really
+ 
+
+ align:start position:0%
+by hard spheres that don't really
+interact when they travel in space apart
+
+ align:start position:0%
+interact when they travel in space apart
+ 
+
+ align:start position:0%
+interact when they travel in space apart
+when they really hit each other so what
+
+ align:start position:0%
+when they really hit each other so what
+ 
+
+ align:start position:0%
+when they really hit each other so what
+is called a contact interaction that is
+
+ align:start position:0%
+is called a contact interaction that is
+ 
+
+ align:start position:0%
+is called a contact interaction that is
+zero all the time apart the instant in
+
+ align:start position:0%
+zero all the time apart the instant in
+ 
+
+ align:start position:0%
+zero all the time apart the instant in
+which they sort of the two spheres
+
+ align:start position:0%
+which they sort of the two spheres
+ 
+
+ align:start position:0%
+which they sort of the two spheres
+Collide can sometimes give you um very
+
+ align:start position:0%
+Collide can sometimes give you um very
+ 
+
+ align:start position:0%
+Collide can sometimes give you um very
+accurate qualitative description of the
+
+ align:start position:0%
+accurate qualitative description of the
+ 
+
+ align:start position:0%
+accurate qualitative description of the
+thermodynamic transition in a problem
+
+ align:start position:0%
+thermodynamic transition in a problem
+ 
+
+ align:start position:0%
+thermodynamic transition in a problem
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um molecular Dynamics actually was sort
+
+ align:start position:0%
+um molecular Dynamics actually was sort
+ 
+
+ align:start position:0%
+um molecular Dynamics actually was sort
+of first introduced really to study
+
+ align:start position:0%
+of first introduced really to study
+ 
+
+ align:start position:0%
+of first introduced really to study
+systems like liquids for which it's very
+
+ align:start position:0%
+systems like liquids for which it's very
+ 
+
+ align:start position:0%
+systems like liquids for which it's very
+difficult to develop analytic techniques
+
+ align:start position:0%
+difficult to develop analytic techniques
+ 
+
+ align:start position:0%
+difficult to develop analytic techniques
+you see if you want to sort of study a
+
+ align:start position:0%
+you see if you want to sort of study a
+ 
+
+ align:start position:0%
+you see if you want to sort of study a
+solid uh you sort of you know you can
+
+ align:start position:0%
+solid uh you sort of you know you can
+ 
+
+ align:start position:0%
+solid uh you sort of you know you can
+actually um choose a potential poal and
+
+ align:start position:0%
+actually um choose a potential poal and
+ 
+
+ align:start position:0%
+actually um choose a potential poal and
+if the potential is simple enough you
+
+ align:start position:0%
+if the potential is simple enough you
+ 
+
+ align:start position:0%
+if the potential is simple enough you
+can analytically calculate the potential
+
+ align:start position:0%
+can analytically calculate the potential
+ 
+
+ align:start position:0%
+can analytically calculate the potential
+energy of a periodic repetition of all
+
+ align:start position:0%
+energy of a periodic repetition of all
+ 
+
+ align:start position:0%
+energy of a periodic repetition of all
+your atoms but if you study um liquid
+
+ align:start position:0%
+your atoms but if you study um liquid
+ 
+
+ align:start position:0%
+your atoms but if you study um liquid
+disorder is really an essential part of
+
+ align:start position:0%
+disorder is really an essential part of
+ 
+
+ align:start position:0%
+disorder is really an essential part of
+the state of the system and so the
+
+ align:start position:0%
+the state of the system and so the
+ 
+
+ align:start position:0%
+the state of the system and so the
+entropic contribution to the free energy
+
+ align:start position:0%
+entropic contribution to the free energy
+ 
+
+ align:start position:0%
+entropic contribution to the free energy
+of this system is fundamental and really
+
+ align:start position:0%
+of this system is fundamental and really
+ 
+
+ align:start position:0%
+of this system is fundamental and really
+there are no uh reasonable analytic ways
+
+ align:start position:0%
+there are no uh reasonable analytic ways
+ 
+
+ align:start position:0%
+there are no uh reasonable analytic ways
+to address a lot of the questions that
+
+ align:start position:0%
+to address a lot of the questions that
+ 
+
+ align:start position:0%
+to address a lot of the questions that
+you have and that's why people really
+
+ align:start position:0%
+you have and that's why people really
+ 
+
+ align:start position:0%
+you have and that's why people really
+sort of moved to solving on the computer
+
+ align:start position:0%
+sort of moved to solving on the computer
+ 
+
+ align:start position:0%
+sort of moved to solving on the computer
+the newon equation of motion and this is
+
+ align:start position:0%
+the newon equation of motion and this is
+ 
+
+ align:start position:0%
+the newon equation of motion and this is
+you know sort of a short history really
+
+ align:start position:0%
+you know sort of a short history really
+ 
+
+ align:start position:0%
+you know sort of a short history really
+of molecular Dynamics reminding you sort
+
+ align:start position:0%
+of molecular Dynamics reminding you sort
+ 
+
+ align:start position:0%
+of molecular Dynamics reminding you sort
+of you know what is the history of
+
+ align:start position:0%
+of you know what is the history of
+ 
+
+ align:start position:0%
+of you know what is the history of
+computer really in
+
+ align:start position:0%
+computer really in
+ 
+
+ align:start position:0%
+computer really in
+1952 one of the first computers Maniac
+
+ align:start position:0%
+1952 one of the first computers Maniac
+ 
+
+ align:start position:0%
+1952 one of the first computers Maniac
+was operational in Los Alamos and that's
+
+ align:start position:0%
+was operational in Los Alamos and that's
+ 
+
+ align:start position:0%
+was operational in Los Alamos and that's
+when Metropolis Nicholas Metropolis
+
+ align:start position:0%
+when Metropolis Nicholas Metropolis
+ 
+
+ align:start position:0%
+when Metropolis Nicholas Metropolis
+collaboration with actually a husband
+
+ align:start position:0%
+collaboration with actually a husband
+ 
+
+ align:start position:0%
+collaboration with actually a husband
+and wife uh couple Rosen blut and Rosen
+
+ align:start position:0%
+and wife uh couple Rosen blut and Rosen
+ 
+
+ align:start position:0%
+and wife uh couple Rosen blut and Rosen
+blut and Teller and Teller developed
+
+ align:start position:0%
+blut and Teller and Teller developed
+ 
+
+ align:start position:0%
+blut and Teller and Teller developed
+what is called the Monte Carlo method
+
+ align:start position:0%
+what is called the Monte Carlo method
+ 
+
+ align:start position:0%
+what is called the Monte Carlo method
+that was sort of a very powerful method
+
+ align:start position:0%
+that was sort of a very powerful method
+ 
+
+ align:start position:0%
+that was sort of a very powerful method
+to address exactly this entropic free
+
+ align:start position:0%
+to address exactly this entropic free
+ 
+
+ align:start position:0%
+to address exactly this entropic free
+energy problem and that you'll see in
+
+ align:start position:0%
+energy problem and that you'll see in
+ 
+
+ align:start position:0%
+energy problem and that you'll see in
+one of the later uh classes but really
+
+ align:start position:0%
+one of the later uh classes but really
+ 
+
+ align:start position:0%
+one of the later uh classes but really
+sort of 1956 is the first molecular
+
+ align:start position:0%
+sort of 1956 is the first molecular
+ 
+
+ align:start position:0%
+sort of 1956 is the first molecular
+Dynamic simulation uh by Alder and Wayne
+
+ align:start position:0%
+Dynamic simulation uh by Alder and Wayne
+ 
+
+ align:start position:0%
+Dynamic simulation uh by Alder and Wayne
+W as I said in looking at the Dynamics
+
+ align:start position:0%
+W as I said in looking at the Dynamics
+ 
+
+ align:start position:0%
+W as I said in looking at the Dynamics
+of hard spheres and sort of these are
+
+ align:start position:0%
+of hard spheres and sort of these are
+ 
+
+ align:start position:0%
+of hard spheres and sort of these are
+sort of the Milestone papers vineard
+
+ align:start position:0%
+sort of the Milestone papers vineard
+ 
+
+ align:start position:0%
+sort of the Milestone papers vineard
+studying radiation damage in Copper what
+
+ align:start position:0%
+studying radiation damage in Copper what
+ 
+
+ align:start position:0%
+studying radiation damage in Copper what
+happens when you have you know a sort of
+
+ align:start position:0%
+happens when you have you know a sort of
+ 
+
+ align:start position:0%
+happens when you have you know a sort of
+copper atom that is really sort of put
+
+ align:start position:0%
+copper atom that is really sort of put
+ 
+
+ align:start position:0%
+copper atom that is really sort of put
+in motion by a very energetic radiation
+
+ align:start position:0%
+in motion by a very energetic radiation
+ 
+
+ align:start position:0%
+in motion by a very energetic radiation
+kicking it and starting sort of running
+
+ align:start position:0%
+kicking it and starting sort of running
+ 
+
+ align:start position:0%
+kicking it and starting sort of running
+around and really this is the the
+
+ align:start position:0%
+around and really this is the the
+ 
+
+ align:start position:0%
+around and really this is the the
+classic paper of anur Raman starting
+
+ align:start position:0%
+classic paper of anur Raman starting
+ 
+
+ align:start position:0%
+classic paper of anur Raman starting
+with Al lener joh potential the Dynamics
+
+ align:start position:0%
+with Al lener joh potential the Dynamics
+ 
+
+ align:start position:0%
+with Al lener joh potential the Dynamics
+of liquid argon again AL lener joh
+
+ align:start position:0%
+of liquid argon again AL lener joh
+ 
+
+ align:start position:0%
+of liquid argon again AL lener joh
+potential is actually accurate to
+
+ align:start position:0%
+potential is actually accurate to
+ 
+
+ align:start position:0%
+potential is actually accurate to
+describe rare gases that ultimately sort
+
+ align:start position:0%
+describe rare gases that ultimately sort
+ 
+
+ align:start position:0%
+describe rare gases that ultimately sort
+of repel each other at very close
+
+ align:start position:0%
+of repel each other at very close
+ 
+
+ align:start position:0%
+of repel each other at very close
+distance and at large distances attract
+
+ align:start position:0%
+distance and at large distances attract
+ 
+
+ align:start position:0%
+distance and at large distances attract
+each other with this weak dipole dipole
+
+ align:start position:0%
+each other with this weak dipole dipole
+ 
+
+ align:start position:0%
+each other with this weak dipole dipole
+interaction that is that goes us one/ R
+
+ align:start position:0%
+interaction that is that goes us one/ R
+ 
+
+ align:start position:0%
+interaction that is that goes us one/ R
+to the 6th and then really the sort of
+
+ align:start position:0%
+to the 6th and then really the sort of
+ 
+
+ align:start position:0%
+to the 6th and then really the sort of
+first abinal molecular Dynamics and the
+
+ align:start position:0%
+first abinal molecular Dynamics and the
+ 
+
+ align:start position:0%
+first abinal molecular Dynamics and the
+first theory for abin molecular Dynamics
+
+ align:start position:0%
+first theory for abin molecular Dynamics
+ 
+
+ align:start position:0%
+first theory for abin molecular Dynamics
+was developed in the mid 80s by Karen
+
+ align:start position:0%
+was developed in the mid 80s by Karen
+ 
+
+ align:start position:0%
+was developed in the mid 80s by Karen
+parinello okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there is a sort of uh Universal way
+
+ align:start position:0%
+now there is a sort of uh Universal way
+ 
+
+ align:start position:0%
+now there is a sort of uh Universal way
+to think at this dynamics of your
+
+ align:start position:0%
+to think at this dynamics of your
+ 
+
+ align:start position:0%
+to think at this dynamics of your
+classical system composed of n particles
+
+ align:start position:0%
+classical system composed of n particles
+ 
+
+ align:start position:0%
+classical system composed of n particles
+and as we have said uh since that they
+
+ align:start position:0%
+and as we have said uh since that they
+ 
+
+ align:start position:0%
+and as we have said uh since that they
+follow Newton equation of motion what we
+
+ align:start position:0%
+follow Newton equation of motion what we
+ 
+
+ align:start position:0%
+follow Newton equation of motion what we
+really need to track the only quantities
+
+ align:start position:0%
+really need to track the only quantities
+ 
+
+ align:start position:0%
+really need to track the only quantities
+that we need to track is their position
+
+ align:start position:0%
+that we need to track is their position
+ 
+
+ align:start position:0%
+that we need to track is their position
+as a function of time and their velocity
+
+ align:start position:0%
+as a function of time and their velocity
+ 
+
+ align:start position:0%
+as a function of time and their velocity
+as a function of time and generally
+
+ align:start position:0%
+as a function of time and generally
+ 
+
+ align:start position:0%
+as a function of time and generally
+speaking the kinetic energy is just a
+
+ align:start position:0%
+speaking the kinetic energy is just a
+ 
+
+ align:start position:0%
+speaking the kinetic energy is just a
+function of the velocities and the
+
+ align:start position:0%
+function of the velocities and the
+ 
+
+ align:start position:0%
+function of the velocities and the
+potential energy is just a function of
+
+ align:start position:0%
+potential energy is just a function of
+ 
+
+ align:start position:0%
+potential energy is just a function of
+the positions so if you have n particles
+
+ align:start position:0%
+the positions so if you have n particles
+ 
+
+ align:start position:0%
+the positions so if you have n particles
+you really have to follow in time six
+
+ align:start position:0%
+you really have to follow in time six
+ 
+
+ align:start position:0%
+you really have to follow in time six
+six n variables and if we Define for a
+
+ align:start position:0%
+six n variables and if we Define for a
+ 
+
+ align:start position:0%
+six n variables and if we Define for a
+moment a six dimensional space what we
+
+ align:start position:0%
+moment a six dimensional space what we
+ 
+
+ align:start position:0%
+moment a six dimensional space what we
+really have is that an instantaneous
+
+ align:start position:0%
+really have is that an instantaneous
+ 
+
+ align:start position:0%
+really have is that an instantaneous
+state of your dynamical system that is
+
+ align:start position:0%
+state of your dynamical system that is
+ 
+
+ align:start position:0%
+state of your dynamical system that is
+all its position and all its velocity
+
+ align:start position:0%
+all its position and all its velocity
+ 
+
+ align:start position:0%
+all its position and all its velocity
+can be represented by a single point
+
+ align:start position:0%
+can be represented by a single point
+ 
+
+ align:start position:0%
+can be represented by a single point
+point in this 6n dimensional space so if
+
+ align:start position:0%
+point in this 6n dimensional space so if
+ 
+
+ align:start position:0%
+point in this 6n dimensional space so if
+you've got just a hydrogen molecule with
+
+ align:start position:0%
+you've got just a hydrogen molecule with
+ 
+
+ align:start position:0%
+you've got just a hydrogen molecule with
+two nuclei what you really need is a
+
+ align:start position:0%
+two nuclei what you really need is a
+ 
+
+ align:start position:0%
+two nuclei what you really need is a
+point in six Dimension if you have a
+
+ align:start position:0%
+point in six Dimension if you have a
+ 
+
+ align:start position:0%
+point in six Dimension if you have a
+water molecule you need a point in nine
+
+ align:start position:0%
+water molecule you need a point in nine
+ 
+
+ align:start position:0%
+water molecule you need a point in nine
+dimensions and the evolution
+
+ align:start position:0%
+dimensions and the evolution
+ 
+
+ align:start position:0%
+dimensions and the evolution
+um sorry if you have a water molecule
+
+ align:start position:0%
+um sorry if you have a water molecule
+ 
+
+ align:start position:0%
+um sorry if you have a water molecule
+you need um point in a 18 dimensions and
+
+ align:start position:0%
+you need um point in a 18 dimensions and
+ 
+
+ align:start position:0%
+you need um point in a 18 dimensions and
+if you have a hydrogen molecule you need
+
+ align:start position:0%
+if you have a hydrogen molecule you need
+ 
+
+ align:start position:0%
+if you have a hydrogen molecule you need
+a point in 12 Dimension and the dynamic
+
+ align:start position:0%
+a point in 12 Dimension and the dynamic
+ 
+
+ align:start position:0%
+a point in 12 Dimension and the dynamic
+IAL evolution of your system is
+
+ align:start position:0%
+IAL evolution of your system is
+ 
+
+ align:start position:0%
+IAL evolution of your system is
+described exactly by the evolution of
+
+ align:start position:0%
+described exactly by the evolution of
+ 
+
+ align:start position:0%
+described exactly by the evolution of
+this point so we often think at this
+
+ align:start position:0%
+this point so we often think at this
+ 
+
+ align:start position:0%
+this point so we often think at this
+phase space uh that we have for n
+
+ align:start position:0%
+phase space uh that we have for n
+ 
+
+ align:start position:0%
+phase space uh that we have for n
+particle 6 n dimension of which uh let's
+
+ align:start position:0%
+particle 6 n dimension of which uh let's
+ 
+
+ align:start position:0%
+particle 6 n dimension of which uh let's
+sort of try to draw a bit Dimension uh
+
+ align:start position:0%
+sort of try to draw a bit Dimension uh
+ 
+
+ align:start position:0%
+sort of try to draw a bit Dimension uh
+three n of them those represented in
+
+ align:start position:0%
+three n of them those represented in
+ 
+
+ align:start position:0%
+three n of them those represented in
+green will really represent the
+
+ align:start position:0%
+green will really represent the
+ 
+
+ align:start position:0%
+green will really represent the
+positions and the other three n will
+
+ align:start position:0%
+positions and the other three n will
+ 
+
+ align:start position:0%
+positions and the other three n will
+represent velocities okay and obviously
+
+ align:start position:0%
+represent velocities okay and obviously
+ 
+
+ align:start position:0%
+represent velocities okay and obviously
+this is all orthogonal Dimension and
+
+ align:start position:0%
+this is all orthogonal Dimension and
+ 
+
+ align:start position:0%
+this is all orthogonal Dimension and
+your point will be somewhere a certain
+
+ align:start position:0%
+your point will be somewhere a certain
+ 
+
+ align:start position:0%
+your point will be somewhere a certain
+instant in time t uh we have a set of
+
+ align:start position:0%
+instant in time t uh we have a set of
+ 
+
+ align:start position:0%
+instant in time t uh we have a set of
+velocities we have a set of position and
+
+ align:start position:0%
+velocities we have a set of position and
+ 
+
+ align:start position:0%
+velocities we have a set of position and
+the Newton equation of motion will make
+
+ align:start position:0%
+the Newton equation of motion will make
+ 
+
+ align:start position:0%
+the Newton equation of motion will make
+it evolve in this phase space so really
+
+ align:start position:0%
+it evolve in this phase space so really
+ 
+
+ align:start position:0%
+it evolve in this phase space so really
+your molecular Dynamic integration
+
+ align:start position:0%
+your molecular Dynamic integration
+ 
+
+ align:start position:0%
+your molecular Dynamic integration
+consists in following in time this uh
+
+ align:start position:0%
+consists in following in time this uh
+ 
+
+ align:start position:0%
+consists in following in time this uh
+this Evolution and that evolution is in
+
+ align:start position:0%
+this Evolution and that evolution is in
+ 
+
+ align:start position:0%
+this Evolution and that evolution is in
+principle analytically and uniquely
+
+ align:start position:0%
+principle analytically and uniquely
+ 
+
+ align:start position:0%
+principle analytically and uniquely
+defined uh once you know the position
+
+ align:start position:0%
+defined uh once you know the position
+ 
+
+ align:start position:0%
+defined uh once you know the position
+and the velocities at every instant uh
+
+ align:start position:0%
+and the velocities at every instant uh
+ 
+
+ align:start position:0%
+and the velocities at every instant uh
+and well we we'll see that later okay so
+
+ align:start position:0%
+and well we we'll see that later okay so
+ 
+
+ align:start position:0%
+and well we we'll see that later okay so
+what do we do once uh we have a
+
+ align:start position:0%
+what do we do once uh we have a
+ 
+
+ align:start position:0%
+what do we do once uh we have a
+computational algorith that allows us to
+
+ align:start position:0%
+computational algorith that allows us to
+ 
+
+ align:start position:0%
+computational algorith that allows us to
+evolve this point in Phase space and I
+
+ align:start position:0%
+evolve this point in Phase space and I
+ 
+
+ align:start position:0%
+evolve this point in Phase space and I
+sort of summarized here sort of the
+
+ align:start position:0%
+sort of summarized here sort of the
+ 
+
+ align:start position:0%
+sort of summarized here sort of the
+three main goals that could follow from
+
+ align:start position:0%
+three main goals that could follow from
+ 
+
+ align:start position:0%
+three main goals that could follow from
+a molecular Dynamic simulation in the
+
+ align:start position:0%
+a molecular Dynamic simulation in the
+ 
+
+ align:start position:0%
+a molecular Dynamic simulation in the
+sort of the order that we'll see them uh
+
+ align:start position:0%
+sort of the order that we'll see them uh
+ 
+
+ align:start position:0%
+sort of the order that we'll see them uh
+really one of the most common ones is to
+
+ align:start position:0%
+really one of the most common ones is to
+ 
+
+ align:start position:0%
+really one of the most common ones is to
+use molecular Dynamic simulations to
+
+ align:start position:0%
+use molecular Dynamic simulations to
+ 
+
+ align:start position:0%
+use molecular Dynamic simulations to
+calculate thermodynamical properties
+
+ align:start position:0%
+calculate thermodynamical properties
+ 
+
+ align:start position:0%
+calculate thermodynamical properties
+that is to calculate what we call
+
+ align:start position:0%
+that is to calculate what we call
+ 
+
+ align:start position:0%
+that is to calculate what we call
+Ensemble averages um suppose that you
+
+ align:start position:0%
+Ensemble averages um suppose that you
+ 
+
+ align:start position:0%
+Ensemble averages um suppose that you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+a system like a solid and you have
+
+ align:start position:0%
+a system like a solid and you have
+ 
+
+ align:start position:0%
+a system like a solid and you have
+calculated say it's latis parameter like
+
+ align:start position:0%
+calculated say it's latis parameter like
+ 
+
+ align:start position:0%
+calculated say it's latis parameter like
+you're doing in lab two or lab three and
+
+ align:start position:0%
+you're doing in lab two or lab three and
+ 
+
+ align:start position:0%
+you're doing in lab two or lab three and
+suppose that you start heating up this
+
+ align:start position:0%
+suppose that you start heating up this
+ 
+
+ align:start position:0%
+suppose that you start heating up this
+solid what happens well the atoms in the
+
+ align:start position:0%
+solid what happens well the atoms in the
+ 
+
+ align:start position:0%
+solid what happens well the atoms in the
+classical sense start oscillating more
+
+ align:start position:0%
+classical sense start oscillating more
+ 
+
+ align:start position:0%
+classical sense start oscillating more
+and more and you know from experience
+
+ align:start position:0%
+and more and you know from experience
+ 
+
+ align:start position:0%
+and more and you know from experience
+that most solids starts expanding when
+
+ align:start position:0%
+that most solids starts expanding when
+ 
+
+ align:start position:0%
+that most solids starts expanding when
+you warm them up so a molecular Dynamic
+
+ align:start position:0%
+you warm them up so a molecular Dynamic
+ 
+
+ align:start position:0%
+you warm them up so a molecular Dynamic
+simulation could tell you how much a
+
+ align:start position:0%
+simulation could tell you how much a
+ 
+
+ align:start position:0%
+simulation could tell you how much a
+solid expands when you heat it up
+
+ align:start position:0%
+solid expands when you heat it up
+ 
+
+ align:start position:0%
+solid expands when you heat it up
+because basically you start evolving
+
+ align:start position:0%
+because basically you start evolving
+ 
+
+ align:start position:0%
+because basically you start evolving
+your system from zero temperature and
+
+ align:start position:0%
+your system from zero temperature and
+ 
+
+ align:start position:0%
+your system from zero temperature and
+then you increase its temperature and
+
+ align:start position:0%
+then you increase its temperature and
+ 
+
+ align:start position:0%
+then you increase its temperature and
+really temperature remember is just the
+
+ align:start position:0%
+really temperature remember is just the
+ 
+
+ align:start position:0%
+really temperature remember is just the
+average kinetic energy of the ions and
+
+ align:start position:0%
+average kinetic energy of the ions and
+ 
+
+ align:start position:0%
+average kinetic energy of the ions and
+as you increase the temperature the ions
+
+ align:start position:0%
+as you increase the temperature the ions
+ 
+
+ align:start position:0%
+as you increase the temperature the ions
+oscillate more and more and if you let
+
+ align:start position:0%
+oscillate more and more and if you let
+ 
+
+ align:start position:0%
+oscillate more and more and if you let
+your unit cell expand or contract in
+
+ align:start position:0%
+your unit cell expand or contract in
+ 
+
+ align:start position:0%
+your unit cell expand or contract in
+time following what is the stress
+
+ align:start position:0%
+time following what is the stress
+ 
+
+ align:start position:0%
+time following what is the stress
+overall of all the atoms in your unit
+
+ align:start position:0%
+overall of all the atoms in your unit
+ 
+
+ align:start position:0%
+overall of all the atoms in your unit
+cell you'll see that your system sort of
+
+ align:start position:0%
+cell you'll see that your system sort of
+ 
+
+ align:start position:0%
+cell you'll see that your system sort of
+you know increases the dimension of the
+
+ align:start position:0%
+you know increases the dimension of the
+ 
+
+ align:start position:0%
+you know increases the dimension of the
+unit cell and starts oscillating around
+
+ align:start position:0%
+unit cell and starts oscillating around
+ 
+
+ align:start position:0%
+unit cell and starts oscillating around
+a value that's really an average
+
+ align:start position:0%
+a value that's really an average
+ 
+
+ align:start position:0%
+a value that's really an average
+depending on temperature and um this all
+
+ align:start position:0%
+depending on temperature and um this all
+ 
+
+ align:start position:0%
+depending on temperature and um this all
+these sort of you know statements can be
+
+ align:start position:0%
+these sort of you know statements can be
+ 
+
+ align:start position:0%
+these sort of you know statements can be
+actually made formally in a way that
+
+ align:start position:0%
+actually made formally in a way that
+ 
+
+ align:start position:0%
+actually made formally in a way that
+we'll see in a moment that is the
+
+ align:start position:0%
+we'll see in a moment that is the
+ 
+
+ align:start position:0%
+we'll see in a moment that is the
+language of thermodynamics that is if we
+
+ align:start position:0%
+language of thermodynamics that is if we
+ 
+
+ align:start position:0%
+language of thermodynamics that is if we
+have a finite temperature
+
+ align:start position:0%
+have a finite temperature
+ 
+
+ align:start position:0%
+have a finite temperature
+will have a certain probability
+
+ align:start position:0%
+will have a certain probability
+ 
+
+ align:start position:0%
+will have a certain probability
+associated with every microscopic
+
+ align:start position:0%
+associated with every microscopic
+ 
+
+ align:start position:0%
+associated with every microscopic
+configuration okay so if you if you are
+
+ align:start position:0%
+configuration okay so if you if you are
+ 
+
+ align:start position:0%
+configuration okay so if you if you are
+at zero temperature really what you have
+
+ align:start position:0%
+at zero temperature really what you have
+ 
+
+ align:start position:0%
+at zero temperature really what you have
+is that you have probability one to be
+
+ align:start position:0%
+is that you have probability one to be
+ 
+
+ align:start position:0%
+is that you have probability one to be
+in the lowest energy State possible and
+
+ align:start position:0%
+in the lowest energy State possible and
+ 
+
+ align:start position:0%
+in the lowest energy State possible and
+probability zero of being in any other
+
+ align:start position:0%
+probability zero of being in any other
+ 
+
+ align:start position:0%
+probability zero of being in any other
+energy state if you start increasing
+
+ align:start position:0%
+energy state if you start increasing
+ 
+
+ align:start position:0%
+energy state if you start increasing
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+temperature states that are
+
+ align:start position:0%
+temperature states that are
+ 
+
+ align:start position:0%
+temperature states that are
+energetically similar to the ground
+
+ align:start position:0%
+energetically similar to the ground
+ 
+
+ align:start position:0%
+energetically similar to the ground
+state but not really the ground state
+
+ align:start position:0%
+state but not really the ground state
+ 
+
+ align:start position:0%
+state but not really the ground state
+start to have a certain probability of
+
+ align:start position:0%
+start to have a certain probability of
+ 
+
+ align:start position:0%
+start to have a certain probability of
+being occupied and the more temperature
+
+ align:start position:0%
+being occupied and the more temperature
+ 
+
+ align:start position:0%
+being occupied and the more temperature
+you have the more very costly
+
+ align:start position:0%
+you have the more very costly
+ 
+
+ align:start position:0%
+you have the more very costly
+configurations can be accessed by your
+
+ align:start position:0%
+configurations can be accessed by your
+ 
+
+ align:start position:0%
+configurations can be accessed by your
+system and really the average properties
+
+ align:start position:0%
+system and really the average properties
+ 
+
+ align:start position:0%
+system and really the average properties
+at a finite temperature need to be an
+
+ align:start position:0%
+at a finite temperature need to be an
+ 
+
+ align:start position:0%
+at a finite temperature need to be an
+average over all this possible State
+
+ align:start position:0%
+average over all this possible State
+ 
+
+ align:start position:0%
+average over all this possible State
+weight with their appropriate
+
+ align:start position:0%
+weight with their appropriate
+ 
+
+ align:start position:0%
+weight with their appropriate
+thermodynamic weight Wade with the
+
+ align:start position:0%
+thermodynamic weight Wade with the
+ 
+
+ align:start position:0%
+thermodynamic weight Wade with the
+probability of being in that state and
+
+ align:start position:0%
+probability of being in that state and
+ 
+
+ align:start position:0%
+probability of being in that state and
+so this is what an ensemble average does
+
+ align:start position:0%
+so this is what an ensemble average does
+ 
+
+ align:start position:0%
+so this is what an ensemble average does
+really it sort of tries to span all the
+
+ align:start position:0%
+really it sort of tries to span all the
+ 
+
+ align:start position:0%
+really it sort of tries to span all the
+possible States in a system with a
+
+ align:start position:0%
+possible States in a system with a
+ 
+
+ align:start position:0%
+possible States in a system with a
+probability that is proportional to
+
+ align:start position:0%
+probability that is proportional to
+ 
+
+ align:start position:0%
+probability that is proportional to
+their thermodynamical weight and then
+
+ align:start position:0%
+their thermodynamical weight and then
+ 
+
+ align:start position:0%
+their thermodynamical weight and then
+for each state you can calculate a
+
+ align:start position:0%
+for each state you can calculate a
+ 
+
+ align:start position:0%
+for each state you can calculate a
+certain property like what is it sort of
+
+ align:start position:0%
+certain property like what is it sort of
+ 
+
+ align:start position:0%
+certain property like what is it sort of
+average potential energy what is it sort
+
+ align:start position:0%
+average potential energy what is it sort
+ 
+
+ align:start position:0%
+average potential energy what is it sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh equilibri what is its
+
+ align:start position:0%
+uh equilibri what is its
+ 
+
+ align:start position:0%
+uh equilibri what is its
+um latis parameter and so on and out of
+
+ align:start position:0%
+um latis parameter and so on and out of
+ 
+
+ align:start position:0%
+um latis parameter and so on and out of
+that you can sort of calculate the
+
+ align:start position:0%
+that you can sort of calculate the
+ 
+
+ align:start position:0%
+that you can sort of calculate the
+average thermodynamical property and
+
+ align:start position:0%
+average thermodynamical property and
+ 
+
+ align:start position:0%
+average thermodynamical property and
+we'll see actually example in a moment
+
+ align:start position:0%
+we'll see actually example in a moment
+ 
+
+ align:start position:0%
+we'll see actually example in a moment
+so we'll see sort of a practical
+
+ align:start position:0%
+so we'll see sort of a practical
+ 
+
+ align:start position:0%
+so we'll see sort of a practical
+application of this um the other thing
+
+ align:start position:0%
+application of this um the other thing
+ 
+
+ align:start position:0%
+application of this um the other thing
+that you can do with a molecular Dynamic
+
+ align:start position:0%
+that you can do with a molecular Dynamic
+ 
+
+ align:start position:0%
+that you can do with a molecular Dynamic
+simulator is actually study the
+
+ align:start position:0%
+simulator is actually study the
+ 
+
+ align:start position:0%
+simulator is actually study the
+evolution in real time of your system so
+
+ align:start position:0%
+evolution in real time of your system so
+ 
+
+ align:start position:0%
+evolution in real time of your system so
+you could actually study a chemical
+
+ align:start position:0%
+you could actually study a chemical
+ 
+
+ align:start position:0%
+you could actually study a chemical
+reaction what happens
+
+ align:start position:0%
+reaction what happens
+ 
+
+ align:start position:0%
+reaction what happens
+if you have say an explosive molecule
+
+ align:start position:0%
+if you have say an explosive molecule
+ 
+
+ align:start position:0%
+if you have say an explosive molecule
+that is decomposing okay and in
+
+ align:start position:0%
+that is decomposing okay and in
+ 
+
+ align:start position:0%
+that is decomposing okay and in
+particular whenever you have sort of you
+
+ align:start position:0%
+particular whenever you have sort of you
+ 
+
+ align:start position:0%
+particular whenever you have sort of you
+know chemical reaction that tends to be
+
+ align:start position:0%
+know chemical reaction that tends to be
+ 
+
+ align:start position:0%
+know chemical reaction that tends to be
+bond breaking and bond forming reaction
+
+ align:start position:0%
+bond breaking and bond forming reaction
+ 
+
+ align:start position:0%
+bond breaking and bond forming reaction
+you'll probably need to use a quantum
+
+ align:start position:0%
+you'll probably need to use a quantum
+ 
+
+ align:start position:0%
+you'll probably need to use a quantum
+mechanical approach but in principle you
+
+ align:start position:0%
+mechanical approach but in principle you
+ 
+
+ align:start position:0%
+mechanical approach but in principle you
+can set up your system in an initial
+
+ align:start position:0%
+can set up your system in an initial
+ 
+
+ align:start position:0%
+can set up your system in an initial
+configuration and see what happens as
+
+ align:start position:0%
+configuration and see what happens as
+ 
+
+ align:start position:0%
+configuration and see what happens as
+you evolve in time you could look at a
+
+ align:start position:0%
+you evolve in time you could look at a
+ 
+
+ align:start position:0%
+you evolve in time you could look at a
+catalytic reaction say maybe you're
+
+ align:start position:0%
+catalytic reaction say maybe you're
+ 
+
+ align:start position:0%
+catalytic reaction say maybe you're
+interested in studying fuel cells and
+
+ align:start position:0%
+interested in studying fuel cells and
+ 
+
+ align:start position:0%
+interested in studying fuel cells and
+you want to see how a hydrogen molecule
+
+ align:start position:0%
+you want to see how a hydrogen molecule
+ 
+
+ align:start position:0%
+you want to see how a hydrogen molecule
+decomposes when it arrives on a platinum
+
+ align:start position:0%
+decomposes when it arrives on a platinum
+ 
+
+ align:start position:0%
+decomposes when it arrives on a platinum
+surface well you can take your hydrogen
+
+ align:start position:0%
+surface well you can take your hydrogen
+ 
+
+ align:start position:0%
+surface well you can take your hydrogen
+molecule and sort of you know project it
+
+ align:start position:0%
+molecule and sort of you know project it
+ 
+
+ align:start position:0%
+molecule and sort of you know project it
+delicately towards the Platinum surface
+
+ align:start position:0%
+delicately towards the Platinum surface
+ 
+
+ align:start position:0%
+delicately towards the Platinum surface
+and follow with your molecular Dynamic
+
+ align:start position:0%
+and follow with your molecular Dynamic
+ 
+
+ align:start position:0%
+and follow with your molecular Dynamic
+techniques the Dynamics of all these
+
+ align:start position:0%
+techniques the Dynamics of all these
+ 
+
+ align:start position:0%
+techniques the Dynamics of all these
+nuclei as the molecule chemisorbs and
+
+ align:start position:0%
+nuclei as the molecule chemisorbs and
+ 
+
+ align:start position:0%
+nuclei as the molecule chemisorbs and
+dissociate in
+
+ align:start position:0%
+dissociate in
+ 
+
+ align:start position:0%
+dissociate in
+time and then really sort of the last
+
+ align:start position:0%
+time and then really sort of the last
+ 
+
+ align:start position:0%
+time and then really sort of the last
+um uh application of molecular Dynamics
+
+ align:start position:0%
+um uh application of molecular Dynamics
+ 
+
+ align:start position:0%
+um uh application of molecular Dynamics
+uh is a sort of more of a
+
+ align:start position:0%
+uh is a sort of more of a
+ 
+
+ align:start position:0%
+uh is a sort of more of a
+optimization algorithm uh there are
+
+ align:start position:0%
+optimization algorithm uh there are
+ 
+
+ align:start position:0%
+optimization algorithm uh there are
+problems in which it's very complex to
+
+ align:start position:0%
+problems in which it's very complex to
+ 
+
+ align:start position:0%
+problems in which it's very complex to
+find what is the lowest possible
+
+ align:start position:0%
+find what is the lowest possible
+ 
+
+ align:start position:0%
+find what is the lowest possible
+solution what is the optimal solution
+
+ align:start position:0%
+solution what is the optimal solution
+ 
+
+ align:start position:0%
+solution what is the optimal solution
+that is you know you could sort of you
+
+ align:start position:0%
+that is you know you could sort of you
+ 
+
+ align:start position:0%
+that is you know you could sort of you
+know try to find out what is the schedle
+
+ align:start position:0%
+know try to find out what is the schedle
+ 
+
+ align:start position:0%
+know try to find out what is the schedle
+of all your flights in a air plane comp
+
+ align:start position:0%
+of all your flights in a air plane comp
+ 
+
+ align:start position:0%
+of all your flights in a air plane comp
+and obviously that's a complex
+
+ align:start position:0%
+and obviously that's a complex
+ 
+
+ align:start position:0%
+and obviously that's a complex
+optimization problem because you can't
+
+ align:start position:0%
+optimization problem because you can't
+ 
+
+ align:start position:0%
+optimization problem because you can't
+move one plane at a time and figure out
+
+ align:start position:0%
+move one plane at a time and figure out
+ 
+
+ align:start position:0%
+move one plane at a time and figure out
+what is the best possible solution
+
+ align:start position:0%
+what is the best possible solution
+ 
+
+ align:start position:0%
+what is the best possible solution
+because there might be a completely
+
+ align:start position:0%
+because there might be a completely
+ 
+
+ align:start position:0%
+because there might be a completely
+different choice of planes and
+
+ align:start position:0%
+different choice of planes and
+ 
+
+ align:start position:0%
+different choice of planes and
+itineraries that actually gives you a
+
+ align:start position:0%
+itineraries that actually gives you a
+ 
+
+ align:start position:0%
+itineraries that actually gives you a
+best performance overall on the net and
+
+ align:start position:0%
+best performance overall on the net and
+ 
+
+ align:start position:0%
+best performance overall on the net and
+so you can always sort of take one
+
+ align:start position:0%
+so you can always sort of take one
+ 
+
+ align:start position:0%
+so you can always sort of take one
+optimization problem and express a cost
+
+ align:start position:0%
+optimization problem and express a cost
+ 
+
+ align:start position:0%
+optimization problem and express a cost
+function that is sort of depending on
+
+ align:start position:0%
+function that is sort of depending on
+ 
+
+ align:start position:0%
+function that is sort of depending on
+what is you're interested sort of
+
+ align:start position:0%
+what is you're interested sort of
+ 
+
+ align:start position:0%
+what is you're interested sort of
+minimize the sort of amount of oil I say
+
+ align:start position:0%
+minimize the sort of amount of oil I say
+ 
+
+ align:start position:0%
+minimize the sort of amount of oil I say
+used in running all these routs so when
+
+ align:start position:0%
+used in running all these routs so when
+ 
+
+ align:start position:0%
+used in running all these routs so when
+you have a cost function of a very
+
+ align:start position:0%
+you have a cost function of a very
+ 
+
+ align:start position:0%
+you have a cost function of a very
+complex problem you have really an
+
+ align:start position:0%
+complex problem you have really an
+ 
+
+ align:start position:0%
+complex problem you have really an
+object that depends on many
+
+ align:start position:0%
+object that depends on many
+ 
+
+ align:start position:0%
+object that depends on many
+variables and that has a lot of possible
+
+ align:start position:0%
+variables and that has a lot of possible
+ 
+
+ align:start position:0%
+variables and that has a lot of possible
+Minima okay so this would be really the
+
+ align:start position:0%
+Minima okay so this would be really the
+ 
+
+ align:start position:0%
+Minima okay so this would be really the
+problem of
+
+ align:start position:0%
+problem of
+ 
+
+ align:start position:0%
+problem of
+optimizing uh the airor roots of a uh
+
+ align:start position:0%
+optimizing uh the airor roots of a uh
+ 
+
+ align:start position:0%
+optimizing uh the airor roots of a uh
+Airline what you have is a lot of
+
+ align:start position:0%
+Airline what you have is a lot of
+ 
+
+ align:start position:0%
+Airline what you have is a lot of
+possible variables and there are a lot
+
+ align:start position:0%
+possible variables and there are a lot
+ 
+
+ align:start position:0%
+possible variables and there are a lot
+of reasonable Solutions but you really
+
+ align:start position:0%
+of reasonable Solutions but you really
+ 
+
+ align:start position:0%
+of reasonable Solutions but you really
+want to find the one that is the best
+
+ align:start position:0%
+want to find the one that is the best
+ 
+
+ align:start position:0%
+want to find the one that is the best
+for you something something like this
+
+ align:start position:0%
+for you something something like this
+ 
+
+ align:start position:0%
+for you something something like this
+and molecular Dynamics can actually help
+
+ align:start position:0%
+and molecular Dynamics can actually help
+ 
+
+ align:start position:0%
+and molecular Dynamics can actually help
+to solve this problem because it's a
+
+ align:start position:0%
+to solve this problem because it's a
+ 
+
+ align:start position:0%
+to solve this problem because it's a
+problem that is absolutely analogous of
+
+ align:start position:0%
+problem that is absolutely analogous of
+ 
+
+ align:start position:0%
+problem that is absolutely analogous of
+having a system of interacting particle
+
+ align:start position:0%
+having a system of interacting particle
+ 
+
+ align:start position:0%
+having a system of interacting particle
+that has a certain potential energy
+
+ align:start position:0%
+that has a certain potential energy
+ 
+
+ align:start position:0%
+that has a certain potential energy
+surface and trying to explore that
+
+ align:start position:0%
+surface and trying to explore that
+ 
+
+ align:start position:0%
+surface and trying to explore that
+potential energy surface moving around
+
+ align:start position:0%
+potential energy surface moving around
+ 
+
+ align:start position:0%
+potential energy surface moving around
+until you find the lowest minimum you
+
+ align:start position:0%
+until you find the lowest minimum you
+ 
+
+ align:start position:0%
+until you find the lowest minimum you
+could think at this as you know a
+
+ align:start position:0%
+could think at this as you know a
+ 
+
+ align:start position:0%
+could think at this as you know a
+mountain range and you have your skares
+
+ align:start position:0%
+mountain range and you have your skares
+ 
+
+ align:start position:0%
+mountain range and you have your skares
+that are really your particles moving
+
+ align:start position:0%
+that are really your particles moving
+ 
+
+ align:start position:0%
+that are really your particles moving
+around and you want to sort of let the
+
+ align:start position:0%
+around and you want to sort of let the
+ 
+
+ align:start position:0%
+around and you want to sort of let the
+skiers ski around as much as possible
+
+ align:start position:0%
+skiers ski around as much as possible
+ 
+
+ align:start position:0%
+skiers ski around as much as possible
+until they find the minimum energy State
+
+ align:start position:0%
+until they find the minimum energy State
+ 
+
+ align:start position:0%
+until they find the minimum energy State
+and so you can use a thermodynamical
+
+ align:start position:0%
+and so you can use a thermodynamical
+ 
+
+ align:start position:0%
+and so you can use a thermodynamical
+analogy you heat up your system that
+
+ align:start position:0%
+analogy you heat up your system that
+ 
+
+ align:start position:0%
+analogy you heat up your system that
+means that every particle has a lot of
+
+ align:start position:0%
+means that every particle has a lot of
+ 
+
+ align:start position:0%
+means that every particle has a lot of
+kinetic energy so sort of you know
+
+ align:start position:0%
+kinetic energy so sort of you know
+ 
+
+ align:start position:0%
+kinetic energy so sort of you know
+having a lot of kinetic energy can
+
+ align:start position:0%
+having a lot of kinetic energy can
+ 
+
+ align:start position:0%
+having a lot of kinetic energy can
+easily overcome any kind of potential
+
+ align:start position:0%
+easily overcome any kind of potential
+ 
+
+ align:start position:0%
+easily overcome any kind of potential
+barrier and you have a lot of this
+
+ align:start position:0%
+barrier and you have a lot of this
+ 
+
+ align:start position:0%
+barrier and you have a lot of this
+particle moving around and then you sort
+
+ align:start position:0%
+particle moving around and then you sort
+ 
+
+ align:start position:0%
+particle moving around and then you sort
+of cool them down slowly and as you cool
+
+ align:start position:0%
+of cool them down slowly and as you cool
+ 
+
+ align:start position:0%
+of cool them down slowly and as you cool
+them down they'll start piling up in the
+
+ align:start position:0%
+them down they'll start piling up in the
+ 
+
+ align:start position:0%
+them down they'll start piling up in the
+lowest possible energy states and once
+
+ align:start position:0%
+lowest possible energy states and once
+ 
+
+ align:start position:0%
+lowest possible energy states and once
+you have reached very slowly zero
+
+ align:start position:0%
+you have reached very slowly zero
+ 
+
+ align:start position:0%
+you have reached very slowly zero
+temperature you look where all your
+
+ align:start position:0%
+temperature you look where all your
+ 
+
+ align:start position:0%
+temperature you look where all your
+particles have ended up and so you have
+
+ align:start position:0%
+particles have ended up and so you have
+ 
+
+ align:start position:0%
+particles have ended up and so you have
+at least you know a good sampling of the
+
+ align:start position:0%
+at least you know a good sampling of the
+ 
+
+ align:start position:0%
+at least you know a good sampling of the
+relevant Minima in your potential energy
+
+ align:start position:0%
+relevant Minima in your potential energy
+ 
+
+ align:start position:0%
+relevant Minima in your potential energy
+surface so moleular Dynamics and this is
+
+ align:start position:0%
+surface so moleular Dynamics and this is
+ 
+
+ align:start position:0%
+surface so moleular Dynamics and this is
+called simulated aning in this context
+
+ align:start position:0%
+called simulated aning in this context
+ 
+
+ align:start position:0%
+called simulated aning in this context
+can actually be used as an optimization
+
+ align:start position:0%
+can actually be used as an optimization
+ 
+
+ align:start position:0%
+can actually be used as an optimization
+as an optimization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technique and uh we don't have sort of
+
+ align:start position:0%
+technique and uh we don't have sort of
+ 
+
+ align:start position:0%
+technique and uh we don't have sort of
+you know to go as far as the case of an
+
+ align:start position:0%
+you know to go as far as the case of an
+ 
+
+ align:start position:0%
+you know to go as far as the case of an
+airline or what is called the traveling
+
+ align:start position:0%
+airline or what is called the traveling
+ 
+
+ align:start position:0%
+airline or what is called the traveling
+salesman problem but often what we have
+
+ align:start position:0%
+salesman problem but often what we have
+ 
+
+ align:start position:0%
+salesman problem but often what we have
+is that we have system that has fairly
+
+ align:start position:0%
+is that we have system that has fairly
+ 
+
+ align:start position:0%
+is that we have system that has fairly
+complicated to
+
+ align:start position:0%
+complicated to
+ 
+
+ align:start position:0%
+complicated to
+characterize uh say we want to describe
+
+ align:start position:0%
+characterize uh say we want to describe
+ 
+
+ align:start position:0%
+characterize uh say we want to describe
+maybe an interface between uh you know
+
+ align:start position:0%
+maybe an interface between uh you know
+ 
+
+ align:start position:0%
+maybe an interface between uh you know
+perfect silicon crystal and the sio2
+
+ align:start position:0%
+perfect silicon crystal and the sio2
+ 
+
+ align:start position:0%
+perfect silicon crystal and the sio2
+substrate because we are in the sort of
+
+ align:start position:0%
+substrate because we are in the sort of
+ 
+
+ align:start position:0%
+substrate because we are in the sort of
+electronic industry well I mean we have
+
+ align:start position:0%
+electronic industry well I mean we have
+ 
+
+ align:start position:0%
+electronic industry well I mean we have
+a problem because how how do we
+
+ align:start position:0%
+a problem because how how do we
+ 
+
+ align:start position:0%
+a problem because how how do we
+construct the interface between a
+
+ align:start position:0%
+construct the interface between a
+ 
+
+ align:start position:0%
+construct the interface between a
+crystalline solid and an amorphous
+
+ align:start position:0%
+crystalline solid and an amorphous
+ 
+
+ align:start position:0%
+crystalline solid and an amorphous
+system I mean we can try putting atoms
+
+ align:start position:0%
+system I mean we can try putting atoms
+ 
+
+ align:start position:0%
+system I mean we can try putting atoms
+in reasonable position but it's never
+
+ align:start position:0%
+in reasonable position but it's never
+ 
+
+ align:start position:0%
+in reasonable position but it's never
+going to work very well and so what we
+
+ align:start position:0%
+going to work very well and so what we
+ 
+
+ align:start position:0%
+going to work very well and so what we
+can do is actually use a molecular
+
+ align:start position:0%
+can do is actually use a molecular
+ 
+
+ align:start position:0%
+can do is actually use a molecular
+Dynamic techniques to let the atoms
+
+ align:start position:0%
+Dynamic techniques to let the atoms
+ 
+
+ align:start position:0%
+Dynamic techniques to let the atoms
+evolve according to their interaction
+
+ align:start position:0%
+evolve according to their interaction
+ 
+
+ align:start position:0%
+evolve according to their interaction
+and to the Newton equation of motion and
+
+ align:start position:0%
+and to the Newton equation of motion and
+ 
+
+ align:start position:0%
+and to the Newton equation of motion and
+somehow find by themselves uh slightly
+
+ align:start position:0%
+somehow find by themselves uh slightly
+ 
+
+ align:start position:0%
+somehow find by themselves uh slightly
+more favorable green Minima instead of
+
+ align:start position:0%
+more favorable green Minima instead of
+ 
+
+ align:start position:0%
+more favorable green Minima instead of
+the initial configuration in which we
+
+ align:start position:0%
+the initial configuration in which we
+ 
+
+ align:start position:0%
+the initial configuration in which we
+have put
+
+ align:start position:0%
+have put
+ 
+
+ align:start position:0%
+have put
+them okay so in principle if you had you
+
+ align:start position:0%
+them okay so in principle if you had you
+ 
+
+ align:start position:0%
+them okay so in principle if you had you
+know um infinite computing power or
+
+ align:start position:0%
+know um infinite computing power or
+ 
+
+ align:start position:0%
+know um infinite computing power or
+infinite mathematical
+
+ align:start position:0%
+infinite mathematical
+ 
+
+ align:start position:0%
+infinite mathematical
+Powers you would have really solved the
+
+ align:start position:0%
+Powers you would have really solved the
+ 
+
+ align:start position:0%
+Powers you would have really solved the
+problem of characterizing on a computer
+
+ align:start position:0%
+problem of characterizing on a computer
+ 
+
+ align:start position:0%
+problem of characterizing on a computer
+any material that you wanted uh the
+
+ align:start position:0%
+any material that you wanted uh the
+ 
+
+ align:start position:0%
+any material that you wanted uh the
+reason why you can't really do that in
+
+ align:start position:0%
+reason why you can't really do that in
+ 
+
+ align:start position:0%
+reason why you can't really do that in
+general and indiscriminate
+
+ align:start position:0%
+general and indiscriminate
+ 
+
+ align:start position:0%
+general and indiscriminate
+indiscriminately um as to do with sort
+
+ align:start position:0%
+indiscriminately um as to do with sort
+ 
+
+ align:start position:0%
+indiscriminately um as to do with sort
+of four
+
+ align:start position:0%
+of four
+ 
+
+ align:start position:0%
+of four
+problems that arises in the approach
+
+ align:start position:0%
+problems that arises in the approach
+ 
+
+ align:start position:0%
+problems that arises in the approach
+that I've mentioned and sort of I've
+
+ align:start position:0%
+that I've mentioned and sort of I've
+ 
+
+ align:start position:0%
+that I've mentioned and sort of I've
+mentioned them here uh I guess in order
+
+ align:start position:0%
+mentioned them here uh I guess in order
+ 
+
+ align:start position:0%
+mentioned them here uh I guess in order
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+importance and uh the first and most
+
+ align:start position:0%
+importance and uh the first and most
+ 
+
+ align:start position:0%
+importance and uh the first and most
+dramatic problem is the one of time
+
+ align:start position:0%
+dramatic problem is the one of time
+ 
+
+ align:start position:0%
+dramatic problem is the one of time
+scales that is atoms move around and
+
+ align:start position:0%
+scales that is atoms move around and
+ 
+
+ align:start position:0%
+scales that is atoms move around and
+vibrate at time scales that are
+
+ align:start position:0%
+vibrate at time scales that are
+ 
+
+ align:start position:0%
+vibrate at time scales that are
+characteristic of atoms that is uh um
+
+ align:start position:0%
+characteristic of atoms that is uh um
+ 
+
+ align:start position:0%
+characteristic of atoms that is uh um
+say in a molecule it will take tens of
+
+ align:start position:0%
+say in a molecule it will take tens of
+ 
+
+ align:start position:0%
+say in a molecule it will take tens of
+ftocs or 100 of ftocs to have a periodic
+
+ align:start position:0%
+ftocs or 100 of ftocs to have a periodic
+ 
+
+ align:start position:0%
+ftocs or 100 of ftocs to have a periodic
+oscillation so these are sort of you
+
+ align:start position:0%
+oscillation so these are sort of you
+ 
+
+ align:start position:0%
+oscillation so these are sort of you
+know uh fto seconds 10 Theus 15 seconds
+
+ align:start position:0%
+know uh fto seconds 10 Theus 15 seconds
+ 
+
+ align:start position:0%
+know uh fto seconds 10 Theus 15 seconds
+is the order of magnitude of the
+
+ align:start position:0%
+is the order of magnitude of the
+ 
+
+ align:start position:0%
+is the order of magnitude of the
+Dynamics of the atoms uh at sort of room
+
+ align:start position:0%
+Dynamics of the atoms uh at sort of room
+ 
+
+ align:start position:0%
+Dynamics of the atoms uh at sort of room
+room temperature now a lot of
+
+ align:start position:0%
+room temperature now a lot of
+ 
+
+ align:start position:0%
+room temperature now a lot of
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+problems take place into sort of times
+
+ align:start position:0%
+problems take place into sort of times
+ 
+
+ align:start position:0%
+problems take place into sort of times
+of seconds me
+
+ align:start position:0%
+of seconds me
+ 
+
+ align:start position:0%
+of seconds me
+or hours you know sort of a classical
+
+ align:start position:0%
+or hours you know sort of a classical
+ 
+
+ align:start position:0%
+or hours you know sort of a classical
+problem is how a protein folds itself in
+
+ align:start position:0%
+problem is how a protein folds itself in
+ 
+
+ align:start position:0%
+problem is how a protein folds itself in
+its native state and you know this is a
+
+ align:start position:0%
+its native state and you know this is a
+ 
+
+ align:start position:0%
+its native state and you know this is a
+process that can take seconds and so we
+
+ align:start position:0%
+process that can take seconds and so we
+ 
+
+ align:start position:0%
+process that can take seconds and so we
+have really the issue that you know all
+
+ align:start position:0%
+have really the issue that you know all
+ 
+
+ align:start position:0%
+have really the issue that you know all
+our calculation takes place on the time
+
+ align:start position:0%
+our calculation takes place on the time
+ 
+
+ align:start position:0%
+our calculation takes place on the time
+scales of 10 to Theus 15 and often we
+
+ align:start position:0%
+scales of 10 to Theus 15 and often we
+ 
+
+ align:start position:0%
+scales of 10 to Theus 15 and often we
+need to reach physical properties that
+
+ align:start position:0%
+need to reach physical properties that
+ 
+
+ align:start position:0%
+need to reach physical properties that
+are of the order of seconds so we need
+
+ align:start position:0%
+are of the order of seconds so we need
+ 
+
+ align:start position:0%
+are of the order of seconds so we need
+to span 15 order of magnitudes and that
+
+ align:start position:0%
+to span 15 order of magnitudes and that
+ 
+
+ align:start position:0%
+to span 15 order of magnitudes and that
+means that you know if it takes a time x
+
+ align:start position:0%
+means that you know if it takes a time x
+ 
+
+ align:start position:0%
+means that you know if it takes a time x
+to perform one single molecular Dynamic
+
+ align:start position:0%
+to perform one single molecular Dynamic
+ 
+
+ align:start position:0%
+to perform one single molecular Dynamic
+operation we have a 10 to the 15 cost to
+
+ align:start position:0%
+operation we have a 10 to the 15 cost to
+ 
+
+ align:start position:0%
+operation we have a 10 to the 15 cost to
+get to the reasonable time scale for a
+
+ align:start position:0%
+get to the reasonable time scale for a
+ 
+
+ align:start position:0%
+get to the reasonable time scale for a
+lot of microscopic processes and that's
+
+ align:start position:0%
+lot of microscopic processes and that's
+ 
+
+ align:start position:0%
+lot of microscopic processes and that's
+really you know a scale that we can't
+
+ align:start position:0%
+really you know a scale that we can't
+ 
+
+ align:start position:0%
+really you know a scale that we can't
+bridge if we do quantum mechanical
+
+ align:start position:0%
+bridge if we do quantum mechanical
+ 
+
+ align:start position:0%
+bridge if we do quantum mechanical
+simulations you know for small system we
+
+ align:start position:0%
+simulations you know for small system we
+ 
+
+ align:start position:0%
+simulations you know for small system we
+can easily sort of reach the times of 10
+
+ align:start position:0%
+can easily sort of reach the times of 10
+ 
+
+ align:start position:0%
+can easily sort of reach the times of 10
+of Picos seconds or hundreds of Picos
+
+ align:start position:0%
+of Picos seconds or hundreds of Picos
+ 
+
+ align:start position:0%
+of Picos seconds or hundreds of Picos
+seconds if we do classical molecular
+
+ align:start position:0%
+seconds if we do classical molecular
+ 
+
+ align:start position:0%
+seconds if we do classical molecular
+Dynamic simulation we can go maybe three
+
+ align:start position:0%
+Dynamic simulation we can go maybe three
+ 
+
+ align:start position:0%
+Dynamic simulation we can go maybe three
+four five orders of magnitude better and
+
+ align:start position:0%
+four five orders of magnitude better and
+ 
+
+ align:start position:0%
+four five orders of magnitude better and
+so we can sort of start accessing
+
+ align:start position:0%
+so we can sort of start accessing
+ 
+
+ align:start position:0%
+so we can sort of start accessing
+Nan and maybe start hitching um start uh
+
+ align:start position:0%
+Nan and maybe start hitching um start uh
+ 
+
+ align:start position:0%
+Nan and maybe start hitching um start uh
+getting closer towards the microc but
+
+ align:start position:0%
+getting closer towards the microc but
+ 
+
+ align:start position:0%
+getting closer towards the microc but
+there is still an enormous Gap to reach
+
+ align:start position:0%
+there is still an enormous Gap to reach
+ 
+
+ align:start position:0%
+there is still an enormous Gap to reach
+and this is really a difficult problem
+
+ align:start position:0%
+and this is really a difficult problem
+ 
+
+ align:start position:0%
+and this is really a difficult problem
+to overcome because we have sort of
+
+ align:start position:0%
+to overcome because we have sort of
+ 
+
+ align:start position:0%
+to overcome because we have sort of
+Dynamics taking place at different
+
+ align:start position:0%
+Dynamics taking place at different
+ 
+
+ align:start position:0%
+Dynamics taking place at different
+levels we have the say think at a
+
+ align:start position:0%
+levels we have the say think at a
+ 
+
+ align:start position:0%
+levels we have the say think at a
+protein we have the atomic dynamics of
+
+ align:start position:0%
+protein we have the atomic dynamics of
+ 
+
+ align:start position:0%
+protein we have the atomic dynamics of
+atom vibrating around and then we have
+
+ align:start position:0%
+atom vibrating around and then we have
+ 
+
+ align:start position:0%
+atom vibrating around and then we have
+sort of dynamics of subunits sort of
+
+ align:start position:0%
+sort of dynamics of subunits sort of
+ 
+
+ align:start position:0%
+sort of dynamics of subunits sort of
+maybe interacting with the different
+
+ align:start position:0%
+maybe interacting with the different
+ 
+
+ align:start position:0%
+maybe interacting with the different
+amino acids along the chain and then we
+
+ align:start position:0%
+amino acids along the chain and then we
+ 
+
+ align:start position:0%
+amino acids along the chain and then we
+have sort of structural motifs that
+
+ align:start position:0%
+have sort of structural motifs that
+ 
+
+ align:start position:0%
+have sort of structural motifs that
+wants to move around and then maybe you
+
+ align:start position:0%
+wants to move around and then maybe you
+ 
+
+ align:start position:0%
+wants to move around and then maybe you
+know sort of they sort of first coil up
+
+ align:start position:0%
+know sort of they sort of first coil up
+ 
+
+ align:start position:0%
+know sort of they sort of first coil up
+in a certain configuration but that's
+
+ align:start position:0%
+in a certain configuration but that's
+ 
+
+ align:start position:0%
+in a certain configuration but that's
+not really very good and then after a
+
+ align:start position:0%
+not really very good and then after a
+ 
+
+ align:start position:0%
+not really very good and then after a
+while they sort of open up and recoil in
+
+ align:start position:0%
+while they sort of open up and recoil in
+ 
+
+ align:start position:0%
+while they sort of open up and recoil in
+a different configuration and so the
+
+ align:start position:0%
+a different configuration and so the
+ 
+
+ align:start position:0%
+a different configuration and so the
+more sort of you look at your system on
+
+ align:start position:0%
+more sort of you look at your system on
+ 
+
+ align:start position:0%
+more sort of you look at your system on
+larger and larger lens scale the more
+
+ align:start position:0%
+larger and larger lens scale the more
+ 
+
+ align:start position:0%
+larger and larger lens scale the more
+you discover that there are dynamics of
+
+ align:start position:0%
+you discover that there are dynamics of
+ 
+
+ align:start position:0%
+you discover that there are dynamics of
+more and more complex groups that are
+
+ align:start position:0%
+more and more complex groups that are
+ 
+
+ align:start position:0%
+more and more complex groups that are
+slower and slower and integrating from
+
+ align:start position:0%
+slower and slower and integrating from
+ 
+
+ align:start position:0%
+slower and slower and integrating from
+the atomic motion up to the mesos scale
+
+ align:start position:0%
+the atomic motion up to the mesos scale
+ 
+
+ align:start position:0%
+the atomic motion up to the mesos scale
+and the microscopic scale this Dynamics
+
+ align:start position:0%
+and the microscopic scale this Dynamics
+ 
+
+ align:start position:0%
+and the microscopic scale this Dynamics
+is really an impossible possible problem
+
+ align:start position:0%
+is really an impossible possible problem
+ 
+
+ align:start position:0%
+is really an impossible possible problem
+to do by brute force and I would say
+
+ align:start position:0%
+to do by brute force and I would say
+ 
+
+ align:start position:0%
+to do by brute force and I would say
+that you know it's still the conceptual
+
+ align:start position:0%
+that you know it's still the conceptual
+ 
+
+ align:start position:0%
+that you know it's still the conceptual
+problem for which less uh progress has
+
+ align:start position:0%
+problem for which less uh progress has
+ 
+
+ align:start position:0%
+problem for which less uh progress has
+been made it's really the most difficult
+
+ align:start position:0%
+been made it's really the most difficult
+ 
+
+ align:start position:0%
+been made it's really the most difficult
+one and you'll hear a lot of talks
+
+ align:start position:0%
+one and you'll hear a lot of talks
+ 
+
+ align:start position:0%
+one and you'll hear a lot of talks
+nowadays in science about multiscale
+
+ align:start position:0%
+nowadays in science about multiscale
+ 
+
+ align:start position:0%
+nowadays in science about multiscale
+modeling and about bridging time scales
+
+ align:start position:0%
+modeling and about bridging time scales
+ 
+
+ align:start position:0%
+modeling and about bridging time scales
+and it's obviously you know very
+
+ align:start position:0%
+and it's obviously you know very
+ 
+
+ align:start position:0%
+and it's obviously you know very
+important challenge but I still think we
+
+ align:start position:0%
+important challenge but I still think we
+ 
+
+ align:start position:0%
+important challenge but I still think we
+are at the stage in which there are very
+
+ align:start position:0%
+are at the stage in which there are very
+ 
+
+ align:start position:0%
+are at the stage in which there are very
+little so Solutions somehow related to
+
+ align:start position:0%
+little so Solutions somehow related to
+ 
+
+ align:start position:0%
+little so Solutions somehow related to
+the length scale problem to the time
+
+ align:start position:0%
+the length scale problem to the time
+ 
+
+ align:start position:0%
+the length scale problem to the time
+scale problem there is the length scale
+
+ align:start position:0%
+scale problem there is the length scale
+ 
+
+ align:start position:0%
+scale problem there is the length scale
+problem um suppose you want to study a
+
+ align:start position:0%
+problem um suppose you want to study a
+ 
+
+ align:start position:0%
+problem um suppose you want to study a
+system close to a phase transition
+
+ align:start position:0%
+system close to a phase transition
+ 
+
+ align:start position:0%
+system close to a phase transition
+suppose that you want to do you know you
+
+ align:start position:0%
+suppose that you want to do you know you
+ 
+
+ align:start position:0%
+suppose that you want to do you know you
+want to see a gas evaporate you want to
+
+ align:start position:0%
+want to see a gas evaporate you want to
+ 
+
+ align:start position:0%
+want to see a gas evaporate you want to
+study a liquid to Vapor transition uh
+
+ align:start position:0%
+study a liquid to Vapor transition uh
+ 
+
+ align:start position:0%
+study a liquid to Vapor transition uh
+what happens exactly at the temperature
+
+ align:start position:0%
+what happens exactly at the temperature
+ 
+
+ align:start position:0%
+what happens exactly at the temperature
+where the liquid and the vapor are in
+
+ align:start position:0%
+where the liquid and the vapor are in
+ 
+
+ align:start position:0%
+where the liquid and the vapor are in
+equilibrium suppose that you're are
+
+ align:start position:0%
+equilibrium suppose that you're are
+ 
+
+ align:start position:0%
+equilibrium suppose that you're are
+studying you know uh water boiling at
+
+ align:start position:0%
+studying you know uh water boiling at
+ 
+
+ align:start position:0%
+studying you know uh water boiling at
+sort of normal condition it boils at uh
+
+ align:start position:0%
+sort of normal condition it boils at uh
+ 
+
+ align:start position:0%
+sort of normal condition it boils at uh
+373 Kelvin uh and at that
+
+ align:start position:0%
+373 Kelvin uh and at that
+ 
+
+ align:start position:0%
+373 Kelvin uh and at that
+temperature uh why there is a phase
+
+ align:start position:0%
+temperature uh why there is a phase
+ 
+
+ align:start position:0%
+temperature uh why there is a phase
+transition basically because the free
+
+ align:start position:0%
+transition basically because the free
+ 
+
+ align:start position:0%
+transition basically because the free
+energy of the liquid and the free energy
+
+ align:start position:0%
+energy of the liquid and the free energy
+ 
+
+ align:start position:0%
+energy of the liquid and the free energy
+of the gas are the same you go a little
+
+ align:start position:0%
+of the gas are the same you go a little
+ 
+
+ align:start position:0%
+of the gas are the same you go a little
+bit above the temperature the free
+
+ align:start position:0%
+bit above the temperature the free
+ 
+
+ align:start position:0%
+bit above the temperature the free
+energy of the gas is lower so the system
+
+ align:start position:0%
+energy of the gas is lower so the system
+ 
+
+ align:start position:0%
+energy of the gas is lower so the system
+wants to be all gas you go a little bit
+
+ align:start position:0%
+wants to be all gas you go a little bit
+ 
+
+ align:start position:0%
+wants to be all gas you go a little bit
+below the boiling temperature the free
+
+ align:start position:0%
+below the boiling temperature the free
+ 
+
+ align:start position:0%
+below the boiling temperature the free
+energy of the liquid is lower so the
+
+ align:start position:0%
+energy of the liquid is lower so the
+ 
+
+ align:start position:0%
+energy of the liquid is lower so the
+system wants to be all liquid but as you
+
+ align:start position:0%
+system wants to be all liquid but as you
+ 
+
+ align:start position:0%
+system wants to be all liquid but as you
+get closer and closer to the temperature
+
+ align:start position:0%
+get closer and closer to the temperature
+ 
+
+ align:start position:0%
+get closer and closer to the temperature
+these two free energies becomes
+
+ align:start position:0%
+these two free energies becomes
+ 
+
+ align:start position:0%
+these two free energies becomes
+comparable that means that the cost of
+
+ align:start position:0%
+comparable that means that the cost of
+ 
+
+ align:start position:0%
+comparable that means that the cost of
+transforming from liquid to the gas and
+
+ align:start position:0%
+transforming from liquid to the gas and
+ 
+
+ align:start position:0%
+transforming from liquid to the gas and
+from gas to liquid becomes smaller and
+
+ align:start position:0%
+from gas to liquid becomes smaller and
+ 
+
+ align:start position:0%
+from gas to liquid becomes smaller and
+smaller and it is zero at the transition
+
+ align:start position:0%
+smaller and it is zero at the transition
+ 
+
+ align:start position:0%
+smaller and it is zero at the transition
+temperature that means in practice that
+
+ align:start position:0%
+temperature that means in practice that
+ 
+
+ align:start position:0%
+temperature that means in practice that
+since that it doesn't cost anything to
+
+ align:start position:0%
+since that it doesn't cost anything to
+ 
+
+ align:start position:0%
+since that it doesn't cost anything to
+transform from one state to the other
+
+ align:start position:0%
+transform from one state to the other
+ 
+
+ align:start position:0%
+transform from one state to the other
+you have lost all possible length scale
+
+ align:start position:0%
+you have lost all possible length scale
+ 
+
+ align:start position:0%
+you have lost all possible length scale
+because you can nucleate a bubble of gas
+
+ align:start position:0%
+because you can nucleate a bubble of gas
+ 
+
+ align:start position:0%
+because you can nucleate a bubble of gas
+of any size with zero cost so if you
+
+ align:start position:0%
+of any size with zero cost so if you
+ 
+
+ align:start position:0%
+of any size with zero cost so if you
+think at the transformation from a
+
+ align:start position:0%
+think at the transformation from a
+ 
+
+ align:start position:0%
+think at the transformation from a
+liquid to a vapor as the nucleation of
+
+ align:start position:0%
+liquid to a vapor as the nucleation of
+ 
+
+ align:start position:0%
+liquid to a vapor as the nucleation of
+bubble of gas exactly at the temperature
+
+ align:start position:0%
+bubble of gas exactly at the temperature
+ 
+
+ align:start position:0%
+bubble of gas exactly at the temperature
+of the transition that cost has become
+
+ align:start position:0%
+of the transition that cost has become
+ 
+
+ align:start position:0%
+of the transition that cost has become
+zero and we can nucleate bubble of any
+
+ align:start position:0%
+zero and we can nucleate bubble of any
+ 
+
+ align:start position:0%
+zero and we can nucleate bubble of any
+size so the phase transition is a moment
+
+ align:start position:0%
+size so the phase transition is a moment
+ 
+
+ align:start position:0%
+size so the phase transition is a moment
+where we lose lens scales the
+
+ align:start position:0%
+where we lose lens scales the
+ 
+
+ align:start position:0%
+where we lose lens scales the
+fluctuation can have any size and so any
+
+ align:start position:0%
+fluctuation can have any size and so any
+ 
+
+ align:start position:0%
+fluctuation can have any size and so any
+kind of finite simulation will break
+
+ align:start position:0%
+kind of finite simulation will break
+ 
+
+ align:start position:0%
+kind of finite simulation will break
+down because it's really only in the
+
+ align:start position:0%
+down because it's really only in the
+ 
+
+ align:start position:0%
+down because it's really only in the
+infinite system that we represent
+
+ align:start position:0%
+infinite system that we represent
+ 
+
+ align:start position:0%
+infinite system that we represent
+appropriately all this sizes popping up
+
+ align:start position:0%
+appropriately all this sizes popping up
+ 
+
+ align:start position:0%
+appropriately all this sizes popping up
+in our system and so that's why it
+
+ align:start position:0%
+in our system and so that's why it
+ 
+
+ align:start position:0%
+in our system and so that's why it
+becomes very difficult to to study
+
+ align:start position:0%
+becomes very difficult to to study
+ 
+
+ align:start position:0%
+becomes very difficult to to study
+accurately say a boundary at a phase
+
+ align:start position:0%
+accurately say a boundary at a phase
+ 
+
+ align:start position:0%
+accurately say a boundary at a phase
+transition we say that the land scale
+
+ align:start position:0%
+transition we say that the land scale
+ 
+
+ align:start position:0%
+transition we say that the land scale
+start diverging and that's why one needs
+
+ align:start position:0%
+start diverging and that's why one needs
+ 
+
+ align:start position:0%
+start diverging and that's why one needs
+to be careful this problem is not as
+
+ align:start position:0%
+to be careful this problem is not as
+ 
+
+ align:start position:0%
+to be careful this problem is not as
+serious as the problem of time scales uh
+
+ align:start position:0%
+serious as the problem of time scales uh
+ 
+
+ align:start position:0%
+serious as the problem of time scales uh
+but it's still you know one that you
+
+ align:start position:0%
+but it's still you know one that you
+ 
+
+ align:start position:0%
+but it's still you know one that you
+want to um consider very carefully and
+
+ align:start position:0%
+want to um consider very carefully and
+ 
+
+ align:start position:0%
+want to um consider very carefully and
+once you need also to spend some time
+
+ align:start position:0%
+once you need also to spend some time
+ 
+
+ align:start position:0%
+once you need also to spend some time
+thinking actually that is uh often we
+
+ align:start position:0%
+thinking actually that is uh often we
+ 
+
+ align:start position:0%
+thinking actually that is uh often we
+use a periodic boundary condition to
+
+ align:start position:0%
+use a periodic boundary condition to
+ 
+
+ align:start position:0%
+use a periodic boundary condition to
+describe an extent system and so the
+
+ align:start position:0%
+describe an extent system and so the
+ 
+
+ align:start position:0%
+describe an extent system and so the
+question that you always have to ask
+
+ align:start position:0%
+question that you always have to ask
+ 
+
+ align:start position:0%
+question that you always have to ask
+yourself is how large should I make my
+
+ align:start position:0%
+yourself is how large should I make my
+ 
+
+ align:start position:0%
+yourself is how large should I make my
+unit system that is periodically
+
+ align:start position:0%
+unit system that is periodically
+ 
+
+ align:start position:0%
+unit system that is periodically
+repeated before it's really describing
+
+ align:start position:0%
+repeated before it's really describing
+ 
+
+ align:start position:0%
+repeated before it's really describing
+accurately the infinite system that is
+
+ align:start position:0%
+accurately the infinite system that is
+ 
+
+ align:start position:0%
+accurately the infinite system that is
+the goal of my simulation suppose that
+
+ align:start position:0%
+the goal of my simulation suppose that
+ 
+
+ align:start position:0%
+the goal of my simulation suppose that
+you want to study water okay or suppose
+
+ align:start position:0%
+you want to study water okay or suppose
+ 
+
+ align:start position:0%
+you want to study water okay or suppose
+that you want to study any
+
+ align:start position:0%
+that you want to study any
+ 
+
+ align:start position:0%
+that you want to study any
+liquid in principle you want an infinite
+
+ align:start position:0%
+liquid in principle you want an infinite
+ 
+
+ align:start position:0%
+liquid in principle you want an infinite
+system in practice you can deal only
+
+ align:start position:0%
+system in practice you can deal only
+ 
+
+ align:start position:0%
+system in practice you can deal only
+with a finite number of degrees of
+
+ align:start position:0%
+with a finite number of degrees of
+ 
+
+ align:start position:0%
+with a finite number of degrees of
+freedom so the two possibilities that
+
+ align:start position:0%
+freedom so the two possibilities that
+ 
+
+ align:start position:0%
+freedom so the two possibilities that
+you have you could study a droplet of
+
+ align:start position:0%
+you have you could study a droplet of
+ 
+
+ align:start position:0%
+you have you could study a droplet of
+water okay but then obviously uh you
+
+ align:start position:0%
+water okay but then obviously uh you
+ 
+
+ align:start position:0%
+water okay but then obviously uh you
+encounter the problem that when you
+
+ align:start position:0%
+encounter the problem that when you
+ 
+
+ align:start position:0%
+encounter the problem that when you
+study a droplet you have a very large
+
+ align:start position:0%
+study a droplet you have a very large
+ 
+
+ align:start position:0%
+study a droplet you have a very large
+influence coming from the surface effect
+
+ align:start position:0%
+influence coming from the surface effect
+ 
+
+ align:start position:0%
+influence coming from the surface effect
+the droplet is a droplet because of the
+
+ align:start position:0%
+the droplet is a droplet because of the
+ 
+
+ align:start position:0%
+the droplet is a droplet because of the
+surface tension and before reaching the
+
+ align:start position:0%
+surface tension and before reaching the
+ 
+
+ align:start position:0%
+surface tension and before reaching the
+thermodynamic limit of that droplet
+
+ align:start position:0%
+thermodynamic limit of that droplet
+ 
+
+ align:start position:0%
+thermodynamic limit of that droplet
+behaving as a bulk liquid you need
+
+ align:start position:0%
+behaving as a bulk liquid you need
+ 
+
+ align:start position:0%
+behaving as a bulk liquid you need
+really to go to a normal most sizes If
+
+ align:start position:0%
+really to go to a normal most sizes If
+ 
+
+ align:start position:0%
+really to go to a normal most sizes If
+instead you study say the same number of
+
+ align:start position:0%
+instead you study say the same number of
+ 
+
+ align:start position:0%
+instead you study say the same number of
+molecules in periodic boundary
+
+ align:start position:0%
+molecules in periodic boundary
+ 
+
+ align:start position:0%
+molecules in periodic boundary
+conditions you eliminate the presence of
+
+ align:start position:0%
+conditions you eliminate the presence of
+ 
+
+ align:start position:0%
+conditions you eliminate the presence of
+the surface and so you can reach the
+
+ align:start position:0%
+the surface and so you can reach the
+ 
+
+ align:start position:0%
+the surface and so you can reach the
+thermodynamic limit of the system
+
+ align:start position:0%
+thermodynamic limit of the system
+ 
+
+ align:start position:0%
+thermodynamic limit of the system
+behaving as a bulk much faster but still
+
+ align:start position:0%
+behaving as a bulk much faster but still
+ 
+
+ align:start position:0%
+behaving as a bulk much faster but still
+you need to always ask your question is
+
+ align:start position:0%
+you need to always ask your question is
+ 
+
+ align:start position:0%
+you need to always ask your question is
+your simulation cell large enough and
+
+ align:start position:0%
+your simulation cell large enough and
+ 
+
+ align:start position:0%
+your simulation cell large enough and
+there is a size that is large enough and
+
+ align:start position:0%
+there is a size that is large enough and
+ 
+
+ align:start position:0%
+there is a size that is large enough and
+that's the other very important concept
+
+ align:start position:0%
+that's the other very important concept
+ 
+
+ align:start position:0%
+that's the other very important concept
+that is whenever your simulation cell is
+
+ align:start position:0%
+that is whenever your simulation cell is
+ 
+
+ align:start position:0%
+that is whenever your simulation cell is
+so large that the Dynamics of one water
+
+ align:start position:0%
+so large that the Dynamics of one water
+ 
+
+ align:start position:0%
+so large that the Dynamics of one water
+molecule doesn't affect the Dynamics of
+
+ align:start position:0%
+molecule doesn't affect the Dynamics of
+ 
+
+ align:start position:0%
+molecule doesn't affect the Dynamics of
+a water molecule that is far away from
+
+ align:start position:0%
+a water molecule that is far away from
+ 
+
+ align:start position:0%
+a water molecule that is far away from
+your as much as it is its periodic image
+
+ align:start position:0%
+your as much as it is its periodic image
+ 
+
+ align:start position:0%
+your as much as it is its periodic image
+your system has become infinite that is
+
+ align:start position:0%
+your system has become infinite that is
+ 
+
+ align:start position:0%
+your system has become infinite that is
+whenever you are sort of a molecule in a
+
+ align:start position:0%
+whenever you are sort of a molecule in a
+ 
+
+ align:start position:0%
+whenever you are sort of a molecule in a
+liquid you really dynamically interact
+
+ align:start position:0%
+liquid you really dynamically interact
+ 
+
+ align:start position:0%
+liquid you really dynamically interact
+not with every other molecule in the
+
+ align:start position:0%
+not with every other molecule in the
+ 
+
+ align:start position:0%
+not with every other molecule in the
+infinite liquid but only with sort of a
+
+ align:start position:0%
+infinite liquid but only with sort of a
+ 
+
+ align:start position:0%
+infinite liquid but only with sort of a
+sphere of neighbors and you need to
+
+ align:start position:0%
+sphere of neighbors and you need to
+ 
+
+ align:start position:0%
+sphere of neighbors and you need to
+understand how large is that sphere of
+
+ align:start position:0%
+understand how large is that sphere of
+ 
+
+ align:start position:0%
+understand how large is that sphere of
+neighbors because those and only those
+
+ align:start position:0%
+neighbors because those and only those
+ 
+
+ align:start position:0%
+neighbors because those and only those
+are the molecules that affect yourself
+
+ align:start position:0%
+are the molecules that affect yourself
+ 
+
+ align:start position:0%
+are the molecules that affect yourself
+in the center of that sphere and if you
+
+ align:start position:0%
+in the center of that sphere and if you
+ 
+
+ align:start position:0%
+in the center of that sphere and if you
+decide that you know for a a water
+
+ align:start position:0%
+decide that you know for a a water
+ 
+
+ align:start position:0%
+decide that you know for a a water
+molecule at room temperature the sphere
+
+ align:start position:0%
+molecule at room temperature the sphere
+ 
+
+ align:start position:0%
+molecule at room temperature the sphere
+of neighbors with which there is a
+
+ align:start position:0%
+of neighbors with which there is a
+ 
+
+ align:start position:0%
+of neighbors with which there is a
+dynamical interaction as only a radius
+
+ align:start position:0%
+dynamical interaction as only a radius
+ 
+
+ align:start position:0%
+dynamical interaction as only a radius
+of 10 anstrom whenever your unit cell is
+
+ align:start position:0%
+of 10 anstrom whenever your unit cell is
+ 
+
+ align:start position:0%
+of 10 anstrom whenever your unit cell is
+larger is a cube say larger than 20
+
+ align:start position:0%
+larger is a cube say larger than 20
+ 
+
+ align:start position:0%
+larger is a cube say larger than 20
+anrom inside you are studying in
+
+ align:start position:0%
+anrom inside you are studying in
+ 
+
+ align:start position:0%
+anrom inside you are studying in
+practice an infinite system because
+
+ align:start position:0%
+practice an infinite system because
+ 
+
+ align:start position:0%
+practice an infinite system because
+every molecule in that system sees all
+
+ align:start position:0%
+every molecule in that system sees all
+ 
+
+ align:start position:0%
+every molecule in that system sees all
+the independent neighbors that needs to
+
+ align:start position:0%
+the independent neighbors that needs to
+ 
+
+ align:start position:0%
+the independent neighbors that needs to
+see okay so even a simulation with a
+
+ align:start position:0%
+see okay so even a simulation with a
+ 
+
+ align:start position:0%
+see okay so even a simulation with a
+finite number of molecules can reproduce
+
+ align:start position:0%
+finite number of molecules can reproduce
+ 
+
+ align:start position:0%
+finite number of molecules can reproduce
+exactly the behavior of an infinite
+
+ align:start position:0%
+exactly the behavior of an infinite
+ 
+
+ align:start position:0%
+exactly the behavior of an infinite
+system provide that a molecule interacts
+
+ align:start position:0%
+system provide that a molecule interacts
+ 
+
+ align:start position:0%
+system provide that a molecule interacts
+with other independent molecules up to a
+
+ align:start position:0%
+with other independent molecules up to a
+ 
+
+ align:start position:0%
+with other independent molecules up to a
+sort of you know maximum range of
+
+ align:start position:0%
+sort of you know maximum range of
+ 
+
+ align:start position:0%
+sort of you know maximum range of
+dynamical correlation and we actually
+
+ align:start position:0%
+dynamical correlation and we actually
+ 
+
+ align:start position:0%
+dynamical correlation and we actually
+sort of Define this quantity in the
+
+ align:start position:0%
+sort of Define this quantity in the
+ 
+
+ align:start position:0%
+sort of Define this quantity in the
+lecture that follows uh so again lens
+
+ align:start position:0%
+lecture that follows uh so again lens
+ 
+
+ align:start position:0%
+lecture that follows uh so again lens
+scale are another problem uh and a
+
+ align:start position:0%
+scale are another problem uh and a
+ 
+
+ align:start position:0%
+scale are another problem uh and a
+problem in which periodic boundary
+
+ align:start position:0%
+problem in which periodic boundary
+ 
+
+ align:start position:0%
+problem in which periodic boundary
+conditions tend to help a lot but again
+
+ align:start position:0%
+conditions tend to help a lot but again
+ 
+
+ align:start position:0%
+conditions tend to help a lot but again
+suppose that you want to study something
+
+ align:start position:0%
+suppose that you want to study something
+ 
+
+ align:start position:0%
+suppose that you want to study something
+like the strength of a metal well you
+
+ align:start position:0%
+like the strength of a metal well you
+ 
+
+ align:start position:0%
+like the strength of a metal well you
+have now a problem in which a lot of
+
+ align:start position:0%
+have now a problem in which a lot of
+ 
+
+ align:start position:0%
+have now a problem in which a lot of
+lens scale becomes intertwined because
+
+ align:start position:0%
+lens scale becomes intertwined because
+ 
+
+ align:start position:0%
+lens scale becomes intertwined because
+in the strength of a metal uh you know
+
+ align:start position:0%
+in the strength of a metal uh you know
+ 
+
+ align:start position:0%
+in the strength of a metal uh you know
+you might want to consider what is the
+
+ align:start position:0%
+you might want to consider what is the
+ 
+
+ align:start position:0%
+you might want to consider what is the
+dynamic dynamics of impurities that
+
+ align:start position:0%
+dynamic dynamics of impurities that
+ 
+
+ align:start position:0%
+dynamic dynamics of impurities that
+strengthen that metal like if you have
+
+ align:start position:0%
+strengthen that metal like if you have
+ 
+
+ align:start position:0%
+strengthen that metal like if you have
+steel you have carbon atoms in between
+
+ align:start position:0%
+steel you have carbon atoms in between
+ 
+
+ align:start position:0%
+steel you have carbon atoms in between
+the iron and so you need to understand
+
+ align:start position:0%
+the iron and so you need to understand
+ 
+
+ align:start position:0%
+the iron and so you need to understand
+what is the atomic Dynamics but then
+
+ align:start position:0%
+what is the atomic Dynamics but then
+ 
+
+ align:start position:0%
+what is the atomic Dynamics but then
+there will be a dynamics of units on a
+
+ align:start position:0%
+there will be a dynamics of units on a
+ 
+
+ align:start position:0%
+there will be a dynamics of units on a
+larger lens scale because in a metal
+
+ align:start position:0%
+larger lens scale because in a metal
+ 
+
+ align:start position:0%
+larger lens scale because in a metal
+there's going to be this location and
+
+ align:start position:0%
+there's going to be this location and
+ 
+
+ align:start position:0%
+there's going to be this location and
+sleep and glide planes and so there is
+
+ align:start position:0%
+sleep and glide planes and so there is
+ 
+
+ align:start position:0%
+sleep and glide planes and so there is
+coordinated
+
+ align:start position:0%
+coordinated
+ 
+
+ align:start position:0%
+coordinated
+motion of thousands of atoms that you
+
+ align:start position:0%
+motion of thousands of atoms that you
+ 
+
+ align:start position:0%
+motion of thousands of atoms that you
+want to consider and then in reality a
+
+ align:start position:0%
+want to consider and then in reality a
+ 
+
+ align:start position:0%
+want to consider and then in reality a
+real metal is never a crystal but it's
+
+ align:start position:0%
+real metal is never a crystal but it's
+ 
+
+ align:start position:0%
+real metal is never a crystal but it's
+always a poly crystalling material so
+
+ align:start position:0%
+always a poly crystalling material so
+ 
+
+ align:start position:0%
+always a poly crystalling material so
+you have grains and inside that grain
+
+ align:start position:0%
+you have grains and inside that grain
+ 
+
+ align:start position:0%
+you have grains and inside that grain
+you have a consistent ordering of the
+
+ align:start position:0%
+you have a consistent ordering of the
+ 
+
+ align:start position:0%
+you have a consistent ordering of the
+atoms but then grains are mismatched and
+
+ align:start position:0%
+atoms but then grains are mismatched and
+ 
+
+ align:start position:0%
+atoms but then grains are mismatched and
+there are grain boundaries and so you
+
+ align:start position:0%
+there are grain boundaries and so you
+ 
+
+ align:start position:0%
+there are grain boundaries and so you
+have a lot of lens scales to consider if
+
+ align:start position:0%
+have a lot of lens scales to consider if
+ 
+
+ align:start position:0%
+have a lot of lens scales to consider if
+you really want to predict what would be
+
+ align:start position:0%
+you really want to predict what would be
+ 
+
+ align:start position:0%
+you really want to predict what would be
+the mechanical response of a real
+
+ align:start position:0%
+the mechanical response of a real
+ 
+
+ align:start position:0%
+the mechanical response of a real
+system okay so this is the challenge if
+
+ align:start position:0%
+system okay so this is the challenge if
+ 
+
+ align:start position:0%
+system okay so this is the challenge if
+you want number two uh the challenge
+
+ align:start position:0%
+you want number two uh the challenge
+ 
+
+ align:start position:0%
+you want number two uh the challenge
+number three is the one that we have
+
+ align:start position:0%
+number three is the one that we have
+ 
+
+ align:start position:0%
+number three is the one that we have
+sort of described more in detail up to
+
+ align:start position:0%
+sort of described more in detail up to
+ 
+
+ align:start position:0%
+sort of described more in detail up to
+now that is determining how accurate
+
+ align:start position:0%
+now that is determining how accurate
+ 
+
+ align:start position:0%
+now that is determining how accurate
+can be your prediction of the
+
+ align:start position:0%
+can be your prediction of the
+ 
+
+ align:start position:0%
+can be your prediction of the
+interaction between nuclei and you have
+
+ align:start position:0%
+interaction between nuclei and you have
+ 
+
+ align:start position:0%
+interaction between nuclei and you have
+seen everything that you know we could
+
+ align:start position:0%
+seen everything that you know we could
+ 
+
+ align:start position:0%
+seen everything that you know we could
+tell you about empirical potential
+
+ align:start position:0%
+tell you about empirical potential
+ 
+
+ align:start position:0%
+tell you about empirical potential
+quantum mechanical simulations and in
+
+ align:start position:0%
+quantum mechanical simulations and in
+ 
+
+ align:start position:0%
+quantum mechanical simulations and in
+principle even if it's obviously very
+
+ align:start position:0%
+principle even if it's obviously very
+ 
+
+ align:start position:0%
+principle even if it's obviously very
+expensive to make very accurate
+
+ align:start position:0%
+expensive to make very accurate
+ 
+
+ align:start position:0%
+expensive to make very accurate
+prediction of the interaction between
+
+ align:start position:0%
+prediction of the interaction between
+ 
+
+ align:start position:0%
+prediction of the interaction between
+atoms in principle is the less
+
+ align:start position:0%
+atoms in principle is the less
+ 
+
+ align:start position:0%
+atoms in principle is the less
+conceptually challenging of the problems
+
+ align:start position:0%
+conceptually challenging of the problems
+ 
+
+ align:start position:0%
+conceptually challenging of the problems
+I mean we can just you know sort of try
+
+ align:start position:0%
+I mean we can just you know sort of try
+ 
+
+ align:start position:0%
+I mean we can just you know sort of try
+all our sort of electronic structure
+
+ align:start position:0%
+all our sort of electronic structure
+ 
+
+ align:start position:0%
+all our sort of electronic structure
+Methods at will and we can sort of to
+
+ align:start position:0%
+Methods at will and we can sort of to
+ 
+
+ align:start position:0%
+Methods at will and we can sort of to
+try to see how accurate we become and
+
+ align:start position:0%
+try to see how accurate we become and
+ 
+
+ align:start position:0%
+try to see how accurate we become and
+the last challenge that is also not
+
+ align:start position:0%
+the last challenge that is also not
+ 
+
+ align:start position:0%
+the last challenge that is also not
+really a conceptual
+
+ align:start position:0%
+really a conceptual
+ 
+
+ align:start position:0%
+really a conceptual
+challenge uh and sort of you know it can
+
+ align:start position:0%
+challenge uh and sort of you know it can
+ 
+
+ align:start position:0%
+challenge uh and sort of you know it can
+be solved but it's just a very um
+
+ align:start position:0%
+be solved but it's just a very um
+ 
+
+ align:start position:0%
+be solved but it's just a very um
+expensive one to overcome is this one in
+
+ align:start position:0%
+expensive one to overcome is this one in
+ 
+
+ align:start position:0%
+expensive one to overcome is this one in
+which we TR we treat the nuclei as
+
+ align:start position:0%
+which we TR we treat the nuclei as
+ 
+
+ align:start position:0%
+which we TR we treat the nuclei as
+classical as classical particles and
+
+ align:start position:0%
+classical as classical particles and
+ 
+
+ align:start position:0%
+classical as classical particles and
+that's s to be in general very good but
+
+ align:start position:0%
+that's s to be in general very good but
+ 
+
+ align:start position:0%
+that's s to be in general very good but
+it's sort of an approximation that
+
+ align:start position:0%
+it's sort of an approximation that
+ 
+
+ align:start position:0%
+it's sort of an approximation that
+breaks down the more you go towards
+
+ align:start position:0%
+breaks down the more you go towards
+ 
+
+ align:start position:0%
+breaks down the more you go towards
+lighter and lighter nuclei because
+
+ align:start position:0%
+lighter and lighter nuclei because
+ 
+
+ align:start position:0%
+lighter and lighter nuclei because
+remember the BR relation your wavelength
+
+ align:start position:0%
+remember the BR relation your wavelength
+ 
+
+ align:start position:0%
+remember the BR relation your wavelength
+times your momentum is equal to the pl
+
+ align:start position:0%
+times your momentum is equal to the pl
+ 
+
+ align:start position:0%
+times your momentum is equal to the pl
+constant so the lighter you are the
+
+ align:start position:0%
+constant so the lighter you are the
+ 
+
+ align:start position:0%
+constant so the lighter you are the
+smaller your momentum the longer your
+
+ align:start position:0%
+smaller your momentum the longer your
+ 
+
+ align:start position:0%
+smaller your momentum the longer your
+wavelength the more Quantum you become
+
+ align:start position:0%
+wavelength the more Quantum you become
+ 
+
+ align:start position:0%
+wavelength the more Quantum you become
+so something like hydrogen that has a
+
+ align:start position:0%
+so something like hydrogen that has a
+ 
+
+ align:start position:0%
+so something like hydrogen that has a
+nucleus that is just one proton so it's
+
+ align:start position:0%
+nucleus that is just one proton so it's
+ 
+
+ align:start position:0%
+nucleus that is just one proton so it's
+fairly light or it's the lightest of all
+
+ align:start position:0%
+fairly light or it's the lightest of all
+ 
+
+ align:start position:0%
+fairly light or it's the lightest of all
+possible nucle tend to still have a
+
+ align:start position:0%
+possible nucle tend to still have a
+ 
+
+ align:start position:0%
+possible nucle tend to still have a
+significant Quantum properties even at
+
+ align:start position:0%
+significant Quantum properties even at
+ 
+
+ align:start position:0%
+significant Quantum properties even at
+relatively high temperatures you see the
+
+ align:start position:0%
+relatively high temperatures you see the
+ 
+
+ align:start position:0%
+relatively high temperatures you see the
+more you increase the temperature the
+
+ align:start position:0%
+more you increase the temperature the
+ 
+
+ align:start position:0%
+more you increase the temperature the
+more the average momentum of your
+
+ align:start position:0%
+more the average momentum of your
+ 
+
+ align:start position:0%
+more the average momentum of your
+particles becomes and the more sort of
+
+ align:start position:0%
+particles becomes and the more sort of
+ 
+
+ align:start position:0%
+particles becomes and the more sort of
+classical they become but the lower the
+
+ align:start position:0%
+classical they become but the lower the
+ 
+
+ align:start position:0%
+classical they become but the lower the
+temperature the more Quantum they become
+
+ align:start position:0%
+temperature the more Quantum they become
+ 
+
+ align:start position:0%
+temperature the more Quantum they become
+and something like hydrogen is still
+
+ align:start position:0%
+and something like hydrogen is still
+ 
+
+ align:start position:0%
+and something like hydrogen is still
+significantly Quantum at room
+
+ align:start position:0%
+significantly Quantum at room
+ 
+
+ align:start position:0%
+significantly Quantum at room
+temperature and what that does that mean
+
+ align:start position:0%
+temperature and what that does that mean
+ 
+
+ align:start position:0%
+temperature and what that does that mean
+well it means that that particle it's
+
+ align:start position:0%
+well it means that that particle it's
+ 
+
+ align:start position:0%
+well it means that that particle it's
+really a delocalized system that can
+
+ align:start position:0%
+really a delocalized system that can
+ 
+
+ align:start position:0%
+really a delocalized system that can
+actually tunnel through through barrier
+
+ align:start position:0%
+actually tunnel through through barrier
+ 
+
+ align:start position:0%
+actually tunnel through through barrier
+that's if you want one of the important
+
+ align:start position:0%
+that's if you want one of the important
+ 
+
+ align:start position:0%
+that's if you want one of the important
+difference between a particle that
+
+ align:start position:0%
+difference between a particle that
+ 
+
+ align:start position:0%
+difference between a particle that
+behaves according to classical mechanics
+
+ align:start position:0%
+behaves according to classical mechanics
+ 
+
+ align:start position:0%
+behaves according to classical mechanics
+and one that behaves according to
+
+ align:start position:0%
+and one that behaves according to
+ 
+
+ align:start position:0%
+and one that behaves according to
+Quantum Mechanics if you are behaving as
+
+ align:start position:0%
+Quantum Mechanics if you are behaving as
+ 
+
+ align:start position:0%
+Quantum Mechanics if you are behaving as
+a classical particle you need to have
+
+ align:start position:0%
+a classical particle you need to have
+ 
+
+ align:start position:0%
+a classical particle you need to have
+enough kinetic energy to overcome a
+
+ align:start position:0%
+enough kinetic energy to overcome a
+ 
+
+ align:start position:0%
+enough kinetic energy to overcome a
+barrier if you are a skier and you are
+
+ align:start position:0%
+barrier if you are a skier and you are
+ 
+
+ align:start position:0%
+barrier if you are a skier and you are
+in a valley and you want to go in the
+
+ align:start position:0%
+in a valley and you want to go in the
+ 
+
+ align:start position:0%
+in a valley and you want to go in the
+other Valley you need to have enough
+
+ align:start position:0%
+other Valley you need to have enough
+ 
+
+ align:start position:0%
+other Valley you need to have enough
+velocity to be able to overcome the
+
+ align:start position:0%
+velocity to be able to overcome the
+ 
+
+ align:start position:0%
+velocity to be able to overcome the
+mountain if you are a Quantum skier you
+
+ align:start position:0%
+mountain if you are a Quantum skier you
+ 
+
+ align:start position:0%
+mountain if you are a Quantum skier you
+can actually have some finite
+
+ align:start position:0%
+can actually have some finite
+ 
+
+ align:start position:0%
+can actually have some finite
+probability of tunnel through and so
+
+ align:start position:0%
+probability of tunnel through and so
+ 
+
+ align:start position:0%
+probability of tunnel through and so
+there are sort of you know tunneling
+
+ align:start position:0%
+there are sort of you know tunneling
+ 
+
+ align:start position:0%
+there are sort of you know tunneling
+problems that are
+
+ align:start position:0%
+problems that are
+ 
+
+ align:start position:0%
+problems that are
+important not only for hydrogen but
+
+ align:start position:0%
+important not only for hydrogen but
+ 
+
+ align:start position:0%
+important not only for hydrogen but
+sometimes even for much more massive
+
+ align:start position:0%
+sometimes even for much more massive
+ 
+
+ align:start position:0%
+sometimes even for much more massive
+particles or even for groups of
+
+ align:start position:0%
+particles or even for groups of
+ 
+
+ align:start position:0%
+particles or even for groups of
+particles provided that the energy
+
+ align:start position:0%
+particles provided that the energy
+ 
+
+ align:start position:0%
+particles provided that the energy
+barrier that they need to overcome is uh
+
+ align:start position:0%
+barrier that they need to overcome is uh
+ 
+
+ align:start position:0%
+barrier that they need to overcome is uh
+small enough and I've shown you in the
+
+ align:start position:0%
+small enough and I've shown you in the
+ 
+
+ align:start position:0%
+small enough and I've shown you in the
+first Quantum class an example in a PA
+
+ align:start position:0%
+first Quantum class an example in a PA
+ 
+
+ align:start position:0%
+first Quantum class an example in a PA
+of Sky crystal in which we have this
+
+ align:start position:0%
+of Sky crystal in which we have this
+ 
+
+ align:start position:0%
+of Sky crystal in which we have this
+cubic structure with an octal cage of
+
+ align:start position:0%
+cubic structure with an octal cage of
+ 
+
+ align:start position:0%
+cubic structure with an octal cage of
+oxygen that can sort of you know
+
+ align:start position:0%
+oxygen that can sort of you know
+ 
+
+ align:start position:0%
+oxygen that can sort of you know
+configure itself in a ground state that
+
+ align:start position:0%
+configure itself in a ground state that
+ 
+
+ align:start position:0%
+configure itself in a ground state that
+is ferroelectric in which the oxygen
+
+ align:start position:0%
+is ferroelectric in which the oxygen
+ 
+
+ align:start position:0%
+is ferroelectric in which the oxygen
+cage displaces with respect to the sort
+
+ align:start position:0%
+cage displaces with respect to the sort
+ 
+
+ align:start position:0%
+cage displaces with respect to the sort
+of cubic Symmetry and induces a
+
+ align:start position:0%
+of cubic Symmetry and induces a
+ 
+
+ align:start position:0%
+of cubic Symmetry and induces a
+permanent electrical diple in your
+
+ align:start position:0%
+permanent electrical diple in your
+ 
+
+ align:start position:0%
+permanent electrical diple in your
+system well there are certain materials
+
+ align:start position:0%
+system well there are certain materials
+ 
+
+ align:start position:0%
+system well there are certain materials
+that have this structure but uh since
+
+ align:start position:0%
+that have this structure but uh since
+ 
+
+ align:start position:0%
+that have this structure but uh since
+that the octal cage can have roughly six
+
+ align:start position:0%
+that the octal cage can have roughly six
+ 
+
+ align:start position:0%
+that the octal cage can have roughly six
+possible choices on where to move off
+
+ align:start position:0%
+possible choices on where to move off
+ 
+
+ align:start position:0%
+possible choices on where to move off
+site if you decrease the temperature
+
+ align:start position:0%
+site if you decrease the temperature
+ 
+
+ align:start position:0%
+site if you decrease the temperature
+enough the oxygen case will start
+
+ align:start position:0%
+enough the oxygen case will start
+ 
+
+ align:start position:0%
+enough the oxygen case will start
+actually tunneling between all the six
+
+ align:start position:0%
+actually tunneling between all the six
+ 
+
+ align:start position:0%
+actually tunneling between all the six
+possibilities instead of sort of finding
+
+ align:start position:0%
+possibilities instead of sort of finding
+ 
+
+ align:start position:0%
+possibilities instead of sort of finding
+itself at zero temperature in a broken
+
+ align:start position:0%
+itself at zero temperature in a broken
+ 
+
+ align:start position:0%
+itself at zero temperature in a broken
+symmetry configuration in which the
+
+ align:start position:0%
+symmetry configuration in which the
+ 
+
+ align:start position:0%
+symmetry configuration in which the
+oxygen cage has chosen one of those six
+
+ align:start position:0%
+oxygen cage has chosen one of those six
+ 
+
+ align:start position:0%
+oxygen cage has chosen one of those six
+possibilities in reality because of
+
+ align:start position:0%
+possibilities in reality because of
+ 
+
+ align:start position:0%
+possibilities in reality because of
+quantum tunneling it keeps tunneling
+
+ align:start position:0%
+quantum tunneling it keeps tunneling
+ 
+
+ align:start position:0%
+quantum tunneling it keeps tunneling
+between all the six possibilities and on
+
+ align:start position:0%
+between all the six possibilities and on
+ 
+
+ align:start position:0%
+between all the six possibilities and on
+average your system looks cubic and on
+
+ align:start position:0%
+average your system looks cubic and on
+ 
+
+ align:start position:0%
+average your system looks cubic and on
+average you don't have really any Fair
+
+ align:start position:0%
+average you don't have really any Fair
+ 
+
+ align:start position:0%
+average you don't have really any Fair
+electricity but the polarizability of
+
+ align:start position:0%
+electricity but the polarizability of
+ 
+
+ align:start position:0%
+electricity but the polarizability of
+the system is going to be different from
+
+ align:start position:0%
+the system is going to be different from
+ 
+
+ align:start position:0%
+the system is going to be different from
+that one in which the octal cage was
+
+ align:start position:0%
+that one in which the octal cage was
+ 
+
+ align:start position:0%
+that one in which the octal cage was
+sitting squarely in the cube so there is
+
+ align:start position:0%
+sitting squarely in the cube so there is
+ 
+
+ align:start position:0%
+sitting squarely in the cube so there is
+a dialectric response that is different
+
+ align:start position:0%
+a dialectric response that is different
+ 
+
+ align:start position:0%
+a dialectric response that is different
+so there are sort of cases that at the
+
+ align:start position:0%
+so there are sort of cases that at the
+ 
+
+ align:start position:0%
+so there are sort of cases that at the
+end are a sort of you know uh fairly
+
+ align:start position:0%
+end are a sort of you know uh fairly
+ 
+
+ align:start position:0%
+end are a sort of you know uh fairly
+exotic I would say for most application
+
+ align:start position:0%
+exotic I would say for most application
+ 
+
+ align:start position:0%
+exotic I would say for most application
+in which tunneling effects of the nuclei
+
+ align:start position:0%
+in which tunneling effects of the nuclei
+ 
+
+ align:start position:0%
+in which tunneling effects of the nuclei
+could become
+
+ align:start position:0%
+could become
+ 
+
+ align:start position:0%
+could become
+important but there is one other
+
+ align:start position:0%
+important but there is one other
+ 
+
+ align:start position:0%
+important but there is one other
+important consequence that comes from
+
+ align:start position:0%
+important consequence that comes from
+ 
+
+ align:start position:0%
+important consequence that comes from
+quantum mechanics that tends to be
+
+ align:start position:0%
+quantum mechanics that tends to be
+ 
+
+ align:start position:0%
+quantum mechanics that tends to be
+important in a lot of cases and that
+
+ align:start position:0%
+important in a lot of cases and that
+ 
+
+ align:start position:0%
+important in a lot of cases and that
+consequence has to do with the
+
+ align:start position:0%
+consequence has to do with the
+ 
+
+ align:start position:0%
+consequence has to do with the
+quantization of vibrational
+
+ align:start position:0%
+quantization of vibrational
+ 
+
+ align:start position:0%
+quantization of vibrational
+excitations that is if you look at the
+
+ align:start position:0%
+excitations that is if you look at the
+ 
+
+ align:start position:0%
+excitations that is if you look at the
+motion of any system a molecule a solid
+
+ align:start position:0%
+motion of any system a molecule a solid
+ 
+
+ align:start position:0%
+motion of any system a molecule a solid
+In classical terms while that molecule
+
+ align:start position:0%
+In classical terms while that molecule
+ 
+
+ align:start position:0%
+In classical terms while that molecule
+or that solid can have any amount of
+
+ align:start position:0%
+or that solid can have any amount of
+ 
+
+ align:start position:0%
+or that solid can have any amount of
+kinetic energy in a hydrogen molecule
+
+ align:start position:0%
+kinetic energy in a hydrogen molecule
+ 
+
+ align:start position:0%
+kinetic energy in a hydrogen molecule
+the atoms can have zero kinetic energy
+
+ align:start position:0%
+the atoms can have zero kinetic energy
+ 
+
+ align:start position:0%
+the atoms can have zero kinetic energy
+if we treat it classically or they can
+
+ align:start position:0%
+if we treat it classically or they can
+ 
+
+ align:start position:0%
+if we treat it classically or they can
+move just a little bit so have a very
+
+ align:start position:0%
+move just a little bit so have a very
+ 
+
+ align:start position:0%
+move just a little bit so have a very
+minute amount of kinetic energy and we
+
+ align:start position:0%
+minute amount of kinetic energy and we
+ 
+
+ align:start position:0%
+minute amount of kinetic energy and we
+can just increase the kinetic energy
+
+ align:start position:0%
+can just increase the kinetic energy
+ 
+
+ align:start position:0%
+can just increase the kinetic energy
+that those atoms can have at
+
+ align:start position:0%
+that those atoms can have at
+ 
+
+ align:start position:0%
+that those atoms can have at
+will in reality because the system is a
+
+ align:start position:0%
+will in reality because the system is a
+ 
+
+ align:start position:0%
+will in reality because the system is a
+Quantum system uh the vibrational modes
+
+ align:start position:0%
+Quantum system uh the vibrational modes
+ 
+
+ align:start position:0%
+Quantum system uh the vibrational modes
+of a molecule or the vibrational modes
+
+ align:start position:0%
+of a molecule or the vibrational modes
+ 
+
+ align:start position:0%
+of a molecule or the vibrational modes
+of a solid are actually quantized and
+
+ align:start position:0%
+of a solid are actually quantized and
+ 
+
+ align:start position:0%
+of a solid are actually quantized and
+you can't have arbitrary amounts of
+
+ align:start position:0%
+you can't have arbitrary amounts of
+ 
+
+ align:start position:0%
+you can't have arbitrary amounts of
+vibrational energy actually in its
+
+ align:start position:0%
+vibrational energy actually in its
+ 
+
+ align:start position:0%
+vibrational energy actually in its
+Quantum ground state a molecule will not
+
+ align:start position:0%
+Quantum ground state a molecule will not
+ 
+
+ align:start position:0%
+Quantum ground state a molecule will not
+be at rest but it will be in what is
+
+ align:start position:0%
+be at rest but it will be in what is
+ 
+
+ align:start position:0%
+be at rest but it will be in what is
+called the zero point Motion state that
+
+ align:start position:0%
+called the zero point Motion state that
+ 
+
+ align:start position:0%
+called the zero point Motion state that
+is what is the quantum mechanical ground
+
+ align:start position:0%
+is what is the quantum mechanical ground
+ 
+
+ align:start position:0%
+is what is the quantum mechanical ground
+state you can think at the analogy with
+
+ align:start position:0%
+state you can think at the analogy with
+ 
+
+ align:start position:0%
+state you can think at the analogy with
+the stability of the atoms uh in its
+
+ align:start position:0%
+the stability of the atoms uh in its
+ 
+
+ align:start position:0%
+the stability of the atoms uh in its
+ground state the electron around the
+
+ align:start position:0%
+ground state the electron around the
+ 
+
+ align:start position:0%
+ground state the electron around the
+proton is not collapsing onto the proton
+
+ align:start position:0%
+proton is not collapsing onto the proton
+ 
+
+ align:start position:0%
+proton is not collapsing onto the proton
+because of the cumic repulsion if the
+
+ align:start position:0%
+because of the cumic repulsion if the
+ 
+
+ align:start position:0%
+because of the cumic repulsion if the
+electron was a classical particle it
+
+ align:start position:0%
+electron was a classical particle it
+ 
+
+ align:start position:0%
+electron was a classical particle it
+would collapse on the nucleus and the
+
+ align:start position:0%
+would collapse on the nucleus and the
+ 
+
+ align:start position:0%
+would collapse on the nucleus and the
+hydrogen atom would be just a proton and
+
+ align:start position:0%
+hydrogen atom would be just a proton and
+ 
+
+ align:start position:0%
+hydrogen atom would be just a proton and
+an electron sitting in the same place
+
+ align:start position:0%
+an electron sitting in the same place
+ 
+
+ align:start position:0%
+an electron sitting in the same place
+but because the electron is quantum it
+
+ align:start position:0%
+but because the electron is quantum it
+ 
+
+ align:start position:0%
+but because the electron is quantum it
+can't really collapse and its lowest
+
+ align:start position:0%
+can't really collapse and its lowest
+ 
+
+ align:start position:0%
+can't really collapse and its lowest
+energy sta is a sta that is you know the
+
+ align:start position:0%
+energy sta is a sta that is you know the
+ 
+
+ align:start position:0%
+energy sta is a sta that is you know the
+1s orbit for the high hydrogen in which
+
+ align:start position:0%
+1s orbit for the high hydrogen in which
+ 
+
+ align:start position:0%
+1s orbit for the high hydrogen in which
+the electron is around that atom but
+
+ align:start position:0%
+the electron is around that atom but
+ 
+
+ align:start position:0%
+the electron is around that atom but
+doesn't collapse onto it and the
+
+ align:start position:0%
+doesn't collapse onto it and the
+ 
+
+ align:start position:0%
+doesn't collapse onto it and the
+excitation of that electron to the next
+
+ align:start position:0%
+excitation of that electron to the next
+ 
+
+ align:start position:0%
+excitation of that electron to the next
+energy state is a quantized excitation
+
+ align:start position:0%
+energy state is a quantized excitation
+ 
+
+ align:start position:0%
+energy state is a quantized excitation
+you can't go to a level of 1 s that has
+
+ align:start position:0%
+you can't go to a level of 1 s that has
+ 
+
+ align:start position:0%
+you can't go to a level of 1 s that has
+an energy for the hydrogen of minus one
+
+ align:start position:0%
+an energy for the hydrogen of minus one
+ 
+
+ align:start position:0%
+an energy for the hydrogen of minus one
+redberg to another state that has energy
+
+ align:start position:0%
+redberg to another state that has energy
+ 
+
+ align:start position:0%
+redberg to another state that has energy
+minus 99 orus 98 or sort of any kind of
+
+ align:start position:0%
+minus 99 orus 98 or sort of any kind of
+ 
+
+ align:start position:0%
+minus 99 orus 98 or sort of any kind of
+amount the next state in which the
+
+ align:start position:0%
+amount the next state in which the
+ 
+
+ align:start position:0%
+amount the next state in which the
+electron can live is a state that has an
+
+ align:start position:0%
+electron can live is a state that has an
+ 
+
+ align:start position:0%
+electron can live is a state that has an
+energy of Min - 1/4 and then minus 1 9th
+
+ align:start position:0%
+energy of Min - 1/4 and then minus 1 9th
+ 
+
+ align:start position:0%
+energy of Min - 1/4 and then minus 1 9th
+and so on and so forth uh the same thing
+
+ align:start position:0%
+and so on and so forth uh the same thing
+ 
+
+ align:start position:0%
+and so on and so forth uh the same thing
+happens for the vibrational level of
+
+ align:start position:0%
+happens for the vibrational level of
+ 
+
+ align:start position:0%
+happens for the vibrational level of
+molecules okay a Quantum molecule at
+
+ align:start position:0%
+molecules okay a Quantum molecule at
+ 
+
+ align:start position:0%
+molecules okay a Quantum molecule at
+sort of you know in its ground state is
+
+ align:start position:0%
+sort of you know in its ground state is
+ 
+
+ align:start position:0%
+sort of you know in its ground state is
+not in a state where the atoms do not
+
+ align:start position:0%
+not in a state where the atoms do not
+ 
+
+ align:start position:0%
+not in a state where the atoms do not
+move but it's in a state where the atoms
+
+ align:start position:0%
+move but it's in a state where the atoms
+ 
+
+ align:start position:0%
+move but it's in a state where the atoms
+have a certain amount of quantum kinetic
+
+ align:start position:0%
+have a certain amount of quantum kinetic
+ 
+
+ align:start position:0%
+have a certain amount of quantum kinetic
+energy and it's in its state called 0
+
+ align:start position:0%
+energy and it's in its state called 0
+ 
+
+ align:start position:0%
+energy and it's in its state called 0
+point motion and if you want to increase
+
+ align:start position:0%
+point motion and if you want to increase
+ 
+
+ align:start position:0%
+point motion and if you want to increase
+the kinetic energy of this molecule you
+
+ align:start position:0%
+the kinetic energy of this molecule you
+ 
+
+ align:start position:0%
+the kinetic energy of this molecule you
+can't do it continuously there is a
+
+ align:start position:0%
+can't do it continuously there is a
+ 
+
+ align:start position:0%
+can't do it continuously there is a
+quantized gap so you need to provide
+
+ align:start position:0%
+quantized gap so you need to provide
+ 
+
+ align:start position:0%
+quantized gap so you need to provide
+enough energy to heat up the system to
+
+ align:start position:0%
+enough energy to heat up the system to
+ 
+
+ align:start position:0%
+enough energy to heat up the system to
+the next state and then to the next
+
+ align:start position:0%
+the next state and then to the next
+ 
+
+ align:start position:0%
+the next state and then to the next
+state and then to the next state and
+
+ align:start position:0%
+state and then to the next state and
+ 
+
+ align:start position:0%
+state and then to the next state and
+that if you think um affects deeply how
+
+ align:start position:0%
+that if you think um affects deeply how
+ 
+
+ align:start position:0%
+that if you think um affects deeply how
+you are going to heat up a system that
+
+ align:start position:0%
+you are going to heat up a system that
+ 
+
+ align:start position:0%
+you are going to heat up a system that
+is if you look at the specific heat of a
+
+ align:start position:0%
+is if you look at the specific heat of a
+ 
+
+ align:start position:0%
+is if you look at the specific heat of a
+solid that is basically the quantity
+
+ align:start position:0%
+solid that is basically the quantity
+ 
+
+ align:start position:0%
+solid that is basically the quantity
+that tells you how much heat this system
+
+ align:start position:0%
+that tells you how much heat this system
+ 
+
+ align:start position:0%
+that tells you how much heat this system
+is going to be able to take and you look
+
+ align:start position:0%
+is going to be able to take and you look
+ 
+
+ align:start position:0%
+is going to be able to take and you look
+at you know what happens at very low
+
+ align:start position:0%
+at you know what happens at very low
+ 
+
+ align:start position:0%
+at you know what happens at very low
+temperature you discover that actually
+
+ align:start position:0%
+temperature you discover that actually
+ 
+
+ align:start position:0%
+temperature you discover that actually
+the system is almost unable to take any
+
+ align:start position:0%
+the system is almost unable to take any
+ 
+
+ align:start position:0%
+the system is almost unable to take any
+heat because all the vibrational
+
+ align:start position:0%
+heat because all the vibrational
+ 
+
+ align:start position:0%
+heat because all the vibrational
+excitation are much larger than the
+
+ align:start position:0%
+excitation are much larger than the
+ 
+
+ align:start position:0%
+excitation are much larger than the
+average amount of kinetic energy that
+
+ align:start position:0%
+average amount of kinetic energy that
+ 
+
+ align:start position:0%
+average amount of kinetic energy that
+you have if you are sort of looking at
+
+ align:start position:0%
+you have if you are sort of looking at
+ 
+
+ align:start position:0%
+you have if you are sort of looking at
+you know what it takes to bring
+
+ align:start position:0%
+you know what it takes to bring
+ 
+
+ align:start position:0%
+you know what it takes to bring
+something from 1 C to 2 Kevin okay but
+
+ align:start position:0%
+something from 1 C to 2 Kevin okay but
+ 
+
+ align:start position:0%
+something from 1 C to 2 Kevin okay but
+this is still relevant if you have you
+
+ align:start position:0%
+this is still relevant if you have you
+ 
+
+ align:start position:0%
+this is still relevant if you have you
+know a system like water even at 300
+
+ align:start position:0%
+know a system like water even at 300
+ 
+
+ align:start position:0%
+know a system like water even at 300
+Kelvin in water say at 300 Kelvin what
+
+ align:start position:0%
+Kelvin in water say at 300 Kelvin what
+ 
+
+ align:start position:0%
+Kelvin in water say at 300 Kelvin what
+you have is you have this water
+
+ align:start position:0%
+you have is you have this water
+ 
+
+ align:start position:0%
+you have is you have this water
+molecules remember what you have you
+
+ align:start position:0%
+molecules remember what you have you
+ 
+
+ align:start position:0%
+molecules remember what you have you
+oxygen hydrogen and hydrogen and you
+
+ align:start position:0%
+oxygen hydrogen and hydrogen and you
+ 
+
+ align:start position:0%
+oxygen hydrogen and hydrogen and you
+know the modes of vibration of these
+
+ align:start position:0%
+know the modes of vibration of these
+ 
+
+ align:start position:0%
+know the modes of vibration of these
+molecules are stretching modes of the
+
+ align:start position:0%
+molecules are stretching modes of the
+ 
+
+ align:start position:0%
+molecules are stretching modes of the
+hydrogens and then there are sort of
+
+ align:start position:0%
+hydrogens and then there are sort of
+ 
+
+ align:start position:0%
+hydrogens and then there are sort of
+scissor like models in which the two
+
+ align:start position:0%
+scissor like models in which the two
+ 
+
+ align:start position:0%
+scissor like models in which the two
+bonds do this and then these are sort of
+
+ align:start position:0%
+bonds do this and then these are sort of
+ 
+
+ align:start position:0%
+bonds do this and then these are sort of
+intramolecular modes just sort of
+
+ align:start position:0%
+intramolecular modes just sort of
+ 
+
+ align:start position:0%
+intramolecular modes just sort of
+relevant to one molecule and then there
+
+ align:start position:0%
+relevant to one molecule and then there
+ 
+
+ align:start position:0%
+relevant to one molecule and then there
+are sort of all the molecules
+
+ align:start position:0%
+are sort of all the molecules
+ 
+
+ align:start position:0%
+are sort of all the molecules
+interacting well at room temperature all
+
+ align:start position:0%
+interacting well at room temperature all
+ 
+
+ align:start position:0%
+interacting well at room temperature all
+the internal modes of the molecule the
+
+ align:start position:0%
+the internal modes of the molecule the
+ 
+
+ align:start position:0%
+the internal modes of the molecule the
+stretching and the scissor modes uh have
+
+ align:start position:0%
+stretching and the scissor modes uh have
+ 
+
+ align:start position:0%
+stretching and the scissor modes uh have
+so much vibrational energy in their
+
+ align:start position:0%
+so much vibrational energy in their
+ 
+
+ align:start position:0%
+so much vibrational energy in their
+ground state that it's almost impossible
+
+ align:start position:0%
+ground state that it's almost impossible
+ 
+
+ align:start position:0%
+ground state that it's almost impossible
+to excite them to the next vibrational
+
+ align:start position:0%
+to excite them to the next vibrational
+ 
+
+ align:start position:0%
+to excite them to the next vibrational
+state with the average temperature that
+
+ align:start position:0%
+state with the average temperature that
+ 
+
+ align:start position:0%
+state with the average temperature that
+you have at 300 Kelvin so even a system
+
+ align:start position:0%
+you have at 300 Kelvin so even a system
+ 
+
+ align:start position:0%
+you have at 300 Kelvin so even a system
+as fundamental as water is really a
+
+ align:start position:0%
+as fundamental as water is really a
+ 
+
+ align:start position:0%
+as fundamental as water is really a
+hybrid behavior in which the vibrational
+
+ align:start position:0%
+hybrid behavior in which the vibrational
+ 
+
+ align:start position:0%
+hybrid behavior in which the vibrational
+interaction between
+
+ align:start position:0%
+interaction between
+ 
+
+ align:start position:0%
+interaction between
+molecules uh can actually be populated
+
+ align:start position:0%
+molecules uh can actually be populated
+ 
+
+ align:start position:0%
+molecules uh can actually be populated
+arbitrarily by the temperature that is
+
+ align:start position:0%
+arbitrarily by the temperature that is
+ 
+
+ align:start position:0%
+arbitrarily by the temperature that is
+surrounding you but it's almost
+
+ align:start position:0%
+surrounding you but it's almost
+ 
+
+ align:start position:0%
+surrounding you but it's almost
+impossible to excite a molecule from a
+
+ align:start position:0%
+impossible to excite a molecule from a
+ 
+
+ align:start position:0%
+impossible to excite a molecule from a
+sort of zero point stretching motion to
+
+ align:start position:0%
+sort of zero point stretching motion to
+ 
+
+ align:start position:0%
+sort of zero point stretching motion to
+the next one and so say the specific
+
+ align:start position:0%
+the next one and so say the specific
+ 
+
+ align:start position:0%
+the next one and so say the specific
+heat of water will be slightly exotic
+
+ align:start position:0%
+heat of water will be slightly exotic
+ 
+
+ align:start position:0%
+heat of water will be slightly exotic
+because really part of its vibration are
+
+ align:start position:0%
+because really part of its vibration are
+ 
+
+ align:start position:0%
+because really part of its vibration are
+quantized and so there are a number of
+
+ align:start position:0%
+quantized and so there are a number of
+ 
+
+ align:start position:0%
+quantized and so there are a number of
+cases in which this classical nuclear
+
+ align:start position:0%
+cases in which this classical nuclear
+ 
+
+ align:start position:0%
+cases in which this classical nuclear
+approximation uh sort of is not is not
+
+ align:start position:0%
+approximation uh sort of is not is not
+ 
+
+ align:start position:0%
+approximation uh sort of is not is not
+exact and luckily they can be studied
+
+ align:start position:0%
+exact and luckily they can be studied
+ 
+
+ align:start position:0%
+exact and luckily they can be studied
+with sort of specific techniques that
+
+ align:start position:0%
+with sort of specific techniques that
+ 
+
+ align:start position:0%
+with sort of specific techniques that
+we'll see in some of the later
+
+ align:start position:0%
+we'll see in some of the later
+ 
+
+ align:start position:0%
+we'll see in some of the later
+application class during this course but
+
+ align:start position:0%
+application class during this course but
+ 
+
+ align:start position:0%
+application class during this course but
+so remember this if there is one thing
+
+ align:start position:0%
+so remember this if there is one thing
+ 
+
+ align:start position:0%
+so remember this if there is one thing
+that you want to remember about the
+
+ align:start position:0%
+that you want to remember about the
+ 
+
+ align:start position:0%
+that you want to remember about the
+behavior of nucle that these vibrational
+
+ align:start position:0%
+behavior of nucle that these vibrational
+ 
+
+ align:start position:0%
+behavior of nucle that these vibrational
+excitation are quantized and we actually
+
+ align:start position:0%
+excitation are quantized and we actually
+ 
+
+ align:start position:0%
+excitation are quantized and we actually
+see this quantization in physical
+
+ align:start position:0%
+see this quantization in physical
+ 
+
+ align:start position:0%
+see this quantization in physical
+properties like the specific like the
+
+ align:start position:0%
+properties like the specific like the
+ 
+
+ align:start position:0%
+properties like the specific like the
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+heat okay so let's
+
+ align:start position:0%
+heat okay so let's
+ 
+
+ align:start position:0%
+heat okay so let's
+discuss uh the
+
+ align:start position:0%
+discuss uh the
+ 
+
+ align:start position:0%
+discuss uh the
+first of the Poss possible application
+
+ align:start position:0%
+first of the Poss possible application
+ 
+
+ align:start position:0%
+first of the Poss possible application
+of molecular dynamics that that I have
+
+ align:start position:0%
+of molecular dynamics that that I have
+ 
+
+ align:start position:0%
+of molecular dynamics that that I have
+mentioned and that using molecular
+
+ align:start position:0%
+mentioned and that using molecular
+ 
+
+ align:start position:0%
+mentioned and that using molecular
+Dynamics to really calculate average
+
+ align:start position:0%
+Dynamics to really calculate average
+ 
+
+ align:start position:0%
+Dynamics to really calculate average
+properties of a system at finite
+
+ align:start position:0%
+properties of a system at finite
+ 
+
+ align:start position:0%
+properties of a system at finite
+temperature and what I written here is
+
+ align:start position:0%
+temperature and what I written here is
+ 
+
+ align:start position:0%
+temperature and what I written here is
+really sort of you know the summary of
+
+ align:start position:0%
+really sort of you know the summary of
+ 
+
+ align:start position:0%
+really sort of you know the summary of
+statistical mechanics that is what if
+
+ align:start position:0%
+statistical mechanics that is what if
+ 
+
+ align:start position:0%
+statistical mechanics that is what if
+you want bolman would tell you you have
+
+ align:start position:0%
+you want bolman would tell you you have
+ 
+
+ align:start position:0%
+you want bolman would tell you you have
+a dynamical system that is described by
+
+ align:start position:0%
+a dynamical system that is described by
+ 
+
+ align:start position:0%
+a dynamical system that is described by
+this point moving around in Phase space
+
+ align:start position:0%
+this point moving around in Phase space
+ 
+
+ align:start position:0%
+this point moving around in Phase space
+okay so with a certain you know possible
+
+ align:start position:0%
+okay so with a certain you know possible
+ 
+
+ align:start position:0%
+okay so with a certain you know possible
+set of position and with a certain
+
+ align:start position:0%
+set of position and with a certain
+ 
+
+ align:start position:0%
+set of position and with a certain
+possible set of momenta and suppose that
+
+ align:start position:0%
+possible set of momenta and suppose that
+ 
+
+ align:start position:0%
+possible set of momenta and suppose that
+we want to calculate I say what is an
+
+ align:start position:0%
+we want to calculate I say what is an
+ 
+
+ align:start position:0%
+we want to calculate I say what is an
+average property at a certain
+
+ align:start position:0%
+average property at a certain
+ 
+
+ align:start position:0%
+average property at a certain
+temperature and we call that property a
+
+ align:start position:0%
+temperature and we call that property a
+ 
+
+ align:start position:0%
+temperature and we call that property a
+it could be the latis parameter of the
+
+ align:start position:0%
+it could be the latis parameter of the
+ 
+
+ align:start position:0%
+it could be the latis parameter of the
+system you have all this or it could be
+
+ align:start position:0%
+system you have all this or it could be
+ 
+
+ align:start position:0%
+system you have all this or it could be
+the diameter say it's even simpler of
+
+ align:start position:0%
+the diameter say it's even simpler of
+ 
+
+ align:start position:0%
+the diameter say it's even simpler of
+your water bubble okay you have this
+
+ align:start position:0%
+your water bubble okay you have this
+ 
+
+ align:start position:0%
+your water bubble okay you have this
+water bubble and you want to see what is
+
+ align:start position:0%
+water bubble and you want to see what is
+ 
+
+ align:start position:0%
+water bubble and you want to see what is
+the diameter of this water Bubble at a
+
+ align:start position:0%
+the diameter of this water Bubble at a
+ 
+
+ align:start position:0%
+the diameter of this water Bubble at a
+certain temperature and this diameter is
+
+ align:start position:0%
+certain temperature and this diameter is
+ 
+
+ align:start position:0%
+certain temperature and this diameter is
+going to increase with temperature and
+
+ align:start position:0%
+going to increase with temperature and
+ 
+
+ align:start position:0%
+going to increase with temperature and
+what you do you just let this system
+
+ align:start position:0%
+what you do you just let this system
+ 
+
+ align:start position:0%
+what you do you just let this system
+evolve and during its Evolution you keep
+
+ align:start position:0%
+evolve and during its Evolution you keep
+ 
+
+ align:start position:0%
+evolve and during its Evolution you keep
+measuring what is its diameter and you
+
+ align:start position:0%
+measuring what is its diameter and you
+ 
+
+ align:start position:0%
+measuring what is its diameter and you
+let this evolve a lot and you measure
+
+ align:start position:0%
+let this evolve a lot and you measure
+ 
+
+ align:start position:0%
+let this evolve a lot and you measure
+what is it's its width well the way
+
+ align:start position:0%
+what is it's its width well the way
+ 
+
+ align:start position:0%
+what is it's its width well the way
+boltman would set this problem is say we
+
+ align:start position:0%
+boltman would set this problem is say we
+ 
+
+ align:start position:0%
+boltman would set this problem is say we
+really need to integrate over all
+
+ align:start position:0%
+really need to integrate over all
+ 
+
+ align:start position:0%
+really need to integrate over all
+possible configuration ation of the
+
+ align:start position:0%
+possible configuration ation of the
+ 
+
+ align:start position:0%
+possible configuration ation of the
+system that is we need to go through all
+
+ align:start position:0%
+system that is we need to go through all
+ 
+
+ align:start position:0%
+system that is we need to go through all
+possible configuration of the system
+
+ align:start position:0%
+possible configuration of the system
+ 
+
+ align:start position:0%
+possible configuration of the system
+that is we need to integrate over the
+
+ align:start position:0%
+that is we need to integrate over the
+ 
+
+ align:start position:0%
+that is we need to integrate over the
+full phase space and for every possible
+
+ align:start position:0%
+full phase space and for every possible
+ 
+
+ align:start position:0%
+full phase space and for every possible
+point in Phase space we need to
+
+ align:start position:0%
+point in Phase space we need to
+ 
+
+ align:start position:0%
+point in Phase space we need to
+calculate the diameter of my water
+
+ align:start position:0%
+calculate the diameter of my water
+ 
+
+ align:start position:0%
+calculate the diameter of my water
+bubble and then we need to sort of take
+
+ align:start position:0%
+bubble and then we need to sort of take
+ 
+
+ align:start position:0%
+bubble and then we need to sort of take
+into account what is the probability of
+
+ align:start position:0%
+into account what is the probability of
+ 
+
+ align:start position:0%
+into account what is the probability of
+being in that configuration and if you
+
+ align:start position:0%
+being in that configuration and if you
+ 
+
+ align:start position:0%
+being in that configuration and if you
+are in a system at a constant
+
+ align:start position:0%
+are in a system at a constant
+ 
+
+ align:start position:0%
+are in a system at a constant
+temperature the probability of finding
+
+ align:start position:0%
+temperature the probability of finding
+ 
+
+ align:start position:0%
+temperature the probability of finding
+yourself at a given temperature is given
+
+ align:start position:0%
+yourself at a given temperature is given
+ 
+
+ align:start position:0%
+yourself at a given temperature is given
+by exponential of minus beta is just one
+
+ align:start position:0%
+by exponential of minus beta is just one
+ 
+
+ align:start position:0%
+by exponential of minus beta is just one
+over the boltzman constant times the
+
+ align:start position:0%
+over the boltzman constant times the
+ 
+
+ align:start position:0%
+over the boltzman constant times the
+temperature times the energy that means
+
+ align:start position:0%
+temperature times the energy that means
+ 
+
+ align:start position:0%
+temperature times the energy that means
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+configuration that have a high internal
+
+ align:start position:0%
+configuration that have a high internal
+ 
+
+ align:start position:0%
+configuration that have a high internal
+energy are very unlikely and
+
+ align:start position:0%
+energy are very unlikely and
+ 
+
+ align:start position:0%
+energy are very unlikely and
+configuration that have low energy are
+
+ align:start position:0%
+configuration that have low energy are
+ 
+
+ align:start position:0%
+configuration that have low energy are
+more likely to the point that if the
+
+ align:start position:0%
+more likely to the point that if the
+ 
+
+ align:start position:0%
+more likely to the point that if the
+temperature is zero that is this beta is
+
+ align:start position:0%
+temperature is zero that is this beta is
+ 
+
+ align:start position:0%
+temperature is zero that is this beta is
+diverging to Infinity only the lowest
+
+ align:start position:0%
+diverging to Infinity only the lowest
+ 
+
+ align:start position:0%
+diverging to Infinity only the lowest
+energy configuration possible is
+
+ align:start position:0%
+energy configuration possible is
+ 
+
+ align:start position:0%
+energy configuration possible is
+represented but so this is the
+
+ align:start position:0%
+represented but so this is the
+ 
+
+ align:start position:0%
+represented but so this is the
+statistical mechanic points to calculate
+
+ align:start position:0%
+statistical mechanic points to calculate
+ 
+
+ align:start position:0%
+statistical mechanic points to calculate
+an average quantity at a finite
+
+ align:start position:0%
+an average quantity at a finite
+ 
+
+ align:start position:0%
+an average quantity at a finite
+temperature we need to sum over all
+
+ align:start position:0%
+temperature we need to sum over all
+ 
+
+ align:start position:0%
+temperature we need to sum over all
+possible configuration in space and
+
+ align:start position:0%
+possible configuration in space and
+ 
+
+ align:start position:0%
+possible configuration in space and
+momentum for each possible rmp
+
+ align:start position:0%
+momentum for each possible rmp
+ 
+
+ align:start position:0%
+momentum for each possible rmp
+configuration we'll have a certain value
+
+ align:start position:0%
+configuration we'll have a certain value
+ 
+
+ align:start position:0%
+configuration we'll have a certain value
+of the diameter of that bubble we weigh
+
+ align:start position:0%
+of the diameter of that bubble we weigh
+ 
+
+ align:start position:0%
+of the diameter of that bubble we weigh
+that with the statistical weight
+
+ align:start position:0%
+that with the statistical weight
+ 
+
+ align:start position:0%
+that with the statistical weight
+of that configuration and we actually
+
+ align:start position:0%
+of that configuration and we actually
+ 
+
+ align:start position:0%
+of that configuration and we actually
+normalize this expectation value and
+
+ align:start position:0%
+normalize this expectation value and
+ 
+
+ align:start position:0%
+normalize this expectation value and
+this is what we obtain so if for a
+
+ align:start position:0%
+this is what we obtain so if for a
+ 
+
+ align:start position:0%
+this is what we obtain so if for a
+moment you think at a facee space that
+
+ align:start position:0%
+moment you think at a facee space that
+ 
+
+ align:start position:0%
+moment you think at a facee space that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+two-dimensional and you know in this
+
+ align:start position:0%
+two-dimensional and you know in this
+ 
+
+ align:start position:0%
+two-dimensional and you know in this
+Square we represent all the possible
+
+ align:start position:0%
+Square we represent all the possible
+ 
+
+ align:start position:0%
+Square we represent all the possible
+position and velocity of our system uh
+
+ align:start position:0%
+position and velocity of our system uh
+ 
+
+ align:start position:0%
+position and velocity of our system uh
+what boltzman tells us is that for every
+
+ align:start position:0%
+what boltzman tells us is that for every
+ 
+
+ align:start position:0%
+what boltzman tells us is that for every
+possible point we will have a certain
+
+ align:start position:0%
+possible point we will have a certain
+ 
+
+ align:start position:0%
+possible point we will have a certain
+value of a and the sum of over all the
+
+ align:start position:0%
+value of a and the sum of over all the
+ 
+
+ align:start position:0%
+value of a and the sum of over all the
+possible value of a weighed with the
+
+ align:start position:0%
+possible value of a weighed with the
+ 
+
+ align:start position:0%
+possible value of a weighed with the
+sort of probability of finding them
+
+ align:start position:0%
+sort of probability of finding them
+ 
+
+ align:start position:0%
+sort of probability of finding them
+gives us the expectation value and so
+
+ align:start position:0%
+gives us the expectation value and so
+ 
+
+ align:start position:0%
+gives us the expectation value and so
+what you really need to do is an
+
+ align:start position:0%
+what you really need to do is an
+ 
+
+ align:start position:0%
+what you really need to do is an
+integral over all space of this and this
+
+ align:start position:0%
+integral over all space of this and this
+ 
+
+ align:start position:0%
+integral over all space of this and this
+the cost of these
+
+ align:start position:0%
+the cost of these
+ 
+
+ align:start position:0%
+the cost of these
+integrals diverges as the number of
+
+ align:start position:0%
+integrals diverges as the number of
+ 
+
+ align:start position:0%
+integrals diverges as the number of
+Dimension diverges because again every
+
+ align:start position:0%
+Dimension diverges because again every
+ 
+
+ align:start position:0%
+Dimension diverges because again every
+time we
+
+ align:start position:0%
+time we
+ 
+
+ align:start position:0%
+time we
+increase you know the size of the system
+
+ align:start position:0%
+increase you know the size of the system
+ 
+
+ align:start position:0%
+increase you know the size of the system
+by one particle we have six more
+
+ align:start position:0%
+by one particle we have six more
+ 
+
+ align:start position:0%
+by one particle we have six more
+Dimension over which to integrate and
+
+ align:start position:0%
+Dimension over which to integrate and
+ 
+
+ align:start position:0%
+Dimension over which to integrate and
+again if you think that you know sort of
+
+ align:start position:0%
+again if you think that you know sort of
+ 
+
+ align:start position:0%
+again if you think that you know sort of
+we do this just by numerical integration
+
+ align:start position:0%
+we do this just by numerical integration
+ 
+
+ align:start position:0%
+we do this just by numerical integration
+by taking points on a grid and maybe we
+
+ align:start position:0%
+by taking points on a grid and maybe we
+ 
+
+ align:start position:0%
+by taking points on a grid and maybe we
+just discretize our system with 10
+
+ align:start position:0%
+just discretize our system with 10
+ 
+
+ align:start position:0%
+just discretize our system with 10
+points along one dimension every time
+
+ align:start position:0%
+points along one dimension every time
+ 
+
+ align:start position:0%
+points along one dimension every time
+you add a particle you have 10 to the
+
+ align:start position:0%
+you add a particle you have 10 to the
+ 
+
+ align:start position:0%
+you add a particle you have 10 to the
+six points that multiplier system so
+
+ align:start position:0%
+six points that multiplier system so
+ 
+
+ align:start position:0%
+six points that multiplier system so
+this this quantity explodes the point of
+
+ align:start position:0%
+this this quantity explodes the point of
+ 
+
+ align:start position:0%
+this this quantity explodes the point of
+view of molecular Dynamics is different
+
+ align:start position:0%
+view of molecular Dynamics is different
+ 
+
+ align:start position:0%
+view of molecular Dynamics is different
+what we say is that well let's just let
+
+ align:start position:0%
+what we say is that well let's just let
+ 
+
+ align:start position:0%
+what we say is that well let's just let
+this system evolve let this system
+
+ align:start position:0%
+this system evolve let this system
+ 
+
+ align:start position:0%
+this system evolve let this system
+evolve in time and let it evolve at a
+
+ align:start position:0%
+evolve in time and let it evolve at a
+ 
+
+ align:start position:0%
+evolve in time and let it evolve at a
+constant temperature and so now our
+
+ align:start position:0%
+constant temperature and so now our
+ 
+
+ align:start position:0%
+constant temperature and so now our
+point in Phase space is going you know
+
+ align:start position:0%
+point in Phase space is going you know
+ 
+
+ align:start position:0%
+point in Phase space is going you know
+to go around following a
+
+ align:start position:0%
+to go around following a
+ 
+
+ align:start position:0%
+to go around following a
+trajectory and if we let it go around
+
+ align:start position:0%
+trajectory and if we let it go around
+ 
+
+ align:start position:0%
+trajectory and if we let it go around
+sort of long enough it will spend more
+
+ align:start position:0%
+sort of long enough it will spend more
+ 
+
+ align:start position:0%
+sort of long enough it will spend more
+time in the parts of phas space that are
+
+ align:start position:0%
+time in the parts of phas space that are
+ 
+
+ align:start position:0%
+time in the parts of phas space that are
+more favorite the one that are sort of
+
+ align:start position:0%
+more favorite the one that are sort of
+ 
+
+ align:start position:0%
+more favorite the one that are sort of
+more likely according to the boltman
+
+ align:start position:0%
+more likely according to the boltman
+ 
+
+ align:start position:0%
+more likely according to the boltman
+factor and so if our Evolution really is
+
+ align:start position:0%
+factor and so if our Evolution really is
+ 
+
+ align:start position:0%
+factor and so if our Evolution really is
+distributed in the trajectory according
+
+ align:start position:0%
+distributed in the trajectory according
+ 
+
+ align:start position:0%
+distributed in the trajectory according
+to this uh um thermodynamical weight
+
+ align:start position:0%
+to this uh um thermodynamical weight
+ 
+
+ align:start position:0%
+to this uh um thermodynamical weight
+thermodynamical Factor then our
+
+ align:start position:0%
+thermodynamical Factor then our
+ 
+
+ align:start position:0%
+thermodynamical Factor then our
+expectation value the thermodynamical
+
+ align:start position:0%
+expectation value the thermodynamical
+ 
+
+ align:start position:0%
+expectation value the thermodynamical
+average for our observable a is just
+
+ align:start position:0%
+average for our observable a is just
+ 
+
+ align:start position:0%
+average for our observable a is just
+trivial obtain by integrating over the
+
+ align:start position:0%
+trivial obtain by integrating over the
+ 
+
+ align:start position:0%
+trivial obtain by integrating over the
+rectories all the values of a that is
+
+ align:start position:0%
+rectories all the values of a that is
+ 
+
+ align:start position:0%
+rectories all the values of a that is
+what I was saying before if you want to
+
+ align:start position:0%
+what I was saying before if you want to
+ 
+
+ align:start position:0%
+what I was saying before if you want to
+calculate the diameter of your bubble uh
+
+ align:start position:0%
+calculate the diameter of your bubble uh
+ 
+
+ align:start position:0%
+calculate the diameter of your bubble uh
+what you do in the molecular Dynamic
+
+ align:start position:0%
+what you do in the molecular Dynamic
+ 
+
+ align:start position:0%
+what you do in the molecular Dynamic
+sense you just let the bubble evolve
+
+ align:start position:0%
+sense you just let the bubble evolve
+ 
+
+ align:start position:0%
+sense you just let the bubble evolve
+according to the equation of motion at a
+
+ align:start position:0%
+according to the equation of motion at a
+ 
+
+ align:start position:0%
+according to the equation of motion at a
+constant temperature and you keep
+
+ align:start position:0%
+constant temperature and you keep
+ 
+
+ align:start position:0%
+constant temperature and you keep
+monitoring its diameter and you will see
+
+ align:start position:0%
+monitoring its diameter and you will see
+ 
+
+ align:start position:0%
+monitoring its diameter and you will see
+that that diameter will have an average
+
+ align:start position:0%
+that that diameter will have an average
+ 
+
+ align:start position:0%
+that that diameter will have an average
+and that this is a much more efficient
+
+ align:start position:0%
+and that this is a much more efficient
+ 
+
+ align:start position:0%
+and that this is a much more efficient
+way than considering all possible
+
+ align:start position:0%
+way than considering all possible
+ 
+
+ align:start position:0%
+way than considering all possible
+configuration of the bubble weighing
+
+ align:start position:0%
+configuration of the bubble weighing
+ 
+
+ align:start position:0%
+configuration of the bubble weighing
+them with how expensive that
+
+ align:start position:0%
+them with how expensive that
+ 
+
+ align:start position:0%
+them with how expensive that
+configuration is and sort of you know
+
+ align:start position:0%
+configuration is and sort of you know
+ 
+
+ align:start position:0%
+configuration is and sort of you know
+doing it for all the possible
+
+ align:start position:0%
+doing it for all the possible
+ 
+
+ align:start position:0%
+doing it for all the possible
+configuration the molecular Dynamic
+
+ align:start position:0%
+configuration the molecular Dynamic
+ 
+
+ align:start position:0%
+configuration the molecular Dynamic
+algorithm automatically if you want keep
+
+ align:start position:0%
+algorithm automatically if you want keep
+ 
+
+ align:start position:0%
+algorithm automatically if you want keep
+spanning the most likely configurations
+
+ align:start position:0%
+spanning the most likely configurations
+ 
+
+ align:start position:0%
+spanning the most likely configurations
+and so it does for you the job of sort
+
+ align:start position:0%
+and so it does for you the job of sort
+ 
+
+ align:start position:0%
+and so it does for you the job of sort
+of you know going in the place where
+
+ align:start position:0%
+of you know going in the place where
+ 
+
+ align:start position:0%
+of you know going in the place where
+it's most likely to be um so in order to
+
+ align:start position:0%
+it's most likely to be um so in order to
+ 
+
+ align:start position:0%
+it's most likely to be um so in order to
+calculate emble average we can actually
+
+ align:start position:0%
+calculate emble average we can actually
+ 
+
+ align:start position:0%
+calculate emble average we can actually
+transform our problem into integration
+
+ align:start position:0%
+transform our problem into integration
+ 
+
+ align:start position:0%
+transform our problem into integration
+over a trajectory and that is almost
+
+ align:start position:0%
+over a trajectory and that is almost
+ 
+
+ align:start position:0%
+over a trajectory and that is almost
+always doable under what is called the
+
+ align:start position:0%
+always doable under what is called the
+ 
+
+ align:start position:0%
+always doable under what is called the
+Criterion of ergodicity so the
+
+ align:start position:0%
+Criterion of ergodicity so the
+ 
+
+ align:start position:0%
+Criterion of ergodicity so the
+equivalence between the two formulation
+
+ align:start position:0%
+equivalence between the two formulation
+ 
+
+ align:start position:0%
+equivalence between the two formulation
+that I written before that is
+
+ align:start position:0%
+that I written before that is
+ 
+
+ align:start position:0%
+that I written before that is
+calculating a thermodynamical observable
+
+ align:start position:0%
+calculating a thermodynamical observable
+ 
+
+ align:start position:0%
+calculating a thermodynamical observable
+as an integral in PH space or as an
+
+ align:start position:0%
+as an integral in PH space or as an
+ 
+
+ align:start position:0%
+as an integral in PH space or as an
+integral over a trajectories are
+
+ align:start position:0%
+integral over a trajectories are
+ 
+
+ align:start position:0%
+integral over a trajectories are
+equivalent provided your trajectory is
+
+ align:start position:0%
+equivalent provided your trajectory is
+ 
+
+ align:start position:0%
+equivalent provided your trajectory is
+really able to go all over the place in
+
+ align:start position:0%
+really able to go all over the place in
+ 
+
+ align:start position:0%
+really able to go all over the place in
+Phase space so if again this were pH
+
+ align:start position:0%
+Phase space so if again this were pH
+ 
+
+ align:start position:0%
+Phase space so if again this were pH
+space you could have in principle the
+
+ align:start position:0%
+space you could have in principle the
+ 
+
+ align:start position:0%
+space you could have in principle the
+problem of a noner godic system if there
+
+ align:start position:0%
+problem of a noner godic system if there
+ 
+
+ align:start position:0%
+problem of a noner godic system if there
+is something that prevents your
+
+ align:start position:0%
+is something that prevents your
+ 
+
+ align:start position:0%
+is something that prevents your
+trajectory to sort of reach certain
+
+ align:start position:0%
+trajectory to sort of reach certain
+ 
+
+ align:start position:0%
+trajectory to sort of reach certain
+so-call forbidden segments in your face
+
+ align:start position:0%
+so-call forbidden segments in your face
+ 
+
+ align:start position:0%
+so-call forbidden segments in your face
+space and I can give you an example
+
+ align:start position:0%
+space and I can give you an example
+ 
+
+ align:start position:0%
+space and I can give you an example
+suppose that you are studying sort of
+
+ align:start position:0%
+suppose that you are studying sort of
+ 
+
+ align:start position:0%
+suppose that you are studying sort of
+something like Silicon and you are in
+
+ align:start position:0%
+something like Silicon and you are in
+ 
+
+ align:start position:0%
+something like Silicon and you are in
+the crystalling state and now you heat
+
+ align:start position:0%
+the crystalling state and now you heat
+ 
+
+ align:start position:0%
+the crystalling state and now you heat
+it up and once you go above the melting
+
+ align:start position:0%
+it up and once you go above the melting
+ 
+
+ align:start position:0%
+it up and once you go above the melting
+temperature your silicon will become
+
+ align:start position:0%
+temperature your silicon will become
+ 
+
+ align:start position:0%
+temperature your silicon will become
+liquid okay now suppose that you cool it
+
+ align:start position:0%
+liquid okay now suppose that you cool it
+ 
+
+ align:start position:0%
+liquid okay now suppose that you cool it
+down again below now the melting
+
+ align:start position:0%
+down again below now the melting
+ 
+
+ align:start position:0%
+down again below now the melting
+temperature okay in principle the liquid
+
+ align:start position:0%
+temperature okay in principle the liquid
+ 
+
+ align:start position:0%
+temperature okay in principle the liquid
+silicon should become again crystalline
+
+ align:start position:0%
+silicon should become again crystalline
+ 
+
+ align:start position:0%
+silicon should become again crystalline
+silicon because at that temperature in
+
+ align:start position:0%
+silicon because at that temperature in
+ 
+
+ align:start position:0%
+silicon because at that temperature in
+which we have sort of you know brought
+
+ align:start position:0%
+which we have sort of you know brought
+ 
+
+ align:start position:0%
+which we have sort of you know brought
+it back to the thermodynamical stable
+
+ align:start position:0%
+it back to the thermodynamical stable
+ 
+
+ align:start position:0%
+it back to the thermodynamical stable
+state is really the crystal in solid if
+
+ align:start position:0%
+state is really the crystal in solid if
+ 
+
+ align:start position:0%
+state is really the crystal in solid if
+you do that in practice with a molecular
+
+ align:start position:0%
+you do that in practice with a molecular
+ 
+
+ align:start position:0%
+you do that in practice with a molecular
+Dynamic simulation you'll see that you
+
+ align:start position:0%
+Dynamic simulation you'll see that you
+ 
+
+ align:start position:0%
+Dynamic simulation you'll see that you
+start from the crystal you heat it up it
+
+ align:start position:0%
+start from the crystal you heat it up it
+ 
+
+ align:start position:0%
+start from the crystal you heat it up it
+becomes a liquid with no problems and
+
+ align:start position:0%
+becomes a liquid with no problems and
+ 
+
+ align:start position:0%
+becomes a liquid with no problems and
+then you cool it back down and instead
+
+ align:start position:0%
+then you cool it back down and instead
+ 
+
+ align:start position:0%
+then you cool it back down and instead
+of going back to a crystal it goes back
+
+ align:start position:0%
+of going back to a crystal it goes back
+ 
+
+ align:start position:0%
+of going back to a crystal it goes back
+to a glassy amorphous State okay silicon
+
+ align:start position:0%
+to a glassy amorphous State okay silicon
+ 
+
+ align:start position:0%
+to a glassy amorphous State okay silicon
+will sort of find itself in a
+
+ align:start position:0%
+will sort of find itself in a
+ 
+
+ align:start position:0%
+will sort of find itself in a
+configuration in which locally all atoms
+
+ align:start position:0%
+configuration in which locally all atoms
+ 
+
+ align:start position:0%
+configuration in which locally all atoms
+are happy to be for for
+
+ align:start position:0%
+are happy to be for for
+ 
+
+ align:start position:0%
+are happy to be for for
+coordinated but if we look at the long R
+
+ align:start position:0%
+coordinated but if we look at the long R
+ 
+
+ align:start position:0%
+coordinated but if we look at the long R
+long range order is completely lost the
+
+ align:start position:0%
+long range order is completely lost the
+ 
+
+ align:start position:0%
+long range order is completely lost the
+system is not crystalling anymore it's
+
+ align:start position:0%
+system is not crystalling anymore it's
+ 
+
+ align:start position:0%
+system is not crystalling anymore it's
+glassy what's happening there well it
+
+ align:start position:0%
+glassy what's happening there well it
+ 
+
+ align:start position:0%
+glassy what's happening there well it
+happens that it's just for a liquid
+
+ align:start position:0%
+happens that it's just for a liquid
+ 
+
+ align:start position:0%
+happens that it's just for a liquid
+cooling down so much easier to sort of
+
+ align:start position:0%
+cooling down so much easier to sort of
+ 
+
+ align:start position:0%
+cooling down so much easier to sort of
+you know trap itself into a set of you
+
+ align:start position:0%
+you know trap itself into a set of you
+ 
+
+ align:start position:0%
+you know trap itself into a set of you
+know configurations in which atoms are
+
+ align:start position:0%
+know configurations in which atoms are
+ 
+
+ align:start position:0%
+know configurations in which atoms are
+really fairly happy as they are because
+
+ align:start position:0%
+really fairly happy as they are because
+ 
+
+ align:start position:0%
+really fairly happy as they are because
+what is important for silicon atoms is
+
+ align:start position:0%
+what is important for silicon atoms is
+ 
+
+ align:start position:0%
+what is important for silicon atoms is
+to be fourfold
+
+ align:start position:0%
+to be fourfold
+ 
+
+ align:start position:0%
+to be fourfold
+coordinated but what is important to be
+
+ align:start position:0%
+coordinated but what is important to be
+ 
+
+ align:start position:0%
+coordinated but what is important to be
+in a crystal is that this fourfold
+
+ align:start position:0%
+in a crystal is that this fourfold
+ 
+
+ align:start position:0%
+in a crystal is that this fourfold
+coordination sort of extends and become
+
+ align:start position:0%
+coordination sort of extends and become
+ 
+
+ align:start position:0%
+coordination sort of extends and become
+long range order but for silicon it's
+
+ align:start position:0%
+long range order but for silicon it's
+ 
+
+ align:start position:0%
+long range order but for silicon it's
+very inexpensive to mess up that long
+
+ align:start position:0%
+very inexpensive to mess up that long
+ 
+
+ align:start position:0%
+very inexpensive to mess up that long
+range order like for many other system
+
+ align:start position:0%
+range order like for many other system
+ 
+
+ align:start position:0%
+range order like for many other system
+and you know in principle same thing
+
+ align:start position:0%
+and you know in principle same thing
+ 
+
+ align:start position:0%
+and you know in principle same thing
+happens for polymers you know sort of
+
+ align:start position:0%
+happens for polymers you know sort of
+ 
+
+ align:start position:0%
+happens for polymers you know sort of
+you lower it down they sort of get
+
+ align:start position:0%
+you lower it down they sort of get
+ 
+
+ align:start position:0%
+you lower it down they sort of get
+chopped in a glassy configuration a lot
+
+ align:start position:0%
+chopped in a glassy configuration a lot
+ 
+
+ align:start position:0%
+chopped in a glassy configuration a lot
+of polymers might want to stay actually
+
+ align:start position:0%
+of polymers might want to stay actually
+ 
+
+ align:start position:0%
+of polymers might want to stay actually
+in a crystalline state but really that
+
+ align:start position:0%
+in a crystalline state but really that
+ 
+
+ align:start position:0%
+in a crystalline state but really that
+is impossible to reach and so if you
+
+ align:start position:0%
+is impossible to reach and so if you
+ 
+
+ align:start position:0%
+is impossible to reach and so if you
+want to study say what are the
+
+ align:start position:0%
+want to study say what are the
+ 
+
+ align:start position:0%
+want to study say what are the
+properties of your silicon and you have
+
+ align:start position:0%
+properties of your silicon and you have
+ 
+
+ align:start position:0%
+properties of your silicon and you have
+are obtaining or you are trying to
+
+ align:start position:0%
+are obtaining or you are trying to
+ 
+
+ align:start position:0%
+are obtaining or you are trying to
+obtain your silicon structure from a
+
+ align:start position:0%
+obtain your silicon structure from a
+ 
+
+ align:start position:0%
+obtain your silicon structure from a
+liquid that you cool it down you'll
+
+ align:start position:0%
+liquid that you cool it down you'll
+ 
+
+ align:start position:0%
+liquid that you cool it down you'll
+actually sort of you know in your
+
+ align:start position:0%
+actually sort of you know in your
+ 
+
+ align:start position:0%
+actually sort of you know in your
+molecular Dynamics you'll keep sort of
+
+ align:start position:0%
+molecular Dynamics you'll keep sort of
+ 
+
+ align:start position:0%
+molecular Dynamics you'll keep sort of
+orbiting around in this sort of glassy
+
+ align:start position:0%
+orbiting around in this sort of glassy
+ 
+
+ align:start position:0%
+orbiting around in this sort of glassy
+masses State and will never reach that
+
+ align:start position:0%
+masses State and will never reach that
+ 
+
+ align:start position:0%
+masses State and will never reach that
+region of face space that is actually
+
+ align:start position:0%
+region of face space that is actually
+ 
+
+ align:start position:0%
+region of face space that is actually
+very very small because it needs to have
+
+ align:start position:0%
+very very small because it needs to have
+ 
+
+ align:start position:0%
+very very small because it needs to have
+all atoms long range in very specific
+
+ align:start position:0%
+all atoms long range in very specific
+ 
+
+ align:start position:0%
+all atoms long range in very specific
+position and so you're really sort of
+
+ align:start position:0%
+position and so you're really sort of
+ 
+
+ align:start position:0%
+position and so you're really sort of
+spanning a system in a non-ergodic way
+
+ align:start position:0%
+spanning a system in a non-ergodic way
+ 
+
+ align:start position:0%
+spanning a system in a non-ergodic way
+that is you spend a lot of time in
+
+ align:start position:0%
+that is you spend a lot of time in
+ 
+
+ align:start position:0%
+that is you spend a lot of time in
+region of face space that are not really
+
+ align:start position:0%
+region of face space that are not really
+ 
+
+ align:start position:0%
+region of face space that are not really
+representative but out of which is very
+
+ align:start position:0%
+representative but out of which is very
+ 
+
+ align:start position:0%
+representative but out of which is very
+difficult to escape okay so there are
+
+ align:start position:0%
+difficult to escape okay so there are
+ 
+
+ align:start position:0%
+difficult to escape okay so there are
+problems in sort of you know again Brute
+
+ align:start position:0%
+problems in sort of you know again Brute
+ 
+
+ align:start position:0%
+problems in sort of you know again Brute
+Force molecular Dynamics approach Roes
+
+ align:start position:0%
+Force molecular Dynamics approach Roes
+ 
+
+ align:start position:0%
+Force molecular Dynamics approach Roes
+that you have to be careful
+
+ align:start position:0%
+that you have to be careful
+ 
+
+ align:start position:0%
+that you have to be careful
+about okay so let's see how we actually
+
+ align:start position:0%
+about okay so let's see how we actually
+ 
+
+ align:start position:0%
+about okay so let's see how we actually
+go and try to do this on a computer
+
+ align:start position:0%
+go and try to do this on a computer
+ 
+
+ align:start position:0%
+go and try to do this on a computer
+experiment and you know I'll start with
+
+ align:start position:0%
+experiment and you know I'll start with
+ 
+
+ align:start position:0%
+experiment and you know I'll start with
+the simplest case that is what is called
+
+ align:start position:0%
+the simplest case that is what is called
+ 
+
+ align:start position:0%
+the simplest case that is what is called
+the microcanonical case that is we
+
+ align:start position:0%
+the microcanonical case that is we
+ 
+
+ align:start position:0%
+the microcanonical case that is we
+perform a simulation where the number of
+
+ align:start position:0%
+perform a simulation where the number of
+ 
+
+ align:start position:0%
+perform a simulation where the number of
+particle is constant the volume is
+
+ align:start position:0%
+particle is constant the volume is
+ 
+
+ align:start position:0%
+particle is constant the volume is
+constant and the total energy of the
+
+ align:start position:0%
+constant and the total energy of the
+ 
+
+ align:start position:0%
+constant and the total energy of the
+system is constant this is you know what
+
+ align:start position:0%
+system is constant this is you know what
+ 
+
+ align:start position:0%
+system is constant this is you know what
+is called a thermodynamical Ensemble
+
+ align:start position:0%
+is called a thermodynamical Ensemble
+ 
+
+ align:start position:0%
+is called a thermodynamical Ensemble
+again these are all sort of extensive
+
+ align:start position:0%
+again these are all sort of extensive
+ 
+
+ align:start position:0%
+again these are all sort of extensive
+variables and you're fixing them uh
+
+ align:start position:0%
+variables and you're fixing them uh
+ 
+
+ align:start position:0%
+variables and you're fixing them uh
+sometimes you know it's appropriate
+
+ align:start position:0%
+sometimes you know it's appropriate
+ 
+
+ align:start position:0%
+sometimes you know it's appropriate
+instead to do a leand transformation and
+
+ align:start position:0%
+instead to do a leand transformation and
+ 
+
+ align:start position:0%
+instead to do a leand transformation and
+go into a different thermodynamical
+
+ align:start position:0%
+go into a different thermodynamical
+ 
+
+ align:start position:0%
+go into a different thermodynamical
+Ensemble so you could want not to be at
+
+ align:start position:0%
+Ensemble so you could want not to be at
+ 
+
+ align:start position:0%
+Ensemble so you could want not to be at
+a constant volume but you might want to
+
+ align:start position:0%
+a constant volume but you might want to
+ 
+
+ align:start position:0%
+a constant volume but you might want to
+study a system at a constant pressure
+
+ align:start position:0%
+study a system at a constant pressure
+ 
+
+ align:start position:0%
+study a system at a constant pressure
+where the volume changes and so we need
+
+ align:start position:0%
+where the volume changes and so we need
+ 
+
+ align:start position:0%
+where the volume changes and so we need
+to describe how we'll actually be able
+
+ align:start position:0%
+to describe how we'll actually be able
+ 
+
+ align:start position:0%
+to describe how we'll actually be able
+to do that that is how we we be able to
+
+ align:start position:0%
+to do that that is how we we be able to
+ 
+
+ align:start position:0%
+to do that that is how we we be able to
+move to a system in which different
+
+ align:start position:0%
+move to a system in which different
+ 
+
+ align:start position:0%
+move to a system in which different
+intensive thermodynamical variables are
+
+ align:start position:0%
+intensive thermodynamical variables are
+ 
+
+ align:start position:0%
+intensive thermodynamical variables are
+constant but if you take a system of
+
+ align:start position:0%
+constant but if you take a system of
+ 
+
+ align:start position:0%
+constant but if you take a system of
+particles in periodic boundary
+
+ align:start position:0%
+particles in periodic boundary
+ 
+
+ align:start position:0%
+particles in periodic boundary
+conditions and you have sort of you know
+
+ align:start position:0%
+conditions and you have sort of you know
+ 
+
+ align:start position:0%
+conditions and you have sort of you know
+10 water molecules in a certain unit
+
+ align:start position:0%
+10 water molecules in a certain unit
+ 
+
+ align:start position:0%
+10 water molecules in a certain unit
+cell and you evolve them with the Newton
+
+ align:start position:0%
+cell and you evolve them with the Newton
+ 
+
+ align:start position:0%
+cell and you evolve them with the Newton
+equation of motion you can obviously
+
+ align:start position:0%
+equation of motion you can obviously
+ 
+
+ align:start position:0%
+equation of motion you can obviously
+know that the number of molecules and
+
+ align:start position:0%
+know that the number of molecules and
+ 
+
+ align:start position:0%
+know that the number of molecules and
+the volume of the unit cell are not
+
+ align:start position:0%
+the volume of the unit cell are not
+ 
+
+ align:start position:0%
+the volume of the unit cell are not
+going to change and if you integrate
+
+ align:start position:0%
+going to change and if you integrate
+ 
+
+ align:start position:0%
+going to change and if you integrate
+your equation of motion appropriately
+
+ align:start position:0%
+your equation of motion appropriately
+ 
+
+ align:start position:0%
+your equation of motion appropriately
+the total energy of the system that is
+
+ align:start position:0%
+the total energy of the system that is
+ 
+
+ align:start position:0%
+the total energy of the system that is
+the kinetic energy plus the potential
+
+ align:start position:0%
+the kinetic energy plus the potential
+ 
+
+ align:start position:0%
+the kinetic energy plus the potential
+energy is not going to change and so as
+
+ align:start position:0%
+energy is not going to change and so as
+ 
+
+ align:start position:0%
+energy is not going to change and so as
+we evolve this point in Phase space it
+
+ align:start position:0%
+we evolve this point in Phase space it
+ 
+
+ align:start position:0%
+we evolve this point in Phase space it
+trajectory is going to span what we call
+
+ align:start position:0%
+trajectory is going to span what we call
+ 
+
+ align:start position:0%
+trajectory is going to span what we call
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+microcanonical Ensemble and you let this
+
+ align:start position:0%
+microcanonical Ensemble and you let this
+ 
+
+ align:start position:0%
+microcanonical Ensemble and you let this
+point evolve long enough and all of a
+
+ align:start position:0%
+point evolve long enough and all of a
+ 
+
+ align:start position:0%
+point evolve long enough and all of a
+sudden you will have a meaningful
+
+ align:start position:0%
+sudden you will have a meaningful
+ 
+
+ align:start position:0%
+sudden you will have a meaningful
+trajectory that is a meaningful assembly
+
+ align:start position:0%
+trajectory that is a meaningful assembly
+ 
+
+ align:start position:0%
+trajectory that is a meaningful assembly
+collection of micro states of
+
+ align:start position:0%
+collection of micro states of
+ 
+
+ align:start position:0%
+collection of micro states of
+Representative configuration in space
+
+ align:start position:0%
+Representative configuration in space
+ 
+
+ align:start position:0%
+Representative configuration in space
+and in velocities of your system out of
+
+ align:start position:0%
+and in velocities of your system out of
+ 
+
+ align:start position:0%
+and in velocities of your system out of
+which you can calculate averages of any
+
+ align:start position:0%
+which you can calculate averages of any
+ 
+
+ align:start position:0%
+which you can calculate averages of any
+of the observables that you want to
+
+ align:start position:0%
+of the observables that you want to
+ 
+
+ align:start position:0%
+of the observables that you want to
+calculate and that you want to
+
+ align:start position:0%
+calculate and that you want to
+ 
+
+ align:start position:0%
+calculate and that you want to
+characterize so what do you do in this
+
+ align:start position:0%
+characterize so what do you do in this
+ 
+
+ align:start position:0%
+characterize so what do you do in this
+sort of molecular Dynamic simulations
+
+ align:start position:0%
+sort of molecular Dynamic simulations
+ 
+
+ align:start position:0%
+sort of molecular Dynamic simulations
+well there are really four important
+
+ align:start position:0%
+well there are really four important
+ 
+
+ align:start position:0%
+well there are really four important
+steps that you need to take into account
+
+ align:start position:0%
+steps that you need to take into account
+ 
+
+ align:start position:0%
+steps that you need to take into account
+and we'll sort of keep thinking at Water
+
+ align:start position:0%
+and we'll sort of keep thinking at Water
+ 
+
+ align:start position:0%
+and we'll sort of keep thinking at Water
+liquid water as an example that is you
+
+ align:start position:0%
+liquid water as an example that is you
+ 
+
+ align:start position:0%
+liquid water as an example that is you
+need to start from something that is you
+
+ align:start position:0%
+need to start from something that is you
+ 
+
+ align:start position:0%
+need to start from something that is you
+need to put your water molecule in
+
+ align:start position:0%
+need to put your water molecule in
+ 
+
+ align:start position:0%
+need to put your water molecule in
+certain position and you need to give
+
+ align:start position:0%
+certain position and you need to give
+ 
+
+ align:start position:0%
+certain position and you need to give
+them initial velocities and you are
+
+ align:start position:0%
+them initial velocities and you are
+ 
+
+ align:start position:0%
+them initial velocities and you are
+almost never going to be good enough in
+
+ align:start position:0%
+almost never going to be good enough in
+ 
+
+ align:start position:0%
+almost never going to be good enough in
+sort of choosing a state of the system
+
+ align:start position:0%
+sort of choosing a state of the system
+ 
+
+ align:start position:0%
+sort of choosing a state of the system
+that is somehow meaningful you'll always
+
+ align:start position:0%
+that is somehow meaningful you'll always
+ 
+
+ align:start position:0%
+that is somehow meaningful you'll always
+when you start building something in
+
+ align:start position:0%
+when you start building something in
+ 
+
+ align:start position:0%
+when you start building something in
+complex put molecules in places that
+
+ align:start position:0%
+complex put molecules in places that
+ 
+
+ align:start position:0%
+complex put molecules in places that
+they don't want to stay and one needs to
+
+ align:start position:0%
+they don't want to stay and one needs to
+ 
+
+ align:start position:0%
+they don't want to stay and one needs to
+be very careful then in in all of this
+
+ align:start position:0%
+be very careful then in in all of this
+ 
+
+ align:start position:0%
+be very careful then in in all of this
+but suppose that we have in any case an
+
+ align:start position:0%
+but suppose that we have in any case an
+ 
+
+ align:start position:0%
+but suppose that we have in any case an
+initial configuration of position and
+
+ align:start position:0%
+initial configuration of position and
+ 
+
+ align:start position:0%
+initial configuration of position and
+velocity then what we need to do is over
+
+ align:start position:0%
+velocity then what we need to do is over
+ 
+
+ align:start position:0%
+velocity then what we need to do is over
+and over again integrate the equation of
+
+ align:start position:0%
+and over again integrate the equation of
+ 
+
+ align:start position:0%
+and over again integrate the equation of
+motion that is from the current position
+
+ align:start position:0%
+motion that is from the current position
+ 
+
+ align:start position:0%
+motion that is from the current position
+and the current velocities predicted the
+
+ align:start position:0%
+and the current velocities predicted the
+ 
+
+ align:start position:0%
+and the current velocities predicted the
+new position after a certain time and
+
+ align:start position:0%
+new position after a certain time and
+ 
+
+ align:start position:0%
+new position after a certain time and
+once you have the new position at
+
+ align:start position:0%
+once you have the new position at
+ 
+
+ align:start position:0%
+once you have the new position at
+certain time you can recalculate what
+
+ align:start position:0%
+certain time you can recalculate what
+ 
+
+ align:start position:0%
+certain time you can recalculate what
+are the forces acting on the particle in
+
+ align:start position:0%
+are the forces acting on the particle in
+ 
+
+ align:start position:0%
+are the forces acting on the particle in
+the new position and with these forces
+
+ align:start position:0%
+the new position and with these forces
+ 
+
+ align:start position:0%
+the new position and with these forces
+you can again sort of move the particles
+
+ align:start position:0%
+you can again sort of move the particles
+ 
+
+ align:start position:0%
+you can again sort of move the particles
+by certain amount and so on and so forth
+
+ align:start position:0%
+by certain amount and so on and so forth
+ 
+
+ align:start position:0%
+by certain amount and so on and so forth
+and that is sort of you know where the
+
+ align:start position:0%
+and that is sort of you know where the
+ 
+
+ align:start position:0%
+and that is sort of you know where the
+molecular Dynamics algorithm comes into
+
+ align:start position:0%
+molecular Dynamics algorithm comes into
+ 
+
+ align:start position:0%
+molecular Dynamics algorithm comes into
+play we need to integrate our equation
+
+ align:start position:0%
+play we need to integrate our equation
+ 
+
+ align:start position:0%
+play we need to integrate our equation
+of motion and with this our system will
+
+ align:start position:0%
+of motion and with this our system will
+ 
+
+ align:start position:0%
+of motion and with this our system will
+start to evolve we have put that point
+
+ align:start position:0%
+start to evolve we have put that point
+ 
+
+ align:start position:0%
+start to evolve we have put that point
+in facee space in motion and just start
+
+ align:start position:0%
+in facee space in motion and just start
+ 
+
+ align:start position:0%
+in facee space in motion and just start
+moving around and if we are integrating
+
+ align:start position:0%
+moving around and if we are integrating
+ 
+
+ align:start position:0%
+moving around and if we are integrating
+correctly the total energy of the system
+
+ align:start position:0%
+correctly the total energy of the system
+ 
+
+ align:start position:0%
+correctly the total energy of the system
+is going to be
+
+ align:start position:0%
+is going to be
+ 
+
+ align:start position:0%
+is going to be
+conserved now what we need to do is we
+
+ align:start position:0%
+conserved now what we need to do is we
+ 
+
+ align:start position:0%
+conserved now what we need to do is we
+need to make sure that our
+
+ align:start position:0%
+need to make sure that our
+ 
+
+ align:start position:0%
+need to make sure that our
+characterization our thermodynamical
+
+ align:start position:0%
+characterization our thermodynamical
+ 
+
+ align:start position:0%
+characterization our thermodynamical
+averages do not depend on our initial
+
+ align:start position:0%
+averages do not depend on our initial
+ 
+
+ align:start position:0%
+averages do not depend on our initial
+condition again we have sort of you know
+
+ align:start position:0%
+condition again we have sort of you know
+ 
+
+ align:start position:0%
+condition again we have sort of you know
+started from a configuration that we
+
+ align:start position:0%
+started from a configuration that we
+ 
+
+ align:start position:0%
+started from a configuration that we
+have built by hand and because of that
+
+ align:start position:0%
+have built by hand and because of that
+ 
+
+ align:start position:0%
+have built by hand and because of that
+it's most likely uh very unfavorable
+
+ align:start position:0%
+it's most likely uh very unfavorable
+ 
+
+ align:start position:0%
+it's most likely uh very unfavorable
+configuration of the system okay so we
+
+ align:start position:0%
+configuration of the system okay so we
+ 
+
+ align:start position:0%
+configuration of the system okay so we
+need to let the system
+
+ align:start position:0%
+need to let the system
+ 
+
+ align:start position:0%
+need to let the system
+evolve and somehow you know start
+
+ align:start position:0%
+evolve and somehow you know start
+ 
+
+ align:start position:0%
+evolve and somehow you know start
+figuring out really in which condition
+
+ align:start position:0%
+figuring out really in which condition
+ 
+
+ align:start position:0%
+figuring out really in which condition
+it would want to stay think at the
+
+ align:start position:0%
+it would want to stay think at the
+ 
+
+ align:start position:0%
+it would want to stay think at the
+previous example of silicon that is
+
+ align:start position:0%
+previous example of silicon that is
+ 
+
+ align:start position:0%
+previous example of silicon that is
+glossifying well you know we had liquid
+
+ align:start position:0%
+glossifying well you know we had liquid
+ 
+
+ align:start position:0%
+glossifying well you know we had liquid
+silicon we have cool it down in a way
+
+ align:start position:0%
+silicon we have cool it down in a way
+ 
+
+ align:start position:0%
+silicon we have cool it down in a way
+what's happening is that we are never
+
+ align:start position:0%
+what's happening is that we are never
+ 
+
+ align:start position:0%
+what's happening is that we are never
+equilibrating it because the system goes
+
+ align:start position:0%
+equilibrating it because the system goes
+ 
+
+ align:start position:0%
+equilibrating it because the system goes
+into a glass phase and so it never loses
+
+ align:start position:0%
+into a glass phase and so it never loses
+ 
+
+ align:start position:0%
+into a glass phase and so it never loses
+memory of its initial Condition it's
+
+ align:start position:0%
+memory of its initial Condition it's
+ 
+
+ align:start position:0%
+memory of its initial Condition it's
+always sort of Trapped In This pseudo
+
+ align:start position:0%
+always sort of Trapped In This pseudo
+ 
+
+ align:start position:0%
+always sort of Trapped In This pseudo
+liquid now glassy State while in reality
+
+ align:start position:0%
+liquid now glassy State while in reality
+ 
+
+ align:start position:0%
+liquid now glassy State while in reality
+at a temperature below the freezing or
+
+ align:start position:0%
+at a temperature below the freezing or
+ 
+
+ align:start position:0%
+at a temperature below the freezing or
+the melting point equilibrium would be
+
+ align:start position:0%
+the melting point equilibrium would be
+ 
+
+ align:start position:0%
+the melting point equilibrium would be
+given by a crystalling state with the
+
+ align:start position:0%
+given by a crystalling state with the
+ 
+
+ align:start position:0%
+given by a crystalling state with the
+ions vibrating so there are cases in
+
+ align:start position:0%
+ions vibrating so there are cases in
+ 
+
+ align:start position:0%
+ions vibrating so there are cases in
+which equilibration is so difficult that
+
+ align:start position:0%
+which equilibration is so difficult that
+ 
+
+ align:start position:0%
+which equilibration is so difficult that
+we actually never reach it silicon never
+
+ align:start position:0%
+we actually never reach it silicon never
+ 
+
+ align:start position:0%
+we actually never reach it silicon never
+go to a crystal and that's why we need
+
+ align:start position:0%
+go to a crystal and that's why we need
+ 
+
+ align:start position:0%
+go to a crystal and that's why we need
+to be careful but in most cases
+
+ align:start position:0%
+to be careful but in most cases
+ 
+
+ align:start position:0%
+to be careful but in most cases
+hopefully we are lucky and we lose
+
+ align:start position:0%
+hopefully we are lucky and we lose
+ 
+
+ align:start position:0%
+hopefully we are lucky and we lose
+memory of initial condition see the
+
+ align:start position:0%
+memory of initial condition see the
+ 
+
+ align:start position:0%
+memory of initial condition see the
+opposite is actually sort of very easy
+
+ align:start position:0%
+opposite is actually sort of very easy
+ 
+
+ align:start position:0%
+opposite is actually sort of very easy
+to achieve if we start from the solid
+
+ align:start position:0%
+to achieve if we start from the solid
+ 
+
+ align:start position:0%
+to achieve if we start from the solid
+and we warm it up it becomes a liquid
+
+ align:start position:0%
+and we warm it up it becomes a liquid
+ 
+
+ align:start position:0%
+and we warm it up it becomes a liquid
+and if we wait long enough that liquid
+
+ align:start position:0%
+and if we wait long enough that liquid
+ 
+
+ align:start position:0%
+and if we wait long enough that liquid
+will have lost all memory of having come
+
+ align:start position:0%
+will have lost all memory of having come
+ 
+
+ align:start position:0%
+will have lost all memory of having come
+from a solid okay so it's actually very
+
+ align:start position:0%
+from a solid okay so it's actually very
+ 
+
+ align:start position:0%
+from a solid okay so it's actually very
+easy in One Direction and very difficult
+
+ align:start position:0%
+easy in One Direction and very difficult
+ 
+
+ align:start position:0%
+easy in One Direction and very difficult
+in the other direction but once sort of
+
+ align:start position:0%
+in the other direction but once sort of
+ 
+
+ align:start position:0%
+in the other direction but once sort of
+this equilibration time has passed fast
+
+ align:start position:0%
+this equilibration time has passed fast
+ 
+
+ align:start position:0%
+this equilibration time has passed fast
+well at that point we have truly
+
+ align:start position:0%
+well at that point we have truly
+ 
+
+ align:start position:0%
+well at that point we have truly
+everything in place our point in face
+
+ align:start position:0%
+everything in place our point in face
+ 
+
+ align:start position:0%
+everything in place our point in face
+space is moving around and is really
+
+ align:start position:0%
+space is moving around and is really
+ 
+
+ align:start position:0%
+space is moving around and is really
+going into the regions of high
+
+ align:start position:0%
+going into the regions of high
+ 
+
+ align:start position:0%
+going into the regions of high
+probability and distributed according to
+
+ align:start position:0%
+probability and distributed according to
+ 
+
+ align:start position:0%
+probability and distributed according to
+bolman distribution and so at that point
+
+ align:start position:0%
+bolman distribution and so at that point
+ 
+
+ align:start position:0%
+bolman distribution and so at that point
+we can sort of start and average among
+
+ align:start position:0%
+we can sort of start and average among
+ 
+
+ align:start position:0%
+we can sort of start and average among
+any of the sort of physical observable
+
+ align:start position:0%
+any of the sort of physical observable
+ 
+
+ align:start position:0%
+any of the sort of physical observable
+that we want uh that we want to
+
+ align:start position:0%
+that we want uh that we want to
+ 
+
+ align:start position:0%
+that we want uh that we want to
+calculate and so there are these four
+
+ align:start position:0%
+calculate and so there are these four
+ 
+
+ align:start position:0%
+calculate and so there are these four
+phases and I'll brief ly sort of you
+
+ align:start position:0%
+phases and I'll brief ly sort of you
+ 
+
+ align:start position:0%
+phases and I'll brief ly sort of you
+know mention how we actually choose them
+
+ align:start position:0%
+know mention how we actually choose them
+ 
+
+ align:start position:0%
+know mention how we actually choose them
+um initialization well again we need
+
+ align:start position:0%
+um initialization well again we need
+ 
+
+ align:start position:0%
+um initialization well again we need
+position and velocities you need to sort
+
+ align:start position:0%
+position and velocities you need to sort
+ 
+
+ align:start position:0%
+position and velocities you need to sort
+of you know be careful in particular to
+
+ align:start position:0%
+of you know be careful in particular to
+ 
+
+ align:start position:0%
+of you know be careful in particular to
+avoid overlap between your molecules if
+
+ align:start position:0%
+avoid overlap between your molecules if
+ 
+
+ align:start position:0%
+avoid overlap between your molecules if
+you put two atoms very close they are
+
+ align:start position:0%
+you put two atoms very close they are
+ 
+
+ align:start position:0%
+you put two atoms very close they are
+going to repel each other with an
+
+ align:start position:0%
+going to repel each other with an
+ 
+
+ align:start position:0%
+going to repel each other with an
+enormous strength and you know sort of
+
+ align:start position:0%
+enormous strength and you know sort of
+ 
+
+ align:start position:0%
+enormous strength and you know sort of
+if you put them close enough they going
+
+ align:start position:0%
+if you put them close enough they going
+ 
+
+ align:start position:0%
+if you put them close enough they going
+to shoot in opposite direction very
+
+ align:start position:0%
+to shoot in opposite direction very
+ 
+
+ align:start position:0%
+to shoot in opposite direction very
+quickly and completely sort of kick off
+
+ align:start position:0%
+quickly and completely sort of kick off
+ 
+
+ align:start position:0%
+quickly and completely sort of kick off
+and mess up everything on the side so
+
+ align:start position:0%
+and mess up everything on the side so
+ 
+
+ align:start position:0%
+and mess up everything on the side so
+what is difficult is really always in
+
+ align:start position:0%
+what is difficult is really always in
+ 
+
+ align:start position:0%
+what is difficult is really always in
+configuration space finding the right
+
+ align:start position:0%
+configuration space finding the right
+ 
+
+ align:start position:0%
+configuration space finding the right
+structures this is the difficult part of
+
+ align:start position:0%
+structures this is the difficult part of
+ 
+
+ align:start position:0%
+structures this is the difficult part of
+choosing initial condition choosing
+
+ align:start position:0%
+choosing initial condition choosing
+ 
+
+ align:start position:0%
+choosing initial condition choosing
+velocities is much easier uh one
+
+ align:start position:0%
+velocities is much easier uh one
+ 
+
+ align:start position:0%
+velocities is much easier uh one
+possibility is just giving zero velocity
+
+ align:start position:0%
+possibility is just giving zero velocity
+ 
+
+ align:start position:0%
+possibility is just giving zero velocity
+to the system or very small velocity and
+
+ align:start position:0%
+to the system or very small velocity and
+ 
+
+ align:start position:0%
+to the system or very small velocity and
+then sort of slowly adding things and
+
+ align:start position:0%
+then sort of slowly adding things and
+ 
+
+ align:start position:0%
+then sort of slowly adding things and
+what we usually say is that
+
+ align:start position:0%
+what we usually say is that
+ 
+
+ align:start position:0%
+what we usually say is that
+configuration in velocity space is much
+
+ align:start position:0%
+configuration in velocity space is much
+ 
+
+ align:start position:0%
+configuration in velocity space is much
+faster and this is the reason think at a
+
+ align:start position:0%
+faster and this is the reason think at a
+ 
+
+ align:start position:0%
+faster and this is the reason think at a
+trajectory for a moment of one particle
+
+ align:start position:0%
+trajectory for a moment of one particle
+ 
+
+ align:start position:0%
+trajectory for a moment of one particle
+and think what happens when you have a
+
+ align:start position:0%
+and think what happens when you have a
+ 
+
+ align:start position:0%
+and think what happens when you have a
+collision suppose that you have
+
+ align:start position:0%
+collision suppose that you have
+ 
+
+ align:start position:0%
+collision suppose that you have
+particles for a moment that are hard
+
+ align:start position:0%
+particles for a moment that are hard
+ 
+
+ align:start position:0%
+particles for a moment that are hard
+spheres in a collision the velocity of
+
+ align:start position:0%
+spheres in a collision the velocity of
+ 
+
+ align:start position:0%
+spheres in a collision the velocity of
+the particle all of a sudden change
+
+ align:start position:0%
+the particle all of a sudden change
+ 
+
+ align:start position:0%
+the particle all of a sudden change
+sign so in the velocity part of the
+
+ align:start position:0%
+sign so in the velocity part of the
+ 
+
+ align:start position:0%
+sign so in the velocity part of the
+phase space your point makes a sudden
+
+ align:start position:0%
+phase space your point makes a sudden
+ 
+
+ align:start position:0%
+phase space your point makes a sudden
+jump okay because the velocity that was
+
+ align:start position:0%
+jump okay because the velocity that was
+ 
+
+ align:start position:0%
+jump okay because the velocity that was
++ 10 has become all of a sudden minus 10
+
+ align:start position:0%
++ 10 has become all of a sudden minus 10
+ 
+
+ align:start position:0%
++ 10 has become all of a sudden minus 10
+so in velocity space for you know the
+
+ align:start position:0%
+so in velocity space for you know the
+ 
+
+ align:start position:0%
+so in velocity space for you know the
+limit case of a system of hard spheres
+
+ align:start position:0%
+limit case of a system of hard spheres
+ 
+
+ align:start position:0%
+limit case of a system of hard spheres
+your representative Point hops
+
+ align:start position:0%
+your representative Point hops
+ 
+
+ align:start position:0%
+your representative Point hops
+everywhere continuously in reality I
+
+ align:start position:0%
+everywhere continuously in reality I
+ 
+
+ align:start position:0%
+everywhere continuously in reality I
+mean you have interaction at all times
+
+ align:start position:0%
+mean you have interaction at all times
+ 
+
+ align:start position:0%
+mean you have interaction at all times
+and you don't really hope but you can
+
+ align:start position:0%
+and you don't really hope but you can
+ 
+
+ align:start position:0%
+and you don't really hope but you can
+sort of you know move very quickly from
+
+ align:start position:0%
+sort of you know move very quickly from
+ 
+
+ align:start position:0%
+sort of you know move very quickly from
+one region to the other region there is
+
+ align:start position:0%
+one region to the other region there is
+ 
+
+ align:start position:0%
+one region to the other region there is
+not anything similar to The Glass
+
+ align:start position:0%
+not anything similar to The Glass
+ 
+
+ align:start position:0%
+not anything similar to The Glass
+entanglement in configuration space so
+
+ align:start position:0%
+entanglement in configuration space so
+ 
+
+ align:start position:0%
+entanglement in configuration space so
+it's very easy to sort of you know
+
+ align:start position:0%
+it's very easy to sort of you know
+ 
+
+ align:start position:0%
+it's very easy to sort of you know
+thermalize velocity it's very difficult
+
+ align:start position:0%
+thermalize velocity it's very difficult
+ 
+
+ align:start position:0%
+thermalize velocity it's very difficult
+to thermalize and equilibrate position
+
+ align:start position:0%
+to thermalize and equilibrate position
+ 
+
+ align:start position:0%
+to thermalize and equilibrate position
+and that's where all sort of you know
+
+ align:start position:0%
+and that's where all sort of you know
+ 
+
+ align:start position:0%
+and that's where all sort of you know
+you need to be careful
+
+ align:start position:0%
+you need to be careful
+ 
+
+ align:start position:0%
+you need to be careful
+and if you really want to be sort of
+
+ align:start position:0%
+and if you really want to be sort of
+ 
+
+ align:start position:0%
+and if you really want to be sort of
+accurate what you can also do instead of
+
+ align:start position:0%
+accurate what you can also do instead of
+ 
+
+ align:start position:0%
+accurate what you can also do instead of
+giving zero velocity to your system you
+
+ align:start position:0%
+giving zero velocity to your system you
+ 
+
+ align:start position:0%
+giving zero velocity to your system you
+can use sort of your concept of
+
+ align:start position:0%
+can use sort of your concept of
+ 
+
+ align:start position:0%
+can use sort of your concept of
+statistical mechanics that is a system
+
+ align:start position:0%
+statistical mechanics that is a system
+ 
+
+ align:start position:0%
+statistical mechanics that is a system
+of classical particles will have a
+
+ align:start position:0%
+of classical particles will have a
+ 
+
+ align:start position:0%
+of classical particles will have a
+distribution of velocities that depends
+
+ align:start position:0%
+distribution of velocities that depends
+ 
+
+ align:start position:0%
+distribution of velocities that depends
+the temperature at which it is and this
+
+ align:start position:0%
+the temperature at which it is and this
+ 
+
+ align:start position:0%
+the temperature at which it is and this
+is Zer in Celsius so it's 273 Kelvin and
+
+ align:start position:0%
+is Zer in Celsius so it's 273 Kelvin and
+ 
+
+ align:start position:0%
+is Zer in Celsius so it's 273 Kelvin and
+sort of the distribution of velocity in
+
+ align:start position:0%
+sort of the distribution of velocity in
+ 
+
+ align:start position:0%
+sort of the distribution of velocity in
+classical system is actually given by
+
+ align:start position:0%
+classical system is actually given by
+ 
+
+ align:start position:0%
+classical system is actually given by
+the Maxwell bolman distribution written
+
+ align:start position:0%
+the Maxwell bolman distribution written
+ 
+
+ align:start position:0%
+the Maxwell bolman distribution written
+above that has basically this shape so
+
+ align:start position:0%
+above that has basically this shape so
+ 
+
+ align:start position:0%
+above that has basically this shape so
+it means that if we are say at 0 Celsius
+
+ align:start position:0%
+it means that if we are say at 0 Celsius
+ 
+
+ align:start position:0%
+it means that if we are say at 0 Celsius
+273 Kelvin we'll have a lot of molecule
+
+ align:start position:0%
+273 Kelvin we'll have a lot of molecule
+ 
+
+ align:start position:0%
+273 Kelvin we'll have a lot of molecule
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+certain uh velocity and then you know
+
+ align:start position:0%
+certain uh velocity and then you know
+ 
+
+ align:start position:0%
+certain uh velocity and then you know
+sort of in principle we can have
+
+ align:start position:0%
+sort of in principle we can have
+ 
+
+ align:start position:0%
+sort of in principle we can have
+molecules with higher and higher
+
+ align:start position:0%
+molecules with higher and higher
+ 
+
+ align:start position:0%
+molecules with higher and higher
+velocity but the probability of finding
+
+ align:start position:0%
+velocity but the probability of finding
+ 
+
+ align:start position:0%
+velocity but the probability of finding
+them decreases and as we increase the
+
+ align:start position:0%
+them decreases and as we increase the
+ 
+
+ align:start position:0%
+them decreases and as we increase the
+temperature the probability distribution
+
+ align:start position:0%
+temperature the probability distribution
+ 
+
+ align:start position:0%
+temperature the probability distribution
+of the velocities for the molecules
+
+ align:start position:0%
+of the velocities for the molecules
+ 
+
+ align:start position:0%
+of the velocities for the molecules
+changes and so as usual you can sort of
+
+ align:start position:0%
+changes and so as usual you can sort of
+ 
+
+ align:start position:0%
+changes and so as usual you can sort of
+you know Define both a median or an
+
+ align:start position:0%
+you know Define both a median or an
+ 
+
+ align:start position:0%
+you know Define both a median or an
+average in your system that is you can
+
+ align:start position:0%
+average in your system that is you can
+ 
+
+ align:start position:0%
+average in your system that is you can
+look at what is the most likely velocity
+
+ align:start position:0%
+look at what is the most likely velocity
+ 
+
+ align:start position:0%
+look at what is the most likely velocity
+that is the top of this curve at 0
+
+ align:start position:0%
+that is the top of this curve at 0
+ 
+
+ align:start position:0%
+that is the top of this curve at 0
+Celsius or you could also Define what is
+
+ align:start position:0%
+Celsius or you could also Define what is
+ 
+
+ align:start position:0%
+Celsius or you could also Define what is
+the average velocity and since that this
+
+ align:start position:0%
+the average velocity and since that this
+ 
+
+ align:start position:0%
+the average velocity and since that this
+curve is asymmetric is going to be
+
+ align:start position:0%
+curve is asymmetric is going to be
+ 
+
+ align:start position:0%
+curve is asymmetric is going to be
+really sort of shifted a little bit and
+
+ align:start position:0%
+really sort of shifted a little bit and
+ 
+
+ align:start position:0%
+really sort of shifted a little bit and
+these are actually the numerical
+
+ align:start position:0%
+these are actually the numerical
+ 
+
+ align:start position:0%
+these are actually the numerical
+expression for these two velocity the
+
+ align:start position:0%
+expression for these two velocity the
+ 
+
+ align:start position:0%
+expression for these two velocity the
+most likely and the average velocity and
+
+ align:start position:0%
+most likely and the average velocity and
+ 
+
+ align:start position:0%
+most likely and the average velocity and
+so you know sort of I've given you the
+
+ align:start position:0%
+so you know sort of I've given you the
+ 
+
+ align:start position:0%
+so you know sort of I've given you the
+example of an oxygen molecule at room
+
+ align:start position:0%
+example of an oxygen molecule at room
+ 
+
+ align:start position:0%
+example of an oxygen molecule at room
+temperature we are talking about you
+
+ align:start position:0%
+temperature we are talking about you
+ 
+
+ align:start position:0%
+temperature we are talking about you
+know 1,000 m/ second so these velocities
+
+ align:start position:0%
+know 1,000 m/ second so these velocities
+ 
+
+ align:start position:0%
+know 1,000 m/ second so these velocities
+if you want are similar to the speed of
+
+ align:start position:0%
+if you want are similar to the speed of
+ 
+
+ align:start position:0%
+if you want are similar to the speed of
+sound in your material because at the
+
+ align:start position:0%
+sound in your material because at the
+ 
+
+ align:start position:0%
+sound in your material because at the
+end you know sound propagates at certain
+
+ align:start position:0%
+end you know sound propagates at certain
+ 
+
+ align:start position:0%
+end you know sound propagates at certain
+speed because that's the velocity of the
+
+ align:start position:0%
+speed because that's the velocity of the
+ 
+
+ align:start position:0%
+speed because that's the velocity of the
+Collision from one molecule to the next
+
+ align:start position:0%
+Collision from one molecule to the next
+ 
+
+ align:start position:0%
+Collision from one molecule to the next
+that are really carrying sound away so
+
+ align:start position:0%
+that are really carrying sound away so
+ 
+
+ align:start position:0%
+that are really carrying sound away so
+if you want to be sophisticated you give
+
+ align:start position:0%
+if you want to be sophisticated you give
+ 
+
+ align:start position:0%
+if you want to be sophisticated you give
+to your system a set of velocity that
+
+ align:start position:0%
+to your system a set of velocity that
+ 
+
+ align:start position:0%
+to your system a set of velocity that
+could be say all identical to the most
+
+ align:start position:0%
+could be say all identical to the most
+ 
+
+ align:start position:0%
+could be say all identical to the most
+likely velocity but again integration
+
+ align:start position:0%
+likely velocity but again integration
+ 
+
+ align:start position:0%
+likely velocity but again integration
+and thermalization in um equilibration
+
+ align:start position:0%
+and thermalization in um equilibration
+ 
+
+ align:start position:0%
+and thermalization in um equilibration
+and thermalization in velocity space is
+
+ align:start position:0%
+and thermalization in velocity space is
+ 
+
+ align:start position:0%
+and thermalization in velocity space is
+very easy so once you have this that is
+
+ align:start position:0%
+very easy so once you have this that is
+ 
+
+ align:start position:0%
+very easy so once you have this that is
+once you have a set of position and a
+
+ align:start position:0%
+once you have a set of position and a
+ 
+
+ align:start position:0%
+once you have a set of position and a
+set of velocity
+
+ align:start position:0%
+set of velocity
+ 
+
+ align:start position:0%
+set of velocity
+you need to use Newton's equation of
+
+ align:start position:0%
+you need to use Newton's equation of
+ 
+
+ align:start position:0%
+you need to use Newton's equation of
+motion of saying of predicting where
+
+ align:start position:0%
+motion of saying of predicting where
+ 
+
+ align:start position:0%
+motion of saying of predicting where
+your system is going is going to
+
+ align:start position:0%
+your system is going is going to
+ 
+
+ align:start position:0%
+your system is going is going to
+go and so that's when sort of you know
+
+ align:start position:0%
+go and so that's when sort of you know
+ 
+
+ align:start position:0%
+go and so that's when sort of you know
+the molecular Dynamic algorithm come
+
+ align:start position:0%
+the molecular Dynamic algorithm come
+ 
+
+ align:start position:0%
+the molecular Dynamic algorithm come
+into play so what you need to do is as
+
+ align:start position:0%
+into play so what you need to do is as
+ 
+
+ align:start position:0%
+into play so what you need to do is as
+we say you need to use an integrator the
+
+ align:start position:0%
+we say you need to use an integrator the
+ 
+
+ align:start position:0%
+we say you need to use an integrator the
+algorithm that tells you what your next
+
+ align:start position:0%
+algorithm that tells you what your next
+ 
+
+ align:start position:0%
+algorithm that tells you what your next
+position and what your next velocities
+
+ align:start position:0%
+position and what your next velocities
+ 
+
+ align:start position:0%
+position and what your next velocities
+are going to be and there are a number
+
+ align:start position:0%
+are going to be and there are a number
+ 
+
+ align:start position:0%
+are going to be and there are a number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+integrators uh you know there are sort
+
+ align:start position:0%
+integrators uh you know there are sort
+ 
+
+ align:start position:0%
+integrators uh you know there are sort
+of subtleties but often you find the
+
+ align:start position:0%
+of subtleties but often you find the
+ 
+
+ align:start position:0%
+of subtleties but often you find the
+name of verlet algorithm this is one
+
+ align:start position:0%
+name of verlet algorithm this is one
+ 
+
+ align:start position:0%
+name of verlet algorithm this is one
+class of algorithm and the other sort of
+
+ align:start position:0%
+class of algorithm and the other sort of
+ 
+
+ align:start position:0%
+class of algorithm and the other sort of
+common class is the gear predictor
+
+ align:start position:0%
+common class is the gear predictor
+ 
+
+ align:start position:0%
+common class is the gear predictor
+corrector just to give you the
+
+ align:start position:0%
+corrector just to give you the
+ 
+
+ align:start position:0%
+corrector just to give you the
+terminology and we look in a moment at
+
+ align:start position:0%
+terminology and we look in a moment at
+ 
+
+ align:start position:0%
+terminology and we look in a moment at
+the verlet algorithm they are all fairly
+
+ align:start position:0%
+the verlet algorithm they are all fairly
+ 
+
+ align:start position:0%
+the verlet algorithm they are all fairly
+simple uh but you know what is really
+
+ align:start position:0%
+simple uh but you know what is really
+ 
+
+ align:start position:0%
+simple uh but you know what is really
+important is that this algorithm should
+
+ align:start position:0%
+important is that this algorithm should
+ 
+
+ align:start position:0%
+important is that this algorithm should
+be robust that is you know they should
+
+ align:start position:0%
+be robust that is you know they should
+ 
+
+ align:start position:0%
+be robust that is you know they should
+sort of give you a trajectory that is
+
+ align:start position:0%
+sort of give you a trajectory that is
+ 
+
+ align:start position:0%
+sort of give you a trajectory that is
+very close to the trajectory that you
+
+ align:start position:0%
+very close to the trajectory that you
+ 
+
+ align:start position:0%
+very close to the trajectory that you
+would get from the perfect analytical
+
+ align:start position:0%
+would get from the perfect analytical
+ 
+
+ align:start position:0%
+would get from the perfect analytical
+integration of the equation of motion
+
+ align:start position:0%
+integration of the equation of motion
+ 
+
+ align:start position:0%
+integration of the equation of motion
+and in particular what is the most
+
+ align:start position:0%
+and in particular what is the most
+ 
+
+ align:start position:0%
+and in particular what is the most
+important thing is that they should be
+
+ align:start position:0%
+important thing is that they should be
+ 
+
+ align:start position:0%
+important thing is that they should be
+accurate in say conserving the constant
+
+ align:start position:0%
+accurate in say conserving the constant
+ 
+
+ align:start position:0%
+accurate in say conserving the constant
+of motion as we have seen from the
+
+ align:start position:0%
+of motion as we have seen from the
+ 
+
+ align:start position:0%
+of motion as we have seen from the
+Newton equation of motion the sum of the
+
+ align:start position:0%
+Newton equation of motion the sum of the
+ 
+
+ align:start position:0%
+Newton equation of motion the sum of the
+kinetic energy and the potential energy
+
+ align:start position:0%
+kinetic energy and the potential energy
+ 
+
+ align:start position:0%
+kinetic energy and the potential energy
+should be a constant if your integration
+
+ align:start position:0%
+should be a constant if your integration
+ 
+
+ align:start position:0%
+should be a constant if your integration
+if your numerical evaluation of that
+
+ align:start position:0%
+if your numerical evaluation of that
+ 
+
+ align:start position:0%
+if your numerical evaluation of that
+equation is poor you will see that the
+
+ align:start position:0%
+equation is poor you will see that the
+ 
+
+ align:start position:0%
+equation is poor you will see that the
+constant of motion is not anymore a
+
+ align:start position:0%
+constant of motion is not anymore a
+ 
+
+ align:start position:0%
+constant of motion is not anymore a
+constant so again this is the sanity
+
+ align:start position:0%
+constant so again this is the sanity
+ 
+
+ align:start position:0%
+constant so again this is the sanity
+check on the accuracy of your
+
+ align:start position:0%
+check on the accuracy of your
+ 
+
+ align:start position:0%
+check on the accuracy of your
+integration and there are sort of you
+
+ align:start position:0%
+integration and there are sort of you
+ 
+
+ align:start position:0%
+integration and there are sort of you
+know more subtle uh elements of you know
+
+ align:start position:0%
+know more subtle uh elements of you know
+ 
+
+ align:start position:0%
+know more subtle uh elements of you know
+the integration algorithm that can
+
+ align:start position:0%
+the integration algorithm that can
+ 
+
+ align:start position:0%
+the integration algorithm that can
+become important but we won't go into
+
+ align:start position:0%
+become important but we won't go into
+ 
+
+ align:start position:0%
+become important but we won't go into
+there and then sort of as I said
+
+ align:start position:0%
+there and then sort of as I said
+ 
+
+ align:start position:0%
+there and then sort of as I said
+straightforward integration of the
+
+ align:start position:0%
+straightforward integration of the
+ 
+
+ align:start position:0%
+straightforward integration of the
+Newton equation of motion gives you the
+
+ align:start position:0%
+Newton equation of motion gives you the
+ 
+
+ align:start position:0%
+Newton equation of motion gives you the
+microcanonical ensemble in which the
+
+ align:start position:0%
+microcanonical ensemble in which the
+ 
+
+ align:start position:0%
+microcanonical ensemble in which the
+total energy is conserved but sometimes
+
+ align:start position:0%
+total energy is conserved but sometimes
+ 
+
+ align:start position:0%
+total energy is conserved but sometimes
+you want to study systems in which the
+
+ align:start position:0%
+you want to study systems in which the
+ 
+
+ align:start position:0%
+you want to study systems in which the
+temperature is fixed or you could want
+
+ align:start position:0%
+temperature is fixed or you could want
+ 
+
+ align:start position:0%
+temperature is fixed or you could want
+to study system in which the pressure is
+
+ align:start position:0%
+to study system in which the pressure is
+ 
+
+ align:start position:0%
+to study system in which the pressure is
+fixed and so you need to sort of augment
+
+ align:start position:0%
+fixed and so you need to sort of augment
+ 
+
+ align:start position:0%
+fixed and so you need to sort of augment
+your molecular Dynamic integrator with
+
+ align:start position:0%
+your molecular Dynamic integrator with
+ 
+
+ align:start position:0%
+your molecular Dynamic integrator with
+uh uh some feature that allows you to
+
+ align:start position:0%
+uh uh some feature that allows you to
+ 
+
+ align:start position:0%
+uh uh some feature that allows you to
+control those intensive variables so if
+
+ align:start position:0%
+control those intensive variables so if
+ 
+
+ align:start position:0%
+control those intensive variables so if
+you want say to control the temperature
+
+ align:start position:0%
+you want say to control the temperature
+ 
+
+ align:start position:0%
+you want say to control the temperature
+of the system what we say usually is
+
+ align:start position:0%
+of the system what we say usually is
+ 
+
+ align:start position:0%
+of the system what we say usually is
+that we couple the system to a
+
+ align:start position:0%
+that we couple the system to a
+ 
+
+ align:start position:0%
+that we couple the system to a
+thermostat that is we make sure that the
+
+ align:start position:0%
+thermostat that is we make sure that the
+ 
+
+ align:start position:0%
+thermostat that is we make sure that the
+temperature in your Evolution doesn't
+
+ align:start position:0%
+temperature in your Evolution doesn't
+ 
+
+ align:start position:0%
+temperature in your Evolution doesn't
+change and you'll see examples in the
+
+ align:start position:0%
+change and you'll see examples in the
+ 
+
+ align:start position:0%
+change and you'll see examples in the
+next class of this and uh uh in the case
+
+ align:start position:0%
+next class of this and uh uh in the case
+ 
+
+ align:start position:0%
+next class of this and uh uh in the case
+in particular of something say like the
+
+ align:start position:0%
+in particular of something say like the
+ 
+
+ align:start position:0%
+in particular of something say like the
+temperature you have a whole set of
+
+ align:start position:0%
+temperature you have a whole set of
+ 
+
+ align:start position:0%
+temperature you have a whole set of
+possible thermostats that is you could
+
+ align:start position:0%
+possible thermostats that is you could
+ 
+
+ align:start position:0%
+possible thermostats that is you could
+use um stochastic approaches that is you
+
+ align:start position:0%
+use um stochastic approaches that is you
+ 
+
+ align:start position:0%
+use um stochastic approaches that is you
+have your evolution of your system and
+
+ align:start position:0%
+have your evolution of your system and
+ 
+
+ align:start position:0%
+have your evolution of your system and
+your system doesn't conserve if it's
+
+ align:start position:0%
+your system doesn't conserve if it's
+ 
+
+ align:start position:0%
+your system doesn't conserve if it's
+microcanonical the temperature sometimes
+
+ align:start position:0%
+microcanonical the temperature sometimes
+ 
+
+ align:start position:0%
+microcanonical the temperature sometimes
+it go towards higher temperature
+
+ align:start position:0%
+it go towards higher temperature
+ 
+
+ align:start position:0%
+it go towards higher temperature
+sometimes it's go towards lower
+
+ align:start position:0%
+sometimes it's go towards lower
+ 
+
+ align:start position:0%
+sometimes it's go towards lower
+temperature and you know what you could
+
+ align:start position:0%
+temperature and you know what you could
+ 
+
+ align:start position:0%
+temperature and you know what you could
+do is either every now and then sort of
+
+ align:start position:0%
+do is either every now and then sort of
+ 
+
+ align:start position:0%
+do is either every now and then sort of
+absorb some energy or give back some
+
+ align:start position:0%
+absorb some energy or give back some
+ 
+
+ align:start position:0%
+absorb some energy or give back some
+energy in your system and that would be
+
+ align:start position:0%
+energy in your system and that would be
+ 
+
+ align:start position:0%
+energy in your system and that would be
+a lan dyamics in order to control the
+
+ align:start position:0%
+a lan dyamics in order to control the
+ 
+
+ align:start position:0%
+a lan dyamics in order to control the
+average kinetic energy of your system or
+
+ align:start position:0%
+average kinetic energy of your system or
+ 
+
+ align:start position:0%
+average kinetic energy of your system or
+you could
+
+ align:start position:0%
+you could
+ 
+
+ align:start position:0%
+you could
+somehow for forbid in the microcanonical
+
+ align:start position:0%
+somehow for forbid in the microcanonical
+ 
+
+ align:start position:0%
+somehow for forbid in the microcanonical
+evolution your system to choose a state
+
+ align:start position:0%
+evolution your system to choose a state
+ 
+
+ align:start position:0%
+evolution your system to choose a state
+in which the temperature changes so if
+
+ align:start position:0%
+in which the temperature changes so if
+ 
+
+ align:start position:0%
+in which the temperature changes so if
+your new positions are such that your
+
+ align:start position:0%
+your new positions are such that your
+ 
+
+ align:start position:0%
+your new positions are such that your
+velocity give an increase in temperature
+
+ align:start position:0%
+velocity give an increase in temperature
+ 
+
+ align:start position:0%
+velocity give an increase in temperature
+you just sort of you know shorten how
+
+ align:start position:0%
+you just sort of you know shorten how
+ 
+
+ align:start position:0%
+you just sort of you know shorten how
+much your atoms move in order to make
+
+ align:start position:0%
+much your atoms move in order to make
+ 
+
+ align:start position:0%
+much your atoms move in order to make
+the velocity smaller and in order to
+
+ align:start position:0%
+the velocity smaller and in order to
+ 
+
+ align:start position:0%
+the velocity smaller and in order to
+make the kinetic energy conserved or
+
+ align:start position:0%
+make the kinetic energy conserved or
+ 
+
+ align:start position:0%
+make the kinetic energy conserved or
+there are sort of more complex dynamical
+
+ align:start position:0%
+there are sort of more complex dynamical
+ 
+
+ align:start position:0%
+there are sort of more complex dynamical
+ways of impose temperature that goes
+
+ align:start position:0%
+ways of impose temperature that goes
+ 
+
+ align:start position:0%
+ways of impose temperature that goes
+under the name of extended aonian or
+
+ align:start position:0%
+under the name of extended aonian or
+ 
+
+ align:start position:0%
+under the name of extended aonian or
+extended system of which we'll see an
+
+ align:start position:0%
+extended system of which we'll see an
+ 
+
+ align:start position:0%
+extended system of which we'll see an
+example that is the no
+
+ align:start position:0%
+example that is the no
+ 
+
+ align:start position:0%
+example that is the no
+U but let me give you sort of you know
+
+ align:start position:0%
+U but let me give you sort of you know
+ 
+
+ align:start position:0%
+U but let me give you sort of you know
+really what is the simplest and still
+
+ align:start position:0%
+really what is the simplest and still
+ 
+
+ align:start position:0%
+really what is the simplest and still
+one of the most used uh sort of
+
+ align:start position:0%
+one of the most used uh sort of
+ 
+
+ align:start position:0%
+one of the most used uh sort of
+numerical integrators and it tends to be
+
+ align:start position:0%
+numerical integrators and it tends to be
+ 
+
+ align:start position:0%
+numerical integrators and it tends to be
+very robust and very accurate so you
+
+ align:start position:0%
+very robust and very accurate so you
+ 
+
+ align:start position:0%
+very robust and very accurate so you
+know it's still used in a lot of
+
+ align:start position:0%
+know it's still used in a lot of
+ 
+
+ align:start position:0%
+know it's still used in a lot of
+molecular Dynamic simulation and there
+
+ align:start position:0%
+molecular Dynamic simulation and there
+ 
+
+ align:start position:0%
+molecular Dynamic simulation and there
+is often no reason to do anything better
+
+ align:start position:0%
+is often no reason to do anything better
+ 
+
+ align:start position:0%
+is often no reason to do anything better
+than this so in a way we are in a luier
+
+ align:start position:0%
+than this so in a way we are in a luier
+ 
+
+ align:start position:0%
+than this so in a way we are in a luier
+situation than sort of in quantum
+
+ align:start position:0%
+situation than sort of in quantum
+ 
+
+ align:start position:0%
+situation than sort of in quantum
+mechanics this is good enough in almost
+
+ align:start position:0%
+mechanics this is good enough in almost
+ 
+
+ align:start position:0%
+mechanics this is good enough in almost
+all cases and this is sort of how we
+
+ align:start position:0%
+all cases and this is sort of how we
+ 
+
+ align:start position:0%
+all cases and this is sort of how we
+look at the problem uh that is what we
+
+ align:start position:0%
+look at the problem uh that is what we
+ 
+
+ align:start position:0%
+look at the problem uh that is what we
+need to do always is we need to
+
+ align:start position:0%
+need to do always is we need to
+ 
+
+ align:start position:0%
+need to do always is we need to
+calculate the
+
+ align:start position:0%
+calculate the
+ 
+
+ align:start position:0%
+calculate the
+position of each
+
+ align:start position:0%
+position of each
+ 
+
+ align:start position:0%
+position of each
+particle at a time t plus delta
+
+ align:start position:0%
+particle at a time t plus delta
+ 
+
+ align:start position:0%
+particle at a time t plus delta
+T once we know the position the velocity
+
+ align:start position:0%
+T once we know the position the velocity
+ 
+
+ align:start position:0%
+T once we know the position the velocity
+and the forces on that particle at time
+
+ align:start position:0%
+and the forces on that particle at time
+ 
+
+ align:start position:0%
+and the forces on that particle at time
+T So suppose I'm at certain instant in
+
+ align:start position:0%
+T So suppose I'm at certain instant in
+ 
+
+ align:start position:0%
+T So suppose I'm at certain instant in
+time that I call T I know everything
+
+ align:start position:0%
+time that I call T I know everything
+ 
+
+ align:start position:0%
+time that I call T I know everything
+about my system position velocity and
+
+ align:start position:0%
+about my system position velocity and
+ 
+
+ align:start position:0%
+about my system position velocity and
+forces what I really need to do is
+
+ align:start position:0%
+forces what I really need to do is
+ 
+
+ align:start position:0%
+forces what I really need to do is
+predict what are the new positions and
+
+ align:start position:0%
+predict what are the new positions and
+ 
+
+ align:start position:0%
+predict what are the new positions and
+when I'm in the new positions I want to
+
+ align:start position:0%
+when I'm in the new positions I want to
+ 
+
+ align:start position:0%
+when I'm in the new positions I want to
+calculate the forces again and um evolve
+
+ align:start position:0%
+calculate the forces again and um evolve
+ 
+
+ align:start position:0%
+calculate the forces again and um evolve
+the system and now what do we do well
+
+ align:start position:0%
+the system and now what do we do well
+ 
+
+ align:start position:0%
+the system and now what do we do well
+let's do a simple tailor expansion that
+
+ align:start position:0%
+let's do a simple tailor expansion that
+ 
+
+ align:start position:0%
+let's do a simple tailor expansion that
+is you know this is R of T is a f
+
+ align:start position:0%
+is you know this is R of T is a f
+ 
+
+ align:start position:0%
+is you know this is R of T is a f
+function of the variable T so we can use
+
+ align:start position:0%
+function of the variable T so we can use
+ 
+
+ align:start position:0%
+function of the variable T so we can use
+a tailor expansion and R of t plus delta
+
+ align:start position:0%
+a tailor expansion and R of t plus delta
+ 
+
+ align:start position:0%
+a tailor expansion and R of t plus delta
+T is going to be R of t plus the
+
+ align:start position:0%
+T is going to be R of t plus the
+ 
+
+ align:start position:0%
+T is going to be R of t plus the
+derivative of r with respect to T *
+
+ align:start position:0%
+derivative of r with respect to T *
+ 
+
+ align:start position:0%
+derivative of r with respect to T *
+delta T and that's the velocity plus 1
+
+ align:start position:0%
+delta T and that's the velocity plus 1
+ 
+
+ align:start position:0%
+delta T and that's the velocity plus 1
+12 the second derivative of uh the
+
+ align:start position:0%
+12 the second derivative of uh the
+ 
+
+ align:start position:0%
+12 the second derivative of uh the
+position with respect to time and that's
+
+ align:start position:0%
+position with respect to time and that's
+ 
+
+ align:start position:0%
+position with respect to time and that's
+the acceleration time delta T square and
+
+ align:start position:0%
+the acceleration time delta T square and
+ 
+
+ align:start position:0%
+the acceleration time delta T square and
+so on for the third derivatives and so
+
+ align:start position:0%
+so on for the third derivatives and so
+ 
+
+ align:start position:0%
+so on for the third derivatives and so
+on for the fourth fifth at infinum this
+
+ align:start position:0%
+on for the fourth fifth at infinum this
+ 
+
+ align:start position:0%
+on for the fourth fifth at infinum this
+is just the tailor expansion as a
+
+ align:start position:0%
+is just the tailor expansion as a
+ 
+
+ align:start position:0%
+is just the tailor expansion as a
+function okay and so it gives us the
+
+ align:start position:0%
+function okay and so it gives us the
+ 
+
+ align:start position:0%
+function okay and so it gives us the
+position at t plus delta T knowing all
+
+ align:start position:0%
+position at t plus delta T knowing all
+ 
+
+ align:start position:0%
+position at t plus delta T knowing all
+the derivatives first second third
+
+ align:start position:0%
+the derivatives first second third
+ 
+
+ align:start position:0%
+the derivatives first second third
+fourth n at times T and once we have the
+
+ align:start position:0%
+fourth n at times T and once we have the
+ 
+
+ align:start position:0%
+fourth n at times T and once we have the
+derivatives we can not only sort of
+
+ align:start position:0%
+derivatives we can not only sort of
+ 
+
+ align:start position:0%
+derivatives we can not only sort of
+predict what the position would be at t
+
+ align:start position:0%
+predict what the position would be at t
+ 
+
+ align:start position:0%
+predict what the position would be at t
+plus delta T but also what the position
+
+ align:start position:0%
+plus delta T but also what the position
+ 
+
+ align:start position:0%
+plus delta T but also what the position
+would be at T minus delta T and it's
+
+ align:start position:0%
+would be at T minus delta T and it's
+ 
+
+ align:start position:0%
+would be at T minus delta T and it's
+written here and if you think the uh
+
+ align:start position:0%
+written here and if you think the uh
+ 
+
+ align:start position:0%
+written here and if you think the uh
+terms with an odd power change sign in
+
+ align:start position:0%
+terms with an odd power change sign in
+ 
+
+ align:start position:0%
+terms with an odd power change sign in
+delta T and the terms with an even power
+
+ align:start position:0%
+delta T and the terms with an even power
+ 
+
+ align:start position:0%
+delta T and the terms with an even power
+in delta T do not change sign so we have
+
+ align:start position:0%
+in delta T do not change sign so we have
+ 
+
+ align:start position:0%
+in delta T do not change sign so we have
+just done a tailor expansion and now
+
+ align:start position:0%
+just done a tailor expansion and now
+ 
+
+ align:start position:0%
+just done a tailor expansion and now
+what we do is we actually sum these two
+
+ align:start position:0%
+what we do is we actually sum these two
+ 
+
+ align:start position:0%
+what we do is we actually sum these two
+quantities together okay and this is
+
+ align:start position:0%
+quantities together okay and this is
+ 
+
+ align:start position:0%
+quantities together okay and this is
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+we obtain okay we sum the two quantities
+
+ align:start position:0%
+we obtain okay we sum the two quantities
+ 
+
+ align:start position:0%
+we obtain okay we sum the two quantities
+together all the odd terms disappear
+
+ align:start position:0%
+together all the odd terms disappear
+ 
+
+ align:start position:0%
+together all the odd terms disappear
+this sum to zero this s to zero the
+
+ align:start position:0%
+this sum to zero this s to zero the
+ 
+
+ align:start position:0%
+this sum to zero this s to zero the
+fifth order seventh order and so s to
+
+ align:start position:0%
+fifth order seventh order and so s to
+ 
+
+ align:start position:0%
+fifth order seventh order and so s to
+zero so what we have is that we have rt
+
+ align:start position:0%
+zero so what we have is that we have rt
+ 
+
+ align:start position:0%
+zero so what we have is that we have rt
++ delta T plus RT minus delta T is equal
+
+ align:start position:0%
++ delta T plus RT minus delta T is equal
+ 
+
+ align:start position:0%
++ delta T plus RT minus delta T is equal
+a 2 * RT plus Alpha sorry acceleration
+
+ align:start position:0%
+a 2 * RT plus Alpha sorry acceleration
+ 
+
+ align:start position:0%
+a 2 * RT plus Alpha sorry acceleration
+time delta T Square it's just written
+
+ align:start position:0%
+time delta T Square it's just written
+ 
+
+ align:start position:0%
+time delta T Square it's just written
+here and then rearrange the terms but
+
+ align:start position:0%
+here and then rearrange the terms but
+ 
+
+ align:start position:0%
+here and then rearrange the terms but
+you see this is the verlet algorithm now
+
+ align:start position:0%
+you see this is the verlet algorithm now
+ 
+
+ align:start position:0%
+you see this is the verlet algorithm now
+what we have when we look at this
+
+ align:start position:0%
+what we have when we look at this
+ 
+
+ align:start position:0%
+what we have when we look at this
+expression we have an expression that
+
+ align:start position:0%
+expression we have an expression that
+ 
+
+ align:start position:0%
+expression we have an expression that
+tells us what is the position at my new
+
+ align:start position:0%
+tells us what is the position at my new
+ 
+
+ align:start position:0%
+tells us what is the position at my new
+time step knowing the position at my
+
+ align:start position:0%
+time step knowing the position at my
+ 
+
+ align:start position:0%
+time step knowing the position at my
+current instant knowing the position at
+
+ align:start position:0%
+current instant knowing the position at
+ 
+
+ align:start position:0%
+current instant knowing the position at
+the previous instant we are sort of
+
+ align:start position:0%
+the previous instant we are sort of
+ 
+
+ align:start position:0%
+the previous instant we are sort of
+keeping configurations from our
+
+ align:start position:0%
+keeping configurations from our
+ 
+
+ align:start position:0%
+keeping configurations from our
+trajectories so we know where we were
+
+ align:start position:0%
+trajectories so we know where we were
+ 
+
+ align:start position:0%
+trajectories so we know where we were
+before we know where we are now and we
+
+ align:start position:0%
+before we know where we are now and we
+ 
+
+ align:start position:0%
+before we know where we are now and we
+know where we are going to be just by
+
+ align:start position:0%
+know where we are going to be just by
+ 
+
+ align:start position:0%
+know where we are going to be just by
+adding to this the term acceleration at
+
+ align:start position:0%
+adding to this the term acceleration at
+ 
+
+ align:start position:0%
+adding to this the term acceleration at
+the present times times Delta t s we
+
+ align:start position:0%
+the present times times Delta t s we
+ 
+
+ align:start position:0%
+the present times times Delta t s we
+make an error because we are not
+
+ align:start position:0%
+make an error because we are not
+ 
+
+ align:start position:0%
+make an error because we are not
+introducing terms
+
+ align:start position:0%
+introducing terms
+ 
+
+ align:start position:0%
+introducing terms
+that are higher order in delta T squ but
+
+ align:start position:0%
+that are higher order in delta T squ but
+ 
+
+ align:start position:0%
+that are higher order in delta T squ but
+you see the term in delta T Cube has
+
+ align:start position:0%
+you see the term in delta T Cube has
+ 
+
+ align:start position:0%
+you see the term in delta T Cube has
+cancelled out so the error that we make
+
+ align:start position:0%
+cancelled out so the error that we make
+ 
+
+ align:start position:0%
+cancelled out so the error that we make
+is just of the order Delta T4 that is
+
+ align:start position:0%
+is just of the order Delta T4 that is
+ 
+
+ align:start position:0%
+is just of the order Delta T4 that is
+that means that the smaller we make the
+
+ align:start position:0%
+that means that the smaller we make the
+ 
+
+ align:start position:0%
+that means that the smaller we make the
+delta T the smaller we make the time
+
+ align:start position:0%
+delta T the smaller we make the time
+ 
+
+ align:start position:0%
+delta T the smaller we make the time
+step the more accurate our integration
+
+ align:start position:0%
+step the more accurate our integration
+ 
+
+ align:start position:0%
+step the more accurate our integration
+is and so this is if you want the most
+
+ align:start position:0%
+is and so this is if you want the most
+ 
+
+ align:start position:0%
+is and so this is if you want the most
+critical parameter in your molecular
+
+ align:start position:0%
+critical parameter in your molecular
+ 
+
+ align:start position:0%
+critical parameter in your molecular
+Dynamic simulation you need to make sure
+
+ align:start position:0%
+Dynamic simulation you need to make sure
+ 
+
+ align:start position:0%
+Dynamic simulation you need to make sure
+that the step steps that you take are
+
+ align:start position:0%
+that the step steps that you take are
+ 
+
+ align:start position:0%
+that the step steps that you take are
+small enough considering what is really
+
+ align:start position:0%
+small enough considering what is really
+ 
+
+ align:start position:0%
+small enough considering what is really
+the variation of your Force as a
+
+ align:start position:0%
+the variation of your Force as a
+ 
+
+ align:start position:0%
+the variation of your Force as a
+function of time because remember that
+
+ align:start position:0%
+function of time because remember that
+ 
+
+ align:start position:0%
+function of time because remember that
+you know now we use Newton's equation of
+
+ align:start position:0%
+you know now we use Newton's equation of
+ 
+
+ align:start position:0%
+you know now we use Newton's equation of
+motion the acceleration at a time T is
+
+ align:start position:0%
+motion the acceleration at a time T is
+ 
+
+ align:start position:0%
+motion the acceleration at a time T is
+just given by the mass the force divided
+
+ align:start position:0%
+just given by the mass the force divided
+ 
+
+ align:start position:0%
+just given by the mass the force divided
+by the mass and because the force is
+
+ align:start position:0%
+by the mass and because the force is
+ 
+
+ align:start position:0%
+by the mass and because the force is
+just the gradient of the potential is
+
+ align:start position:0%
+just the gradient of the potential is
+ 
+
+ align:start position:0%
+just the gradient of the potential is
+just given by this so at a certain in in
+
+ align:start position:0%
+just given by this so at a certain in in
+ 
+
+ align:start position:0%
+just given by this so at a certain in in
+time T you have the acceleration acting
+
+ align:start position:0%
+time T you have the acceleration acting
+ 
+
+ align:start position:0%
+time T you have the acceleration acting
+in your particles just by taking the
+
+ align:start position:0%
+in your particles just by taking the
+ 
+
+ align:start position:0%
+in your particles just by taking the
+force and dividing by the mass so at
+
+ align:start position:0%
+force and dividing by the mass so at
+ 
+
+ align:start position:0%
+force and dividing by the mass so at
+every instant you calculate force and
+
+ align:start position:0%
+every instant you calculate force and
+ 
+
+ align:start position:0%
+every instant you calculate force and
+the force lets you evolve the system and
+
+ align:start position:0%
+the force lets you evolve the system and
+ 
+
+ align:start position:0%
+the force lets you evolve the system and
+it keeps giving you the new positions
+
+ align:start position:0%
+it keeps giving you the new positions
+ 
+
+ align:start position:0%
+it keeps giving you the new positions
+and so you know what is the trajectory
+
+ align:start position:0%
+and so you know what is the trajectory
+ 
+
+ align:start position:0%
+and so you know what is the trajectory
+in configuration space and you can very
+
+ align:start position:0%
+in configuration space and you can very
+ 
+
+ align:start position:0%
+in configuration space and you can very
+simply find out what is your velocity at
+
+ align:start position:0%
+simply find out what is your velocity at
+ 
+
+ align:start position:0%
+simply find out what is your velocity at
+every instant T if you need to calculate
+
+ align:start position:0%
+every instant T if you need to calculate
+ 
+
+ align:start position:0%
+every instant T if you need to calculate
+what is the velocity just by you know
+
+ align:start position:0%
+what is the velocity just by you know
+ 
+
+ align:start position:0%
+what is the velocity just by you know
+doing doing a finite difference
+
+ align:start position:0%
+doing doing a finite difference
+ 
+
+ align:start position:0%
+doing doing a finite difference
+calculation of the tangent basically the
+
+ align:start position:0%
+calculation of the tangent basically the
+ 
+
+ align:start position:0%
+calculation of the tangent basically the
+velocity is the tangent of the
+
+ align:start position:0%
+velocity is the tangent of the
+ 
+
+ align:start position:0%
+velocity is the tangent of the
+trajectory with respect to T okay this
+
+ align:start position:0%
+trajectory with respect to T okay this
+ 
+
+ align:start position:0%
+trajectory with respect to T okay this
+concludes class uh sort of what we'll
+
+ align:start position:0%
+concludes class uh sort of what we'll
+ 
+
+ align:start position:0%
+concludes class uh sort of what we'll
+see in the next lecture is how we
+
+ align:start position:0%
+see in the next lecture is how we
+ 
+
+ align:start position:0%
+see in the next lecture is how we
+actually sort of you know take this
+
+ align:start position:0%
+actually sort of you know take this
+ 
+
+ align:start position:0%
+actually sort of you know take this
+verlet integration and how we use it to
+
+ align:start position:0%
+verlet integration and how we use it to
+ 
+
+ align:start position:0%
+verlet integration and how we use it to
+do the characterization of the
+
+ align:start position:0%
+do the characterization of the
+ 
+
+ align:start position:0%
+do the characterization of the
+thermodynamical properties of a real
+
+ align:start position:0%
+thermodynamical properties of a real
+ 
+
+ align:start position:0%
+thermodynamical properties of a real
+system so um today is Thursday next week
+
+ align:start position:0%
+system so um today is Thursday next week
+ 
+
+ align:start position:0%
+system so um today is Thursday next week
+is spring break so we'll see each other
+
+ align:start position:0%
+is spring break so we'll see each other
+ 
+
+ align:start position:0%
+is spring break so we'll see each other
+again on uh Tuesday
+
+ align:start position:0%
+again on uh Tuesday
+ 
+
+ align:start position:0%
+again on uh Tuesday
+29th and
+
+ align:start position:0%
+29th and
+ 
+
+ align:start position:0%
+29th and
+um I will be at a conference and all the
+
+ align:start position:0%
+um I will be at a conference and all the
+ 
+
+ align:start position:0%
+um I will be at a conference and all the
+Tas will be at a conference next week so
+
+ align:start position:0%
+Tas will be at a conference next week so
+ 
+
+ align:start position:0%
+Tas will be at a conference next week so
+it will be slightly difficult
+
+ align:start position:0%
+it will be slightly difficult
+ 
+
+ align:start position:0%
+it will be slightly difficult
+communicating via email so try to ask a
+
+ align:start position:0%
+communicating via email so try to ask a
+ 
+
+ align:start position:0%
+communicating via email so try to ask a
+lot of questions between now and Sunday
+
+ align:start position:0%
+lot of questions between now and Sunday
+ 
+
+ align:start position:0%
+lot of questions between now and Sunday
+for your problem set that is due the
+
+ align:start position:0%
+for your problem set that is due the
+ 
+
+ align:start position:0%
+for your problem set that is due the
+Tuesday after spring break and that will
+
+ align:start position:0%
+Tuesday after spring break and that will
+ 
+
+ align:start position:0%
+Tuesday after spring break and that will
+be problem set
+
+ align:start position:0%
+be problem set
+ 
+
+ align:start position:0%
+be problem set
+too otherwise enjoy spring break
\ No newline at end of file
diff --git a/gj8RoTm9jxM.txt b/gj8RoTm9jxM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c6332e4f5a82e814cd57bc110400cd9d8dd54685
--- /dev/null
+++ b/gj8RoTm9jxM.txt
@@ -0,0 +1,1291 @@
+align:start position:0%
+ 
+you okay
+
+ align:start position:0%
+you okay
+ 
+
+ align:start position:0%
+you okay
+good morning and welcome thank you for
+
+ align:start position:0%
+good morning and welcome thank you for
+ 
+
+ align:start position:0%
+good morning and welcome thank you for
+agreeing to meet with me to serve on
+
+ align:start position:0%
+agreeing to meet with me to serve on
+ 
+
+ align:start position:0%
+agreeing to meet with me to serve on
+this advisory group to develop a
+
+ align:start position:0%
+this advisory group to develop a
+ 
+
+ align:start position:0%
+this advisory group to develop a
+regional water strategy for metropolitan
+
+ align:start position:0%
+regional water strategy for metropolitan
+ 
+
+ align:start position:0%
+regional water strategy for metropolitan
+area I've called this meeting to give
+
+ align:start position:0%
+area I've called this meeting to give
+ 
+
+ align:start position:0%
+area I've called this meeting to give
+you my advice for how to proceed in this
+
+ align:start position:0%
+you my advice for how to proceed in this
+ 
+
+ align:start position:0%
+you my advice for how to proceed in this
+process during this meeting I will first
+
+ align:start position:0%
+process during this meeting I will first
+ 
+
+ align:start position:0%
+process during this meeting I will first
+clarify our goals in this process then
+
+ align:start position:0%
+clarify our goals in this process then
+ 
+
+ align:start position:0%
+clarify our goals in this process then
+identify some challenges that I see for
+
+ align:start position:0%
+identify some challenges that I see for
+ 
+
+ align:start position:0%
+identify some challenges that I see for
+and what we stand to lose if we don't
+
+ align:start position:0%
+and what we stand to lose if we don't
+ 
+
+ align:start position:0%
+and what we stand to lose if we don't
+conduct this process wisely next I'll
+
+ align:start position:0%
+conduct this process wisely next I'll
+ 
+
+ align:start position:0%
+conduct this process wisely next I'll
+give my thoughts on a strategy to follow
+
+ align:start position:0%
+give my thoughts on a strategy to follow
+ 
+
+ align:start position:0%
+give my thoughts on a strategy to follow
+to reach a sound and politically viable
+
+ align:start position:0%
+to reach a sound and politically viable
+ 
+
+ align:start position:0%
+to reach a sound and politically viable
+regional plan and I'll talk about what I
+
+ align:start position:0%
+regional plan and I'll talk about what I
+ 
+
+ align:start position:0%
+regional plan and I'll talk about what I
+think success in this process would look
+
+ align:start position:0%
+think success in this process would look
+ 
+
+ align:start position:0%
+think success in this process would look
+like for you to keep in mind
+
+ align:start position:0%
+like for you to keep in mind
+ 
+
+ align:start position:0%
+like for you to keep in mind
+prospectively as you carry out the
+
+ align:start position:0%
+prospectively as you carry out the
+ 
+
+ align:start position:0%
+prospectively as you carry out the
+planning process so our goal is to
+
+ align:start position:0%
+planning process so our goal is to
+ 
+
+ align:start position:0%
+planning process so our goal is to
+develop a strategy for administering
+
+ align:start position:0%
+develop a strategy for administering
+ 
+
+ align:start position:0%
+develop a strategy for administering
+water that balances and to whatever
+
+ align:start position:0%
+water that balances and to whatever
+ 
+
+ align:start position:0%
+water that balances and to whatever
+extent possible actually meets the needs
+
+ align:start position:0%
+extent possible actually meets the needs
+ 
+
+ align:start position:0%
+extent possible actually meets the needs
+of the diverse stakeholders from the
+
+ align:start position:0%
+of the diverse stakeholders from the
+ 
+
+ align:start position:0%
+of the diverse stakeholders from the
+industrial residential agricultural and
+
+ align:start position:0%
+industrial residential agricultural and
+ 
+
+ align:start position:0%
+industrial residential agricultural and
+conservation sectors as well as our
+
+ align:start position:0%
+conservation sectors as well as our
+ 
+
+ align:start position:0%
+conservation sectors as well as our
+partners in government I also believe
+
+ align:start position:0%
+partners in government I also believe
+ 
+
+ align:start position:0%
+partners in government I also believe
+that a second but still important goal
+
+ align:start position:0%
+that a second but still important goal
+ 
+
+ align:start position:0%
+that a second but still important goal
+is to get through this process in a way
+
+ align:start position:0%
+is to get through this process in a way
+ 
+
+ align:start position:0%
+is to get through this process in a way
+that this diverse group of stakeholders
+
+ align:start position:0%
+that this diverse group of stakeholders
+ 
+
+ align:start position:0%
+that this diverse group of stakeholders
+feels good about the process they took
+
+ align:start position:0%
+feels good about the process they took
+ 
+
+ align:start position:0%
+feels good about the process they took
+part in has learned from it and thus is
+
+ align:start position:0%
+part in has learned from it and thus is
+ 
+
+ align:start position:0%
+part in has learned from it and thus is
+encouraged to and has a skill set to
+
+ align:start position:0%
+encouraged to and has a skill set to
+ 
+
+ align:start position:0%
+encouraged to and has a skill set to
+collaborate again in the future as you
+
+ align:start position:0%
+collaborate again in the future as you
+ 
+
+ align:start position:0%
+collaborate again in the future as you
+know we face some challenges to
+
+ align:start position:0%
+know we face some challenges to
+ 
+
+ align:start position:0%
+know we face some challenges to
+developing this plan with current
+
+ align:start position:0%
+developing this plan with current
+ 
+
+ align:start position:0%
+developing this plan with current
+distribution and use water supplies are
+
+ align:start position:0%
+distribution and use water supplies are
+ 
+
+ align:start position:0%
+distribution and use water supplies are
+tight and are insufficient to meet the
+
+ align:start position:0%
+tight and are insufficient to meet the
+ 
+
+ align:start position:0%
+tight and are insufficient to meet the
+needs of development that we hope will
+
+ align:start position:0%
+needs of development that we hope will
+ 
+
+ align:start position:0%
+needs of development that we hope will
+return to our region with economic
+
+ align:start position:0%
+return to our region with economic
+ 
+
+ align:start position:0%
+return to our region with economic
+rebound if we don't develop a strategy
+
+ align:start position:0%
+rebound if we don't develop a strategy
+ 
+
+ align:start position:0%
+rebound if we don't develop a strategy
+to as far as possible meet the needs of
+
+ align:start position:0%
+to as far as possible meet the needs of
+ 
+
+ align:start position:0%
+to as far as possible meet the needs of
+all the stakeholder groups involved we
+
+ align:start position:0%
+all the stakeholder groups involved we
+ 
+
+ align:start position:0%
+all the stakeholder groups involved we
+will see rising conflict that could
+
+ align:start position:0%
+will see rising conflict that could
+ 
+
+ align:start position:0%
+will see rising conflict that could
+really strain the relationships in this
+
+ align:start position:0%
+really strain the relationships in this
+ 
+
+ align:start position:0%
+really strain the relationships in this
+community and ultimately tear it apart
+
+ align:start position:0%
+community and ultimately tear it apart
+ 
+
+ align:start position:0%
+community and ultimately tear it apart
+I'm also concerned that if we don't act
+
+ align:start position:0%
+I'm also concerned that if we don't act
+ 
+
+ align:start position:0%
+I'm also concerned that if we don't act
+wisely and proceed in a way that
+
+ align:start position:0%
+wisely and proceed in a way that
+ 
+
+ align:start position:0%
+wisely and proceed in a way that
+everyone is on board with our process
+
+ align:start position:0%
+everyone is on board with our process
+ 
+
+ align:start position:0%
+everyone is on board with our process
+could be undermined who my parties who
+
+ align:start position:0%
+could be undermined who my parties who
+ 
+
+ align:start position:0%
+could be undermined who my parties who
+feel disenfranchised or who don't want
+
+ align:start position:0%
+feel disenfranchised or who don't want
+ 
+
+ align:start position:0%
+feel disenfranchised or who don't want
+to collaborate on a solution so how do
+
+ align:start position:0%
+to collaborate on a solution so how do
+ 
+
+ align:start position:0%
+to collaborate on a solution so how do
+we navigate this delicate task with our
+
+ align:start position:0%
+we navigate this delicate task with our
+ 
+
+ align:start position:0%
+we navigate this delicate task with our
+eyes open to arrive at a sound solution
+
+ align:start position:0%
+eyes open to arrive at a sound solution
+ 
+
+ align:start position:0%
+eyes open to arrive at a sound solution
+I'm very confident in your abilities and
+
+ align:start position:0%
+I'm very confident in your abilities and
+ 
+
+ align:start position:0%
+I'm very confident in your abilities and
+those are the experts that you tap to
+
+ align:start position:0%
+those are the experts that you tap to
+ 
+
+ align:start position:0%
+those are the experts that you tap to
+make sound judgments about a plan to
+
+ align:start position:0%
+make sound judgments about a plan to
+ 
+
+ align:start position:0%
+make sound judgments about a plan to
+share and distribute the water but I
+
+ align:start position:0%
+share and distribute the water but I
+ 
+
+ align:start position:0%
+share and distribute the water but I
+don't want you just to rely on expertise
+
+ align:start position:0%
+don't want you just to rely on expertise
+ 
+
+ align:start position:0%
+don't want you just to rely on expertise
+to engineer the best solution to this
+
+ align:start position:0%
+to engineer the best solution to this
+ 
+
+ align:start position:0%
+to engineer the best solution to this
+problem I want the a plan that is
+
+ align:start position:0%
+problem I want the a plan that is
+ 
+
+ align:start position:0%
+problem I want the a plan that is
+developed to be the result of an
+
+ align:start position:0%
+developed to be the result of an
+ 
+
+ align:start position:0%
+developed to be the result of an
+informed
+
+ align:start position:0%
+informed
+ 
+
+ align:start position:0%
+informed
+that has the backing of everybody needed
+
+ align:start position:0%
+that has the backing of everybody needed
+ 
+
+ align:start position:0%
+that has the backing of everybody needed
+to implement it political viability is
+
+ align:start position:0%
+to implement it political viability is
+ 
+
+ align:start position:0%
+to implement it political viability is
+one key factor we need an an expert
+
+ align:start position:0%
+one key factor we need an an expert
+ 
+
+ align:start position:0%
+one key factor we need an an expert
+solution won't necessarily get us there
+
+ align:start position:0%
+solution won't necessarily get us there
+ 
+
+ align:start position:0%
+solution won't necessarily get us there
+you have been selected to be part of
+
+ align:start position:0%
+you have been selected to be part of
+ 
+
+ align:start position:0%
+you have been selected to be part of
+this advisory group because of your
+
+ align:start position:0%
+this advisory group because of your
+ 
+
+ align:start position:0%
+this advisory group because of your
+expertise and credibility to deal with
+
+ align:start position:0%
+expertise and credibility to deal with
+ 
+
+ align:start position:0%
+expertise and credibility to deal with
+this policy and decision making effort
+
+ align:start position:0%
+this policy and decision making effort
+ 
+
+ align:start position:0%
+this policy and decision making effort
+you have the authority to convene a
+
+ align:start position:0%
+you have the authority to convene a
+ 
+
+ align:start position:0%
+you have the authority to convene a
+credible process however I think we will
+
+ align:start position:0%
+credible process however I think we will
+ 
+
+ align:start position:0%
+credible process however I think we will
+end up with a stronger and more
+
+ align:start position:0%
+end up with a stronger and more
+ 
+
+ align:start position:0%
+end up with a stronger and more
+politically viable solution if we
+
+ align:start position:0%
+politically viable solution if we
+ 
+
+ align:start position:0%
+politically viable solution if we
+directly involve stakeholders who we see
+
+ align:start position:0%
+directly involve stakeholders who we see
+ 
+
+ align:start position:0%
+directly involve stakeholders who we see
+is likely to be in conflict over the
+
+ align:start position:0%
+is likely to be in conflict over the
+ 
+
+ align:start position:0%
+is likely to be in conflict over the
+decision making effort I suggest you
+
+ align:start position:0%
+decision making effort I suggest you
+ 
+
+ align:start position:0%
+decision making effort I suggest you
+bring in a professional neutral
+
+ align:start position:0%
+bring in a professional neutral
+ 
+
+ align:start position:0%
+bring in a professional neutral
+facilitator who can aid in involving
+
+ align:start position:0%
+facilitator who can aid in involving
+ 
+
+ align:start position:0%
+facilitator who can aid in involving
+stakeholders in the proposal generating
+
+ align:start position:0%
+stakeholders in the proposal generating
+ 
+
+ align:start position:0%
+stakeholders in the proposal generating
+process and who could help solidify
+
+ align:start position:0%
+process and who could help solidify
+ 
+
+ align:start position:0%
+process and who could help solidify
+participants confidence in the
+
+ align:start position:0%
+participants confidence in the
+ 
+
+ align:start position:0%
+participants confidence in the
+neutrality of the process since
+
+ align:start position:0%
+neutrality of the process since
+ 
+
+ align:start position:0%
+neutrality of the process since
+disagreements are likely to be
+
+ align:start position:0%
+disagreements are likely to be
+ 
+
+ align:start position:0%
+disagreements are likely to be
+politically charged here's how I suggest
+
+ align:start position:0%
+politically charged here's how I suggest
+ 
+
+ align:start position:0%
+politically charged here's how I suggest
+you proceed hire an experienced neutral
+
+ align:start position:0%
+you proceed hire an experienced neutral
+ 
+
+ align:start position:0%
+you proceed hire an experienced neutral
+as I said begin by conducting situation
+
+ align:start position:0%
+as I said begin by conducting situation
+ 
+
+ align:start position:0%
+as I said begin by conducting situation
+assessment this means meeting with
+
+ align:start position:0%
+assessment this means meeting with
+ 
+
+ align:start position:0%
+assessment this means meeting with
+representatives of each of the
+
+ align:start position:0%
+representatives of each of the
+ 
+
+ align:start position:0%
+representatives of each of the
+stakeholder groups I previously
+
+ align:start position:0%
+stakeholder groups I previously
+ 
+
+ align:start position:0%
+stakeholder groups I previously
+mentioned and anyone else who thinks
+
+ align:start position:0%
+mentioned and anyone else who thinks
+ 
+
+ align:start position:0%
+mentioned and anyone else who thinks
+they should be included in the process
+
+ align:start position:0%
+they should be included in the process
+ 
+
+ align:start position:0%
+they should be included in the process
+and discuss with them what their needs
+
+ align:start position:0%
+and discuss with them what their needs
+ 
+
+ align:start position:0%
+and discuss with them what their needs
+are for water what their interests are
+
+ align:start position:0%
+are for water what their interests are
+ 
+
+ align:start position:0%
+are for water what their interests are
+and how they'd like to see a regional
+
+ align:start position:0%
+and how they'd like to see a regional
+ 
+
+ align:start position:0%
+and how they'd like to see a regional
+plan develop after you've conducted that
+
+ align:start position:0%
+plan develop after you've conducted that
+ 
+
+ align:start position:0%
+plan develop after you've conducted that
+assessment distill down the results of
+
+ align:start position:0%
+assessment distill down the results of
+ 
+
+ align:start position:0%
+assessment distill down the results of
+your research and communicate to the
+
+ align:start position:0%
+your research and communicate to the
+ 
+
+ align:start position:0%
+your research and communicate to the
+public the parameters of the problem and
+
+ align:start position:0%
+public the parameters of the problem and
+ 
+
+ align:start position:0%
+public the parameters of the problem and
+what are some of the preliminary avenues
+
+ align:start position:0%
+what are some of the preliminary avenues
+ 
+
+ align:start position:0%
+what are some of the preliminary avenues
+that could be pursued to reach a plan
+
+ align:start position:0%
+that could be pursued to reach a plan
+ 
+
+ align:start position:0%
+that could be pursued to reach a plan
+ask stakeholder groups to select
+
+ align:start position:0%
+ask stakeholder groups to select
+ 
+
+ align:start position:0%
+ask stakeholder groups to select
+representatives to versus participate in
+
+ align:start position:0%
+representatives to versus participate in
+ 
+
+ align:start position:0%
+representatives to versus participate in
+a formal consensus building process
+
+ align:start position:0%
+a formal consensus building process
+ 
+
+ align:start position:0%
+a formal consensus building process
+conduct joint fact-finding about uses of
+
+ align:start position:0%
+conduct joint fact-finding about uses of
+ 
+
+ align:start position:0%
+conduct joint fact-finding about uses of
+and needs for water in the region and
+
+ align:start position:0%
+and needs for water in the region and
+ 
+
+ align:start position:0%
+and needs for water in the region and
+help participants explore strategies
+
+ align:start position:0%
+help participants explore strategies
+ 
+
+ align:start position:0%
+help participants explore strategies
+that conceptualize water as a flexible
+
+ align:start position:0%
+that conceptualize water as a flexible
+ 
+
+ align:start position:0%
+that conceptualize water as a flexible
+resource where can meet multiple group's
+
+ align:start position:0%
+resource where can meet multiple group's
+ 
+
+ align:start position:0%
+resource where can meet multiple group's
+needs simultaneously here you can bring
+
+ align:start position:0%
+needs simultaneously here you can bring
+ 
+
+ align:start position:0%
+needs simultaneously here you can bring
+in your own expertise and by all means
+
+ align:start position:0%
+in your own expertise and by all means
+ 
+
+ align:start position:0%
+in your own expertise and by all means
+we want everyone to agree together on
+
+ align:start position:0%
+we want everyone to agree together on
+ 
+
+ align:start position:0%
+we want everyone to agree together on
+the facts that we're going to use to
+
+ align:start position:0%
+the facts that we're going to use to
+ 
+
+ align:start position:0%
+the facts that we're going to use to
+make the recommendations together invent
+
+ align:start position:0%
+make the recommendations together invent
+ 
+
+ align:start position:0%
+make the recommendations together invent
+options based on the results of the
+
+ align:start position:0%
+options based on the results of the
+ 
+
+ align:start position:0%
+options based on the results of the
+information gathering help participants
+
+ align:start position:0%
+information gathering help participants
+ 
+
+ align:start position:0%
+information gathering help participants
+in the process find ways to add value to
+
+ align:start position:0%
+in the process find ways to add value to
+ 
+
+ align:start position:0%
+in the process find ways to add value to
+the resources you're dealing with and
+
+ align:start position:0%
+the resources you're dealing with and
+ 
+
+ align:start position:0%
+the resources you're dealing with and
+invent mutually acceptable solutions if
+
+ align:start position:0%
+invent mutually acceptable solutions if
+ 
+
+ align:start position:0%
+invent mutually acceptable solutions if
+necessary bring other issues besides
+
+ align:start position:0%
+necessary bring other issues besides
+ 
+
+ align:start position:0%
+necessary bring other issues besides
+water to the table these groups
+
+ align:start position:0%
+water to the table these groups
+ 
+
+ align:start position:0%
+water to the table these groups
+intersect and overlap in a number of
+
+ align:start position:0%
+intersect and overlap in a number of
+ 
+
+ align:start position:0%
+intersect and overlap in a number of
+areas that affect our planning strategy
+
+ align:start position:0%
+areas that affect our planning strategy
+ 
+
+ align:start position:0%
+areas that affect our planning strategy
+and it might be that if we add in
+
+ align:start position:0%
+and it might be that if we add in
+ 
+
+ align:start position:0%
+and it might be that if we add in
+other ingredients were able to package
+
+ align:start position:0%
+other ingredients were able to package
+ 
+
+ align:start position:0%
+other ingredients were able to package
+solutions that are more acceptable to
+
+ align:start position:0%
+solutions that are more acceptable to
+ 
+
+ align:start position:0%
+solutions that are more acceptable to
+everyone excuse me
+
+ align:start position:0%
+everyone excuse me
+ 
+
+ align:start position:0%
+everyone excuse me
+help representatives caucus the various
+
+ align:start position:0%
+help representatives caucus the various
+ 
+
+ align:start position:0%
+help representatives caucus the various
+options where there consists
+
+ align:start position:0%
+options where there consists
+ 
+
+ align:start position:0%
+options where there consists
+constituencies and clarify their
+
+ align:start position:0%
+constituencies and clarify their
+ 
+
+ align:start position:0%
+constituencies and clarify their
+interests and needs and help them
+
+ align:start position:0%
+interests and needs and help them
+ 
+
+ align:start position:0%
+interests and needs and help them
+package options together in a way that
+
+ align:start position:0%
+package options together in a way that
+ 
+
+ align:start position:0%
+package options together in a way that
+everyone can agree to and knock them all
+
+ align:start position:0%
+everyone can agree to and knock them all
+ 
+
+ align:start position:0%
+everyone can agree to and knock them all
+endorse an agreement for a strategy and
+
+ align:start position:0%
+endorse an agreement for a strategy and
+ 
+
+ align:start position:0%
+endorse an agreement for a strategy and
+then they will turn that recommendation
+
+ align:start position:0%
+then they will turn that recommendation
+ 
+
+ align:start position:0%
+then they will turn that recommendation
+over to you to formalize and then that's
+
+ align:start position:0%
+over to you to formalize and then that's
+ 
+
+ align:start position:0%
+over to you to formalize and then that's
+what we would implement after we engage
+
+ align:start position:0%
+what we would implement after we engage
+ 
+
+ align:start position:0%
+what we would implement after we engage
+in this process how will we know that
+
+ align:start position:0%
+in this process how will we know that
+ 
+
+ align:start position:0%
+in this process how will we know that
+we've succeeded all groups can sign on
+
+ align:start position:0%
+we've succeeded all groups can sign on
+ 
+
+ align:start position:0%
+we've succeeded all groups can sign on
+to the agreement and all agree that it
+
+ align:start position:0%
+to the agreement and all agree that it
+ 
+
+ align:start position:0%
+to the agreement and all agree that it
+is better about an arrangement than
+
+ align:start position:0%
+is better about an arrangement than
+ 
+
+ align:start position:0%
+is better about an arrangement than
+having an agreement at all and
+
+ align:start position:0%
+having an agreement at all and
+ 
+
+ align:start position:0%
+having an agreement at all and
+participating groups will have learned
+
+ align:start position:0%
+participating groups will have learned
+ 
+
+ align:start position:0%
+participating groups will have learned
+about each other's needs and each other
+
+ align:start position:0%
+about each other's needs and each other
+ 
+
+ align:start position:0%
+about each other's needs and each other
+in a way that they can see that coming
+
+ align:start position:0%
+in a way that they can see that coming
+ 
+
+ align:start position:0%
+in a way that they can see that coming
+to consensus is not necessarily a
+
+ align:start position:0%
+to consensus is not necessarily a
+ 
+
+ align:start position:0%
+to consensus is not necessarily a
+zero-sum game I think that this is the
+
+ align:start position:0%
+zero-sum game I think that this is the
+ 
+
+ align:start position:0%
+zero-sum game I think that this is the
+best strategy not only because
+
+ align:start position:0%
+best strategy not only because
+ 
+
+ align:start position:0%
+best strategy not only because
+collaboration improves the quality of
+
+ align:start position:0%
+collaboration improves the quality of
+ 
+
+ align:start position:0%
+collaboration improves the quality of
+the decision but it also makes it more
+
+ align:start position:0%
+the decision but it also makes it more
+ 
+
+ align:start position:0%
+the decision but it also makes it more
+implementable it should help neutralize
+
+ align:start position:0%
+implementable it should help neutralize
+ 
+
+ align:start position:0%
+implementable it should help neutralize
+the process politically if it has
+
+ align:start position:0%
+the process politically if it has
+ 
+
+ align:start position:0%
+the process politically if it has
+extremely widespread support both the
+
+ align:start position:0%
+extremely widespread support both the
+ 
+
+ align:start position:0%
+extremely widespread support both the
+media and the state government who have
+
+ align:start position:0%
+media and the state government who have
+ 
+
+ align:start position:0%
+media and the state government who have
+been less than favorable about
+
+ align:start position:0%
+been less than favorable about
+ 
+
+ align:start position:0%
+been less than favorable about
+developing a regional water plan would
+
+ align:start position:0%
+developing a regional water plan would
+ 
+
+ align:start position:0%
+developing a regional water plan would
+have a hard time criticizing it if
+
+ align:start position:0%
+have a hard time criticizing it if
+ 
+
+ align:start position:0%
+have a hard time criticizing it if
+everyone really backs it up this has
+
+ align:start position:0%
+everyone really backs it up this has
+ 
+
+ align:start position:0%
+everyone really backs it up this has
+been a brief overview and I'm happy to
+
+ align:start position:0%
+been a brief overview and I'm happy to
+ 
+
+ align:start position:0%
+been a brief overview and I'm happy to
+address questions and discuss in more
+
+ align:start position:0%
+address questions and discuss in more
+ 
+
+ align:start position:0%
+address questions and discuss in more
+detail
+
+ align:start position:0%
+detail
+ 
+
+ align:start position:0%
+detail
+[Applause]
\ No newline at end of file
diff --git a/hMUpevQzNzY.txt b/hMUpevQzNzY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c9705efea3336dc8bbe48ec68bfd60156f1a7b11
--- /dev/null
+++ b/hMUpevQzNzY.txt
@@ -0,0 +1,8083 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so we're doing uh
+
+ align:start position:0%
+ocw.mit.edu all right so we're doing uh
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so we're doing uh
+lecture 06 in the course today that's in
+
+ align:start position:0%
+lecture 06 in the course today that's in
+ 
+
+ align:start position:0%
+lecture 06 in the course today that's in
+the just remind people it's in the docs
+
+ align:start position:0%
+the just remind people it's in the docs
+ 
+
+ align:start position:0%
+the just remind people it's in the docs
+directory
+
+ align:start position:0%
+directory
+ 
+
+ align:start position:0%
+directory
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and we're going to be doing a lot
+
+ align:start position:0%
+and we're going to be doing a lot
+ 
+
+ align:start position:0%
+and we're going to be doing a lot
+talking about a particular application
+
+ align:start position:0%
+talking about a particular application
+ 
+
+ align:start position:0%
+talking about a particular application
+which I think is actually representative
+
+ align:start position:0%
+which I think is actually representative
+ 
+
+ align:start position:0%
+which I think is actually representative
+of a variety of applications that we do
+
+ align:start position:0%
+of a variety of applications that we do
+ 
+
+ align:start position:0%
+of a variety of applications that we do
+a lot of things similar statistical
+
+ align:start position:0%
+a lot of things similar statistical
+ 
+
+ align:start position:0%
+a lot of things similar statistical
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+sequence cross
+
+ align:start position:0%
+sequence cross
+ 
+
+ align:start position:0%
+sequence cross
+correlation okay so um
+
+ align:start position:0%
+correlation okay so um
+ 
+
+ align:start position:0%
+correlation okay so um
+diving right
+
+ align:start position:0%
+diving right
+ 
+
+ align:start position:0%
+diving right
+in just going to give an introduction to
+
+ align:start position:0%
+in just going to give an introduction to
+ 
+
+ align:start position:0%
+in just going to give an introduction to
+this particular problem of genetic
+
+ align:start position:0%
+this particular problem of genetic
+ 
+
+ align:start position:0%
+this particular problem of genetic
+sequence analysis from a computational
+
+ align:start position:0%
+sequence analysis from a computational
+ 
+
+ align:start position:0%
+sequence analysis from a computational
+perspective
+
+ align:start position:0%
+perspective
+ 
+
+ align:start position:0%
+perspective
+um and how the d4m technology can really
+
+ align:start position:0%
+um and how the d4m technology can really
+ 
+
+ align:start position:0%
+um and how the d4m technology can really
+make it uh pretty pretty easy to do the
+
+ align:start position:0%
+make it uh pretty pretty easy to do the
+ 
+
+ align:start position:0%
+make it uh pretty pretty easy to do the
+kinds of things that people like to do
+
+ align:start position:0%
+kinds of things that people like to do
+ 
+
+ align:start position:0%
+kinds of things that people like to do
+and then just talk about the pipeline
+
+ align:start position:0%
+and then just talk about the pipeline
+ 
+
+ align:start position:0%
+and then just talk about the pipeline
+that we implemented to implement this
+
+ align:start position:0%
+that we implemented to implement this
+ 
+
+ align:start position:0%
+that we implemented to implement this
+system because as I've said
+
+ align:start position:0%
+system because as I've said
+ 
+
+ align:start position:0%
+system because as I've said
+before um when you're dealing with this
+
+ align:start position:0%
+before um when you're dealing with this
+ 
+
+ align:start position:0%
+before um when you're dealing with this
+type of large data the deform technology
+
+ align:start position:0%
+type of large data the deform technology
+ 
+
+ align:start position:0%
+type of large data the deform technology
+is one piece it's often the piece you
+
+ align:start position:0%
+is one piece it's often the piece you
+ 
+
+ align:start position:0%
+is one piece it's often the piece you
+use to prototype your algorithms
+
+ align:start position:0%
+use to prototype your algorithms
+ 
+
+ align:start position:0%
+use to prototype your algorithms
+but to be a part of a system you usually
+
+ align:start position:0%
+but to be a part of a system you usually
+ 
+
+ align:start position:0%
+but to be a part of a system you usually
+have to stitch together a variety of
+
+ align:start position:0%
+have to stitch together a variety of
+ 
+
+ align:start position:0%
+have to stitch together a variety of
+Technologies databases obviously being
+
+ align:start position:0%
+Technologies databases obviously being
+ 
+
+ align:start position:0%
+Technologies databases obviously being
+an important part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so this is a great chart this is uh
+
+ align:start position:0%
+that so this is a great chart this is uh
+ 
+
+ align:start position:0%
+that so this is a great chart this is uh
+this is the uh relative cost per DNA
+
+ align:start position:0%
+this is the uh relative cost per DNA
+ 
+
+ align:start position:0%
+this is the uh relative cost per DNA
+sequence over time here over the last uh
+
+ align:start position:0%
+sequence over time here over the last uh
+ 
+
+ align:start position:0%
+sequence over time here over the last uh
+uh 20 years uh so we're getting a little
+
+ align:start position:0%
+uh 20 years uh so we're getting a little
+ 
+
+ align:start position:0%
+uh 20 years uh so we're getting a little
+cut off here at the bottom of the screen
+
+ align:start position:0%
+cut off here at the bottom of the screen
+ 
+
+ align:start position:0%
+cut off here at the bottom of the screen
+so I think
+
+ align:start position:0%
+so I think
+ 
+
+ align:start position:0%
+so I think
+I'm so um uh you know this just shows
+
+ align:start position:0%
+I'm so um uh you know this just shows
+ 
+
+ align:start position:0%
+I'm so um uh you know this just shows
+Moore's Law so we all know that that
+
+ align:start position:0%
+Moore's Law so we all know that that
+ 
+
+ align:start position:0%
+Moore's Law so we all know that that
+technology has been increasing at an
+
+ align:start position:0%
+technology has been increasing at an
+ 
+
+ align:start position:0%
+technology has been increasing at an
+incredible rate and as we've seen uh the
+
+ align:start position:0%
+incredible rate and as we've seen uh the
+ 
+
+ align:start position:0%
+incredible rate and as we've seen uh the
+cost of uh DNA sequencing is going down
+
+ align:start position:0%
+cost of uh DNA sequencing is going down
+ 
+
+ align:start position:0%
+cost of uh DNA sequencing is going down
+dramatically so the first DNA
+
+ align:start position:0%
+dramatically so the first DNA
+ 
+
+ align:start position:0%
+dramatically so the first DNA
+sequence you know people nominally say
+
+ align:start position:0%
+sequence you know people nominally say
+ 
+
+ align:start position:0%
+sequence you know people nominally say
+it to to to sequence the first human
+
+ align:start position:0%
+it to to to sequence the first human
+ 
+
+ align:start position:0%
+it to to to sequence the first human
+genome was around a billion
+
+ align:start position:0%
+genome was around a billion
+ 
+
+ align:start position:0%
+genome was around a billion
+dollars and
+
+ align:start position:0%
+dollars and
+ 
+
+ align:start position:0%
+dollars and
+um they're expecting it to be
+
+ align:start position:0%
+um they're expecting it to be
+ 
+
+ align:start position:0%
+um they're expecting it to be
+$100 within the next few years so having
+
+ align:start position:0%
+$100 within the next few years so having
+ 
+
+ align:start position:0%
+$100 within the next few years so having
+your DNA
+
+ align:start position:0%
+your DNA
+ 
+
+ align:start position:0%
+your DNA
+sequenced will become probably a fairly
+
+ align:start position:0%
+sequenced will become probably a fairly
+ 
+
+ align:start position:0%
+sequenced will become probably a fairly
+routine
+
+ align:start position:0%
+routine
+ 
+
+ align:start position:0%
+routine
+medical uh activity in the next the next
+
+ align:start position:0%
+medical uh activity in the next the next
+ 
+
+ align:start position:0%
+medical uh activity in the next the next
+decade um and so
+
+ align:start position:0%
+decade um and so
+ 
+
+ align:start position:0%
+decade um and so
+uh the data generated you know typically
+
+ align:start position:0%
+uh the data generated you know typically
+ 
+
+ align:start position:0%
+uh the data generated you know typically
+a human genm will have
+
+ align:start position:0%
+a human genm will have
+ 
+
+ align:start position:0%
+a human genm will have
+billions of DNA sequences in it and
+
+ align:start position:0%
+billions of DNA sequences in it and
+ 
+
+ align:start position:0%
+billions of DNA sequences in it and
+that's a lot of
+
+ align:start position:0%
+that's a lot of
+ 
+
+ align:start position:0%
+that's a lot of
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+um what's
+
+ align:start position:0%
+um what's
+ 
+
+ align:start position:0%
+um what's
+actually perhaps even more interesting
+
+ align:start position:0%
+actually perhaps even more interesting
+ 
+
+ align:start position:0%
+actually perhaps even more interesting
+than sequencing your
+
+ align:start position:0%
+than sequencing your
+ 
+
+ align:start position:0%
+than sequencing your
+DNA is sequencing the DNA of all the
+
+ align:start position:0%
+DNA is sequencing the DNA of all the
+ 
+
+ align:start position:0%
+DNA is sequencing the DNA of all the
+other things that are in you which is
+
+ align:start position:0%
+other things that are in you which is
+ 
+
+ align:start position:0%
+other things that are in you which is
+sometimes called the metagenome so
+
+ align:start position:0%
+sometimes called the metagenome so
+ 
+
+ align:start position:0%
+sometimes called the metagenome so
+take a swab and not just
+
+ align:start position:0%
+take a swab and not just
+ 
+
+ align:start position:0%
+take a swab and not just
+get the DNA your DNA but also of all the
+
+ align:start position:0%
+get the DNA your DNA but also of all the
+ 
+
+ align:start position:0%
+get the DNA your DNA but also of all the
+other things that are a part of you
+
+ align:start position:0%
+other things that are a part of you
+ 
+
+ align:start position:0%
+other things that are a part of you
+which can be 10 times larger than than
+
+ align:start position:0%
+which can be 10 times larger than than
+ 
+
+ align:start position:0%
+which can be 10 times larger than than
+than your DNA so depending on that so
+
+ align:start position:0%
+than your DNA so depending on that so
+ 
+
+ align:start position:0%
+than your DNA so depending on that so
+they now have developed these high
+
+ align:start position:0%
+they now have developed these high
+ 
+
+ align:start position:0%
+they now have developed these high
+volume sequencers here's an example of
+
+ align:start position:0%
+volume sequencers here's an example of
+ 
+
+ align:start position:0%
+volume sequencers here's an example of
+one that I believe can do uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+600 okay no problem that uh 600 uh
+
+ align:start position:0%
+600 okay no problem that uh 600 uh
+ 
+
+ align:start position:0%
+600 okay no problem that uh 600 uh
+billion base pairs a day so like 600
+
+ align:start position:0%
+billion base pairs a day so like 600
+ 
+
+ align:start position:0%
+billion base pairs a day so like 600
+gigabytes of data a day and this is all
+
+ align:start position:0%
+gigabytes of data a day and this is all
+ 
+
+ align:start position:0%
+gigabytes of data a day and this is all
+data that you want to cross-correlate
+
+ align:start position:0%
+data that you want to cross-correlate
+ 
+
+ align:start position:0%
+data that you want to cross-correlate
+you know I mean it's it's your it's it's
+
+ align:start position:0%
+you know I mean it's it's your it's it's
+ 
+
+ align:start position:0%
+you know I mean it's it's your it's it's
+a it's a so that's what this uh this is
+
+ align:start position:0%
+a it's a so that's what this uh this is
+ 
+
+ align:start position:0%
+a it's a so that's what this uh this is
+a this is a
+
+ align:start position:0%
+a this is a
+ 
+
+ align:start position:0%
+a this is a
+tabletop uh tabletop apparatus here that
+
+ align:start position:0%
+tabletop uh tabletop apparatus here that
+ 
+
+ align:start position:0%
+tabletop uh tabletop apparatus here that
+sells for a few
+
+ align:start position:0%
+sells for a few
+ 
+
+ align:start position:0%
+sells for a few
+hundred, and they are even getting into
+
+ align:start position:0%
+hundred, and they are even getting into
+ 
+
+ align:start position:0%
+hundred, and they are even getting into
+you know portable sequencers that you
+
+ align:start position:0%
+you know portable sequencers that you
+ 
+
+ align:start position:0%
+you know portable sequencers that you
+can plug in with a USB connector
+
+ align:start position:0%
+can plug in with a USB connector
+ 
+
+ align:start position:0%
+can plug in with a USB connector
+connection into a laptop or something
+
+ align:start position:0%
+connection into a laptop or something
+ 
+
+ align:start position:0%
+connection into a laptop or something
+like that to do you know more in the
+
+ align:start position:0%
+like that to do you know more in the
+ 
+
+ align:start position:0%
+like that to do you know more in the
+field types of things so why would you
+
+ align:start position:0%
+field types of things so why would you
+ 
+
+ align:start position:0%
+field types of things so why would you
+want to do this um you know uh I think
+
+ align:start position:0%
+want to do this um you know uh I think
+ 
+
+ align:start position:0%
+want to do this um you know uh I think
+you know abstractly you understand all
+
+ align:start position:0%
+you know abstractly you understand all
+ 
+
+ align:start position:0%
+you know abstractly you understand all
+that would be good um um computation
+
+ align:start position:0%
+that would be good um um computation
+ 
+
+ align:start position:0%
+that would be good um um computation
+plays a a huge role because this data is
+
+ align:start position:0%
+plays a a huge role because this data is
+ 
+
+ align:start position:0%
+plays a a huge role because this data is
+collected and it's just sort of abstract
+
+ align:start position:0%
+collected and it's just sort of abstract
+ 
+
+ align:start position:0%
+collected and it's just sort of abstract
+Snippets of DNA you know just even
+
+ align:start position:0%
+Snippets of DNA you know just even
+ 
+
+ align:start position:0%
+Snippets of DNA you know just even
+assembling them into a you know just
+
+ align:start position:0%
+assembling them into a you know just
+ 
+
+ align:start position:0%
+assembling them into a you know just
+your DNA into a whole process can take a
+
+ align:start position:0%
+your DNA into a whole process can take a
+ 
+
+ align:start position:0%
+your DNA into a whole process can take a
+fair amount of
+
+ align:start position:0%
+fair amount of
+ 
+
+ align:start position:0%
+fair amount of
+computation uh and right now that is
+
+ align:start position:0%
+computation uh and right now that is
+ 
+
+ align:start position:0%
+computation uh and right now that is
+actually something that takes a fair
+
+ align:start position:0%
+actually something that takes a fair
+ 
+
+ align:start position:0%
+actually something that takes a fair
+amount of time and so to give you an
+
+ align:start position:0%
+amount of time and so to give you an
+ 
+
+ align:start position:0%
+amount of time and so to give you an
+example here's a great uh use case uh
+
+ align:start position:0%
+example here's a great uh use case uh
+ 
+
+ align:start position:0%
+example here's a great uh use case uh
+this shows If you recall in the summer
+
+ align:start position:0%
+this shows If you recall in the summer
+ 
+
+ align:start position:0%
+this shows If you recall in the summer
+of 2011 there was a violent ecoli
+
+ align:start position:0%
+of 2011 there was a violent ecoli
+ 
+
+ align:start position:0%
+of 2011 there was a violent ecoli
+outbreak in uh in Germany and not to
+
+ align:start position:0%
+outbreak in uh in Germany and not to
+ 
+
+ align:start position:0%
+outbreak in uh in Germany and not to
+single out the Germans we've certainly
+
+ align:start position:0%
+single out the Germans we've certainly
+ 
+
+ align:start position:0%
+single out the Germans we've certainly
+had the same things occur in the United
+
+ align:start position:0%
+had the same things occur in the United
+ 
+
+ align:start position:0%
+had the same things occur in the United
+States and these these occur all across
+
+ align:start position:0%
+States and these these occur all across
+ 
+
+ align:start position:0%
+States and these these occur all across
+across the world and so you know this
+
+ align:start position:0%
+across the world and so you know this
+ 
+
+ align:start position:0%
+across the world and so you know this
+shows kind of the time course of you
+
+ align:start position:0%
+shows kind of the time course of you
+ 
+
+ align:start position:0%
+shows kind of the time course of you
+know in May you know the first cases
+
+ align:start position:0%
+know in May you know the first cases
+ 
+
+ align:start position:0%
+know in May you know the first cases
+starting appear and then those lead to
+
+ align:start position:0%
+starting appear and then those lead to
+ 
+
+ align:start position:0%
+starting appear and then those lead to
+the first deaths and then you know
+
+ align:start position:0%
+the first deaths and then you know
+ 
+
+ align:start position:0%
+the first deaths and then you know
+spikes and then uh you know that's just
+
+ align:start position:0%
+spikes and then uh you know that's just
+ 
+
+ align:start position:0%
+spikes and then uh you know that's just
+kind of when you hit this peak is when
+
+ align:start position:0%
+kind of when you hit this peak is when
+ 
+
+ align:start position:0%
+kind of when you hit this peak is when
+they really identify the outbrook and
+
+ align:start position:0%
+they really identify the outbrook and
+ 
+
+ align:start position:0%
+they really identify the outbrook and
+then they finally figured out what the
+
+ align:start position:0%
+then they finally figured out what the
+ 
+
+ align:start position:0%
+then they finally figured out what the
+uh what what it what it is that that
+
+ align:start position:0%
+uh what what it what it is that that
+ 
+
+ align:start position:0%
+uh what what it what it is that that
+that's causing people and begin to
+
+ align:start position:0%
+that's causing people and begin to
+ 
+
+ align:start position:0%
+that's causing people and begin to
+remediate it but you know until you've
+
+ align:start position:0%
+remediate it but you know until you've
+ 
+
+ align:start position:0%
+remediate it but you know until you've
+kind of really have this portion you
+
+ align:start position:0%
+kind of really have this portion you
+ 
+
+ align:start position:0%
+kind of really have this portion you
+know people are still getting exposed to
+
+ align:start position:0%
+know people are still getting exposed to
+ 
+
+ align:start position:0%
+know people are still getting exposed to
+the thing um usually before they
+
+ align:start position:0%
+the thing um usually before they
+ 
+
+ align:start position:0%
+the thing um usually before they
+actually nail it down um there's lots of
+
+ align:start position:0%
+actually nail it down um there's lots of
+ 
+
+ align:start position:0%
+actually nail it down um there's lots of
+rumors flying around all other parts of
+
+ align:start position:0%
+rumors flying around all other parts of
+ 
+
+ align:start position:0%
+rumors flying around all other parts of
+uh the food chain are
+
+ align:start position:0%
+uh the food chain are
+ 
+
+ align:start position:0%
+uh the food chain are
+disrupted um you know any single time
+
+ align:start position:0%
+disrupted um you know any single time
+ 
+
+ align:start position:0%
+disrupted um you know any single time
+you know a particular product is
+
+ align:start position:0%
+you know a particular product is
+ 
+
+ align:start position:0%
+you know a particular product is
+implicated that's hundreds of millions
+
+ align:start position:0%
+implicated that's hundreds of millions
+ 
+
+ align:start position:0%
+implicated that's hundreds of millions
+of dollars of lost business as people
+
+ align:start position:0%
+of dollars of lost business as people
+ 
+
+ align:start position:0%
+of dollars of lost business as people
+just basically you know they say it's
+
+ align:start position:0%
+just basically you know they say it's
+ 
+
+ align:start position:0%
+just basically you know they say it's
+spinach then everyone stops buying
+
+ align:start position:0%
+spinach then everyone stops buying
+ 
+
+ align:start position:0%
+spinach then everyone stops buying
+spinach for a while uh oh it wasn't
+
+ align:start position:0%
+spinach for a while uh oh it wasn't
+ 
+
+ align:start position:0%
+spinach for a while uh oh it wasn't
+spinach sorry it was something else and
+
+ align:start position:0%
+spinach sorry it was something else and
+ 
+
+ align:start position:0%
+spinach sorry it was something else and
+so that's so there's a there's a dual
+
+ align:start position:0%
+so that's so there's a there's a dual
+ 
+
+ align:start position:0%
+so that's so there's a there's a dual
+dual uh you know so they started by
+
+ align:start position:0%
+dual uh you know so they started by
+ 
+
+ align:start position:0%
+dual uh you know so they started by
+implicating this the Cucumbers but that
+
+ align:start position:0%
+implicating this the Cucumbers but that
+ 
+
+ align:start position:0%
+implicating this the Cucumbers but that
+wasn't quite right they then sequenced
+
+ align:start position:0%
+wasn't quite right they then sequenced
+ 
+
+ align:start position:0%
+wasn't quite right they then sequenced
+the stuff and then they correctly
+
+ align:start position:0%
+the stuff and then they correctly
+ 
+
+ align:start position:0%
+the stuff and then they correctly
+identified it was the Sprouts um at
+
+ align:start position:0%
+identified it was the Sprouts um at
+ 
+
+ align:start position:0%
+identified it was the Sprouts um at
+least I believe that was the time course
+
+ align:start position:0%
+least I believe that was the time course
+ 
+
+ align:start position:0%
+least I believe that was the time course
+of events here so so um and this is sort
+
+ align:start position:0%
+of events here so so um and this is sort
+ 
+
+ align:start position:0%
+of events here so so um and this is sort
+of the integrated number of deaths and
+
+ align:start position:0%
+of the integrated number of deaths and
+ 
+
+ align:start position:0%
+of the integrated number of deaths and
+so you know the story here is obviously
+
+ align:start position:0%
+so you know the story here is obviously
+ 
+
+ align:start position:0%
+so you know the story here is obviously
+thing we want to do most is when a
+
+ align:start position:0%
+thing we want to do most is when a
+ 
+
+ align:start position:0%
+thing we want to do most is when a
+person gets sick here here wouldn't it
+
+ align:start position:0%
+person gets sick here here wouldn't it
+ 
+
+ align:start position:0%
+person gets sick here here wouldn't it
+be great to sequence them immediately
+
+ align:start position:0%
+be great to sequence them immediately
+ 
+
+ align:start position:0%
+be great to sequence them immediately
+get that information know exactly what's
+
+ align:start position:0%
+get that information know exactly what's
+ 
+
+ align:start position:0%
+get that information know exactly what's
+causing the problem and then be able to
+
+ align:start position:0%
+causing the problem and then be able to
+ 
+
+ align:start position:0%
+causing the problem and then be able to
+start testing the the the the food
+
+ align:start position:0%
+start testing the the the the food
+ 
+
+ align:start position:0%
+start testing the the the the food
+supply channel uh so that you can make a
+
+ align:start position:0%
+supply channel uh so that you can make a
+ 
+
+ align:start position:0%
+supply channel uh so that you can make a
+real impact on the mortality and then
+
+ align:start position:0%
+real impact on the mortality and then
+ 
+
+ align:start position:0%
+real impact on the mortality and then
+likewise not have the econom you know
+
+ align:start position:0%
+likewise not have the econom you know
+ 
+
+ align:start position:0%
+likewise not have the econom you know
+obviously the the the the loss of life
+
+ align:start position:0%
+obviously the the the the loss of life
+ 
+
+ align:start position:0%
+obviously the the the the loss of life
+is the uh
+
+ align:start position:0%
+is the uh
+ 
+
+ align:start position:0%
+is the uh
+preeminent uh issue here um but there's
+
+ align:start position:0%
+preeminent uh issue here um but there's
+ 
+
+ align:start position:0%
+preeminent uh issue here um but there's
+also the economic impact which uh
+
+ align:start position:0%
+also the economic impact which uh
+ 
+
+ align:start position:0%
+also the economic impact which uh
+certainly the people who are in those
+
+ align:start position:0%
+certainly the people who are in those
+ 
+
+ align:start position:0%
+certainly the people who are in those
+businesses would want to address so as
+
+ align:start position:0%
+businesses would want to address so as
+ 
+
+ align:start position:0%
+businesses would want to address so as
+you can see there was a really sort of a
+
+ align:start position:0%
+you can see there was a really sort of a
+ 
+
+ align:start position:0%
+you can see there was a really sort of a
+rather long delay here between sort of
+
+ align:start position:0%
+rather long delay here between sort of
+ 
+
+ align:start position:0%
+rather long delay here between sort of
+when the outbreak started and the DNA uh
+
+ align:start position:0%
+when the outbreak started and the DNA uh
+ 
+
+ align:start position:0%
+when the outbreak started and the DNA uh
+sequence uh release and this was
+
+ align:start position:0%
+sequence uh release and this was
+ 
+
+ align:start position:0%
+sequence uh release and this was
+actually um a big step forward in the
+
+ align:start position:0%
+actually um a big step forward in the
+ 
+
+ align:start position:0%
+actually um a big step forward in the
+sense that DNA sequencing really did
+
+ align:start position:0%
+sense that DNA sequencing really did
+ 
+
+ align:start position:0%
+sense that DNA sequencing really did
+play ended up playing a role in this
+
+ align:start position:0%
+play ended up playing a role in this
+ 
+
+ align:start position:0%
+play ended up playing a role in this
+process as opposed to previously where
+
+ align:start position:0%
+process as opposed to previously where
+ 
+
+ align:start position:0%
+process as opposed to previously where
+it may not have um and uh uh uh and the
+
+ align:start position:0%
+it may not have um and uh uh uh and the
+ 
+
+ align:start position:0%
+it may not have um and uh uh uh and the
+and people see that now and they would
+
+ align:start position:0%
+and people see that now and they would
+ 
+
+ align:start position:0%
+and people see that now and they would
+love to move this move this uh this
+
+ align:start position:0%
+love to move this move this uh this
+ 
+
+ align:start position:0%
+love to move this move this uh this
+earlier so you know and and and
+
+ align:start position:0%
+earlier so you know and and and
+ 
+
+ align:start position:0%
+earlier so you know and and and
+obviously in our business and across
+
+ align:start position:0%
+obviously in our business and across
+ 
+
+ align:start position:0%
+obviously in our business and across
+it's not just this type of example but
+
+ align:start position:0%
+it's not just this type of example but
+ 
+
+ align:start position:0%
+it's not just this type of example but
+there's other types of examples where
+
+ align:start position:0%
+there's other types of examples where
+ 
+
+ align:start position:0%
+there's other types of examples where
+rapid uh sequencing and um and
+
+ align:start position:0%
+rapid uh sequencing and um and
+ 
+
+ align:start position:0%
+rapid uh sequencing and um and
+identification would be very important
+
+ align:start position:0%
+identification would be very important
+ 
+
+ align:start position:0%
+identification would be very important
+and there's certainly Investments being
+
+ align:start position:0%
+and there's certainly Investments being
+ 
+
+ align:start position:0%
+and there's certainly Investments being
+made to try and make that more possible
+
+ align:start position:0%
+made to try and make that more possible
+ 
+
+ align:start position:0%
+made to try and make that more possible
+so an example of what the processing
+
+ align:start position:0%
+so an example of what the processing
+ 
+
+ align:start position:0%
+so an example of what the processing
+timeline looks now I mean you have
+
+ align:start position:0%
+timeline looks now I mean you have
+ 
+
+ align:start position:0%
+timeline looks now I mean you have
+basically starting with the human
+
+ align:start position:0%
+basically starting with the human
+ 
+
+ align:start position:0%
+basically starting with the human
+infection you know it could be a natural
+
+ align:start position:0%
+infection you know it could be a natural
+ 
+
+ align:start position:0%
+infection you know it could be a natural
+disease obviously in the dod they're
+
+ align:start position:0%
+disease obviously in the dod they're
+ 
+
+ align:start position:0%
+disease obviously in the dod they're
+very concerned about bioweapons as well
+
+ align:start position:0%
+very concerned about bioweapons as well
+ 
+
+ align:start position:0%
+very concerned about bioweapons as well
+you know so there's the collection of
+
+ align:start position:0%
+you know so there's the collection of
+ 
+
+ align:start position:0%
+you know so there's the collection of
+the sample the preparation the analysis
+
+ align:start position:0%
+the sample the preparation the analysis
+ 
+
+ align:start position:0%
+the sample the preparation the analysis
+and sort of the overall time to
+
+ align:start position:0%
+and sort of the overall time to
+ 
+
+ align:start position:0%
+and sort of the overall time to
+actionable data and really it's not to
+
+ align:start position:0%
+actionable data and really it's not to
+ 
+
+ align:start position:0%
+actionable data and really it's not to
+say processing plays everything on this
+
+ align:start position:0%
+say processing plays everything on this
+ 
+
+ align:start position:0%
+say processing plays everything on this
+but if is part of a whole system you
+
+ align:start position:0%
+but if is part of a whole system you
+ 
+
+ align:start position:0%
+but if is part of a whole system you
+could imagine if you could do on-site
+
+ align:start position:0%
+could imagine if you could do on-site
+ 
+
+ align:start position:0%
+could imagine if you could do on-site
+collection you know automatic
+
+ align:start position:0%
+collection you know automatic
+ 
+
+ align:start position:0%
+collection you know automatic
+preparation and then you know very quick
+
+ align:start position:0%
+preparation and then you know very quick
+ 
+
+ align:start position:0%
+preparation and then you know very quick
+analysis you could imagine shorting this
+
+ align:start position:0%
+analysis you could imagine shorting this
+ 
+
+ align:start position:0%
+analysis you could imagine shorting this
+cycle down to one day which would be you
+
+ align:start position:0%
+cycle down to one day which would be you
+ 
+
+ align:start position:0%
+cycle down to one day which would be you
+know something that would really make a
+
+ align:start position:0%
+know something that would really make a
+ 
+
+ align:start position:0%
+know something that would really make a
+huge impact
+
+ align:start position:0%
+huge impact
+ 
+
+ align:start position:0%
+huge impact
+some of the other uh useful sequences uh
+
+ align:start position:0%
+some of the other uh useful sequences uh
+ 
+
+ align:start position:0%
+some of the other uh useful sequences uh
+useful I'm sorry uh uh roles for DNA
+
+ align:start position:0%
+useful I'm sorry uh uh roles for DNA
+ 
+
+ align:start position:0%
+useful I'm sorry uh uh roles for DNA
+sequence matching is uh you know quickly
+
+ align:start position:0%
+sequence matching is uh you know quickly
+ 
+
+ align:start position:0%
+sequence matching is uh you know quickly
+comparing two data two sets of DNA um um
+
+ align:start position:0%
+comparing two data two sets of DNA um um
+ 
+
+ align:start position:0%
+comparing two data two sets of DNA um um
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+identification um you know that is you
+
+ align:start position:0%
+identification um you know that is you
+ 
+
+ align:start position:0%
+identification um you know that is you
+know who is it um analysis of mixtures
+
+ align:start position:0%
+know who is it um analysis of mixtures
+ 
+
+ align:start position:0%
+know who is it um analysis of mixtures
+you know what what type of things could
+
+ align:start position:0%
+you know what what type of things could
+ 
+
+ align:start position:0%
+you know what what type of things could
+you determine if someone was related to
+
+ align:start position:0%
+you determine if someone was related to
+ 
+
+ align:start position:0%
+you determine if someone was related to
+somebody else um you know ancestry
+
+ align:start position:0%
+somebody else um you know ancestry
+ 
+
+ align:start position:0%
+somebody else um you know ancestry
+analysis which can be used in disease
+
+ align:start position:0%
+analysis which can be used in disease
+ 
+
+ align:start position:0%
+analysis which can be used in disease
+outbreaks criminal investigation
+
+ align:start position:0%
+outbreaks criminal investigation
+ 
+
+ align:start position:0%
+outbreaks criminal investigation
+personal medicine you know the the set
+
+ align:start position:0%
+personal medicine you know the the set
+ 
+
+ align:start position:0%
+personal medicine you know the the set
+of of things is pretty pretty pretty
+
+ align:start position:0%
+of of things is pretty pretty pretty
+ 
+
+ align:start position:0%
+of of things is pretty pretty pretty
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+here so I'm now going to explain to you
+
+ align:start position:0%
+here so I'm now going to explain to you
+ 
+
+ align:start position:0%
+here so I'm now going to explain to you
+kind of fundamentally what is the
+
+ align:start position:0%
+kind of fundamentally what is the
+ 
+
+ align:start position:0%
+kind of fundamentally what is the
+algorithm that we use for doing this
+
+ align:start position:0%
+algorithm that we use for doing this
+ 
+
+ align:start position:0%
+algorithm that we use for doing this
+matching but we're going to explain it
+
+ align:start position:0%
+matching but we're going to explain it
+ 
+
+ align:start position:0%
+matching but we're going to explain it
+in terms of the mathematics that we've
+
+ align:start position:0%
+in terms of the mathematics that we've
+ 
+
+ align:start position:0%
+in terms of the mathematics that we've
+described before which is these
+
+ align:start position:0%
+described before which is these
+ 
+
+ align:start position:0%
+described before which is these
+associative arrays which actually make
+
+ align:start position:0%
+associative arrays which actually make
+ 
+
+ align:start position:0%
+associative arrays which actually make
+it very very easy to describe what's
+
+ align:start position:0%
+it very very easy to describe what's
+ 
+
+ align:start position:0%
+it very very easy to describe what's
+going on here if I was to describe to
+
+ align:start position:0%
+going on here if I was to describe to
+ 
+
+ align:start position:0%
+going on here if I was to describe to
+you the traditional approaches for how
+
+ align:start position:0%
+you the traditional approaches for how
+ 
+
+ align:start position:0%
+you the traditional approaches for how
+we describe DNA sequence matching it
+
+ align:start position:0%
+we describe DNA sequence matching it
+ 
+
+ align:start position:0%
+we describe DNA sequence matching it
+would actually be that would be a whole
+
+ align:start position:0%
+would actually be that would be a whole
+ 
+
+ align:start position:0%
+would actually be that would be a whole
+lecture in
+
+ align:start position:0%
+lecture in
+ 
+
+ align:start position:0%
+lecture in
+Excel so let me get into that algorithm
+
+ align:start position:0%
+Excel so let me get into that algorithm
+ 
+
+ align:start position:0%
+Excel so let me get into that algorithm
+and so basically this is it one slide Is
+
+ align:start position:0%
+and so basically this is it one slide Is
+ 
+
+ align:start position:0%
+and so basically this is it one slide Is
+How We Do DNA sequence matching so we
+
+ align:start position:0%
+How We Do DNA sequence matching so we
+ 
+
+ align:start position:0%
+How We Do DNA sequence matching so we
+have a reference sequence here this is
+
+ align:start position:0%
+have a reference sequence here this is
+ 
+
+ align:start position:0%
+have a reference sequence here this is
+something that we know a database of
+
+ align:start position:0%
+something that we know a database of
+ 
+
+ align:start position:0%
+something that we know a database of
+data that we know and it consists of a
+
+ align:start position:0%
+data that we know and it consists of a
+ 
+
+ align:start position:0%
+data that we know and it consists of a
+sequence ID and then a whole bunch of
+
+ align:start position:0%
+sequence ID and then a whole bunch of
+ 
+
+ align:start position:0%
+sequence ID and then a whole bunch of
+you know what are called base pairs and
+
+ align:start position:0%
+you know what are called base pairs and
+ 
+
+ align:start position:0%
+you know what are called base pairs and
+this can usually be several hundred long
+
+ align:start position:0%
+this can usually be several hundred long
+ 
+
+ align:start position:0%
+this can usually be several hundred long
+and you'll have thousands of these each
+
+ align:start position:0%
+and you'll have thousands of these each
+ 
+
+ align:start position:0%
+and you'll have thousands of these each
+that are a few hundred maybe a thousand
+
+ align:start position:0%
+that are a few hundred maybe a thousand
+ 
+
+ align:start position:0%
+that are a few hundred maybe a thousand
+base pairs long and so the standard
+
+ align:start position:0%
+base pairs long and so the standard
+ 
+
+ align:start position:0%
+base pairs long and so the standard
+approach to this is to take these
+
+ align:start position:0%
+approach to this is to take these
+ 
+
+ align:start position:0%
+approach to this is to take these
+sequences and break them up into smaller
+
+ align:start position:0%
+sequences and break them up into smaller
+ 
+
+ align:start position:0%
+sequences and break them up into smaller
+units which are called words or
+
+ align:start position:0%
+units which are called words or
+ 
+
+ align:start position:0%
+units which are called words or
+Ms and a standard number is called a
+
+ align:start position:0%
+Ms and a standard number is called a
+ 
+
+ align:start position:0%
+Ms and a standard number is called a
+tenr so the basically what you would say
+
+ align:start position:0%
+tenr so the basically what you would say
+ 
+
+ align:start position:0%
+tenr so the basically what you would say
+is you take the first 10 letters and you
+
+ align:start position:0%
+is you take the first 10 letters and you
+ 
+
+ align:start position:0%
+is you take the first 10 letters and you
+say all right that's one
+
+ align:start position:0%
+say all right that's one
+ 
+
+ align:start position:0%
+say all right that's one
+tenur then you move it over one and you
+
+ align:start position:0%
+tenur then you move it over one and you
+ 
+
+ align:start position:0%
+tenur then you move it over one and you
+say that's another 10mer and so on and
+
+ align:start position:0%
+say that's another 10mer and so on and
+ 
+
+ align:start position:0%
+say that's another 10mer and so on and
+so forth so you have if this was a a
+
+ align:start position:0%
+so forth so you have if this was a a
+ 
+
+ align:start position:0%
+so forth so you have if this was a a
+sequence of four of 400 long you would
+
+ align:start position:0%
+sequence of four of 400 long you would
+ 
+
+ align:start position:0%
+sequence of four of 400 long you would
+have 400
+
+ align:start position:0%
+have 400
+ 
+
+ align:start position:0%
+have 400
+tenm okay and then you're obviously
+
+ align:start position:0%
+tenm okay and then you're obviously
+ 
+
+ align:start position:0%
+tenm okay and then you're obviously
+multiplying the total data volume by a
+
+ align:start position:0%
+multiplying the total data volume by a
+ 
+
+ align:start position:0%
+multiplying the total data volume by a
+factor of 10 because of this thing and
+
+ align:start position:0%
+factor of 10 because of this thing and
+ 
+
+ align:start position:0%
+factor of 10 because of this thing and
+so for those of us who know signal
+
+ align:start position:0%
+so for those of us who know signal
+ 
+
+ align:start position:0%
+so for those of us who know signal
+processing this is just standard
+
+ align:start position:0%
+processing this is just standard
+ 
+
+ align:start position:0%
+processing this is just standard
+filtering nothing new here very very
+
+ align:start position:0%
+filtering nothing new here very very
+ 
+
+ align:start position:0%
+filtering nothing new here very very
+standard type of filtering approach so
+
+ align:start position:0%
+standard type of filtering approach so
+ 
+
+ align:start position:0%
+standard type of filtering approach so
+then what we do is for each sequence
+
+ align:start position:0%
+then what we do is for each sequence
+ 
+
+ align:start position:0%
+then what we do is for each sequence
+ID okay this forms the row key of an
+
+ align:start position:0%
+ID okay this forms the row key of an
+ 
+
+ align:start position:0%
+ID okay this forms the row key of an
+associative array and each 10mer of that
+
+ align:start position:0%
+associative array and each 10mer of that
+ 
+
+ align:start position:0%
+associative array and each 10mer of that
+sequence of forms a column key of that
+
+ align:start position:0%
+sequence of forms a column key of that
+ 
+
+ align:start position:0%
+sequence of forms a column key of that
+tenr so you can see here each of these
+
+ align:start position:0%
+tenr so you can see here each of these
+ 
+
+ align:start position:0%
+tenr so you can see here each of these
+rows shows you all the unique teners
+
+ align:start position:0%
+rows shows you all the unique teners
+ 
+
+ align:start position:0%
+rows shows you all the unique teners
+that appeared in that
+
+ align:start position:0%
+that appeared in that
+ 
+
+ align:start position:0%
+that appeared in that
+sequence and then a column is you know a
+
+ align:start position:0%
+sequence and then a column is you know a
+ 
+
+ align:start position:0%
+sequence and then a column is you know a
+particular tenr so as we can see certain
+
+ align:start position:0%
+particular tenr so as we can see certain
+ 
+
+ align:start position:0%
+particular tenr so as we can see certain
+teners
+
+ align:start position:0%
+teners
+ 
+
+ align:start position:0%
+teners
+appear very commonly and some appear in
+
+ align:start position:0%
+appear very commonly and some appear in
+ 
+
+ align:start position:0%
+appear very commonly and some appear in
+a not so common way so that gives us an
+
+ align:start position:0%
+a not so common way so that gives us an
+ 
+
+ align:start position:0%
+a not so common way so that gives us an
+associative array which is a matri a
+
+ align:start position:0%
+associative array which is a matri a
+ 
+
+ align:start position:0%
+associative array which is a matri a
+sparse Matrix where we have sequence ID
+
+ align:start position:0%
+sparse Matrix where we have sequence ID
+ 
+
+ align:start position:0%
+sparse Matrix where we have sequence ID
+by tenr and then we do the same thing
+
+ align:start position:0%
+by tenr and then we do the same thing
+ 
+
+ align:start position:0%
+by tenr and then we do the same thing
+with a collection so we've collected in
+
+ align:start position:0%
+with a collection so we've collected in
+ 
+
+ align:start position:0%
+with a collection so we've collected in
+this case some unknown bacteria sample
+
+ align:start position:0%
+this case some unknown bacteria sample
+ 
+
+ align:start position:0%
+this case some unknown bacteria sample
+and we have a similar set of sequences
+
+ align:start position:0%
+and we have a similar set of sequences
+ 
+
+ align:start position:0%
+and we have a similar set of sequences
+here and we do the exact same thing we
+
+ align:start position:0%
+here and we do the exact same thing we
+ 
+
+ align:start position:0%
+here and we do the exact same thing we
+have a sequence ID and then the tenr and
+
+ align:start position:0%
+have a sequence ID and then the tenr and
+ 
+
+ align:start position:0%
+have a sequence ID and then the tenr and
+then what we want to do is
+
+ align:start position:0%
+then what we want to do is
+ 
+
+ align:start position:0%
+then what we want to do is
+cross-correlate find all the matches
+
+ align:start position:0%
+cross-correlate find all the matches
+ 
+
+ align:start position:0%
+cross-correlate find all the matches
+between them and so that's just done
+
+ align:start position:0%
+between them and so that's just done
+ 
+
+ align:start position:0%
+between them and so that's just done
+with matri Matrix multiply so A1
+
+ align:start position:0%
+with matri Matrix multiply so A1
+ 
+
+ align:start position:0%
+with matri Matrix multiply so A1
+transpose A2 will then result in a new
+
+ align:start position:0%
+transpose A2 will then result in a new
+ 
+
+ align:start position:0%
+transpose A2 will then result in a new
+Matrix which is reference sequence ID by
+
+ align:start position:0%
+Matrix which is reference sequence ID by
+ 
+
+ align:start position:0%
+Matrix which is reference sequence ID by
+unknown sequence ID and then it will
+
+ align:start position:0%
+unknown sequence ID and then it will
+ 
+
+ align:start position:0%
+unknown sequence ID and then it will
+then the value in here will be how many
+
+ align:start position:0%
+then the value in here will be how many
+ 
+
+ align:start position:0%
+then the value in here will be how many
+matches they had and so generally you
+
+ align:start position:0%
+matches they had and so generally you
+ 
+
+ align:start position:0%
+matches they had and so generally you
+look if say 400 you know was the match
+
+ align:start position:0%
+look if say 400 you know was the match
+ 
+
+ align:start position:0%
+look if say 400 you know was the match
+then you would be looking for things you
+
+ align:start position:0%
+then you would be looking for things you
+ 
+
+ align:start position:0%
+then you would be looking for things you
+know well above 30 or 40 matches between
+
+ align:start position:0%
+know well above 30 or 40 matches between
+ 
+
+ align:start position:0%
+know well above 30 or 40 matches between
+them you know a true match would be
+
+ align:start position:0%
+them you know a true match would be
+ 
+
+ align:start position:0%
+them you know a true match would be
+maybe 50 60 70% of them uh uh match and
+
+ align:start position:0%
+maybe 50 60 70% of them uh uh match and
+ 
+
+ align:start position:0%
+maybe 50 60 70% of them uh uh match and
+so then you can just apply a threshold
+
+ align:start position:0%
+so then you can just apply a threshold
+ 
+
+ align:start position:0%
+so then you can just apply a threshold
+to this to DET to find the true true
+
+ align:start position:0%
+to this to DET to find the true true
+ 
+
+ align:start position:0%
+to this to DET to find the true true
+matches so very simple and you know
+
+ align:start position:0%
+matches so very simple and you know
+ 
+
+ align:start position:0%
+matches so very simple and you know
+there there are large software packages
+
+ align:start position:0%
+there there are large software packages
+ 
+
+ align:start position:0%
+there there are large software packages
+out there that do this they essentially
+
+ align:start position:0%
+out there that do this they essentially
+ 
+
+ align:start position:0%
+out there that do this they essentially
+do this algorithm with various twists
+
+ align:start position:0%
+do this algorithm with various twists
+ 
+
+ align:start position:0%
+do this algorithm with various twists
+and variations and stuff like that but
+
+ align:start position:0%
+and variations and stuff like that but
+ 
+
+ align:start position:0%
+and variations and stuff like that but
+here we can explain the whole thing
+
+ align:start position:0%
+here we can explain the whole thing
+ 
+
+ align:start position:0%
+here we can explain the whole thing
+knowing the mathematics of associative
+
+ align:start position:0%
+knowing the mathematics of associative
+ 
+
+ align:start position:0%
+knowing the mathematics of associative
+arrays on one on one
+
+ align:start position:0%
+arrays on one on one
+ 
+
+ align:start position:0%
+arrays on one on one
+slide
+
+ align:start position:0%
+slide
+ 
+
+ align:start position:0%
+slide
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this calculation is what we call a
+
+ align:start position:0%
+this calculation is what we call a
+ 
+
+ align:start position:0%
+this calculation is what we call a
+direct match calculation we're literally
+
+ align:start position:0%
+direct match calculation we're literally
+ 
+
+ align:start position:0%
+direct match calculation we're literally
+comparing every single sequences 10 ms
+
+ align:start position:0%
+comparing every single sequences 10 ms
+ 
+
+ align:start position:0%
+comparing every single sequences 10 ms
+with all the other ones you know um and
+
+ align:start position:0%
+with all the other ones you know um and
+ 
+
+ align:start position:0%
+with all the other ones you know um and
+uh this is essentially what sequence
+
+ align:start position:0%
+uh this is essentially what sequence
+ 
+
+ align:start position:0%
+uh this is essentially what sequence
+comparison does and um it's takes a lot
+
+ align:start position:0%
+comparison does and um it's takes a lot
+ 
+
+ align:start position:0%
+comparison does and um it's takes a lot
+of computation to do this you know if
+
+ align:start position:0%
+of computation to do this you know if
+ 
+
+ align:start position:0%
+of computation to do this you know if
+you might have you know millions of
+
+ align:start position:0%
+you might have you know millions of
+ 
+
+ align:start position:0%
+you might have you know millions of
+sequence IDs and millions of sequence
+
+ align:start position:0%
+sequence IDs and millions of sequence
+ 
+
+ align:start position:0%
+sequence IDs and millions of sequence
+IDs this very quickly becomes you know
+
+ align:start position:0%
+IDs this very quickly becomes you know
+ 
+
+ align:start position:0%
+IDs this very quickly becomes you know
+uh a large amount of computational
+
+ align:start position:0%
+uh a large amount of computational
+ 
+
+ align:start position:0%
+uh a large amount of computational
+effort so we are of course interested in
+
+ align:start position:0%
+effort so we are of course interested in
+ 
+
+ align:start position:0%
+effort so we are of course interested in
+other techniques that could possibly
+
+ align:start position:0%
+other techniques that could possibly
+ 
+
+ align:start position:0%
+other techniques that could possibly
+accelerate this so one of the things
+
+ align:start position:0%
+accelerate this so one of the things
+ 
+
+ align:start position:0%
+accelerate this so one of the things
+we're able to do using the cumulo
+
+ align:start position:0%
+we're able to do using the cumulo
+ 
+
+ align:start position:0%
+we're able to do using the cumulo
+database is ingest this entire set of
+
+ align:start position:0%
+database is ingest this entire set of
+ 
+
+ align:start position:0%
+database is ingest this entire set of
+data as an associative array into the
+
+ align:start position:0%
+data as an associative array into the
+ 
+
+ align:start position:0%
+data as an associative array into the
+database and using accumulus tally
+
+ align:start position:0%
+database and using accumulus tally
+ 
+
+ align:start position:0%
+database and using accumulus tally
+features then tally have it essentially
+
+ align:start position:0%
+features then tally have it essentially
+ 
+
+ align:start position:0%
+features then tally have it essentially
+as we do the ingestion automatically
+
+ align:start position:0%
+as we do the ingestion automatically
+ 
+
+ align:start position:0%
+as we do the ingestion automatically
+tally the counts for each tenr so we can
+
+ align:start position:0%
+tally the counts for each tenr so we can
+ 
+
+ align:start position:0%
+tally the counts for each tenr so we can
+then essentially construct a histogram
+
+ align:start position:0%
+then essentially construct a histogram
+ 
+
+ align:start position:0%
+then essentially construct a histogram
+of all the tenur some tenur will appear
+
+ align:start position:0%
+of all the tenur some tenur will appear
+ 
+
+ align:start position:0%
+of all the tenur some tenur will appear
+in a very large number of sequences and
+
+ align:start position:0%
+in a very large number of sequences and
+ 
+
+ align:start position:0%
+in a very large number of sequences and
+Sun 10 teners will appear and not very
+
+ align:start position:0%
+Sun 10 teners will appear and not very
+ 
+
+ align:start position:0%
+Sun 10 teners will appear and not very
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+so this is that histogram or essentially
+
+ align:start position:0%
+so this is that histogram or essentially
+ 
+
+ align:start position:0%
+so this is that histogram or essentially
+a degree distribution we talked about
+
+ align:start position:0%
+a degree distribution we talked about
+ 
+
+ align:start position:0%
+a degree distribution we talked about
+degree distributions and other this
+
+ align:start position:0%
+degree distributions and other this
+ 
+
+ align:start position:0%
+degree distributions and other this
+tells us that there's one 10mer that
+
+ align:start position:0%
+tells us that there's one 10mer that
+ 
+
+ align:start position:0%
+tells us that there's one 10mer that
+appears in you know 80 or 90% of all the
+
+ align:start position:0%
+appears in you know 80 or 90% of all the
+ 
+
+ align:start position:0%
+appears in you know 80 or 90% of all the
+sequences and then there's a you know 20
+
+ align:start position:0%
+sequences and then there's a you know 20
+ 
+
+ align:start position:0%
+sequences and then there's a you know 20
+or 30 10 ms that appear in just
+
+ align:start position:0%
+or 30 10 ms that appear in just
+ 
+
+ align:start position:0%
+or 30 10 ms that appear in just
+a few and then there's a distribution in
+
+ align:start position:0%
+a few and then there's a distribution in
+ 
+
+ align:start position:0%
+a few and then there's a distribution in
+this case almost a sort of almost a log
+
+ align:start position:0%
+this case almost a sort of almost a log
+ 
+
+ align:start position:0%
+this case almost a sort of almost a log
+normal curve that shows you um um you
+
+ align:start position:0%
+normal curve that shows you um um you
+ 
+
+ align:start position:0%
+normal curve that shows you um um you
+know that really uh you know most of the
+
+ align:start position:0%
+know that really uh you know most of the
+ 
+
+ align:start position:0%
+know that really uh you know most of the
+10 ms seem to have uh you know appear in
+
+ align:start position:0%
+10 ms seem to have uh you know appear in
+ 
+
+ align:start position:0%
+10 ms seem to have uh you know appear in
+a few hundred
+
+ align:start position:0%
+a few hundred
+ 
+
+ align:start position:0%
+a few hundred
+sequences and so now one thing I've done
+
+ align:start position:0%
+sequences and so now one thing I've done
+ 
+
+ align:start position:0%
+sequences and so now one thing I've done
+here is create certain
+
+ align:start position:0%
+here is create certain
+ 
+
+ align:start position:0%
+here is create certain
+thresholds to say all right
+
+ align:start position:0%
+thresholds to say all right
+ 
+
+ align:start position:0%
+thresholds to say all right
+if I only wanted if I looked at that
+
+ align:start position:0%
+if I only wanted if I looked at that
+ 
+
+ align:start position:0%
+if I only wanted if I looked at that
+large sparse Matrix of the data and I
+
+ align:start position:0%
+large sparse Matrix of the data and I
+ 
+
+ align:start position:0%
+large sparse Matrix of the data and I
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+threshold uh what how many how much of
+
+ align:start position:0%
+threshold uh what how many how much of
+ 
+
+ align:start position:0%
+threshold uh what how many how much of
+the data would I eliminate so if I
+
+ align:start position:0%
+the data would I eliminate so if I
+ 
+
+ align:start position:0%
+the data would I eliminate so if I
+wanted to eliminate 50% of the data I
+
+ align:start position:0%
+wanted to eliminate 50% of the data I
+ 
+
+ align:start position:0%
+wanted to eliminate 50% of the data I
+could set a threshold let's only look at
+
+ align:start position:0%
+could set a threshold let's only look at
+ 
+
+ align:start position:0%
+could set a threshold let's only look at
+things that are less than a degree of
+
+ align:start position:0%
+things that are less than a degree of
+ 
+
+ align:start position:0%
+things that are less than a degree of
+10,000 and you might say well why would
+
+ align:start position:0%
+10,000 and you might say well why would
+ 
+
+ align:start position:0%
+10,000 and you might say well why would
+I want to eliminate these very very
+
+ align:start position:0%
+I want to eliminate these very very
+ 
+
+ align:start position:0%
+I want to eliminate these very very
+popular things well well because they
+
+ align:start position:0%
+popular things well well because they
+ 
+
+ align:start position:0%
+popular things well well because they
+appear everywhere a true match is
+
+ align:start position:0%
+appear everywhere a true match is
+ 
+
+ align:start position:0%
+appear everywhere a true match is
+they're not going to give me any
+
+ align:start position:0%
+they're not going to give me any
+ 
+
+ align:start position:0%
+they're not going to give me any
+information that really tells me about
+
+ align:start position:0%
+information that really tells me about
+ 
+
+ align:start position:0%
+information that really tells me about
+true matches those are going to be
+
+ align:start position:0%
+true matches those are going to be
+ 
+
+ align:start position:0%
+true matches those are going to be
+clutter everything has them that two
+
+ align:start position:0%
+clutter everything has them that two
+ 
+
+ align:start position:0%
+clutter everything has them that two
+sequences share that particular tenr
+
+ align:start position:0%
+sequences share that particular tenr
+ 
+
+ align:start position:0%
+sequences share that particular tenr
+doesn't really give me a lot of power in
+
+ align:start position:0%
+doesn't really give me a lot of power in
+ 
+
+ align:start position:0%
+doesn't really give me a lot of power in
+in in selecting which one it really
+
+ align:start position:0%
+in in selecting which one it really
+ 
+
+ align:start position:0%
+in in selecting which one it really
+belongs
+
+ align:start position:0%
+belongs
+ 
+
+ align:start position:0%
+belongs
+to so like so I can do that if I wanted
+
+ align:start position:0%
+to so like so I can do that if I wanted
+ 
+
+ align:start position:0%
+to so like so I can do that if I wanted
+to go down to only 5% of the data I
+
+ align:start position:0%
+to go down to only 5% of the data I
+ 
+
+ align:start position:0%
+to go down to only 5% of the data I
+could say you know I only want to look
+
+ align:start position:0%
+could say you know I only want to look
+ 
+
+ align:start position:0%
+could say you know I only want to look
+at 10 m
+
+ align:start position:0%
+at 10 m
+ 
+
+ align:start position:0%
+at 10 m
+that are 100 you
+
+ align:start position:0%
+that are 100 you
+ 
+
+ align:start position:0%
+that are 100 you
+know that have that appear in 100 of
+
+ align:start position:0%
+know that have that appear in 100 of
+ 
+
+ align:start position:0%
+know that have that appear in 100 of
+these sequences less and if I wanted to
+
+ align:start position:0%
+these sequences less and if I wanted to
+ 
+
+ align:start position:0%
+these sequences less and if I wanted to
+go even further you know I could go down
+
+ align:start position:0%
+go even further you know I could go down
+ 
+
+ align:start position:0%
+go even further you know I could go down
+to is this 20 30 40 50 and I would only
+
+ align:start position:0%
+to is this 20 30 40 50 and I would only
+ 
+
+ align:start position:0%
+to is this 20 30 40 50 and I would only
+have 1 half% of the data I would have
+
+ align:start position:0%
+have 1 half% of the data I would have
+ 
+
+ align:start position:0%
+have 1 half% of the data I would have
+eliminated from consideration 99.5% of
+
+ align:start position:0%
+eliminated from consideration 99.5% of
+ 
+
+ align:start position:0%
+eliminated from consideration 99.5% of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+so and then if I can do that then that's
+
+ align:start position:0%
+so and then if I can do that then that's
+ 
+
+ align:start position:0%
+so and then if I can do that then that's
+very powerful because I can quickly
+
+ align:start position:0%
+very powerful because I can quickly
+ 
+
+ align:start position:0%
+very powerful because I can quickly
+take my sample data set I know all the
+
+ align:start position:0%
+take my sample data set I know all the
+ 
+
+ align:start position:0%
+take my sample data set I know all the
+teners it has and I can quickly look it
+
+ align:start position:0%
+teners it has and I can quickly look it
+ 
+
+ align:start position:0%
+teners it has and I can quickly look it
+up against this histogram and say no I
+
+ align:start position:0%
+up against this histogram and say no I
+ 
+
+ align:start position:0%
+up against this histogram and say no I
+don't want to do any I only care about
+
+ align:start position:0%
+don't want to do any I only care about
+ 
+
+ align:start position:0%
+don't want to do any I only care about
+this very small section of data and I
+
+ align:start position:0%
+this very small section of data and I
+ 
+
+ align:start position:0%
+this very small section of data and I
+only need to do correlations from that
+
+ align:start position:0%
+only need to do correlations from that
+ 
+
+ align:start position:0%
+only need to do correlations from that
+so let's see how that works
+
+ align:start position:0%
+so let's see how that works
+ 
+
+ align:start position:0%
+so let's see how that works
+out and I should say this technique is
+
+ align:start position:0%
+out and I should say this technique is
+ 
+
+ align:start position:0%
+out and I should say this technique is
+very generic you could do it for text
+
+ align:start position:0%
+very generic you could do it for text
+ 
+
+ align:start position:0%
+very generic you could do it for text
+matching if you have documents you have
+
+ align:start position:0%
+matching if you have documents you have
+ 
+
+ align:start position:0%
+matching if you have documents you have
+the same issue very popular words are
+
+ align:start position:0%
+the same issue very popular words are
+ 
+
+ align:start position:0%
+the same issue very popular words are
+not going to tell you really anything
+
+ align:start position:0%
+not going to tell you really anything
+ 
+
+ align:start position:0%
+not going to tell you really anything
+meaningful about whether two documents
+
+ align:start position:0%
+meaningful about whether two documents
+ 
+
+ align:start position:0%
+meaningful about whether two documents
+are related to an it's going to be
+
+ align:start position:0%
+are related to an it's going to be
+ 
+
+ align:start position:0%
+are related to an it's going to be
+clutter um and other types of records of
+
+ align:start position:0%
+clutter um and other types of records of
+ 
+
+ align:start position:0%
+clutter um and other types of records of
+that thing you know so in the graph
+
+ align:start position:0%
+that thing you know so in the graph
+ 
+
+ align:start position:0%
+that thing you know so in the graph
+Theory perspective we call these super
+
+ align:start position:0%
+Theory perspective we call these super
+ 
+
+ align:start position:0%
+Theory perspective we call these super
+nodes these 10 ms are super nodes they
+
+ align:start position:0%
+nodes these 10 ms are super nodes they
+ 
+
+ align:start position:0%
+nodes these 10 ms are super nodes they
+have connections to many many things and
+
+ align:start position:0%
+have connections to many many things and
+ 
+
+ align:start position:0%
+have connections to many many things and
+therefore if you try and connect through
+
+ align:start position:0%
+therefore if you try and connect through
+ 
+
+ align:start position:0%
+therefore if you try and connect through
+them it's just going to not give you
+
+ align:start position:0%
+them it's just going to not give you
+ 
+
+ align:start position:0%
+them it's just going to not give you
+very useful information um you know it's
+
+ align:start position:0%
+very useful information um you know it's
+ 
+
+ align:start position:0%
+very useful information um you know it's
+like um people visiting
+
+ align:start position:0%
+like um people visiting
+ 
+
+ align:start position:0%
+like um people visiting
+Google looking for all the records where
+
+ align:start position:0%
+Google looking for all the records where
+ 
+
+ align:start position:0%
+Google looking for all the records where
+people connect visited Google is not
+
+ align:start position:0%
+people connect visited Google is not
+ 
+
+ align:start position:0%
+people connect visited Google is not
+really going to tell you much you know
+
+ align:start position:0%
+really going to tell you much you know
+ 
+
+ align:start position:0%
+really going to tell you much you know
+unless you have more information you
+
+ align:start position:0%
+unless you have more information you
+ 
+
+ align:start position:0%
+unless you have more information you
+know and so it's it's not a very big uh
+
+ align:start position:0%
+know and so it's it's not a very big uh
+ 
+
+ align:start position:0%
+know and so it's it's not a very big uh
+distinguishing
+
+ align:start position:0%
+distinguishing
+ 
+
+ align:start position:0%
+distinguishing
+Factor so here's an example of the
+
+ align:start position:0%
+Factor so here's an example of the
+ 
+
+ align:start position:0%
+Factor so here's an example of the
+results of doing of selecting all you
+
+ align:start position:0%
+results of doing of selecting all you
+ 
+
+ align:start position:0%
+results of doing of selecting all you
+know a thresh this low threshold
+
+ align:start position:0%
+know a thresh this low threshold
+ 
+
+ align:start position:0%
+know a thresh this low threshold
+eliminating 99.5% of the data and then
+
+ align:start position:0%
+eliminating 99.5% of the data and then
+ 
+
+ align:start position:0%
+eliminating 99.5% of the data and then
+comparing our matches that we got with
+
+ align:start position:0%
+comparing our matches that we got with
+ 
+
+ align:start position:0%
+comparing our matches that we got with
+what happens when we used 100% % of the
+
+ align:start position:0%
+what happens when we used 100% % of the
+ 
+
+ align:start position:0%
+what happens when we used 100% % of the
+data and so what we have here is the
+
+ align:start position:0%
+data and so what we have here is the
+ 
+
+ align:start position:0%
+data and so what we have here is the
+true 10mer match and then the measured
+
+ align:start position:0%
+true 10mer match and then the measured
+ 
+
+ align:start position:0%
+true 10mer match and then the measured
+subsampled match here and what you see
+
+ align:start position:0%
+subsampled match here and what you see
+ 
+
+ align:start position:0%
+subsampled match here and what you see
+here is that you know we get a very very
+
+ align:start position:0%
+here is that you know we get a very very
+ 
+
+ align:start position:0%
+here is that you know we get a very very
+high success rate in terms of you know
+
+ align:start position:0%
+high success rate in terms of you know
+ 
+
+ align:start position:0%
+high success rate in terms of you know
+uh uh we basically detect all strong
+
+ align:start position:0%
+uh uh we basically detect all strong
+ 
+
+ align:start position:0%
+uh uh we basically detect all strong
+matches using only half percent of the
+
+ align:start position:0%
+matches using only half percent of the
+ 
+
+ align:start position:0%
+matches using only half percent of the
+data and you know uh the number of false
+
+ align:start position:0%
+data and you know uh the number of false
+ 
+
+ align:start position:0%
+data and you know uh the number of false
+positives is extremely low in fact a
+
+ align:start position:0%
+positives is extremely low in fact a
+ 
+
+ align:start position:0%
+positives is extremely low in fact a
+better way to look at that is if we look
+
+ align:start position:0%
+better way to look at that is if we look
+ 
+
+ align:start position:0%
+better way to look at that is if we look
+at the cumul commu probability of
+
+ align:start position:0%
+at the cumul commu probability of
+ 
+
+ align:start position:0%
+at the cumul commu probability of
+detection this shows this that if the
+
+ align:start position:0%
+detection this shows this that if the
+ 
+
+ align:start position:0%
+detection this shows this that if the
+actual match if there was actually 100
+
+ align:start position:0%
+actual match if there was actually 100
+ 
+
+ align:start position:0%
+actual match if there was actually 100
+matches between two sequences we detect
+
+ align:start position:0%
+matches between two sequences we detect
+ 
+
+ align:start position:0%
+matches between two sequences we detect
+all of those using only 12th of the
+
+ align:start position:0%
+all of those using only 12th of the
+ 
+
+ align:start position:0%
+all of those using only 12th of the
+data and likewise in our probability
+
+ align:start position:0%
+data and likewise in our probability
+ 
+
+ align:start position:0%
+data and likewise in our probability
+false alarm rate
+
+ align:start position:0%
+false alarm rate
+ 
+
+ align:start position:0%
+false alarm rate
+we see that if you see more than a match
+
+ align:start position:0%
+we see that if you see more than a match
+ 
+
+ align:start position:0%
+we see that if you see more than a match
+of 10 in the subsample data that is
+
+ align:start position:0%
+of 10 in the subsample data that is
+ 
+
+ align:start position:0%
+of 10 in the subsample data that is
+going to be a true match essentially
+
+ align:start position:0%
+going to be a true match essentially
+ 
+
+ align:start position:0%
+going to be a true match essentially
+100% of the time and so this technique
+
+ align:start position:0%
+100% of the time and so this technique
+ 
+
+ align:start position:0%
+100% of the time and so this technique
+allows us to dramatically speed up the
+
+ align:start position:0%
+allows us to dramatically speed up the
+ 
+
+ align:start position:0%
+allows us to dramatically speed up the
+rate at which we can do these
+
+ align:start position:0%
+rate at which we can do these
+ 
+
+ align:start position:0%
+rate at which we can do these
+comparisons now you do have the price to
+
+ align:start position:0%
+comparisons now you do have the price to
+ 
+
+ align:start position:0%
+comparisons now you do have the price to
+pay that you have to preload your
+
+ align:start position:0%
+pay that you have to preload your
+ 
+
+ align:start position:0%
+pay that you have to preload your
+reference data data into this special
+
+ align:start position:0%
+reference data data into this special
+ 
+
+ align:start position:0%
+reference data data into this special
+database but you since you tend to be
+
+ align:start position:0%
+database but you since you tend to be
+ 
+
+ align:start position:0%
+database but you since you tend to be
+more concerned conned about comparing
+
+ align:start position:0%
+more concerned conned about comparing
+ 
+
+ align:start position:0%
+more concerned conned about comparing
+with respect to it that is a a
+
+ align:start position:0%
+with respect to it that is a a
+ 
+
+ align:start position:0%
+with respect to it that is a a
+worthwhile
+
+ align:start position:0%
+worthwhile
+ 
+
+ align:start position:0%
+worthwhile
+investment so that's just an example of
+
+ align:start position:0%
+investment so that's just an example of
+ 
+
+ align:start position:0%
+investment so that's just an example of
+the how you can use these techniques use
+
+ align:start position:0%
+the how you can use these techniques use
+ 
+
+ align:start position:0%
+the how you can use these techniques use
+the mathematics of associative arrays
+
+ align:start position:0%
+the mathematics of associative arrays
+ 
+
+ align:start position:0%
+the mathematics of associative arrays
+and and these databases uh together in a
+
+ align:start position:0%
+and and these databases uh together in a
+ 
+
+ align:start position:0%
+and and these databases uh together in a
+in a in a coherent
+
+ align:start position:0%
+in a in a coherent
+ 
+
+ align:start position:0%
+in a in a coherent
+way so we can do more than just
+
+ align:start position:0%
+way so we can do more than just
+ 
+
+ align:start position:0%
+way so we can do more than just
+find so the The Matrix multiply I showed
+
+ align:start position:0%
+find so the The Matrix multiply I showed
+ 
+
+ align:start position:0%
+find so the The Matrix multiply I showed
+you before A1 time A2 transpose showed
+
+ align:start position:0%
+you before A1 time A2 transpose showed
+ 
+
+ align:start position:0%
+you before A1 time A2 transpose showed
+us the counts the number of matches but
+
+ align:start position:0%
+us the counts the number of matches but
+ 
+
+ align:start position:0%
+us the counts the number of matches but
+sometimes we don't want to know more
+
+ align:start position:0%
+sometimes we don't want to know more
+ 
+
+ align:start position:0%
+sometimes we don't want to know more
+than that we want to know not just the
+
+ align:start position:0%
+than that we want to know not just the
+ 
+
+ align:start position:0%
+than that we want to know not just the
+number of matches but please show me the
+
+ align:start position:0%
+number of matches but please show me the
+ 
+
+ align:start position:0%
+number of matches but please show me the
+exact set of 10 ms that cause the match
+
+ align:start position:0%
+exact set of 10 ms that cause the match
+ 
+
+ align:start position:0%
+exact set of 10 ms that cause the match
+okay and so this is where and I think we
+
+ align:start position:0%
+okay and so this is where and I think we
+ 
+
+ align:start position:0%
+okay and so this is where and I think we
+talked about this in a previous lecture
+
+ align:start position:0%
+talked about this in a previous lecture
+ 
+
+ align:start position:0%
+talked about this in a previous lecture
+we have these special Matrix multiplies
+
+ align:start position:0%
+we have these special Matrix multiplies
+ 
+
+ align:start position:0%
+we have these special Matrix multiplies
+that will actually
+
+ align:start position:0%
+that will actually
+ 
+
+ align:start position:0%
+that will actually
+take the intersecting key in The Matrix
+
+ align:start position:0%
+take the intersecting key in The Matrix
+ 
+
+ align:start position:0%
+take the intersecting key in The Matrix
+multiply and now assign that to the
+
+ align:start position:0%
+multiply and now assign that to the
+ 
+
+ align:start position:0%
+multiply and now assign that to the
+value field or concatenate and so that's
+
+ align:start position:0%
+value field or concatenate and so that's
+ 
+
+ align:start position:0%
+value field or concatenate and so that's
+why we have this special Matrix multiply
+
+ align:start position:0%
+why we have this special Matrix multiply
+ 
+
+ align:start position:0%
+why we have this special Matrix multiply
+called cat key M and so for instance
+
+ align:start position:0%
+called cat key M and so for instance
+ 
+
+ align:start position:0%
+called cat key M and so for instance
+here if we look at the result of that
+
+ align:start position:0%
+here if we look at the result of that
+ 
+
+ align:start position:0%
+here if we look at the result of that
+which is AK and we say show me all the
+
+ align:start position:0%
+which is AK and we say show me all the
+ 
+
+ align:start position:0%
+which is AK and we say show me all the
+value matches that are you know greater
+
+ align:start position:0%
+value matches that are you know greater
+ 
+
+ align:start position:0%
+value matches that are you know greater
+than six in their rows and their columns
+
+ align:start position:0%
+than six in their rows and their columns
+ 
+
+ align:start position:0%
+than six in their rows and their columns
+together now we can see that this
+
+ align:start position:0%
+together now we can see that this
+ 
+
+ align:start position:0%
+together now we can see that this
+sequence ID matched with this sequence
+
+ align:start position:0%
+sequence ID matched with this sequence
+ 
+
+ align:start position:0%
+sequence ID matched with this sequence
+ID and these were the actual
+
+ align:start position:0%
+ID and these were the actual
+ 
+
+ align:start position:0%
+ID and these were the actual
+10mer that generate that they had in
+
+ align:start position:0%
+10mer that generate that they had in
+ 
+
+ align:start position:0%
+10mer that generate that they had in
+common now clearly six is not true match
+
+ align:start position:0%
+common now clearly six is not true match
+ 
+
+ align:start position:0%
+common now clearly six is not true match
+in this little sample data set we don't
+
+ align:start position:0%
+in this little sample data set we don't
+ 
+
+ align:start position:0%
+in this little sample data set we don't
+have any true matches but this just this
+
+ align:start position:0%
+have any true matches but this just this
+ 
+
+ align:start position:0%
+have any true matches but this just this
+just shows you what what that is like
+
+ align:start position:0%
+just shows you what what that is like
+ 
+
+ align:start position:0%
+just shows you what what that is like
+and so this is what we call a pedigree
+
+ align:start position:0%
+and so this is what we call a pedigree
+ 
+
+ align:start position:0%
+and so this is what we call a pedigree
+preserving correlation that is it shows
+
+ align:start position:0%
+preserving correlation that is it shows
+ 
+
+ align:start position:0%
+preserving correlation that is it shows
+you the the you know it doesn't just
+
+ align:start position:0%
+you the the you know it doesn't just
+ 
+
+ align:start position:0%
+you the the you know it doesn't just
+give you the count it it shows you where
+
+ align:start position:0%
+give you the count it it shows you where
+ 
+
+ align:start position:0%
+give you the count it it shows you where
+that evidence came from and you can
+
+ align:start position:0%
+that evidence came from and you can
+ 
+
+ align:start position:0%
+that evidence came from and you can
+track it back and this is something we
+
+ align:start position:0%
+track it back and this is something we
+ 
+
+ align:start position:0%
+track it back and this is something we
+do want to do all the time if you
+
+ align:start position:0%
+do want to do all the time if you
+ 
+
+ align:start position:0%
+do want to do all the time if you
+imagined two documents that you wanted
+
+ align:start position:0%
+imagined two documents that you wanted
+ 
+
+ align:start position:0%
+imagined two documents that you wanted
+to cross correlate you might say all
+
+ align:start position:0%
+to cross correlate you might say all
+ 
+
+ align:start position:0%
+to cross correlate you might say all
+right I have these two documents and i'
+
+ align:start position:0%
+right I have these two documents and i'
+ 
+
+ align:start position:0%
+right I have these two documents and i'
+i' I've cross-correlated their word
+
+ align:start position:0%
+i' I've cross-correlated their word
+ 
+
+ align:start position:0%
+i' I've cross-correlated their word
+matches well now I want to know the
+
+ align:start position:0%
+matches well now I want to know the
+ 
+
+ align:start position:0%
+matches well now I want to know the
+actual words that matched you know not
+
+ align:start position:0%
+actual words that matched you know not
+ 
+
+ align:start position:0%
+actual words that matched you know not
+just the counts and you would use the
+
+ align:start position:0%
+just the counts and you would use the
+ 
+
+ align:start position:0%
+just the counts and you would use the
+exact same uh multiply to do that you
+
+ align:start position:0%
+exact same uh multiply to do that you
+ 
+
+ align:start position:0%
+exact same uh multiply to do that you
+know likewise you could do the word word
+
+ align:start position:0%
+know likewise you could do the word word
+ 
+
+ align:start position:0%
+know likewise you could do the word word
+correlation of a document so that would
+
+ align:start position:0%
+correlation of a document so that would
+ 
+
+ align:start position:0%
+correlation of a document so that would
+be a transpose time a instead of a a
+
+ align:start position:0%
+be a transpose time a instead of a a
+ 
+
+ align:start position:0%
+be a transpose time a instead of a a
+transpose and then it would show you two
+
+ align:start position:0%
+transpose and then it would show you two
+ 
+
+ align:start position:0%
+transpose and then it would show you two
+words it would show the list of
+
+ align:start position:0%
+words it would show the list of
+ 
+
+ align:start position:0%
+words it would show the list of
+documents that they actually had in
+
+ align:start position:0%
+documents that they actually had in
+ 
+
+ align:start position:0%
+documents that they actually had in
+common so again this is a powerful uh a
+
+ align:start position:0%
+common so again this is a powerful uh a
+ 
+
+ align:start position:0%
+common so again this is a powerful uh a
+powerful tool again I I should remind
+
+ align:start position:0%
+powerful tool again I I should remind
+ 
+
+ align:start position:0%
+powerful tool again I I should remind
+people when using this you do have to be
+
+ align:start position:0%
+people when using this you do have to be
+ 
+
+ align:start position:0%
+people when using this you do have to be
+careful uh when you do say cat keall A1
+
+ align:start position:0%
+careful uh when you do say cat keall A1
+ 
+
+ align:start position:0%
+careful uh when you do say cat keall A1
+time A1 transpose if you do a square
+
+ align:start position:0%
+time A1 transpose if you do a square
+ 
+
+ align:start position:0%
+time A1 transpose if you do a square
+because you will then end up with this
+
+ align:start position:0%
+because you will then end up with this
+ 
+
+ align:start position:0%
+because you will then end up with this
+very dense diagonal and these lists will
+
+ align:start position:0%
+very dense diagonal and these lists will
+ 
+
+ align:start position:0%
+very dense diagonal and these lists will
+get extremely long and you can often run
+
+ align:start position:0%
+get extremely long and you can often run
+ 
+
+ align:start position:0%
+get extremely long and you can often run
+out of memory when that happens so you
+
+ align:start position:0%
+out of memory when that happens so you
+ 
+
+ align:start position:0%
+out of memory when that happens so you
+do have to be careful when you do uh
+
+ align:start position:0%
+do have to be careful when you do uh
+ 
+
+ align:start position:0%
+do have to be careful when you do uh
+correlations these cat Keo correlations
+
+ align:start position:0%
+correlations these cat Keo correlations
+ 
+
+ align:start position:0%
+correlations these cat Keo correlations
+on things that are going to have very
+
+ align:start position:0%
+on things that are going to have very
+ 
+
+ align:start position:0%
+on things that are going to have very
+large uh overlapping matches the regular
+
+ align:start position:0%
+large uh overlapping matches the regular
+ 
+
+ align:start position:0%
+large uh overlapping matches the regular
+Matrix multiply you don't have to worry
+
+ align:start position:0%
+Matrix multiply you don't have to worry
+ 
+
+ align:start position:0%
+Matrix multiply you don't have to worry
+about that creating dense you know that
+
+ align:start position:0%
+about that creating dense you know that
+ 
+
+ align:start position:0%
+about that creating dense you know that
+that's that's that's not a problem but
+
+ align:start position:0%
+that's that's that's not a problem but
+ 
+
+ align:start position:0%
+that's that's that's not a problem but
+that's just a little caveat to be aware
+
+ align:start position:0%
+that's just a little caveat to be aware
+ 
+
+ align:start position:0%
+that's just a little caveat to be aware
+of and there's really nothing we can do
+
+ align:start position:0%
+of and there's really nothing we can do
+ 
+
+ align:start position:0%
+of and there's really nothing we can do
+about that if you do square them you
+
+ align:start position:0%
+about that if you do square them you
+ 
+
+ align:start position:0%
+about that if you do square them you
+know and we thought about creating a new
+
+ align:start position:0%
+know and we thought about creating a new
+ 
+
+ align:start position:0%
+know and we thought about creating a new
+function which is basically squaring
+
+ align:start position:0%
+function which is basically squaring
+ 
+
+ align:start position:0%
+function which is basically squaring
+with and basically not doing the DI
+
+ align:start position:0%
+with and basically not doing the DI
+ 
+
+ align:start position:0%
+with and basically not doing the DI
+diagonal and and we may we may end up
+
+ align:start position:0%
+diagonal and and we may we may end up
+ 
+
+ align:start position:0%
+diagonal and and we may we may end up
+you know making that if we can figure
+
+ align:start position:0%
+you know making that if we can figure
+ 
+
+ align:start position:0%
+you know making that if we can figure
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+out so once you have those actual
+
+ align:start position:0%
+out so once you have those actual
+ 
+
+ align:start position:0%
+out so once you have those actual
+specific matches here so for example we
+
+ align:start position:0%
+specific matches here so for example we
+ 
+
+ align:start position:0%
+specific matches here so for example we
+have our two reference samples and we
+
+ align:start position:0%
+have our two reference samples and we
+ 
+
+ align:start position:0%
+have our two reference samples and we
+looked at the ones that were larger so
+
+ align:start position:0%
+looked at the ones that were larger so
+ 
+
+ align:start position:0%
+looked at the ones that were larger so
+here's our two sequences this this uh we
+
+ align:start position:0%
+here's our two sequences this this uh we
+ 
+
+ align:start position:0%
+here's our two sequences this this uh we
+look back at the original data which uh
+
+ align:start position:0%
+look back at the original data which uh
+ 
+
+ align:start position:0%
+look back at the original data which uh
+which actually stored the locations
+
+ align:start position:0%
+which actually stored the locations
+ 
+
+ align:start position:0%
+which actually stored the locations
+that so now we're saying oh these two
+
+ align:start position:0%
+that so now we're saying oh these two
+ 
+
+ align:start position:0%
+that so now we're saying oh these two
+have a have six matches between them let
+
+ align:start position:0%
+have a have six matches between them let
+ 
+
+ align:start position:0%
+have a have six matches between them let
+me look them up through this oneline
+
+ align:start position:0%
+me look them up through this oneline
+ 
+
+ align:start position:0%
+me look them up through this oneline
+statement here now I can see the actual
+
+ align:start position:0%
+statement here now I can see the actual
+ 
+
+ align:start position:0%
+statement here now I can see the actual
+10mer that match and their actual
+
+ align:start position:0%
+10mer that match and their actual
+ 
+
+ align:start position:0%
+10mer that match and their actual
+locations in the real data and from that
+
+ align:start position:0%
+locations in the real data and from that
+ 
+
+ align:start position:0%
+locations in the real data and from that
+I can then deduce that oh actually this
+
+ align:start position:0%
+I can then deduce that oh actually this
+ 
+
+ align:start position:0%
+I can then deduce that oh actually this
+is not six separate 10mer matches but
+
+ align:start position:0%
+is not six separate 10mer matches but
+ 
+
+ align:start position:0%
+is not six separate 10mer matches but
+it's really two s of uh uh is this 1 2 3
+
+ align:start position:0%
+it's really two s of uh uh is this 1 2 3
+ 
+
+ align:start position:0%
+it's really two s of uh uh is this 1 2 3
+4 5 6 7 8 9 10 one 10 mer match and then
+
+ align:start position:0%
+4 5 6 7 8 9 10 one 10 mer match and then
+ 
+
+ align:start position:0%
+4 5 6 7 8 9 10 one 10 mer match and then
+I guess a I think this is like a 17
+
+ align:start position:0%
+I guess a I think this is like a 17
+ 
+
+ align:start position:0%
+I guess a I think this is like a 17
+match right and likewise over here you
+
+ align:start position:0%
+match right and likewise over here you
+ 
+
+ align:start position:0%
+match right and likewise over here you
+get the a similar type of thing so
+
+ align:start position:0%
+get the a similar type of thing so
+ 
+
+ align:start position:0%
+get the a similar type of thing so
+that's basically stitching it back
+
+ align:start position:0%
+that's basically stitching it back
+ 
+
+ align:start position:0%
+that's basically stitching it back
+together because that's really what
+
+ align:start position:0%
+together because that's really what
+ 
+
+ align:start position:0%
+together because that's really what
+you're trying to do is find these longer
+
+ align:start position:0%
+you're trying to do is find these longer
+ 
+
+ align:start position:0%
+you're trying to do is find these longer
+sequences where it's identical and then
+
+ align:start position:0%
+sequences where it's identical and then
+ 
+
+ align:start position:0%
+sequences where it's identical and then
+people can then use those to determine
+
+ align:start position:0%
+people can then use those to determine
+ 
+
+ align:start position:0%
+people can then use those to determine
+you know functionality and other types
+
+ align:start position:0%
+you know functionality and other types
+ 
+
+ align:start position:0%
+you know functionality and other types
+of things that have to do do with that
+
+ align:start position:0%
+of things that have to do do with that
+ 
+
+ align:start position:0%
+of things that have to do do with that
+so this is just part of the process of
+
+ align:start position:0%
+so this is just part of the process of
+ 
+
+ align:start position:0%
+so this is just part of the process of
+of doing that and it just shows by
+
+ align:start position:0%
+of doing that and it just shows by
+ 
+
+ align:start position:0%
+of doing that and it just shows by
+having this pedigree preserving Matrix
+
+ align:start position:0%
+having this pedigree preserving Matrix
+ 
+
+ align:start position:0%
+having this pedigree preserving Matrix
+multip mly and the ability to store
+
+ align:start position:0%
+multip mly and the ability to store
+ 
+
+ align:start position:0%
+multip mly and the ability to store
+string values in the value that we can
+
+ align:start position:0%
+string values in the value that we can
+ 
+
+ align:start position:0%
+string values in the value that we can
+actually preserve that information and
+
+ align:start position:0%
+actually preserve that information and
+ 
+
+ align:start position:0%
+actually preserve that information and
+um and do
+
+ align:start position:0%
+um and do
+ 
+
+ align:start position:0%
+um and do
+that so that just shows you I think a
+
+ align:start position:0%
+that so that just shows you I think a
+ 
+
+ align:start position:0%
+that so that just shows you I think a
+really great example it's kind of one of
+
+ align:start position:0%
+really great example it's kind of one of
+ 
+
+ align:start position:0%
+really great example it's kind of one of
+the most recent things we did this
+
+ align:start position:0%
+the most recent things we did this
+ 
+
+ align:start position:0%
+the most recent things we did this
+summer in terms of the power of d4m
+
+ align:start position:0%
+summer in terms of the power of d4m
+ 
+
+ align:start position:0%
+summer in terms of the power of d4m
+coupled with databases to really do
+
+ align:start position:0%
+coupled with databases to really do
+ 
+
+ align:start position:0%
+coupled with databases to really do
+algorithms that are completely you
+
+ align:start position:0%
+algorithms that are completely you
+ 
+
+ align:start position:0%
+algorithms that are completely you
+know kind of new and and interesting and
+
+ align:start position:0%
+know kind of new and and interesting and
+ 
+
+ align:start position:0%
+know kind of new and and interesting and
+as algorithm developers I think that's
+
+ align:start position:0%
+as algorithm developers I think that's
+ 
+
+ align:start position:0%
+as algorithm developers I think that's
+something that we all very excited about
+
+ align:start position:0%
+something that we all very excited about
+ 
+
+ align:start position:0%
+something that we all very excited about
+so I'm now I'm going to talk about how
+
+ align:start position:0%
+so I'm now I'm going to talk about how
+ 
+
+ align:start position:0%
+so I'm now I'm going to talk about how
+this fits into an overall pipeline so
+
+ align:start position:0%
+this fits into an overall pipeline so
+ 
+
+ align:start position:0%
+this fits into an overall pipeline so
+once again just for reminders you know
+
+ align:start position:0%
+once again just for reminders you know
+ 
+
+ align:start position:0%
+once again just for reminders you know
+uh d4m you know we've talked mostly
+
+ align:start position:0%
+uh d4m you know we've talked mostly
+ 
+
+ align:start position:0%
+uh d4m you know we've talked mostly
+about working over here in this space in
+
+ align:start position:0%
+about working over here in this space in
+ 
+
+ align:start position:0%
+about working over here in this space in
+the mat lab space um for doing your
+
+ align:start position:0%
+the mat lab space um for doing your
+ 
+
+ align:start position:0%
+the mat lab space um for doing your
+analytics with associative arrays but
+
+ align:start position:0%
+analytics with associative arrays but
+ 
+
+ align:start position:0%
+analytics with associative arrays but
+they also have ways uh we have very nice
+
+ align:start position:0%
+they also have ways uh we have very nice
+ 
+
+ align:start position:0%
+they also have ways uh we have very nice
+bindings to in particular the cumulo
+
+ align:start position:0%
+bindings to in particular the cumulo
+ 
+
+ align:start position:0%
+bindings to in particular the cumulo
+database but we can bind to just about
+
+ align:start position:0%
+database but we can bind to just about
+ 
+
+ align:start position:0%
+database but we can bind to just about
+any database um and here's an example if
+
+ align:start position:0%
+any database um and here's an example if
+ 
+
+ align:start position:0%
+any database um and here's an example if
+I have a table that shows you know all
+
+ align:start position:0%
+I have a table that shows you know all
+ 
+
+ align:start position:0%
+I have a table that shows you know all
+this data and I just wanted to get
+
+ align:start position:0%
+this data and I just wanted to get
+ 
+
+ align:start position:0%
+this data and I just wanted to get
+please give me the column of this 10mer
+
+ align:start position:0%
+please give me the column of this 10mer
+ 
+
+ align:start position:0%
+please give me the column of this 10mer
+sequence I would just type that query
+
+ align:start position:0%
+sequence I would just type that query
+ 
+
+ align:start position:0%
+sequence I would just type that query
+and it will return that column for me
+
+ align:start position:0%
+and it will return that column for me
+ 
+
+ align:start position:0%
+and it will return that column for me
+very nicely so it's a very powerful
+
+ align:start position:0%
+very nicely so it's a very powerful
+ 
+
+ align:start position:0%
+very nicely so it's a very powerful
+binding to to databases it's funny
+
+ align:start position:0%
+binding to to databases it's funny
+ 
+
+ align:start position:0%
+binding to to databases it's funny
+because a lot of people when I talk to
+
+ align:start position:0%
+because a lot of people when I talk to
+ 
+
+ align:start position:0%
+because a lot of people when I talk to
+them they
+
+ align:start position:0%
+them they
+ 
+
+ align:start position:0%
+them they
+like they think dform is either just
+
+ align:start position:0%
+like they think dform is either just
+ 
+
+ align:start position:0%
+like they think dform is either just
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+databases or just about this associative
+
+ align:start position:0%
+databases or just about this associative
+ 
+
+ align:start position:0%
+databases or just about this associative
+R mathematics and because they usually
+
+ align:start position:0%
+R mathematics and because they usually
+ 
+
+ align:start position:0%
+R mathematics and because they usually
+kind of people take sort of they usually
+
+ align:start position:0%
+kind of people take sort of they usually
+ 
+
+ align:start position:0%
+kind of people take sort of they usually
+see it sort of more used in one one
+
+ align:start position:0%
+see it sort of more used in one one
+ 
+
+ align:start position:0%
+see it sort of more used in one one
+context or another and it's really about
+
+ align:start position:0%
+context or another and it's really about
+ 
+
+ align:start position:0%
+context or another and it's really about
+both it's really about connecting the
+
+ align:start position:0%
+both it's really about connecting the
+ 
+
+ align:start position:0%
+both it's really about connecting the
+two worlds
+
+ align:start position:0%
+two worlds
+ 
+
+ align:start position:0%
+two worlds
+together that particular application
+
+ align:start position:0%
+together that particular application
+ 
+
+ align:start position:0%
+together that particular application
+that we showed you this uh genetic
+
+ align:start position:0%
+that we showed you this uh genetic
+ 
+
+ align:start position:0%
+that we showed you this uh genetic
+sequence uh you know comparison uh
+
+ align:start position:0%
+sequence uh you know comparison uh
+ 
+
+ align:start position:0%
+sequence uh you know comparison uh
+application is like you is a part of a
+
+ align:start position:0%
+application is like you is a part of a
+ 
+
+ align:start position:0%
+application is like you is a part of a
+pipeline like you would see in any real
+
+ align:start position:0%
+pipeline like you would see in any real
+ 
+
+ align:start position:0%
+pipeline like you would see in any real
+system and so I'm going to show you that
+
+ align:start position:0%
+system and so I'm going to show you that
+ 
+
+ align:start position:0%
+system and so I'm going to show you that
+that pipeline here and so um you know we
+
+ align:start position:0%
+that pipeline here and so um you know we
+ 
+
+ align:start position:0%
+that pipeline here and so um you know we
+have here uh the the raw data so fasta
+
+ align:start position:0%
+have here uh the the raw data so fasta
+ 
+
+ align:start position:0%
+have here uh the the raw data so fasta
+is just the name of the file format that
+
+ align:start position:0%
+is just the name of the file format that
+ 
+
+ align:start position:0%
+is just the name of the file format that
+all this DNA sequence comes in which
+
+ align:start position:0%
+all this DNA sequence comes in which
+ 
+
+ align:start position:0%
+all this DNA sequence comes in which
+basically looks pretty much like a CSV
+
+ align:start position:0%
+basically looks pretty much like a CSV
+ 
+
+ align:start position:0%
+basically looks pretty much like a CSV
+file of what I just saw you I guess that
+
+ align:start position:0%
+file of what I just saw you I guess that
+ 
+
+ align:start position:0%
+file of what I just saw you I guess that
+deserves a a name as a file format but
+
+ align:start position:0%
+deserves a a name as a file format but
+ 
+
+ align:start position:0%
+deserves a a name as a file format but
+you know uh so it's basically it's
+
+ align:start position:0%
+you know uh so it's basically it's
+ 
+
+ align:start position:0%
+you know uh so it's basically it's
+basically that and then one thing we do
+
+ align:start position:0%
+basically that and then one thing we do
+ 
+
+ align:start position:0%
+basically that and then one thing we do
+is uh is uh we uh parse that data from
+
+ align:start position:0%
+is uh is uh we uh parse that data from
+ 
+
+ align:start position:0%
+is uh is uh we uh parse that data from
+the fasted data into triples
+
+ align:start position:0%
+the fasted data into triples
+ 
+
+ align:start position:0%
+the fasted data into triples
+format which um allows us to then um
+
+ align:start position:0%
+format which um allows us to then um
+ 
+
+ align:start position:0%
+format which um allows us to then um
+really work it with this associative
+
+ align:start position:0%
+really work it with this associative
+ 
+
+ align:start position:0%
+really work it with this associative
+array so it basically creates the 10ms
+
+ align:start position:0%
+array so it basically creates the 10ms
+ 
+
+ align:start position:0%
+array so it basically creates the 10ms
+and puts them into a series of triple
+
+ align:start position:0%
+and puts them into a series of triple
+ 
+
+ align:start position:0%
+and puts them into a series of triple
+files a a row triple file which holds a
+
+ align:start position:0%
+files a a row triple file which holds a
+ 
+
+ align:start position:0%
+files a a row triple file which holds a
+sequence ID uh the actual tenr itself
+
+ align:start position:0%
+sequence ID uh the actual tenr itself
+ 
+
+ align:start position:0%
+sequence ID uh the actual tenr itself
+list of those and then uh the position
+
+ align:start position:0%
+list of those and then uh the position
+ 
+
+ align:start position:0%
+list of those and then uh the position
+of where that tenr appeared in the
+
+ align:start position:0%
+of where that tenr appeared in the
+ 
+
+ align:start position:0%
+of where that tenr appeared in the
+sequence um and then typically what we
+
+ align:start position:0%
+sequence um and then typically what we
+ 
+
+ align:start position:0%
+sequence um and then typically what we
+do then is we
+
+ align:start position:0%
+do then is we
+ 
+
+ align:start position:0%
+do then is we
+read we write a program and this can be
+
+ align:start position:0%
+read we write a program and this can be
+ 
+
+ align:start position:0%
+read we write a program and this can be
+a parallel program if we want it that
+
+ align:start position:0%
+a parallel program if we want it that
+ 
+
+ align:start position:0%
+a parallel program if we want it that
+will then usually in mat lab using D4
+
+ align:start position:0%
+will then usually in mat lab using D4
+ 
+
+ align:start position:0%
+will then usually in mat lab using D4
+that will read these sequences in and
+
+ align:start position:0%
+that will read these sequences in and
+ 
+
+ align:start position:0%
+that will read these sequences in and
+we'll often just directly insert them
+
+ align:start position:0%
+we'll often just directly insert them
+ 
+
+ align:start position:0%
+we'll often just directly insert them
+without any additional formatting just
+
+ align:start position:0%
+without any additional formatting just
+ 
+
+ align:start position:0%
+without any additional formatting just
+we have a way of just inserting triples
+
+ align:start position:0%
+we have a way of just inserting triples
+ 
+
+ align:start position:0%
+we have a way of just inserting triples
+directly into the cumulo database and
+
+ align:start position:0%
+directly into the cumulo database and
+ 
+
+ align:start position:0%
+directly into the cumulo database and
+which is the fastest way that we can do
+
+ align:start position:0%
+which is the fastest way that we can do
+ 
+
+ align:start position:0%
+which is the fastest way that we can do
+inserts um and then it will
+
+ align:start position:0%
+inserts um and then it will
+ 
+
+ align:start position:0%
+inserts um and then it will
+also uh convert these two associative
+
+ align:start position:0%
+also uh convert these two associative
+ 
+
+ align:start position:0%
+also uh convert these two associative
+arrays in mat lab and we'll save them
+
+ align:start position:0%
+arrays in mat lab and we'll save them
+ 
+
+ align:start position:0%
+arrays in mat lab and we'll save them
+out as matte files uh because this will
+
+ align:start position:0%
+out as matte files uh because this will
+ 
+
+ align:start position:0%
+out as matte files uh because this will
+take a little time to convert all of
+
+ align:start position:0%
+take a little time to convert all of
+ 
+
+ align:start position:0%
+take a little time to convert all of
+these things into files you like well
+
+ align:start position:0%
+these things into files you like well
+ 
+
+ align:start position:0%
+these things into files you like well
+why would we do that well there's two
+
+ align:start position:0%
+why would we do that well there's two
+ 
+
+ align:start position:0%
+why would we do that well there's two
+very good reasons for doing that one
+
+ align:start position:0%
+very good reasons for doing that one
+ 
+
+ align:start position:0%
+very good reasons for doing that one
+yukimo database or any database is very
+
+ align:start position:0%
+yukimo database or any database is very
+ 
+
+ align:start position:0%
+yukimo database or any database is very
+good if we want to look up a small part
+
+ align:start position:0%
+good if we want to look up a small part
+ 
+
+ align:start position:0%
+good if we want to look up a small part
+of a large data set okay so we have
+
+ align:start position:0%
+of a large data set okay so we have
+ 
+
+ align:start position:0%
+of a large data set okay so we have
+billions of records and we want millions
+
+ align:start position:0%
+billions of records and we want millions
+ 
+
+ align:start position:0%
+billions of records and we want millions
+of those records that's a great use of a
+
+ align:start position:0%
+of those records that's a great use of a
+ 
+
+ align:start position:0%
+of those records that's a great use of a
+database however there's certain times
+
+ align:start position:0%
+database however there's certain times
+ 
+
+ align:start position:0%
+database however there's certain times
+we're like no we want to Traverse the
+
+ align:start position:0%
+we're like no we want to Traverse the
+ 
+
+ align:start position:0%
+we're like no we want to Traverse the
+entire data set well databases are
+
+ align:start position:0%
+entire data set well databases are
+ 
+
+ align:start position:0%
+entire data set well databases are
+actually bad at doing that if you say I
+
+ align:start position:0%
+actually bad at doing that if you say I
+ 
+
+ align:start position:0%
+actually bad at doing that if you say I
+want to scan over the entire database
+
+ align:start position:0%
+want to scan over the entire database
+ 
+
+ align:start position:0%
+want to scan over the entire database
+it's like doing a billion queries you
+
+ align:start position:0%
+it's like doing a billion queries you
+ 
+
+ align:start position:0%
+it's like doing a billion queries you
+know and so there's overheads associated
+
+ align:start position:0%
+know and so there's overheads associated
+ 
+
+ align:start position:0%
+know and so there's overheads associated
+with that in that instance it's far more
+
+ align:start position:0%
+with that in that instance it's far more
+ 
+
+ align:start position:0%
+with that in that instance it's far more
+efficient to just save the data into
+
+ align:start position:0%
+efficient to just save the data into
+ 
+
+ align:start position:0%
+efficient to just save the data into
+these associate radio files which will
+
+ align:start position:0%
+these associate radio files which will
+ 
+
+ align:start position:0%
+these associate radio files which will
+read in very quickly and then you can
+
+ align:start position:0%
+read in very quickly and then you can
+ 
+
+ align:start position:0%
+read in very quickly and then you can
+just if you're like I want to do an
+
+ align:start position:0%
+just if you're like I want to do an
+ 
+
+ align:start position:0%
+just if you're like I want to do an
+analysis you know of the data uh in that
+
+ align:start position:0%
+analysis you know of the data uh in that
+ 
+
+ align:start position:0%
+analysis you know of the data uh in that
+way where I'm going to want I really
+
+ align:start position:0%
+way where I'm going to want I really
+ 
+
+ align:start position:0%
+way where I'm going to want I really
+want to you know work with 10% or 20% of
+
+ align:start position:0%
+want to you know work with 10% or 20% of
+ 
+
+ align:start position:0%
+want to you know work with 10% or 20% of
+the data then having these these the
+
+ align:start position:0%
+the data then having these these the
+ 
+
+ align:start position:0%
+the data then having these these the
+this data in this you know already
+
+ align:start position:0%
+this data in this you know already
+ 
+
+ align:start position:0%
+this data in this you know already
+parsed into this binary format is a very
+
+ align:start position:0%
+parsed into this binary format is a very
+ 
+
+ align:start position:0%
+parsed into this binary format is a very
+efficient way to run an application or
+
+ align:start position:0%
+efficient way to run an application or
+ 
+
+ align:start position:0%
+efficient way to run an application or
+an analytic that will run over all those
+
+ align:start position:0%
+an analytic that will run over all those
+ 
+
+ align:start position:0%
+an analytic that will run over all those
+files it also U makes parallelism very
+
+ align:start position:0%
+files it also U makes parallelism very
+ 
+
+ align:start position:0%
+files it also U makes parallelism very
+easily you just get let you know
+
+ align:start position:0%
+easily you just get let you know
+ 
+
+ align:start position:0%
+easily you just get let you know
+different processors process different
+
+ align:start position:0%
+different processors process different
+ 
+
+ align:start position:0%
+different processors process different
+files you know that's very easy to do we
+
+ align:start position:0%
+files you know that's very easy to do we
+ 
+
+ align:start position:0%
+files you know that's very easy to do we
+have lots of support for that type of of
+
+ align:start position:0%
+have lots of support for that type of of
+ 
+
+ align:start position:0%
+have lots of support for that type of of
+model and so that's a good reason to do
+
+ align:start position:0%
+model and so that's a good reason to do
+ 
+
+ align:start position:0%
+model and so that's a good reason to do
+that um and you know at worst you're
+
+ align:start position:0%
+that um and you know at worst you're
+ 
+
+ align:start position:0%
+that um and you know at worst you're
+doubling the size of the data in your
+
+ align:start position:0%
+doubling the size of the data in your
+ 
+
+ align:start position:0%
+doubling the size of the data in your
+database don't worry about it we double
+
+ align:start position:0%
+database don't worry about it we double
+ 
+
+ align:start position:0%
+database don't worry about it we double
+data in databases all the time databases
+
+ align:start position:0%
+data in databases all the time databases
+ 
+
+ align:start position:0%
+data in databases all the time databases
+are notoriously if you put a certain
+
+ align:start position:0%
+are notoriously if you put a certain
+ 
+
+ align:start position:0%
+are notoriously if you put a certain
+amount of data in they they they you
+
+ align:start position:0%
+amount of data in they they they you
+ 
+
+ align:start position:0%
+amount of data in they they they you
+know they make it much larger acumulo
+
+ align:start position:0%
+know they make it much larger acumulo
+ 
+
+ align:start position:0%
+know they make it much larger acumulo
+actually does a very good job of that it
+
+ align:start position:0%
+actually does a very good job of that it
+ 
+
+ align:start position:0%
+actually does a very good job of that it
+won't really be that much larger but
+
+ align:start position:0%
+won't really be that much larger but
+ 
+
+ align:start position:0%
+won't really be that much larger but
+there's no reason uh to not as you're
+
+ align:start position:0%
+there's no reason uh to not as you're
+ 
+
+ align:start position:0%
+there's no reason uh to not as you're
+doing the injest to save those files and
+
+ align:start position:0%
+doing the injest to save those files and
+ 
+
+ align:start position:0%
+doing the injest to save those files and
+then you can do various
+
+ align:start position:0%
+then you can do various
+ 
+
+ align:start position:0%
+then you can do various
+comparisons um uh so for example uh you
+
+ align:start position:0%
+comparisons um uh so for example uh you
+ 
+
+ align:start position:0%
+comparisons um uh so for example uh you
+know uh we then can uh if this if we
+
+ align:start position:0%
+know uh we then can uh if this if we
+ 
+
+ align:start position:0%
+know uh we then can uh if this if we
+save the um the sample data as a matlb
+
+ align:start position:0%
+save the um the sample data as a matlb
+ 
+
+ align:start position:0%
+save the um the sample data as a matlb
+file we could read that in and then um
+
+ align:start position:0%
+file we could read that in and then um
+ 
+
+ align:start position:0%
+file we could read that in and then um
+and then uh uh then uh do our comparison
+
+ align:start position:0%
+and then uh uh then uh do our comparison
+ 
+
+ align:start position:0%
+and then uh uh then uh do our comparison
+with the reference data that's sitting
+
+ align:start position:0%
+with the reference data that's sitting
+ 
+
+ align:start position:0%
+with the reference data that's sitting
+inside the database to get our top
+
+ align:start position:0%
+inside the database to get our top
+ 
+
+ align:start position:0%
+inside the database to get our top
+matches and that's exactly how this
+
+ align:start position:0%
+matches and that's exactly how this
+ 
+
+ align:start position:0%
+matches and that's exactly how this
+application actually worked so this pipe
+
+ align:start position:0%
+application actually worked so this pipe
+ 
+
+ align:start position:0%
+application actually worked so this pipe
+P line from raw data to an intermediate
+
+ align:start position:0%
+P line from raw data to an intermediate
+ 
+
+ align:start position:0%
+P line from raw data to an intermediate
+format to you know sort of efficient
+
+ align:start position:0%
+format to you know sort of efficient
+ 
+
+ align:start position:0%
+format to you know sort of efficient
+binary format and insertion uh then to
+
+ align:start position:0%
+binary format and insertion uh then to
+ 
+
+ align:start position:0%
+binary format and insertion uh then to
+then uh doing the analytics and
+
+ align:start position:0%
+then uh doing the analytics and
+ 
+
+ align:start position:0%
+then uh doing the analytics and
+comparisons and eventually you'll
+
+ align:start position:0%
+comparisons and eventually you'll
+ 
+
+ align:start position:0%
+comparisons and eventually you'll
+usually often have another layer which
+
+ align:start position:0%
+usually often have another layer which
+ 
+
+ align:start position:0%
+usually often have another layer which
+is you might create a web interface to
+
+ align:start position:0%
+is you might create a web interface to
+ 
+
+ align:start position:0%
+is you might create a web interface to
+something we're like okay this is now a
+
+ align:start position:0%
+something we're like okay this is now a
+ 
+
+ align:start position:0%
+something we're like okay this is now a
+full system you know person can type in
+
+ align:start position:0%
+full system you know person can type in
+ 
+
+ align:start position:0%
+full system you know person can type in
+you know put in their own data and then
+
+ align:start position:0%
+you know put in their own data and then
+ 
+
+ align:start position:0%
+you know put in their own data and then
+it will then call a function so again
+
+ align:start position:0%
+it will then call a function so again
+ 
+
+ align:start position:0%
+it will then call a function so again
+this is very standard how this stuff
+
+ align:start position:0%
+this is very standard how this stuff
+ 
+
+ align:start position:0%
+this is very standard how this stuff
+ends up uh fitting into an overall
+
+ align:start position:0%
+ends up uh fitting into an overall
+ 
+
+ align:start position:0%
+ends up uh fitting into an overall
+pipeline um and it's certainly a
+
+ align:start position:0%
+pipeline um and it's certainly a
+ 
+
+ align:start position:0%
+pipeline um and it's certainly a
+situation where if you're going to
+
+ align:start position:0%
+situation where if you're going to
+ 
+
+ align:start position:0%
+situation where if you're going to
+deploy a system you might decide you
+
+ align:start position:0%
+deploy a system you might decide you
+ 
+
+ align:start position:0%
+deploy a system you might decide you
+know what I don't want mat lab to be a
+
+ align:start position:0%
+know what I don't want mat lab to be a
+ 
+
+ align:start position:0%
+know what I don't want mat lab to be a
+part of my deployed system I want to do
+
+ align:start position:0%
+part of my deployed system I want to do
+ 
+
+ align:start position:0%
+part of my deployed system I want to do
+that say in Joba or something else
+
+ align:start position:0%
+that say in Joba or something else
+ 
+
+ align:start position:0%
+that say in Joba or something else
+that's sort of more Universal which we
+
+ align:start position:0%
+that's sort of more Universal which we
+ 
+
+ align:start position:0%
+that's sort of more Universal which we
+certainly see people do it still makes
+
+ align:start position:0%
+certainly see people do it still makes
+ 
+
+ align:start position:0%
+certainly see people do it still makes
+sense to do it in this approach because
+
+ align:start position:0%
+sense to do it in this approach because
+ 
+
+ align:start position:0%
+sense to do it in this approach because
+the algorithm development and testing is
+
+ align:start position:0%
+the algorithm development and testing is
+ 
+
+ align:start position:0%
+the algorithm development and testing is
+just much much easier to do in an
+
+ align:start position:0%
+just much much easier to do in an
+ 
+
+ align:start position:0%
+just much much easier to do in an
+environment like d4m and then once you
+
+ align:start position:0%
+environment like d4m and then once you
+ 
+
+ align:start position:0%
+environment like d4m and then once you
+have the algorithm correct it's now much
+
+ align:start position:0%
+have the algorithm correct it's now much
+ 
+
+ align:start position:0%
+have the algorithm correct it's now much
+easier to give that to someone else who
+
+ align:start position:0%
+easier to give that to someone else who
+ 
+
+ align:start position:0%
+easier to give that to someone else who
+is going to do the implementation in
+
+ align:start position:0%
+is going to do the implementation in
+ 
+
+ align:start position:0%
+is going to do the implementation in
+another environment and deal with all
+
+ align:start position:0%
+another environment and deal with all
+ 
+
+ align:start position:0%
+another environment and deal with all
+the issues that are associated with
+
+ align:start position:0%
+the issues that are associated with
+ 
+
+ align:start position:0%
+the issues that are associated with
+maybe doing a deployment type of thing
+
+ align:start position:0%
+maybe doing a deployment type of thing
+ 
+
+ align:start position:0%
+maybe doing a deployment type of thing
+so one certainly could use uh the mat
+
+ align:start position:0%
+so one certainly could use uh the mat
+ 
+
+ align:start position:0%
+so one certainly could use uh the mat
+lab or or G new octave uh code in a
+
+ align:start position:0%
+lab or or G new octave uh code in a
+ 
+
+ align:start position:0%
+lab or or G new octave uh code in a
+production environment we certainly have
+
+ align:start position:0%
+production environment we certainly have
+ 
+
+ align:start position:0%
+production environment we certainly have
+seen that but often in the case one has
+
+ align:start position:0%
+seen that but often in the case one has
+ 
+
+ align:start position:0%
+seen that but often in the case one has
+limitations about what can deploy and so
+
+ align:start position:0%
+limitations about what can deploy and so
+ 
+
+ align:start position:0%
+limitations about what can deploy and so
+it is still better to do the algorithm
+
+ align:start position:0%
+it is still better to do the algorithm
+ 
+
+ align:start position:0%
+it is still better to do the algorithm
+development in this type of environment
+
+ align:start position:0%
+development in this type of environment
+ 
+
+ align:start position:0%
+development in this type of environment
+and than than to uh than to try and do
+
+ align:start position:0%
+and than than to uh than to try and do
+ 
+
+ align:start position:0%
+and than than to uh than to try and do
+the alment in in in a deployment
+
+ align:start position:0%
+the alment in in in a deployment
+ 
+
+ align:start position:0%
+the alment in in in a deployment
+language like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Java one of the things that was very
+
+ align:start position:0%
+Java one of the things that was very
+ 
+
+ align:start position:0%
+Java one of the things that was very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+for this database and it's true of most
+
+ align:start position:0%
+for this database and it's true of most
+ 
+
+ align:start position:0%
+for this database and it's true of most
+parallel
+
+ align:start position:0%
+parallel
+ 
+
+ align:start position:0%
+parallel
+databases so if we want to get the
+
+ align:start position:0%
+databases so if we want to get the
+ 
+
+ align:start position:0%
+databases so if we want to get the
+highest performance insert that is we
+
+ align:start position:0%
+highest performance insert that is we
+ 
+
+ align:start position:0%
+highest performance insert that is we
+want to you know read the data insert it
+
+ align:start position:0%
+want to you know read the data insert it
+ 
+
+ align:start position:0%
+want to you know read the data insert it
+as quickly as possible in the database
+
+ align:start position:0%
+as quickly as possible in the database
+ 
+
+ align:start position:0%
+as quickly as possible in the database
+typically we'll need to have some kind
+
+ align:start position:0%
+typically we'll need to have some kind
+ 
+
+ align:start position:0%
+typically we'll need to have some kind
+of parallel program running in this case
+
+ align:start position:0%
+of parallel program running in this case
+ 
+
+ align:start position:0%
+of parallel program running in this case
+maybe each reading different sets of
+
+ align:start position:0%
+maybe each reading different sets of
+ 
+
+ align:start position:0%
+maybe each reading different sets of
+input files and all inserting them into
+
+ align:start position:0%
+input files and all inserting them into
+ 
+
+ align:start position:0%
+input files and all inserting them into
+the parallel database and so in accumulo
+
+ align:start position:0%
+the parallel database and so in accumulo
+ 
+
+ align:start position:0%
+the parallel database and so in accumulo
+they divide your table amongst the
+
+ align:start position:0%
+they divide your table amongst the
+ 
+
+ align:start position:0%
+they divide your table amongst the
+different computers which they call
+
+ align:start position:0%
+different computers which they call
+ 
+
+ align:start position:0%
+different computers which they call
+tablet
+
+ align:start position:0%
+tablet
+ 
+
+ align:start position:0%
+tablet
+servers and it's very important to avoid
+
+ align:start position:0%
+servers and it's very important to avoid
+ 
+
+ align:start position:0%
+servers and it's very important to avoid
+the situation where everyone is
+
+ align:start position:0%
+the situation where everyone is
+ 
+
+ align:start position:0%
+the situation where everyone is
+inserting and all the data is inserting
+
+ align:start position:0%
+inserting and all the data is inserting
+ 
+
+ align:start position:0%
+inserting and all the data is inserting
+into the same tablet server you're not
+
+ align:start position:0%
+into the same tablet server you're not
+ 
+
+ align:start position:0%
+into the same tablet server you're not
+going to get really very good
+
+ align:start position:0%
+going to get really very good
+ 
+
+ align:start position:0%
+going to get really very good
+performance now the way a cumulo splits
+
+ align:start position:0%
+performance now the way a cumulo splits
+ 
+
+ align:start position:0%
+performance now the way a cumulo splits
+up its data is similar to many other
+
+ align:start position:0%
+up its data is similar to many other
+ 
+
+ align:start position:0%
+up its data is similar to many other
+databases it called it's called sharding
+
+ align:start position:0%
+databases it called it's called sharding
+ 
+
+ align:start position:0%
+databases it called it's called sharding
+sometimes they call it it's just means
+
+ align:start position:0%
+sometimes they call it it's just means
+ 
+
+ align:start position:0%
+sometimes they call it it's just means
+they split up the table but the term in
+
+ align:start position:0%
+they split up the table but the term in
+ 
+
+ align:start position:0%
+they split up the table but the term in
+the database Community use is they call
+
+ align:start position:0%
+the database Community use is they call
+ 
+
+ align:start position:0%
+the database Community use is they call
+it sharding what they'll do is they'll
+
+ align:start position:0%
+it sharding what they'll do is they'll
+ 
+
+ align:start position:0%
+it sharding what they'll do is they'll
+basically take the table and they'll
+
+ align:start position:0%
+basically take the table and they'll
+ 
+
+ align:start position:0%
+basically take the table and they'll
+sign certain row keys in this in a
+
+ align:start position:0%
+sign certain row keys in this in a
+ 
+
+ align:start position:0%
+sign certain row keys in this in a
+cumulous case certain contiguous sets of
+
+ align:start position:0%
+cumulous case certain contiguous sets of
+ 
+
+ align:start position:0%
+cumulous case certain contiguous sets of
+row keys to particular tablet
+
+ align:start position:0%
+row keys to particular tablet
+ 
+
+ align:start position:0%
+row keys to particular tablet
+servers so you know if you had a a data
+
+ align:start position:0%
+servers so you know if you had a a data
+ 
+
+ align:start position:0%
+servers so you know if you had a a data
+set that was
+
+ align:start position:0%
+set that was
+ 
+
+ align:start position:0%
+set that was
+universally uh uh split uh where over
+
+ align:start position:0%
+universally uh uh split uh where over
+ 
+
+ align:start position:0%
+universally uh uh split uh where over
+the alphabet then and you were going to
+
+ align:start position:0%
+the alphabet then and you were going to
+ 
+
+ align:start position:0%
+the alphabet then and you were going to
+split it the first split would be
+
+ align:start position:0%
+split it the first split would be
+ 
+
+ align:start position:0%
+split it the first split would be
+between you know m and n and so this is
+
+ align:start position:0%
+between you know m and n and so this is
+ 
+
+ align:start position:0%
+between you know m and n and so this is
+called splitting and it's very important
+
+ align:start position:0%
+called splitting and it's very important
+ 
+
+ align:start position:0%
+called splitting and it's very important
+to try and get good splits and choose
+
+ align:start position:0%
+to try and get good splits and choose
+ 
+
+ align:start position:0%
+to try and get good splits and choose
+your splits so that you get good
+
+ align:start position:0%
+your splits so that you get good
+ 
+
+ align:start position:0%
+your splits so that you get good
+performance now d4m has a native
+
+ align:start position:0%
+performance now d4m has a native
+ 
+
+ align:start position:0%
+performance now d4m has a native
+interface that allows you to just say
+
+ align:start position:0%
+interface that allows you to just say
+ 
+
+ align:start position:0%
+interface that allows you to just say
+here are the I want these to be the
+
+ align:start position:0%
+here are the I want these to be the
+ 
+
+ align:start position:0%
+here are the I want these to be the
+splits of this table you can actually
+
+ align:start position:0%
+splits of this table you can actually
+ 
+
+ align:start position:0%
+splits of this table you can actually
+compute those and then assign them if
+
+ align:start position:0%
+compute those and then assign them if
+ 
+
+ align:start position:0%
+compute those and then assign them if
+you have a parallel instance in the
+
+ align:start position:0%
+you have a parallel instance in the
+ 
+
+ align:start position:0%
+you have a parallel instance in the
+class you will only be working on the
+
+ align:start position:0%
+class you will only be working on the
+ 
+
+ align:start position:0%
+class you will only be working on the
+databases that we will be set up for you
+
+ align:start position:0%
+databases that we will be set up for you
+ 
+
+ align:start position:0%
+databases that we will be set up for you
+we have set up for you are all single
+
+ align:start position:0%
+we have set up for you are all single
+ 
+
+ align:start position:0%
+we have set up for you are all single
+node instances they do not have multiple
+
+ align:start position:0%
+node instances they do not have multiple
+ 
+
+ align:start position:0%
+node instances they do not have multiple
+tablet servers so you don't really have
+
+ align:start position:0%
+tablet servers so you don't really have
+ 
+
+ align:start position:0%
+tablet servers so you don't really have
+to do deal with splitting uh it's only
+
+ align:start position:0%
+to do deal with splitting uh it's only
+ 
+
+ align:start position:0%
+to do deal with splitting uh it's only
+an issue in parallel but it's certainly
+
+ align:start position:0%
+an issue in parallel but it's certainly
+ 
+
+ align:start position:0%
+an issue in parallel but it's certainly
+something to be aware of and as of the
+
+ align:start position:0%
+something to be aware of and as of the
+ 
+
+ align:start position:0%
+something to be aware of and as of the
+key you know people will often have a
+
+ align:start position:0%
+key you know people will often have a
+ 
+
+ align:start position:0%
+key you know people will often have a
+very large accumulo instance and they
+
+ align:start position:0%
+very large accumulo instance and they
+ 
+
+ align:start position:0%
+very large accumulo instance and they
+may only be getting not very you know
+
+ align:start position:0%
+may only be getting not very you know
+ 
+
+ align:start position:0%
+may only be getting not very you know
+the performance they would get on one on
+
+ align:start position:0%
+the performance they would get on one on
+ 
+
+ align:start position:0%
+the performance they would get on one on
+just a two node instance because and
+
+ align:start position:0%
+just a two node instance because and
+ 
+
+ align:start position:0%
+just a two node instance because and
+usually it's because their splitting
+
+ align:start position:0%
+usually it's because their splitting
+ 
+
+ align:start position:0%
+usually it's because their splitting
+needs to be done in this proper way and
+
+ align:start position:0%
+needs to be done in this proper way and
+ 
+
+ align:start position:0%
+needs to be done in this proper way and
+this is true of all databases not just
+
+ align:start position:0%
+this is true of all databases not just
+ 
+
+ align:start position:0%
+this is true of all databases not just
+accumulo but other databases have the
+
+ align:start position:0%
+accumulo but other databases have the
+ 
+
+ align:start position:0%
+accumulo but other databases have the
+exact same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+issue accumulo is called accumulo
+
+ align:start position:0%
+issue accumulo is called accumulo
+ 
+
+ align:start position:0%
+issue accumulo is called accumulo
+because it has something called
+
+ align:start position:0%
+because it has something called
+ 
+
+ align:start position:0%
+because it has something called
+accumulat
+
+ align:start position:0%
+accumulat
+ 
+
+ align:start position:0%
+accumulat
+which is what actually makes this whole
+
+ align:start position:0%
+which is what actually makes this whole
+ 
+
+ align:start position:0%
+which is what actually makes this whole
+bioinformatics application really go
+
+ align:start position:0%
+bioinformatics application really go
+ 
+
+ align:start position:0%
+bioinformatics application really go
+which is that I can denote a column in a
+
+ align:start position:0%
+which is that I can denote a column in a
+ 
+
+ align:start position:0%
+which is that I can denote a column in a
+table to be an accumulator column which
+
+ align:start position:0%
+table to be an accumulator column which
+ 
+
+ align:start position:0%
+table to be an accumulator column which
+means whenever a new entry is hit some
+
+ align:start position:0%
+means whenever a new entry is hit some
+ 
+
+ align:start position:0%
+means whenever a new entry is hit some
+action will be performed in this case
+
+ align:start position:0%
+action will be performed in this case
+ 
+
+ align:start position:0%
+action will be performed in this case
+the default is
+
+ align:start position:0%
+the default is
+ 
+
+ align:start position:0%
+the default is
+addition and so a standard thing we'll
+
+ align:start position:0%
+addition and so a standard thing we'll
+ 
+
+ align:start position:0%
+addition and so a standard thing we'll
+do in our schemas we've already talked
+
+ align:start position:0%
+do in our schemas we've already talked
+ 
+
+ align:start position:0%
+do in our schemas we've already talked
+about these exploded transpose pair
+
+ align:start position:0%
+about these exploded transpose pair
+ 
+
+ align:start position:0%
+about these exploded transpose pair
+schemas that allow us to do fast lookups
+
+ align:start position:0%
+schemas that allow us to do fast lookups
+ 
+
+ align:start position:0%
+schemas that allow us to do fast lookups
+and rows and columns is it will create
+
+ align:start position:0%
+and rows and columns is it will create
+ 
+
+ align:start position:0%
+and rows and columns is it will create
+two additional tables one of which holds
+
+ align:start position:0%
+two additional tables one of which holds
+ 
+
+ align:start position:0%
+two additional tables one of which holds
+the sums of the rows and one of which
+
+ align:start position:0%
+the sums of the rows and one of which
+ 
+
+ align:start position:0%
+the sums of the rows and one of which
+holds the sums of the columns which then
+
+ align:start position:0%
+holds the sums of the columns which then
+ 
+
+ align:start position:0%
+holds the sums of the columns which then
+allows us to do these very fast lookups
+
+ align:start position:0%
+allows us to do these very fast lookups
+ 
+
+ align:start position:0%
+allows us to do these very fast lookups
+of the statistics which is very useful
+
+ align:start position:0%
+of the statistics which is very useful
+ 
+
+ align:start position:0%
+of the statistics which is very useful
+to know how do we avoid accidentally
+
+ align:start position:0%
+to know how do we avoid accidentally
+ 
+
+ align:start position:0%
+to know how do we avoid accidentally
+looking up columns that we'll have that
+
+ align:start position:0%
+looking up columns that we'll have that
+ 
+
+ align:start position:0%
+looking up columns that we'll have that
+are present in the whole database an
+
+ align:start position:0%
+are present in the whole database an
+ 
+
+ align:start position:0%
+are present in the whole database an
+issue that happens all the time is that
+
+ align:start position:0%
+issue that happens all the time is that
+ 
+
+ align:start position:0%
+issue that happens all the time is that
+you'll have a column that's essentially
+
+ align:start position:0%
+you'll have a column that's essentially
+ 
+
+ align:start position:0%
+you'll have a column that's essentially
+almost a dense column in the database
+
+ align:start position:0%
+almost a dense column in the database
+ 
+
+ align:start position:0%
+almost a dense column in the database
+and you really really really don't want
+
+ align:start position:0%
+and you really really really don't want
+ 
+
+ align:start position:0%
+and you really really really don't want
+to look that up because it's basically
+
+ align:start position:0%
+to look that up because it's basically
+ 
+
+ align:start position:0%
+to look that up because it's basically
+giving you the whole database well with
+
+ align:start position:0%
+giving you the whole database well with
+ 
+
+ align:start position:0%
+giving you the whole database well with
+this accumulator you can look up the
+
+ align:start position:0%
+this accumulator you can look up the
+ 
+
+ align:start position:0%
+this accumulator you can look up the
+column first and it will give you a
+
+ align:start position:0%
+column first and it will give you a
+ 
+
+ align:start position:0%
+column first and it will give you a
+count and be like oh yeah and then you
+
+ align:start position:0%
+count and be like oh yeah and then you
+ 
+
+ align:start position:0%
+count and be like oh yeah and then you
+can just say nope I want to look up
+
+ align:start position:0%
+can just say nope I want to look up
+ 
+
+ align:start position:0%
+can just say nope I want to look up
+everything but that column so very
+
+ align:start position:0%
+everything but that column so very
+ 
+
+ align:start position:0%
+everything but that column so very
+powerful very powerful tool for doing
+
+ align:start position:0%
+powerful very powerful tool for doing
+ 
+
+ align:start position:0%
+powerful very powerful tool for doing
+that that's also another reason why we
+
+ align:start position:0%
+that that's also another reason why we
+ 
+
+ align:start position:0%
+that that's also another reason why we
+construct the associative array when we
+
+ align:start position:0%
+construct the associative array when we
+ 
+
+ align:start position:0%
+construct the associative array when we
+load it for insert because we when we
+
+ align:start position:0%
+load it for insert because we when we
+ 
+
+ align:start position:0%
+load it for insert because we when we
+construct the associa ray we can
+
+ align:start position:0%
+construct the associa ray we can
+ 
+
+ align:start position:0%
+construct the associa ray we can
+actually do a a quick sum right then and
+
+ align:start position:0%
+actually do a a quick sum right then and
+ 
+
+ align:start position:0%
+actually do a a quick sum right then and
+there of whatever piece we've rent in
+
+ align:start position:0%
+there of whatever piece we've rent in
+ 
+
+ align:start position:0%
+there of whatever piece we've rent in
+and so then when we send that into the
+
+ align:start position:0%
+and so then when we send that into the
+ 
+
+ align:start position:0%
+and so then when we send that into the
+database we've dramatically reduced the
+
+ align:start position:0%
+database we've dramatically reduced the
+ 
+
+ align:start position:0%
+database we've dramatically reduced the
+number of the amount of tallying it has
+
+ align:start position:0%
+number of the amount of tallying it has
+ 
+
+ align:start position:0%
+number of the amount of tallying it has
+to do and this can be a huge timesaver
+
+ align:start position:0%
+to do and this can be a huge timesaver
+ 
+
+ align:start position:0%
+to do and this can be a huge timesaver
+because uh if you don't do that you're
+
+ align:start position:0%
+because uh if you don't do that you're
+ 
+
+ align:start position:0%
+because uh if you don't do that you're
+essentially re inserting the data two
+
+ align:start position:0%
+essentially re inserting the data two
+ 
+
+ align:start position:0%
+essentially re inserting the data two
+more times because you know when you
+
+ align:start position:0%
+more times because you know when you
+ 
+
+ align:start position:0%
+more times because you know when you
+you've inserted it into the the the
+
+ align:start position:0%
+you've inserted it into the the the
+ 
+
+ align:start position:0%
+you've inserted it into the the the
+table and it's transpose and to get the
+
+ align:start position:0%
+table and it's transpose and to get the
+ 
+
+ align:start position:0%
+table and it's transpose and to get the
+accumulation effect you would have to
+
+ align:start position:0%
+accumulation effect you would have to
+ 
+
+ align:start position:0%
+accumulation effect you would have to
+directly insert it but if we can do a
+
+ align:start position:0%
+directly insert it but if we can do a
+ 
+
+ align:start position:0%
+directly insert it but if we can do a
+preum that reduces the amount of worked
+
+ align:start position:0%
+preum that reduces the amount of worked
+ 
+
+ align:start position:0%
+preum that reduces the amount of worked
+on that uh on that uh on that
+
+ align:start position:0%
+on that uh on that uh on that
+ 
+
+ align:start position:0%
+on that uh on that uh on that
+accumulator table dramatically and so
+
+ align:start position:0%
+accumulator table dramatically and so
+ 
+
+ align:start position:0%
+accumulator table dramatically and so
+again that's another reason why we we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so let's just talk about some of
+
+ align:start position:0%
+that so let's just talk about some of
+ 
+
+ align:start position:0%
+that so let's just talk about some of
+the results that we see so here's an
+
+ align:start position:0%
+the results that we see so here's an
+ 
+
+ align:start position:0%
+the results that we see so here's an
+example on a uh let's see this is an 8
+
+ align:start position:0%
+example on a uh let's see this is an 8
+ 
+
+ align:start position:0%
+example on a uh let's see this is an 8
+no database and this shows us the ingest
+
+ align:start position:0%
+no database and this shows us the ingest
+ 
+
+ align:start position:0%
+no database and this shows us the ingest
+rate that we get using different numbers
+
+ align:start position:0%
+rate that we get using different numbers
+ 
+
+ align:start position:0%
+rate that we get using different numbers
+of ingestor so this is different
+
+ align:start position:0%
+of ingestor so this is different
+ 
+
+ align:start position:0%
+of ingestor so this is different
+programs all trying to insert into this
+
+ align:start position:0%
+programs all trying to insert into this
+ 
+
+ align:start position:0%
+programs all trying to insert into this
+database simultaneously and this just
+
+ align:start position:0%
+database simultaneously and this just
+ 
+
+ align:start position:0%
+database simultaneously and this just
+shows the difference between having um
+
+ align:start position:0%
+shows the difference between having um
+ 
+
+ align:start position:0%
+shows the difference between having um
+uh uh zero splits and uh in this case 35
+
+ align:start position:0%
+uh uh zero splits and uh in this case 35
+ 
+
+ align:start position:0%
+uh uh zero splits and uh in this case 35
+splits is is was the was the optimal
+
+ align:start position:0%
+splits is is was the was the optimal
+ 
+
+ align:start position:0%
+splits is is was the was the optimal
+number that we had and you see it's a
+
+ align:start position:0%
+number that we had and you see it's a
+ 
+
+ align:start position:0%
+number that we had and you see it's a
+rather large uh uh difference um and you
+
+ align:start position:0%
+rather large uh uh difference um and you
+ 
+
+ align:start position:0%
+rather large uh uh difference um and you
+don't get you know you get some benefit
+
+ align:start position:0%
+don't get you know you get some benefit
+ 
+
+ align:start position:0%
+don't get you know you get some benefit
+with multiple inserters but that sort of
+
+ align:start position:0%
+with multiple inserters but that sort of
+ 
+
+ align:start position:0%
+with multiple inserters but that sort of
+ends when you uh when you don't do this
+
+ align:start position:0%
+ends when you uh when you don't do this
+ 
+
+ align:start position:0%
+ends when you uh when you don't do this
+so this is just an example of why you
+
+ align:start position:0%
+so this is just an example of why you
+ 
+
+ align:start position:0%
+so this is just an example of why you
+want to do
+
+ align:start position:0%
+want to do
+ 
+
+ align:start position:0%
+want to do
+that another example is uh with is the
+
+ align:start position:0%
+that another example is uh with is the
+ 
+
+ align:start position:0%
+that another example is uh with is the
+actual human DNA database this shows us
+
+ align:start position:0%
+actual human DNA database this shows us
+ 
+
+ align:start position:0%
+actual human DNA database this shows us
+our insert rate um uh on doing using
+
+ align:start position:0%
+our insert rate um uh on doing using
+ 
+
+ align:start position:0%
+our insert rate um uh on doing using
+different numbers of uh of
+
+ align:start position:0%
+different numbers of uh of
+ 
+
+ align:start position:0%
+different numbers of uh of
+uh of uh
+
+ align:start position:0%
+uh of uh
+ 
+
+ align:start position:0%
+uh of uh
+inserters and uh oh yeah so this is this
+
+ align:start position:0%
+inserters and uh oh yeah so this is this
+ 
+
+ align:start position:0%
+inserters and uh oh yeah so this is this
+is eight tablet servers and this just
+
+ align:start position:0%
+is eight tablet servers and this just
+ 
+
+ align:start position:0%
+is eight tablet servers and this just
+shows the different number of ingestor
+
+ align:start position:0%
+shows the different number of ingestor
+ 
+
+ align:start position:0%
+shows the different number of ingestor
+here and since we're doing proper
+
+ align:start position:0%
+here and since we're doing proper
+ 
+
+ align:start position:0%
+here and since we're doing proper
+splitting we're getting very nice uh
+
+ align:start position:0%
+splitting we're getting very nice uh
+ 
+
+ align:start position:0%
+splitting we're getting very nice uh
+scaling and this is actually the actual
+
+ align:start position:0%
+scaling and this is actually the actual
+ 
+
+ align:start position:0%
+scaling and this is actually the actual
+output from uh from aimul though it
+
+ align:start position:0%
+output from uh from aimul though it
+ 
+
+ align:start position:0%
+output from uh from aimul though it
+actually has a nice little meter here
+
+ align:start position:0%
+actually has a nice little meter here
+ 
+
+ align:start position:0%
+actually has a nice little meter here
+that shows you what it says you're
+
+ align:start position:0%
+that shows you what it says you're
+ 
+
+ align:start position:0%
+that shows you what it says you're
+actually getting which is very very nice
+
+ align:start position:0%
+actually getting which is very very nice
+ 
+
+ align:start position:0%
+actually getting which is very very nice
+to to be able to verify that you know
+
+ align:start position:0%
+to to be able to verify that you know
+ 
+
+ align:start position:0%
+to to be able to verify that you know
+that you and the database both agree
+
+ align:start position:0%
+that you and the database both agree
+ 
+
+ align:start position:0%
+that you and the database both agree
+that your insert rate is uh so this is
+
+ align:start position:0%
+that your insert rate is uh so this is
+ 
+
+ align:start position:0%
+that your insert rate is uh so this is
+insert rate here so you see we're
+
+ align:start position:0%
+insert rate here so you see we're
+ 
+
+ align:start position:0%
+insert rate here so you see we're
+getting about 4,000 400,000 entries per
+
+ align:start position:0%
+getting about 4,000 400,000 entries per
+ 
+
+ align:start position:0%
+getting about 4,000 400,000 entries per
+second which is an extraordinarily High
+
+ align:start position:0%
+second which is an extraordinarily High
+ 
+
+ align:start position:0%
+second which is an extraordinarily High
+number in the database Community uh just
+
+ align:start position:0%
+number in the database Community uh just
+ 
+
+ align:start position:0%
+number in the database Community uh just
+to give you a comparison uh it would not
+
+ align:start position:0%
+to give you a comparison uh it would not
+ 
+
+ align:start position:0%
+to give you a comparison uh it would not
+be uncommon if you were to set up a
+
+ align:start position:0%
+be uncommon if you were to set up a
+ 
+
+ align:start position:0%
+be uncommon if you were to set up a
+MySQL instance on a single computer and
+
+ align:start position:0%
+MySQL instance on a single computer and
+ 
+
+ align:start position:0%
+MySQL instance on a single computer and
+have one inserter going into it to get
+
+ align:start position:0%
+have one inserter going into it to get
+ 
+
+ align:start position:0%
+have one inserter going into it to get
+maybe a thousand inserts per second on a
+
+ align:start position:0%
+maybe a thousand inserts per second on a
+ 
+
+ align:start position:0%
+maybe a thousand inserts per second on a
+good day and so you know this is this is
+
+ align:start position:0%
+good day and so you know this is this is
+ 
+
+ align:start position:0%
+good day and so you know this is this is
+essentially the core reason why people
+
+ align:start position:0%
+essentially the core reason why people
+ 
+
+ align:start position:0%
+essentially the core reason why people
+use a cumulo is because of this very
+
+ align:start position:0%
+use a cumulo is because of this very
+ 
+
+ align:start position:0%
+use a cumulo is because of this very
+high insert and and query performance um
+
+ align:start position:0%
+high insert and and query performance um
+ 
+
+ align:start position:0%
+high insert and and query performance um
+and this just shows our extrapolated
+
+ align:start position:0%
+and this just shows our extrapolated
+ 
+
+ align:start position:0%
+and this just shows our extrapolated
+runtime if we wanted to for instance
+
+ align:start position:0%
+runtime if we wanted to for instance
+ 
+
+ align:start position:0%
+runtime if we wanted to for instance
+ingest the entire human uh uh fast uh
+
+ align:start position:0%
+ingest the entire human uh uh fast uh
+ 
+
+ align:start position:0%
+ingest the entire human uh uh fast uh
+database here a 4.5 billion entries uh
+
+ align:start position:0%
+database here a 4.5 billion entries uh
+ 
+
+ align:start position:0%
+database here a 4.5 billion entries uh
+we could do that in you know eight hours
+
+ align:start position:0%
+we could do that in you know eight hours
+ 
+
+ align:start position:0%
+we could do that in you know eight hours
+which would be a very reasonable amount
+
+ align:start position:0%
+which would be a very reasonable amount
+ 
+
+ align:start position:0%
+which would be a very reasonable amount
+of time to do that so in summary what we
+
+ align:start position:0%
+of time to do that so in summary what we
+ 
+
+ align:start position:0%
+of time to do that so in summary what we
+were able to achieve with this
+
+ align:start position:0%
+were able to achieve with this
+ 
+
+ align:start position:0%
+were able to achieve with this
+application
+
+ align:start position:0%
+application
+ 
+
+ align:start position:0%
+application
+is this shows one of these diagrams I
+
+ align:start position:0%
+is this shows one of these diagrams I
+ 
+
+ align:start position:0%
+is this shows one of these diagrams I
+think I showed one in the first lecture
+
+ align:start position:0%
+think I showed one in the first lecture
+ 
+
+ align:start position:0%
+think I showed one in the first lecture
+this is a way of of sort of measuring
+
+ align:start position:0%
+this is a way of of sort of measuring
+ 
+
+ align:start position:0%
+this is a way of of sort of measuring
+our productivity and our performance so
+
+ align:start position:0%
+our productivity and our performance so
+ 
+
+ align:start position:0%
+our productivity and our performance so
+this shows the volume of code that we
+
+ align:start position:0%
+this shows the volume of code that we
+ 
+
+ align:start position:0%
+this shows the volume of code that we
+wrote and this shows the runtime so
+
+ align:start position:0%
+wrote and this shows the runtime so
+ 
+
+ align:start position:0%
+wrote and this shows the runtime so
+obviously this is better down here and
+
+ align:start position:0%
+obviously this is better down here and
+ 
+
+ align:start position:0%
+obviously this is better down here and
+this shows blast so blast is the
+
+ align:start position:0%
+this shows blast so blast is the
+ 
+
+ align:start position:0%
+this shows blast so blast is the
+industry standard application for doing
+
+ align:start position:0%
+industry standard application for doing
+ 
+
+ align:start position:0%
+industry standard application for doing
+sequence match and I don't want in any
+
+ align:start position:0%
+sequence match and I don't want in any
+ 
+
+ align:start position:0%
+sequence match and I don't want in any
+way to say that we are doing everything
+
+ align:start position:0%
+way to say that we are doing everything
+ 
+
+ align:start position:0%
+way to say that we are doing everything
+blast does blast is almost a million
+
+ align:start position:0%
+blast does blast is almost a million
+ 
+
+ align:start position:0%
+blast does blast is almost a million
+lines of code it does lots and lots of
+
+ align:start position:0%
+lines of code it does lots and lots of
+ 
+
+ align:start position:0%
+lines of code it does lots and lots of
+different things it handles all
+
+ align:start position:0%
+different things it handles all
+ 
+
+ align:start position:0%
+different things it handles all
+different types of file formats and
+
+ align:start position:0%
+different types of file formats and
+ 
+
+ align:start position:0%
+different types of file formats and
+little nuances and other types of things
+
+ align:start position:0%
+little nuances and other types of things
+ 
+
+ align:start position:0%
+little nuances and other types of things
+but at its core it does what we did and
+
+ align:start position:0%
+but at its core it does what we did and
+ 
+
+ align:start position:0%
+but at its core it does what we did and
+in and we were able to basically do that
+
+ align:start position:0%
+in and we were able to basically do that
+ 
+
+ align:start position:0%
+in and we were able to basically do that
+in you
+
+ align:start position:0%
+in you
+ 
+
+ align:start position:0%
+in you
+know 150 lines of d4m
+
+ align:start position:0%
+know 150 lines of d4m
+ 
+
+ align:start position:0%
+know 150 lines of d4m
+code and using the database we were able
+
+ align:start position:0%
+code and using the database we were able
+ 
+
+ align:start position:0%
+code and using the database we were able
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+that a 100 times faster and so this is
+
+ align:start position:0%
+that a 100 times faster and so this is
+ 
+
+ align:start position:0%
+that a 100 times faster and so this is
+really the power of this technology is
+
+ align:start position:0%
+really the power of this technology is
+ 
+
+ align:start position:0%
+really the power of this technology is
+to allow you to develop these algorithms
+
+ align:start position:0%
+to allow you to develop these algorithms
+ 
+
+ align:start position:0%
+to allow you to develop these algorithms
+and and Implement them and in in this
+
+ align:start position:0%
+and and Implement them and in in this
+ 
+
+ align:start position:0%
+and and Implement them and in in this
+case actually you leverage the database
+
+ align:start position:0%
+case actually you leverage the database
+ 
+
+ align:start position:0%
+case actually you leverage the database
+to essentially replace lookups with
+
+ align:start position:0%
+to essentially replace lookups with
+ 
+
+ align:start position:0%
+to essentially replace lookups with
+computations in a very intelligent way
+
+ align:start position:0%
+computations in a very intelligent way
+ 
+
+ align:start position:0%
+computations in a very intelligent way
+in a way that's knowledgeable about the
+
+ align:start position:0%
+in a way that's knowledgeable about the
+ 
+
+ align:start position:0%
+in a way that's knowledgeable about the
+statistics of your data um and that's
+
+ align:start position:0%
+statistics of your data um and that's
+ 
+
+ align:start position:0%
+statistics of your data um and that's
+really the power and these are the types
+
+ align:start position:0%
+really the power and these are the types
+ 
+
+ align:start position:0%
+really the power and these are the types
+of results that people can get and this
+
+ align:start position:0%
+of results that people can get and this
+ 
+
+ align:start position:0%
+of results that people can get and this
+whole result was done with one summer
+
+ align:start position:0%
+whole result was done with one summer
+ 
+
+ align:start position:0%
+whole result was done with one summer
+student you know very smart summer
+
+ align:start position:0%
+student you know very smart summer
+ 
+
+ align:start position:0%
+student you know very smart summer
+student but you know we were able to put
+
+ align:start position:0%
+student but you know we were able to put
+ 
+
+ align:start position:0%
+student but you know we were able to put
+this whole system together in about a
+
+ align:start position:0%
+this whole system together in about a
+ 
+
+ align:start position:0%
+this whole system together in about a
+couple of months and this is from a
+
+ align:start position:0%
+couple of months and this is from a
+ 
+
+ align:start position:0%
+couple of months and this is from a
+person who knew nothing about accumulo
+
+ align:start position:0%
+person who knew nothing about accumulo
+ 
+
+ align:start position:0%
+person who knew nothing about accumulo
+or deform or anything like that they
+
+ align:start position:0%
+or deform or anything like that they
+ 
+
+ align:start position:0%
+or deform or anything like that they
+were a good they were smart they had a
+
+ align:start position:0%
+were a good they were smart they had a
+ 
+
+ align:start position:0%
+were a good they were smart they had a
+they were good uh good solid Java
+
+ align:start position:0%
+they were good uh good solid Java
+ 
+
+ align:start position:0%
+they were good uh good solid Java
+background and and very energetic but
+
+ align:start position:0%
+background and and very energetic but
+ 
+
+ align:start position:0%
+background and and very energetic but
+you know these are the kinds of things
+
+ align:start position:0%
+you know these are the kinds of things
+ 
+
+ align:start position:0%
+you know these are the kinds of things
+we've been able to
+
+ align:start position:0%
+we've been able to
+ 
+
+ align:start position:0%
+we've been able to
+see so just to summarize you know we
+
+ align:start position:0%
+see so just to summarize you know we
+ 
+
+ align:start position:0%
+see so just to summarize you know we
+again we see uh See uh
+
+ align:start position:0%
+again we see uh See uh
+ 
+
+ align:start position:0%
+again we see uh See uh
+uh uh you know I think just to uh you
+
+ align:start position:0%
+uh uh you know I think just to uh you
+ 
+
+ align:start position:0%
+uh uh you know I think just to uh you
+know we we this types of techniques are
+
+ align:start position:0%
+know we we this types of techniques are
+ 
+
+ align:start position:0%
+know we we this types of techniques are
+useful for document analysis and network
+
+ align:start position:0%
+useful for document analysis and network
+ 
+
+ align:start position:0%
+useful for document analysis and network
+analysis and DNA
+
+ align:start position:0%
+analysis and DNA
+ 
+
+ align:start position:0%
+analysis and DNA
+sequencing um you know this is really
+
+ align:start position:0%
+sequencing um you know this is really
+ 
+
+ align:start position:0%
+sequencing um you know this is really
+summarizing all the applications that
+
+ align:start position:0%
+summarizing all the applications that
+ 
+
+ align:start position:0%
+summarizing all the applications that
+we've talked about you know we we think
+
+ align:start position:0%
+we've talked about you know we we think
+ 
+
+ align:start position:0%
+we've talked about you know we we think
+there's a pretty big gap between doing
+
+ align:start position:0%
+there's a pretty big gap between doing
+ 
+
+ align:start position:0%
+there's a pretty big gap between doing
+the data analysis tools that are really
+
+ align:start position:0%
+the data analysis tools that are really
+ 
+
+ align:start position:0%
+the data analysis tools that are really
+algorithm developers need and really
+
+ align:start position:0%
+algorithm developers need and really
+ 
+
+ align:start position:0%
+algorithm developers need and really
+think d4m is really allowing us to use a
+
+ align:start position:0%
+think d4m is really allowing us to use a
+ 
+
+ align:start position:0%
+think d4m is really allowing us to use a
+tool like mat lab for its traditional
+
+ align:start position:0%
+tool like mat lab for its traditional
+ 
+
+ align:start position:0%
+tool like mat lab for its traditional
+role in this new domain which is
+
+ align:start position:0%
+role in this new domain which is
+ 
+
+ align:start position:0%
+role in this new domain which is
+algorithm development figure things out
+
+ align:start position:0%
+algorithm development figure things out
+ 
+
+ align:start position:0%
+algorithm development figure things out
+getting things right before you can then
+
+ align:start position:0%
+getting things right before you can then
+ 
+
+ align:start position:0%
+getting things right before you can then
+hand it on to someone else to you know
+
+ align:start position:0%
+hand it on to someone else to you know
+ 
+
+ align:start position:0%
+hand it on to someone else to you know
+Implement and and actually you know get
+
+ align:start position:0%
+Implement and and actually you know get
+ 
+
+ align:start position:0%
+Implement and and actually you know get
+in a production
+
+ align:start position:0%
+in a production
+ 
+
+ align:start position:0%
+in a production
+environment so with that that brings the
+
+ align:start position:0%
+environment so with that that brings the
+ 
+
+ align:start position:0%
+environment so with that that brings the
+end to the lecture and then there's some
+
+ align:start position:0%
+end to the lecture and then there's some
+ 
+
+ align:start position:0%
+end to the lecture and then there's some
+examples where we show you the the this
+
+ align:start position:0%
+examples where we show you the the this
+ 
+
+ align:start position:0%
+examples where we show you the the this
+this stuff so uh and there's no homework
+
+ align:start position:0%
+this stuff so uh and there's no homework
+ 
+
+ align:start position:0%
+this stuff so uh and there's no homework
+uh other than I sent you all that
+
+ align:start position:0%
+uh other than I sent you all that
+ 
+
+ align:start position:0%
+uh other than I sent you all that
+link to see if your access to the
+
+ align:start position:0%
+link to see if your access to the
+ 
+
+ align:start position:0%
+link to see if your access to the
+database exists did everyone raise your
+
+ align:start position:0%
+database exists did everyone raise your
+ 
+
+ align:start position:0%
+database exists did everyone raise your
+hand did you check the link out yes you
+
+ align:start position:0%
+hand did you check the link out yes you
+ 
+
+ align:start position:0%
+hand did you check the link out yes you
+logged in it worked you saw a bunch of
+
+ align:start position:0%
+logged in it worked you saw a bunch of
+ 
+
+ align:start position:0%
+logged in it worked you saw a bunch of
+databases there okay it doesn't work cu
+
+ align:start position:0%
+databases there okay it doesn't work cu
+ 
+
+ align:start position:0%
+databases there okay it doesn't work cu
+the next class is the sort of the
+
+ align:start position:0%
+the next class is the sort of the
+ 
+
+ align:start position:0%
+the next class is the sort of the
+penultimate class I'm going to go
+
+ align:start position:0%
+penultimate class I'm going to go
+ 
+
+ align:start position:0%
+penultimate class I'm going to go
+through all these examples and the
+
+ align:start position:0%
+through all these examples and the
+ 
+
+ align:start position:0%
+through all these examples and the
+assignment will be to run those examples
+
+ align:start position:0%
+assignment will be to run those examples
+ 
+
+ align:start position:0%
+assignment will be to run those examples
+on those databases so you will be really
+
+ align:start position:0%
+on those databases so you will be really
+ 
+
+ align:start position:0%
+on those databases so you will be really
+using DM touching a database doing real
+
+ align:start position:0%
+using DM touching a database doing real
+ 
+
+ align:start position:0%
+using DM touching a database doing real
+analytics doing very complicated things
+
+ align:start position:0%
+analytics doing very complicated things
+ 
+
+ align:start position:0%
+analytics doing very complicated things
+the whole class is just going to be a
+
+ align:start position:0%
+the whole class is just going to be a
+ 
+
+ align:start position:0%
+the whole class is just going to be a
+demonstration of that well everything
+
+ align:start position:0%
+demonstration of that well everything
+ 
+
+ align:start position:0%
+demonstration of that well everything
+we've been doing has been leading up so
+
+ align:start position:0%
+we've been doing has been leading up so
+ 
+
+ align:start position:0%
+we've been doing has been leading up so
+the concepts are in place so that you
+
+ align:start position:0%
+the concepts are in place so that you
+ 
+
+ align:start position:0%
+the concepts are in place so that you
+can understand those examples fairly
+
+ align:start position:0%
+can understand those examples fairly
+ 
+
+ align:start position:0%
+can understand those examples fairly
+easily all right so we will take a short
+
+ align:start position:0%
+easily all right so we will take a short
+ 
+
+ align:start position:0%
+easily all right so we will take a short
+break here and then uh we will come back
+
+ align:start position:0%
+break here and then uh we will come back
+ 
+
+ align:start position:0%
+break here and then uh we will come back
+and I will show you the demo uh this
+
+ align:start position:0%
+and I will show you the demo uh this
+ 
+
+ align:start position:0%
+and I will show you the demo uh this
+this week's demo
\ No newline at end of file
diff --git a/hd4roBsrYA8.txt b/hd4roBsrYA8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42ad613a6d5c25478b747311b2a5431088141c33
--- /dev/null
+++ b/hd4roBsrYA8.txt
@@ -0,0 +1,3659 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu um my name is James ji I
+
+ align:start position:0%
+ocw.mit.edu um my name is James ji I
+ 
+
+ align:start position:0%
+ocw.mit.edu um my name is James ji I
+worked with sedarian and jnu on this uh
+
+ align:start position:0%
+worked with sedarian and jnu on this uh
+ 
+
+ align:start position:0%
+worked with sedarian and jnu on this uh
+project and what we did is we took a
+
+ align:start position:0%
+project and what we did is we took a
+ 
+
+ align:start position:0%
+project and what we did is we took a
+numerical simulation electrochemical
+
+ align:start position:0%
+numerical simulation electrochemical
+ 
+
+ align:start position:0%
+numerical simulation electrochemical
+simulation of a battery and ported it to
+
+ align:start position:0%
+simulation of a battery and ported it to
+ 
+
+ align:start position:0%
+simulation of a battery and ported it to
+the PlayStation
+
+ align:start position:0%
+the PlayStation
+ 
+
+ align:start position:0%
+the PlayStation
+3 and so the objective of this project
+
+ align:start position:0%
+3 and so the objective of this project
+ 
+
+ align:start position:0%
+3 and so the objective of this project
+for this situation was to Port a uh
+
+ align:start position:0%
+for this situation was to Port a uh
+ 
+
+ align:start position:0%
+for this situation was to Port a uh
+electrochemical battery simulation to
+
+ align:start position:0%
+electrochemical battery simulation to
+ 
+
+ align:start position:0%
+electrochemical battery simulation to
+the PlayStation 3 and uh try to take
+
+ align:start position:0%
+the PlayStation 3 and uh try to take
+ 
+
+ align:start position:0%
+the PlayStation 3 and uh try to take
+advantage of the unique features of the
+
+ align:start position:0%
+advantage of the unique features of the
+ 
+
+ align:start position:0%
+advantage of the unique features of the
+cell processor to help speed up the
+
+ align:start position:0%
+cell processor to help speed up the
+ 
+
+ align:start position:0%
+cell processor to help speed up the
+computation of the uh simulation so when
+
+ align:start position:0%
+computation of the uh simulation so when
+ 
+
+ align:start position:0%
+computation of the uh simulation so when
+we talk today we're going to talk about
+
+ align:start position:0%
+we talk today we're going to talk about
+ 
+
+ align:start position:0%
+we talk today we're going to talk about
+why we want to do that uh we're going to
+
+ align:start position:0%
+why we want to do that uh we're going to
+ 
+
+ align:start position:0%
+why we want to do that uh we're going to
+discuss the model we're going to discuss
+
+ align:start position:0%
+discuss the model we're going to discuss
+ 
+
+ align:start position:0%
+discuss the model we're going to discuss
+how we uh solved it numerically
+
+ align:start position:0%
+how we uh solved it numerically
+ 
+
+ align:start position:0%
+how we uh solved it numerically
+uh look at some of our performance
+
+ align:start position:0%
+uh look at some of our performance
+ 
+
+ align:start position:0%
+uh look at some of our performance
+results and then discuss what we wish we
+
+ align:start position:0%
+results and then discuss what we wish we
+ 
+
+ align:start position:0%
+results and then discuss what we wish we
+could have
+
+ align:start position:0%
+could have
+ 
+
+ align:start position:0%
+could have
+implemented okay so the justification is
+
+ align:start position:0%
+implemented okay so the justification is
+ 
+
+ align:start position:0%
+implemented okay so the justification is
+basically the world uh needs energy and
+
+ align:start position:0%
+basically the world uh needs energy and
+ 
+
+ align:start position:0%
+basically the world uh needs energy and
+oil has been in the news a lot and
+
+ align:start position:0%
+oil has been in the news a lot and
+ 
+
+ align:start position:0%
+oil has been in the news a lot and
+hasn't been as uh uh reliable source of
+
+ align:start position:0%
+hasn't been as uh uh reliable source of
+ 
+
+ align:start position:0%
+hasn't been as uh uh reliable source of
+energy as we'd like so in the automotive
+
+ align:start position:0%
+energy as we'd like so in the automotive
+ 
+
+ align:start position:0%
+energy as we'd like so in the automotive
+industry hybrids seem to be part of the
+
+ align:start position:0%
+industry hybrids seem to be part of the
+ 
+
+ align:start position:0%
+industry hybrids seem to be part of the
+solution to the uh energy needs now one
+
+ align:start position:0%
+solution to the uh energy needs now one
+ 
+
+ align:start position:0%
+solution to the uh energy needs now one
+of the problems with hybrids is how much
+
+ align:start position:0%
+of the problems with hybrids is how much
+ 
+
+ align:start position:0%
+of the problems with hybrids is how much
+energy is in your battery so the more
+
+ align:start position:0%
+energy is in your battery so the more
+ 
+
+ align:start position:0%
+energy is in your battery so the more
+sophisticated battery model that we can
+
+ align:start position:0%
+sophisticated battery model that we can
+ 
+
+ align:start position:0%
+sophisticated battery model that we can
+put in a hybrid the better that we're
+
+ align:start position:0%
+put in a hybrid the better that we're
+ 
+
+ align:start position:0%
+put in a hybrid the better that we're
+going to be off so uh the a more
+
+ align:start position:0%
+going to be off so uh the a more
+ 
+
+ align:start position:0%
+going to be off so uh the a more
+sophisticated model requires more
+
+ align:start position:0%
+sophisticated model requires more
+ 
+
+ align:start position:0%
+sophisticated model requires more
+computation so you're looking at having
+
+ align:start position:0%
+computation so you're looking at having
+ 
+
+ align:start position:0%
+computation so you're looking at having
+a large supercal processor in your car
+
+ align:start position:0%
+a large supercal processor in your car
+ 
+
+ align:start position:0%
+a large supercal processor in your car
+or you could get see if you could get a
+
+ align:start position:0%
+or you could get see if you could get a
+ 
+
+ align:start position:0%
+or you could get see if you could get a
+lot of small processors to do the same
+
+ align:start position:0%
+lot of small processors to do the same
+ 
+
+ align:start position:0%
+lot of small processors to do the same
+amount of work and the cell represents
+
+ align:start position:0%
+amount of work and the cell represents
+ 
+
+ align:start position:0%
+amount of work and the cell represents
+the kind of the first opportunity to be
+
+ align:start position:0%
+the kind of the first opportunity to be
+ 
+
+ align:start position:0%
+the kind of the first opportunity to be
+able to test that out so the simulation
+
+ align:start position:0%
+able to test that out so the simulation
+ 
+
+ align:start position:0%
+able to test that out so the simulation
+that we ran uh basically consisted of a
+
+ align:start position:0%
+that we ran uh basically consisted of a
+ 
+
+ align:start position:0%
+that we ran uh basically consisted of a
+lead acid battery a cell so un
+
+ align:start position:0%
+lead acid battery a cell so un
+ 
+
+ align:start position:0%
+lead acid battery a cell so un
+fortunately they use the word cell and
+
+ align:start position:0%
+fortunately they use the word cell and
+ 
+
+ align:start position:0%
+fortunately they use the word cell and
+we're also using the word cell so it's
+
+ align:start position:0%
+we're also using the word cell so it's
+ 
+
+ align:start position:0%
+we're also using the word cell so it's
+sort of like the Modern Day Smurf but um
+
+ align:start position:0%
+sort of like the Modern Day Smurf but um
+ 
+
+ align:start position:0%
+sort of like the Modern Day Smurf but um
+so in a Le a battery cell you have a
+
+ align:start position:0%
+so in a Le a battery cell you have a
+ 
+
+ align:start position:0%
+so in a Le a battery cell you have a
+lead dioxide electrode which consists of
+
+ align:start position:0%
+lead dioxide electrode which consists of
+ 
+
+ align:start position:0%
+lead dioxide electrode which consists of
+a number of Parts a lead electrode which
+
+ align:start position:0%
+a number of Parts a lead electrode which
+ 
+
+ align:start position:0%
+a number of Parts a lead electrode which
+also consists of a number of parts and
+
+ align:start position:0%
+also consists of a number of parts and
+ 
+
+ align:start position:0%
+also consists of a number of parts and
+an electrolyte which is five mol
+
+ align:start position:0%
+an electrolyte which is five mol
+ 
+
+ align:start position:0%
+an electrolyte which is five mol
+sulfuric acid which consists of
+
+ align:start position:0%
+sulfuric acid which consists of
+ 
+
+ align:start position:0%
+sulfuric acid which consists of
+h204 okay um when you discharge the
+
+ align:start position:0%
+h204 okay um when you discharge the
+ 
+
+ align:start position:0%
+h204 okay um when you discharge the
+battery you're going to close the
+
+ align:start position:0%
+battery you're going to close the
+ 
+
+ align:start position:0%
+battery you're going to close the
+circuit and basically what ends up
+
+ align:start position:0%
+circuit and basically what ends up
+ 
+
+ align:start position:0%
+circuit and basically what ends up
+happening is you have electrons flowing
+
+ align:start position:0%
+happening is you have electrons flowing
+ 
+
+ align:start position:0%
+happening is you have electrons flowing
+on the Outer Loop and between the
+
+ align:start position:0%
+on the Outer Loop and between the
+ 
+
+ align:start position:0%
+on the Outer Loop and between the
+electrodes you're going to have uh an
+
+ align:start position:0%
+electrodes you're going to have uh an
+ 
+
+ align:start position:0%
+electrodes you're going to have uh an
+ionic current so uh you have a complete
+
+ align:start position:0%
+ionic current so uh you have a complete
+ 
+
+ align:start position:0%
+ionic current so uh you have a complete
+circuit around your Loop and this is the
+
+ align:start position:0%
+circuit around your Loop and this is the
+ 
+
+ align:start position:0%
+circuit around your Loop and this is the
+effect that the simulation is trying to
+
+ align:start position:0%
+effect that the simulation is trying to
+ 
+
+ align:start position:0%
+effect that the simulation is trying to
+simulate the simulation works on a
+
+ align:start position:0%
+simulate the simulation works on a
+ 
+
+ align:start position:0%
+simulate the simulation works on a
+uh uh uh very low physical level and it
+
+ align:start position:0%
+uh uh uh very low physical level and it
+ 
+
+ align:start position:0%
+uh uh uh very low physical level and it
+stimulates the chemical reactions which
+
+ align:start position:0%
+stimulates the chemical reactions which
+ 
+
+ align:start position:0%
+stimulates the chemical reactions which
+at the lead dioxide electrode it
+
+ align:start position:0%
+at the lead dioxide electrode it
+ 
+
+ align:start position:0%
+at the lead dioxide electrode it
+converts lead dioxide into lead sulfate
+
+ align:start position:0%
+converts lead dioxide into lead sulfate
+ 
+
+ align:start position:0%
+converts lead dioxide into lead sulfate
+during this charge reverses it during
+
+ align:start position:0%
+during this charge reverses it during
+ 
+
+ align:start position:0%
+during this charge reverses it during
+charge during uh discharge the lead
+
+ align:start position:0%
+charge during uh discharge the lead
+ 
+
+ align:start position:0%
+charge during uh discharge the lead
+electrode turns lead into lead sulfate
+
+ align:start position:0%
+electrode turns lead into lead sulfate
+ 
+
+ align:start position:0%
+electrode turns lead into lead sulfate
+and during recharge it converts that
+
+ align:start position:0%
+and during recharge it converts that
+ 
+
+ align:start position:0%
+and during recharge it converts that
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+uh to implement the model we took
+
+ align:start position:0%
+uh to implement the model we took
+ 
+
+ align:start position:0%
+uh to implement the model we took
+basically and discretized the system and
+
+ align:start position:0%
+basically and discretized the system and
+ 
+
+ align:start position:0%
+basically and discretized the system and
+just kind of cross-sectioned it okay
+
+ align:start position:0%
+just kind of cross-sectioned it okay
+ 
+
+ align:start position:0%
+just kind of cross-sectioned it okay
+took small sections and cross-sectioned
+
+ align:start position:0%
+took small sections and cross-sectioned
+ 
+
+ align:start position:0%
+took small sections and cross-sectioned
+it um we're going to skip this slide
+
+ align:start position:0%
+it um we're going to skip this slide
+ 
+
+ align:start position:0%
+it um we're going to skip this slide
+make any sense but basically to to uh
+
+ align:start position:0%
+make any sense but basically to to uh
+ 
+
+ align:start position:0%
+make any sense but basically to to uh
+simulate the physics we have a bunch of
+
+ align:start position:0%
+simulate the physics we have a bunch of
+ 
+
+ align:start position:0%
+simulate the physics we have a bunch of
+nasty nonlinear coupled partial
+
+ align:start position:0%
+nasty nonlinear coupled partial
+ 
+
+ align:start position:0%
+nasty nonlinear coupled partial
+differential equations this is an
+
+ align:start position:0%
+differential equations this is an
+ 
+
+ align:start position:0%
+differential equations this is an
+example of two of them and uh there a
+
+ align:start position:0%
+example of two of them and uh there a
+ 
+
+ align:start position:0%
+example of two of them and uh there a
+number of other ones that are included
+
+ align:start position:0%
+number of other ones that are included
+ 
+
+ align:start position:0%
+number of other ones that are included
+in the system but not really worth
+
+ align:start position:0%
+in the system but not really worth
+ 
+
+ align:start position:0%
+in the system but not really worth
+seeing just kind of a feel you get uh
+
+ align:start position:0%
+seeing just kind of a feel you get uh
+ 
+
+ align:start position:0%
+seeing just kind of a feel you get uh
+you see a a a diffusion term you see in
+
+ align:start position:0%
+you see a a a diffusion term you see in
+ 
+
+ align:start position:0%
+you see a a a diffusion term you see in
+the lower equation you see a diffusion
+
+ align:start position:0%
+the lower equation you see a diffusion
+ 
+
+ align:start position:0%
+the lower equation you see a diffusion
+term you see a reaction term and the
+
+ align:start position:0%
+term you see a reaction term and the
+ 
+
+ align:start position:0%
+term you see a reaction term and the
+upper equation you see uh changing of
+
+ align:start position:0%
+upper equation you see uh changing of
+ 
+
+ align:start position:0%
+upper equation you see uh changing of
+the paracity changing the geometry of
+
+ align:start position:0%
+the paracity changing the geometry of
+ 
+
+ align:start position:0%
+the paracity changing the geometry of
+the system this is kind of the output
+
+ align:start position:0%
+the system this is kind of the output
+ 
+
+ align:start position:0%
+the system this is kind of the output
+that you could get from this type of
+
+ align:start position:0%
+that you could get from this type of
+ 
+
+ align:start position:0%
+that you could get from this type of
+battery
+
+ align:start position:0%
+battery
+ 
+
+ align:start position:0%
+battery
+simulation uh and what you're looking at
+
+ align:start position:0%
+simulation uh and what you're looking at
+ 
+
+ align:start position:0%
+simulation uh and what you're looking at
+here is you're looking at if the left
+
+ align:start position:0%
+here is you're looking at if the left
+ 
+
+ align:start position:0%
+here is you're looking at if the left
+hand side is the uh electrodes is the
+
+ align:start position:0%
+hand side is the uh electrodes is the
+ 
+
+ align:start position:0%
+hand side is the uh electrodes is the
+top of the battery uh and the height of
+
+ align:start position:0%
+top of the battery uh and the height of
+ 
+
+ align:start position:0%
+top of the battery uh and the height of
+the battery goes along that way you see
+
+ align:start position:0%
+the battery goes along that way you see
+ 
+
+ align:start position:0%
+the battery goes along that way you see
+that as you discharge the concentration
+
+ align:start position:0%
+that as you discharge the concentration
+ 
+
+ align:start position:0%
+that as you discharge the concentration
+uh at the top of the electrodes is much
+
+ align:start position:0%
+uh at the top of the electrodes is much
+ 
+
+ align:start position:0%
+uh at the top of the electrodes is much
+the acid is used consumed where you're
+
+ align:start position:0%
+the acid is used consumed where you're
+ 
+
+ align:start position:0%
+the acid is used consumed where you're
+drawing current out most readily so
+
+ align:start position:0%
+drawing current out most readily so
+ 
+
+ align:start position:0%
+drawing current out most readily so
+physically the simulation kind of makes
+
+ align:start position:0%
+physically the simulation kind of makes
+ 
+
+ align:start position:0%
+physically the simulation kind of makes
+sense even if my speech didn't um the
+
+ align:start position:0%
+sense even if my speech didn't um the
+ 
+
+ align:start position:0%
+sense even if my speech didn't um the
+battery model that we use is a
+
+ align:start position:0%
+battery model that we use is a
+ 
+
+ align:start position:0%
+battery model that we use is a
+two-dimensional model it has both a lead
+
+ align:start position:0%
+two-dimensional model it has both a lead
+ 
+
+ align:start position:0%
+two-dimensional model it has both a lead
+dioxide electrode and a leg electrode
+
+ align:start position:0%
+dioxide electrode and a leg electrode
+ 
+
+ align:start position:0%
+dioxide electrode and a leg electrode
+and an electrolyte area this is an
+
+ align:start position:0%
+and an electrolyte area this is an
+ 
+
+ align:start position:0%
+and an electrolyte area this is an
+example of just the lead dioxide
+
+ align:start position:0%
+example of just the lead dioxide
+ 
+
+ align:start position:0%
+example of just the lead dioxide
+electrode and if we discretize that in
+
+ align:start position:0%
+electrode and if we discretize that in
+ 
+
+ align:start position:0%
+electrode and if we discretize that in
+two Dimensions we would get uh a
+
+ align:start position:0%
+two Dimensions we would get uh a
+ 
+
+ align:start position:0%
+two Dimensions we would get uh a
+discretization that looks like that if
+
+ align:start position:0%
+discretization that looks like that if
+ 
+
+ align:start position:0%
+discretization that looks like that if
+we were to use a single centered uh
+
+ align:start position:0%
+we were to use a single centered uh
+ 
+
+ align:start position:0%
+we were to use a single centered uh
+finite volume method but it turns out
+
+ align:start position:0%
+finite volume method but it turns out
+ 
+
+ align:start position:0%
+finite volume method but it turns out
+that we have so many discontinuities in
+
+ align:start position:0%
+that we have so many discontinuities in
+ 
+
+ align:start position:0%
+that we have so many discontinuities in
+here that it's much better to use a
+
+ align:start position:0%
+here that it's much better to use a
+ 
+
+ align:start position:0%
+here that it's much better to use a
+staggered grid and so we are using a uh
+
+ align:start position:0%
+staggered grid and so we are using a uh
+ 
+
+ align:start position:0%
+staggered grid and so we are using a uh
+we're using actually two different uh
+
+ align:start position:0%
+we're using actually two different uh
+ 
+
+ align:start position:0%
+we're using actually two different uh
+meshes to simulate the system two
+
+ align:start position:0%
+meshes to simulate the system two
+ 
+
+ align:start position:0%
+meshes to simulate the system two
+different mes well on a single mesh you
+
+ align:start position:0%
+different mes well on a single mesh you
+ 
+
+ align:start position:0%
+different mes well on a single mesh you
+would end up having Four Corners four
+
+ align:start position:0%
+would end up having Four Corners four
+ 
+
+ align:start position:0%
+would end up having Four Corners four
+edges and centers so you'd get uh nine
+
+ align:start position:0%
+edges and centers so you'd get uh nine
+ 
+
+ align:start position:0%
+edges and centers so you'd get uh nine
+different types of objects in one
+
+ align:start position:0%
+different types of objects in one
+ 
+
+ align:start position:0%
+different types of objects in one
+electrode alone and you're talking about
+
+ align:start position:0%
+electrode alone and you're talking about
+ 
+
+ align:start position:0%
+electrode alone and you're talking about
+a rather large and nasty
+
+ align:start position:0%
+a rather large and nasty
+ 
+
+ align:start position:0%
+a rather large and nasty
+simulation on a small scale the
+
+ align:start position:0%
+simulation on a small scale the
+ 
+
+ align:start position:0%
+simulation on a small scale the
+simulation would produce a very sparse
+
+ align:start position:0%
+simulation would produce a very sparse
+ 
+
+ align:start position:0%
+simulation would produce a very sparse
+Matrix that looks something like this
+
+ align:start position:0%
+Matrix that looks something like this
+ 
+
+ align:start position:0%
+Matrix that looks something like this
+and sarian will now come up and talk to
+
+ align:start position:0%
+and sarian will now come up and talk to
+ 
+
+ align:start position:0%
+and sarian will now come up and talk to
+you about the matrices and how solve
+
+ align:start position:0%
+you about the matrices and how solve
+ 
+
+ align:start position:0%
+you about the matrices and how solve
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cont so basically like John said the the
+
+ align:start position:0%
+cont so basically like John said the the
+ 
+
+ align:start position:0%
+cont so basically like John said the the
+problem we essentially trying to
+
+ align:start position:0%
+problem we essentially trying to
+ 
+
+ align:start position:0%
+problem we essentially trying to
+paralyze the most computational
+
+ align:start position:0%
+paralyze the most computational
+ 
+
+ align:start position:0%
+paralyze the most computational
+expensive part of this whole simulation
+
+ align:start position:0%
+expensive part of this whole simulation
+ 
+
+ align:start position:0%
+expensive part of this whole simulation
+is is solving for the Newton at the
+
+ align:start position:0%
+is is solving for the Newton at the
+ 
+
+ align:start position:0%
+is is solving for the Newton at the
+Newton iterations during each load step
+
+ align:start position:0%
+Newton iterations during each load step
+ 
+
+ align:start position:0%
+Newton iterations during each load step
+and and so basically in an abstract I'm
+
+ align:start position:0%
+and and so basically in an abstract I'm
+ 
+
+ align:start position:0%
+and and so basically in an abstract I'm
+sorry any questions
+
+ align:start position:0%
+sorry any questions
+ 
+
+ align:start position:0%
+sorry any questions
+sorry uh I'll try but you you've got to
+
+ align:start position:0%
+sorry uh I'll try but you you've got to
+ 
+
+ align:start position:0%
+sorry uh I'll try but you you've got to
+try and listen harder too TV you have to
+
+ align:start position:0%
+try and listen harder too TV you have to
+ 
+
+ align:start position:0%
+try and listen harder too TV you have to
+yell at that I got it yeah is it is it
+
+ align:start position:0%
+yell at that I got it yeah is it is it
+ 
+
+ align:start position:0%
+yell at that I got it yeah is it is it
+any better now no you got to yell at it
+
+ align:start position:0%
+any better now no you got to yell at it
+ 
+
+ align:start position:0%
+any better now no you got to yell at it
+is it any better now yeah Okay
+
+ align:start position:0%
+is it any better now yeah Okay
+ 
+
+ align:start position:0%
+is it any better now yeah Okay
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so yeah I I always like to say I'll try
+
+ align:start position:0%
+so yeah I I always like to say I'll try
+ 
+
+ align:start position:0%
+so yeah I I always like to say I'll try
+to speak harder you should try to listen
+
+ align:start position:0%
+to speak harder you should try to listen
+ 
+
+ align:start position:0%
+to speak harder you should try to listen
+harder too so we can meet somewhere meet
+
+ align:start position:0%
+harder too so we can meet somewhere meet
+ 
+
+ align:start position:0%
+harder too so we can meet somewhere meet
+somewh in between uh so basically in in
+
+ align:start position:0%
+somewh in between uh so basically in in
+ 
+
+ align:start position:0%
+somewh in between uh so basically in in
+the abstract sense we trying to solve a
+
+ align:start position:0%
+the abstract sense we trying to solve a
+ 
+
+ align:start position:0%
+the abstract sense we trying to solve a
+system of sparse linear equations and
+
+ align:start position:0%
+system of sparse linear equations and
+ 
+
+ align:start position:0%
+system of sparse linear equations and
+for Simplicity uh for the first pass we
+
+ align:start position:0%
+for Simplicity uh for the first pass we
+ 
+
+ align:start position:0%
+for Simplicity uh for the first pass we
+treated The Matrix as as being done so
+
+ align:start position:0%
+treated The Matrix as as being done so
+ 
+
+ align:start position:0%
+treated The Matrix as as being done so
+we did the whole gaus elimination on
+
+ align:start position:0%
+we did the whole gaus elimination on
+ 
+
+ align:start position:0%
+we did the whole gaus elimination on
+treating assuming the ignoring all the
+
+ align:start position:0%
+treating assuming the ignoring all the
+ 
+
+ align:start position:0%
+treating assuming the ignoring all the
+the zeros of the Matrix um and so the
+
+ align:start position:0%
+the zeros of the Matrix um and so the
+ 
+
+ align:start position:0%
+the zeros of the Matrix um and so the
+basic idea is that you you we do the
+
+ align:start position:0%
+basic idea is that you you we do the
+ 
+
+ align:start position:0%
+basic idea is that you you we do the
+full we we do G elimination with partial
+
+ align:start position:0%
+full we we do G elimination with partial
+ 
+
+ align:start position:0%
+full we we do G elimination with partial
+pting and and it's the forward
+
+ align:start position:0%
+pting and and it's the forward
+ 
+
+ align:start position:0%
+pting and and it's the forward
+elimination stage of the G elimination
+
+ align:start position:0%
+elimination stage of the G elimination
+ 
+
+ align:start position:0%
+elimination stage of the G elimination
+that's that's order and Cube there is
+
+ align:start position:0%
+that's that's order and Cube there is
+ 
+
+ align:start position:0%
+that's that's order and Cube there is
+most expensive and that is the thing
+
+ align:start position:0%
+most expensive and that is the thing
+ 
+
+ align:start position:0%
+most expensive and that is the thing
+that we have tried to paraliz between
+
+ align:start position:0%
+that we have tried to paraliz between
+ 
+
+ align:start position:0%
+that we have tried to paraliz between
+among the spus the partial pting and and
+
+ align:start position:0%
+among the spus the partial pting and and
+ 
+
+ align:start position:0%
+among the spus the partial pting and and
+the par pting and the back s is all done
+
+ align:start position:0%
+the par pting and the back s is all done
+ 
+
+ align:start position:0%
+the par pting and the back s is all done
+on the ppus because that that turned out
+
+ align:start position:0%
+on the ppus because that that turned out
+ 
+
+ align:start position:0%
+on the ppus because that that turned out
+to be much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faster so this is the the the the Matrix
+
+ align:start position:0%
+faster so this is the the the the Matrix
+ 
+
+ align:start position:0%
+faster so this is the the the the Matrix
+that that that we are considering at
+
+ align:start position:0%
+that that that we are considering at
+ 
+
+ align:start position:0%
+that that that we are considering at
+during each step filled with random
+
+ align:start position:0%
+during each step filled with random
+ 
+
+ align:start position:0%
+during each step filled with random
+entries and filled with a random uh
+
+ align:start position:0%
+entries and filled with a random uh
+ 
+
+ align:start position:0%
+entries and filled with a random uh
+right hand side um and and the way GA
+
+ align:start position:0%
+right hand side um and and the way GA
+ 
+
+ align:start position:0%
+right hand side um and and the way GA
+elimination works is that we we start
+
+ align:start position:0%
+elimination works is that we we start
+ 
+
+ align:start position:0%
+elimination works is that we we start
+off with with one of the rows which you
+
+ align:start position:0%
+off with with one of the rows which you
+ 
+
+ align:start position:0%
+off with with one of the rows which you
+call the base row or which is where the
+
+ align:start position:0%
+call the base row or which is where the
+ 
+
+ align:start position:0%
+call the base row or which is where the
+pivots come
+
+ align:start position:0%
+pivots come
+ 
+
+ align:start position:0%
+pivots come
+from and then we we we take all and then
+
+ align:start position:0%
+from and then we we we take all and then
+ 
+
+ align:start position:0%
+from and then we we we take all and then
+we we eliminate the variable
+
+ align:start position:0%
+we we eliminate the variable
+ 
+
+ align:start position:0%
+we we eliminate the variable
+corresponding to base R from all the
+
+ align:start position:0%
+corresponding to base R from all the
+ 
+
+ align:start position:0%
+corresponding to base R from all the
+subsequent uh elimination rows and all
+
+ align:start position:0%
+subsequent uh elimination rows and all
+ 
+
+ align:start position:0%
+subsequent uh elimination rows and all
+these eliminations can be done in parall
+
+ align:start position:0%
+these eliminations can be done in parall
+ 
+
+ align:start position:0%
+these eliminations can be done in parall
+and that's what we have tried to
+
+ align:start position:0%
+and that's what we have tried to
+ 
+
+ align:start position:0%
+and that's what we have tried to
+paralyze so each spu grabs hold grabs
+
+ align:start position:0%
+paralyze so each spu grabs hold grabs
+ 
+
+ align:start position:0%
+paralyze so each spu grabs hold grabs
+hold of the next available elimination
+
+ align:start position:0%
+hold of the next available elimination
+ 
+
+ align:start position:0%
+hold of the next available elimination
+row eliminates it and writes the result
+
+ align:start position:0%
+row eliminates it and writes the result
+ 
+
+ align:start position:0%
+row eliminates it and writes the result
+back on on onto the main memory so for
+
+ align:start position:0%
+back on on onto the main memory so for
+ 
+
+ align:start position:0%
+back on on onto the main memory so for
+example if we consider a situation with
+
+ align:start position:0%
+example if we consider a situation with
+ 
+
+ align:start position:0%
+example if we consider a situation with
+with two uh what we what we do is that
+
+ align:start position:0%
+with two uh what we what we do is that
+ 
+
+ align:start position:0%
+with two uh what we what we do is that
+we stream the rows across the we stram
+
+ align:start position:0%
+we stream the rows across the we stram
+ 
+
+ align:start position:0%
+we stream the rows across the we stram
+the El rows across all the spus each spu
+
+ align:start position:0%
+the El rows across all the spus each spu
+ 
+
+ align:start position:0%
+the El rows across all the spus each spu
+performs the elimination and wres the
+
+ align:start position:0%
+performs the elimination and wres the
+ 
+
+ align:start position:0%
+performs the elimination and wres the
+result back to uh back to main memory as
+
+ align:start position:0%
+result back to uh back to main memory as
+ 
+
+ align:start position:0%
+result back to uh back to main memory as
+you can see and and it it for this
+
+ align:start position:0%
+you can see and and it it for this
+ 
+
+ align:start position:0%
+you can see and and it it for this
+happens for every uhow so once the so in
+
+ align:start position:0%
+happens for every uhow so once the so in
+ 
+
+ align:start position:0%
+happens for every uhow so once the so in
+this simulation the first variable has
+
+ align:start position:0%
+this simulation the first variable has
+ 
+
+ align:start position:0%
+this simulation the first variable has
+been eliminated uh as you can see there
+
+ align:start position:0%
+been eliminated uh as you can see there
+ 
+
+ align:start position:0%
+been eliminated uh as you can see there
+are zeros along the First Column and and
+
+ align:start position:0%
+are zeros along the First Column and and
+ 
+
+ align:start position:0%
+are zeros along the First Column and and
+and and then the process is is recursive
+
+ align:start position:0%
+and and then the process is is recursive
+ 
+
+ align:start position:0%
+and and then the process is is recursive
+after after the first variable is
+
+ align:start position:0%
+after after the first variable is
+ 
+
+ align:start position:0%
+after after the first variable is
+completed it moves on to the next
+
+ align:start position:0%
+completed it moves on to the next
+ 
+
+ align:start position:0%
+completed it moves on to the next
+variable so that's basically how and and
+
+ align:start position:0%
+variable so that's basically how and and
+ 
+
+ align:start position:0%
+variable so that's basically how and and
+as you can and the way the the the
+
+ align:start position:0%
+as you can and the way the the the
+ 
+
+ align:start position:0%
+as you can and the way the the the
+alumination rows are delt out they delt
+
+ align:start position:0%
+alumination rows are delt out they delt
+ 
+
+ align:start position:0%
+alumination rows are delt out they delt
+out in a cyclic fashion so there is no
+
+ align:start position:0%
+out in a cyclic fashion so there is no
+ 
+
+ align:start position:0%
+out in a cyclic fashion so there is no
+serial bottleneck it's all perfectly
+
+ align:start position:0%
+serial bottleneck it's all perfectly
+ 
+
+ align:start position:0%
+serial bottleneck it's all perfectly
+load balanced I'm sorry change you
+
+ align:start position:0%
+load balanced I'm sorry change you
+ 
+
+ align:start position:0%
+load balanced I'm sorry change you
+eliminate something lower does the PIV
+
+ align:start position:0%
+eliminate something lower does the PIV
+ 
+
+ align:start position:0%
+eliminate something lower does the PIV
+value change I'm completely not getting
+
+ align:start position:0%
+value change I'm completely not getting
+ 
+
+ align:start position:0%
+value change I'm completely not getting
+what you are saying that's my first
+
+ align:start position:0%
+what you are saying that's my first
+ 
+
+ align:start position:0%
+what you are saying that's my first
+question yes second question is if is
+
+ align:start position:0%
+question yes second question is if is
+ 
+
+ align:start position:0%
+question yes second question is if is
+fast or dense what's your Matrix
+
+ align:start position:0%
+fast or dense what's your Matrix
+ 
+
+ align:start position:0%
+fast or dense what's your Matrix
+representation The Matrix representation
+
+ align:start position:0%
+representation The Matrix representation
+ 
+
+ align:start position:0%
+representation The Matrix representation
+currently is
+
+ align:start position:0%
+currently is
+ 
+
+ align:start position:0%
+currently is
+dense okay yeah so the Val keep changing
+
+ align:start position:0%
+dense okay yeah so the Val keep changing
+ 
+
+ align:start position:0%
+dense okay yeah so the Val keep changing
+when you eliminate so if it completely
+
+ align:start position:0%
+when you eliminate so if it completely
+ 
+
+ align:start position:0%
+when you eliminate so if it completely
+parall and that's what the so are theend
+
+ align:start position:0%
+parall and that's what the so are theend
+ 
+
+ align:start position:0%
+parall and that's what the so are theend
+so so the elimination so the all the
+
+ align:start position:0%
+so so the elimination so the all the
+ 
+
+ align:start position:0%
+so so the elimination so the all the
+subsequent variables that that are
+
+ align:start position:0%
+subsequent variables that that are
+ 
+
+ align:start position:0%
+subsequent variables that that are
+eliminated during for for each variable
+
+ align:start position:0%
+eliminated during for for each variable
+ 
+
+ align:start position:0%
+eliminated during for for each variable
+r r can be done in parall but after
+
+ align:start position:0%
+r r can be done in parall but after
+ 
+
+ align:start position:0%
+r r can be done in parall but after
+after one variable has been eliminated
+
+ align:start position:0%
+after one variable has been eliminated
+ 
+
+ align:start position:0%
+after one variable has been eliminated
+there's a synchronization step where all
+
+ align:start position:0%
+there's a synchronization step where all
+ 
+
+ align:start position:0%
+there's a synchronization step where all
+the spus have to have to synchronize
+
+ align:start position:0%
+the spus have to have to synchronize
+ 
+
+ align:start position:0%
+the spus have to have to synchronize
+there's a barrier after each after each
+
+ align:start position:0%
+there's a barrier after each after each
+ 
+
+ align:start position:0%
+there's a barrier after each after each
+row has been
+
+ align:start position:0%
+row has been
+ 
+
+ align:start position:0%
+row has been
+eliminated okay okay yeah so so so you
+
+ align:start position:0%
+eliminated okay okay yeah so so so you
+ 
+
+ align:start position:0%
+eliminated okay okay yeah so so so you
+started so so there's a triply nested
+
+ align:start position:0%
+started so so there's a triply nested
+ 
+
+ align:start position:0%
+started so so there's a triply nested
+for Loop if you write the algorithm down
+
+ align:start position:0%
+for Loop if you write the algorithm down
+ 
+
+ align:start position:0%
+for Loop if you write the algorithm down
+and you and the first and and then it's
+
+ align:start position:0%
+and you and the first and and then it's
+ 
+
+ align:start position:0%
+and you and the first and and then it's
+the it's it's the inner two Loops that
+
+ align:start position:0%
+the it's it's the inner two Loops that
+ 
+
+ align:start position:0%
+the it's it's the inner two Loops that
+are completely paralyzable and that's
+
+ align:start position:0%
+are completely paralyzable and that's
+ 
+
+ align:start position:0%
+are completely paralyzable and that's
+the second Loop is what you try to
+
+ align:start position:0%
+the second Loop is what you try to
+ 
+
+ align:start position:0%
+the second Loop is what you try to
+paralyze okay is that a little clearer
+
+ align:start position:0%
+paralyze okay is that a little clearer
+ 
+
+ align:start position:0%
+paralyze okay is that a little clearer
+yeah so U this is the this is the basic
+
+ align:start position:0%
+yeah so U this is the this is the basic
+ 
+
+ align:start position:0%
+yeah so U this is the this is the basic
+algorithm and and uh um let John talk
+
+ align:start position:0%
+algorithm and and uh um let John talk
+ 
+
+ align:start position:0%
+algorithm and and uh um let John talk
+about some of the performance numbers uh
+
+ align:start position:0%
+about some of the performance numbers uh
+ 
+
+ align:start position:0%
+about some of the performance numbers uh
+we have got but but uh some of the
+
+ align:start position:0%
+we have got but but uh some of the
+ 
+
+ align:start position:0%
+we have got but but uh some of the
+optimizations that we have tried to that
+
+ align:start position:0%
+optimizations that we have tried to that
+ 
+
+ align:start position:0%
+optimizations that we have tried to that
+we haven't done are are are the use of
+
+ align:start position:0%
+we haven't done are are are the use of
+ 
+
+ align:start position:0%
+we haven't done are are are the use of
+BL three operations where you stream
+
+ align:start position:0%
+BL three operations where you stream
+ 
+
+ align:start position:0%
+BL three operations where you stream
+multiple draws at a time and and uh
+
+ align:start position:0%
+multiple draws at a time and and uh
+ 
+
+ align:start position:0%
+multiple draws at a time and and uh
+use of C operations but I'll let jump
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the um computation of the current
+
+ align:start position:0%
+the um computation of the current
+ 
+
+ align:start position:0%
+the um computation of the current
+elimination row with the fetching of the
+
+ align:start position:0%
+elimination row with the fetching of the
+ 
+
+ align:start position:0%
+elimination row with the fetching of the
+next elimination row um we get roughly a
+
+ align:start position:0%
+next elimination row um we get roughly a
+ 
+
+ align:start position:0%
+next elimination row um we get roughly a
+30% speed up so here's a graph of um uh
+
+ align:start position:0%
+30% speed up so here's a graph of um uh
+ 
+
+ align:start position:0%
+30% speed up so here's a graph of um uh
+to see how both the unbuffered and
+
+ align:start position:0%
+to see how both the unbuffered and
+ 
+
+ align:start position:0%
+to see how both the unbuffered and
+buffer version um performed um with a
+
+ align:start position:0%
+buffer version um performed um with a
+ 
+
+ align:start position:0%
+buffer version um performed um with a
+number of scaling with a number of spus
+
+ align:start position:0%
+number of scaling with a number of spus
+ 
+
+ align:start position:0%
+number of scaling with a number of spus
+so as you can see both look roughly
+
+ align:start position:0%
+so as you can see both look roughly
+ 
+
+ align:start position:0%
+so as you can see both look roughly
+pretty linear um and um that makes sense
+
+ align:start position:0%
+pretty linear um and um that makes sense
+ 
+
+ align:start position:0%
+pretty linear um and um that makes sense
+because uh
+
+ align:start position:0%
+because uh
+ 
+
+ align:start position:0%
+because uh
+the and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so here's here's another graph of um
+
+ align:start position:0%
+so so here's here's another graph of um
+ 
+
+ align:start position:0%
+so so here's here's another graph of um
+how um we how we scale with the size of
+
+ align:start position:0%
+how um we how we scale with the size of
+ 
+
+ align:start position:0%
+how um we how we scale with the size of
+the Matrix that we're working with so
+
+ align:start position:0%
+the Matrix that we're working with so
+ 
+
+ align:start position:0%
+the Matrix that we're working with so
+the smaller the Matrix the higher the
+
+ align:start position:0%
+the smaller the Matrix the higher the
+ 
+
+ align:start position:0%
+the smaller the Matrix the higher the
+communication computation ratio so the
+
+ align:start position:0%
+communication computation ratio so the
+ 
+
+ align:start position:0%
+communication computation ratio so the
+the communication latency should be more
+
+ align:start position:0%
+the communication latency should be more
+ 
+
+ align:start position:0%
+the communication latency should be more
+apparent but as you can see
+
+ align:start position:0%
+apparent but as you can see
+ 
+
+ align:start position:0%
+apparent but as you can see
+um even even as you get smaller um
+
+ align:start position:0%
+um even even as you get smaller um
+ 
+
+ align:start position:0%
+um even even as you get smaller um
+the the computation is still pretty
+
+ align:start position:0%
+the the computation is still pretty
+ 
+
+ align:start position:0%
+the the computation is still pretty
+linear um so yeah it's linear but it's
+
+ align:start position:0%
+linear um so yeah it's linear but it's
+ 
+
+ align:start position:0%
+linear um so yeah it's linear but it's
+not as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B it which not running at two
+
+ align:start position:0%
+B it which not running at two
+ 
+
+ align:start position:0%
+B it which not running at two
+performance Improvement but it has a
+
+ align:start position:0%
+performance Improvement but it has a
+ 
+
+ align:start position:0%
+performance Improvement but it has a
+very it's not fling out so the
+
+ align:start position:0%
+very it's not fling out so the
+ 
+
+ align:start position:0%
+very it's not fling out so the
+interesting thing is why is it only 30%
+
+ align:start position:0%
+interesting thing is why is it only 30%
+ 
+
+ align:start position:0%
+interesting thing is why is it only 30%
+why is it not 2x get 2x performance
+
+ align:start position:0%
+why is it not 2x get 2x performance
+ 
+
+ align:start position:0%
+why is it not 2x get 2x performance
+Improvement so is it because of underlow
+
+ align:start position:0%
+Improvement so is it because of underlow
+ 
+
+ align:start position:0%
+Improvement so is it because of underlow
+if it is underlow this graph shouldn't
+
+ align:start position:0%
+if it is underlow this graph shouldn't
+ 
+
+ align:start position:0%
+if it is underlow this graph shouldn't
+have this kind of a pattern it should
+
+ align:start position:0%
+have this kind of a pattern it should
+ 
+
+ align:start position:0%
+have this kind of a pattern it should
+kind of have a more exponential type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pattern no why so why aren't you getting
+
+ align:start position:0%
+pattern no why so why aren't you getting
+ 
+
+ align:start position:0%
+pattern no why so why aren't you getting
+2x speed up or I mean your your line is
+
+ align:start position:0%
+2x speed up or I mean your your line is
+ 
+
+ align:start position:0%
+2x speed up or I mean your your line is
+straight yeah but it's not increasing
+
+ align:start position:0%
+straight yeah but it's not increasing
+ 
+
+ align:start position:0%
+straight yeah but it's not increasing
+proportional to the number of spus
+
+ align:start position:0%
+proportional to the number of spus
+ 
+
+ align:start position:0%
+proportional to the number of spus
+you're increasing so your efficiency
+
+ align:start position:0%
+you're increasing so your efficiency
+ 
+
+ align:start position:0%
+you're increasing so your efficiency
+might not be at 100% any idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why the two the 2x would only this is a
+
+ align:start position:0%
+why the two the 2x would only this is a
+ 
+
+ align:start position:0%
+why the two the 2x would only this is a
+l Lo so two would only shift it up and
+
+ align:start position:0%
+l Lo so two would only shift it up and
+ 
+
+ align:start position:0%
+l Lo so two would only shift it up and
+down yeah so so looks like you're not
+
+ align:start position:0%
+down yeah so so looks like you're not
+ 
+
+ align:start position:0%
+down yeah so so looks like you're not
+operating at 100% efficiency right oh
+
+ align:start position:0%
+operating at 100% efficiency right oh
+ 
+
+ align:start position:0%
+operating at 100% efficiency right oh
+definely not yeah so I think
+
+ align:start position:0%
+definely not yeah so I think
+ 
+
+ align:start position:0%
+definely not yeah so I think
+the conversation going on there but this
+
+ align:start position:0%
+the conversation going on there but this
+ 
+
+ align:start position:0%
+the conversation going on there but this
+is a stretch type of a gra because
+
+ align:start position:0%
+is a stretch type of a gra because
+ 
+
+ align:start position:0%
+is a stretch type of a gra because
+if it goes actually to do kind of
+
+ align:start position:0%
+if it goes actually to do kind of
+ 
+
+ align:start position:0%
+if it goes actually to do kind of
+improvement and and you get a very nice
+
+ align:start position:0%
+improvement and and you get a very nice
+ 
+
+ align:start position:0%
+improvement and and you get a very nice
+linear T if you have under typ forhead
+
+ align:start position:0%
+linear T if you have under typ forhead
+ 
+
+ align:start position:0%
+linear T if you have under typ forhead
+what you get is you have a good speed up
+
+ align:start position:0%
+what you get is you have a good speed up
+ 
+
+ align:start position:0%
+what you get is you have a good speed up
+at the beginning and then you slow down
+
+ align:start position:0%
+at the beginning and then you slow down
+ 
+
+ align:start position:0%
+at the beginning and then you slow down
+you get a kind of logarithmic type of
+
+ align:start position:0%
+you get a kind of logarithmic type of
+ 
+
+ align:start position:0%
+you get a kind of logarithmic type of
+GRA so it's very I haven't seen things
+
+ align:start position:0%
+GRA so it's very I haven't seen things
+ 
+
+ align:start position:0%
+GRA so it's very I haven't seen things
+like a straight line but not at 45°
+
+ align:start position:0%
+like a straight line but not at 45°
+ 
+
+ align:start position:0%
+like a straight line but not at 45°
+angle Gra is kind of a Str thing it
+
+ align:start position:0%
+angle Gra is kind of a Str thing it
+ 
+
+ align:start position:0%
+angle Gra is kind of a Str thing it
+might be to see where and why this is
+
+ align:start position:0%
+might be to see where and why this is
+ 
+
+ align:start position:0%
+might be to see where and why this is
+happening okay um well yeah so I'll just
+
+ align:start position:0%
+happening okay um well yeah so I'll just
+ 
+
+ align:start position:0%
+happening okay um well yeah so I'll just
+move on um so I'll talk about some of
+
+ align:start position:0%
+move on um so I'll talk about some of
+ 
+
+ align:start position:0%
+move on um so I'll talk about some of
+the further work we're trying to do um
+
+ align:start position:0%
+the further work we're trying to do um
+ 
+
+ align:start position:0%
+the further work we're trying to do um
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+yeah so um we've also tried to Triple
+
+ align:start position:0%
+yeah so um we've also tried to Triple
+ 
+
+ align:start position:0%
+yeah so um we've also tried to Triple
+buffer by um uh pipelining the fetching
+
+ align:start position:0%
+buffer by um uh pipelining the fetching
+ 
+
+ align:start position:0%
+buffer by um uh pipelining the fetching
+of the U of the next row with the
+
+ align:start position:0%
+of the U of the next row with the
+ 
+
+ align:start position:0%
+of the U of the next row with the
+computation of the current row row with
+
+ align:start position:0%
+computation of the current row row with
+ 
+
+ align:start position:0%
+computation of the current row row with
+the um sending of the previous row um we
+
+ align:start position:0%
+the um sending of the previous row um we
+ 
+
+ align:start position:0%
+the um sending of the previous row um we
+did this but it didn't actually give us
+
+ align:start position:0%
+did this but it didn't actually give us
+ 
+
+ align:start position:0%
+did this but it didn't actually give us
+the speed up that um we we thought we
+
+ align:start position:0%
+the speed up that um we we thought we
+ 
+
+ align:start position:0%
+the speed up that um we we thought we
+would get um what we're working on now
+
+ align:start position:0%
+would get um what we're working on now
+ 
+
+ align:start position:0%
+would get um what we're working on now
+is smizing the computation stage so
+
+ align:start position:0%
+is smizing the computation stage so
+ 
+
+ align:start position:0%
+is smizing the computation stage so
+right now we treat the the rows as all
+
+ align:start position:0%
+right now we treat the the rows as all
+ 
+
+ align:start position:0%
+right now we treat the the rows as all
+the doubles and the rows as scalers but
+
+ align:start position:0%
+the doubles and the rows as scalers but
+ 
+
+ align:start position:0%
+the doubles and the rows as scalers but
+we could use the my sying hopefully we
+
+ align:start position:0%
+we could use the my sying hopefully we
+ 
+
+ align:start position:0%
+we could use the my sying hopefully we
+can get a speed up of um by a factor of
+
+ align:start position:0%
+can get a speed up of um by a factor of
+ 
+
+ align:start position:0%
+can get a speed up of um by a factor of
+two um and also right now our Lu
+
+ align:start position:0%
+two um and also right now our Lu
+ 
+
+ align:start position:0%
+two um and also right now our Lu
+algorithm isn't
+
+ align:start position:0%
+algorithm isn't
+ 
+
+ align:start position:0%
+algorithm isn't
+very smart in that when we fetch the
+
+ align:start position:0%
+very smart in that when we fetch the
+ 
+
+ align:start position:0%
+very smart in that when we fetch the
+elimination row as we go on through the
+
+ align:start position:0%
+elimination row as we go on through the
+ 
+
+ align:start position:0%
+elimination row as we go on through the
+algorithm part of the elimination row
+
+ align:start position:0%
+algorithm part of the elimination row
+ 
+
+ align:start position:0%
+algorithm part of the elimination row
+becomes zeros as we move down so um we
+
+ align:start position:0%
+becomes zeros as we move down so um we
+ 
+
+ align:start position:0%
+becomes zeros as we move down so um we
+don't really need to fetch the entire
+
+ align:start position:0%
+don't really need to fetch the entire
+ 
+
+ align:start position:0%
+don't really need to fetch the entire
+elimination row and so by taking that
+
+ align:start position:0%
+elimination row and so by taking that
+ 
+
+ align:start position:0%
+elimination row and so by taking that
+into account um our memory the transfer
+
+ align:start position:0%
+into account um our memory the transfer
+ 
+
+ align:start position:0%
+into account um our memory the transfer
+our dma transfers are smaller and maybe
+
+ align:start position:0%
+our dma transfers are smaller and maybe
+ 
+
+ align:start position:0%
+our dma transfers are smaller and maybe
+that'll speed things up a
+
+ align:start position:0%
+that'll speed things up a
+ 
+
+ align:start position:0%
+that'll speed things up a
+bit so the whole thing is in double
+
+ align:start position:0%
+bit so the whole thing is in double
+ 
+
+ align:start position:0%
+bit so the whole thing is in double
+Precision yes
+
+ align:start position:0%
+Precision yes
+ 
+
+ align:start position:0%
+Precision yes
+it's you know how many flop we have G
+
+ align:start position:0%
+it's you know how many flop we have G
+ 
+
+ align:start position:0%
+it's you know how many flop we have G
+flops I think we around G flops so
+
+ align:start position:0%
+flops I think we around G flops so
+ 
+
+ align:start position:0%
+flops I think we around G flops so
+here's a g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flops you know what the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expected is this a linear scale or on
+
+ align:start position:0%
+expected is this a linear scale or on
+ 
+
+ align:start position:0%
+expected is this a linear scale or on
+the Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AIS idea why you have thisa 3S to use
+
+ align:start position:0%
+AIS idea why you have thisa 3S to use
+ 
+
+ align:start position:0%
+AIS idea why you have thisa 3S to use
+your double buffing result just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drops actually
+
+ align:start position:0%
+drops actually
+ 
+
+ align:start position:0%
+drops actually
+idea I don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know you might want to run a few more
+
+ align:start position:0%
+know you might want to run a few more
+ 
+
+ align:start position:0%
+know you might want to run a few more
+times um there is uh a recent series of
+
+ align:start position:0%
+times um there is uh a recent series of
+ 
+
+ align:start position:0%
+times um there is uh a recent series of
+papers by Jack gar were aiming at Double
+
+ align:start position:0%
+papers by Jack gar were aiming at Double
+ 
+
+ align:start position:0%
+papers by Jack gar were aiming at Double
+Precision calculations they did used
+
+ align:start position:0%
+Precision calculations they did used
+ 
+
+ align:start position:0%
+Precision calculations they did used
+single Precision to get an approximate
+
+ align:start position:0%
+single Precision to get an approximate
+ 
+
+ align:start position:0%
+single Precision to get an approximate
+guess and then did a few iterations of
+
+ align:start position:0%
+guess and then did a few iterations of
+ 
+
+ align:start position:0%
+guess and then did a few iterations of
+an iterative approach to get a double
+
+ align:start position:0%
+an iterative approach to get a double
+ 
+
+ align:start position:0%
+an iterative approach to get a double
+Precision result yeah those don't work
+
+ align:start position:0%
+Precision result yeah those don't work
+ 
+
+ align:start position:0%
+Precision result yeah those don't work
+very well for poly conditioned mates
+
+ align:start position:0%
+very well for poly conditioned mates
+ 
+
+ align:start position:0%
+very well for poly conditioned mates
+what theying and this is conditioned
+
+ align:start position:0%
+what theying and this is conditioned
+ 
+
+ align:start position:0%
+what theying and this is conditioned
+around 10 to the8 so that's kind of out
+
+ align:start position:0%
+around 10 to the8 so that's kind of out
+ 
+
+ align:start position:0%
+around 10 to the8 so that's kind of out
+of the part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of they do they try to
+
+ align:start position:0%
+of they do they try to
+ 
+
+ align:start position:0%
+of they do they try to
+doal the main reason they do is because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we doing things the hope is to
+
+ align:start position:0%
+we doing things the hope is to
+ 
+
+ align:start position:0%
+we doing things the hope is to
+generalize this to to spar metries later
+
+ align:start position:0%
+generalize this to to spar metries later
+ 
+
+ align:start position:0%
+generalize this to to spar metries later
+on and and I don't think I think they
+
+ align:start position:0%
+on and and I don't think I think they
+ 
+
+ align:start position:0%
+on and and I don't think I think they
+are doing trying to do some work with
+
+ align:start position:0%
+are doing trying to do some work with
+ 
+
+ align:start position:0%
+are doing trying to do some work with
+with spars metries but they haven't
+
+ align:start position:0%
+with spars metries but they haven't
+ 
+
+ align:start position:0%
+with spars metries but they haven't
+gotten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one additional question just at at
+
+ align:start position:0%
+that one additional question just at at
+ 
+
+ align:start position:0%
+that one additional question just at at
+a high level is this the right way to
+
+ align:start position:0%
+a high level is this the right way to
+ 
+
+ align:start position:0%
+a high level is this the right way to
+tackle this particular problem it's
+
+ align:start position:0%
+tackle this particular problem it's
+ 
+
+ align:start position:0%
+tackle this particular problem it's
+strikes me that there must be a closed
+
+ align:start position:0%
+strikes me that there must be a closed
+ 
+
+ align:start position:0%
+strikes me that there must be a closed
+form uh you know high level macroscopic
+
+ align:start position:0%
+form uh you know high level macroscopic
+ 
+
+ align:start position:0%
+form uh you know high level macroscopic
+model for you
+
+ align:start position:0%
+model for you
+ 
+
+ align:start position:0%
+model for you
+know battery self-
+
+ align:start position:0%
+know battery self-
+ 
+
+ align:start position:0%
+know battery self-
+discharge I don't know anything about
+
+ align:start position:0%
+discharge I don't know anything about
+ 
+
+ align:start position:0%
+discharge I don't know anything about
+the chemistry of lead acid batteries but
+
+ align:start position:0%
+the chemistry of lead acid batteries but
+ 
+
+ align:start position:0%
+the chemistry of lead acid batteries but
+your your the right up on the website
+
+ align:start position:0%
+your your the right up on the website
+ 
+
+ align:start position:0%
+your your the right up on the website
+mentions black shols which I do know
+
+ align:start position:0%
+mentions black shols which I do know
+ 
+
+ align:start position:0%
+mentions black shols which I do know
+something about and of course there are
+
+ align:start position:0%
+something about and of course there are
+ 
+
+ align:start position:0%
+something about and of course there are
+efficient ways of doing that without
+
+ align:start position:0%
+efficient ways of doing that without
+ 
+
+ align:start position:0%
+efficient ways of doing that without
+sure there there are efficient ways of
+
+ align:start position:0%
+sure there there are efficient ways of
+ 
+
+ align:start position:0%
+sure there there are efficient ways of
+doing blacks there are different ways of
+
+ align:start position:0%
+doing blacks there are different ways of
+ 
+
+ align:start position:0%
+doing blacks there are different ways of
+doing this this is only one of the
+
+ align:start position:0%
+doing this this is only one of the
+ 
+
+ align:start position:0%
+doing this this is only one of the
+equations is similar to Black there are
+
+ align:start position:0%
+equations is similar to Black there are
+ 
+
+ align:start position:0%
+equations is similar to Black there are
+multiple equations that go into this
+
+ align:start position:0%
+multiple equations that go into this
+ 
+
+ align:start position:0%
+multiple equations that go into this
+they're all coupl nonlinear so solving
+
+ align:start position:0%
+they're all coupl nonlinear so solving
+ 
+
+ align:start position:0%
+they're all coupl nonlinear so solving
+this system of equations is in the
+
+ align:start position:0%
+this system of equations is in the
+ 
+
+ align:start position:0%
+this system of equations is in the
+literature if you were going to if you
+
+ align:start position:0%
+literature if you were going to if you
+ 
+
+ align:start position:0%
+literature if you were going to if you
+were going to choose this as your model
+
+ align:start position:0%
+were going to choose this as your model
+ 
+
+ align:start position:0%
+were going to choose this as your model
+but if if you are actually in the
+
+ align:start position:0%
+but if if you are actually in the
+ 
+
+ align:start position:0%
+but if if you are actually in the
+business of of you know well building
+
+ align:start position:0%
+business of of you know well building
+ 
+
+ align:start position:0%
+business of of you know well building
+building and Anda the wouldn't you try
+
+ align:start position:0%
+building and Anda the wouldn't you try
+ 
+
+ align:start position:0%
+building and Anda the wouldn't you try
+and come up with a an efficient
+
+ align:start position:0%
+and come up with a an efficient
+ 
+
+ align:start position:0%
+and come up with a an efficient
+macroscopic model rather than you well
+
+ align:start position:0%
+macroscopic model rather than you well
+ 
+
+ align:start position:0%
+macroscopic model rather than you well
+it depends on what your compute costs
+
+ align:start position:0%
+it depends on what your compute costs
+ 
+
+ align:start position:0%
+it depends on what your compute costs
+are I mean if you know if you going to
+
+ align:start position:0%
+are I mean if you know if you going to
+ 
+
+ align:start position:0%
+are I mean if you know if you going to
+run a model on a supercal processor
+
+ align:start position:0%
+run a model on a supercal processor
+ 
+
+ align:start position:0%
+run a model on a supercal processor
+that's a very expensive processor if
+
+ align:start position:0%
+that's a very expensive processor if
+ 
+
+ align:start position:0%
+that's a very expensive processor if
+however now you have the ability to use
+
+ align:start position:0%
+however now you have the ability to use
+ 
+
+ align:start position:0%
+however now you have the ability to use
+a collection of small cheap you know
+
+ align:start position:0%
+a collection of small cheap you know
+ 
+
+ align:start position:0%
+a collection of small cheap you know
+little processors like this you can
+
+ align:start position:0%
+little processors like this you can
+ 
+
+ align:start position:0%
+little processors like this you can
+maybe have the luxury of using a much
+
+ align:start position:0%
+maybe have the luxury of using a much
+ 
+
+ align:start position:0%
+maybe have the luxury of using a much
+more sophisticated model so is it
+
+ align:start position:0%
+more sophisticated model so is it
+ 
+
+ align:start position:0%
+more sophisticated model so is it
+necessarily more sophisticated I mean is
+
+ align:start position:0%
+necessarily more sophisticated I mean is
+ 
+
+ align:start position:0%
+necessarily more sophisticated I mean is
+there some fundamental reason why you
+
+ align:start position:0%
+there some fundamental reason why you
+ 
+
+ align:start position:0%
+there some fundamental reason why you
+get more information out of this
+
+ align:start position:0%
+get more information out of this
+ 
+
+ align:start position:0%
+get more information out of this
+approach
+
+ align:start position:0%
+approach
+ 
+
+ align:start position:0%
+approach
+than out of a higher level model uh you
+
+ align:start position:0%
+than out of a higher level model uh you
+ 
+
+ align:start position:0%
+than out of a higher level model uh you
+you get a lot more detail as to what's
+
+ align:start position:0%
+you get a lot more detail as to what's
+ 
+
+ align:start position:0%
+you get a lot more detail as to what's
+going on within your battery a high
+
+ align:start position:0%
+going on within your battery a high
+ 
+
+ align:start position:0%
+going on within your battery a high
+level model will give you IO information
+
+ align:start position:0%
+level model will give you IO information
+ 
+
+ align:start position:0%
+level model will give you IO information
+but if you're trying to find failure
+
+ align:start position:0%
+but if you're trying to find failure
+ 
+
+ align:start position:0%
+but if you're trying to find failure
+mechanisms you may want to know how much
+
+ align:start position:0%
+mechanisms you may want to know how much
+ 
+
+ align:start position:0%
+mechanisms you may want to know how much
+pressure is going on at certain points
+
+ align:start position:0%
+pressure is going on at certain points
+ 
+
+ align:start position:0%
+pressure is going on at certain points
+in your battery especially with like
+
+ align:start position:0%
+in your battery especially with like
+ 
+
+ align:start position:0%
+in your battery especially with like
+lithium ion batteries when you inter
+
+ align:start position:0%
+lithium ion batteries when you inter
+ 
+
+ align:start position:0%
+lithium ion batteries when you inter
+this is this differs from a lithium ion
+
+ align:start position:0%
+this is this differs from a lithium ion
+ 
+
+ align:start position:0%
+this is this differs from a lithium ion
+battery in that that we're actually
+
+ align:start position:0%
+battery in that that we're actually
+ 
+
+ align:start position:0%
+battery in that that we're actually
+changing the state the type of matter
+
+ align:start position:0%
+changing the state the type of matter
+ 
+
+ align:start position:0%
+changing the state the type of matter
+that we're using and in lithium ion
+
+ align:start position:0%
+that we're using and in lithium ion
+ 
+
+ align:start position:0%
+that we're using and in lithium ion
+battery we're interpolating and de
+
+ align:start position:0%
+battery we're interpolating and de
+ 
+
+ align:start position:0%
+battery we're interpolating and de
+interpolating and so what we're doing is
+
+ align:start position:0%
+interpolating and so what we're doing is
+ 
+
+ align:start position:0%
+interpolating and so what we're doing is
+we're creating a lot of stress on a
+
+ align:start position:0%
+we're creating a lot of stress on a
+ 
+
+ align:start position:0%
+we're creating a lot of stress on a
+matrix a crystal and that will be a
+
+ align:start position:0%
+matrix a crystal and that will be a
+ 
+
+ align:start position:0%
+matrix a crystal and that will be a
+failure mechanism a simple uh input
+
+ align:start position:0%
+failure mechanism a simple uh input
+ 
+
+ align:start position:0%
+failure mechanism a simple uh input
+output relationship will not give you
+
+ align:start position:0%
+output relationship will not give you
+ 
+
+ align:start position:0%
+output relationship will not give you
+that failure mechanism so you may want
+
+ align:start position:0%
+that failure mechanism so you may want
+ 
+
+ align:start position:0%
+that failure mechanism so you may want
+to know that kind of information you may
+
+ align:start position:0%
+to know that kind of information you may
+ 
+
+ align:start position:0%
+to know that kind of information you may
+want to know heat information also you
+
+ align:start position:0%
+want to know heat information also you
+ 
+
+ align:start position:0%
+want to know heat information also you
+could include you know thermodynamical
+
+ align:start position:0%
+could include you know thermodynamical
+ 
+
+ align:start position:0%
+could include you know thermodynamical
+information into this kind of model okay
+
+ align:start position:0%
+information into this kind of model okay
+ 
+
+ align:start position:0%
+information into this kind of model okay
+that's a good answer I I I take that uh
+
+ align:start position:0%
+that's a good answer I I I take that uh
+ 
+
+ align:start position:0%
+that's a good answer I I I take that uh
+to mean that the the reason for doing
+
+ align:start position:0%
+to mean that the the reason for doing
+ 
+
+ align:start position:0%
+to mean that the the reason for doing
+this is if you're researching the you
+
+ align:start position:0%
+this is if you're researching the you
+ 
+
+ align:start position:0%
+this is if you're researching the you
+know physics of of battery discharge as
+
+ align:start position:0%
+know physics of of battery discharge as
+ 
+
+ align:start position:0%
+know physics of of battery discharge as
+opposed to you know trying to estimate
+
+ align:start position:0%
+opposed to you know trying to estimate
+ 
+
+ align:start position:0%
+opposed to you know trying to estimate
+you know how much uh Power is left in
+
+ align:start position:0%
+you know how much uh Power is left in
+ 
+
+ align:start position:0%
+you know how much uh Power is left in
+your battery well you could you could
+
+ align:start position:0%
+your battery well you could you could
+ 
+
+ align:start position:0%
+your battery well you could you could
+use it if you have the computation power
+
+ align:start position:0%
+use it if you have the computation power
+ 
+
+ align:start position:0%
+use it if you have the computation power
+you could use the same model that does
+
+ align:start position:0%
+you could use the same model that does
+ 
+
+ align:start position:0%
+you could use the same model that does
+the research as the car and so if you
+
+ align:start position:0%
+the research as the car and so if you
+ 
+
+ align:start position:0%
+the research as the car and so if you
+yeah if you can use small processor so
+
+ align:start position:0%
+yeah if you can use small processor so
+ 
+
+ align:start position:0%
+yeah if you can use small processor so
+our demonstration if you guys want to
+
+ align:start position:0%
+our demonstration if you guys want to
+ 
+
+ align:start position:0%
+our demonstration if you guys want to
+see printf statements
+
+ align:start position:0%
+see printf statements
+ 
+
+ align:start position:0%
+see printf statements
+um yeah any last questions wait just so
+
+ align:start position:0%
+um yeah any last questions wait just so
+ 
+
+ align:start position:0%
+um yeah any last questions wait just so
+try understand the sparse versus Den
+
+ align:start position:0%
+try understand the sparse versus Den
+ 
+
+ align:start position:0%
+try understand the sparse versus Den
+issue just do a sparse elimination on a
+
+ align:start position:0%
+issue just do a sparse elimination on a
+ 
+
+ align:start position:0%
+issue just do a sparse elimination on a
+on a unior you get a bigger speed up oh
+
+ align:start position:0%
+on a unior you get a bigger speed up oh
+ 
+
+ align:start position:0%
+on a unior you get a bigger speed up oh
+you get a much bigger speed up okay you
+
+ align:start position:0%
+you get a much bigger speed up okay you
+ 
+
+ align:start position:0%
+you get a much bigger speed up okay you
+know the sparse is the Lu is about the
+
+ align:start position:0%
+know the sparse is the Lu is about the
+ 
+
+ align:start position:0%
+know the sparse is the Lu is about the
+slowest thing you could possibly choose
+
+ align:start position:0%
+slowest thing you could possibly choose
+ 
+
+ align:start position:0%
+slowest thing you could possibly choose
+but it works but what you have would
+
+ align:start position:0%
+but it works but what you have would
+ 
+
+ align:start position:0%
+but it works but what you have would
+still be useful for dense matrices it
+
+ align:start position:0%
+still be useful for dense matrices it
+ 
+
+ align:start position:0%
+still be useful for dense matrices it
+would still be useful for dense matrices
+
+ align:start position:0%
+would still be useful for dense matrices
+ 
+
+ align:start position:0%
+would still be useful for dense matrices
+and did you compare it all to just PPU
+
+ align:start position:0%
+and did you compare it all to just PPU
+ 
+
+ align:start position:0%
+and did you compare it all to just PPU
+performance on a dense Matrix uh no we
+
+ align:start position:0%
+performance on a dense Matrix uh no we
+ 
+
+ align:start position:0%
+performance on a dense Matrix uh no we
+didn't compare it to the PPU we we had a
+
+ align:start position:0%
+didn't compare it to the PPU we we had a
+ 
+
+ align:start position:0%
+didn't compare it to the PPU we we had a
+compare we have the same model running
+
+ align:start position:0%
+compare we have the same model running
+ 
+
+ align:start position:0%
+compare we have the same model running
+on a uh
+
+ align:start position:0%
+on a uh
+ 
+
+ align:start position:0%
+on a uh
+PC okay thanks speakers
+
+ align:start position:0%
+PC okay thanks speakers
+ 
+
+ align:start position:0%
+PC okay thanks speakers
+[Applause]
\ No newline at end of file
diff --git a/j5XdY5wkVTA.txt b/j5XdY5wkVTA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa9482ce11775fde9fd21d21b35fb0c017e9ab84
--- /dev/null
+++ b/j5XdY5wkVTA.txt
@@ -0,0 +1,15195 @@
+align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+welcome everyone this is 1413 psychology
+
+ align:start position:0%
+welcome everyone this is 1413 psychology
+ 
+
+ align:start position:0%
+welcome everyone this is 1413 psychology
+and economics also known as behavioral
+
+ align:start position:0%
+and economics also known as behavioral
+ 
+
+ align:start position:0%
+and economics also known as behavioral
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+my name is frank schilbach i'm a faculty
+
+ align:start position:0%
+my name is frank schilbach i'm a faculty
+ 
+
+ align:start position:0%
+my name is frank schilbach i'm a faculty
+member in the economics department
+
+ align:start position:0%
+member in the economics department
+ 
+
+ align:start position:0%
+member in the economics department
+teaching and doing research in
+
+ align:start position:0%
+teaching and doing research in
+ 
+
+ align:start position:0%
+teaching and doing research in
+behavioral economics and
+
+ align:start position:0%
+behavioral economics and
+ 
+
+ align:start position:0%
+behavioral economics and
+psychology and economics and development
+
+ align:start position:0%
+psychology and economics and development
+ 
+
+ align:start position:0%
+psychology and economics and development
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+there's syllabi over here in case
+
+ align:start position:0%
+there's syllabi over here in case
+ 
+
+ align:start position:0%
+there's syllabi over here in case
+anybody uh uh needs one
+
+ align:start position:0%
+anybody uh uh needs one
+ 
+
+ align:start position:0%
+anybody uh uh needs one
+so let me sort of start with introducing
+
+ align:start position:0%
+so let me sort of start with introducing
+ 
+
+ align:start position:0%
+so let me sort of start with introducing
+ourselves uh including myself
+
+ align:start position:0%
+ourselves uh including myself
+ 
+
+ align:start position:0%
+ourselves uh including myself
+as i said i'm uh frank schilbach i'm an
+
+ align:start position:0%
+as i said i'm uh frank schilbach i'm an
+ 
+
+ align:start position:0%
+as i said i'm uh frank schilbach i'm an
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+phd i'm from harvard recently um i'm
+
+ align:start position:0%
+phd i'm from harvard recently um i'm
+ 
+
+ align:start position:0%
+phd i'm from harvard recently um i'm
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+germany in case uh as you may have
+
+ align:start position:0%
+germany in case uh as you may have
+ 
+
+ align:start position:0%
+germany in case uh as you may have
+noticed i do research at the
+
+ align:start position:0%
+noticed i do research at the
+ 
+
+ align:start position:0%
+noticed i do research at the
+intersection of development behavioral
+
+ align:start position:0%
+intersection of development behavioral
+ 
+
+ align:start position:0%
+intersection of development behavioral
+economics in particular i'm interested
+
+ align:start position:0%
+economics in particular i'm interested
+ 
+
+ align:start position:0%
+economics in particular i'm interested
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+integrating uh psychological issues and
+
+ align:start position:0%
+integrating uh psychological issues and
+ 
+
+ align:start position:0%
+integrating uh psychological issues and
+uh helping us understand better
+
+ align:start position:0%
+uh helping us understand better
+ 
+
+ align:start position:0%
+uh helping us understand better
+um uh the lives of the poor and so they
+
+ align:start position:0%
+um uh the lives of the poor and so they
+ 
+
+ align:start position:0%
+um uh the lives of the poor and so they
+study all sorts of issues related to
+
+ align:start position:0%
+study all sorts of issues related to
+ 
+
+ align:start position:0%
+study all sorts of issues related to
+poverty
+
+ align:start position:0%
+poverty
+ 
+
+ align:start position:0%
+poverty
+how poverty itself affects people's
+
+ align:start position:0%
+how poverty itself affects people's
+ 
+
+ align:start position:0%
+how poverty itself affects people's
+behavior um
+
+ align:start position:0%
+behavior um
+ 
+
+ align:start position:0%
+behavior um
+and how conditions of poverty or things
+
+ align:start position:0%
+and how conditions of poverty or things
+ 
+
+ align:start position:0%
+and how conditions of poverty or things
+that are associated with poverty might
+
+ align:start position:0%
+that are associated with poverty might
+ 
+
+ align:start position:0%
+that are associated with poverty might
+feed back into people's decision making
+
+ align:start position:0%
+feed back into people's decision making
+ 
+
+ align:start position:0%
+feed back into people's decision making
+and their productivity or labor market
+
+ align:start position:0%
+and their productivity or labor market
+ 
+
+ align:start position:0%
+and their productivity or labor market
+behaviors
+
+ align:start position:0%
+behaviors
+ 
+
+ align:start position:0%
+behaviors
+and then perhaps sort of lead to the
+
+ align:start position:0%
+and then perhaps sort of lead to the
+ 
+
+ align:start position:0%
+and then perhaps sort of lead to the
+persistence of poverty through those
+
+ align:start position:0%
+persistence of poverty through those
+ 
+
+ align:start position:0%
+persistence of poverty through those
+kinds of effects
+
+ align:start position:0%
+kinds of effects
+ 
+
+ align:start position:0%
+kinds of effects
+so i have some work on financial
+
+ align:start position:0%
+so i have some work on financial
+ 
+
+ align:start position:0%
+so i have some work on financial
+constraints how financial constraints
+
+ align:start position:0%
+constraints how financial constraints
+ 
+
+ align:start position:0%
+constraints how financial constraints
+affect people's behavior
+
+ align:start position:0%
+affect people's behavior
+ 
+
+ align:start position:0%
+affect people's behavior
+in terms of thinking about money itself
+
+ align:start position:0%
+in terms of thinking about money itself
+ 
+
+ align:start position:0%
+in terms of thinking about money itself
+i have some work on sleep deprivation
+
+ align:start position:0%
+i have some work on sleep deprivation
+ 
+
+ align:start position:0%
+i have some work on sleep deprivation
+among the urban poor
+
+ align:start position:0%
+among the urban poor
+ 
+
+ align:start position:0%
+among the urban poor
+i'm thinking about pain and substance
+
+ align:start position:0%
+i'm thinking about pain and substance
+ 
+
+ align:start position:0%
+i'm thinking about pain and substance
+abuse and how that might affect people's
+
+ align:start position:0%
+abuse and how that might affect people's
+ 
+
+ align:start position:0%
+abuse and how that might affect people's
+choices
+
+ align:start position:0%
+choices
+ 
+
+ align:start position:0%
+choices
+uh uh most recently i'm interested in
+
+ align:start position:0%
+uh uh most recently i'm interested in
+ 
+
+ align:start position:0%
+uh uh most recently i'm interested in
+uh things related to mental health in
+
+ align:start position:0%
+uh things related to mental health in
+ 
+
+ align:start position:0%
+uh things related to mental health in
+particular depression and loneliness
+
+ align:start position:0%
+particular depression and loneliness
+ 
+
+ align:start position:0%
+particular depression and loneliness
+how those might affect people's
+
+ align:start position:0%
+how those might affect people's
+ 
+
+ align:start position:0%
+how those might affect people's
+well-being and then their um behaviors
+
+ align:start position:0%
+well-being and then their um behaviors
+ 
+
+ align:start position:0%
+well-being and then their um behaviors
+um i have um office hours um
+
+ align:start position:0%
+um i have um office hours um
+ 
+
+ align:start position:0%
+um i have um office hours um
+where you can sign up on my website uh
+
+ align:start position:0%
+where you can sign up on my website uh
+ 
+
+ align:start position:0%
+where you can sign up on my website uh
+currently they're on tuesday afternoons
+
+ align:start position:0%
+currently they're on tuesday afternoons
+ 
+
+ align:start position:0%
+currently they're on tuesday afternoons
+but you know if you cannot find
+
+ align:start position:0%
+but you know if you cannot find
+ 
+
+ align:start position:0%
+but you know if you cannot find
+times that work for you please email me
+
+ align:start position:0%
+times that work for you please email me
+ 
+
+ align:start position:0%
+times that work for you please email me
+and you'll find some time that that
+
+ align:start position:0%
+and you'll find some time that that
+ 
+
+ align:start position:0%
+and you'll find some time that that
+works out
+
+ align:start position:0%
+works out
+ 
+
+ align:start position:0%
+works out
+my assistant is krista moody in case you
+
+ align:start position:0%
+my assistant is krista moody in case you
+ 
+
+ align:start position:0%
+my assistant is krista moody in case you
+want to sort of get a hold of me and and
+
+ align:start position:0%
+want to sort of get a hold of me and and
+ 
+
+ align:start position:0%
+want to sort of get a hold of me and and
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+um i'm not available for some reason you
+
+ align:start position:0%
+um i'm not available for some reason you
+ 
+
+ align:start position:0%
+um i'm not available for some reason you
+can reach out to her
+
+ align:start position:0%
+can reach out to her
+ 
+
+ align:start position:0%
+can reach out to her
+um so now let me give you sort of the
+
+ align:start position:0%
+um so now let me give you sort of the
+ 
+
+ align:start position:0%
+um so now let me give you sort of the
+overview of the class
+
+ align:start position:0%
+overview of the class
+ 
+
+ align:start position:0%
+overview of the class
+i'm going to start sort of uh reading
+
+ align:start position:0%
+i'm going to start sort of uh reading
+ 
+
+ align:start position:0%
+i'm going to start sort of uh reading
+through four things one first i'm going
+
+ align:start position:0%
+through four things one first i'm going
+ 
+
+ align:start position:0%
+through four things one first i'm going
+to sort of tell you what is this class
+
+ align:start position:0%
+to sort of tell you what is this class
+ 
+
+ align:start position:0%
+to sort of tell you what is this class
+what is behavioral economics or what is
+
+ align:start position:0%
+what is behavioral economics or what is
+ 
+
+ align:start position:0%
+what is behavioral economics or what is
+psychology economics what do we mean by
+
+ align:start position:0%
+psychology economics what do we mean by
+ 
+
+ align:start position:0%
+psychology economics what do we mean by
+that is it sort of just putting two
+
+ align:start position:0%
+that is it sort of just putting two
+ 
+
+ align:start position:0%
+that is it sort of just putting two
+fields together
+
+ align:start position:0%
+fields together
+ 
+
+ align:start position:0%
+fields together
+or is it something more specific which
+
+ align:start position:0%
+or is it something more specific which
+ 
+
+ align:start position:0%
+or is it something more specific which
+you'll argue uh it is
+
+ align:start position:0%
+you'll argue uh it is
+ 
+
+ align:start position:0%
+you'll argue uh it is
+i'm going to give you some example then
+
+ align:start position:0%
+i'm going to give you some example then
+ 
+
+ align:start position:0%
+i'm going to give you some example then
+about like um uh
+
+ align:start position:0%
+about like um uh
+ 
+
+ align:start position:0%
+about like um uh
+how you might sort of use behavioral
+
+ align:start position:0%
+how you might sort of use behavioral
+ 
+
+ align:start position:0%
+how you might sort of use behavioral
+economics um in a specific example
+
+ align:start position:0%
+economics um in a specific example
+ 
+
+ align:start position:0%
+economics um in a specific example
+uh and a policy that might affect all of
+
+ align:start position:0%
+uh and a policy that might affect all of
+ 
+
+ align:start position:0%
+uh and a policy that might affect all of
+you and in fact it will because we have
+
+ align:start position:0%
+you and in fact it will because we have
+ 
+
+ align:start position:0%
+you and in fact it will because we have
+a specific laptop policy in this class
+
+ align:start position:0%
+a specific laptop policy in this class
+ 
+
+ align:start position:0%
+a specific laptop policy in this class
+uh and we'll tell you a little bit how
+
+ align:start position:0%
+uh and we'll tell you a little bit how
+ 
+
+ align:start position:0%
+uh and we'll tell you a little bit how
+to think about this there will also be a
+
+ align:start position:0%
+to think about this there will also be a
+ 
+
+ align:start position:0%
+to think about this there will also be a
+problem set
+
+ align:start position:0%
+problem set
+ 
+
+ align:start position:0%
+problem set
+that will help you think about this a
+
+ align:start position:0%
+that will help you think about this a
+ 
+
+ align:start position:0%
+that will help you think about this a
+bit more uh then we talk about somewhat
+
+ align:start position:0%
+bit more uh then we talk about somewhat
+ 
+
+ align:start position:0%
+bit more uh then we talk about somewhat
+boring uh course logistics
+
+ align:start position:0%
+boring uh course logistics
+ 
+
+ align:start position:0%
+boring uh course logistics
+um and at the end we do a questionnaire
+
+ align:start position:0%
+um and at the end we do a questionnaire
+ 
+
+ align:start position:0%
+um and at the end we do a questionnaire
+quiz um for everybody
+
+ align:start position:0%
+quiz um for everybody
+ 
+
+ align:start position:0%
+quiz um for everybody
+in part because we want to know some
+
+ align:start position:0%
+in part because we want to know some
+ 
+
+ align:start position:0%
+in part because we want to know some
+information for you in part we want to
+
+ align:start position:0%
+information for you in part we want to
+ 
+
+ align:start position:0%
+information for you in part we want to
+sort of learn a little bit about
+
+ align:start position:0%
+sort of learn a little bit about
+ 
+
+ align:start position:0%
+sort of learn a little bit about
+some decisions that um you might make
+
+ align:start position:0%
+some decisions that um you might make
+ 
+
+ align:start position:0%
+some decisions that um you might make
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+great sorry this is
+
+ align:start position:0%
+great sorry this is
+ 
+
+ align:start position:0%
+great sorry this is
+okay so what is um psychology economics
+
+ align:start position:0%
+okay so what is um psychology economics
+ 
+
+ align:start position:0%
+okay so what is um psychology economics
+so you may have heard of this uh the
+
+ align:start position:0%
+so you may have heard of this uh the
+ 
+
+ align:start position:0%
+so you may have heard of this uh the
+class used to be called economics and
+
+ align:start position:0%
+class used to be called economics and
+ 
+
+ align:start position:0%
+class used to be called economics and
+psychology
+
+ align:start position:0%
+psychology
+ 
+
+ align:start position:0%
+psychology
+or behavioral economics uh for our
+
+ align:start position:0%
+or behavioral economics uh for our
+ 
+
+ align:start position:0%
+or behavioral economics uh for our
+purposes that's kind of like all um
+
+ align:start position:0%
+purposes that's kind of like all um
+ 
+
+ align:start position:0%
+purposes that's kind of like all um
+um uh the same some economists sort of
+
+ align:start position:0%
+um uh the same some economists sort of
+ 
+
+ align:start position:0%
+um uh the same some economists sort of
+argue that um
+
+ align:start position:0%
+argue that um
+ 
+
+ align:start position:0%
+argue that um
+uh all economics is about behavior so
+
+ align:start position:0%
+uh all economics is about behavior so
+ 
+
+ align:start position:0%
+uh all economics is about behavior so
+like you know uh behavioral economics is
+
+ align:start position:0%
+like you know uh behavioral economics is
+ 
+
+ align:start position:0%
+like you know uh behavioral economics is
+sort of a bit of a weird word
+
+ align:start position:0%
+sort of a bit of a weird word
+ 
+
+ align:start position:0%
+sort of a bit of a weird word
+um so that's why partially i'm using
+
+ align:start position:0%
+um so that's why partially i'm using
+ 
+
+ align:start position:0%
+um so that's why partially i'm using
+sort of the word psychology and
+
+ align:start position:0%
+sort of the word psychology and
+ 
+
+ align:start position:0%
+sort of the word psychology and
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+in some sense it's sort of broader than
+
+ align:start position:0%
+in some sense it's sort of broader than
+ 
+
+ align:start position:0%
+in some sense it's sort of broader than
+that one definition is it's a field
+
+ align:start position:0%
+that one definition is it's a field
+ 
+
+ align:start position:0%
+that one definition is it's a field
+of economic academic research that
+
+ align:start position:0%
+of economic academic research that
+ 
+
+ align:start position:0%
+of economic academic research that
+studies the joint influences of
+
+ align:start position:0%
+studies the joint influences of
+ 
+
+ align:start position:0%
+studies the joint influences of
+psychological and economic factors
+
+ align:start position:0%
+psychological and economic factors
+ 
+
+ align:start position:0%
+psychological and economic factors
+on behaviors you could be sort of
+
+ align:start position:0%
+on behaviors you could be sort of
+ 
+
+ align:start position:0%
+on behaviors you could be sort of
+broader and say we're trying to
+
+ align:start position:0%
+broader and say we're trying to
+ 
+
+ align:start position:0%
+broader and say we're trying to
+integrate insights from not just
+
+ align:start position:0%
+integrate insights from not just
+ 
+
+ align:start position:0%
+integrate insights from not just
+psychology but also anthropology
+
+ align:start position:0%
+psychology but also anthropology
+ 
+
+ align:start position:0%
+psychology but also anthropology
+sociology medicine
+
+ align:start position:0%
+sociology medicine
+ 
+
+ align:start position:0%
+sociology medicine
+psychiatry etc and so on into economics
+
+ align:start position:0%
+psychiatry etc and so on into economics
+ 
+
+ align:start position:0%
+psychiatry etc and so on into economics
+and trying with an attempt to make
+
+ align:start position:0%
+and trying with an attempt to make
+ 
+
+ align:start position:0%
+and trying with an attempt to make
+economic models
+
+ align:start position:0%
+economic models
+ 
+
+ align:start position:0%
+economic models
+more realistic and therefore more
+
+ align:start position:0%
+more realistic and therefore more
+ 
+
+ align:start position:0%
+more realistic and therefore more
+predictive and help us understand
+
+ align:start position:0%
+predictive and help us understand
+ 
+
+ align:start position:0%
+predictive and help us understand
+people's behavior better
+
+ align:start position:0%
+people's behavior better
+ 
+
+ align:start position:0%
+people's behavior better
+and then help us uh make better policies
+
+ align:start position:0%
+and then help us uh make better policies
+ 
+
+ align:start position:0%
+and then help us uh make better policies
+perhaps
+
+ align:start position:0%
+perhaps
+ 
+
+ align:start position:0%
+perhaps
+in trying to influence um people's
+
+ align:start position:0%
+in trying to influence um people's
+ 
+
+ align:start position:0%
+in trying to influence um people's
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+now uh as i said you know that's
+
+ align:start position:0%
+now uh as i said you know that's
+ 
+
+ align:start position:0%
+now uh as i said you know that's
+medicine sociology etc
+
+ align:start position:0%
+medicine sociology etc
+ 
+
+ align:start position:0%
+medicine sociology etc
+broadly be trying to use insight from
+
+ align:start position:0%
+broadly be trying to use insight from
+ 
+
+ align:start position:0%
+broadly be trying to use insight from
+those fields and trying to understand
+
+ align:start position:0%
+those fields and trying to understand
+ 
+
+ align:start position:0%
+those fields and trying to understand
+have you missed something by
+
+ align:start position:0%
+have you missed something by
+ 
+
+ align:start position:0%
+have you missed something by
+making the fairly stark assumptions that
+
+ align:start position:0%
+making the fairly stark assumptions that
+ 
+
+ align:start position:0%
+making the fairly stark assumptions that
+economic models um usually
+
+ align:start position:0%
+economic models um usually
+ 
+
+ align:start position:0%
+economic models um usually
+make that leads me to what are the
+
+ align:start position:0%
+make that leads me to what are the
+ 
+
+ align:start position:0%
+make that leads me to what are the
+standard economics
+
+ align:start position:0%
+standard economics
+ 
+
+ align:start position:0%
+standard economics
+models in some sense what we're going to
+
+ align:start position:0%
+models in some sense what we're going to
+ 
+
+ align:start position:0%
+models in some sense what we're going to
+try and study to some degree is
+
+ align:start position:0%
+try and study to some degree is
+ 
+
+ align:start position:0%
+try and study to some degree is
+deviations from the classical or the
+
+ align:start position:0%
+deviations from the classical or the
+ 
+
+ align:start position:0%
+deviations from the classical or the
+the sort of the standard economic model
+
+ align:start position:0%
+the sort of the standard economic model
+ 
+
+ align:start position:0%
+the sort of the standard economic model
+so then of course we need to understand
+
+ align:start position:0%
+so then of course we need to understand
+ 
+
+ align:start position:0%
+so then of course we need to understand
+what is the standard economic models to
+
+ align:start position:0%
+what is the standard economic models to
+ 
+
+ align:start position:0%
+what is the standard economic models to
+start with
+
+ align:start position:0%
+start with
+ 
+
+ align:start position:0%
+start with
+which leads me to in part uh some
+
+ align:start position:0%
+which leads me to in part uh some
+ 
+
+ align:start position:0%
+which leads me to in part uh some
+prerequisites of the class or you should
+
+ align:start position:0%
+prerequisites of the class or you should
+ 
+
+ align:start position:0%
+prerequisites of the class or you should
+have taken at least some economics or
+
+ align:start position:0%
+have taken at least some economics or
+ 
+
+ align:start position:0%
+have taken at least some economics or
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+some economics to start with because i'm
+
+ align:start position:0%
+some economics to start with because i'm
+ 
+
+ align:start position:0%
+some economics to start with because i'm
+going to talk a lot about sort of
+
+ align:start position:0%
+going to talk a lot about sort of
+ 
+
+ align:start position:0%
+going to talk a lot about sort of
+deviations from those models and sort of
+
+ align:start position:0%
+deviations from those models and sort of
+ 
+
+ align:start position:0%
+deviations from those models and sort of
+if you haven't sort of taken any uh
+
+ align:start position:0%
+if you haven't sort of taken any uh
+ 
+
+ align:start position:0%
+if you haven't sort of taken any uh
+class before don't really
+
+ align:start position:0%
+class before don't really
+ 
+
+ align:start position:0%
+class before don't really
+know that very well then understanding
+
+ align:start position:0%
+know that very well then understanding
+ 
+
+ align:start position:0%
+know that very well then understanding
+the deviations will be a little bit
+
+ align:start position:0%
+the deviations will be a little bit
+ 
+
+ align:start position:0%
+the deviations will be a little bit
+tricky so for those of you who have
+
+ align:start position:0%
+tricky so for those of you who have
+ 
+
+ align:start position:0%
+tricky so for those of you who have
+taken economic classes what do we
+
+ align:start position:0%
+taken economic classes what do we
+ 
+
+ align:start position:0%
+taken economic classes what do we
+usually assume about people's behavior
+
+ align:start position:0%
+usually assume about people's behavior
+ 
+
+ align:start position:0%
+usually assume about people's behavior
+what are sort of some of the assumptions
+
+ align:start position:0%
+what are sort of some of the assumptions
+ 
+
+ align:start position:0%
+what are sort of some of the assumptions
+that we make
+
+ align:start position:0%
+that we make
+ 
+
+ align:start position:0%
+that we make
+about economic behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+stable preferences yes um so first well
+
+ align:start position:0%
+stable preferences yes um so first well
+ 
+
+ align:start position:0%
+stable preferences yes um so first well
+defined preferences in the sense of like
+
+ align:start position:0%
+defined preferences in the sense of like
+ 
+
+ align:start position:0%
+defined preferences in the sense of like
+people know what their preferences are
+
+ align:start position:0%
+people know what their preferences are
+ 
+
+ align:start position:0%
+people know what their preferences are
+they can state them
+
+ align:start position:0%
+they can state them
+ 
+
+ align:start position:0%
+they can state them
+and then they're also stable in a sense
+
+ align:start position:0%
+and then they're also stable in a sense
+ 
+
+ align:start position:0%
+and then they're also stable in a sense
+of like when i ask you today
+
+ align:start position:0%
+of like when i ask you today
+ 
+
+ align:start position:0%
+of like when i ask you today
+would you rather have apples or bananas
+
+ align:start position:0%
+would you rather have apples or bananas
+ 
+
+ align:start position:0%
+would you rather have apples or bananas
+um uh that'll
+
+ align:start position:0%
+um uh that'll
+ 
+
+ align:start position:0%
+um uh that'll
+not change unless they're sort of new
+
+ align:start position:0%
+not change unless they're sort of new
+ 
+
+ align:start position:0%
+not change unless they're sort of new
+information or your circumstances change
+
+ align:start position:0%
+information or your circumstances change
+ 
+
+ align:start position:0%
+information or your circumstances change
+of course if i ask you tomorrow and you
+
+ align:start position:0%
+of course if i ask you tomorrow and you
+ 
+
+ align:start position:0%
+of course if i ask you tomorrow and you
+already have a bunch of apples and then
+
+ align:start position:0%
+already have a bunch of apples and then
+ 
+
+ align:start position:0%
+already have a bunch of apples and then
+you'd say you want bananas
+
+ align:start position:0%
+you'd say you want bananas
+ 
+
+ align:start position:0%
+you'd say you want bananas
+that doesn't mean your preferences have
+
+ align:start position:0%
+that doesn't mean your preferences have
+ 
+
+ align:start position:0%
+that doesn't mean your preferences have
+changed but if i ask you about
+
+ align:start position:0%
+changed but if i ask you about
+ 
+
+ align:start position:0%
+changed but if i ask you about
+tomorrow what would you like for lunch
+
+ align:start position:0%
+tomorrow what would you like for lunch
+ 
+
+ align:start position:0%
+tomorrow what would you like for lunch
+you tell me a choice you want apples
+
+ align:start position:0%
+you tell me a choice you want apples
+ 
+
+ align:start position:0%
+you tell me a choice you want apples
+rather than bananas
+
+ align:start position:0%
+rather than bananas
+ 
+
+ align:start position:0%
+rather than bananas
+and then tomorrow you show up and
+
+ align:start position:0%
+and then tomorrow you show up and
+ 
+
+ align:start position:0%
+and then tomorrow you show up and
+nothing else has changed and you say now
+
+ align:start position:0%
+nothing else has changed and you say now
+ 
+
+ align:start position:0%
+nothing else has changed and you say now
+i want bananas well then your
+
+ align:start position:0%
+i want bananas well then your
+ 
+
+ align:start position:0%
+i want bananas well then your
+preferences are not
+
+ align:start position:0%
+preferences are not
+ 
+
+ align:start position:0%
+preferences are not
+stable that's one assumption yes what
+
+ align:start position:0%
+stable that's one assumption yes what
+ 
+
+ align:start position:0%
+stable that's one assumption yes what
+else do you have yeah
+
+ align:start position:0%
+else do you have yeah
+ 
+
+ align:start position:0%
+else do you have yeah
+more broadly they're rational yes and
+
+ align:start position:0%
+more broadly they're rational yes and
+ 
+
+ align:start position:0%
+more broadly they're rational yes and
+what does that mean
+
+ align:start position:0%
+what does that mean
+ 
+
+ align:start position:0%
+what does that mean
+they behave deterministically to
+
+ align:start position:0%
+they behave deterministically to
+ 
+
+ align:start position:0%
+they behave deterministically to
+optimize some utility function
+
+ align:start position:0%
+optimize some utility function
+ 
+
+ align:start position:0%
+optimize some utility function
+right exactly so people essentially
+
+ align:start position:0%
+right exactly so people essentially
+ 
+
+ align:start position:0%
+right exactly so people essentially
+optimize some utility functions so we
+
+ align:start position:0%
+optimize some utility functions so we
+ 
+
+ align:start position:0%
+optimize some utility functions so we
+say here people
+
+ align:start position:0%
+say here people
+ 
+
+ align:start position:0%
+say here people
+have a utility function they know what
+
+ align:start position:0%
+have a utility function they know what
+ 
+
+ align:start position:0%
+have a utility function they know what
+that is and you're sort of saying that
+
+ align:start position:0%
+that is and you're sort of saying that
+ 
+
+ align:start position:0%
+that is and you're sort of saying that
+maximize it to to optimize in a certain
+
+ align:start position:0%
+maximize it to to optimize in a certain
+ 
+
+ align:start position:0%
+maximize it to to optimize in a certain
+way they don't make mistakes in that
+
+ align:start position:0%
+way they don't make mistakes in that
+ 
+
+ align:start position:0%
+way they don't make mistakes in that
+maximization
+
+ align:start position:0%
+maximization
+ 
+
+ align:start position:0%
+maximization
+process so that's to say if you tell me
+
+ align:start position:0%
+process so that's to say if you tell me
+ 
+
+ align:start position:0%
+process so that's to say if you tell me
+you like apples
+
+ align:start position:0%
+you like apples
+ 
+
+ align:start position:0%
+you like apples
+over bananas uh and then you choose
+
+ align:start position:0%
+over bananas uh and then you choose
+ 
+
+ align:start position:0%
+over bananas uh and then you choose
+bananas well then you know something is
+
+ align:start position:0%
+bananas well then you know something is
+ 
+
+ align:start position:0%
+bananas well then you know something is
+sort of going wrong in some ways that we
+
+ align:start position:0%
+sort of going wrong in some ways that we
+ 
+
+ align:start position:0%
+sort of going wrong in some ways that we
+haven't fully understood it might be
+
+ align:start position:0%
+haven't fully understood it might be
+ 
+
+ align:start position:0%
+haven't fully understood it might be
+that you're sort of like just making
+
+ align:start position:0%
+that you're sort of like just making
+ 
+
+ align:start position:0%
+that you're sort of like just making
+uh mistakes that could be construed as
+
+ align:start position:0%
+uh mistakes that could be construed as
+ 
+
+ align:start position:0%
+uh mistakes that could be construed as
+uh irrational it's hard to rationalize
+
+ align:start position:0%
+uh irrational it's hard to rationalize
+ 
+
+ align:start position:0%
+uh irrational it's hard to rationalize
+with a model
+
+ align:start position:0%
+with a model
+ 
+
+ align:start position:0%
+with a model
+what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+self-interest yes so like usually in a
+
+ align:start position:0%
+self-interest yes so like usually in a
+ 
+
+ align:start position:0%
+self-interest yes so like usually in a
+lot of models um
+
+ align:start position:0%
+lot of models um
+ 
+
+ align:start position:0%
+lot of models um
+all like the sort of the the easiest
+
+ align:start position:0%
+all like the sort of the the easiest
+ 
+
+ align:start position:0%
+all like the sort of the the easiest
+models are very narrowly defined
+
+ align:start position:0%
+models are very narrowly defined
+ 
+
+ align:start position:0%
+models are very narrowly defined
+self-interest so people care about
+
+ align:start position:0%
+self-interest so people care about
+ 
+
+ align:start position:0%
+self-interest so people care about
+themselves they care about what they
+
+ align:start position:0%
+themselves they care about what they
+ 
+
+ align:start position:0%
+themselves they care about what they
+consume and not about what others
+
+ align:start position:0%
+consume and not about what others
+ 
+
+ align:start position:0%
+consume and not about what others
+consume or
+
+ align:start position:0%
+consume or
+ 
+
+ align:start position:0%
+consume or
+or or what others think of them sort of
+
+ align:start position:0%
+or or what others think of them sort of
+ 
+
+ align:start position:0%
+or or what others think of them sort of
+narrowly defined
+
+ align:start position:0%
+narrowly defined
+ 
+
+ align:start position:0%
+narrowly defined
+self-interest yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so essentially perfect self-control
+
+ align:start position:0%
+yes so essentially perfect self-control
+ 
+
+ align:start position:0%
+yes so essentially perfect self-control
+usually a sort of
+
+ align:start position:0%
+usually a sort of
+ 
+
+ align:start position:0%
+usually a sort of
+one version of putting that one version
+
+ align:start position:0%
+one version of putting that one version
+ 
+
+ align:start position:0%
+one version of putting that one version
+of putting that is in some sense sort of
+
+ align:start position:0%
+of putting that is in some sense sort of
+ 
+
+ align:start position:0%
+of putting that is in some sense sort of
+going back to what you're saying earlier
+
+ align:start position:0%
+going back to what you're saying earlier
+ 
+
+ align:start position:0%
+going back to what you're saying earlier
+sort of to say stable preferences
+
+ align:start position:0%
+sort of to say stable preferences
+ 
+
+ align:start position:0%
+sort of to say stable preferences
+if i'm telling you i'd like to exercise
+
+ align:start position:0%
+if i'm telling you i'd like to exercise
+ 
+
+ align:start position:0%
+if i'm telling you i'd like to exercise
+tomorrow and that's my preference
+
+ align:start position:0%
+tomorrow and that's my preference
+ 
+
+ align:start position:0%
+tomorrow and that's my preference
+uh tomorrow i'm not gonna sort of be
+
+ align:start position:0%
+uh tomorrow i'm not gonna sort of be
+ 
+
+ align:start position:0%
+uh tomorrow i'm not gonna sort of be
+like oh yeah actually you know i changed
+
+ align:start position:0%
+like oh yeah actually you know i changed
+ 
+
+ align:start position:0%
+like oh yeah actually you know i changed
+my mind and now i'm just watching movies
+
+ align:start position:0%
+my mind and now i'm just watching movies
+ 
+
+ align:start position:0%
+my mind and now i'm just watching movies
+or the like
+
+ align:start position:0%
+or the like
+ 
+
+ align:start position:0%
+or the like
+right so that's the version of sort of
+
+ align:start position:0%
+right so that's the version of sort of
+ 
+
+ align:start position:0%
+right so that's the version of sort of
+preferences being stable but
+
+ align:start position:0%
+preferences being stable but
+ 
+
+ align:start position:0%
+preferences being stable but
+the inherent underlying issue there is
+
+ align:start position:0%
+the inherent underlying issue there is
+ 
+
+ align:start position:0%
+the inherent underlying issue there is
+like self-control problems in the sense
+
+ align:start position:0%
+like self-control problems in the sense
+ 
+
+ align:start position:0%
+like self-control problems in the sense
+of like
+
+ align:start position:0%
+of like
+ 
+
+ align:start position:0%
+of like
+if i like certain things or make certain
+
+ align:start position:0%
+if i like certain things or make certain
+ 
+
+ align:start position:0%
+if i like certain things or make certain
+plans for the future
+
+ align:start position:0%
+plans for the future
+ 
+
+ align:start position:0%
+plans for the future
+i have the self-control to follow
+
+ align:start position:0%
+i have the self-control to follow
+ 
+
+ align:start position:0%
+i have the self-control to follow
+through on those plans that's usually an
+
+ align:start position:0%
+through on those plans that's usually an
+ 
+
+ align:start position:0%
+through on those plans that's usually an
+assumption and that
+
+ align:start position:0%
+assumption and that
+ 
+
+ align:start position:0%
+assumption and that
+then shows up as preferences being
+
+ align:start position:0%
+then shows up as preferences being
+ 
+
+ align:start position:0%
+then shows up as preferences being
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+what else yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so usually there is like a discount
+
+ align:start position:0%
+yeah so usually there is like a discount
+ 
+
+ align:start position:0%
+yeah so usually there is like a discount
+um factor in terms of like how much you
+
+ align:start position:0%
+um factor in terms of like how much you
+ 
+
+ align:start position:0%
+um factor in terms of like how much you
+uh like consumption today versus
+
+ align:start position:0%
+uh like consumption today versus
+ 
+
+ align:start position:0%
+uh like consumption today versus
+consumption tomorrow
+
+ align:start position:0%
+consumption tomorrow
+ 
+
+ align:start position:0%
+consumption tomorrow
+um that is usually in any economic model
+
+ align:start position:0%
+um that is usually in any economic model
+ 
+
+ align:start position:0%
+um that is usually in any economic model
+usually we think of like the discount
+
+ align:start position:0%
+usually we think of like the discount
+ 
+
+ align:start position:0%
+usually we think of like the discount
+factor being
+
+ align:start position:0%
+factor being
+ 
+
+ align:start position:0%
+factor being
+constant as like how you think about
+
+ align:start position:0%
+constant as like how you think about
+ 
+
+ align:start position:0%
+constant as like how you think about
+today versus tomorrow is the same
+
+ align:start position:0%
+today versus tomorrow is the same
+ 
+
+ align:start position:0%
+today versus tomorrow is the same
+as you think about today versus in two
+
+ align:start position:0%
+as you think about today versus in two
+ 
+
+ align:start position:0%
+as you think about today versus in two
+days from now or in like a year from now
+
+ align:start position:0%
+days from now or in like a year from now
+ 
+
+ align:start position:0%
+days from now or in like a year from now
+and a year and a day from now so usually
+
+ align:start position:0%
+and a year and a day from now so usually
+ 
+
+ align:start position:0%
+and a year and a day from now so usually
+there's a constant discount factor for
+
+ align:start position:0%
+there's a constant discount factor for
+ 
+
+ align:start position:0%
+there's a constant discount factor for
+the future usually
+
+ align:start position:0%
+the future usually
+ 
+
+ align:start position:0%
+the future usually
+we sort of employ economic sorry
+
+ align:start position:0%
+we sort of employ economic sorry
+ 
+
+ align:start position:0%
+we sort of employ economic sorry
+constant discounting or exponential
+
+ align:start position:0%
+constant discounting or exponential
+ 
+
+ align:start position:0%
+constant discounting or exponential
+discounting
+
+ align:start position:0%
+discounting
+ 
+
+ align:start position:0%
+discounting
+what else do we have yeah risk reverse
+
+ align:start position:0%
+what else do we have yeah risk reverse
+ 
+
+ align:start position:0%
+what else do we have yeah risk reverse
+yes risk aversion in the sense of like
+
+ align:start position:0%
+yes risk aversion in the sense of like
+ 
+
+ align:start position:0%
+yes risk aversion in the sense of like
+yes people um
+
+ align:start position:0%
+yes people um
+ 
+
+ align:start position:0%
+yes people um
+are risk-averse and people often sort of
+
+ align:start position:0%
+are risk-averse and people often sort of
+ 
+
+ align:start position:0%
+are risk-averse and people often sort of
+define their preferences over
+
+ align:start position:0%
+define their preferences over
+ 
+
+ align:start position:0%
+define their preferences over
+outcome so we have a utility function
+
+ align:start position:0%
+outcome so we have a utility function
+ 
+
+ align:start position:0%
+outcome so we have a utility function
+that we tend to concave and the utility
+
+ align:start position:0%
+that we tend to concave and the utility
+ 
+
+ align:start position:0%
+that we tend to concave and the utility
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+is and we'll get to this in a few
+
+ align:start position:0%
+is and we'll get to this in a few
+ 
+
+ align:start position:0%
+is and we'll get to this in a few
+lectures but the utility function tends
+
+ align:start position:0%
+lectures but the utility function tends
+ 
+
+ align:start position:0%
+lectures but the utility function tends
+is concave and it's defined over outcome
+
+ align:start position:0%
+is concave and it's defined over outcome
+ 
+
+ align:start position:0%
+is concave and it's defined over outcome
+as opposed to over
+
+ align:start position:0%
+as opposed to over
+ 
+
+ align:start position:0%
+as opposed to over
+changes of outcomes that shows up
+
+ align:start position:0%
+changes of outcomes that shows up
+ 
+
+ align:start position:0%
+changes of outcomes that shows up
+usually as sort of like essentially like
+
+ align:start position:0%
+usually as sort of like essentially like
+ 
+
+ align:start position:0%
+usually as sort of like essentially like
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a strictly concave utility function and
+
+ align:start position:0%
+a strictly concave utility function and
+ 
+
+ align:start position:0%
+a strictly concave utility function and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+risk aversion what about information how
+
+ align:start position:0%
+risk aversion what about information how
+ 
+
+ align:start position:0%
+risk aversion what about information how
+do people
+
+ align:start position:0%
+do people
+ 
+
+ align:start position:0%
+do people
+think about information how do they use
+
+ align:start position:0%
+think about information how do they use
+ 
+
+ align:start position:0%
+think about information how do they use
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+bayesian and what what does that mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so people essentially are
+
+ align:start position:0%
+exactly so people essentially are
+ 
+
+ align:start position:0%
+exactly so people essentially are
+perfect uh information
+
+ align:start position:0%
+perfect uh information
+ 
+
+ align:start position:0%
+perfect uh information
+processors you can call them bayesians
+
+ align:start position:0%
+processors you can call them bayesians
+ 
+
+ align:start position:0%
+processors you can call them bayesians
+but essentially it's sort of for those
+
+ align:start position:0%
+but essentially it's sort of for those
+ 
+
+ align:start position:0%
+but essentially it's sort of for those
+of you know that it's sort of the use
+
+ align:start position:0%
+of you know that it's sort of the use
+ 
+
+ align:start position:0%
+of you know that it's sort of the use
+bayes rule essentially
+
+ align:start position:0%
+bayes rule essentially
+ 
+
+ align:start position:0%
+bayes rule essentially
+which is to say uh if you gave a
+
+ align:start position:0%
+which is to say uh if you gave a
+ 
+
+ align:start position:0%
+which is to say uh if you gave a
+statistician a problem how to update
+
+ align:start position:0%
+statistician a problem how to update
+ 
+
+ align:start position:0%
+statistician a problem how to update
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+people are able to do that in their
+
+ align:start position:0%
+people are able to do that in their
+ 
+
+ align:start position:0%
+people are able to do that in their
+heads and you know that's a pretty stark
+
+ align:start position:0%
+heads and you know that's a pretty stark
+ 
+
+ align:start position:0%
+heads and you know that's a pretty stark
+assumption but essentially it's like
+
+ align:start position:0%
+assumption but essentially it's like
+ 
+
+ align:start position:0%
+assumption but essentially it's like
+when you people have certain information
+
+ align:start position:0%
+when you people have certain information
+ 
+
+ align:start position:0%
+when you people have certain information
+uh standard economics does not
+
+ align:start position:0%
+uh standard economics does not
+ 
+
+ align:start position:0%
+uh standard economics does not
+necessarily assume that everybody has
+
+ align:start position:0%
+necessarily assume that everybody has
+ 
+
+ align:start position:0%
+necessarily assume that everybody has
+full information in a sense that
+
+ align:start position:0%
+full information in a sense that
+ 
+
+ align:start position:0%
+full information in a sense that
+everybody knows everything
+
+ align:start position:0%
+everybody knows everything
+ 
+
+ align:start position:0%
+everybody knows everything
+but if you give them some information
+
+ align:start position:0%
+but if you give them some information
+ 
+
+ align:start position:0%
+but if you give them some information
+then they update
+
+ align:start position:0%
+then they update
+ 
+
+ align:start position:0%
+then they update
+their uh beliefs accordingly right so
+
+ align:start position:0%
+their uh beliefs accordingly right so
+ 
+
+ align:start position:0%
+their uh beliefs accordingly right so
+they essentially they optimally use new
+
+ align:start position:0%
+they essentially they optimally use new
+ 
+
+ align:start position:0%
+they essentially they optimally use new
+information and then form their beliefs
+
+ align:start position:0%
+information and then form their beliefs
+ 
+
+ align:start position:0%
+information and then form their beliefs
+their posterior beliefs based on having
+
+ align:start position:0%
+their posterior beliefs based on having
+ 
+
+ align:start position:0%
+their posterior beliefs based on having
+a new information and what they believed
+
+ align:start position:0%
+a new information and what they believed
+ 
+
+ align:start position:0%
+a new information and what they believed
+previously um their priors there's
+
+ align:start position:0%
+previously um their priors there's
+ 
+
+ align:start position:0%
+previously um their priors there's
+another assumption usually and i sort of
+
+ align:start position:0%
+another assumption usually and i sort of
+ 
+
+ align:start position:0%
+another assumption usually and i sort of
+can actually
+
+ align:start position:0%
+can actually
+ 
+
+ align:start position:0%
+can actually
+sort of put this out for you which is
+
+ align:start position:0%
+sort of put this out for you which is
+ 
+
+ align:start position:0%
+sort of put this out for you which is
+there's another assumption that is
+
+ align:start position:0%
+there's another assumption that is
+ 
+
+ align:start position:0%
+there's another assumption that is
+people have no taste for beliefs or
+
+ align:start position:0%
+people have no taste for beliefs or
+ 
+
+ align:start position:0%
+people have no taste for beliefs or
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+what do we mean by that we mean by that
+
+ align:start position:0%
+what do we mean by that we mean by that
+ 
+
+ align:start position:0%
+what do we mean by that we mean by that
+as essentially people use
+
+ align:start position:0%
+as essentially people use
+ 
+
+ align:start position:0%
+as essentially people use
+information only to make decisions so if
+
+ align:start position:0%
+information only to make decisions so if
+ 
+
+ align:start position:0%
+information only to make decisions so if
+you tell me something about like what's
+
+ align:start position:0%
+you tell me something about like what's
+ 
+
+ align:start position:0%
+you tell me something about like what's
+going to happen tomorrow or if you tell
+
+ align:start position:0%
+going to happen tomorrow or if you tell
+ 
+
+ align:start position:0%
+going to happen tomorrow or if you tell
+me something about
+
+ align:start position:0%
+me something about
+ 
+
+ align:start position:0%
+me something about
+my health status or the like i use that
+
+ align:start position:0%
+my health status or the like i use that
+ 
+
+ align:start position:0%
+my health status or the like i use that
+to make better decisions so if you tell
+
+ align:start position:0%
+to make better decisions so if you tell
+ 
+
+ align:start position:0%
+to make better decisions so if you tell
+me i'm sick
+
+ align:start position:0%
+me i'm sick
+ 
+
+ align:start position:0%
+me i'm sick
+i'm going to use that information to go
+
+ align:start position:0%
+i'm going to use that information to go
+ 
+
+ align:start position:0%
+i'm going to use that information to go
+to the doctor
+
+ align:start position:0%
+to the doctor
+ 
+
+ align:start position:0%
+to the doctor
+but people usually don't assume that
+
+ align:start position:0%
+but people usually don't assume that
+ 
+
+ align:start position:0%
+but people usually don't assume that
+people have certain beliefs about
+
+ align:start position:0%
+people have certain beliefs about
+ 
+
+ align:start position:0%
+people have certain beliefs about
+whether they're sick or healthy or
+
+ align:start position:0%
+whether they're sick or healthy or
+ 
+
+ align:start position:0%
+whether they're sick or healthy or
+whether they're smart or not or are they
+
+ align:start position:0%
+whether they're smart or not or are they
+ 
+
+ align:start position:0%
+whether they're smart or not or are they
+good looking or not
+
+ align:start position:0%
+good looking or not
+ 
+
+ align:start position:0%
+good looking or not
+usually the assumption is that beliefs
+
+ align:start position:0%
+usually the assumption is that beliefs
+ 
+
+ align:start position:0%
+usually the assumption is that beliefs
+are only used so information is only
+
+ align:start position:0%
+are only used so information is only
+ 
+
+ align:start position:0%
+are only used so information is only
+used to make better decisions
+
+ align:start position:0%
+used to make better decisions
+ 
+
+ align:start position:0%
+used to make better decisions
+not that people get utility from beliefs
+
+ align:start position:0%
+not that people get utility from beliefs
+ 
+
+ align:start position:0%
+not that people get utility from beliefs
+but instead you might say well i'm
+
+ align:start position:0%
+but instead you might say well i'm
+ 
+
+ align:start position:0%
+but instead you might say well i'm
+really good looking and smart
+
+ align:start position:0%
+really good looking and smart
+ 
+
+ align:start position:0%
+really good looking and smart
+and maybe smarter than you actually are
+
+ align:start position:0%
+and maybe smarter than you actually are
+ 
+
+ align:start position:0%
+and maybe smarter than you actually are
+and the reason why people might believe
+
+ align:start position:0%
+and the reason why people might believe
+ 
+
+ align:start position:0%
+and the reason why people might believe
+that is because that makes them feel
+
+ align:start position:0%
+that is because that makes them feel
+ 
+
+ align:start position:0%
+that is because that makes them feel
+good about themselves
+
+ align:start position:0%
+good about themselves
+ 
+
+ align:start position:0%
+good about themselves
+that's what they're usually an
+
+ align:start position:0%
+that's what they're usually an
+ 
+
+ align:start position:0%
+that's what they're usually an
+assumption that
+
+ align:start position:0%
+assumption that
+ 
+
+ align:start position:0%
+assumption that
+people standard economic models make
+
+ align:start position:0%
+people standard economic models make
+ 
+
+ align:start position:0%
+people standard economic models make
+i think we mentioned almost everything
+
+ align:start position:0%
+i think we mentioned almost everything
+ 
+
+ align:start position:0%
+i think we mentioned almost everything
+we sort of said bayesian information
+
+ align:start position:0%
+we sort of said bayesian information
+ 
+
+ align:start position:0%
+we sort of said bayesian information
+processor essentially
+
+ align:start position:0%
+processor essentially
+ 
+
+ align:start position:0%
+processor essentially
+processing information optimally
+
+ align:start position:0%
+processing information optimally
+ 
+
+ align:start position:0%
+processing information optimally
+well-defined and stable preferences
+
+ align:start position:0%
+well-defined and stable preferences
+ 
+
+ align:start position:0%
+well-defined and stable preferences
+maximize expected utility which is sort
+
+ align:start position:0%
+maximize expected utility which is sort
+ 
+
+ align:start position:0%
+maximize expected utility which is sort
+of like in some sense um
+
+ align:start position:0%
+of like in some sense um
+ 
+
+ align:start position:0%
+of like in some sense um
+rationality if you want apply
+
+ align:start position:0%
+rationality if you want apply
+ 
+
+ align:start position:0%
+rationality if you want apply
+exponential discount weighting
+
+ align:start position:0%
+exponential discount weighting
+ 
+
+ align:start position:0%
+exponential discount weighting
+a current and future well-being people
+
+ align:start position:0%
+a current and future well-being people
+ 
+
+ align:start position:0%
+a current and future well-being people
+are narrowly
+
+ align:start position:0%
+are narrowly
+ 
+
+ align:start position:0%
+are narrowly
+defined in terms of their self-interest
+
+ align:start position:0%
+defined in terms of their self-interest
+ 
+
+ align:start position:0%
+defined in terms of their self-interest
+and people have preferences over final
+
+ align:start position:0%
+and people have preferences over final
+ 
+
+ align:start position:0%
+and people have preferences over final
+outcomes not changes
+
+ align:start position:0%
+outcomes not changes
+ 
+
+ align:start position:0%
+outcomes not changes
+so what you care about is how the
+
+ align:start position:0%
+so what you care about is how the
+ 
+
+ align:start position:0%
+so what you care about is how the
+weather is today not kind of like how
+
+ align:start position:0%
+weather is today not kind of like how
+ 
+
+ align:start position:0%
+weather is today not kind of like how
+the weather changed between yesterday um
+
+ align:start position:0%
+the weather changed between yesterday um
+ 
+
+ align:start position:0%
+the weather changed between yesterday um
+and today or tomorrow and we'll talk
+
+ align:start position:0%
+and today or tomorrow and we'll talk
+ 
+
+ align:start position:0%
+and today or tomorrow and we'll talk
+about all of these
+
+ align:start position:0%
+about all of these
+ 
+
+ align:start position:0%
+about all of these
+by the way these are all sort of like
+
+ align:start position:0%
+by the way these are all sort of like
+ 
+
+ align:start position:0%
+by the way these are all sort of like
+some terms that seem maybe
+
+ align:start position:0%
+some terms that seem maybe
+ 
+
+ align:start position:0%
+some terms that seem maybe
+unfamiliar to you we'll talk about all
+
+ align:start position:0%
+unfamiliar to you we'll talk about all
+ 
+
+ align:start position:0%
+unfamiliar to you we'll talk about all
+of these kinds of assumptions and
+
+ align:start position:0%
+of these kinds of assumptions and
+ 
+
+ align:start position:0%
+of these kinds of assumptions and
+perhaps how to deviate from them
+
+ align:start position:0%
+perhaps how to deviate from them
+ 
+
+ align:start position:0%
+perhaps how to deviate from them
+specifically okay so now now that we
+
+ align:start position:0%
+specifically okay so now now that we
+ 
+
+ align:start position:0%
+specifically okay so now now that we
+have those
+
+ align:start position:0%
+have those
+ 
+
+ align:start position:0%
+have those
+assumptions now what kinds of deviations
+
+ align:start position:0%
+assumptions now what kinds of deviations
+ 
+
+ align:start position:0%
+assumptions now what kinds of deviations
+uh when you look into the world and sort
+
+ align:start position:0%
+uh when you look into the world and sort
+ 
+
+ align:start position:0%
+uh when you look into the world and sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+one part how you think about behavioral
+
+ align:start position:0%
+one part how you think about behavioral
+ 
+
+ align:start position:0%
+one part how you think about behavioral
+economics is uh in some sense think
+
+ align:start position:0%
+economics is uh in some sense think
+ 
+
+ align:start position:0%
+economics is uh in some sense think
+about the world and try to sort of
+
+ align:start position:0%
+about the world and try to sort of
+ 
+
+ align:start position:0%
+about the world and try to sort of
+observe what's going on in the world
+
+ align:start position:0%
+observe what's going on in the world
+ 
+
+ align:start position:0%
+observe what's going on in the world
+and try to see which assumptions might
+
+ align:start position:0%
+and try to see which assumptions might
+ 
+
+ align:start position:0%
+and try to see which assumptions might
+be violated um
+
+ align:start position:0%
+be violated um
+ 
+
+ align:start position:0%
+be violated um
+in an important way and try to sort of
+
+ align:start position:0%
+in an important way and try to sort of
+ 
+
+ align:start position:0%
+in an important way and try to sort of
+improve our models
+
+ align:start position:0%
+improve our models
+ 
+
+ align:start position:0%
+improve our models
+so when you think about the world and
+
+ align:start position:0%
+so when you think about the world and
+ 
+
+ align:start position:0%
+so when you think about the world and
+look at these assumptions can you come
+
+ align:start position:0%
+look at these assumptions can you come
+ 
+
+ align:start position:0%
+look at these assumptions can you come
+up with real world examples
+
+ align:start position:0%
+up with real world examples
+ 
+
+ align:start position:0%
+up with real world examples
+um uh that might sort of violate these
+
+ align:start position:0%
+um uh that might sort of violate these
+ 
+
+ align:start position:0%
+um uh that might sort of violate these
+assumptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um the uh the last assumption
+
+ align:start position:0%
+yes um the uh the last assumption
+ 
+
+ align:start position:0%
+yes um the uh the last assumption
+that you listed uh the one
+
+ align:start position:0%
+that you listed uh the one
+ 
+
+ align:start position:0%
+that you listed uh the one
+beliefs or information is violated on a
+
+ align:start position:0%
+beliefs or information is violated on a
+ 
+
+ align:start position:0%
+beliefs or information is violated on a
+constant basis people
+
+ align:start position:0%
+constant basis people
+ 
+
+ align:start position:0%
+constant basis people
+tend to believe what they want to
+
+ align:start position:0%
+tend to believe what they want to
+ 
+
+ align:start position:0%
+tend to believe what they want to
+believe and you have an example specific
+
+ align:start position:0%
+believe and you have an example specific
+ 
+
+ align:start position:0%
+believe and you have an example specific
+um this is very common as regards like
+
+ align:start position:0%
+um this is very common as regards like
+ 
+
+ align:start position:0%
+um this is very common as regards like
+political matters i'm not gonna name
+
+ align:start position:0%
+political matters i'm not gonna name
+ 
+
+ align:start position:0%
+political matters i'm not gonna name
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obvious reasons but uh like people
+
+ align:start position:0%
+obvious reasons but uh like people
+ 
+
+ align:start position:0%
+obvious reasons but uh like people
+like often like choose to discount
+
+ align:start position:0%
+like often like choose to discount
+ 
+
+ align:start position:0%
+like often like choose to discount
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+that goes against their belief right um
+
+ align:start position:0%
+that goes against their belief right um
+ 
+
+ align:start position:0%
+that goes against their belief right um
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+um so one reason could be and there's uh
+
+ align:start position:0%
+um so one reason could be and there's uh
+ 
+
+ align:start position:0%
+um so one reason could be and there's uh
+quite a bit of work recently we'll talk
+
+ align:start position:0%
+quite a bit of work recently we'll talk
+ 
+
+ align:start position:0%
+quite a bit of work recently we'll talk
+a little bit about this in this class
+
+ align:start position:0%
+a little bit about this in this class
+ 
+
+ align:start position:0%
+a little bit about this in this class
+about sort of
+
+ align:start position:0%
+about sort of
+ 
+
+ align:start position:0%
+about sort of
+how political beliefs or other reasons
+
+ align:start position:0%
+how political beliefs or other reasons
+ 
+
+ align:start position:0%
+how political beliefs or other reasons
+why people might be
+
+ align:start position:0%
+why people might be
+ 
+
+ align:start position:0%
+why people might be
+motivated to believe certain things one
+
+ align:start position:0%
+motivated to believe certain things one
+ 
+
+ align:start position:0%
+motivated to believe certain things one
+clear example would be sort of climate
+
+ align:start position:0%
+clear example would be sort of climate
+ 
+
+ align:start position:0%
+clear example would be sort of climate
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+not just because of political reason
+
+ align:start position:0%
+not just because of political reason
+ 
+
+ align:start position:0%
+not just because of political reason
+there's some interesting work about like
+
+ align:start position:0%
+there's some interesting work about like
+ 
+
+ align:start position:0%
+there's some interesting work about like
+when people live in flood areas for
+
+ align:start position:0%
+when people live in flood areas for
+ 
+
+ align:start position:0%
+when people live in flood areas for
+example what do they think about climate
+
+ align:start position:0%
+example what do they think about climate
+ 
+
+ align:start position:0%
+example what do they think about climate
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+and sort of you might sort of say well
+
+ align:start position:0%
+and sort of you might sort of say well
+ 
+
+ align:start position:0%
+and sort of you might sort of say well
+if you really uh live in an area that's
+
+ align:start position:0%
+if you really uh live in an area that's
+ 
+
+ align:start position:0%
+if you really uh live in an area that's
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+affected by floods you might really want
+
+ align:start position:0%
+affected by floods you might really want
+ 
+
+ align:start position:0%
+affected by floods you might really want
+to know about climate change and know
+
+ align:start position:0%
+to know about climate change and know
+ 
+
+ align:start position:0%
+to know about climate change and know
+what's going on and really try to inform
+
+ align:start position:0%
+what's going on and really try to inform
+ 
+
+ align:start position:0%
+what's going on and really try to inform
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+but what people tend to do is sort of
+
+ align:start position:0%
+but what people tend to do is sort of
+ 
+
+ align:start position:0%
+but what people tend to do is sort of
+try to ignore the issue and try to sort
+
+ align:start position:0%
+try to ignore the issue and try to sort
+ 
+
+ align:start position:0%
+try to ignore the issue and try to sort
+of be happy
+
+ align:start position:0%
+of be happy
+ 
+
+ align:start position:0%
+of be happy
+as long as sort of uh nothing happens
+
+ align:start position:0%
+as long as sort of uh nothing happens
+ 
+
+ align:start position:0%
+as long as sort of uh nothing happens
+now that's one example yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um so purposes might not be well
+
+ align:start position:0%
+yes um so purposes might not be well
+ 
+
+ align:start position:0%
+yes um so purposes might not be well
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+so say like if i have a decision on what
+
+ align:start position:0%
+so say like if i have a decision on what
+ 
+
+ align:start position:0%
+so say like if i have a decision on what
+i want to eat
+
+ align:start position:0%
+i want to eat
+ 
+
+ align:start position:0%
+i want to eat
+i want to eat like steak over chicken if
+
+ align:start position:0%
+i want to eat like steak over chicken if
+ 
+
+ align:start position:0%
+i want to eat like steak over chicken if
+i'm presented with the opportunity
+
+ align:start position:0%
+i'm presented with the opportunity
+ 
+
+ align:start position:0%
+i'm presented with the opportunity
+but i prefer chicken or pork
+
+ align:start position:0%
+but i prefer chicken or pork
+ 
+
+ align:start position:0%
+but i prefer chicken or pork
+but i might also prefer poor purple
+
+ align:start position:0%
+but i might also prefer poor purple
+ 
+
+ align:start position:0%
+but i might also prefer poor purple
+steak right so it's not always
+
+ align:start position:0%
+steak right so it's not always
+ 
+
+ align:start position:0%
+steak right so it's not always
+well defined right so one part that
+
+ align:start position:0%
+well defined right so one part that
+ 
+
+ align:start position:0%
+well defined right so one part that
+you're telling is like essentially so
+
+ align:start position:0%
+you're telling is like essentially so
+ 
+
+ align:start position:0%
+you're telling is like essentially so
+one one part might be it's might not
+
+ align:start position:0%
+one one part might be it's might not
+ 
+
+ align:start position:0%
+one one part might be it's might not
+just be well-defined
+
+ align:start position:0%
+just be well-defined
+ 
+
+ align:start position:0%
+just be well-defined
+there's other issues like for example
+
+ align:start position:0%
+there's other issues like for example
+ 
+
+ align:start position:0%
+there's other issues like for example
+that irrelevant other autism assumption
+
+ align:start position:0%
+that irrelevant other autism assumption
+ 
+
+ align:start position:0%
+that irrelevant other autism assumption
+economics usually is to say if you
+
+ align:start position:0%
+economics usually is to say if you
+ 
+
+ align:start position:0%
+economics usually is to say if you
+choose between a and b
+
+ align:start position:0%
+choose between a and b
+ 
+
+ align:start position:0%
+choose between a and b
+the availability of seed should not
+
+ align:start position:0%
+the availability of seed should not
+ 
+
+ align:start position:0%
+the availability of seed should not
+matter for your choice between a
+
+ align:start position:0%
+matter for your choice between a
+ 
+
+ align:start position:0%
+matter for your choice between a
+and b but often that's not the case
+
+ align:start position:0%
+and b but often that's not the case
+ 
+
+ align:start position:0%
+and b but often that's not the case
+right so if i offer you apples and
+
+ align:start position:0%
+right so if i offer you apples and
+ 
+
+ align:start position:0%
+right so if i offer you apples and
+bananas and you also can get cherries
+
+ align:start position:0%
+bananas and you also can get cherries
+ 
+
+ align:start position:0%
+bananas and you also can get cherries
+now suddenly your choice between apples
+
+ align:start position:0%
+now suddenly your choice between apples
+ 
+
+ align:start position:0%
+now suddenly your choice between apples
+and bananas might change
+
+ align:start position:0%
+and bananas might change
+ 
+
+ align:start position:0%
+and bananas might change
+even if you can't get the cherries like
+
+ align:start position:0%
+even if you can't get the cherries like
+ 
+
+ align:start position:0%
+even if you can't get the cherries like
+if i even if you don't choose the
+
+ align:start position:0%
+if i even if you don't choose the
+ 
+
+ align:start position:0%
+if i even if you don't choose the
+cherries um
+
+ align:start position:0%
+cherries um
+ 
+
+ align:start position:0%
+cherries um
+eventually so exactly so like there
+
+ align:start position:0%
+eventually so exactly so like there
+ 
+
+ align:start position:0%
+eventually so exactly so like there
+might be sort of people's preferences
+
+ align:start position:0%
+might be sort of people's preferences
+ 
+
+ align:start position:0%
+might be sort of people's preferences
+might not be
+
+ align:start position:0%
+might not be
+ 
+
+ align:start position:0%
+might not be
+uh well defined they might also not be
+
+ align:start position:0%
+uh well defined they might also not be
+ 
+
+ align:start position:0%
+uh well defined they might also not be
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+any other example yes um also for the
+
+ align:start position:0%
+any other example yes um also for the
+ 
+
+ align:start position:0%
+any other example yes um also for the
+well-defined preferences like we have
+
+ align:start position:0%
+well-defined preferences like we have
+ 
+
+ align:start position:0%
+well-defined preferences like we have
+information processing constraints if
+
+ align:start position:0%
+information processing constraints if
+ 
+
+ align:start position:0%
+information processing constraints if
+i'm given a menu
+
+ align:start position:0%
+i'm given a menu
+ 
+
+ align:start position:0%
+i'm given a menu
+of 100 choices it's going to be
+
+ align:start position:0%
+of 100 choices it's going to be
+ 
+
+ align:start position:0%
+of 100 choices it's going to be
+difficult for me to
+
+ align:start position:0%
+difficult for me to
+ 
+
+ align:start position:0%
+difficult for me to
+know which one right exactly so the
+
+ align:start position:0%
+know which one right exactly so the
+ 
+
+ align:start position:0%
+know which one right exactly so the
+the people have lots of information
+
+ align:start position:0%
+the people have lots of information
+ 
+
+ align:start position:0%
+the people have lots of information
+around themselves and like if you think
+
+ align:start position:0%
+around themselves and like if you think
+ 
+
+ align:start position:0%
+around themselves and like if you think
+about like
+
+ align:start position:0%
+about like
+ 
+
+ align:start position:0%
+about like
+to process that information if you go to
+
+ align:start position:0%
+to process that information if you go to
+ 
+
+ align:start position:0%
+to process that information if you go to
+a supermarket it's impossible to know
+
+ align:start position:0%
+a supermarket it's impossible to know
+ 
+
+ align:start position:0%
+a supermarket it's impossible to know
+uh all the prices all the goods and make
+
+ align:start position:0%
+uh all the prices all the goods and make
+ 
+
+ align:start position:0%
+uh all the prices all the goods and make
+all these choices so in some sense we're
+
+ align:start position:0%
+all these choices so in some sense we're
+ 
+
+ align:start position:0%
+all these choices so in some sense we're
+like there's an abundance of
+
+ align:start position:0%
+like there's an abundance of
+ 
+
+ align:start position:0%
+like there's an abundance of
+information everywhere and you know we
+
+ align:start position:0%
+information everywhere and you know we
+ 
+
+ align:start position:0%
+information everywhere and you know we
+have to sort of figure out how to how to
+
+ align:start position:0%
+have to sort of figure out how to how to
+ 
+
+ align:start position:0%
+have to sort of figure out how to how to
+deal with
+
+ align:start position:0%
+deal with
+ 
+
+ align:start position:0%
+deal with
+with that any other example yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right exactly so one part is to say
+
+ align:start position:0%
+right exactly so one part is to say
+ 
+
+ align:start position:0%
+right exactly so one part is to say
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+um have preferences of a final outcome
+
+ align:start position:0%
+um have preferences of a final outcome
+ 
+
+ align:start position:0%
+um have preferences of a final outcome
+not changes which would just say
+
+ align:start position:0%
+not changes which would just say
+ 
+
+ align:start position:0%
+not changes which would just say
+uh you know you might feel about the
+
+ align:start position:0%
+uh you know you might feel about the
+ 
+
+ align:start position:0%
+uh you know you might feel about the
+weather in certain ways
+
+ align:start position:0%
+weather in certain ways
+ 
+
+ align:start position:0%
+weather in certain ways
+uh um you know depending on like how the
+
+ align:start position:0%
+uh um you know depending on like how the
+ 
+
+ align:start position:0%
+uh um you know depending on like how the
+weather was yesterday
+
+ align:start position:0%
+weather was yesterday
+ 
+
+ align:start position:0%
+weather was yesterday
+another version of that would be like
+
+ align:start position:0%
+another version of that would be like
+ 
+
+ align:start position:0%
+another version of that would be like
+you evaluate your
+
+ align:start position:0%
+you evaluate your
+ 
+
+ align:start position:0%
+you evaluate your
+the outcomes that you get based on your
+
+ align:start position:0%
+the outcomes that you get based on your
+ 
+
+ align:start position:0%
+the outcomes that you get based on your
+expectations and sort of if you thought
+
+ align:start position:0%
+expectations and sort of if you thought
+ 
+
+ align:start position:0%
+expectations and sort of if you thought
+you know today is going to be really
+
+ align:start position:0%
+you know today is going to be really
+ 
+
+ align:start position:0%
+you know today is going to be really
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+uh or you know today is something that
+
+ align:start position:0%
+uh or you know today is something that
+ 
+
+ align:start position:0%
+uh or you know today is something that
+your day is going to be really good but
+
+ align:start position:0%
+your day is going to be really good but
+ 
+
+ align:start position:0%
+your day is going to be really good but
+then it happened to be not as good for
+
+ align:start position:0%
+then it happened to be not as good for
+ 
+
+ align:start position:0%
+then it happened to be not as good for
+whatever reason the weather is bad
+
+ align:start position:0%
+whatever reason the weather is bad
+ 
+
+ align:start position:0%
+whatever reason the weather is bad
+or you know something bad happened to
+
+ align:start position:0%
+or you know something bad happened to
+ 
+
+ align:start position:0%
+or you know something bad happened to
+you today the typical assumption would
+
+ align:start position:0%
+you today the typical assumption would
+ 
+
+ align:start position:0%
+you today the typical assumption would
+be to say well
+
+ align:start position:0%
+be to say well
+ 
+
+ align:start position:0%
+be to say well
+um you should just evaluate the final
+
+ align:start position:0%
+um you should just evaluate the final
+ 
+
+ align:start position:0%
+um you should just evaluate the final
+outcome it shouldn't matter what you
+
+ align:start position:0%
+outcome it shouldn't matter what you
+ 
+
+ align:start position:0%
+outcome it shouldn't matter what you
+thought about previously would what
+
+ align:start position:0%
+thought about previously would what
+ 
+
+ align:start position:0%
+thought about previously would what
+might happen
+
+ align:start position:0%
+might happen
+ 
+
+ align:start position:0%
+might happen
+you're going to look at like what
+
+ align:start position:0%
+you're going to look at like what
+ 
+
+ align:start position:0%
+you're going to look at like what
+happens at the end and that's how you
+
+ align:start position:0%
+happens at the end and that's how you
+ 
+
+ align:start position:0%
+happens at the end and that's how you
+evaluate your
+
+ align:start position:0%
+evaluate your
+ 
+
+ align:start position:0%
+evaluate your
+uh your well-being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um you might need a commitment
+
+ align:start position:0%
+yes um you might need a commitment
+ 
+
+ align:start position:0%
+yes um you might need a commitment
+device
+
+ align:start position:0%
+device
+ 
+
+ align:start position:0%
+device
+so that you don't uh like you might
+
+ align:start position:0%
+so that you don't uh like you might
+ 
+
+ align:start position:0%
+so that you don't uh like you might
+avoid buying
+
+ align:start position:0%
+avoid buying
+ 
+
+ align:start position:0%
+avoid buying
+potato chips because you think you'll
+
+ align:start position:0%
+potato chips because you think you'll
+ 
+
+ align:start position:0%
+potato chips because you think you'll
+eat them that doesn't really make sense
+
+ align:start position:0%
+eat them that doesn't really make sense
+ 
+
+ align:start position:0%
+eat them that doesn't really make sense
+right so people might on purpose
+
+ align:start position:0%
+right so people might on purpose
+ 
+
+ align:start position:0%
+right so people might on purpose
+restrict their choices in certain ways
+
+ align:start position:0%
+restrict their choices in certain ways
+ 
+
+ align:start position:0%
+restrict their choices in certain ways
+right so you might sort of um and this
+
+ align:start position:0%
+right so you might sort of um and this
+ 
+
+ align:start position:0%
+right so you might sort of um and this
+is what gets me eventually to the
+
+ align:start position:0%
+is what gets me eventually to the
+ 
+
+ align:start position:0%
+is what gets me eventually to the
+laptop policy but people might sort of
+
+ align:start position:0%
+laptop policy but people might sort of
+ 
+
+ align:start position:0%
+laptop policy but people might sort of
+essentially know that in the future they
+
+ align:start position:0%
+essentially know that in the future they
+ 
+
+ align:start position:0%
+essentially know that in the future they
+make certain choices
+
+ align:start position:0%
+make certain choices
+ 
+
+ align:start position:0%
+make certain choices
+you might um for example
+
+ align:start position:0%
+you might um for example
+ 
+
+ align:start position:0%
+you might um for example
+in the laptop case you might say i'm
+
+ align:start position:0%
+in the laptop case you might say i'm
+ 
+
+ align:start position:0%
+in the laptop case you might say i'm
+gonna use a laptop in class
+
+ align:start position:0%
+gonna use a laptop in class
+ 
+
+ align:start position:0%
+gonna use a laptop in class
+with all the best intentions to taking
+
+ align:start position:0%
+with all the best intentions to taking
+ 
+
+ align:start position:0%
+with all the best intentions to taking
+notes and uh paying attention
+
+ align:start position:0%
+notes and uh paying attention
+ 
+
+ align:start position:0%
+notes and uh paying attention
+but you know at the end of the day you
+
+ align:start position:0%
+but you know at the end of the day you
+ 
+
+ align:start position:0%
+but you know at the end of the day you
+know you're gonna like watch the
+
+ align:start position:0%
+know you're gonna like watch the
+ 
+
+ align:start position:0%
+know you're gonna like watch the
+football review from yesterday or
+
+ align:start position:0%
+football review from yesterday or
+ 
+
+ align:start position:0%
+football review from yesterday or
+whatever other stuff comes up you're
+
+ align:start position:0%
+whatever other stuff comes up you're
+ 
+
+ align:start position:0%
+whatever other stuff comes up you're
+going to chat with your friends and so
+
+ align:start position:0%
+going to chat with your friends and so
+ 
+
+ align:start position:0%
+going to chat with your friends and so
+on and so forth
+
+ align:start position:0%
+on and so forth
+ 
+
+ align:start position:0%
+on and so forth
+so now in some sense if you're
+
+ align:start position:0%
+so now in some sense if you're
+ 
+
+ align:start position:0%
+so now in some sense if you're
+sophisticated as in like if you know
+
+ align:start position:0%
+sophisticated as in like if you know
+ 
+
+ align:start position:0%
+sophisticated as in like if you know
+um what you're going to do in case you
+
+ align:start position:0%
+um what you're going to do in case you
+ 
+
+ align:start position:0%
+um what you're going to do in case you
+sort of make certain choices
+
+ align:start position:0%
+sort of make certain choices
+ 
+
+ align:start position:0%
+sort of make certain choices
+you might say i choose not to even allow
+
+ align:start position:0%
+you might say i choose not to even allow
+ 
+
+ align:start position:0%
+you might say i choose not to even allow
+myself to use a laptop
+
+ align:start position:0%
+myself to use a laptop
+ 
+
+ align:start position:0%
+myself to use a laptop
+at all the reason being because i know
+
+ align:start position:0%
+at all the reason being because i know
+ 
+
+ align:start position:0%
+at all the reason being because i know
+that essentially
+
+ align:start position:0%
+that essentially
+ 
+
+ align:start position:0%
+that essentially
+i'm going to misbehave in the future and
+
+ align:start position:0%
+i'm going to misbehave in the future and
+ 
+
+ align:start position:0%
+i'm going to misbehave in the future and
+that's sort of we'll talk about this um
+
+ align:start position:0%
+that's sort of we'll talk about this um
+ 
+
+ align:start position:0%
+that's sort of we'll talk about this um
+soon i think in lecture three or four
+
+ align:start position:0%
+soon i think in lecture three or four
+ 
+
+ align:start position:0%
+soon i think in lecture three or four
+which is essentially people's demand for
+
+ align:start position:0%
+which is essentially people's demand for
+ 
+
+ align:start position:0%
+which is essentially people's demand for
+commitment as we call it which is to say
+
+ align:start position:0%
+commitment as we call it which is to say
+ 
+
+ align:start position:0%
+commitment as we call it which is to say
+people have demand for restricting their
+
+ align:start position:0%
+people have demand for restricting their
+ 
+
+ align:start position:0%
+people have demand for restricting their
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+and in any neoclassical model does this
+
+ align:start position:0%
+and in any neoclassical model does this
+ 
+
+ align:start position:0%
+and in any neoclassical model does this
+make any sense because like you're going
+
+ align:start position:0%
+make any sense because like you're going
+ 
+
+ align:start position:0%
+make any sense because like you're going
+to choose optimally anyway and then you
+
+ align:start position:0%
+to choose optimally anyway and then you
+ 
+
+ align:start position:0%
+to choose optimally anyway and then you
+need to make
+
+ align:start position:0%
+need to make
+ 
+
+ align:start position:0%
+need to make
+the best choice for yourself in any case
+
+ align:start position:0%
+the best choice for yourself in any case
+ 
+
+ align:start position:0%
+the best choice for yourself in any case
+that's an assumption so why would you
+
+ align:start position:0%
+that's an assumption so why would you
+ 
+
+ align:start position:0%
+that's an assumption so why would you
+ever sort of shut down certain choices
+
+ align:start position:0%
+ever sort of shut down certain choices
+ 
+
+ align:start position:0%
+ever sort of shut down certain choices
+because for example in an emergency or
+
+ align:start position:0%
+because for example in an emergency or
+ 
+
+ align:start position:0%
+because for example in an emergency or
+there might be something really
+
+ align:start position:0%
+there might be something really
+ 
+
+ align:start position:0%
+there might be something really
+important coming up in class
+
+ align:start position:0%
+important coming up in class
+ 
+
+ align:start position:0%
+important coming up in class
+where you might want to use your laptop
+
+ align:start position:0%
+where you might want to use your laptop
+ 
+
+ align:start position:0%
+where you might want to use your laptop
+regardless of what's happening uh why
+
+ align:start position:0%
+regardless of what's happening uh why
+ 
+
+ align:start position:0%
+regardless of what's happening uh why
+would you shut that
+
+ align:start position:0%
+would you shut that
+ 
+
+ align:start position:0%
+would you shut that
+uh down exactly so demand for commitment
+
+ align:start position:0%
+uh down exactly so demand for commitment
+ 
+
+ align:start position:0%
+uh down exactly so demand for commitment
+is is is another example
+
+ align:start position:0%
+is is is another example
+ 
+
+ align:start position:0%
+is is is another example
+uh yes people are also not
+
+ align:start position:0%
+uh yes people are also not
+ 
+
+ align:start position:0%
+uh yes people are also not
+like anywhere near perfect uh invasion
+
+ align:start position:0%
+like anywhere near perfect uh invasion
+ 
+
+ align:start position:0%
+like anywhere near perfect uh invasion
+information processors either
+
+ align:start position:0%
+information processors either
+ 
+
+ align:start position:0%
+information processors either
+we are as a general rule
+
+ align:start position:0%
+we are as a general rule
+ 
+
+ align:start position:0%
+we are as a general rule
+people are pretty bad at uh
+
+ align:start position:0%
+people are pretty bad at uh
+ 
+
+ align:start position:0%
+people are pretty bad at uh
+updating their um you know
+
+ align:start position:0%
+updating their um you know
+ 
+
+ align:start position:0%
+updating their um you know
+their their beliefs based on new
+
+ align:start position:0%
+their their beliefs based on new
+ 
+
+ align:start position:0%
+their their beliefs based on new
+information and we frequently traffic
+
+ align:start position:0%
+information and we frequently traffic
+ 
+
+ align:start position:0%
+information and we frequently traffic
+in 100 and zero percent certainties
+
+ align:start position:0%
+in 100 and zero percent certainties
+ 
+
+ align:start position:0%
+in 100 and zero percent certainties
+like very often which um you know
+
+ align:start position:0%
+like very often which um you know
+ 
+
+ align:start position:0%
+like very often which um you know
+far more often than like what you would
+
+ align:start position:0%
+far more often than like what you would
+ 
+
+ align:start position:0%
+far more often than like what you would
+um expect from
+
+ align:start position:0%
+um expect from
+ 
+
+ align:start position:0%
+um expect from
+an invasion information right
+
+ align:start position:0%
+an invasion information right
+ 
+
+ align:start position:0%
+an invasion information right
+exactly so you know uh one summary of
+
+ align:start position:0%
+exactly so you know uh one summary of
+ 
+
+ align:start position:0%
+exactly so you know uh one summary of
+that is to say bayes rule a lot of this
+
+ align:start position:0%
+that is to say bayes rule a lot of this
+ 
+
+ align:start position:0%
+that is to say bayes rule a lot of this
+sort of updating uh behavior is really
+
+ align:start position:0%
+sort of updating uh behavior is really
+ 
+
+ align:start position:0%
+sort of updating uh behavior is really
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+it's actually tough to do um and for
+
+ align:start position:0%
+it's actually tough to do um and for
+ 
+
+ align:start position:0%
+it's actually tough to do um and for
+those of you who do statistics math etc
+
+ align:start position:0%
+those of you who do statistics math etc
+ 
+
+ align:start position:0%
+those of you who do statistics math etc
+you might be able to do that very well
+
+ align:start position:0%
+you might be able to do that very well
+ 
+
+ align:start position:0%
+you might be able to do that very well
+but in way you're like a very small
+
+ align:start position:0%
+but in way you're like a very small
+ 
+
+ align:start position:0%
+but in way you're like a very small
+share of the population
+
+ align:start position:0%
+share of the population
+ 
+
+ align:start position:0%
+share of the population
+who actually uh uh does that well
+
+ align:start position:0%
+who actually uh uh does that well
+ 
+
+ align:start position:0%
+who actually uh uh does that well
+but even among those you know there's a
+
+ align:start position:0%
+but even among those you know there's a
+ 
+
+ align:start position:0%
+but even among those you know there's a
+bunch of
+
+ align:start position:0%
+bunch of
+ 
+
+ align:start position:0%
+bunch of
+stuff that's really hard to compute in
+
+ align:start position:0%
+stuff that's really hard to compute in
+ 
+
+ align:start position:0%
+stuff that's really hard to compute in
+your head uh you might be able to write
+
+ align:start position:0%
+your head uh you might be able to write
+ 
+
+ align:start position:0%
+your head uh you might be able to write
+it down and figure it out eventually
+
+ align:start position:0%
+it down and figure it out eventually
+ 
+
+ align:start position:0%
+it down and figure it out eventually
+but usually the assumption is that
+
+ align:start position:0%
+but usually the assumption is that
+ 
+
+ align:start position:0%
+but usually the assumption is that
+people just do all of this stuff in
+
+ align:start position:0%
+people just do all of this stuff in
+ 
+
+ align:start position:0%
+people just do all of this stuff in
+their heads and really complicated
+
+ align:start position:0%
+their heads and really complicated
+ 
+
+ align:start position:0%
+their heads and really complicated
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+and you know that's that's sort of
+
+ align:start position:0%
+and you know that's that's sort of
+ 
+
+ align:start position:0%
+and you know that's that's sort of
+clearly not the case in many situations
+
+ align:start position:0%
+clearly not the case in many situations
+ 
+
+ align:start position:0%
+clearly not the case in many situations
+and then of course like um uh that's
+
+ align:start position:0%
+and then of course like um uh that's
+ 
+
+ align:start position:0%
+and then of course like um uh that's
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+one part of that sort of among mit
+
+ align:start position:0%
+one part of that sort of among mit
+ 
+
+ align:start position:0%
+one part of that sort of among mit
+students uh but then you know
+
+ align:start position:0%
+students uh but then you know
+ 
+
+ align:start position:0%
+students uh but then you know
+um there's other populations that are um
+
+ align:start position:0%
+um there's other populations that are um
+ 
+
+ align:start position:0%
+um there's other populations that are um
+uh less educated they might not even
+
+ align:start position:0%
+uh less educated they might not even
+ 
+
+ align:start position:0%
+uh less educated they might not even
+know what bayes rule is
+
+ align:start position:0%
+know what bayes rule is
+ 
+
+ align:start position:0%
+know what bayes rule is
+uh uh they might be illiterate and so on
+
+ align:start position:0%
+uh uh they might be illiterate and so on
+ 
+
+ align:start position:0%
+uh uh they might be illiterate and so on
+and so forth so is there the assumption
+
+ align:start position:0%
+and so forth so is there the assumption
+ 
+
+ align:start position:0%
+and so forth so is there the assumption
+of like
+
+ align:start position:0%
+of like
+ 
+
+ align:start position:0%
+of like
+people's perfectly processing
+
+ align:start position:0%
+people's perfectly processing
+ 
+
+ align:start position:0%
+people's perfectly processing
+information is even perhaps more
+
+ align:start position:0%
+information is even perhaps more
+ 
+
+ align:start position:0%
+information is even perhaps more
+um um uh you know 10 years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so there's two parts to that
+
+ align:start position:0%
+right so there's two parts to that
+ 
+
+ align:start position:0%
+right so there's two parts to that
+there's essentially people
+
+ align:start position:0%
+there's essentially people
+ 
+
+ align:start position:0%
+there's essentially people
+uh this is essentially the assumption of
+
+ align:start position:0%
+uh this is essentially the assumption of
+ 
+
+ align:start position:0%
+uh this is essentially the assumption of
+narrowly defined self-interest people
+
+ align:start position:0%
+narrowly defined self-interest people
+ 
+
+ align:start position:0%
+narrowly defined self-interest people
+caring only about themselves of their
+
+ align:start position:0%
+caring only about themselves of their
+ 
+
+ align:start position:0%
+caring only about themselves of their
+own consumption
+
+ align:start position:0%
+own consumption
+ 
+
+ align:start position:0%
+own consumption
+so there's two parts to that one is you
+
+ align:start position:0%
+so there's two parts to that one is you
+ 
+
+ align:start position:0%
+so there's two parts to that one is you
+might care about your friends you might
+
+ align:start position:0%
+might care about your friends you might
+ 
+
+ align:start position:0%
+might care about your friends you might
+give money to your friends you might
+
+ align:start position:0%
+give money to your friends you might
+ 
+
+ align:start position:0%
+give money to your friends you might
+sort of help them out you might help
+
+ align:start position:0%
+sort of help them out you might help
+ 
+
+ align:start position:0%
+sort of help them out you might help
+them with homework you might help them
+
+ align:start position:0%
+them with homework you might help them
+ 
+
+ align:start position:0%
+them with homework you might help them
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh you know any other situations you
+
+ align:start position:0%
+uh you know any other situations you
+ 
+
+ align:start position:0%
+uh you know any other situations you
+might send money to charity and so on
+
+ align:start position:0%
+might send money to charity and so on
+ 
+
+ align:start position:0%
+might send money to charity and so on
+and so forth this is kind of like
+
+ align:start position:0%
+and so forth this is kind of like
+ 
+
+ align:start position:0%
+and so forth this is kind of like
+you care about other people like the
+
+ align:start position:0%
+you care about other people like the
+ 
+
+ align:start position:0%
+you care about other people like the
+well-being of other people is in your
+
+ align:start position:0%
+well-being of other people is in your
+ 
+
+ align:start position:0%
+well-being of other people is in your
+utility function one way or the other
+
+ align:start position:0%
+utility function one way or the other
+ 
+
+ align:start position:0%
+utility function one way or the other
+the second part is what you uh uh
+
+ align:start position:0%
+the second part is what you uh uh
+ 
+
+ align:start position:0%
+the second part is what you uh uh
+already uh
+
+ align:start position:0%
+already uh
+ 
+
+ align:start position:0%
+already uh
+discuss as well which is kind of like
+
+ align:start position:0%
+discuss as well which is kind of like
+ 
+
+ align:start position:0%
+discuss as well which is kind of like
+social influences call it which is
+
+ align:start position:0%
+social influences call it which is
+ 
+
+ align:start position:0%
+social influences call it which is
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+peer effects you care a lot about what
+
+ align:start position:0%
+peer effects you care a lot about what
+ 
+
+ align:start position:0%
+peer effects you care a lot about what
+other people think about you
+
+ align:start position:0%
+other people think about you
+ 
+
+ align:start position:0%
+other people think about you
+you care a lot about what other people
+
+ align:start position:0%
+you care a lot about what other people
+ 
+
+ align:start position:0%
+you care a lot about what other people
+do people get jealous
+
+ align:start position:0%
+do people get jealous
+ 
+
+ align:start position:0%
+do people get jealous
+people get angry people get envious and
+
+ align:start position:0%
+people get angry people get envious and
+ 
+
+ align:start position:0%
+people get angry people get envious and
+sort of their behavior about what they
+
+ align:start position:0%
+sort of their behavior about what they
+ 
+
+ align:start position:0%
+sort of their behavior about what they
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+at the end of the day is very um
+
+ align:start position:0%
+at the end of the day is very um
+ 
+
+ align:start position:0%
+at the end of the day is very um
+volatile or malleable essentially based
+
+ align:start position:0%
+volatile or malleable essentially based
+ 
+
+ align:start position:0%
+volatile or malleable essentially based
+on uh influences from others
+
+ align:start position:0%
+on uh influences from others
+ 
+
+ align:start position:0%
+on uh influences from others
+right and that might sort of show up uh
+
+ align:start position:0%
+right and that might sort of show up uh
+ 
+
+ align:start position:0%
+right and that might sort of show up uh
+in all sorts of ways
+
+ align:start position:0%
+in all sorts of ways
+ 
+
+ align:start position:0%
+in all sorts of ways
+including in terms of like peer effects
+
+ align:start position:0%
+including in terms of like peer effects
+ 
+
+ align:start position:0%
+including in terms of like peer effects
+um people do all sorts of things because
+
+ align:start position:0%
+um people do all sorts of things because
+ 
+
+ align:start position:0%
+um people do all sorts of things because
+other people think
+
+ align:start position:0%
+other people think
+ 
+
+ align:start position:0%
+other people think
+that's cool but it's not necessarily
+
+ align:start position:0%
+that's cool but it's not necessarily
+ 
+
+ align:start position:0%
+that's cool but it's not necessarily
+what's best for
+
+ align:start position:0%
+what's best for
+ 
+
+ align:start position:0%
+what's best for
+them if they had to choose on their own
+
+ align:start position:0%
+them if they had to choose on their own
+ 
+
+ align:start position:0%
+them if they had to choose on their own
+okay great so let me stop here there's a
+
+ align:start position:0%
+okay great so let me stop here there's a
+ 
+
+ align:start position:0%
+okay great so let me stop here there's a
+lot of other examples that we can come
+
+ align:start position:0%
+lot of other examples that we can come
+ 
+
+ align:start position:0%
+lot of other examples that we can come
+up with
+
+ align:start position:0%
+up with
+ 
+
+ align:start position:0%
+up with
+i have a few here so one is sort of
+
+ align:start position:0%
+i have a few here so one is sort of
+ 
+
+ align:start position:0%
+i have a few here so one is sort of
+limited self-control that's one of my
+
+ align:start position:0%
+limited self-control that's one of my
+ 
+
+ align:start position:0%
+limited self-control that's one of my
+favorite pictures about
+
+ align:start position:0%
+favorite pictures about
+ 
+
+ align:start position:0%
+favorite pictures about
+a gym attendance where you say well uh
+
+ align:start position:0%
+a gym attendance where you say well uh
+ 
+
+ align:start position:0%
+a gym attendance where you say well uh
+you know they seem to be people have
+
+ align:start position:0%
+you know they seem to be people have
+ 
+
+ align:start position:0%
+you know they seem to be people have
+preferences for going to the gym
+
+ align:start position:0%
+preferences for going to the gym
+ 
+
+ align:start position:0%
+preferences for going to the gym
+um but then you know there's an
+
+ align:start position:0%
+um but then you know there's an
+ 
+
+ align:start position:0%
+um but then you know there's an
+escalator um and people like you know
+
+ align:start position:0%
+escalator um and people like you know
+ 
+
+ align:start position:0%
+escalator um and people like you know
+not working out so much so in some sense
+
+ align:start position:0%
+not working out so much so in some sense
+ 
+
+ align:start position:0%
+not working out so much so in some sense
+uh something is is perhaps um a miss
+
+ align:start position:0%
+uh something is is perhaps um a miss
+ 
+
+ align:start position:0%
+uh something is is perhaps um a miss
+here when you look at sort of
+
+ align:start position:0%
+here when you look at sort of
+ 
+
+ align:start position:0%
+here when you look at sort of
+i mean this is one of my favorite things
+
+ align:start position:0%
+i mean this is one of my favorite things
+ 
+
+ align:start position:0%
+i mean this is one of my favorite things
+to do is like in or not just not quite
+
+ align:start position:0%
+to do is like in or not just not quite
+ 
+
+ align:start position:0%
+to do is like in or not just not quite
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+it's a it's a fun thing to do i mean one
+
+ align:start position:0%
+it's a it's a fun thing to do i mean one
+ 
+
+ align:start position:0%
+it's a it's a fun thing to do i mean one
+of my favorite things um
+
+ align:start position:0%
+of my favorite things um
+ 
+
+ align:start position:0%
+of my favorite things um
+uh um uh uh when you sort of google um
+
+ align:start position:0%
+uh um uh uh when you sort of google um
+ 
+
+ align:start position:0%
+uh um uh uh when you sort of google um
+uh terms and this is um calories or
+
+ align:start position:0%
+uh terms and this is um calories or
+ 
+
+ align:start position:0%
+uh terms and this is um calories or
+weight watchers or the like
+
+ align:start position:0%
+weight watchers or the like
+ 
+
+ align:start position:0%
+weight watchers or the like
+where you say well what is people's
+
+ align:start position:0%
+where you say well what is people's
+ 
+
+ align:start position:0%
+where you say well what is people's
+interest in googling those kinds of
+
+ align:start position:0%
+interest in googling those kinds of
+ 
+
+ align:start position:0%
+interest in googling those kinds of
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+over the course of a year and as you can
+
+ align:start position:0%
+over the course of a year and as you can
+ 
+
+ align:start position:0%
+over the course of a year and as you can
+imagine what you see are these spikes
+
+ align:start position:0%
+imagine what you see are these spikes
+ 
+
+ align:start position:0%
+imagine what you see are these spikes
+are essentially
+
+ align:start position:0%
+are essentially
+ 
+
+ align:start position:0%
+are essentially
+january 1st people start sort of like
+
+ align:start position:0%
+january 1st people start sort of like
+ 
+
+ align:start position:0%
+january 1st people start sort of like
+googling calories they like start
+
+ align:start position:0%
+googling calories they like start
+ 
+
+ align:start position:0%
+googling calories they like start
+googling weight watchers and so on and
+
+ align:start position:0%
+googling weight watchers and so on and
+ 
+
+ align:start position:0%
+googling weight watchers and so on and
+so forth
+
+ align:start position:0%
+so forth
+ 
+
+ align:start position:0%
+so forth
+and now of course you can sort of think
+
+ align:start position:0%
+and now of course you can sort of think
+ 
+
+ align:start position:0%
+and now of course you can sort of think
+about some models that sort of can
+
+ align:start position:0%
+about some models that sort of can
+ 
+
+ align:start position:0%
+about some models that sort of can
+rationalize
+
+ align:start position:0%
+rationalize
+ 
+
+ align:start position:0%
+rationalize
+in some sense in saying like well
+
+ align:start position:0%
+in some sense in saying like well
+ 
+
+ align:start position:0%
+in some sense in saying like well
+january is just a good way to start a
+
+ align:start position:0%
+january is just a good way to start a
+ 
+
+ align:start position:0%
+january is just a good way to start a
+a diet and so on but you know really the
+
+ align:start position:0%
+a diet and so on but you know really the
+ 
+
+ align:start position:0%
+a diet and so on but you know really the
+the right thing to do is sort of people
+
+ align:start position:0%
+the right thing to do is sort of people
+ 
+
+ align:start position:0%
+the right thing to do is sort of people
+and january 1st they have all the best
+
+ align:start position:0%
+and january 1st they have all the best
+ 
+
+ align:start position:0%
+and january 1st they have all the best
+of it
+
+ align:start position:0%
+of it
+ 
+
+ align:start position:0%
+of it
+intentions to lose weight uh uh eat
+
+ align:start position:0%
+intentions to lose weight uh uh eat
+ 
+
+ align:start position:0%
+intentions to lose weight uh uh eat
+healthier um
+
+ align:start position:0%
+healthier um
+ 
+
+ align:start position:0%
+healthier um
+exercise more and so on and so forth and
+
+ align:start position:0%
+exercise more and so on and so forth and
+ 
+
+ align:start position:0%
+exercise more and so on and so forth and
+then you know um
+
+ align:start position:0%
+then you know um
+ 
+
+ align:start position:0%
+then you know um
+uh the year starts the semester um
+
+ align:start position:0%
+uh the year starts the semester um
+ 
+
+ align:start position:0%
+uh the year starts the semester um
+happens and so on and so forth
+
+ align:start position:0%
+happens and so on and so forth
+ 
+
+ align:start position:0%
+happens and so on and so forth
+and the good attention sort of like um a
+
+ align:start position:0%
+and the good attention sort of like um a
+ 
+
+ align:start position:0%
+and the good attention sort of like um a
+fade away which is essentially as
+
+ align:start position:0%
+fade away which is essentially as
+ 
+
+ align:start position:0%
+fade away which is essentially as
+um limited self-control um
+
+ align:start position:0%
+um limited self-control um
+ 
+
+ align:start position:0%
+um limited self-control um
+there's some interesting things about
+
+ align:start position:0%
+there's some interesting things about
+ 
+
+ align:start position:0%
+there's some interesting things about
+demand for information especially when
+
+ align:start position:0%
+demand for information especially when
+ 
+
+ align:start position:0%
+demand for information especially when
+it comes to
+
+ align:start position:0%
+it comes to
+ 
+
+ align:start position:0%
+it comes to
+health you know every time i ask this
+
+ align:start position:0%
+health you know every time i ask this
+ 
+
+ align:start position:0%
+health you know every time i ask this
+um and i've taught this class a few
+
+ align:start position:0%
+um and i've taught this class a few
+ 
+
+ align:start position:0%
+um and i've taught this class a few
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+so far every time i ask this i should
+
+ align:start position:0%
+so far every time i ask this i should
+ 
+
+ align:start position:0%
+so far every time i ask this i should
+have realized how old i am who knows dr
+
+ align:start position:0%
+have realized how old i am who knows dr
+ 
+
+ align:start position:0%
+have realized how old i am who knows dr
+house
+
+ align:start position:0%
+house
+ 
+
+ align:start position:0%
+house
+oh not bad so can anybody explain to me
+
+ align:start position:0%
+oh not bad so can anybody explain to me
+ 
+
+ align:start position:0%
+oh not bad so can anybody explain to me
+13 and dr house and what is sort of
+
+ align:start position:0%
+13 and dr house and what is sort of
+ 
+
+ align:start position:0%
+13 and dr house and what is sort of
+their deal and what does this have to do
+
+ align:start position:0%
+their deal and what does this have to do
+ 
+
+ align:start position:0%
+their deal and what does this have to do
+with demand for information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so who's 13 or what is her health issues
+
+ align:start position:0%
+so who's 13 or what is her health issues
+ 
+
+ align:start position:0%
+so who's 13 or what is her health issues
+she's got like i think yes she has
+
+ align:start position:0%
+she's got like i think yes she has
+ 
+
+ align:start position:0%
+she's got like i think yes she has
+huntington's yes right so
+
+ align:start position:0%
+huntington's yes right so
+ 
+
+ align:start position:0%
+huntington's yes right so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+right so she has a disease which is
+
+ align:start position:0%
+right so she has a disease which is
+ 
+
+ align:start position:0%
+right so she has a disease which is
+called huntington's disease which we'll
+
+ align:start position:0%
+called huntington's disease which we'll
+ 
+
+ align:start position:0%
+called huntington's disease which we'll
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+talk about more in the class which
+
+ align:start position:0%
+talk about more in the class which
+ 
+
+ align:start position:0%
+talk about more in the class which
+essentially is a brain disease
+
+ align:start position:0%
+essentially is a brain disease
+ 
+
+ align:start position:0%
+essentially is a brain disease
+where over time your brain more or less
+
+ align:start position:0%
+where over time your brain more or less
+ 
+
+ align:start position:0%
+where over time your brain more or less
+degenerates and that's a
+
+ align:start position:0%
+degenerates and that's a
+ 
+
+ align:start position:0%
+degenerates and that's a
+it's a really a bad condition and uh
+
+ align:start position:0%
+it's a really a bad condition and uh
+ 
+
+ align:start position:0%
+it's a really a bad condition and uh
+where like at age 40 50 that manifests
+
+ align:start position:0%
+where like at age 40 50 that manifests
+ 
+
+ align:start position:0%
+where like at age 40 50 that manifests
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it's a very serious condition it's a
+
+ align:start position:0%
+it's a very serious condition it's a
+ 
+
+ align:start position:0%
+it's a very serious condition it's a
+genetic disease in the
+
+ align:start position:0%
+genetic disease in the
+ 
+
+ align:start position:0%
+genetic disease in the
+in the sense that like if your parents
+
+ align:start position:0%
+in the sense that like if your parents
+ 
+
+ align:start position:0%
+in the sense that like if your parents
+have that disease the chance of you
+
+ align:start position:0%
+have that disease the chance of you
+ 
+
+ align:start position:0%
+have that disease the chance of you
+having it is way way higher than
+
+ align:start position:0%
+having it is way way higher than
+ 
+
+ align:start position:0%
+having it is way way higher than
+in the general population uh there's a
+
+ align:start position:0%
+in the general population uh there's a
+ 
+
+ align:start position:0%
+in the general population uh there's a
+test for it but there's no cure
+
+ align:start position:0%
+test for it but there's no cure
+ 
+
+ align:start position:0%
+test for it but there's no cure
+so now um the dilemma and the show then
+
+ align:start position:0%
+so now um the dilemma and the show then
+ 
+
+ align:start position:0%
+so now um the dilemma and the show then
+comes where
+
+ align:start position:0%
+comes where
+ 
+
+ align:start position:0%
+comes where
+uh she essentially is thinking about
+
+ align:start position:0%
+uh she essentially is thinking about
+ 
+
+ align:start position:0%
+uh she essentially is thinking about
+getting tested
+
+ align:start position:0%
+getting tested
+ 
+
+ align:start position:0%
+getting tested
+and dr house who's in some ways very
+
+ align:start position:0%
+and dr house who's in some ways very
+ 
+
+ align:start position:0%
+and dr house who's in some ways very
+rational and others not so much
+
+ align:start position:0%
+rational and others not so much
+ 
+
+ align:start position:0%
+rational and others not so much
+essentially encourages her to test or
+
+ align:start position:0%
+essentially encourages her to test or
+ 
+
+ align:start position:0%
+essentially encourages her to test or
+get that test
+
+ align:start position:0%
+get that test
+ 
+
+ align:start position:0%
+get that test
+and any rational model would say well
+
+ align:start position:0%
+and any rational model would say well
+ 
+
+ align:start position:0%
+and any rational model would say well
+you should really get that
+
+ align:start position:0%
+you should really get that
+ 
+
+ align:start position:0%
+you should really get that
+or any sort of neoclassical model would
+
+ align:start position:0%
+or any sort of neoclassical model would
+ 
+
+ align:start position:0%
+or any sort of neoclassical model would
+say you should get that test why why
+
+ align:start position:0%
+say you should get that test why why
+ 
+
+ align:start position:0%
+say you should get that test why why
+should you get the test
+
+ align:start position:0%
+should you get the test
+ 
+
+ align:start position:0%
+should you get the test
+why is that helpful and what's that
+
+ align:start position:0%
+why is that helpful and what's that
+ 
+
+ align:start position:0%
+why is that helpful and what's that
+health information helpful for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right exactly you would say information
+
+ align:start position:0%
+right exactly you would say information
+ 
+
+ align:start position:0%
+right exactly you would say information
+is good why is information good because
+
+ align:start position:0%
+is good why is information good because
+ 
+
+ align:start position:0%
+is good why is information good because
+there's lots of important choices that
+
+ align:start position:0%
+there's lots of important choices that
+ 
+
+ align:start position:0%
+there's lots of important choices that
+you might make
+
+ align:start position:0%
+you might make
+ 
+
+ align:start position:0%
+you might make
+that depend on that information you
+
+ align:start position:0%
+that depend on that information you
+ 
+
+ align:start position:0%
+that depend on that information you
+might think about like how much money
+
+ align:start position:0%
+might think about like how much money
+ 
+
+ align:start position:0%
+might think about like how much money
+you want to save you think about like
+
+ align:start position:0%
+you want to save you think about like
+ 
+
+ align:start position:0%
+you want to save you think about like
+your choices
+
+ align:start position:0%
+your choices
+ 
+
+ align:start position:0%
+your choices
+about taking vacation about
+
+ align:start position:0%
+about taking vacation about
+ 
+
+ align:start position:0%
+about taking vacation about
+career choices about partner choices
+
+ align:start position:0%
+career choices about partner choices
+ 
+
+ align:start position:0%
+career choices about partner choices
+about having children
+
+ align:start position:0%
+about having children
+ 
+
+ align:start position:0%
+about having children
+all sorts of issues about health
+
+ align:start position:0%
+all sorts of issues about health
+ 
+
+ align:start position:0%
+all sorts of issues about health
+behaviors you might sort of take better
+
+ align:start position:0%
+behaviors you might sort of take better
+ 
+
+ align:start position:0%
+behaviors you might sort of take better
+care of yourself
+
+ align:start position:0%
+care of yourself
+ 
+
+ align:start position:0%
+care of yourself
+there's all sorts of really important
+
+ align:start position:0%
+there's all sorts of really important
+ 
+
+ align:start position:0%
+there's all sorts of really important
+decision that might hinge on the fact
+
+ align:start position:0%
+decision that might hinge on the fact
+ 
+
+ align:start position:0%
+decision that might hinge on the fact
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+your life will be dramatically different
+
+ align:start position:0%
+your life will be dramatically different
+ 
+
+ align:start position:0%
+your life will be dramatically different
+whether you have huntington's disease
+
+ align:start position:0%
+whether you have huntington's disease
+ 
+
+ align:start position:0%
+whether you have huntington's disease
+or not now 13 does not want to i think
+
+ align:start position:0%
+or not now 13 does not want to i think
+ 
+
+ align:start position:0%
+or not now 13 does not want to i think
+she actually does the test and then
+
+ align:start position:0%
+she actually does the test and then
+ 
+
+ align:start position:0%
+she actually does the test and then
+doesn't want to see the result
+
+ align:start position:0%
+doesn't want to see the result
+ 
+
+ align:start position:0%
+doesn't want to see the result
+and why is that yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so that's one view to view that i
+
+ align:start position:0%
+and so that's one view to view that i
+ 
+
+ align:start position:0%
+and so that's one view to view that i
+think you know in some things as i said
+
+ align:start position:0%
+think you know in some things as i said
+ 
+
+ align:start position:0%
+think you know in some things as i said
+you may could make other decisions like
+
+ align:start position:0%
+you may could make other decisions like
+ 
+
+ align:start position:0%
+you may could make other decisions like
+economic choices you could save more you
+
+ align:start position:0%
+economic choices you could save more you
+ 
+
+ align:start position:0%
+economic choices you could save more you
+could see the doctor more you could
+
+ align:start position:0%
+could see the doctor more you could
+ 
+
+ align:start position:0%
+could see the doctor more you could
+go more on vacations or whatever do fun
+
+ align:start position:0%
+go more on vacations or whatever do fun
+ 
+
+ align:start position:0%
+go more on vacations or whatever do fun
+things in life but you could say well
+
+ align:start position:0%
+things in life but you could say well
+ 
+
+ align:start position:0%
+things in life but you could say well
+maybe that's not that important but the
+
+ align:start position:0%
+maybe that's not that important but the
+ 
+
+ align:start position:0%
+maybe that's not that important but the
+neoclassical or the the classical
+
+ align:start position:0%
+neoclassical or the the classical
+ 
+
+ align:start position:0%
+neoclassical or the the classical
+economics model
+
+ align:start position:0%
+economics model
+ 
+
+ align:start position:0%
+economics model
+would still argue that you should get
+
+ align:start position:0%
+would still argue that you should get
+ 
+
+ align:start position:0%
+would still argue that you should get
+that information it wouldn't hurt you
+
+ align:start position:0%
+that information it wouldn't hurt you
+ 
+
+ align:start position:0%
+that information it wouldn't hurt you
+you wouldn't want to refuse it
+
+ align:start position:0%
+you wouldn't want to refuse it
+ 
+
+ align:start position:0%
+you wouldn't want to refuse it
+so why is she but why is she refusing it
+
+ align:start position:0%
+so why is she but why is she refusing it
+ 
+
+ align:start position:0%
+so why is she but why is she refusing it
+yes i think maybe she doesn't want to
+
+ align:start position:0%
+yes i think maybe she doesn't want to
+ 
+
+ align:start position:0%
+yes i think maybe she doesn't want to
+leave the rest of her life
+
+ align:start position:0%
+leave the rest of her life
+ 
+
+ align:start position:0%
+leave the rest of her life
+exactly so she essentially derives
+
+ align:start position:0%
+exactly so she essentially derives
+ 
+
+ align:start position:0%
+exactly so she essentially derives
+utility from
+
+ align:start position:0%
+utility from
+ 
+
+ align:start position:0%
+utility from
+information if you want from her beliefs
+
+ align:start position:0%
+information if you want from her beliefs
+ 
+
+ align:start position:0%
+information if you want from her beliefs
+she likes to sort of pretend to herself
+
+ align:start position:0%
+she likes to sort of pretend to herself
+ 
+
+ align:start position:0%
+she likes to sort of pretend to herself
+that she's healthy or like the chance of
+
+ align:start position:0%
+that she's healthy or like the chance of
+ 
+
+ align:start position:0%
+that she's healthy or like the chance of
+her being healthy is very high
+
+ align:start position:0%
+her being healthy is very high
+ 
+
+ align:start position:0%
+her being healthy is very high
+now under some assumptions you might
+
+ align:start position:0%
+now under some assumptions you might
+ 
+
+ align:start position:0%
+now under some assumptions you might
+want to not get tested and sort of see
+
+ align:start position:0%
+want to not get tested and sort of see
+ 
+
+ align:start position:0%
+want to not get tested and sort of see
+the results
+
+ align:start position:0%
+the results
+ 
+
+ align:start position:0%
+the results
+of that test because once you have the
+
+ align:start position:0%
+of that test because once you have the
+ 
+
+ align:start position:0%
+of that test because once you have the
+test it's very hard to pretend
+
+ align:start position:0%
+test it's very hard to pretend
+ 
+
+ align:start position:0%
+test it's very hard to pretend
+if it's positive it's very hard to
+
+ align:start position:0%
+if it's positive it's very hard to
+ 
+
+ align:start position:0%
+if it's positive it's very hard to
+pretend to yourself uh
+
+ align:start position:0%
+pretend to yourself uh
+ 
+
+ align:start position:0%
+pretend to yourself uh
+uh uh that you're healthy because
+
+ align:start position:0%
+uh uh that you're healthy because
+ 
+
+ align:start position:0%
+uh uh that you're healthy because
+there's a hard test saying that
+
+ align:start position:0%
+there's a hard test saying that
+ 
+
+ align:start position:0%
+there's a hard test saying that
+um before the test you can still sort of
+
+ align:start position:0%
+um before the test you can still sort of
+ 
+
+ align:start position:0%
+um before the test you can still sort of
+think like try to forget about it and
+
+ align:start position:0%
+think like try to forget about it and
+ 
+
+ align:start position:0%
+think like try to forget about it and
+try to sort of live a happy life
+
+ align:start position:0%
+try to sort of live a happy life
+ 
+
+ align:start position:0%
+try to sort of live a happy life
+sort of until the symptoms set in
+
+ align:start position:0%
+sort of until the symptoms set in
+ 
+
+ align:start position:0%
+sort of until the symptoms set in
+but that's a clear violation of the
+
+ align:start position:0%
+but that's a clear violation of the
+ 
+
+ align:start position:0%
+but that's a clear violation of the
+classical model of the assumptions that
+
+ align:start position:0%
+classical model of the assumptions that
+ 
+
+ align:start position:0%
+classical model of the assumptions that
+i was showing you
+
+ align:start position:0%
+i was showing you
+ 
+
+ align:start position:0%
+i was showing you
+above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next part is uh default effects so
+
+ align:start position:0%
+the next part is uh default effects so
+ 
+
+ align:start position:0%
+the next part is uh default effects so
+what i'm showing here here is the
+
+ align:start position:0%
+what i'm showing here here is the
+ 
+
+ align:start position:0%
+what i'm showing here here is the
+fraction of organ
+
+ align:start position:0%
+fraction of organ
+ 
+
+ align:start position:0%
+fraction of organ
+donors by country and type of default
+
+ align:start position:0%
+donors by country and type of default
+ 
+
+ align:start position:0%
+donors by country and type of default
+there's uh
+
+ align:start position:0%
+there's uh
+ 
+
+ align:start position:0%
+there's uh
+two types of defaults um often for organ
+
+ align:start position:0%
+two types of defaults um often for organ
+ 
+
+ align:start position:0%
+two types of defaults um often for organ
+donations
+
+ align:start position:0%
+donations
+ 
+
+ align:start position:0%
+donations
+this is from a few years ago but i think
+
+ align:start position:0%
+this is from a few years ago but i think
+ 
+
+ align:start position:0%
+this is from a few years ago but i think
+overall things have not changed that
+
+ align:start position:0%
+overall things have not changed that
+ 
+
+ align:start position:0%
+overall things have not changed that
+much um there's opt-in versus
+
+ align:start position:0%
+much um there's opt-in versus
+ 
+
+ align:start position:0%
+much um there's opt-in versus
+opt-out so in the countries on the left
+
+ align:start position:0%
+opt-out so in the countries on the left
+ 
+
+ align:start position:0%
+opt-out so in the countries on the left
+essentially you have an opt-in policy in
+
+ align:start position:0%
+essentially you have an opt-in policy in
+ 
+
+ align:start position:0%
+essentially you have an opt-in policy in
+a sense like if you don't do anything
+
+ align:start position:0%
+a sense like if you don't do anything
+ 
+
+ align:start position:0%
+a sense like if you don't do anything
+you're not an organ donor
+
+ align:start position:0%
+you're not an organ donor
+ 
+
+ align:start position:0%
+you're not an organ donor
+so you have to like actively say in some
+
+ align:start position:0%
+so you have to like actively say in some
+ 
+
+ align:start position:0%
+so you have to like actively say in some
+form or some form of like declaration
+
+ align:start position:0%
+form or some form of like declaration
+ 
+
+ align:start position:0%
+form or some form of like declaration
+that you want to be
+
+ align:start position:0%
+that you want to be
+ 
+
+ align:start position:0%
+that you want to be
+an organ donor on the right there's like
+
+ align:start position:0%
+an organ donor on the right there's like
+ 
+
+ align:start position:0%
+an organ donor on the right there's like
+opt
+
+ align:start position:0%
+opt
+ 
+
+ align:start position:0%
+opt
+out policies which means essentially if
+
+ align:start position:0%
+out policies which means essentially if
+ 
+
+ align:start position:0%
+out policies which means essentially if
+you don't do anything you'll be
+
+ align:start position:0%
+you don't do anything you'll be
+ 
+
+ align:start position:0%
+you don't do anything you'll be
+automatically
+
+ align:start position:0%
+automatically
+ 
+
+ align:start position:0%
+automatically
+registered or viewed as an organ donor
+
+ align:start position:0%
+registered or viewed as an organ donor
+ 
+
+ align:start position:0%
+registered or viewed as an organ donor
+you can opt
+
+ align:start position:0%
+you can opt
+ 
+
+ align:start position:0%
+you can opt
+out but only um uh only if you do so
+
+ align:start position:0%
+out but only um uh only if you do so
+ 
+
+ align:start position:0%
+out but only um uh only if you do so
+you'll actually be opted out otherwise
+
+ align:start position:0%
+you'll actually be opted out otherwise
+ 
+
+ align:start position:0%
+you'll actually be opted out otherwise
+if there's an accident in the lake
+
+ align:start position:0%
+if there's an accident in the lake
+ 
+
+ align:start position:0%
+if there's an accident in the lake
+you'll be viewed as an organ donor
+
+ align:start position:0%
+you'll be viewed as an organ donor
+ 
+
+ align:start position:0%
+you'll be viewed as an organ donor
+now what's weird about this graph or why
+
+ align:start position:0%
+now what's weird about this graph or why
+ 
+
+ align:start position:0%
+now what's weird about this graph or why
+is this sort of uh
+
+ align:start position:0%
+is this sort of uh
+ 
+
+ align:start position:0%
+is this sort of uh
+potentially a violation of the
+
+ align:start position:0%
+potentially a violation of the
+ 
+
+ align:start position:0%
+potentially a violation of the
+neoclassical or the typical economics
+
+ align:start position:0%
+neoclassical or the typical economics
+ 
+
+ align:start position:0%
+neoclassical or the typical economics
+assumptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes the
+
+ align:start position:0%
+yes the
+ 
+
+ align:start position:0%
+yes the
+people have the same preference of
+
+ align:start position:0%
+people have the same preference of
+ 
+
+ align:start position:0%
+people have the same preference of
+whether they want to opt-in or opt-out
+
+ align:start position:0%
+whether they want to opt-in or opt-out
+ 
+
+ align:start position:0%
+whether they want to opt-in or opt-out
+that everyone should have this would be
+
+ align:start position:0%
+that everyone should have this would be
+ 
+
+ align:start position:0%
+that everyone should have this would be
+the same proportion across
+
+ align:start position:0%
+the same proportion across
+ 
+
+ align:start position:0%
+the same proportion across
+but the difference is that um the effort
+
+ align:start position:0%
+but the difference is that um the effort
+ 
+
+ align:start position:0%
+but the difference is that um the effort
+required to make that change or the
+
+ align:start position:0%
+required to make that change or the
+ 
+
+ align:start position:0%
+required to make that change or the
+difference the lack of indifference
+
+ align:start position:0%
+difference the lack of indifference
+ 
+
+ align:start position:0%
+difference the lack of indifference
+causes there to be the imbalance between
+
+ align:start position:0%
+causes there to be the imbalance between
+ 
+
+ align:start position:0%
+causes there to be the imbalance between
+the opt-out and the opt-in
+
+ align:start position:0%
+the opt-out and the opt-in
+ 
+
+ align:start position:0%
+the opt-out and the opt-in
+right exactly so um some people on uh
+
+ align:start position:0%
+right exactly so um some people on uh
+ 
+
+ align:start position:0%
+right exactly so um some people on uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+don't want to get in trouble but some
+
+ align:start position:0%
+don't want to get in trouble but some
+ 
+
+ align:start position:0%
+don't want to get in trouble but some
+people argue germany and austria is
+
+ align:start position:0%
+people argue germany and austria is
+ 
+
+ align:start position:0%
+people argue germany and austria is
+actually not that different so i'm
+
+ align:start position:0%
+actually not that different so i'm
+ 
+
+ align:start position:0%
+actually not that different so i'm
+german so you know some austrians might
+
+ align:start position:0%
+german so you know some austrians might
+ 
+
+ align:start position:0%
+german so you know some austrians might
+disagree but you would say you know
+
+ align:start position:0%
+disagree but you would say you know
+ 
+
+ align:start position:0%
+disagree but you would say you know
+overall germans and austrians are not
+
+ align:start position:0%
+overall germans and austrians are not
+ 
+
+ align:start position:0%
+overall germans and austrians are not
+that different overall and you think you
+
+ align:start position:0%
+that different overall and you think you
+ 
+
+ align:start position:0%
+that different overall and you think you
+know their preferences in particular
+
+ align:start position:0%
+know their preferences in particular
+ 
+
+ align:start position:0%
+know their preferences in particular
+they might be different but their
+
+ align:start position:0%
+they might be different but their
+ 
+
+ align:start position:0%
+they might be different but their
+preferences for organ donations
+
+ align:start position:0%
+preferences for organ donations
+ 
+
+ align:start position:0%
+preferences for organ donations
+are probably pretty similar across those
+
+ align:start position:0%
+are probably pretty similar across those
+ 
+
+ align:start position:0%
+are probably pretty similar across those
+two countries which is a reasonable
+
+ align:start position:0%
+two countries which is a reasonable
+ 
+
+ align:start position:0%
+two countries which is a reasonable
+assumption
+
+ align:start position:0%
+assumption
+ 
+
+ align:start position:0%
+assumption
+second lots of people care a lot about
+
+ align:start position:0%
+second lots of people care a lot about
+ 
+
+ align:start position:0%
+second lots of people care a lot about
+what happens to them after they die
+
+ align:start position:0%
+what happens to them after they die
+ 
+
+ align:start position:0%
+what happens to them after they die
+right so they for whatever reasons
+
+ align:start position:0%
+right so they for whatever reasons
+ 
+
+ align:start position:0%
+right so they for whatever reasons
+religious or others they might actually
+
+ align:start position:0%
+religious or others they might actually
+ 
+
+ align:start position:0%
+religious or others they might actually
+care a lot about at the end of the day
+
+ align:start position:0%
+care a lot about at the end of the day
+ 
+
+ align:start position:0%
+care a lot about at the end of the day
+um uh what happens to their body and so
+
+ align:start position:0%
+um uh what happens to their body and so
+ 
+
+ align:start position:0%
+um uh what happens to their body and so
+on and that's obviously their choice
+
+ align:start position:0%
+on and that's obviously their choice
+ 
+
+ align:start position:0%
+on and that's obviously their choice
+um to make now if you assume those two
+
+ align:start position:0%
+um to make now if you assume those two
+ 
+
+ align:start position:0%
+um to make now if you assume those two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+then it's very hard to reconcile this
+
+ align:start position:0%
+then it's very hard to reconcile this
+ 
+
+ align:start position:0%
+then it's very hard to reconcile this
+this picture
+
+ align:start position:0%
+this picture
+ 
+
+ align:start position:0%
+this picture
+because essentially um the opt in and
+
+ align:start position:0%
+because essentially um the opt in and
+ 
+
+ align:start position:0%
+because essentially um the opt in and
+out out is a very small change to make
+
+ align:start position:0%
+out out is a very small change to make
+ 
+
+ align:start position:0%
+out out is a very small change to make
+it's very um simple and easy to do you
+
+ align:start position:0%
+it's very um simple and easy to do you
+ 
+
+ align:start position:0%
+it's very um simple and easy to do you
+just have to like fill out some form
+
+ align:start position:0%
+just have to like fill out some form
+ 
+
+ align:start position:0%
+just have to like fill out some form
+maybe it takes you an hour maybe two you
+
+ align:start position:0%
+maybe it takes you an hour maybe two you
+ 
+
+ align:start position:0%
+maybe it takes you an hour maybe two you
+have to maybe go to some office or the
+
+ align:start position:0%
+have to maybe go to some office or the
+ 
+
+ align:start position:0%
+have to maybe go to some office or the
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+but if you really care you could easily
+
+ align:start position:0%
+but if you really care you could easily
+ 
+
+ align:start position:0%
+but if you really care you could easily
+do it
+
+ align:start position:0%
+do it
+ 
+
+ align:start position:0%
+do it
+yet you see huge differences in outcome
+
+ align:start position:0%
+yet you see huge differences in outcome
+ 
+
+ align:start position:0%
+yet you see huge differences in outcome
+based on this very simple
+
+ align:start position:0%
+based on this very simple
+ 
+
+ align:start position:0%
+based on this very simple
+um small change which it's very hard to
+
+ align:start position:0%
+um small change which it's very hard to
+ 
+
+ align:start position:0%
+um small change which it's very hard to
+model a right on a model that sort of
+
+ align:start position:0%
+model a right on a model that sort of
+ 
+
+ align:start position:0%
+model a right on a model that sort of
+rationalizes this behavior
+
+ align:start position:0%
+rationalizes this behavior
+ 
+
+ align:start position:0%
+rationalizes this behavior
+so somehow the default sort of the way
+
+ align:start position:0%
+so somehow the default sort of the way
+ 
+
+ align:start position:0%
+so somehow the default sort of the way
+in which the decision is presented
+
+ align:start position:0%
+in which the decision is presented
+ 
+
+ align:start position:0%
+in which the decision is presented
+seems to really affect people's behavior
+
+ align:start position:0%
+seems to really affect people's behavior
+ 
+
+ align:start position:0%
+seems to really affect people's behavior
+in a fundamental
+
+ align:start position:0%
+in a fundamental
+ 
+
+ align:start position:0%
+in a fundamental
+way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay next one is glow caps this is like
+
+ align:start position:0%
+okay next one is glow caps this is like
+ 
+
+ align:start position:0%
+okay next one is glow caps this is like
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+help for people to take their medication
+
+ align:start position:0%
+help for people to take their medication
+ 
+
+ align:start position:0%
+help for people to take their medication
+in particular for the elderly
+
+ align:start position:0%
+in particular for the elderly
+ 
+
+ align:start position:0%
+in particular for the elderly
+which essentially is a reminder um uh
+
+ align:start position:0%
+which essentially is a reminder um uh
+ 
+
+ align:start position:0%
+which essentially is a reminder um uh
+for people you can sort of program this
+
+ align:start position:0%
+for people you can sort of program this
+ 
+
+ align:start position:0%
+for people you can sort of program this
+in certain ways
+
+ align:start position:0%
+in certain ways
+ 
+
+ align:start position:0%
+in certain ways
+like every day or every few hours um a
+
+ align:start position:0%
+like every day or every few hours um a
+ 
+
+ align:start position:0%
+like every day or every few hours um a
+glow cap
+
+ align:start position:0%
+glow cap
+ 
+
+ align:start position:0%
+glow cap
+starts either sort of making sounds or
+
+ align:start position:0%
+starts either sort of making sounds or
+ 
+
+ align:start position:0%
+starts either sort of making sounds or
+like starts blinking and the like
+
+ align:start position:0%
+like starts blinking and the like
+ 
+
+ align:start position:0%
+like starts blinking and the like
+and gets you to take your medication and
+
+ align:start position:0%
+and gets you to take your medication and
+ 
+
+ align:start position:0%
+and gets you to take your medication and
+it's a very sort of simple proof of
+
+ align:start position:0%
+it's a very sort of simple proof of
+ 
+
+ align:start position:0%
+it's a very sort of simple proof of
+concept that you know reminders are
+
+ align:start position:0%
+concept that you know reminders are
+ 
+
+ align:start position:0%
+concept that you know reminders are
+important and can save people's lives
+
+ align:start position:0%
+important and can save people's lives
+ 
+
+ align:start position:0%
+important and can save people's lives
+and people have done studies on that and
+
+ align:start position:0%
+and people have done studies on that and
+ 
+
+ align:start position:0%
+and people have done studies on that and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+but essentially it's a very simple proof
+
+ align:start position:0%
+but essentially it's a very simple proof
+ 
+
+ align:start position:0%
+but essentially it's a very simple proof
+of concept that memory is limited
+
+ align:start position:0%
+of concept that memory is limited
+ 
+
+ align:start position:0%
+of concept that memory is limited
+right if your memory was perfect if you
+
+ align:start position:0%
+right if your memory was perfect if you
+ 
+
+ align:start position:0%
+right if your memory was perfect if you
+could remember everything if you sort of
+
+ align:start position:0%
+could remember everything if you sort of
+ 
+
+ align:start position:0%
+could remember everything if you sort of
+had all sorts of if you're a perfect
+
+ align:start position:0%
+had all sorts of if you're a perfect
+ 
+
+ align:start position:0%
+had all sorts of if you're a perfect
+information processor
+
+ align:start position:0%
+information processor
+ 
+
+ align:start position:0%
+information processor
+you would not forget about your
+
+ align:start position:0%
+you would not forget about your
+ 
+
+ align:start position:0%
+you would not forget about your
+medication especially if it's important
+
+ align:start position:0%
+medication especially if it's important
+ 
+
+ align:start position:0%
+medication especially if it's important
+especially if it's medication
+
+ align:start position:0%
+especially if it's medication
+ 
+
+ align:start position:0%
+especially if it's medication
+uh that potentially saves your lives yet
+
+ align:start position:0%
+uh that potentially saves your lives yet
+ 
+
+ align:start position:0%
+uh that potentially saves your lives yet
+you know we see that people's demand
+
+ align:start position:0%
+you know we see that people's demand
+ 
+
+ align:start position:0%
+you know we see that people's demand
+people's uh uh medication usage um
+
+ align:start position:0%
+people's uh uh medication usage um
+ 
+
+ align:start position:0%
+people's uh uh medication usage um
+is uh strongly affected by sort of types
+
+ align:start position:0%
+is uh strongly affected by sort of types
+ 
+
+ align:start position:0%
+is uh strongly affected by sort of types
+of policies or products
+
+ align:start position:0%
+of policies or products
+ 
+
+ align:start position:0%
+of policies or products
+um that can help people uh remember so
+
+ align:start position:0%
+um that can help people uh remember so
+ 
+
+ align:start position:0%
+um that can help people uh remember so
+that's essentially a rejection of um
+
+ align:start position:0%
+that's essentially a rejection of um
+ 
+
+ align:start position:0%
+that's essentially a rejection of um
+perfect memory
+
+ align:start position:0%
+perfect memory
+ 
+
+ align:start position:0%
+perfect memory
+um next one is charity so if you think
+
+ align:start position:0%
+um next one is charity so if you think
+ 
+
+ align:start position:0%
+um next one is charity so if you think
+about you know um
+
+ align:start position:0%
+about you know um
+ 
+
+ align:start position:0%
+about you know um
+people in all sorts of ways seem to care
+
+ align:start position:0%
+people in all sorts of ways seem to care
+ 
+
+ align:start position:0%
+people in all sorts of ways seem to care
+about others in the sense of like just
+
+ align:start position:0%
+about others in the sense of like just
+ 
+
+ align:start position:0%
+about others in the sense of like just
+giving
+
+ align:start position:0%
+giving
+ 
+
+ align:start position:0%
+giving
+uh money uh here's one charity that's
+
+ align:start position:0%
+uh money uh here's one charity that's
+ 
+
+ align:start position:0%
+uh money uh here's one charity that's
+called gift directly which is
+
+ align:start position:0%
+called gift directly which is
+ 
+
+ align:start position:0%
+called gift directly which is
+a very nice charity in a sense that like
+
+ align:start position:0%
+a very nice charity in a sense that like
+ 
+
+ align:start position:0%
+a very nice charity in a sense that like
+what it does essentially is
+
+ align:start position:0%
+what it does essentially is
+ 
+
+ align:start position:0%
+what it does essentially is
+a very simple way of helping the poor by
+
+ align:start position:0%
+a very simple way of helping the poor by
+ 
+
+ align:start position:0%
+a very simple way of helping the poor by
+just directly transferring money
+
+ align:start position:0%
+just directly transferring money
+ 
+
+ align:start position:0%
+just directly transferring money
+to poorer countries so on the right you
+
+ align:start position:0%
+to poorer countries so on the right you
+ 
+
+ align:start position:0%
+to poorer countries so on the right you
+see an actual recipient from
+
+ align:start position:0%
+see an actual recipient from
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+
+ align:start position:0%
+see an actual recipient from
+give directly that person has a phone
+
+ align:start position:0%
+give directly that person has a phone
+ 
+
+ align:start position:0%
+give directly that person has a phone
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+
+ align:start position:0%
+they're sort of a mobile
+ 
+
+ align:start position:0%
+they're sort of a mobile
+phone based uh transfers where
+
+ align:start position:0%
+phone based uh transfers where
+ 
+
+ align:start position:0%
+phone based uh transfers where
+essentially you can send money to people
+
+ align:start position:0%
+essentially you can send money to people
+ 
+
+ align:start position:0%
+essentially you can send money to people
+with mobile phones
+
+ align:start position:0%
+with mobile phones
+ 
+
+ align:start position:0%
+with mobile phones
+so if you decided now to give hundred
+
+ align:start position:0%
+so if you decided now to give hundred
+ 
+
+ align:start position:0%
+so if you decided now to give hundred
+dollars um
+
+ align:start position:0%
+dollars um
+ 
+
+ align:start position:0%
+dollars um
+to that person it could be that person
+
+ align:start position:0%
+to that person it could be that person
+ 
+
+ align:start position:0%
+to that person it could be that person
+or a similar person
+
+ align:start position:0%
+or a similar person
+ 
+
+ align:start position:0%
+or a similar person
+uh 95 of those or 90 of those dollars
+
+ align:start position:0%
+uh 95 of those or 90 of those dollars
+ 
+
+ align:start position:0%
+uh 95 of those or 90 of those dollars
+would then in fact arrive at the phone
+
+ align:start position:0%
+would then in fact arrive at the phone
+ 
+
+ align:start position:0%
+would then in fact arrive at the phone
+a cell phone of that person now um
+
+ align:start position:0%
+a cell phone of that person now um
+ 
+
+ align:start position:0%
+a cell phone of that person now um
+why are people doing this presumably
+
+ align:start position:0%
+why are people doing this presumably
+ 
+
+ align:start position:0%
+why are people doing this presumably
+because they care about others one way
+
+ align:start position:0%
+because they care about others one way
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+
+ align:start position:0%
+because they care about others one way
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+ align:start position:0%
+or the other
+ 
+
+ align:start position:0%
+or the other
+um it could be either that you know in
+
+ align:start position:0%
+um it could be either that you know in
+ 
+
+ align:start position:0%
+um it could be either that you know in
+some sense that's part of the utility
+
+ align:start position:0%
+some sense that's part of the utility
+ 
+
+ align:start position:0%
+some sense that's part of the utility
+function just donating money to others
+
+ align:start position:0%
+function just donating money to others
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+
+ align:start position:0%
+function just donating money to others
+makes you happier and that's essentially
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+ align:start position:0%
+makes you happier and that's essentially
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+
+ align:start position:0%
+makes you happier and that's essentially
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+
+ align:start position:0%
+a way in which you improve your
+ 
+
+ align:start position:0%
+a way in which you improve your
+well-being you just have
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+ align:start position:0%
+well-being you just have
+ 
+
+ align:start position:0%
+well-being you just have
+others well-being in your utility
+
+ align:start position:0%
+others well-being in your utility
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+
+ align:start position:0%
+others well-being in your utility
+function or it could be things like what
+
+ align:start position:0%
+function or it could be things like what
+ 
+
+ align:start position:0%
+function or it could be things like what
+we said previously it could be like you
+
+ align:start position:0%
+we said previously it could be like you
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+
+ align:start position:0%
+we said previously it could be like you
+sort of think it's like appropriate
+
+ align:start position:0%
+sort of think it's like appropriate
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+
+ align:start position:0%
+sort of think it's like appropriate
+thing to do maybe other people's do it's
+
+ align:start position:0%
+thing to do maybe other people's do it's
+ 
+
+ align:start position:0%
+thing to do maybe other people's do it's
+like an important thing to do maybe you
+
+ align:start position:0%
+like an important thing to do maybe you
+ 
+
+ align:start position:0%
+like an important thing to do maybe you
+could tell your friends about it and so
+
+ align:start position:0%
+could tell your friends about it and so
+ 
+
+ align:start position:0%
+could tell your friends about it and so
+on and so forth
+
+ align:start position:0%
+on and so forth
+ 
+
+ align:start position:0%
+on and so forth
+but one way the other people give lots
+
+ align:start position:0%
+but one way the other people give lots
+ 
+
+ align:start position:0%
+but one way the other people give lots
+of money to charity which in some sense
+
+ align:start position:0%
+of money to charity which in some sense
+ 
+
+ align:start position:0%
+of money to charity which in some sense
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+
+ align:start position:0%
+says one way or the other you must care
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+
+ align:start position:0%
+says one way or the other you must care
+about others
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+ align:start position:0%
+about others
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+
+ align:start position:0%
+about others
+overall so others are in your utility
+
+ align:start position:0%
+overall so others are in your utility
+ 
+
+ align:start position:0%
+overall so others are in your utility
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+so now attention um if you've seen this
+
+ align:start position:0%
+so now attention um if you've seen this
+ 
+
+ align:start position:0%
+so now attention um if you've seen this
+before um uh
+
+ align:start position:0%
+before um uh
+ 
+
+ align:start position:0%
+before um uh
+don't tell your friends about it here's
+
+ align:start position:0%
+don't tell your friends about it here's
+ 
+
+ align:start position:0%
+don't tell your friends about it here's
+a simple attention test that i want you
+
+ align:start position:0%
+a simple attention test that i want you
+ 
+
+ align:start position:0%
+a simple attention test that i want you
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do what's interesting about this is in
+
+ align:start position:0%
+do what's interesting about this is in
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+
+ align:start position:0%
+do what's interesting about this is in
+some ways like
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+ align:start position:0%
+some ways like
+ 
+
+ align:start position:0%
+some ways like
+um you know you might have seen this
+
+ align:start position:0%
+um you know you might have seen this
+ 
+
+ align:start position:0%
+um you know you might have seen this
+before some of them may have she's seen
+
+ align:start position:0%
+before some of them may have she's seen
+ 
+
+ align:start position:0%
+before some of them may have she's seen
+the gorilla before
+
+ align:start position:0%
+the gorilla before
+ 
+
+ align:start position:0%
+the gorilla before
+uh who didn't see the gorilla it's okay
+
+ align:start position:0%
+uh who didn't see the gorilla it's okay
+ 
+
+ align:start position:0%
+uh who didn't see the gorilla it's okay
+i didn't see it either but something
+
+ align:start position:0%
+i didn't see it either but something
+ 
+
+ align:start position:0%
+i didn't see it either but something
+some people have seen it before that
+
+ align:start position:0%
+some people have seen it before that
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+
+ align:start position:0%
+some people have seen it before that
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+
+ align:start position:0%
+there's a bunch of experiments that
+ 
+
+ align:start position:0%
+there's a bunch of experiments that
+people have done that essentially show
+
+ align:start position:0%
+people have done that essentially show
+ 
+
+ align:start position:0%
+people have done that essentially show
+that you know often
+
+ align:start position:0%
+that you know often
+ 
+
+ align:start position:0%
+that you know often
+a large fraction of people don't see
+
+ align:start position:0%
+a large fraction of people don't see
+ 
+
+ align:start position:0%
+a large fraction of people don't see
+this gorilla
+
+ align:start position:0%
+this gorilla
+ 
+
+ align:start position:0%
+this gorilla
+and there's various ways in which people
+
+ align:start position:0%
+and there's various ways in which people
+ 
+
+ align:start position:0%
+and there's various ways in which people
+do other types of experiments
+
+ align:start position:0%
+do other types of experiments
+ 
+
+ align:start position:0%
+do other types of experiments
+there's types of experiments where
+
+ align:start position:0%
+there's types of experiments where
+ 
+
+ align:start position:0%
+there's types of experiments where
+essentially people
+
+ align:start position:0%
+essentially people
+ 
+
+ align:start position:0%
+essentially people
+they go to like some bank teller the
+
+ align:start position:0%
+they go to like some bank teller the
+ 
+
+ align:start position:0%
+they go to like some bank teller the
+bank teller says i'm going to go away
+
+ align:start position:0%
+bank teller says i'm going to go away
+ 
+
+ align:start position:0%
+bank teller says i'm going to go away
+and then comes back and then there's a
+
+ align:start position:0%
+and then comes back and then there's a
+ 
+
+ align:start position:0%
+and then comes back and then there's a
+different person who comes back and
+
+ align:start position:0%
+different person who comes back and
+ 
+
+ align:start position:0%
+different person who comes back and
+people don't notice
+
+ align:start position:0%
+people don't notice
+ 
+
+ align:start position:0%
+people don't notice
+there's various versions of that and so
+
+ align:start position:0%
+there's various versions of that and so
+ 
+
+ align:start position:0%
+there's various versions of that and so
+what's interesting about this in some
+
+ align:start position:0%
+what's interesting about this in some
+ 
+
+ align:start position:0%
+what's interesting about this in some
+sense is
+
+ align:start position:0%
+sense is
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+
+ align:start position:0%
+sense is
+so a it proves in some ways that
+
+ align:start position:0%
+so a it proves in some ways that
+ 
+
+ align:start position:0%
+so a it proves in some ways that
+attention is limited
+
+ align:start position:0%
+attention is limited
+ 
+
+ align:start position:0%
+attention is limited
+you just focus your attention on some
+
+ align:start position:0%
+you just focus your attention on some
+ 
+
+ align:start position:0%
+you just focus your attention on some
+things and not others
+
+ align:start position:0%
+things and not others
+ 
+
+ align:start position:0%
+things and not others
+and you might miss important things now
+
+ align:start position:0%
+and you might miss important things now
+ 
+
+ align:start position:0%
+and you might miss important things now
+that's okay in some ways there's sort of
+
+ align:start position:0%
+that's okay in some ways there's sort of
+ 
+
+ align:start position:0%
+that's okay in some ways there's sort of
+a version of that that says well
+
+ align:start position:0%
+a version of that that says well
+ 
+
+ align:start position:0%
+a version of that that says well
+it might be sort of like rational
+
+ align:start position:0%
+it might be sort of like rational
+ 
+
+ align:start position:0%
+it might be sort of like rational
+inattention in some sense you focus on
+
+ align:start position:0%
+inattention in some sense you focus on
+ 
+
+ align:start position:0%
+inattention in some sense you focus on
+the important things in life and you
+
+ align:start position:0%
+the important things in life and you
+ 
+
+ align:start position:0%
+the important things in life and you
+might miss some things and that's okay
+
+ align:start position:0%
+might miss some things and that's okay
+ 
+
+ align:start position:0%
+might miss some things and that's okay
+in some sense
+
+ align:start position:0%
+in some sense
+ 
+
+ align:start position:0%
+in some sense
+i ask you or the video asks you to count
+
+ align:start position:0%
+i ask you or the video asks you to count
+ 
+
+ align:start position:0%
+i ask you or the video asks you to count
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+passes so in some sense the gorilla is
+
+ align:start position:0%
+passes so in some sense the gorilla is
+ 
+
+ align:start position:0%
+passes so in some sense the gorilla is
+irrelevant and that's true in this case
+
+ align:start position:0%
+irrelevant and that's true in this case
+ 
+
+ align:start position:0%
+irrelevant and that's true in this case
+but in many other cases people might
+
+ align:start position:0%
+but in many other cases people might
+ 
+
+ align:start position:0%
+but in many other cases people might
+sort of not rationally pay attention
+
+ align:start position:0%
+sort of not rationally pay attention
+ 
+
+ align:start position:0%
+sort of not rationally pay attention
+they might sort of miss
+
+ align:start position:0%
+they might sort of miss
+ 
+
+ align:start position:0%
+they might sort of miss
+some really important things in their
+
+ align:start position:0%
+some really important things in their
+ 
+
+ align:start position:0%
+some really important things in their
+lives in part because you know they're
+
+ align:start position:0%
+lives in part because you know they're
+ 
+
+ align:start position:0%
+lives in part because you know they're
+distracted and part because they don't
+
+ align:start position:0%
+distracted and part because they don't
+ 
+
+ align:start position:0%
+distracted and part because they don't
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+pay attention and so on um and sort of
+
+ align:start position:0%
+pay attention and so on um and sort of
+ 
+
+ align:start position:0%
+pay attention and so on um and sort of
+some of the strand of behavioral
+
+ align:start position:0%
+some of the strand of behavioral
+ 
+
+ align:start position:0%
+some of the strand of behavioral
+economics which we'll talk about is sort
+
+ align:start position:0%
+economics which we'll talk about is sort
+ 
+
+ align:start position:0%
+economics which we'll talk about is sort
+of like
+
+ align:start position:0%
+of like
+ 
+
+ align:start position:0%
+of like
+when people do not pay attention and
+
+ align:start position:0%
+when people do not pay attention and
+ 
+
+ align:start position:0%
+when people do not pay attention and
+then make mistakes
+
+ align:start position:0%
+then make mistakes
+ 
+
+ align:start position:0%
+then make mistakes
+because of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i could go on and on with lots
+
+ align:start position:0%
+okay so i could go on and on with lots
+ 
+
+ align:start position:0%
+okay so i could go on and on with lots
+of different examples but
+
+ align:start position:0%
+of different examples but
+ 
+
+ align:start position:0%
+of different examples but
+the bottom line here is that most
+
+ align:start position:0%
+the bottom line here is that most
+ 
+
+ align:start position:0%
+the bottom line here is that most
+researchers in psychology economics
+
+ align:start position:0%
+researchers in psychology economics
+ 
+
+ align:start position:0%
+researchers in psychology economics
+believe that the classical um model of
+
+ align:start position:0%
+believe that the classical um model of
+ 
+
+ align:start position:0%
+believe that the classical um model of
+behavior to the homo economics is too
+
+ align:start position:0%
+behavior to the homo economics is too
+ 
+
+ align:start position:0%
+behavior to the homo economics is too
+too extreme in various ways uh that that
+
+ align:start position:0%
+too extreme in various ways uh that that
+ 
+
+ align:start position:0%
+too extreme in various ways uh that that
+person is too selfish
+
+ align:start position:0%
+person is too selfish
+ 
+
+ align:start position:0%
+person is too selfish
+um too rational and too willful and um
+
+ align:start position:0%
+um too rational and too willful and um
+ 
+
+ align:start position:0%
+um too rational and too willful and um
+you know in some ways we want to kind of
+
+ align:start position:0%
+you know in some ways we want to kind of
+ 
+
+ align:start position:0%
+you know in some ways we want to kind of
+understand how relaxing some of these
+
+ align:start position:0%
+understand how relaxing some of these
+ 
+
+ align:start position:0%
+understand how relaxing some of these
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+might make economic models more
+
+ align:start position:0%
+might make economic models more
+ 
+
+ align:start position:0%
+might make economic models more
+realistic now in some sense
+
+ align:start position:0%
+realistic now in some sense
+ 
+
+ align:start position:0%
+realistic now in some sense
+no economist would in fact argue that
+
+ align:start position:0%
+no economist would in fact argue that
+ 
+
+ align:start position:0%
+no economist would in fact argue that
+the assumptions of the standard models
+
+ align:start position:0%
+the assumptions of the standard models
+ 
+
+ align:start position:0%
+the assumptions of the standard models
+are exactly correct
+
+ align:start position:0%
+are exactly correct
+ 
+
+ align:start position:0%
+are exactly correct
+the questions are are these deviations
+
+ align:start position:0%
+the questions are are these deviations
+ 
+
+ align:start position:0%
+the questions are are these deviations
+important do they actually matter for
+
+ align:start position:0%
+important do they actually matter for
+ 
+
+ align:start position:0%
+important do they actually matter for
+something important
+
+ align:start position:0%
+something important
+ 
+
+ align:start position:0%
+something important
+in explaining people's behavior and you
+
+ align:start position:0%
+in explaining people's behavior and you
+ 
+
+ align:start position:0%
+in explaining people's behavior and you
+know which of those assumptions for
+
+ align:start position:0%
+know which of those assumptions for
+ 
+
+ align:start position:0%
+know which of those assumptions for
+deviations
+
+ align:start position:0%
+deviations
+ 
+
+ align:start position:0%
+deviations
+uh actually matter and that's kind of
+
+ align:start position:0%
+uh actually matter and that's kind of
+ 
+
+ align:start position:0%
+uh actually matter and that's kind of
+like the name of the the game here
+
+ align:start position:0%
+like the name of the the game here
+ 
+
+ align:start position:0%
+like the name of the the game here
+um in fact when you look at sort of like
+
+ align:start position:0%
+um in fact when you look at sort of like
+ 
+
+ align:start position:0%
+um in fact when you look at sort of like
+when you talk to cognitive
+
+ align:start position:0%
+when you talk to cognitive
+ 
+
+ align:start position:0%
+when you talk to cognitive
+scientists uh psychologists etc um
+
+ align:start position:0%
+scientists uh psychologists etc um
+ 
+
+ align:start position:0%
+scientists uh psychologists etc um
+they will tell you the world is full of
+
+ align:start position:0%
+they will tell you the world is full of
+ 
+
+ align:start position:0%
+they will tell you the world is full of
+uh cognitive biases and uh you
+
+ align:start position:0%
+uh cognitive biases and uh you
+ 
+
+ align:start position:0%
+uh cognitive biases and uh you
+might not be able to read this and
+
+ align:start position:0%
+might not be able to read this and
+ 
+
+ align:start position:0%
+might not be able to read this and
+that's kind of the point there's like so
+
+ align:start position:0%
+that's kind of the point there's like so
+ 
+
+ align:start position:0%
+that's kind of the point there's like so
+many different things in which we're
+
+ align:start position:0%
+many different things in which we're
+ 
+
+ align:start position:0%
+many different things in which we're
+biased in some sense every choice that
+
+ align:start position:0%
+biased in some sense every choice that
+ 
+
+ align:start position:0%
+biased in some sense every choice that
+we make or anything
+
+ align:start position:0%
+we make or anything
+ 
+
+ align:start position:0%
+we make or anything
+we do there's lots of biases that
+
+ align:start position:0%
+we do there's lots of biases that
+ 
+
+ align:start position:0%
+we do there's lots of biases that
+interfere with people's choices
+
+ align:start position:0%
+interfere with people's choices
+ 
+
+ align:start position:0%
+interfere with people's choices
+and almost any choice you can think of
+
+ align:start position:0%
+and almost any choice you can think of
+ 
+
+ align:start position:0%
+and almost any choice you can think of
+or any behavior they can think about
+
+ align:start position:0%
+or any behavior they can think about
+ 
+
+ align:start position:0%
+or any behavior they can think about
+there will be a psychology or other
+
+ align:start position:0%
+there will be a psychology or other
+ 
+
+ align:start position:0%
+there will be a psychology or other
+experiments showing that people do not
+
+ align:start position:0%
+experiments showing that people do not
+ 
+
+ align:start position:0%
+experiments showing that people do not
+uh behave perfectly now
+
+ align:start position:0%
+uh behave perfectly now
+ 
+
+ align:start position:0%
+uh behave perfectly now
+the key question then is which of those
+
+ align:start position:0%
+the key question then is which of those
+ 
+
+ align:start position:0%
+the key question then is which of those
+assumptions are are important or which
+
+ align:start position:0%
+assumptions are are important or which
+ 
+
+ align:start position:0%
+assumptions are are important or which
+of those assumptions
+
+ align:start position:0%
+of those assumptions
+ 
+
+ align:start position:0%
+of those assumptions
+violations of assumptions should we
+
+ align:start position:0%
+violations of assumptions should we
+ 
+
+ align:start position:0%
+violations of assumptions should we
+focus on and for that i want to step
+
+ align:start position:0%
+focus on and for that i want to step
+ 
+
+ align:start position:0%
+focus on and for that i want to step
+back a little bit and say okay what is
+
+ align:start position:0%
+back a little bit and say okay what is
+ 
+
+ align:start position:0%
+back a little bit and say okay what is
+actually a model
+
+ align:start position:0%
+actually a model
+ 
+
+ align:start position:0%
+actually a model
+what are economic models are trying to
+
+ align:start position:0%
+what are economic models are trying to
+ 
+
+ align:start position:0%
+what are economic models are trying to
+do and so what is a model a model
+
+ align:start position:0%
+do and so what is a model a model
+ 
+
+ align:start position:0%
+do and so what is a model a model
+is a simplified representation of the
+
+ align:start position:0%
+is a simplified representation of the
+ 
+
+ align:start position:0%
+is a simplified representation of the
+world um
+
+ align:start position:0%
+world um
+ 
+
+ align:start position:0%
+world um
+and we we know in some sense that the
+
+ align:start position:0%
+and we we know in some sense that the
+ 
+
+ align:start position:0%
+and we we know in some sense that the
+assumptions of the models are not true
+
+ align:start position:0%
+assumptions of the models are not true
+ 
+
+ align:start position:0%
+assumptions of the models are not true
+they're sort of supposed to be
+
+ align:start position:0%
+they're sort of supposed to be
+ 
+
+ align:start position:0%
+they're sort of supposed to be
+approximately true and
+
+ align:start position:0%
+approximately true and
+ 
+
+ align:start position:0%
+approximately true and
+exactly uh false so when you think about
+
+ align:start position:0%
+exactly uh false so when you think about
+ 
+
+ align:start position:0%
+exactly uh false so when you think about
+like used models of the earth
+
+ align:start position:0%
+like used models of the earth
+ 
+
+ align:start position:0%
+like used models of the earth
+in some sense they're like flat
+
+ align:start position:0%
+in some sense they're like flat
+ 
+
+ align:start position:0%
+in some sense they're like flat
+spherical ellipsoid and so on and so
+
+ align:start position:0%
+spherical ellipsoid and so on and so
+ 
+
+ align:start position:0%
+spherical ellipsoid and so on and so
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+um models so good models do not accounts
+
+ align:start position:0%
+um models so good models do not accounts
+ 
+
+ align:start position:0%
+um models so good models do not accounts
+for bumps and and grooves and so on
+
+ align:start position:0%
+for bumps and and grooves and so on
+ 
+
+ align:start position:0%
+for bumps and and grooves and so on
+a perfect replica of the earth is not a
+
+ align:start position:0%
+a perfect replica of the earth is not a
+ 
+
+ align:start position:0%
+a perfect replica of the earth is not a
+useful model to use
+
+ align:start position:0%
+useful model to use
+ 
+
+ align:start position:0%
+useful model to use
+you kind of want to simplify and capture
+
+ align:start position:0%
+you kind of want to simplify and capture
+ 
+
+ align:start position:0%
+you kind of want to simplify and capture
+the essence of what's what's um
+
+ align:start position:0%
+the essence of what's what's um
+ 
+
+ align:start position:0%
+the essence of what's what's um
+important so now then what's a good
+
+ align:start position:0%
+important so now then what's a good
+ 
+
+ align:start position:0%
+important so now then what's a good
+model well a good model and you can read
+
+ align:start position:0%
+model well a good model and you can read
+ 
+
+ align:start position:0%
+model well a good model and you can read
+a bit about this in
+
+ align:start position:0%
+a bit about this in
+ 
+
+ align:start position:0%
+a bit about this in
+and get back in lapses paper a good
+
+ align:start position:0%
+and get back in lapses paper a good
+ 
+
+ align:start position:0%
+and get back in lapses paper a good
+model is supposed to be simple
+
+ align:start position:0%
+model is supposed to be simple
+ 
+
+ align:start position:0%
+model is supposed to be simple
+it's supposed to be easy to work with
+
+ align:start position:0%
+it's supposed to be easy to work with
+ 
+
+ align:start position:0%
+it's supposed to be easy to work with
+and tractable so in some sense you have
+
+ align:start position:0%
+and tractable so in some sense you have
+ 
+
+ align:start position:0%
+and tractable so in some sense you have
+only like a few variables or a few
+
+ align:start position:0%
+only like a few variables or a few
+ 
+
+ align:start position:0%
+only like a few variables or a few
+things that you uh
+
+ align:start position:0%
+things that you uh
+ 
+
+ align:start position:0%
+things that you uh
+that matter it's conceptually insightful
+
+ align:start position:0%
+that matter it's conceptually insightful
+ 
+
+ align:start position:0%
+that matter it's conceptually insightful
+in the sense that like
+
+ align:start position:0%
+in the sense that like
+ 
+
+ align:start position:0%
+in the sense that like
+it it focuses on important things it
+
+ align:start position:0%
+it it focuses on important things it
+ 
+
+ align:start position:0%
+it it focuses on important things it
+tells you about behavior that we really
+
+ align:start position:0%
+tells you about behavior that we really
+ 
+
+ align:start position:0%
+tells you about behavior that we really
+care about and important ideas
+
+ align:start position:0%
+care about and important ideas
+ 
+
+ align:start position:0%
+care about and important ideas
+it's generalizable in a sense like
+
+ align:start position:0%
+it's generalizable in a sense like
+ 
+
+ align:start position:0%
+it's generalizable in a sense like
+ideally we are trying to look for some
+
+ align:start position:0%
+ideally we are trying to look for some
+ 
+
+ align:start position:0%
+ideally we are trying to look for some
+behaviors
+
+ align:start position:0%
+behaviors
+ 
+
+ align:start position:0%
+behaviors
+that are general in some sense so if i
+
+ align:start position:0%
+that are general in some sense so if i
+ 
+
+ align:start position:0%
+that are general in some sense so if i
+can just explain you one simple choice
+
+ align:start position:0%
+can just explain you one simple choice
+ 
+
+ align:start position:0%
+can just explain you one simple choice
+in one domain
+
+ align:start position:0%
+in one domain
+ 
+
+ align:start position:0%
+in one domain
+and write a model about it but that
+
+ align:start position:0%
+and write a model about it but that
+ 
+
+ align:start position:0%
+and write a model about it but that
+model doesn't apply for anything else
+
+ align:start position:0%
+model doesn't apply for anything else
+ 
+
+ align:start position:0%
+model doesn't apply for anything else
+that's not a good model um to work with
+
+ align:start position:0%
+that's not a good model um to work with
+ 
+
+ align:start position:0%
+that's not a good model um to work with
+the model is supposed to be falsifiable
+
+ align:start position:0%
+the model is supposed to be falsifiable
+ 
+
+ align:start position:0%
+the model is supposed to be falsifiable
+in a sense like we can actually test
+
+ align:start position:0%
+in a sense like we can actually test
+ 
+
+ align:start position:0%
+in a sense like we can actually test
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and that's kind of what we do in
+
+ align:start position:0%
+and that's kind of what we do in
+ 
+
+ align:start position:0%
+and that's kind of what we do in
+experimental and behavioral economics we
+
+ align:start position:0%
+experimental and behavioral economics we
+ 
+
+ align:start position:0%
+experimental and behavioral economics we
+try to test people's theories or
+
+ align:start position:0%
+try to test people's theories or
+ 
+
+ align:start position:0%
+try to test people's theories or
+our theories and then sort of empirical
+
+ align:start position:0%
+our theories and then sort of empirical
+ 
+
+ align:start position:0%
+our theories and then sort of empirical
+work and then sort of falsify
+
+ align:start position:0%
+work and then sort of falsify
+ 
+
+ align:start position:0%
+work and then sort of falsify
+or reject models that are wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we should be able to make good
+
+ align:start position:0%
+and we should be able to make good
+ 
+
+ align:start position:0%
+and we should be able to make good
+predictions for people's
+
+ align:start position:0%
+predictions for people's
+ 
+
+ align:start position:0%
+predictions for people's
+behavior now are the assumptions of the
+
+ align:start position:0%
+behavior now are the assumptions of the
+ 
+
+ align:start position:0%
+behavior now are the assumptions of the
+standard models true for most people
+
+ align:start position:0%
+standard models true for most people
+ 
+
+ align:start position:0%
+standard models true for most people
+the answer is no but the key insight
+
+ align:start position:0%
+the answer is no but the key insight
+ 
+
+ align:start position:0%
+the answer is no but the key insight
+here is that
+
+ align:start position:0%
+here is that
+ 
+
+ align:start position:0%
+here is that
+the key properties of good models is
+
+ align:start position:0%
+the key properties of good models is
+ 
+
+ align:start position:0%
+the key properties of good models is
+simplicity so in some sense
+
+ align:start position:0%
+simplicity so in some sense
+ 
+
+ align:start position:0%
+simplicity so in some sense
+assuming perfect rationality selfishness
+
+ align:start position:0%
+assuming perfect rationality selfishness
+ 
+
+ align:start position:0%
+assuming perfect rationality selfishness
+and willpower is actually a simple thing
+
+ align:start position:0%
+and willpower is actually a simple thing
+ 
+
+ align:start position:0%
+and willpower is actually a simple thing
+to do in some sense
+
+ align:start position:0%
+to do in some sense
+ 
+
+ align:start position:0%
+to do in some sense
+the reason why economists have made
+
+ align:start position:0%
+the reason why economists have made
+ 
+
+ align:start position:0%
+the reason why economists have made
+those assumptions to start with
+
+ align:start position:0%
+those assumptions to start with
+ 
+
+ align:start position:0%
+those assumptions to start with
+is not necessarily because i thought
+
+ align:start position:0%
+is not necessarily because i thought
+ 
+
+ align:start position:0%
+is not necessarily because i thought
+people are perfectly rational or or
+
+ align:start position:0%
+people are perfectly rational or or
+ 
+
+ align:start position:0%
+people are perfectly rational or or
+that they're not these uh psychological
+
+ align:start position:0%
+that they're not these uh psychological
+ 
+
+ align:start position:0%
+that they're not these uh psychological
+issues going on
+
+ align:start position:0%
+issues going on
+ 
+
+ align:start position:0%
+issues going on
+the reason is actually simplicity it's
+
+ align:start position:0%
+the reason is actually simplicity it's
+ 
+
+ align:start position:0%
+the reason is actually simplicity it's
+an easy thing to do you model how you
+
+ align:start position:0%
+an easy thing to do you model how you
+ 
+
+ align:start position:0%
+an easy thing to do you model how you
+think people should behave
+
+ align:start position:0%
+think people should behave
+ 
+
+ align:start position:0%
+think people should behave
+and how you behave perfectly and
+
+ align:start position:0%
+and how you behave perfectly and
+ 
+
+ align:start position:0%
+and how you behave perfectly and
+making some of these models sort of
+
+ align:start position:0%
+making some of these models sort of
+ 
+
+ align:start position:0%
+making some of these models sort of
+richer in their psychology is actually
+
+ align:start position:0%
+richer in their psychology is actually
+ 
+
+ align:start position:0%
+richer in their psychology is actually
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+and makes the models more complex and
+
+ align:start position:0%
+and makes the models more complex and
+ 
+
+ align:start position:0%
+and makes the models more complex and
+harder to analyze
+
+ align:start position:0%
+harder to analyze
+ 
+
+ align:start position:0%
+harder to analyze
+so that is just to say well then the
+
+ align:start position:0%
+so that is just to say well then the
+ 
+
+ align:start position:0%
+so that is just to say well then the
+question is like can we find some
+
+ align:start position:0%
+question is like can we find some
+ 
+
+ align:start position:0%
+question is like can we find some
+assumptions of economics can we make
+
+ align:start position:0%
+assumptions of economics can we make
+ 
+
+ align:start position:0%
+assumptions of economics can we make
+them more realistic in a tractable way
+
+ align:start position:0%
+them more realistic in a tractable way
+ 
+
+ align:start position:0%
+them more realistic in a tractable way
+in a sense can we find key things that
+
+ align:start position:0%
+in a sense can we find key things that
+ 
+
+ align:start position:0%
+in a sense can we find key things that
+we change that
+
+ align:start position:0%
+we change that
+ 
+
+ align:start position:0%
+we change that
+keep the models tractable while then
+
+ align:start position:0%
+keep the models tractable while then
+ 
+
+ align:start position:0%
+keep the models tractable while then
+also explaining important things better
+
+ align:start position:0%
+also explaining important things better
+ 
+
+ align:start position:0%
+also explaining important things better
+than we can before
+
+ align:start position:0%
+than we can before
+ 
+
+ align:start position:0%
+than we can before
+right so it's not about just taking all
+
+ align:start position:0%
+right so it's not about just taking all
+ 
+
+ align:start position:0%
+right so it's not about just taking all
+sorts of like psychological issues that
+
+ align:start position:0%
+sorts of like psychological issues that
+ 
+
+ align:start position:0%
+sorts of like psychological issues that
+might be going on and say well
+
+ align:start position:0%
+might be going on and say well
+ 
+
+ align:start position:0%
+might be going on and say well
+economic assumptions are wrong or models
+
+ align:start position:0%
+economic assumptions are wrong or models
+ 
+
+ align:start position:0%
+economic assumptions are wrong or models
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+economics are wrong or the assumptions
+
+ align:start position:0%
+economics are wrong or the assumptions
+ 
+
+ align:start position:0%
+economics are wrong or the assumptions
+of those are wrong we know that these
+
+ align:start position:0%
+of those are wrong we know that these
+ 
+
+ align:start position:0%
+of those are wrong we know that these
+assumptions are wrong
+
+ align:start position:0%
+assumptions are wrong
+ 
+
+ align:start position:0%
+assumptions are wrong
+the question is can we make somewhat
+
+ align:start position:0%
+the question is can we make somewhat
+ 
+
+ align:start position:0%
+the question is can we make somewhat
+simple assumptions or improvements of
+
+ align:start position:0%
+simple assumptions or improvements of
+ 
+
+ align:start position:0%
+simple assumptions or improvements of
+those assumptions
+
+ align:start position:0%
+those assumptions
+ 
+
+ align:start position:0%
+those assumptions
+based on insights from psychology and
+
+ align:start position:0%
+based on insights from psychology and
+ 
+
+ align:start position:0%
+based on insights from psychology and
+other fields that help us improve those
+
+ align:start position:0%
+other fields that help us improve those
+ 
+
+ align:start position:0%
+other fields that help us improve those
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+and then make better uh predictions and
+
+ align:start position:0%
+and then make better uh predictions and
+ 
+
+ align:start position:0%
+and then make better uh predictions and
+all of that in a tractable
+
+ align:start position:0%
+all of that in a tractable
+ 
+
+ align:start position:0%
+all of that in a tractable
+way so now this is very important here
+
+ align:start position:0%
+way so now this is very important here
+ 
+
+ align:start position:0%
+way so now this is very important here
+i'm a good behavioral economic economist
+
+ align:start position:0%
+i'm a good behavioral economic economist
+ 
+
+ align:start position:0%
+i'm a good behavioral economic economist
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+a good student in this class is also a
+
+ align:start position:0%
+a good student in this class is also a
+ 
+
+ align:start position:0%
+a good student in this class is also a
+good economist
+
+ align:start position:0%
+good economist
+ 
+
+ align:start position:0%
+good economist
+behavioral economics is not sort of
+
+ align:start position:0%
+behavioral economics is not sort of
+ 
+
+ align:start position:0%
+behavioral economics is not sort of
+trying to replace standard economics
+
+ align:start position:0%
+trying to replace standard economics
+ 
+
+ align:start position:0%
+trying to replace standard economics
+so i don't want you to go to my
+
+ align:start position:0%
+so i don't want you to go to my
+ 
+
+ align:start position:0%
+so i don't want you to go to my
+colleagues and say you know 1401 1402
+
+ align:start position:0%
+colleagues and say you know 1401 1402
+ 
+
+ align:start position:0%
+colleagues and say you know 1401 1402
+and so on this is all garbage frank is
+
+ align:start position:0%
+and so on this is all garbage frank is
+ 
+
+ align:start position:0%
+and so on this is all garbage frank is
+telling you
+
+ align:start position:0%
+telling you
+ 
+
+ align:start position:0%
+telling you
+um we do things differently in fact you
+
+ align:start position:0%
+um we do things differently in fact you
+ 
+
+ align:start position:0%
+um we do things differently in fact you
+very much need to know those kinds of
+
+ align:start position:0%
+very much need to know those kinds of
+ 
+
+ align:start position:0%
+very much need to know those kinds of
+things from like standard economics
+
+ align:start position:0%
+things from like standard economics
+ 
+
+ align:start position:0%
+things from like standard economics
+to understand what the assumptions are
+
+ align:start position:0%
+to understand what the assumptions are
+ 
+
+ align:start position:0%
+to understand what the assumptions are
+and how to best to deviate
+
+ align:start position:0%
+and how to best to deviate
+ 
+
+ align:start position:0%
+and how to best to deviate
+from that and so as such then like key
+
+ align:start position:0%
+from that and so as such then like key
+ 
+
+ align:start position:0%
+from that and so as such then like key
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+principles of mainstream economics
+
+ align:start position:0%
+principles of mainstream economics
+ 
+
+ align:start position:0%
+principles of mainstream economics
+continue to apply
+
+ align:start position:0%
+continue to apply
+ 
+
+ align:start position:0%
+continue to apply
+decision makers are still highly
+
+ align:start position:0%
+decision makers are still highly
+ 
+
+ align:start position:0%
+decision makers are still highly
+sophisticated markets and incentives
+
+ align:start position:0%
+sophisticated markets and incentives
+ 
+
+ align:start position:0%
+sophisticated markets and incentives
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+they're in fact play a key role in
+
+ align:start position:0%
+they're in fact play a key role in
+ 
+
+ align:start position:0%
+they're in fact play a key role in
+shaping behavior
+
+ align:start position:0%
+shaping behavior
+ 
+
+ align:start position:0%
+shaping behavior
+and markets allocate resources well most
+
+ align:start position:0%
+and markets allocate resources well most
+ 
+
+ align:start position:0%
+and markets allocate resources well most
+of the time the question is can we sort
+
+ align:start position:0%
+of the time the question is can we sort
+ 
+
+ align:start position:0%
+of the time the question is can we sort
+of focus on important deviations and try
+
+ align:start position:0%
+of focus on important deviations and try
+ 
+
+ align:start position:0%
+of focus on important deviations and try
+to fix
+
+ align:start position:0%
+to fix
+ 
+
+ align:start position:0%
+to fix
+those and then again like sort of
+
+ align:start position:0%
+those and then again like sort of
+ 
+
+ align:start position:0%
+those and then again like sort of
+methodological principles still apply
+
+ align:start position:0%
+methodological principles still apply
+ 
+
+ align:start position:0%
+methodological principles still apply
+you use observational experimental data
+
+ align:start position:0%
+you use observational experimental data
+ 
+
+ align:start position:0%
+you use observational experimental data
+mathematical models are good and so on
+
+ align:start position:0%
+mathematical models are good and so on
+ 
+
+ align:start position:0%
+mathematical models are good and so on
+and so forth
+
+ align:start position:0%
+and so forth
+ 
+
+ align:start position:0%
+and so forth
+and ideally models would sort of nest
+
+ align:start position:0%
+and ideally models would sort of nest
+ 
+
+ align:start position:0%
+and ideally models would sort of nest
+the special case stuff
+
+ align:start position:0%
+the special case stuff
+ 
+
+ align:start position:0%
+the special case stuff
+perfect rationality or perfectly sort of
+
+ align:start position:0%
+perfect rationality or perfectly sort of
+ 
+
+ align:start position:0%
+perfect rationality or perfectly sort of
+standard economic models i mean trying
+
+ align:start position:0%
+standard economic models i mean trying
+ 
+
+ align:start position:0%
+standard economic models i mean trying
+to build in some parameters that
+
+ align:start position:0%
+to build in some parameters that
+ 
+
+ align:start position:0%
+to build in some parameters that
+deviates from that and try to understand
+
+ align:start position:0%
+deviates from that and try to understand
+ 
+
+ align:start position:0%
+deviates from that and try to understand
+can we make better
+
+ align:start position:0%
+can we make better
+ 
+
+ align:start position:0%
+can we make better
+predictions and then so often prices are
+
+ align:start position:0%
+predictions and then so often prices are
+ 
+
+ align:start position:0%
+predictions and then so often prices are
+actually the most important aspects of
+
+ align:start position:0%
+actually the most important aspects of
+ 
+
+ align:start position:0%
+actually the most important aspects of
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+here's one experiment by ito at all that
+
+ align:start position:0%
+here's one experiment by ito at all that
+ 
+
+ align:start position:0%
+here's one experiment by ito at all that
+try to essentially sort of change
+
+ align:start position:0%
+try to essentially sort of change
+ 
+
+ align:start position:0%
+try to essentially sort of change
+people's um
+
+ align:start position:0%
+people's um
+ 
+
+ align:start position:0%
+people's um
+energy usage and so on and they have
+
+ align:start position:0%
+energy usage and so on and they have
+ 
+
+ align:start position:0%
+energy usage and so on and they have
+like two treatments one is uh
+
+ align:start position:0%
+like two treatments one is uh
+ 
+
+ align:start position:0%
+like two treatments one is uh
+called moral suration which essentially
+
+ align:start position:0%
+called moral suration which essentially
+ 
+
+ align:start position:0%
+called moral suration which essentially
+is telling people uh uh sort of
+
+ align:start position:0%
+is telling people uh uh sort of
+ 
+
+ align:start position:0%
+is telling people uh uh sort of
+appealing to their morals in some ways
+
+ align:start position:0%
+appealing to their morals in some ways
+ 
+
+ align:start position:0%
+appealing to their morals in some ways
+and the other one is essentially just
+
+ align:start position:0%
+and the other one is essentially just
+ 
+
+ align:start position:0%
+and the other one is essentially just
+financial incentives straight up
+
+ align:start position:0%
+financial incentives straight up
+ 
+
+ align:start position:0%
+financial incentives straight up
+changing the price of people's choices
+
+ align:start position:0%
+changing the price of people's choices
+ 
+
+ align:start position:0%
+changing the price of people's choices
+and what you see in this experiment
+
+ align:start position:0%
+and what you see in this experiment
+ 
+
+ align:start position:0%
+and what you see in this experiment
+essentially is
+
+ align:start position:0%
+essentially is
+ 
+
+ align:start position:0%
+essentially is
+um uh there's a in red you have the
+
+ align:start position:0%
+um uh there's a in red you have the
+ 
+
+ align:start position:0%
+um uh there's a in red you have the
+impact is all treatment effects over
+
+ align:start position:0%
+impact is all treatment effects over
+ 
+
+ align:start position:0%
+impact is all treatment effects over
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+comparing like a treatment group and a
+
+ align:start position:0%
+comparing like a treatment group and a
+ 
+
+ align:start position:0%
+comparing like a treatment group and a
+control group and you see
+
+ align:start position:0%
+control group and you see
+ 
+
+ align:start position:0%
+control group and you see
+and read the treatment effects of the
+
+ align:start position:0%
+and read the treatment effects of the
+ 
+
+ align:start position:0%
+and read the treatment effects of the
+incentives and you see these are
+
+ align:start position:0%
+incentives and you see these are
+ 
+
+ align:start position:0%
+incentives and you see these are
+relatively large and persists over time
+
+ align:start position:0%
+relatively large and persists over time
+ 
+
+ align:start position:0%
+relatively large and persists over time
+and you see the treatment effects of the
+
+ align:start position:0%
+and you see the treatment effects of the
+ 
+
+ align:start position:0%
+and you see the treatment effects of the
+moral suasion treatment which
+
+ align:start position:0%
+moral suasion treatment which
+ 
+
+ align:start position:0%
+moral suasion treatment which
+happens to be you know reasonably large
+
+ align:start position:0%
+happens to be you know reasonably large
+ 
+
+ align:start position:0%
+happens to be you know reasonably large
+to start with but essentially just goes
+
+ align:start position:0%
+to start with but essentially just goes
+ 
+
+ align:start position:0%
+to start with but essentially just goes
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+what we learned from that we were
+
+ align:start position:0%
+what we learned from that we were
+ 
+
+ align:start position:0%
+what we learned from that we were
+learned from that prices matter and
+
+ align:start position:0%
+learned from that prices matter and
+ 
+
+ align:start position:0%
+learned from that prices matter and
+maybe in this case
+
+ align:start position:0%
+maybe in this case
+ 
+
+ align:start position:0%
+maybe in this case
+moral surveillance is just not that
+
+ align:start position:0%
+moral surveillance is just not that
+ 
+
+ align:start position:0%
+moral surveillance is just not that
+important and that's perfectly fine
+
+ align:start position:0%
+important and that's perfectly fine
+ 
+
+ align:start position:0%
+important and that's perfectly fine
+we're trying to identify sort of
+
+ align:start position:0%
+we're trying to identify sort of
+ 
+
+ align:start position:0%
+we're trying to identify sort of
+situations or cases where some of the
+
+ align:start position:0%
+situations or cases where some of the
+ 
+
+ align:start position:0%
+situations or cases where some of the
+underlying psychological issues are
+
+ align:start position:0%
+underlying psychological issues are
+ 
+
+ align:start position:0%
+underlying psychological issues are
+important and we've learned from
+
+ align:start position:0%
+important and we've learned from
+ 
+
+ align:start position:0%
+important and we've learned from
+an experiment that in some cases this
+
+ align:start position:0%
+an experiment that in some cases this
+ 
+
+ align:start position:0%
+an experiment that in some cases this
+doesn't apply well so be it then we
+
+ align:start position:0%
+doesn't apply well so be it then we
+ 
+
+ align:start position:0%
+doesn't apply well so be it then we
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+focus on other cases where the
+
+ align:start position:0%
+focus on other cases where the
+ 
+
+ align:start position:0%
+focus on other cases where the
+psychological issues are
+
+ align:start position:0%
+psychological issues are
+ 
+
+ align:start position:0%
+psychological issues are
+are more important okay so then um
+
+ align:start position:0%
+are more important okay so then um
+ 
+
+ align:start position:0%
+are more important okay so then um
+what sort of our broad approach to each
+
+ align:start position:0%
+what sort of our broad approach to each
+ 
+
+ align:start position:0%
+what sort of our broad approach to each
+topic we're trying to sort of start with
+
+ align:start position:0%
+topic we're trying to sort of start with
+ 
+
+ align:start position:0%
+topic we're trying to sort of start with
+intuitive empirical and uh experimental
+
+ align:start position:0%
+intuitive empirical and uh experimental
+ 
+
+ align:start position:0%
+intuitive empirical and uh experimental
+examples how people behave in in some
+
+ align:start position:0%
+examples how people behave in in some
+ 
+
+ align:start position:0%
+examples how people behave in in some
+situations
+
+ align:start position:0%
+situations
+ 
+
+ align:start position:0%
+situations
+we're trying to think about their
+
+ align:start position:0%
+we're trying to think about their
+ 
+
+ align:start position:0%
+we're trying to think about their
+motivations trying to see about how they
+
+ align:start position:0%
+motivations trying to see about how they
+ 
+
+ align:start position:0%
+motivations trying to see about how they
+make choices and behaviors and how they
+
+ align:start position:0%
+make choices and behaviors and how they
+ 
+
+ align:start position:0%
+make choices and behaviors and how they
+behave in certain situations and then
+
+ align:start position:0%
+behave in certain situations and then
+ 
+
+ align:start position:0%
+behave in certain situations and then
+we're going to try to sort of model this
+
+ align:start position:0%
+we're going to try to sort of model this
+ 
+
+ align:start position:0%
+we're going to try to sort of model this
+in a more precise way
+
+ align:start position:0%
+in a more precise way
+ 
+
+ align:start position:0%
+in a more precise way
+and try to consider how the modeling of
+
+ align:start position:0%
+and try to consider how the modeling of
+ 
+
+ align:start position:0%
+and try to consider how the modeling of
+that perhaps deviates from the
+
+ align:start position:0%
+that perhaps deviates from the
+ 
+
+ align:start position:0%
+that perhaps deviates from the
+neoclassical
+
+ align:start position:0%
+neoclassical
+ 
+
+ align:start position:0%
+neoclassical
+uh or sort of the classical model of
+
+ align:start position:0%
+uh or sort of the classical model of
+ 
+
+ align:start position:0%
+uh or sort of the classical model of
+economics some other times you also just
+
+ align:start position:0%
+economics some other times you also just
+ 
+
+ align:start position:0%
+economics some other times you also just
+start from the classical model of
+
+ align:start position:0%
+start from the classical model of
+ 
+
+ align:start position:0%
+start from the classical model of
+economics look at the predictions and
+
+ align:start position:0%
+economics look at the predictions and
+ 
+
+ align:start position:0%
+economics look at the predictions and
+say well
+
+ align:start position:0%
+say well
+ 
+
+ align:start position:0%
+say well
+can we reject that or do we make certain
+
+ align:start position:0%
+can we reject that or do we make certain
+ 
+
+ align:start position:0%
+can we reject that or do we make certain
+predictions that are just not true and
+
+ align:start position:0%
+predictions that are just not true and
+ 
+
+ align:start position:0%
+predictions that are just not true and
+then say can we sort of improve those
+
+ align:start position:0%
+then say can we sort of improve those
+ 
+
+ align:start position:0%
+then say can we sort of improve those
+types of
+
+ align:start position:0%
+types of
+ 
+
+ align:start position:0%
+types of
+assumptions and then overall they're
+
+ align:start position:0%
+assumptions and then overall they're
+ 
+
+ align:start position:0%
+assumptions and then overall they're
+trying to think about then you know how
+
+ align:start position:0%
+trying to think about then you know how
+ 
+
+ align:start position:0%
+trying to think about then you know how
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+hypotheses or deviations might be able
+
+ align:start position:0%
+hypotheses or deviations might be able
+ 
+
+ align:start position:0%
+hypotheses or deviations might be able
+to explain how people behave and markets
+
+ align:start position:0%
+to explain how people behave and markets
+ 
+
+ align:start position:0%
+to explain how people behave and markets
+and what choices they make
+
+ align:start position:0%
+and what choices they make
+ 
+
+ align:start position:0%
+and what choices they make
+and how perhaps we can think about
+
+ align:start position:0%
+and how perhaps we can think about
+ 
+
+ align:start position:0%
+and how perhaps we can think about
+policies that might affect the people's
+
+ align:start position:0%
+policies that might affect the people's
+ 
+
+ align:start position:0%
+policies that might affect the people's
+well-being
+
+ align:start position:0%
+well-being
+ 
+
+ align:start position:0%
+well-being
+their welfare or any other consequences
+
+ align:start position:0%
+their welfare or any other consequences
+ 
+
+ align:start position:0%
+their welfare or any other consequences
+any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um now i want to give you one
+
+ align:start position:0%
+okay so um now i want to give you one
+ 
+
+ align:start position:0%
+okay so um now i want to give you one
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+simple and some sense stylized example
+
+ align:start position:0%
+simple and some sense stylized example
+ 
+
+ align:start position:0%
+simple and some sense stylized example
+of uh which would
+
+ align:start position:0%
+of uh which would
+ 
+
+ align:start position:0%
+of uh which would
+demonstrate a little bit what sort of
+
+ align:start position:0%
+demonstrate a little bit what sort of
+ 
+
+ align:start position:0%
+demonstrate a little bit what sort of
+like you know classical economic
+
+ align:start position:0%
+like you know classical economic
+ 
+
+ align:start position:0%
+like you know classical economic
+uh standard uh economic assumptions are
+
+ align:start position:0%
+uh standard uh economic assumptions are
+ 
+
+ align:start position:0%
+uh standard uh economic assumptions are
+and may
+
+ align:start position:0%
+and may
+ 
+
+ align:start position:0%
+and may
+how sort of enriching a model with
+
+ align:start position:0%
+how sort of enriching a model with
+ 
+
+ align:start position:0%
+how sort of enriching a model with
+psychological considerations
+
+ align:start position:0%
+psychological considerations
+ 
+
+ align:start position:0%
+psychological considerations
+um might be more powerful so
+
+ align:start position:0%
+um might be more powerful so
+ 
+
+ align:start position:0%
+um might be more powerful so
+um when you think about laptops in class
+
+ align:start position:0%
+um when you think about laptops in class
+ 
+
+ align:start position:0%
+um when you think about laptops in class
+what are sort of
+
+ align:start position:0%
+what are sort of
+ 
+
+ align:start position:0%
+what are sort of
+standard economic concept considerations
+
+ align:start position:0%
+standard economic concept considerations
+ 
+
+ align:start position:0%
+standard economic concept considerations
+should you allow laptops should they be
+
+ align:start position:0%
+should you allow laptops should they be
+ 
+
+ align:start position:0%
+should you allow laptops should they be
+laptops in class is that a good thing or
+
+ align:start position:0%
+laptops in class is that a good thing or
+ 
+
+ align:start position:0%
+laptops in class is that a good thing or
+a bad thing or
+
+ align:start position:0%
+a bad thing or
+ 
+
+ align:start position:0%
+a bad thing or
+what do we think about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now i'm asking for like standard
+
+ align:start position:0%
+and now i'm asking for like standard
+ 
+
+ align:start position:0%
+and now i'm asking for like standard
+non-psychological issues just saying
+
+ align:start position:0%
+non-psychological issues just saying
+ 
+
+ align:start position:0%
+non-psychological issues just saying
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+he went to like a classical economist
+
+ align:start position:0%
+he went to like a classical economist
+ 
+
+ align:start position:0%
+he went to like a classical economist
+and says should we allow laptops in
+
+ align:start position:0%
+and says should we allow laptops in
+ 
+
+ align:start position:0%
+and says should we allow laptops in
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+what would be considerations for that
+
+ align:start position:0%
+what would be considerations for that
+ 
+
+ align:start position:0%
+what would be considerations for that
+yeah uh
+
+ align:start position:0%
+yeah uh
+ 
+
+ align:start position:0%
+yeah uh
+yes so you know you could call that
+
+ align:start position:0%
+yes so you know you could call that
+ 
+
+ align:start position:0%
+yes so you know you could call that
+a psychological or not but essentially
+
+ align:start position:0%
+a psychological or not but essentially
+ 
+
+ align:start position:0%
+a psychological or not but essentially
+it could distract people essentially and
+
+ align:start position:0%
+it could distract people essentially and
+ 
+
+ align:start position:0%
+it could distract people essentially and
+that's uh externalities tend to be sort
+
+ align:start position:0%
+that's uh externalities tend to be sort
+ 
+
+ align:start position:0%
+that's uh externalities tend to be sort
+of like
+
+ align:start position:0%
+of like
+ 
+
+ align:start position:0%
+of like
+uh very much like in classical economics
+
+ align:start position:0%
+uh very much like in classical economics
+ 
+
+ align:start position:0%
+uh very much like in classical economics
+essentially if you smoke it affects
+
+ align:start position:0%
+essentially if you smoke it affects
+ 
+
+ align:start position:0%
+essentially if you smoke it affects
+others similarly if a laptop it might
+
+ align:start position:0%
+others similarly if a laptop it might
+ 
+
+ align:start position:0%
+others similarly if a laptop it might
+affect others
+
+ align:start position:0%
+affect others
+ 
+
+ align:start position:0%
+affect others
+it's a little bit sort of in the middle
+
+ align:start position:0%
+it's a little bit sort of in the middle
+ 
+
+ align:start position:0%
+it's a little bit sort of in the middle
+between psychological and economic
+
+ align:start position:0%
+between psychological and economic
+ 
+
+ align:start position:0%
+between psychological and economic
+considerations because in some sense
+
+ align:start position:0%
+considerations because in some sense
+ 
+
+ align:start position:0%
+considerations because in some sense
+uh you know if somebody next to you
+
+ align:start position:0%
+uh you know if somebody next to you
+ 
+
+ align:start position:0%
+uh you know if somebody next to you
+would use a laptop
+
+ align:start position:0%
+would use a laptop
+ 
+
+ align:start position:0%
+would use a laptop
+and i would just say well why don't you
+
+ align:start position:0%
+and i would just say well why don't you
+ 
+
+ align:start position:0%
+and i would just say well why don't you
+just focus on class anyway you should be
+
+ align:start position:0%
+just focus on class anyway you should be
+ 
+
+ align:start position:0%
+just focus on class anyway you should be
+able to just ignore that
+
+ align:start position:0%
+able to just ignore that
+ 
+
+ align:start position:0%
+able to just ignore that
+but setting that aside that exactly
+
+ align:start position:0%
+but setting that aside that exactly
+ 
+
+ align:start position:0%
+but setting that aside that exactly
+externalities are surely one
+
+ align:start position:0%
+externalities are surely one
+ 
+
+ align:start position:0%
+externalities are surely one
+considerations that we have
+
+ align:start position:0%
+considerations that we have
+ 
+
+ align:start position:0%
+considerations that we have
+what's the pro side why would we allow
+
+ align:start position:0%
+what's the pro side why would we allow
+ 
+
+ align:start position:0%
+what's the pro side why would we allow
+laptops
+
+ align:start position:0%
+laptops
+ 
+
+ align:start position:0%
+laptops
+what's good about laptops in class yeah
+
+ align:start position:0%
+what's good about laptops in class yeah
+ 
+
+ align:start position:0%
+what's good about laptops in class yeah
+like it could just be efficient for
+
+ align:start position:0%
+like it could just be efficient for
+ 
+
+ align:start position:0%
+like it could just be efficient for
+taking notes some people might need to
+
+ align:start position:0%
+taking notes some people might need to
+ 
+
+ align:start position:0%
+taking notes some people might need to
+use them some people maybe are
+
+ align:start position:0%
+use them some people maybe are
+ 
+
+ align:start position:0%
+use them some people maybe are
+dispensing
+
+ align:start position:0%
+dispensing
+ 
+
+ align:start position:0%
+dispensing
+stuff like that so it's just good
+
+ align:start position:0%
+stuff like that so it's just good
+ 
+
+ align:start position:0%
+stuff like that so it's just good
+exactly it's like a useful technology
+
+ align:start position:0%
+exactly it's like a useful technology
+ 
+
+ align:start position:0%
+exactly it's like a useful technology
+to take notes and you might just be
+
+ align:start position:0%
+to take notes and you might just be
+ 
+
+ align:start position:0%
+to take notes and you might just be
+better that it might be more comfortable
+
+ align:start position:0%
+better that it might be more comfortable
+ 
+
+ align:start position:0%
+better that it might be more comfortable
+it's easier for it to do
+
+ align:start position:0%
+it's easier for it to do
+ 
+
+ align:start position:0%
+it's easier for it to do
+maybe it's also saved some paper or
+
+ align:start position:0%
+maybe it's also saved some paper or
+ 
+
+ align:start position:0%
+maybe it's also saved some paper or
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+what else are laptops good for yeah i
+
+ align:start position:0%
+what else are laptops good for yeah i
+ 
+
+ align:start position:0%
+what else are laptops good for yeah i
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+more choices just always better so if
+
+ align:start position:0%
+more choices just always better so if
+ 
+
+ align:start position:0%
+more choices just always better so if
+each person has their laptop they can
+
+ align:start position:0%
+each person has their laptop they can
+ 
+
+ align:start position:0%
+each person has their laptop they can
+choose what's better for them
+
+ align:start position:0%
+choose what's better for them
+ 
+
+ align:start position:0%
+choose what's better for them
+yes exactly if you are so inclined and
+
+ align:start position:0%
+yes exactly if you are so inclined and
+ 
+
+ align:start position:0%
+yes exactly if you are so inclined and
+want to watch football from yesterday
+
+ align:start position:0%
+want to watch football from yesterday
+ 
+
+ align:start position:0%
+want to watch football from yesterday
+the replay and so on if you prefer that
+
+ align:start position:0%
+the replay and so on if you prefer that
+ 
+
+ align:start position:0%
+the replay and so on if you prefer that
+and that's good for you
+
+ align:start position:0%
+and that's good for you
+ 
+
+ align:start position:0%
+and that's good for you
+uh you know who should be stopping you
+
+ align:start position:0%
+uh you know who should be stopping you
+ 
+
+ align:start position:0%
+uh you know who should be stopping you
+right and so
+
+ align:start position:0%
+right and so
+ 
+
+ align:start position:0%
+right and so
+uh at some sense laptops are useful for
+
+ align:start position:0%
+uh at some sense laptops are useful for
+ 
+
+ align:start position:0%
+uh at some sense laptops are useful for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+note-taking they're also useful for uh
+
+ align:start position:0%
+note-taking they're also useful for uh
+ 
+
+ align:start position:0%
+note-taking they're also useful for uh
+non-class activities
+
+ align:start position:0%
+non-class activities
+ 
+
+ align:start position:0%
+non-class activities
+and as you say each student should be
+
+ align:start position:0%
+and as you say each student should be
+ 
+
+ align:start position:0%
+and as you say each student should be
+able to choose for themselves
+
+ align:start position:0%
+able to choose for themselves
+ 
+
+ align:start position:0%
+able to choose for themselves
+um what's good and um uh that may be
+
+ align:start position:0%
+um what's good and um uh that may be
+ 
+
+ align:start position:0%
+um what's good and um uh that may be
+involved like paying attention or or or
+
+ align:start position:0%
+involved like paying attention or or or
+ 
+
+ align:start position:0%
+involved like paying attention or or or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+now what else sort of some psychological
+
+ align:start position:0%
+now what else sort of some psychological
+ 
+
+ align:start position:0%
+now what else sort of some psychological
+conservations we had one of them which
+
+ align:start position:0%
+conservations we had one of them which
+ 
+
+ align:start position:0%
+conservations we had one of them which
+is essentially distracting others which
+
+ align:start position:0%
+is essentially distracting others which
+ 
+
+ align:start position:0%
+is essentially distracting others which
+essentially is the externality
+
+ align:start position:0%
+essentially is the externality
+ 
+
+ align:start position:0%
+essentially is the externality
+um what else yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right exactly you might sort of uh have
+
+ align:start position:0%
+right exactly you might sort of uh have
+ 
+
+ align:start position:0%
+right exactly you might sort of uh have
+all the best intentions of taking notes
+
+ align:start position:0%
+all the best intentions of taking notes
+ 
+
+ align:start position:0%
+all the best intentions of taking notes
+of the what i said previously but then
+
+ align:start position:0%
+of the what i said previously but then
+ 
+
+ align:start position:0%
+of the what i said previously but then
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+it gets a little dull and boring at
+
+ align:start position:0%
+it gets a little dull and boring at
+ 
+
+ align:start position:0%
+it gets a little dull and boring at
+minutes when it's 40
+
+ align:start position:0%
+minutes when it's 40
+ 
+
+ align:start position:0%
+minutes when it's 40
+and you might sort of be inclined to
+
+ align:start position:0%
+and you might sort of be inclined to
+ 
+
+ align:start position:0%
+and you might sort of be inclined to
+sort of think about other uh stuff and
+
+ align:start position:0%
+sort of think about other uh stuff and
+ 
+
+ align:start position:0%
+sort of think about other uh stuff and
+sort of start surfing in the internet or
+
+ align:start position:0%
+sort of start surfing in the internet or
+ 
+
+ align:start position:0%
+sort of start surfing in the internet or
+the like or start chatting or whatever
+
+ align:start position:0%
+the like or start chatting or whatever
+ 
+
+ align:start position:0%
+the like or start chatting or whatever
+that sort of essentially limited
+
+ align:start position:0%
+that sort of essentially limited
+ 
+
+ align:start position:0%
+that sort of essentially limited
+self-control one way or the other
+
+ align:start position:0%
+self-control one way or the other
+ 
+
+ align:start position:0%
+self-control one way or the other
+yeah yeah i think so i think even if you
+
+ align:start position:0%
+yeah yeah i think so i think even if you
+ 
+
+ align:start position:0%
+yeah yeah i think so i think even if you
+don't fall into the limitation
+
+ align:start position:0%
+don't fall into the limitation
+ 
+
+ align:start position:0%
+don't fall into the limitation
+you kind of have to spend energy
+
+ align:start position:0%
+you kind of have to spend energy
+ 
+
+ align:start position:0%
+you kind of have to spend energy
+resisting that temptation and that might
+
+ align:start position:0%
+resisting that temptation and that might
+ 
+
+ align:start position:0%
+resisting that temptation and that might
+kind of distract you
+
+ align:start position:0%
+kind of distract you
+ 
+
+ align:start position:0%
+kind of distract you
+right so there's some cognitive
+
+ align:start position:0%
+right so there's some cognitive
+ 
+
+ align:start position:0%
+right so there's some cognitive
+resources potentially from
+
+ align:start position:0%
+resources potentially from
+ 
+
+ align:start position:0%
+resources potentially from
+from that that's a very nice observation
+
+ align:start position:0%
+from that that's a very nice observation
+ 
+
+ align:start position:0%
+from that that's a very nice observation
+exactly that that also might be true
+
+ align:start position:0%
+exactly that that also might be true
+ 
+
+ align:start position:0%
+exactly that that also might be true
+there's another part to that which is
+
+ align:start position:0%
+there's another part to that which is
+ 
+
+ align:start position:0%
+there's another part to that which is
+people tend to overestimate how much
+
+ align:start position:0%
+people tend to overestimate how much
+ 
+
+ align:start position:0%
+people tend to overestimate how much
+they can multitask and there's
+
+ align:start position:0%
+they can multitask and there's
+ 
+
+ align:start position:0%
+they can multitask and there's
+like a large number of experiments that
+
+ align:start position:0%
+like a large number of experiments that
+ 
+
+ align:start position:0%
+like a large number of experiments that
+say well i'm actually paying attention
+
+ align:start position:0%
+say well i'm actually paying attention
+ 
+
+ align:start position:0%
+say well i'm actually paying attention
+i'm look you know i'm just sort of
+
+ align:start position:0%
+i'm look you know i'm just sort of
+ 
+
+ align:start position:0%
+i'm look you know i'm just sort of
+reading some other stuff i'm chatting
+
+ align:start position:0%
+reading some other stuff i'm chatting
+ 
+
+ align:start position:0%
+reading some other stuff i'm chatting
+with my friend
+
+ align:start position:0%
+with my friend
+ 
+
+ align:start position:0%
+with my friend
+um and people actually think they pay
+
+ align:start position:0%
+um and people actually think they pay
+ 
+
+ align:start position:0%
+um and people actually think they pay
+attention and they learn
+
+ align:start position:0%
+attention and they learn
+ 
+
+ align:start position:0%
+attention and they learn
+trust me they do not so essentially
+
+ align:start position:0%
+trust me they do not so essentially
+ 
+
+ align:start position:0%
+trust me they do not so essentially
+there's a large large literature on
+
+ align:start position:0%
+there's a large large literature on
+ 
+
+ align:start position:0%
+there's a large large literature on
+people thinking that they can
+
+ align:start position:0%
+people thinking that they can
+ 
+
+ align:start position:0%
+people thinking that they can
+multitask when in fact they cannot
+
+ align:start position:0%
+multitask when in fact they cannot
+ 
+
+ align:start position:0%
+multitask when in fact they cannot
+there's a very human thing to do
+
+ align:start position:0%
+there's a very human thing to do
+ 
+
+ align:start position:0%
+there's a very human thing to do
+you might think you know you can study
+
+ align:start position:0%
+you might think you know you can study
+ 
+
+ align:start position:0%
+you might think you know you can study
+for an exam by watching tv
+
+ align:start position:0%
+for an exam by watching tv
+ 
+
+ align:start position:0%
+for an exam by watching tv
+chances are you're not studying um very
+
+ align:start position:0%
+chances are you're not studying um very
+ 
+
+ align:start position:0%
+chances are you're not studying um very
+well so that's essentially some form of
+
+ align:start position:0%
+well so that's essentially some form of
+ 
+
+ align:start position:0%
+well so that's essentially some form of
+like um
+
+ align:start position:0%
+like um
+ 
+
+ align:start position:0%
+like um
+um overconfidence um
+
+ align:start position:0%
+um overconfidence um
+ 
+
+ align:start position:0%
+um overconfidence um
+right and then there's another part
+
+ align:start position:0%
+right and then there's another part
+ 
+
+ align:start position:0%
+right and then there's another part
+which is sort of like uh
+
+ align:start position:0%
+which is sort of like uh
+ 
+
+ align:start position:0%
+which is sort of like uh
+uh sort of some with different
+
+ align:start position:0%
+uh sort of some with different
+ 
+
+ align:start position:0%
+uh sort of some with different
+psychological consideration which is
+
+ align:start position:0%
+psychological consideration which is
+ 
+
+ align:start position:0%
+psychological consideration which is
+people tend to not like hard paternalism
+
+ align:start position:0%
+people tend to not like hard paternalism
+ 
+
+ align:start position:0%
+people tend to not like hard paternalism
+as in like if you sort of like we talk
+
+ align:start position:0%
+as in like if you sort of like we talk
+ 
+
+ align:start position:0%
+as in like if you sort of like we talk
+about this at the very end when we talk
+
+ align:start position:0%
+about this at the very end when we talk
+ 
+
+ align:start position:0%
+about this at the very end when we talk
+about policy
+
+ align:start position:0%
+about policy
+ 
+
+ align:start position:0%
+about policy
+people don't like certain hard rules
+
+ align:start position:0%
+people don't like certain hard rules
+ 
+
+ align:start position:0%
+people don't like certain hard rules
+about like you're allowed to do this
+
+ align:start position:0%
+about like you're allowed to do this
+ 
+
+ align:start position:0%
+about like you're allowed to do this
+where you don't allow to do x or y you
+
+ align:start position:0%
+where you don't allow to do x or y you
+ 
+
+ align:start position:0%
+where you don't allow to do x or y you
+have to come to class or whatever
+
+ align:start position:0%
+have to come to class or whatever
+ 
+
+ align:start position:0%
+have to come to class or whatever
+people tend to not like that um that's
+
+ align:start position:0%
+people tend to not like that um that's
+ 
+
+ align:start position:0%
+people tend to not like that um that's
+more like another sort of consideration
+
+ align:start position:0%
+more like another sort of consideration
+ 
+
+ align:start position:0%
+more like another sort of consideration
+you think about like what is the right
+
+ align:start position:0%
+you think about like what is the right
+ 
+
+ align:start position:0%
+you think about like what is the right
+policy um
+
+ align:start position:0%
+policy um
+ 
+
+ align:start position:0%
+policy um
+to do now what policy solutions could we
+
+ align:start position:0%
+to do now what policy solutions could we
+ 
+
+ align:start position:0%
+to do now what policy solutions could we
+do what what laptop policies have you
+
+ align:start position:0%
+do what what laptop policies have you
+ 
+
+ align:start position:0%
+do what what laptop policies have you
+seen or how do you think about them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe somebody else yes
+
+ align:start position:0%
+maybe somebody else yes
+ 
+
+ align:start position:0%
+maybe somebody else yes
+i haven't seen it but let the people
+
+ align:start position:0%
+i haven't seen it but let the people
+ 
+
+ align:start position:0%
+i haven't seen it but let the people
+with laptops sit in the back
+
+ align:start position:0%
+with laptops sit in the back
+ 
+
+ align:start position:0%
+with laptops sit in the back
+yes you could have you could do that um
+
+ align:start position:0%
+yes you could have you could do that um
+ 
+
+ align:start position:0%
+yes you could have you could do that um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and sort of that's kind of like
+
+ align:start position:0%
+and sort of that's kind of like
+ 
+
+ align:start position:0%
+and sort of that's kind of like
+minimizing the the externality
+
+ align:start position:0%
+minimizing the the externality
+ 
+
+ align:start position:0%
+minimizing the the externality
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+um it's not really helping with
+
+ align:start position:0%
+um it's not really helping with
+ 
+
+ align:start position:0%
+um it's not really helping with
+self-control i guess
+
+ align:start position:0%
+self-control i guess
+ 
+
+ align:start position:0%
+self-control i guess
+right because if particularly if you sit
+
+ align:start position:0%
+right because if particularly if you sit
+ 
+
+ align:start position:0%
+right because if particularly if you sit
+in the back nobody sees what you're
+
+ align:start position:0%
+in the back nobody sees what you're
+ 
+
+ align:start position:0%
+in the back nobody sees what you're
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+um and you might be so inclined to to do
+
+ align:start position:0%
+um and you might be so inclined to to do
+ 
+
+ align:start position:0%
+um and you might be so inclined to to do
+all sorts of things
+
+ align:start position:0%
+all sorts of things
+ 
+
+ align:start position:0%
+all sorts of things
+uh yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that's sort of like hard
+
+ align:start position:0%
+right so that's sort of like hard
+ 
+
+ align:start position:0%
+right so that's sort of like hard
+paternalism with some uh
+
+ align:start position:0%
+paternalism with some uh
+ 
+
+ align:start position:0%
+paternalism with some uh
+exceptions potentially yeah
+
+ align:start position:0%
+exceptions potentially yeah
+ 
+
+ align:start position:0%
+exceptions potentially yeah
+um i've seen like only devices that are
+
+ align:start position:0%
+um i've seen like only devices that are
+ 
+
+ align:start position:0%
+um i've seen like only devices that are
+flat on the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for note-taking yeah i've seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+track of class um so if they see you
+
+ align:start position:0%
+track of class um so if they see you
+ 
+
+ align:start position:0%
+track of class um so if they see you
+doing something
+
+ align:start position:0%
+doing something
+ 
+
+ align:start position:0%
+doing something
+not academic they can technically take
+
+ align:start position:0%
+not academic they can technically take
+ 
+
+ align:start position:0%
+not academic they can technically take
+you forward
+
+ align:start position:0%
+you forward
+ 
+
+ align:start position:0%
+you forward
+yeah that's what they're for no no
+
+ align:start position:0%
+yeah that's what they're for no no
+ 
+
+ align:start position:0%
+yeah that's what they're for no no
+um anything else
+
+ align:start position:0%
+um anything else
+ 
+
+ align:start position:0%
+um anything else
+i've seen classes where you're just
+
+ align:start position:0%
+i've seen classes where you're just
+ 
+
+ align:start position:0%
+i've seen classes where you're just
+allowed to use your laptop because i
+
+ align:start position:0%
+allowed to use your laptop because i
+ 
+
+ align:start position:0%
+allowed to use your laptop because i
+guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right exactly that's sort of less affair
+
+ align:start position:0%
+right exactly that's sort of less affair
+ 
+
+ align:start position:0%
+right exactly that's sort of less affair
+saying like you know what's best for you
+
+ align:start position:0%
+saying like you know what's best for you
+ 
+
+ align:start position:0%
+saying like you know what's best for you
+in some sense since this is sort of like
+
+ align:start position:0%
+in some sense since this is sort of like
+ 
+
+ align:start position:0%
+in some sense since this is sort of like
+a psychology income behavioral class
+
+ align:start position:0%
+a psychology income behavioral class
+ 
+
+ align:start position:0%
+a psychology income behavioral class
+uh you know i i tend to
+
+ align:start position:0%
+uh you know i i tend to
+ 
+
+ align:start position:0%
+uh you know i i tend to
+tend to disagree with some of those
+
+ align:start position:0%
+tend to disagree with some of those
+ 
+
+ align:start position:0%
+tend to disagree with some of those
+assumptions but yes exactly that's less
+
+ align:start position:0%
+assumptions but yes exactly that's less
+ 
+
+ align:start position:0%
+assumptions but yes exactly that's less
+affair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other thoughts
+
+ align:start position:0%
+any other thoughts
+ 
+
+ align:start position:0%
+any other thoughts
+uh okay so then uh here they are so
+
+ align:start position:0%
+uh okay so then uh here they are so
+ 
+
+ align:start position:0%
+uh okay so then uh here they are so
+there's um less affair
+
+ align:start position:0%
+there's um less affair
+ 
+
+ align:start position:0%
+there's um less affair
+there's educational intervention which
+
+ align:start position:0%
+there's educational intervention which
+ 
+
+ align:start position:0%
+there's educational intervention which
+essentially just providing people
+
+ align:start position:0%
+essentially just providing people
+ 
+
+ align:start position:0%
+essentially just providing people
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+about um um laptops or what laptops do
+
+ align:start position:0%
+about um um laptops or what laptops do
+ 
+
+ align:start position:0%
+about um um laptops or what laptops do
+for learning
+
+ align:start position:0%
+for learning
+ 
+
+ align:start position:0%
+for learning
+uh there's some experiments i'll show
+
+ align:start position:0%
+uh there's some experiments i'll show
+ 
+
+ align:start position:0%
+uh there's some experiments i'll show
+you in a second educational
+
+ align:start position:0%
+you in a second educational
+ 
+
+ align:start position:0%
+you in a second educational
+interventions tend to actually not
+
+ align:start position:0%
+interventions tend to actually not
+ 
+
+ align:start position:0%
+interventions tend to actually not
+work particularly well so essentially
+
+ align:start position:0%
+work particularly well so essentially
+ 
+
+ align:start position:0%
+work particularly well so essentially
+just giving people information tends to
+
+ align:start position:0%
+just giving people information tends to
+ 
+
+ align:start position:0%
+just giving people information tends to
+not change behavior
+
+ align:start position:0%
+not change behavior
+ 
+
+ align:start position:0%
+not change behavior
+um often in the way we'd like to do that
+
+ align:start position:0%
+um often in the way we'd like to do that
+ 
+
+ align:start position:0%
+um often in the way we'd like to do that
+you could tax laptop users
+
+ align:start position:0%
+you could tax laptop users
+ 
+
+ align:start position:0%
+you could tax laptop users
+say it's costly to do that would be the
+
+ align:start position:0%
+say it's costly to do that would be the
+ 
+
+ align:start position:0%
+say it's costly to do that would be the
+typical sort of like public economic
+
+ align:start position:0%
+typical sort of like public economic
+ 
+
+ align:start position:0%
+typical sort of like public economic
+sort of solution
+
+ align:start position:0%
+sort of solution
+ 
+
+ align:start position:0%
+sort of solution
+i think i'm not allowed to take money
+
+ align:start position:0%
+i think i'm not allowed to take money
+ 
+
+ align:start position:0%
+i think i'm not allowed to take money
+from you guys so so i might not not do
+
+ align:start position:0%
+from you guys so so i might not not do
+ 
+
+ align:start position:0%
+from you guys so so i might not not do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you could ban laptops this is from um
+
+ align:start position:0%
+you could ban laptops this is from um
+ 
+
+ align:start position:0%
+you could ban laptops this is from um
+that was a previous suggestion to say
+
+ align:start position:0%
+that was a previous suggestion to say
+ 
+
+ align:start position:0%
+that was a previous suggestion to say
+except for students with medical need
+
+ align:start position:0%
+except for students with medical need
+ 
+
+ align:start position:0%
+except for students with medical need
+you could make a non-laptop section the
+
+ align:start position:0%
+you could make a non-laptop section the
+ 
+
+ align:start position:0%
+you could make a non-laptop section the
+default and let students opt out or
+
+ align:start position:0%
+default and let students opt out or
+ 
+
+ align:start position:0%
+default and let students opt out or
+opt in depending on that and essentially
+
+ align:start position:0%
+opt in depending on that and essentially
+ 
+
+ align:start position:0%
+opt in depending on that and essentially
+saying like
+
+ align:start position:0%
+saying like
+ 
+
+ align:start position:0%
+saying like
+the default choice is one uh essentially
+
+ align:start position:0%
+the default choice is one uh essentially
+ 
+
+ align:start position:0%
+the default choice is one uh essentially
+no laptops but you can opt into that
+
+ align:start position:0%
+no laptops but you can opt into that
+ 
+
+ align:start position:0%
+no laptops but you can opt into that
+by emailing the a ta and then use it in
+
+ align:start position:0%
+by emailing the a ta and then use it in
+ 
+
+ align:start position:0%
+by emailing the a ta and then use it in
+a certain section uh
+
+ align:start position:0%
+a certain section uh
+ 
+
+ align:start position:0%
+a certain section uh
+we'll talk about in the problems in a
+
+ align:start position:0%
+we'll talk about in the problems in a
+ 
+
+ align:start position:0%
+we'll talk about in the problems in a
+little bit why that might be a good idea
+
+ align:start position:0%
+little bit why that might be a good idea
+ 
+
+ align:start position:0%
+little bit why that might be a good idea
+you could also set up an active choice
+
+ align:start position:0%
+you could also set up an active choice
+ 
+
+ align:start position:0%
+you could also set up an active choice
+between the laptop and the no laptop
+
+ align:start position:0%
+between the laptop and the no laptop
+ 
+
+ align:start position:0%
+between the laptop and the no laptop
+sections so here's the educational
+
+ align:start position:0%
+sections so here's the educational
+ 
+
+ align:start position:0%
+sections so here's the educational
+interventions the the evidence and
+
+ align:start position:0%
+interventions the the evidence and
+ 
+
+ align:start position:0%
+interventions the the evidence and
+there's very clear evidence from various
+
+ align:start position:0%
+there's very clear evidence from various
+ 
+
+ align:start position:0%
+there's very clear evidence from various
+settings that shows that laptops in
+
+ align:start position:0%
+settings that shows that laptops in
+ 
+
+ align:start position:0%
+settings that shows that laptops in
+class are not good for learning
+
+ align:start position:0%
+class are not good for learning
+ 
+
+ align:start position:0%
+class are not good for learning
+on average there's a very nice article
+
+ align:start position:0%
+on average there's a very nice article
+ 
+
+ align:start position:0%
+on average there's a very nice article
+by susan
+
+ align:start position:0%
+by susan
+ 
+
+ align:start position:0%
+by susan
+donarski in the new york times he'll put
+
+ align:start position:0%
+donarski in the new york times he'll put
+ 
+
+ align:start position:0%
+donarski in the new york times he'll put
+this this online as well that you can
+
+ align:start position:0%
+this this online as well that you can
+ 
+
+ align:start position:0%
+this this online as well that you can
+read
+
+ align:start position:0%
+read
+ 
+
+ align:start position:0%
+read
+but essentially one of these studies is
+
+ align:start position:0%
+but essentially one of these studies is
+ 
+
+ align:start position:0%
+but essentially one of these studies is
+a randomized control trial that um
+
+ align:start position:0%
+a randomized control trial that um
+ 
+
+ align:start position:0%
+a randomized control trial that um
+mit a grad student a former mit grad
+
+ align:start position:0%
+mit a grad student a former mit grad
+ 
+
+ align:start position:0%
+mit a grad student a former mit grad
+student had done
+
+ align:start position:0%
+student had done
+ 
+
+ align:start position:0%
+student had done
+in an intro econ class this is carter
+
+ align:start position:0%
+in an intro econ class this is carter
+ 
+
+ align:start position:0%
+in an intro econ class this is carter
+adal and essentially what they find is
+
+ align:start position:0%
+adal and essentially what they find is
+ 
+
+ align:start position:0%
+adal and essentially what they find is
+that allowing computers in class reduced
+
+ align:start position:0%
+that allowing computers in class reduced
+ 
+
+ align:start position:0%
+that allowing computers in class reduced
+test scores by 0.18 standard deviations
+
+ align:start position:0%
+test scores by 0.18 standard deviations
+ 
+
+ align:start position:0%
+test scores by 0.18 standard deviations
+that's quite a large
+
+ align:start position:0%
+that's quite a large
+ 
+
+ align:start position:0%
+that's quite a large
+number that's essentially saying they
+
+ align:start position:0%
+number that's essentially saying they
+ 
+
+ align:start position:0%
+number that's essentially saying they
+didn't randomize across classes like
+
+ align:start position:0%
+didn't randomize across classes like
+ 
+
+ align:start position:0%
+didn't randomize across classes like
+at the classroom level whether they
+
+ align:start position:0%
+at the classroom level whether they
+ 
+
+ align:start position:0%
+at the classroom level whether they
+allowed laptops in class or not
+
+ align:start position:0%
+allowed laptops in class or not
+ 
+
+ align:start position:0%
+allowed laptops in class or not
+interestingly they found negative
+
+ align:start position:0%
+interestingly they found negative
+ 
+
+ align:start position:0%
+interestingly they found negative
+effects both of like unconstrained
+
+ align:start position:0%
+effects both of like unconstrained
+ 
+
+ align:start position:0%
+effects both of like unconstrained
+laptops like
+
+ align:start position:0%
+laptops like
+ 
+
+ align:start position:0%
+laptops like
+any laptop use but also the flat tablet
+
+ align:start position:0%
+any laptop use but also the flat tablet
+ 
+
+ align:start position:0%
+any laptop use but also the flat tablet
+solutions so even the flat tablet
+
+ align:start position:0%
+solutions so even the flat tablet
+ 
+
+ align:start position:0%
+solutions so even the flat tablet
+solution was worse than sort of the note
+
+ align:start position:0%
+solution was worse than sort of the note
+ 
+
+ align:start position:0%
+solution was worse than sort of the note
+taking
+
+ align:start position:0%
+taking
+ 
+
+ align:start position:0%
+taking
+which pen and paper um you know and
+
+ align:start position:0%
+which pen and paper um you know and
+ 
+
+ align:start position:0%
+which pen and paper um you know and
+there's a bunch of evidence that sort of
+
+ align:start position:0%
+there's a bunch of evidence that sort of
+ 
+
+ align:start position:0%
+there's a bunch of evidence that sort of
+shows that
+
+ align:start position:0%
+shows that
+ 
+
+ align:start position:0%
+shows that
+so in this class what we're going to
+
+ align:start position:0%
+so in this class what we're going to
+ 
+
+ align:start position:0%
+so in this class what we're going to
+have is sort of a version of opt-in
+
+ align:start position:0%
+have is sort of a version of opt-in
+ 
+
+ align:start position:0%
+have is sort of a version of opt-in
+policy which is there's going to be a
+
+ align:start position:0%
+policy which is there's going to be a
+ 
+
+ align:start position:0%
+policy which is there's going to be a
+laptop
+
+ align:start position:0%
+laptop
+ 
+
+ align:start position:0%
+laptop
+section starting next class which is
+
+ align:start position:0%
+section starting next class which is
+ 
+
+ align:start position:0%
+section starting next class which is
+going to be on the front and one side of
+
+ align:start position:0%
+going to be on the front and one side of
+ 
+
+ align:start position:0%
+going to be on the front and one side of
+the class
+
+ align:start position:0%
+the class
+ 
+
+ align:start position:0%
+the class
+the reason being we're trying to sort of
+
+ align:start position:0%
+the reason being we're trying to sort of
+ 
+
+ align:start position:0%
+the reason being we're trying to sort of
+minimize externalities
+
+ align:start position:0%
+minimize externalities
+ 
+
+ align:start position:0%
+minimize externalities
+uh it's in the front not in the back um
+
+ align:start position:0%
+uh it's in the front not in the back um
+ 
+
+ align:start position:0%
+uh it's in the front not in the back um
+the reason being that
+
+ align:start position:0%
+the reason being that
+ 
+
+ align:start position:0%
+the reason being that
+if you're in the very back then there's
+
+ align:start position:0%
+if you're in the very back then there's
+ 
+
+ align:start position:0%
+if you're in the very back then there's
+no supervision i'll i guess ask some uh
+
+ align:start position:0%
+no supervision i'll i guess ask some uh
+ 
+
+ align:start position:0%
+no supervision i'll i guess ask some uh
+tas to sit sort of like in the back if
+
+ align:start position:0%
+tas to sit sort of like in the back if
+ 
+
+ align:start position:0%
+tas to sit sort of like in the back if
+there's too much uh
+
+ align:start position:0%
+there's too much uh
+ 
+
+ align:start position:0%
+there's too much uh
+other activities going on maybe there
+
+ align:start position:0%
+other activities going on maybe there
+ 
+
+ align:start position:0%
+other activities going on maybe there
+won't be a laptop section um
+
+ align:start position:0%
+won't be a laptop section um
+ 
+
+ align:start position:0%
+won't be a laptop section um
+anymore anyway there will be sort of
+
+ align:start position:0%
+anymore anyway there will be sort of
+ 
+
+ align:start position:0%
+anymore anyway there will be sort of
+conservations about that and the problem
+
+ align:start position:0%
+conservations about that and the problem
+ 
+
+ align:start position:0%
+conservations about that and the problem
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+but the point of all of that is to say
+
+ align:start position:0%
+but the point of all of that is to say
+ 
+
+ align:start position:0%
+but the point of all of that is to say
+if you just had the standard economic
+
+ align:start position:0%
+if you just had the standard economic
+ 
+
+ align:start position:0%
+if you just had the standard economic
+considerations you would make certain
+
+ align:start position:0%
+considerations you would make certain
+ 
+
+ align:start position:0%
+considerations you would make certain
+policies um
+
+ align:start position:0%
+policies um
+ 
+
+ align:start position:0%
+policies um
+on very sort of simple considerations by
+
+ align:start position:0%
+on very sort of simple considerations by
+ 
+
+ align:start position:0%
+on very sort of simple considerations by
+missing important facts
+
+ align:start position:0%
+missing important facts
+ 
+
+ align:start position:0%
+missing important facts
+and that might be sort of the
+
+ align:start position:0%
+and that might be sort of the
+ 
+
+ align:start position:0%
+and that might be sort of the
+psychological externality might be the
+
+ align:start position:0%
+psychological externality might be the
+ 
+
+ align:start position:0%
+psychological externality might be the
+self-control problems
+
+ align:start position:0%
+self-control problems
+ 
+
+ align:start position:0%
+self-control problems
+the overestimation of people's ability
+
+ align:start position:0%
+the overestimation of people's ability
+ 
+
+ align:start position:0%
+the overestimation of people's ability
+to multitask and so on and so forth
+
+ align:start position:0%
+to multitask and so on and so forth
+ 
+
+ align:start position:0%
+to multitask and so on and so forth
+and all of those things might sort of
+
+ align:start position:0%
+and all of those things might sort of
+ 
+
+ align:start position:0%
+and all of those things might sort of
+like interfere with people's optimal
+
+ align:start position:0%
+like interfere with people's optimal
+ 
+
+ align:start position:0%
+like interfere with people's optimal
+choices
+
+ align:start position:0%
+choices
+ 
+
+ align:start position:0%
+choices
+and that that makes certain more
+
+ align:start position:0%
+and that that makes certain more
+ 
+
+ align:start position:0%
+and that that makes certain more
+paternalistic policies uh
+
+ align:start position:0%
+paternalistic policies uh
+ 
+
+ align:start position:0%
+paternalistic policies uh
+potentially more promising but again
+
+ align:start position:0%
+potentially more promising but again
+ 
+
+ align:start position:0%
+potentially more promising but again
+in the problem said you'll you'll think
+
+ align:start position:0%
+in the problem said you'll you'll think
+ 
+
+ align:start position:0%
+in the problem said you'll you'll think
+about some of these um uh solutions
+
+ align:start position:0%
+about some of these um uh solutions
+ 
+
+ align:start position:0%
+about some of these um uh solutions
+any questions on the laptops yes i might
+
+ align:start position:0%
+any questions on the laptops yes i might
+ 
+
+ align:start position:0%
+any questions on the laptops yes i might
+be thinking of a different study but it
+
+ align:start position:0%
+be thinking of a different study but it
+ 
+
+ align:start position:0%
+be thinking of a different study but it
+is the same one it i thought that in
+
+ align:start position:0%
+is the same one it i thought that in
+ 
+
+ align:start position:0%
+is the same one it i thought that in
+their other classes they
+
+ align:start position:0%
+their other classes they
+ 
+
+ align:start position:0%
+their other classes they
+previously were not like allowed to use
+
+ align:start position:0%
+previously were not like allowed to use
+ 
+
+ align:start position:0%
+previously were not like allowed to use
+laptops so
+
+ align:start position:0%
+laptops so
+ 
+
+ align:start position:0%
+laptops so
+it might be that they had not optimized
+
+ align:start position:0%
+it might be that they had not optimized
+ 
+
+ align:start position:0%
+it might be that they had not optimized
+themselves for
+
+ align:start position:0%
+themselves for
+ 
+
+ align:start position:0%
+themselves for
+laptop usage during class that's
+
+ align:start position:0%
+laptop usage during class that's
+ 
+
+ align:start position:0%
+laptop usage during class that's
+interesting uh
+
+ align:start position:0%
+interesting uh
+ 
+
+ align:start position:0%
+interesting uh
+so i think there are several studies
+
+ align:start position:0%
+so i think there are several studies
+ 
+
+ align:start position:0%
+so i think there are several studies
+that show that um i don't know the
+
+ align:start position:0%
+that show that um i don't know the
+ 
+
+ align:start position:0%
+that show that um i don't know the
+details on
+
+ align:start position:0%
+details on
+ 
+
+ align:start position:0%
+details on
+that uh but if you can send that to me
+
+ align:start position:0%
+that uh but if you can send that to me
+ 
+
+ align:start position:0%
+that uh but if you can send that to me
+i'm happy to
+
+ align:start position:0%
+i'm happy to
+ 
+
+ align:start position:0%
+i'm happy to
+to just look at that and reconsider i
+
+ align:start position:0%
+to just look at that and reconsider i
+ 
+
+ align:start position:0%
+to just look at that and reconsider i
+think my my view overall is that sort of
+
+ align:start position:0%
+think my my view overall is that sort of
+ 
+
+ align:start position:0%
+think my my view overall is that sort of
+the the existing evidence essentially
+
+ align:start position:0%
+the the existing evidence essentially
+ 
+
+ align:start position:0%
+the the existing evidence essentially
+shows laptops
+
+ align:start position:0%
+shows laptops
+ 
+
+ align:start position:0%
+shows laptops
+are bad since i'm interested in your uh
+
+ align:start position:0%
+are bad since i'm interested in your uh
+ 
+
+ align:start position:0%
+are bad since i'm interested in your uh
+learning um um and that's what i go with
+
+ align:start position:0%
+learning um um and that's what i go with
+ 
+
+ align:start position:0%
+learning um um and that's what i go with
+but i'm happy to be um to be educated
+
+ align:start position:0%
+but i'm happy to be um to be educated
+ 
+
+ align:start position:0%
+but i'm happy to be um to be educated
+um i'll try and put the slides online
+
+ align:start position:0%
+um i'll try and put the slides online
+ 
+
+ align:start position:0%
+um i'll try and put the slides online
+um i was the night before in case you
+
+ align:start position:0%
+um i was the night before in case you
+ 
+
+ align:start position:0%
+um i was the night before in case you
+want to print them out or look at them
+
+ align:start position:0%
+want to print them out or look at them
+ 
+
+ align:start position:0%
+want to print them out or look at them
+or whatever during class
+
+ align:start position:0%
+or whatever during class
+ 
+
+ align:start position:0%
+or whatever during class
+i'm um you're welcome um to do that
+
+ align:start position:0%
+i'm um you're welcome um to do that
+ 
+
+ align:start position:0%
+i'm um you're welcome um to do that
+okay so then let me tell you very
+
+ align:start position:0%
+okay so then let me tell you very
+ 
+
+ align:start position:0%
+okay so then let me tell you very
+briefly about like um
+
+ align:start position:0%
+briefly about like um
+ 
+
+ align:start position:0%
+briefly about like um
+uh different topics of the class and
+
+ align:start position:0%
+uh different topics of the class and
+ 
+
+ align:start position:0%
+uh different topics of the class and
+what we're gonna
+
+ align:start position:0%
+what we're gonna
+ 
+
+ align:start position:0%
+what we're gonna
+cover so first we're gonna have an
+
+ align:start position:0%
+cover so first we're gonna have an
+ 
+
+ align:start position:0%
+cover so first we're gonna have an
+introduction uh and overview
+
+ align:start position:0%
+introduction uh and overview
+ 
+
+ align:start position:0%
+introduction uh and overview
+today's introduction lecture the
+
+ align:start position:0%
+today's introduction lecture the
+ 
+
+ align:start position:0%
+today's introduction lecture the
+overview um will be on wednesday we'll
+
+ align:start position:0%
+overview um will be on wednesday we'll
+ 
+
+ align:start position:0%
+overview um will be on wednesday we'll
+show a cover kind of like
+
+ align:start position:0%
+show a cover kind of like
+ 
+
+ align:start position:0%
+show a cover kind of like
+providing an overview what the different
+
+ align:start position:0%
+providing an overview what the different
+ 
+
+ align:start position:0%
+providing an overview what the different
+topics are and how to think about them
+
+ align:start position:0%
+topics are and how to think about them
+ 
+
+ align:start position:0%
+topics are and how to think about them
+and what evidence do we actually have
+
+ align:start position:0%
+and what evidence do we actually have
+ 
+
+ align:start position:0%
+and what evidence do we actually have
+so i was kind of like a little bit hand
+
+ align:start position:0%
+so i was kind of like a little bit hand
+ 
+
+ align:start position:0%
+so i was kind of like a little bit hand
+wavy in a sense of like showing you lots
+
+ align:start position:0%
+wavy in a sense of like showing you lots
+ 
+
+ align:start position:0%
+wavy in a sense of like showing you lots
+of like
+
+ align:start position:0%
+of like
+ 
+
+ align:start position:0%
+of like
+flashy pictures of people misbehaving
+
+ align:start position:0%
+flashy pictures of people misbehaving
+ 
+
+ align:start position:0%
+flashy pictures of people misbehaving
+but in fact um you know i'm going to
+
+ align:start position:0%
+but in fact um you know i'm going to
+ 
+
+ align:start position:0%
+but in fact um you know i'm going to
+show you some more sort of rigorous
+
+ align:start position:0%
+show you some more sort of rigorous
+ 
+
+ align:start position:0%
+show you some more sort of rigorous
+evidence that we have that in fact
+
+ align:start position:0%
+evidence that we have that in fact
+ 
+
+ align:start position:0%
+evidence that we have that in fact
+uh some of the assumptions of the um
+
+ align:start position:0%
+uh some of the assumptions of the um
+ 
+
+ align:start position:0%
+uh some of the assumptions of the um
+classical
+
+ align:start position:0%
+classical
+ 
+
+ align:start position:0%
+classical
+model are violated and sort of like how
+
+ align:start position:0%
+model are violated and sort of like how
+ 
+
+ align:start position:0%
+model are violated and sort of like how
+we think about them and how we might
+
+ align:start position:0%
+we think about them and how we might
+ 
+
+ align:start position:0%
+we think about them and how we might
+sort of incorporate them into economics
+
+ align:start position:0%
+sort of incorporate them into economics
+ 
+
+ align:start position:0%
+sort of incorporate them into economics
+so that's going to be an overview on
+
+ align:start position:0%
+so that's going to be an overview on
+ 
+
+ align:start position:0%
+so that's going to be an overview on
+wednesday
+
+ align:start position:0%
+wednesday
+ 
+
+ align:start position:0%
+wednesday
+then we're going to talk a lot about
+
+ align:start position:0%
+then we're going to talk a lot about
+ 
+
+ align:start position:0%
+then we're going to talk a lot about
+preferences you can think about
+
+ align:start position:0%
+preferences you can think about
+ 
+
+ align:start position:0%
+preferences you can think about
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+when people make choices there's a
+
+ align:start position:0%
+when people make choices there's a
+ 
+
+ align:start position:0%
+when people make choices there's a
+utility function and sort of
+
+ align:start position:0%
+utility function and sort of
+ 
+
+ align:start position:0%
+utility function and sort of
+one set of behavioral economics issues
+
+ align:start position:0%
+one set of behavioral economics issues
+ 
+
+ align:start position:0%
+one set of behavioral economics issues
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+changes to the utility function this
+
+ align:start position:0%
+changes to the utility function this
+ 
+
+ align:start position:0%
+changes to the utility function this
+might be time preferences and people's
+
+ align:start position:0%
+might be time preferences and people's
+ 
+
+ align:start position:0%
+might be time preferences and people's
+self-control
+
+ align:start position:0%
+self-control
+ 
+
+ align:start position:0%
+self-control
+which we already discussed it might be
+
+ align:start position:0%
+which we already discussed it might be
+ 
+
+ align:start position:0%
+which we already discussed it might be
+risk preferences how people think about
+
+ align:start position:0%
+risk preferences how people think about
+ 
+
+ align:start position:0%
+risk preferences how people think about
+risk or they think about gains and
+
+ align:start position:0%
+risk or they think about gains and
+ 
+
+ align:start position:0%
+risk or they think about gains and
+losses and how their preferences are
+
+ align:start position:0%
+losses and how their preferences are
+ 
+
+ align:start position:0%
+losses and how their preferences are
+reference dependent
+
+ align:start position:0%
+reference dependent
+ 
+
+ align:start position:0%
+reference dependent
+this is what um a student was saying
+
+ align:start position:0%
+this is what um a student was saying
+ 
+
+ align:start position:0%
+this is what um a student was saying
+earlier about like
+
+ align:start position:0%
+earlier about like
+ 
+
+ align:start position:0%
+earlier about like
+how you evaluate something might it
+
+ align:start position:0%
+how you evaluate something might it
+ 
+
+ align:start position:0%
+how you evaluate something might it
+depend a lot on your expectation of that
+
+ align:start position:0%
+depend a lot on your expectation of that
+ 
+
+ align:start position:0%
+depend a lot on your expectation of that
+outcome
+
+ align:start position:0%
+outcome
+ 
+
+ align:start position:0%
+outcome
+as opposed to just the outcome itself
+
+ align:start position:0%
+as opposed to just the outcome itself
+ 
+
+ align:start position:0%
+as opposed to just the outcome itself
+uh let me talk quite a bit about social
+
+ align:start position:0%
+uh let me talk quite a bit about social
+ 
+
+ align:start position:0%
+uh let me talk quite a bit about social
+preferences this is sort of like how
+
+ align:start position:0%
+preferences this is sort of like how
+ 
+
+ align:start position:0%
+preferences this is sort of like how
+much we
+
+ align:start position:0%
+much we
+ 
+
+ align:start position:0%
+much we
+uh uh how much we weigh others um
+
+ align:start position:0%
+uh uh how much we weigh others um
+ 
+
+ align:start position:0%
+uh uh how much we weigh others um
+utility uh in our youtube our utility
+
+ align:start position:0%
+utility uh in our youtube our utility
+ 
+
+ align:start position:0%
+utility uh in our youtube our utility
+function or their consumption and our
+
+ align:start position:0%
+function or their consumption and our
+ 
+
+ align:start position:0%
+function or their consumption and our
+utility function
+
+ align:start position:0%
+utility function
+ 
+
+ align:start position:0%
+utility function
+uh we'll do some experiments in class um
+
+ align:start position:0%
+uh we'll do some experiments in class um
+ 
+
+ align:start position:0%
+uh we'll do some experiments in class um
+on that which which
+
+ align:start position:0%
+on that which which
+ 
+
+ align:start position:0%
+on that which which
+should be a lot of fun and then discuss
+
+ align:start position:0%
+should be a lot of fun and then discuss
+ 
+
+ align:start position:0%
+should be a lot of fun and then discuss
+various issues about a how much people
+
+ align:start position:0%
+various issues about a how much people
+ 
+
+ align:start position:0%
+various issues about a how much people
+care about others and how they're
+
+ align:start position:0%
+care about others and how they're
+ 
+
+ align:start position:0%
+care about others and how they're
+affected by others behavior and social
+
+ align:start position:0%
+affected by others behavior and social
+ 
+
+ align:start position:0%
+affected by others behavior and social
+influences so that's kind of like the
+
+ align:start position:0%
+influences so that's kind of like the
+ 
+
+ align:start position:0%
+influences so that's kind of like the
+first half of the class broadly about
+
+ align:start position:0%
+first half of the class broadly about
+ 
+
+ align:start position:0%
+first half of the class broadly about
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+changes in people's then preferences
+
+ align:start position:0%
+changes in people's then preferences
+ 
+
+ align:start position:0%
+changes in people's then preferences
+going to talk more about beliefs
+
+ align:start position:0%
+going to talk more about beliefs
+ 
+
+ align:start position:0%
+going to talk more about beliefs
+broadly speaking and sort of people's
+
+ align:start position:0%
+broadly speaking and sort of people's
+ 
+
+ align:start position:0%
+broadly speaking and sort of people's
+how people
+
+ align:start position:0%
+how people
+ 
+
+ align:start position:0%
+how people
+view information in the world you talk a
+
+ align:start position:0%
+view information in the world you talk a
+ 
+
+ align:start position:0%
+view information in the world you talk a
+little about emotions what's called
+
+ align:start position:0%
+little about emotions what's called
+ 
+
+ align:start position:0%
+little about emotions what's called
+projection and attribution bias
+
+ align:start position:0%
+projection and attribution bias
+ 
+
+ align:start position:0%
+projection and attribution bias
+these are issues about for example when
+
+ align:start position:0%
+these are issues about for example when
+ 
+
+ align:start position:0%
+these are issues about for example when
+people are hungry
+
+ align:start position:0%
+people are hungry
+ 
+
+ align:start position:0%
+people are hungry
+or tired they might make quite different
+
+ align:start position:0%
+or tired they might make quite different
+ 
+
+ align:start position:0%
+or tired they might make quite different
+choices
+
+ align:start position:0%
+choices
+ 
+
+ align:start position:0%
+choices
+um and and so that might affect their
+
+ align:start position:0%
+um and and so that might affect their
+ 
+
+ align:start position:0%
+um and and so that might affect their
+preferences
+
+ align:start position:0%
+preferences
+ 
+
+ align:start position:0%
+preferences
+but it might also affect their their
+
+ align:start position:0%
+but it might also affect their their
+ 
+
+ align:start position:0%
+but it might also affect their their
+beliefs in some sense if you think about
+
+ align:start position:0%
+beliefs in some sense if you think about
+ 
+
+ align:start position:0%
+beliefs in some sense if you think about
+how you're going to behave if you're
+
+ align:start position:0%
+how you're going to behave if you're
+ 
+
+ align:start position:0%
+how you're going to behave if you're
+hungry right now it's very hard for you
+
+ align:start position:0%
+hungry right now it's very hard for you
+ 
+
+ align:start position:0%
+hungry right now it's very hard for you
+to believe or
+
+ align:start position:0%
+to believe or
+ 
+
+ align:start position:0%
+to believe or
+think about like that you're not might
+
+ align:start position:0%
+think about like that you're not might
+ 
+
+ align:start position:0%
+think about like that you're not might
+not be hungry in the future this is sort
+
+ align:start position:0%
+not be hungry in the future this is sort
+ 
+
+ align:start position:0%
+not be hungry in the future this is sort
+of the classical example of
+
+ align:start position:0%
+of the classical example of
+ 
+
+ align:start position:0%
+of the classical example of
+shopping on an empty stomach um there's
+
+ align:start position:0%
+shopping on an empty stomach um there's
+ 
+
+ align:start position:0%
+shopping on an empty stomach um there's
+lots of different applications of that
+
+ align:start position:0%
+lots of different applications of that
+ 
+
+ align:start position:0%
+lots of different applications of that
+it's like people buy convertibles when
+
+ align:start position:0%
+it's like people buy convertibles when
+ 
+
+ align:start position:0%
+it's like people buy convertibles when
+it's sunny um and then return them when
+
+ align:start position:0%
+it's sunny um and then return them when
+ 
+
+ align:start position:0%
+it's sunny um and then return them when
+it rains
+
+ align:start position:0%
+it rains
+ 
+
+ align:start position:0%
+it rains
+but there's also much more serious
+
+ align:start position:0%
+but there's also much more serious
+ 
+
+ align:start position:0%
+but there's also much more serious
+issues in particular things like
+
+ align:start position:0%
+issues in particular things like
+ 
+
+ align:start position:0%
+issues in particular things like
+depression for example when people are
+
+ align:start position:0%
+depression for example when people are
+ 
+
+ align:start position:0%
+depression for example when people are
+depressed it's very hard for them to
+
+ align:start position:0%
+depressed it's very hard for them to
+ 
+
+ align:start position:0%
+depressed it's very hard for them to
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+how it might feel when they're not
+
+ align:start position:0%
+how it might feel when they're not
+ 
+
+ align:start position:0%
+how it might feel when they're not
+depressed anymore in the future
+
+ align:start position:0%
+depressed anymore in the future
+ 
+
+ align:start position:0%
+depressed anymore in the future
+so we'll talk about sort of production
+
+ align:start position:0%
+so we'll talk about sort of production
+ 
+
+ align:start position:0%
+so we'll talk about sort of production
+and attribution bytes which is kind of
+
+ align:start position:0%
+and attribution bytes which is kind of
+ 
+
+ align:start position:0%
+and attribution bytes which is kind of
+these biases and how to think about
+
+ align:start position:0%
+these biases and how to think about
+ 
+
+ align:start position:0%
+these biases and how to think about
+people's
+
+ align:start position:0%
+people's
+ 
+
+ align:start position:0%
+people's
+states of the world we talk about
+
+ align:start position:0%
+states of the world we talk about
+ 
+
+ align:start position:0%
+states of the world we talk about
+limited attention that people sort of
+
+ align:start position:0%
+limited attention that people sort of
+ 
+
+ align:start position:0%
+limited attention that people sort of
+don't pay attention to certain things in
+
+ align:start position:0%
+don't pay attention to certain things in
+ 
+
+ align:start position:0%
+don't pay attention to certain things in
+the world and sort of how that might
+
+ align:start position:0%
+the world and sort of how that might
+ 
+
+ align:start position:0%
+the world and sort of how that might
+affect people's behavior
+
+ align:start position:0%
+affect people's behavior
+ 
+
+ align:start position:0%
+affect people's behavior
+how we might sort of exploit that
+
+ align:start position:0%
+how we might sort of exploit that
+ 
+
+ align:start position:0%
+how we might sort of exploit that
+potentially for taxing them or how we
+
+ align:start position:0%
+potentially for taxing them or how we
+ 
+
+ align:start position:0%
+potentially for taxing them or how we
+might sort of direct their attention to
+
+ align:start position:0%
+might sort of direct their attention to
+ 
+
+ align:start position:0%
+might sort of direct their attention to
+certain things and might improve their
+
+ align:start position:0%
+certain things and might improve their
+ 
+
+ align:start position:0%
+certain things and might improve their
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+similarly then we talk about beliefs and
+
+ align:start position:0%
+similarly then we talk about beliefs and
+ 
+
+ align:start position:0%
+similarly then we talk about beliefs and
+learning this is kind of like
+
+ align:start position:0%
+learning this is kind of like
+ 
+
+ align:start position:0%
+learning this is kind of like
+how what information do they have
+
+ align:start position:0%
+how what information do they have
+ 
+
+ align:start position:0%
+how what information do they have
+available a you know how they
+
+ align:start position:0%
+available a you know how they
+ 
+
+ align:start position:0%
+available a you know how they
+update uh their beliefs when they get
+
+ align:start position:0%
+update uh their beliefs when they get
+ 
+
+ align:start position:0%
+update uh their beliefs when they get
+information and are they able to process
+
+ align:start position:0%
+information and are they able to process
+ 
+
+ align:start position:0%
+information and are they able to process
+information well
+
+ align:start position:0%
+information well
+ 
+
+ align:start position:0%
+information well
+b is the demand for information do
+
+ align:start position:0%
+b is the demand for information do
+ 
+
+ align:start position:0%
+b is the demand for information do
+people get utility from beliefs this is
+
+ align:start position:0%
+people get utility from beliefs this is
+ 
+
+ align:start position:0%
+people get utility from beliefs this is
+what i was talking about like
+
+ align:start position:0%
+what i was talking about like
+ 
+
+ align:start position:0%
+what i was talking about like
+health behaviors other health
+
+ align:start position:0%
+health behaviors other health
+ 
+
+ align:start position:0%
+health behaviors other health
+information where people might have
+
+ align:start position:0%
+information where people might have
+ 
+
+ align:start position:0%
+information where people might have
+motivated beliefs in the sense that like
+
+ align:start position:0%
+motivated beliefs in the sense that like
+ 
+
+ align:start position:0%
+motivated beliefs in the sense that like
+they like to
+
+ align:start position:0%
+they like to
+ 
+
+ align:start position:0%
+they like to
+believe certain things uh um
+
+ align:start position:0%
+believe certain things uh um
+ 
+
+ align:start position:0%
+believe certain things uh um
+when in fact they're not true in part
+
+ align:start position:0%
+when in fact they're not true in part
+ 
+
+ align:start position:0%
+when in fact they're not true in part
+because it makes them happy or in part
+
+ align:start position:0%
+because it makes them happy or in part
+ 
+
+ align:start position:0%
+because it makes them happy or in part
+because they want to be right about
+
+ align:start position:0%
+because they want to be right about
+ 
+
+ align:start position:0%
+because they want to be right about
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+or their party or whatever uh you'll
+
+ align:start position:0%
+or their party or whatever uh you'll
+ 
+
+ align:start position:0%
+or their party or whatever uh you'll
+talk a little about mental accounting
+
+ align:start position:0%
+talk a little about mental accounting
+ 
+
+ align:start position:0%
+talk a little about mental accounting
+which is like
+
+ align:start position:0%
+which is like
+ 
+
+ align:start position:0%
+which is like
+people tend to sort of narrowly bracket
+
+ align:start position:0%
+people tend to sort of narrowly bracket
+ 
+
+ align:start position:0%
+people tend to sort of narrowly bracket
+their choices they might sort of have
+
+ align:start position:0%
+their choices they might sort of have
+ 
+
+ align:start position:0%
+their choices they might sort of have
+certain accounts in their behavior and
+
+ align:start position:0%
+certain accounts in their behavior and
+ 
+
+ align:start position:0%
+certain accounts in their behavior and
+decide sort of separately
+
+ align:start position:0%
+decide sort of separately
+ 
+
+ align:start position:0%
+decide sort of separately
+as opposed to aggregating their behavior
+
+ align:start position:0%
+as opposed to aggregating their behavior
+ 
+
+ align:start position:0%
+as opposed to aggregating their behavior
+as a whole
+
+ align:start position:0%
+as a whole
+ 
+
+ align:start position:0%
+as a whole
+and that sort of issue that's less
+
+ align:start position:0%
+and that sort of issue that's less
+ 
+
+ align:start position:0%
+and that sort of issue that's less
+research but quite interesting overall
+
+ align:start position:0%
+research but quite interesting overall
+ 
+
+ align:start position:0%
+research but quite interesting overall
+then we're going to move towards sort of
+
+ align:start position:0%
+then we're going to move towards sort of
+ 
+
+ align:start position:0%
+then we're going to move towards sort of
+more radical deviations if you want from
+
+ align:start position:0%
+more radical deviations if you want from
+ 
+
+ align:start position:0%
+more radical deviations if you want from
+the standard model which is
+
+ align:start position:0%
+the standard model which is
+ 
+
+ align:start position:0%
+the standard model which is
+things like malleability and
+
+ align:start position:0%
+things like malleability and
+ 
+
+ align:start position:0%
+things like malleability and
+inaccessibility of preferences which is
+
+ align:start position:0%
+inaccessibility of preferences which is
+ 
+
+ align:start position:0%
+inaccessibility of preferences which is
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+people might not actually know what they
+
+ align:start position:0%
+people might not actually know what they
+ 
+
+ align:start position:0%
+people might not actually know what they
+want they might not even understand what
+
+ align:start position:0%
+want they might not even understand what
+ 
+
+ align:start position:0%
+want they might not even understand what
+their preferences are
+
+ align:start position:0%
+their preferences are
+ 
+
+ align:start position:0%
+their preferences are
+or their preferences are easily
+
+ align:start position:0%
+or their preferences are easily
+ 
+
+ align:start position:0%
+or their preferences are easily
+manipulable i can sort of like make you
+
+ align:start position:0%
+manipulable i can sort of like make you
+ 
+
+ align:start position:0%
+manipulable i can sort of like make you
+choose a or b
+
+ align:start position:0%
+choose a or b
+ 
+
+ align:start position:0%
+choose a or b
+or b or a versus b or b versus a
+
+ align:start position:0%
+or b or a versus b or b versus a
+ 
+
+ align:start position:0%
+or b or a versus b or b versus a
+depending on what kind of situation i
+
+ align:start position:0%
+depending on what kind of situation i
+ 
+
+ align:start position:0%
+depending on what kind of situation i
+put you in
+
+ align:start position:0%
+put you in
+ 
+
+ align:start position:0%
+put you in
+and you might not even notice that i'm
+
+ align:start position:0%
+and you might not even notice that i'm
+ 
+
+ align:start position:0%
+and you might not even notice that i'm
+doing that um and in fact
+
+ align:start position:0%
+doing that um and in fact
+ 
+
+ align:start position:0%
+doing that um and in fact
+and that makes things a lot trickier
+
+ align:start position:0%
+and that makes things a lot trickier
+ 
+
+ align:start position:0%
+and that makes things a lot trickier
+because then in some sense it's much
+
+ align:start position:0%
+because then in some sense it's much
+ 
+
+ align:start position:0%
+because then in some sense it's much
+harder to sort of say
+
+ align:start position:0%
+harder to sort of say
+ 
+
+ align:start position:0%
+harder to sort of say
+should the government or any sort of
+
+ align:start position:0%
+should the government or any sort of
+ 
+
+ align:start position:0%
+should the government or any sort of
+other policymaker choose a or b
+
+ align:start position:0%
+other policymaker choose a or b
+ 
+
+ align:start position:0%
+other policymaker choose a or b
+if we don't even know what people's
+
+ align:start position:0%
+if we don't even know what people's
+ 
+
+ align:start position:0%
+if we don't even know what people's
+preferences are people don't even know
+
+ align:start position:0%
+preferences are people don't even know
+ 
+
+ align:start position:0%
+preferences are people don't even know
+what their own preferences are
+
+ align:start position:0%
+what their own preferences are
+ 
+
+ align:start position:0%
+what their own preferences are
+we're going to talk about happiness and
+
+ align:start position:0%
+we're going to talk about happiness and
+ 
+
+ align:start position:0%
+we're going to talk about happiness and
+mental health this kind of broadly
+
+ align:start position:0%
+mental health this kind of broadly
+ 
+
+ align:start position:0%
+mental health this kind of broadly
+speaking what makes people happy and can
+
+ align:start position:0%
+speaking what makes people happy and can
+ 
+
+ align:start position:0%
+speaking what makes people happy and can
+we think about that in particular sort
+
+ align:start position:0%
+we think about that in particular sort
+ 
+
+ align:start position:0%
+we think about that in particular sort
+of like financial choices and others
+
+ align:start position:0%
+of like financial choices and others
+ 
+
+ align:start position:0%
+of like financial choices and others
+i'll tell you a little bit about some of
+
+ align:start position:0%
+i'll tell you a little bit about some of
+ 
+
+ align:start position:0%
+i'll tell you a little bit about some of
+the work on mental health that i have
+
+ align:start position:0%
+the work on mental health that i have
+ 
+
+ align:start position:0%
+the work on mental health that i have
+been
+
+ align:start position:0%
+been
+ 
+
+ align:start position:0%
+been
+doing thinking about kind of like how
+
+ align:start position:0%
+doing thinking about kind of like how
+ 
+
+ align:start position:0%
+doing thinking about kind of like how
+mental health might affect economic
+
+ align:start position:0%
+mental health might affect economic
+ 
+
+ align:start position:0%
+mental health might affect economic
+behaviors and choices and in part how
+
+ align:start position:0%
+behaviors and choices and in part how
+ 
+
+ align:start position:0%
+behaviors and choices and in part how
+people's demand for mental health
+
+ align:start position:0%
+people's demand for mental health
+ 
+
+ align:start position:0%
+people's demand for mental health
+interventions
+
+ align:start position:0%
+interventions
+ 
+
+ align:start position:0%
+interventions
+might be shaped by influences of others
+
+ align:start position:0%
+might be shaped by influences of others
+ 
+
+ align:start position:0%
+might be shaped by influences of others
+uh we're going to talk about gender and
+
+ align:start position:0%
+uh we're going to talk about gender and
+ 
+
+ align:start position:0%
+uh we're going to talk about gender and
+racial discrimination um which sometimes
+
+ align:start position:0%
+racial discrimination um which sometimes
+ 
+
+ align:start position:0%
+racial discrimination um which sometimes
+there's sort of
+
+ align:start position:0%
+there's sort of
+ 
+
+ align:start position:0%
+there's sort of
+classical and neoclassical models of
+
+ align:start position:0%
+classical and neoclassical models of
+ 
+
+ align:start position:0%
+classical and neoclassical models of
+discrimination
+
+ align:start position:0%
+discrimination
+ 
+
+ align:start position:0%
+discrimination
+when we in particular think about sort
+
+ align:start position:0%
+when we in particular think about sort
+ 
+
+ align:start position:0%
+when we in particular think about sort
+of issues of discriminations that are
+
+ align:start position:0%
+of issues of discriminations that are
+ 
+
+ align:start position:0%
+of issues of discriminations that are
+sort of not
+
+ align:start position:0%
+sort of not
+ 
+
+ align:start position:0%
+sort of not
+uh rational in the sense of like uh
+
+ align:start position:0%
+uh rational in the sense of like uh
+ 
+
+ align:start position:0%
+uh rational in the sense of like uh
+think about like unfair in some sense um
+
+ align:start position:0%
+think about like unfair in some sense um
+ 
+
+ align:start position:0%
+think about like unfair in some sense um
+discrimination
+
+ align:start position:0%
+discrimination
+ 
+
+ align:start position:0%
+discrimination
+um finally going to talk about sort of
+
+ align:start position:0%
+um finally going to talk about sort of
+ 
+
+ align:start position:0%
+um finally going to talk about sort of
+policy and paternalism
+
+ align:start position:0%
+policy and paternalism
+ 
+
+ align:start position:0%
+policy and paternalism
+uh one broad issue is about and this
+
+ align:start position:0%
+uh one broad issue is about and this
+ 
+
+ align:start position:0%
+uh one broad issue is about and this
+goes back to malleability and
+
+ align:start position:0%
+goes back to malleability and
+ 
+
+ align:start position:0%
+goes back to malleability and
+inaccessibility of of preferences which
+
+ align:start position:0%
+inaccessibility of of preferences which
+ 
+
+ align:start position:0%
+inaccessibility of of preferences which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+essentially ways in which choices can be
+
+ align:start position:0%
+essentially ways in which choices can be
+ 
+
+ align:start position:0%
+essentially ways in which choices can be
+affected through frames defaults and
+
+ align:start position:0%
+affected through frames defaults and
+ 
+
+ align:start position:0%
+affected through frames defaults and
+nudges assumptions that say
+
+ align:start position:0%
+nudges assumptions that say
+ 
+
+ align:start position:0%
+nudges assumptions that say
+i can manipulate your choice
+
+ align:start position:0%
+i can manipulate your choice
+ 
+
+ align:start position:0%
+i can manipulate your choice
+architecture in certain ways that make
+
+ align:start position:0%
+architecture in certain ways that make
+ 
+
+ align:start position:0%
+architecture in certain ways that make
+you choose certain things
+
+ align:start position:0%
+you choose certain things
+ 
+
+ align:start position:0%
+you choose certain things
+uh you know i might sort of send you
+
+ align:start position:0%
+uh you know i might sort of send you
+ 
+
+ align:start position:0%
+uh you know i might sort of send you
+letters to do your taxes i can sort of
+
+ align:start position:0%
+letters to do your taxes i can sort of
+ 
+
+ align:start position:0%
+letters to do your taxes i can sort of
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+frame certain or set certain defaults
+
+ align:start position:0%
+frame certain or set certain defaults
+ 
+
+ align:start position:0%
+frame certain or set certain defaults
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+organ donations or for uh savings
+
+ align:start position:0%
+organ donations or for uh savings
+ 
+
+ align:start position:0%
+organ donations or for uh savings
+choices and the like
+
+ align:start position:0%
+choices and the like
+ 
+
+ align:start position:0%
+choices and the like
+and that might have profound effects on
+
+ align:start position:0%
+and that might have profound effects on
+ 
+
+ align:start position:0%
+and that might have profound effects on
+people's behavior
+
+ align:start position:0%
+people's behavior
+ 
+
+ align:start position:0%
+people's behavior
+uh once we go through that in the sense
+
+ align:start position:0%
+uh once we go through that in the sense
+ 
+
+ align:start position:0%
+uh once we go through that in the sense
+of like showing you some evidence that
+
+ align:start position:0%
+of like showing you some evidence that
+ 
+
+ align:start position:0%
+of like showing you some evidence that
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+it's possible to do that we're going to
+
+ align:start position:0%
+it's possible to do that we're going to
+ 
+
+ align:start position:0%
+it's possible to do that we're going to
+talk a little bit about policy and
+
+ align:start position:0%
+talk a little bit about policy and
+ 
+
+ align:start position:0%
+talk a little bit about policy and
+paternalism in a sense of like say
+
+ align:start position:0%
+paternalism in a sense of like say
+ 
+
+ align:start position:0%
+paternalism in a sense of like say
+okay now if i know i can change your
+
+ align:start position:0%
+okay now if i know i can change your
+ 
+
+ align:start position:0%
+okay now if i know i can change your
+behavior in certain ways
+
+ align:start position:0%
+behavior in certain ways
+ 
+
+ align:start position:0%
+behavior in certain ways
+what kinds of policies should we do and
+
+ align:start position:0%
+what kinds of policies should we do and
+ 
+
+ align:start position:0%
+what kinds of policies should we do and
+should we in fact do that
+
+ align:start position:0%
+should we in fact do that
+ 
+
+ align:start position:0%
+should we in fact do that
+or you know should we tax people should
+
+ align:start position:0%
+or you know should we tax people should
+ 
+
+ align:start position:0%
+or you know should we tax people should
+we set certain frames and defaults
+
+ align:start position:0%
+we set certain frames and defaults
+ 
+
+ align:start position:0%
+we set certain frames and defaults
+and you know i'll be potentially making
+
+ align:start position:0%
+and you know i'll be potentially making
+ 
+
+ align:start position:0%
+and you know i'll be potentially making
+some people worse off while making some
+
+ align:start position:0%
+some people worse off while making some
+ 
+
+ align:start position:0%
+some people worse off while making some
+people better off by doing these kinds
+
+ align:start position:0%
+people better off by doing these kinds
+ 
+
+ align:start position:0%
+people better off by doing these kinds
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+policies there's often also some ethical
+
+ align:start position:0%
+policies there's often also some ethical
+ 
+
+ align:start position:0%
+policies there's often also some ethical
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+associated with that and then finally i
+
+ align:start position:0%
+associated with that and then finally i
+ 
+
+ align:start position:0%
+associated with that and then finally i
+talk about poverty this is sort of
+
+ align:start position:0%
+talk about poverty this is sort of
+ 
+
+ align:start position:0%
+talk about poverty this is sort of
+mostly the research
+
+ align:start position:0%
+mostly the research
+ 
+
+ align:start position:0%
+mostly the research
+that i do and thinking about sort of
+
+ align:start position:0%
+that i do and thinking about sort of
+ 
+
+ align:start position:0%
+that i do and thinking about sort of
+poverty issues through the lens of of
+
+ align:start position:0%
+poverty issues through the lens of of
+ 
+
+ align:start position:0%
+poverty issues through the lens of of
+psychology again i'll tell you a little
+
+ align:start position:0%
+psychology again i'll tell you a little
+ 
+
+ align:start position:0%
+psychology again i'll tell you a little
+bit about the the work i do myself
+
+ align:start position:0%
+bit about the the work i do myself
+ 
+
+ align:start position:0%
+bit about the the work i do myself
+um partially to talk a little bit about
+
+ align:start position:0%
+um partially to talk a little bit about
+ 
+
+ align:start position:0%
+um partially to talk a little bit about
+so how
+
+ align:start position:0%
+so how
+ 
+
+ align:start position:0%
+so how
+financial constraints are just thinking
+
+ align:start position:0%
+financial constraints are just thinking
+ 
+
+ align:start position:0%
+financial constraints are just thinking
+about money affects people's behavior
+
+ align:start position:0%
+about money affects people's behavior
+ 
+
+ align:start position:0%
+about money affects people's behavior
+and then second how other issues related
+
+ align:start position:0%
+and then second how other issues related
+ 
+
+ align:start position:0%
+and then second how other issues related
+to poverty might
+
+ align:start position:0%
+to poverty might
+ 
+
+ align:start position:0%
+to poverty might
+shape people's choices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decision making and their sort of labor
+
+ align:start position:0%
+decision making and their sort of labor
+ 
+
+ align:start position:0%
+decision making and their sort of labor
+market outcomes earnings and so on
+
+ align:start position:0%
+market outcomes earnings and so on
+ 
+
+ align:start position:0%
+market outcomes earnings and so on
+and whether it's potentially something
+
+ align:start position:0%
+and whether it's potentially something
+ 
+
+ align:start position:0%
+and whether it's potentially something
+that you might want to call a
+
+ align:start position:0%
+that you might want to call a
+ 
+
+ align:start position:0%
+that you might want to call a
+psychological or behavioral
+
+ align:start position:0%
+psychological or behavioral
+ 
+
+ align:start position:0%
+psychological or behavioral
+poverty trap any questions on these
+
+ align:start position:0%
+poverty trap any questions on these
+ 
+
+ align:start position:0%
+poverty trap any questions on these
+topics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then readings for next time this
+
+ align:start position:0%
+okay so then readings for next time this
+ 
+
+ align:start position:0%
+okay so then readings for next time this
+is wednesday please read
+
+ align:start position:0%
+is wednesday please read
+ 
+
+ align:start position:0%
+is wednesday please read
+um there's a paper on the course website
+
+ align:start position:0%
+um there's a paper on the course website
+ 
+
+ align:start position:0%
+um there's a paper on the course website
+um by matthew raven who is one of sort
+
+ align:start position:0%
+um by matthew raven who is one of sort
+ 
+
+ align:start position:0%
+um by matthew raven who is one of sort
+of like the
+
+ align:start position:0%
+of like the
+ 
+
+ align:start position:0%
+of like the
+uh all-stars in behavioral economics
+
+ align:start position:0%
+uh all-stars in behavioral economics
+ 
+
+ align:start position:0%
+uh all-stars in behavioral economics
+uh 20 years ago he already wrote a very
+
+ align:start position:0%
+uh 20 years ago he already wrote a very
+ 
+
+ align:start position:0%
+uh 20 years ago he already wrote a very
+useful perspective on psychology and
+
+ align:start position:0%
+useful perspective on psychology and
+ 
+
+ align:start position:0%
+useful perspective on psychology and
+economics that sort of discusses a lot
+
+ align:start position:0%
+economics that sort of discusses a lot
+ 
+
+ align:start position:0%
+economics that sort of discusses a lot
+of the issues of
+
+ align:start position:0%
+of the issues of
+ 
+
+ align:start position:0%
+of the issues of
+behavioral economics how to think about
+
+ align:start position:0%
+behavioral economics how to think about
+ 
+
+ align:start position:0%
+behavioral economics how to think about
+that um again read sections one and two
+
+ align:start position:0%
+that um again read sections one and two
+ 
+
+ align:start position:0%
+that um again read sections one and two
+we're not going to sort of test you
+
+ align:start position:0%
+we're not going to sort of test you
+ 
+
+ align:start position:0%
+we're not going to sort of test you
+specifically on like very specific
+
+ align:start position:0%
+specifically on like very specific
+ 
+
+ align:start position:0%
+specifically on like very specific
+things but you should sort of be able to
+
+ align:start position:0%
+things but you should sort of be able to
+ 
+
+ align:start position:0%
+things but you should sort of be able to
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+uh remember at least roughly what's
+
+ align:start position:0%
+uh remember at least roughly what's
+ 
+
+ align:start position:0%
+uh remember at least roughly what's
+what's in that paper
\ No newline at end of file
diff --git a/jtOxRPQDuJs.txt b/jtOxRPQDuJs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..80d1a146813169afccb8aa953770073d3e999238
--- /dev/null
+++ b/jtOxRPQDuJs.txt
@@ -0,0 +1,459 @@
+align:start position:0%
+ 
+let's consider a one-dimensional motion
+
+ align:start position:0%
+let's consider a one-dimensional motion
+ 
+
+ align:start position:0%
+let's consider a one-dimensional motion
+that has a non uniform acceleration what
+
+ align:start position:0%
+that has a non uniform acceleration what
+ 
+
+ align:start position:0%
+that has a non uniform acceleration what
+we'd like to do is explore how do you
+
+ align:start position:0%
+we'd like to do is explore how do you
+ 
+
+ align:start position:0%
+we'd like to do is explore how do you
+differentiate position functions to get
+
+ align:start position:0%
+differentiate position functions to get
+ 
+
+ align:start position:0%
+differentiate position functions to get
+philosophy functions to get acceleration
+
+ align:start position:0%
+philosophy functions to get acceleration
+ 
+
+ align:start position:0%
+philosophy functions to get acceleration
+function so what we're going to consider
+
+ align:start position:0%
+function so what we're going to consider
+ 
+
+ align:start position:0%
+function so what we're going to consider
+is a rocket so I'm going to choose a
+
+ align:start position:0%
+is a rocket so I'm going to choose a
+ 
+
+ align:start position:0%
+is a rocket so I'm going to choose a
+coordinate system Y and here's my rocket
+
+ align:start position:0%
+coordinate system Y and here's my rocket
+ 
+
+ align:start position:0%
+coordinate system Y and here's my rocket
+and I have the function y of T and I'll
+
+ align:start position:0%
+and I have the function y of T and I'll
+ 
+
+ align:start position:0%
+and I have the function y of T and I'll
+have a J hat direction but this will be
+
+ align:start position:0%
+have a J hat direction but this will be
+ 
+
+ align:start position:0%
+have a J hat direction but this will be
+a one-dimensional motion now I want to
+
+ align:start position:0%
+a one-dimensional motion now I want to
+ 
+
+ align:start position:0%
+a one-dimensional motion now I want to
+express while the rocket is thrusting
+
+ align:start position:0%
+express while the rocket is thrusting
+ 
+
+ align:start position:0%
+express while the rocket is thrusting
+upwards and the engine is burning we can
+
+ align:start position:0%
+upwards and the engine is burning we can
+ 
+
+ align:start position:0%
+upwards and the engine is burning we can
+describe a function y of T to be equal
+
+ align:start position:0%
+describe a function y of T to be equal
+ 
+
+ align:start position:0%
+describe a function y of T to be equal
+to one-half a constant a naught minus
+
+ align:start position:0%
+to one-half a constant a naught minus
+ 
+
+ align:start position:0%
+to one-half a constant a naught minus
+the gravitational acceleration times T
+
+ align:start position:0%
+the gravitational acceleration times T
+ 
+
+ align:start position:0%
+the gravitational acceleration times T
+squared and we're going to have a
+
+ align:start position:0%
+squared and we're going to have a
+ 
+
+ align:start position:0%
+squared and we're going to have a
+separate term here which is minus 1 over
+
+ align:start position:0%
+separate term here which is minus 1 over
+ 
+
+ align:start position:0%
+separate term here which is minus 1 over
+30 and you'll see where this 30 comes in
+
+ align:start position:0%
+30 and you'll see where this 30 comes in
+ 
+
+ align:start position:0%
+30 and you'll see where this 30 comes in
+as we start to differentiate same
+
+ align:start position:0%
+as we start to differentiate same
+ 
+
+ align:start position:0%
+as we start to differentiate same
+constant a naught T to the sixth over T
+
+ align:start position:0%
+constant a naught T to the sixth over T
+ 
+
+ align:start position:0%
+constant a naught T to the sixth over T
+naught to the fourth now in this
+
+ align:start position:0%
+naught to the fourth now in this
+ 
+
+ align:start position:0%
+naught to the fourth now in this
+expression a naught is bigger than G and
+
+ align:start position:0%
+expression a naught is bigger than G and
+ 
+
+ align:start position:0%
+expression a naught is bigger than G and
+also this is only true this holds for
+
+ align:start position:0%
+also this is only true this holds for
+ 
+
+ align:start position:0%
+also this is only true this holds for
+the time interval 0 less than or equal
+
+ align:start position:0%
+the time interval 0 less than or equal
+ 
+
+ align:start position:0%
+the time interval 0 less than or equal
+to t less than T naught and at time T
+
+ align:start position:0%
+to t less than T naught and at time T
+ 
+
+ align:start position:0%
+to t less than T naught and at time T
+equals to T naught the engine shuts off
+
+ align:start position:0%
+equals to T naught the engine shuts off
+ 
+
+ align:start position:0%
+equals to T naught the engine shuts off
+and at that moment our expectation will
+
+ align:start position:0%
+and at that moment our expectation will
+ 
+
+ align:start position:0%
+and at that moment our expectation will
+be that the Y component of the
+
+ align:start position:0%
+be that the Y component of the
+ 
+
+ align:start position:0%
+be that the Y component of the
+acceleration should just be minus G for
+
+ align:start position:0%
+acceleration should just be minus G for
+ 
+
+ align:start position:0%
+acceleration should just be minus G for
+T greater than T naught so now let's
+
+ align:start position:0%
+T greater than T naught so now let's
+ 
+
+ align:start position:0%
+T greater than T naught so now let's
+calculate the acceleration as the
+
+ align:start position:0%
+calculate the acceleration as the
+ 
+
+ align:start position:0%
+calculate the acceleration as the
+velocity and the position as functions
+
+ align:start position:0%
+velocity and the position as functions
+ 
+
+ align:start position:0%
+velocity and the position as functions
+of time so the velocity in each case
+
+ align:start position:0%
+of time so the velocity in each case
+ 
+
+ align:start position:0%
+of time so the velocity in each case
+we're going to use the polynomial rule
+
+ align:start position:0%
+we're going to use the polynomial rule
+ 
+
+ align:start position:0%
+we're going to use the polynomial rule
+so the Y component of the velocity is
+
+ align:start position:0%
+so the Y component of the velocity is
+ 
+
+ align:start position:0%
+so the Y component of the velocity is
+just the different derivative of T
+
+ align:start position:0%
+just the different derivative of T
+ 
+
+ align:start position:0%
+just the different derivative of T
+squared which is just 2t and so we get a
+
+ align:start position:0%
+squared which is just 2t and so we get a
+ 
+
+ align:start position:0%
+squared which is just 2t and so we get a
+naught minus G times T and when we
+
+ align:start position:0%
+naught minus G times T and when we
+ 
+
+ align:start position:0%
+naught minus G times T and when we
+differentiate T to the sixth the 6 over
+
+ align:start position:0%
+differentiate T to the sixth the 6 over
+ 
+
+ align:start position:0%
+differentiate T to the sixth the 6 over
+30 gives us a factor 1 over 5 so we have
+
+ align:start position:0%
+30 gives us a factor 1 over 5 so we have
+ 
+
+ align:start position:0%
+30 gives us a factor 1 over 5 so we have
+minus 1 over 5 times a naught T to the
+
+ align:start position:0%
+minus 1 over 5 times a naught T to the
+ 
+
+ align:start position:0%
+minus 1 over 5 times a naught T to the
+fifth
+
+ align:start position:0%
+fifth
+ 
+
+ align:start position:0%
+fifth
+over T not to the fourth and this is a
+
+ align:start position:0%
+over T not to the fourth and this is a
+ 
+
+ align:start position:0%
+over T not to the fourth and this is a
+combination of a linear term and a term
+
+ align:start position:0%
+combination of a linear term and a term
+ 
+
+ align:start position:0%
+combination of a linear term and a term
+that is decreasing by this T to the
+
+ align:start position:0%
+that is decreasing by this T to the
+ 
+
+ align:start position:0%
+that is decreasing by this T to the
+fifth factor and finally we now take the
+
+ align:start position:0%
+fifth factor and finally we now take the
+ 
+
+ align:start position:0%
+fifth factor and finally we now take the
+next derivative a Y of T which is d dy
+
+ align:start position:0%
+next derivative a Y of T which is d dy
+ 
+
+ align:start position:0%
+next derivative a Y of T which is d dy
+DT I'll just keep functions of T but we
+
+ align:start position:0%
+DT I'll just keep functions of T but we
+ 
+
+ align:start position:0%
+DT I'll just keep functions of T but we
+don't really need that and when we
+
+ align:start position:0%
+don't really need that and when we
+ 
+
+ align:start position:0%
+don't really need that and when we
+differentiate here we get a naught minus
+
+ align:start position:0%
+differentiate here we get a naught minus
+ 
+
+ align:start position:0%
+differentiate here we get a naught minus
+G now you see the 5s are cancelling and
+
+ align:start position:0%
+G now you see the 5s are cancelling and
+ 
+
+ align:start position:0%
+G now you see the 5s are cancelling and
+we have minus a naught T to the fourth
+
+ align:start position:0%
+we have minus a naught T to the fourth
+ 
+
+ align:start position:0%
+we have minus a naught T to the fourth
+over T naught to the fourth now at time
+
+ align:start position:0%
+over T naught to the fourth now at time
+ 
+
+ align:start position:0%
+over T naught to the fourth now at time
+T equals T naught what do we have well a
+
+ align:start position:0%
+T equals T naught what do we have well a
+ 
+
+ align:start position:0%
+T equals T naught what do we have well a
+Y at T equals T naught this is just a
+
+ align:start position:0%
+Y at T equals T naught this is just a
+ 
+
+ align:start position:0%
+Y at T equals T naught this is just a
+factor minus a naught those cancel and
+
+ align:start position:0%
+factor minus a naught those cancel and
+ 
+
+ align:start position:0%
+factor minus a naught those cancel and
+we get minus G which is what we expected
\ No newline at end of file
diff --git a/k3AiUhwHQ28.txt b/k3AiUhwHQ28.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fed166d593bb7b68cb96616f428e21596b195fdb
--- /dev/null
+++ b/k3AiUhwHQ28.txt
@@ -0,0 +1,8331 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he graciously agreed to come today
+
+ align:start position:0%
+so he graciously agreed to come today
+ 
+
+ align:start position:0%
+so he graciously agreed to come today
+and so everything is ready then and in
+
+ align:start position:0%
+and so everything is ready then and in
+ 
+
+ align:start position:0%
+and so everything is ready then and in
+your cutoff is like 155 yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know somebody changed the resolution
+
+ align:start position:0%
+you know somebody changed the resolution
+ 
+
+ align:start position:0%
+you know somebody changed the resolution
+it seems but that's fine doesn't doesn't
+
+ align:start position:0%
+it seems but that's fine doesn't doesn't
+ 
+
+ align:start position:0%
+it seems but that's fine doesn't doesn't
+bother us so I'm gonna tell you about
+
+ align:start position:0%
+bother us so I'm gonna tell you about
+ 
+
+ align:start position:0%
+bother us so I'm gonna tell you about
+let's say one of the most ancient
+
+ align:start position:0%
+let's say one of the most ancient
+ 
+
+ align:start position:0%
+let's say one of the most ancient
+optimization methods much simpler than
+
+ align:start position:0%
+optimization methods much simpler than
+ 
+
+ align:start position:0%
+optimization methods much simpler than
+in fact the more advanced methods you
+
+ align:start position:0%
+in fact the more advanced methods you
+ 
+
+ align:start position:0%
+in fact the more advanced methods you
+have already seen in class and
+
+ align:start position:0%
+have already seen in class and
+ 
+
+ align:start position:0%
+have already seen in class and
+interestingly this more ancient method
+
+ align:start position:0%
+interestingly this more ancient method
+ 
+
+ align:start position:0%
+interestingly this more ancient method
+remains the method for training
+
+ align:start position:0%
+remains the method for training
+ 
+
+ align:start position:0%
+remains the method for training
+large-scale machine learning systems and
+
+ align:start position:0%
+large-scale machine learning systems and
+ 
+
+ align:start position:0%
+large-scale machine learning systems and
+so there's a little bit of history
+
+ align:start position:0%
+so there's a little bit of history
+ 
+
+ align:start position:0%
+so there's a little bit of history
+around that I'm not gonna go too much
+
+ align:start position:0%
+around that I'm not gonna go too much
+ 
+
+ align:start position:0%
+around that I'm not gonna go too much
+into the history but the bottom line
+
+ align:start position:0%
+into the history but the bottom line
+ 
+
+ align:start position:0%
+into the history but the bottom line
+which probably Gil has also mentioned to
+
+ align:start position:0%
+which probably Gil has also mentioned to
+ 
+
+ align:start position:0%
+which probably Gil has also mentioned to
+you in class that at least for large
+
+ align:start position:0%
+you in class that at least for large
+ 
+
+ align:start position:0%
+you in class that at least for large
+data science problems in the end stuff
+
+ align:start position:0%
+data science problems in the end stuff
+ 
+
+ align:start position:0%
+data science problems in the end stuff
+reduces to solving an optimization
+
+ align:start position:0%
+reduces to solving an optimization
+ 
+
+ align:start position:0%
+reduces to solving an optimization
+problem and in current times these
+
+ align:start position:0%
+problem and in current times these
+ 
+
+ align:start position:0%
+problem and in current times these
+optimization problems are pretty large
+
+ align:start position:0%
+optimization problems are pretty large
+ 
+
+ align:start position:0%
+optimization problems are pretty large
+so people actually started liking stuff
+
+ align:start position:0%
+so people actually started liking stuff
+ 
+
+ align:start position:0%
+so people actually started liking stuff
+like gradient descent which was invented
+
+ align:start position:0%
+like gradient descent which was invented
+ 
+
+ align:start position:0%
+like gradient descent which was invented
+by Cauchy back in the day and this is
+
+ align:start position:0%
+by Cauchy back in the day and this is
+ 
+
+ align:start position:0%
+by Cauchy back in the day and this is
+how I'm writing the abstract problem and
+
+ align:start position:0%
+how I'm writing the abstract problem and
+ 
+
+ align:start position:0%
+how I'm writing the abstract problem and
+what I wanna see is okay is it fitting
+
+ align:start position:0%
+what I wanna see is okay is it fitting
+ 
+
+ align:start position:0%
+what I wanna see is okay is it fitting
+on the page this is my implementation in
+
+ align:start position:0%
+on the page this is my implementation in
+ 
+
+ align:start position:0%
+on the page this is my implementation in
+MATLAB of gradient descent just to set
+
+ align:start position:0%
+MATLAB of gradient descent just to set
+ 
+
+ align:start position:0%
+MATLAB of gradient descent just to set
+the stage that you know this stuff
+
+ align:start position:0%
+the stage that you know this stuff
+ 
+
+ align:start position:0%
+the stage that you know this stuff
+really looks simple you've already seen
+
+ align:start position:0%
+really looks simple you've already seen
+ 
+
+ align:start position:0%
+really looks simple you've already seen
+gradient descent and today essentially
+
+ align:start position:0%
+gradient descent and today essentially
+ 
+
+ align:start position:0%
+gradient descent and today essentially
+in a nutshell what really changes in
+
+ align:start position:0%
+in a nutshell what really changes in
+ 
+
+ align:start position:0%
+in a nutshell what really changes in
+this implementation of gradient descent
+
+ align:start position:0%
+this implementation of gradient descent
+ 
+
+ align:start position:0%
+this implementation of gradient descent
+today is this part that's it
+
+ align:start position:0%
+today is this part that's it
+ 
+
+ align:start position:0%
+today is this part that's it
+so you've seen gradient descent I'm only
+
+ align:start position:0%
+so you've seen gradient descent I'm only
+ 
+
+ align:start position:0%
+so you've seen gradient descent I'm only
+going to change this one line and the
+
+ align:start position:0%
+going to change this one line and the
+ 
+
+ align:start position:0%
+going to change this one line and the
+change of that one line surprisingly is
+
+ align:start position:0%
+change of that one line surprisingly is
+ 
+
+ align:start position:0%
+change of that one line surprisingly is
+driving you know all the deep learning
+
+ align:start position:0%
+driving you know all the deep learning
+ 
+
+ align:start position:0%
+driving you know all the deep learning
+toolboxes and all of large scale machine
+
+ align:start position:0%
+toolboxes and all of large scale machine
+ 
+
+ align:start position:0%
+toolboxes and all of large scale machine
+learning etc this is an
+
+ align:start position:0%
+learning etc this is an
+ 
+
+ align:start position:0%
+learning etc this is an
+oversimplification but morally that's it
+
+ align:start position:0%
+oversimplification but morally that's it
+ 
+
+ align:start position:0%
+oversimplification but morally that's it
+so let's look at what's happening so I
+
+ align:start position:0%
+so let's look at what's happening so I
+ 
+
+ align:start position:0%
+so let's look at what's happening so I
+will become very concrete pretty soon
+
+ align:start position:0%
+will become very concrete pretty soon
+ 
+
+ align:start position:0%
+will become very concrete pretty soon
+but abstractly what I want you to look
+
+ align:start position:0%
+but abstractly what I want you to look
+ 
+
+ align:start position:0%
+but abstractly what I want you to look
+at is the
+
+ align:start position:0%
+at is the
+ 
+
+ align:start position:0%
+at is the
+kinds of optimization problems we are
+
+ align:start position:0%
+kinds of optimization problems we are
+ 
+
+ align:start position:0%
+kinds of optimization problems we are
+solving in machine learning and I'll
+
+ align:start position:0%
+solving in machine learning and I'll
+ 
+
+ align:start position:0%
+solving in machine learning and I'll
+give you very concrete examples of these
+
+ align:start position:0%
+give you very concrete examples of these
+ 
+
+ align:start position:0%
+give you very concrete examples of these
+optimization problems so that you can
+
+ align:start position:0%
+optimization problems so that you can
+ 
+
+ align:start position:0%
+optimization problems so that you can
+relate to them better but I'm just
+
+ align:start position:0%
+relate to them better but I'm just
+ 
+
+ align:start position:0%
+relate to them better but I'm just
+writing this as the key topic that all
+
+ align:start position:0%
+writing this as the key topic that all
+ 
+
+ align:start position:0%
+writing this as the key topic that all
+the optimization problems that I'm going
+
+ align:start position:0%
+the optimization problems that I'm going
+ 
+
+ align:start position:0%
+the optimization problems that I'm going
+to talk about today they look like that
+
+ align:start position:0%
+to talk about today they look like that
+ 
+
+ align:start position:0%
+to talk about today they look like that
+we're trying to find an x over a cost
+
+ align:start position:0%
+we're trying to find an x over a cost
+ 
+
+ align:start position:0%
+we're trying to find an x over a cost
+function where the cost function can be
+
+ align:start position:0%
+function where the cost function can be
+ 
+
+ align:start position:0%
+function where the cost function can be
+written as a sum in modern day machine
+
+ align:start position:0%
+written as a sum in modern day machine
+ 
+
+ align:start position:0%
+written as a sum in modern day machine
+learning parlance these are also called
+
+ align:start position:0%
+learning parlance these are also called
+ 
+
+ align:start position:0%
+learning parlance these are also called
+finite sum problems in case you run into
+
+ align:start position:0%
+finite sum problems in case you run into
+ 
+
+ align:start position:0%
+finite sum problems in case you run into
+that term and this is called finite
+
+ align:start position:0%
+that term and this is called finite
+ 
+
+ align:start position:0%
+that term and this is called finite
+because n is finite here in pure
+
+ align:start position:0%
+because n is finite here in pure
+ 
+
+ align:start position:0%
+because n is finite here in pure
+optimization Theory parlance n can
+
+ align:start position:0%
+optimization Theory parlance n can
+ 
+
+ align:start position:0%
+optimization Theory parlance n can
+actually go to infinity and then they
+
+ align:start position:0%
+actually go to infinity and then they
+ 
+
+ align:start position:0%
+actually go to infinity and then they
+are called stochastic optimization
+
+ align:start position:0%
+are called stochastic optimization
+ 
+
+ align:start position:0%
+are called stochastic optimization
+problems just for terminology if while
+
+ align:start position:0%
+problems just for terminology if while
+ 
+
+ align:start position:0%
+problems just for terminology if while
+searching the internet you run into some
+
+ align:start position:0%
+searching the internet you run into some
+ 
+
+ align:start position:0%
+searching the internet you run into some
+such terminology so you kind of know
+
+ align:start position:0%
+such terminology so you kind of know
+ 
+
+ align:start position:0%
+such terminology so you kind of know
+what it means so here is our set up in
+
+ align:start position:0%
+what it means so here is our set up in
+ 
+
+ align:start position:0%
+what it means so here is our set up in
+machine learning we have a bunch of
+
+ align:start position:0%
+machine learning we have a bunch of
+ 
+
+ align:start position:0%
+machine learning we have a bunch of
+training data ok on this slide I am
+
+ align:start position:0%
+training data ok on this slide I am
+ 
+
+ align:start position:0%
+training data ok on this slide I am
+calling x1 through xn these are the
+
+ align:start position:0%
+calling x1 through xn these are the
+ 
+
+ align:start position:0%
+calling x1 through xn these are the
+training data the raw features later
+
+ align:start position:0%
+training data the raw features later
+ 
+
+ align:start position:0%
+training data the raw features later
+actually I stopped writing X for them
+
+ align:start position:0%
+actually I stopped writing X for them
+ 
+
+ align:start position:0%
+actually I stopped writing X for them
+and write them with the letter A but
+
+ align:start position:0%
+and write them with the letter A but
+ 
+
+ align:start position:0%
+and write them with the letter A but
+hopefully that's okay so x1 through xn
+
+ align:start position:0%
+hopefully that's okay so x1 through xn
+ 
+
+ align:start position:0%
+hopefully that's okay so x1 through xn
+these could be just raw images for
+
+ align:start position:0%
+these could be just raw images for
+ 
+
+ align:start position:0%
+these could be just raw images for
+instance in imagenet or some other image
+
+ align:start position:0%
+instance in imagenet or some other image
+ 
+
+ align:start position:0%
+instance in imagenet or some other image
+data set there could be text documents
+
+ align:start position:0%
+data set there could be text documents
+ 
+
+ align:start position:0%
+data set there could be text documents
+they could be anything y1 through yn in
+
+ align:start position:0%
+they could be anything y1 through yn in
+ 
+
+ align:start position:0%
+they could be anything y1 through yn in
+classical machine learning think of them
+
+ align:start position:0%
+classical machine learning think of them
+ 
+
+ align:start position:0%
+classical machine learning think of them
+as plus minus 1 labels cat not cat or in
+
+ align:start position:0%
+as plus minus 1 labels cat not cat or in
+ 
+
+ align:start position:0%
+as plus minus 1 labels cat not cat or in
+a regression setup as some real number
+
+ align:start position:0%
+a regression setup as some real number
+ 
+
+ align:start position:0%
+a regression setup as some real number
+so that's a training data we have D
+
+ align:start position:0%
+so that's a training data we have D
+ 
+
+ align:start position:0%
+so that's a training data we have D
+dimensional raw vectors and of those and
+
+ align:start position:0%
+dimensional raw vectors and of those and
+ 
+
+ align:start position:0%
+dimensional raw vectors and of those and
+we have corresponding labels which can
+
+ align:start position:0%
+we have corresponding labels which can
+ 
+
+ align:start position:0%
+we have corresponding labels which can
+be either plus minus 1 in a
+
+ align:start position:0%
+be either plus minus 1 in a
+ 
+
+ align:start position:0%
+be either plus minus 1 in a
+classification setting or a real number
+
+ align:start position:0%
+classification setting or a real number
+ 
+
+ align:start position:0%
+classification setting or a real number
+in a regression setting it's kind of
+
+ align:start position:0%
+in a regression setting it's kind of
+ 
+
+ align:start position:0%
+in a regression setting it's kind of
+immaterial for my lecture right now so
+
+ align:start position:0%
+immaterial for my lecture right now so
+ 
+
+ align:start position:0%
+immaterial for my lecture right now so
+that's the input and whenever anybody
+
+ align:start position:0%
+that's the input and whenever anybody
+ 
+
+ align:start position:0%
+that's the input and whenever anybody
+says large-scale machine learning what
+
+ align:start position:0%
+says large-scale machine learning what
+ 
+
+ align:start position:0%
+says large-scale machine learning what
+do we really mean
+
+ align:start position:0%
+do we really mean
+ 
+
+ align:start position:0%
+do we really mean
+what we mean is that both N and D can be
+
+ align:start position:0%
+what we mean is that both N and D can be
+ 
+
+ align:start position:0%
+what we mean is that both N and D can be
+large so what does that mean in words
+
+ align:start position:0%
+large so what does that mean in words
+ 
+
+ align:start position:0%
+large so what does that mean in words
+there n is the number of training data
+
+ align:start position:0%
+there n is the number of training data
+ 
+
+ align:start position:0%
+there n is the number of training data
+points so n could be these days what
+
+ align:start position:0%
+points so n could be these days what
+ 
+
+ align:start position:0%
+points so n could be these days what
+million ten million hundred million
+
+ align:start position:0%
+million ten million hundred million
+ 
+
+ align:start position:0%
+million ten million hundred million
+depends on how big computers and data
+
+ align:start position:0%
+depends on how big computers and data
+ 
+
+ align:start position:0%
+depends on how big computers and data
+sets you got so n can be huge d the
+
+ align:start position:0%
+sets you got so n can be huge d the
+ 
+
+ align:start position:0%
+sets you got so n can be huge d the
+dimensionality the vectors that we are
+
+ align:start position:0%
+dimensionality the vectors that we are
+ 
+
+ align:start position:0%
+dimensionality the vectors that we are
+working with the raw vectors that can
+
+ align:start position:0%
+working with the raw vectors that can
+ 
+
+ align:start position:0%
+working with the raw vectors that can
+also be pretty large think if X is an
+
+ align:start position:0%
+also be pretty large think if X is an
+ 
+
+ align:start position:0%
+also be pretty large think if X is an
+image if it's a megapixel image wow
+
+ align:start position:0%
+image if it's a megapixel image wow
+ 
+
+ align:start position:0%
+image if it's a megapixel image wow
+these like a million already if you are
+
+ align:start position:0%
+these like a million already if you are
+ 
+
+ align:start position:0%
+these like a million already if you are
+somebody like kriti o or Facebook or
+
+ align:start position:0%
+somebody like kriti o or Facebook or
+ 
+
+ align:start position:0%
+somebody like kriti o or Facebook or
+Google and you're serving web
+
+ align:start position:0%
+Google and you're serving web
+ 
+
+ align:start position:0%
+Google and you're serving web
+advertisements D these are the features
+
+ align:start position:0%
+advertisements D these are the features
+ 
+
+ align:start position:0%
+advertisements D these are the features
+could be like in 700 million even a
+
+ align:start position:0%
+could be like in 700 million even a
+ 
+
+ align:start position:0%
+could be like in 700 million even a
+billion where they encode all sorts of
+
+ align:start position:0%
+billion where they encode all sorts of
+ 
+
+ align:start position:0%
+billion where they encode all sorts of
+nasty stuff and information they collect
+
+ align:start position:0%
+nasty stuff and information they collect
+ 
+
+ align:start position:0%
+nasty stuff and information they collect
+about you as users so so many nasty
+
+ align:start position:0%
+about you as users so so many nasty
+ 
+
+ align:start position:0%
+about you as users so so many nasty
+things they can collect right so DNN are
+
+ align:start position:0%
+things they can collect right so DNN are
+ 
+
+ align:start position:0%
+things they can collect right so DNN are
+huge and it's because both D and n are
+
+ align:start position:0%
+huge and it's because both D and n are
+ 
+
+ align:start position:0%
+huge and it's because both D and n are
+huge we are interested in thinking of
+
+ align:start position:0%
+huge we are interested in thinking of
+ 
+
+ align:start position:0%
+huge we are interested in thinking of
+optimization methods for large-scale
+
+ align:start position:0%
+optimization methods for large-scale
+ 
+
+ align:start position:0%
+optimization methods for large-scale
+machine learning that can handle such
+
+ align:start position:0%
+machine learning that can handle such
+ 
+
+ align:start position:0%
+machine learning that can handle such
+big dnl and this is driving a lot of
+
+ align:start position:0%
+big dnl and this is driving a lot of
+ 
+
+ align:start position:0%
+big dnl and this is driving a lot of
+research also in theoretical computer
+
+ align:start position:0%
+research also in theoretical computer
+ 
+
+ align:start position:0%
+research also in theoretical computer
+science including the search for sub
+
+ align:start position:0%
+science including the search for sub
+ 
+
+ align:start position:0%
+science including the search for sub
+linear time algorithms in all sorts of
+
+ align:start position:0%
+linear time algorithms in all sorts of
+ 
+
+ align:start position:0%
+linear time algorithms in all sorts of
+data structures in hashing tricks just
+
+ align:start position:0%
+data structures in hashing tricks just
+ 
+
+ align:start position:0%
+data structures in hashing tricks just
+to deal with these two quantities so
+
+ align:start position:0%
+to deal with these two quantities so
+ 
+
+ align:start position:0%
+to deal with these two quantities so
+here is an example super toy example and
+
+ align:start position:0%
+here is an example super toy example and
+ 
+
+ align:start position:0%
+here is an example super toy example and
+I hope really you know by that I can
+
+ align:start position:0%
+I hope really you know by that I can
+ 
+
+ align:start position:0%
+I hope really you know by that I can
+squeeze in a little bit of a proof later
+
+ align:start position:0%
+squeeze in a little bit of a proof later
+ 
+
+ align:start position:0%
+squeeze in a little bit of a proof later
+on towards the end I'll take a vote here
+
+ align:start position:0%
+on towards the end I'll take a vote here
+ 
+
+ align:start position:0%
+on towards the end I'll take a vote here
+in class to see if you are interested
+
+ align:start position:0%
+in class to see if you are interested
+ 
+
+ align:start position:0%
+in class to see if you are interested
+let's look at the most classic question
+
+ align:start position:0%
+let's look at the most classic question
+ 
+
+ align:start position:0%
+let's look at the most classic question
+least squares regression is a matrix of
+
+ align:start position:0%
+least squares regression is a matrix of
+ 
+
+ align:start position:0%
+least squares regression is a matrix of
+observations or sorry measurements B are
+
+ align:start position:0%
+observations or sorry measurements B are
+ 
+
+ align:start position:0%
+observations or sorry measurements B are
+the observations you're trying to solve
+
+ align:start position:0%
+the observations you're trying to solve
+ 
+
+ align:start position:0%
+the observations you're trying to solve
+ax minus B whole square
+
+ align:start position:0%
+ax minus B whole square
+ 
+
+ align:start position:0%
+ax minus B whole square
+of course a linear system of equations
+
+ align:start position:0%
+of course a linear system of equations
+ 
+
+ align:start position:0%
+of course a linear system of equations
+the most classical problem in linear
+
+ align:start position:0%
+the most classical problem in linear
+ 
+
+ align:start position:0%
+the most classical problem in linear
+algebra can also be written like that
+
+ align:start position:0%
+algebra can also be written like that
+ 
+
+ align:start position:0%
+algebra can also be written like that
+let's say this can be expanded hopefully
+
+ align:start position:0%
+let's say this can be expanded hopefully
+ 
+
+ align:start position:0%
+let's say this can be expanded hopefully
+you are comfortable with this norm right
+
+ align:start position:0%
+you are comfortable with this norm right
+ 
+
+ align:start position:0%
+you are comfortable with this norm right
+so x2 square this is just defined as
+
+ align:start position:0%
+so x2 square this is just defined as
+ 
+
+ align:start position:0%
+so x2 square this is just defined as
+that's the definition of that notation
+
+ align:start position:0%
+that's the definition of that notation
+ 
+
+ align:start position:0%
+that's the definition of that notation
+but I'll just write it only once now I
+
+ align:start position:0%
+but I'll just write it only once now I
+ 
+
+ align:start position:0%
+but I'll just write it only once now I
+hope you are fully familiar with that so
+
+ align:start position:0%
+hope you are fully familiar with that so
+ 
+
+ align:start position:0%
+hope you are fully familiar with that so
+by expanding that I managed to write
+
+ align:start position:0%
+by expanding that I managed to write
+ 
+
+ align:start position:0%
+by expanding that I managed to write
+least squares problem in terms of what I
+
+ align:start position:0%
+least squares problem in terms of what I
+ 
+
+ align:start position:0%
+least squares problem in terms of what I
+call the finite sum right so it's just
+
+ align:start position:0%
+call the finite sum right so it's just
+ 
+
+ align:start position:0%
+call the finite sum right so it's just
+going over all the rows in a their end
+
+ align:start position:0%
+going over all the rows in a their end
+ 
+
+ align:start position:0%
+going over all the rows in a their end
+rows let's say so that's the least
+
+ align:start position:0%
+rows let's say so that's the least
+ 
+
+ align:start position:0%
+rows let's say so that's the least
+squares classical least squares problem
+
+ align:start position:0%
+squares classical least squares problem
+ 
+
+ align:start position:0%
+squares classical least squares problem
+it assumes this finite sum form that we
+
+ align:start position:0%
+it assumes this finite sum form that we
+ 
+
+ align:start position:0%
+it assumes this finite sum form that we
+care about another random example
+
+ align:start position:0%
+care about another random example
+ 
+
+ align:start position:0%
+care about another random example
+something called la so maybe you have if
+
+ align:start position:0%
+something called la so maybe you have if
+ 
+
+ align:start position:0%
+something called la so maybe you have if
+anybody of you has played with machine
+
+ align:start position:0%
+anybody of you has played with machine
+ 
+
+ align:start position:0%
+anybody of you has played with machine
+learning statistics toolkits you may
+
+ align:start position:0%
+learning statistics toolkits you may
+ 
+
+ align:start position:0%
+learning statistics toolkits you may
+have seen something called la Sol la Sol
+
+ align:start position:0%
+have seen something called la Sol la Sol
+ 
+
+ align:start position:0%
+have seen something called la Sol la Sol
+is essentially least squares but there's
+
+ align:start position:0%
+is essentially least squares but there's
+ 
+
+ align:start position:0%
+is essentially least squares but there's
+another simple term at the end that
+
+ align:start position:0%
+another simple term at the end that
+ 
+
+ align:start position:0%
+another simple term at the end that
+again looks like F of I support vector
+
+ align:start position:0%
+again looks like F of I support vector
+ 
+
+ align:start position:0%
+again looks like F of I support vector
+machines once over horse of they're
+
+ align:start position:0%
+machines once over horse of they're
+ 
+
+ align:start position:0%
+machines once over horse of they're
+still a workhorse horse of people who
+
+ align:start position:0%
+still a workhorse horse of people who
+ 
+
+ align:start position:0%
+still a workhorse horse of people who
+work with small to medium sized data
+
+ align:start position:0%
+work with small to medium sized data
+ 
+
+ align:start position:0%
+work with small to medium sized data
+deep learning stuff requires huge amount
+
+ align:start position:0%
+deep learning stuff requires huge amount
+ 
+
+ align:start position:0%
+deep learning stuff requires huge amount
+of data if you have small to medium
+
+ align:start position:0%
+of data if you have small to medium
+ 
+
+ align:start position:0%
+of data if you have small to medium
+amount of data logistic regression
+
+ align:start position:0%
+amount of data logistic regression
+ 
+
+ align:start position:0%
+amount of data logistic regression
+support vector machines trees etc this
+
+ align:start position:0%
+support vector machines trees etc this
+ 
+
+ align:start position:0%
+support vector machines trees etc this
+will be a first go to methods they still
+
+ align:start position:0%
+will be a first go to methods they still
+ 
+
+ align:start position:0%
+will be a first go to methods they still
+very widely used these problems are
+
+ align:start position:0%
+very widely used these problems are
+ 
+
+ align:start position:0%
+very widely used these problems are
+again written in terms of a loss over
+
+ align:start position:0%
+again written in terms of a loss over
+ 
+
+ align:start position:0%
+again written in terms of a loss over
+training data so this again has this
+
+ align:start position:0%
+training data so this again has this
+ 
+
+ align:start position:0%
+training data so this again has this
+awesome format which I'll just now
+
+ align:start position:0%
+awesome format which I'll just now
+ 
+
+ align:start position:0%
+awesome format which I'll just now
+record here I may not even need to
+
+ align:start position:0%
+record here I may not even need to
+ 
+
+ align:start position:0%
+record here I may not even need to
+repeat it sometimes I write it with a
+
+ align:start position:0%
+repeat it sometimes I write it with a
+ 
+
+ align:start position:0%
+repeat it sometimes I write it with a
+normalization you may wonder at some
+
+ align:start position:0%
+normalization you may wonder at some
+ 
+
+ align:start position:0%
+normalization you may wonder at some
+point why as that finite sum problem and
+
+ align:start position:0%
+point why as that finite sum problem and
+ 
+
+ align:start position:0%
+point why as that finite sum problem and
+maybe the example that you want it to
+
+ align:start position:0%
+maybe the example that you want it to
+ 
+
+ align:start position:0%
+maybe the example that you want it to
+see is something like that so deep
+
+ align:start position:0%
+see is something like that so deep
+ 
+
+ align:start position:0%
+see is something like that so deep
+neural networks that are very popular
+
+ align:start position:0%
+neural networks that are very popular
+ 
+
+ align:start position:0%
+neural networks that are very popular
+these days they are just yet another
+
+ align:start position:0%
+these days they are just yet another
+ 
+
+ align:start position:0%
+these days they are just yet another
+example of this finite sum problem how
+
+ align:start position:0%
+example of this finite sum problem how
+ 
+
+ align:start position:0%
+example of this finite sum problem how
+are they an example of that so you have
+
+ align:start position:0%
+are they an example of that so you have
+ 
+
+ align:start position:0%
+are they an example of that so you have
+n training data points there's a neural
+
+ align:start position:0%
+n training data points there's a neural
+ 
+
+ align:start position:0%
+n training data points there's a neural
+network loss like cross-entropy or what
+
+ align:start position:0%
+network loss like cross-entropy or what
+ 
+
+ align:start position:0%
+network loss like cross-entropy or what
+have you squared loss cross into any
+
+ align:start position:0%
+have you squared loss cross into any
+ 
+
+ align:start position:0%
+have you squared loss cross into any
+kind of loss why eyes are the labels cat
+
+ align:start position:0%
+kind of loss why eyes are the labels cat
+ 
+
+ align:start position:0%
+kind of loss why eyes are the labels cat
+not cat or whatever or they may be her
+
+ align:start position:0%
+not cat or whatever or they may be her
+ 
+
+ align:start position:0%
+not cat or whatever or they may be her
+multi class
+
+ align:start position:0%
+multi class
+ 
+
+ align:start position:0%
+multi class
+and then you have a transfer function
+
+ align:start position:0%
+and then you have a transfer function
+ 
+
+ align:start position:0%
+and then you have a transfer function
+called a deep neural network which takes
+
+ align:start position:0%
+called a deep neural network which takes
+ 
+
+ align:start position:0%
+called a deep neural network which takes
+raw images as input and generates a
+
+ align:start position:0%
+raw images as input and generates a
+ 
+
+ align:start position:0%
+raw images as input and generates a
+prediction whether this is a dog or not
+
+ align:start position:0%
+prediction whether this is a dog or not
+ 
+
+ align:start position:0%
+prediction whether this is a dog or not
+that whole thing I'm just calling DN n
+
+ align:start position:0%
+that whole thing I'm just calling DN n
+ 
+
+ align:start position:0%
+that whole thing I'm just calling DN n
+so it's a function of a eyes which are
+
+ align:start position:0%
+so it's a function of a eyes which are
+ 
+
+ align:start position:0%
+so it's a function of a eyes which are
+the training data X are the weight
+
+ align:start position:0%
+the training data X are the weight
+ 
+
+ align:start position:0%
+the training data X are the weight
+matrices of the neural network so I'm
+
+ align:start position:0%
+matrices of the neural network so I'm
+ 
+
+ align:start position:0%
+matrices of the neural network so I'm
+just compressed the whole neural network
+
+ align:start position:0%
+just compressed the whole neural network
+ 
+
+ align:start position:0%
+just compressed the whole neural network
+into this notation
+
+ align:start position:0%
+into this notation
+ 
+
+ align:start position:0%
+into this notation
+once again it's nothing but an instance
+
+ align:start position:0%
+once again it's nothing but an instance
+ 
+
+ align:start position:0%
+once again it's nothing but an instance
+of that finite sum so that F I in there
+
+ align:start position:0%
+of that finite sum so that F I in there
+ 
+
+ align:start position:0%
+of that finite sum so that F I in there
+captures the entire neural network
+
+ align:start position:0%
+captures the entire neural network
+ 
+
+ align:start position:0%
+captures the entire neural network
+architecture but mathematically it's
+
+ align:start position:0%
+architecture but mathematically it's
+ 
+
+ align:start position:0%
+architecture but mathematically it's
+still just one particular instance of
+
+ align:start position:0%
+still just one particular instance of
+ 
+
+ align:start position:0%
+still just one particular instance of
+this finite sum problem and in people
+
+ align:start position:0%
+this finite sum problem and in people
+ 
+
+ align:start position:0%
+this finite sum problem and in people
+who do lot of statistics maximum
+
+ align:start position:0%
+who do lot of statistics maximum
+ 
+
+ align:start position:0%
+who do lot of statistics maximum
+likelihood estimation this is log
+
+ align:start position:0%
+likelihood estimation this is log
+ 
+
+ align:start position:0%
+likelihood estimation this is log
+likelihood over n observations we want
+
+ align:start position:0%
+likelihood over n observations we want
+ 
+
+ align:start position:0%
+likelihood over n observations we want
+to maximize log likelihood once again
+
+ align:start position:0%
+to maximize log likelihood once again
+ 
+
+ align:start position:0%
+to maximize log likelihood once again
+just a finite sum so pretty much most of
+
+ align:start position:0%
+just a finite sum so pretty much most of
+ 
+
+ align:start position:0%
+just a finite sum so pretty much most of
+the problems that we are interested in
+
+ align:start position:0%
+the problems that we are interested in
+ 
+
+ align:start position:0%
+the problems that we are interested in
+machine learning and statistics when I
+
+ align:start position:0%
+machine learning and statistics when I
+ 
+
+ align:start position:0%
+machine learning and statistics when I
+write them write them down as an
+
+ align:start position:0%
+write them write them down as an
+ 
+
+ align:start position:0%
+write them write them down as an
+optimization problem they look like this
+
+ align:start position:0%
+optimization problem they look like this
+ 
+
+ align:start position:0%
+optimization problem they look like this
+finite sum problems and that's the
+
+ align:start position:0%
+finite sum problems and that's the
+ 
+
+ align:start position:0%
+finite sum problems and that's the
+reason to develop specialized
+
+ align:start position:0%
+reason to develop specialized
+ 
+
+ align:start position:0%
+reason to develop specialized
+optimization procedures to solve such
+
+ align:start position:0%
+optimization procedures to solve such
+ 
+
+ align:start position:0%
+optimization procedures to solve such
+finite sum problems and that's where SGD
+
+ align:start position:0%
+finite sum problems and that's where SGD
+ 
+
+ align:start position:0%
+finite sum problems and that's where SGD
+comes in ok so that's kind of just the
+
+ align:start position:0%
+comes in ok so that's kind of just the
+ 
+
+ align:start position:0%
+comes in ok so that's kind of just the
+backdrop let's look at now how to go
+
+ align:start position:0%
+backdrop let's look at now how to go
+ 
+
+ align:start position:0%
+backdrop let's look at now how to go
+about solving these problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so hopefully this iteration is familiar
+
+ align:start position:0%
+so hopefully this iteration is familiar
+ 
+
+ align:start position:0%
+so hopefully this iteration is familiar
+to you gradient descent right ok so just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for notation f of X refers to that
+
+ align:start position:0%
+for notation f of X refers to that
+ 
+
+ align:start position:0%
+for notation f of X refers to that
+entire summation F sub I of X refers to
+
+ align:start position:0%
+entire summation F sub I of X refers to
+ 
+
+ align:start position:0%
+entire summation F sub I of X refers to
+a single component ok so if you were to
+
+ align:start position:0%
+a single component ok so if you were to
+ 
+
+ align:start position:0%
+a single component ok so if you were to
+try to solve that is to minimize this
+
+ align:start position:0%
+try to solve that is to minimize this
+ 
+
+ align:start position:0%
+try to solve that is to minimize this
+cost function neural network SVM
+
+ align:start position:0%
+cost function neural network SVM
+ 
+
+ align:start position:0%
+cost function neural network SVM
+what-have-you using gradient descent
+
+ align:start position:0%
+what-have-you using gradient descent
+ 
+
+ align:start position:0%
+what-have-you using gradient descent
+that's what one iteration would look
+
+ align:start position:0%
+that's what one iteration would look
+ 
+
+ align:start position:0%
+that's what one iteration would look
+like because it's a finite sum gradients
+
+ align:start position:0%
+like because it's a finite sum gradients
+ 
+
+ align:start position:0%
+like because it's a finite sum gradients
+are linear operators
+
+ align:start position:0%
+are linear operators
+ 
+
+ align:start position:0%
+are linear operators
+you know gradient of the sum is the sum
+
+ align:start position:0%
+you know gradient of the sum is the sum
+ 
+
+ align:start position:0%
+you know gradient of the sum is the sum
+of the gradients so that's gradient
+
+ align:start position:0%
+of the gradients so that's gradient
+ 
+
+ align:start position:0%
+of the gradients so that's gradient
+descent for you and now I'll just ask a
+
+ align:start position:0%
+descent for you and now I'll just ask a
+ 
+
+ align:start position:0%
+descent for you and now I'll just ask a
+rhetoric question that if you put
+
+ align:start position:0%
+rhetoric question that if you put
+ 
+
+ align:start position:0%
+rhetoric question that if you put
+yourself in the shoes of you know
+
+ align:start position:0%
+yourself in the shoes of you know
+ 
+
+ align:start position:0%
+yourself in the shoes of you know
+algorithm designers some things that you
+
+ align:start position:0%
+algorithm designers some things that you
+ 
+
+ align:start position:0%
+algorithm designers some things that you
+may want to think about what may you not
+
+ align:start position:0%
+may want to think about what may you not
+ 
+
+ align:start position:0%
+may want to think about what may you not
+like about this iteration given that big
+
+ align:start position:0%
+like about this iteration given that big
+ 
+
+ align:start position:0%
+like about this iteration given that big
+and Big D story that I told you so
+
+ align:start position:0%
+and Big D story that I told you so
+ 
+
+ align:start position:0%
+and Big D story that I told you so
+anybody have any reservations or about
+
+ align:start position:0%
+anybody have any reservations or about
+ 
+
+ align:start position:0%
+anybody have any reservations or about
+drawbacks of this iteration any comments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a pretty big sum especially
+
+ align:start position:0%
+it's a pretty big sum especially
+ 
+
+ align:start position:0%
+it's a pretty big sum especially
+anything that is a big drawback and
+
+ align:start position:0%
+anything that is a big drawback and
+ 
+
+ align:start position:0%
+anything that is a big drawback and
+there is that is the prime drawback for
+
+ align:start position:0%
+there is that is the prime drawback for
+ 
+
+ align:start position:0%
+there is that is the prime drawback for
+large scale that n can be huge there can
+
+ align:start position:0%
+large scale that n can be huge there can
+ 
+
+ align:start position:0%
+large scale that n can be huge there can
+be variety of other drawbacks some of
+
+ align:start position:0%
+be variety of other drawbacks some of
+ 
+
+ align:start position:0%
+be variety of other drawbacks some of
+those you may have seen previously if
+
+ align:start position:0%
+those you may have seen previously if
+ 
+
+ align:start position:0%
+those you may have seen previously if
+when people compare whether to do
+
+ align:start position:0%
+when people compare whether to do
+ 
+
+ align:start position:0%
+when people compare whether to do
+gradient or to do Newton etc but for
+
+ align:start position:0%
+gradient or to do Newton etc but for
+ 
+
+ align:start position:0%
+gradient or to do Newton etc but for
+purpose of today for finite sums the big
+
+ align:start position:0%
+purpose of today for finite sums the big
+ 
+
+ align:start position:0%
+purpose of today for finite sums the big
+drawback is computing gradient at a
+
+ align:start position:0%
+drawback is computing gradient at a
+ 
+
+ align:start position:0%
+drawback is computing gradient at a
+single point this is a subscript XK
+
+ align:start position:0%
+single point this is a subscript XK
+ 
+
+ align:start position:0%
+single point this is a subscript XK
+missing there involves computing the
+
+ align:start position:0%
+missing there involves computing the
+ 
+
+ align:start position:0%
+missing there involves computing the
+gradient of that entire sum that sum is
+
+ align:start position:0%
+gradient of that entire sum that sum is
+ 
+
+ align:start position:0%
+gradient of that entire sum that sum is
+huge so getting a single gradient to do
+
+ align:start position:0%
+huge so getting a single gradient to do
+ 
+
+ align:start position:0%
+huge so getting a single gradient to do
+a single step of gradient descent for a
+
+ align:start position:0%
+a single step of gradient descent for a
+ 
+
+ align:start position:0%
+a single step of gradient descent for a
+large data set could take you hours or
+
+ align:start position:0%
+large data set could take you hours or
+ 
+
+ align:start position:0%
+large data set could take you hours or
+days so that's a major drawback but then
+
+ align:start position:0%
+days so that's a major drawback but then
+ 
+
+ align:start position:0%
+days so that's a major drawback but then
+okay if you identify that drawback
+
+ align:start position:0%
+okay if you identify that drawback
+ 
+
+ align:start position:0%
+okay if you identify that drawback
+anybody have any ideas how to counter
+
+ align:start position:0%
+anybody have any ideas how to counter
+ 
+
+ align:start position:0%
+anybody have any ideas how to counter
+that drawback at least say purely from
+
+ align:start position:0%
+that drawback at least say purely from
+ 
+
+ align:start position:0%
+that drawback at least say purely from
+an engineering perspective I heard
+
+ align:start position:0%
+an engineering perspective I heard
+ 
+
+ align:start position:0%
+an engineering perspective I heard
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using LexA and a batch of mash lights to
+
+ align:start position:0%
+using LexA and a batch of mash lights to
+ 
+
+ align:start position:0%
+using LexA and a batch of mash lights to
+defend us and maybe somebody else has
+
+ align:start position:0%
+defend us and maybe somebody else has
+ 
+
+ align:start position:0%
+defend us and maybe somebody else has
+essentially the same idea anybody wants
+
+ align:start position:0%
+essentially the same idea anybody wants
+ 
+
+ align:start position:0%
+essentially the same idea anybody wants
+to suggest how to circumvent that big
+
+ align:start position:0%
+to suggest how to circumvent that big
+ 
+
+ align:start position:0%
+to suggest how to circumvent that big
+end stuff in there anything suppose you
+
+ align:start position:0%
+end stuff in there anything suppose you
+ 
+
+ align:start position:0%
+end stuff in there anything suppose you
+can implement in this what would you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+andum sample of the full n so these are
+
+ align:start position:0%
+andum sample of the full n so these are
+ 
+
+ align:start position:0%
+andum sample of the full n so these are
+all excellent ideas and hence you folks
+
+ align:start position:0%
+all excellent ideas and hence you folks
+ 
+
+ align:start position:0%
+all excellent ideas and hence you folks
+in the class have discovered the most
+
+ align:start position:0%
+in the class have discovered the most
+ 
+
+ align:start position:0%
+in the class have discovered the most
+important method for optimizing machine
+
+ align:start position:0%
+important method for optimizing machine
+ 
+
+ align:start position:0%
+important method for optimizing machine
+learning problems sitting here in a few
+
+ align:start position:0%
+learning problems sitting here in a few
+ 
+
+ align:start position:0%
+learning problems sitting here in a few
+moments isn't that great so the part
+
+ align:start position:0%
+moments isn't that great so the part
+ 
+
+ align:start position:0%
+moments isn't that great so the part
+that is missing is of course to make
+
+ align:start position:0%
+that is missing is of course to make
+ 
+
+ align:start position:0%
+that is missing is of course to make
+sense of does this idea work why does it
+
+ align:start position:0%
+sense of does this idea work why does it
+ 
+
+ align:start position:0%
+sense of does this idea work why does it
+work so this idea is really at the heart
+
+ align:start position:0%
+work so this idea is really at the heart
+ 
+
+ align:start position:0%
+work so this idea is really at the heart
+of stochastic gradient descent so let's
+
+ align:start position:0%
+of stochastic gradient descent so let's
+ 
+
+ align:start position:0%
+of stochastic gradient descent so let's
+see I maybe I can show you an example
+
+ align:start position:0%
+see I maybe I can show you an example
+ 
+
+ align:start position:0%
+see I maybe I can show you an example
+actually that I I'll show you a
+
+ align:start position:0%
+actually that I I'll show you a
+ 
+
+ align:start position:0%
+actually that I I'll show you a
+simulation I found on somebody's nice
+
+ align:start position:0%
+simulation I found on somebody's nice
+ 
+
+ align:start position:0%
+simulation I found on somebody's nice
+web page about that so exactly your idea
+
+ align:start position:0%
+web page about that so exactly your idea
+ 
+
+ align:start position:0%
+web page about that so exactly your idea
+just put in slight mathematical notation
+
+ align:start position:0%
+just put in slight mathematical notation
+ 
+
+ align:start position:0%
+just put in slight mathematical notation
+that what if at each iteration we
+
+ align:start position:0%
+that what if at each iteration we
+ 
+
+ align:start position:0%
+that what if at each iteration we
+randomly pick some integer I K out of
+
+ align:start position:0%
+randomly pick some integer I K out of
+ 
+
+ align:start position:0%
+randomly pick some integer I K out of
+the n training data points and and we
+
+ align:start position:0%
+the n training data points and and we
+ 
+
+ align:start position:0%
+the n training data points and and we
+instead just perform this update right
+
+ align:start position:0%
+instead just perform this update right
+ 
+
+ align:start position:0%
+instead just perform this update right
+so you instead of using the full
+
+ align:start position:0%
+so you instead of using the full
+ 
+
+ align:start position:0%
+so you instead of using the full
+gradient you just compute the gradient
+
+ align:start position:0%
+gradient you just compute the gradient
+ 
+
+ align:start position:0%
+gradient you just compute the gradient
+of a single randomly chosen data point
+
+ align:start position:0%
+of a single randomly chosen data point
+ 
+
+ align:start position:0%
+of a single randomly chosen data point
+so what have you done with that one
+
+ align:start position:0%
+so what have you done with that one
+ 
+
+ align:start position:0%
+so what have you done with that one
+iteration is now n times faster if n
+
+ align:start position:0%
+iteration is now n times faster if n
+ 
+
+ align:start position:0%
+iteration is now n times faster if n
+were a million or a billion wow that's
+
+ align:start position:0%
+were a million or a billion wow that's
+ 
+
+ align:start position:0%
+were a million or a billion wow that's
+super fast but why should this work
+
+ align:start position:0%
+super fast but why should this work
+ 
+
+ align:start position:0%
+super fast but why should this work
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean I could have done many other
+
+ align:start position:0%
+I mean I could have done many other
+ 
+
+ align:start position:0%
+I mean I could have done many other
+things I could have constant I could
+
+ align:start position:0%
+things I could have constant I could
+ 
+
+ align:start position:0%
+things I could have constant I could
+have not done any update and just output
+
+ align:start position:0%
+have not done any update and just output
+ 
+
+ align:start position:0%
+have not done any update and just output
+the zero vector that would take even
+
+ align:start position:0%
+the zero vector that would take even
+ 
+
+ align:start position:0%
+the zero vector that would take even
+lesser time that's also an idea means a
+
+ align:start position:0%
+lesser time that's also an idea means a
+ 
+
+ align:start position:0%
+lesser time that's also an idea means a
+bad idea but it's an idea in the similar
+
+ align:start position:0%
+bad idea but it's an idea in the similar
+ 
+
+ align:start position:0%
+bad idea but it's an idea in the similar
+league I could have done a variety of
+
+ align:start position:0%
+league I could have done a variety of
+ 
+
+ align:start position:0%
+league I could have done a variety of
+other things why would you think that
+
+ align:start position:0%
+other things why would you think that
+ 
+
+ align:start position:0%
+other things why would you think that
+just you know replacing that some with
+
+ align:start position:0%
+just you know replacing that some with
+ 
+
+ align:start position:0%
+just you know replacing that some with
+just one random example may work let's
+
+ align:start position:0%
+just one random example may work let's
+ 
+
+ align:start position:0%
+just one random example may work let's
+see a little bit more about that so of
+
+ align:start position:0%
+see a little bit more about that so of
+ 
+
+ align:start position:0%
+see a little bit more about that so of
+course it's n times faster and the key
+
+ align:start position:0%
+course it's n times faster and the key
+ 
+
+ align:start position:0%
+course it's n times faster and the key
+question for us here right now the
+
+ align:start position:0%
+question for us here right now the
+ 
+
+ align:start position:0%
+question for us here right now the
+scientific question is does this make
+
+ align:start position:0%
+scientific question is does this make
+ 
+
+ align:start position:0%
+scientific question is does this make
+sense it makes great engineering sense
+
+ align:start position:0%
+sense it makes great engineering sense
+ 
+
+ align:start position:0%
+sense it makes great engineering sense
+does it make algorithmic or mathematical
+
+ align:start position:0%
+does it make algorithmic or mathematical
+ 
+
+ align:start position:0%
+does it make algorithmic or mathematical
+sense so this idea of doing stuff in the
+
+ align:start position:0%
+sense so this idea of doing stuff in the
+ 
+
+ align:start position:0%
+sense so this idea of doing stuff in the
+stochastic manner was actually
+
+ align:start position:0%
+stochastic manner was actually
+ 
+
+ align:start position:0%
+stochastic manner was actually
+originally proposed by Robbins in Monro
+
+ align:start position:0%
+originally proposed by Robbins in Monro
+ 
+
+ align:start position:0%
+originally proposed by Robbins in Monro
+somewhere I think around 1951 and that's
+
+ align:start position:0%
+somewhere I think around 1951 and that's
+ 
+
+ align:start position:0%
+somewhere I think around 1951 and that's
+the most advanced method that we are
+
+ align:start position:0%
+the most advanced method that we are
+ 
+
+ align:start position:0%
+the most advanced method that we are
+essentially using currently so I'll show
+
+ align:start position:0%
+essentially using currently so I'll show
+ 
+
+ align:start position:0%
+essentially using currently so I'll show
+you that this idea makes sense but maybe
+
+ align:start position:0%
+you that this idea makes sense but maybe
+ 
+
+ align:start position:0%
+you that this idea makes sense but maybe
+let's first just look at a comparison of
+
+ align:start position:0%
+let's first just look at a comparison of
+ 
+
+ align:start position:0%
+let's first just look at a comparison of
+SGD with gradient descent in this
+
+ align:start position:0%
+SGD with gradient descent in this
+ 
+
+ align:start position:0%
+SGD with gradient descent in this
+simulation so this is that MATLAB code
+
+ align:start position:0%
+simulation so this is that MATLAB code
+ 
+
+ align:start position:0%
+simulation so this is that MATLAB code
+of gradient descent and this is just a
+
+ align:start position:0%
+of gradient descent and this is just a
+ 
+
+ align:start position:0%
+of gradient descent and this is just a
+simulation of gradient descent as you
+
+ align:start position:0%
+simulation of gradient descent as you
+ 
+
+ align:start position:0%
+simulation of gradient descent as you
+pick a different step size that gamma in
+
+ align:start position:0%
+pick a different step size that gamma in
+ 
+
+ align:start position:0%
+pick a different step size that gamma in
+there you move towards the optimum if
+
+ align:start position:0%
+there you move towards the optimum if
+ 
+
+ align:start position:0%
+there you move towards the optimum if
+the step size is small you make many
+
+ align:start position:0%
+the step size is small you make many
+ 
+
+ align:start position:0%
+the step size is small you make many
+small steps progress and you reach there
+
+ align:start position:0%
+small steps progress and you reach there
+ 
+
+ align:start position:0%
+small steps progress and you reach there
+that's for a well-conditioned problem in
+
+ align:start position:0%
+that's for a well-conditioned problem in
+ 
+
+ align:start position:0%
+that's for a well-conditioned problem in
+an ill-conditioned problem it takes you
+
+ align:start position:0%
+an ill-conditioned problem it takes you
+ 
+
+ align:start position:0%
+an ill-conditioned problem it takes you
+even larger in a neural network type
+
+ align:start position:0%
+even larger in a neural network type
+ 
+
+ align:start position:0%
+even larger in a neural network type
+problem which is non convex you have to
+
+ align:start position:0%
+problem which is non convex you have to
+ 
+
+ align:start position:0%
+problem which is non convex you have to
+typically work with smaller step sizes
+
+ align:start position:0%
+typically work with smaller step sizes
+ 
+
+ align:start position:0%
+typically work with smaller step sizes
+and if you take bigger ones you can get
+
+ align:start position:0%
+and if you take bigger ones you can get
+ 
+
+ align:start position:0%
+and if you take bigger ones you can get
+crazy oscillations but that's gradient
+
+ align:start position:0%
+crazy oscillations but that's gradient
+ 
+
+ align:start position:0%
+crazy oscillations but that's gradient
+descent in comparison let's hope that
+
+ align:start position:0%
+descent in comparison let's hope that
+ 
+
+ align:start position:0%
+descent in comparison let's hope that
+this loads correctly well there's even a
+
+ align:start position:0%
+this loads correctly well there's even a
+ 
+
+ align:start position:0%
+this loads correctly well there's even a
+picture of Robbins who's a core
+
+ align:start position:0%
+picture of Robbins who's a core
+ 
+
+ align:start position:0%
+picture of Robbins who's a core
+discoverer of the stochastic gradient
+
+ align:start position:0%
+discoverer of the stochastic gradient
+ 
+
+ align:start position:0%
+discoverer of the stochastic gradient
+method there's a nice simulation that
+
+ align:start position:0%
+method there's a nice simulation that
+ 
+
+ align:start position:0%
+method there's a nice simulation that
+instead of me
+
+ align:start position:0%
+instead of me
+ 
+
+ align:start position:0%
+instead of me
+King that kind of deterministic descent
+
+ align:start position:0%
+King that kind of deterministic descent
+ 
+
+ align:start position:0%
+King that kind of deterministic descent
+after all gradient descent is called
+
+ align:start position:0%
+after all gradient descent is called
+ 
+
+ align:start position:0%
+after all gradient descent is called
+gradient descent at every step it
+
+ align:start position:0%
+gradient descent at every step it
+ 
+
+ align:start position:0%
+gradient descent at every step it
+descends it decreases the cost function
+
+ align:start position:0%
+descends it decreases the cost function
+ 
+
+ align:start position:0%
+descends it decreases the cost function
+stochastic gradient descent is actually
+
+ align:start position:0%
+stochastic gradient descent is actually
+ 
+
+ align:start position:0%
+stochastic gradient descent is actually
+a misnomer at every step it doesn't do
+
+ align:start position:0%
+a misnomer at every step it doesn't do
+ 
+
+ align:start position:0%
+a misnomer at every step it doesn't do
+any descent it does not decrease the
+
+ align:start position:0%
+any descent it does not decrease the
+ 
+
+ align:start position:0%
+any descent it does not decrease the
+cost function so you can see at every
+
+ align:start position:0%
+cost function so you can see at every
+ 
+
+ align:start position:0%
+cost function so you can see at every
+step those are the contours of the cost
+
+ align:start position:0%
+step those are the contours of the cost
+ 
+
+ align:start position:0%
+step those are the contours of the cost
+function sometimes it goes up sometimes
+
+ align:start position:0%
+function sometimes it goes up sometimes
+ 
+
+ align:start position:0%
+function sometimes it goes up sometimes
+it goes down it fluctuates around but it
+
+ align:start position:0%
+it goes down it fluctuates around but it
+ 
+
+ align:start position:0%
+it goes down it fluctuates around but it
+kind of stochastically still seems to be
+
+ align:start position:0%
+kind of stochastically still seems to be
+ 
+
+ align:start position:0%
+kind of stochastically still seems to be
+making progress towards the optimum and
+
+ align:start position:0%
+making progress towards the optimum and
+ 
+
+ align:start position:0%
+making progress towards the optimum and
+stochastic gradient descent because it's
+
+ align:start position:0%
+stochastic gradient descent because it's
+ 
+
+ align:start position:0%
+stochastic gradient descent because it's
+not using exact gradients just working
+
+ align:start position:0%
+not using exact gradients just working
+ 
+
+ align:start position:0%
+not using exact gradients just working
+with these random examples it actually
+
+ align:start position:0%
+with these random examples it actually
+ 
+
+ align:start position:0%
+with these random examples it actually
+is much more sensitive to step sizes and
+
+ align:start position:0%
+is much more sensitive to step sizes and
+ 
+
+ align:start position:0%
+is much more sensitive to step sizes and
+you can see as I increase the step size
+
+ align:start position:0%
+you can see as I increase the step size
+ 
+
+ align:start position:0%
+you can see as I increase the step size
+its behavior this is like actually full
+
+ align:start position:0%
+its behavior this is like actually full
+ 
+
+ align:start position:0%
+its behavior this is like actually full
+simulation for a toy problem so
+
+ align:start position:0%
+simulation for a toy problem so
+ 
+
+ align:start position:0%
+simulation for a toy problem so
+initially so what I want you to notice
+
+ align:start position:0%
+initially so what I want you to notice
+ 
+
+ align:start position:0%
+initially so what I want you to notice
+is let me go through this you know a few
+
+ align:start position:0%
+is let me go through this you know a few
+ 
+
+ align:start position:0%
+is let me go through this you know a few
+times keep looking at what patterns you
+
+ align:start position:0%
+times keep looking at what patterns you
+ 
+
+ align:start position:0%
+times keep looking at what patterns you
+may notice in how that line is
+
+ align:start position:0%
+may notice in how that line is
+ 
+
+ align:start position:0%
+may notice in how that line is
+fluctuating hopefully this is big enough
+
+ align:start position:0%
+fluctuating hopefully this is big enough
+ 
+
+ align:start position:0%
+fluctuating hopefully this is big enough
+for everybody to see okay so this slider
+
+ align:start position:0%
+for everybody to see okay so this slider
+ 
+
+ align:start position:0%
+for everybody to see okay so this slider
+that I'm shifting is just the step size
+
+ align:start position:0%
+that I'm shifting is just the step size
+ 
+
+ align:start position:0%
+that I'm shifting is just the step size
+so let me just remind you in case you
+
+ align:start position:0%
+so let me just remind you in case you
+ 
+
+ align:start position:0%
+so let me just remind you in case you
+forgot the iteration we are running XK
+
+ align:start position:0%
+forgot the iteration we are running XK
+ 
+
+ align:start position:0%
+forgot the iteration we are running XK
+plus 1 is XK minus some it okay okay
+
+ align:start position:0%
+plus 1 is XK minus some it okay okay
+ 
+
+ align:start position:0%
+plus 1 is XK minus some it okay okay
+it's called alpha there times some
+
+ align:start position:0%
+it's called alpha there times some
+ 
+
+ align:start position:0%
+it's called alpha there times some
+randomly chosen data point you compute
+
+ align:start position:0%
+randomly chosen data point you compute
+ 
+
+ align:start position:0%
+randomly chosen data point you compute
+its gradient this is SGD that's what we
+
+ align:start position:0%
+its gradient this is SGD that's what we
+ 
+
+ align:start position:0%
+its gradient this is SGD that's what we
+are running and we threw away tons of
+
+ align:start position:0%
+are running and we threw away tons of
+ 
+
+ align:start position:0%
+are running and we threw away tons of
+information we didn't use the full
+
+ align:start position:0%
+information we didn't use the full
+ 
+
+ align:start position:0%
+information we didn't use the full
+gradient we just using this crude crude
+
+ align:start position:0%
+gradient we just using this crude crude
+ 
+
+ align:start position:0%
+gradient we just using this crude crude
+gradient so this process is very
+
+ align:start position:0%
+gradient so this process is very
+ 
+
+ align:start position:0%
+gradient so this process is very
+sensitive to the other parameter in the
+
+ align:start position:0%
+sensitive to the other parameter in the
+ 
+
+ align:start position:0%
+sensitive to the other parameter in the
+system which is the step size much more
+
+ align:start position:0%
+system which is the step size much more
+ 
+
+ align:start position:0%
+system which is the step size much more
+sensitive than gradient descent in fact
+
+ align:start position:0%
+sensitive than gradient descent in fact
+ 
+
+ align:start position:0%
+sensitive than gradient descent in fact
+and you let's see as I vary the step
+
+ align:start position:0%
+and you let's see as I vary the step
+ 
+
+ align:start position:0%
+and you let's see as I vary the step
+size see if you can notice some parents
+
+ align:start position:0%
+size see if you can notice some parents
+ 
+
+ align:start position:0%
+size see if you can notice some parents
+on how it tries to go towards an optimum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a zoomed in version also of this
+
+ align:start position:0%
+is a zoomed in version also of this
+ 
+
+ align:start position:0%
+is a zoomed in version also of this
+later here and come to that shortly
+
+ align:start position:0%
+later here and come to that shortly
+ 
+
+ align:start position:0%
+later here and come to that shortly
+again I'll repeat again and then I'll
+
+ align:start position:0%
+again I'll repeat again and then I'll
+ 
+
+ align:start position:0%
+again I'll repeat again and then I'll
+ask you for your observations if you
+
+ align:start position:0%
+ask you for your observations if you
+ 
+
+ align:start position:0%
+ask you for your observations if you
+notice some patterns I don't know if
+
+ align:start position:0%
+notice some patterns I don't know if
+ 
+
+ align:start position:0%
+notice some patterns I don't know if
+they're necessarily apparent you know
+
+ align:start position:0%
+they're necessarily apparent you know
+ 
+
+ align:start position:0%
+they're necessarily apparent you know
+that's the thing with patterns because I
+
+ align:start position:0%
+that's the thing with patterns because I
+ 
+
+ align:start position:0%
+that's the thing with patterns because I
+know the answer so I see the pattern if
+
+ align:start position:0%
+know the answer so I see the pattern if
+ 
+
+ align:start position:0%
+know the answer so I see the pattern if
+you don't know the answer you may or may
+
+ align:start position:0%
+you don't know the answer you may or may
+ 
+
+ align:start position:0%
+you don't know the answer you may or may
+not see the pattern but I want to see if
+
+ align:start position:0%
+not see the pattern but I want to see if
+ 
+
+ align:start position:0%
+not see the pattern but I want to see if
+you actually see the pattern as I move
+
+ align:start position:0%
+you actually see the pattern as I move
+ 
+
+ align:start position:0%
+you actually see the pattern as I move
+change the step size so maybe that was
+
+ align:start position:0%
+change the step size so maybe that was
+ 
+
+ align:start position:0%
+change the step size so maybe that was
+enough simulation anybody have any
+
+ align:start position:0%
+enough simulation anybody have any
+ 
+
+ align:start position:0%
+enough simulation anybody have any
+comments on what kind of pattern you may
+
+ align:start position:0%
+comments on what kind of pattern you may
+ 
+
+ align:start position:0%
+comments on what kind of pattern you may
+have observed any other comments there's
+
+ align:start position:0%
+have observed any other comments there's
+ 
+
+ align:start position:0%
+have observed any other comments there's
+one more interesting thing happening
+
+ align:start position:0%
+one more interesting thing happening
+ 
+
+ align:start position:0%
+one more interesting thing happening
+here which is a very very typical thing
+
+ align:start position:0%
+here which is a very very typical thing
+ 
+
+ align:start position:0%
+here which is a very very typical thing
+for SGD in one of the reasons why people
+
+ align:start position:0%
+for SGD in one of the reasons why people
+ 
+
+ align:start position:0%
+for SGD in one of the reasons why people
+love SGD let me do that once again
+
+ align:start position:0%
+love SGD let me do that once again
+ 
+
+ align:start position:0%
+love SGD let me do that once again
+briefly okay this is tiny step size
+
+ align:start position:0%
+briefly okay this is tiny step size
+ 
+
+ align:start position:0%
+briefly okay this is tiny step size
+almost zero close to zero is not exactly
+
+ align:start position:0%
+almost zero close to zero is not exactly
+ 
+
+ align:start position:0%
+almost zero close to zero is not exactly
+zero so you see what happens for a very
+
+ align:start position:0%
+zero so you see what happens for a very
+ 
+
+ align:start position:0%
+zero so you see what happens for a very
+tiny step size it doesn't look that
+
+ align:start position:0%
+tiny step size it doesn't look that
+ 
+
+ align:start position:0%
+tiny step size it doesn't look that
+stochastic right but that's kind of
+
+ align:start position:0%
+stochastic right but that's kind of
+ 
+
+ align:start position:0%
+stochastic right but that's kind of
+obvious from there if a Takei is very
+
+ align:start position:0%
+obvious from there if a Takei is very
+ 
+
+ align:start position:0%
+obvious from there if a Takei is very
+tiny you'll hardly make any move so
+
+ align:start position:0%
+tiny you'll hardly make any move so
+ 
+
+ align:start position:0%
+tiny you'll hardly make any move so
+things will look very stable and in fact
+
+ align:start position:0%
+things will look very stable and in fact
+ 
+
+ align:start position:0%
+things will look very stable and in fact
+the speed at which stochastic gradient
+
+ align:start position:0%
+the speed at which stochastic gradient
+ 
+
+ align:start position:0%
+the speed at which stochastic gradient
+converges that's why extremely sensitive
+
+ align:start position:0%
+converges that's why extremely sensitive
+ 
+
+ align:start position:0%
+converges that's why extremely sensitive
+to how you pick the step size it's still
+
+ align:start position:0%
+to how you pick the step size it's still
+ 
+
+ align:start position:0%
+to how you pick the step size it's still
+an open research problem to come up with
+
+ align:start position:0%
+an open research problem to come up with
+ 
+
+ align:start position:0%
+an open research problem to come up with
+the best way to pick step sizes okay so
+
+ align:start position:0%
+the best way to pick step sizes okay so
+ 
+
+ align:start position:0%
+the best way to pick step sizes okay so
+it's even though it's simple it doesn't
+
+ align:start position:0%
+it's even though it's simple it doesn't
+ 
+
+ align:start position:0%
+it's even though it's simple it doesn't
+mean it's trivial and as I vary the step
+
+ align:start position:0%
+mean it's trivial and as I vary the step
+ 
+
+ align:start position:0%
+mean it's trivial and as I vary the step
+size okay to make some progress and it
+
+ align:start position:0%
+size okay to make some progress and it
+ 
+
+ align:start position:0%
+size okay to make some progress and it
+goes towards the solution are you know
+
+ align:start position:0%
+goes towards the solution are you know
+ 
+
+ align:start position:0%
+goes towards the solution are you know
+beginning to say that it seems to be
+
+ align:start position:0%
+beginning to say that it seems to be
+ 
+
+ align:start position:0%
+beginning to say that it seems to be
+making a more stable progress in the
+
+ align:start position:0%
+making a more stable progress in the
+ 
+
+ align:start position:0%
+making a more stable progress in the
+beginning and when it comes close to the
+
+ align:start position:0%
+beginning and when it comes close to the
+ 
+
+ align:start position:0%
+beginning and when it comes close to the
+solution it's fluctuating more and the
+
+ align:start position:0%
+solution it's fluctuating more and the
+ 
+
+ align:start position:0%
+solution it's fluctuating more and the
+bigger the step size the amount of
+
+ align:start position:0%
+bigger the step size the amount of
+ 
+
+ align:start position:0%
+bigger the step size the amount of
+fluctuation near the solution is Wilder
+
+ align:start position:0%
+fluctuation near the solution is Wilder
+ 
+
+ align:start position:0%
+fluctuation near the solution is Wilder
+as he noticed back there but one
+
+ align:start position:0%
+as he noticed back there but one
+ 
+
+ align:start position:0%
+as he noticed back there but one
+very interesting thing is more or less
+
+ align:start position:0%
+very interesting thing is more or less
+ 
+
+ align:start position:0%
+very interesting thing is more or less
+constant there is more fluctuation also
+
+ align:start position:0%
+constant there is more fluctuation also
+ 
+
+ align:start position:0%
+constant there is more fluctuation also
+on the outside but you see that the
+
+ align:start position:0%
+on the outside but you see that the
+ 
+
+ align:start position:0%
+on the outside but you see that the
+initial part still seems to be making
+
+ align:start position:0%
+initial part still seems to be making
+ 
+
+ align:start position:0%
+initial part still seems to be making
+pretty good progress and as you come
+
+ align:start position:0%
+pretty good progress and as you come
+ 
+
+ align:start position:0%
+pretty good progress and as you come
+close to the solution it fluctuates more
+
+ align:start position:0%
+close to the solution it fluctuates more
+ 
+
+ align:start position:0%
+close to the solution it fluctuates more
+and that is a very principally typical
+
+ align:start position:0%
+and that is a very principally typical
+ 
+
+ align:start position:0%
+and that is a very principally typical
+behavior of stochastic gradient descent
+
+ align:start position:0%
+behavior of stochastic gradient descent
+ 
+
+ align:start position:0%
+behavior of stochastic gradient descent
+that in the beginning it makes rapid
+
+ align:start position:0%
+that in the beginning it makes rapid
+ 
+
+ align:start position:0%
+that in the beginning it makes rapid
+strides so you may see your training
+
+ align:start position:0%
+strides so you may see your training
+ 
+
+ align:start position:0%
+strides so you may see your training
+loss decrease whoops super fast and then
+
+ align:start position:0%
+loss decrease whoops super fast and then
+ 
+
+ align:start position:0%
+loss decrease whoops super fast and then
+kind of you know peter out and it's this
+
+ align:start position:0%
+kind of you know peter out and it's this
+ 
+
+ align:start position:0%
+kind of you know peter out and it's this
+particular behavior which got people
+
+ align:start position:0%
+particular behavior which got people
+ 
+
+ align:start position:0%
+particular behavior which got people
+super excited that hey in machine
+
+ align:start position:0%
+super excited that hey in machine
+ 
+
+ align:start position:0%
+super excited that hey in machine
+learning we are working with all sorts
+
+ align:start position:0%
+learning we are working with all sorts
+ 
+
+ align:start position:0%
+learning we are working with all sorts
+of big data I just want a quick and
+
+ align:start position:0%
+of big data I just want a quick and
+ 
+
+ align:start position:0%
+of big data I just want a quick and
+dirty progress on my training training I
+
+ align:start position:0%
+dirty progress on my training training I
+ 
+
+ align:start position:0%
+dirty progress on my training training I
+don't care about getting to the best
+
+ align:start position:0%
+don't care about getting to the best
+ 
+
+ align:start position:0%
+don't care about getting to the best
+optimum because in machine learning you
+
+ align:start position:0%
+optimum because in machine learning you
+ 
+
+ align:start position:0%
+optimum because in machine learning you
+don't just care about solving the
+
+ align:start position:0%
+don't just care about solving the
+ 
+
+ align:start position:0%
+don't just care about solving the
+optimization problem you actually care
+
+ align:start position:0%
+optimization problem you actually care
+ 
+
+ align:start position:0%
+optimization problem you actually care
+about finding solutions that work well
+
+ align:start position:0%
+about finding solutions that work well
+ 
+
+ align:start position:0%
+about finding solutions that work well
+on unseen data so that means you don't
+
+ align:start position:0%
+on unseen data so that means you don't
+ 
+
+ align:start position:0%
+on unseen data so that means you don't
+want to over fit and solve the
+
+ align:start position:0%
+want to over fit and solve the
+ 
+
+ align:start position:0%
+want to over fit and solve the
+optimization problem supremely well so
+
+ align:start position:0%
+optimization problem supremely well so
+ 
+
+ align:start position:0%
+optimization problem supremely well so
+it's great to make rapid initial
+
+ align:start position:0%
+it's great to make rapid initial
+ 
+
+ align:start position:0%
+it's great to make rapid initial
+progress and if after that progress
+
+ align:start position:0%
+progress and if after that progress
+ 
+
+ align:start position:0%
+progress and if after that progress
+Peters out it's okay
+
+ align:start position:0%
+Peters out it's okay
+ 
+
+ align:start position:0%
+Peters out it's okay
+this intuitionistic statements that are
+
+ align:start position:0%
+this intuitionistic statements that are
+ 
+
+ align:start position:0%
+this intuitionistic statements that are
+making in some nice cases like convex
+
+ align:start position:0%
+making in some nice cases like convex
+ 
+
+ align:start position:0%
+making in some nice cases like convex
+optimization problems one can
+
+ align:start position:0%
+optimization problems one can
+ 
+
+ align:start position:0%
+optimization problems one can
+mathematically fully quantify this one
+
+ align:start position:0%
+mathematically fully quantify this one
+ 
+
+ align:start position:0%
+mathematically fully quantify this one
+can prove theorems to quantify its thing
+
+ align:start position:0%
+can prove theorems to quantify its thing
+ 
+
+ align:start position:0%
+can prove theorems to quantify its thing
+that I said in terms of how close how
+
+ align:start position:0%
+that I said in terms of how close how
+ 
+
+ align:start position:0%
+that I said in terms of how close how
+fast and so on we'll see a little bit of
+
+ align:start position:0%
+fast and so on we'll see a little bit of
+ 
+
+ align:start position:0%
+fast and so on we'll see a little bit of
+that and this is what really happens to
+
+ align:start position:0%
+that and this is what really happens to
+ 
+
+ align:start position:0%
+that and this is what really happens to
+SGD you know it makes great initial
+
+ align:start position:0%
+SGD you know it makes great initial
+ 
+
+ align:start position:0%
+SGD you know it makes great initial
+progress and regardless of how you use
+
+ align:start position:0%
+progress and regardless of how you use
+ 
+
+ align:start position:0%
+progress and regardless of how you use
+step sizes close to the optimum it can
+
+ align:start position:0%
+step sizes close to the optimum it can
+ 
+
+ align:start position:0%
+step sizes close to the optimum it can
+either get stuck or enter some kind of
+
+ align:start position:0%
+either get stuck or enter some kind of
+ 
+
+ align:start position:0%
+either get stuck or enter some kind of
+chaos dynamics or just behave like crazy
+
+ align:start position:0%
+chaos dynamics or just behave like crazy
+ 
+
+ align:start position:0%
+chaos dynamics or just behave like crazy
+so that's typical of SGD and let's look
+
+ align:start position:0%
+so that's typical of SGD and let's look
+ 
+
+ align:start position:0%
+so that's typical of SGD and let's look
+at no slight mathematical insight into
+
+ align:start position:0%
+at no slight mathematical insight into
+ 
+
+ align:start position:0%
+at no slight mathematical insight into
+roughly why this behavior may happen
+
+ align:start position:0%
+roughly why this behavior may happen
+ 
+
+ align:start position:0%
+roughly why this behavior may happen
+this is a trivial 1 dimensional
+
+ align:start position:0%
+this is a trivial 1 dimensional
+ 
+
+ align:start position:0%
+this is a trivial 1 dimensional
+optimization problem but it conveys the
+
+ align:start position:0%
+optimization problem but it conveys the
+ 
+
+ align:start position:0%
+optimization problem but it conveys the
+crux of why this behavior is displayed
+
+ align:start position:0%
+crux of why this behavior is displayed
+ 
+
+ align:start position:0%
+crux of why this behavior is displayed
+by stochastic gradient methods that it
+
+ align:start position:0%
+by stochastic gradient methods that it
+ 
+
+ align:start position:0%
+by stochastic gradient methods that it
+works really well in the beginning
+
+ align:start position:0%
+works really well in the beginning
+ 
+
+ align:start position:0%
+works really well in the beginning
+then it can God knows what happens when
+
+ align:start position:0%
+then it can God knows what happens when
+ 
+
+ align:start position:0%
+then it can God knows what happens when
+it comes close to the optimum anything
+
+ align:start position:0%
+it comes close to the optimum anything
+ 
+
+ align:start position:0%
+it comes close to the optimum anything
+can happen so let's look at that okay so
+
+ align:start position:0%
+can happen so let's look at that okay so
+ 
+
+ align:start position:0%
+can happen so let's look at that okay so
+let's look at a simple one dimensional
+
+ align:start position:0%
+let's look at a simple one dimensional
+ 
+
+ align:start position:0%
+let's look at a simple one dimensional
+optimization problem I'll kind of draw
+
+ align:start position:0%
+optimization problem I'll kind of draw
+ 
+
+ align:start position:0%
+optimization problem I'll kind of draw
+it out maybe on the other side so that
+
+ align:start position:0%
+it out maybe on the other side so that
+ 
+
+ align:start position:0%
+it out maybe on the other side so that
+people on this side are not
+
+ align:start position:0%
+people on this side are not
+ 
+
+ align:start position:0%
+people on this side are not
+disadvantaged so I'll just draw out a
+
+ align:start position:0%
+disadvantaged so I'll just draw out a
+ 
+
+ align:start position:0%
+disadvantaged so I'll just draw out a
+least squares problem X is one
+
+ align:start position:0%
+least squares problem X is one
+ 
+
+ align:start position:0%
+least squares problem X is one
+dimensional previously I had AI
+
+ align:start position:0%
+dimensional previously I had AI
+ 
+
+ align:start position:0%
+dimensional previously I had AI
+transpose X now AI is also a scalar so
+
+ align:start position:0%
+transpose X now AI is also a scalar so
+ 
+
+ align:start position:0%
+transpose X now AI is also a scalar so
+it's just 1d stuff everything is 1d so
+
+ align:start position:0%
+it's just 1d stuff everything is 1d so
+ 
+
+ align:start position:0%
+it's just 1d stuff everything is 1d so
+this is our set up think of AI into X
+
+ align:start position:0%
+this is our set up think of AI into X
+ 
+
+ align:start position:0%
+this is our set up think of AI into X
+minus bi these are quadratic functions
+
+ align:start position:0%
+minus bi these are quadratic functions
+ 
+
+ align:start position:0%
+minus bi these are quadratic functions
+right so they look like this
+
+ align:start position:0%
+right so they look like this
+ 
+
+ align:start position:0%
+right so they look like this
+corresponding to different eyes there's
+
+ align:start position:0%
+corresponding to different eyes there's
+ 
+
+ align:start position:0%
+corresponding to different eyes there's
+like some different functions sitting
+
+ align:start position:0%
+like some different functions sitting
+ 
+
+ align:start position:0%
+like some different functions sitting
+and so on so these are my n different
+
+ align:start position:0%
+and so on so these are my n different
+ 
+
+ align:start position:0%
+and so on so these are my n different
+loss functions and I want to minimize
+
+ align:start position:0%
+loss functions and I want to minimize
+ 
+
+ align:start position:0%
+loss functions and I want to minimize
+those we know we can actually explicitly
+
+ align:start position:0%
+those we know we can actually explicitly
+ 
+
+ align:start position:0%
+those we know we can actually explicitly
+compute the solution of that problem
+
+ align:start position:0%
+compute the solution of that problem
+ 
+
+ align:start position:0%
+compute the solution of that problem
+right you set so you set the derivative
+
+ align:start position:0%
+right you set so you set the derivative
+ 
+
+ align:start position:0%
+right you set so you set the derivative
+of f of X to 0 so you set the gradient
+
+ align:start position:0%
+of f of X to 0 so you set the gradient
+ 
+
+ align:start position:0%
+of f of X to 0 so you set the gradient
+of f of X to 0 hopefully that's easy for
+
+ align:start position:0%
+of f of X to 0 hopefully that's easy for
+ 
+
+ align:start position:0%
+of f of X to 0 hopefully that's easy for
+you to do so if you do that
+
+ align:start position:0%
+you to do so if you do that
+ 
+
+ align:start position:0%
+you to do so if you do that
+differentiation will get gradient of f
+
+ align:start position:0%
+differentiation will get gradient of f
+ 
+
+ align:start position:0%
+differentiation will get gradient of f
+of X will be just given by well you can
+
+ align:start position:0%
+of X will be just given by well you can
+ 
+
+ align:start position:0%
+of X will be just given by well you can
+do that in your head I'll just write it
+
+ align:start position:0%
+do that in your head I'll just write it
+ 
+
+ align:start position:0%
+do that in your head I'll just write it
+out explicitly AI X minus bi times AI is
+
+ align:start position:0%
+out explicitly AI X minus bi times AI is
+ 
+
+ align:start position:0%
+out explicitly AI X minus bi times AI is
+equal to 0 and you solve that for X you
+
+ align:start position:0%
+equal to 0 and you solve that for X you
+ 
+
+ align:start position:0%
+equal to 0 and you solve that for X you
+get X star the optimum of this least
+
+ align:start position:0%
+get X star the optimum of this least
+ 
+
+ align:start position:0%
+get X star the optimum of this least
+squares problem right so we actually
+
+ align:start position:0%
+squares problem right so we actually
+ 
+
+ align:start position:0%
+squares problem right so we actually
+know how to solve it pretty easily it's
+
+ align:start position:0%
+know how to solve it pretty easily it's
+ 
+
+ align:start position:0%
+know how to solve it pretty easily it's
+a really cool example actually I got
+
+ align:start position:0%
+a really cool example actually I got
+ 
+
+ align:start position:0%
+a really cool example actually I got
+that from textbook by Professor Dimitri
+
+ align:start position:0%
+that from textbook by Professor Dimitri
+ 
+
+ align:start position:0%
+that from textbook by Professor Dimitri
+butts acres now a very interesting thing
+
+ align:start position:0%
+butts acres now a very interesting thing
+ 
+
+ align:start position:0%
+butts acres now a very interesting thing
+we are not going to use the full
+
+ align:start position:0%
+we are not going to use the full
+ 
+
+ align:start position:0%
+we are not going to use the full
+gradient we are only you going to use
+
+ align:start position:0%
+gradient we are only you going to use
+ 
+
+ align:start position:0%
+gradient we are only you going to use
+the gradients of individual components
+
+ align:start position:0%
+the gradients of individual components
+ 
+
+ align:start position:0%
+the gradients of individual components
+right so what does the minimum of an
+
+ align:start position:0%
+right so what does the minimum of an
+ 
+
+ align:start position:0%
+right so what does the minimum of an
+individual component look like well the
+
+ align:start position:0%
+individual component look like well the
+ 
+
+ align:start position:0%
+individual component look like well the
+minimum of an individual component is
+
+ align:start position:0%
+minimum of an individual component is
+ 
+
+ align:start position:0%
+minimum of an individual component is
+attained when we can set this thing to
+
+ align:start position:0%
+attained when we can set this thing to
+ 
+
+ align:start position:0%
+attained when we can set this thing to
+zero and that thing becomes zero if you
+
+ align:start position:0%
+zero and that thing becomes zero if you
+ 
+
+ align:start position:0%
+zero and that thing becomes zero if you
+just pick X equal to B I divided by AI
+
+ align:start position:0%
+just pick X equal to B I divided by AI
+ 
+
+ align:start position:0%
+just pick X equal to B I divided by AI
+right so a single component we can be
+
+ align:start position:0%
+right so a single component we can be
+ 
+
+ align:start position:0%
+right so a single component we can be
+minimized by that choice so you can do a
+
+ align:start position:0%
+minimized by that choice so you can do a
+ 
+
+ align:start position:0%
+minimized by that choice so you can do a
+little bit of arithmetic mean geometric
+
+ align:start position:0%
+little bit of arithmetic mean geometric
+ 
+
+ align:start position:0%
+little bit of arithmetic mean geometric
+mean type inequalities to draw this
+
+ align:start position:0%
+mean type inequalities to draw this
+ 
+
+ align:start position:0%
+mean type inequalities to draw this
+picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so overall I from 1 through n this is
+
+ align:start position:0%
+so overall I from 1 through n this is
+ 
+
+ align:start position:0%
+so overall I from 1 through n this is
+the minimum value of this ratio AI bi bi
+
+ align:start position:0%
+the minimum value of this ratio AI bi bi
+ 
+
+ align:start position:0%
+the minimum value of this ratio AI bi bi
+and let's say this is the max value of
+
+ align:start position:0%
+and let's say this is the max value of
+ 
+
+ align:start position:0%
+and let's say this is the max value of
+AI bi bi and we know that closed-form
+
+ align:start position:0%
+AI bi bi and we know that closed-form
+ 
+
+ align:start position:0%
+AI bi bi and we know that closed-form
+solution that is the true solution so
+
+ align:start position:0%
+solution that is the true solution so
+ 
+
+ align:start position:0%
+solution that is the true solution so
+you can verify with some algebra that
+
+ align:start position:0%
+you can verify with some algebra that
+ 
+
+ align:start position:0%
+you can verify with some algebra that
+that solution will lie in this interval
+
+ align:start position:0%
+that solution will lie in this interval
+ 
+
+ align:start position:0%
+that solution will lie in this interval
+so let's so you you may want to this is
+
+ align:start position:0%
+so let's so you you may want to this is
+ 
+
+ align:start position:0%
+so let's so you you may want to this is
+a tiny exercise for you hopefully some
+
+ align:start position:0%
+a tiny exercise for you hopefully some
+ 
+
+ align:start position:0%
+a tiny exercise for you hopefully some
+of you love inequalities like me so this
+
+ align:start position:0%
+of you love inequalities like me so this
+ 
+
+ align:start position:0%
+of you love inequalities like me so this
+is hopefully not such a bad exercise but
+
+ align:start position:0%
+is hopefully not such a bad exercise but
+ 
+
+ align:start position:0%
+is hopefully not such a bad exercise but
+you can verify that within this range of
+
+ align:start position:0%
+you can verify that within this range of
+ 
+
+ align:start position:0%
+you can verify that within this range of
+the individual mins and max is where the
+
+ align:start position:0%
+the individual mins and max is where the
+ 
+
+ align:start position:0%
+the individual mins and max is where the
+combined solution lies so of course
+
+ align:start position:0%
+combined solution lies so of course
+ 
+
+ align:start position:0%
+combined solution lies so of course
+intuitively you would have physics style
+
+ align:start position:0%
+intuitively you would have physics style
+ 
+
+ align:start position:0%
+intuitively you would have physics style
+thinking you would have guessed that
+
+ align:start position:0%
+thinking you would have guessed that
+ 
+
+ align:start position:0%
+thinking you would have guessed that
+right away so it means when you are
+
+ align:start position:0%
+right away so it means when you are
+ 
+
+ align:start position:0%
+right away so it means when you are
+outside where the individual solutions
+
+ align:start position:0%
+outside where the individual solutions
+ 
+
+ align:start position:0%
+outside where the individual solutions
+let's call this the far out zone and
+
+ align:start position:0%
+let's call this the far out zone and
+ 
+
+ align:start position:0%
+let's call this the far out zone and
+also this side is the far out zone and
+
+ align:start position:0%
+also this side is the far out zone and
+ 
+
+ align:start position:0%
+also this side is the far out zone and
+this region within which the true
+
+ align:start position:0%
+this region within which the true
+ 
+
+ align:start position:0%
+this region within which the true
+minimum can lie you can say okay that's
+
+ align:start position:0%
+minimum can lie you can say okay that's
+ 
+
+ align:start position:0%
+minimum can lie you can say okay that's
+the region of confusion why I'm calling
+
+ align:start position:0%
+the region of confusion why I'm calling
+ 
+
+ align:start position:0%
+the region of confusion why I'm calling
+it the region of confusion because there
+
+ align:start position:0%
+it the region of confusion because there
+ 
+
+ align:start position:0%
+it the region of confusion because there
+by minimizing an individual fi you're
+
+ align:start position:0%
+by minimizing an individual fi you're
+ 
+
+ align:start position:0%
+by minimizing an individual fi you're
+not going to be able to tell what is the
+
+ align:start position:0%
+not going to be able to tell what is the
+ 
+
+ align:start position:0%
+not going to be able to tell what is the
+combined X star that's all and a very
+
+ align:start position:0%
+combined X star that's all and a very
+ 
+
+ align:start position:0%
+combined X star that's all and a very
+interesting thing happens now just to
+
+ align:start position:0%
+interesting thing happens now just to
+ 
+
+ align:start position:0%
+interesting thing happens now just to
+gain some mathematical insight into that
+
+ align:start position:0%
+gain some mathematical insight into that
+ 
+
+ align:start position:0%
+gain some mathematical insight into that
+simulation that I showed you that if you
+
+ align:start position:0%
+simulation that I showed you that if you
+ 
+
+ align:start position:0%
+simulation that I showed you that if you
+have a scalar X that is outside this
+
+ align:start position:0%
+have a scalar X that is outside this
+ 
+
+ align:start position:0%
+have a scalar X that is outside this
+region of confusion which states that if
+
+ align:start position:0%
+region of confusion which states that if
+ 
+
+ align:start position:0%
+region of confusion which states that if
+you are far from the region within which
+
+ align:start position:0%
+you are far from the region within which
+ 
+
+ align:start position:0%
+you are far from the region within which
+an optimum can lie so you're far away
+
+ align:start position:0%
+an optimum can lie so you're far away
+ 
+
+ align:start position:0%
+an optimum can lie so you're far away
+you've just started out your progress
+
+ align:start position:0%
+you've just started out your progress
+ 
+
+ align:start position:0%
+you've just started out your progress
+you made a random initialization most
+
+ align:start position:0%
+you made a random initialization most
+ 
+
+ align:start position:0%
+you made a random initialization most
+likely a far away from where the
+
+ align:start position:0%
+likely a far away from where the
+ 
+
+ align:start position:0%
+likely a far away from where the
+solution is so suppose that's where you
+
+ align:start position:0%
+solution is so suppose that's where you
+ 
+
+ align:start position:0%
+solution is so suppose that's where you
+are what happens when you're in that far
+
+ align:start position:0%
+are what happens when you're in that far
+ 
+
+ align:start position:0%
+are what happens when you're in that far
+out region so if you're in that far out
+
+ align:start position:0%
+out region so if you're in that far out
+ 
+
+ align:start position:0%
+out region so if you're in that far out
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+you use a stochastic gradient of some
+
+ align:start position:0%
+you use a stochastic gradient of some
+ 
+
+ align:start position:0%
+you use a stochastic gradient of some
+eyuth component so the full gradient
+
+ align:start position:0%
+eyuth component so the full gradient
+ 
+
+ align:start position:0%
+eyuth component so the full gradient
+will look like that a stochastic
+
+ align:start position:0%
+will look like that a stochastic
+ 
+
+ align:start position:0%
+will look like that a stochastic
+gradient looks like this one component
+
+ align:start position:0%
+gradient looks like this one component
+ 
+
+ align:start position:0%
+gradient looks like this one component
+and when you are far out outside that
+
+ align:start position:0%
+and when you are far out outside that
+ 
+
+ align:start position:0%
+and when you are far out outside that
+min and Max regime then you can check by
+
+ align:start position:0%
+min and Max regime then you can check by
+ 
+
+ align:start position:0%
+min and Max regime then you can check by
+just by just looking at it that a
+
+ align:start position:0%
+just by just looking at it that a
+ 
+
+ align:start position:0%
+just by just looking at it that a
+stochastic gradient in the far away
+
+ align:start position:0%
+stochastic gradient in the far away
+ 
+
+ align:start position:0%
+stochastic gradient in the far away
+regime has exactly the same sign as the
+
+ align:start position:0%
+regime has exactly the same sign as the
+ 
+
+ align:start position:0%
+regime has exactly the same sign as the
+full gradient
+
+ align:start position:0%
+full gradient
+ 
+
+ align:start position:0%
+full gradient
+what does gradient descent do it says
+
+ align:start position:0%
+what does gradient descent do it says
+ 
+
+ align:start position:0%
+what does gradient descent do it says
+well walk in the direction of the
+
+ align:start position:0%
+well walk in the direction of the
+ 
+
+ align:start position:0%
+well walk in the direction of the
+negative gradient and if far away from
+
+ align:start position:0%
+negative gradient and if far away from
+ 
+
+ align:start position:0%
+negative gradient and if far away from
+the optimum outside the region of
+
+ align:start position:0%
+the optimum outside the region of
+ 
+
+ align:start position:0%
+the optimum outside the region of
+confusion your stochastic gradient has
+
+ align:start position:0%
+confusion your stochastic gradient has
+ 
+
+ align:start position:0%
+confusion your stochastic gradient has
+the same sign as the true gradient may
+
+ align:start position:0%
+the same sign as the true gradient may
+ 
+
+ align:start position:0%
+the same sign as the true gradient may
+be in more linear algebra terms it makes
+
+ align:start position:0%
+be in more linear algebra terms it makes
+ 
+
+ align:start position:0%
+be in more linear algebra terms it makes
+you know it makes an acute angle with
+
+ align:start position:0%
+you know it makes an acute angle with
+ 
+
+ align:start position:0%
+you know it makes an acute angle with
+your gradient that means if even though
+
+ align:start position:0%
+your gradient that means if even though
+ 
+
+ align:start position:0%
+your gradient that means if even though
+a stochastic gradient is not exactly the
+
+ align:start position:0%
+a stochastic gradient is not exactly the
+ 
+
+ align:start position:0%
+a stochastic gradient is not exactly the
+full gradient it has some component in
+
+ align:start position:0%
+full gradient it has some component in
+ 
+
+ align:start position:0%
+full gradient it has some component in
+the direction of the true gradient this
+
+ align:start position:0%
+the direction of the true gradient this
+ 
+
+ align:start position:0%
+the direction of the true gradient this
+is 1d here it is exactly the same sign
+
+ align:start position:0%
+is 1d here it is exactly the same sign
+ 
+
+ align:start position:0%
+is 1d here it is exactly the same sign
+in multiple dimensions this is the idea
+
+ align:start position:0%
+in multiple dimensions this is the idea
+ 
+
+ align:start position:0%
+in multiple dimensions this is the idea
+that it will have some component in the
+
+ align:start position:0%
+that it will have some component in the
+ 
+
+ align:start position:0%
+that it will have some component in the
+direction of the true gradient when
+
+ align:start position:0%
+direction of the true gradient when
+ 
+
+ align:start position:0%
+direction of the true gradient when
+you're far away which means if you then
+
+ align:start position:0%
+you're far away which means if you then
+ 
+
+ align:start position:0%
+you're far away which means if you then
+use that direction to make an update in
+
+ align:start position:0%
+use that direction to make an update in
+ 
+
+ align:start position:0%
+use that direction to make an update in
+that style you will end up making solid
+
+ align:start position:0%
+that style you will end up making solid
+ 
+
+ align:start position:0%
+that style you will end up making solid
+progress and the beauty is in the time
+
+ align:start position:0%
+progress and the beauty is in the time
+ 
+
+ align:start position:0%
+progress and the beauty is in the time
+it would have taken you to do one single
+
+ align:start position:0%
+it would have taken you to do one single
+ 
+
+ align:start position:0%
+it would have taken you to do one single
+iteration of batch gradient descent far
+
+ align:start position:0%
+iteration of batch gradient descent far
+ 
+
+ align:start position:0%
+iteration of batch gradient descent far
+away you can do million stochastic steps
+
+ align:start position:0%
+away you can do million stochastic steps
+ 
+
+ align:start position:0%
+away you can do million stochastic steps
+and each step will make some progress
+
+ align:start position:0%
+and each step will make some progress
+ 
+
+ align:start position:0%
+and each step will make some progress
+and that's why you we see this dramatic
+
+ align:start position:0%
+and that's why you we see this dramatic
+ 
+
+ align:start position:0%
+and that's why you we see this dramatic
+initial again this is in the 1d case
+
+ align:start position:0%
+initial again this is in the 1d case
+ 
+
+ align:start position:0%
+initial again this is in the 1d case
+this is explicit mathematically in the
+
+ align:start position:0%
+this is explicit mathematically in the
+ 
+
+ align:start position:0%
+this is explicit mathematically in the
+high D case this is more intuitive ok
+
+ align:start position:0%
+high D case this is more intuitive ok
+ 
+
+ align:start position:0%
+high D case this is more intuitive ok
+without further assumptions about angles
+
+ align:start position:0%
+without further assumptions about angles
+ 
+
+ align:start position:0%
+without further assumptions about angles
+etc one can't make such a broad claim
+
+ align:start position:0%
+etc one can't make such a broad claim
+ 
+
+ align:start position:0%
+etc one can't make such a broad claim
+but intuitively this is what's happening
+
+ align:start position:0%
+but intuitively this is what's happening
+ 
+
+ align:start position:0%
+but intuitively this is what's happening
+on why you see this awesome initial
+
+ align:start position:0%
+on why you see this awesome initial
+ 
+
+ align:start position:0%
+on why you see this awesome initial
+speed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and once you inside the region of
+
+ align:start position:0%
+and once you inside the region of
+ 
+
+ align:start position:0%
+and once you inside the region of
+confusion then this behavior breaks down
+
+ align:start position:0%
+confusion then this behavior breaks down
+ 
+
+ align:start position:0%
+confusion then this behavior breaks down
+some stochastic gradient we have the
+
+ align:start position:0%
+some stochastic gradient we have the
+ 
+
+ align:start position:0%
+some stochastic gradient we have the
+same sign as the full gradient some may
+
+ align:start position:0%
+same sign as the full gradient some may
+ 
+
+ align:start position:0%
+same sign as the full gradient some may
+not and that's why you can get at crazy
+
+ align:start position:0%
+not and that's why you can get at crazy
+ 
+
+ align:start position:0%
+not and that's why you can get at crazy
+fluctuations so this simple 1d example
+
+ align:start position:0%
+fluctuations so this simple 1d example
+ 
+
+ align:start position:0%
+fluctuations so this simple 1d example
+kind of exactly shows you what we saw in
+
+ align:start position:0%
+kind of exactly shows you what we saw in
+ 
+
+ align:start position:0%
+kind of exactly shows you what we saw in
+that picture and people really loved
+
+ align:start position:0%
+that picture and people really loved
+ 
+
+ align:start position:0%
+that picture and people really loved
+this initial progress because often we
+
+ align:start position:0%
+this initial progress because often we
+ 
+
+ align:start position:0%
+this initial progress because often we
+also do early stopping you know train
+
+ align:start position:0%
+also do early stopping you know train
+ 
+
+ align:start position:0%
+also do early stopping you know train
+for some time and then you say ok I'm
+
+ align:start position:0%
+for some time and then you say ok I'm
+ 
+
+ align:start position:0%
+for some time and then you say ok I'm
+done so importantly if you are purely an
+
+ align:start position:0%
+done so importantly if you are purely an
+ 
+
+ align:start position:0%
+done so importantly if you are purely an
+optimization person not thinking so much
+
+ align:start position:0%
+optimization person not thinking so much
+ 
+
+ align:start position:0%
+optimization person not thinking so much
+in terms of machine learning when please
+
+ align:start position:0%
+in terms of machine learning when please
+ 
+
+ align:start position:0%
+in terms of machine learning when please
+keep in mind that stochastic gradient
+
+ align:start position:0%
+keep in mind that stochastic gradient
+ 
+
+ align:start position:0%
+keep in mind that stochastic gradient
+descent or stochastic gradient method is
+
+ align:start position:0%
+descent or stochastic gradient method is
+ 
+
+ align:start position:0%
+descent or stochastic gradient method is
+not such a great optimization method
+
+ align:start position:0%
+not such a great optimization method
+ 
+
+ align:start position:0%
+not such a great optimization method
+because once in the region of confusion
+
+ align:start position:0%
+because once in the region of confusion
+ 
+
+ align:start position:0%
+because once in the region of confusion
+it can just fluctuate all over forever
+
+ align:start position:0%
+it can just fluctuate all over forever
+ 
+
+ align:start position:0%
+it can just fluctuate all over forever
+and in machine learning you say oh the
+
+ align:start position:0%
+and in machine learning you say oh the
+ 
+
+ align:start position:0%
+and in machine learning you say oh the
+region of confusion that's fine it'll
+
+ align:start position:0%
+region of confusion that's fine it'll
+ 
+
+ align:start position:0%
+region of confusion that's fine it'll
+make my method robust gonna make my
+
+ align:start position:0%
+make my method robust gonna make my
+ 
+
+ align:start position:0%
+make my method robust gonna make my
+neural network training more robust will
+
+ align:start position:0%
+neural network training more robust will
+ 
+
+ align:start position:0%
+neural network training more robust will
+generalize better etcetera etcetera we
+
+ align:start position:0%
+generalize better etcetera etcetera we
+ 
+
+ align:start position:0%
+generalize better etcetera etcetera we
+like that so it depends on which frame
+
+ align:start position:0%
+like that so it depends on which frame
+ 
+
+ align:start position:0%
+like that so it depends on which frame
+of mind you are in ok so that's that's
+
+ align:start position:0%
+of mind you are in ok so that's that's
+ 
+
+ align:start position:0%
+of mind you are in ok so that's that's
+the awesome thing about the stochastic
+
+ align:start position:0%
+the awesome thing about the stochastic
+ 
+
+ align:start position:0%
+the awesome thing about the stochastic
+gradient method so I'll give you now the
+
+ align:start position:0%
+gradient method so I'll give you now the
+ 
+
+ align:start position:0%
+gradient method so I'll give you now the
+key mathematical ideas behind the
+
+ align:start position:0%
+key mathematical ideas behind the
+ 
+
+ align:start position:0%
+key mathematical ideas behind the
+success of SGD this was like little
+
+ align:start position:0%
+success of SGD this was like little
+ 
+
+ align:start position:0%
+success of SGD this was like little
+illustration very abstractly this is an
+
+ align:start position:0%
+illustration very abstractly this is an
+ 
+
+ align:start position:0%
+illustration very abstractly this is an
+idea that records throughout machine
+
+ align:start position:0%
+idea that records throughout machine
+ 
+
+ align:start position:0%
+idea that records throughout machine
+learning and throughout theoretical
+
+ align:start position:0%
+learning and throughout theoretical
+ 
+
+ align:start position:0%
+learning and throughout theoretical
+computer science and statistics any time
+
+ align:start position:0%
+computer science and statistics any time
+ 
+
+ align:start position:0%
+computer science and statistics any time
+you're faced with the need to compute an
+
+ align:start position:0%
+you're faced with the need to compute an
+ 
+
+ align:start position:0%
+you're faced with the need to compute an
+expensive quantity resort to
+
+ align:start position:0%
+expensive quantity resort to
+ 
+
+ align:start position:0%
+expensive quantity resort to
+randomization to speed up the
+
+ align:start position:0%
+randomization to speed up the
+ 
+
+ align:start position:0%
+randomization to speed up the
+computation SGD is one example the true
+
+ align:start position:0%
+computation SGD is one example the true
+ 
+
+ align:start position:0%
+computation SGD is one example the true
+gradient was expensive to compute so we
+
+ align:start position:0%
+gradient was expensive to compute so we
+ 
+
+ align:start position:0%
+gradient was expensive to compute so we
+create a randomized estimate of the true
+
+ align:start position:0%
+create a randomized estimate of the true
+ 
+
+ align:start position:0%
+create a randomized estimate of the true
+gradient and the randomized estimate is
+
+ align:start position:0%
+gradient and the randomized estimate is
+ 
+
+ align:start position:0%
+gradient and the randomized estimate is
+much faster to compute and
+
+ align:start position:0%
+much faster to compute and
+ 
+
+ align:start position:0%
+much faster to compute and
+mathematically what will start happening
+
+ align:start position:0%
+mathematically what will start happening
+ 
+
+ align:start position:0%
+mathematically what will start happening
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+depending on how good your randomized
+
+ align:start position:0%
+depending on how good your randomized
+ 
+
+ align:start position:0%
+depending on how good your randomized
+estimate is your method may or may not
+
+ align:start position:0%
+estimate is your method may or may not
+ 
+
+ align:start position:0%
+estimate is your method may or may not
+converge to the right answer so you of
+
+ align:start position:0%
+converge to the right answer so you of
+ 
+
+ align:start position:0%
+converge to the right answer so you of
+course one has to be careful about what
+
+ align:start position:0%
+course one has to be careful about what
+ 
+
+ align:start position:0%
+course one has to be careful about what
+particular randomized estimate one makes
+
+ align:start position:0%
+particular randomized estimate one makes
+ 
+
+ align:start position:0%
+particular randomized estimate one makes
+so but really abstractly even if I
+
+ align:start position:0%
+so but really abstractly even if I
+ 
+
+ align:start position:0%
+so but really abstractly even if I
+hadn't shown you the main idea this idea
+
+ align:start position:0%
+hadn't shown you the main idea this idea
+ 
+
+ align:start position:0%
+hadn't shown you the main idea this idea
+you can apply in many other settings if
+
+ align:start position:0%
+you can apply in many other settings if
+ 
+
+ align:start position:0%
+you can apply in many other settings if
+you have a difficult quantity come up
+
+ align:start position:0%
+you have a difficult quantity come up
+ 
+
+ align:start position:0%
+you have a difficult quantity come up
+with a randomized estimate and save on
+
+ align:start position:0%
+with a randomized estimate and save on
+ 
+
+ align:start position:0%
+with a randomized estimate and save on
+computation this is a very important
+
+ align:start position:0%
+computation this is a very important
+ 
+
+ align:start position:0%
+computation this is a very important
+theme throughout machine learning and
+
+ align:start position:0%
+theme throughout machine learning and
+ 
+
+ align:start position:0%
+theme throughout machine learning and
+data science okay and this is the key
+
+ align:start position:0%
+data science okay and this is the key
+ 
+
+ align:start position:0%
+data science okay and this is the key
+property so stochastic gradient descent
+
+ align:start position:0%
+property so stochastic gradient descent
+ 
+
+ align:start position:0%
+property so stochastic gradient descent
+it uses stochastic gradients stochastic
+
+ align:start position:0%
+it uses stochastic gradients stochastic
+ 
+
+ align:start position:0%
+it uses stochastic gradients stochastic
+is here just used very loosely you know
+
+ align:start position:0%
+is here just used very loosely you know
+ 
+
+ align:start position:0%
+is here just used very loosely you know
+it just means there's some randomization
+
+ align:start position:0%
+it just means there's some randomization
+ 
+
+ align:start position:0%
+it just means there's some randomization
+that's all it means
+
+ align:start position:0%
+that's all it means
+ 
+
+ align:start position:0%
+that's all it means
+and the property the key property that
+
+ align:start position:0%
+and the property the key property that
+ 
+
+ align:start position:0%
+and the property the key property that
+we have is in expectation the
+
+ align:start position:0%
+we have is in expectation the
+ 
+
+ align:start position:0%
+we have is in expectation the
+expectation is over
+
+ align:start position:0%
+expectation is over
+ 
+
+ align:start position:0%
+expectation is over
+whatever randomness you used so if you
+
+ align:start position:0%
+whatever randomness you used so if you
+ 
+
+ align:start position:0%
+whatever randomness you used so if you
+picked you know some random training
+
+ align:start position:0%
+picked you know some random training
+ 
+
+ align:start position:0%
+picked you know some random training
+data point out of the million then it is
+
+ align:start position:0%
+data point out of the million then it is
+ 
+
+ align:start position:0%
+data point out of the million then it is
+the expectation is over the probability
+
+ align:start position:0%
+the expectation is over the probability
+ 
+
+ align:start position:0%
+the expectation is over the probability
+distribution over what kind of
+
+ align:start position:0%
+distribution over what kind of
+ 
+
+ align:start position:0%
+distribution over what kind of
+randomness you used if you like picked
+
+ align:start position:0%
+randomness you used if you like picked
+ 
+
+ align:start position:0%
+randomness you used if you like picked
+uniformly at random from a million
+
+ align:start position:0%
+uniformly at random from a million
+ 
+
+ align:start position:0%
+uniformly at random from a million
+points then this expectation is over
+
+ align:start position:0%
+points then this expectation is over
+ 
+
+ align:start position:0%
+points then this expectation is over
+that uniform probability but the key
+
+ align:start position:0%
+that uniform probability but the key
+ 
+
+ align:start position:0%
+that uniform probability but the key
+property for SGD or at least the version
+
+ align:start position:0%
+property for SGD or at least the version
+ 
+
+ align:start position:0%
+property for SGD or at least the version
+of SGD i am talking about is that in
+
+ align:start position:0%
+of SGD i am talking about is that in
+ 
+
+ align:start position:0%
+of SGD i am talking about is that in
+expectation over that randomness the
+
+ align:start position:0%
+expectation over that randomness the
+ 
+
+ align:start position:0%
+expectation over that randomness the
+thing that you are pretending to use
+
+ align:start position:0%
+thing that you are pretending to use
+ 
+
+ align:start position:0%
+thing that you are pretending to use
+instead of the true gradient in
+
+ align:start position:0%
+instead of the true gradient in
+ 
+
+ align:start position:0%
+instead of the true gradient in
+expectation actually it is the true
+
+ align:start position:0%
+expectation actually it is the true
+ 
+
+ align:start position:0%
+expectation actually it is the true
+gradient so in statistics language this
+
+ align:start position:0%
+gradient so in statistics language this
+ 
+
+ align:start position:0%
+gradient so in statistics language this
+is called the stochastic gradient that
+
+ align:start position:0%
+is called the stochastic gradient that
+ 
+
+ align:start position:0%
+is called the stochastic gradient that
+we use is an unbiased estimate of the
+
+ align:start position:0%
+we use is an unbiased estimate of the
+ 
+
+ align:start position:0%
+we use is an unbiased estimate of the
+true gradient and this is a very
+
+ align:start position:0%
+true gradient and this is a very
+ 
+
+ align:start position:0%
+true gradient and this is a very
+important property in the mathematical
+
+ align:start position:0%
+important property in the mathematical
+ 
+
+ align:start position:0%
+important property in the mathematical
+analysis of stochastic gradient descent
+
+ align:start position:0%
+analysis of stochastic gradient descent
+ 
+
+ align:start position:0%
+analysis of stochastic gradient descent
+that it is an unbiased estimate and
+
+ align:start position:0%
+that it is an unbiased estimate and
+ 
+
+ align:start position:0%
+that it is an unbiased estimate and
+intuitively speaking anytime you did any
+
+ align:start position:0%
+intuitively speaking anytime you did any
+ 
+
+ align:start position:0%
+intuitively speaking anytime you did any
+proof in class or in the book or lecture
+
+ align:start position:0%
+proof in class or in the book or lecture
+ 
+
+ align:start position:0%
+proof in class or in the book or lecture
+notes wherever where you were using true
+
+ align:start position:0%
+notes wherever where you were using true
+ 
+
+ align:start position:0%
+notes wherever where you were using true
+gradients more or less you can do those
+
+ align:start position:0%
+gradients more or less you can do those
+ 
+
+ align:start position:0%
+gradients more or less you can do those
+same proofs more
+
+ align:start position:0%
+same proofs more
+ 
+
+ align:start position:0%
+same proofs more
+less not always using stochastic
+
+ align:start position:0%
+less not always using stochastic
+ 
+
+ align:start position:0%
+less not always using stochastic
+gradients by replace by encapsulating
+
+ align:start position:0%
+gradients by replace by encapsulating
+ 
+
+ align:start position:0%
+gradients by replace by encapsulating
+everything within expectations over the
+
+ align:start position:0%
+everything within expectations over the
+ 
+
+ align:start position:0%
+everything within expectations over the
+randomness I'll show you an example of
+
+ align:start position:0%
+randomness I'll show you an example of
+ 
+
+ align:start position:0%
+randomness I'll show you an example of
+what I mean by that I'm just trying to
+
+ align:start position:0%
+what I mean by that I'm just trying to
+ 
+
+ align:start position:0%
+what I mean by that I'm just trying to
+simplify that for you and in particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the unbiasness is great so it means I
+
+ align:start position:0%
+the unbiasness is great so it means I
+ 
+
+ align:start position:0%
+the unbiasness is great so it means I
+can kind of plug in these stochastic
+
+ align:start position:0%
+can kind of plug in these stochastic
+ 
+
+ align:start position:0%
+can kind of plug in these stochastic
+gradients in place of the true gradient
+
+ align:start position:0%
+gradients in place of the true gradient
+ 
+
+ align:start position:0%
+gradients in place of the true gradient
+and I'm still doing something meaningful
+
+ align:start position:0%
+and I'm still doing something meaningful
+ 
+
+ align:start position:0%
+and I'm still doing something meaningful
+so this is answering that earlier
+
+ align:start position:0%
+so this is answering that earlier
+ 
+
+ align:start position:0%
+so this is answering that earlier
+question you know why this random stuff
+
+ align:start position:0%
+question you know why this random stuff
+ 
+
+ align:start position:0%
+question you know why this random stuff
+why it should we think it may work but
+
+ align:start position:0%
+why it should we think it may work but
+ 
+
+ align:start position:0%
+why it should we think it may work but
+there's another very important aspect to
+
+ align:start position:0%
+there's another very important aspect to
+ 
+
+ align:start position:0%
+there's another very important aspect to
+it why it works beyond this unbiasness
+
+ align:start position:0%
+it why it works beyond this unbiasness
+ 
+
+ align:start position:0%
+it why it works beyond this unbiasness
+that the amount of noise or like the
+
+ align:start position:0%
+that the amount of noise or like the
+ 
+
+ align:start position:0%
+that the amount of noise or like the
+amount of amount of stochasticity is
+
+ align:start position:0%
+amount of amount of stochasticity is
+ 
+
+ align:start position:0%
+amount of amount of stochasticity is
+controlled so just because it is an
+
+ align:start position:0%
+controlled so just because it is an
+ 
+
+ align:start position:0%
+controlled so just because it is an
+unbiased estimate doesn't mean that it's
+
+ align:start position:0%
+unbiased estimate doesn't mean that it's
+ 
+
+ align:start position:0%
+unbiased estimate doesn't mean that it's
+going to work that well why because it
+
+ align:start position:0%
+going to work that well why because it
+ 
+
+ align:start position:0%
+going to work that well why because it
+could still fluctuate hugely right
+
+ align:start position:0%
+could still fluctuate hugely right
+ 
+
+ align:start position:0%
+could still fluctuate hugely right
+essentially plus infinity here minus
+
+ align:start position:0%
+essentially plus infinity here minus
+ 
+
+ align:start position:0%
+essentially plus infinity here minus
+infinity here you take an average you
+
+ align:start position:0%
+infinity here you take an average you
+ 
+
+ align:start position:0%
+infinity here you take an average you
+get zero so that is essentially unbiased
+
+ align:start position:0%
+get zero so that is essentially unbiased
+ 
+
+ align:start position:0%
+get zero so that is essentially unbiased
+but the fluctuation is gigantic
+
+ align:start position:0%
+but the fluctuation is gigantic
+ 
+
+ align:start position:0%
+but the fluctuation is gigantic
+so whenever talking about estimates
+
+ align:start position:0%
+so whenever talking about estimates
+ 
+
+ align:start position:0%
+so whenever talking about estimates
+what's the other key quantity we need to
+
+ align:start position:0%
+what's the other key quantity we need to
+ 
+
+ align:start position:0%
+what's the other key quantity we need to
+care about beyond expectation
+
+ align:start position:0%
+care about beyond expectation
+ 
+
+ align:start position:0%
+care about beyond expectation
+in clearance and really the key thing
+
+ align:start position:0%
+in clearance and really the key thing
+ 
+
+ align:start position:0%
+in clearance and really the key thing
+that governs the speed at which
+
+ align:start position:0%
+that governs the speed at which
+ 
+
+ align:start position:0%
+that governs the speed at which
+stochastic gradient descent does the job
+
+ align:start position:0%
+stochastic gradient descent does the job
+ 
+
+ align:start position:0%
+stochastic gradient descent does the job
+that we want it to do is how much
+
+ align:start position:0%
+that we want it to do is how much
+ 
+
+ align:start position:0%
+that we want it to do is how much
+variance do the stochastic gradient have
+
+ align:start position:0%
+variance do the stochastic gradient have
+ 
+
+ align:start position:0%
+variance do the stochastic gradient have
+just this simple statistical point in
+
+ align:start position:0%
+just this simple statistical point in
+ 
+
+ align:start position:0%
+just this simple statistical point in
+fact is at the heart of a sequence of
+
+ align:start position:0%
+fact is at the heart of a sequence of
+ 
+
+ align:start position:0%
+fact is at the heart of a sequence of
+research progress in the past five years
+
+ align:start position:0%
+research progress in the past five years
+ 
+
+ align:start position:0%
+research progress in the past five years
+in the field of stochastic gradient
+
+ align:start position:0%
+in the field of stochastic gradient
+ 
+
+ align:start position:0%
+in the field of stochastic gradient
+where people have worked really hard to
+
+ align:start position:0%
+where people have worked really hard to
+ 
+
+ align:start position:0%
+where people have worked really hard to
+come up with newer and newer fancier and
+
+ align:start position:0%
+come up with newer and newer fancier and
+ 
+
+ align:start position:0%
+come up with newer and newer fancier and
+fancier versions of stochastic gradient
+
+ align:start position:0%
+fancier versions of stochastic gradient
+ 
+
+ align:start position:0%
+fancier versions of stochastic gradient
+which have the unbiasness property but
+
+ align:start position:0%
+which have the unbiasness property but
+ 
+
+ align:start position:0%
+which have the unbiasness property but
+have smaller and smaller variants and
+
+ align:start position:0%
+have smaller and smaller variants and
+ 
+
+ align:start position:0%
+have smaller and smaller variants and
+the smaller the variance you have the
+
+ align:start position:0%
+the smaller the variance you have the
+ 
+
+ align:start position:0%
+the smaller the variance you have the
+better your stochastic gradient is as a
+
+ align:start position:0%
+better your stochastic gradient is as a
+ 
+
+ align:start position:0%
+better your stochastic gradient is as a
+replacement of the true gradient and of
+
+ align:start position:0%
+replacement of the true gradient and of
+ 
+
+ align:start position:0%
+replacement of the true gradient and of
+course the better is the replacement of
+
+ align:start position:0%
+course the better is the replacement of
+ 
+
+ align:start position:0%
+course the better is the replacement of
+the true gradient then you truly get
+
+ align:start position:0%
+the true gradient then you truly get
+ 
+
+ align:start position:0%
+the true gradient then you truly get
+that you know n time speed-up okay so
+
+ align:start position:0%
+that you know n time speed-up okay so
+ 
+
+ align:start position:0%
+that you know n time speed-up okay so
+the speed of convergence depends on how
+
+ align:start position:0%
+the speed of convergence depends on how
+ 
+
+ align:start position:0%
+the speed of convergence depends on how
+noisy the stochastic gradients are it
+
+ align:start position:0%
+noisy the stochastic gradients are it
+ 
+
+ align:start position:0%
+noisy the stochastic gradients are it
+seems like I'm going too slow I won't be
+
+ align:start position:0%
+seems like I'm going too slow I won't be
+ 
+
+ align:start position:0%
+seems like I'm going too slow I won't be
+able to do a proof i if it sucks but
+
+ align:start position:0%
+able to do a proof i if it sucks but
+ 
+
+ align:start position:0%
+able to do a proof i if it sucks but
+I'll but let's let me actually tell you
+
+ align:start position:0%
+I'll but let's let me actually tell you
+ 
+
+ align:start position:0%
+I'll but let's let me actually tell you
+then about rather than the the proof
+
+ align:start position:0%
+then about rather than the the proof
+ 
+
+ align:start position:0%
+then about rather than the the proof
+I think I'll share the proof with Gil
+
+ align:start position:0%
+I think I'll share the proof with Gil
+ 
+
+ align:start position:0%
+I think I'll share the proof with Gil
+because the proof that I want to want
+
+ align:start position:0%
+because the proof that I want to want
+ 
+
+ align:start position:0%
+because the proof that I want to want
+you to actually show you talk gives a
+
+ align:start position:0%
+you to actually show you talk gives a
+ 
+
+ align:start position:0%
+you to actually show you talk gives a
+proof of stochastic gradient is
+
+ align:start position:0%
+proof of stochastic gradient is
+ 
+
+ align:start position:0%
+proof of stochastic gradient is
+well-behaved on both convex and non
+
+ align:start position:0%
+well-behaved on both convex and non
+ 
+
+ align:start position:0%
+well-behaved on both convex and non
+convex problems and the proof I wanted
+
+ align:start position:0%
+convex problems and the proof I wanted
+ 
+
+ align:start position:0%
+convex problems and the proof I wanted
+to show was for the non convex case
+
+ align:start position:0%
+to show was for the non convex case
+ 
+
+ align:start position:0%
+to show was for the non convex case
+because it applies to neural networks so
+
+ align:start position:0%
+because it applies to neural networks so
+ 
+
+ align:start position:0%
+because it applies to neural networks so
+you may be curious about that proof and
+
+ align:start position:0%
+you may be curious about that proof and
+ 
+
+ align:start position:0%
+you may be curious about that proof and
+remarkably that proof is much simpler
+
+ align:start position:0%
+remarkably that proof is much simpler
+ 
+
+ align:start position:0%
+remarkably that proof is much simpler
+than the case of convex problems so let
+
+ align:start position:0%
+than the case of convex problems so let
+ 
+
+ align:start position:0%
+than the case of convex problems so let
+me just mention some very important
+
+ align:start position:0%
+me just mention some very important
+ 
+
+ align:start position:0%
+me just mention some very important
+points about stochastic gradient so even
+
+ align:start position:0%
+points about stochastic gradient so even
+ 
+
+ align:start position:0%
+points about stochastic gradient so even
+though this method has been around since
+
+ align:start position:0%
+though this method has been around since
+ 
+
+ align:start position:0%
+though this method has been around since
+1951 every deep learning toolkit has it
+
+ align:start position:0%
+1951 every deep learning toolkit has it
+ 
+
+ align:start position:0%
+1951 every deep learning toolkit has it
+and we are studying it in class there
+
+ align:start position:0%
+and we are studying it in class there
+ 
+
+ align:start position:0%
+and we are studying it in class there
+are still gaps between what we can say
+
+ align:start position:0%
+are still gaps between what we can say
+ 
+
+ align:start position:0%
+are still gaps between what we can say
+theoretically and what happens in
+
+ align:start position:0%
+theoretically and what happens in
+ 
+
+ align:start position:0%
+theoretically and what happens in
+practice and I'll show you those gaps
+
+ align:start position:0%
+practice and I'll show you those gaps
+ 
+
+ align:start position:0%
+practice and I'll show you those gaps
+already and encourage you to think about
+
+ align:start position:0%
+already and encourage you to think about
+ 
+
+ align:start position:0%
+already and encourage you to think about
+those if you wish
+
+ align:start position:0%
+those if you wish
+ 
+
+ align:start position:0%
+those if you wish
+so let's look back at our problem and
+
+ align:start position:0%
+so let's look back at our problem and
+ 
+
+ align:start position:0%
+so let's look back at our problem and
+tell you about two variants so here are
+
+ align:start position:0%
+tell you about two variants so here are
+ 
+
+ align:start position:0%
+tell you about two variants so here are
+the two variants I'm going to ask if any
+
+ align:start position:0%
+the two variants I'm going to ask if any
+ 
+
+ align:start position:0%
+the two variants I'm going to ask if any
+of you is familiar with this variant
+
+ align:start position:0%
+of you is familiar with this variant
+ 
+
+ align:start position:0%
+of you is familiar with this variant
+in some way or the other so let's I just
+
+ align:start position:0%
+in some way or the other so let's I just
+ 
+
+ align:start position:0%
+in some way or the other so let's I just
+call it feasible here there are no
+
+ align:start position:0%
+call it feasible here there are no
+ 
+
+ align:start position:0%
+call it feasible here there are no
+constraints so I start with any random
+
+ align:start position:0%
+constraints so I start with any random
+ 
+
+ align:start position:0%
+constraints so I start with any random
+vector of your choice in deep network
+
+ align:start position:0%
+vector of your choice in deep network
+ 
+
+ align:start position:0%
+vector of your choice in deep network
+training you have to work harder and
+
+ align:start position:0%
+training you have to work harder and
+ 
+
+ align:start position:0%
+training you have to work harder and
+then this is the iteration you run right
+
+ align:start position:0%
+then this is the iteration you run right
+ 
+
+ align:start position:0%
+then this is the iteration you run right
+option one and option two so option one
+
+ align:start position:0%
+option one and option two so option one
+ 
+
+ align:start position:0%
+option one and option two so option one
+says that was the idea we had in class
+
+ align:start position:0%
+says that was the idea we had in class
+ 
+
+ align:start position:0%
+says that was the idea we had in class
+randomly pick some training data point
+
+ align:start position:0%
+randomly pick some training data point
+ 
+
+ align:start position:0%
+randomly pick some training data point
+use it stochastic gradient well what do
+
+ align:start position:0%
+use it stochastic gradient well what do
+ 
+
+ align:start position:0%
+use it stochastic gradient well what do
+we mean by randomly pick the moment you
+
+ align:start position:0%
+we mean by randomly pick the moment you
+ 
+
+ align:start position:0%
+we mean by randomly pick the moment you
+use the word random you have to define
+
+ align:start position:0%
+use the word random you have to define
+ 
+
+ align:start position:0%
+use the word random you have to define
+what's the randomness so one randomness
+
+ align:start position:0%
+what's the randomness so one randomness
+ 
+
+ align:start position:0%
+what's the randomness so one randomness
+is uniform probability of our n training
+
+ align:start position:0%
+is uniform probability of our n training
+ 
+
+ align:start position:0%
+is uniform probability of our n training
+data points that is one randomness the
+
+ align:start position:0%
+data points that is one randomness the
+ 
+
+ align:start position:0%
+data points that is one randomness the
+other version is you pick a training
+
+ align:start position:0%
+other version is you pick a training
+ 
+
+ align:start position:0%
+other version is you pick a training
+data point without replacement so I so
+
+ align:start position:0%
+data point without replacement so I so
+ 
+
+ align:start position:0%
+data point without replacement so I so
+with replacement means you know just
+
+ align:start position:0%
+with replacement means you know just
+ 
+
+ align:start position:0%
+with replacement means you know just
+uniformly at random each time you draw a
+
+ align:start position:0%
+uniformly at random each time you draw a
+ 
+
+ align:start position:0%
+uniformly at random each time you draw a
+number from one through n use that
+
+ align:start position:0%
+number from one through n use that
+ 
+
+ align:start position:0%
+number from one through n use that
+stochastic gradient move on which means
+
+ align:start position:0%
+stochastic gradient move on which means
+ 
+
+ align:start position:0%
+stochastic gradient move on which means
+the same point can easily be picked
+
+ align:start position:0%
+the same point can easily be picked
+ 
+
+ align:start position:0%
+the same point can easily be picked
+twice also and without replacement means
+
+ align:start position:0%
+twice also and without replacement means
+ 
+
+ align:start position:0%
+twice also and without replacement means
+if you've picked a point number three
+
+ align:start position:0%
+if you've picked a point number three
+ 
+
+ align:start position:0%
+if you've picked a point number three
+you're not going to pick it again until
+
+ align:start position:0%
+you're not going to pick it again until
+ 
+
+ align:start position:0%
+you're not going to pick it again until
+you've gone through the entire training
+
+ align:start position:0%
+you've gone through the entire training
+ 
+
+ align:start position:0%
+you've gone through the entire training
+data set those are two types of
+
+ align:start position:0%
+data set those are two types of
+ 
+
+ align:start position:0%
+data set those are two types of
+randomness which version would you use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is no right or wrong answer to
+
+ align:start position:0%
+there is no right or wrong answer to
+ 
+
+ align:start position:0%
+there is no right or wrong answer to
+this I'm just taking a poll what would
+
+ align:start position:0%
+this I'm just taking a poll what would
+ 
+
+ align:start position:0%
+this I'm just taking a poll what would
+you use think that you're writing a
+
+ align:start position:0%
+you use think that you're writing a
+ 
+
+ align:start position:0%
+you use think that you're writing a
+program for this and maybe think really
+
+ align:start position:0%
+program for this and maybe think really
+ 
+
+ align:start position:0%
+program for this and maybe think really
+pragmatically practically so that's
+
+ align:start position:0%
+pragmatically practically so that's
+ 
+
+ align:start position:0%
+pragmatically practically so that's
+enough of an hint which version would
+
+ align:start position:0%
+enough of an hint which version would
+ 
+
+ align:start position:0%
+enough of an hint which version would
+you use I'm just curious who would use
+
+ align:start position:0%
+you use I'm just curious who would use
+ 
+
+ align:start position:0%
+you use I'm just curious who would use
+one please raise hands who and the the
+
+ align:start position:0%
+one please raise hands who and the the
+ 
+
+ align:start position:0%
+one please raise hands who and the the
+exclusion the compliment they reform I
+
+ align:start position:0%
+exclusion the compliment they reform I
+ 
+
+ align:start position:0%
+exclusion the compliment they reform I
+don't know maybe some people are
+
+ align:start position:0%
+don't know maybe some people are
+ 
+
+ align:start position:0%
+don't know maybe some people are
+undecided who would use two very few
+
+ align:start position:0%
+undecided who would use two very few
+ 
+
+ align:start position:0%
+undecided who would use two very few
+people okay how many of you use neural
+
+ align:start position:0%
+people okay how many of you use neural
+ 
+
+ align:start position:0%
+people okay how many of you use neural
+network training tool kits like
+
+ align:start position:0%
+network training tool kits like
+ 
+
+ align:start position:0%
+network training tool kits like
+tensorflow pi torch whatnot which
+
+ align:start position:0%
+tensorflow pi torch whatnot which
+ 
+
+ align:start position:0%
+tensorflow pi torch whatnot which
+version are they using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually every person in the real world
+
+ align:start position:0%
+actually every person in the real world
+ 
+
+ align:start position:0%
+actually every person in the real world
+is using version 2 are you really gonna
+
+ align:start position:0%
+is using version 2 are you really gonna
+ 
+
+ align:start position:0%
+is using version 2 are you really gonna
+randomly go through your RAAM each time
+
+ align:start position:0%
+randomly go through your RAAM each time
+ 
+
+ align:start position:0%
+randomly go through your RAAM each time
+to pick random points they'll kill your
+
+ align:start position:0%
+to pick random points they'll kill your
+ 
+
+ align:start position:0%
+to pick random points they'll kill your
+GPU performance like anything what
+
+ align:start position:0%
+GPU performance like anything what
+ 
+
+ align:start position:0%
+GPU performance like anything what
+people do is take a data set use a pre
+
+ align:start position:0%
+people do is take a data set use a pre
+ 
+
+ align:start position:0%
+people do is take a data set use a pre
+shuffle operation and then just Boop
+
+ align:start position:0%
+shuffle operation and then just Boop
+ 
+
+ align:start position:0%
+shuffle operation and then just Boop
+stream through the data what the
+
+ align:start position:0%
+stream through the data what the
+ 
+
+ align:start position:0%
+stream through the data what the
+streaming through the data mean without
+
+ align:start position:0%
+streaming through the data mean without
+ 
+
+ align:start position:0%
+streaming through the data mean without
+replacement so all the toolkits actually
+
+ align:start position:0%
+replacement so all the toolkits actually
+ 
+
+ align:start position:0%
+replacement so all the toolkits actually
+are using the without replacement
+
+ align:start position:0%
+are using the without replacement
+ 
+
+ align:start position:0%
+are using the without replacement
+version even though intuitively the rent
+
+ align:start position:0%
+version even though intuitively the rent
+ 
+
+ align:start position:0%
+version even though intuitively the rent
+just uniform random feels much nicer and
+
+ align:start position:0%
+just uniform random feels much nicer and
+ 
+
+ align:start position:0%
+just uniform random feels much nicer and
+that feeling is not ill-founded because
+
+ align:start position:0%
+that feeling is not ill-founded because
+ 
+
+ align:start position:0%
+that feeling is not ill-founded because
+that's the only version we know how to
+
+ align:start position:0%
+that's the only version we know how to
+ 
+
+ align:start position:0%
+that's the only version we know how to
+analyze mathematically so even for this
+
+ align:start position:0%
+analyze mathematically so even for this
+ 
+
+ align:start position:0%
+analyze mathematically so even for this
+method everybody studies it their
+
+ align:start position:0%
+method everybody studies it their
+ 
+
+ align:start position:0%
+method everybody studies it their
+million papers on it the version that is
+
+ align:start position:0%
+million papers on it the version that is
+ 
+
+ align:start position:0%
+million papers on it the version that is
+used in practice is not the version we
+
+ align:start position:0%
+used in practice is not the version we
+ 
+
+ align:start position:0%
+used in practice is not the version we
+know how to analyze it's a major open
+
+ align:start position:0%
+know how to analyze it's a major open
+ 
+
+ align:start position:0%
+know how to analyze it's a major open
+problem in the field of stochastic
+
+ align:start position:0%
+problem in the field of stochastic
+ 
+
+ align:start position:0%
+problem in the field of stochastic
+gradient to actually analyze the version
+
+ align:start position:0%
+gradient to actually analyze the version
+ 
+
+ align:start position:0%
+gradient to actually analyze the version
+that we use in practice it's kind of
+
+ align:start position:0%
+that we use in practice it's kind of
+ 
+
+ align:start position:0%
+that we use in practice it's kind of
+embarrassing but it's without
+
+ align:start position:0%
+embarrassing but it's without
+ 
+
+ align:start position:0%
+embarrassing but it's without
+replacement means non iid probability
+
+ align:start position:0%
+replacement means non iid probability
+ 
+
+ align:start position:0%
+replacement means non iid probability
+theory and non iid probability theory is
+
+ align:start position:0%
+theory and non iid probability theory is
+ 
+
+ align:start position:0%
+theory and non iid probability theory is
+not so easy
+
+ align:start position:0%
+not so easy
+ 
+
+ align:start position:0%
+not so easy
+that's the answer okay so the other
+
+ align:start position:0%
+that's the answer okay so the other
+ 
+
+ align:start position:0%
+that's the answer okay so the other
+version is this mini batch idea which
+
+ align:start position:0%
+version is this mini batch idea which
+ 
+
+ align:start position:0%
+version is this mini batch idea which
+you mentioned really early on is that
+
+ align:start position:0%
+you mentioned really early on is that
+ 
+
+ align:start position:0%
+you mentioned really early on is that
+rather than pick one random point I'll
+
+ align:start position:0%
+rather than pick one random point I'll
+ 
+
+ align:start position:0%
+rather than pick one random point I'll
+pick a mini batch so I had a million
+
+ align:start position:0%
+pick a mini batch so I had a million
+ 
+
+ align:start position:0%
+pick a mini batch so I had a million
+points each time instead of picking one
+
+ align:start position:0%
+points each time instead of picking one
+ 
+
+ align:start position:0%
+points each time instead of picking one
+maybe I'll pick 10 or 100 or thousand or
+
+ align:start position:0%
+maybe I'll pick 10 or 100 or thousand or
+ 
+
+ align:start position:0%
+maybe I'll pick 10 or 100 or thousand or
+what have you
+
+ align:start position:0%
+what have you
+ 
+
+ align:start position:0%
+what have you
+so this averages things averaging things
+
+ align:start position:0%
+so this averages things averaging things
+ 
+
+ align:start position:0%
+so this averages things averaging things
+reduces the variance so this is actually
+
+ align:start position:0%
+reduces the variance so this is actually
+ 
+
+ align:start position:0%
+reduces the variance so this is actually
+a good thing because the more quantities
+
+ align:start position:0%
+a good thing because the more quantities
+ 
+
+ align:start position:0%
+a good thing because the more quantities
+you averaged the less noise you have
+
+ align:start position:0%
+you averaged the less noise you have
+ 
+
+ align:start position:0%
+you averaged the less noise you have
+that's kind of what happens in
+
+ align:start position:0%
+that's kind of what happens in
+ 
+
+ align:start position:0%
+that's kind of what happens in
+probability right so we pick a mini
+
+ align:start position:0%
+probability right so we pick a mini
+ 
+
+ align:start position:0%
+probability right so we pick a mini
+batch and the stochastic estimate now is
+
+ align:start position:0%
+batch and the stochastic estimate now is
+ 
+
+ align:start position:0%
+batch and the stochastic estimate now is
+this you know not just a single gradient
+
+ align:start position:0%
+this you know not just a single gradient
+ 
+
+ align:start position:0%
+this you know not just a single gradient
+but averaged over a mini batch so mini
+
+ align:start position:0%
+but averaged over a mini batch so mini
+ 
+
+ align:start position:0%
+but averaged over a mini batch so mini
+batch of size one is the pure vanilla
+
+ align:start position:0%
+batch of size one is the pure vanilla
+ 
+
+ align:start position:0%
+batch of size one is the pure vanilla
+SGD mini batch of size n is nothing
+
+ align:start position:0%
+SGD mini batch of size n is nothing
+ 
+
+ align:start position:0%
+SGD mini batch of size n is nothing
+other than pure gradient descent
+
+ align:start position:0%
+other than pure gradient descent
+ 
+
+ align:start position:0%
+other than pure gradient descent
+something in between is what people
+
+ align:start position:0%
+something in between is what people
+ 
+
+ align:start position:0%
+something in between is what people
+actually use
+
+ align:start position:0%
+actually use
+ 
+
+ align:start position:0%
+actually use
+and again the theoretical analysis only
+
+ align:start position:0%
+and again the theoretical analysis only
+ 
+
+ align:start position:0%
+and again the theoretical analysis only
+exists if the mini-batch is picked with
+
+ align:start position:0%
+exists if the mini-batch is picked with
+ 
+
+ align:start position:0%
+exists if the mini-batch is picked with
+replacement not without replacement so
+
+ align:start position:0%
+replacement not without replacement so
+ 
+
+ align:start position:0%
+replacement not without replacement so
+one of the reasons actually a very
+
+ align:start position:0%
+one of the reasons actually a very
+ 
+
+ align:start position:0%
+one of the reasons actually a very
+important thing in theory you don't gain
+
+ align:start position:0%
+important thing in theory you don't gain
+ 
+
+ align:start position:0%
+important thing in theory you don't gain
+too much in terms of computational gains
+
+ align:start position:0%
+too much in terms of computational gains
+ 
+
+ align:start position:0%
+too much in terms of computational gains
+on convergence speed by using mini
+
+ align:start position:0%
+on convergence speed by using mini
+ 
+
+ align:start position:0%
+on convergence speed by using mini
+matches but mini batches are really
+
+ align:start position:0%
+matches but mini batches are really
+ 
+
+ align:start position:0%
+matches but mini batches are really
+crucial especially in you know deep
+
+ align:start position:0%
+crucial especially in you know deep
+ 
+
+ align:start position:0%
+crucial especially in you know deep
+learning GPU style training because they
+
+ align:start position:0%
+learning GPU style training because they
+ 
+
+ align:start position:0%
+learning GPU style training because they
+allow you to do things in parallel each
+
+ align:start position:0%
+allow you to do things in parallel each
+ 
+
+ align:start position:0%
+allow you to do things in parallel each
+thread or each core or sub core or small
+
+ align:start position:0%
+thread or each core or sub core or small
+ 
+
+ align:start position:0%
+thread or each core or sub core or small
+chip or what-have-you depending on your
+
+ align:start position:0%
+chip or what-have-you depending on your
+ 
+
+ align:start position:0%
+chip or what-have-you depending on your
+hardware can be working with one
+
+ align:start position:0%
+hardware can be working with one
+ 
+
+ align:start position:0%
+hardware can be working with one
+stochastic gradient so mini batch is the
+
+ align:start position:0%
+stochastic gradient so mini batch is the
+ 
+
+ align:start position:0%
+stochastic gradient so mini batch is the
+larger the mini batch the more things
+
+ align:start position:0%
+larger the mini batch the more things
+ 
+
+ align:start position:0%
+larger the mini batch the more things
+you can do in parallel so mini batches
+
+ align:start position:0%
+you can do in parallel so mini batches
+ 
+
+ align:start position:0%
+you can do in parallel so mini batches
+are greatly exploited by people to give
+
+ align:start position:0%
+are greatly exploited by people to give
+ 
+
+ align:start position:0%
+are greatly exploited by people to give
+you a cheap version of parallelism and
+
+ align:start position:0%
+you a cheap version of parallelism and
+ 
+
+ align:start position:0%
+you a cheap version of parallelism and
+where does the parallelism happen you
+
+ align:start position:0%
+where does the parallelism happen you
+ 
+
+ align:start position:0%
+where does the parallelism happen you
+can think that each core computes a
+
+ align:start position:0%
+can think that each core computes a
+ 
+
+ align:start position:0%
+can think that each core computes a
+stochastic gradient so the hard part is
+
+ align:start position:0%
+stochastic gradient so the hard part is
+ 
+
+ align:start position:0%
+stochastic gradient so the hard part is
+not adding these things up and making
+
+ align:start position:0%
+not adding these things up and making
+ 
+
+ align:start position:0%
+not adding these things up and making
+the update to X the hard part is
+
+ align:start position:0%
+the update to X the hard part is
+ 
+
+ align:start position:0%
+the update to X the hard part is
+computing a stochastic gradient so if
+
+ align:start position:0%
+computing a stochastic gradient so if
+ 
+
+ align:start position:0%
+computing a stochastic gradient so if
+you can compute 10,000 of those in
+
+ align:start position:0%
+you can compute 10,000 of those in
+ 
+
+ align:start position:0%
+you can compute 10,000 of those in
+parallel because you have 10,000 cores
+
+ align:start position:0%
+parallel because you have 10,000 cores
+ 
+
+ align:start position:0%
+parallel because you have 10,000 cores
+great for you and that's the reason
+
+ align:start position:0%
+great for you and that's the reason
+ 
+
+ align:start position:0%
+great for you and that's the reason
+people love using mini batches but a
+
+ align:start position:0%
+people love using mini batches but a
+ 
+
+ align:start position:0%
+people love using mini batches but a
+nice side remark here this is also this
+
+ align:start position:0%
+nice side remark here this is also this
+ 
+
+ align:start position:0%
+nice side remark here this is also this
+brings us close to the research edge of
+
+ align:start position:0%
+brings us close to the research edge of
+ 
+
+ align:start position:0%
+brings us close to the research edge of
+things again that well you'd love to use
+
+ align:start position:0%
+things again that well you'd love to use
+ 
+
+ align:start position:0%
+things again that well you'd love to use
+very large mini batches so that you can
+
+ align:start position:0%
+very large mini batches so that you can
+ 
+
+ align:start position:0%
+very large mini batches so that you can
+fully max out on the parallelism
+
+ align:start position:0%
+fully max out on the parallelism
+ 
+
+ align:start position:0%
+fully max out on the parallelism
+available to you right maybe you have a
+
+ align:start position:0%
+available to you right maybe you have a
+ 
+
+ align:start position:0%
+available to you right maybe you have a
+multi GPU system if you're friends with
+
+ align:start position:0%
+multi GPU system if you're friends with
+ 
+
+ align:start position:0%
+multi GPU system if you're friends with
+NVDA or Google I only have like two GPUs
+
+ align:start position:0%
+NVDA or Google I only have like two GPUs
+ 
+
+ align:start position:0%
+NVDA or Google I only have like two GPUs
+but it depends on how many GPUs you have
+
+ align:start position:0%
+but it depends on how many GPUs you have
+ 
+
+ align:start position:0%
+but it depends on how many GPUs you have
+you'd like to really max out on
+
+ align:start position:0%
+you'd like to really max out on
+ 
+
+ align:start position:0%
+you'd like to really max out on
+parallelism so that you can really
+
+ align:start position:0%
+parallelism so that you can really
+ 
+
+ align:start position:0%
+parallelism so that you can really
+crunch through big datasets as fast as
+
+ align:start position:0%
+crunch through big datasets as fast as
+ 
+
+ align:start position:0%
+crunch through big datasets as fast as
+possible but you know what happens with
+
+ align:start position:0%
+possible but you know what happens with
+ 
+
+ align:start position:0%
+possible but you know what happens with
+very large mini batches so if you have
+
+ align:start position:0%
+very large mini batches so if you have
+ 
+
+ align:start position:0%
+very large mini batches so if you have
+very large mini batches stochastic
+
+ align:start position:0%
+very large mini batches stochastic
+ 
+
+ align:start position:0%
+very large mini batches stochastic
+gradient starts looking more like full
+
+ align:start position:0%
+gradient starts looking more like full
+ 
+
+ align:start position:0%
+gradient starts looking more like full
+gradient descent which is also called
+
+ align:start position:0%
+gradient descent which is also called
+ 
+
+ align:start position:0%
+gradient descent which is also called
+batch gradient descent that's not a bad
+
+ align:start position:0%
+batch gradient descent that's not a bad
+ 
+
+ align:start position:0%
+batch gradient descent that's not a bad
+thing that's awesome for optimization
+
+ align:start position:0%
+thing that's awesome for optimization
+ 
+
+ align:start position:0%
+thing that's awesome for optimization
+but it is a weird conundrum that happens
+
+ align:start position:0%
+but it is a weird conundrum that happens
+ 
+
+ align:start position:0%
+but it is a weird conundrum that happens
+in training deep neural networks this
+
+ align:start position:0%
+in training deep neural networks this
+ 
+
+ align:start position:0%
+in training deep neural networks this
+type of problem we wouldn't have for
+
+ align:start position:0%
+type of problem we wouldn't have for
+ 
+
+ align:start position:0%
+type of problem we wouldn't have for
+convex optimization but in deep neural
+
+ align:start position:0%
+convex optimization but in deep neural
+ 
+
+ align:start position:0%
+convex optimization but in deep neural
+networks this is really disturbing thing
+
+ align:start position:0%
+networks this is really disturbing thing
+ 
+
+ align:start position:0%
+networks this is really disturbing thing
+happens that if you use this very large
+
+ align:start position:0%
+happens that if you use this very large
+ 
+
+ align:start position:0%
+happens that if you use this very large
+mini-batches your method starts
+
+ align:start position:0%
+mini-batches your method starts
+ 
+
+ align:start position:0%
+mini-batches your method starts
+resembling gradient descent that means
+
+ align:start position:0%
+resembling gradient descent that means
+ 
+
+ align:start position:0%
+resembling gradient descent that means
+it decreases noise so much so that this
+
+ align:start position:0%
+it decreases noise so much so that this
+ 
+
+ align:start position:0%
+it decreases noise so much so that this
+region of confusion shrinks so much
+
+ align:start position:0%
+region of confusion shrinks so much
+ 
+
+ align:start position:0%
+region of confusion shrinks so much
+which all sounds good but it ends up
+
+ align:start position:0%
+which all sounds good but it ends up
+ 
+
+ align:start position:0%
+which all sounds good but it ends up
+being really bad for machine learning
+
+ align:start position:0%
+being really bad for machine learning
+ 
+
+ align:start position:0%
+being really bad for machine learning
+that's what I said that in machine
+
+ align:start position:0%
+that's what I said that in machine
+ 
+
+ align:start position:0%
+that's what I said that in machine
+learning you want some region of
+
+ align:start position:0%
+learning you want some region of
+ 
+
+ align:start position:0%
+learning you want some region of
+uncertainty and what it means actually
+
+ align:start position:0%
+uncertainty and what it means actually
+ 
+
+ align:start position:0%
+uncertainty and what it means actually
+is a lot of people are have been working
+
+ align:start position:0%
+is a lot of people are have been working
+ 
+
+ align:start position:0%
+is a lot of people are have been working
+on this including at big companies that
+
+ align:start position:0%
+on this including at big companies that
+ 
+
+ align:start position:0%
+on this including at big companies that
+if you reduce that region of uncertainty
+
+ align:start position:0%
+if you reduce that region of uncertainty
+ 
+
+ align:start position:0%
+if you reduce that region of uncertainty
+too much you end up overfitting your
+
+ align:start position:0%
+too much you end up overfitting your
+ 
+
+ align:start position:0%
+too much you end up overfitting your
+neural network and then it starts
+
+ align:start position:0%
+neural network and then it starts
+ 
+
+ align:start position:0%
+neural network and then it starts
+sucking in its test data unseen data
+
+ align:start position:0%
+sucking in its test data unseen data
+ 
+
+ align:start position:0%
+sucking in its test data unseen data
+performance so even though for
+
+ align:start position:0%
+performance so even though for
+ 
+
+ align:start position:0%
+performance so even though for
+parallelism programming optimization
+
+ align:start position:0%
+parallelism programming optimization
+ 
+
+ align:start position:0%
+parallelism programming optimization
+Theory big mini-batch is awesome
+
+ align:start position:0%
+Theory big mini-batch is awesome
+ 
+
+ align:start position:0%
+Theory big mini-batch is awesome
+unfortunately there's price to be paid
+
+ align:start position:0%
+unfortunately there's price to be paid
+ 
+
+ align:start position:0%
+unfortunately there's price to be paid
+it hurts your test error performance and
+
+ align:start position:0%
+it hurts your test error performance and
+ 
+
+ align:start position:0%
+it hurts your test error performance and
+there all sorts of methods people are
+
+ align:start position:0%
+there all sorts of methods people are
+ 
+
+ align:start position:0%
+there all sorts of methods people are
+trying to cook up including shrinking
+
+ align:start position:0%
+trying to cook up including shrinking
+ 
+
+ align:start position:0%
+trying to cook up including shrinking
+data accordingly or changing neural
+
+ align:start position:0%
+data accordingly or changing neural
+ 
+
+ align:start position:0%
+data accordingly or changing neural
+network architecture and all sorts of
+
+ align:start position:0%
+network architecture and all sorts of
+ 
+
+ align:start position:0%
+network architecture and all sorts of
+ideas you can cook up your ideas for
+
+ align:start position:0%
+ideas you can cook up your ideas for
+ 
+
+ align:start position:0%
+ideas you can cook up your ideas for
+your favorite architecture how to make a
+
+ align:start position:0%
+your favorite architecture how to make a
+ 
+
+ align:start position:0%
+your favorite architecture how to make a
+large mini batch without hurting the
+
+ align:start position:0%
+large mini batch without hurting the
+ 
+
+ align:start position:0%
+large mini batch without hurting the
+final performance but it's still
+
+ align:start position:0%
+final performance but it's still
+ 
+
+ align:start position:0%
+final performance but it's still
+somewhat of an open question on how to
+
+ align:start position:0%
+somewhat of an open question on how to
+ 
+
+ align:start position:0%
+somewhat of an open question on how to
+optimally select which many larger
+
+ align:start position:0%
+optimally select which many larger
+ 
+
+ align:start position:0%
+optimally select which many larger
+mini-batch so should be so even though
+
+ align:start position:0%
+mini-batch so should be so even though
+ 
+
+ align:start position:0%
+mini-batch so should be so even though
+these ideas are simple you see that
+
+ align:start position:0%
+these ideas are simple you see that
+ 
+
+ align:start position:0%
+these ideas are simple you see that
+every simple idea leads to an entire sub
+
+ align:start position:0%
+every simple idea leads to an entire sub
+ 
+
+ align:start position:0%
+every simple idea leads to an entire sub
+area of SGD so here are practical
+
+ align:start position:0%
+area of SGD so here are practical
+ 
+
+ align:start position:0%
+area of SGD so here are practical
+challenges people have various
+
+ align:start position:0%
+challenges people have various
+ 
+
+ align:start position:0%
+challenges people have various
+heuristics for solving these challenges
+
+ align:start position:0%
+heuristics for solving these challenges
+ 
+
+ align:start position:0%
+heuristics for solving these challenges
+you can cook up your own but it's not
+
+ align:start position:0%
+you can cook up your own but it's not
+ 
+
+ align:start position:0%
+you can cook up your own but it's not
+that one idea always works so if you
+
+ align:start position:0%
+that one idea always works so if you
+ 
+
+ align:start position:0%
+that one idea always works so if you
+look at SGD what are the moving parts
+
+ align:start position:0%
+look at SGD what are the moving parts
+ 
+
+ align:start position:0%
+look at SGD what are the moving parts
+the moving parts in SGD the gradients
+
+ align:start position:0%
+the moving parts in SGD the gradients
+ 
+
+ align:start position:0%
+the moving parts in SGD the gradients
+stochastic gradients the step size the
+
+ align:start position:0%
+stochastic gradients the step size the
+ 
+
+ align:start position:0%
+stochastic gradients the step size the
+mini batch so
+
+ align:start position:0%
+mini batch so
+ 
+
+ align:start position:0%
+mini batch so
+how should I pick step sizes very
+
+ align:start position:0%
+how should I pick step sizes very
+ 
+
+ align:start position:0%
+how should I pick step sizes very
+non-trivial problem different deep
+
+ align:start position:0%
+non-trivial problem different deep
+ 
+
+ align:start position:0%
+non-trivial problem different deep
+learning toolkits may have different
+
+ align:start position:0%
+learning toolkits may have different
+ 
+
+ align:start position:0%
+learning toolkits may have different
+ways of automating that tuning but it's
+
+ align:start position:0%
+ways of automating that tuning but it's
+ 
+
+ align:start position:0%
+ways of automating that tuning but it's
+one of the painful things which
+
+ align:start position:0%
+one of the painful things which
+ 
+
+ align:start position:0%
+one of the painful things which
+mini-batch to use with replacement
+
+ align:start position:0%
+mini-batch to use with replacement
+ 
+
+ align:start position:0%
+mini-batch to use with replacement
+without replacement I already showed you
+
+ align:start position:0%
+without replacement I already showed you
+ 
+
+ align:start position:0%
+without replacement I already showed you
+but which mini-batch should I use how
+
+ align:start position:0%
+but which mini-batch should I use how
+ 
+
+ align:start position:0%
+but which mini-batch should I use how
+large that should be again not an easy
+
+ align:start position:0%
+large that should be again not an easy
+ 
+
+ align:start position:0%
+large that should be again not an easy
+question to answer how to compute
+
+ align:start position:0%
+question to answer how to compute
+ 
+
+ align:start position:0%
+question to answer how to compute
+stochastic gradients does anybody know
+
+ align:start position:0%
+stochastic gradients does anybody know
+ 
+
+ align:start position:0%
+stochastic gradients does anybody know
+how stochastic gradients are computed
+
+ align:start position:0%
+how stochastic gradients are computed
+ 
+
+ align:start position:0%
+how stochastic gradients are computed
+for deep Network training anybody know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is a very famous algorithm called
+
+ align:start position:0%
+there is a very famous algorithm called
+ 
+
+ align:start position:0%
+there is a very famous algorithm called
+back propagation that back propagation
+
+ align:start position:0%
+back propagation that back propagation
+ 
+
+ align:start position:0%
+back propagation that back propagation
+algorithm is used to compute a single
+
+ align:start position:0%
+algorithm is used to compute a single
+ 
+
+ align:start position:0%
+algorithm is used to compute a single
+stochastic gradient some people use the
+
+ align:start position:0%
+stochastic gradient some people use the
+ 
+
+ align:start position:0%
+stochastic gradient some people use the
+word back prop to mean SGD but what back
+
+ align:start position:0%
+word back prop to mean SGD but what back
+ 
+
+ align:start position:0%
+word back prop to mean SGD but what back
+prop really means is some some kind of
+
+ align:start position:0%
+prop really means is some some kind of
+ 
+
+ align:start position:0%
+prop really means is some some kind of
+algorithm which computes for you a
+
+ align:start position:0%
+algorithm which computes for you a
+ 
+
+ align:start position:0%
+algorithm which computes for you a
+single stochastic gradient and hence you
+
+ align:start position:0%
+single stochastic gradient and hence you
+ 
+
+ align:start position:0%
+single stochastic gradient and hence you
+know this tensorflow etc these toolkits
+
+ align:start position:0%
+know this tensorflow etc these toolkits
+ 
+
+ align:start position:0%
+know this tensorflow etc these toolkits
+they come up with all sorts of ways to
+
+ align:start position:0%
+they come up with all sorts of ways to
+ 
+
+ align:start position:0%
+they come up with all sorts of ways to
+automate the computation of a gradient
+
+ align:start position:0%
+automate the computation of a gradient
+ 
+
+ align:start position:0%
+automate the computation of a gradient
+because really that's the main thing and
+
+ align:start position:0%
+because really that's the main thing and
+ 
+
+ align:start position:0%
+because really that's the main thing and
+then other ideas like gradient clipping
+
+ align:start position:0%
+then other ideas like gradient clipping
+ 
+
+ align:start position:0%
+then other ideas like gradient clipping
+and momentum etc there's a bunch of
+
+ align:start position:0%
+and momentum etc there's a bunch of
+ 
+
+ align:start position:0%
+and momentum etc there's a bunch of
+other ideas and the theoretical
+
+ align:start position:0%
+other ideas and the theoretical
+ 
+
+ align:start position:0%
+other ideas and the theoretical
+challenges I mentioned to you already
+
+ align:start position:0%
+challenges I mentioned to you already
+ 
+
+ align:start position:0%
+challenges I mentioned to you already
+proving that it works that it actually
+
+ align:start position:0%
+proving that it works that it actually
+ 
+
+ align:start position:0%
+proving that it works that it actually
+solves what it set out to do
+
+ align:start position:0%
+solves what it set out to do
+ 
+
+ align:start position:0%
+solves what it set out to do
+unfortunately I was too slow I couldn't
+
+ align:start position:0%
+unfortunately I was too slow I couldn't
+ 
+
+ align:start position:0%
+unfortunately I was too slow I couldn't
+show you the awesome five line proof
+
+ align:start position:0%
+show you the awesome five line proof
+ 
+
+ align:start position:0%
+show you the awesome five line proof
+that I have that SGD works for neural
+
+ align:start position:0%
+that I have that SGD works for neural
+ 
+
+ align:start position:0%
+that I have that SGD works for neural
+networks and theoretical analysis as I
+
+ align:start position:0%
+networks and theoretical analysis as I
+ 
+
+ align:start position:0%
+networks and theoretical analysis as I
+said it's really lagging my proof also
+
+ align:start position:0%
+said it's really lagging my proof also
+ 
+
+ align:start position:0%
+said it's really lagging my proof also
+uses the with replacement and the
+
+ align:start position:0%
+uses the with replacement and the
+ 
+
+ align:start position:0%
+uses the with replacement and the
+without replacement version which is the
+
+ align:start position:0%
+without replacement version which is the
+ 
+
+ align:start position:0%
+without replacement version which is the
+one that is actually implemented there's
+
+ align:start position:0%
+one that is actually implemented there's
+ 
+
+ align:start position:0%
+one that is actually implemented there's
+very little progress on that there is
+
+ align:start position:0%
+very little progress on that there is
+ 
+
+ align:start position:0%
+very little progress on that there is
+some progress there's a bunch of papers
+
+ align:start position:0%
+some progress there's a bunch of papers
+ 
+
+ align:start position:0%
+some progress there's a bunch of papers
+including from our colleagues at MIT but
+
+ align:start position:0%
+including from our colleagues at MIT but
+ 
+
+ align:start position:0%
+including from our colleagues at MIT but
+it's quite unsolved and the biggest
+
+ align:start position:0%
+it's quite unsolved and the biggest
+ 
+
+ align:start position:0%
+it's quite unsolved and the biggest
+question which most of the people in
+
+ align:start position:0%
+question which most of the people in
+ 
+
+ align:start position:0%
+question which most of the people in
+machine learning are currently excited
+
+ align:start position:0%
+machine learning are currently excited
+ 
+
+ align:start position:0%
+machine learning are currently excited
+about these days is stuff like why does
+
+ align:start position:0%
+about these days is stuff like why does
+ 
+
+ align:start position:0%
+about these days is stuff like why does
+SGD work so well for neural networks we
+
+ align:start position:0%
+SGD work so well for neural networks we
+ 
+
+ align:start position:0%
+SGD work so well for neural networks we
+use this crappy optimization method it
+
+ align:start position:0%
+use this crappy optimization method it
+ 
+
+ align:start position:0%
+use this crappy optimization method it
+very rapidly does some fitting data is
+
+ align:start position:0%
+very rapidly does some fitting data is
+ 
+
+ align:start position:0%
+very rapidly does some fitting data is
+large neural network is large
+
+ align:start position:0%
+large neural network is large
+ 
+
+ align:start position:0%
+large neural network is large
+and then this neural network ends up
+
+ align:start position:0%
+and then this neural network ends up
+ 
+
+ align:start position:0%
+and then this neural network ends up
+having great classification performance
+
+ align:start position:0%
+having great classification performance
+ 
+
+ align:start position:0%
+having great classification performance
+why is that happening
+
+ align:start position:0%
+why is that happening
+ 
+
+ align:start position:0%
+why is that happening
+it's called trying to explain build a
+
+ align:start position:0%
+it's called trying to explain build a
+ 
+
+ align:start position:0%
+it's called trying to explain build a
+theory of generalization why does this
+
+ align:start position:0%
+theory of generalization why does this
+ 
+
+ align:start position:0%
+theory of generalization why does this
+an SGD train neural network work better
+
+ align:start position:0%
+an SGD train neural network work better
+ 
+
+ align:start position:0%
+an SGD train neural network work better
+than neural networks train with more
+
+ align:start position:0%
+than neural networks train with more
+ 
+
+ align:start position:0%
+than neural networks train with more
+fancy optimization methods it's a
+
+ align:start position:0%
+fancy optimization methods it's a
+ 
+
+ align:start position:0%
+fancy optimization methods it's a
+mystery and most of the people who take
+
+ align:start position:0%
+mystery and most of the people who take
+ 
+
+ align:start position:0%
+mystery and most of the people who take
+interest in theoretical machine learning
+
+ align:start position:0%
+interest in theoretical machine learning
+ 
+
+ align:start position:0%
+interest in theoretical machine learning
+and statistics that is one of the
+
+ align:start position:0%
+and statistics that is one of the
+ 
+
+ align:start position:0%
+and statistics that is one of the
+mysteries they are trying to understand
+
+ align:start position:0%
+mysteries they are trying to understand
+ 
+
+ align:start position:0%
+mysteries they are trying to understand
+so I think that's my story of SGD and
+
+ align:start position:0%
+so I think that's my story of SGD and
+ 
+
+ align:start position:0%
+so I think that's my story of SGD and
+this is the part we skip but it's ok the
+
+ align:start position:0%
+this is the part we skip but it's ok the
+ 
+
+ align:start position:0%
+this is the part we skip but it's ok the
+the intuition behind SGD is much more
+
+ align:start position:0%
+the intuition behind SGD is much more
+ 
+
+ align:start position:0%
+the intuition behind SGD is much more
+important than this so I think exactly
+
+ align:start position:0%
+important than this so I think exactly
+ 
+
+ align:start position:0%
+important than this so I think exactly
+yeah I think so that they'll be great
\ No newline at end of file
diff --git a/kZkLqCdMXWY.txt b/kZkLqCdMXWY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..14d4227cac904804ec57a15a85a33468bde0fe75
--- /dev/null
+++ b/kZkLqCdMXWY.txt
@@ -0,0 +1,15963 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu there are a lot of ideas in
+
+ align:start position:0%
+ocw.mit.edu there are a lot of ideas in
+ 
+
+ align:start position:0%
+ocw.mit.edu there are a lot of ideas in
+chapter
+
+ align:start position:0%
+chapter
+ 
+
+ align:start position:0%
+chapter
+for uh about a quarter of them are uh
+
+ align:start position:0%
+for uh about a quarter of them are uh
+ 
+
+ align:start position:0%
+for uh about a quarter of them are uh
+Rewritten from the Society of
+
+ align:start position:0%
+Rewritten from the Society of
+ 
+
+ align:start position:0%
+Rewritten from the Society of
+Mind and
+
+ align:start position:0%
+Mind and
+ 
+
+ align:start position:0%
+Mind and
+uh it isn't until the next chapter that
+
+ align:start position:0%
+uh it isn't until the next chapter that
+ 
+
+ align:start position:0%
+uh it isn't until the next chapter that
+right in the middle of the book that I
+
+ align:start position:0%
+right in the middle of the book that I
+ 
+
+ align:start position:0%
+right in the middle of the book that I
+try to describe the mind is made of a
+
+ align:start position:0%
+try to describe the mind is made of a
+ 
+
+ align:start position:0%
+try to describe the mind is made of a
+big stack of six different layers of I
+
+ align:start position:0%
+big stack of six different layers of I
+ 
+
+ align:start position:0%
+big stack of six different layers of I
+guess the introduction mentioned that
+
+ align:start position:0%
+guess the introduction mentioned that
+ 
+
+ align:start position:0%
+guess the introduction mentioned that
+but uh six different layers of
+
+ align:start position:0%
+but uh six different layers of
+ 
+
+ align:start position:0%
+but uh six different layers of
+structures Each of which reacts to
+
+ align:start position:0%
+structures Each of which reacts to
+ 
+
+ align:start position:0%
+structures Each of which reacts to
+what's happening in the layer below it
+
+ align:start position:0%
+what's happening in the layer below it
+ 
+
+ align:start position:0%
+what's happening in the layer below it
+and and that's something we sometimes
+
+ align:start position:0%
+and and that's something we sometimes
+ 
+
+ align:start position:0%
+and and that's something we sometimes
+call model six for no particular
+
+ align:start position:0%
+call model six for no particular
+ 
+
+ align:start position:0%
+call model six for no particular
+reason and uh so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sort of at this section in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the in chapter 4 it talks about the idea
+
+ align:start position:0%
+the in chapter 4 it talks about the idea
+ 
+
+ align:start position:0%
+the in chapter 4 it talks about the idea
+that in the early days of psychology
+
+ align:start position:0%
+that in the early days of psychology
+ 
+
+ align:start position:0%
+that in the early days of psychology
+well around
+
+ align:start position:0%
+well around
+ 
+
+ align:start position:0%
+well around
+1900 uh there were some very simple
+
+ align:start position:0%
+1900 uh there were some very simple
+ 
+
+ align:start position:0%
+1900 uh there were some very simple
+theories based on uh various experiments
+
+ align:start position:0%
+theories based on uh various experiments
+ 
+
+ align:start position:0%
+theories based on uh various experiments
+with rats and other
+
+ align:start position:0%
+with rats and other
+ 
+
+ align:start position:0%
+with rats and other
+uh shouldn't call them simple
+
+ align:start position:0%
+uh shouldn't call them simple
+ 
+
+ align:start position:0%
+uh shouldn't call them simple
+mammals if you think about it the animal
+
+ align:start position:0%
+mammals if you think about it the animal
+ 
+
+ align:start position:0%
+mammals if you think about it the animal
+the small mammals like rats and
+
+ align:start position:0%
+the small mammals like rats and
+ 
+
+ align:start position:0%
+the small mammals like rats and
+mice what did it
+
+ align:start position:0%
+mice what did it
+ 
+
+ align:start position:0%
+mice what did it
+do in the
+
+ align:start position:0%
+do in the
+ 
+
+ align:start position:0%
+do in the
+very when I say early days of psychology
+
+ align:start position:0%
+very when I say early days of psychology
+ 
+
+ align:start position:0%
+very when I say early days of psychology
+that's a strange thing to say because if
+
+ align:start position:0%
+that's a strange thing to say because if
+ 
+
+ align:start position:0%
+that's a strange thing to say because if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+read
+
+ align:start position:0%
+read
+ 
+
+ align:start position:0%
+read
+Aristotle's book on rhetoric which is a
+
+ align:start position:0%
+Aristotle's book on rhetoric which is a
+ 
+
+ align:start position:0%
+Aristotle's book on rhetoric which is a
+fairly big one it's full of ideas about
+
+ align:start position:0%
+fairly big one it's full of ideas about
+ 
+
+ align:start position:0%
+fairly big one it's full of ideas about
+how the mind works and then if uh then I
+
+ align:start position:0%
+how the mind works and then if uh then I
+ 
+
+ align:start position:0%
+how the mind works and then if uh then I
+don't know very much in between but if
+
+ align:start position:0%
+don't know very much in between but if
+ 
+
+ align:start position:0%
+don't know very much in between but if
+you go to the era of English
+
+ align:start position:0%
+you go to the era of English
+ 
+
+ align:start position:0%
+you go to the era of English
+philosophers like
+
+ align:start position:0%
+philosophers like
+ 
+
+ align:start position:0%
+philosophers like
+Hume and so forth then you uh see
+
+ align:start position:0%
+Hume and so forth then you uh see
+ 
+
+ align:start position:0%
+Hume and so forth then you uh see
+theories well hum is kind of strange
+
+ align:start position:0%
+theories well hum is kind of strange
+ 
+
+ align:start position:0%
+theories well hum is kind of strange
+theories about the associations of ideas
+
+ align:start position:0%
+theories about the associations of ideas
+ 
+
+ align:start position:0%
+theories about the associations of ideas
+and so forth and at the beginning of the
+
+ align:start position:0%
+and so forth and at the beginning of the
+ 
+
+ align:start position:0%
+and so forth and at the beginning of the
+19th century we find people like Watson
+
+ align:start position:0%
+19th century we find people like Watson
+ 
+
+ align:start position:0%
+19th century we find people like Watson
+and Pavlov who invent a very simple form
+
+ align:start position:0%
+and Pavlov who invent a very simple form
+ 
+
+ align:start position:0%
+and Pavlov who invent a very simple form
+of rule-based system uh that Pavlov
+
+ align:start position:0%
+of rule-based system uh that Pavlov
+ 
+
+ align:start position:0%
+of rule-based system uh that Pavlov
+called conditioned
+
+ align:start position:0%
+called conditioned
+ 
+
+ align:start position:0%
+called conditioned
+reflexes
+
+ align:start position:0%
+reflexes
+ 
+
+ align:start position:0%
+reflexes
+and uh in these descriptions of
+
+ align:start position:0%
+and uh in these descriptions of
+ 
+
+ align:start position:0%
+and uh in these descriptions of
+psychology This was later elaborated by
+
+ align:start position:0%
+psychology This was later elaborated by
+ 
+
+ align:start position:0%
+psychology This was later elaborated by
+B F Skinner who was a very famous
+
+ align:start position:0%
+B F Skinner who was a very famous
+ 
+
+ align:start position:0%
+B F Skinner who was a very famous
+psychologist of the
+
+ align:start position:0%
+psychologist of the
+ 
+
+ align:start position:0%
+psychologist of the
+1930s through
+
+ align:start position:0%
+1930s through
+ 
+
+ align:start position:0%
+1930s through
+7s and
+
+ align:start position:0%
+7s and
+ 
+
+ align:start position:0%
+7s and
+uh I made friends with him when I was an
+
+ align:start position:0%
+uh I made friends with him when I was an
+ 
+
+ align:start position:0%
+uh I made friends with him when I was an
+undergraduate at Harvard
+
+ align:start position:0%
+undergraduate at Harvard
+ 
+
+ align:start position:0%
+undergraduate at Harvard
+and played around with I was good at
+
+ align:start position:0%
+and played around with I was good at
+ 
+
+ align:start position:0%
+and played around with I was good at
+Electronics so I helped with the
+
+ align:start position:0%
+Electronics so I helped with the
+ 
+
+ align:start position:0%
+Electronics so I helped with the
+instrumentation uh what Pavlov and and
+
+ align:start position:0%
+instrumentation uh what Pavlov and and
+ 
+
+ align:start position:0%
+instrumentation uh what Pavlov and and
+those people did at the beginning of the
+
+ align:start position:0%
+those people did at the beginning of the
+ 
+
+ align:start position:0%
+those people did at the beginning of the
+19th century was do systematic
+
+ align:start position:0%
+19th century was do systematic
+ 
+
+ align:start position:0%
+19th century was do systematic
+experiments on animals
+
+ align:start position:0%
+experiments on animals
+ 
+
+ align:start position:0%
+experiments on animals
+and the standard Theory became what is
+
+ align:start position:0%
+and the standard Theory became what is
+ 
+
+ align:start position:0%
+and the standard Theory became what is
+now called reinforcement Theory you put
+
+ align:start position:0%
+now called reinforcement Theory you put
+ 
+
+ align:start position:0%
+now called reinforcement Theory you put
+the animal in a situation uh for
+
+ align:start position:0%
+the animal in a situation uh for
+ 
+
+ align:start position:0%
+the animal in a situation uh for
+example uh in Skinner what Skinner did
+
+ align:start position:0%
+example uh in Skinner what Skinner did
+ 
+
+ align:start position:0%
+example uh in Skinner what Skinner did
+was make the study of animal behavior
+
+ align:start position:0%
+was make the study of animal behavior
+ 
+
+ align:start position:0%
+was make the study of animal behavior
+sort of scientific in the sense that he
+
+ align:start position:0%
+sort of scientific in the sense that he
+ 
+
+ align:start position:0%
+sort of scientific in the sense that he
+restricted all sorts of variables what
+
+ align:start position:0%
+restricted all sorts of variables what
+ 
+
+ align:start position:0%
+restricted all sorts of variables what
+Pavlov did is he would uh
+
+ align:start position:0%
+Pavlov did is he would uh
+ 
+
+ align:start position:0%
+Pavlov did is he would uh
+uh uh show something to a dog maybe a
+
+ align:start position:0%
+uh uh show something to a dog maybe a
+ 
+
+ align:start position:0%
+uh uh show something to a dog maybe a
+piece of meat uh I'm sorry maybe uh play
+
+ align:start position:0%
+piece of meat uh I'm sorry maybe uh play
+ 
+
+ align:start position:0%
+piece of meat uh I'm sorry maybe uh play
+a certain sound and if the dog uh did
+
+ align:start position:0%
+a certain sound and if the dog uh did
+ 
+
+ align:start position:0%
+a certain sound and if the dog uh did
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+sit uh then Pavlov would reward it with
+
+ align:start position:0%
+sit uh then Pavlov would reward it with
+ 
+
+ align:start position:0%
+sit uh then Pavlov would reward it with
+something that acts as a reward for the
+
+ align:start position:0%
+something that acts as a reward for the
+ 
+
+ align:start position:0%
+something that acts as a reward for the
+animal uh so that's called a conditioned
+
+ align:start position:0%
+animal uh so that's called a conditioned
+ 
+
+ align:start position:0%
+animal uh so that's called a conditioned
+reflex uh you have a certain stimulus
+
+ align:start position:0%
+reflex uh you have a certain stimulus
+ 
+
+ align:start position:0%
+reflex uh you have a certain stimulus
+the animal could do a variety of things
+
+ align:start position:0%
+the animal could do a variety of things
+ 
+
+ align:start position:0%
+the animal could do a variety of things
+and you pick a particular one and you
+
+ align:start position:0%
+and you pick a particular one and you
+ 
+
+ align:start position:0%
+and you pick a particular one and you
+reward the animal if it does that
+
+ align:start position:0%
+reward the animal if it does that
+ 
+
+ align:start position:0%
+reward the animal if it does that
+particular one and then after a couple
+
+ align:start position:0%
+particular one and then after a couple
+ 
+
+ align:start position:0%
+particular one and then after a couple
+of 100 trials the dog will do exactly
+
+ align:start position:0%
+of 100 trials the dog will do exactly
+ 
+
+ align:start position:0%
+of 100 trials the dog will do exactly
+what you have been rewarding it for very
+
+ align:start position:0%
+what you have been rewarding it for very
+ 
+
+ align:start position:0%
+what you have been rewarding it for very
+reliably then if
+
+ align:start position:0%
+reliably then if
+ 
+
+ align:start position:0%
+reliably then if
+you provide the stimulus
+
+ align:start position:0%
+you provide the stimulus
+ 
+
+ align:start position:0%
+you provide the stimulus
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+uh and the animal sits or whatever you
+
+ align:start position:0%
+uh and the animal sits or whatever you
+ 
+
+ align:start position:0%
+uh and the animal sits or whatever you
+want it to
+
+ align:start position:0%
+want it to
+ 
+
+ align:start position:0%
+want it to
+do if you well the stimulus could just
+
+ align:start position:0%
+do if you well the stimulus could just
+ 
+
+ align:start position:0%
+do if you well the stimulus could just
+sit if you say sit the dog will do
+
+ align:start position:0%
+sit if you say sit the dog will do
+ 
+
+ align:start position:0%
+sit if you say sit the dog will do
+something or other or whatever it does
+
+ align:start position:0%
+something or other or whatever it does
+ 
+
+ align:start position:0%
+something or other or whatever it does
+you can regard as its response and uh if
+
+ align:start position:0%
+you can regard as its response and uh if
+ 
+
+ align:start position:0%
+you can regard as its response and uh if
+it's the response you like you reward it
+
+ align:start position:0%
+it's the response you like you reward it
+ 
+
+ align:start position:0%
+it's the response you like you reward it
+after it's very well trained to do
+
+ align:start position:0%
+after it's very well trained to do
+ 
+
+ align:start position:0%
+after it's very well trained to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh what happens if you say sit and it
+
+ align:start position:0%
+uh what happens if you say sit and it
+ 
+
+ align:start position:0%
+uh what happens if you say sit and it
+doesn't sit I'm sorry and you don't if
+
+ align:start position:0%
+doesn't sit I'm sorry and you don't if
+ 
+
+ align:start position:0%
+doesn't sit I'm sorry and you don't if
+it sits and you don't reward it uh well
+
+ align:start position:0%
+it sits and you don't reward it uh well
+ 
+
+ align:start position:0%
+it sits and you don't reward it uh well
+then it'll look
+
+ align:start position:0%
+then it'll look
+ 
+
+ align:start position:0%
+then it'll look
+puzzled and uh if you do that a few
+
+ align:start position:0%
+puzzled and uh if you do that a few
+ 
+
+ align:start position:0%
+puzzled and uh if you do that a few
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+then you'll find that when you say sit
+
+ align:start position:0%
+then you'll find that when you say sit
+ 
+
+ align:start position:0%
+then you'll find that when you say sit
+it doesn't properly sit and in fact if
+
+ align:start position:0%
+it doesn't properly sit and in fact if
+ 
+
+ align:start position:0%
+it doesn't properly sit and in fact if
+youve rewarded it a thousand times and
+
+ align:start position:0%
+youve rewarded it a thousand times and
+ 
+
+ align:start position:0%
+youve rewarded it a thousand times and
+then you give this command uh maybe 20
+
+ align:start position:0%
+then you give this command uh maybe 20
+ 
+
+ align:start position:0%
+then you give this command uh maybe 20
+times in a row and don't reward it then
+
+ align:start position:0%
+times in a row and don't reward it then
+ 
+
+ align:start position:0%
+times in a row and don't reward it then
+the 21st time it probably won't
+
+ align:start position:0%
+the 21st time it probably won't
+ 
+
+ align:start position:0%
+the 21st time it probably won't
+sit it's as though it erased the rule
+
+ align:start position:0%
+sit it's as though it erased the rule
+ 
+
+ align:start position:0%
+sit it's as though it erased the rule
+what Skinner
+
+ align:start position:0%
+what Skinner
+ 
+
+ align:start position:0%
+what Skinner
+discovered
+
+ align:start position:0%
+discovered
+ 
+
+ align:start position:0%
+discovered
+uh made a revolution in animal training
+
+ align:start position:0%
+uh made a revolution in animal training
+ 
+
+ align:start position:0%
+uh made a revolution in animal training
+I imagine a lot of lot of animal
+
+ align:start position:0%
+I imagine a lot of lot of animal
+ 
+
+ align:start position:0%
+I imagine a lot of lot of animal
+trainers knew this but they didn't
+
+ align:start position:0%
+trainers knew this but they didn't
+ 
+
+ align:start position:0%
+trainers knew this but they didn't
+publish in journals Skinner discovered
+
+ align:start position:0%
+publish in journals Skinner discovered
+ 
+
+ align:start position:0%
+publish in journals Skinner discovered
+that uh if you reward the animal every
+
+ align:start position:0%
+that uh if you reward the animal every
+ 
+
+ align:start position:0%
+that uh if you reward the animal every
+time then it's then it gets trained to
+
+ align:start position:0%
+time then it's then it gets trained to
+ 
+
+ align:start position:0%
+time then it's then it gets trained to
+produce this stimulus response event
+
+ align:start position:0%
+produce this stimulus response event
+ 
+
+ align:start position:0%
+produce this stimulus response event
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+reliably and if you stop rewarding it
+
+ align:start position:0%
+reliably and if you stop rewarding it
+ 
+
+ align:start position:0%
+reliably and if you stop rewarding it
+then it rather quickly uh stops
+
+ align:start position:0%
+then it rather quickly uh stops
+ 
+
+ align:start position:0%
+then it rather quickly uh stops
+responding in the way you've trained it
+
+ align:start position:0%
+responding in the way you've trained it
+ 
+
+ align:start position:0%
+responding in the way you've trained it
+and you might say it's
+
+ align:start position:0%
+and you might say it's
+ 
+
+ align:start position:0%
+and you might say it's
+forgotten uh
+
+ align:start position:0%
+forgotten uh
+ 
+
+ align:start position:0%
+forgotten uh
+however Skinner discovered that if you
+
+ align:start position:0%
+however Skinner discovered that if you
+ 
+
+ align:start position:0%
+however Skinner discovered that if you
+start to train it again it will very
+
+ align:start position:0%
+start to train it again it will very
+ 
+
+ align:start position:0%
+start to train it again it will very
+quickly learn maybe it will start
+
+ align:start position:0%
+quickly learn maybe it will start
+ 
+
+ align:start position:0%
+quickly learn maybe it will start
+reliably responding in just 20 trials
+
+ align:start position:0%
+reliably responding in just 20 trials
+ 
+
+ align:start position:0%
+reliably responding in just 20 trials
+instead of the maybe couple of hundred
+
+ align:start position:0%
+instead of the maybe couple of hundred
+ 
+
+ align:start position:0%
+instead of the maybe couple of hundred
+or whatever it took the first time but
+
+ align:start position:0%
+or whatever it took the first time but
+ 
+
+ align:start position:0%
+or whatever it took the first time but
+Skinner discovered another thing that
+
+ align:start position:0%
+Skinner discovered another thing that
+ 
+
+ align:start position:0%
+Skinner discovered another thing that
+hadn't uh been observed by animal
+
+ align:start position:0%
+hadn't uh been observed by animal
+ 
+
+ align:start position:0%
+hadn't uh been observed by animal
+behaviorists what happens if you tell
+
+ align:start position:0%
+behaviorists what happens if you tell
+ 
+
+ align:start position:0%
+behaviorists what happens if you tell
+the dog to sit and it does and you
+
+ align:start position:0%
+the dog to sit and it does and you
+ 
+
+ align:start position:0%
+the dog to sit and it does and you
+rewarded only say one out of every five
+
+ align:start position:0%
+rewarded only say one out of every five
+ 
+
+ align:start position:0%
+rewarded only say one out of every five
+times then it'll take a little longer to
+
+ align:start position:0%
+times then it'll take a little longer to
+ 
+
+ align:start position:0%
+times then it'll take a little longer to
+train but not
+
+ align:start position:0%
+train but not
+ 
+
+ align:start position:0%
+train but not
+much and then if you start saying sit
+
+ align:start position:0%
+much and then if you start saying sit
+ 
+
+ align:start position:0%
+much and then if you start saying sit
+and don't reward it it
+
+ align:start position:0%
+and don't reward it it
+ 
+
+ align:start position:0%
+and don't reward it it
+might continue to obey the command
+
+ align:start position:0%
+might continue to obey the command
+ 
+
+ align:start position:0%
+might continue to obey the command
+reliably for a couple of hundred times
+
+ align:start position:0%
+reliably for a couple of hundred times
+ 
+
+ align:start position:0%
+reliably for a couple of hundred times
+in other words intermittent unreliable
+
+ align:start position:0%
+in other words intermittent unreliable
+ 
+
+ align:start position:0%
+in other words intermittent unreliable
+reinforcement and and Skinner would have
+
+ align:start position:0%
+reinforcement and and Skinner would have
+ 
+
+ align:start position:0%
+reinforcement and and Skinner would have
+a random interval uh if you in fact
+
+ align:start position:0%
+a random interval uh if you in fact
+ 
+
+ align:start position:0%
+a random interval uh if you in fact
+rewarded it every five times uh some
+
+ align:start position:0%
+rewarded it every five times uh some
+ 
+
+ align:start position:0%
+rewarded it every five times uh some
+dogs would actually
+
+ align:start position:0%
+dogs would actually
+ 
+
+ align:start position:0%
+dogs would actually
+uh wait for you to order it five times
+
+ align:start position:0%
+uh wait for you to order it five times
+ 
+
+ align:start position:0%
+uh wait for you to order it five times
+before it sits uh but if you did it
+
+ align:start position:0%
+before it sits uh but if you did it
+ 
+
+ align:start position:0%
+before it sits uh but if you did it
+randomly so that it couldn't predict
+
+ align:start position:0%
+randomly so that it couldn't predict
+ 
+
+ align:start position:0%
+randomly so that it couldn't predict
+when the next reward was then it
+
+ align:start position:0%
+when the next reward was then it
+ 
+
+ align:start position:0%
+when the next reward was then it
+sometimes took as many as 50 or a 100
+
+ align:start position:0%
+sometimes took as many as 50 or a 100
+ 
+
+ align:start position:0%
+sometimes took as many as 50 or a 100
+times as long to make that response
+
+ align:start position:0%
+times as long to make that response
+ 
+
+ align:start position:0%
+times as long to make that response
+disappear U anyway that's that's
+
+ align:start position:0%
+disappear U anyway that's that's
+ 
+
+ align:start position:0%
+disappear U anyway that's that's
+something that uh isn't really often
+
+ align:start position:0%
+something that uh isn't really often
+ 
+
+ align:start position:0%
+something that uh isn't really often
+described in in the older
+
+ align:start position:0%
+described in in the older
+ 
+
+ align:start position:0%
+described in in the older
+textbooks on conditioned reflexes
+
+ align:start position:0%
+textbooks on conditioned reflexes
+ 
+
+ align:start position:0%
+textbooks on conditioned reflexes
+because it hadn't been
+
+ align:start position:0%
+because it hadn't been
+ 
+
+ align:start position:0%
+because it hadn't been
+known uh so there's when you extinguish
+
+ align:start position:0%
+known uh so there's when you extinguish
+ 
+
+ align:start position:0%
+known uh so there's when you extinguish
+a response in an animal that's been reli
+
+ align:start position:0%
+a response in an animal that's been reli
+ 
+
+ align:start position:0%
+a response in an animal that's been reli
+been constantly trained it hasn't really
+
+ align:start position:0%
+been constantly trained it hasn't really
+ 
+
+ align:start position:0%
+been constantly trained it hasn't really
+forgotten it it's somehow suppressing it
+
+ align:start position:0%
+forgotten it it's somehow suppressing it
+ 
+
+ align:start position:0%
+forgotten it it's somehow suppressing it
+and uh that was one of the reasons that
+
+ align:start position:0%
+and uh that was one of the reasons that
+ 
+
+ align:start position:0%
+and uh that was one of the reasons that
+I began to think about critics and about
+
+ align:start position:0%
+I began to think about critics and about
+ 
+
+ align:start position:0%
+I began to think about critics and about
+sensors that a memory isn't erased by
+
+ align:start position:0%
+sensors that a memory isn't erased by
+ 
+
+ align:start position:0%
+sensors that a memory isn't erased by
+non-use but it may actually get
+
+ align:start position:0%
+non-use but it may actually get
+ 
+
+ align:start position:0%
+non-use but it may actually get
+suppressed if it turns out that that
+
+ align:start position:0%
+suppressed if it turns out that that
+ 
+
+ align:start position:0%
+suppressed if it turns out that that
+response doesn't
+
+ align:start position:0%
+response doesn't
+ 
+
+ align:start position:0%
+response doesn't
+lead to success for a while so in other
+
+ align:start position:0%
+lead to success for a while so in other
+ 
+
+ align:start position:0%
+lead to success for a while so in other
+words the animal will persist much
+
+ align:start position:0%
+words the animal will persist much
+ 
+
+ align:start position:0%
+words the animal will persist much
+longer if it was randomly rewarded and
+
+ align:start position:0%
+longer if it was randomly rewarded and
+ 
+
+ align:start position:0%
+longer if it was randomly rewarded and
+again when you start rewarding it more
+
+ align:start position:0%
+again when you start rewarding it more
+ 
+
+ align:start position:0%
+again when you start rewarding it more
+often it will almost instantly jump back
+
+ align:start position:0%
+often it will almost instantly jump back
+ 
+
+ align:start position:0%
+often it will almost instantly jump back
+to the previous level of of responding
+
+ align:start position:0%
+to the previous level of of responding
+ 
+
+ align:start position:0%
+to the previous level of of responding
+reliably so that suggests that uh you're
+
+ align:start position:0%
+reliably so that suggests that uh you're
+ 
+
+ align:start position:0%
+reliably so that suggests that uh you're
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+changing now you can look at conditioned
+
+ align:start position:0%
+changing now you can look at conditioned
+ 
+
+ align:start position:0%
+changing now you can look at conditioned
+reflexes as what uh AI researchers call
+
+ align:start position:0%
+reflexes as what uh AI researchers call
+ 
+
+ align:start position:0%
+reflexes as what uh AI researchers call
+rule-based systems namely the you can
+
+ align:start position:0%
+rule-based systems namely the you can
+ 
+
+ align:start position:0%
+rule-based systems namely the you can
+think of the poor animal as just a
+
+ align:start position:0%
+think of the poor animal as just a
+ 
+
+ align:start position:0%
+think of the poor animal as just a
+catalog of uh two-part rules if this
+
+ align:start position:0%
+catalog of uh two-part rules if this
+ 
+
+ align:start position:0%
+catalog of uh two-part rules if this
+happens do that if this happens do that
+
+ align:start position:0%
+happens do that if this happens do that
+ 
+
+ align:start position:0%
+happens do that if this happens do that
+and around
+
+ align:start position:0%
+and around
+ 
+
+ align:start position:0%
+and around
+1980 one of the reasons why artificial
+
+ align:start position:0%
+1980 one of the reasons why artificial
+ 
+
+ align:start position:0%
+1980 one of the reasons why artificial
+intelligence stopped making
+
+ align:start position:0%
+intelligence stopped making
+ 
+
+ align:start position:0%
+intelligence stopped making
+progress is that before
+
+ align:start position:0%
+progress is that before
+ 
+
+ align:start position:0%
+progress is that before
+1980 uh lots of us worked on uh getting
+
+ align:start position:0%
+1980 uh lots of us worked on uh getting
+ 
+
+ align:start position:0%
+1980 uh lots of us worked on uh getting
+computers to solve really hard problems
+
+ align:start position:0%
+computers to solve really hard problems
+ 
+
+ align:start position:0%
+computers to solve really hard problems
+like uh problems in calculus or or
+
+ align:start position:0%
+like uh problems in calculus or or
+ 
+
+ align:start position:0%
+like uh problems in calculus or or
+finding new ways to uh make them better
+
+ align:start position:0%
+finding new ways to uh make them better
+ 
+
+ align:start position:0%
+finding new ways to uh make them better
+at playing games I mean people still
+
+ align:start position:0%
+at playing games I mean people still
+ 
+
+ align:start position:0%
+at playing games I mean people still
+worked on making them play games better
+
+ align:start position:0%
+worked on making them play games better
+ 
+
+ align:start position:0%
+worked on making them play games better
+but as I think I said the other day uh
+
+ align:start position:0%
+but as I think I said the other day uh
+ 
+
+ align:start position:0%
+but as I think I said the other day uh
+when deep blue W the world championship
+
+ align:start position:0%
+when deep blue W the world championship
+ 
+
+ align:start position:0%
+when deep blue W the world championship
+it didn't have a significantly larger
+
+ align:start position:0%
+it didn't have a significantly larger
+ 
+
+ align:start position:0%
+it didn't have a significantly larger
+collection of
+
+ align:start position:0%
+collection of
+ 
+
+ align:start position:0%
+collection of
+strategic uh ideas or knowledge about
+
+ align:start position:0%
+strategic uh ideas or knowledge about
+ 
+
+ align:start position:0%
+strategic uh ideas or knowledge about
+Chess than uh green blats program in 197
+
+ align:start position:0%
+Chess than uh green blats program in 197
+ 
+
+ align:start position:0%
+Chess than uh green blats program in 197
+uh which was the first U chess program
+
+ align:start position:0%
+uh which was the first U chess program
+ 
+
+ align:start position:0%
+uh which was the first U chess program
+that would reliably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beat uh not beginner chess players
+
+ align:start position:0%
+beat uh not beginner chess players
+ 
+
+ align:start position:0%
+beat uh not beginner chess players
+couldn't beat Master chess players but
+
+ align:start position:0%
+couldn't beat Master chess players but
+ 
+
+ align:start position:0%
+couldn't beat Master chess players but
+at an amateur tournament it it turned
+
+ align:start position:0%
+at an amateur tournament it it turned
+ 
+
+ align:start position:0%
+at an amateur tournament it it turned
+over one a few
+
+ align:start position:0%
+over one a few
+ 
+
+ align:start position:0%
+over one a few
+games so there was this idea of a
+
+ align:start position:0%
+games so there was this idea of a
+ 
+
+ align:start position:0%
+games so there was this idea of a
+rule-based system that became very
+
+ align:start position:0%
+rule-based system that became very
+ 
+
+ align:start position:0%
+rule-based system that became very
+popular around 1980 mainly from a PhD
+
+ align:start position:0%
+popular around 1980 mainly from a PhD
+ 
+
+ align:start position:0%
+popular around 1980 mainly from a PhD
+thesis by Ed tigan
+
+ align:start position:0%
+thesis by Ed tigan
+ 
+
+ align:start position:0%
+thesis by Ed tigan
+mam I think was a graduate student at
+
+ align:start position:0%
+mam I think was a graduate student at
+ 
+
+ align:start position:0%
+mam I think was a graduate student at
+Stanford at that time and uh it became
+
+ align:start position:0%
+Stanford at that time and uh it became
+ 
+
+ align:start position:0%
+Stanford at that time and uh it became
+very popular to say could we make
+
+ align:start position:0%
+very popular to say could we make
+ 
+
+ align:start position:0%
+very popular to say could we make
+systems that are just based on rules
+
+ align:start position:0%
+systems that are just based on rules
+ 
+
+ align:start position:0%
+systems that are just based on rules
+without any internal models or
+
+ align:start position:0%
+without any internal models or
+ 
+
+ align:start position:0%
+without any internal models or
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+reflective searches or
+
+ align:start position:0%
+reflective searches or
+ 
+
+ align:start position:0%
+reflective searches or
+whatever uh in the 1980s and progress on
+
+ align:start position:0%
+whatever uh in the 1980s and progress on
+ 
+
+ align:start position:0%
+whatever uh in the 1980s and progress on
+finding good heuristics for improving
+
+ align:start position:0%
+finding good heuristics for improving
+ 
+
+ align:start position:0%
+finding good heuristics for improving
+search processes and so forth sort of
+
+ align:start position:0%
+search processes and so forth sort of
+ 
+
+ align:start position:0%
+search processes and so forth sort of
+appeared
+
+ align:start position:0%
+appeared
+ 
+
+ align:start position:0%
+appeared
+um I just mentioned all that
+
+ align:start position:0%
+um I just mentioned all that
+ 
+
+ align:start position:0%
+um I just mentioned all that
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh you don't you see lots of commercial
+
+ align:start position:0%
+uh you don't you see lots of commercial
+ 
+
+ align:start position:0%
+uh you don't you see lots of commercial
+applications of artificial intelligence
+
+ align:start position:0%
+applications of artificial intelligence
+ 
+
+ align:start position:0%
+applications of artificial intelligence
+systems but you don't see ones that do
+
+ align:start position:0%
+systems but you don't see ones that do
+ 
+
+ align:start position:0%
+systems but you don't see ones that do
+dramatically interesting kinds of
+
+ align:start position:0%
+dramatically interesting kinds of
+ 
+
+ align:start position:0%
+dramatically interesting kinds of
+reasoning or problem solving very much
+
+ align:start position:0%
+reasoning or problem solving very much
+ 
+
+ align:start position:0%
+reasoning or problem solving very much
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+that uh so this idea of a rule-based
+
+ align:start position:0%
+that uh so this idea of a rule-based
+ 
+
+ align:start position:0%
+that uh so this idea of a rule-based
+system a collection of if then rules
+
+ align:start position:0%
+system a collection of if then rules
+ 
+
+ align:start position:0%
+system a collection of if then rules
+became popular and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh what I'm suggesting in this early
+
+ align:start position:0%
+uh uh what I'm suggesting in this early
+ 
+
+ align:start position:0%
+uh uh what I'm suggesting in this early
+part of the chapter is
+
+ align:start position:0%
+part of the chapter is
+ 
+
+ align:start position:0%
+part of the chapter is
+that if you're looking at something like
+
+ align:start position:0%
+that if you're looking at something like
+ 
+
+ align:start position:0%
+that if you're looking at something like
+human thinking uh there aren't just
+
+ align:start position:0%
+human thinking uh there aren't just
+ 
+
+ align:start position:0%
+human thinking uh there aren't just
+rules about how to react to an external
+
+ align:start position:0%
+rules about how to react to an external
+ 
+
+ align:start position:0%
+rules about how to react to an external
+situation but there might be a second
+
+ align:start position:0%
+situation but there might be a second
+ 
+
+ align:start position:0%
+situation but there might be a second
+level of the
+
+ align:start position:0%
+level of the
+ 
+
+ align:start position:0%
+level of the
+brain which is regarding the the Pavlov
+
+ align:start position:0%
+brain which is regarding the the Pavlov
+ 
+
+ align:start position:0%
+brain which is regarding the the Pavlov
+and the uh rule based system as its
+
+ align:start position:0%
+and the uh rule based system as its
+ 
+
+ align:start position:0%
+and the uh rule based system as its
+world and the second
+
+ align:start position:0%
+world and the second
+ 
+
+ align:start position:0%
+world and the second
+layer of the brain might be learning
+
+ align:start position:0%
+layer of the brain might be learning
+ 
+
+ align:start position:0%
+layer of the brain might be learning
+some ways to manipulate what happens in
+
+ align:start position:0%
+some ways to manipulate what happens in
+ 
+
+ align:start position:0%
+some ways to manipulate what happens in
+the first world in the U sensory motor
+
+ align:start position:0%
+the first world in the U sensory motor
+ 
+
+ align:start position:0%
+the first world in the U sensory motor
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+system uh why is this
+
+ align:start position:0%
+system uh why is this
+ 
+
+ align:start position:0%
+system uh why is this
+important because if you go back and
+
+ align:start position:0%
+important because if you go back and
+ 
+
+ align:start position:0%
+important because if you go back and
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+at uh Pavlov and even
+
+ align:start position:0%
+at uh Pavlov and even
+ 
+
+ align:start position:0%
+at uh Pavlov and even
+Skinner uh they kept improving their
+
+ align:start position:0%
+Skinner uh they kept improving their
+ 
+
+ align:start position:0%
+Skinner uh they kept improving their
+ideas of under what conditions a rule
+
+ align:start position:0%
+ideas of under what conditions a rule
+ 
+
+ align:start position:0%
+ideas of under what conditions a rule
+gets
+
+ align:start position:0%
+gets
+ 
+
+ align:start position:0%
+gets
+reinforced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh when you present the dog or the
+
+ align:start position:0%
+but uh when you present the dog or the
+ 
+
+ align:start position:0%
+but uh when you present the dog or the
+rat with a
+
+ align:start position:0%
+rat with a
+ 
+
+ align:start position:0%
+rat with a
+stimulus
+
+ align:start position:0%
+stimulus
+ 
+
+ align:start position:0%
+stimulus
+uh how does it decide what response to
+
+ align:start position:0%
+uh how does it decide what response to
+ 
+
+ align:start position:0%
+uh how does it decide what response to
+try and you don't see any discussion of
+
+ align:start position:0%
+try and you don't see any discussion of
+ 
+
+ align:start position:0%
+try and you don't see any discussion of
+that uh Skinner made a name for that
+
+ align:start position:0%
+that uh Skinner made a name for that
+ 
+
+ align:start position:0%
+that uh Skinner made a name for that
+that's called operant conditioning
+
+ align:start position:0%
+that's called operant conditioning
+ 
+
+ align:start position:0%
+that's called operant conditioning
+namely put the animal in situation and
+
+ align:start position:0%
+namely put the animal in situation and
+ 
+
+ align:start position:0%
+namely put the animal in situation and
+somehow animal makes a response and then
+
+ align:start position:0%
+somehow animal makes a response and then
+ 
+
+ align:start position:0%
+somehow animal makes a response and then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+reinforcement May sort of suppress or uh
+
+ align:start position:0%
+reinforcement May sort of suppress or uh
+ 
+
+ align:start position:0%
+reinforcement May sort of suppress or uh
+increase the probability or whatever
+
+ align:start position:0%
+increase the probability or whatever
+ 
+
+ align:start position:0%
+increase the probability or whatever
+however you want to describe it of that
+
+ align:start position:0%
+however you want to describe it of that
+ 
+
+ align:start position:0%
+however you want to describe it of that
+response but there isn't much talk about
+
+ align:start position:0%
+response but there isn't much talk about
+ 
+
+ align:start position:0%
+response but there isn't much talk about
+how it decides what to how to respond
+
+ align:start position:0%
+how it decides what to how to respond
+ 
+
+ align:start position:0%
+how it decides what to how to respond
+does the dog just look up in a table
+
+ align:start position:0%
+does the dog just look up in a table
+ 
+
+ align:start position:0%
+does the dog just look up in a table
+what to do when it hears the phon names
+
+ align:start position:0%
+what to do when it hears the phon names
+ 
+
+ align:start position:0%
+what to do when it hears the phon names
+in the word
+
+ align:start position:0%
+in the word
+ 
+
+ align:start position:0%
+in the word
+sit U well that's what the rulebase
+
+ align:start position:0%
+sit U well that's what the rulebase
+ 
+
+ align:start position:0%
+sit U well that's what the rulebase
+system would require that there's some
+
+ align:start position:0%
+system would require that there's some
+ 
+
+ align:start position:0%
+system would require that there's some
+sort of table which says for each uh
+
+ align:start position:0%
+sort of table which says for each uh
+ 
+
+ align:start position:0%
+sort of table which says for each uh
+input condition what should you do uh
+
+ align:start position:0%
+input condition what should you do uh
+ 
+
+ align:start position:0%
+input condition what should you do uh
+but does the dog say well
+
+ align:start position:0%
+but does the dog say well
+ 
+
+ align:start position:0%
+but does the dog say well
+uh I could do a lot of things uh the
+
+ align:start position:0%
+uh I could do a lot of things uh the
+ 
+
+ align:start position:0%
+uh I could do a lot of things uh the
+last few times that I sat I got a reward
+
+ align:start position:0%
+last few times that I sat I got a reward
+ 
+
+ align:start position:0%
+last few times that I sat I got a reward
+and uh when I didn't sit I didn't get a
+
+ align:start position:0%
+and uh when I didn't sit I didn't get a
+ 
+
+ align:start position:0%
+and uh when I didn't sit I didn't get a
+reward you don't see that kind of
+
+ align:start position:0%
+reward you don't see that kind of
+ 
+
+ align:start position:0%
+reward you don't see that kind of
+thinking in the so-called behaviorist
+
+ align:start position:0%
+thinking in the so-called behaviorist
+ 
+
+ align:start position:0%
+thinking in the so-called behaviorist
+tradition that I've been described ing
+
+ align:start position:0%
+tradition that I've been described ing
+ 
+
+ align:start position:0%
+tradition that I've been described ing
+where you just make a catalog of what
+
+ align:start position:0%
+where you just make a catalog of what
+ 
+
+ align:start position:0%
+where you just make a catalog of what
+are the behavior of the what are the
+
+ align:start position:0%
+are the behavior of the what are the
+ 
+
+ align:start position:0%
+are the behavior of the what are the
+behaviors of the animal and then try to
+
+ align:start position:0%
+behaviors of the animal and then try to
+ 
+
+ align:start position:0%
+behaviors of the animal and then try to
+make a set of rules that explains the
+
+ align:start position:0%
+make a set of rules that explains the
+ 
+
+ align:start position:0%
+make a set of rules that explains the
+behaviors that you've
+
+ align:start position:0%
+behaviors that you've
+ 
+
+ align:start position:0%
+behaviors that you've
+observed where are the rules that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say which behaviors to not
+
+ align:start position:0%
+say which behaviors to not
+ 
+
+ align:start position:0%
+say which behaviors to not
+produce and uh in an ironical way uh uh
+
+ align:start position:0%
+produce and uh in an ironical way uh uh
+ 
+
+ align:start position:0%
+produce and uh in an ironical way uh uh
+Professor Nome Chomsky who's very well
+
+ align:start position:0%
+Professor Nome Chomsky who's very well
+ 
+
+ align:start position:0%
+Professor Nome Chomsky who's very well
+known for having uh sort of won a big
+
+ align:start position:0%
+known for having uh sort of won a big
+ 
+
+ align:start position:0%
+known for having uh sort of won a big
+public argument with
+
+ align:start position:0%
+public argument with
+ 
+
+ align:start position:0%
+public argument with
+Skinner
+
+ align:start position:0%
+Skinner
+ 
+
+ align:start position:0%
+Skinner
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+has uh been described as the person
+
+ align:start position:0%
+has uh been described as the person
+ 
+
+ align:start position:0%
+has uh been described as the person
+who uh conquered the
+
+ align:start position:0%
+who uh conquered the
+ 
+
+ align:start position:0%
+who uh conquered the
+behaviorists but chsky
+
+ align:start position:0%
+behaviorists but chsky
+ 
+
+ align:start position:0%
+behaviorists but chsky
+himself is very much like Skinner in the
+
+ align:start position:0%
+himself is very much like Skinner in the
+ 
+
+ align:start position:0%
+himself is very much like Skinner in the
+sense that he's taking all the sentences
+
+ align:start position:0%
+sense that he's taking all the sentences
+ 
+
+ align:start position:0%
+sense that he's taking all the sentences
+people you say a lot of sentences to
+
+ align:start position:0%
+people you say a lot of sentences to
+ 
+
+ align:start position:0%
+people you say a lot of sentences to
+people or a lot of strings of words and
+
+ align:start position:0%
+people or a lot of strings of words and
+ 
+
+ align:start position:0%
+people or a lot of strings of words and
+the person has two responses that's a
+
+ align:start position:0%
+the person has two responses that's a
+ 
+
+ align:start position:0%
+the person has two responses that's a
+sentence that's not a
+
+ align:start position:0%
+sentence that's not a
+ 
+
+ align:start position:0%
+sentence that's not a
+sentence then uh Chomsky asks uh what
+
+ align:start position:0%
+sentence then uh Chomsky asks uh what
+ 
+
+ align:start position:0%
+sentence then uh Chomsky asks uh what
+kind
+
+ align:start position:0%
+kind
+ 
+
+ align:start position:0%
+kind
+of Machinery could produce this
+
+ align:start position:0%
+of Machinery could produce this
+ 
+
+ align:start position:0%
+of Machinery could produce this
+particular kind of
+
+ align:start position:0%
+particular kind of
+ 
+
+ align:start position:0%
+particular kind of
+behavior not the behavior of saying
+
+ align:start position:0%
+behavior not the behavior of saying
+ 
+
+ align:start position:0%
+behavior not the behavior of saying
+sentences exactly but the behavior of
+
+ align:start position:0%
+sentences exactly but the behavior of
+ 
+
+ align:start position:0%
+sentences exactly but the behavior of
+which speech actions are called
+
+ align:start position:0%
+which speech actions are called
+ 
+
+ align:start position:0%
+which speech actions are called
+sentences and then he explains that by a
+
+ align:start position:0%
+sentences and then he explains that by a
+ 
+
+ align:start position:0%
+sentences and then he explains that by a
+collection of rules which are at a table
+
+ align:start position:0%
+collection of rules which are at a table
+ 
+
+ align:start position:0%
+collection of rules which are at a table
+because they're more sophisticated and
+
+ align:start position:0%
+because they're more sophisticated and
+ 
+
+ align:start position:0%
+because they're more sophisticated and
+nested which describe the set of all
+
+ align:start position:0%
+nested which describe the set of all
+ 
+
+ align:start position:0%
+nested which describe the set of all
+possible sentences but at least in the
+
+ align:start position:0%
+possible sentences but at least in the
+ 
+
+ align:start position:0%
+possible sentences but at least in the
+older I don't know what chsky has
+
+ align:start position:0%
+older I don't know what chsky has
+ 
+
+ align:start position:0%
+older I don't know what chsky has
+written in the the last decade or so
+
+ align:start position:0%
+written in the the last decade or so
+ 
+
+ align:start position:0%
+written in the the last decade or so
+because I gave up and I may have missed
+
+ align:start position:0%
+because I gave up and I may have missed
+ 
+
+ align:start position:0%
+because I gave up and I may have missed
+some great new ideas but generally his
+
+ align:start position:0%
+some great new ideas but generally his
+ 
+
+ align:start position:0%
+some great new ideas but generally his
+descriptions
+
+ align:start position:0%
+descriptions
+ 
+
+ align:start position:0%
+descriptions
+are ways to describe the set of
+
+ align:start position:0%
+are ways to describe the set of
+ 
+
+ align:start position:0%
+are ways to describe the set of
+acceptable responses or the set of
+
+ align:start position:0%
+acceptable responses or the set of
+ 
+
+ align:start position:0%
+acceptable responses or the set of
+accept of Expressions that are regarded
+
+ align:start position:0%
+accept of Expressions that are regarded
+ 
+
+ align:start position:0%
+accept of Expressions that are regarded
+as s es without a theory of what
+
+ align:start position:0%
+as s es without a theory of what
+ 
+
+ align:start position:0%
+as s es without a theory of what
+produces them so the grammar rules are
+
+ align:start position:0%
+produces them so the grammar rules are
+ 
+
+ align:start position:0%
+produces them so the grammar rules are
+sort of like a rule-based system which
+
+ align:start position:0%
+sort of like a rule-based system which
+ 
+
+ align:start position:0%
+sort of like a rule-based system which
+when apply to an utterance will either
+
+ align:start position:0%
+when apply to an utterance will either
+ 
+
+ align:start position:0%
+when apply to an utterance will either
+accept or uh if you can find a set of
+
+ align:start position:0%
+accept or uh if you can find a set of
+ 
+
+ align:start position:0%
+accept or uh if you can find a set of
+grammar rules which produces that
+
+ align:start position:0%
+grammar rules which produces that
+ 
+
+ align:start position:0%
+grammar rules which produces that
+utterance then it's a sentence and if
+
+ align:start position:0%
+utterance then it's a sentence and if
+ 
+
+ align:start position:0%
+utterance then it's a sentence and if
+you can't then it's not so in some sense
+
+ align:start position:0%
+you can't then it's not so in some sense
+ 
+
+ align:start position:0%
+you can't then it's not so in some sense
+he's as much of a behaviorist as Skinner
+
+ align:start position:0%
+he's as much of a behaviorist as Skinner
+ 
+
+ align:start position:0%
+he's as much of a behaviorist as Skinner
+was because neither of them ask under
+
+ align:start position:0%
+was because neither of them ask under
+ 
+
+ align:start position:0%
+was because neither of them ask under
+what conditions will you produce a
+
+ align:start position:0%
+what conditions will you produce a
+ 
+
+ align:start position:0%
+what conditions will you produce a
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+sentence or even more important perhaps
+
+ align:start position:0%
+sentence or even more important perhaps
+ 
+
+ align:start position:0%
+sentence or even more important perhaps
+uh because a lot of what people say
+
+ align:start position:0%
+uh because a lot of what people say
+ 
+
+ align:start position:0%
+uh because a lot of what people say
+aren't
+
+ align:start position:0%
+aren't
+ 
+
+ align:start position:0%
+aren't
+sentences like the one I just finishing
+
+ align:start position:0%
+sentences like the one I just finishing
+ 
+
+ align:start position:0%
+sentences like the one I just finishing
+now that wasn't a sentence and you know
+
+ align:start position:0%
+now that wasn't a sentence and you know
+ 
+
+ align:start position:0%
+now that wasn't a sentence and you know
+exactly what it meant uh so it doesn't
+
+ align:start position:0%
+exactly what it meant uh so it doesn't
+ 
+
+ align:start position:0%
+exactly what it meant uh so it doesn't
+explain uh very much of human verbal
+
+ align:start position:0%
+explain uh very much of human verbal
+ 
+
+ align:start position:0%
+explain uh very much of human verbal
+Behavior Uh it does explain in in many
+
+ align:start position:0%
+Behavior Uh it does explain in in many
+ 
+
+ align:start position:0%
+Behavior Uh it does explain in in many
+cases uh which utterances after careful
+
+ align:start position:0%
+cases uh which utterances after careful
+ 
+
+ align:start position:0%
+cases uh which utterances after careful
+analysis you will
+
+ align:start position:0%
+analysis you will
+ 
+
+ align:start position:0%
+analysis you will
+decide is a sentence and that's a sort
+
+ align:start position:0%
+decide is a sentence and that's a sort
+ 
+
+ align:start position:0%
+decide is a sentence and that's a sort
+of behavioristic criteria not a
+
+ align:start position:0%
+of behavioristic criteria not a
+ 
+
+ align:start position:0%
+of behavioristic criteria not a
+cognitive one oh well enough denouncing
+
+ align:start position:0%
+cognitive one oh well enough denouncing
+ 
+
+ align:start position:0%
+cognitive one oh well enough denouncing
+chsky it's it's one of my hobbies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but it's interesting that neither
+
+ align:start position:0%
+so but it's interesting that neither
+ 
+
+ align:start position:0%
+so but it's interesting that neither
+Pavlov or Skinner discuss very much how
+
+ align:start position:0%
+Pavlov or Skinner discuss very much how
+ 
+
+ align:start position:0%
+Pavlov or Skinner discuss very much how
+does the animal decide what to
+
+ align:start position:0%
+does the animal decide what to
+ 
+
+ align:start position:0%
+does the animal decide what to
+try and obviously when you think about
+
+ align:start position:0%
+try and obviously when you think about
+ 
+
+ align:start position:0%
+try and obviously when you think about
+that for about 10 seconds you say well
+
+ align:start position:0%
+that for about 10 seconds you say well
+ 
+
+ align:start position:0%
+that for about 10 seconds you say well
+that's much more important than making a
+
+ align:start position:0%
+that's much more important than making a
+ 
+
+ align:start position:0%
+that's much more important than making a
+description from the outside of just
+
+ align:start position:0%
+description from the outside of just
+ 
+
+ align:start position:0%
+description from the outside of just
+which responses come how often to to
+
+ align:start position:0%
+which responses come how often to to
+ 
+
+ align:start position:0%
+which responses come how often to to
+which stimuli where did the responses
+
+ align:start position:0%
+which stimuli where did the responses
+ 
+
+ align:start position:0%
+which stimuli where did the responses
+themselves come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from so then the next theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is well why have two levels why not have
+
+ align:start position:0%
+is well why have two levels why not have
+ 
+
+ align:start position:0%
+is well why have two levels why not have
+another level and the main model of the
+
+ align:start position:0%
+another level and the main model of the
+ 
+
+ align:start position:0%
+another level and the main model of the
+book I shouldn't say the main one
+
+ align:start position:0%
+book I shouldn't say the main one
+ 
+
+ align:start position:0%
+book I shouldn't say the main one
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh really the strategy in the the
+
+ align:start position:0%
+uh really the strategy in the the
+ 
+
+ align:start position:0%
+uh really the strategy in the the
+emotion machine project or the the whole
+
+ align:start position:0%
+emotion machine project or the the whole
+ 
+
+ align:start position:0%
+emotion machine project or the the whole
+idea is that uh we don't want to be like
+
+ align:start position:0%
+idea is that uh we don't want to be like
+ 
+
+ align:start position:0%
+idea is that uh we don't want to be like
+physicists and say here are the laws of
+
+ align:start position:0%
+physicists and say here are the laws of
+ 
+
+ align:start position:0%
+physicists and say here are the laws of
+thought the reason for that is that uh
+
+ align:start position:0%
+thought the reason for that is that uh
+ 
+
+ align:start position:0%
+thought the reason for that is that uh
+what a physicist does is to look for a
+
+ align:start position:0%
+what a physicist does is to look for a
+ 
+
+ align:start position:0%
+what a physicist does is to look for a
+very small number of rules in the case
+
+ align:start position:0%
+very small number of rules in the case
+ 
+
+ align:start position:0%
+very small number of rules in the case
+of the human brain you know that there
+
+ align:start position:0%
+of the human brain you know that there
+ 
+
+ align:start position:0%
+of the human brain you know that there
+are 400 different pieces of machinery
+
+ align:start position:0%
+are 400 different pieces of machinery
+ 
+
+ align:start position:0%
+are 400 different pieces of machinery
+and uh the behavior of all the different
+
+ align:start position:0%
+and uh the behavior of all the different
+ 
+
+ align:start position:0%
+and uh the behavior of all the different
+mammals are quite different in some
+
+ align:start position:0%
+mammals are quite different in some
+ 
+
+ align:start position:0%
+mammals are quite different in some
+respects all they're all similar in
+
+ align:start position:0%
+respects all they're all similar in
+ 
+
+ align:start position:0%
+respects all they're all similar in
+others and so no very simple Theory
+
+ align:start position:0%
+others and so no very simple Theory
+ 
+
+ align:start position:0%
+others and so no very simple Theory
+could explain it uh the biggest part of
+
+ align:start position:0%
+could explain it uh the biggest part of
+ 
+
+ align:start position:0%
+could explain it uh the biggest part of
+the evidence from neurology is that
+
+ align:start position:0%
+the evidence from neurology is that
+ 
+
+ align:start position:0%
+the evidence from neurology is that
+there are lots of different parts of the
+
+ align:start position:0%
+there are lots of different parts of the
+ 
+
+ align:start position:0%
+there are lots of different parts of the
+brain and if you uh injure one then the
+
+ align:start position:0%
+brain and if you uh injure one then the
+ 
+
+ align:start position:0%
+brain and if you uh injure one then the
+animal's behavior changes in various
+
+ align:start position:0%
+animal's behavior changes in various
+ 
+
+ align:start position:0%
+animal's behavior changes in various
+ways it's uh usually can still solve
+
+ align:start position:0%
+ways it's uh usually can still solve
+ 
+
+ align:start position:0%
+ways it's uh usually can still solve
+lots of problems in some Realms but not
+
+ align:start position:0%
+lots of problems in some Realms but not
+ 
+
+ align:start position:0%
+lots of problems in some Realms but not
+in others and uh
+
+ align:start position:0%
+in others and uh
+ 
+
+ align:start position:0%
+in others and uh
+and uh so it wouldn't be a matter of a
+
+ align:start position:0%
+and uh so it wouldn't be a matter of a
+ 
+
+ align:start position:0%
+and uh so it wouldn't be a matter of a
+small number of uh basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principles uh then the rest of the book
+
+ align:start position:0%
+principles uh then the rest of the book
+ 
+
+ align:start position:0%
+principles uh then the rest of the book
+jumps into this idea of
+
+ align:start position:0%
+jumps into this idea of
+ 
+
+ align:start position:0%
+jumps into this idea of
+asking
+
+ align:start position:0%
+asking
+ 
+
+ align:start position:0%
+asking
+uh oh I didn't realize I had that in
+
+ align:start position:0%
+uh oh I didn't realize I had that in
+ 
+
+ align:start position:0%
+uh oh I didn't realize I had that in
+that chapter I talked a lot about the uh
+
+ align:start position:0%
+that chapter I talked a lot about the uh
+ 
+
+ align:start position:0%
+that chapter I talked a lot about the uh
+duplication and diversity there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the chapter is called
+
+ align:start position:0%
+but the chapter is called
+ 
+
+ align:start position:0%
+but the chapter is called
+Consciousness
+
+ align:start position:0%
+Consciousness
+ 
+
+ align:start position:0%
+Consciousness
+and anybody want to describe what they
+
+ align:start position:0%
+and anybody want to describe what they
+ 
+
+ align:start position:0%
+and anybody want to describe what they
+how do you how would you describe or
+
+ align:start position:0%
+how do you how would you describe or
+ 
+
+ align:start position:0%
+how do you how would you describe or
+explain when a human action is conscious
+
+ align:start position:0%
+explain when a human action is conscious
+ 
+
+ align:start position:0%
+explain when a human action is conscious
+or not anybody want to try a
+
+ align:start position:0%
+or not anybody want to try a
+ 
+
+ align:start position:0%
+or not anybody want to try a
+description when would you say you made
+
+ align:start position:0%
+description when would you say you made
+ 
+
+ align:start position:0%
+description when would you say you made
+a conscious
+
+ align:start position:0%
+a conscious
+ 
+
+ align:start position:0%
+a conscious
+decision you predicted what you wanted
+
+ align:start position:0%
+decision you predicted what you wanted
+ 
+
+ align:start position:0%
+decision you predicted what you wanted
+to do and then did it realize that all
+
+ align:start position:0%
+to do and then did it realize that all
+ 
+
+ align:start position:0%
+to do and then did it realize that all
+those things matched the conscious that
+
+ align:start position:0%
+those things matched the conscious that
+ 
+
+ align:start position:0%
+those things matched the conscious that
+you did when you had a description of
+
+ align:start position:0%
+you did when you had a description of
+ 
+
+ align:start position:0%
+you did when you had a description of
+what you were going to do already
+
+ align:start position:0%
+what you were going to do already
+ 
+
+ align:start position:0%
+what you were going to do already
+right but it needs a little more than
+
+ align:start position:0%
+right but it needs a little more than
+ 
+
+ align:start position:0%
+right but it needs a little more than
+that you have to know that you had the
+
+ align:start position:0%
+that you have to know that you had the
+ 
+
+ align:start position:0%
+that you have to know that you had the
+description what if the description were
+
+ align:start position:0%
+description what if the description were
+ 
+
+ align:start position:0%
+description what if the description were
+in in this part of your brain and and
+
+ align:start position:0%
+in in this part of your brain and and
+ 
+
+ align:start position:0%
+in in this part of your brain and and
+the part that's well actually the part
+
+ align:start position:0%
+the part that's well actually the part
+ 
+
+ align:start position:0%
+the part that's well actually the part
+of your brain that's talking is uh in
+
+ align:start position:0%
+of your brain that's talking is uh in
+ 
+
+ align:start position:0%
+of your brain that's talking is uh in
+most people on the left side so what if
+
+ align:start position:0%
+most people on the left side so what if
+ 
+
+ align:start position:0%
+most people on the left side so what if
+the description were over here
+
+ align:start position:0%
+the description were over here
+ 
+
+ align:start position:0%
+the description were over here
+and uh you weren't able to say that you
+
+ align:start position:0%
+and uh you weren't able to say that you
+ 
+
+ align:start position:0%
+and uh you weren't able to say that you
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+one what if the description were
+
+ align:start position:0%
+one what if the description were
+ 
+
+ align:start position:0%
+one what if the description were
+actually there in some other part of the
+
+ align:start position:0%
+actually there in some other part of the
+ 
+
+ align:start position:0%
+actually there in some other part of the
+brain would that be conscious or would
+
+ align:start position:0%
+brain would that be conscious or would
+ 
+
+ align:start position:0%
+brain would that be conscious or would
+it just be a matter of your being able
+
+ align:start position:0%
+it just be a matter of your being able
+ 
+
+ align:start position:0%
+it just be a matter of your being able
+to uh describe it uh with your verbal
+
+ align:start position:0%
+to uh describe it uh with your verbal
+ 
+
+ align:start position:0%
+to uh describe it uh with your verbal
+output other words how do you know what
+
+ align:start position:0%
+output other words how do you know what
+ 
+
+ align:start position:0%
+output other words how do you know what
+you're conscious of is it just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh only verbal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well of course it's not verbal uh for
+
+ align:start position:0%
+well of course it's not verbal uh for
+ 
+
+ align:start position:0%
+well of course it's not verbal uh for
+example if I'm thinking about picking up
+
+ align:start position:0%
+example if I'm thinking about picking up
+ 
+
+ align:start position:0%
+example if I'm thinking about picking up
+this coke
+
+ align:start position:0%
+this coke
+ 
+
+ align:start position:0%
+this coke
+bottle uh I'm aware
+
+ align:start position:0%
+bottle uh I'm aware
+ 
+
+ align:start position:0%
+bottle uh I'm aware
+of what would you call it a virtual in I
+
+ align:start position:0%
+of what would you call it a virtual in I
+ 
+
+ align:start position:0%
+of what would you call it a virtual in I
+have a little virtual world and I can
+
+ align:start position:0%
+have a little virtual world and I can
+ 
+
+ align:start position:0%
+have a little virtual world and I can
+feel my arm going out and uh I can feel
+
+ align:start position:0%
+feel my arm going out and uh I can feel
+ 
+
+ align:start position:0%
+feel my arm going out and uh I can feel
+that when it gets about here in touches
+
+ align:start position:0%
+that when it gets about here in touches
+ 
+
+ align:start position:0%
+that when it gets about here in touches
+it I'll get a sensation of cold and so
+
+ align:start position:0%
+it I'll get a sensation of cold and so
+ 
+
+ align:start position:0%
+it I'll get a sensation of cold and so
+forth and I presumably could do that
+
+ align:start position:0%
+forth and I presumably could do that
+ 
+
+ align:start position:0%
+forth and I presumably could do that
+without uh having had any verbal
+
+ align:start position:0%
+without uh having had any verbal
+ 
+
+ align:start position:0%
+without uh having had any verbal
+conception or of course I can't be sure
+
+ align:start position:0%
+conception or of course I can't be sure
+ 
+
+ align:start position:0%
+conception or of course I can't be sure
+that uh maybe there's a second language
+
+ align:start position:0%
+that uh maybe there's a second language
+ 
+
+ align:start position:0%
+that uh maybe there's a second language
+area that deals with
+
+ align:start position:0%
+area that deals with
+ 
+
+ align:start position:0%
+area that deals with
+semantics uh with semantic symbols that
+
+ align:start position:0%
+semantics uh with semantic symbols that
+ 
+
+ align:start position:0%
+semantics uh with semantic symbols that
+aren't words and before you speak uh
+
+ align:start position:0%
+aren't words and before you speak uh
+ 
+
+ align:start position:0%
+aren't words and before you speak uh
+that other thing is operating and if you
+
+ align:start position:0%
+that other thing is operating and if you
+ 
+
+ align:start position:0%
+that other thing is operating and if you
+don't happen to feel like talking you
+
+ align:start position:0%
+don't happen to feel like talking you
+ 
+
+ align:start position:0%
+don't happen to feel like talking you
+might never realize that you had
+
+ align:start position:0%
+might never realize that you had
+ 
+
+ align:start position:0%
+might never realize that you had
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+just below the surface of of a verbal
+
+ align:start position:0%
+just below the surface of of a verbal
+ 
+
+ align:start position:0%
+just below the surface of of a verbal
+expression for I was looking at Japanese
+
+ align:start position:0%
+expression for I was looking at Japanese
+ 
+
+ align:start position:0%
+expression for I was looking at Japanese
+characters and they they feel completely
+
+ align:start position:0%
+characters and they they feel completely
+ 
+
+ align:start position:0%
+characters and they they feel completely
+different uh from English characters
+
+ align:start position:0%
+different uh from English characters
+ 
+
+ align:start position:0%
+different uh from English characters
+because uh the words go straight up u in
+
+ align:start position:0%
+because uh the words go straight up u in
+ 
+
+ align:start position:0%
+because uh the words go straight up u in
+columns did you mean or uh straight up
+
+ align:start position:0%
+columns did you mean or uh straight up
+ 
+
+ align:start position:0%
+columns did you mean or uh straight up
+in terms of you know the features um of
+
+ align:start position:0%
+in terms of you know the features um of
+ 
+
+ align:start position:0%
+in terms of you know the features um of
+of the letters the ink I'm not conscious
+
+ align:start position:0%
+of the letters the ink I'm not conscious
+ 
+
+ align:start position:0%
+of the letters the ink I'm not conscious
+all of that I'm not conscious of the
+
+ align:start position:0%
+all of that I'm not conscious of the
+ 
+
+ align:start position:0%
+all of that I'm not conscious of the
+lines that are very particular in
+
+ align:start position:0%
+lines that are very particular in
+ 
+
+ align:start position:0%
+lines that are very particular in
+Japanese characters um but uh when I
+
+ align:start position:0%
+Japanese characters um but uh when I
+ 
+
+ align:start position:0%
+Japanese characters um but uh when I
+look at English words I I I'm instantly
+
+ align:start position:0%
+look at English words I I I'm instantly
+ 
+
+ align:start position:0%
+look at English words I I I'm instantly
+aware of the meaning of it instead of
+
+ align:start position:0%
+aware of the meaning of it instead of
+ 
+
+ align:start position:0%
+aware of the meaning of it instead of
+looking at the low level descriptions
+
+ align:start position:0%
+looking at the low level descriptions
+ 
+
+ align:start position:0%
+looking at the low level descriptions
+that are being buil that are being built
+
+ align:start position:0%
+that are being buil that are being built
+ 
+
+ align:start position:0%
+that are being buil that are being built
+up I think sometimes you can have two
+
+ align:start position:0%
+up I think sometimes you can have two
+ 
+
+ align:start position:0%
+up I think sometimes you can have two
+Japanese characters that have the same
+
+ align:start position:0%
+Japanese characters that have the same
+ 
+
+ align:start position:0%
+Japanese characters that have the same
+pronunciation can't
+
+ align:start position:0%
+pronunciation can't
+ 
+
+ align:start position:0%
+pronunciation can't
+you yeah
+
+ align:start position:0%
+you yeah
+ 
+
+ align:start position:0%
+you yeah
+because I was once uh
+
+ align:start position:0%
+because I was once uh
+ 
+
+ align:start position:0%
+because I was once uh
+watching two people talk and in Japan
+
+ align:start position:0%
+watching two people talk and in Japan
+ 
+
+ align:start position:0%
+watching two people talk and in Japan
+and the first one said something the
+
+ align:start position:0%
+and the first one said something the
+ 
+
+ align:start position:0%
+and the first one said something the
+others said didn't understand the first
+
+ align:start position:0%
+others said didn't understand the first
+ 
+
+ align:start position:0%
+others said didn't understand the first
+one as well I mean this and he made a
+
+ align:start position:0%
+one as well I mean this and he made a
+ 
+
+ align:start position:0%
+one as well I mean this and he made a
+few brush
+
+ align:start position:0%
+few brush
+ 
+
+ align:start position:0%
+few brush
+Strokes because there wasn't
+
+ align:start position:0%
+Strokes because there wasn't
+ 
+
+ align:start position:0%
+Strokes because there wasn't
+any pronouncing it more clearly wouldn't
+
+ align:start position:0%
+any pronouncing it more clearly wouldn't
+ 
+
+ align:start position:0%
+any pronouncing it more clearly wouldn't
+help what I'm try to say is that uh when
+
+ align:start position:0%
+help what I'm try to say is that uh when
+ 
+
+ align:start position:0%
+help what I'm try to say is that uh when
+we learning a language or learning
+
+ align:start position:0%
+we learning a language or learning
+ 
+
+ align:start position:0%
+we learning a language or learning
+symbols then we might be conscious of
+
+ align:start position:0%
+symbols then we might be conscious of
+ 
+
+ align:start position:0%
+symbols then we might be conscious of
+the processings that you know we are
+
+ align:start position:0%
+the processings that you know we are
+ 
+
+ align:start position:0%
+the processings that you know we are
+trying to learn from yes or the
+
+ align:start position:0%
+trying to learn from yes or the
+ 
+
+ align:start position:0%
+trying to learn from yes or the
+representations that we building but
+
+ align:start position:0%
+representations that we building but
+ 
+
+ align:start position:0%
+representations that we building but
+once we've done
+
+ align:start position:0%
+once we've done
+ 
+
+ align:start position:0%
+once we've done
+that uh then maybe we have lost the
+
+ align:start position:0%
+that uh then maybe we have lost the
+ 
+
+ align:start position:0%
+that uh then maybe we have lost the
+intermediate descriptions that build
+
+ align:start position:0%
+intermediate descriptions that build
+ 
+
+ align:start position:0%
+intermediate descriptions that build
+things on exactly it's like uh the
+
+ align:start position:0%
+things on exactly it's like uh the
+ 
+
+ align:start position:0%
+things on exactly it's like uh the
+difference between a highlevel program
+
+ align:start position:0%
+difference between a highlevel program
+ 
+
+ align:start position:0%
+difference between a highlevel program
+and a compiled
+
+ align:start position:0%
+and a compiled
+ 
+
+ align:start position:0%
+and a compiled
+one presumably when you're an
+
+ align:start position:0%
+one presumably when you're an
+ 
+
+ align:start position:0%
+one presumably when you're an
+expert uh when you're a beginner this
+
+ align:start position:0%
+expert uh when you're a beginner this
+ 
+
+ align:start position:0%
+expert uh when you're a beginner this
+teacher tells you all these rules or or
+
+ align:start position:0%
+teacher tells you all these rules or or
+ 
+
+ align:start position:0%
+teacher tells you all these rules or or
+you learn them somehow or look them up
+
+ align:start position:0%
+you learn them somehow or look them up
+ 
+
+ align:start position:0%
+you learn them somehow or look them up
+uh I actually remember
+
+ align:start position:0%
+uh I actually remember
+ 
+
+ align:start position:0%
+uh I actually remember
+uh when my father uh explained how chess
+
+ align:start position:0%
+uh when my father uh explained how chess
+ 
+
+ align:start position:0%
+uh when my father uh explained how chess
+worked and I couldn't believe anybody
+
+ align:start position:0%
+worked and I couldn't believe anybody
+ 
+
+ align:start position:0%
+worked and I couldn't believe anybody
+could do that in real time because he
+
+ align:start position:0%
+could do that in real time because he
+ 
+
+ align:start position:0%
+could do that in real time because he
+would explain that well the night can
+
+ align:start position:0%
+would explain that well the night can
+ 
+
+ align:start position:0%
+would explain that well the night can
+move two two forward and one this way or
+
+ align:start position:0%
+move two two forward and one this way or
+ 
+
+ align:start position:0%
+move two two forward and one this way or
+two this way or one this way and and
+
+ align:start position:0%
+two this way or one this way and and
+ 
+
+ align:start position:0%
+two this way or one this way and and
+there are eight different ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh after a few games uh those rules
+
+ align:start position:0%
+and uh after a few games uh those rules
+ 
+
+ align:start position:0%
+and uh after a few games uh those rules
+have disappeared and you're you've
+
+ align:start position:0%
+have disappeared and you're you've
+ 
+
+ align:start position:0%
+have disappeared and you're you've
+compiled it uh um each person must have
+
+ align:start position:0%
+compiled it uh um each person must have
+ 
+
+ align:start position:0%
+compiled it uh um each person must have
+a different uh new compiled
+
+ align:start position:0%
+a different uh new compiled
+ 
+
+ align:start position:0%
+a different uh new compiled
+representation but mine is that the
+
+ align:start position:0%
+representation but mine is that the
+ 
+
+ align:start position:0%
+representation but mine is that the
+Knight has this uh jaggedy circle around
+
+ align:start position:0%
+Knight has this uh jaggedy circle around
+ 
+
+ align:start position:0%
+Knight has this uh jaggedy circle around
+it and uh it's perfectly obvious uh if
+
+ align:start position:0%
+it and uh it's perfectly obvious uh if
+ 
+
+ align:start position:0%
+it and uh it's perfectly obvious uh if
+the night is on this black Square then
+
+ align:start position:0%
+the night is on this black Square then
+ 
+
+ align:start position:0%
+the night is on this black Square then
+these eight uh white squares uh just
+
+ align:start position:0%
+these eight uh white squares uh just
+ 
+
+ align:start position:0%
+these eight uh white squares uh just
+turn pink or something you can think of
+
+ align:start position:0%
+turn pink or something you can think of
+ 
+
+ align:start position:0%
+turn pink or something you can think of
+it as colors or something but they just
+
+ align:start position:0%
+it as colors or something but they just
+ 
+
+ align:start position:0%
+it as colors or something but they just
+jump out and wherever the night is it
+
+ align:start position:0%
+jump out and wherever the night is it
+ 
+
+ align:start position:0%
+jump out and wherever the night is it
+has this Aura around it and uh happens
+
+ align:start position:0%
+has this Aura around it and uh happens
+ 
+
+ align:start position:0%
+has this Aura around it and uh happens
+without thinking uh if you had to think
+
+ align:start position:0%
+without thinking uh if you had to think
+ 
+
+ align:start position:0%
+without thinking uh if you had to think
+you would never have time to make your
+
+ align:start position:0%
+you would never have time to make your
+ 
+
+ align:start position:0%
+you would never have time to make your
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+move well
+
+ align:start position:0%
+move well
+ 
+
+ align:start position:0%
+move well
+uh as the chapter says at the beginning
+
+ align:start position:0%
+uh as the chapter says at the beginning
+ 
+
+ align:start position:0%
+uh as the chapter says at the beginning
+there's a lot of uh great many very
+
+ align:start position:0%
+there's a lot of uh great many very
+ 
+
+ align:start position:0%
+there's a lot of uh great many very
+smart
+
+ align:start position:0%
+smart
+ 
+
+ align:start position:0%
+smart
+people uh feel that there's a big
+
+ align:start position:0%
+people uh feel that there's a big
+ 
+
+ align:start position:0%
+people uh feel that there's a big
+mystery about Consciousness could could
+
+ align:start position:0%
+mystery about Consciousness could could
+ 
+
+ align:start position:0%
+mystery about Consciousness could could
+you have a zombie machine as it's been
+
+ align:start position:0%
+you have a zombie machine as it's been
+ 
+
+ align:start position:0%
+you have a zombie machine as it's been
+called which does exactly could you have
+
+ align:start position:0%
+called which does exactly could you have
+ 
+
+ align:start position:0%
+called which does exactly could you have
+a brain uh which is just like your brain
+
+ align:start position:0%
+a brain uh which is just like your brain
+ 
+
+ align:start position:0%
+a brain uh which is just like your brain
+and it does everything uh you do it's
+
+ align:start position:0%
+and it does everything uh you do it's
+ 
+
+ align:start position:0%
+and it does everything uh you do it's
+absolutely identical to you except that
+
+ align:start position:0%
+absolutely identical to you except that
+ 
+
+ align:start position:0%
+absolutely identical to you except that
+it does it's not conscious of what it's
+
+ align:start position:0%
+it does it's not conscious of what it's
+ 
+
+ align:start position:0%
+it does it's not conscious of what it's
+doing and people like uh David Chalmer
+
+ align:start position:0%
+doing and people like uh David Chalmer
+ 
+
+ align:start position:0%
+doing and people like uh David Chalmer
+who's a well-known philosopher of
+
+ align:start position:0%
+who's a well-known philosopher of
+ 
+
+ align:start position:0%
+who's a well-known philosopher of
+Consciousness says well it's logically
+
+ align:start position:0%
+Consciousness says well it's logically
+ 
+
+ align:start position:0%
+Consciousness says well it's logically
+perfectly possible that they could be
+
+ align:start position:0%
+perfectly possible that they could be
+ 
+
+ align:start position:0%
+perfectly possible that they could be
+another person just like you with a
+
+ align:start position:0%
+another person just like you with a
+ 
+
+ align:start position:0%
+another person just like you with a
+brain just like
+
+ align:start position:0%
+brain just like
+ 
+
+ align:start position:0%
+brain just like
+yours uh except that it doesn't have any
+
+ align:start position:0%
+yours uh except that it doesn't have any
+ 
+
+ align:start position:0%
+yours uh except that it doesn't have any
+conscious
+
+ align:start position:0%
+conscious
+ 
+
+ align:start position:0%
+conscious
+experience and
+
+ align:start position:0%
+experience and
+ 
+
+ align:start position:0%
+experience and
+uh I think I might have mentioned that
+
+ align:start position:0%
+uh I think I might have mentioned that
+ 
+
+ align:start position:0%
+uh I think I might have mentioned that
+somewhere in this book when he says
+
+ align:start position:0%
+somewhere in this book when he says
+ 
+
+ align:start position:0%
+somewhere in this book when he says
+logically
+
+ align:start position:0%
+logically
+ 
+
+ align:start position:0%
+logically
+possible I think he's confused what do
+
+ align:start position:0%
+possible I think he's confused what do
+ 
+
+ align:start position:0%
+possible I think he's confused what do
+you mean log uh to say that
+
+ align:start position:0%
+you mean log uh to say that
+ 
+
+ align:start position:0%
+you mean log uh to say that
+something follows logically from another
+
+ align:start position:0%
+something follows logically from another
+ 
+
+ align:start position:0%
+something follows logically from another
+thing one statement follows logically
+
+ align:start position:0%
+thing one statement follows logically
+ 
+
+ align:start position:0%
+thing one statement follows logically
+from another statement doesn't mean
+
+ align:start position:0%
+from another statement doesn't mean
+ 
+
+ align:start position:0%
+from another statement doesn't mean
+anything by itself because the word
+
+ align:start position:0%
+anything by itself because the word
+ 
+
+ align:start position:0%
+anything by itself because the word
+logic refers generally to a set of
+
+ align:start position:0%
+logic refers generally to a set of
+ 
+
+ align:start position:0%
+logic refers generally to a set of
+axioms a set of assumptions of which the
+
+ align:start position:0%
+axioms a set of assumptions of which the
+ 
+
+ align:start position:0%
+axioms a set of assumptions of which the
+average person probably has 60 million
+
+ align:start position:0%
+average person probably has 60 million
+ 
+
+ align:start position:0%
+average person probably has 60 million
+or something like that that's that's
+
+ align:start position:0%
+or something like that that's that's
+ 
+
+ align:start position:0%
+or something like that that's that's
+my one of one of the estimates I like
+
+ align:start position:0%
+my one of one of the estimates I like
+ 
+
+ align:start position:0%
+my one of one of the estimates I like
+that a person knows the order of 50 or
+
+ align:start position:0%
+that a person knows the order of 50 or
+ 
+
+ align:start position:0%
+that a person knows the order of 50 or
+100 million fragments of information so
+
+ align:start position:0%
+100 million fragments of information so
+ 
+
+ align:start position:0%
+100 million fragments of information so
+when you say something is logic Ally
+
+ align:start position:0%
+when you say something is logic Ally
+ 
+
+ align:start position:0%
+when you say something is logic Ally
+possible that means that given these 100
+
+ align:start position:0%
+possible that means that given these 100
+ 
+
+ align:start position:0%
+possible that means that given these 100
+million uh axioms and
+
+ align:start position:0%
+million uh axioms and
+ 
+
+ align:start position:0%
+million uh axioms and
+given the rules by which you can derive
+
+ align:start position:0%
+given the rules by which you can derive
+ 
+
+ align:start position:0%
+given the rules by which you can derive
+a new sentence from one or two or more
+
+ align:start position:0%
+a new sentence from one or two or more
+ 
+
+ align:start position:0%
+a new sentence from one or two or more
+uh already established axioms or axioms
+
+ align:start position:0%
+uh already established axioms or axioms
+ 
+
+ align:start position:0%
+uh already established axioms or axioms
+or already established conclusions
+
+ align:start position:0%
+or already established conclusions
+ 
+
+ align:start position:0%
+or already established conclusions
+that's what logically possible
+
+ align:start position:0%
+that's what logically possible
+ 
+
+ align:start position:0%
+that's what logically possible
+means and chers is saying it's logically
+
+ align:start position:0%
+means and chers is saying it's logically
+ 
+
+ align:start position:0%
+means and chers is saying it's logically
+possible in the sense that uh he thinks
+
+ align:start position:0%
+possible in the sense that uh he thinks
+ 
+
+ align:start position:0%
+possible in the sense that uh he thinks
+he can imagine
+
+ align:start position:0%
+he can imagine
+ 
+
+ align:start position:0%
+he can imagine
+these two machines one of which is
+
+ align:start position:0%
+these two machines one of which is
+ 
+
+ align:start position:0%
+these two machines one of which is
+conscious and one isn't but they're
+
+ align:start position:0%
+conscious and one isn't but they're
+ 
+
+ align:start position:0%
+conscious and one isn't but they're
+otherwise the
+
+ align:start position:0%
+otherwise the
+ 
+
+ align:start position:0%
+otherwise the
+same there's nothing logical about it I
+
+ align:start position:0%
+same there's nothing logical about it I
+ 
+
+ align:start position:0%
+same there's nothing logical about it I
+don't believe he can imagine either of
+
+ align:start position:0%
+don't believe he can imagine either of
+ 
+
+ align:start position:0%
+don't believe he can imagine either of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+machines he can only make sentences
+
+ align:start position:0%
+machines he can only make sentences
+ 
+
+ align:start position:0%
+machines he can only make sentences
+about them and publish them and convince
+
+ align:start position:0%
+about them and publish them and convince
+ 
+
+ align:start position:0%
+about them and publish them and convince
+other people that they make sense how do
+
+ align:start position:0%
+other people that they make sense how do
+ 
+
+ align:start position:0%
+other people that they make sense how do
+you imagine a machine that's the same as
+
+ align:start position:0%
+you imagine a machine that's the same as
+ 
+
+ align:start position:0%
+you imagine a machine that's the same as
+you but it's not
+
+ align:start position:0%
+you but it's not
+ 
+
+ align:start position:0%
+you but it's not
+conscious all you can do is Imagine that
+
+ align:start position:0%
+conscious all you can do is Imagine that
+ 
+
+ align:start position:0%
+conscious all you can do is Imagine that
+somebody would uh would understand that
+
+ align:start position:0%
+somebody would uh would understand that
+ 
+
+ align:start position:0%
+somebody would uh would understand that
+sentence in some way
+
+ align:start position:0%
+sentence in some way
+ 
+
+ align:start position:0%
+sentence in some way
+yeah could we could we build like a very
+
+ align:start position:0%
+yeah could we could we build like a very
+ 
+
+ align:start position:0%
+yeah could we could we build like a very
+simple block world uh with a character
+
+ align:start position:0%
+simple block world uh with a character
+ 
+
+ align:start position:0%
+simple block world uh with a character
+there doing something that people would
+
+ align:start position:0%
+there doing something that people would
+ 
+
+ align:start position:0%
+there doing something that people would
+agree that it's conscious of
+
+ align:start position:0%
+agree that it's conscious of
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+
+ align:start position:0%
+agree that it's conscious of
+itself well they'd have to Define
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+ align:start position:0%
+itself well they'd have to Define
+ 
+
+ align:start position:0%
+itself well they'd have to Define
+conscious well I mean that agree that
+
+ align:start position:0%
+conscious well I mean that agree that
+ 
+
+ align:start position:0%
+conscious well I mean that agree that
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+
+ align:start position:0%
+you know if I think that this guy's
+ 
+
+ align:start position:0%
+you know if I think that this guy's
+conscious then that guy's conscious mhm
+
+ align:start position:0%
+conscious then that guy's conscious mhm
+ 
+
+ align:start position:0%
+conscious then that guy's conscious mhm
+I'm not sure what you're saying you're
+
+ align:start position:0%
+I'm not sure what you're saying you're
+ 
+
+ align:start position:0%
+I'm not sure what you're saying you're
+saying well let's assume that he's
+
+ align:start position:0%
+saying well let's assume that he's
+ 
+
+ align:start position:0%
+saying well let's assume that he's
+conscious and he and the and they behave
+
+ align:start position:0%
+conscious and he and the and they behave
+ 
+
+ align:start position:0%
+conscious and he and the and they behave
+the same they behave the same they speak
+
+ align:start position:0%
+the same they behave the same they speak
+ 
+
+ align:start position:0%
+the same they behave the same they speak
+the same language all right but what is
+
+ align:start position:0%
+the same language all right but what is
+ 
+
+ align:start position:0%
+the same language all right but what is
+it you're
+
+ align:start position:0%
+it you're
+ 
+
+ align:start position:0%
+it you're
+imagining uh I'm I'm imagining uh a
+
+ align:start position:0%
+imagining uh I'm I'm imagining uh a
+ 
+
+ align:start position:0%
+imagining uh I'm I'm imagining uh a
+blocks world uh system which has uh a
+
+ align:start position:0%
+blocks world uh system which has uh a
+ 
+
+ align:start position:0%
+blocks world uh system which has uh a
+few guys in it uh who are building
+
+ align:start position:0%
+few guys in it uh who are building
+ 
+
+ align:start position:0%
+few guys in it uh who are building
+something or doing something M and
+
+ align:start position:0%
+something or doing something M and
+ 
+
+ align:start position:0%
+something or doing something M and
+uh and it has a lot of is that let's say
+
+ align:start position:0%
+uh and it has a lot of is that let's say
+ 
+
+ align:start position:0%
+uh and it has a lot of is that let's say
+you were talking about and would would
+
+ align:start position:0%
+you were talking about and would would
+ 
+
+ align:start position:0%
+you were talking about and would would
+people agree that those characters are
+
+ align:start position:0%
+people agree that those characters are
+ 
+
+ align:start position:0%
+people agree that those characters are
+conscious what's the test like what's
+
+ align:start position:0%
+conscious what's the test like what's
+ 
+
+ align:start position:0%
+conscious what's the test like what's
+the how would they what would it mean
+
+ align:start position:0%
+the how would they what would it mean
+ 
+
+ align:start position:0%
+the how would they what would it mean
+what matter would it be if they agreed
+
+ align:start position:0%
+what matter would it be if they agreed
+ 
+
+ align:start position:0%
+what matter would it be if they agreed
+what would they
+
+ align:start position:0%
+what would they
+ 
+
+ align:start position:0%
+what would they
+mean um well if the machines are the
+
+ align:start position:0%
+mean um well if the machines are the
+ 
+
+ align:start position:0%
+mean um well if the machines are the
+same and you're saying well I can
+
+ align:start position:0%
+same and you're saying well I can
+ 
+
+ align:start position:0%
+same and you're saying well I can
+imagine that this machine isn't
+
+ align:start position:0%
+imagine that this machine isn't
+ 
+
+ align:start position:0%
+imagine that this machine isn't
+conscious and this one is I don't see
+
+ align:start position:0%
+conscious and this one is I don't see
+ 
+
+ align:start position:0%
+conscious and this one is I don't see
+what you're imagining well finding the
+
+ align:start position:0%
+what you're imagining well finding the
+ 
+
+ align:start position:0%
+what you're imagining well finding the
+word Consciousness but I don't even know
+
+ align:start position:0%
+word Consciousness but I don't even know
+ 
+
+ align:start position:0%
+word Consciousness but I don't even know
+what it means M then how can you imagine
+
+ align:start position:0%
+what it means M then how can you imagine
+ 
+
+ align:start position:0%
+what it means M then how can you imagine
+what it would be from this one not to be
+
+ align:start position:0%
+what it would be from this one not to be
+ 
+
+ align:start position:0%
+what it would be from this one not to be
+conscious if you have no idea what it
+
+ align:start position:0%
+conscious if you have no idea what it
+ 
+
+ align:start position:0%
+conscious if you have no idea what it
+means yeah but but I'm saying those
+
+ align:start position:0%
+means yeah but but I'm saying those
+ 
+
+ align:start position:0%
+means yeah but but I'm saying those
+people aree those people who who are
+
+ align:start position:0%
+people aree those people who who are
+ 
+
+ align:start position:0%
+people aree those people who who are
+trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find well I'm just saying in my opinion
+
+ align:start position:0%
+find well I'm just saying in my opinion
+ 
+
+ align:start position:0%
+find well I'm just saying in my opinion
+Chalmer doesn't have any idea of what
+
+ align:start position:0%
+Chalmer doesn't have any idea of what
+ 
+
+ align:start position:0%
+Chalmer doesn't have any idea of what
+that would
+
+ align:start position:0%
+that would
+ 
+
+ align:start position:0%
+that would
+mean and so he says it's logically
+
+ align:start position:0%
+mean and so he says it's logically
+ 
+
+ align:start position:0%
+mean and so he says it's logically
+possible meaning I can't imagine anyone
+
+ align:start position:0%
+possible meaning I can't imagine anyone
+ 
+
+ align:start position:0%
+possible meaning I can't imagine anyone
+objecting to this or something like that
+
+ align:start position:0%
+objecting to this or something like that
+ 
+
+ align:start position:0%
+objecting to this or something like that
+it's he's not making a statement about
+
+ align:start position:0%
+it's he's not making a statement about
+ 
+
+ align:start position:0%
+it's he's not making a statement about
+Consciousness because he's saying that's
+
+ align:start position:0%
+Consciousness because he's saying that's
+ 
+
+ align:start position:0%
+Consciousness because he's saying that's
+a mystery I don't know what it is I
+
+ align:start position:0%
+a mystery I don't know what it is I
+ 
+
+ align:start position:0%
+a mystery I don't know what it is I
+don't think it's describable in physical
+
+ align:start position:0%
+don't think it's describable in physical
+ 
+
+ align:start position:0%
+don't think it's describable in physical
+terms he has all these negative things
+
+ align:start position:0%
+terms he has all these negative things
+ 
+
+ align:start position:0%
+terms he has all these negative things
+he says this is a very hard problem
+
+ align:start position:0%
+he says this is a very hard problem
+ 
+
+ align:start position:0%
+he says this is a very hard problem
+which probably no one will ever
+
+ align:start position:0%
+which probably no one will ever
+ 
+
+ align:start position:0%
+which probably no one will ever
+solve but I don't think when he says
+
+ align:start position:0%
+solve but I don't think when he says
+ 
+
+ align:start position:0%
+solve but I don't think when he says
+it's logically possible that there's
+
+ align:start position:0%
+it's logically possible that there's
+ 
+
+ align:start position:0%
+it's logically possible that there's
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+difference as uh pen Gillette would say
+
+ align:start position:0%
+difference as uh pen Gillette would say
+ 
+
+ align:start position:0%
+difference as uh pen Gillette would say
+I I think that's just word
+
+ align:start position:0%
+I I think that's just word
+ 
+
+ align:start position:0%
+I I think that's just word
+salad that you look at that and say
+
+ align:start position:0%
+salad that you look at that and say
+ 
+
+ align:start position:0%
+salad that you look at that and say
+well Chalmer is saying that he sees some
+
+ align:start position:0%
+well Chalmer is saying that he sees some
+ 
+
+ align:start position:0%
+well Chalmer is saying that he sees some
+meaning in this
+
+ align:start position:0%
+meaning in this
+ 
+
+ align:start position:0%
+meaning in this
+assertion but I don't see any reason to
+
+ align:start position:0%
+assertion but I don't see any reason to
+ 
+
+ align:start position:0%
+assertion but I don't see any reason to
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+him U maybe because I don't see him as
+
+ align:start position:0%
+him U maybe because I don't see him as
+ 
+
+ align:start position:0%
+him U maybe because I don't see him as
+ever having any other good ideas about
+
+ align:start position:0%
+ever having any other good ideas about
+ 
+
+ align:start position:0%
+ever having any other good ideas about
+psychology well that's
+
+ align:start position:0%
+psychology well that's
+ 
+
+ align:start position:0%
+psychology well that's
+mean maybe he has
+
+ align:start position:0%
+mean maybe he has
+ 
+
+ align:start position:0%
+mean maybe he has
+had but in fact what I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the trick in this chapter I think this
+
+ align:start position:0%
+the trick in this chapter I think this
+ 
+
+ align:start position:0%
+the trick in this chapter I think this
+is sort of original maybe you've seen
+
+ align:start position:0%
+is sort of original maybe you've seen
+ 
+
+ align:start position:0%
+is sort of original maybe you've seen
+something like it but uh what I try to
+
+ align:start position:0%
+something like it but uh what I try to
+ 
+
+ align:start position:0%
+something like it but uh what I try to
+do is be a little more
+
+ align:start position:0%
+do is be a little more
+ 
+
+ align:start position:0%
+do is be a little more
+behavioristic and
+
+ align:start position:0%
+behavioristic and
+ 
+
+ align:start position:0%
+behavioristic and
+say uh what's going on when a person
+
+ align:start position:0%
+say uh what's going on when a person
+ 
+
+ align:start position:0%
+say uh what's going on when a person
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+uh I consciously decided to uh pick up
+
+ align:start position:0%
+uh I consciously decided to uh pick up
+ 
+
+ align:start position:0%
+uh I consciously decided to uh pick up
+that bottle of
+
+ align:start position:0%
+that bottle of
+ 
+
+ align:start position:0%
+that bottle of
+coke uh something like that what do what
+
+ align:start position:0%
+coke uh something like that what do what
+ 
+
+ align:start position:0%
+coke uh something like that what do what
+do you think is happening in a person's
+
+ align:start position:0%
+do you think is happening in a person's
+ 
+
+ align:start position:0%
+do you think is happening in a person's
+mind when they use the word conscious
+
+ align:start position:0%
+mind when they use the word conscious
+ 
+
+ align:start position:0%
+mind when they use the word conscious
+and the first chap part of the chapter
+
+ align:start position:0%
+and the first chap part of the chapter
+ 
+
+ align:start position:0%
+and the first chap part of the chapter
+you remember about Joan crossing the
+
+ align:start position:0%
+you remember about Joan crossing the
+ 
+
+ align:start position:0%
+you remember about Joan crossing the
+street describes about uh 20 or 30
+
+ align:start position:0%
+street describes about uh 20 or 30
+ 
+
+ align:start position:0%
+street describes about uh 20 or 30
+different kinds of things that must have
+
+ align:start position:0%
+different kinds of things that must have
+ 
+
+ align:start position:0%
+different kinds of things that must have
+been going on in her mind uh when when
+
+ align:start position:0%
+been going on in her mind uh when when
+ 
+
+ align:start position:0%
+been going on in her mind uh when when
+she was making that decision and I left
+
+ align:start position:0%
+she was making that decision and I left
+ 
+
+ align:start position:0%
+she was making that decision and I left
+it to the reader to say well I think
+
+ align:start position:0%
+it to the reader to say well I think
+ 
+
+ align:start position:0%
+it to the reader to say well I think
+this one where she's thinking about her
+
+ align:start position:0%
+this one where she's thinking about her
+ 
+
+ align:start position:0%
+this one where she's thinking about her
+recent thoughts as conscious or or not
+
+ align:start position:0%
+recent thoughts as conscious or or not
+ 
+
+ align:start position:0%
+recent thoughts as conscious or or not
+and so forth so I didn't say when I
+
+ align:start position:0%
+and so forth so I didn't say when I
+ 
+
+ align:start position:0%
+and so forth so I didn't say when I
+listed those 30 things mental activities
+
+ align:start position:0%
+listed those 30 things mental activities
+ 
+
+ align:start position:0%
+listed those 30 things mental activities
+that she was in I didn't
+
+ align:start position:0%
+that she was in I didn't
+ 
+
+ align:start position:0%
+that she was in I didn't
+uh actually in the first draft I tried
+
+ align:start position:0%
+uh actually in the first draft I tried
+ 
+
+ align:start position:0%
+uh actually in the first draft I tried
+to make a judgment about which ones the
+
+ align:start position:0%
+to make a judgment about which ones the
+ 
+
+ align:start position:0%
+to make a judgment about which ones the
+average person would call conscious and
+
+ align:start position:0%
+average person would call conscious and
+ 
+
+ align:start position:0%
+average person would call conscious and
+then I gave up but uh but then I thought
+
+ align:start position:0%
+then I gave up but uh but then I thought
+ 
+
+ align:start position:0%
+then I gave up but uh but then I thought
+about it a lot more and so in this
+
+ align:start position:0%
+about it a lot more and so in this
+ 
+
+ align:start position:0%
+about it a lot more and so in this
+section I was saying well
+
+ align:start position:0%
+section I was saying well
+ 
+
+ align:start position:0%
+section I was saying well
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+somebody says that uh they did something
+
+ align:start position:0%
+somebody says that uh they did something
+ 
+
+ align:start position:0%
+somebody says that uh they did something
+consciously uh what could they be saying
+
+ align:start position:0%
+consciously uh what could they be saying
+ 
+
+ align:start position:0%
+consciously uh what could they be saying
+and after a while I decided
+
+ align:start position:0%
+and after a while I decided
+ 
+
+ align:start position:0%
+and after a while I decided
+that it uh very likely uses these four
+
+ align:start position:0%
+that it uh very likely uses these four
+ 
+
+ align:start position:0%
+that it uh very likely uses these four
+properties which are sort of
+
+ align:start position:0%
+properties which are sort of
+ 
+
+ align:start position:0%
+properties which are sort of
+computational ones so one thing is when
+
+ align:start position:0%
+computational ones so one thing is when
+ 
+
+ align:start position:0%
+computational ones so one thing is when
+you talk about conscious uh one feature
+
+ align:start position:0%
+you talk about conscious uh one feature
+ 
+
+ align:start position:0%
+you talk about conscious uh one feature
+is that you're talking about yourself
+
+ align:start position:0%
+is that you're talking about yourself
+ 
+
+ align:start position:0%
+is that you're talking about yourself
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+explicitly you don't say a conscious
+
+ align:start position:0%
+explicitly you don't say a conscious
+ 
+
+ align:start position:0%
+explicitly you don't say a conscious
+decision was made you say I made this
+
+ align:start position:0%
+decision was made you say I made this
+ 
+
+ align:start position:0%
+decision was made you say I made this
+decision consciously what do you mean by
+
+ align:start position:0%
+decision consciously what do you mean by
+ 
+
+ align:start position:0%
+decision consciously what do you mean by
+I and I doesn't mean you I means or me I
+
+ align:start position:0%
+I and I doesn't mean you I means or me I
+ 
+
+ align:start position:0%
+I and I doesn't mean you I means or me I
+means uh the current process is using a
+
+ align:start position:0%
+means uh the current process is using a
+ 
+
+ align:start position:0%
+means uh the current process is using a
+model of
+
+ align:start position:0%
+model of
+ 
+
+ align:start position:0%
+model of
+myself I'm a big machine somewhere in
+
+ align:start position:0%
+myself I'm a big machine somewhere in
+ 
+
+ align:start position:0%
+myself I'm a big machine somewhere in
+this machine is something that it often
+
+ align:start position:0%
+this machine is something that it often
+ 
+
+ align:start position:0%
+this machine is something that it often
+uses to make predictions of what uh what
+
+ align:start position:0%
+uses to make predictions of what uh what
+ 
+
+ align:start position:0%
+uses to make predictions of what uh what
+the body of this machine will do or what
+
+ align:start position:0%
+the body of this machine will do or what
+ 
+
+ align:start position:0%
+the body of this machine will do or what
+the mouth of this words the mouth of
+
+ align:start position:0%
+the mouth of this words the mouth of
+ 
+
+ align:start position:0%
+the mouth of this words the mouth of
+this machine will speak or something and
+
+ align:start position:0%
+this machine will speak or something and
+ 
+
+ align:start position:0%
+this machine will speak or something and
+so the word I means that you're thinking
+
+ align:start position:0%
+so the word I means that you're thinking
+ 
+
+ align:start position:0%
+so the word I means that you're thinking
+about some representation or uh theory
+
+ align:start position:0%
+about some representation or uh theory
+ 
+
+ align:start position:0%
+about some representation or uh theory
+about what's inside your head assuming
+
+ align:start position:0%
+about what's inside your head assuming
+ 
+
+ align:start position:0%
+about what's inside your head assuming
+that uh like most westerners you think
+
+ align:start position:0%
+that uh like most westerners you think
+ 
+
+ align:start position:0%
+that uh like most westerners you think
+your mind is in your head I've been told
+
+ align:start position:0%
+your mind is in your head I've been told
+ 
+
+ align:start position:0%
+your mind is in your head I've been told
+that uh in some other cultures people
+
+ align:start position:0%
+that uh in some other cultures people
+ 
+
+ align:start position:0%
+that uh in some other cultures people
+think the mind is in your chest or your
+
+ align:start position:0%
+think the mind is in your chest or your
+ 
+
+ align:start position:0%
+think the mind is in your chest or your
+belly but uh I don't believe them
+
+ align:start position:0%
+belly but uh I don't believe them
+ 
+
+ align:start position:0%
+belly but uh I don't believe them
+exuse me yeah we have very simplistic uh
+
+ align:start position:0%
+exuse me yeah we have very simplistic uh
+ 
+
+ align:start position:0%
+exuse me yeah we have very simplistic uh
+descriptions of
+
+ align:start position:0%
+descriptions of
+ 
+
+ align:start position:0%
+descriptions of
+self among your descriptions of self are
+
+ align:start position:0%
+self among your descriptions of self are
+ 
+
+ align:start position:0%
+self among your descriptions of self are
+some simplistic ones is that what you're
+
+ align:start position:0%
+some simplistic ones is that what you're
+ 
+
+ align:start position:0%
+some simplistic ones is that what you're
+saying I'm saying most people have
+
+ align:start position:0%
+saying I'm saying most people have
+ 
+
+ align:start position:0%
+saying I'm saying most people have
+simple descriptions of the self
+
+ align:start position:0%
+simple descriptions of the self
+ 
+
+ align:start position:0%
+simple descriptions of the self
+otherwise they would find it very hard
+
+ align:start position:0%
+otherwise they would find it very hard
+ 
+
+ align:start position:0%
+otherwise they would find it very hard
+to say something like I did well no
+
+ align:start position:0%
+to say something like I did well no
+ 
+
+ align:start position:0%
+to say something like I did well no
+they're when they say I they're
+
+ align:start position:0%
+they're when they say I they're
+ 
+
+ align:start position:0%
+they're when they say I they're
+using if you had if you understood your
+
+ align:start position:0%
+using if you had if you understood your
+ 
+
+ align:start position:0%
+using if you had if you understood your
+conflix then you would be like oh it
+
+ align:start position:0%
+conflix then you would be like oh it
+ 
+
+ align:start position:0%
+conflix then you would be like oh it
+doesn't mean anything this part of my
+
+ align:start position:0%
+doesn't mean anything this part of my
+ 
+
+ align:start position:0%
+doesn't mean anything this part of my
+brain said this and this part of my
+
+ align:start position:0%
+brain said this and this part of my
+ 
+
+ align:start position:0%
+brain said this and this part of my
+brain said this and this hand yeah but
+
+ align:start position:0%
+brain said this and this hand yeah but
+ 
+
+ align:start position:0%
+brain said this and this hand yeah but
+the Talking part of your brain is using
+
+ align:start position:0%
+the Talking part of your brain is using
+ 
+
+ align:start position:0%
+the Talking part of your brain is using
+this word I and like any a matter ofing
+
+ align:start position:0%
+this word I and like any a matter ofing
+ 
+
+ align:start position:0%
+this word I and like any a matter ofing
+I mean you could P yourself to
+
+ align:start position:0%
+I mean you could P yourself to
+ 
+
+ align:start position:0%
+I mean you could P yourself to
+completely make the word I not mean
+
+ align:start position:0%
+completely make the word I not mean
+ 
+
+ align:start position:0%
+completely make the word I not mean
+anything well Freud says my SEC super
+
+ align:start position:0%
+anything well Freud says my SEC super
+ 
+
+ align:start position:0%
+anything well Freud says my SEC super
+ego does this and my ID does this and my
+
+ align:start position:0%
+ego does this and my ID does this and my
+ 
+
+ align:start position:0%
+ego does this and my ID does this and my
+ego does this so yes you can train
+
+ align:start position:0%
+ego does this so yes you can train
+ 
+
+ align:start position:0%
+ego does this so yes you can train
+yourself to regard yourself is made of
+
+ align:start position:0%
+yourself to regard yourself is made of
+ 
+
+ align:start position:0%
+yourself to regard yourself is made of
+three parts and most people don't but
+
+ align:start position:0%
+three parts and most people don't but
+ 
+
+ align:start position:0%
+three parts and most people don't but
+even if you don't you still may have 16
+
+ align:start position:0%
+even if you don't you still may have 16
+ 
+
+ align:start position:0%
+even if you don't you still may have 16
+models and just like the word chair uh
+
+ align:start position:0%
+models and just like the word chair uh
+ 
+
+ align:start position:0%
+models and just like the word chair uh
+you use it as though it were you don't
+
+ align:start position:0%
+you use it as though it were you don't
+ 
+
+ align:start position:0%
+you use it as though it were you don't
+disambiguate it uh because a at the
+
+ align:start position:0%
+disambiguate it uh because a at the
+ 
+
+ align:start position:0%
+disambiguate it uh because a at the
+moment you're not you don't have a
+
+ align:start position:0%
+moment you're not you don't have a
+ 
+
+ align:start position:0%
+moment you're not you don't have a
+representation of yourself as a lot of
+
+ align:start position:0%
+representation of yourself as a lot of
+ 
+
+ align:start position:0%
+representation of yourself as a lot of
+subs or as a chair uh you might have a
+
+ align:start position:0%
+subs or as a chair uh you might have a
+ 
+
+ align:start position:0%
+subs or as a chair uh you might have a
+representation as something that you
+
+ align:start position:0%
+representation as something that you
+ 
+
+ align:start position:0%
+representation as something that you
+could sit on and you don't say uh it's a
+
+ align:start position:0%
+could sit on and you don't say uh it's a
+ 
+
+ align:start position:0%
+could sit on and you don't say uh it's a
+chair like this or it's a bamboo chair
+
+ align:start position:0%
+chair like this or it's a bamboo chair
+ 
+
+ align:start position:0%
+chair like this or it's a bamboo chair
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+um or a five-legged office chair and so
+
+ align:start position:0%
+um or a five-legged office chair and so
+ 
+
+ align:start position:0%
+um or a five-legged office chair and so
+forth even though every one of you
+
+ align:start position:0%
+forth even though every one of you
+ 
+
+ align:start position:0%
+forth even though every one of you
+probably has 50 or 60 rather different
+
+ align:start position:0%
+probably has 50 or 60 rather different
+ 
+
+ align:start position:0%
+probably has 50 or 60 rather different
+objects that you'd recognize as a chair
+
+ align:start position:0%
+objects that you'd recognize as a chair
+ 
+
+ align:start position:0%
+objects that you'd recognize as a chair
+that doesn't bother you when say I'm
+
+ align:start position:0%
+that doesn't bother you when say I'm
+ 
+
+ align:start position:0%
+that doesn't bother you when say I'm
+looking for something to a chair to sit
+
+ align:start position:0%
+looking for something to a chair to sit
+ 
+
+ align:start position:0%
+looking for something to a chair to sit
+on there's a dollhouse chair which you
+
+ align:start position:0%
+on there's a dollhouse chair which you
+ 
+
+ align:start position:0%
+on there's a dollhouse chair which you
+can't sit on but it's still a chair
+
+ align:start position:0%
+can't sit on but it's still a chair
+ 
+
+ align:start position:0%
+can't sit on but it's still a chair
+right I think in society Society of Mind
+
+ align:start position:0%
+right I think in society Society of Mind
+ 
+
+ align:start position:0%
+right I think in society Society of Mind
+I don't know if I had it in this book
+
+ align:start position:0%
+I don't know if I had it in this book
+ 
+
+ align:start position:0%
+I don't know if I had it in this book
+there's a picture of a broken chair
+
+ align:start position:0%
+there's a picture of a broken chair
+ 
+
+ align:start position:0%
+there's a picture of a broken chair
+which which if you sat on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would you would break your hip or
+
+ align:start position:0%
+would you would break your hip or
+ 
+
+ align:start position:0%
+would you would break your hip or
+something so when you use conscious I
+
+ align:start position:0%
+something so when you use conscious I
+ 
+
+ align:start position:0%
+something so when you use conscious I
+think one thing that you do is uh you're
+
+ align:start position:0%
+think one thing that you do is uh you're
+ 
+
+ align:start position:0%
+think one thing that you do is uh you're
+using some representation of yourself or
+
+ align:start position:0%
+using some representation of yourself or
+ 
+
+ align:start position:0%
+using some representation of yourself or
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+several another thing I think although
+
+ align:start position:0%
+several another thing I think although
+ 
+
+ align:start position:0%
+several another thing I think although
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is that doesn't seem quite in fact the
+
+ align:start position:0%
+is that doesn't seem quite in fact the
+ 
+
+ align:start position:0%
+is that doesn't seem quite in fact the
+next two aren't aren't quite so
+
+ align:start position:0%
+next two aren't aren't quite so
+ 
+
+ align:start position:0%
+next two aren't aren't quite so
+necessary I think when people talk about
+
+ align:start position:0%
+necessary I think when people talk about
+ 
+
+ align:start position:0%
+necessary I think when people talk about
+being conscious of something they
+
+ align:start position:0%
+being conscious of something they
+ 
+
+ align:start position:0%
+being conscious of something they
+usually mean that they're aware of some
+
+ align:start position:0%
+usually mean that they're aware of some
+ 
+
+ align:start position:0%
+usually mean that they're aware of some
+kind of Serial sequential process they
+
+ align:start position:0%
+kind of Serial sequential process they
+ 
+
+ align:start position:0%
+kind of Serial sequential process they
+can they can say uh I thought this first
+
+ align:start position:0%
+can they can say uh I thought this first
+ 
+
+ align:start position:0%
+can they can say uh I thought this first
+and that first and and so forth uh not
+
+ align:start position:0%
+and that first and and so forth uh not
+ 
+
+ align:start position:0%
+and that first and and so forth uh not
+too insistent on that uh I'm pretty sure
+
+ align:start position:0%
+too insistent on that uh I'm pretty sure
+ 
+
+ align:start position:0%
+too insistent on that uh I'm pretty sure
+that there that it means that of course
+
+ align:start position:0%
+that there that it means that of course
+ 
+
+ align:start position:0%
+that there that it means that of course
+parts of their brain are reacting in a
+
+ align:start position:0%
+parts of their brain are reacting in a
+ 
+
+ align:start position:0%
+parts of their brain are reacting in a
+St using a statistical baset or
+
+ align:start position:0%
+St using a statistical baset or
+ 
+
+ align:start position:0%
+St using a statistical baset or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+and one of the features of a statistical
+
+ align:start position:0%
+and one of the features of a statistical
+ 
+
+ align:start position:0%
+and one of the features of a statistical
+baset is inputs come in and outputs go
+
+ align:start position:0%
+baset is inputs come in and outputs go
+ 
+
+ align:start position:0%
+baset is inputs come in and outputs go
+out and if you stuck some probes in the
+
+ align:start position:0%
+out and if you stuck some probes in the
+ 
+
+ align:start position:0%
+out and if you stuck some probes in the
+middle you wouldn't get any information
+
+ align:start position:0%
+middle you wouldn't get any information
+ 
+
+ align:start position:0%
+middle you wouldn't get any information
+about uh How It produced that output
+
+ align:start position:0%
+about uh How It produced that output
+ 
+
+ align:start position:0%
+about uh How It produced that output
+because uh there's a great book that
+
+ align:start position:0%
+because uh there's a great book that
+ 
+
+ align:start position:0%
+because uh there's a great book that
+came out in the early 1980s called
+
+ align:start position:0%
+came out in the early 1980s called
+ 
+
+ align:start position:0%
+came out in the early 1980s called
+parallel distributed
+
+ align:start position:0%
+parallel distributed
+ 
+
+ align:start position:0%
+parallel distributed
+processing which was sort of a who's it
+
+ align:start position:0%
+processing which was sort of a who's it
+ 
+
+ align:start position:0%
+processing which was sort of a who's it
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+um I might remember in a minute
+
+ align:start position:0%
+um I might remember in a minute
+ 
+
+ align:start position:0%
+um I might remember in a minute
+the trouble is I thought Hinton and my
+
+ align:start position:0%
+the trouble is I thought Hinton and my
+ 
+
+ align:start position:0%
+the trouble is I thought Hinton and my
+theory of name recognition
+
+ align:start position:0%
+theory of name recognition
+ 
+
+ align:start position:0%
+theory of name recognition
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+what is it by mclan mlen rumel Hart
+
+ align:start position:0%
+what is it by mclan mlen rumel Hart
+ 
+
+ align:start position:0%
+what is it by mclan mlen rumel Hart
+and one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more who's the neuro one out in West
+
+ align:start position:0%
+more who's the neuro one out in West
+ 
+
+ align:start position:0%
+more who's the neuro one out in West
+Coast Three
+
+ align:start position:0%
+Coast Three
+ 
+
+ align:start position:0%
+Coast Three
+Guys yes it's Mand rumelhart and hint I
+
+ align:start position:0%
+Guys yes it's Mand rumelhart and hint I
+ 
+
+ align:start position:0%
+Guys yes it's Mand rumelhart and hint I
+don't think Hinton was an author of that
+
+ align:start position:0%
+don't think Hinton was an author of that
+ 
+
+ align:start position:0%
+don't think Hinton was an author of that
+book is he really I think so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe well it says rart ment and the PDP
+
+ align:start position:0%
+maybe well it says rart ment and the PDP
+ 
+
+ align:start position:0%
+maybe well it says rart ment and the PDP
+research group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh that's pretty good did you look that
+
+ align:start position:0%
+oh that's pretty good did you look that
+ 
+
+ align:start position:0%
+oh that's pretty good did you look that
+up on the
+
+ align:start position:0%
+up on the
+ 
+
+ align:start position:0%
+up on the
+web
+
+ align:start position:0%
+web
+ 
+
+ align:start position:0%
+web
+uh and you're using symbolic
+
+ align:start position:0%
+uh and you're using symbolic
+ 
+
+ align:start position:0%
+uh and you're using symbolic
+descriptions I think that's fairly
+
+ align:start position:0%
+descriptions I think that's fairly
+ 
+
+ align:start position:0%
+descriptions I think that's fairly
+necessary you can say I was conscious of
+
+ align:start position:0%
+necessary you can say I was conscious of
+ 
+
+ align:start position:0%
+necessary you can say I was conscious of
+a feeling in the pit of my
+
+ align:start position:0%
+a feeling in the pit of my
+ 
+
+ align:start position:0%
+a feeling in the pit of my
+stomach but I still claim you're using a
+
+ align:start position:0%
+stomach but I still claim you're using a
+ 
+
+ align:start position:0%
+stomach but I still claim you're using a
+symbolic description of that or you
+
+ align:start position:0%
+symbolic description of that or you
+ 
+
+ align:start position:0%
+symbolic description of that or you
+couldn't say it uh and maybe most
+
+ align:start position:0%
+couldn't say it uh and maybe most
+ 
+
+ align:start position:0%
+couldn't say it uh and maybe most
+important uh you couldn't say anything
+
+ align:start position:0%
+important uh you couldn't say anything
+ 
+
+ align:start position:0%
+important uh you couldn't say anything
+about how you made the decision unless
+
+ align:start position:0%
+about how you made the decision unless
+ 
+
+ align:start position:0%
+about how you made the decision unless
+you uh the process that's making that
+
+ align:start position:0%
+you uh the process that's making that
+ 
+
+ align:start position:0%
+you uh the process that's making that
+statement and finding the words and
+
+ align:start position:0%
+statement and finding the words and
+ 
+
+ align:start position:0%
+statement and finding the words and
+assembling that utterance um had access
+
+ align:start position:0%
+assembling that utterance um had access
+ 
+
+ align:start position:0%
+assembling that utterance um had access
+to some record of what your mind was
+
+ align:start position:0%
+to some record of what your mind was
+ 
+
+ align:start position:0%
+to some record of what your mind was
+doing recently namely
+
+ align:start position:0%
+doing recently namely
+ 
+
+ align:start position:0%
+doing recently namely
+it was trying to solve this problem and
+
+ align:start position:0%
+it was trying to solve this problem and
+ 
+
+ align:start position:0%
+it was trying to solve this problem and
+it had two Alternatives and it uh after
+
+ align:start position:0%
+it had two Alternatives and it uh after
+ 
+
+ align:start position:0%
+it had two Alternatives and it uh after
+a long time it chose this one rather
+
+ align:start position:0%
+a long time it chose this one rather
+ 
+
+ align:start position:0%
+a long time it chose this one rather
+than that one which means that uh it had
+
+ align:start position:0%
+than that one which means that uh it had
+ 
+
+ align:start position:0%
+than that one which means that uh it had
+to have a sort of symbolic
+
+ align:start position:0%
+to have a sort of symbolic
+ 
+
+ align:start position:0%
+to have a sort of symbolic
+representation it couldn't have been
+
+ align:start position:0%
+representation it couldn't have been
+ 
+
+ align:start position:0%
+representation it couldn't have been
+just a big neural net that had these
+
+ align:start position:0%
+just a big neural net that had these
+ 
+
+ align:start position:0%
+just a big neural net that had these
+waves of activity and then uh a appeared
+
+ align:start position:0%
+waves of activity and then uh a appeared
+ 
+
+ align:start position:0%
+waves of activity and then uh a appeared
+at the output instead of B because uh
+
+ align:start position:0%
+at the output instead of B because uh
+ 
+
+ align:start position:0%
+at the output instead of B because uh
+you wouldn't say I was I was deciding or
+
+ align:start position:0%
+you wouldn't say I was I was deciding or
+ 
+
+ align:start position:0%
+you wouldn't say I was I was deciding or
+you might say something was going on and
+
+ align:start position:0%
+you might say something was going on and
+ 
+
+ align:start position:0%
+you might say something was going on and
+suddenly I found myself forced to do
+
+ align:start position:0%
+suddenly I found myself forced to do
+ 
+
+ align:start position:0%
+suddenly I found myself forced to do
+this or that though which wouldn't fit
+
+ align:start position:0%
+this or that though which wouldn't fit
+ 
+
+ align:start position:0%
+this or that though which wouldn't fit
+the idea of a
+
+ align:start position:0%
+the idea of a
+ 
+
+ align:start position:0%
+the idea of a
+conscious and then the chapter has a a
+
+ align:start position:0%
+conscious and then the chapter has a a
+ 
+
+ align:start position:0%
+conscious and then the chapter has a a
+long discussion of those four
+
+ align:start position:0%
+long discussion of those four
+ 
+
+ align:start position:0%
+long discussion of those four
+ideas
+
+ align:start position:0%
+ideas
+ 
+
+ align:start position:0%
+ideas
+and I'm really not particularly happy
+
+ align:start position:0%
+and I'm really not particularly happy
+ 
+
+ align:start position:0%
+and I'm really not particularly happy
+with that particular description except
+
+ align:start position:0%
+with that particular description except
+ 
+
+ align:start position:0%
+with that particular description except
+that it leads to this
+
+ align:start position:0%
+that it leads to this
+ 
+
+ align:start position:0%
+that it leads to this
+diagram which this is a diagram
+
+ align:start position:0%
+diagram which this is a diagram
+ 
+
+ align:start position:0%
+diagram which this is a diagram
+which you could
+
+ align:start position:0%
+which you could
+ 
+
+ align:start position:0%
+which you could
+use to say when a person is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likely oops this is the wrong
+
+ align:start position:0%
+likely oops this is the wrong
+ 
+
+ align:start position:0%
+likely oops this is the wrong
+diagram imagine all the arrows going the
+
+ align:start position:0%
+diagram imagine all the arrows going the
+ 
+
+ align:start position:0%
+diagram imagine all the arrows going the
+other way then this this is this is what
+
+ align:start position:0%
+other way then this this is this is what
+ 
+
+ align:start position:0%
+other way then this this is this is what
+I keep pointing to that instead of that
+
+ align:start position:0%
+I keep pointing to that instead of that
+ 
+
+ align:start position:0%
+I keep pointing to that instead of that
+and I didn't bring the light
+
+ align:start position:0%
+and I didn't bring the light
+ 
+
+ align:start position:0%
+and I didn't bring the light
+pen uh but if you think of that model of
+
+ align:start position:0%
+pen uh but if you think of that model of
+ 
+
+ align:start position:0%
+pen uh but if you think of that model of
+that diagram backwards you could say
+
+ align:start position:0%
+that diagram backwards you could say
+ 
+
+ align:start position:0%
+that diagram backwards you could say
+here's a piece of machinery that would
+
+ align:start position:0%
+here's a piece of machinery that would
+ 
+
+ align:start position:0%
+here's a piece of machinery that would
+account in many cases for when a person
+
+ align:start position:0%
+account in many cases for when a person
+ 
+
+ align:start position:0%
+account in many cases for when a person
+is likely to use the word
+
+ align:start position:0%
+is likely to use the word
+ 
+
+ align:start position:0%
+is likely to use the word
+conscious and you don't see anything
+
+ align:start position:0%
+conscious and you don't see anything
+ 
+
+ align:start position:0%
+conscious and you don't see anything
+like that in in in the Journal of
+
+ align:start position:0%
+like that in in in the Journal of
+ 
+
+ align:start position:0%
+like that in in in the Journal of
+Consciousness studies because they think
+
+ align:start position:0%
+Consciousness studies because they think
+ 
+
+ align:start position:0%
+Consciousness studies because they think
+Consciousness is a mysterious single
+
+ align:start position:0%
+Consciousness is a mysterious single
+ 
+
+ align:start position:0%
+Consciousness is a mysterious single
+thing and this is saying uh there isn't
+
+ align:start position:0%
+thing and this is saying uh there isn't
+ 
+
+ align:start position:0%
+thing and this is saying uh there isn't
+any such thing as Consciousness but
+
+ align:start position:0%
+any such thing as Consciousness but
+ 
+
+ align:start position:0%
+any such thing as Consciousness but
+there are a lot of mental
+
+ align:start position:0%
+there are a lot of mental
+ 
+
+ align:start position:0%
+there are a lot of mental
+activities
+
+ align:start position:0%
+activities
+ 
+
+ align:start position:0%
+activities
+which uh any of which any combination of
+
+ align:start position:0%
+which uh any of which any combination of
+ 
+
+ align:start position:0%
+which uh any of which any combination of
+which might lead a person to use the
+
+ align:start position:0%
+which might lead a person to use the
+ 
+
+ align:start position:0%
+which might lead a person to use the
+word conscious and how can you help from
+
+ align:start position:0%
+word conscious and how can you help from
+ 
+
+ align:start position:0%
+word conscious and how can you help from
+pointing to that uh and when that
+
+ align:start position:0%
+pointing to that uh and when that
+ 
+
+ align:start position:0%
+pointing to that uh and when that
+trouble detector notices that all four
+
+ align:start position:0%
+trouble detector notices that all four
+ 
+
+ align:start position:0%
+trouble detector notices that all four
+of those kinds of processes are
+
+ align:start position:0%
+of those kinds of processes are
+ 
+
+ align:start position:0%
+of those kinds of processes are
+operating
+
+ align:start position:0%
+operating
+ 
+
+ align:start position:0%
+operating
+uh perhaps in the frontal lobe of your
+
+ align:start position:0%
+uh perhaps in the frontal lobe of your
+ 
+
+ align:start position:0%
+uh perhaps in the frontal lobe of your
+brain I don't know if people who have
+
+ align:start position:0%
+brain I don't know if people who have
+ 
+
+ align:start position:0%
+brain I don't know if people who have
+lost their frontal lobe or claim to be
+
+ align:start position:0%
+lost their frontal lobe or claim to be
+ 
+
+ align:start position:0%
+lost their frontal lobe or claim to be
+conscious or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not so there's a theory of
+
+ align:start position:0%
+not so there's a theory of
+ 
+
+ align:start position:0%
+not so there's a theory of
+of when a person might say conscious and
+
+ align:start position:0%
+of when a person might say conscious and
+ 
+
+ align:start position:0%
+of when a person might say conscious and
+I think it fits a lot of the
+
+ align:start position:0%
+I think it fits a lot of the
+ 
+
+ align:start position:0%
+I think it fits a lot of the
+descriptions of of the uh conditions
+
+ align:start position:0%
+descriptions of of the uh conditions
+ 
+
+ align:start position:0%
+descriptions of of the uh conditions
+under which people say they're conscious
+
+ align:start position:0%
+under which people say they're conscious
+ 
+
+ align:start position:0%
+under which people say they're conscious
+and uh that's the kind of theory I like
+
+ align:start position:0%
+and uh that's the kind of theory I like
+ 
+
+ align:start position:0%
+and uh that's the kind of theory I like
+to see it does still doesn't say
+
+ align:start position:0%
+to see it does still doesn't say
+ 
+
+ align:start position:0%
+to see it does still doesn't say
+what's maybe those are the four wrong
+
+ align:start position:0%
+what's maybe those are the four wrong
+ 
+
+ align:start position:0%
+what's maybe those are the four wrong
+parameters and I'd love somebody to
+
+ align:start position:0%
+parameters and I'd love somebody to
+ 
+
+ align:start position:0%
+parameters and I'd love somebody to
+suggested one that I've obviously left
+
+ align:start position:0%
+suggested one that I've obviously left
+ 
+
+ align:start position:0%
+suggested one that I've obviously left
+out and shouldn't have or or that you
+
+ align:start position:0%
+out and shouldn't have or or that you
+ 
+
+ align:start position:0%
+out and shouldn't have or or that you
+don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need maybe there's no reason to think
+
+ align:start position:0%
+need maybe there's no reason to think
+ 
+
+ align:start position:0%
+need maybe there's no reason to think
+that you need serial processes for this
+
+ align:start position:0%
+that you need serial processes for this
+ 
+
+ align:start position:0%
+that you need serial processes for this
+to happen or whatever I don't
+
+ align:start position:0%
+to happen or whatever I don't
+ 
+
+ align:start position:0%
+to happen or whatever I don't
+know so then there are four long
+
+ align:start position:0%
+know so then there are four long
+ 
+
+ align:start position:0%
+know so then there are four long
+sections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about actually yeah think about it uh
+
+ align:start position:0%
+about actually yeah think about it uh
+ 
+
+ align:start position:0%
+about actually yeah think about it uh
+you probably have seral processing for
+
+ align:start position:0%
+you probably have seral processing for
+ 
+
+ align:start position:0%
+you probably have seral processing for
+langage langage processing yes if you
+
+ align:start position:0%
+langage langage processing yes if you
+ 
+
+ align:start position:0%
+langage langage processing yes if you
+are p
+
+ align:start position:0%
+are p
+ 
+
+ align:start position:0%
+are p
+feure uh on a canas might is some kind
+
+ align:start position:0%
+feure uh on a canas might is some kind
+ 
+
+ align:start position:0%
+feure uh on a canas might is some kind
+of par processing to imagine different
+
+ align:start position:0%
+of par processing to imagine different
+ 
+
+ align:start position:0%
+of par processing to imagine different
+elements in that picture or composing or
+
+ align:start position:0%
+elements in that picture or composing or
+ 
+
+ align:start position:0%
+elements in that picture or composing or
+something for harmony well certainly
+
+ align:start position:0%
+something for harmony well certainly
+ 
+
+ align:start position:0%
+something for harmony well certainly
+there so much data in a two-dimensional
+
+ align:start position:0%
+there so much data in a two-dimensional
+ 
+
+ align:start position:0%
+there so much data in a two-dimensional
+thing that uh if you had to look at each
+
+ align:start position:0%
+thing that uh if you had to look at each
+ 
+
+ align:start position:0%
+thing that uh if you had to look at each
+point separately uh you would lose track
+
+ align:start position:0%
+point separately uh you would lose track
+ 
+
+ align:start position:0%
+point separately uh you would lose track
+and you'd have to keep starting over so
+
+ align:start position:0%
+and you'd have to keep starting over so
+ 
+
+ align:start position:0%
+and you'd have to keep starting over so
+but uh I think what an artist would you
+
+ align:start position:0%
+but uh I think what an artist would you
+ 
+
+ align:start position:0%
+but uh I think what an artist would you
+ask the artist why did you uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why did you put that figure of a
+
+ align:start position:0%
+why did you put that figure of a
+ 
+
+ align:start position:0%
+why did you put that figure of a
+person not in the center but a little
+
+ align:start position:0%
+person not in the center but a little
+ 
+
+ align:start position:0%
+person not in the center but a little
+over to the right and uh if he were a
+
+ align:start position:0%
+over to the right and uh if he were a
+ 
+
+ align:start position:0%
+over to the right and uh if he were a
+traditional artist he might say well
+
+ align:start position:0%
+traditional artist he might say well
+ 
+
+ align:start position:0%
+traditional artist he might say well
+everyone knows that if you put something
+
+ align:start position:0%
+everyone knows that if you put something
+ 
+
+ align:start position:0%
+everyone knows that if you put something
+right in the center then the reader uh
+
+ align:start position:0%
+right in the center then the reader uh
+ 
+
+ align:start position:0%
+right in the center then the reader uh
+the viewer doesn't know whether to look
+
+ align:start position:0%
+the viewer doesn't know whether to look
+ 
+
+ align:start position:0%
+the viewer doesn't know whether to look
+left or right after they've seen the
+
+ align:start position:0%
+left or right after they've seen the
+ 
+
+ align:start position:0%
+left or right after they've seen the
+figure that people have little uh
+
+ align:start position:0%
+figure that people have little uh
+ 
+
+ align:start position:0%
+figure that people have little uh
+amateur psychological theories of of why
+
+ align:start position:0%
+amateur psychological theories of of why
+ 
+
+ align:start position:0%
+amateur psychological theories of of why
+you shouldn't put in in fact if you look
+
+ align:start position:0%
+you shouldn't put in in fact if you look
+ 
+
+ align:start position:0%
+you shouldn't put in in fact if you look
+at a book on drawing you'll find
+
+ align:start position:0%
+at a book on drawing you'll find
+ 
+
+ align:start position:0%
+at a book on drawing you'll find
+statements like it's best to put the
+
+ align:start position:0%
+statements like it's best to put the
+ 
+
+ align:start position:0%
+statements like it's best to put the
+center figure 30% from one side or the
+
+ align:start position:0%
+center figure 30% from one side or the
+ 
+
+ align:start position:0%
+center figure 30% from one side or the
+other uh not 50% and uh you certainly
+
+ align:start position:0%
+other uh not 50% and uh you certainly
+ 
+
+ align:start position:0%
+other uh not 50% and uh you certainly
+don't want to put it right in the middle
+
+ align:start position:0%
+don't want to put it right in the middle
+ 
+
+ align:start position:0%
+don't want to put it right in the middle
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+uh how many of you have tried to learn
+
+ align:start position:0%
+uh how many of you have tried to learn
+ 
+
+ align:start position:0%
+uh how many of you have tried to learn
+to draw from a drawing book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they have a lot of principles and
+
+ align:start position:0%
+they have a lot of principles and
+ 
+
+ align:start position:0%
+they have a lot of principles and
+they're not all compatible oh yes but my
+
+ align:start position:0%
+they're not all compatible oh yes but my
+ 
+
+ align:start position:0%
+they're not all compatible oh yes but my
+theory of that art is the same as
+
+ align:start position:0%
+theory of that art is the same as
+ 
+
+ align:start position:0%
+theory of that art is the same as
+engineering uh there's just one big
+
+ align:start position:0%
+engineering uh there's just one big
+ 
+
+ align:start position:0%
+engineering uh there's just one big
+difference in engineering you normally
+
+ align:start position:0%
+difference in engineering you normally
+ 
+
+ align:start position:0%
+difference in engineering you normally
+have a lot of specification you have a
+
+ align:start position:0%
+have a lot of specification you have a
+ 
+
+ align:start position:0%
+have a lot of specification you have a
+lot of goals you have to achieve if
+
+ align:start position:0%
+lot of goals you have to achieve if
+ 
+
+ align:start position:0%
+lot of goals you have to achieve if
+you're making a DVD player
+
+ align:start position:0%
+you're making a DVD player
+ 
+
+ align:start position:0%
+you're making a DVD player
+uh there are a lot of constraints like
+
+ align:start position:0%
+uh there are a lot of constraints like
+ 
+
+ align:start position:0%
+uh there are a lot of constraints like
+the power button ought to be at the left
+
+ align:start position:0%
+the power button ought to be at the left
+ 
+
+ align:start position:0%
+the power button ought to be at the left
+only it isn't always there but since
+
+ align:start position:0%
+only it isn't always there but since
+ 
+
+ align:start position:0%
+only it isn't always there but since
+it's on the left in 90% of devices why
+
+ align:start position:0%
+it's on the left in 90% of devices why
+ 
+
+ align:start position:0%
+it's on the left in 90% of devices why
+is is that
+
+ align:start position:0%
+is is that
+ 
+
+ align:start position:0%
+is is that
+right raise your hand if you have
+
+ align:start position:0%
+right raise your hand if you have
+ 
+
+ align:start position:0%
+right raise your hand if you have
+a DV DVD player with the button on the
+
+ align:start position:0%
+a DV DVD player with the button on the
+ 
+
+ align:start position:0%
+a DV DVD player with the button on the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+side what mine on the left most of them
+
+ align:start position:0%
+side what mine on the left most of them
+ 
+
+ align:start position:0%
+side what mine on the left most of them
+are on the left I have this motor rol of
+
+ align:start position:0%
+are on the left I have this motor rol of
+ 
+
+ align:start position:0%
+are on the left I have this motor rol of
+phone which
+
+ align:start position:0%
+phone which
+ 
+
+ align:start position:0%
+phone which
+uh has the
+
+ align:start position:0%
+uh has the
+ 
+
+ align:start position:0%
+uh has the
+wrong I think if you press this it goes
+
+ align:start position:0%
+wrong I think if you press this it goes
+ 
+
+ align:start position:0%
+wrong I think if you press this it goes
+off off the left side this one is on the
+
+ align:start position:0%
+off off the left side this one is on the
+ 
+
+ align:start position:0%
+off off the left side this one is on the
+right is it a Motorola
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uhhuh isn't everyone else's on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left yes mine's on the right
+
+ align:start position:0%
+left yes mine's on the right
+ 
+
+ align:start position:0%
+left yes mine's on the right
+uh but I used to use a some other brand
+
+ align:start position:0%
+uh but I used to use a some other brand
+ 
+
+ align:start position:0%
+uh but I used to use a some other brand
+so when the phone rings I press the one
+
+ align:start position:0%
+so when the phone rings I press the one
+ 
+
+ align:start position:0%
+so when the phone rings I press the one
+on the left and it shuts off the
+
+ align:start position:0%
+on the left and it shuts off the
+ 
+
+ align:start position:0%
+on the left and it shuts off the
+call how many of you have phones with
+
+ align:start position:0%
+call how many of you have phones with
+ 
+
+ align:start position:0%
+call how many of you have phones with
+the talk button on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left how many of those are motor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rollers I talked to some executive and
+
+ align:start position:0%
+rollers I talked to some executive and
+ 
+
+ align:start position:0%
+rollers I talked to some executive and
+he said yes this was a big mistake but
+
+ align:start position:0%
+he said yes this was a big mistake but
+ 
+
+ align:start position:0%
+he said yes this was a big mistake but
+we're afraid to change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+so what I described the last few minutes
+
+ align:start position:0%
+so what I described the last few minutes
+ 
+
+ align:start position:0%
+so what I described the last few minutes
+was the Consciousness
+
+ align:start position:0%
+was the Consciousness
+ 
+
+ align:start position:0%
+was the Consciousness
+recognizer you were talking about how
+
+ align:start position:0%
+recognizer you were talking about how
+ 
+
+ align:start position:0%
+recognizer you were talking about how
+art is like engineering thank you uh yes
+
+ align:start position:0%
+art is like engineering thank you uh yes
+ 
+
+ align:start position:0%
+art is like engineering thank you uh yes
+and so in uh in
+
+ align:start position:0%
+and so in uh in
+ 
+
+ align:start position:0%
+and so in uh in
+engineering uh you have a bunch of goals
+
+ align:start position:0%
+engineering uh you have a bunch of goals
+ 
+
+ align:start position:0%
+engineering uh you have a bunch of goals
+you want to achieve and uh in fact
+
+ align:start position:0%
+you want to achieve and uh in fact
+ 
+
+ align:start position:0%
+you want to achieve and uh in fact
+there's a
+
+ align:start position:0%
+there's a
+ 
+
+ align:start position:0%
+there's a
+sublist which you absolutely have to
+
+ align:start position:0%
+sublist which you absolutely have to
+ 
+
+ align:start position:0%
+sublist which you absolutely have to
+achieve or the product won't work and so
+
+ align:start position:0%
+achieve or the product won't work and so
+ 
+
+ align:start position:0%
+achieve or the product won't work and so
+forth and so you focus on those and if
+
+ align:start position:0%
+forth and so you focus on those and if
+ 
+
+ align:start position:0%
+forth and so you focus on those and if
+you can make it have a few other virtues
+
+ align:start position:0%
+you can make it have a few other virtues
+ 
+
+ align:start position:0%
+you can make it have a few other virtues
+that's fine uh so there's a lot of
+
+ align:start position:0%
+that's fine uh so there's a lot of
+ 
+
+ align:start position:0%
+that's fine uh so there's a lot of
+problem solving and how do you make a
+
+ align:start position:0%
+problem solving and how do you make a
+ 
+
+ align:start position:0%
+problem solving and how do you make a
+thing that achieves these 12 goals uh in
+
+ align:start position:0%
+thing that achieves these 12 goals uh in
+ 
+
+ align:start position:0%
+thing that achieves these 12 goals uh in
+art I think it's uh the process is the
+
+ align:start position:0%
+art I think it's uh the process is the
+ 
+
+ align:start position:0%
+art I think it's uh the process is the
+same except an artist always has more
+
+ align:start position:0%
+same except an artist always has more
+ 
+
+ align:start position:0%
+same except an artist always has more
+goals than you can achieve maybe he
+
+ align:start position:0%
+goals than you can achieve maybe he
+ 
+
+ align:start position:0%
+goals than you can achieve maybe he
+wants this painting to do everything and
+
+ align:start position:0%
+wants this painting to do everything and
+ 
+
+ align:start position:0%
+wants this painting to do everything and
+uh uh I know a lot of artists and my
+
+ align:start position:0%
+uh uh I know a lot of artists and my
+ 
+
+ align:start position:0%
+uh uh I know a lot of artists and my
+impression is they spend a lot of time
+
+ align:start position:0%
+impression is they spend a lot of time
+ 
+
+ align:start position:0%
+impression is they spend a lot of time
+deciding which goals to scrap for this
+
+ align:start position:0%
+deciding which goals to scrap for this
+ 
+
+ align:start position:0%
+deciding which goals to scrap for this
+particular work like
+
+ align:start position:0%
+particular work like
+ 
+
+ align:start position:0%
+particular work like
+uh if they're going to make a bronze
+
+ align:start position:0%
+uh if they're going to make a bronze
+ 
+
+ align:start position:0%
+uh if they're going to make a bronze
+statue uh they'd like it to be eight
+
+ align:start position:0%
+statue uh they'd like it to be eight
+ 
+
+ align:start position:0%
+statue uh they'd like it to be eight
+feet tall but that would cost $60,000 so
+
+ align:start position:0%
+feet tall but that would cost $60,000 so
+ 
+
+ align:start position:0%
+feet tall but that would cost $60,000 so
+they'll make it this tall and so they
+
+ align:start position:0%
+they'll make it this tall and so they
+ 
+
+ align:start position:0%
+they'll make it this tall and so they
+give up the goal of being 8T tall
+
+ align:start position:0%
+give up the goal of being 8T tall
+ 
+
+ align:start position:0%
+give up the goal of being 8T tall
+because uh they want it to be made of
+
+ align:start position:0%
+because uh they want it to be made of
+ 
+
+ align:start position:0%
+because uh they want it to be made of
+bronze and so forth so my par this is a
+
+ align:start position:0%
+bronze and so forth so my par this is a
+ 
+
+ align:start position:0%
+bronze and so forth so my par this is a
+parody my parody of an artist is an
+
+ align:start position:0%
+parody my parody of an artist is an
+ 
+
+ align:start position:0%
+parody my parody of an artist is an
+artist is just like an engineer only the
+
+ align:start position:0%
+artist is just like an engineer only the
+ 
+
+ align:start position:0%
+artist is just like an engineer only the
+main problem is that the artist has a
+
+ align:start position:0%
+main problem is that the artist has a
+ 
+
+ align:start position:0%
+main problem is that the artist has a
+wider range of possible goals uh
+
+ align:start position:0%
+wider range of possible goals uh
+ 
+
+ align:start position:0%
+wider range of possible goals uh
+he wants to make a lot of people feel
+
+ align:start position:0%
+he wants to make a lot of people feel
+ 
+
+ align:start position:0%
+he wants to make a lot of people feel
+happy or he makes he wants to make all
+
+ align:start position:0%
+happy or he makes he wants to make all
+ 
+
+ align:start position:0%
+happy or he makes he wants to make all
+the people in the world feel terrible
+
+ align:start position:0%
+the people in the world feel terrible
+ 
+
+ align:start position:0%
+the people in the world feel terrible
+and uh but he can't achieve that so he
+
+ align:start position:0%
+and uh but he can't achieve that so he
+ 
+
+ align:start position:0%
+and uh but he can't achieve that so he
+has to make some kind of compromise so a
+
+ align:start position:0%
+has to make some kind of compromise so a
+ 
+
+ align:start position:0%
+has to make some kind of compromise so a
+lot of the artist's work goes into
+
+ align:start position:0%
+lot of the artist's work goes into
+ 
+
+ align:start position:0%
+lot of the artist's work goes into
+deciding uh what set of goals should I
+
+ align:start position:0%
+deciding uh what set of goals should I
+ 
+
+ align:start position:0%
+deciding uh what set of goals should I
+achieve in my next painting or or uh
+
+ align:start position:0%
+achieve in my next painting or or uh
+ 
+
+ align:start position:0%
+achieve in my next painting or or uh
+composition or uh sculpture or
+
+ align:start position:0%
+composition or uh sculpture or
+ 
+
+ align:start position:0%
+composition or uh sculpture or
+whatever and uh once those settle down
+
+ align:start position:0%
+whatever and uh once those settle down
+ 
+
+ align:start position:0%
+whatever and uh once those settle down
+then there's no difference between the
+
+ align:start position:0%
+then there's no difference between the
+ 
+
+ align:start position:0%
+then there's no difference between the
+artist and the engineer and he has to
+
+ align:start position:0%
+artist and the engineer and he has to
+ 
+
+ align:start position:0%
+artist and the engineer and he has to
+get this thing enough off center but not
+
+ align:start position:0%
+get this thing enough off center but not
+ 
+
+ align:start position:0%
+get this thing enough off center but not
+too much and if it if he can't get it
+
+ align:start position:0%
+too much and if it if he can't get it
+ 
+
+ align:start position:0%
+too much and if it if he can't get it
+there well maybe he can uh make a little
+
+ align:start position:0%
+there well maybe he can uh make a little
+ 
+
+ align:start position:0%
+there well maybe he can uh make a little
+more crowded stuff over here to make it
+
+ align:start position:0%
+more crowded stuff over here to make it
+ 
+
+ align:start position:0%
+more crowded stuff over here to make it
+look like it's further you know all
+
+ align:start position:0%
+look like it's further you know all
+ 
+
+ align:start position:0%
+look like it's further you know all
+those uh little interactions that every
+
+ align:start position:0%
+those uh little interactions that every
+ 
+
+ align:start position:0%
+those uh little interactions that every
+artist uh that many artists exploit so
+
+ align:start position:0%
+artist uh that many artists exploit so
+ 
+
+ align:start position:0%
+artist uh that many artists exploit so
+there's not very much difference as far
+
+ align:start position:0%
+there's not very much difference as far
+ 
+
+ align:start position:0%
+there's not very much difference as far
+as I can see they're both doing
+
+ align:start position:0%
+as I can see they're both doing
+ 
+
+ align:start position:0%
+as I can see they're both doing
+heuristic searches they have slightly
+
+ align:start position:0%
+heuristic searches they have slightly
+ 
+
+ align:start position:0%
+heuristic searches they have slightly
+different heuristics but the artist is
+
+ align:start position:0%
+different heuristics but the artist is
+ 
+
+ align:start position:0%
+different heuristics but the artist is
+more ambitious in a sense the artist
+
+ align:start position:0%
+more ambitious in a sense the artist
+ 
+
+ align:start position:0%
+more ambitious in a sense the artist
+wants to make
+
+ align:start position:0%
+wants to make
+ 
+
+ align:start position:0%
+wants to make
+everybody I don't know what the artist
+
+ align:start position:0%
+everybody I don't know what the artist
+ 
+
+ align:start position:0%
+everybody I don't know what the artist
+wants but you get the
+
+ align:start position:0%
+wants but you get the
+ 
+
+ align:start position:0%
+wants but you get the
+idea ambitious too yeah uh Steve Jobs
+
+ align:start position:0%
+idea ambitious too yeah uh Steve Jobs
+ 
+
+ align:start position:0%
+idea ambitious too yeah uh Steve Jobs
+wants everybody to not use anything
+
+ align:start position:0%
+wants everybody to not use anything
+ 
+
+ align:start position:0%
+wants everybody to not use anything
+except a Mac ever again and uh he does
+
+ align:start position:0%
+except a Mac ever again and uh he does
+ 
+
+ align:start position:0%
+except a Mac ever again and uh he does
+all sorts of things to uh make this
+
+ align:start position:0%
+all sorts of things to uh make this
+ 
+
+ align:start position:0%
+all sorts of things to uh make this
+happen and they don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but he's as much as an artist as any
+
+ align:start position:0%
+but but he's as much as an artist as any
+ 
+
+ align:start position:0%
+but but he's as much as an artist as any
+artist I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know and then the uh the other half of
+
+ align:start position:0%
+know and then the uh the other half of
+ 
+
+ align:start position:0%
+know and then the uh the other half of
+the theory is exactly the opposite
+
+ align:start position:0%
+the theory is exactly the opposite
+ 
+
+ align:start position:0%
+the theory is exactly the opposite
+namely uh why would you why are people
+
+ align:start position:0%
+namely uh why would you why are people
+ 
+
+ align:start position:0%
+namely uh why would you why are people
+conscious and the answer is when you're
+
+ align:start position:0%
+conscious and the answer is when you're
+ 
+
+ align:start position:0%
+conscious and the answer is when you're
+stuck you've been working on this
+
+ align:start position:0%
+stuck you've been working on this
+ 
+
+ align:start position:0%
+stuck you've been working on this
+problem puttering around and nothing's
+
+ align:start position:0%
+problem puttering around and nothing's
+ 
+
+ align:start position:0%
+problem puttering around and nothing's
+happening and you and you say to
+
+ align:start position:0%
+happening and you and you say to
+ 
+
+ align:start position:0%
+happening and you and you say to
+yourself well this is terrible I must
+
+ align:start position:0%
+yourself well this is terrible I must
+ 
+
+ align:start position:0%
+yourself well this is terrible I must
+think I must focus on this I have to
+
+ align:start position:0%
+think I must focus on this I have to
+ 
+
+ align:start position:0%
+think I must focus on this I have to
+concentrate I ought to crystallize what
+
+ align:start position:0%
+concentrate I ought to crystallize what
+ 
+
+ align:start position:0%
+concentrate I ought to crystallize what
+I'm doing I uh I've got to uh evaluate
+
+ align:start position:0%
+I'm doing I uh I've got to uh evaluate
+ 
+
+ align:start position:0%
+I'm doing I uh I've got to uh evaluate
+the procedures I'm using and blah blah
+
+ align:start position:0%
+the procedures I'm using and blah blah
+ 
+
+ align:start position:0%
+the procedures I'm using and blah blah
+blah and
+
+ align:start position:0%
+blah and
+ 
+
+ align:start position:0%
+blah and
+uh so I summarized this by
+
+ align:start position:0%
+uh so I summarized this by
+ 
+
+ align:start position:0%
+uh so I summarized this by
+saying that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh Consciousness is a great thing uh
+
+ align:start position:0%
+uh Consciousness is a great thing uh
+ 
+
+ align:start position:0%
+uh Consciousness is a great thing uh
+because uh when you're in trouble and
+
+ align:start position:0%
+because uh when you're in trouble and
+ 
+
+ align:start position:0%
+because uh when you're in trouble and
+you're not solving a problem uh I mean
+
+ align:start position:0%
+you're not solving a problem uh I mean
+ 
+
+ align:start position:0%
+you're not solving a problem uh I mean
+you can solve a lot of problems by Zen
+
+ align:start position:0%
+you can solve a lot of problems by Zen
+ 
+
+ align:start position:0%
+you can solve a lot of problems by Zen
+Buddhism uh where you just don't do
+
+ align:start position:0%
+Buddhism uh where you just don't do
+ 
+
+ align:start position:0%
+Buddhism uh where you just don't do
+anything and you don't think about the
+
+ align:start position:0%
+anything and you don't think about the
+ 
+
+ align:start position:0%
+anything and you don't think about the
+Target and and you pull this thing back
+
+ align:start position:0%
+Target and and you pull this thing back
+ 
+
+ align:start position:0%
+Target and and you pull this thing back
+and the arrow flies right into the
+
+ align:start position:0%
+and the arrow flies right into the
+ 
+
+ align:start position:0%
+and the arrow flies right into the
+bullseye uh but uh I don't care what the
+
+ align:start position:0%
+bullseye uh but uh I don't care what the
+ 
+
+ align:start position:0%
+bullseye uh but uh I don't care what the
+Zen people say the idea is if you have
+
+ align:start position:0%
+Zen people say the idea is if you have
+ 
+
+ align:start position:0%
+Zen people say the idea is if you have
+pretty good compiled code then uh
+
+ align:start position:0%
+pretty good compiled code then uh
+ 
+
+ align:start position:0%
+pretty good compiled code then uh
+thinking about it will mess it up and uh
+
+ align:start position:0%
+thinking about it will mess it up and uh
+ 
+
+ align:start position:0%
+thinking about it will mess it up and uh
+the idea that you should not think about
+
+ align:start position:0%
+the idea that you should not think about
+ 
+
+ align:start position:0%
+the idea that you should not think about
+keeping your gun steady I have great
+
+ align:start position:0%
+keeping your gun steady I have great
+ 
+
+ align:start position:0%
+keeping your gun steady I have great
+example uh
+
+ align:start position:0%
+example uh
+ 
+
+ align:start position:0%
+example uh
+I once went to the Rockefeller Institute
+
+ align:start position:0%
+I once went to the Rockefeller Institute
+ 
+
+ align:start position:0%
+I once went to the Rockefeller Institute
+with Seymour paper to talk
+
+ align:start position:0%
+with Seymour paper to talk
+ 
+
+ align:start position:0%
+with Seymour paper to talk
+to some guy about
+
+ align:start position:0%
+to some guy about
+ 
+
+ align:start position:0%
+to some guy about
+something but instead of discussing that
+
+ align:start position:0%
+something but instead of discussing that
+ 
+
+ align:start position:0%
+something but instead of discussing that
+he said well let's play
+
+ align:start position:0%
+he said well let's play
+ 
+
+ align:start position:0%
+he said well let's play
+pool they had a pool table in
+
+ align:start position:0%
+pool they had a pool table in
+ 
+
+ align:start position:0%
+pool they had a pool table in
+the recreation
+
+ align:start position:0%
+the recreation
+ 
+
+ align:start position:0%
+the recreation
+room and uh I'd never played pool so I
+
+ align:start position:0%
+room and uh I'd never played pool so I
+ 
+
+ align:start position:0%
+room and uh I'd never played pool so I
+went like that and the ball went the
+
+ align:start position:0%
+went like that and the ball went the
+ 
+
+ align:start position:0%
+went like that and the ball went the
+wrong way and uh nothing worked and he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said I know what's wrong I said what's
+
+ align:start position:0%
+said I know what's wrong I said what's
+ 
+
+ align:start position:0%
+said I know what's wrong I said what's
+wrong and he said you're trying to hit
+
+ align:start position:0%
+wrong and he said you're trying to hit
+ 
+
+ align:start position:0%
+wrong and he said you're trying to hit
+the ball with the end of the Q stick and
+
+ align:start position:0%
+the ball with the end of the Q stick and
+ 
+
+ align:start position:0%
+the ball with the end of the Q stick and
+I said
+
+ align:start position:0%
+I said
+ 
+
+ align:start position:0%
+I said
+so and he said uh it's a very bad
+
+ align:start position:0%
+so and he said uh it's a very bad
+ 
+
+ align:start position:0%
+so and he said uh it's a very bad
+strategy what you must do is here's the
+
+ align:start position:0%
+strategy what you must do is here's the
+ 
+
+ align:start position:0%
+strategy what you must do is here's the
+bull don't try to hit the bull with the
+
+ align:start position:0%
+bull don't try to hit the bull with the
+ 
+
+ align:start position:0%
+bull don't try to hit the bull with the
+end of your Q stick imagine another bll
+
+ align:start position:0%
+end of your Q stick imagine another bll
+ 
+
+ align:start position:0%
+end of your Q stick imagine another bll
+4 in
+
+ align:start position:0%
+4 in
+ 
+
+ align:start position:0%
+4 in
+away past it and try to hit that ball
+
+ align:start position:0%
+away past it and try to hit that ball
+ 
+
+ align:start position:0%
+away past it and try to hit that ball
+with the end of your Q stick so I tried
+
+ align:start position:0%
+with the end of your Q stick so I tried
+ 
+
+ align:start position:0%
+with the end of your Q stick so I tried
+that and thing went right in the pocket
+
+ align:start position:0%
+that and thing went right in the pocket
+ 
+
+ align:start position:0%
+that and thing went right in the pocket
+and I got eight in a row without any
+
+ align:start position:0%
+and I got eight in a row without any
+ 
+
+ align:start position:0%
+and I got eight in a row without any
+practice so he said well do you know why
+
+ align:start position:0%
+practice so he said well do you know why
+ 
+
+ align:start position:0%
+practice so he said well do you know why
+that works I said well no and he said
+
+ align:start position:0%
+that works I said well no and he said
+ 
+
+ align:start position:0%
+that works I said well no and he said
+whenever you make a motion like
+
+ align:start position:0%
+whenever you make a motion like
+ 
+
+ align:start position:0%
+whenever you make a motion like
+that bring your hand as close to the
+
+ align:start position:0%
+that bring your hand as close to the
+ 
+
+ align:start position:0%
+that bring your hand as close to the
+nose as fast as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible well what you don't do is
+
+ align:start position:0%
+possible well what you don't do is
+ 
+
+ align:start position:0%
+possible well what you don't do is
+contract your back biceps with maximum
+
+ align:start position:0%
+contract your back biceps with maximum
+ 
+
+ align:start position:0%
+contract your back biceps with maximum
+Force because then you'll smash your
+
+ align:start position:0%
+Force because then you'll smash your
+ 
+
+ align:start position:0%
+Force because then you'll smash your
+nose what you do is you make you make
+
+ align:start position:0%
+nose what you do is you make you make
+ 
+
+ align:start position:0%
+nose what you do is you make you make
+this plan although you don't know you've
+
+ align:start position:0%
+this plan although you don't know you've
+ 
+
+ align:start position:0%
+this plan although you don't know you've
+made this plan and the plan says I'm
+
+ align:start position:0%
+made this plan and the plan says I'm
+ 
+
+ align:start position:0%
+made this plan and the plan says I'm
+going to contract my biceps until about
+
+ align:start position:0%
+going to contract my biceps until about
+ 
+
+ align:start position:0%
+going to contract my biceps until about
+gets about here and then I'm going to
+
+ align:start position:0%
+gets about here and then I'm going to
+ 
+
+ align:start position:0%
+gets about here and then I'm going to
+contract my triceps so that it stops
+
+ align:start position:0%
+contract my triceps so that it stops
+ 
+
+ align:start position:0%
+contract my triceps so that it stops
+because you see if you just
+
+ align:start position:0%
+because you see if you just
+ 
+
+ align:start position:0%
+because you see if you just
+if you don't have another muscle uh in
+
+ align:start position:0%
+if you don't have another muscle uh in
+ 
+
+ align:start position:0%
+if you don't have another muscle uh in
+the opp Opposite Direction then if you
+
+ align:start position:0%
+the opp Opposite Direction then if you
+ 
+
+ align:start position:0%
+the opp Opposite Direction then if you
+stop here it'll just coast and you'll
+
+ align:start position:0%
+stop here it'll just coast and you'll
+ 
+
+ align:start position:0%
+stop here it'll just coast and you'll
+still get a bloody nose so you're trying
+
+ align:start position:0%
+still get a bloody nose so you're trying
+ 
+
+ align:start position:0%
+still get a bloody nose so you're trying
+to stop at at the ball if you try to
+
+ align:start position:0%
+to stop at at the ball if you try to
+ 
+
+ align:start position:0%
+to stop at at the ball if you try to
+stop at the ball then your antagonist
+
+ align:start position:0%
+stop at the ball then your antagonist
+ 
+
+ align:start position:0%
+stop at the ball then your antagonist
+muscle will engage 4 Ines before you hit
+
+ align:start position:0%
+muscle will engage 4 Ines before you hit
+ 
+
+ align:start position:0%
+muscle will engage 4 Ines before you hit
+the ball and spoil your aim because this
+
+ align:start position:0%
+the ball and spoil your aim because this
+ 
+
+ align:start position:0%
+the ball and spoil your aim because this
+muscle pulls your arm here but this
+
+ align:start position:0%
+muscle pulls your arm here but this
+ 
+
+ align:start position:0%
+muscle pulls your arm here but this
+muscle is not exactly at the opposite
+
+ align:start position:0%
+muscle is not exactly at the opposite
+ 
+
+ align:start position:0%
+muscle is not exactly at the opposite
+part but it's about 10° off so you see
+
+ align:start position:0%
+part but it's about 10° off so you see
+ 
+
+ align:start position:0%
+part but it's about 10° off so you see
+as soon as that one go you're it's very
+
+ align:start position:0%
+as soon as that one go you're it's very
+ 
+
+ align:start position:0%
+as soon as that one go you're it's very
+cute so this way you fool your
+
+ align:start position:0%
+cute so this way you fool your
+ 
+
+ align:start position:0%
+cute so this way you fool your
+uh you fool your uh cerebellum and
+
+ align:start position:0%
+uh you fool your uh cerebellum and
+ 
+
+ align:start position:0%
+uh you fool your uh cerebellum and
+spinal cord from turning on it's called
+
+ align:start position:0%
+spinal cord from turning on it's called
+ 
+
+ align:start position:0%
+spinal cord from turning on it's called
+the decelerator muscle for almost every
+
+ align:start position:0%
+the decelerator muscle for almost every
+ 
+
+ align:start position:0%
+the decelerator muscle for almost every
+action there's an accelerating part and
+
+ align:start position:0%
+action there's an accelerating part and
+ 
+
+ align:start position:0%
+action there's an accelerating part and
+a decelerating part and uh as far as I
+
+ align:start position:0%
+a decelerating part and uh as far as I
+ 
+
+ align:start position:0%
+a decelerating part and uh as far as I
+can see most of what people have told me
+
+ align:start position:0%
+can see most of what people have told me
+ 
+
+ align:start position:0%
+can see most of what people have told me
+about Zen Buddhism has nothing to do
+
+ align:start position:0%
+about Zen Buddhism has nothing to do
+ 
+
+ align:start position:0%
+about Zen Buddhism has nothing to do
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+uh the simultaneous consciousness of
+
+ align:start position:0%
+uh the simultaneous consciousness of
+ 
+
+ align:start position:0%
+uh the simultaneous consciousness of
+everything in the universe or stuff like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that almost all of it is explained by
+
+ align:start position:0%
+that almost all of it is explained by
+ 
+
+ align:start position:0%
+that almost all of it is explained by
+this is a really stupid trick for
+
+ align:start position:0%
+this is a really stupid trick for
+ 
+
+ align:start position:0%
+this is a really stupid trick for
+fooling your decelerator muscle not to
+
+ align:start position:0%
+fooling your decelerator muscle not to
+ 
+
+ align:start position:0%
+fooling your decelerator muscle not to
+spoil your aim and
+
+ align:start position:0%
+spoil your aim and
+ 
+
+ align:start position:0%
+spoil your aim and
+uh I'm very mistrustful of ancient
+
+ align:start position:0%
+uh I'm very mistrustful of ancient
+ 
+
+ align:start position:0%
+uh I'm very mistrustful of ancient
+wisdom just because if it hasn't changed
+
+ align:start position:0%
+wisdom just because if it hasn't changed
+ 
+
+ align:start position:0%
+wisdom just because if it hasn't changed
+for a thousand years then there must be
+
+ align:start position:0%
+for a thousand years then there must be
+ 
+
+ align:start position:0%
+for a thousand years then there must be
+something in the executive bureaucracy
+
+ align:start position:0%
+something in the executive bureaucracy
+ 
+
+ align:start position:0%
+something in the executive bureaucracy
+that's keeping science
+
+ align:start position:0%
+that's keeping science
+ 
+
+ align:start position:0%
+that's keeping science
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+the uh what was true in uh
+
+ align:start position:0%
+the uh what was true in uh
+ 
+
+ align:start position:0%
+the uh what was true in uh
+1700 was that there was this great
+
+ align:start position:0%
+1700 was that there was this great
+ 
+
+ align:start position:0%
+1700 was that there was this great
+caloric theory of heat that heat was a
+
+ align:start position:0%
+caloric theory of heat that heat was a
+ 
+
+ align:start position:0%
+caloric theory of heat that heat was a
+fluid and it flowed uh from the hot
+
+ align:start position:0%
+fluid and it flowed uh from the hot
+ 
+
+ align:start position:0%
+fluid and it flowed uh from the hot
+places to the cold places because
+
+ align:start position:0%
+places to the cold places because
+ 
+
+ align:start position:0%
+places to the cold places because
+there's more of it and if there was room
+
+ align:start position:0%
+there's more of it and if there was room
+ 
+
+ align:start position:0%
+there's more of it and if there was room
+to go somewhere else and it explained a
+
+ align:start position:0%
+to go somewhere else and it explained a
+ 
+
+ align:start position:0%
+to go somewhere else and it explained a
+lot of uh hiders of thermodynamics but
+
+ align:start position:0%
+lot of uh hiders of thermodynamics but
+ 
+
+ align:start position:0%
+lot of uh hiders of thermodynamics but
+not enough and the caloric theory was
+
+ align:start position:0%
+not enough and the caloric theory was
+ 
+
+ align:start position:0%
+not enough and the caloric theory was
+the best theory there had been for a
+
+ align:start position:0%
+the best theory there had been for a
+ 
+
+ align:start position:0%
+the best theory there had been for a
+couple of thousand years and it took
+
+ align:start position:0%
+couple of thousand years and it took
+ 
+
+ align:start position:0%
+couple of thousand years and it took
+about a hundred years to go away as
+
+ align:start position:0%
+about a hundred years to go away as
+ 
+
+ align:start position:0%
+about a hundred years to go away as
+the uh as the uh kinetic theory of heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appeared however the Zan Buddhist theory
+
+ align:start position:0%
+appeared however the Zan Buddhist theory
+ 
+
+ align:start position:0%
+appeared however the Zan Buddhist theory
+of archery doesn't go away now that we
+
+ align:start position:0%
+of archery doesn't go away now that we
+ 
+
+ align:start position:0%
+of archery doesn't go away now that we
+know about
+
+ align:start position:0%
+know about
+ 
+
+ align:start position:0%
+know about
+physiology because of you know
+
+ align:start position:0%
+physiology because of you know
+ 
+
+ align:start position:0%
+physiology because of you know
+what because there a lot of very wise
+
+ align:start position:0%
+what because there a lot of very wise
+ 
+
+ align:start position:0%
+what because there a lot of very wise
+people who make their living from it
+
+ align:start position:0%
+people who make their living from it
+ 
+
+ align:start position:0%
+people who make their living from it
+so anyway you see once you've got that
+
+ align:start position:0%
+so anyway you see once you've got that
+ 
+
+ align:start position:0%
+so anyway you see once you've got that
+theory of how you know when you're being
+
+ align:start position:0%
+theory of how you know when you're being
+ 
+
+ align:start position:0%
+theory of how you know when you're being
+conscious you see that it's not a
+
+ align:start position:0%
+conscious you see that it's not a
+ 
+
+ align:start position:0%
+conscious you see that it's not a
+complete Theory because having
+
+ align:start position:0%
+complete Theory because having
+ 
+
+ align:start position:0%
+complete Theory because having
+the concept is great uh because then if
+
+ align:start position:0%
+the concept is great uh because then if
+ 
+
+ align:start position:0%
+the concept is great uh because then if
+you're stuck and you're not doing very
+
+ align:start position:0%
+you're stuck and you're not doing very
+ 
+
+ align:start position:0%
+you're stuck and you're not doing very
+well you say well I must be more
+
+ align:start position:0%
+well you say well I must be more
+ 
+
+ align:start position:0%
+well you say well I must be more
+deliberate or conscious or
+
+ align:start position:0%
+deliberate or conscious or
+ 
+
+ align:start position:0%
+deliberate or conscious or
+uh any more synonyms for that uh
+
+ align:start position:0%
+uh any more synonyms for that uh
+ 
+
+ align:start position:0%
+uh any more synonyms for that uh
+reflective what aware yeah I should be
+
+ align:start position:0%
+reflective what aware yeah I should be
+ 
+
+ align:start position:0%
+reflective what aware yeah I should be
+more aware of what I'm doing and so as
+
+ align:start position:0%
+more aware of what I'm doing and so as
+ 
+
+ align:start position:0%
+more aware of what I'm doing and so as
+soon as you say that uh your compiler
+
+ align:start position:0%
+soon as you say that uh your compiler
+ 
+
+ align:start position:0%
+soon as you say that uh your compiler
+has compiled that into oh turn on more
+
+ align:start position:0%
+has compiled that into oh turn on more
+ 
+
+ align:start position:0%
+has compiled that into oh turn on more
+uh self models turn on more reflective
+
+ align:start position:0%
+uh self models turn on more reflective
+ 
+
+ align:start position:0%
+uh self models turn on more reflective
+processes uh get yourself working
+
+ align:start position:0%
+processes uh get yourself working
+ 
+
+ align:start position:0%
+processes uh get yourself working
+serially so that if something goes wrong
+
+ align:start position:0%
+serially so that if something goes wrong
+ 
+
+ align:start position:0%
+serially so that if something goes wrong
+with the process you'll detect it right
+
+ align:start position:0%
+with the process you'll detect it right
+ 
+
+ align:start position:0%
+with the process you'll detect it right
+away instead of it being buried in noise
+
+ align:start position:0%
+away instead of it being buried in noise
+ 
+
+ align:start position:0%
+away instead of it being buried in noise
+and uh start sorting through your recent
+
+ align:start position:0%
+and uh start sorting through your recent
+ 
+
+ align:start position:0%
+and uh start sorting through your recent
+memories to to see where you might have
+
+ align:start position:0%
+memories to to see where you might have
+ 
+
+ align:start position:0%
+memories to to see where you might have
+made your mistake and so forth so
+
+ align:start position:0%
+made your mistake and so forth so
+ 
+
+ align:start position:0%
+made your mistake and so forth so
+Consciousness is a great idea provided
+
+ align:start position:0%
+Consciousness is a great idea provided
+ 
+
+ align:start position:0%
+Consciousness is a great idea provided
+you don't believe it's it's a mysterious
+
+ align:start position:0%
+you don't believe it's it's a mysterious
+ 
+
+ align:start position:0%
+you don't believe it's it's a mysterious
+thing but say um I'm saying it's these
+
+ align:start position:0%
+thing but say um I'm saying it's these
+ 
+
+ align:start position:0%
+thing but say um I'm saying it's these
+four things I'm really hoping somebody
+
+ align:start position:0%
+four things I'm really hoping somebody
+ 
+
+ align:start position:0%
+four things I'm really hoping somebody
+will find five others that are pretty
+
+ align:start position:0%
+will find five others that are pretty
+ 
+
+ align:start position:0%
+will find five others that are pretty
+different that yeah isn't isn't the it
+
+ align:start position:0%
+different that yeah isn't isn't the it
+ 
+
+ align:start position:0%
+different that yeah isn't isn't the it
+seems like the trouble detector is kind
+
+ align:start position:0%
+seems like the trouble detector is kind
+ 
+
+ align:start position:0%
+seems like the trouble detector is kind
+of the hard part right like so what the
+
+ align:start position:0%
+of the hard part right like so what the
+ 
+
+ align:start position:0%
+of the hard part right like so what the
+trouble detector is kind of so I mean if
+
+ align:start position:0%
+trouble detector is kind of so I mean if
+ 
+
+ align:start position:0%
+trouble detector is kind of so I mean if
+I'm if I'm doing a task and my brain is
+
+ align:start position:0%
+I'm if I'm doing a task and my brain is
+ 
+
+ align:start position:0%
+I'm if I'm doing a task and my brain is
+sort of involved in something it's sort
+
+ align:start position:0%
+sort of involved in something it's sort
+ 
+
+ align:start position:0%
+sort of involved in something it's sort
+of like when do you know
+
+ align:start position:0%
+of like when do you know
+ 
+
+ align:start position:0%
+of like when do you know
+that you know enough now is the time to
+
+ align:start position:0%
+that you know enough now is the time to
+ 
+
+ align:start position:0%
+that you know enough now is the time to
+you know bring it up level well the rest
+
+ align:start position:0%
+you know bring it up level well the rest
+ 
+
+ align:start position:0%
+you know bring it up level well the rest
+of the book is about uh these things
+
+ align:start position:0%
+of the book is about uh these things
+ 
+
+ align:start position:0%
+of the book is about uh these things
+called critics and maybe this trouble
+
+ align:start position:0%
+called critics and maybe this trouble
+ 
+
+ align:start position:0%
+called critics and maybe this trouble
+detector is one of the first examples
+
+ align:start position:0%
+detector is one of the first examples
+ 
+
+ align:start position:0%
+detector is one of the first examples
+then I generalize it and say all all
+
+ align:start position:0%
+then I generalize it and say all all
+ 
+
+ align:start position:0%
+then I generalize it and say all all
+thinking involves doing stuff you know
+
+ align:start position:0%
+thinking involves doing stuff you know
+ 
+
+ align:start position:0%
+thinking involves doing stuff you know
+how to do but having other things
+
+ align:start position:0%
+how to do but having other things
+ 
+
+ align:start position:0%
+how to do but having other things
+recognizing not that you're in trouble
+
+ align:start position:0%
+recognizing not that you're in trouble
+ 
+
+ align:start position:0%
+recognizing not that you're in trouble
+but what kind of trouble you're in and
+
+ align:start position:0%
+but what kind of trouble you're in and
+ 
+
+ align:start position:0%
+but what kind of trouble you're in and
+this Consciousness detector is maybe
+
+ align:start position:0%
+this Consciousness detector is maybe
+ 
+
+ align:start position:0%
+this Consciousness detector is maybe
+what you do when everything else has
+
+ align:start position:0%
+what you do when everything else has
+ 
+
+ align:start position:0%
+what you do when everything else has
+failed at lower levels and you're still
+
+ align:start position:0%
+failed at lower levels and you're still
+ 
+
+ align:start position:0%
+failed at lower levels and you're still
+screwing up and it says well uh screw
+
+ align:start position:0%
+screwing up and it says well uh screw
+ 
+
+ align:start position:0%
+screwing up and it says well uh screw
+those lower levels let's get some
+
+ align:start position:0%
+those lower levels let's get some
+ 
+
+ align:start position:0%
+those lower levels let's get some
+reflective symbolic analytical serial
+
+ align:start position:0%
+reflective symbolic analytical serial
+ 
+
+ align:start position:0%
+reflective symbolic analytical serial
+logical processes going and see if we
+
+ align:start position:0%
+logical processes going and see if we
+ 
+
+ align:start position:0%
+logical processes going and see if we
+can take this thing apart and find in
+
+ align:start position:0%
+can take this thing apart and find in
+ 
+
+ align:start position:0%
+can take this thing apart and find in
+other words instead of I'm I'm made of
+
+ align:start position:0%
+other words instead of I'm I'm made of
+ 
+
+ align:start position:0%
+other words instead of I'm I'm made of
+bad protoplasm I can't aim you're saying
+
+ align:start position:0%
+bad protoplasm I can't aim you're saying
+ 
+
+ align:start position:0%
+bad protoplasm I can't aim you're saying
+well uh is there some other way I can
+
+ align:start position:0%
+well uh is there some other way I can
+ 
+
+ align:start position:0%
+well uh is there some other way I can
+fool my uh
+
+ align:start position:0%
+fool my uh
+ 
+
+ align:start position:0%
+fool my uh
+whatever I'm doing for
+
+ align:start position:0%
+whatever I'm doing for
+ 
+
+ align:start position:0%
+whatever I'm doing for
+example uh if you've ever shot a gun
+
+ align:start position:0%
+example uh if you've ever shot a gun
+ 
+
+ align:start position:0%
+example uh if you've ever shot a gun
+which I uh once I was once in the Navy
+
+ align:start position:0%
+which I uh once I was once in the Navy
+ 
+
+ align:start position:0%
+which I uh once I was once in the Navy
+and we got some
+
+ align:start position:0%
+and we got some
+ 
+
+ align:start position:0%
+and we got some
+training and one of the things is that
+
+ align:start position:0%
+training and one of the things is that
+ 
+
+ align:start position:0%
+training and one of the things is that
+uh if you're firing a 3030 rifle it's a
+
+ align:start position:0%
+uh if you're firing a 3030 rifle it's a
+ 
+
+ align:start position:0%
+uh if you're firing a 3030 rifle it's a
+big bang and it really hurts and so
+
+ align:start position:0%
+big bang and it really hurts and so
+ 
+
+ align:start position:0%
+big bang and it really hurts and so
+forth so just as about to pull the
+
+ align:start position:0%
+forth so just as about to pull the
+ 
+
+ align:start position:0%
+forth so just as about to pull the
+trigger you wince because you're
+
+ align:start position:0%
+trigger you wince because you're
+ 
+
+ align:start position:0%
+trigger you wince because you're
+expecting this terrible noise and and
+
+ align:start position:0%
+expecting this terrible noise and and
+ 
+
+ align:start position:0%
+expecting this terrible noise and and
+uh so uh you have to turn off
+
+ align:start position:0%
+uh so uh you have to turn off
+ 
+
+ align:start position:0%
+uh so uh you have to turn off
+uh you have to figure out some way to uh
+
+ align:start position:0%
+uh you have to figure out some way to uh
+ 
+
+ align:start position:0%
+uh you have to figure out some way to uh
+and what some people say is uh you
+
+ align:start position:0%
+and what some people say is uh you
+ 
+
+ align:start position:0%
+and what some people say is uh you
+should squeeze the trigger so slowly
+
+ align:start position:0%
+should squeeze the trigger so slowly
+ 
+
+ align:start position:0%
+should squeeze the trigger so slowly
+that you don't know when it's going to
+
+ align:start position:0%
+that you don't know when it's going to
+ 
+
+ align:start position:0%
+that you don't know when it's going to
+go off and that way you won't wince just
+
+ align:start position:0%
+go off and that way you won't wince just
+ 
+
+ align:start position:0%
+go off and that way you won't wince just
+as as it happens because it takes 100
+
+ align:start position:0%
+as as it happens because it takes 100
+ 
+
+ align:start position:0%
+as as it happens because it takes 100
+milliseconds to react to something by
+
+ align:start position:0%
+milliseconds to react to something by
+ 
+
+ align:start position:0%
+milliseconds to react to something by
+that time the bullet is on its
+
+ align:start position:0%
+that time the bullet is on its
+ 
+
+ align:start position:0%
+that time the bullet is on its
+way you know human reaction time is
+
+ align:start position:0%
+way you know human reaction time is
+ 
+
+ align:start position:0%
+way you know human reaction time is
+a between 100 and
+
+ align:start position:0%
+a between 100 and
+ 
+
+ align:start position:0%
+a between 100 and
+200 one and two 2 t0 of a
+
+ align:start position:0%
+200 one and two 2 t0 of a
+ 
+
+ align:start position:0%
+200 one and two 2 t0 of a
+second so
+
+ align:start position:0%
+second so
+ 
+
+ align:start position:0%
+second so
+uh my colleague Seymour papert did a lot
+
+ align:start position:0%
+uh my colleague Seymour papert did a lot
+ 
+
+ align:start position:0%
+uh my colleague Seymour papert did a lot
+of research on juggling and in fact uh
+
+ align:start position:0%
+of research on juggling and in fact uh
+ 
+
+ align:start position:0%
+of research on juggling and in fact uh
+we hired uh professional jugglers to
+
+ align:start position:0%
+we hired uh professional jugglers to
+ 
+
+ align:start position:0%
+we hired uh professional jugglers to
+tell us how they did it and the most
+
+ align:start position:0%
+tell us how they did it and the most
+ 
+
+ align:start position:0%
+tell us how they did it and the most
+important piece of advice is don't keep
+
+ align:start position:0%
+important piece of advice is don't keep
+ 
+
+ align:start position:0%
+important piece of advice is don't keep
+your eye on the
+
+ align:start position:0%
+your eye on the
+ 
+
+ align:start position:0%
+your eye on the
+bull because if you juggle one bll and
+
+ align:start position:0%
+bull because if you juggle one bll and
+ 
+
+ align:start position:0%
+bull because if you juggle one bll and
+you track it there's no problem if there
+
+ align:start position:0%
+you track it there's no problem if there
+ 
+
+ align:start position:0%
+you track it there's no problem if there
+two the first place you can't keep your
+
+ align:start position:0%
+two the first place you can't keep your
+ 
+
+ align:start position:0%
+two the first place you can't keep your
+eye on the bll and the second place if
+
+ align:start position:0%
+eye on the bll and the second place if
+ 
+
+ align:start position:0%
+eye on the bll and the second place if
+the ball is over here and your hand is
+
+ align:start position:0%
+the ball is over here and your hand is
+ 
+
+ align:start position:0%
+the ball is over here and your hand is
+here it's too
+
+ align:start position:0%
+here it's too
+ 
+
+ align:start position:0%
+here it's too
+late so in fact what a good juggler does
+
+ align:start position:0%
+late so in fact what a good juggler does
+ 
+
+ align:start position:0%
+late so in fact what a good juggler does
+is you only look up here and you look at
+
+ align:start position:0%
+is you only look up here and you look at
+ 
+
+ align:start position:0%
+is you only look up here and you look at
+you look for the top of the parabola
+
+ align:start position:0%
+you look for the top of the parabola
+ 
+
+ align:start position:0%
+you look for the top of the parabola
+which is a great time because the Bull's
+
+ align:start position:0%
+which is a great time because the Bull's
+ 
+
+ align:start position:0%
+which is a great time because the Bull's
+going really slowly and you've got
+
+ align:start position:0%
+going really slowly and you've got
+ 
+
+ align:start position:0%
+going really slowly and you've got
+plenty of time and then some part of
+
+ align:start position:0%
+plenty of time and then some part of
+ 
+
+ align:start position:0%
+plenty of time and then some part of
+your brain extrapolates that and gets
+
+ align:start position:0%
+your brain extrapolates that and gets
+ 
+
+ align:start position:0%
+your brain extrapolates that and gets
+your hand ready to go there of course in
+
+ align:start position:0%
+your hand ready to go there of course in
+ 
+
+ align:start position:0%
+your hand ready to go there of course in
+the meantime there's another Bowl that's
+
+ align:start position:0%
+the meantime there's another Bowl that's
+ 
+
+ align:start position:0%
+the meantime there's another Bowl that's
+already gone by and your hand is was
+
+ align:start position:0%
+already gone by and your hand is was
+ 
+
+ align:start position:0%
+already gone by and your hand is was
+here to receive it but uh after about 40
+
+ align:start position:0%
+here to receive it but uh after about 40
+ 
+
+ align:start position:0%
+here to receive it but uh after about 40
+minutes the average person is able to uh
+
+ align:start position:0%
+minutes the average person is able to uh
+ 
+
+ align:start position:0%
+minutes the average person is able to uh
+get two or two of these going and uh
+
+ align:start position:0%
+get two or two of these going and uh
+ 
+
+ align:start position:0%
+get two or two of these going and uh
+less than two hours if you really focus
+
+ align:start position:0%
+less than two hours if you really focus
+ 
+
+ align:start position:0%
+less than two hours if you really focus
+you can start doing three Ball Juggling
+
+ align:start position:0%
+you can start doing three Ball Juggling
+ 
+
+ align:start position:0%
+you can start doing three Ball Juggling
+uh we actually had a PhD thesis on this
+
+ align:start position:0%
+uh we actually had a PhD thesis on this
+ 
+
+ align:start position:0%
+uh we actually had a PhD thesis on this
+by a clever guy named Howard Austin and
+
+ align:start position:0%
+by a clever guy named Howard Austin and
+ 
+
+ align:start position:0%
+by a clever guy named Howard Austin and
+Austin uh took all these notes that we
+
+ align:start position:0%
+Austin uh took all these notes that we
+ 
+
+ align:start position:0%
+Austin uh took all these notes that we
+had made from The Professional uh
+
+ align:start position:0%
+had made from The Professional uh
+ 
+
+ align:start position:0%
+had made from The Professional uh
+jugglers and uh set up a course and the
+
+ align:start position:0%
+jugglers and uh set up a course and the
+ 
+
+ align:start position:0%
+jugglers and uh set up a course and the
+course was how to juggle and it had
+
+ align:start position:0%
+course was how to juggle and it had
+ 
+
+ align:start position:0%
+course was how to juggle and it had
+three basic principles the most
+
+ align:start position:0%
+three basic principles the most
+ 
+
+ align:start position:0%
+three basic principles the most
+important principle was that uh one
+
+ align:start position:0%
+important principle was that uh one
+ 
+
+ align:start position:0%
+important principle was that uh one
+mistake you're liable to make is that
+
+ align:start position:0%
+mistake you're liable to make is that
+ 
+
+ align:start position:0%
+mistake you're liable to make is that
+the ball goes forward so you step
+
+ align:start position:0%
+the ball goes forward so you step
+ 
+
+ align:start position:0%
+the ball goes forward so you step
+forward to get it well then you're
+
+ align:start position:0%
+forward to get it well then you're
+ 
+
+ align:start position:0%
+forward to get it well then you're
+doomed because the next ball is going to
+
+ align:start position:0%
+doomed because the next ball is going to
+ 
+
+ align:start position:0%
+doomed because the next ball is going to
+go further and you crash into the wool
+
+ align:start position:0%
+go further and you crash into the wool
+ 
+
+ align:start position:0%
+go further and you crash into the wool
+uh and the way the pros deal with
+
+ align:start position:0%
+uh and the way the pros deal with
+ 
+
+ align:start position:0%
+uh and the way the pros deal with
+beginners is that is that you juggle
+
+ align:start position:0%
+beginners is that is that you juggle
+ 
+
+ align:start position:0%
+beginners is that is that you juggle
+right next to the wall so you can't walk
+
+ align:start position:0%
+right next to the wall so you can't walk
+ 
+
+ align:start position:0%
+right next to the wall so you can't walk
+forward and that cures
+
+ align:start position:0%
+forward and that cures
+ 
+
+ align:start position:0%
+forward and that cures
+that and then there's the uh looking at
+
+ align:start position:0%
+that and then there's the uh looking at
+ 
+
+ align:start position:0%
+that and then there's the uh looking at
+the looking up here with what going on
+
+ align:start position:0%
+the looking up here with what going on
+ 
+
+ align:start position:0%
+the looking up here with what going on
+and because if you look here it's too
+
+ align:start position:0%
+and because if you look here it's too
+ 
+
+ align:start position:0%
+and because if you look here it's too
+late you can't react and you can't learn
+
+ align:start position:0%
+late you can't react and you can't learn
+ 
+
+ align:start position:0%
+late you can't react and you can't learn
+much and I forget the third
+
+ align:start position:0%
+much and I forget the third
+ 
+
+ align:start position:0%
+much and I forget the third
+rule but the joke was that it took uh
+
+ align:start position:0%
+rule but the joke was that it took uh
+ 
+
+ align:start position:0%
+rule but the joke was that it took uh
+the untrained people about 40 minutes to
+
+ align:start position:0%
+the untrained people about 40 minutes to
+ 
+
+ align:start position:0%
+the untrained people about 40 minutes to
+reach a certain skill level uh and with
+
+ align:start position:0%
+reach a certain skill level uh and with
+ 
+
+ align:start position:0%
+reach a certain skill level uh and with
+Howard's 20 minute course then it took
+
+ align:start position:0%
+Howard's 20 minute course then it took
+ 
+
+ align:start position:0%
+Howard's 20 minute course then it took
+them only 20 more minutes
+
+ align:start position:0%
+them only 20 more minutes
+ 
+
+ align:start position:0%
+them only 20 more minutes
+to reach that skill level and uh he came
+
+ align:start position:0%
+to reach that skill level and uh he came
+ 
+
+ align:start position:0%
+to reach that skill level and uh he came
+out with this wonderful collection of
+
+ align:start position:0%
+out with this wonderful collection of
+ 
+
+ align:start position:0%
+out with this wonderful collection of
+data which says it takes 40 minutes to
+
+ align:start position:0%
+data which says it takes 40 minutes to
+ 
+
+ align:start position:0%
+data which says it takes 40 minutes to
+learn to juggle this well whether you
+
+ align:start position:0%
+learn to juggle this well whether you
+ 
+
+ align:start position:0%
+learn to juggle this well whether you
+teach your whether you're trained or
+
+ align:start position:0%
+teach your whether you're trained or
+ 
+
+ align:start position:0%
+teach your whether you're trained or
+not um which we regarded as a great
+
+ align:start position:0%
+not um which we regarded as a great
+ 
+
+ align:start position:0%
+not um which we regarded as a great
+positive result but other people said
+
+ align:start position:0%
+positive result but other people said
+ 
+
+ align:start position:0%
+positive result but other people said
+what's the use then if it
+
+ align:start position:0%
+what's the use then if it
+ 
+
+ align:start position:0%
+what's the use then if it
+doesn't uh but the conjecture is maybe
+
+ align:start position:0%
+doesn't uh but the conjecture is maybe
+ 
+
+ align:start position:0%
+doesn't uh but the conjecture is maybe
+for five bow got juggling
+
+ align:start position:0%
+for five bow got juggling
+ 
+
+ align:start position:0%
+for five bow got juggling
+juggling something like that would help
+
+ align:start position:0%
+juggling something like that would help
+ 
+
+ align:start position:0%
+juggling something like that would help
+even more since no normal person ever
+
+ align:start position:0%
+even more since no normal person ever
+ 
+
+ align:start position:0%
+even more since no normal person ever
+gets that far any of you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+juggle
+
+ align:start position:0%
+juggle
+ 
+
+ align:start position:0%
+juggle
+problem who a Juggle problem set
+
+ align:start position:0%
+problem who a Juggle problem set
+ 
+
+ align:start position:0%
+problem who a Juggle problem set
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+yes yes how do you decide which problem
+
+ align:start position:0%
+yes yes how do you decide which problem
+ 
+
+ align:start position:0%
+yes yes how do you decide which problem
+to work on next the one that's most
+
+ align:start position:0%
+to work on next the one that's most
+ 
+
+ align:start position:0%
+to work on next the one that's most
+attractive or the one that you want to
+
+ align:start position:0%
+attractive or the one that you want to
+ 
+
+ align:start position:0%
+attractive or the one that you want to
+get it over with we were
+
+ align:start position:0%
+get it over with we were
+ 
+
+ align:start position:0%
+get it over with we were
+just anyway I that's all I wanted to say
+
+ align:start position:0%
+just anyway I that's all I wanted to say
+ 
+
+ align:start position:0%
+just anyway I that's all I wanted to say
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+there's all sorts of other stories in
+
+ align:start position:0%
+there's all sorts of other stories in
+ 
+
+ align:start position:0%
+there's all sorts of other stories in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and toward the end of the
+
+ align:start position:0%
+and toward the end of the
+ 
+
+ align:start position:0%
+and toward the end of the
+chapter oh here's here's where I start
+
+ align:start position:0%
+chapter oh here's here's where I start
+ 
+
+ align:start position:0%
+chapter oh here's here's where I start
+talking about Chalmer I didn't discuss
+
+ align:start position:0%
+talking about Chalmer I didn't discuss
+ 
+
+ align:start position:0%
+talking about Chalmer I didn't discuss
+the zombie machine problem here uh maybe
+
+ align:start position:0%
+the zombie machine problem here uh maybe
+ 
+
+ align:start position:0%
+the zombie machine problem here uh maybe
+I'll uh I have a draft of it which I
+
+ align:start position:0%
+I'll uh I have a draft of it which I
+ 
+
+ align:start position:0%
+I'll uh I have a draft of it which I
+didn't put in the book about why it's
+
+ align:start position:0%
+didn't put in the book about why it's
+ 
+
+ align:start position:0%
+didn't put in the book about why it's
+not logically possible that there there
+
+ align:start position:0%
+not logically possible that there there
+ 
+
+ align:start position:0%
+not logically possible that there there
+could be two machines I might be wrong
+
+ align:start position:0%
+could be two machines I might be wrong
+ 
+
+ align:start position:0%
+could be two machines I might be wrong
+it's a nice argument though uh however
+
+ align:start position:0%
+it's a nice argument though uh however
+ 
+
+ align:start position:0%
+it's a nice argument though uh however
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+right uh this week I we have a
+
+ align:start position:0%
+right uh this week I we have a
+ 
+
+ align:start position:0%
+right uh this week I we have a
+visitor Professor takabayashi from uh
+
+ align:start position:0%
+visitor Professor takabayashi from uh
+ 
+
+ align:start position:0%
+visitor Professor takabayashi from uh
+what's it called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+University uh uh I've known him for more
+
+ align:start position:0%
+University uh uh I've known him for more
+ 
+
+ align:start position:0%
+University uh uh I've known him for more
+than 20 years and we've worked together
+
+ align:start position:0%
+than 20 years and we've worked together
+ 
+
+ align:start position:0%
+than 20 years and we've worked together
+from time to time on all sorts of
+
+ align:start position:0%
+from time to time on all sorts of
+ 
+
+ align:start position:0%
+from time to time on all sorts of
+different problems uh he's uh expert in
+
+ align:start position:0%
+different problems uh he's uh expert in
+ 
+
+ align:start position:0%
+different problems uh he's uh expert in
+Signal processing
+
+ align:start position:0%
+Signal processing
+ 
+
+ align:start position:0%
+Signal processing
+made any number of inventions I think he
+
+ align:start position:0%
+made any number of inventions I think he
+ 
+
+ align:start position:0%
+made any number of inventions I think he
+you made the first telephone where you
+
+ align:start position:0%
+you made the first telephone where you
+ 
+
+ align:start position:0%
+you made the first telephone where you
+could speak numbers and it would dial
+
+ align:start position:0%
+could speak numbers and it would dial
+ 
+
+ align:start position:0%
+could speak numbers and it would dial
+and did did toi at toiba did they ever
+
+ align:start position:0%
+and did did toi at toiba did they ever
+ 
+
+ align:start position:0%
+and did did toi at toiba did they ever
+make a product of that did it sell yes
+
+ align:start position:0%
+make a product of that did it sell yes
+ 
+
+ align:start position:0%
+make a product of that did it sell yes
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and he made some speech recognition
+
+ align:start position:0%
+good and he made some speech recognition
+ 
+
+ align:start position:0%
+good and he made some speech recognition
+systems that were quite good uh I know
+
+ align:start position:0%
+systems that were quite good uh I know
+ 
+
+ align:start position:0%
+systems that were quite good uh I know
+some people here who made speech
+
+ align:start position:0%
+some people here who made speech
+ 
+
+ align:start position:0%
+some people here who made speech
+recognition systems and they wanted to
+
+ align:start position:0%
+recognition systems and they wanted to
+ 
+
+ align:start position:0%
+recognition systems and they wanted to
+make one which would still work if there
+
+ align:start position:0%
+make one which would still work if there
+ 
+
+ align:start position:0%
+make one which would still work if there
+were a lot of noise so because they had
+
+ align:start position:0%
+were a lot of noise so because they had
+ 
+
+ align:start position:0%
+were a lot of noise so because they had
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+mathematical training they said well of
+
+ align:start position:0%
+mathematical training they said well of
+ 
+
+ align:start position:0%
+mathematical training they said well of
+course White gaussian Noise would be the
+
+ align:start position:0%
+course White gaussian Noise would be the
+ 
+
+ align:start position:0%
+course White gaussian Noise would be the
+best thing and
+
+ align:start position:0%
+best thing and
+ 
+
+ align:start position:0%
+best thing and
+uh yoichi
+
+ align:start position:0%
+uh yoichi
+ 
+
+ align:start position:0%
+uh yoichi
+takabayashi didn't think white noise was
+
+ align:start position:0%
+takabayashi didn't think white noise was
+ 
+
+ align:start position:0%
+takabayashi didn't think white noise was
+good so uh he made a lot of tapes of
+
+ align:start position:0%
+good so uh he made a lot of tapes of
+ 
+
+ align:start position:0%
+good so uh he made a lot of tapes of
+people saying numbers in the middle of
+
+ align:start position:0%
+people saying numbers in the middle of
+ 
+
+ align:start position:0%
+people saying numbers in the middle of
+Tokyo Station which is the noisiest
+
+ align:start position:0%
+Tokyo Station which is the noisiest
+ 
+
+ align:start position:0%
+Tokyo Station which is the noisiest
+place in the world maybe and it's full
+
+ align:start position:0%
+place in the world maybe and it's full
+ 
+
+ align:start position:0%
+place in the world maybe and it's full
+of every kind of noise so uh somehow
+
+ align:start position:0%
+of every kind of noise so uh somehow
+ 
+
+ align:start position:0%
+of every kind of noise so uh somehow
+that made his system robust enough to be
+
+ align:start position:0%
+that made his system robust enough to be
+ 
+
+ align:start position:0%
+that made his system robust enough to be
+a product but anyway uh for the last few
+
+ align:start position:0%
+a product but anyway uh for the last few
+ 
+
+ align:start position:0%
+a product but anyway uh for the last few
+years he he quit industry became a
+
+ align:start position:0%
+years he he quit industry became a
+ 
+
+ align:start position:0%
+years he he quit industry became a
+professor and is doing some very
+
+ align:start position:0%
+professor and is doing some very
+ 
+
+ align:start position:0%
+professor and is doing some very
+interesting things on Common Sense and
+
+ align:start position:0%
+interesting things on Common Sense and
+ 
+
+ align:start position:0%
+interesting things on Common Sense and
+uh this kind of uh highlevel cognitive
+
+ align:start position:0%
+uh this kind of uh highlevel cognitive
+ 
+
+ align:start position:0%
+uh this kind of uh highlevel cognitive
+theory so he's going to show you some
+
+ align:start position:0%
+theory so he's going to show you some
+ 
+
+ align:start position:0%
+theory so he's going to show you some
+interesting examples of that that we're
+
+ align:start position:0%
+interesting examples of that that we're
+ 
+
+ align:start position:0%
+interesting examples of that that we're
+we're very interested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in as m inod uce me um I used to work
+
+ align:start position:0%
+in as m inod uce me um I used to work
+ 
+
+ align:start position:0%
+in as m inod uce me um I used to work
+for the signal processing and uh speech
+
+ align:start position:0%
+for the signal processing and uh speech
+ 
+
+ align:start position:0%
+for the signal processing and uh speech
+recognition and also multimod speech
+
+ align:start position:0%
+recognition and also multimod speech
+ 
+
+ align:start position:0%
+recognition and also multimod speech
+dialogue system I'm the first person to
+
+ align:start position:0%
+dialogue system I'm the first person to
+ 
+
+ align:start position:0%
+dialogue system I'm the first person to
+develop the spontaneous speech dialogue
+
+ align:start position:0%
+develop the spontaneous speech dialogue
+ 
+
+ align:start position:0%
+develop the spontaneous speech dialogue
+system it
+
+ align:start position:0%
+system it
+ 
+
+ align:start position:0%
+system it
+works um very uh NOA NOA but the problem
+
+ align:start position:0%
+works um very uh NOA NOA but the problem
+ 
+
+ align:start position:0%
+works um very uh NOA NOA but the problem
+is is Task
+
+ align:start position:0%
+is is Task
+ 
+
+ align:start position:0%
+is is Task
+oriented then the Marin criticize me
+
+ align:start position:0%
+oriented then the Marin criticize me
+ 
+
+ align:start position:0%
+oriented then the Marin criticize me
+it's a toy system so I decided to
+
+ align:start position:0%
+it's a toy system so I decided to
+ 
+
+ align:start position:0%
+it's a toy system so I decided to
+develop a system
+
+ align:start position:0%
+develop a system
+ 
+
+ align:start position:0%
+develop a system
+um uh which have the common sense but uh
+
+ align:start position:0%
+um uh which have the common sense but uh
+ 
+
+ align:start position:0%
+um uh which have the common sense but uh
+uh still the common sense means just a
+
+ align:start position:0%
+uh still the common sense means just a
+ 
+
+ align:start position:0%
+uh still the common sense means just a
+white color common sense then I um
+
+ align:start position:0%
+white color common sense then I um
+ 
+
+ align:start position:0%
+white color common sense then I um
+attended the Marvin class that more than
+
+ align:start position:0%
+attended the Marvin class that more than
+ 
+
+ align:start position:0%
+attended the Marvin class that more than
+20 years ago to be exact
+
+ align:start position:0%
+20 years ago to be exact
+ 
+
+ align:start position:0%
+20 years ago to be exact
+1986 and uh at that time he wrote a book
+
+ align:start position:0%
+1986 and uh at that time he wrote a book
+ 
+
+ align:start position:0%
+1986 and uh at that time he wrote a book
+and Society mind I learn lot from him
+
+ align:start position:0%
+and Society mind I learn lot from him
+ 
+
+ align:start position:0%
+and Society mind I learn lot from him
+then the I and now um so I have been
+
+ align:start position:0%
+then the I and now um so I have been
+ 
+
+ align:start position:0%
+then the I and now um so I have been
+working for uh TOA for more than 20
+
+ align:start position:0%
+working for uh TOA for more than 20
+ 
+
+ align:start position:0%
+working for uh TOA for more than 20
+years then I moved to the shiza
+
+ align:start position:0%
+years then I moved to the shiza
+ 
+
+ align:start position:0%
+years then I moved to the shiza
+university as a professor then I have a
+
+ align:start position:0%
+university as a professor then I have a
+ 
+
+ align:start position:0%
+university as a professor then I have a
+lot of freedom to do the basic research
+
+ align:start position:0%
+lot of freedom to do the basic research
+ 
+
+ align:start position:0%
+lot of freedom to do the basic research
+then I started the
+
+ align:start position:0%
+then I started the
+ 
+
+ align:start position:0%
+then I started the
+infant and the uh learning and research
+
+ align:start position:0%
+infant and the uh learning and research
+ 
+
+ align:start position:0%
+infant and the uh learning and research
+so today I I'll introduce about the
+
+ align:start position:0%
+so today I I'll introduce about the
+ 
+
+ align:start position:0%
+so today I I'll introduce about the
+present research on the um infant the
+
+ align:start position:0%
+present research on the um infant the
+ 
+
+ align:start position:0%
+present research on the um infant the
+learning actually it's a common sense
+
+ align:start position:0%
+learning actually it's a common sense
+ 
+
+ align:start position:0%
+learning actually it's a common sense
+computing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is a whole um the
+
+ align:start position:0%
+um this is a whole um the
+ 
+
+ align:start position:0%
+um this is a whole um the
+um scope of our uh infant learning
+
+ align:start position:0%
+um scope of our uh infant learning
+ 
+
+ align:start position:0%
+um scope of our uh infant learning
+project so um the Japanese people are
+
+ align:start position:0%
+project so um the Japanese people are
+ 
+
+ align:start position:0%
+project so um the Japanese people are
+good at are making a product in real
+
+ align:start position:0%
+good at are making a product in real
+ 
+
+ align:start position:0%
+good at are making a product in real
+world not conceptually but uh I used to
+
+ align:start position:0%
+world not conceptually but uh I used to
+ 
+
+ align:start position:0%
+world not conceptually but uh I used to
+work for under the speech recognition
+
+ align:start position:0%
+work for under the speech recognition
+ 
+
+ align:start position:0%
+work for under the speech recognition
+system for practical system as a
+
+ align:start position:0%
+system for practical system as a
+ 
+
+ align:start position:0%
+system for practical system as a
+commercial product uh we observed lots
+
+ align:start position:0%
+commercial product uh we observed lots
+ 
+
+ align:start position:0%
+commercial product uh we observed lots
+of data to extract the very essential
+
+ align:start position:0%
+of data to extract the very essential
+ 
+
+ align:start position:0%
+of data to extract the very essential
+component and uh uh so uh I myself I
+
+ align:start position:0%
+component and uh uh so uh I myself I
+ 
+
+ align:start position:0%
+component and uh uh so uh I myself I
+think I believe I know that's important
+
+ align:start position:0%
+think I believe I know that's important
+ 
+
+ align:start position:0%
+think I believe I know that's important
+and that's trivial so uh uh then we
+
+ align:start position:0%
+and that's trivial so uh uh then we
+ 
+
+ align:start position:0%
+and that's trivial so uh uh then we
+started this uh infant running product
+
+ align:start position:0%
+started this uh infant running product
+ 
+
+ align:start position:0%
+started this uh infant running product
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+project um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops the uh we have the classroom the uh
+
+ align:start position:0%
+oops the uh we have the classroom the uh
+ 
+
+ align:start position:0%
+oops the uh we have the classroom the uh
+actually the co education environment
+
+ align:start position:0%
+actually the co education environment
+ 
+
+ align:start position:0%
+actually the co education environment
+for parents and infants
+
+ align:start position:0%
+for parents and infants
+ 
+
+ align:start position:0%
+for parents and infants
+because um in
+
+ align:start position:0%
+because um in
+ 
+
+ align:start position:0%
+because um in
+Japan um the infants are changing and
+
+ align:start position:0%
+Japan um the infants are changing and
+ 
+
+ align:start position:0%
+Japan um the infants are changing and
+parents are
+
+ align:start position:0%
+parents are
+ 
+
+ align:start position:0%
+parents are
+changing uh Japan used to be very safe
+
+ align:start position:0%
+changing uh Japan used to be very safe
+ 
+
+ align:start position:0%
+changing uh Japan used to be very safe
+country um very few the um the crimes
+
+ align:start position:0%
+country um very few the um the crimes
+ 
+
+ align:start position:0%
+country um very few the um the crimes
+and uh uh when I was the
+
+ align:start position:0%
+and uh uh when I was the
+ 
+
+ align:start position:0%
+and uh uh when I was the
+kid uh we we didn't lock my house it's
+
+ align:start position:0%
+kid uh we we didn't lock my house it's
+ 
+
+ align:start position:0%
+kid uh we we didn't lock my house it's
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+safe um the first time I went to Japan I
+
+ align:start position:0%
+safe um the first time I went to Japan I
+ 
+
+ align:start position:0%
+safe um the first time I went to Japan I
+had a 12-year-old daughter uh-huh and uh
+
+ align:start position:0%
+had a 12-year-old daughter uh-huh and uh
+ 
+
+ align:start position:0%
+had a 12-year-old daughter uh-huh and uh
+she wanted to go and look at Kyoto and
+
+ align:start position:0%
+she wanted to go and look at Kyoto and
+ 
+
+ align:start position:0%
+she wanted to go and look at Kyoto and
+everybody said it's perfectly
+
+ align:start position:0%
+everybody said it's perfectly
+ 
+
+ align:start position:0%
+everybody said it's perfectly
+safe so she went all by herself and uh
+
+ align:start position:0%
+safe so she went all by herself and uh
+ 
+
+ align:start position:0%
+safe so she went all by herself and uh
+but now it's very dangerous it's
+
+ align:start position:0%
+but now it's very dangerous it's
+ 
+
+ align:start position:0%
+but now it's very dangerous it's
+dangerous so that I never tell you the
+
+ align:start position:0%
+dangerous so that I never tell you the
+ 
+
+ align:start position:0%
+dangerous so that I never tell you the
+story she went to an arcade uhhuh which
+
+ align:start position:0%
+story she went to an arcade uhhuh which
+ 
+
+ align:start position:0%
+story she went to an arcade uhhuh which
+had a uh arcade game called gallaga mhm
+
+ align:start position:0%
+had a uh arcade game called gallaga mhm
+ 
+
+ align:start position:0%
+had a uh arcade game called gallaga mhm
+and it had a lot of boys playing it and
+
+ align:start position:0%
+and it had a lot of boys playing it and
+ 
+
+ align:start position:0%
+and it had a lot of boys playing it and
+uh so she had some coins so she got a
+
+ align:start position:0%
+uh so she had some coins so she got a
+ 
+
+ align:start position:0%
+uh so she had some coins so she got a
+turn and then uh she broke the
+
+ align:start position:0%
+turn and then uh she broke the
+ 
+
+ align:start position:0%
+turn and then uh she broke the
+record uh she kept uh shooting down more
+
+ align:start position:0%
+record uh she kept uh shooting down more
+ 
+
+ align:start position:0%
+record uh she kept uh shooting down more
+whatever they were and when she finished
+
+ align:start position:0%
+whatever they were and when she finished
+ 
+
+ align:start position:0%
+whatever they were and when she finished
+all the boys had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disappeared but anyway the we are
+
+ align:start position:0%
+disappeared but anyway the we are
+ 
+
+ align:start position:0%
+disappeared but anyway the we are
+designing the um the classroom infant
+
+ align:start position:0%
+designing the um the classroom infant
+ 
+
+ align:start position:0%
+designing the um the classroom infant
+classroom and the playroom and the uh so
+
+ align:start position:0%
+classroom and the playroom and the uh so
+ 
+
+ align:start position:0%
+classroom and the playroom and the uh so
+the um the the the the purpose um for
+
+ align:start position:0%
+the um the the the the purpose um for
+ 
+
+ align:start position:0%
+the um the the the the purpose um for
+our research is to develop the common
+
+ align:start position:0%
+our research is to develop the common
+ 
+
+ align:start position:0%
+our research is to develop the common
+sense Computing model and also the um
+
+ align:start position:0%
+sense Computing model and also the um
+ 
+
+ align:start position:0%
+sense Computing model and also the um
+the uh designing and developing the the
+
+ align:start position:0%
+the uh designing and developing the the
+ 
+
+ align:start position:0%
+the uh designing and developing the the
+good materials for uh infant education
+
+ align:start position:0%
+good materials for uh infant education
+ 
+
+ align:start position:0%
+good materials for uh infant education
+and the infant learning so the uh we are
+
+ align:start position:0%
+and the infant learning so the uh we are
+ 
+
+ align:start position:0%
+and the infant learning so the uh we are
+focusing on the um um
+
+ align:start position:0%
+focusing on the um um
+ 
+
+ align:start position:0%
+focusing on the um um
+the um constructing infant Behavior
+
+ align:start position:0%
+the um constructing infant Behavior
+ 
+
+ align:start position:0%
+the um constructing infant Behavior
+Corpus so Marin told um many um good the
+
+ align:start position:0%
+Corpus so Marin told um many um good the
+ 
+
+ align:start position:0%
+Corpus so Marin told um many um good the
+Articles related to the how mind works
+
+ align:start position:0%
+Articles related to the how mind works
+ 
+
+ align:start position:0%
+Articles related to the how mind works
+and and the common sense that works but
+
+ align:start position:0%
+and and the common sense that works but
+ 
+
+ align:start position:0%
+and and the common sense that works but
+U um infant is very uh simple relatively
+
+ align:start position:0%
+U um infant is very uh simple relatively
+ 
+
+ align:start position:0%
+U um infant is very uh simple relatively
+uh much simpler than the adults so we
+
+ align:start position:0%
+uh much simpler than the adults so we
+ 
+
+ align:start position:0%
+uh much simpler than the adults so we
+started this research um and this kind
+
+ align:start position:0%
+started this research um and this kind
+ 
+
+ align:start position:0%
+started this research um and this kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+research so the again the purpose of the
+
+ align:start position:0%
+research so the again the purpose of the
+ 
+
+ align:start position:0%
+research so the again the purpose of the
+project is constru um conduct basic
+
+ align:start position:0%
+project is constru um conduct basic
+ 
+
+ align:start position:0%
+project is constru um conduct basic
+Common Sense resarch Bas based on the
+
+ align:start position:0%
+Common Sense resarch Bas based on the
+ 
+
+ align:start position:0%
+Common Sense resarch Bas based on the
+scientific data real world data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um infant expressions are genuine and
+
+ align:start position:0%
+um infant expressions are genuine and
+ 
+
+ align:start position:0%
+um infant expressions are genuine and
+good for modeling it's easy easier and
+
+ align:start position:0%
+good for modeling it's easy easier and
+ 
+
+ align:start position:0%
+good for modeling it's easy easier and
+uh um then produce Rich theories for
+
+ align:start position:0%
+uh um then produce Rich theories for
+ 
+
+ align:start position:0%
+uh um then produce Rich theories for
+common sense
+
+ align:start position:0%
+common sense
+ 
+
+ align:start position:0%
+common sense
+Computing um the and the other purpose
+
+ align:start position:0%
+Computing um the and the other purpose
+ 
+
+ align:start position:0%
+Computing um the and the other purpose
+is support healthy development of the
+
+ align:start position:0%
+is support healthy development of the
+ 
+
+ align:start position:0%
+is support healthy development of the
+infant as I mentioned earlier the
+
+ align:start position:0%
+infant as I mentioned earlier the
+ 
+
+ align:start position:0%
+infant as I mentioned earlier the
+parents is an important is parenting is
+
+ align:start position:0%
+parents is an important is parenting is
+ 
+
+ align:start position:0%
+parents is an important is parenting is
+an important issu in Japan now and I
+
+ align:start position:0%
+an important issu in Japan now and I
+ 
+
+ align:start position:0%
+an important issu in Japan now and I
+think in this country
+
+ align:start position:0%
+think in this country
+ 
+
+ align:start position:0%
+think in this country
+and uh and also created multimodal
+
+ align:start position:0%
+and uh and also created multimodal
+ 
+
+ align:start position:0%
+and uh and also created multimodal
+knowledge contents for parir
+
+ align:start position:0%
+knowledge contents for parir
+ 
+
+ align:start position:0%
+knowledge contents for parir
+renting so uh this is this is a trick
+
+ align:start position:0%
+renting so uh this is this is a trick
+ 
+
+ align:start position:0%
+renting so uh this is this is a trick
+the this um infant learning itself is
+
+ align:start position:0%
+the this um infant learning itself is
+ 
+
+ align:start position:0%
+the this um infant learning itself is
+very good
+
+ align:start position:0%
+very good
+ 
+
+ align:start position:0%
+very good
+applications um I hope Japanese
+
+ align:start position:0%
+applications um I hope Japanese
+ 
+
+ align:start position:0%
+applications um I hope Japanese
+government and the US government fing it
+
+ align:start position:0%
+government and the US government fing it
+ 
+
+ align:start position:0%
+government and the US government fing it
+now now oh Japanese government
+
+ align:start position:0%
+now now oh Japanese government
+ 
+
+ align:start position:0%
+now now oh Japanese government
+uhuh that's more funding and this is our
+
+ align:start position:0%
+uhuh that's more funding and this is our
+ 
+
+ align:start position:0%
+uhuh that's more funding and this is our
+the cross room um I'll show you this
+
+ align:start position:0%
+the cross room um I'll show you this
+ 
+
+ align:start position:0%
+the cross room um I'll show you this
+demos brief
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explanations it's very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usual so um this is made by CA trees um
+
+ align:start position:0%
+usual so um this is made by CA trees um
+ 
+
+ align:start position:0%
+usual so um this is made by CA trees um
+CA Tre is that causes lots of allergy in
+
+ align:start position:0%
+CA Tre is that causes lots of allergy in
+ 
+
+ align:start position:0%
+CA Tre is that causes lots of allergy in
+in your country country but it's good
+
+ align:start position:0%
+in your country country but it's good
+ 
+
+ align:start position:0%
+in your country country but it's good
+for the um uh child classroom infant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classroom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Goku it's faster this afternoon yeah
+
+ align:start position:0%
+Goku it's faster this afternoon yeah
+ 
+
+ align:start position:0%
+Goku it's faster this afternoon yeah
+it's the building yeah building yeah uh
+
+ align:start position:0%
+it's the building yeah building yeah uh
+ 
+
+ align:start position:0%
+it's the building yeah building yeah uh
+the uh see that three um the trees and
+
+ align:start position:0%
+the uh see that three um the trees and
+ 
+
+ align:start position:0%
+the uh see that three um the trees and
+the uh four cameras
+
+ align:start position:0%
+the uh four cameras
+ 
+
+ align:start position:0%
+the uh four cameras
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'll be back to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the oh this is a um the scenary of the
+
+ align:start position:0%
+the oh this is a um the scenary of the
+ 
+
+ align:start position:0%
+the oh this is a um the scenary of the
+education okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the um the mothers and the
+
+ align:start position:0%
+the um the mothers and the
+ 
+
+ align:start position:0%
+the um the mothers and the
+infants they're working together
+
+ align:start position:0%
+infants they're working together
+ 
+
+ align:start position:0%
+infants they're working together
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hardly any of our kids go to school at
+
+ align:start position:0%
+hardly any of our kids go to school at
+ 
+
+ align:start position:0%
+hardly any of our kids go to school at
+age one sorry we don't have many
+
+ align:start position:0%
+age one sorry we don't have many
+ 
+
+ align:start position:0%
+age one sorry we don't have many
+children in school at age one yeah same
+
+ align:start position:0%
+children in school at age one yeah same
+ 
+
+ align:start position:0%
+children in school at age one yeah same
+thing happen in Japan and uh uh it's
+
+ align:start position:0%
+thing happen in Japan and uh uh it's
+ 
+
+ align:start position:0%
+thing happen in Japan and uh uh it's
+good actually in Japan the um the
+
+ align:start position:0%
+good actually in Japan the um the
+ 
+
+ align:start position:0%
+good actually in Japan the um the
+government controlled the um the
+
+ align:start position:0%
+government controlled the um the
+ 
+
+ align:start position:0%
+government controlled the um the
+elementary school but uh before the
+
+ align:start position:0%
+elementary school but uh before the
+ 
+
+ align:start position:0%
+elementary school but uh before the
+elementary SCH it's very free oh so we
+
+ align:start position:0%
+elementary SCH it's very free oh so we
+ 
+
+ align:start position:0%
+elementary SCH it's very free oh so we
+can do our own you know sat to do the
+
+ align:start position:0%
+can do our own you know sat to do the
+ 
+
+ align:start position:0%
+can do our own you know sat to do the
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+educations so the um practice of of
+
+ align:start position:0%
+educations so the um practice of of
+ 
+
+ align:start position:0%
+educations so the um practice of of
+infant school is uh we are now U have
+
+ align:start position:0%
+infant school is uh we are now U have
+ 
+
+ align:start position:0%
+infant school is uh we are now U have
+participants of one two three year old
+
+ align:start position:0%
+participants of one two three year old
+ 
+
+ align:start position:0%
+participants of one two three year old
+the children and their mothers but from
+
+ align:start position:0%
+the children and their mothers but from
+ 
+
+ align:start position:0%
+the children and their mothers but from
+the uh next April we have one two four
+
+ align:start position:0%
+the uh next April we have one two four
+ 
+
+ align:start position:0%
+the uh next April we have one two four
+years children so we are
+
+ align:start position:0%
+years children so we are
+ 
+
+ align:start position:0%
+years children so we are
+continuously doing the experiment to do
+
+ align:start position:0%
+continuously doing the experiment to do
+ 
+
+ align:start position:0%
+continuously doing the experiment to do
+research and for Designing the good uh
+
+ align:start position:0%
+research and for Designing the good uh
+ 
+
+ align:start position:0%
+research and for Designing the good uh
+environment that's very good because in
+
+ align:start position:0%
+environment that's very good because in
+ 
+
+ align:start position:0%
+environment that's very good because in
+a 100 Years you'll have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everyone so uh yeah you can have a
+
+ align:start position:0%
+everyone so uh yeah you can have a
+ 
+
+ align:start position:0%
+everyone so uh yeah you can have a
+chance to do this kind
+
+ align:start position:0%
+chance to do this kind
+ 
+
+ align:start position:0%
+chance to do this kind
+of so the um the classroom is uh uh half
+
+ align:start position:0%
+of so the um the classroom is uh uh half
+ 
+
+ align:start position:0%
+of so the um the classroom is uh uh half
+an hour and the prum and parenting and
+
+ align:start position:0%
+an hour and the prum and parenting and
+ 
+
+ align:start position:0%
+an hour and the prum and parenting and
+counseling is a half half half an hour
+
+ align:start position:0%
+counseling is a half half half an hour
+ 
+
+ align:start position:0%
+counseling is a half half half an hour
+again this is a trick it's good for the
+
+ align:start position:0%
+again this is a trick it's good for the
+ 
+
+ align:start position:0%
+again this is a trick it's good for the
+the U parents so we can get scientific
+
+ align:start position:0%
+the U parents so we can get scientific
+ 
+
+ align:start position:0%
+the U parents so we can get scientific
+data to do research to the basic
+
+ align:start position:0%
+data to do research to the basic
+ 
+
+ align:start position:0%
+data to do research to the basic
+research so the um the at this moment
+
+ align:start position:0%
+research so the um the at this moment
+ 
+
+ align:start position:0%
+research so the um the at this moment
+the long-term recording of data we um 22
+
+ align:start position:0%
+the long-term recording of data we um 22
+ 
+
+ align:start position:0%
+the long-term recording of data we um 22
+months uh um since um
+
+ align:start position:0%
+months uh um since um
+ 
+
+ align:start position:0%
+months uh um since um
+June of
+
+ align:start position:0%
+June of
+ 
+
+ align:start position:0%
+June of
+2005 and
+
+ align:start position:0%
+2005 and
+ 
+
+ align:start position:0%
+2005 and
+uh 146 occasions of classroom and
+
+ align:start position:0%
+uh 146 occasions of classroom and
+ 
+
+ align:start position:0%
+uh 146 occasions of classroom and
+playrooms the more than 200 hours of
+
+ align:start position:0%
+playrooms the more than 200 hours of
+ 
+
+ align:start position:0%
+playrooms the more than 200 hours of
+recording the movie of the speech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data and uh um we we we are trying to
+
+ align:start position:0%
+data and uh um we we we are trying to
+ 
+
+ align:start position:0%
+data and uh um we we we are trying to
+accumulate of um Child Care knoow from
+
+ align:start position:0%
+accumulate of um Child Care knoow from
+ 
+
+ align:start position:0%
+accumulate of um Child Care knoow from
+Child Care the clinic to the
+
+ align:start position:0%
+Child Care the clinic to the
+ 
+
+ align:start position:0%
+Child Care the clinic to the
+family uh uh it is the um good for the
+
+ align:start position:0%
+family uh uh it is the um good for the
+ 
+
+ align:start position:0%
+family uh uh it is the um good for the
+family and uh um so that's why we can um
+
+ align:start position:0%
+family and uh um so that's why we can um
+ 
+
+ align:start position:0%
+family and uh um so that's why we can um
+and do the very useful the um
+
+ align:start position:0%
+and do the very useful the um
+ 
+
+ align:start position:0%
+and do the very useful the um
+experiment like um
+
+ align:start position:0%
+experiment like um
+ 
+
+ align:start position:0%
+experiment like um
+parents
+
+ align:start position:0%
+parents
+ 
+
+ align:start position:0%
+parents
+uh um um connecting to the uh our uh the
+
+ align:start position:0%
+uh um um connecting to the uh our uh the
+ 
+
+ align:start position:0%
+uh um um connecting to the uh our uh the
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+and other schools are related can be
+
+ align:start position:0%
+and other schools are related can be
+ 
+
+ align:start position:0%
+and other schools are related can be
+related to the um our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classes
+
+ align:start position:0%
+classes
+ 
+
+ align:start position:0%
+classes
+okay and uh the um the but the um the
+
+ align:start position:0%
+okay and uh the um the but the um the
+ 
+
+ align:start position:0%
+okay and uh the um the but the um the
+reason five that to do our the um
+
+ align:start position:0%
+reason five that to do our the um
+ 
+
+ align:start position:0%
+reason five that to do our the um
+project is a
+
+ align:start position:0%
+project is a
+ 
+
+ align:start position:0%
+project is a
+um the um based on the the Marvin's the
+
+ align:start position:0%
+um the um based on the the Marvin's the
+ 
+
+ align:start position:0%
+um the um based on the the Marvin's the
+emotion machine book especially the the
+
+ align:start position:0%
+emotion machine book especially the the
+ 
+
+ align:start position:0%
+emotion machine book especially the the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+practice of a pushes scenario um
+
+ align:start position:0%
+practice of a pushes scenario um
+ 
+
+ align:start position:0%
+practice of a pushes scenario um
+we uh I'll will show you very
+
+ align:start position:0%
+we uh I'll will show you very
+ 
+
+ align:start position:0%
+we uh I'll will show you very
+interesting uh the um experimental data
+
+ align:start position:0%
+interesting uh the um experimental data
+ 
+
+ align:start position:0%
+interesting uh the um experimental data
+um the uh we put the blocks in the
+
+ align:start position:0%
+um the uh we put the blocks in the
+ 
+
+ align:start position:0%
+um the uh we put the blocks in the
+playroom and uh infants did
+
+ align:start position:0%
+playroom and uh infants did
+ 
+
+ align:start position:0%
+playroom and uh infants did
+collaboration by accident the this is uh
+
+ align:start position:0%
+collaboration by accident the this is uh
+ 
+
+ align:start position:0%
+collaboration by accident the this is uh
+I'll show you the which is the driver
+
+ align:start position:0%
+I'll show you the which is the driver
+ 
+
+ align:start position:0%
+I'll show you the which is the driver
+task
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not the want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a truck
+
+ align:start position:0%
+so it's a truck
+ 
+
+ align:start position:0%
+so it's a truck
+car yeah yeah truck um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the like a bus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now audio doesn't work well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sound yeah no no no actually the uh some
+
+ align:start position:0%
+sound yeah no no no actually the uh some
+ 
+
+ align:start position:0%
+sound yeah no no no actually the uh some
+the background program is right
+
+ align:start position:0%
+the background program is right
+ 
+
+ align:start position:0%
+the background program is right
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Microsoft that's how babies cry in
+
+ align:start position:0%
+Microsoft that's how babies cry in
+ 
+
+ align:start position:0%
+Microsoft that's how babies cry in
+Japanese
+
+ align:start position:0%
+Japanese
+ 
+
+ align:start position:0%
+Japanese
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um the among the lots of recorded
+
+ align:start position:0%
+so um the among the lots of recorded
+ 
+
+ align:start position:0%
+so um the among the lots of recorded
+data we can choose the very the uh
+
+ align:start position:0%
+data we can choose the very the uh
+ 
+
+ align:start position:0%
+data we can choose the very the uh
+interesting the parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's actually giving the steering wheel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah how old are they two um three and
+
+ align:start position:0%
+yeah how old are they two um three and
+ 
+
+ align:start position:0%
+yeah how old are they two um three and
+four okay
+
+ align:start position:0%
+four okay
+ 
+
+ align:start position:0%
+four okay
+so because younger ones wouldn't
+
+ align:start position:0%
+so because younger ones wouldn't
+ 
+
+ align:start position:0%
+so because younger ones wouldn't
+negotiate that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well have they seen the movie from push
+
+ align:start position:0%
+well have they seen the movie from push
+ 
+
+ align:start position:0%
+well have they seen the movie from push
+Theses I don't think so push sing wrote
+
+ align:start position:0%
+Theses I don't think so push sing wrote
+ 
+
+ align:start position:0%
+Theses I don't think so push sing wrote
+his PhD Theses with a model of the first
+
+ align:start position:0%
+his PhD Theses with a model of the first
+ 
+
+ align:start position:0%
+his PhD Theses with a model of the first
+three layers of
+
+ align:start position:0%
+three layers of
+ 
+
+ align:start position:0%
+three layers of
+the motion machine architecture that has
+
+ align:start position:0%
+the motion machine architecture that has
+ 
+
+ align:start position:0%
+the motion machine architecture that has
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+robots and one runs into trouble and the
+
+ align:start position:0%
+robots and one runs into trouble and the
+ 
+
+ align:start position:0%
+robots and one runs into trouble and the
+other figures out
+
+ align:start position:0%
+other figures out
+ 
+
+ align:start position:0%
+other figures out
+how to help
+
+ align:start position:0%
+how to help
+ 
+
+ align:start position:0%
+how to help
+it you program at threeyear Old to
+
+ align:start position:0%
+it you program at threeyear Old to
+ 
+
+ align:start position:0%
+it you program at threeyear Old to
+do yeah um actually the um oh and this
+
+ align:start position:0%
+do yeah um actually the um oh and this
+ 
+
+ align:start position:0%
+do yeah um actually the um oh and this
+is a problem solving um and is a example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sometimes um they use a he use a
+
+ align:start position:0%
+so sometimes um they use a he use a
+ 
+
+ align:start position:0%
+so sometimes um they use a he use a
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+level the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowledge for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spee speech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we have cameras the on the top
+
+ align:start position:0%
+now we have cameras the on the top
+ 
+
+ align:start position:0%
+now we have cameras the on the top
+what's the speed record yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry the audio doesn't work
+
+ align:start position:0%
+sorry the audio doesn't work
+ 
+
+ align:start position:0%
+sorry the audio doesn't work
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+well they usually the more cute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we are uh describing this Behavior
+
+ align:start position:0%
+uh we are uh describing this Behavior
+ 
+
+ align:start position:0%
+uh we are uh describing this Behavior
+using a knowledge representation langage
+
+ align:start position:0%
+using a knowledge representation langage
+ 
+
+ align:start position:0%
+using a knowledge representation langage
+like e EMR emotion machine and the type
+
+ align:start position:0%
+like e EMR emotion machine and the type
+ 
+
+ align:start position:0%
+like e EMR emotion machine and the type
+representation by push
+
+ align:start position:0%
+representation by push
+ 
+
+ align:start position:0%
+representation by push
+and did you ask him what his goals are
+
+ align:start position:0%
+and did you ask him what his goals are
+ 
+
+ align:start position:0%
+and did you ask him what his goals are
+yeah but uh we uh we uh we have a
+
+ align:start position:0%
+yeah but uh we uh we uh we have a
+ 
+
+ align:start position:0%
+yeah but uh we uh we uh we have a
+conference what the and the the about
+
+ align:start position:0%
+conference what the and the the about
+ 
+
+ align:start position:0%
+conference what the and the the about
+the goals and what the uh the reasons or
+
+ align:start position:0%
+the goals and what the uh the reasons or
+ 
+
+ align:start position:0%
+the goals and what the uh the reasons or
+some the behaviors so every uh um the um
+
+ align:start position:0%
+some the behaviors so every uh um the um
+ 
+
+ align:start position:0%
+some the behaviors so every uh um the um
+week we have discussions what's going on
+
+ align:start position:0%
+week we have discussions what's going on
+ 
+
+ align:start position:0%
+week we have discussions what's going on
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and but it's hard to tell ask the infant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s think worth mentioning that in uh in
+
+ align:start position:0%
+s think worth mentioning that in uh in
+ 
+
+ align:start position:0%
+s think worth mentioning that in uh in
+modern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+psychology people are trained to do
+
+ align:start position:0%
+psychology people are trained to do
+ 
+
+ align:start position:0%
+psychology people are trained to do
+experiments and they have large numbers
+
+ align:start position:0%
+experiments and they have large numbers
+ 
+
+ align:start position:0%
+experiments and they have large numbers
+of subjects and control groups and they
+
+ align:start position:0%
+of subjects and control groups and they
+ 
+
+ align:start position:0%
+of subjects and control groups and they
+do the same thing with 50 Children and
+
+ align:start position:0%
+do the same thing with 50 Children and
+ 
+
+ align:start position:0%
+do the same thing with 50 Children and
+then some slightly different thing with
+
+ align:start position:0%
+then some slightly different thing with
+ 
+
+ align:start position:0%
+then some slightly different thing with
+50 others and there's very little
+
+ align:start position:0%
+50 others and there's very little
+ 
+
+ align:start position:0%
+50 others and there's very little
+support for experiments like this uh but
+
+ align:start position:0%
+support for experiments like this uh but
+ 
+
+ align:start position:0%
+support for experiments like this uh but
+historically almost a very large
+
+ align:start position:0%
+historically almost a very large
+ 
+
+ align:start position:0%
+historically almost a very large
+fraction of what we know about young
+
+ align:start position:0%
+fraction of what we know about young
+ 
+
+ align:start position:0%
+fraction of what we know about young
+children comes from the
+
+ align:start position:0%
+children comes from the
+ 
+
+ align:start position:0%
+children comes from the
+psychology psychologist John P who
+
+ align:start position:0%
+psychology psychologist John P who
+ 
+
+ align:start position:0%
+psychology psychologist John P who
+studied three children for many
+
+ align:start position:0%
+studied three children for many
+ 
+
+ align:start position:0%
+studied three children for many
+years uh also my friend Bob ller studied
+
+ align:start position:0%
+years uh also my friend Bob ller studied
+ 
+
+ align:start position:0%
+years uh also my friend Bob ller studied
+three children for many years and they
+
+ align:start position:0%
+three children for many years and they
+ 
+
+ align:start position:0%
+three children for many years and they
+learn a lot about the child's
+
+ align:start position:0%
+learn a lot about the child's
+ 
+
+ align:start position:0%
+learn a lot about the child's
+development whereas it's very hard in
+
+ align:start position:0%
+development whereas it's very hard in
+ 
+
+ align:start position:0%
+development whereas it's very hard in
+modern psychology
+
+ align:start position:0%
+modern psychology
+ 
+
+ align:start position:0%
+modern psychology
+because they want statisticians to say
+
+ align:start position:0%
+because they want statisticians to say
+ 
+
+ align:start position:0%
+because they want statisticians to say
+What's significant so you need 50
+
+ align:start position:0%
+What's significant so you need 50
+ 
+
+ align:start position:0%
+What's significant so you need 50
+Children and then if uh enough of the
+
+ align:start position:0%
+Children and then if uh enough of the
+ 
+
+ align:start position:0%
+Children and then if uh enough of the
+children do the same thing then that's
+
+ align:start position:0%
+children do the same thing then that's
+ 
+
+ align:start position:0%
+children do the same thing then that's
+that's what you publish but what you
+
+ align:start position:0%
+that's what you publish but what you
+ 
+
+ align:start position:0%
+that's what you publish but what you
+really want all children are different
+
+ align:start position:0%
+really want all children are different
+ 
+
+ align:start position:0%
+really want all children are different
+you really want to know what happens in
+
+ align:start position:0%
+you really want to know what happens in
+ 
+
+ align:start position:0%
+you really want to know what happens in
+the course of one child's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+development
+
+ align:start position:0%
+development
+ 
+
+ align:start position:0%
+development
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fore spee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so she knows it's to be broken yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so this is the audio and video data and
+
+ align:start position:0%
+so this is the audio and video data and
+ 
+
+ align:start position:0%
+so this is the audio and video data and
+uh again we uh we we're trying to to
+
+ align:start position:0%
+uh again we uh we we're trying to to
+ 
+
+ align:start position:0%
+uh again we uh we we're trying to to
+describe the um this Behavior by natural
+
+ align:start position:0%
+describe the um this Behavior by natural
+ 
+
+ align:start position:0%
+describe the um this Behavior by natural
+language and also the um knowledge um um
+
+ align:start position:0%
+language and also the um knowledge um um
+ 
+
+ align:start position:0%
+language and also the um knowledge um um
+AI type knowledge representation
+
+ align:start position:0%
+AI type knowledge representation
+ 
+
+ align:start position:0%
+AI type knowledge representation
+language so did he switch to building
+
+ align:start position:0%
+language so did he switch to building
+ 
+
+ align:start position:0%
+language so did he switch to building
+because she said
+
+ align:start position:0%
+because she said
+ 
+
+ align:start position:0%
+because she said
+to oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah very good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speech spee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um I don't U give the good
+
+ align:start position:0%
+so um I don't U give the good
+ 
+
+ align:start position:0%
+so um I don't U give the good
+demo so um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so have you assembled a sequence of
+
+ align:start position:0%
+um so have you assembled a sequence of
+ 
+
+ align:start position:0%
+um so have you assembled a sequence of
+one of the child's development yet
+
+ align:start position:0%
+one of the child's development yet
+ 
+
+ align:start position:0%
+one of the child's development yet
+sorry have you have you got snaps of
+
+ align:start position:0%
+sorry have you have you got snaps of
+ 
+
+ align:start position:0%
+sorry have you have you got snaps of
+what one child does for 3 years yeah um
+
+ align:start position:0%
+what one child does for 3 years yeah um
+ 
+
+ align:start position:0%
+what one child does for 3 years yeah um
+the again um um this year um the um just
+
+ align:start position:0%
+the again um um this year um the um just
+ 
+
+ align:start position:0%
+the again um um this year um the um just
+the um the third year so we can um
+
+ align:start position:0%
+the um the third year so we can um
+ 
+
+ align:start position:0%
+the um the third year so we can um
+collect the the the fourth the same
+
+ align:start position:0%
+collect the the the fourth the same
+ 
+
+ align:start position:0%
+collect the the the fourth the same
+child now for three years the Child
+
+ align:start position:0%
+child now for three years the Child
+ 
+
+ align:start position:0%
+child now for three years the Child
+Development because it would be nice to
+
+ align:start position:0%
+Development because it would be nice to
+ 
+
+ align:start position:0%
+Development because it would be nice to
+know how she gets the idea of
+
+ align:start position:0%
+know how she gets the idea of
+ 
+
+ align:start position:0%
+know how she gets the idea of
+cooperating yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you mention that you use the EM1
+
+ align:start position:0%
+so you mention that you use the EM1
+ 
+
+ align:start position:0%
+so you mention that you use the EM1
+representation yes example that
+
+ align:start position:0%
+representation yes example that
+ 
+
+ align:start position:0%
+representation yes example that
+yeah oh so we can see I think uses it
+
+ align:start position:0%
+yeah oh so we can see I think uses it
+ 
+
+ align:start position:0%
+yeah oh so we can see I think uses it
+for taking notes by saying this action
+
+ align:start position:0%
+for taking notes by saying this action
+ 
+
+ align:start position:0%
+for taking notes by saying this action
+might show level
+
+ align:start position:0%
+might show level
+ 
+
+ align:start position:0%
+might show level
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+okay so I I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give so uh this kind of explanation um
+
+ align:start position:0%
+give so uh this kind of explanation um
+ 
+
+ align:start position:0%
+give so uh this kind of explanation um
+this reflective thinking level and
+
+ align:start position:0%
+this reflective thinking level and
+ 
+
+ align:start position:0%
+this reflective thinking level and
+self-reflective thinking and uh uh so we
+
+ align:start position:0%
+self-reflective thinking and uh uh so we
+ 
+
+ align:start position:0%
+self-reflective thinking and uh uh so we
+can describe the behavior using multi-
+
+ align:start position:0%
+can describe the behavior using multi-
+ 
+
+ align:start position:0%
+can describe the behavior using multi-
+level the representation the that uh uh
+
+ align:start position:0%
+level the representation the that uh uh
+ 
+
+ align:start position:0%
+level the representation the that uh uh
+you are learning in this class but you
+
+ align:start position:0%
+you are learning in this class but you
+ 
+
+ align:start position:0%
+you are learning in this class but you
+don't know if the boy yeah thinks that
+
+ align:start position:0%
+don't know if the boy yeah thinks that
+ 
+
+ align:start position:0%
+don't know if the boy yeah thinks that
+about the mother in that case does he is
+
+ align:start position:0%
+about the mother in that case does he is
+ 
+
+ align:start position:0%
+about the mother in that case does he is
+there any evidence oh it's a just a
+
+ align:start position:0%
+there any evidence oh it's a just a
+ 
+
+ align:start position:0%
+there any evidence oh it's a just a
+assumption and uh we are just um the um
+
+ align:start position:0%
+assumption and uh we are just um the um
+ 
+
+ align:start position:0%
+assumption and uh we are just um the um
+the thinking and discussing what's going
+
+ align:start position:0%
+the thinking and discussing what's going
+ 
+
+ align:start position:0%
+the thinking and discussing what's going
+on so um the uh description is not just
+
+ align:start position:0%
+on so um the uh description is not just
+ 
+
+ align:start position:0%
+on so um the uh description is not just
+a single multi
+
+ align:start position:0%
+a single multi
+ 
+
+ align:start position:0%
+a single multi
+ways but uh the um getting more and more
+
+ align:start position:0%
+ways but uh the um getting more and more
+ 
+
+ align:start position:0%
+ways but uh the um getting more and more
+data and uh um making the model I think
+
+ align:start position:0%
+data and uh um making the model I think
+ 
+
+ align:start position:0%
+data and uh um making the model I think
+um in the room now yes oh so you could
+
+ align:start position:0%
+um in the room now yes oh so you could
+ 
+
+ align:start position:0%
+um in the room now yes oh so you could
+see if he looks over it her yeah uh
+
+ align:start position:0%
+see if he looks over it her yeah uh
+ 
+
+ align:start position:0%
+see if he looks over it her yeah uh
+sometime oh this case is not no uh no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parents so um this is such kind of
+
+ align:start position:0%
+parents so um this is such kind of
+ 
+
+ align:start position:0%
+parents so um this is such kind of
+representations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have a graphical user interface
+
+ align:start position:0%
+and we have a graphical user interface
+ 
+
+ align:start position:0%
+and we have a graphical user interface
+to put the um the um the functions of
+
+ align:start position:0%
+to put the um the um the functions of
+ 
+
+ align:start position:0%
+to put the um the um the functions of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+EM1 if you had a picture of mother it
+
+ align:start position:0%
+EM1 if you had a picture of mother it
+ 
+
+ align:start position:0%
+EM1 if you had a picture of mother it
+would be interesting to see if his
+
+ align:start position:0%
+would be interesting to see if his
+ 
+
+ align:start position:0%
+would be interesting to see if his
+strategy is different yeah actually the
+
+ align:start position:0%
+strategy is different yeah actually the
+ 
+
+ align:start position:0%
+strategy is different yeah actually the
+uh we I gave up the um videos for one
+
+ align:start position:0%
+uh we I gave up the um videos for one
+ 
+
+ align:start position:0%
+uh we I gave up the um videos for one
+year long you
+
+ align:start position:0%
+year long you
+ 
+
+ align:start position:0%
+year long you
+know uh infant development
+
+ align:start position:0%
+know uh infant development
+ 
+
+ align:start position:0%
+know uh infant development
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+service it's a good souvenir for
+
+ align:start position:0%
+service it's a good souvenir for
+ 
+
+ align:start position:0%
+service it's a good souvenir for
+grandparents
+
+ align:start position:0%
+grandparents
+ 
+
+ align:start position:0%
+grandparents
+and as a d DVD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+format but P has a nice
+
+ align:start position:0%
+format but P has a nice
+ 
+
+ align:start position:0%
+format but P has a nice
+story I'm sure you all know the famous
+
+ align:start position:0%
+story I'm sure you all know the famous
+ 
+
+ align:start position:0%
+story I'm sure you all know the famous
+experiment of P where you pour water
+
+ align:start position:0%
+experiment of P where you pour water
+ 
+
+ align:start position:0%
+experiment of P where you pour water
+from a whole thin glass into a short fat
+
+ align:start position:0%
+from a whole thin glass into a short fat
+ 
+
+ align:start position:0%
+from a whole thin glass into a short fat
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+U paper did a lot of those experiments
+
+ align:start position:0%
+U paper did a lot of those experiments
+ 
+
+ align:start position:0%
+U paper did a lot of those experiments
+in Geneva with
+
+ align:start position:0%
+in Geneva with
+ 
+
+ align:start position:0%
+in Geneva with
+P so typically the 5-year-old thinks
+
+ align:start position:0%
+P so typically the 5-year-old thinks
+ 
+
+ align:start position:0%
+P so typically the 5-year-old thinks
+there's more in the OR says there's more
+
+ align:start position:0%
+there's more in the OR says there's more
+ 
+
+ align:start position:0%
+there's more in the OR says there's more
+water in the to one so he had a boy who
+
+ align:start position:0%
+water in the to one so he had a boy who
+ 
+
+ align:start position:0%
+water in the to one so he had a boy who
+had had a movie of a boy doing that and
+
+ align:start position:0%
+had had a movie of a boy doing that and
+ 
+
+ align:start position:0%
+had had a movie of a boy doing that and
+then when the boy was seven seven years
+
+ align:start position:0%
+then when the boy was seven seven years
+ 
+
+ align:start position:0%
+then when the boy was seven seven years
+old uh he did the same experiment and
+
+ align:start position:0%
+old uh he did the same experiment and
+ 
+
+ align:start position:0%
+old uh he did the same experiment and
+the boy said well of course equal it's
+
+ align:start position:0%
+the boy said well of course equal it's
+ 
+
+ align:start position:0%
+the boy said well of course equal it's
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+order and then peer showed the boy the
+
+ align:start position:0%
+order and then peer showed the boy the
+ 
+
+ align:start position:0%
+order and then peer showed the boy the
+movie two years ago where he said
+
+ align:start position:0%
+movie two years ago where he said
+ 
+
+ align:start position:0%
+movie two years ago where he said
+there's more and the boy gets very angry
+
+ align:start position:0%
+there's more and the boy gets very angry
+ 
+
+ align:start position:0%
+there's more and the boy gets very angry
+and said I never believed that and uh
+
+ align:start position:0%
+and said I never believed that and uh
+ 
+
+ align:start position:0%
+and said I never believed that and uh
+ABT said well there's the movie and the
+
+ align:start position:0%
+ABT said well there's the movie and the
+ 
+
+ align:start position:0%
+ABT said well there's the movie and the
+boy said you must have uh had somebody
+
+ align:start position:0%
+boy said you must have uh had somebody
+ 
+
+ align:start position:0%
+boy said you must have uh had somebody
+make up this fake movie I was never so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stupid it's kind of infant Amnesia of
+
+ align:start position:0%
+stupid it's kind of infant Amnesia of
+ 
+
+ align:start position:0%
+stupid it's kind of infant Amnesia of
+very strong
+
+ align:start position:0%
+very strong
+ 
+
+ align:start position:0%
+very strong
+form boy didn't believe any he could
+
+ align:start position:0%
+form boy didn't believe any he could
+ 
+
+ align:start position:0%
+form boy didn't believe any he could
+ever have made that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mistake so you can use that on yeah you
+
+ align:start position:0%
+mistake so you can use that on yeah you
+ 
+
+ align:start position:0%
+mistake so you can use that on yeah you
+can show them the video in three years
+
+ align:start position:0%
+can show them the video in three years
+ 
+
+ align:start position:0%
+can show them the video in three years
+and see they believe
+
+ align:start position:0%
+and see they believe
+ 
+
+ align:start position:0%
+and see they believe
+it so the um it's a just ongoing project
+
+ align:start position:0%
+it so the um it's a just ongoing project
+ 
+
+ align:start position:0%
+it so the um it's a just ongoing project
+but uh um we want to U develop the um
+
+ align:start position:0%
+but uh um we want to U develop the um
+ 
+
+ align:start position:0%
+but uh um we want to U develop the um
+computational model for common sense
+
+ align:start position:0%
+computational model for common sense
+ 
+
+ align:start position:0%
+computational model for common sense
+reason uh I I think it is not only for
+
+ align:start position:0%
+reason uh I I think it is not only for
+ 
+
+ align:start position:0%
+reason uh I I think it is not only for
+the infant um some of some part of this
+
+ align:start position:0%
+the infant um some of some part of this
+ 
+
+ align:start position:0%
+the infant um some of some part of this
+uh the common sense reasoning model uh
+
+ align:start position:0%
+uh the common sense reasoning model uh
+ 
+
+ align:start position:0%
+uh the common sense reasoning model uh
+work for the U adults I we believe and
+
+ align:start position:0%
+work for the U adults I we believe and
+ 
+
+ align:start position:0%
+work for the U adults I we believe and
+uh so um this is just a the six months
+
+ align:start position:0%
+uh so um this is just a the six months
+ 
+
+ align:start position:0%
+uh so um this is just a the six months
+long project and as far as the the
+
+ align:start position:0%
+long project and as far as the the
+ 
+
+ align:start position:0%
+long project and as far as the the
+modeling we are collecting the data um
+
+ align:start position:0%
+modeling we are collecting the data um
+ 
+
+ align:start position:0%
+modeling we are collecting the data um
+we the building more the models for the
+
+ align:start position:0%
+we the building more the models for the
+ 
+
+ align:start position:0%
+we the building more the models for the
+um Common Sense Computing U de Roy is
+
+ align:start position:0%
+um Common Sense Computing U de Roy is
+ 
+
+ align:start position:0%
+um Common Sense Computing U de Roy is
+collecting a huge amount of data but I'm
+
+ align:start position:0%
+collecting a huge amount of data but I'm
+ 
+
+ align:start position:0%
+collecting a huge amount of data but I'm
+not sure it's so organized as this oh
+
+ align:start position:0%
+not sure it's so organized as this oh
+ 
+
+ align:start position:0%
+not sure it's so organized as this oh
+the different thing is uh we have a you
+
+ align:start position:0%
+the different thing is uh we have a you
+ 
+
+ align:start position:0%
+the different thing is uh we have a you
+know increment we are our data is
+
+ align:start position:0%
+know increment we are our data is
+ 
+
+ align:start position:0%
+know increment we are our data is
+incremental so the uh so it's I I think
+
+ align:start position:0%
+incremental so the uh so it's I I think
+ 
+
+ align:start position:0%
+incremental so the uh so it's I I think
+it's a slightly different the boy uh uh
+
+ align:start position:0%
+it's a slightly different the boy uh uh
+ 
+
+ align:start position:0%
+it's a slightly different the boy uh uh
+was has been doing a good research for
+
+ align:start position:0%
+was has been doing a good research for
+ 
+
+ align:start position:0%
+was has been doing a good research for
+the very the um theep model of the the
+
+ align:start position:0%
+the very the um theep model of the the
+ 
+
+ align:start position:0%
+the very the um theep model of the the
+speech and language development that but
+
+ align:start position:0%
+speech and language development that but
+ 
+
+ align:start position:0%
+speech and language development that but
+our data is a multimodel including
+
+ align:start position:0%
+our data is a multimodel including
+ 
+
+ align:start position:0%
+our data is a multimodel including
+gestures for for instance at the
+
+ align:start position:0%
+gestures for for instance at the
+ 
+
+ align:start position:0%
+gestures for for instance at the
+beginning um just a behavior then the
+
+ align:start position:0%
+beginning um just a behavior then the
+ 
+
+ align:start position:0%
+beginning um just a behavior then the
+the communications is not um the um is
+
+ align:start position:0%
+the communications is not um the um is
+ 
+
+ align:start position:0%
+the communications is not um the um is
+uh useful then the behaviors changes to
+
+ align:start position:0%
+uh useful then the behaviors changes to
+ 
+
+ align:start position:0%
+uh useful then the behaviors changes to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gestures so um some symbolic meaning
+
+ align:start position:0%
+gestures so um some symbolic meaning
+ 
+
+ align:start position:0%
+gestures so um some symbolic meaning
+appears
+
+ align:start position:0%
+appears
+ 
+
+ align:start position:0%
+appears
+so our research is a um
+
+ align:start position:0%
+so our research is a um
+ 
+
+ align:start position:0%
+so our research is a um
+um um language development and uh just
+
+ align:start position:0%
+um um language development and uh just
+ 
+
+ align:start position:0%
+um um language development and uh just
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+development yeah if there's just one
+
+ align:start position:0%
+development yeah if there's just one
+ 
+
+ align:start position:0%
+development yeah if there's just one
+child you can't get all that yeah
+
+ align:start position:0%
+child you can't get all that yeah
+ 
+
+ align:start position:0%
+child you can't get all that yeah
+especially the um my colleague kirama he
+
+ align:start position:0%
+especially the um my colleague kirama he
+ 
+
+ align:start position:0%
+especially the um my colleague kirama he
+has a um two months old baby yes so uh
+
+ align:start position:0%
+has a um two months old baby yes so uh
+ 
+
+ align:start position:0%
+has a um two months old baby yes so uh
+it's good and the opportunity for
+
+ align:start position:0%
+it's good and the opportunity for
+ 
+
+ align:start position:0%
+it's good and the opportunity for
+him to observe the the
+
+ align:start position:0%
+him to observe the the
+ 
+
+ align:start position:0%
+him to observe the the
+babye babysitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so U sorry um um um this evening um
+
+ align:start position:0%
+yeah so U sorry um um um this evening um
+ 
+
+ align:start position:0%
+yeah so U sorry um um um this evening um
+our computer doesn't work well thank you
+
+ align:start position:0%
+our computer doesn't work well thank you
+ 
+
+ align:start position:0%
+our computer doesn't work well thank you
+thank you very much for
+
+ align:start position:0%
+thank you very much for
+ 
+
+ align:start position:0%
+thank you very much for
+attentions
+
+ align:start position:0%
+attentions
+ 
+
+ align:start position:0%
+attentions
+yeah facts we've been able to collect so
+
+ align:start position:0%
+yeah facts we've been able to collect so
+ 
+
+ align:start position:0%
+yeah facts we've been able to collect so
+far those first months sorry how how
+
+ align:start position:0%
+far those first months sorry how how
+ 
+
+ align:start position:0%
+far those first months sorry how how
+manys Common Sense facts have you've
+
+ align:start position:0%
+manys Common Sense facts have you've
+ 
+
+ align:start position:0%
+manys Common Sense facts have you've
+been able to collect uhuh it's how to
+
+ align:start position:0%
+been able to collect uhuh it's how to
+ 
+
+ align:start position:0%
+been able to collect uhuh it's how to
+the um the
+
+ align:start position:0%
+the um the
+ 
+
+ align:start position:0%
+the um the
+count because uh uh um as I mentioned
+
+ align:start position:0%
+count because uh uh um as I mentioned
+ 
+
+ align:start position:0%
+count because uh uh um as I mentioned
+the multi um model infant Behavior
+
+ align:start position:0%
+the multi um model infant Behavior
+ 
+
+ align:start position:0%
+the multi um model infant Behavior
+Corpus the copass means the collecting
+
+ align:start position:0%
+Corpus the copass means the collecting
+ 
+
+ align:start position:0%
+Corpus the copass means the collecting
+video and audio data and annot with
+
+ align:start position:0%
+video and audio data and annot with
+ 
+
+ align:start position:0%
+video and audio data and annot with
+annotation annotation is a natural
+
+ align:start position:0%
+annotation annotation is a natural
+ 
+
+ align:start position:0%
+annotation annotation is a natural
+language and also the uh the some sort
+
+ align:start position:0%
+language and also the uh the some sort
+ 
+
+ align:start position:0%
+language and also the uh the some sort
+of knowledge representation language
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so the huge amount of data and
+
+ align:start position:0%
+so yeah so the huge amount of data and
+ 
+
+ align:start position:0%
+so yeah so the huge amount of data and
+uh we are the the changing the
+
+ align:start position:0%
+uh we are the the changing the
+ 
+
+ align:start position:0%
+uh we are the the changing the
+representation that you know our
+
+ align:start position:0%
+representation that you know our
+ 
+
+ align:start position:0%
+representation that you know our
+representations are evolving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have any of
+
+ align:start position:0%
+have any of
+ 
+
+ align:start position:0%
+have any of
+you try to analyze what a child is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doing of course no one really knows how
+
+ align:start position:0%
+doing of course no one really knows how
+ 
+
+ align:start position:0%
+doing of course no one really knows how
+you so who do you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+annota how many people are oh the trying
+
+ align:start position:0%
+annota how many people are oh the trying
+ 
+
+ align:start position:0%
+annota how many people are oh the trying
+to describe basically the the graduate
+
+ align:start position:0%
+to describe basically the the graduate
+ 
+
+ align:start position:0%
+to describe basically the the graduate
+students and uh for the the conference
+
+ align:start position:0%
+students and uh for the the conference
+ 
+
+ align:start position:0%
+students and uh for the the conference
+the um about 10 mhm the people join the
+
+ align:start position:0%
+the um about 10 mhm the people join the
+ 
+
+ align:start position:0%
+the um about 10 mhm the people join the
+um like uh you know the U medical
+
+ align:start position:0%
+um like uh you know the U medical
+ 
+
+ align:start position:0%
+um like uh you know the U medical
+doctors have a conference yes so you
+
+ align:start position:0%
+doctors have a conference yes so you
+ 
+
+ align:start position:0%
+doctors have a conference yes so you
+have Conference of child yeah interest
+
+ align:start position:0%
+have Conference of child yeah interest
+ 
+
+ align:start position:0%
+have Conference of child yeah interest
+yeah and also sometimes the
+
+ align:start position:0%
+yeah and also sometimes the
+ 
+
+ align:start position:0%
+yeah and also sometimes the
+parents
+
+ align:start position:0%
+parents
+ 
+
+ align:start position:0%
+parents
+collabora I wonder if it be any use to
+
+ align:start position:0%
+collabora I wonder if it be any use to
+ 
+
+ align:start position:0%
+collabora I wonder if it be any use to
+try to get volunteers toate
+
+ align:start position:0%
+try to get volunteers toate
+ 
+
+ align:start position:0%
+try to get volunteers toate
+have to learn your way of describing
+
+ align:start position:0%
+have to learn your way of describing
+ 
+
+ align:start position:0%
+have to learn your way of describing
+things yeah um our system um can be used
+
+ align:start position:0%
+things yeah um our system um can be used
+ 
+
+ align:start position:0%
+things yeah um our system um can be used
+a web based system so you can join
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us but everybody would use a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language yeah U as far as the um the
+
+ align:start position:0%
+language yeah U as far as the um the
+ 
+
+ align:start position:0%
+language yeah U as far as the um the
+audio and video
+
+ align:start position:0%
+audio and video
+ 
+
+ align:start position:0%
+audio and video
+data it's the r data
+
+ align:start position:0%
+data it's the r data
+ 
+
+ align:start position:0%
+data it's the r data
+so in ph's laboratory which
+
+ align:start position:0%
+so in ph's laboratory which
+ 
+
+ align:start position:0%
+so in ph's laboratory which
+I guess closed in
+
+ align:start position:0%
+I guess closed in
+ 
+
+ align:start position:0%
+I guess closed in
+around the late
+
+ align:start position:0%
+around the late
+ 
+
+ align:start position:0%
+around the late
+1970s in Geneva there
+
+ align:start position:0%
+1970s in Geneva there
+ 
+
+ align:start position:0%
+1970s in Geneva there
+were many wonderful experiments it was a
+
+ align:start position:0%
+were many wonderful experiments it was a
+ 
+
+ align:start position:0%
+were many wonderful experiments it was a
+small lab I think it had about 8 or 10
+
+ align:start position:0%
+small lab I think it had about 8 or 10
+ 
+
+ align:start position:0%
+small lab I think it had about 8 or 10
+people uh
+
+ align:start position:0%
+people uh
+ 
+
+ align:start position:0%
+people uh
+and there were long studies watching one
+
+ align:start position:0%
+and there were long studies watching one
+ 
+
+ align:start position:0%
+and there were long studies watching one
+child learn to build things with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blocks I knew I knew one of the
+
+ align:start position:0%
+blocks I knew I knew one of the
+ 
+
+ align:start position:0%
+blocks I knew I knew one of the
+researchers I'm looking for two
+
+ align:start position:0%
+researchers I'm looking for two
+ 
+
+ align:start position:0%
+researchers I'm looking for two
+blocks but uh and that I'll names again
+
+ align:start position:0%
+blocks but uh and that I'll names again
+ 
+
+ align:start position:0%
+blocks but uh and that I'll names again
+uh she did experiments where uh the
+
+ align:start position:0%
+uh she did experiments where uh the
+ 
+
+ align:start position:0%
+uh she did experiments where uh the
+child uh had seen someone else build a
+
+ align:start position:0%
+child uh had seen someone else build a
+ 
+
+ align:start position:0%
+child uh had seen someone else build a
+t-shape just just a thing like
+
+ align:start position:0%
+t-shape just just a thing like
+ 
+
+ align:start position:0%
+t-shape just just a thing like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Sor and
+
+ align:start position:0%
+Sor and
+ 
+
+ align:start position:0%
+Sor and
+uh so after a while all children learned
+
+ align:start position:0%
+uh so after a while all children learned
+ 
+
+ align:start position:0%
+uh so after a while all children learned
+that um if you have the vertical block
+
+ align:start position:0%
+that um if you have the vertical block
+ 
+
+ align:start position:0%
+that um if you have the vertical block
+you should put the long horizontal block
+
+ align:start position:0%
+you should put the long horizontal block
+ 
+
+ align:start position:0%
+you should put the long horizontal block
+around in the
+
+ align:start position:0%
+around in the
+ 
+
+ align:start position:0%
+around in the
+middle and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I'm blocked on the name of the
+
+ align:start position:0%
+uh I'm blocked on the name of the
+ 
+
+ align:start position:0%
+uh I'm blocked on the name of the
+experimenter so she made a block that uh
+
+ align:start position:0%
+experimenter so she made a block that uh
+ 
+
+ align:start position:0%
+experimenter so she made a block that uh
+like a loaded dice uh she drilled a
+
+ align:start position:0%
+like a loaded dice uh she drilled a
+ 
+
+ align:start position:0%
+like a loaded dice uh she drilled a
+little hole and put a lead weight in one
+
+ align:start position:0%
+little hole and put a lead weight in one
+ 
+
+ align:start position:0%
+little hole and put a lead weight in one
+end covered it up and varnished it so
+
+ align:start position:0%
+end covered it up and varnished it so
+ 
+
+ align:start position:0%
+end covered it up and varnished it so
+you couldn't tell and so then the block
+
+ align:start position:0%
+you couldn't tell and so then the block
+ 
+
+ align:start position:0%
+you couldn't tell and so then the block
+would have to be offset
+
+ align:start position:0%
+would have to be offset
+ 
+
+ align:start position:0%
+would have to be offset
+so what was interesting is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the three-year-olds had a lot of
+
+ align:start position:0%
+uh the three-year-olds had a lot of
+ 
+
+ align:start position:0%
+uh the three-year-olds had a lot of
+trouble with
+
+ align:start position:0%
+trouble with
+ 
+
+ align:start position:0%
+trouble with
+that and uh they would keep putting it
+
+ align:start position:0%
+that and uh they would keep putting it
+ 
+
+ align:start position:0%
+that and uh they would keep putting it
+in in the center it would fall over and
+
+ align:start position:0%
+in in the center it would fall over and
+ 
+
+ align:start position:0%
+in in the center it would fall over and
+they wouldn't know what to do and then
+
+ align:start position:0%
+they wouldn't know what to do and then
+ 
+
+ align:start position:0%
+they wouldn't know what to do and then
+slightly older children would realize
+
+ align:start position:0%
+slightly older children would realize
+ 
+
+ align:start position:0%
+slightly older children would realize
+there was something wrong with the block
+
+ align:start position:0%
+there was something wrong with the block
+ 
+
+ align:start position:0%
+there was something wrong with the block
+and they would just push it until it
+
+ align:start position:0%
+and they would just push it until it
+ 
+
+ align:start position:0%
+and they would just push it until it
+balanced nicely even though it was off
+
+ align:start position:0%
+balanced nicely even though it was off
+ 
+
+ align:start position:0%
+balanced nicely even though it was off
+center it was sort of unusual uh that
+
+ align:start position:0%
+center it was sort of unusual uh that
+ 
+
+ align:start position:0%
+center it was sort of unusual uh that
+developmental scenario because then a
+
+ align:start position:0%
+developmental scenario because then a
+ 
+
+ align:start position:0%
+developmental scenario because then a
+slightly older child uh would be as bad
+
+ align:start position:0%
+slightly older child uh would be as bad
+ 
+
+ align:start position:0%
+slightly older child uh would be as bad
+as the the
+
+ align:start position:0%
+as the the
+ 
+
+ align:start position:0%
+as the the
+three-year-old because the older child
+
+ align:start position:0%
+three-year-old because the older child
+ 
+
+ align:start position:0%
+three-year-old because the older child
+knew that it had to be
+
+ align:start position:0%
+knew that it had to be
+ 
+
+ align:start position:0%
+knew that it had to be
+symmetrical didn't know the imbalance
+
+ align:start position:0%
+symmetrical didn't know the imbalance
+ 
+
+ align:start position:0%
+symmetrical didn't know the imbalance
+was very uh very small so the older
+
+ align:start position:0%
+was very uh very small so the older
+ 
+
+ align:start position:0%
+was very uh very small so the older
+child persisted much longer in trying to
+
+ align:start position:0%
+child persisted much longer in trying to
+ 
+
+ align:start position:0%
+child persisted much longer in trying to
+make it centered because he knew it had
+
+ align:start position:0%
+make it centered because he knew it had
+ 
+
+ align:start position:0%
+make it centered because he knew it had
+to be centered so you had a
+
+ align:start position:0%
+to be centered so you had a
+ 
+
+ align:start position:0%
+to be centered so you had a
+developmental curve like that instead of
+
+ align:start position:0%
+developmental curve like that instead of
+ 
+
+ align:start position:0%
+developmental curve like that instead of
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+usual uh getting better and
+
+ align:start position:0%
+usual uh getting better and
+ 
+
+ align:start position:0%
+usual uh getting better and
+better and then of course a yet older
+
+ align:start position:0%
+better and then of course a yet older
+ 
+
+ align:start position:0%
+better and then of course a yet older
+child would quickly say Well it must
+
+ align:start position:0%
+child would quickly say Well it must
+ 
+
+ align:start position:0%
+child would quickly say Well it must
+have a weight in this end so uh they'd
+
+ align:start position:0%
+have a weight in this end so uh they'd
+ 
+
+ align:start position:0%
+have a weight in this end so uh they'd
+be happy at the first try
+
+ align:start position:0%
+be happy at the first try
+ 
+
+ align:start position:0%
+be happy at the first try
+because it wouldn't have fallen over in
+
+ align:start position:0%
+because it wouldn't have fallen over in
+ 
+
+ align:start position:0%
+because it wouldn't have fallen over in
+the middle if it
+
+ align:start position:0%
+the middle if it
+ 
+
+ align:start position:0%
+the middle if it
+didn't so you could see I mean you're
+
+ align:start position:0%
+didn't so you could see I mean you're
+ 
+
+ align:start position:0%
+didn't so you could see I mean you're
+I'm just inferring all that from just
+
+ align:start position:0%
+I'm just inferring all that from just
+ 
+
+ align:start position:0%
+I'm just inferring all that from just
+seeing
+
+ align:start position:0%
+seeing
+ 
+
+ align:start position:0%
+seeing
+the seeing what happened and you're
+
+ align:start position:0%
+the seeing what happened and you're
+ 
+
+ align:start position:0%
+the seeing what happened and you're
+guessing that why the really old child
+
+ align:start position:0%
+guessing that why the really old child
+ 
+
+ align:start position:0%
+guessing that why the really old child
+instantly makes the Right theory and uh
+
+ align:start position:0%
+instantly makes the Right theory and uh
+ 
+
+ align:start position:0%
+instantly makes the Right theory and uh
+doesn't mind that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unsymmetrical so until we can actually
+
+ align:start position:0%
+unsymmetrical so until we can actually
+ 
+
+ align:start position:0%
+unsymmetrical so until we can actually
+look into their brain we just have to
+
+ align:start position:0%
+look into their brain we just have to
+ 
+
+ align:start position:0%
+look into their brain we just have to
+guess how
+
+ align:start position:0%
+guess how
+ 
+
+ align:start position:0%
+guess how
+to what's going on
+
+ align:start position:0%
+to what's going on
+ 
+
+ align:start position:0%
+to what's going on
+there but if P hadn't done the
+
+ align:start position:0%
+there but if P hadn't done the
+ 
+
+ align:start position:0%
+there but if P hadn't done the
+experiments maybe the question would
+
+ align:start position:0%
+experiments maybe the question would
+ 
+
+ align:start position:0%
+experiments maybe the question would
+never
+
+ align:start position:0%
+never
+ 
+
+ align:start position:0%
+never
+arise uh in fact I did some experiments
+
+ align:start position:0%
+arise uh in fact I did some experiments
+ 
+
+ align:start position:0%
+arise uh in fact I did some experiments
+after that uh making complicated things
+
+ align:start position:0%
+after that uh making complicated things
+ 
+
+ align:start position:0%
+after that uh making complicated things
+and asking children where the center
+
+ align:start position:0%
+and asking children where the center
+ 
+
+ align:start position:0%
+and asking children where the center
+was and it wasn't a scientific study but
+
+ align:start position:0%
+was and it wasn't a scientific study but
+ 
+
+ align:start position:0%
+was and it wasn't a scientific study but
+it was
+
+ align:start position:0%
+it was
+ 
+
+ align:start position:0%
+it was
+amazing uh even very young
+
+ align:start position:0%
+amazing uh even very young
+ 
+
+ align:start position:0%
+amazing uh even very young
+children would instantly find this the
+
+ align:start position:0%
+children would instantly find this the
+ 
+
+ align:start position:0%
+children would instantly find this the
+center of an object once once they knew
+
+ align:start position:0%
+center of an object once once they knew
+ 
+
+ align:start position:0%
+center of an object once once they knew
+I was looking for even if it were
+
+ align:start position:0%
+I was looking for even if it were
+ 
+
+ align:start position:0%
+I was looking for even if it were
+complicated Swirls and things I have no
+
+ align:start position:0%
+complicated Swirls and things I have no
+ 
+
+ align:start position:0%
+complicated Swirls and things I have no
+idea how they do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you think about more more
+
+ align:start position:0%
+what do you think about more more
+ 
+
+ align:start position:0%
+what do you think about more more
+research the the brain research using
+
+ align:start position:0%
+research the the brain research using
+ 
+
+ align:start position:0%
+research the the brain research using
+MRI or well every clue gives
+
+ align:start position:0%
+MRI or well every clue gives
+ 
+
+ align:start position:0%
+MRI or well every clue gives
+you I think once you have a a scanner
+
+ align:start position:0%
+you I think once you have a a scanner
+ 
+
+ align:start position:0%
+you I think once you have a a scanner
+that's not interfering with the child
+
+ align:start position:0%
+that's not interfering with the child
+ 
+
+ align:start position:0%
+that's not interfering with the child
+then then you take all your theories
+
+ align:start position:0%
+then then you take all your theories
+ 
+
+ align:start position:0%
+then then you take all your theories
+that came from this and maybe in a much
+
+ align:start position:0%
+that came from this and maybe in a much
+ 
+
+ align:start position:0%
+that came from this and maybe in a much
+shorter time you can say well uh we can
+
+ align:start position:0%
+shorter time you can say well uh we can
+ 
+
+ align:start position:0%
+shorter time you can say well uh we can
+throw half those theories out right away
+
+ align:start position:0%
+throw half those theories out right away
+ 
+
+ align:start position:0%
+throw half those theories out right away
+because of something we saw in the
+
+ align:start position:0%
+because of something we saw in the
+ 
+
+ align:start position:0%
+because of something we saw in the
+brain nobody knows what'll happen if you
+
+ align:start position:0%
+brain nobody knows what'll happen if you
+ 
+
+ align:start position:0%
+brain nobody knows what'll happen if you
+get if we can get fast high resolution
+
+ align:start position:0%
+get if we can get fast high resolution
+ 
+
+ align:start position:0%
+get if we can get fast high resolution
+pictures of the brain
+
+ align:start position:0%
+pictures of the brain
+ 
+
+ align:start position:0%
+pictures of the brain
+then then we might as well start over
+
+ align:start position:0%
+then then we might as well start over
+ 
+
+ align:start position:0%
+then then we might as well start over
+with everything
+
+ align:start position:0%
+with everything
+ 
+
+ align:start position:0%
+with everything
+because generally the brain scientist
+
+ align:start position:0%
+because generally the brain scientist
+ 
+
+ align:start position:0%
+because generally the brain scientist
+doesn't have any interest the high level
+
+ align:start position:0%
+doesn't have any interest the high level
+ 
+
+ align:start position:0%
+doesn't have any interest the high level
+theor well they sort of have very high
+
+ align:start position:0%
+theor well they sort of have very high
+ 
+
+ align:start position:0%
+theor well they sort of have very high
+level theories from Clinical mhm and
+
+ align:start position:0%
+level theories from Clinical mhm and
+ 
+
+ align:start position:0%
+level theories from Clinical mhm and
+very low-level theories from from uh
+
+ align:start position:0%
+very low-level theories from from uh
+ 
+
+ align:start position:0%
+very low-level theories from from uh
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+cells and uh they're trying to find
+
+ align:start position:0%
+cells and uh they're trying to find
+ 
+
+ align:start position:0%
+cells and uh they're trying to find
+theories in between but since they as
+
+ align:start position:0%
+theories in between but since they as
+ 
+
+ align:start position:0%
+theories in between but since they as
+far as I can see what you have to do is
+
+ align:start position:0%
+far as I can see what you have to do is
+ 
+
+ align:start position:0%
+far as I can see what you have to do is
+take the AI thing and work down because
+
+ align:start position:0%
+take the AI thing and work down because
+ 
+
+ align:start position:0%
+take the AI thing and work down because
+otherwise you wouldn't guess what to
+
+ align:start position:0%
+otherwise you wouldn't guess what to
+ 
+
+ align:start position:0%
+otherwise you wouldn't guess what to
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+for like in in uh there's this old idea
+
+ align:start position:0%
+for like in in uh there's this old idea
+ 
+
+ align:start position:0%
+for like in in uh there's this old idea
+uh that I call a Difference
+
+ align:start position:0%
+uh that I call a Difference
+ 
+
+ align:start position:0%
+uh that I call a Difference
+Engine which I got from new Simon it
+
+ align:start position:0%
+Engine which I got from new Simon it
+ 
+
+ align:start position:0%
+Engine which I got from new Simon it
+says uh if you you have a goal uh then
+
+ align:start position:0%
+says uh if you you have a goal uh then
+ 
+
+ align:start position:0%
+says uh if you you have a goal uh then
+the simplest explanation is the old
+
+ align:start position:0%
+the simplest explanation is the old
+ 
+
+ align:start position:0%
+the simplest explanation is the old
+cybernetic idea there's something that
+
+ align:start position:0%
+cybernetic idea there's something that
+ 
+
+ align:start position:0%
+cybernetic idea there's something that
+has a representation of uh the
+
+ align:start position:0%
+has a representation of uh the
+ 
+
+ align:start position:0%
+has a representation of uh the
+properties that you want and there's
+
+ align:start position:0%
+properties that you want and there's
+ 
+
+ align:start position:0%
+properties that you want and there's
+something else that is making a
+
+ align:start position:0%
+something else that is making a
+ 
+
+ align:start position:0%
+something else that is making a
+representation of what it observes and
+
+ align:start position:0%
+representation of what it observes and
+ 
+
+ align:start position:0%
+representation of what it observes and
+there has to be something to see what's
+
+ align:start position:0%
+there has to be something to see what's
+ 
+
+ align:start position:0%
+there has to be something to see what's
+the difference between those lists and
+
+ align:start position:0%
+the difference between those lists and
+ 
+
+ align:start position:0%
+the difference between those lists and
+then there has to be something to say
+
+ align:start position:0%
+then there has to be something to say
+ 
+
+ align:start position:0%
+then there has to be something to say
+well which of those features should I
+
+ align:start position:0%
+well which of those features should I
+ 
+
+ align:start position:0%
+well which of those features should I
+try to reduce
+
+ align:start position:0%
+try to reduce
+ 
+
+ align:start position:0%
+try to reduce
+next and uh unless you have a theory
+
+ align:start position:0%
+next and uh unless you have a theory
+ 
+
+ align:start position:0%
+next and uh unless you have a theory
+like that that you you wouldn't know
+
+ align:start position:0%
+like that that you you wouldn't know
+ 
+
+ align:start position:0%
+like that that you you wouldn't know
+what to look
+
+ align:start position:0%
+what to look
+ 
+
+ align:start position:0%
+what to look
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm sure eventually somebody will
+
+ align:start position:0%
+and I'm sure eventually somebody will
+ 
+
+ align:start position:0%
+and I'm sure eventually somebody will
+think of two or three other ideas for
+
+ align:start position:0%
+think of two or three other ideas for
+ 
+
+ align:start position:0%
+think of two or three other ideas for
+representing goals but but uh this is
+
+ align:start position:0%
+representing goals but but uh this is
+ 
+
+ align:start position:0%
+representing goals but but uh this is
+the only one that's ever worked in in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+programs there's series of
+
+ align:start position:0%
+programs there's series of
+ 
+
+ align:start position:0%
+programs there's series of
+papers right around 1960 by Allan Newell
+
+ align:start position:0%
+papers right around 1960 by Allan Newell
+ 
+
+ align:start position:0%
+papers right around 1960 by Allan Newell
+and Herbert Simon where they made
+
+ align:start position:0%
+and Herbert Simon where they made
+ 
+
+ align:start position:0%
+and Herbert Simon where they made
+programs that uh solved some problems by
+
+ align:start position:0%
+programs that uh solved some problems by
+ 
+
+ align:start position:0%
+programs that uh solved some problems by
+formulating things as goals and uh
+
+ align:start position:0%
+formulating things as goals and uh
+ 
+
+ align:start position:0%
+formulating things as goals and uh
+processes that would look for
+
+ align:start position:0%
+processes that would look for
+ 
+
+ align:start position:0%
+processes that would look for
+differences between situations and try
+
+ align:start position:0%
+differences between situations and try
+ 
+
+ align:start position:0%
+differences between situations and try
+to remove them it's sort of
+
+ align:start position:0%
+to remove them it's sort of
+ 
+
+ align:start position:0%
+to remove them it's sort of
+obvious but
+
+ align:start position:0%
+obvious but
+ 
+
+ align:start position:0%
+obvious but
+uh but uh I haven't seen that idea
+
+ align:start position:0%
+uh but uh I haven't seen that idea
+ 
+
+ align:start position:0%
+uh but uh I haven't seen that idea
+lately it sort of died out for some
+
+ align:start position:0%
+lately it sort of died out for some
+ 
+
+ align:start position:0%
+lately it sort of died out for some
+reason
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time's up but if anybody has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a thanks yoi CH
+
+ align:start position:0%
+a thanks yoi CH
+ 
+
+ align:start position:0%
+a thanks yoi CH
+that's have to come back in a year or
+
+ align:start position:0%
+that's have to come back in a year or
+ 
+
+ align:start position:0%
+that's have to come back in a year or
+two and see what the five-year-olds are
+
+ align:start position:0%
+two and see what the five-year-olds are
+ 
+
+ align:start position:0%
+two and see what the five-year-olds are
+doing well you when do they go to school
+
+ align:start position:0%
+doing well you when do they go to school
+ 
+
+ align:start position:0%
+doing well you when do they go to school
+and then you lose
+
+ align:start position:0%
+and then you lose
+ 
+
+ align:start position:0%
+and then you lose
+them six six year old uhhuh plenty of
+
+ align:start position:0%
+them six six year old uhhuh plenty of
+ 
+
+ align:start position:0%
+them six six year old uhhuh plenty of
+time then uh weend Saturday on
+
+ align:start position:0%
+time then uh weend Saturday on
+ 
+
+ align:start position:0%
+time then uh weend Saturday on
+Sundays but in any case I think if you
+
+ align:start position:0%
+Sundays but in any case I think if you
+ 
+
+ align:start position:0%
+Sundays but in any case I think if you
+knew how a 5-year-old worked you would
+
+ align:start position:0%
+knew how a 5-year-old worked you would
+ 
+
+ align:start position:0%
+knew how a 5-year-old worked you would
+be almost all the way
+
+ align:start position:0%
+be almost all the way
+ 
+
+ align:start position:0%
+be almost all the way
+home
+
+ align:start position:0%
+home
+ 
+
+ align:start position:0%
+home
+so if you take all the things robots can
+
+ align:start position:0%
+so if you take all the things robots can
+ 
+
+ align:start position:0%
+so if you take all the things robots can
+do today
+
+ align:start position:0%
+do today
+ 
+
+ align:start position:0%
+do today
+uh that includes almost none of what a
+
+ align:start position:0%
+uh that includes almost none of what a
+ 
+
+ align:start position:0%
+uh that includes almost none of what a
+five-year-old can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do in fact why do we need school
+
+ align:start position:0%
+do in fact why do we need school
+ 
+
+ align:start position:0%
+do in fact why do we need school
+pleas
\ No newline at end of file
diff --git a/klPt8DrL5tc.txt b/klPt8DrL5tc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..378a150ba0e276248ab174d8f951474c9d23fb2f
--- /dev/null
+++ b/klPt8DrL5tc.txt
@@ -0,0 +1,1347 @@
+align:start position:0%
+ 
+my name is Devon Neary I'm the cleaning
+
+ align:start position:0%
+my name is Devon Neary I'm the cleaning
+ 
+
+ align:start position:0%
+my name is Devon Neary I'm the cleaning
+the outreach manager here at the cma as
+
+ align:start position:0%
+the outreach manager here at the cma as
+ 
+
+ align:start position:0%
+the outreach manager here at the cma as
+you all know our members across the
+
+ align:start position:0%
+you all know our members across the
+ 
+
+ align:start position:0%
+you all know our members across the
+country face constant opposition from
+
+ align:start position:0%
+country face constant opposition from
+ 
+
+ align:start position:0%
+country face constant opposition from
+environmental groups I'm here today to
+
+ align:start position:0%
+environmental groups I'm here today to
+ 
+
+ align:start position:0%
+environmental groups I'm here today to
+propose some solutions for working with
+
+ align:start position:0%
+propose some solutions for working with
+ 
+
+ align:start position:0%
+propose some solutions for working with
+these groups right hence then our most
+
+ align:start position:0%
+these groups right hence then our most
+ 
+
+ align:start position:0%
+these groups right hence then our most
+recent conflict involved an
+
+ align:start position:0%
+recent conflict involved an
+ 
+
+ align:start position:0%
+recent conflict involved an
+environmental group trying to block the
+
+ align:start position:0%
+environmental group trying to block the
+ 
+
+ align:start position:0%
+environmental group trying to block the
+expansion of our Southwest computer chip
+
+ align:start position:0%
+expansion of our Southwest computer chip
+ 
+
+ align:start position:0%
+expansion of our Southwest computer chip
+factory on the grounds that pollution is
+
+ align:start position:0%
+factory on the grounds that pollution is
+ 
+
+ align:start position:0%
+factory on the grounds that pollution is
+causing a spike in local cancer rates so
+
+ align:start position:0%
+causing a spike in local cancer rates so
+ 
+
+ align:start position:0%
+causing a spike in local cancer rates so
+what's our goal be in designing a
+
+ align:start position:0%
+what's our goal be in designing a
+ 
+
+ align:start position:0%
+what's our goal be in designing a
+working plan with this environmental
+
+ align:start position:0%
+working plan with this environmental
+ 
+
+ align:start position:0%
+working plan with this environmental
+group I propose a strategy that is
+
+ align:start position:0%
+group I propose a strategy that is
+ 
+
+ align:start position:0%
+group I propose a strategy that is
+different from how the CMA usually
+
+ align:start position:0%
+different from how the CMA usually
+ 
+
+ align:start position:0%
+different from how the CMA usually
+conducts business I propose me sit down
+
+ align:start position:0%
+conducts business I propose me sit down
+ 
+
+ align:start position:0%
+conducts business I propose me sit down
+in a mediated negotiation with the
+
+ align:start position:0%
+in a mediated negotiation with the
+ 
+
+ align:start position:0%
+in a mediated negotiation with the
+environmental groups and explain our
+
+ align:start position:0%
+environmental groups and explain our
+ 
+
+ align:start position:0%
+environmental groups and explain our
+side of the issue allow them to explain
+
+ align:start position:0%
+side of the issue allow them to explain
+ 
+
+ align:start position:0%
+side of the issue allow them to explain
+their side of the issue and find a
+
+ align:start position:0%
+their side of the issue and find a
+ 
+
+ align:start position:0%
+their side of the issue and find a
+consensus for moving forward that
+
+ align:start position:0%
+consensus for moving forward that
+ 
+
+ align:start position:0%
+consensus for moving forward that
+enables both sides to achieve their
+
+ align:start position:0%
+enables both sides to achieve their
+ 
+
+ align:start position:0%
+enables both sides to achieve their
+long-term aims given the constraints of
+
+ align:start position:0%
+long-term aims given the constraints of
+ 
+
+ align:start position:0%
+long-term aims given the constraints of
+reality we want to open up a space to
+
+ align:start position:0%
+reality we want to open up a space to
+ 
+
+ align:start position:0%
+reality we want to open up a space to
+collaborate and brainstorm non-binding
+
+ align:start position:0%
+collaborate and brainstorm non-binding
+ 
+
+ align:start position:0%
+collaborate and brainstorm non-binding
+options as a means of moving towards a
+
+ align:start position:0%
+options as a means of moving towards a
+ 
+
+ align:start position:0%
+options as a means of moving towards a
+binding agreement why should this be our
+
+ align:start position:0%
+binding agreement why should this be our
+ 
+
+ align:start position:0%
+binding agreement why should this be our
+goal environmental groups pressure us
+
+ align:start position:0%
+goal environmental groups pressure us
+ 
+
+ align:start position:0%
+goal environmental groups pressure us
+and attempt to block us at our sites
+
+ align:start position:0%
+and attempt to block us at our sites
+ 
+
+ align:start position:0%
+and attempt to block us at our sites
+throughout the country these disputes
+
+ align:start position:0%
+throughout the country these disputes
+ 
+
+ align:start position:0%
+throughout the country these disputes
+have not improved over the last few
+
+ align:start position:0%
+have not improved over the last few
+ 
+
+ align:start position:0%
+have not improved over the last few
+decades and it's time for a new approach
+
+ align:start position:0%
+decades and it's time for a new approach
+ 
+
+ align:start position:0%
+decades and it's time for a new approach
+to make sure our projects progressed
+
+ align:start position:0%
+to make sure our projects progressed
+ 
+
+ align:start position:0%
+to make sure our projects progressed
+according to time and financial
+
+ align:start position:0%
+according to time and financial
+ 
+
+ align:start position:0%
+according to time and financial
+constraints my research on this issue
+
+ align:start position:0%
+constraints my research on this issue
+ 
+
+ align:start position:0%
+constraints my research on this issue
+supports the idea that a consensus
+
+ align:start position:0%
+supports the idea that a consensus
+ 
+
+ align:start position:0%
+supports the idea that a consensus
+building approach can improve outcomes
+
+ align:start position:0%
+building approach can improve outcomes
+ 
+
+ align:start position:0%
+building approach can improve outcomes
+for all parties just for a little bit of
+
+ align:start position:0%
+for all parties just for a little bit of
+ 
+
+ align:start position:0%
+for all parties just for a little bit of
+context in reality our partners in the
+
+ align:start position:0%
+context in reality our partners in the
+ 
+
+ align:start position:0%
+context in reality our partners in the
+environments organization do not have a
+
+ align:start position:0%
+environments organization do not have a
+ 
+
+ align:start position:0%
+environments organization do not have a
+lot of legal ground to stand on proving
+
+ align:start position:0%
+lot of legal ground to stand on proving
+ 
+
+ align:start position:0%
+lot of legal ground to stand on proving
+the cause of a specific cancer in a
+
+ align:start position:0%
+the cause of a specific cancer in a
+ 
+
+ align:start position:0%
+the cause of a specific cancer in a
+specific individual and tying it to a
+
+ align:start position:0%
+specific individual and tying it to a
+ 
+
+ align:start position:0%
+specific individual and tying it to a
+specific chemical that came out of our
+
+ align:start position:0%
+specific chemical that came out of our
+ 
+
+ align:start position:0%
+specific chemical that came out of our
+chip plant on a specific day is very
+
+ align:start position:0%
+chip plant on a specific day is very
+ 
+
+ align:start position:0%
+chip plant on a specific day is very
+challenging and costly in a courtroom we
+
+ align:start position:0%
+challenging and costly in a courtroom we
+ 
+
+ align:start position:0%
+challenging and costly in a courtroom we
+can gently remind environmentalists that
+
+ align:start position:0%
+can gently remind environmentalists that
+ 
+
+ align:start position:0%
+can gently remind environmentalists that
+court is expensive adversarial and often
+
+ align:start position:0%
+court is expensive adversarial and often
+ 
+
+ align:start position:0%
+court is expensive adversarial and often
+drawn-out
+
+ align:start position:0%
+drawn-out
+ 
+
+ align:start position:0%
+drawn-out
+similarly our funding and legal
+
+ align:start position:0%
+similarly our funding and legal
+ 
+
+ align:start position:0%
+similarly our funding and legal
+capabilities will defeat theirs in
+
+ align:start position:0%
+capabilities will defeat theirs in
+ 
+
+ align:start position:0%
+capabilities will defeat theirs in
+addition in times of economic duress and
+
+ align:start position:0%
+addition in times of economic duress and
+ 
+
+ align:start position:0%
+addition in times of economic duress and
+uncertainty local authorities are going
+
+ align:start position:0%
+uncertainty local authorities are going
+ 
+
+ align:start position:0%
+uncertainty local authorities are going
+to make way for our great industry to
+
+ align:start position:0%
+to make way for our great industry to
+ 
+
+ align:start position:0%
+to make way for our great industry to
+create jobs and capital
+
+ align:start position:0%
+create jobs and capital
+ 
+
+ align:start position:0%
+create jobs and capital
+so in some sense there's no need for us
+
+ align:start position:0%
+so in some sense there's no need for us
+ 
+
+ align:start position:0%
+so in some sense there's no need for us
+to engage with the environmentalists
+
+ align:start position:0%
+to engage with the environmentalists
+ 
+
+ align:start position:0%
+to engage with the environmentalists
+without the negotiation we'll probably
+
+ align:start position:0%
+without the negotiation we'll probably
+ 
+
+ align:start position:0%
+without the negotiation we'll probably
+still get our expansion however what I
+
+ align:start position:0%
+still get our expansion however what I
+ 
+
+ align:start position:0%
+still get our expansion however what I
+want to point out is that we can do
+
+ align:start position:0%
+want to point out is that we can do
+ 
+
+ align:start position:0%
+want to point out is that we can do
+better than that
+
+ align:start position:0%
+better than that
+ 
+
+ align:start position:0%
+better than that
+the negotiation we can improve our
+
+ align:start position:0%
+the negotiation we can improve our
+ 
+
+ align:start position:0%
+the negotiation we can improve our
+relationships with the environmentalists
+
+ align:start position:0%
+relationships with the environmentalists
+ 
+
+ align:start position:0%
+relationships with the environmentalists
+and we can make it easier and less
+
+ align:start position:0%
+and we can make it easier and less
+ 
+
+ align:start position:0%
+and we can make it easier and less
+costly to do business in the future I
+
+ align:start position:0%
+costly to do business in the future I
+ 
+
+ align:start position:0%
+costly to do business in the future I
+know many of you probably have some
+
+ align:start position:0%
+know many of you probably have some
+ 
+
+ align:start position:0%
+know many of you probably have some
+hesitations about this perhaps you feel
+
+ align:start position:0%
+hesitations about this perhaps you feel
+ 
+
+ align:start position:0%
+hesitations about this perhaps you feel
+a fear of the unknown a fear that the
+
+ align:start position:0%
+a fear of the unknown a fear that the
+ 
+
+ align:start position:0%
+a fear of the unknown a fear that the
+process will fail or fear that the
+
+ align:start position:0%
+process will fail or fear that the
+ 
+
+ align:start position:0%
+process will fail or fear that the
+negotiation will be slow and costly but
+
+ align:start position:0%
+negotiation will be slow and costly but
+ 
+
+ align:start position:0%
+negotiation will be slow and costly but
+remember we're investing for long term
+
+ align:start position:0%
+remember we're investing for long term
+ 
+
+ align:start position:0%
+remember we're investing for long term
+gains in our relationships with
+
+ align:start position:0%
+gains in our relationships with
+ 
+
+ align:start position:0%
+gains in our relationships with
+surrounding communities I understands is
+
+ align:start position:0%
+surrounding communities I understands is
+ 
+
+ align:start position:0%
+surrounding communities I understands is
+atypical for our powerful industry and
+
+ align:start position:0%
+atypical for our powerful industry and
+ 
+
+ align:start position:0%
+atypical for our powerful industry and
+there will be challenges as the views of
+
+ align:start position:0%
+there will be challenges as the views of
+ 
+
+ align:start position:0%
+there will be challenges as the views of
+the CMA and the views of the
+
+ align:start position:0%
+the CMA and the views of the
+ 
+
+ align:start position:0%
+the CMA and the views of the
+environmental groups differ radically
+
+ align:start position:0%
+environmental groups differ radically
+ 
+
+ align:start position:0%
+environmental groups differ radically
+the environmentalists may not be ready
+
+ align:start position:0%
+the environmentalists may not be ready
+ 
+
+ align:start position:0%
+the environmentalists may not be ready
+or willing to negotiate they may be
+
+ align:start position:0%
+or willing to negotiate they may be
+ 
+
+ align:start position:0%
+or willing to negotiate they may be
+intent on filing a lawsuit or they could
+
+ align:start position:0%
+intent on filing a lawsuit or they could
+ 
+
+ align:start position:0%
+intent on filing a lawsuit or they could
+draw out the negotiations in a
+
+ align:start position:0%
+draw out the negotiations in a
+ 
+
+ align:start position:0%
+draw out the negotiations in a
+disruptive manner their strategy is
+
+ align:start position:0%
+disruptive manner their strategy is
+ 
+
+ align:start position:0%
+disruptive manner their strategy is
+going to be to eliminate the earth their
+
+ align:start position:0%
+going to be to eliminate the earth their
+ 
+
+ align:start position:0%
+going to be to eliminate the earth their
+ultimate goal would probably be to
+
+ align:start position:0%
+ultimate goal would probably be to
+ 
+
+ align:start position:0%
+ultimate goal would probably be to
+eliminate art plan but this is not a
+
+ align:start position:0%
+eliminate art plan but this is not a
+ 
+
+ align:start position:0%
+eliminate art plan but this is not a
+realistic demand our plan is already
+
+ align:start position:0%
+realistic demand our plan is already
+ 
+
+ align:start position:0%
+realistic demand our plan is already
+they're not breeding well so eliminating
+
+ align:start position:0%
+they're not breeding well so eliminating
+ 
+
+ align:start position:0%
+they're not breeding well so eliminating
+the potential carcinogens is not a
+
+ align:start position:0%
+the potential carcinogens is not a
+ 
+
+ align:start position:0%
+the potential carcinogens is not a
+feasible option for them so what is the
+
+ align:start position:0%
+feasible option for them so what is the
+ 
+
+ align:start position:0%
+feasible option for them so what is the
+next next best option for the community
+
+ align:start position:0%
+next next best option for the community
+ 
+
+ align:start position:0%
+next next best option for the community
+our strategy is to think in terms what
+
+ align:start position:0%
+our strategy is to think in terms what
+ 
+
+ align:start position:0%
+our strategy is to think in terms what
+we can offer them to appease some of
+
+ align:start position:0%
+we can offer them to appease some of
+ 
+
+ align:start position:0%
+we can offer them to appease some of
+their concerns without giving up
+
+ align:start position:0%
+their concerns without giving up
+ 
+
+ align:start position:0%
+their concerns without giving up
+anything precious to us do they need
+
+ align:start position:0%
+anything precious to us do they need
+ 
+
+ align:start position:0%
+anything precious to us do they need
+health clinics in their community do
+
+ align:start position:0%
+health clinics in their community do
+ 
+
+ align:start position:0%
+health clinics in their community do
+they want a community buy out so they
+
+ align:start position:0%
+they want a community buy out so they
+ 
+
+ align:start position:0%
+they want a community buy out so they
+can relocate what they like a new nature
+
+ align:start position:0%
+can relocate what they like a new nature
+ 
+
+ align:start position:0%
+can relocate what they like a new nature
+preserve or funding for education for
+
+ align:start position:0%
+preserve or funding for education for
+ 
+
+ align:start position:0%
+preserve or funding for education for
+our part our members have to decide away
+
+ align:start position:0%
+our part our members have to decide away
+ 
+
+ align:start position:0%
+our part our members have to decide away
+from the table how much we are willing
+
+ align:start position:0%
+from the table how much we are willing
+ 
+
+ align:start position:0%
+from the table how much we are willing
+to give to smooth out these
+
+ align:start position:0%
+to give to smooth out these
+ 
+
+ align:start position:0%
+to give to smooth out these
+relationships and leverage these
+
+ align:start position:0%
+relationships and leverage these
+ 
+
+ align:start position:0%
+relationships and leverage these
+concessions and negotiations we need to
+
+ align:start position:0%
+concessions and negotiations we need to
+ 
+
+ align:start position:0%
+concessions and negotiations we need to
+find out what people on both sides are
+
+ align:start position:0%
+find out what people on both sides are
+ 
+
+ align:start position:0%
+find out what people on both sides are
+really willing to live with we can begin
+
+ align:start position:0%
+really willing to live with we can begin
+ 
+
+ align:start position:0%
+really willing to live with we can begin
+by addressing their environmental
+
+ align:start position:0%
+by addressing their environmental
+ 
+
+ align:start position:0%
+by addressing their environmental
+concerns talking about issues of leaks
+
+ align:start position:0%
+concerns talking about issues of leaks
+ 
+
+ align:start position:0%
+concerns talking about issues of leaks
+accidents the increased rates of cancer
+
+ align:start position:0%
+accidents the increased rates of cancer
+ 
+
+ align:start position:0%
+accidents the increased rates of cancer
+that they're observing how can you prove
+
+ align:start position:0%
+that they're observing how can you prove
+ 
+
+ align:start position:0%
+that they're observing how can you prove
+to them that we are in compliance of
+
+ align:start position:0%
+to them that we are in compliance of
+ 
+
+ align:start position:0%
+to them that we are in compliance of
+regulations and protecting the abutting
+
+ align:start position:0%
+regulations and protecting the abutting
+ 
+
+ align:start position:0%
+regulations and protecting the abutting
+communities we can also leverage what we
+
+ align:start position:0%
+communities we can also leverage what we
+ 
+
+ align:start position:0%
+communities we can also leverage what we
+do well for the community we create jobs
+
+ align:start position:0%
+do well for the community we create jobs
+ 
+
+ align:start position:0%
+do well for the community we create jobs
+we spur economic development we make
+
+ align:start position:0%
+we spur economic development we make
+ 
+
+ align:start position:0%
+we spur economic development we make
+philanthropic donations provide job
+
+ align:start position:0%
+philanthropic donations provide job
+ 
+
+ align:start position:0%
+philanthropic donations provide job
+training my job is to get people excited
+
+ align:start position:0%
+training my job is to get people excited
+ 
+
+ align:start position:0%
+training my job is to get people excited
+about chemical manufacturing and all the
+
+ align:start position:0%
+about chemical manufacturing and all the
+ 
+
+ align:start position:0%
+about chemical manufacturing and all the
+wonderful things we do for the country
+
+ align:start position:0%
+wonderful things we do for the country
+ 
+
+ align:start position:0%
+wonderful things we do for the country
+and for the world the chips
+
+ align:start position:0%
+and for the world the chips
+ 
+
+ align:start position:0%
+and for the world the chips
+manufacturing plant in question while
+
+ align:start position:0%
+manufacturing plant in question while
+ 
+
+ align:start position:0%
+manufacturing plant in question while
+may be causing some pollution is
+
+ align:start position:0%
+may be causing some pollution is
+ 
+
+ align:start position:0%
+may be causing some pollution is
+manufacturing computer chips used in a
+
+ align:start position:0%
+manufacturing computer chips used in a
+ 
+
+ align:start position:0%
+manufacturing computer chips used in a
+wide range of industries and clean
+
+ align:start position:0%
+wide range of industries and clean
+ 
+
+ align:start position:0%
+wide range of industries and clean
+defense medical research
+
+ align:start position:0%
+defense medical research
+ 
+
+ align:start position:0%
+defense medical research
+shishun and so on we believe that if
+
+ align:start position:0%
+shishun and so on we believe that if
+ 
+
+ align:start position:0%
+shishun and so on we believe that if
+residents realize the contribution we
+
+ align:start position:0%
+residents realize the contribution we
+ 
+
+ align:start position:0%
+residents realize the contribution we
+have for their community and for the
+
+ align:start position:0%
+have for their community and for the
+ 
+
+ align:start position:0%
+have for their community and for the
+country they'll be more amenable to
+
+ align:start position:0%
+country they'll be more amenable to
+ 
+
+ align:start position:0%
+country they'll be more amenable to
+negotiating with us so you want to focus
+
+ align:start position:0%
+negotiating with us so you want to focus
+ 
+
+ align:start position:0%
+negotiating with us so you want to focus
+on two principles we want to focus on
+
+ align:start position:0%
+on two principles we want to focus on
+ 
+
+ align:start position:0%
+on two principles we want to focus on
+maintaining relationships throughout you
+
+ align:start position:0%
+maintaining relationships throughout you
+ 
+
+ align:start position:0%
+maintaining relationships throughout you
+want to focus on mutual gains so we'll
+
+ align:start position:0%
+want to focus on mutual gains so we'll
+ 
+
+ align:start position:0%
+want to focus on mutual gains so we'll
+follow a process based on a research
+
+ align:start position:0%
+follow a process based on a research
+ 
+
+ align:start position:0%
+follow a process based on a research
+consensus building approach when we are
+
+ align:start position:0%
+consensus building approach when we are
+ 
+
+ align:start position:0%
+consensus building approach when we are
+a to negotiate and the environmentalists
+
+ align:start position:0%
+a to negotiate and the environmentalists
+ 
+
+ align:start position:0%
+a to negotiate and the environmentalists
+expressed that they already first we
+
+ align:start position:0%
+expressed that they already first we
+ 
+
+ align:start position:0%
+expressed that they already first we
+will convene and assign roles for
+
+ align:start position:0%
+will convene and assign roles for
+ 
+
+ align:start position:0%
+will convene and assign roles for
+example we need to identify a mediator
+
+ align:start position:0%
+example we need to identify a mediator
+ 
+
+ align:start position:0%
+example we need to identify a mediator
+the mediator will schedule and
+
+ align:start position:0%
+the mediator will schedule and
+ 
+
+ align:start position:0%
+the mediator will schedule and
+facilitate the meetings consult
+
+ align:start position:0%
+facilitate the meetings consult
+ 
+
+ align:start position:0%
+facilitate the meetings consult
+privately with groups and push us to
+
+ align:start position:0%
+privately with groups and push us to
+ 
+
+ align:start position:0%
+privately with groups and push us to
+build consensus we also want to focus on
+
+ align:start position:0%
+build consensus we also want to focus on
+ 
+
+ align:start position:0%
+build consensus we also want to focus on
+group problem solving how can we create
+
+ align:start position:0%
+group problem solving how can we create
+ 
+
+ align:start position:0%
+group problem solving how can we create
+value as a group by brainstorming
+
+ align:start position:0%
+value as a group by brainstorming
+ 
+
+ align:start position:0%
+value as a group by brainstorming
+different options together based on our
+
+ align:start position:0%
+different options together based on our
+ 
+
+ align:start position:0%
+different options together based on our
+interests and being creative we can
+
+ align:start position:0%
+interests and being creative we can
+ 
+
+ align:start position:0%
+interests and being creative we can
+present alternative designs we can
+
+ align:start position:0%
+present alternative designs we can
+ 
+
+ align:start position:0%
+present alternative designs we can
+expand the means of dealing with
+
+ align:start position:0%
+expand the means of dealing with
+ 
+
+ align:start position:0%
+expand the means of dealing with
+externalities and try to create
+
+ align:start position:0%
+externalities and try to create
+ 
+
+ align:start position:0%
+externalities and try to create
+different packages of benefits we can
+
+ align:start position:0%
+different packages of benefits we can
+ 
+
+ align:start position:0%
+different packages of benefits we can
+offer the community once we have created
+
+ align:start position:0%
+offer the community once we have created
+ 
+
+ align:start position:0%
+offer the community once we have created
+value we can talk about ways to
+
+ align:start position:0%
+value we can talk about ways to
+ 
+
+ align:start position:0%
+value we can talk about ways to
+distribute value to implement these
+
+ align:start position:0%
+distribute value to implement these
+ 
+
+ align:start position:0%
+distribute value to implement these
+goals and to hold parties accountable
+
+ align:start position:0%
+goals and to hold parties accountable
+ 
+
+ align:start position:0%
+goals and to hold parties accountable
+for their commitments so just to review
+
+ align:start position:0%
+for their commitments so just to review
+ 
+
+ align:start position:0%
+for their commitments so just to review
+the benefits of engaging in a successful
+
+ align:start position:0%
+the benefits of engaging in a successful
+ 
+
+ align:start position:0%
+the benefits of engaging in a successful
+negotiation for our company it's an
+
+ align:start position:0%
+negotiation for our company it's an
+ 
+
+ align:start position:0%
+negotiation for our company it's an
+opportunity to educate the community
+
+ align:start position:0%
+opportunity to educate the community
+ 
+
+ align:start position:0%
+opportunity to educate the community
+about our work and our constraints to
+
+ align:start position:0%
+about our work and our constraints to
+ 
+
+ align:start position:0%
+about our work and our constraints to
+gain some flexibility in when and how
+
+ align:start position:0%
+gain some flexibility in when and how
+ 
+
+ align:start position:0%
+gain some flexibility in when and how
+requirements are met and to smooth out
+
+ align:start position:0%
+requirements are met and to smooth out
+ 
+
+ align:start position:0%
+requirements are met and to smooth out
+these long-standing and disruptive
+
+ align:start position:0%
+these long-standing and disruptive
+ 
+
+ align:start position:0%
+these long-standing and disruptive
+conflicts with environmentalists with
+
+ align:start position:0%
+conflicts with environmentalists with
+ 
+
+ align:start position:0%
+conflicts with environmentalists with
+the environmentalists they can achieve
+
+ align:start position:0%
+the environmentalists they can achieve
+ 
+
+ align:start position:0%
+the environmentalists they can achieve
+better environmental gains we've added
+
+ align:start position:0%
+better environmental gains we've added
+ 
+
+ align:start position:0%
+better environmental gains we've added
+value and enforce stronger business
+
+ align:start position:0%
+value and enforce stronger business
+ 
+
+ align:start position:0%
+value and enforce stronger business
+practices in their community all at a
+
+ align:start position:0%
+practices in their community all at a
+ 
+
+ align:start position:0%
+practices in their community all at a
+lower cost
\ No newline at end of file
diff --git a/lET4uQLpmM0.txt b/lET4uQLpmM0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6fd197cd2f5824e7fecb5449e88278701730ba4e
--- /dev/null
+++ b/lET4uQLpmM0.txt
@@ -0,0 +1,1091 @@
+align:start position:0%
+ 
+in this segment we discuss a little more
+
+ align:start position:0%
+in this segment we discuss a little more
+ 
+
+ align:start position:0%
+in this segment we discuss a little more
+the mean squared error consider some
+
+ align:start position:0%
+the mean squared error consider some
+ 
+
+ align:start position:0%
+the mean squared error consider some
+estimator it can be any estimator not
+
+ align:start position:0%
+estimator it can be any estimator not
+ 
+
+ align:start position:0%
+estimator it can be any estimator not
+just the sample mean we can decompose
+
+ align:start position:0%
+just the sample mean we can decompose
+ 
+
+ align:start position:0%
+just the sample mean we can decompose
+the mean squared error as a sum of two
+
+ align:start position:0%
+the mean squared error as a sum of two
+ 
+
+ align:start position:0%
+the mean squared error as a sum of two
+terms where does this formula come from
+
+ align:start position:0%
+terms where does this formula come from
+ 
+
+ align:start position:0%
+terms where does this formula come from
+well we know that for any random
+
+ align:start position:0%
+well we know that for any random
+ 
+
+ align:start position:0%
+well we know that for any random
+variable Z this formula is valid and if
+
+ align:start position:0%
+variable Z this formula is valid and if
+ 
+
+ align:start position:0%
+variable Z this formula is valid and if
+we let Z be equal to the difference
+
+ align:start position:0%
+we let Z be equal to the difference
+ 
+
+ align:start position:0%
+we let Z be equal to the difference
+between the estimator and the value that
+
+ align:start position:0%
+between the estimator and the value that
+ 
+
+ align:start position:0%
+between the estimator and the value that
+we're trying to estimate then we obtain
+
+ align:start position:0%
+we're trying to estimate then we obtain
+ 
+
+ align:start position:0%
+we're trying to estimate then we obtain
+this formula here we expected value of
+
+ align:start position:0%
+this formula here we expected value of
+ 
+
+ align:start position:0%
+this formula here we expected value of
+our random variable Z squared is equal
+
+ align:start position:0%
+our random variable Z squared is equal
+ 
+
+ align:start position:0%
+our random variable Z squared is equal
+to the variance of that random variable
+
+ align:start position:0%
+to the variance of that random variable
+ 
+
+ align:start position:0%
+to the variance of that random variable
+plus the square of its mean let us now
+
+ align:start position:0%
+plus the square of its mean let us now
+ 
+
+ align:start position:0%
+plus the square of its mean let us now
+rewrite these two terms in a more
+
+ align:start position:0%
+rewrite these two terms in a more
+ 
+
+ align:start position:0%
+rewrite these two terms in a more
+suggestive way we first noticed that
+
+ align:start position:0%
+suggestive way we first noticed that
+ 
+
+ align:start position:0%
+suggestive way we first noticed that
+theta is a constant when you add or
+
+ align:start position:0%
+theta is a constant when you add or
+ 
+
+ align:start position:0%
+theta is a constant when you add or
+subtract a constant from a random
+
+ align:start position:0%
+subtract a constant from a random
+ 
+
+ align:start position:0%
+subtract a constant from a random
+variable the variance does not change so
+
+ align:start position:0%
+variable the variance does not change so
+ 
+
+ align:start position:0%
+variable the variance does not change so
+this term is the same as the variance of
+
+ align:start position:0%
+this term is the same as the variance of
+ 
+
+ align:start position:0%
+this term is the same as the variance of
+theta hat this quantity here we will
+
+ align:start position:0%
+theta hat this quantity here we will
+ 
+
+ align:start position:0%
+theta hat this quantity here we will
+call it the bias of the estimator it
+
+ align:start position:0%
+call it the bias of the estimator it
+ 
+
+ align:start position:0%
+call it the bias of the estimator it
+tells us whether theta hat is
+
+ align:start position:0%
+tells us whether theta hat is
+ 
+
+ align:start position:0%
+tells us whether theta hat is
+systematically above or below than the
+
+ align:start position:0%
+systematically above or below than the
+ 
+
+ align:start position:0%
+systematically above or below than the
+unknown parameter theta that we are
+
+ align:start position:0%
+unknown parameter theta that we are
+ 
+
+ align:start position:0%
+unknown parameter theta that we are
+trying to estimate and using this
+
+ align:start position:0%
+trying to estimate and using this
+ 
+
+ align:start position:0%
+trying to estimate and using this
+terminology this term here is just equal
+
+ align:start position:0%
+terminology this term here is just equal
+ 
+
+ align:start position:0%
+terminology this term here is just equal
+to the square of the bias so the mean
+
+ align:start position:0%
+to the square of the bias so the mean
+ 
+
+ align:start position:0%
+to the square of the bias so the mean
+squared error consists of two components
+
+ align:start position:0%
+squared error consists of two components
+ 
+
+ align:start position:0%
+squared error consists of two components
+and these capture different aspects of
+
+ align:start position:0%
+and these capture different aspects of
+ 
+
+ align:start position:0%
+and these capture different aspects of
+an estimators performance let us see
+
+ align:start position:0%
+an estimators performance let us see
+ 
+
+ align:start position:0%
+an estimators performance let us see
+what they are in the concrete setting
+
+ align:start position:0%
+what they are in the concrete setting
+ 
+
+ align:start position:0%
+what they are in the concrete setting
+suppose that were estimating the unknown
+
+ align:start position:0%
+suppose that were estimating the unknown
+ 
+
+ align:start position:0%
+suppose that were estimating the unknown
+mean of some distribution and that our
+
+ align:start position:0%
+mean of some distribution and that our
+ 
+
+ align:start position:0%
+mean of some distribution and that our
+estimator is the sample mean in this
+
+ align:start position:0%
+estimator is the sample mean in this
+ 
+
+ align:start position:0%
+estimator is the sample mean in this
+case the mean squared error is the
+
+ align:start position:0%
+case the mean squared error is the
+ 
+
+ align:start position:0%
+case the mean squared error is the
+variance which we know to be Sigma
+
+ align:start position:0%
+variance which we know to be Sigma
+ 
+
+ align:start position:0%
+variance which we know to be Sigma
+squared over n plus the bias term but we
+
+ align:start position:0%
+squared over n plus the bias term but we
+ 
+
+ align:start position:0%
+squared over n plus the bias term but we
+know that the sample mean is unbiased
+
+ align:start position:0%
+know that the sample mean is unbiased
+ 
+
+ align:start position:0%
+know that the sample mean is unbiased
+the expected value of the sample mean is
+
+ align:start position:0%
+the expected value of the sample mean is
+ 
+
+ align:start position:0%
+the expected value of the sample mean is
+equal to the unknown mean and so the
+
+ align:start position:0%
+equal to the unknown mean and so the
+ 
+
+ align:start position:0%
+equal to the unknown mean and so the
+bias contribution is equal to 0 now for
+
+ align:start position:0%
+bias contribution is equal to 0 now for
+ 
+
+ align:start position:0%
+bias contribution is equal to 0 now for
+the sake of a comparison let us consider
+
+ align:start position:0%
+the sake of a comparison let us consider
+ 
+
+ align:start position:0%
+the sake of a comparison let us consider
+a somewhat silly estimator which ignores
+
+ align:start position:0%
+a somewhat silly estimator which ignores
+ 
+
+ align:start position:0%
+a somewhat silly estimator which ignores
+the data altogether and always gives you
+
+ align:start position:0%
+the data altogether and always gives you
+ 
+
+ align:start position:0%
+the data altogether and always gives you
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+estimate of zero in this case the mean
+
+ align:start position:0%
+estimate of zero in this case the mean
+ 
+
+ align:start position:0%
+estimate of zero in this case the mean
+squared error is as follows
+
+ align:start position:0%
+squared error is as follows
+ 
+
+ align:start position:0%
+squared error is as follows
+since our estimator is just a constant
+
+ align:start position:0%
+since our estimator is just a constant
+ 
+
+ align:start position:0%
+since our estimator is just a constant
+it's variance is going to be equal to
+
+ align:start position:0%
+it's variance is going to be equal to
+ 
+
+ align:start position:0%
+it's variance is going to be equal to
+zero on the other hand since theta hat
+
+ align:start position:0%
+zero on the other hand since theta hat
+ 
+
+ align:start position:0%
+zero on the other hand since theta hat
+is zero this term here is just the
+
+ align:start position:0%
+is zero this term here is just the
+ 
+
+ align:start position:0%
+is zero this term here is just the
+constant theta squared and this gives us
+
+ align:start position:0%
+constant theta squared and this gives us
+ 
+
+ align:start position:0%
+constant theta squared and this gives us
+the corresponding mean squared error let
+
+ align:start position:0%
+the corresponding mean squared error let
+ 
+
+ align:start position:0%
+the corresponding mean squared error let
+us now compare the two estimators we
+
+ align:start position:0%
+us now compare the two estimators we
+ 
+
+ align:start position:0%
+us now compare the two estimators we
+will plot the mean squared error as a
+
+ align:start position:0%
+will plot the mean squared error as a
+ 
+
+ align:start position:0%
+will plot the mean squared error as a
+function of the unknown parameter theta
+
+ align:start position:0%
+function of the unknown parameter theta
+ 
+
+ align:start position:0%
+function of the unknown parameter theta
+for the sample mean estimator the mean
+
+ align:start position:0%
+for the sample mean estimator the mean
+ 
+
+ align:start position:0%
+for the sample mean estimator the mean
+squared error is constant does not
+
+ align:start position:0%
+squared error is constant does not
+ 
+
+ align:start position:0%
+squared error is constant does not
+depend on theta and is equal to this
+
+ align:start position:0%
+depend on theta and is equal to this
+ 
+
+ align:start position:0%
+depend on theta and is equal to this
+value Sigma squared over N on the other
+
+ align:start position:0%
+value Sigma squared over N on the other
+ 
+
+ align:start position:0%
+value Sigma squared over N on the other
+hand for the zero estimator the mean
+
+ align:start position:0%
+hand for the zero estimator the mean
+ 
+
+ align:start position:0%
+hand for the zero estimator the mean
+squared error is equal to theta squared
+
+ align:start position:0%
+squared error is equal to theta squared
+ 
+
+ align:start position:0%
+squared error is equal to theta squared
+how do they compare which one is better
+
+ align:start position:0%
+how do they compare which one is better
+ 
+
+ align:start position:0%
+how do they compare which one is better
+at this point there is no way to say
+
+ align:start position:0%
+at this point there is no way to say
+ 
+
+ align:start position:0%
+at this point there is no way to say
+that one is better than the other for
+
+ align:start position:0%
+that one is better than the other for
+ 
+
+ align:start position:0%
+that one is better than the other for
+some theta the sample mean has a smaller
+
+ align:start position:0%
+some theta the sample mean has a smaller
+ 
+
+ align:start position:0%
+some theta the sample mean has a smaller
+mean squared error but for other theta
+
+ align:start position:0%
+mean squared error but for other theta
+ 
+
+ align:start position:0%
+mean squared error but for other theta
+the 0 estimator has a smaller mean
+
+ align:start position:0%
+the 0 estimator has a smaller mean
+ 
+
+ align:start position:0%
+the 0 estimator has a smaller mean
+squared error but we do not know where
+
+ align:start position:0%
+squared error but we do not know where
+ 
+
+ align:start position:0%
+squared error but we do not know where
+the true value of theta is it could be
+
+ align:start position:0%
+the true value of theta is it could be
+ 
+
+ align:start position:0%
+the true value of theta is it could be
+anything so we cannot say that one is
+
+ align:start position:0%
+anything so we cannot say that one is
+ 
+
+ align:start position:0%
+anything so we cannot say that one is
+better than the other of course we know
+
+ align:start position:0%
+better than the other of course we know
+ 
+
+ align:start position:0%
+better than the other of course we know
+that the sample mean is a consistent
+
+ align:start position:0%
+that the sample mean is a consistent
+ 
+
+ align:start position:0%
+that the sample mean is a consistent
+estimator as n goes to infinity it will
+
+ align:start position:0%
+estimator as n goes to infinity it will
+ 
+
+ align:start position:0%
+estimator as n goes to infinity it will
+give you the true value of theta and
+
+ align:start position:0%
+give you the true value of theta and
+ 
+
+ align:start position:0%
+give you the true value of theta and
+this is a very desirable property that
+
+ align:start position:0%
+this is a very desirable property that
+ 
+
+ align:start position:0%
+this is a very desirable property that
+the zero estimator does not have but if
+
+ align:start position:0%
+the zero estimator does not have but if
+ 
+
+ align:start position:0%
+the zero estimator does not have but if
+n is moderate the situation is less
+
+ align:start position:0%
+n is moderate the situation is less
+ 
+
+ align:start position:0%
+n is moderate the situation is less
+clear if we have some good reason to
+
+ align:start position:0%
+clear if we have some good reason to
+ 
+
+ align:start position:0%
+clear if we have some good reason to
+expect that the true value of theta is
+
+ align:start position:0%
+expect that the true value of theta is
+ 
+
+ align:start position:0%
+expect that the true value of theta is
+somewhere in the vicinity of zero then
+
+ align:start position:0%
+somewhere in the vicinity of zero then
+ 
+
+ align:start position:0%
+somewhere in the vicinity of zero then
+the zero estimator might be a better one
+
+ align:start position:0%
+the zero estimator might be a better one
+ 
+
+ align:start position:0%
+the zero estimator might be a better one
+because it that will achieve a smaller
+
+ align:start position:0%
+because it that will achieve a smaller
+ 
+
+ align:start position:0%
+because it that will achieve a smaller
+mean squared error but in a classical
+
+ align:start position:0%
+mean squared error but in a classical
+ 
+
+ align:start position:0%
+mean squared error but in a classical
+statistical framework there is no way to
+
+ align:start position:0%
+statistical framework there is no way to
+ 
+
+ align:start position:0%
+statistical framework there is no way to
+express a belief of this kind
+
+ align:start position:0%
+express a belief of this kind
+ 
+
+ align:start position:0%
+express a belief of this kind
+in contrast if we were following a
+
+ align:start position:0%
+in contrast if we were following a
+ 
+
+ align:start position:0%
+in contrast if we were following a
+Bayesian approach you could provide a
+
+ align:start position:0%
+Bayesian approach you could provide a
+ 
+
+ align:start position:0%
+Bayesian approach you could provide a
+prior distribution for theta that would
+
+ align:start position:0%
+prior distribution for theta that would
+ 
+
+ align:start position:0%
+prior distribution for theta that would
+be highly concentrated around zero this
+
+ align:start position:0%
+be highly concentrated around zero this
+ 
+
+ align:start position:0%
+be highly concentrated around zero this
+would express your beliefs about theta
+
+ align:start position:0%
+would express your beliefs about theta
+ 
+
+ align:start position:0%
+would express your beliefs about theta
+and would provide you with the guidance
+
+ align:start position:0%
+and would provide you with the guidance
+ 
+
+ align:start position:0%
+and would provide you with the guidance
+to choose between the two estimators or
+
+ align:start position:0%
+to choose between the two estimators or
+ 
+
+ align:start position:0%
+to choose between the two estimators or
+maybe suggest an even better estimator
+
+ align:start position:0%
+maybe suggest an even better estimator
+ 
+
+ align:start position:0%
+maybe suggest an even better estimator
+in any case going back to this formula
+
+ align:start position:0%
+in any case going back to this formula
+ 
+
+ align:start position:0%
+in any case going back to this formula
+this quantity the variance of the
+
+ align:start position:0%
+this quantity the variance of the
+ 
+
+ align:start position:0%
+this quantity the variance of the
+estimator plays an important role in the
+
+ align:start position:0%
+estimator plays an important role in the
+ 
+
+ align:start position:0%
+estimator plays an important role in the
+analysis of different estimators and the
+
+ align:start position:0%
+analysis of different estimators and the
+ 
+
+ align:start position:0%
+analysis of different estimators and the
+more intuitive variant of this quantity
+
+ align:start position:0%
+more intuitive variant of this quantity
+ 
+
+ align:start position:0%
+more intuitive variant of this quantity
+is its square root which is the standard
+
+ align:start position:0%
+is its square root which is the standard
+ 
+
+ align:start position:0%
+is its square root which is the standard
+deviation of the estimator and is
+
+ align:start position:0%
+deviation of the estimator and is
+ 
+
+ align:start position:0%
+deviation of the estimator and is
+usually called the standard error of the
+
+ align:start position:0%
+usually called the standard error of the
+ 
+
+ align:start position:0%
+usually called the standard error of the
+estimator we can interpret the standard
+
+ align:start position:0%
+estimator we can interpret the standard
+ 
+
+ align:start position:0%
+estimator we can interpret the standard
+error as follows we have the true value
+
+ align:start position:0%
+error as follows we have the true value
+ 
+
+ align:start position:0%
+error as follows we have the true value
+of theta then on day one we collect some
+
+ align:start position:0%
+of theta then on day one we collect some
+ 
+
+ align:start position:0%
+of theta then on day one we collect some
+data we perform the estimation procedure
+
+ align:start position:0%
+data we perform the estimation procedure
+ 
+
+ align:start position:0%
+data we perform the estimation procedure
+and we come up with an estimate on day
+
+ align:start position:0%
+and we come up with an estimate on day
+ 
+
+ align:start position:0%
+and we come up with an estimate on day
+two we do the same thing but
+
+ align:start position:0%
+two we do the same thing but
+ 
+
+ align:start position:0%
+two we do the same thing but
+independently we collect a new set of
+
+ align:start position:0%
+independently we collect a new set of
+ 
+
+ align:start position:0%
+independently we collect a new set of
+data and we come up with another
+
+ align:start position:0%
+data and we come up with another
+ 
+
+ align:start position:0%
+data and we come up with another
+estimate and so on we do this many times
+
+ align:start position:0%
+estimate and so on we do this many times
+ 
+
+ align:start position:0%
+estimate and so on we do this many times
+we use different data sets to come up
+
+ align:start position:0%
+we use different data sets to come up
+ 
+
+ align:start position:0%
+we use different data sets to come up
+with different estimates and because of
+
+ align:start position:0%
+with different estimates and because of
+ 
+
+ align:start position:0%
+with different estimates and because of
+the randomness in the data these
+
+ align:start position:0%
+the randomness in the data these
+ 
+
+ align:start position:0%
+the randomness in the data these
+estimates may be all over the place well
+
+ align:start position:0%
+estimates may be all over the place well
+ 
+
+ align:start position:0%
+estimates may be all over the place well
+the standard error tells us how spread
+
+ align:start position:0%
+the standard error tells us how spread
+ 
+
+ align:start position:0%
+the standard error tells us how spread
+out all these estimates will be it is
+
+ align:start position:0%
+out all these estimates will be it is
+ 
+
+ align:start position:0%
+out all these estimates will be it is
+the standard deviation of this
+
+ align:start position:0%
+the standard deviation of this
+ 
+
+ align:start position:0%
+the standard deviation of this
+collection of estimates having a large
+
+ align:start position:0%
+collection of estimates having a large
+ 
+
+ align:start position:0%
+collection of estimates having a large
+standard error means that our estimation
+
+ align:start position:0%
+standard error means that our estimation
+ 
+
+ align:start position:0%
+standard error means that our estimation
+procedure is quite noisy and that our
+
+ align:start position:0%
+procedure is quite noisy and that our
+ 
+
+ align:start position:0%
+procedure is quite noisy and that our
+estimates have some inherent randomness
+
+ align:start position:0%
+estimates have some inherent randomness
+ 
+
+ align:start position:0%
+estimates have some inherent randomness
+and therefore also have a lack of
+
+ align:start position:0%
+and therefore also have a lack of
+ 
+
+ align:start position:0%
+and therefore also have a lack of
+accuracy that is they cannot be trusted
+
+ align:start position:0%
+accuracy that is they cannot be trusted
+ 
+
+ align:start position:0%
+accuracy that is they cannot be trusted
+too much that's the case of a large
+
+ align:start position:0%
+too much that's the case of a large
+ 
+
+ align:start position:0%
+too much that's the case of a large
+standard error conversely a small
+
+ align:start position:0%
+standard error conversely a small
+ 
+
+ align:start position:0%
+standard error conversely a small
+standard error would tell us that the
+
+ align:start position:0%
+standard error would tell us that the
+ 
+
+ align:start position:0%
+standard error would tell us that the
+estimates would tend to be concentrated
+
+ align:start position:0%
+estimates would tend to be concentrated
+ 
+
+ align:start position:0%
+estimates would tend to be concentrated
+close to each other as such the standard
+
+ align:start position:0%
+close to each other as such the standard
+ 
+
+ align:start position:0%
+close to each other as such the standard
+error is a very useful piece of
+
+ align:start position:0%
+error is a very useful piece of
+ 
+
+ align:start position:0%
+error is a very useful piece of
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+to have besides designing and
+
+ align:start position:0%
+to have besides designing and
+ 
+
+ align:start position:0%
+to have besides designing and
+implementing an estimator one usually
+
+ align:start position:0%
+implementing an estimator one usually
+ 
+
+ align:start position:0%
+implementing an estimator one usually
+also tries to find a way to calculate
+
+ align:start position:0%
+also tries to find a way to calculate
+ 
+
+ align:start position:0%
+also tries to find a way to calculate
+and report the associated standard error
\ No newline at end of file
diff --git a/lJOuPmI--5c.txt b/lJOuPmI--5c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..763cba99052b7d2eeb351fc22ddf1749b4930f71
--- /dev/null
+++ b/lJOuPmI--5c.txt
@@ -0,0 +1,1833 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK, so let's
+start to discuss ion traps.
+
+Now, in many situations, ions
+are just charged neutral atoms.
+
+And if the charge
+doesn't matter,
+
+you can do very similar physics
+with ions and neutral atoms.
+
+However, the charge
+makes major differences
+
+when it comes to confining
+and manipulating particles.
+
+So when I compare
+neutrals to ions,
+
+the forces which we
+exert on neutral atoms
+
+are magnetic forces,
+optical forces.
+
+And typically, the
+traps we can create
+
+have a depth of about 1 kelvin.
+
+Actually, you just need
+superconducting magnets.
+
+The magnetic traps we build here
+at MIT have millikelvin depths.
+
+So the trap depth is
+often on the order
+
+of microkelvin, millikelvin,
+and kelvin at the high scale.
+
+Well, this is very
+different in ions.
+
+In ions, you have
+the Coulomb force.
+
+If you take electric fields
+of 100 volts per millimeter,
+
+you can create confinement
+forces for 10,000 kelvin.
+
+So you have no problem in
+confining room temperature
+
+ions.
+
+When it comes to-- so this
+is trapping and confinement.
+
+If you talk about cooling,
+well, our workhorses
+
+are Doppler cooling and
+evaporative cooling.
+
+You can actually cool
+ions by evaporation.
+
+You can also cool ions
+by evaporative cooling.
+
+But what has been very
+common and special to ions
+
+is the ability to resolve
+sidebands, sidebands
+
+of the vibration and motion in
+the harmonic oscillator trap.
+
+And in problem
+set number 10, you
+
+have looked through the
+physics of sideband cooling.
+
+However, sideband cooling
+is now also coming back
+
+to neutral atoms.
+
+For instance, if you have
+neutral atoms in a very tightly
+
+confining dipole trap,
+you can resolve sidebands
+
+and use those for cooling.
+
+OK, what is the science?
+
+Well, a driving force for
+both ions and neutral atoms
+
+has been clocks.
+
+If atoms are cold,
+you can use them
+
+to have very accurate
+ways of keeping time.
+
+And I think currently,
+there is a race
+
+between the based neutral
+atom atomic clocks,
+
+neutral [INAUDIBLE]
+optical lattices,
+
+and ion traps in particular,
+the aluminum ion at Boulder.
+
+So we have clocks.
+
+In ions-- and this is what I
+want to talk a little bit more
+
+about today-- a major driving
+force was quantum information.
+
+You have two ions and get
+quantum gates between them,
+
+or you have eight
+ions and can have now
+
+eight qubits in a
+prototypical quantum computer.
+
+So quantum information
+science and quantum algorithms
+
+was quite important.
+
+But I would say
+some of the physics
+
+is at least discussed
+and partially pursued
+
+with atoms in optical lattices.
+
+We have talked a lot
+about, for neutral atoms,
+
+quantum simulations,
+studying super fluidity,
+
+studying phase transitions,
+magnetic properties
+
+of many body systems.
+
+But there are more efforts
+to do that with ions.
+
+Chris Monroe's
+group in Maryland is
+
+studying antiferromagnetic
+ordering of a spin chain.
+
+And the spin chain consists of
+a string of ions in an ion trap.
+
+So see actually on
+the science side
+
+that all three-- clocks,
+precision measurements, quantum
+
+information, qubits, quantum
+algorithms, and quantum
+
+simulation of many
+body systems--
+
+are done with both
+neutral atoms and ions.
+
+So these are now two
+very different platforms.
+
+So I could spend a
+long time teaching
+
+about special aspects of ions.
+
+How do you do a trap?
+
+How do you cool ions?
+
+How do you do quantum
+state control?
+
+Because this is
+our last lecture,
+
+I decided to focus
+on two aspects.
+
+One is, I want to talk about a
+special way of trapping ions.
+
+Because there is one
+difference for ions.
+
+Ions, until recently,
+have not been
+
+trapped in stationary traps.
+
+They've only been
+trapped in dynamic traps.
+
+So you cannot trap ions by
+simply putting an electric
+
+potential around it.
+
+Because the divergence of
+the electric field is 0.
+
+And that means there's
+always one direction in space
+
+where the ions are dragged out.
+
+You cannot have an inward
+force from all directions.
+
+So therefore, when you want
+to use electric fields,
+
+you can only use dynamic traps.
+
+Well, for the
+experts I should say,
+
+this does not apply for
+the optical dipole trap.
+
+We know how we can create
+trapping potentials
+
+for neutral atoms using
+the optical dipole trap.
+
+And very recently, a group
+was able to trap ions
+
+not with electric and magnetic
+fields provided by electrodes
+
+or radio frequency, but by
+inner focused laser beams.
+
+So it's a very new development.
+
+But it uses exactly
+the mechanism
+
+which has been used
+for neutral atoms.
+
+So when it comes
+to dynamic traps,
+
+the standard two
+traps which have
+
+been used for ion trapping--
+one is the Penning trap,
+
+which I do not want
+to describe in detail.
+
+The Penning trap uses a
+quadrupole configuration
+
+of two positive charges.
+
+And then you have a ring
+with negative charge.
+
+That means that an
+ion is confined here
+
+but would see anti-confinement
+in the outward direction.
+
+Now, what you do with
+the anti-confinement?
+
+Well, the solution is that
+you add a magnetic field.
+
+And what happens
+now is the particle
+
+is well-confined axially.
+
+But radially, when
+it wants to move out,
+
+it's turned into
+a cyclotron orbit,
+
+and therefore stays trapped.
+
+So this is the principal
+of Penning traps
+
+where the confinement
+in the axial direction
+
+is electrostatic, and
+the confinement in x, y
+
+is through cyclotron motion.
+
+OK, it's wonderful
+physics to describe
+
+the motion of ions in this trap.
+
+It's the combination
+of an axial motion,
+
+cyclotron motion,
+magnetron motion.
+
+It's very interesting physics.
+
+And for many years, Dave
+Pritchard here at MIT
+
+used such Penning traps to
+measure the masses, determine
+
+the masses, of ions with
+the highest precision ever
+
+possible.
+
+MIT still has the world
+record of the most precise
+
+mass measurements at the
+10 to the minus 11 level.
+
+And this was done
+in Penning traps.
+
+But I want to talk more today
+about RF traps, or Paul traps,
+
+because the are used in the
+majority of experiments.
+
+And they're used in pretty
+much all experiments
+
+on quantum information
+processing with ions.
+
+So the neat thing--
+and I try to teach you
+
+concepts in physics-- the
+interesting thing about Paul
+
+traps or RF traps is that
+you alternate at a radio
+
+frequency between confinement
+and anti-confinement.
+
+You can say you have a
+settle point potential, which
+
+is confining in x and
+anti-confining in y.
+
+But then, you switch x and y.
+
+So therefore, the situation
+is just imagine you're an ion,
+
+and you feel half of the time
+a confining harmonic oscillator
+
+and half of the time an
+anti-confining harmonic
+
+oscillator.
+
+The question I have for you,
+and this is a general physics
+
+question, well, is
+the sum of a confining
+
+and an anti-confining potential
+of the same strength give 0,
+
+or does it give something
+which in the end is confining?
+
+So if you were in a potential,
+and the potential switches
+
+permanently form parabolic
+upward to parabolic
+
+downward, at any given position,
+the average force is 0.
+
+Because in one phase, you
+have a force to the left.
+
+In the other case,
+you have the opposite.
+
+You have the same
+force but to the right
+
+with the opposite sign.
+
+But what's going on here?
+
+Yes.
+
+AUDIENCE: So I can't answer
+this mathematically or even
+
+physically.
+
+But I just remember
+this very cool example
+
+that someone showed me once
+where they took a saddle shape
+
+in space, put a
+ball in the middle,
+
+and then you spin the saddle.
+
+And as soon as the ball
+tries to fall to one side,
+
+the saddle will spin
+over and pick it up.
+
+So I know the answer has
+to be, it is confining.
+
+But I can't explain why.
+
+PROFESSOR: OK, Colin?
+
+AUDIENCE: Could it possibly
+be like a threshold?
+
+Because if you consider
+spinning it sort of slowly,
+
+then the particle can
+just sort of roll off.
+
+Maybe there's a threshold.
+
+PROFESSOR: Yeah,
+there is a threshold.
+
+I mean, if there's a
+confining potential
+
+for a long, long
+time, and then there's
+
+an anti-confining potential,
+and I just fall down
+
+the anti-confining potential,
+and I disappear to infinity,
+
+the confining part
+doesn't help me.
+
+So there will definitely
+be a threshold in time.
+
+We have to switch between
+confining and anti-confining
+
+sufficiently rapidly.
+
+Yes.
+
+AUDIENCE: Does it
+have something to do
+
+with fictitious
+force [INAUDIBLE]?
+
+PROFESSOR: No, but this would
+have been a possibility.
+
+Maybe there is a formalism.
+
+But the standard formalism does
+not use the rotating frame.
+
+Let me--
+
+AUDIENCE: You could think
+of the classical analog
+
+where you have a bead on a wire,
+and you have a stable position
+
+at sort of a finite angle
+only at certain frequencies.
+
+PROFESSOR: Yes, I'm not sure.
+
+Anyway, you all-- I think
+everybody here works
+
+with optics or knows
+what optics is.
+
+So why don't I
+discuss the following.
+
+If you take a positive
+lens and a negative lens
+
+with equal strength, what
+happens now to your laser beam?
+
+You send a laser
+beam through, it
+
+gets an inward bend by the
+convex lens, an outward bend
+
+by the concave lens.
+
+Is the net effect nothing,
+or is it focusing?
+
+Well, it depends.
+
+What happens is the following.
+
+If the lenses are put
+in close proximity,
+
+the two bending actions on the
+rays just completely cancel.
+
+But now we can do the following.
+
+We can put the two
+lenses further apart.
+
+And now the following happens.
+
+We have a laser beam
+which is bent inward.
+
+And you probably all know
+the lens maker's equation,
+
+that the further
+out the rays are,
+
+the more they have to be bent
+inward to come to a focus.
+
+So what happens is those
+beams are now bent inward.
+
+But when they reach
+the other lens,
+
+they are now bent
+outward somewhat.
+
+I'm not very accurate
+in my drawing.
+
+But the angle by
+which they're bent
+
+inward is proportional
+to the separation here.
+
+The angle by which
+they're bent outward
+
+is proportional to
+the separation there.
+
+So the inward bend is stronger
+than the outward bend.
+
+So therefore what
+I'm telling you
+
+is convex and concave,
+with a certain distance
+
+between the two,
+results in focusing.
+
+Now maybe you can
+think about it.
+
+What happens if I reverse
+convex and concave?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Is it
+now still focusing,
+
+or is it the opposite
+of the example above?
+
+Now the first lens bends
+the beam outward, yes?
+
+And the second lens
+bends it inward.
+
+But since we reach the
+second lens further out,
+
+the invert kick is stronger
+than the outward bend initially.
+
+So therefore, when you have
+positive and negative lenses
+
+of equal strength, no matter
+in what order you apply it,
+
+you always get an inward force.
+
+So this should
+actually explain--
+
+AUDIENCE: As long as they're
+within the focal length.
+
+Could you imagine if I
+had positive and negative
+
+that was larger than
+the focal length away?
+
+PROFESSOR: Yeah,
+everything within reason
+
+here-- there will be
+a stability diagram.
+
+But I want to first make it
+very plausible what happens.
+
+And just to address the
+question which I raised before,
+
+if I'm in a potential,
+and I get an equal amount
+
+of inward and outward force,
+shouldn't that average to 0?
+
+The question is how you average.
+
+If I would keep the distance
+from the x as constant,
+
+I would say here as a function
+of-- let me call it x.
+
+The bending angle as a
+function of x is positive.
+
+The bending angle at
+the same x is negative.
+
+So if I would do the average
+at constant x, I would get 0.
+
+But what I do is I do
+the average following
+
+the trajectory of the beam.
+
+So in other words,
+if I'm sitting
+
+on this potential, which
+switches from attractive
+
+to repulsive, if I would
+be here at my position,
+
+the average force is 0.
+
+But when the potential is
+repulsive, in 1/2 cycle
+
+I'm pushed outwards.
+
+And further out,
+the attractive force
+
+is now stronger
+than it was before.
+
+And therefore, if you average
+the force at my position,
+
+you will always find
+an inward force.
+
+But if you average the
+force at a fixed location,
+
+it averages out to 0.
+
+So this is exactly
+how RF ion traps work.
+
+And well, the rest are just
+equations to describe that.
+
+So I think we have
+to make a choice.
+
+I could derive for
+you the equations, how
+
+you average over the rapid
+oscillations of the potential,
+
+and you get a harmonic
+oscillator potential,
+
+and this is how you trap ions.
+
+But it's pretty
+much showing to you
+
+how the concept I've
+just explained to you
+
+is reflected in equations.
+
+Or the second option we have
+that takes about 20 minutes
+
+is to explain to you how
+quantum computation is
+
+done with two
+ions, in particular
+
+how the famous
+Zoller-Cirac gate works.
+
+Do you have a clear preference?
+
+AUDIENCE: Second one.
+
+PROFESSOR: OK, fine,
+but there is one piece
+
+of mathematics you
+should understand.
+
+Really, and this
+is the only essence
+
+of the mathematical derivation.
+
+If I'm standing here, and I
+feel the alternating force,
+
+it's a cosine omega t,
+and it averages to 0.
+
+But if the force drives
+me, it shakes me.
+
+This is micromotion.
+
+Like the beam here, if you
+go through many lasers,
+
+the beam goes up and
+down, up and down.
+
+This is micromotion.
+
+The micromotion is
+at cosine omega t.
+
+And the net
+attractive force comes
+
+because the force which
+oscillates at cosine omega t,
+
+and I'm oscillating
+at cosine omega t,
+
+then you get cosine
+squared omega t.
+
+And this gives you
+the net force which
+
+provides the net
+attractive force.
+
+And it's the cosine square term
+averaged over the micromotion,
+
+which is one half, which is
+responsible for the trapping
+
+potential in ion traps.
+
+Anyway, you know the
+physics very well.
+
+You understand where the math
+comes form in that it's really
+
+just the product of the two.
+
+It's a rectification.
+
+It's an alternating force.
+
+But since the system
+itself, the particle itself,
+
+is driven at the micromotion,
+there's rectification going on,
+
+which leads to the
+cosine squared term.
+
+[? Timor, ?] yes?
+
+AUDIENCE: Two quick questions.
+
+So I think ion trappers always
+complain about the micromotion.
+
+But in fact, they
+need it for trapping
+
+to work-- is pretty much
+what's going on here, right?
+
+PROFESSOR: Yes, actually,
+the one interesting side
+
+of the mathematics is the
+micromotion is kinetic energy.
+
+The harmonic
+trapping potential is
+
+nothing else than
+the micromotion.
+
+In other words, if people
+show in an ion trap
+
+that you have a
+harmonic oscillator,
+
+the harmonic oscillator
+potential is high here.
+
+But mathematically, this
+harmonic oscillator potential
+
+is the kinetic energy
+of the micromotion.
+
+In other words, if you
+look at the micromotion,
+
+it has a kinetic energy.
+
+The kinetic energy appears
+as the potential energy
+
+in this slow secular motion.
+
+So in other words, the
+potential energy for the trap
+
+is the kinetic energy
+of the micromotion.
+
+So you can't avoid it.
+
+This is responsible for
+the restoring force.
+
+AUDIENCE: Is it a really
+conservative trap,
+
+or can I have an out
+of phase component
+
+to the micromotion response?
+
+Is there like a sine
+part to the response?
+
+PROFESSOR: Well, the secular
+motion is conservative.
+
+You're now asking--
+
+AUDIENCE: I'm trying to think
+if there would be a reason why
+
+my response, my
+dipole response, would
+
+have a different [INAUDIBLE].
+
+Is there a reason?
+
+PROFESSOR: Well, to the
+best of my knowledge,
+
+everything is
+wonderfully conservative
+
+if you have a
+separation of timescale.
+
+If you want to sort
+of get something
+
+strange and non-conservative
+out of the micromotion,
+
+you have to violate the
+adiabatic separation
+
+of timescales.
+
+There is a possibility that
+if particles move quickly
+
+through the
+potential, they're not
+
+following the micromotion
+adiabatically.
+
+And then there is a
+collision where micromotion
+
+is released as
+collisional energy.
+
+But on the similar
+particle level,
+
+it's a pretty good
+approximation.
+
+OK, we want to talk about
+quantum computation with ions.
+
+[INAUDIBLE] has a
+wonderful write-up
+
+on the wiki on the basic
+concept of quantum computation
+
+and how it applies to ions.
+
+But let me immediately
+jump to qubit operations.
+
+You've heard many, many
+times that a general quantum
+
+algorithm can be constructed
+out of single qubit
+
+rotations and two qubit gates.
+
+Single qubit rotations
+are just oscillations
+
+on the Bloch sphere.
+
+If you excite a particle, move
+it around on the Bloch sphere,
+
+this is how you can rotate a
+single qubit from ground state
+
+to excited state, any
+possible superposition state.
+
+So the physics of single
+atoms, Rabi oscillation,
+
+rotation on the Bloch
+sphere, this is all you
+
+have to know about
+single qubit operations.
+
+The interesting thing is how do
+we create two qubit operations?
+
+And two qubit
+operation would mean
+
+you want to do something
+to one ion here depending
+
+what the state of
+the other ion is.
+
+And this is much more subtle.
+
+So what I want to
+explain to you now
+
+is the famous Cirac-Zoller
+gate, which was really
+
+a pioneering paper which has
+thousands of citations now.
+
+Because it showed that
+quantum computation
+
+can be experimentally realized
+in a rather straightforward
+
+way.
+
+So it's a fundamental theorem of
+quantum information processing
+
+that if you have single
+qubit operations, and one
+
+to qubit gate, which is
+a CNOT gate, that this
+
+is a universal set
+of quantum gates,
+
+any arbitrary quantum algorithm
+can be constructed out
+
+of those gate operations.
+
+So let me just remind you
+what the CNOT gate is.
+
+We have qubits ion one, ion two.
+
+They can be in 0 or 1.
+
+These can be two different
+hyperfine states.
+
+Or in the case of the calcium
+ion, it can be the ground state
+
+or metastable excited state--
+just two different states
+
+of ion one, two different
+states of ion two.
+
+The CNOT gate would
+now say the following.
+
+The first ion is
+the control bit.
+
+And whenever the
+control bit is 1,
+
+it flips the qubit,
+the second qubit.
+
+If the control bit is 0, it
+does nothing to the second ion.
+
+So therefore, the table
+which shows how the quantum
+
+states perform is
+1, 1, 0, 0, 1, 1.
+
+It just shows that
+I'm writing down
+
+the matrix in these spaces.
+
+It's a truth table 0,
+0, 0, 1, 1, 0, 1, 1.
+
+And it shows that when you
+have 1, 1 at the input,
+
+you get 1, 0 at the output.
+
+If you have 1, 0 at the input,
+you get 1, 1 at the output.
+
+Well, the two qubit
+gate I want to discuss,
+
+which can be realized in
+the simplest possible way
+
+with the Cirac-Zoller algorithm,
+is the controlled phase qubit,
+
+which has a truth table
+of 1, 1, 1, minus 1.
+
+And it means it simply
+changes the face of the two
+
+qubit states when
+both qubits are 1.
+
+Now, the CNOT gate
+can be constructed out
+
+of the controlled phase gate
+by having two single qubit
+
+rotations done with
+the Hadamard gate.
+
+The Hadamard gate is taking
+the bases 1 and 2 and creates 1
+
+plus 2, 1 minus 2, the
+symmetric and anti-symmetric
+
+superposition state.
+
+So therefore, the CPHASE gate
+is S general as the CNOT gate.
+
+Because one can be used
+to construct the other.
+
+So how do we create
+the Cirac-Zoller gate?
+
+So how do we get now
+the controlled phase
+
+gate out of trapped ions?
+
+So the effect is the following.
+
+Remember, if we
+have two ions, we
+
+want to change the phase
+to minus 1 of the state
+
+only if the two
+ions are qubit up.
+
+So in other words, we want to do
+180 degree rotation of the wave
+
+function, but only
+if both ions are up.
+
+And the question is,
+how do we do that?
+
+How does one ion feel what
+the other ion is doing?
+
+And let me explain that now.
+
+The critical element in
+the Cirac-Zoller case
+
+is a center of mass motion.
+
+We want at some point-- say
+when this ion is spin up,
+
+we swap the quantum
+information from the ion
+
+to the center of mass motion.
+
+In other words, when this ion
+is up, we use laser pulses.
+
+I will explain that to you.
+
+Then all the ions
+are moving together.
+
+And then, this ion,
+because they're all moving,
+
+knows that this ion
+was spin up before.
+
+So the center of mass motion,
+the common dipole oscillation
+
+of all ions together in the
+trap, this is the data bus.
+
+So this is the key idea.
+
+But in order to explain it to
+you, I have to go in two steps.
+
+So let's just take that as
+a genetic level structure.
+
+We have an S state.
+
+And it has two different
+hyperfine states,
+
+spin up and spin down.
+
+And these are our two qubits.
+
+There may be a P state, which
+we have used for laser cooling.
+
+But everything is in the
+ground state of motion
+
+using sideband
+cooling, which you've
+
+studied in your homework.
+
+And what I want
+to show you first
+
+is how we can
+create a phase gate.
+
+But I'm only
+focusing on ion one.
+
+So hold the thought.
+
+Ion two will come in a few
+moments, will come back.
+
+So what we can do
+is the following.
+
+Each qubit state has vibrational
+structure-- ground state,
+
+excited state without
+center of mass motion.
+
+But then, as a function of
+vibrational quantum number
+
+for the center of
+mass motion, we
+
+have g1, g2, e1, e2, and such.
+
+And what we can now
+do is, let's assume
+
+we have another state,
+a D state, which
+
+is an auxiliary state here.
+
+Fortunately, ions and
+atoms have many states.
+
+And we can drive a
+laser transition from S
+
+to D, which is only in resonance
+with the first vibrational
+
+excited state to the D state.
+
+So we use a [INAUDIBLE]
+sideband here,
+
+which only drives the
+transition from e1
+
+to the non-vibrational state
+of the auxiliary state.
+
+And that means automatically
+that this laser does nothing
+
+to e0, does nothing to
+g0, does nothing to g1.
+
+So if you have this Hilbert
+space of g0, g1, e0, e1,
+
+the only transition
+which is effected here,
+
+or the only state which is
+effected here, is the e1 state.
+
+OK, I'm talking
+about a single ion.
+
+I'm just talking about talking
+to a single ion right now.
+
+It's really simple.
+
+So if we switch on this
+laser, what happens
+
+is we simply induce Rabi
+oscillations-- simple physics.
+
+The Rabi oscillation,
+however, after one Rabi period
+
+has changed the phase of the
+initial state by minus 1.
+
+If you carefully look what
+Rabi oscillations are,
+
+the wave function goes
+up, down, up, down.
+
+But we usually discuss what
+happens to the probability.
+
+And this is shown in green.
+
+So when we are back
+in the original state,
+
+we have changed the phase of
+the wave function by minus 1.
+
+So let's just assume that
+we switch on this laser
+
+to this auxiliary state,
+and we have a-- well,
+
+it's a 2 pi pulse in population.
+
+But it makes a phase shift
+of pi to the wave function,
+
+which is minus 1.
+
+So what we have
+accomplished now is
+
+a phase gate not
+between two ions.
+
+But we have a phase gate
+which, in this Hilbert space,
+
+between the qubit
+up, qubit down--
+
+I call it ground
+and excited state.
+
+But the other
+qubit, so to speak,
+
+is the center of mass
+motion 0, 1, 0, 1.
+
+So this is the truth
+table of the phase gate.
+
+And so technically, we have
+now done a local phase gate
+
+with one ion where
+the two qubits are
+
+ground and excited
+state of the ion.
+
+This is our qubit we
+want to work with.
+
+But then, the second qubit
+to realize the phase gate
+
+was 0, 1 of the center
+of mass vibration.
+
+But once we have
+realized that, we
+
+can now immediately
+take this idea
+
+and get a phase gate
+between two ions.
+
+Because the center of mass
+vibration is everywhere.
+
+So therefore, what we can
+do is this was ion one.
+
+We can now-- and this
+is the missing step
+
+I want to show
+you-- go to ion two.
+
+And we can swap the qubit
+information-- ground, excited,
+
+spin up, spin down.
+
+We can swap that with the
+center of mass motion.
+
+So therefore, what we can do is,
+when the second ion is spin up,
+
+we do a swapping
+of the information
+
+from spin up, spin down
+to center of mass motion
+
+being 0 or 1.
+
+So the idea is the following.
+
+Ion two should control
+what ion one is doing.
+
+So we first focus on ion two.
+
+We swap the qubit of ion two
+into the center of mass motion.
+
+Then, we do what I just
+said, the controlled phase
+
+gate for ion one with the
+center of mass motion.
+
+And after this is done, we write
+the center of mass motion back
+
+into ion two.
+
+And then we have
+nothing to ion two.
+
+Ion two was just
+putting its information
+
+into the center of mass motion.
+
+It helped ion one to do
+the controlled phase gate.
+
+And then, we swapped
+the information back.
+
+So this is the sequence.
+
+After preparing the center of
+mass, the first of two lasers
+
+cool everything in the center
+of mass motion into the 0 state.
+
+Then we swap from ion
+two the information
+
+to this phonon state
+center of mass vibration.
+
+Then we do the controlled
+phase gate on ion one.
+
+And then, we swap
+the information back.
+
+So what I should show
+you-- you may have seen it.
+
+But what I should
+show you explicitly--
+
+how do we swap
+the information ge
+
+from the internal
+state of ion two?
+
+How do we write this information
+into the data bus, which
+
+is the phonon,
+which is the center
+
+of mass vibration in the trap?
+
+Well, we again use
+[INAUDIBLE] side pulse.
+
+We do a pi pulse
+driving this transition.
+
+And just look how beautifully
+the math works out.
+
+We have an arbitrary
+qubit state,
+
+a superposition of
+ground and excited.
+
+And the center of
+mass motion was
+
+laser cooled to
+the ground state.
+
+So let me just
+multiply that out.
+
+So we have coefficient a times
+g0 plus coefficient b times e0.
+
+If we now do a pi pulse, we
+transfer the population from e0
+
+into g1.
+
+And this is what I've done here.
+
+But now you see I
+can factor out the g.
+
+And what I have now is I have
+the same qubit information
+
+with coefficients e and b, but
+no longer in the internal state
+
+of the ion but in
+the phonon state
+
+in the qubit, which is
+the center of mass motion.
+
+So the idea here is you can have
+an arbitrary number of ions.
+
+And now you want to
+have a quantum gate.
+
+What you do with a
+quantum gate, you say,
+
+I want to now take this
+ion here and have a quantum
+
+gate with 10 ions further down.
+
+So you first go
+to your first ion,
+
+transfer the information of
+this qubit into the data bus,
+
+into the center of mass motion.
+
+And now with a local
+operation here,
+
+you can do something to this
+ion conditionally on the motion,
+
+the center of mass motion.
+
+But the center of mass
+motion reflects the ion
+
+over there, in
+which state it was.
+
+And after you have
+done the two qubit
+
+operation between
+those two ions,
+
+you take the center
+of mass motion,
+
+put it back into this ion.
+
+And at the end of the
+day what you have done
+
+is you have done a
+two qubit operation.
+
+You've changed the
+state of this ion.
+
+But all the other ions
+have remained the same.
+
+And with that, you can
+now, in a chain of ion,
+
+implement arbitrary
+two qubit operations.
+
+I think I said it
+clearer in words here.
+
+It is in a little
+bit more formal way
+
+the steps you will do
+to the wave function.
+
+You initialize.
+
+Your transfer the
+information to the data bus,
+
+you execute the
+controlled phase gate,
+
+and you put the information
+from the data bus
+
+back into the control ion.
+
+And now your data bus
+is free, is back again
+
+to the initial value and
+ready for the next operation.
+
+I should mention that
+this was pioneering paper.
+
+Right now, this quantum gate
+is not the most popular one.
+
+Because it has
+severe requirements.
+
+One is you really have to cool
+to the absolute ground state.
+
+The center of mass
+motion has to be
+
+cooled to the
+absolute ground state.
+
+There are other
+quantum gates which
+
+do not require such
+extreme cooling.
+
+And secondly, the center of mass
+motion, because all particles
+
+move together, is one of the
+slowest vibrational motions
+
+in the system.
+
+And if you want to
+scale up the system
+
+to more and more particles,
+the speed of the gate operation
+
+has to be slower than
+the vibrational period
+
+of the center of mass motion.
+
+So these are two disadvantages.
+
+But there are different
+gates, like geometric gates,
+
+like Sorensen gates.
+
+There are other possibilities
+to involve the same quantum
+
+logic with ions.
+
+But the one of
+Cirac-Zoller really
+
+stands out by it's pedagogy.
+
+It's really a
+wonderful way to see
+
+how we take the information,
+put it in a data bus,
+
+do the controlled
+phase operation,
+
+and then proceed to the
+next two qubit gate.
+
+OK, so that's the end of
+ions, the end of this class.
+
+Do you have any questions
+about the last topic?
+
+If not, let me say thanks.
+
+You were a fabulous class.
+
+I really enjoyed the
+classroom atmosphere.
+
+I enjoyed all the
+questions, whether it
+
+was after class or during class.
+
+And, well, I'm happy
+that most of you
+
+I will see around for
+a number of years.
+
+All right.
+
+[APPLAUSE]
\ No newline at end of file
diff --git a/leXa7EKUPFk.txt b/leXa7EKUPFk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e914b3f2bdab5f6dd2f957f89c11e52cbc33d855
--- /dev/null
+++ b/leXa7EKUPFk.txt
@@ -0,0 +1,2353 @@
+PROFESSOR PATRICK WINSTON:
+Ladies and gentlemen, the
+
+engineers drinking song.
+
+Back in the day, I've drunk
+quite a lot to that song.
+
+And as drinking songs
+go, it's not bad.
+
+I caution you, however, before
+playing this song in the
+
+presence of small children,
+audition it first.
+
+Some of the verses are
+sufficiently gross as to make
+
+a sailor go beyond blushing.
+
+It's an interesting song because
+there are an infinite
+
+number of verses.
+
+Here's the mathematical proof.
+
+Suppose there were a finite
+number of verses.
+
+Then there would be
+a last verse.
+
+And if there were a last verse,
+then some drunk alumni
+
+would compose a new one.
+
+Therefore, there is no last
+verse, the size is not finite,
+
+and there are an infinite
+number of verses.
+
+I play it for you today because
+I'm an engineer.
+
+I like to build stuff.
+
+I build stuff out of wood.
+
+I build stuff out of metal.
+
+I build stuff out of rocks.
+
+And I especially like
+to write programs.
+
+I don't know, sometimes people
+come to me and say, I'm
+
+majoring in computer science,
+but I don't
+
+like to write programs.
+
+I've always been mystified
+by that.
+
+I mean, if you want to show how
+tough you are, you can go
+
+bungee jumping or drive a nail
+through your hand or something
+
+like that instead.
+
+But I've written quite a few
+programs for demonstrating
+
+stuff in this subject.
+
+They're all written in Java,
+principally because I can
+
+therefore make them available to
+you and to the rest of the
+
+world by way of Web Start.
+
+A few weeks ago, I was mucking
+around with the system and
+
+broke the version on the server,
+and within 15 minutes,
+
+I got an email from somebody
+in the depths of Anatolia
+
+complaining about it and asking
+me to bring it back up.
+
+This particular program
+is patterned
+
+after an early AI classic.
+
+And it was the business end of
+a program written by Terry
+
+Winograd, who became, and is,
+a professor of computer
+
+science at Stanford
+University--
+
+which is on the west coast
+for those of you--
+
+on the strength of his work on
+the natural language front end
+
+of this program.
+
+But the natural language part
+is not what makes it of
+
+interest for us today.
+
+It's more the other
+kinds of stuff.
+
+Let's pile these things up.
+
+Now, I'm going to ask to
+do something, maybe put
+
+B2 on top of B7.
+
+Not bad.
+
+How about B6 on B3?
+
+This program's kind of clever.
+
+Let me do one more.
+
+Let's put B7 on B2.
+
+OK, now let's see.
+
+Maybe B5 on B2?
+
+B4 on B3 first, maybe?
+
+Oh, I must have clicked
+the wrong button.
+
+Oh, there it goes.
+
+OK.
+
+Let's put B4 on B1.
+
+Agh, my mouse keeps getting
+out of control.
+
+Now, let's put B1 on B2.
+
+This is an example I'm
+actually going to
+
+work out on the board.
+
+Oh, I see.
+
+My touch pad accidentally
+got activated.
+
+B1 on B2.
+
+Now, let's ask a question.
+
+OK.
+
+Well.
+
+SPEAKER 2: [SINGING]
+
+PROFESSOR PATRICK
+WINSTON: Stop.
+
+SPEAKER 3: [LAUGHTER]
+
+PROFESSOR PATRICK WINSTON:
+Had enough of that.
+
+Let's see.
+
+Why did you put--
+
+why did you want to
+get rid of B4?
+
+OK, one--
+
+SPEAKER 2: [SINGING]
+
+PROFESSOR PATRICK WINSTON: Maybe
+they think, that's what
+
+happens when you use software
+you write yourself.
+
+Why did you want to clear
+the top of B2?
+
+Did I do that?
+
+Why did you clear
+the top of B1?
+
+OK.
+
+SPEAKER 2: [SINGING]
+
+SPEAKER 3: [LAUGHTER]
+
+PROFESSOR PATRICK WINSTON:
+Oh, it's haunting me.
+
+Yeah.
+
+So the drinking song is easily
+offended, I guess.
+
+But I won't develop that
+scenario again.
+
+What I want to show you is that
+this program looks like
+
+it's kind of smart, and it
+somehow can answer questions
+
+about its own behavior.
+
+Have you ever written a program
+that's answered
+
+questions about its
+own behavior?
+
+Probably not.
+
+Would you like to learn
+how to do that?
+
+OK.
+
+So by the end of the hour,
+you'll be able to write this
+
+program and many more like it
+that know how to answer
+
+questions about their
+own behavior.
+
+There have been tens of
+thousands of such programs
+
+written, but only by people who
+know the stuff I'm going
+
+to tell you about
+right now, OK?
+
+So what I want to do is I want
+to start by taking this
+
+program apart on the board and
+talking to you about the
+
+modules, the subroutines
+that it contains.
+
+So here it is.
+
+The first thing we need
+to think about,
+
+here are some blocks.
+
+What has to happen if I'm going
+to put the bottom block
+
+on the larger block?
+
+Well, first of all, I have
+to find space for it.
+
+Then I have to grasp
+the lower block.
+
+And I have to move it and
+I have to ungrasp it.
+
+So those are four things I need
+to do in order to achieve
+
+what I want to do.
+
+So therefore, I know that the
+put-on method has four pieces.
+
+It has to find space on
+the target block.
+
+It has to grasp the block that
+it's been commanded to move.
+
+Then it has to move, and
+then it has to ungrasp.
+
+But taking hints from some of
+the questions that it did
+
+answer before I got haunted by
+the music, taking our cue from
+
+that, we know that in order to
+grasp something, in this
+
+particular world, you can't have
+anything on top of it.
+
+So grasp, therefore, may call
+clear top in order to get
+
+stuff off from the
+target object.
+
+And that may happen in an
+iterative loop because there
+
+may be several things on top.
+
+And how do you get
+rid of stuff?
+
+Well, by calling get rid of.
+
+And that may go around
+a loop several times.
+
+And then, the way you get rid of
+stuff is by calling put-on.
+
+So that gives us recursion, and
+it's from the recursion
+
+that we get a lot of the
+apparent complexity of the
+
+program's behavior when
+it solves a problem.
+
+Now, in order to find space,
+you also have to
+
+call get rid of.
+
+So that's where I meant to
+put this other iterative
+
+loop, not down here.
+
+Cleat top has got the iterative
+loop inside of it.
+
+So that's the structure
+of the program.
+
+It's extremely simple.
+
+And you might say to me, well,
+how can you get such
+
+apparently complex-looking
+behavior out of
+
+such a simple program?
+
+A legitimate question.
+
+But before we tackle that one
+head on, I'd like to do a
+
+simulation of this program
+with a very
+
+simple blocks problem.
+
+And it's the one I almost
+showed you, but
+
+it goes like this.
+
+Here's B1.
+
+We'll call this BX because
+I forgot its name.
+
+Here's BY.
+
+And here's B2.
+
+And the task is to
+put B1 on B2.
+
+And according to our system
+diagram, that results in four
+
+calls to subroutines.
+
+We have to find space.
+
+We have to grasp B1.
+
+We have to move, and
+then we ungrasp.
+
+Now, the way we grasp something
+is the first thing
+
+we have to do is clear
+off its top.
+
+So grasp calls clear top.
+
+And clear top in turn
+calls get rid of.
+
+And let me see.
+
+Let me keep track of these.
+
+This is clearing the top
+of B1, and this is
+
+getting rid of BX.
+
+And the way we get rid of BX is
+by putting BX on the table.
+
+And then that in turn causes
+calls to another find space,
+
+another grasp, another move,
+and another ungrasp.
+
+So that's a little trace of
+the program as it works on
+
+this simple problem.
+
+So how does it go about
+answering the questions that I
+
+demonstrated to you
+a moment ago?
+
+Let's do that by using
+this trace.
+
+So how, for example, does it
+answer the question, why did
+
+you get rid of BX?
+
+[INAUDIBLE], what
+do you think?
+
+How can it answer
+that question?
+
+SPEAKER 4: [INAUDIBLE]
+
+PROFESSOR PATRICK WINSTON: So
+it goes up one level and
+
+reports what it sees.
+
+So it says, and said in the
+demonstration, I got rid of BX
+
+because I was trying to
+clear the top of B1.
+
+So if I were to say why did you
+clear the top of B1, it
+
+would say because I was
+trying to grasp it.
+
+If I were to say, why did you
+grasp B1, it would say because
+
+I was putting B1 on B2.
+
+If I say, why did you put
+B1 on B2, it would say,
+
+slavishly, because
+you told me to.
+
+OK, so that's how it deals
+with why questions.
+
+How about how questions?
+
+Timothy, what do you think
+about that one?
+
+How would it go about answering
+a question about how
+
+you did something?
+
+Do you have a thought?
+
+TIMOTHY: Um, yeah, it would
+think about what I was trying
+
+to accomplish.
+
+PROFESSOR PATRICK WINSTON:
+Yeah, but
+
+how would it do that?
+
+How would the program do that?
+
+We know that answering
+a why question makes
+
+it go up one level.
+
+How does it answer
+a how question?
+
+Sebastian?
+
+SEBASTIAN: It goes
+down one level.
+
+PROFESSOR PATRICK WINSTON:
+You go down one level.
+
+So you start off all the way
+up here with a put-on.
+
+You will say, oh, well I
+did these four things.
+
+You say, why did you grasp B1?
+
+It will say because I was
+trying to clear its top.
+
+Why did you clear its top?
+
+Because I was trying
+to get rid of it.
+
+Why were you trying
+to get rid of it?
+
+Because I was trying to
+put it on the table.
+
+So that's how it answers how
+questions, by going down in
+
+this tree and this trace of the
+program of action so as to
+
+see how things are
+put together.
+
+What are these things that
+are being put together?
+
+What's the word I've been
+avoiding so as to bring this
+
+to a crescendo?
+
+What are these objectives, these
+things it wants to do?
+
+They're goals.
+
+So this thing is leaving a
+trace, which is a goal tree.
+
+Does that sound familiar?
+
+Three days ago, we talked about
+goal trees in connection
+
+with integration.
+
+So this thing is building a goal
+tree, also known as an
+
+and-or tree.
+
+So this must be an and tree.
+
+And if this is an and tree,
+are there any and nodes?
+
+Sure, there's one right there.
+
+So do you think then that you
+can answer questions about
+
+your own behavior as long as
+you build an and-or tree?
+
+Sure.
+
+Does this mean that the
+integration program could
+
+answer questions about
+its own behavior?
+
+Sure.
+
+Because they both build goal
+trees, and wherever you got a
+
+goal tree, you can answer
+certain kinds of questions
+
+about your own behavior.
+
+So let me see if in fact it
+really does build itself a
+
+goal tree as it solves
+problems.
+
+So this time, we'll put
+B6 on B3 this time.
+
+But watch it develop
+its goal tree.
+
+So in contrast to the simple
+example I was working on the
+
+board, this gets to be a pretty
+complicated goal tree.
+
+But I could still answers
+questions about behavior.
+
+For example, I could say, why
+did you put B6 on B3?
+
+Because you told me to.
+
+All right, so the complexity of
+the behavior is largely a
+
+consequence not of the
+complexity of the program in
+
+this particular case, but the
+building of this giant goal
+
+tree as a consequence of the
+complexity of the problem.
+
+This brings us to one of
+our previous matters--
+
+early on to one of the gold
+star ideas of today.
+
+And this gold star idea goes
+back to a lecture given in the
+
+late '60s by Herb Simon, who was
+the first Nobel Laureate
+
+in the pseudo Nobel Prize
+for economics.
+
+Is that right, Bob?
+
+Was he the first?
+
+All right, he was the first
+winner of the Nobel Prize,
+
+pseudo Nobel Prize
+in economics.
+
+And in this lecture, which was
+titled "The Sciences of the
+
+Artificial," he said imagine
+that you're looking on a beach
+
+at the path of a ant.
+
+And he said, well, you know,
+the path of the ant looks
+
+extremely complicated.
+
+And you're tempted to think the
+ant is some kind of genius
+
+or monster brain ant.
+
+But in fact, when you take a
+closer look, what you discover
+
+is that there are a bunch of
+pebbles on the beach, and all
+
+the ant is doing is avoiding
+those pebbles on his way home.
+
+So the complexity of the
+behavior, said Simon, is a
+
+consequence of the complexity
+of the environment, not the
+
+complexity of the program.
+
+So that's the metaphoric
+Simon's ant.
+
+And what it says is that the
+complexity of the behavior is
+
+the max of the complexity of the
+program and the complexity
+
+of the environment.
+
+So that's something we'll see
+many times during the rest of
+
+the semester.
+
+Complex behavior,
+simple program.
+
+You think it's going
+to be complicated.
+
+It turns out to be simple
+because the problem has the
+
+complexity, not the program.
+
+So that brings us to check box
+three in today's talk, and
+
+there's a little bit of a scene
+here because now I want
+
+to stop talking about
+goal-centered programming and
+
+start talking about rule-based
+expert systems.
+
+The rule-based expert systems
+were developed in a burst of
+
+enthusiasm about the prospects
+for commercial applications of
+
+artificial intelligence
+in the mid-1980s.
+
+At that time, it was supposed
+lengthy articles are written,
+
+but you could account for
+useful aspects of human
+
+intelligence by writing all the
+knowledge in the form of
+
+simple rules.
+
+So if this is true,
+then that's true.
+
+If you want to achieve
+this, then do that.
+
+But all the knowledge had to be
+encapsulated in the form of
+
+simple rules.
+
+So what might you want
+to do with this?
+
+All sorts of things.
+
+Thousands of these systems
+were written,
+
+as I indicated before.
+
+But here's an example.
+
+I'm going to work out an example
+having to do with
+
+identification.
+
+And this example is patterned
+off of a classic program,
+
+strangely also written at
+Stanford, called MYCIN.
+
+It was developed to
+diagnose bacterial
+
+infections in the blood.
+
+So you come in.
+
+You got some horrible disease,
+and the doctor gets curious
+
+about what antibiotic would be
+perfect for your disease.
+
+He starts asking a
+lot of questions.
+
+So I'm not going to deal with
+that because that world has
+
+all kinds of unpronounceable
+terms like bacterioides and
+
+anaerobic and stuff like that.
+
+So it's completely analogous
+to talk about identifying
+
+animals in a little zoo, sort
+of a small town type of zoo.
+
+So I'm going to suggest that
+we write down on a piece of
+
+paper all the things we can
+observe about an animal, and
+
+then we'll try to figure
+out what the animal is.
+
+So I don't know, what
+can we start with?
+
+Has hair.
+
+Then there are some
+characteristics of the
+
+following form.
+
+Has claws.
+
+Sharp teeth.
+
+And forward-pointing eyes.
+
+And these are all
+characteristics of carnivores.
+
+We happen to have
+forward-pointing eyes too, but
+
+that's more because we used to
+swing around the trees a lot,
+
+and we needed the
+stereo vision.
+
+And we don't have the claws
+and the sharp teeth
+
+that go with it.
+
+But anyhow, those are typically
+characteristics of
+
+carnivores, as is eating meat.
+
+And this particular little
+animal we're looking at has
+
+also got spots, and
+it's very fast.
+
+What is it?
+
+Well, everybody says
+it's a cheetah.
+
+Let's see how our program
+would figure that out.
+
+Well, program might say, let's
+see if it has hair, then rule
+
+one says that that means
+it must be a mammal.
+
+We can imagine another rule that
+says if you have sharp
+
+claws, sharp teeth, and
+forward-pointing eyes, then
+
+you're a carnivore.
+
+And I'm using sort of hardware
+notation here.
+
+That's an and gate, right?
+
+So that means we have to have
+all of these characteristics
+
+before we will conclude that
+the animal is a carnivore.
+
+Now, this animal has been also
+observed to eat meat.
+
+So that means we've got extra
+evidence that the animal is
+
+carnivorous.
+
+And now, because the animal is
+a mammal and a carnivore and
+
+has spots, and it's very fast,
+then the animal is a cheetah.
+
+And I hope all of our African
+students agree that
+
+it must be a cheetah.
+
+It's a small zoo--
+
+I mean, a big zoo.
+
+Who knows what it is?
+
+It's probably got some
+unpronouncable name--
+
+there's possibilities.
+
+But for our small zoo,
+that will do.
+
+So we have group now written
+down in the form
+
+of these and gates.
+
+Several rules, R1, R2--
+and there needs to
+
+be an and gate here--
+
+that's R3 and an R4.
+
+All of which indicate that
+this animal is a cheetah.
+
+So we built ourself a little
+rule-based expert system that
+
+can recognize exactly one
+animal, but you could imagine
+
+filling out this system with
+other rules so that you could
+
+recognize giraffes and penguins
+and all the other
+
+sorts of things you find
+in a small zoo.
+
+So when you have a system like
+this that works as I've
+
+indicated, then what we're
+going to call that, we're
+
+going to give that a special
+name, and we're going to call
+
+that a forward-chaining
+rule-based--
+
+because it uses rules--
+
+expert system.
+
+And we're going to put expert
+in parentheses because when
+
+these things were developed,
+for marketing reasons, they
+
+called them expert systems
+instead of novice systems.
+
+But are they really experts
+in a human sense?
+
+Not really, because they have
+these knee-jerk rules.
+
+They're not equipped with
+anything you might want to
+
+call common sense.
+
+They don't have an ability to
+deal with previous cases, like
+
+we do when we go to
+medical school.
+
+So they really ought to be
+called rule-based novice
+
+systems because they reason
+like novices on
+
+the basis of rules.
+
+But the tradition
+is to call them
+
+rule-based expert systems.
+
+And this one works forward from
+the facts we give it to
+
+the conclusion off
+on the right.
+
+That's why it's a
+forward-chaining system.
+
+Can this system answer
+questions
+
+about its own behavior?
+
+[INAUDIBLE], what
+do you think?
+
+SPEAKER 5: [INAUDIBLE].
+
+PROFESSOR PATRICK
+WINSTON: Why?
+
+SPEAKER 5: [INAUDIBLE].
+
+PROFESSOR PATRICK WINSTON:
+Because it
+
+looks like a goal tree.
+
+Right.
+
+This is, in fact, building a
+goal tree because each of
+
+these rules that require several
+things to be true is
+
+creating an and node.
+
+And each of these situations
+here where you have multiple
+
+reasons for believing that the
+thing is a carnivore, that's
+
+creating an or node.
+
+And we already know that you
+can answer questions about
+
+your own behavior if you leave
+behind a trace of a goal tree.
+
+So look at this.
+
+If I say to it, why were
+you interested in
+
+the animal's claws?
+
+Because I was trying to see
+if it was a carnivore.
+
+How did you know that the
+animal is a mammal?
+
+Because it has hair.
+
+Why did you think it
+was a cheetah?
+
+Because it's a mammal,
+a carnivore, has
+
+spots, and very fast.
+
+So by working forward and
+backward in this goal tree,
+
+this too can answer questions
+about its own behavior.
+
+So now you know how, going
+forward, you can write
+
+programs that answer questions
+about their behavior.
+
+Either you write the subroutines
+so that each one
+
+is wrapped around a goal, so
+you've got goal-centered
+
+programming, or you build a
+so-called expert system using
+
+rules, in which case it's easy
+to make it leave behind a
+
+trace of a goal tree, which
+makes it possible to answer
+
+questions about its own
+behavior, just as this
+
+[INAUDIBLE]
+
+program did.
+
+But now, a little
+more vocabulary.
+
+I'm going to save time by
+erasing all of these things
+
+that I previously drew by
+way of connections.
+
+And I'm going to approach this
+zoo in a little different way.
+
+I'm going to not ask any
+questions about the animal.
+
+Instead, I'm going to say,
+mommy, is this thing I'm
+
+looking at a cheetah?
+
+And how would mommy go about
+figuring it out.
+
+In her head, she would say,
+well, I don't know.
+
+If it's going to be a cheetah,
+then it must be the case that
+
+it's a carnivore, and it must be
+the case that it has spots.
+
+And it must be the case
+that it's very fast.
+
+So so far, what we've
+established is that if it's
+
+going to be a cheetah, it
+has to have the four
+
+characteristics that
+mommy finds behind
+
+this rule are four.
+
+So instead of working forward
+from facts, what I'm going to
+
+do is work backward
+from a hypothesis.
+
+So here the hypothesis is
+this thing is a cheetah.
+
+How do I go about showing
+whether that's true or not?
+
+Well, I haven't done anything so
+far because all I know is a
+
+cheetah if all these things are
+true, but are they true?
+
+Well, to find out if it's a
+mammal, I can use rule one.
+
+And if I know or can determine
+that the animal has hair, then
+
+that part of it is
+taken care of.
+
+And I can similarly work my way
+back through carnivore.
+
+I say, well, it's a carnivore if
+it has claws, sharp teeth,
+
+and forward-pointing eyes.
+
+And then as much as the
+animal in question
+
+does, then I'm through.
+
+I know it's a carnivore.
+
+I don't have to go through and
+show that it's a carnivore
+
+another way.
+
+So I never actually ask
+questions about
+
+whether it eats meat.
+
+Finally, the final two
+conditions are met by just an
+
+inspection of the animal.
+
+That's to say, it's
+in the database.
+
+I don't have to use any rules
+to determine that the animal
+
+has spots and is very fast.
+
+So now, I've got everything in
+place to say that it's a
+
+cheetah, because it's a
+carnivore, because it has
+
+claws, sharp teeth, and
+forward-pointing eyes, and all
+
+the rest of this stuff is
+similarly determined by going
+
+backwards, backwards from the
+hypothesis toward the facts,
+
+instead of from the facts
+forward to the conclusions.
+
+So building a system that works
+like that, I have a
+
+backward-chaining rule-based
+expert system.
+
+But there's a very important
+characteristic of this system
+
+in both backward and forward
+mode, and that is that this
+
+thing is a deduction system.
+
+That's because it's
+working with facts
+
+to produce new facts.
+
+When you have a deduction
+system, you can never take
+
+anything away.
+
+But these rule-based systems are
+also used in another mode,
+
+where it's possible to
+take something away.
+
+See, in fact world, in deduction
+world, you're
+
+talking about proving things.
+
+And once you prove something
+is true, it can't be false.
+
+If it is, you've got a
+contradiction in your system.
+
+But if you think of this as a
+programming language, if you
+
+think of using rules as a
+programming language, then you
+
+can think of arranging it so
+these rules add or subtract
+
+from the database.
+
+Let me show you an example
+of a couple of systems.
+
+First of all, since I've talked
+about the MYCIN system,
+
+let me show you an example
+of a MYCIN dialogue.
+
+That's a MYCIN dialogue.
+
+And you can see the appearance
+of words you have to go to
+
+medical school to learn.
+
+And here's a typical MYCIN rule,
+just like the rules for
+
+doing zoo analysis, only a
+more complicated domain.
+
+But here's another example of a
+system that was written, not
+
+in the '80s, but just a couple
+of years ago by a student in
+
+the architecture department,
+Ph.D. thesis.
+
+He was interested in the
+architecture of a Portuguese
+
+architect named Siza.
+
+And Siza's done a lot of
+mass housing stuff.
+
+And Siza has the idea that you
+ought to be able to design
+
+your own house.
+
+And so Jose Duarte, a Portuguese
+student, a Ph.D.
+
+student in architecture, wrote
+a rule-based system that was
+
+capable of designing Siza-like
+houses in response to the
+
+requirements and recommendations
+and desires of
+
+the people who are going
+to occupy the houses.
+
+So the most compelling part of
+this thing, of this exercise,
+
+was that Duarte took some of
+the designs of the program,
+
+mixed them up with some of the
+designs of Siza, and put them
+
+in front of Siza, and said,
+which ones did you do?
+
+And Siza couldn't tell.
+
+So somehow, the rule-based
+system that was built using
+
+this kind of technology was
+sufficient to confuse even the
+
+expert that they were
+patterned after.
+
+But this program is a
+little complicated.
+
+It, too, has its own
+specialized lingo.
+
+So I'm not going to talk about
+it in detail, but rather talk
+
+instead about an analogous
+problem.
+
+And that is a problem that
+everyone has faced at one
+
+point or another, and that
+is the problem of putting
+
+groceries in a bag at
+a grocery store.
+
+It's the same thing, right?
+
+Instead of putting rooms in
+a house, you're putting
+
+groceries in a bag.
+
+And there must be some rules
+about how to do that.
+
+In fact, maybe some of you have
+been professional grocery
+
+store baggers?
+
+[INAUDIBLE] a grocery store
+professional bagger.
+
+You're a--
+
+which one?
+
+LISA: [INAUDIBLE]
+
+PROFESSOR PATRICK WINSTON:
+Yeah, what is your name?
+
+LISA: Lisa.
+
+PROFESSOR PATRICK
+WINSTON: Lisa.
+
+OK, well we got two
+professional
+
+grocery store baggers.
+
+And I'm going to be now
+simulating a highly paid
+
+knowledge engineer desirous of
+building a program that knows
+
+how to bag groceries.
+
+So I'm going to visit your site,
+Market Basket, and I'm
+
+going to ask Lisa, now fearful
+of losing her job, if she
+
+would tell me about how
+she bags groceries.
+
+So could you suggest a rule?
+
+LISA: Sure.
+
+Large items in the bottom.
+
+PROFESSOR PATRICK WINSTON: Large
+items in the bottom.
+
+You see, that's why I'm a
+highly paid knowledge
+
+engineer, because I translate
+what she said
+
+into an if-then rule.
+
+So if large, then bottom.
+
+So now I--
+
+SPEAKER 3: [LAUGHTER]
+
+PROFESSOR PATRICK WINSTON: So
+how about you, [INAUDIBLE]?
+
+Have you got a suggestion?
+
+About how to bag groceries?
+
+SPEAKER 6: The small
+things on top.
+
+PROFESSOR PATRICK WINSTON:
+If small, then on top.
+
+Lisa, have you got anything
+else you could tell me?
+
+LISA: Don't put too many heavy
+things in the same bag.
+
+PROFESSOR PATRICK WINSTON:
+Don't put too many heavy
+
+things in the same bag.
+
+So if heavy greater than
+three, then new bag, or
+
+something like that.
+
+Is that all we're going to be
+able to-- does anybody else
+
+want to volunteer?
+
+[INAUDIBLE], have you bagged
+groceries in Turkey?
+
+LISA: So they don't
+have grocery
+
+baggers, so we have to--
+
+PROFESSOR PATRICK WINSTON: So
+everybody's a professional
+
+bagger in Turkey.
+
+Yeah.
+
+It's outsourced to
+the customers.
+
+SPEAKER 7: So no squishies
+on the bottom.
+
+So if you have--
+
+PROFESSOR PATRICK WINSTON: No
+squishies on the bottom.
+
+SPEAKER 7: If you
+have tomatoes--
+
+PROFESSOR PATRICK WINSTON:
+That's good.
+
+Tomatoes.
+
+SPEAKER 7: You don't want
+them to get squished.
+
+PROFESSOR PATRICK WINSTON: Now,
+there's a very different
+
+thing about squishies and
+tomatoes because tomato is
+
+specific, and squishy isn't.
+
+Now, one tendency of MIT
+students, of course, is that
+
+we all tend to generalize.
+
+I once knew a professor
+in the Sloan School
+
+who seemed real smart.
+
+And--
+
+SPEAKER 3: [LAUGHTER]
+
+PROFESSOR PATRICK
+WINSTON: Then I
+
+figured out what he did.
+
+If I were to say, I'm thinking
+about a red apple.
+
+They'd sit back and say, oh,
+I see you're contemplating
+
+colored fruit today.
+
+They're just taking it up one
+level of abstraction.
+
+Not a genius.
+
+He also was able to talk for
+an hour after he drew a
+
+triangle on the board.
+
+Amazing people.
+
+Anyhow, where were we?
+
+Oh, yes, bagging groceries.
+
+So we're making some progress,
+but not as
+
+much as I would like.
+
+And so in order to really make
+progress on tasks like this,
+
+you have to exercise--
+
+you know about some principles
+of knowledge engineering.
+
+So principle number one, which
+I've listed over here as part
+
+of a gold star idea, is deal
+with specific cases.
+
+So while you're at the site, if
+all you do is talk to the
+
+experts like Lisa and
+[INAUDIBLE], all you're going
+
+to get is vague generalities
+because they won't think of
+
+everything.
+
+So what you do is you
+say, well, let me
+
+watch you on the line.
+
+And then you'll see that they
+have to have some way of
+
+dealing with the milk.
+
+And then you'll see that they
+have to have some way of
+
+dealing with the potato chips.
+
+Nobody mentioned potato chips,
+except insofar as they might
+
+be squishy.
+
+We don't have a definition
+for squishy.
+
+Nobody talked about
+the macaroni.
+
+And no one talked about
+the motor oil.
+
+This is a convenience store.
+
+I don't want that in the
+same bag with the meat.
+
+And then no one talked
+about canned stuff.
+
+Here's a can of olives.
+
+So by looking at specific cases,
+you elicit from people
+
+knowledge they otherwise would
+not have thought to give you.
+
+That's knowledge engineering
+rule number one.
+
+And within a very few minutes,
+you'll have all three
+
+knowledge engineering rules and
+be prepared to be a highly
+
+paid knowledge engineer.
+
+Heuristic, let's call
+these heuristics.
+
+Heuristic number one,
+specific cases.
+
+Heuristic number two is ask
+questions about things that
+
+appear to be the same, but are
+actually handled differently.
+
+So there's some Birds Eye
+frozen peas, and here--
+
+ugh, some fresh cut
+sweet peas.
+
+And to me, the person who's
+never touched a grocery bag in
+
+my life-- maybe I'm
+from Mars--
+
+I can't tell the difference.
+
+They're both peas.
+
+But I observe that the experts
+are handling these objects
+
+differently.
+
+So I say, why did you handle
+those peas differently from
+
+those peas, and what
+do they say?
+
+One's canned, and
+one's frozen.
+
+So what happens?
+
+Bingo, I've got some new
+words in my vocabulary.
+
+And those new vocabulary words
+are going to give me power
+
+over the domain because
+I can now use
+
+those words in my rules.
+
+And I can write rules like if
+frozen, then put them all
+
+together in a little
+plastic bag.
+
+Actually, that's too
+complicated, but that's what
+
+we end up doing, right?
+
+Why do we put them
+all together in a
+
+little plastic bag?
+
+SPEAKER 8: [INAUDIBLE]
+
+PROFESSOR PATRICK WINSTON:
+What's that?
+
+SPEAKER 8: [INAUDIBLE]
+
+PROFESSOR PATRICK WINSTON:
+Well, there are two
+
+explanations.
+
+There's the MIT explanation.
+
+We know that temperature flow
+is equal to the fourth power
+
+of the temperature difference
+and the surface area and all
+
+that kind of stuff.
+
+We want to get them all together
+in a ball, sphere.
+
+The normal explanation is that
+they're going to melt anyway,
+
+so they might as well not
+get everything else wet.
+
+All right.
+
+SPEAKER 3: [LAUGHTER]
+
+PROFESSOR PATRICK WINSTON: So
+that's heuristic number two.
+
+And actually, there's heuristic
+number three, that I
+
+just want to relate to you for
+the first time because I have
+
+been dealing with it a lot
+over this past summer.
+
+Heuristic number three is you
+build a system, and you see
+
+when it cracks.
+
+And when it cracks is when you
+don't have one of the rules
+
+you need in order to execute--
+
+in order to get the program
+to execute as
+
+you want it to execute.
+
+So if I were to write a grocery
+store bagging program
+
+and have it bag some groceries,
+again, eventually
+
+it would either make a mistake
+or come to a grinding halt,
+
+and bingo, I know that there's
+a missing rule.
+
+Isn't that what happens when you
+do a problem set, and you
+
+hit an impasse?
+
+You're performing an experiment
+on yourself, and
+
+you're discovering that you
+don't have the whole program.
+
+In fact, I've listed this as a
+gold star idea having to do
+
+with engineering yourself
+because all of these things
+
+that you can do for knowledge
+engineering are things you can
+
+do when you learn a new
+subject yourself.
+
+Because essentially, you're
+making yourself into an expert
+
+system when you're learning
+circuit theory or
+
+electromagnetism or something
+of that sort.
+
+You're saying to yourself,
+well, let's look at some
+
+specific cases.
+
+Well, what are the vocabulary
+items here that tell me why
+
+this problem is different
+from that problem?
+
+Oh, this is a cylinder
+instead of a sphere.
+
+Or you're working with a problem
+set, and you discover
+
+you can't work with the problem,
+and you need to get
+
+another chunk of knowledge
+that makes it possible
+
+for you to do it.
+
+So this sort of thing, which
+you think of primarily as a
+
+mechanism, heuristics for doing
+knowledge engineering,
+
+are also mechanisms for making
+yourself smarter.
+
+So that concludes what I want to
+talk with you about today.
+
+But the bottom line is, that
+if you build a rule-based
+
+expert system, it can
+answer questions
+
+about its own behavior.
+
+If you build a program that's
+centered on goals, it can
+
+answer questions about
+its own behavior.
+
+If you build an integration
+program, it can answer
+
+questions about its
+own behavior.
+
+And if you want to build one of
+these systems, and you need
+
+to extract knowledge from an
+expert, you need to approach
+
+it with these kinds of
+heuristics because the expert
+
+won't think what to tell you
+unless you elicit that
+
+information by specific cases,
+by asking questions about
+
+differences, and by ultimately
+doing some experiments to see
+
+where your program is correct.
+
+So that really concludes what I
+had to say, except I want to
+
+ask the question, is this all
+we need to know about human
+
+intelligence?
+
+Can these things be--
+
+are these things really smart?
+
+And the traditional answer is
+no, they're not really smart
+
+because their intelligence is
+this sort of thin veneer.
+
+And when you try to get
+underneath it, as written,
+
+they tend to crack.
+
+For example, we talk about a
+rule, we could talk about a
+
+rule that knows that you should
+put the potato chips on
+
+the top of the bag.
+
+But a program that knows that
+would have no idea why you
+
+would want to put the potato
+chips on top of the bag.
+
+They wouldn't know that if you
+put them on the bottom of the
+
+bag, they'll get crushed.
+
+And it wouldn't know that if
+they get crushed, the customer
+
+will get angry, because people
+don't like to eat crushed
+
+potato chips.
+
+So that's what I mean when I
+say the knowledge of these
+
+things tends to be a veneer.
+
+So the MYCIN program, during
+debugging, once prescribed a
+
+barrel of penicillin to be
+administered to a patient for
+
+its disease.
+
+They don't know, they don't
+have any common sense.
+
+So the question then becomes,
+well, I don't know.
+
+Does rule-based--
+
+do rules have anything to
+do with common sense?
+
+And I'm becoming a little bit
+agnostic on that subject.
+
+Because there are certain
+indications, there are certain
+
+situations, in which rules could
+be said to play a role
+
+in our ordinary understanding
+of things.
+
+Would you like to see
+a demonstration?
+
+What I'm going to show you,
+when the clip speaks up--
+
+well, before I make any
+promises, let me see if I'm
+
+actually connected to the web.
+
+MIT, good.
+
+MIT.
+
+Guest.
+
+Yeah, that's me.
+
+Sounds good.
+
+OK, I just tested the system,
+and I've seen it is actually
+
+connected to the web.
+
+And I'm going to adjust some
+systems options here.
+
+I'll get rid of the text box.
+
+And we'll get rid of those
+changes scale a little bit.
+
+What I'm going to do is I'm
+going to read a little
+
+synopsis of the Macbeth plot.
+
+You're MIT students.
+
+I'm sure you're all classically
+educated and very
+
+familiar with Shakespearean
+plots.
+
+So I'm going to read one.
+
+I'm going to read a version
+of a Macbeth plot.
+
+And it's going to go
+along like this.
+
+It's basically reading
+a rule base so far.
+
+And pretty soon, it's going to
+get beyond the rule base and
+
+start reading the
+Macbeth story.
+
+And there it is.
+
+It's read the Macbeth story.
+
+Let me show you what the Macbeth
+story looks like as
+
+it's actually retained
+by the system.
+
+That's it.
+
+Read that.
+
+OK, you ran out of
+time because the
+
+machine's already finished.
+
+It takes about five seconds
+to read this story.
+
+Now, as you look at this little
+synopsis of Macbeth,
+
+there are a couple
+things to note.
+
+For one thing, it says that
+Duncan is murdered.
+
+Duncan, I hope this doesn't
+bother you.
+
+Duncan is murdered by Macbeth.
+
+But at no time does it say
+that Duncan is dead.
+
+But you know Duncan's dead
+because he was murdered.
+
+If murdered, then dead.
+
+SPEAKER 3: [LAUGHTER].
+
+PROFESSOR PATRICK WINSTON: So
+if you look a little further
+
+down, what you see is that
+Macduff kills Macbeth.
+
+Fourth line up from
+the bottom.
+
+Why did Macduff kill Macbeth?
+
+Doesn't say why in this story,
+but you have no trouble
+
+figuring out that it's
+because he got angry.
+
+And when you get angry, you
+don't necessarily kill
+
+somebody, but it's possible.
+
+SPEAKER 3: [LAUGHTER].
+
+PROFESSOR PATRICK WINSTON: So
+now that you see what's in the
+
+story, let me take you
+back to this display.
+
+It's what we call an
+elaboration graph.
+
+And when I blow it up, you can
+see that there's some familiar
+
+looking things in there.
+
+For example, up here in the
+left-hand corner, Macbeth
+
+murders Duncan, right
+over there.
+
+And over here, Macduff
+kills Macbeth.
+
+And if you look at what is a
+consequence of that, it looks
+
+like there must be a rule that
+says if you murder somebody,
+
+you harm them.
+
+And if you murder somebody,
+then they're dead.
+
+And one reason why you might
+kill somebody is because they
+
+angered you.
+
+And if you go the other way,
+one consequence of killing
+
+somebody is that you harm them,
+and that they die too.
+
+And if you harm somebody, they
+get angry, and their state
+
+goes negative.
+
+So that suggests that there are
+some things that we have
+
+on our hands that are very
+compiled and very, strangely
+
+enough, very rule-like
+in their character.
+
+Now, to close, I'm just
+going to read Hamlet.
+
+The Hamlet demonstration is
+much like the Macbeth one.
+
+In fact, Hamlet and Macbeth are
+very alike in their plot.
+
+But there's one thing that's
+well-illustrated by our
+
+particular capturing
+of Hamlet here.
+
+And that is that you'll note
+that the ratio of gray stuff
+
+to white stuff is
+considerable.
+
+The gray stuff is stuff that
+has been deduced by rules.
+
+And the reason there's so much
+gray stuff in this Hamlet
+
+story is because everybody's
+related to everybody else.
+
+So when you kill anybody, you
+irritate everybody else.
+
+So look at that.
+
+A few white things, those are
+the things that are explicit
+
+in the story, and lots
+of gray stuff.
+
+So what this is suggesting is
+that when we tell a story,
+
+it's mostly a matter of
+controlled hallucination.
+
+I know what rules are in your
+head, so I could take
+
+advantage of that in telling the
+story and not have to tell
+
+you anything I'm sure you're
+going to know.
+
+And so that's why, we've
+discovered, that storytelling
+
+is largely a matter of just
+controlling how you're going
+
+along, a kind of controlled
+hallucination.
\ No newline at end of file
diff --git a/lw9W32ezQhM.txt b/lw9W32ezQhM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b5dafe3e8d8133cbc73f7be9bff83ef028a30d24
--- /dev/null
+++ b/lw9W32ezQhM.txt
@@ -0,0 +1,499 @@
+align:start position:0%
+ 
+we are now in position to find the
+
+ align:start position:0%
+we are now in position to find the
+ 
+
+ align:start position:0%
+we are now in position to find the
+accelerations a1 a2 in the tension
+
+ align:start position:0%
+accelerations a1 a2 in the tension
+ 
+
+ align:start position:0%
+accelerations a1 a2 in the tension
+because we have Newton's second law and
+
+ align:start position:0%
+because we have Newton's second law and
+ 
+
+ align:start position:0%
+because we have Newton's second law and
+our constraint condition for the
+
+ align:start position:0%
+our constraint condition for the
+ 
+
+ align:start position:0%
+our constraint condition for the
+acceleration let's recall the equations
+
+ align:start position:0%
+acceleration let's recall the equations
+ 
+
+ align:start position:0%
+acceleration let's recall the equations
+that we found we had M 1 G minus T was
+
+ align:start position:0%
+that we found we had M 1 G minus T was
+ 
+
+ align:start position:0%
+that we found we had M 1 G minus T was
+m1 a1 and we had m2 G minus 2 T was
+
+ align:start position:0%
+m1 a1 and we had m2 G minus 2 T was
+ 
+
+ align:start position:0%
+m1 a1 and we had m2 G minus 2 T was
+equal to m2 a2 and we also had the
+
+ align:start position:0%
+equal to m2 a2 and we also had the
+ 
+
+ align:start position:0%
+equal to m2 a2 and we also had the
+condition constraint condition between
+
+ align:start position:0%
+condition constraint condition between
+ 
+
+ align:start position:0%
+condition constraint condition between
+the accelerations that a1 was minus 2 a
+
+ align:start position:0%
+the accelerations that a1 was minus 2 a
+ 
+
+ align:start position:0%
+the accelerations that a1 was minus 2 a
+2 so now we have a system of three
+
+ align:start position:0%
+2 so now we have a system of three
+ 
+
+ align:start position:0%
+2 so now we have a system of three
+equations and we can find we can solve
+
+ align:start position:0%
+equations and we can find we can solve
+ 
+
+ align:start position:0%
+equations and we can find we can solve
+for any of these quantities that we want
+
+ align:start position:0%
+for any of these quantities that we want
+ 
+
+ align:start position:0%
+for any of these quantities that we want
+so one way to do it is to identify an
+
+ align:start position:0%
+so one way to do it is to identify an
+ 
+
+ align:start position:0%
+so one way to do it is to identify an
+equation and to identify the quantity
+
+ align:start position:0%
+equation and to identify the quantity
+ 
+
+ align:start position:0%
+equation and to identify the quantity
+that we would like to solve for so for
+
+ align:start position:0%
+that we would like to solve for so for
+ 
+
+ align:start position:0%
+that we would like to solve for so for
+instance let's identify that we want to
+
+ align:start position:0%
+instance let's identify that we want to
+ 
+
+ align:start position:0%
+instance let's identify that we want to
+solve for a 1 first
+
+ align:start position:0%
+solve for a 1 first
+ 
+
+ align:start position:0%
+solve for a 1 first
+so how are we going to develop a
+
+ align:start position:0%
+so how are we going to develop a
+ 
+
+ align:start position:0%
+so how are we going to develop a
+strategy for that well I'll choose
+
+ align:start position:0%
+strategy for that well I'll choose
+ 
+
+ align:start position:0%
+strategy for that well I'll choose
+equation 1 as my backbone equation and I
+
+ align:start position:0%
+equation 1 as my backbone equation and I
+ 
+
+ align:start position:0%
+equation 1 as my backbone equation and I
+have an unknown T but in equation 2 that
+
+ align:start position:0%
+have an unknown T but in equation 2 that
+ 
+
+ align:start position:0%
+have an unknown T but in equation 2 that
+unknown T is appearing there but it's
+
+ align:start position:0%
+unknown T is appearing there but it's
+ 
+
+ align:start position:0%
+unknown T is appearing there but it's
+expressed in terms of a 2 and a 2 though
+
+ align:start position:0%
+expressed in terms of a 2 and a 2 though
+ 
+
+ align:start position:0%
+expressed in terms of a 2 and a 2 though
+from Equation 3 is expressed in terms of
+
+ align:start position:0%
+from Equation 3 is expressed in terms of
+ 
+
+ align:start position:0%
+from Equation 3 is expressed in terms of
+a 1 so my first step is to write
+
+ align:start position:0%
+a 1 so my first step is to write
+ 
+
+ align:start position:0%
+a 1 so my first step is to write
+equation rewrite equation 2 as m2 G
+
+ align:start position:0%
+equation rewrite equation 2 as m2 G
+ 
+
+ align:start position:0%
+equation rewrite equation 2 as m2 G
+minus 2 T equals m2 now here is I'm
+
+ align:start position:0%
+minus 2 T equals m2 now here is I'm
+ 
+
+ align:start position:0%
+minus 2 T equals m2 now here is I'm
+going to make the substitution which is
+
+ align:start position:0%
+going to make the substitution which is
+ 
+
+ align:start position:0%
+going to make the substitution which is
+minus a 1 over 2 so we'll call that 2a
+
+ align:start position:0%
+minus a 1 over 2 so we'll call that 2a
+ 
+
+ align:start position:0%
+minus a 1 over 2 so we'll call that 2a
+and now I have equation 1 and equation 2
+
+ align:start position:0%
+and now I have equation 1 and equation 2
+ 
+
+ align:start position:0%
+and now I have equation 1 and equation 2
+a 2 unknowns T and a 1 and what I can do
+
+ align:start position:0%
+a 2 unknowns T and a 1 and what I can do
+ 
+
+ align:start position:0%
+a 2 unknowns T and a 1 and what I can do
+is I can solve for either equation and I
+
+ align:start position:0%
+is I can solve for either equation and I
+ 
+
+ align:start position:0%
+is I can solve for either equation and I
+can make a choice what's easiest when I
+
+ align:start position:0%
+can make a choice what's easiest when I
+ 
+
+ align:start position:0%
+can make a choice what's easiest when I
+look at these equations it's easiest for
+
+ align:start position:0%
+look at these equations it's easiest for
+ 
+
+ align:start position:0%
+look at these equations it's easiest for
+me to identify what T is in terms of a 1
+
+ align:start position:0%
+me to identify what T is in terms of a 1
+ 
+
+ align:start position:0%
+me to identify what T is in terms of a 1
+so I'll write M 1 G minus M 1 a 1 is
+
+ align:start position:0%
+so I'll write M 1 G minus M 1 a 1 is
+ 
+
+ align:start position:0%
+so I'll write M 1 G minus M 1 a 1 is
+equal to T I'll call that equation 1 a
+
+ align:start position:0%
+equal to T I'll call that equation 1 a
+ 
+
+ align:start position:0%
+equal to T I'll call that equation 1 a
+and now I can substitute that value of T
+
+ align:start position:0%
+and now I can substitute that value of T
+ 
+
+ align:start position:0%
+and now I can substitute that value of T
+into equation 2 a and I get m2 G minus 2
+
+ align:start position:0%
+into equation 2 a and I get m2 G minus 2
+ 
+
+ align:start position:0%
+into equation 2 a and I get m2 G minus 2
+times M 1 G minus M 1
+
+ align:start position:0%
+times M 1 G minus M 1
+ 
+
+ align:start position:0%
+times M 1 G minus M 1
+and that's equal to minus em 2 over 2
+
+ align:start position:0%
+and that's equal to minus em 2 over 2
+ 
+
+ align:start position:0%
+and that's equal to minus em 2 over 2
+times a 1 and now I'd like to collect my
+
+ align:start position:0%
+times a 1 and now I'd like to collect my
+ 
+
+ align:start position:0%
+times a 1 and now I'd like to collect my
+a 1 terms and what I have over here
+
+ align:start position:0%
+a 1 terms and what I have over here
+ 
+
+ align:start position:0%
+a 1 terms and what I have over here
+let's bring all the a 1 terms to this
+
+ align:start position:0%
+let's bring all the a 1 terms to this
+ 
+
+ align:start position:0%
+let's bring all the a 1 terms to this
+side and I get em 2 gee minus 2 & 1 gee
+
+ align:start position:0%
+side and I get em 2 gee minus 2 & 1 gee
+ 
+
+ align:start position:0%
+side and I get em 2 gee minus 2 & 1 gee
+I have a plus so I'm going to bring that
+
+ align:start position:0%
+I have a plus so I'm going to bring that
+ 
+
+ align:start position:0%
+I have a plus so I'm going to bring that
+over to this side and I get equal to
+
+ align:start position:0%
+over to this side and I get equal to
+ 
+
+ align:start position:0%
+over to this side and I get equal to
+that's plus plus so I'll have 2 minus
+
+ align:start position:0%
+that's plus plus so I'll have 2 minus
+ 
+
+ align:start position:0%
+that's plus plus so I'll have 2 minus
+signs and I'll have to M 1 plus M 2 over
+
+ align:start position:0%
+signs and I'll have to M 1 plus M 2 over
+ 
+
+ align:start position:0%
+signs and I'll have to M 1 plus M 2 over
+2 a 1 and now I can solve for a 1 and
+
+ align:start position:0%
+2 a 1 and now I can solve for a 1 and
+ 
+
+ align:start position:0%
+2 a 1 and now I can solve for a 1 and
+what I get is I get 2 & 1 G minus m2g
+
+ align:start position:0%
+what I get is I get 2 & 1 G minus m2g
+ 
+
+ align:start position:0%
+what I get is I get 2 & 1 G minus m2g
+and I want to divide through by this
+
+ align:start position:0%
+and I want to divide through by this
+ 
+
+ align:start position:0%
+and I want to divide through by this
+denominator and what I have downstairs
+
+ align:start position:0%
+denominator and what I have downstairs
+ 
+
+ align:start position:0%
+denominator and what I have downstairs
+is 2 m 1 plus M 2 divided by 2 and
+
+ align:start position:0%
+is 2 m 1 plus M 2 divided by 2 and
+ 
+
+ align:start position:0%
+is 2 m 1 plus M 2 divided by 2 and
+that's my expression for a 1 once I have
+
+ align:start position:0%
+that's my expression for a 1 once I have
+ 
+
+ align:start position:0%
+that's my expression for a 1 once I have
+that expression for a 1 I can easily
+
+ align:start position:0%
+that expression for a 1 I can easily
+ 
+
+ align:start position:0%
+that expression for a 1 I can easily
+come back and find out what a 2 is or I
+
+ align:start position:0%
+come back and find out what a 2 is or I
+ 
+
+ align:start position:0%
+come back and find out what a 2 is or I
+can substitute into the equation here
+
+ align:start position:0%
+can substitute into the equation here
+ 
+
+ align:start position:0%
+can substitute into the equation here
+for a 1 and find out what the tension is
+
+ align:start position:0%
+for a 1 and find out what the tension is
+ 
+
+ align:start position:0%
+for a 1 and find out what the tension is
+and so I can now easily find my
+
+ align:start position:0%
+and so I can now easily find my
+ 
+
+ align:start position:0%
+and so I can now easily find my
+expressions for a 2 and T but I will
+
+ align:start position:0%
+expressions for a 2 and T but I will
+ 
+
+ align:start position:0%
+expressions for a 2 and T but I will
+leave that as an exercise
\ No newline at end of file
diff --git a/lxpXowuUdKw.txt b/lxpXowuUdKw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7e66ecd8dfb0f1e5f6e6a32fbd14e6086e8822e7
--- /dev/null
+++ b/lxpXowuUdKw.txt
@@ -0,0 +1,10795 @@
+align:start position:0%
+ 
+that says choices for your gaining
+
+ align:start position:0%
+that says choices for your gaining
+ 
+
+ align:start position:0%
+that says choices for your gaining
+project these are the six choices that
+
+ align:start position:0%
+project these are the six choices that
+ 
+
+ align:start position:0%
+project these are the six choices that
+we want to make available to you the
+
+ align:start position:0%
+we want to make available to you the
+ 
+
+ align:start position:0%
+we want to make available to you the
+next one is perhaps the most challenging
+
+ align:start position:0%
+next one is perhaps the most challenging
+ 
+
+ align:start position:0%
+next one is perhaps the most challenging
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+intellectually it's about new funding
+
+ align:start position:0%
+intellectually it's about new funding
+ 
+
+ align:start position:0%
+intellectually it's about new funding
+mechanisms for disas
+
+ align:start position:0%
+mechanisms for disas
+ 
+
+ align:start position:0%
+mechanisms for disas
+Bri I will explain this we call it
+
+ align:start position:0%
+Bri I will explain this we call it
+ 
+
+ align:start position:0%
+Bri I will explain this we call it
+forecast based financing or
+
+ align:start position:0%
+forecast based financing or
+ 
+
+ align:start position:0%
+forecast based financing or
+FBF and it's the the one that has the
+
+ align:start position:0%
+FBF and it's the the one that has the
+ 
+
+ align:start position:0%
+FBF and it's the the one that has the
+most potential to transform the
+
+ align:start position:0%
+most potential to transform the
+ 
+
+ align:start position:0%
+most potential to transform the
+humanitarian
+
+ align:start position:0%
+humanitarian
+ 
+
+ align:start position:0%
+humanitarian
+world all right moving to the next
+
+ align:start position:0%
+world all right moving to the next
+ 
+
+ align:start position:0%
+world all right moving to the next
+one the next one is the most
+
+ align:start position:0%
+one the next one is the most
+ 
+
+ align:start position:0%
+one the next one is the most
+complex um do you see the drawing of the
+
+ align:start position:0%
+complex um do you see the drawing of the
+ 
+
+ align:start position:0%
+complex um do you see the drawing of the
+time bomb with the fuse
+
+ align:start position:0%
+time bomb with the fuse
+ 
+
+ align:start position:0%
+time bomb with the fuse
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+okay so allow me to give a little bit of
+
+ align:start position:0%
+okay so allow me to give a little bit of
+ 
+
+ align:start position:0%
+okay so allow me to give a little bit of
+context we did a little bit of this
+
+ align:start position:0%
+context we did a little bit of this
+ 
+
+ align:start position:0%
+context we did a little bit of this
+conversation when I showed up a few
+
+ align:start position:0%
+conversation when I showed up a few
+ 
+
+ align:start position:0%
+conversation when I showed up a few
+weeks ago but I imagine you all Forgot
+
+ align:start position:0%
+weeks ago but I imagine you all Forgot
+ 
+
+ align:start position:0%
+weeks ago but I imagine you all Forgot
+by now the humanitarian sector has two
+
+ align:start position:0%
+by now the humanitarian sector has two
+ 
+
+ align:start position:0%
+by now the humanitarian sector has two
+main funding
+
+ align:start position:0%
+main funding
+ 
+
+ align:start position:0%
+main funding
+mechanisms imagine a pot of
+
+ align:start position:0%
+mechanisms imagine a pot of
+ 
+
+ align:start position:0%
+mechanisms imagine a pot of
+money even if there's almost no money
+
+ align:start position:0%
+money even if there's almost no money
+ 
+
+ align:start position:0%
+money even if there's almost no money
+there if the pot exists money can go in
+
+ align:start position:0%
+there if the pot exists money can go in
+ 
+
+ align:start position:0%
+there if the pot exists money can go in
+to then be taken out to spend one of the
+
+ align:start position:0%
+to then be taken out to spend one of the
+ 
+
+ align:start position:0%
+to then be taken out to spend one of the
+pots of money that exists one of the
+
+ align:start position:0%
+pots of money that exists one of the
+ 
+
+ align:start position:0%
+pots of money that exists one of the
+funding mechanisms that exist is for
+
+ align:start position:0%
+funding mechanisms that exist is for
+ 
+
+ align:start position:0%
+funding mechanisms that exist is for
+Disaster Response meaning a hurricane a
+
+ align:start position:0%
+Disaster Response meaning a hurricane a
+ 
+
+ align:start position:0%
+Disaster Response meaning a hurricane a
+flood a volcanic eruption something has
+
+ align:start position:0%
+flood a volcanic eruption something has
+ 
+
+ align:start position:0%
+flood a volcanic eruption something has
+already happened is happening and is
+
+ align:start position:0%
+already happened is happening and is
+ 
+
+ align:start position:0%
+already happened is happening and is
+killing people people are dying but if
+
+ align:start position:0%
+killing people people are dying but if
+ 
+
+ align:start position:0%
+killing people people are dying but if
+you did something you could save lives
+
+ align:start position:0%
+you did something you could save lives
+ 
+
+ align:start position:0%
+you did something you could save lives
+for example get on a boat and rescue
+
+ align:start position:0%
+for example get on a boat and rescue
+ 
+
+ align:start position:0%
+for example get on a boat and rescue
+people who are stranding on a roof or
+
+ align:start position:0%
+people who are stranding on a roof or
+ 
+
+ align:start position:0%
+people who are stranding on a roof or
+people are sick go give them medicine
+
+ align:start position:0%
+people are sick go give them medicine
+ 
+
+ align:start position:0%
+people are sick go give them medicine
+this is Disaster Response and if you
+
+ align:start position:0%
+this is Disaster Response and if you
+ 
+
+ align:start position:0%
+this is Disaster Response and if you
+spend money you can do very good things
+
+ align:start position:0%
+spend money you can do very good things
+ 
+
+ align:start position:0%
+spend money you can do very good things
+and the funding mechanism exists there
+
+ align:start position:0%
+and the funding mechanism exists there
+ 
+
+ align:start position:0%
+and the funding mechanism exists there
+is another pot of money which is for a
+
+ align:start position:0%
+is another pot of money which is for a
+ 
+
+ align:start position:0%
+is another pot of money which is for a
+normal day the Red Cross has Vehicles
+
+ align:start position:0%
+normal day the Red Cross has Vehicles
+ 
+
+ align:start position:0%
+normal day the Red Cross has Vehicles
+the vehicles need maintenance they need
+
+ align:start position:0%
+the vehicles need maintenance they need
+ 
+
+ align:start position:0%
+the vehicles need maintenance they need
+to change tires you need to buy a new
+
+ align:start position:0%
+to change tires you need to buy a new
+ 
+
+ align:start position:0%
+to change tires you need to buy a new
+computer you need to pay rent and uh
+
+ align:start position:0%
+computer you need to pay rent and uh
+ 
+
+ align:start position:0%
+computer you need to pay rent and uh
+electricity bills you need to train
+
+ align:start position:0%
+electricity bills you need to train
+ 
+
+ align:start position:0%
+electricity bills you need to train
+stuff so on a normal day you have a
+
+ align:start position:0%
+stuff so on a normal day you have a
+ 
+
+ align:start position:0%
+stuff so on a normal day you have a
+budget for you know either maintenance
+
+ align:start position:0%
+budget for you know either maintenance
+ 
+
+ align:start position:0%
+budget for you know either maintenance
+or development of new projects or
+
+ align:start position:0%
+or development of new projects or
+ 
+
+ align:start position:0%
+or development of new projects or
+writing proposal and so on and that pot
+
+ align:start position:0%
+writing proposal and so on and that pot
+ 
+
+ align:start position:0%
+writing proposal and so on and that pot
+of money exists we call it the annual
+
+ align:start position:0%
+of money exists we call it the annual
+ 
+
+ align:start position:0%
+of money exists we call it the annual
+appeal every year we appeal for help and
+
+ align:start position:0%
+appeal every year we appeal for help and
+ 
+
+ align:start position:0%
+appeal every year we appeal for help and
+the people or donors or governments give
+
+ align:start position:0%
+the people or donors or governments give
+ 
+
+ align:start position:0%
+the people or donors or governments give
+us some money what does not exist is
+
+ align:start position:0%
+us some money what does not exist is
+ 
+
+ align:start position:0%
+us some money what does not exist is
+what the drawing the cartoon depicts
+
+ align:start position:0%
+what the drawing the cartoon depicts
+ 
+
+ align:start position:0%
+what the drawing the cartoon depicts
+which is when there's a signal from
+
+ align:start position:0%
+which is when there's a signal from
+ 
+
+ align:start position:0%
+which is when there's a signal from
+science that a disaster that something
+
+ align:start position:0%
+science that a disaster that something
+ 
+
+ align:start position:0%
+science that a disaster that something
+bad is likely to happen soon we don't
+
+ align:start position:0%
+bad is likely to happen soon we don't
+ 
+
+ align:start position:0%
+bad is likely to happen soon we don't
+have money to f action before the
+
+ align:start position:0%
+have money to f action before the
+ 
+
+ align:start position:0%
+have money to f action before the
+disaster after the forecast so if you
+
+ align:start position:0%
+disaster after the forecast so if you
+ 
+
+ align:start position:0%
+disaster after the forecast so if you
+click to see the text the context is
+
+ align:start position:0%
+click to see the text the context is
+ 
+
+ align:start position:0%
+click to see the text the context is
+that there's that missing money pot we
+
+ align:start position:0%
+that there's that missing money pot we
+ 
+
+ align:start position:0%
+that there's that missing money pot we
+have money for after the disaster we
+
+ align:start position:0%
+have money for after the disaster we
+ 
+
+ align:start position:0%
+have money for after the disaster we
+have money for the normal day but we
+
+ align:start position:0%
+have money for the normal day but we
+ 
+
+ align:start position:0%
+have money for the normal day but we
+don't have money for before the disaster
+
+ align:start position:0%
+don't have money for before the disaster
+ 
+
+ align:start position:0%
+don't have money for before the disaster
+after the forecast the issue is that if
+
+ align:start position:0%
+after the forecast the issue is that if
+ 
+
+ align:start position:0%
+after the forecast the issue is that if
+you spend money in that time window
+
+ align:start position:0%
+you spend money in that time window
+ 
+
+ align:start position:0%
+you spend money in that time window
+before the disaster after science says
+
+ align:start position:0%
+before the disaster after science says
+ 
+
+ align:start position:0%
+before the disaster after science says
+the disaster is likely you can do very
+
+ align:start position:0%
+the disaster is likely you can do very
+ 
+
+ align:start position:0%
+the disaster is likely you can do very
+good things for very cheap and and
+
+ align:start position:0%
+good things for very cheap and and
+ 
+
+ align:start position:0%
+good things for very cheap and and
+relative be simply and much more
+
+ align:start position:0%
+relative be simply and much more
+ 
+
+ align:start position:0%
+relative be simply and much more
+reliably it's not only more expensive
+
+ align:start position:0%
+reliably it's not only more expensive
+ 
+
+ align:start position:0%
+reliably it's not only more expensive
+but more difficult to Save a Life when
+
+ align:start position:0%
+but more difficult to Save a Life when
+ 
+
+ align:start position:0%
+but more difficult to Save a Life when
+the when the storm waters are flashing
+
+ align:start position:0%
+the when the storm waters are flashing
+ 
+
+ align:start position:0%
+the when the storm waters are flashing
+through a city and people are about to
+
+ align:start position:0%
+through a city and people are about to
+ 
+
+ align:start position:0%
+through a city and people are about to
+drown the boat is unstable whereas if
+
+ align:start position:0%
+drown the boat is unstable whereas if
+ 
+
+ align:start position:0%
+drown the boat is unstable whereas if
+you do it the day before when the water
+
+ align:start position:0%
+you do it the day before when the water
+ 
+
+ align:start position:0%
+you do it the day before when the water
+has come down from the sky but it's
+
+ align:start position:0%
+has come down from the sky but it's
+ 
+
+ align:start position:0%
+has come down from the sky but it's
+still in the river and not in the city
+
+ align:start position:0%
+still in the river and not in the city
+ 
+
+ align:start position:0%
+still in the river and not in the city
+people can take action by just walking
+
+ align:start position:0%
+people can take action by just walking
+ 
+
+ align:start position:0%
+people can take action by just walking
+away on their own means with their
+
+ align:start position:0%
+away on their own means with their
+ 
+
+ align:start position:0%
+away on their own means with their
+valuables and not just depending on
+
+ align:start position:0%
+valuables and not just depending on
+ 
+
+ align:start position:0%
+valuables and not just depending on
+someone to show with the boat so we came
+
+ align:start position:0%
+someone to show with the boat so we came
+ 
+
+ align:start position:0%
+someone to show with the boat so we came
+up with a financial mechanism we call it
+
+ align:start position:0%
+up with a financial mechanism we call it
+ 
+
+ align:start position:0%
+up with a financial mechanism we call it
+forecast based financing for disaster
+
+ align:start position:0%
+forecast based financing for disaster
+ 
+
+ align:start position:0%
+forecast based financing for disaster
+preparedness which is nuanced in how
+
+ align:start position:0%
+preparedness which is nuanced in how
+ 
+
+ align:start position:0%
+preparedness which is nuanced in how
+it's implemented there's a pot of money
+
+ align:start position:0%
+it's implemented there's a pot of money
+ 
+
+ align:start position:0%
+it's implemented there's a pot of money
+it's like a bank account you need to
+
+ align:start position:0%
+it's like a bank account you need to
+ 
+
+ align:start position:0%
+it's like a bank account you need to
+have a threshold of disaster risk that
+
+ align:start position:0%
+have a threshold of disaster risk that
+ 
+
+ align:start position:0%
+have a threshold of disaster risk that
+needs to be exceeded so it cannot be two
+
+ align:start position:0%
+needs to be exceeded so it cannot be two
+ 
+
+ align:start position:0%
+needs to be exceeded so it cannot be two
+drops of rain it has to be a lot of rain
+
+ align:start position:0%
+drops of rain it has to be a lot of rain
+ 
+
+ align:start position:0%
+drops of rain it has to be a lot of rain
+it cannot be some Breeze it has to be a
+
+ align:start position:0%
+it cannot be some Breeze it has to be a
+ 
+
+ align:start position:0%
+it cannot be some Breeze it has to be a
+hurricane category one or more but once
+
+ align:start position:0%
+hurricane category one or more but once
+ 
+
+ align:start position:0%
+hurricane category one or more but once
+the threshold is established and reached
+
+ align:start position:0%
+the threshold is established and reached
+ 
+
+ align:start position:0%
+the threshold is established and reached
+by the forecast then there some standard
+
+ align:start position:0%
+by the forecast then there some standard
+ 
+
+ align:start position:0%
+by the forecast then there some standard
+operating procedures some actions that
+
+ align:start position:0%
+operating procedures some actions that
+ 
+
+ align:start position:0%
+operating procedures some actions that
+people have to take spending money to
+
+ align:start position:0%
+people have to take spending money to
+ 
+
+ align:start position:0%
+people have to take spending money to
+save lives and that is something that if
+
+ align:start position:0%
+save lives and that is something that if
+ 
+
+ align:start position:0%
+save lives and that is something that if
+you could come up with a game that
+
+ align:start position:0%
+you could come up with a game that
+ 
+
+ align:start position:0%
+you could come up with a game that
+captures that this is the one that if we
+
+ align:start position:0%
+captures that this is the one that if we
+ 
+
+ align:start position:0%
+captures that this is the one that if we
+help communicate forecast based
+
+ align:start position:0%
+help communicate forecast based
+ 
+
+ align:start position:0%
+help communicate forecast based
+financing i s to the public because it
+
+ align:start position:0%
+financing i s to the public because it
+ 
+
+ align:start position:0%
+financing i s to the public because it
+can work for a broad audience digitally
+
+ align:start position:0%
+can work for a broad audience digitally
+ 
+
+ align:start position:0%
+can work for a broad audience digitally
+ideally would reach those who can
+
+ align:start position:0%
+ideally would reach those who can
+ 
+
+ align:start position:0%
+ideally would reach those who can
+contribute either money or decisions
+
+ align:start position:0%
+contribute either money or decisions
+ 
+
+ align:start position:0%
+contribute either money or decisions
+muscle power and
+
+ align:start position:0%
+muscle power and
+ 
+
+ align:start position:0%
+muscle power and
+the chances of embrace for this one are
+
+ align:start position:0%
+the chances of embrace for this one are
+ 
+
+ align:start position:0%
+the chances of embrace for this one are
+not as high as all the previous one but
+
+ align:start position:0%
+not as high as all the previous one but
+ 
+
+ align:start position:0%
+not as high as all the previous one but
+if it were to happen it would have the
+
+ align:start position:0%
+if it were to happen it would have the
+ 
+
+ align:start position:0%
+if it were to happen it would have the
+highest impact because right now there's
+
+ align:start position:0%
+highest impact because right now there's
+ 
+
+ align:start position:0%
+highest impact because right now there's
+billions of dollars being spent in the
+
+ align:start position:0%
+billions of dollars being spent in the
+ 
+
+ align:start position:0%
+billions of dollars being spent in the
+two extremes and if a small fraction
+
+ align:start position:0%
+two extremes and if a small fraction
+ 
+
+ align:start position:0%
+two extremes and if a small fraction
+were spent invested in that precious
+
+ align:start position:0%
+were spent invested in that precious
+ 
+
+ align:start position:0%
+were spent invested in that precious
+window of opportunity when you see the
+
+ align:start position:0%
+window of opportunity when you see the
+ 
+
+ align:start position:0%
+window of opportunity when you see the
+fuse getting close that time of effort
+
+ align:start position:0%
+fuse getting close that time of effort
+ 
+
+ align:start position:0%
+fuse getting close that time of effort
+can really have a very very high impact
+
+ align:start position:0%
+can really have a very very high impact
+ 
+
+ align:start position:0%
+can really have a very very high impact
+there's a link to a journal article that
+
+ align:start position:0%
+there's a link to a journal article that
+ 
+
+ align:start position:0%
+there's a link to a journal article that
+is should be very clear for students uh
+
+ align:start position:0%
+is should be very clear for students uh
+ 
+
+ align:start position:0%
+is should be very clear for students uh
+we also have some simpler readings and
+
+ align:start position:0%
+we also have some simpler readings and
+ 
+
+ align:start position:0%
+we also have some simpler readings and
+Jano and I have been engaged with it and
+
+ align:start position:0%
+Jano and I have been engaged with it and
+ 
+
+ align:start position:0%
+Jano and I have been engaged with it and
+are ready to help this is I insist the
+
+ align:start position:0%
+are ready to help this is I insist the
+ 
+
+ align:start position:0%
+are ready to help this is I insist the
+one that is intellectually most
+
+ align:start position:0%
+one that is intellectually most
+ 
+
+ align:start position:0%
+one that is intellectually most
+challenging but I think if you nail it
+
+ align:start position:0%
+challenging but I think if you nail it
+ 
+
+ align:start position:0%
+challenging but I think if you nail it
+it will also be the most
+
+ align:start position:0%
+it will also be the most
+ 
+
+ align:start position:0%
+it will also be the most
+rewarding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions questions this
+
+ align:start position:0%
+questions questions this
+ 
+
+ align:start position:0%
+questions questions this
+one so one thing when we first started
+
+ align:start position:0%
+one so one thing when we first started
+ 
+
+ align:start position:0%
+one so one thing when we first started
+um designing this class this was
+
+ align:start position:0%
+um designing this class this was
+ 
+
+ align:start position:0%
+um designing this class this was
+actually our the the problem that we
+
+ align:start position:0%
+actually our the the problem that we
+ 
+
+ align:start position:0%
+actually our the the problem that we
+were most interested in um mainly
+
+ align:start position:0%
+were most interested in um mainly
+ 
+
+ align:start position:0%
+were most interested in um mainly
+because the other problems we just
+
+ align:start position:0%
+because the other problems we just
+ 
+
+ align:start position:0%
+because the other problems we just
+didn't hadn't heard about since um the
+
+ align:start position:0%
+didn't hadn't heard about since um the
+ 
+
+ align:start position:0%
+didn't hadn't heard about since um the
+kalera was a recent um yes proposal that
+
+ align:start position:0%
+kalera was a recent um yes proposal that
+ 
+
+ align:start position:0%
+kalera was a recent um yes proposal that
+was asked for and Abola of course um
+
+ align:start position:0%
+was asked for and Abola of course um
+ 
+
+ align:start position:0%
+was asked for and Abola of course um
+very very recent as well um so if you
+
+ align:start position:0%
+very very recent as well um so if you
+ 
+
+ align:start position:0%
+very very recent as well um so if you
+really enjoyed some of the challenges
+
+ align:start position:0%
+really enjoyed some of the challenges
+ 
+
+ align:start position:0%
+really enjoyed some of the challenges
+from projects two and three and you
+
+ align:start position:0%
+from projects two and three and you
+ 
+
+ align:start position:0%
+from projects two and three and you
+really took on the the planning aspects
+
+ align:start position:0%
+really took on the the planning aspects
+ 
+
+ align:start position:0%
+really took on the the planning aspects
+the trade-offs as aspects of those two
+
+ align:start position:0%
+the trade-offs as aspects of those two
+ 
+
+ align:start position:0%
+the trade-offs as aspects of those two
+games um if you're looking at kind of
+
+ align:start position:0%
+games um if you're looking at kind of
+ 
+
+ align:start position:0%
+games um if you're looking at kind of
+trying to trying to communicate to
+
+ align:start position:0%
+trying to trying to communicate to
+ 
+
+ align:start position:0%
+trying to trying to communicate to
+another person how these kind of
+
+ align:start position:0%
+another person how these kind of
+ 
+
+ align:start position:0%
+another person how these kind of
+probabilities works this is probably a
+
+ align:start position:0%
+probabilities works this is probably a
+ 
+
+ align:start position:0%
+probabilities works this is probably a
+really good project you might be
+
+ align:start position:0%
+really good project you might be
+ 
+
+ align:start position:0%
+really good project you might be
+interested in
+
+ align:start position:0%
+interested in
+ 
+
+ align:start position:0%
+interested in
+and I should say also that working with
+
+ align:start position:0%
+and I should say also that working with
+ 
+
+ align:start position:0%
+and I should say also that working with
+a few MIT teams including the
+
+ align:start position:0%
+a few MIT teams including the
+ 
+
+ align:start position:0%
+a few MIT teams including the
+humanitarian response lab including the
+
+ align:start position:0%
+humanitarian response lab including the
+ 
+
+ align:start position:0%
+humanitarian response lab including the
+environmental engineering and we have
+
+ align:start position:0%
+environmental engineering and we have
+ 
+
+ align:start position:0%
+environmental engineering and we have
+two generations of three students plus
+
+ align:start position:0%
+two generations of three students plus
+ 
+
+ align:start position:0%
+two generations of three students plus
+one Professor go to Uganda to work on on
+
+ align:start position:0%
+one Professor go to Uganda to work on on
+ 
+
+ align:start position:0%
+one Professor go to Uganda to work on on
+making this happen for real we got
+
+ align:start position:0%
+making this happen for real we got
+ 
+
+ align:start position:0%
+making this happen for real we got
+German money to do it in Togo and in
+
+ align:start position:0%
+German money to do it in Togo and in
+ 
+
+ align:start position:0%
+German money to do it in Togo and in
+Uganda so it's beginning to happen but
+
+ align:start position:0%
+Uganda so it's beginning to happen but
+ 
+
+ align:start position:0%
+Uganda so it's beginning to happen but
+it's hard to explain because it's dry
+
+ align:start position:0%
+it's hard to explain because it's dry
+ 
+
+ align:start position:0%
+it's hard to explain because it's dry
+it's like explaining Insurance you know
+
+ align:start position:0%
+it's like explaining Insurance you know
+ 
+
+ align:start position:0%
+it's like explaining Insurance you know
+people get bored before they get it so
+
+ align:start position:0%
+people get bored before they get it so
+ 
+
+ align:start position:0%
+people get bored before they get it so
+media game can
+
+ align:start position:0%
+media game can
+ 
+
+ align:start position:0%
+media game can
+help
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motivate our team is working on forecast
+
+ align:start position:0%
+motivate our team is working on forecast
+ 
+
+ align:start position:0%
+motivate our team is working on forecast
+based financing so because we're about
+
+ align:start position:0%
+based financing so because we're about
+ 
+
+ align:start position:0%
+based financing so because we're about
+planning for disasters our game is
+
+ align:start position:0%
+planning for disasters our game is
+ 
+
+ align:start position:0%
+planning for disasters our game is
+pretty heavy on chance but what we want
+
+ align:start position:0%
+pretty heavy on chance but what we want
+ 
+
+ align:start position:0%
+pretty heavy on chance but what we want
+to teach the players to do is to use
+
+ align:start position:0%
+to teach the players to do is to use
+ 
+
+ align:start position:0%
+to teach the players to do is to use
+planning and forecasting in order to
+
+ align:start position:0%
+planning and forecasting in order to
+ 
+
+ align:start position:0%
+planning and forecasting in order to
+reduce the effects of that chance and
+
+ align:start position:0%
+reduce the effects of that chance and
+ 
+
+ align:start position:0%
+reduce the effects of that chance and
+sort of gain valuable skills in in uh
+
+ align:start position:0%
+sort of gain valuable skills in in uh
+ 
+
+ align:start position:0%
+sort of gain valuable skills in in uh
+mitigating that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically if you
+
+ align:start position:0%
+so basically if you
+ 
+
+ align:start position:0%
+so basically if you
+have there's one two three four five
+
+ align:start position:0%
+have there's one two three four five
+ 
+
+ align:start position:0%
+have there's one two three four five
+testers plus let's say each team send
+
+ align:start position:0%
+testers plus let's say each team send
+ 
+
+ align:start position:0%
+testers plus let's say each team send
+out two two people to test other games
+
+ align:start position:0%
+out two two people to test other games
+ 
+
+ align:start position:0%
+out two two people to test other games
+um remember remember to rotate we're
+
+ align:start position:0%
+um remember remember to rotate we're
+ 
+
+ align:start position:0%
+um remember remember to rotate we're
+going to do this for about 20 minutes as
+
+ align:start position:0%
+going to do this for about 20 minutes as
+ 
+
+ align:start position:0%
+going to do this for about 20 minutes as
+long as it takes and then see where we
+
+ align:start position:0%
+long as it takes and then see where we
+ 
+
+ align:start position:0%
+long as it takes and then see where we
+are and do it again um to get some just
+
+ align:start position:0%
+are and do it again um to get some just
+ 
+
+ align:start position:0%
+are and do it again um to get some just
+quick testing and make sure that the
+
+ align:start position:0%
+quick testing and make sure that the
+ 
+
+ align:start position:0%
+quick testing and make sure that the
+five of us get to play um a good number
+
+ align:start position:0%
+five of us get to play um a good number
+ 
+
+ align:start position:0%
+five of us get to play um a good number
+of your games and give you some some
+
+ align:start position:0%
+of your games and give you some some
+ 
+
+ align:start position:0%
+of your games and give you some some
+feedback on that so remember if you're
+
+ align:start position:0%
+feedback on that so remember if you're
+ 
+
+ align:start position:0%
+feedback on that so remember if you're
+using digital if you're not if a
+
+ align:start position:0%
+using digital if you're not if a
+ 
+
+ align:start position:0%
+using digital if you're not if a
+computer is not being used for testing
+
+ align:start position:0%
+computer is not being used for testing
+ 
+
+ align:start position:0%
+computer is not being used for testing
+close it or make it look like it's not
+
+ align:start position:0%
+close it or make it look like it's not
+ 
+
+ align:start position:0%
+close it or make it look like it's not
+being used for testing by typing on
+
+ align:start position:0%
+being used for testing by typing on
+ 
+
+ align:start position:0%
+being used for testing by typing on
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um all right let's get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+started I we forecast based funding the
+
+ align:start position:0%
+started I we forecast based funding the
+ 
+
+ align:start position:0%
+started I we forecast based funding the
+general idea behind our concept is that
+
+ align:start position:0%
+general idea behind our concept is that
+ 
+
+ align:start position:0%
+general idea behind our concept is that
+planning ahead for disasters is much
+
+ align:start position:0%
+planning ahead for disasters is much
+ 
+
+ align:start position:0%
+planning ahead for disasters is much
+better than trying to react to them so
+
+ align:start position:0%
+better than trying to react to them so
+ 
+
+ align:start position:0%
+better than trying to react to them so
+if you can have operating procedures or
+
+ align:start position:0%
+if you can have operating procedures or
+ 
+
+ align:start position:0%
+if you can have operating procedures or
+ways of planning for them and money
+
+ align:start position:0%
+ways of planning for them and money
+ 
+
+ align:start position:0%
+ways of planning for them and money
+allocated for that you can reduce loss
+
+ align:start position:0%
+allocated for that you can reduce loss
+ 
+
+ align:start position:0%
+allocated for that you can reduce loss
+of lives in the event of disasters we
+
+ align:start position:0%
+of lives in the event of disasters we
+ 
+
+ align:start position:0%
+of lives in the event of disasters we
+are actually between two prototypes
+
+ align:start position:0%
+are actually between two prototypes
+ 
+
+ align:start position:0%
+are actually between two prototypes
+right now that we're testing to try and
+
+ align:start position:0%
+right now that we're testing to try and
+ 
+
+ align:start position:0%
+right now that we're testing to try and
+get at the ideas the first one is a sort
+
+ align:start position:0%
+get at the ideas the first one is a sort
+ 
+
+ align:start position:0%
+get at the ideas the first one is a sort
+of higher level city-based simulation of
+
+ align:start position:0%
+of higher level city-based simulation of
+ 
+
+ align:start position:0%
+of higher level city-based simulation of
+cities at risk of disaster which you
+
+ align:start position:0%
+cities at risk of disaster which you
+ 
+
+ align:start position:0%
+cities at risk of disaster which you
+then have to fortify by training
+
+ align:start position:0%
+then have to fortify by training
+ 
+
+ align:start position:0%
+then have to fortify by training
+volunteers or preparing for upcoming
+
+ align:start position:0%
+volunteers or preparing for upcoming
+ 
+
+ align:start position:0%
+volunteers or preparing for upcoming
+disasters uh in order to prevent too
+
+ align:start position:0%
+disasters uh in order to prevent too
+ 
+
+ align:start position:0%
+disasters uh in order to prevent too
+much damage from happening to them uh
+
+ align:start position:0%
+much damage from happening to them uh
+ 
+
+ align:start position:0%
+much damage from happening to them uh
+one of the problems that we're seeing
+
+ align:start position:0%
+one of the problems that we're seeing
+ 
+
+ align:start position:0%
+one of the problems that we're seeing
+with the game is that it's kind of
+
+ align:start position:0%
+with the game is that it's kind of
+ 
+
+ align:start position:0%
+with the game is that it's kind of
+abstract and not as uh interactive for
+
+ align:start position:0%
+abstract and not as uh interactive for
+ 
+
+ align:start position:0%
+abstract and not as uh interactive for
+players to connect with but they are
+
+ align:start position:0%
+players to connect with but they are
+ 
+
+ align:start position:0%
+players to connect with but they are
+getting a good understanding of the idea
+
+ align:start position:0%
+getting a good understanding of the idea
+ 
+
+ align:start position:0%
+getting a good understanding of the idea
+of planning ahead yeah and so to try and
+
+ align:start position:0%
+of planning ahead yeah and so to try and
+ 
+
+ align:start position:0%
+of planning ahead yeah and so to try and
+address those issues we have a second
+
+ align:start position:0%
+address those issues we have a second
+ 
+
+ align:start position:0%
+address those issues we have a second
+prototype right now which is about um
+
+ align:start position:0%
+prototype right now which is about um
+ 
+
+ align:start position:0%
+prototype right now which is about um
+trying to actually like rescue
+
+ align:start position:0%
+trying to actually like rescue
+ 
+
+ align:start position:0%
+trying to actually like rescue
+volunteers in a flooding I uh rescue
+
+ align:start position:0%
+volunteers in a flooding I uh rescue
+ 
+
+ align:start position:0%
+volunteers in a flooding I uh rescue
+people in a flooding City and so that
+
+ align:start position:0%
+people in a flooding City and so that
+ 
+
+ align:start position:0%
+people in a flooding City and so that
+hits the other end of this scale where
+
+ align:start position:0%
+hits the other end of this scale where
+ 
+
+ align:start position:0%
+hits the other end of this scale where
+the player is told ahead of time this um
+
+ align:start position:0%
+the player is told ahead of time this um
+ 
+
+ align:start position:0%
+the player is told ahead of time this um
+This Disaster was planned for versus
+
+ align:start position:0%
+This Disaster was planned for versus
+ 
+
+ align:start position:0%
+This Disaster was planned for versus
+This Disaster was not planned for and
+
+ align:start position:0%
+This Disaster was not planned for and
+ 
+
+ align:start position:0%
+This Disaster was not planned for and
+the like the uh appropriate effects for
+
+ align:start position:0%
+the like the uh appropriate effects for
+ 
+
+ align:start position:0%
+the like the uh appropriate effects for
+each and then they have to rescue people
+
+ align:start position:0%
+each and then they have to rescue people
+ 
+
+ align:start position:0%
+each and then they have to rescue people
+under those two different conditions and
+
+ align:start position:0%
+under those two different conditions and
+ 
+
+ align:start position:0%
+under those two different conditions and
+then they get to directly compare like
+
+ align:start position:0%
+then they get to directly compare like
+ 
+
+ align:start position:0%
+then they get to directly compare like
+what the experience of is for like um
+
+ align:start position:0%
+what the experience of is for like um
+ 
+
+ align:start position:0%
+what the experience of is for like um
+acting in one circumstance versus the
+
+ align:start position:0%
+acting in one circumstance versus the
+ 
+
+ align:start position:0%
+acting in one circumstance versus the
+other over the next couple days we'll be
+
+ align:start position:0%
+other over the next couple days we'll be
+ 
+
+ align:start position:0%
+other over the next couple days we'll be
+looking at what we learn from both of
+
+ align:start position:0%
+looking at what we learn from both of
+ 
+
+ align:start position:0%
+looking at what we learn from both of
+them trying to either combine them or
+
+ align:start position:0%
+them trying to either combine them or
+ 
+
+ align:start position:0%
+them trying to either combine them or
+pull out the parts that we thought were
+
+ align:start position:0%
+pull out the parts that we thought were
+ 
+
+ align:start position:0%
+pull out the parts that we thought were
+really useful to make a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comp this's the hard one yeah we ass
+
+ align:start position:0%
+comp this's the hard one yeah we ass
+ 
+
+ align:start position:0%
+comp this's the hard one yeah we ass
+this uh it was I think it was stated a
+
+ align:start position:0%
+this uh it was I think it was stated a
+ 
+
+ align:start position:0%
+this uh it was I think it was stated a
+couple of times that we should be
+
+ align:start position:0%
+couple of times that we should be
+ 
+
+ align:start position:0%
+couple of times that we should be
+looking at people like policy makers or
+
+ align:start position:0%
+looking at people like policy makers or
+ 
+
+ align:start position:0%
+looking at people like policy makers or
+donors in the sense of sort of people
+
+ align:start position:0%
+donors in the sense of sort of people
+ 
+
+ align:start position:0%
+donors in the sense of sort of people
+who would be allocating funds from
+
+ align:start position:0%
+who would be allocating funds from
+ 
+
+ align:start position:0%
+who would be allocating funds from
+governments or nonprofits things like
+
+ align:start position:0%
+governments or nonprofits things like
+ 
+
+ align:start position:0%
+governments or nonprofits things like
+that uh basically to make it clear that
+
+ align:start position:0%
+that uh basically to make it clear that
+ 
+
+ align:start position:0%
+that uh basically to make it clear that
+this type of planning ahead is a good
+
+ align:start position:0%
+this type of planning ahead is a good
+ 
+
+ align:start position:0%
+this type of planning ahead is a good
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um oh and what have you decided on
+
+ align:start position:0%
+um oh and what have you decided on
+ 
+
+ align:start position:0%
+um oh and what have you decided on
+technology yet or you still not there
+
+ align:start position:0%
+technology yet or you still not there
+ 
+
+ align:start position:0%
+technology yet or you still not there
+yet uh we're probably using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phaser all right thank
+
+ align:start position:0%
+phaser all right thank
+ 
+
+ align:start position:0%
+phaser all right thank
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you our game uh is called hello waves we
+
+ align:start position:0%
+you our game uh is called hello waves we
+ 
+
+ align:start position:0%
+you our game uh is called hello waves we
+don't have a title screen in yet but the
+
+ align:start position:0%
+don't have a title screen in yet but the
+ 
+
+ align:start position:0%
+don't have a title screen in yet but the
+idea is still forecast based
+
+ align:start position:0%
+idea is still forecast based
+ 
+
+ align:start position:0%
+idea is still forecast based
+financing uh so it's a little washed out
+
+ align:start position:0%
+financing uh so it's a little washed out
+ 
+
+ align:start position:0%
+financing uh so it's a little washed out
+on there but if you can see there these
+
+ align:start position:0%
+on there but if you can see there these
+ 
+
+ align:start position:0%
+on there but if you can see there these
+different these five different sand
+
+ align:start position:0%
+different these five different sand
+ 
+
+ align:start position:0%
+different these five different sand
+castles with workers associated with
+
+ align:start position:0%
+castles with workers associated with
+ 
+
+ align:start position:0%
+castles with workers associated with
+each and up here in the corner we have a
+
+ align:start position:0%
+each and up here in the corner we have a
+ 
+
+ align:start position:0%
+each and up here in the corner we have a
+forecast of what the water level will be
+
+ align:start position:0%
+forecast of what the water level will be
+ 
+
+ align:start position:0%
+forecast of what the water level will be
+like in a couple days this is the water
+
+ align:start position:0%
+like in a couple days this is the water
+ 
+
+ align:start position:0%
+like in a couple days this is the water
+level right here and throughout the game
+
+ align:start position:0%
+level right here and throughout the game
+ 
+
+ align:start position:0%
+level right here and throughout the game
+it'll rise and fall and the idea is not
+
+ align:start position:0%
+it'll rise and fall and the idea is not
+ 
+
+ align:start position:0%
+it'll rise and fall and the idea is not
+to let your workers uh get drowned by
+
+ align:start position:0%
+to let your workers uh get drowned by
+ 
+
+ align:start position:0%
+to let your workers uh get drowned by
+the rising water the other aspect of the
+
+ align:start position:0%
+the rising water the other aspect of the
+ 
+
+ align:start position:0%
+the rising water the other aspect of the
+game though is that you have a certain
+
+ align:start position:0%
+game though is that you have a certain
+ 
+
+ align:start position:0%
+game though is that you have a certain
+amount of supplies and whenever you move
+
+ align:start position:0%
+amount of supplies and whenever you move
+ 
+
+ align:start position:0%
+amount of supplies and whenever you move
+someone from their Castle in order to
+
+ align:start position:0%
+someone from their Castle in order to
+ 
+
+ align:start position:0%
+someone from their Castle in order to
+prevent them from getting drowned they
+
+ align:start position:0%
+prevent them from getting drowned they
+ 
+
+ align:start position:0%
+prevent them from getting drowned they
+will consume supplies from that stock
+
+ align:start position:0%
+will consume supplies from that stock
+ 
+
+ align:start position:0%
+will consume supplies from that stock
+and if you don't have enough supplies
+
+ align:start position:0%
+and if you don't have enough supplies
+ 
+
+ align:start position:0%
+and if you don't have enough supplies
+and they'll take
+
+ align:start position:0%
+and they'll take
+ 
+
+ align:start position:0%
+and they'll take
+damage
+
+ align:start position:0%
+damage
+ 
+
+ align:start position:0%
+damage
+so as you can see right now everybody's
+
+ align:start position:0%
+so as you can see right now everybody's
+ 
+
+ align:start position:0%
+so as you can see right now everybody's
+in their own castle if we click next
+
+ align:start position:0%
+in their own castle if we click next
+ 
+
+ align:start position:0%
+in their own castle if we click next
+turn the water level will change and
+
+ align:start position:0%
+turn the water level will change and
+ 
+
+ align:start position:0%
+turn the water level will change and
+we'll see that the forecast will update
+
+ align:start position:0%
+we'll see that the forecast will update
+ 
+
+ align:start position:0%
+we'll see that the forecast will update
+we have a range of values on this
+
+ align:start position:0%
+we have a range of values on this
+ 
+
+ align:start position:0%
+we have a range of values on this
+forecast uh a high prediction and a low
+
+ align:start position:0%
+forecast uh a high prediction and a low
+ 
+
+ align:start position:0%
+forecast uh a high prediction and a low
+prediction and if if you Mouse over any
+
+ align:start position:0%
+prediction and if if you Mouse over any
+ 
+
+ align:start position:0%
+prediction and if if you Mouse over any
+of the castles you'll see a red line
+
+ align:start position:0%
+of the castles you'll see a red line
+ 
+
+ align:start position:0%
+of the castles you'll see a red line
+appear on the forecast just to help you
+
+ align:start position:0%
+appear on the forecast just to help you
+ 
+
+ align:start position:0%
+appear on the forecast just to help you
+Orient what Heights uh are on the
+
+ align:start position:0%
+Orient what Heights uh are on the
+ 
+
+ align:start position:0%
+Orient what Heights uh are on the
+forecast or if you're looking at the
+
+ align:start position:0%
+forecast or if you're looking at the
+ 
+
+ align:start position:0%
+forecast or if you're looking at the
+forecast what it is in the real world so
+
+ align:start position:0%
+forecast what it is in the real world so
+ 
+
+ align:start position:0%
+forecast what it is in the real world so
+you can see the water move over these
+
+ align:start position:0%
+you can see the water move over these
+ 
+
+ align:start position:0%
+you can see the water move over these
+couple days right now the forecast is
+
+ align:start position:0%
+couple days right now the forecast is
+ 
+
+ align:start position:0%
+couple days right now the forecast is
+pretty low if we see that it's kind of
+
+ align:start position:0%
+pretty low if we see that it's kind of
+ 
+
+ align:start position:0%
+pretty low if we see that it's kind of
+getting close and we're worried about
+
+ align:start position:0%
+getting close and we're worried about
+ 
+
+ align:start position:0%
+getting close and we're worried about
+someone we can click and drag them to
+
+ align:start position:0%
+someone we can click and drag them to
+ 
+
+ align:start position:0%
+someone we can click and drag them to
+another castle and on the next turn
+
+ align:start position:0%
+another castle and on the next turn
+ 
+
+ align:start position:0%
+another castle and on the next turn
+they'll move
+
+ align:start position:0%
+they'll move
+ 
+
+ align:start position:0%
+they'll move
+over you can also click people to toggle
+
+ align:start position:0%
+over you can also click people to toggle
+ 
+
+ align:start position:0%
+over you can also click people to toggle
+between building and Gathering uh it's
+
+ align:start position:0%
+between building and Gathering uh it's
+ 
+
+ align:start position:0%
+between building and Gathering uh it's
+very hard to see the status text right
+
+ align:start position:0%
+very hard to see the status text right
+ 
+
+ align:start position:0%
+very hard to see the status text right
+now because it's small we threw that in
+
+ align:start position:0%
+now because it's small we threw that in
+ 
+
+ align:start position:0%
+now because it's small we threw that in
+quickly for right now uh but he is set
+
+ align:start position:0%
+quickly for right now uh but he is set
+ 
+
+ align:start position:0%
+quickly for right now uh but he is set
+to building and he these three are set
+
+ align:start position:0%
+to building and he these three are set
+ 
+
+ align:start position:0%
+to building and he these three are set
+to Gathering so we'll see that each turn
+
+ align:start position:0%
+to Gathering so we'll see that each turn
+ 
+
+ align:start position:0%
+to Gathering so we'll see that each turn
+these three will gather one Supply each
+
+ align:start position:0%
+these three will gather one Supply each
+ 
+
+ align:start position:0%
+these three will gather one Supply each
+this teddy bear will consume one so
+
+ align:start position:0%
+this teddy bear will consume one so
+ 
+
+ align:start position:0%
+this teddy bear will consume one so
+we'll see supplies go up by two and
+
+ align:start position:0%
+we'll see supplies go up by two and
+ 
+
+ align:start position:0%
+we'll see supplies go up by two and
+victory progress will go up by
+
+ align:start position:0%
+victory progress will go up by
+ 
+
+ align:start position:0%
+victory progress will go up by
+one what we have planned for the rest of
+
+ align:start position:0%
+one what we have planned for the rest of
+ 
+
+ align:start position:0%
+one what we have planned for the rest of
+the game is we've made a lot of progress
+
+ align:start position:0%
+the game is we've made a lot of progress
+ 
+
+ align:start position:0%
+the game is we've made a lot of progress
+in terms of the intuitiveness of our
+
+ align:start position:0%
+in terms of the intuitiveness of our
+ 
+
+ align:start position:0%
+in terms of the intuitiveness of our
+game once you understand it but right
+
+ align:start position:0%
+game once you understand it but right
+ 
+
+ align:start position:0%
+game once you understand it but right
+now there's a lot in the game that isn't
+
+ align:start position:0%
+now there's a lot in the game that isn't
+ 
+
+ align:start position:0%
+now there's a lot in the game that isn't
+explained from the get-go and so uh if I
+
+ align:start position:0%
+explained from the get-go and so uh if I
+ 
+
+ align:start position:0%
+explained from the get-go and so uh if I
+give that Spiel to anyone they can play
+
+ align:start position:0%
+give that Spiel to anyone they can play
+ 
+
+ align:start position:0%
+give that Spiel to anyone they can play
+the game fine and uh they do pretty well
+
+ align:start position:0%
+the game fine and uh they do pretty well
+ 
+
+ align:start position:0%
+the game fine and uh they do pretty well
+with it but if you just open up the game
+
+ align:start position:0%
+with it but if you just open up the game
+ 
+
+ align:start position:0%
+with it but if you just open up the game
+you're lost so a lot of our work is
+
+ align:start position:0%
+you're lost so a lot of our work is
+ 
+
+ align:start position:0%
+you're lost so a lot of our work is
+going to be on the UI of making things
+
+ align:start position:0%
+going to be on the UI of making things
+ 
+
+ align:start position:0%
+going to be on the UI of making things
+more self-evident and making sure that
+
+ align:start position:0%
+more self-evident and making sure that
+ 
+
+ align:start position:0%
+more self-evident and making sure that
+people can understand what's going on
+
+ align:start position:0%
+people can understand what's going on
+ 
+
+ align:start position:0%
+people can understand what's going on
+and what their actions will do without
+
+ align:start position:0%
+and what their actions will do without
+ 
+
+ align:start position:0%
+and what their actions will do without
+me having to stand there and tell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I'm G to ask you again um
+
+ align:start position:0%
+all right so I'm G to ask you again um
+ 
+
+ align:start position:0%
+all right so I'm G to ask you again um
+what is your biggest risk going forward
+
+ align:start position:0%
+what is your biggest risk going forward
+ 
+
+ align:start position:0%
+what is your biggest risk going forward
+so I mean I think um in terms of our
+
+ align:start position:0%
+so I mean I think um in terms of our
+ 
+
+ align:start position:0%
+so I mean I think um in terms of our
+technical implementation we've already
+
+ align:start position:0%
+technical implementation we've already
+ 
+
+ align:start position:0%
+technical implementation we've already
+got good play tests of our work done and
+
+ align:start position:0%
+got good play tests of our work done and
+ 
+
+ align:start position:0%
+got good play tests of our work done and
+we have like all of our major Graphics
+
+ align:start position:0%
+we have like all of our major Graphics
+ 
+
+ align:start position:0%
+we have like all of our major Graphics
+in and things like that so I think our
+
+ align:start position:0%
+in and things like that so I think our
+ 
+
+ align:start position:0%
+in and things like that so I think our
+major risk going ahead is not being able
+
+ align:start position:0%
+major risk going ahead is not being able
+ 
+
+ align:start position:0%
+major risk going ahead is not being able
+to explain the game properly and so even
+
+ align:start position:0%
+to explain the game properly and so even
+ 
+
+ align:start position:0%
+to explain the game properly and so even
+if we have a finished product like it
+
+ align:start position:0%
+if we have a finished product like it
+ 
+
+ align:start position:0%
+if we have a finished product like it
+may may may still not be playable if we
+
+ align:start position:0%
+may may may still not be playable if we
+ 
+
+ align:start position:0%
+may may may still not be playable if we
+don't write good
+
+ align:start position:0%
+don't write good
+ 
+
+ align:start position:0%
+don't write good
+instructions all right so on that front
+
+ align:start position:0%
+instructions all right so on that front
+ 
+
+ align:start position:0%
+instructions all right so on that front
+think of uh
+
+ align:start position:0%
+think of uh
+ 
+
+ align:start position:0%
+think of uh
+incremental uh addition of features so
+
+ align:start position:0%
+incremental uh addition of features so
+ 
+
+ align:start position:0%
+incremental uh addition of features so
+the game begins with a super simple even
+
+ align:start position:0%
+the game begins with a super simple even
+ 
+
+ align:start position:0%
+the game begins with a super simple even
+maybe too boring choice but then a new
+
+ align:start position:0%
+maybe too boring choice but then a new
+ 
+
+ align:start position:0%
+maybe too boring choice but then a new
+Choice arrives so the the learning by
+
+ align:start position:0%
+Choice arrives so the the learning by
+ 
+
+ align:start position:0%
+Choice arrives so the the learning by
+playing can be staggered uh in a way
+
+ align:start position:0%
+playing can be staggered uh in a way
+ 
+
+ align:start position:0%
+playing can be staggered uh in a way
+that is that is intuitive good good luck
+
+ align:start position:0%
+that is that is intuitive good good luck
+ 
+
+ align:start position:0%
+that is that is intuitive good good luck
+to you and uh we'll talk more about uh
+
+ align:start position:0%
+to you and uh we'll talk more about uh
+ 
+
+ align:start position:0%
+to you and uh we'll talk more about uh
+choices later but okay I by I should say
+
+ align:start position:0%
+choices later but okay I by I should say
+ 
+
+ align:start position:0%
+choices later but okay I by I should say
+that this High versus low prediction is
+
+ align:start position:0%
+that this High versus low prediction is
+ 
+
+ align:start position:0%
+that this High versus low prediction is
+something that I wish scientists did
+
+ align:start position:0%
+something that I wish scientists did
+ 
+
+ align:start position:0%
+something that I wish scientists did
+like you're doing because most people
+
+ align:start position:0%
+like you're doing because most people
+ 
+
+ align:start position:0%
+like you're doing because most people
+say one value and then it's not that
+
+ align:start position:0%
+say one value and then it's not that
+ 
+
+ align:start position:0%
+say one value and then it's not that
+value here everyone does for good thank
+
+ align:start position:0%
+value here everyone does for good thank
+ 
+
+ align:start position:0%
+value here everyone does for good thank
+you thank
+
+ align:start position:0%
+you thank
+ 
+
+ align:start position:0%
+you thank
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+you anyway come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down okay so it's a little light on
+
+ align:start position:0%
+down okay so it's a little light on
+ 
+
+ align:start position:0%
+down okay so it's a little light on
+there but our game is hello waves it's a
+
+ align:start position:0%
+there but our game is hello waves it's a
+ 
+
+ align:start position:0%
+there but our game is hello waves it's a
+game about forecast based financing that
+
+ align:start position:0%
+game about forecast based financing that
+ 
+
+ align:start position:0%
+game about forecast based financing that
+we're developing for the Red Cross the
+
+ align:start position:0%
+we're developing for the Red Cross the
+ 
+
+ align:start position:0%
+we're developing for the Red Cross the
+idea of forecast based financing is
+
+ align:start position:0%
+idea of forecast based financing is
+ 
+
+ align:start position:0%
+idea of forecast based financing is
+using the idea of forecast about the
+
+ align:start position:0%
+using the idea of forecast about the
+ 
+
+ align:start position:0%
+using the idea of forecast about the
+future in order to make decisions that
+
+ align:start position:0%
+future in order to make decisions that
+ 
+
+ align:start position:0%
+future in order to make decisions that
+are more effective than just reacting to
+
+ align:start position:0%
+are more effective than just reacting to
+ 
+
+ align:start position:0%
+are more effective than just reacting to
+disasters when they happen so uh I'd
+
+ align:start position:0%
+disasters when they happen so uh I'd
+ 
+
+ align:start position:0%
+disasters when they happen so uh I'd
+like to show you a playthrough of our
+
+ align:start position:0%
+like to show you a playthrough of our
+ 
+
+ align:start position:0%
+like to show you a playthrough of our
+game so uh I said hello waves here are
+
+ align:start position:0%
+game so uh I said hello waves here are
+ 
+
+ align:start position:0%
+game so uh I said hello waves here are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+instructions uh we would have done a
+
+ align:start position:0%
+instructions uh we would have done a
+ 
+
+ align:start position:0%
+instructions uh we would have done a
+tutorial if we had enough time but this
+
+ align:start position:0%
+tutorial if we had enough time but this
+ 
+
+ align:start position:0%
+tutorial if we had enough time but this
+gets the idea across uh and uh designing
+
+ align:start position:0%
+gets the idea across uh and uh designing
+ 
+
+ align:start position:0%
+gets the idea across uh and uh designing
+a a good tutorial that actually teaches
+
+ align:start position:0%
+a a good tutorial that actually teaches
+ 
+
+ align:start position:0%
+a a good tutorial that actually teaches
+the player well is kind of hard to do in
+
+ align:start position:0%
+the player well is kind of hard to do in
+ 
+
+ align:start position:0%
+the player well is kind of hard to do in
+a a logical flow so we have these
+
+ align:start position:0%
+a a logical flow so we have these
+ 
+
+ align:start position:0%
+a a logical flow so we have these
+instructions that explain how to play
+
+ align:start position:0%
+instructions that explain how to play
+ 
+
+ align:start position:0%
+instructions that explain how to play
+what the point of the game is and uh a
+
+ align:start position:0%
+what the point of the game is and uh a
+ 
+
+ align:start position:0%
+what the point of the game is and uh a
+couple of tips about how the game
+
+ align:start position:0%
+couple of tips about how the game
+ 
+
+ align:start position:0%
+couple of tips about how the game
+works so if we go into the play screen
+
+ align:start position:0%
+works so if we go into the play screen
+ 
+
+ align:start position:0%
+works so if we go into the play screen
+you can see something similar to uh what
+
+ align:start position:0%
+you can see something similar to uh what
+ 
+
+ align:start position:0%
+you can see something similar to uh what
+we showed you a couple weeks ago where
+
+ align:start position:0%
+we showed you a couple weeks ago where
+ 
+
+ align:start position:0%
+we showed you a couple weeks ago where
+you have all these different toys at
+
+ align:start position:0%
+you have all these different toys at
+ 
+
+ align:start position:0%
+you have all these different toys at
+their castles and as you go through the
+
+ align:start position:0%
+their castles and as you go through the
+ 
+
+ align:start position:0%
+their castles and as you go through the
+days you'll see a forecast of what the
+
+ align:start position:0%
+days you'll see a forecast of what the
+ 
+
+ align:start position:0%
+days you'll see a forecast of what the
+water level's going to be at over time
+
+ align:start position:0%
+water level's going to be at over time
+ 
+
+ align:start position:0%
+water level's going to be at over time
+and so you can see that right now
+
+ align:start position:0%
+and so you can see that right now
+ 
+
+ align:start position:0%
+and so you can see that right now
+Gathering candy the water level will
+
+ align:start position:0%
+Gathering candy the water level will
+ 
+
+ align:start position:0%
+Gathering candy the water level will
+change this character is underwater and
+
+ align:start position:0%
+change this character is underwater and
+ 
+
+ align:start position:0%
+change this character is underwater and
+so he takes damage and so what you
+
+ align:start position:0%
+so he takes damage and so what you
+ 
+
+ align:start position:0%
+so he takes damage and so what you
+actually want to do is you want to move
+
+ align:start position:0%
+actually want to do is you want to move
+ 
+
+ align:start position:0%
+actually want to do is you want to move
+toys out of the water so that they don't
+
+ align:start position:0%
+toys out of the water so that they don't
+ 
+
+ align:start position:0%
+toys out of the water so that they don't
+get damaged however they can only move
+
+ align:start position:0%
+get damaged however they can only move
+ 
+
+ align:start position:0%
+get damaged however they can only move
+one Castle over at a time so because we
+
+ align:start position:0%
+one Castle over at a time so because we
+ 
+
+ align:start position:0%
+one Castle over at a time so because we
+didn't think ahead well enough we'll see
+
+ align:start position:0%
+didn't think ahead well enough we'll see
+ 
+
+ align:start position:0%
+didn't think ahead well enough we'll see
+that this truck will actually take
+
+ align:start position:0%
+that this truck will actually take
+ 
+
+ align:start position:0%
+that this truck will actually take
+damage on the next turn because he's
+
+ align:start position:0%
+damage on the next turn because he's
+ 
+
+ align:start position:0%
+damage on the next turn because he's
+underwater actually he ended up not
+
+ align:start position:0%
+underwater actually he ended up not
+ 
+
+ align:start position:0%
+underwater actually he ended up not
+underwater we got lucky there but
+
+ align:start position:0%
+underwater we got lucky there but
+ 
+
+ align:start position:0%
+underwater we got lucky there but
+theoretically he he would have and so as
+
+ align:start position:0%
+theoretically he he would have and so as
+ 
+
+ align:start position:0%
+theoretically he he would have and so as
+you go through it the end goal of the
+
+ align:start position:0%
+you go through it the end goal of the
+ 
+
+ align:start position:0%
+you go through it the end goal of the
+game is to build a castle uh and so
+
+ align:start position:0%
+game is to build a castle uh and so
+ 
+
+ align:start position:0%
+game is to build a castle uh and so
+every toy when they're home can either
+
+ align:start position:0%
+every toy when they're home can either
+ 
+
+ align:start position:0%
+every toy when they're home can either
+choose between Gathering candy to feed
+
+ align:start position:0%
+choose between Gathering candy to feed
+ 
+
+ align:start position:0%
+choose between Gathering candy to feed
+evacuated toys or building the castle to
+
+ align:start position:0%
+evacuated toys or building the castle to
+ 
+
+ align:start position:0%
+evacuated toys or building the castle to
+reach your end goal of the game and then
+
+ align:start position:0%
+reach your end goal of the game and then
+ 
+
+ align:start position:0%
+reach your end goal of the game and then
+the idea of the forecast is that you
+
+ align:start position:0%
+the idea of the forecast is that you
+ 
+
+ align:start position:0%
+the idea of the forecast is that you
+want to use the forecast in order to
+
+ align:start position:0%
+want to use the forecast in order to
+ 
+
+ align:start position:0%
+want to use the forecast in order to
+know how much candy you're going to need
+
+ align:start position:0%
+know how much candy you're going to need
+ 
+
+ align:start position:0%
+know how much candy you're going to need
+over the next couple days and to use it
+
+ align:start position:0%
+over the next couple days and to use it
+ 
+
+ align:start position:0%
+over the next couple days and to use it
+to know when you are going to need to
+
+ align:start position:0%
+to know when you are going to need to
+ 
+
+ align:start position:0%
+to know when you are going to need to
+evacuate various toys from their
+
+ align:start position:0%
+evacuate various toys from their
+ 
+
+ align:start position:0%
+evacuate various toys from their
+variously heighted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+homes so back to the presid
+
+ align:start position:0%
+homes so back to the presid
+ 
+
+ align:start position:0%
+homes so back to the presid
+presentation full
+
+ align:start position:0%
+presentation full
+ 
+
+ align:start position:0%
+presentation full
+screen so we had a couple of challenges
+
+ align:start position:0%
+screen so we had a couple of challenges
+ 
+
+ align:start position:0%
+screen so we had a couple of challenges
+in the design process the first and the
+
+ align:start position:0%
+in the design process the first and the
+ 
+
+ align:start position:0%
+in the design process the first and the
+major one is really that we were trying
+
+ align:start position:0%
+major one is really that we were trying
+ 
+
+ align:start position:0%
+major one is really that we were trying
+to teach about forecast-based
+
+ align:start position:0%
+to teach about forecast-based
+ 
+
+ align:start position:0%
+to teach about forecast-based
+financing which was a bit of an abstract
+
+ align:start position:0%
+financing which was a bit of an abstract
+ 
+
+ align:start position:0%
+financing which was a bit of an abstract
+topic it's a little different than just
+
+ align:start position:0%
+topic it's a little different than just
+ 
+
+ align:start position:0%
+topic it's a little different than just
+thinking long term because you have to
+
+ align:start position:0%
+thinking long term because you have to
+ 
+
+ align:start position:0%
+thinking long term because you have to
+use the idea of there's some information
+
+ align:start position:0%
+use the idea of there's some information
+ 
+
+ align:start position:0%
+use the idea of there's some information
+we know about the future that we want to
+
+ align:start position:0%
+we know about the future that we want to
+ 
+
+ align:start position:0%
+we know about the future that we want to
+use to make optimal decisions or at
+
+ align:start position:0%
+use to make optimal decisions or at
+ 
+
+ align:start position:0%
+use to make optimal decisions or at
+least decisions based on some idea of
+
+ align:start position:0%
+least decisions based on some idea of
+ 
+
+ align:start position:0%
+least decisions based on some idea of
+the risk that that's out there but we
+
+ align:start position:0%
+the risk that that's out there but we
+ 
+
+ align:start position:0%
+the risk that that's out there but we
+also wanted to avoid things like just
+
+ align:start position:0%
+also wanted to avoid things like just
+ 
+
+ align:start position:0%
+also wanted to avoid things like just
+pushing a button to win where you have
+
+ align:start position:0%
+pushing a button to win where you have
+ 
+
+ align:start position:0%
+pushing a button to win where you have
+all the information you ever need and
+
+ align:start position:0%
+all the information you ever need and
+ 
+
+ align:start position:0%
+all the information you ever need and
+there's just one option that you know
+
+ align:start position:0%
+there's just one option that you know
+ 
+
+ align:start position:0%
+there's just one option that you know
+you're going to pick every time and the
+
+ align:start position:0%
+you're going to pick every time and the
+ 
+
+ align:start position:0%
+you're going to pick every time and the
+game has no thought whatsoever and we
+
+ align:start position:0%
+game has no thought whatsoever and we
+ 
+
+ align:start position:0%
+game has no thought whatsoever and we
+also needed to think about how we are
+
+ align:start position:0%
+also needed to think about how we are
+ 
+
+ align:start position:0%
+also needed to think about how we are
+going to communicate the forecast to the
+
+ align:start position:0%
+going to communicate the forecast to the
+ 
+
+ align:start position:0%
+going to communicate the forecast to the
+player so that they could then use that
+
+ align:start position:0%
+player so that they could then use that
+ 
+
+ align:start position:0%
+player so that they could then use that
+to make
+
+ align:start position:0%
+to make
+ 
+
+ align:start position:0%
+to make
+decisions uh one of the problems that we
+
+ align:start position:0%
+decisions uh one of the problems that we
+ 
+
+ align:start position:0%
+decisions uh one of the problems that we
+also ran into related to this was that
+
+ align:start position:0%
+also ran into related to this was that
+ 
+
+ align:start position:0%
+also ran into related to this was that
+we focused a lot on the idea of forecast
+
+ align:start position:0%
+we focused a lot on the idea of forecast
+ 
+
+ align:start position:0%
+we focused a lot on the idea of forecast
+based financing as the topic and then
+
+ align:start position:0%
+based financing as the topic and then
+ 
+
+ align:start position:0%
+based financing as the topic and then
+tried to build a game built on top of
+
+ align:start position:0%
+tried to build a game built on top of
+ 
+
+ align:start position:0%
+tried to build a game built on top of
+that topic instead of building a game
+
+ align:start position:0%
+that topic instead of building a game
+ 
+
+ align:start position:0%
+that topic instead of building a game
+that use forecast based financing so
+
+ align:start position:0%
+that use forecast based financing so
+ 
+
+ align:start position:0%
+that use forecast based financing so
+that held us back a lot in the beginning
+
+ align:start position:0%
+that held us back a lot in the beginning
+ 
+
+ align:start position:0%
+that held us back a lot in the beginning
+when we were trying to come up with
+
+ align:start position:0%
+when we were trying to come up with
+ 
+
+ align:start position:0%
+when we were trying to come up with
+ideas we also had a really difficult
+
+ align:start position:0%
+ideas we also had a really difficult
+ 
+
+ align:start position:0%
+ideas we also had a really difficult
+initial targeted audience of policy
+
+ align:start position:0%
+initial targeted audience of policy
+ 
+
+ align:start position:0%
+initial targeted audience of policy
+makers 50 60 year-old uh government
+
+ align:start position:0%
+makers 50 60 year-old uh government
+ 
+
+ align:start position:0%
+makers 50 60 year-old uh government
+officials or people at NOS who are going
+
+ align:start position:0%
+officials or people at NOS who are going
+ 
+
+ align:start position:0%
+officials or people at NOS who are going
+to be using forecast to make decisions
+
+ align:start position:0%
+to be using forecast to make decisions
+ 
+
+ align:start position:0%
+to be using forecast to make decisions
+of some sort and it was supposed to
+
+ align:start position:0%
+of some sort and it was supposed to
+ 
+
+ align:start position:0%
+of some sort and it was supposed to
+teach them about how they can use
+
+ align:start position:0%
+teach them about how they can use
+ 
+
+ align:start position:0%
+teach them about how they can use
+forecast to make these decisions except
+
+ align:start position:0%
+forecast to make these decisions except
+ 
+
+ align:start position:0%
+forecast to make these decisions except
+this was a really difficult audience
+
+ align:start position:0%
+this was a really difficult audience
+ 
+
+ align:start position:0%
+this was a really difficult audience
+because they don't generally play games
+
+ align:start position:0%
+because they don't generally play games
+ 
+
+ align:start position:0%
+because they don't generally play games
+and uh they don't have a lot of time to
+
+ align:start position:0%
+and uh they don't have a lot of time to
+ 
+
+ align:start position:0%
+and uh they don't have a lot of time to
+learn about this kind of thing and so we
+
+ align:start position:0%
+learn about this kind of thing and so we
+ 
+
+ align:start position:0%
+learn about this kind of thing and so we
+couldn't really expect to get them to
+
+ align:start position:0%
+couldn't really expect to get them to
+ 
+
+ align:start position:0%
+couldn't really expect to get them to
+sit down for a long period of time and
+
+ align:start position:0%
+sit down for a long period of time and
+ 
+
+ align:start position:0%
+sit down for a long period of time and
+play around with our
+
+ align:start position:0%
+play around with our
+ 
+
+ align:start position:0%
+play around with our
+game in order to deal with these
+
+ align:start position:0%
+game in order to deal with these
+ 
+
+ align:start position:0%
+game in order to deal with these
+problems we came up with a couple
+
+ align:start position:0%
+problems we came up with a couple
+ 
+
+ align:start position:0%
+problems we came up with a couple
+Solutions the first thing was that we
+
+ align:start position:0%
+Solutions the first thing was that we
+ 
+
+ align:start position:0%
+Solutions the first thing was that we
+had no idea what kind of game would work
+
+ align:start position:0%
+had no idea what kind of game would work
+ 
+
+ align:start position:0%
+had no idea what kind of game would work
+or would make sense or anything like
+
+ align:start position:0%
+or would make sense or anything like
+ 
+
+ align:start position:0%
+or would make sense or anything like
+that so what we did is we just broke up
+
+ align:start position:0%
+that so what we did is we just broke up
+ 
+
+ align:start position:0%
+that so what we did is we just broke up
+into group into our team up into
+
+ align:start position:0%
+into group into our team up into
+ 
+
+ align:start position:0%
+into group into our team up into
+multiple groups and came up with a bunch
+
+ align:start position:0%
+multiple groups and came up with a bunch
+ 
+
+ align:start position:0%
+multiple groups and came up with a bunch
+of different prototypes uh on paper we
+
+ align:start position:0%
+of different prototypes uh on paper we
+ 
+
+ align:start position:0%
+of different prototypes uh on paper we
+had two different prototypes one that
+
+ align:start position:0%
+had two different prototypes one that
+ 
+
+ align:start position:0%
+had two different prototypes one that
+focused on the idea of managing a city
+
+ align:start position:0%
+focused on the idea of managing a city
+ 
+
+ align:start position:0%
+focused on the idea of managing a city
+and it's resources and its response to
+
+ align:start position:0%
+and it's resources and its response to
+ 
+
+ align:start position:0%
+and it's resources and its response to
+disasters versus focusing on individual
+
+ align:start position:0%
+disasters versus focusing on individual
+ 
+
+ align:start position:0%
+disasters versus focusing on individual
+people and how you're going to move them
+
+ align:start position:0%
+people and how you're going to move them
+ 
+
+ align:start position:0%
+people and how you're going to move them
+around to keep them safe from the
+
+ align:start position:0%
+around to keep them safe from the
+ 
+
+ align:start position:0%
+around to keep them safe from the
+disasters and then we went into a whole
+
+ align:start position:0%
+disasters and then we went into a whole
+ 
+
+ align:start position:0%
+disasters and then we went into a whole
+bunch of different digital prototypes
+
+ align:start position:0%
+bunch of different digital prototypes
+ 
+
+ align:start position:0%
+bunch of different digital prototypes
+one that was a text based game about
+
+ align:start position:0%
+one that was a text based game about
+ 
+
+ align:start position:0%
+one that was a text based game about
+managing a city we
+
+ align:start position:0%
+managing a city we
+ 
+
+ align:start position:0%
+managing a city we
+had one that looked like this where you
+
+ align:start position:0%
+had one that looked like this where you
+ 
+
+ align:start position:0%
+had one that looked like this where you
+had two different cities and you were
+
+ align:start position:0%
+had two different cities and you were
+ 
+
+ align:start position:0%
+had two different cities and you were
+specifying what workers were going to do
+
+ align:start position:0%
+specifying what workers were going to do
+ 
+
+ align:start position:0%
+specifying what workers were going to do
+or when they would leave the city in
+
+ align:start position:0%
+or when they would leave the city in
+ 
+
+ align:start position:0%
+or when they would leave the city in
+order to stay
+
+ align:start position:0%
+order to stay
+ 
+
+ align:start position:0%
+order to stay
+safe and then we would take the
+
+ align:start position:0%
+safe and then we would take the
+ 
+
+ align:start position:0%
+safe and then we would take the
+different ideas that we were learning
+
+ align:start position:0%
+different ideas that we were learning
+ 
+
+ align:start position:0%
+different ideas that we were learning
+from both of these prototypes combine
+
+ align:start position:0%
+from both of these prototypes combine
+ 
+
+ align:start position:0%
+from both of these prototypes combine
+them together take things out out and
+
+ align:start position:0%
+them together take things out out and
+ 
+
+ align:start position:0%
+them together take things out out and
+our final prototype actually uses ideas
+
+ align:start position:0%
+our final prototype actually uses ideas
+ 
+
+ align:start position:0%
+our final prototype actually uses ideas
+from all of
+
+ align:start position:0%
+from all of
+ 
+
+ align:start position:0%
+from all of
+these another solution that uh we kind
+
+ align:start position:0%
+these another solution that uh we kind
+ 
+
+ align:start position:0%
+these another solution that uh we kind
+of got lucky with is when Pablo came to
+
+ align:start position:0%
+of got lucky with is when Pablo came to
+ 
+
+ align:start position:0%
+of got lucky with is when Pablo came to
+play our game he told us that we
+
+ align:start position:0%
+play our game he told us that we
+ 
+
+ align:start position:0%
+play our game he told us that we
+actually shouldn't focus on the policy
+
+ align:start position:0%
+actually shouldn't focus on the policy
+ 
+
+ align:start position:0%
+actually shouldn't focus on the policy
+makers because he wasn't confident that
+
+ align:start position:0%
+makers because he wasn't confident that
+ 
+
+ align:start position:0%
+makers because he wasn't confident that
+he could actually get them to play the
+
+ align:start position:0%
+he could actually get them to play the
+ 
+
+ align:start position:0%
+he could actually get them to play the
+game and so we switched our Target to
+
+ align:start position:0%
+game and so we switched our Target to
+ 
+
+ align:start position:0%
+game and so we switched our Target to
+being grade schoolers which is why you
+
+ align:start position:0%
+being grade schoolers which is why you
+ 
+
+ align:start position:0%
+being grade schoolers which is why you
+saw the sort of cuty art with the beach
+
+ align:start position:0%
+saw the sort of cuty art with the beach
+ 
+
+ align:start position:0%
+saw the sort of cuty art with the beach
+and the toys this actually made it a lot
+
+ align:start position:0%
+and the toys this actually made it a lot
+ 
+
+ align:start position:0%
+and the toys this actually made it a lot
+easier for us because we could Target
+
+ align:start position:0%
+easier for us because we could Target
+ 
+
+ align:start position:0%
+easier for us because we could Target
+people who probably had some experience
+
+ align:start position:0%
+people who probably had some experience
+ 
+
+ align:start position:0%
+people who probably had some experience
+with games or at least wanted to do
+
+ align:start position:0%
+with games or at least wanted to do
+ 
+
+ align:start position:0%
+with games or at least wanted to do
+something fun and would be curious to
+
+ align:start position:0%
+something fun and would be curious to
+ 
+
+ align:start position:0%
+something fun and would be curious to
+learn about our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topic so another um for our development
+
+ align:start position:0%
+topic so another um for our development
+ 
+
+ align:start position:0%
+topic so another um for our development
+process uh or I can just speak here
+
+ align:start position:0%
+process uh or I can just speak here
+ 
+
+ align:start position:0%
+process uh or I can just speak here
+right yeah you can speak right okay so
+
+ align:start position:0%
+right yeah you can speak right okay so
+ 
+
+ align:start position:0%
+right yeah you can speak right okay so
+another uh big issue we uh another set
+
+ align:start position:0%
+another uh big issue we uh another set
+ 
+
+ align:start position:0%
+another uh big issue we uh another set
+of challenges that we ran into was
+
+ align:start position:0%
+of challenges that we ran into was
+ 
+
+ align:start position:0%
+of challenges that we ran into was
+through our development process and so
+
+ align:start position:0%
+through our development process and so
+ 
+
+ align:start position:0%
+through our development process and so
+um we had initially issues with
+
+ align:start position:0%
+um we had initially issues with
+ 
+
+ align:start position:0%
+um we had initially issues with
+communication and facilitation our team
+
+ align:start position:0%
+communication and facilitation our team
+ 
+
+ align:start position:0%
+communication and facilitation our team
+had a wide variety of like uh
+
+ align:start position:0%
+had a wide variety of like uh
+ 
+
+ align:start position:0%
+had a wide variety of like uh
+experiences and backgrounds some were
+
+ align:start position:0%
+experiences and backgrounds some were
+ 
+
+ align:start position:0%
+experiences and backgrounds some were
+hardcore Gamers some mostly mobile
+
+ align:start position:0%
+hardcore Gamers some mostly mobile
+ 
+
+ align:start position:0%
+hardcore Gamers some mostly mobile
+Gamers and so there were initially a lot
+
+ align:start position:0%
+Gamers and so there were initially a lot
+ 
+
+ align:start position:0%
+Gamers and so there were initially a lot
+of disagreements on what level of game
+
+ align:start position:0%
+of disagreements on what level of game
+ 
+
+ align:start position:0%
+of disagreements on what level of game
+uh we wanted to create and like what
+
+ align:start position:0%
+uh we wanted to create and like what
+ 
+
+ align:start position:0%
+uh we wanted to create and like what
+sort of game casual versus hardcore that
+
+ align:start position:0%
+sort of game casual versus hardcore that
+ 
+
+ align:start position:0%
+sort of game casual versus hardcore that
+we wanted to create and so we needed to
+
+ align:start position:0%
+we wanted to create and so we needed to
+ 
+
+ align:start position:0%
+we wanted to create and so we needed to
+overcome like challenges of facilitation
+
+ align:start position:0%
+overcome like challenges of facilitation
+ 
+
+ align:start position:0%
+overcome like challenges of facilitation
+and communication within our team
+
+ align:start position:0%
+and communication within our team
+ 
+
+ align:start position:0%
+and communication within our team
+another major challenge in our devel
+
+ align:start position:0%
+another major challenge in our devel
+ 
+
+ align:start position:0%
+another major challenge in our devel
+vment process that we had to face came
+
+ align:start position:0%
+vment process that we had to face came
+ 
+
+ align:start position:0%
+vment process that we had to face came
+from our design issues where for a very
+
+ align:start position:0%
+from our design issues where for a very
+ 
+
+ align:start position:0%
+from our design issues where for a very
+long time we had kind of a vague vision
+
+ align:start position:0%
+long time we had kind of a vague vision
+ 
+
+ align:start position:0%
+long time we had kind of a vague vision
+of what to do we didn't know what kind
+
+ align:start position:0%
+of what to do we didn't know what kind
+ 
+
+ align:start position:0%
+of what to do we didn't know what kind
+of game we wanted to make and so we
+
+ align:start position:0%
+of game we wanted to make and so we
+ 
+
+ align:start position:0%
+of game we wanted to make and so we
+purposely tried to keep our game ideas
+
+ align:start position:0%
+purposely tried to keep our game ideas
+ 
+
+ align:start position:0%
+purposely tried to keep our game ideas
+vague as we built prototypes but then we
+
+ align:start position:0%
+vague as we built prototypes but then we
+ 
+
+ align:start position:0%
+vague as we built prototypes but then we
+ran into issues where um we would have
+
+ align:start position:0%
+ran into issues where um we would have
+ 
+
+ align:start position:0%
+ran into issues where um we would have
+Solutions but like no consensus on which
+
+ align:start position:0%
+Solutions but like no consensus on which
+ 
+
+ align:start position:0%
+Solutions but like no consensus on which
+solution was best and where we would um
+
+ align:start position:0%
+solution was best and where we would um
+ 
+
+ align:start position:0%
+solution was best and where we would um
+and where we went from long periods of
+
+ align:start position:0%
+and where we went from long periods of
+ 
+
+ align:start position:0%
+and where we went from long periods of
+time without having a clear direction of
+
+ align:start position:0%
+time without having a clear direction of
+ 
+
+ align:start position:0%
+time without having a clear direction of
+where we wanted our final game to
+
+ align:start position:0%
+where we wanted our final game to
+ 
+
+ align:start position:0%
+where we wanted our final game to
+be so um our solutions
+
+ align:start position:0%
+be so um our solutions
+ 
+
+ align:start position:0%
+be so um our solutions
+for uh the challenges proposed by the
+
+ align:start position:0%
+for uh the challenges proposed by the
+ 
+
+ align:start position:0%
+for uh the challenges proposed by the
+development were a team structure and so
+
+ align:start position:0%
+development were a team structure and so
+ 
+
+ align:start position:0%
+development were a team structure and so
+we structured our team
+
+ align:start position:0%
+we structured our team
+ 
+
+ align:start position:0%
+we structured our team
+Loosely uh into three sub teams a
+
+ align:start position:0%
+Loosely uh into three sub teams a
+ 
+
+ align:start position:0%
+Loosely uh into three sub teams a
+production sub team which would uh take
+
+ align:start position:0%
+production sub team which would uh take
+ 
+
+ align:start position:0%
+production sub team which would uh take
+care of uh production like the uh
+
+ align:start position:0%
+care of uh production like the uh
+ 
+
+ align:start position:0%
+care of uh production like the uh
+deliverables and making sure that the uh
+
+ align:start position:0%
+deliverables and making sure that the uh
+ 
+
+ align:start position:0%
+deliverables and making sure that the uh
+game ideas are being uh communicated
+
+ align:start position:0%
+game ideas are being uh communicated
+ 
+
+ align:start position:0%
+game ideas are being uh communicated
+properly a technical team which um
+
+ align:start position:0%
+properly a technical team which um
+ 
+
+ align:start position:0%
+properly a technical team which um
+worked primarily with the code and
+
+ align:start position:0%
+worked primarily with the code and
+ 
+
+ align:start position:0%
+worked primarily with the code and
+making sure the game got done and then a
+
+ align:start position:0%
+making sure the game got done and then a
+ 
+
+ align:start position:0%
+making sure the game got done and then a
+user experience team which handled art
+
+ align:start position:0%
+user experience team which handled art
+ 
+
+ align:start position:0%
+user experience team which handled art
+UI and uh sound and so we kept a
+
+ align:start position:0%
+UI and uh sound and so we kept a
+ 
+
+ align:start position:0%
+UI and uh sound and so we kept a
+flexible responsibility I uh we kept the
+
+ align:start position:0%
+flexible responsibility I uh we kept the
+ 
+
+ align:start position:0%
+flexible responsibility I uh we kept the
+responsibilities flexible so you know as
+
+ align:start position:0%
+responsibilities flexible so you know as
+ 
+
+ align:start position:0%
+responsibilities flexible so you know as
+team members got busy over the semester
+
+ align:start position:0%
+team members got busy over the semester
+ 
+
+ align:start position:0%
+team members got busy over the semester
+or as like changing conditions led to
+
+ align:start position:0%
+or as like changing conditions led to
+ 
+
+ align:start position:0%
+or as like changing conditions led to
+different people contributing um
+
+ align:start position:0%
+different people contributing um
+ 
+
+ align:start position:0%
+different people contributing um
+we kept UH responsibilities were able to
+
+ align:start position:0%
+we kept UH responsibilities were able to
+ 
+
+ align:start position:0%
+we kept UH responsibilities were able to
+easily flow between teams and team
+
+ align:start position:0%
+easily flow between teams and team
+ 
+
+ align:start position:0%
+easily flow between teams and team
+members and um additionally another idea
+
+ align:start position:0%
+members and um additionally another idea
+ 
+
+ align:start position:0%
+members and um additionally another idea
+we uh started with in the beginning was
+
+ align:start position:0%
+we uh started with in the beginning was
+ 
+
+ align:start position:0%
+we uh started with in the beginning was
+the idea of sub team leaders um which
+
+ align:start position:0%
+the idea of sub team leaders um which
+ 
+
+ align:start position:0%
+the idea of sub team leaders um which
+are the two people marked with the L's
+
+ align:start position:0%
+are the two people marked with the L's
+ 
+
+ align:start position:0%
+are the two people marked with the L's
+but that was an idea we later abandoned
+
+ align:start position:0%
+but that was an idea we later abandoned
+ 
+
+ align:start position:0%
+but that was an idea we later abandoned
+in favor of just having a more flexible
+
+ align:start position:0%
+in favor of just having a more flexible
+ 
+
+ align:start position:0%
+in favor of just having a more flexible
+team structure or flat team
+
+ align:start position:0%
+team structure or flat team
+ 
+
+ align:start position:0%
+team structure or flat team
+structure um another solution for
+
+ align:start position:0%
+structure um another solution for
+ 
+
+ align:start position:0%
+structure um another solution for
+helping our development process was the
+
+ align:start position:0%
+helping our development process was the
+ 
+
+ align:start position:0%
+helping our development process was the
+use of good code practices and I cannot
+
+ align:start position:0%
+use of good code practices and I cannot
+ 
+
+ align:start position:0%
+use of good code practices and I cannot
+emphasize enough that this really helped
+
+ align:start position:0%
+emphasize enough that this really helped
+ 
+
+ align:start position:0%
+emphasize enough that this really helped
+speed up our development because of we
+
+ align:start position:0%
+speed up our development because of we
+ 
+
+ align:start position:0%
+speed up our development because of we
+didn't run into trouble with code it was
+
+ align:start position:0%
+didn't run into trouble with code it was
+ 
+
+ align:start position:0%
+didn't run into trouble with code it was
+mostly with design so we used um we used
+
+ align:start position:0%
+mostly with design so we used um we used
+ 
+
+ align:start position:0%
+mostly with design so we used um we used
+dooman which is a JavaScript uh SC
+
+ align:start position:0%
+dooman which is a JavaScript uh SC
+ 
+
+ align:start position:0%
+dooman which is a JavaScript uh SC
+module system and basically it allowed
+
+ align:start position:0%
+module system and basically it allowed
+ 
+
+ align:start position:0%
+module system and basically it allowed
+our code to be interoperable we could
+
+ align:start position:0%
+our code to be interoperable we could
+ 
+
+ align:start position:0%
+our code to be interoperable we could
+write one module separately from another
+
+ align:start position:0%
+write one module separately from another
+ 
+
+ align:start position:0%
+write one module separately from another
+module so that solved a lot of issues
+
+ align:start position:0%
+module so that solved a lot of issues
+ 
+
+ align:start position:0%
+module so that solved a lot of issues
+with like dependencies or like um people
+
+ align:start position:0%
+with like dependencies or like um people
+ 
+
+ align:start position:0%
+with like dependencies or like um people
+working in parallel because it allowed
+
+ align:start position:0%
+working in parallel because it allowed
+ 
+
+ align:start position:0%
+working in parallel because it allowed
+people to you know work in parallel
+
+ align:start position:0%
+people to you know work in parallel
+ 
+
+ align:start position:0%
+people to you know work in parallel
+without overwriting each other's code um
+
+ align:start position:0%
+without overwriting each other's code um
+ 
+
+ align:start position:0%
+without overwriting each other's code um
+we also used good code practice with
+
+ align:start position:0%
+we also used good code practice with
+ 
+
+ align:start position:0%
+we also used good code practice with
+State machines and MVC which is mod view
+
+ align:start position:0%
+State machines and MVC which is mod view
+ 
+
+ align:start position:0%
+State machines and MVC which is mod view
+control and so we had a very you know
+
+ align:start position:0%
+control and so we had a very you know
+ 
+
+ align:start position:0%
+control and so we had a very you know
+objectoriented code very modular and
+
+ align:start position:0%
+objectoriented code very modular and
+ 
+
+ align:start position:0%
+objectoriented code very modular and
+when we did need to you know uh change
+
+ align:start position:0%
+when we did need to you know uh change
+ 
+
+ align:start position:0%
+when we did need to you know uh change
+our code rip it all out and put it back
+
+ align:start position:0%
+our code rip it all out and put it back
+ 
+
+ align:start position:0%
+our code rip it all out and put it back
+in it actually didn't turn out to be too
+
+ align:start position:0%
+in it actually didn't turn out to be too
+ 
+
+ align:start position:0%
+in it actually didn't turn out to be too
+painful because we just had to switch a
+
+ align:start position:0%
+painful because we just had to switch a
+ 
+
+ align:start position:0%
+painful because we just had to switch a
+couple objects around
+
+ align:start position:0%
+couple objects around
+ 
+
+ align:start position:0%
+couple objects around
+um all right and then one final solution
+
+ align:start position:0%
+um all right and then one final solution
+ 
+
+ align:start position:0%
+um all right and then one final solution
+that we used for uh for our development
+
+ align:start position:0%
+that we used for uh for our development
+ 
+
+ align:start position:0%
+that we used for uh for our development
+processes were slack and scrum so slack
+
+ align:start position:0%
+processes were slack and scrum so slack
+ 
+
+ align:start position:0%
+processes were slack and scrum so slack
+is like a modernized IRC chat room and
+
+ align:start position:0%
+is like a modernized IRC chat room and
+ 
+
+ align:start position:0%
+is like a modernized IRC chat room and
+it's very featur rich it has a lot of
+
+ align:start position:0%
+it's very featur rich it has a lot of
+ 
+
+ align:start position:0%
+it's very featur rich it has a lot of
+Integrations with uh GitHub and Google
+
+ align:start position:0%
+Integrations with uh GitHub and Google
+ 
+
+ align:start position:0%
+Integrations with uh GitHub and Google
+Drive and things like that and so that
+
+ align:start position:0%
+Drive and things like that and so that
+ 
+
+ align:start position:0%
+Drive and things like that and so that
+sort of realtime communication actually
+
+ align:start position:0%
+sort of realtime communication actually
+ 
+
+ align:start position:0%
+sort of realtime communication actually
+made it so that we didn't really have to
+
+ align:start position:0%
+made it so that we didn't really have to
+ 
+
+ align:start position:0%
+made it so that we didn't really have to
+meet outside of cloud too often uh we if
+
+ align:start position:0%
+meet outside of cloud too often uh we if
+ 
+
+ align:start position:0%
+meet outside of cloud too often uh we if
+someone was working we would just email
+
+ align:start position:0%
+someone was working we would just email
+ 
+
+ align:start position:0%
+someone was working we would just email
+out saying we're I'm on the slack and
+
+ align:start position:0%
+out saying we're I'm on the slack and
+ 
+
+ align:start position:0%
+out saying we're I'm on the slack and
+then people could meet on the slack and
+
+ align:start position:0%
+then people could meet on the slack and
+ 
+
+ align:start position:0%
+then people could meet on the slack and
+it was full featured enough like we
+
+ align:start position:0%
+it was full featured enough like we
+ 
+
+ align:start position:0%
+it was full featured enough like we
+could send attachments and things like
+
+ align:start position:0%
+could send attachments and things like
+ 
+
+ align:start position:0%
+could send attachments and things like
+that that yeah most of our communication
+
+ align:start position:0%
+that that yeah most of our communication
+ 
+
+ align:start position:0%
+that that yeah most of our communication
+in-person communication could be done in
+
+ align:start position:0%
+in-person communication could be done in
+ 
+
+ align:start position:0%
+in-person communication could be done in
+class and in class we adopted a uh sort
+
+ align:start position:0%
+class and in class we adopted a uh sort
+ 
+
+ align:start position:0%
+class and in class we adopted a uh sort
+of like daily scrum format where uh we
+
+ align:start position:0%
+of like daily scrum format where uh we
+ 
+
+ align:start position:0%
+of like daily scrum format where uh we
+simply said what we had done since the
+
+ align:start position:0%
+simply said what we had done since the
+ 
+
+ align:start position:0%
+simply said what we had done since the
+previous class and what our goals were
+
+ align:start position:0%
+previous class and what our goals were
+ 
+
+ align:start position:0%
+previous class and what our goals were
+uh until next
+
+ align:start position:0%
+uh until next
+ 
+
+ align:start position:0%
+uh until next
+class yeah so in the end though we did
+
+ align:start position:0%
+class yeah so in the end though we did
+ 
+
+ align:start position:0%
+class yeah so in the end though we did
+have to cut some features
+
+ align:start position:0%
+have to cut some features
+ 
+
+ align:start position:0%
+have to cut some features
+uh um these features mainly were the
+
+ align:start position:0%
+uh um these features mainly were the
+ 
+
+ align:start position:0%
+uh um these features mainly were the
+idea of multi again m a tutorial or
+
+ align:start position:0%
+idea of multi again m a tutorial or
+ 
+
+ align:start position:0%
+idea of multi again m a tutorial or
+multiple levels uh simply because there
+
+ align:start position:0%
+multiple levels uh simply because there
+ 
+
+ align:start position:0%
+multiple levels uh simply because there
+would just be too much content that we
+
+ align:start position:0%
+would just be too much content that we
+ 
+
+ align:start position:0%
+would just be too much content that we
+would need to play test in order to make
+
+ align:start position:0%
+would need to play test in order to make
+ 
+
+ align:start position:0%
+would need to play test in order to make
+sure that it like was a consistent
+
+ align:start position:0%
+sure that it like was a consistent
+ 
+
+ align:start position:0%
+sure that it like was a consistent
+quality and like got our message
+
+ align:start position:0%
+quality and like got our message
+ 
+
+ align:start position:0%
+quality and like got our message
+across um and also trying to to add more
+
+ align:start position:0%
+across um and also trying to to add more
+ 
+
+ align:start position:0%
+across um and also trying to to add more
+individuality to the uh to the toys that
+
+ align:start position:0%
+individuality to the uh to the toys that
+ 
+
+ align:start position:0%
+individuality to the uh to the toys that
+you saw um they have different Graphics
+
+ align:start position:0%
+you saw um they have different Graphics
+ 
+
+ align:start position:0%
+you saw um they have different Graphics
+but that's as much as we could do given
+
+ align:start position:0%
+but that's as much as we could do given
+ 
+
+ align:start position:0%
+but that's as much as we could do given
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+constraints and so kind of just bring it
+
+ align:start position:0%
+constraints and so kind of just bring it
+ 
+
+ align:start position:0%
+constraints and so kind of just bring it
+back um and our worst three worst
+
+ align:start position:0%
+back um and our worst three worst
+ 
+
+ align:start position:0%
+back um and our worst three worst
+decisions um where first we spent a lot
+
+ align:start position:0%
+decisions um where first we spent a lot
+ 
+
+ align:start position:0%
+decisions um where first we spent a lot
+we did end up spending a lot of time on
+
+ align:start position:0%
+we did end up spending a lot of time on
+ 
+
+ align:start position:0%
+we did end up spending a lot of time on
+code and assets that never got used we
+
+ align:start position:0%
+code and assets that never got used we
+ 
+
+ align:start position:0%
+code and assets that never got used we
+maybe like
+
+ align:start position:0%
+maybe like
+ 
+
+ align:start position:0%
+maybe like
+use 10% of our final 10 to 20% of our
+
+ align:start position:0%
+use 10% of our final 10 to 20% of our
+ 
+
+ align:start position:0%
+use 10% of our final 10 to 20% of our
+final work in our final project actually
+
+ align:start position:0%
+final work in our final project actually
+ 
+
+ align:start position:0%
+final work in our final project actually
+maybe that is a bit uh Overkill but um
+
+ align:start position:0%
+maybe that is a bit uh Overkill but um
+ 
+
+ align:start position:0%
+maybe that is a bit uh Overkill but um
+okay maybe 30% of our final uh code and
+
+ align:start position:0%
+okay maybe 30% of our final uh code and
+ 
+
+ align:start position:0%
+okay maybe 30% of our final uh code and
+Assets in our final
+
+ align:start position:0%
+Assets in our final
+ 
+
+ align:start position:0%
+Assets in our final
+project um this really was due to uh
+
+ align:start position:0%
+project um this really was due to uh
+ 
+
+ align:start position:0%
+project um this really was due to uh
+this second bad decision that we kept
+
+ align:start position:0%
+this second bad decision that we kept
+ 
+
+ align:start position:0%
+this second bad decision that we kept
+the game and its direction too vague for
+
+ align:start position:0%
+the game and its direction too vague for
+ 
+
+ align:start position:0%
+the game and its direction too vague for
+too long we always were holding out that
+
+ align:start position:0%
+too long we always were holding out that
+ 
+
+ align:start position:0%
+too long we always were holding out that
+oh maybe we'll be able to come up with a
+
+ align:start position:0%
+oh maybe we'll be able to come up with a
+ 
+
+ align:start position:0%
+oh maybe we'll be able to come up with a
+better game idea or maybe we'll find
+
+ align:start position:0%
+better game idea or maybe we'll find
+ 
+
+ align:start position:0%
+better game idea or maybe we'll find
+some magic solution to how we can make
+
+ align:start position:0%
+some magic solution to how we can make
+ 
+
+ align:start position:0%
+some magic solution to how we can make
+for forecast based financing into a game
+
+ align:start position:0%
+for forecast based financing into a game
+ 
+
+ align:start position:0%
+for forecast based financing into a game
+and because of this mindset we spent
+
+ align:start position:0%
+and because of this mindset we spent
+ 
+
+ align:start position:0%
+and because of this mindset we spent
+probably the first half of the project
+
+ align:start position:0%
+probably the first half of the project
+ 
+
+ align:start position:0%
+probably the first half of the project
+like just staying too vague and that
+
+ align:start position:0%
+like just staying too vague and that
+ 
+
+ align:start position:0%
+like just staying too vague and that
+hurt us in the end because we spent so
+
+ align:start position:0%
+hurt us in the end because we spent so
+ 
+
+ align:start position:0%
+hurt us in the end because we spent so
+much time going in all these different
+
+ align:start position:0%
+much time going in all these different
+ 
+
+ align:start position:0%
+much time going in all these different
+directions and really um really the uh
+
+ align:start position:0%
+directions and really um really the uh
+ 
+
+ align:start position:0%
+directions and really um really the uh
+decision that kind of capture those
+
+ align:start position:0%
+decision that kind of capture those
+ 
+
+ align:start position:0%
+decision that kind of capture those
+first two though is the fact that we
+
+ align:start position:0%
+first two though is the fact that we
+ 
+
+ align:start position:0%
+first two though is the fact that we
+tried to make a game on top of forecast
+
+ align:start position:0%
+tried to make a game on top of forecast
+ 
+
+ align:start position:0%
+tried to make a game on top of forecast
+based financing so we had forecast based
+
+ align:start position:0%
+based financing so we had forecast based
+ 
+
+ align:start position:0%
+based financing so we had forecast based
+financing and we were like how can we
+
+ align:start position:0%
+financing and we were like how can we
+ 
+
+ align:start position:0%
+financing and we were like how can we
+skin this as a game whereas once we
+
+ align:start position:0%
+skin this as a game whereas once we
+ 
+
+ align:start position:0%
+skin this as a game whereas once we
+switched that mindset and thought let's
+
+ align:start position:0%
+switched that mindset and thought let's
+ 
+
+ align:start position:0%
+switched that mindset and thought let's
+have a game and how can we put forecast
+
+ align:start position:0%
+have a game and how can we put forecast
+ 
+
+ align:start position:0%
+have a game and how can we put forecast
+based financing into it I think uh that
+
+ align:start position:0%
+based financing into it I think uh that
+ 
+
+ align:start position:0%
+based financing into it I think uh that
+was the moment that we then came
+
+ align:start position:0%
+was the moment that we then came
+ 
+
+ align:start position:0%
+was the moment that we then came
+together as a team and really started
+
+ align:start position:0%
+together as a team and really started
+ 
+
+ align:start position:0%
+together as a team and really started
+making the final game that we
+
+ align:start position:0%
+making the final game that we
+ 
+
+ align:start position:0%
+making the final game that we
+wanted so our best
+
+ align:start position:0%
+wanted so our best
+ 
+
+ align:start position:0%
+wanted so our best
+decision um yeah so uh one of our best
+
+ align:start position:0%
+decision um yeah so uh one of our best
+ 
+
+ align:start position:0%
+decision um yeah so uh one of our best
+decisions was that we chose good tools
+
+ align:start position:0%
+decisions was that we chose good tools
+ 
+
+ align:start position:0%
+decisions was that we chose good tools
+at the beginning which meant that as we
+
+ align:start position:0%
+at the beginning which meant that as we
+ 
+
+ align:start position:0%
+at the beginning which meant that as we
+went through all these different digital
+
+ align:start position:0%
+went through all these different digital
+ 
+
+ align:start position:0%
+went through all these different digital
+prototypes we actually didn't have to
+
+ align:start position:0%
+prototypes we actually didn't have to
+ 
+
+ align:start position:0%
+prototypes we actually didn't have to
+completely rewrite our game we could
+
+ align:start position:0%
+completely rewrite our game we could
+ 
+
+ align:start position:0%
+completely rewrite our game we could
+pull out the way that workers worked in
+
+ align:start position:0%
+pull out the way that workers worked in
+ 
+
+ align:start position:0%
+pull out the way that workers worked in
+one game we could pull out the view that
+
+ align:start position:0%
+one game we could pull out the view that
+ 
+
+ align:start position:0%
+one game we could pull out the view that
+we were using in another game and then
+
+ align:start position:0%
+we were using in another game and then
+ 
+
+ align:start position:0%
+we were using in another game and then
+we could just combine them together and
+
+ align:start position:0%
+we could just combine them together and
+ 
+
+ align:start position:0%
+we could just combine them together and
+that allowed us to move quickly whenever
+
+ align:start position:0%
+that allowed us to move quickly whenever
+ 
+
+ align:start position:0%
+that allowed us to move quickly whenever
+we were changing our
+
+ align:start position:0%
+we were changing our
+ 
+
+ align:start position:0%
+we were changing our
+prototype we also weren't afraid to
+
+ align:start position:0%
+prototype we also weren't afraid to
+ 
+
+ align:start position:0%
+prototype we also weren't afraid to
+trust each other uh both in terms of
+
+ align:start position:0%
+trust each other uh both in terms of
+ 
+
+ align:start position:0%
+trust each other uh both in terms of
+what everyone was working on but also in
+
+ align:start position:0%
+what everyone was working on but also in
+ 
+
+ align:start position:0%
+what everyone was working on but also in
+terms of the decisions that we were
+
+ align:start position:0%
+terms of the decisions that we were
+ 
+
+ align:start position:0%
+terms of the decisions that we were
+making and so when we said that we had
+
+ align:start position:0%
+making and so when we said that we had
+ 
+
+ align:start position:0%
+making and so when we said that we had
+throw something out we all understood
+
+ align:start position:0%
+throw something out we all understood
+ 
+
+ align:start position:0%
+throw something out we all understood
+that it was for the best uh the good of
+
+ align:start position:0%
+that it was for the best uh the good of
+ 
+
+ align:start position:0%
+that it was for the best uh the good of
+the project and we we didn't have a lot
+
+ align:start position:0%
+the project and we we didn't have a lot
+ 
+
+ align:start position:0%
+the project and we we didn't have a lot
+of complaining or hurt feelings when
+
+ align:start position:0%
+of complaining or hurt feelings when
+ 
+
+ align:start position:0%
+of complaining or hurt feelings when
+something didn't get put in or when we
+
+ align:start position:0%
+something didn't get put in or when we
+ 
+
+ align:start position:0%
+something didn't get put in or when we
+decided to throw out our assets or code
+
+ align:start position:0%
+decided to throw out our assets or code
+ 
+
+ align:start position:0%
+decided to throw out our assets or code
+and when we got to the end we had been
+
+ align:start position:0%
+and when we got to the end we had been
+ 
+
+ align:start position:0%
+and when we got to the end we had been
+through enough of sort of this vagueness
+
+ align:start position:0%
+through enough of sort of this vagueness
+ 
+
+ align:start position:0%
+through enough of sort of this vagueness
+that we were all kind of frustrated with
+
+ align:start position:0%
+that we were all kind of frustrated with
+ 
+
+ align:start position:0%
+that we were all kind of frustrated with
+it and we realized that we had an idea
+
+ align:start position:0%
+it and we realized that we had an idea
+ 
+
+ align:start position:0%
+it and we realized that we had an idea
+that we all liked and we really got on
+
+ align:start position:0%
+that we all liked and we really got on
+ 
+
+ align:start position:0%
+that we all liked and we really got on
+board with it and made it happen once we
+
+ align:start position:0%
+board with it and made it happen once we
+ 
+
+ align:start position:0%
+board with it and made it happen once we
+started working on our final idea and we
+
+ align:start position:0%
+started working on our final idea and we
+ 
+
+ align:start position:0%
+started working on our final idea and we
+saw that it worked uh basically every
+
+ align:start position:0%
+saw that it worked uh basically every
+ 
+
+ align:start position:0%
+saw that it worked uh basically every
+decision from that point on was how do
+
+ align:start position:0%
+decision from that point on was how do
+ 
+
+ align:start position:0%
+decision from that point on was how do
+we make this game better uh and we were
+
+ align:start position:0%
+we make this game better uh and we were
+ 
+
+ align:start position:0%
+we make this game better uh and we were
+all on board with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vision thank you any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions anyone in the audience have
+
+ align:start position:0%
+questions anyone in the audience have
+ 
+
+ align:start position:0%
+questions anyone in the audience have
+feedback for them first
+
+ align:start position:0%
+feedback for them first
+ 
+
+ align:start position:0%
+feedback for them first
+before you can't see that s very well
+
+ align:start position:0%
+before you can't see that s very well
+ 
+
+ align:start position:0%
+before you can't see that s very well
+yeah we'll have to make all of our
+
+ align:start position:0%
+yeah we'll have to make all of our
+ 
+
+ align:start position:0%
+yeah we'll have to make all of our
+slides darker yeah yellow and white yeah
+
+ align:start position:0%
+slides darker yeah yellow and white yeah
+ 
+
+ align:start position:0%
+slides darker yeah yellow and white yeah
+like the yellow and white on your on
+
+ align:start position:0%
+like the yellow and white on your on
+ 
+
+ align:start position:0%
+like the yellow and white on your on
+your early screen yeah I was doing this
+
+ align:start position:0%
+your early screen yeah I was doing this
+ 
+
+ align:start position:0%
+your early screen yeah I was doing this
+on yourp screen I realized that's the
+
+ align:start position:0%
+on yourp screen I realized that's the
+ 
+
+ align:start position:0%
+on yourp screen I realized that's the
+game not the the
+
+ align:start position:0%
+game not the the
+ 
+
+ align:start position:0%
+game not the the
+um presentation but wow it's also a
+
+ align:start position:0%
+um presentation but wow it's also a
+ 
+
+ align:start position:0%
+um presentation but wow it's also a
+little faded in the game itself it could
+
+ align:start position:0%
+little faded in the game itself it could
+ 
+
+ align:start position:0%
+little faded in the game itself it could
+be the display resolution you're using
+
+ align:start position:0%
+be the display resolution you're using
+ 
+
+ align:start position:0%
+be the display resolution you're using
+so after CL after we're done with
+
+ align:start position:0%
+so after CL after we're done with
+ 
+
+ align:start position:0%
+so after CL after we're done with
+everything try a different resolution
+
+ align:start position:0%
+everything try a different resolution
+ 
+
+ align:start position:0%
+everything try a different resolution
+see if it makes a difference yeah be
+
+ align:start position:0%
+see if it makes a difference yeah be
+ 
+
+ align:start position:0%
+see if it makes a difference yeah be
+great um the music in the game Deo was
+
+ align:start position:0%
+great um the music in the game Deo was
+ 
+
+ align:start position:0%
+great um the music in the game Deo was
+too high um it was overpowering your
+
+ align:start position:0%
+too high um it was overpowering your
+ 
+
+ align:start position:0%
+too high um it was overpowering your
+voice okay uh so you know I think you
+
+ align:start position:0%
+voice okay uh so you know I think you
+ 
+
+ align:start position:0%
+voice okay uh so you know I think you
+were almost hollering just to be able to
+
+ align:start position:0%
+were almost hollering just to be able to
+ 
+
+ align:start position:0%
+were almost hollering just to be able to
+be heard uh doesn't need to be that loud
+
+ align:start position:0%
+be heard uh doesn't need to be that loud
+ 
+
+ align:start position:0%
+be heard uh doesn't need to be that loud
+so you can just crank down the volume I
+
+ align:start position:0%
+so you can just crank down the volume I
+ 
+
+ align:start position:0%
+so you can just crank down the volume I
+or on the computer or on the controls
+
+ align:start position:0%
+or on the computer or on the controls
+ 
+
+ align:start position:0%
+or on the computer or on the controls
+over there um something that I that I
+
+ align:start position:0%
+over there um something that I that I
+ 
+
+ align:start position:0%
+over there um something that I that I
+had a question for uh you don't have to
+
+ align:start position:0%
+had a question for uh you don't have to
+ 
+
+ align:start position:0%
+had a question for uh you don't have to
+answer it today um but you might want to
+
+ align:start position:0%
+answer it today um but you might want to
+ 
+
+ align:start position:0%
+answer it today um but you might want to
+put it in your presentation was how long
+
+ align:start position:0%
+put it in your presentation was how long
+ 
+
+ align:start position:0%
+put it in your presentation was how long
+was the design of what you've what you
+
+ align:start position:0%
+was the design of what you've what you
+ 
+
+ align:start position:0%
+was the design of what you've what you
+eventually established on the table
+
+ align:start position:0%
+eventually established on the table
+ 
+
+ align:start position:0%
+eventually established on the table
+before you decided that this was the
+
+ align:start position:0%
+before you decided that this was the
+ 
+
+ align:start position:0%
+before you decided that this was the
+thing that you were going for right
+
+ align:start position:0%
+thing that you were going for right
+ 
+
+ align:start position:0%
+thing that you were going for right
+because I'm assuming it was one of your
+
+ align:start position:0%
+because I'm assuming it was one of your
+ 
+
+ align:start position:0%
+because I'm assuming it was one of your
+vague it came up during your vague idea
+
+ align:start position:0%
+vague it came up during your vague idea
+ 
+
+ align:start position:0%
+vague it came up during your vague idea
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+and you're and you're implying that you
+
+ align:start position:0%
+and you're and you're implying that you
+ 
+
+ align:start position:0%
+and you're and you're implying that you
+were in that mode for too long but I
+
+ align:start position:0%
+were in that mode for too long but I
+ 
+
+ align:start position:0%
+were in that mode for too long but I
+don't know how long it was on the table
+
+ align:start position:0%
+don't know how long it was on the table
+ 
+
+ align:start position:0%
+don't know how long it was on the table
+or was it only something you figured out
+
+ align:start position:0%
+or was it only something you figured out
+ 
+
+ align:start position:0%
+or was it only something you figured out
+at the end of the vague idea phase um
+
+ align:start position:0%
+at the end of the vague idea phase um
+ 
+
+ align:start position:0%
+at the end of the vague idea phase um
+because you otherwise you wouldn't have
+
+ align:start position:0%
+because you otherwise you wouldn't have
+ 
+
+ align:start position:0%
+because you otherwise you wouldn't have
+been able to switch to this idea if it
+
+ align:start position:0%
+been able to switch to this idea if it
+ 
+
+ align:start position:0%
+been able to switch to this idea if it
+was not on the table in the first place
+
+ align:start position:0%
+was not on the table in the first place
+ 
+
+ align:start position:0%
+was not on the table in the first place
+um so uh and how did you decide this was
+
+ align:start position:0%
+um so uh and how did you decide this was
+ 
+
+ align:start position:0%
+um so uh and how did you decide this was
+it that that the San hustle game was
+
+ align:start position:0%
+it that that the San hustle game was
+ 
+
+ align:start position:0%
+it that that the San hustle game was
+going to be it um I understand I think
+
+ align:start position:0%
+going to be it um I understand I think
+ 
+
+ align:start position:0%
+going to be it um I understand I think
+you you very clearly explained the
+
+ align:start position:0%
+you you very clearly explained the
+ 
+
+ align:start position:0%
+you you very clearly explained the
+benefits of deciding this was it but how
+
+ align:start position:0%
+benefits of deciding this was it but how
+ 
+
+ align:start position:0%
+benefits of deciding this was it but how
+did you come to that conclusion sure was
+
+ align:start position:0%
+did you come to that conclusion sure was
+ 
+
+ align:start position:0%
+did you come to that conclusion sure was
+that stuff I want to hear more about but
+
+ align:start position:0%
+that stuff I want to hear more about but
+ 
+
+ align:start position:0%
+that stuff I want to hear more about but
+you don't have to answer it
+
+ align:start position:0%
+you don't have to answer it
+ 
+
+ align:start position:0%
+you don't have to answer it
+now yeah I might also um just a little
+
+ align:start position:0%
+now yeah I might also um just a little
+ 
+
+ align:start position:0%
+now yeah I might also um just a little
+bit speci you mentioned you spent too
+
+ align:start position:0%
+bit speci you mentioned you spent too
+ 
+
+ align:start position:0%
+bit speci you mentioned you spent too
+long on that design phase I wonder how
+
+ align:start position:0%
+long on that design phase I wonder how
+ 
+
+ align:start position:0%
+long on that design phase I wonder how
+long that was
+
+ align:start position:0%
+long that was
+ 
+
+ align:start position:0%
+long that was
+okay um you said Pablo switched your
+
+ align:start position:0%
+okay um you said Pablo switched your
+ 
+
+ align:start position:0%
+okay um you said Pablo switched your
+target audience for you um telling us
+
+ align:start position:0%
+target audience for you um telling us
+ 
+
+ align:start position:0%
+target audience for you um telling us
+whether that was because of the game
+
+ align:start position:0%
+whether that was because of the game
+ 
+
+ align:start position:0%
+whether that was because of the game
+that he saw or because of something else
+
+ align:start position:0%
+that he saw or because of something else
+ 
+
+ align:start position:0%
+that he saw or because of something else
+if you know that information throw it in
+
+ align:start position:0%
+if you know that information throw it in
+ 
+
+ align:start position:0%
+if you know that information throw it in
+there if you don't know that information
+
+ align:start position:0%
+there if you don't know that information
+ 
+
+ align:start position:0%
+there if you don't know that information
+that's fine
+
+ align:start position:0%
+that's fine
+ 
+
+ align:start position:0%
+that's fine
+um knowing why you you dropped the team
+
+ align:start position:0%
+um knowing why you you dropped the team
+ 
+
+ align:start position:0%
+um knowing why you you dropped the team
+lead you mentioned you you dropped it
+
+ align:start position:0%
+lead you mentioned you you dropped it
+ 
+
+ align:start position:0%
+lead you mentioned you you dropped it
+but you didn't exactly say why again
+
+ align:start position:0%
+but you didn't exactly say why again
+ 
+
+ align:start position:0%
+but you didn't exactly say why again
+really quick this is what it this we
+
+ align:start position:0%
+really quick this is what it this we
+ 
+
+ align:start position:0%
+really quick this is what it this we
+weren't getting blah out of it or the
+
+ align:start position:0%
+weren't getting blah out of it or the
+ 
+
+ align:start position:0%
+weren't getting blah out of it or the
+flexibility was more whatever um and
+
+ align:start position:0%
+flexibility was more whatever um and
+ 
+
+ align:start position:0%
+flexibility was more whatever um and
+then yeah to oh um defining your terms
+
+ align:start position:0%
+then yeah to oh um defining your terms
+ 
+
+ align:start position:0%
+then yeah to oh um defining your terms
+you're saying things like casual versus
+
+ align:start position:0%
+you're saying things like casual versus
+ 
+
+ align:start position:0%
+you're saying things like casual versus
+hardcore give a little bit of definition
+
+ align:start position:0%
+hardcore give a little bit of definition
+ 
+
+ align:start position:0%
+hardcore give a little bit of definition
+of what you what you mean by that um it
+
+ align:start position:0%
+of what you what you mean by that um it
+ 
+
+ align:start position:0%
+of what you what you mean by that um it
+means different things for everybody so
+
+ align:start position:0%
+means different things for everybody so
+ 
+
+ align:start position:0%
+means different things for everybody so
+what is your what is your use of that
+
+ align:start position:0%
+what is your what is your use of that
+ 
+
+ align:start position:0%
+what is your what is your use of that
+yeah I think you specifically said
+
+ align:start position:0%
+yeah I think you specifically said
+ 
+
+ align:start position:0%
+yeah I think you specifically said
+hardcore and mobile uh but there are
+
+ align:start position:0%
+hardcore and mobile uh but there are
+ 
+
+ align:start position:0%
+hardcore and mobile uh but there are
+hardcore mobile players out there so
+
+ align:start position:0%
+hardcore mobile players out there so
+ 
+
+ align:start position:0%
+hardcore mobile players out there so
+this is this is like and Casual can be
+
+ align:start position:0%
+this is this is like and Casual can be
+ 
+
+ align:start position:0%
+this is this is like and Casual can be
+considered a version of Hardcore just in
+
+ align:start position:0%
+considered a version of Hardcore just in
+ 
+
+ align:start position:0%
+considered a version of Hardcore just in
+a different way so just be really just
+
+ align:start position:0%
+a different way so just be really just
+ 
+
+ align:start position:0%
+a different way so just be really just
+be a little bit more clear about because
+
+ align:start position:0%
+be a little bit more clear about because
+ 
+
+ align:start position:0%
+be a little bit more clear about because
+I think you're talking about the target
+
+ align:start position:0%
+I think you're talking about the target
+ 
+
+ align:start position:0%
+I think you're talking about the target
+audience and the kind of players and the
+
+ align:start position:0%
+audience and the kind of players and the
+ 
+
+ align:start position:0%
+audience and the kind of players and the
+kind of games they might play so just be
+
+ align:start position:0%
+kind of games they might play so just be
+ 
+
+ align:start position:0%
+kind of games they might play so just be
+a little bit more more focused on what
+
+ align:start position:0%
+a little bit more more focused on what
+ 
+
+ align:start position:0%
+a little bit more more focused on what
+exactly you mean by
+
+ align:start position:0%
+exactly you mean by
+ 
+
+ align:start position:0%
+exactly you mean by
+that um that's it for me yeah so just a
+
+ align:start position:0%
+that um that's it for me yeah so just a
+ 
+
+ align:start position:0%
+that um that's it for me yeah so just a
+techical observation young man is not
+
+ align:start position:0%
+techical observation young man is not
+ 
+
+ align:start position:0%
+techical observation young man is not
+really a module frame it's just a system
+
+ align:start position:0%
+really a module frame it's just a system
+ 
+
+ align:start position:0%
+really a module frame it's just a system
+to generate a project and puts different
+
+ align:start position:0%
+to generate a project and puts different
+ 
+
+ align:start position:0%
+to generate a project and puts different
+Frameworks so
+
+ align:start position:0%
+Frameworks so
+ 
+
+ align:start position:0%
+Frameworks so
+just so that's terminology issue
+
+ align:start position:0%
+just so that's terminology issue
+ 
+
+ align:start position:0%
+just so that's terminology issue
+yeah CLE clear clearly it worked out for
+
+ align:start position:0%
+yeah CLE clear clearly it worked out for
+ 
+
+ align:start position:0%
+yeah CLE clear clearly it worked out for
+your team so we're not saying like don't
+
+ align:start position:0%
+your team so we're not saying like don't
+ 
+
+ align:start position:0%
+your team so we're not saying like don't
+mention your man it's clearly a good
+
+ align:start position:0%
+mention your man it's clearly a good
+ 
+
+ align:start position:0%
+mention your man it's clearly a good
+thing but just check your definition of
+
+ align:start position:0%
+thing but just check your definition of
+ 
+
+ align:start position:0%
+thing but just check your definition of
+what it of what it is because because
+
+ align:start position:0%
+what it of what it is because because
+ 
+
+ align:start position:0%
+what it of what it is because because
+it'll be more helpful for other people
+
+ align:start position:0%
+it'll be more helpful for other people
+ 
+
+ align:start position:0%
+it'll be more helpful for other people
+to understand what it is so that they
+
+ align:start position:0%
+to understand what it is so that they
+ 
+
+ align:start position:0%
+to understand what it is so that they
+can think about where they want to use
+
+ align:start position:0%
+can think about where they want to use
+ 
+
+ align:start position:0%
+can think about where they want to use
+it in the future oh actually so your
+
+ align:start position:0%
+it in the future oh actually so your
+ 
+
+ align:start position:0%
+it in the future oh actually so your
+demo you spent about three minutes doing
+
+ align:start position:0%
+demo you spent about three minutes doing
+ 
+
+ align:start position:0%
+demo you spent about three minutes doing
+it um we are going to have you have the
+
+ align:start position:0%
+it um we are going to have you have the
+ 
+
+ align:start position:0%
+it um we are going to have you have the
+a player from the audience play your
+
+ align:start position:0%
+a player from the audience play your
+ 
+
+ align:start position:0%
+a player from the audience play your
+your game live okay without do or
+
+ align:start position:0%
+your game live okay without do or
+ 
+
+ align:start position:0%
+your game live okay without do or
+without getting a lot of help you can
+
+ align:start position:0%
+without getting a lot of help you can
+ 
+
+ align:start position:0%
+without getting a lot of help you can
+talk over it you can after a while start
+
+ align:start position:0%
+talk over it you can after a while start
+ 
+
+ align:start position:0%
+talk over it you can after a while start
+helping them we need we want to see them
+
+ align:start position:0%
+helping them we need we want to see them
+ 
+
+ align:start position:0%
+helping them we need we want to see them
+at least just start playing it on their
+
+ align:start position:0%
+at least just start playing it on their
+ 
+
+ align:start position:0%
+at least just start playing it on their
+own decide when you're going to put that
+
+ align:start position:0%
+own decide when you're going to put that
+ 
+
+ align:start position:0%
+own decide when you're going to put that
+demo in you could actually combine them
+
+ align:start position:0%
+demo in you could actually combine them
+ 
+
+ align:start position:0%
+demo in you could actually combine them
+both together if you do it at the
+
+ align:start position:0%
+both together if you do it at the
+ 
+
+ align:start position:0%
+both together if you do it at the
+beginning or end um but if you do that
+
+ align:start position:0%
+beginning or end um but if you do that
+ 
+
+ align:start position:0%
+beginning or end um but if you do that
+give give the player a little bit of
+
+ align:start position:0%
+give give the player a little bit of
+ 
+
+ align:start position:0%
+give give the player a little bit of
+time before you start talking okay
+
+ align:start position:0%
+time before you start talking okay
+ 
+
+ align:start position:0%
+time before you start talking okay
+sure that's all I got great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks snap come on down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hello we are hello waves we're a game
+
+ align:start position:0%
+hello we are hello waves we're a game
+ 
+
+ align:start position:0%
+hello we are hello waves we're a game
+about forecasting uh specifically this
+
+ align:start position:0%
+about forecasting uh specifically this
+ 
+
+ align:start position:0%
+about forecasting uh specifically this
+idea called forecast based financing of
+
+ align:start position:0%
+idea called forecast based financing of
+ 
+
+ align:start position:0%
+idea called forecast based financing of
+using forecast to make decisions about
+
+ align:start position:0%
+using forecast to make decisions about
+ 
+
+ align:start position:0%
+using forecast to make decisions about
+possible disasters in the future and how
+
+ align:start position:0%
+possible disasters in the future and how
+ 
+
+ align:start position:0%
+possible disasters in the future and how
+to prepare for them we'd actually like
+
+ align:start position:0%
+to prepare for them we'd actually like
+ 
+
+ align:start position:0%
+to prepare for them we'd actually like
+to start with a playthrough of our game
+
+ align:start position:0%
+to start with a playthrough of our game
+ 
+
+ align:start position:0%
+to start with a playthrough of our game
+so if anybody would like to be a
+
+ align:start position:0%
+so if anybody would like to be a
+ 
+
+ align:start position:0%
+so if anybody would like to be a
+volunteer to to try it out a guest from
+
+ align:start position:0%
+volunteer to to try it out a guest from
+ 
+
+ align:start position:0%
+volunteer to to try it out a guest from
+not our class if one could please come
+
+ align:start position:0%
+not our class if one could please come
+ 
+
+ align:start position:0%
+not our class if one could please come
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Andrew thank you for
+
+ align:start position:0%
+Andrew thank you for
+ 
+
+ align:start position:0%
+Andrew thank you for
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+volunteering hi
+
+ align:start position:0%
+volunteering hi
+ 
+
+ align:start position:0%
+volunteering hi
+I'm you a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chair not sure how got full screen but
+
+ align:start position:0%
+chair not sure how got full screen but
+ 
+
+ align:start position:0%
+chair not sure how got full screen but
+um anyways this is our game I'd
+
+ align:start position:0%
+um anyways this is our game I'd
+ 
+
+ align:start position:0%
+um anyways this is our game I'd
+recommend looking at the instructions
+
+ align:start position:0%
+recommend looking at the instructions
+ 
+
+ align:start position:0%
+recommend looking at the instructions
+first and reading through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them and
+
+ align:start position:0%
+them and
+ 
+
+ align:start position:0%
+them and
+we'll keep the description minimal as
+
+ align:start position:0%
+we'll keep the description minimal as
+ 
+
+ align:start position:0%
+we'll keep the description minimal as
+you read through it just to to sure to
+
+ align:start position:0%
+you read through it just to to sure to
+ 
+
+ align:start position:0%
+you read through it just to to sure to
+show the player's initial reaction to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it music
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah start
+
+ align:start position:0%
+okay so yeah start
+ 
+
+ align:start position:0%
+okay so yeah start
+again so as you can see our game as I
+
+ align:start position:0%
+again so as you can see our game as I
+ 
+
+ align:start position:0%
+again so as you can see our game as I
+said before you uh control some toys at
+
+ align:start position:0%
+said before you uh control some toys at
+ 
+
+ align:start position:0%
+said before you uh control some toys at
+uh on a day at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beach and so by dragging and dropping
+
+ align:start position:0%
+beach and so by dragging and dropping
+ 
+
+ align:start position:0%
+beach and so by dragging and dropping
+them between the castles you'll see that
+
+ align:start position:0%
+them between the castles you'll see that
+ 
+
+ align:start position:0%
+them between the castles you'll see that
+their status is Chang change and say
+
+ align:start position:0%
+their status is Chang change and say
+ 
+
+ align:start position:0%
+their status is Chang change and say
+that they want to move on their next
+
+ align:start position:0%
+that they want to move on their next
+ 
+
+ align:start position:0%
+that they want to move on their next
+turn or that they want to be collecting
+
+ align:start position:0%
+turn or that they want to be collecting
+ 
+
+ align:start position:0%
+turn or that they want to be collecting
+or that they're going to be collecting
+
+ align:start position:0%
+or that they're going to be collecting
+ 
+
+ align:start position:0%
+or that they're going to be collecting
+candy or anything like that and the game
+
+ align:start position:0%
+candy or anything like that and the game
+ 
+
+ align:start position:0%
+candy or anything like that and the game
+is turn-based
+
+ align:start position:0%
+is turn-based
+ 
+
+ align:start position:0%
+is turn-based
+so uh all the actions will resolve on
+
+ align:start position:0%
+so uh all the actions will resolve on
+ 
+
+ align:start position:0%
+so uh all the actions will resolve on
+the next turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+am I reading this
+
+ align:start position:0%
+am I reading this
+ 
+
+ align:start position:0%
+am I reading this
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um yeah you can also access the the
+
+ align:start position:0%
+um yeah you can also access the the
+ 
+
+ align:start position:0%
+um yeah you can also access the the
+right corner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so uh when you go to the next to
+
+ align:start position:0%
+and so uh when you go to the next to
+ 
+
+ align:start position:0%
+and so uh when you go to the next to
+turn you'll see all the toys
+
+ align:start position:0%
+turn you'll see all the toys
+ 
+
+ align:start position:0%
+turn you'll see all the toys
+move uh as specified by the status
+
+ align:start position:0%
+move uh as specified by the status
+ 
+
+ align:start position:0%
+move uh as specified by the status
+bubble above their
+
+ align:start position:0%
+bubble above their
+ 
+
+ align:start position:0%
+bubble above their
+heads so to next turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next but unfortunately you'll find that
+
+ align:start position:0%
+next but unfortunately you'll find that
+ 
+
+ align:start position:0%
+next but unfortunately you'll find that
+when toys have been evacuated they're
+
+ align:start position:0%
+when toys have been evacuated they're
+ 
+
+ align:start position:0%
+when toys have been evacuated they're
+unhappy and need candy to survive so
+
+ align:start position:0%
+unhappy and need candy to survive so
+ 
+
+ align:start position:0%
+unhappy and need candy to survive so
+they'll all take
+
+ align:start position:0%
+they'll all take
+ 
+
+ align:start position:0%
+they'll all take
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+damage they don't want
+
+ align:start position:0%
+damage they don't want
+ 
+
+ align:start position:0%
+damage they don't want
+to you can try returning them to their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+homes and so you'll see that on this
+
+ align:start position:0%
+homes and so you'll see that on this
+ 
+
+ align:start position:0%
+homes and so you'll see that on this
+turn instead uh now they have their
+
+ align:start position:0%
+turn instead uh now they have their
+ 
+
+ align:start position:0%
+turn instead uh now they have their
+statuses set to Gathering candy except
+
+ align:start position:0%
+statuses set to Gathering candy except
+ 
+
+ align:start position:0%
+statuses set to Gathering candy except
+for the dun dump truck who's still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+evacuated
+
+ align:start position:0%
+evacuated
+ 
+
+ align:start position:0%
+evacuated
+okay need to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evacuated
+
+ align:start position:0%
+evacuated
+ 
+
+ align:start position:0%
+evacuated
+exactly and so the the idea is that as
+
+ align:start position:0%
+exactly and so the the idea is that as
+ 
+
+ align:start position:0%
+exactly and so the the idea is that as
+the player plays through it they get
+
+ align:start position:0%
+the player plays through it they get
+ 
+
+ align:start position:0%
+the player plays through it they get
+better at understanding how to use the
+
+ align:start position:0%
+better at understanding how to use the
+ 
+
+ align:start position:0%
+better at understanding how to use the
+forecast to make decisions about the
+
+ align:start position:0%
+forecast to make decisions about the
+ 
+
+ align:start position:0%
+forecast to make decisions about the
+future uh both in terms of how much
+
+ align:start position:0%
+future uh both in terms of how much
+ 
+
+ align:start position:0%
+future uh both in terms of how much
+candy that they need to have stocked up
+
+ align:start position:0%
+candy that they need to have stocked up
+ 
+
+ align:start position:0%
+candy that they need to have stocked up
+in order to weather out the rising tides
+
+ align:start position:0%
+in order to weather out the rising tides
+ 
+
+ align:start position:0%
+in order to weather out the rising tides
+and also in terms of uh when they're
+
+ align:start position:0%
+and also in terms of uh when they're
+ 
+
+ align:start position:0%
+and also in terms of uh when they're
+going to need to move their workers out
+
+ align:start position:0%
+going to need to move their workers out
+ 
+
+ align:start position:0%
+going to need to move their workers out
+of their toys out of areas that are in
+
+ align:start position:0%
+of their toys out of areas that are in
+ 
+
+ align:start position:0%
+of their toys out of areas that are in
+danger they're going to be really imp
+
+ align:start position:0%
+danger they're going to be really imp
+ 
+
+ align:start position:0%
+danger they're going to be really imp
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I think you have those two guys
+
+ align:start position:0%
+um I think you have those two guys
+ 
+
+ align:start position:0%
+um I think you have those two guys
+so is there a reminder of where they
+
+ align:start position:0%
+so is there a reminder of where they
+ 
+
+ align:start position:0%
+so is there a reminder of where they
+started yeah it's on the castle it's
+
+ align:start position:0%
+started yeah it's on the castle it's
+ 
+
+ align:start position:0%
+started yeah it's on the castle it's
+actually blocked out right now by by the
+
+ align:start position:0%
+actually blocked out right now by by the
+ 
+
+ align:start position:0%
+actually blocked out right now by by the
+toys in front of it but there's a little
+
+ align:start position:0%
+toys in front of it but there's a little
+ 
+
+ align:start position:0%
+toys in front of it but there's a little
+Shadow on there an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imprint and because because he ran out
+
+ align:start position:0%
+imprint and because because he ran out
+ 
+
+ align:start position:0%
+imprint and because because he ran out
+of candy and then or actually sorry
+
+ align:start position:0%
+of candy and then or actually sorry
+ 
+
+ align:start position:0%
+of candy and then or actually sorry
+because he went to a place that was
+
+ align:start position:0%
+because he went to a place that was
+ 
+
+ align:start position:0%
+because he went to a place that was
+underwater uh he took too much damage
+
+ align:start position:0%
+underwater uh he took too much damage
+ 
+
+ align:start position:0%
+underwater uh he took too much damage
+and then was Swept Away by the waves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on the forecast you can see that
+
+ align:start position:0%
+and so on the forecast you can see that
+ 
+
+ align:start position:0%
+and so on the forecast you can see that
+high water is coming for quite a while
+
+ align:start position:0%
+high water is coming for quite a while
+ 
+
+ align:start position:0%
+high water is coming for quite a while
+uh which is going to be a danger for the
+
+ align:start position:0%
+uh which is going to be a danger for the
+ 
+
+ align:start position:0%
+uh which is going to be a danger for the
+toys both in terms of possibly getting
+
+ align:start position:0%
+toys both in terms of possibly getting
+ 
+
+ align:start position:0%
+toys both in terms of possibly getting
+swept away and not having enough candy
+
+ align:start position:0%
+swept away and not having enough candy
+ 
+
+ align:start position:0%
+swept away and not having enough candy
+uh for all the toys that you're going to
+
+ align:start position:0%
+uh for all the toys that you're going to
+ 
+
+ align:start position:0%
+uh for all the toys that you're going to
+have to move out of the way
+
+ align:start position:0%
+have to move out of the way
+ 
+
+ align:start position:0%
+have to move out of the way
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh he may be out of luck
+
+ align:start position:0%
+oh he may be out of luck
+ 
+
+ align:start position:0%
+oh he may be out of luck
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah and when you've lost two toys you
+
+ align:start position:0%
+yeah and when you've lost two toys you
+ 
+
+ align:start position:0%
+yeah and when you've lost two toys you
+lose the
+
+ align:start position:0%
+lose the
+ 
+
+ align:start position:0%
+lose the
+game okay thank you for
+
+ align:start position:0%
+game okay thank you for
+ 
+
+ align:start position:0%
+game okay thank you for
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+playing so that's hello
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in our game we had uh a few
+
+ align:start position:0%
+so in our game we had uh a few
+ 
+
+ align:start position:0%
+so in our game we had uh a few
+challenges to overcome the first was
+
+ align:start position:0%
+challenges to overcome the first was
+ 
+
+ align:start position:0%
+challenges to overcome the first was
+that our game was based on forecast
+
+ align:start position:0%
+that our game was based on forecast
+ 
+
+ align:start position:0%
+that our game was based on forecast
+based financing which is a very abstract
+
+ align:start position:0%
+based financing which is a very abstract
+ 
+
+ align:start position:0%
+based financing which is a very abstract
+topic it's it's a pretty understandable
+
+ align:start position:0%
+topic it's it's a pretty understandable
+ 
+
+ align:start position:0%
+topic it's it's a pretty understandable
+idea of using information about the
+
+ align:start position:0%
+idea of using information about the
+ 
+
+ align:start position:0%
+idea of using information about the
+future and ideas of risk in order to
+
+ align:start position:0%
+future and ideas of risk in order to
+ 
+
+ align:start position:0%
+future and ideas of risk in order to
+decide where to allocate resources but
+
+ align:start position:0%
+decide where to allocate resources but
+ 
+
+ align:start position:0%
+decide where to allocate resources but
+it's still a bit abstract and building a
+
+ align:start position:0%
+it's still a bit abstract and building a
+ 
+
+ align:start position:0%
+it's still a bit abstract and building a
+game around it uh took a little bit of
+
+ align:start position:0%
+game around it uh took a little bit of
+ 
+
+ align:start position:0%
+game around it uh took a little bit of
+work it's useful to note that it's
+
+ align:start position:0%
+work it's useful to note that it's
+ 
+
+ align:start position:0%
+work it's useful to note that it's
+different than long-term planning it's
+
+ align:start position:0%
+different than long-term planning it's
+ 
+
+ align:start position:0%
+different than long-term planning it's
+not just thinking about what what will
+
+ align:start position:0%
+not just thinking about what what will
+ 
+
+ align:start position:0%
+not just thinking about what what will
+happen in the future you know building a
+
+ align:start position:0%
+happen in the future you know building a
+ 
+
+ align:start position:0%
+happen in the future you know building a
+dam to prevent water or things like that
+
+ align:start position:0%
+dam to prevent water or things like that
+ 
+
+ align:start position:0%
+dam to prevent water or things like that
+it's actually about using the
+
+ align:start position:0%
+it's actually about using the
+ 
+
+ align:start position:0%
+it's actually about using the
+information you have to make the best
+
+ align:start position:0%
+information you have to make the best
+ 
+
+ align:start position:0%
+information you have to make the best
+decision for events that may be upcoming
+
+ align:start position:0%
+decision for events that may be upcoming
+ 
+
+ align:start position:0%
+decision for events that may be upcoming
+in the semi near
+
+ align:start position:0%
+in the semi near
+ 
+
+ align:start position:0%
+in the semi near
+future we also wanted to avoid making a
+
+ align:start position:0%
+future we also wanted to avoid making a
+ 
+
+ align:start position:0%
+future we also wanted to avoid making a
+game that was overly preachy or
+
+ align:start position:0%
+game that was overly preachy or
+ 
+
+ align:start position:0%
+game that was overly preachy or
+simplified where it was clear H exactly
+
+ align:start position:0%
+simplified where it was clear H exactly
+ 
+
+ align:start position:0%
+simplified where it was clear H exactly
+how you're going to win and you could
+
+ align:start position:0%
+how you're going to win and you could
+ 
+
+ align:start position:0%
+how you're going to win and you could
+just basically push the forecast based
+
+ align:start position:0%
+just basically push the forecast based
+ 
+
+ align:start position:0%
+just basically push the forecast based
+financing button to win the game we want
+
+ align:start position:0%
+financing button to win the game we want
+ 
+
+ align:start position:0%
+financing button to win the game we want
+players to actually think and understand
+
+ align:start position:0%
+players to actually think and understand
+ 
+
+ align:start position:0%
+players to actually think and understand
+the concepts there instead of just you
+
+ align:start position:0%
+the concepts there instead of just you
+ 
+
+ align:start position:0%
+the concepts there instead of just you
+know coming up with the buzzword of
+
+ align:start position:0%
+know coming up with the buzzword of
+ 
+
+ align:start position:0%
+know coming up with the buzzword of
+forecast based financing and finally we
+
+ align:start position:0%
+forecast based financing and finally we
+ 
+
+ align:start position:0%
+forecast based financing and finally we
+had the challenge of actually
+
+ align:start position:0%
+had the challenge of actually
+ 
+
+ align:start position:0%
+had the challenge of actually
+communicating that forecast 2 players in
+
+ align:start position:0%
+communicating that forecast 2 players in
+ 
+
+ align:start position:0%
+communicating that forecast 2 players in
+a way that they would be able to
+
+ align:start position:0%
+a way that they would be able to
+ 
+
+ align:start position:0%
+a way that they would be able to
+understand and then make use of you
+
+ align:start position:0%
+understand and then make use of you
+ 
+
+ align:start position:0%
+understand and then make use of you
+could see in that game that we had water
+
+ align:start position:0%
+could see in that game that we had water
+ 
+
+ align:start position:0%
+could see in that game that we had water
+levels and it would show on the map and
+
+ align:start position:0%
+levels and it would show on the map and
+ 
+
+ align:start position:0%
+levels and it would show on the map and
+we found that players were pretty good
+
+ align:start position:0%
+we found that players were pretty good
+ 
+
+ align:start position:0%
+we found that players were pretty good
+at using that in order to decide to make
+
+ align:start position:0%
+at using that in order to decide to make
+ 
+
+ align:start position:0%
+at using that in order to decide to make
+decisions about what was going to happen
+
+ align:start position:0%
+decisions about what was going to happen
+ 
+
+ align:start position:0%
+decisions about what was going to happen
+in the future and how to allocate their
+
+ align:start position:0%
+in the future and how to allocate their
+ 
+
+ align:start position:0%
+in the future and how to allocate their
+resources the other big challenge that
+
+ align:start position:0%
+resources the other big challenge that
+ 
+
+ align:start position:0%
+resources the other big challenge that
+we had in the beginning was that our
+
+ align:start position:0%
+we had in the beginning was that our
+ 
+
+ align:start position:0%
+we had in the beginning was that our
+initial target audience was policy
+
+ align:start position:0%
+initial target audience was policy
+ 
+
+ align:start position:0%
+initial target audience was policy
+makers uh like for SNAP Pablo had come
+
+ align:start position:0%
+makers uh like for SNAP Pablo had come
+ 
+
+ align:start position:0%
+makers uh like for SNAP Pablo had come
+in and pitched us to this game idea and
+
+ align:start position:0%
+in and pitched us to this game idea and
+ 
+
+ align:start position:0%
+in and pitched us to this game idea and
+originally he had wanted us to build a
+
+ align:start position:0%
+originally he had wanted us to build a
+ 
+
+ align:start position:0%
+originally he had wanted us to build a
+game for policy makers that would help
+
+ align:start position:0%
+game for policy makers that would help
+ 
+
+ align:start position:0%
+game for policy makers that would help
+them understand the benefits of forecast
+
+ align:start position:0%
+them understand the benefits of forecast
+ 
+
+ align:start position:0%
+them understand the benefits of forecast
+based financing and therefore convinc
+
+ align:start position:0%
+based financing and therefore convinc
+ 
+
+ align:start position:0%
+based financing and therefore convinc
+them that they should develop policies
+
+ align:start position:0%
+them that they should develop policies
+ 
+
+ align:start position:0%
+them that they should develop policies
+that would uh give resources to plans
+
+ align:start position:0%
+that would uh give resources to plans
+ 
+
+ align:start position:0%
+that would uh give resources to plans
+based on forecast based
+
+ align:start position:0%
+based on forecast based
+ 
+
+ align:start position:0%
+based on forecast based
+financing so i' would like to take you
+
+ align:start position:0%
+financing so i' would like to take you
+ 
+
+ align:start position:0%
+financing so i' would like to take you
+through a couple of our prototypes just
+
+ align:start position:0%
+through a couple of our prototypes just
+ 
+
+ align:start position:0%
+through a couple of our prototypes just
+to show you the evolution and comment
+
+ align:start position:0%
+to show you the evolution and comment
+ 
+
+ align:start position:0%
+to show you the evolution and comment
+sort of on our
+
+ align:start position:0%
+sort of on our
+ 
+
+ align:start position:0%
+sort of on our
+process uh actually and to to preface
+
+ align:start position:0%
+process uh actually and to to preface
+ 
+
+ align:start position:0%
+process uh actually and to to preface
+that we had a lot of prototypes because
+
+ align:start position:0%
+that we had a lot of prototypes because
+ 
+
+ align:start position:0%
+that we had a lot of prototypes because
+because our idea was so abstract and
+
+ align:start position:0%
+because our idea was so abstract and
+ 
+
+ align:start position:0%
+because our idea was so abstract and
+because we weren't sure how to address
+
+ align:start position:0%
+because we weren't sure how to address
+ 
+
+ align:start position:0%
+because we weren't sure how to address
+our audience so we built a lot of
+
+ align:start position:0%
+our audience so we built a lot of
+ 
+
+ align:start position:0%
+our audience so we built a lot of
+prototypes to start with uh we had ideas
+
+ align:start position:0%
+prototypes to start with uh we had ideas
+ 
+
+ align:start position:0%
+prototypes to start with uh we had ideas
+that ranged across sort of levels of
+
+ align:start position:0%
+that ranged across sort of levels of
+ 
+
+ align:start position:0%
+that ranged across sort of levels of
+scope of what you controlled where you
+
+ align:start position:0%
+scope of what you controlled where you
+ 
+
+ align:start position:0%
+scope of what you controlled where you
+controlled entire cities or where you
+
+ align:start position:0%
+controlled entire cities or where you
+ 
+
+ align:start position:0%
+controlled entire cities or where you
+controlled individual workers and moved
+
+ align:start position:0%
+controlled individual workers and moved
+ 
+
+ align:start position:0%
+controlled individual workers and moved
+them around and then we would pull from
+
+ align:start position:0%
+them around and then we would pull from
+ 
+
+ align:start position:0%
+them around and then we would pull from
+all these different kinds of ideas what
+
+ align:start position:0%
+all these different kinds of ideas what
+ 
+
+ align:start position:0%
+all these different kinds of ideas what
+worked what didn't what did people
+
+ align:start position:0%
+worked what didn't what did people
+ 
+
+ align:start position:0%
+worked what didn't what did people
+understand what confused them and from
+
+ align:start position:0%
+understand what confused them and from
+ 
+
+ align:start position:0%
+understand what confused them and from
+that we got a really good idea of what
+
+ align:start position:0%
+that we got a really good idea of what
+ 
+
+ align:start position:0%
+that we got a really good idea of what
+concepts helped people understand the
+
+ align:start position:0%
+concepts helped people understand the
+ 
+
+ align:start position:0%
+concepts helped people understand the
+idea and brought them into this final
+
+ align:start position:0%
+idea and brought them into this final
+ 
+
+ align:start position:0%
+idea and brought them into this final
+game that we ended up with
+
+ align:start position:0%
+game that we ended up with
+ 
+
+ align:start position:0%
+game that we ended up with
+so the project started on October 15th
+
+ align:start position:0%
+so the project started on October 15th
+ 
+
+ align:start position:0%
+so the project started on October 15th
+and this was our first prototype it was
+
+ align:start position:0%
+and this was our first prototype it was
+ 
+
+ align:start position:0%
+and this was our first prototype it was
+a terminal based game where you had some
+
+ align:start position:0%
+a terminal based game where you had some
+ 
+
+ align:start position:0%
+a terminal based game where you had some
+kind of information about a future
+
+ align:start position:0%
+kind of information about a future
+ 
+
+ align:start position:0%
+kind of information about a future
+rainfall and then you had to type in
+
+ align:start position:0%
+rainfall and then you had to type in
+ 
+
+ align:start position:0%
+rainfall and then you had to type in
+your commands of how you control
+
+ align:start position:0%
+your commands of how you control
+ 
+
+ align:start position:0%
+your commands of how you control
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+cities this actually people found it fun
+
+ align:start position:0%
+cities this actually people found it fun
+ 
+
+ align:start position:0%
+cities this actually people found it fun
+but as you might expect the feedback
+
+ align:start position:0%
+but as you might expect the feedback
+ 
+
+ align:start position:0%
+but as you might expect the feedback
+wasn't very good and people didn't quite
+
+ align:start position:0%
+wasn't very good and people didn't quite
+ 
+
+ align:start position:0%
+wasn't very good and people didn't quite
+understand how to move forward with it
+
+ align:start position:0%
+understand how to move forward with it
+ 
+
+ align:start position:0%
+understand how to move forward with it
+it made it it put a lot of cognitive
+
+ align:start position:0%
+it made it it put a lot of cognitive
+ 
+
+ align:start position:0%
+it made it it put a lot of cognitive
+load on people so when we move forward
+
+ align:start position:0%
+load on people so when we move forward
+ 
+
+ align:start position:0%
+load on people so when we move forward
+we tried to give people more easily
+
+ align:start position:0%
+we tried to give people more easily
+ 
+
+ align:start position:0%
+we tried to give people more easily
+understandable actions to use but the
+
+ align:start position:0%
+understandable actions to use but the
+ 
+
+ align:start position:0%
+understandable actions to use but the
+problem with this game was that it was
+
+ align:start position:0%
+problem with this game was that it was
+ 
+
+ align:start position:0%
+problem with this game was that it was
+time based and it updated every second
+
+ align:start position:0%
+time based and it updated every second
+ 
+
+ align:start position:0%
+time based and it updated every second
+and so there were so many numbers flying
+
+ align:start position:0%
+and so there were so many numbers flying
+ 
+
+ align:start position:0%
+and so there were so many numbers flying
+at people that even MIT students who
+
+ align:start position:0%
+at people that even MIT students who
+ 
+
+ align:start position:0%
+at people that even MIT students who
+play tested it couldn't understand so we
+
+ align:start position:0%
+play tested it couldn't understand so we
+ 
+
+ align:start position:0%
+play tested it couldn't understand so we
+figured that people like policy makers
+
+ align:start position:0%
+figured that people like policy makers
+ 
+
+ align:start position:0%
+figured that people like policy makers
+who didn't have much experience with
+
+ align:start position:0%
+who didn't have much experience with
+ 
+
+ align:start position:0%
+who didn't have much experience with
+games really wouldn't be able to
+
+ align:start position:0%
+games really wouldn't be able to
+ 
+
+ align:start position:0%
+games really wouldn't be able to
+understand the game at all so instead we
+
+ align:start position:0%
+understand the game at all so instead we
+ 
+
+ align:start position:0%
+understand the game at all so instead we
+went to turn-based
+
+ align:start position:0%
+went to turn-based
+ 
+
+ align:start position:0%
+went to turn-based
+and that helped but at the same time
+
+ align:start position:0%
+and that helped but at the same time
+ 
+
+ align:start position:0%
+and that helped but at the same time
+it's tough to see on this projector but
+
+ align:start position:0%
+it's tough to see on this projector but
+ 
+
+ align:start position:0%
+it's tough to see on this projector but
+we have a forecast underneath that says
+
+ align:start position:0%
+we have a forecast underneath that says
+ 
+
+ align:start position:0%
+we have a forecast underneath that says
+how much rainfall is it expected and
+
+ align:start position:0%
+how much rainfall is it expected and
+ 
+
+ align:start position:0%
+how much rainfall is it expected and
+again that wasn't understandable to
+
+ align:start position:0%
+again that wasn't understandable to
+ 
+
+ align:start position:0%
+again that wasn't understandable to
+people cuz they couldn't understand what
+
+ align:start position:0%
+people cuz they couldn't understand what
+ 
+
+ align:start position:0%
+people cuz they couldn't understand what
+3 in of rainfall meant for their city
+
+ align:start position:0%
+3 in of rainfall meant for their city
+ 
+
+ align:start position:0%
+3 in of rainfall meant for their city
+and they couldn't understand how that
+
+ align:start position:0%
+and they couldn't understand how that
+ 
+
+ align:start position:0%
+and they couldn't understand how that
+contributed to a possible disaster at
+
+ align:start position:0%
+contributed to a possible disaster at
+ 
+
+ align:start position:0%
+contributed to a possible disaster at
+this point Pablo actually came by the
+
+ align:start position:0%
+this point Pablo actually came by the
+ 
+
+ align:start position:0%
+this point Pablo actually came by the
+class and played the game and then he
+
+ align:start position:0%
+class and played the game and then he
+ 
+
+ align:start position:0%
+class and played the game and then he
+told us that he wasn't even sure that he
+
+ align:start position:0%
+told us that he wasn't even sure that he
+ 
+
+ align:start position:0%
+told us that he wasn't even sure that he
+could get policy makers to play the game
+
+ align:start position:0%
+could get policy makers to play the game
+ 
+
+ align:start position:0%
+could get policy makers to play the game
+because they may not have enough time
+
+ align:start position:0%
+because they may not have enough time
+ 
+
+ align:start position:0%
+because they may not have enough time
+instead he wanted us to switch to grade
+
+ align:start position:0%
+instead he wanted us to switch to grade
+ 
+
+ align:start position:0%
+instead he wanted us to switch to grade
+schoolers because we could teach them
+
+ align:start position:0%
+schoolers because we could teach them
+ 
+
+ align:start position:0%
+schoolers because we could teach them
+something about forecast based financing
+
+ align:start position:0%
+something about forecast based financing
+ 
+
+ align:start position:0%
+something about forecast based financing
+and help them understand as they grew
+
+ align:start position:0%
+and help them understand as they grew
+ 
+
+ align:start position:0%
+and help them understand as they grew
+up and this was great for us because
+
+ align:start position:0%
+up and this was great for us because
+ 
+
+ align:start position:0%
+up and this was great for us because
+making a game that was serious easy for
+
+ align:start position:0%
+making a game that was serious easy for
+ 
+
+ align:start position:0%
+making a game that was serious easy for
+somebody who didn't have experience with
+
+ align:start position:0%
+somebody who didn't have experience with
+ 
+
+ align:start position:0%
+somebody who didn't have experience with
+games to play and also fun and engaging
+
+ align:start position:0%
+games to play and also fun and engaging
+ 
+
+ align:start position:0%
+games to play and also fun and engaging
+was too difficult for us actually so
+
+ align:start position:0%
+was too difficult for us actually so
+ 
+
+ align:start position:0%
+was too difficult for us actually so
+moving to grade schoolers was awesome he
+
+ align:start position:0%
+moving to grade schoolers was awesome he
+ 
+
+ align:start position:0%
+moving to grade schoolers was awesome he
+also suggested that we try to make the
+
+ align:start position:0%
+also suggested that we try to make the
+ 
+
+ align:start position:0%
+also suggested that we try to make the
+idea of rainfall or water levels more
+
+ align:start position:0%
+idea of rainfall or water levels more
+ 
+
+ align:start position:0%
+idea of rainfall or water levels more
+visceral and that's when we came upon
+
+ align:start position:0%
+visceral and that's when we came upon
+ 
+
+ align:start position:0%
+visceral and that's when we came upon
+this idea of the rising Waters whenever
+
+ align:start position:0%
+this idea of the rising Waters whenever
+ 
+
+ align:start position:0%
+this idea of the rising Waters whenever
+players looked at this they instantly
+
+ align:start position:0%
+players looked at this they instantly
+ 
+
+ align:start position:0%
+players looked at this they instantly
+understood the concept of the game the
+
+ align:start position:0%
+understood the concept of the game the
+ 
+
+ align:start position:0%
+understood the concept of the game the
+feedback might not be there the
+
+ align:start position:0%
+feedback might not be there the
+ 
+
+ align:start position:0%
+feedback might not be there the
+Beautiful You might not be there but the
+
+ align:start position:0%
+Beautiful You might not be there but the
+ 
+
+ align:start position:0%
+Beautiful You might not be there but the
+idea of having cities with workers in
+
+ align:start position:0%
+idea of having cities with workers in
+ 
+
+ align:start position:0%
+idea of having cities with workers in
+them and a rising water level coming
+
+ align:start position:0%
+them and a rising water level coming
+ 
+
+ align:start position:0%
+them and a rising water level coming
+towards them everybody understood that
+
+ align:start position:0%
+towards them everybody understood that
+ 
+
+ align:start position:0%
+towards them everybody understood that
+and it made it a lot easier for players
+
+ align:start position:0%
+and it made it a lot easier for players
+ 
+
+ align:start position:0%
+and it made it a lot easier for players
+to reason about the game from there we
+
+ align:start position:0%
+to reason about the game from there we
+ 
+
+ align:start position:0%
+to reason about the game from there we
+added things like nicer art better
+
+ align:start position:0%
+added things like nicer art better
+ 
+
+ align:start position:0%
+added things like nicer art better
+feedback which you can't quite see in
+
+ align:start position:0%
+feedback which you can't quite see in
+ 
+
+ align:start position:0%
+feedback which you can't quite see in
+the static picture uh more improvements
+
+ align:start position:0%
+the static picture uh more improvements
+ 
+
+ align:start position:0%
+the static picture uh more improvements
+to how the forecast worked and uh
+
+ align:start position:0%
+to how the forecast worked and uh
+ 
+
+ align:start position:0%
+to how the forecast worked and uh
+eventually we ended up with our final
+
+ align:start position:0%
+eventually we ended up with our final
+ 
+
+ align:start position:0%
+eventually we ended up with our final
+version
+
+ align:start position:0%
+version
+ 
+
+ align:start position:0%
+version
+today uh yeah so to talk a little bit
+
+ align:start position:0%
+today uh yeah so to talk a little bit
+ 
+
+ align:start position:0%
+today uh yeah so to talk a little bit
+about our actual development process so
+
+ align:start position:0%
+about our actual development process so
+ 
+
+ align:start position:0%
+about our actual development process so
+our team was structured into three main
+
+ align:start position:0%
+our team was structured into three main
+ 
+
+ align:start position:0%
+our team was structured into three main
+sub teams production which was in charge
+
+ align:start position:0%
+sub teams production which was in charge
+ 
+
+ align:start position:0%
+sub teams production which was in charge
+of managerial roles deliverables and
+
+ align:start position:0%
+of managerial roles deliverables and
+ 
+
+ align:start position:0%
+of managerial roles deliverables and
+play testing and so there was a shared
+
+ align:start position:0%
+play testing and so there was a shared
+ 
+
+ align:start position:0%
+play testing and so there was a shared
+responsibility of like um their uh
+
+ align:start position:0%
+responsibility of like um their uh
+ 
+
+ align:start position:0%
+responsibility of like um their uh
+technical team which was in charge of
+
+ align:start position:0%
+technical team which was in charge of
+ 
+
+ align:start position:0%
+technical team which was in charge of
+the bulk of the uh coding work and a
+
+ align:start position:0%
+the bulk of the uh coding work and a
+ 
+
+ align:start position:0%
+the bulk of the uh coding work and a
+user experience team which would be in
+
+ align:start position:0%
+user experience team which would be in
+ 
+
+ align:start position:0%
+user experience team which would be in
+charge of assets UI design and UI design
+
+ align:start position:0%
+charge of assets UI design and UI design
+ 
+
+ align:start position:0%
+charge of assets UI design and UI design
+um we also initially invisioned like a
+
+ align:start position:0%
+um we also initially invisioned like a
+ 
+
+ align:start position:0%
+um we also initially invisioned like a
+sub team leaders where we'd be kind of
+
+ align:start position:0%
+sub team leaders where we'd be kind of
+ 
+
+ align:start position:0%
+sub team leaders where we'd be kind of
+communicating through those but uh we
+
+ align:start position:0%
+communicating through those but uh we
+ 
+
+ align:start position:0%
+communicating through those but uh we
+found the concept kind of redundant and
+
+ align:start position:0%
+found the concept kind of redundant and
+ 
+
+ align:start position:0%
+found the concept kind of redundant and
+so we worked pretty much with like a
+
+ align:start position:0%
+so we worked pretty much with like a
+ 
+
+ align:start position:0%
+so we worked pretty much with like a
+flat structure between the three
+
+ align:start position:0%
+flat structure between the three
+ 
+
+ align:start position:0%
+flat structure between the three
+teams um so from the beginning we
+
+ align:start position:0%
+teams um so from the beginning we
+ 
+
+ align:start position:0%
+teams um so from the beginning we
+encouraged good coding practice and so
+
+ align:start position:0%
+encouraged good coding practice and so
+ 
+
+ align:start position:0%
+encouraged good coding practice and so
+we used uh good tools available to us
+
+ align:start position:0%
+we used uh good tools available to us
+ 
+
+ align:start position:0%
+we used uh good tools available to us
+one of these is um Yen which is a
+
+ align:start position:0%
+one of these is um Yen which is a
+ 
+
+ align:start position:0%
+one of these is um Yen which is a
+JavaScript scaffolding framework um and
+
+ align:start position:0%
+JavaScript scaffolding framework um and
+ 
+
+ align:start position:0%
+JavaScript scaffolding framework um and
+this helped us out a lot by basically
+
+ align:start position:0%
+this helped us out a lot by basically
+ 
+
+ align:start position:0%
+this helped us out a lot by basically
+automating a lot of our JavaScript tasks
+
+ align:start position:0%
+automating a lot of our JavaScript tasks
+ 
+
+ align:start position:0%
+automating a lot of our JavaScript tasks
+and making our code
+
+ align:start position:0%
+and making our code
+ 
+
+ align:start position:0%
+and making our code
+modular um we also used pH State machine
+
+ align:start position:0%
+modular um we also used pH State machine
+ 
+
+ align:start position:0%
+modular um we also used pH State machine
+which is this kind of kind of badly
+
+ align:start position:0%
+which is this kind of kind of badly
+ 
+
+ align:start position:0%
+which is this kind of kind of badly
+documented like new Fe feature in the
+
+ align:start position:0%
+documented like new Fe feature in the
+ 
+
+ align:start position:0%
+documented like new Fe feature in the
+phaser game engine which was the uh
+
+ align:start position:0%
+phaser game engine which was the uh
+ 
+
+ align:start position:0%
+phaser game engine which was the uh
+JavaScript game engine that we used um
+
+ align:start position:0%
+JavaScript game engine that we used um
+ 
+
+ align:start position:0%
+JavaScript game engine that we used um
+it's a bit badly documented so um but it
+
+ align:start position:0%
+it's a bit badly documented so um but it
+ 
+
+ align:start position:0%
+it's a bit badly documented so um but it
+did save us a lot of headaches and once
+
+ align:start position:0%
+did save us a lot of headaches and once
+ 
+
+ align:start position:0%
+did save us a lot of headaches and once
+we figured that out that was uh proved
+
+ align:start position:0%
+we figured that out that was uh proved
+ 
+
+ align:start position:0%
+we figured that out that was uh proved
+immensely helpful and we also used MVC
+
+ align:start position:0%
+immensely helpful and we also used MVC
+ 
+
+ align:start position:0%
+immensely helpful and we also used MVC
+which is a computer uh computer software
+
+ align:start position:0%
+which is a computer uh computer software
+ 
+
+ align:start position:0%
+which is a computer uh computer software
+engineering term standing for model view
+
+ align:start position:0%
+engineering term standing for model view
+ 
+
+ align:start position:0%
+engineering term standing for model view
+controller and again um by by
+
+ align:start position:0%
+controller and again um by by
+ 
+
+ align:start position:0%
+controller and again um by by
+encouraging these good coding practices
+
+ align:start position:0%
+encouraging these good coding practices
+ 
+
+ align:start position:0%
+encouraging these good coding practices
+we reduced dependencies and uh made sure
+
+ align:start position:0%
+we reduced dependencies and uh made sure
+ 
+
+ align:start position:0%
+we reduced dependencies and uh made sure
+that our team was
+
+ align:start position:0%
+that our team was
+ 
+
+ align:start position:0%
+that our team was
+productive um in terms of communication
+
+ align:start position:0%
+productive um in terms of communication
+ 
+
+ align:start position:0%
+productive um in terms of communication
+we also similar to snap use slack which
+
+ align:start position:0%
+we also similar to snap use slack which
+ 
+
+ align:start position:0%
+we also similar to snap use slack which
+is kind of like a modernized chat room
+
+ align:start position:0%
+is kind of like a modernized chat room
+ 
+
+ align:start position:0%
+is kind of like a modernized chat room
+it's very featur rich and so you can
+
+ align:start position:0%
+it's very featur rich and so you can
+ 
+
+ align:start position:0%
+it's very featur rich and so you can
+share files Channel and things like that
+
+ align:start position:0%
+share files Channel and things like that
+ 
+
+ align:start position:0%
+share files Channel and things like that
+and we also use the idea of the uh daily
+
+ align:start position:0%
+and we also use the idea of the uh daily
+ 
+
+ align:start position:0%
+and we also use the idea of the uh daily
+scrum we implemented it in class and we
+
+ align:start position:0%
+scrum we implemented it in class and we
+ 
+
+ align:start position:0%
+scrum we implemented it in class and we
+would say what we had done that class
+
+ align:start position:0%
+would say what we had done that class
+ 
+
+ align:start position:0%
+would say what we had done that class
+what we would be doing um and what we
+
+ align:start position:0%
+what we would be doing um and what we
+ 
+
+ align:start position:0%
+what we would be doing um and what we
+wanted to do uh until next
+
+ align:start position:0%
+wanted to do uh until next
+ 
+
+ align:start position:0%
+wanted to do uh until next
+class and so now the major challenges
+
+ align:start position:0%
+class and so now the major challenges
+ 
+
+ align:start position:0%
+class and so now the major challenges
+that we faced during the development
+
+ align:start position:0%
+that we faced during the development
+ 
+
+ align:start position:0%
+that we faced during the development
+process though um where that our team
+
+ align:start position:0%
+process though um where that our team
+ 
+
+ align:start position:0%
+process though um where that our team
+members came from very different
+
+ align:start position:0%
+members came from very different
+ 
+
+ align:start position:0%
+members came from very different
+backgrounds and had very different
+
+ align:start position:0%
+backgrounds and had very different
+ 
+
+ align:start position:0%
+backgrounds and had very different
+preferences about games you know some of
+
+ align:start position:0%
+preferences about games you know some of
+ 
+
+ align:start position:0%
+preferences about games you know some of
+our some of our team members were
+
+ align:start position:0%
+our some of our team members were
+ 
+
+ align:start position:0%
+our some of our team members were
+hardcore Starcraft players and you know
+
+ align:start position:0%
+hardcore Starcraft players and you know
+ 
+
+ align:start position:0%
+hardcore Starcraft players and you know
+very good at RTS games while other
+
+ align:start position:0%
+very good at RTS games while other
+ 
+
+ align:start position:0%
+very good at RTS games while other
+members of our team preferred like a
+
+ align:start position:0%
+members of our team preferred like a
+ 
+
+ align:start position:0%
+members of our team preferred like a
+more laid-back you know mobile game
+
+ align:start position:0%
+more laid-back you know mobile game
+ 
+
+ align:start position:0%
+more laid-back you know mobile game
+Fruit Ninja kind of approach and so
+
+ align:start position:0%
+Fruit Ninja kind of approach and so
+ 
+
+ align:start position:0%
+Fruit Ninja kind of approach and so
+trying to like mediate those two
+
+ align:start position:0%
+trying to like mediate those two
+ 
+
+ align:start position:0%
+trying to like mediate those two
+viewpoints and trying to create a game
+
+ align:start position:0%
+viewpoints and trying to create a game
+ 
+
+ align:start position:0%
+viewpoints and trying to create a game
+that would engage both uh both types of
+
+ align:start position:0%
+that would engage both uh both types of
+ 
+
+ align:start position:0%
+that would engage both uh both types of
+Gamers was a challenge that we had to
+
+ align:start position:0%
+Gamers was a challenge that we had to
+ 
+
+ align:start position:0%
+Gamers was a challenge that we had to
+overcome um and so another big challenge
+
+ align:start position:0%
+overcome um and so another big challenge
+ 
+
+ align:start position:0%
+overcome um and so another big challenge
+that we had in our development process
+
+ align:start position:0%
+that we had in our development process
+ 
+
+ align:start position:0%
+that we had in our development process
+you know as you saw through our uh uh
+
+ align:start position:0%
+you know as you saw through our uh uh
+ 
+
+ align:start position:0%
+you know as you saw through our uh uh
+progression through our different
+
+ align:start position:0%
+progression through our different
+ 
+
+ align:start position:0%
+progression through our different
+prototypes was that our Direction was
+
+ align:start position:0%
+prototypes was that our Direction was
+ 
+
+ align:start position:0%
+prototypes was that our Direction was
+not very clear until about halfway
+
+ align:start position:0%
+not very clear until about halfway
+ 
+
+ align:start position:0%
+not very clear until about halfway
+through the project and so partially
+
+ align:start position:0%
+through the project and so partially
+ 
+
+ align:start position:0%
+through the project and so partially
+because we had uh different ideas on
+
+ align:start position:0%
+because we had uh different ideas on
+ 
+
+ align:start position:0%
+because we had uh different ideas on
+what the game should look like and also
+
+ align:start position:0%
+what the game should look like and also
+ 
+
+ align:start position:0%
+what the game should look like and also
+partially because we had such an
+
+ align:start position:0%
+partially because we had such an
+ 
+
+ align:start position:0%
+partially because we had such an
+abstract idea of forecast based
+
+ align:start position:0%
+abstract idea of forecast based
+ 
+
+ align:start position:0%
+abstract idea of forecast based
+financing that you know even we didn't
+
+ align:start position:0%
+financing that you know even we didn't
+ 
+
+ align:start position:0%
+financing that you know even we didn't
+have that good of a grass Bond initially
+
+ align:start position:0%
+have that good of a grass Bond initially
+ 
+
+ align:start position:0%
+have that good of a grass Bond initially
+um it took us a while to really get
+
+ align:start position:0%
+um it took us a while to really get
+ 
+
+ align:start position:0%
+um it took us a while to really get
+settled on what we wanted to build and
+
+ align:start position:0%
+settled on what we wanted to build and
+ 
+
+ align:start position:0%
+settled on what we wanted to build and
+so this really challenged our
+
+ align:start position:0%
+so this really challenged our
+ 
+
+ align:start position:0%
+so this really challenged our
+development process and um and made us
+
+ align:start position:0%
+development process and um and made us
+ 
+
+ align:start position:0%
+development process and um and made us
+have to kind of build a lot before we
+
+ align:start position:0%
+have to kind of build a lot before we
+ 
+
+ align:start position:0%
+have to kind of build a lot before we
+got something that we
+
+ align:start position:0%
+got something that we
+ 
+
+ align:start position:0%
+got something that we
+liked and so um eventually we did end up
+
+ align:start position:0%
+liked and so um eventually we did end up
+ 
+
+ align:start position:0%
+liked and so um eventually we did end up
+having to cut some features uh like
+
+ align:start position:0%
+having to cut some features uh like
+ 
+
+ align:start position:0%
+having to cut some features uh like
+multiple levels or like a guided
+
+ align:start position:0%
+multiple levels or like a guided
+ 
+
+ align:start position:0%
+multiple levels or like a guided
+tutorial for the player um we thought
+
+ align:start position:0%
+tutorial for the player um we thought
+ 
+
+ align:start position:0%
+tutorial for the player um we thought
+that this would introduce too much new
+
+ align:start position:0%
+that this would introduce too much new
+ 
+
+ align:start position:0%
+that this would introduce too much new
+content that would need to be play
+
+ align:start position:0%
+content that would need to be play
+ 
+
+ align:start position:0%
+content that would need to be play
+tested balanced and you know um tested
+
+ align:start position:0%
+tested balanced and you know um tested
+ 
+
+ align:start position:0%
+tested balanced and you know um tested
+to ensure consistency with the rest of
+
+ align:start position:0%
+to ensure consistency with the rest of
+ 
+
+ align:start position:0%
+to ensure consistency with the rest of
+our game which we viewed as taking up
+
+ align:start position:0%
+our game which we viewed as taking up
+ 
+
+ align:start position:0%
+our game which we viewed as taking up
+too much time and we also cut the idea
+
+ align:start position:0%
+too much time and we also cut the idea
+ 
+
+ align:start position:0%
+too much time and we also cut the idea
+of adding more individuality to the
+
+ align:start position:0%
+of adding more individuality to the
+ 
+
+ align:start position:0%
+of adding more individuality to the
+indiv uh to the workers or to the toys
+
+ align:start position:0%
+indiv uh to the workers or to the toys
+ 
+
+ align:start position:0%
+indiv uh to the workers or to the toys
+that use saw um other than different
+
+ align:start position:0%
+that use saw um other than different
+ 
+
+ align:start position:0%
+that use saw um other than different
+graphics for
+
+ align:start position:0%
+graphics for
+ 
+
+ align:start position:0%
+graphics for
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+so some of the worst things that we did
+
+ align:start position:0%
+so some of the worst things that we did
+ 
+
+ align:start position:0%
+so some of the worst things that we did
+on our team is that we spent a lot of
+
+ align:start position:0%
+on our team is that we spent a lot of
+ 
+
+ align:start position:0%
+on our team is that we spent a lot of
+time on work that got thrown out
+
+ align:start position:0%
+time on work that got thrown out
+ 
+
+ align:start position:0%
+time on work that got thrown out
+entirely all the prototypes we did they
+
+ align:start position:0%
+entirely all the prototypes we did they
+ 
+
+ align:start position:0%
+entirely all the prototypes we did they
+were actually pretty useful because of
+
+ align:start position:0%
+were actually pretty useful because of
+ 
+
+ align:start position:0%
+were actually pretty useful because of
+the things we learned about the concept
+
+ align:start position:0%
+the things we learned about the concept
+ 
+
+ align:start position:0%
+the things we learned about the concept
+and about how people would play the game
+
+ align:start position:0%
+and about how people would play the game
+ 
+
+ align:start position:0%
+and about how people would play the game
+but we did spend a lot of time on things
+
+ align:start position:0%
+but we did spend a lot of time on things
+ 
+
+ align:start position:0%
+but we did spend a lot of time on things
+like art or you know nitty-gritty
+
+ align:start position:0%
+like art or you know nitty-gritty
+ 
+
+ align:start position:0%
+like art or you know nitty-gritty
+details that didn't really need to be
+
+ align:start position:0%
+details that didn't really need to be
+ 
+
+ align:start position:0%
+details that didn't really need to be
+figured out and that we could have put
+
+ align:start position:0%
+figured out and that we could have put
+ 
+
+ align:start position:0%
+figured out and that we could have put
+off until later in the project
+
+ align:start position:0%
+off until later in the project
+ 
+
+ align:start position:0%
+off until later in the project
+we also kept the game Direction too
+
+ align:start position:0%
+we also kept the game Direction too
+ 
+
+ align:start position:0%
+we also kept the game Direction too
+vague for too long uh as Norman said we
+
+ align:start position:0%
+vague for too long uh as Norman said we
+ 
+
+ align:start position:0%
+vague for too long uh as Norman said we
+spent a lot of time with that and it
+
+ align:start position:0%
+spent a lot of time with that and it
+ 
+
+ align:start position:0%
+spent a lot of time with that and it
+probably ate up too much of our time
+
+ align:start position:0%
+probably ate up too much of our time
+ 
+
+ align:start position:0%
+probably ate up too much of our time
+although it helped us learn we could
+
+ align:start position:0%
+although it helped us learn we could
+ 
+
+ align:start position:0%
+although it helped us learn we could
+have moved faster in the beginning to
+
+ align:start position:0%
+have moved faster in the beginning to
+ 
+
+ align:start position:0%
+have moved faster in the beginning to
+get to a solid idea because once we got
+
+ align:start position:0%
+get to a solid idea because once we got
+ 
+
+ align:start position:0%
+get to a solid idea because once we got
+to a solid idea of the rising Waters our
+
+ align:start position:0%
+to a solid idea of the rising Waters our
+ 
+
+ align:start position:0%
+to a solid idea of the rising Waters our
+team started to centralize around it a
+
+ align:start position:0%
+team started to centralize around it a
+ 
+
+ align:start position:0%
+team started to centralize around it a
+lot better because we could actually
+
+ align:start position:0%
+lot better because we could actually
+ 
+
+ align:start position:0%
+lot better because we could actually
+deal with something concrete while we
+
+ align:start position:0%
+deal with something concrete while we
+ 
+
+ align:start position:0%
+deal with something concrete while we
+were dealing with the abstract ideas
+
+ align:start position:0%
+were dealing with the abstract ideas
+ 
+
+ align:start position:0%
+were dealing with the abstract ideas
+everybody was all over the place and
+
+ align:start position:0%
+everybody was all over the place and
+ 
+
+ align:start position:0%
+everybody was all over the place and
+arguing about things that didn't quite
+
+ align:start position:0%
+arguing about things that didn't quite
+ 
+
+ align:start position:0%
+arguing about things that didn't quite
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+up and the worst decision of all that we
+
+ align:start position:0%
+up and the worst decision of all that we
+ 
+
+ align:start position:0%
+up and the worst decision of all that we
+started with and that sort of made the
+
+ align:start position:0%
+started with and that sort of made the
+ 
+
+ align:start position:0%
+started with and that sort of made the
+problem of going too vague and all these
+
+ align:start position:0%
+problem of going too vague and all these
+ 
+
+ align:start position:0%
+problem of going too vague and all these
+other things happen is that we were
+
+ align:start position:0%
+other things happen is that we were
+ 
+
+ align:start position:0%
+other things happen is that we were
+originally thinking how do we skin
+
+ align:start position:0%
+originally thinking how do we skin
+ 
+
+ align:start position:0%
+originally thinking how do we skin
+forecast based financing as a game how
+
+ align:start position:0%
+forecast based financing as a game how
+ 
+
+ align:start position:0%
+forecast based financing as a game how
+do we take this idea of using forecast
+
+ align:start position:0%
+do we take this idea of using forecast
+ 
+
+ align:start position:0%
+do we take this idea of using forecast
+to make decisions and then just gamify
+
+ align:start position:0%
+to make decisions and then just gamify
+ 
+
+ align:start position:0%
+to make decisions and then just gamify
+it which we eventually realized wasn't
+
+ align:start position:0%
+it which we eventually realized wasn't
+ 
+
+ align:start position:0%
+it which we eventually realized wasn't
+fun and didn't help us actually come up
+
+ align:start position:0%
+fun and didn't help us actually come up
+ 
+
+ align:start position:0%
+fun and didn't help us actually come up
+with any ideas instead when we flipped
+
+ align:start position:0%
+with any ideas instead when we flipped
+ 
+
+ align:start position:0%
+with any ideas instead when we flipped
+it and started talking about what game
+
+ align:start position:0%
+it and started talking about what game
+ 
+
+ align:start position:0%
+it and started talking about what game
+could we create and use forecast based
+
+ align:start position:0%
+could we create and use forecast based
+ 
+
+ align:start position:0%
+could we create and use forecast based
+financing to improve it and teach
+
+ align:start position:0%
+financing to improve it and teach
+ 
+
+ align:start position:0%
+financing to improve it and teach
+something teach players how to play the
+
+ align:start position:0%
+something teach players how to play the
+ 
+
+ align:start position:0%
+something teach players how to play the
+game and therefore allow them to come
+
+ align:start position:0%
+game and therefore allow them to come
+ 
+
+ align:start position:0%
+game and therefore allow them to come
+out of the game Having learned about
+
+ align:start position:0%
+out of the game Having learned about
+ 
+
+ align:start position:0%
+out of the game Having learned about
+forecast based financing the world sort
+
+ align:start position:0%
+forecast based financing the world sort
+ 
+
+ align:start position:0%
+forecast based financing the world sort
+of opened up everything became a lot
+
+ align:start position:0%
+of opened up everything became a lot
+ 
+
+ align:start position:0%
+of opened up everything became a lot
+more interesting and we found that we
+
+ align:start position:0%
+more interesting and we found that we
+ 
+
+ align:start position:0%
+more interesting and we found that we
+started to move
+
+ align:start position:0%
+started to move
+ 
+
+ align:start position:0%
+started to move
+faster some of the best decisions that
+
+ align:start position:0%
+faster some of the best decisions that
+ 
+
+ align:start position:0%
+faster some of the best decisions that
+we made on the other hand as Norman said
+
+ align:start position:0%
+we made on the other hand as Norman said
+ 
+
+ align:start position:0%
+we made on the other hand as Norman said
+we had good tools which meant that even
+
+ align:start position:0%
+we had good tools which meant that even
+ 
+
+ align:start position:0%
+we had good tools which meant that even
+when we threw out prototypes although we
+
+ align:start position:0%
+when we threw out prototypes although we
+ 
+
+ align:start position:0%
+when we threw out prototypes although we
+wasted things like art resources and uh
+
+ align:start position:0%
+wasted things like art resources and uh
+ 
+
+ align:start position:0%
+wasted things like art resources and uh
+things like that we actually didn't end
+
+ align:start position:0%
+things like that we actually didn't end
+ 
+
+ align:start position:0%
+things like that we actually didn't end
+up wasting very much code because things
+
+ align:start position:0%
+up wasting very much code because things
+ 
+
+ align:start position:0%
+up wasting very much code because things
+like the idea of workers or cities could
+
+ align:start position:0%
+like the idea of workers or cities could
+ 
+
+ align:start position:0%
+like the idea of workers or cities could
+literally be pulled out of the old games
+
+ align:start position:0%
+literally be pulled out of the old games
+ 
+
+ align:start position:0%
+literally be pulled out of the old games
+we had put into our new game and then
+
+ align:start position:0%
+we had put into our new game and then
+ 
+
+ align:start position:0%
+we had put into our new game and then
+reworked to build our our new
+
+ align:start position:0%
+reworked to build our our new
+ 
+
+ align:start position:0%
+reworked to build our our new
+structure we also weren't afraid to
+
+ align:start position:0%
+structure we also weren't afraid to
+ 
+
+ align:start position:0%
+structure we also weren't afraid to
+trust each other and throw out the
+
+ align:start position:0%
+trust each other and throw out the
+ 
+
+ align:start position:0%
+trust each other and throw out the
+things that didn't work once we started
+
+ align:start position:0%
+things that didn't work once we started
+ 
+
+ align:start position:0%
+things that didn't work once we started
+moving fast we had a lot of ideas that
+
+ align:start position:0%
+moving fast we had a lot of ideas that
+ 
+
+ align:start position:0%
+moving fast we had a lot of ideas that
+would come out and we'd say okay this
+
+ align:start position:0%
+would come out and we'd say okay this
+ 
+
+ align:start position:0%
+would come out and we'd say okay this
+doesn't work we're actually going to
+
+ align:start position:0%
+doesn't work we're actually going to
+ 
+
+ align:start position:0%
+doesn't work we're actually going to
+scrap it or uh you know we think that
+
+ align:start position:0%
+scrap it or uh you know we think that
+ 
+
+ align:start position:0%
+scrap it or uh you know we think that
+this isn't the direction we need to go
+
+ align:start position:0%
+this isn't the direction we need to go
+ 
+
+ align:start position:0%
+this isn't the direction we need to go
+in and everybody was willing to go along
+
+ align:start position:0%
+in and everybody was willing to go along
+ 
+
+ align:start position:0%
+in and everybody was willing to go along
+with it it's not good to feel it's not a
+
+ align:start position:0%
+with it it's not good to feel it's not a
+ 
+
+ align:start position:0%
+with it it's not good to feel it's not a
+good feeling to see your things thrown
+
+ align:start position:0%
+good feeling to see your things thrown
+ 
+
+ align:start position:0%
+good feeling to see your things thrown
+out but everybody understood that was
+
+ align:start position:0%
+out but everybody understood that was
+ 
+
+ align:start position:0%
+out but everybody understood that was
+for the best of the game and I really
+
+ align:start position:0%
+for the best of the game and I really
+ 
+
+ align:start position:0%
+for the best of the game and I really
+appreciate their understanding with
+
+ align:start position:0%
+appreciate their understanding with
+ 
+
+ align:start position:0%
+appreciate their understanding with
+everything too and part of that all
+
+ align:start position:0%
+everything too and part of that all
+ 
+
+ align:start position:0%
+everything too and part of that all
+comes down to the fact that we were on
+
+ align:start position:0%
+comes down to the fact that we were on
+ 
+
+ align:start position:0%
+comes down to the fact that we were on
+board with our final idea we were all
+
+ align:start position:0%
+board with our final idea we were all
+ 
+
+ align:start position:0%
+board with our final idea we were all
+excited about the concept that we had
+
+ align:start position:0%
+excited about the concept that we had
+ 
+
+ align:start position:0%
+excited about the concept that we had
+part of that might have been the relief
+
+ align:start position:0%
+part of that might have been the relief
+ 
+
+ align:start position:0%
+part of that might have been the relief
+of coming to a concrete idea after
+
+ align:start position:0%
+of coming to a concrete idea after
+ 
+
+ align:start position:0%
+of coming to a concrete idea after
+spending so much time being vague but
+
+ align:start position:0%
+spending so much time being vague but
+ 
+
+ align:start position:0%
+spending so much time being vague but
+once we had that conquered idea we
+
+ align:start position:0%
+once we had that conquered idea we
+ 
+
+ align:start position:0%
+once we had that conquered idea we
+really moved fast and worked well around
+
+ align:start position:0%
+really moved fast and worked well around
+ 
+
+ align:start position:0%
+really moved fast and worked well around
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so thank you and any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+questions who did your sound it's
+
+ align:start position:0%
+questions who did your sound it's
+ 
+
+ align:start position:0%
+questions who did your sound it's
+awesome that was from our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you yeah where did you find it um so
+
+ align:start position:0%
+you yeah where did you find it um so
+ 
+
+ align:start position:0%
+you yeah where did you find it um so
+it's on our credits page most of it was
+
+ align:start position:0%
+it's on our credits page most of it was
+ 
+
+ align:start position:0%
+it's on our credits page most of it was
+online uh the credits page in our game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it's a little small I guess up
+
+ align:start position:0%
+here it's a little small I guess up
+ 
+
+ align:start position:0%
+here it's a little small I guess up
+there but it looks yeah hold my hand AGP
+
+ align:start position:0%
+there but it looks yeah hold my hand AGP
+ 
+
+ align:start position:0%
+there but it looks yeah hold my hand AGP
+by would it be possible be to create
+
+ align:start position:0%
+by would it be possible be to create
+ 
+
+ align:start position:0%
+by would it be possible be to create
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+shorturl bitly link uh yeah sure we can
+
+ align:start position:0%
+shorturl bitly link uh yeah sure we can
+ 
+
+ align:start position:0%
+shorturl bitly link uh yeah sure we can
+we can make a bitly link and we'll send
+
+ align:start position:0%
+we can make a bitly link and we'll send
+ 
+
+ align:start position:0%
+we can make a bitly link and we'll send
+it out to everyone just
+
+ align:start position:0%
+it out to everyone just
+ 
+
+ align:start position:0%
+it out to everyone just
+yeah that's a good call
+
+ align:start position:0%
+yeah that's a good call
+ 
+
+ align:start position:0%
+yeah that's a good call
+yes having watched the the early crash
+
+ align:start position:0%
+yes having watched the the early crash
+ 
+
+ align:start position:0%
+yes having watched the the early crash
+and burn at the playr um how often do
+
+ align:start position:0%
+and burn at the playr um how often do
+ 
+
+ align:start position:0%
+and burn at the playr um how often do
+people I don't know if you've actually
+
+ align:start position:0%
+people I don't know if you've actually
+ 
+
+ align:start position:0%
+people I don't know if you've actually
+had a lot of people to play your your
+
+ align:start position:0%
+had a lot of people to play your your
+ 
+
+ align:start position:0%
+had a lot of people to play your your
+current version of your game um do
+
+ align:start position:0%
+current version of your game um do
+ 
+
+ align:start position:0%
+current version of your game um do
+people usually take a playthrough or two
+
+ align:start position:0%
+people usually take a playthrough or two
+ 
+
+ align:start position:0%
+people usually take a playthrough or two
+before they start getting the concept
+
+ align:start position:0%
+before they start getting the concept
+ 
+
+ align:start position:0%
+before they start getting the concept
+yes that's why something like a tutorial
+
+ align:start position:0%
+yes that's why something like a tutorial
+ 
+
+ align:start position:0%
+yes that's why something like a tutorial
+would be really nice um unfortunately we
+
+ align:start position:0%
+would be really nice um unfortunately we
+ 
+
+ align:start position:0%
+would be really nice um unfortunately we
+didn't have the time to put it in yeah
+
+ align:start position:0%
+didn't have the time to put it in yeah
+ 
+
+ align:start position:0%
+didn't have the time to put it in yeah
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+no okay yeah usually what happens is
+
+ align:start position:0%
+no okay yeah usually what happens is
+ 
+
+ align:start position:0%
+no okay yeah usually what happens is
+even if after Maybe a couple turns of
+
+ align:start position:0%
+even if after Maybe a couple turns of
+ 
+
+ align:start position:0%
+even if after Maybe a couple turns of
+playing through they start to get the
+
+ align:start position:0%
+playing through they start to get the
+ 
+
+ align:start position:0%
+playing through they start to get the
+idea the problem is that as the water
+
+ align:start position:0%
+idea the problem is that as the water
+ 
+
+ align:start position:0%
+idea the problem is that as the water
+starts to rise they haven't prepared
+
+ align:start position:0%
+starts to rise they haven't prepared
+ 
+
+ align:start position:0%
+starts to rise they haven't prepared
+enough and so all their workers all the
+
+ align:start position:0%
+enough and so all their workers all the
+ 
+
+ align:start position:0%
+enough and so all their workers all the
+toys will starve or get carried away by
+
+ align:start position:0%
+toys will starve or get carried away by
+ 
+
+ align:start position:0%
+toys will starve or get carried away by
+the waves which is a bit unfortunate and
+
+ align:start position:0%
+the waves which is a bit unfortunate and
+ 
+
+ align:start position:0%
+the waves which is a bit unfortunate and
+probably makes the players feel bad on
+
+ align:start position:0%
+probably makes the players feel bad on
+ 
+
+ align:start position:0%
+probably makes the players feel bad on
+the first time but then they it actually
+
+ align:start position:0%
+the first time but then they it actually
+ 
+
+ align:start position:0%
+the first time but then they it actually
+teaches them to think ahead about it so
+
+ align:start position:0%
+teaches them to think ahead about it so
+ 
+
+ align:start position:0%
+teaches them to think ahead about it so
+the next play through they're much more
+
+ align:start position:0%
+the next play through they're much more
+ 
+
+ align:start position:0%
+the next play through they're much more
+careful and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+understanding yes um I was wondering if
+
+ align:start position:0%
+understanding yes um I was wondering if
+ 
+
+ align:start position:0%
+understanding yes um I was wondering if
+um you were play any other games or
+
+ align:start position:0%
+um you were play any other games or
+ 
+
+ align:start position:0%
+um you were play any other games or
+thinking about other games as
+
+ align:start position:0%
+thinking about other games as
+ 
+
+ align:start position:0%
+thinking about other games as
+inspiration or thinking about how to
+
+ align:start position:0%
+inspiration or thinking about how to
+ 
+
+ align:start position:0%
+inspiration or thinking about how to
+deal with sort of getting the right
+
+ align:start position:0%
+deal with sort of getting the right
+ 
+
+ align:start position:0%
+deal with sort of getting the right
+level of strategic thinking
+
+ align:start position:0%
+level of strategic thinking
+ 
+
+ align:start position:0%
+level of strategic thinking
+in yeah well so I guess in terms of uh
+
+ align:start position:0%
+in yeah well so I guess in terms of uh
+ 
+
+ align:start position:0%
+in yeah well so I guess in terms of uh
+early on because we had a very different
+
+ align:start position:0%
+early on because we had a very different
+ 
+
+ align:start position:0%
+early on because we had a very different
+idea of uh what we wanted to do early on
+
+ align:start position:0%
+idea of uh what we wanted to do early on
+ 
+
+ align:start position:0%
+idea of uh what we wanted to do early on
+in the process we were thinking about
+
+ align:start position:0%
+in the process we were thinking about
+ 
+
+ align:start position:0%
+in the process we were thinking about
+games like Civilization and how did they
+
+ align:start position:0%
+games like Civilization and how did they
+ 
+
+ align:start position:0%
+games like Civilization and how did they
+communicate all these complex you know
+
+ align:start position:0%
+communicate all these complex you know
+ 
+
+ align:start position:0%
+communicate all these complex you know
+worker movements and managing multiple
+
+ align:start position:0%
+worker movements and managing multiple
+ 
+
+ align:start position:0%
+worker movements and managing multiple
+cities
+
+ align:start position:0%
+cities
+ 
+
+ align:start position:0%
+cities
+but uh once we actually came up with
+
+ align:start position:0%
+but uh once we actually came up with
+ 
+
+ align:start position:0%
+but uh once we actually came up with
+this game concept uh I think we had much
+
+ align:start position:0%
+this game concept uh I think we had much
+ 
+
+ align:start position:0%
+this game concept uh I think we had much
+much smaller goals and so um do we have
+
+ align:start position:0%
+much smaller goals and so um do we have
+ 
+
+ align:start position:0%
+much smaller goals and so um do we have
+any specific game models do you think or
+
+ align:start position:0%
+any specific game models do you think or
+ 
+
+ align:start position:0%
+any specific game models do you think or
+there's none that I specifically think
+
+ align:start position:0%
+there's none that I specifically think
+ 
+
+ align:start position:0%
+there's none that I specifically think
+of there were some things that you know
+
+ align:start position:0%
+of there were some things that you know
+ 
+
+ align:start position:0%
+of there were some things that you know
+we were sort of inspired by standard
+
+ align:start position:0%
+we were sort of inspired by standard
+ 
+
+ align:start position:0%
+we were sort of inspired by standard
+tricks like when you hover over one of
+
+ align:start position:0%
+tricks like when you hover over one of
+ 
+
+ align:start position:0%
+tricks like when you hover over one of
+the characters they got bigger some idea
+
+ align:start position:0%
+the characters they got bigger some idea
+ 
+
+ align:start position:0%
+the characters they got bigger some idea
+of showing off that this is clickable
+
+ align:start position:0%
+of showing off that this is clickable
+ 
+
+ align:start position:0%
+of showing off that this is clickable
+things like that but specific game
+
+ align:start position:0%
+things like that but specific game
+ 
+
+ align:start position:0%
+things like that but specific game
+themselves uh not really I was just
+
+ align:start position:0%
+themselves uh not really I was just
+ 
+
+ align:start position:0%
+themselves uh not really I was just
+thinking it's it ended up being kind of
+
+ align:start position:0%
+thinking it's it ended up being kind of
+ 
+
+ align:start position:0%
+thinking it's it ended up being kind of
+board gamey and I feel like there's a
+
+ align:start position:0%
+board gamey and I feel like there's a
+ 
+
+ align:start position:0%
+board gamey and I feel like there's a
+lot of War games where they've been
+
+ align:start position:0%
+lot of War games where they've been
+ 
+
+ align:start position:0%
+lot of War games where they've been
+thinking a lot about getting that right
+
+ align:start position:0%
+thinking a lot about getting that right
+ 
+
+ align:start position:0%
+thinking a lot about getting that right
+level of uh of I guess tactics rather
+
+ align:start position:0%
+level of uh of I guess tactics rather
+ 
+
+ align:start position:0%
+level of uh of I guess tactics rather
+than strategy but yeah I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wor so this you you mentioned that you
+
+ align:start position:0%
+wor so this you you mentioned that you
+ 
+
+ align:start position:0%
+wor so this you you mentioned that you
+were able to completely change how your
+
+ align:start position:0%
+were able to completely change how your
+ 
+
+ align:start position:0%
+were able to completely change how your
+workers looked and just keep your models
+
+ align:start position:0%
+workers looked and just keep your models
+ 
+
+ align:start position:0%
+workers looked and just keep your models
+so that's sort of the Holy Grail of
+
+ align:start position:0%
+so that's sort of the Holy Grail of
+ 
+
+ align:start position:0%
+so that's sort of the Holy Grail of
+object oriented programming that you
+
+ align:start position:0%
+object oriented programming that you
+ 
+
+ align:start position:0%
+object oriented programming that you
+have an object that's reusable and you
+
+ align:start position:0%
+have an object that's reusable and you
+ 
+
+ align:start position:0%
+have an object that's reusable and you
+don't have to throw out the code um do
+
+ align:start position:0%
+don't have to throw out the code um do
+ 
+
+ align:start position:0%
+don't have to throw out the code um do
+you think there's like a reason why in
+
+ align:start position:0%
+you think there's like a reason why in
+ 
+
+ align:start position:0%
+you think there's like a reason why in
+particular you were able to achieve that
+
+ align:start position:0%
+particular you were able to achieve that
+ 
+
+ align:start position:0%
+particular you were able to achieve that
+because I think that's not that's not
+
+ align:start position:0%
+because I think that's not that's not
+ 
+
+ align:start position:0%
+because I think that's not that's not
+common necessarily in object-oriented
+
+ align:start position:0%
+common necessarily in object-oriented
+ 
+
+ align:start position:0%
+common necessarily in object-oriented
+programming
+
+ align:start position:0%
+programming
+ 
+
+ align:start position:0%
+programming
+uh um partially a little bit of OCD like
+
+ align:start position:0%
+uh um partially a little bit of OCD like
+ 
+
+ align:start position:0%
+uh um partially a little bit of OCD like
+very early on very strictly saying um
+
+ align:start position:0%
+very early on very strictly saying um
+ 
+
+ align:start position:0%
+very early on very strictly saying um
+we're going to write this objectoriented
+
+ align:start position:0%
+we're going to write this objectoriented
+ 
+
+ align:start position:0%
+we're going to write this objectoriented
+code and we're not just going to hack
+
+ align:start position:0%
+code and we're not just going to hack
+ 
+
+ align:start position:0%
+code and we're not just going to hack
+things together I think that helped a
+
+ align:start position:0%
+things together I think that helped a
+ 
+
+ align:start position:0%
+things together I think that helped a
+lot because um we actually spended time
+
+ align:start position:0%
+lot because um we actually spended time
+ 
+
+ align:start position:0%
+lot because um we actually spended time
+in the very beginning to think about
+
+ align:start position:0%
+in the very beginning to think about
+ 
+
+ align:start position:0%
+in the very beginning to think about
+like which which objects were
+
+ align:start position:0%
+like which which objects were
+ 
+
+ align:start position:0%
+like which which objects were
+responsible for what and what their
+
+ align:start position:0%
+responsible for what and what their
+ 
+
+ align:start position:0%
+responsible for what and what their
+purpose should be so yeah basically I
+
+ align:start position:0%
+purpose should be so yeah basically I
+ 
+
+ align:start position:0%
+purpose should be so yeah basically I
+think because we moved more slowly in
+
+ align:start position:0%
+think because we moved more slowly in
+ 
+
+ align:start position:0%
+think because we moved more slowly in
+the start and thought more carefully
+
+ align:start position:0%
+the start and thought more carefully
+ 
+
+ align:start position:0%
+the start and thought more carefully
+about how that code should be structured
+
+ align:start position:0%
+about how that code should be structured
+ 
+
+ align:start position:0%
+about how that code should be structured
+we ended up with having an easier time
+
+ align:start position:0%
+we ended up with having an easier time
+ 
+
+ align:start position:0%
+we ended up with having an easier time
+later on there's also the fact that
+
+ align:start position:0%
+later on there's also the fact that
+ 
+
+ align:start position:0%
+later on there's also the fact that
+because we had learned these things from
+
+ align:start position:0%
+because we had learned these things from
+ 
+
+ align:start position:0%
+because we had learned these things from
+the Prototype that we were putting into
+
+ align:start position:0%
+the Prototype that we were putting into
+ 
+
+ align:start position:0%
+the Prototype that we were putting into
+this game that also meant that
+
+ align:start position:0%
+this game that also meant that
+ 
+
+ align:start position:0%
+this game that also meant that
+the the objects that we
+
+ align:start position:0%
+the the objects that we
+ 
+
+ align:start position:0%
+the the objects that we
+created because we wanted similar
+
+ align:start position:0%
+created because we wanted similar
+ 
+
+ align:start position:0%
+created because we wanted similar
+functionality to things that we had
+
+ align:start position:0%
+functionality to things that we had
+ 
+
+ align:start position:0%
+functionality to things that we had
+already seen and we knew worked it meant
+
+ align:start position:0%
+already seen and we knew worked it meant
+ 
+
+ align:start position:0%
+already seen and we knew worked it meant
+that we were comfortable pulling out the
+
+ align:start position:0%
+that we were comfortable pulling out the
+ 
+
+ align:start position:0%
+that we were comfortable pulling out the
+functionality into that uh so I won't I
+
+ align:start position:0%
+functionality into that uh so I won't I
+ 
+
+ align:start position:0%
+functionality into that uh so I won't I
+don't want to say it was designed to fit
+
+ align:start position:0%
+don't want to say it was designed to fit
+ 
+
+ align:start position:0%
+don't want to say it was designed to fit
+but there is some there is the fact that
+
+ align:start position:0%
+but there is some there is the fact that
+ 
+
+ align:start position:0%
+but there is some there is the fact that
+we moved it on purpose
+
+ align:start position:0%
+we moved it on purpose
+ 
+
+ align:start position:0%
+we moved it on purpose
+really I something so uh we had a very
+
+ align:start position:0%
+really I something so uh we had a very
+ 
+
+ align:start position:0%
+really I something so uh we had a very
+good NBC model uh so models were
+
+ align:start position:0%
+good NBC model uh so models were
+ 
+
+ align:start position:0%
+good NBC model uh so models were
+three like structure and it was very
+
+ align:start position:0%
+three like structure and it was very
+ 
+
+ align:start position:0%
+three like structure and it was very
+easy to change models so models knew
+
+ align:start position:0%
+easy to change models so models knew
+ 
+
+ align:start position:0%
+easy to change models so models knew
+about uh sorry use knew about models but
+
+ align:start position:0%
+about uh sorry use knew about models but
+ 
+
+ align:start position:0%
+about uh sorry use knew about models but
+models and no idea about use so
+
+ align:start position:0%
+models and no idea about use so
+ 
+
+ align:start position:0%
+models and no idea about use so
+basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
\ No newline at end of file
diff --git a/muLn57VrGAA.txt b/muLn57VrGAA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..712643765c3cf89f27256e42fc8af941e4c6f46c
--- /dev/null
+++ b/muLn57VrGAA.txt
@@ -0,0 +1,907 @@
+align:start position:0%
+ 
+in the last lecture we introduced the
+
+ align:start position:0%
+in the last lecture we introduced the
+ 
+
+ align:start position:0%
+in the last lecture we introduced the
+notion of virtual memory and added a
+
+ align:start position:0%
+notion of virtual memory and added a
+ 
+
+ align:start position:0%
+notion of virtual memory and added a
+memory management unit MMU to translate
+
+ align:start position:0%
+memory management unit MMU to translate
+ 
+
+ align:start position:0%
+memory management unit MMU to translate
+the virtual addresses generated by the
+
+ align:start position:0%
+the virtual addresses generated by the
+ 
+
+ align:start position:0%
+the virtual addresses generated by the
+CPU to the physical address is sent to
+
+ align:start position:0%
+CPU to the physical address is sent to
+ 
+
+ align:start position:0%
+CPU to the physical address is sent to
+main memory this gave us the ability to
+
+ align:start position:0%
+main memory this gave us the ability to
+ 
+
+ align:start position:0%
+main memory this gave us the ability to
+share physical memory between many
+
+ align:start position:0%
+share physical memory between many
+ 
+
+ align:start position:0%
+share physical memory between many
+running programs while still giving each
+
+ align:start position:0%
+running programs while still giving each
+ 
+
+ align:start position:0%
+running programs while still giving each
+program the illusion of having its own
+
+ align:start position:0%
+program the illusion of having its own
+ 
+
+ align:start position:0%
+program the illusion of having its own
+large address space both the virtual and
+
+ align:start position:0%
+large address space both the virtual and
+ 
+
+ align:start position:0%
+large address space both the virtual and
+physical address spaces are divided into
+
+ align:start position:0%
+physical address spaces are divided into
+ 
+
+ align:start position:0%
+physical address spaces are divided into
+a sequence of pages each holding some
+
+ align:start position:0%
+a sequence of pages each holding some
+ 
+
+ align:start position:0%
+a sequence of pages each holding some
+fixed number of locations for example if
+
+ align:start position:0%
+fixed number of locations for example if
+ 
+
+ align:start position:0%
+fixed number of locations for example if
+each page holds 2 to the 12th bytes a
+
+ align:start position:0%
+each page holds 2 to the 12th bytes a
+ 
+
+ align:start position:0%
+each page holds 2 to the 12th bytes a
+32-bit address would have 2 to the 32
+
+ align:start position:0%
+32-bit address would have 2 to the 32
+ 
+
+ align:start position:0%
+32-bit address would have 2 to the 32
+divided by 2 to the 12th or 2 to the
+
+ align:start position:0%
+divided by 2 to the 12th or 2 to the
+ 
+
+ align:start position:0%
+divided by 2 to the 12th or 2 to the
+20th pages in this example the 32-bit
+
+ align:start position:0%
+20th pages in this example the 32-bit
+ 
+
+ align:start position:0%
+20th pages in this example the 32-bit
+address can be thought of as having 2
+
+ align:start position:0%
+address can be thought of as having 2
+ 
+
+ align:start position:0%
+address can be thought of as having 2
+fields a 20-bit page number form from
+
+ align:start position:0%
+fields a 20-bit page number form from
+ 
+
+ align:start position:0%
+fields a 20-bit page number form from
+the higher-order address bits and a 12
+
+ align:start position:0%
+the higher-order address bits and a 12
+ 
+
+ align:start position:0%
+the higher-order address bits and a 12
+bit page offset form from the low order
+
+ align:start position:0%
+bit page offset form from the low order
+ 
+
+ align:start position:0%
+bit page offset form from the low order
+address bits this arrangement
+
+ align:start position:0%
+address bits this arrangement
+ 
+
+ align:start position:0%
+address bits this arrangement
+ensures that nearby data will be located
+
+ align:start position:0%
+ensures that nearby data will be located
+ 
+
+ align:start position:0%
+ensures that nearby data will be located
+on the same page the MMU translates
+
+ align:start position:0%
+on the same page the MMU translates
+ 
+
+ align:start position:0%
+on the same page the MMU translates
+virtual page numbers into physical page
+
+ align:start position:0%
+virtual page numbers into physical page
+ 
+
+ align:start position:0%
+virtual page numbers into physical page
+numbers using a page map conceptually
+
+ align:start position:0%
+numbers using a page map conceptually
+ 
+
+ align:start position:0%
+numbers using a page map conceptually
+the page map is an array where each
+
+ align:start position:0%
+the page map is an array where each
+ 
+
+ align:start position:0%
+the page map is an array where each
+entry in the array contains a physical
+
+ align:start position:0%
+entry in the array contains a physical
+ 
+
+ align:start position:0%
+entry in the array contains a physical
+page number along with a couple of bits
+
+ align:start position:0%
+page number along with a couple of bits
+ 
+
+ align:start position:0%
+page number along with a couple of bits
+indicating the page status the
+
+ align:start position:0%
+indicating the page status the
+ 
+
+ align:start position:0%
+indicating the page status the
+translation process is simple the
+
+ align:start position:0%
+translation process is simple the
+ 
+
+ align:start position:0%
+translation process is simple the
+virtual page number is used as an index
+
+ align:start position:0%
+virtual page number is used as an index
+ 
+
+ align:start position:0%
+virtual page number is used as an index
+into the array to fetch the
+
+ align:start position:0%
+into the array to fetch the
+ 
+
+ align:start position:0%
+into the array to fetch the
+corresponding physical page number the
+
+ align:start position:0%
+corresponding physical page number the
+ 
+
+ align:start position:0%
+corresponding physical page number the
+physical page number is then combined
+
+ align:start position:0%
+physical page number is then combined
+ 
+
+ align:start position:0%
+physical page number is then combined
+with the page offset to form the
+
+ align:start position:0%
+with the page offset to form the
+ 
+
+ align:start position:0%
+with the page offset to form the
+complete physical address in the actual
+
+ align:start position:0%
+complete physical address in the actual
+ 
+
+ align:start position:0%
+complete physical address in the actual
+implementation the page map is usually
+
+ align:start position:0%
+implementation the page map is usually
+ 
+
+ align:start position:0%
+implementation the page map is usually
+organized into multiple levels which
+
+ align:start position:0%
+organized into multiple levels which
+ 
+
+ align:start position:0%
+organized into multiple levels which
+permits us to have resident only the
+
+ align:start position:0%
+permits us to have resident only the
+ 
+
+ align:start position:0%
+permits us to have resident only the
+portion of the page map we're actively
+
+ align:start position:0%
+portion of the page map we're actively
+ 
+
+ align:start position:0%
+portion of the page map we're actively
+using and to avoid the cost of accessing
+
+ align:start position:0%
+using and to avoid the cost of accessing
+ 
+
+ align:start position:0%
+using and to avoid the cost of accessing
+the page map on each address translation
+
+ align:start position:0%
+the page map on each address translation
+ 
+
+ align:start position:0%
+the page map on each address translation
+we use a cache called the translation
+
+ align:start position:0%
+we use a cache called the translation
+ 
+
+ align:start position:0%
+we use a cache called the translation
+lookaside buffer to remember the results
+
+ align:start position:0%
+lookaside buffer to remember the results
+ 
+
+ align:start position:0%
+lookaside buffer to remember the results
+of recent VPN to PPN translations all
+
+ align:start position:0%
+of recent VPN to PPN translations all
+ 
+
+ align:start position:0%
+of recent VPN to PPN translations all
+allocated locations of each virtual
+
+ align:start position:0%
+allocated locations of each virtual
+ 
+
+ align:start position:0%
+allocated locations of each virtual
+address space can be found on secondary
+
+ align:start position:0%
+address space can be found on secondary
+ 
+
+ align:start position:0%
+address space can be found on secondary
+storage note that they may not
+
+ align:start position:0%
+storage note that they may not
+ 
+
+ align:start position:0%
+storage note that they may not
+necessarily be resident in main
+
+ align:start position:0%
+necessarily be resident in main
+ 
+
+ align:start position:0%
+necessarily be resident in main
+Marie if the CPU attempts to access a
+
+ align:start position:0%
+Marie if the CPU attempts to access a
+ 
+
+ align:start position:0%
+Marie if the CPU attempts to access a
+virtual address that's not resident in
+
+ align:start position:0%
+virtual address that's not resident in
+ 
+
+ align:start position:0%
+virtual address that's not resident in
+main memory a page fault is signaled and
+
+ align:start position:0%
+main memory a page fault is signaled and
+ 
+
+ align:start position:0%
+main memory a page fault is signaled and
+the operating system will arrange to
+
+ align:start position:0%
+the operating system will arrange to
+ 
+
+ align:start position:0%
+the operating system will arrange to
+move the desired page from secondary
+
+ align:start position:0%
+move the desired page from secondary
+ 
+
+ align:start position:0%
+move the desired page from secondary
+storage into main memory in practice
+
+ align:start position:0%
+storage into main memory in practice
+ 
+
+ align:start position:0%
+storage into main memory in practice
+only the active pages for each program
+
+ align:start position:0%
+only the active pages for each program
+ 
+
+ align:start position:0%
+only the active pages for each program
+are resident in main memory at any given
+
+ align:start position:0%
+are resident in main memory at any given
+ 
+
+ align:start position:0%
+are resident in main memory at any given
+time here's a diagram showing the
+
+ align:start position:0%
+time here's a diagram showing the
+ 
+
+ align:start position:0%
+time here's a diagram showing the
+translation process first we check to
+
+ align:start position:0%
+translation process first we check to
+ 
+
+ align:start position:0%
+translation process first we check to
+see if the required VPN to PPN mapping
+
+ align:start position:0%
+see if the required VPN to PPN mapping
+ 
+
+ align:start position:0%
+see if the required VPN to PPN mapping
+is cached in the TLB if not we have to
+
+ align:start position:0%
+is cached in the TLB if not we have to
+ 
+
+ align:start position:0%
+is cached in the TLB if not we have to
+access the hierarchical page map to see
+
+ align:start position:0%
+access the hierarchical page map to see
+ 
+
+ align:start position:0%
+access the hierarchical page map to see
+if the page is resident and if so look
+
+ align:start position:0%
+if the page is resident and if so look
+ 
+
+ align:start position:0%
+if the page is resident and if so look
+up its physical page number if we
+
+ align:start position:0%
+up its physical page number if we
+ 
+
+ align:start position:0%
+up its physical page number if we
+discover that the page is not resident a
+
+ align:start position:0%
+discover that the page is not resident a
+ 
+
+ align:start position:0%
+discover that the page is not resident a
+page fault exception is signaled to the
+
+ align:start position:0%
+page fault exception is signaled to the
+ 
+
+ align:start position:0%
+page fault exception is signaled to the
+CPU so that it can run a handler to load
+
+ align:start position:0%
+CPU so that it can run a handler to load
+ 
+
+ align:start position:0%
+CPU so that it can run a handler to load
+the page from secondary storage note
+
+ align:start position:0%
+the page from secondary storage note
+ 
+
+ align:start position:0%
+the page from secondary storage note
+that access to a particular mapping
+
+ align:start position:0%
+that access to a particular mapping
+ 
+
+ align:start position:0%
+that access to a particular mapping
+context is controlled by two registers
+
+ align:start position:0%
+context is controlled by two registers
+ 
+
+ align:start position:0%
+context is controlled by two registers
+the context number register controls
+
+ align:start position:0%
+the context number register controls
+ 
+
+ align:start position:0%
+the context number register controls
+which mappings are accessible in the TLB
+
+ align:start position:0%
+which mappings are accessible in the TLB
+ 
+
+ align:start position:0%
+which mappings are accessible in the TLB
+and the page directory register
+
+ align:start position:0%
+and the page directory register
+ 
+
+ align:start position:0%
+and the page directory register
+indicates which physical page holds the
+
+ align:start position:0%
+indicates which physical page holds the
+ 
+
+ align:start position:0%
+indicates which physical page holds the
+top tier of the hierarchical page map we
+
+ align:start position:0%
+top tier of the hierarchical page map we
+ 
+
+ align:start position:0%
+top tier of the hierarchical page map we
+can switch to another context by simply
+
+ align:start position:0%
+can switch to another context by simply
+ 
+
+ align:start position:0%
+can switch to another context by simply
+reloading these two registers to
+
+ align:start position:0%
+reloading these two registers to
+ 
+
+ align:start position:0%
+reloading these two registers to
+effectively accommodate multiple
+
+ align:start position:0%
+effectively accommodate multiple
+ 
+
+ align:start position:0%
+effectively accommodate multiple
+contacts we'll need to have sufficient
+
+ align:start position:0%
+contacts we'll need to have sufficient
+ 
+
+ align:start position:0%
+contacts we'll need to have sufficient
+TLB capacity to simultaneously cache the
+
+ align:start position:0%
+TLB capacity to simultaneously cache the
+ 
+
+ align:start position:0%
+TLB capacity to simultaneously cache the
+most frequent mappings for all the
+
+ align:start position:0%
+most frequent mappings for all the
+ 
+
+ align:start position:0%
+most frequent mappings for all the
+processes and we'll need some number of
+
+ align:start position:0%
+processes and we'll need some number of
+ 
+
+ align:start position:0%
+processes and we'll need some number of
+physical pages to hold the required page
+
+ align:start position:0%
+physical pages to hold the required page
+ 
+
+ align:start position:0%
+physical pages to hold the required page
+directories and segments of the page
+
+ align:start position:0%
+directories and segments of the page
+ 
+
+ align:start position:0%
+directories and segments of the page
+tables for example for a particular
+
+ align:start position:0%
+tables for example for a particular
+ 
+
+ align:start position:0%
+tables for example for a particular
+process three pages will suffice to hold
+
+ align:start position:0%
+process three pages will suffice to hold
+ 
+
+ align:start position:0%
+process three pages will suffice to hold
+the resident two-level page map for 1024
+
+ align:start position:0%
+the resident two-level page map for 1024
+ 
+
+ align:start position:0%
+the resident two-level page map for 1024
+pages at each end of the virtual address
+
+ align:start position:0%
+pages at each end of the virtual address
+ 
+
+ align:start position:0%
+pages at each end of the virtual address
+space providing access to up to eight
+
+ align:start position:0%
+space providing access to up to eight
+ 
+
+ align:start position:0%
+space providing access to up to eight
+megabytes of code stack and heap more
+
+ align:start position:0%
+megabytes of code stack and heap more
+ 
+
+ align:start position:0%
+megabytes of code stack and heap more
+than enough for many simple programs the
+
+ align:start position:0%
+than enough for many simple programs the
+ 
+
+ align:start position:0%
+than enough for many simple programs the
+page map creates the context needed to
+
+ align:start position:0%
+page map creates the context needed to
+ 
+
+ align:start position:0%
+page map creates the context needed to
+translate virtual addresses to physical
+
+ align:start position:0%
+translate virtual addresses to physical
+ 
+
+ align:start position:0%
+translate virtual addresses to physical
+addresses in a computer system that's
+
+ align:start position:0%
+addresses in a computer system that's
+ 
+
+ align:start position:0%
+addresses in a computer system that's
+working on multiple tasks at the same
+
+ align:start position:0%
+working on multiple tasks at the same
+ 
+
+ align:start position:0%
+working on multiple tasks at the same
+time we would like to support multiple
+
+ align:start position:0%
+time we would like to support multiple
+ 
+
+ align:start position:0%
+time we would like to support multiple
+contexts and to be able to quickly
+
+ align:start position:0%
+contexts and to be able to quickly
+ 
+
+ align:start position:0%
+contexts and to be able to quickly
+switch from one context to another
+
+ align:start position:0%
+switch from one context to another
+ 
+
+ align:start position:0%
+switch from one context to another
+multiple contexts would allow us to
+
+ align:start position:0%
+multiple contexts would allow us to
+ 
+
+ align:start position:0%
+multiple contexts would allow us to
+share physical memory between multiple
+
+ align:start position:0%
+share physical memory between multiple
+ 
+
+ align:start position:0%
+share physical memory between multiple
+programs
+
+ align:start position:0%
+programs
+ 
+
+ align:start position:0%
+programs
+each program would have an independent
+
+ align:start position:0%
+each program would have an independent
+ 
+
+ align:start position:0%
+each program would have an independent
+virtual address space for example two
+
+ align:start position:0%
+virtual address space for example two
+ 
+
+ align:start position:0%
+virtual address space for example two
+programs could both access virtual zero
+
+ align:start position:0%
+programs could both access virtual zero
+ 
+
+ align:start position:0%
+programs could both access virtual zero
+as the address of the first instruction
+
+ align:start position:0%
+as the address of the first instruction
+ 
+
+ align:start position:0%
+as the address of the first instruction
+and would end up accessing different
+
+ align:start position:0%
+and would end up accessing different
+ 
+
+ align:start position:0%
+and would end up accessing different
+physical locations in main memory when
+
+ align:start position:0%
+physical locations in main memory when
+ 
+
+ align:start position:0%
+physical locations in main memory when
+switching between programs we perform a
+
+ align:start position:0%
+switching between programs we perform a
+ 
+
+ align:start position:0%
+switching between programs we perform a
+context switch to move to the
+
+ align:start position:0%
+context switch to move to the
+ 
+
+ align:start position:0%
+context switch to move to the
+appropriate MMU context the ability to
+
+ align:start position:0%
+appropriate MMU context the ability to
+ 
+
+ align:start position:0%
+appropriate MMU context the ability to
+share the CPU between many programs
+
+ align:start position:0%
+share the CPU between many programs
+ 
+
+ align:start position:0%
+share the CPU between many programs
+seems like a great idea let's figure out
+
+ align:start position:0%
+seems like a great idea let's figure out
+ 
+
+ align:start position:0%
+seems like a great idea let's figure out
+the details of how that might work
\ No newline at end of file
diff --git a/n1cXiw3s72k.txt b/n1cXiw3s72k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f55df9b005130826f91017f5025094d1a6245a73
--- /dev/null
+++ b/n1cXiw3s72k.txt
@@ -0,0 +1,475 @@
+align:start position:0%
+ 
+up until now we have analyzed the motion
+
+ align:start position:0%
+up until now we have analyzed the motion
+ 
+
+ align:start position:0%
+up until now we have analyzed the motion
+of objects that we treated as so-called
+
+ align:start position:0%
+of objects that we treated as so-called
+ 
+
+ align:start position:0%
+of objects that we treated as so-called
+point masses we're literally all of the
+
+ align:start position:0%
+point masses we're literally all of the
+ 
+
+ align:start position:0%
+point masses we're literally all of the
+mass of the object was treated as lying
+
+ align:start position:0%
+mass of the object was treated as lying
+ 
+
+ align:start position:0%
+mass of the object was treated as lying
+at a single point this is obviously an
+
+ align:start position:0%
+at a single point this is obviously an
+ 
+
+ align:start position:0%
+at a single point this is obviously an
+unrealistic idealization real objects
+
+ align:start position:0%
+unrealistic idealization real objects
+ 
+
+ align:start position:0%
+unrealistic idealization real objects
+have spatial extent and come in various
+
+ align:start position:0%
+have spatial extent and come in various
+ 
+
+ align:start position:0%
+have spatial extent and come in various
+sizes and shapes some regular and some
+
+ align:start position:0%
+sizes and shapes some regular and some
+ 
+
+ align:start position:0%
+sizes and shapes some regular and some
+highly irregular the mass distribution
+
+ align:start position:0%
+highly irregular the mass distribution
+ 
+
+ align:start position:0%
+highly irregular the mass distribution
+within these extended objects might be
+
+ align:start position:0%
+within these extended objects might be
+ 
+
+ align:start position:0%
+within these extended objects might be
+smooth and uniform or highly non-uniform
+
+ align:start position:0%
+smooth and uniform or highly non-uniform
+ 
+
+ align:start position:0%
+smooth and uniform or highly non-uniform
+and lumpy moreover sometimes we will be
+
+ align:start position:0%
+and lumpy moreover sometimes we will be
+ 
+
+ align:start position:0%
+and lumpy moreover sometimes we will be
+interested in simultaneously analyzing a
+
+ align:start position:0%
+interested in simultaneously analyzing a
+ 
+
+ align:start position:0%
+interested in simultaneously analyzing a
+large system of particles or objects to
+
+ align:start position:0%
+large system of particles or objects to
+ 
+
+ align:start position:0%
+large system of particles or objects to
+deal properly with such situations it is
+
+ align:start position:0%
+deal properly with such situations it is
+ 
+
+ align:start position:0%
+deal properly with such situations it is
+necessary to introduce a new physical
+
+ align:start position:0%
+necessary to introduce a new physical
+ 
+
+ align:start position:0%
+necessary to introduce a new physical
+quantity called the momentum which is a
+
+ align:start position:0%
+quantity called the momentum which is a
+ 
+
+ align:start position:0%
+quantity called the momentum which is a
+vector that we traditionally denote with
+
+ align:start position:0%
+vector that we traditionally denote with
+ 
+
+ align:start position:0%
+vector that we traditionally denote with
+the symbol P for a single point mass the
+
+ align:start position:0%
+the symbol P for a single point mass the
+ 
+
+ align:start position:0%
+the symbol P for a single point mass the
+momentum is a product of the mass and
+
+ align:start position:0%
+momentum is a product of the mass and
+ 
+
+ align:start position:0%
+momentum is a product of the mass and
+the velocity vector the form of Newton's
+
+ align:start position:0%
+the velocity vector the form of Newton's
+ 
+
+ align:start position:0%
+the velocity vector the form of Newton's
+second law that we have used so far F
+
+ align:start position:0%
+second law that we have used so far F
+ 
+
+ align:start position:0%
+second law that we have used so far F
+equals MA is actually only true for the
+
+ align:start position:0%
+equals MA is actually only true for the
+ 
+
+ align:start position:0%
+equals MA is actually only true for the
+special case of a point mass the more
+
+ align:start position:0%
+special case of a point mass the more
+ 
+
+ align:start position:0%
+special case of a point mass the more
+general form of Newton's second law is
+
+ align:start position:0%
+general form of Newton's second law is
+ 
+
+ align:start position:0%
+general form of Newton's second law is
+that F equals DP DT that is that the
+
+ align:start position:0%
+that F equals DP DT that is that the
+ 
+
+ align:start position:0%
+that F equals DP DT that is that the
+force is equal to the time derivative of
+
+ align:start position:0%
+force is equal to the time derivative of
+ 
+
+ align:start position:0%
+force is equal to the time derivative of
+the momentum vector this is applicable
+
+ align:start position:0%
+the momentum vector this is applicable
+ 
+
+ align:start position:0%
+the momentum vector this is applicable
+to either a single particle or to a
+
+ align:start position:0%
+to either a single particle or to a
+ 
+
+ align:start position:0%
+to either a single particle or to a
+system of particles this more general
+
+ align:start position:0%
+system of particles this more general
+ 
+
+ align:start position:0%
+system of particles this more general
+form provides us a way to address
+
+ align:start position:0%
+form provides us a way to address
+ 
+
+ align:start position:0%
+form provides us a way to address
+extended objects or multi particle
+
+ align:start position:0%
+extended objects or multi particle
+ 
+
+ align:start position:0%
+extended objects or multi particle
+systems we will once again appeal to a
+
+ align:start position:0%
+systems we will once again appeal to a
+ 
+
+ align:start position:0%
+systems we will once again appeal to a
+calculus like argument breaking down an
+
+ align:start position:0%
+calculus like argument breaking down an
+ 
+
+ align:start position:0%
+calculus like argument breaking down an
+extended distribution into a large
+
+ align:start position:0%
+extended distribution into a large
+ 
+
+ align:start position:0%
+extended distribution into a large
+number of small elements treating each
+
+ align:start position:0%
+number of small elements treating each
+ 
+
+ align:start position:0%
+number of small elements treating each
+element separately and then summing the
+
+ align:start position:0%
+element separately and then summing the
+ 
+
+ align:start position:0%
+element separately and then summing the
+results as part of this process we will
+
+ align:start position:0%
+results as part of this process we will
+ 
+
+ align:start position:0%
+results as part of this process we will
+introduce the concept of the center of
+
+ align:start position:0%
+introduce the concept of the center of
+ 
+
+ align:start position:0%
+introduce the concept of the center of
+mass a sort of mass weighted average
+
+ align:start position:0%
+mass a sort of mass weighted average
+ 
+
+ align:start position:0%
+mass a sort of mass weighted average
+position for an extended object or
+
+ align:start position:0%
+position for an extended object or
+ 
+
+ align:start position:0%
+position for an extended object or
+system momentum is also the first of
+
+ align:start position:0%
+system momentum is also the first of
+ 
+
+ align:start position:0%
+system momentum is also the first of
+several special measurable quantities
+
+ align:start position:0%
+several special measurable quantities
+ 
+
+ align:start position:0%
+several special measurable quantities
+that we will discuss that obey special
+
+ align:start position:0%
+that we will discuss that obey special
+ 
+
+ align:start position:0%
+that we will discuss that obey special
+powerful rules called conservation laws
+
+ align:start position:0%
+powerful rules called conservation laws
+ 
+
+ align:start position:0%
+powerful rules called conservation laws
+the other two quantities are energy and
+
+ align:start position:0%
+the other two quantities are energy and
+ 
+
+ align:start position:0%
+the other two quantities are energy and
+angular momentum conservation laws are
+
+ align:start position:0%
+angular momentum conservation laws are
+ 
+
+ align:start position:0%
+angular momentum conservation laws are
+principles that provide that the given
+
+ align:start position:0%
+principles that provide that the given
+ 
+
+ align:start position:0%
+principles that provide that the given
+measurable quantity remains unchanged
+
+ align:start position:0%
+measurable quantity remains unchanged
+ 
+
+ align:start position:0%
+measurable quantity remains unchanged
+during the evolution of a system with
+
+ align:start position:0%
+during the evolution of a system with
+ 
+
+ align:start position:0%
+during the evolution of a system with
+time as long as certain requirements are
+
+ align:start position:0%
+time as long as certain requirements are
+ 
+
+ align:start position:0%
+time as long as certain requirements are
+met essentially the requirement that a
+
+ align:start position:0%
+met essentially the requirement that a
+ 
+
+ align:start position:0%
+met essentially the requirement that a
+system remains isolated with this
+
+ align:start position:0%
+system remains isolated with this
+ 
+
+ align:start position:0%
+system remains isolated with this
+restriction in place the possible
+
+ align:start position:0%
+restriction in place the possible
+ 
+
+ align:start position:0%
+restriction in place the possible
+evolution of motion of a particle
+
+ align:start position:0%
+evolution of motion of a particle
+ 
+
+ align:start position:0%
+evolution of motion of a particle
+or system of particles is greatly
+
+ align:start position:0%
+or system of particles is greatly
+ 
+
+ align:start position:0%
+or system of particles is greatly
+restricted simplifying this calculation
+
+ align:start position:0%
+restricted simplifying this calculation
+ 
+
+ align:start position:0%
+restricted simplifying this calculation
+we will see how this can be used to our
+
+ align:start position:0%
+we will see how this can be used to our
+ 
+
+ align:start position:0%
+we will see how this can be used to our
+advantage in understanding what will
+
+ align:start position:0%
+advantage in understanding what will
+ 
+
+ align:start position:0%
+advantage in understanding what will
+happen
\ No newline at end of file
diff --git a/nmuXpvSIm3k.txt b/nmuXpvSIm3k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..860497c3bbfe9d60b867954beeab3f5f710ff5d0
--- /dev/null
+++ b/nmuXpvSIm3k.txt
@@ -0,0 +1,14651 @@
+align:start position:0%
+ 
+it's our last class which is happy
+
+ align:start position:0%
+it's our last class which is happy
+ 
+
+ align:start position:0%
+it's our last class which is happy
+because we get to go on break but
+
+ align:start position:0%
+because we get to go on break but
+ 
+
+ align:start position:0%
+because we get to go on break but
+there's so much more I want to tell you
+
+ align:start position:0%
+there's so much more I want to tell you
+ 
+
+ align:start position:0%
+there's so much more I want to tell you
+guys so but you know that's all we have
+
+ align:start position:0%
+guys so but you know that's all we have
+ 
+
+ align:start position:0%
+guys so but you know that's all we have
+time for uh there are cookies here for
+
+ align:start position:0%
+time for uh there are cookies here for
+ 
+
+ align:start position:0%
+time for uh there are cookies here for
+to make our last class sweet so please
+
+ align:start position:0%
+to make our last class sweet so please
+ 
+
+ align:start position:0%
+to make our last class sweet so please
+come and get some if you want they're
+
+ align:start position:0%
+come and get some if you want they're
+ 
+
+ align:start position:0%
+come and get some if you want they're
+very small so you can take to uh or you
+
+ align:start position:0%
+very small so you can take to uh or you
+ 
+
+ align:start position:0%
+very small so you can take to uh or you
+know if you didn't want to commit a
+
+ align:start position:0%
+know if you didn't want to commit a
+ 
+
+ align:start position:0%
+know if you didn't want to commit a
+large cookie you don't need
+
+ align:start position:0%
+large cookie you don't need
+ 
+
+ align:start position:0%
+large cookie you don't need
+to so uh okay so today uh finally we're
+
+ align:start position:0%
+to so uh okay so today uh finally we're
+ 
+
+ align:start position:0%
+to so uh okay so today uh finally we're
+going to actually construct the snars
+
+ align:start position:0%
+going to actually construct the snars
+ 
+
+ align:start position:0%
+going to actually construct the snars
+that we've been after that was kind of
+
+ align:start position:0%
+that we've been after that was kind of
+ 
+
+ align:start position:0%
+that we've been after that was kind of
+the goal uh is to uh construct uh snars
+
+ align:start position:0%
+the goal uh is to uh construct uh snars
+ 
+
+ align:start position:0%
+the goal uh is to uh construct uh snars
+s interactive arguments and like this
+
+ align:start position:0%
+s interactive arguments and like this
+ 
+
+ align:start position:0%
+s interactive arguments and like this
+entire course was a buildup to construct
+
+ align:start position:0%
+entire course was a buildup to construct
+ 
+
+ align:start position:0%
+entire course was a buildup to construct
+uh these snars and today we're going to
+
+ align:start position:0%
+uh these snars and today we're going to
+ 
+
+ align:start position:0%
+uh these snars and today we're going to
+see how to construct them uh they
+
+ align:start position:0%
+see how to construct them uh they
+ 
+
+ align:start position:0%
+see how to construct them uh they
+cookies
+
+ align:start position:0%
+cookies
+ 
+
+ align:start position:0%
+cookies
+guys cookies if you want from flower
+
+ align:start position:0%
+guys cookies if you want from flower
+ 
+
+ align:start position:0%
+guys cookies if you want from flower
+really good ones so feel free to take
+
+ align:start position:0%
+really good ones so feel free to take
+ 
+
+ align:start position:0%
+really good ones so feel free to take
+some um okay so uh what we're going to
+
+ align:start position:0%
+some um okay so uh what we're going to
+ 
+
+ align:start position:0%
+some um okay so uh what we're going to
+do today is show how to construct these
+
+ align:start position:0%
+do today is show how to construct these
+ 
+
+ align:start position:0%
+do today is show how to construct these
+snarks uh and uh we're gonna last class
+
+ align:start position:0%
+snarks uh and uh we're gonna last class
+ 
+
+ align:start position:0%
+snarks uh and uh we're gonna last class
+Jen Jang uh uh showed you is a really
+
+ align:start position:0%
+Jen Jang uh uh showed you is a really
+ 
+
+ align:start position:0%
+Jen Jang uh uh showed you is a really
+beautiful work on constructing bargs
+
+ align:start position:0%
+beautiful work on constructing bargs
+ 
+
+ align:start position:0%
+beautiful work on constructing bargs
+which are batch
+
+ align:start position:0%
+which are batch
+ 
+
+ align:start position:0%
+which are batch
+argument and you know on their own you
+
+ align:start position:0%
+argument and you know on their own you
+ 
+
+ align:start position:0%
+argument and you know on their own you
+can say uh why do we care about B
+
+ align:start position:0%
+can say uh why do we care about B
+ 
+
+ align:start position:0%
+can say uh why do we care about B
+argument I'm going to recall the
+
+ align:start position:0%
+argument I'm going to recall the
+ 
+
+ align:start position:0%
+argument I'm going to recall the
+definition but the I mean it's
+
+ align:start position:0%
+definition but the I mean it's
+ 
+
+ align:start position:0%
+definition but the I mean it's
+interesting on its own but what makes it
+
+ align:start position:0%
+interesting on its own but what makes it
+ 
+
+ align:start position:0%
+interesting on its own but what makes it
+super interesting is that we can use it
+
+ align:start position:0%
+super interesting is that we can use it
+ 
+
+ align:start position:0%
+super interesting is that we can use it
+in a pretty straightforward manner to
+
+ align:start position:0%
+in a pretty straightforward manner to
+ 
+
+ align:start position:0%
+in a pretty straightforward manner to
+construct snars so that's what we're
+
+ align:start position:0%
+construct snars so that's what we're
+ 
+
+ align:start position:0%
+construct snars so that's what we're
+going to see today we're going to see
+
+ align:start position:0%
+going to see today we're going to see
+ 
+
+ align:start position:0%
+going to see today we're going to see
+how to use these bars that I'm going to
+
+ align:start position:0%
+how to use these bars that I'm going to
+ 
+
+ align:start position:0%
+how to use these bars that I'm going to
+recall the definition in a second and
+
+ align:start position:0%
+recall the definition in a second and
+ 
+
+ align:start position:0%
+recall the definition in a second and
+also how to use I think Jen Jong called
+
+ align:start position:0%
+also how to use I think Jen Jong called
+ 
+
+ align:start position:0%
+also how to use I think Jen Jong called
+it a somewhere statistically binding
+
+ align:start position:0%
+it a somewhere statistically binding
+ 
+
+ align:start position:0%
+it a somewhere statistically binding
+hash functions it's also known in the
+
+ align:start position:0%
+hash functions it's also known in the
+ 
+
+ align:start position:0%
+hash functions it's also known in the
+literature as somewh extractable hash
+
+ align:start position:0%
+literature as somewh extractable hash
+ 
+
+ align:start position:0%
+literature as somewh extractable hash
+functions both are used so I'm just
+
+ align:start position:0%
+functions both are used so I'm just
+ 
+
+ align:start position:0%
+functions both are used so I'm just
+going to use the other just so familiar
+
+ align:start position:0%
+going to use the other just so familiar
+ 
+
+ align:start position:0%
+going to use the other just so familiar
+with both uh a uh formulations uh both
+
+ align:start position:0%
+with both uh a uh formulations uh both
+ 
+
+ align:start position:0%
+with both uh a uh formulations uh both
+names uh so what we're going to see
+
+ align:start position:0%
+names uh so what we're going to see
+ 
+
+ align:start position:0%
+names uh so what we're going to see
+today is how to use these bars with with
+
+ align:start position:0%
+today is how to use these bars with with
+ 
+
+ align:start position:0%
+today is how to use these bars with with
+these hash functions to get
+
+ align:start position:0%
+these hash functions to get
+ 
+
+ align:start position:0%
+these hash functions to get
+snars that's kind of uh the plan for
+
+ align:start position:0%
+snars that's kind of uh the plan for
+ 
+
+ align:start position:0%
+snars that's kind of uh the plan for
+today uh so let me first recall what a
+
+ align:start position:0%
+today uh so let me first recall what a
+ 
+
+ align:start position:0%
+today uh so let me first recall what a
+barg is really uh fast so a bar you want
+
+ align:start position:0%
+barg is really uh fast so a bar you want
+ 
+
+ align:start position:0%
+barg is really uh fast so a bar you want
+to kind of prove that many instances
+
+ align:start position:0%
+to kind of prove that many instances
+ 
+
+ align:start position:0%
+to kind of prove that many instances
+belong to an NP language so about Mark
+
+ align:start position:0%
+belong to an NP language so about Mark
+ 
+
+ align:start position:0%
+belong to an NP language so about Mark
+for an NP language L consists of three
+
+ align:start position:0%
+for an NP language L consists of three
+ 
+
+ align:start position:0%
+for an NP language L consists of three
+algorithm gen uh takes as input a
+
+ align:start position:0%
+algorithm gen uh takes as input a
+ 
+
+ align:start position:0%
+algorithm gen uh takes as input a
+security parameter the number of
+
+ align:start position:0%
+security parameter the number of
+ 
+
+ align:start position:0%
+security parameter the number of
+instances you want to batch maybe I'll
+
+ align:start position:0%
+instances you want to batch maybe I'll
+ 
+
+ align:start position:0%
+instances you want to batch maybe I'll
+close thank you can you close the door
+
+ align:start position:0%
+close thank you can you close the door
+ 
+
+ align:start position:0%
+close thank you can you close the door
+thanks uh K which is the number of
+
+ align:start position:0%
+thanks uh K which is the number of
+ 
+
+ align:start position:0%
+thanks uh K which is the number of
+instances you want to batch and N with
+
+ align:start position:0%
+instances you want to batch and N with
+ 
+
+ align:start position:0%
+instances you want to batch and N with
+which is the length of each instance and
+
+ align:start position:0%
+which is the length of each instance and
+ 
+
+ align:start position:0%
+which is the length of each instance and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+output uh some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CRS note Lambda is given in unary
+
+ align:start position:0%
+CRS note Lambda is given in unary
+ 
+
+ align:start position:0%
+CRS note Lambda is given in unary
+because we want them to run in time poly
+
+ align:start position:0%
+because we want them to run in time poly
+ 
+
+ align:start position:0%
+because we want them to run in time poly
+Lambda but K and N are given in binary
+
+ align:start position:0%
+Lambda but K and N are given in binary
+ 
+
+ align:start position:0%
+Lambda but K and N are given in binary
+so because it's polinomial time
+
+ align:start position:0%
+so because it's polinomial time
+ 
+
+ align:start position:0%
+so because it's polinomial time
+algorithm it runs in time poog in K poog
+
+ align:start position:0%
+algorithm it runs in time poog in K poog
+ 
+
+ align:start position:0%
+algorithm it runs in time poog in K poog
+in N the instant size okay and then the
+
+ align:start position:0%
+in N the instant size okay and then the
+ 
+
+ align:start position:0%
+in N the instant size okay and then the
+Prov algorithm takes as input uh the
+
+ align:start position:0%
+Prov algorithm takes as input uh the
+ 
+
+ align:start position:0%
+Prov algorithm takes as input uh the
+CRS and then X1 up to xn uh XK sorry so
+
+ align:start position:0%
+CRS and then X1 up to xn uh XK sorry so
+ 
+
+ align:start position:0%
+CRS and then X1 up to xn uh XK sorry so
+K elements with
+
+ align:start position:0%
+K elements with
+ 
+
+ align:start position:0%
+K elements with
+Witnesses and outputs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh proof
+
+ align:start position:0%
+uh proof
+ 
+
+ align:start position:0%
+uh proof
+Pi but importantly this proof should be
+
+ align:start position:0%
+Pi but importantly this proof should be
+ 
+
+ align:start position:0%
+Pi but importantly this proof should be
+small so this Pi is of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size uh poly log or poly in security
+
+ align:start position:0%
+size uh poly log or poly in security
+ 
+
+ align:start position:0%
+size uh poly log or poly in security
+parameter but log K that's
+
+ align:start position:0%
+parameter but log K that's
+ 
+
+ align:start position:0%
+parameter but log K that's
+important okay we want it to depend only
+
+ align:start position:0%
+important okay we want it to depend only
+ 
+
+ align:start position:0%
+important okay we want it to depend only
+Poly arthic on on K that's kind of our
+
+ align:start position:0%
+Poly arthic on on K that's kind of our
+ 
+
+ align:start position:0%
+Poly arthic on on K that's kind of our
+goal okay okay and then maybe ideally
+
+ align:start position:0%
+goal okay okay and then maybe ideally
+ 
+
+ align:start position:0%
+goal okay okay and then maybe ideally
+also log n but the point is we want it
+
+ align:start position:0%
+also log n but the point is we want it
+ 
+
+ align:start position:0%
+also log n but the point is we want it
+to be succinct okay otherwise it's
+
+ align:start position:0%
+to be succinct okay otherwise it's
+ 
+
+ align:start position:0%
+to be succinct okay otherwise it's
+trivial you just output the witnesses
+
+ align:start position:0%
+trivial you just output the witnesses
+ 
+
+ align:start position:0%
+trivial you just output the witnesses
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+verifier takes his input CRS the
+
+ align:start position:0%
+verifier takes his input CRS the
+ 
+
+ align:start position:0%
+verifier takes his input CRS the
+instances and a proof and it output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+01 accept or reject okay and this but
+
+ align:start position:0%
+01 accept or reject okay and this but
+ 
+
+ align:start position:0%
+01 accept or reject okay and this but
+when I say the size of the proof is this
+
+ align:start position:0%
+when I say the size of the proof is this
+ 
+
+ align:start position:0%
+when I say the size of the proof is this
+actually you can make it bigger smaller
+
+ align:start position:0%
+actually you can make it bigger smaller
+ 
+
+ align:start position:0%
+actually you can make it bigger smaller
+but we want it to be SU
+
+ align:start position:0%
+but we want it to be SU
+ 
+
+ align:start position:0%
+but we want it to be SU
+okay that's oh sorry I uh sorry I
+
+ align:start position:0%
+okay that's oh sorry I uh sorry I
+ 
+
+ align:start position:0%
+okay that's oh sorry I uh sorry I
+didn't we wanted to depend only
+
+ align:start position:0%
+didn't we wanted to depend only
+ 
+
+ align:start position:0%
+didn't we wanted to depend only
+logarithmically and K so on
+
+ align:start position:0%
+logarithmically and K so on
+ 
+
+ align:start position:0%
+logarithmically and K so on
+but we allow it to depend uh L polom and
+
+ align:start position:0%
+but we allow it to depend uh L polom and
+ 
+
+ align:start position:0%
+but we allow it to depend uh L polom and
+one in one witness okay so I can put it
+
+ align:start position:0%
+one in one witness okay so I can put it
+ 
+
+ align:start position:0%
+one in one witness okay so I can put it
+here a single witness one not many
+
+ align:start position:0%
+here a single witness one not many
+ 
+
+ align:start position:0%
+here a single witness one not many
+ideally we want to be as exing as
+
+ align:start position:0%
+ideally we want to be as exing as
+ 
+
+ align:start position:0%
+ideally we want to be as exing as
+possible but what we can get is a as a
+
+ align:start position:0%
+possible but what we can get is a as a
+ 
+
+ align:start position:0%
+possible but what we can get is a as a
+bar that depends grows with one instance
+
+ align:start position:0%
+bar that depends grows with one instance
+ 
+
+ align:start position:0%
+bar that depends grows with one instance
+one witness as opposed to K
+
+ align:start position:0%
+one witness as opposed to K
+ 
+
+ align:start position:0%
+one witness as opposed to K
+instances okay so uh so this is kind of
+
+ align:start position:0%
+instances okay so uh so this is kind of
+ 
+
+ align:start position:0%
+instances okay so uh so this is kind of
+the the algorithms uh then we want
+
+ align:start position:0%
+the the algorithms uh then we want
+ 
+
+ align:start position:0%
+the the algorithms uh then we want
+completeness and soundness completeness
+
+ align:start position:0%
+completeness and soundness completeness
+ 
+
+ align:start position:0%
+completeness and soundness completeness
+is the usual thing that just says if P
+
+ align:start position:0%
+is the usual thing that just says if P
+ 
+
+ align:start position:0%
+is the usual thing that just says if P
+has valid Witnesses and he generates a
+
+ align:start position:0%
+has valid Witnesses and he generates a
+ 
+
+ align:start position:0%
+has valid Witnesses and he generates a
+bar this bar is going to be accepting
+
+ align:start position:0%
+bar this bar is going to be accepting
+ 
+
+ align:start position:0%
+bar this bar is going to be accepting
+with probability one over kind of the
+
+ align:start position:0%
+with probability one over kind of the
+ 
+
+ align:start position:0%
+with probability one over kind of the
+CRS generation so that's the standard
+
+ align:start position:0%
+CRS generation so that's the standard
+ 
+
+ align:start position:0%
+CRS generation so that's the standard
+completeness and then uh the soundness
+
+ align:start position:0%
+completeness and then uh the soundness
+ 
+
+ align:start position:0%
+completeness and then uh the soundness
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+that uh that we have ideally you would
+
+ align:start position:0%
+that uh that we have ideally you would
+ 
+
+ align:start position:0%
+that uh that we have ideally you would
+want to say that uh so in soundless
+
+ align:start position:0%
+want to say that uh so in soundless
+ 
+
+ align:start position:0%
+want to say that uh so in soundless
+computational soundness we have adaptive
+
+ align:start position:0%
+computational soundness we have adaptive
+ 
+
+ align:start position:0%
+computational soundness we have adaptive
+soundness and nonadaptive soundness and
+
+ align:start position:0%
+soundness and nonadaptive soundness and
+ 
+
+ align:start position:0%
+soundness and nonadaptive soundness and
+we want to we want to say that the a
+
+ align:start position:0%
+we want to we want to say that the a
+ 
+
+ align:start position:0%
+we want to we want to say that the a
+cheating prover cannot convince you of a
+
+ align:start position:0%
+cheating prover cannot convince you of a
+ 
+
+ align:start position:0%
+cheating prover cannot convince you of a
+false statement so he cannot generate he
+
+ align:start position:0%
+false statement so he cannot generate he
+ 
+
+ align:start position:0%
+false statement so he cannot generate he
+cannot give you X's that are not all in
+
+ align:start position:0%
+cannot give you X's that are not all in
+ 
+
+ align:start position:0%
+cannot give you X's that are not all in
+the language with a valid proof that
+
+ align:start position:0%
+the language with a valid proof that
+ 
+
+ align:start position:0%
+the language with a valid proof that
+soundless okay there's an issue is when
+
+ align:start position:0%
+soundless okay there's an issue is when
+ 
+
+ align:start position:0%
+soundless okay there's an issue is when
+does the cheating Pro gets to choose
+
+ align:start position:0%
+does the cheating Pro gets to choose
+ 
+
+ align:start position:0%
+does the cheating Pro gets to choose
+these X's is it before he sees the CRS
+
+ align:start position:0%
+these X's is it before he sees the CRS
+ 
+
+ align:start position:0%
+these X's is it before he sees the CRS
+or after he sees the CRS if he needs to
+
+ align:start position:0%
+or after he sees the CRS if he needs to
+ 
+
+ align:start position:0%
+or after he sees the CRS if he needs to
+decide them before he sees the CRS then
+
+ align:start position:0%
+decide them before he sees the CRS then
+ 
+
+ align:start position:0%
+decide them before he sees the CRS then
+it's non adaptive if you get to decide
+
+ align:start position:0%
+it's non adaptive if you get to decide
+ 
+
+ align:start position:0%
+it's non adaptive if you get to decide
+it after then it's
+
+ align:start position:0%
+it after then it's
+ 
+
+ align:start position:0%
+it after then it's
+adaptive ideally we want to say it's
+
+ align:start position:0%
+adaptive ideally we want to say it's
+ 
+
+ align:start position:0%
+adaptive ideally we want to say it's
+secure for all like very uh all as big
+
+ align:start position:0%
+secure for all like very uh all as big
+ 
+
+ align:start position:0%
+secure for all like very uh all as big
+classes provs as possible and thus we
+
+ align:start position:0%
+classes provs as possible and thus we
+ 
+
+ align:start position:0%
+classes provs as possible and thus we
+would like to have sounds against
+
+ align:start position:0%
+would like to have sounds against
+ 
+
+ align:start position:0%
+would like to have sounds against
+adaptive provs to say even if a cheating
+
+ align:start position:0%
+adaptive provs to say even if a cheating
+ 
+
+ align:start position:0%
+adaptive provs to say even if a cheating
+prover chooses this X1 of XC
+
+ align:start position:0%
+prover chooses this X1 of XC
+ 
+
+ align:start position:0%
+prover chooses this X1 of XC
+adaptably after seeing the CRS if one of
+
+ align:start position:0%
+adaptably after seeing the CRS if one of
+ 
+
+ align:start position:0%
+adaptably after seeing the CRS if one of
+them is false he cannot generate a proof
+
+ align:start position:0%
+them is false he cannot generate a proof
+ 
+
+ align:start position:0%
+them is false he cannot generate a proof
+that's what we would like to say what we
+
+ align:start position:0%
+that's what we would like to say what we
+ 
+
+ align:start position:0%
+that's what we would like to say what we
+can say is what's called a semi adaptive
+
+ align:start position:0%
+can say is what's called a semi adaptive
+ 
+
+ align:start position:0%
+can say is what's called a semi adaptive
+something in between okay so let me just
+
+ align:start position:0%
+something in between okay so let me just
+ 
+
+ align:start position:0%
+something in between okay so let me just
+write it here so semi-adaptive sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is just says the adversary needs to tell
+
+ align:start position:0%
+is just says the adversary needs to tell
+ 
+
+ align:start position:0%
+is just says the adversary needs to tell
+you which in so he's going to give you K
+
+ align:start position:0%
+you which in so he's going to give you K
+ 
+
+ align:start position:0%
+you which in so he's going to give you K
+instances he can choose them adaptively
+
+ align:start position:0%
+instances he can choose them adaptively
+ 
+
+ align:start position:0%
+instances he can choose them adaptively
+but he needs to choose the ion which is
+
+ align:start position:0%
+but he needs to choose the ion which is
+ 
+
+ align:start position:0%
+but he needs to choose the ion which is
+going to cheat so he's a cheater so one
+
+ align:start position:0%
+going to cheat so he's a cheater so one
+ 
+
+ align:start position:0%
+going to cheat so he's a cheater so one
+of that eyes is not in the
+
+ align:start position:0%
+of that eyes is not in the
+ 
+
+ align:start position:0%
+of that eyes is not in the
+language which ey which location I the
+
+ align:start position:0%
+language which ey which location I the
+ 
+
+ align:start position:0%
+language which ey which location I the
+XI is going to be not in the language
+
+ align:start position:0%
+XI is going to be not in the language
+ 
+
+ align:start position:0%
+XI is going to be not in the language
+that should not depend on the CRS okay
+
+ align:start position:0%
+that should not depend on the CRS okay
+ 
+
+ align:start position:0%
+that should not depend on the CRS okay
+so so it says that for any poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size P star and for for every I which of
+
+ align:start position:0%
+size P star and for for every I which of
+ 
+
+ align:start position:0%
+size P star and for for every I which of
+course may depend on on Lambda because
+
+ align:start position:0%
+course may depend on on Lambda because
+ 
+
+ align:start position:0%
+course may depend on on Lambda because
+for any Lambda you have an i because the
+
+ align:start position:0%
+for any Lambda you have an i because the
+ 
+
+ align:start position:0%
+for any Lambda you have an i because the
+I is between one and K and K grows with
+
+ align:start position:0%
+I is between one and K and K grows with
+ 
+
+ align:start position:0%
+I is between one and K and K grows with
+can grow with Lambda so for any I you
+
+ align:start position:0%
+can grow with Lambda so for any I you
+ 
+
+ align:start position:0%
+can grow with Lambda so for any I you
+want to say the probability that P star
+
+ align:start position:0%
+want to say the probability that P star
+ 
+
+ align:start position:0%
+want to say the probability that P star
+given a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CRS outputs X1 up to XK and
+
+ align:start position:0%
+CRS outputs X1 up to XK and
+ 
+
+ align:start position:0%
+CRS outputs X1 up to XK and
+Pi such that x i is not in the language
+
+ align:start position:0%
+Pi such that x i is not in the language
+ 
+
+ align:start position:0%
+Pi such that x i is not in the language
+and Pi is accepted is negligible so XI
+
+ align:start position:0%
+and Pi is accepted is negligible so XI
+ 
+
+ align:start position:0%
+and Pi is accepted is negligible so XI
+one of them is the XI one is not in the
+
+ align:start position:0%
+one of them is the XI one is not in the
+ 
+
+ align:start position:0%
+one of them is the XI one is not in the
+language and the I was chosen before he
+
+ align:start position:0%
+language and the I was chosen before he
+ 
+
+ align:start position:0%
+language and the I was chosen before he
+saw the CRS okay so for any P star he
+
+ align:start position:0%
+saw the CRS okay so for any P star he
+ 
+
+ align:start position:0%
+saw the CRS okay so for any P star he
+tells you I'm going to cheat on location
+
+ align:start position:0%
+tells you I'm going to cheat on location
+ 
+
+ align:start position:0%
+tells you I'm going to cheat on location
+I now he's given a CRS the probability
+
+ align:start position:0%
+I now he's given a CRS the probability
+ 
+
+ align:start position:0%
+I now he's given a CRS the probability
+that he gives you an accepting proof for
+
+ align:start position:0%
+that he gives you an accepting proof for
+ 
+
+ align:start position:0%
+that he gives you an accepting proof for
+X on of dek that he chose adaptively
+
+ align:start position:0%
+X on of dek that he chose adaptively
+ 
+
+ align:start position:0%
+X on of dek that he chose adaptively
+after seeing the CRS the probability
+
+ align:start position:0%
+after seeing the CRS the probability
+ 
+
+ align:start position:0%
+after seeing the CRS the probability
+that it's accepting so
+
+ align:start position:0%
+that it's accepting so
+ 
+
+ align:start position:0%
+that it's accepting so
+CRS uh X1 up to XK and Pi is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and X is not in the language x i is
+
+ align:start position:0%
+one and X is not in the language x i is
+ 
+
+ align:start position:0%
+one and X is not in the language x i is
+not is
+
+ align:start position:0%
+not is
+ 
+
+ align:start position:0%
+not is
+negligible this equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible okay so again for any
+
+ align:start position:0%
+negligible okay so again for any
+ 
+
+ align:start position:0%
+negligible okay so again for any
+cheating prover he needs to ahead of
+
+ align:start position:0%
+cheating prover he needs to ahead of
+ 
+
+ align:start position:0%
+cheating prover he needs to ahead of
+time I'm going to choose my xon XK
+
+ align:start position:0%
+time I'm going to choose my xon XK
+ 
+
+ align:start position:0%
+time I'm going to choose my xon XK
+adaptively after I see the CRS but I'm
+
+ align:start position:0%
+adaptively after I see the CRS but I'm
+ 
+
+ align:start position:0%
+adaptively after I see the CRS but I'm
+going to I'm going to cheat on location
+
+ align:start position:0%
+going to I'm going to cheat on location
+ 
+
+ align:start position:0%
+going to I'm going to cheat on location
+I the probability that he succeeds in
+
+ align:start position:0%
+I the probability that he succeeds in
+ 
+
+ align:start position:0%
+I the probability that he succeeds in
+cheating in location
+
+ align:start position:0%
+cheating in location
+ 
+
+ align:start position:0%
+cheating in location
+I in an accepting way is
+
+ align:start position:0%
+I in an accepting way is
+ 
+
+ align:start position:0%
+I in an accepting way is
+negligible that's the semi-adaptive
+
+ align:start position:0%
+negligible that's the semi-adaptive
+ 
+
+ align:start position:0%
+negligible that's the semi-adaptive
+soundness okay so and uh last class
+
+ align:start position:0%
+soundness okay so and uh last class
+ 
+
+ align:start position:0%
+soundness okay so and uh last class
+jenong kind of showed you the high level
+
+ align:start position:0%
+jenong kind of showed you the high level
+ 
+
+ align:start position:0%
+jenong kind of showed you the high level
+of how you construct such a like the
+
+ align:start position:0%
+of how you construct such a like the
+ 
+
+ align:start position:0%
+of how you construct such a like the
+construction of such a
+
+ align:start position:0%
+construction of such a
+ 
+
+ align:start position:0%
+construction of such a
+bar okay any questions yes uh is piz
+
+ align:start position:0%
+bar okay any questions yes uh is piz
+ 
+
+ align:start position:0%
+bar okay any questions yes uh is piz
+required like the indices other than I
+
+ align:start position:0%
+required like the indices other than I
+ 
+
+ align:start position:0%
+required like the indices other than I
+are those required to be act like in the
+
+ align:start position:0%
+are those required to be act like in the
+ 
+
+ align:start position:0%
+are those required to be act like in the
+language or no no we don't care so yeah
+
+ align:start position:0%
+language or no no we don't care so yeah
+ 
+
+ align:start position:0%
+language or no no we don't care so yeah
+good question so the P star can choose
+
+ align:start position:0%
+good question so the P star can choose
+ 
+
+ align:start position:0%
+good question so the P star can choose
+the rest of the X's however he wants in
+
+ align:start position:0%
+the rest of the X's however he wants in
+ 
+
+ align:start position:0%
+the rest of the X's however he wants in
+the language outside the language
+
+ align:start position:0%
+the language outside the language
+ 
+
+ align:start position:0%
+the language outside the language
+however he
+
+ align:start position:0%
+however he
+ 
+
+ align:start position:0%
+however he
+wants okay but he wins if the XI is not
+
+ align:start position:0%
+wants okay but he wins if the XI is not
+ 
+
+ align:start position:0%
+wants okay but he wins if the XI is not
+in the language and the pi is
+
+ align:start position:0%
+in the language and the pi is
+ 
+
+ align:start position:0%
+in the language and the pi is
+accepting and he wins with probability
+
+ align:start position:0%
+accepting and he wins with probability
+ 
+
+ align:start position:0%
+accepting and he wins with probability
+yes transforming this into fully
+
+ align:start position:0%
+yes transforming this into fully
+ 
+
+ align:start position:0%
+yes transforming this into fully
+adaptive will imply
+
+ align:start position:0%
+adaptive will imply
+ 
+
+ align:start position:0%
+adaptive will imply
+guessing
+
+ align:start position:0%
+guessing
+ 
+
+ align:start position:0%
+guessing
+yeah okay uh good so the question is can
+
+ align:start position:0%
+yeah okay uh good so the question is can
+ 
+
+ align:start position:0%
+yeah okay uh good so the question is can
+why like can we transform this into a
+
+ align:start position:0%
+why like can we transform this into a
+ 
+
+ align:start position:0%
+why like can we transform this into a
+fully adaptive snar so ah converting it
+
+ align:start position:0%
+fully adaptive snar so ah converting it
+ 
+
+ align:start position:0%
+fully adaptive snar so ah converting it
+into a fully adaptive
+
+ align:start position:0%
+into a fully adaptive
+ 
+
+ align:start position:0%
+into a fully adaptive
+snar is um non-trial and I'll tell you
+
+ align:start position:0%
+snar is um non-trial and I'll tell you
+ 
+
+ align:start position:0%
+snar is um non-trial and I'll tell you
+why you can you can guess I you can
+
+ align:start position:0%
+why you can you can guess I you can
+ 
+
+ align:start position:0%
+why you can you can guess I you can
+guess I and you'll guess it correctly
+
+ align:start position:0%
+guess I and you'll guess it correctly
+ 
+
+ align:start position:0%
+guess I and you'll guess it correctly
+with probability one over k
+
+ align:start position:0%
+with probability one over k
+ 
+
+ align:start position:0%
+with probability one over k
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+general but here is so you you can do
+
+ align:start position:0%
+general but here is so you you can do
+ 
+
+ align:start position:0%
+general but here is so you you can do
+the you can do it but here is the issue
+
+ align:start position:0%
+the you can do it but here is the issue
+ 
+
+ align:start position:0%
+the you can do it but here is the issue
+I'll tell you what what um complication
+
+ align:start position:0%
+I'll tell you what what um complication
+ 
+
+ align:start position:0%
+I'll tell you what what um complication
+is in the analysis so I I don't want to
+
+ align:start position:0%
+is in the analysis so I I don't want to
+ 
+
+ align:start position:0%
+is in the analysis so I I don't want to
+recall too much the construction but the
+
+ align:start position:0%
+recall too much the construction but the
+ 
+
+ align:start position:0%
+recall too much the construction but the
+high level idea of how these bars are
+
+ align:start position:0%
+high level idea of how these bars are
+ 
+
+ align:start position:0%
+high level idea of how these bars are
+analyzed even without kind of knowing
+
+ align:start position:0%
+analyzed even without kind of knowing
+ 
+
+ align:start position:0%
+analyzed even without kind of knowing
+the construction uh the way they're
+
+ align:start position:0%
+the construction uh the way they're
+ 
+
+ align:start position:0%
+the construction uh the way they're
+analyzed in this CRS so in the proof in
+
+ align:start position:0%
+analyzed in this CRS so in the proof in
+ 
+
+ align:start position:0%
+analyzed in this CRS so in the proof in
+the analysis we say Suppose there exists
+
+ align:start position:0%
+the analysis we say Suppose there exists
+ 
+
+ align:start position:0%
+the analysis we say Suppose there exists
+some cheating
+
+ align:start position:0%
+some cheating
+ 
+
+ align:start position:0%
+some cheating
+prover that Che on some
+
+ align:start position:0%
+prover that Che on some
+ 
+
+ align:start position:0%
+prover that Che on some
+ey in the
+
+ align:start position:0%
+ey in the
+ 
+
+ align:start position:0%
+ey in the
+CRS I'm going to I'm going to change the
+
+ align:start position:0%
+CRS I'm going to I'm going to change the
+ 
+
+ align:start position:0%
+CRS I'm going to I'm going to change the
+CRS now I'm going to tell the cheating
+
+ align:start position:0%
+CRS now I'm going to tell the cheating
+ 
+
+ align:start position:0%
+CRS now I'm going to tell the cheating
+Pro here's a new CRS and in this new CRS
+
+ align:start position:0%
+Pro here's a new CRS and in this new CRS
+ 
+
+ align:start position:0%
+Pro here's a new CRS and in this new CRS
+I'm going to kind of hardwire I I'm
+
+ align:start position:0%
+I'm going to kind of hardwire I I'm
+ 
+
+ align:start position:0%
+I'm going to kind of hardwire I I'm
+going to put some information about I in
+
+ align:start position:0%
+going to put some information about I in
+ 
+
+ align:start position:0%
+going to put some information about I in
+a way that's
+
+ align:start position:0%
+a way that's
+ 
+
+ align:start position:0%
+a way that's
+unnoticeable okay and when we'll see I'm
+
+ align:start position:0%
+unnoticeable okay and when we'll see I'm
+ 
+
+ align:start position:0%
+unnoticeable okay and when we'll see I'm
+going to call the somewh extractable
+
+ align:start position:0%
+going to call the somewh extractable
+ 
+
+ align:start position:0%
+going to call the somewh extractable
+hash or what J called SSB hash some more
+
+ align:start position:0%
+hash or what J called SSB hash some more
+ 
+
+ align:start position:0%
+hash or what J called SSB hash some more
+statistically binding and then you I'll
+
+ align:start position:0%
+statistically binding and then you I'll
+ 
+
+ align:start position:0%
+statistically binding and then you I'll
+remind you a little bit how we where we
+
+ align:start position:0%
+remind you a little bit how we where we
+ 
+
+ align:start position:0%
+remind you a little bit how we where we
+stick the the index ey but in analysis
+
+ align:start position:0%
+stick the the index ey but in analysis
+ 
+
+ align:start position:0%
+stick the the index ey but in analysis
+we say you know let me change the CRS to
+
+ align:start position:0%
+we say you know let me change the CRS to
+ 
+
+ align:start position:0%
+we say you know let me change the CRS to
+a CRS a different CRS it has a very
+
+ align:start position:0%
+a CRS a different CRS it has a very
+ 
+
+ align:start position:0%
+a CRS a different CRS it has a very
+different distribution but it's
+
+ align:start position:0%
+different distribution but it's
+ 
+
+ align:start position:0%
+different distribution but it's
+indistinguishable it looks the like the
+
+ align:start position:0%
+indistinguishable it looks the like the
+ 
+
+ align:start position:0%
+indistinguishable it looks the like the
+original CRS so P star can't distinguish
+
+ align:start position:0%
+original CRS so P star can't distinguish
+ 
+
+ align:start position:0%
+original CRS so P star can't distinguish
+between the two so he'll still give me a
+
+ align:start position:0%
+between the two so he'll still give me a
+ 
+
+ align:start position:0%
+between the two so he'll still give me a
+valid bar okay and now I'm going to say
+
+ align:start position:0%
+valid bar okay and now I'm going to say
+ 
+
+ align:start position:0%
+valid bar okay and now I'm going to say
+in this new CRS actually there's no way
+
+ align:start position:0%
+in this new CRS actually there's no way
+ 
+
+ align:start position:0%
+in this new CRS actually there's no way
+he can cheat on location I there's no
+
+ align:start position:0%
+he can cheat on location I there's no
+ 
+
+ align:start position:0%
+he can cheat on location I there's no
+way he can cheat okay what is the issue
+
+ align:start position:0%
+way he can cheat okay what is the issue
+ 
+
+ align:start position:0%
+way he can cheat okay what is the issue
+so now you're saying why why do we need
+
+ align:start position:0%
+so now you're saying why why do we need
+ 
+
+ align:start position:0%
+so now you're saying why why do we need
+why can't we do fully
+
+ align:start position:0%
+why can't we do fully
+ 
+
+ align:start position:0%
+why can't we do fully
+adaptive the the issue is it may be the
+
+ align:start position:0%
+adaptive the the issue is it may be the
+ 
+
+ align:start position:0%
+adaptive the the issue is it may be the
+case that once we switch the CRS it
+
+ align:start position:0%
+case that once we switch the CRS it
+ 
+
+ align:start position:0%
+case that once we switch the CRS it
+switches where he's cheating so here's
+
+ align:start position:0%
+switches where he's cheating so here's
+ 
+
+ align:start position:0%
+switches where he's cheating so here's
+an here's an alternative way let's say
+
+ align:start position:0%
+an here's an alternative way let's say
+ 
+
+ align:start position:0%
+an here's an alternative way let's say
+the approver tells you here you know I'm
+
+ align:start position:0%
+the approver tells you here you know I'm
+ 
+
+ align:start position:0%
+the approver tells you here you know I'm
+going to cheat in location I but I can
+
+ align:start position:0%
+going to cheat in location I but I can
+ 
+
+ align:start position:0%
+going to cheat in location I but I can
+be adaptive chosen based on the
+
+ align:start position:0%
+be adaptive chosen based on the
+ 
+
+ align:start position:0%
+be adaptive chosen based on the
+CRS so now in the analysis I'm going to
+
+ align:start position:0%
+CRS so now in the analysis I'm going to
+ 
+
+ align:start position:0%
+CRS so now in the analysis I'm going to
+say I'm GNA guess where he cheated I'm
+
+ align:start position:0%
+say I'm GNA guess where he cheated I'm
+ 
+
+ align:start position:0%
+say I'm GNA guess where he cheated I'm
+GNA say let's guess he cheated location
+
+ align:start position:0%
+GNA say let's guess he cheated location
+ 
+
+ align:start position:0%
+GNA say let's guess he cheated location
+seven I'm GNA hardwire kind of the CRS
+
+ align:start position:0%
+seven I'm GNA hardwire kind of the CRS
+ 
+
+ align:start position:0%
+seven I'm GNA hardwire kind of the CRS
+to depend on this location and then the
+
+ align:start position:0%
+to depend on this location and then the
+ 
+
+ align:start position:0%
+to depend on this location and then the
+cheatting pro doesn't cheat on seven it
+
+ align:start position:0%
+cheatting pro doesn't cheat on seven it
+ 
+
+ align:start position:0%
+cheatting pro doesn't cheat on seven it
+cheat on something else he can kind of
+
+ align:start position:0%
+cheat on something else he can kind of
+ 
+
+ align:start position:0%
+cheat on something else he can kind of
+evade me now you're saying oh if he
+
+ align:start position:0%
+evade me now you're saying oh if he
+ 
+
+ align:start position:0%
+evade me now you're saying oh if he
+cheat something else I can tell I can
+
+ align:start position:0%
+cheat something else I can tell I can
+ 
+
+ align:start position:0%
+cheat something else I can tell I can
+tell the difference so like I shouldn't
+
+ align:start position:0%
+tell the difference so like I shouldn't
+ 
+
+ align:start position:0%
+tell the difference so like I shouldn't
+be able to tell but the thing is you
+
+ align:start position:0%
+be able to tell but the thing is you
+ 
+
+ align:start position:0%
+be able to tell but the thing is you
+don't know what's in the language it's
+
+ align:start position:0%
+don't know what's in the language it's
+ 
+
+ align:start position:0%
+don't know what's in the language it's
+not what's not in the language so the
+
+ align:start position:0%
+not what's not in the language so the
+ 
+
+ align:start position:0%
+not what's not in the language so the
+the problem is whether XI is in the
+
+ align:start position:0%
+the problem is whether XI is in the
+ 
+
+ align:start position:0%
+the problem is whether XI is in the
+language or not in the language can be
+
+ align:start position:0%
+language or not in the language can be
+ 
+
+ align:start position:0%
+language or not in the language can be
+very hard to tell it may
+
+ align:start position:0%
+very hard to tell it may
+ 
+
+ align:start position:0%
+very hard to tell it may
+take and that's why kind of getting
+
+ align:start position:0%
+take and that's why kind of getting
+ 
+
+ align:start position:0%
+take and that's why kind of getting
+adaptive like just guessing is
+
+ align:start position:0%
+adaptive like just guessing is
+ 
+
+ align:start position:0%
+adaptive like just guessing is
+not is not uh good enough because he
+
+ align:start position:0%
+not is not uh good enough because he
+ 
+
+ align:start position:0%
+not is not uh good enough because he
+needs to the the issue is if you could
+
+ align:start position:0%
+needs to the the issue is if you could
+ 
+
+ align:start position:0%
+needs to the the issue is if you could
+tell efficiently whether exi is in the
+
+ align:start position:0%
+tell efficiently whether exi is in the
+ 
+
+ align:start position:0%
+tell efficiently whether exi is in the
+language or not in the language then yes
+
+ align:start position:0%
+language or not in the language then yes
+ 
+
+ align:start position:0%
+language or not in the language then yes
+but because it can be very
+
+ align:start position:0%
+but because it can be very
+ 
+
+ align:start position:0%
+but because it can be very
+hard that's where things become tricky
+
+ align:start position:0%
+hard that's where things become tricky
+ 
+
+ align:start position:0%
+hard that's where things become tricky
+so that's so you can guess but it's not
+
+ align:start position:0%
+so that's so you can guess but it's not
+ 
+
+ align:start position:0%
+so that's so you can guess but it's not
+good enough is is uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer okay any yeah
+
+ align:start position:0%
+answer okay any yeah
+ 
+
+ align:start position:0%
+answer okay any yeah
+even huh even if he commits to
+
+ align:start position:0%
+even huh even if he commits to
+ 
+
+ align:start position:0%
+even huh even if he commits to
+do will that
+
+ align:start position:0%
+do will that
+ 
+
+ align:start position:0%
+do will that
+be well he can com what do you mean he
+
+ align:start position:0%
+be well he can com what do you mean he
+ 
+
+ align:start position:0%
+be well he can com what do you mean he
+commits the so you're saying let's
+
+ align:start position:0%
+commits the so you're saying let's
+ 
+
+ align:start position:0%
+commits the so you're saying let's
+change the scheme kind of and have him
+
+ align:start position:0%
+change the scheme kind of and have him
+ 
+
+ align:start position:0%
+change the scheme kind of and have him
+add commitment
+
+ align:start position:0%
+add commitment
+ 
+
+ align:start position:0%
+add commitment
+or I guess not be
+
+ align:start position:0%
+or I guess not be
+ 
+
+ align:start position:0%
+or I guess not be
+that I I guess the issue is look when
+
+ align:start position:0%
+that I I guess the issue is look when
+ 
+
+ align:start position:0%
+that I I guess the issue is look when
+he's cheating we don't know whether like
+
+ align:start position:0%
+he's cheating we don't know whether like
+ 
+
+ align:start position:0%
+he's cheating we don't know whether like
+he gives you X1 of to XK and and approve
+
+ align:start position:0%
+he gives you X1 of to XK and and approve
+ 
+
+ align:start position:0%
+he gives you X1 of to XK and and approve
+Pi now he cheats if one of them is not
+
+ align:start position:0%
+Pi now he cheats if one of them is not
+ 
+
+ align:start position:0%
+Pi now he cheats if one of them is not
+in the language that's when he cheats
+
+ align:start position:0%
+in the language that's when he cheats
+ 
+
+ align:start position:0%
+in the language that's when he cheats
+it's hard to know whether one of them is
+
+ align:start position:0%
+it's hard to know whether one of them is
+ 
+
+ align:start position:0%
+it's hard to know whether one of them is
+in the language are not in the language
+
+ align:start position:0%
+in the language are not in the language
+ 
+
+ align:start position:0%
+in the language are not in the language
+and the concern is he can say I he can
+
+ align:start position:0%
+and the concern is he can say I he can
+ 
+
+ align:start position:0%
+and the concern is he can say I he can
+say whatever he wants he's going to
+
+ align:start position:0%
+say whatever he wants he's going to
+ 
+
+ align:start position:0%
+say whatever he wants he's going to
+cheat so nothing he says we we we
+
+ align:start position:0%
+cheat so nothing he says we we we
+ 
+
+ align:start position:0%
+cheat so nothing he says we we we
+believe right and the concern is that
+
+ align:start position:0%
+believe right and the concern is that
+ 
+
+ align:start position:0%
+believe right and the concern is that
+maybe when we switch the CRS to kind of
+
+ align:start position:0%
+maybe when we switch the CRS to kind of
+ 
+
+ align:start position:0%
+maybe when we switch the CRS to kind of
+depend on I all the exite becomes in the
+
+ align:start position:0%
+depend on I all the exite becomes in the
+ 
+
+ align:start position:0%
+depend on I all the exite becomes in the
+language and then what do you do and now
+
+ align:start position:0%
+language and then what do you do and now
+ 
+
+ align:start position:0%
+language and then what do you do and now
+you can say you can't tell the
+
+ align:start position:0%
+you can say you can't tell the
+ 
+
+ align:start position:0%
+you can say you can't tell the
+difference because exide in the language
+
+ align:start position:0%
+difference because exide in the language
+ 
+
+ align:start position:0%
+difference because exide in the language
+and outside the language they look the
+
+ align:start position:0%
+and outside the language they look the
+ 
+
+ align:start position:0%
+and outside the language they look the
+same so that's why kind of guessing is
+
+ align:start position:0%
+same so that's why kind of guessing is
+ 
+
+ align:start position:0%
+same so that's why kind of guessing is
+is in some sense not good enough like
+
+ align:start position:0%
+is in some sense not good enough like
+ 
+
+ align:start position:0%
+is in some sense not good enough like
+it's not helpful
+
+ align:start position:0%
+it's not helpful
+ 
+
+ align:start position:0%
+it's not helpful
+okay so this is uh any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so this is one ingredient
+
+ align:start position:0%
+questions okay so this is one ingredient
+ 
+
+ align:start position:0%
+questions okay so this is one ingredient
+that we're going to use to construct our
+
+ align:start position:0%
+that we're going to use to construct our
+ 
+
+ align:start position:0%
+that we're going to use to construct our
+snar the other ingredient is uh what's
+
+ align:start position:0%
+snar the other ingredient is uh what's
+ 
+
+ align:start position:0%
+snar the other ingredient is uh what's
+what uh the some extractable hash or SSB
+
+ align:start position:0%
+what uh the some extractable hash or SSB
+ 
+
+ align:start position:0%
+what uh the some extractable hash or SSB
+has so let me write it out I'm going to
+
+ align:start position:0%
+has so let me write it out I'm going to
+ 
+
+ align:start position:0%
+has so let me write it out I'm going to
+write it here uh so we'll keep it on the
+
+ align:start position:0%
+write it here uh so we'll keep it on the
+ 
+
+ align:start position:0%
+write it here uh so we'll keep it on the
+board so that's so let me just recall
+
+ align:start position:0%
+board so that's so let me just recall
+ 
+
+ align:start position:0%
+board so that's so let me just recall
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+definition uh somewhere extractable hash
+
+ align:start position:0%
+definition uh somewhere extractable hash
+ 
+
+ align:start position:0%
+definition uh somewhere extractable hash
+family uh
+
+ align:start position:0%
+family uh
+ 
+
+ align:start position:0%
+family uh
+consists of uh many several PPT
+
+ align:start position:0%
+consists of uh many several PPT
+ 
+
+ align:start position:0%
+consists of uh many several PPT
+algorithm let me start writing so so the
+
+ align:start position:0%
+algorithm let me start writing so so the
+ 
+
+ align:start position:0%
+algorithm let me start writing so so the
+first one is uh
+
+ align:start position:0%
+first one is uh
+ 
+
+ align:start position:0%
+first one is uh
+gen gen so now we're constructing a hash
+
+ align:start position:0%
+gen gen so now we're constructing a hash
+ 
+
+ align:start position:0%
+gen gen so now we're constructing a hash
+okay so gen takes a security
+
+ align:start position:0%
+okay so gen takes a security
+ 
+
+ align:start position:0%
+okay so gen takes a security
+parameter the length how many bits we're
+
+ align:start position:0%
+parameter the length how many bits we're
+ 
+
+ align:start position:0%
+parameter the length how many bits we're
+going to Hash so let's say n Bits we're
+
+ align:start position:0%
+going to Hash so let's say n Bits we're
+ 
+
+ align:start position:0%
+going to Hash so let's say n Bits we're
+going to hash and how many and okay so
+
+ align:start position:0%
+going to hash and how many and okay so
+ 
+
+ align:start position:0%
+going to hash and how many and okay so
+let's say in the location I this is
+
+ align:start position:0%
+let's say in the location I this is
+ 
+
+ align:start position:0%
+let's say in the location I this is
+going to be I and N this is where we're
+
+ align:start position:0%
+going to be I and N this is where we're
+ 
+
+ align:start position:0%
+going to be I and N this is where we're
+going to be binding on or where want to
+
+ align:start position:0%
+going to be binding on or where want to
+ 
+
+ align:start position:0%
+going to be binding on or where want to
+be extractable on and it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outputs a hash key and a trap door this
+
+ align:start position:0%
+outputs a hash key and a trap door this
+ 
+
+ align:start position:0%
+outputs a hash key and a trap door this
+trapid door is going to be we're going
+
+ align:start position:0%
+trapid door is going to be we're going
+ 
+
+ align:start position:0%
+trapid door is going to be we're going
+to use it to kind of extract from the
+
+ align:start position:0%
+to use it to kind of extract from the
+ 
+
+ align:start position:0%
+to use it to kind of extract from the
+hash the I location of what we hashed
+
+ align:start position:0%
+hash the I location of what we hashed
+ 
+
+ align:start position:0%
+hash the I location of what we hashed
+okay so there's a hash key and a trapo I
+
+ align:start position:0%
+okay so there's a hash key and a trapo I
+ 
+
+ align:start position:0%
+okay so there's a hash key and a trapo I
+know when Jen Jen taught it then he just
+
+ align:start position:0%
+know when Jen Jen taught it then he just
+ 
+
+ align:start position:0%
+know when Jen Jen taught it then he just
+said hash key and he put kind of the
+
+ align:start position:0%
+said hash key and he put kind of the
+ 
+
+ align:start position:0%
+said hash key and he put kind of the
+trapo at the end so I'm I'm going to
+
+ align:start position:0%
+trapo at the end so I'm I'm going to
+ 
+
+ align:start position:0%
+trapo at the end so I'm I'm going to
+write it with a
+
+ align:start position:0%
+write it with a
+ 
+
+ align:start position:0%
+write it with a
+trapdoor okay so Jen outputs a hash key
+
+ align:start position:0%
+trapdoor okay so Jen outputs a hash key
+ 
+
+ align:start position:0%
+trapdoor okay so Jen outputs a hash key
+and a trapo and then you have eval
+
+ align:start position:0%
+and a trapo and then you have eval
+ 
+
+ align:start position:0%
+and a trapo and then you have eval
+algorithm it just takes the hash key uh
+
+ align:start position:0%
+algorithm it just takes the hash key uh
+ 
+
+ align:start position:0%
+algorithm it just takes the hash key uh
+uh input X and 01 to the
+
+ align:start position:0%
+uh input X and 01 to the
+ 
+
+ align:start position:0%
+uh input X and 01 to the
+n and then output a hash value
+
+ align:start position:0%
+n and then output a hash value
+ 
+
+ align:start position:0%
+n and then output a hash value
+V uh and then you have
+
+ align:start position:0%
+V uh and then you have
+ 
+
+ align:start position:0%
+V uh and then you have
+open where you take a hash key the X and
+
+ align:start position:0%
+open where you take a hash key the X and
+ 
+
+ align:start position:0%
+open where you take a hash key the X and
+some index J that you want to open
+
+ align:start position:0%
+some index J that you want to open
+ 
+
+ align:start position:0%
+some index J that you want to open
+to and it outputs an opening row or row
+
+ align:start position:0%
+to and it outputs an opening row or row
+ 
+
+ align:start position:0%
+to and it outputs an opening row or row
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+and this should be in 01 to the Lambda
+
+ align:start position:0%
+and this should be in 01 to the Lambda
+ 
+
+ align:start position:0%
+and this should be in 01 to the Lambda
+or poly Lambda similar here this should
+
+ align:start position:0%
+or poly Lambda similar here this should
+ 
+
+ align:start position:0%
+or poly Lambda similar here this should
+be small 01 to the Lambda or poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda and then there's ver that
+
+ align:start position:0%
+Lambda and then there's ver that
+ 
+
+ align:start position:0%
+Lambda and then there's ver that
+verifies so ver takes a hash key a value
+
+ align:start position:0%
+verifies so ver takes a hash key a value
+ 
+
+ align:start position:0%
+verifies so ver takes a hash key a value
+and now you you let's say you want to
+
+ align:start position:0%
+and now you you let's say you want to
+ 
+
+ align:start position:0%
+and now you you let's say you want to
+say I'm going to open location J here's
+
+ align:start position:0%
+say I'm going to open location J here's
+ 
+
+ align:start position:0%
+say I'm going to open location J here's
+my B that opens and here's the
+
+ align:start position:0%
+my B that opens and here's the
+ 
+
+ align:start position:0%
+my B that opens and here's the
+opening and he checks is it valid
+
+ align:start position:0%
+opening and he checks is it valid
+ 
+
+ align:start position:0%
+opening and he checks is it valid
+opening or not so it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outputs zero or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and finally so consist of
+
+ align:start position:0%
+one and finally so consist of
+ 
+
+ align:start position:0%
+one and finally so consist of
+five vpt
+
+ align:start position:0%
+five vpt
+ 
+
+ align:start position:0%
+five vpt
+algorithms so first you generate a hash
+
+ align:start position:0%
+algorithms so first you generate a hash
+ 
+
+ align:start position:0%
+algorithms so first you generate a hash
+key with a trapo then uh there's an eval
+
+ align:start position:0%
+key with a trapo then uh there's an eval
+ 
+
+ align:start position:0%
+key with a trapo then uh there's an eval
+algorithm that given nbit string outputs
+
+ align:start position:0%
+algorithm that given nbit string outputs
+ 
+
+ align:start position:0%
+algorithm that given nbit string outputs
+the hash value v short succinct then
+
+ align:start position:0%
+the hash value v short succinct then
+ 
+
+ align:start position:0%
+the hash value v short succinct then
+there's open that you can open given uh
+
+ align:start position:0%
+there's open that you can open given uh
+ 
+
+ align:start position:0%
+there's open that you can open given uh
+that you can generate an opening for
+
+ align:start position:0%
+that you can generate an opening for
+ 
+
+ align:start position:0%
+that you can generate an opening for
+specific index J so you generate row J
+
+ align:start position:0%
+specific index J so you generate row J
+ 
+
+ align:start position:0%
+specific index J so you generate row J
+which is an opening and anybody can
+
+ align:start position:0%
+which is an opening and anybody can
+ 
+
+ align:start position:0%
+which is an opening and anybody can
+verify the opening using only the
+
+ align:start position:0%
+verify the opening using only the
+ 
+
+ align:start position:0%
+verify the opening using only the
+succinct hash value okay so given a hash
+
+ align:start position:0%
+succinct hash value okay so given a hash
+ 
+
+ align:start position:0%
+succinct hash value okay so given a hash
+key the succinct hash value the index
+
+ align:start position:0%
+key the succinct hash value the index
+ 
+
+ align:start position:0%
+key the succinct hash value the index
+the bit you can verify the opening and
+
+ align:start position:0%
+the bit you can verify the opening and
+ 
+
+ align:start position:0%
+the bit you can verify the opening and
+finally that's the extract algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it takes the
+
+ align:start position:0%
+and it takes the
+ 
+
+ align:start position:0%
+and it takes the
+trapo and the value and it outputs a
+
+ align:start position:0%
+trapo and the value and it outputs a
+ 
+
+ align:start position:0%
+trapo and the value and it outputs a
+bit and this bit should be
+
+ align:start position:0%
+bit and this bit should be
+ 
+
+ align:start position:0%
+bit and this bit should be
+XI okay so let me say the the uh
+
+ align:start position:0%
+XI okay so let me say the the uh
+ 
+
+ align:start position:0%
+XI okay so let me say the the uh
+properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first property is completeness
+
+ align:start position:0%
+so the first property is completeness
+ 
+
+ align:start position:0%
+so the first property is completeness
+that's kind of usually the a
+
+ align:start position:0%
+that's kind of usually the a
+ 
+
+ align:start position:0%
+that's kind of usually the a
+straightforward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property which essentially says look if
+
+ align:start position:0%
+property which essentially says look if
+ 
+
+ align:start position:0%
+property which essentially says look if
+everybody's honest you get what you
+
+ align:start position:0%
+everybody's honest you get what you
+ 
+
+ align:start position:0%
+everybody's honest you get what you
+expect which means one the verifier
+
+ align:start position:0%
+expect which means one the verifier
+ 
+
+ align:start position:0%
+expect which means one the verifier
+would accept the opening and B the
+
+ align:start position:0%
+would accept the opening and B the
+ 
+
+ align:start position:0%
+would accept the opening and B the
+extract will output the I bit so it says
+
+ align:start position:0%
+extract will output the I bit so it says
+ 
+
+ align:start position:0%
+extract will output the I bit so it says
+that the probability okay so for every X
+
+ align:start position:0%
+that the probability okay so for every X
+ 
+
+ align:start position:0%
+that the probability okay so for every X
+for every Lambda for
+
+ align:start position:0%
+for every Lambda for
+ 
+
+ align:start position:0%
+for every Lambda for
+every uh n which is at most two to the
+
+ align:start position:0%
+every uh n which is at most two to the
+ 
+
+ align:start position:0%
+every uh n which is at most two to the
+Lambda we always restrict the length of
+
+ align:start position:0%
+Lambda we always restrict the length of
+ 
+
+ align:start position:0%
+Lambda we always restrict the length of
+what we're we're hashing to be at most 2
+
+ align:start position:0%
+what we're we're hashing to be at most 2
+ 
+
+ align:start position:0%
+what we're we're hashing to be at most 2
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+Lambda and for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I we say that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a open sorry that
+
+ align:start position:0%
+a open sorry that
+ 
+
+ align:start position:0%
+a open sorry that
+there an hash key generated from gen V
+
+ align:start position:0%
+there an hash key generated from gen V
+ 
+
+ align:start position:0%
+there an hash key generated from gen V
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+theal ah and for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J J row
+
+ align:start position:0%
+J J row
+ 
+
+ align:start position:0%
+J J row
+generated by
+
+ align:start position:0%
+generated by
+ 
+
+ align:start position:0%
+generated by
+open it always outputs one it outputs on
+
+ align:start position:0%
+open it always outputs one it outputs on
+ 
+
+ align:start position:0%
+open it always outputs one it outputs on
+probability one and
+
+ align:start position:0%
+probability one and
+ 
+
+ align:start position:0%
+probability one and
+extract I'll just denote by okay extract
+
+ align:start position:0%
+extract I'll just denote by okay extract
+ 
+
+ align:start position:0%
+extract I'll just denote by okay extract
+let me denote by just X for Simplicity
+
+ align:start position:0%
+let me denote by just X for Simplicity
+ 
+
+ align:start position:0%
+let me denote by just X for Simplicity
+uh given trap door and V output x i and
+
+ align:start position:0%
+uh given trap door and V output x i and
+ 
+
+ align:start position:0%
+uh given trap door and V output x i and
+this hold with probability one where the
+
+ align:start position:0%
+this hold with probability one where the
+ 
+
+ align:start position:0%
+this hold with probability one where the
+probability is over what hash key and
+
+ align:start position:0%
+probability is over what hash key and
+ 
+
+ align:start position:0%
+probability is over what hash key and
+trapo are in gen so essentially I won't
+
+ align:start position:0%
+trapo are in gen so essentially I won't
+ 
+
+ align:start position:0%
+trapo are in gen so essentially I won't
+write it but the hash key is generated
+
+ align:start position:0%
+write it but the hash key is generated
+ 
+
+ align:start position:0%
+write it but the hash key is generated
+by this V is generated by this eval row
+
+ align:start position:0%
+by this V is generated by this eval row
+ 
+
+ align:start position:0%
+by this V is generated by this eval row
+or I'll call row J is
+
+ align:start position:0%
+or I'll call row J is
+ 
+
+ align:start position:0%
+or I'll call row J is
+generated by
+
+ align:start position:0%
+generated by
+ 
+
+ align:start position:0%
+generated by
+open and this just says if if everything
+
+ align:start position:0%
+open and this just says if if everything
+ 
+
+ align:start position:0%
+open and this just says if if everything
+was done correctly the ver always
+
+ align:start position:0%
+was done correctly the ver always
+ 
+
+ align:start position:0%
+was done correctly the ver always
+accepts and the extract indeed will
+
+ align:start position:0%
+accepts and the extract indeed will
+ 
+
+ align:start position:0%
+accepts and the extract indeed will
+extract the correct bit
+
+ align:start position:0%
+extract the correct bit
+ 
+
+ align:start position:0%
+extract the correct bit
+so this is just if everybody follows the
+
+ align:start position:0%
+so this is just if everybody follows the
+ 
+
+ align:start position:0%
+so this is just if everybody follows the
+protocol everything should be as you
+
+ align:start position:0%
+protocol everything should be as you
+ 
+
+ align:start position:0%
+protocol everything should be as you
+expect okay uh the soundness or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+binding or the statistical binding I
+
+ align:start position:0%
+binding or the statistical binding I
+ 
+
+ align:start position:0%
+binding or the statistical binding I
+should say somewh or I can call the SSB
+
+ align:start position:0%
+should say somewh or I can call the SSB
+ 
+
+ align:start position:0%
+should say somewh or I can call the SSB
+somewh statistically binding condition
+
+ align:start position:0%
+somewh statistically binding condition
+ 
+
+ align:start position:0%
+somewh statistically binding condition
+says that on
+
+ align:start position:0%
+says that on
+ 
+
+ align:start position:0%
+says that on
+location oh before I go to SSB uh
+
+ align:start position:0%
+location oh before I go to SSB uh
+ 
+
+ align:start position:0%
+location oh before I go to SSB uh
+there's another property which is index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hiding index hiding
+
+ align:start position:0%
+hiding index hiding
+ 
+
+ align:start position:0%
+hiding index hiding
+means that the hash key hides the index
+
+ align:start position:0%
+means that the hash key hides the index
+ 
+
+ align:start position:0%
+means that the hash key hides the index
+okay if you see just hash key you have
+
+ align:start position:0%
+okay if you see just hash key you have
+ 
+
+ align:start position:0%
+okay if you see just hash key you have
+no idea what I is okay so it just says
+
+ align:start position:0%
+no idea what I is okay so it just says
+ 
+
+ align:start position:0%
+no idea what I is okay so it just says
+that for every I and
+
+ align:start position:0%
+that for every I and
+ 
+
+ align:start position:0%
+that for every I and
+J if you look at hash key generated by
+
+ align:start position:0%
+J if you look at hash key generated by
+ 
+
+ align:start position:0%
+J if you look at hash key generated by
+and I'll call it I or hash key generated
+
+ align:start position:0%
+and I'll call it I or hash key generated
+ 
+
+ align:start position:0%
+and I'll call it I or hash key generated
+by J
+
+ align:start position:0%
+by J
+ 
+
+ align:start position:0%
+by J
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+indistinguishable okay this is just a
+
+ align:start position:0%
+indistinguishable okay this is just a
+ 
+
+ align:start position:0%
+indistinguishable okay this is just a
+notation to say hash key generated where
+
+ align:start position:0%
+notation to say hash key generated where
+ 
+
+ align:start position:0%
+notation to say hash key generated where
+here I have I and this is just a
+
+ align:start position:0%
+here I have I and this is just a
+ 
+
+ align:start position:0%
+here I have I and this is just a
+notation saying this is Hash key
+
+ align:start position:0%
+notation saying this is Hash key
+ 
+
+ align:start position:0%
+notation saying this is Hash key
+generated by uh giving J to gen okay so
+
+ align:start position:0%
+generated by uh giving J to gen okay so
+ 
+
+ align:start position:0%
+generated by uh giving J to gen okay so
+this the the hashy HIDs the index for
+
+ align:start position:0%
+this the the hashy HIDs the index for
+ 
+
+ align:start position:0%
+this the the hashy HIDs the index for
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+inj uh the hashy generated with I the
+
+ align:start position:0%
+inj uh the hashy generated with I the
+ 
+
+ align:start position:0%
+inj uh the hashy generated with I the
+has generate J they look the
+
+ align:start position:0%
+has generate J they look the
+ 
+
+ align:start position:0%
+has generate J they look the
+same okay so that's the index hiding and
+
+ align:start position:0%
+same okay so that's the index hiding and
+ 
+
+ align:start position:0%
+same okay so that's the index hiding and
+finally is The Binding
+
+ align:start position:0%
+finally is The Binding
+ 
+
+ align:start position:0%
+finally is The Binding
+condition and The Binding condition says
+
+ align:start position:0%
+condition and The Binding condition says
+ 
+
+ align:start position:0%
+condition and The Binding condition says
+that so the SSB the somewhere
+
+ align:start position:0%
+that so the SSB the somewhere
+ 
+
+ align:start position:0%
+that so the SSB the somewhere
+statistical binding says that for the
+
+ align:start position:0%
+statistical binding says that for the
+ 
+
+ align:start position:0%
+statistical binding says that for the
+location
+
+ align:start position:0%
+location
+ 
+
+ align:start position:0%
+location
+I that we that we're binding on even an
+
+ align:start position:0%
+I that we that we're binding on even an
+ 
+
+ align:start position:0%
+I that we that we're binding on even an
+all powerful adversary that is given
+
+ align:start position:0%
+all powerful adversary that is given
+ 
+
+ align:start position:0%
+all powerful adversary that is given
+hash key cannot generate V and and two
+
+ align:start position:0%
+hash key cannot generate V and and two
+ 
+
+ align:start position:0%
+hash key cannot generate V and and two
+different openings to location I an
+
+ align:start position:0%
+different openings to location I an
+ 
+
+ align:start position:0%
+different openings to location I an
+opening to zero and opening to one on
+
+ align:start position:0%
+opening to zero and opening to one on
+ 
+
+ align:start position:0%
+opening to zero and opening to one on
+location I so on location I you're
+
+ align:start position:0%
+location I so on location I you're
+ 
+
+ align:start position:0%
+location I so on location I you're
+really information theoretically bounded
+
+ align:start position:0%
+really information theoretically bounded
+ 
+
+ align:start position:0%
+really information theoretically bounded
+okay so again even in all powerful
+
+ align:start position:0%
+okay so again even in all powerful
+ 
+
+ align:start position:0%
+okay so again even in all powerful
+adversary that is given hash key with
+
+ align:start position:0%
+adversary that is given hash key with
+ 
+
+ align:start position:0%
+adversary that is given hash key with
+respect to a i on location I cannot open
+
+ align:start position:0%
+respect to a i on location I cannot open
+ 
+
+ align:start position:0%
+respect to a i on location I cannot open
+both to zero and to one except with Neal
+
+ align:start position:0%
+both to zero and to one except with Neal
+ 
+
+ align:start position:0%
+both to zero and to one except with Neal
+probability Okay so ah I hoped to put
+
+ align:start position:0%
+probability Okay so ah I hoped to put
+ 
+
+ align:start position:0%
+probability Okay so ah I hoped to put
+everything on that but I I'll I'll add
+
+ align:start position:0%
+everything on that but I I'll I'll add
+ 
+
+ align:start position:0%
+everything on that but I I'll I'll add
+one here so I'll put here The Binding
+
+ align:start position:0%
+one here so I'll put here The Binding
+ 
+
+ align:start position:0%
+one here so I'll put here The Binding
+condition so the SSB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+binding The summ Binding says that for
+
+ align:start position:0%
+binding The summ Binding says that for
+ 
+
+ align:start position:0%
+binding The summ Binding says that for
+every all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+powerful adversary a the probability
+
+ align:start position:0%
+powerful adversary a the probability
+ 
+
+ align:start position:0%
+powerful adversary a the probability
+that a and hash key where hash key is
+
+ align:start position:0%
+that a and hash key where hash key is
+ 
+
+ align:start position:0%
+that a and hash key where hash key is
+generated
+
+ align:start position:0%
+generated
+ 
+
+ align:start position:0%
+generated
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+gen 1 Lambda n and I the probability
+
+ align:start position:0%
+gen 1 Lambda n and I the probability
+ 
+
+ align:start position:0%
+gen 1 Lambda n and I the probability
+that he outputs any value
+
+ align:start position:0%
+that he outputs any value
+ 
+
+ align:start position:0%
+that he outputs any value
+V and row zero and Row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one such that there would accept both so
+
+ align:start position:0%
+one such that there would accept both so
+ 
+
+ align:start position:0%
+one such that there would accept both so
+that for every B both zero and
+
+ align:start position:0%
+that for every B both zero and
+ 
+
+ align:start position:0%
+that for every B both zero and
+one there on hash key v i b Robby
+
+ align:start position:0%
+one there on hash key v i b Robby
+ 
+
+ align:start position:0%
+one there on hash key v i b Robby
+outputs one this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible okay so
+
+ align:start position:0%
+negligible okay so
+ 
+
+ align:start position:0%
+negligible okay so
+on on index I the one that we're the
+
+ align:start position:0%
+on on index I the one that we're the
+ 
+
+ align:start position:0%
+on on index I the one that we're the
+hatch came from that we're binding on he
+
+ align:start position:0%
+hatch came from that we're binding on he
+ 
+
+ align:start position:0%
+hatch came from that we're binding on he
+cannot open to both zero and open to one
+
+ align:start position:0%
+cannot open to both zero and open to one
+ 
+
+ align:start position:0%
+cannot open to both zero and open to one
+uh in an accepting way with uh accept
+
+ align:start position:0%
+uh in an accepting way with uh accept
+ 
+
+ align:start position:0%
+uh in an accepting way with uh accept
+probability yeah does have to be
+
+ align:start position:0%
+probability yeah does have to be
+ 
+
+ align:start position:0%
+probability yeah does have to be
+generated from eval here or no good good
+
+ align:start position:0%
+generated from eval here or no good good
+ 
+
+ align:start position:0%
+generated from eval here or no good good
+good good great question V malicious
+
+ align:start position:0%
+good good great question V malicious
+ 
+
+ align:start position:0%
+good good great question V malicious
+there's no a can be so the adversary
+
+ align:start position:0%
+there's no a can be so the adversary
+ 
+
+ align:start position:0%
+there's no a can be so the adversary
+he's not following any guidelines he's
+
+ align:start position:0%
+he's not following any guidelines he's
+ 
+
+ align:start position:0%
+he's not following any guidelines he's
+completely malicious he generates V
+
+ align:start position:0%
+completely malicious he generates V
+ 
+
+ align:start position:0%
+completely malicious he generates V
+according to his own will generating row
+
+ align:start position:0%
+according to his own will generating row
+ 
+
+ align:start position:0%
+according to his own will generating row
+zero and Row one however he wants he's
+
+ align:start position:0%
+zero and Row one however he wants he's
+ 
+
+ align:start position:0%
+zero and Row one however he wants he's
+still and he's all powerful he's still
+
+ align:start position:0%
+still and he's all powerful he's still
+ 
+
+ align:start position:0%
+still and he's all powerful he's still
+cannot uh generate two accepting
+
+ align:start position:0%
+cannot uh generate two accepting
+ 
+
+ align:start position:0%
+cannot uh generate two accepting
+openings for location
+
+ align:start position:0%
+openings for location
+ 
+
+ align:start position:0%
+openings for location
+I yeah just to follow up on that that's
+
+ align:start position:0%
+I yeah just to follow up on that that's
+ 
+
+ align:start position:0%
+I yeah just to follow up on that that's
+the only reason that we don't get this
+
+ align:start position:0%
+the only reason that we don't get this
+ 
+
+ align:start position:0%
+the only reason that we don't get this
+free from extraction right exactly good
+
+ align:start position:0%
+free from extraction right exactly good
+ 
+
+ align:start position:0%
+free from extraction right exactly good
+good good very good so let me just uh uh
+
+ align:start position:0%
+good good very good so let me just uh uh
+ 
+
+ align:start position:0%
+good good very good so let me just uh uh
+uh repeat what s said look in extraction
+
+ align:start position:0%
+uh repeat what s said look in extraction
+ 
+
+ align:start position:0%
+uh repeat what s said look in extraction
+we said that we're binding completely
+
+ align:start position:0%
+we said that we're binding completely
+ 
+
+ align:start position:0%
+we said that we're binding completely
+binding because guess what from V we can
+
+ align:start position:0%
+binding because guess what from V we can
+ 
+
+ align:start position:0%
+binding because guess what from V we can
+actually uh we can actually learn the
+
+ align:start position:0%
+actually uh we can actually learn the
+ 
+
+ align:start position:0%
+actually uh we can actually learn the
+the bit XI so XI is sitting there so
+
+ align:start position:0%
+the bit XI so XI is sitting there so
+ 
+
+ align:start position:0%
+the bit XI so XI is sitting there so
+yeah if you're honest XI is sitting
+
+ align:start position:0%
+yeah if you're honest XI is sitting
+ 
+
+ align:start position:0%
+yeah if you're honest XI is sitting
+there but if you're malicious you know
+
+ align:start position:0%
+there but if you're malicious you know
+ 
+
+ align:start position:0%
+there but if you're malicious you know
+you can do whatever you want and maybe
+
+ align:start position:0%
+you can do whatever you want and maybe
+ 
+
+ align:start position:0%
+you can do whatever you want and maybe
+if for malicious V maybe there's no you
+
+ align:start position:0%
+if for malicious V maybe there's no you
+ 
+
+ align:start position:0%
+if for malicious V maybe there's no you
+can't extract anything from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah right good good good very good yes
+
+ align:start position:0%
+yeah right good good good very good yes
+ 
+
+ align:start position:0%
+yeah right good good good very good yes
+yes yes this is the same as saying that
+
+ align:start position:0%
+yes yes this is the same as saying that
+ 
+
+ align:start position:0%
+yes yes this is the same as saying that
+there exists a
+
+ align:start position:0%
+there exists a
+ 
+
+ align:start position:0%
+there exists a
+v row zero for any H okay for almost all
+
+ align:start position:0%
+v row zero for any H okay for almost all
+ 
+
+ align:start position:0%
+v row zero for any H okay for almost all
+hash Keys the probability that there
+
+ align:start position:0%
+hash Keys the probability that there
+ 
+
+ align:start position:0%
+hash Keys the probability that there
+exists v r z and R1 is is is uh zero
+
+ align:start position:0%
+exists v r z and R1 is is is uh zero
+ 
+
+ align:start position:0%
+exists v r z and R1 is is is uh zero
+they don't exist for almost all hash
+
+ align:start position:0%
+they don't exist for almost all hash
+ 
+
+ align:start position:0%
+they don't exist for almost all hash
+keys this triplet that satisfies this
+
+ align:start position:0%
+keys this triplet that satisfies this
+ 
+
+ align:start position:0%
+keys this triplet that satisfies this
+does not exist yes yeah very
+
+ align:start position:0%
+does not exist yes yeah very
+ 
+
+ align:start position:0%
+does not exist yes yeah very
+good any any other
+
+ align:start position:0%
+good any any other
+ 
+
+ align:start position:0%
+good any any other
+questions okay so the plan for today is
+
+ align:start position:0%
+questions okay so the plan for today is
+ 
+
+ align:start position:0%
+questions okay so the plan for today is
+to show how to use these two building
+
+ align:start position:0%
+to show how to use these two building
+ 
+
+ align:start position:0%
+to show how to use these two building
+blocks to get a snar but before I do
+
+ align:start position:0%
+blocks to get a snar but before I do
+ 
+
+ align:start position:0%
+blocks to get a snar but before I do
+that I want to say a few more to first I
+
+ align:start position:0%
+that I want to say a few more to first I
+ 
+
+ align:start position:0%
+that I want to say a few more to first I
+want to give you time to digest and ask
+
+ align:start position:0%
+want to give you time to digest and ask
+ 
+
+ align:start position:0%
+want to give you time to digest and ask
+questions uh also I want to say a few
+
+ align:start position:0%
+questions uh also I want to say a few
+ 
+
+ align:start position:0%
+questions uh also I want to say a few
+more things about these two Primitives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions before
+
+ align:start position:0%
+any questions before
+ 
+
+ align:start position:0%
+any questions before
+I okay so one thing I want to mention is
+
+ align:start position:0%
+I okay so one thing I want to mention is
+ 
+
+ align:start position:0%
+I okay so one thing I want to mention is
+even though the binding condition was
+
+ align:start position:0%
+even though the binding condition was
+ 
+
+ align:start position:0%
+even though the binding condition was
+only an I I said only on the specific
+
+ align:start position:0%
+only an I I said only on the specific
+ 
+
+ align:start position:0%
+only an I I said only on the specific
+eye I promise you you can't open two
+
+ align:start position:0%
+eye I promise you you can't open two
+ 
+
+ align:start position:0%
+eye I promise you you can't open two
+different ways now say what about the
+
+ align:start position:0%
+different ways now say what about the
+ 
+
+ align:start position:0%
+different ways now say what about the
+other eye what about J Jay can an ADV
+
+ align:start position:0%
+other eye what about J Jay can an ADV
+ 
+
+ align:start position:0%
+other eye what about J Jay can an ADV
+open two different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways and the answer is no actually he
+
+ align:start position:0%
+ways and the answer is no actually he
+ 
+
+ align:start position:0%
+ways and the answer is no actually he
+can't and we don't need to state that
+
+ align:start position:0%
+can't and we don't need to state that
+ 
+
+ align:start position:0%
+can't and we don't need to state that
+explicitly from from the SSB and the
+
+ align:start position:0%
+explicitly from from the SSB and the
+ 
+
+ align:start position:0%
+explicitly from from the SSB and the
+index hiding I want to argue already we
+
+ align:start position:0%
+index hiding I want to argue already we
+ 
+
+ align:start position:0%
+index hiding I want to argue already we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+conclude that a poliz
+
+ align:start position:0%
+conclude that a poliz
+ 
+
+ align:start position:0%
+conclude that a poliz
+adversary cannot open a poze not all
+
+ align:start position:0%
+adversary cannot open a poze not all
+ 
+
+ align:start position:0%
+adversary cannot open a poze not all
+powerful but a poliz
+
+ align:start position:0%
+powerful but a poliz
+ 
+
+ align:start position:0%
+powerful but a poliz
+adversary cannot generate V any index
+
+ align:start position:0%
+adversary cannot generate V any index
+ 
+
+ align:start position:0%
+adversary cannot generate V any index
+J and two
+
+ align:start position:0%
+J and two
+ 
+
+ align:start position:0%
+J and two
+openings that will be accepted except NE
+
+ align:start position:0%
+openings that will be accepted except NE
+ 
+
+ align:start position:0%
+openings that will be accepted except NE
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+okay so in other words I'm saying
+
+ align:start position:0%
+okay so in other words I'm saying
+ 
+
+ align:start position:0%
+okay so in other words I'm saying
+binding holes this local binding holes
+
+ align:start position:0%
+binding holes this local binding holes
+ 
+
+ align:start position:0%
+binding holes this local binding holes
+for every J not against all powerful but
+
+ align:start position:0%
+for every J not against all powerful but
+ 
+
+ align:start position:0%
+for every J not against all powerful but
+for any PPT or poly sizing we get this
+
+ align:start position:0%
+for any PPT or poly sizing we get this
+ 
+
+ align:start position:0%
+for any PPT or poly sizing we get this
+binding condition for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why so because of the index hiding
+
+ align:start position:0%
+why so because of the index hiding
+ 
+
+ align:start position:0%
+why so because of the index hiding
+property where we cannot distinguish
+
+ align:start position:0%
+property where we cannot distinguish
+ 
+
+ align:start position:0%
+property where we cannot distinguish
+like index I or something else precisely
+
+ align:start position:0%
+like index I or something else precisely
+ 
+
+ align:start position:0%
+like index I or something else precisely
+so the reason is this a he doesn't know
+
+ align:start position:0%
+so the reason is this a he doesn't know
+ 
+
+ align:start position:0%
+so the reason is this a he doesn't know
+if hash key came from index I or index J
+
+ align:start position:0%
+if hash key came from index I or index J
+ 
+
+ align:start position:0%
+if hash key came from index I or index J
+they're they're indistinguishable so now
+
+ align:start position:0%
+they're they're indistinguishable so now
+ 
+
+ align:start position:0%
+they're they're indistinguishable so now
+if he can generate it for index
+
+ align:start position:0%
+if he can generate it for index
+ 
+
+ align:start position:0%
+if he can generate it for index
+J then he should be able to generate
+
+ align:start position:0%
+J then he should be able to generate
+ 
+
+ align:start position:0%
+J then he should be able to generate
+also for index so let's replace this
+
+ align:start position:0%
+also for index so let's replace this
+ 
+
+ align:start position:0%
+also for index so let's replace this
+with an J he can't distinguish so he'll
+
+ align:start position:0%
+with an J he can't distinguish so he'll
+ 
+
+ align:start position:0%
+with an J he can't distinguish so he'll
+fall in the same J again at some point
+
+ align:start position:0%
+fall in the same J again at some point
+ 
+
+ align:start position:0%
+fall in the same J again at some point
+and that that'll be a
+
+ align:start position:0%
+and that that'll be a
+ 
+
+ align:start position:0%
+and that that'll be a
+contradiction okay so because he has no
+
+ align:start position:0%
+contradiction okay so because he has no
+ 
+
+ align:start position:0%
+contradiction okay so because he has no
+idea what's sitting here the fact that
+
+ align:start position:0%
+idea what's sitting here the fact that
+ 
+
+ align:start position:0%
+idea what's sitting here the fact that
+he cannot do it for that index I even
+
+ align:start position:0%
+he cannot do it for that index I even
+ 
+
+ align:start position:0%
+he cannot do it for that index I even
+information theoretically means he can't
+
+ align:start position:0%
+information theoretically means he can't
+ 
+
+ align:start position:0%
+information theoretically means he can't
+do it for for any other
+
+ align:start position:0%
+do it for for any other
+ 
+
+ align:start position:0%
+do it for for any other
+index yeah so this indexing really
+
+ align:start position:0%
+index yeah so this indexing really
+ 
+
+ align:start position:0%
+index yeah so this indexing really
+statistical no this index hiding is
+
+ align:start position:0%
+statistical no this index hiding is
+ 
+
+ align:start position:0%
+statistical no this index hiding is
+computational
+
+ align:start position:0%
+computational
+ 
+
+ align:start position:0%
+computational
+actually oh good good good good so the
+
+ align:start position:0%
+actually oh good good good good so the
+ 
+
+ align:start position:0%
+actually oh good good good good so the
+corollary
+
+ align:start position:0%
+corollary
+ 
+
+ align:start position:0%
+corollary
+is for any poly
+
+ align:start position:0%
+is for any poly
+ 
+
+ align:start position:0%
+is for any poly
+size the cor say is that for only any
+
+ align:start position:0%
+size the cor say is that for only any
+ 
+
+ align:start position:0%
+size the cor say is that for only any
+poly size a the
+
+ align:start position:0%
+poly size a the
+ 
+
+ align:start position:0%
+poly size a the
+probability that a on hash key let's say
+
+ align:start position:0%
+probability that a on hash key let's say
+ 
+
+ align:start position:0%
+probability that a on hash key let's say
+from I same hash key outputs V or v j
+
+ align:start position:0%
+from I same hash key outputs V or v j
+ 
+
+ align:start position:0%
+from I same hash key outputs V or v j
+row zero and Row
+
+ align:start position:0%
+row zero and Row
+ 
+
+ align:start position:0%
+row zero and Row
+one such that the same thing here holds
+
+ align:start position:0%
+one such that the same thing here holds
+ 
+
+ align:start position:0%
+one such that the same thing here holds
+namely for every B he generates
+
+ align:start position:0%
+namely for every B he generates
+ 
+
+ align:start position:0%
+namely for every B he generates
+accepting answers for both zero and one
+
+ align:start position:0%
+accepting answers for both zero and one
+ 
+
+ align:start position:0%
+accepting answers for both zero and one
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible because if there exist some J
+
+ align:start position:0%
+negligible because if there exist some J
+ 
+
+ align:start position:0%
+negligible because if there exist some J
+that he does that for non- Negal
+
+ align:start position:0%
+that he does that for non- Negal
+ 
+
+ align:start position:0%
+that he does that for non- Negal
+probability then let's replate replace
+
+ align:start position:0%
+probability then let's replate replace
+ 
+
+ align:start position:0%
+probability then let's replate replace
+HK with hash key generating like that's
+
+ align:start position:0%
+HK with hash key generating like that's
+ 
+
+ align:start position:0%
+HK with hash key generating like that's
+binding on this that actually
+
+ align:start position:0%
+binding on this that actually
+ 
+
+ align:start position:0%
+binding on this that actually
+statistically binding on this J A can
+
+ align:start position:0%
+statistically binding on this J A can
+ 
+
+ align:start position:0%
+statistically binding on this J A can
+distinguish so we'll still do this for
+
+ align:start position:0%
+distinguish so we'll still do this for
+ 
+
+ align:start position:0%
+distinguish so we'll still do this for
+that J with some prob non- negligent
+
+ align:start position:0%
+that J with some prob non- negligent
+ 
+
+ align:start position:0%
+that J with some prob non- negligent
+probability and that he cannot do even
+
+ align:start position:0%
+probability and that he cannot do even
+ 
+
+ align:start position:0%
+probability and that he cannot do even
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+theoretically so that's why we get like
+
+ align:start position:0%
+theoretically so that's why we get like
+ 
+
+ align:start position:0%
+theoretically so that's why we get like
+because index hiding actually just
+
+ align:start position:0%
+because index hiding actually just
+ 
+
+ align:start position:0%
+because index hiding actually just
+getting statistically binding on one of
+
+ align:start position:0%
+getting statistically binding on one of
+ 
+
+ align:start position:0%
+getting statistically binding on one of
+them is good enough it will imply
+
+ align:start position:0%
+them is good enough it will imply
+ 
+
+ align:start position:0%
+them is good enough it will imply
+computational binding and all the
+
+ align:start position:0%
+computational binding and all the
+ 
+
+ align:start position:0%
+computational binding and all the
+rest okay another thing I want to
+
+ align:start position:0%
+rest okay another thing I want to
+ 
+
+ align:start position:0%
+rest okay another thing I want to
+mention and this we'll use actually in
+
+ align:start position:0%
+mention and this we'll use actually in
+ 
+
+ align:start position:0%
+mention and this we'll use actually in
+our construction
+
+ align:start position:0%
+our construction
+ 
+
+ align:start position:0%
+our construction
+today I said that the hash is binding on
+
+ align:start position:0%
+today I said that the hash is binding on
+ 
+
+ align:start position:0%
+today I said that the hash is binding on
+one location and XI we can get it
+
+ align:start position:0%
+one location and XI we can get it
+ 
+
+ align:start position:0%
+one location and XI we can get it
+binding actually on L locations not just
+
+ align:start position:0%
+binding actually on L locations not just
+ 
+
+ align:start position:0%
+binding actually on L locations not just
+one how do I get it binding on L
+
+ align:start position:0%
+one how do I get it binding on L
+ 
+
+ align:start position:0%
+one how do I get it binding on L
+locations I'm going to just generate hk1
+
+ align:start position:0%
+locations I'm going to just generate hk1
+ 
+
+ align:start position:0%
+locations I'm going to just generate hk1
+hk2 up to hkl where the first L is Bing
+
+ align:start position:0%
+hk2 up to hkl where the first L is Bing
+ 
+
+ align:start position:0%
+hk2 up to hkl where the first L is Bing
+on the first I'm just going to
+
+ align:start position:0%
+on the first I'm just going to
+ 
+
+ align:start position:0%
+on the first I'm just going to
+generate L
+
+ align:start position:0%
+generate L
+ 
+
+ align:start position:0%
+generate L
+hashes I'm going to ask to generate the
+
+ align:start position:0%
+hashes I'm going to ask to generate the
+ 
+
+ align:start position:0%
+hashes I'm going to ask to generate the
+AAL on all these hashes so the hash
+
+ align:start position:0%
+AAL on all these hashes so the hash
+ 
+
+ align:start position:0%
+AAL on all these hashes so the hash
+value now is going to be V1 up to VL
+
+ align:start position:0%
+value now is going to be V1 up to VL
+ 
+
+ align:start position:0%
+value now is going to be V1 up to VL
+where the honest uh evalid is going to
+
+ align:start position:0%
+where the honest uh evalid is going to
+ 
+
+ align:start position:0%
+where the honest uh evalid is going to
+take X you want to hash and do eval hk1
+
+ align:start position:0%
+take X you want to hash and do eval hk1
+ 
+
+ align:start position:0%
+take X you want to hash and do eval hk1
+of X eval hk2 of X so just hash the same
+
+ align:start position:0%
+of X eval hk2 of X so just hash the same
+ 
+
+ align:start position:0%
+of X eval hk2 of X so just hash the same
+x with all L keys so now the hatch value
+
+ align:start position:0%
+x with all L keys so now the hatch value
+ 
+
+ align:start position:0%
+x with all L keys so now the hatch value
+is Grows by a factor of L and then when
+
+ align:start position:0%
+is Grows by a factor of L and then when
+ 
+
+ align:start position:0%
+is Grows by a factor of L and then when
+you open a certain bit a certain
+
+ align:start position:0%
+you open a certain bit a certain
+ 
+
+ align:start position:0%
+you open a certain bit a certain
+location you'll generate all the
+
+ align:start position:0%
+location you'll generate all the
+ 
+
+ align:start position:0%
+location you'll generate all the
+openings so just do the same thing kind
+
+ align:start position:0%
+openings so just do the same thing kind
+ 
+
+ align:start position:0%
+openings so just do the same thing kind
+of all times just repeat it all times
+
+ align:start position:0%
+of all times just repeat it all times
+ 
+
+ align:start position:0%
+of all times just repeat it all times
+and now what do we have from that if you
+
+ align:start position:0%
+and now what do we have from that if you
+ 
+
+ align:start position:0%
+and now what do we have from that if you
+by repeating our time so let me uh write
+
+ align:start position:0%
+by repeating our time so let me uh write
+ 
+
+ align:start position:0%
+by repeating our time so let me uh write
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh let me erase the quary so I'll
+
+ align:start position:0%
+so uh let me erase the quary so I'll
+ 
+
+ align:start position:0%
+so uh let me erase the quary so I'll
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+room
+
+ align:start position:0%
+room
+ 
+
+ align:start position:0%
+room
+so uh no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remark by repeating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times we
+
+ align:start position:0%
+times we
+ 
+
+ align:start position:0%
+times we
+get uh somewhere extractable hash that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extractable on L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+locations and moreover another property
+
+ align:start position:0%
+locations and moreover another property
+ 
+
+ align:start position:0%
+locations and moreover another property
+that's we're going to need even if I
+
+ align:start position:0%
+that's we're going to need even if I
+ 
+
+ align:start position:0%
+that's we're going to need even if I
+let's say gave you the trapo
+
+ align:start position:0%
+let's say gave you the trapo
+ 
+
+ align:start position:0%
+let's say gave you the trapo
+corresponding to some of the alloc not
+
+ align:start position:0%
+corresponding to some of the alloc not
+ 
+
+ align:start position:0%
+corresponding to some of the alloc not
+all the allocations let's say gave you
+
+ align:start position:0%
+all the allocations let's say gave you
+ 
+
+ align:start position:0%
+all the allocations let's say gave you
+trap door one trap door two and trap
+
+ align:start position:0%
+trap door one trap door two and trap
+ 
+
+ align:start position:0%
+trap door one trap door two and trap
+door
+
+ align:start position:0%
+door
+ 
+
+ align:start position:0%
+door
+three still what's in the location
+
+ align:start position:0%
+three still what's in the location
+ 
+
+ align:start position:0%
+three still what's in the location
+hidden in hq4 you have no idea what it
+
+ align:start position:0%
+hidden in hq4 you have no idea what it
+ 
+
+ align:start position:0%
+hidden in hq4 you have no idea what it
+is so even if I reveal some of the trap
+
+ align:start position:0%
+is so even if I reveal some of the trap
+ 
+
+ align:start position:0%
+is so even if I reveal some of the trap
+doors the other IND indic sees remain
+
+ align:start position:0%
+doors the other IND indic sees remain
+ 
+
+ align:start position:0%
+doors the other IND indic sees remain
+hidden okay and we're going to use this
+
+ align:start position:0%
+hidden okay and we're going to use this
+ 
+
+ align:start position:0%
+hidden okay and we're going to use this
+property okay so again if we repeat all
+
+ align:start position:0%
+property okay so again if we repeat all
+ 
+
+ align:start position:0%
+property okay so again if we repeat all
+times we're binding an L location
+
+ align:start position:0%
+times we're binding an L location
+ 
+
+ align:start position:0%
+times we're binding an L location
+but even if I destroy I kind of reveal
+
+ align:start position:0%
+but even if I destroy I kind of reveal
+ 
+
+ align:start position:0%
+but even if I destroy I kind of reveal
+the trapo corresponding to I don't know
+
+ align:start position:0%
+the trapo corresponding to I don't know
+ 
+
+ align:start position:0%
+the trapo corresponding to I don't know
+location to a couple
+
+ align:start position:0%
+location to a couple
+ 
+
+ align:start position:0%
+location to a couple
+locations the rest of the so of course
+
+ align:start position:0%
+locations the rest of the so of course
+ 
+
+ align:start position:0%
+locations the rest of the so of course
+if I give you the trapo then all bets
+
+ align:start position:0%
+if I give you the trapo then all bets
+ 
+
+ align:start position:0%
+if I give you the trapo then all bets
+are off you learn everything you learn
+
+ align:start position:0%
+are off you learn everything you learn
+ 
+
+ align:start position:0%
+are off you learn everything you learn
+the eye you learn everything that's
+
+ align:start position:0%
+the eye you learn everything that's
+ 
+
+ align:start position:0%
+the eye you learn everything that's
+that's the trapo our trap doors are such
+
+ align:start position:0%
+that's the trapo our trap doors are such
+ 
+
+ align:start position:0%
+that's the trapo our trap doors are such
+that once I give you the trap door you
+
+ align:start position:0%
+that once I give you the trap door you
+ 
+
+ align:start position:0%
+that once I give you the trap door you
+learn the index you learn
+
+ align:start position:0%
+learn the index you learn
+ 
+
+ align:start position:0%
+learn the index you learn
+everything but the other indices that
+
+ align:start position:0%
+everything but the other indices that
+ 
+
+ align:start position:0%
+everything but the other indices that
+are not in the not corresponding to the
+
+ align:start position:0%
+are not in the not corresponding to the
+ 
+
+ align:start position:0%
+are not in the not corresponding to the
+trap doors that I give that I gave are
+
+ align:start position:0%
+trap doors that I give that I gave are
+ 
+
+ align:start position:0%
+trap doors that I give that I gave are
+still completely hidden CU I did them
+
+ align:start position:0%
+still completely hidden CU I did them
+ 
+
+ align:start position:0%
+still completely hidden CU I did them
+completely in
+
+ align:start position:0%
+completely in
+ 
+
+ align:start position:0%
+completely in
+independent and this is something we're
+
+ align:start position:0%
+independent and this is something we're
+ 
+
+ align:start position:0%
+independent and this is something we're
+going to use when we're going to
+
+ align:start position:0%
+going to use when we're going to
+ 
+
+ align:start position:0%
+going to use when we're going to
+construct our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+snars okay so that's one thing we're
+
+ align:start position:0%
+snars okay so that's one thing we're
+ 
+
+ align:start position:0%
+snars okay so that's one thing we're
+going to use a I I want to mention a
+
+ align:start position:0%
+going to use a I I want to mention a
+ 
+
+ align:start position:0%
+going to use a I I want to mention a
+little I want to talk a little bit about
+
+ align:start position:0%
+little I want to talk a little bit about
+ 
+
+ align:start position:0%
+little I want to talk a little bit about
+the construction because I think maybe
+
+ align:start position:0%
+the construction because I think maybe
+ 
+
+ align:start position:0%
+the construction because I think maybe
+in Jen jang's uh lecture last time this
+
+ align:start position:0%
+in Jen jang's uh lecture last time this
+ 
+
+ align:start position:0%
+in Jen jang's uh lecture last time this
+was missed a little because he said it I
+
+ align:start position:0%
+was missed a little because he said it I
+ 
+
+ align:start position:0%
+was missed a little because he said it I
+think a little too fast so I want to say
+
+ align:start position:0%
+think a little too fast so I want to say
+ 
+
+ align:start position:0%
+think a little too fast so I want to say
+a few words about the construction but
+
+ align:start position:0%
+a few words about the construction but
+ 
+
+ align:start position:0%
+a few words about the construction but
+before I talk about the construction I
+
+ align:start position:0%
+before I talk about the construction I
+ 
+
+ align:start position:0%
+before I talk about the construction I
+want to say one more property about the
+
+ align:start position:0%
+want to say one more property about the
+ 
+
+ align:start position:0%
+want to say one more property about the
+bar that we're going to also use so what
+
+ align:start position:0%
+bar that we're going to also use so what
+ 
+
+ align:start position:0%
+bar that we're going to also use so what
+we're going to use about the bar so we
+
+ align:start position:0%
+we're going to use about the bar so we
+ 
+
+ align:start position:0%
+we're going to use about the bar so we
+said that these gen p and v are
+
+ align:start position:0%
+said that these gen p and v are
+ 
+
+ align:start position:0%
+said that these gen p and v are
+polinomial time algorithm probabilistic
+
+ align:start position:0%
+polinomial time algorithm probabilistic
+ 
+
+ align:start position:0%
+polinomial time algorithm probabilistic
+polinomial time algorithms in particular
+
+ align:start position:0%
+polinomial time algorithms in particular
+ 
+
+ align:start position:0%
+polinomial time algorithms in particular
+V I want to talk about v v is a
+
+ align:start position:0%
+V I want to talk about v v is a
+ 
+
+ align:start position:0%
+V I want to talk about v v is a
+polinomial Time algorithm but V's input
+
+ align:start position:0%
+polinomial Time algorithm but V's input
+ 
+
+ align:start position:0%
+polinomial Time algorithm but V's input
+is really large it has X1 up to XK so
+
+ align:start position:0%
+is really large it has X1 up to XK so
+ 
+
+ align:start position:0%
+is really large it has X1 up to XK so
+poom time means it runs at least in time
+
+ align:start position:0%
+poom time means it runs at least in time
+ 
+
+ align:start position:0%
+poom time means it runs at least in time
+poly K it needs to read its
+
+ align:start position:0%
+poly K it needs to read its
+ 
+
+ align:start position:0%
+poly K it needs to read its
+input ever turns out that the bars we
+
+ align:start position:0%
+input ever turns out that the bars we
+ 
+
+ align:start position:0%
+input ever turns out that the bars we
+have this is what J called bar for index
+
+ align:start position:0%
+have this is what J called bar for index
+ 
+
+ align:start position:0%
+have this is what J called bar for index
+languages if there exists a suing
+
+ align:start position:0%
+languages if there exists a suing
+ 
+
+ align:start position:0%
+languages if there exists a suing
+description of these X1 of to XK the
+
+ align:start position:0%
+description of these X1 of to XK the
+ 
+
+ align:start position:0%
+description of these X1 of to XK the
+verifier only needs to run in time that
+
+ align:start position:0%
+verifier only needs to run in time that
+ 
+
+ align:start position:0%
+verifier only needs to run in time that
+depends on the description in other
+
+ align:start position:0%
+depends on the description in other
+ 
+
+ align:start position:0%
+depends on the description in other
+words we can replace so uh
+
+ align:start position:0%
+words we can replace so uh
+ 
+
+ align:start position:0%
+words we can replace so uh
+if I didn't bring
+
+ align:start position:0%
+if I didn't bring
+ 
+
+ align:start position:0%
+if I didn't bring
+my okay I forgot to bring my colorful uh
+
+ align:start position:0%
+my okay I forgot to bring my colorful uh
+ 
+
+ align:start position:0%
+my okay I forgot to bring my colorful uh
+chalk so uh sorry but at least you have
+
+ align:start position:0%
+chalk so uh sorry but at least you have
+ 
+
+ align:start position:0%
+chalk so uh sorry but at least you have
+cookies I mean what would you prefer
+
+ align:start position:0%
+cookies I mean what would you prefer
+ 
+
+ align:start position:0%
+cookies I mean what would you prefer
+colorful chalks or
+
+ align:start position:0%
+colorful chalks or
+ 
+
+ align:start position:0%
+colorful chalks or
+cookies so if a if you can generate
+
+ align:start position:0%
+cookies so if a if you can generate
+ 
+
+ align:start position:0%
+cookies so if a if you can generate
+these X1 up to XK if there's kind of
+
+ align:start position:0%
+these X1 up to XK if there's kind of
+ 
+
+ align:start position:0%
+these X1 up to XK if there's kind of
+succinct
+
+ align:start position:0%
+succinct
+ 
+
+ align:start position:0%
+succinct
+description then the verify runs in
+
+ align:start position:0%
+description then the verify runs in
+ 
+
+ align:start position:0%
+description then the verify runs in
+polinomial time in the description okay
+
+ align:start position:0%
+polinomial time in the description okay
+ 
+
+ align:start position:0%
+polinomial time in the description okay
+so if let's say there exists some
+
+ align:start position:0%
+so if let's say there exists some
+ 
+
+ align:start position:0%
+so if let's say there exists some
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+M such
+
+ align:start position:0%
+M such
+ 
+
+ align:start position:0%
+M such
+that for every I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XI is just kind of the train
+
+ align:start position:0%
+XI is just kind of the train
+ 
+
+ align:start position:0%
+XI is just kind of the train
+machine on on input I so this kind of
+
+ align:start position:0%
+machine on on input I so this kind of
+ 
+
+ align:start position:0%
+machine on on input I so this kind of
+machine you can you should think this
+
+ align:start position:0%
+machine you can you should think this
+ 
+
+ align:start position:0%
+machine you can you should think this
+algorithm you should think of has kind
+
+ align:start position:0%
+algorithm you should think of has kind
+ 
+
+ align:start position:0%
+algorithm you should think of has kind
+of a succinct description of all the X
+
+ align:start position:0%
+of a succinct description of all the X
+ 
+
+ align:start position:0%
+of a succinct description of all the X
+on up to x k and you give him I you get
+
+ align:start position:0%
+on up to x k and you give him I you get
+ 
+
+ align:start position:0%
+on up to x k and you give him I you get
+it it gives you the X I if this is the
+
+ align:start position:0%
+it it gives you the X I if this is the
+ 
+
+ align:start position:0%
+it it gives you the X I if this is the
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+then V the runtime
+
+ align:start position:0%
+then V the runtime
+ 
+
+ align:start position:0%
+then V the runtime
+or I say
+
+ align:start position:0%
+or I say
+ 
+
+ align:start position:0%
+or I say
+time of v it grows with with the size of
+
+ align:start position:0%
+time of v it grows with with the size of
+ 
+
+ align:start position:0%
+time of v it grows with with the size of
+M as opposed to
+
+ align:start position:0%
+M as opposed to
+ 
+
+ align:start position:0%
+M as opposed to
+K okay so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grows with M and does not grow with K so
+
+ align:start position:0%
+grows with M and does not grow with K so
+ 
+
+ align:start position:0%
+grows with M and does not grow with K so
+of course if you give him xon to XK he
+
+ align:start position:0%
+of course if you give him xon to XK he
+ 
+
+ align:start position:0%
+of course if you give him xon to XK he
+need to read his input his run times
+
+ align:start position:0%
+need to read his input his run times
+ 
+
+ align:start position:0%
+need to read his input his run times
+grow K but if you can kind of generate
+
+ align:start position:0%
+grow K but if you can kind of generate
+ 
+
+ align:start position:0%
+grow K but if you can kind of generate
+in succinct way then he doesn't need to
+
+ align:start position:0%
+in succinct way then he doesn't need to
+ 
+
+ align:start position:0%
+in succinct way then he doesn't need to
+grow grow with
+
+ align:start position:0%
+grow grow with
+ 
+
+ align:start position:0%
+grow grow with
+K okay so the you should another way to
+
+ align:start position:0%
+K okay so the you should another way to
+ 
+
+ align:start position:0%
+K okay so the you should another way to
+think about it you can think of x i as
+
+ align:start position:0%
+think about it you can think of x i as
+ 
+
+ align:start position:0%
+think about it you can think of x i as
+like M comma
+
+ align:start position:0%
+like M comma
+ 
+
+ align:start position:0%
+like M comma
+I and the instance just says if you run
+
+ align:start position:0%
+I and the instance just says if you run
+ 
+
+ align:start position:0%
+I and the instance just says if you run
+M on i x i then XI in the language and
+
+ align:start position:0%
+M on i x i then XI in the language and
+ 
+
+ align:start position:0%
+M on i x i then XI in the language and
+that's why it's called index language
+
+ align:start position:0%
+that's why it's called index language
+ 
+
+ align:start position:0%
+that's why it's called index language
+because it's like there's an index yeah
+
+ align:start position:0%
+because it's like there's an index yeah
+ 
+
+ align:start position:0%
+because it's like there's an index yeah
+so this means that there still like a
+
+ align:start position:0%
+so this means that there still like a
+ 
+
+ align:start position:0%
+so this means that there still like a
+depend in these R time right yeah yeah
+
+ align:start position:0%
+depend in these R time right yeah yeah
+ 
+
+ align:start position:0%
+depend in these R time right yeah yeah
+yeah there is a lock dependence 100%
+
+ align:start position:0%
+yeah there is a lock dependence 100%
+ 
+
+ align:start position:0%
+yeah there is a lock dependence 100%
+sorry yeah yeah it just means yeah
+
+ align:start position:0%
+sorry yeah yeah it just means yeah
+ 
+
+ align:start position:0%
+sorry yeah yeah it just means yeah
+exactly that runs into time uh log K
+
+ align:start position:0%
+exactly that runs into time uh log K
+ 
+
+ align:start position:0%
+exactly that runs into time uh log K
+actually yeah you have I here which is
+
+ align:start position:0%
+actually yeah you have I here which is
+ 
+
+ align:start position:0%
+actually yeah you have I here which is
+log K so there is a log K dependence
+
+ align:start position:0%
+log K so there is a log K dependence
+ 
+
+ align:start position:0%
+log K so there is a log K dependence
+yeah the CRS is sublinear in K as well
+
+ align:start position:0%
+yeah the CRS is sublinear in K as well
+ 
+
+ align:start position:0%
+yeah the CRS is sublinear in K as well
+is that true the length of the CRS in
+
+ align:start position:0%
+is that true the length of the CRS in
+ 
+
+ align:start position:0%
+is that true the length of the CRS in
+general you want it to be sublinear in K
+
+ align:start position:0%
+general you want it to be sublinear in K
+ 
+
+ align:start position:0%
+general you want it to be sublinear in K
+in the snar construction it's po okay
+
+ align:start position:0%
+in the snar construction it's po okay
+ 
+
+ align:start position:0%
+in the snar construction it's po okay
+but yes but when we'll talk about snar
+
+ align:start position:0%
+but yes but when we'll talk about snar
+ 
+
+ align:start position:0%
+but yes but when we'll talk about snar
+so yeah in the the in the bar the bar
+
+ align:start position:0%
+so yeah in the the in the bar the bar
+ 
+
+ align:start position:0%
+so yeah in the the in the bar the bar
+construction we have the
+
+ align:start position:0%
+construction we have the
+ 
+
+ align:start position:0%
+construction we have the
+CRS MO most of our construction the SS
+
+ align:start position:0%
+CRS MO most of our construction the SS
+ 
+
+ align:start position:0%
+CRS MO most of our construction the SS
+is of size
+
+ align:start position:0%
+is of size
+ 
+
+ align:start position:0%
+is of size
+pology uh the one under lwe that Jing
+
+ align:start position:0%
+pology uh the one under lwe that Jing
+ 
+
+ align:start position:0%
+pology uh the one under lwe that Jing
+Jang showed is is of size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+poly so I know that if we have a bar
+
+ align:start position:0%
+poly so I know that if we have a bar
+ 
+
+ align:start position:0%
+poly so I know that if we have a bar
+that size these properties and function
+
+ align:start position:0%
+that size these properties and function
+ 
+
+ align:start position:0%
+that size these properties and function
+I guess you can always kind of like like
+
+ align:start position:0%
+I guess you can always kind of like like
+ 
+
+ align:start position:0%
+I guess you can always kind of like like
+add the property that you want here
+
+ align:start position:0%
+add the property that you want here
+ 
+
+ align:start position:0%
+add the property that you want here
+being able to extract a witness from the
+
+ align:start position:0%
+being able to extract a witness from the
+ 
+
+ align:start position:0%
+being able to extract a witness from the
+group itself is there a world like do we
+
+ align:start position:0%
+group itself is there a world like do we
+ 
+
+ align:start position:0%
+group itself is there a world like do we
+have any bars without the assumptions
+
+ align:start position:0%
+have any bars without the assumptions
+ 
+
+ align:start position:0%
+have any bars without the assumptions
+that we need for
+
+ align:start position:0%
+that we need for
+ 
+
+ align:start position:0%
+that we need for
+function you're asking is there a bar
+
+ align:start position:0%
+function you're asking is there a bar
+ 
+
+ align:start position:0%
+function you're asking is there a bar
+for which we we we don't know how to
+
+ align:start position:0%
+for which we we we don't know how to
+ 
+
+ align:start position:0%
+for which we we we don't know how to
+extract is that what you're asking okay
+
+ align:start position:0%
+extract is that what you're asking okay
+ 
+
+ align:start position:0%
+extract is that what you're asking okay
+okay so okay so let me you're asking a
+
+ align:start position:0%
+okay so okay so let me you're asking a
+ 
+
+ align:start position:0%
+okay so okay so let me you're asking a
+great question let me kind of uh
+
+ align:start position:0%
+great question let me kind of uh
+ 
+
+ align:start position:0%
+great question let me kind of uh
+uh okay so when we said when I when the
+
+ align:start position:0%
+uh okay so when we said when I when the
+ 
+
+ align:start position:0%
+uh okay so when we said when I when the
+soundness condition just says that a
+
+ align:start position:0%
+soundness condition just says that a
+ 
+
+ align:start position:0%
+soundness condition just says that a
+cheating prover cannot uh you know cheat
+
+ align:start position:0%
+cheating prover cannot uh you know cheat
+ 
+
+ align:start position:0%
+cheating prover cannot uh you know cheat
+cannot generate X1 up to XK that one of
+
+ align:start position:0%
+cannot generate X1 up to XK that one of
+ 
+
+ align:start position:0%
+cannot generate X1 up to XK that one of
+them the I is not in the language and
+
+ align:start position:0%
+them the I is not in the language and
+ 
+
+ align:start position:0%
+them the I is not in the language and
+yet convinced
+
+ align:start position:0%
+yet convinced
+ 
+
+ align:start position:0%
+yet convinced
+often time also in our snar in our snar
+
+ align:start position:0%
+often time also in our snar in our snar
+ 
+
+ align:start position:0%
+often time also in our snar in our snar
+construction we want something stronger
+
+ align:start position:0%
+construction we want something stronger
+ 
+
+ align:start position:0%
+construction we want something stronger
+what we want is that I can actually
+
+ align:start position:0%
+what we want is that I can actually
+ 
+
+ align:start position:0%
+what we want is that I can actually
+extract a
+
+ align:start position:0%
+extract a
+ 
+
+ align:start position:0%
+extract a
+witness from from this cheating prover
+
+ align:start position:0%
+witness from from this cheating prover
+ 
+
+ align:start position:0%
+witness from from this cheating prover
+so I want to say this cheating prover I
+
+ align:start position:0%
+so I want to say this cheating prover I
+ 
+
+ align:start position:0%
+so I want to say this cheating prover I
+can't extract all the
+
+ align:start position:0%
+can't extract all the
+ 
+
+ align:start position:0%
+can't extract all the
+witnesses but for some ey I can generate
+
+ align:start position:0%
+witnesses but for some ey I can generate
+ 
+
+ align:start position:0%
+witnesses but for some ey I can generate
+a CRS that looks like just standard CRS
+
+ align:start position:0%
+a CRS that looks like just standard CRS
+ 
+
+ align:start position:0%
+a CRS that looks like just standard CRS
+but I can kind of change the
+
+ align:start position:0%
+but I can kind of change the
+ 
+
+ align:start position:0%
+but I can kind of change the
+distribution a CRS to be such that using
+
+ align:start position:0%
+distribution a CRS to be such that using
+ 
+
+ align:start position:0%
+distribution a CRS to be such that using
+some trapo about the CRS I can actually
+
+ align:start position:0%
+some trapo about the CRS I can actually
+ 
+
+ align:start position:0%
+some trapo about the CRS I can actually
+extract from P star a witness for XI and
+
+ align:start position:0%
+extract from P star a witness for XI and
+ 
+
+ align:start position:0%
+extract from P star a witness for XI and
+once I extract a witness of course it
+
+ align:start position:0%
+once I extract a witness of course it
+ 
+
+ align:start position:0%
+once I extract a witness of course it
+has to be in the language I I argue not
+
+ align:start position:0%
+has to be in the language I I argue not
+ 
+
+ align:start position:0%
+has to be in the language I I argue not
+only it's in the language I can even
+
+ align:start position:0%
+only it's in the language I can even
+ 
+
+ align:start position:0%
+only it's in the language I can even
+find you know get a witness from him so
+
+ align:start position:0%
+find you know get a witness from him so
+ 
+
+ align:start position:0%
+find you know get a witness from him so
+that's called somewhere this is like
+
+ align:start position:0%
+that's called somewhere this is like
+ 
+
+ align:start position:0%
+that's called somewhere this is like
+somewh extractable bar now what Li was
+
+ align:start position:0%
+somewh extractable bar now what Li was
+ 
+
+ align:start position:0%
+somewh extractable bar now what Li was
+saying is that the bar that Jen Jong uh
+
+ align:start position:0%
+saying is that the bar that Jen Jong uh
+ 
+
+ align:start position:0%
+saying is that the bar that Jen Jong uh
+showed you last time was extra had the
+
+ align:start position:0%
+showed you last time was extra had the
+ 
+
+ align:start position:0%
+showed you last time was extra had the
+somewh extractable property okay was
+
+ align:start position:0%
+somewh extractable property okay was
+ 
+
+ align:start position:0%
+somewh extractable property okay was
+extractable actually let me tell you we
+
+ align:start position:0%
+extractable actually let me tell you we
+ 
+
+ align:start position:0%
+extractable actually let me tell you we
+also will need bar that are somewhere
+
+ align:start position:0%
+also will need bar that are somewhere
+ 
+
+ align:start position:0%
+also will need bar that are somewhere
+extractable I didn't write that here why
+
+ align:start position:0%
+extractable I didn't write that here why
+ 
+
+ align:start position:0%
+extractable I didn't write that here why
+didn't I write it here and this is where
+
+ align:start position:0%
+didn't I write it here and this is where
+ 
+
+ align:start position:0%
+didn't I write it here and this is where
+the exactly the answer is any bar we can
+
+ align:start position:0%
+the exactly the answer is any bar we can
+ 
+
+ align:start position:0%
+the exactly the answer is any bar we can
+make it somewhere extractable by just
+
+ align:start position:0%
+make it somewhere extractable by just
+ 
+
+ align:start position:0%
+make it somewhere extractable by just
+adding a hash so we can kind of up we
+
+ align:start position:0%
+adding a hash so we can kind of up we
+ 
+
+ align:start position:0%
+adding a hash so we can kind of up we
+don't need to worry about summer
+
+ align:start position:0%
+don't need to worry about summer
+ 
+
+ align:start position:0%
+don't need to worry about summer
+extractability of a bar because what we
+
+ align:start position:0%
+extractability of a bar because what we
+ 
+
+ align:start position:0%
+extractability of a bar because what we
+can always do is add put a hash of all
+
+ align:start position:0%
+can always do is add put a hash of all
+ 
+
+ align:start position:0%
+can always do is add put a hash of all
+the witnesses a some if you have some
+
+ align:start position:0%
+the witnesses a some if you have some
+ 
+
+ align:start position:0%
+the witnesses a some if you have some
+extractable hash if you have a somewh
+
+ align:start position:0%
+extractable hash if you have a somewh
+ 
+
+ align:start position:0%
+extractable hash if you have a somewh
+extractable hash you can tell the
+
+ align:start position:0%
+extractable hash you can tell the
+ 
+
+ align:start position:0%
+extractable hash you can tell the
+verifier put a somewh extractable hash
+
+ align:start position:0%
+verifier put a somewh extractable hash
+ 
+
+ align:start position:0%
+verifier put a somewh extractable hash
+of all your Witnesses so take witness
+
+ align:start position:0%
+of all your Witnesses so take witness
+ 
+
+ align:start position:0%
+of all your Witnesses so take witness
+one witness two witness three up to
+
+ align:start position:0%
+one witness two witness three up to
+ 
+
+ align:start position:0%
+one witness two witness three up to
+witness K hash them and in the analysis
+
+ align:start position:0%
+witness K hash them and in the analysis
+ 
+
+ align:start position:0%
+witness K hash them and in the analysis
+just jumping ahead we're going to be
+
+ align:start position:0%
+just jumping ahead we're going to be
+ 
+
+ align:start position:0%
+just jumping ahead we're going to be
+extractable on all the locations
+
+ align:start position:0%
+extractable on all the locations
+ 
+
+ align:start position:0%
+extractable on all the locations
+corresponding to witness I and now we're
+
+ align:start position:0%
+corresponding to witness I and now we're
+ 
+
+ align:start position:0%
+corresponding to witness I and now we're
+going to tell him we're going to say
+
+ align:start position:0%
+going to tell him we're going to say
+ 
+
+ align:start position:0%
+going to tell him we're going to say
+give me a bar the bar is not for the
+
+ align:start position:0%
+give me a bar the bar is not for the
+ 
+
+ align:start position:0%
+give me a bar the bar is not for the
+original language L the bar says
+
+ align:start position:0%
+original language L the bar says
+ 
+
+ align:start position:0%
+original language L the bar says
+the bar that X eyes in the language now
+
+ align:start position:0%
+the bar that X eyes in the language now
+ 
+
+ align:start position:0%
+the bar that X eyes in the language now
+says there is an opening for the hash
+
+ align:start position:0%
+says there is an opening for the hash
+ 
+
+ align:start position:0%
+says there is an opening for the hash
+value that in the locations conf find to
+
+ align:start position:0%
+value that in the locations conf find to
+ 
+
+ align:start position:0%
+value that in the locations conf find to
+Wi if you opened you would get a valid
+
+ align:start position:0%
+Wi if you opened you would get a valid
+ 
+
+ align:start position:0%
+Wi if you opened you would get a valid
+witness bar that language so instead of
+
+ align:start position:0%
+witness bar that language so instead of
+ 
+
+ align:start position:0%
+witness bar that language so instead of
+barging the original language bark a
+
+ align:start position:0%
+barging the original language bark a
+ 
+
+ align:start position:0%
+barging the original language bark a
+little bit kind of upgraded language
+
+ align:start position:0%
+little bit kind of upgraded language
+ 
+
+ align:start position:0%
+little bit kind of upgraded language
+that again says there's a so the
+
+ align:start position:0%
+that again says there's a so the
+ 
+
+ align:start position:0%
+that again says there's a so the
+verifier will give you a hash of all the
+
+ align:start position:0%
+verifier will give you a hash of all the
+ 
+
+ align:start position:0%
+verifier will give you a hash of all the
+witnesses and he will prove for every
+
+ align:start position:0%
+witnesses and he will prove for every
+ 
+
+ align:start position:0%
+witnesses and he will prove for every
+eye he won't won't prove just XIs in the
+
+ align:start position:0%
+eye he won't won't prove just XIs in the
+ 
+
+ align:start position:0%
+eye he won't won't prove just XIs in the
+language he's going to prove for every
+
+ align:start position:0%
+language he's going to prove for every
+ 
+
+ align:start position:0%
+language he's going to prove for every
+eye I have openings corresponding to
+
+ align:start position:0%
+eye I have openings corresponding to
+ 
+
+ align:start position:0%
+eye I have openings corresponding to
+witness eye so that the a the openings
+
+ align:start position:0%
+witness eye so that the a the openings
+ 
+
+ align:start position:0%
+witness eye so that the a the openings
+are valid and B wi is in the is in the
+
+ align:start position:0%
+are valid and B wi is in the is in the
+ 
+
+ align:start position:0%
+are valid and B wi is in the is in the
+language L that's the bar he's going to
+
+ align:start position:0%
+language L that's the bar he's going to
+ 
+
+ align:start position:0%
+language L that's the bar he's going to
+give you and now the fact that you're in
+
+ align:start position:0%
+give you and now the fact that you're in
+ 
+
+ align:start position:0%
+give you and now the fact that you're in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+language means that it must be that if
+
+ align:start position:0%
+language means that it must be that if
+ 
+
+ align:start position:0%
+language means that it must be that if
+you take the trap door and look into it
+
+ align:start position:0%
+you take the trap door and look into it
+ 
+
+ align:start position:0%
+you take the trap door and look into it
+it must be by by
+
+ align:start position:0%
+it must be by by
+ 
+
+ align:start position:0%
+it must be by by
+soundless must be that's what's sitting
+
+ align:start position:0%
+soundless must be that's what's sitting
+ 
+
+ align:start position:0%
+soundless must be that's what's sitting
+there because you're binding if if
+
+ align:start position:0%
+there because you're binding if if
+ 
+
+ align:start position:0%
+there because you're binding if if
+you're going to be binding on that part
+
+ align:start position:0%
+you're going to be binding on that part
+ 
+
+ align:start position:0%
+you're going to be binding on that part
+you know that what's sitting there must
+
+ align:start position:0%
+you know that what's sitting there must
+ 
+
+ align:start position:0%
+you know that what's sitting there must
+be the correct
+
+ align:start position:0%
+be the correct
+ 
+
+ align:start position:0%
+be the correct
+witness so that's uh that's kind of uh
+
+ align:start position:0%
+witness so that's uh that's kind of uh
+ 
+
+ align:start position:0%
+witness so that's uh that's kind of uh
+why why actually we don't need to
+
+ align:start position:0%
+why why actually we don't need to
+ 
+
+ align:start position:0%
+why why actually we don't need to
+construct bars with with extractability
+
+ align:start position:0%
+construct bars with with extractability
+ 
+
+ align:start position:0%
+construct bars with with extractability
+we can always attach uh uh some
+
+ align:start position:0%
+we can always attach uh uh some
+ 
+
+ align:start position:0%
+we can always attach uh uh some
+constructible hash to them yeah I guess
+
+ align:start position:0%
+constructible hash to them yeah I guess
+ 
+
+ align:start position:0%
+constructible hash to them yeah I guess
+actually Wonder something assumptions do
+
+ align:start position:0%
+actually Wonder something assumptions do
+ 
+
+ align:start position:0%
+actually Wonder something assumptions do
+we have any constructions of bars from
+
+ align:start position:0%
+we have any constructions of bars from
+ 
+
+ align:start position:0%
+we have any constructions of bars from
+assumptions weaker than those needed to
+
+ align:start position:0%
+assumptions weaker than those needed to
+ 
+
+ align:start position:0%
+assumptions weaker than those needed to
+construct which would make it I guess
+
+ align:start position:0%
+construct which would make it I guess
+ 
+
+ align:start position:0%
+construct which would make it I guess
+interesting I see what you're saying I
+
+ align:start position:0%
+interesting I see what you're saying I
+ 
+
+ align:start position:0%
+interesting I see what you're saying I
+see uh um I don't think not that I yeah
+
+ align:start position:0%
+see uh um I don't think not that I yeah
+ 
+
+ align:start position:0%
+see uh um I don't think not that I yeah
+I don't think so I don't think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah I don't know how to construct a
+
+ align:start position:0%
+so yeah I don't know how to construct a
+ 
+
+ align:start position:0%
+so yeah I don't know how to construct a
+bar from an assumption for which I don't
+
+ align:start position:0%
+bar from an assumption for which I don't
+ 
+
+ align:start position:0%
+bar from an assumption for which I don't
+know how to construct a some
+
+ align:start position:0%
+know how to construct a some
+ 
+
+ align:start position:0%
+know how to construct a some
+constructible hash
+
+ align:start position:0%
+constructible hash
+ 
+
+ align:start position:0%
+constructible hash
+yeah okay a any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so I want to get to the
+
+ align:start position:0%
+questions okay so I want to get to the
+ 
+
+ align:start position:0%
+questions okay so I want to get to the
+bar to the construction of the snar but
+
+ align:start position:0%
+bar to the construction of the snar but
+ 
+
+ align:start position:0%
+bar to the construction of the snar but
+before I do so I I I do want to spend a
+
+ align:start position:0%
+before I do so I I I do want to spend a
+ 
+
+ align:start position:0%
+before I do so I I I do want to spend a
+little more time on the summer
+
+ align:start position:0%
+little more time on the summer
+ 
+
+ align:start position:0%
+little more time on the summer
+extractable hash and say a little bit
+
+ align:start position:0%
+extractable hash and say a little bit
+ 
+
+ align:start position:0%
+extractable hash and say a little bit
+about the way we construct it because
+
+ align:start position:0%
+about the way we construct it because
+ 
+
+ align:start position:0%
+about the way we construct it because
+I'm just want to make sure that a
+
+ align:start position:0%
+I'm just want to make sure that a
+ 
+
+ align:start position:0%
+I'm just want to make sure that a
+a that you you you you didn't miss a
+
+ align:start position:0%
+a that you you you you didn't miss a
+ 
+
+ align:start position:0%
+a that you you you you didn't miss a
+part from last lecture that I think was
+
+ align:start position:0%
+part from last lecture that I think was
+ 
+
+ align:start position:0%
+part from last lecture that I think was
+a bit said too succinctly so the high
+
+ align:start position:0%
+a bit said too succinctly so the high
+ 
+
+ align:start position:0%
+a bit said too succinctly so the high
+level idea of how you construct a Sumer
+
+ align:start position:0%
+level idea of how you construct a Sumer
+ 
+
+ align:start position:0%
+level idea of how you construct a Sumer
+extractable hash is using uh fully
+
+ align:start position:0%
+extractable hash is using uh fully
+ 
+
+ align:start position:0%
+extractable hash is using uh fully
+homomorphic encryption okay so I don't
+
+ align:start position:0%
+homomorphic encryption okay so I don't
+ 
+
+ align:start position:0%
+homomorphic encryption okay so I don't
+want to get into uh uh I don't want to
+
+ align:start position:0%
+want to get into uh uh I don't want to
+ 
+
+ align:start position:0%
+want to get into uh uh I don't want to
+recall too much the definition but I'll
+
+ align:start position:0%
+recall too much the definition but I'll
+ 
+
+ align:start position:0%
+recall too much the definition but I'll
+I'll give you a high level so the basic
+
+ align:start position:0%
+I'll give you a high level so the basic
+ 
+
+ align:start position:0%
+I'll give you a high level so the basic
+idea which doesn't work okay let me
+
+ align:start position:0%
+idea which doesn't work okay let me
+ 
+
+ align:start position:0%
+idea which doesn't work okay let me
+first tell you the idea that doesn't
+
+ align:start position:0%
+first tell you the idea that doesn't
+ 
+
+ align:start position:0%
+first tell you the idea that doesn't
+work because that's very natural and I
+
+ align:start position:0%
+work because that's very natural and I
+ 
+
+ align:start position:0%
+work because that's very natural and I
+think maybe that's what you got from
+
+ align:start position:0%
+think maybe that's what you got from
+ 
+
+ align:start position:0%
+think maybe that's what you got from
+last lecture so the basic idea that
+
+ align:start position:0%
+last lecture so the basic idea that
+ 
+
+ align:start position:0%
+last lecture so the basic idea that
+doesn't work is to say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gen will just output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+encryption so it'll give you a public
+
+ align:start position:0%
+encryption so it'll give you a public
+ 
+
+ align:start position:0%
+encryption so it'll give you a public
+key an encryption of I with this public
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key and the trap door that's going to be
+
+ align:start position:0%
+key and the trap door that's going to be
+ 
+
+ align:start position:0%
+key and the trap door that's going to be
+the hash
+
+ align:start position:0%
+the hash
+ 
+
+ align:start position:0%
+the hash
+key and the trap door is going to be the
+
+ align:start position:0%
+key and the trap door is going to be the
+ 
+
+ align:start position:0%
+key and the trap door is going to be the
+secret
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key okay so I'm just the hash key is
+
+ align:start position:0%
+key okay so I'm just the hash key is
+ 
+
+ align:start position:0%
+key okay so I'm just the hash key is
+going to be an encryption of of the
+
+ align:start position:0%
+going to be an encryption of of the
+ 
+
+ align:start position:0%
+going to be an encryption of of the
+index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I want X1 to X n Let Me Assume for
+
+ align:start position:0%
+now I want X1 to X n Let Me Assume for
+ 
+
+ align:start position:0%
+now I want X1 to X n Let Me Assume for
+Simplicity that n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose N is a power of two otherwise
+
+ align:start position:0%
+suppose N is a power of two otherwise
+ 
+
+ align:start position:0%
+suppose N is a power of two otherwise
+you know pad okay so let's say big n is
+
+ align:start position:0%
+you know pad okay so let's say big n is
+ 
+
+ align:start position:0%
+you know pad okay so let's say big n is
+a power of two so it's some two to the
+
+ align:start position:0%
+a power of two so it's some two to the
+ 
+
+ align:start position:0%
+a power of two so it's some two to the
+small n now here's what I'm going to do
+
+ align:start position:0%
+small n now here's what I'm going to do
+ 
+
+ align:start position:0%
+small n now here's what I'm going to do
+let me so when I say encryption of I
+
+ align:start position:0%
+let me so when I say encryption of I
+ 
+
+ align:start position:0%
+let me so when I say encryption of I
+let's think of it as bid by bit
+
+ align:start position:0%
+let's think of it as bid by bit
+ 
+
+ align:start position:0%
+let's think of it as bid by bit
+encryption so it's
+
+ align:start position:0%
+encryption so it's
+ 
+
+ align:start position:0%
+encryption so it's
+encryption of
+
+ align:start position:0%
+encryption of
+ 
+
+ align:start position:0%
+encryption of
+i1 up to encryption
+
+ align:start position:0%
+i1 up to encryption
+ 
+
+ align:start position:0%
+i1 up to encryption
+of I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in okay and now the idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is what we'll do is for for each like
+
+ align:start position:0%
+is what we'll do is for for each like
+ 
+
+ align:start position:0%
+is what we'll do is for for each like
+pair so I'm going to do kind of a Merkle
+
+ align:start position:0%
+pair so I'm going to do kind of a Merkle
+ 
+
+ align:start position:0%
+pair so I'm going to do kind of a Merkle
+hash and for each pair I'm going to
+
+ align:start position:0%
+hash and for each pair I'm going to
+ 
+
+ align:start position:0%
+hash and for each pair I'm going to
+encrypt so I'm going to do this Merle
+
+ align:start position:0%
+encrypt so I'm going to do this Merle
+ 
+
+ align:start position:0%
+encrypt so I'm going to do this Merle
+hash where for each node I'm going to
+
+ align:start position:0%
+hash where for each node I'm going to
+ 
+
+ align:start position:0%
+hash where for each node I'm going to
+associate a cipher text and the output
+
+ align:start position:0%
+associate a cipher text and the output
+ 
+
+ align:start position:0%
+associate a cipher text and the output
+is going to be the cipher text of the
+
+ align:start position:0%
+is going to be the cipher text of the
+ 
+
+ align:start position:0%
+is going to be the cipher text of the
+root that's my hash value the hash Val
+
+ align:start position:0%
+root that's my hash value the hash Val
+ 
+
+ align:start position:0%
+root that's my hash value the hash Val
+is give be a cipher text of the root and
+
+ align:start position:0%
+is give be a cipher text of the root and
+ 
+
+ align:start position:0%
+is give be a cipher text of the root and
+this Cypher text going be a cyppher text
+
+ align:start position:0%
+this Cypher text going be a cyppher text
+ 
+
+ align:start position:0%
+this Cypher text going be a cyppher text
+it's encryption of
+
+ align:start position:0%
+it's encryption of
+ 
+
+ align:start position:0%
+it's encryption of
+XI okay how do I asso so of course I can
+
+ align:start position:0%
+XI okay how do I asso so of course I can
+ 
+
+ align:start position:0%
+XI okay how do I asso so of course I can
+comp encryption of x i this is a
+
+ align:start position:0%
+comp encryption of x i this is a
+ 
+
+ align:start position:0%
+comp encryption of x i this is a
+homomorphic encryption given X an
+
+ align:start position:0%
+homomorphic encryption given X an
+ 
+
+ align:start position:0%
+homomorphic encryption given X an
+encryption of I I can do computation
+
+ align:start position:0%
+encryption of I I can do computation
+ 
+
+ align:start position:0%
+encryption of I I can do computation
+under the hood so I can compute
+
+ align:start position:0%
+under the hood so I can compute
+ 
+
+ align:start position:0%
+under the hood so I can compute
+encryption of xabi okay so because this
+
+ align:start position:0%
+encryption of xabi okay so because this
+ 
+
+ align:start position:0%
+encryption of xabi okay so because this
+is a a fully homomorphic
+
+ align:start position:0%
+is a a fully homomorphic
+ 
+
+ align:start position:0%
+is a a fully homomorphic
+encryption
+
+ align:start position:0%
+encryption
+ 
+
+ align:start position:0%
+encryption
+given X and encryption of I
+
+ align:start position:0%
+given X and encryption of I
+ 
+
+ align:start position:0%
+given X and encryption of I
+I can compute encryption of
+
+ align:start position:0%
+I can compute encryption of
+ 
+
+ align:start position:0%
+I can compute encryption of
+xabi of course there's public keys I'm
+
+ align:start position:0%
+xabi of course there's public keys I'm
+ 
+
+ align:start position:0%
+xabi of course there's public keys I'm
+omitting them for sness of
+
+ align:start position:0%
+omitting them for sness of
+ 
+
+ align:start position:0%
+omitting them for sness of
+rotation okay this is because I can
+
+ align:start position:0%
+rotation okay this is because I can
+ 
+
+ align:start position:0%
+rotation okay this is because I can
+compute under the
+
+ align:start position:0%
+compute under the
+ 
+
+ align:start position:0%
+compute under the
+hood the value of the root is going to
+
+ align:start position:0%
+hood the value of the root is going to
+ 
+
+ align:start position:0%
+hood the value of the root is going to
+be encryption of
+
+ align:start position:0%
+be encryption of
+ 
+
+ align:start position:0%
+be encryption of
+XI but what kind of encryption it's not
+
+ align:start position:0%
+XI but what kind of encryption it's not
+ 
+
+ align:start position:0%
+XI but what kind of encryption it's not
+any ENC so let me tell you how exactly
+
+ align:start position:0%
+any ENC so let me tell you how exactly
+ 
+
+ align:start position:0%
+any ENC so let me tell you how exactly
+how I compute this encryption so the
+
+ align:start position:0%
+how I compute this encryption so the
+ 
+
+ align:start position:0%
+how I compute this encryption so the
+idea would be so and and not only that
+
+ align:start position:0%
+idea would be so and and not only that
+ 
+
+ align:start position:0%
+idea would be so and and not only that
+how do I open
+
+ align:start position:0%
+how do I open
+ 
+
+ align:start position:0%
+how do I open
+okay I want to do local opening so the
+
+ align:start position:0%
+okay I want to do local opening so the
+ 
+
+ align:start position:0%
+okay I want to do local opening so the
+the way I'm going to do it is as follows
+
+ align:start position:0%
+the way I'm going to do it is as follows
+ 
+
+ align:start position:0%
+the way I'm going to do it is as follows
+for each for each pair I'm going to
+
+ align:start position:0%
+for each for each pair I'm going to
+ 
+
+ align:start position:0%
+for each for each pair I'm going to
+encrypt only one of them I'm going to
+
+ align:start position:0%
+encrypt only one of them I'm going to
+ 
+
+ align:start position:0%
+encrypt only one of them I'm going to
+either put here encryption of X1 or
+
+ align:start position:0%
+either put here encryption of X1 or
+ 
+
+ align:start position:0%
+either put here encryption of X1 or
+encryption of X2 which one depending on
+
+ align:start position:0%
+encryption of X2 which one depending on
+ 
+
+ align:start position:0%
+encryption of X2 which one depending on
+i1 so let's start with i1 if i1 is zero
+
+ align:start position:0%
+i1 so let's start with i1 if i1 is zero
+ 
+
+ align:start position:0%
+i1 so let's start with i1 if i1 is zero
+I'm gonna so I'm I'm GNA let's say
+
+ align:start position:0%
+I'm gonna so I'm I'm GNA let's say
+ 
+
+ align:start position:0%
+I'm gonna so I'm I'm GNA let's say
+choose X1 if i1 is one I'm going to
+
+ align:start position:0%
+choose X1 if i1 is one I'm going to
+ 
+
+ align:start position:0%
+choose X1 if i1 is one I'm going to
+choose X2 it's I'm gonna choose even
+
+ align:start position:0%
+choose X2 it's I'm gonna choose even
+ 
+
+ align:start position:0%
+choose X2 it's I'm gonna choose even
+other so that the output will be the
+
+ align:start position:0%
+other so that the output will be the
+ 
+
+ align:start position:0%
+other so that the output will be the
+correct one uh okay so I'm gonna the the
+
+ align:start position:0%
+correct one uh okay so I'm gonna the the
+ 
+
+ align:start position:0%
+correct one uh okay so I'm gonna the the
+i1 depending on encryption of i1 that's
+
+ align:start position:0%
+i1 depending on encryption of i1 that's
+ 
+
+ align:start position:0%
+i1 depending on encryption of i1 that's
+going to tell me which one to put here
+
+ align:start position:0%
+going to tell me which one to put here
+ 
+
+ align:start position:0%
+going to tell me which one to put here
+zero I put all the
+
+ align:start position:0%
+zero I put all the
+ 
+
+ align:start position:0%
+zero I put all the
+left like the left children or one I put
+
+ align:start position:0%
+left like the left children or one I put
+ 
+
+ align:start position:0%
+left like the left children or one I put
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+children and then I do the exact same
+
+ align:start position:0%
+children and then I do the exact same
+ 
+
+ align:start position:0%
+children and then I do the exact same
+thing given
+
+ align:start position:0%
+thing given
+ 
+
+ align:start position:0%
+thing given
+these whether I choose the left or right
+
+ align:start position:0%
+these whether I choose the left or right
+ 
+
+ align:start position:0%
+these whether I choose the left or right
+depends on encryption of I2 if I2 is
+
+ align:start position:0%
+depends on encryption of I2 if I2 is
+ 
+
+ align:start position:0%
+depends on encryption of I2 if I2 is
+zero I choose the left if I2 is one I
+
+ align:start position:0%
+zero I choose the left if I2 is one I
+ 
+
+ align:start position:0%
+zero I choose the left if I2 is one I
+choose the right and so on so forth
+
+ align:start position:0%
+choose the right and so on so forth
+ 
+
+ align:start position:0%
+choose the right and so on so forth
+that's the idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's it's like an OT it's really like an
+
+ align:start position:0%
+it's it's like an OT it's really like an
+ 
+
+ align:start position:0%
+it's it's like an OT it's really like an
+OT exactly exact I didn't Define what OT
+
+ align:start position:0%
+OT exactly exact I didn't Define what OT
+ 
+
+ align:start position:0%
+OT exactly exact I didn't Define what OT
+is but it's exactly like an
+
+ align:start position:0%
+is but it's exactly like an
+ 
+
+ align:start position:0%
+is but it's exactly like an
+OT okay this does not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work okay it it almost works but it does
+
+ align:start position:0%
+work okay it it almost works but it does
+ 
+
+ align:start position:0%
+work okay it it almost works but it does
+not work so let me tell you why it seems
+
+ align:start position:0%
+not work so let me tell you why it seems
+ 
+
+ align:start position:0%
+not work so let me tell you why it seems
+like it should work and then I just want
+
+ align:start position:0%
+like it should work and then I just want
+ 
+
+ align:start position:0%
+like it should work and then I just want
+to mention the uh the um the the a the
+
+ align:start position:0%
+to mention the uh the um the the a the
+ 
+
+ align:start position:0%
+to mention the uh the um the the a the
+subtlety here so the reason it you so
+
+ align:start position:0%
+subtlety here so the reason it you so
+ 
+
+ align:start position:0%
+subtlety here so the reason it you so
+okay so first how do you generate local
+
+ align:start position:0%
+okay so first how do you generate local
+ 
+
+ align:start position:0%
+okay so first how do you generate local
+opening well you check so if you want to
+
+ align:start position:0%
+opening well you check so if you want to
+ 
+
+ align:start position:0%
+opening well you check so if you want to
+open XI I I'll tell you okay give me X1
+
+ align:start position:0%
+open XI I I'll tell you okay give me X1
+ 
+
+ align:start position:0%
+open XI I I'll tell you okay give me X1
+and X2 so I can check that this is
+
+ align:start position:0%
+and X2 so I can check that this is
+ 
+
+ align:start position:0%
+and X2 so I can check that this is
+corrected and then give me the hash the
+
+ align:start position:0%
+corrected and then give me the hash the
+ 
+
+ align:start position:0%
+corrected and then give me the hash the
+cipher text here and I can check that
+
+ align:start position:0%
+cipher text here and I can check that
+ 
+
+ align:start position:0%
+cipher text here and I can check that
+this is correct because each each Cipher
+
+ align:start position:0%
+this is correct because each each Cipher
+ 
+
+ align:start position:0%
+this is correct because each each Cipher
+text is some f valuation that depends on
+
+ align:start position:0%
+text is some f valuation that depends on
+ 
+
+ align:start position:0%
+text is some f valuation that depends on
+the two children and on the the hash key
+
+ align:start position:0%
+the two children and on the the hash key
+ 
+
+ align:start position:0%
+the two children and on the the hash key
+which is encryption so in in layer J it
+
+ align:start position:0%
+which is encryption so in in layer J it
+ 
+
+ align:start position:0%
+which is encryption so in in layer J it
+depends on the two children and
+
+ align:start position:0%
+depends on the two children and
+ 
+
+ align:start position:0%
+depends on the two children and
+encryption of
+
+ align:start position:0%
+encryption of
+ 
+
+ align:start position:0%
+encryption of
+IG okay each time the the the the
+
+ align:start position:0%
+IG okay each time the the the the
+ 
+
+ align:start position:0%
+IG okay each time the the the the
+node the the cipher text corresponding
+
+ align:start position:0%
+node the the cipher text corresponding
+ 
+
+ align:start position:0%
+node the the cipher text corresponding
+to some node is a deterministic function
+
+ align:start position:0%
+to some node is a deterministic function
+ 
+
+ align:start position:0%
+to some node is a deterministic function
+of the cipher text corresponding to the
+
+ align:start position:0%
+of the cipher text corresponding to the
+ 
+
+ align:start position:0%
+of the cipher text corresponding to the
+children and the hash key corresponding
+
+ align:start position:0%
+children and the hash key corresponding
+ 
+
+ align:start position:0%
+children and the hash key corresponding
+to that level so encryption of let's say
+
+ align:start position:0%
+to that level so encryption of let's say
+ 
+
+ align:start position:0%
+to that level so encryption of let's say
+JJ okay cu because remember if if I'm
+
+ align:start position:0%
+JJ okay cu because remember if if I'm
+ 
+
+ align:start position:0%
+JJ okay cu because remember if if I'm
+let's say in level two I have here
+
+ align:start position:0%
+let's say in level two I have here
+ 
+
+ align:start position:0%
+let's say in level two I have here
+Cipher text I don't know one and Cipher
+
+ align:start position:0%
+Cipher text I don't know one and Cipher
+ 
+
+ align:start position:0%
+Cipher text I don't know one and Cipher
+text two then I do
+
+ align:start position:0%
+text two then I do
+ 
+
+ align:start position:0%
+text two then I do
+U the way I compute the the parent uh
+
+ align:start position:0%
+U the way I compute the the parent uh
+ 
+
+ align:start position:0%
+U the way I compute the the parent uh
+Cipher text is just a homomorphic
+
+ align:start position:0%
+Cipher text is just a homomorphic
+ 
+
+ align:start position:0%
+Cipher text is just a homomorphic
+evaluation that takes if I uh if I to is
+
+ align:start position:0%
+evaluation that takes if I uh if I to is
+ 
+
+ align:start position:0%
+evaluation that takes if I uh if I to is
+zero it it takes cyppher text two if I
+
+ align:start position:0%
+zero it it takes cyppher text two if I
+ 
+
+ align:start position:0%
+zero it it takes cyppher text two if I
+two is one it takes sorry c one
+
+ align:start position:0%
+two is one it takes sorry c one
+ 
+
+ align:start position:0%
+two is one it takes sorry c one
+otherwise t i verx 2 okay so this is
+
+ align:start position:0%
+otherwise t i verx 2 okay so this is
+ 
+
+ align:start position:0%
+otherwise t i verx 2 okay so this is
+really just a deterministic homomorphic
+
+ align:start position:0%
+really just a deterministic homomorphic
+ 
+
+ align:start position:0%
+really just a deterministic homomorphic
+evaluation and so that's how I open I
+
+ align:start position:0%
+evaluation and so that's how I open I
+ 
+
+ align:start position:0%
+evaluation and so that's how I open I
+just open all the relevant CER Tex and
+
+ align:start position:0%
+just open all the relevant CER Tex and
+ 
+
+ align:start position:0%
+just open all the relevant CER Tex and
+the verifier will check that the
+
+ align:start position:0%
+the verifier will check that the
+ 
+
+ align:start position:0%
+the verifier will check that the
+homomorphic evaluation was done
+
+ align:start position:0%
+homomorphic evaluation was done
+ 
+
+ align:start position:0%
+homomorphic evaluation was done
+correctly so you can local opening you
+
+ align:start position:0%
+correctly so you can local opening you
+ 
+
+ align:start position:0%
+correctly so you can local opening you
+can do local opening but it's not
+
+ align:start position:0%
+can do local opening but it's not
+ 
+
+ align:start position:0%
+can do local opening but it's not
+binding or I don't know how to prove
+
+ align:start position:0%
+binding or I don't know how to prove
+ 
+
+ align:start position:0%
+binding or I don't know how to prove
+that it's binding is the problem okay
+
+ align:start position:0%
+that it's binding is the problem okay
+ 
+
+ align:start position:0%
+that it's binding is the problem okay
+and probably you can find a weird FHA
+
+ align:start position:0%
+and probably you can find a weird FHA
+ 
+
+ align:start position:0%
+and probably you can find a weird FHA
+for which it's not binding I don't know
+
+ align:start position:0%
+for which it's not binding I don't know
+ 
+
+ align:start position:0%
+for which it's not binding I don't know
+maybe for natural constructions it is
+
+ align:start position:0%
+maybe for natural constructions it is
+ 
+
+ align:start position:0%
+maybe for natural constructions it is
+binding I don't know I don't know how to
+
+ align:start position:0%
+binding I don't know I don't know how to
+ 
+
+ align:start position:0%
+binding I don't know I don't know how to
+prove it
+
+ align:start position:0%
+prove it
+ 
+
+ align:start position:0%
+prove it
+but there's a problem with binding and
+
+ align:start position:0%
+but there's a problem with binding and
+ 
+
+ align:start position:0%
+but there's a problem with binding and
+the problem with binding is that a
+
+ align:start position:0%
+the problem with binding is that a
+ 
+
+ align:start position:0%
+the problem with binding is that a
+cheating so it seems like it should be
+
+ align:start position:0%
+cheating so it seems like it should be
+ 
+
+ align:start position:0%
+cheating so it seems like it should be
+binding because look here is sitting
+
+ align:start position:0%
+binding because look here is sitting
+ 
+
+ align:start position:0%
+binding because look here is sitting
+encryption of
+
+ align:start position:0%
+encryption of
+ 
+
+ align:start position:0%
+encryption of
+XI but the thing is the reason why it's
+
+ align:start position:0%
+XI but the thing is the reason why it's
+ 
+
+ align:start position:0%
+XI but the thing is the reason why it's
+not binding is because a
+
+ align:start position:0%
+not binding is because a
+ 
+
+ align:start position:0%
+not binding is because a
+malicious
+
+ align:start position:0%
+malicious
+ 
+
+ align:start position:0%
+malicious
+ah a malicious
+
+ align:start position:0%
+ah a malicious
+ 
+
+ align:start position:0%
+ah a malicious
+adversary he may give Cipher Texs that
+
+ align:start position:0%
+adversary he may give Cipher Texs that
+ 
+
+ align:start position:0%
+adversary he may give Cipher Texs that
+are are garbage are completely garbage
+
+ align:start position:0%
+are are garbage are completely garbage
+ 
+
+ align:start position:0%
+are are garbage are completely garbage
+they don't actually they're not legal
+
+ align:start position:0%
+they don't actually they're not legal
+ 
+
+ align:start position:0%
+they don't actually they're not legal
+Cipher texts and and he if he gives
+
+ align:start position:0%
+Cipher texts and and he if he gives
+ 
+
+ align:start position:0%
+Cipher texts and and he if he gives
+Cypher Texs that are garbage I don't
+
+ align:start position:0%
+Cypher Texs that are garbage I don't
+ 
+
+ align:start position:0%
+Cypher Texs that are garbage I don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+why why would there be binding so I mean
+
+ align:start position:0%
+why why would there be binding so I mean
+ 
+
+ align:start position:0%
+why why would there be binding so I mean
+maybe extract doesn't work okay here's
+
+ align:start position:0%
+maybe extract doesn't work okay here's
+ 
+
+ align:start position:0%
+maybe extract doesn't work okay here's
+me I'm a malicious person I nothing ex
+
+ align:start position:0%
+me I'm a malicious person I nothing ex
+ 
+
+ align:start position:0%
+me I'm a malicious person I nothing ex
+no you can't extract anything I just
+
+ align:start position:0%
+no you can't extract anything I just
+ 
+
+ align:start position:0%
+no you can't extract anything I just
+want to ruin the binding my whole goal
+
+ align:start position:0%
+want to ruin the binding my whole goal
+ 
+
+ align:start position:0%
+want to ruin the binding my whole goal
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+to kind of Ruin binding here okay I'm
+
+ align:start position:0%
+to kind of Ruin binding here okay I'm
+ 
+
+ align:start position:0%
+to kind of Ruin binding here okay I'm
+going to give you V that doesn't encrypt
+
+ align:start position:0%
+going to give you V that doesn't encrypt
+ 
+
+ align:start position:0%
+going to give you V that doesn't encrypt
+anything it's a junk V and I'm going to
+
+ align:start position:0%
+anything it's a junk V and I'm going to
+ 
+
+ align:start position:0%
+anything it's a junk V and I'm going to
+open it in two different ways Maybe
+
+ align:start position:0%
+open it in two different ways Maybe
+ 
+
+ align:start position:0%
+open it in two different ways Maybe
+maybe I can generate a v like it's I
+
+ align:start position:0%
+maybe I can generate a v like it's I
+ 
+
+ align:start position:0%
+maybe I can generate a v like it's I
+call it Cypher text but it's just a
+
+ align:start position:0%
+call it Cypher text but it's just a
+ 
+
+ align:start position:0%
+call it Cypher text but it's just a
+bunch of bits that have no meaning
+
+ align:start position:0%
+bunch of bits that have no meaning
+ 
+
+ align:start position:0%
+bunch of bits that have no meaning
+cannot be decrypted at all and maybe I
+
+ align:start position:0%
+cannot be decrypted at all and maybe I
+ 
+
+ align:start position:0%
+cannot be decrypted at all and maybe I
+can somehow generate valid
+
+ align:start position:0%
+can somehow generate valid
+ 
+
+ align:start position:0%
+can somehow generate valid
+openings so and I we don't know how to
+
+ align:start position:0%
+openings so and I we don't know how to
+ 
+
+ align:start position:0%
+openings so and I we don't know how to
+argue that you cannot do that so in
+
+ align:start position:0%
+argue that you cannot do that so in
+ 
+
+ align:start position:0%
+argue that you cannot do that so in
+order to actually get soundness I need
+
+ align:start position:0%
+order to actually get soundness I need
+ 
+
+ align:start position:0%
+order to actually get soundness I need
+to make sure that the things are well
+
+ align:start position:0%
+to make sure that the things are well
+ 
+
+ align:start position:0%
+to make sure that the things are well
+formed that these are actually valid
+
+ align:start position:0%
+formed that these are actually valid
+ 
+
+ align:start position:0%
+formed that these are actually valid
+Cipher text or what I open to is a valid
+
+ align:start position:0%
+Cipher text or what I open to is a valid
+ 
+
+ align:start position:0%
+Cipher text or what I open to is a valid
+Cipher text
+
+ align:start position:0%
+Cipher text
+ 
+
+ align:start position:0%
+Cipher text
+and the way we get this is by making
+
+ align:start position:0%
+and the way we get this is by making
+ 
+
+ align:start position:0%
+and the way we get this is by making
+this a little more
+
+ align:start position:0%
+this a little more
+ 
+
+ align:start position:0%
+this a little more
+cumbersome so the way we get this is we
+
+ align:start position:0%
+cumbersome so the way we get this is we
+ 
+
+ align:start position:0%
+cumbersome so the way we get this is we
+actually don't use one public key we use
+
+ align:start position:0%
+actually don't use one public key we use
+ 
+
+ align:start position:0%
+actually don't use one public key we use
+small n public keys so for each layer
+
+ align:start position:0%
+small n public keys so for each layer
+ 
+
+ align:start position:0%
+small n public keys so for each layer
+we'll use a different public key and
+
+ align:start position:0%
+we'll use a different public key and
+ 
+
+ align:start position:0%
+we'll use a different public key and
+what we encrypt so what okay so what we
+
+ align:start position:0%
+what we encrypt so what okay so what we
+ 
+
+ align:start position:0%
+what we encrypt so what okay so what we
+do is we
+
+ align:start position:0%
+do is we
+ 
+
+ align:start position:0%
+do is we
+have public key
+
+ align:start position:0%
+have public key
+ 
+
+ align:start position:0%
+have public key
+j for J goes from one to n okay so we
+
+ align:start position:0%
+j for J goes from one to n okay so we
+ 
+
+ align:start position:0%
+j for J goes from one to n okay so we
+have n public keys and with public key
+
+ align:start position:0%
+have n public keys and with public key
+ 
+
+ align:start position:0%
+have n public keys and with public key
+j we encrypt i j but also so the you one
+
+ align:start position:0%
+j we encrypt i j but also so the you one
+ 
+
+ align:start position:0%
+j we encrypt i j but also so the you one
+I has I want up to i n we encrypt i j
+
+ align:start position:0%
+I has I want up to i n we encrypt i j
+ 
+
+ align:start position:0%
+I has I want up to i n we encrypt i j
+but we also
+
+ align:start position:0%
+but we also
+ 
+
+ align:start position:0%
+but we also
+encrypt skj minus one we I want to have
+
+ align:start position:0%
+encrypt skj minus one we I want to have
+ 
+
+ align:start position:0%
+encrypt skj minus one we I want to have
+the decryption it's important me to have
+
+ align:start position:0%
+the decryption it's important me to have
+ 
+
+ align:start position:0%
+the decryption it's important me to have
+the decryption
+
+ align:start position:0%
+the decryption
+ 
+
+ align:start position:0%
+the decryption
+key now okay so the the the bit the
+
+ align:start position:0%
+key now okay so the the the bit the
+ 
+
+ align:start position:0%
+key now okay so the the the bit the
+important bit is that homomorphic
+
+ align:start position:0%
+important bit is that homomorphic
+ 
+
+ align:start position:0%
+important bit is that homomorphic
+evaluation I'm doing here I need to know
+
+ align:start position:0%
+evaluation I'm doing here I need to know
+ 
+
+ align:start position:0%
+evaluation I'm doing here I need to know
+the secret key because I'm not just
+
+ align:start position:0%
+the secret key because I'm not just
+ 
+
+ align:start position:0%
+the secret key because I'm not just
+gonna say before I said what's going on
+
+ align:start position:0%
+gonna say before I said what's going on
+ 
+
+ align:start position:0%
+gonna say before I said what's going on
+underneath under the hood I'm saying
+
+ align:start position:0%
+underneath under the hood I'm saying
+ 
+
+ align:start position:0%
+underneath under the hood I'm saying
+look I have I one I have two Cipher
+
+ align:start position:0%
+look I have I one I have two Cipher
+ 
+
+ align:start position:0%
+look I have I one I have two Cipher
+texts give me one of them no no no no
+
+ align:start position:0%
+texts give me one of them no no no no
+ 
+
+ align:start position:0%
+texts give me one of them no no no no
+what I want to do is to say the
+
+ align:start position:0%
+what I want to do is to say the
+ 
+
+ align:start position:0%
+what I want to do is to say the
+following under the hood decrypt
+
+ align:start position:0%
+following under the hood decrypt
+ 
+
+ align:start position:0%
+following under the hood decrypt
+this decrypt this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and give me only the relevant one so
+
+ align:start position:0%
+and give me only the relevant one so
+ 
+
+ align:start position:0%
+and give me only the relevant one so
+that even if this does not
+
+ align:start position:0%
+that even if this does not
+ 
+
+ align:start position:0%
+that even if this does not
+decrypt so okay so here's the point
+
+ align:start position:0%
+decrypt so okay so here's the point
+ 
+
+ align:start position:0%
+decrypt so okay so here's the point
+let's say I want to open to
+
+ align:start position:0%
+let's say I want to open to
+ 
+
+ align:start position:0%
+let's say I want to open to
+X2 okay so okay he gives me X1 these are
+
+ align:start position:0%
+X2 okay so okay he gives me X1 these are
+ 
+
+ align:start position:0%
+X2 okay so okay he gives me X1 these are
+valid so this is valid good but
+
+ align:start position:0%
+valid so this is valid good but
+ 
+
+ align:start position:0%
+valid so this is valid good but
+now Cypher Tex 2 can be completely not
+
+ align:start position:0%
+now Cypher Tex 2 can be completely not
+ 
+
+ align:start position:0%
+now Cypher Tex 2 can be completely not
+valid cuz when he opens he gives me
+
+ align:start position:0%
+valid cuz when he opens he gives me
+ 
+
+ align:start position:0%
+valid cuz when he opens he gives me
+Cypher Tex one with these two so I know
+
+ align:start position:0%
+Cypher Tex one with these two so I know
+ 
+
+ align:start position:0%
+Cypher Tex one with these two so I know
+this was valid because this is
+
+ align:start position:0%
+this was valid because this is
+ 
+
+ align:start position:0%
+this was valid because this is
+computation and then they give me Cypher
+
+ align:start position:0%
+computation and then they give me Cypher
+ 
+
+ align:start position:0%
+computation and then they give me Cypher
+Tex 2 and I do this evaluation then they
+
+ align:start position:0%
+Tex 2 and I do this evaluation then they
+ 
+
+ align:start position:0%
+Tex 2 and I do this evaluation then they
+G me so the The Sibling Cipher Tex that
+
+ align:start position:0%
+G me so the The Sibling Cipher Tex that
+ 
+
+ align:start position:0%
+G me so the The Sibling Cipher Tex that
+he gives me they may not be valid I want
+
+ align:start position:0%
+he gives me they may not be valid I want
+ 
+
+ align:start position:0%
+he gives me they may not be valid I want
+to Ure even if they're not valid even if
+
+ align:start position:0%
+to Ure even if they're not valid even if
+ 
+
+ align:start position:0%
+to Ure even if they're not valid even if
+they're not valid this is going to be
+
+ align:start position:0%
+they're not valid this is going to be
+ 
+
+ align:start position:0%
+they're not valid this is going to be
+valid the openings are going to be valid
+
+ align:start position:0%
+valid the openings are going to be valid
+ 
+
+ align:start position:0%
+valid the openings are going to be valid
+kind of the on the path things are going
+
+ align:start position:0%
+kind of the on the path things are going
+ 
+
+ align:start position:0%
+kind of the on the path things are going
+to be valid even though the siblings
+
+ align:start position:0%
+to be valid even though the siblings
+ 
+
+ align:start position:0%
+to be valid even though the siblings
+that are given in order to just kind of
+
+ align:start position:0%
+that are given in order to just kind of
+ 
+
+ align:start position:0%
+that are given in order to just kind of
+do the verify the opening even if
+
+ align:start position:0%
+do the verify the opening even if
+ 
+
+ align:start position:0%
+do the verify the opening even if
+they're not valid the opening path will
+
+ align:start position:0%
+they're not valid the opening path will
+ 
+
+ align:start position:0%
+they're not valid the opening path will
+be kind of valid Cipher texts so why are
+
+ align:start position:0%
+be kind of valid Cipher texts so why are
+ 
+
+ align:start position:0%
+be kind of valid Cipher texts so why are
+they going to be valid because the way
+
+ align:start position:0%
+they going to be valid because the way
+ 
+
+ align:start position:0%
+they going to be valid because the way
+that what is so now let's what is the
+
+ align:start position:0%
+that what is so now let's what is the
+ 
+
+ align:start position:0%
+that what is so now let's what is the
+deterministic computation that's
+
+ align:start position:0%
+deterministic computation that's
+ 
+
+ align:start position:0%
+deterministic computation that's
+happening here the deter or the
+
+ align:start position:0%
+happening here the deter or the
+ 
+
+ align:start position:0%
+happening here the deter or the
+evaluation the the evaluated Cipher Tech
+
+ align:start position:0%
+evaluation the the evaluated Cipher Tech
+ 
+
+ align:start position:0%
+evaluation the the evaluated Cipher Tech
+the way we do the evaluation is the
+
+ align:start position:0%
+the way we do the evaluation is the
+ 
+
+ align:start position:0%
+the way we do the evaluation is the
+following I decrypt this and I decrypt
+
+ align:start position:0%
+following I decrypt this and I decrypt
+ 
+
+ align:start position:0%
+following I decrypt this and I decrypt
+this and then I take the decrypted value
+
+ align:start position:0%
+this and then I take the decrypted value
+ 
+
+ align:start position:0%
+this and then I take the decrypted value
+and I encrypted with the next public key
+
+ align:start position:0%
+and I encrypted with the next public key
+ 
+
+ align:start position:0%
+and I encrypted with the next public key
+so the point is even if this didn't
+
+ align:start position:0%
+so the point is even if this didn't
+ 
+
+ align:start position:0%
+so the point is even if this didn't
+decrypt maybe this didn't decrypt I
+
+ align:start position:0%
+decrypt maybe this didn't decrypt I
+ 
+
+ align:start position:0%
+decrypt maybe this didn't decrypt I
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+care I'm this is still going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valid okay so the point is even if the
+
+ align:start position:0%
+valid okay so the point is even if the
+ 
+
+ align:start position:0%
+valid okay so the point is even if the
+The Sibling Cipher texts that are given
+
+ align:start position:0%
+The Sibling Cipher texts that are given
+ 
+
+ align:start position:0%
+The Sibling Cipher texts that are given
+only for verifying the opening even if
+
+ align:start position:0%
+only for verifying the opening even if
+ 
+
+ align:start position:0%
+only for verifying the opening even if
+these sibling Cipher text are malale
+
+ align:start position:0%
+these sibling Cipher text are malale
+ 
+
+ align:start position:0%
+these sibling Cipher text are malale
+formed if you give me the open openings
+
+ align:start position:0%
+formed if you give me the open openings
+ 
+
+ align:start position:0%
+formed if you give me the open openings
+in the entire path I get the guarantee
+
+ align:start position:0%
+in the entire path I get the guarantee
+ 
+
+ align:start position:0%
+in the entire path I get the guarantee
+that on the path not on the siblings on
+
+ align:start position:0%
+that on the path not on the siblings on
+ 
+
+ align:start position:0%
+that on the path not on the siblings on
+the path things are well formed and I
+
+ align:start position:0%
+the path things are well formed and I
+ 
+
+ align:start position:0%
+the path things are well formed and I
+mean well formed cyer these are Cipher
+
+ align:start position:0%
+mean well formed cyer these are Cipher
+ 
+
+ align:start position:0%
+mean well formed cyer these are Cipher
+Texs that decrypt
+
+ align:start position:0%
+Texs that decrypt
+ 
+
+ align:start position:0%
+Texs that decrypt
+correctly and that's what I need for for
+
+ align:start position:0%
+correctly and that's what I need for for
+ 
+
+ align:start position:0%
+correctly and that's what I need for for
+the soundness so it's important to do
+
+ align:start position:0%
+the soundness so it's important to do
+ 
+
+ align:start position:0%
+the soundness so it's important to do
+the decryption this is really uh crucial
+
+ align:start position:0%
+the decryption this is really uh crucial
+ 
+
+ align:start position:0%
+the decryption this is really uh crucial
+okay you doing each I follow okay again
+
+ align:start position:0%
+okay you doing each I follow okay again
+ 
+
+ align:start position:0%
+okay you doing each I follow okay again
+what what am I doing on each note good
+
+ align:start position:0%
+what what am I doing on each note good
+ 
+
+ align:start position:0%
+what what am I doing on each note good
+good good so here's what I'm doing on
+
+ align:start position:0%
+good good so here's what I'm doing on
+ 
+
+ align:start position:0%
+good good so here's what I'm doing on
+each Noe H the evaluation function takes
+
+ align:start position:0%
+each Noe H the evaluation function takes
+ 
+
+ align:start position:0%
+each Noe H the evaluation function takes
+kind of i j
+
+ align:start position:0%
+kind of i j
+ 
+
+ align:start position:0%
+kind of i j
+secret key j minus one and two Cipher
+
+ align:start position:0%
+secret key j minus one and two Cipher
+ 
+
+ align:start position:0%
+secret key j minus one and two Cipher
+Tex Cipher Tex zero and Cipher Tex
+
+ align:start position:0%
+Tex Cipher Tex zero and Cipher Tex
+ 
+
+ align:start position:0%
+Tex Cipher Tex zero and Cipher Tex
+one and what it does is the following
+
+ align:start position:0%
+one and what it does is the following
+ 
+
+ align:start position:0%
+one and what it does is the following
+decrypt cyppher Tex zero so it
+
+ align:start position:0%
+decrypt cyppher Tex zero so it
+ 
+
+ align:start position:0%
+decrypt cyppher Tex zero so it
+decrypts with SK J minus one uh cyppher
+
+ align:start position:0%
+decrypts with SK J minus one uh cyppher
+ 
+
+ align:start position:0%
+decrypts with SK J minus one uh cyppher
+Tex Z cyppher text B for every B get get
+
+ align:start position:0%
+Tex Z cyppher text B for every B get get
+ 
+
+ align:start position:0%
+Tex Z cyppher text B for every B get get
+some uh bit I don't know a a alpha
+
+ align:start position:0%
+some uh bit I don't know a a alpha
+ 
+
+ align:start position:0%
+some uh bit I don't know a a alpha
+B and then it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outputs one of them I know Alpha B Star
+
+ align:start position:0%
+outputs one of them I know Alpha B Star
+ 
+
+ align:start position:0%
+outputs one of them I know Alpha B Star
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+i j so so it gets to bits and he he he
+
+ align:start position:0%
+i j so so it gets to bits and he he he
+ 
+
+ align:start position:0%
+i j so so it gets to bits and he he he
+chooses one of them which one depending
+
+ align:start position:0%
+chooses one of them which one depending
+ 
+
+ align:start position:0%
+chooses one of them which one depending
+on the IG you want so what you will get
+
+ align:start position:0%
+on the IG you want so what you will get
+ 
+
+ align:start position:0%
+on the IG you want so what you will get
+the point is what you will get is really
+
+ align:start position:0%
+the point is what you will get is really
+ 
+
+ align:start position:0%
+the point is what you will get is really
+an encryption so the point is let's
+
+ align:start position:0%
+an encryption so the point is let's
+ 
+
+ align:start position:0%
+an encryption so the point is let's
+say I do it under the hood this isn't a
+
+ align:start position:0%
+say I do it under the hood this isn't a
+ 
+
+ align:start position:0%
+say I do it under the hood this isn't a
+computation that is done under the hood
+
+ align:start position:0%
+computation that is done under the hood
+ 
+
+ align:start position:0%
+computation that is done under the hood
+yes so this is going to be encrypted in
+
+ align:start position:0%
+yes so this is going to be encrypted in
+ 
+
+ align:start position:0%
+yes so this is going to be encrypted in
+and in in a box but what I'm going to do
+
+ align:start position:0%
+and in in a box but what I'm going to do
+ 
+
+ align:start position:0%
+and in in a box but what I'm going to do
+Under the box is to say so these I have
+
+ align:start position:0%
+Under the box is to say so these I have
+ 
+
+ align:start position:0%
+Under the box is to say so these I have
+so sorry these two are i j and skj minus
+
+ align:start position:0%
+so sorry these two are i j and skj minus
+ 
+
+ align:start position:0%
+so sorry these two are i j and skj minus
+one are in a box and the computation
+
+ align:start position:0%
+one are in a box and the computation
+ 
+
+ align:start position:0%
+one are in a box and the computation
+that I'm doing inside the box as I'm
+
+ align:start position:0%
+that I'm doing inside the box as I'm
+ 
+
+ align:start position:0%
+that I'm doing inside the box as I'm
+saying I have these in a box I have
+
+ align:start position:0%
+saying I have these in a box I have
+ 
+
+ align:start position:0%
+saying I have these in a box I have
+these in the clear Inside the Box what I
+
+ align:start position:0%
+these in the clear Inside the Box what I
+ 
+
+ align:start position:0%
+these in the clear Inside the Box what I
+do is the following I say I have the
+
+ align:start position:0%
+do is the following I say I have the
+ 
+
+ align:start position:0%
+do is the following I say I have the
+secret key j minus one and these two
+
+ align:start position:0%
+secret key j minus one and these two
+ 
+
+ align:start position:0%
+secret key j minus one and these two
+Cipher texts let me decrypt both of them
+
+ align:start position:0%
+Cipher texts let me decrypt both of them
+ 
+
+ align:start position:0%
+Cipher texts let me decrypt both of them
+I'm going to get two bits Alpha zero and
+
+ align:start position:0%
+I'm going to get two bits Alpha zero and
+ 
+
+ align:start position:0%
+I'm going to get two bits Alpha zero and
+Alpha One now maybe one of them is bad
+
+ align:start position:0%
+Alpha One now maybe one of them is bad
+ 
+
+ align:start position:0%
+Alpha One now maybe one of them is bad
+so but so maybe one of them doesn't
+
+ align:start position:0%
+so but so maybe one of them doesn't
+ 
+
+ align:start position:0%
+so but so maybe one of them doesn't
+decrypt so the one that doesn't decrypt
+
+ align:start position:0%
+decrypt so the one that doesn't decrypt
+ 
+
+ align:start position:0%
+decrypt so the one that doesn't decrypt
+I'll put
+
+ align:start position:0%
+I'll put
+ 
+
+ align:start position:0%
+I'll put
+bot and then the output will be the
+
+ align:start position:0%
+bot and then the output will be the
+ 
+
+ align:start position:0%
+bot and then the output will be the
+relevant one that according if if it's
+
+ align:start position:0%
+relevant one that according if if it's
+ 
+
+ align:start position:0%
+relevant one that according if if it's
+zero I'm going to Output Alpha zero if
+
+ align:start position:0%
+zero I'm going to Output Alpha zero if
+ 
+
+ align:start position:0%
+zero I'm going to Output Alpha zero if
+it's one I'm going to Output Alpha One
+
+ align:start position:0%
+it's one I'm going to Output Alpha One
+ 
+
+ align:start position:0%
+it's one I'm going to Output Alpha One
+and now what I can argue is on the path
+
+ align:start position:0%
+and now what I can argue is on the path
+ 
+
+ align:start position:0%
+and now what I can argue is on the path
+itself everything has to be well formed
+
+ align:start position:0%
+itself everything has to be well formed
+ 
+
+ align:start position:0%
+itself everything has to be well formed
+so I'm actually going to get the the
+
+ align:start position:0%
+so I'm actually going to get the the
+ 
+
+ align:start position:0%
+so I'm actually going to get the the
+correct Cipher text and I can argue that
+
+ align:start position:0%
+correct Cipher text and I can argue that
+ 
+
+ align:start position:0%
+correct Cipher text and I can argue that
+by induction Okay so
+
+ align:start position:0%
+by induction Okay so
+ 
+
+ align:start position:0%
+by induction Okay so
+here of course this is well form because
+
+ align:start position:0%
+here of course this is well form because
+ 
+
+ align:start position:0%
+here of course this is well form because
+I this is just a deterministic
+
+ align:start position:0%
+I this is just a deterministic
+ 
+
+ align:start position:0%
+I this is just a deterministic
+computation that's done locally now the
+
+ align:start position:0%
+computation that's done locally now the
+ 
+
+ align:start position:0%
+computation that's done locally now the
+point is so let's say like I I want to
+
+ align:start position:0%
+point is so let's say like I I want to
+ 
+
+ align:start position:0%
+point is so let's say like I I want to
+Output I want to I'm binding an X1 this
+
+ align:start position:0%
+Output I want to I'm binding an X1 this
+ 
+
+ align:start position:0%
+Output I want to I'm binding an X1 this
+is X1 is what I want to open Okay so
+
+ align:start position:0%
+is X1 is what I want to open Okay so
+ 
+
+ align:start position:0%
+is X1 is what I want to open Okay so
+this must be well formed and now the
+
+ align:start position:0%
+this must be well formed and now the
+ 
+
+ align:start position:0%
+this must be well formed and now the
+point is even if this is not well
+
+ align:start position:0%
+point is even if this is not well
+ 
+
+ align:start position:0%
+point is even if this is not well
+formed what will I do under the hood I'm
+
+ align:start position:0%
+formed what will I do under the hood I'm
+ 
+
+ align:start position:0%
+formed what will I do under the hood I'm
+going to open this and open this this is
+
+ align:start position:0%
+going to open this and open this this is
+ 
+
+ align:start position:0%
+going to open this and open this this is
+going to be the correct value this is
+
+ align:start position:0%
+going to be the correct value this is
+ 
+
+ align:start position:0%
+going to be the correct value this is
+not going to be maybe the correct this
+
+ align:start position:0%
+not going to be maybe the correct this
+ 
+
+ align:start position:0%
+not going to be maybe the correct this
+may be bot but this is the one I choose
+
+ align:start position:0%
+may be bot but this is the one I choose
+ 
+
+ align:start position:0%
+may be bot but this is the one I choose
+and then I encrypt it so I have it here
+
+ align:start position:0%
+and then I encrypt it so I have it here
+ 
+
+ align:start position:0%
+and then I encrypt it so I have it here
+and then again this may be bad I'm going
+
+ align:start position:0%
+and then again this may be bad I'm going
+ 
+
+ align:start position:0%
+and then again this may be bad I'm going
+to decrypt it it may be bot but this is
+
+ align:start position:0%
+to decrypt it it may be bot but this is
+ 
+
+ align:start position:0%
+to decrypt it it may be bot but this is
+going to be good and this is the one I
+
+ align:start position:0%
+going to be good and this is the one I
+ 
+
+ align:start position:0%
+going to be good and this is the one I
+choose so one can argue kind of by
+
+ align:start position:0%
+choose so one can argue kind of by
+ 
+
+ align:start position:0%
+choose so one can argue kind of by
+induction that this is going to be inp x
+
+ align:start position:0%
+induction that this is going to be inp x
+ 
+
+ align:start position:0%
+induction that this is going to be inp x
+one this is going be inp everything in
+
+ align:start position:0%
+one this is going be inp everything in
+ 
+
+ align:start position:0%
+one this is going be inp everything in
+of X1 until the end so there's no way
+
+ align:start position:0%
+of X1 until the end so there's no way
+ 
+
+ align:start position:0%
+of X1 until the end so there's no way
+you can open two different ways you have
+
+ align:start position:0%
+you can open two different ways you have
+ 
+
+ align:start position:0%
+you can open two different ways you have
+to open to
+
+ align:start position:0%
+to open to
+ 
+
+ align:start position:0%
+to open to
+X1 and the verifier is also going to do
+
+ align:start position:0%
+X1 and the verifier is also going to do
+ 
+
+ align:start position:0%
+X1 and the verifier is also going to do
+the same computation to check exactly
+
+ align:start position:0%
+the same computation to check exactly
+ 
+
+ align:start position:0%
+the same computation to check exactly
+the verifier does the exact same
+
+ align:start position:0%
+the verifier does the exact same
+ 
+
+ align:start position:0%
+the verifier does the exact same
+computation to check yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+only right this is not opening a general
+
+ align:start position:0%
+only right this is not opening a general
+ 
+
+ align:start position:0%
+only right this is not opening a general
+good so this exactly this shows that the
+
+ align:start position:0%
+good so this exactly this shows that the
+ 
+
+ align:start position:0%
+good so this exactly this shows that the
+specific uh so this
+
+ align:start position:0%
+specific uh so this
+ 
+
+ align:start position:0%
+specific uh so this
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay this shows that the specific eye
+
+ align:start position:0%
+uh okay this shows that the specific eye
+ 
+
+ align:start position:0%
+uh okay this shows that the specific eye
+that's encrypted here so there's one the
+
+ align:start position:0%
+that's encrypted here so there's one the
+ 
+
+ align:start position:0%
+that's encrypted here so there's one the
+hash key is binding on one eye on
+
+ align:start position:0%
+hash key is binding on one eye on
+ 
+
+ align:start position:0%
+hash key is binding on one eye on
+specific eye the the eye on which you're
+
+ align:start position:0%
+specific eye the the eye on which you're
+ 
+
+ align:start position:0%
+specific eye the the eye on which you're
+binding you can only open in one way uh
+
+ align:start position:0%
+binding you can only open in one way uh
+ 
+
+ align:start position:0%
+binding you can only open in one way uh
+statistically and then by the index
+
+ align:start position:0%
+statistically and then by the index
+ 
+
+ align:start position:0%
+statistically and then by the index
+hiding it means that you can only for
+
+ align:start position:0%
+hiding it means that you can only for
+ 
+
+ align:start position:0%
+hiding it means that you can only for
+any J you can only open one way
+
+ align:start position:0%
+any J you can only open one way
+ 
+
+ align:start position:0%
+any J you can only open one way
+computationally because you can
+
+ align:start position:0%
+computationally because you can
+ 
+
+ align:start position:0%
+computationally because you can
+distinguish yeah you avoid this chain of
+
+ align:start position:0%
+distinguish yeah you avoid this chain of
+ 
+
+ align:start position:0%
+distinguish yeah you avoid this chain of
+keys if you happy to
+
+ align:start position:0%
+keys if you happy to
+ 
+
+ align:start position:0%
+keys if you happy to
+ENC good very good good good yes so you
+
+ align:start position:0%
+ENC good very good good good yes so you
+ 
+
+ align:start position:0%
+ENC good very good good good yes so you
+can avoid uh you can avoid avoid using
+
+ align:start position:0%
+can avoid uh you can avoid avoid using
+ 
+
+ align:start position:0%
+can avoid uh you can avoid avoid using
+many public Keys you can just use one
+
+ align:start position:0%
+many public Keys you can just use one
+ 
+
+ align:start position:0%
+many public Keys you can just use one
+public key encrypt the secret key and
+
+ align:start position:0%
+public key encrypt the secret key and
+ 
+
+ align:start position:0%
+public key encrypt the secret key and
+and rely on what's called circular
+
+ align:start position:0%
+and rely on what's called circular
+ 
+
+ align:start position:0%
+and rely on what's called circular
+security that's another option if you
+
+ align:start position:0%
+security that's another option if you
+ 
+
+ align:start position:0%
+security that's another option if you
+wish s doesn't want to do
+
+ align:start position:0%
+wish s doesn't want to do
+ 
+
+ align:start position:0%
+wish s doesn't want to do
+that but yes
+
+ align:start position:0%
+that but yes
+ 
+
+ align:start position:0%
+that but yes
+exactly exactly
+
+ align:start position:0%
+exactly exactly
+ 
+
+ align:start position:0%
+exactly exactly
+yeah you see get
+
+ align:start position:0%
+yeah you see get
+ 
+
+ align:start position:0%
+yeah you see get
+resistance you okay so yeah so you're
+
+ align:start position:0%
+resistance you okay so yeah so you're
+ 
+
+ align:start position:0%
+resistance you okay so yeah so you're
+asking will you get uh Collision like
+
+ align:start position:0%
+asking will you get uh Collision like
+ 
+
+ align:start position:0%
+asking will you get uh Collision like
+Collision resistance and the answer is
+
+ align:start position:0%
+Collision resistance and the answer is
+ 
+
+ align:start position:0%
+Collision resistance and the answer is
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+because for the specific eye that you
+
+ align:start position:0%
+because for the specific eye that you
+ 
+
+ align:start position:0%
+because for the specific eye that you
+for the specific ey that kind of you en
+
+ align:start position:0%
+for the specific ey that kind of you en
+ 
+
+ align:start position:0%
+for the specific ey that kind of you en
+encrypted in the hash key you get uh
+
+ align:start position:0%
+encrypted in the hash key you get uh
+ 
+
+ align:start position:0%
+encrypted in the hash key you get uh
+binding kind of statistically okay
+
+ align:start position:0%
+binding kind of statistically okay
+ 
+
+ align:start position:0%
+binding kind of statistically okay
+there's no way you can open two
+
+ align:start position:0%
+there's no way you can open two
+ 
+
+ align:start position:0%
+there's no way you can open two
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+and what you have at the end is just the
+
+ align:start position:0%
+and what you have at the end is just the
+ 
+
+ align:start position:0%
+and what you have at the end is just the
+encryption of that Index right right so
+
+ align:start position:0%
+encryption of that Index right right so
+ 
+
+ align:start position:0%
+encryption of that Index right right so
+you're asking about a different J oh
+
+ align:start position:0%
+you're asking about a different J oh
+ 
+
+ align:start position:0%
+you're asking about a different J oh
+sorry no that you you have two x's that
+
+ align:start position:0%
+sorry no that you you have two x's that
+ 
+
+ align:start position:0%
+sorry no that you you have two x's that
+have the same uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+index have the same that index and then
+
+ align:start position:0%
+index have the same that index and then
+ 
+
+ align:start position:0%
+index have the same that index and then
+but the are
+
+ align:start position:0%
+but the are
+ 
+
+ align:start position:0%
+but the are
+different you get a different outut of
+
+ align:start position:0%
+different you get a different outut of
+ 
+
+ align:start position:0%
+different you get a different outut of
+the if you take those two different X
+
+ align:start position:0%
+the if you take those two different X
+ 
+
+ align:start position:0%
+the if you take those two different X
+good good good okay so if you take two
+
+ align:start position:0%
+good good good okay so if you take two
+ 
+
+ align:start position:0%
+good good good okay so if you take two
+different X's for which let's say they
+
+ align:start position:0%
+different X's for which let's say they
+ 
+
+ align:start position:0%
+different X's for which let's say they
+have the same X1 and let's say the hash
+
+ align:start position:0%
+have the same X1 and let's say the hash
+ 
+
+ align:start position:0%
+have the same X1 and let's say the hash
+key is binding on location
+
+ align:start position:0%
+key is binding on location
+ 
+
+ align:start position:0%
+key is binding on location
+one the value would get if you if you
+
+ align:start position:0%
+one the value would get if you if you
+ 
+
+ align:start position:0%
+one the value would get if you if you
+hash them honestly will be actually very
+
+ align:start position:0%
+hash them honestly will be actually very
+ 
+
+ align:start position:0%
+hash them honestly will be actually very
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+but because you use different X's but so
+
+ align:start position:0%
+but because you use different X's but so
+ 
+
+ align:start position:0%
+but because you use different X's but so
+you'll get different values but if you
+
+ align:start position:0%
+you'll get different values but if you
+ 
+
+ align:start position:0%
+you'll get different values but if you
+decrypt these values correspond to a
+
+ align:start position:0%
+decrypt these values correspond to a
+ 
+
+ align:start position:0%
+decrypt these values correspond to a
+cyppher text as values they're going to
+
+ align:start position:0%
+cyppher text as values they're going to
+ 
+
+ align:start position:0%
+cyppher text as values they're going to
+look very different but if you decrypt
+
+ align:start position:0%
+look very different but if you decrypt
+ 
+
+ align:start position:0%
+look very different but if you decrypt
+you will get the same bit which is
+
+ align:start position:0%
+you will get the same bit which is
+ 
+
+ align:start position:0%
+you will get the same bit which is
+X1 yeah good okay so anyway if you if
+
+ align:start position:0%
+X1 yeah good okay so anyway if you if
+ 
+
+ align:start position:0%
+X1 yeah good okay so anyway if you if
+you didn't follow the exact construction
+
+ align:start position:0%
+you didn't follow the exact construction
+ 
+
+ align:start position:0%
+you didn't follow the exact construction
+it doesn't really matter I just wanted
+
+ align:start position:0%
+it doesn't really matter I just wanted
+ 
+
+ align:start position:0%
+it doesn't really matter I just wanted
+to make sure that uh uh you know this it
+
+ align:start position:0%
+to make sure that uh uh you know this it
+ 
+
+ align:start position:0%
+to make sure that uh uh you know this it
+was clear that you really needed to do
+
+ align:start position:0%
+was clear that you really needed to do
+ 
+
+ align:start position:0%
+was clear that you really needed to do
+this decryption uh yeah the reason you
+
+ align:start position:0%
+this decryption uh yeah the reason you
+ 
+
+ align:start position:0%
+this decryption uh yeah the reason you
+don't need circular security as it is
+
+ align:start position:0%
+don't need circular security as it is
+ 
+
+ align:start position:0%
+don't need circular security as it is
+for this F is that each of these
+
+ align:start position:0%
+for this F is that each of these
+ 
+
+ align:start position:0%
+for this F is that each of these
+computations is simple enough that you
+
+ align:start position:0%
+computations is simple enough that you
+ 
+
+ align:start position:0%
+computations is simple enough that you
+don't need to like the bo strap is that
+
+ align:start position:0%
+don't need to like the bo strap is that
+ 
+
+ align:start position:0%
+don't need to like the bo strap is that
+the reason Okay the reason I don't need
+
+ align:start position:0%
+the reason Okay the reason I don't need
+ 
+
+ align:start position:0%
+the reason Okay the reason I don't need
+uh uh um circular security is I'm I'm
+
+ align:start position:0%
+uh uh um circular security is I'm I'm
+ 
+
+ align:start position:0%
+uh uh um circular security is I'm I'm
+never
+
+ align:start position:0%
+never
+ 
+
+ align:start position:0%
+never
+encrypting a secret key under its
+
+ align:start position:0%
+encrypting a secret key under its
+ 
+
+ align:start position:0%
+encrypting a secret key under its
+publicy so sorry asking why the you're
+
+ align:start position:0%
+publicy so sorry asking why the you're
+ 
+
+ align:start position:0%
+publicy so sorry asking why the you're
+using not need to be
+
+ align:start position:0%
+using not need to be
+ 
+
+ align:start position:0%
+using not need to be
+unbounded oh oh oh okay okay okay you're
+
+ align:start position:0%
+unbounded oh oh oh okay okay okay you're
+ 
+
+ align:start position:0%
+unbounded oh oh oh okay okay okay you're
+saying okay sorry sorry you're you're
+
+ align:start position:0%
+saying okay sorry sorry you're you're
+ 
+
+ align:start position:0%
+saying okay sorry sorry you're you're
+asking okay got it you're saying well in
+
+ align:start position:0%
+asking okay got it you're saying well in
+ 
+
+ align:start position:0%
+asking okay got it you're saying well in
+general if we want arbitrary FHA we need
+
+ align:start position:0%
+general if we want arbitrary FHA we need
+ 
+
+ align:start position:0%
+general if we want arbitrary FHA we need
+to assume circular secure LW inside it
+
+ align:start position:0%
+to assume circular secure LW inside it
+ 
+
+ align:start position:0%
+to assume circular secure LW inside it
+kind of and you're asking do we not need
+
+ align:start position:0%
+kind of and you're asking do we not need
+ 
+
+ align:start position:0%
+kind of and you're asking do we not need
+to assum like you're kind of going into
+
+ align:start position:0%
+to assum like you're kind of going into
+ 
+
+ align:start position:0%
+to assum like you're kind of going into
+the you're saying do we actually need
+
+ align:start position:0%
+the you're saying do we actually need
+ 
+
+ align:start position:0%
+the you're saying do we actually need
+fully fully fully homomorphic encryption
+
+ align:start position:0%
+fully fully fully homomorphic encryption
+ 
+
+ align:start position:0%
+fully fully fully homomorphic encryption
+because if we do then actually we need
+
+ align:start position:0%
+because if we do then actually we need
+ 
+
+ align:start position:0%
+because if we do then actually we need
+to rely on like a circle security
+
+ align:start position:0%
+to rely on like a circle security
+ 
+
+ align:start position:0%
+to rely on like a circle security
+assumption inside too the answer is we
+
+ align:start position:0%
+assumption inside too the answer is we
+ 
+
+ align:start position:0%
+assumption inside too the answer is we
+we because the computation is very
+
+ align:start position:0%
+we because the computation is very
+ 
+
+ align:start position:0%
+we because the computation is very
+specific and very small depth you don't
+
+ align:start position:0%
+specific and very small depth you don't
+ 
+
+ align:start position:0%
+specific and very small depth you don't
+need to there's no you don't need like
+
+ align:start position:0%
+need to there's no you don't need like
+ 
+
+ align:start position:0%
+need to there's no you don't need like
+full full FH you need FH for very
+
+ align:start position:0%
+full full FH you need FH for very
+ 
+
+ align:start position:0%
+full full FH you need FH for very
+bounded depth
+
+ align:start position:0%
+bounded depth
+ 
+
+ align:start position:0%
+bounded depth
+computations yeah great thank you a any
+
+ align:start position:0%
+computations yeah great thank you a any
+ 
+
+ align:start position:0%
+computations yeah great thank you a any
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so let's
+
+ align:start position:0%
+questions okay so let's
+ 
+
+ align:start position:0%
+questions okay so let's
+snar well let me just make sure I
+
+ align:start position:0%
+snar well let me just make sure I
+ 
+
+ align:start position:0%
+snar well let me just make sure I
+covered everything I wanted
+
+ align:start position:0%
+covered everything I wanted
+ 
+
+ align:start position:0%
+covered everything I wanted
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to okay after three months we SN we snar
+
+ align:start position:0%
+to okay after three months we SN we snar
+ 
+
+ align:start position:0%
+to okay after three months we SN we snar
+okay the last kind of two hours in class
+
+ align:start position:0%
+okay the last kind of two hours in class
+ 
+
+ align:start position:0%
+okay the last kind of two hours in class
+last we're going to
+
+ align:start position:0%
+last we're going to
+ 
+
+ align:start position:0%
+last we're going to
+snar okay
+
+ align:start position:0%
+snar okay
+ 
+
+ align:start position:0%
+snar okay
+so okay so now the snar is really simple
+
+ align:start position:0%
+so okay so now the snar is really simple
+ 
+
+ align:start position:0%
+so okay so now the snar is really simple
+it's like as simple as one can like you
+
+ align:start position:0%
+it's like as simple as one can like you
+ 
+
+ align:start position:0%
+it's like as simple as one can like you
+essentially can do it done we're done
+
+ align:start position:0%
+essentially can do it done we're done
+ 
+
+ align:start position:0%
+essentially can do it done we're done
+okay so how do we we can go home uh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so anybody want a cookie before we
+
+ align:start position:0%
+so anybody want a cookie before we
+ 
+
+ align:start position:0%
+so anybody want a cookie before we
+snar I feel like these grandmothers that
+
+ align:start position:0%
+snar I feel like these grandmothers that
+ 
+
+ align:start position:0%
+snar I feel like these grandmothers that
+kind of you know constantly feed
+
+ align:start position:0%
+kind of you know constantly feed
+ 
+
+ align:start position:0%
+kind of you know constantly feed
+you okay so here's the idea the idea is
+
+ align:start position:0%
+you okay so here's the idea the idea is
+ 
+
+ align:start position:0%
+you okay so here's the idea the idea is
+very simple take any so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+snar okay so let me first say kind of
+
+ align:start position:0%
+snar okay so let me first say kind of
+ 
+
+ align:start position:0%
+snar okay so let me first say kind of
+the high level idea the high level idea
+
+ align:start position:0%
+the high level idea the high level idea
+ 
+
+ align:start position:0%
+the high level idea the high level idea
+is the following here's what the prover
+
+ align:start position:0%
+is the following here's what the prover
+ 
+
+ align:start position:0%
+is the following here's what the prover
+will do the so the prover wants to
+
+ align:start position:0%
+will do the so the prover wants to
+ 
+
+ align:start position:0%
+will do the so the prover wants to
+convince that X is in the language
+
+ align:start position:0%
+convince that X is in the language
+ 
+
+ align:start position:0%
+convince that X is in the language
+there's some verification circuit so you
+
+ align:start position:0%
+there's some verification circuit so you
+ 
+
+ align:start position:0%
+there's some verification circuit so you
+have X let's start with let's take X in
+
+ align:start position:0%
+have X let's start with let's take X in
+ 
+
+ align:start position:0%
+have X let's start with let's take X in
+the language
+
+ align:start position:0%
+the language
+ 
+
+ align:start position:0%
+the language
+or there is some for any X you know it
+
+ align:start position:0%
+or there is some for any X you know it
+ 
+
+ align:start position:0%
+or there is some for any X you know it
+doesn't matter for any
+
+ align:start position:0%
+doesn't matter for any
+ 
+
+ align:start position:0%
+doesn't matter for any
+X you have a circuit C
+
+ align:start position:0%
+X you have a circuit C
+ 
+
+ align:start position:0%
+X you have a circuit C
+subx and C subx takes a
+
+ align:start position:0%
+subx and C subx takes a
+ 
+
+ align:start position:0%
+subx and C subx takes a
+witness and now put 0 one like it's a
+
+ align:start position:0%
+witness and now put 0 one like it's a
+ 
+
+ align:start position:0%
+witness and now put 0 one like it's a
+verification circuit you can also think
+
+ align:start position:0%
+verification circuit you can also think
+ 
+
+ align:start position:0%
+verification circuit you can also think
+of it if you want
+
+ align:start position:0%
+of it if you want
+ 
+
+ align:start position:0%
+of it if you want
+c as taking X and a witness and I'll put
+
+ align:start position:0%
+c as taking X and a witness and I'll put
+ 
+
+ align:start position:0%
+c as taking X and a witness and I'll put
+zero if it's a not valid witness and one
+
+ align:start position:0%
+zero if it's a not valid witness and one
+ 
+
+ align:start position:0%
+zero if it's a not valid witness and one
+if it's a valid Witness if it's a
+
+ align:start position:0%
+if it's a valid Witness if it's a
+ 
+
+ align:start position:0%
+if it's a valid Witness if it's a
+deterministic computation there's no
+
+ align:start position:0%
+deterministic computation there's no
+ 
+
+ align:start position:0%
+deterministic computation there's no
+witness just say x and output zero or
+
+ align:start position:0%
+witness just say x and output zero or
+ 
+
+ align:start position:0%
+witness just say x and output zero or
+one that's the
+
+ align:start position:0%
+one that's the
+ 
+
+ align:start position:0%
+one that's the
+computation okay so when when I talk
+
+ align:start position:0%
+computation okay so when when I talk
+ 
+
+ align:start position:0%
+computation okay so when when I talk
+about snarky you can think of snar of
+
+ align:start position:0%
+about snarky you can think of snar of
+ 
+
+ align:start position:0%
+about snarky you can think of snar of
+non- deterministic snar of deterministic
+
+ align:start position:0%
+non- deterministic snar of deterministic
+ 
+
+ align:start position:0%
+non- deterministic snar of deterministic
+any language L I don't even want to go
+
+ align:start position:0%
+any language L I don't even want to go
+ 
+
+ align:start position:0%
+any language L I don't even want to go
+to specific okay but when I have a
+
+ align:start position:0%
+to specific okay but when I have a
+ 
+
+ align:start position:0%
+to specific okay but when I have a
+language L you know what how what does
+
+ align:start position:0%
+language L you know what how what does
+ 
+
+ align:start position:0%
+language L you know what how what does
+it mean a language well there's some
+
+ align:start position:0%
+it mean a language well there's some
+ 
+
+ align:start position:0%
+it mean a language well there's some
+circuit it takes the instance maybe with
+
+ align:start position:0%
+circuit it takes the instance maybe with
+ 
+
+ align:start position:0%
+circuit it takes the instance maybe with
+a witness and the circuit kind of does
+
+ align:start position:0%
+a witness and the circuit kind of does
+ 
+
+ align:start position:0%
+a witness and the circuit kind of does
+some checks to decide if it's valid or
+
+ align:start position:0%
+some checks to decide if it's valid or
+ 
+
+ align:start position:0%
+some checks to decide if it's valid or
+not valid
+
+ align:start position:0%
+not valid
+ 
+
+ align:start position:0%
+not valid
+okay now I want to convince you I have
+
+ align:start position:0%
+okay now I want to convince you I have
+ 
+
+ align:start position:0%
+okay now I want to convince you I have
+an X I want to give you a snar that this
+
+ align:start position:0%
+an X I want to give you a snar that this
+ 
+
+ align:start position:0%
+an X I want to give you a snar that this
+C an X outputs one either that there's a
+
+ align:start position:0%
+C an X outputs one either that there's a
+ 
+
+ align:start position:0%
+C an X outputs one either that there's a
+witness say that outputs one or maybe
+
+ align:start position:0%
+witness say that outputs one or maybe
+ 
+
+ align:start position:0%
+witness say that outputs one or maybe
+it's DET terministic so just C of X Out
+
+ align:start position:0%
+it's DET terministic so just C of X Out
+ 
+
+ align:start position:0%
+it's DET terministic so just C of X Out
+outputs one here's what I'm going to do
+
+ align:start position:0%
+outputs one here's what I'm going to do
+ 
+
+ align:start position:0%
+outputs one here's what I'm going to do
+what I'm going to do I'm going to
+
+ align:start position:0%
+what I'm going to do I'm going to
+ 
+
+ align:start position:0%
+what I'm going to do I'm going to
+compute all the wires of this circuit
+
+ align:start position:0%
+compute all the wires of this circuit
+ 
+
+ align:start position:0%
+compute all the wires of this circuit
+I'm all the wires and I'm going to give
+
+ align:start position:0%
+I'm all the wires and I'm going to give
+ 
+
+ align:start position:0%
+I'm all the wires and I'm going to give
+you a hash of all the wires now there's
+
+ align:start position:0%
+you a hash of all the wires now there's
+ 
+
+ align:start position:0%
+you a hash of all the wires now there's
+a lot of wires so it's going to be a
+
+ align:start position:0%
+a lot of wires so it's going to be a
+ 
+
+ align:start position:0%
+a lot of wires so it's going to be a
+shrinking
+
+ align:start position:0%
+shrinking
+ 
+
+ align:start position:0%
+shrinking
+hash I'm gonna actually use a somewh
+
+ align:start position:0%
+hash I'm gonna actually use a somewh
+ 
+
+ align:start position:0%
+hash I'm gonna actually use a somewh
+extractable
+
+ align:start position:0%
+extractable
+ 
+
+ align:start position:0%
+extractable
+hash
+
+ align:start position:0%
+hash
+ 
+
+ align:start position:0%
+hash
+so let's say we agreed on a hash key for
+
+ align:start position:0%
+so let's say we agreed on a hash key for
+ 
+
+ align:start position:0%
+so let's say we agreed on a hash key for
+somewhere extractable hash I the prover
+
+ align:start position:0%
+somewhere extractable hash I the prover
+ 
+
+ align:start position:0%
+somewhere extractable hash I the prover
+I'm going to compute all the wires of
+
+ align:start position:0%
+I'm going to compute all the wires of
+ 
+
+ align:start position:0%
+I'm going to compute all the wires of
+this verification
+
+ align:start position:0%
+this verification
+ 
+
+ align:start position:0%
+this verification
+circuit and I'm going to give you the
+
+ align:start position:0%
+circuit and I'm going to give you the
+ 
+
+ align:start position:0%
+circuit and I'm going to give you the
+hash the hash of the the values of all
+
+ align:start position:0%
+hash the hash of the the values of all
+ 
+
+ align:start position:0%
+hash the hash of the the values of all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+wires okay hash what are you going to do
+
+ align:start position:0%
+wires okay hash what are you going to do
+ 
+
+ align:start position:0%
+wires okay hash what are you going to do
+with that so the other thing I'm going
+
+ align:start position:0%
+with that so the other thing I'm going
+ 
+
+ align:start position:0%
+with that so the other thing I'm going
+to give you is I'm going to give you a
+
+ align:start position:0%
+to give you is I'm going to give you a
+ 
+
+ align:start position:0%
+to give you is I'm going to give you a
+bar a proof a bar of what the bark I'm
+
+ align:start position:0%
+bar a proof a bar of what the bark I'm
+ 
+
+ align:start position:0%
+bar a proof a bar of what the bark I'm
+going to give you is that every gate
+
+ align:start position:0%
+going to give you is that every gate
+ 
+
+ align:start position:0%
+going to give you is that every gate
+here is satisfied so I committed to all
+
+ align:start position:0%
+here is satisfied so I committed to all
+ 
+
+ align:start position:0%
+here is satisfied so I committed to all
+the wires I can commit to anything I I
+
+ align:start position:0%
+the wires I can commit to anything I I
+ 
+
+ align:start position:0%
+the wires I can commit to anything I I
+mean I hashed all the wires now I'm
+
+ align:start position:0%
+mean I hashed all the wires now I'm
+ 
+
+ align:start position:0%
+mean I hashed all the wires now I'm
+going to prove to you that for any gate
+
+ align:start position:0%
+going to prove to you that for any gate
+ 
+
+ align:start position:0%
+going to prove to you that for any gate
+if you look at kind of the
+
+ align:start position:0%
+if you look at kind of the
+ 
+
+ align:start position:0%
+if you look at kind of the
+two the in the two input wires to the
+
+ align:start position:0%
+two the in the two input wires to the
+ 
+
+ align:start position:0%
+two the in the two input wires to the
+gate and the output wire of the gate
+
+ align:start position:0%
+gate and the output wire of the gate
+ 
+
+ align:start position:0%
+gate and the output wire of the gate
+they satisfy the gate so for any for all
+
+ align:start position:0%
+they satisfy the gate so for any for all
+ 
+
+ align:start position:0%
+they satisfy the gate so for any for all
+every gate in the circuit I'm going to
+
+ align:start position:0%
+every gate in the circuit I'm going to
+ 
+
+ align:start position:0%
+every gate in the circuit I'm going to
+prove to you that there exists an
+
+ align:start position:0%
+prove to you that there exists an
+ 
+
+ align:start position:0%
+prove to you that there exists an
+opening to this wire and an opening to
+
+ align:start position:0%
+opening to this wire and an opening to
+ 
+
+ align:start position:0%
+opening to this wire and an opening to
+this wire and to this wire such that
+
+ align:start position:0%
+this wire and to this wire such that
+ 
+
+ align:start position:0%
+this wire and to this wire such that
+these openings are valid and that the
+
+ align:start position:0%
+these openings are valid and that the
+ 
+
+ align:start position:0%
+these openings are valid and that the
+values that I opened accept the the kind
+
+ align:start position:0%
+values that I opened accept the the kind
+ 
+
+ align:start position:0%
+values that I opened accept the the kind
+of respect the
+
+ align:start position:0%
+of respect the
+ 
+
+ align:start position:0%
+of respect the
+gate and I'm going to prove to you that
+
+ align:start position:0%
+gate and I'm going to prove to you that
+ 
+
+ align:start position:0%
+gate and I'm going to prove to you that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+output that so I I I I said that I I
+
+ align:start position:0%
+output that so I I I I said that I I
+ 
+
+ align:start position:0%
+output that so I I I I said that I I
+hashed all the wires I'm going to argue
+
+ align:start position:0%
+hashed all the wires I'm going to argue
+ 
+
+ align:start position:0%
+hashed all the wires I'm going to argue
+I'm going to open the output wire so you
+
+ align:start position:0%
+I'm going to open the output wire so you
+ 
+
+ align:start position:0%
+I'm going to open the output wire so you
+see the end output is one so again what
+
+ align:start position:0%
+see the end output is one so again what
+ 
+
+ align:start position:0%
+see the end output is one so again what
+am I going to do I want to I want to
+
+ align:start position:0%
+am I going to do I want to I want to
+ 
+
+ align:start position:0%
+am I going to do I want to I want to
+convince you that the output here is
+
+ align:start position:0%
+convince you that the output here is
+ 
+
+ align:start position:0%
+convince you that the output here is
+one I'm going to Hash all the wires the
+
+ align:start position:0%
+one I'm going to Hash all the wires the
+ 
+
+ align:start position:0%
+one I'm going to Hash all the wires the
+value of all the wires in the
+
+ align:start position:0%
+value of all the wires in the
+ 
+
+ align:start position:0%
+value of all the wires in the
+circuit I'm going to prove that every
+
+ align:start position:0%
+circuit I'm going to prove that every
+ 
+
+ align:start position:0%
+circuit I'm going to prove that every
+gate is kind of satisfied I have an
+
+ align:start position:0%
+gate is kind of satisfied I have an
+ 
+
+ align:start position:0%
+gate is kind of satisfied I have an
+opening that's kind of respects each and
+
+ align:start position:0%
+opening that's kind of respects each and
+ 
+
+ align:start position:0%
+opening that's kind of respects each and
+every gate and the output wire is
+
+ align:start position:0%
+every gate and the output wire is
+ 
+
+ align:start position:0%
+every gate and the output wire is
+one that's my SN yeah how's this
+
+ align:start position:0%
+one that's my SN yeah how's this
+ 
+
+ align:start position:0%
+one that's my SN yeah how's this
+different from gkr okay how is this
+
+ align:start position:0%
+different from gkr okay how is this
+ 
+
+ align:start position:0%
+different from gkr okay how is this
+different from gkr uh G okay so gkr is
+
+ align:start position:0%
+different from gkr uh G okay so gkr is
+ 
+
+ align:start position:0%
+different from gkr uh G okay so gkr is
+uh is very different in many ways first
+
+ align:start position:0%
+uh is very different in many ways first
+ 
+
+ align:start position:0%
+uh is very different in many ways first
+of all it's a interactive protocol now
+
+ align:start position:0%
+of all it's a interactive protocol now
+ 
+
+ align:start position:0%
+of all it's a interactive protocol now
+you can apply F to it but essentially in
+
+ align:start position:0%
+you can apply F to it but essentially in
+ 
+
+ align:start position:0%
+you can apply F to it but essentially in
+gkr you kind of take the circuit you
+
+ align:start position:0%
+gkr you kind of take the circuit you
+ 
+
+ align:start position:0%
+gkr you kind of take the circuit you
+compute all the wires in the circuit but
+
+ align:start position:0%
+compute all the wires in the circuit but
+ 
+
+ align:start position:0%
+compute all the wires in the circuit but
+actually I don't bar say look all the
+
+ align:start position:0%
+actually I don't bar say look all the
+ 
+
+ align:start position:0%
+actually I don't bar say look all the
+wires are satisfied instead I'm going to
+
+ align:start position:0%
+wires are satisfied instead I'm going to
+ 
+
+ align:start position:0%
+wires are satisfied instead I'm going to
+kind of we're doing an interactive
+
+ align:start position:0%
+kind of we're doing an interactive
+ 
+
+ align:start position:0%
+kind of we're doing an interactive
+process saying oh I'm going to I argue
+
+ align:start position:0%
+process saying oh I'm going to I argue
+ 
+
+ align:start position:0%
+process saying oh I'm going to I argue
+the output wies one and then we do kind
+
+ align:start position:0%
+the output wies one and then we do kind
+ 
+
+ align:start position:0%
+the output wies one and then we do kind
+of a little sum check or some inve
+
+ align:start position:0%
+of a little sum check or some inve
+ 
+
+ align:start position:0%
+of a little sum check or some inve
+process to reduce checking that value to
+
+ align:start position:0%
+process to reduce checking that value to
+ 
+
+ align:start position:0%
+process to reduce checking that value to
+checking a value in one layer below and
+
+ align:start position:0%
+checking a value in one layer below and
+ 
+
+ align:start position:0%
+checking a value in one layer below and
+then we do an instructive process to say
+
+ align:start position:0%
+then we do an instructive process to say
+ 
+
+ align:start position:0%
+then we do an instructive process to say
+Okay if that was false you know then the
+
+ align:start position:0%
+Okay if that was false you know then the
+ 
+
+ align:start position:0%
+Okay if that was false you know then the
+layer below needs to be false until we
+
+ align:start position:0%
+layer below needs to be false until we
+ 
+
+ align:start position:0%
+layer below needs to be false until we
+reach the the leaves and then you can
+
+ align:start position:0%
+reach the the leaves and then you can
+ 
+
+ align:start position:0%
+reach the the leaves and then you can
+apply F chamir to that to kind of make
+
+ align:start position:0%
+apply F chamir to that to kind of make
+ 
+
+ align:start position:0%
+apply F chamir to that to kind of make
+it a
+
+ align:start position:0%
+it a
+ 
+
+ align:start position:0%
+it a
+snar here we're doing something very
+
+ align:start position:0%
+snar here we're doing something very
+ 
+
+ align:start position:0%
+snar here we're doing something very
+differently we're starting with a bar
+
+ align:start position:0%
+differently we're starting with a bar
+ 
+
+ align:start position:0%
+differently we're starting with a bar
+now it's true that the construction you
+
+ align:start position:0%
+now it's true that the construction you
+ 
+
+ align:start position:0%
+now it's true that the construction you
+saw for bar uses F also but some
+
+ align:start position:0%
+saw for bar uses F also but some
+ 
+
+ align:start position:0%
+saw for bar uses F also but some
+constructions don't use f actually for
+
+ align:start position:0%
+constructions don't use f actually for
+ 
+
+ align:start position:0%
+constructions don't use f actually for
+bar there are various constructions of
+
+ align:start position:0%
+bar there are various constructions of
+ 
+
+ align:start position:0%
+bar there are various constructions of
+bargs you saw one of them but there are
+
+ align:start position:0%
+bargs you saw one of them but there are
+ 
+
+ align:start position:0%
+bargs you saw one of them but there are
+others so we say take any
+
+ align:start position:0%
+others so we say take any
+ 
+
+ align:start position:0%
+others so we say take any
+bar and there's no interaction here like
+
+ align:start position:0%
+bar and there's no interaction here like
+ 
+
+ align:start position:0%
+bar and there's no interaction here like
+besides maybe they're inside the bark
+
+ align:start position:0%
+besides maybe they're inside the bark
+ 
+
+ align:start position:0%
+besides maybe they're inside the bark
+but maybe the bark doesn't have any F or
+
+ align:start position:0%
+but maybe the bark doesn't have any F or
+ 
+
+ align:start position:0%
+but maybe the bark doesn't have any F or
+anything to it and we're saying just
+
+ align:start position:0%
+anything to it and we're saying just
+ 
+
+ align:start position:0%
+anything to it and we're saying just
+hash all the wires of the circuit and
+
+ align:start position:0%
+hash all the wires of the circuit and
+ 
+
+ align:start position:0%
+hash all the wires of the circuit and
+prove that everything is consistent
+
+ align:start position:0%
+prove that everything is consistent
+ 
+
+ align:start position:0%
+prove that everything is consistent
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+it that's really what we're
+
+ align:start position:0%
+it that's really what we're
+ 
+
+ align:start position:0%
+it that's really what we're
+doing so let me write this down so it
+
+ align:start position:0%
+doing so let me write this down so it
+ 
+
+ align:start position:0%
+doing so let me write this down so it
+will be so that my ingredients that I
+
+ align:start position:0%
+will be so that my ingredients that I
+ 
+
+ align:start position:0%
+will be so that my ingredients that I
+have for my snar is uh so okay so
+
+ align:start position:0%
+have for my snar is uh so okay so
+ 
+
+ align:start position:0%
+have for my snar is uh so okay so
+ingredients maybe I'll write it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ingredients is a
+
+ align:start position:0%
+ingredients is a
+ 
+
+ align:start position:0%
+ingredients is a
+bar and Sumer extractable
+
+ align:start position:0%
+bar and Sumer extractable
+ 
+
+ align:start position:0%
+bar and Sumer extractable
+hash these are my ingredients and I'm
+
+ align:start position:0%
+hash these are my ingredients and I'm
+ 
+
+ align:start position:0%
+hash these are my ingredients and I'm
+going to show you my snar okay so snar
+
+ align:start position:0%
+going to show you my snar okay so snar
+ 
+
+ align:start position:0%
+going to show you my snar okay so snar
+has uh three algorithms we have a gen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm and here's what my gen
+
+ align:start position:0%
+algorithm and here's what my gen
+ 
+
+ align:start position:0%
+algorithm and here's what my gen
+algorithm is going to
+
+ align:start position:0%
+algorithm is going to
+ 
+
+ align:start position:0%
+algorithm is going to
+do it's going to let's say the Gen also
+
+ align:start position:0%
+do it's going to let's say the Gen also
+ 
+
+ align:start position:0%
+do it's going to let's say the Gen also
+has an input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length ah we don't need it
+
+ align:start position:0%
+length ah we don't need it
+ 
+
+ align:start position:0%
+length ah we don't need it
+okay here's what it's going to okay
+
+ align:start position:0%
+okay here's what it's going to okay
+ 
+
+ align:start position:0%
+okay here's what it's going to okay
+let's say it has an input
+
+ align:start position:0%
+let's say it has an input
+ 
+
+ align:start position:0%
+let's say it has an input
+length so this says you know you're
+
+ align:start position:0%
+length so this says you know you're
+ 
+
+ align:start position:0%
+length so this says you know you're
+going to prove to me statements of
+
+ align:start position:0%
+going to prove to me statements of
+ 
+
+ align:start position:0%
+going to prove to me statements of
+length that the input X is of length n
+
+ align:start position:0%
+length that the input X is of length n
+ 
+
+ align:start position:0%
+length that the input X is of length n
+okay so here's what we're going to do
+
+ align:start position:0%
+okay so here's what we're going to do
+ 
+
+ align:start position:0%
+okay so here's what we're going to do
+first thing we do is we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generate a hash
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key for Gen of the Sumer extractable
+
+ align:start position:0%
+key for Gen of the Sumer extractable
+ 
+
+ align:start position:0%
+key for Gen of the Sumer extractable
+hash so generate a hash key
+
+ align:start position:0%
+hash so generate a hash key
+ 
+
+ align:start position:0%
+hash so generate a hash key
+corresponding to the summer extractable
+
+ align:start position:0%
+corresponding to the summer extractable
+ 
+
+ align:start position:0%
+corresponding to the summer extractable
+hash this is going to be with security
+
+ align:start position:0%
+hash this is going to be with security
+ 
+
+ align:start position:0%
+hash this is going to be with security
+parameter n is going to
+
+ align:start position:0%
+parameter n is going to
+ 
+
+ align:start position:0%
+parameter n is going to
+be this is going to be number of
+
+ align:start position:0%
+be this is going to be number of
+ 
+
+ align:start position:0%
+be this is going to be number of
+wires in the circuit C this is the
+
+ align:start position:0%
+wires in the circuit C this is the
+ 
+
+ align:start position:0%
+wires in the circuit C this is the
+circuit that takes X of length n
+
+ align:start position:0%
+circuit that takes X of length n
+ 
+
+ align:start position:0%
+circuit that takes X of length n
+possibly a witness and output zero or
+
+ align:start position:0%
+possibly a witness and output zero or
+ 
+
+ align:start position:0%
+possibly a witness and output zero or
+one okay so this is going to be the
+
+ align:start position:0%
+one okay so this is going to be the
+ 
+
+ align:start position:0%
+one okay so this is going to be the
+number of wires and take any I I don't
+
+ align:start position:0%
+number of wires and take any I I don't
+ 
+
+ align:start position:0%
+number of wires and take any I I don't
+know whatever I equals 1 take any I in
+
+ align:start position:0%
+know whatever I equals 1 take any I in
+ 
+
+ align:start position:0%
+know whatever I equals 1 take any I in
+between one to n it doesn't matter
+
+ align:start position:0%
+between one to n it doesn't matter
+ 
+
+ align:start position:0%
+between one to n it doesn't matter
+choose it arbitrarily your favorite
+
+ align:start position:0%
+choose it arbitrarily your favorite
+ 
+
+ align:start position:0%
+choose it arbitrarily your favorite
+number okay so that's first thing and
+
+ align:start position:0%
+number okay so that's first thing and
+ 
+
+ align:start position:0%
+number okay so that's first thing and
+then you also generate a CRS for the bar
+
+ align:start position:0%
+then you also generate a CRS for the bar
+ 
+
+ align:start position:0%
+then you also generate a CRS for the bar
+so you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generate a CRS for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar this is for the
+
+ align:start position:0%
+bar this is for the
+ 
+
+ align:start position:0%
+bar this is for the
+bar and this will be with input one to
+
+ align:start position:0%
+bar and this will be with input one to
+ 
+
+ align:start position:0%
+bar and this will be with input one to
+the with the sc one to the Lambda K the
+
+ align:start position:0%
+the with the sc one to the Lambda K the
+ 
+
+ align:start position:0%
+the with the sc one to the Lambda K the
+number of statements is like the number
+
+ align:start position:0%
+number of statements is like the number
+ 
+
+ align:start position:0%
+number of statements is like the number
+of gates in the circuit so K is going to
+
+ align:start position:0%
+of gates in the circuit so K is going to
+ 
+
+ align:start position:0%
+of gates in the circuit so K is going to
+be number of
+
+ align:start position:0%
+be number of
+ 
+
+ align:start position:0%
+be number of
+gates in C because we're going to
+
+ align:start position:0%
+gates in C because we're going to
+ 
+
+ align:start position:0%
+gates in C because we're going to
+remember we're going to say we're going
+
+ align:start position:0%
+remember we're going to say we're going
+ 
+
+ align:start position:0%
+remember we're going to say we're going
+to prove that for every gate is
+
+ align:start position:0%
+to prove that for every gate is
+ 
+
+ align:start position:0%
+to prove that for every gate is
+satisfied so usually K and N are very
+
+ align:start position:0%
+satisfied so usually K and N are very
+ 
+
+ align:start position:0%
+satisfied so usually K and N are very
+similar it's like essentially the same
+
+ align:start position:0%
+similar it's like essentially the same
+ 
+
+ align:start position:0%
+similar it's like essentially the same
+number but you know uh let me just be
+
+ align:start position:0%
+number but you know uh let me just be
+ 
+
+ align:start position:0%
+number but you know uh let me just be
+clear that this is we're going to have
+
+ align:start position:0%
+clear that this is we're going to have
+ 
+
+ align:start position:0%
+clear that this is we're going to have
+the number of gates and the length n
+
+ align:start position:0%
+the number of gates and the length n
+ 
+
+ align:start position:0%
+the number of gates and the length n
+there and let me call it n Prime we'll
+
+ align:start position:0%
+there and let me call it n Prime we'll
+ 
+
+ align:start position:0%
+there and let me call it n Prime we'll
+see what it is it's a we'll see what
+
+ align:start position:0%
+see what it is it's a we'll see what
+ 
+
+ align:start position:0%
+see what it is it's a we'll see what
+this n Prime is in a in a minute so the
+
+ align:start position:0%
+this n Prime is in a in a minute so the
+ 
+
+ align:start position:0%
+this n Prime is in a in a minute so the
+we're going to Bar statements not of
+
+ align:start position:0%
+we're going to Bar statements not of
+ 
+
+ align:start position:0%
+we're going to Bar statements not of
+length n but of a different length n
+
+ align:start position:0%
+length n but of a different length n
+ 
+
+ align:start position:0%
+length n but of a different length n
+Prime we're going to see what that is
+
+ align:start position:0%
+Prime we're going to see what that is
+ 
+
+ align:start position:0%
+Prime we're going to see what that is
+but the output is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a uh let me call this CRS bar so you
+
+ align:start position:0%
+a uh let me call this CRS bar so you
+ 
+
+ align:start position:0%
+a uh let me call this CRS bar so you
+output CRS which is equal to Hash key
+
+ align:start position:0%
+output CRS which is equal to Hash key
+ 
+
+ align:start position:0%
+output CRS which is equal to Hash key
+and CRS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar okay so that's how you generate so
+
+ align:start position:0%
+bar okay so that's how you generate so
+ 
+
+ align:start position:0%
+bar okay so that's how you generate so
+the key generation the CRS has a CRS for
+
+ align:start position:0%
+the key generation the CRS has a CRS for
+ 
+
+ align:start position:0%
+the key generation the CRS has a CRS for
+the bar and a hash
+
+ align:start position:0%
+the bar and a hash
+ 
+
+ align:start position:0%
+the bar and a hash
+key now we're going going
+
+ align:start position:0%
+key now we're going going
+ 
+
+ align:start position:0%
+key now we're going going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+a uh what does the prover do so the
+
+ align:start position:0%
+a uh what does the prover do so the
+ 
+
+ align:start position:0%
+a uh what does the prover do so the
+prover gets his input X maybe a witness
+
+ align:start position:0%
+prover gets his input X maybe a witness
+ 
+
+ align:start position:0%
+prover gets his input X maybe a witness
+if it's an
+
+ align:start position:0%
+if it's an
+ 
+
+ align:start position:0%
+if it's an
+NP maybe there's no witness let me say
+
+ align:start position:0%
+NP maybe there's no witness let me say
+ 
+
+ align:start position:0%
+NP maybe there's no witness let me say
+generally with a witness but uh actually
+
+ align:start position:0%
+generally with a witness but uh actually
+ 
+
+ align:start position:0%
+generally with a witness but uh actually
+the bar we're going to construct today
+
+ align:start position:0%
+the bar we're going to construct today
+ 
+
+ align:start position:0%
+the bar we're going to construct today
+is going to be for deterministic
+
+ align:start position:0%
+is going to be for deterministic
+ 
+
+ align:start position:0%
+is going to be for deterministic
+languages but let me write it also for
+
+ align:start position:0%
+languages but let me write it also for
+ 
+
+ align:start position:0%
+languages but let me write it also for
+because I'm going to show you kind of a
+
+ align:start position:0%
+because I'm going to show you kind of a
+ 
+
+ align:start position:0%
+because I'm going to show you kind of a
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+framework so p is going to get a CRS
+
+ align:start position:0%
+framework so p is going to get a CRS
+ 
+
+ align:start position:0%
+framework so p is going to get a CRS
+X and maybe a witness if it's an
+
+ align:start position:0%
+X and maybe a witness if it's an
+ 
+
+ align:start position:0%
+X and maybe a witness if it's an
+NP and he needs to generate a snar so
+
+ align:start position:0%
+NP and he needs to generate a snar so
+ 
+
+ align:start position:0%
+NP and he needs to generate a snar so
+what does he what does it do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute all the wires in the circuit so
+
+ align:start position:0%
+compute all the wires in the circuit so
+ 
+
+ align:start position:0%
+compute all the wires in the circuit so
+X is fixed let's think of X is like
+
+ align:start position:0%
+X is fixed let's think of X is like
+ 
+
+ align:start position:0%
+X is fixed let's think of X is like
+that's not part of the wires because
+
+ align:start position:0%
+that's not part of the wires because
+ 
+
+ align:start position:0%
+that's not part of the wires because
+it's fixed but let's compute all the
+
+ align:start position:0%
+it's fixed but let's compute all the
+ 
+
+ align:start position:0%
+it's fixed but let's compute all the
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+W1 up to w a n which is the wires of the
+
+ align:start position:0%
+W1 up to w a n which is the wires of the
+ 
+
+ align:start position:0%
+W1 up to w a n which is the wires of the
+circuit you can think of the first m has
+
+ align:start position:0%
+circuit you can think of the first m has
+ 
+
+ align:start position:0%
+circuit you can think of the first m has
+kind of the actual witness let's say the
+
+ align:start position:0%
+kind of the actual witness let's say the
+ 
+
+ align:start position:0%
+kind of the actual witness let's say the
+if you have a witness and it's of length
+
+ align:start position:0%
+if you have a witness and it's of length
+ 
+
+ align:start position:0%
+if you have a witness and it's of length
+M W1 w m is the witness but then the
+
+ align:start position:0%
+M W1 w m is the witness but then the
+ 
+
+ align:start position:0%
+M W1 w m is the witness but then the
+rest are the wires so I'm thinking the
+
+ align:start position:0%
+rest are the wires so I'm thinking the
+ 
+
+ align:start position:0%
+rest are the wires so I'm thinking the
+wires include kind of the witness and
+
+ align:start position:0%
+wires include kind of the witness and
+ 
+
+ align:start position:0%
+wires include kind of the witness and
+everything above and if there's no
+
+ align:start position:0%
+everything above and if there's no
+ 
+
+ align:start position:0%
+everything above and if there's no
+witness then it doesn't include a
+
+ align:start position:0%
+witness then it doesn't include a
+ 
+
+ align:start position:0%
+witness then it doesn't include a
+witness so I compute these are all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wires in
+
+ align:start position:0%
+wires in
+ 
+
+ align:start position:0%
+wires in
+C except
+
+ align:start position:0%
+C except
+ 
+
+ align:start position:0%
+C except
+X except the input Y is corresponding
+
+ align:start position:0%
+X except the input Y is corresponding
+ 
+
+ align:start position:0%
+X except the input Y is corresponding
+the input Y is corresponding to X cuz
+
+ align:start position:0%
+the input Y is corresponding to X cuz
+ 
+
+ align:start position:0%
+the input Y is corresponding to X cuz
+that's kind of we know what it is the
+
+ align:start position:0%
+that's kind of we know what it is the
+ 
+
+ align:start position:0%
+that's kind of we know what it is the
+verifier knows
+
+ align:start position:0%
+verifier knows
+ 
+
+ align:start position:0%
+verifier knows
+it okay so you compute all the wires and
+
+ align:start position:0%
+it okay so you compute all the wires and
+ 
+
+ align:start position:0%
+it okay so you compute all the wires and
+then you
+
+ align:start position:0%
+then you
+ 
+
+ align:start position:0%
+then you
+compute hash of the you compute V which
+
+ align:start position:0%
+compute hash of the you compute V which
+ 
+
+ align:start position:0%
+compute hash of the you compute V which
+is a hash the
+
+ align:start position:0%
+is a hash the
+ 
+
+ align:start position:0%
+is a hash the
+eval with hash key of W1 up to
+
+ align:start position:0%
+eval with hash key of W1 up to
+ 
+
+ align:start position:0%
+eval with hash key of W1 up to
+WN so you hash all these wires together
+
+ align:start position:0%
+WN so you hash all these wires together
+ 
+
+ align:start position:0%
+WN so you hash all these wires together
+okay so the verifier computed all the
+
+ align:start position:0%
+okay so the verifier computed all the
+ 
+
+ align:start position:0%
+okay so the verifier computed all the
+wires of the
+
+ align:start position:0%
+wires of the
+ 
+
+ align:start position:0%
+wires of the
+circuit hashed all the
+
+ align:start position:0%
+circuit hashed all the
+ 
+
+ align:start position:0%
+circuit hashed all the
+wires oh uh okay actually let me just
+
+ align:start position:0%
+wires oh uh okay actually let me just
+ 
+
+ align:start position:0%
+wires oh uh okay actually let me just
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry when you generate a key I said you
+
+ align:start position:0%
+sorry when you generate a key I said you
+ 
+
+ align:start position:0%
+sorry when you generate a key I said you
+know use a a a su constructible hash yes
+
+ align:start position:0%
+know use a a a su constructible hash yes
+ 
+
+ align:start position:0%
+know use a a a su constructible hash yes
+exactly but let's you don't need to just
+
+ align:start position:0%
+exactly but let's you don't need to just
+ 
+
+ align:start position:0%
+exactly but let's you don't need to just
+use one index okay so let's use it with
+
+ align:start position:0%
+use one index okay so let's use it with
+ 
+
+ align:start position:0%
+use one index okay so let's use it with
+few index i l now you can ask what is
+
+ align:start position:0%
+few index i l now you can ask what is
+ 
+
+ align:start position:0%
+few index i l now you can ask what is
+L we'll see you know you can think of it
+
+ align:start position:0%
+L we'll see you know you can think of it
+ 
+
+ align:start position:0%
+L we'll see you know you can think of it
+as a few L's you can think of poly log l
+
+ align:start position:0%
+as a few L's you can think of poly log l
+ 
+
+ align:start position:0%
+as a few L's you can think of poly log l
+the bigger the is the less extinct the
+
+ align:start position:0%
+the bigger the is the less extinct the
+ 
+
+ align:start position:0%
+the bigger the is the less extinct the
+snar is going to be so the snar is going
+
+ align:start position:0%
+snar is going to be so the snar is going
+ 
+
+ align:start position:0%
+snar is going to be so the snar is going
+to grow with L because the hash key
+
+ align:start position:0%
+to grow with L because the hash key
+ 
+
+ align:start position:0%
+to grow with L because the hash key
+grows with L it's like L hash Keys
+
+ align:start position:0%
+grows with L it's like L hash Keys
+ 
+
+ align:start position:0%
+grows with L it's like L hash Keys
+essentially because we're
+
+ align:start position:0%
+essentially because we're
+ 
+
+ align:start position:0%
+essentially because we're
+repeating so here I'm going to be
+
+ align:start position:0%
+repeating so here I'm going to be
+ 
+
+ align:start position:0%
+repeating so here I'm going to be
+binding on L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+locations the hash value grow with L
+
+ align:start position:0%
+locations the hash value grow with L
+ 
+
+ align:start position:0%
+locations the hash value grow with L
+because you're like you're Computing
+
+ align:start position:0%
+because you're like you're Computing
+ 
+
+ align:start position:0%
+because you're like you're Computing
+essentially L hash values so the more
+
+ align:start position:0%
+essentially L hash values so the more
+ 
+
+ align:start position:0%
+essentially L hash values so the more
+the bigger L is in some sense the more
+
+ align:start position:0%
+the bigger L is in some sense the more
+ 
+
+ align:start position:0%
+the bigger L is in some sense the more
+secure we're going to we're going to get
+
+ align:start position:0%
+secure we're going to we're going to get
+ 
+
+ align:start position:0%
+secure we're going to we're going to get
+we'll see but the more non succinct it's
+
+ align:start position:0%
+we'll see but the more non succinct it's
+ 
+
+ align:start position:0%
+we'll see but the more non succinct it's
+going to be so L now is going to be a
+
+ align:start position:0%
+going to be so L now is going to be a
+ 
+
+ align:start position:0%
+going to be so L now is going to be a
+parameter and when we talk about then
+
+ align:start position:0%
+parameter and when we talk about then
+ 
+
+ align:start position:0%
+parameter and when we talk about then
+Elis we'll see which L we want yeah is
+
+ align:start position:0%
+Elis we'll see which L we want yeah is
+ 
+
+ align:start position:0%
+Elis we'll see which L we want yeah is
+there any hope for getting like
+
+ align:start position:0%
+there any hope for getting like
+ 
+
+ align:start position:0%
+there any hope for getting like
+sublinear dependence in L like any other
+
+ align:start position:0%
+sublinear dependence in L like any other
+ 
+
+ align:start position:0%
+sublinear dependence in L like any other
+construction instead of a direct product
+
+ align:start position:0%
+construction instead of a direct product
+ 
+
+ align:start position:0%
+construction instead of a direct product
+construction so okay in V there's no way
+
+ align:start position:0%
+construction so okay in V there's no way
+ 
+
+ align:start position:0%
+construction so okay in V there's no way
+to get sublinear and L because you need
+
+ align:start position:0%
+to get sublinear and L because you need
+ 
+
+ align:start position:0%
+to get sublinear and L because you need
+to extract it's like a there's must have
+
+ align:start position:0%
+to extract it's like a there's must have
+ 
+
+ align:start position:0%
+to extract it's like a there's must have
+information so in V there's no way to
+
+ align:start position:0%
+information so in V there's no way to
+ 
+
+ align:start position:0%
+information so in V there's no way to
+have to have in the Hat key on the other
+
+ align:start position:0%
+have to have in the Hat key on the other
+ 
+
+ align:start position:0%
+have to have in the Hat key on the other
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+um okay if the I I want up to I L can be
+
+ align:start position:0%
+um okay if the I I want up to I L can be
+ 
+
+ align:start position:0%
+um okay if the I I want up to I L can be
+shrunk somehow if there's a sucin
+
+ align:start position:0%
+shrunk somehow if there's a sucin
+ 
+
+ align:start position:0%
+shrunk somehow if there's a sucin
+description of i1 to I for example in
+
+ align:start position:0%
+description of i1 to I for example in
+ 
+
+ align:start position:0%
+description of i1 to I for example in
+the case of a witness you know I'm I
+
+ align:start position:0%
+the case of a witness you know I'm I
+ 
+
+ align:start position:0%
+the case of a witness you know I'm I
+want to be extractable and witness I
+
+ align:start position:0%
+want to be extractable and witness I
+ 
+
+ align:start position:0%
+want to be extractable and witness I
+these are consecutive locations so I
+
+ align:start position:0%
+these are consecutive locations so I
+ 
+
+ align:start position:0%
+these are consecutive locations so I
+don't need to write location I I plus
+
+ align:start position:0%
+don't need to write location I I plus
+ 
+
+ align:start position:0%
+don't need to write location I I plus
+one I plus you can just say I and go
+
+ align:start position:0%
+one I plus you can just say I and go
+ 
+
+ align:start position:0%
+one I plus you can just say I and go
+from I to n there's a very suin
+
+ align:start position:0%
+from I to n there's a very suin
+ 
+
+ align:start position:0%
+from I to n there's a very suin
+description in the case where there's Su
+
+ align:start position:0%
+description in the case where there's Su
+ 
+
+ align:start position:0%
+description in the case where there's Su
+description
+
+ align:start position:0%
+description
+ 
+
+ align:start position:0%
+description
+you can hope to get the hash key
+
+ align:start position:0%
+you can hope to get the hash key
+ 
+
+ align:start position:0%
+you can hope to get the hash key
+smaller and we do know how to get the
+
+ align:start position:0%
+smaller and we do know how to get the
+ 
+
+ align:start position:0%
+smaller and we do know how to get the
+hash key smaller but in general uh for
+
+ align:start position:0%
+hash key smaller but in general uh for
+ 
+
+ align:start position:0%
+hash key smaller but in general uh for
+the Val value there's no way information
+
+ align:start position:0%
+the Val value there's no way information
+ 
+
+ align:start position:0%
+the Val value there's no way information
+theoretically great great
+
+ align:start position:0%
+theoretically great great
+ 
+
+ align:start position:0%
+theoretically great great
+question okay so a okay so you compute
+
+ align:start position:0%
+question okay so a okay so you compute
+ 
+
+ align:start position:0%
+question okay so a okay so you compute
+the the hash value of all the wires and
+
+ align:start position:0%
+the the hash value of all the wires and
+ 
+
+ align:start position:0%
+the the hash value of all the wires and
+then you add a Barb so the last thing
+
+ align:start position:0%
+then you add a Barb so the last thing
+ 
+
+ align:start position:0%
+then you add a Barb so the last thing
+you do is you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute uh the P bar like you take the a
+
+ align:start position:0%
+compute uh the P bar like you take the a
+ 
+
+ align:start position:0%
+compute uh the P bar like you take the a
+bar
+
+ align:start position:0%
+bar
+ 
+
+ align:start position:0%
+bar
+prover and here's our bar prover you
+
+ align:start position:0%
+prover and here's our bar prover you
+ 
+
+ align:start position:0%
+prover and here's our bar prover you
+give it CRS of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar and you have axes and Witnesses now
+
+ align:start position:0%
+bar and you have axes and Witnesses now
+ 
+
+ align:start position:0%
+bar and you have axes and Witnesses now
+what are the axes and the witnesses okay
+
+ align:start position:0%
+what are the axes and the witnesses okay
+ 
+
+ align:start position:0%
+what are the axes and the witnesses okay
+I want to use I want to argue I'm going
+
+ align:start position:0%
+I want to use I want to argue I'm going
+ 
+
+ align:start position:0%
+I want to use I want to argue I'm going
+to generate a bunch of axes and
+
+ align:start position:0%
+to generate a bunch of axes and
+ 
+
+ align:start position:0%
+to generate a bunch of axes and
+Witnesses and generate a proof so what
+
+ align:start position:0%
+Witnesses and generate a proof so what
+ 
+
+ align:start position:0%
+Witnesses and generate a proof so what
+is it that I'm what are so I'm going to
+
+ align:start position:0%
+is it that I'm what are so I'm going to
+ 
+
+ align:start position:0%
+is it that I'm what are so I'm going to
+give you X1 star x k star and W1 star
+
+ align:start position:0%
+give you X1 star x k star and W1 star
+ 
+
+ align:start position:0%
+give you X1 star x k star and W1 star
+I'll tell you what these are in a second
+
+ align:start position:0%
+I'll tell you what these are in a second
+ 
+
+ align:start position:0%
+I'll tell you what these are in a second
+w k star so this is going to be Pi this
+
+ align:start position:0%
+w k star so this is going to be Pi this
+ 
+
+ align:start position:0%
+w k star so this is going to be Pi this
+is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute Pi
+
+ align:start position:0%
+compute Pi
+ 
+
+ align:start position:0%
+compute Pi
+Bar so you bar case statements but what
+
+ align:start position:0%
+Bar so you bar case statements but what
+ 
+
+ align:start position:0%
+Bar so you bar case statements but what
+are these statements so so let me just
+
+ align:start position:0%
+are these statements so so let me just
+ 
+
+ align:start position:0%
+are these statements so so let me just
+tell you what these and these
+
+ align:start position:0%
+tell you what these and these
+ 
+
+ align:start position:0%
+tell you what these and these
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+X star J
+
+ align:start position:0%
+X star J
+ 
+
+ align:start position:0%
+X star J
+is essentially it's going to it's going
+
+ align:start position:0%
+is essentially it's going to it's going
+ 
+
+ align:start position:0%
+is essentially it's going to it's going
+to be hash
+
+ align:start position:0%
+to be hash
+ 
+
+ align:start position:0%
+to be hash
+key value and
+
+ align:start position:0%
+key value and
+ 
+
+ align:start position:0%
+key value and
+J okay that's X that so what I'm going
+
+ align:start position:0%
+J okay that's X that so what I'm going
+ 
+
+ align:start position:0%
+J okay that's X that so what I'm going
+to prove that for each gate
+
+ align:start position:0%
+to prove that for each gate
+ 
+
+ align:start position:0%
+to prove that for each gate
+J I have an opening to the input wires
+
+ align:start position:0%
+J I have an opening to the input wires
+ 
+
+ align:start position:0%
+J I have an opening to the input wires
+of the gate and the out wire of the gate
+
+ align:start position:0%
+of the gate and the out wire of the gate
+ 
+
+ align:start position:0%
+of the gate and the out wire of the gate
+with respect I have an opening with
+
+ align:start position:0%
+with respect I have an opening with
+ 
+
+ align:start position:0%
+with respect I have an opening with
+respect to V that satisfi the gate okay
+
+ align:start position:0%
+respect to V that satisfi the gate okay
+ 
+
+ align:start position:0%
+respect to V that satisfi the gate okay
+so the XJ is going to be well I have the
+
+ align:start position:0%
+so the XJ is going to be well I have the
+ 
+
+ align:start position:0%
+so the XJ is going to be well I have the
+hash ke I have the hash value and gate J
+
+ align:start position:0%
+hash ke I have the hash value and gate J
+ 
+
+ align:start position:0%
+hash ke I have the hash value and gate J
+and the witness for gate J is going to
+
+ align:start position:0%
+and the witness for gate J is going to
+ 
+
+ align:start position:0%
+and the witness for gate J is going to
+be opening so I'm going to have a like
+
+ align:start position:0%
+be opening so I'm going to have a like
+ 
+
+ align:start position:0%
+be opening so I'm going to have a like
+bit uh like a left child right child
+
+ align:start position:0%
+bit uh like a left child right child
+ 
+
+ align:start position:0%
+bit uh like a left child right child
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+child not child I'll put the
+
+ align:start position:0%
+child not child I'll put the
+ 
+
+ align:start position:0%
+child not child I'll put the
+parent uh so left child right right
+
+ align:start position:0%
+parent uh so left child right right
+ 
+
+ align:start position:0%
+parent uh so left child right right
+child and parent of the
+
+ align:start position:0%
+child and parent of the
+ 
+
+ align:start position:0%
+child and parent of the
+gate opening row of left child row of
+
+ align:start position:0%
+gate opening row of left child row of
+ 
+
+ align:start position:0%
+gate opening row of left child row of
+right child row of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output that's going to be a witness and
+
+ align:start position:0%
+output that's going to be a witness and
+ 
+
+ align:start position:0%
+output that's going to be a witness and
+it's a valid witness
+
+ align:start position:0%
+it's a valid witness
+ 
+
+ align:start position:0%
+it's a valid witness
+if b0 row zero are valid opening of the
+
+ align:start position:0%
+if b0 row zero are valid opening of the
+ 
+
+ align:start position:0%
+if b0 row zero are valid opening of the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+child of
+
+ align:start position:0%
+child of
+ 
+
+ align:start position:0%
+child of
+GJ B1 Row one are a valid opening of the
+
+ align:start position:0%
+GJ B1 Row one are a valid opening of the
+ 
+
+ align:start position:0%
+GJ B1 Row one are a valid opening of the
+right child of gate J B out and row out
+
+ align:start position:0%
+right child of gate J B out and row out
+ 
+
+ align:start position:0%
+right child of gate J B out and row out
+are valid openings of the output wire of
+
+ align:start position:0%
+are valid openings of the output wire of
+ 
+
+ align:start position:0%
+are valid openings of the output wire of
+gate J
+
+ align:start position:0%
+gate J
+ 
+
+ align:start position:0%
+gate J
+and these satisfy the gate so if it's a
+
+ align:start position:0%
+and these satisfy the gate so if it's a
+ 
+
+ align:start position:0%
+and these satisfy the gate so if it's a
+end gate this and this is
+
+ align:start position:0%
+end gate this and this is
+ 
+
+ align:start position:0%
+end gate this and this is
+this okay that's gonna that's what
+
+ align:start position:0%
+this okay that's gonna that's what
+ 
+
+ align:start position:0%
+this okay that's gonna that's what
+that's G to that's so a valid witness is
+
+ align:start position:0%
+that's G to that's so a valid witness is
+ 
+
+ align:start position:0%
+that's G to that's so a valid witness is
+a six tupo like this that all these
+
+ align:start position:0%
+a six tupo like this that all these
+ 
+
+ align:start position:0%
+a six tupo like this that all these
+openings are accepted and these bits
+
+ align:start position:0%
+openings are accepted and these bits
+ 
+
+ align:start position:0%
+openings are accepted and these bits
+satisfy the gate
+
+ align:start position:0%
+satisfy the gate
+ 
+
+ align:start position:0%
+satisfy the gate
+and are valid opening with respect to
+
+ align:start position:0%
+and are valid opening with respect to
+ 
+
+ align:start position:0%
+and are valid opening with respect to
+which wires the wires that are defined
+
+ align:start position:0%
+which wires the wires that are defined
+ 
+
+ align:start position:0%
+which wires the wires that are defined
+by the gate so think of that you know we
+
+ align:start position:0%
+by the gate so think of that you know we
+ 
+
+ align:start position:0%
+by the gate so think of that you know we
+have this circuit C the gates are kind
+
+ align:start position:0%
+have this circuit C the gates are kind
+ 
+
+ align:start position:0%
+have this circuit C the gates are kind
+of uh numbered and for any Gates J we
+
+ align:start position:0%
+of uh numbered and for any Gates J we
+ 
+
+ align:start position:0%
+of uh numbered and for any Gates J we
+know there's we know the number of the
+
+ align:start position:0%
+know there's we know the number of the
+ 
+
+ align:start position:0%
+know there's we know the number of the
+input an output wire okay because it's
+
+ align:start position:0%
+input an output wire okay because it's
+ 
+
+ align:start position:0%
+input an output wire okay because it's
+this is uniform everything the circuit
+
+ align:start position:0%
+this is uniform everything the circuit
+ 
+
+ align:start position:0%
+this is uniform everything the circuit
+is uniform so for every gate J we
+
+ align:start position:0%
+is uniform so for every gate J we
+ 
+
+ align:start position:0%
+is uniform so for every gate J we
+corresponds to you know I know I yre I
+
+ align:start position:0%
+corresponds to you know I know I yre I
+ 
+
+ align:start position:0%
+corresponds to you know I know I yre I
+yre J and yre K yeah and so these
+
+ align:start position:0%
+yre J and yre K yeah and so these
+ 
+
+ align:start position:0%
+yre J and yre K yeah and so these
+openings should be with respect to y i y
+
+ align:start position:0%
+openings should be with respect to y i y
+ 
+
+ align:start position:0%
+openings should be with respect to y i y
+j and y k the same hash key for same
+
+ align:start position:0%
+j and y k the same hash key for same
+ 
+
+ align:start position:0%
+j and y k the same hash key for same
+hash key for all of them yeah because I
+
+ align:start position:0%
+hash key for all of them yeah because I
+ 
+
+ align:start position:0%
+hash key for all of them yeah because I
+used one hash key I mean it's one hash
+
+ align:start position:0%
+used one hash key I mean it's one hash
+ 
+
+ align:start position:0%
+used one hash key I mean it's one hash
+key that's binding and and allocations
+
+ align:start position:0%
+key that's binding and and allocations
+ 
+
+ align:start position:0%
+key that's binding and and allocations
+but I'm uh now I'm thinking just just
+
+ align:start position:0%
+but I'm uh now I'm thinking just just
+ 
+
+ align:start position:0%
+but I'm uh now I'm thinking just just
+one hash key that's binding how I
+
+ align:start position:0%
+one hash key that's binding how I
+ 
+
+ align:start position:0%
+one hash key that's binding how I
+construct it
+
+ align:start position:0%
+construct it
+ 
+
+ align:start position:0%
+construct it
+will abstract that for now but yeah I
+
+ align:start position:0%
+will abstract that for now but yeah I
+ 
+
+ align:start position:0%
+will abstract that for now but yeah I
+have one hash key that's binding on a
+
+ align:start position:0%
+have one hash key that's binding on a
+ 
+
+ align:start position:0%
+have one hash key that's binding on a
+location I hash all the values of the
+
+ align:start position:0%
+location I hash all the values of the
+ 
+
+ align:start position:0%
+location I hash all the values of the
+the W the values of all the wires to
+
+ align:start position:0%
+the W the values of all the wires to
+ 
+
+ align:start position:0%
+the W the values of all the wires to
+this specific hash key and then add a
+
+ align:start position:0%
+this specific hash key and then add a
+ 
+
+ align:start position:0%
+this specific hash key and then add a
+bar for any uh gate J that I have an
+
+ align:start position:0%
+bar for any uh gate J that I have an
+ 
+
+ align:start position:0%
+bar for any uh gate J that I have an
+opening for the input the two input
+
+ align:start position:0%
+opening for the input the two input
+ 
+
+ align:start position:0%
+opening for the input the two input
+children the output output uh um wire of
+
+ align:start position:0%
+children the output output uh um wire of
+ 
+
+ align:start position:0%
+children the output output uh um wire of
+gate J that satisfy the gate yeah only
+
+ align:start position:0%
+gate J that satisfy the gate yeah only
+ 
+
+ align:start position:0%
+gate J that satisfy the gate yeah only
+differ index itself so it's like one of
+
+ align:start position:0%
+differ index itself so it's like one of
+ 
+
+ align:start position:0%
+differ index itself so it's like one of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+index yeah yeah yeah yeah good so you're
+
+ align:start position:0%
+index yeah yeah yeah yeah good so you're
+ 
+
+ align:start position:0%
+index yeah yeah yeah yeah good so you're
+saying where's J here where's
+
+ align:start position:0%
+saying where's J here where's
+ 
+
+ align:start position:0%
+saying where's J here where's
+J is that you're saying no more like
+
+ align:start position:0%
+J is that you're saying no more like
+ 
+
+ align:start position:0%
+J is that you're saying no more like
+like J star and XJ the only difference
+
+ align:start position:0%
+like J star and XJ the only difference
+ 
+
+ align:start position:0%
+like J star and XJ the only difference
+is J okay so this is an index kind of
+
+ align:start position:0%
+is J okay so this is an index kind of
+ 
+
+ align:start position:0%
+is J okay so this is an index kind of
+language yeah this note this is kind of
+
+ align:start position:0%
+language yeah this note this is kind of
+ 
+
+ align:start position:0%
+language yeah this note this is kind of
+it's that X1 X1 star X2 star are the
+
+ align:start position:0%
+it's that X1 X1 star X2 star are the
+ 
+
+ align:start position:0%
+it's that X1 X1 star X2 star are the
+same hash KV K one two 3 four up to K so
+
+ align:start position:0%
+same hash KV K one two 3 four up to K so
+ 
+
+ align:start position:0%
+same hash KV K one two 3 four up to K so
+it's kind of an index language we're
+
+ align:start position:0%
+it's kind of an index language we're
+ 
+
+ align:start position:0%
+it's kind of an index language we're
+going to get back to it when uh because
+
+ align:start position:0%
+going to get back to it when uh because
+ 
+
+ align:start position:0%
+going to get back to it when uh because
+we want the efficiency of V so we'll
+
+ align:start position:0%
+we want the efficiency of V so we'll
+ 
+
+ align:start position:0%
+we want the efficiency of V so we'll
+talk about that but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes any question about the the prover
+
+ align:start position:0%
+yes any question about the the prover
+ 
+
+ align:start position:0%
+yes any question about the the prover
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now the verifier what the
+
+ align:start position:0%
+okay so now the verifier what the
+ 
+
+ align:start position:0%
+okay so now the verifier what the
+verifier
+
+ align:start position:0%
+verifier
+ 
+
+ align:start position:0%
+verifier
+does is uh okay so now let's write the
+
+ align:start position:0%
+does is uh okay so now let's write the
+ 
+
+ align:start position:0%
+does is uh okay so now let's write the
+verifier
+
+ align:start position:0%
+verifier
+ 
+
+ align:start position:0%
+verifier
+somewhere oh that's sad I want to keep
+
+ align:start position:0%
+somewhere oh that's sad I want to keep
+ 
+
+ align:start position:0%
+somewhere oh that's sad I want to keep
+this okay if you don't mind we'll write
+
+ align:start position:0%
+this okay if you don't mind we'll write
+ 
+
+ align:start position:0%
+this okay if you don't mind we'll write
+the verifier
+
+ align:start position:0%
+the verifier
+ 
+
+ align:start position:0%
+the verifier
+here okay so what does the verifier do V
+
+ align:start position:0%
+here okay so what does the verifier do V
+ 
+
+ align:start position:0%
+here okay so what does the verifier do V
+takes his input a CRS which
+
+ align:start position:0%
+takes his input a CRS which
+ 
+
+ align:start position:0%
+takes his input a CRS which
+is hash key and CRS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar that's the CRS and it takes an
+
+ align:start position:0%
+bar that's the CRS and it takes an
+ 
+
+ align:start position:0%
+bar that's the CRS and it takes an
+instance X and a proof what is the proof
+
+ align:start position:0%
+instance X and a proof what is the proof
+ 
+
+ align:start position:0%
+instance X and a proof what is the proof
+a proof is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value and um a
+
+ align:start position:0%
+value and um a
+ 
+
+ align:start position:0%
+value and um a
+bar a hash value and a bar okay so the
+
+ align:start position:0%
+bar a hash value and a bar okay so the
+ 
+
+ align:start position:0%
+bar a hash value and a bar okay so the
+verifier he gets the CRS which is of
+
+ align:start position:0%
+verifier he gets the CRS which is of
+ 
+
+ align:start position:0%
+verifier he gets the CRS which is of
+this form he gets an input X and he gets
+
+ align:start position:0%
+this form he gets an input X and he gets
+ 
+
+ align:start position:0%
+this form he gets an input X and he gets
+snar a snar is oh did I say what did
+
+ align:start position:0%
+snar a snar is oh did I say what did
+ 
+
+ align:start position:0%
+snar a snar is oh did I say what did
+output sorry okay sorry compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output V and P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar so now he takes the The Snug which
+
+ align:start position:0%
+bar so now he takes the The Snug which
+ 
+
+ align:start position:0%
+bar so now he takes the The Snug which
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+hash and uh and a bar
+
+ align:start position:0%
+hash and uh and a bar
+ 
+
+ align:start position:0%
+hash and uh and a bar
+and it just outputs
+
+ align:start position:0%
+and it just outputs
+ 
+
+ align:start position:0%
+and it just outputs
+one and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output the output of V bar he accepts if
+
+ align:start position:0%
+output the output of V bar he accepts if
+ 
+
+ align:start position:0%
+output the output of V bar he accepts if
+and only if the bar is accepting what do
+
+ align:start position:0%
+and only if the bar is accepting what do
+ 
+
+ align:start position:0%
+and only if the bar is accepting what do
+I mean the bar V bar takes CRS
+
+ align:start position:0%
+I mean the bar V bar takes CRS
+ 
+
+ align:start position:0%
+I mean the bar V bar takes CRS
+bar and X1 star up to XK star which are
+
+ align:start position:0%
+bar and X1 star up to XK star which are
+ 
+
+ align:start position:0%
+bar and X1 star up to XK star which are
+essentially an index language
+
+ align:start position:0%
+essentially an index language
+ 
+
+ align:start position:0%
+essentially an index language
+corresponding to
+
+ align:start position:0%
+corresponding to
+ 
+
+ align:start position:0%
+corresponding to
+HK V
+
+ align:start position:0%
+HK V
+ 
+
+ align:start position:0%
+HK V
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J so it
+
+ align:start position:0%
+J so it
+ 
+
+ align:start position:0%
+J so it
+accepts if and only if the bar is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accepted that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+snar one thing I so again you a the
+
+ align:start position:0%
+snar one thing I so again you a the
+ 
+
+ align:start position:0%
+snar one thing I so again you a the
+again what is the snar in the CRS
+
+ align:start position:0%
+again what is the snar in the CRS
+ 
+
+ align:start position:0%
+again what is the snar in the CRS
+generated generation you generate a hash
+
+ align:start position:0%
+generated generation you generate a hash
+ 
+
+ align:start position:0%
+generated generation you generate a hash
+key for the sum extractable hash and you
+
+ align:start position:0%
+key for the sum extractable hash and you
+ 
+
+ align:start position:0%
+key for the sum extractable hash and you
+generate a CRS for the barg the
+
+ align:start position:0%
+generate a CRS for the barg the
+ 
+
+ align:start position:0%
+generate a CRS for the barg the
+prover computes the values of all the
+
+ align:start position:0%
+prover computes the values of all the
+ 
+
+ align:start position:0%
+prover computes the values of all the
+wires in the circuits hashes it using
+
+ align:start position:0%
+wires in the circuits hashes it using
+ 
+
+ align:start position:0%
+wires in the circuits hashes it using
+the hash key to generate a value a hash
+
+ align:start position:0%
+the hash key to generate a value a hash
+ 
+
+ align:start position:0%
+the hash key to generate a value a hash
+value V and then he proves he gives a
+
+ align:start position:0%
+value V and then he proves he gives a
+ 
+
+ align:start position:0%
+value V and then he proves he gives a
+bar that all the gates are satisfied
+
+ align:start position:0%
+bar that all the gates are satisfied
+ 
+
+ align:start position:0%
+bar that all the gates are satisfied
+namely for every gate he has an opening
+
+ align:start position:0%
+namely for every gate he has an opening
+ 
+
+ align:start position:0%
+namely for every gate he has an opening
+valid that's satisfi that respects the
+
+ align:start position:0%
+valid that's satisfi that respects the
+ 
+
+ align:start position:0%
+valid that's satisfi that respects the
+gate gate and that the upper gate is one
+
+ align:start position:0%
+gate gate and that the upper gate is one
+ 
+
+ align:start position:0%
+gate gate and that the upper gate is one
+that's another thing you also prove that
+
+ align:start position:0%
+that's another thing you also prove that
+ 
+
+ align:start position:0%
+that's another thing you also prove that
+in the B you also prove that the upper
+
+ align:start position:0%
+in the B you also prove that the upper
+ 
+
+ align:start position:0%
+in the B you also prove that the upper
+gate is one so for the upper gate you
+
+ align:start position:0%
+gate is one so for the upper gate you
+ 
+
+ align:start position:0%
+gate is one so for the upper gate you
+prove it respects namely you prove it's
+
+ align:start position:0%
+prove it respects namely you prove it's
+ 
+
+ align:start position:0%
+prove it respects namely you prove it's
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um good so that's and and how do you
+
+ align:start position:0%
+um good so that's and and how do you
+ 
+
+ align:start position:0%
+um good so that's and and how do you
+verify you just verify the
+
+ align:start position:0%
+verify you just verify the
+ 
+
+ align:start position:0%
+verify you just verify the
+bar now here's one important thing to
+
+ align:start position:0%
+bar now here's one important thing to
+ 
+
+ align:start position:0%
+bar now here's one important thing to
+note this V bar takes his input the bar
+
+ align:start position:0%
+note this V bar takes his input the bar
+ 
+
+ align:start position:0%
+note this V bar takes his input the bar
+of length k k is like the number of
+
+ align:start position:0%
+of length k k is like the number of
+ 
+
+ align:start position:0%
+of length k k is like the number of
+wires in the circuit we do not want want
+
+ align:start position:0%
+wires in the circuit we do not want want
+ 
+
+ align:start position:0%
+wires in the circuit we do not want want
+the verifier to run in time K that would
+
+ align:start position:0%
+the verifier to run in time K that would
+ 
+
+ align:start position:0%
+the verifier to run in time K that would
+be the the size of the circuit no we
+
+ align:start position:0%
+be the the size of the circuit no we
+ 
+
+ align:start position:0%
+be the the size of the circuit no we
+want the verifier to be very
+
+ align:start position:0%
+want the verifier to be very
+ 
+
+ align:start position:0%
+want the verifier to be very
+efficient but that's but that's okay
+
+ align:start position:0%
+efficient but that's but that's okay
+ 
+
+ align:start position:0%
+efficient but that's but that's okay
+because he actually doesn't need to run
+
+ align:start position:0%
+because he actually doesn't need to run
+ 
+
+ align:start position:0%
+because he actually doesn't need to run
+in time K because actually it's an in
+
+ align:start position:0%
+in time K because actually it's an in
+ 
+
+ align:start position:0%
+in time K because actually it's an in
+it's what's called an index language
+
+ align:start position:0%
+it's what's called an index language
+ 
+
+ align:start position:0%
+it's what's called an index language
+namely X1 up to XK
+
+ align:start position:0%
+namely X1 up to XK
+ 
+
+ align:start position:0%
+namely X1 up to XK
+star essentially it's like an index on
+
+ align:start position:0%
+star essentially it's like an index on
+ 
+
+ align:start position:0%
+star essentially it's like an index on
+an Hash k and V so the the you can
+
+ align:start position:0%
+an Hash k and V so the the you can
+ 
+
+ align:start position:0%
+an Hash k and V so the the you can
+generate them kind of you can um Express
+
+ align:start position:0%
+generate them kind of you can um Express
+ 
+
+ align:start position:0%
+generate them kind of you can um Express
+them very
+
+ align:start position:0%
+them very
+ 
+
+ align:start position:0%
+them very
+succinctly right the you can you can
+
+ align:start position:0%
+succinctly right the you can you can
+ 
+
+ align:start position:0%
+succinctly right the you can you can
+express them by hash key V and all the
+
+ align:start position:0%
+express them by hash key V and all the
+ 
+
+ align:start position:0%
+express them by hash key V and all the
+index between one and K that's it so
+
+ align:start position:0%
+index between one and K that's it so
+ 
+
+ align:start position:0%
+index between one and K that's it so
+because they have a succinct
+
+ align:start position:0%
+because they have a succinct
+ 
+
+ align:start position:0%
+because they have a succinct
+representation the RM of the verifier
+
+ align:start position:0%
+representation the RM of the verifier
+ 
+
+ align:start position:0%
+representation the RM of the verifier
+only grows with hash key and V PO with
+
+ align:start position:0%
+only grows with hash key and V PO with
+ 
+
+ align:start position:0%
+only grows with hash key and V PO with
+hash and V he does not need to grow with
+
+ align:start position:0%
+hash and V he does not need to grow with
+ 
+
+ align:start position:0%
+hash and V he does not need to grow with
+K that's kind of the um efficiency
+
+ align:start position:0%
+K that's kind of the um efficiency
+ 
+
+ align:start position:0%
+K that's kind of the um efficiency
+property of index languages and that's
+
+ align:start position:0%
+property of index languages and that's
+ 
+
+ align:start position:0%
+property of index languages and that's
+very important without it we can't use
+
+ align:start position:0%
+very important without it we can't use
+ 
+
+ align:start position:0%
+very important without it we can't use
+it for the bar for the
+
+ align:start position:0%
+it for the bar for the
+ 
+
+ align:start position:0%
+it for the bar for the
+snar so the so in terms of efficiency if
+
+ align:start position:0%
+snar so the so in terms of efficiency if
+ 
+
+ align:start position:0%
+snar so the so in terms of efficiency if
+the bar has good efficiency and let's
+
+ align:start position:0%
+the bar has good efficiency and let's
+ 
+
+ align:start position:0%
+the bar has good efficiency and let's
+say the the dependence is poly log on K
+
+ align:start position:0%
+say the the dependence is poly log on K
+ 
+
+ align:start position:0%
+say the the dependence is poly log on K
+then the V is going to be so what what
+
+ align:start position:0%
+then the V is going to be so what what
+ 
+
+ align:start position:0%
+then the V is going to be so what what
+is the what's the the snar grows with v
+
+ align:start position:0%
+is the what's the the snar grows with v
+ 
+
+ align:start position:0%
+is the what's the the snar grows with v
+and with a bar proof the bar proof is
+
+ align:start position:0%
+and with a bar proof the bar proof is
+ 
+
+ align:start position:0%
+and with a bar proof the bar proof is
+very if it grows with poly
+
+ align:start position:0%
+very if it grows with poly
+ 
+
+ align:start position:0%
+very if it grows with poly
+logarithmically with K it's like poly
+
+ align:start position:0%
+logarithmically with K it's like poly
+ 
+
+ align:start position:0%
+logarithmically with K it's like poly
+log the circuit sign very
+
+ align:start position:0%
+log the circuit sign very
+ 
+
+ align:start position:0%
+log the circuit sign very
+efficient V grows with the number of
+
+ align:start position:0%
+efficient V grows with the number of
+ 
+
+ align:start position:0%
+efficient V grows with the number of
+indices we're binding on so it grows
+
+ align:start position:0%
+indices we're binding on so it grows
+ 
+
+ align:start position:0%
+indices we're binding on so it grows
+with L so okay grows with L we'll try to
+
+ align:start position:0%
+with L so okay grows with L we'll try to
+ 
+
+ align:start position:0%
+with L so okay grows with L we'll try to
+minimize L we ideally want L to be poly
+
+ align:start position:0%
+minimize L we ideally want L to be poly
+ 
+
+ align:start position:0%
+minimize L we ideally want L to be poly
+log K okay so that's what we want we'll
+
+ align:start position:0%
+log K okay so that's what we want we'll
+ 
+
+ align:start position:0%
+log K okay so that's what we want we'll
+see what we get but ideally this should
+
+ align:start position:0%
+see what we get but ideally this should
+ 
+
+ align:start position:0%
+see what we get but ideally this should
+be polylog K and the runtime of the
+
+ align:start position:0%
+be polylog K and the runtime of the
+ 
+
+ align:start position:0%
+be polylog K and the runtime of the
+verifier because it's an index language
+
+ align:start position:0%
+verifier because it's an index language
+ 
+
+ align:start position:0%
+verifier because it's an index language
+is also going to be poog K assuming uh
+
+ align:start position:0%
+is also going to be poog K assuming uh
+ 
+
+ align:start position:0%
+is also going to be poog K assuming uh
+a sorry uh and he needs to to um to
+
+ align:start position:0%
+a sorry uh and he needs to to um to
+ 
+
+ align:start position:0%
+a sorry uh and he needs to to um to
+uh he does run in time x because he also
+
+ align:start position:0%
+uh he does run in time x because he also
+ 
+
+ align:start position:0%
+uh he does run in time x because he also
+needs to check to check this Pi Bar is
+
+ align:start position:0%
+needs to check to check this Pi Bar is
+ 
+
+ align:start position:0%
+needs to check to check this Pi Bar is
+Pi Bar comma of X because when you check
+
+ align:start position:0%
+Pi Bar comma of X because when you check
+ 
+
+ align:start position:0%
+Pi Bar comma of X because when you check
+the validity of the of that each gate is
+
+ align:start position:0%
+the validity of the of that each gate is
+ 
+
+ align:start position:0%
+the validity of the of that each gate is
+satisfied the the gates in layer one
+
+ align:start position:0%
+satisfied the the gates in layer one
+ 
+
+ align:start position:0%
+satisfied the the gates in layer one
+depend on the on X so to the gates in
+
+ align:start position:0%
+depend on the on X so to the gates in
+ 
+
+ align:start position:0%
+depend on the on X so to the gates in
+layer one the input wires are x x i XJ
+
+ align:start position:0%
+layer one the input wires are x x i XJ
+ 
+
+ align:start position:0%
+layer one the input wires are x x i XJ
+so the bug needs to know X the verifier
+
+ align:start position:0%
+so the bug needs to know X the verifier
+ 
+
+ align:start position:0%
+so the bug needs to know X the verifier
+of course needs to know X but but uh
+
+ align:start position:0%
+of course needs to know X but but uh
+ 
+
+ align:start position:0%
+of course needs to know X but but uh
+that's it so he doesn't need to run in
+
+ align:start position:0%
+that's it so he doesn't need to run in
+ 
+
+ align:start position:0%
+that's it so he doesn't need to run in
+time linear in X but the bar itself s is
+
+ align:start position:0%
+time linear in X but the bar itself s is
+ 
+
+ align:start position:0%
+time linear in X but the bar itself s is
+very short so the The Snug is very short
+
+ align:start position:0%
+very short so the The Snug is very short
+ 
+
+ align:start position:0%
+very short so the The Snug is very short
+the verify of course run needs to run
+
+ align:start position:0%
+the verify of course run needs to run
+ 
+
+ align:start position:0%
+the verify of course run needs to run
+time x he needs to read the input but
+
+ align:start position:0%
+time x he needs to read the input but
+ 
+
+ align:start position:0%
+time x he needs to read the input but
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+it okay so any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so let's take a break a
+
+ align:start position:0%
+questions okay so let's take a break a
+ 
+
+ align:start position:0%
+questions okay so let's take a break a
+cookie break a fun break and let's start
+
+ align:start position:0%
+cookie break a fun break and let's start
+ 
+
+ align:start position:0%
+cookie break a fun break and let's start
+again like 10 minutes and then we'll
+
+ align:start position:0%
+again like 10 minutes and then we'll
+ 
+
+ align:start position:0%
+again like 10 minutes and then we'll
+talk about the analysis and when but
+
+ align:start position:0%
+talk about the analysis and when but
+ 
+
+ align:start position:0%
+talk about the analysis and when but
+this is all that's done we're done with
+
+ align:start position:0%
+this is all that's done we're done with
+ 
+
+ align:start position:0%
+this is all that's done we're done with
+the construction this is your snar okay
+
+ align:start position:0%
+the construction this is your snar okay
+ 
+
+ align:start position:0%
+the construction this is your snar okay
+and we built up to it here it is and
+
+ align:start position:0%
+and we built up to it here it is and
+ 
+
+ align:start position:0%
+and we built up to it here it is and
+then we'll analyze it uh after the break
\ No newline at end of file
diff --git a/oAFufZvbBb0.txt b/oAFufZvbBb0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..605caaedcdb7c5d5a335219945a1b99d4ea443f9
--- /dev/null
+++ b/oAFufZvbBb0.txt
@@ -0,0 +1,8131 @@
+align:start position:0%
+ 
+We have a a very exciting uh group of of
+
+ align:start position:0%
+We have a a very exciting uh group of of
+ 
+
+ align:start position:0%
+We have a a very exciting uh group of of
+people to talk to you this morning. And
+
+ align:start position:0%
+people to talk to you this morning. And
+ 
+
+ align:start position:0%
+people to talk to you this morning. And
+the way we structure this, as Steve
+
+ align:start position:0%
+the way we structure this, as Steve
+ 
+
+ align:start position:0%
+the way we structure this, as Steve
+said, is is I'm going to give each uh
+
+ align:start position:0%
+said, is is I'm going to give each uh
+ 
+
+ align:start position:0%
+said, is is I'm going to give each uh
+each person about 15 or 20 minutes to
+
+ align:start position:0%
+each person about 15 or 20 minutes to
+ 
+
+ align:start position:0%
+each person about 15 or 20 minutes to
+make their presentation and then we're
+
+ align:start position:0%
+make their presentation and then we're
+ 
+
+ align:start position:0%
+make their presentation and then we're
+going to reserve about 20 minutes at the
+
+ align:start position:0%
+going to reserve about 20 minutes at the
+ 
+
+ align:start position:0%
+going to reserve about 20 minutes at the
+end for questions. I ask that you hold
+
+ align:start position:0%
+end for questions. I ask that you hold
+ 
+
+ align:start position:0%
+end for questions. I ask that you hold
+your questions until until we finish,
+
+ align:start position:0%
+your questions until until we finish,
+ 
+
+ align:start position:0%
+your questions until until we finish,
+but we will uh then be up here as a
+
+ align:start position:0%
+but we will uh then be up here as a
+ 
+
+ align:start position:0%
+but we will uh then be up here as a
+panel to answer the questions. And the
+
+ align:start position:0%
+panel to answer the questions. And the
+ 
+
+ align:start position:0%
+panel to answer the questions. And the
+way we've got it structured is that um
+
+ align:start position:0%
+way we've got it structured is that um
+ 
+
+ align:start position:0%
+way we've got it structured is that um
+I'm going to start off and I'm going to
+
+ align:start position:0%
+I'm going to start off and I'm going to
+ 
+
+ align:start position:0%
+I'm going to start off and I'm going to
+talk about a few things that that we're
+
+ align:start position:0%
+talk about a few things that that we're
+ 
+
+ align:start position:0%
+talk about a few things that that we're
+doing at the University of Arkansas and
+
+ align:start position:0%
+doing at the University of Arkansas and
+ 
+
+ align:start position:0%
+doing at the University of Arkansas and
+some of the the holes that that we see
+
+ align:start position:0%
+some of the the holes that that we see
+ 
+
+ align:start position:0%
+some of the the holes that that we see
+that are out there that need to be
+
+ align:start position:0%
+that are out there that need to be
+ 
+
+ align:start position:0%
+that are out there that need to be
+filled. And uh then we have um Simon
+
+ align:start position:0%
+filled. And uh then we have um Simon
+ 
+
+ align:start position:0%
+filled. And uh then we have um Simon
+Langford from from Walmart. Um we have
+
+ align:start position:0%
+Langford from from Walmart. Um we have
+ 
+
+ align:start position:0%
+Langford from from Walmart. Um we have
+Terry Crawford from Publix and that's
+
+ align:start position:0%
+Terry Crawford from Publix and that's
+ 
+
+ align:start position:0%
+Terry Crawford from Publix and that's
+the the retailer side of things. Uh then
+
+ align:start position:0%
+the the retailer side of things. Uh then
+ 
+
+ align:start position:0%
+the the retailer side of things. Uh then
+we have Dick Canwell from PNG Gillette
+
+ align:start position:0%
+we have Dick Canwell from PNG Gillette
+ 
+
+ align:start position:0%
+we have Dick Canwell from PNG Gillette
+from the supplier perspective and we
+
+ align:start position:0%
+from the supplier perspective and we
+ 
+
+ align:start position:0%
+from the supplier perspective and we
+have Klaus Garbish from DHL from the
+
+ align:start position:0%
+have Klaus Garbish from DHL from the
+ 
+
+ align:start position:0%
+have Klaus Garbish from DHL from the
+logistics side. So we've we've tried to
+
+ align:start position:0%
+logistics side. So we've we've tried to
+ 
+
+ align:start position:0%
+logistics side. So we've we've tried to
+cover the supply chain with uh as much
+
+ align:start position:0%
+cover the supply chain with uh as much
+ 
+
+ align:start position:0%
+cover the supply chain with uh as much
+as possible with our panelists here and
+
+ align:start position:0%
+as possible with our panelists here and
+ 
+
+ align:start position:0%
+as possible with our panelists here and
+and then we'll we'll wrap up then with
+
+ align:start position:0%
+and then we'll we'll wrap up then with
+ 
+
+ align:start position:0%
+and then we'll we'll wrap up then with
+Brian Subberan from from
+
+ align:start position:0%
+Brian Subberan from from
+ 
+
+ align:start position:0%
+Brian Subberan from from
+MIT again. So we'll start with academic
+
+ align:start position:0%
+MIT again. So we'll start with academic
+ 
+
+ align:start position:0%
+MIT again. So we'll start with academic
+we'll end it with academic and and
+
+ align:start position:0%
+we'll end it with academic and and
+ 
+
+ align:start position:0%
+we'll end it with academic and and
+industry in between. So, uh, let's go
+
+ align:start position:0%
+industry in between. So, uh, let's go
+ 
+
+ align:start position:0%
+industry in between. So, uh, let's go
+ahead and get started. And again,
+
+ align:start position:0%
+ahead and get started. And again,
+ 
+
+ align:start position:0%
+ahead and get started. And again,
+welcome welcome to our panelist. And,
+
+ align:start position:0%
+welcome welcome to our panelist. And,
+ 
+
+ align:start position:0%
+welcome welcome to our panelist. And,
+um, I'll keep myself my my job is going
+
+ align:start position:0%
+um, I'll keep myself my my job is going
+ 
+
+ align:start position:0%
+um, I'll keep myself my my job is going
+to be timekeeper, so I'll keep myself on
+
+ align:start position:0%
+to be timekeeper, so I'll keep myself on
+ 
+
+ align:start position:0%
+to be timekeeper, so I'll keep myself on
+time here. Uh, I want to talk about what
+
+ align:start position:0%
+time here. Uh, I want to talk about what
+ 
+
+ align:start position:0%
+time here. Uh, I want to talk about what
+we're doing again at the at the
+
+ align:start position:0%
+we're doing again at the at the
+ 
+
+ align:start position:0%
+we're doing again at the at the
+University of Arkansas and then and to
+
+ align:start position:0%
+University of Arkansas and then and to
+ 
+
+ align:start position:0%
+University of Arkansas and then and to
+talk about some of the research
+
+ align:start position:0%
+talk about some of the research
+ 
+
+ align:start position:0%
+talk about some of the research
+areas. We we have research in several
+
+ align:start position:0%
+areas. We we have research in several
+ 
+
+ align:start position:0%
+areas. We we have research in several
+areas. I'm going to restrict it because
+
+ align:start position:0%
+areas. I'm going to restrict it because
+ 
+
+ align:start position:0%
+areas. I'm going to restrict it because
+of our topic here being supply chain to
+
+ align:start position:0%
+of our topic here being supply chain to
+ 
+
+ align:start position:0%
+of our topic here being supply chain to
+to those specific topics. But we are we
+
+ align:start position:0%
+to those specific topics. But we are we
+ 
+
+ align:start position:0%
+to those specific topics. But we are we
+are heavily involved in the at this
+
+ align:start position:0%
+are heavily involved in the at this
+ 
+
+ align:start position:0%
+are heavily involved in the at this
+point technology deployment. Uh we've
+
+ align:start position:0%
+point technology deployment. Uh we've
+ 
+
+ align:start position:0%
+point technology deployment. Uh we've
+got some groups that are looking at u
+
+ align:start position:0%
+got some groups that are looking at u
+ 
+
+ align:start position:0%
+got some groups that are looking at u
+developing some technology but but for
+
+ align:start position:0%
+developing some technology but but for
+ 
+
+ align:start position:0%
+developing some technology but but for
+the most part we are we're very heavy in
+
+ align:start position:0%
+the most part we are we're very heavy in
+ 
+
+ align:start position:0%
+the most part we are we're very heavy in
+in deploying that technology static
+
+ align:start position:0%
+in deploying that technology static
+ 
+
+ align:start position:0%
+in deploying that technology static
+versus uh mobile readers uh gen two uh
+
+ align:start position:0%
+versus uh mobile readers uh gen two uh
+ 
+
+ align:start position:0%
+versus uh mobile readers uh gen two uh
+those type of things. Uh we we've just
+
+ align:start position:0%
+those type of things. Uh we we've just
+ 
+
+ align:start position:0%
+those type of things. Uh we we've just
+our lab was just converted over and now
+
+ align:start position:0%
+our lab was just converted over and now
+ 
+
+ align:start position:0%
+our lab was just converted over and now
+was just telling Simon we uh we're now
+
+ align:start position:0%
+was just telling Simon we uh we're now
+ 
+
+ align:start position:0%
+was just telling Simon we uh we're now
+totally gen two uh no more gen one
+
+ align:start position:0%
+totally gen two uh no more gen one
+ 
+
+ align:start position:0%
+totally gen two uh no more gen one
+testing for us at this point. Um and
+
+ align:start position:0%
+testing for us at this point. Um and
+ 
+
+ align:start position:0%
+testing for us at this point. Um and
+that's really from the demands that
+
+ align:start position:0%
+that's really from the demands that
+ 
+
+ align:start position:0%
+that's really from the demands that
+we're seeing from from industry data
+
+ align:start position:0%
+we're seeing from from industry data
+ 
+
+ align:start position:0%
+we're seeing from from industry data
+analytics. I'll talk more about that in
+
+ align:start position:0%
+analytics. I'll talk more about that in
+ 
+
+ align:start position:0%
+analytics. I'll talk more about that in
+in depth making the business case. I'll
+
+ align:start position:0%
+in depth making the business case. I'll
+ 
+
+ align:start position:0%
+in depth making the business case. I'll
+talk more about that, but we're doing
+
+ align:start position:0%
+talk more about that, but we're doing
+ 
+
+ align:start position:0%
+talk more about that, but we're doing
+doing projects in middleware, open-
+
+ align:start position:0%
+doing projects in middleware, open-
+ 
+
+ align:start position:0%
+doing projects in middleware, open-
+source um development, uh lots of work
+
+ align:start position:0%
+source um development, uh lots of work
+ 
+
+ align:start position:0%
+source um development, uh lots of work
+around public policy, consumer reaction
+
+ align:start position:0%
+around public policy, consumer reaction
+ 
+
+ align:start position:0%
+around public policy, consumer reaction
+type issues, um animal ID. We've got a
+
+ align:start position:0%
+type issues, um animal ID. We've got a
+ 
+
+ align:start position:0%
+type issues, um animal ID. We've got a
+group in our a department uh and also
+
+ align:start position:0%
+group in our a department uh and also
+ 
+
+ align:start position:0%
+group in our a department uh and also
+with our close affiliation with our
+
+ align:start position:0%
+with our close affiliation with our
+ 
+
+ align:start position:0%
+with our close affiliation with our
+friends at Tyson down the street uh
+
+ align:start position:0%
+friends at Tyson down the street uh
+ 
+
+ align:start position:0%
+friends at Tyson down the street uh
+doing a lot of in animal ID trailer
+
+ align:start position:0%
+doing a lot of in animal ID trailer
+ 
+
+ align:start position:0%
+doing a lot of in animal ID trailer
+tracking load status uh trying to move
+
+ align:start position:0%
+tracking load status uh trying to move
+ 
+
+ align:start position:0%
+tracking load status uh trying to move
+more into the logistics area there and
+
+ align:start position:0%
+more into the logistics area there and
+ 
+
+ align:start position:0%
+more into the logistics area there and
+also as we move up the supply chain into
+
+ align:start position:0%
+also as we move up the supply chain into
+ 
+
+ align:start position:0%
+also as we move up the supply chain into
+manufacturing uh as well. Let me drill
+
+ align:start position:0%
+manufacturing uh as well. Let me drill
+ 
+
+ align:start position:0%
+manufacturing uh as well. Let me drill
+down to a couple of areas here and start
+
+ align:start position:0%
+down to a couple of areas here and start
+ 
+
+ align:start position:0%
+down to a couple of areas here and start
+off with with data analytics. And that's
+
+ align:start position:0%
+off with with data analytics. And that's
+ 
+
+ align:start position:0%
+off with with data analytics. And that's
+one area that we've spent a great deal
+
+ align:start position:0%
+one area that we've spent a great deal
+ 
+
+ align:start position:0%
+one area that we've spent a great deal
+of time uh and trying to look at what
+
+ align:start position:0%
+of time uh and trying to look at what
+ 
+
+ align:start position:0%
+of time uh and trying to look at what
+the data um really trying to tell us.
+
+ align:start position:0%
+the data um really trying to tell us.
+ 
+
+ align:start position:0%
+the data um really trying to tell us.
+And um we we were I was having a
+
+ align:start position:0%
+And um we we were I was having a
+ 
+
+ align:start position:0%
+And um we we were I was having a
+conversation with Jazelle this morning
+
+ align:start position:0%
+conversation with Jazelle this morning
+ 
+
+ align:start position:0%
+conversation with Jazelle this morning
+and uh a couple of conversations last
+
+ align:start position:0%
+and uh a couple of conversations last
+ 
+
+ align:start position:0%
+and uh a couple of conversations last
+night and that's an area that really
+
+ align:start position:0%
+night and that's an area that really
+ 
+
+ align:start position:0%
+night and that's an area that really
+needs a lot of work. Uh you know, we're
+
+ align:start position:0%
+needs a lot of work. Uh you know, we're
+ 
+
+ align:start position:0%
+needs a lot of work. Uh you know, we're
+getting the technology in place. The
+
+ align:start position:0%
+getting the technology in place. The
+ 
+
+ align:start position:0%
+getting the technology in place. The
+technology will come along. We've got a
+
+ align:start position:0%
+technology will come along. We've got a
+ 
+
+ align:start position:0%
+technology will come along. We've got a
+we've got a lot of things we can do
+
+ align:start position:0%
+we've got a lot of things we can do
+ 
+
+ align:start position:0%
+we've got a lot of things we can do
+there, but it's but it's about creating
+
+ align:start position:0%
+there, but it's but it's about creating
+ 
+
+ align:start position:0%
+there, but it's but it's about creating
+that data and then turning that data
+
+ align:start position:0%
+that data and then turning that data
+ 
+
+ align:start position:0%
+that data and then turning that data
+into business value. And so that data is
+
+ align:start position:0%
+into business value. And so that data is
+ 
+
+ align:start position:0%
+into business value. And so that data is
+a very very very important piece and uh
+
+ align:start position:0%
+a very very very important piece and uh
+ 
+
+ align:start position:0%
+a very very very important piece and uh
+you know we we first look at this idea
+
+ align:start position:0%
+you know we we first look at this idea
+ 
+
+ align:start position:0%
+you know we we first look at this idea
+of of the 100% read rates and we've
+
+ align:start position:0%
+of of the 100% read rates and we've
+ 
+
+ align:start position:0%
+of of the 100% read rates and we've
+we've heard all kinds of things about
+
+ align:start position:0%
+we've heard all kinds of things about
+ 
+
+ align:start position:0%
+we've heard all kinds of things about
+we've got to see 100% of those read
+
+ align:start position:0%
+we've got to see 100% of those read
+ 
+
+ align:start position:0%
+we've got to see 100% of those read
+rates for it to make sense. And it
+
+ align:start position:0%
+rates for it to make sense. And it
+ 
+
+ align:start position:0%
+rates for it to make sense. And it
+really doesn't. You know we there's an
+
+ align:start position:0%
+really doesn't. You know we there's an
+ 
+
+ align:start position:0%
+really doesn't. You know we there's an
+implicit read versus an explicit read.
+
+ align:start position:0%
+implicit read versus an explicit read.
+ 
+
+ align:start position:0%
+implicit read versus an explicit read.
+Yeah. Did you see it or can you imply
+
+ align:start position:0%
+Yeah. Did you see it or can you imply
+ 
+
+ align:start position:0%
+Yeah. Did you see it or can you imply
+that if it went from point A to point C
+
+ align:start position:0%
+that if it went from point A to point C
+ 
+
+ align:start position:0%
+that if it went from point A to point C
+that it went past point B? And um Sanjay
+
+ align:start position:0%
+that it went past point B? And um Sanjay
+ 
+
+ align:start position:0%
+that it went past point B? And um Sanjay
+talked about yesterday the idea of of
+
+ align:start position:0%
+talked about yesterday the idea of of
+ 
+
+ align:start position:0%
+talked about yesterday the idea of of
+this phantom inventory. If you were to
+
+ align:start position:0%
+this phantom inventory. If you were to
+ 
+
+ align:start position:0%
+this phantom inventory. If you were to
+miss it, that's extremely important.
+
+ align:start position:0%
+miss it, that's extremely important.
+ 
+
+ align:start position:0%
+miss it, that's extremely important.
+Obviously, if if you're not going to get
+
+ align:start position:0%
+Obviously, if if you're not going to get
+ 
+
+ align:start position:0%
+Obviously, if if you're not going to get
+100% reads, can you infer those 100%
+
+ align:start position:0%
+100% reads, can you infer those 100%
+ 
+
+ align:start position:0%
+100% reads, can you infer those 100%
+reads or how can you get that? And I
+
+ align:start position:0%
+reads or how can you get that? And I
+ 
+
+ align:start position:0%
+reads or how can you get that? And I
+think that's going to be very important
+
+ align:start position:0%
+think that's going to be very important
+ 
+
+ align:start position:0%
+think that's going to be very important
+as we as we go on that we when we reach
+
+ align:start position:0%
+as we as we go on that we when we reach
+ 
+
+ align:start position:0%
+as we as we go on that we when we reach
+this 100% read again whether it's
+
+ align:start position:0%
+this 100% read again whether it's
+ 
+
+ align:start position:0%
+this 100% read again whether it's
+implicit or explicit. You've got to be
+
+ align:start position:0%
+implicit or explicit. You've got to be
+ 
+
+ align:start position:0%
+implicit or explicit. You've got to be
+able to draw some inferences from where
+
+ align:start position:0%
+able to draw some inferences from where
+ 
+
+ align:start position:0%
+able to draw some inferences from where
+you saw that uh the data at this point
+
+ align:start position:0%
+you saw that uh the data at this point
+ 
+
+ align:start position:0%
+you saw that uh the data at this point
+is is very noisy. Uh and those of you in
+
+ align:start position:0%
+is is very noisy. Uh and those of you in
+ 
+
+ align:start position:0%
+is is very noisy. Uh and those of you in
+the room have seen the the data you know
+
+ align:start position:0%
+the room have seen the the data you know
+ 
+
+ align:start position:0%
+the room have seen the the data you know
+there there's there's a there's a lot of
+
+ align:start position:0%
+there there's there's a there's a lot of
+ 
+
+ align:start position:0%
+there there's there's a there's a lot of
+noise in that data. You know you may
+
+ align:start position:0%
+noise in that data. You know you may
+ 
+
+ align:start position:0%
+noise in that data. You know you may
+have uh hundreds of reads at a
+
+ align:start position:0%
+have uh hundreds of reads at a
+ 
+
+ align:start position:0%
+have uh hundreds of reads at a
+particular reader. maybe maybe was
+
+ align:start position:0%
+particular reader. maybe maybe was
+ 
+
+ align:start position:0%
+particular reader. maybe maybe was
+sitting near the reader and moving in
+
+ align:start position:0%
+sitting near the reader and moving in
+ 
+
+ align:start position:0%
+sitting near the reader and moving in
+and out of the field or maybe it passed
+
+ align:start position:0%
+and out of the field or maybe it passed
+ 
+
+ align:start position:0%
+and out of the field or maybe it passed
+back and forth or as the forklift was
+
+ align:start position:0%
+back and forth or as the forklift was
+ 
+
+ align:start position:0%
+back and forth or as the forklift was
+pulling it down through by the dock
+
+ align:start position:0%
+pulling it down through by the dock
+ 
+
+ align:start position:0%
+pulling it down through by the dock
+doors, it was reading at every dock
+
+ align:start position:0%
+doors, it was reading at every dock
+ 
+
+ align:start position:0%
+doors, it was reading at every dock
+door. There's a lot of noise there and
+
+ align:start position:0%
+door. There's a lot of noise there and
+ 
+
+ align:start position:0%
+door. There's a lot of noise there and
+and you know, we've we've did um early
+
+ align:start position:0%
+and you know, we've we've did um early
+ 
+
+ align:start position:0%
+and you know, we've we've did um early
+on quite a bit of work in in using um
+
+ align:start position:0%
+on quite a bit of work in in using um
+ 
+
+ align:start position:0%
+on quite a bit of work in in using um
+such things as neural networks to try to
+
+ align:start position:0%
+such things as neural networks to try to
+ 
+
+ align:start position:0%
+such things as neural networks to try to
+predict when something might be late or
+
+ align:start position:0%
+predict when something might be late or
+ 
+
+ align:start position:0%
+predict when something might be late or
+when it's outside of its its uh uh
+
+ align:start position:0%
+when it's outside of its its uh uh
+ 
+
+ align:start position:0%
+when it's outside of its its uh uh
+normal schedule or using such things as
+
+ align:start position:0%
+normal schedule or using such things as
+ 
+
+ align:start position:0%
+normal schedule or using such things as
+genetic algorithms to try to pull out
+
+ align:start position:0%
+genetic algorithms to try to pull out
+ 
+
+ align:start position:0%
+genetic algorithms to try to pull out
+those patterns in the data. and the the
+
+ align:start position:0%
+those patterns in the data. and the the
+ 
+
+ align:start position:0%
+those patterns in the data. and the the
+data is just very noisy. And we can
+
+ align:start position:0%
+data is just very noisy. And we can
+ 
+
+ align:start position:0%
+data is just very noisy. And we can
+artificially take that data and create
+
+ align:start position:0%
+artificially take that data and create
+ 
+
+ align:start position:0%
+artificially take that data and create
+some good models, but at this point we
+
+ align:start position:0%
+some good models, but at this point we
+ 
+
+ align:start position:0%
+some good models, but at this point we
+haven't been that successful in creating
+
+ align:start position:0%
+haven't been that successful in creating
+ 
+
+ align:start position:0%
+haven't been that successful in creating
+good models with the data as it is. Data
+
+ align:start position:0%
+good models with the data as it is. Data
+ 
+
+ align:start position:0%
+good models with the data as it is. Data
+has got to get cleaner. We got to find a
+
+ align:start position:0%
+has got to get cleaner. We got to find a
+ 
+
+ align:start position:0%
+has got to get cleaner. We got to find a
+way to to clean that data up. And one of
+
+ align:start position:0%
+way to to clean that data up. And one of
+ 
+
+ align:start position:0%
+way to to clean that data up. And one of
+those starts with business rules for
+
+ align:start position:0%
+those starts with business rules for
+ 
+
+ align:start position:0%
+those starts with business rules for
+interpretation. Uh I really feel that
+
+ align:start position:0%
+interpretation. Uh I really feel that
+ 
+
+ align:start position:0%
+interpretation. Uh I really feel that
+we've got to have and there's going to
+
+ align:start position:0%
+we've got to have and there's going to
+ 
+
+ align:start position:0%
+we've got to have and there's going to
+be multiple levels of these. There's
+
+ align:start position:0%
+be multiple levels of these. There's
+ 
+
+ align:start position:0%
+be multiple levels of these. There's
+going to be mo business rules that help
+
+ align:start position:0%
+going to be mo business rules that help
+ 
+
+ align:start position:0%
+going to be mo business rules that help
+us decipher what's a what what was a
+
+ align:start position:0%
+us decipher what's a what what was a
+ 
+
+ align:start position:0%
+us decipher what's a what what was a
+good read, what was a bad read, how do
+
+ align:start position:0%
+good read, what was a bad read, how do
+ 
+
+ align:start position:0%
+good read, what was a bad read, how do
+we make that implicit read then if it's
+
+ align:start position:0%
+we make that implicit read then if it's
+ 
+
+ align:start position:0%
+we make that implicit read then if it's
+not there. And unfortunately, these
+
+ align:start position:0%
+not there. And unfortunately, these
+ 
+
+ align:start position:0%
+not there. And unfortunately, these
+business rules, I think there's going to
+
+ align:start position:0%
+business rules, I think there's going to
+ 
+
+ align:start position:0%
+business rules, I think there's going to
+be some that are global in nature, but
+
+ align:start position:0%
+be some that are global in nature, but
+ 
+
+ align:start position:0%
+be some that are global in nature, but
+then there's going to be some that vary
+
+ align:start position:0%
+then there's going to be some that vary
+ 
+
+ align:start position:0%
+then there's going to be some that vary
+by industry. There's going to be some
+
+ align:start position:0%
+by industry. There's going to be some
+ 
+
+ align:start position:0%
+by industry. There's going to be some
+then that are going to be specific to
+
+ align:start position:0%
+then that are going to be specific to
+ 
+
+ align:start position:0%
+then that are going to be specific to
+companies. And we've got to have some
+
+ align:start position:0%
+companies. And we've got to have some
+ 
+
+ align:start position:0%
+companies. And we've got to have some
+type of architecture, data architecture
+
+ align:start position:0%
+type of architecture, data architecture
+ 
+
+ align:start position:0%
+type of architecture, data architecture
+that allows us to to specify those
+
+ align:start position:0%
+that allows us to to specify those
+ 
+
+ align:start position:0%
+that allows us to to specify those
+business rules all the way down, maybe
+
+ align:start position:0%
+business rules all the way down, maybe
+ 
+
+ align:start position:0%
+business rules all the way down, maybe
+even to a product level. I'm not sure
+
+ align:start position:0%
+even to a product level. I'm not sure
+ 
+
+ align:start position:0%
+even to a product level. I'm not sure
+what that architecture looks like yet.
+
+ align:start position:0%
+what that architecture looks like yet.
+ 
+
+ align:start position:0%
+what that architecture looks like yet.
+We're still trying to conceptualize what
+
+ align:start position:0%
+We're still trying to conceptualize what
+ 
+
+ align:start position:0%
+We're still trying to conceptualize what
+that thing is, but we've got to be able
+
+ align:start position:0%
+that thing is, but we've got to be able
+ 
+
+ align:start position:0%
+that thing is, but we've got to be able
+to to do a better job of of um
+
+ align:start position:0%
+to to do a better job of of um
+ 
+
+ align:start position:0%
+to to do a better job of of um
+interpreting that data. uh Sanjay
+
+ align:start position:0%
+interpreting that data. uh Sanjay
+ 
+
+ align:start position:0%
+interpreting that data. uh Sanjay
+mentioned yesterday the idea of control
+
+ align:start position:0%
+mentioned yesterday the idea of control
+ 
+
+ align:start position:0%
+mentioned yesterday the idea of control
+charts and I think that's going to be
+
+ align:start position:0%
+charts and I think that's going to be
+ 
+
+ align:start position:0%
+charts and I think that's going to be
+important is once we can start
+
+ align:start position:0%
+important is once we can start
+ 
+
+ align:start position:0%
+important is once we can start
+establishing these patterns and
+
+ align:start position:0%
+establishing these patterns and
+ 
+
+ align:start position:0%
+establishing these patterns and
+establishing what these these uh
+
+ align:start position:0%
+establishing what these these uh
+ 
+
+ align:start position:0%
+establishing what these these uh
+products should be doing then we can use
+
+ align:start position:0%
+products should be doing then we can use
+ 
+
+ align:start position:0%
+products should be doing then we can use
+this to to help us determine when things
+
+ align:start position:0%
+this to to help us determine when things
+ 
+
+ align:start position:0%
+this to to help us determine when things
+aren't operating properly um you know
+
+ align:start position:0%
+aren't operating properly um you know
+ 
+
+ align:start position:0%
+aren't operating properly um you know
+the idea of how much uh data will RFID
+
+ align:start position:0%
+the idea of how much uh data will RFID
+ 
+
+ align:start position:0%
+the idea of how much uh data will RFID
+generate you know there's been a lot of
+
+ align:start position:0%
+generate you know there's been a lot of
+ 
+
+ align:start position:0%
+generate you know there's been a lot of
+speculation about the the terabytes of
+
+ align:start position:0%
+speculation about the the terabytes of
+ 
+
+ align:start position:0%
+speculation about the the terabytes of
+data that will be generated and again
+
+ align:start position:0%
+data that will be generated and again
+ 
+
+ align:start position:0%
+data that will be generated and again
+that goes back to you know once we can
+
+ align:start position:0%
+that goes back to you know once we can
+ 
+
+ align:start position:0%
+that goes back to you know once we can
+get this data filtered and cleansed and
+
+ align:start position:0%
+get this data filtered and cleansed and
+ 
+
+ align:start position:0%
+get this data filtered and cleansed and
+and worked on I don't think it's going
+
+ align:start position:0%
+and worked on I don't think it's going
+ 
+
+ align:start position:0%
+and worked on I don't think it's going
+going to be that much and it's not the
+
+ align:start position:0%
+going to be that much and it's not the
+ 
+
+ align:start position:0%
+going to be that much and it's not the
+quantity so much as it is the quality of
+
+ align:start position:0%
+quantity so much as it is the quality of
+ 
+
+ align:start position:0%
+quantity so much as it is the quality of
+the data that's going to matter. You
+
+ align:start position:0%
+the data that's going to matter. You
+ 
+
+ align:start position:0%
+the data that's going to matter. You
+know, storage is cheap, but it's it's
+
+ align:start position:0%
+know, storage is cheap, but it's it's
+ 
+
+ align:start position:0%
+know, storage is cheap, but it's it's
+really extracting that quality. Um, and
+
+ align:start position:0%
+really extracting that quality. Um, and
+ 
+
+ align:start position:0%
+really extracting that quality. Um, and
+a couple issues that were mentioned
+
+ align:start position:0%
+a couple issues that were mentioned
+ 
+
+ align:start position:0%
+a couple issues that were mentioned
+yesterday, it's going to be extremely
+
+ align:start position:0%
+yesterday, it's going to be extremely
+ 
+
+ align:start position:0%
+yesterday, it's going to be extremely
+important data consistency.
+
+ align:start position:0%
+important data consistency.
+ 
+
+ align:start position:0%
+important data consistency.
+uh you know Walmart provides data via
+
+ align:start position:0%
+uh you know Walmart provides data via
+ 
+
+ align:start position:0%
+uh you know Walmart provides data via
+their retail link system and uh you know
+
+ align:start position:0%
+their retail link system and uh you know
+ 
+
+ align:start position:0%
+their retail link system and uh you know
+Target has their own system and Kmart
+
+ align:start position:0%
+Target has their own system and Kmart
+ 
+
+ align:start position:0%
+Target has their own system and Kmart
+has their own system and I know that uh
+
+ align:start position:0%
+has their own system and I know that uh
+ 
+
+ align:start position:0%
+has their own system and I know that uh
+I haven't talked to Simon uh yet but I
+
+ align:start position:0%
+I haven't talked to Simon uh yet but I
+ 
+
+ align:start position:0%
+I haven't talked to Simon uh yet but I
+know that I saw something in the in the
+
+ align:start position:0%
+know that I saw something in the in the
+ 
+
+ align:start position:0%
+know that I saw something in the in the
+news about Target and Walmart working on
+
+ align:start position:0%
+news about Target and Walmart working on
+ 
+
+ align:start position:0%
+news about Target and Walmart working on
+a program where there might be some some
+
+ align:start position:0%
+a program where there might be some some
+ 
+
+ align:start position:0%
+a program where there might be some some
+um efforts to make this data more
+
+ align:start position:0%
+um efforts to make this data more
+ 
+
+ align:start position:0%
+um efforts to make this data more
+consistent. It has to be that way. I
+
+ align:start position:0%
+consistent. It has to be that way. I
+ 
+
+ align:start position:0%
+consistent. It has to be that way. I
+mean we can't have every retailer with
+
+ align:start position:0%
+mean we can't have every retailer with
+ 
+
+ align:start position:0%
+mean we can't have every retailer with
+their own data format for this thing to
+
+ align:start position:0%
+their own data format for this thing to
+ 
+
+ align:start position:0%
+their own data format for this thing to
+work and same thing goes for suppliers.
+
+ align:start position:0%
+work and same thing goes for suppliers.
+ 
+
+ align:start position:0%
+work and same thing goes for suppliers.
+And then of course data integration into
+
+ align:start position:0%
+And then of course data integration into
+ 
+
+ align:start position:0%
+And then of course data integration into
+one's own own organization. I think
+
+ align:start position:0%
+one's own own organization. I think
+ 
+
+ align:start position:0%
+one's own own organization. I think
+we've got a lot of work there into
+
+ align:start position:0%
+we've got a lot of work there into
+ 
+
+ align:start position:0%
+we've got a lot of work there into
+pulling those into the enterprise
+
+ align:start position:0%
+pulling those into the enterprise
+ 
+
+ align:start position:0%
+pulling those into the enterprise
+systems that we have in place. And again
+
+ align:start position:0%
+systems that we have in place. And again
+ 
+
+ align:start position:0%
+systems that we have in place. And again
+with those things, you know, if you pull
+
+ align:start position:0%
+with those things, you know, if you pull
+ 
+
+ align:start position:0%
+with those things, you know, if you pull
+in in noisy or dirty data, uh it's it's
+
+ align:start position:0%
+in in noisy or dirty data, uh it's it's
+ 
+
+ align:start position:0%
+in in noisy or dirty data, uh it's it's
+very bad. So along the bottom you see
+
+ align:start position:0%
+very bad. So along the bottom you see
+ 
+
+ align:start position:0%
+very bad. So along the bottom you see
+there the idea of filter and cleanse,
+
+ align:start position:0%
+there the idea of filter and cleanse,
+ 
+
+ align:start position:0%
+there the idea of filter and cleanse,
+integrate, interpret and understand.
+
+ align:start position:0%
+integrate, interpret and understand.
+ 
+
+ align:start position:0%
+integrate, interpret and understand.
+We've got to move toward that model of
+
+ align:start position:0%
+We've got to move toward that model of
+ 
+
+ align:start position:0%
+We've got to move toward that model of
+filtering that data, cleansing that
+
+ align:start position:0%
+filtering that data, cleansing that
+ 
+
+ align:start position:0%
+filtering that data, cleansing that
+data, integrating with what we have,
+
+ align:start position:0%
+data, integrating with what we have,
+ 
+
+ align:start position:0%
+data, integrating with what we have,
+interpreting what it means and
+
+ align:start position:0%
+interpreting what it means and
+ 
+
+ align:start position:0%
+interpreting what it means and
+understanding. And that then will lead
+
+ align:start position:0%
+understanding. And that then will lead
+ 
+
+ align:start position:0%
+understanding. And that then will lead
+to action based upon that
+
+ align:start position:0%
+to action based upon that
+ 
+
+ align:start position:0%
+to action based upon that
+data. Now making the business case, we
+
+ align:start position:0%
+data. Now making the business case, we
+ 
+
+ align:start position:0%
+data. Now making the business case, we
+could we could spend the rest of the day
+
+ align:start position:0%
+could we could spend the rest of the day
+ 
+
+ align:start position:0%
+could we could spend the rest of the day
+talking about this this area and the
+
+ align:start position:0%
+talking about this this area and the
+ 
+
+ align:start position:0%
+talking about this this area and the
+opportunities that lie within and we had
+
+ align:start position:0%
+opportunities that lie within and we had
+ 
+
+ align:start position:0%
+opportunities that lie within and we had
+some questions yesterday. So, so in in
+
+ align:start position:0%
+some questions yesterday. So, so in in
+ 
+
+ align:start position:0%
+some questions yesterday. So, so in in
+the interest of just keeping it brief,
+
+ align:start position:0%
+the interest of just keeping it brief,
+ 
+
+ align:start position:0%
+the interest of just keeping it brief,
+what I've done is I want to throw out a
+
+ align:start position:0%
+what I've done is I want to throw out a
+ 
+
+ align:start position:0%
+what I've done is I want to throw out a
+couple of things just for you to think
+
+ align:start position:0%
+couple of things just for you to think
+ 
+
+ align:start position:0%
+couple of things just for you to think
+about and and again this is necessarily
+
+ align:start position:0%
+about and and again this is necessarily
+ 
+
+ align:start position:0%
+about and and again this is necessarily
+very narrow so that you can understand
+
+ align:start position:0%
+very narrow so that you can understand
+ 
+
+ align:start position:0%
+very narrow so that you can understand
+the scope at which which we could look
+
+ align:start position:0%
+the scope at which which we could look
+ 
+
+ align:start position:0%
+the scope at which which we could look
+at this. When we look at RFID, we can we
+
+ align:start position:0%
+at this. When we look at RFID, we can we
+ 
+
+ align:start position:0%
+at this. When we look at RFID, we can we
+can view this as an incremental
+
+ align:start position:0%
+can view this as an incremental
+ 
+
+ align:start position:0%
+can view this as an incremental
+technology. We can go in and we can
+
+ align:start position:0%
+technology. We can go in and we can
+ 
+
+ align:start position:0%
+technology. We can go in and we can
+tweak what's already there. Okay. Now,
+
+ align:start position:0%
+tweak what's already there. Okay. Now,
+ 
+
+ align:start position:0%
+tweak what's already there. Okay. Now,
+I'm going to I'm going to kind of look
+
+ align:start position:0%
+I'm going to I'm going to kind of look
+ 
+
+ align:start position:0%
+I'm going to I'm going to kind of look
+at, you know, primarily the store level,
+
+ align:start position:0%
+at, you know, primarily the store level,
+ 
+
+ align:start position:0%
+at, you know, primarily the store level,
+maybe a little bit at the DC level. But
+
+ align:start position:0%
+maybe a little bit at the DC level. But
+ 
+
+ align:start position:0%
+maybe a little bit at the DC level. But
+one thing we could do is say, "All
+
+ align:start position:0%
+one thing we could do is say, "All
+ 
+
+ align:start position:0%
+one thing we could do is say, "All
+right, we'll take RFID and it will just
+
+ align:start position:0%
+right, we'll take RFID and it will just
+ 
+
+ align:start position:0%
+right, we'll take RFID and it will just
+we we'll we'll just use it to make our
+
+ align:start position:0%
+we we'll we'll just use it to make our
+ 
+
+ align:start position:0%
+we we'll we'll just use it to make our
+process a little faster, a little more
+
+ align:start position:0%
+process a little faster, a little more
+ 
+
+ align:start position:0%
+process a little faster, a little more
+efficient, or we'll use it to to make
+
+ align:start position:0%
+efficient, or we'll use it to to make
+ 
+
+ align:start position:0%
+efficient, or we'll use it to to make
+our process a little better. Maybe our
+
+ align:start position:0%
+our process a little better. Maybe our
+ 
+
+ align:start position:0%
+our process a little better. Maybe our
+process isn't broke, it's it's just bent
+
+ align:start position:0%
+process isn't broke, it's it's just bent
+ 
+
+ align:start position:0%
+process isn't broke, it's it's just bent
+a little bit, and we'll use it to just
+
+ align:start position:0%
+a little bit, and we'll use it to just
+ 
+
+ align:start position:0%
+a little bit, and we'll use it to just
+tweak it." Okay, very incremental. We're
+
+ align:start position:0%
+tweak it." Okay, very incremental. We're
+ 
+
+ align:start position:0%
+tweak it." Okay, very incremental. We're
+not we're not radically changing
+
+ align:start position:0%
+not we're not radically changing
+ 
+
+ align:start position:0%
+not we're not radically changing
+anything. So I I just gave some examples
+
+ align:start position:0%
+anything. So I I just gave some examples
+ 
+
+ align:start position:0%
+anything. So I I just gave some examples
+there under the heading of process
+
+ align:start position:0%
+there under the heading of process
+ 
+
+ align:start position:0%
+there under the heading of process
+efficiencies for example promotions you
+
+ align:start position:0%
+efficiencies for example promotions you
+ 
+
+ align:start position:0%
+efficiencies for example promotions you
+know we we may be good at promotions but
+
+ align:start position:0%
+know we we may be good at promotions but
+ 
+
+ align:start position:0%
+know we we may be good at promotions but
+if we don't get it out to the to the
+
+ align:start position:0%
+if we don't get it out to the to the
+ 
+
+ align:start position:0%
+if we don't get it out to the to the
+shelf in a timely manner doesn't matter.
+
+ align:start position:0%
+shelf in a timely manner doesn't matter.
+ 
+
+ align:start position:0%
+shelf in a timely manner doesn't matter.
+So, you know, we can use RFID there. And
+
+ align:start position:0%
+So, you know, we can use RFID there. And
+ 
+
+ align:start position:0%
+So, you know, we can use RFID there. And
+I think there's been some, you know, you
+
+ align:start position:0%
+I think there's been some, you know, you
+ 
+
+ align:start position:0%
+I think there's been some, you know, you
+you probably have all seen this, the
+
+ align:start position:0%
+you probably have all seen this, the
+ 
+
+ align:start position:0%
+you probably have all seen this, the
+early studies. I know Gillette uh
+
+ align:start position:0%
+early studies. I know Gillette uh
+ 
+
+ align:start position:0%
+early studies. I know Gillette uh
+released some data from a study they did
+
+ align:start position:0%
+released some data from a study they did
+ 
+
+ align:start position:0%
+released some data from a study they did
+um working with MIT on on some uh
+
+ align:start position:0%
+um working with MIT on on some uh
+ 
+
+ align:start position:0%
+um working with MIT on on some uh
+opportunities for improvements just
+
+ align:start position:0%
+opportunities for improvements just
+ 
+
+ align:start position:0%
+opportunities for improvements just
+based upon promotions. Uh out of stocks
+
+ align:start position:0%
+based upon promotions. Uh out of stocks
+ 
+
+ align:start position:0%
+based upon promotions. Uh out of stocks
+is another one of those. Again, getting
+
+ align:start position:0%
+is another one of those. Again, getting
+ 
+
+ align:start position:0%
+is another one of those. Again, getting
+it to the shelf when the when the
+
+ align:start position:0%
+it to the shelf when the when the
+ 
+
+ align:start position:0%
+it to the shelf when the when the
+customer wants it in a timely manner.
+
+ align:start position:0%
+customer wants it in a timely manner.
+ 
+
+ align:start position:0%
+customer wants it in a timely manner.
+So, just speeding up that process that's
+
+ align:start position:0%
+So, just speeding up that process that's
+ 
+
+ align:start position:0%
+So, just speeding up that process that's
+already in place. We can also use it
+
+ align:start position:0%
+already in place. We can also use it
+ 
+
+ align:start position:0%
+already in place. We can also use it
+incrementally to to uh fix a process or
+
+ align:start position:0%
+incrementally to to uh fix a process or
+ 
+
+ align:start position:0%
+incrementally to to uh fix a process or
+or make that process a little better.
+
+ align:start position:0%
+or make that process a little better.
+ 
+
+ align:start position:0%
+or make that process a little better.
+Product rotation. Okay, we know how to
+
+ align:start position:0%
+Product rotation. Okay, we know how to
+ 
+
+ align:start position:0%
+Product rotation. Okay, we know how to
+do product rotation. It's not a matter
+
+ align:start position:0%
+do product rotation. It's not a matter
+ 
+
+ align:start position:0%
+do product rotation. It's not a matter
+of timeliness. It's a matter of are we
+
+ align:start position:0%
+of timeliness. It's a matter of are we
+ 
+
+ align:start position:0%
+of timeliness. It's a matter of are we
+doing it correctly? Well, with RFID, we
+
+ align:start position:0%
+doing it correctly? Well, with RFID, we
+ 
+
+ align:start position:0%
+doing it correctly? Well, with RFID, we
+know what's coming in, what's going out.
+
+ align:start position:0%
+know what's coming in, what's going out.
+ 
+
+ align:start position:0%
+know what's coming in, what's going out.
+We can maybe fix some of those problems.
+
+ align:start position:0%
+We can maybe fix some of those problems.
+ 
+
+ align:start position:0%
+We can maybe fix some of those problems.
+Uh better use of merchandisers. Instead
+
+ align:start position:0%
+Uh better use of merchandisers. Instead
+ 
+
+ align:start position:0%
+Uh better use of merchandisers. Instead
+of sending merchandisers to various
+
+ align:start position:0%
+of sending merchandisers to various
+ 
+
+ align:start position:0%
+of sending merchandisers to various
+stores uh just at random or or better or
+
+ align:start position:0%
+stores uh just at random or or better or
+ 
+
+ align:start position:0%
+stores uh just at random or or better or
+worse yet just on a set schedule, maybe
+
+ align:start position:0%
+worse yet just on a set schedule, maybe
+ 
+
+ align:start position:0%
+worse yet just on a set schedule, maybe
+target those merchandisers to where we
+
+ align:start position:0%
+target those merchandisers to where we
+ 
+
+ align:start position:0%
+target those merchandisers to where we
+see product in the back room or when we
+
+ align:start position:0%
+see product in the back room or when we
+ 
+
+ align:start position:0%
+see product in the back room or when we
+see an out of stock event based upon uh
+
+ align:start position:0%
+see an out of stock event based upon uh
+ 
+
+ align:start position:0%
+see an out of stock event based upon uh
+the RFID data. Target those
+
+ align:start position:0%
+the RFID data. Target those
+ 
+
+ align:start position:0%
+the RFID data. Target those
+merchandisers again improving that
+
+ align:start position:0%
+merchandisers again improving that
+ 
+
+ align:start position:0%
+merchandisers again improving that
+process. uh the the manual orders that
+
+ align:start position:0%
+process. uh the the manual orders that
+ 
+
+ align:start position:0%
+process. uh the the manual orders that
+um for example that that Walmart is um
+
+ align:start position:0%
+um for example that that Walmart is um
+ 
+
+ align:start position:0%
+um for example that that Walmart is um
+is doing with with RFID trying to
+
+ align:start position:0%
+is doing with with RFID trying to
+ 
+
+ align:start position:0%
+is doing with with RFID trying to
+restrict those those overrides of those
+
+ align:start position:0%
+restrict those those overrides of those
+ 
+
+ align:start position:0%
+restrict those those overrides of those
+manual orders when we know that
+
+ align:start position:0%
+manual orders when we know that
+ 
+
+ align:start position:0%
+manual orders when we know that
+something's in the back room um
+
+ align:start position:0%
+something's in the back room um
+ 
+
+ align:start position:0%
+something's in the back room um
+electronic proof of delivery um at the
+
+ align:start position:0%
+electronic proof of delivery um at the
+ 
+
+ align:start position:0%
+electronic proof of delivery um at the
+at the DC for example trying to fix that
+
+ align:start position:0%
+at the DC for example trying to fix that
+ 
+
+ align:start position:0%
+at the DC for example trying to fix that
+process where we really see what's
+
+ align:start position:0%
+process where we really see what's
+ 
+
+ align:start position:0%
+process where we really see what's
+coming into the DC and then also I'll
+
+ align:start position:0%
+coming into the DC and then also I'll
+ 
+
+ align:start position:0%
+coming into the DC and then also I'll
+put out a stocks under the idea
+
+ align:start position:0%
+put out a stocks under the idea
+ 
+
+ align:start position:0%
+put out a stocks under the idea
+effectiveness of of uh not only getting
+
+ align:start position:0%
+effectiveness of of uh not only getting
+ 
+
+ align:start position:0%
+effectiveness of of uh not only getting
+out there as a as as an efficiency of
+
+ align:start position:0%
+out there as a as as an efficiency of
+ 
+
+ align:start position:0%
+out there as a as as an efficiency of
+getting out there in a time but also
+
+ align:start position:0%
+getting out there in a time but also
+ 
+
+ align:start position:0%
+getting out there in a time but also
+improving that process. Um there was
+
+ align:start position:0%
+improving that process. Um there was
+ 
+
+ align:start position:0%
+improving that process. Um there was
+there was some data released earlier uh
+
+ align:start position:0%
+there was some data released earlier uh
+ 
+
+ align:start position:0%
+there was some data released earlier uh
+in 2005 that that from Walmart suggested
+
+ align:start position:0%
+in 2005 that that from Walmart suggested
+ 
+
+ align:start position:0%
+in 2005 that that from Walmart suggested
+that you know one out of 12 products was
+
+ align:start position:0%
+that you know one out of 12 products was
+ 
+
+ align:start position:0%
+that you know one out of 12 products was
+actually making it uh from the from the
+
+ align:start position:0%
+actually making it uh from the from the
+ 
+
+ align:start position:0%
+actually making it uh from the from the
+pick list to the shelf and and Simon you
+
+ align:start position:0%
+pick list to the shelf and and Simon you
+ 
+
+ align:start position:0%
+pick list to the shelf and and Simon you
+may have to correct that stat if it's
+
+ align:start position:0%
+may have to correct that stat if it's
+ 
+
+ align:start position:0%
+may have to correct that stat if it's
+not entirely correct but something you
+
+ align:start position:0%
+not entirely correct but something you
+ 
+
+ align:start position:0%
+not entirely correct but something you
+know on a busy Saturday you know by the
+
+ align:start position:0%
+know on a busy Saturday you know by the
+ 
+
+ align:start position:0%
+know on a busy Saturday you know by the
+time it got on the pick list and then
+
+ align:start position:0%
+time it got on the pick list and then
+ 
+
+ align:start position:0%
+time it got on the pick list and then
+got to shelf one out of 12. Well, that
+
+ align:start position:0%
+got to shelf one out of 12. Well, that
+ 
+
+ align:start position:0%
+got to shelf one out of 12. Well, that
+that process can be helped with
+
+ align:start position:0%
+that process can be helped with
+ 
+
+ align:start position:0%
+that process can be helped with
+RFID. Now again, so if you view it as an
+
+ align:start position:0%
+RFID. Now again, so if you view it as an
+ 
+
+ align:start position:0%
+RFID. Now again, so if you view it as an
+incremental technology and some
+
+ align:start position:0%
+incremental technology and some
+ 
+
+ align:start position:0%
+incremental technology and some
+companies are doing that, they look at
+
+ align:start position:0%
+companies are doing that, they look at
+ 
+
+ align:start position:0%
+companies are doing that, they look at
+it and they say, "Okay, RFID is just
+
+ align:start position:0%
+it and they say, "Okay, RFID is just
+ 
+
+ align:start position:0%
+it and they say, "Okay, RFID is just
+going to help us improve the speed of
+
+ align:start position:0%
+going to help us improve the speed of
+ 
+
+ align:start position:0%
+going to help us improve the speed of
+our process or help us tweak our process
+
+ align:start position:0%
+our process or help us tweak our process
+ 
+
+ align:start position:0%
+our process or help us tweak our process
+a little bit." Others are viewing it as
+
+ align:start position:0%
+a little bit." Others are viewing it as
+ 
+
+ align:start position:0%
+a little bit." Others are viewing it as
+more as a radical or disruptive
+
+ align:start position:0%
+more as a radical or disruptive
+ 
+
+ align:start position:0%
+more as a radical or disruptive
+technology. And and that is giving us an
+
+ align:start position:0%
+technology. And and that is giving us an
+ 
+
+ align:start position:0%
+technology. And and that is giving us an
+opportunity to use RFID as a process
+
+ align:start position:0%
+opportunity to use RFID as a process
+ 
+
+ align:start position:0%
+opportunity to use RFID as a process
+enabler. Let's go in and and create new
+
+ align:start position:0%
+enabler. Let's go in and and create new
+ 
+
+ align:start position:0%
+enabler. Let's go in and and create new
+ways of doing business that were never
+
+ align:start position:0%
+ways of doing business that were never
+ 
+
+ align:start position:0%
+ways of doing business that were never
+before possible using RFID as that
+
+ align:start position:0%
+before possible using RFID as that
+ 
+
+ align:start position:0%
+before possible using RFID as that
+technology that drives that. And um I
+
+ align:start position:0%
+technology that drives that. And um I
+ 
+
+ align:start position:0%
+technology that drives that. And um I
+just give you some examples there. It
+
+ align:start position:0%
+just give you some examples there. It
+ 
+
+ align:start position:0%
+just give you some examples there. It
+may be that we could use RFID as to
+
+ align:start position:0%
+may be that we could use RFID as to
+ 
+
+ align:start position:0%
+may be that we could use RFID as to
+radically change the way that retail
+
+ align:start position:0%
+radically change the way that retail
+ 
+
+ align:start position:0%
+radically change the way that retail
+stores stock their shelves. I don't know
+
+ align:start position:0%
+stores stock their shelves. I don't know
+ 
+
+ align:start position:0%
+stores stock their shelves. I don't know
+what that process might look like, but
+
+ align:start position:0%
+what that process might look like, but
+ 
+
+ align:start position:0%
+what that process might look like, but
+that might be a possibility. Obviously,
+
+ align:start position:0%
+that might be a possibility. Obviously,
+ 
+
+ align:start position:0%
+that might be a possibility. Obviously,
+as we move on down the line, the idea of
+
+ align:start position:0%
+as we move on down the line, the idea of
+ 
+
+ align:start position:0%
+as we move on down the line, the idea of
+the contactless checkout, you know,
+
+ align:start position:0%
+the contactless checkout, you know,
+ 
+
+ align:start position:0%
+the contactless checkout, you know,
+that's that would radically change that
+
+ align:start position:0%
+that's that would radically change that
+ 
+
+ align:start position:0%
+that's that would radically change that
+process, right, of of going up and
+
+ align:start position:0%
+process, right, of of going up and
+ 
+
+ align:start position:0%
+process, right, of of going up and
+handing your stuff off to a a cashier
+
+ align:start position:0%
+handing your stuff off to a a cashier
+ 
+
+ align:start position:0%
+handing your stuff off to a a cashier
+that swipes your items and puts it back
+
+ align:start position:0%
+that swipes your items and puts it back
+ 
+
+ align:start position:0%
+that swipes your items and puts it back
+in the cart. Radically changes that. Um,
+
+ align:start position:0%
+in the cart. Radically changes that. Um,
+ 
+
+ align:start position:0%
+in the cart. Radically changes that. Um,
+Sanjay mentioned yesterday the idea of
+
+ align:start position:0%
+Sanjay mentioned yesterday the idea of
+ 
+
+ align:start position:0%
+Sanjay mentioned yesterday the idea of
+the paper scan is radically changing
+
+ align:start position:0%
+the paper scan is radically changing
+ 
+
+ align:start position:0%
+the paper scan is radically changing
+that relationship between suppliers and
+
+ align:start position:0%
+that relationship between suppliers and
+ 
+
+ align:start position:0%
+that relationship between suppliers and
+retailers, changing that supply chain,
+
+ align:start position:0%
+retailers, changing that supply chain,
+ 
+
+ align:start position:0%
+retailers, changing that supply chain,
+okay? where where we get directtore
+
+ align:start position:0%
+okay? where where we get directtore
+ 
+
+ align:start position:0%
+okay? where where we get directtore
+deliveries and you know the retailer
+
+ align:start position:0%
+deliveries and you know the retailer
+ 
+
+ align:start position:0%
+deliveries and you know the retailer
+simply acts as a as a facilitator or a
+
+ align:start position:0%
+simply acts as a as a facilitator or a
+ 
+
+ align:start position:0%
+simply acts as a as a facilitator or a
+broker of those goods until they're
+
+ align:start position:0%
+broker of those goods until they're
+ 
+
+ align:start position:0%
+broker of those goods until they're
+sold. That's a radical change. But but
+
+ align:start position:0%
+sold. That's a radical change. But but
+ 
+
+ align:start position:0%
+sold. That's a radical change. But but
+what I think that we're seeing and and
+
+ align:start position:0%
+what I think that we're seeing and and
+ 
+
+ align:start position:0%
+what I think that we're seeing and and
+if you start looking at the case studies
+
+ align:start position:0%
+if you start looking at the case studies
+ 
+
+ align:start position:0%
+if you start looking at the case studies
+closely, what you what you'll find is
+
+ align:start position:0%
+closely, what you what you'll find is
+ 
+
+ align:start position:0%
+closely, what you what you'll find is
+that some companies are treating it as a
+
+ align:start position:0%
+that some companies are treating it as a
+ 
+
+ align:start position:0%
+that some companies are treating it as a
+as an incremental and and necessarily
+
+ align:start position:0%
+as an incremental and and necessarily
+ 
+
+ align:start position:0%
+as an incremental and and necessarily
+so. There there are many companies and
+
+ align:start position:0%
+so. There there are many companies and
+ 
+
+ align:start position:0%
+so. There there are many companies and
+and I've worked with several of the
+
+ align:start position:0%
+and I've worked with several of the
+ 
+
+ align:start position:0%
+and I've worked with several of the
+suppliers that you know are very very
+
+ align:start position:0%
+suppliers that you know are very very
+ 
+
+ align:start position:0%
+suppliers that you know are very very
+very good at what they do. All the
+
+ align:start position:0%
+very good at what they do. All the
+ 
+
+ align:start position:0%
+very good at what they do. All the
+lowhanging fruit has already been
+
+ align:start position:0%
+lowhanging fruit has already been
+ 
+
+ align:start position:0%
+lowhanging fruit has already been
+picked. So you have to look hard to find
+
+ align:start position:0%
+picked. So you have to look hard to find
+ 
+
+ align:start position:0%
+picked. So you have to look hard to find
+that incremental value. Now that doesn't
+
+ align:start position:0%
+that incremental value. Now that doesn't
+ 
+
+ align:start position:0%
+that incremental value. Now that doesn't
+mean they can't use it as a radical
+
+ align:start position:0%
+mean they can't use it as a radical
+ 
+
+ align:start position:0%
+mean they can't use it as a radical
+technology but there but they first look
+
+ align:start position:0%
+technology but there but they first look
+ 
+
+ align:start position:0%
+technology but there but they first look
+for that incremental change. Other
+
+ align:start position:0%
+for that incremental change. Other
+ 
+
+ align:start position:0%
+for that incremental change. Other
+companies however have actually
+
+ align:start position:0%
+companies however have actually
+ 
+
+ align:start position:0%
+companies however have actually
+purposely used RFID as a way to
+
+ align:start position:0%
+purposely used RFID as a way to
+ 
+
+ align:start position:0%
+purposely used RFID as a way to
+radically change their business. they
+
+ align:start position:0%
+radically change their business. they
+ 
+
+ align:start position:0%
+radically change their business. they
+weren't very good at what they were
+
+ align:start position:0%
+weren't very good at what they were
+ 
+
+ align:start position:0%
+weren't very good at what they were
+doing and RFID then actually becomes an
+
+ align:start position:0%
+doing and RFID then actually becomes an
+ 
+
+ align:start position:0%
+doing and RFID then actually becomes an
+excuse to really change what they're
+
+ align:start position:0%
+excuse to really change what they're
+ 
+
+ align:start position:0%
+excuse to really change what they're
+doing and uh as with most things the
+
+ align:start position:0%
+doing and uh as with most things the
+ 
+
+ align:start position:0%
+doing and uh as with most things the
+higher the risk the higher the return
+
+ align:start position:0%
+higher the risk the higher the return
+ 
+
+ align:start position:0%
+higher the risk the higher the return
+right so uh with with those following
+
+ align:start position:0%
+right so uh with with those following
+ 
+
+ align:start position:0%
+right so uh with with those following
+that radical or disruptive path the the
+
+ align:start position:0%
+that radical or disruptive path the the
+ 
+
+ align:start position:0%
+that radical or disruptive path the the
+opportunity for return is greater but
+
+ align:start position:0%
+opportunity for return is greater but
+ 
+
+ align:start position:0%
+opportunity for return is greater but
+the risk is higher that it won't work
+
+ align:start position:0%
+the risk is higher that it won't work
+ 
+
+ align:start position:0%
+the risk is higher that it won't work
+right now the the third element that we
+
+ align:start position:0%
+right now the the third element that we
+ 
+
+ align:start position:0%
+right now the the third element that we
+have to keep in mind here is who are the
+
+ align:start position:0%
+have to keep in mind here is who are the
+ 
+
+ align:start position:0%
+have to keep in mind here is who are the
+beneficiary beneficiaries of of these
+
+ align:start position:0%
+beneficiary beneficiaries of of these
+ 
+
+ align:start position:0%
+beneficiary beneficiaries of of these
+changes. Could it could be the retailer,
+
+ align:start position:0%
+changes. Could it could be the retailer,
+ 
+
+ align:start position:0%
+changes. Could it could be the retailer,
+it could be the supplier, could be the
+
+ align:start position:0%
+it could be the supplier, could be the
+ 
+
+ align:start position:0%
+it could be the supplier, could be the
+logistics provider, could be the
+
+ align:start position:0%
+logistics provider, could be the
+ 
+
+ align:start position:0%
+logistics provider, could be the
+consumer. Now, we we did a an out of
+
+ align:start position:0%
+consumer. Now, we we did a an out of
+ 
+
+ align:start position:0%
+consumer. Now, we we did a an out of
+stock study working with with Walmart,
+
+ align:start position:0%
+stock study working with with Walmart,
+ 
+
+ align:start position:0%
+stock study working with with Walmart,
+and we necessarily looked
+
+ align:start position:0%
+and we necessarily looked
+ 
+
+ align:start position:0%
+and we necessarily looked
+at one particular area that would
+
+ align:start position:0%
+at one particular area that would
+ 
+
+ align:start position:0%
+at one particular area that would
+provide benefit to several
+
+ align:start position:0%
+provide benefit to several
+ 
+
+ align:start position:0%
+provide benefit to several
+beneficiaries.
+
+ align:start position:0%
+beneficiaries.
+ 
+
+ align:start position:0%
+beneficiaries.
+look at a fairly constrained or a fairly
+
+ align:start position:0%
+look at a fairly constrained or a fairly
+ 
+
+ align:start position:0%
+look at a fairly constrained or a fairly
+narrow area. And that was how
+
+ align:start position:0%
+narrow area. And that was how
+ 
+
+ align:start position:0%
+narrow area. And that was how
+we kind of tweak that out of stock
+
+ align:start position:0%
+we kind of tweak that out of stock
+ 
+
+ align:start position:0%
+we kind of tweak that out of stock
+process to make it just a little bit
+
+ align:start position:0%
+process to make it just a little bit
+ 
+
+ align:start position:0%
+process to make it just a little bit
+better using RFID and in this case
+
+ align:start position:0%
+better using RFID and in this case
+ 
+
+ align:start position:0%
+better using RFID and in this case
+creating those automatic pick list for
+
+ align:start position:0%
+creating those automatic pick list for
+ 
+
+ align:start position:0%
+creating those automatic pick list for
+them to go to the back room and find
+
+ align:start position:0%
+them to go to the back room and find
+ 
+
+ align:start position:0%
+them to go to the back room and find
+that that product and take it to the
+
+ align:start position:0%
+that that product and take it to the
+ 
+
+ align:start position:0%
+that that product and take it to the
+shelf. So we so we tweaked it just a
+
+ align:start position:0%
+shelf. So we so we tweaked it just a
+ 
+
+ align:start position:0%
+shelf. So we so we tweaked it just a
+little bit. And so I wanted to put it in
+
+ align:start position:0%
+little bit. And so I wanted to put it in
+ 
+
+ align:start position:0%
+little bit. And so I wanted to put it in
+context of what we studied and and uh
+
+ align:start position:0%
+context of what we studied and and uh
+ 
+
+ align:start position:0%
+context of what we studied and and uh
+many of you I know have seen the white
+
+ align:start position:0%
+many of you I know have seen the white
+ 
+
+ align:start position:0%
+many of you I know have seen the white
+paper that was released because it's
+
+ align:start position:0%
+paper that was released because it's
+ 
+
+ align:start position:0%
+paper that was released because it's
+it's important that you put this thing
+
+ align:start position:0%
+it's important that you put this thing
+ 
+
+ align:start position:0%
+it's important that you put this thing
+in perspective. Keep in mind that what
+
+ align:start position:0%
+in perspective. Keep in mind that what
+ 
+
+ align:start position:0%
+in perspective. Keep in mind that what
+we looked at was an incremental use of
+
+ align:start position:0%
+we looked at was an incremental use of
+ 
+
+ align:start position:0%
+we looked at was an incremental use of
+the technology in a very narrow
+
+ align:start position:0%
+the technology in a very narrow
+ 
+
+ align:start position:0%
+the technology in a very narrow
+domain. It did help I mean out of stocks
+
+ align:start position:0%
+domain. It did help I mean out of stocks
+ 
+
+ align:start position:0%
+domain. It did help I mean out of stocks
+can help the supplier. It can help the
+
+ align:start position:0%
+can help the supplier. It can help the
+ 
+
+ align:start position:0%
+can help the supplier. It can help the
+retailer. It can help the consumer. So
+
+ align:start position:0%
+retailer. It can help the consumer. So
+ 
+
+ align:start position:0%
+retailer. It can help the consumer. So
+the beneficiary side was great, but the
+
+ align:start position:0%
+the beneficiary side was great, but the
+ 
+
+ align:start position:0%
+the beneficiary side was great, but the
+fact that we
+
+ align:start position:0%
+fact that we
+ 
+
+ align:start position:0%
+fact that we
+found changes that RFID that we could
+
+ align:start position:0%
+found changes that RFID that we could
+ 
+
+ align:start position:0%
+found changes that RFID that we could
+attribute to
+
+ align:start position:0%
+attribute to
+ 
+
+ align:start position:0%
+attribute to
+RFID is tells a lot because we were
+
+ align:start position:0%
+RFID is tells a lot because we were
+ 
+
+ align:start position:0%
+RFID is tells a lot because we were
+looking at a very narrow thing. Now to
+
+ align:start position:0%
+looking at a very narrow thing. Now to
+ 
+
+ align:start position:0%
+looking at a very narrow thing. Now to
+me, that's extremely encouraging because
+
+ align:start position:0%
+me, that's extremely encouraging because
+ 
+
+ align:start position:0%
+me, that's extremely encouraging because
+if you've narrowed it down to this much
+
+ align:start position:0%
+if you've narrowed it down to this much
+ 
+
+ align:start position:0%
+if you've narrowed it down to this much
+and you still found a fairly uh big
+
+ align:start position:0%
+and you still found a fairly uh big
+ 
+
+ align:start position:0%
+and you still found a fairly uh big
+difference, then what if we expand that
+
+ align:start position:0%
+difference, then what if we expand that
+ 
+
+ align:start position:0%
+difference, then what if we expand that
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+out? Okay. I think the possibilities I I
+
+ align:start position:0%
+out? Okay. I think the possibilities I I
+ 
+
+ align:start position:0%
+out? Okay. I think the possibilities I I
+I think we we've only set a very very
+
+ align:start position:0%
+I think we we've only set a very very
+ 
+
+ align:start position:0%
+I think we we've only set a very very
+small bar to clear and and and we we
+
+ align:start position:0%
+small bar to clear and and and we we
+ 
+
+ align:start position:0%
+small bar to clear and and and we we
+cleared it easily, but there's a lot
+
+ align:start position:0%
+cleared it easily, but there's a lot
+ 
+
+ align:start position:0%
+cleared it easily, but there's a lot
+more there that we can we can get at.
+
+ align:start position:0%
+more there that we can we can get at.
+ 
+
+ align:start position:0%
+more there that we can we can get at.
+And also keep in mind that that this
+
+ align:start position:0%
+And also keep in mind that that this
+ 
+
+ align:start position:0%
+And also keep in mind that that this
+idea of incremental versus radical, it's
+
+ align:start position:0%
+idea of incremental versus radical, it's
+ 
+
+ align:start position:0%
+idea of incremental versus radical, it's
+going to vary by the company. We're
+
+ align:start position:0%
+going to vary by the company. We're
+ 
+
+ align:start position:0%
+going to vary by the company. We're
+looking at a very abbreviated supply
+
+ align:start position:0%
+looking at a very abbreviated supply
+ 
+
+ align:start position:0%
+looking at a very abbreviated supply
+chain at this point. Okay, this is from
+
+ align:start position:0%
+chain at this point. Okay, this is from
+ 
+
+ align:start position:0%
+chain at this point. Okay, this is from
+the DC basically to the back room of the
+
+ align:start position:0%
+the DC basically to the back room of the
+ 
+
+ align:start position:0%
+the DC basically to the back room of the
+store and and so far the logistics
+
+ align:start position:0%
+store and and so far the logistics
+ 
+
+ align:start position:0%
+store and and so far the logistics
+segment has been largely
+
+ align:start position:0%
+segment has been largely
+ 
+
+ align:start position:0%
+segment has been largely
+overlooked. You notice that they're
+
+ align:start position:0%
+overlooked. You notice that they're
+ 
+
+ align:start position:0%
+overlooked. You notice that they're
+listed there, but there's not a lot
+
+ align:start position:0%
+listed there, but there's not a lot
+ 
+
+ align:start position:0%
+listed there, but there's not a lot
+going on when we talk about the supply
+
+ align:start position:0%
+going on when we talk about the supply
+ 
+
+ align:start position:0%
+going on when we talk about the supply
+chain and how it's involving the
+
+ align:start position:0%
+chain and how it's involving the
+ 
+
+ align:start position:0%
+chain and how it's involving the
+logistics
+
+ align:start position:0%
+logistics
+ 
+
+ align:start position:0%
+logistics
+arm. Okay. And just uh just very quickly
+
+ align:start position:0%
+arm. Okay. And just uh just very quickly
+ 
+
+ align:start position:0%
+arm. Okay. And just uh just very quickly
+on the on the the out of stocks uh
+
+ align:start position:0%
+on the on the the out of stocks uh
+ 
+
+ align:start position:0%
+on the on the the out of stocks uh
+keeping in in perspective of where that
+
+ align:start position:0%
+keeping in in perspective of where that
+ 
+
+ align:start position:0%
+keeping in in perspective of where that
+was on that chart, you know, the fact
+
+ align:start position:0%
+was on that chart, you know, the fact
+ 
+
+ align:start position:0%
+was on that chart, you know, the fact
+that we were able to find, you know,
+
+ align:start position:0%
+that we were able to find, you know,
+ 
+
+ align:start position:0%
+that we were able to find, you know,
+improvements between pre and post RFID
+
+ align:start position:0%
+improvements between pre and post RFID
+ 
+
+ align:start position:0%
+improvements between pre and post RFID
+and then and in between the pilot and
+
+ align:start position:0%
+and then and in between the pilot and
+ 
+
+ align:start position:0%
+and then and in between the pilot and
+control stores, we we found those
+
+ align:start position:0%
+control stores, we we found those
+ 
+
+ align:start position:0%
+control stores, we we found those
+differences even though we were
+
+ align:start position:0%
+differences even though we were
+ 
+
+ align:start position:0%
+differences even though we were
+constraining ourselves to an incremental
+
+ align:start position:0%
+constraining ourselves to an incremental
+ 
+
+ align:start position:0%
+constraining ourselves to an incremental
+change uh in a very small
+
+ align:start position:0%
+change uh in a very small
+ 
+
+ align:start position:0%
+change uh in a very small
+area. Okay, that that's that just give
+
+ align:start position:0%
+area. Okay, that that's that just give
+ 
+
+ align:start position:0%
+area. Okay, that that's that just give
+you some things to think about there. I
+
+ align:start position:0%
+you some things to think about there. I
+ 
+
+ align:start position:0%
+you some things to think about there. I
+want to very quickly run through, you
+
+ align:start position:0%
+want to very quickly run through, you
+ 
+
+ align:start position:0%
+want to very quickly run through, you
+know, also it's important we're doing
+
+ align:start position:0%
+know, also it's important we're doing
+ 
+
+ align:start position:0%
+know, also it's important we're doing
+the research, but we're also teaching
+
+ align:start position:0%
+the research, but we're also teaching
+ 
+
+ align:start position:0%
+the research, but we're also teaching
+students and others about RFID. We're
+
+ align:start position:0%
+students and others about RFID. We're
+ 
+
+ align:start position:0%
+students and others about RFID. We're
+trying to we're trying to turn out
+
+ align:start position:0%
+trying to we're trying to turn out
+ 
+
+ align:start position:0%
+trying to we're trying to turn out
+people. Michael O'Shea said uh last year
+
+ align:start position:0%
+people. Michael O'Shea said uh last year
+ 
+
+ align:start position:0%
+people. Michael O'Shea said uh last year
+that that the CIO of Kimberly Clark said
+
+ align:start position:0%
+that that the CIO of Kimberly Clark said
+ 
+
+ align:start position:0%
+that that the CIO of Kimberly Clark said
+that uh you know there's such a der of
+
+ align:start position:0%
+that uh you know there's such a der of
+ 
+
+ align:start position:0%
+that uh you know there's such a der of
+experience out there that if somebody
+
+ align:start position:0%
+experience out there that if somebody
+ 
+
+ align:start position:0%
+experience out there that if somebody
+walks by a reader and and says RFID and
+
+ align:start position:0%
+walks by a reader and and says RFID and
+ 
+
+ align:start position:0%
+walks by a reader and and says RFID and
+not riffid, that makes them an RFID
+
+ align:start position:0%
+not riffid, that makes them an RFID
+ 
+
+ align:start position:0%
+not riffid, that makes them an RFID
+expert. Well, we're trying to to stamp
+
+ align:start position:0%
+expert. Well, we're trying to to stamp
+ 
+
+ align:start position:0%
+expert. Well, we're trying to to stamp
+out some of that ignorance by by
+
+ align:start position:0%
+out some of that ignorance by by
+ 
+
+ align:start position:0%
+out some of that ignorance by by
+training people and uh so we've got
+
+ align:start position:0%
+training people and uh so we've got
+ 
+
+ align:start position:0%
+training people and uh so we've got
+dedicated courses in in the the business
+
+ align:start position:0%
+dedicated courses in in the the business
+ 
+
+ align:start position:0%
+dedicated courses in in the the business
+school which which I personally teach uh
+
+ align:start position:0%
+school which which I personally teach uh
+ 
+
+ align:start position:0%
+school which which I personally teach uh
+where we have students uh from across
+
+ align:start position:0%
+where we have students uh from across
+ 
+
+ align:start position:0%
+where we have students uh from across
+the college and and graduate students as
+
+ align:start position:0%
+the college and and graduate students as
+ 
+
+ align:start position:0%
+the college and and graduate students as
+well. So it's undergraduate and graduate
+
+ align:start position:0%
+well. So it's undergraduate and graduate
+ 
+
+ align:start position:0%
+well. So it's undergraduate and graduate
+uh we they're doing live projects for
+
+ align:start position:0%
+uh we they're doing live projects for
+ 
+
+ align:start position:0%
+uh we they're doing live projects for
+companies uh we've got dedicated courses
+
+ align:start position:0%
+companies uh we've got dedicated courses
+ 
+
+ align:start position:0%
+companies uh we've got dedicated courses
+computer science computer engineering
+
+ align:start position:0%
+computer science computer engineering
+ 
+
+ align:start position:0%
+computer science computer engineering
+and then and then interwoven into a lot
+
+ align:start position:0%
+and then and then interwoven into a lot
+ 
+
+ align:start position:0%
+and then and then interwoven into a lot
+of different courses. So we we've got
+
+ align:start position:0%
+of different courses. So we we've got
+ 
+
+ align:start position:0%
+of different courses. So we we've got
+about this semester or last semester we
+
+ align:start position:0%
+about this semester or last semester we
+ 
+
+ align:start position:0%
+about this semester or last semester we
+about had about 80 students uh involved
+
+ align:start position:0%
+about had about 80 students uh involved
+ 
+
+ align:start position:0%
+about had about 80 students uh involved
+in RFID in some some form or fashion. Uh
+
+ align:start position:0%
+in RFID in some some form or fashion. Uh
+ 
+
+ align:start position:0%
+in RFID in some some form or fashion. Uh
+that's over 100 this semester. Um we
+
+ align:start position:0%
+that's over 100 this semester. Um we
+ 
+
+ align:start position:0%
+that's over 100 this semester. Um we
+also uh provide testing and training
+
+ align:start position:0%
+also uh provide testing and training
+ 
+
+ align:start position:0%
+also uh provide testing and training
+services to the industry. Uh one of the
+
+ align:start position:0%
+services to the industry. Uh one of the
+ 
+
+ align:start position:0%
+services to the industry. Uh one of the
+things that we do is we help um
+
+ align:start position:0%
+things that we do is we help um
+ 
+
+ align:start position:0%
+things that we do is we help um
+companies determine tag and tag
+
+ align:start position:0%
+companies determine tag and tag
+ 
+
+ align:start position:0%
+companies determine tag and tag
+placement on their products so that it's
+
+ align:start position:0%
+placement on their products so that it's
+ 
+
+ align:start position:0%
+placement on their products so that it's
+ready to go through an RFID enabled
+
+ align:start position:0%
+ready to go through an RFID enabled
+ 
+
+ align:start position:0%
+ready to go through an RFID enabled
+supply chain. Uh and we've started
+
+ align:start position:0%
+supply chain. Uh and we've started
+ 
+
+ align:start position:0%
+supply chain. Uh and we've started
+coupling our testing with training. One
+
+ align:start position:0%
+coupling our testing with training. One
+ 
+
+ align:start position:0%
+coupling our testing with training. One
+of the things we found out was that, you
+
+ align:start position:0%
+of the things we found out was that, you
+ 
+
+ align:start position:0%
+of the things we found out was that, you
+know, people would just send us a box of
+
+ align:start position:0%
+know, people would just send us a box of
+ 
+
+ align:start position:0%
+know, people would just send us a box of
+their product or case or pallet of their
+
+ align:start position:0%
+their product or case or pallet of their
+ 
+
+ align:start position:0%
+their product or case or pallet of their
+product and say, "Here, help me figure
+
+ align:start position:0%
+product and say, "Here, help me figure
+ 
+
+ align:start position:0%
+product and say, "Here, help me figure
+this out." But they didn't understand
+
+ align:start position:0%
+this out." But they didn't understand
+ 
+
+ align:start position:0%
+this out." But they didn't understand
+RFID. And our most successful um
+
+ align:start position:0%
+RFID. And our most successful um
+ 
+
+ align:start position:0%
+RFID. And our most successful um
+uh projects were when they actually came
+
+ align:start position:0%
+uh projects were when they actually came
+ 
+
+ align:start position:0%
+uh projects were when they actually came
+in and spent time with us going through
+
+ align:start position:0%
+in and spent time with us going through
+ 
+
+ align:start position:0%
+in and spent time with us going through
+the testing and understanding RFID. So,
+
+ align:start position:0%
+the testing and understanding RFID. So,
+ 
+
+ align:start position:0%
+the testing and understanding RFID. So,
+we've actually started coupling that uh
+
+ align:start position:0%
+we've actually started coupling that uh
+ 
+
+ align:start position:0%
+we've actually started coupling that uh
+now formally where we bring the
+
+ align:start position:0%
+now formally where we bring the
+ 
+
+ align:start position:0%
+now formally where we bring the
+companies in, they spend a couple of
+
+ align:start position:0%
+companies in, they spend a couple of
+ 
+
+ align:start position:0%
+companies in, they spend a couple of
+days with us learning about RFID as we
+
+ align:start position:0%
+days with us learning about RFID as we
+ 
+
+ align:start position:0%
+days with us learning about RFID as we
+uh test their products. Um, our lab
+
+ align:start position:0%
+uh test their products. Um, our lab
+ 
+
+ align:start position:0%
+uh test their products. Um, our lab
+facility there at the University of
+
+ align:start position:0%
+facility there at the University of
+ 
+
+ align:start position:0%
+facility there at the University of
+Arkansas, we we're actually off-campus a
+
+ align:start position:0%
+Arkansas, we we're actually off-campus a
+ 
+
+ align:start position:0%
+Arkansas, we we're actually off-campus a
+few miles uh in a working warehouse and
+
+ align:start position:0%
+few miles uh in a working warehouse and
+ 
+
+ align:start position:0%
+few miles uh in a working warehouse and
+manufacturing environment. We have about
+
+ align:start position:0%
+manufacturing environment. We have about
+ 
+
+ align:start position:0%
+manufacturing environment. We have about
+8,000 square feet in Hannah's Candle
+
+ align:start position:0%
+8,000 square feet in Hannah's Candle
+ 
+
+ align:start position:0%
+8,000 square feet in Hannah's Candle
+Company uh which uh they manufacture and
+
+ align:start position:0%
+Company uh which uh they manufacture and
+ 
+
+ align:start position:0%
+Company uh which uh they manufacture and
+then their distribution center is there
+
+ align:start position:0%
+then their distribution center is there
+ 
+
+ align:start position:0%
+then their distribution center is there
+as well. Uh and that's um unfortunately
+
+ align:start position:0%
+as well. Uh and that's um unfortunately
+ 
+
+ align:start position:0%
+as well. Uh and that's um unfortunately
+it is in the distribution center uh
+
+ align:start position:0%
+it is in the distribution center uh
+ 
+
+ align:start position:0%
+it is in the distribution center uh
+part. So the there is no control over
+
+ align:start position:0%
+part. So the there is no control over
+ 
+
+ align:start position:0%
+part. So the there is no control over
+the temperature. So the temperature
+
+ align:start position:0%
+the temperature. So the temperature
+ 
+
+ align:start position:0%
+the temperature. So the temperature
+inside is plus or - 10° what it is
+
+ align:start position:0%
+inside is plus or - 10° what it is
+ 
+
+ align:start position:0%
+inside is plus or - 10° what it is
+outside. Uh, so we also have um when we
+
+ align:start position:0%
+outside. Uh, so we also have um when we
+ 
+
+ align:start position:0%
+outside. Uh, so we also have um when we
+have to test stuff in the cold chain,
+
+ align:start position:0%
+have to test stuff in the cold chain,
+ 
+
+ align:start position:0%
+have to test stuff in the cold chain,
+we've got about a 4,500 square foot
+
+ align:start position:0%
+we've got about a 4,500 square foot
+ 
+
+ align:start position:0%
+we've got about a 4,500 square foot
+square foot facility in Zero Mountain,
+
+ align:start position:0%
+square foot facility in Zero Mountain,
+ 
+
+ align:start position:0%
+square foot facility in Zero Mountain,
+which is a a cold storage facility. And
+
+ align:start position:0%
+which is a a cold storage facility. And
+ 
+
+ align:start position:0%
+which is a a cold storage facility. And
+we've got two labs there, one at 36
+
+ align:start position:0%
+we've got two labs there, one at 36
+ 
+
+ align:start position:0%
+we've got two labs there, one at 36
+degrees and one in minus 10. Uh, so we
+
+ align:start position:0%
+degrees and one in minus 10. Uh, so we
+ 
+
+ align:start position:0%
+degrees and one in minus 10. Uh, so we
+can test stuff there. Our lab is set up
+
+ align:start position:0%
+can test stuff there. Our lab is set up
+ 
+
+ align:start position:0%
+can test stuff there. Our lab is set up
+to replicate really everything that a
+
+ align:start position:0%
+to replicate really everything that a
+ 
+
+ align:start position:0%
+to replicate really everything that a
+that a box sees at this point through
+
+ align:start position:0%
+that a box sees at this point through
+ 
+
+ align:start position:0%
+that a box sees at this point through
+the abbreviated supply chain. And we are
+
+ align:start position:0%
+the abbreviated supply chain. And we are
+ 
+
+ align:start position:0%
+the abbreviated supply chain. And we are
+one of only four labs at this point
+
+ align:start position:0%
+one of only four labs at this point
+ 
+
+ align:start position:0%
+one of only four labs at this point
+that's accredited by EPC Global uh as a
+
+ align:start position:0%
+that's accredited by EPC Global uh as a
+ 
+
+ align:start position:0%
+that's accredited by EPC Global uh as a
+testing facility and the only academic
+
+ align:start position:0%
+testing facility and the only academic
+ 
+
+ align:start position:0%
+testing facility and the only academic
+lab in the world. And just to give you
+
+ align:start position:0%
+lab in the world. And just to give you
+ 
+
+ align:start position:0%
+lab in the world. And just to give you
+some quick quick pictures here of our
+
+ align:start position:0%
+some quick quick pictures here of our
+ 
+
+ align:start position:0%
+some quick quick pictures here of our
+lab and I'm I'm got two minutes to wrap
+
+ align:start position:0%
+lab and I'm I'm got two minutes to wrap
+ 
+
+ align:start position:0%
+lab and I'm I'm got two minutes to wrap
+up. That's the outside of our lab. A
+
+ align:start position:0%
+up. That's the outside of our lab. A
+ 
+
+ align:start position:0%
+up. That's the outside of our lab. A
+truck backed up to our dock. Uh that's
+
+ align:start position:0%
+truck backed up to our dock. Uh that's
+ 
+
+ align:start position:0%
+truck backed up to our dock. Uh that's
+the inside of the lab looking out that
+
+ align:start position:0%
+the inside of the lab looking out that
+ 
+
+ align:start position:0%
+the inside of the lab looking out that
+that same dock door. Um uh view from our
+
+ align:start position:0%
+that same dock door. Um uh view from our
+ 
+
+ align:start position:0%
+that same dock door. Um uh view from our
+lab. The conveyor system that we have in
+
+ align:start position:0%
+lab. The conveyor system that we have in
+ 
+
+ align:start position:0%
+lab. The conveyor system that we have in
+um in there. We we had actually were
+
+ align:start position:0%
+um in there. We we had actually were
+ 
+
+ align:start position:0%
+um in there. We we had actually were
+fortunate to have a conveyor system that
+
+ align:start position:0%
+fortunate to have a conveyor system that
+ 
+
+ align:start position:0%
+fortunate to have a conveyor system that
+was custom designed and built for our
+
+ align:start position:0%
+was custom designed and built for our
+ 
+
+ align:start position:0%
+was custom designed and built for our
+lab that replicates uh um you know
+
+ align:start position:0%
+lab that replicates uh um you know
+ 
+
+ align:start position:0%
+lab that replicates uh um you know
+sorting and merging and and up to 700 ft
+
+ align:start position:0%
+sorting and merging and and up to 700 ft
+ 
+
+ align:start position:0%
+sorting and merging and and up to 700 ft
+per minute. The the whole works um and
+
+ align:start position:0%
+per minute. The the whole works um and
+ 
+
+ align:start position:0%
+per minute. The the whole works um and
+then um pallet rack and and backroom
+
+ align:start position:0%
+then um pallet rack and and backroom
+ 
+
+ align:start position:0%
+then um pallet rack and and backroom
+storage facilities, forklifts,
+
+ align:start position:0%
+storage facilities, forklifts,
+ 
+
+ align:start position:0%
+storage facilities, forklifts,
+etc. Okay. Uh at this point um I believe
+
+ align:start position:0%
+etc. Okay. Uh at this point um I believe
+ 
+
+ align:start position:0%
+etc. Okay. Uh at this point um I believe
+the next on the agenda is is Simon. So
+
+ align:start position:0%
+the next on the agenda is is Simon. So
+ 
+
+ align:start position:0%
+the next on the agenda is is Simon. So
+I'll turn it over to you, Simon. And let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. Thanks, Bill. And good
+
+ align:start position:0%
+Okay. Okay. Thanks, Bill. And good
+ 
+
+ align:start position:0%
+Okay. Okay. Thanks, Bill. And good
+morning, everybody. um really want to
+
+ align:start position:0%
+morning, everybody. um really want to
+ 
+
+ align:start position:0%
+morning, everybody. um really want to
+touch on the the opportunities and
+
+ align:start position:0%
+touch on the the opportunities and
+ 
+
+ align:start position:0%
+touch on the the opportunities and
+issues that that we see in the retail
+
+ align:start position:0%
+issues that that we see in the retail
+ 
+
+ align:start position:0%
+issues that that we see in the retail
+supply chain. Um before I do that, just
+
+ align:start position:0%
+supply chain. Um before I do that, just
+ 
+
+ align:start position:0%
+supply chain. Um before I do that, just
+to to step back a little bit and see
+
+ align:start position:0%
+to to step back a little bit and see
+ 
+
+ align:start position:0%
+to to step back a little bit and see
+what uh we've all accomplished in the
+
+ align:start position:0%
+what uh we've all accomplished in the
+ 
+
+ align:start position:0%
+what uh we've all accomplished in the
+last last few years. Uh so in 2001 2002
+
+ align:start position:0%
+last last few years. Uh so in 2001 2002
+ 
+
+ align:start position:0%
+last last few years. Uh so in 2001 2002
+uh we had the auto ID center field
+
+ align:start position:0%
+uh we had the auto ID center field
+ 
+
+ align:start position:0%
+uh we had the auto ID center field
+trials and uh installation points around
+
+ align:start position:0%
+trials and uh installation points around
+ 
+
+ align:start position:0%
+trials and uh installation points around
+a dock door for instance took hours to
+
+ align:start position:0%
+a dock door for instance took hours to
+ 
+
+ align:start position:0%
+a dock door for instance took hours to
+install and and probably minutes to
+
+ align:start position:0%
+install and and probably minutes to
+ 
+
+ align:start position:0%
+install and and probably minutes to
+destroy or somebody to to go move those
+
+ align:start position:0%
+destroy or somebody to to go move those
+ 
+
+ align:start position:0%
+destroy or somebody to to go move those
+things. Um so it wasn't scalable, wasn't
+
+ align:start position:0%
+things. Um so it wasn't scalable, wasn't
+ 
+
+ align:start position:0%
+things. Um so it wasn't scalable, wasn't
+deployable and certainly wasn't wasn't
+
+ align:start position:0%
+deployable and certainly wasn't wasn't
+ 
+
+ align:start position:0%
+deployable and certainly wasn't wasn't
+supportable. Uh but a lot of learning
+
+ align:start position:0%
+supportable. Uh but a lot of learning
+ 
+
+ align:start position:0%
+supportable. Uh but a lot of learning
+came out of that uh for us all then to
+
+ align:start position:0%
+came out of that uh for us all then to
+ 
+
+ align:start position:0%
+came out of that uh for us all then to
+focus on what we needed for deployable
+
+ align:start position:0%
+focus on what we needed for deployable
+ 
+
+ align:start position:0%
+focus on what we needed for deployable
+solutions. And the one key message that
+
+ align:start position:0%
+solutions. And the one key message that
+ 
+
+ align:start position:0%
+solutions. And the one key message that
+we were putting out at the time is that
+
+ align:start position:0%
+we were putting out at the time is that
+ 
+
+ align:start position:0%
+we were putting out at the time is that
+they should be futurep proofed as far as
+
+ align:start position:0%
+they should be futurep proofed as far as
+ 
+
+ align:start position:0%
+they should be futurep proofed as far as
+possible knowing that Gen 2 was on the
+
+ align:start position:0%
+possible knowing that Gen 2 was on the
+ 
+
+ align:start position:0%
+possible knowing that Gen 2 was on the
+horizon that we wanted to deploy things
+
+ align:start position:0%
+horizon that we wanted to deploy things
+ 
+
+ align:start position:0%
+horizon that we wanted to deploy things
+that were software
+
+ align:start position:0%
+that were software
+ 
+
+ align:start position:0%
+that were software
+upgradable. And in 2004 then we really
+
+ align:start position:0%
+upgradable. And in 2004 then we really
+ 
+
+ align:start position:0%
+upgradable. And in 2004 then we really
+stepped up a notch to to drive for
+
+ align:start position:0%
+stepped up a notch to to drive for
+ 
+
+ align:start position:0%
+stepped up a notch to to drive for
+mobile solutions whether that be
+
+ align:start position:0%
+mobile solutions whether that be
+ 
+
+ align:start position:0%
+mobile solutions whether that be
+handheld solutions uh in particular
+
+ align:start position:0%
+handheld solutions uh in particular
+ 
+
+ align:start position:0%
+handheld solutions uh in particular
+forklift solutions which uh is important
+
+ align:start position:0%
+forklift solutions which uh is important
+ 
+
+ align:start position:0%
+forklift solutions which uh is important
+both to the retailer and a lot of
+
+ align:start position:0%
+both to the retailer and a lot of
+ 
+
+ align:start position:0%
+both to the retailer and a lot of
+suppliers. A lot of those things are
+
+ align:start position:0%
+suppliers. A lot of those things are
+ 
+
+ align:start position:0%
+suppliers. A lot of those things are
+still in the the early stages especially
+
+ align:start position:0%
+still in the the early stages especially
+ 
+
+ align:start position:0%
+still in the the early stages especially
+around mobile
+
+ align:start position:0%
+around mobile
+ 
+
+ align:start position:0%
+around mobile
+solutions. So current situation is we
+
+ align:start position:0%
+solutions. So current situation is we
+ 
+
+ align:start position:0%
+solutions. So current situation is we
+have robust fixed reader solutions
+
+ align:start position:0%
+have robust fixed reader solutions
+ 
+
+ align:start position:0%
+have robust fixed reader solutions
+allowing us to deploy up to 20 read
+
+ align:start position:0%
+allowing us to deploy up to 20 read
+ 
+
+ align:start position:0%
+allowing us to deploy up to 20 read
+points in a in a store in a matter of
+
+ align:start position:0%
+points in a in a store in a matter of
+ 
+
+ align:start position:0%
+points in a in a store in a matter of
+hours in a couple of hours. So taking
+
+ align:start position:0%
+hours in a couple of hours. So taking
+ 
+
+ align:start position:0%
+hours in a couple of hours. So taking
+that time down from days to hours that
+
+ align:start position:0%
+that time down from days to hours that
+ 
+
+ align:start position:0%
+that time down from days to hours that
+reduces the cost cost of deployment. So
+
+ align:start position:0%
+reduces the cost cost of deployment. So
+ 
+
+ align:start position:0%
+reduces the cost cost of deployment. So
+the cost of deployment isn't just around
+
+ align:start position:0%
+the cost of deployment isn't just around
+ 
+
+ align:start position:0%
+the cost of deployment isn't just around
+readers and antenna. A lot of the cost
+
+ align:start position:0%
+readers and antenna. A lot of the cost
+ 
+
+ align:start position:0%
+readers and antenna. A lot of the cost
+is in cabling and actual insulation of
+
+ align:start position:0%
+is in cabling and actual insulation of
+ 
+
+ align:start position:0%
+is in cabling and actual insulation of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+equipment. So it's a little bit like
+
+ align:start position:0%
+equipment. So it's a little bit like
+ 
+
+ align:start position:0%
+equipment. So it's a little bit like
+tags. It's not just the IC chip that we
+
+ align:start position:0%
+tags. It's not just the IC chip that we
+ 
+
+ align:start position:0%
+tags. It's not just the IC chip that we
+can take cost out of. It's that whole
+
+ align:start position:0%
+can take cost out of. It's that whole
+ 
+
+ align:start position:0%
+can take cost out of. It's that whole
+process driving for common operating
+
+ align:start position:0%
+process driving for common operating
+ 
+
+ align:start position:0%
+process driving for common operating
+systems so that we can support it
+
+ align:start position:0%
+systems so that we can support it
+ 
+
+ align:start position:0%
+systems so that we can support it
+centrally and
+
+ align:start position:0%
+centrally and
+ 
+
+ align:start position:0%
+centrally and
+maintain the robustness of that that
+
+ align:start position:0%
+maintain the robustness of that that
+ 
+
+ align:start position:0%
+maintain the robustness of that that
+system. We're starting to deploy
+
+ align:start position:0%
+system. We're starting to deploy
+ 
+
+ align:start position:0%
+system. We're starting to deploy
+handhelds in the the next few months. So
+
+ align:start position:0%
+handhelds in the the next few months. So
+ 
+
+ align:start position:0%
+handhelds in the the next few months. So
+getting the first mobile devices out
+
+ align:start position:0%
+getting the first mobile devices out
+ 
+
+ align:start position:0%
+getting the first mobile devices out
+there. And I think that's when our store
+
+ align:start position:0%
+there. And I think that's when our store
+ 
+
+ align:start position:0%
+there. And I think that's when our store
+associates will start to see some of
+
+ align:start position:0%
+associates will start to see some of
+ 
+
+ align:start position:0%
+associates will start to see some of
+those transformational changes rather
+
+ align:start position:0%
+those transformational changes rather
+ 
+
+ align:start position:0%
+those transformational changes rather
+than just the iterative process changes
+
+ align:start position:0%
+than just the iterative process changes
+ 
+
+ align:start position:0%
+than just the iterative process changes
+that we've had out there in the uh in
+
+ align:start position:0%
+that we've had out there in the uh in
+ 
+
+ align:start position:0%
+that we've had out there in the uh in
+the store so far. Things that they can
+
+ align:start position:0%
+the store so far. Things that they can
+ 
+
+ align:start position:0%
+the store so far. Things that they can
+actually touch and feel and see the
+
+ align:start position:0%
+actually touch and feel and see the
+ 
+
+ align:start position:0%
+actually touch and feel and see the
+difference with RFID. So our fixed read
+
+ align:start position:0%
+difference with RFID. So our fixed read
+ 
+
+ align:start position:0%
+difference with RFID. So our fixed read
+points are collecting data in the
+
+ align:start position:0%
+points are collecting data in the
+ 
+
+ align:start position:0%
+points are collecting data in the
+background and suggesting items to pick.
+
+ align:start position:0%
+background and suggesting items to pick.
+ 
+
+ align:start position:0%
+background and suggesting items to pick.
+But really to a store associate today,
+
+ align:start position:0%
+But really to a store associate today,
+ 
+
+ align:start position:0%
+But really to a store associate today,
+what is RFI doing? They don't know. They
+
+ align:start position:0%
+what is RFI doing? They don't know. They
+ 
+
+ align:start position:0%
+what is RFI doing? They don't know. They
+don't see that as visible. Sure, they're
+
+ align:start position:0%
+don't see that as visible. Sure, they're
+ 
+
+ align:start position:0%
+don't see that as visible. Sure, they're
+picking more product and moving it out
+
+ align:start position:0%
+picking more product and moving it out
+ 
+
+ align:start position:0%
+picking more product and moving it out
+to the the floor quicker, but once we
+
+ align:start position:0%
+to the the floor quicker, but once we
+ 
+
+ align:start position:0%
+to the the floor quicker, but once we
+get these mobile devices in their hands,
+
+ align:start position:0%
+get these mobile devices in their hands,
+ 
+
+ align:start position:0%
+get these mobile devices in their hands,
+then that will help them home in on
+
+ align:start position:0%
+then that will help them home in on
+ 
+
+ align:start position:0%
+then that will help them home in on
+where that product is and really start
+
+ align:start position:0%
+where that product is and really start
+ 
+
+ align:start position:0%
+where that product is and really start
+to streamline their
+
+ align:start position:0%
+to streamline their
+ 
+
+ align:start position:0%
+to streamline their
+process. We're very close to deploying
+
+ align:start position:0%
+process. We're very close to deploying
+ 
+
+ align:start position:0%
+process. We're very close to deploying
+the first forklift solution in our
+
+ align:start position:0%
+the first forklift solution in our
+ 
+
+ align:start position:0%
+the first forklift solution in our
+enterprise to read pallet tags and
+
+ align:start position:0%
+enterprise to read pallet tags and
+ 
+
+ align:start position:0%
+enterprise to read pallet tags and
+location tags. So, we can have a a
+
+ align:start position:0%
+location tags. So, we can have a a
+ 
+
+ align:start position:0%
+location tags. So, we can have a a
+pallet locating system in our Sam's Club
+
+ align:start position:0%
+pallet locating system in our Sam's Club
+ 
+
+ align:start position:0%
+pallet locating system in our Sam's Club
+operation, for example.
+
+ align:start position:0%
+operation, for example.
+ 
+
+ align:start position:0%
+operation, for example.
+Taking that learning, then we can then
+
+ align:start position:0%
+Taking that learning, then we can then
+ 
+
+ align:start position:0%
+Taking that learning, then we can then
+take that to our distribution
+
+ align:start position:0%
+take that to our distribution
+ 
+
+ align:start position:0%
+take that to our distribution
+centers to see how we can use location
+
+ align:start position:0%
+centers to see how we can use location
+ 
+
+ align:start position:0%
+centers to see how we can use location
+tracking and putting pallets away and
+
+ align:start position:0%
+tracking and putting pallets away and
+ 
+
+ align:start position:0%
+tracking and putting pallets away and
+dropping them down and start to
+
+ align:start position:0%
+dropping them down and start to
+ 
+
+ align:start position:0%
+dropping them down and start to
+streamline processes there as we move
+
+ align:start position:0%
+streamline processes there as we move
+ 
+
+ align:start position:0%
+streamline processes there as we move
+move forward in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future. But even those forklift
+
+ align:start position:0%
+future. But even those forklift
+ 
+
+ align:start position:0%
+future. But even those forklift
+solutions are still at the early stages.
+
+ align:start position:0%
+solutions are still at the early stages.
+ 
+
+ align:start position:0%
+solutions are still at the early stages.
+So we can read a pallet tag today.
+
+ align:start position:0%
+So we can read a pallet tag today.
+ 
+
+ align:start position:0%
+So we can read a pallet tag today.
+In the future, we need to to be able to
+
+ align:start position:0%
+In the future, we need to to be able to
+ 
+
+ align:start position:0%
+In the future, we need to to be able to
+read cases or the same amount of cases
+
+ align:start position:0%
+read cases or the same amount of cases
+ 
+
+ align:start position:0%
+read cases or the same amount of cases
+we do today on a dock door from that
+
+ align:start position:0%
+we do today on a dock door from that
+ 
+
+ align:start position:0%
+we do today on a dock door from that
+pallet read on the
+
+ align:start position:0%
+pallet read on the
+ 
+
+ align:start position:0%
+pallet read on the
+forklift. That way we can start to
+
+ align:start position:0%
+forklift. That way we can start to
+ 
+
+ align:start position:0%
+forklift. That way we can start to
+eliminate deploying readers around dock
+
+ align:start position:0%
+eliminate deploying readers around dock
+ 
+
+ align:start position:0%
+eliminate deploying readers around dock
+doors and reduce our overall costs and
+
+ align:start position:0%
+doors and reduce our overall costs and
+ 
+
+ align:start position:0%
+doors and reduce our overall costs and
+just have those readers on
+
+ align:start position:0%
+just have those readers on
+ 
+
+ align:start position:0%
+just have those readers on
+forklifts. We're at the very early
+
+ align:start position:0%
+forklifts. We're at the very early
+ 
+
+ align:start position:0%
+forklifts. We're at the very early
+stages, the infant stages of wearable
+
+ align:start position:0%
+stages, the infant stages of wearable
+ 
+
+ align:start position:0%
+stages, the infant stages of wearable
+solutions.
+
+ align:start position:0%
+solutions.
+ 
+
+ align:start position:0%
+solutions.
+So whether that be something that an
+
+ align:start position:0%
+So whether that be something that an
+ 
+
+ align:start position:0%
+So whether that be something that an
+associate would wear on their the belt
+
+ align:start position:0%
+associate would wear on their the belt
+ 
+
+ align:start position:0%
+associate would wear on their the belt
+or within a vest and the system is
+
+ align:start position:0%
+or within a vest and the system is
+ 
+
+ align:start position:0%
+or within a vest and the system is
+reading in the
+
+ align:start position:0%
+reading in the
+ 
+
+ align:start position:0%
+reading in the
+background and talking back to them and
+
+ align:start position:0%
+background and talking back to them and
+ 
+
+ align:start position:0%
+background and talking back to them and
+give them work to
+
+ align:start position:0%
+give them work to
+ 
+
+ align:start position:0%
+give them work to
+do. And as Bill mentioned, Gen Two is
+
+ align:start position:0%
+do. And as Bill mentioned, Gen Two is
+ 
+
+ align:start position:0%
+do. And as Bill mentioned, Gen Two is
+starting to roll out. We're enabled in
+
+ align:start position:0%
+starting to roll out. We're enabled in
+ 
+
+ align:start position:0%
+starting to roll out. We're enabled in
+our supply chain and starting to receive
+
+ align:start position:0%
+our supply chain and starting to receive
+ 
+
+ align:start position:0%
+our supply chain and starting to receive
+product uh on Gen Two uh tags and prices
+
+ align:start position:0%
+product uh on Gen Two uh tags and prices
+ 
+
+ align:start position:0%
+product uh on Gen Two uh tags and prices
+are falling. tag prices are are falling
+
+ align:start position:0%
+are falling. tag prices are are falling
+ 
+
+ align:start position:0%
+are falling. tag prices are are falling
+through the the
+
+ align:start position:0%
+through the the
+ 
+
+ align:start position:0%
+through the the
+floor. So what has all that technology
+
+ align:start position:0%
+floor. So what has all that technology
+ 
+
+ align:start position:0%
+floor. So what has all that technology
+delivered so far? What are the benefits
+
+ align:start position:0%
+delivered so far? What are the benefits
+ 
+
+ align:start position:0%
+delivered so far? What are the benefits
+of that? So it's allowed the first sort
+
+ align:start position:0%
+of that? So it's allowed the first sort
+ 
+
+ align:start position:0%
+of that? So it's allowed the first sort
+of automation of tasks around pick lists
+
+ align:start position:0%
+of automation of tasks around pick lists
+ 
+
+ align:start position:0%
+of automation of tasks around pick lists
+and manual order controls and our
+
+ align:start position:0%
+and manual order controls and our
+ 
+
+ align:start position:0%
+and manual order controls and our
+associates to work more efficiently.
+
+ align:start position:0%
+associates to work more efficiently.
+ 
+
+ align:start position:0%
+associates to work more efficiently.
+That's improved our customer service and
+
+ align:start position:0%
+That's improved our customer service and
+ 
+
+ align:start position:0%
+That's improved our customer service and
+our offering of product on the shelf at
+
+ align:start position:0%
+our offering of product on the shelf at
+ 
+
+ align:start position:0%
+our offering of product on the shelf at
+the right time. It's really taken the
+
+ align:start position:0%
+the right time. It's really taken the
+ 
+
+ align:start position:0%
+the right time. It's really taken the
+theory out of the lab environment into
+
+ align:start position:0%
+theory out of the lab environment into
+ 
+
+ align:start position:0%
+theory out of the lab environment into
+the real world. And I think once you
+
+ align:start position:0%
+the real world. And I think once you
+ 
+
+ align:start position:0%
+the real world. And I think once you
+take that step, that's when a lot of the
+
+ align:start position:0%
+take that step, that's when a lot of the
+ 
+
+ align:start position:0%
+take that step, that's when a lot of the
+the real learning comes
+
+ align:start position:0%
+the real learning comes
+ 
+
+ align:start position:0%
+the real learning comes
+about. And Bill mentioned the study that
+
+ align:start position:0%
+about. And Bill mentioned the study that
+ 
+
+ align:start position:0%
+about. And Bill mentioned the study that
+they performed on our first changes
+
+ align:start position:0%
+they performed on our first changes
+ 
+
+ align:start position:0%
+they performed on our first changes
+where out of stocks were reduced by 16%.
+
+ align:start position:0%
+where out of stocks were reduced by 16%.
+ 
+
+ align:start position:0%
+where out of stocks were reduced by 16%.
+So you can see from a a nonrfid
+
+ align:start position:0%
+So you can see from a a nonrfid
+ 
+
+ align:start position:0%
+So you can see from a a nonrfid
+environment in the different store
+
+ align:start position:0%
+environment in the different store
+ 
+
+ align:start position:0%
+environment in the different store
+formats here to a partial implementation
+
+ align:start position:0%
+formats here to a partial implementation
+ 
+
+ align:start position:0%
+formats here to a partial implementation
+that we did uh we had some caps on the
+
+ align:start position:0%
+that we did uh we had some caps on the
+ 
+
+ align:start position:0%
+that we did uh we had some caps on the
+number of autopicks that we would
+
+ align:start position:0%
+number of autopicks that we would
+ 
+
+ align:start position:0%
+number of autopicks that we would
+actually suggest to to store associates
+
+ align:start position:0%
+actually suggest to to store associates
+ 
+
+ align:start position:0%
+actually suggest to to store associates
+and then to a full-blown RFID solution
+
+ align:start position:0%
+and then to a full-blown RFID solution
+ 
+
+ align:start position:0%
+and then to a full-blown RFID solution
+on those products that were enabled at
+
+ align:start position:0%
+on those products that were enabled at
+ 
+
+ align:start position:0%
+on those products that were enabled at
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+measuring the out of stocks in the
+
+ align:start position:0%
+measuring the out of stocks in the
+ 
+
+ align:start position:0%
+measuring the out of stocks in the
+control stores versus um sorry the the
+
+ align:start position:0%
+control stores versus um sorry the the
+ 
+
+ align:start position:0%
+control stores versus um sorry the the
+pilot stores versus control stores.
+
+ align:start position:0%
+pilot stores versus control stores.
+ 
+
+ align:start position:0%
+pilot stores versus control stores.
+Those RFID stores performed 63% better
+
+ align:start position:0%
+Those RFID stores performed 63% better
+ 
+
+ align:start position:0%
+Those RFID stores performed 63% better
+in stocking the shelves than the control
+
+ align:start position:0%
+in stocking the shelves than the control
+ 
+
+ align:start position:0%
+in stocking the shelves than the control
+stores
+
+ align:start position:0%
+stores
+ 
+
+ align:start position:0%
+stores
+did. And within the same store, within
+
+ align:start position:0%
+did. And within the same store, within
+ 
+
+ align:start position:0%
+did. And within the same store, within
+the pilot store, looking at tagged
+
+ align:start position:0%
+the pilot store, looking at tagged
+ 
+
+ align:start position:0%
+the pilot store, looking at tagged
+product versus non-tagged product, we
+
+ align:start position:0%
+product versus non-tagged product, we
+ 
+
+ align:start position:0%
+product versus non-tagged product, we
+saw those replenish three times
+
+ align:start position:0%
+saw those replenish three times
+ 
+
+ align:start position:0%
+saw those replenish three times
+faster, those products with RFID tags.
+
+ align:start position:0%
+faster, those products with RFID tags.
+ 
+
+ align:start position:0%
+faster, those products with RFID tags.
+So, as Bill said, those first iterative
+
+ align:start position:0%
+So, as Bill said, those first iterative
+ 
+
+ align:start position:0%
+So, as Bill said, those first iterative
+process changes were starting to deliver
+
+ align:start position:0%
+process changes were starting to deliver
+ 
+
+ align:start position:0%
+process changes were starting to deliver
+dramatic results on the tag product we
+
+ align:start position:0%
+dramatic results on the tag product we
+ 
+
+ align:start position:0%
+dramatic results on the tag product we
+had in those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stores. So, what about the issues and
+
+ align:start position:0%
+stores. So, what about the issues and
+ 
+
+ align:start position:0%
+stores. So, what about the issues and
+opportunities? Well, the issues remain
+
+ align:start position:0%
+opportunities? Well, the issues remain
+ 
+
+ align:start position:0%
+opportunities? Well, the issues remain
+the same as they did four years ago, 10
+
+ align:start position:0%
+the same as they did four years ago, 10
+ 
+
+ align:start position:0%
+the same as they did four years ago, 10
+years ago. It's all about data accuracy
+
+ align:start position:0%
+years ago. It's all about data accuracy
+ 
+
+ align:start position:0%
+years ago. It's all about data accuracy
+and real-time data. Data accuracy drives
+
+ align:start position:0%
+and real-time data. Data accuracy drives
+ 
+
+ align:start position:0%
+and real-time data. Data accuracy drives
+both availability of product in the
+
+ align:start position:0%
+both availability of product in the
+ 
+
+ align:start position:0%
+both availability of product in the
+whole supply
+
+ align:start position:0%
+whole supply
+ 
+
+ align:start position:0%
+whole supply
+chain, the speed of that that
+
+ align:start position:0%
+chain, the speed of that that
+ 
+
+ align:start position:0%
+chain, the speed of that that
+merchandise flowing through the supply
+
+ align:start position:0%
+merchandise flowing through the supply
+ 
+
+ align:start position:0%
+merchandise flowing through the supply
+chain and the amount of inventory we
+
+ align:start position:0%
+chain and the amount of inventory we
+ 
+
+ align:start position:0%
+chain and the amount of inventory we
+have to hold that has a direct relation
+
+ align:start position:0%
+have to hold that has a direct relation
+ 
+
+ align:start position:0%
+have to hold that has a direct relation
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+costs. And as Bill said, it's important
+
+ align:start position:0%
+costs. And as Bill said, it's important
+ 
+
+ align:start position:0%
+costs. And as Bill said, it's important
+to to see how we use that data that we
+
+ align:start position:0%
+to to see how we use that data that we
+ 
+
+ align:start position:0%
+to to see how we use that data that we
+don't get swamped with data. We're using
+
+ align:start position:0%
+don't get swamped with data. We're using
+ 
+
+ align:start position:0%
+don't get swamped with data. We're using
+it. It's actionable for store
+
+ align:start position:0%
+it. It's actionable for store
+ 
+
+ align:start position:0%
+it. It's actionable for store
+associates, for replenishment
+
+ align:start position:0%
+associates, for replenishment
+ 
+
+ align:start position:0%
+associates, for replenishment
+associates, and for our
+
+ align:start position:0%
+associates, and for our
+ 
+
+ align:start position:0%
+associates, and for our
+suppliers. But it opens up a new world
+
+ align:start position:0%
+suppliers. But it opens up a new world
+ 
+
+ align:start position:0%
+suppliers. But it opens up a new world
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+granularity, new windows that we can see
+
+ align:start position:0%
+granularity, new windows that we can see
+ 
+
+ align:start position:0%
+granularity, new windows that we can see
+into the supply chain that we just
+
+ align:start position:0%
+into the supply chain that we just
+ 
+
+ align:start position:0%
+into the supply chain that we just
+didn't realize
+
+ align:start position:0%
+didn't realize
+ 
+
+ align:start position:0%
+didn't realize
+before. We're starting to drive
+
+ align:start position:0%
+before. We're starting to drive
+ 
+
+ align:start position:0%
+before. We're starting to drive
+efficiencies around manual processes,
+
+ align:start position:0%
+efficiencies around manual processes,
+ 
+
+ align:start position:0%
+efficiencies around manual processes,
+but lots of inefficiencies still exist
+
+ align:start position:0%
+but lots of inefficiencies still exist
+ 
+
+ align:start position:0%
+but lots of inefficiencies still exist
+today.
+
+ align:start position:0%
+today.
+ 
+
+ align:start position:0%
+today.
+And a lot of changes will only occur say
+
+ align:start position:0%
+And a lot of changes will only occur say
+ 
+
+ align:start position:0%
+And a lot of changes will only occur say
+in a distribution center once we start
+
+ align:start position:0%
+in a distribution center once we start
+ 
+
+ align:start position:0%
+in a distribution center once we start
+to get a critical mass of product
+
+ align:start position:0%
+to get a critical mass of product
+ 
+
+ align:start position:0%
+to get a critical mass of product
+flowing through those
+
+ align:start position:0%
+flowing through those
+ 
+
+ align:start position:0%
+flowing through those
+facilities. We've got a big opportunity
+
+ align:start position:0%
+facilities. We've got a big opportunity
+ 
+
+ align:start position:0%
+facilities. We've got a big opportunity
+to reduce lead times in the whole supply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain. So in the short term, as I've
+
+ align:start position:0%
+chain. So in the short term, as I've
+ 
+
+ align:start position:0%
+chain. So in the short term, as I've
+mentioned, we're rolling out handhelds,
+
+ align:start position:0%
+mentioned, we're rolling out handhelds,
+ 
+
+ align:start position:0%
+mentioned, we're rolling out handhelds,
+but the choice of handhelds today is
+
+ align:start position:0%
+but the choice of handhelds today is
+ 
+
+ align:start position:0%
+but the choice of handhelds today is
+limited. The functionality of those
+
+ align:start position:0%
+limited. The functionality of those
+ 
+
+ align:start position:0%
+limited. The functionality of those
+handhelds is limited.
+
+ align:start position:0%
+handhelds is limited.
+ 
+
+ align:start position:0%
+handhelds is limited.
+We need to move to
+
+ align:start position:0%
+We need to move to
+ 
+
+ align:start position:0%
+We need to move to
+wearable mobile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+devices systems that help us fasttrack
+
+ align:start position:0%
+devices systems that help us fasttrack
+ 
+
+ align:start position:0%
+devices systems that help us fasttrack
+product to the sales floor. It's always
+
+ align:start position:0%
+product to the sales floor. It's always
+ 
+
+ align:start position:0%
+product to the sales floor. It's always
+that last 50 yards in the store where
+
+ align:start position:0%
+that last 50 yards in the store where
+ 
+
+ align:start position:0%
+that last 50 yards in the store where
+we're most
+
+ align:start position:0%
+we're most
+ 
+
+ align:start position:0%
+we're most
+inefficient. So, how do we get what I
+
+ align:start position:0%
+inefficient. So, how do we get what I
+ 
+
+ align:start position:0%
+inefficient. So, how do we get what I
+would turn oneway stock? It comes in,
+
+ align:start position:0%
+would turn oneway stock? It comes in,
+ 
+
+ align:start position:0%
+would turn oneway stock? It comes in,
+goes straight to the sales floor to the
+
+ align:start position:0%
+goes straight to the sales floor to the
+ 
+
+ align:start position:0%
+goes straight to the sales floor to the
+shelf. It's put on the shelf and the box
+
+ align:start position:0%
+shelf. It's put on the shelf and the box
+ 
+
+ align:start position:0%
+shelf. It's put on the shelf and the box
+is thrown away. We don't get this
+
+ align:start position:0%
+is thrown away. We don't get this
+ 
+
+ align:start position:0%
+is thrown away. We don't get this
+double, treble, quadruple handling back
+
+ align:start position:0%
+double, treble, quadruple handling back
+ 
+
+ align:start position:0%
+double, treble, quadruple handling back
+and forth from the back room to the
+
+ align:start position:0%
+and forth from the back room to the
+ 
+
+ align:start position:0%
+and forth from the back room to the
+sales
+
+ align:start position:0%
+sales
+ 
+
+ align:start position:0%
+sales
+floor. Bill mentioned about execution
+
+ align:start position:0%
+floor. Bill mentioned about execution
+ 
+
+ align:start position:0%
+floor. Bill mentioned about execution
+tools for promotions, new item
+
+ align:start position:0%
+tools for promotions, new item
+ 
+
+ align:start position:0%
+tools for promotions, new item
+launches. So, how can we work more
+
+ align:start position:0%
+launches. So, how can we work more
+ 
+
+ align:start position:0%
+launches. So, how can we work more
+efficiently in that aspect? And that's
+
+ align:start position:0%
+efficiently in that aspect? And that's
+ 
+
+ align:start position:0%
+efficiently in that aspect? And that's
+not just a suppliers responsibility or a
+
+ align:start position:0%
+not just a suppliers responsibility or a
+ 
+
+ align:start position:0%
+not just a suppliers responsibility or a
+retailer's responsibility. It's how do
+
+ align:start position:0%
+retailer's responsibility. It's how do
+ 
+
+ align:start position:0%
+retailer's responsibility. It's how do
+we collaborate together and make that
+
+ align:start position:0%
+we collaborate together and make that
+ 
+
+ align:start position:0%
+we collaborate together and make that
+work?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+driving execution. So I mentioned the
+
+ align:start position:0%
+driving execution. So I mentioned the
+ 
+
+ align:start position:0%
+driving execution. So I mentioned the
+new windows and and the the new data
+
+ align:start position:0%
+new windows and and the the new data
+ 
+
+ align:start position:0%
+new windows and and the the new data
+streams that that RFI gives
+
+ align:start position:0%
+streams that that RFI gives
+ 
+
+ align:start position:0%
+streams that that RFI gives
+us. How do we use
+
+ align:start position:0%
+us. How do we use
+ 
+
+ align:start position:0%
+us. How do we use
+that to drive that execution? So in the
+
+ align:start position:0%
+that to drive that execution? So in the
+ 
+
+ align:start position:0%
+that to drive that execution? So in the
+real world today, people tick boxes and
+
+ align:start position:0%
+real world today, people tick boxes and
+ 
+
+ align:start position:0%
+real world today, people tick boxes and
+make reports look pretty and say they've
+
+ align:start position:0%
+make reports look pretty and say they've
+ 
+
+ align:start position:0%
+make reports look pretty and say they've
+done task when they may not have done
+
+ align:start position:0%
+done task when they may not have done
+ 
+
+ align:start position:0%
+done task when they may not have done
+that task. RFID gives us that ability to
+
+ align:start position:0%
+that task. RFID gives us that ability to
+ 
+
+ align:start position:0%
+that task. RFID gives us that ability to
+see whether that task has been done,
+
+ align:start position:0%
+see whether that task has been done,
+ 
+
+ align:start position:0%
+see whether that task has been done,
+whether that new modular has been laid
+
+ align:start position:0%
+whether that new modular has been laid
+ 
+
+ align:start position:0%
+whether that new modular has been laid
+out on the shelf, whether those new
+
+ align:start position:0%
+out on the shelf, whether those new
+ 
+
+ align:start position:0%
+out on the shelf, whether those new
+items have made it out to the shelf
+
+ align:start position:0%
+items have made it out to the shelf
+ 
+
+ align:start position:0%
+items have made it out to the shelf
+without anybody having to go and and
+
+ align:start position:0%
+without anybody having to go and and
+ 
+
+ align:start position:0%
+without anybody having to go and and
+take a a check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sheet. Bill mentioned electronic proof
+
+ align:start position:0%
+sheet. Bill mentioned electronic proof
+ 
+
+ align:start position:0%
+sheet. Bill mentioned electronic proof
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+delivery, big efficiency gain for both
+
+ align:start position:0%
+delivery, big efficiency gain for both
+ 
+
+ align:start position:0%
+delivery, big efficiency gain for both
+the supplier and retailer.
+
+ align:start position:0%
+the supplier and retailer.
+ 
+
+ align:start position:0%
+the supplier and retailer.
+So how do we we make that happen across
+
+ align:start position:0%
+So how do we we make that happen across
+ 
+
+ align:start position:0%
+So how do we we make that happen across
+all retailers, all
+
+ align:start position:0%
+all retailers, all
+ 
+
+ align:start position:0%
+all retailers, all
+suppliers with a common
+
+ align:start position:0%
+suppliers with a common
+ 
+
+ align:start position:0%
+suppliers with a common
+understanding? I mentioned about the
+
+ align:start position:0%
+understanding? I mentioned about the
+ 
+
+ align:start position:0%
+understanding? I mentioned about the
+pallet locator system for
+
+ align:start position:0%
+pallet locator system for
+ 
+
+ align:start position:0%
+pallet locator system for
+SAMs. The benefits we're starting to see
+
+ align:start position:0%
+SAMs. The benefits we're starting to see
+ 
+
+ align:start position:0%
+SAMs. The benefits we're starting to see
+today, as Bill mentioned, it's a very
+
+ align:start position:0%
+today, as Bill mentioned, it's a very
+ 
+
+ align:start position:0%
+today, as Bill mentioned, it's a very
+small sort of subset of products, an
+
+ align:start position:0%
+small sort of subset of products, an
+ 
+
+ align:start position:0%
+small sort of subset of products, an
+area that we've started to change. So
+
+ align:start position:0%
+area that we've started to change. So
+ 
+
+ align:start position:0%
+area that we've started to change. So
+that is truly the tip of the
+
+ align:start position:0%
+that is truly the tip of the
+ 
+
+ align:start position:0%
+that is truly the tip of the
+iceberg. But many benefits are reliant
+
+ align:start position:0%
+iceberg. But many benefits are reliant
+ 
+
+ align:start position:0%
+iceberg. But many benefits are reliant
+on the technology continue to develop
+
+ align:start position:0%
+on the technology continue to develop
+ 
+
+ align:start position:0%
+on the technology continue to develop
+and mature and reducing the cost of
+
+ align:start position:0%
+and mature and reducing the cost of
+ 
+
+ align:start position:0%
+and mature and reducing the cost of
+deployment. So we start to get that
+
+ align:start position:0%
+deployment. So we start to get that
+ 
+
+ align:start position:0%
+deployment. So we start to get that
+critical mass of products flowing
+
+ align:start position:0%
+critical mass of products flowing
+ 
+
+ align:start position:0%
+critical mass of products flowing
+through. Gen two is showing step change
+
+ align:start position:0%
+through. Gen two is showing step change
+ 
+
+ align:start position:0%
+through. Gen two is showing step change
+in performance, a real step change. I
+
+ align:start position:0%
+in performance, a real step change. I
+ 
+
+ align:start position:0%
+in performance, a real step change. I
+know as end users when we came together
+
+ align:start position:0%
+know as end users when we came together
+ 
+
+ align:start position:0%
+know as end users when we came together
+we all said well you know we need a
+
+ align:start position:0%
+we all said well you know we need a
+ 
+
+ align:start position:0%
+we all said well you know we need a
+global tag but it's no point in in
+
+ align:start position:0%
+global tag but it's no point in in
+ 
+
+ align:start position:0%
+global tag but it's no point in in
+developing this this tag if it's just an
+
+ align:start position:0%
+developing this this tag if it's just an
+ 
+
+ align:start position:0%
+developing this this tag if it's just an
+iterative process we need a real step
+
+ align:start position:0%
+iterative process we need a real step
+ 
+
+ align:start position:0%
+iterative process we need a real step
+change and pleas to say Gen two is is
+
+ align:start position:0%
+change and pleas to say Gen two is is
+ 
+
+ align:start position:0%
+change and pleas to say Gen two is is
+delivering that today but we still need
+
+ align:start position:0%
+delivering that today but we still need
+ 
+
+ align:start position:0%
+delivering that today but we still need
+to drive for cheaper faster and added
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+features. So what are some of the
+
+ align:start position:0%
+features. So what are some of the
+ 
+
+ align:start position:0%
+features. So what are some of the
+barriers to continuing adoption and
+
+ align:start position:0%
+barriers to continuing adoption and
+ 
+
+ align:start position:0%
+barriers to continuing adoption and
+accelerating
+
+ align:start position:0%
+accelerating
+ 
+
+ align:start position:0%
+accelerating
+adoption? I think if you ask most
+
+ align:start position:0%
+adoption? I think if you ask most
+ 
+
+ align:start position:0%
+adoption? I think if you ask most
+suppliers, tag cost
+
+ align:start position:0%
+suppliers, tag cost
+ 
+
+ align:start position:0%
+suppliers, tag cost
+is the primary barrier.
+
+ align:start position:0%
+is the primary barrier.
+ 
+
+ align:start position:0%
+is the primary barrier.
+Many process
+
+ align:start position:0%
+Many process
+ 
+
+ align:start position:0%
+Many process
+efficiencies require that critical mass
+
+ align:start position:0%
+efficiencies require that critical mass
+ 
+
+ align:start position:0%
+efficiencies require that critical mass
+I've spoken about and we need to be
+
+ align:start position:0%
+I've spoken about and we need to be
+ 
+
+ align:start position:0%
+I've spoken about and we need to be
+smart of how we introduce
+
+ align:start position:0%
+smart of how we introduce
+ 
+
+ align:start position:0%
+smart of how we introduce
+RFID into areas so we're not running
+
+ align:start position:0%
+RFID into areas so we're not running
+ 
+
+ align:start position:0%
+RFID into areas so we're not running
+dual
+
+ align:start position:0%
+dual
+ 
+
+ align:start position:0%
+dual
+processes and turning people's worlds
+
+ align:start position:0%
+processes and turning people's worlds
+ 
+
+ align:start position:0%
+processes and turning people's worlds
+upside down. That's what we started to
+
+ align:start position:0%
+upside down. That's what we started to
+ 
+
+ align:start position:0%
+upside down. That's what we started to
+do with our picking
+
+ align:start position:0%
+do with our picking
+ 
+
+ align:start position:0%
+do with our picking
+list. So it's behind the scenes and it's
+
+ align:start position:0%
+list. So it's behind the scenes and it's
+ 
+
+ align:start position:0%
+list. So it's behind the scenes and it's
+just dovetailing with the current
+
+ align:start position:0%
+just dovetailing with the current
+ 
+
+ align:start position:0%
+just dovetailing with the current
+process. And as we move forward, we need
+
+ align:start position:0%
+process. And as we move forward, we need
+ 
+
+ align:start position:0%
+process. And as we move forward, we need
+to minimize the impact on associates
+
+ align:start position:0%
+to minimize the impact on associates
+ 
+
+ align:start position:0%
+to minimize the impact on associates
+throughout the supply chain to enable us
+
+ align:start position:0%
+throughout the supply chain to enable us
+ 
+
+ align:start position:0%
+throughout the supply chain to enable us
+to execute and to get buy
+
+ align:start position:0%
+to execute and to get buy
+ 
+
+ align:start position:0%
+to execute and to get buy
+in. So what are the kind of things that
+
+ align:start position:0%
+in. So what are the kind of things that
+ 
+
+ align:start position:0%
+in. So what are the kind of things that
+that we're looking that that we need to
+
+ align:start position:0%
+that we're looking that that we need to
+ 
+
+ align:start position:0%
+that we're looking that that we need to
+work on and we need to collaborate on?
+
+ align:start position:0%
+work on and we need to collaborate on?
+ 
+
+ align:start position:0%
+work on and we need to collaborate on?
+And it's those transformational
+
+ align:start position:0%
+And it's those transformational
+ 
+
+ align:start position:0%
+And it's those transformational
+changes that Bill spoke about. So sensor
+
+ align:start position:0%
+changes that Bill spoke about. So sensor
+ 
+
+ align:start position:0%
+changes that Bill spoke about. So sensor
+tags seems like we've been talking about
+
+ align:start position:0%
+tags seems like we've been talking about
+ 
+
+ align:start position:0%
+tags seems like we've been talking about
+cold chain compliance and sensor
+
+ align:start position:0%
+cold chain compliance and sensor
+ 
+
+ align:start position:0%
+cold chain compliance and sensor
+tags since a year
+
+ align:start position:0%
+tags since a year
+ 
+
+ align:start position:0%
+tags since a year
+dot and it's not really becoming a
+
+ align:start position:0%
+dot and it's not really becoming a
+ 
+
+ align:start position:0%
+dot and it's not really becoming a
+reality yet. So you look at semipassive
+
+ align:start position:0%
+reality yet. So you look at semipassive
+ 
+
+ align:start position:0%
+reality yet. So you look at semipassive
+tags, they're far too expensive
+
+ align:start position:0%
+tags, they're far too expensive
+ 
+
+ align:start position:0%
+tags, they're far too expensive
+currently to put into a a deployable uh
+
+ align:start position:0%
+currently to put into a a deployable uh
+ 
+
+ align:start position:0%
+currently to put into a a deployable uh
+solution. So we need to move that up a
+
+ align:start position:0%
+solution. So we need to move that up a
+ 
+
+ align:start position:0%
+solution. So we need to move that up a
+notch.
+
+ align:start position:0%
+notch.
+ 
+
+ align:start position:0%
+notch.
+We'll start piloting some proof of
+
+ align:start position:0%
+We'll start piloting some proof of
+ 
+
+ align:start position:0%
+We'll start piloting some proof of
+concepts this year again to to show
+
+ align:start position:0%
+concepts this year again to to show
+ 
+
+ align:start position:0%
+concepts this year again to to show
+everybody what the benefit would
+
+ align:start position:0%
+everybody what the benefit would
+ 
+
+ align:start position:0%
+everybody what the benefit would
+be. But looking at passive temperature
+
+ align:start position:0%
+be. But looking at passive temperature
+ 
+
+ align:start position:0%
+be. But looking at passive temperature
+sensing. So what is a true real business
+
+ align:start position:0%
+sensing. So what is a true real business
+ 
+
+ align:start position:0%
+sensing. So what is a true real business
+case? Is it that we want to with a
+
+ align:start position:0%
+case? Is it that we want to with a
+ 
+
+ align:start position:0%
+case? Is it that we want to with a
+passive uh sensor tag read that
+
+ align:start position:0%
+passive uh sensor tag read that
+ 
+
+ align:start position:0%
+passive uh sensor tag read that
+temperature as it passes certain read
+
+ align:start position:0%
+temperature as it passes certain read
+ 
+
+ align:start position:0%
+temperature as it passes certain read
+points or in a trailer that may have um
+
+ align:start position:0%
+points or in a trailer that may have um
+ 
+
+ align:start position:0%
+points or in a trailer that may have um
+RF equipment on board already for things
+
+ align:start position:0%
+RF equipment on board already for things
+ 
+
+ align:start position:0%
+RF equipment on board already for things
+like GPS that we can tie into.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theft prevention
+
+ align:start position:0%
+theft prevention
+ 
+
+ align:start position:0%
+theft prevention
+systems. A lot of work was done on this
+
+ align:start position:0%
+systems. A lot of work was done on this
+ 
+
+ align:start position:0%
+systems. A lot of work was done on this
+through the auto center and the
+
+ align:start position:0%
+through the auto center and the
+ 
+
+ align:start position:0%
+through the auto center and the
+labs you probably four or five years
+
+ align:start position:0%
+labs you probably four or five years
+ 
+
+ align:start position:0%
+labs you probably four or five years
+ago. But how do we really replace EAS
+
+ align:start position:0%
+ago. But how do we really replace EAS
+ 
+
+ align:start position:0%
+ago. But how do we really replace EAS
+systems because that will start to
+
+ align:start position:0%
+systems because that will start to
+ 
+
+ align:start position:0%
+systems because that will start to
+reduce
+
+ align:start position:0%
+reduce
+ 
+
+ align:start position:0%
+reduce
+costs in that aspect. We can't have EAS
+
+ align:start position:0%
+costs in that aspect. We can't have EAS
+ 
+
+ align:start position:0%
+costs in that aspect. We can't have EAS
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+RFID tags on the same product.
+
+ align:start position:0%
+RFID tags on the same product.
+ 
+
+ align:start position:0%
+RFID tags on the same product.
+because that's just increasing costs.
+
+ align:start position:0%
+because that's just increasing costs.
+ 
+
+ align:start position:0%
+because that's just increasing costs.
+So, how do we get down to one solution
+
+ align:start position:0%
+So, how do we get down to one solution
+ 
+
+ align:start position:0%
+So, how do we get down to one solution
+that will achieve
+
+ align:start position:0%
+that will achieve
+ 
+
+ align:start position:0%
+that will achieve
+both true true sort at high
+
+ align:start position:0%
+both true true sort at high
+ 
+
+ align:start position:0%
+both true true sort at high
+speeds? So, we're close to 600 feet a
+
+ align:start position:0%
+speeds? So, we're close to 600 feet a
+ 
+
+ align:start position:0%
+speeds? So, we're close to 600 feet a
+minute on our sortation systems. How do
+
+ align:start position:0%
+minute on our sortation systems. How do
+ 
+
+ align:start position:0%
+minute on our sortation systems. How do
+we singulate tag reads to know it's that
+
+ align:start position:0%
+we singulate tag reads to know it's that
+ 
+
+ align:start position:0%
+we singulate tag reads to know it's that
+case that needs to go to store 50?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I spoke quite a bit about mobile devices
+
+ align:start position:0%
+I spoke quite a bit about mobile devices
+ 
+
+ align:start position:0%
+I spoke quite a bit about mobile devices
+but robust deployable mobile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+devices and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+international we need true global tags
+
+ align:start position:0%
+international we need true global tags
+ 
+
+ align:start position:0%
+international we need true global tags
+mentioned about Gen two being a global
+
+ align:start position:0%
+mentioned about Gen two being a global
+ 
+
+ align:start position:0%
+mentioned about Gen two being a global
+solution but I think what you'll see out
+
+ align:start position:0%
+solution but I think what you'll see out
+ 
+
+ align:start position:0%
+solution but I think what you'll see out
+there today with Gen two is those tags
+
+ align:start position:0%
+there today with Gen two is those tags
+ 
+
+ align:start position:0%
+there today with Gen two is those tags
+are tuned to each geographic area so the
+
+ align:start position:0%
+are tuned to each geographic area so the
+ 
+
+ align:start position:0%
+are tuned to each geographic area so the
+tags that we're testing
+
+ align:start position:0%
+tags that we're testing
+ 
+
+ align:start position:0%
+tags that we're testing
+here I'm sure are tuned
+
+ align:start position:0%
+here I'm sure are tuned
+ 
+
+ align:start position:0%
+here I'm sure are tuned
+to the US. The tags that we're testing
+
+ align:start position:0%
+to the US. The tags that we're testing
+ 
+
+ align:start position:0%
+to the US. The tags that we're testing
+in Europe are tuned to
+
+ align:start position:0%
+in Europe are tuned to
+ 
+
+ align:start position:0%
+in Europe are tuned to
+Europe. That's not going to work. That
+
+ align:start position:0%
+Europe. That's not going to work. That
+ 
+
+ align:start position:0%
+Europe. That's not going to work. That
+wasn't the idea of Gen
+
+ align:start position:0%
+wasn't the idea of Gen
+ 
+
+ align:start position:0%
+wasn't the idea of Gen
+Two. So, we need to to tune the
+
+ align:start position:0%
+Two. So, we need to to tune the
+ 
+
+ align:start position:0%
+Two. So, we need to to tune the
+tags to to one sort of format that will
+
+ align:start position:0%
+tags to to one sort of format that will
+ 
+
+ align:start position:0%
+tags to to one sort of format that will
+work around the
+
+ align:start position:0%
+work around the
+ 
+
+ align:start position:0%
+work around the
+world. And we need to move the EPC
+
+ align:start position:0%
+world. And we need to move the EPC
+ 
+
+ align:start position:0%
+world. And we need to move the EPC
+network from theory and powerpoints into
+
+ align:start position:0%
+network from theory and powerpoints into
+ 
+
+ align:start position:0%
+network from theory and powerpoints into
+reality.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of talk about farmer and I think
+
+ align:start position:0%
+a lot of talk about farmer and I think
+ 
+
+ align:start position:0%
+a lot of talk about farmer and I think
+there was a a separate session yesterday
+
+ align:start position:0%
+there was a a separate session yesterday
+ 
+
+ align:start position:0%
+there was a a separate session yesterday
+on farmer which uh I wasn't able to
+
+ align:start position:0%
+on farmer which uh I wasn't able to
+ 
+
+ align:start position:0%
+on farmer which uh I wasn't able to
+make but in the UHF space you know
+
+ align:start position:0%
+make but in the UHF space you know
+ 
+
+ align:start position:0%
+make but in the UHF space you know
+there's been a lot of focus on case and
+
+ align:start position:0%
+there's been a lot of focus on case and
+ 
+
+ align:start position:0%
+there's been a lot of focus on case and
+pallet and large form factors of
+
+ align:start position:0%
+pallet and large form factors of
+ 
+
+ align:start position:0%
+pallet and large form factors of
+tags little emphasis on the small form
+
+ align:start position:0%
+tags little emphasis on the small form
+ 
+
+ align:start position:0%
+tags little emphasis on the small form
+factors but we need to to work on that
+
+ align:start position:0%
+factors but we need to to work on that
+ 
+
+ align:start position:0%
+factors but we need to to work on that
+there's initiatives uh happening right
+
+ align:start position:0%
+there's initiatives uh happening right
+ 
+
+ align:start position:0%
+there's initiatives uh happening right
+now showing some good results in labs
+
+ align:start position:0%
+now showing some good results in labs
+ 
+
+ align:start position:0%
+now showing some good results in labs
+but again we need to move this out to to
+
+ align:start position:0%
+but again we need to move this out to to
+ 
+
+ align:start position:0%
+but again we need to move this out to to
+the field to get real world
+
+ align:start position:0%
+the field to get real world
+ 
+
+ align:start position:0%
+the field to get real world
+learning and then have the proper debate
+
+ align:start position:0%
+learning and then have the proper debate
+ 
+
+ align:start position:0%
+learning and then have the proper debate
+whether HF or UHF is a correct method to
+
+ align:start position:0%
+whether HF or UHF is a correct method to
+ 
+
+ align:start position:0%
+whether HF or UHF is a correct method to
+to move forward
+
+ align:start position:0%
+to move forward
+ 
+
+ align:start position:0%
+to move forward
+with and a big need not just for pharma
+
+ align:start position:0%
+with and a big need not just for pharma
+ 
+
+ align:start position:0%
+with and a big need not just for pharma
+but other areas as well for
+
+ align:start position:0%
+but other areas as well for
+ 
+
+ align:start position:0%
+but other areas as well for
+security you know so what are the
+
+ align:start position:0%
+security you know so what are the
+ 
+
+ align:start position:0%
+security you know so what are the
+security measures that we would want and
+
+ align:start position:0%
+security measures that we would want and
+ 
+
+ align:start position:0%
+security measures that we would want and
+need on such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products mentioned about international
+
+ align:start position:0%
+products mentioned about international
+ 
+
+ align:start position:0%
+products mentioned about international
+and the EPC
+
+ align:start position:0%
+and the EPC
+ 
+
+ align:start position:0%
+and the EPC
+network and direction. This is probably
+
+ align:start position:0%
+network and direction. This is probably
+ 
+
+ align:start position:0%
+network and direction. This is probably
+my number one um objective for this
+
+ align:start position:0%
+my number one um objective for this
+ 
+
+ align:start position:0%
+my number one um objective for this
+year is through RFID to sense direction.
+
+ align:start position:0%
+year is through RFID to sense direction.
+ 
+
+ align:start position:0%
+year is through RFID to sense direction.
+So, Bill mentioned about read rates, you
+
+ align:start position:0%
+So, Bill mentioned about read rates, you
+ 
+
+ align:start position:0%
+So, Bill mentioned about read rates, you
+know, not 100% and we don't need them to
+
+ align:start position:0%
+know, not 100% and we don't need them to
+ 
+
+ align:start position:0%
+know, not 100% and we don't need them to
+be 100% today, but having direction,
+
+ align:start position:0%
+be 100% today, but having direction,
+ 
+
+ align:start position:0%
+be 100% today, but having direction,
+knowing that something is either leaving
+
+ align:start position:0%
+knowing that something is either leaving
+ 
+
+ align:start position:0%
+knowing that something is either leaving
+this room or coming into this
+
+ align:start position:0%
+this room or coming into this
+ 
+
+ align:start position:0%
+this room or coming into this
+room then actually gives us much more
+
+ align:start position:0%
+room then actually gives us much more
+ 
+
+ align:start position:0%
+room then actually gives us much more
+accurate data than we have today.
+
+ align:start position:0%
+accurate data than we have today.
+ 
+
+ align:start position:0%
+accurate data than we have today.
+The last thing I want to do is tell an
+
+ align:start position:0%
+The last thing I want to do is tell an
+ 
+
+ align:start position:0%
+The last thing I want to do is tell an
+associate to go and pick a case that's
+
+ align:start position:0%
+associate to go and pick a case that's
+ 
+
+ align:start position:0%
+associate to go and pick a case that's
+sat in the back
+
+ align:start position:0%
+sat in the back
+ 
+
+ align:start position:0%
+sat in the back
+room of a store and they go there and
+
+ align:start position:0%
+room of a store and they go there and
+ 
+
+ align:start position:0%
+room of a store and they go there and
+it's not not there can't be found. That
+
+ align:start position:0%
+it's not not there can't be found. That
+ 
+
+ align:start position:0%
+it's not not there can't be found. That
+discredits the whole system. So the
+
+ align:start position:0%
+discredits the whole system. So the
+ 
+
+ align:start position:0%
+discredits the whole system. So the
+cleaner data we can get then the better
+
+ align:start position:0%
+cleaner data we can get then the better
+ 
+
+ align:start position:0%
+cleaner data we can get then the better
+position we are the better execution
+
+ align:start position:0%
+position we are the better execution
+ 
+
+ align:start position:0%
+position we are the better execution
+we'll get and direction will give us
+
+ align:start position:0%
+we'll get and direction will give us
+ 
+
+ align:start position:0%
+we'll get and direction will give us
+that. And there's various uh theories
+
+ align:start position:0%
+that. And there's various uh theories
+ 
+
+ align:start position:0%
+that. And there's various uh theories
+and uh solutions thrown out there from
+
+ align:start position:0%
+and uh solutions thrown out there from
+ 
+
+ align:start position:0%
+and uh solutions thrown out there from
+using RFID and complimentary
+
+ align:start position:0%
+using RFID and complimentary
+ 
+
+ align:start position:0%
+using RFID and complimentary
+technologies such as sensors that we
+
+ align:start position:0%
+technologies such as sensors that we
+ 
+
+ align:start position:0%
+technologies such as sensors that we
+could use or things like the Doppler
+
+ align:start position:0%
+could use or things like the Doppler
+ 
+
+ align:start position:0%
+could use or things like the Doppler
+effect that we could use through through
+
+ align:start position:0%
+effect that we could use through through
+ 
+
+ align:start position:0%
+effect that we could use through through
+readers, but really need to get out
+
+ align:start position:0%
+readers, but really need to get out
+ 
+
+ align:start position:0%
+readers, but really need to get out
+there and try four or five the four or
+
+ align:start position:0%
+there and try four or five the four or
+ 
+
+ align:start position:0%
+there and try four or five the four or
+five of these different methods to see
+
+ align:start position:0%
+five of these different methods to see
+ 
+
+ align:start position:0%
+five of these different methods to see
+which is most appropriate and cost
+
+ align:start position:0%
+which is most appropriate and cost
+ 
+
+ align:start position:0%
+which is most appropriate and cost
+effective.
+
+ align:start position:0%
+effective.
+ 
+
+ align:start position:0%
+effective.
+And then some of the holy grails,
+
+ align:start position:0%
+And then some of the holy grails,
+ 
+
+ align:start position:0%
+And then some of the holy grails,
+reading all cases on a
+
+ align:start position:0%
+reading all cases on a
+ 
+
+ align:start position:0%
+reading all cases on a
+pallet, not possible
+
+ align:start position:0%
+pallet, not possible
+ 
+
+ align:start position:0%
+pallet, not possible
+today, but how can we achieve that in
+
+ align:start position:0%
+today, but how can we achieve that in
+ 
+
+ align:start position:0%
+today, but how can we achieve that in
+the future? And how do we get to the sub
+
+ align:start position:0%
+the future? And how do we get to the sub
+ 
+
+ align:start position:0%
+the future? And how do we get to the sub
+5 cent
+
+ align:start position:0%
+5 cent
+ 
+
+ align:start position:0%
+5 cent
+tag so that the automated checkout
+
+ align:start position:0%
+tag so that the automated checkout
+ 
+
+ align:start position:0%
+tag so that the automated checkout
+becomes a reality in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future? What do we need to keep doing?
+
+ align:start position:0%
+future? What do we need to keep doing?
+ 
+
+ align:start position:0%
+future? What do we need to keep doing?
+We need to keep educating.
+
+ align:start position:0%
+We need to keep educating.
+ 
+
+ align:start position:0%
+We need to keep educating.
+We need to keep educating governing
+
+ align:start position:0%
+We need to keep educating governing
+ 
+
+ align:start position:0%
+We need to keep educating governing
+bodies around the world so that Gen 2 is
+
+ align:start position:0%
+bodies around the world so that Gen 2 is
+ 
+
+ align:start position:0%
+bodies around the world so that Gen 2 is
+endorsed in every region, every
+
+ align:start position:0%
+endorsed in every region, every
+ 
+
+ align:start position:0%
+endorsed in every region, every
+country so that global tag can be
+
+ align:start position:0%
+country so that global tag can be
+ 
+
+ align:start position:0%
+country so that global tag can be
+used. We need to educate end users what
+
+ align:start position:0%
+used. We need to educate end users what
+ 
+
+ align:start position:0%
+used. We need to educate end users what
+are the benefits of RFID, how best to
+
+ align:start position:0%
+are the benefits of RFID, how best to
+ 
+
+ align:start position:0%
+are the benefits of RFID, how best to
+deploy it, where to start. There's some
+
+ align:start position:0%
+deploy it, where to start. There's some
+ 
+
+ align:start position:0%
+deploy it, where to start. There's some
+great work being done in this area
+
+ align:start position:0%
+great work being done in this area
+ 
+
+ align:start position:0%
+great work being done in this area
+already. And as Bill mentioned,
+
+ align:start position:0%
+already. And as Bill mentioned,
+ 
+
+ align:start position:0%
+already. And as Bill mentioned,
+developing and nurturing people
+
+ align:start position:0%
+developing and nurturing people
+ 
+
+ align:start position:0%
+developing and nurturing people
+today to help in the future
+
+ align:start position:0%
+today to help in the future
+ 
+
+ align:start position:0%
+today to help in the future
+uh build these systems and manage these
+
+ align:start position:0%
+uh build these systems and manage these
+ 
+
+ align:start position:0%
+uh build these systems and manage these
+systems and quality
+
+ align:start position:0%
+systems and quality
+ 
+
+ align:start position:0%
+systems and quality
+improvements. So cost isn't just about
+
+ align:start position:0%
+improvements. So cost isn't just about
+ 
+
+ align:start position:0%
+improvements. So cost isn't just about
+this tag's costing me 12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cents. Yield rates are important too
+
+ align:start position:0%
+cents. Yield rates are important too
+ 
+
+ align:start position:0%
+cents. Yield rates are important too
+because that c cost gets passed on
+
+ align:start position:0%
+because that c cost gets passed on
+ 
+
+ align:start position:0%
+because that c cost gets passed on
+somewhere down the
+
+ align:start position:0%
+somewhere down the
+ 
+
+ align:start position:0%
+somewhere down the
+line. and testing testing for true
+
+ align:start position:0%
+line. and testing testing for true
+ 
+
+ align:start position:0%
+line. and testing testing for true
+interoperability. Testing for what is
+
+ align:start position:0%
+interoperability. Testing for what is
+ 
+
+ align:start position:0%
+interoperability. Testing for what is
+the best tag or the antenna design for
+
+ align:start position:0%
+the best tag or the antenna design for
+ 
+
+ align:start position:0%
+the best tag or the antenna design for
+that product that you're shipping.
+
+ align:start position:0%
+that product that you're shipping.
+ 
+
+ align:start position:0%
+that product that you're shipping.
+Bill shared with me a while ago an
+
+ align:start position:0%
+Bill shared with me a while ago an
+ 
+
+ align:start position:0%
+Bill shared with me a while ago an
+interesting story from a supplier where
+
+ align:start position:0%
+interesting story from a supplier where
+ 
+
+ align:start position:0%
+interesting story from a supplier where
+there it was two cases of a product, one
+
+ align:start position:0%
+there it was two cases of a product, one
+ 
+
+ align:start position:0%
+there it was two cases of a product, one
+of our suppliers, and uh it was the same
+
+ align:start position:0%
+of our suppliers, and uh it was the same
+ 
+
+ align:start position:0%
+of our suppliers, and uh it was the same
+product except a different flavor and uh
+
+ align:start position:0%
+product except a different flavor and uh
+ 
+
+ align:start position:0%
+product except a different flavor and uh
+they were getting good read rates on one
+
+ align:start position:0%
+they were getting good read rates on one
+ 
+
+ align:start position:0%
+they were getting good read rates on one
+and poor read rates on the other and
+
+ align:start position:0%
+and poor read rates on the other and
+ 
+
+ align:start position:0%
+and poor read rates on the other and
+couldn't understand why why that was and
+
+ align:start position:0%
+couldn't understand why why that was and
+ 
+
+ align:start position:0%
+couldn't understand why why that was and
+uh went along to Bill and said, "Can you
+
+ align:start position:0%
+uh went along to Bill and said, "Can you
+ 
+
+ align:start position:0%
+uh went along to Bill and said, "Can you
+help us with this?"
+
+ align:start position:0%
+help us with this?"
+ 
+
+ align:start position:0%
+help us with this?"
+And after some trial and error and
+
+ align:start position:0%
+And after some trial and error and
+ 
+
+ align:start position:0%
+And after some trial and error and
+swapping the product between the two
+
+ align:start position:0%
+swapping the product between the two
+ 
+
+ align:start position:0%
+swapping the product between the two
+boxes, found out that one of the flavors
+
+ align:start position:0%
+boxes, found out that one of the flavors
+ 
+
+ align:start position:0%
+boxes, found out that one of the flavors
+had some metallic paint within the
+
+ align:start position:0%
+had some metallic paint within the
+ 
+
+ align:start position:0%
+had some metallic paint within the
+packaging. And it was that that was that
+
+ align:start position:0%
+packaging. And it was that that was that
+ 
+
+ align:start position:0%
+packaging. And it was that that was that
+was causing the uh poor read rate on
+
+ align:start position:0%
+was causing the uh poor read rate on
+ 
+
+ align:start position:0%
+was causing the uh poor read rate on
+that second product. So to a supplier,
+
+ align:start position:0%
+that second product. So to a supplier,
+ 
+
+ align:start position:0%
+that second product. So to a supplier,
+it was the same product, the same same
+
+ align:start position:0%
+it was the same product, the same same
+ 
+
+ align:start position:0%
+it was the same product, the same same
+packaging as they thought, same density
+
+ align:start position:0%
+packaging as they thought, same density
+ 
+
+ align:start position:0%
+packaging as they thought, same density
+of product inside, but two different
+
+ align:start position:0%
+of product inside, but two different
+ 
+
+ align:start position:0%
+of product inside, but two different
+results.
+
+ align:start position:0%
+results.
+ 
+
+ align:start position:0%
+results.
+And so how can we uh test and get best
+
+ align:start position:0%
+And so how can we uh test and get best
+ 
+
+ align:start position:0%
+And so how can we uh test and get best
+practice out there and so every supplier
+
+ align:start position:0%
+practice out there and so every supplier
+ 
+
+ align:start position:0%
+practice out there and so every supplier
+doesn't have to go through that learning
+
+ align:start position:0%
+doesn't have to go through that learning
+ 
+
+ align:start position:0%
+doesn't have to go through that learning
+process because that reduces costs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+overall. And then we should all be
+
+ align:start position:0%
+overall. And then we should all be
+ 
+
+ align:start position:0%
+overall. And then we should all be
+mindful that you know as we move forward
+
+ align:start position:0%
+mindful that you know as we move forward
+ 
+
+ align:start position:0%
+mindful that you know as we move forward
+as we move forward to the sales floor to
+
+ align:start position:0%
+as we move forward to the sales floor to
+ 
+
+ align:start position:0%
+as we move forward to the sales floor to
+items to theft prevention that we need
+
+ align:start position:0%
+items to theft prevention that we need
+ 
+
+ align:start position:0%
+items to theft prevention that we need
+to ensure that privacy concerns are
+
+ align:start position:0%
+to ensure that privacy concerns are
+ 
+
+ align:start position:0%
+to ensure that privacy concerns are
+taken into account and addressed.
+
+ align:start position:0%
+taken into account and addressed.
+ 
+
+ align:start position:0%
+taken into account and addressed.
+This should only equal lowering the cost
+
+ align:start position:0%
+This should only equal lowering the cost
+ 
+
+ align:start position:0%
+This should only equal lowering the cost
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+implementation. So just to wrap
+
+ align:start position:0%
+implementation. So just to wrap
+ 
+
+ align:start position:0%
+implementation. So just to wrap
+up, we're just scratching the surface
+
+ align:start position:0%
+up, we're just scratching the surface
+ 
+
+ align:start position:0%
+up, we're just scratching the surface
+today. We need to get mobile devices out
+
+ align:start position:0%
+today. We need to get mobile devices out
+ 
+
+ align:start position:0%
+today. We need to get mobile devices out
+there so that people can go about their
+
+ align:start position:0%
+there so that people can go about their
+ 
+
+ align:start position:0%
+there so that people can go about their
+everyday job and the system is just
+
+ align:start position:0%
+everyday job and the system is just
+ 
+
+ align:start position:0%
+everyday job and the system is just
+talking to them and give them work to do
+
+ align:start position:0%
+talking to them and give them work to do
+ 
+
+ align:start position:0%
+talking to them and give them work to do
+in a prioritized way. We need to lower
+
+ align:start position:0%
+in a prioritized way. We need to lower
+ 
+
+ align:start position:0%
+in a prioritized way. We need to lower
+the cost of deployment.
+
+ align:start position:0%
+the cost of deployment.
+ 
+
+ align:start position:0%
+the cost of deployment.
+And then finally, we should never lose a
+
+ align:start position:0%
+And then finally, we should never lose a
+ 
+
+ align:start position:0%
+And then finally, we should never lose a
+sight of of why we're using this
+
+ align:start position:0%
+sight of of why we're using this
+ 
+
+ align:start position:0%
+sight of of why we're using this
+technology, why we're pushing this
+
+ align:start position:0%
+technology, why we're pushing this
+ 
+
+ align:start position:0%
+technology, why we're pushing this
+technology and driving forward. It's all
+
+ align:start position:0%
+technology and driving forward. It's all
+ 
+
+ align:start position:0%
+technology and driving forward. It's all
+about the customer at the end of the
+
+ align:start position:0%
+about the customer at the end of the
+ 
+
+ align:start position:0%
+about the customer at the end of the
+day. So whether you're a supplier or
+
+ align:start position:0%
+day. So whether you're a supplier or
+ 
+
+ align:start position:0%
+day. So whether you're a supplier or
+retailer, at the end of the day, we need
+
+ align:start position:0%
+retailer, at the end of the day, we need
+ 
+
+ align:start position:0%
+retailer, at the end of the day, we need
+to service our customers better. Whether
+
+ align:start position:0%
+to service our customers better. Whether
+ 
+
+ align:start position:0%
+to service our customers better. Whether
+that's working more efficiently and
+
+ align:start position:0%
+that's working more efficiently and
+ 
+
+ align:start position:0%
+that's working more efficiently and
+taking cost out of the supply chain that
+
+ align:start position:0%
+taking cost out of the supply chain that
+ 
+
+ align:start position:0%
+taking cost out of the supply chain that
+then can be passed on to the customer,
+
+ align:start position:0%
+then can be passed on to the customer,
+ 
+
+ align:start position:0%
+then can be passed on to the customer,
+that's our end goal. Thank you.
\ No newline at end of file
diff --git a/oLIMFmEgaWo.txt b/oLIMFmEgaWo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9d8ab9df4cc36055572e01c93ad691db32f7eda7
--- /dev/null
+++ b/oLIMFmEgaWo.txt
@@ -0,0 +1,2307 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay most of the hour we'll
+
+ align:start position:0%
+ocw.mit.edu okay most of the hour we'll
+ 
+
+ align:start position:0%
+ocw.mit.edu okay most of the hour we'll
+be watching the first half of the uh the
+
+ align:start position:0%
+be watching the first half of the uh the
+ 
+
+ align:start position:0%
+be watching the first half of the uh the
+video on chimpanzees but yeah I wanted
+
+ align:start position:0%
+video on chimpanzees but yeah I wanted
+ 
+
+ align:start position:0%
+video on chimpanzees but yeah I wanted
+to finish
+
+ align:start position:0%
+to finish
+ 
+
+ align:start position:0%
+to finish
+uh Revis I revised a little bit on motor
+
+ align:start position:0%
+uh Revis I revised a little bit on motor
+ 
+
+ align:start position:0%
+uh Revis I revised a little bit on motor
+learning to try to make it clear what
+
+ align:start position:0%
+learning to try to make it clear what
+ 
+
+ align:start position:0%
+learning to try to make it clear what
+I'm trying to get across so let's just
+
+ align:start position:0%
+I'm trying to get across so let's just
+ 
+
+ align:start position:0%
+I'm trying to get across so let's just
+go through motor learning again this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the acquisition of path habits I talked
+
+ align:start position:0%
+the acquisition of path habits I talked
+ 
+
+ align:start position:0%
+the acquisition of path habits I talked
+about but the main point here is that
+
+ align:start position:0%
+about but the main point here is that
+ 
+
+ align:start position:0%
+about but the main point here is that
+the movements acquired independence from
+
+ align:start position:0%
+the movements acquired independence from
+ 
+
+ align:start position:0%
+the movements acquired independence from
+sensory input so it's not that they're
+
+ align:start position:0%
+sensory input so it's not that they're
+ 
+
+ align:start position:0%
+sensory input so it's not that they're
+continually responding to things all
+
+ align:start position:0%
+continually responding to things all
+ 
+
+ align:start position:0%
+continually responding to things all
+along their path if if it becomes
+
+ align:start position:0%
+along their path if if it becomes
+ 
+
+ align:start position:0%
+along their path if if it becomes
+learned in the motor system they just
+
+ align:start position:0%
+learned in the motor system they just
+ 
+
+ align:start position:0%
+learned in the motor system they just
+run it off like like a fixed motor
+
+ align:start position:0%
+run it off like like a fixed motor
+ 
+
+ align:start position:0%
+run it off like like a fixed motor
+pattern you'll remember when we talked
+
+ align:start position:0%
+pattern you'll remember when we talked
+ 
+
+ align:start position:0%
+pattern you'll remember when we talked
+about fix action patterns in bir the the
+
+ align:start position:0%
+about fix action patterns in bir the the
+ 
+
+ align:start position:0%
+about fix action patterns in bir the the
+geese and Ducks the way roll the eggs in
+
+ align:start position:0%
+geese and Ducks the way roll the eggs in
+ 
+
+ align:start position:0%
+geese and Ducks the way roll the eggs in
+if you interrupt it you
+
+ align:start position:0%
+if you interrupt it you
+ 
+
+ align:start position:0%
+if you interrupt it you
+know they need they just have to start
+
+ align:start position:0%
+know they need they just have to start
+ 
+
+ align:start position:0%
+know they need they just have to start
+all over again if they going to do it at
+
+ align:start position:0%
+all over again if they going to do it at
+ 
+
+ align:start position:0%
+all over again if they going to do it at
+all it's a single pattern and that's
+
+ align:start position:0%
+all it's a single pattern and that's
+ 
+
+ align:start position:0%
+all it's a single pattern and that's
+what these path this path learning
+
+ align:start position:0%
+what these path this path learning
+ 
+
+ align:start position:0%
+what these path this path learning
+amounts
+
+ align:start position:0%
+amounts
+ 
+
+ align:start position:0%
+amounts
+to it becomes encoded in the
+
+ align:start position:0%
+to it becomes encoded in the
+ 
+
+ align:start position:0%
+to it becomes encoded in the
+cerebellum okay so it's like when you
+
+ align:start position:0%
+cerebellum okay so it's like when you
+ 
+
+ align:start position:0%
+cerebellum okay so it's like when you
+recite something from memory or learn to
+
+ align:start position:0%
+recite something from memory or learn to
+ 
+
+ align:start position:0%
+recite something from memory or learn to
+play a musical instrument you probably
+
+ align:start position:0%
+play a musical instrument you probably
+ 
+
+ align:start position:0%
+play a musical instrument you probably
+have all had the experience of you're
+
+ align:start position:0%
+have all had the experience of you're
+ 
+
+ align:start position:0%
+have all had the experience of you're
+reciting something and you don't have it
+
+ align:start position:0%
+reciting something and you don't have it
+ 
+
+ align:start position:0%
+reciting something and you don't have it
+quite learned perfectly so you get stuck
+
+ align:start position:0%
+quite learned perfectly so you get stuck
+ 
+
+ align:start position:0%
+quite learned perfectly so you get stuck
+and then to remember it you have to go
+
+ align:start position:0%
+and then to remember it you have to go
+ 
+
+ align:start position:0%
+and then to remember it you have to go
+back either to the beginning or to
+
+ align:start position:0%
+back either to the beginning or to
+ 
+
+ align:start position:0%
+back either to the beginning or to
+some chunk beginning of some chunk
+
+ align:start position:0%
+some chunk beginning of some chunk
+ 
+
+ align:start position:0%
+some chunk beginning of some chunk
+before you can do it that's because
+
+ align:start position:0%
+before you can do it that's because
+ 
+
+ align:start position:0%
+before you can do it that's because
+you've learned it if you memorize
+
+ align:start position:0%
+you've learned it if you memorize
+ 
+
+ align:start position:0%
+you've learned it if you memorize
+something it often becomes motor
+
+ align:start position:0%
+something it often becomes motor
+ 
+
+ align:start position:0%
+something it often becomes motor
+learning okay so and it acquires some
+
+ align:start position:0%
+learning okay so and it acquires some
+ 
+
+ align:start position:0%
+learning okay so and it acquires some
+similarities to the motor component of
+
+ align:start position:0%
+similarities to the motor component of
+ 
+
+ align:start position:0%
+similarities to the motor component of
+fix action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns um as I mention here and then
+
+ align:start position:0%
+patterns um as I mention here and then
+ 
+
+ align:start position:0%
+patterns um as I mention here and then
+it's it's very resistant to change and
+
+ align:start position:0%
+it's it's very resistant to change and
+ 
+
+ align:start position:0%
+it's it's very resistant to change and
+perhaps most interesting is that in many
+
+ align:start position:0%
+perhaps most interesting is that in many
+ 
+
+ align:start position:0%
+perhaps most interesting is that in many
+cases it seems to acquire its own uh
+
+ align:start position:0%
+cases it seems to acquire its own uh
+ 
+
+ align:start position:0%
+cases it seems to acquire its own uh
+action specific potential that is it
+
+ align:start position:0%
+action specific potential that is it
+ 
+
+ align:start position:0%
+action specific potential that is it
+requires a motivation the animal to do
+
+ align:start position:0%
+requires a motivation the animal to do
+ 
+
+ align:start position:0%
+requires a motivation the animal to do
+it or the person it usually requires a
+
+ align:start position:0%
+it or the person it usually requires a
+ 
+
+ align:start position:0%
+it or the person it usually requires a
+lot of repetition is like when you learn
+
+ align:start position:0%
+lot of repetition is like when you learn
+ 
+
+ align:start position:0%
+lot of repetition is like when you learn
+skills in
+
+ align:start position:0%
+skills in
+ 
+
+ align:start position:0%
+skills in
+sport we talked about the difference in
+
+ align:start position:0%
+sport we talked about the difference in
+ 
+
+ align:start position:0%
+sport we talked about the difference in
+Locomotion between these different
+
+ align:start position:0%
+Locomotion between these different
+ 
+
+ align:start position:0%
+Locomotion between these different
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ulates and what surf footedness is it's
+
+ align:start position:0%
+ulates and what surf footedness is it's
+ 
+
+ align:start position:0%
+ulates and what surf footedness is it's
+an example of the more surefooted
+
+ align:start position:0%
+an example of the more surefooted
+ 
+
+ align:start position:0%
+an example of the more surefooted
+animals simply there's more separate
+
+ align:start position:0%
+animals simply there's more separate
+ 
+
+ align:start position:0%
+animals simply there's more separate
+elements in their action
+
+ align:start position:0%
+elements in their action
+ 
+
+ align:start position:0%
+elements in their action
+pattern so more subject we would say to
+
+ align:start position:0%
+pattern so more subject we would say to
+ 
+
+ align:start position:0%
+pattern so more subject we would say to
+subject to voluntary control they can
+
+ align:start position:0%
+subject to voluntary control they can
+ 
+
+ align:start position:0%
+subject to voluntary control they can
+decide to use
+
+ align:start position:0%
+decide to use
+ 
+
+ align:start position:0%
+decide to use
+it and so I've rewarded this just a
+
+ align:start position:0%
+it and so I've rewarded this just a
+ 
+
+ align:start position:0%
+it and so I've rewarded this just a
+little bit to help you understand what
+
+ align:start position:0%
+little bit to help you understand what
+ 
+
+ align:start position:0%
+little bit to help you understand what
+that's all about and
+
+ align:start position:0%
+that's all about and
+ 
+
+ align:start position:0%
+that's all about and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but I think it's it's clear enough
+
+ align:start position:0%
+uh but I think it's it's clear enough
+ 
+
+ align:start position:0%
+uh but I think it's it's clear enough
+with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I wanted to add this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh about the exploratory uh sorry what
+
+ align:start position:0%
+uh about the exploratory uh sorry what
+ 
+
+ align:start position:0%
+uh about the exploratory uh sorry what
+did I do
+
+ align:start position:0%
+did I do
+ 
+
+ align:start position:0%
+did I do
+here oh this got out of place okay this
+
+ align:start position:0%
+here oh this got out of place okay this
+ 
+
+ align:start position:0%
+here oh this got out of place okay this
+belongs with discussion of voluntary
+
+ align:start position:0%
+belongs with discussion of voluntary
+ 
+
+ align:start position:0%
+belongs with discussion of voluntary
+Behavior animals that have evolved
+
+ align:start position:0%
+Behavior animals that have evolved
+ 
+
+ align:start position:0%
+Behavior animals that have evolved
+direct axonal projections from the
+
+ align:start position:0%
+direct axonal projections from the
+ 
+
+ align:start position:0%
+direct axonal projections from the
+neocortex to the motor
+
+ align:start position:0%
+neocortex to the motor
+ 
+
+ align:start position:0%
+neocortex to the motor
+neurons uh there aren't all that many
+
+ align:start position:0%
+neurons uh there aren't all that many
+ 
+
+ align:start position:0%
+neurons uh there aren't all that many
+but but higher primates have that
+
+ align:start position:0%
+but but higher primates have that
+ 
+
+ align:start position:0%
+but but higher primates have that
+raccoons have it uh a few other species
+
+ align:start position:0%
+raccoons have it uh a few other species
+ 
+
+ align:start position:0%
+raccoons have it uh a few other species
+then the unit of movement is just the
+
+ align:start position:0%
+then the unit of movement is just the
+ 
+
+ align:start position:0%
+then the unit of movement is just the
+digital movement now that's the smallest
+
+ align:start position:0%
+digital movement now that's the smallest
+ 
+
+ align:start position:0%
+digital movement now that's the smallest
+unit you can get and and animals that
+
+ align:start position:0%
+unit you can get and and animals that
+ 
+
+ align:start position:0%
+unit you can get and and animals that
+have that like us you know yes we have
+
+ align:start position:0%
+have that like us you know yes we have
+ 
+
+ align:start position:0%
+have that like us you know yes we have
+voluntary control over individual digits
+
+ align:start position:0%
+voluntary control over individual digits
+ 
+
+ align:start position:0%
+voluntary control over individual digits
+we someone can tell you can you move
+
+ align:start position:0%
+we someone can tell you can you move
+ 
+
+ align:start position:0%
+we someone can tell you can you move
+just you know your little finger and you
+
+ align:start position:0%
+just you know your little finger and you
+ 
+
+ align:start position:0%
+just you know your little finger and you
+can do it we can't do it very well for
+
+ align:start position:0%
+can do it we can't do it very well for
+ 
+
+ align:start position:0%
+can do it we can't do it very well for
+the fourth finger but in general we have
+
+ align:start position:0%
+the fourth finger but in general we have
+ 
+
+ align:start position:0%
+the fourth finger but in general we have
+that kind of control but most movements
+
+ align:start position:0%
+that kind of control but most movements
+ 
+
+ align:start position:0%
+that kind of control but most movements
+are not that we can't control just
+
+ align:start position:0%
+are not that we can't control just
+ 
+
+ align:start position:0%
+are not that we can't control just
+individual set of muscles like that most
+
+ align:start position:0%
+individual set of muscles like that most
+ 
+
+ align:start position:0%
+individual set of muscles like that most
+movements
+
+ align:start position:0%
+movements
+ 
+
+ align:start position:0%
+movements
+uh we don't have that kind of voluntary
+
+ align:start position:0%
+uh we don't have that kind of voluntary
+ 
+
+ align:start position:0%
+uh we don't have that kind of voluntary
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+over and that uh is true for other
+
+ align:start position:0%
+over and that uh is true for other
+ 
+
+ align:start position:0%
+over and that uh is true for other
+animals of course even
+
+ align:start position:0%
+animals of course even
+ 
+
+ align:start position:0%
+animals of course even
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+and I mentioned here that you know I
+
+ align:start position:0%
+and I mentioned here that you know I
+ 
+
+ align:start position:0%
+and I mentioned here that you know I
+talk about these projections from motor
+
+ align:start position:0%
+talk about these projections from motor
+ 
+
+ align:start position:0%
+talk about these projections from motor
+cortex and or the motor areas of Cortex
+
+ align:start position:0%
+cortex and or the motor areas of Cortex
+ 
+
+ align:start position:0%
+cortex and or the motor areas of Cortex
+in a mammal but if you talk about birds
+
+ align:start position:0%
+in a mammal but if you talk about birds
+ 
+
+ align:start position:0%
+in a mammal but if you talk about birds
+they don't have a neocortex but they
+
+ align:start position:0%
+they don't have a neocortex but they
+ 
+
+ align:start position:0%
+they don't have a neocortex but they
+have equivalent structures especially
+
+ align:start position:0%
+have equivalent structures especially
+ 
+
+ align:start position:0%
+have equivalent structures especially
+this hyper palum region and it becomes
+
+ align:start position:0%
+this hyper palum region and it becomes
+ 
+
+ align:start position:0%
+this hyper palum region and it becomes
+so welldeveloped and the more advanced
+
+ align:start position:0%
+so welldeveloped and the more advanced
+ 
+
+ align:start position:0%
+so welldeveloped and the more advanced
+birds like the corvids parrots uh it
+
+ align:start position:0%
+birds like the corvids parrots uh it
+ 
+
+ align:start position:0%
+birds like the corvids parrots uh it
+forms a bulge and they actually have a
+
+ align:start position:0%
+forms a bulge and they actually have a
+ 
+
+ align:start position:0%
+forms a bulge and they actually have a
+motor
+
+ align:start position:0%
+motor
+ 
+
+ align:start position:0%
+motor
+wolst they have aat of sensory wolst a
+
+ align:start position:0%
+wolst they have aat of sensory wolst a
+ 
+
+ align:start position:0%
+wolst they have aat of sensory wolst a
+visual wolst okay that's the equivalent
+
+ align:start position:0%
+visual wolst okay that's the equivalent
+ 
+
+ align:start position:0%
+visual wolst okay that's the equivalent
+to those areas and they also have these
+
+ align:start position:0%
+to those areas and they also have these
+ 
+
+ align:start position:0%
+to those areas and they also have these
+direct projections to the spinal cord um
+
+ align:start position:0%
+direct projections to the spinal cord um
+ 
+
+ align:start position:0%
+direct projections to the spinal cord um
+I'm not sure if they go directly to
+
+ align:start position:0%
+I'm not sure if they go directly to
+ 
+
+ align:start position:0%
+I'm not sure if they go directly to
+motor neurons as they do in higher
+
+ align:start position:0%
+motor neurons as they do in higher
+ 
+
+ align:start position:0%
+motor neurons as they do in higher
+primates uh but uh that's
+
+ align:start position:0%
+primates uh but uh that's
+ 
+
+ align:start position:0%
+primates uh but uh that's
+possible so okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh although I rewarded this a little bit
+
+ align:start position:0%
+uh although I rewarded this a little bit
+ 
+
+ align:start position:0%
+uh although I rewarded this a little bit
+we talked about exploratory behavior and
+
+ align:start position:0%
+we talked about exploratory behavior and
+ 
+
+ align:start position:0%
+we talked about exploratory behavior and
+curiosity before so I don't think we
+
+ align:start position:0%
+curiosity before so I don't think we
+ 
+
+ align:start position:0%
+curiosity before so I don't think we
+have to go through
+
+ align:start position:0%
+have to go through
+ 
+
+ align:start position:0%
+have to go through
+that I just want to point out here in
+
+ align:start position:0%
+that I just want to point out here in
+ 
+
+ align:start position:0%
+that I just want to point out here in
+the functions of play he actually
+
+ align:start position:0%
+the functions of play he actually
+ 
+
+ align:start position:0%
+the functions of play he actually
+introduced introduces what amounts to
+
+ align:start position:0%
+introduced introduces what amounts to
+ 
+
+ align:start position:0%
+introduced introduces what amounts to
+three additional types of
+
+ align:start position:0%
+three additional types of
+ 
+
+ align:start position:0%
+three additional types of
+learning U all learned in place so they
+
+ align:start position:0%
+learning U all learned in place so they
+ 
+
+ align:start position:0%
+learning U all learned in place so they
+amount to a different kind of learning
+
+ align:start position:0%
+amount to a different kind of learning
+ 
+
+ align:start position:0%
+amount to a different kind of learning
+than learned in other situations so I
+
+ align:start position:0%
+than learned in other situations so I
+ 
+
+ align:start position:0%
+than learned in other situations so I
+list them
+
+ align:start position:0%
+list them
+ 
+
+ align:start position:0%
+list them
+there and then we talked about research
+
+ align:start position:0%
+there and then we talked about research
+ 
+
+ align:start position:0%
+there and then we talked about research
+in art in humans but that's where we
+
+ align:start position:0%
+in art in humans but that's where we
+ 
+
+ align:start position:0%
+in art in humans but that's where we
+ended yesterday and you can go through
+
+ align:start position:0%
+ended yesterday and you can go through
+ 
+
+ align:start position:0%
+ended yesterday and you can go through
+all these different kinds of learning
+
+ align:start position:0%
+all these different kinds of learning
+ 
+
+ align:start position:0%
+all these different kinds of learning
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+neuroscientist uh can relate them to
+
+ align:start position:0%
+neuroscientist uh can relate them to
+ 
+
+ align:start position:0%
+neuroscientist uh can relate them to
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+structures um for example the
+
+ align:start position:0%
+structures um for example the
+ 
+
+ align:start position:0%
+structures um for example the
+habituation and sensitization the these
+
+ align:start position:0%
+habituation and sensitization the these
+ 
+
+ align:start position:0%
+habituation and sensitization the these
+Learning Without
+
+ align:start position:0%
+Learning Without
+ 
+
+ align:start position:0%
+Learning Without
+Association
+
+ align:start position:0%
+Association
+ 
+
+ align:start position:0%
+Association
+uh it can even happen in in spinal
+
+ align:start position:0%
+uh it can even happen in in spinal
+ 
+
+ align:start position:0%
+uh it can even happen in in spinal
+Pathways uh so all the sensory and motor
+
+ align:start position:0%
+Pathways uh so all the sensory and motor
+ 
+
+ align:start position:0%
+Pathways uh so all the sensory and motor
+pathways can can be subject to that kind
+
+ align:start position:0%
+pathways can can be subject to that kind
+ 
+
+ align:start position:0%
+pathways can can be subject to that kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+change uh the other things of interest
+
+ align:start position:0%
+change uh the other things of interest
+ 
+
+ align:start position:0%
+change uh the other things of interest
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the not just the cerebellar mechanisms
+
+ align:start position:0%
+the not just the cerebellar mechanisms
+ 
+
+ align:start position:0%
+the not just the cerebellar mechanisms
+for motor learning but for uh these
+
+ align:start position:0%
+for motor learning but for uh these
+ 
+
+ align:start position:0%
+for motor learning but for uh these
+simple habit formation including
+
+ align:start position:0%
+simple habit formation including
+ 
+
+ align:start position:0%
+simple habit formation including
+avoidance responses learned through
+
+ align:start position:0%
+avoidance responses learned through
+ 
+
+ align:start position:0%
+avoidance responses learned through
+trauma they involve the Corpus
+
+ align:start position:0%
+trauma they involve the Corpus
+ 
+
+ align:start position:0%
+trauma they involve the Corpus
+trium responsible for many habits it's
+
+ align:start position:0%
+trium responsible for many habits it's
+ 
+
+ align:start position:0%
+trium responsible for many habits it's
+especially true of a this type of a
+
+ align:start position:0%
+especially true of a this type of a
+ 
+
+ align:start position:0%
+especially true of a this type of a
+learning affected by the consequences of
+
+ align:start position:0%
+learning affected by the consequences of
+ 
+
+ align:start position:0%
+learning affected by the consequences of
+behavior and here's what we were going
+
+ align:start position:0%
+behavior and here's what we were going
+ 
+
+ align:start position:0%
+behavior and here's what we were going
+through before but one more thing I
+
+ align:start position:0%
+through before but one more thing I
+ 
+
+ align:start position:0%
+through before but one more thing I
+wanted to go through in just a little
+
+ align:start position:0%
+wanted to go through in just a little
+ 
+
+ align:start position:0%
+wanted to go through in just a little
+bit and that is another way to classify
+
+ align:start position:0%
+bit and that is another way to classify
+ 
+
+ align:start position:0%
+bit and that is another way to classify
+learning is to begin with the brain
+
+ align:start position:0%
+learning is to begin with the brain
+ 
+
+ align:start position:0%
+learning is to begin with the brain
+mechanisms and here I just focus on the
+
+ align:start position:0%
+mechanisms and here I just focus on the
+ 
+
+ align:start position:0%
+mechanisms and here I just focus on the
+forbrain I've not tried to do it for
+
+ align:start position:0%
+forbrain I've not tried to do it for
+ 
+
+ align:start position:0%
+forbrain I've not tried to do it for
+because we don't know enough really
+
+ align:start position:0%
+because we don't know enough really
+ 
+
+ align:start position:0%
+because we don't know enough really
+about the various kinds of synaptic
+
+ align:start position:0%
+about the various kinds of synaptic
+ 
+
+ align:start position:0%
+about the various kinds of synaptic
+mechanisms various kinds of of
+
+ align:start position:0%
+mechanisms various kinds of of
+ 
+
+ align:start position:0%
+mechanisms various kinds of of
+anatomical changes this field is still
+
+ align:start position:0%
+anatomical changes this field is still
+ 
+
+ align:start position:0%
+anatomical changes this field is still
+pretty young but we do know quite a bit
+
+ align:start position:0%
+pretty young but we do know quite a bit
+ 
+
+ align:start position:0%
+pretty young but we do know quite a bit
+about involvement of forbrain Pathways
+
+ align:start position:0%
+about involvement of forbrain Pathways
+ 
+
+ align:start position:0%
+about involvement of forbrain Pathways
+and the kinds of learning they're
+
+ align:start position:0%
+and the kinds of learning they're
+ 
+
+ align:start position:0%
+and the kinds of learning they're
+involved in so we can separate then
+
+ align:start position:0%
+involved in so we can separate then
+ 
+
+ align:start position:0%
+involved in so we can separate then
+learning of object location in the sense
+
+ align:start position:0%
+learning of object location in the sense
+ 
+
+ align:start position:0%
+learning of object location in the sense
+of an egocentric localization so if I if
+
+ align:start position:0%
+of an egocentric localization so if I if
+ 
+
+ align:start position:0%
+of an egocentric localization so if I if
+I glance at this group here you know I
+
+ align:start position:0%
+I glance at this group here you know I
+ 
+
+ align:start position:0%
+I glance at this group here you know I
+can retain In My Memory at least very
+
+ align:start position:0%
+can retain In My Memory at least very
+ 
+
+ align:start position:0%
+can retain In My Memory at least very
+briefly a working memory of of where
+
+ align:start position:0%
+briefly a working memory of of where
+ 
+
+ align:start position:0%
+briefly a working memory of of where
+various things are in this room in fact
+
+ align:start position:0%
+various things are in this room in fact
+ 
+
+ align:start position:0%
+various things are in this room in fact
+some people can actually see it if they
+
+ align:start position:0%
+some people can actually see it if they
+ 
+
+ align:start position:0%
+some people can actually see it if they
+shut their eyes I can I was talking to
+
+ align:start position:0%
+shut their eyes I can I was talking to
+ 
+
+ align:start position:0%
+shut their eyes I can I was talking to
+one of the students in this class about
+
+ align:start position:0%
+one of the students in this class about
+ 
+
+ align:start position:0%
+one of the students in this class about
+this probably 5 to 10% of you can do it
+
+ align:start position:0%
+this probably 5 to 10% of you can do it
+ 
+
+ align:start position:0%
+this probably 5 to 10% of you can do it
+but uh well you all have that ability
+
+ align:start position:0%
+but uh well you all have that ability
+ 
+
+ align:start position:0%
+but uh well you all have that ability
+you can remember briefly in your what we
+
+ align:start position:0%
+you can remember briefly in your what we
+ 
+
+ align:start position:0%
+you can remember briefly in your what we
+call working memory okay the egocentric
+
+ align:start position:0%
+call working memory okay the egocentric
+ 
+
+ align:start position:0%
+call working memory okay the egocentric
+position meaning where from position of
+
+ align:start position:0%
+position meaning where from position of
+ 
+
+ align:start position:0%
+position meaning where from position of
+my head and eyes something is you know I
+
+ align:start position:0%
+my head and eyes something is you know I
+ 
+
+ align:start position:0%
+my head and eyes something is you know I
+know the doors over there I know the
+
+ align:start position:0%
+know the doors over there I know the
+ 
+
+ align:start position:0%
+know the doors over there I know the
+clocks over there I know that's a wall
+
+ align:start position:0%
+clocks over there I know that's a wall
+ 
+
+ align:start position:0%
+clocks over there I know that's a wall
+and so on so forth and some of these
+
+ align:start position:0%
+and so on so forth and some of these
+ 
+
+ align:start position:0%
+and so on so forth and some of these
+even if I've seen it only briefly I will
+
+ align:start position:0%
+even if I've seen it only briefly I will
+ 
+
+ align:start position:0%
+even if I've seen it only briefly I will
+retain so that's a very simple kind of
+
+ align:start position:0%
+retain so that's a very simple kind of
+ 
+
+ align:start position:0%
+retain so that's a very simple kind of
+learning and we know about the pathways
+
+ align:start position:0%
+learning and we know about the pathways
+ 
+
+ align:start position:0%
+learning and we know about the pathways
+involved in
+
+ align:start position:0%
+involved in
+ 
+
+ align:start position:0%
+involved in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh as for object identity we we know
+
+ align:start position:0%
+uh as for object identity we we know
+ 
+
+ align:start position:0%
+uh as for object identity we we know
+it's another kind of learning but we
+
+ align:start position:0%
+it's another kind of learning but we
+ 
+
+ align:start position:0%
+it's another kind of learning but we
+also now have another kind of
+
+ align:start position:0%
+also now have another kind of
+ 
+
+ align:start position:0%
+also now have another kind of
+localization namely allocentric
+
+ align:start position:0%
+localization namely allocentric
+ 
+
+ align:start position:0%
+localization namely allocentric
+localization where am I in this
+
+ align:start position:0%
+localization where am I in this
+ 
+
+ align:start position:0%
+localization where am I in this
+environment where am I in this building
+
+ align:start position:0%
+environment where am I in this building
+ 
+
+ align:start position:0%
+environment where am I in this building
+where am I in Cambridge and so on so
+
+ align:start position:0%
+where am I in Cambridge and so on so
+ 
+
+ align:start position:0%
+where am I in Cambridge and so on so
+forth and we are learning that all the
+
+ align:start position:0%
+forth and we are learning that all the
+ 
+
+ align:start position:0%
+forth and we are learning that all the
+time and then I've listed other things
+
+ align:start position:0%
+time and then I've listed other things
+ 
+
+ align:start position:0%
+time and then I've listed other things
+like learning of sensor motor
+
+ align:start position:0%
+like learning of sensor motor
+ 
+
+ align:start position:0%
+like learning of sensor motor
+coordination movement patterns that's
+
+ align:start position:0%
+coordination movement patterns that's
+ 
+
+ align:start position:0%
+coordination movement patterns that's
+easier to relate to the things that
+
+ align:start position:0%
+easier to relate to the things that
+ 
+
+ align:start position:0%
+easier to relate to the things that
+Lawrence is talking about what about the
+
+ align:start position:0%
+Lawrence is talking about what about the
+ 
+
+ align:start position:0%
+Lawrence is talking about what about the
+formation of plants that's a kind of
+
+ align:start position:0%
+formation of plants that's a kind of
+ 
+
+ align:start position:0%
+formation of plants that's a kind of
+learning because we're changing them all
+
+ align:start position:0%
+learning because we're changing them all
+ 
+
+ align:start position:0%
+learning because we're changing them all
+the time in our brain okay involving
+
+ align:start position:0%
+the time in our brain okay involving
+ 
+
+ align:start position:0%
+the time in our brain okay involving
+prefrontal areas of the
+
+ align:start position:0%
+prefrontal areas of the
+ 
+
+ align:start position:0%
+prefrontal areas of the
+cortex and then I go through this a
+
+ align:start position:0%
+cortex and then I go through this a
+ 
+
+ align:start position:0%
+cortex and then I go through this a
+little more uh expanding the object
+
+ align:start position:0%
+little more uh expanding the object
+ 
+
+ align:start position:0%
+little more uh expanding the object
+location to include objects associated
+
+ align:start position:0%
+location to include objects associated
+ 
+
+ align:start position:0%
+location to include objects associated
+with places so the places are kind of we
+
+ align:start position:0%
+with places so the places are kind of we
+ 
+
+ align:start position:0%
+with places so the places are kind of we
+remember those by a kind of allocentric
+
+ align:start position:0%
+remember those by a kind of allocentric
+ 
+
+ align:start position:0%
+remember those by a kind of allocentric
+orientation to place that's with respect
+
+ align:start position:0%
+orientation to place that's with respect
+ 
+
+ align:start position:0%
+orientation to place that's with respect
+to the environment not with respect to
+
+ align:start position:0%
+to the environment not with respect to
+ 
+
+ align:start position:0%
+to the environment not with respect to
+where we are at the
+
+ align:start position:0%
+where we are at the
+ 
+
+ align:start position:0%
+where we are at the
+moment but that's a kind of Association
+
+ align:start position:0%
+moment but that's a kind of Association
+ 
+
+ align:start position:0%
+moment but that's a kind of Association
+learning we we associate objects with
+
+ align:start position:0%
+learning we we associate objects with
+ 
+
+ align:start position:0%
+learning we we associate objects with
+specific places and we're only in the
+
+ align:start position:0%
+specific places and we're only in the
+ 
+
+ align:start position:0%
+specific places and we're only in the
+last few years are learning how that is
+
+ align:start position:0%
+last few years are learning how that is
+ 
+
+ align:start position:0%
+last few years are learning how that is
+done in the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and of course we know a lot about
+
+ align:start position:0%
+uh and of course we know a lot about
+ 
+
+ align:start position:0%
+uh and of course we know a lot about
+learning of object identity I've just
+
+ align:start position:0%
+learning of object identity I've just
+ 
+
+ align:start position:0%
+learning of object identity I've just
+mentioned some of the characteristics
+
+ align:start position:0%
+mentioned some of the characteristics
+ 
+
+ align:start position:0%
+mentioned some of the characteristics
+from a behavioral point of view and then
+
+ align:start position:0%
+from a behavioral point of view and then
+ 
+
+ align:start position:0%
+from a behavioral point of view and then
+ways to classify them according to their
+
+ align:start position:0%
+ways to classify them according to their
+ 
+
+ align:start position:0%
+ways to classify them according to their
+potential uses which neuroscientists
+
+ align:start position:0%
+potential uses which neuroscientists
+ 
+
+ align:start position:0%
+potential uses which neuroscientists
+don't pay a lot of attention
+
+ align:start position:0%
+don't pay a lot of attention
+ 
+
+ align:start position:0%
+don't pay a lot of attention
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um here's the thing about learning
+
+ align:start position:0%
+um here's the thing about learning
+ 
+
+ align:start position:0%
+um here's the thing about learning
+knowledge of
+
+ align:start position:0%
+knowledge of
+ 
+
+ align:start position:0%
+knowledge of
+place uh besides a very rapid assessment
+
+ align:start position:0%
+place uh besides a very rapid assessment
+ 
+
+ align:start position:0%
+place uh besides a very rapid assessment
+of where we are what we call seene
+
+ align:start position:0%
+of where we are what we call seene
+ 
+
+ align:start position:0%
+of where we are what we call seene
+perception um we
+
+ align:start position:0%
+perception um we
+ 
+
+ align:start position:0%
+perception um we
+learn where we are with respect to
+
+ align:start position:0%
+learn where we are with respect to
+ 
+
+ align:start position:0%
+learn where we are with respect to
+visual landmarks and for primates that's
+
+ align:start position:0%
+visual landmarks and for primates that's
+ 
+
+ align:start position:0%
+visual landmarks and for primates that's
+probably major but for many animals it's
+
+ align:start position:0%
+probably major but for many animals it's
+ 
+
+ align:start position:0%
+probably major but for many animals it's
+still Factory the smell of a place
+
+ align:start position:0%
+still Factory the smell of a place
+ 
+
+ align:start position:0%
+still Factory the smell of a place
+that's more
+
+ align:start position:0%
+that's more
+ 
+
+ align:start position:0%
+that's more
+important uh but we also many animals we
+
+ align:start position:0%
+important uh but we also many animals we
+ 
+
+ align:start position:0%
+important uh but we also many animals we
+know learn where they are with respect
+
+ align:start position:0%
+know learn where they are with respect
+ 
+
+ align:start position:0%
+know learn where they are with respect
+to more Global a more global map
+
+ align:start position:0%
+to more Global a more global map
+ 
+
+ align:start position:0%
+to more Global a more global map
+magnetic cues infr infrasound
+
+ align:start position:0%
+magnetic cues infr infrasound
+ 
+
+ align:start position:0%
+magnetic cues infr infrasound
+patterns um we even learn place in a
+
+ align:start position:0%
+patterns um we even learn place in a
+ 
+
+ align:start position:0%
+patterns um we even learn place in a
+Time cycle but we know the least about
+
+ align:start position:0%
+Time cycle but we know the least about
+ 
+
+ align:start position:0%
+Time cycle but we know the least about
+that and I also want to point out that
+
+ align:start position:0%
+that and I also want to point out that
+ 
+
+ align:start position:0%
+that and I also want to point out that
+we have we we have this knowledge we've
+
+ align:start position:0%
+we have we we have this knowledge we've
+ 
+
+ align:start position:0%
+we have we we have this knowledge we've
+acquired of anticipated positions
+
+ align:start position:0%
+acquired of anticipated positions
+ 
+
+ align:start position:0%
+acquired of anticipated positions
+because every time we move our head
+
+ align:start position:0%
+because every time we move our head
+ 
+
+ align:start position:0%
+because every time we move our head
+around and our eyes we're activating
+
+ align:start position:0%
+around and our eyes we're activating
+ 
+
+ align:start position:0%
+around and our eyes we're activating
+we're say we're activating long-term
+
+ align:start position:0%
+we're say we're activating long-term
+ 
+
+ align:start position:0%
+we're say we're activating long-term
+memories but in the spatial system
+
+ align:start position:0%
+memories but in the spatial system
+ 
+
+ align:start position:0%
+memories but in the spatial system
+putting it in our anatomical terms we're
+
+ align:start position:0%
+putting it in our anatomical terms we're
+ 
+
+ align:start position:0%
+putting it in our anatomical terms we're
+activating a system uh connected with
+
+ align:start position:0%
+activating a system uh connected with
+ 
+
+ align:start position:0%
+activating a system uh connected with
+our head head Direction that's
+
+ align:start position:0%
+our head head Direction that's
+ 
+
+ align:start position:0%
+our head head Direction that's
+activating
+
+ align:start position:0%
+activating
+ 
+
+ align:start position:0%
+activating
+memories we're aware of what's in that
+
+ align:start position:0%
+memories we're aware of what's in that
+ 
+
+ align:start position:0%
+memories we're aware of what's in that
+direction what's in this direction and
+
+ align:start position:0%
+direction what's in this direction and
+ 
+
+ align:start position:0%
+direction what's in this direction and
+so forth that's how we know which way to
+
+ align:start position:0%
+so forth that's how we know which way to
+ 
+
+ align:start position:0%
+so forth that's how we know which way to
+go so it's connected with our
+
+ align:start position:0%
+go so it's connected with our
+ 
+
+ align:start position:0%
+go so it's connected with our
+motivational system as well as the
+
+ align:start position:0%
+motivational system as well as the
+ 
+
+ align:start position:0%
+motivational system as well as the
+highest systems of the brain and the
+
+ align:start position:0%
+highest systems of the brain and the
+ 
+
+ align:start position:0%
+highest systems of the brain and the
+hippoc cample formation is involved in
+
+ align:start position:0%
+hippoc cample formation is involved in
+ 
+
+ align:start position:0%
+hippoc cample formation is involved in
+learning those
+
+ align:start position:0%
+learning those
+ 
+
+ align:start position:0%
+learning those
+things all
+
+ align:start position:0%
+things all
+ 
+
+ align:start position:0%
+things all
+right so we need to fill in a lot of
+
+ align:start position:0%
+right so we need to fill in a lot of
+ 
+
+ align:start position:0%
+right so we need to fill in a lot of
+gaps in this the in lawence types and
+
+ align:start position:0%
+gaps in this the in lawence types and
+ 
+
+ align:start position:0%
+gaps in this the in lawence types and
+I've count about 19 separate types in
+
+ align:start position:0%
+I've count about 19 separate types in
+ 
+
+ align:start position:0%
+I've count about 19 separate types in
+Lawrence
+
+ align:start position:0%
+Lawrence
+ 
+
+ align:start position:0%
+Lawrence
+descriptions and uh if you include those
+
+ align:start position:0%
+descriptions and uh if you include those
+ 
+
+ align:start position:0%
+descriptions and uh if you include those
+iel iisf types he
+
+ align:start position:0%
+iel iisf types he
+ 
+
+ align:start position:0%
+iel iisf types he
+describes uh that hasn't been fully
+
+ align:start position:0%
+describes uh that hasn't been fully
+ 
+
+ align:start position:0%
+describes uh that hasn't been fully
+integrated with the other means of
+
+ align:start position:0%
+integrated with the other means of
+ 
+
+ align:start position:0%
+integrated with the other means of
+classifying
+
+ align:start position:0%
+classifying
+ 
+
+ align:start position:0%
+classifying
+learning okay I'm going to stop there
+
+ align:start position:0%
+learning okay I'm going to stop there
+ 
+
+ align:start position:0%
+learning okay I'm going to stop there
+and turn on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+video this is some of you may have seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some content has been removed due to
+
+ align:start position:0%
+some content has been removed due to
+ 
+
+ align:start position:0%
+some content has been removed due to
+copyright restrictions see the readings
+
+ align:start position:0%
+copyright restrictions see the readings
+ 
+
+ align:start position:0%
+copyright restrictions see the readings
+and viewings page for more information
\ No newline at end of file
diff --git a/pi1IagGYJ3E.txt b/pi1IagGYJ3E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e93116b235a45e00c93c62bde68b15884deefe16
--- /dev/null
+++ b/pi1IagGYJ3E.txt
@@ -0,0 +1,2084 @@
+PROFESSOR: Another strange
+observation about mirrors that
+
+I've never really understood--
+
+the mirror plane is reflecting
+me left to right, so it looks
+
+as though a mirror has
+a grain to it.
+
+It knows what line to reflect
+me back and forth.
+
+But if I kept the mirror in
+fixed orientation and I lay
+
+down, the thing should
+reflect me side to
+
+side, but it doesn't.
+
+It still reflects me
+from top to bottom.
+
+So how can that be?
+
+Why does a mirror plane, if I
+hold it in one orientation,
+
+appear to have a direction
+across which I'm reflected but
+
+it doesn't follow
+me if I move?
+
+Know what I mean?
+
+You have any explanation
+of that?
+
+Hmm?
+
+AUDIENCE: Rotate
+your eyes, too.
+
+PROFESSOR: Rotate my eyes.
+
+I can roll them around.
+
+I can't rotate in any
+other fashion.
+
+That's strange.
+
+I mean, you look at yourself
+every morning--
+
+several times, perhaps,
+and you're reflected
+
+always left to right.
+
+And if you turn the
+mirror, it doesn't
+
+reflect you top to bottom.
+
+Or conversely, you can leave the
+mirror alone and you can--
+
+why does a mirror plane just
+reflect you left to right?
+
+Ah.
+
+I'll let you stew about
+that one for a while.
+
+And I can tell you that I know
+of three papers in scientific
+
+journals that tried
+to explain this.
+
+I can give you literature
+citations, but you think about
+
+it until our next meeting.
+
+Why does it know which
+way I'm oriented?
+
+Ah, I can't think about it.
+
+Alright, back to more
+straightforward questions.
+
+We are now about to embark on
+a grand process of synthesis
+
+which will take us the better
+part of half a semester.
+
+And we've identified our
+four basic operations--
+
+four basic one step
+operations--
+
+namely translation, reflection,
+rotation, and for
+
+the time being I'm going to look
+just at two-dimensional
+
+symmetries, so I'll leave
+inversion out of the picture.
+
+It's only defined in three
+dimensions, and the logic
+
+which I will follow will be to
+first build up two-dimensional
+
+symmetries and then we'll turn
+them into three-dimensional
+
+symmetries by picking another
+translation that's not
+
+coplanar with the first two.
+
+So we're going to look for
+the time being at just
+
+two-dimensional symmetries.
+
+The nice thing about doing this
+is that the number of
+
+two-dimensional symmetries is
+relatively small, so we can
+
+derive them rigorously
+and exhaustively.
+
+To do so in three dimensions is
+a much more time consuming
+
+and elaborate exercise.
+
+It's no different in principle,
+
+there's just more work.
+
+So if we do two-dimensional
+symmetries first,
+
+it's an easy case.
+
+We can do it rigorously and
+completely, and then what
+
+we'll do is just look at a few
+examples in three dimensions
+
+and look at how the results are
+designated and tabulated.
+
+So the first combination I will
+choose to make is one
+
+that I set up last time and
+should not have started when
+
+there was no time
+to finish it.
+
+So let me take an initially
+pristine space and say that to
+
+this I'm going to the operation
+of translation.
+
+That immediately implies a
+string of translations and a
+
+string of lattice points, but
+I'm just going to focus my
+
+attention on the first one.
+
+Then what I said I'll do is add
+to the space a rotation
+
+operation A alpha.
+
+I'm going to for convenience
+put it right at the lattice
+
+point, but as there is no
+unique origin to the
+
+translation, I can start
+and stop the
+
+translation anywhere I like.
+
+So here's my translation.
+
+The rotation operation is going
+to take that translation
+
+and repeat it at angular
+intervals alpha so that I get
+
+a radiating porcupine-like
+sheaf of translations all
+
+coming out of a common point.
+
+Alpha, we observed, has to be
+a submultiple of 2 pi, so I
+
+will have a cluster of
+translations separated by the
+
+equal interval alpha--
+
+angular interval alpha--
+
+and I'm going to choose to
+focus my attention on
+
+just the first one.
+
+So this, since it's repeated
+by rotation, has the same
+
+length T.
+
+And then I'm going to look
+at the other end of the
+
+translation and say that
+similarly I must have a set of
+
+equally spaced angular-wise
+translations all separated by
+
+alpha, and I'm going to choose
+to focus my attention
+
+just on this one.
+
+So this angle is alpha, and
+this angle here is alpha.
+
+And now there's big trouble
+in River City.
+
+This is a translation, here's
+a lattice point, here's a
+
+lattice point.
+
+This is a translation--
+
+a lattice point sits up here.
+
+This is a translation--
+
+a lattice points sits up here.
+
+Now I've got two lattice points
+eyeball to eyeball, and
+
+they jolly well better be
+separated by either the
+
+interval T or some multiple
+P times T,
+
+where P is some integer.
+
+It would be quite all right if
+there were two translation
+
+separation or five translation
+separation, but it must be
+
+some multiple of translation or
+I have violated my initial
+
+premise that everything in this
+space is periodic at a
+
+translational interval T.
+
+So let me take this geometrical
+constraint and
+
+very quickly convert it into
+analytical form so that we can
+
+proceed to systematically
+find out what the
+
+possibilities are.
+
+Let me drop a perpendicular
+down to the original
+
+translation.
+
+So this distance in here is PT,
+this distance will be T
+
+times the cosine of alpha, and
+this distance in here will be
+
+T times the cosine of alpha.
+
+So in analytic form, then, I
+can say that my original
+
+translation T is equal
+to T cosine of alpha
+
+plus T cosine of alpha.
+
+That's 2T cosine of
+alpha plus PT.
+
+And the first thing we can see
+is that the magnitude of T
+
+drops out because this
+construction and the
+
+constraint it embodies in no way
+depends on the magnitude
+
+of the translation.
+
+So this says, then, that 1 is
+equal to 2 cosine of alpha
+
+plus the integer P. And if I
+solve for the value of cosine
+
+of alpha, cosine of alpha will
+be 1 minus an integer P
+
+divided by 2.
+
+So there is the constraint that
+must be followed if my
+
+construction is to be
+self-consistent.
+
+So we've got this now in a
+plug and chug situation.
+
+So what I'm going to put down is
+the value of P, taking all
+
+possible integers for
+which a value of
+
+cosine of alpha exists.
+
+I'm then going to evaluate
+cosine of alpha, which is 1
+
+minus P over 2, and then I'm
+going to identify the n-fold
+
+axis that corresponds to that
+particular value of alpha.
+
+Let's put in P equals 3,
+and this is as far
+
+as we got last time.
+
+Well, if we put 4, then cosine
+of alpha is minus 3/2--
+
+it's not defined.
+
+If we drop P down to 3, then
+cosine of alpha is minus 1, 1
+
+minus 3 over 2.
+
+And the angle whose cosine
+is minus 1 is a--
+
+let me put down the
+value of alpha and
+
+then the n-fold axis.
+
+The angle whose cosine is minus
+1 is 180 degrees, and
+
+that would describe quite nicely
+the rotational throw of
+
+a twofold axis.
+
+If I let P drop down to the
+value 2, then I have minus 1/2
+
+of the cosine of alpha.
+
+The angle whose cosine is minus
+1/2 is 120 degrees.
+
+And guess what?
+
+That's the angular throw
+of a threefold axis.
+
+Let P drop down to 1, and then
+cosine of alpha is 0.
+
+The angle whose cosine is 0 is
+90 degrees, and that would be
+
+a fourfold axis.
+
+Looks like we're done, except
+P could be equal to 0.
+
+In that case, cosine of
+alpha is plus 1/2.
+
+The angle whose cosine is plus
+1/2 is equal to 60 degrees,
+
+and that's a sixfold access.
+
+What about negative integers?
+
+Minus one, will that work?
+
+This says that cosine of alpha
+is 1, and the angle whose
+
+cosine is one is 0 degrees
+or 360 degrees.
+
+And that would be no rotational
+symmetry all.
+
+It's rather amusing that the
+trivial case of no symmetry at
+
+all also falls out of
+this construction.
+
+So this is a momentous result.
+
+We've shown that if you're going
+to have a pattern that
+
+has a repetition by translation
+in it, the number
+
+of rotational symmetries that
+can be added are either no
+
+symmetry at all, a twofold
+rotational symmetry,
+
+threefold, fourfold,
+or sixfold.
+
+In other words, the axis--
+
+no symmetry at all, twofold,
+threefold, fourfold, or
+
+sixfold, nothing else.
+
+This tells you a lot about the
+shapes that you can see
+
+macroscopically on crystals.
+
+You could have a crystal that
+had the shape of the trigonal
+
+prism, and that would
+be perfectly fine.
+
+You could have a crystal that
+had the shape of an orthogonal
+
+brick that would have twofold
+axes coming out of the faces.
+
+You could have a crystal in
+the shape of a hexagonal
+
+present, or you could have a
+crystal in the shape of the
+
+square prism.
+
+But something thing like a
+crystal with a pentagonal
+
+cross section that would
+be a fivefold access--
+
+that is strictly forbidden,
+because the external shape of
+
+the crystal has to reflect the
+internal symmetry among the
+
+arrangement of atoms.
+
+There are lots of things
+in nature that have
+
+crystallographic symmetry.
+
+There is a little cactus that
+looks like this with some
+
+little spines coming out like
+this on the top, and its
+
+proper name is astrophytum
+myriostigma, also known as the
+
+ornamented bishops cap.
+
+Beautiful example of fivefold
+symmetry, but the cells inside
+
+of that cactus can not have the
+same size and shape and be
+
+repeated by translation.
+
+There are flowers that have
+very common examples of
+
+fivefold and even sevenfold
+symmetry.
+
+There's one little purple flower
+that looks like this
+
+that comes out in the spring,
+and that's called periwinkle.
+
+Fivefold symmetry-- fine for a
+plant, but if you got down
+
+inside the stem of this flower,
+the cells cannot be
+
+repeated by translation.
+
+There are astronomically
+high symmetries.
+
+These big giant cacti in the
+Southwest, the saguaro, they
+
+have rotational symmetries
+that run from 18-fold,
+
+19-fold, 23-fold, so that if
+you picked up one of these
+
+guys very carefully, because
+they're covered with spines,
+
+and if you could lift it--
+which would be very hard
+
+because they weigh a
+couple of tons--
+
+take that guy and rotate them
+through 1/27 of a circle, and
+
+if he had 27-fold symmetry, you
+could plop them down and
+
+you couldn't tell that
+it had been moved.
+
+There is no crystallographer
+who can resist cacti.
+
+All sorts of symmetry, even
+symmetries that violate
+
+crystal graphic symmetries--
+
+wonderful textures and colors.
+
+And they have another really
+remarkable property, which
+
+commends them as house plants.
+
+If they die, this sheath of
+spines stays intact until
+
+someday when you're watering it,
+you brush against it and
+
+you poke a hole right through
+the spines and
+
+there's nothing inside.
+
+So a house plant that dies and
+you can't tell for two years
+
+or so is a very good plant
+to have as a companion.
+
+So cacti have all sorts
+of strange symmetries.
+
+Fine, but you can say something
+about the internal
+
+structure of that flower
+or that cactus.
+
+But this little almost trivial
+proof has told us something
+
+else about crystals, because
+the presence of translation
+
+imposes a constraint on the
+rotational symmetry that can
+
+be present, and the rotational
+symmetry tells us something
+
+about the nature of the
+two-dimensional lattice which
+
+can accommodate that symmetry.
+
+So let's go through this list
+once more, and let's pay
+
+attention to the value of P.
+
+For a twofold rotational
+symmetry, what we would do
+
+would be to take this original
+translation, we put the
+
+twofold axis here, and that
+takes the translation and
+
+rotates it around.
+
+So here's a lattice point here,
+one here, one here, and
+
+the twofold axis here, takes the
+translation and we rotate
+
+in a counterclockwise sense.
+
+Here's another lattice
+point here.
+
+P was equal to three
+translations, and I'll be
+
+darned if that isn't exactly
+what we have.
+
+Three translations from
+this lattice point A--
+
+let me put some labels
+up here.
+
+This was lattice point A, this
+was lattice point B, and this
+
+was our translation PT.
+
+Three translations, just
+as advertised.
+
+What constraint does this
+put on a lattice?
+
+None whatsoever, because all
+this says is that if you have
+
+a translation that translation
+must be repeated into an
+
+extended one-dimensional row.
+
+So you can put this an any
+2D lattice whatsoever.
+
+In other words, the magnitudes
+of the two translations--
+
+let's call them T1 and T2 are
+under no constraint to be
+
+related one to another--
+
+and this angle between
+them, alpha, can be
+
+anything that it likes.
+
+You could have a twofold axis,
+but that requires simply a
+
+lattice row parallel to T1 and
+a lattice row parallel to T2.
+
+The next integer we
+hit was minus 1/2.
+
+That was cosine of minus 1/2,
+this was P equals 3, and that
+
+corresponded to something
+that could
+
+accept a threefold symmetry.
+
+So let me put a guide to the
+I in here and make an
+
+equilateral triangle.
+
+If we translate and rotate
+up by 120 degrees using a
+
+threefold axis and then rotate
+minus 120 degrees about the
+
+other lattice point, that
+puts another translation
+
+up here, and now--
+
+I'm sorry, this was P equals 2
+And as required, this is PT,
+
+and that's equal to
+two translations.
+
+This has put a constraint on the
+sort of lattice which can
+
+exist in this space because we
+have two translations, T1 and
+
+T2, which are equal in
+magnitude, identical in
+
+magnitude, because they're
+related by symmetry.
+
+And consequently, we have
+defined a space lattice, a
+
+two-dimensional space lattice.
+
+We'll call this T1
+and call this T2.
+
+This lattice has the constraint
+that magnitude of
+
+T1 must be identical to the
+magnitude of T2, and the angle
+
+between T1 and T2 is again
+identically 120 degrees.
+
+Not 119.9, but exactly 120
+degrees because there is a
+
+threefold axis in here that
+demands that that be so.
+
+So this is a very specialized
+kind of lattice, restricted to
+
+have two translations identical
+in magnitude.
+
+And if there's a threefold axis
+there, you should be able
+
+to find these two.
+
+And if there's a threefold axis
+there, then the angle
+
+between these two specialized
+translations is 120 degrees.
+
+Our next magic integer was 1,
+and that corresponded to a
+
+fourfold axis.
+
+And if we do what we claimed we
+did in that construction,
+
+we'd put a fold axis here.
+
+That takes T1 and rotates it
+exactly 90 degrees to a
+
+translation T2.
+
+Once again, two noncollinear
+translations, so we have
+
+defined a two-dimensional net.
+
+If we complete the cell, this
+is one translation.
+
+PT is equal to one translation
+in here, and this angle is 90
+
+degrees because it's produced
+by a fourfold axis.
+
+So we have a very
+special lattice.
+
+Again, the magnitudes of two
+translations are identical--
+
+not approximately the same,
+they're identical--
+
+and the angle between them is
+identically 90 degrees.
+
+Only a couple to go.
+
+P could be equal to 0, and that
+was the case for a 60
+
+degree rotation,
+a sixfold axis.
+
+So again, let's draw what
+came out of this
+
+particular special case.
+
+Here's T1, here is T2.
+
+This angle is 60 degrees exactly
+because there's a
+
+six-fold rotation axis here, a
+sixfold rotation axis here,
+
+and the rotation of 60 in the
+opposite sense gives us
+
+another translation here.
+
+These two lattice points
+coincide and there is PT equal
+
+to 0T, and these two
+points coincide.
+
+Now if I complete a standard
+unit cell with T1 T2 as I've
+
+done in other cases--
+
+this was T1, this was T2, this
+was a translation which I'm
+
+not going to use.
+
+So this is the shape of the
+lattice and these now are
+
+lattice points with a sixfold
+axis on them.
+
+The dimensional specialization
+is exactly the same as I found
+
+for a threefold axis,
+T1 identical to T2.
+
+If I pick this cell, T1 to T2
+can be described as an angle
+
+of 120 degrees.
+
+Exactly the same lattice that we
+found for a threefold axis.
+
+So with this simple minded
+little construction we've
+
+found two profound things--
+
+that there are five kinds of
+rotation axes, including the
+
+onefold no rotational
+symmetry at all.
+
+And it turns out that there are
+one, a general lattice, a
+
+hexagonal lattice, and
+the square lattice.
+
+There are three kinds of
+two-dimensional lattices that
+
+are required by these
+symmetry elements.
+
+So these guys require that
+there be three lattice of
+
+different specializations that
+are able to accommodate them.
+
+So let me call this a
+parallelogram net, and that
+
+has T1 not equal to
+T2, the angle
+
+between T1 and T2 general.
+
+And this is a lattice that can
+accommodate either no symmetry
+
+at all or a twofold
+rotation access.
+
+Then there was a net that I'll
+call the hexagonal net, and
+
+this had T1 identical to T2 in
+magnitude, and it had the
+
+angle between them, the angle
+between T1 and T2 as
+
+identically 120 degrees.
+
+And this could accommodate
+either a threefold or a
+
+sixfold axis.
+
+And then finally, the general
+net, which I call a
+
+parallelogram net, and that
+has magnitudes of the two
+
+translations not equal
+to one another.
+
+They can have any values they
+like, and the angle between T1
+
+and T2 is completely general.
+
+And that's exactly what I had
+up here for the-- oh, we did
+
+that once already.
+
+The one that I'm missing, the
+third one, is the square net.
+
+Square net has T1
+identical to T2.
+
+In magnitude, the angle between
+them is exactly 90
+
+degrees, and that is required
+by a fourfold axis.
+
+Let me pause here to see if
+there are any questions.
+
+Yes, sir.
+
+AUDIENCE: When you write on the
+last one with the sixfold,
+
+it's only 120.
+
+You could have also written
+60, correct?
+
+PROFESSOR: Yes, I could have.
+
+And this lattice is actually the
+same as what I found for a
+
+threefold axis.
+
+I could pick either this or this
+as the cell, but the two
+
+translations in those
+two cells are equal.
+
+And again at various stages
+along the way, we'll need a
+
+convention.
+
+And if I have a net that looks
+like this, a parallelogram,
+
+whether a specialized
+parallelogram or not, I have a
+
+choice of two angles
+that I could use.
+
+We call that alpha.
+
+This is going to be 180
+degrees minus alpha.
+
+Which do I pick?
+
+You need a rule, and the rule is
+that for labeling the cell,
+
+pick alpha so that it's greater
+
+or equal to 90 degrees.
+
+That's pure convention, but you
+want to have a rule just
+
+like a language so people use
+the same words to describe the
+
+same thing.
+
+Here we want to use the same
+geometry to describe one and
+
+the same thing.
+
+The other convention is that
+there are no unique
+
+translations that
+define a net.
+
+We could take linear
+combinations of these vectors
+
+and define the same lattice,
+so we need another rule for
+
+selecting the standard
+translations--
+
+again, so that two people can
+do an x-ray diffraction
+
+experiment and report the
+results in terms of the same
+
+lattice, and this is a fairly
+reasonable thing.
+
+This is pick the two shortest
+translations, and that clearly
+
+makes sense.
+
+There's absolutely nothing at
+all to commend a cell that has
+
+this as T2 and this as
+T1 so you get a long,
+
+skinny oblique things.
+
+Your natural inclination would
+pick the two shortest
+
+translations in the net.
+
+OK, so these are conventions.
+
+This has nothing to do with the
+nature of the symmetry or
+
+what makes it unique, but just
+so that people have one
+
+defined way of labeling
+things.
+
+AUDIENCE: Right.
+
+[INAUDIBLE] my question
+was actually that--
+
+PROFESSOR: It was a good answer,
+even if was not to the
+
+question that you asked.
+
+AUDIENCE: I said the sixfold and
+the threefold are exactly
+
+the same, but then I realized
+they are because there is no
+
+crystal that can have threefold
+
+symmetry without sixfold.
+
+PROFESSOR: You were
+doing fine.
+
+You should have quit just before
+that last statement.
+
+How can you have a hexagonal
+lattice that sometimes has
+
+sixfold symmetry and sometimes
+has threefold symmetry?
+
+Well, let me give you an example
+for that, and it makes
+
+a very useful point.
+
+Let me draw two hexagonal nets,
+and in this one I'll put
+
+a threefold axis.
+
+So I'll have one motif here,
+I'll go 120 degrees away.
+
+Here is a motif here, and I'll
+go 120 degrees away, and here
+
+is a third motif.
+
+So these three guys form
+a triangle about
+
+this lattice point.
+
+And we would have about the
+other lattice points at the
+
+corners of the cell exactly the
+same triangle of motifs,
+
+and the same thing over here.
+
+So there is a pattern.
+
+It has a hexagonal lattice,
+and it has a triangle of
+
+objects related by
+a threefold axis.
+
+And now let me take exactly the
+same lattice, and now I'll
+
+put in instead a sixfold axis.
+
+And that means I'm going to have
+a hexagon of objects, and
+
+it'll do something like this.
+
+And I don't want to push my
+luck and try to draw that
+
+twice, but there would be a
+hexagon here and a hexagon of
+
+motifs here, another one at
+this lattice point, and
+
+another one at this lattice
+point here.
+
+Same lattice, same shape,
+same dimensions--
+
+although that's not critical--
+
+but one of them has only
+a threefold axis.
+
+One of them has only a
+sixfold axis in it.
+
+Why?
+
+Because I decided to put a
+threefold axis in this
+
+pattern, and I decided to put
+a sixfold axis in this
+
+pattern, but they both end up
+being contented and happy with
+
+a lattice with the same degree
+of specialization.
+
+Now we will come as we
+progressed a little bit
+
+further that we have to
+go in two dimensions
+
+to the reverse situation.
+
+We have a particular symmetry
+and it's happy with two
+
+different sorts of lattices
+with different shapes and
+
+different specializations,
+and that's
+
+going to come up directly.
+
+Any other questions?
+
+Yeah.
+
+AUDIENCE: In this example,
+the sixfold [INAUDIBLE]
+
+axis [INAUDIBLE].
+
+It's just that [INAUDIBLE].
+
+PROFESSOR: Yes.
+
+You're saying that here hanging
+at this lattice point
+
+is something that has
+sixfold symmetry.
+
+Here is something has only
+threefold symmetry.
+
+The nature of the lattice and
+the symmetry that is in that
+
+lattice are two inseparable
+aspects of the pattern.
+
+But often, as we've seen here,
+there's more than one
+
+possibility for a
+given lattice.
+
+And as we'll see very shortly,
+for some other symmetries, for
+
+one given symmetry, there are
+two kinds of lattices.
+
+But nevertheless, the thing to
+keep fixed in your mind is
+
+that we call this a
+hexagonal lattice.
+
+Why?
+
+Because this translation is
+equal to this one, and they
+
+are exactly 120 degrees apart.
+
+That lattice can have that
+specialness only if there's
+
+either a threefold or a
+sixfold axis in it.
+
+So the specialization of a
+lattice is inseparable from
+
+the symmetry that is in the
+lattice that demands that
+
+specialization of the lattice.
+
+Conversely, a lattice can have
+the specialization only if you
+
+place in a symmetry which
+demands precisely that
+
+specialization.
+
+So if you measure a lattice,
+and this turns out to be
+
+119.99 degrees and these turn
+out to be 3.21 angstroms and
+
+3.21 angstroms, that is not a
+hexagonal lattice, because
+
+there's no symmetry in there
+that demands that this angle
+
+be 120 degrees.
+
+And that may seem to be an
+academic fine point, but we'll
+
+see that in due course the
+properties of a crystal depend
+
+on the symmetry of
+that crystal.
+
+If the crystal has symmetry, the
+property also has to have
+
+that symmetry.
+
+And it is the atoms inside the
+cell which determine the
+
+symmetry of the property, and
+the properties is one aspect
+
+of the symmetry that goes along
+with lattice dimensions
+
+and lattice angles.
+
+Is that clear?
+
+So let me say it again,
+because this is
+
+an important point.
+
+The specialness of a lattice
+is inseparable from the
+
+symmetry that is existing in
+that lattice that demands that
+
+specialness.
+
+So if you have a crystal with
+three orthogonal translations
+
+that is equal in length as you
+might care to measure, that
+
+crystal is not cubic unless
+there's symmetry in that
+
+lattice that demands that the
+edges of the cell conform to
+
+the geometry of a cube.
+
+Any other questions?
+
+Let's then in the time that's
+remaining look at the other
+
+symmetry element that could be
+present in a two-dimensional
+
+crystal, and that's
+the mirror plane.
+
+So here's a mirror plane.
+
+That's the one remaining
+symmetry element in two
+
+dimensions, and let's ask how we
+might combine in this space
+
+along with the mirror
+plane a translation.
+
+If I just pop in a translation,
+and call this T1,
+
+and for convenience, I'll take
+the lattice point on the
+
+mirror plane.
+
+Here's another lattice
+point that sits here.
+
+The mirror plane acts
+on everything.
+
+It's going to take this lattice
+point and flip it over
+
+to here, and it's going to take
+the translation that goes
+
+from the origin lattice point to
+this lattice point and give
+
+me a T1 prime that sits here.
+
+And now I have two non collinear
+translations, so
+
+these have defined for me a
+cell that looks like this.
+
+This is T1, this is T2, and
+this is some angle alpha
+
+between them.
+
+That's a special lattice.
+
+This is a lattice which has,
+just as in the hexagonal or
+
+square net, two translations
+that are
+
+identical in magnitude.
+
+Why?
+
+Because they're repeated by a
+mirror plane, and the angle
+
+between them-- the angle
+between T1 and T2--
+
+is completely general.
+
+It can be anything it likes.
+
+It can close up to a very narrow
+angle or it can open up
+
+to an almost flat angle.
+
+That's a new kind of lattice.
+
+None of the preceding lattices
+could make that claim.
+
+Now let me point out that this
+is for the first time a case
+
+where it would be much to our
+advantage to not choose a cell
+
+that contains one
+lattice point.
+
+Let me put some dotted
+lines in here.
+
+And let me submit--
+
+these will also be
+lattice points--
+
+that I could pick a larger cell
+that would have this as
+
+T1, it would have this as T2,
+and the angle between them now
+
+would be identically 90
+degrees because of the
+
+geometry that gives
+us a rhombus here.
+
+This would have two translations
+that are not
+
+equal in magnitude, and it would
+have an angle between
+
+these two translations that is
+identically 90 degrees, but it
+
+is no longer a cell that
+contains one lattice point.
+
+It now catches a second
+lattice point
+
+that's in the middle.
+
+So this is a double cell, and
+it has a rectangular shape.
+
+It's a centered rectangular
+lattice.
+
+Being a double cell that's
+redundant has twice the area
+
+that is unique in the pattern,
+and anything that's hanging up
+
+here is going to be hanging down
+here, so it has a twofold
+
+redundancy.
+
+But the thing that you get in
+return for paying the price of
+
+that redundancy is a cell that
+has a right angle in it.
+
+And as we'll see, we're going
+to use the edges of the unit
+
+cell as the basis of a
+coordinate system for
+
+describing what goes on at
+positions xy within the cell.
+
+And the advantages of an
+orthogonal coordinate system,
+
+whenever you can take advantage
+of it, far outweighs
+
+the price of pain--
+
+twice the area to describe
+the same pattern.
+
+So this is what is generally
+taken as the standard cell.
+
+It's a double cell.
+
+But I think you're used to
+that sort of compromise,
+
+because you've all heard of face
+centered cubic lattices.
+
+The primitive cell in a face
+centered cubic lattice is a
+
+rhombohedron.
+
+But, oh, that Cartesian
+coordinate system is so great
+
+to use rather than something
+that has an
+
+oblique coordinate system.
+
+So is this is a definition
+of convenience.
+
+Notice the curious duality--
+
+either special relation between
+the translations angle
+
+general or special relation
+between the translations, an
+
+angle special.
+
+General translation, special
+angle, relation between the
+
+translation, general angle--
+
+so, it's a curious
+sort of duality.
+
+You can have one but not the
+other or vice versa.
+
+So this is a fourth
+sort of lattice.
+
+Number one, number two, number
+three, and now we have number
+
+four, which is a centered
+rectangular lattice.
+
+And this particular lattice
+has T1 not equal to T2 in
+
+magnitude, but it has the
+angle between T1 and T2
+
+exactly 90 degrees, and
+it's a double cell.
+
+It's centered.
+
+Are we done?
+
+The reason I asked that silly
+rhetorical question is that
+
+obviously I suspect that we're
+not done, and what
+
+else might we do?
+
+We got our centered rectangular
+net by starting
+
+with a translation--
+
+starting with an mirror
+plane, really--
+
+and then we added a general
+translation, and that
+
+reflected it across and gave us
+a diamond shaped net which
+
+we could define as a rectangular
+double shell.
+
+Does that always happen?
+
+Do I always get that oblique
+diamond shaped cell?
+
+No.
+
+Suppose I put in my first
+translation deliberately in a
+
+fashion such that it was at
+exactly right angles to the
+
+mirror plane.
+
+That mirror plane will then
+reflect the translation and
+
+change its direction, and
+now I have generated a
+
+one-dimensional lattice
+row with
+
+translational periodicity T1.
+
+And I've got a translation
+that's exactly perpendicular
+
+to the mirror plane.
+
+How do I now make a space
+lattice, a two-dimensional
+
+space lattice?
+
+And the answer is
+very carefully.
+
+Suppose I throw in a second
+translation T2 and the mirror
+
+plane reflects it
+across to here.
+
+This interval between lattice
+points up here is totally in
+
+commensurate with the
+first translation,
+
+and that won't work.
+
+It's violated my initial choice
+of the translational
+
+periodicity unless I do one of
+two things, and let's try them
+
+both and dispose of
+this quickly--
+
+this is straight away.
+
+Here's my one-dimensional
+lattice row.
+
+I do not violate this
+periodicity
+
+T1 if I do two things.
+
+I could pick T2 so that it fell
+exactly along the mirror
+
+line, and that's going to
+generate for me a new type of
+
+lattice in which this is 90
+degrees and these two
+
+translations are unequal
+in length.
+
+So this is a lattice that
+has a rectangular shape.
+
+It's a primitive rectangular
+cell, and it has T1 not equal
+
+to T2 in magnitude, and
+it has T1 and T2
+
+exactly 90 degrees apart.
+
+The second choice that would
+not result in any
+
+contradiction would be to have
+this as T1, and then pick T2
+
+very carefully so that it
+spanned the mirror line with
+
+one half of T1 exactly
+up here and one half
+
+of T1 exactly here.
+
+And this would be compatible
+with the separation T1 down at
+
+the start of this translation.
+
+I think you can see that what
+this is going to give me is
+
+the centered rectangular net
+right back again, so this is
+
+the centered rectangular net--
+
+nothing new.
+
+But we did pick up one
+additional two-dimensional
+
+lattice of distinct character.
+
+Number 5 is a primitive
+rectangular network, and it
+
+has the characteristics T1 is
+not equal to T2 in magnitude.
+
+Just as in the centered
+rectangular net, T1 is at
+
+exactly 90 degrees to T2, but
+this is a primitive cell.
+
+And that's it.
+
+We really set up the ground
+rules for the geometry of a
+
+periodic two-dimensional
+space.
+
+There are five kinds
+of rotation axes--
+
+one, two, three,
+four, and six.
+
+Each one requires one or
+more of the specialized
+
+two-dimensional lattices.
+
+We have a case where
+interestingly two different
+
+symmetries are compatible with
+a lattice of the same
+
+specialization.
+
+In the case of the [? hexagon ?]
+on that, either
+
+three or sixfold symmetry
+could require that.
+
+In the case of the mirror plane
+we have one symmetry
+
+element, M, that can
+fit into two
+
+different kinds of lattices.
+
+So in one case, the same lattice
+can take two different
+
+symmetries.
+
+In this case, two different
+lattices can accommodate the
+
+same symmetry.
+
+So that's the story for two
+dimensions, and we have just
+
+one final thing to do.
+
+That is to add to the lattices
+that we have found, and there
+
+are five of them, and add
+to the lattice point the
+
+symmetries that we have
+found require them.
+
+And there are a limited number
+of these-- one, two, three,
+
+four, or sixfold rotational
+symmetry in a mirror plane.
+
+And when we have finished these
+additions, we will end
+
+up with a combination of lattice
+and symmetry, which is
+
+something that is called
+a plane group--
+
+group because the operations
+that are present in the space
+
+follow the requirements of the
+mathematical entity called a
+
+group, plane because this is
+a distribution of symmetry
+
+elements throughout a plane
+and not just fixed at one
+
+particular point.
+
+Let me finish with some general
+observation, and we
+
+will obtain some of these
+rules later on.
+
+Suppose I take a pristine
+space--
+
+and this blackboard is
+no longer pristine--
+
+and I put in the space a
+first operation, and
+
+there's a motif in there.
+
+This first operation moves
+around this first motif and
+
+gives me a second
+one, number two.
+
+Then I say let me put in
+another operation.
+
+I'd like to combine these
+things and see how many
+
+different combinations
+I have, so I put in
+
+operation number two.
+
+Operation number two will take
+the second object and repeat
+
+it to a third object.
+
+Number two is identical to
+number one, so this gives me a
+
+third object reproduced
+from the second by
+
+operation number two.
+
+Now I have a space, and
+sitting in it are two
+
+different operations and
+three different motifs.
+
+Motif number one and motif
+number three are the same darn
+
+thing because they've been
+repeated by symmetry steps, so
+
+there must automatically be some
+third transformation that
+
+is equal to the combined effect
+of going from one to
+
+two and then from
+two to three--
+
+going from one to
+three directly.
+
+So this is another truth
+about these symmetries.
+
+Whenever you take two operations
+and combine them in
+
+a space, the net effect of those
+two operations is equal
+
+to a third operation.
+
+So a question we're going to ask
+all along the way until we
+
+are at the end of the month--
+
+if you take a translation and
+combine it with a mirror
+
+plane, what new operation
+has to arise?
+
+If you take two rotation
+operations and put them
+
+together, what third net
+operation has to arrive?
+
+If we have some general rules,
+then we can automatically say,
+
+OK, I'm going to take a square
+lattice and I'm going to put
+
+in a fourfold axis.
+
+What else is going to pop up
+elsewhere within the cell?
+
+We'll be able to do this
+systematically but fairly
+
+automatically.
+
+So that's where we're
+going from here.
+
+When we're done, we will have
+derived systematically and
+
+rigorously the sorts of
+symmetries that can combine
+
+symmetries such as rotation and
+reflection with a lattice,
+
+and we will know completely
+the different sorts of
+
+patterns that exist around
+us in two dimensions--
+
+in floor tiles, brick
+work, wrapping
+
+paper, and plaid shirts.
+
+We'll pick up at this
+point on Thursday.
+
+Let me caution you we are going
+into territory that is
+
+not covered in Berger's book.
+
+I've just passed
+it out to you.
+
+What we've said in the early
+parts of the term are in
+
+there, but we're going to do
+things in a slightly different
+
+way and then return to
+his text later on.
\ No newline at end of file
diff --git a/pjLbxB9TXJs.txt b/pjLbxB9TXJs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5c02b80ba26fc8341dc6e885005a68b34a08d4f2
--- /dev/null
+++ b/pjLbxB9TXJs.txt
@@ -0,0 +1,1627 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: I want to finish up
+our little excursion into
+
+searching and sorting, a very
+important topic in computing.
+
+How do you sort lists
+or databases?
+
+How do you search them?
+
+And I want to finish
+it up with hashing.
+
+Hashing is how dictionaries
+are implemented in Python.
+
+And this leads to a
+very efficient--
+
+at least most of the
+time-- search.
+
+But it comes at the
+cost of space.
+
+So this is an example where one
+can trade space for time.
+
+So I want to start
+with a simple
+
+example to explain hashing.
+
+And I'm going to begin by
+assuming that what we're
+
+hashing is a set of integers.
+
+So we want to build a set of
+integers and detect whether or
+
+not a particular integer
+is in that set.
+
+And we want to do
+that quickly.
+
+So the basic idea is we're going
+to take an integer--
+
+call it i--
+
+and we're going to hash it.
+
+I'll tell you what that
+means in a minute.
+
+And what a hash function does
+is it converts i to a
+
+different integer, perhaps,
+in some range.
+
+So it, say, converts i to some
+integer in the range 0 to k,
+
+for some constant k.
+
+We're going to then use
+this integer to index
+
+into a list of lists.
+
+So each of these is
+called a bucket.
+
+And a bucket will itself
+be a list.
+
+So this together is
+called a bucket.
+
+We've already seen that we can
+find the i-th element of a
+
+list in constant time.
+
+So when we ask whether some
+integers in this set will hash
+
+it, we'll go immediately to the
+correct bucket, the bucket
+
+associated with that integer.
+
+And then we'll search the list
+at that bucket to see if the
+
+integer is there.
+
+If this list is short enough,
+it will be very efficient.
+
+All, right I realize that's
+very abstract.
+
+But let's look at the code,
+which will make
+
+it much less abstract.
+
+So the code starts with
+something very ugly that I'll
+
+apologize for.
+
+But very soon, we'll see
+how to get rid of that.
+
+I'm using a global variable here
+to say how many buckets
+
+there are going to be.
+
+And I've very arbitrarily
+chosen 47.
+
+I then have a function called
+create, which uses this global
+
+variable and creates a
+list of lists, each
+
+element of which is empty.
+
+Because initially, we have
+no elements in the set.
+
+When I want to insert an element
+in the set, I'll call
+
+the function insert, which
+will hash the element.
+
+It doesn't actually even need
+to use the global numBuckets
+
+in this case, in fact.
+
+And then append it to
+the correct list.
+
+So it calls this function
+hashElem, which could hardly
+
+be simpler.
+
+It just takes the remainder, the
+modulus of the element and
+
+the number of buckets.
+
+So that will give me a
+value between 0 and
+
+numBuckets minus 1.
+
+It gives me one of the
+list, and I'll just
+
+insert it at the end.
+
+When I want to check for
+membership, you'll see it's
+
+quite simple.
+
+All I do is ask the question,
+is i in the list associated
+
+with the correct bucket?
+
+Remove is a little bit more
+complicated, but in fact, we
+
+don't need to spend much
+time looking at it now.
+
+It's just some code.
+
+And the only reason it's
+complicated is Insert doesn't
+
+look whether or not the element
+is already there.
+
+So it may occur multiple
+times in the list.
+
+So I would have to remove
+each one of them.
+
+People see the basic
+structure of this?
+
+Why a list of lists?
+
+Why don't I just, say, have a
+list of Booleans, where I hash
+
+the integer, and it's true or
+false, whether or not I've
+
+seen it, depending upon the
+value of that bucket?
+
+Why can't I do that?
+
+Somebody?
+
+Well, what's the property
+of this hash function?
+
+The key issue here is
+the hash function --
+
+is many-to-one.
+
+That is to say, an infinite
+number of different integers
+
+will hash to the same value.
+
+Because after all, I have
+a set in which I
+
+can store any integer--
+
+or any positive integer,
+at least--
+
+and there are only 47 buckets.
+
+So it's pretty obvious that many
+integers will hash to the
+
+same bucket.
+
+When two different elements hash
+to the same bucket, we
+
+have what is called
+a collision.
+
+There are lots of different
+ways to handle collisions.
+
+What I've shown you here is
+probably the simplest way,
+
+which is called linear
+rehashing.
+
+I'm not actually rehashing.
+
+I'm just keeping a list.
+
+Does that makes sense?
+
+Yes, thank you for--
+
+I'm glad somebody
+has a question.
+
+You have to ask loudly.
+
+AUDIENCE: When you take
+the modulus 47,
+
+what does that return?
+
+PROFESSOR: 0.
+
+AUDIENCE: So hashElem
+always returns 0?
+
+PROFESSOR: Well, no, sorry.
+
+It depends what I'm hashing.
+
+Sorry, I thought if you
+were saying that if I
+
+asked 47 mod 47.
+
+If I take 48 mod 47, I get 1.
+
+If I take 49 mod 47--
+
+it's the remainder.
+
+Maybe I should have called
+it just the remainder.
+
+Look up.
+
+I'm about to throw
+something at you.
+
+Ooh, I threw a curve ball.
+
+OK.
+
+What's the complexity here
+of the membership test?
+
+Kind of hard to analyze.
+
+Roughly speaking, or exactly,
+it will be the length of the
+
+bucket, the size
+of the bucket.
+
+Now, I don't know how
+many elements
+
+will be in the bucket.
+
+But what will this depend on?
+
+It will depend upon the
+number of buckets.
+
+If I have a million buckets,
+I'll get a lot fewer
+
+collisions than if I
+have two buckets.
+
+So let's look at an
+example here.
+
+There's a small program
+called test.
+
+I said numBuckets to
+47 in this case.
+
+And then I'm going to create
+it, create a set.
+
+And then I'm going to put a
+bunch of integers in it, then
+
+a few more, just for fun,
+including one very big
+
+integer, just to show
+that it works.
+
+Then I'm going to show you
+what the set looks like.
+
+And in fact, what we'll do is
+we'll stop it here and see
+
+what we get.
+
+So what we'll see here is, as
+you would expect with that
+
+number of buckets, each of the
+small numbers hashes to a
+
+separate thing.
+
+That's just the way
+remainder works.
+
+Not surprisingly--
+
+in fact, it would be
+disappointing if 325 didn't
+
+have the same value both
+times I inserted it.
+
+So we say we happen to have
+one bucket that's got two
+
+elements in it.
+
+Happen to be the same.
+
+But this very big number
+happened to hash to the same
+
+value of 30 as 34.
+
+So here we have two
+elements in it.
+
+A good hash function has the
+property that it will widely
+
+disperse the values you hash.
+
+So they end up in different
+buckets, rather than some
+
+stupid hash function that tends
+to put everything in the
+
+same bucket.
+
+Now, let's see what happens if I
+change the number of buckets
+
+to, say, 3.
+
+Well, not surprisingly, we get
+some very big buckets, because
+
+there are relatively
+few choices.
+
+So what we see here is we have
+a genuine trade off between
+
+time and space.
+
+If the number of buckets is
+large relative to the number
+
+of elements that we insert in
+the table, then looking at
+
+whether or not an element in
+it is roughly order one.
+
+Because these lists will
+be very short.
+
+So we can actually look up
+something in constant time if
+
+we dedicate enough space
+to the hash table.
+
+If the hash table
+is very small--
+
+the reduction ad absurdium
+case of one bucket--
+
+then it's order n.
+
+It's not constant time.
+
+It's linear in the number
+of elements.
+
+Typically, when people use hash
+tables, they make the
+
+hash tables big enough that for
+all intents and purposes,
+
+you can assume that looking
+something up is
+
+constant time, order 1.
+
+And that, in fact, is what
+Python does with dictionaries.
+
+It hashes the keys and chooses
+a big enough table so that
+
+looking up whether or not
+something is in a dictionary
+
+can be done in constant time.
+
+If it then notices that the
+table is too small, because
+
+you've ended up putting a lot
+of elements in it, it just
+
+re-does it and gets
+a bigger table.
+
+So hashing is an extremely
+powerful technique.
+
+And it's used all the time for
+quite complicated things.
+
+Now is it useful here only when
+we want to store ints?
+
+No.
+
+It would be kind of bad
+if that were the case.
+
+In fact, any kind of immutable
+object can be hashed.
+
+Now, you may have wondered
+why the keys in
+
+dicts have to be immutable.
+
+And that's so that they
+can be hashed.
+
+Why does it have to
+be immutable?
+
+Well, imagine that you
+used a list as a key.
+
+You'd hash it when you put the
+list in the hash table.
+
+But then you might mutate it,
+and the next time you hashed
+
+it, you'd get a different value,
+and so you wouldn't be
+
+able to find it again.
+
+So you need it to be a kind of
+object, where every time you
+
+apply the hash function,
+you get the same value.
+
+I don't need to show you
+that this works.
+
+You'll just believe
+me, I'm sure.
+
+Let's look at a slightly more
+complicated hash function.
+
+Here, I want to hash something
+that could be
+
+either an int or a string.
+
+So I first check and
+see if it's an int.
+
+If so, I'll set the
+value to be e.
+
+Then down at the bottom, I'll do
+the modulus operator again.
+
+But if it's a string,
+I'm going to first
+
+convert e to an int.
+
+And this is basically the trick
+that people typically
+
+use when they're doing hashing,
+is they convert
+
+whatever thing they have,
+to some integer.
+
+People do this with all
+sorts of things.
+
+For example, this is the way
+airport security systems today
+
+do face recognition.
+
+They hash every picture of a
+face to an integer, and then
+
+look it up.
+
+So we can see it here.
+
+The way I'm doing it--
+and the details
+
+don't very much matter--
+
+is I'm going to do it a
+character at a time, do a
+
+shift ord of C, takes the
+ASCII, the internal
+
+representation bits
+of each character.
+
+And again, I don't care
+if you understand how
+
+the code works here.
+
+What I just want you to see is
+that it's not very long.
+
+And in, fact it's typically
+fairly simple to hash almost
+
+any kind of an object.
+
+Because deep down, we know
+that every object is
+
+represented by some string of
+bits in the computer's memory.
+
+And we can always convert a
+string of bits to an integer.
+
+All right, so that's hashing, a
+very powerful and extremely
+
+useful technique.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+you're returning something,
+will you always find the
+
+remainder, or can you
+use [INAUDIBLE]?
+
+PROFESSOR: There are many
+different ways of doing hash.
+
+All the hash function has to
+do is convert its argument
+
+into an integer in some way or
+another within a fixed range.
+
+It happens to be that remainder
+is a very simple way
+
+to do that and is often used.
+
+There's a whole theory
+about hash functions.
+
+You can read about them in
+gory detail on Wikipedia.
+
+The math can actually be quite
+complicated, and there's no
+
+real need to understand it.
+
+I typically do something like
+dividing by a prime number,
+
+which is known to have
+good properties.
+
+But, again, you can get carried
+away with this.
+
+And it's usually not worth the
+trouble, unless you're very
+
+deeply involved in something.
+
+OK?
+
+And then I've got another
+program that does this, but
+
+again, I don't think much
+would be served by
+
+running it for you.
+
+Any questions about hashing?
+
+Yes?
+
+AUDIENCE: So does this only
+work because you said
+
+[INAUDIBLE]
+
+Python treats lists
+in a certain way?
+
+You said other languages, you
+can't have this constant time
+
+list search.
+
+So how would hashing work?
+
+PROFESSOR: So the question is
+that, because Python gives us
+
+constant-time looking up for
+lists is the key to making
+
+this work --
+
+every programming language
+I know has some
+
+concept that's similar.
+
+In, say, C, it's not a list,
+but it's an array.
+
+And so in C, you would use
+array for this purpose?
+
+In Java, you would use the
+arrays for this purpose?
+
+But yes, you can do this in
+any programming language,
+
+because every reasonable
+programming language has some
+
+way to create the equivalent
+of a list, in which you can
+
+get a particular index
+in constant time.
+
+So it's a universally
+useful technique.
+
+Good question.
+
+Anything else?
+
+If not, we're about to abandon
+searching and sorting, and in
+
+fact, abandon algorithms
+in general for a while.
+
+Bounced right off his hands.
+
+I will not sign you to
+a baseball contract.
+
+Pardon?
+
+Yes, I threw him
+a Butterfinger?
+
+Oh, it's terrible.
+
+Boy, your jokes are
+worse than mine.
+
+I now want to move
+on to the last--
+
+go back to Python, away from
+algorithms, away from computer
+
+science in general, and talk
+about the last three major
+
+linguistic concepts in Python,
+exceptions, classes, and then
+
+later iterators.
+
+Let's start with exceptions,
+because we've already seen
+
+them, and they're
+pretty simple.
+
+Exceptions are everywhere
+in Python.
+
+And we've certainly seen
+plenty of them
+
+all semester already.
+
+We get them if we set some
+list to, say [1,2]
+
+and then I asked for a test of
+12, I get an index error.
+
+This is an exception.
+
+We've got exceptions when we've
+tried to convert things
+
+to incorrect types.
+
+So if I go into test, I'll
+get a type error.
+
+Anything that ends in the word
+"error" is a built-in kind of
+
+exception in Python.
+
+We've got them when we
+accessed, nonexistent
+
+variables, a name error.
+
+So there are a whole bunch
+of these things.
+
+In each of these cases--
+
+here, I'm just kind of playing
+around in Python.
+
+And it printed an error message,
+and it stopped.
+
+These kind of exceptions are
+called unhandled exceptions,
+
+where they cause the program
+to effectively crash.
+
+The program just
+stops running.
+
+And I suspect that some of you
+have written programs in which
+
+this has happened.
+
+In fact, is there anybody here
+who has not written a program
+
+that crashed because of an
+unhandled exception?
+
+Good.
+
+For those of you watching
+on TV, no hands went up.
+
+Almost every day, I write a
+program that crashes because
+
+of an unhandled exception.
+
+On the other hand, once my
+program is debugged--
+
+once your program is
+debugged-- this
+
+should never happen.
+
+Because there are mechanisms
+in Python for handling
+
+exceptions.
+
+And in fact, as we'll see, it's
+a perfectly valid flow of
+
+control concept.
+
+You will sometimes write
+programs that are intended to
+
+raise exceptions.
+
+And then you'll catch the
+exception and do something
+
+useful with it.
+
+The way we use exceptions
+is in something called a
+
+try-except block.
+
+So you write the word "try," and
+then you have some code,
+
+and then "except," and
+then some more code.
+
+What the interpreter does is it
+starts executing this code.
+
+If it gets through this code
+without raising any kind of an
+
+exception, it jumps to the code
+
+following the except block.
+
+On the other hand, if an
+exception gets raised here, it
+
+immediately stops executing
+this code and jumps to the
+
+start of this code, the code
+associated with the except,
+
+and executes that.
+
+And, then when it finishes this,
+it again goes to the
+
+code following the except.
+
+Just like an if, you can
+nest these things.
+
+It's just a control concept.
+
+It's nothing more.
+
+Let's look at an example.
+
+So here's readVal.
+
+This is a function.
+
+It's a polymorphic function.
+
+Its first argument is
+of type 'type'.
+
+Remember--
+
+and you'll hear me say this a
+1,000 more times at least--
+
+in Python, everything is an
+object and can be manipulated
+
+by the program.
+
+It's one of the beauties
+of Python.
+
+It's something that's not true
+in many programming languages.
+
+So types are objects, just
+like ints or floats.
+
+So the first argument to
+readVal is a type.
+
+And then there are two strings,
+the request message
+
+and the error message.
+
+It then sets a local variable,
+numTries, to 0.
+
+And while numTries is less than
+4, it sets val equal to
+
+raw input, printing the
+request message.
+
+And then it tries to convert val
+to valType, whatever that
+
+happens to be.
+
+And if it succeeds,
+it returns it.
+
+On the other hand, if during
+this attempt to convert it an
+
+exception is raised--
+
+for example, the user is asked
+to input an integer, and they
+
+type in the letter b, which
+can't be converted to an int--
+
+then a type error exception
+will be raised, or a value
+
+error exception.
+
+And if a value error exception
+is raised, it prints the error
+
+message, increases numTries by
+1, and goes back to the top of
+
+the y loop.
+
+If it goes through this y loop
+too many times, it leaves,
+
+raising the type error with the
+message that the argument
+
+"numTries
+
+exceeded." All right.
+
+Let's run this and
+see what happens.
+
+Every once in a while,
+funny things happen.
+
+When that happens, somehow,
+clicking in this window, and
+
+then clicking back in
+that window tends to
+
+make it work again.
+
+This is a bug in Python.
+
+So it's now asked me
+to enter an int.
+
+If I enter an int, everything
+is good.
+
+It just prints it.
+
+On the other hand, if I run it,
+and I enter the letter A,
+
+it will give me another
+chance.
+
+And now I can enter an
+int, and it's happy.
+
+All right.
+
+Now, suppose I am unhappy with
+the fact that if four times in
+
+a row I've failed to enter an
+int, something bad happens.
+
+It comes back, and it
+raises an exception.
+
+Well, I can catch that in the
+code that calls readVal.
+
+So here at the top level, I'm
+going to try readVal.
+
+And then I'm going to say,
+except if a type error is
+
+raised, print the argument
+returned by that exception.
+
+So this is what's called the
+handler for the exception.
+
+And so I don't have to crash
+when the exception is raised.
+
+But I can actually deal with it
+and do something sensible.
+
+If following the word "except,"
+as you see over
+
+there, I have not listed any
+exception names, then I'll go
+
+to the except clause
+for all exceptions.
+
+Doesn't matter what
+the exception is.
+
+I will go there.
+
+So I can write code that
+captures any exception.
+
+OK.
+
+Usually, that's not as good a
+thing, because it shows that I
+
+did not anticipate what the
+exception might be.
+
+But you can see that
+this is a pretty
+
+powerful programming paradigm.
+
+I can write this fairly compact
+readVal function
+
+that's pretty robust.
+
+It's polymorphic, it can take
+in what the error messages
+
+are, and it can try as
+many times as I want.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE] after
+type error [INAUDIBLE]?
+
+AUDIENCE: PROFESSOR: You'll note
+that when I raised the
+
+exception type error after it, I
+had an open [UNINTELLIGIBLE]
+
+a string.
+
+So what this basically says is
+that an exception can have
+
+associated with it a
+set of arguments,
+
+a sequence of arguments.
+
+And I've just chosen to call the
+first of the arguments s,
+
+so that I could then print it.
+
+So this is a fairly common
+paradigm, that you associate a
+
+message with an exception,
+explaining the exception.
+
+Since after all, type error is
+not all that meaningful.
+
+And this tells me why it
+was raised, that I
+
+tried too many times.
+
+OK, does it make sense?
+
+Anything else?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+before you said [INAUDIBLE]?
+
+PROFESSOR: Well, what we'll see
+when I execute something
+
+like assert false, it's actually
+raising an exception.
+
+It's raising an assertion
+error exception.
+
+And so I can actually catch that
+and do something with it.
+
+I've been using these
+asserts just
+
+basically to stop the program.
+
+But we've also seen that
+sometimes in functions, we use
+
+assertions to check the types
+of the arguments.
+
+But if you don't catch that
+exception, then the program
+
+crashes with the wrong
+arguments, without doing
+
+anything useful.
+
+Because that's just an
+exception, I can catch it, and
+
+then do something useful.
+
+So it's, again, just
+an example of that.
+
+We're going to try your
+hands once more.
+
+I'll throw you a different
+kind of candy.
+
+And this time he caught it.
+
+Two for two.
+
+Very powerful.
+
+A very useful mechanism.
+
+You can use them for sort
+of catching errors,
+
+as we've done here.
+
+They are frequently used in
+situations where you are
+
+getting input from a user.
+
+So for example, if you were
+writing a text editor, and you
+
+wanted to open up a file, and
+you typed in the file name,
+
+and it didn't exist, you would
+in Python get an error message
+
+when you try to open
+that file.
+
+It would raise an exception,
+"File Not Found," basically,
+
+which you could then catch, and
+then print to the user a
+
+useful error message saying,
+"File Not Found."
+
+Similarly, if you try and write
+to a file that already
+
+exists, you can get an exception
+saying, do you
+
+really want to overwrite
+this file?
+
+And ask the user.
+
+So it's very commonly
+used in a lot of
+
+programs as a mechanism.
+
+And now, as we go on and see
+more and more code, you'll see
+
+that I'm going to start using
+exceptions fairly frequently
+
+as a flow of control
+mechanism.
+
+It makes certain kinds of
+code easier to write.
+
+All right.
+
+That's all I have to say
+about exceptions.
+
+Simple but useful mechanism.
+
+Now, on to something
+that's even more
+
+useful, but not so simple.
+
+It is probably the
+distinguishing thing, not only
+
+in Python, but in
+a whole class of
+
+modern programming languages.
+
+And that's the notion
+of a class.
+
+I'm not going to finish
+it today.
+
+I'm barely going to scratch
+the surface of it today.
+
+But we're going to start leading
+up and I will pretty
+
+much finish it on Thursday.
+
+We've already seen the notion of
+a module, which has been a
+
+collection of related
+functions.
+
+So, for example, we've seen code
+that includes something
+
+like import math.
+
+And that provided me
+with access to
+
+functions like math.log.
+
+What the module mechanism does
+in the import mechanism, it
+
+makes it convenient
+to import a lot of
+
+related things at once.
+
+And then we use this dot
+notation to disambiguate, to
+
+tell us, well, which log.
+
+Typically, there's probably
+only one log function.
+
+But certainly, you might imagine
+that set.member and
+
+table.member would
+be different, and
+
+that both might exist.
+
+And as we've said before, the
+dot notation avoids conflicts
+
+by disambiguating.
+
+OK.
+
+That's a module.
+
+What a class is, it is like a
+module, but it's not just a
+
+collection of functions.
+
+A class is a collection of data
+and functions, functions
+
+that operate on that data.
+
+They are bound together, so that
+you can pass an object
+
+from one part of a program
+to another.
+
+And the part of the program
+to which you pass it
+
+automatically gets access to the
+functions associated with
+
+that type of object.
+
+And this is really the key
+to what people call
+
+object-oriented programming,
+a very popular buzzword.
+
+So we've already seen that kind
+of thing, where if we
+
+pass a list from one function
+to another, we can write
+
+something like L.append,
+some value.
+
+The data and functions
+associated with an object are
+
+called that object's
+attributes.
+
+So you can think of this as a
+way to associate attributes
+
+with objects.
+
+Now, I've been talking about
+data and functions as if
+
+they're different
+kinds of things.
+
+In fact, they're not really,
+because they're just objects.
+
+In Python, everything is an
+object, including, as we'll
+
+see on Thursday, the class
+itself is an object.
+
+When people talk about objects
+and object-oriented
+
+programming, they often use a
+message passing metaphor.
+
+And I want to emphasize it's
+nothing more than a metaphor.
+
+And I almost hesitate to bring
+it up, because it makes it all
+
+sound more complicated
+than it is.
+
+But you will see this phrase
+in the literature.
+
+People will use it.
+
+So you need to know
+what it is.
+
+The basic metaphor is that when
+I write something like
+
+L.append, I am passing the
+message append e to the object
+
+L. And then there's a mechanism
+for looking up what
+
+that object means, what
+that message means.
+
+And then the object, L, executes
+that message, and
+
+does something.
+
+So, for example, if I had a
+class called Circle, I might
+
+pass the object C --
+
+the message area, which would
+cause this object to return
+
+the area of its own area, the
+area of the circle that is
+
+that object.
+
+Again, nothing dramatic
+going on here.
+
+If you just think of this as
+a fancy way of writing
+
+functions, you'll be
+absolutely correct.
+
+But I did think you should
+hear about this metaphor.
+
+I add by the way --
+should have--
+
+I've been using the word...
+
+Method is a function associated
+with an object.
+
+So in this case, the method area
+is associated with the
+
+object C. And purists would say,
+always refer to append as
+
+a method, rather than a
+function, because we use the
+
+dot notation to get to it, and
+it's always associated with
+
+some object of type list.
+
+Now, just as data can have
+types, objects, as we know,
+
+have types.
+
+What a class is is it's a
+collection of objects with
+
+identical characteristics
+that form a type.
+
+So we can use classes to
+introduce new types into the
+
+programming environment.
+
+So as you think about
+existing things--
+
+now, I won't put that up,
+because it will disappear
+
+behind the screen.
+
+We've looked at things
+like lists and dict.
+
+What these are are
+built-in classes.
+
+They happen to be classes that
+are so useful that somebody
+
+decided they should be part of
+the language, they should have
+
+efficient implementations,
+they should be built-in,
+
+people shouldn't have to
+reimplement them themselves.
+
+And in fact, there are a whole
+bunch of interesting built-in
+
+classes in Python.
+
+And there are a whole bunch of
+libraries of classes you can
+
+bring in-- and we'll look
+at many of those--
+
+that extend it.
+
+And that's the beauty of
+the class mechanism.
+
+It lets you add new types to
+the language that are every
+
+bit as easy to use as
+the built-in types.
+
+So in effect, the language can
+be extended to add new and
+
+useful types.
+
+And we'll look at several
+examples of
+
+that starting on Thursday.
\ No newline at end of file
diff --git a/pyJJ3oRlorM.txt b/pyJJ3oRlorM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5add1c13e169f0ea9a3bbc7497dfe9f25f1b9961
--- /dev/null
+++ b/pyJJ3oRlorM.txt
@@ -0,0 +1,11547 @@
+align:start position:0%
+ 
+today we are going to be discussing
+
+ align:start position:0%
+today we are going to be discussing
+ 
+
+ align:start position:0%
+today we are going to be discussing
+neutral particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Diagnostics
+
+ align:start position:0%
+Diagnostics
+ 
+
+ align:start position:0%
+Diagnostics
+so the fact of the matter is we have
+
+ align:start position:0%
+so the fact of the matter is we have
+ 
+
+ align:start position:0%
+so the fact of the matter is we have
+some plasma like a
+
+ align:start position:0%
+some plasma like a
+ 
+
+ align:start position:0%
+some plasma like a
+and it has some flux surfaces and we
+
+ align:start position:0%
+and it has some flux surfaces and we
+ 
+
+ align:start position:0%
+and it has some flux surfaces and we
+want to know what's going on inside the
+
+ align:start position:0%
+want to know what's going on inside the
+ 
+
+ align:start position:0%
+want to know what's going on inside the
+core because this is where the fusion is
+
+ align:start position:0%
+core because this is where the fusion is
+ 
+
+ align:start position:0%
+core because this is where the fusion is
+happening in particular we want to know
+
+ align:start position:0%
+happening in particular we want to know
+ 
+
+ align:start position:0%
+happening in particular we want to know
+what the distribution function of the
+
+ align:start position:0%
+what the distribution function of the
+ 
+
+ align:start position:0%
+what the distribution function of the
+ions is it's probably maxwellian is but
+
+ align:start position:0%
+ions is it's probably maxwellian is but
+ 
+
+ align:start position:0%
+ions is it's probably maxwellian is but
+the ish is the interesting bit there may
+
+ align:start position:0%
+the ish is the interesting bit there may
+ 
+
+ align:start position:0%
+the ish is the interesting bit there may
+be some lovely Tales of particles here
+
+ align:start position:0%
+be some lovely Tales of particles here
+ 
+
+ align:start position:0%
+be some lovely Tales of particles here
+and those are the ones that might be
+
+ align:start position:0%
+and those are the ones that might be
+ 
+
+ align:start position:0%
+and those are the ones that might be
+doing most of our Fusion reactions so
+
+ align:start position:0%
+doing most of our Fusion reactions so
+ 
+
+ align:start position:0%
+doing most of our Fusion reactions so
+we'd like to be able to measure this
+
+ align:start position:0%
+we'd like to be able to measure this
+ 
+
+ align:start position:0%
+we'd like to be able to measure this
+distribution function f ofi the trouble
+
+ align:start position:0%
+distribution function f ofi the trouble
+ 
+
+ align:start position:0%
+distribution function f ofi the trouble
+is the particles the core are hopefully
+
+ align:start position:0%
+is the particles the core are hopefully
+ 
+
+ align:start position:0%
+is the particles the core are hopefully
+very well
+
+ align:start position:0%
+very well
+ 
+
+ align:start position:0%
+very well
+confined if they're not confined we
+
+ align:start position:0%
+confined if they're not confined we
+ 
+
+ align:start position:0%
+confined if they're not confined we
+haven't done a very good job so we can't
+
+ align:start position:0%
+haven't done a very good job so we can't
+ 
+
+ align:start position:0%
+haven't done a very good job so we can't
+exactly wait for them to wander out and
+
+ align:start position:0%
+exactly wait for them to wander out and
+ 
+
+ align:start position:0%
+exactly wait for them to wander out and
+see what they're up to uh and so we need
+
+ align:start position:0%
+see what they're up to uh and so we need
+ 
+
+ align:start position:0%
+see what they're up to uh and so we need
+some technique of measuring uh this core
+
+ align:start position:0%
+some technique of measuring uh this core
+ 
+
+ align:start position:0%
+some technique of measuring uh this core
+distribution function f of IV now we
+
+ align:start position:0%
+distribution function f of IV now we
+ 
+
+ align:start position:0%
+distribution function f of IV now we
+have some ideas based on some of the
+
+ align:start position:0%
+have some ideas based on some of the
+ 
+
+ align:start position:0%
+have some ideas based on some of the
+other Diagnostics we've looked at
+
+ align:start position:0%
+other Diagnostics we've looked at
+ 
+
+ align:start position:0%
+other Diagnostics we've looked at
+already for example we could use
+
+ align:start position:0%
+already for example we could use
+ 
+
+ align:start position:0%
+already for example we could use
+electron cyclotron emission that gave us
+
+ align:start position:0%
+electron cyclotron emission that gave us
+ 
+
+ align:start position:0%
+electron cyclotron emission that gave us
+information about what's going on in the
+
+ align:start position:0%
+information about what's going on in the
+ 
+
+ align:start position:0%
+information about what's going on in the
+core but this gives us a measurement of
+
+ align:start position:0%
+core but this gives us a measurement of
+ 
+
+ align:start position:0%
+core but this gives us a measurement of
+te and te does not necessarily have to
+
+ align:start position:0%
+te and te does not necessarily have to
+ 
+
+ align:start position:0%
+te and te does not necessarily have to
+be the same as ti so that's not a very
+
+ align:start position:0%
+be the same as ti so that's not a very
+ 
+
+ align:start position:0%
+be the same as ti so that's not a very
+good diagnostic we could do something
+
+ align:start position:0%
+good diagnostic we could do something
+ 
+
+ align:start position:0%
+good diagnostic we could do something
+using uh laser induced fluoresence or
+
+ align:start position:0%
+using uh laser induced fluoresence or
+ 
+
+ align:start position:0%
+using uh laser induced fluoresence or
+two Photon absorption laser induced
+
+ align:start position:0%
+two Photon absorption laser induced
+ 
+
+ align:start position:0%
+two Photon absorption laser induced
+fluoresence like this if you remember
+
+ align:start position:0%
+fluoresence like this if you remember
+ 
+
+ align:start position:0%
+fluoresence like this if you remember
+that's where we had an upper level and a
+
+ align:start position:0%
+that's where we had an upper level and a
+ 
+
+ align:start position:0%
+that's where we had an upper level and a
+lower level and we scanned our laser
+
+ align:start position:0%
+lower level and we scanned our laser
+ 
+
+ align:start position:0%
+lower level and we scanned our laser
+wavelength in frequency space here so
+
+ align:start position:0%
+wavelength in frequency space here so
+ 
+
+ align:start position:0%
+wavelength in frequency space here so
+that we could address particles which
+
+ align:start position:0%
+that we could address particles which
+ 
+
+ align:start position:0%
+that we could address particles which
+were doter shifted towards us and do
+
+ align:start position:0%
+were doter shifted towards us and do
+ 
+
+ align:start position:0%
+were doter shifted towards us and do
+shifted away from us and by looking at
+
+ align:start position:0%
+shifted away from us and by looking at
+ 
+
+ align:start position:0%
+shifted away from us and by looking at
+the intensity of light coming out we
+
+ align:start position:0%
+the intensity of light coming out we
+ 
+
+ align:start position:0%
+the intensity of light coming out we
+could measure this distribution function
+
+ align:start position:0%
+could measure this distribution function
+ 
+
+ align:start position:0%
+could measure this distribution function
+here so this looks like a pretty good
+
+ align:start position:0%
+here so this looks like a pretty good
+ 
+
+ align:start position:0%
+here so this looks like a pretty good
+technique for measuring the core uh the
+
+ align:start position:0%
+technique for measuring the core uh the
+ 
+
+ align:start position:0%
+technique for measuring the core uh the
+trouble is that in the core all of our
+
+ align:start position:0%
+trouble is that in the core all of our
+ 
+
+ align:start position:0%
+trouble is that in the core all of our
+particles are fully ionized and so there
+
+ align:start position:0%
+particles are fully ionized and so there
+ 
+
+ align:start position:0%
+particles are fully ionized and so there
+are no electrons here so we can't use
+
+ align:start position:0%
+are no electrons here so we can't use
+ 
+
+ align:start position:0%
+are no electrons here so we can't use
+these techniques because there are no
+
+ align:start position:0%
+these techniques because there are no
+ 
+
+ align:start position:0%
+these techniques because there are no
+ions with an electron in them in order
+
+ align:start position:0%
+ions with an electron in them in order
+ 
+
+ align:start position:0%
+ions with an electron in them in order
+for us to be able to address it using
+
+ align:start position:0%
+for us to be able to address it using
+ 
+
+ align:start position:0%
+for us to be able to address it using
+our laser and thirdly we could also use
+
+ align:start position:0%
+our laser and thirdly we could also use
+ 
+
+ align:start position:0%
+our laser and thirdly we could also use
+Thompson scattering which we haven't
+
+ align:start position:0%
+Thompson scattering which we haven't
+ 
+
+ align:start position:0%
+Thompson scattering which we haven't
+about yet but we will do in detail soon
+
+ align:start position:0%
+about yet but we will do in detail soon
+ 
+
+ align:start position:0%
+about yet but we will do in detail soon
+the trouble with Thompson scattering is
+
+ align:start position:0%
+the trouble with Thompson scattering is
+ 
+
+ align:start position:0%
+the trouble with Thompson scattering is
+that it tends to give us information
+
+ align:start position:0%
+that it tends to give us information
+ 
+
+ align:start position:0%
+that it tends to give us information
+scattering about the electron
+
+ align:start position:0%
+scattering about the electron
+ 
+
+ align:start position:0%
+scattering about the electron
+distribution function f of or Fe V like
+
+ align:start position:0%
+distribution function f of or Fe V like
+ 
+
+ align:start position:0%
+distribution function f of or Fe V like
+that and again that doesn't have to
+
+ align:start position:0%
+that and again that doesn't have to
+ 
+
+ align:start position:0%
+that and again that doesn't have to
+necessarily be the same as the ion
+
+ align:start position:0%
+necessarily be the same as the ion
+ 
+
+ align:start position:0%
+necessarily be the same as the ion
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+function so we're going to need a new
+
+ align:start position:0%
+function so we're going to need a new
+ 
+
+ align:start position:0%
+function so we're going to need a new
+technique in order to measure the
+
+ align:start position:0%
+technique in order to measure the
+ 
+
+ align:start position:0%
+technique in order to measure the
+distribution of these core particles so
+
+ align:start position:0%
+distribution of these core particles so
+ 
+
+ align:start position:0%
+distribution of these core particles so
+the idea
+
+ align:start position:0%
+the idea
+ 
+
+ align:start position:0%
+the idea
+is well what if spontaneously some of
+
+ align:start position:0%
+is well what if spontaneously some of
+ 
+
+ align:start position:0%
+is well what if spontaneously some of
+these core ions turned into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neutrals
+
+ align:start position:0%
+neutrals
+ 
+
+ align:start position:0%
+neutrals
+well if some of these core ions turned
+
+ align:start position:0%
+well if some of these core ions turned
+ 
+
+ align:start position:0%
+well if some of these core ions turned
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+neutrals then they would no longer be
+
+ align:start position:0%
+neutrals then they would no longer be
+ 
+
+ align:start position:0%
+neutrals then they would no longer be
+confined they would be able to wander
+
+ align:start position:0%
+confined they would be able to wander
+ 
+
+ align:start position:0%
+confined they would be able to wander
+freely
+
+ align:start position:0%
+freely
+ 
+
+ align:start position:0%
+freely
+out and perhaps we could stick a
+
+ align:start position:0%
+out and perhaps we could stick a
+ 
+
+ align:start position:0%
+out and perhaps we could stick a
+detector on the outside of the plasma
+
+ align:start position:0%
+detector on the outside of the plasma
+ 
+
+ align:start position:0%
+detector on the outside of the plasma
+and measure these neutrals which will
+
+ align:start position:0%
+and measure these neutrals which will
+ 
+
+ align:start position:0%
+and measure these neutrals which will
+carry with them some information about
+
+ align:start position:0%
+carry with them some information about
+ 
+
+ align:start position:0%
+carry with them some information about
+the ion distribution they came from and
+
+ align:start position:0%
+the ion distribution they came from and
+ 
+
+ align:start position:0%
+the ion distribution they came from and
+that will allow us to indirectly measure
+
+ align:start position:0%
+that will allow us to indirectly measure
+ 
+
+ align:start position:0%
+that will allow us to indirectly measure
+the ion
+
+ align:start position:0%
+the ion
+ 
+
+ align:start position:0%
+the ion
+distribution so uh what's a good way to
+
+ align:start position:0%
+distribution so uh what's a good way to
+ 
+
+ align:start position:0%
+distribution so uh what's a good way to
+summarize they're gonna these neutrals
+
+ align:start position:0%
+summarize they're gonna these neutrals
+ 
+
+ align:start position:0%
+summarize they're gonna these neutrals
+would give us information
+
+ align:start position:0%
+would give us information
+ 
+
+ align:start position:0%
+would give us information
+on the distribution function so there's
+
+ align:start position:0%
+on the distribution function so there's
+ 
+
+ align:start position:0%
+on the distribution function so there's
+two problems that's come to your mind
+
+ align:start position:0%
+two problems that's come to your mind
+ 
+
+ align:start position:0%
+two problems that's come to your mind
+straight away why exactly was an ion
+
+ align:start position:0%
+straight away why exactly was an ion
+ 
+
+ align:start position:0%
+straight away why exactly was an ion
+suddenly turn itself into a neutral in
+
+ align:start position:0%
+suddenly turn itself into a neutral in
+ 
+
+ align:start position:0%
+suddenly turn itself into a neutral in
+the core and does it stand a chance of
+
+ align:start position:0%
+the core and does it stand a chance of
+ 
+
+ align:start position:0%
+the core and does it stand a chance of
+actually escaping from the core to the
+
+ align:start position:0%
+actually escaping from the core to the
+ 
+
+ align:start position:0%
+actually escaping from the core to the
+outside where we can detect it uh and so
+
+ align:start position:0%
+outside where we can detect it uh and so
+ 
+
+ align:start position:0%
+outside where we can detect it uh and so
+we'll talk about those two issues one
+
+ align:start position:0%
+we'll talk about those two issues one
+ 
+
+ align:start position:0%
+we'll talk about those two issues one
+after the other so first of all is the
+
+ align:start position:0%
+after the other so first of all is the
+ 
+
+ align:start position:0%
+after the other so first of all is the
+uh NE neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+production and I guess we could call the
+
+ align:start position:0%
+production and I guess we could call the
+ 
+
+ align:start position:0%
+production and I guess we could call the
+second problem neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transport so in terms of neutral
+
+ align:start position:0%
+transport so in terms of neutral
+ 
+
+ align:start position:0%
+transport so in terms of neutral
+production there are two major processes
+
+ align:start position:0%
+production there are two major processes
+ 
+
+ align:start position:0%
+production there are two major processes
+that we could have we could have a
+
+ align:start position:0%
+that we could have we could have a
+ 
+
+ align:start position:0%
+that we could have we could have a
+charge exchange so I'm just going to
+
+ align:start position:0%
+charge exchange so I'm just going to
+ 
+
+ align:start position:0%
+charge exchange so I'm just going to
+write that as CX uh we talked about
+
+ align:start position:0%
+write that as CX uh we talked about
+ 
+
+ align:start position:0%
+write that as CX uh we talked about
+charge exchange before this is where a
+
+ align:start position:0%
+charge exchange before this is where a
+ 
+
+ align:start position:0%
+charge exchange before this is where a
+neutral collides with an ion and the
+
+ align:start position:0%
+neutral collides with an ion and the
+ 
+
+ align:start position:0%
+neutral collides with an ion and the
+neutral loses an electron and the ion
+
+ align:start position:0%
+neutral loses an electron and the ion
+ 
+
+ align:start position:0%
+neutral loses an electron and the ion
+gains an electron so we could have
+
+ align:start position:0%
+gains an electron so we could have
+ 
+
+ align:start position:0%
+gains an electron so we could have
+charge exchange with Edge
+
+ align:start position:0%
+charge exchange with Edge
+ 
+
+ align:start position:0%
+charge exchange with Edge
+neutrals so they could be neutrals
+
+ align:start position:0%
+neutrals so they could be neutrals
+ 
+
+ align:start position:0%
+neutrals so they could be neutrals
+coming in from the edge of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma and that would look like some
+
+ align:start position:0%
+plasma and that would look like some
+ 
+
+ align:start position:0%
+plasma and that would look like some
+neutrals coming in like this and I'll
+
+ align:start position:0%
+neutrals coming in like this and I'll
+ 
+
+ align:start position:0%
+neutrals coming in like this and I'll
+use N Sub a to be like some density of
+
+ align:start position:0%
+use N Sub a to be like some density of
+ 
+
+ align:start position:0%
+use N Sub a to be like some density of
+neutral atoms these are going to be
+
+ align:start position:0%
+neutral atoms these are going to be
+ 
+
+ align:start position:0%
+neutral atoms these are going to be
+wandering in from the edge all the time
+
+ align:start position:0%
+wandering in from the edge all the time
+ 
+
+ align:start position:0%
+wandering in from the edge all the time
+maybe a few of them make it to the
+
+ align:start position:0%
+maybe a few of them make it to the
+ 
+
+ align:start position:0%
+maybe a few of them make it to the
+center and then they charge exchange of
+
+ align:start position:0%
+center and then they charge exchange of
+ 
+
+ align:start position:0%
+center and then they charge exchange of
+our core and then those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core then the ions make it back out
+
+ align:start position:0%
+core then the ions make it back out
+ 
+
+ align:start position:0%
+core then the ions make it back out
+again and we can detect it that's one
+
+ align:start position:0%
+again and we can detect it that's one
+ 
+
+ align:start position:0%
+again and we can detect it that's one
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+mechanism uh a more active mechanism
+
+ align:start position:0%
+mechanism uh a more active mechanism
+ 
+
+ align:start position:0%
+mechanism uh a more active mechanism
+will be taking a neutral beam and
+
+ align:start position:0%
+will be taking a neutral beam and
+ 
+
+ align:start position:0%
+will be taking a neutral beam and
+putting a neutral beam into the center
+
+ align:start position:0%
+putting a neutral beam into the center
+ 
+
+ align:start position:0%
+putting a neutral beam into the center
+of the core here this is neutral beam
+
+ align:start position:0%
+of the core here this is neutral beam
+ 
+
+ align:start position:0%
+of the core here this is neutral beam
+injection we use neutral beam injection
+
+ align:start position:0%
+injection we use neutral beam injection
+ 
+
+ align:start position:0%
+injection we use neutral beam injection
+for all sorts of things like current
+
+ align:start position:0%
+for all sorts of things like current
+ 
+
+ align:start position:0%
+for all sorts of things like current
+drive and heating of the plasma and so
+
+ align:start position:0%
+drive and heating of the plasma and so
+ 
+
+ align:start position:0%
+drive and heating of the plasma and so
+we often have this process happening
+
+ align:start position:0%
+we often have this process happening
+ 
+
+ align:start position:0%
+we often have this process happening
+automatically the whole point of the
+
+ align:start position:0%
+automatically the whole point of the
+ 
+
+ align:start position:0%
+automatically the whole point of the
+neutral beam here is that as these
+
+ align:start position:0%
+neutral beam here is that as these
+ 
+
+ align:start position:0%
+neutral beam here is that as these
+neutral particles come into the center
+
+ align:start position:0%
+neutral particles come into the center
+ 
+
+ align:start position:0%
+neutral particles come into the center
+they'll charge exchange with the ions
+
+ align:start position:0%
+they'll charge exchange with the ions
+ 
+
+ align:start position:0%
+they'll charge exchange with the ions
+and become ions but that means that the
+
+ align:start position:0%
+and become ions but that means that the
+ 
+
+ align:start position:0%
+and become ions but that means that the
+ions they've charge exchange will become
+
+ align:start position:0%
+ions they've charge exchange will become
+ 
+
+ align:start position:0%
+ions they've charge exchange will become
+neutrals and so those neutrals May uh
+
+ align:start position:0%
+neutrals and so those neutrals May uh
+ 
+
+ align:start position:0%
+neutrals and so those neutrals May uh
+come out the the plasma here where we
+
+ align:start position:0%
+come out the the plasma here where we
+ 
+
+ align:start position:0%
+come out the the plasma here where we
+can detect them so we have charge
+
+ align:start position:0%
+can detect them so we have charge
+ 
+
+ align:start position:0%
+can detect them so we have charge
+exchange with Edge neutrals and charge
+
+ align:start position:0%
+exchange with Edge neutrals and charge
+ 
+
+ align:start position:0%
+exchange with Edge neutrals and charge
+exchange with neutral beam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+injection neutral transport is asking
+
+ align:start position:0%
+injection neutral transport is asking
+ 
+
+ align:start position:0%
+injection neutral transport is asking
+can the neutral make it from the center
+
+ align:start position:0%
+can the neutral make it from the center
+ 
+
+ align:start position:0%
+can the neutral make it from the center
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core here can that neutral make it
+
+ align:start position:0%
+core here can that neutral make it
+ 
+
+ align:start position:0%
+core here can that neutral make it
+out along some path and so there's going
+
+ align:start position:0%
+out along some path and so there's going
+ 
+
+ align:start position:0%
+out along some path and so there's going
+to be a series of processes which are
+
+ align:start position:0%
+to be a series of processes which are
+ 
+
+ align:start position:0%
+to be a series of processes which are
+trying to to reionize this neutral as it
+
+ align:start position:0%
+trying to to reionize this neutral as it
+ 
+
+ align:start position:0%
+trying to to reionize this neutral as it
+tries to leave the plasma so these
+
+ align:start position:0%
+tries to leave the plasma so these
+ 
+
+ align:start position:0%
+tries to leave the plasma so these
+processes are going to be things like
+
+ align:start position:0%
+processes are going to be things like
+ 
+
+ align:start position:0%
+processes are going to be things like
+I'm going to give them their
+
+ align:start position:0%
+I'm going to give them their
+ 
+
+ align:start position:0%
+I'm going to give them their
+cross-sections Sigma sub this is
+
+ align:start position:0%
+cross-sections Sigma sub this is
+ 
+
+ align:start position:0%
+cross-sections Sigma sub this is
+electron impact ionization which we
+
+ align:start position:0%
+electron impact ionization which we
+ 
+
+ align:start position:0%
+electron impact ionization which we
+talked about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before this is going to be we're going
+
+ align:start position:0%
+before this is going to be we're going
+ 
+
+ align:start position:0%
+before this is going to be we're going
+to use Sigma subscript P this is Ion
+
+ align:start position:0%
+to use Sigma subscript P this is Ion
+ 
+
+ align:start position:0%
+to use Sigma subscript P this is Ion
+impact ionization because we can also
+
+ align:start position:0%
+impact ionization because we can also
+ 
+
+ align:start position:0%
+impact ionization because we can also
+have collisions of ions causing
+
+ align:start position:0%
+have collisions of ions causing
+ 
+
+ align:start position:0%
+have collisions of ions causing
+ionization here and finally we can have
+
+ align:start position:0%
+ionization here and finally we can have
+ 
+
+ align:start position:0%
+ionization here and finally we can have
+the probability of charge exchange with
+
+ align:start position:0%
+the probability of charge exchange with
+ 
+
+ align:start position:0%
+the probability of charge exchange with
+ions so if we've charge exchanged once
+
+ align:start position:0%
+ions so if we've charge exchanged once
+ 
+
+ align:start position:0%
+ions so if we've charge exchanged once
+in order to get our Neutron in the first
+
+ align:start position:0%
+in order to get our Neutron in the first
+ 
+
+ align:start position:0%
+in order to get our Neutron in the first
+place it's not at all impossible for us
+
+ align:start position:0%
+place it's not at all impossible for us
+ 
+
+ align:start position:0%
+place it's not at all impossible for us
+to charge exchange again as we head out
+
+ align:start position:0%
+to charge exchange again as we head out
+ 
+
+ align:start position:0%
+to charge exchange again as we head out
+and then our core neutral that was
+
+ align:start position:0%
+and then our core neutral that was
+ 
+
+ align:start position:0%
+and then our core neutral that was
+heading out and giving us information
+
+ align:start position:0%
+heading out and giving us information
+ 
+
+ align:start position:0%
+heading out and giving us information
+about the core will become an ion it be
+
+ align:start position:0%
+about the core will become an ion it be
+ 
+
+ align:start position:0%
+about the core will become an ion it be
+trapped again and now we'll have a ion
+
+ align:start position:0%
+trapped again and now we'll have a ion
+ 
+
+ align:start position:0%
+trapped again and now we'll have a ion
+from further out become a neutral and
+
+ align:start position:0%
+from further out become a neutral and
+ 
+
+ align:start position:0%
+from further out become a neutral and
+that will try and Le so this charge EXT
+
+ align:start position:0%
+that will try and Le so this charge EXT
+ 
+
+ align:start position:0%
+that will try and Le so this charge EXT
+change process is particularly
+
+ align:start position:0%
+change process is particularly
+ 
+
+ align:start position:0%
+change process is particularly
+problematic because what we're ending up
+
+ align:start position:0%
+problematic because what we're ending up
+ 
+
+ align:start position:0%
+problematic because what we're ending up
+with is something that looks like a
+
+ align:start position:0%
+with is something that looks like a
+ 
+
+ align:start position:0%
+with is something that looks like a
+hydrogen neutral plus a hydrogen ion
+
+ align:start position:0%
+hydrogen neutral plus a hydrogen ion
+ 
+
+ align:start position:0%
+hydrogen neutral plus a hydrogen ion
+going to a hydrogen ion plus a hydrogen
+
+ align:start position:0%
+going to a hydrogen ion plus a hydrogen
+ 
+
+ align:start position:0%
+going to a hydrogen ion plus a hydrogen
+neutral now the beautiful symmetry in
+
+ align:start position:0%
+neutral now the beautiful symmetry in
+ 
+
+ align:start position:0%
+neutral now the beautiful symmetry in
+this equation here means that this is
+
+ align:start position:0%
+this equation here means that this is
+ 
+
+ align:start position:0%
+this equation here means that this is
+resonant and so it's quite likely to
+
+ align:start position:0%
+resonant and so it's quite likely to
+ 
+
+ align:start position:0%
+resonant and so it's quite likely to
+happen so this Sigma C is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large okay so that's an overview of what
+
+ align:start position:0%
+large okay so that's an overview of what
+ 
+
+ align:start position:0%
+large okay so that's an overview of what
+we're going to try and do I'm going to
+
+ align:start position:0%
+we're going to try and do I'm going to
+ 
+
+ align:start position:0%
+we're going to try and do I'm going to
+talk a little bit about the neutral
+
+ align:start position:0%
+talk a little bit about the neutral
+ 
+
+ align:start position:0%
+talk a little bit about the neutral
+transport estimate the size of these
+
+ align:start position:0%
+transport estimate the size of these
+ 
+
+ align:start position:0%
+transport estimate the size of these
+different coefficients and work out How
+
+ align:start position:0%
+different coefficients and work out How
+ 
+
+ align:start position:0%
+different coefficients and work out How
+likely it is we can actually get any
+
+ align:start position:0%
+likely it is we can actually get any
+ 
+
+ align:start position:0%
+likely it is we can actually get any
+neutrals from the core back out again
+
+ align:start position:0%
+neutrals from the core back out again
+ 
+
+ align:start position:0%
+neutrals from the core back out again
+and then we'll talk about the neutral
+
+ align:start position:0%
+and then we'll talk about the neutral
+ 
+
+ align:start position:0%
+and then we'll talk about the neutral
+Productions I'm going to go two and then
+
+ align:start position:0%
+Productions I'm going to go two and then
+ 
+
+ align:start position:0%
+Productions I'm going to go two and then
+one but that's an overview if you have
+
+ align:start position:0%
+one but that's an overview if you have
+ 
+
+ align:start position:0%
+one but that's an overview if you have
+any questions before we get going this
+
+ align:start position:0%
+any questions before we get going this
+ 
+
+ align:start position:0%
+any questions before we get going this
+is a good time to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you should take a closer look at
+
+ align:start position:0%
+yes you should take a closer look at
+ 
+
+ align:start position:0%
+yes you should take a closer look at
+Hutchinson's Book for a more formal
+
+ align:start position:0%
+Hutchinson's Book for a more formal
+ 
+
+ align:start position:0%
+Hutchinson's Book for a more formal
+definition um but Quantum mechanically
+
+ align:start position:0%
+definition um but Quantum mechanically
+ 
+
+ align:start position:0%
+definition um but Quantum mechanically
+this is nice and likely to happen
+
+ align:start position:0%
+this is nice and likely to happen
+ 
+
+ align:start position:0%
+this is nice and likely to happen
+because we're sort of starting or ending
+
+ align:start position:0%
+because we're sort of starting or ending
+ 
+
+ align:start position:0%
+because we're sort of starting or ending
+up with something very similar to what
+
+ align:start position:0%
+up with something very similar to what
+ 
+
+ align:start position:0%
+up with something very similar to what
+we've started and so this process is is
+
+ align:start position:0%
+we've started and so this process is is
+ 
+
+ align:start position:0%
+we've started and so this process is is
+likely to occur
+
+ align:start position:0%
+likely to occur
+ 
+
+ align:start position:0%
+likely to occur
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again we've got some blob of
+
+ align:start position:0%
+okay so again we've got some blob of
+ 
+
+ align:start position:0%
+okay so again we've got some blob of
+plasma here we've got some particle
+
+ align:start position:0%
+plasma here we've got some particle
+ 
+
+ align:start position:0%
+plasma here we've got some particle
+which is born at a point a and we want
+
+ align:start position:0%
+which is born at a point a and we want
+ 
+
+ align:start position:0%
+which is born at a point a and we want
+to know if we can get to a point B like
+
+ align:start position:0%
+to know if we can get to a point B like
+ 
+
+ align:start position:0%
+to know if we can get to a point B like
+this so this is the
+
+ align:start position:0%
+this so this is the
+ 
+
+ align:start position:0%
+this so this is the
+core and B is where we have our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detector if you look at this you say oh
+
+ align:start position:0%
+detector if you look at this you say oh
+ 
+
+ align:start position:0%
+detector if you look at this you say oh
+this looks an awful lot like our
+
+ align:start position:0%
+this looks an awful lot like our
+ 
+
+ align:start position:0%
+this looks an awful lot like our
+radiation transport problem and so we
+
+ align:start position:0%
+radiation transport problem and so we
+ 
+
+ align:start position:0%
+radiation transport problem and so we
+could say that there's a probability of
+
+ align:start position:0%
+could say that there's a probability of
+ 
+
+ align:start position:0%
+could say that there's a probability of
+the particle getting from A to B or this
+
+ align:start position:0%
+the particle getting from A to B or this
+ 
+
+ align:start position:0%
+the particle getting from A to B or this
+could be a power of particles as well if
+
+ align:start position:0%
+could be a power of particles as well if
+ 
+
+ align:start position:0%
+could be a power of particles as well if
+I multiply it by the particle energy per
+
+ align:start position:0%
+I multiply it by the particle energy per
+ 
+
+ align:start position:0%
+I multiply it by the particle energy per
+unit time and that's going to look like
+
+ align:start position:0%
+unit time and that's going to look like
+ 
+
+ align:start position:0%
+unit time and that's going to look like
+the exponential of the line integral
+
+ align:start position:0%
+the exponential of the line integral
+ 
+
+ align:start position:0%
+the exponential of the line integral
+from A to B of some opacity in this case
+
+ align:start position:0%
+from A to B of some opacity in this case
+ 
+
+ align:start position:0%
+from A to B of some opacity in this case
+sort of more to do with scattering than
+
+ align:start position:0%
+sort of more to do with scattering than
+ 
+
+ align:start position:0%
+sort of more to do with scattering than
+it is to do with
+
+ align:start position:0%
+it is to do with
+ 
+
+ align:start position:0%
+it is to do with
+absorption which varies along the path
+
+ align:start position:0%
+absorption which varies along the path
+ 
+
+ align:start position:0%
+absorption which varies along the path
+integrated along the path the L and as a
+
+ align:start position:0%
+integrated along the path the L and as a
+ 
+
+ align:start position:0%
+integrated along the path the L and as a
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+sign okay so again this looks like
+
+ align:start position:0%
+sign okay so again this looks like
+ 
+
+ align:start position:0%
+sign okay so again this looks like
+radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we talked about three different
+
+ align:start position:0%
+so we talked about three different
+ 
+
+ align:start position:0%
+so we talked about three different
+processes over there which might be
+
+ align:start position:0%
+processes over there which might be
+ 
+
+ align:start position:0%
+processes over there which might be
+important um and the importance of those
+
+ align:start position:0%
+important um and the importance of those
+ 
+
+ align:start position:0%
+important um and the importance of those
+different processes will depend a lot on
+
+ align:start position:0%
+different processes will depend a lot on
+ 
+
+ align:start position:0%
+different processes will depend a lot on
+the distribution functions that we have
+
+ align:start position:0%
+the distribution functions that we have
+ 
+
+ align:start position:0%
+the distribution functions that we have
+here so if this is V and this is f of V
+
+ align:start position:0%
+here so if this is V and this is f of V
+ 
+
+ align:start position:0%
+here so if this is V and this is f of V
+here we'll have an ion distribution
+
+ align:start position:0%
+here we'll have an ion distribution
+ 
+
+ align:start position:0%
+here we'll have an ion distribution
+function that's just the ions making up
+
+ align:start position:0%
+function that's just the ions making up
+ 
+
+ align:start position:0%
+function that's just the ions making up
+the plasma and that will be relatively
+
+ align:start position:0%
+the plasma and that will be relatively
+ 
+
+ align:start position:0%
+the plasma and that will be relatively
+uh small in velocity space here so this
+
+ align:start position:0%
+uh small in velocity space here so this
+ 
+
+ align:start position:0%
+uh small in velocity space here so this
+is f of I and we'll also have an
+
+ align:start position:0%
+is f of I and we'll also have an
+ 
+
+ align:start position:0%
+is f of I and we'll also have an
+electron distribution
+
+ align:start position:0%
+electron distribution
+ 
+
+ align:start position:0%
+electron distribution
+function which is much broader and
+
+ align:start position:0%
+function which is much broader and
+ 
+
+ align:start position:0%
+function which is much broader and
+that's because the electrons are less
+
+ align:start position:0%
+that's because the electrons are less
+ 
+
+ align:start position:0%
+that's because the electrons are less
+massive so for a similar temperature
+
+ align:start position:0%
+massive so for a similar temperature
+ 
+
+ align:start position:0%
+massive so for a similar temperature
+they have fire higher velocities and
+
+ align:start position:0%
+they have fire higher velocities and
+ 
+
+ align:start position:0%
+they have fire higher velocities and
+we'll also assume that our neutrals
+
+ align:start position:0%
+we'll also assume that our neutrals
+ 
+
+ align:start position:0%
+we'll also assume that our neutrals
+coming out here have some
+
+ align:start position:0%
+coming out here have some
+ 
+
+ align:start position:0%
+coming out here have some
+distribution that is relatively narrow
+
+ align:start position:0%
+distribution that is relatively narrow
+ 
+
+ align:start position:0%
+distribution that is relatively narrow
+and uh shifted like this so this is at a
+
+ align:start position:0%
+and uh shifted like this so this is at a
+ 
+
+ align:start position:0%
+and uh shifted like this so this is at a
+velocity e like this for the
+
+ align:start position:0%
+velocity e like this for the
+ 
+
+ align:start position:0%
+velocity e like this for the
+neutrals and so we're assuming here to
+
+ align:start position:0%
+neutrals and so we're assuming here to
+ 
+
+ align:start position:0%
+neutrals and so we're assuming here to
+make our calculations that the ion
+
+ align:start position:0%
+make our calculations that the ion
+ 
+
+ align:start position:0%
+make our calculations that the ion
+velocities are all much less than these
+
+ align:start position:0%
+velocities are all much less than these
+ 
+
+ align:start position:0%
+velocities are all much less than these
+core neutral velocities and this means
+
+ align:start position:0%
+core neutral velocities and this means
+ 
+
+ align:start position:0%
+core neutral velocities and this means
+that VI minus VA is
+
+ align:start position:0%
+that VI minus VA is
+ 
+
+ align:start position:0%
+that VI minus VA is
+about VA is useful when we're working
+
+ align:start position:0%
+about VA is useful when we're working
+ 
+
+ align:start position:0%
+about VA is useful when we're working
+out these cross-sections that have the
+
+ align:start position:0%
+out these cross-sections that have the
+ 
+
+ align:start position:0%
+out these cross-sections that have the
+difference between the two velocity
+
+ align:start position:0%
+difference between the two velocity
+ 
+
+ align:start position:0%
+difference between the two velocity
+populations and then we can write down
+
+ align:start position:0%
+populations and then we can write down
+ 
+
+ align:start position:0%
+populations and then we can write down
+that our attenuation coefficient Alpha
+
+ align:start position:0%
+that our attenuation coefficient Alpha
+ 
+
+ align:start position:0%
+that our attenuation coefficient Alpha
+here is going to look like one upon the
+
+ align:start position:0%
+here is going to look like one upon the
+ 
+
+ align:start position:0%
+here is going to look like one upon the
+a the electron impact uh cross-section
+
+ align:start position:0%
+a the electron impact uh cross-section
+ 
+
+ align:start position:0%
+a the electron impact uh cross-section
+Sigma e v evaluated
+
+ align:start position:0%
+Sigma e v evaluated
+ 
+
+ align:start position:0%
+Sigma e v evaluated
+VA
+
+ align:start position:0%
+VA
+ 
+
+ align:start position:0%
+VA
+NE
+
+ align:start position:0%
+NE
+ 
+
+ align:start position:0%
+NE
+plus the ion impact ionization Sigma P
+
+ align:start position:0%
+plus the ion impact ionization Sigma P
+ 
+
+ align:start position:0%
+plus the ion impact ionization Sigma P
+VI evaluated
+
+ align:start position:0%
+VI evaluated
+ 
+
+ align:start position:0%
+VI evaluated
+VA and that's times ni
+
+ align:start position:0%
+VA and that's times ni
+ 
+
+ align:start position:0%
+VA and that's times ni
+plus the charge exchange cross-section
+
+ align:start position:0%
+plus the charge exchange cross-section
+ 
+
+ align:start position:0%
+plus the charge exchange cross-section
+Sigma C VI evaluated at VA Times by N
+
+ align:start position:0%
+Sigma C VI evaluated at VA Times by N
+ 
+
+ align:start position:0%
+Sigma C VI evaluated at VA Times by N
+I like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that um and we'll also now assume that
+
+ align:start position:0%
+that um and we'll also now assume that
+ 
+
+ align:start position:0%
+that um and we'll also now assume that
+our beam velocity is much less than or
+
+ align:start position:0%
+our beam velocity is much less than or
+ 
+
+ align:start position:0%
+our beam velocity is much less than or
+the sorry the neutral atom velocity the
+
+ align:start position:0%
+the sorry the neutral atom velocity the
+ 
+
+ align:start position:0%
+the sorry the neutral atom velocity the
+neutrals trying to get out of the plasma
+
+ align:start position:0%
+neutrals trying to get out of the plasma
+ 
+
+ align:start position:0%
+neutrals trying to get out of the plasma
+is much less than the sort of average
+
+ align:start position:0%
+is much less than the sort of average
+ 
+
+ align:start position:0%
+is much less than the sort of average
+thermal velocity of the electrons so
+
+ align:start position:0%
+thermal velocity of the electrons so
+ 
+
+ align:start position:0%
+thermal velocity of the electrons so
+that we can have this nice ordering
+
+ align:start position:0%
+that we can have this nice ordering
+ 
+
+ align:start position:0%
+that we can have this nice ordering
+where VI is much less than VA much less
+
+ align:start position:0%
+where VI is much less than VA much less
+ 
+
+ align:start position:0%
+where VI is much less than VA much less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+VTE and that allows us to further
+
+ align:start position:0%
+VTE and that allows us to further
+ 
+
+ align:start position:0%
+VTE and that allows us to further
+simplify this um we'll simplify it in
+
+ align:start position:0%
+simplify this um we'll simplify it in
+ 
+
+ align:start position:0%
+simplify this um we'll simplify it in
+two ways the first one is that from the
+
+ align:start position:0%
+two ways the first one is that from the
+ 
+
+ align:start position:0%
+two ways the first one is that from the
+point of view of the
+
+ align:start position:0%
+point of view of the
+ 
+
+ align:start position:0%
+point of view of the
+electrons the ions sorry the neutrals
+
+ align:start position:0%
+electrons the ions sorry the neutrals
+ 
+
+ align:start position:0%
+electrons the ions sorry the neutrals
+are basically not moving so we can set
+
+ align:start position:0%
+are basically not moving so we can set
+ 
+
+ align:start position:0%
+are basically not moving so we can set
+this to zero uh and from the point of
+
+ align:start position:0%
+this to zero uh and from the point of
+ 
+
+ align:start position:0%
+this to zero uh and from the point of
+view of the neutrals uh this VI is
+
+ align:start position:0%
+view of the neutrals uh this VI is
+ 
+
+ align:start position:0%
+view of the neutrals uh this VI is
+approximately constant it's a small
+
+ align:start position:0%
+approximately constant it's a small
+ 
+
+ align:start position:0%
+approximately constant it's a small
+value and it's approximately constant
+
+ align:start position:0%
+value and it's approximately constant
+ 
+
+ align:start position:0%
+value and it's approximately constant
+and so we can just take this VI out
+
+ align:start position:0%
+and so we can just take this VI out
+ 
+
+ align:start position:0%
+and so we can just take this VI out
+sorry we can evaluate
+
+ align:start position:0%
+sorry we can evaluate
+ 
+
+ align:start position:0%
+sorry we can evaluate
+this VI is just being VA and we can take
+
+ align:start position:0%
+this VI is just being VA and we can take
+ 
+
+ align:start position:0%
+this VI is just being VA and we can take
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside where it will nicely cancel with
+
+ align:start position:0%
+outside where it will nicely cancel with
+ 
+
+ align:start position:0%
+outside where it will nicely cancel with
+this VA so this gives us an expression
+
+ align:start position:0%
+this VA so this gives us an expression
+ 
+
+ align:start position:0%
+this VA so this gives us an expression
+that looks like one upon
+
+ align:start position:0%
+that looks like one upon
+ 
+
+ align:start position:0%
+that looks like one upon
+VA Sigma
+
+ align:start position:0%
+VA Sigma
+ 
+
+ align:start position:0%
+VA Sigma
+e v
+
+ align:start position:0%
+e v
+ 
+
+ align:start position:0%
+e v
+evaluated for effectiv the zero neutral
+
+ align:start position:0%
+evaluated for effectiv the zero neutral
+ 
+
+ align:start position:0%
+evaluated for effectiv the zero neutral
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+plus just these two cross-section Sigma
+
+ align:start position:0%
+plus just these two cross-section Sigma
+ 
+
+ align:start position:0%
+plus just these two cross-section Sigma
+p and sigma c times
+
+ align:start position:0%
+p and sigma c times
+ 
+
+ align:start position:0%
+p and sigma c times
+ni and we see that this term goes as one
+
+ align:start position:0%
+ni and we see that this term goes as one
+ 
+
+ align:start position:0%
+ni and we see that this term goes as one
+upon VA and this term doesn't so if
+
+ align:start position:0%
+upon VA and this term doesn't so if
+ 
+
+ align:start position:0%
+upon VA and this term doesn't so if
+we're dealing with energetic enough uh
+
+ align:start position:0%
+we're dealing with energetic enough uh
+ 
+
+ align:start position:0%
+we're dealing with energetic enough uh
+neutrals coming out of the core then we
+
+ align:start position:0%
+neutrals coming out of the core then we
+ 
+
+ align:start position:0%
+neutrals coming out of the core then we
+could imagine that this term could be
+
+ align:start position:0%
+could imagine that this term could be
+ 
+
+ align:start position:0%
+could imagine that this term could be
+relatively small it will depend exactly
+
+ align:start position:0%
+relatively small it will depend exactly
+ 
+
+ align:start position:0%
+relatively small it will depend exactly
+on Sigma e Sigma p and sigma C are but
+
+ align:start position:0%
+on Sigma e Sigma p and sigma C are but
+ 
+
+ align:start position:0%
+on Sigma e Sigma p and sigma C are but
+we can imagine for reasonable values
+
+ align:start position:0%
+we can imagine for reasonable values
+ 
+
+ align:start position:0%
+we can imagine for reasonable values
+this term will cancel so we end up with
+
+ align:start position:0%
+this term will cancel so we end up with
+ 
+
+ align:start position:0%
+this term will cancel so we end up with
+an expression that just has this so This
+
+ align:start position:0%
+an expression that just has this so This
+ 
+
+ align:start position:0%
+an expression that just has this so This
+Again is just
+
+ align:start position:0%
+Again is just
+ 
+
+ align:start position:0%
+Again is just
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+Alpha neglecting this for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then you can put this back up
+
+ align:start position:0%
+okay so then you can put this back up
+ 
+
+ align:start position:0%
+okay so then you can put this back up
+into our probability of the particle
+
+ align:start position:0%
+into our probability of the particle
+ 
+
+ align:start position:0%
+into our probability of the particle
+getting through and we just get
+
+ align:start position:0%
+getting through and we just get
+ 
+
+ align:start position:0%
+getting through and we just get
+exponential of
+
+ align:start position:0%
+exponential of
+ 
+
+ align:start position:0%
+exponential of
+minus Sigma P plus Sigma
+
+ align:start position:0%
+minus Sigma P plus Sigma
+ 
+
+ align:start position:0%
+minus Sigma P plus Sigma
+C integral of Ni D like
+
+ align:start position:0%
+C integral of Ni D like
+ 
+
+ align:start position:0%
+C integral of Ni D like
+this and you can go into Hutchinson's
+
+ align:start position:0%
+this and you can go into Hutchinson's
+ 
+
+ align:start position:0%
+this and you can go into Hutchinson's
+book and see graphs of Sigma p and sigma
+
+ align:start position:0%
+book and see graphs of Sigma p and sigma
+ 
+
+ align:start position:0%
+book and see graphs of Sigma p and sigma
+C and and e as well for different plasma
+
+ align:start position:0%
+C and and e as well for different plasma
+ 
+
+ align:start position:0%
+C and and e as well for different plasma
+conditions and so if we just use an
+
+ align:start position:0%
+conditions and so if we just use an
+ 
+
+ align:start position:0%
+conditions and so if we just use an
+example that maybe we have 10
+
+ align:start position:0%
+example that maybe we have 10
+ 
+
+ align:start position:0%
+example that maybe we have 10
+KV neutrals streaming out of the core
+
+ align:start position:0%
+KV neutrals streaming out of the core
+ 
+
+ align:start position:0%
+KV neutrals streaming out of the core
+because that's the sort of temperature
+
+ align:start position:0%
+because that's the sort of temperature
+ 
+
+ align:start position:0%
+because that's the sort of temperature
+we'd like in a fusion reactor so 10 KV
+
+ align:start position:0%
+we'd like in a fusion reactor so 10 KV
+ 
+
+ align:start position:0%
+we'd like in a fusion reactor so 10 KV
+neutrals we got a
+
+ align:start position:0%
+neutrals we got a
+ 
+
+ align:start position:0%
+neutrals we got a
+density of
+
+ align:start position:0%
+density of
+ 
+
+ align:start position:0%
+density of
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+10 20 per meter cubed so this is on the
+
+ align:start position:0%
+10 20 per meter cubed so this is on the
+ 
+
+ align:start position:0%
+10 20 per meter cubed so this is on the
+dense side for an mcf reactor but that's
+
+ align:start position:0%
+dense side for an mcf reactor but that's
+ 
+
+ align:start position:0%
+dense side for an mcf reactor but that's
+the sort of density we might need to
+
+ align:start position:0%
+the sort of density we might need to
+ 
+
+ align:start position:0%
+the sort of density we might need to
+react to relevant conditions then using
+
+ align:start position:0%
+react to relevant conditions then using
+ 
+
+ align:start position:0%
+react to relevant conditions then using
+this we will get a length scale in this
+
+ align:start position:0%
+this we will get a length scale in this
+ 
+
+ align:start position:0%
+this we will get a length scale in this
+exponent uh which is effectively the
+
+ align:start position:0%
+exponent uh which is effectively the
+ 
+
+ align:start position:0%
+exponent uh which is effectively the
+mean-free path the neutrals trying to
+
+ align:start position:0%
+mean-free path the neutrals trying to
+ 
+
+ align:start position:0%
+mean-free path the neutrals trying to
+leave the plasma and that is going to be
+
+ align:start position:0%
+leave the plasma and that is going to be
+ 
+
+ align:start position:0%
+leave the plasma and that is going to be
+about 10
+
+ align:start position:0%
+about 10
+ 
+
+ align:start position:0%
+about 10
+cm so for this relatively hot relatively
+
+ align:start position:0%
+cm so for this relatively hot relatively
+ 
+
+ align:start position:0%
+cm so for this relatively hot relatively
+dense plasma we're not going to see very
+
+ align:start position:0%
+dense plasma we're not going to see very
+ 
+
+ align:start position:0%
+dense plasma we're not going to see very
+many neutrals more than 10 centimeters
+
+ align:start position:0%
+many neutrals more than 10 centimeters
+ 
+
+ align:start position:0%
+many neutrals more than 10 centimeters
+away from the core and probably our
+
+ align:start position:0%
+away from the core and probably our
+ 
+
+ align:start position:0%
+away from the core and probably our
+reactor is going to have a
+
+ align:start position:0%
+reactor is going to have a
+ 
+
+ align:start position:0%
+reactor is going to have a
+diameter a of about 100 cm or so so
+
+ align:start position:0%
+diameter a of about 100 cm or so so
+ 
+
+ align:start position:0%
+diameter a of about 100 cm or so so
+we're not going to see very many of
+
+ align:start position:0%
+we're not going to see very many of
+ 
+
+ align:start position:0%
+we're not going to see very many of
+these particles which means that in
+
+ align:start position:0%
+these particles which means that in
+ 
+
+ align:start position:0%
+these particles which means that in
+order for these neutral Diagnostics to
+
+ align:start position:0%
+order for these neutral Diagnostics to
+ 
+
+ align:start position:0%
+order for these neutral Diagnostics to
+work at all we're going to
+
+ align:start position:0%
+work at all we're going to
+ 
+
+ align:start position:0%
+work at all we're going to
+require that the
+
+ align:start position:0%
+require that the
+ 
+
+ align:start position:0%
+require that the
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+having okay thank you um so we're going
+
+ align:start position:0%
+having okay thank you um so we're going
+ 
+
+ align:start position:0%
+having okay thank you um so we're going
+to require that the line
+
+ align:start position:0%
+to require that the line
+ 
+
+ align:start position:0%
+to require that the line
+integrated density here is going to be
+
+ align:start position:0%
+integrated density here is going to be
+ 
+
+ align:start position:0%
+integrated density here is going to be
+less than about 10 to the
+
+ align:start position:0%
+less than about 10 to the
+ 
+
+ align:start position:0%
+less than about 10 to the
+19 per meter squar here and if you do
+
+ align:start position:0%
+19 per meter squar here and if you do
+ 
+
+ align:start position:0%
+19 per meter squar here and if you do
+that then you get Lambda a more like a
+
+ align:start position:0%
+that then you get Lambda a more like a
+ 
+
+ align:start position:0%
+that then you get Lambda a more like a
+meter or
+
+ align:start position:0%
+meter or
+ 
+
+ align:start position:0%
+meter or
+so so we need low
+
+ align:start position:0%
+so so we need low
+ 
+
+ align:start position:0%
+so so we need low
+density I put it in quote marks because
+
+ align:start position:0%
+density I put it in quote marks because
+ 
+
+ align:start position:0%
+density I put it in quote marks because
+low means different things for different
+
+ align:start position:0%
+low means different things for different
+ 
+
+ align:start position:0%
+low means different things for different
+people but we need a relatively low
+
+ align:start position:0%
+people but we need a relatively low
+ 
+
+ align:start position:0%
+people but we need a relatively low
+density toac or magnetic confir Fusion
+
+ align:start position:0%
+density toac or magnetic confir Fusion
+ 
+
+ align:start position:0%
+density toac or magnetic confir Fusion
+device in order to get neutrals escaping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes this is just like a a speed of the
+
+ align:start position:0%
+yes this is just like a a speed of the
+ 
+
+ align:start position:0%
+yes this is just like a a speed of the
+neutrals coming out here I realize
+
+ align:start position:0%
+neutrals coming out here I realize
+ 
+
+ align:start position:0%
+neutrals coming out here I realize
+actually drawing this I don't think this
+
+ align:start position:0%
+actually drawing this I don't think this
+ 
+
+ align:start position:0%
+actually drawing this I don't think this
+is right at all I don't think this is a
+
+ align:start position:0%
+is right at all I don't think this is a
+ 
+
+ align:start position:0%
+is right at all I don't think this is a
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+function because we're talking about a
+
+ align:start position:0%
+function because we're talking about a
+ 
+
+ align:start position:0%
+function because we're talking about a
+distribution that's the whole thing
+
+ align:start position:0%
+distribution that's the whole thing
+ 
+
+ align:start position:0%
+distribution that's the whole thing
+we're trying to measure here so I think
+
+ align:start position:0%
+we're trying to measure here so I think
+ 
+
+ align:start position:0%
+we're trying to measure here so I think
+that actually I should be drawing it
+
+ align:start position:0%
+that actually I should be drawing it
+ 
+
+ align:start position:0%
+that actually I should be drawing it
+like this and call it f of a so this is
+
+ align:start position:0%
+like this and call it f of a so this is
+ 
+
+ align:start position:0%
+like this and call it f of a so this is
+the distribution the neutrals it's
+
+ align:start position:0%
+the distribution the neutrals it's
+ 
+
+ align:start position:0%
+the distribution the neutrals it's
+something Max wanish um but the average
+
+ align:start position:0%
+something Max wanish um but the average
+ 
+
+ align:start position:0%
+something Max wanish um but the average
+velocity here which I could call
+
+ align:start position:0%
+velocity here which I could call
+ 
+
+ align:start position:0%
+velocity here which I could call
+VTA which is maybe here is much larger
+
+ align:start position:0%
+VTA which is maybe here is much larger
+ 
+
+ align:start position:0%
+VTA which is maybe here is much larger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+vti but much smaller
+
+ align:start position:0%
+vti but much smaller
+ 
+
+ align:start position:0%
+vti but much smaller
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+VTE so this is just the idea that um for
+
+ align:start position:0%
+VTE so this is just the idea that um for
+ 
+
+ align:start position:0%
+VTE so this is just the idea that um for
+these neutrals here uh from the point of
+
+ align:start position:0%
+these neutrals here uh from the point of
+ 
+
+ align:start position:0%
+these neutrals here uh from the point of
+view of the neutrals the I are basically
+
+ align:start position:0%
+view of the neutrals the I are basically
+ 
+
+ align:start position:0%
+view of the neutrals the I are basically
+stationary and from the point of view of
+
+ align:start position:0%
+stationary and from the point of view of
+ 
+
+ align:start position:0%
+stationary and from the point of view of
+the electrons the neutrals are basically
+
+ align:start position:0%
+the electrons the neutrals are basically
+ 
+
+ align:start position:0%
+the electrons the neutrals are basically
+stationary as well and that allows us to
+
+ align:start position:0%
+stationary as well and that allows us to
+ 
+
+ align:start position:0%
+stationary as well and that allows us to
+simplify all of these angle brackets
+
+ align:start position:0%
+simplify all of these angle brackets
+ 
+
+ align:start position:0%
+simplify all of these angle brackets
+which are actually averaging over the
+
+ align:start position:0%
+which are actually averaging over the
+ 
+
+ align:start position:0%
+which are actually averaging over the
+difference between the two velocity
+
+ align:start position:0%
+difference between the two velocity
+ 
+
+ align:start position:0%
+difference between the two velocity
+distributions we can either set it to
+
+ align:start position:0%
+distributions we can either set it to
+ 
+
+ align:start position:0%
+distributions we can either set it to
+zero or just be the velocity of the
+
+ align:start position:0%
+zero or just be the velocity of the
+ 
+
+ align:start position:0%
+zero or just be the velocity of the
+neutrals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah well we imagine there's some
+
+ align:start position:0%
+yeah yeah well we imagine there's some
+ 
+
+ align:start position:0%
+yeah yeah well we imagine there's some
+temperature distribution inside this so
+
+ align:start position:0%
+temperature distribution inside this so
+ 
+
+ align:start position:0%
+temperature distribution inside this so
+we're talking about these these neutrals
+
+ align:start position:0%
+we're talking about these these neutrals
+ 
+
+ align:start position:0%
+we're talking about these these neutrals
+here are neutral that are in the core of
+
+ align:start position:0%
+here are neutral that are in the core of
+ 
+
+ align:start position:0%
+here are neutral that are in the core of
+the plasma so we hope they're hotter
+
+ align:start position:0%
+the plasma so we hope they're hotter
+ 
+
+ align:start position:0%
+the plasma so we hope they're hotter
+than the neutral than the ions in the
+
+ align:start position:0%
+than the neutral than the ions in the
+ 
+
+ align:start position:0%
+than the neutral than the ions in the
+rest of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plas no these are like the ions out here
+
+ align:start position:0%
+plas no these are like the ions out here
+ 
+
+ align:start position:0%
+plas no these are like the ions out here
+or something like that further out yeah
+
+ align:start position:0%
+or something like that further out yeah
+ 
+
+ align:start position:0%
+or something like that further out yeah
+that's a good question so if we have a
+
+ align:start position:0%
+that's a good question so if we have a
+ 
+
+ align:start position:0%
+that's a good question so if we have a
+sort of radius and temperature type
+
+ align:start position:0%
+sort of radius and temperature type
+ 
+
+ align:start position:0%
+sort of radius and temperature type
+thing we assume for a good reactor that
+
+ align:start position:0%
+thing we assume for a good reactor that
+ 
+
+ align:start position:0%
+thing we assume for a good reactor that
+it's peaked in some way and so we're
+
+ align:start position:0%
+it's peaked in some way and so we're
+ 
+
+ align:start position:0%
+it's peaked in some way and so we're
+asking about this the F of I VI I at R
+
+ align:start position:0%
+asking about this the F of I VI I at R
+ 
+
+ align:start position:0%
+asking about this the F of I VI I at R
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+becomes our F of neutrals V
+
+ align:start position:0%
+becomes our F of neutrals V
+ 
+
+ align:start position:0%
+becomes our F of neutrals V
+neutral at r equal Z but they're
+
+ align:start position:0%
+neutral at r equal Z but they're
+ 
+
+ align:start position:0%
+neutral at r equal Z but they're
+streaming through
+
+ align:start position:0%
+streaming through
+ 
+
+ align:start position:0%
+streaming through
+some f ofi VI I at R greater than zero
+
+ align:start position:0%
+some f ofi VI I at R greater than zero
+ 
+
+ align:start position:0%
+some f ofi VI I at R greater than zero
+which in general is going to be a lower
+
+ align:start position:0%
+which in general is going to be a lower
+ 
+
+ align:start position:0%
+which in general is going to be a lower
+temperature so the distribution is
+
+ align:start position:0%
+temperature so the distribution is
+ 
+
+ align:start position:0%
+temperature so the distribution is
+smaller yeah you know all of this is
+
+ align:start position:0%
+smaller yeah you know all of this is
+ 
+
+ align:start position:0%
+smaller yeah you know all of this is
+very handwavy of course if you want to
+
+ align:start position:0%
+very handwavy of course if you want to
+ 
+
+ align:start position:0%
+very handwavy of course if you want to
+do this properly you have to keep track
+
+ align:start position:0%
+do this properly you have to keep track
+ 
+
+ align:start position:0%
+do this properly you have to keep track
+and all these integrals correctly but
+
+ align:start position:0%
+and all these integrals correctly but
+ 
+
+ align:start position:0%
+and all these integrals correctly but
+just to give an idea of the the the most
+
+ align:start position:0%
+just to give an idea of the the the most
+ 
+
+ align:start position:0%
+just to give an idea of the the the most
+important effect it turns out are the
+
+ align:start position:0%
+important effect it turns out are the
+ 
+
+ align:start position:0%
+important effect it turns out are the
+ion ion impact ionization and the charge
+
+ align:start position:0%
+ion ion impact ionization and the charge
+ 
+
+ align:start position:0%
+ion ion impact ionization and the charge
+exchange and the charge exchange
+
+ align:start position:0%
+exchange and the charge exchange
+ 
+
+ align:start position:0%
+exchange and the charge exchange
+dominates this pretty strongly actually
+
+ align:start position:0%
+dominates this pretty strongly actually
+ 
+
+ align:start position:0%
+dominates this pretty strongly actually
+mostly just Char exchange with some of
+
+ align:start position:0%
+mostly just Char exchange with some of
+ 
+
+ align:start position:0%
+mostly just Char exchange with some of
+the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we haven't talked about that no no
+
+ align:start position:0%
+yeah we haven't talked about that no no
+ 
+
+ align:start position:0%
+yeah we haven't talked about that no no
+so what I'm saying is Imagine somehow
+
+ align:start position:0%
+so what I'm saying is Imagine somehow
+ 
+
+ align:start position:0%
+so what I'm saying is Imagine somehow
+you have created neutrals in core would
+
+ align:start position:0%
+you have created neutrals in core would
+ 
+
+ align:start position:0%
+you have created neutrals in core would
+they actually be able to get out because
+
+ align:start position:0%
+they actually be able to get out because
+ 
+
+ align:start position:0%
+they actually be able to get out because
+if they can't get out there's no point
+
+ align:start position:0%
+if they can't get out there's no point
+ 
+
+ align:start position:0%
+if they can't get out there's no point
+even trying to create them in the first
+
+ align:start position:0%
+even trying to create them in the first
+ 
+
+ align:start position:0%
+even trying to create them in the first
+place so we're sort of working our way
+
+ align:start position:0%
+place so we're sort of working our way
+ 
+
+ align:start position:0%
+place so we're sort of working our way
+backwards through the problem the next
+
+ align:start position:0%
+backwards through the problem the next
+ 
+
+ align:start position:0%
+backwards through the problem the next
+step is okay now that we know if we
+
+ align:start position:0%
+step is okay now that we know if we
+ 
+
+ align:start position:0%
+step is okay now that we know if we
+create some neutrals they can escape we
+
+ align:start position:0%
+create some neutrals they can escape we
+ 
+
+ align:start position:0%
+create some neutrals they can escape we
+can probably measure them in some way
+
+ align:start position:0%
+can probably measure them in some way
+ 
+
+ align:start position:0%
+can probably measure them in some way
+and learn about the core ion
+
+ align:start position:0%
+and learn about the core ion
+ 
+
+ align:start position:0%
+and learn about the core ion
+distribution now that we know that
+
+ align:start position:0%
+distribution now that we know that
+ 
+
+ align:start position:0%
+distribution now that we know that
+that's the case can we now work out how
+
+ align:start position:0%
+that's the case can we now work out how
+ 
+
+ align:start position:0%
+that's the case can we now work out how
+to create the neutrals and we'll talk
+
+ align:start position:0%
+to create the neutrals and we'll talk
+ 
+
+ align:start position:0%
+to create the neutrals and we'll talk
+about some techniques for that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah I mean this is very crude
+
+ align:start position:0%
+yeah yeah I mean this is very crude
+ 
+
+ align:start position:0%
+yeah yeah I mean this is very crude
+you're quite right I mean this should be
+
+ align:start position:0%
+you're quite right I mean this should be
+ 
+
+ align:start position:0%
+you're quite right I mean this should be
+inside here but if we assume these don't
+
+ align:start position:0%
+inside here but if we assume these don't
+ 
+
+ align:start position:0%
+inside here but if we assume these don't
+vary too much as the particle travels
+
+ align:start position:0%
+vary too much as the particle travels
+ 
+
+ align:start position:0%
+vary too much as the particle travels
+from the core to the edge then it allows
+
+ align:start position:0%
+from the core to the edge then it allows
+ 
+
+ align:start position:0%
+from the core to the edge then it allows
+us just to pull out this factor of nidl
+
+ align:start position:0%
+us just to pull out this factor of nidl
+ 
+
+ align:start position:0%
+us just to pull out this factor of nidl
+and make it clear that it's like the
+
+ align:start position:0%
+and make it clear that it's like the
+ 
+
+ align:start position:0%
+and make it clear that it's like the
+line integrated density that's important
+
+ align:start position:0%
+line integrated density that's important
+ 
+
+ align:start position:0%
+line integrated density that's important
+thing in reality it would have to stay
+
+ align:start position:0%
+thing in reality it would have to stay
+ 
+
+ align:start position:0%
+thing in reality it would have to stay
+inside you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online all right let's go find out how
+
+ align:start position:0%
+online all right let's go find out how
+ 
+
+ align:start position:0%
+online all right let's go find out how
+to put some neutrals in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trying to spell neutrals with an a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay so again let's have some flux
+
+ align:start position:0%
+there okay so again let's have some flux
+ 
+
+ align:start position:0%
+there okay so again let's have some flux
+surfaces some plasma like this so one of
+
+ align:start position:0%
+surfaces some plasma like this so one of
+ 
+
+ align:start position:0%
+surfaces some plasma like this so one of
+the ways the neutrals could get there as
+
+ align:start position:0%
+the ways the neutrals could get there as
+ 
+
+ align:start position:0%
+the ways the neutrals could get there as
+we discussed before is from The Edge so
+
+ align:start position:0%
+we discussed before is from The Edge so
+ 
+
+ align:start position:0%
+we discussed before is from The Edge so
+around the edge of plasma there's um for
+
+ align:start position:0%
+around the edge of plasma there's um for
+ 
+
+ align:start position:0%
+around the edge of plasma there's um for
+example the scrape off layer and then
+
+ align:start position:0%
+example the scrape off layer and then
+ 
+
+ align:start position:0%
+example the scrape off layer and then
+there's going to be a region which is in
+
+ align:start position:0%
+there's going to be a region which is in
+ 
+
+ align:start position:0%
+there's going to be a region which is in
+contact with the wall which is
+
+ align:start position:0%
+contact with the wall which is
+ 
+
+ align:start position:0%
+contact with the wall which is
+relatively cold and so we can have
+
+ align:start position:0%
+relatively cold and so we can have
+ 
+
+ align:start position:0%
+relatively cold and so we can have
+neutrals uh being produced here and
+
+ align:start position:0%
+neutrals uh being produced here and
+ 
+
+ align:start position:0%
+neutrals uh being produced here and
+these neutrals will wander in and they
+
+ align:start position:0%
+these neutrals will wander in and they
+ 
+
+ align:start position:0%
+these neutrals will wander in and they
+won't see the magnetic field lines and
+
+ align:start position:0%
+won't see the magnetic field lines and
+ 
+
+ align:start position:0%
+won't see the magnetic field lines and
+so maybe one of them will only get so
+
+ align:start position:0%
+so maybe one of them will only get so
+ 
+
+ align:start position:0%
+so maybe one of them will only get so
+far here before the charge exchanges and
+
+ align:start position:0%
+far here before the charge exchanges and
+ 
+
+ align:start position:0%
+far here before the charge exchanges and
+this one will get a little bit further
+
+ align:start position:0%
+this one will get a little bit further
+ 
+
+ align:start position:0%
+this one will get a little bit further
+but you can imagine that maybe a couple
+
+ align:start position:0%
+but you can imagine that maybe a couple
+ 
+
+ align:start position:0%
+but you can imagine that maybe a couple
+of these neutrals wander into the center
+
+ align:start position:0%
+of these neutrals wander into the center
+ 
+
+ align:start position:0%
+of these neutrals wander into the center
+they charge exchange and then we can
+
+ align:start position:0%
+they charge exchange and then we can
+ 
+
+ align:start position:0%
+they charge exchange and then we can
+start getting
+
+ align:start position:0%
+start getting
+ 
+
+ align:start position:0%
+start getting
+those the new neutrals the ones that
+
+ align:start position:0%
+those the new neutrals the ones that
+ 
+
+ align:start position:0%
+those the new neutrals the ones that
+represent the core ions start moving
+
+ align:start position:0%
+represent the core ions start moving
+ 
+
+ align:start position:0%
+represent the core ions start moving
+back out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so one possibility is we'll call
+
+ align:start position:0%
+again so one possibility is we'll call
+ 
+
+ align:start position:0%
+again so one possibility is we'll call
+it Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fueling and we know how to calculate the
+
+ align:start position:0%
+fueling and we know how to calculate the
+ 
+
+ align:start position:0%
+fueling and we know how to calculate the
+probability of that because we just
+
+ align:start position:0%
+probability of that because we just
+ 
+
+ align:start position:0%
+probability of that because we just
+spent a long time trying to calculate
+
+ align:start position:0%
+spent a long time trying to calculate
+ 
+
+ align:start position:0%
+spent a long time trying to calculate
+the probability of the opposite process
+
+ align:start position:0%
+the probability of the opposite process
+ 
+
+ align:start position:0%
+the probability of the opposite process
+so now we know that it's basically p b
+
+ align:start position:0%
+so now we know that it's basically p b
+ 
+
+ align:start position:0%
+so now we know that it's basically p b
+a which is the probability of going from
+
+ align:start position:0%
+a which is the probability of going from
+ 
+
+ align:start position:0%
+a which is the probability of going from
+the outside B into the core which we
+
+ align:start position:0%
+the outside B into the core which we
+ 
+
+ align:start position:0%
+the outside B into the core which we
+called a in our previous diagram so we
+
+ align:start position:0%
+called a in our previous diagram so we
+ 
+
+ align:start position:0%
+called a in our previous diagram so we
+can estimate How likely it is that any
+
+ align:start position:0%
+can estimate How likely it is that any
+ 
+
+ align:start position:0%
+can estimate How likely it is that any
+of these particles get through and the
+
+ align:start position:0%
+of these particles get through and the
+ 
+
+ align:start position:0%
+of these particles get through and the
+answer is that this actually does create
+
+ align:start position:0%
+answer is that this actually does create
+ 
+
+ align:start position:0%
+answer is that this actually does create
+a fair amount of neutrals in the core
+
+ align:start position:0%
+a fair amount of neutrals in the core
+ 
+
+ align:start position:0%
+a fair amount of neutrals in the core
+just because there are so many neutrals
+
+ align:start position:0%
+just because there are so many neutrals
+ 
+
+ align:start position:0%
+just because there are so many neutrals
+in the edge some of them will get
+
+ align:start position:0%
+in the edge some of them will get
+ 
+
+ align:start position:0%
+in the edge some of them will get
+through so this technique by itself will
+
+ align:start position:0%
+through so this technique by itself will
+ 
+
+ align:start position:0%
+through so this technique by itself will
+create a detectable flux of core
+
+ align:start position:0%
+create a detectable flux of core
+ 
+
+ align:start position:0%
+create a detectable flux of core
+neutrals coming back out again okay so
+
+ align:start position:0%
+neutrals coming back out again okay so
+ 
+
+ align:start position:0%
+neutrals coming back out again okay so
+PBA which is Edge decor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another thing you might say well trapped
+
+ align:start position:0%
+another thing you might say well trapped
+ 
+
+ align:start position:0%
+another thing you might say well trapped
+just by some Atomic processes in the
+
+ align:start position:0%
+just by some Atomic processes in the
+ 
+
+ align:start position:0%
+just by some Atomic processes in the
+core here we could get neutrals
+
+ align:start position:0%
+core here we could get neutrals
+ 
+
+ align:start position:0%
+core here we could get neutrals
+developing here so we could have
+
+ align:start position:0%
+developing here so we could have
+ 
+
+ align:start position:0%
+developing here so we could have
+radiative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recombination because after all there's
+
+ align:start position:0%
+recombination because after all there's
+ 
+
+ align:start position:0%
+recombination because after all there's
+a load of electrons flying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+these electrons are up above the
+
+ align:start position:0%
+these electrons are up above the
+ 
+
+ align:start position:0%
+these electrons are up above the
+ionization energy so they're
+
+ align:start position:0%
+ionization energy so they're
+ 
+
+ align:start position:0%
+ionization energy so they're
+free but this electron could be caught
+
+ align:start position:0%
+free but this electron could be caught
+ 
+
+ align:start position:0%
+free but this electron could be caught
+by the electric potential of the ion and
+
+ align:start position:0%
+by the electric potential of the ion and
+ 
+
+ align:start position:0%
+by the electric potential of the ion and
+become a bound electron and then we
+
+ align:start position:0%
+become a bound electron and then we
+ 
+
+ align:start position:0%
+become a bound electron and then we
+would get out our recombination
+
+ align:start position:0%
+would get out our recombination
+ 
+
+ align:start position:0%
+would get out our recombination
+Photon that process could happen but of
+
+ align:start position:0%
+Photon that process could happen but of
+ 
+
+ align:start position:0%
+Photon that process could happen but of
+course the other process we've already
+
+ align:start position:0%
+course the other process we've already
+ 
+
+ align:start position:0%
+course the other process we've already
+discussed is when we have an electron
+
+ align:start position:0%
+discussed is when we have an electron
+ 
+
+ align:start position:0%
+discussed is when we have an electron
+come in and collide with one of the
+
+ align:start position:0%
+come in and collide with one of the
+ 
+
+ align:start position:0%
+come in and collide with one of the
+inner shell electrons and we end up with
+
+ align:start position:0%
+inner shell electrons and we end up with
+ 
+
+ align:start position:0%
+inner shell electrons and we end up with
+two electrons coming back out again this
+
+ align:start position:0%
+two electrons coming back out again this
+ 
+
+ align:start position:0%
+two electrons coming back out again this
+is electron
+
+ align:start position:0%
+is electron
+ 
+
+ align:start position:0%
+is electron
+impact
+
+ align:start position:0%
+impact
+ 
+
+ align:start position:0%
+impact
+ionization um
+
+ align:start position:0%
+ionization um
+ 
+
+ align:start position:0%
+ionization um
+and there'll be a balance in steady
+
+ align:start position:0%
+and there'll be a balance in steady
+ 
+
+ align:start position:0%
+and there'll be a balance in steady
+States between these two processes and
+
+ align:start position:0%
+States between these two processes and
+ 
+
+ align:start position:0%
+States between these two processes and
+that balance will look like the density
+
+ align:start position:0%
+that balance will look like the density
+ 
+
+ align:start position:0%
+that balance will look like the density
+of electrons the density of ions uh the
+
+ align:start position:0%
+of electrons the density of ions uh the
+ 
+
+ align:start position:0%
+of electrons the density of ions uh the
+reactivity or the cross-section for the
+
+ align:start position:0%
+reactivity or the cross-section for the
+ 
+
+ align:start position:0%
+reactivity or the cross-section for the
+radiative rec
+
+ align:start position:0%
+radiative rec
+ 
+
+ align:start position:0%
+radiative rec
+combination Times by the electron
+
+ align:start position:0%
+combination Times by the electron
+ 
+
+ align:start position:0%
+combination Times by the electron
+velocity and that will be balanced by
+
+ align:start position:0%
+velocity and that will be balanced by
+ 
+
+ align:start position:0%
+velocity and that will be balanced by
+the electron density the density of
+
+ align:start position:0%
+the electron density the density of
+ 
+
+ align:start position:0%
+the electron density the density of
+neutrals
+
+ align:start position:0%
+neutrals
+ 
+
+ align:start position:0%
+neutrals
+here Sigma e for electron impact
+
+ align:start position:0%
+here Sigma e for electron impact
+ 
+
+ align:start position:0%
+here Sigma e for electron impact
+ionization de like that so that means
+
+ align:start position:0%
+ionization de like that so that means
+ 
+
+ align:start position:0%
+ionization de like that so that means
+that we can look at this and go okay
+
+ align:start position:0%
+that we can look at this and go okay
+ 
+
+ align:start position:0%
+that we can look at this and go okay
+what is the steady state density of
+
+ align:start position:0%
+what is the steady state density of
+ 
+
+ align:start position:0%
+what is the steady state density of
+neutrals that's going to be n over ni I
+
+ align:start position:0%
+neutrals that's going to be n over ni I
+ 
+
+ align:start position:0%
+neutrals that's going to be n over ni I
+the ne's cancel so it's just going to be
+
+ align:start position:0%
+the ne's cancel so it's just going to be
+ 
+
+ align:start position:0%
+the ne's cancel so it's just going to be
+the ratio of these reactivities Sigma r
+
+ align:start position:0%
+the ratio of these reactivities Sigma r
+ 
+
+ align:start position:0%
+the ratio of these reactivities Sigma r
+v over Sigma e e e like
+
+ align:start position:0%
+v over Sigma e e e like
+ 
+
+ align:start position:0%
+v over Sigma e e e like
+that and at 1
+
+ align:start position:0%
+that and at 1
+ 
+
+ align:start position:0%
+that and at 1
+KV which is a reasonable temperature for
+
+ align:start position:0%
+KV which is a reasonable temperature for
+ 
+
+ align:start position:0%
+KV which is a reasonable temperature for
+you to have in your core um this is
+
+ align:start position:0%
+you to have in your core um this is
+ 
+
+ align:start position:0%
+you to have in your core um this is
+about 10 to the minus 8 so the point I'm
+
+ align:start position:0%
+about 10 to the minus 8 so the point I'm
+ 
+
+ align:start position:0%
+about 10 to the minus 8 so the point I'm
+trying to make here is although you
+
+ align:start position:0%
+trying to make here is although you
+ 
+
+ align:start position:0%
+trying to make here is although you
+might occasionally have some
+
+ align:start position:0%
+might occasionally have some
+ 
+
+ align:start position:0%
+might occasionally have some
+recombination process because the other
+
+ align:start position:0%
+recombination process because the other
+ 
+
+ align:start position:0%
+recombination process because the other
+processes which lead to ionization again
+
+ align:start position:0%
+processes which lead to ionization again
+ 
+
+ align:start position:0%
+processes which lead to ionization again
+are so rapid you quickly will reionize
+
+ align:start position:0%
+are so rapid you quickly will reionize
+ 
+
+ align:start position:0%
+are so rapid you quickly will reionize
+and so if you have 10 to 13 or 10 to 20
+
+ align:start position:0%
+and so if you have 10 to 13 or 10 to 20
+ 
+
+ align:start position:0%
+and so if you have 10 to 13 or 10 to 20
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+ions per cubic meter they'll only have
+
+ align:start position:0%
+ions per cubic meter they'll only have
+ 
+
+ align:start position:0%
+ions per cubic meter they'll only have
+10 to 12 neutral and that's not really
+
+ align:start position:0%
+10 to 12 neutral and that's not really
+ 
+
+ align:start position:0%
+10 to 12 neutral and that's not really
+enough to detect so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible so Edge fueling yes could be
+
+ align:start position:0%
+negligible so Edge fueling yes could be
+ 
+
+ align:start position:0%
+negligible so Edge fueling yes could be
+a way of getting neutrals in the core
+
+ align:start position:0%
+a way of getting neutrals in the core
+ 
+
+ align:start position:0%
+a way of getting neutrals in the core
+radiative recombination is not a way and
+
+ align:start position:0%
+radiative recombination is not a way and
+ 
+
+ align:start position:0%
+radiative recombination is not a way and
+you kind of know this because if this
+
+ align:start position:0%
+you kind of know this because if this
+ 
+
+ align:start position:0%
+you kind of know this because if this
+was an effective process then you would
+
+ align:start position:0%
+was an effective process then you would
+ 
+
+ align:start position:0%
+was an effective process then you would
+end up with a large neutral fraction in
+
+ align:start position:0%
+end up with a large neutral fraction in
+ 
+
+ align:start position:0%
+end up with a large neutral fraction in
+the cor of your toac and that's not
+
+ align:start position:0%
+the cor of your toac and that's not
+ 
+
+ align:start position:0%
+the cor of your toac and that's not
+something that we generally think about
+
+ align:start position:0%
+something that we generally think about
+ 
+
+ align:start position:0%
+something that we generally think about
+and doesn't generally happen Okay and
+
+ align:start position:0%
+and doesn't generally happen Okay and
+ 
+
+ align:start position:0%
+and doesn't generally happen Okay and
+then finally there are beans and I'll
+
+ align:start position:0%
+then finally there are beans and I'll
+ 
+
+ align:start position:0%
+then finally there are beans and I'll
+talk a little bit more about beam in a
+
+ align:start position:0%
+talk a little bit more about beam in a
+ 
+
+ align:start position:0%
+talk a little bit more about beam in a
+second as like an active version of the
+
+ align:start position:0%
+second as like an active version of the
+ 
+
+ align:start position:0%
+second as like an active version of the
+diagnostic but I just want to talk about
+
+ align:start position:0%
+diagnostic but I just want to talk about
+ 
+
+ align:start position:0%
+diagnostic but I just want to talk about
+how we actually
+
+ align:start position:0%
+how we actually
+ 
+
+ align:start position:0%
+how we actually
+measure these neutrals coming out in
+
+ align:start position:0%
+measure these neutrals coming out in
+ 
+
+ align:start position:0%
+measure these neutrals coming out in
+this passive version where we just let
+
+ align:start position:0%
+this passive version where we just let
+ 
+
+ align:start position:0%
+this passive version where we just let
+Edge fueling do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so pass it
+
+ align:start position:0%
+so pass it
+ 
+
+ align:start position:0%
+so pass it
+CX with Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neutrals so we've got
+
+ align:start position:0%
+neutrals so we've got
+ 
+
+ align:start position:0%
+neutrals so we've got
+some hocak vacuum chamber some mcf
+
+ align:start position:0%
+some hocak vacuum chamber some mcf
+ 
+
+ align:start position:0%
+some hocak vacuum chamber some mcf
+vacuum chamber with some plasma like
+
+ align:start position:0%
+vacuum chamber with some plasma like
+ 
+
+ align:start position:0%
+vacuum chamber with some plasma like
+this we have all of
+
+ align:start position:0%
+this we have all of
+ 
+
+ align:start position:0%
+this we have all of
+the particles coming in from the edge
+
+ align:start position:0%
+the particles coming in from the edge
+ 
+
+ align:start position:0%
+the particles coming in from the edge
+and then the charge exchanging with
+
+ align:start position:0%
+and then the charge exchanging with
+ 
+
+ align:start position:0%
+and then the charge exchanging with
+particles in the core and and they're
+
+ align:start position:0%
+particles in the core and and they're
+ 
+
+ align:start position:0%
+particles in the core and and they're
+producing for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example a hydrogen neutral that's coming
+
+ align:start position:0%
+example a hydrogen neutral that's coming
+ 
+
+ align:start position:0%
+example a hydrogen neutral that's coming
+out from the core and we put that
+
+ align:start position:0%
+out from the core and we put that
+ 
+
+ align:start position:0%
+out from the core and we put that
+hydrogen neutral into something called a
+
+ align:start position:0%
+hydrogen neutral into something called a
+ 
+
+ align:start position:0%
+hydrogen neutral into something called a
+stripping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell and it comes out as a hydrogen ion
+
+ align:start position:0%
+cell and it comes out as a hydrogen ion
+ 
+
+ align:start position:0%
+cell and it comes out as a hydrogen ion
+again but a hydrogen ion with the same
+
+ align:start position:0%
+again but a hydrogen ion with the same
+ 
+
+ align:start position:0%
+again but a hydrogen ion with the same
+velocity or effectively the same
+
+ align:start position:0%
+velocity or effectively the same
+ 
+
+ align:start position:0%
+velocity or effectively the same
+distribution function as the neutral
+
+ align:start position:0%
+distribution function as the neutral
+ 
+
+ align:start position:0%
+distribution function as the neutral
+coming in the stripping cell has a very
+
+ align:start position:0%
+coming in the stripping cell has a very
+ 
+
+ align:start position:0%
+coming in the stripping cell has a very
+uh electropositive gas so it wants to
+
+ align:start position:0%
+uh electropositive gas so it wants to
+ 
+
+ align:start position:0%
+uh electropositive gas so it wants to
+take off the electrons and it will
+
+ align:start position:0%
+take off the electrons and it will
+ 
+
+ align:start position:0%
+take off the electrons and it will
+charge exchange about really changing
+
+ align:start position:0%
+charge exchange about really changing
+ 
+
+ align:start position:0%
+charge exchange about really changing
+the trajectory of this very much and
+
+ align:start position:0%
+the trajectory of this very much and
+ 
+
+ align:start position:0%
+the trajectory of this very much and
+then we have for example a large
+
+ align:start position:0%
+then we have for example a large
+ 
+
+ align:start position:0%
+then we have for example a large
+magnetic field in this region that bends
+
+ align:start position:0%
+magnetic field in this region that bends
+ 
+
+ align:start position:0%
+magnetic field in this region that bends
+the particles according to their
+
+ align:start position:0%
+the particles according to their
+ 
+
+ align:start position:0%
+the particles according to their
+velocity and then we have a detector
+
+ align:start position:0%
+velocity and then we have a detector
+ 
+
+ align:start position:0%
+velocity and then we have a detector
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this with bins in it and the bins have
+
+ align:start position:0%
+this with bins in it and the bins have
+ 
+
+ align:start position:0%
+this with bins in it and the bins have
+different sensitivity to different
+
+ align:start position:0%
+different sensitivity to different
+ 
+
+ align:start position:0%
+different sensitivity to different
+velocities here and so by counting out
+
+ align:start position:0%
+velocities here and so by counting out
+ 
+
+ align:start position:0%
+velocities here and so by counting out
+the number of particles in each
+
+ align:start position:0%
+the number of particles in each
+ 
+
+ align:start position:0%
+the number of particles in each
+bin we get out that distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function like
+
+ align:start position:0%
+function like
+ 
+
+ align:start position:0%
+function like
+that and we hope that during their
+
+ align:start position:0%
+that and we hope that during their
+ 
+
+ align:start position:0%
+that and we hope that during their
+travels from the core through our
+
+ align:start position:0%
+travels from the core through our
+ 
+
+ align:start position:0%
+travels from the core through our
+stripping cell onto our detector the
+
+ align:start position:0%
+stripping cell onto our detector the
+ 
+
+ align:start position:0%
+stripping cell onto our detector the
+distribution function has not been
+
+ align:start position:0%
+distribution function has not been
+ 
+
+ align:start position:0%
+distribution function has not been
+changed very much so we really are
+
+ align:start position:0%
+changed very much so we really are
+ 
+
+ align:start position:0%
+changed very much so we really are
+measuring the distribution function of
+
+ align:start position:0%
+measuring the distribution function of
+ 
+
+ align:start position:0%
+measuring the distribution function of
+the particles in the center there so if
+
+ align:start position:0%
+the particles in the center there so if
+ 
+
+ align:start position:0%
+the particles in the center there so if
+we look at that on our detector and I
+
+ align:start position:0%
+we look at that on our detector and I
+ 
+
+ align:start position:0%
+we look at that on our detector and I
+plot it on a logarithmic scale the log
+
+ align:start position:0%
+plot it on a logarithmic scale the log
+ 
+
+ align:start position:0%
+plot it on a logarithmic scale the log
+of intensity which is equal to log of
+
+ align:start position:0%
+of intensity which is equal to log of
+ 
+
+ align:start position:0%
+of intensity which is equal to log of
+particle number
+
+ align:start position:0%
+particle number
+ 
+
+ align:start position:0%
+particle number
+versus particle energy here so not
+
+ align:start position:0%
+versus particle energy here so not
+ 
+
+ align:start position:0%
+versus particle energy here so not
+velocity but energy which is half mv^
+
+ align:start position:0%
+velocity but energy which is half mv^
+ 
+
+ align:start position:0%
+velocity but energy which is half mv^
+s we see that we
+
+ align:start position:0%
+s we see that we
+ 
+
+ align:start position:0%
+s we see that we
+have a region that is approximately
+
+ align:start position:0%
+have a region that is approximately
+ 
+
+ align:start position:0%
+have a region that is approximately
+straight and that has a slope of one
+
+ align:start position:0%
+straight and that has a slope of one
+ 
+
+ align:start position:0%
+straight and that has a slope of one
+over TI because our distribution
+
+ align:start position:0%
+over TI because our distribution
+ 
+
+ align:start position:0%
+over TI because our distribution
+function from mellan is exponential of
+
+ align:start position:0%
+function from mellan is exponential of
+ 
+
+ align:start position:0%
+function from mellan is exponential of
+minus E over TI like that and then we
+
+ align:start position:0%
+minus E over TI like that and then we
+ 
+
+ align:start position:0%
+minus E over TI like that and then we
+might have some interesting features
+
+ align:start position:0%
+might have some interesting features
+ 
+
+ align:start position:0%
+might have some interesting features
+down at the bottom here where it become
+
+ align:start position:0%
+down at the bottom here where it become
+ 
+
+ align:start position:0%
+down at the bottom here where it become
+looks non- maxwelli and so this can be
+
+ align:start position:0%
+looks non- maxwelli and so this can be
+ 
+
+ align:start position:0%
+looks non- maxwelli and so this can be
+the pale and this will correspond to
+
+ align:start position:0%
+the pale and this will correspond to
+ 
+
+ align:start position:0%
+the pale and this will correspond to
+fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ions and measuring fast Downs is very
+
+ align:start position:0%
+ions and measuring fast Downs is very
+ 
+
+ align:start position:0%
+ions and measuring fast Downs is very
+important in magnetic confinement Fusion
+
+ align:start position:0%
+important in magnetic confinement Fusion
+ 
+
+ align:start position:0%
+important in magnetic confinement Fusion
+these fast ions might be due to things
+
+ align:start position:0%
+these fast ions might be due to things
+ 
+
+ align:start position:0%
+these fast ions might be due to things
+like RF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heating or they might be due to runaways
+
+ align:start position:0%
+heating or they might be due to runaways
+ 
+
+ align:start position:0%
+heating or they might be due to runaways
+being produced by inductively driven
+
+ align:start position:0%
+being produced by inductively driven
+ 
+
+ align:start position:0%
+being produced by inductively driven
+electric fields or other cool physics so
+
+ align:start position:0%
+electric fields or other cool physics so
+ 
+
+ align:start position:0%
+electric fields or other cool physics so
+it's nice to be able to measure those
+
+ align:start position:0%
+it's nice to be able to measure those
+ 
+
+ align:start position:0%
+it's nice to be able to measure those
+fast ands as well the main problem with
+
+ align:start position:0%
+fast ands as well the main problem with
+ 
+
+ align:start position:0%
+fast ands as well the main problem with
+this technique of course is it's line
+
+ align:start position:0%
+this technique of course is it's line
+ 
+
+ align:start position:0%
+this technique of course is it's line
+integrated if I have my detector set up
+
+ align:start position:0%
+integrated if I have my detector set up
+ 
+
+ align:start position:0%
+integrated if I have my detector set up
+like this and collecting all the
+
+ align:start position:0%
+like this and collecting all the
+ 
+
+ align:start position:0%
+like this and collecting all the
+particles in this region that come down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and so you don't really know
+
+ align:start position:0%
+here and so you don't really know
+ 
+
+ align:start position:0%
+here and so you don't really know
+exactly where those particles have come
+
+ align:start position:0%
+exactly where those particles have come
+ 
+
+ align:start position:0%
+exactly where those particles have come
+from and so we have the same problem we
+
+ align:start position:0%
+from and so we have the same problem we
+ 
+
+ align:start position:0%
+from and so we have the same problem we
+have with all of our other line
+
+ align:start position:0%
+have with all of our other line
+ 
+
+ align:start position:0%
+have with all of our other line
+integrated
+
+ align:start position:0%
+integrated
+ 
+
+ align:start position:0%
+integrated
+Diagnostics but it's you know pretty
+
+ align:start position:0%
+Diagnostics but it's you know pretty
+ 
+
+ align:start position:0%
+Diagnostics but it's you know pretty
+free we don't actually have to put any
+
+ align:start position:0%
+free we don't actually have to put any
+ 
+
+ align:start position:0%
+free we don't actually have to put any
+effort into making neutrals in the
+
+ align:start position:0%
+effort into making neutrals in the
+ 
+
+ align:start position:0%
+effort into making neutrals in the
+center there we just let the fact that
+
+ align:start position:0%
+center there we just let the fact that
+ 
+
+ align:start position:0%
+center there we just let the fact that
+we have a crappy vacuum chamber do the
+
+ align:start position:0%
+we have a crappy vacuum chamber do the
+ 
+
+ align:start position:0%
+we have a crappy vacuum chamber do the
+work for so this is a nice way to do it
+
+ align:start position:0%
+work for so this is a nice way to do it
+ 
+
+ align:start position:0%
+work for so this is a nice way to do it
+if you don't have a neutral beam any
+
+ align:start position:0%
+if you don't have a neutral beam any
+ 
+
+ align:start position:0%
+if you don't have a neutral beam any
+questions on that before you put a
+
+ align:start position:0%
+questions on that before you put a
+ 
+
+ align:start position:0%
+questions on that before you put a
+neutral beam in system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm oh you would just have a magnetic
+
+ align:start position:0%
+mhm oh you would just have a magnetic
+ 
+
+ align:start position:0%
+mhm oh you would just have a magnetic
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and frankly the magnetic field of
+
+ align:start position:0%
+yeah and frankly the magnetic field of
+ 
+
+ align:start position:0%
+yeah and frankly the magnetic field of
+your toac does a pretty good job of that
+
+ align:start position:0%
+your toac does a pretty good job of that
+ 
+
+ align:start position:0%
+your toac does a pretty good job of that
+yeah yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how does what depend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like yeah uh I mean we tend to be
+
+ align:start position:0%
+like yeah uh I mean we tend to be
+ 
+
+ align:start position:0%
+like yeah uh I mean we tend to be
+thinking about we still tend to be
+
+ align:start position:0%
+thinking about we still tend to be
+ 
+
+ align:start position:0%
+thinking about we still tend to be
+thinking about these neutrals coming
+
+ align:start position:0%
+thinking about these neutrals coming
+ 
+
+ align:start position:0%
+thinking about these neutrals coming
+from the Ed as being hydrogen so when we
+
+ align:start position:0%
+from the Ed as being hydrogen so when we
+ 
+
+ align:start position:0%
+from the Ed as being hydrogen so when we
+have when we have the pl hydrogen plasma
+
+ align:start position:0%
+have when we have the pl hydrogen plasma
+ 
+
+ align:start position:0%
+have when we have the pl hydrogen plasma
+by hydrogen I mean duum and Trum are
+
+ align:start position:0%
+by hydrogen I mean duum and Trum are
+ 
+
+ align:start position:0%
+by hydrogen I mean duum and Trum are
+fuel so when we have our fuel in contact
+
+ align:start position:0%
+fuel so when we have our fuel in contact
+ 
+
+ align:start position:0%
+fuel so when we have our fuel in contact
+with the wall there will be a layer of
+
+ align:start position:0%
+with the wall there will be a layer of
+ 
+
+ align:start position:0%
+with the wall there will be a layer of
+like low ionization state partially
+
+ align:start position:0%
+like low ionization state partially
+ 
+
+ align:start position:0%
+like low ionization state partially
+neutral gas around the edge just gets
+
+ align:start position:0%
+neutral gas around the edge just gets
+ 
+
+ align:start position:0%
+neutral gas around the edge just gets
+into contact with a wall and so most of
+
+ align:start position:0%
+into contact with a wall and so most of
+ 
+
+ align:start position:0%
+into contact with a wall and so most of
+this will be coming from I don't know
+
+ align:start position:0%
+this will be coming from I don't know
+ 
+
+ align:start position:0%
+this will be coming from I don't know
+what happens if you start looking at
+
+ align:start position:0%
+what happens if you start looking at
+ 
+
+ align:start position:0%
+what happens if you start looking at
+this and you start looking at all the
+
+ align:start position:0%
+this and you start looking at all the
+ 
+
+ align:start position:0%
+this and you start looking at all the
+neutrals as well presuming you now need
+
+ align:start position:0%
+neutrals as well presuming you now need
+ 
+
+ align:start position:0%
+neutrals as well presuming you now need
+many more coefficients to calculate and
+
+ align:start position:0%
+many more coefficients to calculate and
+ 
+
+ align:start position:0%
+many more coefficients to calculate and
+probably if you're doing it properly you
+
+ align:start position:0%
+probably if you're doing it properly you
+ 
+
+ align:start position:0%
+probably if you're doing it properly you
+should take into account those but I
+
+ align:start position:0%
+should take into account those but I
+ 
+
+ align:start position:0%
+should take into account those but I
+think although impurities can dominate
+
+ align:start position:0%
+think although impurities can dominate
+ 
+
+ align:start position:0%
+think although impurities can dominate
+things like line radiation this really
+
+ align:start position:0%
+things like line radiation this really
+ 
+
+ align:start position:0%
+things like line radiation this really
+depends on the ion
+
+ align:start position:0%
+depends on the ion
+ 
+
+ align:start position:0%
+depends on the ion
+number so we're going to be thinking
+
+ align:start position:0%
+number so we're going to be thinking
+ 
+
+ align:start position:0%
+number so we're going to be thinking
+probably about the num the the the
+
+ align:start position:0%
+probably about the num the the the
+ 
+
+ align:start position:0%
+probably about the num the the the
+impurities probably don't have a higher
+
+ align:start position:0%
+impurities probably don't have a higher
+ 
+
+ align:start position:0%
+impurities probably don't have a higher
+number density in the fuel or you've
+
+ align:start position:0%
+number density in the fuel or you've
+ 
+
+ align:start position:0%
+number density in the fuel or you've
+done something very wrong that's happen
+
+ align:start position:0%
+done something very wrong that's happen
+ 
+
+ align:start position:0%
+done something very wrong that's happen
+so I think you're still going to be
+
+ align:start position:0%
+so I think you're still going to be
+ 
+
+ align:start position:0%
+so I think you're still going to be
+dominated by your fuel I
+
+ align:start position:0%
+dominated by your fuel I
+ 
+
+ align:start position:0%
+dominated by your fuel I
+yeah yes so if you start with a neutral
+
+ align:start position:0%
+yeah yes so if you start with a neutral
+ 
+
+ align:start position:0%
+yeah yes so if you start with a neutral
+at the and then it goes into the plasma
+
+ align:start position:0%
+at the and then it goes into the plasma
+ 
+
+ align:start position:0%
+at the and then it goes into the plasma
+4 Char exchange and the new neutral that
+
+ align:start position:0%
+4 Char exchange and the new neutral that
+ 
+
+ align:start position:0%
+4 Char exchange and the new neutral that
+leaks out was an
+
+ align:start position:0%
+leaks out was an
+ 
+
+ align:start position:0%
+leaks out was an
+IR and then you're measuring that Neal
+
+ align:start position:0%
+IR and then you're measuring that Neal
+ 
+
+ align:start position:0%
+IR and then you're measuring that Neal
+out how do you know that you're only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measuring yeah so the question how do we
+
+ align:start position:0%
+measuring yeah so the question how do we
+ 
+
+ align:start position:0%
+measuring yeah so the question how do we
+know that none of our signal is due to
+
+ align:start position:0%
+know that none of our signal is due to
+ 
+
+ align:start position:0%
+know that none of our signal is due to
+the neutrals at the edge well the
+
+ align:start position:0%
+the neutrals at the edge well the
+ 
+
+ align:start position:0%
+the neutrals at the edge well the
+neutrals at the edge are very cold so
+
+ align:start position:0%
+neutrals at the edge are very cold so
+ 
+
+ align:start position:0%
+neutrals at the edge are very cold so
+their energy is very low so we probably
+
+ align:start position:0%
+their energy is very low so we probably
+ 
+
+ align:start position:0%
+their energy is very low so we probably
+will have a Spectra that looks like this
+
+ align:start position:0%
+will have a Spectra that looks like this
+ 
+
+ align:start position:0%
+will have a Spectra that looks like this
+or something with some noise up here or
+
+ align:start position:0%
+or something with some noise up here or
+ 
+
+ align:start position:0%
+or something with some noise up here or
+some some spous signal that's due to
+
+ align:start position:0%
+some some spous signal that's due to
+ 
+
+ align:start position:0%
+some some spous signal that's due to
+other neutrals in the system so I'll
+
+ align:start position:0%
+other neutrals in the system so I'll
+ 
+
+ align:start position:0%
+other neutrals in the system so I'll
+just start my fit at some nice high
+
+ align:start position:0%
+just start my fit at some nice high
+ 
+
+ align:start position:0%
+just start my fit at some nice high
+energy which can't be due to any of
+
+ align:start position:0%
+energy which can't be due to any of
+ 
+
+ align:start position:0%
+energy which can't be due to any of
+these uh cold ions or cold neutrals from
+
+ align:start position:0%
+these uh cold ions or cold neutrals from
+ 
+
+ align:start position:0%
+these uh cold ions or cold neutrals from
+The Edge has to just be due to the core
+
+ align:start position:0%
+The Edge has to just be due to the core
+ 
+
+ align:start position:0%
+The Edge has to just be due to the core
+ions
+
+ align:start position:0%
+ions
+ 
+
+ align:start position:0%
+ions
+instead okay any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so I mean that that's what's
+
+ align:start position:0%
+yeah yeah so I mean that that's what's
+ 
+
+ align:start position:0%
+yeah yeah so I mean that that's what's
+very challenging about this here because
+
+ align:start position:0%
+very challenging about this here because
+ 
+
+ align:start position:0%
+very challenging about this here because
+in fact this will be like the sum of a
+
+ align:start position:0%
+in fact this will be like the sum of a
+ 
+
+ align:start position:0%
+in fact this will be like the sum of a
+load of lines which will be weighted by
+
+ align:start position:0%
+load of lines which will be weighted by
+ 
+
+ align:start position:0%
+load of lines which will be weighted by
+their density so I think it is difficult
+
+ align:start position:0%
+their density so I think it is difficult
+ 
+
+ align:start position:0%
+their density so I think it is difficult
+to interpret the passive version of it
+
+ align:start position:0%
+to interpret the passive version of it
+ 
+
+ align:start position:0%
+to interpret the passive version of it
+of course if you go high enough out in
+
+ align:start position:0%
+of course if you go high enough out in
+ 
+
+ align:start position:0%
+of course if you go high enough out in
+energy and you can still fit a bit of a
+
+ align:start position:0%
+energy and you can still fit a bit of a
+ 
+
+ align:start position:0%
+energy and you can still fit a bit of a
+straight line you can be like there is
+
+ align:start position:0%
+straight line you can be like there is
+ 
+
+ align:start position:0%
+straight line you can be like there is
+some part of my plasma right because
+
+ align:start position:0%
+some part of my plasma right because
+ 
+
+ align:start position:0%
+some part of my plasma right because
+you'll have different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slopes and there'll only be one slope
+
+ align:start position:0%
+slopes and there'll only be one slope
+ 
+
+ align:start position:0%
+slopes and there'll only be one slope
+that still extends all the way out here
+
+ align:start position:0%
+that still extends all the way out here
+ 
+
+ align:start position:0%
+that still extends all the way out here
+because each of these will eventually
+
+ align:start position:0%
+because each of these will eventually
+ 
+
+ align:start position:0%
+because each of these will eventually
+sort of drop off so if you're like aha
+
+ align:start position:0%
+sort of drop off so if you're like aha
+ 
+
+ align:start position:0%
+sort of drop off so if you're like aha
+still out here there's some region then
+
+ align:start position:0%
+still out here there's some region then
+ 
+
+ align:start position:0%
+still out here there's some region then
+that's probably your core ISS so you
+
+ align:start position:0%
+that's probably your core ISS so you
+ 
+
+ align:start position:0%
+that's probably your core ISS so you
+might have a chance of identifying but
+
+ align:start position:0%
+might have a chance of identifying but
+ 
+
+ align:start position:0%
+might have a chance of identifying but
+in general your signal look more comp
+
+ align:start position:0%
+in general your signal look more comp
+ 
+
+ align:start position:0%
+in general your signal look more comp
+which leads me very neatly onto using a
+
+ align:start position:0%
+which leads me very neatly onto using a
+ 
+
+ align:start position:0%
+which leads me very neatly onto using a
+neutral beam you do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead so this actually is very similar
+
+ align:start position:0%
+instead so this actually is very similar
+ 
+
+ align:start position:0%
+instead so this actually is very similar
+to some of those active spectroscopy
+
+ align:start position:0%
+to some of those active spectroscopy
+ 
+
+ align:start position:0%
+to some of those active spectroscopy
+Diagnostics we talked about before we've
+
+ align:start position:0%
+Diagnostics we talked about before we've
+ 
+
+ align:start position:0%
+Diagnostics we talked about before we've
+again got our vacuum chamber under our
+
+ align:start position:0%
+again got our vacuum chamber under our
+ 
+
+ align:start position:0%
+again got our vacuum chamber under our
+plasma like this but now we have a
+
+ align:start position:0%
+plasma like this but now we have a
+ 
+
+ align:start position:0%
+plasma like this but now we have a
+neutral beam going through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma and if we have our detector
+
+ align:start position:0%
+plasma and if we have our detector
+ 
+
+ align:start position:0%
+plasma and if we have our detector
+oriented perpendicularly for
+
+ align:start position:0%
+oriented perpendicularly for
+ 
+
+ align:start position:0%
+oriented perpendicularly for
+this now we know that the majority of
+
+ align:start position:0%
+this now we know that the majority of
+ 
+
+ align:start position:0%
+this now we know that the majority of
+the neutrals are being born by charge
+
+ align:start position:0%
+the neutrals are being born by charge
+ 
+
+ align:start position:0%
+the neutrals are being born by charge
+exchange between the neutral beam and
+
+ align:start position:0%
+exchange between the neutral beam and
+ 
+
+ align:start position:0%
+exchange between the neutral beam and
+this small core region here which
+
+ align:start position:0%
+this small core region here which
+ 
+
+ align:start position:0%
+this small core region here which
+overlaps the field of view of our
+
+ align:start position:0%
+overlaps the field of view of our
+ 
+
+ align:start position:0%
+overlaps the field of view of our
+detector and the neutral beam
+
+ align:start position:0%
+detector and the neutral beam
+ 
+
+ align:start position:0%
+detector and the neutral beam
+here and so now we know very well when
+
+ align:start position:0%
+here and so now we know very well when
+ 
+
+ align:start position:0%
+here and so now we know very well when
+these particles come
+
+ align:start position:0%
+these particles come
+ 
+
+ align:start position:0%
+these particles come
+out that we are detecting F ofi VI are
+
+ align:start position:0%
+out that we are detecting F ofi VI are
+ 
+
+ align:start position:0%
+out that we are detecting F ofi VI are
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+zero from the core here so this allows
+
+ align:start position:0%
+zero from the core here so this allows
+ 
+
+ align:start position:0%
+zero from the core here so this allows
+us to actively Pro That central region
+
+ align:start position:0%
+us to actively Pro That central region
+ 
+
+ align:start position:0%
+us to actively Pro That central region
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+localizes
+
+ align:start position:0%
+localizes
+ 
+
+ align:start position:0%
+localizes
+um and this is often convenient because
+
+ align:start position:0%
+um and this is often convenient because
+ 
+
+ align:start position:0%
+um and this is often convenient because
+we often have neutral beams as we said
+
+ align:start position:0%
+we often have neutral beams as we said
+ 
+
+ align:start position:0%
+we often have neutral beams as we said
+these neutral beams are already being
+
+ align:start position:0%
+these neutral beams are already being
+ 
+
+ align:start position:0%
+these neutral beams are already being
+used for
+
+ align:start position:0%
+used for
+ 
+
+ align:start position:0%
+used for
+heating and
+
+ align:start position:0%
+heating and
+ 
+
+ align:start position:0%
+heating and
+for current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Drive of course the neutral beam has the
+
+ align:start position:0%
+Drive of course the neutral beam has the
+ 
+
+ align:start position:0%
+Drive of course the neutral beam has the
+same problem uh that we found out when
+
+ align:start position:0%
+same problem uh that we found out when
+ 
+
+ align:start position:0%
+same problem uh that we found out when
+we were talking about how far these
+
+ align:start position:0%
+we were talking about how far these
+ 
+
+ align:start position:0%
+we were talking about how far these
+neutrals can penetrate if you have a
+
+ align:start position:0%
+neutrals can penetrate if you have a
+ 
+
+ align:start position:0%
+neutrals can penetrate if you have a
+density that's high enough inside your
+
+ align:start position:0%
+density that's high enough inside your
+ 
+
+ align:start position:0%
+density that's high enough inside your
+machine you're not going to be able to
+
+ align:start position:0%
+machine you're not going to be able to
+ 
+
+ align:start position:0%
+machine you're not going to be able to
+use a neutral beam to heat Al new
+
+ align:start position:0%
+use a neutral beam to heat Al new
+ 
+
+ align:start position:0%
+use a neutral beam to heat Al new
+current driv so beams tend to be limited
+
+ align:start position:0%
+current driv so beams tend to be limited
+ 
+
+ align:start position:0%
+current driv so beams tend to be limited
+to lower density machines which is why
+
+ align:start position:0%
+to lower density machines which is why
+ 
+
+ align:start position:0%
+to lower density machines which is why
+we've never had much use for them on
+
+ align:start position:0%
+we've never had much use for them on
+ 
+
+ align:start position:0%
+we've never had much use for them on
+devices like cod where the magnetic
+
+ align:start position:0%
+devices like cod where the magnetic
+ 
+
+ align:start position:0%
+devices like cod where the magnetic
+field in the density is very very high
+
+ align:start position:0%
+field in the density is very very high
+ 
+
+ align:start position:0%
+field in the density is very very high
+but for other devices you may well have
+
+ align:start position:0%
+but for other devices you may well have
+ 
+
+ align:start position:0%
+but for other devices you may well have
+a neutral beam already there so this is
+
+ align:start position:0%
+a neutral beam already there so this is
+ 
+
+ align:start position:0%
+a neutral beam already there so this is
+again kind of a freebie to have this as
+
+ align:start position:0%
+again kind of a freebie to have this as
+ 
+
+ align:start position:0%
+again kind of a freebie to have this as
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagnostic okay let's talk about some
+
+ align:start position:0%
+diagnostic okay let's talk about some
+ 
+
+ align:start position:0%
+diagnostic okay let's talk about some
+other things you can do with uh a
+
+ align:start position:0%
+other things you can do with uh a
+ 
+
+ align:start position:0%
+other things you can do with uh a
+neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam so there's a very nice technique
+
+ align:start position:0%
+beam so there's a very nice technique
+ 
+
+ align:start position:0%
+beam so there's a very nice technique
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called my green there we
+
+ align:start position:0%
+called my green there we
+ 
+
+ align:start position:0%
+called my green there we
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectroscopy this technique has
+
+ align:start position:0%
+spectroscopy this technique has
+ 
+
+ align:start position:0%
+spectroscopy this technique has
+developed a number of acronyms in the
+
+ align:start position:0%
+developed a number of acronyms in the
+ 
+
+ align:start position:0%
+developed a number of acronyms in the
+literature which are all uh identical in
+
+ align:start position:0%
+literature which are all uh identical in
+ 
+
+ align:start position:0%
+literature which are all uh identical in
+meaning so some people call it charge
+
+ align:start position:0%
+meaning so some people call it charge
+ 
+
+ align:start position:0%
+meaning so some people call it charge
+exchange re com ation spectroscopy and
+
+ align:start position:0%
+exchange re com ation spectroscopy and
+ 
+
+ align:start position:0%
+exchange re com ation spectroscopy and
+some people call it charge exchange
+
+ align:start position:0%
+some people call it charge exchange
+ 
+
+ align:start position:0%
+some people call it charge exchange
+recombination spectroscopy so if you see
+
+ align:start position:0%
+recombination spectroscopy so if you see
+ 
+
+ align:start position:0%
+recombination spectroscopy so if you see
+an acronym that looks something like
+
+ align:start position:0%
+an acronym that looks something like
+ 
+
+ align:start position:0%
+an acronym that looks something like
+this they're probably talking about the
+
+ align:start position:0%
+this they're probably talking about the
+ 
+
+ align:start position:0%
+this they're probably talking about the
+same diagnostic these are not two
+
+ align:start position:0%
+same diagnostic these are not two
+ 
+
+ align:start position:0%
+same diagnostic these are not two
+separate Diagnostics they are the same
+
+ align:start position:0%
+separate Diagnostics they are the same
+ 
+
+ align:start position:0%
+separate Diagnostics they are the same
+thing here um so the idea of charge
+
+ align:start position:0%
+thing here um so the idea of charge
+ 
+
+ align:start position:0%
+thing here um so the idea of charge
+exchange recombination spectroscopy is
+
+ align:start position:0%
+exchange recombination spectroscopy is
+ 
+
+ align:start position:0%
+exchange recombination spectroscopy is
+within our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma we will have some neutrals oh
+
+ align:start position:0%
+plasma we will have some neutrals oh
+ 
+
+ align:start position:0%
+plasma we will have some neutrals oh
+sorry we will have some ions which are
+
+ align:start position:0%
+sorry we will have some ions which are
+ 
+
+ align:start position:0%
+sorry we will have some ions which are
+impurity ions sorry so an impurity like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a we'll just use a symbol a I'll make it
+
+ align:start position:0%
+a we'll just use a symbol a I'll make it
+ 
+
+ align:start position:0%
+a we'll just use a symbol a I'll make it
+clear what it is in a moment these
+
+ align:start position:0%
+clear what it is in a moment these
+ 
+
+ align:start position:0%
+clear what it is in a moment these
+impurities will things like oxygen or
+
+ align:start position:0%
+impurities will things like oxygen or
+ 
+
+ align:start position:0%
+impurities will things like oxygen or
+carbon or Boron and although these
+
+ align:start position:0%
+carbon or Boron and although these
+ 
+
+ align:start position:0%
+carbon or Boron and although these
+impurities have many more electrons than
+
+ align:start position:0%
+impurities have many more electrons than
+ 
+
+ align:start position:0%
+impurities have many more electrons than
+hydrogen um they are in the center of
+
+ align:start position:0%
+hydrogen um they are in the center of
+ 
+
+ align:start position:0%
+hydrogen um they are in the center of
+the machine probably fully stripped
+
+ align:start position:0%
+the machine probably fully stripped
+ 
+
+ align:start position:0%
+the machine probably fully stripped
+they've lost all of their electrons so
+
+ align:start position:0%
+they've lost all of their electrons so
+ 
+
+ align:start position:0%
+they've lost all of their electrons so
+they no longer can produce any line so
+
+ align:start position:0%
+they no longer can produce any line so
+ 
+
+ align:start position:0%
+they no longer can produce any line so
+we can't detect their presence in the
+
+ align:start position:0%
+we can't detect their presence in the
+ 
+
+ align:start position:0%
+we can't detect their presence in the
+machine so we don't know where these
+
+ align:start position:0%
+machine so we don't know where these
+ 
+
+ align:start position:0%
+machine so we don't know where these
+impurities are so the idea of charge
+
+ align:start position:0%
+impurities are so the idea of charge
+ 
+
+ align:start position:0%
+impurities are so the idea of charge
+exchange recombination spectroscopy is
+
+ align:start position:0%
+exchange recombination spectroscopy is
+ 
+
+ align:start position:0%
+exchange recombination spectroscopy is
+we put our neutral beam through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+machine and we end up uh charge
+
+ align:start position:0%
+machine and we end up uh charge
+ 
+
+ align:start position:0%
+machine and we end up uh charge
+exchanging on these impurities so we
+
+ align:start position:0%
+exchanging on these impurities so we
+ 
+
+ align:start position:0%
+exchanging on these impurities so we
+have some neutral beam uh and some
+
+ align:start position:0%
+have some neutral beam uh and some
+ 
+
+ align:start position:0%
+have some neutral beam uh and some
+impurity in a
+
+ align:start position:0%
+impurity in a
+ 
+
+ align:start position:0%
+impurity in a
+state Z Plus where it's ionized Z times
+
+ align:start position:0%
+state Z Plus where it's ionized Z times
+ 
+
+ align:start position:0%
+state Z Plus where it's ionized Z times
+and this charge exchanges and gives us a
+
+ align:start position:0%
+and this charge exchanges and gives us a
+ 
+
+ align:start position:0%
+and this charge exchanges and gives us a
+neutral beam ion
+
+ align:start position:0%
+neutral beam ion
+ 
+
+ align:start position:0%
+neutral beam ion
+plus an impurity in a state Z minus one
+
+ align:start position:0%
+plus an impurity in a state Z minus one
+ 
+
+ align:start position:0%
+plus an impurity in a state Z minus one
+plus and most importantly it's likely
+
+ align:start position:0%
+plus and most importantly it's likely
+ 
+
+ align:start position:0%
+plus and most importantly it's likely
+that the impurity will end up in an
+
+ align:start position:0%
+that the impurity will end up in an
+ 
+
+ align:start position:0%
+that the impurity will end up in an
+excited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state so then our impurity which is in
+
+ align:start position:0%
+state so then our impurity which is in
+ 
+
+ align:start position:0%
+state so then our impurity which is in
+some excited state it will spontaneously
+
+ align:start position:0%
+some excited state it will spontaneously
+ 
+
+ align:start position:0%
+some excited state it will spontaneously
+Decay down and we'll get out a photon
+
+ align:start position:0%
+Decay down and we'll get out a photon
+ 
+
+ align:start position:0%
+Decay down and we'll get out a photon
+like that and because this Photon will
+
+ align:start position:0%
+like that and because this Photon will
+ 
+
+ align:start position:0%
+like that and because this Photon will
+have a characteristic energy that we're
+
+ align:start position:0%
+have a characteristic energy that we're
+ 
+
+ align:start position:0%
+have a characteristic energy that we're
+looking for with our spectrometer we can
+
+ align:start position:0%
+looking for with our spectrometer we can
+ 
+
+ align:start position:0%
+looking for with our spectrometer we can
+say aha this is from an
+
+ align:start position:0%
+say aha this is from an
+ 
+
+ align:start position:0%
+say aha this is from an
+impurity and now the invisible
+
+ align:start position:0%
+impurity and now the invisible
+ 
+
+ align:start position:0%
+impurity and now the invisible
+impurities are visible
+
+ align:start position:0%
+impurities are visible
+ 
+
+ align:start position:0%
+impurities are visible
+again so there are a few things that we
+
+ align:start position:0%
+again so there are a few things that we
+ 
+
+ align:start position:0%
+again so there are a few things that we
+can measure from charge exchange
+
+ align:start position:0%
+can measure from charge exchange
+ 
+
+ align:start position:0%
+can measure from charge exchange
+recombination spectroscopy we can
+
+ align:start position:0%
+recombination spectroscopy we can
+ 
+
+ align:start position:0%
+recombination spectroscopy we can
+measure the density of impurities from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+so you need sum Atomic models and you
+
+ align:start position:0%
+so you need sum Atomic models and you
+ 
+
+ align:start position:0%
+so you need sum Atomic models and you
+need an absolute calibration for your
+
+ align:start position:0%
+need an absolute calibration for your
+ 
+
+ align:start position:0%
+need an absolute calibration for your
+detector but you can work out the
+
+ align:start position:0%
+detector but you can work out the
+ 
+
+ align:start position:0%
+detector but you can work out the
+density of these impurities that's
+
+ align:start position:0%
+density of these impurities that's
+ 
+
+ align:start position:0%
+density of these impurities that's
+pretty useful we can also measure TI and
+
+ align:start position:0%
+pretty useful we can also measure TI and
+ 
+
+ align:start position:0%
+pretty useful we can also measure TI and
+V flow from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Doppler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broadening and the doler shift
+
+ align:start position:0%
+broadening and the doler shift
+ 
+
+ align:start position:0%
+broadening and the doler shift
+respectively so as we discussed in the
+
+ align:start position:0%
+respectively so as we discussed in the
+ 
+
+ align:start position:0%
+respectively so as we discussed in the
+spectroscopy you weeks ago or a week ago
+
+ align:start position:0%
+spectroscopy you weeks ago or a week ago
+ 
+
+ align:start position:0%
+spectroscopy you weeks ago or a week ago
+when we're talking about different
+
+ align:start position:0%
+when we're talking about different
+ 
+
+ align:start position:0%
+when we're talking about different
+broadening mechanisms uh these
+
+ align:start position:0%
+broadening mechanisms uh these
+ 
+
+ align:start position:0%
+broadening mechanisms uh these
+effectively can be the impurities which
+
+ align:start position:0%
+effectively can be the impurities which
+ 
+
+ align:start position:0%
+effectively can be the impurities which
+are acting as a tracer for the flow
+
+ align:start position:0%
+are acting as a tracer for the flow
+ 
+
+ align:start position:0%
+are acting as a tracer for the flow
+velocity so like our bulk motion of the
+
+ align:start position:0%
+velocity so like our bulk motion of the
+ 
+
+ align:start position:0%
+velocity so like our bulk motion of the
+entire plasma around the Taurus and for
+
+ align:start position:0%
+entire plasma around the Taurus and for
+ 
+
+ align:start position:0%
+entire plasma around the Taurus and for
+the temperature and again the reason is
+
+ align:start position:0%
+the temperature and again the reason is
+ 
+
+ align:start position:0%
+the temperature and again the reason is
+that uh maybe you could r on an impurity
+
+ align:start position:0%
+that uh maybe you could r on an impurity
+ 
+
+ align:start position:0%
+that uh maybe you could r on an impurity
+that was very high Z and still had some
+
+ align:start position:0%
+that was very high Z and still had some
+ 
+
+ align:start position:0%
+that was very high Z and still had some
+electrons left but if you done a really
+
+ align:start position:0%
+electrons left but if you done a really
+ 
+
+ align:start position:0%
+electrons left but if you done a really
+good job of reducing all of the tonsen
+
+ align:start position:0%
+good job of reducing all of the tonsen
+ 
+
+ align:start position:0%
+good job of reducing all of the tonsen
+and nasty things in your machine and all
+
+ align:start position:0%
+and nasty things in your machine and all
+ 
+
+ align:start position:0%
+and nasty things in your machine and all
+your left is oxygen carbon and Boron uh
+
+ align:start position:0%
+your left is oxygen carbon and Boron uh
+ 
+
+ align:start position:0%
+your left is oxygen carbon and Boron uh
+then you need to effectively give them
+
+ align:start position:0%
+then you need to effectively give them
+ 
+
+ align:start position:0%
+then you need to effectively give them
+back an electrons so you can do
+
+ align:start position:0%
+back an electrons so you can do
+ 
+
+ align:start position:0%
+back an electrons so you can do
+spectroscopy on them and again this is a
+
+ align:start position:0%
+spectroscopy on them and again this is a
+ 
+
+ align:start position:0%
+spectroscopy on them and again this is a
+nice active diagnostic because you can
+
+ align:start position:0%
+nice active diagnostic because you can
+ 
+
+ align:start position:0%
+nice active diagnostic because you can
+localize the region where you know the
+
+ align:start position:0%
+localize the region where you know the
+ 
+
+ align:start position:0%
+localize the region where you know the
+particles are sitting in by putting your
+
+ align:start position:0%
+particles are sitting in by putting your
+ 
+
+ align:start position:0%
+particles are sitting in by putting your
+spectrometer perpendicular to the line
+
+ align:start position:0%
+spectrometer perpendicular to the line
+ 
+
+ align:start position:0%
+spectrometer perpendicular to the line
+of sight of your neutral
+
+ align:start position:0%
+of sight of your neutral
+ 
+
+ align:start position:0%
+of sight of your neutral
+beam and
+
+ align:start position:0%
+beam and
+ 
+
+ align:start position:0%
+beam and
+again you can localize it flat region
+
+ align:start position:0%
+again you can localize it flat region
+ 
+
+ align:start position:0%
+again you can localize it flat region
+here so this gives you these two and
+
+ align:start position:0%
+here so this gives you these two and
+ 
+
+ align:start position:0%
+here so this gives you these two and
+they're all localized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measurements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there there are can be problems with
+
+ align:start position:0%
+um there there are can be problems with
+ 
+
+ align:start position:0%
+um there there are can be problems with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um so one issue is you get uh charge
+
+ align:start position:0%
+um so one issue is you get uh charge
+ 
+
+ align:start position:0%
+um so one issue is you get uh charge
+exchange with Edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impurities I know I said this
+
+ align:start position:0%
+impurities I know I said this
+ 
+
+ align:start position:0%
+impurities I know I said this
+measurement localizes this but you could
+
+ align:start position:0%
+measurement localizes this but you could
+ 
+
+ align:start position:0%
+measurement localizes this but you could
+imagine that you could get light
+
+ align:start position:0%
+imagine that you could get light
+ 
+
+ align:start position:0%
+imagine that you could get light
+reflecting from here fill back down into
+
+ align:start position:0%
+reflecting from here fill back down into
+ 
+
+ align:start position:0%
+reflecting from here fill back down into
+your detector and you can also just have
+
+ align:start position:0%
+your detector and you can also just have
+ 
+
+ align:start position:0%
+your detector and you can also just have
+background so something like Ram stong
+
+ align:start position:0%
+background so something like Ram stong
+ 
+
+ align:start position:0%
+background so something like Ram stong
+radiation at this Photon energy and
+
+ align:start position:0%
+radiation at this Photon energy and
+ 
+
+ align:start position:0%
+radiation at this Photon energy and
+because there's not so many impurities
+
+ align:start position:0%
+because there's not so many impurities
+ 
+
+ align:start position:0%
+because there's not so many impurities
+we hope and not so many of them are
+
+ align:start position:0%
+we hope and not so many of them are
+ 
+
+ align:start position:0%
+we hope and not so many of them are
+charging exchanging neutral beam the
+
+ align:start position:0%
+charging exchanging neutral beam the
+ 
+
+ align:start position:0%
+charging exchanging neutral beam the
+signal could be relatively weak so this
+
+ align:start position:0%
+signal could be relatively weak so this
+ 
+
+ align:start position:0%
+signal could be relatively weak so this
+brem ston at that uh the the photon
+
+ align:start position:0%
+brem ston at that uh the the photon
+ 
+
+ align:start position:0%
+brem ston at that uh the the photon
+energy of the charge exchange with
+
+ align:start position:0%
+energy of the charge exchange with
+ 
+
+ align:start position:0%
+energy of the charge exchange with
+impurities that could be a significant
+
+ align:start position:0%
+impurities that could be a significant
+ 
+
+ align:start position:0%
+impurities that could be a significant
+uh amount so we may not be able to see
+
+ align:start position:0%
+uh amount so we may not be able to see
+ 
+
+ align:start position:0%
+uh amount so we may not be able to see
+this signal very clearly so a really
+
+ align:start position:0%
+this signal very clearly so a really
+ 
+
+ align:start position:0%
+this signal very clearly so a really
+neat trick that you can
+
+ align:start position:0%
+neat trick that you can
+ 
+
+ align:start position:0%
+neat trick that you can
+do is to modulate the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be so you
+
+ align:start position:0%
+be so you
+ 
+
+ align:start position:0%
+be so you
+take the intensity of your neutral beam
+
+ align:start position:0%
+take the intensity of your neutral beam
+ 
+
+ align:start position:0%
+take the intensity of your neutral beam
+and you just turn it on and
+
+ align:start position:0%
+and you just turn it on and
+ 
+
+ align:start position:0%
+and you just turn it on and
+off like that and then when you look at
+
+ align:start position:0%
+off like that and then when you look at
+ 
+
+ align:start position:0%
+off like that and then when you look at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+intensity at this specific wavelength
+
+ align:start position:0%
+intensity at this specific wavelength
+ 
+
+ align:start position:0%
+intensity at this specific wavelength
+that you're on the lookout for you
+
+ align:start position:0%
+that you're on the lookout for you
+ 
+
+ align:start position:0%
+that you're on the lookout for you
+should see that there's maybe some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+background but that background is being
+
+ align:start position:0%
+background but that background is being
+ 
+
+ align:start position:0%
+background but that background is being
+modulated by the neutral beam and then
+
+ align:start position:0%
+modulated by the neutral beam and then
+ 
+
+ align:start position:0%
+modulated by the neutral beam and then
+you can do tricks with like phase lock
+
+ align:start position:0%
+you can do tricks with like phase lock
+ 
+
+ align:start position:0%
+you can do tricks with like phase lock
+loops and all your other favorite for
+
+ align:start position:0%
+loops and all your other favorite for
+ 
+
+ align:start position:0%
+loops and all your other favorite for
+transform techniques and you can isolate
+
+ align:start position:0%
+transform techniques and you can isolate
+ 
+
+ align:start position:0%
+transform techniques and you can isolate
+out which part of this signal is
+
+ align:start position:0%
+out which part of this signal is
+ 
+
+ align:start position:0%
+out which part of this signal is
+actually due
+
+ align:start position:0%
+actually due
+ 
+
+ align:start position:0%
+actually due
+to exchange and which part of the signal
+
+ align:start position:0%
+to exchange and which part of the signal
+ 
+
+ align:start position:0%
+to exchange and which part of the signal
+is due to
+
+ align:start position:0%
+is due to
+ 
+
+ align:start position:0%
+is due to
+RS that's pretty neat okay questions on
+
+ align:start position:0%
+RS that's pretty neat okay questions on
+ 
+
+ align:start position:0%
+RS that's pretty neat okay questions on
+CH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theoretically we have just a single line
+
+ align:start position:0%
+theoretically we have just a single line
+ 
+
+ align:start position:0%
+theoretically we have just a single line
+like this if all the particles were
+
+ align:start position:0%
+like this if all the particles were
+ 
+
+ align:start position:0%
+like this if all the particles were
+stationary and uh the temperature was
+
+ align:start position:0%
+stationary and uh the temperature was
+ 
+
+ align:start position:0%
+stationary and uh the temperature was
+Zero all the particles moving at the
+
+ align:start position:0%
+Zero all the particles moving at the
+ 
+
+ align:start position:0%
+Zero all the particles moving at the
+same speed and we just have a line at
+
+ align:start position:0%
+same speed and we just have a line at
+ 
+
+ align:start position:0%
+same speed and we just have a line at
+Omega 0 if all the particles are moving
+
+ align:start position:0%
+Omega 0 if all the particles are moving
+ 
+
+ align:start position:0%
+Omega 0 if all the particles are moving
+in the same direction this will be
+
+ align:start position:0%
+in the same direction this will be
+ 
+
+ align:start position:0%
+in the same direction this will be
+Doppler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shifted and that Doppler shift will be P
+
+ align:start position:0%
+shifted and that Doppler shift will be P
+ 
+
+ align:start position:0%
+shifted and that Doppler shift will be P
+doted into the flow velocity and if we
+
+ align:start position:0%
+doted into the flow velocity and if we
+ 
+
+ align:start position:0%
+doted into the flow velocity and if we
+have some broadening on top of that
+
+ align:start position:0%
+have some broadening on top of that
+ 
+
+ align:start position:0%
+have some broadening on top of that
+because we've got nonzero temperature
+
+ align:start position:0%
+because we've got nonzero temperature
+ 
+
+ align:start position:0%
+because we've got nonzero temperature
+some of the particles although they're
+
+ align:start position:0%
+some of the particles although they're
+ 
+
+ align:start position:0%
+some of the particles although they're
+all moving in One Direction some of them
+
+ align:start position:0%
+all moving in One Direction some of them
+ 
+
+ align:start position:0%
+all moving in One Direction some of them
+moving back a little bit and some are
+
+ align:start position:0%
+moving back a little bit and some are
+ 
+
+ align:start position:0%
+moving back a little bit and some are
+moving forwards and then the width of
+
+ align:start position:0%
+moving forwards and then the width of
+ 
+
+ align:start position:0%
+moving forwards and then the width of
+this feature full width of half maximum
+
+ align:start position:0%
+this feature full width of half maximum
+ 
+
+ align:start position:0%
+this feature full width of half maximum
+is proportional to vtii which is square
+
+ align:start position:0%
+is proportional to vtii which is square
+ 
+
+ align:start position:0%
+is proportional to vtii which is square
+root of temperature so you measure the
+
+ align:start position:0%
+root of temperature so you measure the
+ 
+
+ align:start position:0%
+root of temperature so you measure the
+shift of the feature and the broading of
+
+ align:start position:0%
+shift of the feature and the broading of
+ 
+
+ align:start position:0%
+shift of the feature and the broading of
+the feature that gives you the velocity
+
+ align:start position:0%
+the feature that gives you the velocity
+ 
+
+ align:start position:0%
+the feature that gives you the velocity
+and the temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topic there are yet more fun things you
+
+ align:start position:0%
+topic there are yet more fun things you
+ 
+
+ align:start position:0%
+topic there are yet more fun things you
+can do with a neutral beam who would
+
+ align:start position:0%
+can do with a neutral beam who would
+ 
+
+ align:start position:0%
+can do with a neutral beam who would
+have thought
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next one thing you can do as a neutral
+
+ align:start position:0%
+next one thing you can do as a neutral
+ 
+
+ align:start position:0%
+next one thing you can do as a neutral
+beam is something called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectroscopy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bees the idea here once again vacuum
+
+ align:start position:0%
+bees the idea here once again vacuum
+ 
+
+ align:start position:0%
+bees the idea here once again vacuum
+chamber
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam as the beam goes through the plasma
+
+ align:start position:0%
+beam as the beam goes through the plasma
+ 
+
+ align:start position:0%
+beam as the beam goes through the plasma
+remember our beam is going to be
+
+ align:start position:0%
+remember our beam is going to be
+ 
+
+ align:start position:0%
+remember our beam is going to be
+hydrogen or uterum or something like
+
+ align:start position:0%
+hydrogen or uterum or something like
+ 
+
+ align:start position:0%
+hydrogen or uterum or something like
+that the neutrals inside here and these
+
+ align:start position:0%
+that the neutrals inside here and these
+ 
+
+ align:start position:0%
+that the neutrals inside here and these
+are all neutrals so I'll just put a
+
+ align:start position:0%
+are all neutrals so I'll just put a
+ 
+
+ align:start position:0%
+are all neutrals so I'll just put a
+little zero to remind ourselves they're
+
+ align:start position:0%
+little zero to remind ourselves they're
+ 
+
+ align:start position:0%
+little zero to remind ourselves they're
+neutrals um will have some glancing
+
+ align:start position:0%
+neutrals um will have some glancing
+ 
+
+ align:start position:0%
+neutrals um will have some glancing
+collisions of the electrons and ions not
+
+ align:start position:0%
+collisions of the electrons and ions not
+ 
+
+ align:start position:0%
+collisions of the electrons and ions not
+enough to ionize them some of the
+
+ align:start position:0%
+enough to ionize them some of the
+ 
+
+ align:start position:0%
+enough to ionize them some of the
+collisions will ionize them but some of
+
+ align:start position:0%
+collisions will ionize them but some of
+ 
+
+ align:start position:0%
+collisions will ionize them but some of
+the collisions will be enough to excite
+
+ align:start position:0%
+the collisions will be enough to excite
+ 
+
+ align:start position:0%
+the collisions will be enough to excite
+these right and so we'll end up inside
+
+ align:start position:0%
+these right and so we'll end up inside
+ 
+
+ align:start position:0%
+these right and so we'll end up inside
+our Beam with excited neutral hydrogen
+
+ align:start position:0%
+our Beam with excited neutral hydrogen
+ 
+
+ align:start position:0%
+our Beam with excited neutral hydrogen
+and excited neutral uterum or something
+
+ align:start position:0%
+and excited neutral uterum or something
+ 
+
+ align:start position:0%
+and excited neutral uterum or something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that and we can then put our
+
+ align:start position:0%
+that and we can then put our
+ 
+
+ align:start position:0%
+that and we can then put our
+spectrometer down here or our detector
+
+ align:start position:0%
+spectrometer down here or our detector
+ 
+
+ align:start position:0%
+spectrometer down here or our detector
+down here and we can look for the
+
+ align:start position:0%
+down here and we can look for the
+ 
+
+ align:start position:0%
+down here and we can look for the
+characteristic I actually have some
+
+ align:start position:0%
+characteristic I actually have some
+ 
+
+ align:start position:0%
+characteristic I actually have some
+drawings of
+
+ align:start position:0%
+drawings of
+ 
+
+ align:start position:0%
+drawings of
+this no okay we can look for these
+
+ align:start position:0%
+this no okay we can look for these
+ 
+
+ align:start position:0%
+this no okay we can look for these
+characteristic uh decays here and if you
+
+ align:start position:0%
+characteristic uh decays here and if you
+ 
+
+ align:start position:0%
+characteristic uh decays here and if you
+remember before we we talked about the
+
+ align:start position:0%
+remember before we we talked about the
+ 
+
+ align:start position:0%
+remember before we we talked about the
+Lyman Alpha and beta and the balma
+
+ align:start position:0%
+Lyman Alpha and beta and the balma
+ 
+
+ align:start position:0%
+Lyman Alpha and beta and the balma
+series as well so we know very well
+
+ align:start position:0%
+series as well so we know very well
+ 
+
+ align:start position:0%
+series as well so we know very well
+defined what these uh energies of the
+
+ align:start position:0%
+defined what these uh energies of the
+ 
+
+ align:start position:0%
+defined what these uh energies of the
+photons coming out are going to be now
+
+ align:start position:0%
+photons coming out are going to be now
+ 
+
+ align:start position:0%
+photons coming out are going to be now
+the neat thing about this is the
+
+ align:start position:0%
+the neat thing about this is the
+ 
+
+ align:start position:0%
+the neat thing about this is the
+intensity of these
+
+ align:start position:0%
+intensity of these
+ 
+
+ align:start position:0%
+intensity of these
+lines is proportional to or is I'll make
+
+ align:start position:0%
+lines is proportional to or is I'll make
+ 
+
+ align:start position:0%
+lines is proportional to or is I'll make
+it stronger is directly proportional to
+
+ align:start position:0%
+it stronger is directly proportional to
+ 
+
+ align:start position:0%
+it stronger is directly proportional to
+the number of electrons in the plasma
+
+ align:start position:0%
+the number of electrons in the plasma
+ 
+
+ align:start position:0%
+the number of electrons in the plasma
+because this is a collisional excitation
+
+ align:start position:0%
+because this is a collisional excitation
+ 
+
+ align:start position:0%
+because this is a collisional excitation
+process and we know that that is propal
+
+ align:start position:0%
+process and we know that that is propal
+ 
+
+ align:start position:0%
+process and we know that that is propal
+to any and then whatever the
+
+ align:start position:0%
+to any and then whatever the
+ 
+
+ align:start position:0%
+to any and then whatever the
+relevant collisional excitation
+
+ align:start position:0%
+relevant collisional excitation
+ 
+
+ align:start position:0%
+relevant collisional excitation
+crosssection is okay but the main thing
+
+ align:start position:0%
+crosssection is okay but the main thing
+ 
+
+ align:start position:0%
+crosssection is okay but the main thing
+is it's proportional to the
+
+ align:start position:0%
+is it's proportional to the
+ 
+
+ align:start position:0%
+is it's proportional to the
+density so the neat thing is if I now
+
+ align:start position:0%
+density so the neat thing is if I now
+ 
+
+ align:start position:0%
+density so the neat thing is if I now
+have density
+
+ align:start position:0%
+have density
+ 
+
+ align:start position:0%
+have density
+fluctuations so this is we've got some
+
+ align:start position:0%
+fluctuations so this is we've got some
+ 
+
+ align:start position:0%
+fluctuations so this is we've got some
+background density but the density is
+
+ align:start position:0%
+background density but the density is
+ 
+
+ align:start position:0%
+background density but the density is
+fluctuating on top of that so you know
+
+ align:start position:0%
+fluctuating on top of that so you know
+ 
+
+ align:start position:0%
+fluctuating on top of that so you know
+any Z Plus Delta NE of T then that's
+
+ align:start position:0%
+any Z Plus Delta NE of T then that's
+ 
+
+ align:start position:0%
+any Z Plus Delta NE of T then that's
+going to give me
+
+ align:start position:0%
+going to give me
+ 
+
+ align:start position:0%
+going to give me
+an intensity fluctuation as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so by carefully measuring the
+
+ align:start position:0%
+well so by carefully measuring the
+ 
+
+ align:start position:0%
+well so by carefully measuring the
+intensity of these lines and again we
+
+ align:start position:0%
+intensity of these lines and again we
+ 
+
+ align:start position:0%
+intensity of these lines and again we
+can localize this relatively well
+
+ align:start position:0%
+can localize this relatively well
+ 
+
+ align:start position:0%
+can localize this relatively well
+because I have a specific field of view
+
+ align:start position:0%
+because I have a specific field of view
+ 
+
+ align:start position:0%
+because I have a specific field of view
+of my detector and I know where this uh
+
+ align:start position:0%
+of my detector and I know where this uh
+ 
+
+ align:start position:0%
+of my detector and I know where this uh
+beam emission is coming from so I can
+
+ align:start position:0%
+beam emission is coming from so I can
+ 
+
+ align:start position:0%
+beam emission is coming from so I can
+localize it to a little region I could
+
+ align:start position:0%
+localize it to a little region I could
+ 
+
+ align:start position:0%
+localize it to a little region I could
+have multiple detectors and I can have
+
+ align:start position:0%
+have multiple detectors and I can have
+ 
+
+ align:start position:0%
+have multiple detectors and I can have
+another one looking here I can measure
+
+ align:start position:0%
+another one looking here I can measure
+ 
+
+ align:start position:0%
+another one looking here I can measure
+density fluctuations in very precise
+
+ align:start position:0%
+density fluctuations in very precise
+ 
+
+ align:start position:0%
+density fluctuations in very precise
+regions here and density fluctuations
+
+ align:start position:0%
+regions here and density fluctuations
+ 
+
+ align:start position:0%
+regions here and density fluctuations
+are very important especially in
+
+ align:start position:0%
+are very important especially in
+ 
+
+ align:start position:0%
+are very important especially in
+magnetic confinement Fusion because
+
+ align:start position:0%
+magnetic confinement Fusion because
+ 
+
+ align:start position:0%
+magnetic confinement Fusion because
+these fluctuations lead to transport
+
+ align:start position:0%
+these fluctuations lead to transport
+ 
+
+ align:start position:0%
+these fluctuations lead to transport
+turbulent transport so we really really
+
+ align:start position:0%
+turbulent transport so we really really
+ 
+
+ align:start position:0%
+turbulent transport so we really really
+want to be
+
+ align:start position:0%
+want to be
+ 
+
+ align:start position:0%
+want to be
+a um so beam emission spectroscopy I
+
+ align:start position:0%
+a um so beam emission spectroscopy I
+ 
+
+ align:start position:0%
+a um so beam emission spectroscopy I
+think this is the only slide I have on
+
+ align:start position:0%
+think this is the only slide I have on
+ 
+
+ align:start position:0%
+think this is the only slide I have on
+this yes um well I have another one
+
+ align:start position:0%
+this yes um well I have another one
+ 
+
+ align:start position:0%
+this yes um well I have another one
+that's related this is a very cool
+
+ align:start position:0%
+that's related this is a very cool
+ 
+
+ align:start position:0%
+that's related this is a very cool
+technique um the trouble is that what I
+
+ align:start position:0%
+technique um the trouble is that what I
+ 
+
+ align:start position:0%
+technique um the trouble is that what I
+just said
+
+ align:start position:0%
+just said
+ 
+
+ align:start position:0%
+just said
+here about just being proportional to
+
+ align:start position:0%
+here about just being proportional to
+ 
+
+ align:start position:0%
+here about just being proportional to
+density here this is rather simple
+
+ align:start position:0%
+density here this is rather simple
+ 
+
+ align:start position:0%
+density here this is rather simple
+it's not actually true in reality so
+
+ align:start position:0%
+it's not actually true in reality so
+ 
+
+ align:start position:0%
+it's not actually true in reality so
+what we actually have to do um is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+include all relevant processes this is
+
+ align:start position:0%
+include all relevant processes this is
+ 
+
+ align:start position:0%
+include all relevant processes this is
+going back to spectroscopy again where
+
+ align:start position:0%
+going back to spectroscopy again where
+ 
+
+ align:start position:0%
+going back to spectroscopy again where
+if you're not quite in a simple
+
+ align:start position:0%
+if you're not quite in a simple
+ 
+
+ align:start position:0%
+if you're not quite in a simple
+equilibrium you need to include lots
+
+ align:start position:0%
+equilibrium you need to include lots
+ 
+
+ align:start position:0%
+equilibrium you need to include lots
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes and you also need to include
+
+ align:start position:0%
+processes and you also need to include
+ 
+
+ align:start position:0%
+processes and you also need to include
+the beam's attenuation because of course
+
+ align:start position:0%
+the beam's attenuation because of course
+ 
+
+ align:start position:0%
+the beam's attenuation because of course
+the point of launching a neutral beam
+
+ align:start position:0%
+the point of launching a neutral beam
+ 
+
+ align:start position:0%
+the point of launching a neutral beam
+into your system is not to hit the far
+
+ align:start position:0%
+into your system is not to hit the far
+ 
+
+ align:start position:0%
+into your system is not to hit the far
+wall of your vacuum chamber and melt it
+
+ align:start position:0%
+wall of your vacuum chamber and melt it
+ 
+
+ align:start position:0%
+wall of your vacuum chamber and melt it
+but it's actually to charge exchange
+
+ align:start position:0%
+but it's actually to charge exchange
+ 
+
+ align:start position:0%
+but it's actually to charge exchange
+with the plasma and heat it and drive
+
+ align:start position:0%
+with the plasma and heat it and drive
+ 
+
+ align:start position:0%
+with the plasma and heat it and drive
+current so this beam is going to be
+
+ align:start position:0%
+current so this beam is going to be
+ 
+
+ align:start position:0%
+current so this beam is going to be
+getting less and less intense as it goes
+
+ align:start position:0%
+getting less and less intense as it goes
+ 
+
+ align:start position:0%
+getting less and less intense as it goes
+through the plasma and so if you want to
+
+ align:start position:0%
+through the plasma and so if you want to
+ 
+
+ align:start position:0%
+through the plasma and so if you want to
+do all this properly you also need to
+
+ align:start position:0%
+do all this properly you also need to
+ 
+
+ align:start position:0%
+do all this properly you also need to
+track the beam attenuation because this
+
+ align:start position:0%
+track the beam attenuation because this
+ 
+
+ align:start position:0%
+track the beam attenuation because this
+density is also proportional to the
+
+ align:start position:0%
+density is also proportional to the
+ 
+
+ align:start position:0%
+density is also proportional to the
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+of beam particles as well or number
+
+ align:start position:0%
+of beam particles as well or number
+ 
+
+ align:start position:0%
+of beam particles as well or number
+density of beam particles so we need to
+
+ align:start position:0%
+density of beam particles so we need to
+ 
+
+ align:start position:0%
+density of beam particles so we need to
+attct the beam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attenuation but if you can do that this
+
+ align:start position:0%
+attenuation but if you can do that this
+ 
+
+ align:start position:0%
+attenuation but if you can do that this
+is potentially a very powerful
+
+ align:start position:0%
+is potentially a very powerful
+ 
+
+ align:start position:0%
+is potentially a very powerful
+diagnostic for measuring density
+
+ align:start position:0%
+diagnostic for measuring density
+ 
+
+ align:start position:0%
+diagnostic for measuring density
+fluctuations which are otherwise quite
+
+ align:start position:0%
+fluctuations which are otherwise quite
+ 
+
+ align:start position:0%
+fluctuations which are otherwise quite
+challenging for
+
+ align:start position:0%
+challenging for
+ 
+
+ align:start position:0%
+challenging for
+meas questions on beam Mission
+
+ align:start position:0%
+meas questions on beam Mission
+ 
+
+ align:start position:0%
+meas questions on beam Mission
+spectroscopy uh Professor yes um so do
+
+ align:start position:0%
+spectroscopy uh Professor yes um so do
+ 
+
+ align:start position:0%
+spectroscopy uh Professor yes um so do
+you need to specialize your neutral Beam
+
+ align:start position:0%
+you need to specialize your neutral Beam
+ 
+
+ align:start position:0%
+you need to specialize your neutral Beam
+for these kind of readings or is it
+
+ align:start position:0%
+for these kind of readings or is it
+ 
+
+ align:start position:0%
+for these kind of readings or is it
+something you can do while using the
+
+ align:start position:0%
+something you can do while using the
+ 
+
+ align:start position:0%
+something you can do while using the
+neutral beam as a heating Source already
+
+ align:start position:0%
+neutral beam as a heating Source already
+ 
+
+ align:start position:0%
+neutral beam as a heating Source already
+yes the nice thing about all of these
+
+ align:start position:0%
+yes the nice thing about all of these
+ 
+
+ align:start position:0%
+yes the nice thing about all of these
+things is you tend to just be able to
+
+ align:start position:0%
+things is you tend to just be able to
+ 
+
+ align:start position:0%
+things is you tend to just be able to
+use your standard neutral beam so some
+
+ align:start position:0%
+use your standard neutral beam so some
+ 
+
+ align:start position:0%
+use your standard neutral beam so some
+people do have specifically made
+
+ align:start position:0%
+people do have specifically made
+ 
+
+ align:start position:0%
+people do have specifically made
+diagnostic neutral beams so on eer they
+
+ align:start position:0%
+diagnostic neutral beams so on eer they
+ 
+
+ align:start position:0%
+diagnostic neutral beams so on eer they
+have several neutral beams specifically
+
+ align:start position:0%
+have several neutral beams specifically
+ 
+
+ align:start position:0%
+have several neutral beams specifically
+designed for heating and they also have
+
+ align:start position:0%
+designed for heating and they also have
+ 
+
+ align:start position:0%
+designed for heating and they also have
+diagnostic neutral beams so the heating
+
+ align:start position:0%
+diagnostic neutral beams so the heating
+ 
+
+ align:start position:0%
+diagnostic neutral beams so the heating
+beams are up at Mega electron volts and
+
+ align:start position:0%
+beams are up at Mega electron volts and
+ 
+
+ align:start position:0%
+beams are up at Mega electron volts and
+the diagnostic beam is at a lower energy
+
+ align:start position:0%
+the diagnostic beam is at a lower energy
+ 
+
+ align:start position:0%
+the diagnostic beam is at a lower energy
+and I believe that lower energy is
+
+ align:start position:0%
+and I believe that lower energy is
+ 
+
+ align:start position:0%
+and I believe that lower energy is
+because it gives you better
+
+ align:start position:0%
+because it gives you better
+ 
+
+ align:start position:0%
+because it gives you better
+cross-sections for all these processes
+
+ align:start position:0%
+cross-sections for all these processes
+ 
+
+ align:start position:0%
+cross-sections for all these processes
+so I'm not sure um an amusing example of
+
+ align:start position:0%
+so I'm not sure um an amusing example of
+ 
+
+ align:start position:0%
+so I'm not sure um an amusing example of
+that is that there was a diagnostic
+
+ align:start position:0%
+that is that there was a diagnostic
+ 
+
+ align:start position:0%
+that is that there was a diagnostic
+neutral be
+
+ align:start position:0%
+neutral be
+ 
+
+ align:start position:0%
+neutral be
+developed for the national compact
+
+ align:start position:0%
+developed for the national compact
+ 
+
+ align:start position:0%
+developed for the national compact
+accelerator experiment of Princeton
+
+ align:start position:0%
+accelerator experiment of Princeton
+ 
+
+ align:start position:0%
+accelerator experiment of Princeton
+which was cancelled and that diagnostic
+
+ align:start position:0%
+which was cancelled and that diagnostic
+ 
+
+ align:start position:0%
+which was cancelled and that diagnostic
+neutral beam then went on to be the
+
+ align:start position:0%
+neutral beam then went on to be the
+ 
+
+ align:start position:0%
+neutral beam then went on to be the
+heating neutral Beam for a much smaller
+
+ align:start position:0%
+heating neutral Beam for a much smaller
+ 
+
+ align:start position:0%
+heating neutral Beam for a much smaller
+device so you know you can build a
+
+ align:start position:0%
+device so you know you can build a
+ 
+
+ align:start position:0%
+device so you know you can build a
+diagnostic neutral beam but at the end
+
+ align:start position:0%
+diagnostic neutral beam but at the end
+ 
+
+ align:start position:0%
+diagnostic neutral beam but at the end
+of the day it's still a neutral beam it
+
+ align:start position:0%
+of the day it's still a neutral beam it
+ 
+
+ align:start position:0%
+of the day it's still a neutral beam it
+can do whatever you you normally want
+
+ align:start position:0%
+can do whatever you you normally want
+ 
+
+ align:start position:0%
+can do whatever you you normally want
+this is going to be coming in at 300 K
+
+ align:start position:0%
+this is going to be coming in at 300 K
+ 
+
+ align:start position:0%
+this is going to be coming in at 300 K
+or whatever energy you can generate and
+
+ align:start position:0%
+or whatever energy you can generate and
+ 
+
+ align:start position:0%
+or whatever energy you can generate and
+all these processes are going to be
+
+ align:start position:0%
+all these processes are going to be
+ 
+
+ align:start position:0%
+all these processes are going to be
+happening and the fact that the beam
+
+ align:start position:0%
+happening and the fact that the beam
+ 
+
+ align:start position:0%
+happening and the fact that the beam
+slows down and converts into ions and
+
+ align:start position:0%
+slows down and converts into ions and
+ 
+
+ align:start position:0%
+slows down and converts into ions and
+does all the heating relies on all of
+
+ align:start position:0%
+does all the heating relies on all of
+ 
+
+ align:start position:0%
+does all the heating relies on all of
+the same atomic processes that we then
+
+ align:start position:0%
+the same atomic processes that we then
+ 
+
+ align:start position:0%
+the same atomic processes that we then
+use to observe beam emission
+
+ align:start position:0%
+use to observe beam emission
+ 
+
+ align:start position:0%
+use to observe beam emission
+spectroscopy and charge exchange and all
+
+ align:start position:0%
+spectroscopy and charge exchange and all
+ 
+
+ align:start position:0%
+spectroscopy and charge exchange and all
+that sort of stuff so like those
+
+ align:start position:0%
+that sort of stuff so like those
+ 
+
+ align:start position:0%
+that sort of stuff so like those
+processes have to happen for the beam to
+
+ align:start position:0%
+processes have to happen for the beam to
+ 
+
+ align:start position:0%
+processes have to happen for the beam to
+work and now you're just observing the
+
+ align:start position:0%
+work and now you're just observing the
+ 
+
+ align:start position:0%
+work and now you're just observing the
+obvious consequence of the yeah good
+
+ align:start position:0%
+obvious consequence of the yeah good
+ 
+
+ align:start position:0%
+obvious consequence of the yeah good
+question great thank you other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question now we're going to be done
+
+ align:start position:0%
+question now we're going to be done
+ 
+
+ align:start position:0%
+question now we're going to be done
+early all right final thing as we
+
+ align:start position:0%
+early all right final thing as we
+ 
+
+ align:start position:0%
+early all right final thing as we
+discussed it the other day is emotional
+
+ align:start position:0%
+discussed it the other day is emotional
+ 
+
+ align:start position:0%
+discussed it the other day is emotional
+Stark effect which I had forgotten was
+
+ align:start position:0%
+Stark effect which I had forgotten was
+ 
+
+ align:start position:0%
+Stark effect which I had forgotten was
+to do with this and in fact I was
+
+ align:start position:0%
+to do with this and in fact I was
+ 
+
+ align:start position:0%
+to do with this and in fact I was
+looking through my notes today and I was
+
+ align:start position:0%
+looking through my notes today and I was
+ 
+
+ align:start position:0%
+looking through my notes today and I was
+like oh I actually wrote several pages
+
+ align:start position:0%
+like oh I actually wrote several pages
+ 
+
+ align:start position:0%
+like oh I actually wrote several pages
+of notes on emotional star effect and
+
+ align:start position:0%
+of notes on emotional star effect and
+ 
+
+ align:start position:0%
+of notes on emotional star effect and
+then told people I had no idea what it
+
+ align:start position:0%
+then told people I had no idea what it
+ 
+
+ align:start position:0%
+then told people I had no idea what it
+was so that just shows how good my
+
+ align:start position:0%
+was so that just shows how good my
+ 
+
+ align:start position:0%
+was so that just shows how good my
+memory is so now you will have the
+
+ align:start position:0%
+memory is so now you will have the
+ 
+
+ align:start position:0%
+memory is so now you will have the
+pleasure of learning about and then
+
+ align:start position:0%
+pleasure of learning about and then
+ 
+
+ align:start position:0%
+pleasure of learning about and then
+instantly forgetting about the emotional
+
+ align:start position:0%
+instantly forgetting about the emotional
+ 
+
+ align:start position:0%
+instantly forgetting about the emotional
+Stark effect no it's actually really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool say often abbreviated as
+
+ align:start position:0%
+cool say often abbreviated as
+ 
+
+ align:start position:0%
+cool say often abbreviated as
+M okay so we already talked
+
+ align:start position:0%
+M okay so we already talked
+ 
+
+ align:start position:0%
+M okay so we already talked
+about the Stark effect and in the Stark
+
+ align:start position:0%
+about the Stark effect and in the Stark
+ 
+
+ align:start position:0%
+about the Stark effect and in the Stark
+effect we said that there was an
+
+ align:start position:0%
+effect we said that there was an
+ 
+
+ align:start position:0%
+effect we said that there was an
+electric field and I'm going to continue
+
+ align:start position:0%
+electric field and I'm going to continue
+ 
+
+ align:start position:0%
+electric field and I'm going to continue
+writing electric with this weird curly e
+
+ align:start position:0%
+writing electric with this weird curly e
+ 
+
+ align:start position:0%
+writing electric with this weird curly e
+because we're GNA have capital E for
+
+ align:start position:0%
+because we're GNA have capital E for
+ 
+
+ align:start position:0%
+because we're GNA have capital E for
+energy later I don't want us to get
+
+ align:start position:0%
+energy later I don't want us to get
+ 
+
+ align:start position:0%
+energy later I don't want us to get
+confused so this is the electric field
+
+ align:start position:0%
+confused so this is the electric field
+ 
+
+ align:start position:0%
+confused so this is the electric field
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shifts the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+of some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atom so we could do this just in a
+
+ align:start position:0%
+atom so we could do this just in a
+ 
+
+ align:start position:0%
+atom so we could do this just in a
+laboratory was a strong electric field
+
+ align:start position:0%
+laboratory was a strong electric field
+ 
+
+ align:start position:0%
+laboratory was a strong electric field
+and a neutral gas
+
+ align:start position:0%
+and a neutral gas
+ 
+
+ align:start position:0%
+and a neutral gas
+um and we then considered what this does
+
+ align:start position:0%
+um and we then considered what this does
+ 
+
+ align:start position:0%
+um and we then considered what this does
+inside a plasma so in a plasma we have
+
+ align:start position:0%
+inside a plasma so in a plasma we have
+ 
+
+ align:start position:0%
+inside a plasma so in a plasma we have
+lots of electrons moving around as we
+
+ align:start position:0%
+lots of electrons moving around as we
+ 
+
+ align:start position:0%
+lots of electrons moving around as we
+said and those electrons will be
+
+ align:start position:0%
+said and those electrons will be
+ 
+
+ align:start position:0%
+said and those electrons will be
+colliding with our ions or our atoms
+
+ align:start position:0%
+colliding with our ions or our atoms
+ 
+
+ align:start position:0%
+colliding with our ions or our atoms
+that have bound electrons and those
+
+ align:start position:0%
+that have bound electrons and those
+ 
+
+ align:start position:0%
+that have bound electrons and those
+electrons get close they will be
+
+ align:start position:0%
+electrons get close they will be
+ 
+
+ align:start position:0%
+electrons get close they will be
+Shifting the uh electric field and
+
+ align:start position:0%
+Shifting the uh electric field and
+ 
+
+ align:start position:0%
+Shifting the uh electric field and
+therefore the energy level in the
+
+ align:start position:0%
+therefore the energy level in the
+ 
+
+ align:start position:0%
+therefore the energy level in the
+vicinity that atom so we saw there that
+
+ align:start position:0%
+vicinity that atom so we saw there that
+ 
+
+ align:start position:0%
+vicinity that atom so we saw there that
+we got a change in the energy of the
+
+ align:start position:0%
+we got a change in the energy of the
+ 
+
+ align:start position:0%
+we got a change in the energy of the
+photons being emitted which was
+
+ align:start position:0%
+photons being emitted which was
+ 
+
+ align:start position:0%
+photons being emitted which was
+proportional to the electric field and
+
+ align:start position:0%
+proportional to the electric field and
+ 
+
+ align:start position:0%
+proportional to the electric field and
+that electric field was proportional to
+
+ align:start position:0%
+that electric field was proportional to
+ 
+
+ align:start position:0%
+that electric field was proportional to
+density of the 1/3 and this was just a
+
+ align:start position:0%
+density of the 1/3 and this was just a
+ 
+
+ align:start position:0%
+density of the 1/3 and this was just a
+electric field one over r s i this
+
+ align:start position:0%
+electric field one over r s i this
+ 
+
+ align:start position:0%
+electric field one over r s i this
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+two3 there we go okay this was from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collisions
+
+ align:start position:0%
+collisions
+ 
+
+ align:start position:0%
+collisions
+but this whole picture here required a
+
+ align:start position:0%
+but this whole picture here required a
+ 
+
+ align:start position:0%
+but this whole picture here required a
+thermal plasma with lots of particles
+
+ align:start position:0%
+thermal plasma with lots of particles
+ 
+
+ align:start position:0%
+thermal plasma with lots of particles
+moving in all sorts of ways here so this
+
+ align:start position:0%
+moving in all sorts of ways here so this
+ 
+
+ align:start position:0%
+moving in all sorts of ways here so this
+was with the distribution F of e v that
+
+ align:start position:0%
+was with the distribution F of e v that
+ 
+
+ align:start position:0%
+was with the distribution F of e v that
+was exponential of I don't know minus
+
+ align:start position:0%
+was exponential of I don't know minus
+ 
+
+ align:start position:0%
+was exponential of I don't know minus
+v^2 over V3 e
+
+ align:start position:0%
+v^2 over V3 e
+ 
+
+ align:start position:0%
+v^2 over V3 e
+squ but in this case here for a neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam we have a very Peak distribution
+
+ align:start position:0%
+beam we have a very Peak distribution
+ 
+
+ align:start position:0%
+beam we have a very Peak distribution
+function so our distribution of neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam
+
+ align:start position:0%
+beam
+ 
+
+ align:start position:0%
+beam
+ions is a roughly a Delta function right
+
+ align:start position:0%
+ions is a roughly a Delta function right
+ 
+
+ align:start position:0%
+ions is a roughly a Delta function right
+so they're all at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VB so we don't expect to see a broadness
+
+ align:start position:0%
+VB so we don't expect to see a broadness
+ 
+
+ align:start position:0%
+VB so we don't expect to see a broadness
+what we would expect to see maybe is
+
+ align:start position:0%
+what we would expect to see maybe is
+ 
+
+ align:start position:0%
+what we would expect to see maybe is
+some sort of shift in a single Direction
+
+ align:start position:0%
+some sort of shift in a single Direction
+ 
+
+ align:start position:0%
+some sort of shift in a single Direction
+here but where is the electric field
+
+ align:start position:0%
+here but where is the electric field
+ 
+
+ align:start position:0%
+here but where is the electric field
+coming up from in a plasma like this
+
+ align:start position:0%
+coming up from in a plasma like this
+ 
+
+ align:start position:0%
+coming up from in a plasma like this
+where we're just talking about our
+
+ align:start position:0%
+where we're just talking about our
+ 
+
+ align:start position:0%
+where we're just talking about our
+particles moving because here we argued
+
+ align:start position:0%
+particles moving because here we argued
+ 
+
+ align:start position:0%
+particles moving because here we argued
+this was the electric field from
+
+ align:start position:0%
+this was the electric field from
+ 
+
+ align:start position:0%
+this was the electric field from
+particles close in within the div
+
+ align:start position:0%
+particles close in within the div
+ 
+
+ align:start position:0%
+particles close in within the div
+bisphere but on large scales we don't
+
+ align:start position:0%
+bisphere but on large scales we don't
+ 
+
+ align:start position:0%
+bisphere but on large scales we don't
+see this electric field but what we do
+
+ align:start position:0%
+see this electric field but what we do
+ 
+
+ align:start position:0%
+see this electric field but what we do
+have is a magnetic field we have a
+
+ align:start position:0%
+have is a magnetic field we have a
+ 
+
+ align:start position:0%
+have is a magnetic field we have a
+magnetic field B like this and so we
+
+ align:start position:0%
+magnetic field B like this and so we
+ 
+
+ align:start position:0%
+magnetic field B like this and so we
+have some
+
+ align:start position:0%
+have some
+ 
+
+ align:start position:0%
+have some
+beam
+
+ align:start position:0%
+beam
+ 
+
+ align:start position:0%
+beam
+velocity V cross B and in the frame of
+
+ align:start position:0%
+velocity V cross B and in the frame of
+ 
+
+ align:start position:0%
+velocity V cross B and in the frame of
+the particle that creates an electric
+
+ align:start position:0%
+the particle that creates an electric
+ 
+
+ align:start position:0%
+the particle that creates an electric
+field which is equal to minus B cross B
+
+ align:start position:0%
+field which is equal to minus B cross B
+ 
+
+ align:start position:0%
+field which is equal to minus B cross B
+so this is our Lorent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transform so in the frame of the lab we
+
+ align:start position:0%
+transform so in the frame of the lab we
+ 
+
+ align:start position:0%
+transform so in the frame of the lab we
+see particles moving with velocity the
+
+ align:start position:0%
+see particles moving with velocity the
+ 
+
+ align:start position:0%
+see particles moving with velocity the
+beam and we see a magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field but in the frame of the particle
+
+ align:start position:0%
+field but in the frame of the particle
+ 
+
+ align:start position:0%
+field but in the frame of the particle
+when we do the Laurence
+
+ align:start position:0%
+when we do the Laurence
+ 
+
+ align:start position:0%
+when we do the Laurence
+transformation the particle of course
+
+ align:start position:0%
+transformation the particle of course
+ 
+
+ align:start position:0%
+transformation the particle of course
+doesn't know it's moving we're in its
+
+ align:start position:0%
+doesn't know it's moving we're in its
+ 
+
+ align:start position:0%
+doesn't know it's moving we're in its
+frame and instead of seeing a magnetic
+
+ align:start position:0%
+frame and instead of seeing a magnetic
+ 
+
+ align:start position:0%
+frame and instead of seeing a magnetic
+field it sees this electric field
+
+ align:start position:0%
+field it sees this electric field
+ 
+
+ align:start position:0%
+field it sees this electric field
+instead okay and so that means that now
+
+ align:start position:0%
+instead okay and so that means that now
+ 
+
+ align:start position:0%
+instead okay and so that means that now
+we're expecting to get ngg shifts Delta
+
+ align:start position:0%
+we're expecting to get ngg shifts Delta
+ 
+
+ align:start position:0%
+we're expecting to get ngg shifts Delta
+e which are again proportional to the
+
+ align:start position:0%
+e which are again proportional to the
+ 
+
+ align:start position:0%
+e which are again proportional to the
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+field which are now proportional to V
+
+ align:start position:0%
+field which are now proportional to V
+ 
+
+ align:start position:0%
+field which are now proportional to V
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+and I just want to point out and
+
+ align:start position:0%
+and I just want to point out and
+ 
+
+ align:start position:0%
+and I just want to point out and
+Hutchinson goes into this in some detail
+
+ align:start position:0%
+Hutchinson goes into this in some detail
+ 
+
+ align:start position:0%
+Hutchinson goes into this in some detail
+we've assumed here that we're talking
+
+ align:start position:0%
+we've assumed here that we're talking
+ 
+
+ align:start position:0%
+we've assumed here that we're talking
+about the linear Stark
+
+ align:start position:0%
+about the linear Stark
+ 
+
+ align:start position:0%
+about the linear Stark
+effect and depending on exactly what's
+
+ align:start position:0%
+effect and depending on exactly what's
+ 
+
+ align:start position:0%
+effect and depending on exactly what's
+going on you may need more complicated
+
+ align:start position:0%
+going on you may need more complicated
+ 
+
+ align:start position:0%
+going on you may need more complicated
+things like the quadratic Stark effect
+
+ align:start position:0%
+things like the quadratic Stark effect
+ 
+
+ align:start position:0%
+things like the quadratic Stark effect
+but this is the linear Stark effect it
+
+ align:start position:0%
+but this is the linear Stark effect it
+ 
+
+ align:start position:0%
+but this is the linear Stark effect it
+turns out the linear Stark effect is
+
+ align:start position:0%
+turns out the linear Stark effect is
+ 
+
+ align:start position:0%
+turns out the linear Stark effect is
+good when this Delta e is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large so as long as you have
+
+ align:start position:0%
+large so as long as you have
+ 
+
+ align:start position:0%
+large so as long as you have
+sufficiently large magnetic field and uh
+
+ align:start position:0%
+sufficiently large magnetic field and uh
+ 
+
+ align:start position:0%
+sufficiently large magnetic field and uh
+beam velocities then you end up in this
+
+ align:start position:0%
+beam velocities then you end up in this
+ 
+
+ align:start position:0%
+beam velocities then you end up in this
+linear regim which is much easier to
+
+ align:start position:0%
+linear regim which is much easier to
+ 
+
+ align:start position:0%
+linear regim which is much easier to
+analyze
+
+ align:start position:0%
+analyze
+ 
+
+ align:start position:0%
+analyze
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay um I'm gonna erase this because I
+
+ align:start position:0%
+okay um I'm gonna erase this because I
+ 
+
+ align:start position:0%
+okay um I'm gonna erase this because I
+want to keep that on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+now some voodoo magic happens and we
+
+ align:start position:0%
+now some voodoo magic happens and we
+ 
+
+ align:start position:0%
+now some voodoo magic happens and we
+find out that we each energy level
+
+ align:start position:0%
+find out that we each energy level
+ 
+
+ align:start position:0%
+find out that we each energy level
+splits into multiple energy levels so
+
+ align:start position:0%
+splits into multiple energy levels so
+ 
+
+ align:start position:0%
+splits into multiple energy levels so
+this is reminiscent of the Zan spliting
+
+ align:start position:0%
+this is reminiscent of the Zan spliting
+ 
+
+ align:start position:0%
+this is reminiscent of the Zan spliting
+again so each energy level splits into
+
+ align:start position:0%
+again so each energy level splits into
+ 
+
+ align:start position:0%
+again so each energy level splits into
+energy levels whose energy is given by
+
+ align:start position:0%
+energy levels whose energy is given by
+ 
+
+ align:start position:0%
+energy levels whose energy is given by
+three n k I'll explain all of these
+
+ align:start position:0%
+three n k I'll explain all of these
+ 
+
+ align:start position:0%
+three n k I'll explain all of these
+symbols mean in a
+
+ align:start position:0%
+symbols mean in a
+ 
+
+ align:start position:0%
+symbols mean in a
+moment electric field
+
+ align:start position:0%
+moment electric field
+ 
+
+ align:start position:0%
+moment electric field
+over z
+
+ align:start position:0%
+over z
+ 
+
+ align:start position:0%
+over z
+e over 4 Pi Epsilon do a z
+
+ align:start position:0%
+e over 4 Pi Epsilon do a z
+ 
+
+ align:start position:0%
+e over 4 Pi Epsilon do a z
+Z squar I haven't got in my notes what a
+
+ align:start position:0%
+Z squar I haven't got in my notes what a
+ 
+
+ align:start position:0%
+Z squar I haven't got in my notes what a
+Zer is and I've forgotten what it is off
+
+ align:start position:0%
+Zer is and I've forgotten what it is off
+ 
+
+ align:start position:0%
+Zer is and I've forgotten what it is off
+to my head so that's not very
+
+ align:start position:0%
+to my head so that's not very
+ 
+
+ align:start position:0%
+to my head so that's not very
+useful some constant is the most
+
+ align:start position:0%
+useful some constant is the most
+ 
+
+ align:start position:0%
+useful some constant is the most
+important thing and all this times the
+
+ align:start position:0%
+important thing and all this times the
+ 
+
+ align:start position:0%
+important thing and all this times the
+rigberg energy which you all remember
+
+ align:start position:0%
+rigberg energy which you all remember
+ 
+
+ align:start position:0%
+rigberg energy which you all remember
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+13.6 electron volts and this electric
+
+ align:start position:0%
+13.6 electron volts and this electric
+ 
+
+ align:start position:0%
+13.6 electron volts and this electric
+field is B cross B modulus of it okay so
+
+ align:start position:0%
+field is B cross B modulus of it okay so
+ 
+
+ align:start position:0%
+field is B cross B modulus of it okay so
+n here is the Quant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number n equal 1 2 3 and K here for each
+
+ align:start position:0%
+number n equal 1 2 3 and K here for each
+ 
+
+ align:start position:0%
+number n equal 1 2 3 and K here for each
+quantum number n can take multiple
+
+ align:start position:0%
+quantum number n can take multiple
+ 
+
+ align:start position:0%
+quantum number n can take multiple
+values k equals Zer plus or minus one
+
+ align:start position:0%
+values k equals Zer plus or minus one
+ 
+
+ align:start position:0%
+values k equals Zer plus or minus one
+plus or minus
+
+ align:start position:0%
+plus or minus
+ 
+
+ align:start position:0%
+plus or minus
+2 up to plus or minus n minus
+
+ align:start position:0%
+2 up to plus or minus n minus
+ 
+
+ align:start position:0%
+2 up to plus or minus n minus
+1 so for Nal 1 K can only take the value
+
+ align:start position:0%
+1 so for Nal 1 K can only take the value
+ 
+
+ align:start position:0%
+1 so for Nal 1 K can only take the value
+zero for nals two it can take three
+
+ align:start position:0%
+zero for nals two it can take three
+ 
+
+ align:start position:0%
+zero for nals two it can take three
+values for n equals three it can take
+
+ align:start position:0%
+values for n equals three it can take
+ 
+
+ align:start position:0%
+values for n equals three it can take
+five values like
+
+ align:start position:0%
+five values like
+ 
+
+ align:start position:0%
+five values like
+this and because these energy levels are
+
+ align:start position:0%
+this and because these energy levels are
+ 
+
+ align:start position:0%
+this and because these energy levels are
+all split and I'll draw some now so that
+
+ align:start position:0%
+all split and I'll draw some now so that
+ 
+
+ align:start position:0%
+all split and I'll draw some now so that
+you get some feel what's going
+
+ align:start position:0%
+you get some feel what's going
+ 
+
+ align:start position:0%
+you get some feel what's going
+on see if I've got space to do it here
+
+ align:start position:0%
+on see if I've got space to do it here
+ 
+
+ align:start position:0%
+on see if I've got space to do it here
+we start out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with n = 1 n = 2 Nal three this nals 1
+
+ align:start position:0%
+with n = 1 n = 2 Nal three this nals 1
+ 
+
+ align:start position:0%
+with n = 1 n = 2 Nal three this nals 1
+will just be split to an N equals one
+
+ align:start position:0%
+will just be split to an N equals one
+ 
+
+ align:start position:0%
+will just be split to an N equals one
+level the N equals 2 will be split to
+
+ align:start position:0%
+level the N equals 2 will be split to
+ 
+
+ align:start position:0%
+level the N equals 2 will be split to
+three levels and the N equals three we
+
+ align:start position:0%
+three levels and the N equals three we
+ 
+
+ align:start position:0%
+three levels and the N equals three we
+split to five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+levels and each of these levels is going
+
+ align:start position:0%
+levels and each of these levels is going
+ 
+
+ align:start position:0%
+levels and each of these levels is going
+to have an energy Delta
+
+ align:start position:0%
+to have an energy Delta
+ 
+
+ align:start position:0%
+to have an energy Delta
+e between them which is given by this
+
+ align:start position:0%
+e between them which is given by this
+ 
+
+ align:start position:0%
+e between them which is given by this
+formula here and so by measuring the
+
+ align:start position:0%
+formula here and so by measuring the
+ 
+
+ align:start position:0%
+formula here and so by measuring the
+splitting we can measure the magnetic
+
+ align:start position:0%
+splitting we can measure the magnetic
+ 
+
+ align:start position:0%
+splitting we can measure the magnetic
+field because
+
+ align:start position:0%
+field because
+ 
+
+ align:start position:0%
+field because
+most of the stuff in here is just a
+
+ align:start position:0%
+most of the stuff in here is just a
+ 
+
+ align:start position:0%
+most of the stuff in here is just a
+constant we should know our beam
+
+ align:start position:0%
+constant we should know our beam
+ 
+
+ align:start position:0%
+constant we should know our beam
+velocity because we're the ones
+
+ align:start position:0%
+velocity because we're the ones
+ 
+
+ align:start position:0%
+velocity because we're the ones
+objecting neutral beam so the only thing
+
+ align:start position:0%
+objecting neutral beam so the only thing
+ 
+
+ align:start position:0%
+objecting neutral beam so the only thing
+we don't know is the size of the
+
+ align:start position:0%
+we don't know is the size of the
+ 
+
+ align:start position:0%
+we don't know is the size of the
+magnetic
+
+ align:start position:0%
+magnetic
+ 
+
+ align:start position:0%
+magnetic
+field so we could try and use uh so
+
+ align:start position:0%
+field so we could try and use uh so
+ 
+
+ align:start position:0%
+field so we could try and use uh so
+again this is still a neutral beam so
+
+ align:start position:0%
+again this is still a neutral beam so
+ 
+
+ align:start position:0%
+again this is still a neutral beam so
+we've got one electron so we could try
+
+ align:start position:0%
+we've got one electron so we could try
+ 
+
+ align:start position:0%
+we've got one electron so we could try
+and look at transitions from here down
+
+ align:start position:0%
+and look at transitions from here down
+ 
+
+ align:start position:0%
+and look at transitions from here down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+here and there should be a triplet of
+
+ align:start position:0%
+here and there should be a triplet of
+ 
+
+ align:start position:0%
+here and there should be a triplet of
+transitions all coming out with slightly
+
+ align:start position:0%
+transitions all coming out with slightly
+ 
+
+ align:start position:0%
+transitions all coming out with slightly
+different energies what is the problem
+
+ align:start position:0%
+different energies what is the problem
+ 
+
+ align:start position:0%
+different energies what is the problem
+with using
+
+ align:start position:0%
+with using
+ 
+
+ align:start position:0%
+with using
+this oh first of all does anyone
+
+ align:start position:0%
+this oh first of all does anyone
+ 
+
+ align:start position:0%
+this oh first of all does anyone
+remember the name for this transition
+
+ align:start position:0%
+remember the name for this transition
+ 
+
+ align:start position:0%
+remember the name for this transition
+and what's the problem with using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is it a forbidden transition it's not
+
+ align:start position:0%
+it is it a forbidden transition it's not
+ 
+
+ align:start position:0%
+it is it a forbidden transition it's not
+forbidden but good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hydrogen transition from the first
+
+ align:start position:0%
+hydrogen transition from the first
+ 
+
+ align:start position:0%
+hydrogen transition from the first
+excited state down to ground state is
+
+ align:start position:0%
+excited state down to ground state is
+ 
+
+ align:start position:0%
+excited state down to ground state is
+the Lyman Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the wavelength of the L
+
+ align:start position:0%
+what's the wavelength of the L
+ 
+
+ align:start position:0%
+what's the wavelength of the L
+Alpha yeah it's 121
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nom so this is what's called vacuum
+
+ align:start position:0%
+Nom so this is what's called vacuum
+ 
+
+ align:start position:0%
+Nom so this is what's called vacuum
+ultraviolet and the reason it's called
+
+ align:start position:0%
+ultraviolet and the reason it's called
+ 
+
+ align:start position:0%
+ultraviolet and the reason it's called
+vacuum ultraviolet is it only propagates
+
+ align:start position:0%
+vacuum ultraviolet is it only propagates
+ 
+
+ align:start position:0%
+vacuum ultraviolet is it only propagates
+in a vacuum so it's a real pain to deal
+
+ align:start position:0%
+in a vacuum so it's a real pain to deal
+ 
+
+ align:start position:0%
+in a vacuum so it's a real pain to deal
+with so we don't want to work with this
+
+ align:start position:0%
+with so we don't want to work with this
+ 
+
+ align:start position:0%
+with so we don't want to work with this
+transition here instead what we want to
+
+ align:start position:0%
+transition here instead what we want to
+ 
+
+ align:start position:0%
+transition here instead what we want to
+do is use a transition from nals 3 down
+
+ align:start position:0%
+do is use a transition from nals 3 down
+ 
+
+ align:start position:0%
+do is use a transition from nals 3 down
+to nals 2 what's the name of this
+
+ align:start position:0%
+to nals 2 what's the name of this
+ 
+
+ align:start position:0%
+to nals 2 what's the name of this
+transition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah H alpha balber
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alpha and this is where the Forbidden
+
+ align:start position:0%
+alpha and this is where the Forbidden
+ 
+
+ align:start position:0%
+alpha and this is where the Forbidden
+transitions that were mentioned come in
+
+ align:start position:0%
+transitions that were mentioned come in
+ 
+
+ align:start position:0%
+transitions that were mentioned come in
+here so these have a angular momentum
+
+ align:start position:0%
+here so these have a angular momentum
+ 
+
+ align:start position:0%
+here so these have a angular momentum
+quantum number m m of 2 1 0 minus oneus
+
+ align:start position:0%
+quantum number m m of 2 1 0 minus oneus
+ 
+
+ align:start position:0%
+quantum number m m of 2 1 0 minus oneus
+2 1 Z minus one like this and the
+
+ align:start position:0%
+2 1 Z minus one like this and the
+ 
+
+ align:start position:0%
+2 1 Z minus one like this and the
+transit the uh selection rule for these
+
+ align:start position:0%
+transit the uh selection rule for these
+ 
+
+ align:start position:0%
+transit the uh selection rule for these
+that tells you whether this transition
+
+ align:start position:0%
+that tells you whether this transition
+ 
+
+ align:start position:0%
+that tells you whether this transition
+is forbidden or not is Delta m is equal
+
+ align:start position:0%
+is forbidden or not is Delta m is equal
+ 
+
+ align:start position:0%
+is forbidden or not is Delta m is equal
+to uh I got it written down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here yeah zero and plus or minus
+
+ align:start position:0%
+here yeah zero and plus or minus
+ 
+
+ align:start position:0%
+here yeah zero and plus or minus
+one okay so From Any Given level here
+
+ align:start position:0%
+one okay so From Any Given level here
+ 
+
+ align:start position:0%
+one okay so From Any Given level here
+for this one for example the m equals z
+
+ align:start position:0%
+for this one for example the m equals z
+ 
+
+ align:start position:0%
+for this one for example the m equals z
+in the N equals 3 we can have a
+
+ align:start position:0%
+in the N equals 3 we can have a
+ 
+
+ align:start position:0%
+in the N equals 3 we can have a
+transition down to zero down to minus
+
+ align:start position:0%
+transition down to zero down to minus
+ 
+
+ align:start position:0%
+transition down to zero down to minus
+one and down to one we'll get a triple
+
+ align:start position:0%
+one and down to one we'll get a triple
+ 
+
+ align:start position:0%
+one and down to one we'll get a triple
+of lines from that we'll also get
+
+ align:start position:0%
+of lines from that we'll also get
+ 
+
+ align:start position:0%
+of lines from that we'll also get
+another set of lines you can see this
+
+ align:start position:0%
+another set of lines you can see this
+ 
+
+ align:start position:0%
+another set of lines you can see this
+starts to get quite complicated quite
+
+ align:start position:0%
+starts to get quite complicated quite
+ 
+
+ align:start position:0%
+starts to get quite complicated quite
+quickly like
+
+ align:start position:0%
+quickly like
+ 
+
+ align:start position:0%
+quickly like
+this there is no transition down to
+
+ align:start position:0%
+this there is no transition down to
+ 
+
+ align:start position:0%
+this there is no transition down to
+minus two because it doesn't exist and
+
+ align:start position:0%
+minus two because it doesn't exist and
+ 
+
+ align:start position:0%
+minus two because it doesn't exist and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+finally uh we'll have well the minus two
+
+ align:start position:0%
+finally uh we'll have well the minus two
+ 
+
+ align:start position:0%
+finally uh we'll have well the minus two
+could guess can go to minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and the m equals 1 can go down to uh m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals zero and m equal 1 I'm running
+
+ align:start position:0%
+equals zero and m equal 1 I'm running
+ 
+
+ align:start position:0%
+equals zero and m equal 1 I'm running
+out of
+
+ align:start position:0%
+out of
+ 
+
+ align:start position:0%
+out of
+colors and the m equals 2 can go down to
+
+ align:start position:0%
+colors and the m equals 2 can go down to
+ 
+
+ align:start position:0%
+colors and the m equals 2 can go down to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+m f time so you see there's all sorts of
+
+ align:start position:0%
+m f time so you see there's all sorts of
+ 
+
+ align:start position:0%
+m f time so you see there's all sorts of
+different lines but you notice that
+
+ align:start position:0%
+different lines but you notice that
+ 
+
+ align:start position:0%
+different lines but you notice that
+their spacings of these levels are the
+
+ align:start position:0%
+their spacings of these levels are the
+ 
+
+ align:start position:0%
+their spacings of these levels are the
+same as the spacings of these no it's
+
+ align:start position:0%
+same as the spacings of these no it's
+ 
+
+ align:start position:0%
+same as the spacings of these no it's
+not because n is different yeah you're
+
+ align:start position:0%
+not because n is different yeah you're
+ 
+
+ align:start position:0%
+not because n is different yeah you're
+going to get clusters of different lines
+
+ align:start position:0%
+going to get clusters of different lines
+ 
+
+ align:start position:0%
+going to get clusters of different lines
+at slightly different energy so you need
+
+ align:start position:0%
+at slightly different energy so you need
+ 
+
+ align:start position:0%
+at slightly different energy so you need
+a very nice spectrometer be able to
+
+ align:start position:0%
+a very nice spectrometer be able to
+ 
+
+ align:start position:0%
+a very nice spectrometer be able to
+distinguish between these lines so as
+
+ align:start position:0%
+distinguish between these lines so as
+ 
+
+ align:start position:0%
+distinguish between these lines so as
+you increase the magnetic field the
+
+ align:start position:0%
+you increase the magnetic field the
+ 
+
+ align:start position:0%
+you increase the magnetic field the
+energy gap gets bigger and so you need a
+
+ align:start position:0%
+energy gap gets bigger and so you need a
+ 
+
+ align:start position:0%
+energy gap gets bigger and so you need a
+less and less nice Spectrum so um your
+
+ align:start position:0%
+less and less nice Spectrum so um your
+ 
+
+ align:start position:0%
+less and less nice Spectrum so um your
+resolution requirements go down for a
+
+ align:start position:0%
+resolution requirements go down for a
+ 
+
+ align:start position:0%
+resolution requirements go down for a
+bigger magnetic field but in general
+
+ align:start position:0%
+bigger magnetic field but in general
+ 
+
+ align:start position:0%
+bigger magnetic field but in general
+you're going to see a forest of light
+
+ align:start position:0%
+you're going to see a forest of light
+ 
+
+ align:start position:0%
+you're going to see a forest of light
+you're going to
+
+ align:start position:0%
+you're going to
+ 
+
+ align:start position:0%
+you're going to
+see instead of just your H Alpha line
+
+ align:start position:0%
+see instead of just your H Alpha line
+ 
+
+ align:start position:0%
+see instead of just your H Alpha line
+that you had originally you're going to
+
+ align:start position:0%
+that you had originally you're going to
+ 
+
+ align:start position:0%
+that you had originally you're going to
+get I'm not going to try and draw this
+
+ align:start position:0%
+get I'm not going to try and draw this
+ 
+
+ align:start position:0%
+get I'm not going to try and draw this
+accurately a set of lines like this and
+
+ align:start position:0%
+accurately a set of lines like this and
+ 
+
+ align:start position:0%
+accurately a set of lines like this and
+then you might get another line over up
+
+ align:start position:0%
+then you might get another line over up
+ 
+
+ align:start position:0%
+then you might get another line over up
+here and you might get another line down
+
+ align:start position:0%
+here and you might get another line down
+ 
+
+ align:start position:0%
+here and you might get another line down
+here and all sorts of things like that
+
+ align:start position:0%
+here and all sorts of things like that
+ 
+
+ align:start position:0%
+here and all sorts of things like that
+and other sets of triplets and dbls
+
+ align:start position:0%
+and other sets of triplets and dbls
+ 
+
+ align:start position:0%
+and other sets of triplets and dbls
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+places if that's not quite right it's
+
+ align:start position:0%
+places if that's not quite right it's
+ 
+
+ align:start position:0%
+places if that's not quite right it's
+not completely okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool why are we bothering with this this
+
+ align:start position:0%
+cool why are we bothering with this this
+ 
+
+ align:start position:0%
+cool why are we bothering with this this
+looks an awful lot like Zan splitting
+
+ align:start position:0%
+looks an awful lot like Zan splitting
+ 
+
+ align:start position:0%
+looks an awful lot like Zan splitting
+couldn't we have just done Zan splitting
+
+ align:start position:0%
+couldn't we have just done Zan splitting
+ 
+
+ align:start position:0%
+couldn't we have just done Zan splitting
+okay so the main thing about this is
+
+ align:start position:0%
+okay so the main thing about this is
+ 
+
+ align:start position:0%
+okay so the main thing about this is
+this Delta e is much much larger than we
+
+ align:start position:0%
+this Delta e is much much larger than we
+ 
+
+ align:start position:0%
+this Delta e is much much larger than we
+get for
+
+ align:start position:0%
+get for
+ 
+
+ align:start position:0%
+get for
+Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by much much larger I mean about 10
+
+ align:start position:0%
+by much much larger I mean about 10
+ 
+
+ align:start position:0%
+by much much larger I mean about 10
+times larger so it's much easier to
+
+ align:start position:0%
+times larger so it's much easier to
+ 
+
+ align:start position:0%
+times larger so it's much easier to
+distinguish between the lines and once
+
+ align:start position:0%
+distinguish between the lines and once
+ 
+
+ align:start position:0%
+distinguish between the lines and once
+again we can use our neutral beam that
+
+ align:start position:0%
+again we can use our neutral beam that
+ 
+
+ align:start position:0%
+again we can use our neutral beam that
+we already have to do this so this is
+
+ align:start position:0%
+we already have to do this so this is
+ 
+
+ align:start position:0%
+we already have to do this so this is
+very nice use of a neutral beam now we
+
+ align:start position:0%
+very nice use of a neutral beam now we
+ 
+
+ align:start position:0%
+very nice use of a neutral beam now we
+talked about with Zan before it's not
+
+ align:start position:0%
+talked about with Zan before it's not
+ 
+
+ align:start position:0%
+talked about with Zan before it's not
+actually super useful to be able to
+
+ align:start position:0%
+actually super useful to be able to
+ 
+
+ align:start position:0%
+actually super useful to be able to
+measure the straight for a magnetic
+
+ align:start position:0%
+measure the straight for a magnetic
+ 
+
+ align:start position:0%
+measure the straight for a magnetic
+field in a toac because we know what it
+
+ align:start position:0%
+field in a toac because we know what it
+ 
+
+ align:start position:0%
+field in a toac because we know what it
+is it's the toid magnetic field
+
+ align:start position:0%
+is it's the toid magnetic field
+ 
+
+ align:start position:0%
+is it's the toid magnetic field
+basically the poloidal magnetic field is
+
+ align:start position:0%
+basically the poloidal magnetic field is
+ 
+
+ align:start position:0%
+basically the poloidal magnetic field is
+very small so this is our condition that
+
+ align:start position:0%
+very small so this is our condition that
+ 
+
+ align:start position:0%
+very small so this is our condition that
+b poloidal is much much less than B
+
+ align:start position:0%
+b poloidal is much much less than B
+ 
+
+ align:start position:0%
+b poloidal is much much less than B
+thidal that we have in a toac um the
+
+ align:start position:0%
+thidal that we have in a toac um the
+ 
+
+ align:start position:0%
+thidal that we have in a toac um the
+nice thing about this is that each of
+
+ align:start position:0%
+nice thing about this is that each of
+ 
+
+ align:start position:0%
+nice thing about this is that each of
+these different transitions has a
+
+ align:start position:0%
+these different transitions has a
+ 
+
+ align:start position:0%
+these different transitions has a
+different polarization this is going
+
+ align:start position:0%
+different polarization this is going
+ 
+
+ align:start position:0%
+different polarization this is going
+back to what we were talking about
+
+ align:start position:0%
+back to what we were talking about
+ 
+
+ align:start position:0%
+back to what we were talking about
+before where we had these pi
+
+ align:start position:0%
+before where we had these pi
+ 
+
+ align:start position:0%
+before where we had these pi
+polarizations and sigma
+
+ align:start position:0%
+polarizations and sigma
+ 
+
+ align:start position:0%
+polarizations and sigma
+polarizations and I'm running out of
+
+ align:start position:0%
+polarizations and I'm running out of
+ 
+
+ align:start position:0%
+polarizations and I'm running out of
+room to draw it but if you go back to
+
+ align:start position:0%
+room to draw it but if you go back to
+ 
+
+ align:start position:0%
+room to draw it but if you go back to
+the notes that we had on Zan
+
+ align:start position:0%
+the notes that we had on Zan
+ 
+
+ align:start position:0%
+the notes that we had on Zan
+spectroscopy here
+
+ align:start position:0%
+spectroscopy here
+ 
+
+ align:start position:0%
+spectroscopy here
+this polarization for example will come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out we've got some magnetic fields here
+
+ align:start position:0%
+out we've got some magnetic fields here
+ 
+
+ align:start position:0%
+out we've got some magnetic fields here
+which is the thidal field plus the the
+
+ align:start position:0%
+which is the thidal field plus the the
+ 
+
+ align:start position:0%
+which is the thidal field plus the the
+loyal field will have the P polarization
+
+ align:start position:0%
+loyal field will have the P polarization
+ 
+
+ align:start position:0%
+loyal field will have the P polarization
+coming out of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma perpendicular to be and we'll
+
+ align:start position:0%
+plasma perpendicular to be and we'll
+ 
+
+ align:start position:0%
+plasma perpendicular to be and we'll
+have the stigma polarizations coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out parallel to B so by having two
+
+ align:start position:0%
+out parallel to B so by having two
+ 
+
+ align:start position:0%
+out parallel to B so by having two
+spectrometers with two different
+
+ align:start position:0%
+spectrometers with two different
+ 
+
+ align:start position:0%
+spectrometers with two different
+polarizers Cross of each other and
+
+ align:start position:0%
+polarizers Cross of each other and
+ 
+
+ align:start position:0%
+polarizers Cross of each other and
+measuring the relative strength of these
+
+ align:start position:0%
+measuring the relative strength of these
+ 
+
+ align:start position:0%
+measuring the relative strength of these
+two lines you can actually determine the
+
+ align:start position:0%
+two lines you can actually determine the
+ 
+
+ align:start position:0%
+two lines you can actually determine the
+angle of the magnetic field and then
+
+ align:start position:0%
+angle of the magnetic field and then
+ 
+
+ align:start position:0%
+angle of the magnetic field and then
+from that you can work out the size of
+
+ align:start position:0%
+from that you can work out the size of
+ 
+
+ align:start position:0%
+from that you can work out the size of
+this bidal component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and from the bidal component you can
+
+ align:start position:0%
+and from the bidal component you can
+ 
+
+ align:start position:0%
+and from the bidal component you can
+start to guess at distribution of
+
+ align:start position:0%
+start to guess at distribution of
+ 
+
+ align:start position:0%
+start to guess at distribution of
+current inside your toac which is very
+
+ align:start position:0%
+current inside your toac which is very
+ 
+
+ align:start position:0%
+current inside your toac which is very
+very important especially when we're
+
+ align:start position:0%
+very important especially when we're
+ 
+
+ align:start position:0%
+very important especially when we're
+doing things like bootstrap current
+
+ align:start position:0%
+doing things like bootstrap current
+ 
+
+ align:start position:0%
+doing things like bootstrap current
+where we need very specific current
+
+ align:start position:0%
+where we need very specific current
+ 
+
+ align:start position:0%
+where we need very specific current
+profiles in order to induce it so
+
+ align:start position:0%
+profiles in order to induce it so
+ 
+
+ align:start position:0%
+profiles in order to induce it so
+basically motional star effect here is
+
+ align:start position:0%
+basically motional star effect here is
+ 
+
+ align:start position:0%
+basically motional star effect here is
+very useful for
+
+ align:start position:0%
+very useful for
+ 
+
+ align:start position:0%
+very useful for
+magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reconstruction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so the Zan effect requires certain
+
+ align:start position:0%
+yes so the Zan effect requires certain
+ 
+
+ align:start position:0%
+yes so the Zan effect requires certain
+electronic configurations to actually
+
+ align:start position:0%
+electronic configurations to actually
+ 
+
+ align:start position:0%
+electronic configurations to actually
+occur and I believe that you don't get
+
+ align:start position:0%
+occur and I believe that you don't get
+ 
+
+ align:start position:0%
+occur and I believe that you don't get
+Zan splitting in hydrogen normally so
+
+ align:start position:0%
+Zan splitting in hydrogen normally so
+ 
+
+ align:start position:0%
+Zan splitting in hydrogen normally so
+this emotional star effect is therefore
+
+ align:start position:0%
+this emotional star effect is therefore
+ 
+
+ align:start position:0%
+this emotional star effect is therefore
+more more like more useful in that case
+
+ align:start position:0%
+more more like more useful in that case
+ 
+
+ align:start position:0%
+more more like more useful in that case
+yeah and this motional star effect is
+
+ align:start position:0%
+yeah and this motional star effect is
+ 
+
+ align:start position:0%
+yeah and this motional star effect is
+particularly big because we're talking
+
+ align:start position:0%
+particularly big because we're talking
+ 
+
+ align:start position:0%
+particularly big because we're talking
+about very fast moving neutral beam
+
+ align:start position:0%
+about very fast moving neutral beam
+ 
+
+ align:start position:0%
+about very fast moving neutral beam
+particles so or you know this this isn't
+
+ align:start position:0%
+particles so or you know this this isn't
+ 
+
+ align:start position:0%
+particles so or you know this this isn't
+useful in a plasma in just looking at
+
+ align:start position:0%
+useful in a plasma in just looking at
+ 
+
+ align:start position:0%
+useful in a plasma in just looking at
+the thermal ions because all these
+
+ align:start position:0%
+the thermal ions because all these
+ 
+
+ align:start position:0%
+the thermal ions because all these
+velocities are in different directions
+
+ align:start position:0%
+velocities are in different directions
+ 
+
+ align:start position:0%
+velocities are in different directions
+and they're relatively small so all that
+
+ align:start position:0%
+and they're relatively small so all that
+ 
+
+ align:start position:0%
+and they're relatively small so all that
+will give you is a broadening the point
+
+ align:start position:0%
+will give you is a broadening the point
+ 
+
+ align:start position:0%
+will give you is a broadening the point
+is that this V is large and All in One
+
+ align:start position:0%
+is that this V is large and All in One
+ 
+
+ align:start position:0%
+is that this V is large and All in One
+Direction so you get a big splitting and
+
+ align:start position:0%
+Direction so you get a big splitting and
+ 
+
+ align:start position:0%
+Direction so you get a big splitting and
+it consists every single particle is
+
+ align:start position:0%
+it consists every single particle is
+ 
+
+ align:start position:0%
+it consists every single particle is
+emitting light with the same Spectra and
+
+ align:start position:0%
+emitting light with the same Spectra and
+ 
+
+ align:start position:0%
+emitting light with the same Spectra and
+so you can actually stand a chance of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online all right you can have quarter of
+
+ align:start position:0%
+online all right you can have quarter of
+ 
+
+ align:start position:0%
+online all right you can have quarter of
+your H quarter of an hour of your lives
+
+ align:start position:0%
+your H quarter of an hour of your lives
+ 
+
+ align:start position:0%
+your H quarter of an hour of your lives
+back do whatever you want and Happy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thanksgiving
\ No newline at end of file
diff --git a/qhOVXxNXAug.txt b/qhOVXxNXAug.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bdedb5b0fade723cb7da8c9f4621996be0bd4a19
--- /dev/null
+++ b/qhOVXxNXAug.txt
@@ -0,0 +1,379 @@
+align:start position:0%
+ 
+okay now it's time to construct and
+
+ align:start position:0%
+okay now it's time to construct and
+ 
+
+ align:start position:0%
+okay now it's time to construct and
+pre-process the corpus so we'll start by
+
+ align:start position:0%
+pre-process the corpus so we'll start by
+ 
+
+ align:start position:0%
+pre-process the corpus so we'll start by
+loading the TM package with library of
+
+ align:start position:0%
+loading the TM package with library of
+ 
+
+ align:start position:0%
+loading the TM package with library of
+TM and now that we have done that we'll
+
+ align:start position:0%
+TM and now that we have done that we'll
+ 
+
+ align:start position:0%
+TM and now that we have done that we'll
+construct a variable called corpus using
+
+ align:start position:0%
+construct a variable called corpus using
+ 
+
+ align:start position:0%
+construct a variable called corpus using
+the corpus and vector source functions
+
+ align:start position:0%
+the corpus and vector source functions
+ 
+
+ align:start position:0%
+the corpus and vector source functions
+and passing in all of the emails in our
+
+ align:start position:0%
+and passing in all of the emails in our
+ 
+
+ align:start position:0%
+and passing in all of the emails in our
+data set which is emails dollar sign
+
+ align:start position:0%
+data set which is emails dollar sign
+ 
+
+ align:start position:0%
+data set which is emails dollar sign
+email okay so now that we've constructed
+
+ align:start position:0%
+email okay so now that we've constructed
+ 
+
+ align:start position:0%
+email okay so now that we've constructed
+the corpus we can output the first email
+
+ align:start position:0%
+the corpus we can output the first email
+ 
+
+ align:start position:0%
+the corpus we can output the first email
+in the corpus we'll start out by calling
+
+ align:start position:0%
+in the corpus we'll start out by calling
+ 
+
+ align:start position:0%
+in the corpus we'll start out by calling
+this to our wrap function to get it on
+
+ align:start position:0%
+this to our wrap function to get it on
+ 
+
+ align:start position:0%
+this to our wrap function to get it on
+multiple lines and then we can select
+
+ align:start position:0%
+multiple lines and then we can select
+ 
+
+ align:start position:0%
+multiple lines and then we can select
+the first element in the corpus using
+
+ align:start position:0%
+the first element in the corpus using
+ 
+
+ align:start position:0%
+the first element in the corpus using
+the double square bracket notation and
+
+ align:start position:0%
+the double square bracket notation and
+ 
+
+ align:start position:0%
+the double square bracket notation and
+selecting element 1 and we can see that
+
+ align:start position:0%
+selecting element 1 and we can see that
+ 
+
+ align:start position:0%
+selecting element 1 and we can see that
+this is exactly the same email that we
+
+ align:start position:0%
+this is exactly the same email that we
+ 
+
+ align:start position:0%
+this is exactly the same email that we
+saw originally so email about the
+
+ align:start position:0%
+saw originally so email about the
+ 
+
+ align:start position:0%
+saw originally so email about the
+working paper alright so now we're ready
+
+ align:start position:0%
+working paper alright so now we're ready
+ 
+
+ align:start position:0%
+working paper alright so now we're ready
+to pre-process the corpus using the TM
+
+ align:start position:0%
+to pre-process the corpus using the TM
+ 
+
+ align:start position:0%
+to pre-process the corpus using the TM
+map function
+
+ align:start position:0%
+map function
+ 
+
+ align:start position:0%
+map function
+so first we'll convert the corpus to
+
+ align:start position:0%
+so first we'll convert the corpus to
+ 
+
+ align:start position:0%
+so first we'll convert the corpus to
+lowercase using TM map and the two lower
+
+ align:start position:0%
+lowercase using TM map and the two lower
+ 
+
+ align:start position:0%
+lowercase using TM map and the two lower
+function still have corpus is equal to
+
+ align:start position:0%
+function still have corpus is equal to
+ 
+
+ align:start position:0%
+function still have corpus is equal to
+TM map of corpus and pass it along to
+
+ align:start position:0%
+TM map of corpus and pass it along to
+ 
+
+ align:start position:0%
+TM map of corpus and pass it along to
+lower alright and then we'll do the
+
+ align:start position:0%
+lower alright and then we'll do the
+ 
+
+ align:start position:0%
+lower alright and then we'll do the
+exact same thing except removing
+
+ align:start position:0%
+exact same thing except removing
+ 
+
+ align:start position:0%
+exact same thing except removing
+punctuation so I have corpus is equal to
+
+ align:start position:0%
+punctuation so I have corpus is equal to
+ 
+
+ align:start position:0%
+punctuation so I have corpus is equal to
+TM map of the corpus with the remove
+
+ align:start position:0%
+TM map of the corpus with the remove
+ 
+
+ align:start position:0%
+TM map of the corpus with the remove
+punctuation ok we'll remove the stop
+
+ align:start position:0%
+punctuation ok we'll remove the stop
+ 
+
+ align:start position:0%
+punctuation ok we'll remove the stop
+words with remove words function and
+
+ align:start position:0%
+words with remove words function and
+ 
+
+ align:start position:0%
+words with remove words function and
+we'll pass along to stop words of the
+
+ align:start position:0%
+we'll pass along to stop words of the
+ 
+
+ align:start position:0%
+we'll pass along to stop words of the
+English language as the words we want to
+
+ align:start position:0%
+English language as the words we want to
+ 
+
+ align:start position:0%
+English language as the words we want to
+remove and lastly we're going to send
+
+ align:start position:0%
+remove and lastly we're going to send
+ 
+
+ align:start position:0%
+remove and lastly we're going to send
+the document so if corpus is you put a
+
+ align:start position:0%
+the document so if corpus is you put a
+ 
+
+ align:start position:0%
+the document so if corpus is you put a
+TM map of corpus with the stem document
+
+ align:start position:0%
+TM map of corpus with the stem document
+ 
+
+ align:start position:0%
+TM map of corpus with the stem document
+function ok and now that we've gone
+
+ align:start position:0%
+function ok and now that we've gone
+ 
+
+ align:start position:0%
+function ok and now that we've gone
+through those for pre-processing steps
+
+ align:start position:0%
+through those for pre-processing steps
+ 
+
+ align:start position:0%
+through those for pre-processing steps
+we can take a second look at the first
+
+ align:start position:0%
+we can take a second look at the first
+ 
+
+ align:start position:0%
+we can take a second look at the first
+email in the corpus so again call STR
+
+ align:start position:0%
+email in the corpus so again call STR
+ 
+
+ align:start position:0%
+email in the corpus so again call STR
+wrap on corpus
+
+ align:start position:0%
+wrap on corpus
+ 
+
+ align:start position:0%
+wrap on corpus
+selecting the first email and now it
+
+ align:start position:0%
+selecting the first email and now it
+ 
+
+ align:start position:0%
+selecting the first email and now it
+looks quite a bit different let me come
+
+ align:start position:0%
+looks quite a bit different let me come
+ 
+
+ align:start position:0%
+looks quite a bit different let me come
+up to the top here it's a lot harder to
+
+ align:start position:0%
+up to the top here it's a lot harder to
+ 
+
+ align:start position:0%
+up to the top here it's a lot harder to
+read now that we removed all the stop
+
+ align:start position:0%
+read now that we removed all the stop
+ 
+
+ align:start position:0%
+read now that we removed all the stop
+words and punctuation and word stems but
+
+ align:start position:0%
+words and punctuation and word stems but
+ 
+
+ align:start position:0%
+words and punctuation and word stems but
+now the emails and this corpus are ready
+
+ align:start position:0%
+now the emails and this corpus are ready
+ 
+
+ align:start position:0%
+now the emails and this corpus are ready
+for our machine learning algorithms
\ No newline at end of file
diff --git a/qpdtzW8py0c.txt b/qpdtzW8py0c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07c988e73d58e7cf494b49be89368f9c2bccc0ec
--- /dev/null
+++ b/qpdtzW8py0c.txt
@@ -0,0 +1,2907 @@
+align:start position:0%
+ 
+Hello, I'm Mary Rudder from the Harvey
+
+ align:start position:0%
+Hello, I'm Mary Rudder from the Harvey
+ 
+
+ align:start position:0%
+Hello, I'm Mary Rudder from the Harvey
+Ken School in Charles Town and I teach
+
+ align:start position:0%
+Ken School in Charles Town and I teach
+ 
+
+ align:start position:0%
+Ken School in Charles Town and I teach
+kindergarten. Um, I use the Star
+
+ align:start position:0%
+kindergarten. Um, I use the Star
+ 
+
+ align:start position:0%
+kindergarten. Um, I use the Star
+Festival CD ROM as part of our unit on
+
+ align:start position:0%
+Festival CD ROM as part of our unit on
+ 
+
+ align:start position:0%
+Festival CD ROM as part of our unit on
+Japan and places in the world. I also
+
+ align:start position:0%
+Japan and places in the world. I also
+ 
+
+ align:start position:0%
+Japan and places in the world. I also
+use it as a connection between family
+
+ align:start position:0%
+use it as a connection between family
+ 
+
+ align:start position:0%
+use it as a connection between family
+life, um, family roots and just to make
+
+ align:start position:0%
+life, um, family roots and just to make
+ 
+
+ align:start position:0%
+life, um, family roots and just to make
+the adventure more real. We start our
+
+ align:start position:0%
+the adventure more real. We start our
+ 
+
+ align:start position:0%
+the adventure more real. We start our
+adventure on our airplane which the kids
+
+ align:start position:0%
+adventure on our airplane which the kids
+ 
+
+ align:start position:0%
+adventure on our airplane which the kids
+painted and designed and then we prepare
+
+ align:start position:0%
+painted and designed and then we prepare
+ 
+
+ align:start position:0%
+painted and designed and then we prepare
+for our trip by packing our suitcases
+
+ align:start position:0%
+for our trip by packing our suitcases
+ 
+
+ align:start position:0%
+for our trip by packing our suitcases
+which of course are made of paper since
+
+ align:start position:0%
+which of course are made of paper since
+ 
+
+ align:start position:0%
+which of course are made of paper since
+kindergarten is the paper capital of the
+
+ align:start position:0%
+kindergarten is the paper capital of the
+ 
+
+ align:start position:0%
+kindergarten is the paper capital of the
+world. Um, inside the suitcase is a
+
+ align:start position:0%
+world. Um, inside the suitcase is a
+ 
+
+ align:start position:0%
+world. Um, inside the suitcase is a
+plain piece of white paper and the
+
+ align:start position:0%
+plain piece of white paper and the
+ 
+
+ align:start position:0%
+plain piece of white paper and the
+children are asked to draw the things
+
+ align:start position:0%
+children are asked to draw the things
+ 
+
+ align:start position:0%
+children are asked to draw the things
+that they think they will need on their
+
+ align:start position:0%
+that they think they will need on their
+ 
+
+ align:start position:0%
+that they think they will need on their
+trip. And sometimes you get what they
+
+ align:start position:0%
+trip. And sometimes you get what they
+ 
+
+ align:start position:0%
+trip. And sometimes you get what they
+would need. Some children want to bring
+
+ align:start position:0%
+would need. Some children want to bring
+ 
+
+ align:start position:0%
+would need. Some children want to bring
+all the toys they own. And one of the
+
+ align:start position:0%
+all the toys they own. And one of the
+ 
+
+ align:start position:0%
+all the toys they own. And one of the
+boys this year wanted to bring an ice
+
+ align:start position:0%
+boys this year wanted to bring an ice
+ 
+
+ align:start position:0%
+boys this year wanted to bring an ice
+cream machine. Unfortunately, when he
+
+ align:start position:0%
+cream machine. Unfortunately, when he
+ 
+
+ align:start position:0%
+cream machine. Unfortunately, when he
+went through customs in Japan, they
+
+ align:start position:0%
+went through customs in Japan, they
+ 
+
+ align:start position:0%
+went through customs in Japan, they
+would not let him in. They made him take
+
+ align:start position:0%
+would not let him in. They made him take
+ 
+
+ align:start position:0%
+would not let him in. They made him take
+it out of his suitcase cuz I am the
+
+ align:start position:0%
+it out of his suitcase cuz I am the
+ 
+
+ align:start position:0%
+it out of his suitcase cuz I am the
+customs official.
+
+ align:start position:0%
+customs official.
+ 
+
+ align:start position:0%
+customs official.
+Um after we prepare we also
+
+ align:start position:0%
+Um after we prepare we also
+ 
+
+ align:start position:0%
+Um after we prepare we also
+have our airline tickets and since we
+
+ align:start position:0%
+have our airline tickets and since we
+ 
+
+ align:start position:0%
+have our airline tickets and since we
+will be traveling to several places on
+
+ align:start position:0%
+will be traveling to several places on
+ 
+
+ align:start position:0%
+will be traveling to several places on
+the earth on the world um there are
+
+ align:start position:0%
+the earth on the world um there are
+ 
+
+ align:start position:0%
+the earth on the world um there are
+several categories that it lists the
+
+ align:start position:0%
+several categories that it lists the
+ 
+
+ align:start position:0%
+several categories that it lists the
+places we we will be going. Tokyo is our
+
+ align:start position:0%
+places we we will be going. Tokyo is our
+ 
+
+ align:start position:0%
+places we we will be going. Tokyo is our
+first stop although our trip will bring
+
+ align:start position:0%
+first stop although our trip will bring
+ 
+
+ align:start position:0%
+first stop although our trip will bring
+us all the way to Haratska which is
+
+ align:start position:0%
+us all the way to Haratska which is
+ 
+
+ align:start position:0%
+us all the way to Haratska which is
+where the star festival takes place. Um
+
+ align:start position:0%
+where the star festival takes place. Um
+ 
+
+ align:start position:0%
+where the star festival takes place. Um
+the children have a ticket in their
+
+ align:start position:0%
+the children have a ticket in their
+ 
+
+ align:start position:0%
+the children have a ticket in their
+boarding pass and quite a few children
+
+ align:start position:0%
+boarding pass and quite a few children
+ 
+
+ align:start position:0%
+boarding pass and quite a few children
+real understand what a boarding pass is.
+
+ align:start position:0%
+real understand what a boarding pass is.
+ 
+
+ align:start position:0%
+real understand what a boarding pass is.
+So when they receive this they thought
+
+ align:start position:0%
+So when they receive this they thought
+ 
+
+ align:start position:0%
+So when they receive this they thought
+the trip was almost real. A few of the
+
+ align:start position:0%
+the trip was almost real. A few of the
+ 
+
+ align:start position:0%
+the trip was almost real. A few of the
+children went home and said I'm going to
+
+ align:start position:0%
+children went home and said I'm going to
+ 
+
+ align:start position:0%
+children went home and said I'm going to
+Japan tomorrow but you don't need to
+
+ align:start position:0%
+Japan tomorrow but you don't need to
+ 
+
+ align:start position:0%
+Japan tomorrow but you don't need to
+worry mom cuz I'm going to be home by
+
+ align:start position:0%
+worry mom cuz I'm going to be home by
+ 
+
+ align:start position:0%
+worry mom cuz I'm going to be home by
+8:00 tonight. So I also issued them a
+
+ align:start position:0%
+8:00 tonight. So I also issued them a
+ 
+
+ align:start position:0%
+8:00 tonight. So I also issued them a
+passport. Put their picture in it. Had
+
+ align:start position:0%
+passport. Put their picture in it. Had
+ 
+
+ align:start position:0%
+passport. Put their picture in it. Had
+them sign their name. checked to see if
+
+ align:start position:0%
+them sign their name. checked to see if
+ 
+
+ align:start position:0%
+them sign their name. checked to see if
+they knew their address because this is
+
+ align:start position:0%
+they knew their address because this is
+ 
+
+ align:start position:0%
+they knew their address because this is
+an important fact u fact toy the
+
+ align:start position:0%
+an important fact u fact toy the
+ 
+
+ align:start position:0%
+an important fact u fact toy the
+kindergarten children are expected to
+
+ align:start position:0%
+kindergarten children are expected to
+ 
+
+ align:start position:0%
+kindergarten children are expected to
+learn a few didn't know went home and
+
+ align:start position:0%
+learn a few didn't know went home and
+ 
+
+ align:start position:0%
+learn a few didn't know went home and
+found out their birth date again a few
+
+ align:start position:0%
+found out their birth date again a few
+ 
+
+ align:start position:0%
+found out their birth date again a few
+didn't know left a space on the back for
+
+ align:start position:0%
+didn't know left a space on the back for
+ 
+
+ align:start position:0%
+didn't know left a space on the back for
+the stamps for when they go through
+
+ align:start position:0%
+the stamps for when they go through
+ 
+
+ align:start position:0%
+the stamps for when they go through
+customs so as you can see we are in
+
+ align:start position:0%
+customs so as you can see we are in
+ 
+
+ align:start position:0%
+customs so as you can see we are in
+Japan so in the afternoon because it's
+
+ align:start position:0%
+Japan so in the afternoon because it's
+ 
+
+ align:start position:0%
+Japan so in the afternoon because it's
+an 18-hour flight from
+
+ align:start position:0%
+an 18-hour flight from
+ 
+
+ align:start position:0%
+an 18-hour flight from
+Boston we board the ship we board the
+
+ align:start position:0%
+Boston we board the ship we board the
+ 
+
+ align:start position:0%
+Boston we board the ship we board the
+airship just before we're leaving and
+
+ align:start position:0%
+airship just before we're leaving and
+ 
+
+ align:start position:0%
+airship just before we're leaving and
+for the day. And I collect their tickets
+
+ align:start position:0%
+for the day. And I collect their tickets
+ 
+
+ align:start position:0%
+for the day. And I collect their tickets
+and their suitcases and stow them under
+
+ align:start position:0%
+and their suitcases and stow them under
+ 
+
+ align:start position:0%
+and their suitcases and stow them under
+board and behind the airplane is seats.
+
+ align:start position:0%
+board and behind the airplane is seats.
+ 
+
+ align:start position:0%
+board and behind the airplane is seats.
+And they sit in
+
+ align:start position:0%
+And they sit in
+ 
+
+ align:start position:0%
+And they sit in
+rows just as they would in a airplane.
+
+ align:start position:0%
+rows just as they would in a airplane.
+ 
+
+ align:start position:0%
+rows just as they would in a airplane.
+And they say, "Oh, uh, when are we going
+
+ align:start position:0%
+And they say, "Oh, uh, when are we going
+ 
+
+ align:start position:0%
+And they say, "Oh, uh, when are we going
+to be in Japan?" And I I will tell them,
+
+ align:start position:0%
+to be in Japan?" And I I will tell them,
+ 
+
+ align:start position:0%
+to be in Japan?" And I I will tell them,
+"You have to go home tonight. Go to bed
+
+ align:start position:0%
+"You have to go home tonight. Go to bed
+ 
+
+ align:start position:0%
+"You have to go home tonight. Go to bed
+in your own bed. And when you come back
+
+ align:start position:0%
+in your own bed. And when you come back
+ 
+
+ align:start position:0%
+in your own bed. And when you come back
+in the morning, we will be almost in
+
+ align:start position:0%
+in the morning, we will be almost in
+ 
+
+ align:start position:0%
+in the morning, we will be almost in
+Japan. So they come in the following
+
+ align:start position:0%
+Japan. So they come in the following
+ 
+
+ align:start position:0%
+Japan. So they come in the following
+morning. And when they came in, the
+
+ align:start position:0%
+morning. And when they came in, the
+ 
+
+ align:start position:0%
+morning. And when they came in, the
+Japanese house is up. So we'll talk
+
+ align:start position:0%
+Japanese house is up. So we'll talk
+ 
+
+ align:start position:0%
+Japanese house is up. So we'll talk
+about that in a few minutes. Before we
+
+ align:start position:0%
+about that in a few minutes. Before we
+ 
+
+ align:start position:0%
+about that in a few minutes. Before we
+start our trip, I want the children to
+
+ align:start position:0%
+start our trip, I want the children to
+ 
+
+ align:start position:0%
+start our trip, I want the children to
+know where in the world they are and
+
+ align:start position:0%
+know where in the world they are and
+ 
+
+ align:start position:0%
+know where in the world they are and
+where they've come from. So we make a
+
+ align:start position:0%
+where they've come from. So we make a
+ 
+
+ align:start position:0%
+where they've come from. So we make a
+big mural map, which they help paint. Of
+
+ align:start position:0%
+big mural map, which they help paint. Of
+ 
+
+ align:start position:0%
+big mural map, which they help paint. Of
+course, you will notice that some of the
+
+ align:start position:0%
+course, you will notice that some of the
+ 
+
+ align:start position:0%
+course, you will notice that some of the
+continents aren't quite correct because
+
+ align:start position:0%
+continents aren't quite correct because
+ 
+
+ align:start position:0%
+continents aren't quite correct because
+when they get the paint in their hand,
+
+ align:start position:0%
+when they get the paint in their hand,
+ 
+
+ align:start position:0%
+when they get the paint in their hand,
+they tend to start painting areas that
+
+ align:start position:0%
+they tend to start painting areas that
+ 
+
+ align:start position:0%
+they tend to start painting areas that
+should be water and end up to be land
+
+ align:start position:0%
+should be water and end up to be land
+ 
+
+ align:start position:0%
+should be water and end up to be land
+and land that should be water or land
+
+ align:start position:0%
+and land that should be water or land
+ 
+
+ align:start position:0%
+and land that should be water or land
+that ends up to be water. So, but it has
+
+ align:start position:0%
+that ends up to be water. So, but it has
+ 
+
+ align:start position:0%
+that ends up to be water. So, but it has
+a general feeling for it. And I send
+
+ align:start position:0%
+a general feeling for it. And I send
+ 
+
+ align:start position:0%
+a general feeling for it. And I send
+home a
+
+ align:start position:0%
+home a
+ 
+
+ align:start position:0%
+home a
+questionnaire asking the parents because
+
+ align:start position:0%
+questionnaire asking the parents because
+ 
+
+ align:start position:0%
+questionnaire asking the parents because
+most of the children in the class come
+
+ align:start position:0%
+most of the children in the class come
+ 
+
+ align:start position:0%
+most of the children in the class come
+from other countries. In fact, just
+
+ align:start position:0%
+from other countries. In fact, just
+ 
+
+ align:start position:0%
+from other countries. In fact, just
+about everybody in America comes from
+
+ align:start position:0%
+about everybody in America comes from
+ 
+
+ align:start position:0%
+about everybody in America comes from
+another country if you trace back far
+
+ align:start position:0%
+another country if you trace back far
+ 
+
+ align:start position:0%
+another country if you trace back far
+enough. And they are asked just to write
+
+ align:start position:0%
+enough. And they are asked just to write
+ 
+
+ align:start position:0%
+enough. And they are asked just to write
+the child's name and if you have I
+
+ align:start position:0%
+the child's name and if you have I
+ 
+
+ align:start position:0%
+the child's name and if you have I
+mentioned mom, dad, grandparents, what
+
+ align:start position:0%
+mentioned mom, dad, grandparents, what
+ 
+
+ align:start position:0%
+mentioned mom, dad, grandparents, what
+countries they come from. And when they
+
+ align:start position:0%
+countries they come from. And when they
+ 
+
+ align:start position:0%
+countries they come from. And when they
+come in, I've already used the same
+
+ align:start position:0%
+come in, I've already used the same
+ 
+
+ align:start position:0%
+come in, I've already used the same
+pictures that we have on the passports
+
+ align:start position:0%
+pictures that we have on the passports
+ 
+
+ align:start position:0%
+pictures that we have on the passports
+to make a little um card which will
+
+ align:start position:0%
+to make a little um card which will
+ 
+
+ align:start position:0%
+to make a little um card which will
+mount on our map with a line that will
+
+ align:start position:0%
+mount on our map with a line that will
+ 
+
+ align:start position:0%
+mount on our map with a line that will
+go from the girl's name or boy's name to
+
+ align:start position:0%
+go from the girl's name or boy's name to
+ 
+
+ align:start position:0%
+go from the girl's name or boy's name to
+Boston to wherever they came from. So
+
+ align:start position:0%
+Boston to wherever they came from. So
+ 
+
+ align:start position:0%
+Boston to wherever they came from. So
+the children will actually be able to
+
+ align:start position:0%
+the children will actually be able to
+ 
+
+ align:start position:0%
+the children will actually be able to
+see where in the world their family came
+
+ align:start position:0%
+see where in the world their family came
+ 
+
+ align:start position:0%
+see where in the world their family came
+from. And it's quite interesting and
+
+ align:start position:0%
+from. And it's quite interesting and
+ 
+
+ align:start position:0%
+from. And it's quite interesting and
+they become very proud. In fact, the
+
+ align:start position:0%
+they become very proud. In fact, the
+ 
+
+ align:start position:0%
+they become very proud. In fact, the
+parents came in when they saw the map up
+
+ align:start position:0%
+parents came in when they saw the map up
+ 
+
+ align:start position:0%
+parents came in when they saw the map up
+and said, "Oh, this is where I come
+
+ align:start position:0%
+and said, "Oh, this is where I come
+ 
+
+ align:start position:0%
+and said, "Oh, this is where I come
+from. This is so they didn't know I was
+
+ align:start position:0%
+from. This is so they didn't know I was
+ 
+
+ align:start position:0%
+from. This is so they didn't know I was
+going to ask them the question." So,
+
+ align:start position:0%
+going to ask them the question." So,
+ 
+
+ align:start position:0%
+going to ask them the question." So,
+they'll I think they'll really be
+
+ align:start position:0%
+they'll I think they'll really be
+ 
+
+ align:start position:0%
+they'll I think they'll really be
+thrilled when they see their kids up
+
+ align:start position:0%
+thrilled when they see their kids up
+ 
+
+ align:start position:0%
+thrilled when they see their kids up
+with the name connected. I think it's
+
+ align:start position:0%
+with the name connected. I think it's
+ 
+
+ align:start position:0%
+with the name connected. I think it's
+just important because it gives them a
+
+ align:start position:0%
+just important because it gives them a
+ 
+
+ align:start position:0%
+just important because it gives them a
+sense of, you know, where where they
+
+ align:start position:0%
+sense of, you know, where where they
+ 
+
+ align:start position:0%
+sense of, you know, where where they
+came from and it also sort of gives
+
+ align:start position:0%
+came from and it also sort of gives
+ 
+
+ align:start position:0%
+came from and it also sort of gives
+value to their background. It was
+
+ align:start position:0%
+value to their background. It was
+ 
+
+ align:start position:0%
+value to their background. It was
+interesting that I sent home because we
+
+ align:start position:0%
+interesting that I sent home because we
+ 
+
+ align:start position:0%
+interesting that I sent home because we
+will be doing this paper. Um, and we
+
+ align:start position:0%
+will be doing this paper. Um, and we
+ 
+
+ align:start position:0%
+will be doing this paper. Um, and we
+will be doing a family tree, but I
+
+ align:start position:0%
+will be doing a family tree, but I
+ 
+
+ align:start position:0%
+will be doing a family tree, but I
+didn't ask for a family tree. One of the
+
+ align:start position:0%
+didn't ask for a family tree. One of the
+ 
+
+ align:start position:0%
+didn't ask for a family tree. One of the
+kids came back with it all written on
+
+ align:start position:0%
+kids came back with it all written on
+ 
+
+ align:start position:0%
+kids came back with it all written on
+the back of the paper. So, I thought
+
+ align:start position:0%
+the back of the paper. So, I thought
+ 
+
+ align:start position:0%
+the back of the paper. So, I thought
+this is perfect because when we start
+
+ align:start position:0%
+this is perfect because when we start
+ 
+
+ align:start position:0%
+this is perfect because when we start
+looking at Shagaru's family tree and we
+
+ align:start position:0%
+looking at Shagaru's family tree and we
+ 
+
+ align:start position:0%
+looking at Shagaru's family tree and we
+start doing our own here, Juan has his
+
+ align:start position:0%
+start doing our own here, Juan has his
+ 
+
+ align:start position:0%
+start doing our own here, Juan has his
+all done. Only we'll probably do it on a
+
+ align:start position:0%
+all done. Only we'll probably do it on a
+ 
+
+ align:start position:0%
+all done. Only we'll probably do it on a
+bigger piece of drawing paper so you can
+
+ align:start position:0%
+bigger piece of drawing paper so you can
+ 
+
+ align:start position:0%
+bigger piece of drawing paper so you can
+see it and I'll have him script the
+
+ align:start position:0%
+see it and I'll have him script the
+ 
+
+ align:start position:0%
+see it and I'll have him script the
+words. So I think that um it's
+
+ align:start position:0%
+words. So I think that um it's
+ 
+
+ align:start position:0%
+words. So I think that um it's
+interesting the things you come out with
+
+ align:start position:0%
+interesting the things you come out with
+ 
+
+ align:start position:0%
+interesting the things you come out with
+and the things that come out of the
+
+ align:start position:0%
+and the things that come out of the
+ 
+
+ align:start position:0%
+and the things that come out of the
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because um I want to go to Haratzka
+
+ align:start position:0%
+because um I want to go to Haratzka
+ 
+
+ align:start position:0%
+because um I want to go to Haratzka
+because part of our adventure in Japan
+
+ align:start position:0%
+because part of our adventure in Japan
+ 
+
+ align:start position:0%
+because part of our adventure in Japan
+is the big festival and what we will be
+
+ align:start position:0%
+is the big festival and what we will be
+ 
+
+ align:start position:0%
+is the big festival and what we will be
+doing as we travel with Shagarro through
+
+ align:start position:0%
+doing as we travel with Shagarro through
+ 
+
+ align:start position:0%
+doing as we travel with Shagarro through
+the different points going to the um
+
+ align:start position:0%
+the different points going to the um
+ 
+
+ align:start position:0%
+the different points going to the um
+train station or from the train station
+
+ align:start position:0%
+train station or from the train station
+ 
+
+ align:start position:0%
+train station or from the train station
+on the bus looking to see how it's the
+
+ align:start position:0%
+on the bus looking to see how it's the
+ 
+
+ align:start position:0%
+on the bus looking to see how it's the
+same as what they're used to or how it's
+
+ align:start position:0%
+same as what they're used to or how it's
+ 
+
+ align:start position:0%
+same as what they're used to or how it's
+different from what they know. They were
+
+ align:start position:0%
+different from what they know. They were
+ 
+
+ align:start position:0%
+different from what they know. They were
+thrilled to see the subway station, the
+
+ align:start position:0%
+thrilled to see the subway station, the
+ 
+
+ align:start position:0%
+thrilled to see the subway station, the
+train station, because they noticed
+
+ align:start position:0%
+train station, because they noticed
+ 
+
+ align:start position:0%
+train station, because they noticed
+right away it didn't look like a train
+
+ align:start position:0%
+right away it didn't look like a train
+ 
+
+ align:start position:0%
+right away it didn't look like a train
+station that they are familiar with and
+
+ align:start position:0%
+station that they are familiar with and
+ 
+
+ align:start position:0%
+station that they are familiar with and
+um they could see the little shops in
+
+ align:start position:0%
+um they could see the little shops in
+ 
+
+ align:start position:0%
+um they could see the little shops in
+the background. So, they were, "Wow,
+
+ align:start position:0%
+the background. So, they were, "Wow,
+ 
+
+ align:start position:0%
+the background. So, they were, "Wow,
+that's really pretty." So, I think
+
+ align:start position:0%
+that's really pretty." So, I think
+ 
+
+ align:start position:0%
+that's really pretty." So, I think
+that's um interesting that now they're
+
+ align:start position:0%
+that's um interesting that now they're
+ 
+
+ align:start position:0%
+that's um interesting that now they're
+thinking of what they know and they're
+
+ align:start position:0%
+thinking of what they know and they're
+ 
+
+ align:start position:0%
+thinking of what they know and they're
+learning something different. Um going
+
+ align:start position:0%
+learning something different. Um going
+ 
+
+ align:start position:0%
+learning something different. Um going
+to bring you over to our house.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the bell's going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to I should sit on the floor, but I
+
+ align:start position:0%
+to I should sit on the floor, but I
+ 
+
+ align:start position:0%
+to I should sit on the floor, but I
+won't cuz I'll never get up
+
+ align:start position:0%
+won't cuz I'll never get up
+ 
+
+ align:start position:0%
+won't cuz I'll never get up
+again. Um, this is
+
+ align:start position:0%
+again. Um, this is
+ 
+
+ align:start position:0%
+again. Um, this is
+Haruku and she's named after a little
+
+ align:start position:0%
+Haruku and she's named after a little
+ 
+
+ align:start position:0%
+Haruku and she's named after a little
+girl I met in Japan when I went on a
+
+ align:start position:0%
+girl I met in Japan when I went on a
+ 
+
+ align:start position:0%
+girl I met in Japan when I went on a
+visit. And so when I came back, I
+
+ align:start position:0%
+visit. And so when I came back, I
+ 
+
+ align:start position:0%
+visit. And so when I came back, I
+thought kids like to relate to other
+
+ align:start position:0%
+thought kids like to relate to other
+ 
+
+ align:start position:0%
+thought kids like to relate to other
+kids. Um, and before I introduce Shagaru
+
+ align:start position:0%
+kids. Um, and before I introduce Shagaru
+ 
+
+ align:start position:0%
+kids. Um, and before I introduce Shagaru
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+CD, uh, Heruku introduces her
+
+ align:start position:0%
+CD, uh, Heruku introduces her
+ 
+
+ align:start position:0%
+CD, uh, Heruku introduces her
+grandmother's house because I don't want
+
+ align:start position:0%
+grandmother's house because I don't want
+ 
+
+ align:start position:0%
+grandmother's house because I don't want
+the children thinking that the every
+
+ align:start position:0%
+the children thinking that the every
+ 
+
+ align:start position:0%
+the children thinking that the every
+child in Japan lives in a house that's a
+
+ align:start position:0%
+child in Japan lives in a house that's a
+ 
+
+ align:start position:0%
+child in Japan lives in a house that's a
+traditional Japanese style house that
+
+ align:start position:0%
+traditional Japanese style house that
+ 
+
+ align:start position:0%
+traditional Japanese style house that
+most of the children when they talk to
+
+ align:start position:0%
+most of the children when they talk to
+ 
+
+ align:start position:0%
+most of the children when they talk to
+them would probably live in an
+
+ align:start position:0%
+them would probably live in an
+ 
+
+ align:start position:0%
+them would probably live in an
+apartment. U, but they might they would
+
+ align:start position:0%
+apartment. U, but they might they would
+ 
+
+ align:start position:0%
+apartment. U, but they might they would
+probably have a tatami mat on the floor
+
+ align:start position:0%
+probably have a tatami mat on the floor
+ 
+
+ align:start position:0%
+probably have a tatami mat on the floor
+and they might have the kadatu. um at
+
+ align:start position:0%
+and they might have the kadatu. um at
+ 
+
+ align:start position:0%
+and they might have the kadatu. um at
+their table or they might have a western
+
+ align:start position:0%
+their table or they might have a western
+ 
+
+ align:start position:0%
+their table or they might have a western
+table. So I think it's important that
+
+ align:start position:0%
+table. So I think it's important that
+ 
+
+ align:start position:0%
+table. So I think it's important that
+they know some of the things that um the
+
+ align:start position:0%
+they know some of the things that um the
+ 
+
+ align:start position:0%
+they know some of the things that um the
+the children in Japan are doing now. In
+
+ align:start position:0%
+the children in Japan are doing now. In
+ 
+
+ align:start position:0%
+the children in Japan are doing now. In
+fact, we have Japanese eels which is
+
+ align:start position:0%
+fact, we have Japanese eels which is
+ 
+
+ align:start position:0%
+fact, we have Japanese eels which is
+really a great great deal of fun.
+
+ align:start position:0%
+really a great great deal of fun.
+ 
+
+ align:start position:0%
+really a great great deal of fun.
+They're first graders, but they uh are
+
+ align:start position:0%
+They're first graders, but they uh are
+ 
+
+ align:start position:0%
+They're first graders, but they uh are
+kind enough to write to us. I show um
+
+ align:start position:0%
+kind enough to write to us. I show um
+ 
+
+ align:start position:0%
+kind enough to write to us. I show um
+Haku Haku in her regular clothes, but I
+
+ align:start position:0%
+Haku Haku in her regular clothes, but I
+ 
+
+ align:start position:0%
+Haku Haku in her regular clothes, but I
+have this little angel that was sitting
+
+ align:start position:0%
+have this little angel that was sitting
+ 
+
+ align:start position:0%
+have this little angel that was sitting
+up here and the kids all said, "What is
+
+ align:start position:0%
+up here and the kids all said, "What is
+ 
+
+ align:start position:0%
+up here and the kids all said, "What is
+that? What is that?" And then they said,
+
+ align:start position:0%
+that? What is that?" And then they said,
+ 
+
+ align:start position:0%
+that? What is that?" And then they said,
+"She has wings. She has wings." So I
+
+ align:start position:0%
+"She has wings. She has wings." So I
+ 
+
+ align:start position:0%
+"She has wings. She has wings." So I
+said, "Oh, what do you think this is?"
+
+ align:start position:0%
+said, "Oh, what do you think this is?"
+ 
+
+ align:start position:0%
+said, "Oh, what do you think this is?"
+And they recognized right away she's an
+
+ align:start position:0%
+And they recognized right away she's an
+ 
+
+ align:start position:0%
+And they recognized right away she's an
+angel. And I said, "Why would I want to
+
+ align:start position:0%
+angel. And I said, "Why would I want to
+ 
+
+ align:start position:0%
+angel. And I said, "Why would I want to
+have her around?" And oh, she's good
+
+ align:start position:0%
+have her around?" And oh, she's good
+ 
+
+ align:start position:0%
+have her around?" And oh, she's good
+luck. And I said, "But what's she
+
+ align:start position:0%
+luck. And I said, "But what's she
+ 
+
+ align:start position:0%
+luck. And I said, "But what's she
+wearing?" And we talked about she has
+
+ align:start position:0%
+wearing?" And we talked about she has
+ 
+
+ align:start position:0%
+wearing?" And we talked about she has
+the kimono on and she has the Gita
+
+ align:start position:0%
+the kimono on and she has the Gita
+ 
+
+ align:start position:0%
+the kimono on and she has the Gita
+shoes. So, it's sort of like a a tie
+
+ align:start position:0%
+shoes. So, it's sort of like a a tie
+ 
+
+ align:start position:0%
+shoes. So, it's sort of like a a tie
+between the old and the the new. And I
+
+ align:start position:0%
+between the old and the the new. And I
+ 
+
+ align:start position:0%
+between the old and the the new. And I
+think the CD ROM does that a lot when
+
+ align:start position:0%
+think the CD ROM does that a lot when
+ 
+
+ align:start position:0%
+think the CD ROM does that a lot when
+you see the older pictures and um you
+
+ align:start position:0%
+you see the older pictures and um you
+ 
+
+ align:start position:0%
+you see the older pictures and um you
+know the festival dress. Uh you know, I
+
+ align:start position:0%
+know the festival dress. Uh you know, I
+ 
+
+ align:start position:0%
+know the festival dress. Uh you know, I
+think it's important for them to
+
+ align:start position:0%
+think it's important for them to
+ 
+
+ align:start position:0%
+think it's important for them to
+recognize it. Um I tie in a lot of
+
+ align:start position:0%
+recognize it. Um I tie in a lot of
+ 
+
+ align:start position:0%
+recognize it. Um I tie in a lot of
+literature and I introduced the story by
+
+ align:start position:0%
+literature and I introduced the story by
+ 
+
+ align:start position:0%
+literature and I introduced the story by
+saying it's her
+
+ align:start position:0%
+saying it's her
+ 
+
+ align:start position:0%
+saying it's her
+favorite. So they think this is great if
+
+ align:start position:0%
+favorite. So they think this is great if
+ 
+
+ align:start position:0%
+favorite. So they think this is great if
+she liked this story and they sit with
+
+ align:start position:0%
+she liked this story and they sit with
+ 
+
+ align:start position:0%
+she liked this story and they sit with
+her after the story is read and um we'll
+
+ align:start position:0%
+her after the story is read and um we'll
+ 
+
+ align:start position:0%
+her after the story is read and um we'll
+reread it or go through the pages
+
+ align:start position:0%
+reread it or go through the pages
+ 
+
+ align:start position:0%
+reread it or go through the pages
+together or they'll all sit around the
+
+ align:start position:0%
+together or they'll all sit around the
+ 
+
+ align:start position:0%
+together or they'll all sit around the
+table and try to oh look at the pictures
+
+ align:start position:0%
+table and try to oh look at the pictures
+ 
+
+ align:start position:0%
+table and try to oh look at the pictures
+and talk to her. They were we had our
+
+ align:start position:0%
+and talk to her. They were we had our
+ 
+
+ align:start position:0%
+and talk to her. They were we had our
+friends in and we were singing songs
+
+ align:start position:0%
+friends in and we were singing songs
+ 
+
+ align:start position:0%
+friends in and we were singing songs
+together and they were making her hands
+
+ align:start position:0%
+together and they were making her hands
+ 
+
+ align:start position:0%
+together and they were making her hands
+clap because they wanted her to you know
+
+ align:start position:0%
+clap because they wanted her to you know
+ 
+
+ align:start position:0%
+clap because they wanted her to you know
+while we're doing we're clapping they
+
+ align:start position:0%
+while we're doing we're clapping they
+ 
+
+ align:start position:0%
+while we're doing we're clapping they
+wanted her to clap so they were like
+
+ align:start position:0%
+wanted her to clap so they were like
+ 
+
+ align:start position:0%
+wanted her to clap so they were like
+really including her as part of the
+
+ align:start position:0%
+really including her as part of the
+ 
+
+ align:start position:0%
+really including her as part of the
+classroom. I think it's important for
+
+ align:start position:0%
+classroom. I think it's important for
+ 
+
+ align:start position:0%
+classroom. I think it's important for
+the children to really become involved
+
+ align:start position:0%
+the children to really become involved
+ 
+
+ align:start position:0%
+the children to really become involved
+in things to make it important to them.
+
+ align:start position:0%
+in things to make it important to them.
+ 
+
+ align:start position:0%
+in things to make it important to them.
+Um we and I told them today they noticed
+
+ align:start position:0%
+Um we and I told them today they noticed
+ 
+
+ align:start position:0%
+Um we and I told them today they noticed
+the festival decorations on the uh
+
+ align:start position:0%
+the festival decorations on the uh
+ 
+
+ align:start position:0%
+the festival decorations on the uh
+opening screen and on some of the
+
+ align:start position:0%
+opening screen and on some of the
+ 
+
+ align:start position:0%
+opening screen and on some of the
+pictures that they saw and they said,
+
+ align:start position:0%
+pictures that they saw and they said,
+ 
+
+ align:start position:0%
+pictures that they saw and they said,
+"Oh, look at that." Uh especially the
+
+ align:start position:0%
+"Oh, look at that." Uh especially the
+ 
+
+ align:start position:0%
+"Oh, look at that." Uh especially the
+dragon. Look at the dragon. I said, "Oh,
+
+ align:start position:0%
+dragon. Look at the dragon. I said, "Oh,
+ 
+
+ align:start position:0%
+dragon. Look at the dragon. I said, "Oh,
+that's part of the festival." And we're
+
+ align:start position:0%
+that's part of the festival." And we're
+ 
+
+ align:start position:0%
+that's part of the festival." And we're
+traveling on this train to go to
+
+ align:start position:0%
+traveling on this train to go to
+ 
+
+ align:start position:0%
+traveling on this train to go to
+Haratska because we're going to be part
+
+ align:start position:0%
+Haratska because we're going to be part
+ 
+
+ align:start position:0%
+Haratska because we're going to be part
+of the festival. And we will plan at the
+
+ align:start position:0%
+of the festival. And we will plan at the
+ 
+
+ align:start position:0%
+of the festival. And we will plan at the
+end of uh two weeks of reading stories
+
+ align:start position:0%
+end of uh two weeks of reading stories
+ 
+
+ align:start position:0%
+end of uh two weeks of reading stories
+about Japan. True. And mostly folk a lot
+
+ align:start position:0%
+about Japan. True. And mostly folk a lot
+ 
+
+ align:start position:0%
+about Japan. True. And mostly folk a lot
+of folk tales. They are it allows them
+
+ align:start position:0%
+of folk tales. They are it allows them
+ 
+
+ align:start position:0%
+of folk tales. They are it allows them
+to process the story, tell what it's
+
+ align:start position:0%
+to process the story, tell what it's
+ 
+
+ align:start position:0%
+to process the story, tell what it's
+about. They pick out their favorite
+
+ align:start position:0%
+about. They pick out their favorite
+ 
+
+ align:start position:0%
+about. They pick out their favorite
+part. They read it. And um they thrilled
+
+ align:start position:0%
+part. They read it. And um they thrilled
+ 
+
+ align:start position:0%
+part. They read it. And um they thrilled
+me today. They read they they read the
+
+ align:start position:0%
+me today. They read they they read the
+ 
+
+ align:start position:0%
+me today. They read they they read the
+um wise old woman. And it sort of
+
+ align:start position:0%
+um wise old woman. And it sort of
+ 
+
+ align:start position:0%
+um wise old woman. And it sort of
+teaches why um the it's so important to
+
+ align:start position:0%
+teaches why um the it's so important to
+ 
+
+ align:start position:0%
+teaches why um the it's so important to
+respect elderly. And they took their
+
+ align:start position:0%
+respect elderly. And they took their
+ 
+
+ align:start position:0%
+respect elderly. And they took their
+favorite part and then they all stood
+
+ align:start position:0%
+favorite part and then they all stood
+ 
+
+ align:start position:0%
+favorite part and then they all stood
+and they started to write all the
+
+ align:start position:0%
+and they started to write all the
+ 
+
+ align:start position:0%
+and they started to write all the
+they're sounding out their words which
+
+ align:start position:0%
+they're sounding out their words which
+ 
+
+ align:start position:0%
+they're sounding out their words which
+is we're doing writers workshop. So this
+
+ align:start position:0%
+is we're doing writers workshop. So this
+ 
+
+ align:start position:0%
+is we're doing writers workshop. So this
+is like a big thing. I was so proud of
+
+ align:start position:0%
+is like a big thing. I was so proud of
+ 
+
+ align:start position:0%
+is like a big thing. I was so proud of
+them and they're going, "Oh, I got
+
+ align:start position:0%
+them and they're going, "Oh, I got
+ 
+
+ align:start position:0%
+them and they're going, "Oh, I got
+this." And they could read it. So I
+
+ align:start position:0%
+this." And they could read it. So I
+ 
+
+ align:start position:0%
+this." And they could read it. So I
+think it's um you know even though we're
+
+ align:start position:0%
+think it's um you know even though we're
+ 
+
+ align:start position:0%
+think it's um you know even though we're
+doing Japan, we're still doing language
+
+ align:start position:0%
+doing Japan, we're still doing language
+ 
+
+ align:start position:0%
+doing Japan, we're still doing language
+arts. We're still doing writing.
+
+ align:start position:0%
+arts. We're still doing writing.
+ 
+
+ align:start position:0%
+arts. We're still doing writing.
+So um I try to keep that connection and
+
+ align:start position:0%
+So um I try to keep that connection and
+ 
+
+ align:start position:0%
+So um I try to keep that connection and
+keep it tied in. So I told them that the
+
+ align:start position:0%
+keep it tied in. So I told them that the
+ 
+
+ align:start position:0%
+keep it tied in. So I told them that the
+festival we will be having a festival
+
+ align:start position:0%
+festival we will be having a festival
+ 
+
+ align:start position:0%
+festival we will be having a festival
+and we will need to do all the
+
+ align:start position:0%
+and we will need to do all the
+ 
+
+ align:start position:0%
+and we will need to do all the
+decorations just like they see in the
+
+ align:start position:0%
+decorations just like they see in the
+ 
+
+ align:start position:0%
+decorations just like they see in the
+movie and um or film and that we will be
+
+ align:start position:0%
+movie and um or film and that we will be
+ 
+
+ align:start position:0%
+movie and um or film and that we will be
+inviting our pals down the hall to come
+
+ align:start position:0%
+inviting our pals down the hall to come
+ 
+
+ align:start position:0%
+inviting our pals down the hall to come
+in and partake of all the festivities.
+
+ align:start position:0%
+in and partake of all the festivities.
+ 
+
+ align:start position:0%
+in and partake of all the festivities.
+And I said um because I knew I didn't
+
+ align:start position:0%
+And I said um because I knew I didn't
+ 
+
+ align:start position:0%
+And I said um because I knew I didn't
+want to have five kindergarten groups
+
+ align:start position:0%
+want to have five kindergarten groups
+ 
+
+ align:start position:0%
+want to have five kindergarten groups
+all in here at once. I said, you know,
+
+ align:start position:0%
+all in here at once. I said, you know,
+ 
+
+ align:start position:0%
+all in here at once. I said, you know,
+it takes a few days, so we'll probably
+
+ align:start position:0%
+it takes a few days, so we'll probably
+ 
+
+ align:start position:0%
+it takes a few days, so we'll probably
+have it several days with one class in,
+
+ align:start position:0%
+have it several days with one class in,
+ 
+
+ align:start position:0%
+have it several days with one class in,
+you know, each sitting. So, they were,
+
+ align:start position:0%
+you know, each sitting. So, they were,
+ 
+
+ align:start position:0%
+you know, each sitting. So, they were,
+oh, okay, we're ready. So, I think
+
+ align:start position:0%
+oh, okay, we're ready. So, I think
+ 
+
+ align:start position:0%
+oh, okay, we're ready. So, I think
+they're u I think this is really going
+
+ align:start position:0%
+they're u I think this is really going
+ 
+
+ align:start position:0%
+they're u I think this is really going
+to be a great adventure. All the past
+
+ align:start position:0%
+to be a great adventure. All the past
+ 
+
+ align:start position:0%
+to be a great adventure. All the past
+years I've done it, it's been a learning
+
+ align:start position:0%
+years I've done it, it's been a learning
+ 
+
+ align:start position:0%
+years I've done it, it's been a learning
+experience for the children and for
+
+ align:start position:0%
+experience for the children and for
+ 
+
+ align:start position:0%
+experience for the children and for
+myself. They always find a new angle or
+
+ align:start position:0%
+myself. They always find a new angle or
+ 
+
+ align:start position:0%
+myself. They always find a new angle or
+a different part to um key in on. And
+
+ align:start position:0%
+a different part to um key in on. And
+ 
+
+ align:start position:0%
+a different part to um key in on. And
+this especially this class, I think
+
+ align:start position:0%
+this especially this class, I think
+ 
+
+ align:start position:0%
+this especially this class, I think
+they're really keyed in on just they
+
+ align:start position:0%
+they're really keyed in on just they
+ 
+
+ align:start position:0%
+they're really keyed in on just they
+really think they're there. They're
+
+ align:start position:0%
+really think they're there. They're
+ 
+
+ align:start position:0%
+really think they're there. They're
+really and I think that hearing the
+
+ align:start position:0%
+really and I think that hearing the
+ 
+
+ align:start position:0%
+really and I think that hearing the
+noises, seeing the sights, going on the
+
+ align:start position:0%
+noises, seeing the sights, going on the
+ 
+
+ align:start position:0%
+noises, seeing the sights, going on the
+bus ride, seeing the fish market. I have
+
+ align:start position:0%
+bus ride, seeing the fish market. I have
+ 
+
+ align:start position:0%
+bus ride, seeing the fish market. I have
+to tell you the fish market. The girls
+
+ align:start position:0%
+to tell you the fish market. The girls
+ 
+
+ align:start position:0%
+to tell you the fish market. The girls
+saw the fish market. One girl goes, "I
+
+ align:start position:0%
+saw the fish market. One girl goes, "I
+ 
+
+ align:start position:0%
+saw the fish market. One girl goes, "I
+love fish sticks." And so I'm like,
+
+ align:start position:0%
+love fish sticks." And so I'm like,
+ 
+
+ align:start position:0%
+love fish sticks." And so I'm like,
+"They're cutting the fish up into big
+
+ align:start position:0%
+"They're cutting the fish up into big
+ 
+
+ align:start position:0%
+"They're cutting the fish up into big
+sections." I said, "Oh, that's nice.
+
+ align:start position:0%
+sections." I said, "Oh, that's nice.
+ 
+
+ align:start position:0%
+sections." I said, "Oh, that's nice.
+Well, you'll see all the fish later."
+
+ align:start position:0%
+Well, you'll see all the fish later."
+ 
+
+ align:start position:0%
+Well, you'll see all the fish later."
+And she goes, "I love." And I said,
+
+ align:start position:0%
+And she goes, "I love." And I said,
+ 
+
+ align:start position:0%
+And she goes, "I love." And I said,
+"Well, this is where it comes from. This
+
+ align:start position:0%
+"Well, this is where it comes from. This
+ 
+
+ align:start position:0%
+"Well, this is where it comes from. This
+is what happens before it's made into
+
+ align:start position:0%
+is what happens before it's made into
+ 
+
+ align:start position:0%
+is what happens before it's made into
+fish sticks." So, here we'll be talking
+
+ align:start position:0%
+fish sticks." So, here we'll be talking
+ 
+
+ align:start position:0%
+fish sticks." So, here we'll be talking
+about how food comes to the table. You
+
+ align:start position:0%
+about how food comes to the table. You
+ 
+
+ align:start position:0%
+about how food comes to the table. You
+know, what happens? It doesn't just
+
+ align:start position:0%
+know, what happens? It doesn't just
+ 
+
+ align:start position:0%
+know, what happens? It doesn't just
+materialize into fish sticks. We didn't
+
+ align:start position:0%
+materialize into fish sticks. We didn't
+ 
+
+ align:start position:0%
+materialize into fish sticks. We didn't
+just go out to the river and pull up the
+
+ align:start position:0%
+just go out to the river and pull up the
+ 
+
+ align:start position:0%
+just go out to the river and pull up the
+fish sticks. So, I think it's important
+
+ align:start position:0%
+fish sticks. So, I think it's important
+ 
+
+ align:start position:0%
+fish sticks. So, I think it's important
+for um you know, to see that we need
+
+ align:start position:0%
+for um you know, to see that we need
+ 
+
+ align:start position:0%
+for um you know, to see that we need
+food. People in Japan need food. People
+
+ align:start position:0%
+food. People in Japan need food. People
+ 
+
+ align:start position:0%
+food. People in Japan need food. People
+in China need food. We basically are all
+
+ align:start position:0%
+in China need food. We basically are all
+ 
+
+ align:start position:0%
+in China need food. We basically are all
+different, but we all have the same
+
+ align:start position:0%
+different, but we all have the same
+ 
+
+ align:start position:0%
+different, but we all have the same
+kinds of needs. So,
+
+ align:start position:0%
+kinds of needs. So,
+ 
+
+ align:start position:0%
+kinds of needs. So,
+um I don't know. It's an
+
+ align:start position:0%
+um I don't know. It's an
+ 
+
+ align:start position:0%
+um I don't know. It's an
+adventure. Want to see the old picture?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is a class I had that even at the
+
+ align:start position:0%
+This is a class I had that even at the
+ 
+
+ align:start position:0%
+This is a class I had that even at the
+very end of the
+
+ align:start position:0%
+very end of the
+ 
+
+ align:start position:0%
+very end of the
+day, they were trying to
+
+ align:start position:0%
+day, they were trying to
+ 
+
+ align:start position:0%
+day, they were trying to
+work because I totally identified
+
+ align:start position:0%
+work because I totally identified
+ 
+
+ align:start position:0%
+work because I totally identified
+with Chagarro on the uh film and they
+
+ align:start position:0%
+with Chagarro on the uh film and they
+ 
+
+ align:start position:0%
+with Chagarro on the uh film and they
+were looking at it and even when they
+
+ align:start position:0%
+were looking at it and even when they
+ 
+
+ align:start position:0%
+were looking at it and even when they
+were had their coat on and they're
+
+ align:start position:0%
+were had their coat on and they're
+ 
+
+ align:start position:0%
+were had their coat on and they're
+waiting for their parents to take them
+
+ align:start position:0%
+waiting for their parents to take them
+ 
+
+ align:start position:0%
+waiting for their parents to take them
+home, they would still go and explore in
+
+ align:start position:0%
+home, they would still go and explore in
+ 
+
+ align:start position:0%
+home, they would still go and explore in
+different parts of the um computer.
+
+ align:start position:0%
+different parts of the um computer.
+ 
+
+ align:start position:0%
+different parts of the um computer.
+Do I have a minute to tell you about the
+
+ align:start position:0%
+Do I have a minute to tell you about the
+ 
+
+ align:start position:0%
+Do I have a minute to tell you about the
+book? Sorry, I'm so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hot. This is a project I was involved
+
+ align:start position:0%
+hot. This is a project I was involved
+ 
+
+ align:start position:0%
+hot. This is a project I was involved
+in. It's a real I mean really adventure.
+
+ align:start position:0%
+in. It's a real I mean really adventure.
+ 
+
+ align:start position:0%
+in. It's a real I mean really adventure.
+And so um this is the story of Shagira
+
+ align:start position:0%
+And so um this is the story of Shagira
+ 
+
+ align:start position:0%
+And so um this is the story of Shagira
+when he was in Japan because the story
+
+ align:start position:0%
+when he was in Japan because the story
+ 
+
+ align:start position:0%
+when he was in Japan because the story
+on the CD ROM is when he's grown up. So,
+
+ align:start position:0%
+on the CD ROM is when he's grown up. So,
+ 
+
+ align:start position:0%
+on the CD ROM is when he's grown up. So,
+this takes all the information from the
+
+ align:start position:0%
+this takes all the information from the
+ 
+
+ align:start position:0%
+this takes all the information from the
+CD ROM and makes it into a story
+
+ align:start position:0%
+CD ROM and makes it into a story
+ 
+
+ align:start position:0%
+CD ROM and makes it into a story
+that a teacher or a parent or librarian
+
+ align:start position:0%
+that a teacher or a parent or librarian
+ 
+
+ align:start position:0%
+that a teacher or a parent or librarian
+could read to the children and it shows
+
+ align:start position:0%
+could read to the children and it shows
+ 
+
+ align:start position:0%
+could read to the children and it shows
+real pictures and it also shows
+
+ align:start position:0%
+real pictures and it also shows
+ 
+
+ align:start position:0%
+real pictures and it also shows
+beautiful drawings and I think that um
+
+ align:start position:0%
+beautiful drawings and I think that um
+ 
+
+ align:start position:0%
+beautiful drawings and I think that um
+just it it's a story that about his
+
+ align:start position:0%
+just it it's a story that about his
+ 
+
+ align:start position:0%
+just it it's a story that about his
+family before he left and sort of how he
+
+ align:start position:0%
+family before he left and sort of how he
+ 
+
+ align:start position:0%
+family before he left and sort of how he
+had a very happy joy joyful life with
+
+ align:start position:0%
+had a very happy joy joyful life with
+ 
+
+ align:start position:0%
+had a very happy joy joyful life with
+his family. And he's after it shows them
+
+ align:start position:0%
+his family. And he's after it shows them
+ 
+
+ align:start position:0%
+his family. And he's after it shows them
+all the things he does with his going to
+
+ align:start position:0%
+all the things he does with his going to
+ 
+
+ align:start position:0%
+all the things he does with his going to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+shrine, fishing with his grandfather,
+
+ align:start position:0%
+shrine, fishing with his grandfather,
+ 
+
+ align:start position:0%
+shrine, fishing with his grandfather,
+um visiting his grandfather's shoe shop,
+
+ align:start position:0%
+um visiting his grandfather's shoe shop,
+ 
+
+ align:start position:0%
+um visiting his grandfather's shoe shop,
+things that were just an intricral part
+
+ align:start position:0%
+things that were just an intricral part
+ 
+
+ align:start position:0%
+things that were just an intricral part
+of his life. going to the model shop and
+
+ align:start position:0%
+of his life. going to the model shop and
+ 
+
+ align:start position:0%
+of his life. going to the model shop and
+then to
+
+ align:start position:0%
+then to
+ 
+
+ align:start position:0%
+then to
+have, you know, when he's nine or 10 to
+
+ align:start position:0%
+have, you know, when he's nine or 10 to
+ 
+
+ align:start position:0%
+have, you know, when he's nine or 10 to
+be taken from his home roots and just
+
+ align:start position:0%
+be taken from his home roots and just
+ 
+
+ align:start position:0%
+be taken from his home roots and just
+brought over into a very strange world
+
+ align:start position:0%
+brought over into a very strange world
+ 
+
+ align:start position:0%
+brought over into a very strange world
+where he didn't speak the language and
+
+ align:start position:0%
+where he didn't speak the language and
+ 
+
+ align:start position:0%
+where he didn't speak the language and
+he didn't, you know, really understand
+
+ align:start position:0%
+he didn't, you know, really understand
+ 
+
+ align:start position:0%
+he didn't, you know, really understand
+or know any of the culture because he
+
+ align:start position:0%
+or know any of the culture because he
+ 
+
+ align:start position:0%
+or know any of the culture because he
+wasn't exposed to it. and then to have
+
+ align:start position:0%
+wasn't exposed to it. and then to have
+ 
+
+ align:start position:0%
+wasn't exposed to it. and then to have
+to deal with that. Um, and how he
+
+ align:start position:0%
+to deal with that. Um, and how he
+ 
+
+ align:start position:0%
+to deal with that. Um, and how he
+quickly became more Americanized that
+
+ align:start position:0%
+quickly became more Americanized that
+ 
+
+ align:start position:0%
+quickly became more Americanized that
+after a short or a year or so when
+
+ align:start position:0%
+after a short or a year or so when
+ 
+
+ align:start position:0%
+after a short or a year or so when
+um he found out that a letter he had
+
+ align:start position:0%
+um he found out that a letter he had
+ 
+
+ align:start position:0%
+um he found out that a letter he had
+sent to his grandfather was totally in
+
+ align:start position:0%
+sent to his grandfather was totally in
+ 
+
+ align:start position:0%
+sent to his grandfather was totally in
+in English and his grandfather couldn't
+
+ align:start position:0%
+in English and his grandfather couldn't
+ 
+
+ align:start position:0%
+in English and his grandfather couldn't
+read it and he didn't hadn't even
+
+ align:start position:0%
+read it and he didn't hadn't even
+ 
+
+ align:start position:0%
+read it and he didn't hadn't even
+realized that he had done that. So, um I
+
+ align:start position:0%
+realized that he had done that. So, um I
+ 
+
+ align:start position:0%
+realized that he had done that. So, um I
+think it a lot of the children I have
+
+ align:start position:0%
+think it a lot of the children I have
+ 
+
+ align:start position:0%
+think it a lot of the children I have
+bilingual children and a lot of them
+
+ align:start position:0%
+bilingual children and a lot of them
+ 
+
+ align:start position:0%
+bilingual children and a lot of them
+have um you know two languages or even
+
+ align:start position:0%
+have um you know two languages or even
+ 
+
+ align:start position:0%
+have um you know two languages or even
+three languages and I think this sort of
+
+ align:start position:0%
+three languages and I think this sort of
+ 
+
+ align:start position:0%
+three languages and I think this sort of
+really they understand that maybe
+
+ align:start position:0%
+really they understand that maybe
+ 
+
+ align:start position:0%
+really they understand that maybe
+sometimes I say things to them they
+
+ align:start position:0%
+sometimes I say things to them they
+ 
+
+ align:start position:0%
+sometimes I say things to them they
+don't quite understand what it is
+
+ align:start position:0%
+don't quite understand what it is
+ 
+
+ align:start position:0%
+don't quite understand what it is
+because it's not familiar to them but
+
+ align:start position:0%
+because it's not familiar to them but
+ 
+
+ align:start position:0%
+because it's not familiar to them but
+this sort of connects to their own their
+
+ align:start position:0%
+this sort of connects to their own their
+ 
+
+ align:start position:0%
+this sort of connects to their own their
+own life and I think that when you see
+
+ align:start position:0%
+own life and I think that when you see
+ 
+
+ align:start position:0%
+own life and I think that when you see
+Shagarro going back into Haratska and
+
+ align:start position:0%
+Shagarro going back into Haratska and
+ 
+
+ align:start position:0%
+Shagarro going back into Haratska and
+visiting the old haunts that he went to.
+
+ align:start position:0%
+visiting the old haunts that he went to.
+ 
+
+ align:start position:0%
+visiting the old haunts that he went to.
+And looking at the old photographs, you
+
+ align:start position:0%
+And looking at the old photographs, you
+ 
+
+ align:start position:0%
+And looking at the old photographs, you
+can see um you know how much he changed
+
+ align:start position:0%
+can see um you know how much he changed
+ 
+
+ align:start position:0%
+can see um you know how much he changed
+and how much he grew and how he would
+
+ align:start position:0%
+and how much he grew and how he would
+ 
+
+ align:start position:0%
+and how much he grew and how he would
+have that feeling. He's not quite sure
+
+ align:start position:0%
+have that feeling. He's not quite sure
+ 
+
+ align:start position:0%
+have that feeling. He's not quite sure
+which culture he belongs to. And maybe
+
+ align:start position:0%
+which culture he belongs to. And maybe
+ 
+
+ align:start position:0%
+which culture he belongs to. And maybe
+that's how a lot of our children feel.
\ No newline at end of file
diff --git a/rFGvvlsveOk.txt b/rFGvvlsveOk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4e7bdc766303661373b4fad99c9cceb6c771eed6
--- /dev/null
+++ b/rFGvvlsveOk.txt
@@ -0,0 +1,579 @@
+align:start position:0%
+ 
+This insulating cylinder is free to
+
+ align:start position:0%
+This insulating cylinder is free to
+ 
+
+ align:start position:0%
+This insulating cylinder is free to
+rotate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's centered between these
+
+ align:start position:0%
+It's centered between these
+ 
+
+ align:start position:0%
+It's centered between these
+electrodes which will be used to impose
+
+ align:start position:0%
+electrodes which will be used to impose
+ 
+
+ align:start position:0%
+electrodes which will be used to impose
+an electric
+
+ align:start position:0%
+an electric
+ 
+
+ align:start position:0%
+an electric
+field transverse to the axis of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation. The electrodes and cylinder
+
+ align:start position:0%
+rotation. The electrodes and cylinder
+ 
+
+ align:start position:0%
+rotation. The electrodes and cylinder
+are immersed in slightly conducting corn
+
+ align:start position:0%
+are immersed in slightly conducting corn
+ 
+
+ align:start position:0%
+are immersed in slightly conducting corn
+oil. As we apply the potential to the
+
+ align:start position:0%
+oil. As we apply the potential to the
+ 
+
+ align:start position:0%
+oil. As we apply the potential to the
+plates, the threshold of about 20
+
+ align:start position:0%
+plates, the threshold of about 20
+ 
+
+ align:start position:0%
+plates, the threshold of about 20
+kovolts is reached and the cylinder
+
+ align:start position:0%
+kovolts is reached and the cylinder
+ 
+
+ align:start position:0%
+kovolts is reached and the cylinder
+begins to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotate. Which direction is a matter of
+
+ align:start position:0%
+rotate. Which direction is a matter of
+ 
+
+ align:start position:0%
+rotate. Which direction is a matter of
+chance?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You need two more pieces of information
+
+ align:start position:0%
+You need two more pieces of information
+ 
+
+ align:start position:0%
+You need two more pieces of information
+to explain this experiment. The Teflon
+
+ align:start position:0%
+to explain this experiment. The Teflon
+ 
+
+ align:start position:0%
+to explain this experiment. The Teflon
+rotor is a very good insulator compared
+
+ align:start position:0%
+rotor is a very good insulator compared
+ 
+
+ align:start position:0%
+rotor is a very good insulator compared
+to the corn oil and the oil has a
+
+ align:start position:0%
+to the corn oil and the oil has a
+ 
+
+ align:start position:0%
+to the corn oil and the oil has a
+relaxation time on the same order as the
+
+ align:start position:0%
+relaxation time on the same order as the
+ 
+
+ align:start position:0%
+relaxation time on the same order as the
+period of rotation.
+
+ align:start position:0%
+period of rotation.
+ 
+
+ align:start position:0%
+period of rotation.
+The rotor acts as an insulator in series
+
+ align:start position:0%
+The rotor acts as an insulator in series
+ 
+
+ align:start position:0%
+The rotor acts as an insulator in series
+with the regions of conducting liquid
+
+ align:start position:0%
+with the regions of conducting liquid
+ 
+
+ align:start position:0%
+with the regions of conducting liquid
+adjacent to the
+
+ align:start position:0%
+adjacent to the
+ 
+
+ align:start position:0%
+adjacent to the
+electrodes. As surface charges build up
+
+ align:start position:0%
+electrodes. As surface charges build up
+ 
+
+ align:start position:0%
+electrodes. As surface charges build up
+on the electrodes, they induce
+
+ align:start position:0%
+on the electrodes, they induce
+ 
+
+ align:start position:0%
+on the electrodes, they induce
+neighboring surface charges of the same
+
+ align:start position:0%
+neighboring surface charges of the same
+ 
+
+ align:start position:0%
+neighboring surface charges of the same
+sign on the rotor liquid
+
+ align:start position:0%
+sign on the rotor liquid
+ 
+
+ align:start position:0%
+sign on the rotor liquid
+interface. A perturbation of the static
+
+ align:start position:0%
+interface. A perturbation of the static
+ 
+
+ align:start position:0%
+interface. A perturbation of the static
+cylinder carries these charges
+
+ align:start position:0%
+cylinder carries these charges
+ 
+
+ align:start position:0%
+cylinder carries these charges
+along. The motion affects the field.
+
+ align:start position:0%
+along. The motion affects the field.
+ 
+
+ align:start position:0%
+along. The motion affects the field.
+In return, there is a repulsion of the
+
+ align:start position:0%
+In return, there is a repulsion of the
+ 
+
+ align:start position:0%
+In return, there is a repulsion of the
+like charges that tends to sustain the
+
+ align:start position:0%
+like charges that tends to sustain the
+ 
+
+ align:start position:0%
+like charges that tends to sustain the
+rotation. The field affects the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion. Steady rotation is maintained
+
+ align:start position:0%
+motion. Steady rotation is maintained
+ 
+
+ align:start position:0%
+motion. Steady rotation is maintained
+because the convection of the surface
+
+ align:start position:0%
+because the convection of the surface
+ 
+
+ align:start position:0%
+because the convection of the surface
+charge is just compensated by its
+
+ align:start position:0%
+charge is just compensated by its
+ 
+
+ align:start position:0%
+charge is just compensated by its
+relaxation through conduction in the
+
+ align:start position:0%
+relaxation through conduction in the
+ 
+
+ align:start position:0%
+relaxation through conduction in the
+corn oil.
+
+ align:start position:0%
+corn oil.
+ 
+
+ align:start position:0%
+corn oil.
+The cylinder begins to rotate only
+
+ align:start position:0%
+The cylinder begins to rotate only
+ 
+
+ align:start position:0%
+The cylinder begins to rotate only
+because there is both an effect of the
+
+ align:start position:0%
+because there is both an effect of the
+ 
+
+ align:start position:0%
+because there is both an effect of the
+field on the motion and of the motion on
+
+ align:start position:0%
+field on the motion and of the motion on
+ 
+
+ align:start position:0%
+field on the motion and of the motion on
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field. The rotation alters the charge
+
+ align:start position:0%
+field. The rotation alters the charge
+ 
+
+ align:start position:0%
+field. The rotation alters the charge
+distribution because the ratio of
+
+ align:start position:0%
+distribution because the ratio of
+ 
+
+ align:start position:0%
+distribution because the ratio of
+relaxation time in the oil to the time
+
+ align:start position:0%
+relaxation time in the oil to the time
+ 
+
+ align:start position:0%
+relaxation time in the oil to the time
+required for a point on the cylinder
+
+ align:start position:0%
+required for a point on the cylinder
+ 
+
+ align:start position:0%
+required for a point on the cylinder
+surface to make one revolution is about
+
+ align:start position:0%
+surface to make one revolution is about
+ 
+
+ align:start position:0%
+surface to make one revolution is about
+unity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The field induced rotations of the
+
+ align:start position:0%
+The field induced rotations of the
+ 
+
+ align:start position:0%
+The field induced rotations of the
+cylinder also are responsible for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion. These cells of fluid are
+
+ align:start position:0%
+motion. These cells of fluid are
+ 
+
+ align:start position:0%
+motion. These cells of fluid are
+spinning on the free surface of corn
+
+ align:start position:0%
+spinning on the free surface of corn
+ 
+
+ align:start position:0%
+spinning on the free surface of corn
+oil.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The fluid is contained in this box which
+
+ align:start position:0%
+The fluid is contained in this box which
+ 
+
+ align:start position:0%
+The fluid is contained in this box which
+has two electrodes lying flat on its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bottom. They're separated by about 1/4
+
+ align:start position:0%
+bottom. They're separated by about 1/4
+ 
+
+ align:start position:0%
+bottom. They're separated by about 1/4
+in.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bubbles injected on the surface show how
+
+ align:start position:0%
+Bubbles injected on the surface show how
+ 
+
+ align:start position:0%
+Bubbles injected on the surface show how
+the rotations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+develop. Passage of current through the
+
+ align:start position:0%
+develop. Passage of current through the
+ 
+
+ align:start position:0%
+develop. Passage of current through the
+oil results in a potential drop along
+
+ align:start position:0%
+oil results in a potential drop along
+ 
+
+ align:start position:0%
+oil results in a potential drop along
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interface. From above, we see the
+
+ align:start position:0%
+interface. From above, we see the
+ 
+
+ align:start position:0%
+interface. From above, we see the
+charges on the
+
+ align:start position:0%
+charges on the
+ 
+
+ align:start position:0%
+charges on the
+electrodes and on the
+
+ align:start position:0%
+electrodes and on the
+ 
+
+ align:start position:0%
+electrodes and on the
+interface.
+
+ align:start position:0%
+interface.
+ 
+
+ align:start position:0%
+interface.
+Any slight fluid rotation results in
+
+ align:start position:0%
+Any slight fluid rotation results in
+ 
+
+ align:start position:0%
+Any slight fluid rotation results in
+charge redistribution which encourages
+
+ align:start position:0%
+charge redistribution which encourages
+ 
+
+ align:start position:0%
+charge redistribution which encourages
+further rotation.
+
+ align:start position:0%
+further rotation.
+ 
+
+ align:start position:0%
+further rotation.
+The interface is unstable to cellular
+
+ align:start position:0%
+The interface is unstable to cellular
+ 
+
+ align:start position:0%
+The interface is unstable to cellular
+motions in its own plane and the
+
+ align:start position:0%
+motions in its own plane and the
+ 
+
+ align:start position:0%
+motions in its own plane and the
+resulting cell pattern is one which
+
+ align:start position:0%
+resulting cell pattern is one which
+ 
+
+ align:start position:0%
+resulting cell pattern is one which
+reduces viscous drag to a minimum.
\ No newline at end of file
diff --git a/rkFY8WB8tfs.txt b/rkFY8WB8tfs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..481ab59c2fb2d4b5c7a2d2f65fbba860f173d8d1
--- /dev/null
+++ b/rkFY8WB8tfs.txt
@@ -0,0 +1,9835 @@
+align:start position:0%
+ 
+so we're going to talk a little bit
+
+ align:start position:0%
+so we're going to talk a little bit
+ 
+
+ align:start position:0%
+so we're going to talk a little bit
+about bohr and then we're going to talk
+
+ align:start position:0%
+about bohr and then we're going to talk
+ 
+
+ align:start position:0%
+about bohr and then we're going to talk
+about ionization energy which is a theme
+
+ align:start position:0%
+about ionization energy which is a theme
+ 
+
+ align:start position:0%
+about ionization energy which is a theme
+that's going to come back
+
+ align:start position:0%
+that's going to come back
+ 
+
+ align:start position:0%
+that's going to come back
+a couple more times very important
+
+ align:start position:0%
+a couple more times very important
+ 
+
+ align:start position:0%
+a couple more times very important
+and then we're going quantum
+
+ align:start position:0%
+and then we're going quantum
+ 
+
+ align:start position:0%
+and then we're going quantum
+we're going quantum and that's why this
+
+ align:start position:0%
+we're going quantum and that's why this
+ 
+
+ align:start position:0%
+we're going quantum and that's why this
+is a very exciting day
+
+ align:start position:0%
+is a very exciting day
+ 
+
+ align:start position:0%
+is a very exciting day
+uh for me and i i'm hoping it will be
+
+ align:start position:0%
+uh for me and i i'm hoping it will be
+ 
+
+ align:start position:0%
+uh for me and i i'm hoping it will be
+for you too
+
+ align:start position:0%
+for you too
+ 
+
+ align:start position:0%
+for you too
+it's why i have t-shirts it's also a
+
+ align:start position:0%
+it's why i have t-shirts it's also a
+ 
+
+ align:start position:0%
+it's why i have t-shirts it's also a
+goody bag day there's just all sorts of
+
+ align:start position:0%
+goody bag day there's just all sorts of
+ 
+
+ align:start position:0%
+goody bag day there's just all sorts of
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+happening today so i'm very excited
+
+ align:start position:0%
+happening today so i'm very excited
+ 
+
+ align:start position:0%
+happening today so i'm very excited
+this is how we ended our lecture on
+
+ align:start position:0%
+this is how we ended our lecture on
+ 
+
+ align:start position:0%
+this is how we ended our lecture on
+wednesday
+
+ align:start position:0%
+wednesday
+ 
+
+ align:start position:0%
+wednesday
+okay i was showing you this as part of
+
+ align:start position:0%
+okay i was showing you this as part of
+ 
+
+ align:start position:0%
+okay i was showing you this as part of
+my why this matters which started with
+
+ align:start position:0%
+my why this matters which started with
+ 
+
+ align:start position:0%
+my why this matters which started with
+refrigerators
+
+ align:start position:0%
+refrigerators
+ 
+
+ align:start position:0%
+refrigerators
+and then we talked about a chemistry
+
+ align:start position:0%
+and then we talked about a chemistry
+ 
+
+ align:start position:0%
+and then we talked about a chemistry
+problem cfcs
+
+ align:start position:0%
+problem cfcs
+ 
+
+ align:start position:0%
+problem cfcs
+and we talked about how those were
+
+ align:start position:0%
+and we talked about how those were
+ 
+
+ align:start position:0%
+and we talked about how those were
+destroying the ozone layer of this
+
+ align:start position:0%
+destroying the ozone layer of this
+ 
+
+ align:start position:0%
+destroying the ozone layer of this
+planet
+
+ align:start position:0%
+planet
+ 
+
+ align:start position:0%
+planet
+now why is that important and i had this
+
+ align:start position:0%
+now why is that important and i had this
+ 
+
+ align:start position:0%
+now why is that important and i had this
+picture up there
+
+ align:start position:0%
+picture up there
+ 
+
+ align:start position:0%
+picture up there
+to help explain it this is
+
+ align:start position:0%
+to help explain it this is
+ 
+
+ align:start position:0%
+to help explain it this is
+just to to make sure we all see what
+
+ align:start position:0%
+just to to make sure we all see what
+ 
+
+ align:start position:0%
+just to to make sure we all see what
+this is you know i'm
+
+ align:start position:0%
+this is you know i'm
+ 
+
+ align:start position:0%
+this is you know i'm
+showing it here again this is the energy
+
+ align:start position:0%
+showing it here again this is the energy
+ 
+
+ align:start position:0%
+showing it here again this is the energy
+watts per meter squared
+
+ align:start position:0%
+watts per meter squared
+ 
+
+ align:start position:0%
+watts per meter squared
+that we get from the sun right and
+
+ align:start position:0%
+that we get from the sun right and
+ 
+
+ align:start position:0%
+that we get from the sun right and
+and you can measure that up on top of
+
+ align:start position:0%
+and you can measure that up on top of
+ 
+
+ align:start position:0%
+and you can measure that up on top of
+the atmosphere so there's no atmosphere
+
+ align:start position:0%
+the atmosphere so there's no atmosphere
+ 
+
+ align:start position:0%
+the atmosphere so there's no atmosphere
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and this is what it looks like right
+
+ align:start position:0%
+and this is what it looks like right
+ 
+
+ align:start position:0%
+and this is what it looks like right
+that's the energy
+
+ align:start position:0%
+that's the energy
+ 
+
+ align:start position:0%
+that's the energy
+as a function of the wavelength or
+
+ align:start position:0%
+as a function of the wavelength or
+ 
+
+ align:start position:0%
+as a function of the wavelength or
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+or energy of the photon you now know how
+
+ align:start position:0%
+or energy of the photon you now know how
+ 
+
+ align:start position:0%
+or energy of the photon you now know how
+to go back and forth between those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but see on the planet here once you once
+
+ align:start position:0%
+but see on the planet here once you once
+ 
+
+ align:start position:0%
+but see on the planet here once you once
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+have the atmosphere you get a different
+
+ align:start position:0%
+have the atmosphere you get a different
+ 
+
+ align:start position:0%
+have the atmosphere you get a different
+spectrum and the reason is and it's
+
+ align:start position:0%
+spectrum and the reason is and it's
+ 
+
+ align:start position:0%
+spectrum and the reason is and it's
+shown here that
+
+ align:start position:0%
+shown here that
+ 
+
+ align:start position:0%
+shown here that
+some of the molecules in the atmosphere
+
+ align:start position:0%
+some of the molecules in the atmosphere
+ 
+
+ align:start position:0%
+some of the molecules in the atmosphere
+are absorbing
+
+ align:start position:0%
+are absorbing
+ 
+
+ align:start position:0%
+are absorbing
+parts of that spectrum so what we see on
+
+ align:start position:0%
+parts of that spectrum so what we see on
+ 
+
+ align:start position:0%
+parts of that spectrum so what we see on
+the planet is different
+
+ align:start position:0%
+the planet is different
+ 
+
+ align:start position:0%
+the planet is different
+right and we talk about this in terms of
+
+ align:start position:0%
+right and we talk about this in terms of
+ 
+
+ align:start position:0%
+right and we talk about this in terms of
+why this matters
+
+ align:start position:0%
+why this matters
+ 
+
+ align:start position:0%
+why this matters
+and and how ozone you know so you say
+
+ align:start position:0%
+and and how ozone you know so you say
+ 
+
+ align:start position:0%
+and and how ozone you know so you say
+well i said i mentioned oh if you could
+
+ align:start position:0%
+well i said i mentioned oh if you could
+ 
+
+ align:start position:0%
+well i said i mentioned oh if you could
+only if we could only see out here
+
+ align:start position:0%
+only if we could only see out here
+ 
+
+ align:start position:0%
+only if we could only see out here
+right the visible is here that's the
+
+ align:start position:0%
+right the visible is here that's the
+ 
+
+ align:start position:0%
+right the visible is here that's the
+visible okay there's the
+
+ align:start position:0%
+visible okay there's the
+ 
+
+ align:start position:0%
+visible okay there's the
+frequencies of the visible but what if
+
+ align:start position:0%
+frequencies of the visible but what if
+ 
+
+ align:start position:0%
+frequencies of the visible but what if
+it were here the planet would be totally
+
+ align:start position:0%
+it were here the planet would be totally
+ 
+
+ align:start position:0%
+it were here the planet would be totally
+dark
+
+ align:start position:0%
+dark
+ 
+
+ align:start position:0%
+dark
+because no light would get through the
+
+ align:start position:0%
+because no light would get through the
+ 
+
+ align:start position:0%
+because no light would get through the
+absorption that happens from
+
+ align:start position:0%
+absorption that happens from
+ 
+
+ align:start position:0%
+absorption that happens from
+those molecules on the other hand over
+
+ align:start position:0%
+those molecules on the other hand over
+ 
+
+ align:start position:0%
+those molecules on the other hand over
+here we've got ozone that's protecting
+
+ align:start position:0%
+here we've got ozone that's protecting
+ 
+
+ align:start position:0%
+here we've got ozone that's protecting
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+it is absorbing light in the higher
+
+ align:start position:0%
+it is absorbing light in the higher
+ 
+
+ align:start position:0%
+it is absorbing light in the higher
+frequency in the higher frequency
+
+ align:start position:0%
+frequency in the higher frequency
+ 
+
+ align:start position:0%
+frequency in the higher frequency
+which means lower wavelength that's the
+
+ align:start position:0%
+which means lower wavelength that's the
+ 
+
+ align:start position:0%
+which means lower wavelength that's the
+uv
+
+ align:start position:0%
+uv
+ 
+
+ align:start position:0%
+uv
+and that's why that was such an
+
+ align:start position:0%
+and that's why that was such an
+ 
+
+ align:start position:0%
+and that's why that was such an
+important problem is to not destroy
+
+ align:start position:0%
+important problem is to not destroy
+ 
+
+ align:start position:0%
+important problem is to not destroy
+those precious ozone molecules
+
+ align:start position:0%
+those precious ozone molecules
+ 
+
+ align:start position:0%
+those precious ozone molecules
+okay so i want to make sure that we and
+
+ align:start position:0%
+okay so i want to make sure that we and
+ 
+
+ align:start position:0%
+okay so i want to make sure that we and
+we understood this in terms of
+
+ align:start position:0%
+we understood this in terms of
+ 
+
+ align:start position:0%
+we understood this in terms of
+energy transitions because how do these
+
+ align:start position:0%
+energy transitions because how do these
+ 
+
+ align:start position:0%
+energy transitions because how do these
+things absorb light
+
+ align:start position:0%
+things absorb light
+ 
+
+ align:start position:0%
+things absorb light
+well they do just what we said which is
+
+ align:start position:0%
+well they do just what we said which is
+ 
+
+ align:start position:0%
+well they do just what we said which is
+they take the energy from
+
+ align:start position:0%
+they take the energy from
+ 
+
+ align:start position:0%
+they take the energy from
+a kind of light and and an electron then
+
+ align:start position:0%
+a kind of light and and an electron then
+ 
+
+ align:start position:0%
+a kind of light and and an electron then
+takes that energy absorbs it to be
+
+ align:start position:0%
+takes that energy absorbs it to be
+ 
+
+ align:start position:0%
+takes that energy absorbs it to be
+excited and it goes from one energy
+
+ align:start position:0%
+excited and it goes from one energy
+ 
+
+ align:start position:0%
+excited and it goes from one energy
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+to another right we did that in terms of
+
+ align:start position:0%
+to another right we did that in terms of
+ 
+
+ align:start position:0%
+to another right we did that in terms of
+the board levels
+
+ align:start position:0%
+the board levels
+ 
+
+ align:start position:0%
+the board levels
+so i want to do that and that is what
+
+ align:start position:0%
+so i want to do that and that is what
+ 
+
+ align:start position:0%
+so i want to do that and that is what
+you have right here
+
+ align:start position:0%
+you have right here
+ 
+
+ align:start position:0%
+you have right here
+right you have a way to see that visible
+
+ align:start position:0%
+right you have a way to see that visible
+ 
+
+ align:start position:0%
+right you have a way to see that visible
+spectrum so we'll talk about that
+
+ align:start position:0%
+spectrum so we'll talk about that
+ 
+
+ align:start position:0%
+spectrum so we'll talk about that
+as well oh we'll talk about it right now
+
+ align:start position:0%
+as well oh we'll talk about it right now
+ 
+
+ align:start position:0%
+as well oh we'll talk about it right now
+because i have a slide on it
+
+ align:start position:0%
+because i have a slide on it
+ 
+
+ align:start position:0%
+because i have a slide on it
+so you have what is known as
+
+ align:start position:0%
+so you have what is known as
+ 
+
+ align:start position:0%
+so you have what is known as
+a spectroscope or the most powerful way
+
+ align:start position:0%
+a spectroscope or the most powerful way
+ 
+
+ align:start position:0%
+a spectroscope or the most powerful way
+to see light
+
+ align:start position:0%
+to see light
+ 
+
+ align:start position:0%
+to see light
+ever designed and and if you look
+
+ align:start position:0%
+ever designed and and if you look
+ 
+
+ align:start position:0%
+ever designed and and if you look
+through this
+
+ align:start position:0%
+through this
+ 
+
+ align:start position:0%
+through this
+okay don't look at the uv please don't
+
+ align:start position:0%
+okay don't look at the uv please don't
+ 
+
+ align:start position:0%
+okay don't look at the uv please don't
+look at the sun
+
+ align:start position:0%
+look at the sun
+ 
+
+ align:start position:0%
+look at the sun
+with this please don't do that but we
+
+ align:start position:0%
+with this please don't do that but we
+ 
+
+ align:start position:0%
+with this please don't do that but we
+gave you
+
+ align:start position:0%
+gave you
+ 
+
+ align:start position:0%
+gave you
+light sources to look at like that right
+
+ align:start position:0%
+light sources to look at like that right
+ 
+
+ align:start position:0%
+light sources to look at like that right
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+you could look at that or you could look
+
+ align:start position:0%
+you could look at that or you could look
+ 
+
+ align:start position:0%
+you could look at that or you could look
+at like things around you with it
+
+ align:start position:0%
+at like things around you with it
+ 
+
+ align:start position:0%
+at like things around you with it
+and what are you seeing you're seeing
+
+ align:start position:0%
+and what are you seeing you're seeing
+ 
+
+ align:start position:0%
+and what are you seeing you're seeing
+this you're seeing the spectrum
+
+ align:start position:0%
+this you're seeing the spectrum
+ 
+
+ align:start position:0%
+this you're seeing the spectrum
+in the visible you're seeing it in this
+
+ align:start position:0%
+in the visible you're seeing it in this
+ 
+
+ align:start position:0%
+in the visible you're seeing it in this
+part okay
+
+ align:start position:0%
+part okay
+ 
+
+ align:start position:0%
+part okay
+but from this you are also what you are
+
+ align:start position:0%
+but from this you are also what you are
+ 
+
+ align:start position:0%
+but from this you are also what you are
+seeing
+
+ align:start position:0%
+seeing
+ 
+
+ align:start position:0%
+seeing
+are literally electron transitions you
+
+ align:start position:0%
+are literally electron transitions you
+ 
+
+ align:start position:0%
+are literally electron transitions you
+are literally
+
+ align:start position:0%
+are literally
+ 
+
+ align:start position:0%
+are literally
+and that's what i want you to think
+
+ align:start position:0%
+and that's what i want you to think
+ 
+
+ align:start position:0%
+and that's what i want you to think
+about that's why i wanted you to have
+
+ align:start position:0%
+about that's why i wanted you to have
+ 
+
+ align:start position:0%
+about that's why i wanted you to have
+this power
+
+ align:start position:0%
+this power
+ 
+
+ align:start position:0%
+this power
+this power which means responsibility as
+
+ align:start position:0%
+this power which means responsibility as
+ 
+
+ align:start position:0%
+this power which means responsibility as
+we know but
+
+ align:start position:0%
+we know but
+ 
+
+ align:start position:0%
+we know but
+now you can not only see light you can
+
+ align:start position:0%
+now you can not only see light you can
+ 
+
+ align:start position:0%
+now you can not only see light you can
+see electron transitions
+
+ align:start position:0%
+see electron transitions
+ 
+
+ align:start position:0%
+see electron transitions
+i want you to think about that as you're
+
+ align:start position:0%
+i want you to think about that as you're
+ 
+
+ align:start position:0%
+i want you to think about that as you're
+seeing light
+
+ align:start position:0%
+seeing light
+ 
+
+ align:start position:0%
+seeing light
+and and i want you to think about it in
+
+ align:start position:0%
+and and i want you to think about it in
+ 
+
+ align:start position:0%
+and and i want you to think about it in
+terms of what we learned on wednesday
+
+ align:start position:0%
+terms of what we learned on wednesday
+ 
+
+ align:start position:0%
+terms of what we learned on wednesday
+which is bore
+
+ align:start position:0%
+which is bore
+ 
+
+ align:start position:0%
+which is bore
+right and so let's let's just put that
+
+ align:start position:0%
+right and so let's let's just put that
+ 
+
+ align:start position:0%
+right and so let's let's just put that
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so we had bohr and
+
+ align:start position:0%
+okay so we had bohr and
+ 
+
+ align:start position:0%
+okay so we had bohr and
+in the bohr model we said the energy
+
+ align:start position:0%
+in the bohr model we said the energy
+ 
+
+ align:start position:0%
+in the bohr model we said the energy
+is going to be quantized minus 13.6
+
+ align:start position:0%
+is going to be quantized minus 13.6
+ 
+
+ align:start position:0%
+is going to be quantized minus 13.6
+electron volts times the atomic number
+
+ align:start position:0%
+electron volts times the atomic number
+ 
+
+ align:start position:0%
+electron volts times the atomic number
+squared divided by n squared
+
+ align:start position:0%
+squared divided by n squared
+ 
+
+ align:start position:0%
+squared divided by n squared
+right and so like for hydrogen
+
+ align:start position:0%
+right and so like for hydrogen
+ 
+
+ align:start position:0%
+right and so like for hydrogen
+for example this is equal to uh minus
+
+ align:start position:0%
+for example this is equal to uh minus
+ 
+
+ align:start position:0%
+for example this is equal to uh minus
+13.6 ev
+
+ align:start position:0%
+13.6 ev
+ 
+
+ align:start position:0%
+13.6 ev
+right because z is one over n squared so
+
+ align:start position:0%
+right because z is one over n squared so
+ 
+
+ align:start position:0%
+right because z is one over n squared so
+that was our
+
+ align:start position:0%
+that was our
+ 
+
+ align:start position:0%
+that was our
+for hydrogen z equals
+
+ align:start position:0%
+for hydrogen z equals
+ 
+
+ align:start position:0%
+for hydrogen z equals
+one all right and so that that's one and
+
+ align:start position:0%
+one all right and so that that's one and
+ 
+
+ align:start position:0%
+one all right and so that that's one and
+that's it
+
+ align:start position:0%
+that's it
+ 
+
+ align:start position:0%
+that's it
+but n is equal to one two
+
+ align:start position:0%
+but n is equal to one two
+ 
+
+ align:start position:0%
+but n is equal to one two
+three etc it's quantized right this was
+
+ align:start position:0%
+three etc it's quantized right this was
+ 
+
+ align:start position:0%
+three etc it's quantized right this was
+this was the whole uh kind of discussion
+
+ align:start position:0%
+this was the whole uh kind of discussion
+ 
+
+ align:start position:0%
+this was the whole uh kind of discussion
+and theme of wednesday's lecture
+
+ align:start position:0%
+and theme of wednesday's lecture
+ 
+
+ align:start position:0%
+and theme of wednesday's lecture
+and and and that got us to these levels
+
+ align:start position:0%
+and and and that got us to these levels
+ 
+
+ align:start position:0%
+and and and that got us to these levels
+these bore levels which are places where
+
+ align:start position:0%
+these bore levels which are places where
+ 
+
+ align:start position:0%
+these bore levels which are places where
+energetic places energies of the
+
+ align:start position:0%
+energetic places energies of the
+ 
+
+ align:start position:0%
+energetic places energies of the
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+right so we'd have these levels
+
+ align:start position:0%
+right so we'd have these levels
+ 
+
+ align:start position:0%
+right so we'd have these levels
+that kept on going until you're at
+
+ align:start position:0%
+that kept on going until you're at
+ 
+
+ align:start position:0%
+that kept on going until you're at
+somehow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if this is energy
+
+ align:start position:0%
+right so if this is energy
+ 
+
+ align:start position:0%
+right so if this is energy
+right and and this would be like n
+
+ align:start position:0%
+right and and this would be like n
+ 
+
+ align:start position:0%
+right and and this would be like n
+equals one
+
+ align:start position:0%
+equals one
+ 
+
+ align:start position:0%
+equals one
+n equals two these are the energies
+
+ align:start position:0%
+n equals two these are the energies
+ 
+
+ align:start position:0%
+n equals two these are the energies
+right right there i'm just plugging in
+
+ align:start position:0%
+right right there i'm just plugging in
+ 
+
+ align:start position:0%
+right right there i'm just plugging in
+and this would be like n equals infinity
+
+ align:start position:0%
+and this would be like n equals infinity
+ 
+
+ align:start position:0%
+and this would be like n equals infinity
+so the energy here
+
+ align:start position:0%
+so the energy here
+ 
+
+ align:start position:0%
+so the energy here
+would be zero and for the hydrogen atom
+
+ align:start position:0%
+would be zero and for the hydrogen atom
+ 
+
+ align:start position:0%
+would be zero and for the hydrogen atom
+the energy here would be minus 13.6
+
+ align:start position:0%
+the energy here would be minus 13.6
+ 
+
+ align:start position:0%
+the energy here would be minus 13.6
+electron volts right if that's hydrogen
+
+ align:start position:0%
+electron volts right if that's hydrogen
+ 
+
+ align:start position:0%
+electron volts right if that's hydrogen
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+now i'm leaving this here i want to use
+
+ align:start position:0%
+now i'm leaving this here i want to use
+ 
+
+ align:start position:0%
+now i'm leaving this here i want to use
+this that's why i'm putting it back up
+
+ align:start position:0%
+this that's why i'm putting it back up
+ 
+
+ align:start position:0%
+this that's why i'm putting it back up
+okay because look now you can use this
+
+ align:start position:0%
+okay because look now you can use this
+ 
+
+ align:start position:0%
+okay because look now you can use this
+to start
+
+ align:start position:0%
+to start
+ 
+
+ align:start position:0%
+to start
+understanding light and so you use this
+
+ align:start position:0%
+understanding light and so you use this
+ 
+
+ align:start position:0%
+understanding light and so you use this
+and you look at light sources
+
+ align:start position:0%
+and you look at light sources
+ 
+
+ align:start position:0%
+and you look at light sources
+and you can start thinking about things
+
+ align:start position:0%
+and you can start thinking about things
+ 
+
+ align:start position:0%
+and you can start thinking about things
+in terms of energy transitions so let's
+
+ align:start position:0%
+in terms of energy transitions so let's
+ 
+
+ align:start position:0%
+in terms of energy transitions so let's
+take a look so what if i
+
+ align:start position:0%
+take a look so what if i
+ 
+
+ align:start position:0%
+take a look so what if i
+uh just look at some light sources right
+
+ align:start position:0%
+uh just look at some light sources right
+ 
+
+ align:start position:0%
+uh just look at some light sources right
+okay so that's what you see that's like
+
+ align:start position:0%
+okay so that's what you see that's like
+ 
+
+ align:start position:0%
+okay so that's what you see that's like
+the sun
+
+ align:start position:0%
+the sun
+ 
+
+ align:start position:0%
+the sun
+right so that's daylight and now we're
+
+ align:start position:0%
+right so that's daylight and now we're
+ 
+
+ align:start position:0%
+right so that's daylight and now we're
+getting into the the mode of seeing
+
+ align:start position:0%
+getting into the the mode of seeing
+ 
+
+ align:start position:0%
+getting into the the mode of seeing
+light like this right it's in intensity
+
+ align:start position:0%
+light like this right it's in intensity
+ 
+
+ align:start position:0%
+light like this right it's in intensity
+salute versus uh wavelength right
+
+ align:start position:0%
+salute versus uh wavelength right
+ 
+
+ align:start position:0%
+salute versus uh wavelength right
+and there you go you go and now if you
+
+ align:start position:0%
+and there you go you go and now if you
+ 
+
+ align:start position:0%
+and there you go you go and now if you
+look at sort of an incandescent light
+
+ align:start position:0%
+look at sort of an incandescent light
+ 
+
+ align:start position:0%
+look at sort of an incandescent light
+bulb
+
+ align:start position:0%
+bulb
+ 
+
+ align:start position:0%
+bulb
+all right it'll look something like this
+
+ align:start position:0%
+all right it'll look something like this
+ 
+
+ align:start position:0%
+all right it'll look something like this
+so it's it's warm
+
+ align:start position:0%
+so it's it's warm
+ 
+
+ align:start position:0%
+so it's it's warm
+there's a little more red right you
+
+ align:start position:0%
+there's a little more red right you
+ 
+
+ align:start position:0%
+there's a little more red right you
+can't get up to the sun's temperature
+
+ align:start position:0%
+can't get up to the sun's temperature
+ 
+
+ align:start position:0%
+can't get up to the sun's temperature
+but you get pretty hot
+
+ align:start position:0%
+but you get pretty hot
+ 
+
+ align:start position:0%
+but you get pretty hot
+so you see this nice kind of looking
+
+ align:start position:0%
+so you see this nice kind of looking
+ 
+
+ align:start position:0%
+so you see this nice kind of looking
+spectrum and oh here's a halogen
+
+ align:start position:0%
+spectrum and oh here's a halogen
+ 
+
+ align:start position:0%
+spectrum and oh here's a halogen
+all right that looks kind of closer
+
+ align:start position:0%
+all right that looks kind of closer
+ 
+
+ align:start position:0%
+all right that looks kind of closer
+maybe look at what happens when we go
+
+ align:start position:0%
+maybe look at what happens when we go
+ 
+
+ align:start position:0%
+maybe look at what happens when we go
+fluorescent ah
+
+ align:start position:0%
+fluorescent ah
+ 
+
+ align:start position:0%
+fluorescent ah
+look at that why does fluorescent light
+
+ align:start position:0%
+look at that why does fluorescent light
+ 
+
+ align:start position:0%
+look at that why does fluorescent light
+give us headaches
+
+ align:start position:0%
+give us headaches
+ 
+
+ align:start position:0%
+give us headaches
+well that might be other reasons but but
+
+ align:start position:0%
+well that might be other reasons but but
+ 
+
+ align:start position:0%
+well that might be other reasons but but
+look at this spectrum
+
+ align:start position:0%
+look at this spectrum
+ 
+
+ align:start position:0%
+look at this spectrum
+that doesn't look like that that's why
+
+ align:start position:0%
+that doesn't look like that that's why
+ 
+
+ align:start position:0%
+that doesn't look like that that's why
+we all have so much trouble with floor
+
+ align:start position:0%
+we all have so much trouble with floor
+ 
+
+ align:start position:0%
+we all have so much trouble with floor
+and here's leds and you can buy your
+
+ align:start position:0%
+and here's leds and you can buy your
+ 
+
+ align:start position:0%
+and here's leds and you can buy your
+cool white leds and your warm white leds
+
+ align:start position:0%
+cool white leds and your warm white leds
+ 
+
+ align:start position:0%
+cool white leds and your warm white leds
+but look
+
+ align:start position:0%
+but look
+ 
+
+ align:start position:0%
+but look
+they're still not they're not that right
+
+ align:start position:0%
+they're still not they're not that right
+ 
+
+ align:start position:0%
+they're still not they're not that right
+there's been a lot of work on this
+
+ align:start position:0%
+there's been a lot of work on this
+ 
+
+ align:start position:0%
+there's been a lot of work on this
+can we get this to be that right
+
+ align:start position:0%
+can we get this to be that right
+ 
+
+ align:start position:0%
+can we get this to be that right
+and and so so now we are armed
+
+ align:start position:0%
+and and so so now we are armed
+ 
+
+ align:start position:0%
+and and so so now we are armed
+with with great power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you can look at things you see oh
+
+ align:start position:0%
+and so you can look at things you see oh
+ 
+
+ align:start position:0%
+and so you can look at things you see oh
+i see that it has
+
+ align:start position:0%
+i see that it has
+ 
+
+ align:start position:0%
+i see that it has
+uh this large peak because i'm looking
+
+ align:start position:0%
+uh this large peak because i'm looking
+ 
+
+ align:start position:0%
+uh this large peak because i'm looking
+at a fluorescent light
+
+ align:start position:0%
+at a fluorescent light
+ 
+
+ align:start position:0%
+at a fluorescent light
+within and i see that it's got this
+
+ align:start position:0%
+within and i see that it's got this
+ 
+
+ align:start position:0%
+within and i see that it's got this
+stronger peak in the blue
+
+ align:start position:0%
+stronger peak in the blue
+ 
+
+ align:start position:0%
+stronger peak in the blue
+maybe i could just absorb a little of
+
+ align:start position:0%
+maybe i could just absorb a little of
+ 
+
+ align:start position:0%
+maybe i could just absorb a little of
+that what if i came up with a coating
+
+ align:start position:0%
+that what if i came up with a coating
+ 
+
+ align:start position:0%
+that what if i came up with a coating
+right that i could put on that cool led
+
+ align:start position:0%
+right that i could put on that cool led
+ 
+
+ align:start position:0%
+right that i could put on that cool led
+bulb to make it just a little bit more
+
+ align:start position:0%
+bulb to make it just a little bit more
+ 
+
+ align:start position:0%
+bulb to make it just a little bit more
+look like that
+
+ align:start position:0%
+look like that
+ 
+
+ align:start position:0%
+look like that
+well now we know how to we might be able
+
+ align:start position:0%
+well now we know how to we might be able
+ 
+
+ align:start position:0%
+well now we know how to we might be able
+to use bore to do this
+
+ align:start position:0%
+to use bore to do this
+ 
+
+ align:start position:0%
+to use bore to do this
+right because because what if i say okay
+
+ align:start position:0%
+right because because what if i say okay
+ 
+
+ align:start position:0%
+right because because what if i say okay
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the wavelength of that is around 450.
+
+ align:start position:0%
+the wavelength of that is around 450.
+ 
+
+ align:start position:0%
+the wavelength of that is around 450.
+so if the wavelength is 450 nanometers
+
+ align:start position:0%
+so if the wavelength is 450 nanometers
+ 
+
+ align:start position:0%
+so if the wavelength is 450 nanometers
+then i know you know remember we did
+
+ align:start position:0%
+then i know you know remember we did
+ 
+
+ align:start position:0%
+then i know you know remember we did
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+waves right light waves we can go back
+
+ align:start position:0%
+waves right light waves we can go back
+ 
+
+ align:start position:0%
+waves right light waves we can go back
+and forth
+
+ align:start position:0%
+and forth
+ 
+
+ align:start position:0%
+and forth
+between uh frequency below
+
+ align:start position:0%
+between uh frequency below
+ 
+
+ align:start position:0%
+between uh frequency below
+how's it going all right welcome to
+
+ align:start position:0%
+how's it going all right welcome to
+ 
+
+ align:start position:0%
+how's it going all right welcome to
+class um
+
+ align:start position:0%
+class um
+ 
+
+ align:start position:0%
+class um
+and uh and energy energy
+
+ align:start position:0%
+and uh and energy energy
+ 
+
+ align:start position:0%
+and uh and energy energy
+equals h c over lambda
+
+ align:start position:0%
+equals h c over lambda
+ 
+
+ align:start position:0%
+equals h c over lambda
+oh plank thank you
+
+ align:start position:0%
+oh plank thank you
+ 
+
+ align:start position:0%
+oh plank thank you
+and this is roughly 2.75
+
+ align:start position:0%
+and this is roughly 2.75
+ 
+
+ align:start position:0%
+and this is roughly 2.75
+electron volts for that wavelength
+
+ align:start position:0%
+electron volts for that wavelength
+ 
+
+ align:start position:0%
+electron volts for that wavelength
+2.75 electron volts right okay well but
+
+ align:start position:0%
+2.75 electron volts right okay well but
+ 
+
+ align:start position:0%
+2.75 electron volts right okay well but
+see now
+
+ align:start position:0%
+see now
+ 
+
+ align:start position:0%
+see now
+but i want to absorb some of those
+
+ align:start position:0%
+but i want to absorb some of those
+ 
+
+ align:start position:0%
+but i want to absorb some of those
+photons
+
+ align:start position:0%
+photons
+ 
+
+ align:start position:0%
+photons
+i'll pose a problem what if i have
+
+ align:start position:0%
+i'll pose a problem what if i have
+ 
+
+ align:start position:0%
+i'll pose a problem what if i have
+an atom so question right
+
+ align:start position:0%
+an atom so question right
+ 
+
+ align:start position:0%
+an atom so question right
+so i have an atom an atom
+
+ align:start position:0%
+so i have an atom an atom
+ 
+
+ align:start position:0%
+so i have an atom an atom
+that has
+
+ align:start position:0%
+that has
+ 
+
+ align:start position:0%
+that has
+an n equal 4 to n
+
+ align:start position:0%
+an n equal 4 to n
+ 
+
+ align:start position:0%
+an n equal 4 to n
+equal 5 transition
+
+ align:start position:0%
+equal 5 transition
+ 
+
+ align:start position:0%
+equal 5 transition
+that absorbs so i'm i'm telling you now
+
+ align:start position:0%
+that absorbs so i'm i'm telling you now
+ 
+
+ align:start position:0%
+that absorbs so i'm i'm telling you now
+this energy so i'm telling you now
+
+ align:start position:0%
+this energy so i'm telling you now
+ 
+
+ align:start position:0%
+this energy so i'm telling you now
+i've got some atom and i know there's a
+
+ align:start position:0%
+i've got some atom and i know there's a
+ 
+
+ align:start position:0%
+i've got some atom and i know there's a
+transition in it
+
+ align:start position:0%
+transition in it
+ 
+
+ align:start position:0%
+transition in it
+it has an electron transition because
+
+ align:start position:0%
+it has an electron transition because
+ 
+
+ align:start position:0%
+it has an electron transition because
+remember we're going from electron
+
+ align:start position:0%
+remember we're going from electron
+ 
+
+ align:start position:0%
+remember we're going from electron
+transitions to light energy back and
+
+ align:start position:0%
+transitions to light energy back and
+ 
+
+ align:start position:0%
+transitions to light energy back and
+forth back but this right here
+
+ align:start position:0%
+forth back but this right here
+ 
+
+ align:start position:0%
+forth back but this right here
+i'm just saying look okay n equal just
+
+ align:start position:0%
+i'm just saying look okay n equal just
+ 
+
+ align:start position:0%
+i'm just saying look okay n equal just
+keep going n equals three
+
+ align:start position:0%
+keep going n equals three
+ 
+
+ align:start position:0%
+keep going n equals three
+n equals four n equals five so what i
+
+ align:start position:0%
+n equals four n equals five so what i
+ 
+
+ align:start position:0%
+n equals four n equals five so what i
+just asked you is i said well look
+
+ align:start position:0%
+just asked you is i said well look
+ 
+
+ align:start position:0%
+just asked you is i said well look
+some atom has
+
+ align:start position:0%
+some atom has
+ 
+
+ align:start position:0%
+some atom has
+a transition between n equals four and
+
+ align:start position:0%
+a transition between n equals four and
+ 
+
+ align:start position:0%
+a transition between n equals four and
+equals five that means that
+
+ align:start position:0%
+equals five that means that
+ 
+
+ align:start position:0%
+equals five that means that
+if an electron happens to be here it can
+
+ align:start position:0%
+if an electron happens to be here it can
+ 
+
+ align:start position:0%
+if an electron happens to be here it can
+absorb
+
+ align:start position:0%
+absorb
+ 
+
+ align:start position:0%
+absorb
+energy to promote it up to here of
+
+ align:start position:0%
+energy to promote it up to here of
+ 
+
+ align:start position:0%
+energy to promote it up to here of
+exactly 2.75 ev
+
+ align:start position:0%
+exactly 2.75 ev
+ 
+
+ align:start position:0%
+exactly 2.75 ev
+well i can use bore i can use bore now
+
+ align:start position:0%
+well i can use bore i can use bore now
+ 
+
+ align:start position:0%
+well i can use bore i can use bore now
+right because
+
+ align:start position:0%
+right because
+ 
+
+ align:start position:0%
+right because
+so i can actually answer this problem
+
+ align:start position:0%
+so i can actually answer this problem
+ 
+
+ align:start position:0%
+so i can actually answer this problem
+answer this question if i know that
+
+ align:start position:0%
+answer this question if i know that
+ 
+
+ align:start position:0%
+answer this question if i know that
+then i can say well okay if the initial
+
+ align:start position:0%
+then i can say well okay if the initial
+ 
+
+ align:start position:0%
+then i can say well okay if the initial
+state is
+
+ align:start position:0%
+state is
+ 
+
+ align:start position:0%
+state is
+four and the final state is five right
+
+ align:start position:0%
+four and the final state is five right
+ 
+
+ align:start position:0%
+four and the final state is five right
+i've gone from four to five i've
+
+ align:start position:0%
+i've gone from four to five i've
+ 
+
+ align:start position:0%
+i've gone from four to five i've
+promoted an electron
+
+ align:start position:0%
+promoted an electron
+ 
+
+ align:start position:0%
+promoted an electron
+up in energy lifting it up like a ball
+
+ align:start position:0%
+up in energy lifting it up like a ball
+ 
+
+ align:start position:0%
+up in energy lifting it up like a ball
+against gravity
+
+ align:start position:0%
+against gravity
+ 
+
+ align:start position:0%
+against gravity
+all right then if then i can use boar to
+
+ align:start position:0%
+all right then if then i can use boar to
+ 
+
+ align:start position:0%
+all right then if then i can use boar to
+say that 2.75
+
+ align:start position:0%
+say that 2.75
+ 
+
+ align:start position:0%
+say that 2.75
+ev is equal to minus 13.6
+
+ align:start position:0%
+ev is equal to minus 13.6
+ 
+
+ align:start position:0%
+ev is equal to minus 13.6
+z squared times 1 over 5
+
+ align:start position:0%
+z squared times 1 over 5
+ 
+
+ align:start position:0%
+z squared times 1 over 5
+squared minus 1 over 4 squared
+
+ align:start position:0%
+squared minus 1 over 4 squared
+ 
+
+ align:start position:0%
+squared minus 1 over 4 squared
+that would be the transition energy this
+
+ align:start position:0%
+that would be the transition energy this
+ 
+
+ align:start position:0%
+that would be the transition energy this
+dictated by bohr and oh i have
+
+ align:start position:0%
+dictated by bohr and oh i have
+ 
+
+ align:start position:0%
+dictated by bohr and oh i have
+everything except z
+
+ align:start position:0%
+everything except z
+ 
+
+ align:start position:0%
+everything except z
+which i can solve for z equals three
+
+ align:start position:0%
+which i can solve for z equals three
+ 
+
+ align:start position:0%
+which i can solve for z equals three
+z equals three all right so so i've now
+
+ align:start position:0%
+z equals three all right so so i've now
+ 
+
+ align:start position:0%
+z equals three all right so so i've now
+all i need to do is come up with a way
+
+ align:start position:0%
+all i need to do is come up with a way
+ 
+
+ align:start position:0%
+all i need to do is come up with a way
+to coat all the cool
+
+ align:start position:0%
+to coat all the cool
+ 
+
+ align:start position:0%
+to coat all the cool
+leds with lithium right
+
+ align:start position:0%
+leds with lithium right
+ 
+
+ align:start position:0%
+leds with lithium right
+because this is lithium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll be fine except there's a
+
+ align:start position:0%
+and we'll be fine except there's a
+ 
+
+ align:start position:0%
+and we'll be fine except there's a
+problem and this is part of the problem
+
+ align:start position:0%
+problem and this is part of the problem
+ 
+
+ align:start position:0%
+problem and this is part of the problem
+that we need to address and solve today
+
+ align:start position:0%
+that we need to address and solve today
+ 
+
+ align:start position:0%
+that we need to address and solve today
+before the weekend and that is that
+
+ align:start position:0%
+before the weekend and that is that
+ 
+
+ align:start position:0%
+before the weekend and that is that
+see bohr only works
+
+ align:start position:0%
+see bohr only works
+ 
+
+ align:start position:0%
+see bohr only works
+war only works for one electron now it's
+
+ align:start position:0%
+war only works for one electron now it's
+ 
+
+ align:start position:0%
+war only works for one electron now it's
+okay z can be higher
+
+ align:start position:0%
+okay z can be higher
+ 
+
+ align:start position:0%
+okay z can be higher
+z is three and it works here but i've
+
+ align:start position:0%
+z is three and it works here but i've
+ 
+
+ align:start position:0%
+z is three and it works here but i've
+assumed only one
+
+ align:start position:0%
+assumed only one
+ 
+
+ align:start position:0%
+assumed only one
+electron which means this really would
+
+ align:start position:0%
+electron which means this really would
+ 
+
+ align:start position:0%
+electron which means this really would
+be like li-2 plus
+
+ align:start position:0%
+be like li-2 plus
+ 
+
+ align:start position:0%
+be like li-2 plus
+okay we're going to come back to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but bohr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only for
+
+ align:start position:0%
+only for
+ 
+
+ align:start position:0%
+only for
+one electron
+
+ align:start position:0%
+one electron
+ 
+
+ align:start position:0%
+one electron
+right so so if i'm going to get
+
+ align:start position:0%
+right so so if i'm going to get
+ 
+
+ align:start position:0%
+right so so if i'm going to get
+something like like z
+
+ align:start position:0%
+something like like z
+ 
+
+ align:start position:0%
+something like like z
+is three that's fine but it can only
+
+ align:start position:0%
+is three that's fine but it can only
+ 
+
+ align:start position:0%
+is three that's fine but it can only
+have one electron there
+
+ align:start position:0%
+have one electron there
+ 
+
+ align:start position:0%
+have one electron there
+can only have one electron there or the
+
+ align:start position:0%
+can only have one electron there or the
+ 
+
+ align:start position:0%
+can only have one electron there or the
+model doesn't work it was one electron
+
+ align:start position:0%
+model doesn't work it was one electron
+ 
+
+ align:start position:0%
+model doesn't work it was one electron
+with some z of protons right
+
+ align:start position:0%
+with some z of protons right
+ 
+
+ align:start position:0%
+with some z of protons right
+so this could be li-2 plus that sounds
+
+ align:start position:0%
+so this could be li-2 plus that sounds
+ 
+
+ align:start position:0%
+so this could be li-2 plus that sounds
+harder
+
+ align:start position:0%
+harder
+ 
+
+ align:start position:0%
+harder
+to put into a film okay
+
+ align:start position:0%
+to put into a film okay
+ 
+
+ align:start position:0%
+to put into a film okay
+we will be coming back to this that is a
+
+ align:start position:0%
+we will be coming back to this that is a
+ 
+
+ align:start position:0%
+we will be coming back to this that is a
+serious limitation
+
+ align:start position:0%
+serious limitation
+ 
+
+ align:start position:0%
+serious limitation
+of the bohr model and we can't do a lot
+
+ align:start position:0%
+of the bohr model and we can't do a lot
+ 
+
+ align:start position:0%
+of the bohr model and we can't do a lot
+if we can only do one electron
+
+ align:start position:0%
+if we can only do one electron
+ 
+
+ align:start position:0%
+if we can only do one electron
+right you do a lot of ions
+
+ align:start position:0%
+right you do a lot of ions
+ 
+
+ align:start position:0%
+right you do a lot of ions
+but that's it okay
+
+ align:start position:0%
+but that's it okay
+ 
+
+ align:start position:0%
+but that's it okay
+so i just said the word ion
+
+ align:start position:0%
+so i just said the word ion
+ 
+
+ align:start position:0%
+so i just said the word ion
+what happens now if
+
+ align:start position:0%
+what happens now if
+ 
+
+ align:start position:0%
+what happens now if
+you take an electron not from one level
+
+ align:start position:0%
+you take an electron not from one level
+ 
+
+ align:start position:0%
+you take an electron not from one level
+up in energy but up up up up up all the
+
+ align:start position:0%
+up in energy but up up up up up all the
+ 
+
+ align:start position:0%
+up in energy but up up up up up all the
+way until it's free
+
+ align:start position:0%
+way until it's free
+ 
+
+ align:start position:0%
+way until it's free
+what happens if you do that well that is
+
+ align:start position:0%
+what happens if you do that well that is
+ 
+
+ align:start position:0%
+what happens if you do that well that is
+called ionization
+
+ align:start position:0%
+called ionization
+ 
+
+ align:start position:0%
+called ionization
+that's ionization and in fact when you
+
+ align:start position:0%
+that's ionization and in fact when you
+ 
+
+ align:start position:0%
+that's ionization and in fact when you
+look out into the beautiful world
+
+ align:start position:0%
+look out into the beautiful world
+ 
+
+ align:start position:0%
+look out into the beautiful world
+the universe remember i said on
+
+ align:start position:0%
+the universe remember i said on
+ 
+
+ align:start position:0%
+the universe remember i said on
+wednesday 75
+
+ align:start position:0%
+wednesday 75
+ 
+
+ align:start position:0%
+wednesday 75
+of this is hydrogen a whole lot of it is
+
+ align:start position:0%
+of this is hydrogen a whole lot of it is
+ 
+
+ align:start position:0%
+of this is hydrogen a whole lot of it is
+ionized it's getting ionized
+
+ align:start position:0%
+ionized it's getting ionized
+ 
+
+ align:start position:0%
+ionized it's getting ionized
+from energy that's that's knocking
+
+ align:start position:0%
+from energy that's that's knocking
+ 
+
+ align:start position:0%
+from energy that's that's knocking
+electrons out and then electrons are
+
+ align:start position:0%
+electrons out and then electrons are
+ 
+
+ align:start position:0%
+electrons out and then electrons are
+coming back
+
+ align:start position:0%
+coming back
+ 
+
+ align:start position:0%
+coming back
+and cascading through these levels
+
+ align:start position:0%
+and cascading through these levels
+ 
+
+ align:start position:0%
+and cascading through these levels
+emitting discrete
+
+ align:start position:0%
+emitting discrete
+ 
+
+ align:start position:0%
+emitting discrete
+frequencies of light and this is what
+
+ align:start position:0%
+frequencies of light and this is what
+ 
+
+ align:start position:0%
+frequencies of light and this is what
+you see it's beautiful
+
+ align:start position:0%
+you see it's beautiful
+ 
+
+ align:start position:0%
+you see it's beautiful
+right what you're looking at is ionized
+
+ align:start position:0%
+right what you're looking at is ionized
+ 
+
+ align:start position:0%
+right what you're looking at is ionized
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+getting electrons coming in and
+
+ align:start position:0%
+getting electrons coming in and
+ 
+
+ align:start position:0%
+getting electrons coming in and
+cascading through the bore levels
+
+ align:start position:0%
+cascading through the bore levels
+ 
+
+ align:start position:0%
+cascading through the bore levels
+right ah but what does ionized hydrogen
+
+ align:start position:0%
+right ah but what does ionized hydrogen
+ 
+
+ align:start position:0%
+right ah but what does ionized hydrogen
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+right okay we can now understand it
+
+ align:start position:0%
+right okay we can now understand it
+ 
+
+ align:start position:0%
+right okay we can now understand it
+we can now understand it because now
+
+ align:start position:0%
+we can now understand it because now
+ 
+
+ align:start position:0%
+we can now understand it because now
+instead of going from like four to five
+
+ align:start position:0%
+instead of going from like four to five
+ 
+
+ align:start position:0%
+instead of going from like four to five
+i'm going from anything to infinity it's
+
+ align:start position:0%
+i'm going from anything to infinity it's
+ 
+
+ align:start position:0%
+i'm going from anything to infinity it's
+like escape velocity right
+
+ align:start position:0%
+like escape velocity right
+ 
+
+ align:start position:0%
+like escape velocity right
+it's like how much velocity do i need to
+
+ align:start position:0%
+it's like how much velocity do i need to
+ 
+
+ align:start position:0%
+it's like how much velocity do i need to
+give something so it just gets away
+
+ align:start position:0%
+give something so it just gets away
+ 
+
+ align:start position:0%
+give something so it just gets away
+from the earth and it's not going to
+
+ align:start position:0%
+from the earth and it's not going to
+ 
+
+ align:start position:0%
+from the earth and it's not going to
+feel the earth's
+
+ align:start position:0%
+feel the earth's
+ 
+
+ align:start position:0%
+feel the earth's
+gravitational pull well here i don't
+
+ align:start position:0%
+gravitational pull well here i don't
+ 
+
+ align:start position:0%
+gravitational pull well here i don't
+want this electron to
+
+ align:start position:0%
+want this electron to
+ 
+
+ align:start position:0%
+want this electron to
+feel the potential of the atom anymore
+
+ align:start position:0%
+feel the potential of the atom anymore
+ 
+
+ align:start position:0%
+feel the potential of the atom anymore
+the z the positive charge i want it to
+
+ align:start position:0%
+the z the positive charge i want it to
+ 
+
+ align:start position:0%
+the z the positive charge i want it to
+just be free
+
+ align:start position:0%
+just be free
+ 
+
+ align:start position:0%
+just be free
+that's here that's infinity that's n
+
+ align:start position:0%
+that's here that's infinity that's n
+ 
+
+ align:start position:0%
+that's here that's infinity that's n
+equals infinity
+
+ align:start position:0%
+equals infinity
+ 
+
+ align:start position:0%
+equals infinity
+right so if if i think about this
+
+ align:start position:0%
+right so if if i think about this
+ 
+
+ align:start position:0%
+right so if if i think about this
+that that's actually quite easy to put
+
+ align:start position:0%
+that that's actually quite easy to put
+ 
+
+ align:start position:0%
+that that's actually quite easy to put
+into bohr ionization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy so
+
+ align:start position:0%
+energy so
+ 
+
+ align:start position:0%
+energy so
+to save time we'll write ie right
+
+ align:start position:0%
+to save time we'll write ie right
+ 
+
+ align:start position:0%
+to save time we'll write ie right
+and this is equal to the energy
+
+ align:start position:0%
+and this is equal to the energy
+ 
+
+ align:start position:0%
+and this is equal to the energy
+required oh i'm going to save time here
+
+ align:start position:0%
+required oh i'm going to save time here
+ 
+
+ align:start position:0%
+required oh i'm going to save time here
+look at that requida
+
+ align:start position:0%
+look at that requida
+ 
+
+ align:start position:0%
+look at that requida
+to remove
+
+ align:start position:0%
+to remove
+ 
+
+ align:start position:0%
+to remove
+the electron from the atom
+
+ align:start position:0%
+the electron from the atom
+ 
+
+ align:start position:0%
+the electron from the atom
+okay good and and if we think about this
+
+ align:start position:0%
+okay good and and if we think about this
+ 
+
+ align:start position:0%
+okay good and and if we think about this
+in terms of bore
+
+ align:start position:0%
+in terms of bore
+ 
+
+ align:start position:0%
+in terms of bore
+it would be like minus 13.6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say for hydrogen because i've got
+
+ align:start position:0%
+let's say for hydrogen because i've got
+ 
+
+ align:start position:0%
+let's say for hydrogen because i've got
+hydrogen up there so for hydrogen
+
+ align:start position:0%
+hydrogen up there so for hydrogen
+ 
+
+ align:start position:0%
+hydrogen up there so for hydrogen
+meaning z equals 1 it'd be minus 13.6
+
+ align:start position:0%
+meaning z equals 1 it'd be minus 13.6
+ 
+
+ align:start position:0%
+meaning z equals 1 it'd be minus 13.6
+times 1
+
+ align:start position:0%
+times 1
+ 
+
+ align:start position:0%
+times 1
+squared that's the z squared right
+
+ align:start position:0%
+squared that's the z squared right
+ 
+
+ align:start position:0%
+squared that's the z squared right
+times 1 over
+
+ align:start position:0%
+times 1 over
+ 
+
+ align:start position:0%
+times 1 over
+nf squared minus 1 over
+
+ align:start position:0%
+nf squared minus 1 over
+ 
+
+ align:start position:0%
+nf squared minus 1 over
+n i squared that's that delta e which
+
+ align:start position:0%
+n i squared that's that delta e which
+ 
+
+ align:start position:0%
+n i squared that's that delta e which
+equals minus 13.6
+
+ align:start position:0%
+equals minus 13.6
+ 
+
+ align:start position:0%
+equals minus 13.6
+times 1 over infinity
+
+ align:start position:0%
+times 1 over infinity
+ 
+
+ align:start position:0%
+times 1 over infinity
+minus 1 over n i squared
+
+ align:start position:0%
+minus 1 over n i squared
+ 
+
+ align:start position:0%
+minus 1 over n i squared
+right now the last i checked with my
+
+ align:start position:0%
+right now the last i checked with my
+ 
+
+ align:start position:0%
+right now the last i checked with my
+colleagues in the math department that's
+
+ align:start position:0%
+colleagues in the math department that's
+ 
+
+ align:start position:0%
+colleagues in the math department that's
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+that's zero right so the ionization
+
+ align:start position:0%
+that's zero right so the ionization
+ 
+
+ align:start position:0%
+that's zero right so the ionization
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+you literally can just read off here if
+
+ align:start position:0%
+you literally can just read off here if
+ 
+
+ align:start position:0%
+you literally can just read off here if
+an electron is in the ground
+
+ align:start position:0%
+an electron is in the ground
+ 
+
+ align:start position:0%
+an electron is in the ground
+state if there's a happy electron right
+
+ align:start position:0%
+state if there's a happy electron right
+ 
+
+ align:start position:0%
+state if there's a happy electron right
+here in this orbital
+
+ align:start position:0%
+here in this orbital
+ 
+
+ align:start position:0%
+here in this orbital
+the amount of energy i need to input
+
+ align:start position:0%
+the amount of energy i need to input
+ 
+
+ align:start position:0%
+the amount of energy i need to input
+into that atom
+
+ align:start position:0%
+into that atom
+ 
+
+ align:start position:0%
+into that atom
+to knock the electron fully out the
+
+ align:start position:0%
+to knock the electron fully out the
+ 
+
+ align:start position:0%
+to knock the electron fully out the
+ionization energy
+
+ align:start position:0%
+ionization energy
+ 
+
+ align:start position:0%
+ionization energy
+is 13.6 electron volts right it's just
+
+ align:start position:0%
+is 13.6 electron volts right it's just
+ 
+
+ align:start position:0%
+is 13.6 electron volts right it's just
+the energy of that orbital
+
+ align:start position:0%
+the energy of that orbital
+ 
+
+ align:start position:0%
+the energy of that orbital
+i could get a little fancier i could say
+
+ align:start position:0%
+i could get a little fancier i could say
+ 
+
+ align:start position:0%
+i could get a little fancier i could say
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+okay what about this question
+
+ align:start position:0%
+okay what about this question
+ 
+
+ align:start position:0%
+okay what about this question
+what if i had light with a hundred
+
+ align:start position:0%
+what if i had light with a hundred
+ 
+
+ align:start position:0%
+what if i had light with a hundred
+nanometers
+
+ align:start position:0%
+nanometers
+ 
+
+ align:start position:0%
+nanometers
+so now i'm telling you my source right
+
+ align:start position:0%
+so now i'm telling you my source right
+ 
+
+ align:start position:0%
+so now i'm telling you my source right
+before i didn't tell you
+
+ align:start position:0%
+before i didn't tell you
+ 
+
+ align:start position:0%
+before i didn't tell you
+something goes into it and knocks it all
+
+ align:start position:0%
+something goes into it and knocks it all
+ 
+
+ align:start position:0%
+something goes into it and knocks it all
+out no now i know what's going in
+
+ align:start position:0%
+out no now i know what's going in
+ 
+
+ align:start position:0%
+out no now i know what's going in
+the the uh the wavelength or the energy
+
+ align:start position:0%
+the the uh the wavelength or the energy
+ 
+
+ align:start position:0%
+the the uh the wavelength or the energy
+of the photons is a hundred nanometers
+
+ align:start position:0%
+of the photons is a hundred nanometers
+ 
+
+ align:start position:0%
+of the photons is a hundred nanometers
+and i'm shining that on hydrogen well
+
+ align:start position:0%
+and i'm shining that on hydrogen well
+ 
+
+ align:start position:0%
+and i'm shining that on hydrogen well
+now okay let's see here so let's stop oh
+
+ align:start position:0%
+now okay let's see here so let's stop oh
+ 
+
+ align:start position:0%
+now okay let's see here so let's stop oh
+i'm asking a question what's the
+
+ align:start position:0%
+i'm asking a question what's the
+ 
+
+ align:start position:0%
+i'm asking a question what's the
+question what is the lowest energy level
+
+ align:start position:0%
+question what is the lowest energy level
+ 
+
+ align:start position:0%
+question what is the lowest energy level
+that the electron could be in such that
+
+ align:start position:0%
+that the electron could be in such that
+ 
+
+ align:start position:0%
+that the electron could be in such that
+a photon from this light source
+
+ align:start position:0%
+a photon from this light source
+ 
+
+ align:start position:0%
+a photon from this light source
+ionizes the atom okay let's see
+
+ align:start position:0%
+ionizes the atom okay let's see
+ 
+
+ align:start position:0%
+ionizes the atom okay let's see
+because i now i now know the pieces and
+
+ align:start position:0%
+because i now i now know the pieces and
+ 
+
+ align:start position:0%
+because i now i now know the pieces and
+i know the definition
+
+ align:start position:0%
+i know the definition
+ 
+
+ align:start position:0%
+i know the definition
+right so now if i have the energy
+
+ align:start position:0%
+right so now if i have the energy
+ 
+
+ align:start position:0%
+right so now if i have the energy
+of a hundred nanometer photon
+
+ align:start position:0%
+of a hundred nanometer photon
+ 
+
+ align:start position:0%
+of a hundred nanometer photon
+well that i'm not going to go through it
+
+ align:start position:0%
+well that i'm not going to go through it
+ 
+
+ align:start position:0%
+well that i'm not going to go through it
+is equal to 12.4 ev
+
+ align:start position:0%
+is equal to 12.4 ev
+ 
+
+ align:start position:0%
+is equal to 12.4 ev
+but see if i now want to use this to
+
+ align:start position:0%
+but see if i now want to use this to
+ 
+
+ align:start position:0%
+but see if i now want to use this to
+ionize hydrogen
+
+ align:start position:0%
+ionize hydrogen
+ 
+
+ align:start position:0%
+ionize hydrogen
+then i get something like this i get
+
+ align:start position:0%
+then i get something like this i get
+ 
+
+ align:start position:0%
+then i get something like this i get
+that delta e
+
+ align:start position:0%
+that delta e
+ 
+
+ align:start position:0%
+that delta e
+equals minus 13.6
+
+ align:start position:0%
+equals minus 13.6
+ 
+
+ align:start position:0%
+equals minus 13.6
+okay times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh one over infinity squared okay fine
+
+ align:start position:0%
+uh one over infinity squared okay fine
+ 
+
+ align:start position:0%
+uh one over infinity squared okay fine
+we'll keep that for a sec
+
+ align:start position:0%
+we'll keep that for a sec
+ 
+
+ align:start position:0%
+we'll keep that for a sec
+minus one over n i squared right
+
+ align:start position:0%
+minus one over n i squared right
+ 
+
+ align:start position:0%
+minus one over n i squared right
+this is how much this is how much uh uh
+
+ align:start position:0%
+this is how much this is how much uh uh
+ 
+
+ align:start position:0%
+this is how much this is how much uh uh
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+i need to ionize from any given place
+
+ align:start position:0%
+i need to ionize from any given place
+ 
+
+ align:start position:0%
+i need to ionize from any given place
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+given energy level and i right
+
+ align:start position:0%
+given energy level and i right
+ 
+
+ align:start position:0%
+given energy level and i right
+okay but but i have 12. so what if i set
+
+ align:start position:0%
+okay but but i have 12. so what if i set
+ 
+
+ align:start position:0%
+okay but but i have 12. so what if i set
+this equal to 12
+
+ align:start position:0%
+this equal to 12
+ 
+
+ align:start position:0%
+this equal to 12
+right if i set this equal to 12.4 that's
+
+ align:start position:0%
+right if i set this equal to 12.4 that's
+ 
+
+ align:start position:0%
+right if i set this equal to 12.4 that's
+what i have
+
+ align:start position:0%
+what i have
+ 
+
+ align:start position:0%
+what i have
+then what i get is n i
+
+ align:start position:0%
+then what i get is n i
+ 
+
+ align:start position:0%
+then what i get is n i
+equals 1.05
+
+ align:start position:0%
+equals 1.05
+ 
+
+ align:start position:0%
+equals 1.05
+okay good that's my answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no panic everybody should be panicking
+
+ align:start position:0%
+no panic everybody should be panicking
+ 
+
+ align:start position:0%
+no panic everybody should be panicking
+no that can't be my answer
+
+ align:start position:0%
+no that can't be my answer
+ 
+
+ align:start position:0%
+no that can't be my answer
+i can't i can't have something that's
+
+ align:start position:0%
+i can't i can't have something that's
+ 
+
+ align:start position:0%
+i can't i can't have something that's
+not an integer
+
+ align:start position:0%
+not an integer
+ 
+
+ align:start position:0%
+not an integer
+because i said it over there that n is a
+
+ align:start position:0%
+because i said it over there that n is a
+ 
+
+ align:start position:0%
+because i said it over there that n is a
+quantum number
+
+ align:start position:0%
+quantum number
+ 
+
+ align:start position:0%
+quantum number
+one two three nothing is allowed in
+
+ align:start position:0%
+one two three nothing is allowed in
+ 
+
+ align:start position:0%
+one two three nothing is allowed in
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+so what you can see is that i got so
+
+ align:start position:0%
+so what you can see is that i got so
+ 
+
+ align:start position:0%
+so what you can see is that i got so
+close
+
+ align:start position:0%
+close
+ 
+
+ align:start position:0%
+close
+i almost had enough energy to get n to
+
+ align:start position:0%
+i almost had enough energy to get n to
+ 
+
+ align:start position:0%
+i almost had enough energy to get n to
+b1 but i don't
+
+ align:start position:0%
+b1 but i don't
+ 
+
+ align:start position:0%
+b1 but i don't
+so i cannot use this light to ionize an
+
+ align:start position:0%
+so i cannot use this light to ionize an
+ 
+
+ align:start position:0%
+so i cannot use this light to ionize an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+in n equals one i can't but i could use
+
+ align:start position:0%
+in n equals one i can't but i could use
+ 
+
+ align:start position:0%
+in n equals one i can't but i could use
+it to ionize an electron in n equals two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because there if n is two
+
+ align:start position:0%
+right because there if n is two
+ 
+
+ align:start position:0%
+right because there if n is two
+well then i've got actually plenty of
+
+ align:start position:0%
+well then i've got actually plenty of
+ 
+
+ align:start position:0%
+well then i've got actually plenty of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cannot ionize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from n i equals one
+
+ align:start position:0%
+from n i equals one
+ 
+
+ align:start position:0%
+from n i equals one
+but n i equals two
+
+ align:start position:0%
+but n i equals two
+ 
+
+ align:start position:0%
+but n i equals two
+is okay right so that's the outcome of
+
+ align:start position:0%
+is okay right so that's the outcome of
+ 
+
+ align:start position:0%
+is okay right so that's the outcome of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+now i could also use that same 12.4 ev
+
+ align:start position:0%
+now i could also use that same 12.4 ev
+ 
+
+ align:start position:0%
+now i could also use that same 12.4 ev
+photon
+
+ align:start position:0%
+photon
+ 
+
+ align:start position:0%
+photon
+to ionize from n equals three or four or
+
+ align:start position:0%
+to ionize from n equals three or four or
+ 
+
+ align:start position:0%
+to ionize from n equals three or four or
+any of these
+
+ align:start position:0%
+any of these
+ 
+
+ align:start position:0%
+any of these
+but i can't get to one and there's one
+
+ align:start position:0%
+but i can't get to one and there's one
+ 
+
+ align:start position:0%
+but i can't get to one and there's one
+other concept that's important because
+
+ align:start position:0%
+other concept that's important because
+ 
+
+ align:start position:0%
+other concept that's important because
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+i gave it 12.4 ev
+
+ align:start position:0%
+i gave it 12.4 ev
+ 
+
+ align:start position:0%
+i gave it 12.4 ev
+what did i actually need well i mean you
+
+ align:start position:0%
+what did i actually need well i mean you
+ 
+
+ align:start position:0%
+what did i actually need well i mean you
+can even see it here
+
+ align:start position:0%
+can even see it here
+ 
+
+ align:start position:0%
+can even see it here
+you can just you know what these levels
+
+ align:start position:0%
+you can just you know what these levels
+ 
+
+ align:start position:0%
+you can just you know what these levels
+are from the bohr model
+
+ align:start position:0%
+are from the bohr model
+ 
+
+ align:start position:0%
+are from the bohr model
+here this is 13.6 this is
+
+ align:start position:0%
+here this is 13.6 this is
+ 
+
+ align:start position:0%
+here this is 13.6 this is
+minus 3.4 okay that's telling me this is
+
+ align:start position:0%
+minus 3.4 okay that's telling me this is
+ 
+
+ align:start position:0%
+minus 3.4 okay that's telling me this is
+definitely not drawn to scale
+
+ align:start position:0%
+definitely not drawn to scale
+ 
+
+ align:start position:0%
+definitely not drawn to scale
+but still you you get the point 3.4
+
+ align:start position:0%
+but still you you get the point 3.4
+ 
+
+ align:start position:0%
+but still you you get the point 3.4
+and and i just said well i could
+
+ align:start position:0%
+and and i just said well i could
+ 
+
+ align:start position:0%
+and and i just said well i could
+probably get it out of 3.4 and i can
+
+ align:start position:0%
+probably get it out of 3.4 and i can
+ 
+
+ align:start position:0%
+probably get it out of 3.4 and i can
+because i've got 12.4
+
+ align:start position:0%
+because i've got 12.4
+ 
+
+ align:start position:0%
+because i've got 12.4
+and so if i did this so if n
+
+ align:start position:0%
+and so if i did this so if n
+ 
+
+ align:start position:0%
+and so if i did this so if n
+i equals two then i would have excess
+
+ align:start position:0%
+i equals two then i would have excess
+ 
+
+ align:start position:0%
+i equals two then i would have excess
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+excess energy would be nine electron
+
+ align:start position:0%
+excess energy would be nine electron
+ 
+
+ align:start position:0%
+excess energy would be nine electron
+volts
+
+ align:start position:0%
+volts
+ 
+
+ align:start position:0%
+volts
+and that is kinetic right so i've shot
+
+ align:start position:0%
+and that is kinetic right so i've shot
+ 
+
+ align:start position:0%
+and that is kinetic right so i've shot
+this thing out of the atom
+
+ align:start position:0%
+this thing out of the atom
+ 
+
+ align:start position:0%
+this thing out of the atom
+with light that's got way more energy
+
+ align:start position:0%
+with light that's got way more energy
+ 
+
+ align:start position:0%
+with light that's got way more energy
+than i needed to ionize it but that
+
+ align:start position:0%
+than i needed to ionize it but that
+ 
+
+ align:start position:0%
+than i needed to ionize it but that
+energy didn't it's still in the electron
+
+ align:start position:0%
+energy didn't it's still in the electron
+ 
+
+ align:start position:0%
+energy didn't it's still in the electron
+i transferred that photon energy to the
+
+ align:start position:0%
+i transferred that photon energy to the
+ 
+
+ align:start position:0%
+i transferred that photon energy to the
+electron energy
+
+ align:start position:0%
+electron energy
+ 
+
+ align:start position:0%
+electron energy
+and so that is going to be
+
+ align:start position:0%
+and so that is going to be
+ 
+
+ align:start position:0%
+and so that is going to be
+in the kinetic energy of
+
+ align:start position:0%
+in the kinetic energy of
+ 
+
+ align:start position:0%
+in the kinetic energy of
+the electron that's now free the
+
+ align:start position:0%
+the electron that's now free the
+ 
+
+ align:start position:0%
+the electron that's now free the
+electron free
+
+ align:start position:0%
+electron free
+ 
+
+ align:start position:0%
+electron free
+i should have said free electron right
+
+ align:start position:0%
+i should have said free electron right
+ 
+
+ align:start position:0%
+i should have said free electron right
+excess kinetic energy comes after
+
+ align:start position:0%
+excess kinetic energy comes after
+ 
+
+ align:start position:0%
+excess kinetic energy comes after
+ionizing it right so these things
+
+ align:start position:0%
+ionizing it right so these things
+ 
+
+ align:start position:0%
+ionizing it right so these things
+are the things we can do with bohr so i
+
+ align:start position:0%
+are the things we can do with bohr so i
+ 
+
+ align:start position:0%
+are the things we can do with bohr so i
+wanted to kind of
+
+ align:start position:0%
+wanted to kind of
+ 
+
+ align:start position:0%
+wanted to kind of
+you know take what we learned wednesday
+
+ align:start position:0%
+you know take what we learned wednesday
+ 
+
+ align:start position:0%
+you know take what we learned wednesday
+and apply it to a few problems
+
+ align:start position:0%
+and apply it to a few problems
+ 
+
+ align:start position:0%
+and apply it to a few problems
+and go back and forth with
+
+ align:start position:0%
+and go back and forth with
+ 
+
+ align:start position:0%
+and go back and forth with
+with this idea of photon energy uh
+
+ align:start position:0%
+with this idea of photon energy uh
+ 
+
+ align:start position:0%
+with this idea of photon energy uh
+to bore level changes and that's what i
+
+ align:start position:0%
+to bore level changes and that's what i
+ 
+
+ align:start position:0%
+to bore level changes and that's what i
+want you to do in
+
+ align:start position:0%
+want you to do in
+ 
+
+ align:start position:0%
+want you to do in
+this week's goodie bag as well okay
+
+ align:start position:0%
+this week's goodie bag as well okay
+ 
+
+ align:start position:0%
+this week's goodie bag as well okay
+now ionization is an important concept
+
+ align:start position:0%
+now ionization is an important concept
+ 
+
+ align:start position:0%
+now ionization is an important concept
+like i said we'll be coming back to it
+
+ align:start position:0%
+like i said we'll be coming back to it
+ 
+
+ align:start position:0%
+like i said we'll be coming back to it
+um and you can you can actually uh
+
+ align:start position:0%
+um and you can you can actually uh
+ 
+
+ align:start position:0%
+um and you can you can actually uh
+plot and many people have measured and
+
+ align:start position:0%
+plot and many people have measured and
+ 
+
+ align:start position:0%
+plot and many people have measured and
+and this is very important
+
+ align:start position:0%
+and this is very important
+ 
+
+ align:start position:0%
+and this is very important
+the ionization energy of elements like
+
+ align:start position:0%
+the ionization energy of elements like
+ 
+
+ align:start position:0%
+the ionization energy of elements like
+as a function of
+
+ align:start position:0%
+as a function of
+ 
+
+ align:start position:0%
+as a function of
+atomic number and the first ionization
+
+ align:start position:0%
+atomic number and the first ionization
+ 
+
+ align:start position:0%
+atomic number and the first ionization
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+is important right the first ionization
+
+ align:start position:0%
+is important right the first ionization
+ 
+
+ align:start position:0%
+is important right the first ionization
+energy is the energy
+
+ align:start position:0%
+energy is the energy
+ 
+
+ align:start position:0%
+energy is the energy
+required to remove the outermost
+
+ align:start position:0%
+required to remove the outermost
+ 
+
+ align:start position:0%
+required to remove the outermost
+electron right
+
+ align:start position:0%
+electron right
+ 
+
+ align:start position:0%
+electron right
+right so if i did have a whole bunch of
+
+ align:start position:0%
+right so if i did have a whole bunch of
+ 
+
+ align:start position:0%
+right so if i did have a whole bunch of
+of electrons so if i had
+
+ align:start position:0%
+of electrons so if i had
+ 
+
+ align:start position:0%
+of electrons so if i had
+a whole bunch of electrons the first
+
+ align:start position:0%
+a whole bunch of electrons the first
+ 
+
+ align:start position:0%
+a whole bunch of electrons the first
+ionization the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ionization energy is the energy
+
+ align:start position:0%
+ionization energy is the energy
+ 
+
+ align:start position:0%
+ionization energy is the energy
+required
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to remove the outermost one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's an important number to know if
+
+ align:start position:0%
+so that's an important number to know if
+ 
+
+ align:start position:0%
+so that's an important number to know if
+you want to take an electron off of an
+
+ align:start position:0%
+you want to take an electron off of an
+ 
+
+ align:start position:0%
+you want to take an electron off of an
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+and we will be doing that because that's
+
+ align:start position:0%
+and we will be doing that because that's
+ 
+
+ align:start position:0%
+and we will be doing that because that's
+how we're going to make our first
+
+ align:start position:0%
+how we're going to make our first
+ 
+
+ align:start position:0%
+how we're going to make our first
+bond next week if you want to take an
+
+ align:start position:0%
+bond next week if you want to take an
+ 
+
+ align:start position:0%
+bond next week if you want to take an
+electron off an atom this is one of the
+
+ align:start position:0%
+electron off an atom this is one of the
+ 
+
+ align:start position:0%
+electron off an atom this is one of the
+first things you ask
+
+ align:start position:0%
+first things you ask
+ 
+
+ align:start position:0%
+first things you ask
+how much energy does it take right how
+
+ align:start position:0%
+how much energy does it take right how
+ 
+
+ align:start position:0%
+how much energy does it take right how
+much energy does it take so that's an
+
+ align:start position:0%
+much energy does it take so that's an
+ 
+
+ align:start position:0%
+much energy does it take so that's an
+important concept that we'll be coming
+
+ align:start position:0%
+important concept that we'll be coming
+ 
+
+ align:start position:0%
+important concept that we'll be coming
+back to now
+
+ align:start position:0%
+back to now
+ 
+
+ align:start position:0%
+back to now
+okay i alluded to the fact that we
+
+ align:start position:0%
+okay i alluded to the fact that we
+ 
+
+ align:start position:0%
+okay i alluded to the fact that we
+needed a new theory
+
+ align:start position:0%
+needed a new theory
+ 
+
+ align:start position:0%
+needed a new theory
+i already alluded to that and i said
+
+ align:start position:0%
+i already alluded to that and i said
+ 
+
+ align:start position:0%
+i already alluded to that and i said
+that's where we're going today
+
+ align:start position:0%
+that's where we're going today
+ 
+
+ align:start position:0%
+that's where we're going today
+the bohr model works for one electron as
+
+ align:start position:0%
+the bohr model works for one electron as
+ 
+
+ align:start position:0%
+the bohr model works for one electron as
+i said all right that means it's good
+
+ align:start position:0%
+i said all right that means it's good
+ 
+
+ align:start position:0%
+i said all right that means it's good
+for hydrogen
+
+ align:start position:0%
+for hydrogen
+ 
+
+ align:start position:0%
+for hydrogen
+oh we just ionized hydrogen that was a
+
+ align:start position:0%
+oh we just ionized hydrogen that was a
+ 
+
+ align:start position:0%
+oh we just ionized hydrogen that was a
+lot of fun
+
+ align:start position:0%
+lot of fun
+ 
+
+ align:start position:0%
+lot of fun
+and it's good for like he plus
+
+ align:start position:0%
+and it's good for like he plus
+ 
+
+ align:start position:0%
+and it's good for like he plus
+or li2 plus or osmium 75 plus
+
+ align:start position:0%
+or li2 plus or osmium 75 plus
+ 
+
+ align:start position:0%
+or li2 plus or osmium 75 plus
+yeah that's real but what about two
+
+ align:start position:0%
+yeah that's real but what about two
+ 
+
+ align:start position:0%
+yeah that's real but what about two
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+what about two just two forget about ten
+
+ align:start position:0%
+what about two just two forget about ten
+ 
+
+ align:start position:0%
+what about two just two forget about ten
+twenty thirty
+
+ align:start position:0%
+twenty thirty
+ 
+
+ align:start position:0%
+twenty thirty
+two the bohr model can't do it it
+
+ align:start position:0%
+two the bohr model can't do it it
+ 
+
+ align:start position:0%
+two the bohr model can't do it it
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+it it doesn't work for anything more
+
+ align:start position:0%
+it it doesn't work for anything more
+ 
+
+ align:start position:0%
+it it doesn't work for anything more
+than one electron it was derived for one
+
+ align:start position:0%
+than one electron it was derived for one
+ 
+
+ align:start position:0%
+than one electron it was derived for one
+electron and that's where it stays so
+
+ align:start position:0%
+electron and that's where it stays so
+ 
+
+ align:start position:0%
+electron and that's where it stays so
+we're at this point now
+
+ align:start position:0%
+we're at this point now
+ 
+
+ align:start position:0%
+we're at this point now
+this is a picture i started to draw this
+
+ align:start position:0%
+this is a picture i started to draw this
+ 
+
+ align:start position:0%
+this is a picture i started to draw this
+week on monday and we're at a point
+
+ align:start position:0%
+week on monday and we're at a point
+ 
+
+ align:start position:0%
+week on monday and we're at a point
+where we need something deeper
+
+ align:start position:0%
+where we need something deeper
+ 
+
+ align:start position:0%
+where we need something deeper
+and some of the work that went into this
+
+ align:start position:0%
+and some of the work that went into this
+ 
+
+ align:start position:0%
+and some of the work that went into this
+was really critical
+
+ align:start position:0%
+was really critical
+ 
+
+ align:start position:0%
+was really critical
+and i'm not going to go into too much
+
+ align:start position:0%
+and i'm not going to go into too much
+ 
+
+ align:start position:0%
+and i'm not going to go into too much
+detail but there's one thing i want you
+
+ align:start position:0%
+detail but there's one thing i want you
+ 
+
+ align:start position:0%
+detail but there's one thing i want you
+to know so remember
+
+ align:start position:0%
+to know so remember
+ 
+
+ align:start position:0%
+to know so remember
+you know plank and einstein they were
+
+ align:start position:0%
+you know plank and einstein they were
+ 
+
+ align:start position:0%
+you know plank and einstein they were
+playing with quantization of light
+
+ align:start position:0%
+playing with quantization of light
+ 
+
+ align:start position:0%
+playing with quantization of light
+and einstein's photoelectric effect
+
+ align:start position:0%
+and einstein's photoelectric effect
+ 
+
+ align:start position:0%
+and einstein's photoelectric effect
+found the particle nature of light
+
+ align:start position:0%
+found the particle nature of light
+ 
+
+ align:start position:0%
+found the particle nature of light
+with planks you know with together their
+
+ align:start position:0%
+with planks you know with together their
+ 
+
+ align:start position:0%
+with planks you know with together their
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+right equals h nu that quantized energy
+
+ align:start position:0%
+right equals h nu that quantized energy
+ 
+
+ align:start position:0%
+right equals h nu that quantized energy
+of the photon
+
+ align:start position:0%
+of the photon
+ 
+
+ align:start position:0%
+of the photon
+and they they saw it's a particle but it
+
+ align:start position:0%
+and they they saw it's a particle but it
+ 
+
+ align:start position:0%
+and they they saw it's a particle but it
+also is is a
+
+ align:start position:0%
+also is is a
+ 
+
+ align:start position:0%
+also is is a
+is a wave right there's a lot of
+
+ align:start position:0%
+is a wave right there's a lot of
+ 
+
+ align:start position:0%
+is a wave right there's a lot of
+discussion and
+
+ align:start position:0%
+discussion and
+ 
+
+ align:start position:0%
+discussion and
+and interest and and attempts to
+
+ align:start position:0%
+and interest and and attempts to
+ 
+
+ align:start position:0%
+and interest and and attempts to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+what it was was it a wave or a particle
+
+ align:start position:0%
+what it was was it a wave or a particle
+ 
+
+ align:start position:0%
+what it was was it a wave or a particle
+and compton did some beautiful
+
+ align:start position:0%
+and compton did some beautiful
+ 
+
+ align:start position:0%
+and compton did some beautiful
+experiments to show again
+
+ align:start position:0%
+experiments to show again
+ 
+
+ align:start position:0%
+experiments to show again
+evidence that it was a particle because
+
+ align:start position:0%
+evidence that it was a particle because
+ 
+
+ align:start position:0%
+evidence that it was a particle because
+he he saw how
+
+ align:start position:0%
+he he saw how
+ 
+
+ align:start position:0%
+he he saw how
+light interacted with electrons and it
+
+ align:start position:0%
+light interacted with electrons and it
+ 
+
+ align:start position:0%
+light interacted with electrons and it
+was like this collision
+
+ align:start position:0%
+was like this collision
+ 
+
+ align:start position:0%
+was like this collision
+that particles do and then de broglie
+
+ align:start position:0%
+that particles do and then de broglie
+ 
+
+ align:start position:0%
+that particles do and then de broglie
+or as where's jerome de bruyne
+
+ align:start position:0%
+or as where's jerome de bruyne
+ 
+
+ align:start position:0%
+or as where's jerome de bruyne
+i don't know would say he went
+
+ align:start position:0%
+i don't know would say he went
+ 
+
+ align:start position:0%
+i don't know would say he went
+further de broglie went further he said
+
+ align:start position:0%
+further de broglie went further he said
+ 
+
+ align:start position:0%
+further de broglie went further he said
+everything is both light you guys don't
+
+ align:start position:0%
+everything is both light you guys don't
+ 
+
+ align:start position:0%
+everything is both light you guys don't
+know if light is a particle or wave well
+
+ align:start position:0%
+know if light is a particle or wave well
+ 
+
+ align:start position:0%
+know if light is a particle or wave well
+i'm saying everything is a wave
+
+ align:start position:0%
+i'm saying everything is a wave
+ 
+
+ align:start position:0%
+i'm saying everything is a wave
+everything and everything has this
+
+ align:start position:0%
+everything and everything has this
+ 
+
+ align:start position:0%
+everything and everything has this
+duality
+
+ align:start position:0%
+duality
+ 
+
+ align:start position:0%
+duality
+so he wrote something very important
+
+ align:start position:0%
+so he wrote something very important
+ 
+
+ align:start position:0%
+so he wrote something very important
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+the relationship between anything's
+
+ align:start position:0%
+the relationship between anything's
+ 
+
+ align:start position:0%
+the relationship between anything's
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+and it's wavelength so we'll come back
+
+ align:start position:0%
+and it's wavelength so we'll come back
+ 
+
+ align:start position:0%
+and it's wavelength so we'll come back
+to this so i want to write it down so
+
+ align:start position:0%
+to this so i want to write it down so
+ 
+
+ align:start position:0%
+to this so i want to write it down so
+de brush he said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the wavelength of anything can be
+
+ align:start position:0%
+that the wavelength of anything can be
+ 
+
+ align:start position:0%
+that the wavelength of anything can be
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+as oh that same quantization number
+
+ align:start position:0%
+as oh that same quantization number
+ 
+
+ align:start position:0%
+as oh that same quantization number
+constant from planck divided by its
+
+ align:start position:0%
+constant from planck divided by its
+ 
+
+ align:start position:0%
+constant from planck divided by its
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+literally just its momentum anything has
+
+ align:start position:0%
+literally just its momentum anything has
+ 
+
+ align:start position:0%
+literally just its momentum anything has
+a wave nature
+
+ align:start position:0%
+a wave nature
+ 
+
+ align:start position:0%
+a wave nature
+anything and light has a particle nature
+
+ align:start position:0%
+anything and light has a particle nature
+ 
+
+ align:start position:0%
+anything and light has a particle nature
+what's going on
+
+ align:start position:0%
+what's going on
+ 
+
+ align:start position:0%
+what's going on
+and it led einstein to say at the time
+
+ align:start position:0%
+and it led einstein to say at the time
+ 
+
+ align:start position:0%
+and it led einstein to say at the time
+he said quote it seems as though we must
+
+ align:start position:0%
+he said quote it seems as though we must
+ 
+
+ align:start position:0%
+he said quote it seems as though we must
+use sometimes the one theory and
+
+ align:start position:0%
+use sometimes the one theory and
+ 
+
+ align:start position:0%
+use sometimes the one theory and
+sometimes the other
+
+ align:start position:0%
+sometimes the other
+ 
+
+ align:start position:0%
+sometimes the other
+while at times we may use either we are
+
+ align:start position:0%
+while at times we may use either we are
+ 
+
+ align:start position:0%
+while at times we may use either we are
+faced with a new kind of difficulty we
+
+ align:start position:0%
+faced with a new kind of difficulty we
+ 
+
+ align:start position:0%
+faced with a new kind of difficulty we
+have two contradictory pictures of
+
+ align:start position:0%
+have two contradictory pictures of
+ 
+
+ align:start position:0%
+have two contradictory pictures of
+reality
+
+ align:start position:0%
+reality
+ 
+
+ align:start position:0%
+reality
+separately neither of them fully
+
+ align:start position:0%
+separately neither of them fully
+ 
+
+ align:start position:0%
+separately neither of them fully
+explains the phenomena of light
+
+ align:start position:0%
+explains the phenomena of light
+ 
+
+ align:start position:0%
+explains the phenomena of light
+but together they do this was the
+
+ align:start position:0%
+but together they do this was the
+ 
+
+ align:start position:0%
+but together they do this was the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+of quantum mechanics this is where they
+
+ align:start position:0%
+of quantum mechanics this is where they
+ 
+
+ align:start position:0%
+of quantum mechanics this is where they
+were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and later once they once they really
+
+ align:start position:0%
+and and later once they once they really
+ 
+
+ align:start position:0%
+and and later once they once they really
+got the quantum mechanics kind of going
+
+ align:start position:0%
+got the quantum mechanics kind of going
+ 
+
+ align:start position:0%
+got the quantum mechanics kind of going
+he said this the more success the
+
+ align:start position:0%
+he said this the more success the
+ 
+
+ align:start position:0%
+he said this the more success the
+quantum mechanics has the sillier it
+
+ align:start position:0%
+quantum mechanics has the sillier it
+ 
+
+ align:start position:0%
+quantum mechanics has the sillier it
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+why well there's only one way
+
+ align:start position:0%
+why well there's only one way
+ 
+
+ align:start position:0%
+why well there's only one way
+uh to really learn about quantum
+
+ align:start position:0%
+uh to really learn about quantum
+ 
+
+ align:start position:0%
+uh to really learn about quantum
+especially if it's the first time and
+
+ align:start position:0%
+especially if it's the first time and
+ 
+
+ align:start position:0%
+especially if it's the first time and
+that's from dr quantum himself
+
+ align:start position:0%
+that's from dr quantum himself
+ 
+
+ align:start position:0%
+that's from dr quantum himself
+and so i do have a video of dr quanum
+
+ align:start position:0%
+and so i do have a video of dr quanum
+ 
+
+ align:start position:0%
+and so i do have a video of dr quanum
+and i'm hoping you will enjoy this with
+
+ align:start position:0%
+and i'm hoping you will enjoy this with
+ 
+
+ align:start position:0%
+and i'm hoping you will enjoy this with
+me i enjoy it every time i see it
+
+ align:start position:0%
+me i enjoy it every time i see it
+ 
+
+ align:start position:0%
+me i enjoy it every time i see it
+most friday nights um so
+
+ align:start position:0%
+most friday nights um so
+ 
+
+ align:start position:0%
+most friday nights um so
+let's watch dr quantum explain
+
+ align:start position:0%
+let's watch dr quantum explain
+ 
+
+ align:start position:0%
+let's watch dr quantum explain
+because there was one really important
+
+ align:start position:0%
+because there was one really important
+ 
+
+ align:start position:0%
+because there was one really important
+experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that happened that he's going to explain
+
+ align:start position:0%
+that happened that he's going to explain
+ 
+
+ align:start position:0%
+that happened that he's going to explain
+right now called the double slit
+
+ align:start position:0%
+right now called the double slit
+ 
+
+ align:start position:0%
+right now called the double slit
+experiment and it changed everything
+
+ align:start position:0%
+experiment and it changed everything
+ 
+
+ align:start position:0%
+experiment and it changed everything
+and i don't care if you see it in
+
+ align:start position:0%
+and i don't care if you see it in
+ 
+
+ align:start position:0%
+and i don't care if you see it in
+another class we're seeing it here
+
+ align:start position:0%
+another class we're seeing it here
+ 
+
+ align:start position:0%
+another class we're seeing it here
+because this sets up
+
+ align:start position:0%
+because this sets up
+ 
+
+ align:start position:0%
+because this sets up
+what happens next in chemistry let's
+
+ align:start position:0%
+what happens next in chemistry let's
+ 
+
+ align:start position:0%
+what happens next in chemistry let's
+watch dr quantum
+
+ align:start position:0%
+watch dr quantum
+ 
+
+ align:start position:0%
+watch dr quantum
+we are the granddaddy of all quantum
+
+ align:start position:0%
+we are the granddaddy of all quantum
+ 
+
+ align:start position:0%
+we are the granddaddy of all quantum
+weirdness
+
+ align:start position:0%
+weirdness
+ 
+
+ align:start position:0%
+weirdness
+the infamous double slit experiment
+
+ align:start position:0%
+the infamous double slit experiment
+ 
+
+ align:start position:0%
+the infamous double slit experiment
+to understand this experiment we first
+
+ align:start position:0%
+to understand this experiment we first
+ 
+
+ align:start position:0%
+to understand this experiment we first
+need to see
+
+ align:start position:0%
+need to see
+ 
+
+ align:start position:0%
+need to see
+how particles or little balls of matter
+
+ align:start position:0%
+how particles or little balls of matter
+ 
+
+ align:start position:0%
+how particles or little balls of matter
+act if we randomly shoot a small
+
+ align:start position:0%
+act if we randomly shoot a small
+ 
+
+ align:start position:0%
+act if we randomly shoot a small
+object say a marble at the screen
+
+ align:start position:0%
+object say a marble at the screen
+ 
+
+ align:start position:0%
+object say a marble at the screen
+we see a pattern on the back wall where
+
+ align:start position:0%
+we see a pattern on the back wall where
+ 
+
+ align:start position:0%
+we see a pattern on the back wall where
+they went through the slit
+
+ align:start position:0%
+they went through the slit
+ 
+
+ align:start position:0%
+they went through the slit
+and hit now if we add a second slit
+
+ align:start position:0%
+and hit now if we add a second slit
+ 
+
+ align:start position:0%
+and hit now if we add a second slit
+we would expect to see a second band
+
+ align:start position:0%
+we would expect to see a second band
+ 
+
+ align:start position:0%
+we would expect to see a second band
+duplicated
+
+ align:start position:0%
+duplicated
+ 
+
+ align:start position:0%
+duplicated
+to the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's look at waves
+
+ align:start position:0%
+now let's look at waves
+ 
+
+ align:start position:0%
+now let's look at waves
+the waves hit the slit and radiate out
+
+ align:start position:0%
+the waves hit the slit and radiate out
+ 
+
+ align:start position:0%
+the waves hit the slit and radiate out
+striking the back wall with the most
+
+ align:start position:0%
+striking the back wall with the most
+ 
+
+ align:start position:0%
+striking the back wall with the most
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+directly in line with the slit
+
+ align:start position:0%
+directly in line with the slit
+ 
+
+ align:start position:0%
+directly in line with the slit
+the line of brightness on the back
+
+ align:start position:0%
+the line of brightness on the back
+ 
+
+ align:start position:0%
+the line of brightness on the back
+screen shows that intensity
+
+ align:start position:0%
+screen shows that intensity
+ 
+
+ align:start position:0%
+screen shows that intensity
+this is similar to the line the marbles
+
+ align:start position:0%
+this is similar to the line the marbles
+ 
+
+ align:start position:0%
+this is similar to the line the marbles
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+but when we add the second slit
+
+ align:start position:0%
+but when we add the second slit
+ 
+
+ align:start position:0%
+but when we add the second slit
+something different happens if the top
+
+ align:start position:0%
+something different happens if the top
+ 
+
+ align:start position:0%
+something different happens if the top
+of one wave
+
+ align:start position:0%
+of one wave
+ 
+
+ align:start position:0%
+of one wave
+meets the bottom of another wave
+
+ align:start position:0%
+meets the bottom of another wave
+ 
+
+ align:start position:0%
+meets the bottom of another wave
+they cancel each other out so now
+
+ align:start position:0%
+they cancel each other out so now
+ 
+
+ align:start position:0%
+they cancel each other out so now
+there is an interference pattern on the
+
+ align:start position:0%
+there is an interference pattern on the
+ 
+
+ align:start position:0%
+there is an interference pattern on the
+back wall
+
+ align:start position:0%
+back wall
+ 
+
+ align:start position:0%
+back wall
+places where the two tops meet are the
+
+ align:start position:0%
+places where the two tops meet are the
+ 
+
+ align:start position:0%
+places where the two tops meet are the
+highest intensity
+
+ align:start position:0%
+highest intensity
+ 
+
+ align:start position:0%
+highest intensity
+the bright lines and where they cancel
+
+ align:start position:0%
+the bright lines and where they cancel
+ 
+
+ align:start position:0%
+the bright lines and where they cancel
+there is nothing
+
+ align:start position:0%
+there is nothing
+ 
+
+ align:start position:0%
+there is nothing
+so when we throw things
+
+ align:start position:0%
+so when we throw things
+ 
+
+ align:start position:0%
+so when we throw things
+that is matter through two slits
+
+ align:start position:0%
+that is matter through two slits
+ 
+
+ align:start position:0%
+that is matter through two slits
+we get this two bands of hits
+
+ align:start position:0%
+we get this two bands of hits
+ 
+
+ align:start position:0%
+we get this two bands of hits
+and with waves we get an interference
+
+ align:start position:0%
+and with waves we get an interference
+ 
+
+ align:start position:0%
+and with waves we get an interference
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+of many bands good
+
+ align:start position:0%
+of many bands good
+ 
+
+ align:start position:0%
+of many bands good
+so far now let's go
+
+ align:start position:0%
+so far now let's go
+ 
+
+ align:start position:0%
+so far now let's go
+quantum my favorite line i love that
+
+ align:start position:0%
+quantum my favorite line i love that
+ 
+
+ align:start position:0%
+quantum my favorite line i love that
+line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an electron is a tiny tiny bit
+
+ align:start position:0%
+an electron is a tiny tiny bit
+ 
+
+ align:start position:0%
+an electron is a tiny tiny bit
+of matter like a tiny marble
+
+ align:start position:0%
+of matter like a tiny marble
+ 
+
+ align:start position:0%
+of matter like a tiny marble
+let's fire a stream through one slit
+
+ align:start position:0%
+let's fire a stream through one slit
+ 
+
+ align:start position:0%
+let's fire a stream through one slit
+it behaves just like the marble a single
+
+ align:start position:0%
+it behaves just like the marble a single
+ 
+
+ align:start position:0%
+it behaves just like the marble a single
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+so if we shoot these tiny bits through
+
+ align:start position:0%
+so if we shoot these tiny bits through
+ 
+
+ align:start position:0%
+so if we shoot these tiny bits through
+two slits we should get like the marbles
+
+ align:start position:0%
+two slits we should get like the marbles
+ 
+
+ align:start position:0%
+two slits we should get like the marbles
+two bands what
+
+ align:start position:0%
+two bands what
+ 
+
+ align:start position:0%
+two bands what
+an interference pattern we fired
+
+ align:start position:0%
+an interference pattern we fired
+ 
+
+ align:start position:0%
+an interference pattern we fired
+electrons tiny bits of matter through
+
+ align:start position:0%
+electrons tiny bits of matter through
+ 
+
+ align:start position:0%
+electrons tiny bits of matter through
+but we get a pattern like waves not like
+
+ align:start position:0%
+but we get a pattern like waves not like
+ 
+
+ align:start position:0%
+but we get a pattern like waves not like
+little marbles
+
+ align:start position:0%
+little marbles
+ 
+
+ align:start position:0%
+little marbles
+how how could pieces of matter
+
+ align:start position:0%
+how how could pieces of matter
+ 
+
+ align:start position:0%
+how how could pieces of matter
+create an interference pattern like a
+
+ align:start position:0%
+create an interference pattern like a
+ 
+
+ align:start position:0%
+create an interference pattern like a
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+it doesn't make sense but
+
+ align:start position:0%
+it doesn't make sense but
+ 
+
+ align:start position:0%
+it doesn't make sense but
+physicists are clever they thought maybe
+
+ align:start position:0%
+physicists are clever they thought maybe
+ 
+
+ align:start position:0%
+physicists are clever they thought maybe
+those little balls are bouncing off each
+
+ align:start position:0%
+those little balls are bouncing off each
+ 
+
+ align:start position:0%
+those little balls are bouncing off each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+and creating that pattern so
+
+ align:start position:0%
+and creating that pattern so
+ 
+
+ align:start position:0%
+and creating that pattern so
+they decide to shoot electrons through
+
+ align:start position:0%
+they decide to shoot electrons through
+ 
+
+ align:start position:0%
+they decide to shoot electrons through
+one at a time
+
+ align:start position:0%
+one at a time
+ 
+
+ align:start position:0%
+one at a time
+there is no way they can interfere with
+
+ align:start position:0%
+there is no way they can interfere with
+ 
+
+ align:start position:0%
+there is no way they can interfere with
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+but after an hour of this the same
+
+ align:start position:0%
+but after an hour of this the same
+ 
+
+ align:start position:0%
+but after an hour of this the same
+interference pattern is seen to emerge
+
+ align:start position:0%
+interference pattern is seen to emerge
+ 
+
+ align:start position:0%
+interference pattern is seen to emerge
+the conclusion is inescapable the single
+
+ align:start position:0%
+the conclusion is inescapable the single
+ 
+
+ align:start position:0%
+the conclusion is inescapable the single
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+leaves as a particle becomes a wave of
+
+ align:start position:0%
+leaves as a particle becomes a wave of
+ 
+
+ align:start position:0%
+leaves as a particle becomes a wave of
+potentials
+
+ align:start position:0%
+potentials
+ 
+
+ align:start position:0%
+potentials
+goes through both slits and interferes
+
+ align:start position:0%
+goes through both slits and interferes
+ 
+
+ align:start position:0%
+goes through both slits and interferes
+with itself to hit the wall like a
+
+ align:start position:0%
+with itself to hit the wall like a
+ 
+
+ align:start position:0%
+with itself to hit the wall like a
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+but mathematically it's even stranger it
+
+ align:start position:0%
+but mathematically it's even stranger it
+ 
+
+ align:start position:0%
+but mathematically it's even stranger it
+goes through both slits
+
+ align:start position:0%
+goes through both slits
+ 
+
+ align:start position:0%
+goes through both slits
+and it goes through neither and it goes
+
+ align:start position:0%
+and it goes through neither and it goes
+ 
+
+ align:start position:0%
+and it goes through neither and it goes
+through just one
+
+ align:start position:0%
+through just one
+ 
+
+ align:start position:0%
+through just one
+and it goes through just the other all
+
+ align:start position:0%
+and it goes through just the other all
+ 
+
+ align:start position:0%
+and it goes through just the other all
+of these possibilities
+
+ align:start position:0%
+of these possibilities
+ 
+
+ align:start position:0%
+of these possibilities
+are in superposition with each other but
+
+ align:start position:0%
+are in superposition with each other but
+ 
+
+ align:start position:0%
+are in superposition with each other but
+physicists were completely baffled by
+
+ align:start position:0%
+physicists were completely baffled by
+ 
+
+ align:start position:0%
+physicists were completely baffled by
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so they decided to peek and see which
+
+ align:start position:0%
+so they decided to peek and see which
+ 
+
+ align:start position:0%
+so they decided to peek and see which
+slit
+
+ align:start position:0%
+slit
+ 
+
+ align:start position:0%
+slit
+it actually goes through
+
+ align:start position:0%
+it actually goes through
+ 
+
+ align:start position:0%
+it actually goes through
+they put a measuring device by one slip
+
+ align:start position:0%
+they put a measuring device by one slip
+ 
+
+ align:start position:0%
+they put a measuring device by one slip
+to see which one it went through
+
+ align:start position:0%
+to see which one it went through
+ 
+
+ align:start position:0%
+to see which one it went through
+and let it fly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the quantum world is far more
+
+ align:start position:0%
+but the quantum world is far more
+ 
+
+ align:start position:0%
+but the quantum world is far more
+mysterious than they could have imagined
+
+ align:start position:0%
+mysterious than they could have imagined
+ 
+
+ align:start position:0%
+mysterious than they could have imagined
+when they observed the electron went
+
+ align:start position:0%
+when they observed the electron went
+ 
+
+ align:start position:0%
+when they observed the electron went
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+to behaving like a little marble it
+
+ align:start position:0%
+to behaving like a little marble it
+ 
+
+ align:start position:0%
+to behaving like a little marble it
+produced a pattern of two
+
+ align:start position:0%
+produced a pattern of two
+ 
+
+ align:start position:0%
+produced a pattern of two
+bands not an interference pattern of
+
+ align:start position:0%
+bands not an interference pattern of
+ 
+
+ align:start position:0%
+bands not an interference pattern of
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+the very act of measuring
+
+ align:start position:0%
+the very act of measuring
+ 
+
+ align:start position:0%
+the very act of measuring
+or observing which slit it went through
+
+ align:start position:0%
+or observing which slit it went through
+ 
+
+ align:start position:0%
+or observing which slit it went through
+meant it only went through one not both
+
+ align:start position:0%
+meant it only went through one not both
+ 
+
+ align:start position:0%
+meant it only went through one not both
+the electron decided to act
+
+ align:start position:0%
+the electron decided to act
+ 
+
+ align:start position:0%
+the electron decided to act
+differently though it was aware
+
+ align:start position:0%
+differently though it was aware
+ 
+
+ align:start position:0%
+differently though it was aware
+it was being watched and it was here
+
+ align:start position:0%
+it was being watched and it was here
+ 
+
+ align:start position:0%
+it was being watched and it was here
+that physicists stepped forever into the
+
+ align:start position:0%
+that physicists stepped forever into the
+ 
+
+ align:start position:0%
+that physicists stepped forever into the
+strange
+
+ align:start position:0%
+strange
+ 
+
+ align:start position:0%
+strange
+never world of quantum events
+
+ align:start position:0%
+never world of quantum events
+ 
+
+ align:start position:0%
+never world of quantum events
+what is matter marbles or waves
+
+ align:start position:0%
+what is matter marbles or waves
+ 
+
+ align:start position:0%
+what is matter marbles or waves
+and waves of what and what does an
+
+ align:start position:0%
+and waves of what and what does an
+ 
+
+ align:start position:0%
+and waves of what and what does an
+observer have to do with
+
+ align:start position:0%
+observer have to do with
+ 
+
+ align:start position:0%
+observer have to do with
+any of this the observer
+
+ align:start position:0%
+any of this the observer
+ 
+
+ align:start position:0%
+any of this the observer
+collapsed the wave function
+
+ align:start position:0%
+collapsed the wave function
+ 
+
+ align:start position:0%
+collapsed the wave function
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+simply by observing
+
+ align:start position:0%
+simply by observing
+ 
+
+ align:start position:0%
+simply by observing
+you you can see why i show this uh we do
+
+ align:start position:0%
+you you can see why i show this uh we do
+ 
+
+ align:start position:0%
+you you can see why i show this uh we do
+movie night at home a lot
+
+ align:start position:0%
+movie night at home a lot
+ 
+
+ align:start position:0%
+movie night at home a lot
+it's friday night guys like seriously um
+
+ align:start position:0%
+it's friday night guys like seriously um
+ 
+
+ align:start position:0%
+it's friday night guys like seriously um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+that uh you know you might have like a
+
+ align:start position:0%
+that uh you know you might have like a
+ 
+
+ align:start position:0%
+that uh you know you might have like a
+little free time
+
+ align:start position:0%
+little free time
+ 
+
+ align:start position:0%
+little free time
+you get together with some friends
+
+ align:start position:0%
+you get together with some friends
+ 
+
+ align:start position:0%
+you get together with some friends
+there's no better way but look
+
+ align:start position:0%
+there's no better way but look
+ 
+
+ align:start position:0%
+there's no better way but look
+let me you know this is why i hope
+
+ align:start position:0%
+let me you know this is why i hope
+ 
+
+ align:start position:0%
+let me you know this is why i hope
+that's as mind-blowing to you as it is
+
+ align:start position:0%
+that's as mind-blowing to you as it is
+ 
+
+ align:start position:0%
+that's as mind-blowing to you as it is
+to me it was mind-blowing to them
+
+ align:start position:0%
+to me it was mind-blowing to them
+ 
+
+ align:start position:0%
+to me it was mind-blowing to them
+at the time um this led border famously
+
+ align:start position:0%
+at the time um this led border famously
+ 
+
+ align:start position:0%
+at the time um this led border famously
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+anyone who is not shocked by quantum
+
+ align:start position:0%
+anyone who is not shocked by quantum
+ 
+
+ align:start position:0%
+anyone who is not shocked by quantum
+theory has not understood it
+
+ align:start position:0%
+theory has not understood it
+ 
+
+ align:start position:0%
+theory has not understood it
+and and here's the thing there's uh
+
+ align:start position:0%
+and and here's the thing there's uh
+ 
+
+ align:start position:0%
+and and here's the thing there's uh
+you know there are some things in life
+
+ align:start position:0%
+you know there are some things in life
+ 
+
+ align:start position:0%
+you know there are some things in life
+where you can ask questions and and you
+
+ align:start position:0%
+where you can ask questions and and you
+ 
+
+ align:start position:0%
+where you can ask questions and and you
+can understand them you can answer them
+
+ align:start position:0%
+can understand them you can answer them
+ 
+
+ align:start position:0%
+can understand them you can answer them
+i can ask the question why do or
+
+ align:start position:0%
+i can ask the question why do or
+ 
+
+ align:start position:0%
+i can ask the question why do or
+somebody might say
+
+ align:start position:0%
+somebody might say
+ 
+
+ align:start position:0%
+somebody might say
+why do i wear a a t-shirt under a sport
+
+ align:start position:0%
+why do i wear a a t-shirt under a sport
+ 
+
+ align:start position:0%
+why do i wear a a t-shirt under a sport
+coat
+
+ align:start position:0%
+coat
+ 
+
+ align:start position:0%
+coat
+that's weird stylistically
+
+ align:start position:0%
+that's weird stylistically
+ 
+
+ align:start position:0%
+that's weird stylistically
+i mean stylistically that's and i say
+
+ align:start position:0%
+i mean stylistically that's and i say
+ 
+
+ align:start position:0%
+i mean stylistically that's and i say
+well okay here's the answer
+
+ align:start position:0%
+well okay here's the answer
+ 
+
+ align:start position:0%
+well okay here's the answer
+because i put you know comfort over
+
+ align:start position:0%
+because i put you know comfort over
+ 
+
+ align:start position:0%
+because i put you know comfort over
+stylistic norms whatever
+
+ align:start position:0%
+stylistic norms whatever
+ 
+
+ align:start position:0%
+stylistic norms whatever
+that's an answer i could ask a harder
+
+ align:start position:0%
+that's an answer i could ask a harder
+ 
+
+ align:start position:0%
+that's an answer i could ask a harder
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+i could ask a harder question why did
+
+ align:start position:0%
+i could ask a harder question why did
+ 
+
+ align:start position:0%
+i could ask a harder question why did
+justin and celina break up
+
+ align:start position:0%
+justin and celina break up
+ 
+
+ align:start position:0%
+justin and celina break up
+because jelena was totally hashtag
+
+ align:start position:0%
+because jelena was totally hashtag
+ 
+
+ align:start position:0%
+because jelena was totally hashtag
+couple goals
+
+ align:start position:0%
+couple goals
+ 
+
+ align:start position:0%
+couple goals
+just saying okay anyway now i'm just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why oh but still that's a harder
+
+ align:start position:0%
+why oh but still that's a harder
+ 
+
+ align:start position:0%
+why oh but still that's a harder
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+why because they were so good but
+
+ align:start position:0%
+why because they were so good but
+ 
+
+ align:start position:0%
+why because they were so good but
+there's probably an answer to that too
+
+ align:start position:0%
+there's probably an answer to that too
+ 
+
+ align:start position:0%
+there's probably an answer to that too
+that's a harder question
+
+ align:start position:0%
+that's a harder question
+ 
+
+ align:start position:0%
+that's a harder question
+this was mind-blowing how can something
+
+ align:start position:0%
+this was mind-blowing how can something
+ 
+
+ align:start position:0%
+this was mind-blowing how can something
+be both how can something that they know
+
+ align:start position:0%
+be both how can something that they know
+ 
+
+ align:start position:0%
+be both how can something that they know
+is a part of how can everything
+
+ align:start position:0%
+is a part of how can everything
+ 
+
+ align:start position:0%
+is a part of how can everything
+be both this was really
+
+ align:start position:0%
+be both this was really
+ 
+
+ align:start position:0%
+be both this was really
+difficult to answer and in fact
+
+ align:start position:0%
+difficult to answer and in fact
+ 
+
+ align:start position:0%
+difficult to answer and in fact
+the real answer came with a mathematical
+
+ align:start position:0%
+the real answer came with a mathematical
+ 
+
+ align:start position:0%
+the real answer came with a mathematical
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+which we'll learn next but not quite
+
+ align:start position:0%
+which we'll learn next but not quite
+ 
+
+ align:start position:0%
+which we'll learn next but not quite
+understanding
+
+ align:start position:0%
+understanding
+ 
+
+ align:start position:0%
+understanding
+we still don't really understand quantum
+
+ align:start position:0%
+we still don't really understand quantum
+ 
+
+ align:start position:0%
+we still don't really understand quantum
+mechanics even after 100 years
+
+ align:start position:0%
+mechanics even after 100 years
+ 
+
+ align:start position:0%
+mechanics even after 100 years
+we don't um and
+
+ align:start position:0%
+we don't um and
+ 
+
+ align:start position:0%
+we don't um and
+and so so this is just i think a
+
+ align:start position:0%
+and so so this is just i think a
+ 
+
+ align:start position:0%
+and so so this is just i think a
+beautiful part of
+
+ align:start position:0%
+beautiful part of
+ 
+
+ align:start position:0%
+beautiful part of
+our story of our detective story
+
+ align:start position:0%
+our story of our detective story
+ 
+
+ align:start position:0%
+our story of our detective story
+and just to show like people are still
+
+ align:start position:0%
+and just to show like people are still
+ 
+
+ align:start position:0%
+and just to show like people are still
+working on this right
+
+ align:start position:0%
+working on this right
+ 
+
+ align:start position:0%
+working on this right
+how much quantum can we see how much
+
+ align:start position:0%
+how much quantum can we see how much
+ 
+
+ align:start position:0%
+how much quantum can we see how much
+quantum can we see
+
+ align:start position:0%
+quantum can we see
+ 
+
+ align:start position:0%
+quantum can we see
+well look here's some here's somebody
+
+ align:start position:0%
+well look here's some here's somebody
+ 
+
+ align:start position:0%
+well look here's some here's somebody
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+about 15 years ago and it's published in
+
+ align:start position:0%
+about 15 years ago and it's published in
+ 
+
+ align:start position:0%
+about 15 years ago and it's published in
+this paper i'm a little more almost 20
+
+ align:start position:0%
+this paper i'm a little more almost 20
+ 
+
+ align:start position:0%
+this paper i'm a little more almost 20
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+they actually took forget about
+
+ align:start position:0%
+they actually took forget about
+ 
+
+ align:start position:0%
+they actually took forget about
+electrons those are teeny tiny things
+
+ align:start position:0%
+electrons those are teeny tiny things
+ 
+
+ align:start position:0%
+electrons those are teeny tiny things
+this is a whole group of of 60 carbon
+
+ align:start position:0%
+this is a whole group of of 60 carbon
+ 
+
+ align:start position:0%
+this is a whole group of of 60 carbon
+atoms that's called a fullerene
+
+ align:start position:0%
+atoms that's called a fullerene
+ 
+
+ align:start position:0%
+atoms that's called a fullerene
+and they shot this through they did the
+
+ align:start position:0%
+and they shot this through they did the
+ 
+
+ align:start position:0%
+and they shot this through they did the
+double slit experiment with this
+
+ align:start position:0%
+double slit experiment with this
+ 
+
+ align:start position:0%
+double slit experiment with this
+and they showed that with the grating
+
+ align:start position:0%
+and they showed that with the grating
+ 
+
+ align:start position:0%
+and they showed that with the grating
+right without you get the single p
+
+ align:start position:0%
+right without you get the single p
+ 
+
+ align:start position:0%
+right without you get the single p
+just like we saw and with you get
+
+ align:start position:0%
+just like we saw and with you get
+ 
+
+ align:start position:0%
+just like we saw and with you get
+diffract you get interference
+
+ align:start position:0%
+diffract you get interference
+ 
+
+ align:start position:0%
+diffract you get interference
+you get interference so they were able
+
+ align:start position:0%
+you get interference so they were able
+ 
+
+ align:start position:0%
+you get interference so they were able
+to show all the way up to
+
+ align:start position:0%
+to show all the way up to
+ 
+
+ align:start position:0%
+to show all the way up to
+a large molecule 60 carbon atoms
+
+ align:start position:0%
+a large molecule 60 carbon atoms
+ 
+
+ align:start position:0%
+a large molecule 60 carbon atoms
+that these things are still they have
+
+ align:start position:0%
+that these things are still they have
+ 
+
+ align:start position:0%
+that these things are still they have
+wavelength they have these
+
+ align:start position:0%
+wavelength they have these
+ 
+
+ align:start position:0%
+wavelength they have these
+these incredibly strange properties that
+
+ align:start position:0%
+these incredibly strange properties that
+ 
+
+ align:start position:0%
+these incredibly strange properties that
+you just saw
+
+ align:start position:0%
+you just saw
+ 
+
+ align:start position:0%
+you just saw
+in the double slit experiment all
+
+ align:start position:0%
+in the double slit experiment all
+ 
+
+ align:start position:0%
+in the double slit experiment all
+everything has
+
+ align:start position:0%
+everything has
+ 
+
+ align:start position:0%
+everything has
+this duality this this duality between
+
+ align:start position:0%
+this duality this this duality between
+ 
+
+ align:start position:0%
+this duality this this duality between
+uh waves and particles
+
+ align:start position:0%
+uh waves and particles
+ 
+
+ align:start position:0%
+uh waves and particles
+now um okay
+
+ align:start position:0%
+now um okay
+ 
+
+ align:start position:0%
+now um okay
+we said we needed a new model right bohr
+
+ align:start position:0%
+we said we needed a new model right bohr
+ 
+
+ align:start position:0%
+we said we needed a new model right bohr
+can only do one electron
+
+ align:start position:0%
+can only do one electron
+ 
+
+ align:start position:0%
+can only do one electron
+and meanwhile there's all this stuff
+
+ align:start position:0%
+and meanwhile there's all this stuff
+ 
+
+ align:start position:0%
+and meanwhile there's all this stuff
+going on at the time
+
+ align:start position:0%
+going on at the time
+ 
+
+ align:start position:0%
+going on at the time
+you know showing that that there you
+
+ align:start position:0%
+you know showing that that there you
+ 
+
+ align:start position:0%
+you know showing that that there you
+need a new theory
+
+ align:start position:0%
+need a new theory
+ 
+
+ align:start position:0%
+need a new theory
+how do we explain waves and to kind of
+
+ align:start position:0%
+how do we explain waves and to kind of
+ 
+
+ align:start position:0%
+how do we explain waves and to kind of
+put a little bit more of of the nail in
+
+ align:start position:0%
+put a little bit more of of the nail in
+ 
+
+ align:start position:0%
+put a little bit more of of the nail in
+the coffin for for bore
+
+ align:start position:0%
+the coffin for for bore
+ 
+
+ align:start position:0%
+the coffin for for bore
+you had um you had heisenberg so i'll
+
+ align:start position:0%
+you had um you had heisenberg so i'll
+ 
+
+ align:start position:0%
+you had um you had heisenberg so i'll
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+write this on the board before i go to
+
+ align:start position:0%
+write this on the board before i go to
+ 
+
+ align:start position:0%
+write this on the board before i go to
+my why this matters
+
+ align:start position:0%
+my why this matters
+ 
+
+ align:start position:0%
+my why this matters
+um and what heisenberg said
+
+ align:start position:0%
+um and what heisenberg said
+ 
+
+ align:start position:0%
+um and what heisenberg said
+is that you cannot
+
+ align:start position:0%
+is that you cannot
+ 
+
+ align:start position:0%
+is that you cannot
+measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+position and
+
+ align:start position:0%
+position and
+ 
+
+ align:start position:0%
+position and
+momentum exactly
+
+ align:start position:0%
+momentum exactly
+ 
+
+ align:start position:0%
+momentum exactly
+you can't get them both okay and that
+
+ align:start position:0%
+you can't get them both okay and that
+ 
+
+ align:start position:0%
+you can't get them both okay and that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that's called the heisenberg uncertainty
+
+ align:start position:0%
+that's called the heisenberg uncertainty
+ 
+
+ align:start position:0%
+that's called the heisenberg uncertainty
+principle but that was it because look
+
+ align:start position:0%
+principle but that was it because look
+ 
+
+ align:start position:0%
+principle but that was it because look
+you look at that so he he's saying this
+
+ align:start position:0%
+you look at that so he he's saying this
+ 
+
+ align:start position:0%
+you look at that so he he's saying this
+and said but
+
+ align:start position:0%
+and said but
+ 
+
+ align:start position:0%
+and said but
+in board you've got them both you've got
+
+ align:start position:0%
+in board you've got them both you've got
+ 
+
+ align:start position:0%
+in board you've got them both you've got
+them both exactly
+
+ align:start position:0%
+them both exactly
+ 
+
+ align:start position:0%
+them both exactly
+remember we i put energy down there but
+
+ align:start position:0%
+remember we i put energy down there but
+ 
+
+ align:start position:0%
+remember we i put energy down there but
+we also put r
+
+ align:start position:0%
+we also put r
+ 
+
+ align:start position:0%
+we also put r
+on wednesday exactly because then type
+
+ align:start position:0%
+on wednesday exactly because then type
+ 
+
+ align:start position:0%
+on wednesday exactly because then type
+you can't get them both
+
+ align:start position:0%
+you can't get them both
+ 
+
+ align:start position:0%
+you can't get them both
+and if you can't get them both that's
+
+ align:start position:0%
+and if you can't get them both that's
+ 
+
+ align:start position:0%
+and if you can't get them both that's
+another problem with bohr because bohr
+
+ align:start position:0%
+another problem with bohr because bohr
+ 
+
+ align:start position:0%
+another problem with bohr because bohr
+says you can get them exactly right
+
+ align:start position:0%
+says you can get them exactly right
+ 
+
+ align:start position:0%
+says you can get them exactly right
+so we had these pointers double sid
+
+ align:start position:0%
+so we had these pointers double sid
+ 
+
+ align:start position:0%
+so we had these pointers double sid
+experiment heisenberg's theories
+
+ align:start position:0%
+experiment heisenberg's theories
+ 
+
+ align:start position:0%
+experiment heisenberg's theories
+right saying we need something more we
+
+ align:start position:0%
+right saying we need something more we
+ 
+
+ align:start position:0%
+right saying we need something more we
+need something more
+
+ align:start position:0%
+need something more
+ 
+
+ align:start position:0%
+need something more
+and i'll i'll get to that um i want to
+
+ align:start position:0%
+and i'll i'll get to that um i want to
+ 
+
+ align:start position:0%
+and i'll i'll get to that um i want to
+do my why this matters and then i'll get
+
+ align:start position:0%
+do my why this matters and then i'll get
+ 
+
+ align:start position:0%
+do my why this matters and then i'll get
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the more that came which will then
+
+ align:start position:0%
+the more that came which will then
+ 
+
+ align:start position:0%
+the more that came which will then
+expand on on monday
+
+ align:start position:0%
+expand on on monday
+ 
+
+ align:start position:0%
+expand on on monday
+um before i do that let's do wise
+
+ align:start position:0%
+um before i do that let's do wise
+ 
+
+ align:start position:0%
+um before i do that let's do wise
+matters so why
+
+ align:start position:0%
+matters so why
+ 
+
+ align:start position:0%
+matters so why
+why are why is the fact that an electron
+
+ align:start position:0%
+why are why is the fact that an electron
+ 
+
+ align:start position:0%
+why are why is the fact that an electron
+is a wave why is that so
+
+ align:start position:0%
+is a wave why is that so
+ 
+
+ align:start position:0%
+is a wave why is that so
+important first of all because it sets
+
+ align:start position:0%
+important first of all because it sets
+ 
+
+ align:start position:0%
+important first of all because it sets
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+you know this this detective story of
+
+ align:start position:0%
+you know this this detective story of
+ 
+
+ align:start position:0%
+you know this this detective story of
+the electron
+
+ align:start position:0%
+the electron
+ 
+
+ align:start position:0%
+the electron
+set up this new theory that's coming
+
+ align:start position:0%
+set up this new theory that's coming
+ 
+
+ align:start position:0%
+set up this new theory that's coming
+quantum mechanics right
+
+ align:start position:0%
+quantum mechanics right
+ 
+
+ align:start position:0%
+quantum mechanics right
+um but also it immediately just like
+
+ align:start position:0%
+um but also it immediately just like
+ 
+
+ align:start position:0%
+um but also it immediately just like
+just like we started painting with them
+
+ align:start position:0%
+just like we started painting with them
+ 
+
+ align:start position:0%
+just like we started painting with them
+right remember that was one of my widest
+
+ align:start position:0%
+right remember that was one of my widest
+ 
+
+ align:start position:0%
+right remember that was one of my widest
+matters we also realized that we could
+
+ align:start position:0%
+matters we also realized that we could
+ 
+
+ align:start position:0%
+matters we also realized that we could
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+with them we could see with electrons
+
+ align:start position:0%
+with them we could see with electrons
+ 
+
+ align:start position:0%
+with them we could see with electrons
+because you know if electrons are waves
+
+ align:start position:0%
+because you know if electrons are waves
+ 
+
+ align:start position:0%
+because you know if electrons are waves
+then i can shine them just like i shine
+
+ align:start position:0%
+then i can shine them just like i shine
+ 
+
+ align:start position:0%
+then i can shine them just like i shine
+light and see what it shows me
+
+ align:start position:0%
+light and see what it shows me
+ 
+
+ align:start position:0%
+light and see what it shows me
+right it can illuminate matter
+
+ align:start position:0%
+right it can illuminate matter
+ 
+
+ align:start position:0%
+right it can illuminate matter
+so you know if you look at the frequency
+
+ align:start position:0%
+so you know if you look at the frequency
+ 
+
+ align:start position:0%
+so you know if you look at the frequency
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+of light right this is this is a
+
+ align:start position:0%
+of light right this is this is a
+ 
+
+ align:start position:0%
+of light right this is this is a
+electromagnetic spectrum
+
+ align:start position:0%
+electromagnetic spectrum
+ 
+
+ align:start position:0%
+electromagnetic spectrum
+radio right microwave infrared visible
+
+ align:start position:0%
+radio right microwave infrared visible
+ 
+
+ align:start position:0%
+radio right microwave infrared visible
+uv now here's the thing
+
+ align:start position:0%
+uv now here's the thing
+ 
+
+ align:start position:0%
+uv now here's the thing
+if you want to see something
+
+ align:start position:0%
+if you want to see something
+ 
+
+ align:start position:0%
+if you want to see something
+some feature size you're limited
+
+ align:start position:0%
+some feature size you're limited
+ 
+
+ align:start position:0%
+some feature size you're limited
+by the wavelength of the light it can't
+
+ align:start position:0%
+by the wavelength of the light it can't
+ 
+
+ align:start position:0%
+by the wavelength of the light it can't
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+bigger than the features you're looking
+
+ align:start position:0%
+bigger than the features you're looking
+ 
+
+ align:start position:0%
+bigger than the features you're looking
+at roughly ish
+
+ align:start position:0%
+at roughly ish
+ 
+
+ align:start position:0%
+at roughly ish
+okay that's what you're so if you're
+
+ align:start position:0%
+okay that's what you're so if you're
+ 
+
+ align:start position:0%
+okay that's what you're so if you're
+trying to see something tiny but the
+
+ align:start position:0%
+trying to see something tiny but the
+ 
+
+ align:start position:0%
+trying to see something tiny but the
+wavelength of light is really big
+
+ align:start position:0%
+wavelength of light is really big
+ 
+
+ align:start position:0%
+wavelength of light is really big
+you won't see it so we need if we want
+
+ align:start position:0%
+you won't see it so we need if we want
+ 
+
+ align:start position:0%
+you won't see it so we need if we want
+let's say we want to see atoms
+
+ align:start position:0%
+let's say we want to see atoms
+ 
+
+ align:start position:0%
+let's say we want to see atoms
+let's say we want to see atoms or or or
+
+ align:start position:0%
+let's say we want to see atoms or or or
+ 
+
+ align:start position:0%
+let's say we want to see atoms or or or
+even more nuclei
+
+ align:start position:0%
+even more nuclei
+ 
+
+ align:start position:0%
+even more nuclei
+look at how tight those are 10 to the
+
+ align:start position:0%
+look at how tight those are 10 to the
+ 
+
+ align:start position:0%
+look at how tight those are 10 to the
+minus 10 centimeters 12 meters
+
+ align:start position:0%
+minus 10 centimeters 12 meters
+ 
+
+ align:start position:0%
+minus 10 centimeters 12 meters
+those are x-rays or gamma rays but the
+
+ align:start position:0%
+those are x-rays or gamma rays but the
+ 
+
+ align:start position:0%
+those are x-rays or gamma rays but the
+problem is if we shine
+
+ align:start position:0%
+problem is if we shine
+ 
+
+ align:start position:0%
+problem is if we shine
+x-rays on things and we will do that
+
+ align:start position:0%
+x-rays on things and we will do that
+ 
+
+ align:start position:0%
+x-rays on things and we will do that
+when we look at crystals
+
+ align:start position:0%
+when we look at crystals
+ 
+
+ align:start position:0%
+when we look at crystals
+but if we shine x-rays it's very hard to
+
+ align:start position:0%
+but if we shine x-rays it's very hard to
+ 
+
+ align:start position:0%
+but if we shine x-rays it's very hard to
+then collect them and make a
+
+ align:start position:0%
+then collect them and make a
+ 
+
+ align:start position:0%
+then collect them and make a
+photographic image
+
+ align:start position:0%
+photographic image
+ 
+
+ align:start position:0%
+photographic image
+okay right i mean at least one that gets
+
+ align:start position:0%
+okay right i mean at least one that gets
+ 
+
+ align:start position:0%
+okay right i mean at least one that gets
+you that resolution
+
+ align:start position:0%
+you that resolution
+ 
+
+ align:start position:0%
+you that resolution
+and gamma rays are even harder to catch
+
+ align:start position:0%
+and gamma rays are even harder to catch
+ 
+
+ align:start position:0%
+and gamma rays are even harder to catch
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+oh but see here's the thing electrons
+
+ align:start position:0%
+oh but see here's the thing electrons
+ 
+
+ align:start position:0%
+oh but see here's the thing electrons
+electrons give you exactly what you need
+
+ align:start position:0%
+electrons give you exactly what you need
+ 
+
+ align:start position:0%
+electrons give you exactly what you need
+because you know if we do this math
+
+ align:start position:0%
+because you know if we do this math
+ 
+
+ align:start position:0%
+because you know if we do this math
+for an electron let's bring this one
+
+ align:start position:0%
+for an electron let's bring this one
+ 
+
+ align:start position:0%
+for an electron let's bring this one
+back down
+
+ align:start position:0%
+back down
+ 
+
+ align:start position:0%
+back down
+if we do this math for an electron well
+
+ align:start position:0%
+if we do this math for an electron well
+ 
+
+ align:start position:0%
+if we do this math for an electron well
+i'm going to use
+
+ align:start position:0%
+i'm going to use
+ 
+
+ align:start position:0%
+i'm going to use
+ah i thought i had the middle one so if
+
+ align:start position:0%
+ah i thought i had the middle one so if
+ 
+
+ align:start position:0%
+ah i thought i had the middle one so if
+i have an electron let's suppose i have
+
+ align:start position:0%
+i have an electron let's suppose i have
+ 
+
+ align:start position:0%
+i have an electron let's suppose i have
+an electron
+
+ align:start position:0%
+an electron
+ 
+
+ align:start position:0%
+an electron
+that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron i'm going to say i accelerate
+
+ align:start position:0%
+electron i'm going to say i accelerate
+ 
+
+ align:start position:0%
+electron i'm going to say i accelerate
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over 100 volts
+
+ align:start position:0%
+over 100 volts
+ 
+
+ align:start position:0%
+over 100 volts
+i'm going to take an electron i'm going
+
+ align:start position:0%
+i'm going to take an electron i'm going
+ 
+
+ align:start position:0%
+i'm going to take an electron i'm going
+to put it over 100 volts i'm going to
+
+ align:start position:0%
+to put it over 100 volts i'm going to
+ 
+
+ align:start position:0%
+to put it over 100 volts i'm going to
+give it some kinetic energy
+
+ align:start position:0%
+give it some kinetic energy
+ 
+
+ align:start position:0%
+give it some kinetic energy
+right so its kinetic energy
+
+ align:start position:0%
+right so its kinetic energy
+ 
+
+ align:start position:0%
+right so its kinetic energy
+is then going to equal 100 ev right
+
+ align:start position:0%
+is then going to equal 100 ev right
+ 
+
+ align:start position:0%
+is then going to equal 100 ev right
+okay so now i've got an electron moving
+
+ align:start position:0%
+okay so now i've got an electron moving
+ 
+
+ align:start position:0%
+okay so now i've got an electron moving
+with a kinetic energy that's 100 ev now
+
+ align:start position:0%
+with a kinetic energy that's 100 ev now
+ 
+
+ align:start position:0%
+with a kinetic energy that's 100 ev now
+you can convert this to joules and you
+
+ align:start position:0%
+you can convert this to joules and you
+ 
+
+ align:start position:0%
+you can convert this to joules and you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+set this equal to one-half mv squared
+
+ align:start position:0%
+set this equal to one-half mv squared
+ 
+
+ align:start position:0%
+set this equal to one-half mv squared
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+mass of the electron times its velocity
+
+ align:start position:0%
+mass of the electron times its velocity
+ 
+
+ align:start position:0%
+mass of the electron times its velocity
+squared and
+
+ align:start position:0%
+squared and
+ 
+
+ align:start position:0%
+squared and
+then once you have the velocity so you
+
+ align:start position:0%
+then once you have the velocity so you
+ 
+
+ align:start position:0%
+then once you have the velocity so you
+get the v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then once you have that you get the
+
+ align:start position:0%
+and then once you have that you get the
+ 
+
+ align:start position:0%
+and then once you have that you get the
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+the p right and then once you have that
+
+ align:start position:0%
+the p right and then once you have that
+ 
+
+ align:start position:0%
+the p right and then once you have that
+you get the wavelength right so i can go
+
+ align:start position:0%
+you get the wavelength right so i can go
+ 
+
+ align:start position:0%
+you get the wavelength right so i can go
+now from like
+
+ align:start position:0%
+now from like
+ 
+
+ align:start position:0%
+now from like
+something that's easy to do 100 volts is
+
+ align:start position:0%
+something that's easy to do 100 volts is
+ 
+
+ align:start position:0%
+something that's easy to do 100 volts is
+a lot but
+
+ align:start position:0%
+a lot but
+ 
+
+ align:start position:0%
+a lot but
+in a lab safe not in your dorm you could
+
+ align:start position:0%
+in a lab safe not in your dorm you could
+ 
+
+ align:start position:0%
+in a lab safe not in your dorm you could
+apply 100 volts
+
+ align:start position:0%
+apply 100 volts
+ 
+
+ align:start position:0%
+apply 100 volts
+to an electron get it going at this
+
+ align:start position:0%
+to an electron get it going at this
+ 
+
+ align:start position:0%
+to an electron get it going at this
+speed
+
+ align:start position:0%
+speed
+ 
+
+ align:start position:0%
+speed
+and once you know the speed you know the
+
+ align:start position:0%
+and once you know the speed you know the
+ 
+
+ align:start position:0%
+and once you know the speed you know the
+momentum and if you know mv
+
+ align:start position:0%
+momentum and if you know mv
+ 
+
+ align:start position:0%
+momentum and if you know mv
+then you know it's wavelength and that
+
+ align:start position:0%
+then you know it's wavelength and that
+ 
+
+ align:start position:0%
+then you know it's wavelength and that
+in that case
+
+ align:start position:0%
+in that case
+ 
+
+ align:start position:0%
+in that case
+from this relationship you would get
+
+ align:start position:0%
+from this relationship you would get
+ 
+
+ align:start position:0%
+from this relationship you would get
+that it's about 0.12
+
+ align:start position:0%
+that it's about 0.12
+ 
+
+ align:start position:0%
+that it's about 0.12
+nanometers but look at this the
+
+ align:start position:0%
+nanometers but look at this the
+ 
+
+ align:start position:0%
+nanometers but look at this the
+wavelength of a
+
+ align:start position:0%
+wavelength of a
+ 
+
+ align:start position:0%
+wavelength of a
+simply accelerated electron is right
+
+ align:start position:0%
+simply accelerated electron is right
+ 
+
+ align:start position:0%
+simply accelerated electron is right
+where i need it
+
+ align:start position:0%
+where i need it
+ 
+
+ align:start position:0%
+where i need it
+it's right where i need it it's an
+
+ align:start position:0%
+it's right where i need it it's an
+ 
+
+ align:start position:0%
+it's right where i need it it's an
+angstrom
+
+ align:start position:0%
+angstrom
+ 
+
+ align:start position:0%
+angstrom
+right so now i think if i take advantage
+
+ align:start position:0%
+right so now i think if i take advantage
+ 
+
+ align:start position:0%
+right so now i think if i take advantage
+of the wavelengths of the wave nature of
+
+ align:start position:0%
+of the wavelengths of the wave nature of
+ 
+
+ align:start position:0%
+of the wavelengths of the wave nature of
+electrons and i shine them
+
+ align:start position:0%
+electrons and i shine them
+ 
+
+ align:start position:0%
+electrons and i shine them
+on materials then i can see materials
+
+ align:start position:0%
+on materials then i can see materials
+ 
+
+ align:start position:0%
+on materials then i can see materials
+that way and i can see them at that
+
+ align:start position:0%
+that way and i can see them at that
+ 
+
+ align:start position:0%
+that way and i can see them at that
+scale and we do that all the time
+
+ align:start position:0%
+scale and we do that all the time
+ 
+
+ align:start position:0%
+scale and we do that all the time
+all the time in in many many different
+
+ align:start position:0%
+all the time in in many many different
+ 
+
+ align:start position:0%
+all the time in in many many different
+areas of technology
+
+ align:start position:0%
+areas of technology
+ 
+
+ align:start position:0%
+areas of technology
+and of research today we use electrons
+
+ align:start position:0%
+and of research today we use electrons
+ 
+
+ align:start position:0%
+and of research today we use electrons
+to image in fact the best images you can
+
+ align:start position:0%
+to image in fact the best images you can
+ 
+
+ align:start position:0%
+to image in fact the best images you can
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+are made with electrons right here's an
+
+ align:start position:0%
+are made with electrons right here's an
+ 
+
+ align:start position:0%
+are made with electrons right here's an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+of using scanning what's called a
+
+ align:start position:0%
+of using scanning what's called a
+ 
+
+ align:start position:0%
+of using scanning what's called a
+scanning electron microscope
+
+ align:start position:0%
+scanning electron microscope
+ 
+
+ align:start position:0%
+scanning electron microscope
+right so you see a butterfly but you
+
+ align:start position:0%
+right so you see a butterfly but you
+ 
+
+ align:start position:0%
+right so you see a butterfly but you
+want to really see a butterfly
+
+ align:start position:0%
+want to really see a butterfly
+ 
+
+ align:start position:0%
+want to really see a butterfly
+or we can go even further and instead of
+
+ align:start position:0%
+or we can go even further and instead of
+ 
+
+ align:start position:0%
+or we can go even further and instead of
+just drawing pictures
+
+ align:start position:0%
+just drawing pictures
+ 
+
+ align:start position:0%
+just drawing pictures
+of this these beautiful materials made
+
+ align:start position:0%
+of this these beautiful materials made
+ 
+
+ align:start position:0%
+of this these beautiful materials made
+of carbon those are called nanotubes
+
+ align:start position:0%
+of carbon those are called nanotubes
+ 
+
+ align:start position:0%
+of carbon those are called nanotubes
+these are called this is called graphene
+
+ align:start position:0%
+these are called this is called graphene
+ 
+
+ align:start position:0%
+these are called this is called graphene
+because in tight
+
+ align:start position:0%
+because in tight
+ 
+
+ align:start position:0%
+because in tight
+it's a single sheet of carbon atoms one
+
+ align:start position:0%
+it's a single sheet of carbon atoms one
+ 
+
+ align:start position:0%
+it's a single sheet of carbon atoms one
+atom thick material notice with these
+
+ align:start position:0%
+atom thick material notice with these
+ 
+
+ align:start position:0%
+atom thick material notice with these
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+every single atom is a surface atom
+
+ align:start position:0%
+every single atom is a surface atom
+ 
+
+ align:start position:0%
+every single atom is a surface atom
+that's pretty cool
+
+ align:start position:0%
+that's pretty cool
+ 
+
+ align:start position:0%
+that's pretty cool
+they also have lots of other cool
+
+ align:start position:0%
+they also have lots of other cool
+ 
+
+ align:start position:0%
+they also have lots of other cool
+properties and i'll give you examples
+
+ align:start position:0%
+properties and i'll give you examples
+ 
+
+ align:start position:0%
+properties and i'll give you examples
+throughout you know in other other
+
+ align:start position:0%
+throughout you know in other other
+ 
+
+ align:start position:0%
+throughout you know in other other
+lectures of how these kinds of materials
+
+ align:start position:0%
+lectures of how these kinds of materials
+ 
+
+ align:start position:0%
+lectures of how these kinds of materials
+can be used
+
+ align:start position:0%
+can be used
+ 
+
+ align:start position:0%
+can be used
+but for now i'm talking about seeing
+
+ align:start position:0%
+but for now i'm talking about seeing
+ 
+
+ align:start position:0%
+but for now i'm talking about seeing
+them and this is what happens
+
+ align:start position:0%
+them and this is what happens
+ 
+
+ align:start position:0%
+them and this is what happens
+when you actually look at them with an
+
+ align:start position:0%
+when you actually look at them with an
+ 
+
+ align:start position:0%
+when you actually look at them with an
+electron that's a nanotube and here
+
+ align:start position:0%
+electron that's a nanotube and here
+ 
+
+ align:start position:0%
+electron that's a nanotube and here
+is a picture of graphene the only reason
+
+ align:start position:0%
+is a picture of graphene the only reason
+ 
+
+ align:start position:0%
+is a picture of graphene the only reason
+we can see graphene
+
+ align:start position:0%
+we can see graphene
+ 
+
+ align:start position:0%
+we can see graphene
+is because we have electrons and we take
+
+ align:start position:0%
+is because we have electrons and we take
+ 
+
+ align:start position:0%
+is because we have electrons and we take
+advantage of the wave nature
+
+ align:start position:0%
+advantage of the wave nature
+ 
+
+ align:start position:0%
+advantage of the wave nature
+of those electrons we say well okay but
+
+ align:start position:0%
+of those electrons we say well okay but
+ 
+
+ align:start position:0%
+of those electrons we say well okay but
+why does that matter
+
+ align:start position:0%
+why does that matter
+ 
+
+ align:start position:0%
+why does that matter
+well that matters tremendously because
+
+ align:start position:0%
+well that matters tremendously because
+ 
+
+ align:start position:0%
+well that matters tremendously because
+one of the first experiments
+
+ align:start position:0%
+one of the first experiments
+ 
+
+ align:start position:0%
+one of the first experiments
+that really did what feynman what
+
+ align:start position:0%
+that really did what feynman what
+ 
+
+ align:start position:0%
+that really did what feynman what
+richard feynman wanted
+
+ align:start position:0%
+richard feynman wanted
+ 
+
+ align:start position:0%
+richard feynman wanted
+richard feynman predicted the the field
+
+ align:start position:0%
+richard feynman predicted the the field
+ 
+
+ align:start position:0%
+richard feynman predicted the the field
+of nanotechnology
+
+ align:start position:0%
+of nanotechnology
+ 
+
+ align:start position:0%
+of nanotechnology
+50 years ago he gave a famous speech at
+
+ align:start position:0%
+50 years ago he gave a famous speech at
+ 
+
+ align:start position:0%
+50 years ago he gave a famous speech at
+caltech it's called there's plenty of
+
+ align:start position:0%
+caltech it's called there's plenty of
+ 
+
+ align:start position:0%
+caltech it's called there's plenty of
+room at the bottom
+
+ align:start position:0%
+room at the bottom
+ 
+
+ align:start position:0%
+room at the bottom
+he's also an amazing teacher and he
+
+ align:start position:0%
+he's also an amazing teacher and he
+ 
+
+ align:start position:0%
+he's also an amazing teacher and he
+taught actually the double slit
+
+ align:start position:0%
+taught actually the double slit
+ 
+
+ align:start position:0%
+taught actually the double slit
+experiment i highly recommend you
+
+ align:start position:0%
+experiment i highly recommend you
+ 
+
+ align:start position:0%
+experiment i highly recommend you
+googling that lecture and he said that
+
+ align:start position:0%
+googling that lecture and he said that
+ 
+
+ align:start position:0%
+googling that lecture and he said that
+you know someday you can put the atom
+
+ align:start position:0%
+you know someday you can put the atom
+ 
+
+ align:start position:0%
+you know someday you can put the atom
+where you want
+
+ align:start position:0%
+where you want
+ 
+
+ align:start position:0%
+where you want
+right and the first time that was done
+
+ align:start position:0%
+right and the first time that was done
+ 
+
+ align:start position:0%
+right and the first time that was done
+was in 1989 by ibm
+
+ align:start position:0%
+was in 1989 by ibm
+ 
+
+ align:start position:0%
+was in 1989 by ibm
+they had 35 xenon atoms they moved them
+
+ align:start position:0%
+they had 35 xenon atoms they moved them
+ 
+
+ align:start position:0%
+they had 35 xenon atoms they moved them
+around the point is you couldn't realize
+
+ align:start position:0%
+around the point is you couldn't realize
+ 
+
+ align:start position:0%
+around the point is you couldn't realize
+nanotechnology you couldn't
+
+ align:start position:0%
+nanotechnology you couldn't
+ 
+
+ align:start position:0%
+nanotechnology you couldn't
+realize the ability to actually move
+
+ align:start position:0%
+realize the ability to actually move
+ 
+
+ align:start position:0%
+realize the ability to actually move
+atoms if you can't see them
+
+ align:start position:0%
+atoms if you can't see them
+ 
+
+ align:start position:0%
+atoms if you can't see them
+right and so this you know the ability
+
+ align:start position:0%
+right and so this you know the ability
+ 
+
+ align:start position:0%
+right and so this you know the ability
+to see
+
+ align:start position:0%
+to see
+ 
+
+ align:start position:0%
+to see
+what you were doing changed everything
+
+ align:start position:0%
+what you were doing changed everything
+ 
+
+ align:start position:0%
+what you were doing changed everything
+it changed everything and you know
+
+ align:start position:0%
+it changed everything and you know
+ 
+
+ align:start position:0%
+it changed everything and you know
+nature had been doing this and i love
+
+ align:start position:0%
+nature had been doing this and i love
+ 
+
+ align:start position:0%
+nature had been doing this and i love
+these examples so you know nature has
+
+ align:start position:0%
+these examples so you know nature has
+ 
+
+ align:start position:0%
+these examples so you know nature has
+been doing nanotech for a long time
+
+ align:start position:0%
+been doing nanotech for a long time
+ 
+
+ align:start position:0%
+been doing nanotech for a long time
+right uh so you have uh the inner ear of
+
+ align:start position:0%
+right uh so you have uh the inner ear of
+ 
+
+ align:start position:0%
+right uh so you have uh the inner ear of
+the frog it's a cantilever that uh
+
+ align:start position:0%
+the frog it's a cantilever that uh
+ 
+
+ align:start position:0%
+the frog it's a cantilever that uh
+sensitive to a few nanometers of
+
+ align:start position:0%
+sensitive to a few nanometers of
+ 
+
+ align:start position:0%
+sensitive to a few nanometers of
+movement the frog can actually hear that
+
+ align:start position:0%
+movement the frog can actually hear that
+ 
+
+ align:start position:0%
+movement the frog can actually hear that
+you've got features in the ant's eye i
+
+ align:start position:0%
+you've got features in the ant's eye i
+ 
+
+ align:start position:0%
+you've got features in the ant's eye i
+love the the silk moth
+
+ align:start position:0%
+love the the silk moth
+ 
+
+ align:start position:0%
+love the the silk moth
+the male silk moth has a single
+
+ align:start position:0%
+the male silk moth has a single
+ 
+
+ align:start position:0%
+the male silk moth has a single
+molecule detection system on board
+
+ align:start position:0%
+molecule detection system on board
+ 
+
+ align:start position:0%
+molecule detection system on board
+that can sense a single molecule
+
+ align:start position:0%
+that can sense a single molecule
+ 
+
+ align:start position:0%
+that can sense a single molecule
+pheromone it can detect a female silk
+
+ align:start position:0%
+pheromone it can detect a female silk
+ 
+
+ align:start position:0%
+pheromone it can detect a female silk
+moth two miles away
+
+ align:start position:0%
+moth two miles away
+ 
+
+ align:start position:0%
+moth two miles away
+two miles away we have nothing like that
+
+ align:start position:0%
+two miles away we have nothing like that
+ 
+
+ align:start position:0%
+two miles away we have nothing like that
+we have no technologies like that i
+
+ align:start position:0%
+we have no technologies like that i
+ 
+
+ align:start position:0%
+we have no technologies like that i
+can't even tell if someone's in the next
+
+ align:start position:0%
+can't even tell if someone's in the next
+ 
+
+ align:start position:0%
+can't even tell if someone's in the next
+room
+
+ align:start position:0%
+room
+ 
+
+ align:start position:0%
+room
+i have to look at my phone or something
+
+ align:start position:0%
+i have to look at my phone or something
+ 
+
+ align:start position:0%
+i have to look at my phone or something
+this is because of nanotechnology
+
+ align:start position:0%
+this is because of nanotechnology
+ 
+
+ align:start position:0%
+this is because of nanotechnology
+that kind of detection system right but
+
+ align:start position:0%
+that kind of detection system right but
+ 
+
+ align:start position:0%
+that kind of detection system right but
+it was the ability to see
+
+ align:start position:0%
+it was the ability to see
+ 
+
+ align:start position:0%
+it was the ability to see
+atoms and molecules with electrons that
+
+ align:start position:0%
+atoms and molecules with electrons that
+ 
+
+ align:start position:0%
+atoms and molecules with electrons that
+that kind of blew open this entire field
+
+ align:start position:0%
+that kind of blew open this entire field
+ 
+
+ align:start position:0%
+that kind of blew open this entire field
+right and it's made it so that we can
+
+ align:start position:0%
+right and it's made it so that we can
+ 
+
+ align:start position:0%
+right and it's made it so that we can
+now try at least to rival nature
+
+ align:start position:0%
+now try at least to rival nature
+ 
+
+ align:start position:0%
+now try at least to rival nature
+here's one example you're not just
+
+ align:start position:0%
+here's one example you're not just
+ 
+
+ align:start position:0%
+here's one example you're not just
+seeing graphene but check this out
+
+ align:start position:0%
+seeing graphene but check this out
+ 
+
+ align:start position:0%
+seeing graphene but check this out
+you're seeing a single atom of graphene
+
+ align:start position:0%
+you're seeing a single atom of graphene
+ 
+
+ align:start position:0%
+you're seeing a single atom of graphene
+and you're seeing what happens
+
+ align:start position:0%
+and you're seeing what happens
+ 
+
+ align:start position:0%
+and you're seeing what happens
+under a certain kind of ra irradiation
+
+ align:start position:0%
+under a certain kind of ra irradiation
+ 
+
+ align:start position:0%
+under a certain kind of ra irradiation
+and you're seeing this hole
+
+ align:start position:0%
+and you're seeing this hole
+ 
+
+ align:start position:0%
+and you're seeing this hole
+and you're seeing the whole grow and
+
+ align:start position:0%
+and you're seeing the whole grow and
+ 
+
+ align:start position:0%
+and you're seeing the whole grow and
+that's really important because
+
+ align:start position:0%
+that's really important because
+ 
+
+ align:start position:0%
+that's really important because
+something i care a lot about our
+
+ align:start position:0%
+something i care a lot about our
+ 
+
+ align:start position:0%
+something i care a lot about our
+membranes
+
+ align:start position:0%
+membranes
+ 
+
+ align:start position:0%
+membranes
+right and another why this matters i'll
+
+ align:start position:0%
+right and another why this matters i'll
+ 
+
+ align:start position:0%
+right and another why this matters i'll
+tell you about membranes but here
+
+ align:start position:0%
+tell you about membranes but here
+ 
+
+ align:start position:0%
+tell you about membranes but here
+you know i'm actually making the
+
+ align:start position:0%
+you know i'm actually making the
+ 
+
+ align:start position:0%
+you know i'm actually making the
+thinnest possible membrane that
+
+ align:start position:0%
+thinnest possible membrane that
+ 
+
+ align:start position:0%
+thinnest possible membrane that
+that you could make because it's only
+
+ align:start position:0%
+that you could make because it's only
+ 
+
+ align:start position:0%
+that you could make because it's only
+one atom thick and i'm controlling
+
+ align:start position:0%
+one atom thick and i'm controlling
+ 
+
+ align:start position:0%
+one atom thick and i'm controlling
+how i make that but i would never know
+
+ align:start position:0%
+how i make that but i would never know
+ 
+
+ align:start position:0%
+how i make that but i would never know
+what my controls do if i couldn't see it
+
+ align:start position:0%
+what my controls do if i couldn't see it
+ 
+
+ align:start position:0%
+what my controls do if i couldn't see it
+in real time right so this is this is my
+
+ align:start position:0%
+in real time right so this is this is my
+ 
+
+ align:start position:0%
+in real time right so this is this is my
+my why this matters it's seeing things
+
+ align:start position:0%
+my why this matters it's seeing things
+ 
+
+ align:start position:0%
+my why this matters it's seeing things
+at this scale
+
+ align:start position:0%
+at this scale
+ 
+
+ align:start position:0%
+at this scale
+okay so back to so there's heisenberg
+
+ align:start position:0%
+okay so back to so there's heisenberg
+ 
+
+ align:start position:0%
+okay so back to so there's heisenberg
+right so at every moment
+
+ align:start position:0%
+right so at every moment
+ 
+
+ align:start position:0%
+right so at every moment
+the electron is only inaccurate position
+
+ align:start position:0%
+the electron is only inaccurate position
+ 
+
+ align:start position:0%
+the electron is only inaccurate position
+and inaccurate velocity this was
+
+ align:start position:0%
+and inaccurate velocity this was
+ 
+
+ align:start position:0%
+and inaccurate velocity this was
+again saying bohr you got to think
+
+ align:start position:0%
+again saying bohr you got to think
+ 
+
+ align:start position:0%
+again saying bohr you got to think
+harder
+
+ align:start position:0%
+harder
+ 
+
+ align:start position:0%
+harder
+um and we had all of this these
+
+ align:start position:0%
+um and we had all of this these
+ 
+
+ align:start position:0%
+um and we had all of this these
+experiments showing the
+
+ align:start position:0%
+experiments showing the
+ 
+
+ align:start position:0%
+experiments showing the
+the the particle wave duality of nature
+
+ align:start position:0%
+the the particle wave duality of nature
+ 
+
+ align:start position:0%
+the the particle wave duality of nature
+and of
+
+ align:start position:0%
+and of
+ 
+
+ align:start position:0%
+and of
+of atoms um and so the question then
+
+ align:start position:0%
+of atoms um and so the question then
+ 
+
+ align:start position:0%
+of atoms um and so the question then
+became
+
+ align:start position:0%
+became
+ 
+
+ align:start position:0%
+became
+all these pointers from all these
+
+ align:start position:0%
+all these pointers from all these
+ 
+
+ align:start position:0%
+all these pointers from all these
+different places the question became
+
+ align:start position:0%
+different places the question became
+ 
+
+ align:start position:0%
+different places the question became
+how do we describe these this wave
+
+ align:start position:0%
+how do we describe these this wave
+ 
+
+ align:start position:0%
+how do we describe these this wave
+nature
+
+ align:start position:0%
+nature
+ 
+
+ align:start position:0%
+nature
+of matter how do we describe an electron
+
+ align:start position:0%
+of matter how do we describe an electron
+ 
+
+ align:start position:0%
+of matter how do we describe an electron
+as a wave and i like this
+
+ align:start position:0%
+as a wave and i like this
+ 
+
+ align:start position:0%
+as a wave and i like this
+because not only do i think if
+
+ align:start position:0%
+because not only do i think if
+ 
+
+ align:start position:0%
+because not only do i think if
+schrodinger had a swimming pool
+
+ align:start position:0%
+schrodinger had a swimming pool
+ 
+
+ align:start position:0%
+schrodinger had a swimming pool
+this is what he would do with it but
+
+ align:start position:0%
+this is what he would do with it but
+ 
+
+ align:start position:0%
+this is what he would do with it but
+also i thought maybe this would be cool
+
+ align:start position:0%
+also i thought maybe this would be cool
+ 
+
+ align:start position:0%
+also i thought maybe this would be cool
+for like an mit
+
+ align:start position:0%
+for like an mit
+ 
+
+ align:start position:0%
+for like an mit
+kind of swim test thing um in the future
+
+ align:start position:0%
+kind of swim test thing um in the future
+ 
+
+ align:start position:0%
+kind of swim test thing um in the future
+because you can see what happens
+
+ align:start position:0%
+because you can see what happens
+ 
+
+ align:start position:0%
+because you can see what happens
+um this just i i want to do this
+
+ align:start position:0%
+um this just i i want to do this
+ 
+
+ align:start position:0%
+um this just i i want to do this
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+um but this looks really fun they're
+
+ align:start position:0%
+um but this looks really fun they're
+ 
+
+ align:start position:0%
+um but this looks really fun they're
+making waves they're
+
+ align:start position:0%
+making waves they're
+ 
+
+ align:start position:0%
+making waves they're
+they're literally making waves right um
+
+ align:start position:0%
+they're literally making waves right um
+ 
+
+ align:start position:0%
+they're literally making waves right um
+but and so the question now look at that
+
+ align:start position:0%
+but and so the question now look at that
+ 
+
+ align:start position:0%
+but and so the question now look at that
+see but the question is how do you
+
+ align:start position:0%
+see but the question is how do you
+ 
+
+ align:start position:0%
+see but the question is how do you
+describe it well there are wave
+
+ align:start position:0%
+describe it well there are wave
+ 
+
+ align:start position:0%
+describe it well there are wave
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+there are wave equations that we know
+
+ align:start position:0%
+there are wave equations that we know
+ 
+
+ align:start position:0%
+there are wave equations that we know
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that relate the position of a wave to
+
+ align:start position:0%
+that relate the position of a wave to
+ 
+
+ align:start position:0%
+that relate the position of a wave to
+its time change and velocity
+
+ align:start position:0%
+its time change and velocity
+ 
+
+ align:start position:0%
+its time change and velocity
+right and and the thing is this is it
+
+ align:start position:0%
+right and and the thing is this is it
+ 
+
+ align:start position:0%
+right and and the thing is this is it
+this is how we need to describe an
+
+ align:start position:0%
+this is how we need to describe an
+ 
+
+ align:start position:0%
+this is how we need to describe an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+now think about it for a second an
+
+ align:start position:0%
+now think about it for a second an
+ 
+
+ align:start position:0%
+now think about it for a second an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+by the way it just occurred to me that
+
+ align:start position:0%
+by the way it just occurred to me that
+ 
+
+ align:start position:0%
+by the way it just occurred to me that
+you should take this on that same date
+
+ align:start position:0%
+you should take this on that same date
+ 
+
+ align:start position:0%
+you should take this on that same date
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+if they don't have real candles and they
+
+ align:start position:0%
+if they don't have real candles and they
+ 
+
+ align:start position:0%
+if they don't have real candles and they
+only have these
+
+ align:start position:0%
+only have these
+ 
+
+ align:start position:0%
+only have these
+you should have this handy because you
+
+ align:start position:0%
+you should have this handy because you
+ 
+
+ align:start position:0%
+you should have this handy because you
+might need to pull it out and see what
+
+ align:start position:0%
+might need to pull it out and see what
+ 
+
+ align:start position:0%
+might need to pull it out and see what
+kind of led
+
+ align:start position:0%
+kind of led
+ 
+
+ align:start position:0%
+kind of led
+they gave you what does it look like
+
+ align:start position:0%
+they gave you what does it look like
+ 
+
+ align:start position:0%
+they gave you what does it look like
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+okay that was a side point
+
+ align:start position:0%
+okay that was a side point
+ 
+
+ align:start position:0%
+okay that was a side point
+bohr says electrons can only be in
+
+ align:start position:0%
+bohr says electrons can only be in
+ 
+
+ align:start position:0%
+bohr says electrons can only be in
+certain places
+
+ align:start position:0%
+certain places
+ 
+
+ align:start position:0%
+certain places
+well that's mind-blowing because but by
+
+ align:start position:0%
+well that's mind-blowing because but by
+ 
+
+ align:start position:0%
+well that's mind-blowing because but by
+the way think about that
+
+ align:start position:0%
+the way think about that
+ 
+
+ align:start position:0%
+the way think about that
+an electron can only be here here oh by
+
+ align:start position:0%
+an electron can only be here here oh by
+ 
+
+ align:start position:0%
+an electron can only be here here oh by
+the way it can transition between them
+
+ align:start position:0%
+the way it can transition between them
+ 
+
+ align:start position:0%
+the way it can transition between them
+but it can never be
+
+ align:start position:0%
+but it can never be
+ 
+
+ align:start position:0%
+but it can never be
+between them did anyone catch that
+
+ align:start position:0%
+between them did anyone catch that
+ 
+
+ align:start position:0%
+between them did anyone catch that
+what's up with that it can't be between
+
+ align:start position:0%
+what's up with that it can't be between
+ 
+
+ align:start position:0%
+what's up with that it can't be between
+them i am
+
+ align:start position:0%
+them i am
+ 
+
+ align:start position:0%
+them i am
+telling you that but it can transition
+
+ align:start position:0%
+telling you that but it can transition
+ 
+
+ align:start position:0%
+telling you that but it can transition
+where did it go
+
+ align:start position:0%
+where did it go
+ 
+
+ align:start position:0%
+where did it go
+oh okay that's a weekend kind of
+
+ align:start position:0%
+oh okay that's a weekend kind of
+ 
+
+ align:start position:0%
+oh okay that's a weekend kind of
+thinking exercise
+
+ align:start position:0%
+thinking exercise
+ 
+
+ align:start position:0%
+thinking exercise
+and now we're saying they're not even
+
+ align:start position:0%
+and now we're saying they're not even
+ 
+
+ align:start position:0%
+and now we're saying they're not even
+they're not even like
+
+ align:start position:0%
+they're not even like
+ 
+
+ align:start position:0%
+they're not even like
+in one place they're waves
+
+ align:start position:0%
+in one place they're waves
+ 
+
+ align:start position:0%
+in one place they're waves
+they're like the water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's cra that that really was at the
+
+ align:start position:0%
+that's cra that that really was at the
+ 
+
+ align:start position:0%
+that's cra that that really was at the
+time they thought how is this possible
+
+ align:start position:0%
+time they thought how is this possible
+ 
+
+ align:start position:0%
+time they thought how is this possible
+right but schrodinger came along and he
+
+ align:start position:0%
+right but schrodinger came along and he
+ 
+
+ align:start position:0%
+right but schrodinger came along and he
+said i'm gonna write down the equation
+
+ align:start position:0%
+said i'm gonna write down the equation
+ 
+
+ align:start position:0%
+said i'm gonna write down the equation
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+and and that's that was the the
+
+ align:start position:0%
+and and that's that was the the
+ 
+
+ align:start position:0%
+and and that's that was the the
+the big contribution the the really
+
+ align:start position:0%
+the big contribution the the really
+ 
+
+ align:start position:0%
+the big contribution the the really
+critical contribution that schroedinger
+
+ align:start position:0%
+critical contribution that schroedinger
+ 
+
+ align:start position:0%
+critical contribution that schroedinger
+did
+
+ align:start position:0%
+did
+ 
+
+ align:start position:0%
+did
+is he said i'm gonna i'm gonna write
+
+ align:start position:0%
+is he said i'm gonna i'm gonna write
+ 
+
+ align:start position:0%
+is he said i'm gonna i'm gonna write
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+kind of like a newton's equation like an
+
+ align:start position:0%
+kind of like a newton's equation like an
+ 
+
+ align:start position:0%
+kind of like a newton's equation like an
+f equals ma but for
+
+ align:start position:0%
+f equals ma but for
+ 
+
+ align:start position:0%
+f equals ma but for
+for quantum mechanics and for waves like
+
+ align:start position:0%
+for quantum mechanics and for waves like
+ 
+
+ align:start position:0%
+for quantum mechanics and for waves like
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+and i'm going to describe them so he
+
+ align:start position:0%
+and i'm going to describe them so he
+ 
+
+ align:start position:0%
+and i'm going to describe them so he
+developed the equation
+
+ align:start position:0%
+developed the equation
+ 
+
+ align:start position:0%
+developed the equation
+that we solved that on monday we'll
+
+ align:start position:0%
+that we solved that on monday we'll
+ 
+
+ align:start position:0%
+that we solved that on monday we'll
+solve to describe the wave nature
+
+ align:start position:0%
+solve to describe the wave nature
+ 
+
+ align:start position:0%
+solve to describe the wave nature
+of quantum mechanics and and just to
+
+ align:start position:0%
+of quantum mechanics and and just to
+ 
+
+ align:start position:0%
+of quantum mechanics and and just to
+to end so on on monday we'll pick up
+
+ align:start position:0%
+to end so on on monday we'll pick up
+ 
+
+ align:start position:0%
+to end so on on monday we'll pick up
+with schrodinger's equation
+
+ align:start position:0%
+with schrodinger's equation
+ 
+
+ align:start position:0%
+with schrodinger's equation
+for the atom you know the question is
+
+ align:start position:0%
+for the atom you know the question is
+ 
+
+ align:start position:0%
+for the atom you know the question is
+what does this all mean for chemistry
+
+ align:start position:0%
+what does this all mean for chemistry
+ 
+
+ align:start position:0%
+what does this all mean for chemistry
+what does this mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're not i'm not teaching you quantum
+
+ align:start position:0%
+we're not i'm not teaching you quantum
+ 
+
+ align:start position:0%
+we're not i'm not teaching you quantum
+i'm not teaching you quantum just so you
+
+ align:start position:0%
+i'm not teaching you quantum just so you
+ 
+
+ align:start position:0%
+i'm not teaching you quantum just so you
+know quantum in isolation i'm telling
+
+ align:start position:0%
+know quantum in isolation i'm telling
+ 
+
+ align:start position:0%
+know quantum in isolation i'm telling
+you about it
+
+ align:start position:0%
+you about it
+ 
+
+ align:start position:0%
+you about it
+because it completely revolutionized
+
+ align:start position:0%
+because it completely revolutionized
+ 
+
+ align:start position:0%
+because it completely revolutionized
+chemistry and and that is where we will
+
+ align:start position:0%
+chemistry and and that is where we will
+ 
+
+ align:start position:0%
+chemistry and and that is where we will
+answer that question
+
+ align:start position:0%
+answer that question
+ 
+
+ align:start position:0%
+answer that question
+on monday have a really good weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/s67DO7fFM14.txt b/s67DO7fFM14.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a5192c1f9028a88158a71eb21e9fe3fd248f7df1
--- /dev/null
+++ b/s67DO7fFM14.txt
@@ -0,0 +1,3843 @@
+align:start position:0%
+ 
+there's no pizza for me cuz I'm going to
+
+ align:start position:0%
+there's no pizza for me cuz I'm going to
+ 
+
+ align:start position:0%
+there's no pizza for me cuz I'm going to
+talk about Oshkosh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is it it's end of July every
+
+ align:start position:0%
+so what is it it's end of July every
+ 
+
+ align:start position:0%
+so what is it it's end of July every
+year and a big physically big but
+
+ align:start position:0%
+year and a big physically big but
+ 
+
+ align:start position:0%
+year and a big physically big but
+otherwise not very busy Airport in
+
+ align:start position:0%
+otherwise not very busy Airport in
+ 
+
+ align:start position:0%
+otherwise not very busy Airport in
+Wisconsin and about 10,000 airplanes
+
+ align:start position:0%
+Wisconsin and about 10,000 airplanes
+ 
+
+ align:start position:0%
+Wisconsin and about 10,000 airplanes
+come in people camp out people hang out
+
+ align:start position:0%
+come in people camp out people hang out
+ 
+
+ align:start position:0%
+come in people camp out people hang out
+usually at least a hundred thousand
+
+ align:start position:0%
+usually at least a hundred thousand
+ 
+
+ align:start position:0%
+usually at least a hundred thousand
+people a day there's a Boeing there's a
+
+ align:start position:0%
+people a day there's a Boeing there's a
+ 
+
+ align:start position:0%
+people a day there's a Boeing there's a
+c-17 cargo plane a lot of experimentals
+
+ align:start position:0%
+c-17 cargo plane a lot of experimentals
+ 
+
+ align:start position:0%
+c-17 cargo plane a lot of experimentals
+it's founded by the Experimental
+
+ align:start position:0%
+it's founded by the Experimental
+ 
+
+ align:start position:0%
+it's founded by the Experimental
+Aircraft Association so there's a lot of
+
+ align:start position:0%
+Aircraft Association so there's a lot of
+ 
+
+ align:start position:0%
+Aircraft Association so there's a lot of
+people who are passionate about home
+
+ align:start position:0%
+people who are passionate about home
+ 
+
+ align:start position:0%
+people who are passionate about home
+building there you can see all the
+
+ align:start position:0%
+building there you can see all the
+ 
+
+ align:start position:0%
+building there you can see all the
+airplanes parked
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there's 12,000 camping sites 40,000
+
+ align:start position:0%
+yeah there's 12,000 camping sites 40,000
+ 
+
+ align:start position:0%
+yeah there's 12,000 camping sites 40,000
+campers there's 1,500 workshops and
+
+ align:start position:0%
+campers there's 1,500 workshops and
+ 
+
+ align:start position:0%
+campers there's 1,500 workshops and
+seminars that you can take to learn or
+
+ align:start position:0%
+seminars that you can take to learn or
+ 
+
+ align:start position:0%
+seminars that you can take to learn or
+you can just walk around and talk to
+
+ align:start position:0%
+you can just walk around and talk to
+ 
+
+ align:start position:0%
+you can just walk around and talk to
+people and hang out so I planned this
+
+ align:start position:0%
+people and hang out so I planned this
+ 
+
+ align:start position:0%
+people and hang out so I planned this
+trip for me and my friend ray he's a
+
+ align:start position:0%
+trip for me and my friend ray he's a
+ 
+
+ align:start position:0%
+trip for me and my friend ray he's a
+helicopter pilot from Ireland and the
+
+ align:start position:0%
+helicopter pilot from Ireland and the
+ 
+
+ align:start position:0%
+helicopter pilot from Ireland and the
+idea was to fly to Niagara Falls and
+
+ align:start position:0%
+idea was to fly to Niagara Falls and
+ 
+
+ align:start position:0%
+idea was to fly to Niagara Falls and
+show him Niagara Falls and on the way
+
+ align:start position:0%
+show him Niagara Falls and on the way
+ 
+
+ align:start position:0%
+show him Niagara Falls and on the way
+back up to Mackinac Island they saw
+
+ align:start position:0%
+back up to Mackinac Island they saw
+ 
+
+ align:start position:0%
+back up to Mackinac Island they saw
+automobiles about 120 years ago and they
+
+ align:start position:0%
+automobiles about 120 years ago and they
+ 
+
+ align:start position:0%
+automobiles about 120 years ago and they
+said this is a terrible technology
+
+ align:start position:0%
+said this is a terrible technology
+ 
+
+ align:start position:0%
+said this is a terrible technology
+that'll ruin everything
+
+ align:start position:0%
+that'll ruin everything
+ 
+
+ align:start position:0%
+that'll ruin everything
+they banned cars the only powered air
+
+ align:start position:0%
+they banned cars the only powered air
+ 
+
+ align:start position:0%
+they banned cars the only powered air
+the only powered vehicle you can legally
+
+ align:start position:0%
+the only powered vehicle you can legally
+ 
+
+ align:start position:0%
+the only powered vehicle you can legally
+have on Mackinac Island is an aircraft
+
+ align:start position:0%
+have on Mackinac Island is an aircraft
+ 
+
+ align:start position:0%
+have on Mackinac Island is an aircraft
+they do have an airport anyway in the
+
+ align:start position:0%
+they do have an airport anyway in the
+ 
+
+ align:start position:0%
+they do have an airport anyway in the
+back and we were gonna go to Toronto as
+
+ align:start position:0%
+back and we were gonna go to Toronto as
+ 
+
+ align:start position:0%
+back and we were gonna go to Toronto as
+well so we had to get all this stuff
+
+ align:start position:0%
+well so we had to get all this stuff
+ 
+
+ align:start position:0%
+well so we had to get all this stuff
+ready for international flying I had it
+
+ align:start position:0%
+ready for international flying I had it
+ 
+
+ align:start position:0%
+ready for international flying I had it
+all carefully planned out where we're
+
+ align:start position:0%
+all carefully planned out where we're
+ 
+
+ align:start position:0%
+all carefully planned out where we're
+gonna have 540 pounds of stuff which is
+
+ align:start position:0%
+gonna have 540 pounds of stuff which is
+ 
+
+ align:start position:0%
+gonna have 540 pounds of stuff which is
+right at the payload of the airplane
+
+ align:start position:0%
+right at the payload of the airplane
+ 
+
+ align:start position:0%
+right at the payload of the airplane
+with full fuel but then Alex Anna who
+
+ align:start position:0%
+with full fuel but then Alex Anna who
+ 
+
+ align:start position:0%
+with full fuel but then Alex Anna who
+was just here she's an aerobatic pilot
+
+ align:start position:0%
+was just here she's an aerobatic pilot
+ 
+
+ align:start position:0%
+was just here she's an aerobatic pilot
+at East Coast Aero clubs she said she
+
+ align:start position:0%
+at East Coast Aero clubs she said she
+ 
+
+ align:start position:0%
+at East Coast Aero clubs she said she
+wanted to come too so then we had we had
+
+ align:start position:0%
+wanted to come too so then we had we had
+ 
+
+ align:start position:0%
+wanted to come too so then we had we had
+to add a fuel stop there's all our merry
+
+ align:start position:0%
+to add a fuel stop there's all our merry
+ 
+
+ align:start position:0%
+to add a fuel stop there's all our merry
+band of three people there's a whole
+
+ align:start position:0%
+band of three people there's a whole
+ 
+
+ align:start position:0%
+band of three people there's a whole
+bunch of camping gear in the back that
+
+ align:start position:0%
+bunch of camping gear in the back that
+ 
+
+ align:start position:0%
+bunch of camping gear in the back that
+you can't quite see option Cox becomes
+
+ align:start position:0%
+you can't quite see option Cox becomes
+ 
+
+ align:start position:0%
+you can't quite see option Cox becomes
+temporarily the business busiest airport
+
+ align:start position:0%
+temporarily the business busiest airport
+ 
+
+ align:start position:0%
+temporarily the business busiest airport
+in the world and you might say well how
+
+ align:start position:0%
+in the world and you might say well how
+ 
+
+ align:start position:0%
+in the world and you might say well how
+can that be O'Hare has more flights but
+
+ align:start position:0%
+can that be O'Hare has more flights but
+ 
+
+ align:start position:0%
+can that be O'Hare has more flights but
+their only option has only open about 10
+
+ align:start position:0%
+their only option has only open about 10
+ 
+
+ align:start position:0%
+their only option has only open about 10
+hours a day because they close the
+
+ align:start position:0%
+hours a day because they close the
+ 
+
+ align:start position:0%
+hours a day because they close the
+airport at night and they close it also
+
+ align:start position:0%
+airport at night and they close it also
+ 
+
+ align:start position:0%
+airport at night and they close it also
+for a few hours
+
+ align:start position:0%
+for a few hours
+ 
+
+ align:start position:0%
+for a few hours
+every afternoon for an airshow this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody's iPad
+
+ align:start position:0%
+somebody's iPad
+ 
+
+ align:start position:0%
+somebody's iPad
+I think screen capture of airplanes
+
+ align:start position:0%
+I think screen capture of airplanes
+ 
+
+ align:start position:0%
+I think screen capture of airplanes
+flying in and around Oshkosh and these
+
+ align:start position:0%
+flying in and around Oshkosh and these
+ 
+
+ align:start position:0%
+flying in and around Oshkosh and these
+are only the ones with the newest ad s
+
+ align:start position:0%
+are only the ones with the newest ad s
+ 
+
+ align:start position:0%
+are only the ones with the newest ad s
+be out transponders so it doesn't show
+
+ align:start position:0%
+be out transponders so it doesn't show
+ 
+
+ align:start position:0%
+be out transponders so it doesn't show
+probably this is probably only 20
+
+ align:start position:0%
+probably this is probably only 20
+ 
+
+ align:start position:0%
+probably this is probably only 20
+percent of the total airplanes you have
+
+ align:start position:0%
+percent of the total airplanes you have
+ 
+
+ align:start position:0%
+percent of the total airplanes you have
+special arrival rules if you're not a
+
+ align:start position:0%
+special arrival rules if you're not a
+ 
+
+ align:start position:0%
+special arrival rules if you're not a
+ then you have to fly and visually
+
+ align:start position:0%
+ then you have to fly and visually
+ 
+
+ align:start position:0%
+ then you have to fly and visually
+circle around until it's your turn and
+
+ align:start position:0%
+circle around until it's your turn and
+ 
+
+ align:start position:0%
+circle around until it's your turn and
+then they'll tell you you can't use the
+
+ align:start position:0%
+then they'll tell you you can't use the
+ 
+
+ align:start position:0%
+then they'll tell you you can't use the
+whole runway you have to land on one of
+
+ align:start position:0%
+whole runway you have to land on one of
+ 
+
+ align:start position:0%
+whole runway you have to land on one of
+these dots they'll say land on the green
+
+ align:start position:0%
+these dots they'll say land on the green
+ 
+
+ align:start position:0%
+these dots they'll say land on the green
+dot if you are a you file IFR get
+
+ align:start position:0%
+dot if you are a you file IFR get
+ 
+
+ align:start position:0%
+dot if you are a you file IFR get
+your IFR reservation when this daus
+
+ align:start position:0%
+your IFR reservation when this daus
+ 
+
+ align:start position:0%
+your IFR reservation when this daus
+grade computer system confirm it with
+
+ align:start position:0%
+grade computer system confirm it with
+ 
+
+ align:start position:0%
+grade computer system confirm it with
+this daus grade computer system that
+
+ align:start position:0%
+this daus grade computer system that
+ 
+
+ align:start position:0%
+this daus grade computer system that
+nobody else wants to deal with and then
+
+ align:start position:0%
+nobody else wants to deal with and then
+ 
+
+ align:start position:0%
+nobody else wants to deal with and then
+you get the whole runway and you just
+
+ align:start position:0%
+you get the whole runway and you just
+ 
+
+ align:start position:0%
+you get the whole runway and you just
+land all right here's a picture of the
+
+ align:start position:0%
+land all right here's a picture of the
+ 
+
+ align:start position:0%
+land all right here's a picture of the
+multifunction display and no actually I
+
+ align:start position:0%
+multifunction display and no actually I
+ 
+
+ align:start position:0%
+multifunction display and no actually I
+guess this was some flat fried up
+
+ align:start position:0%
+guess this was some flat fried up
+ 
+
+ align:start position:0%
+guess this was some flat fried up
+FlightAware later this shows that we
+
+ align:start position:0%
+FlightAware later this shows that we
+ 
+
+ align:start position:0%
+FlightAware later this shows that we
+diverted a bit from Bedford we ended up
+
+ align:start position:0%
+diverted a bit from Bedford we ended up
+ 
+
+ align:start position:0%
+diverted a bit from Bedford we ended up
+going up to Watertown New York so we
+
+ align:start position:0%
+going up to Watertown New York so we
+ 
+
+ align:start position:0%
+going up to Watertown New York so we
+didn't we could have legally where
+
+ align:start position:0%
+didn't we could have legally where
+ 
+
+ align:start position:0%
+didn't we could have legally where
+instrument-rated and everything we could
+
+ align:start position:0%
+instrument-rated and everything we could
+ 
+
+ align:start position:0%
+instrument-rated and everything we could
+have flown through this you know these
+
+ align:start position:0%
+have flown through this you know these
+ 
+
+ align:start position:0%
+have flown through this you know these
+rain showers but it's always smarter
+
+ align:start position:0%
+rain showers but it's always smarter
+ 
+
+ align:start position:0%
+rain showers but it's always smarter
+just to go around if you can okay so we
+
+ align:start position:0%
+just to go around if you can okay so we
+ 
+
+ align:start position:0%
+just to go around if you can okay so we
+flew over Niagara Falls we landed we had
+
+ align:start position:0%
+flew over Niagara Falls we landed we had
+ 
+
+ align:start position:0%
+flew over Niagara Falls we landed we had
+that whole runway to ourself about
+
+ align:start position:0%
+that whole runway to ourself about
+ 
+
+ align:start position:0%
+that whole runway to ourself about
+10,000 foot runway and it's actually
+
+ align:start position:0%
+10,000 foot runway and it's actually
+ 
+
+ align:start position:0%
+10,000 foot runway and it's actually
+oriented east-west so we actually just
+
+ align:start position:0%
+oriented east-west so we actually just
+ 
+
+ align:start position:0%
+oriented east-west so we actually just
+essentially we could have done the same
+
+ align:start position:0%
+essentially we could have done the same
+ 
+
+ align:start position:0%
+essentially we could have done the same
+heading basically from Hanscom field all
+
+ align:start position:0%
+heading basically from Hanscom field all
+ 
+
+ align:start position:0%
+heading basically from Hanscom field all
+the way to the end of the runway and
+
+ align:start position:0%
+the way to the end of the runway and
+ 
+
+ align:start position:0%
+the way to the end of the runway and
+where we turned off you get there and
+
+ align:start position:0%
+where we turned off you get there and
+ 
+
+ align:start position:0%
+where we turned off you get there and
+there's just on a thirty p-51 Mustangs
+
+ align:start position:0%
+there's just on a thirty p-51 Mustangs
+ 
+
+ align:start position:0%
+there's just on a thirty p-51 Mustangs
+right next to your tent there are people
+
+ align:start position:0%
+right next to your tent there are people
+ 
+
+ align:start position:0%
+right next to your tent there are people
+building this one-week Wonder an RV kit
+
+ align:start position:0%
+building this one-week Wonder an RV kit
+ 
+
+ align:start position:0%
+building this one-week Wonder an RV kit
+where you get to pull rivets Oksana's
+
+ align:start position:0%
+where you get to pull rivets Oksana's
+ 
+
+ align:start position:0%
+where you get to pull rivets Oksana's
+actually here and she can tell you about
+
+ align:start position:0%
+actually here and she can tell you about
+ 
+
+ align:start position:0%
+actually here and she can tell you about
+her experience helping to build that
+
+ align:start position:0%
+her experience helping to build that
+ 
+
+ align:start position:0%
+her experience helping to build that
+airplane
+
+ align:start position:0%
+airplane
+ 
+
+ align:start position:0%
+airplane
+there's your b-1 bomber I love the
+
+ align:start position:0%
+there's your b-1 bomber I love the
+ 
+
+ align:start position:0%
+there's your b-1 bomber I love the
+antiques here's one from the late 20s a
+
+ align:start position:0%
+antiques here's one from the late 20s a
+ 
+
+ align:start position:0%
+antiques here's one from the late 20s a
+Lincoln Age airplane that has been
+
+ align:start position:0%
+Lincoln Age airplane that has been
+ 
+
+ align:start position:0%
+Lincoln Age airplane that has been
+recently restored and flying there's
+
+ align:start position:0%
+recently restored and flying there's
+ 
+
+ align:start position:0%
+recently restored and flying there's
+that replica autogyro beautiful Cessna
+
+ align:start position:0%
+that replica autogyro beautiful Cessna
+ 
+
+ align:start position:0%
+that replica autogyro beautiful Cessna
+172 mold piper Comanche there on the
+
+ align:start position:0%
+172 mold piper Comanche there on the
+ 
+
+ align:start position:0%
+172 mold piper Comanche there on the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+there's not a whole lot of helicopter
+
+ align:start position:0%
+there's not a whole lot of helicopter
+ 
+
+ align:start position:0%
+there's not a whole lot of helicopter
+action there's a little bit this is
+
+ align:start position:0%
+action there's a little bit this is
+ 
+
+ align:start position:0%
+action there's a little bit this is
+what's called a safari helicopter kit
+
+ align:start position:0%
+what's called a safari helicopter kit
+ 
+
+ align:start position:0%
+what's called a safari helicopter kit
+that's how you know that you have real
+
+ align:start position:0%
+that's how you know that you have real
+ 
+
+ align:start position:0%
+that's how you know that you have real
+confidence in your mechanical abilities
+
+ align:start position:0%
+confidence in your mechanical abilities
+ 
+
+ align:start position:0%
+confidence in your mechanical abilities
+if you build and then fly your own
+
+ align:start position:0%
+if you build and then fly your own
+ 
+
+ align:start position:0%
+if you build and then fly your own
+helicopter Piper Cub this is a guy who
+
+ align:start position:0%
+helicopter Piper Cub this is a guy who
+ 
+
+ align:start position:0%
+helicopter Piper Cub this is a guy who
+stuck a Pratt and Whitney I think it's a
+
+ align:start position:0%
+stuck a Pratt and Whitney I think it's a
+ 
+
+ align:start position:0%
+stuck a Pratt and Whitney I think it's a
+Pratt pt6 engine into a Polish Wilgus
+
+ align:start position:0%
+Pratt pt6 engine into a Polish Wilgus
+ 
+
+ align:start position:0%
+Pratt pt6 engine into a Polish Wilgus
+short field landing airplane he added
+
+ align:start position:0%
+short field landing airplane he added
+ 
+
+ align:start position:0%
+short field landing airplane he added
+fuel tanks it's such a fuel log now that
+
+ align:start position:0%
+fuel tanks it's such a fuel log now that
+ 
+
+ align:start position:0%
+fuel tanks it's such a fuel log now that
+they had to add extra fuel capacity in
+
+ align:start position:0%
+they had to add extra fuel capacity in
+ 
+
+ align:start position:0%
+they had to add extra fuel capacity in
+the struts and flies all around the West
+
+ align:start position:0%
+the struts and flies all around the West
+ 
+
+ align:start position:0%
+the struts and flies all around the West
+going camping with his family all right
+
+ align:start position:0%
+going camping with his family all right
+ 
+
+ align:start position:0%
+going camping with his family all right
+and that's called a traveler there were
+
+ align:start position:0%
+and that's called a traveler there were
+ 
+
+ align:start position:0%
+and that's called a traveler there were
+a bunch of these so these are airplanes
+
+ align:start position:0%
+a bunch of these so these are airplanes
+ 
+
+ align:start position:0%
+a bunch of these so these are airplanes
+from the 20s people are just using them
+
+ align:start position:0%
+from the 20s people are just using them
+ 
+
+ align:start position:0%
+from the 20s people are just using them
+for transportation throwing a friend in
+
+ align:start position:0%
+for transportation throwing a friend in
+ 
+
+ align:start position:0%
+for transportation throwing a friend in
+the back maybe and a tent and that going
+
+ align:start position:0%
+the back maybe and a tent and that going
+ 
+
+ align:start position:0%
+the back maybe and a tent and that going
+and camping out of Oshkosh so I think
+
+ align:start position:0%
+and camping out of Oshkosh so I think
+ 
+
+ align:start position:0%
+and camping out of Oshkosh so I think
+that's pretty cool all right there are
+
+ align:start position:0%
+that's pretty cool all right there are
+ 
+
+ align:start position:0%
+that's pretty cool all right there are
+only five of these Piaggio seaplanes P
+
+ align:start position:0%
+only five of these Piaggio seaplanes P
+ 
+
+ align:start position:0%
+only five of these Piaggio seaplanes P
+31 thirty Six's that still exist out of
+
+ align:start position:0%
+31 thirty Six's that still exist out of
+ 
+
+ align:start position:0%
+31 thirty Six's that still exist out of
+63 that were built from 1948 to 1961 I
+
+ align:start position:0%
+63 that were built from 1948 to 1961 I
+ 
+
+ align:start position:0%
+63 that were built from 1948 to 1961 I
+saw two of them parked next to each
+
+ align:start position:0%
+saw two of them parked next to each
+ 
+
+ align:start position:0%
+saw two of them parked next to each
+other Oshkosh that's what makes it a
+
+ align:start position:0%
+other Oshkosh that's what makes it a
+ 
+
+ align:start position:0%
+other Oshkosh that's what makes it a
+unique experience here's some kind of
+
+ align:start position:0%
+unique experience here's some kind of
+ 
+
+ align:start position:0%
+unique experience here's some kind of
+airplane doing a simulated bombing run
+
+ align:start position:0%
+airplane doing a simulated bombing run
+ 
+
+ align:start position:0%
+airplane doing a simulated bombing run
+meanwhile a family is there and their
+
+ align:start position:0%
+meanwhile a family is there and their
+ 
+
+ align:start position:0%
+meanwhile a family is there and their
+personal dc-3 camping out here's our
+
+ align:start position:0%
+personal dc-3 camping out here's our
+ 
+
+ align:start position:0%
+personal dc-3 camping out here's our
+little plane and the $99 tent from
+
+ align:start position:0%
+little plane and the $99 tent from
+ 
+
+ align:start position:0%
+little plane and the $99 tent from
+Costco it seemed like a great idea
+
+ align:start position:0%
+Costco it seemed like a great idea
+ 
+
+ align:start position:0%
+Costco it seemed like a great idea
+at the time I think we have a slide on
+
+ align:start position:0%
+at the time I think we have a slide on
+ 
+
+ align:start position:0%
+at the time I think we have a slide on
+that okay this kind of summarizes 8:00
+
+ align:start position:0%
+that okay this kind of summarizes 8:00
+ 
+
+ align:start position:0%
+that okay this kind of summarizes 8:00
+this is the unfortunate state of general
+
+ align:start position:0%
+this is the unfortunate state of general
+ 
+
+ align:start position:0%
+this is the unfortunate state of general
+aviation now so we have the innovation
+
+ align:start position:0%
+aviation now so we have the innovation
+ 
+
+ align:start position:0%
+aviation now so we have the innovation
+showcase and right in front of it a
+
+ align:start position:0%
+showcase and right in front of it a
+ 
+
+ align:start position:0%
+showcase and right in front of it a
+piper Seminole which I think was
+
+ align:start position:0%
+piper Seminole which I think was
+ 
+
+ align:start position:0%
+piper Seminole which I think was
+certified in the 1970s and certainly a
+
+ align:start position:0%
+certified in the 1970s and certainly a
+ 
+
+ align:start position:0%
+certified in the 1970s and certainly a
+derivative of things going back a lot
+
+ align:start position:0%
+derivative of things going back a lot
+ 
+
+ align:start position:0%
+derivative of things going back a lot
+harder than that
+
+ align:start position:0%
+harder than that
+ 
+
+ align:start position:0%
+harder than that
+there were some interesting talks there
+
+ align:start position:0%
+there were some interesting talks there
+ 
+
+ align:start position:0%
+there were some interesting talks there
+some heavy-hitters this guy Pat Anderson
+
+ align:start position:0%
+some heavy-hitters this guy Pat Anderson
+ 
+
+ align:start position:0%
+some heavy-hitters this guy Pat Anderson
+is a professor at embry-riddle and he
+
+ align:start position:0%
+is a professor at embry-riddle and he
+ 
+
+ align:start position:0%
+is a professor at embry-riddle and he
+said actually that we haven't really
+
+ align:start position:0%
+said actually that we haven't really
+ 
+
+ align:start position:0%
+said actually that we haven't really
+seen anything in the electric aircraft
+
+ align:start position:0%
+seen anything in the electric aircraft
+ 
+
+ align:start position:0%
+seen anything in the electric aircraft
+world because in the early days of Jets
+
+ align:start position:0%
+world because in the early days of Jets
+ 
+
+ align:start position:0%
+world because in the early days of Jets
+they just took these piston airframes
+
+ align:start position:0%
+they just took these piston airframes
+ 
+
+ align:start position:0%
+they just took these piston airframes
+and stuck a jet engine in them and they
+
+ align:start position:0%
+and stuck a jet engine in them and they
+ 
+
+ align:start position:0%
+and stuck a jet engine in them and they
+didn't perform that differently from the
+
+ align:start position:0%
+didn't perform that differently from the
+ 
+
+ align:start position:0%
+didn't perform that differently from the
+piston fighters but then you know five
+
+ align:start position:0%
+piston fighters but then you know five
+ 
+
+ align:start position:0%
+piston fighters but then you know five
+years later they had the swept wings and
+
+ align:start position:0%
+years later they had the swept wings and
+ 
+
+ align:start position:0%
+years later they had the swept wings and
+we would recognize as the modern fighter
+
+ align:start position:0%
+we would recognize as the modern fighter
+ 
+
+ align:start position:0%
+we would recognize as the modern fighter
+jet so it completely was it was the jet
+
+ align:start position:0%
+jet so it completely was it was the jet
+ 
+
+ align:start position:0%
+jet so it completely was it was the jet
+engine did completely transform the
+
+ align:start position:0%
+engine did completely transform the
+ 
+
+ align:start position:0%
+engine did completely transform the
+aircraft but not immediately so he said
+
+ align:start position:0%
+aircraft but not immediately so he said
+ 
+
+ align:start position:0%
+aircraft but not immediately so he said
+you know you're seeing some of this now
+
+ align:start position:0%
+you know you're seeing some of this now
+ 
+
+ align:start position:0%
+you know you're seeing some of this now
+our people take a little two-seat
+
+ align:start position:0%
+our people take a little two-seat
+ 
+
+ align:start position:0%
+our people take a little two-seat
+trainer and they remove the piston
+
+ align:start position:0%
+trainer and they remove the piston
+ 
+
+ align:start position:0%
+trainer and they remove the piston
+engine and put in a electric motor with
+
+ align:start position:0%
+engine and put in a electric motor with
+ 
+
+ align:start position:0%
+engine and put in a electric motor with
+the propeller but that's not really what
+
+ align:start position:0%
+the propeller but that's not really what
+ 
+
+ align:start position:0%
+the propeller but that's not really what
+what we're really going to see is are
+
+ align:start position:0%
+what we're really going to see is are
+ 
+
+ align:start position:0%
+what we're really going to see is are
+things that are much more like drones
+
+ align:start position:0%
+things that are much more like drones
+ 
+
+ align:start position:0%
+things that are much more like drones
+there's an uber there was a guy from
+
+ align:start position:0%
+there's an uber there was a guy from
+ 
+
+ align:start position:0%
+there's an uber there was a guy from
+uber that was very interesting
+
+ align:start position:0%
+uber that was very interesting
+ 
+
+ align:start position:0%
+uber that was very interesting
+uber has aeronautical engineers working
+
+ align:start position:0%
+uber has aeronautical engineers working
+ 
+
+ align:start position:0%
+uber has aeronautical engineers working
+for them designing aircraft and then
+
+ align:start position:0%
+for them designing aircraft and then
+ 
+
+ align:start position:0%
+for them designing aircraft and then
+releasing the designs for free hoping
+
+ align:start position:0%
+releasing the designs for free hoping
+ 
+
+ align:start position:0%
+releasing the designs for free hoping
+that well people will make them they're
+
+ align:start position:0%
+that well people will make them they're
+ 
+
+ align:start position:0%
+that well people will make them they're
+claiming that they're gonna I don't know
+
+ align:start position:0%
+claiming that they're gonna I don't know
+ 
+
+ align:start position:0%
+claiming that they're gonna I don't know
+they gotta I gotta pay somebody off in
+
+ align:start position:0%
+they gotta I gotta pay somebody off in
+ 
+
+ align:start position:0%
+they gotta I gotta pay somebody off in
+the government to make this happen 2023
+
+ align:start position:0%
+the government to make this happen 2023
+ 
+
+ align:start position:0%
+the government to make this happen 2023
+they say they're gonna be operating in
+
+ align:start position:0%
+they say they're gonna be operating in
+ 
+
+ align:start position:0%
+they say they're gonna be operating in
+Los Angeles their idea is that you know
+
+ align:start position:0%
+Los Angeles their idea is that you know
+ 
+
+ align:start position:0%
+Los Angeles their idea is that you know
+the world is going to be so congested
+
+ align:start position:0%
+the world is going to be so congested
+ 
+
+ align:start position:0%
+the world is going to be so congested
+that people will pay up happily to hop
+
+ align:start position:0%
+that people will pay up happily to hop
+ 
+
+ align:start position:0%
+that people will pay up happily to hop
+over the congestion and in relatively
+
+ align:start position:0%
+over the congestion and in relatively
+ 
+
+ align:start position:0%
+over the congestion and in relatively
+short hops so ubers putting a lot of
+
+ align:start position:0%
+short hops so ubers putting a lot of
+ 
+
+ align:start position:0%
+short hops so ubers putting a lot of
+money into this they have some partners
+
+ align:start position:0%
+money into this they have some partners
+ 
+
+ align:start position:0%
+money into this they have some partners
+like Airbus pipistrelle the Slovenian
+
+ align:start position:0%
+like Airbus pipistrelle the Slovenian
+ 
+
+ align:start position:0%
+like Airbus pipistrelle the Slovenian
+company we'll see what happens so some
+
+ align:start position:0%
+company we'll see what happens so some
+ 
+
+ align:start position:0%
+company we'll see what happens so some
+round-the-world pilots were there
+
+ align:start position:0%
+round-the-world pilots were there
+ 
+
+ align:start position:0%
+round-the-world pilots were there
+actually I don't know how many you guys
+
+ align:start position:0%
+actually I don't know how many you guys
+ 
+
+ align:start position:0%
+actually I don't know how many you guys
+know this but Matt Guf Miller who was an
+
+ align:start position:0%
+know this but Matt Guf Miller who was an
+ 
+
+ align:start position:0%
+know this but Matt Guf Miller who was an
+MIT between freshman and sophomore years
+
+ align:start position:0%
+MIT between freshman and sophomore years
+ 
+
+ align:start position:0%
+MIT between freshman and sophomore years
+became the youngest person ever to fly
+
+ align:start position:0%
+became the youngest person ever to fly
+ 
+
+ align:start position:0%
+became the youngest person ever to fly
+around the world in a Beechcraft Bonanza
+
+ align:start position:0%
+around the world in a Beechcraft Bonanza
+ 
+
+ align:start position:0%
+around the world in a Beechcraft Bonanza
+I mean he was he was in there bonanza
+
+ align:start position:0%
+I mean he was he was in there bonanza
+ 
+
+ align:start position:0%
+I mean he was he was in there bonanza
+and he he was the youngest person to fly
+
+ align:start position:0%
+and he he was the youngest person to fly
+ 
+
+ align:start position:0%
+and he he was the youngest person to fly
+around the world but there's also at
+
+ align:start position:0%
+around the world but there's also at
+ 
+
+ align:start position:0%
+around the world but there's also at
+Oshkosh we met this guy dick Rutan who
+
+ align:start position:0%
+Oshkosh we met this guy dick Rutan who
+ 
+
+ align:start position:0%
+Oshkosh we met this guy dick Rutan who
+flew around the world
+
+ align:start position:0%
+flew around the world
+ 
+
+ align:start position:0%
+flew around the world
+non-stop unrefueled in a clean design by
+
+ align:start position:0%
+non-stop unrefueled in a clean design by
+ 
+
+ align:start position:0%
+non-stop unrefueled in a clean design by
+his brother Burt Rutan what else is Burt
+
+ align:start position:0%
+his brother Burt Rutan what else is Burt
+ 
+
+ align:start position:0%
+his brother Burt Rutan what else is Burt
+Rutan famous for besides designing
+
+ align:start position:0%
+Rutan famous for besides designing
+ 
+
+ align:start position:0%
+Rutan famous for besides designing
+aircraft does anybody know
+
+ align:start position:0%
+aircraft does anybody know
+ 
+
+ align:start position:0%
+aircraft does anybody know
+what spacecraft that's true but yeah
+
+ align:start position:0%
+what spacecraft that's true but yeah
+ 
+
+ align:start position:0%
+what spacecraft that's true but yeah
+spacecraft and aircraft but what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+canard plane so there are airplanes
+
+ align:start position:0%
+canard plane so there are airplanes
+ 
+
+ align:start position:0%
+canard plane so there are airplanes
+climate change denial look it up he's
+
+ align:start position:0%
+climate change denial look it up he's
+ 
+
+ align:start position:0%
+climate change denial look it up he's
+got like a hundred page book about the
+
+ align:start position:0%
+got like a hundred page book about the
+ 
+
+ align:start position:0%
+got like a hundred page book about the
+scientific fraud of climate change but
+
+ align:start position:0%
+scientific fraud of climate change but
+ 
+
+ align:start position:0%
+scientific fraud of climate change but
+anyway dick Rutan the other interesting
+
+ align:start position:0%
+anyway dick Rutan the other interesting
+ 
+
+ align:start position:0%
+anyway dick Rutan the other interesting
+thing is before this nine-day flight he
+
+ align:start position:0%
+thing is before this nine-day flight he
+ 
+
+ align:start position:0%
+thing is before this nine-day flight he
+was engaged to be married to Jeana
+
+ align:start position:0%
+was engaged to be married to Jeana
+ 
+
+ align:start position:0%
+was engaged to be married to Jeana
+Jaeger and supposedly I what I heard was
+
+ align:start position:0%
+Jaeger and supposedly I what I heard was
+ 
+
+ align:start position:0%
+Jaeger and supposedly I what I heard was
+it at Oshkosh was they have not spoken
+
+ align:start position:0%
+it at Oshkosh was they have not spoken
+ 
+
+ align:start position:0%
+it at Oshkosh was they have not spoken
+since they landed in 1986
+
+ align:start position:0%
+since they landed in 1986
+ 
+
+ align:start position:0%
+since they landed in 1986
+so in nine days there can be quite a
+
+ align:start position:0%
+so in nine days there can be quite a
+ 
+
+ align:start position:0%
+so in nine days there can be quite a
+change in a relationship apparently we
+
+ align:start position:0%
+change in a relationship apparently we
+ 
+
+ align:start position:0%
+change in a relationship apparently we
+met this this pilot shyest hawaii's I
+
+ align:start position:0%
+met this this pilot shyest hawaii's I
+ 
+
+ align:start position:0%
+met this this pilot shyest hawaii's I
+don't know if that's the correct
+
+ align:start position:0%
+don't know if that's the correct
+ 
+
+ align:start position:0%
+don't know if that's the correct
+pronunciation she grew up in California
+
+ align:start position:0%
+pronunciation she grew up in California
+ 
+
+ align:start position:0%
+pronunciation she grew up in California
+and learned to fly relatively recently
+
+ align:start position:0%
+and learned to fly relatively recently
+ 
+
+ align:start position:0%
+and learned to fly relatively recently
+and she also flew a bonanza all the way
+
+ align:start position:0%
+and she also flew a bonanza all the way
+ 
+
+ align:start position:0%
+and she also flew a bonanza all the way
+around the world over 145 days so that
+
+ align:start position:0%
+around the world over 145 days so that
+ 
+
+ align:start position:0%
+around the world over 145 days so that
+was interesting she actually said it
+
+ align:start position:0%
+was interesting she actually said it
+ 
+
+ align:start position:0%
+was interesting she actually said it
+gets a little bit easier once you're out
+
+ align:start position:0%
+gets a little bit easier once you're out
+ 
+
+ align:start position:0%
+gets a little bit easier once you're out
+over the ocean from a weather point of
+
+ align:start position:0%
+over the ocean from a weather point of
+ 
+
+ align:start position:0%
+over the ocean from a weather point of
+view she said except for the
+
+ align:start position:0%
+view she said except for the
+ 
+
+ align:start position:0%
+view she said except for the
+Intertropical Convergence of the equator
+
+ align:start position:0%
+Intertropical Convergence of the equator
+ 
+
+ align:start position:0%
+Intertropical Convergence of the equator
+most weather is kind of a phenomenon of
+
+ align:start position:0%
+most weather is kind of a phenomenon of
+ 
+
+ align:start position:0%
+most weather is kind of a phenomenon of
+being overland to me the most impressive
+
+ align:start position:0%
+being overland to me the most impressive
+ 
+
+ align:start position:0%
+being overland to me the most impressive
+round-the-world pilot though was
+
+ align:start position:0%
+round-the-world pilot though was
+ 
+
+ align:start position:0%
+round-the-world pilot though was
+actually an Italian guy that I met he
+
+ align:start position:0%
+actually an Italian guy that I met he
+ 
+
+ align:start position:0%
+actually an Italian guy that I met he
+was in a Cirrus sr22 and he just flies
+
+ align:start position:0%
+was in a Cirrus sr22 and he just flies
+ 
+
+ align:start position:0%
+was in a Cirrus sr22 and he just flies
+to Oshkosh every year he just loads up
+
+ align:start position:0%
+to Oshkosh every year he just loads up
+ 
+
+ align:start position:0%
+to Oshkosh every year he just loads up
+in Italy turns the key and goes every
+
+ align:start position:0%
+in Italy turns the key and goes every
+ 
+
+ align:start position:0%
+in Italy turns the key and goes every
+year flies over the Atlantic and then
+
+ align:start position:0%
+year flies over the Atlantic and then
+ 
+
+ align:start position:0%
+year flies over the Atlantic and then
+flies back to Italy when it's over so I
+
+ align:start position:0%
+flies back to Italy when it's over so I
+ 
+
+ align:start position:0%
+flies back to Italy when it's over so I
+thought you know that is actually the
+
+ align:start position:0%
+thought you know that is actually the
+ 
+
+ align:start position:0%
+thought you know that is actually the
+coolest thing when it's not you know
+
+ align:start position:0%
+coolest thing when it's not you know
+ 
+
+ align:start position:0%
+coolest thing when it's not you know
+even an adventure you're not gonna write
+
+ align:start position:0%
+even an adventure you're not gonna write
+ 
+
+ align:start position:0%
+even an adventure you're not gonna write
+about it you're not gonna build a
+
+ align:start position:0%
+about it you're not gonna build a
+ 
+
+ align:start position:0%
+about it you're not gonna build a
+webpage you're not gonna say you're you
+
+ align:start position:0%
+webpage you're not gonna say you're you
+ 
+
+ align:start position:0%
+webpage you're not gonna say you're you
+know changing the world or helping to
+
+ align:start position:0%
+know changing the world or helping to
+ 
+
+ align:start position:0%
+know changing the world or helping to
+achieve something you're not gonna set a
+
+ align:start position:0%
+achieve something you're not gonna set a
+ 
+
+ align:start position:0%
+achieve something you're not gonna set a
+record you're just using your airplane
+
+ align:start position:0%
+record you're just using your airplane
+ 
+
+ align:start position:0%
+record you're just using your airplane
+for transportation you want to get to
+
+ align:start position:0%
+for transportation you want to get to
+ 
+
+ align:start position:0%
+for transportation you want to get to
+Oshkosh you have an airplane so why
+
+ align:start position:0%
+Oshkosh you have an airplane so why
+ 
+
+ align:start position:0%
+Oshkosh you have an airplane so why
+should the fact that you're on a
+
+ align:start position:0%
+should the fact that you're on a
+ 
+
+ align:start position:0%
+should the fact that you're on a
+different continent stopped you from
+
+ align:start position:0%
+different continent stopped you from
+ 
+
+ align:start position:0%
+different continent stopped you from
+doing it you know a lot of people have
+
+ align:start position:0%
+doing it you know a lot of people have
+ 
+
+ align:start position:0%
+doing it you know a lot of people have
+stopped doing home projects home repairs
+
+ align:start position:0%
+stopped doing home projects home repairs
+ 
+
+ align:start position:0%
+stopped doing home projects home repairs
+so Oshkosh they actually have people to
+
+ align:start position:0%
+so Oshkosh they actually have people to
+ 
+
+ align:start position:0%
+so Oshkosh they actually have people to
+teach kids you know how to hammer how to
+
+ align:start position:0%
+teach kids you know how to hammer how to
+ 
+
+ align:start position:0%
+teach kids you know how to hammer how to
+drill how to cut sheet metal there's a
+
+ align:start position:0%
+drill how to cut sheet metal there's a
+ 
+
+ align:start position:0%
+drill how to cut sheet metal there's a
+lot of great workshops there for kids we
+
+ align:start position:0%
+lot of great workshops there for kids we
+ 
+
+ align:start position:0%
+lot of great workshops there for kids we
+were over by the Pioneer Airport and the
+
+ align:start position:0%
+were over by the Pioneer Airport and the
+ 
+
+ align:start position:0%
+were over by the Pioneer Airport and the
+museum
+
+ align:start position:0%
+museum
+ 
+
+ align:start position:0%
+museum
+here's the museum they have a replica
+
+ align:start position:0%
+here's the museum they have a replica
+ 
+
+ align:start position:0%
+here's the museum they have a replica
+right flyer
+
+ align:start position:0%
+right flyer
+ 
+
+ align:start position:0%
+right flyer
+the whole area devoted to the route and
+
+ align:start position:0%
+the whole area devoted to the route and
+ 
+
+ align:start position:0%
+the whole area devoted to the route and
+designs I don't know how many I don't
+
+ align:start position:0%
+designs I don't know how many I don't
+ 
+
+ align:start position:0%
+designs I don't know how many I don't
+know how many you know the MIT spin-off
+
+ align:start position:0%
+know how many you know the MIT spin-off
+ 
+
+ align:start position:0%
+know how many you know the MIT spin-off
+Terrafugia I guess I think it was 12 at
+
+ align:start position:0%
+Terrafugia I guess I think it was 12 at
+ 
+
+ align:start position:0%
+Terrafugia I guess I think it was 12 at
+least 12 years ago they said they were
+
+ align:start position:0%
+least 12 years ago they said they were
+ 
+
+ align:start position:0%
+least 12 years ago they said they were
+gonna build a flying car so I took a
+
+ align:start position:0%
+gonna build a flying car so I took a
+ 
+
+ align:start position:0%
+gonna build a flying car so I took a
+picture of this 1949 Taylor Aero car
+
+ align:start position:0%
+picture of this 1949 Taylor Aero car
+ 
+
+ align:start position:0%
+picture of this 1949 Taylor Aero car
+which is actually a certificated flying
+
+ align:start position:0%
+which is actually a certificated flying
+ 
+
+ align:start position:0%
+which is actually a certificated flying
+car and unfairly associated with
+
+ align:start position:0%
+car and unfairly associated with
+ 
+
+ align:start position:0%
+car and unfairly associated with
+Terrafugia okay so this guy is kind of
+
+ align:start position:0%
+Terrafugia okay so this guy is kind of
+ 
+
+ align:start position:0%
+Terrafugia okay so this guy is kind of
+an inspiration I think Paul po Perez nee
+
+ align:start position:0%
+an inspiration I think Paul po Perez nee
+ 
+
+ align:start position:0%
+an inspiration I think Paul po Perez nee
+the founder of the Experimental Aircraft
+
+ align:start position:0%
+the founder of the Experimental Aircraft
+ 
+
+ align:start position:0%
+the founder of the Experimental Aircraft
+Association he flew the most expensive
+
+ align:start position:0%
+Association he flew the most expensive
+ 
+
+ align:start position:0%
+Association he flew the most expensive
+and highest performance aircraft of the
+
+ align:start position:0%
+and highest performance aircraft of the
+ 
+
+ align:start position:0%
+and highest performance aircraft of the
+day he flew the p-51 Mustang the p-38
+
+ align:start position:0%
+day he flew the p-51 Mustang the p-38
+ 
+
+ align:start position:0%
+day he flew the p-51 Mustang the p-38
+lightning and then he came home and said
+
+ align:start position:0%
+lightning and then he came home and said
+ 
+
+ align:start position:0%
+lightning and then he came home and said
+well what's cool to do after flying you
+
+ align:start position:0%
+well what's cool to do after flying you
+ 
+
+ align:start position:0%
+well what's cool to do after flying you
+know a 12,000 pound plus p-51 Mustang
+
+ align:start position:0%
+know a 12,000 pound plus p-51 Mustang
+ 
+
+ align:start position:0%
+know a 12,000 pound plus p-51 Mustang
+why not just you know go to the basement
+
+ align:start position:0%
+why not just you know go to the basement
+ 
+
+ align:start position:0%
+why not just you know go to the basement
+get some plywood nail it together and
+
+ align:start position:0%
+get some plywood nail it together and
+ 
+
+ align:start position:0%
+get some plywood nail it together and
+build a really crummy plywood airplane
+
+ align:start position:0%
+build a really crummy plywood airplane
+ 
+
+ align:start position:0%
+build a really crummy plywood airplane
+and that's what he did so it just shows
+
+ align:start position:0%
+and that's what he did so it just shows
+ 
+
+ align:start position:0%
+and that's what he did so it just shows
+the joy you know you don't have to have
+
+ align:start position:0%
+the joy you know you don't have to have
+ 
+
+ align:start position:0%
+the joy you know you don't have to have
+a high-performance state-of-the-art
+
+ align:start position:0%
+a high-performance state-of-the-art
+ 
+
+ align:start position:0%
+a high-performance state-of-the-art
+airplane if you build it yourself or
+
+ align:start position:0%
+airplane if you build it yourself or
+ 
+
+ align:start position:0%
+airplane if you build it yourself or
+you're goofing around you can have fun
+
+ align:start position:0%
+you're goofing around you can have fun
+ 
+
+ align:start position:0%
+you're goofing around you can have fun
+and he did and he was a better pilot you
+
+ align:start position:0%
+and he did and he was a better pilot you
+ 
+
+ align:start position:0%
+and he did and he was a better pilot you
+know then an alibi B I'm sure you know
+
+ align:start position:0%
+know then an alibi B I'm sure you know
+ 
+
+ align:start position:0%
+know then an alibi B I'm sure you know
+in his p-51 so that that made me think
+
+ align:start position:0%
+in his p-51 so that that made me think
+ 
+
+ align:start position:0%
+in his p-51 so that that made me think
+you know maybe we shouldn't be snobby
+
+ align:start position:0%
+you know maybe we shouldn't be snobby
+ 
+
+ align:start position:0%
+you know maybe we shouldn't be snobby
+about these slim build airplanes because
+
+ align:start position:0%
+about these slim build airplanes because
+ 
+
+ align:start position:0%
+about these slim build airplanes because
+if it was good enough you know po Perez
+
+ align:start position:0%
+if it was good enough you know po Perez
+ 
+
+ align:start position:0%
+if it was good enough you know po Perez
+and you had fun with it all right so
+
+ align:start position:0%
+and you had fun with it all right so
+ 
+
+ align:start position:0%
+and you had fun with it all right so
+here's some examples of homebuilts up at
+
+ align:start position:0%
+here's some examples of homebuilts up at
+ 
+
+ align:start position:0%
+here's some examples of homebuilts up at
+the left there there's some kind of
+
+ align:start position:0%
+the left there there's some kind of
+ 
+
+ align:start position:0%
+the left there there's some kind of
+canard velocity these folks spent 15
+
+ align:start position:0%
+canard velocity these folks spent 15
+ 
+
+ align:start position:0%
+canard velocity these folks spent 15
+years building this helicopter and they
+
+ align:start position:0%
+years building this helicopter and they
+ 
+
+ align:start position:0%
+years building this helicopter and they
+add about 40 hours of flight time on it
+
+ align:start position:0%
+add about 40 hours of flight time on it
+ 
+
+ align:start position:0%
+add about 40 hours of flight time on it
+so it's you know to me you know in a
+
+ align:start position:0%
+so it's you know to me you know in a
+ 
+
+ align:start position:0%
+so it's you know to me you know in a
+good in a good month at a flight school
+
+ align:start position:0%
+good in a good month at a flight school
+ 
+
+ align:start position:0%
+good in a good month at a flight school
+a Robinson helicopter might fly 90 hours
+
+ align:start position:0%
+a Robinson helicopter might fly 90 hours
+ 
+
+ align:start position:0%
+a Robinson helicopter might fly 90 hours
+or 100 hours in just a month so it was
+
+ align:start position:0%
+or 100 hours in just a month so it was
+ 
+
+ align:start position:0%
+or 100 hours in just a month so it was
+taking them you know take them 15 years
+
+ align:start position:0%
+taking them you know take them 15 years
+ 
+
+ align:start position:0%
+taking them you know take them 15 years
+plus to get to where a flight school
+
+ align:start position:0%
+plus to get to where a flight school
+ 
+
+ align:start position:0%
+plus to get to where a flight school
+would get in a month but you know that's
+
+ align:start position:0%
+would get in a month but you know that's
+ 
+
+ align:start position:0%
+would get in a month but you know that's
+kind of not the point it's not about
+
+ align:start position:0%
+kind of not the point it's not about
+ 
+
+ align:start position:0%
+kind of not the point it's not about
+efficiency apparently that's a rotor way
+
+ align:start position:0%
+efficiency apparently that's a rotor way
+ 
+
+ align:start position:0%
+efficiency apparently that's a rotor way
+kid I bet and they modified it by
+
+ align:start position:0%
+kid I bet and they modified it by
+ 
+
+ align:start position:0%
+kid I bet and they modified it by
+sticking in a little tiny turbine engine
+
+ align:start position:0%
+sticking in a little tiny turbine engine
+ 
+
+ align:start position:0%
+sticking in a little tiny turbine engine
+this is another modification this is a
+
+ align:start position:0%
+this is another modification this is a
+ 
+
+ align:start position:0%
+this is another modification this is a
+Rutan design that became the bear coot
+
+ align:start position:0%
+Rutan design that became the bear coot
+ 
+
+ align:start position:0%
+Rutan design that became the bear coot
+with a big piston engine this guy stuck
+
+ align:start position:0%
+with a big piston engine this guy stuck
+ 
+
+ align:start position:0%
+with a big piston engine this guy stuck
+hey a turbojet engine here's the company
+
+ align:start position:0%
+hey a turbojet engine here's the company
+ 
+
+ align:start position:0%
+hey a turbojet engine here's the company
+42,000 I think that doesn't include the
+
+ align:start position:0%
+42,000 I think that doesn't include the
+ 
+
+ align:start position:0%
+42,000 I think that doesn't include the
+engine which is another 50 you can build
+
+ align:start position:0%
+engine which is another 50 you can build
+ 
+
+ align:start position:0%
+engine which is another 50 you can build
+your own little single-seat jet Cirrus
+
+ align:start position:0%
+your own little single-seat jet Cirrus
+ 
+
+ align:start position:0%
+your own little single-seat jet Cirrus
+was there serious actually has been kind
+
+ align:start position:0%
+was there serious actually has been kind
+ 
+
+ align:start position:0%
+was there serious actually has been kind
+of a industry change in company it
+
+ align:start position:0%
+of a industry change in company it
+ 
+
+ align:start position:0%
+of a industry change in company it
+didn't seem that way at the time because
+
+ align:start position:0%
+didn't seem that way at the time because
+ 
+
+ align:start position:0%
+didn't seem that way at the time because
+it's very similar in performance the
+
+ align:start position:0%
+it's very similar in performance the
+ 
+
+ align:start position:0%
+it's very similar in performance the
+Moonies and Piper's and Cessnas but they
+
+ align:start position:0%
+Moonies and Piper's and Cessnas but they
+ 
+
+ align:start position:0%
+Moonies and Piper's and Cessnas but they
+really have revolutionized the way that
+
+ align:start position:0%
+really have revolutionized the way that
+ 
+
+ align:start position:0%
+really have revolutionized the way that
+you know families buy airplanes now and
+
+ align:start position:0%
+you know families buy airplanes now and
+ 
+
+ align:start position:0%
+you know families buy airplanes now and
+they've got over 7,000 of them the
+
+ align:start position:0%
+they've got over 7,000 of them the
+ 
+
+ align:start position:0%
+they've got over 7,000 of them the
+parachute is I think critical to getting
+
+ align:start position:0%
+parachute is I think critical to getting
+ 
+
+ align:start position:0%
+parachute is I think critical to getting
+modern people to accept this design and
+
+ align:start position:0%
+modern people to accept this design and
+ 
+
+ align:start position:0%
+modern people to accept this design and
+also the glass cockpit does make life
+
+ align:start position:0%
+also the glass cockpit does make life
+ 
+
+ align:start position:0%
+also the glass cockpit does make life
+easier although everybody else has
+
+ align:start position:0%
+easier although everybody else has
+ 
+
+ align:start position:0%
+easier although everybody else has
+caught up there here's the icon a5 they
+
+ align:start position:0%
+caught up there here's the icon a5 they
+ 
+
+ align:start position:0%
+caught up there here's the icon a5 they
+had the same booth every year a huge
+
+ align:start position:0%
+had the same booth every year a huge
+ 
+
+ align:start position:0%
+had the same booth every year a huge
+amount of excitement people love it a
+
+ align:start position:0%
+amount of excitement people love it a
+ 
+
+ align:start position:0%
+amount of excitement people love it a
+lot of people have ordered it they
+
+ align:start position:0%
+lot of people have ordered it they
+ 
+
+ align:start position:0%
+lot of people have ordered it they
+haven't figured out how to build it you
+
+ align:start position:0%
+haven't figured out how to build it you
+ 
+
+ align:start position:0%
+haven't figured out how to build it you
+know the price has gotten got to the
+
+ align:start position:0%
+know the price has gotten got to the
+ 
+
+ align:start position:0%
+know the price has gotten got to the
+point where you can almost buy a Cessna
+
+ align:start position:0%
+point where you can almost buy a Cessna
+ 
+
+ align:start position:0%
+point where you can almost buy a Cessna
+Caravan on floats with a jet engine for
+
+ align:start position:0%
+Caravan on floats with a jet engine for
+ 
+
+ align:start position:0%
+Caravan on floats with a jet engine for
+the same price here's a retired airforce
+
+ align:start position:0%
+the same price here's a retired airforce
+ 
+
+ align:start position:0%
+the same price here's a retired airforce
+and Southwest Airlines pilot with his
+
+ align:start position:0%
+and Southwest Airlines pilot with his
+ 
+
+ align:start position:0%
+and Southwest Airlines pilot with his
+electric self launching pipistrelle
+
+ align:start position:0%
+electric self launching pipistrelle
+ 
+
+ align:start position:0%
+electric self launching pipistrelle
+glider the past role is the company to
+
+ align:start position:0%
+glider the past role is the company to
+ 
+
+ align:start position:0%
+glider the past role is the company to
+watch they do a lot of interesting stuff
+
+ align:start position:0%
+watch they do a lot of interesting stuff
+ 
+
+ align:start position:0%
+watch they do a lot of interesting stuff
+in Slovenia
+
+ align:start position:0%
+in Slovenia
+ 
+
+ align:start position:0%
+in Slovenia
+especially with electrics this is not
+
+ align:start position:0%
+especially with electrics this is not
+ 
+
+ align:start position:0%
+especially with electrics this is not
+the kind of radar picture you want to
+
+ align:start position:0%
+the kind of radar picture you want to
+ 
+
+ align:start position:0%
+the kind of radar picture you want to
+see when you're in the $99 tent I will
+
+ align:start position:0%
+see when you're in the $99 tent I will
+ 
+
+ align:start position:0%
+see when you're in the $99 tent I will
+say I will say to Costco that it did
+
+ align:start position:0%
+say I will say to Costco that it did
+ 
+
+ align:start position:0%
+say I will say to Costco that it did
+hold up remarkably well but it was scary
+
+ align:start position:0%
+hold up remarkably well but it was scary
+ 
+
+ align:start position:0%
+hold up remarkably well but it was scary
+the seaplane base a few miles away from
+
+ align:start position:0%
+the seaplane base a few miles away from
+ 
+
+ align:start position:0%
+the seaplane base a few miles away from
+Oshkosh they have the Oshkosh seaplane
+
+ align:start position:0%
+Oshkosh they have the Oshkosh seaplane
+ 
+
+ align:start position:0%
+Oshkosh they have the Oshkosh seaplane
+base
+
+ align:start position:0%
+base
+ 
+
+ align:start position:0%
+base
+I think it's on Lake Winnebago so you
+
+ align:start position:0%
+I think it's on Lake Winnebago so you
+ 
+
+ align:start position:0%
+I think it's on Lake Winnebago so you
+take the shuttle bus or you drive over
+
+ align:start position:0%
+take the shuttle bus or you drive over
+ 
+
+ align:start position:0%
+take the shuttle bus or you drive over
+there if you have a rental car so you'll
+
+ align:start position:0%
+there if you have a rental car so you'll
+ 
+
+ align:start position:0%
+there if you have a rental car so you'll
+see you know they call it the quiet part
+
+ align:start position:0%
+see you know they call it the quiet part
+ 
+
+ align:start position:0%
+see you know they call it the quiet part
+of Akasha it's quiet because you only
+
+ align:start position:0%
+of Akasha it's quiet because you only
+ 
+
+ align:start position:0%
+of Akasha it's quiet because you only
+hear about three or four aircraft
+
+ align:start position:0%
+hear about three or four aircraft
+ 
+
+ align:start position:0%
+hear about three or four aircraft
+engines running at any one time and
+
+ align:start position:0%
+engines running at any one time and
+ 
+
+ align:start position:0%
+engines running at any one time and
+maybe two takeoffs or landings they have
+
+ align:start position:0%
+maybe two takeoffs or landings they have
+ 
+
+ align:start position:0%
+maybe two takeoffs or landings they have
+four hangars vendors if you want to take
+
+ align:start position:0%
+four hangars vendors if you want to take
+ 
+
+ align:start position:0%
+four hangars vendors if you want to take
+your dog and an unpressurized airplane
+
+ align:start position:0%
+your dog and an unpressurized airplane
+ 
+
+ align:start position:0%
+your dog and an unpressurized airplane
+up to 18,000 feet you can buy this kit I
+
+ align:start position:0%
+up to 18,000 feet you can buy this kit I
+ 
+
+ align:start position:0%
+up to 18,000 feet you can buy this kit I
+don't know what our golden retriever
+
+ align:start position:0%
+don't know what our golden retriever
+ 
+
+ align:start position:0%
+don't know what our golden retriever
+would say about that
+
+ align:start position:0%
+would say about that
+ 
+
+ align:start position:0%
+would say about that
+there's affinity groups
+
+ align:start position:0%
+there's affinity groups
+ 
+
+ align:start position:0%
+there's affinity groups
+you know four different slices here's
+
+ align:start position:0%
+you know four different slices here's
+ 
+
+ align:start position:0%
+you know four different slices here's
+one a woman who just like just for
+
+ align:start position:0%
+one a woman who just like just for
+ 
+
+ align:start position:0%
+one a woman who just like just for
+female pilots of Muniz air shows every
+
+ align:start position:0%
+female pilots of Muniz air shows every
+ 
+
+ align:start position:0%
+female pilots of Muniz air shows every
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+my favorite acts actually were I did
+
+ align:start position:0%
+my favorite acts actually were I did
+ 
+
+ align:start position:0%
+my favorite acts actually were I did
+like the game bird that was cool but I
+
+ align:start position:0%
+like the game bird that was cool but I
+ 
+
+ align:start position:0%
+like the game bird that was cool but I
+also liked this first two were kind of
+
+ align:start position:0%
+also liked this first two were kind of
+ 
+
+ align:start position:0%
+also liked this first two were kind of
+regular family airplanes just being
+
+ align:start position:0%
+regular family airplanes just being
+ 
+
+ align:start position:0%
+regular family airplanes just being
+pushed to their limits it wouldn't be
+
+ align:start position:0%
+pushed to their limits it wouldn't be
+ 
+
+ align:start position:0%
+pushed to their limits it wouldn't be
+legal just to go out and do that in a
+
+ align:start position:0%
+legal just to go out and do that in a
+ 
+
+ align:start position:0%
+legal just to go out and do that in a
+barren because you can't do acrobatics
+
+ align:start position:0%
+barren because you can't do acrobatics
+ 
+
+ align:start position:0%
+barren because you can't do acrobatics
+but he would help put it into
+
+ align:start position:0%
+but he would help put it into
+ 
+
+ align:start position:0%
+but he would help put it into
+experimental category and then just fly
+
+ align:start position:0%
+experimental category and then just fly
+ 
+
+ align:start position:0%
+experimental category and then just fly
+it right up to the G limits for which it
+
+ align:start position:0%
+it right up to the G limits for which it
+ 
+
+ align:start position:0%
+it right up to the G limits for which it
+was designed and it's amazing to see
+
+ align:start position:0%
+was designed and it's amazing to see
+ 
+
+ align:start position:0%
+was designed and it's amazing to see
+what these you know ordinary family or
+
+ align:start position:0%
+what these you know ordinary family or
+ 
+
+ align:start position:0%
+what these you know ordinary family or
+business airplanes can do when pushed
+
+ align:start position:0%
+business airplanes can do when pushed
+ 
+
+ align:start position:0%
+business airplanes can do when pushed
+there were one thing is interesting
+
+ align:start position:0%
+there were one thing is interesting
+ 
+
+ align:start position:0%
+there were one thing is interesting
+about 150 Beechcraft aerobatic bonanzas
+
+ align:start position:0%
+about 150 Beechcraft aerobatic bonanzas
+ 
+
+ align:start position:0%
+about 150 Beechcraft aerobatic bonanzas
+were built they were strengthened and it
+
+ align:start position:0%
+were built they were strengthened and it
+ 
+
+ align:start position:0%
+were built they were strengthened and it
+is legal to do aerobatics in your four
+
+ align:start position:0%
+is legal to do aerobatics in your four
+ 
+
+ align:start position:0%
+is legal to do aerobatics in your four
+seed Bonanza night airshow I guess
+
+ align:start position:0%
+seed Bonanza night airshow I guess
+ 
+
+ align:start position:0%
+seed Bonanza night airshow I guess
+that's worth showing it is so unusual
+
+ align:start position:0%
+that's worth showing it is so unusual
+ 
+
+ align:start position:0%
+that's worth showing it is so unusual
+they had explosives and fireworks
+
+ align:start position:0%
+they had explosives and fireworks
+ 
+
+ align:start position:0%
+they had explosives and fireworks
+mounted on the aircraft so they fly
+
+ align:start position:0%
+mounted on the aircraft so they fly
+ 
+
+ align:start position:0%
+mounted on the aircraft so they fly
+around at night shooting fireworks off I
+
+ align:start position:0%
+around at night shooting fireworks off I
+ 
+
+ align:start position:0%
+around at night shooting fireworks off I
+guess you may have to you may have to
+
+ align:start position:0%
+guess you may have to you may have to
+ 
+
+ align:start position:0%
+guess you may have to you may have to
+view that on your own which isn't so bad
+
+ align:start position:0%
+view that on your own which isn't so bad
+ 
+
+ align:start position:0%
+view that on your own which isn't so bad
+a lot of warbirds everything from World
+
+ align:start position:0%
+a lot of warbirds everything from World
+ 
+
+ align:start position:0%
+a lot of warbirds everything from World
+War two is still flying pretty much at
+
+ align:start position:0%
+War two is still flying pretty much at
+ 
+
+ align:start position:0%
+War two is still flying pretty much at
+Oshkosh that Grumman tiger cat on the
+
+ align:start position:0%
+Oshkosh that Grumman tiger cat on the
+ 
+
+ align:start position:0%
+Oshkosh that Grumman tiger cat on the
+right I'd never even heard of that
+
+ align:start position:0%
+right I'd never even heard of that
+ 
+
+ align:start position:0%
+right I'd never even heard of that
+airplane until I saw it at Oshkosh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's I think this is EA's own b-17
+
+ align:start position:0%
+that's I think this is EA's own b-17
+ 
+
+ align:start position:0%
+that's I think this is EA's own b-17
+which they fly around and sell rides and
+
+ align:start position:0%
+which they fly around and sell rides and
+ 
+
+ align:start position:0%
+which they fly around and sell rides and
+and stuff
+
+ align:start position:0%
+and stuff
+ 
+
+ align:start position:0%
+and stuff
+oh and up on the top right is a flying
+
+ align:start position:0%
+oh and up on the top right is a flying
+ 
+
+ align:start position:0%
+oh and up on the top right is a flying
+1/3 scale b-17 that some crazy guy spent
+
+ align:start position:0%
+1/3 scale b-17 that some crazy guy spent
+ 
+
+ align:start position:0%
+1/3 scale b-17 that some crazy guy spent
+15 years building or more
+
+ align:start position:0%
+15 years building or more
+ 
+
+ align:start position:0%
+15 years building or more
+that's EAA also they have a b-29 up
+
+ align:start position:0%
+that's EAA also they have a b-29 up
+ 
+
+ align:start position:0%
+that's EAA also they have a b-29 up
+there the top right is my friend Erik
+
+ align:start position:0%
+there the top right is my friend Erik
+ 
+
+ align:start position:0%
+there the top right is my friend Erik
+with his personal I guess he hasn't
+
+ align:start position:0%
+with his personal I guess he hasn't
+ 
+
+ align:start position:0%
+with his personal I guess he hasn't
+found a ssin with a few other people but
+
+ align:start position:0%
+found a ssin with a few other people but
+ 
+
+ align:start position:0%
+found a ssin with a few other people but
+he's essentially a personal dc-3 oh and
+
+ align:start position:0%
+he's essentially a personal dc-3 oh and
+ 
+
+ align:start position:0%
+he's essentially a personal dc-3 oh and
+he's flying up to Europe this year for
+
+ align:start position:0%
+he's flying up to Europe this year for
+ 
+
+ align:start position:0%
+he's flying up to Europe this year for
+the 50th anniversary of d-day is it the
+
+ align:start position:0%
+the 50th anniversary of d-day is it the
+ 
+
+ align:start position:0%
+the 50th anniversary of d-day is it the
+50th no it can't be
+
+ align:start position:0%
+50th no it can't be
+ 
+
+ align:start position:0%
+50th no it can't be
+what seventy-fifth sorry thank you I was
+
+ align:start position:0%
+what seventy-fifth sorry thank you I was
+ 
+
+ align:start position:0%
+what seventy-fifth sorry thank you I was
+in math undergrad good illustration of
+
+ align:start position:0%
+in math undergrad good illustration of
+ 
+
+ align:start position:0%
+in math undergrad good illustration of
+the value of a course 18 degree and
+
+ align:start position:0%
+the value of a course 18 degree and
+ 
+
+ align:start position:0%
+the value of a course 18 degree and
+actually when I was in undergrad people
+
+ align:start position:0%
+actually when I was in undergrad people
+ 
+
+ align:start position:0%
+actually when I was in undergrad people
+said how will you ever get a job if
+
+ align:start position:0%
+said how will you ever get a job if
+ 
+
+ align:start position:0%
+said how will you ever get a job if
+you're a math major the engineers all
+
+ align:start position:0%
+you're a math major the engineers all
+ 
+
+ align:start position:0%
+you're a math major the engineers all
+said that when you said well we can
+
+ align:start position:0%
+said that when you said well we can
+ 
+
+ align:start position:0%
+said that when you said well we can
+become actuaries we can become actuaries
+
+ align:start position:0%
+become actuaries we can become actuaries
+ 
+
+ align:start position:0%
+become actuaries we can become actuaries
+if there's a group of folks who are
+
+ align:start position:0%
+if there's a group of folks who are
+ 
+
+ align:start position:0%
+if there's a group of folks who are
+passionate about warbirds down in the
+
+ align:start position:0%
+passionate about warbirds down in the
+ 
+
+ align:start position:0%
+passionate about warbirds down in the
+south and they called their organization
+
+ align:start position:0%
+south and they called their organization
+ 
+
+ align:start position:0%
+south and they called their organization
+the Confederate air Confederate Air
+
+ align:start position:0%
+the Confederate air Confederate Air
+ 
+
+ align:start position:0%
+the Confederate air Confederate Air
+Force well they've had to change that
+
+ align:start position:0%
+Force well they've had to change that
+ 
+
+ align:start position:0%
+Force well they've had to change that
+now they're the commemorative Air Force
+
+ align:start position:0%
+now they're the commemorative Air Force
+ 
+
+ align:start position:0%
+now they're the commemorative Air Force
+and they're big into they brought the
+
+ align:start position:0%
+and they're big into they brought the
+ 
+
+ align:start position:0%
+and they're big into they brought the
+Tuskeegee Airmen some of the remaining
+
+ align:start position:0%
+Tuskeegee Airmen some of the remaining
+ 
+
+ align:start position:0%
+Tuskeegee Airmen some of the remaining
+p-51 guys from World War two there I
+
+ align:start position:0%
+p-51 guys from World War two there I
+ 
+
+ align:start position:0%
+p-51 guys from World War two there I
+gave a talk with Noah that's Kate from
+
+ align:start position:0%
+gave a talk with Noah that's Kate from
+ 
+
+ align:start position:0%
+gave a talk with Noah that's Kate from
+NOAA trying to get volunteer pilots to
+
+ align:start position:0%
+NOAA trying to get volunteer pilots to
+ 
+
+ align:start position:0%
+NOAA trying to get volunteer pilots to
+fly sea turtles back from Cape Cod and
+
+ align:start position:0%
+fly sea turtles back from Cape Cod and
+ 
+
+ align:start position:0%
+fly sea turtles back from Cape Cod and
+other northern places to Florida Sunday
+
+ align:start position:0%
+other northern places to Florida Sunday
+ 
+
+ align:start position:0%
+other northern places to Florida Sunday
+morning it was time to leave I for me I
+
+ align:start position:0%
+morning it was time to leave I for me I
+ 
+
+ align:start position:0%
+morning it was time to leave I for me I
+saw a 30% of what we'd hope to see and
+
+ align:start position:0%
+saw a 30% of what we'd hope to see and
+ 
+
+ align:start position:0%
+saw a 30% of what we'd hope to see and
+1% of what there was to see as you can
+
+ align:start position:0%
+1% of what there was to see as you can
+ 
+
+ align:start position:0%
+1% of what there was to see as you can
+see from the right that one week wonder
+
+ align:start position:0%
+see from the right that one week wonder
+ 
+
+ align:start position:0%
+see from the right that one week wonder
+is coming together it actually did fly I
+
+ align:start position:0%
+is coming together it actually did fly I
+ 
+
+ align:start position:0%
+is coming together it actually did fly I
+believe on Sunday so they they got it
+
+ align:start position:0%
+believe on Sunday so they they got it
+ 
+
+ align:start position:0%
+believe on Sunday so they they got it
+built in seven or eight days we went to
+
+ align:start position:0%
+built in seven or eight days we went to
+ 
+
+ align:start position:0%
+built in seven or eight days we went to
+Mackinac Island beautiful place up near
+
+ align:start position:0%
+Mackinac Island beautiful place up near
+ 
+
+ align:start position:0%
+Mackinac Island beautiful place up near
+the Canadian border
+
+ align:start position:0%
+the Canadian border
+ 
+
+ align:start position:0%
+the Canadian border
+everything is horse-drawn or bicycle fun
+
+ align:start position:0%
+everything is horse-drawn or bicycle fun
+ 
+
+ align:start position:0%
+everything is horse-drawn or bicycle fun
+place to go in the airplane we went we
+
+ align:start position:0%
+place to go in the airplane we went we
+ 
+
+ align:start position:0%
+place to go in the airplane we went we
+went and landed to Toronto City Island
+
+ align:start position:0%
+went and landed to Toronto City Island
+ 
+
+ align:start position:0%
+went and landed to Toronto City Island
+Airport which is right in front of
+
+ align:start position:0%
+Airport which is right in front of
+ 
+
+ align:start position:0%
+Airport which is right in front of
+downtown we had Chinese food
+
+ align:start position:0%
+downtown we had Chinese food
+ 
+
+ align:start position:0%
+downtown we had Chinese food
+so the aquarium landed back in Bedford
+
+ align:start position:0%
+so the aquarium landed back in Bedford
+ 
+
+ align:start position:0%
+so the aquarium landed back in Bedford
+so we burned up 15 hours of Hobbes time
+
+ align:start position:0%
+so we burned up 15 hours of Hobbes time
+ 
+
+ align:start position:0%
+so we burned up 15 hours of Hobbes time
+split by three people that wouldn't be
+
+ align:start position:0%
+split by three people that wouldn't be
+ 
+
+ align:start position:0%
+split by three people that wouldn't be
+too horrible it was about three thousand
+
+ align:start position:0%
+too horrible it was about three thousand
+ 
+
+ align:start position:0%
+too horrible it was about three thousand
+dollars at retail next year I think it
+
+ align:start position:0%
+dollars at retail next year I think it
+ 
+
+ align:start position:0%
+dollars at retail next year I think it
+might be time to go JetBlue so the
+
+ align:start position:0%
+might be time to go JetBlue so the
+ 
+
+ align:start position:0%
+might be time to go JetBlue so the
+summary is that you know even as the
+
+ align:start position:0%
+summary is that you know even as the
+ 
+
+ align:start position:0%
+summary is that you know even as the
+regulation has made light aircraft
+
+ align:start position:0%
+regulation has made light aircraft
+ 
+
+ align:start position:0%
+regulation has made light aircraft
+almost as expensive to operate
+
+ align:start position:0%
+almost as expensive to operate
+ 
+
+ align:start position:0%
+almost as expensive to operate
+commercially at least or for charter has
+
+ align:start position:0%
+commercially at least or for charter has
+ 
+
+ align:start position:0%
+commercially at least or for charter has
+the big aircraft so but Oshkosh keeps
+
+ align:start position:0%
+the big aircraft so but Oshkosh keeps
+ 
+
+ align:start position:0%
+the big aircraft so but Oshkosh keeps
+growing every year more people are
+
+ align:start position:0%
+growing every year more people are
+ 
+
+ align:start position:0%
+growing every year more people are
+passionate about it so what you're
+
+ align:start position:0%
+passionate about it so what you're
+ 
+
+ align:start position:0%
+passionate about it so what you're
+seeing in the aircraft world is like the
+
+ align:start position:0%
+seeing in the aircraft world is like the
+ 
+
+ align:start position:0%
+seeing in the aircraft world is like the
+very high-end and the very low end or
+
+ align:start position:0%
+very high-end and the very low end or
+ 
+
+ align:start position:0%
+very high-end and the very low end or
+kind of prospering
+
+ align:start position:0%
+kind of prospering
+ 
+
+ align:start position:0%
+kind of prospering
+this is Oksana Stang she asked everybody
+
+ align:start position:0%
+this is Oksana Stang she asked everybody
+ 
+
+ align:start position:0%
+this is Oksana Stang she asked everybody
+like what brings you to ash cops and
+
+ align:start position:0%
+like what brings you to ash cops and
+ 
+
+ align:start position:0%
+like what brings you to ash cops and
+they always said the people I love
+
+ align:start position:0%
+they always said the people I love
+ 
+
+ align:start position:0%
+they always said the people I love
+talking to the people here and I feel
+
+ align:start position:0%
+talking to the people here and I feel
+ 
+
+ align:start position:0%
+talking to the people here and I feel
+that way too people go you know year
+
+ align:start position:0%
+that way too people go you know year
+ 
+
+ align:start position:0%
+that way too people go you know year
+after year there's a whole bunch of
+
+ align:start position:0%
+after year there's a whole bunch of
+ 
+
+ align:start position:0%
+after year there's a whole bunch of
+Link's here in the presentation and
+
+ align:start position:0%
+Link's here in the presentation and
+ 
+
+ align:start position:0%
+Link's here in the presentation and
+finally you know what I like most about
+
+ align:start position:0%
+finally you know what I like most about
+ 
+
+ align:start position:0%
+finally you know what I like most about
+it is and the reason I'm going back I
+
+ align:start position:0%
+it is and the reason I'm going back I
+ 
+
+ align:start position:0%
+it is and the reason I'm going back I
+think is it's it's my safe space outside
+
+ align:start position:0%
+think is it's it's my safe space outside
+ 
+
+ align:start position:0%
+think is it's it's my safe space outside
+of this room if I tell people you know I
+
+ align:start position:0%
+of this room if I tell people you know I
+ 
+
+ align:start position:0%
+of this room if I tell people you know I
+have to go over to Hanscom field and buy
+
+ align:start position:0%
+have to go over to Hanscom field and buy
+ 
+
+ align:start position:0%
+have to go over to Hanscom field and buy
+this little four seat airplane with a
+
+ align:start position:0%
+this little four seat airplane with a
+ 
+
+ align:start position:0%
+this little four seat airplane with a
+piston engine they're horrified that's
+
+ align:start position:0%
+piston engine they're horrified that's
+ 
+
+ align:start position:0%
+piston engine they're horrified that's
+just so dumb you could just drive to New
+
+ align:start position:0%
+just so dumb you could just drive to New
+ 
+
+ align:start position:0%
+just so dumb you could just drive to New
+York in your Honda you could get a
+
+ align:start position:0%
+York in your Honda you could get a
+ 
+
+ align:start position:0%
+York in your Honda you could get a
+ticket on JetBlue for no money like why
+
+ align:start position:0%
+ticket on JetBlue for no money like why
+ 
+
+ align:start position:0%
+ticket on JetBlue for no money like why
+would you do that it's dumb but Oshkosh
+
+ align:start position:0%
+would you do that it's dumb but Oshkosh
+ 
+
+ align:start position:0%
+would you do that it's dumb but Oshkosh
+is the one place where nobody will say
+
+ align:start position:0%
+is the one place where nobody will say
+ 
+
+ align:start position:0%
+is the one place where nobody will say
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/srjNMMtPATo.txt b/srjNMMtPATo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..453995513c544c4e6dd5c31f3952fd35341186b0
--- /dev/null
+++ b/srjNMMtPATo.txt
@@ -0,0 +1,1823 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Alright.
+
+Well, we've been looking in the
+last couple lectures at a
+
+really important topic
+in thermodynamics.
+
+Which is, how do you tell
+what's going to happen.
+
+Which way does a process
+want to go?
+
+Which way will it go
+spontaneously?
+
+And if it goes in one direction
+or another, where
+
+does is lead?
+
+In other words, what is
+the equilibrium state?
+
+And this is just an incredibly
+important area that
+
+thermodynamics allows
+us to speak to.
+
+So we started to see this.
+
+Sort of direction of
+spontaneous change.
+
+And where the equilibrium
+lies.
+
+So what we did is, remember we
+started with the second law.
+
+Right?
+
+That dS is greater than
+dq over T. And for the
+
+spontaneous change which happens
+irreversibly That
+
+means that'll be dq
+irreversible.
+
+It would be equal for
+the reversible case.
+
+And we combine this with first
+law, which for the case of
+
+pressure volume changes
+we write as this.
+
+And so what this gave us was
+a very, very useful general
+
+criterion for determining
+whether something happened
+
+spontaneously.
+
+Namely, du plus p external dV
+minus T for the surroundings
+
+dS, is greater than zero.
+
+Sorry.
+
+It's less than zero.
+
+And this is for any spontaneous
+change.
+
+If it equals zero, then
+we're at equilibrium.
+
+And if it's greater than
+zero, then the process
+
+goes the other way.
+
+We would write the process in
+the reverse to have it be less
+
+than 0 and it would
+go spontaneously.
+
+And based on this one result,
+we then looked under various
+
+constraints and said OK, what
+about looking at our
+
+variables, volume, pressure,
+temperature, other things,
+
+entropy, if we constrain those,
+what's the condition
+
+for equilibrium?
+
+And that's what led us to a
+number of results to determine
+
+what quantities we even
+need to be looking at.
+
+To figure out equilibrium.
+
+And what the conditions were.
+
+And so what we discovered
+were the following.
+
+This one, which we already
+had seen, which is dS, is
+
+greater than zero.
+
+Change in entropy is
+greater than zero,
+
+for an isolated system.
+
+We also saw that dS for constant
+H and p was greater
+
+than zero. du, regular energy,
+at constant entropy and volume
+
+is less then zero.
+
+And u is minimized
+at equilibrium.
+
+And this is the familiar
+result from ordinary
+
+mechanics, where you're not
+worrying about something like
+
+entropy for a whole collection
+of particles.
+
+That is, you minimize potential
+energy and you see
+
+things falling under the force
+of gravity and so forth, going
+
+to potential energy minima in
+conformance with this result.
+
+dH, S and p is less than zero.
+
+So our H is u plus
+pV, as you know.
+
+And H is minimized
+at equilibrium.
+
+And this is, of course, with
+constant S V. This is
+
+constant S and p.
+
+But of course, the need to have
+entropy constrained is
+
+never going to be the most
+convenient one experimental.
+
+There may be circumstances under
+which it's the case, but
+
+it's often difficult
+to control.
+
+On the other hand, temperature,
+volume and
+
+pressure are variables that are
+much easier in the lab to
+
+keep constant.
+
+To keep control over.
+
+And so that led us to the
+definitions of other energy
+
+quantities, the Helmholtz
+and Gibbs free energy.
+
+We discovered that the quantity
+dA, under conditions
+
+of constant volume
+and temperature,
+
+is less than zero.
+
+And A is u minus TS.
+
+And A is minimized at
+equilibrium, under conditions
+
+of constant T and V. And
+finally, and in many cases the
+
+most important of the results,
+because of the conditions it
+
+applies to, we saw that this
+Gibbs free energy is less than
+
+zero, that's our condition
+for spontaneous change.
+
+Where the Gibbs free energy,
+u plus pV minus
+
+TS is H minus TS.
+
+Also A plus pV and G is
+minimized at equilibrium with
+
+constant temperature
+and pressure.
+
+And that's why the Gibbs
+free energy is just
+
+so enormously important.
+
+Because so much of what we do
+in chemistry does take place
+
+with constant temperature
+and pressure.
+
+So we have this condition
+that's established in a
+
+quantity that we know
+how to calculate.
+
+That tells us the direction
+of spontaneous change for
+
+ordinary processes, chemical
+processes, mixing and you name
+
+it, under conditions that are
+easy to achieve in the lab.
+
+OK, now what we'd like to do is
+be able to calculate any of
+
+these quantities in terms of
+temperature, pressure, volume
+
+properties.
+
+That is, in terms of
+equations of state.
+
+For any material.
+
+Then we would really be able to
+
+essentially calculate anything.
+
+Anything thermodynamic.
+
+About a material.
+
+Of course, that's assuming we
+know the equation of state.
+
+We may or may not.
+
+But because in many cases we can
+reasonably either model or
+
+measure equations of state,
+collect data for a material
+
+for its temperature, pressure,
+volume relations, then in fact
+
+if we can relate all these
+quantities to those, then in
+
+fact we really can calculate
+essentially all of the
+
+thermodynamics.
+
+For the material.
+
+So let's relate the
+thermodynamic quantities to
+
+equation of state
+p, V, T data.
+
+And we can do that by going
+through and deriving what
+
+we'll call the fundamental
+equations of thermodynamics.
+
+that'll provide these
+relations.
+
+And at this point we know
+enough to do this in a
+
+straightforward way.
+
+So if we start with a relation
+for energy, T dS minus p dV.
+
+Where u is written
+as a function
+
+of entropy and volume.
+
+And we've seen that that's
+generally the case.
+
+It comes from the fact that dq
+reversible is T dS, and dw
+
+reversible is minus p dV.
+
+And of course du is
+the some of those.
+
+So, this is generally true.
+
+Since these are all
+state functions.
+
+That is, this is derived in the
+case for reversible paths.
+
+But since these are all simply
+state functions and
+
+quantities, this is
+generally true.
+
+Now we can use it to derive
+differential relations for all
+
+of the thermodynamics
+quantities.
+
+So let's just go through
+and do that.
+
+So H is u plus pV.
+
+So dH is just du plus
+p dV plus V dp.
+
+And now we're just going to
+substitute du in here.
+
+And the p dV terms are
+going to cancel.
+
+So we have the result that
+dH is T dS plus V dp.
+
+Right?
+
+And that shows us that H is
+written naturally as a
+
+function of entropy
+and pressure.
+
+And now let's keep going.
+
+A is u minus TS.
+
+dA is du minus T
+dS minus S dT.
+
+We're going to do
+the same thing.
+
+Substitute this for du.
+
+This time, the T dS terms
+are going to cancel.
+
+So we have dA is minus
+S dT minus T dS.
+
+That can't be right.
+
+And it isn't.
+
+Minus S dT, that's the p dV term
+that's left, minus p dV.
+
+And it shows us that A is
+written naturally as a
+
+function of T and V. G,
+we can write in any
+
+of a number of ways.
+
+Let's write it as H minus TS.
+
+So dG is dH minus
+T dS minus S dT.
+
+Here's dH.
+
+We'll substitute that in,
+and the T dS terms
+
+are going to cancel.
+
+So dG is minus S dT plus V dp.
+
+And this shows that G is
+written naturally as a
+
+function of T and p.
+
+So these, which we will exalt
+and celebrate by our
+
+sparingly-used colored chalk,
+are our fundamental equations
+
+of thermodynamics.
+
+So what they do is, they're
+describing how these
+
+thermodynamic properties change,
+in terms of only state
+
+functions and state variables.
+
+Very, very useful.
+
+And that's what it means, when
+we say well, it's natural
+
+then, to express say, G as a
+function of T and p, that's
+
+what we're saying.
+
+Is that we can express
+its changes in
+
+terms of these variables.
+
+Related only through
+quantities that are
+
+functions of state.
+
+I don't need to know about
+a specific path here.
+
+If I know about the states
+involved, I just need to know
+
+what the volume was
+in each of them.
+
+Now, before, of course, in the
+first part of the class we
+
+started out looking at u and
+then looking at H not as
+
+functions of S and V or S and
+p, but as functions of
+
+temperature, mostly.
+
+In general, temperature and
+volume or pressure.
+
+And it doesn't mean
+that something was
+
+somehow wrong with that.
+
+It certainly is, it still is
+going to be useful to do
+
+thermochemistry.
+
+To ask questions like how much
+heat is released in a chemical
+
+reaction that takes place
+at constant temperature.
+
+Not one of these variables.
+
+And we can calculate that.
+
+So it's not that we're somehow
+throwing away our
+
+ability to do that.
+
+However, the thing to remember
+is, when you look at heats of
+
+reaction under those
+conditions it's
+
+all well and good.
+
+But it doesn't tell you, this
+is the direction that the
+
+reaction is going to go.
+
+It doesn't tell you, this is the
+equilibrium concentration
+
+that you'll end up with.
+
+That doesn't come out of what
+we calculated before in
+
+thermochemistry.
+
+What does come out, which is
+very useful is, if you do run
+
+the reaction, here's how
+much heat comes out.
+
+And if you want to run a furnace
+and provide energy,
+
+that's an extremely important
+thing to be able to calculate.
+
+Because you're going to run it
+and you'll probably find
+
+conditions under which you can
+run it more or less to
+
+completion.
+
+But it doesn't tell you,
+by itself, which
+
+direction things run in.
+
+Whereas under these conditions,
+these quantities,
+
+if you look at free energy
+change, for example, at
+
+constant temperature and
+pressure, you can still
+
+calculate H. You can
+still calculate
+
+the heat that's released.
+
+This is what will tell you
+under some particular
+
+conditions what will
+actually happen.
+
+Where will you end up.
+
+Very, very important, of
+course, to be able to
+
+understand that.
+
+Now, it's also very useful to
+look at some of the relations
+
+that come out of these
+fundamental equations.
+
+And they're straightforward
+to derive.
+
+So, all I want to do now is look
+at the derivatives of the
+
+free energies with respect
+to temperature
+
+and volume and pressure.
+
+So for example, if I look at A,
+which we now have written
+
+as the function of T and V, of
+course, in general I can
+
+always write dA as partial of
+A, with respect to T at
+
+constant volume dT, plus partial
+of A with respect to
+
+V, at constant temperature dV.
+
+And I know what those
+turn out to be.
+
+It's minus S dT minus p dV.
+
+So what does that tell me?
+
+It tells me that the partial
+of A with respect to T at
+
+constant V is minus S. Right?
+
+In other words, now I know how
+to tell how the Helmholtz free
+
+energy changes as a function
+of temperature.
+
+Or as a function of volume.
+dA/dV, at constant T, must be
+
+negative p.
+
+Things that I can measure.
+
+So I can in a very
+straightforward way say, OK,
+
+well, here is my Helmholtz
+free energy.
+
+If I'm working under conditions
+of constant
+
+temperature and volume,
+that's very useful.
+
+Now, if I want to change those
+quantities; change the
+
+temperature, change the volume,
+how will it change?
+
+Well, I can, for any given case,
+measure the pressure,
+
+determine the entropy and
+I'll know what the slope
+
+of change will be.
+
+Similarly for G as a function of
+temperature and pressure, I
+
+can go through the
+same procedure.
+
+That is, it's easy to write down
+straight away that dG,
+
+with respect to temperature at
+constant pressure is minus S.
+
+That is, this is, dG/dT
+at constant pressure.
+
+And this is dG/dp at constant
+temperature.
+
+So again with the Gibbs free
+energy, now I see how to
+
+determine, if I change the
+pressure, if I change the
+
+temperature by some modest
+amount, how much is the Gibbs
+
+free energy going to change?
+
+Well, it's easy to see.
+
+These two relations involving
+entropy are also useful
+
+because they'll let us see
+how entropy depends
+
+on volume and pressure.
+
+And let me show you
+how that goes.
+
+Now, you've already seen
+how entropy depends on
+
+temperature.
+
+We've already seen that, going
+to write dS as dq reversible
+
+over T. And it's Cv dT over
+T at constant volume.
+
+It's Cp dT over T at
+constant pressure.
+
+So we know that dS/dT at
+constant volume is Cv over T,
+
+and dS/dT at constant pressure
+is Cp, over T. And we've seen
+
+that on a number of occasions.
+
+So that tells us what to do
+to know the entropy as the
+
+temperature changes.
+
+But now, what happens if,
+instead we look at what
+
+happens when we go to some state
+one to some other state
+
+two and it's the pressure.
+
+Or the volume, that changes.
+
+And by the way, just to be
+explicit about this, let's
+
+take this example, it means that
+delta S, if we undergo a
+
+change from, say, T1 to T2.
+
+There's Cp over T dT.
+
+So it's Cp log of T2 over T1,
+and we saw this before.
+
+So now, instead, let's
+look at some process.
+
+State one goes to state two.
+
+Let's have constant T. And
+look at what happens if
+
+pressure goes from p1 to p2.
+
+Or volume goes from V1 to V2.
+
+And see what happens there.
+
+We looked at pressure change
+before, actually, in
+
+discussing the third law, the
+fact that the entropy goes to
+
+zero as the absolute temperature
+goes to zero for a
+
+pure, perfect crystal.
+
+But, actually, we didn't do
+that in a general way.
+
+We just treated the one case
+of an ideal gas as the
+
+temperature is reduced.
+
+But we can do this, generally,
+by using what are called
+
+Maxwell relations.
+
+And all this is, is saying that
+when you take a mixed
+
+second derivative, it doesn't
+matter in which order you take
+
+the two derivatives.
+
+So, let's, we're going to
+use this relationship.
+
+And we're going to
+use these two.
+
+So, using those, now, what
+happens if we take the second
+
+derivative of A, the mixed
+derivative, partial with
+
+respect to T and the partial
+with respect to V. So let's
+
+leave these off for a moment,
+and now let's try that.
+
+And the point is that the second
+derivative of A, with
+
+respect to V and T in this
+order is the same as the
+
+second derivative of
+a with respect to T
+
+and V in this order.
+
+It doesn't matter which order.
+
+But that turns out
+to be useful.
+
+So let's do this explicitly.
+
+Which means we're going to
+take the derivative with
+
+respect to volume of dA/dT.
+
+Now, the dA/dT isn't
+constant volume.
+
+The derivative we're taking with
+respect to volume, when
+
+we take that it's at constant
+temperature.
+
+But what is it?
+
+Well, we already know what
+dA/dT at constant V is.
+
+It's negative S. So this
+is negative dS/dV.
+
+At constant temperature.
+
+Now let's take it in
+the other order.
+
+So d/dT of dA/dV,
+just like this.
+
+The dA/dV is calculated at
+constant temperature.
+
+We know it.
+
+Then we can take the derivative
+of that quantity,
+
+when we vary the temperature,
+holding the volume constant.
+
+But again, dA/dV dT,
+there it is.
+
+It's negative p.
+
+So this is just negative dp/dT
+at constant volume.
+
+These things have to be
+equal to each other.
+
+Because these mixed
+second derivatives
+
+are the same thing.
+
+But that's very useful.
+
+Because this is what comes
+directly out of an equation of
+
+state, right?
+
+You know how pressure changes
+with temperature at constant
+
+volume if you know the
+equation of state.
+
+It relates the pressure,
+volume,
+
+and temperature together.
+
+So from measured equation of
+state data, or from a model
+
+like the ideal gas or the van
+der Waal's gas or another
+
+equation of state,
+you know this.
+
+Can determine how entropy
+is going to behave
+
+as the volume changes.
+
+If we try that for an ideal
+gas, pV is nRT.
+
+So dp/dT at constant volume,
+it's just nR over V. And that,
+
+now, we know must equal dS/dV,
+with a positive sign.
+
+At constant temperature.
+
+So now let's try looking
+at something where
+
+are V1 goes to V2.
+
+The volume is going to change,
+and we can see
+
+how the entropy changes.
+
+So, if one goes to two and V1
+goes to V2, and it's constant
+
+temperature, just what we've
+specified there.
+
+Delta S is S(T, V2) minus S(T,
+V1), T's staying the same.
+
+So it's just the integral from
+V1 to V2 of dS/dV At constant
+
+temperature dV.
+
+And now we know what that is.
+
+So it's nR integral from V1 to
+V2 dV over V. So it's nR log
+
+V2 over V1.
+
+There's our delta S. So we
+know how to calculate it.
+
+Make sense?
+
+Now, we can do the same
+procedure for
+
+the pressure change.
+
+And all we do is, I'll just
+outline this, I think.
+
+I won't write it all
+on the board.
+
+But, of course, it's going to
+come from the fact that these
+
+second derivatives
+are also equal.
+
+So d squared G dT dp is equal
+to d squared G dp dT.
+
+In other words, the order of
+taking the derivatives with
+
+respect to pressure and
+temperature doesn't matter.
+
+And what this will show is
+that dS/dp at constant
+
+temperature, here we saw how
+entropy varies with volume,
+
+this is going to show us how
+it varies with pressure.
+
+Is equal to minus dV/dT
+at constant pressure.
+
+And again, this is something
+that comes from
+
+an equation of state.
+
+We know how the volume and
+temperature vary with respect
+
+to each other at constant
+pressure.
+
+That's what the equation
+of state tells us.
+
+So, again, I can just
+use that result.
+
+So, if we do a process where
+one goes to two at constant
+
+temperature, and now the
+pressure, p1, goes to p2, well
+
+then delta S is just the
+integral from p1 to p2 of
+
+dS/dp times dS, so
+it's just this.
+
+And so of course it's
+still pV equals nRT.
+
+So now we just have
+nR over p dp.
+
+Right?
+
+So we're going to see
+the same story.
+
+It's nR log of p2 over p1 for
+the process where there's a
+
+pressure change.
+
+Any questions about this part?
+
+So what we've done is take
+one step further.
+
+We've used the fundamental
+equations that are hiding down
+
+here, out of sight but
+never out of mind.
+
+And what we've done is look at
+the derivatives of the new
+
+free energies that we've just
+recently introduced, A and G.
+
+And then, the only thing we've
+done beyond that is say, OK,
+
+well now let's just take the
+mixed second derivatives, they
+
+have to be equal
+to each other.
+
+And what's fallen out when we do
+that, because in each case,
+
+one of the first derivatives
+gives us the entropy.
+
+Then the second derivative gives
+the change in entropy
+
+with respect to the variable
+that we're differentiating,
+
+with respect to which is either
+pressure or volume.
+
+And the useful outcome of all
+that is that we get to see how
+
+entropy changes with one of
+those variables in terms of
+
+only V, T, and p, which come out
+of some equation of state.
+
+And all we did, further, is take
+that second derivative.
+
+That mixed second derivative.
+
+And, of course, see that either
+way we do that we'll
+
+have an equality.
+
+Now, let's go back to our older
+friends u and H. Which
+
+we've expressed now in terms
+of S and V, S and p.
+
+So, so far we don't have a way
+to just write off, relate them
+
+to equation of state data.
+
+Which also would
+be very useful.
+
+Here, A and G, we've already
+got as functions of these
+
+easily controlled, conveniently
+
+controlled state variables.
+
+Let's look at those quantities.
+u and H. And look
+
+at, for example, the
+V dependence of u.
+
+The volume dependence.
+
+And in particular let's look
+at, for example, du/dV at
+
+constant temperature.
+
+Now, we can immediately
+see what du/dV at
+
+constant entropy is.
+
+Experimentally, though, that's
+not such an easy
+
+situation to arrange.
+
+Of course, this is a much
+more practical one.
+
+But it doesn't just fall out
+immediately from the one
+
+fundamental equation for du.
+
+But we can start there.
+
+So, du is T dS minus p dV.
+
+And I can take this derivative.
+du/dV at constant
+
+T. And so, what is it?
+
+Well, it's not just p because
+there's some dS/dV at constant
+
+T. This isn't zero.
+
+There's some variation, dS/dV,
+at constant temperature.
+
+That's going to matter.
+
+This part, of course,
+is just minus p.
+
+But we just figured out what
+dS/dV at constant T is.
+
+This is dp/dT at constant
+V. So that's neat.
+
+So in other words, we can write
+this as T, dp/dT at
+
+constant V, minus p.
+
+Let's just check T, p, T, V, p.
+
+Right?
+
+In other words, we just
+have pressure,
+
+temperature and volume.
+
+Again, if we know the equation
+of state, we
+
+know all this stuff.
+
+So again, we can measure
+equation of state data.
+
+Or, if we know the equation of
+state from a model, ideal gas,
+
+van der Waal's gas, whatever,
+now we can determine u.
+
+From equation of state data.
+
+Terrific, right?
+
+So let's take our one model that
+we keep going back to.
+
+Equation of state, and just
+see how it works.
+
+That is, ideal gas.
+
+And see how it works
+with that.
+
+Now, we saw before, or really
+I should say we accepted
+
+before, that for an ideal
+gas, u was a function of
+
+temperature only.
+
+Well, now let's try it.
+
+So, dp/dT, for our ideal gas,
+at constant volume,
+
+remember pV is nRT.
+
+So this nR over V. And then,
+using the relation again, we
+
+can just write this as p over
+T. In other words, we're
+
+taking advantage of
+the fact that we
+
+now know that quantity.
+
+In the case of the ideal
+gas, we just have a
+
+simple model for it.
+
+More generally, we
+could measure it.
+
+We could just collect
+a bunch of data.
+
+For a material.
+
+What's the volume it occupies
+at some pressure and
+
+temperature?
+
+Now let's change the pressure
+and temperature and sweep
+
+through a whole range of
+pressures and temperatures and
+
+measure the volume in
+every one of them.
+
+Well, then, we could
+just use that for
+
+our equation of state.
+
+One way or another, we can
+determine this quantity.
+
+For the ideal gas it's this.
+
+So now our du/dV, at constant T
+is just T times dp/dT, which
+
+is just p over T minus
+p, it's zero.
+
+Remember the Joule expansion.
+
+And we saw that, you saw that
+the Joule coefficient for an
+
+ideal gas was zero.
+
+So that you could see that for
+the ideal gas, u would not be
+
+a function of volume, but
+only of temperature.
+
+But actually, when you saw that
+before, you weren't given
+
+any proof of that.
+
+It was just that when the
+good Mr. Joule made the
+
+measurements, to the precision
+that he could measure, he
+
+discovered that for some gases
+it was extremely small.
+
+At least, smaller than anything
+he could detect.
+
+So it sure seemed like it was
+going to zero, under ideal gas
+
+conditions.
+
+And that was the result that
+we came to accept.
+
+Here, though, you can just
+derive straight away.
+
+That for an ideal gas it has to
+be the case that there's no
+
+volume dependence
+of the energy.
+
+Only a temperature dependence.
+
+It's the same for H. Just like
+u, we'd like to be able to
+
+express it in a way that allows
+us to calculate what
+
+happens only from equation
+of state data.
+
+But, again, our fundamental
+equations show us how it
+
+changes as a function of
+entropy and pressure.
+
+So, dH is T dS plus V dp.
+
+So let's look at dH/dp.
+
+We know how to get it
+immediately if we
+
+keep entropy constant.
+
+But we'd like to relate it to
+what happens if we keep the
+
+temperature constant.
+
+So then, just like we saw,
+analogous to what saw just
+
+before, it's T dS/dp at constant
+T. Plus V. But now
+
+we've seen from the Maxwell
+relations that dS/dp is minus
+
+dV/dT, for constant p.
+
+Again, this is this quantity,
+one of these quantities that
+
+again we can determine from
+equation of state data.
+
+Only V, p and T appear.
+
+So it's minus T dV/dT at
+constant p, plus V. And so,
+
+again, this can come from
+equation of state data.
+
+And if you do this again for
+an ideal gas, let me see.
+
+So we have pV is nRT.
+
+So dV/dT at constant pressure
+is just nR over p.
+
+But we can plug that in again
+just like we did before.
+
+It's just equal to V over T.
+And so dH/dp under our
+
+condition of constant
+temperature is just minus T
+
+times V over T plus
+V, everything
+
+cancels, and that's zero.
+
+That's our Joule - Thompson
+expansion.
+
+That was a constant
+enthalpy change.
+
+And again there, too, you saw
+an experimental result you
+
+were presented with that says,
+well at least to the extent
+
+that it could be measured,
+it was obviously
+
+getting very small.
+
+For gases that approach
+ideal gas conditions.
+
+Well, there you can see it.
+
+Sure better have gotten
+small because in fact
+
+it has to be zero.
+
+Now let's take just
+one somewhat
+
+more complicated case.
+
+Let's look at a van
+der Waal's gas.
+
+Let's try it with a different
+equation of state, that isn't
+
+quite as simple as the
+ideal gas case.
+
+So, then p plus a over molar
+volume squared times V minus b
+
+molar volume V minus b is
+equal to RT, remember?
+
+This was back from the
+first or second
+
+lecture in the course.
+
+So, we can separate out p.
+
+It's RT over molar volume minus
+b minus a over molar
+
+volume V squared.
+
+And then we can take the
+derivative with respect to
+
+temperature, it's just R over
+molar volume minus b.
+
+So it's dp/dT at constant V is
+just R over V bar minus b.
+
+Well, let's now look, given
+this, let's now look in that
+
+case, at what happens to u as a
+function of V. For the ideal
+
+gas, we know that u is
+volume independent.
+
+It only depends on
+the temperature.
+
+But for the van der
+Waal's gas, now
+
+it's going to be different.
+
+And that's because this is
+different from what it is in
+
+the ideal gas case.
+
+Namely, now du/dV at constant T,
+for the van der Waal's gas.
+
+So it's this.
+
+So it's RT over molar
+volume minus b.
+
+Minus p, right?
+
+But in fact, if you go back to
+the van der Waal's equation of
+
+state, here's RT
+over v minus b.
+
+If we put it as minus
+b, that's just
+
+equal to a over V squared.
+
+Equals a over molar
+volume squared.
+
+But the point is, the main
+point is, it's not zero.
+
+It's some number. a over the
+molar volume squared. a is a
+
+positive number in the van der
+Waal's equation of state.
+
+So this is greater than zero.
+
+In other words, u is a function
+of T and V. If we
+
+don't have an ideal gas.
+
+By the way, just to think about
+it a little bit, it's a
+
+positive number.
+
+What that means is, I've got my
+
+ideal gas in some container.
+
+There's some energy, some
+internal energy.
+
+Now I make the volume bigger.
+
+I allow it to expand.
+
+And the energy changes,
+it goes up.
+
+In some sense it's less
+favorable energetically.
+
+What's happening there, that a
+term in the van der Waal's
+
+equation of state, is describing
+interactions,
+
+favorable attractions, between
+gas molecules.
+
+The b is describing
+repulsions.
+
+Effectively, the
+volume changes.
+
+The molar volume is being
+changed a little bit by the
+
+fact that if you're really
+trying to make things collide
+
+with each other, they can't
+occupy the same volume.
+
+And that is being
+expressed here.
+
+The a, though is expressing
+attraction between molecules
+
+at somewhat longer range.
+
+So now, if you make the
+volume bigger, those
+
+attractions die out.
+
+Because the molecules are
+farther apart from each other.
+
+So the energy goes up.
+
+Now, you might ask, well why
+does it do that, right?
+
+I mean, if the energy is lower
+to occupy a smaller volume,
+
+then if I have this room and a
+bunch of molecules of oxygen,
+
+and nitrogen and what have you
+in the air, and there are weak
+
+attractions between them, why
+don't they all just sort of
+
+glum together and find whatever
+volume they like.
+
+So that the attractive
+forces can exert
+
+themselves a little bit.
+
+Not too close, right?
+
+Not so close that the
+repulsions dominate.
+
+Why don't they do that?
+
+What else matters besides any
+of those considerations?
+
+What else matters that I haven't
+considered in this
+
+little discussion?
+
+Yeah.
+
+What about entropy, right?
+
+If I only worry about
+minimizing the
+
+energy, it's true.
+
+They'll stick together
+a little bit.
+
+But entropy also matters.
+
+And there's disorder achieved
+by occupying the full
+
+available volume.
+
+Many more states possible.
+
+And that will end up winning out
+at basically any realistic
+
+temperature where the stuff
+really is a gas.
+
+OK.
+
+Next time, what you're going
+to see is the following.
+
+It turns out we can express all
+these functions in terms
+
+of G, we wouldn't need to choose
+G, but it's a very
+
+useful function to choose.
+
+Because of its natural
+expression in
+
+terms of T and p.
+
+So we can write any of these
+functions in terms of G. Which
+
+means that we can really
+calculate all the
+
+thermodynamics in
+terms of only g.
+
+It's not necessary to do that,
+but it can be quite
+
+convenient.
+
+And then we can say, OK, if we
+have many constituents, what
+
+if we have a mixture of stuff?
+
+We can take the derivative of
+G with respect to how much
+
+material there is.
+
+With respect to n, the
+number of moles.
+
+And if there are one, and two,
+and three constituents with
+
+respect to n1, and n2, and n3.
+
+Each individual amount
+of stuff.
+
+What that's going to allow us to
+do is, if we say, OK I have
+
+a mixture of stuff, how does
+the free energy change?
+
+If I change the composition
+of the mixture?
+
+If I take something away, or
+put something else in?
+
+And we'll be able to determine
+equilibrium under those
+
+conditions.
+
+That's very useful for things
+like chemical reactions, where
+
+this constituent changes
+to this one.
+
+And I can calculate what happens
+to G under those
+
+conditions.
+
+And that's what you'll see
+starting next time.
+
+And professor Blendi
+will be taking over
+
+for that set of lectures.
\ No newline at end of file
diff --git a/tBhR9hZLf0c.txt b/tBhR9hZLf0c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f208c0674b93a5a9ed996185599d79cee3ec5e8e
--- /dev/null
+++ b/tBhR9hZLf0c.txt
@@ -0,0 +1,13163 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
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+to offer highquality educational
+ 
+
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+to offer highquality educational
+resources for free to make a donation or
+
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+resources for free to make a donation or
+ 
+
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+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu question Contin so again I
+
+ align:start position:0%
+ocw.mit.edu question Contin so again I
+ 
+
+ align:start position:0%
+ocw.mit.edu question Contin so again I
+think what you're saying is a
+
+ align:start position:0%
+think what you're saying is a
+ 
+
+ align:start position:0%
+think what you're saying is a
+trajectory that uh we start so it's it's
+
+ align:start position:0%
+trajectory that uh we start so it's it's
+ 
+
+ align:start position:0%
+trajectory that uh we start so it's it's
+a very steep time we start from a very
+
+ align:start position:0%
+a very steep time we start from a very
+ 
+
+ align:start position:0%
+a very steep time we start from a very
+basic thinking and then really trying to
+
+ align:start position:0%
+basic thinking and then really trying to
+ 
+
+ align:start position:0%
+basic thinking and then really trying to
+understand the materials what determin
+
+ align:start position:0%
+understand the materials what determin
+ 
+
+ align:start position:0%
+understand the materials what determin
+the material
+
+ align:start position:0%
+the material
+ 
+
+ align:start position:0%
+the material
+properties and uh uh this lecture I what
+
+ align:start position:0%
+properties and uh uh this lecture I what
+ 
+
+ align:start position:0%
+properties and uh uh this lecture I what
+I'm hoping after I close up with you uh
+
+ align:start position:0%
+I'm hoping after I close up with you uh
+ 
+
+ align:start position:0%
+I'm hoping after I close up with you uh
+listen topic conductivity what I'm Hing
+
+ align:start position:0%
+listen topic conductivity what I'm Hing
+ 
+
+ align:start position:0%
+listen topic conductivity what I'm Hing
+hoping is bring you to re from here what
+
+ align:start position:0%
+hoping is bring you to re from here what
+ 
+
+ align:start position:0%
+hoping is bring you to re from here what
+people are thinking in making materials
+
+ align:start position:0%
+people are thinking in making materials
+ 
+
+ align:start position:0%
+people are thinking in making materials
+better so uh but uh let me start with uh
+
+ align:start position:0%
+better so uh but uh let me start with uh
+ 
+
+ align:start position:0%
+better so uh but uh let me start with uh
+a very brief
+
+ align:start position:0%
+a very brief
+ 
+
+ align:start position:0%
+a very brief
+review uh of last lecture um uh we show
+
+ align:start position:0%
+review uh of last lecture um uh we show
+ 
+
+ align:start position:0%
+review uh of last lecture um uh we show
+uh one is simple remember my picture
+
+ align:start position:0%
+uh one is simple remember my picture
+ 
+
+ align:start position:0%
+uh one is simple remember my picture
+always simple picture always from left
+
+ align:start position:0%
+always simple picture always from left
+ 
+
+ align:start position:0%
+always simple picture always from left
+to right and right to left and the
+
+ align:start position:0%
+to right and right to left and the
+ 
+
+ align:start position:0%
+to right and right to left and the
+difference gives the the FL uh so from
+
+ align:start position:0%
+difference gives the the FL uh so from
+ 
+
+ align:start position:0%
+difference gives the the FL uh so from
+there we show General relation uh the
+
+ align:start position:0%
+there we show General relation uh the
+ 
+
+ align:start position:0%
+there we show General relation uh the
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+flux this the uh current flux is related
+
+ align:start position:0%
+flux this the uh current flux is related
+ 
+
+ align:start position:0%
+flux this the uh current flux is related
+to electrostatic potential so that's the
+
+ align:start position:0%
+to electrostatic potential so that's the
+ 
+
+ align:start position:0%
+to electrostatic potential so that's the
+charge driving force for charge flow and
+
+ align:start position:0%
+charge driving force for charge flow and
+ 
+
+ align:start position:0%
+charge driving force for charge flow and
+then we will have a gradient is
+
+ align:start position:0%
+then we will have a gradient is
+ 
+
+ align:start position:0%
+then we will have a gradient is
+toter so now you see the electricity to
+
+ align:start position:0%
+toter so now you see the electricity to
+ 
+
+ align:start position:0%
+toter so now you see the electricity to
+he and then this one shows the Heat
+
+ align:start position:0%
+he and then this one shows the Heat
+ 
+
+ align:start position:0%
+he and then this one shows the Heat
+current so really now electron is
+
+ align:start position:0%
+current so really now electron is
+ 
+
+ align:start position:0%
+current so really now electron is
+carrying the heat as Heat current
+
+ align:start position:0%
+carrying the heat as Heat current
+ 
+
+ align:start position:0%
+carrying the heat as Heat current
+electric current Heat current is again
+
+ align:start position:0%
+electric current Heat current is again
+ 
+
+ align:start position:0%
+electric current Heat current is again
+coupl in this Cas not just
+
+ align:start position:0%
+coupl in this Cas not just
+ 
+
+ align:start position:0%
+coupl in this Cas not just
+to but also to the elal
+
+ align:start position:0%
+to but also to the elal
+ 
+
+ align:start position:0%
+to but also to the elal
+potential and uh this is a very general
+
+ align:start position:0%
+potential and uh this is a very general
+ 
+
+ align:start position:0%
+potential and uh this is a very general
+answer relation if I have read this
+
+ align:start position:0%
+answer relation if I have read this
+ 
+
+ align:start position:0%
+answer relation if I have read this
+really this radi in terms of generalized
+
+ align:start position:0%
+really this radi in terms of generalized
+ 
+
+ align:start position:0%
+really this radi in terms of generalized
+force uh is this coefficient
+
+ align:start position:0%
+force uh is this coefficient
+ 
+
+ align:start position:0%
+force uh is this coefficient
+CR this
+
+ align:start position:0%
+CR this
+ 
+
+ align:start position:0%
+CR this
+what the price
+
+ align:start position:0%
+what the price
+ 
+
+ align:start position:0%
+what the price
+before and uh then uh I gave some we use
+
+ align:start position:0%
+before and uh then uh I gave some we use
+ 
+
+ align:start position:0%
+before and uh then uh I gave some we use
+the some of the concept we learned
+
+ align:start position:0%
+the some of the concept we learned
+ 
+
+ align:start position:0%
+the some of the concept we learned
+before for example density of states and
+
+ align:start position:0%
+before for example density of states and
+ 
+
+ align:start position:0%
+before for example density of states and
+uh uh the uh uh we have expression for
+
+ align:start position:0%
+uh uh the uh uh we have expression for
+ 
+
+ align:start position:0%
+uh uh the uh uh we have expression for
+this coefficient l11 is the electric
+
+ align:start position:0%
+this coefficient l11 is the electric
+ 
+
+ align:start position:0%
+this coefficient l11 is the electric
+conductivity uh and those other
+
+ align:start position:0%
+conductivity uh and those other
+ 
+
+ align:start position:0%
+conductivity uh and those other
+coefficient from those other
+
+ align:start position:0%
+coefficient from those other
+ 
+
+ align:start position:0%
+coefficient from those other
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+and uh let me just uh one remark that
+
+ align:start position:0%
+and uh let me just uh one remark that
+ 
+
+ align:start position:0%
+and uh let me just uh one remark that
+those expressions are not uh uh most
+
+ align:start position:0%
+those expressions are not uh uh most
+ 
+
+ align:start position:0%
+those expressions are not uh uh most
+General uh you can have different
+
+ align:start position:0%
+General uh you can have different
+ 
+
+ align:start position:0%
+General uh you can have different
+transort regim this is the regime that
+
+ align:start position:0%
+transort regim this is the regime that
+ 
+
+ align:start position:0%
+transort regim this is the regime that
+most people do the Boardman transort
+
+ align:start position:0%
+most people do the Boardman transort
+ 
+
+ align:start position:0%
+most people do the Boardman transort
+regime so those expression can rather
+
+ align:start position:0%
+regime so those expression can rather
+ 
+
+ align:start position:0%
+regime so those expression can rather
+than my time deration uh you can
+
+ align:start position:0%
+than my time deration uh you can
+ 
+
+ align:start position:0%
+than my time deration uh you can
+actually start from my equation derive
+
+ align:start position:0%
+actually start from my equation derive
+ 
+
+ align:start position:0%
+actually start from my equation derive
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+coefficients and uh uh I showed
+
+ align:start position:0%
+coefficients and uh uh I showed
+ 
+
+ align:start position:0%
+coefficients and uh uh I showed
+examples uh one thing that I want to uh
+
+ align:start position:0%
+examples uh one thing that I want to uh
+ 
+
+ align:start position:0%
+examples uh one thing that I want to uh
+emphasize is that the properties depends
+
+ align:start position:0%
+emphasize is that the properties depends
+ 
+
+ align:start position:0%
+emphasize is that the properties depends
+on temperature so different temperature
+
+ align:start position:0%
+on temperature so different temperature
+ 
+
+ align:start position:0%
+on temperature so different temperature
+uh you can see the property are changing
+
+ align:start position:0%
+uh you can see the property are changing
+ 
+
+ align:start position:0%
+uh you can see the property are changing
+uh for electric conductivity if you
+
+ align:start position:0%
+uh for electric conductivity if you
+ 
+
+ align:start position:0%
+uh for electric conductivity if you
+follow the simple Bo
+
+ align:start position:0%
+follow the simple Bo
+ 
+
+ align:start position:0%
+follow the simple Bo
+statistics uh you actually get the
+
+ align:start position:0%
+statistics uh you actually get the
+ 
+
+ align:start position:0%
+statistics uh you actually get the
+electric conductive in semiconductor we
+
+ align:start position:0%
+electric conductive in semiconductor we
+ 
+
+ align:start position:0%
+electric conductive in semiconductor we
+know typical micro electronic type of
+
+ align:start position:0%
+know typical micro electronic type of
+ 
+
+ align:start position:0%
+know typical micro electronic type of
+doping Electa the increase with
+
+ align:start position:0%
+doping Electa the increase with
+ 
+
+ align:start position:0%
+doping Electa the increase with
+temperature but for thric material so
+
+ align:start position:0%
+temperature but for thric material so
+ 
+
+ align:start position:0%
+temperature but for thric material so
+this is not right for thric material you
+
+ align:start position:0%
+this is not right for thric material you
+ 
+
+ align:start position:0%
+this is not right for thric material you
+can say theal contivity electric
+
+ align:start position:0%
+can say theal contivity electric
+ 
+
+ align:start position:0%
+can say theal contivity electric
+contivity decrease this temperature and
+
+ align:start position:0%
+contivity decrease this temperature and
+ 
+
+ align:start position:0%
+contivity decrease this temperature and
+that's because we doping very heavily
+
+ align:start position:0%
+that's because we doping very heavily
+ 
+
+ align:start position:0%
+that's because we doping very heavily
+metal is like this metal in metal the
+
+ align:start position:0%
+metal is like this metal in metal the
+ 
+
+ align:start position:0%
+metal is like this metal in metal the
+electric connectivity decreases because
+
+ align:start position:0%
+electric connectivity decreases because
+ 
+
+ align:start position:0%
+electric connectivity decreases because
+when you get a top they're not more Fon
+
+ align:start position:0%
+when you get a top they're not more Fon
+ 
+
+ align:start position:0%
+when you get a top they're not more Fon
+the Aton atoms are vibrating more
+
+ align:start position:0%
+the Aton atoms are vibrating more
+ 
+
+ align:start position:0%
+the Aton atoms are vibrating more
+violently and that's scatter electron
+
+ align:start position:0%
+violently and that's scatter electron
+ 
+
+ align:start position:0%
+violently and that's scatter electron
+that's when why they will
+
+ align:start position:0%
+that's when why they will
+ 
+
+ align:start position:0%
+that's when why they will
+decrease and uh the
+
+ align:start position:0%
+decrease and uh the
+ 
+
+ align:start position:0%
+decrease and uh the
+CAC uh is typically have a peak and if
+
+ align:start position:0%
+CAC uh is typically have a peak and if
+ 
+
+ align:start position:0%
+CAC uh is typically have a peak and if
+you just talk simply one B Transport so
+
+ align:start position:0%
+you just talk simply one B Transport so
+ 
+
+ align:start position:0%
+you just talk simply one B Transport so
+one b means if I have a conduction B and
+
+ align:start position:0%
+one b means if I have a conduction B and
+ 
+
+ align:start position:0%
+one b means if I have a conduction B and
+if electron only uh going one through
+
+ align:start position:0%
+if electron only uh going one through
+ 
+
+ align:start position:0%
+if electron only uh going one through
+one conduction B then the theory say it
+
+ align:start position:0%
+one conduction B then the theory say it
+ 
+
+ align:start position:0%
+one conduction B then the theory say it
+should increase temperature because as
+
+ align:start position:0%
+should increase temperature because as
+ 
+
+ align:start position:0%
+should increase temperature because as
+the temperature increases the separation
+
+ align:start position:0%
+the temperature increases the separation
+ 
+
+ align:start position:0%
+the temperature increases the separation
+of the chemical potential from the
+
+ align:start position:0%
+of the chemical potential from the
+ 
+
+ align:start position:0%
+of the chemical potential from the
+bottom so you drive chemal potential to
+
+ align:start position:0%
+bottom so you drive chemal potential to
+ 
+
+ align:start position:0%
+bottom so you drive chemal potential to
+the center of the B but uh in uh almost
+
+ align:start position:0%
+the center of the B but uh in uh almost
+ 
+
+ align:start position:0%
+the center of the B but uh in uh almost
+all materials the behavior is will peit
+
+ align:start position:0%
+all materials the behavior is will peit
+ 
+
+ align:start position:0%
+all materials the behavior is will peit
+at some temperature and start to
+
+ align:start position:0%
+at some temperature and start to
+ 
+
+ align:start position:0%
+at some temperature and start to
+decrease and the reason is uh as the
+
+ align:start position:0%
+decrease and the reason is uh as the
+ 
+
+ align:start position:0%
+decrease and the reason is uh as the
+temperature increase you exide uh the
+
+ align:start position:0%
+temperature increase you exide uh the
+ 
+
+ align:start position:0%
+temperature increase you exide uh the
+intrinsically you you you leave the
+
+ align:start position:0%
+intrinsically you you you leave the
+ 
+
+ align:start position:0%
+intrinsically you you you leave the
+thermal energy leave electron from the
+
+ align:start position:0%
+thermal energy leave electron from the
+ 
+
+ align:start position:0%
+thermal energy leave electron from the
+bance band with a hole behind D electron
+
+ align:start position:0%
+bance band with a hole behind D electron
+ 
+
+ align:start position:0%
+bance band with a hole behind D electron
+can so in this case now you have both
+
+ align:start position:0%
+can so in this case now you have both
+ 
+
+ align:start position:0%
+can so in this case now you have both
+electron a hole so when you flow current
+
+ align:start position:0%
+electron a hole so when you flow current
+ 
+
+ align:start position:0%
+electron a hole so when you flow current
+electron carry energy in One Direction F
+
+ align:start position:0%
+electron carry energy in One Direction F
+ 
+
+ align:start position:0%
+electron carry energy in One Direction F
+carrent energy in the opposite direction
+
+ align:start position:0%
+carrent energy in the opposite direction
+ 
+
+ align:start position:0%
+carrent energy in the opposite direction
+so they cancel each other in this case
+
+ align:start position:0%
+so they cancel each other in this case
+ 
+
+ align:start position:0%
+so they cancel each other in this case
+you actually could get a higher electric
+
+ align:start position:0%
+you actually could get a higher electric
+ 
+
+ align:start position:0%
+you actually could get a higher electric
+conductivity but the C canel each other
+
+ align:start position:0%
+conductivity but the C canel each other
+ 
+
+ align:start position:0%
+conductivity but the C canel each other
+so this is when you look at experimental
+
+ align:start position:0%
+so this is when you look at experimental
+ 
+
+ align:start position:0%
+so this is when you look at experimental
+data it turns out the many C we do that
+
+ align:start position:0%
+data it turns out the many C we do that
+ 
+
+ align:start position:0%
+data it turns out the many C we do that
+say we cannot calculate exactly so we
+
+ align:start position:0%
+say we cannot calculate exactly so we
+ 
+
+ align:start position:0%
+say we cannot calculate exactly so we
+look at experiment this is what
+
+ align:start position:0%
+look at experiment this is what
+ 
+
+ align:start position:0%
+look at experiment this is what
+happening this is the why div and this
+
+ align:start position:0%
+happening this is the why div and this
+ 
+
+ align:start position:0%
+happening this is the why div and this
+is where okay how you can move this to
+
+ align:start position:0%
+is where okay how you can move this to
+ 
+
+ align:start position:0%
+is where okay how you can move this to
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+temperature you if you have more
+
+ align:start position:0%
+temperature you if you have more
+ 
+
+ align:start position:0%
+temperature you if you have more
+electron you you do it more heavily you
+
+ align:start position:0%
+electron you you do it more heavily you
+ 
+
+ align:start position:0%
+electron you you do it more heavily you
+will go to higher temperature and if you
+
+ align:start position:0%
+will go to higher temperature and if you
+ 
+
+ align:start position:0%
+will go to higher temperature and if you
+have larger back Gap it's it's more
+
+ align:start position:0%
+have larger back Gap it's it's more
+ 
+
+ align:start position:0%
+have larger back Gap it's it's more
+difficult to generate the seral electron
+
+ align:start position:0%
+difficult to generate the seral electron
+ 
+
+ align:start position:0%
+difficult to generate the seral electron
+pole pair and then you can move this so
+
+ align:start position:0%
+pole pair and then you can move this so
+ 
+
+ align:start position:0%
+pole pair and then you can move this so
+that's how you look at different these
+
+ align:start position:0%
+that's how you look at different these
+ 
+
+ align:start position:0%
+that's how you look at different these
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+materials so that's where we were in the
+
+ align:start position:0%
+materials so that's where we were in the
+ 
+
+ align:start position:0%
+materials so that's where we were in the
+uh last uh lecture and those were many
+
+ align:start position:0%
+uh last uh lecture and those were many
+ 
+
+ align:start position:0%
+uh last uh lecture and those were many
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+electrons and uh uh we also talk about
+
+ align:start position:0%
+electrons and uh uh we also talk about
+ 
+
+ align:start position:0%
+electrons and uh uh we also talk about
+the colon the concept of lce vibration
+
+ align:start position:0%
+the colon the concept of lce vibration
+ 
+
+ align:start position:0%
+the colon the concept of lce vibration
+and we give a very simple expression
+
+ align:start position:0%
+and we give a very simple expression
+ 
+
+ align:start position:0%
+and we give a very simple expression
+before on the phon thermal conductivity
+
+ align:start position:0%
+before on the phon thermal conductivity
+ 
+
+ align:start position:0%
+before on the phon thermal conductivity
+and again my picture is left to right
+
+ align:start position:0%
+and again my picture is left to right
+ 
+
+ align:start position:0%
+and again my picture is left to right
+right to left right so when I want to
+
+ align:start position:0%
+right to left right so when I want to
+ 
+
+ align:start position:0%
+right to left right so when I want to
+find out the heat flock going through
+
+ align:start position:0%
+find out the heat flock going through
+ 
+
+ align:start position:0%
+find out the heat flock going through
+any plan I see how much heat is going
+
+ align:start position:0%
+any plan I see how much heat is going
+ 
+
+ align:start position:0%
+any plan I see how much heat is going
+from one side to the other without
+
+ align:start position:0%
+from one side to the other without
+ 
+
+ align:start position:0%
+from one side to the other without
+scattering so this is with one
+
+ align:start position:0%
+scattering so this is with one
+ 
+
+ align:start position:0%
+scattering so this is with one
+relaxation time and how much from left
+
+ align:start position:0%
+relaxation time and how much from left
+ 
+
+ align:start position:0%
+relaxation time and how much from left
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+right time the difference give me the
+
+ align:start position:0%
+right time the difference give me the
+ 
+
+ align:start position:0%
+right time the difference give me the
+and what I want to do a little bit more
+
+ align:start position:0%
+and what I want to do a little bit more
+ 
+
+ align:start position:0%
+and what I want to do a little bit more
+better compy uh meaning before I just
+
+ align:start position:0%
+better compy uh meaning before I just
+ 
+
+ align:start position:0%
+better compy uh meaning before I just
+say this is lber density n right per
+
+ align:start position:0%
+say this is lber density n right per
+ 
+
+ align:start position:0%
+say this is lber density n right per
+unit volume now I'm going to do modes so
+
+ align:start position:0%
+unit volume now I'm going to do modes so
+ 
+
+ align:start position:0%
+unit volume now I'm going to do modes so
+I'm going to sum up so this is a uh it's
+
+ align:start position:0%
+I'm going to sum up so this is a uh it's
+ 
+
+ align:start position:0%
+I'm going to sum up so this is a uh it's
+the same as as what I draw here but here
+
+ align:start position:0%
+the same as as what I draw here but here
+ 
+
+ align:start position:0%
+the same as as what I draw here but here
+is uh more rigorous so this is the
+
+ align:start position:0%
+is uh more rigorous so this is the
+ 
+
+ align:start position:0%
+is uh more rigorous so this is the
+energy of
+
+ align:start position:0%
+energy of
+ 
+
+ align:start position:0%
+energy of
+one lce vibration form of lce vibration
+
+ align:start position:0%
+one lce vibration form of lce vibration
+ 
+
+ align:start position:0%
+one lce vibration form of lce vibration
+so one F and then this is perum mechanic
+
+ align:start position:0%
+so one F and then this is perum mechanic
+ 
+
+ align:start position:0%
+so one F and then this is perum mechanic
+modes that's both Einstein distribution
+
+ align:start position:0%
+modes that's both Einstein distribution
+ 
+
+ align:start position:0%
+modes that's both Einstein distribution
+right per mole per state Quantum State
+
+ align:start position:0%
+right per mole per state Quantum State
+ 
+
+ align:start position:0%
+right per mole per state Quantum State
+how many Fon you
+
+ align:start position:0%
+how many Fon you
+ 
+
+ align:start position:0%
+how many Fon you
+have right and this is the velocity so
+
+ align:start position:0%
+have right and this is the velocity so
+ 
+
+ align:start position:0%
+have right and this is the velocity so
+this is a so this is really telling me
+
+ align:start position:0%
+this is a so this is really telling me
+ 
+
+ align:start position:0%
+this is a so this is really telling me
+per quantum mechanical mode how many
+
+ align:start position:0%
+per quantum mechanical mode how many
+ 
+
+ align:start position:0%
+per quantum mechanical mode how many
+Fons is moving to the forward positive X
+
+ align:start position:0%
+Fons is moving to the forward positive X
+ 
+
+ align:start position:0%
+Fons is moving to the forward positive X
+Direction the one half gives me half
+
+ align:start position:0%
+Direction the one half gives me half
+ 
+
+ align:start position:0%
+Direction the one half gives me half
+random motion so the idea is the same
+
+ align:start position:0%
+random motion so the idea is the same
+ 
+
+ align:start position:0%
+random motion so the idea is the same
+but now I'm trying to do little a better
+
+ align:start position:0%
+but now I'm trying to do little a better
+ 
+
+ align:start position:0%
+but now I'm trying to do little a better
+job cting better cting job and here what
+
+ align:start position:0%
+job cting better cting job and here what
+ 
+
+ align:start position:0%
+job cting better cting job and here what
+we have this is remember in the second
+
+ align:start position:0%
+we have this is remember in the second
+ 
+
+ align:start position:0%
+we have this is remember in the second
+lecture I was doing black body black
+
+ align:start position:0%
+lecture I was doing black body black
+ 
+
+ align:start position:0%
+lecture I was doing black body black
+body radiation right so this is the
+
+ align:start position:0%
+body radiation right so this is the
+ 
+
+ align:start position:0%
+body radiation right so this is the
+counting all the mechanic allow M KX
+
+ align:start position:0%
+counting all the mechanic allow M KX
+ 
+
+ align:start position:0%
+counting all the mechanic allow M KX
+with vectors right it's a for on with KX
+
+ align:start position:0%
+with vectors right it's a for on with KX
+ 
+
+ align:start position:0%
+with vectors right it's a for on with KX
+KY k z so I'm suing up all those modes
+
+ align:start position:0%
+KY k z so I'm suing up all those modes
+ 
+
+ align:start position:0%
+KY k z so I'm suing up all those modes
+and that's from left to right minus from
+
+ align:start position:0%
+and that's from left to right minus from
+ 
+
+ align:start position:0%
+and that's from left to right minus from
+right to left give me the left FL so
+
+ align:start position:0%
+right to left give me the left FL so
+ 
+
+ align:start position:0%
+right to left give me the left FL so
+that's what I uh we show before in
+
+ align:start position:0%
+that's what I uh we show before in
+ 
+
+ align:start position:0%
+that's what I uh we show before in
+simpler form but if I do
+
+ align:start position:0%
+simpler form but if I do
+ 
+
+ align:start position:0%
+simpler form but if I do
+this okay and I will get the integral no
+
+ align:start position:0%
+this okay and I will get the integral no
+ 
+
+ align:start position:0%
+this okay and I will get the integral no
+longer just a simple 1/3 CB GMA that's
+
+ align:start position:0%
+longer just a simple 1/3 CB GMA that's
+ 
+
+ align:start position:0%
+longer just a simple 1/3 CB GMA that's
+what we have before and now it's
+
+ align:start position:0%
+what we have before and now it's
+ 
+
+ align:start position:0%
+what we have before and now it's
+integration of all the frequency
+
+ align:start position:0%
+integration of all the frequency
+ 
+
+ align:start position:0%
+integration of all the frequency
+frequency remember fall so the acoustic
+
+ align:start position:0%
+frequency remember fall so the acoustic
+ 
+
+ align:start position:0%
+frequency remember fall so the acoustic
+wave the uh for example low frequency
+
+ align:start position:0%
+wave the uh for example low frequency
+ 
+
+ align:start position:0%
+wave the uh for example low frequency
+acoustic wave that's what you hear and
+
+ align:start position:0%
+acoustic wave that's what you hear and
+ 
+
+ align:start position:0%
+acoustic wave that's what you hear and
+uh they have uh uh the different mean
+
+ align:start position:0%
+uh they have uh uh the different mean
+ 
+
+ align:start position:0%
+uh they have uh uh the different mean
+free paths different group velocity the
+
+ align:start position:0%
+free paths different group velocity the
+ 
+
+ align:start position:0%
+free paths different group velocity the
+higher frequency ones so this can all
+
+ align:start position:0%
+higher frequency ones so this can all
+ 
+
+ align:start position:0%
+higher frequency ones so this can all
+change as a function frequency what we
+
+ align:start position:0%
+change as a function frequency what we
+ 
+
+ align:start position:0%
+change as a function frequency what we
+writing now is the more RoR form for the
+
+ align:start position:0%
+writing now is the more RoR form for the
+ 
+
+ align:start position:0%
+writing now is the more RoR form for the
+thermal conductivity uh carry e
+
+ align:start position:0%
+thermal conductivity uh carry e
+ 
+
+ align:start position:0%
+thermal conductivity uh carry e
+conduction by the L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L okay so this is a about material right
+
+ align:start position:0%
+L okay so this is a about material right
+ 
+
+ align:start position:0%
+L okay so this is a about material right
+and people have measur the theral
+
+ align:start position:0%
+and people have measur the theral
+ 
+
+ align:start position:0%
+and people have measur the theral
+conductivity and this is a typical curve
+
+ align:start position:0%
+conductivity and this is a typical curve
+ 
+
+ align:start position:0%
+conductivity and this is a typical curve
+of Thal conductivity of material versus
+
+ align:start position:0%
+of Thal conductivity of material versus
+ 
+
+ align:start position:0%
+of Thal conductivity of material versus
+temperature and this is specific example
+
+ align:start position:0%
+temperature and this is specific example
+ 
+
+ align:start position:0%
+temperature and this is specific example
+ofum oite and you can say uh there's a
+
+ align:start position:0%
+ofum oite and you can say uh there's a
+ 
+
+ align:start position:0%
+ofum oite and you can say uh there's a
+peak this is B matal this peak is
+
+ align:start position:0%
+peak this is B matal this peak is
+ 
+
+ align:start position:0%
+peak this is B matal this peak is
+typically between 10 to 20
+
+ align:start position:0%
+typically between 10 to 20
+ 
+
+ align:start position:0%
+typically between 10 to 20
+K and then after the PE the drops below
+
+ align:start position:0%
+K and then after the PE the drops below
+ 
+
+ align:start position:0%
+K and then after the PE the drops below
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+in and this actually reflects different
+
+ align:start position:0%
+in and this actually reflects different
+ 
+
+ align:start position:0%
+in and this actually reflects different
+physics so at a very high
+
+ align:start position:0%
+physics so at a very high
+ 
+
+ align:start position:0%
+physics so at a very high
+temperature okay the uh each mold carry
+
+ align:start position:0%
+temperature okay the uh each mold carry
+ 
+
+ align:start position:0%
+temperature okay the uh each mold carry
+energy KT right so the L uh the L of
+
+ align:start position:0%
+energy KT right so the L uh the L of
+ 
+
+ align:start position:0%
+energy KT right so the L uh the L of
+fance is also proportional to T
+
+ align:start position:0%
+fance is also proportional to T
+ 
+
+ align:start position:0%
+fance is also proportional to T
+temperature and in this case case what
+
+ align:start position:0%
+temperature and in this case case what
+ 
+
+ align:start position:0%
+temperature and in this case case what
+happens because as the temperature
+
+ align:start position:0%
+happens because as the temperature
+ 
+
+ align:start position:0%
+happens because as the temperature
+increases you inside more
+
+ align:start position:0%
+increases you inside more
+ 
+
+ align:start position:0%
+increases you inside more
+Fons and they scatter each other they
+
+ align:start position:0%
+Fons and they scatter each other they
+ 
+
+ align:start position:0%
+Fons and they scatter each other they
+scatter each other and they drop the Cal
+
+ align:start position:0%
+scatter each other and they drop the Cal
+ 
+
+ align:start position:0%
+scatter each other and they drop the Cal
+conductivity so that's why the Cal
+
+ align:start position:0%
+conductivity so that's why the Cal
+ 
+
+ align:start position:0%
+conductivity so that's why the Cal
+conductiv is dropping and in fact if you
+
+ align:start position:0%
+conductiv is dropping and in fact if you
+ 
+
+ align:start position:0%
+conductiv is dropping and in fact if you
+follow the arum I
+
+ align:start position:0%
+follow the arum I
+ 
+
+ align:start position:0%
+follow the arum I
+saying the L is proportional to T the
+
+ align:start position:0%
+saying the L is proportional to T the
+ 
+
+ align:start position:0%
+saying the L is proportional to T the
+contivity iners proportional to Surf to
+
+ align:start position:0%
+contivity iners proportional to Surf to
+ 
+
+ align:start position:0%
+contivity iners proportional to Surf to
+temperature but see that's a simple
+
+ align:start position:0%
+temperature but see that's a simple
+ 
+
+ align:start position:0%
+temperature but see that's a simple
+picture and then
+
+ align:start position:0%
+picture and then
+ 
+
+ align:start position:0%
+picture and then
+this exponent is not one it's typic
+
+ align:start position:0%
+this exponent is not one it's typic
+ 
+
+ align:start position:0%
+this exponent is not one it's typic
+depend on matal 1.5 people Z are trying
+
+ align:start position:0%
+depend on matal 1.5 people Z are trying
+ 
+
+ align:start position:0%
+depend on matal 1.5 people Z are trying
+to figure out Y is not exactly
+
+ align:start position:0%
+to figure out Y is not exactly
+ 
+
+ align:start position:0%
+to figure out Y is not exactly
+one okay so this is a higher temperature
+
+ align:start position:0%
+one okay so this is a higher temperature
+ 
+
+ align:start position:0%
+one okay so this is a higher temperature
+range and as you go to lower temperature
+
+ align:start position:0%
+range and as you go to lower temperature
+ 
+
+ align:start position:0%
+range and as you go to lower temperature
+the foron foron scal the lightest W
+
+ align:start position:0%
+the foron foron scal the lightest W
+ 
+
+ align:start position:0%
+the foron foron scal the lightest W
+interaction with itself becomes weaker
+
+ align:start position:0%
+interaction with itself becomes weaker
+ 
+
+ align:start position:0%
+interaction with itself becomes weaker
+so in this case what so the ther cond
+
+ align:start position:0%
+so in this case what so the ther cond
+ 
+
+ align:start position:0%
+so in this case what so the ther cond
+increase right even though if you go to
+
+ align:start position:0%
+increase right even though if you go to
+ 
+
+ align:start position:0%
+increase right even though if you go to
+check specific heat specific heat of the
+
+ align:start position:0%
+check specific heat specific heat of the
+ 
+
+ align:start position:0%
+check specific heat specific heat of the
+which in in this dialectric is due to FS
+
+ align:start position:0%
+which in in this dialectric is due to FS
+ 
+
+ align:start position:0%
+which in in this dialectric is due to FS
+specific is typically this curve okay I
+
+ align:start position:0%
+specific is typically this curve okay I
+ 
+
+ align:start position:0%
+specific is typically this curve okay I
+Q one and it's not a constant uh it
+
+ align:start position:0%
+Q one and it's not a constant uh it
+ 
+
+ align:start position:0%
+Q one and it's not a constant uh it
+increase from low time to high
+
+ align:start position:0%
+increase from low time to high
+ 
+
+ align:start position:0%
+increase from low time to high
+temperature but Thal conductivity so
+
+ align:start position:0%
+temperature but Thal conductivity so
+ 
+
+ align:start position:0%
+temperature but Thal conductivity so
+even though there less energy
+
+ align:start position:0%
+even though there less energy
+ 
+
+ align:start position:0%
+even though there less energy
+specifically the measure of full energy
+
+ align:start position:0%
+specifically the measure of full energy
+ 
+
+ align:start position:0%
+specifically the measure of full energy
+less energy in this region compared this
+
+ align:start position:0%
+less energy in this region compared this
+ 
+
+ align:start position:0%
+less energy in this region compared this
+region but because L scatter the goes
+
+ align:start position:0%
+region but because L scatter the goes
+ 
+
+ align:start position:0%
+region but because L scatter the goes
+longer so the Thal conductivity actually
+
+ align:start position:0%
+longer so the Thal conductivity actually
+ 
+
+ align:start position:0%
+longer so the Thal conductivity actually
+incre okay so the uh so in this region
+
+ align:start position:0%
+incre okay so the uh so in this region
+ 
+
+ align:start position:0%
+incre okay so the uh so in this region
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+typically scatter is no longer dominant
+
+ align:start position:0%
+typically scatter is no longer dominant
+ 
+
+ align:start position:0%
+typically scatter is no longer dominant
+is you got a impurity atoms so for
+
+ align:start position:0%
+is you got a impurity atoms so for
+ 
+
+ align:start position:0%
+is you got a impurity atoms so for
+example in Silicon if you
+
+ align:start position:0%
+example in Silicon if you
+ 
+
+ align:start position:0%
+example in Silicon if you
+have phosphor or Boron you dop it right
+
+ align:start position:0%
+have phosphor or Boron you dop it right
+ 
+
+ align:start position:0%
+have phosphor or Boron you dop it right
+they are lighter so you think about it
+
+ align:start position:0%
+they are lighter so you think about it
+ 
+
+ align:start position:0%
+they are lighter so you think about it
+you have a Str again Fon is the larest
+
+ align:start position:0%
+you have a Str again Fon is the larest
+ 
+
+ align:start position:0%
+you have a Str again Fon is the larest
+you have the same mass for and suddenly
+
+ align:start position:0%
+you have the same mass for and suddenly
+ 
+
+ align:start position:0%
+you have the same mass for and suddenly
+you put a different
+
+ align:start position:0%
+you put a different
+ 
+
+ align:start position:0%
+you put a different
+mass that created some scaling of the of
+
+ align:start position:0%
+mass that created some scaling of the of
+ 
+
+ align:start position:0%
+mass that created some scaling of the of
+the waves and so this is the region
+
+ align:start position:0%
+the waves and so this is the region
+ 
+
+ align:start position:0%
+the waves and so this is the region
+where the
+
+ align:start position:0%
+where the
+ 
+
+ align:start position:0%
+where the
+limit uh the peak here is very much
+
+ align:start position:0%
+limit uh the peak here is very much
+ 
+
+ align:start position:0%
+limit uh the peak here is very much
+limited by this impurities in the
+
+ align:start position:0%
+limited by this impurities in the
+ 
+
+ align:start position:0%
+limited by this impurities in the
+material and
+
+ align:start position:0%
+material and
+ 
+
+ align:start position:0%
+material and
+then when you go to very low temperature
+
+ align:start position:0%
+then when you go to very low temperature
+ 
+
+ align:start position:0%
+then when you go to very low temperature
+so the M pass becomes very long in fact
+
+ align:start position:0%
+so the M pass becomes very long in fact
+ 
+
+ align:start position:0%
+so the M pass becomes very long in fact
+even you make a make a measure make a b
+
+ align:start position:0%
+even you make a make a measure make a b
+ 
+
+ align:start position:0%
+even you make a make a measure make a b
+material the the me fre pass is longer
+
+ align:start position:0%
+material the the me fre pass is longer
+ 
+
+ align:start position:0%
+material the the me fre pass is longer
+than your
+
+ align:start position:0%
+than your
+ 
+
+ align:start position:0%
+than your
+sze so in this case the boundary scatter
+
+ align:start position:0%
+sze so in this case the boundary scatter
+ 
+
+ align:start position:0%
+sze so in this case the boundary scatter
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+dominant and the mean free pass L longer
+
+ align:start position:0%
+dominant and the mean free pass L longer
+ 
+
+ align:start position:0%
+dominant and the mean free pass L longer
+dependent on the frequency but depend on
+
+ align:start position:0%
+dependent on the frequency but depend on
+ 
+
+ align:start position:0%
+dependent on the frequency but depend on
+is limited by the sample size so in this
+
+ align:start position:0%
+is limited by the sample size so in this
+ 
+
+ align:start position:0%
+is limited by the sample size so in this
+region the theral conductivity that is
+
+ align:start position:0%
+region the theral conductivity that is
+ 
+
+ align:start position:0%
+region the theral conductivity that is
+exactly due
+
+ align:start position:0%
+exactly due
+ 
+
+ align:start position:0%
+exactly due
+to uh yeah due to the specific so the
+
+ align:start position:0%
+to uh yeah due to the specific so the
+ 
+
+ align:start position:0%
+to uh yeah due to the specific so the
+behavior just
+
+ align:start position:0%
+behavior just
+ 
+
+ align:start position:0%
+behavior just
+speciic
+
+ align:start position:0%
+speciic
+ 
+
+ align:start position:0%
+speciic
+sample so yes no question because I just
+
+ align:start position:0%
+sample so yes no question because I just
+ 
+
+ align:start position:0%
+sample so yes no question because I just
+think because spef
+
+ align:start position:0%
+think because spef
+ 
+
+ align:start position:0%
+think because spef
+all why that's exactly the reason right
+
+ align:start position:0%
+all why that's exactly the reason right
+ 
+
+ align:start position:0%
+all why that's exactly the reason right
+so by the way this is why black body
+
+ align:start position:0%
+so by the way this is why black body
+ 
+
+ align:start position:0%
+so by the way this is why black body
+radiation the fourth power right
+
+ align:start position:0%
+radiation the fourth power right
+ 
+
+ align:start position:0%
+radiation the fourth power right
+specific is the third power the energy
+
+ align:start position:0%
+specific is the third power the energy
+ 
+
+ align:start position:0%
+specific is the third power the energy
+is Du DT so if you integrate the energy
+
+ align:start position:0%
+is Du DT so if you integrate the energy
+ 
+
+ align:start position:0%
+is Du DT so if you integrate the energy
+is the temperature Force Power and Fon
+
+ align:start position:0%
+is the temperature Force Power and Fon
+ 
+
+ align:start position:0%
+is the temperature Force Power and Fon
+Photon this is regime unfortunately this
+
+ align:start position:0%
+Photon this is regime unfortunately this
+ 
+
+ align:start position:0%
+Photon this is regime unfortunately this
+is very low temperature regime but this
+
+ align:start position:0%
+is very low temperature regime but this
+ 
+
+ align:start position:0%
+is very low temperature regime but this
+is regime Fon behave almost identically
+
+ align:start position:0%
+is regime Fon behave almost identically
+ 
+
+ align:start position:0%
+is regime Fon behave almost identically
+to full no scatter very weak scatter so
+
+ align:start position:0%
+to full no scatter very weak scatter so
+ 
+
+ align:start position:0%
+to full no scatter very weak scatter so
+uh you can see the
+
+ align:start position:0%
+uh you can see the
+ 
+
+ align:start position:0%
+uh you can see the
+temperature power is the
+
+ align:start position:0%
+temperature power is the
+ 
+
+ align:start position:0%
+temperature power is the
+same okay so that's that's a typical
+
+ align:start position:0%
+same okay so that's that's a typical
+ 
+
+ align:start position:0%
+same okay so that's that's a typical
+behavior of lat theral conductivity in C
+
+ align:start position:0%
+behavior of lat theral conductivity in C
+ 
+
+ align:start position:0%
+behavior of lat theral conductivity in C
+and just give one example the highest
+
+ align:start position:0%
+and just give one example the highest
+ 
+
+ align:start position:0%
+and just give one example the highest
+thermal conductivity materal
+
+ align:start position:0%
+thermal conductivity materal
+ 
+
+ align:start position:0%
+thermal conductivity materal
+diamond and if you purify the diamond
+
+ align:start position:0%
+diamond and if you purify the diamond
+ 
+
+ align:start position:0%
+diamond and if you purify the diamond
+you can change this P by uh from uh this
+
+ align:start position:0%
+you can change this P by uh from uh this
+ 
+
+ align:start position:0%
+you can change this P by uh from uh this
+P di at room temperature is about 2,000
+
+ align:start position:0%
+P di at room temperature is about 2,000
+ 
+
+ align:start position:0%
+P di at room temperature is about 2,000
+and that PE will go very high and if you
+
+ align:start position:0%
+and that PE will go very high and if you
+ 
+
+ align:start position:0%
+and that PE will go very high and if you
+purify just say even
+
+ align:start position:0%
+purify just say even
+ 
+
+ align:start position:0%
+purify just say even
+Isotopes right carbon 12 versus carbon
+
+ align:start position:0%
+Isotopes right carbon 12 versus carbon
+ 
+
+ align:start position:0%
+Isotopes right carbon 12 versus carbon
+13 can significant limit this uh the you
+
+ align:start position:0%
+13 can significant limit this uh the you
+ 
+
+ align:start position:0%
+13 can significant limit this uh the you
+my room temperature uh the theral
+
+ align:start position:0%
+my room temperature uh the theral
+ 
+
+ align:start position:0%
+my room temperature uh the theral
+connectivity will be influenced by the
+
+ align:start position:0%
+connectivity will be influenced by the
+ 
+
+ align:start position:0%
+connectivity will be influenced by the
+just the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is okay so now if I combine the theral
+
+ align:start position:0%
+is okay so now if I combine the theral
+ 
+
+ align:start position:0%
+is okay so now if I combine the theral
+conductivity right it turns out lce has
+
+ align:start position:0%
+conductivity right it turns out lce has
+ 
+
+ align:start position:0%
+conductivity right it turns out lce has
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+contribution the electron also carry
+
+ align:start position:0%
+contribution the electron also carry
+ 
+
+ align:start position:0%
+contribution the electron also carry
+here so if I have electron I have hole
+
+ align:start position:0%
+here so if I have electron I have hole
+ 
+
+ align:start position:0%
+here so if I have electron I have hole
+hole also carries here right so I have
+
+ align:start position:0%
+hole also carries here right so I have
+ 
+
+ align:start position:0%
+hole also carries here right so I have
+electron hole and then I mention uh the
+
+ align:start position:0%
+electron hole and then I mention uh the
+ 
+
+ align:start position:0%
+electron hole and then I mention uh the
+uh when they move when electron hold or
+
+ align:start position:0%
+uh when they move when electron hold or
+ 
+
+ align:start position:0%
+uh when they move when electron hold or
+fuse they uh at the higher temperature
+
+ align:start position:0%
+fuse they uh at the higher temperature
+ 
+
+ align:start position:0%
+fuse they uh at the higher temperature
+region you may get more electron ho when
+
+ align:start position:0%
+region you may get more electron ho when
+ 
+
+ align:start position:0%
+region you may get more electron ho when
+you go to lower temperature region they
+
+ align:start position:0%
+you go to lower temperature region they
+ 
+
+ align:start position:0%
+you go to lower temperature region they
+have less electron hole what happens the
+
+ align:start position:0%
+have less electron hole what happens the
+ 
+
+ align:start position:0%
+have less electron hole what happens the
+electron and the hole will combine each
+
+ align:start position:0%
+electron and the hole will combine each
+ 
+
+ align:start position:0%
+electron and the hole will combine each
+with each other and give up heat so in
+
+ align:start position:0%
+with each other and give up heat so in
+ 
+
+ align:start position:0%
+with each other and give up heat so in
+that case they they carry really
+
+ align:start position:0%
+that case they they carry really
+ 
+
+ align:start position:0%
+that case they they carry really
+potential energy from one place to other
+
+ align:start position:0%
+potential energy from one place to other
+ 
+
+ align:start position:0%
+potential energy from one place to other
+and this is a bipol contribution which
+
+ align:start position:0%
+and this is a bipol contribution which
+ 
+
+ align:start position:0%
+and this is a bipol contribution which
+is really bad for Thermo elrics so uh uh
+
+ align:start position:0%
+is really bad for Thermo elrics so uh uh
+ 
+
+ align:start position:0%
+is really bad for Thermo elrics so uh uh
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+example most people do Thermo
+
+ align:start position:0%
+example most people do Thermo
+ 
+
+ align:start position:0%
+example most people do Thermo
+electrics don't pay attention to this
+
+ align:start position:0%
+electrics don't pay attention to this
+ 
+
+ align:start position:0%
+electrics don't pay attention to this
+and uh uh that's wrong okay uh for
+
+ align:start position:0%
+and uh uh that's wrong okay uh for
+ 
+
+ align:start position:0%
+and uh uh that's wrong okay uh for
+example the electronic contribution you
+
+ align:start position:0%
+example the electronic contribution you
+ 
+
+ align:start position:0%
+example the electronic contribution you
+can calculate from with right the
+
+ align:start position:0%
+can calculate from with right the
+ 
+
+ align:start position:0%
+can calculate from with right the
+electric conductivity divide by
+
+ align:start position:0%
+electric conductivity divide by
+ 
+
+ align:start position:0%
+electric conductivity divide by
+conductivity temp constant mention so
+
+ align:start position:0%
+conductivity temp constant mention so
+ 
+
+ align:start position:0%
+conductivity temp constant mention so
+many people would do this they will
+
+ align:start position:0%
+many people would do this they will
+ 
+
+ align:start position:0%
+many people would do this they will
+calculate this term and this term and
+
+ align:start position:0%
+calculate this term and this term and
+ 
+
+ align:start position:0%
+calculate this term and this term and
+they measure this term and they subtract
+
+ align:start position:0%
+they measure this term and they subtract
+ 
+
+ align:start position:0%
+they measure this term and they subtract
+the difference to give you the L but
+
+ align:start position:0%
+the difference to give you the L but
+ 
+
+ align:start position:0%
+the difference to give you the L but
+they don't calculate this term okay and
+
+ align:start position:0%
+they don't calculate this term okay and
+ 
+
+ align:start position:0%
+they don't calculate this term okay and
+this is actually difficult to calculate
+
+ align:start position:0%
+this is actually difficult to calculate
+ 
+
+ align:start position:0%
+this is actually difficult to calculate
+see and that's the reason and but you
+
+ align:start position:0%
+see and that's the reason and but you
+ 
+
+ align:start position:0%
+see and that's the reason and but you
+can see that the Thal conductivity at
+
+ align:start position:0%
+can see that the Thal conductivity at
+ 
+
+ align:start position:0%
+can see that the Thal conductivity at
+higher temperature goes
+
+ align:start position:0%
+higher temperature goes
+ 
+
+ align:start position:0%
+higher temperature goes
+up okay the lat Thal conductivity always
+
+ align:start position:0%
+up okay the lat Thal conductivity always
+ 
+
+ align:start position:0%
+up okay the lat Thal conductivity always
+goes down and the reason for this goes
+
+ align:start position:0%
+goes down and the reason for this goes
+ 
+
+ align:start position:0%
+goes down and the reason for this goes
+up is due to this term a very strong
+
+ align:start position:0%
+up is due to this term a very strong
+ 
+
+ align:start position:0%
+up is due to this term a very strong
+signature of bipolar C conductivity from
+
+ align:start position:0%
+signature of bipolar C conductivity from
+ 
+
+ align:start position:0%
+signature of bipolar C conductivity from
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+and and and corresponding the cback goes
+
+ align:start position:0%
+and and and corresponding the cback goes
+ 
+
+ align:start position:0%
+and and and corresponding the cback goes
+down right the catback because the
+
+ align:start position:0%
+down right the catback because the
+ 
+
+ align:start position:0%
+down right the catback because the
+electron hold cancel that Fe but the Cal
+
+ align:start position:0%
+electron hold cancel that Fe but the Cal
+ 
+
+ align:start position:0%
+electron hold cancel that Fe but the Cal
+conductivity is still getting both terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inal okay so now let's go back I've
+
+ align:start position:0%
+inal okay so now let's go back I've
+ 
+
+ align:start position:0%
+inal okay so now let's go back I've
+talked a long time on this figure of
+
+ align:start position:0%
+talked a long time on this figure of
+ 
+
+ align:start position:0%
+talked a long time on this figure of
+marriage this parameter
+
+ align:start position:0%
+marriage this parameter
+ 
+
+ align:start position:0%
+marriage this parameter
+electric C conductivity and we SP the C
+
+ align:start position:0%
+electric C conductivity and we SP the C
+ 
+
+ align:start position:0%
+electric C conductivity and we SP the C
+conductivity into electronic part colon
+
+ align:start position:0%
+conductivity into electronic part colon
+ 
+
+ align:start position:0%
+conductivity into electronic part colon
+part and uh now if I divide this uh by
+
+ align:start position:0%
+part and uh now if I divide this uh by
+ 
+
+ align:start position:0%
+part and uh now if I divide this uh by
+the uh electric conductivity so here I
+
+ align:start position:0%
+the uh electric conductivity so here I
+ 
+
+ align:start position:0%
+the uh electric conductivity so here I
+have laen
+
+ align:start position:0%
+have laen
+ 
+
+ align:start position:0%
+have laen
+L and here I full on by so Sigma T right
+
+ align:start position:0%
+L and here I full on by so Sigma T right
+ 
+
+ align:start position:0%
+L and here I full on by so Sigma T right
+that's just the um say simple
+
+ align:start position:0%
+that's just the um say simple
+ 
+
+ align:start position:0%
+that's just the um say simple
+manipulation and the lawence L
+
+ align:start position:0%
+manipulation and the lawence L
+ 
+
+ align:start position:0%
+manipulation and the lawence L
+in metal that's the exact L but when you
+
+ align:start position:0%
+in metal that's the exact L but when you
+ 
+
+ align:start position:0%
+in metal that's the exact L but when you
+go semiconductor this depends on L so I
+
+ align:start position:0%
+go semiconductor this depends on L so I
+ 
+
+ align:start position:0%
+go semiconductor this depends on L so I
+have that's why I WR L function n but
+
+ align:start position:0%
+have that's why I WR L function n but
+ 
+
+ align:start position:0%
+have that's why I WR L function n but
+see if you look at it me C cancel each
+
+ align:start position:0%
+see if you look at it me C cancel each
+ 
+
+ align:start position:0%
+see if you look at it me C cancel each
+other the electron above the fir level
+
+ align:start position:0%
+other the electron above the fir level
+ 
+
+ align:start position:0%
+other the electron above the fir level
+electron below the fir level cancel each
+
+ align:start position:0%
+electron below the fir level cancel each
+ 
+
+ align:start position:0%
+electron below the fir level cancel each
+other you don't get
+
+ align:start position:0%
+other you don't get
+ 
+
+ align:start position:0%
+other you don't get
+a so you plug in those lepers the best
+
+ align:start position:0%
+a so you plug in those lepers the best
+ 
+
+ align:start position:0%
+a so you plug in those lepers the best
+you get most metal is about 01
+
+ align:start position:0%
+you get most metal is about 01
+ 
+
+ align:start position:0%
+you get most metal is about 01
+okay when I first get into Ru the C
+
+ align:start position:0%
+okay when I first get into Ru the C
+ 
+
+ align:start position:0%
+okay when I first get into Ru the C
+Electric proposal I didn't know whether
+
+ align:start position:0%
+Electric proposal I didn't know whether
+ 
+
+ align:start position:0%
+Electric proposal I didn't know whether
+metal was good or bad or semiconductor
+
+ align:start position:0%
+metal was good or bad or semiconductor
+ 
+
+ align:start position:0%
+metal was good or bad or semiconductor
+so well now you take a
+
+ align:start position:0%
+so well now you take a
+ 
+
+ align:start position:0%
+so well now you take a
+good right B that's a example and C is
+
+ align:start position:0%
+good right B that's a example and C is
+ 
+
+ align:start position:0%
+good right B that's a example and C is
+about 200 microw
+
+ align:start position:0%
+about 200 microw
+ 
+
+ align:start position:0%
+about 200 microw
+per and is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one per meter so C is just the inverse
+
+ align:start position:0%
+one per meter so C is just the inverse
+ 
+
+ align:start position:0%
+one per meter so C is just the inverse
+of all right so that's the unit of
+
+ align:start position:0%
+of all right so that's the unit of
+ 
+
+ align:start position:0%
+of all right so that's the unit of
+connectivity and you plug in all those
+
+ align:start position:0%
+connectivity and you plug in all those
+ 
+
+ align:start position:0%
+connectivity and you plug in all those
+numbers and then you find that's of the
+
+ align:start position:0%
+numbers and then you find that's of the
+ 
+
+ align:start position:0%
+numbers and then you find that's of the
+order one so uh for from 1950s to 1990s
+
+ align:start position:0%
+order one so uh for from 1950s to 1990s
+ 
+
+ align:start position:0%
+order one so uh for from 1950s to 1990s
+the best thero electric material have a
+
+ align:start position:0%
+the best thero electric material have a
+ 
+
+ align:start position:0%
+the best thero electric material have a
+figure matter about one people have
+
+ align:start position:0%
+figure matter about one people have
+ 
+
+ align:start position:0%
+figure matter about one people have
+because of experimental you can't get
+
+ align:start position:0%
+because of experimental you can't get
+ 
+
+ align:start position:0%
+because of experimental you can't get
+better so people reading lot of papers
+
+ align:start position:0%
+better so people reading lot of papers
+ 
+
+ align:start position:0%
+better so people reading lot of papers
+on why we can't break this is the
+
+ align:start position:0%
+on why we can't break this is the
+ 
+
+ align:start position:0%
+on why we can't break this is the
+absolute maximum so whe they question
+
+ align:start position:0%
+absolute maximum so whe they question
+ 
+
+ align:start position:0%
+absolute maximum so whe they question
+whether their Theory trying to say why
+
+ align:start position:0%
+whether their Theory trying to say why
+ 
+
+ align:start position:0%
+whether their Theory trying to say why
+this is the maximum okay so this is the
+
+ align:start position:0%
+this is the maximum okay so this is the
+ 
+
+ align:start position:0%
+this is the maximum okay so this is the
+U uh uh the really the thetical
+
+ align:start position:0%
+U uh uh the really the thetical
+ 
+
+ align:start position:0%
+U uh uh the really the thetical
+foundation we talk and the last slides
+
+ align:start position:0%
+foundation we talk and the last slides
+ 
+
+ align:start position:0%
+foundation we talk and the last slides
+on this is a uh material I said
+
+ align:start position:0%
+on this is a uh material I said
+ 
+
+ align:start position:0%
+on this is a uh material I said
+sometimes you may get a really good one
+
+ align:start position:0%
+sometimes you may get a really good one
+ 
+
+ align:start position:0%
+sometimes you may get a really good one
+but you throw away because the do isn't
+
+ align:start position:0%
+but you throw away because the do isn't
+ 
+
+ align:start position:0%
+but you throw away because the do isn't
+right you can say that say because the
+
+ align:start position:0%
+right you can say that say because the
+ 
+
+ align:start position:0%
+right you can say that say because the
+dop determine where is the chemical
+
+ align:start position:0%
+dop determine where is the chemical
+ 
+
+ align:start position:0%
+dop determine where is the chemical
+potential right so the properties are so
+
+ align:start position:0%
+potential right so the properties are so
+ 
+
+ align:start position:0%
+potential right so the properties are so
+uh intertrend with each other C by
+
+ align:start position:0%
+uh intertrend with each other C by
+ 
+
+ align:start position:0%
+uh intertrend with each other C by
+coefficient as a function of dopin right
+
+ align:start position:0%
+coefficient as a function of dopin right
+ 
+
+ align:start position:0%
+coefficient as a function of dopin right
+here is bipolar in fact in fact this one
+
+ align:start position:0%
+here is bipolar in fact in fact this one
+ 
+
+ align:start position:0%
+here is bipolar in fact in fact this one
+why I have to check uh the electric
+
+ align:start position:0%
+why I have to check uh the electric
+ 
+
+ align:start position:0%
+why I have to check uh the electric
+conduc this looks better electric
+
+ align:start position:0%
+conduc this looks better electric
+ 
+
+ align:start position:0%
+conduc this looks better electric
+conductivity
+
+ align:start position:0%
+conductivity
+ 
+
+ align:start position:0%
+conductivity
+increases and thermal conductivity and
+
+ align:start position:0%
+increases and thermal conductivity and
+ 
+
+ align:start position:0%
+increases and thermal conductivity and
+you t z at certain
+
+ align:start position:0%
+you t z at certain
+ 
+
+ align:start position:0%
+you t z at certain
+value right so this is a clearly so you
+
+ align:start position:0%
+value right so this is a clearly so you
+ 
+
+ align:start position:0%
+value right so this is a clearly so you
+have to really TW your dopen that's say
+
+ align:start position:0%
+have to really TW your dopen that's say
+ 
+
+ align:start position:0%
+have to really TW your dopen that's say
+adding other materials or creating their
+
+ align:start position:0%
+adding other materials or creating their
+ 
+
+ align:start position:0%
+adding other materials or creating their
+different ways creating dopen carriers
+
+ align:start position:0%
+different ways creating dopen carriers
+ 
+
+ align:start position:0%
+different ways creating dopen carriers
+so this is uh the uh uh the difficulty
+
+ align:start position:0%
+so this is uh the uh uh the difficulty
+ 
+
+ align:start position:0%
+so this is uh the uh uh the difficulty
+with ther electric optimization not of
+
+ align:start position:0%
+with ther electric optimization not of
+ 
+
+ align:start position:0%
+with ther electric optimization not of
+work one has to
+
+ align:start position:0%
+work one has to
+ 
+
+ align:start position:0%
+work one has to
+do okay now we're going to really say
+
+ align:start position:0%
+do okay now we're going to really say
+ 
+
+ align:start position:0%
+do okay now we're going to really say
+What are the
+
+ align:start position:0%
+What are the
+ 
+
+ align:start position:0%
+What are the
+uh yes so that gra was it actually
+
+ align:start position:0%
+uh yes so that gra was it actually
+ 
+
+ align:start position:0%
+uh yes so that gra was it actually
+experim this Cur yeah this Cur for
+
+ align:start position:0%
+experim this Cur yeah this Cur for
+ 
+
+ align:start position:0%
+experim this Cur yeah this Cur for
+calculated right yeah the the typically
+
+ align:start position:0%
+calculated right yeah the the typically
+ 
+
+ align:start position:0%
+calculated right yeah the the typically
+when you say show dots that's mostly
+
+ align:start position:0%
+when you say show dots that's mostly
+ 
+
+ align:start position:0%
+when you say show dots that's mostly
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+okay okay those are experiment what do
+
+ align:start position:0%
+okay okay those are experiment what do
+ 
+
+ align:start position:0%
+okay okay those are experiment what do
+you see here in the experiment so this
+
+ align:start position:0%
+you see here in the experiment so this
+ 
+
+ align:start position:0%
+you see here in the experiment so this
+is a um uh say summary not always
+
+ align:start position:0%
+is a um uh say summary not always
+ 
+
+ align:start position:0%
+is a um uh say summary not always
+updated and people always recording
+
+ align:start position:0%
+updated and people always recording
+ 
+
+ align:start position:0%
+updated and people always recording
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+those days so uh here is a summary of ZT
+
+ align:start position:0%
+those days so uh here is a summary of ZT
+ 
+
+ align:start position:0%
+those days so uh here is a summary of ZT
+of different materials and what people
+
+ align:start position:0%
+of different materials and what people
+ 
+
+ align:start position:0%
+of different materials and what people
+have traditionally been using this cite
+
+ align:start position:0%
+have traditionally been using this cite
+ 
+
+ align:start position:0%
+have traditionally been using this cite
+that's in all modules uh commercial
+
+ align:start position:0%
+that's in all modules uh commercial
+ 
+
+ align:start position:0%
+that's in all modules uh commercial
+module you buy and this is the function
+
+ align:start position:0%
+module you buy and this is the function
+ 
+
+ align:start position:0%
+module you buy and this is the function
+of temperature right so this commercial
+
+ align:start position:0%
+of temperature right so this commercial
+ 
+
+ align:start position:0%
+of temperature right so this commercial
+uh CT kcks around room
+
+ align:start position:0%
+uh CT kcks around room
+ 
+
+ align:start position:0%
+uh CT kcks around room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+one and left and right is in the
+
+ align:start position:0%
+one and left and right is in the
+ 
+
+ align:start position:0%
+one and left and right is in the
+intermediate temperature 400° 500° right
+
+ align:start position:0%
+intermediate temperature 400° 500° right
+ 
+
+ align:start position:0%
+intermediate temperature 400° 500° right
+and the p is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one89 and the SEC manual this is what
+
+ align:start position:0%
+one89 and the SEC manual this is what
+ 
+
+ align:start position:0%
+one89 and the SEC manual this is what
+Lassa has been using Lassa uses for
+
+ align:start position:0%
+Lassa has been using Lassa uses for
+ 
+
+ align:start position:0%
+Lassa has been using Lassa uses for
+space machines they use nuclear as a
+
+ align:start position:0%
+space machines they use nuclear as a
+ 
+
+ align:start position:0%
+space machines they use nuclear as a
+heat source and but they they build
+
+ align:start position:0%
+heat source and but they they build
+ 
+
+ align:start position:0%
+heat source and but they they build
+their system so the H side offer very
+
+ align:start position:0%
+their system so the H side offer very
+ 
+
+ align:start position:0%
+their system so the H side offer very
+high temperature so 6 manum is what L
+
+ align:start position:0%
+high temperature so 6 manum is what L
+ 
+
+ align:start position:0%
+high temperature so 6 manum is what L
+used in the past and remember if you
+
+ align:start position:0%
+used in the past and remember if you
+ 
+
+ align:start position:0%
+used in the past and remember if you
+want to build device you have to have
+
+ align:start position:0%
+want to build device you have to have
+ 
+
+ align:start position:0%
+want to build device you have to have
+both n type and P type materials so uh
+
+ align:start position:0%
+both n type and P type materials so uh
+ 
+
+ align:start position:0%
+both n type and P type materials so uh
+uh it's not all shown whether it's p
+
+ align:start position:0%
+uh it's not all shown whether it's p
+ 
+
+ align:start position:0%
+uh it's not all shown whether it's p
+type or n type but for each time you you
+
+ align:start position:0%
+type or n type but for each time you you
+ 
+
+ align:start position:0%
+type or n type but for each time you you
+build device you need both n and T and
+
+ align:start position:0%
+build device you need both n and T and
+ 
+
+ align:start position:0%
+build device you need both n and T and
+also ideally if we look uh go back to
+
+ align:start position:0%
+also ideally if we look uh go back to
+ 
+
+ align:start position:0%
+also ideally if we look uh go back to
+look at the notes in the uh device
+
+ align:start position:0%
+look at the notes in the uh device
+ 
+
+ align:start position:0%
+look at the notes in the uh device
+section when we talk about device you
+
+ align:start position:0%
+section when we talk about device you
+ 
+
+ align:start position:0%
+section when we talk about device you
+want this two materials closed
+
+ align:start position:0%
+want this two materials closed
+ 
+
+ align:start position:0%
+want this two materials closed
+properties closed otherwise it's not the
+
+ align:start position:0%
+properties closed otherwise it's not the
+ 
+
+ align:start position:0%
+properties closed otherwise it's not the
+material that determine your efficiency
+
+ align:start position:0%
+material that determine your efficiency
+ 
+
+ align:start position:0%
+material that determine your efficiency
+so uh you look at say the same P range
+
+ align:start position:0%
+so uh you look at say the same P range
+ 
+
+ align:start position:0%
+so uh you look at say the same P range
+what mats are
+
+ align:start position:0%
+what mats are
+ 
+
+ align:start position:0%
+what mats are
+below and uh like I said uh ZT has been
+
+ align:start position:0%
+below and uh like I said uh ZT has been
+ 
+
+ align:start position:0%
+below and uh like I said uh ZT has been
+one most of the time and there are some
+
+ align:start position:0%
+one most of the time and there are some
+ 
+
+ align:start position:0%
+one most of the time and there are some
+recent progress will discuss those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+progresses okay this is a more
+
+ align:start position:0%
+progresses okay this is a more
+ 
+
+ align:start position:0%
+progresses okay this is a more
+traditional
+
+ align:start position:0%
+traditional
+ 
+
+ align:start position:0%
+traditional
+material uh like I said this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tye and P Tye
+
+ align:start position:0%
+Tye and P Tye
+ 
+
+ align:start position:0%
+Tye and P Tye
+materials and SC is newer material so
+
+ align:start position:0%
+materials and SC is newer material so
+ 
+
+ align:start position:0%
+materials and SC is newer material so
+the uh commercial is
+
+ align:start position:0%
+the uh commercial is
+ 
+
+ align:start position:0%
+the uh commercial is
+Bid right bid go to periodic table I I
+
+ align:start position:0%
+Bid right bid go to periodic table I I
+ 
+
+ align:start position:0%
+Bid right bid go to periodic table I I
+can't remember all this positions every
+
+ align:start position:0%
+can't remember all this positions every
+ 
+
+ align:start position:0%
+can't remember all this positions every
+time I'm sit in my office look at
+
+ align:start position:0%
+time I'm sit in my office look at
+ 
+
+ align:start position:0%
+time I'm sit in my office look at
+periodic table but this a heavy that's
+
+ align:start position:0%
+periodic table but this a heavy that's
+ 
+
+ align:start position:0%
+periodic table but this a heavy that's
+so dismus colorum heavy elements and why
+
+ align:start position:0%
+so dismus colorum heavy elements and why
+ 
+
+ align:start position:0%
+so dismus colorum heavy elements and why
+uh we want heavy elements in this case
+
+ align:start position:0%
+uh we want heavy elements in this case
+ 
+
+ align:start position:0%
+uh we want heavy elements in this case
+why why it's good so you look at it as
+
+ align:start position:0%
+why why it's good so you look at it as
+ 
+
+ align:start position:0%
+why why it's good so you look at it as
+the uh it becomes heavier the bank Gap
+
+ align:start position:0%
+the uh it becomes heavier the bank Gap
+ 
+
+ align:start position:0%
+the uh it becomes heavier the bank Gap
+decreases here this is the bank Gap the
+
+ align:start position:0%
+decreases here this is the bank Gap the
+ 
+
+ align:start position:0%
+decreases here this is the bank Gap the
+bank Gap decrease uh it's typically
+
+ align:start position:0%
+bank Gap decrease uh it's typically
+ 
+
+ align:start position:0%
+bank Gap decrease uh it's typically
+about you need for the bank Gap versus
+
+ align:start position:0%
+about you need for the bank Gap versus
+ 
+
+ align:start position:0%
+about you need for the bank Gap versus
+temperature range around 10 KT okay 10
+
+ align:start position:0%
+temperature range around 10 KT okay 10
+ 
+
+ align:start position:0%
+temperature range around 10 KT okay 10
+times KBT KT so at room temperature the
+
+ align:start position:0%
+times KBT KT so at room temperature the
+ 
+
+ align:start position:0%
+times KBT KT so at room temperature the
+KT is 26 M electron volts so 10 is
+
+ align:start position:0%
+KT is 26 M electron volts so 10 is
+ 
+
+ align:start position:0%
+KT is 26 M electron volts so 10 is
+a26 turns out the VIS ter back Gap is
+
+ align:start position:0%
+a26 turns out the VIS ter back Gap is
+ 
+
+ align:start position:0%
+a26 turns out the VIS ter back Gap is
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+.15 uh uh range so uh you go to uh see
+
+ align:start position:0%
+.15 uh uh range so uh you go to uh see
+ 
+
+ align:start position:0%
+.15 uh uh range so uh you go to uh see
+heavier material your bank Gap
+
+ align:start position:0%
+heavier material your bank Gap
+ 
+
+ align:start position:0%
+heavier material your bank Gap
+decreases and uh now you think about
+
+ align:start position:0%
+decreases and uh now you think about
+ 
+
+ align:start position:0%
+decreases and uh now you think about
+thermal
+
+ align:start position:0%
+thermal
+ 
+
+ align:start position:0%
+thermal
+conductivity uh recall that when I say
+
+ align:start position:0%
+conductivity uh recall that when I say
+ 
+
+ align:start position:0%
+conductivity uh recall that when I say
+the vibrational frequency right
+
+ align:start position:0%
+the vibrational frequency right
+ 
+
+ align:start position:0%
+the vibrational frequency right
+vibrational frequency is spring constant
+
+ align:start position:0%
+vibrational frequency is spring constant
+ 
+
+ align:start position:0%
+vibrational frequency is spring constant
+divide the mass square root
+
+ align:start position:0%
+divide the mass square root
+ 
+
+ align:start position:0%
+divide the mass square root
+so h mass you got uh the lower
+
+ align:start position:0%
+so h mass you got uh the lower
+ 
+
+ align:start position:0%
+so h mass you got uh the lower
+vibrational frequency lower vibrational
+
+ align:start position:0%
+vibrational frequency lower vibrational
+ 
+
+ align:start position:0%
+vibrational frequency lower vibrational
+frequency you look at the group velocity
+
+ align:start position:0%
+frequency you look at the group velocity
+ 
+
+ align:start position:0%
+frequency you look at the group velocity
+it travels slower so the fall on that
+
+ align:start position:0%
+it travels slower so the fall on that
+ 
+
+ align:start position:0%
+it travels slower so the fall on that
+waves go slow more slowly than lighter
+
+ align:start position:0%
+waves go slow more slowly than lighter
+ 
+
+ align:start position:0%
+waves go slow more slowly than lighter
+ATS so that's why the thermal
+
+ align:start position:0%
+ATS so that's why the thermal
+ 
+
+ align:start position:0%
+ATS so that's why the thermal
+conductivity uh is lower when you go to
+
+ align:start position:0%
+conductivity uh is lower when you go to
+ 
+
+ align:start position:0%
+conductivity uh is lower when you go to
+heavier materials so B ter right uh has
+
+ align:start position:0%
+heavier materials so B ter right uh has
+ 
+
+ align:start position:0%
+heavier materials so B ter right uh has
+a very complicated unit this is really
+
+ align:start position:0%
+a very complicated unit this is really
+ 
+
+ align:start position:0%
+a very complicated unit this is really
+in in terms of full periodicity when you
+
+ align:start position:0%
+in in terms of full periodicity when you
+ 
+
+ align:start position:0%
+in in terms of full periodicity when you
+consider a
+
+ align:start position:0%
+consider a
+ 
+
+ align:start position:0%
+consider a
+hexagonal unic cell is really uh 30.7
+
+ align:start position:0%
+hexagonal unic cell is really uh 30.7
+ 
+
+ align:start position:0%
+hexagonal unic cell is really uh 30.7
+Armstrong many atoms here and uh uh it's
+
+ align:start position:0%
+Armstrong many atoms here and uh uh it's
+ 
+
+ align:start position:0%
+Armstrong many atoms here and uh uh it's
+it's interesting this is where when you
+
+ align:start position:0%
+it's interesting this is where when you
+ 
+
+ align:start position:0%
+it's interesting this is where when you
+really want to understand the material
+
+ align:start position:0%
+really want to understand the material
+ 
+
+ align:start position:0%
+really want to understand the material
+so uh it's a tum BM tum so layer
+
+ align:start position:0%
+so uh it's a tum BM tum so layer
+ 
+
+ align:start position:0%
+so uh it's a tum BM tum so layer
+structure right and this is the tum this
+
+ align:start position:0%
+structure right and this is the tum this
+ 
+
+ align:start position:0%
+structure right and this is the tum this
+is bmus to
+
+ align:start position:0%
+is bmus to
+ 
+
+ align:start position:0%
+is bmus to
+and the in between the layers you got
+
+ align:start position:0%
+and the in between the layers you got
+ 
+
+ align:start position:0%
+and the in between the layers you got
+you see here is T this are one bonding
+
+ align:start position:0%
+you see here is T this are one bonding
+ 
+
+ align:start position:0%
+you see here is T this are one bonding
+and here is more mixture of coent and
+
+ align:start position:0%
+and here is more mixture of coent and
+ 
+
+ align:start position:0%
+and here is more mixture of coent and
+ionic bonding uh and there lot of study
+
+ align:start position:0%
+ionic bonding uh and there lot of study
+ 
+
+ align:start position:0%
+ionic bonding uh and there lot of study
+people looking at which layer is
+
+ align:start position:0%
+people looking at which layer is
+ 
+
+ align:start position:0%
+people looking at which layer is
+conducting electron which layer is
+
+ align:start position:0%
+conducting electron which layer is
+ 
+
+ align:start position:0%
+conducting electron which layer is
+conducting hole and uh uh it's a really
+
+ align:start position:0%
+conducting hole and uh uh it's a really
+ 
+
+ align:start position:0%
+conducting hole and uh uh it's a really
+if you we're still working on
+
+ align:start position:0%
+if you we're still working on
+ 
+
+ align:start position:0%
+if you we're still working on
+buide and it's important to understand
+
+ align:start position:0%
+buide and it's important to understand
+ 
+
+ align:start position:0%
+buide and it's important to understand
+those details because people have been
+
+ align:start position:0%
+those details because people have been
+ 
+
+ align:start position:0%
+those details because people have been
+working this many years you want to do
+
+ align:start position:0%
+working this many years you want to do
+ 
+
+ align:start position:0%
+working this many years you want to do
+something you need to look at detail
+
+ align:start position:0%
+something you need to look at detail
+ 
+
+ align:start position:0%
+something you need to look at detail
+where are the which are the layers that
+
+ align:start position:0%
+where are the which are the layers that
+ 
+
+ align:start position:0%
+where are the which are the layers that
+electron can you think about something
+
+ align:start position:0%
+electron can you think about something
+ 
+
+ align:start position:0%
+electron can you think about something
+that you can for example still get the
+
+ align:start position:0%
+that you can for example still get the
+ 
+
+ align:start position:0%
+that you can for example still get the
+electron transer well in this layer but
+
+ align:start position:0%
+electron transer well in this layer but
+ 
+
+ align:start position:0%
+electron transer well in this layer but
+screw up the Fon kill the Fon
+
+ align:start position:0%
+screw up the Fon kill the Fon
+ 
+
+ align:start position:0%
+screw up the Fon kill the Fon
+propagation in the materials so uh
+
+ align:start position:0%
+propagation in the materials so uh
+ 
+
+ align:start position:0%
+propagation in the materials so uh
+people calculate the B structure I'm not
+
+ align:start position:0%
+people calculate the B structure I'm not
+ 
+
+ align:start position:0%
+people calculate the B structure I'm not
+going to detail this is a really uh how
+
+ align:start position:0%
+going to detail this is a really uh how
+ 
+
+ align:start position:0%
+going to detail this is a really uh how
+you do this uh the span structure
+
+ align:start position:0%
+you do this uh the span structure
+ 
+
+ align:start position:0%
+you do this uh the span structure
+calculation is also relative standard
+
+ align:start position:0%
+calculation is also relative standard
+ 
+
+ align:start position:0%
+calculation is also relative standard
+you do density function Theory
+
+ align:start position:0%
+you do density function Theory
+ 
+
+ align:start position:0%
+you do density function Theory
+calculation and uh this is a pure
+
+ align:start position:0%
+calculation and uh this is a pure
+ 
+
+ align:start position:0%
+calculation and uh this is a pure
+business turn right uh uh uh if you just
+
+ align:start position:0%
+business turn right uh uh uh if you just
+ 
+
+ align:start position:0%
+business turn right uh uh uh if you just
+do pure business turn right the Z the
+
+ align:start position:0%
+do pure business turn right the Z the
+ 
+
+ align:start position:0%
+do pure business turn right the Z the
+best is
+
+ align:start position:0%
+best is
+ 
+
+ align:start position:0%
+best is
+about6 okay and how you get one is
+
+ align:start position:0%
+about6 okay and how you get one is
+ 
+
+ align:start position:0%
+about6 okay and how you get one is
+really by alloying alloying you so you
+
+ align:start position:0%
+really by alloying alloying you so you
+ 
+
+ align:start position:0%
+really by alloying alloying you so you
+can further reduce Thal conductivity by
+
+ align:start position:0%
+can further reduce Thal conductivity by
+ 
+
+ align:start position:0%
+can further reduce Thal conductivity by
+allo so B ter is a Compound
+
+ align:start position:0%
+allo so B ter is a Compound
+ 
+
+ align:start position:0%
+allo so B ter is a Compound
+Semiconductor and they look at the same
+
+ align:start position:0%
+Semiconductor and they look at the same
+ 
+
+ align:start position:0%
+Semiconductor and they look at the same
+column of the periodic table when we are
+
+ align:start position:0%
+column of the periodic table when we are
+ 
+
+ align:start position:0%
+column of the periodic table when we are
+thinking Al is same column periodic
+
+ align:start position:0%
+thinking Al is same column periodic
+ 
+
+ align:start position:0%
+thinking Al is same column periodic
+table and you substitute for example
+
+ align:start position:0%
+table and you substitute for example
+ 
+
+ align:start position:0%
+table and you substitute for example
+buus by
+
+ align:start position:0%
+buus by
+ 
+
+ align:start position:0%
+buus by
+antimony and that way you could reduce
+
+ align:start position:0%
+antimony and that way you could reduce
+ 
+
+ align:start position:0%
+antimony and that way you could reduce
+thermal
+
+ align:start position:0%
+thermal
+ 
+
+ align:start position:0%
+thermal
+conductivity and the best example of
+
+ align:start position:0%
+conductivity and the best example of
+ 
+
+ align:start position:0%
+conductivity and the best example of
+allo reduced th
+
+ align:start position:0%
+allo reduced th
+ 
+
+ align:start position:0%
+allo reduced th
+conductivity is
+
+ align:start position:0%
+conductivity is
+ 
+
+ align:start position:0%
+conductivity is
+Sy okay and the SEC manual uh this is a
+
+ align:start position:0%
+Sy okay and the SEC manual uh this is a
+ 
+
+ align:start position:0%
+Sy okay and the SEC manual uh this is a
+another Thal conductivity unit this is
+
+ align:start position:0%
+another Thal conductivity unit this is
+ 
+
+ align:start position:0%
+another Thal conductivity unit this is
+the inverse thermal
+
+ align:start position:0%
+the inverse thermal
+ 
+
+ align:start position:0%
+the inverse thermal
+conductivity uh uh unit so uh here is
+
+ align:start position:0%
+conductivity uh uh unit so uh here is
+ 
+
+ align:start position:0%
+conductivity uh uh unit so uh here is
+cicon very conductive the theral
+
+ align:start position:0%
+cicon very conductive the theral
+ 
+
+ align:start position:0%
+cicon very conductive the theral
+conductivity of silicon is about
+
+ align:start position:0%
+conductivity of silicon is about
+ 
+
+ align:start position:0%
+conductivity of silicon is about
+150 wat per meter per
+
+ align:start position:0%
+150 wat per meter per
+ 
+
+ align:start position:0%
+150 wat per meter per
+K and the geranium is also very
+
+ align:start position:0%
+K and the geranium is also very
+ 
+
+ align:start position:0%
+K and the geranium is also very
+conductive about 60 wat per meter per K
+
+ align:start position:0%
+conductive about 60 wat per meter per K
+ 
+
+ align:start position:0%
+conductive about 60 wat per meter per K
+okay now you mix a little bit you can
+
+ align:start position:0%
+okay now you mix a little bit you can
+ 
+
+ align:start position:0%
+okay now you mix a little bit you can
+see this is not a linear curve right you
+
+ align:start position:0%
+see this is not a linear curve right you
+ 
+
+ align:start position:0%
+see this is not a linear curve right you
+mix a little bit silicon with Germania
+
+ align:start position:0%
+mix a little bit silicon with Germania
+ 
+
+ align:start position:0%
+mix a little bit silicon with Germania
+your thermal conductivity drop
+
+ align:start position:0%
+your thermal conductivity drop
+ 
+
+ align:start position:0%
+your thermal conductivity drop
+sharply and the lowest thermal
+
+ align:start position:0%
+sharply and the lowest thermal
+ 
+
+ align:start position:0%
+sharply and the lowest thermal
+conductivity here your un state is about
+
+ align:start position:0%
+conductivity here your un state is about
+ 
+
+ align:start position:0%
+conductivity here your un state is about
+67 wat met kin so you drop from 100 to
+
+ align:start position:0%
+67 wat met kin so you drop from 100 to
+ 
+
+ align:start position:0%
+67 wat met kin so you drop from 100 to
+67 by alloy and this is because again if
+
+ align:start position:0%
+67 by alloy and this is because again if
+ 
+
+ align:start position:0%
+67 by alloy and this is because again if
+you think about it you have Atomic chain
+
+ align:start position:0%
+you think about it you have Atomic chain
+ 
+
+ align:start position:0%
+you think about it you have Atomic chain
+right first you do you can try with a
+
+ align:start position:0%
+right first you do you can try with a
+ 
+
+ align:start position:0%
+right first you do you can try with a
+pure atom Ste second you you MX up the
+
+ align:start position:0%
+pure atom Ste second you you MX up the
+ 
+
+ align:start position:0%
+pure atom Ste second you you MX up the
+atom ticity the wave becomes frustrated
+
+ align:start position:0%
+atom ticity the wave becomes frustrated
+ 
+
+ align:start position:0%
+atom ticity the wave becomes frustrated
+and so the theral
+
+ align:start position:0%
+and so the theral
+ 
+
+ align:start position:0%
+and so the theral
+conductivity uh will drop so this is one
+
+ align:start position:0%
+conductivity uh will drop so this is one
+ 
+
+ align:start position:0%
+conductivity uh will drop so this is one
+way of scattering and that's the all th
+
+ align:start position:0%
+way of scattering and that's the all th
+ 
+
+ align:start position:0%
+way of scattering and that's the all th
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+materials that are made of Alloys and uh
+
+ align:start position:0%
+materials that are made of Alloys and uh
+ 
+
+ align:start position:0%
+materials that are made of Alloys and uh
+uh the typical thinking of the alloy is
+
+ align:start position:0%
+uh the typical thinking of the alloy is
+ 
+
+ align:start position:0%
+uh the typical thinking of the alloy is
+in terms of scn create additional
+
+ align:start position:0%
+in terms of scn create additional
+ 
+
+ align:start position:0%
+in terms of scn create additional
+statter and you can see here this is a
+
+ align:start position:0%
+statter and you can see here this is a
+ 
+
+ align:start position:0%
+statter and you can see here this is a
+really statter relation
+
+ align:start position:0%
+really statter relation
+ 
+
+ align:start position:0%
+really statter relation
+what is really scanner you go outside in
+
+ align:start position:0%
+what is really scanner you go outside in
+ 
+
+ align:start position:0%
+what is really scanner you go outside in
+sunny day you see blue
+
+ align:start position:0%
+sunny day you see blue
+ 
+
+ align:start position:0%
+sunny day you see blue
+skies and the blue sky is the blue light
+
+ align:start position:0%
+skies and the blue sky is the blue light
+ 
+
+ align:start position:0%
+skies and the blue sky is the blue light
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+scattered and high frequency blue light
+
+ align:start position:0%
+scattered and high frequency blue light
+ 
+
+ align:start position:0%
+scattered and high frequency blue light
+compared to red right solar radiation
+
+ align:start position:0%
+compared to red right solar radiation
+ 
+
+ align:start position:0%
+compared to red right solar radiation
+The High Frequency scatter more so here
+
+ align:start position:0%
+The High Frequency scatter more so here
+ 
+
+ align:start position:0%
+The High Frequency scatter more so here
+is the really scatter regime that's
+
+ align:start position:0%
+is the really scatter regime that's
+ 
+
+ align:start position:0%
+is the really scatter regime that's
+that's really scatter high frequency and
+
+ align:start position:0%
+that's really scatter high frequency and
+ 
+
+ align:start position:0%
+that's really scatter high frequency and
+the some wave is typical as people model
+
+ align:start position:0%
+the some wave is typical as people model
+ 
+
+ align:start position:0%
+the some wave is typical as people model
+uh high frequency it's a inverse time so
+
+ align:start position:0%
+uh high frequency it's a inverse time so
+ 
+
+ align:start position:0%
+uh high frequency it's a inverse time so
+scatter time relaxation time is shorter
+
+ align:start position:0%
+scatter time relaxation time is shorter
+ 
+
+ align:start position:0%
+scatter time relaxation time is shorter
+so that's really scatter and uh uh then
+
+ align:start position:0%
+so that's really scatter and uh uh then
+ 
+
+ align:start position:0%
+so that's really scatter and uh uh then
+this depends on the mass contrast and
+
+ align:start position:0%
+this depends on the mass contrast and
+ 
+
+ align:start position:0%
+this depends on the mass contrast and
+also depends on lce uh parameter lce
+
+ align:start position:0%
+also depends on lce uh parameter lce
+ 
+
+ align:start position:0%
+also depends on lce uh parameter lce
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+contast those series were done in the
+
+ align:start position:0%
+contast those series were done in the
+ 
+
+ align:start position:0%
+contast those series were done in the
+50s and in fact I have a lot of
+
+ align:start position:0%
+50s and in fact I have a lot of
+ 
+
+ align:start position:0%
+50s and in fact I have a lot of
+Suspicion whether they are truly valid
+
+ align:start position:0%
+Suspicion whether they are truly valid
+ 
+
+ align:start position:0%
+Suspicion whether they are truly valid
+or not and uh uh but say that's what
+
+ align:start position:0%
+or not and uh uh but say that's what
+ 
+
+ align:start position:0%
+or not and uh uh but say that's what
+people doing uh this is the just the
+
+ align:start position:0%
+people doing uh this is the just the
+ 
+
+ align:start position:0%
+people doing uh this is the just the
+Curr St most
+
+ align:start position:0%
+Curr St most
+ 
+
+ align:start position:0%
+Curr St most
+of and the the problem is you go to
+
+ align:start position:0%
+of and the the problem is you go to
+ 
+
+ align:start position:0%
+of and the the problem is you go to
+think about theral conductivity I show
+
+ align:start position:0%
+think about theral conductivity I show
+ 
+
+ align:start position:0%
+think about theral conductivity I show
+payal 13 c v GMA
+
+ align:start position:0%
+payal 13 c v GMA
+ 
+
+ align:start position:0%
+payal 13 c v GMA
+integration and integration is very
+
+ align:start position:0%
+integration and integration is very
+ 
+
+ align:start position:0%
+integration and integration is very
+forgiven okay in the sense if you make
+
+ align:start position:0%
+forgiven okay in the sense if you make
+ 
+
+ align:start position:0%
+forgiven okay in the sense if you make
+the error one place you make up the
+
+ align:start position:0%
+the error one place you make up the
+ 
+
+ align:start position:0%
+the error one place you make up the
+other place and when you don't have
+
+ align:start position:0%
+other place and when you don't have
+ 
+
+ align:start position:0%
+other place and when you don't have
+exact uh Theory there and you got a lot
+
+ align:start position:0%
+exact uh Theory there and you got a lot
+ 
+
+ align:start position:0%
+exact uh Theory there and you got a lot
+of feeding parameter and that
+
+ align:start position:0%
+of feeding parameter and that
+ 
+
+ align:start position:0%
+of feeding parameter and that
+integration can help you publish your
+
+ align:start position:0%
+integration can help you publish your
+ 
+
+ align:start position:0%
+integration can help you publish your
+paper okay
+
+ align:start position:0%
+paper okay
+ 
+
+ align:start position:0%
+paper okay
+but uh the details very often are
+
+ align:start position:0%
+but uh the details very often are
+ 
+
+ align:start position:0%
+but uh the details very often are
+amazing okay like I said uh this is a
+
+ align:start position:0%
+amazing okay like I said uh this is a
+ 
+
+ align:start position:0%
+amazing okay like I said uh this is a
+typically that's how people uh make the
+
+ align:start position:0%
+typically that's how people uh make the
+ 
+
+ align:start position:0%
+typically that's how people uh make the
+material dismus in P5 dismus antimony
+
+ align:start position:0%
+material dismus in P5 dismus antimony
+ 
+
+ align:start position:0%
+material dismus in P5 dismus antimony
+and this x is about 33
+
+ align:start position:0%
+and this x is about 33
+ 
+
+ align:start position:0%
+and this x is about 33
+to.5 and then the end type material
+
+ align:start position:0%
+to.5 and then the end type material
+ 
+
+ align:start position:0%
+to.5 and then the end type material
+dismus anony and with
+
+ align:start position:0%
+dismus anony and with
+ 
+
+ align:start position:0%
+dismus anony and with
+senum and if any of you actually are uh
+
+ align:start position:0%
+senum and if any of you actually are uh
+ 
+
+ align:start position:0%
+senum and if any of you actually are uh
+from physics Department uh you probably
+
+ align:start position:0%
+from physics Department uh you probably
+ 
+
+ align:start position:0%
+from physics Department uh you probably
+went to I remember a few weeks ago there
+
+ align:start position:0%
+went to I remember a few weeks ago there
+ 
+
+ align:start position:0%
+went to I remember a few weeks ago there
+was a seminar on topological conductor
+
+ align:start position:0%
+was a seminar on topological conductor
+ 
+
+ align:start position:0%
+was a seminar on topological conductor
+turns out that this material now it's
+
+ align:start position:0%
+turns out that this material now it's
+ 
+
+ align:start position:0%
+turns out that this material now it's
+very hard in the physics people are
+
+ align:start position:0%
+very hard in the physics people are
+ 
+
+ align:start position:0%
+very hard in the physics people are
+looking at Anon turn right and it's
+
+ align:start position:0%
+looking at Anon turn right and it's
+ 
+
+ align:start position:0%
+looking at Anon turn right and it's
+topological conductor uh so very hot to
+
+ align:start position:0%
+topological conductor uh so very hot to
+ 
+
+ align:start position:0%
+topological conductor uh so very hot to
+clear but see uh we don't know whether
+
+ align:start position:0%
+clear but see uh we don't know whether
+ 
+
+ align:start position:0%
+clear but see uh we don't know whether
+that has any implication of thermo
+
+ align:start position:0%
+that has any implication of thermo
+ 
+
+ align:start position:0%
+that has any implication of thermo
+electrics or
+
+ align:start position:0%
+electrics or
+ 
+
+ align:start position:0%
+electrics or
+not and dopin you can uh always add
+
+ align:start position:0%
+not and dopin you can uh always add
+ 
+
+ align:start position:0%
+not and dopin you can uh always add
+other materials as dopin but say uh here
+
+ align:start position:0%
+other materials as dopin but say uh here
+ 
+
+ align:start position:0%
+other materials as dopin but say uh here
+typically is by Def effect the soal anti
+
+ align:start position:0%
+typically is by Def effect the soal anti
+ 
+
+ align:start position:0%
+typically is by Def effect the soal anti
+side so if you look at it it's possible
+
+ align:start position:0%
+side so if you look at it it's possible
+ 
+
+ align:start position:0%
+side so if you look at it it's possible
+that buiness go to torum side and this
+
+ align:start position:0%
+that buiness go to torum side and this
+ 
+
+ align:start position:0%
+that buiness go to torum side and this
+is a particularly because bmus and torum
+
+ align:start position:0%
+is a particularly because bmus and torum
+ 
+
+ align:start position:0%
+is a particularly because bmus and torum
+there are soall Char say uh electro
+
+ align:start position:0%
+there are soall Char say uh electro
+ 
+
+ align:start position:0%
+there are soall Char say uh electro
+negativity is very similar so they can
+
+ align:start position:0%
+negativity is very similar so they can
+ 
+
+ align:start position:0%
+negativity is very similar so they can
+uh uh the when they exchange positions
+
+ align:start position:0%
+uh uh the when they exchange positions
+ 
+
+ align:start position:0%
+uh uh the when they exchange positions
+uh uh the uh the uh disturbance PR is
+
+ align:start position:0%
+uh uh the uh the uh disturbance PR is
+ 
+
+ align:start position:0%
+uh uh the uh the uh disturbance PR is
+small but the number of charge is
+
+ align:start position:0%
+small but the number of charge is
+ 
+
+ align:start position:0%
+small but the number of charge is
+different so that cre either F or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons okay so now we're moving to so
+
+ align:start position:0%
+electrons okay so now we're moving to so
+ 
+
+ align:start position:0%
+electrons okay so now we're moving to so
+that's traditional material we're now
+
+ align:start position:0%
+that's traditional material we're now
+ 
+
+ align:start position:0%
+that's traditional material we're now
+moving to more uh current materials
+
+ align:start position:0%
+moving to more uh current materials
+ 
+
+ align:start position:0%
+moving to more uh current materials
+people are
+
+ align:start position:0%
+people are
+ 
+
+ align:start position:0%
+people are
+talking uh this is a uh uh oxide um it's
+
+ align:start position:0%
+talking uh this is a uh uh oxide um it's
+ 
+
+ align:start position:0%
+talking uh this is a uh uh oxide um it's
+sodium cobal uh oxide and uh uh this
+
+ align:start position:0%
+sodium cobal uh oxide and uh uh this
+ 
+
+ align:start position:0%
+sodium cobal uh oxide and uh uh this
+were originally started in Japan terak
+
+ align:start position:0%
+were originally started in Japan terak
+ 
+
+ align:start position:0%
+were originally started in Japan terak
+more contribution to this and uh turns
+
+ align:start position:0%
+more contribution to this and uh turns
+ 
+
+ align:start position:0%
+more contribution to this and uh turns
+out people are interested in oxide since
+
+ align:start position:0%
+out people are interested in oxide since
+ 
+
+ align:start position:0%
+out people are interested in oxide since
+1980s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why that's because the high temperature
+
+ align:start position:0%
+why that's because the high temperature
+ 
+
+ align:start position:0%
+why that's because the high temperature
+superconductor was discovered out of
+
+ align:start position:0%
+superconductor was discovered out of
+ 
+
+ align:start position:0%
+superconductor was discovered out of
+oxide it's is
+
+ align:start position:0%
+oxide it's is
+ 
+
+ align:start position:0%
+oxide it's is
+surprising yd you s copper oxygen
+
+ align:start position:0%
+surprising yd you s copper oxygen
+ 
+
+ align:start position:0%
+surprising yd you s copper oxygen
+and that got lower price right see so uh
+
+ align:start position:0%
+and that got lower price right see so uh
+ 
+
+ align:start position:0%
+and that got lower price right see so uh
+the transitional temperature now in this
+
+ align:start position:0%
+the transitional temperature now in this
+ 
+
+ align:start position:0%
+the transitional temperature now in this
+High tempure super conductor uh has
+
+ align:start position:0%
+High tempure super conductor uh has
+ 
+
+ align:start position:0%
+High tempure super conductor uh has
+reached probably around 130 K
+
+ align:start position:0%
+reached probably around 130 K
+ 
+
+ align:start position:0%
+reached probably around 130 K
+140 uh but say uh super conductor itself
+
+ align:start position:0%
+140 uh but say uh super conductor itself
+ 
+
+ align:start position:0%
+140 uh but say uh super conductor itself
+is not interesting for
+
+ align:start position:0%
+is not interesting for
+ 
+
+ align:start position:0%
+is not interesting for
+thermoelectrics why this is because
+
+ align:start position:0%
+thermoelectrics why this is because
+ 
+
+ align:start position:0%
+thermoelectrics why this is because
+there's only one common state so the
+
+ align:start position:0%
+there's only one common state so the
+ 
+
+ align:start position:0%
+there's only one common state so the
+entropy is is zero log of quum state
+
+ align:start position:0%
+entropy is is zero log of quum state
+ 
+
+ align:start position:0%
+entropy is is zero log of quum state
+right that's the for man relation uh uh
+
+ align:start position:0%
+right that's the for man relation uh uh
+ 
+
+ align:start position:0%
+right that's the for man relation uh uh
+entropy carried by say is a l state so
+
+ align:start position:0%
+entropy carried by say is a l state so
+ 
+
+ align:start position:0%
+entropy carried by say is a l state so
+super conductor is not interesting but
+
+ align:start position:0%
+super conductor is not interesting but
+ 
+
+ align:start position:0%
+super conductor is not interesting but
+this one is lot of super conductor and
+
+ align:start position:0%
+this one is lot of super conductor and
+ 
+
+ align:start position:0%
+this one is lot of super conductor and
+uh people have achieve about ZT for one
+
+ align:start position:0%
+uh people have achieve about ZT for one
+ 
+
+ align:start position:0%
+uh people have achieve about ZT for one
+at I think this is around 800 de CS so
+
+ align:start position:0%
+at I think this is around 800 de CS so
+ 
+
+ align:start position:0%
+at I think this is around 800 de CS so
+it's a high temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application uh half poer uh I mentioned
+
+ align:start position:0%
+application uh half poer uh I mentioned
+ 
+
+ align:start position:0%
+application uh half poer uh I mentioned
+this material uh
+
+ align:start position:0%
+this material uh
+ 
+
+ align:start position:0%
+this material uh
+because if you go to Japan I talk a lot
+
+ align:start position:0%
+because if you go to Japan I talk a lot
+ 
+
+ align:start position:0%
+because if you go to Japan I talk a lot
+to uh uh Japan uh C ELC guys and also
+
+ align:start position:0%
+to uh uh Japan uh C ELC guys and also
+ 
+
+ align:start position:0%
+to uh uh Japan uh C ELC guys and also
+from a
+
+ align:start position:0%
+from a
+ 
+
+ align:start position:0%
+from a
+company uh whenever you work on you look
+
+ align:start position:0%
+company uh whenever you work on you look
+ 
+
+ align:start position:0%
+company uh whenever you work on you look
+at the disos ter uh they they whereare
+
+ align:start position:0%
+at the disos ter uh they they whereare
+ 
+
+ align:start position:0%
+at the disos ter uh they they whereare
+Japan is very sensitive this
+
+ align:start position:0%
+Japan is very sensitive this
+ 
+
+ align:start position:0%
+Japan is very sensitive this
+because uh they have limited amount of
+
+ align:start position:0%
+because uh they have limited amount of
+ 
+
+ align:start position:0%
+because uh they have limited amount of
+materials right small country and the
+
+ align:start position:0%
+materials right small country and the
+ 
+
+ align:start position:0%
+materials right small country and the
+resources very limited so they don't
+
+ align:start position:0%
+resources very limited so they don't
+ 
+
+ align:start position:0%
+resources very limited so they don't
+want they always say can you make out of
+
+ align:start position:0%
+want they always say can you make out of
+ 
+
+ align:start position:0%
+want they always say can you make out of
+this abond material what are the abond
+
+ align:start position:0%
+this abond material what are the abond
+ 
+
+ align:start position:0%
+this abond material what are the abond
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+City and aluminum so those type of
+
+ align:start position:0%
+City and aluminum so those type of
+ 
+
+ align:start position:0%
+City and aluminum so those type of
+materials and uh uh so this is one
+
+ align:start position:0%
+materials and uh uh so this is one
+ 
+
+ align:start position:0%
+materials and uh uh so this is one
+example where the material is called
+
+ align:start position:0%
+example where the material is called
+ 
+
+ align:start position:0%
+example where the material is called
+abundant
+
+ align:start position:0%
+abundant
+ 
+
+ align:start position:0%
+abundant
+ni uh uh kin and tanium and it has
+
+ align:start position:0%
+ni uh uh kin and tanium and it has
+ 
+
+ align:start position:0%
+ni uh uh kin and tanium and it has
+reached a reasonable uh fig of marage
+
+ align:start position:0%
+reached a reasonable uh fig of marage
+ 
+
+ align:start position:0%
+reached a reasonable uh fig of marage
+and this is where for example you look
+
+ align:start position:0%
+and this is where for example you look
+ 
+
+ align:start position:0%
+and this is where for example you look
+at even with this biger merage C cond is
+
+ align:start position:0%
+at even with this biger merage C cond is
+ 
+
+ align:start position:0%
+at even with this biger merage C cond is
+still very high why is still very high
+
+ align:start position:0%
+still very high why is still very high
+ 
+
+ align:start position:0%
+still very high why is still very high
+why I say it's very high because you
+
+ align:start position:0%
+why I say it's very high because you
+ 
+
+ align:start position:0%
+why I say it's very high because you
+always think of BU St right that's a
+
+ align:start position:0%
+always think of BU St right that's a
+ 
+
+ align:start position:0%
+always think of BU St right that's a
+good number to remember Cal conductivity
+
+ align:start position:0%
+good number to remember Cal conductivity
+ 
+
+ align:start position:0%
+good number to remember Cal conductivity
+is about one or 1.5 C is 100 microwatt
+
+ align:start position:0%
+is about one or 1.5 C is 100 microwatt
+ 
+
+ align:start position:0%
+is about one or 1.5 C is 100 microwatt
+per celvin and
+
+ align:start position:0%
+per celvin and
+ 
+
+ align:start position:0%
+per celvin and
+electric so if you look at this the
+
+ align:start position:0%
+electric so if you look at this the
+ 
+
+ align:start position:0%
+electric so if you look at this the
+ctivity is in the denominator and they
+
+ align:start position:0%
+ctivity is in the denominator and they
+ 
+
+ align:start position:0%
+ctivity is in the denominator and they
+get this good uh ZT that means electron
+
+ align:start position:0%
+get this good uh ZT that means electron
+ 
+
+ align:start position:0%
+get this good uh ZT that means electron
+is really good right s sare Sigma that's
+
+ align:start position:0%
+is really good right s sare Sigma that's
+ 
+
+ align:start position:0%
+is really good right s sare Sigma that's
+the power factor is pretty good can you
+
+ align:start position:0%
+the power factor is pretty good can you
+ 
+
+ align:start position:0%
+the power factor is pretty good can you
+kill this guy can you kill it thermal
+
+ align:start position:0%
+kill this guy can you kill it thermal
+ 
+
+ align:start position:0%
+kill this guy can you kill it thermal
+conductivity reduce it how
+
+ align:start position:0%
+conductivity reduce it how
+ 
+
+ align:start position:0%
+conductivity reduce it how
+can you reduce the F part you don't just
+
+ align:start position:0%
+can you reduce the F part you don't just
+ 
+
+ align:start position:0%
+can you reduce the F part you don't just
+want to reduce because the electronic
+
+ align:start position:0%
+want to reduce because the electronic
+ 
+
+ align:start position:0%
+want to reduce because the electronic
+also part of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z okay so uh people now looking into if
+
+ align:start position:0%
+Z okay so uh people now looking into if
+ 
+
+ align:start position:0%
+Z okay so uh people now looking into if
+you look at the P materials right uh
+
+ align:start position:0%
+you look at the P materials right uh
+ 
+
+ align:start position:0%
+you look at the P materials right uh
+it's typically bu ter let ter manual
+
+ align:start position:0%
+it's typically bu ter let ter manual
+ 
+
+ align:start position:0%
+it's typically bu ter let ter manual
+those are simple structures simple
+
+ align:start position:0%
+those are simple structures simple
+ 
+
+ align:start position:0%
+those are simple structures simple
+compounds Two element binary
+
+ align:start position:0%
+compounds Two element binary
+ 
+
+ align:start position:0%
+compounds Two element binary
+right and now people are looking going
+
+ align:start position:0%
+right and now people are looking going
+ 
+
+ align:start position:0%
+right and now people are looking going
+more into more complex
+
+ align:start position:0%
+more into more complex
+ 
+
+ align:start position:0%
+more into more complex
+structures and the why complex
+
+ align:start position:0%
+structures and the why complex
+ 
+
+ align:start position:0%
+structures and the why complex
+structure yeah from Thal connectivity
+
+ align:start position:0%
+structure yeah from Thal connectivity
+ 
+
+ align:start position:0%
+structure yeah from Thal connectivity
+point of view there is a good reason
+
+ align:start position:0%
+point of view there is a good reason
+ 
+
+ align:start position:0%
+point of view there is a good reason
+there uh uh this is a few lecture back I
+
+ align:start position:0%
+there uh uh this is a few lecture back I
+ 
+
+ align:start position:0%
+there uh uh this is a few lecture back I
+was talking about the mes right uh in
+
+ align:start position:0%
+was talking about the mes right uh in
+ 
+
+ align:start position:0%
+was talking about the mes right uh in
+terms of op forong acoustic forong op
+
+ align:start position:0%
+terms of op forong acoustic forong op
+ 
+
+ align:start position:0%
+terms of op forong acoustic forong op
+Fon is very flat and acoustic Fon is
+
+ align:start position:0%
+Fon is very flat and acoustic Fon is
+ 
+
+ align:start position:0%
+Fon is very flat and acoustic Fon is
+really the one that carries Heat
+
+ align:start position:0%
+really the one that carries Heat
+ 
+
+ align:start position:0%
+really the one that carries Heat
+so when you got a lot of atem in the
+
+ align:start position:0%
+so when you got a lot of atem in the
+ 
+
+ align:start position:0%
+so when you got a lot of atem in the
+Unis
+
+ align:start position:0%
+Unis
+ 
+
+ align:start position:0%
+Unis
+cell you have lot of op branches so
+
+ align:start position:0%
+cell you have lot of op branches so
+ 
+
+ align:start position:0%
+cell you have lot of op branches so
+those out brand don't carry much GE so
+
+ align:start position:0%
+those out brand don't carry much GE so
+ 
+
+ align:start position:0%
+those out brand don't carry much GE so
+the uh that's the more complex Crystal
+
+ align:start position:0%
+the uh that's the more complex Crystal
+ 
+
+ align:start position:0%
+the uh that's the more complex Crystal
+typically the lower is their C
+
+ align:start position:0%
+typically the lower is their C
+ 
+
+ align:start position:0%
+typically the lower is their C
+connectivity and that's only a very
+
+ align:start position:0%
+connectivity and that's only a very
+ 
+
+ align:start position:0%
+connectivity and that's only a very
+simple uh handen uh uh way of saying and
+
+ align:start position:0%
+simple uh handen uh uh way of saying and
+ 
+
+ align:start position:0%
+simple uh handen uh uh way of saying and
+of course you can say some of this
+
+ align:start position:0%
+of course you can say some of this
+ 
+
+ align:start position:0%
+of course you can say some of this
+material have really low of conductivity
+
+ align:start position:0%
+material have really low of conductivity
+ 
+
+ align:start position:0%
+material have really low of conductivity
+bu turn right is is here right and this
+
+ align:start position:0%
+bu turn right is is here right and this
+ 
+
+ align:start position:0%
+bu turn right is is here right and this
+like want to find out this Z
+
+ align:start position:0%
+like want to find out this Z
+ 
+
+ align:start position:0%
+like want to find out this Z
+zinc zinc is a b if you can make zinc
+
+ align:start position:0%
+zinc zinc is a b if you can make zinc
+ 
+
+ align:start position:0%
+zinc zinc is a b if you can make zinc
+zinc zinc is a good one if you can make
+
+ align:start position:0%
+zinc zinc is a good one if you can make
+ 
+
+ align:start position:0%
+zinc zinc is a good one if you can make
+the work right uh and it has very low
+
+ align:start position:0%
+the work right uh and it has very low
+ 
+
+ align:start position:0%
+the work right uh and it has very low
+Thal conductivity and in fact
+
+ align:start position:0%
+Thal conductivity and in fact
+ 
+
+ align:start position:0%
+Thal conductivity and in fact
+zinc electric F mer now has reached I
+
+ align:start position:0%
+zinc electric F mer now has reached I
+ 
+
+ align:start position:0%
+zinc electric F mer now has reached I
+think it's about 1.4
+
+ align:start position:0%
+think it's about 1.4
+ 
+
+ align:start position:0%
+think it's about 1.4
+um pretty good except there are also
+
+ align:start position:0%
+um pretty good except there are also
+ 
+
+ align:start position:0%
+um pretty good except there are also
+issues material stability and when you
+
+ align:start position:0%
+issues material stability and when you
+ 
+
+ align:start position:0%
+issues material stability and when you
+heat up to high
+
+ align:start position:0%
+heat up to high
+ 
+
+ align:start position:0%
+heat up to high
+temperature zinc speed up I have seen
+
+ align:start position:0%
+temperature zinc speed up I have seen
+ 
+
+ align:start position:0%
+temperature zinc speed up I have seen
+pictures showing that the under tempure
+
+ align:start position:0%
+pictures showing that the under tempure
+ 
+
+ align:start position:0%
+pictures showing that the under tempure
+gradient is the material grew here okay
+
+ align:start position:0%
+gradient is the material grew here okay
+ 
+
+ align:start position:0%
+gradient is the material grew here okay
+the here are Z coming out so You' got a
+
+ align:start position:0%
+the here are Z coming out so You' got a
+ 
+
+ align:start position:0%
+the here are Z coming out so You' got a
+lot of material reliability issues also
+
+ align:start position:0%
+lot of material reliability issues also
+ 
+
+ align:start position:0%
+lot of material reliability issues also
+and uh uh so the uh but uh generally
+
+ align:start position:0%
+and uh uh so the uh but uh generally
+ 
+
+ align:start position:0%
+and uh uh so the uh but uh generally
+there are L people into a lot more
+
+ align:start position:0%
+there are L people into a lot more
+ 
+
+ align:start position:0%
+there are L people into a lot more
+complex structures Crystal
+
+ align:start position:0%
+complex structures Crystal
+ 
+
+ align:start position:0%
+complex structures Crystal
+structures and a broader much broader
+
+ align:start position:0%
+structures and a broader much broader
+ 
+
+ align:start position:0%
+structures and a broader much broader
+range of some electric materials I
+
+ align:start position:0%
+range of some electric materials I
+ 
+
+ align:start position:0%
+range of some electric materials I
+mentioned this already but now let's
+
+ align:start position:0%
+mentioned this already but now let's
+ 
+
+ align:start position:0%
+mentioned this already but now let's
+look at the ideas right uh which the
+
+ align:start position:0%
+look at the ideas right uh which the
+ 
+
+ align:start position:0%
+look at the ideas right uh which the
+complex structure and this is another
+
+ align:start position:0%
+complex structure and this is another
+ 
+
+ align:start position:0%
+complex structure and this is another
+idea uh that's really interesting
+
+ align:start position:0%
+idea uh that's really interesting
+ 
+
+ align:start position:0%
+idea uh that's really interesting
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh uh alloy if you think about silicon
+
+ align:start position:0%
+uh uh alloy if you think about silicon
+ 
+
+ align:start position:0%
+uh uh alloy if you think about silicon
+gum
+
+ align:start position:0%
+gum
+ 
+
+ align:start position:0%
+gum
+alloy and it's really geranium go to
+
+ align:start position:0%
+alloy and it's really geranium go to
+ 
+
+ align:start position:0%
+alloy and it's really geranium go to
+Silicon Atomic side so you can think
+
+ align:start position:0%
+Silicon Atomic side so you can think
+ 
+
+ align:start position:0%
+Silicon Atomic side so you can think
+about that as a substitution right so
+
+ align:start position:0%
+about that as a substitution right so
+ 
+
+ align:start position:0%
+about that as a substitution right so
+silicon germanium substitute silicon
+
+ align:start position:0%
+silicon germanium substitute silicon
+ 
+
+ align:start position:0%
+silicon germanium substitute silicon
+atom the L is the if you think about
+
+ align:start position:0%
+atom the L is the if you think about
+ 
+
+ align:start position:0%
+atom the L is the if you think about
+cube right and let's take a cry right
+
+ align:start position:0%
+cube right and let's take a cry right
+ 
+
+ align:start position:0%
+cube right and let's take a cry right
+think about Cube and silicon sits in the
+
+ align:start position:0%
+think about Cube and silicon sits in the
+ 
+
+ align:start position:0%
+think about Cube and silicon sits in the
+corner of the cube now you take out one
+
+ align:start position:0%
+corner of the cube now you take out one
+ 
+
+ align:start position:0%
+corner of the cube now you take out one
+of the corner you put a gtic and so the
+
+ align:start position:0%
+of the corner you put a gtic and so the
+ 
+
+ align:start position:0%
+of the corner you put a gtic and so the
+this is a uh substitutional uh type of I
+
+ align:start position:0%
+this is a uh substitutional uh type of I
+ 
+
+ align:start position:0%
+this is a uh substitutional uh type of I
+call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and Scar is a simple interesting
+
+ align:start position:0%
+that and Scar is a simple interesting
+ 
+
+ align:start position:0%
+that and Scar is a simple interesting
+material uh this is a SC Cal antim
+
+ align:start position:0%
+material uh this is a SC Cal antim
+ 
+
+ align:start position:0%
+material uh this is a SC Cal antim
+orium IR that type of
+
+ align:start position:0%
+orium IR that type of
+ 
+
+ align:start position:0%
+orium IR that type of
+structure and what's interesting is it
+
+ align:start position:0%
+structure and what's interesting is it
+ 
+
+ align:start position:0%
+structure and what's interesting is it
+has a very large Unis cell lot of atoms
+
+ align:start position:0%
+has a very large Unis cell lot of atoms
+ 
+
+ align:start position:0%
+has a very large Unis cell lot of atoms
+there and also in those unic cell so
+
+ align:start position:0%
+there and also in those unic cell so
+ 
+
+ align:start position:0%
+there and also in those unic cell so
+uh uh here we got two V so you can see
+
+ align:start position:0%
+uh uh here we got two V so you can see
+ 
+
+ align:start position:0%
+uh uh here we got two V so you can see
+this each is a square right but in uh
+
+ align:start position:0%
+this each is a square right but in uh
+ 
+
+ align:start position:0%
+this each is a square right but in uh
+this eight uh how many we have eight
+
+ align:start position:0%
+this eight uh how many we have eight
+ 
+
+ align:start position:0%
+this eight uh how many we have eight
+cubes six of the square has a atoms
+
+ align:start position:0%
+cubes six of the square has a atoms
+ 
+
+ align:start position:0%
+cubes six of the square has a atoms
+inside two of them don't have anything
+
+ align:start position:0%
+inside two of them don't have anything
+ 
+
+ align:start position:0%
+inside two of them don't have anything
+inside so there is a open space
+
+ align:start position:0%
+inside so there is a open space
+ 
+
+ align:start position:0%
+inside so there is a open space
+here uh the open space give you
+
+ align:start position:0%
+here uh the open space give you
+ 
+
+ align:start position:0%
+here uh the open space give you
+opportunity let's put another at
+
+ align:start position:0%
+opportunity let's put another at
+ 
+
+ align:start position:0%
+opportunity let's put another at
+there another this atom has a very
+
+ align:start position:0%
+there another this atom has a very
+ 
+
+ align:start position:0%
+there another this atom has a very
+different characteristic from the host
+
+ align:start position:0%
+different characteristic from the host
+ 
+
+ align:start position:0%
+different characteristic from the host
+atom cob UL so the idea is like a r
+
+ align:start position:0%
+atom cob UL so the idea is like a r
+ 
+
+ align:start position:0%
+atom cob UL so the idea is like a r
+slate you put the atom the r wrong and
+
+ align:start position:0%
+slate you put the atom the r wrong and
+ 
+
+ align:start position:0%
+slate you put the atom the r wrong and
+this rine will disturb the normally
+
+ align:start position:0%
+this rine will disturb the normally
+ 
+
+ align:start position:0%
+this rine will disturb the normally
+periodical L waves in the surrounding
+
+ align:start position:0%
+periodical L waves in the surrounding
+ 
+
+ align:start position:0%
+periodical L waves in the surrounding
+material surrounding the the lat itself
+
+ align:start position:0%
+material surrounding the the lat itself
+ 
+
+ align:start position:0%
+material surrounding the the lat itself
+so that was called fullon r
+
+ align:start position:0%
+so that was called fullon r
+ 
+
+ align:start position:0%
+so that was called fullon r
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh next one it's example
+
+ align:start position:0%
+uh next one it's example
+ 
+
+ align:start position:0%
+uh next one it's example
+of you can see
+
+ align:start position:0%
+of you can see
+ 
+
+ align:start position:0%
+of you can see
+C and you feel this with other rular Lum
+
+ align:start position:0%
+C and you feel this with other rular Lum
+ 
+
+ align:start position:0%
+C and you feel this with other rular Lum
+and people try it many different way
+
+ align:start position:0%
+and people try it many different way
+ 
+
+ align:start position:0%
+and people try it many different way
+this is a steel I said uh I was in the
+
+ align:start position:0%
+this is a steel I said uh I was in the
+ 
+
+ align:start position:0%
+this is a steel I said uh I was in the
+meeting last week and people are still
+
+ align:start position:0%
+meeting last week and people are still
+ 
+
+ align:start position:0%
+meeting last week and people are still
+putting first with one r one atom one
+
+ align:start position:0%
+putting first with one r one atom one
+ 
+
+ align:start position:0%
+putting first with one r one atom one
+type of atom now people gotone to three
+
+ align:start position:0%
+type of atom now people gotone to three
+ 
+
+ align:start position:0%
+type of atom now people gotone to three
+rackers well the hope is each rler have
+
+ align:start position:0%
+rackers well the hope is each rler have
+ 
+
+ align:start position:0%
+rackers well the hope is each rler have
+its own rling
+
+ align:start position:0%
+its own rling
+ 
+
+ align:start position:0%
+its own rling
+frequency and you kill the whole uh
+
+ align:start position:0%
+frequency and you kill the whole uh
+ 
+
+ align:start position:0%
+frequency and you kill the whole uh
+acoustic frequency of the whole uh LS
+
+ align:start position:0%
+acoustic frequency of the whole uh LS
+ 
+
+ align:start position:0%
+acoustic frequency of the whole uh LS
+waves so uh this is a clearly a very
+
+ align:start position:0%
+waves so uh this is a clearly a very
+ 
+
+ align:start position:0%
+waves so uh this is a clearly a very
+dramatic decrease in the latest thermal
+
+ align:start position:0%
+dramatic decrease in the latest thermal
+ 
+
+ align:start position:0%
+dramatic decrease in the latest thermal
+connectivity and people have done uh
+
+ align:start position:0%
+connectivity and people have done uh
+ 
+
+ align:start position:0%
+connectivity and people have done uh
+Neutron scattering to actually look at
+
+ align:start position:0%
+Neutron scattering to actually look at
+ 
+
+ align:start position:0%
+Neutron scattering to actually look at
+the Atomic
+
+ align:start position:0%
+the Atomic
+ 
+
+ align:start position:0%
+the Atomic
+displacement in this materials so you
+
+ align:start position:0%
+displacement in this materials so you
+ 
+
+ align:start position:0%
+displacement in this materials so you
+can see here this is a lum uh uh cobal
+
+ align:start position:0%
+can see here this is a lum uh uh cobal
+ 
+
+ align:start position:0%
+can see here this is a lum uh uh cobal
+anite right so uh here you have ion
+
+ align:start position:0%
+anite right so uh here you have ion
+ 
+
+ align:start position:0%
+anite right so uh here you have ion
+cobal that's their atomic display of it
+
+ align:start position:0%
+cobal that's their atomic display of it
+ 
+
+ align:start position:0%
+cobal that's their atomic display of it
+so inside is doing Browning motion and
+
+ align:start position:0%
+so inside is doing Browning motion and
+ 
+
+ align:start position:0%
+so inside is doing Browning motion and
+this measurement you can actually
+
+ align:start position:0%
+this measurement you can actually
+ 
+
+ align:start position:0%
+this measurement you can actually
+measure what's the amplitude this is
+
+ align:start position:0%
+measure what's the amplitude this is
+ 
+
+ align:start position:0%
+measure what's the amplitude this is
+Armstrong Square you here and what's the
+
+ align:start position:0%
+Armstrong Square you here and what's the
+ 
+
+ align:start position:0%
+Armstrong Square you here and what's the
+amplitude of the motion and the Lum they
+
+ align:start position:0%
+amplitude of the motion and the Lum they
+ 
+
+ align:start position:0%
+amplitude of the motion and the Lum they
+put into the cage there seems to be have
+
+ align:start position:0%
+put into the cage there seems to be have
+ 
+
+ align:start position:0%
+put into the cage there seems to be have
+a very large uh ude here you can see and
+
+ align:start position:0%
+a very large uh ude here you can see and
+ 
+
+ align:start position:0%
+a very large uh ude here you can see and
+the uh the theory is that this uh
+
+ align:start position:0%
+the uh the theory is that this uh
+ 
+
+ align:start position:0%
+the uh the theory is that this uh
+scatter the fors I think the again the
+
+ align:start position:0%
+scatter the fors I think the again the
+ 
+
+ align:start position:0%
+scatter the fors I think the again the
+theory is still evolving okay and the
+
+ align:start position:0%
+theory is still evolving okay and the
+ 
+
+ align:start position:0%
+theory is still evolving okay and the
+explanation people have came up with
+
+ align:start position:0%
+explanation people have came up with
+ 
+
+ align:start position:0%
+explanation people have came up with
+different explanations but you try to uh
+
+ align:start position:0%
+different explanations but you try to uh
+ 
+
+ align:start position:0%
+different explanations but you try to uh
+uh do the uh uh modeling experiment to
+
+ align:start position:0%
+uh do the uh uh modeling experiment to
+ 
+
+ align:start position:0%
+uh do the uh uh modeling experiment to
+really make this
+
+ align:start position:0%
+really make this
+ 
+
+ align:start position:0%
+really make this
+muchal uh here
+
+ align:start position:0%
+muchal uh here
+ 
+
+ align:start position:0%
+muchal uh here
+uh is the uh this is a I I think I
+
+ align:start position:0%
+uh is the uh this is a I I think I
+ 
+
+ align:start position:0%
+uh is the uh this is a I I think I
+forgot whether this is G type and N type
+
+ align:start position:0%
+forgot whether this is G type and N type
+ 
+
+ align:start position:0%
+forgot whether this is G type and N type
+and but I do want to tell you a
+
+ align:start position:0%
+and but I do want to tell you a
+ 
+
+ align:start position:0%
+and but I do want to tell you a
+story uh many uh years ago people
+
+ align:start position:0%
+story uh many uh years ago people
+ 
+
+ align:start position:0%
+story uh many uh years ago people
+reported P type uh scites cob timite
+
+ align:start position:0%
+reported P type uh scites cob timite
+ 
+
+ align:start position:0%
+reported P type uh scites cob timite
+have figure merital
+
+ align:start position:0%
+have figure merital
+ 
+
+ align:start position:0%
+have figure merital
+1.4 and now nobody can get
+
+ align:start position:0%
+1.4 and now nobody can get
+ 
+
+ align:start position:0%
+1.4 and now nobody can get
+1.4 everybody the best you can get is
+
+ align:start position:0%
+1.4 everybody the best you can get is
+ 
+
+ align:start position:0%
+1.4 everybody the best you can get is
+.95 and the reason this is bring up a
+
+ align:start position:0%
+.95 and the reason this is bring up a
+ 
+
+ align:start position:0%
+.95 and the reason this is bring up a
+very important Point Thal electrical
+
+ align:start position:0%
+very important Point Thal electrical
+ 
+
+ align:start position:0%
+very important Point Thal electrical
+research measuring this property is
+
+ align:start position:0%
+research measuring this property is
+ 
+
+ align:start position:0%
+research measuring this property is
+tricky okay and it has three property to
+
+ align:start position:0%
+tricky okay and it has three property to
+ 
+
+ align:start position:0%
+tricky okay and it has three property to
+measure electric conductivity thermal
+
+ align:start position:0%
+measure electric conductivity thermal
+ 
+
+ align:start position:0%
+measure electric conductivity thermal
+conductivity cack and even if you are
+
+ align:start position:0%
+conductivity cack and even if you are
+ 
+
+ align:start position:0%
+conductivity cack and even if you are
+very good each property you say okay I
+
+ align:start position:0%
+very good each property you say okay I
+ 
+
+ align:start position:0%
+very good each property you say okay I
+have about 5% uncertainty which I think
+
+ align:start position:0%
+have about 5% uncertainty which I think
+ 
+
+ align:start position:0%
+have about 5% uncertainty which I think
+is pretty good right
+
+ align:start position:0%
+is pretty good right
+ 
+
+ align:start position:0%
+is pretty good right
+and you go to calc our certainty range
+
+ align:start position:0%
+and you go to calc our certainty range
+ 
+
+ align:start position:0%
+and you go to calc our certainty range
+and that's about
+
+ align:start position:0%
+and that's about
+ 
+
+ align:start position:0%
+and that's about
+15% right and it turns out that many
+
+ align:start position:0%
+15% right and it turns out that many
+ 
+
+ align:start position:0%
+15% right and it turns out that many
+times your system can take the same
+
+ align:start position:0%
+times your system can take the same
+ 
+
+ align:start position:0%
+times your system can take the same
+sample so you do Cal conductivity take a
+
+ align:start position:0%
+sample so you do Cal conductivity take a
+ 
+
+ align:start position:0%
+sample so you do Cal conductivity take a
+sample you go to pick another sample for
+
+ align:start position:0%
+sample you go to pick another sample for
+ 
+
+ align:start position:0%
+sample you go to pick another sample for
+electric conductivity and uh you
+
+ align:start position:0%
+electric conductivity and uh you
+ 
+
+ align:start position:0%
+electric conductivity and uh you
+measure wrong
+
+ align:start position:0%
+measure wrong
+ 
+
+ align:start position:0%
+measure wrong
+things and sometimes if you look at bu
+
+ align:start position:0%
+things and sometimes if you look at bu
+ 
+
+ align:start position:0%
+things and sometimes if you look at bu
+uh Chate it's layer structure right the
+
+ align:start position:0%
+uh Chate it's layer structure right the
+ 
+
+ align:start position:0%
+uh Chate it's layer structure right the
+property is very
+
+ align:start position:0%
+property is very
+ 
+
+ align:start position:0%
+property is very
+isotropic this will be uh uh really
+
+ align:start position:0%
+isotropic this will be uh uh really
+ 
+
+ align:start position:0%
+isotropic this will be uh uh really
+dangerous you you measure even the same
+
+ align:start position:0%
+dangerous you you measure even the same
+ 
+
+ align:start position:0%
+dangerous you you measure even the same
+sample you you measure property C in One
+
+ align:start position:0%
+sample you you measure property C in One
+ 
+
+ align:start position:0%
+sample you you measure property C in One
+Direction measure Electric in other
+
+ align:start position:0%
+Direction measure Electric in other
+ 
+
+ align:start position:0%
+Direction measure Electric in other
+direction and you can just get a good ZT
+
+ align:start position:0%
+direction and you can just get a good ZT
+ 
+
+ align:start position:0%
+direction and you can just get a good ZT
+that's not true so this is a every time
+
+ align:start position:0%
+that's not true so this is a every time
+ 
+
+ align:start position:0%
+that's not true so this is a every time
+you going to mean it people will be
+
+ align:start position:0%
+you going to mean it people will be
+ 
+
+ align:start position:0%
+you going to mean it people will be
+debating and most of time people are
+
+ align:start position:0%
+debating and most of time people are
+ 
+
+ align:start position:0%
+debating and most of time people are
+skep of any
+
+ align:start position:0%
+skep of any
+ 
+
+ align:start position:0%
+skep of any
+report okay it's just difficult because
+
+ align:start position:0%
+report okay it's just difficult because
+ 
+
+ align:start position:0%
+report okay it's just difficult because
+measurement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difficult okay now uh I turn to my cvor
+
+ align:start position:0%
+difficult okay now uh I turn to my cvor
+ 
+
+ align:start position:0%
+difficult okay now uh I turn to my cvor
+right n structure I said that they bulk
+
+ align:start position:0%
+right n structure I said that they bulk
+ 
+
+ align:start position:0%
+right n structure I said that they bulk
+material people look at different
+
+ align:start position:0%
+material people look at different
+ 
+
+ align:start position:0%
+material people look at different
+material different structures uh uh full
+
+ align:start position:0%
+material different structures uh uh full
+ 
+
+ align:start position:0%
+material different structures uh uh full
+rular those are all working on crystal
+
+ align:start position:0%
+rular those are all working on crystal
+ 
+
+ align:start position:0%
+rular those are all working on crystal
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+materials and there was say this another
+
+ align:start position:0%
+materials and there was say this another
+ 
+
+ align:start position:0%
+materials and there was say this another
+structur
+
+ align:start position:0%
+structur
+ 
+
+ align:start position:0%
+structur
+approach uh was really uh a m gr house
+
+ align:start position:0%
+approach uh was really uh a m gr house
+ 
+
+ align:start position:0%
+approach uh was really uh a m gr house
+in the E Department uh at the time and
+
+ align:start position:0%
+in the E Department uh at the time and
+ 
+
+ align:start position:0%
+in the E Department uh at the time and
+the story is this is a really a good
+
+ align:start position:0%
+the story is this is a really a good
+ 
+
+ align:start position:0%
+the story is this is a really a good
+story okay uh in around the 990 uh US
+
+ align:start position:0%
+story okay uh in around the 990 uh US
+ 
+
+ align:start position:0%
+story okay uh in around the 990 uh US
+Navy uh start to rethink thero electrics
+
+ align:start position:0%
+Navy uh start to rethink thero electrics
+ 
+
+ align:start position:0%
+Navy uh start to rethink thero electrics
+so they went ask around and they came to
+
+ align:start position:0%
+so they went ask around and they came to
+ 
+
+ align:start position:0%
+so they went ask around and they came to
+Millie whether she had any idea on ther
+
+ align:start position:0%
+Millie whether she had any idea on ther
+ 
+
+ align:start position:0%
+Millie whether she had any idea on ther
+elrics Millie didn't uh work on Elric
+
+ align:start position:0%
+elrics Millie didn't uh work on Elric
+ 
+
+ align:start position:0%
+elrics Millie didn't uh work on Elric
+before and uh but she s about it and
+
+ align:start position:0%
+before and uh but she s about it and
+ 
+
+ align:start position:0%
+before and uh but she s about it and
+there was a pH student walked into her
+
+ align:start position:0%
+there was a pH student walked into her
+ 
+
+ align:start position:0%
+there was a pH student walked into her
+office want to do was ask her whether
+
+ align:start position:0%
+office want to do was ask her whether
+ 
+
+ align:start position:0%
+office want to do was ask her whether
+she had a topic so she said oh why don't
+
+ align:start position:0%
+she had a topic so she said oh why don't
+ 
+
+ align:start position:0%
+she had a topic so she said oh why don't
+you look at the uh condom well whether
+
+ align:start position:0%
+you look at the uh condom well whether
+ 
+
+ align:start position:0%
+you look at the uh condom well whether
+you can give better uh super electric
+
+ align:start position:0%
+you can give better uh super electric
+ 
+
+ align:start position:0%
+you can give better uh super electric
+properties uh so the student looked and
+
+ align:start position:0%
+properties uh so the student looked and
+ 
+
+ align:start position:0%
+properties uh so the student looked and
+did it's really a homework problem I
+
+ align:start position:0%
+did it's really a homework problem I
+ 
+
+ align:start position:0%
+did it's really a homework problem I
+I'll show you later and but the
+
+ align:start position:0%
+I'll show you later and but the
+ 
+
+ align:start position:0%
+I'll show you later and but the
+calculation turns out to be really
+
+ align:start position:0%
+calculation turns out to be really
+ 
+
+ align:start position:0%
+calculation turns out to be really
+interesting and lot people start working
+
+ align:start position:0%
+interesting and lot people start working
+ 
+
+ align:start position:0%
+interesting and lot people start working
+on that so sometimes a simple idea
+
+ align:start position:0%
+on that so sometimes a simple idea
+ 
+
+ align:start position:0%
+on that so sometimes a simple idea
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+research and here uh I'm this is a slide
+
+ align:start position:0%
+research and here uh I'm this is a slide
+ 
+
+ align:start position:0%
+research and here uh I'm this is a slide
+that I triy to make and they seeing the
+
+ align:start position:0%
+that I triy to make and they seeing the
+ 
+
+ align:start position:0%
+that I triy to make and they seeing the
+potential of using n so uh you think
+
+ align:start position:0%
+potential of using n so uh you think
+ 
+
+ align:start position:0%
+potential of using n so uh you think
+about the electron and Fon electron is
+
+ align:start position:0%
+about the electron and Fon electron is
+ 
+
+ align:start position:0%
+about the electron and Fon electron is
+what carries heat around and of course
+
+ align:start position:0%
+what carries heat around and of course
+ 
+
+ align:start position:0%
+what carries heat around and of course
+they are Quant mechanic they all waves
+
+ align:start position:0%
+they are Quant mechanic they all waves
+ 
+
+ align:start position:0%
+they are Quant mechanic they all waves
+we we mentioned those W before but they
+
+ align:start position:0%
+we we mentioned those W before but they
+ 
+
+ align:start position:0%
+we we mentioned those W before but they
+have different wavelengths okay and in
+
+ align:start position:0%
+have different wavelengths okay and in
+ 
+
+ align:start position:0%
+have different wavelengths okay and in
+terms of it's a spread okay in real
+
+ align:start position:0%
+terms of it's a spread okay in real
+ 
+
+ align:start position:0%
+terms of it's a spread okay in real
+material it's all a spread and uh U we
+
+ align:start position:0%
+material it's all a spread and uh U we
+ 
+
+ align:start position:0%
+material it's all a spread and uh U we
+need to look into details but in general
+
+ align:start position:0%
+need to look into details but in general
+ 
+
+ align:start position:0%
+need to look into details but in general
+actually electron winess can be long
+
+ align:start position:0%
+actually electron winess can be long
+ 
+
+ align:start position:0%
+actually electron winess can be long
+average speaking then the fullon he
+
+ align:start position:0%
+average speaking then the fullon he
+ 
+
+ align:start position:0%
+average speaking then the fullon he
+carrying for ons and so uh so that's uh
+
+ align:start position:0%
+carrying for ons and so uh so that's uh
+ 
+
+ align:start position:0%
+carrying for ons and so uh so that's uh
+sort of order magnitud that I could I I
+
+ align:start position:0%
+sort of order magnitud that I could I I
+ 
+
+ align:start position:0%
+sort of order magnitud that I could I I
+often use but again each material is
+
+ align:start position:0%
+often use but again each material is
+ 
+
+ align:start position:0%
+often use but again each material is
+different temp is
+
+ align:start position:0%
+different temp is
+ 
+
+ align:start position:0%
+different temp is
+different and the other is me free
+
+ align:start position:0%
+different and the other is me free
+ 
+
+ align:start position:0%
+different and the other is me free
+pa okay that's the average distance
+
+ align:start position:0%
+pa okay that's the average distance
+ 
+
+ align:start position:0%
+pa okay that's the average distance
+electron fall on
+
+ align:start position:0%
+electron fall on
+ 
+
+ align:start position:0%
+electron fall on
+TRS so uh we you look at one possibility
+
+ align:start position:0%
+TRS so uh we you look at one possibility
+ 
+
+ align:start position:0%
+TRS so uh we you look at one possibility
+is really look at the wavelength
+
+ align:start position:0%
+is really look at the wavelength
+ 
+
+ align:start position:0%
+is really look at the wavelength
+difference and uh because the wavelength
+
+ align:start position:0%
+difference and uh because the wavelength
+ 
+
+ align:start position:0%
+difference and uh because the wavelength
+difference means uh intutive picture is
+
+ align:start position:0%
+difference means uh intutive picture is
+ 
+
+ align:start position:0%
+difference means uh intutive picture is
+that if you have a surface whether it's
+
+ align:start position:0%
+that if you have a surface whether it's
+ 
+
+ align:start position:0%
+that if you have a surface whether it's
+smooth or rough right really depends on
+
+ align:start position:0%
+smooth or rough right really depends on
+ 
+
+ align:start position:0%
+smooth or rough right really depends on
+the feature on the on the surface versus
+
+ align:start position:0%
+the feature on the on the surface versus
+ 
+
+ align:start position:0%
+the feature on the on the surface versus
+the feature of the wave wavess right if
+
+ align:start position:0%
+the feature of the wave wavess right if
+ 
+
+ align:start position:0%
+the feature of the wave wavess right if
+you have uh visible light coming towards
+
+ align:start position:0%
+you have uh visible light coming towards
+ 
+
+ align:start position:0%
+you have uh visible light coming towards
+a surface like this it look rough it's
+
+ align:start position:0%
+a surface like this it look rough it's
+ 
+
+ align:start position:0%
+a surface like this it look rough it's
+scatter light to all Direction but if
+
+ align:start position:0%
+scatter light to all Direction but if
+ 
+
+ align:start position:0%
+scatter light to all Direction but if
+you have really a microwave coming in
+
+ align:start position:0%
+you have really a microwave coming in
+ 
+
+ align:start position:0%
+you have really a microwave coming in
+very long wavelength this surface will
+
+ align:start position:0%
+very long wavelength this surface will
+ 
+
+ align:start position:0%
+very long wavelength this surface will
+be smooth much say uh we larger than the
+
+ align:start position:0%
+be smooth much say uh we larger than the
+ 
+
+ align:start position:0%
+be smooth much say uh we larger than the
+roughness
+
+ align:start position:0%
+roughness
+ 
+
+ align:start position:0%
+roughness
+fees uh so one of this idea was if you
+
+ align:start position:0%
+fees uh so one of this idea was if you
+ 
+
+ align:start position:0%
+fees uh so one of this idea was if you
+recall the thermal conductivity right
+
+ align:start position:0%
+recall the thermal conductivity right
+ 
+
+ align:start position:0%
+recall the thermal conductivity right
+the Curve at a very low temperature the
+
+ align:start position:0%
+the Curve at a very low temperature the
+ 
+
+ align:start position:0%
+the Curve at a very low temperature the
+Cal conductivity increase with the
+
+ align:start position:0%
+Cal conductivity increase with the
+ 
+
+ align:start position:0%
+Cal conductivity increase with the
+specific heat because the mean free pass
+
+ align:start position:0%
+specific heat because the mean free pass
+ 
+
+ align:start position:0%
+specific heat because the mean free pass
+equals sample size is limited by sample
+
+ align:start position:0%
+equals sample size is limited by sample
+ 
+
+ align:start position:0%
+equals sample size is limited by sample
+size so low temperature already have the
+
+ align:start position:0%
+size so low temperature already have the
+ 
+
+ align:start position:0%
+size so low temperature already have the
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+effect and if I make this structure very
+
+ align:start position:0%
+effect and if I make this structure very
+ 
+
+ align:start position:0%
+effect and if I make this structure very
+small that size effect can shift to high
+
+ align:start position:0%
+small that size effect can shift to high
+ 
+
+ align:start position:0%
+small that size effect can shift to high
+temperature as long as small enough so
+
+ align:start position:0%
+temperature as long as small enough so
+ 
+
+ align:start position:0%
+temperature as long as small enough so
+that the let's take a wire or
+
+ align:start position:0%
+that the let's take a wire or
+ 
+
+ align:start position:0%
+that the let's take a wire or
+fi if the diameter or thickness is
+
+ align:start position:0%
+fi if the diameter or thickness is
+ 
+
+ align:start position:0%
+fi if the diameter or thickness is
+comparable to MRE PA now the Fallon will
+
+ align:start position:0%
+comparable to MRE PA now the Fallon will
+ 
+
+ align:start position:0%
+comparable to MRE PA now the Fallon will
+no longer is a Fallon Fon pooll they are
+
+ align:start position:0%
+no longer is a Fallon Fon pooll they are
+ 
+
+ align:start position:0%
+no longer is a Fallon Fon pooll they are
+colled with
+
+ align:start position:0%
+colled with
+ 
+
+ align:start position:0%
+colled with
+surface right and uh another simple
+
+ align:start position:0%
+surface right and uh another simple
+ 
+
+ align:start position:0%
+surface right and uh another simple
+intuitive picture is okay what happens
+
+ align:start position:0%
+intuitive picture is okay what happens
+ 
+
+ align:start position:0%
+intuitive picture is okay what happens
+have the interface of to material right
+
+ align:start position:0%
+have the interface of to material right
+ 
+
+ align:start position:0%
+have the interface of to material right
+uh you have the L wave coming in and at
+
+ align:start position:0%
+uh you have the L wave coming in and at
+ 
+
+ align:start position:0%
+uh you have the L wave coming in and at
+the interface you hear Echo High well we
+
+ align:start position:0%
+the interface you hear Echo High well we
+ 
+
+ align:start position:0%
+the interface you hear Echo High well we
+he Echo for the visible R audible range
+
+ align:start position:0%
+he Echo for the visible R audible range
+ 
+
+ align:start position:0%
+he Echo for the visible R audible range
+but see in the heat caring is terz Right
+
+ align:start position:0%
+but see in the heat caring is terz Right
+ 
+
+ align:start position:0%
+but see in the heat caring is terz Right
+depends on so those are high frequency
+
+ align:start position:0%
+depends on so those are high frequency
+ 
+
+ align:start position:0%
+depends on so those are high frequency
+you still got the same phenomena happen
+
+ align:start position:0%
+you still got the same phenomena happen
+ 
+
+ align:start position:0%
+you still got the same phenomena happen
+and the echo means some he go don't go
+
+ align:start position:0%
+and the echo means some he go don't go
+ 
+
+ align:start position:0%
+and the echo means some he go don't go
+forward anymore so you have you could
+
+ align:start position:0%
+forward anymore so you have you could
+ 
+
+ align:start position:0%
+forward anymore so you have you could
+use those phenomena to drop the Thal
+
+ align:start position:0%
+use those phenomena to drop the Thal
+ 
+
+ align:start position:0%
+use those phenomena to drop the Thal
+connectivity and uh M idea uh at the
+
+ align:start position:0%
+connectivity and uh M idea uh at the
+ 
+
+ align:start position:0%
+connectivity and uh M idea uh at the
+time was squeeze
+
+ align:start position:0%
+time was squeeze
+ 
+
+ align:start position:0%
+time was squeeze
+electrons okay so Quantum effect which
+
+ align:start position:0%
+electrons okay so Quantum effect which
+ 
+
+ align:start position:0%
+electrons okay so Quantum effect which
+I'll talk more but
+
+ align:start position:0%
+I'll talk more but
+ 
+
+ align:start position:0%
+I'll talk more but
+now think about the the quantum effect
+
+ align:start position:0%
+now think about the the quantum effect
+ 
+
+ align:start position:0%
+now think about the the quantum effect
+electron is a b wave wave function is a
+
+ align:start position:0%
+electron is a b wave wave function is a
+ 
+
+ align:start position:0%
+electron is a b wave wave function is a
+function this the S
+
+ align:start position:0%
+function this the S
+ 
+
+ align:start position:0%
+function this the S
+orbital we function is a ball okay and
+
+ align:start position:0%
+orbital we function is a ball okay and
+ 
+
+ align:start position:0%
+orbital we function is a ball okay and
+uh let's see this is the size of the
+
+ align:start position:0%
+uh let's see this is the size of the
+ 
+
+ align:start position:0%
+uh let's see this is the size of the
+ball let's say
+
+ align:start position:0%
+ball let's say
+ 
+
+ align:start position:0%
+ball let's say
+100 right now you fit this this electron
+
+ align:start position:0%
+100 right now you fit this this electron
+ 
+
+ align:start position:0%
+100 right now you fit this this electron
+you make a film only 10 Armstrong or 50
+
+ align:start position:0%
+you make a film only 10 Armstrong or 50
+ 
+
+ align:start position:0%
+you make a film only 10 Armstrong or 50
+Armstrong What Happens the the ball is
+
+ align:start position:0%
+Armstrong What Happens the the ball is
+ 
+
+ align:start position:0%
+Armstrong What Happens the the ball is
+long longer a b right I once when I was
+
+ align:start position:0%
+long longer a b right I once when I was
+ 
+
+ align:start position:0%
+long longer a b right I once when I was
+student visiting lbl there was
+
+ align:start position:0%
+student visiting lbl there was
+ 
+
+ align:start position:0%
+student visiting lbl there was
+interesting analogy made by professor
+
+ align:start position:0%
+interesting analogy made by professor
+ 
+
+ align:start position:0%
+interesting analogy made by professor
+said think this you put a box ball into
+
+ align:start position:0%
+said think this you put a box ball into
+ 
+
+ align:start position:0%
+said think this you put a box ball into
+a piz of
+
+ align:start position:0%
+a piz of
+ 
+
+ align:start position:0%
+a piz of
+box you squeeze that wall you have
+
+ align:start position:0%
+box you squeeze that wall you have
+ 
+
+ align:start position:0%
+box you squeeze that wall you have
+energy compensation so that's the so you
+
+ align:start position:0%
+energy compensation so that's the so you
+ 
+
+ align:start position:0%
+energy compensation so that's the so you
+have this wave and when you size is
+
+ align:start position:0%
+have this wave and when you size is
+ 
+
+ align:start position:0%
+have this wave and when you size is
+small you you you quti the wave and uh
+
+ align:start position:0%
+small you you you quti the wave and uh
+ 
+
+ align:start position:0%
+small you you you quti the wave and uh
+you ideally what you want is this way is
+
+ align:start position:0%
+you ideally what you want is this way is
+ 
+
+ align:start position:0%
+you ideally what you want is this way is
+a under ideal pation you want this
+
+ align:start position:0%
+a under ideal pation you want this
+ 
+
+ align:start position:0%
+a under ideal pation you want this
+smooth surface okay you don't want the
+
+ align:start position:0%
+smooth surface okay you don't want the
+ 
+
+ align:start position:0%
+smooth surface okay you don't want the
+interface scatter
+
+ align:start position:0%
+interface scatter
+ 
+
+ align:start position:0%
+interface scatter
+electrons and it's possible again you
+
+ align:start position:0%
+electrons and it's possible again you
+ 
+
+ align:start position:0%
+electrons and it's possible again you
+think about the wavelength range right
+
+ align:start position:0%
+think about the wavelength range right
+ 
+
+ align:start position:0%
+think about the wavelength range right
+because we surface smooth or a rough
+
+ align:start position:0%
+because we surface smooth or a rough
+ 
+
+ align:start position:0%
+because we surface smooth or a rough
+depends on wavess for the case of
+
+ align:start position:0%
+depends on wavess for the case of
+ 
+
+ align:start position:0%
+depends on wavess for the case of
+electron the scatter is electrical
+
+ align:start position:0%
+electron the scatter is electrical
+ 
+
+ align:start position:0%
+electron the scatter is electrical
+potential your potential whether is
+
+ align:start position:0%
+potential your potential whether is
+ 
+
+ align:start position:0%
+potential your potential whether is
+rough or not and for the case of full on
+
+ align:start position:0%
+rough or not and for the case of full on
+ 
+
+ align:start position:0%
+rough or not and for the case of full on
+that way fundament is all electrostatic
+
+ align:start position:0%
+that way fundament is all electrostatic
+ 
+
+ align:start position:0%
+that way fundament is all electrostatic
+but it's really the you can think of
+
+ align:start position:0%
+but it's really the you can think of
+ 
+
+ align:start position:0%
+but it's really the you can think of
+mass Sprint whether this uh the force is
+
+ align:start position:0%
+mass Sprint whether this uh the force is
+ 
+
+ align:start position:0%
+mass Sprint whether this uh the force is
+RO
+
+ align:start position:0%
+RO
+ 
+
+ align:start position:0%
+RO
+now okay and so you actually have the
+
+ align:start position:0%
+now okay and so you actually have the
+ 
+
+ align:start position:0%
+now okay and so you actually have the
+potential if you think about the Fon and
+
+ align:start position:0%
+potential if you think about the Fon and
+ 
+
+ align:start position:0%
+potential if you think about the Fon and
+electron your your electron if you quiz
+
+ align:start position:0%
+electron your your electron if you quiz
+ 
+
+ align:start position:0%
+electron your your electron if you quiz
+it is the
+
+ align:start position:0%
+it is the
+ 
+
+ align:start position:0%
+it is the
+smooth and because the wance difference
+
+ align:start position:0%
+smooth and because the wance difference
+ 
+
+ align:start position:0%
+smooth and because the wance difference
+you can potentially actually have the
+
+ align:start position:0%
+you can potentially actually have the
+ 
+
+ align:start position:0%
+you can potentially actually have the
+same surface be Rock right for full the
+
+ align:start position:0%
+same surface be Rock right for full the
+ 
+
+ align:start position:0%
+same surface be Rock right for full the
+acoustic W so this will be idea your
+
+ align:start position:0%
+acoustic W so this will be idea your
+ 
+
+ align:start position:0%
+acoustic W so this will be idea your
+dreft you you want to screw up the
+
+ align:start position:0%
+dreft you you want to screw up the
+ 
+
+ align:start position:0%
+dreft you you want to screw up the
+atomical vibration but electron can go
+
+ align:start position:0%
+atomical vibration but electron can go
+ 
+
+ align:start position:0%
+atomical vibration but electron can go
+as a wave guide that that would be one
+
+ align:start position:0%
+as a wave guide that that would be one
+ 
+
+ align:start position:0%
+as a wave guide that that would be one
+scenario and people started uh uh a lot
+
+ align:start position:0%
+scenario and people started uh uh a lot
+ 
+
+ align:start position:0%
+scenario and people started uh uh a lot
+uh since many and in fact I should say
+
+ align:start position:0%
+uh since many and in fact I should say
+ 
+
+ align:start position:0%
+uh since many and in fact I should say
+at the same time they go to other places
+
+ align:start position:0%
+at the same time they go to other places
+ 
+
+ align:start position:0%
+at the same time they go to other places
+and people have similar idea although M
+
+ align:start position:0%
+and people have similar idea although M
+ 
+
+ align:start position:0%
+and people have similar idea although M
+did the really a good calculation uh uh
+
+ align:start position:0%
+did the really a good calculation uh uh
+ 
+
+ align:start position:0%
+did the really a good calculation uh uh
+this uh uh superl idea was from Rama Ron
+
+ align:start position:0%
+this uh uh superl idea was from Rama Ron
+ 
+
+ align:start position:0%
+this uh uh superl idea was from Rama Ron
+and what he did is the perpendicular
+
+ align:start position:0%
+and what he did is the perpendicular
+ 
+
+ align:start position:0%
+and what he did is the perpendicular
+direction to
+
+ align:start position:0%
+direction to
+ 
+
+ align:start position:0%
+direction to
+superus and this is a you can say uh the
+
+ align:start position:0%
+superus and this is a you can say uh the
+ 
+
+ align:start position:0%
+superus and this is a you can say uh the
+experiment Cal
+
+ align:start position:0%
+experiment Cal
+ 
+
+ align:start position:0%
+experiment Cal
+connectivity had uh dropped right say uh
+
+ align:start position:0%
+connectivity had uh dropped right say uh
+ 
+
+ align:start position:0%
+connectivity had uh dropped right say uh
+say the uh dis cite B is about 1.2 and
+
+ align:start position:0%
+say the uh dis cite B is about 1.2 and
+ 
+
+ align:start position:0%
+say the uh dis cite B is about 1.2 and
+they Dro
+
+ align:start position:0%
+they Dro
+ 
+
+ align:start position:0%
+they Dro
+to5 very difficult measurement and this
+
+ align:start position:0%
+to5 very difficult measurement and this
+ 
+
+ align:start position:0%
+to5 very difficult measurement and this
+is where I start getting into ther
+
+ align:start position:0%
+is where I start getting into ther
+ 
+
+ align:start position:0%
+is where I start getting into ther
+electrics my my thesis my wife my PhD I
+
+ align:start position:0%
+electrics my my thesis my wife my PhD I
+ 
+
+ align:start position:0%
+electrics my my thesis my wife my PhD I
+was looking at the superus he conduction
+
+ align:start position:0%
+was looking at the superus he conduction
+ 
+
+ align:start position:0%
+was looking at the superus he conduction
+I was aware about lasers not therm Elric
+
+ align:start position:0%
+I was aware about lasers not therm Elric
+ 
+
+ align:start position:0%
+I was aware about lasers not therm Elric
+I didn't know anything
+
+ align:start position:0%
+I didn't know anything
+ 
+
+ align:start position:0%
+I didn't know anything
+thric and uh uh the but the electron
+
+ align:start position:0%
+thric and uh uh the but the electron
+ 
+
+ align:start position:0%
+thric and uh uh the but the electron
+here decrease a little bit this s Square
+
+ align:start position:0%
+here decrease a little bit this s Square
+ 
+
+ align:start position:0%
+here decrease a little bit this s Square
+Sigma the power Factor s sare Sigma
+
+ align:start position:0%
+Sigma the power Factor s sare Sigma
+ 
+
+ align:start position:0%
+Sigma the power Factor s sare Sigma
+decre a little bit and in the case of
+
+ align:start position:0%
+decre a little bit and in the case of
+ 
+
+ align:start position:0%
+decre a little bit and in the case of
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+a he grew this Le
+
+ align:start position:0%
+a he grew this Le
+ 
+
+ align:start position:0%
+a he grew this Le
+torite on Le site on Le torite and
+
+ align:start position:0%
+torite on Le site on Le torite and
+ 
+
+ align:start position:0%
+torite on Le site on Le torite and
+because the lce constant is very
+
+ align:start position:0%
+because the lce constant is very
+ 
+
+ align:start position:0%
+because the lce constant is very
+different the string so you grw certain
+
+ align:start position:0%
+different the string so you grw certain
+ 
+
+ align:start position:0%
+different the string so you grw certain
+sickness the string will break up the
+
+ align:start position:0%
+sickness the string will break up the
+ 
+
+ align:start position:0%
+sickness the string will break up the
+film and form dots so he grew those
+
+ align:start position:0%
+film and form dots so he grew those
+ 
+
+ align:start position:0%
+film and form dots so he grew those
+multi-layer
+
+ align:start position:0%
+multi-layer
+ 
+
+ align:start position:0%
+multi-layer
+structures and uh uh this picture I
+
+ align:start position:0%
+structures and uh uh this picture I
+ 
+
+ align:start position:0%
+structures and uh uh this picture I
+don't think it from him I don't remember
+
+ align:start position:0%
+don't think it from him I don't remember
+ 
+
+ align:start position:0%
+don't think it from him I don't remember
+but uh uh what he show was again no
+
+ align:start position:0%
+but uh uh what he show was again no
+ 
+
+ align:start position:0%
+but uh uh what he show was again no
+contivity and the par Factor so at the
+
+ align:start position:0%
+contivity and the par Factor so at the
+ 
+
+ align:start position:0%
+contivity and the par Factor so at the
+end it turns out
+
+ align:start position:0%
+end it turns out
+ 
+
+ align:start position:0%
+end it turns out
+that uh historically the connectivity
+
+ align:start position:0%
+that uh historically the connectivity
+ 
+
+ align:start position:0%
+that uh historically the connectivity
+alloy institutional right and now with
+
+ align:start position:0%
+alloy institutional right and now with
+ 
+
+ align:start position:0%
+alloy institutional right and now with
+the uh this Nan structure in terms of
+
+ align:start position:0%
+the uh this Nan structure in terms of
+ 
+
+ align:start position:0%
+the uh this Nan structure in terms of
+the really Thal contivity seems to be a
+
+ align:start position:0%
+the really Thal contivity seems to be a
+ 
+
+ align:start position:0%
+the really Thal contivity seems to be a
+very effective
+
+ align:start position:0%
+very effective
+ 
+
+ align:start position:0%
+very effective
+strategy but let me again
+
+ align:start position:0%
+strategy but let me again
+ 
+
+ align:start position:0%
+strategy but let me again
+o almost now see everybody question
+
+ align:start position:0%
+o almost now see everybody question
+ 
+
+ align:start position:0%
+o almost now see everybody question
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+results it's a a very interesting
+
+ align:start position:0%
+results it's a a very interesting
+ 
+
+ align:start position:0%
+results it's a a very interesting
+results very intriguant but it's a very
+
+ align:start position:0%
+results very intriguant but it's a very
+ 
+
+ align:start position:0%
+results very intriguant but it's a very
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+measurement and uh uh uh retire is I
+
+ align:start position:0%
+measurement and uh uh uh retire is I
+ 
+
+ align:start position:0%
+measurement and uh uh uh retire is I
+very respected and I I talk to him a
+
+ align:start position:0%
+very respected and I I talk to him a
+ 
+
+ align:start position:0%
+very respected and I I talk to him a
+lot he has a book if you want to
+
+ align:start position:0%
+lot he has a book if you want to
+ 
+
+ align:start position:0%
+lot he has a book if you want to
+understand Thermo Elric he has a very
+
+ align:start position:0%
+understand Thermo Elric he has a very
+ 
+
+ align:start position:0%
+understand Thermo Elric he has a very
+good book not many people read because
+
+ align:start position:0%
+good book not many people read because
+ 
+
+ align:start position:0%
+good book not many people read because
+it's too
+
+ align:start position:0%
+it's too
+ 
+
+ align:start position:0%
+it's too
+difficult but very good if you if you
+
+ align:start position:0%
+difficult but very good if you if you
+ 
+
+ align:start position:0%
+difficult but very good if you if you
+read and the first picture I remember
+
+ align:start position:0%
+read and the first picture I remember
+ 
+
+ align:start position:0%
+read and the first picture I remember
+first two pages was talking about
+
+ align:start position:0%
+first two pages was talking about
+ 
+
+ align:start position:0%
+first two pages was talking about
+electrostatic potential as a mechanical
+
+ align:start position:0%
+electrostatic potential as a mechanical
+ 
+
+ align:start position:0%
+electrostatic potential as a mechanical
+engineer that always being har um
+
+ align:start position:0%
+engineer that always being har um
+ 
+
+ align:start position:0%
+engineer that always being har um
+understand what's the electrical
+
+ align:start position:0%
+understand what's the electrical
+ 
+
+ align:start position:0%
+understand what's the electrical
+potential what's the C
+
+ align:start position:0%
+potential what's the C
+ 
+
+ align:start position:0%
+potential what's the C
+po okay and uh uh Rama wonan this from
+
+ align:start position:0%
+po okay and uh uh Rama wonan this from
+ 
+
+ align:start position:0%
+po okay and uh uh Rama wonan this from
+RTI they have a uh spin up company
+
+ align:start position:0%
+RTI they have a uh spin up company
+ 
+
+ align:start position:0%
+RTI they have a uh spin up company
+trying to do the super lysis for micro
+
+ align:start position:0%
+trying to do the super lysis for micro
+ 
+
+ align:start position:0%
+trying to do the super lysis for micro
+electronics coing and if you're
+
+ align:start position:0%
+electronics coing and if you're
+ 
+
+ align:start position:0%
+electronics coing and if you're
+interested you can check Le they have
+
+ align:start position:0%
+interested you can check Le they have
+ 
+
+ align:start position:0%
+interested you can check Le they have
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+startups and uh uh uh the the uh the
+
+ align:start position:0%
+startups and uh uh uh the the uh the
+ 
+
+ align:start position:0%
+startups and uh uh uh the the uh the
+super L is uh I guess say the the
+
+ align:start position:0%
+super L is uh I guess say the the
+ 
+
+ align:start position:0%
+super L is uh I guess say the the
+challenge is grew very thck and also
+
+ align:start position:0%
+challenge is grew very thck and also
+ 
+
+ align:start position:0%
+challenge is grew very thck and also
+reduce the
+
+ align:start position:0%
+reduce the
+ 
+
+ align:start position:0%
+reduce the
+cost so this is where my story is I I
+
+ align:start position:0%
+cost so this is where my story is I I
+ 
+
+ align:start position:0%
+cost so this is where my story is I I
+said I have been working on this for a
+
+ align:start position:0%
+said I have been working on this for a
+ 
+
+ align:start position:0%
+said I have been working on this for a
+long time uh since my uh
+
+ align:start position:0%
+long time uh since my uh
+ 
+
+ align:start position:0%
+long time uh since my uh
+was really use for
+
+ align:start position:0%
+was really use for
+ 
+
+ align:start position:0%
+was really use for
+leers and uh uh uh so those are
+
+ align:start position:0%
+leers and uh uh uh so those are
+ 
+
+ align:start position:0%
+leers and uh uh uh so those are
+experiments uh in the along the film
+
+ align:start position:0%
+experiments uh in the along the film
+ 
+
+ align:start position:0%
+experiments uh in the along the film
+Direction you can see isotopic this
+
+ align:start position:0%
+Direction you can see isotopic this
+ 
+
+ align:start position:0%
+Direction you can see isotopic this
+is but's see uh the super structure
+
+ align:start position:0%
+is but's see uh the super structure
+ 
+
+ align:start position:0%
+is but's see uh the super structure
+right so this is a perpendicular to the
+
+ align:start position:0%
+right so this is a perpendicular to the
+ 
+
+ align:start position:0%
+right so this is a perpendicular to the
+fil plan Direction parallel to film plan
+
+ align:start position:0%
+fil plan Direction parallel to film plan
+ 
+
+ align:start position:0%
+fil plan Direction parallel to film plan
+Direction and the problem is if you
+
+ align:start position:0%
+Direction and the problem is if you
+ 
+
+ align:start position:0%
+Direction and the problem is if you
+think about this super l space l this
+
+ align:start position:0%
+think about this super l space l this
+ 
+
+ align:start position:0%
+think about this super l space l this
+were super ltis was
+
+ align:start position:0%
+were super ltis was
+ 
+
+ align:start position:0%
+were super ltis was
+invented by uh R2 and isak isaki got the
+
+ align:start position:0%
+invented by uh R2 and isak isaki got the
+ 
+
+ align:start position:0%
+invented by uh R2 and isak isaki got the
+low price uh for his work in resent dial
+
+ align:start position:0%
+low price uh for his work in resent dial
+ 
+
+ align:start position:0%
+low price uh for his work in resent dial
+okay that's before he even super
+
+ align:start position:0%
+okay that's before he even super
+ 
+
+ align:start position:0%
+okay that's before he even super
+this and the L of super litis means you
+
+ align:start position:0%
+this and the L of super litis means you
+ 
+
+ align:start position:0%
+this and the L of super litis means you
+have a super
+
+ align:start position:0%
+have a super
+ 
+
+ align:start position:0%
+have a super
+freal and so you see say this is one
+
+ align:start position:0%
+freal and so you see say this is one
+ 
+
+ align:start position:0%
+freal and so you see say this is one
+layer this another layer now you look at
+
+ align:start position:0%
+layer this another layer now you look at
+ 
+
+ align:start position:0%
+layer this another layer now you look at
+a Unis is no longer CU but the uh
+
+ align:start position:0%
+a Unis is no longer CU but the uh
+ 
+
+ align:start position:0%
+a Unis is no longer CU but the uh
+cedra that cover from here to here one
+
+ align:start position:0%
+cedra that cover from here to here one
+ 
+
+ align:start position:0%
+cedra that cover from here to here one
+period of a crystal right so that's what
+
+ align:start position:0%
+period of a crystal right so that's what
+ 
+
+ align:start position:0%
+period of a crystal right so that's what
+the Lan implies if you have this
+
+ align:start position:0%
+the Lan implies if you have this
+ 
+
+ align:start position:0%
+the Lan implies if you have this
+according to the Lan this is new Crystal
+
+ align:start position:0%
+according to the Lan this is new Crystal
+ 
+
+ align:start position:0%
+according to the Lan this is new Crystal
+you can calculate the new energy for on
+
+ align:start position:0%
+you can calculate the new energy for on
+ 
+
+ align:start position:0%
+you can calculate the new energy for on
+Spectrum you calc grou velocity you C
+
+ align:start position:0%
+Spectrum you calc grou velocity you C
+ 
+
+ align:start position:0%
+Spectrum you calc grou velocity you C
+sub states do all this calculation and
+
+ align:start position:0%
+sub states do all this calculation and
+ 
+
+ align:start position:0%
+sub states do all this calculation and
+then you do one c v gamma I don't know
+
+ align:start position:0%
+then you do one c v gamma I don't know
+ 
+
+ align:start position:0%
+then you do one c v gamma I don't know
+gamma so but I know I can from that
+
+ align:start position:0%
+gamma so but I know I can from that
+ 
+
+ align:start position:0%
+gamma so but I know I can from that
+calculation I know see and not weak from
+
+ align:start position:0%
+calculation I know see and not weak from
+ 
+
+ align:start position:0%
+calculation I know see and not weak from
+density of St and dis and that's the
+
+ align:start position:0%
+density of St and dis and that's the
+ 
+
+ align:start position:0%
+density of St and dis and that's the
+curve you get as a function of thickness
+
+ align:start position:0%
+curve you get as a function of thickness
+ 
+
+ align:start position:0%
+curve you get as a function of thickness
+just it's not correct okay so basically
+
+ align:start position:0%
+just it's not correct okay so basically
+ 
+
+ align:start position:0%
+just it's not correct okay so basically
+the picture is not
+
+ align:start position:0%
+the picture is not
+ 
+
+ align:start position:0%
+the picture is not
+about forming a coherent structure
+
+ align:start position:0%
+about forming a coherent structure
+ 
+
+ align:start position:0%
+about forming a coherent structure
+people are still debating so I don't
+
+ align:start position:0%
+people are still debating so I don't
+ 
+
+ align:start position:0%
+people are still debating so I don't
+want to prejuce you you should read
+
+ align:start position:0%
+want to prejuce you you should read
+ 
+
+ align:start position:0%
+want to prejuce you you should read
+literature and that's my own Prejudice
+
+ align:start position:0%
+literature and that's my own Prejudice
+ 
+
+ align:start position:0%
+literature and that's my own Prejudice
+because I been doing research in that
+
+ align:start position:0%
+because I been doing research in that
+ 
+
+ align:start position:0%
+because I been doing research in that
+but when you get into it say oh I don't
+
+ align:start position:0%
+but when you get into it say oh I don't
+ 
+
+ align:start position:0%
+but when you get into it say oh I don't
+believe that look into literature look
+
+ align:start position:0%
+believe that look into literature look
+ 
+
+ align:start position:0%
+believe that look into literature look
+at the different sides of the
+
+ align:start position:0%
+at the different sides of the
+ 
+
+ align:start position:0%
+at the different sides of the
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+okay and uh so when I go to look into
+
+ align:start position:0%
+okay and uh so when I go to look into
+ 
+
+ align:start position:0%
+okay and uh so when I go to look into
+the other picture just say okay now I
+
+ align:start position:0%
+the other picture just say okay now I
+ 
+
+ align:start position:0%
+the other picture just say okay now I
+got a
+
+ align:start position:0%
+got a
+ 
+
+ align:start position:0%
+got a
+surface I I only just consider not this
+
+ align:start position:0%
+surface I I only just consider not this
+ 
+
+ align:start position:0%
+surface I I only just consider not this
+super cell just two layers and of course
+
+ align:start position:0%
+super cell just two layers and of course
+ 
+
+ align:start position:0%
+super cell just two layers and of course
+periodic structure we consider all that
+
+ align:start position:0%
+periodic structure we consider all that
+ 
+
+ align:start position:0%
+periodic structure we consider all that
+and then we got the interface
+
+ align:start position:0%
+and then we got the interface
+ 
+
+ align:start position:0%
+and then we got the interface
+roughness and that roughness scatter
+
+ align:start position:0%
+roughness and that roughness scatter
+ 
+
+ align:start position:0%
+roughness and that roughness scatter
+foron diffuse the and that can cause the
+
+ align:start position:0%
+foron diffuse the and that can cause the
+ 
+
+ align:start position:0%
+foron diffuse the and that can cause the
+reduction and here I got a fuding
+
+ align:start position:0%
+reduction and here I got a fuding
+ 
+
+ align:start position:0%
+reduction and here I got a fuding
+parameter yes when you say roughness are
+
+ align:start position:0%
+parameter yes when you say roughness are
+ 
+
+ align:start position:0%
+parameter yes when you say roughness are
+you talking about just like obstacle
+
+ align:start position:0%
+you talking about just like obstacle
+ 
+
+ align:start position:0%
+you talking about just like obstacle
+spacing like an electron defraction or
+
+ align:start position:0%
+spacing like an electron defraction or
+ 
+
+ align:start position:0%
+spacing like an electron defraction or
+any other defraction experiment that
+
+ align:start position:0%
+any other defraction experiment that
+ 
+
+ align:start position:0%
+any other defraction experiment that
+like you expect something to be
+
+ align:start position:0%
+like you expect something to be
+ 
+
+ align:start position:0%
+like you expect something to be
+scattered by something with spacing your
+
+ align:start position:0%
+scattered by something with spacing your
+ 
+
+ align:start position:0%
+scattered by something with spacing your
+right right so so that's a very good
+
+ align:start position:0%
+right right so so that's a very good
+ 
+
+ align:start position:0%
+right right so so that's a very good
+question and what's the mechanism of
+
+ align:start position:0%
+question and what's the mechanism of
+ 
+
+ align:start position:0%
+question and what's the mechanism of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+roughness and it turns
+
+ align:start position:0%
+roughness and it turns
+ 
+
+ align:start position:0%
+roughness and it turns
+out that say when you grw super L
+
+ align:start position:0%
+out that say when you grw super L
+ 
+
+ align:start position:0%
+out that say when you grw super L
+molecular
+
+ align:start position:0%
+molecular
+ 
+
+ align:start position:0%
+molecular
+and you find out there in the 80s there
+
+ align:start position:0%
+and you find out there in the 80s there
+ 
+
+ align:start position:0%
+and you find out there in the 80s there
+a lot of study gas is best study system
+
+ align:start position:0%
+a lot of study gas is best study system
+ 
+
+ align:start position:0%
+a lot of study gas is best study system
+and there are diffusion of atoms between
+
+ align:start position:0%
+and there are diffusion of atoms between
+ 
+
+ align:start position:0%
+and there are diffusion of atoms between
+the layers about one two three mon
+
+ align:start position:0%
+the layers about one two three mon
+ 
+
+ align:start position:0%
+the layers about one two three mon
+Atomic
+
+ align:start position:0%
+Atomic
+ 
+
+ align:start position:0%
+Atomic
+layer and I said the full weakness is
+
+ align:start position:0%
+layer and I said the full weakness is
+ 
+
+ align:start position:0%
+layer and I said the full weakness is
+very short right so my picture is really
+
+ align:start position:0%
+very short right so my picture is really
+ 
+
+ align:start position:0%
+very short right so my picture is really
+the atom if it's a perfect periodic you
+
+ align:start position:0%
+the atom if it's a perfect periodic you
+ 
+
+ align:start position:0%
+the atom if it's a perfect periodic you
+see the atomic space is all PR the same
+
+ align:start position:0%
+see the atomic space is all PR the same
+ 
+
+ align:start position:0%
+see the atomic space is all PR the same
+atom then you should not have that but
+
+ align:start position:0%
+atom then you should not have that but
+ 
+
+ align:start position:0%
+atom then you should not have that but
+now if you just have one atom per two
+
+ align:start position:0%
+now if you just have one atom per two
+ 
+
+ align:start position:0%
+now if you just have one atom per two
+and then random distance later another
+
+ align:start position:0%
+and then random distance later another
+ 
+
+ align:start position:0%
+and then random distance later another
+atom protr and that's say a surface
+
+ align:start position:0%
+atom protr and that's say a surface
+ 
+
+ align:start position:0%
+atom protr and that's say a surface
+whether is rough or or smooth is about
+
+ align:start position:0%
+whether is rough or or smooth is about
+ 
+
+ align:start position:0%
+whether is rough or or smooth is about
+one1 of the wavelength so if you go the
+
+ align:start position:0%
+one1 of the wavelength so if you go the
+ 
+
+ align:start position:0%
+one1 of the wavelength so if you go the
+Optics so here again we do know exactly
+
+ align:start position:0%
+Optics so here again we do know exactly
+ 
+
+ align:start position:0%
+Optics so here again we do know exactly
+so good Optics when people say whether
+
+ align:start position:0%
+so good Optics when people say whether
+ 
+
+ align:start position:0%
+so good Optics when people say whether
+surface is smooth or not is about one1
+
+ align:start position:0%
+surface is smooth or not is about one1
+ 
+
+ align:start position:0%
+surface is smooth or not is about one1
+Wess right one you look at the uh the
+
+ align:start position:0%
+Wess right one you look at the uh the
+ 
+
+ align:start position:0%
+Wess right one you look at the uh the
+face of the wave so uh here because the
+
+ align:start position:0%
+face of the wave so uh here because the
+ 
+
+ align:start position:0%
+face of the wave so uh here because the
+weakness of foron is about 1 n to 10 NM
+
+ align:start position:0%
+weakness of foron is about 1 n to 10 NM
+ 
+
+ align:start position:0%
+weakness of foron is about 1 n to 10 NM
+R so a little bit atom diffusion can PA
+
+ align:start position:0%
+R so a little bit atom diffusion can PA
+ 
+
+ align:start position:0%
+R so a little bit atom diffusion can PA
+that but there are a lot of puzzles at
+
+ align:start position:0%
+that but there are a lot of puzzles at
+ 
+
+ align:start position:0%
+that but there are a lot of puzzles at
+this stage okay you should read uh D
+
+ align:start position:0%
+this stage okay you should read uh D
+ 
+
+ align:start position:0%
+this stage okay you should read uh D
+paper from U and they have done constant
+
+ align:start position:0%
+paper from U and they have done constant
+ 
+
+ align:start position:0%
+paper from U and they have done constant
+dite and some newer material system and
+
+ align:start position:0%
+dite and some newer material system and
+ 
+
+ align:start position:0%
+dite and some newer material system and
+they found that they can have S
+
+ align:start position:0%
+they found that they can have S
+ 
+
+ align:start position:0%
+they found that they can have S
+connectivity really really the noise
+
+ align:start position:0%
+connectivity really really the noise
+ 
+
+ align:start position:0%
+connectivity really really the noise
+they have is twice air solid fully uh
+
+ align:start position:0%
+they have is twice air solid fully uh
+ 
+
+ align:start position:0%
+they have is twice air solid fully uh
+solid anyway so I I say uh uh this is a
+
+ align:start position:0%
+solid anyway so I I say uh uh this is a
+ 
+
+ align:start position:0%
+solid anyway so I I say uh uh this is a
+uh the picture I have but I think there
+
+ align:start position:0%
+uh the picture I have but I think there
+ 
+
+ align:start position:0%
+uh the picture I have but I think there
+are probably more things uh that that we
+
+ align:start position:0%
+are probably more things uh that that we
+ 
+
+ align:start position:0%
+are probably more things uh that that we
+need to
+
+ align:start position:0%
+need to
+ 
+
+ align:start position:0%
+need to
+develop okay so but see from this
+
+ align:start position:0%
+develop okay so but see from this
+ 
+
+ align:start position:0%
+develop okay so but see from this
+picture what I conclude is okay we don't
+
+ align:start position:0%
+picture what I conclude is okay we don't
+ 
+
+ align:start position:0%
+picture what I conclude is okay we don't
+need the P structure because if it's not
+
+ align:start position:0%
+need the P structure because if it's not
+ 
+
+ align:start position:0%
+need the P structure because if it's not
+unic cell type of picture then I don't
+
+ align:start position:0%
+unic cell type of picture then I don't
+ 
+
+ align:start position:0%
+unic cell type of picture then I don't
+need a pure disy so that's what need us
+
+ align:start position:0%
+need a pure disy so that's what need us
+ 
+
+ align:start position:0%
+need a pure disy so that's what need us
+to to do this random composite
+
+ align:start position:0%
+to to do this random composite
+ 
+
+ align:start position:0%
+to to do this random composite
+structures because that way I can do Cod
+
+ align:start position:0%
+structures because that way I can do Cod
+ 
+
+ align:start position:0%
+structures because that way I can do Cod
+lower cost and
+
+ align:start position:0%
+lower cost and
+ 
+
+ align:start position:0%
+lower cost and
+uh uh so we we try this and it works in
+
+ align:start position:0%
+uh uh so we we try this and it works in
+ 
+
+ align:start position:0%
+uh uh so we we try this and it works in
+some materials right this is a
+
+ align:start position:0%
+some materials right this is a
+ 
+
+ align:start position:0%
+some materials right this is a
+uh lat right uh this is the this is a b
+
+ align:start position:0%
+uh lat right uh this is the this is a b
+ 
+
+ align:start position:0%
+uh lat right uh this is the this is a b
+that right and this is n no dis right
+
+ align:start position:0%
+that right and this is n no dis right
+ 
+
+ align:start position:0%
+that right and this is n no dis right
+dis right B and N and uh uh it turn what
+
+ align:start position:0%
+dis right B and N and uh uh it turn what
+ 
+
+ align:start position:0%
+dis right B and N and uh uh it turn what
+we do is just B material and we compact
+
+ align:start position:0%
+we do is just B material and we compact
+ 
+
+ align:start position:0%
+we do is just B material and we compact
+them into n form in work in dis ter
+
+ align:start position:0%
+them into n form in work in dis ter
+ 
+
+ align:start position:0%
+them into n form in work in dis ter
+works on SEC gtic also didn't quite work
+
+ align:start position:0%
+works on SEC gtic also didn't quite work
+ 
+
+ align:start position:0%
+works on SEC gtic also didn't quite work
+in that that the green
+
+ align:start position:0%
+in that that the green
+ 
+
+ align:start position:0%
+in that that the green
+gr and uh SC that didn't work out either
+
+ align:start position:0%
+gr and uh SC that didn't work out either
+ 
+
+ align:start position:0%
+gr and uh SC that didn't work out either
+and because GRE so we're still trying to
+
+ align:start position:0%
+and because GRE so we're still trying to
+ 
+
+ align:start position:0%
+and because GRE so we're still trying to
+figure out how we can prevent stop that
+
+ align:start position:0%
+figure out how we can prevent stop that
+ 
+
+ align:start position:0%
+figure out how we can prevent stop that
+grth of the GD and we drop the ther
+
+ align:start position:0%
+grth of the GD and we drop the ther
+ 
+
+ align:start position:0%
+grth of the GD and we drop the ther
+activity yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's that's a very good uh uh uh
+
+ align:start position:0%
+yeah that's that's a very good uh uh uh
+ 
+
+ align:start position:0%
+yeah that's that's a very good uh uh uh
+suggestion and I didn't look in C
+
+ align:start position:0%
+suggestion and I didn't look in C
+ 
+
+ align:start position:0%
+suggestion and I didn't look in C
+Crystal but but there are people looking
+
+ align:start position:0%
+Crystal but but there are people looking
+ 
+
+ align:start position:0%
+Crystal but but there are people looking
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+CL classro is a very complicated like uh
+
+ align:start position:0%
+CL classro is a very complicated like uh
+ 
+
+ align:start position:0%
+CL classro is a very complicated like uh
+you can have cicon in the crossroad
+
+ align:start position:0%
+you can have cicon in the crossroad
+ 
+
+ align:start position:0%
+you can have cicon in the crossroad
+geranium in Closs it's
+
+ align:start position:0%
+geranium in Closs it's
+ 
+
+ align:start position:0%
+geranium in Closs it's
+a it has a say has holes
+
+ align:start position:0%
+a it has a say has holes
+ 
+
+ align:start position:0%
+a it has a say has holes
+and uh they have
+
+ align:start position:0%
+and uh they have
+ 
+
+ align:start position:0%
+and uh they have
+little uh but for that c the
+
+ align:start position:0%
+little uh but for that c the
+ 
+
+ align:start position:0%
+little uh but for that c the
+CATE the case whether you can make the
+
+ align:start position:0%
+CATE the case whether you can make the
+ 
+
+ align:start position:0%
+CATE the case whether you can make the
+electron to move remember you can kill
+
+ align:start position:0%
+electron to move remember you can kill
+ 
+
+ align:start position:0%
+electron to move remember you can kill
+fullon if you just want to kill Fon
+
+ align:start position:0%
+fullon if you just want to kill Fon
+ 
+
+ align:start position:0%
+fullon if you just want to kill Fon
+that's easy but you also want to keep
+
+ align:start position:0%
+that's easy but you also want to keep
+ 
+
+ align:start position:0%
+that's easy but you also want to keep
+the electron moving so the idea the good
+
+ align:start position:0%
+the electron moving so the idea the good
+ 
+
+ align:start position:0%
+the electron moving so the idea the good
+a very good terminology came from glance
+
+ align:start position:0%
+a very good terminology came from glance
+ 
+
+ align:start position:0%
+a very good terminology came from glance
+SL and he said what do you want is
+
+ align:start position:0%
+SL and he said what do you want is
+ 
+
+ align:start position:0%
+SL and he said what do you want is
+electron Crystal for Fon glass in one
+
+ align:start position:0%
+electron Crystal for Fon glass in one
+ 
+
+ align:start position:0%
+electron Crystal for Fon glass in one
+material because Fon in glass this glass
+
+ align:start position:0%
+material because Fon in glass this glass
+ 
+
+ align:start position:0%
+material because Fon in glass this glass
+here am off us random Atomic Arrangement
+
+ align:start position:0%
+here am off us random Atomic Arrangement
+ 
+
+ align:start position:0%
+here am off us random Atomic Arrangement
+so the full onity is very cool but this
+
+ align:start position:0%
+so the full onity is very cool but this
+ 
+
+ align:start position:0%
+so the full onity is very cool but this
+super L is is
+
+ align:start position:0%
+super L is is
+ 
+
+ align:start position:0%
+super L is is
+different right it's still
+
+ align:start position:0%
+different right it's still
+ 
+
+ align:start position:0%
+different right it's still
+Crystal so you are uh whether we can for
+
+ align:start position:0%
+Crystal so you are uh whether we can for
+ 
+
+ align:start position:0%
+Crystal so you are uh whether we can for
+example we're looking randomized wave
+
+ align:start position:0%
+example we're looking randomized wave
+ 
+
+ align:start position:0%
+example we're looking randomized wave
+localize you you localize
+
+ align:start position:0%
+localize you you localize
+ 
+
+ align:start position:0%
+localize you you localize
+way very difficult I think but it's
+
+ align:start position:0%
+way very difficult I think but it's
+ 
+
+ align:start position:0%
+way very difficult I think but it's
+worth trying right and uh because say
+
+ align:start position:0%
+worth trying right and uh because say
+ 
+
+ align:start position:0%
+worth trying right and uh because say
+you need a crystal structure to get
+
+ align:start position:0%
+you need a crystal structure to get
+ 
+
+ align:start position:0%
+you need a crystal structure to get
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+propagated very difficult because the
+
+ align:start position:0%
+propagated very difficult because the
+ 
+
+ align:start position:0%
+propagated very difficult because the
+sure wance you can do photonic Crystal
+
+ align:start position:0%
+sure wance you can do photonic Crystal
+ 
+
+ align:start position:0%
+sure wance you can do photonic Crystal
+or that for electromagnetic wave because
+
+ align:start position:0%
+or that for electromagnetic wave because
+ 
+
+ align:start position:0%
+or that for electromagnetic wave because
+the wav is pretty long but it's very
+
+ align:start position:0%
+the wav is pretty long but it's very
+ 
+
+ align:start position:0%
+the wav is pretty long but it's very
+hard to do this for fullon because wance
+
+ align:start position:0%
+hard to do this for fullon because wance
+ 
+
+ align:start position:0%
+hard to do this for fullon because wance
+is short and they don't propagate very
+
+ align:start position:0%
+is short and they don't propagate very
+ 
+
+ align:start position:0%
+is short and they don't propagate very
+long you need a long cerence to have the
+
+ align:start position:0%
+long you need a long cerence to have the
+ 
+
+ align:start position:0%
+long you need a long cerence to have the
+waves distract each other so those are
+
+ align:start position:0%
+waves distract each other so those are
+ 
+
+ align:start position:0%
+waves distract each other so those are
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difficulties okay so here more detailed
+
+ align:start position:0%
+difficulties okay so here more detailed
+ 
+
+ align:start position:0%
+difficulties okay so here more detailed
+example this you can say the theral is
+
+ align:start position:0%
+example this you can say the theral is
+ 
+
+ align:start position:0%
+example this you can say the theral is
+Dro so when I started
+
+ align:start position:0%
+Dro so when I started
+ 
+
+ align:start position:0%
+Dro so when I started
+this everybody was saying electron what
+
+ align:start position:0%
+this everybody was saying electron what
+ 
+
+ align:start position:0%
+this everybody was saying electron what
+you to do with electron and said I don't
+
+ align:start position:0%
+you to do with electron and said I don't
+ 
+
+ align:start position:0%
+you to do with electron and said I don't
+know I wish it work out uh but when I
+
+ align:start position:0%
+know I wish it work out uh but when I
+ 
+
+ align:start position:0%
+know I wish it work out uh but when I
+think back you actually have good reason
+
+ align:start position:0%
+think back you actually have good reason
+ 
+
+ align:start position:0%
+think back you actually have good reason
+the general idea is okay let's don't get
+
+ align:start position:0%
+the general idea is okay let's don't get
+ 
+
+ align:start position:0%
+the general idea is okay let's don't get
+a too much electrical potential offset
+
+ align:start position:0%
+a too much electrical potential offset
+ 
+
+ align:start position:0%
+a too much electrical potential offset
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+interface right that's what the scatter
+
+ align:start position:0%
+interface right that's what the scatter
+ 
+
+ align:start position:0%
+interface right that's what the scatter
+electron and uh but say it turns out uh
+
+ align:start position:0%
+electron and uh but say it turns out uh
+ 
+
+ align:start position:0%
+electron and uh but say it turns out uh
+in bu right you can see the electron is
+
+ align:start position:0%
+in bu right you can see the electron is
+ 
+
+ align:start position:0%
+in bu right you can see the electron is
+is better when I first look at this I
+
+ align:start position:0%
+is better when I first look at this I
+ 
+
+ align:start position:0%
+is better when I first look at this I
+couldn't believe right and the reason is
+
+ align:start position:0%
+couldn't believe right and the reason is
+ 
+
+ align:start position:0%
+couldn't believe right and the reason is
+of course it's semiconductor the
+
+ align:start position:0%
+of course it's semiconductor the
+ 
+
+ align:start position:0%
+of course it's semiconductor the
+electric conductivity depends on the
+
+ align:start position:0%
+electric conductivity depends on the
+ 
+
+ align:start position:0%
+electric conductivity depends on the
+carer concentration right it's a
+
+ align:start position:0%
+carer concentration right it's a
+ 
+
+ align:start position:0%
+carer concentration right it's a
+Mobility times n the car concentration
+
+ align:start position:0%
+Mobility times n the car concentration
+ 
+
+ align:start position:0%
+Mobility times n the car concentration
+times charge so turn out the dis ter
+
+ align:start position:0%
+times charge so turn out the dis ter
+ 
+
+ align:start position:0%
+times charge so turn out the dis ter
+when you it you generate defect that
+
+ align:start position:0%
+when you it you generate defect that
+ 
+
+ align:start position:0%
+when you it you generate defect that
+generate more electron or in this case
+
+ align:start position:0%
+generate more electron or in this case
+ 
+
+ align:start position:0%
+generate more electron or in this case
+more P because it's a positive you C is
+
+ align:start position:0%
+more P because it's a positive you C is
+ 
+
+ align:start position:0%
+more P because it's a positive you C is
+positive that's P again you can say
+
+ align:start position:0%
+positive that's P again you can say
+ 
+
+ align:start position:0%
+positive that's P again you can say
+that's the typical Behavior so at the
+
+ align:start position:0%
+that's the typical Behavior so at the
+ 
+
+ align:start position:0%
+that's the typical Behavior so at the
+end if I PL the s s here so higher
+
+ align:start position:0%
+end if I PL the s s here so higher
+ 
+
+ align:start position:0%
+end if I PL the s s here so higher
+electron density lower catback
+
+ align:start position:0%
+electron density lower catback
+ 
+
+ align:start position:0%
+electron density lower catback
+right higher electron density fir level
+
+ align:start position:0%
+right higher electron density fir level
+ 
+
+ align:start position:0%
+right higher electron density fir level
+is closer to the B Edge or even get into
+
+ align:start position:0%
+is closer to the B Edge or even get into
+ 
+
+ align:start position:0%
+is closer to the B Edge or even get into
+the B the C is the average distance
+
+ align:start position:0%
+the B the C is the average distance
+ 
+
+ align:start position:0%
+the B the C is the average distance
+thermal energy of electron Rel to C
+
+ align:start position:0%
+thermal energy of electron Rel to C
+ 
+
+ align:start position:0%
+thermal energy of electron Rel to C
+Potential from so higher electric
+
+ align:start position:0%
+Potential from so higher electric
+ 
+
+ align:start position:0%
+Potential from so higher electric
+connectivity lower C that's all but
+
+ align:start position:0%
+connectivity lower C that's all but
+ 
+
+ align:start position:0%
+connectivity lower C that's all but
+because it have higher car
+
+ align:start position:0%
+because it have higher car
+ 
+
+ align:start position:0%
+because it have higher car
+concentration the bipolar decrease start
+
+ align:start position:0%
+concentration the bipolar decrease start
+ 
+
+ align:start position:0%
+concentration the bipolar decrease start
+later you can see here right go to
+
+ align:start position:0%
+later you can see here right go to
+ 
+
+ align:start position:0%
+later you can see here right go to
+higher temperature
+
+ align:start position:0%
+higher temperature
+ 
+
+ align:start position:0%
+higher temperature
+and then uh so if you PL s sare Sigma
+
+ align:start position:0%
+and then uh so if you PL s sare Sigma
+ 
+
+ align:start position:0%
+and then uh so if you PL s sare Sigma
+this is actually better than
+
+ align:start position:0%
+this is actually better than
+ 
+
+ align:start position:0%
+this is actually better than
+this we try that very hard in superla we
+
+ align:start position:0%
+this we try that very hard in superla we
+ 
+
+ align:start position:0%
+this we try that very hard in superla we
+didn't get S squ Sigma both decreased
+
+ align:start position:0%
+didn't get S squ Sigma both decreased
+ 
+
+ align:start position:0%
+didn't get S squ Sigma both decreased
+Thal connectivity incre power factor and
+
+ align:start position:0%
+Thal connectivity incre power factor and
+ 
+
+ align:start position:0%
+Thal connectivity incre power factor and
+this actually work so um but we still
+
+ align:start position:0%
+this actually work so um but we still
+ 
+
+ align:start position:0%
+this actually work so um but we still
+don't know how exactly to model it very
+
+ align:start position:0%
+don't know how exactly to model it very
+ 
+
+ align:start position:0%
+don't know how exactly to model it very
+difficult to model in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+romu we do not and we another only one
+
+ align:start position:0%
+romu we do not and we another only one
+ 
+
+ align:start position:0%
+romu we do not and we another only one
+let me see uh in fact uh Mercury
+
+ align:start position:0%
+let me see uh in fact uh Mercury
+ 
+
+ align:start position:0%
+let me see uh in fact uh Mercury
+KES uh has been working this material
+
+ align:start position:0%
+KES uh has been working this material
+ 
+
+ align:start position:0%
+KES uh has been working this material
+system which play
+
+ align:start position:0%
+system which play
+ 
+
+ align:start position:0%
+system which play
+for last and so that
+
+ align:start position:0%
+for last and so that
+ 
+
+ align:start position:0%
+for last and so that
+turn and the single free store he grew
+
+ align:start position:0%
+turn and the single free store he grew
+ 
+
+ align:start position:0%
+turn and the single free store he grew
+single free spent several days to GRE
+
+ align:start position:0%
+single free spent several days to GRE
+ 
+
+ align:start position:0%
+single free spent several days to GRE
+single fre stores coing feeding and got
+
+ align:start position:0%
+single fre stores coing feeding and got
+ 
+
+ align:start position:0%
+single fre stores coing feeding and got
+a very good
+
+ align:start position:0%
+a very good
+ 
+
+ align:start position:0%
+a very good
+properties and again let me question you
+
+ align:start position:0%
+properties and again let me question you
+ 
+
+ align:start position:0%
+properties and again let me question you
+I can't believe this for point this he
+
+ align:start position:0%
+I can't believe this for point this he
+ 
+
+ align:start position:0%
+I can't believe this for point this he
+extrapolated no he doesn't show this
+
+ align:start position:0%
+extrapolated no he doesn't show this
+ 
+
+ align:start position:0%
+extrapolated no he doesn't show this
+anymore and measurement is always a hard
+
+ align:start position:0%
+anymore and measurement is always a hard
+ 
+
+ align:start position:0%
+anymore and measurement is always a hard
+problem this is a one has to realize
+
+ align:start position:0%
+problem this is a one has to realize
+ 
+
+ align:start position:0%
+problem this is a one has to realize
+sometimes I steare people away by saying
+
+ align:start position:0%
+sometimes I steare people away by saying
+ 
+
+ align:start position:0%
+sometimes I steare people away by saying
+that but that's reality have Cas and
+
+ align:start position:0%
+that but that's reality have Cas and
+ 
+
+ align:start position:0%
+that but that's reality have Cas and
+what they found later on is that in this
+
+ align:start position:0%
+what they found later on is that in this
+ 
+
+ align:start position:0%
+what they found later on is that in this
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+actually even though it's a single
+
+ align:start position:0%
+actually even though it's a single
+ 
+
+ align:start position:0%
+actually even though it's a single
+Crystal but a lot of precipi are from n
+
+ align:start position:0%
+Crystal but a lot of precipi are from n
+ 
+
+ align:start position:0%
+Crystal but a lot of precipi are from n
+Dot and uh and with that the his is also
+
+ align:start position:0%
+Dot and uh and with that the his is also
+ 
+
+ align:start position:0%
+Dot and uh and with that the his is also
+low so we got a a good uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+figure this is a really interesting
+
+ align:start position:0%
+figure this is a really interesting
+ 
+
+ align:start position:0%
+figure this is a really interesting
+system uh I've been talking to je
+
+ align:start position:0%
+system uh I've been talking to je
+ 
+
+ align:start position:0%
+system uh I've been talking to je
+paramas
+
+ align:start position:0%
+paramas
+ 
+
+ align:start position:0%
+paramas
+uh and I still can really give you very
+
+ align:start position:0%
+uh and I still can really give you very
+ 
+
+ align:start position:0%
+uh and I still can really give you very
+simple picture and it's a uh basically
+
+ align:start position:0%
+simple picture and it's a uh basically
+ 
+
+ align:start position:0%
+simple picture and it's a uh basically
+uh I give me a very simple picture so I
+
+ align:start position:0%
+uh I give me a very simple picture so I
+ 
+
+ align:start position:0%
+uh I give me a very simple picture so I
+can exp my students and uh I don't think
+
+ align:start position:0%
+can exp my students and uh I don't think
+ 
+
+ align:start position:0%
+can exp my students and uh I don't think
+I got his simple picture yet uh but the
+
+ align:start position:0%
+I got his simple picture yet uh but the
+ 
+
+ align:start position:0%
+I got his simple picture yet uh but the
+the idea is looking at is uh here is a
+
+ align:start position:0%
+the idea is looking at is uh here is a
+ 
+
+ align:start position:0%
+the idea is looking at is uh here is a
+silver uh site by site it's cuic
+
+ align:start position:0%
+silver uh site by site it's cuic
+ 
+
+ align:start position:0%
+silver uh site by site it's cuic
+structure right so right all those are
+
+ align:start position:0%
+structure right so right all those are
+ 
+
+ align:start position:0%
+structure right so right all those are
+similar and uh one is see is uh the
+
+ align:start position:0%
+similar and uh one is see is uh the
+ 
+
+ align:start position:0%
+similar and uh one is see is uh the
+electron clouds between the atoms
+
+ align:start position:0%
+electron clouds between the atoms
+ 
+
+ align:start position:0%
+electron clouds between the atoms
+uh have overlap and when one set of atom
+
+ align:start position:0%
+uh have overlap and when one set of atom
+ 
+
+ align:start position:0%
+uh have overlap and when one set of atom
+is moving let squeeze this CL clouds
+
+ align:start position:0%
+is moving let squeeze this CL clouds
+ 
+
+ align:start position:0%
+is moving let squeeze this CL clouds
+very significant so electron CLA very
+
+ align:start position:0%
+very significant so electron CLA very
+ 
+
+ align:start position:0%
+very significant so electron CLA very
+significant squeezing cause the the
+
+ align:start position:0%
+significant squeezing cause the the
+ 
+
+ align:start position:0%
+significant squeezing cause the the
+force UNH
+
+ align:start position:0%
+force UNH
+ 
+
+ align:start position:0%
+force UNH
+harmonis and this
+
+ align:start position:0%
+harmonis and this
+ 
+
+ align:start position:0%
+harmonis and this
+anharmonicity gives a very low so what
+
+ align:start position:0%
+anharmonicity gives a very low so what
+ 
+
+ align:start position:0%
+anharmonicity gives a very low so what
+you want is you want to make the atom
+
+ align:start position:0%
+you want is you want to make the atom
+ 
+
+ align:start position:0%
+you want is you want to make the atom
+strongly scatter each other okay uh High
+
+ align:start position:0%
+strongly scatter each other okay uh High
+ 
+
+ align:start position:0%
+strongly scatter each other okay uh High
+connectivity is you just have a pure
+
+ align:start position:0%
+connectivity is you just have a pure
+ 
+
+ align:start position:0%
+connectivity is you just have a pure
+Sprint honic oscillator you have
+
+ align:start position:0%
+Sprint honic oscillator you have
+ 
+
+ align:start position:0%
+Sprint honic oscillator you have
+infinite thermal
+
+ align:start position:0%
+infinite thermal
+ 
+
+ align:start position:0%
+infinite thermal
+conductivity and this the final thermal
+
+ align:start position:0%
+conductivity and this the final thermal
+ 
+
+ align:start position:0%
+conductivity and this the final thermal
+connectivity really comes from the third
+
+ align:start position:0%
+connectivity really comes from the third
+ 
+
+ align:start position:0%
+connectivity really comes from the third
+term of the potential okay it's not fals
+
+ align:start position:0%
+term of the potential okay it's not fals
+ 
+
+ align:start position:0%
+term of the potential okay it's not fals
+KX is for FAL KX plus perturbation KX
+
+ align:start position:0%
+KX is for FAL KX plus perturbation KX
+ 
+
+ align:start position:0%
+KX is for FAL KX plus perturbation KX
+squ so that square makees the two
+
+ align:start position:0%
+squ so that square makees the two
+ 
+
+ align:start position:0%
+squ so that square makees the two
+different frequency W interact with each
+
+ align:start position:0%
+different frequency W interact with each
+ 
+
+ align:start position:0%
+different frequency W interact with each
+other that's so hard for optical wave
+
+ align:start position:0%
+other that's so hard for optical wave
+ 
+
+ align:start position:0%
+other that's so hard for optical wave
+it's much easier for f but when you want
+
+ align:start position:0%
+it's much easier for f but when you want
+ 
+
+ align:start position:0%
+it's much easier for f but when you want
+to push to very low uh very small limit
+
+ align:start position:0%
+to push to very low uh very small limit
+ 
+
+ align:start position:0%
+to push to very low uh very small limit
+you got to say get this aity very large
+
+ align:start position:0%
+you got to say get this aity very large
+ 
+
+ align:start position:0%
+you got to say get this aity very large
+and one way to to gaug that is this
+
+ align:start position:0%
+and one way to to gaug that is this
+ 
+
+ align:start position:0%
+and one way to to gaug that is this
+reason parameter which is related to
+
+ align:start position:0%
+reason parameter which is related to
+ 
+
+ align:start position:0%
+reason parameter which is related to
+theral expansion and theral expansion so
+
+ align:start position:0%
+theral expansion and theral expansion so
+ 
+
+ align:start position:0%
+theral expansion and theral expansion so
+higher large th expansion material
+
+ align:start position:0%
+higher large th expansion material
+ 
+
+ align:start position:0%
+higher large th expansion material
+typically is more
+
+ align:start position:0%
+typically is more
+ 
+
+ align:start position:0%
+typically is more
+unod
+
+ align:start position:0%
+unod
+ 
+
+ align:start position:0%
+unod
+okay and uh what is showing is this
+
+ align:start position:0%
+okay and uh what is showing is this
+ 
+
+ align:start position:0%
+okay and uh what is showing is this
+minimum theral conductivity Theory uh
+
+ align:start position:0%
+minimum theral conductivity Theory uh
+ 
+
+ align:start position:0%
+minimum theral conductivity Theory uh
+that's also another thing I never
+
+ align:start position:0%
+that's also another thing I never
+ 
+
+ align:start position:0%
+that's also another thing I never
+believe minimum Ser contivity uh what
+
+ align:start position:0%
+believe minimum Ser contivity uh what
+ 
+
+ align:start position:0%
+believe minimum Ser contivity uh what
+the idea is one thir K 1 c v gamma right
+
+ align:start position:0%
+the idea is one thir K 1 c v gamma right
+ 
+
+ align:start position:0%
+the idea is one thir K 1 c v gamma right
+that's the ktic theory and the minimum
+
+ align:start position:0%
+that's the ktic theory and the minimum
+ 
+
+ align:start position:0%
+that's the ktic theory and the minimum
+server conductivity is replacing the
+
+ align:start position:0%
+server conductivity is replacing the
+ 
+
+ align:start position:0%
+server conductivity is replacing the
+mean free pass by the
+
+ align:start position:0%
+mean free pass by the
+ 
+
+ align:start position:0%
+mean free pass by the
+wavelength okay so that's the minimum
+
+ align:start position:0%
+wavelength okay so that's the minimum
+ 
+
+ align:start position:0%
+wavelength okay so that's the minimum
+mean free pass you could have and this
+
+ align:start position:0%
+mean free pass you could have and this
+ 
+
+ align:start position:0%
+mean free pass you could have and this
+was a glen slack originary Theory and
+
+ align:start position:0%
+was a glen slack originary Theory and
+ 
+
+ align:start position:0%
+was a glen slack originary Theory and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+and Bobby Paul from uh Corel uh said
+
+ align:start position:0%
+and Bobby Paul from uh Corel uh said
+ 
+
+ align:start position:0%
+and Bobby Paul from uh Corel uh said
+that oh you should not be just mean free
+
+ align:start position:0%
+that oh you should not be just mean free
+ 
+
+ align:start position:0%
+that oh you should not be just mean free
+pass equals wance it should be mean free
+
+ align:start position:0%
+pass equals wance it should be mean free
+ 
+
+ align:start position:0%
+pass equals wance it should be mean free
+pass equals half wance Einstein based on
+
+ align:start position:0%
+pass equals half wance Einstein based on
+ 
+
+ align:start position:0%
+pass equals half wance Einstein based on
+Einstein the
+
+ align:start position:0%
+Einstein the
+ 
+
+ align:start position:0%
+Einstein the
+argument so that reduce th minimum by
+
+ align:start position:0%
+argument so that reduce th minimum by
+ 
+
+ align:start position:0%
+argument so that reduce th minimum by
+another half and so very often people
+
+ align:start position:0%
+another half and so very often people
+ 
+
+ align:start position:0%
+another half and so very often people
+will draw theal connectivity against
+
+ align:start position:0%
+will draw theal connectivity against
+ 
+
+ align:start position:0%
+will draw theal connectivity against
+minimum so this is the one example say
+
+ align:start position:0%
+minimum so this is the one example say
+ 
+
+ align:start position:0%
+minimum so this is the one example say
+okay you reach the minimum you can
+
+ align:start position:0%
+okay you reach the minimum you can
+ 
+
+ align:start position:0%
+okay you reach the minimum you can
+reduce
+
+ align:start position:0%
+reduce
+ 
+
+ align:start position:0%
+reduce
+anymore but in fact I said D key help
+
+ align:start position:0%
+anymore but in fact I said D key help
+ 
+
+ align:start position:0%
+anymore but in fact I said D key help
+because he measur layer structure his
+
+ align:start position:0%
+because he measur layer structure his
+ 
+
+ align:start position:0%
+because he measur layer structure his
+server connectivity is twice air it's
+
+ align:start position:0%
+server connectivity is twice air it's
+ 
+
+ align:start position:0%
+server connectivity is twice air it's
+order magnitude smaller than the minimum
+
+ align:start position:0%
+order magnitude smaller than the minimum
+ 
+
+ align:start position:0%
+order magnitude smaller than the minimum
+so his own minimal Theory now there's a
+
+ align:start position:0%
+so his own minimal Theory now there's a
+ 
+
+ align:start position:0%
+so his own minimal Theory now there's a
+minimal experiment as an order Corner
+
+ align:start position:0%
+minimal experiment as an order Corner
+ 
+
+ align:start position:0%
+minimal experiment as an order Corner
+that's why I say I don't believe in the
+
+ align:start position:0%
+that's why I say I don't believe in the
+ 
+
+ align:start position:0%
+that's why I say I don't believe in the
+because you should go uh look at that
+
+ align:start position:0%
+because you should go uh look at that
+ 
+
+ align:start position:0%
+because you should go uh look at that
+there better formulation when you have
+
+ align:start position:0%
+there better formulation when you have
+ 
+
+ align:start position:0%
+there better formulation when you have
+iron s you don't you don't have one3
+
+ align:start position:0%
+iron s you don't you don't have one3
+ 
+
+ align:start position:0%
+iron s you don't you don't have one3
+M if you're interested this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to okay this is something that uh I
+
+ align:start position:0%
+to okay this is something that uh I
+ 
+
+ align:start position:0%
+to okay this is something that uh I
+really want I said I have okay I bring
+
+ align:start position:0%
+really want I said I have okay I bring
+ 
+
+ align:start position:0%
+really want I said I have okay I bring
+you from the basics to really the
+
+ align:start position:0%
+you from the basics to really the
+ 
+
+ align:start position:0%
+you from the basics to really the
+Forefront that's just a few uh uh month
+
+ align:start position:0%
+Forefront that's just a few uh uh month
+ 
+
+ align:start position:0%
+Forefront that's just a few uh uh month
+ago there was paper um uh Indian
+
+ align:start position:0%
+ago there was paper um uh Indian
+ 
+
+ align:start position:0%
+ago there was paper um uh Indian
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+satellite and uh what is the saying this
+
+ align:start position:0%
+satellite and uh what is the saying this
+ 
+
+ align:start position:0%
+satellite and uh what is the saying this
+is this is a charge
+
+ align:start position:0%
+is this is a charge
+ 
+
+ align:start position:0%
+is this is a charge
+density and the PES
+
+ align:start position:0%
+density and the PES
+ 
+
+ align:start position:0%
+density and the PES
+instability and this this got really uh
+
+ align:start position:0%
+instability and this this got really uh
+ 
+
+ align:start position:0%
+instability and this this got really uh
+uh so uh but let me f uh so what what
+
+ align:start position:0%
+uh so uh but let me f uh so what what
+ 
+
+ align:start position:0%
+uh so uh but let me f uh so what what
+happens is uh this direction is wward
+
+ align:start position:0%
+happens is uh this direction is wward
+ 
+
+ align:start position:0%
+happens is uh this direction is wward
+for that's more like a layer structure
+
+ align:start position:0%
+for that's more like a layer structure
+ 
+
+ align:start position:0%
+for that's more like a layer structure
+and then into the C axis that's the uh
+
+ align:start position:0%
+and then into the C axis that's the uh
+ 
+
+ align:start position:0%
+and then into the C axis that's the uh
+uh see calent bonding but because the uh
+
+ align:start position:0%
+uh see calent bonding but because the uh
+ 
+
+ align:start position:0%
+uh see calent bonding but because the uh
+uh charge Distortion so in the C axis
+
+ align:start position:0%
+uh charge Distortion so in the C axis
+ 
+
+ align:start position:0%
+uh charge Distortion so in the C axis
+this actually charg is strongly
+
+ align:start position:0%
+this actually charg is strongly
+ 
+
+ align:start position:0%
+this actually charg is strongly
+distorted and create a very large ANH
+
+ align:start position:0%
+distorted and create a very large ANH
+ 
+
+ align:start position:0%
+distorted and create a very large ANH
+harmonicity to the L W scatter so the
+
+ align:start position:0%
+harmonicity to the L W scatter so the
+ 
+
+ align:start position:0%
+harmonicity to the L W scatter so the
+theral conductivity is really strange
+
+ align:start position:0%
+theral conductivity is really strange
+ 
+
+ align:start position:0%
+theral conductivity is really strange
+because the onear direction Force weak
+
+ align:start position:0%
+because the onear direction Force weak
+ 
+
+ align:start position:0%
+because the onear direction Force weak
+Force typically means low th contivity
+
+ align:start position:0%
+Force typically means low th contivity
+ 
+
+ align:start position:0%
+Force typically means low th contivity
+right but in this case what you have
+
+ align:start position:0%
+right but in this case what you have
+ 
+
+ align:start position:0%
+right but in this case what you have
+this is the CX coent Direction has lower
+
+ align:start position:0%
+this is the CX coent Direction has lower
+ 
+
+ align:start position:0%
+this is the CX coent Direction has lower
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+the and very interesting uh uh and
+
+ align:start position:0%
+the and very interesting uh uh and
+ 
+
+ align:start position:0%
+the and very interesting uh uh and
+definitely wor more study
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay now let me go to m
+
+ align:start position:0%
+here okay now let me go to m
+ 
+
+ align:start position:0%
+here okay now let me go to m
+side right uh this is the quantization
+
+ align:start position:0%
+side right uh this is the quantization
+ 
+
+ align:start position:0%
+side right uh this is the quantization
+menion and uh uh the pza Box problem
+
+ align:start position:0%
+menion and uh uh the pza Box problem
+ 
+
+ align:start position:0%
+menion and uh uh the pza Box problem
+right the
+
+ align:start position:0%
+right the
+ 
+
+ align:start position:0%
+right the
+possible so you have a simple uh see
+
+ align:start position:0%
+possible so you have a simple uh see
+ 
+
+ align:start position:0%
+possible so you have a simple uh see
+this is a simple homework I said before
+
+ align:start position:0%
+this is a simple homework I said before
+ 
+
+ align:start position:0%
+this is a simple homework I said before
+uh the uh this is the Z Direction energy
+
+ align:start position:0%
+uh the uh this is the Z Direction energy
+ 
+
+ align:start position:0%
+uh the uh this is the Z Direction energy
+cont and you can do the same standing
+
+ align:start position:0%
+cont and you can do the same standing
+ 
+
+ align:start position:0%
+cont and you can do the same standing
+wave argument I did before and say
+
+ align:start position:0%
+wave argument I did before and say
+ 
+
+ align:start position:0%
+wave argument I did before and say
+what's the wavelength and what's the
+
+ align:start position:0%
+what's the wavelength and what's the
+ 
+
+ align:start position:0%
+what's the wavelength and what's the
+corresponding
+
+ align:start position:0%
+corresponding
+ 
+
+ align:start position:0%
+corresponding
+energy and uh uh so x y direction the is
+
+ align:start position:0%
+energy and uh uh so x y direction the is
+ 
+
+ align:start position:0%
+energy and uh uh so x y direction the is
+qu continuous W Vector so now for
+
+ align:start position:0%
+qu continuous W Vector so now for
+ 
+
+ align:start position:0%
+qu continuous W Vector so now for
+different end uh we have the sub bance
+
+ align:start position:0%
+different end uh we have the sub bance
+ 
+
+ align:start position:0%
+different end uh we have the sub bance
+so this energy P
+
+ align:start position:0%
+so this energy P
+ 
+
+ align:start position:0%
+so this energy P
+has different energy levels in the due
+
+ align:start position:0%
+has different energy levels in the due
+ 
+
+ align:start position:0%
+has different energy levels in the due
+to the uh thickness in the direction so
+
+ align:start position:0%
+to the uh thickness in the direction so
+ 
+
+ align:start position:0%
+to the uh thickness in the direction so
+that's a basic F Well idea okay and now
+
+ align:start position:0%
+that's a basic F Well idea okay and now
+ 
+
+ align:start position:0%
+that's a basic F Well idea okay and now
+you go to do
+
+ align:start position:0%
+you go to do
+ 
+
+ align:start position:0%
+you go to do
+this uh you calculate the density of
+
+ align:start position:0%
+this uh you calculate the density of
+ 
+
+ align:start position:0%
+this uh you calculate the density of
+space I I uh I don't want to go through
+
+ align:start position:0%
+space I I uh I don't want to go through
+ 
+
+ align:start position:0%
+space I I uh I don't want to go through
+this MTH but you can say this is the the
+
+ align:start position:0%
+this MTH but you can say this is the the
+ 
+
+ align:start position:0%
+this MTH but you can say this is the the
+same thing we did before except in the
+
+ align:start position:0%
+same thing we did before except in the
+ 
+
+ align:start position:0%
+same thing we did before except in the
+direction now I don't do uh I do not
+
+ align:start position:0%
+direction now I don't do uh I do not
+ 
+
+ align:start position:0%
+direction now I don't do uh I do not
+convert this summation into into
+
+ align:start position:0%
+convert this summation into into
+ 
+
+ align:start position:0%
+convert this summation into into
+integration in Z Direction I convert the
+
+ align:start position:0%
+integration in Z Direction I convert the
+ 
+
+ align:start position:0%
+integration in Z Direction I convert the
+XY Direction because the direction that
+
+ align:start position:0%
+XY Direction because the direction that
+ 
+
+ align:start position:0%
+XY Direction because the direction that
+separation is too large and the the
+
+ align:start position:0%
+separation is too large and the the
+ 
+
+ align:start position:0%
+separation is too large and the the
+summation to integration that conversion
+
+ align:start position:0%
+summation to integration that conversion
+ 
+
+ align:start position:0%
+summation to integration that conversion
+is not rigorous not mathematically
+
+ align:start position:0%
+is not rigorous not mathematically
+ 
+
+ align:start position:0%
+is not rigorous not mathematically
+accurate so I still keep this summation
+
+ align:start position:0%
+accurate so I still keep this summation
+ 
+
+ align:start position:0%
+accurate so I still keep this summation
+here and at the end what you show is
+
+ align:start position:0%
+here and at the end what you show is
+ 
+
+ align:start position:0%
+here and at the end what you show is
+density of States now is a
+
+ align:start position:0%
+density of States now is a
+ 
+
+ align:start position:0%
+density of States now is a
+staircase uh or in typical parabolic
+
+ align:start position:0%
+staircase uh or in typical parabolic
+ 
+
+ align:start position:0%
+staircase uh or in typical parabolic
+band approximation we got this is 3D
+
+ align:start position:0%
+band approximation we got this is 3D
+ 
+
+ align:start position:0%
+band approximation we got this is 3D
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+2D okay and now with that there's
+
+ align:start position:0%
+2D okay and now with that there's
+ 
+
+ align:start position:0%
+2D okay and now with that there's
+Advantage where is the
+
+ align:start position:0%
+Advantage where is the
+ 
+
+ align:start position:0%
+Advantage where is the
+advantage let's go back to the picture I
+
+ align:start position:0%
+advantage let's go back to the picture I
+ 
+
+ align:start position:0%
+advantage let's go back to the picture I
+show before right see back in the
+
+ align:start position:0%
+show before right see back in the
+ 
+
+ align:start position:0%
+show before right see back in the
+measure of the average energy of the
+
+ align:start position:0%
+measure of the average energy of the
+ 
+
+ align:start position:0%
+measure of the average energy of the
+electron relative chical potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the number the electron electric
+
+ align:start position:0%
+the number the electron electric
+ 
+
+ align:start position:0%
+the number the electron electric
+conductivity is really proportional to
+
+ align:start position:0%
+conductivity is really proportional to
+ 
+
+ align:start position:0%
+conductivity is really proportional to
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+electrons right now when I have this if
+
+ align:start position:0%
+electrons right now when I have this if
+ 
+
+ align:start position:0%
+electrons right now when I have this if
+you look at this is den of States this
+
+ align:start position:0%
+you look at this is den of States this
+ 
+
+ align:start position:0%
+you look at this is den of States this
+is DF per direct derivative now this is
+
+ align:start position:0%
+is DF per direct derivative now this is
+ 
+
+ align:start position:0%
+is DF per direct derivative now this is
+very small this this times this that's
+
+ align:start position:0%
+very small this this times this that's
+ 
+
+ align:start position:0%
+very small this this times this that's
+the region where it's contributing to
+
+ align:start position:0%
+the region where it's contributing to
+ 
+
+ align:start position:0%
+the region where it's contributing to
+electrons right because of the parabolic
+
+ align:start position:0%
+electrons right because of the parabolic
+ 
+
+ align:start position:0%
+electrons right because of the parabolic
+this is a small L time small
+
+ align:start position:0%
+this is a small L time small
+ 
+
+ align:start position:0%
+this is a small L time small
+l so the electric conduction the number
+
+ align:start position:0%
+l so the electric conduction the number
+ 
+
+ align:start position:0%
+l so the electric conduction the number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+charges that carry this C back most of
+
+ align:start position:0%
+charges that carry this C back most of
+ 
+
+ align:start position:0%
+charges that carry this C back most of
+them is very low energy the average
+
+ align:start position:0%
+them is very low energy the average
+ 
+
+ align:start position:0%
+them is very low energy the average
+energy is here those are low energy
+
+ align:start position:0%
+energy is here those are low energy
+ 
+
+ align:start position:0%
+energy is here those are low energy
+electron they carry more electrical
+
+ align:start position:0%
+electron they carry more electrical
+ 
+
+ align:start position:0%
+electron they carry more electrical
+charge so that's a problem with
+
+ align:start position:0%
+charge so that's a problem with
+ 
+
+ align:start position:0%
+charge so that's a problem with
+parabolic than with the density the
+
+ align:start position:0%
+parabolic than with the density the
+ 
+
+ align:start position:0%
+parabolic than with the density the
+parabolic density of
+
+ align:start position:0%
+parabolic density of
+ 
+
+ align:start position:0%
+parabolic density of
+stat okay now do the conent right you
+
+ align:start position:0%
+stat okay now do the conent right you
+ 
+
+ align:start position:0%
+stat okay now do the conent right you
+have a sharp
+
+ align:start position:0%
+have a sharp
+ 
+
+ align:start position:0%
+have a sharp
+staircase and uh you can put in you see
+
+ align:start position:0%
+staircase and uh you can put in you see
+ 
+
+ align:start position:0%
+staircase and uh you can put in you see
+here you can put in more charge or still
+
+ align:start position:0%
+here you can put in more charge or still
+ 
+
+ align:start position:0%
+here you can put in more charge or still
+have the same
+
+ align:start position:0%
+have the same
+ 
+
+ align:start position:0%
+have the same
+SE or if you have S electric
+
+ align:start position:0%
+SE or if you have S electric
+ 
+
+ align:start position:0%
+SE or if you have S electric
+conductivity they you then you can
+
+ align:start position:0%
+conductivity they you then you can
+ 
+
+ align:start position:0%
+conductivity they you then you can
+increase your
+
+ align:start position:0%
+increase your
+ 
+
+ align:start position:0%
+increase your
+C at the end what you want is s sare
+
+ align:start position:0%
+C at the end what you want is s sare
+ 
+
+ align:start position:0%
+C at the end what you want is s sare
+Sigma to be larger right so that's why
+
+ align:start position:0%
+Sigma to be larger right so that's why
+ 
+
+ align:start position:0%
+Sigma to be larger right so that's why
+why those Quantum structures like the
+
+ align:start position:0%
+why those Quantum structures like the
+ 
+
+ align:start position:0%
+why those Quantum structures like the
+quantum Wells gave you larger s Square
+
+ align:start position:0%
+quantum Wells gave you larger s Square
+ 
+
+ align:start position:0%
+quantum Wells gave you larger s Square
+Sigma and then you look at the other
+
+ align:start position:0%
+Sigma and then you look at the other
+ 
+
+ align:start position:0%
+Sigma and then you look at the other
+structures the D of States this is the
+
+ align:start position:0%
+structures the D of States this is the
+ 
+
+ align:start position:0%
+structures the D of States this is the
+Ser case for the uh two dimensional and
+
+ align:start position:0%
+Ser case for the uh two dimensional and
+ 
+
+ align:start position:0%
+Ser case for the uh two dimensional and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+wires is a sharp Pi here and dots are
+
+ align:start position:0%
+wires is a sharp Pi here and dots are
+ 
+
+ align:start position:0%
+wires is a sharp Pi here and dots are
+just discrete
+
+ align:start position:0%
+just discrete
+ 
+
+ align:start position:0%
+just discrete
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+so progressively going from 3D 2D 1D z d
+
+ align:start position:0%
+so progressively going from 3D 2D 1D z d
+ 
+
+ align:start position:0%
+so progressively going from 3D 2D 1D z d
+it's better progressively it's better
+
+ align:start position:0%
+it's better progressively it's better
+ 
+
+ align:start position:0%
+it's better progressively it's better
+okay so that's what the theory says and
+
+ align:start position:0%
+okay so that's what the theory says and
+ 
+
+ align:start position:0%
+okay so that's what the theory says and
+at the time Milly and uh Ham N lab did
+
+ align:start position:0%
+at the time Milly and uh Ham N lab did
+ 
+
+ align:start position:0%
+at the time Milly and uh Ham N lab did
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+experiment and uh uh they show that that
+
+ align:start position:0%
+experiment and uh uh they show that that
+ 
+
+ align:start position:0%
+experiment and uh uh they show that that
+this but I don't I want first to show
+
+ align:start position:0%
+this but I don't I want first to show
+ 
+
+ align:start position:0%
+this but I don't I want first to show
+the trend right except there's one
+
+ align:start position:0%
+the trend right except there's one
+ 
+
+ align:start position:0%
+the trend right except there's one
+cop you see there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not s squ Sigma this is s squ n
+
+ align:start position:0%
+this is not s squ Sigma this is s squ n
+ 
+
+ align:start position:0%
+this is not s squ Sigma this is s squ n
+right electric conductivity is n time
+
+ align:start position:0%
+right electric conductivity is n time
+ 
+
+ align:start position:0%
+right electric conductivity is n time
+Mobility
+
+ align:start position:0%
+Mobility
+ 
+
+ align:start position:0%
+Mobility
+times the carrier charge electron
+
+ align:start position:0%
+times the carrier charge electron
+ 
+
+ align:start position:0%
+times the carrier charge electron
+charge okay and what what's the reason
+
+ align:start position:0%
+charge okay and what what's the reason
+ 
+
+ align:start position:0%
+charge okay and what what's the reason
+is that the super was not the the
+
+ align:start position:0%
+is that the super was not the the
+ 
+
+ align:start position:0%
+is that the super was not the the
+quantum W was not very good interface
+
+ align:start position:0%
+quantum W was not very good interface
+ 
+
+ align:start position:0%
+quantum W was not very good interface
+scal
+
+ align:start position:0%
+scal
+ 
+
+ align:start position:0%
+scal
+electrons Electric conductiv
+
+ align:start position:0%
+electrons Electric conductiv
+ 
+
+ align:start position:0%
+electrons Electric conductiv
+if you PL uh that I don't I don't know
+
+ align:start position:0%
+if you PL uh that I don't I don't know
+ 
+
+ align:start position:0%
+if you PL uh that I don't I don't know
+the detail but let see uh there are
+
+ align:start position:0%
+the detail but let see uh there are
+ 
+
+ align:start position:0%
+the detail but let see uh there are
+still questions here right because you
+
+ align:start position:0%
+still questions here right because you
+ 
+
+ align:start position:0%
+still questions here right because you
+this is s Square Sigma s Square n not s
+
+ align:start position:0%
+this is s Square Sigma s Square n not s
+ 
+
+ align:start position:0%
+this is s Square Sigma s Square n not s
+squ Sigma but the trend is there and
+
+ align:start position:0%
+squ Sigma but the trend is there and
+ 
+
+ align:start position:0%
+squ Sigma but the trend is there and
+that generate a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interest and uh this is just a more
+
+ align:start position:0%
+interest and uh this is just a more
+ 
+
+ align:start position:0%
+interest and uh this is just a more
+calculation I
+
+ align:start position:0%
+calculation I
+ 
+
+ align:start position:0%
+calculation I
+took from a book that Jo Paras and
+
+ align:start position:0%
+took from a book that Jo Paras and
+ 
+
+ align:start position:0%
+took from a book that Jo Paras and
+myself wri we never have finished finish
+
+ align:start position:0%
+myself wri we never have finished finish
+ 
+
+ align:start position:0%
+myself wri we never have finished finish
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+but anyone want to read there gra 3D 2D
+
+ align:start position:0%
+but anyone want to read there gra 3D 2D
+ 
+
+ align:start position:0%
+but anyone want to read there gra 3D 2D
+1D progressiv is
+
+ align:start position:0%
+1D progressiv is
+ 
+
+ align:start position:0%
+1D progressiv is
+better uh that's a theory and to do it
+
+ align:start position:0%
+better uh that's a theory and to do it
+ 
+
+ align:start position:0%
+better uh that's a theory and to do it
+in the experiment like I said you you
+
+ align:start position:0%
+in the experiment like I said you you
+ 
+
+ align:start position:0%
+in the experiment like I said you you
+can't scatter electrons you have to be
+
+ align:start position:0%
+can't scatter electrons you have to be
+ 
+
+ align:start position:0%
+can't scatter electrons you have to be
+very careful right so
+
+ align:start position:0%
+very careful right so
+ 
+
+ align:start position:0%
+very careful right so
+um and there's another problem okay so
+
+ align:start position:0%
+um and there's another problem okay so
+ 
+
+ align:start position:0%
+um and there's another problem okay so
+of course superl is uh well is just the
+
+ align:start position:0%
+of course superl is uh well is just the
+ 
+
+ align:start position:0%
+of course superl is uh well is just the
+film that's conducting electron
+
+ align:start position:0%
+film that's conducting electron
+ 
+
+ align:start position:0%
+film that's conducting electron
+and uh the problem is you have to
+
+ align:start position:0%
+and uh the problem is you have to
+ 
+
+ align:start position:0%
+and uh the problem is you have to
+sandwich this right or you can use air
+
+ align:start position:0%
+sandwich this right or you can use air
+ 
+
+ align:start position:0%
+sandwich this right or you can use air
+or vacuum or Quon wire in vacuum then
+
+ align:start position:0%
+or vacuum or Quon wire in vacuum then
+ 
+
+ align:start position:0%
+or vacuum or Quon wire in vacuum then
+there's no
+
+ align:start position:0%
+there's no
+ 
+
+ align:start position:0%
+there's no
+leakage but see normally when you use
+
+ align:start position:0%
+leakage but see normally when you use
+ 
+
+ align:start position:0%
+leakage but see normally when you use
+another materal to create a barrier to
+
+ align:start position:0%
+another materal to create a barrier to
+ 
+
+ align:start position:0%
+another materal to create a barrier to
+confine electron in the film then you
+
+ align:start position:0%
+confine electron in the film then you
+ 
+
+ align:start position:0%
+confine electron in the film then you
+got a colons in this
+
+ align:start position:0%
+got a colons in this
+ 
+
+ align:start position:0%
+got a colons in this
+barrier forance in this varus will kill
+
+ align:start position:0%
+barrier forance in this varus will kill
+ 
+
+ align:start position:0%
+barrier forance in this varus will kill
+your conduction right so kill your
+
+ align:start position:0%
+your conduction right so kill your
+ 
+
+ align:start position:0%
+your conduction right so kill your
+create a more Lage
+
+ align:start position:0%
+create a more Lage
+ 
+
+ align:start position:0%
+create a more Lage
+there and there are solutions on this
+
+ align:start position:0%
+there and there are solutions on this
+ 
+
+ align:start position:0%
+there and there are solutions on this
+theoretically I worked with M uh on this
+
+ align:start position:0%
+theoretically I worked with M uh on this
+ 
+
+ align:start position:0%
+theoretically I worked with M uh on this
+before uh let's say uh just the CIA one
+
+ align:start position:0%
+before uh let's say uh just the CIA one
+ 
+
+ align:start position:0%
+before uh let's say uh just the CIA one
+has to pay attention for example uh
+
+ align:start position:0%
+has to pay attention for example uh
+ 
+
+ align:start position:0%
+has to pay attention for example uh
+there are also also study by Jer and
+
+ align:start position:0%
+there are also also study by Jer and
+ 
+
+ align:start position:0%
+there are also also study by Jer and
+others say if you reduce the sickness
+
+ align:start position:0%
+others say if you reduce the sickness
+ 
+
+ align:start position:0%
+others say if you reduce the sickness
+okay you want to reduce barrier hequ you
+
+ align:start position:0%
+okay you want to reduce barrier hequ you
+ 
+
+ align:start position:0%
+okay you want to reduce barrier hequ you
+reduce sickness and then the different
+
+ align:start position:0%
+reduce sickness and then the different
+ 
+
+ align:start position:0%
+reduce sickness and then the different
+then you have another qu this two start
+
+ align:start position:0%
+then you have another qu this two start
+ 
+
+ align:start position:0%
+then you have another qu this two start
+talking to each other colony and that
+
+ align:start position:0%
+talking to each other colony and that
+ 
+
+ align:start position:0%
+talking to each other colony and that
+Colony actually is not good that can uh
+
+ align:start position:0%
+Colony actually is not good that can uh
+ 
+
+ align:start position:0%
+Colony actually is not good that can uh
+the uh the den stat become less sharper
+
+ align:start position:0%
+the uh the den stat become less sharper
+ 
+
+ align:start position:0%
+the uh the den stat become less sharper
+than uh the pure Quant we is there are
+
+ align:start position:0%
+than uh the pure Quant we is there are
+ 
+
+ align:start position:0%
+than uh the pure Quant we is there are
+there are potential Solutions uh I
+
+ align:start position:0%
+there are potential Solutions uh I
+ 
+
+ align:start position:0%
+there are potential Solutions uh I
+encourage you read the literature M and
+
+ align:start position:0%
+encourage you read the literature M and
+ 
+
+ align:start position:0%
+encourage you read the literature M and
+work on
+
+ align:start position:0%
+work on
+ 
+
+ align:start position:0%
+work on
+this but turns
+
+ align:start position:0%
+this but turns
+ 
+
+ align:start position:0%
+this but turns
+out this general idea of sh feature in
+
+ align:start position:0%
+out this general idea of sh feature in
+ 
+
+ align:start position:0%
+out this general idea of sh feature in
+den of
+
+ align:start position:0%
+den of
+ 
+
+ align:start position:0%
+den of
+States is Universal not only in th films
+
+ align:start position:0%
+States is Universal not only in th films
+ 
+
+ align:start position:0%
+States is Universal not only in th films
+but in both
+
+ align:start position:0%
+but in both
+ 
+
+ align:start position:0%
+but in both
+materials and uh there was a one paper
+
+ align:start position:0%
+materials and uh there was a one paper
+ 
+
+ align:start position:0%
+materials and uh there was a one paper
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+Jeran and uh he wrote a paper around 97
+
+ align:start position:0%
+Jeran and uh he wrote a paper around 97
+ 
+
+ align:start position:0%
+Jeran and uh he wrote a paper around 97
+and he did he is he's a very good
+
+ align:start position:0%
+and he did he is he's a very good
+ 
+
+ align:start position:0%
+and he did he is he's a very good
+theoretician he just took a simple math
+
+ align:start position:0%
+theoretician he just took a simple math
+ 
+
+ align:start position:0%
+theoretician he just took a simple math
+problem he said I'm going to optimize
+
+ align:start position:0%
+problem he said I'm going to optimize
+ 
+
+ align:start position:0%
+problem he said I'm going to optimize
+thiss of States just write the
+
+ align:start position:0%
+thiss of States just write the
+ 
+
+ align:start position:0%
+thiss of States just write the
+expression I wrote before treat as a
+
+ align:start position:0%
+expression I wrote before treat as a
+ 
+
+ align:start position:0%
+expression I wrote before treat as a
+functional that D this sub stat as a
+
+ align:start position:0%
+functional that D this sub stat as a
+ 
+
+ align:start position:0%
+functional that D this sub stat as a
+functional mathematics what's the
+
+ align:start position:0%
+functional mathematics what's the
+ 
+
+ align:start position:0%
+functional mathematics what's the
+functional that will give you maximum s
+
+ align:start position:0%
+functional that will give you maximum s
+ 
+
+ align:start position:0%
+functional that will give you maximum s
+s Sigma or give you maximum ZT and at
+
+ align:start position:0%
+s Sigma or give you maximum ZT and at
+ 
+
+ align:start position:0%
+s Sigma or give you maximum ZT and at
+the end he conclud this Delta
+
+ align:start position:0%
+the end he conclud this Delta
+ 
+
+ align:start position:0%
+the end he conclud this Delta
+function okay so Delta function is the
+
+ align:start position:0%
+function okay so Delta function is the
+ 
+
+ align:start position:0%
+function okay so Delta function is the
+best and if you go back to what I show
+
+ align:start position:0%
+best and if you go back to what I show
+ 
+
+ align:start position:0%
+best and if you go back to what I show
+here quum dot is best except the
+
+ align:start position:0%
+here quum dot is best except the
+ 
+
+ align:start position:0%
+here quum dot is best except the
+electron what how you going move quom
+
+ align:start position:0%
+electron what how you going move quom
+ 
+
+ align:start position:0%
+electron what how you going move quom
+dots electron going to except the delta
+
+ align:start position:0%
+dots electron going to except the delta
+ 
+
+ align:start position:0%
+dots electron going to except the delta
+T over quom dots right
+
+ align:start position:0%
+T over quom dots right
+ 
+
+ align:start position:0%
+T over quom dots right
+so wire is is is also good so this is
+
+ align:start position:0%
+so wire is is is also good so this is
+ 
+
+ align:start position:0%
+so wire is is is also good so this is
+General principle another interesting
+
+ align:start position:0%
+General principle another interesting
+ 
+
+ align:start position:0%
+General principle another interesting
+comment I want to make is you go to
+
+ align:start position:0%
+comment I want to make is you go to
+ 
+
+ align:start position:0%
+comment I want to make is you go to
+check the Lawrence Lum uh and that's
+
+ align:start position:0%
+check the Lawrence Lum uh and that's
+ 
+
+ align:start position:0%
+check the Lawrence Lum uh and that's
+what I suspected the Lawrence number in
+
+ align:start position:0%
+what I suspected the Lawrence number in
+ 
+
+ align:start position:0%
+what I suspected the Lawrence number in
+Quantum do can be
+
+ align:start position:0%
+Quantum do can be
+ 
+
+ align:start position:0%
+Quantum do can be
+zero very strange nobody demonstrated
+
+ align:start position:0%
+zero very strange nobody demonstrated
+ 
+
+ align:start position:0%
+zero very strange nobody demonstrated
+that okay it very will be interesting
+
+ align:start position:0%
+that okay it very will be interesting
+ 
+
+ align:start position:0%
+that okay it very will be interesting
+experiment electric
+
+ align:start position:0%
+experiment electric
+ 
+
+ align:start position:0%
+experiment electric
+conductivity is not zero but the
+
+ align:start position:0%
+conductivity is not zero but the
+ 
+
+ align:start position:0%
+conductivity is not zero but the
+electronic thermal conductivity is zero
+
+ align:start position:0%
+electronic thermal conductivity is zero
+ 
+
+ align:start position:0%
+electronic thermal conductivity is zero
+very easy to
+
+ align:start position:0%
+very easy to
+ 
+
+ align:start position:0%
+very easy to
+check okay let me go here so so this is
+
+ align:start position:0%
+check okay let me go here so so this is
+ 
+
+ align:start position:0%
+check okay let me go here so so this is
+really recent
+
+ align:start position:0%
+really recent
+ 
+
+ align:start position:0%
+really recent
+Herman and he said weing we talk a lot
+
+ align:start position:0%
+Herman and he said weing we talk a lot
+ 
+
+ align:start position:0%
+Herman and he said weing we talk a lot
+but the very smart guy and he
+
+ align:start position:0%
+but the very smart guy and he
+ 
+
+ align:start position:0%
+but the very smart guy and he
+say uh he worked on Nano Nano work with
+
+ align:start position:0%
+say uh he worked on Nano Nano work with
+ 
+
+ align:start position:0%
+say uh he worked on Nano Nano work with
+million say I'm going to turn to B mat
+
+ align:start position:0%
+million say I'm going to turn to B mat
+ 
+
+ align:start position:0%
+million say I'm going to turn to B mat
+so he when they uh he he read Russian
+
+ align:start position:0%
+so he when they uh he he read Russian
+ 
+
+ align:start position:0%
+so he when they uh he he read Russian
+literature and this all actually in
+
+ align:start position:0%
+literature and this all actually in
+ 
+
+ align:start position:0%
+literature and this all actually in
+Russian literature it turns out there
+
+ align:start position:0%
+Russian literature it turns out there
+ 
+
+ align:start position:0%
+Russian literature it turns out there
+are some
+
+ align:start position:0%
+are some
+ 
+
+ align:start position:0%
+are some
+doping when we think about doping we
+
+ align:start position:0%
+doping when we think about doping we
+ 
+
+ align:start position:0%
+doping when we think about doping we
+think about doping the energy level is
+
+ align:start position:0%
+think about doping the energy level is
+ 
+
+ align:start position:0%
+think about doping the energy level is
+inside the b in the uh Bank Gap but
+
+ align:start position:0%
+inside the b in the uh Bank Gap but
+ 
+
+ align:start position:0%
+inside the b in the uh Bank Gap but
+there are some other atoms you dop it
+
+ align:start position:0%
+there are some other atoms you dop it
+ 
+
+ align:start position:0%
+there are some other atoms you dop it
+the dopen level is within the conduction
+
+ align:start position:0%
+the dopen level is within the conduction
+ 
+
+ align:start position:0%
+the dopen level is within the conduction
+of Valance B and in this case is in the
+
+ align:start position:0%
+of Valance B and in this case is in the
+ 
+
+ align:start position:0%
+of Valance B and in this case is in the
+viance band and this viance band they
+
+ align:start position:0%
+viance band and this viance band they
+ 
+
+ align:start position:0%
+viance band and this viance band they
+don't the form additional energy state
+
+ align:start position:0%
+don't the form additional energy state
+ 
+
+ align:start position:0%
+don't the form additional energy state
+that create a Shar feature in the
+
+ align:start position:0%
+that create a Shar feature in the
+ 
+
+ align:start position:0%
+that create a Shar feature in the
+density of
+
+ align:start position:0%
+density of
+ 
+
+ align:start position:0%
+density of
+state and this Shar feature led to a
+
+ align:start position:0%
+state and this Shar feature led to a
+ 
+
+ align:start position:0%
+state and this Shar feature led to a
+very good C coefficient and a very high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C the question is you whether you can
+
+ align:start position:0%
+C the question is you whether you can
+ 
+
+ align:start position:0%
+C the question is you whether you can
+replicate in different
+
+ align:start position:0%
+replicate in different
+ 
+
+ align:start position:0%
+replicate in different
+materials without nobody wants to touch
+
+ align:start position:0%
+materials without nobody wants to touch
+ 
+
+ align:start position:0%
+materials without nobody wants to touch
+it okay a very poison uh uh because say
+
+ align:start position:0%
+it okay a very poison uh uh because say
+ 
+
+ align:start position:0%
+it okay a very poison uh uh because say
+it's not that terrible I have a friend
+
+ align:start position:0%
+it's not that terrible I have a friend
+ 
+
+ align:start position:0%
+it's not that terrible I have a friend
+that he said I work with son for more
+
+ align:start position:0%
+that he said I work with son for more
+ 
+
+ align:start position:0%
+that he said I work with son for more
+than 15 years Super conductor and uh
+
+ align:start position:0%
+than 15 years Super conductor and uh
+ 
+
+ align:start position:0%
+than 15 years Super conductor and uh
+nothing happened but but uh of
+
+ align:start position:0%
+nothing happened but but uh of
+ 
+
+ align:start position:0%
+nothing happened but but uh of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+careful now this is another
+
+ align:start position:0%
+careful now this is another
+ 
+
+ align:start position:0%
+careful now this is another
+idea uh I think again come back to uh
+
+ align:start position:0%
+idea uh I think again come back to uh
+ 
+
+ align:start position:0%
+idea uh I think again come back to uh
+the uh you can interpret the same as
+
+ align:start position:0%
+the uh you can interpret the same as
+ 
+
+ align:start position:0%
+the uh you can interpret the same as
+dens of State this is a Okay C efficient
+
+ align:start position:0%
+dens of State this is a Okay C efficient
+ 
+
+ align:start position:0%
+dens of State this is a Okay C efficient
+if your C potential is here
+
+ align:start position:0%
+if your C potential is here
+ 
+
+ align:start position:0%
+if your C potential is here
+this is negative this is positive so
+
+ align:start position:0%
+this is negative this is positive so
+ 
+
+ align:start position:0%
+this is negative this is positive so
+they cancel each other right of course
+
+ align:start position:0%
+they cancel each other right of course
+ 
+
+ align:start position:0%
+they cancel each other right of course
+this is larger so you still have the
+
+ align:start position:0%
+this is larger so you still have the
+ 
+
+ align:start position:0%
+this is larger so you still have the
+cancellation small but if you put a
+
+ align:start position:0%
+cancellation small but if you put a
+ 
+
+ align:start position:0%
+cancellation small but if you put a
+potential so you you have a particle or
+
+ align:start position:0%
+potential so you you have a particle or
+ 
+
+ align:start position:0%
+potential so you you have a particle or
+you have an interface that just happen
+
+ align:start position:0%
+you have an interface that just happen
+ 
+
+ align:start position:0%
+you have an interface that just happen
+to have this potential height then those
+
+ align:start position:0%
+to have this potential height then those
+ 
+
+ align:start position:0%
+to have this potential height then those
+electrons are scatter so that's called
+
+ align:start position:0%
+electrons are scatter so that's called
+ 
+
+ align:start position:0%
+electrons are scatter so that's called
+the energy fi term or emission I'll talk
+
+ align:start position:0%
+the energy fi term or emission I'll talk
+ 
+
+ align:start position:0%
+the energy fi term or emission I'll talk
+about th mission in the last lecture we
+
+ align:start position:0%
+about th mission in the last lecture we
+ 
+
+ align:start position:0%
+about th mission in the last lecture we
+talk about theran engines that's a
+
+ align:start position:0%
+talk about theran engines that's a
+ 
+
+ align:start position:0%
+talk about theran engines that's a
+different way but this is doing in solid
+
+ align:start position:0%
+different way but this is doing in solid
+ 
+
+ align:start position:0%
+different way but this is doing in solid
+so you scatter this low energy electron
+
+ align:start position:0%
+so you scatter this low energy electron
+ 
+
+ align:start position:0%
+so you scatter this low energy electron
+and then you only have high energy
+
+ align:start position:0%
+and then you only have high energy
+ 
+
+ align:start position:0%
+and then you only have high energy
+electron and if I dra the den of State
+
+ align:start position:0%
+electron and if I dra the den of State
+ 
+
+ align:start position:0%
+electron and if I dra the den of State
+picture is although there are electron
+
+ align:start position:0%
+picture is although there are electron
+ 
+
+ align:start position:0%
+picture is although there are electron
+in this region but I scatter them they
+
+ align:start position:0%
+in this region but I scatter them they
+ 
+
+ align:start position:0%
+in this region but I scatter them they
+do not move so now the in terms of this
+
+ align:start position:0%
+do not move so now the in terms of this
+ 
+
+ align:start position:0%
+do not move so now the in terms of this
+St what's really moving is still have
+
+ align:start position:0%
+St what's really moving is still have
+ 
+
+ align:start position:0%
+St what's really moving is still have
+per Char picture so that's my
+
+ align:start position:0%
+per Char picture so that's my
+ 
+
+ align:start position:0%
+per Char picture so that's my
+interpretation to this picture uh this
+
+ align:start position:0%
+interpretation to this picture uh this
+ 
+
+ align:start position:0%
+interpretation to this picture uh this
+this different idea can think about the
+
+ align:start position:0%
+this different idea can think about the
+ 
+
+ align:start position:0%
+this different idea can think about the
+state features for electron but really
+
+ align:start position:0%
+state features for electron but really
+ 
+
+ align:start position:0%
+state features for electron but really
+the one that has went so far in the only
+
+ align:start position:0%
+the one that has went so far in the only
+ 
+
+ align:start position:0%
+the one that has went so far in the only
+successful example I
+
+ align:start position:0%
+successful example I
+ 
+
+ align:start position:0%
+successful example I
+know is this one okay truly uh work in
+
+ align:start position:0%
+know is this one okay truly uh work in
+ 
+
+ align:start position:0%
+know is this one okay truly uh work in
+materials so most other approach that's
+
+ align:start position:0%
+materials so most other approach that's
+ 
+
+ align:start position:0%
+materials so most other approach that's
+successful is in
+
+ align:start position:0%
+successful is in
+ 
+
+ align:start position:0%
+successful is in
+PH so with that I brought you from this
+
+ align:start position:0%
+PH so with that I brought you from this
+ 
+
+ align:start position:0%
+PH so with that I brought you from this
+very simple since I don't know you
+
+ align:start position:0%
+very simple since I don't know you
+ 
+
+ align:start position:0%
+very simple since I don't know you
+figure out okay
\ No newline at end of file
diff --git a/tnmQ8gytqyc.txt b/tnmQ8gytqyc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..393dacc53e7296f974b558c4bc8ffdddd72e1a3a
--- /dev/null
+++ b/tnmQ8gytqyc.txt
@@ -0,0 +1,12380 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
+ align:start position:0%
+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
+
+ align:start position:0%
+will help mit opencourseware continue to
+ 
+
+ align:start position:0%
+will help mit opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things here
+
+ align:start position:0%
+things here
+ 
+
+ align:start position:0%
+things here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+x and theta and how they can be
+
+ align:start position:0%
+x and theta and how they can be
+ 
+
+ align:start position:0%
+x and theta and how they can be
+represented
+
+ align:start position:0%
+represented
+ 
+
+ align:start position:0%
+represented
+uh but you can create some really
+
+ align:start position:0%
+uh but you can create some really
+ 
+
+ align:start position:0%
+uh but you can create some really
+beautiful images out of that you can
+
+ align:start position:0%
+beautiful images out of that you can
+ 
+
+ align:start position:0%
+beautiful images out of that you can
+even create
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can create some really interesting
+
+ align:start position:0%
+you can create some really interesting
+ 
+
+ align:start position:0%
+you can create some really interesting
+pictures like this
+
+ align:start position:0%
+pictures like this
+ 
+
+ align:start position:0%
+pictures like this
+so if i
+
+ align:start position:0%
+so if i
+ 
+
+ align:start position:0%
+so if i
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this picture
+
+ align:start position:0%
+this picture
+ 
+
+ align:start position:0%
+this picture
+is made
+
+ align:start position:0%
+is made
+ 
+
+ align:start position:0%
+is made
+in that x theta space the coordinates
+
+ align:start position:0%
+in that x theta space the coordinates
+ 
+
+ align:start position:0%
+in that x theta space the coordinates
+are a little bit
+
+ align:start position:0%
+are a little bit
+ 
+
+ align:start position:0%
+are a little bit
+uh changed here this is a this is a
+
+ align:start position:0%
+uh changed here this is a this is a
+ 
+
+ align:start position:0%
+uh changed here this is a this is a
+slide from
+
+ align:start position:0%
+slide from
+ 
+
+ align:start position:0%
+slide from
+uh samus enough
+
+ align:start position:0%
+uh samus enough
+ 
+
+ align:start position:0%
+uh samus enough
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's a robot that
+
+ align:start position:0%
+there's a robot that
+ 
+
+ align:start position:0%
+there's a robot that
+andrew adams built at stanford just
+
+ align:start position:0%
+andrew adams built at stanford just
+ 
+
+ align:start position:0%
+andrew adams built at stanford just
+using legos and you can do this for your
+
+ align:start position:0%
+using legos and you can do this for your
+ 
+
+ align:start position:0%
+using legos and you can do this for your
+assignment as well
+
+ align:start position:0%
+assignment as well
+ 
+
+ align:start position:0%
+assignment as well
+you can build a lego based
+
+ align:start position:0%
+you can build a lego based
+ 
+
+ align:start position:0%
+you can build a lego based
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+gang tree
+
+ align:start position:0%
+gang tree
+ 
+
+ align:start position:0%
+gang tree
+that can
+
+ align:start position:0%
+that can
+ 
+
+ align:start position:0%
+that can
+you know shift and take these pictures
+
+ align:start position:0%
+you know shift and take these pictures
+ 
+
+ align:start position:0%
+you know shift and take these pictures
+for your assignment you're just doing
+
+ align:start position:0%
+for your assignment you're just doing
+ 
+
+ align:start position:0%
+for your assignment you're just doing
+one day translation
+
+ align:start position:0%
+one day translation
+ 
+
+ align:start position:0%
+one day translation
+but you could even do 2d translation
+
+ align:start position:0%
+but you could even do 2d translation
+ 
+
+ align:start position:0%
+but you could even do 2d translation
+and then imagine if i put a camera here
+
+ align:start position:0%
+and then imagine if i put a camera here
+ 
+
+ align:start position:0%
+and then imagine if i put a camera here
+and i simply translate it
+
+ align:start position:0%
+and i simply translate it
+ 
+
+ align:start position:0%
+and i simply translate it
+and now we are in flatline when
+
+ align:start position:0%
+and now we are in flatline when
+ 
+
+ align:start position:0%
+and now we are in flatline when
+the camera is here i will take a picture
+
+ align:start position:0%
+the camera is here i will take a picture
+ 
+
+ align:start position:0%
+the camera is here i will take a picture
+and put it over here this launcher
+
+ align:start position:0%
+and put it over here this launcher
+ 
+
+ align:start position:0%
+and put it over here this launcher
+okay then i'll move the camera and i'll
+
+ align:start position:0%
+okay then i'll move the camera and i'll
+ 
+
+ align:start position:0%
+okay then i'll move the camera and i'll
+stack those images
+
+ align:start position:0%
+stack those images
+ 
+
+ align:start position:0%
+stack those images
+so for example when i am
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah if you look at this particular
+
+ align:start position:0%
+so yeah if you look at this particular
+ 
+
+ align:start position:0%
+so yeah if you look at this particular
+green object
+
+ align:start position:0%
+green object
+ 
+
+ align:start position:0%
+green object
+over here you'll see that it creates
+
+ align:start position:0%
+over here you'll see that it creates
+ 
+
+ align:start position:0%
+over here you'll see that it creates
+actually a line
+
+ align:start position:0%
+actually a line
+ 
+
+ align:start position:0%
+actually a line
+because when i'm gonna start
+
+ align:start position:0%
+because when i'm gonna start
+ 
+
+ align:start position:0%
+because when i'm gonna start
+transferring it it creates that line on
+
+ align:start position:0%
+transferring it it creates that line on
+ 
+
+ align:start position:0%
+transferring it it creates that line on
+the other hand this particular white
+
+ align:start position:0%
+the other hand this particular white
+ 
+
+ align:start position:0%
+the other hand this particular white
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+ends up mapping with this really strange
+
+ align:start position:0%
+ends up mapping with this really strange
+ 
+
+ align:start position:0%
+ends up mapping with this really strange
+object here
+
+ align:start position:0%
+object here
+ 
+
+ align:start position:0%
+object here
+so this is the visualization of the same
+
+ align:start position:0%
+so this is the visualization of the same
+ 
+
+ align:start position:0%
+so this is the visualization of the same
+space that you saw earlier which looks
+
+ align:start position:0%
+space that you saw earlier which looks
+ 
+
+ align:start position:0%
+space that you saw earlier which looks
+you know maybe simple and very boring
+
+ align:start position:0%
+you know maybe simple and very boring
+ 
+
+ align:start position:0%
+you know maybe simple and very boring
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so once you start putting interesting
+
+ align:start position:0%
+so once you start putting interesting
+ 
+
+ align:start position:0%
+so once you start putting interesting
+objects
+
+ align:start position:0%
+objects
+ 
+
+ align:start position:0%
+objects
+that's how your like fit starts looking
+
+ align:start position:0%
+that's how your like fit starts looking
+ 
+
+ align:start position:0%
+that's how your like fit starts looking
+and this is basically a light fill here
+
+ align:start position:0%
+and this is basically a light fill here
+ 
+
+ align:start position:0%
+and this is basically a light fill here
+t and theta but it's same as x and theta
+
+ align:start position:0%
+t and theta but it's same as x and theta
+ 
+
+ align:start position:0%
+t and theta but it's same as x and theta
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the the appearance of this room
+
+ align:start position:0%
+the the appearance of this room
+ 
+
+ align:start position:0%
+the the appearance of this room
+through this window
+
+ align:start position:0%
+through this window
+ 
+
+ align:start position:0%
+through this window
+all you have to do is look at this world
+
+ align:start position:0%
+all you have to do is look at this world
+ 
+
+ align:start position:0%
+all you have to do is look at this world
+through this window you cannot go inside
+
+ align:start position:0%
+through this window you cannot go inside
+ 
+
+ align:start position:0%
+through this window you cannot go inside
+to list it from outside
+
+ align:start position:0%
+to list it from outside
+ 
+
+ align:start position:0%
+to list it from outside
+everything that can be captured about
+
+ align:start position:0%
+everything that can be captured about
+ 
+
+ align:start position:0%
+everything that can be captured about
+the scene through this window is
+
+ align:start position:0%
+the scene through this window is
+ 
+
+ align:start position:0%
+the scene through this window is
+represented
+
+ align:start position:0%
+represented
+ 
+
+ align:start position:0%
+represented
+in this 2d electrode
+
+ align:start position:0%
+in this 2d electrode
+ 
+
+ align:start position:0%
+in this 2d electrode
+so now if i want to create any
+
+ align:start position:0%
+so now if i want to create any
+ 
+
+ align:start position:0%
+so now if i want to create any
+refocusing effects any depth of field
+
+ align:start position:0%
+refocusing effects any depth of field
+ 
+
+ align:start position:0%
+refocusing effects any depth of field
+effects all the information is available
+
+ align:start position:0%
+effects all the information is available
+ 
+
+ align:start position:0%
+effects all the information is available
+here and if i just
+
+ align:start position:0%
+here and if i just
+ 
+
+ align:start position:0%
+here and if i just
+reuse the pixels from here and take
+
+ align:start position:0%
+reuse the pixels from here and take
+ 
+
+ align:start position:0%
+reuse the pixels from here and take
+projections and so on i can create the
+
+ align:start position:0%
+projections and so on i can create the
+ 
+
+ align:start position:0%
+projections and so on i can create the
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're going to twist your twist your
+
+ align:start position:0%
+if you're going to twist your twist your
+ 
+
+ align:start position:0%
+if you're going to twist your twist your
+mind around it and then it starts making
+
+ align:start position:0%
+mind around it and then it starts making
+ 
+
+ align:start position:0%
+mind around it and then it starts making
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for those of you who have a computer
+
+ align:start position:0%
+for those of you who have a computer
+ 
+
+ align:start position:0%
+for those of you who have a computer
+vision background
+
+ align:start position:0%
+vision background
+ 
+
+ align:start position:0%
+vision background
+this is also known as ap polar plane
+
+ align:start position:0%
+this is also known as ap polar plane
+ 
+
+ align:start position:0%
+this is also known as ap polar plane
+images or epi
+
+ align:start position:0%
+images or epi
+ 
+
+ align:start position:0%
+images or epi
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's go back to some of this concept
+
+ align:start position:0%
+so let's go back to some of this concept
+ 
+
+ align:start position:0%
+so let's go back to some of this concept
+we were talking about earlier
+
+ align:start position:0%
+we were talking about earlier
+ 
+
+ align:start position:0%
+we were talking about earlier
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+you know you're going to represent
+
+ align:start position:0%
+you know you're going to represent
+ 
+
+ align:start position:0%
+you know you're going to represent
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+part of the lens as a different camera
+
+ align:start position:0%
+part of the lens as a different camera
+ 
+
+ align:start position:0%
+part of the lens as a different camera
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+five subsections five games
+
+ align:start position:0%
+five subsections five games
+ 
+
+ align:start position:0%
+five subsections five games
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+we know that
+
+ align:start position:0%
+we know that
+ 
+
+ align:start position:0%
+we know that
+we found the focus at infinity
+
+ align:start position:0%
+we found the focus at infinity
+ 
+
+ align:start position:0%
+we found the focus at infinity
+i can just take the sum of all these
+
+ align:start position:0%
+i can just take the sum of all these
+ 
+
+ align:start position:0%
+i can just take the sum of all these
+images and i'm done
+
+ align:start position:0%
+images and i'm done
+ 
+
+ align:start position:0%
+images and i'm done
+right or average of these images but for
+
+ align:start position:0%
+right or average of these images but for
+ 
+
+ align:start position:0%
+right or average of these images but for
+focus closer
+
+ align:start position:0%
+focus closer
+ 
+
+ align:start position:0%
+focus closer
+then i cannot just take the average i
+
+ align:start position:0%
+then i cannot just take the average i
+ 
+
+ align:start position:0%
+then i cannot just take the average i
+would shift
+
+ align:start position:0%
+would shift
+ 
+
+ align:start position:0%
+would shift
+and what this prism is doing
+
+ align:start position:0%
+and what this prism is doing
+ 
+
+ align:start position:0%
+and what this prism is doing
+in the real world is doing the shifting
+
+ align:start position:0%
+in the real world is doing the shifting
+ 
+
+ align:start position:0%
+in the real world is doing the shifting
+for you
+
+ align:start position:0%
+for you
+ 
+
+ align:start position:0%
+for you
+okay so let's go back to this example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this notion of shifting and adding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i'm going to compare this with
+
+ align:start position:0%
+i'm going to compare this with
+ 
+
+ align:start position:0%
+i'm going to compare this with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+five camera situation see if i have a
+
+ align:start position:0%
+five camera situation see if i have a
+ 
+
+ align:start position:0%
+five camera situation see if i have a
+point here
+
+ align:start position:0%
+point here
+ 
+
+ align:start position:0%
+point here
+from the first camera the image goes
+
+ align:start position:0%
+from the first camera the image goes
+ 
+
+ align:start position:0%
+from the first camera the image goes
+here the second one it goes there third
+
+ align:start position:0%
+here the second one it goes there third
+ 
+
+ align:start position:0%
+here the second one it goes there third
+one it goes there both front goes here
+
+ align:start position:0%
+one it goes there both front goes here
+ 
+
+ align:start position:0%
+one it goes there both front goes here
+this one is here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's my pinball camera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so as you can see if the point is
+
+ align:start position:0%
+okay so as you can see if the point is
+ 
+
+ align:start position:0%
+okay so as you can see if the point is
+close by the coordinates here are not
+
+ align:start position:0%
+close by the coordinates here are not
+ 
+
+ align:start position:0%
+close by the coordinates here are not
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+here it's near the zero and here's a
+
+ align:start position:0%
+here it's near the zero and here's a
+ 
+
+ align:start position:0%
+here it's near the zero and here's a
+little bit further up from the center
+
+ align:start position:0%
+little bit further up from the center
+ 
+
+ align:start position:0%
+little bit further up from the center
+and here is
+
+ align:start position:0%
+and here is
+ 
+
+ align:start position:0%
+and here is
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+so when i have to bring these five
+
+ align:start position:0%
+so when i have to bring these five
+ 
+
+ align:start position:0%
+so when i have to bring these five
+images i need to shift these images so
+
+ align:start position:0%
+images i need to shift these images so
+ 
+
+ align:start position:0%
+images i need to shift these images so
+that these are all guys overlap on top
+
+ align:start position:0%
+that these are all guys overlap on top
+ 
+
+ align:start position:0%
+that these are all guys overlap on top
+of each other so that this point will be
+
+ align:start position:0%
+of each other so that this point will be
+ 
+
+ align:start position:0%
+of each other so that this point will be
+sharp focus
+
+ align:start position:0%
+sharp focus
+ 
+
+ align:start position:0%
+sharp focus
+the lens does that for you automatically
+
+ align:start position:0%
+the lens does that for you automatically
+ 
+
+ align:start position:0%
+the lens does that for you automatically
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+because of the prism if i put a painting
+
+ align:start position:0%
+because of the prism if i put a painting
+ 
+
+ align:start position:0%
+because of the prism if i put a painting
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and there is just a
+
+ align:start position:0%
+and there is just a
+ 
+
+ align:start position:0%
+and there is just a
+pinhole here
+
+ align:start position:0%
+pinhole here
+ 
+
+ align:start position:0%
+pinhole here
+this is abc
+
+ align:start position:0%
+this is abc
+ 
+
+ align:start position:0%
+this is abc
+right this will come back as abc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but this one here
+
+ align:start position:0%
+okay but this one here
+ 
+
+ align:start position:0%
+okay but this one here
+would have created an image that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but because of the prism
+
+ align:start position:0%
+but because of the prism
+ 
+
+ align:start position:0%
+but because of the prism
+it rotates the image and then this thing
+
+ align:start position:0%
+it rotates the image and then this thing
+ 
+
+ align:start position:0%
+it rotates the image and then this thing
+shifts down
+
+ align:start position:0%
+shifts down
+ 
+
+ align:start position:0%
+shifts down
+so they are on top of each other
+
+ align:start position:0%
+so they are on top of each other
+ 
+
+ align:start position:0%
+so they are on top of each other
+and because of this part of the prism it
+
+ align:start position:0%
+and because of this part of the prism it
+ 
+
+ align:start position:0%
+and because of this part of the prism it
+shifts
+
+ align:start position:0%
+shifts
+ 
+
+ align:start position:0%
+shifts
+it would have the image would have been
+
+ align:start position:0%
+it would have the image would have been
+ 
+
+ align:start position:0%
+it would have the image would have been
+created here the abc
+
+ align:start position:0%
+created here the abc
+ 
+
+ align:start position:0%
+created here the abc
+but shifts just a little bit
+
+ align:start position:0%
+but shifts just a little bit
+ 
+
+ align:start position:0%
+but shifts just a little bit
+and so on and for the other one the
+
+ align:start position:0%
+and so on and for the other one the
+ 
+
+ align:start position:0%
+and so on and for the other one the
+image would have been formed here it
+
+ align:start position:0%
+image would have been formed here it
+ 
+
+ align:start position:0%
+image would have been formed here it
+shifts up so the prism does the job for
+
+ align:start position:0%
+shifts up so the prism does the job for
+ 
+
+ align:start position:0%
+shifts up so the prism does the job for
+you basically of shifting these images
+
+ align:start position:0%
+you basically of shifting these images
+ 
+
+ align:start position:0%
+you basically of shifting these images
+so that's so very simple we are thinking
+
+ align:start position:0%
+so that's so very simple we are thinking
+ 
+
+ align:start position:0%
+so that's so very simple we are thinking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+we can emulate a very large lens by an
+
+ align:start position:0%
+we can emulate a very large lens by an
+ 
+
+ align:start position:0%
+we can emulate a very large lens by an
+array of canvas
+
+ align:start position:0%
+array of canvas
+ 
+
+ align:start position:0%
+array of canvas
+so the top cameras here should shift
+
+ align:start position:0%
+so the top cameras here should shift
+ 
+
+ align:start position:0%
+so the top cameras here should shift
+jump shift down into images and the
+
+ align:start position:0%
+jump shift down into images and the
+ 
+
+ align:start position:0%
+jump shift down into images and the
+bottom cameras should shift up and by
+
+ align:start position:0%
+bottom cameras should shift up and by
+ 
+
+ align:start position:0%
+bottom cameras should shift up and by
+doing that you can focus anyway
+
+ align:start position:0%
+doing that you can focus anyway
+ 
+
+ align:start position:0%
+doing that you can focus anyway
+except that in case of a traditional
+
+ align:start position:0%
+except that in case of a traditional
+ 
+
+ align:start position:0%
+except that in case of a traditional
+lens once the photo is taken you are
+
+ align:start position:0%
+lens once the photo is taken you are
+ 
+
+ align:start position:0%
+lens once the photo is taken you are
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+in case of an area of cameras
+
+ align:start position:0%
+in case of an area of cameras
+ 
+
+ align:start position:0%
+in case of an area of cameras
+you can take those pictures and shift as
+
+ align:start position:0%
+you can take those pictures and shift as
+ 
+
+ align:start position:0%
+you can take those pictures and shift as
+much as you want you want and add them
+
+ align:start position:0%
+much as you want you want and add them
+ 
+
+ align:start position:0%
+much as you want you want and add them
+in interesting
+
+ align:start position:0%
+in interesting
+ 
+
+ align:start position:0%
+in interesting
+and that's why like fits are so powerful
+
+ align:start position:0%
+and that's why like fits are so powerful
+ 
+
+ align:start position:0%
+and that's why like fits are so powerful
+so instead of using now an area of
+
+ align:start position:0%
+so instead of using now an area of
+ 
+
+ align:start position:0%
+so instead of using now an area of
+cameras
+
+ align:start position:0%
+cameras
+ 
+
+ align:start position:0%
+cameras
+we're going to build landslide arrays or
+
+ align:start position:0%
+we're going to build landslide arrays or
+ 
+
+ align:start position:0%
+we're going to build landslide arrays or
+some other
+
+ align:start position:0%
+some other
+ 
+
+ align:start position:0%
+some other
+fantasy optics so that i can directly
+
+ align:start position:0%
+fantasy optics so that i can directly
+ 
+
+ align:start position:0%
+fantasy optics so that i can directly
+capture these five images
+
+ align:start position:0%
+capture these five images
+ 
+
+ align:start position:0%
+capture these five images
+in a single function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there is three ways
+
+ align:start position:0%
+okay there is three ways
+ 
+
+ align:start position:0%
+okay there is three ways
+of creating
+
+ align:start position:0%
+of creating
+ 
+
+ align:start position:0%
+of creating
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you think about the stanford camera
+
+ align:start position:0%
+when you think about the stanford camera
+ 
+
+ align:start position:0%
+when you think about the stanford camera
+you want each of these cameras to have
+
+ align:start position:0%
+you want each of these cameras to have
+ 
+
+ align:start position:0%
+you want each of these cameras to have
+independent depth of it so everything is
+
+ align:start position:0%
+independent depth of it so everything is
+ 
+
+ align:start position:0%
+independent depth of it so everything is
+sharp focus which means it's a pinhole
+
+ align:start position:0%
+sharp focus which means it's a pinhole
+ 
+
+ align:start position:0%
+sharp focus which means it's a pinhole
+camera so conceptually yes it's a
+
+ align:start position:0%
+camera so conceptually yes it's a
+ 
+
+ align:start position:0%
+camera so conceptually yes it's a
+pinhole camera but in real world you
+
+ align:start position:0%
+pinhole camera but in real world you
+ 
+
+ align:start position:0%
+pinhole camera but in real world you
+cannot help in the camera
+
+ align:start position:0%
+cannot help in the camera
+ 
+
+ align:start position:0%
+cannot help in the camera
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+they try to keep that aperture small but
+
+ align:start position:0%
+they try to keep that aperture small but
+ 
+
+ align:start position:0%
+they try to keep that aperture small but
+you know if you use a really cheap
+
+ align:start position:0%
+you know if you use a really cheap
+ 
+
+ align:start position:0%
+you know if you use a really cheap
+camera like a cell phone camera
+
+ align:start position:0%
+camera like a cell phone camera
+ 
+
+ align:start position:0%
+camera like a cell phone camera
+they usually have a pretty large depth
+
+ align:start position:0%
+they usually have a pretty large depth
+ 
+
+ align:start position:0%
+they usually have a pretty large depth
+of field on you so they're as close to
+
+ align:start position:0%
+of field on you so they're as close to
+ 
+
+ align:start position:0%
+of field on you so they're as close to
+pinhole as you can get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so basically three ways of
+
+ align:start position:0%
+okay so basically three ways of
+ 
+
+ align:start position:0%
+okay so basically three ways of
+capturing
+
+ align:start position:0%
+capturing
+ 
+
+ align:start position:0%
+capturing
+light for you
+
+ align:start position:0%
+light for you
+ 
+
+ align:start position:0%
+light for you
+something that exploits shadows and
+
+ align:start position:0%
+something that exploits shadows and
+ 
+
+ align:start position:0%
+something that exploits shadows and
+pinhole array 1908
+
+ align:start position:0%
+pinhole array 1908
+ 
+
+ align:start position:0%
+pinhole array 1908
+something that uses landslide array also
+
+ align:start position:0%
+something that uses landslide array also
+ 
+
+ align:start position:0%
+something that uses landslide array also
+uh early 1900s
+
+ align:start position:0%
+uh early 1900s
+ 
+
+ align:start position:0%
+uh early 1900s
+and so-called heterodyne
+
+ align:start position:0%
+and so-called heterodyne
+ 
+
+ align:start position:0%
+and so-called heterodyne
+after 100 years in my group
+
+ align:start position:0%
+after 100 years in my group
+ 
+
+ align:start position:0%
+after 100 years in my group
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so took 100 years to come up with a
+
+ align:start position:0%
+so took 100 years to come up with a
+ 
+
+ align:start position:0%
+so took 100 years to come up with a
+third solution
+
+ align:start position:0%
+third solution
+ 
+
+ align:start position:0%
+third solution
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+how you can uh you know as i said a sub
+
+ align:start position:0%
+how you can uh you know as i said a sub
+ 
+
+ align:start position:0%
+how you can uh you know as i said a sub
+aperture is basically a pinhole with a
+
+ align:start position:0%
+aperture is basically a pinhole with a
+ 
+
+ align:start position:0%
+aperture is basically a pinhole with a
+prism
+
+ align:start position:0%
+prism
+ 
+
+ align:start position:0%
+prism
+so i can take each of these pinholes
+
+ align:start position:0%
+so i can take each of these pinholes
+ 
+
+ align:start position:0%
+so i can take each of these pinholes
+and just so
+
+ align:start position:0%
+and just so
+ 
+
+ align:start position:0%
+and just so
+you have this you have this and the
+
+ align:start position:0%
+you have this you have this and the
+ 
+
+ align:start position:0%
+you have this you have this and the
+third one would be i can just put a
+
+ align:start position:0%
+third one would be i can just put a
+ 
+
+ align:start position:0%
+third one would be i can just put a
+pinhole
+
+ align:start position:0%
+pinhole
+ 
+
+ align:start position:0%
+pinhole
+and in front of this i can put a prism
+
+ align:start position:0%
+and in front of this i can put a prism
+ 
+
+ align:start position:0%
+and in front of this i can put a prism
+in front of this i'll put a
+
+ align:start position:0%
+in front of this i'll put a
+ 
+
+ align:start position:0%
+in front of this i'll put a
+shower present in front of this piece of
+
+ align:start position:0%
+shower present in front of this piece of
+ 
+
+ align:start position:0%
+shower present in front of this piece of
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so lens is basically area of pimples
+
+ align:start position:0%
+so lens is basically area of pimples
+ 
+
+ align:start position:0%
+so lens is basically area of pimples
+with a set of pistons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as you saw
+
+ align:start position:0%
+and as you saw
+ 
+
+ align:start position:0%
+and as you saw
+if you have two
+
+ align:start position:0%
+if you have two
+ 
+
+ align:start position:0%
+if you have two
+corners of this pinhole the image will
+
+ align:start position:0%
+corners of this pinhole the image will
+ 
+
+ align:start position:0%
+corners of this pinhole the image will
+be formed with large sensor
+
+ align:start position:0%
+be formed with large sensor
+ 
+
+ align:start position:0%
+be formed with large sensor
+but the lens does a smart job of just
+
+ align:start position:0%
+but the lens does a smart job of just
+ 
+
+ align:start position:0%
+but the lens does a smart job of just
+bending like
+
+ align:start position:0%
+bending like
+ 
+
+ align:start position:0%
+bending like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this figure is from uh from from
+
+ align:start position:0%
+okay so this figure is from uh from from
+ 
+
+ align:start position:0%
+okay so this figure is from uh from from
+lipman i believe in 1930 sorry this one
+
+ align:start position:0%
+lipman i believe in 1930 sorry this one
+ 
+
+ align:start position:0%
+lipman i believe in 1930 sorry this one
+is lipman this one is in 1933 and he
+
+ align:start position:0%
+is lipman this one is in 1933 and he
+ 
+
+ align:start position:0%
+is lipman this one is in 1933 and he
+said okay if you really want to capture
+
+ align:start position:0%
+said okay if you really want to capture
+ 
+
+ align:start position:0%
+said okay if you really want to capture
+each of these individually
+
+ align:start position:0%
+each of these individually
+ 
+
+ align:start position:0%
+each of these individually
+you can just put a pin for that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if i put a pinhole area there
+
+ align:start position:0%
+if i put a pinhole area there
+ 
+
+ align:start position:0%
+if i put a pinhole area there
+and and and take a picture so no
+
+ align:start position:0%
+and and and take a picture so no
+ 
+
+ align:start position:0%
+and and and take a picture so no
+legislate array just a pin hole
+
+ align:start position:0%
+legislate array just a pin hole
+ 
+
+ align:start position:0%
+legislate array just a pin hole
+then you end up getting a picture that
+
+ align:start position:0%
+then you end up getting a picture that
+ 
+
+ align:start position:0%
+then you end up getting a picture that
+looks like this
+
+ align:start position:0%
+looks like this
+ 
+
+ align:start position:0%
+looks like this
+and if you zoom in on that
+
+ align:start position:0%
+and if you zoom in on that
+ 
+
+ align:start position:0%
+and if you zoom in on that
+you'll see that under each pinhole it
+
+ align:start position:0%
+you'll see that under each pinhole it
+ 
+
+ align:start position:0%
+you'll see that under each pinhole it
+will create a disc
+
+ align:start position:0%
+will create a disc
+ 
+
+ align:start position:0%
+will create a disc
+so remember we had a lens light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's that's an example of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is our solution number one
+
+ align:start position:0%
+so this is our solution number one
+ 
+
+ align:start position:0%
+so this is our solution number one
+is our solution number two and solution
+
+ align:start position:0%
+is our solution number two and solution
+ 
+
+ align:start position:0%
+is our solution number two and solution
+number three
+
+ align:start position:0%
+number three
+ 
+
+ align:start position:0%
+number three
+will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and it turns out if you think about a
+
+ align:start position:0%
+uh and it turns out if you think about a
+ 
+
+ align:start position:0%
+uh and it turns out if you think about a
+glare in a scene
+
+ align:start position:0%
+glare in a scene
+ 
+
+ align:start position:0%
+glare in a scene
+like a lens flare
+
+ align:start position:0%
+like a lens flare
+ 
+
+ align:start position:0%
+like a lens flare
+uh a 2d image might look like that on
+
+ align:start position:0%
+uh a 2d image might look like that on
+ 
+
+ align:start position:0%
+uh a 2d image might look like that on
+the top right
+
+ align:start position:0%
+the top right
+ 
+
+ align:start position:0%
+the top right
+but if you zoom in
+
+ align:start position:0%
+but if you zoom in
+ 
+
+ align:start position:0%
+but if you zoom in
+it turns out in the 4d space
+
+ align:start position:0%
+it turns out in the 4d space
+ 
+
+ align:start position:0%
+it turns out in the 4d space
+the glare manifests itself as this
+
+ align:start position:0%
+the glare manifests itself as this
+ 
+
+ align:start position:0%
+the glare manifests itself as this
+bright spots in a corner can match so
+
+ align:start position:0%
+bright spots in a corner can match so
+ 
+
+ align:start position:0%
+bright spots in a corner can match so
+you can just go through this image and
+
+ align:start position:0%
+you can just go through this image and
+ 
+
+ align:start position:0%
+you can just go through this image and
+eliminate all the all the bright spots
+
+ align:start position:0%
+eliminate all the all the bright spots
+ 
+
+ align:start position:0%
+eliminate all the all the bright spots
+and you can get rid of lens flare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know so you can remove the
+
+ align:start position:0%
+and you know so you can remove the
+ 
+
+ align:start position:0%
+and you know so you can remove the
+outliers just do some kind of a medium
+
+ align:start position:0%
+outliers just do some kind of a medium
+ 
+
+ align:start position:0%
+outliers just do some kind of a medium
+filtering in a neighborhood
+
+ align:start position:0%
+filtering in a neighborhood
+ 
+
+ align:start position:0%
+filtering in a neighborhood
+and the lens flare is removed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so the second way of doing it
+
+ align:start position:0%
+all right so the second way of doing it
+ 
+
+ align:start position:0%
+all right so the second way of doing it
+is by using lenslet array which we
+
+ align:start position:0%
+is by using lenslet array which we
+ 
+
+ align:start position:0%
+is by using lenslet array which we
+already saw so i'm going to repeat that
+
+ align:start position:0%
+already saw so i'm going to repeat that
+ 
+
+ align:start position:0%
+already saw so i'm going to repeat that
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+and now comes the question of
+
+ align:start position:0%
+and now comes the question of
+ 
+
+ align:start position:0%
+and now comes the question of
+what happens to points that are in focus
+
+ align:start position:0%
+what happens to points that are in focus
+ 
+
+ align:start position:0%
+what happens to points that are in focus
+versus order focus okay and this is a
+
+ align:start position:0%
+versus order focus okay and this is a
+ 
+
+ align:start position:0%
+versus order focus okay and this is a
+very key concept uh you have to
+
+ align:start position:0%
+very key concept uh you have to
+ 
+
+ align:start position:0%
+very key concept uh you have to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+so let's say
+
+ align:start position:0%
+so let's say
+ 
+
+ align:start position:0%
+so let's say
+i have a level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and i have a point that's in sharp
+
+ align:start position:0%
+uh and i have a point that's in sharp
+ 
+
+ align:start position:0%
+uh and i have a point that's in sharp
+focus
+
+ align:start position:0%
+focus
+ 
+
+ align:start position:0%
+focus
+at one of these
+
+ align:start position:0%
+at one of these
+ 
+
+ align:start position:0%
+at one of these
+and same situation
+
+ align:start position:0%
+and same situation
+ 
+
+ align:start position:0%
+and same situation
+if the point is in sharp focus
+
+ align:start position:0%
+if the point is in sharp focus
+ 
+
+ align:start position:0%
+if the point is in sharp focus
+at this pin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+light will go back
+
+ align:start position:0%
+light will go back
+ 
+
+ align:start position:0%
+light will go back
+and i will create a disk
+
+ align:start position:0%
+and i will create a disk
+ 
+
+ align:start position:0%
+and i will create a disk
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+but let's say this is the this is the
+
+ align:start position:0%
+but let's say this is the this is the
+ 
+
+ align:start position:0%
+but let's say this is the this is the
+red
+
+ align:start position:0%
+red
+ 
+
+ align:start position:0%
+red
+crayon
+
+ align:start position:0%
+crayon
+ 
+
+ align:start position:0%
+crayon
+all the rays are red
+
+ align:start position:0%
+all the rays are red
+ 
+
+ align:start position:0%
+all the rays are red
+and when we come back to the spin hole
+
+ align:start position:0%
+and when we come back to the spin hole
+ 
+
+ align:start position:0%
+and when we come back to the spin hole
+this whole thing looks wet
+
+ align:start position:0%
+this whole thing looks wet
+ 
+
+ align:start position:0%
+this whole thing looks wet
+so that's why
+
+ align:start position:0%
+so that's why
+ 
+
+ align:start position:0%
+so that's why
+in this part of the image
+
+ align:start position:0%
+in this part of the image
+ 
+
+ align:start position:0%
+in this part of the image
+where in the original photo with the
+
+ align:start position:0%
+where in the original photo with the
+ 
+
+ align:start position:0%
+where in the original photo with the
+original camera
+
+ align:start position:0%
+original camera
+ 
+
+ align:start position:0%
+original camera
+the the red crayons are in sharp focus
+
+ align:start position:0%
+the the red crayons are in sharp focus
+ 
+
+ align:start position:0%
+the the red crayons are in sharp focus
+the whole disc is right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means that
+
+ align:start position:0%
+which means that
+ 
+
+ align:start position:0%
+which means that
+the whole
+
+ align:start position:0%
+the whole
+ 
+
+ align:start position:0%
+the whole
+every part of the lens
+
+ align:start position:0%
+every part of the lens
+ 
+
+ align:start position:0%
+every part of the lens
+is getting
+
+ align:start position:0%
+is getting
+ 
+
+ align:start position:0%
+is getting
+a red ray as in
+
+ align:start position:0%
+a red ray as in
+ 
+
+ align:start position:0%
+a red ray as in
+from this point
+
+ align:start position:0%
+from this point
+ 
+
+ align:start position:0%
+from this point
+but let's go to a part that's actually
+
+ align:start position:0%
+but let's go to a part that's actually
+ 
+
+ align:start position:0%
+but let's go to a part that's actually
+uh outer force okay so i believe this
+
+ align:start position:0%
+uh outer force okay so i believe this
+ 
+
+ align:start position:0%
+uh outer force okay so i believe this
+one is over here so that's on the
+
+ align:start position:0%
+one is over here so that's on the
+ 
+
+ align:start position:0%
+one is over here so that's on the
+boundary between uh maybe a yellow
+
+ align:start position:0%
+boundary between uh maybe a yellow
+ 
+
+ align:start position:0%
+boundary between uh maybe a yellow
+crayon and a blue cream
+
+ align:start position:0%
+crayon and a blue cream
+ 
+
+ align:start position:0%
+crayon and a blue cream
+so even in the original photo it's all
+
+ align:start position:0%
+so even in the original photo it's all
+ 
+
+ align:start position:0%
+so even in the original photo it's all
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+we didn't have a necessary array to the
+
+ align:start position:0%
+we didn't have a necessary array to the
+ 
+
+ align:start position:0%
+we didn't have a necessary array to the
+outputs and here you can see
+
+ align:start position:0%
+outputs and here you can see
+ 
+
+ align:start position:0%
+outputs and here you can see
+part of the each block
+
+ align:start position:0%
+part of the each block
+ 
+
+ align:start position:0%
+part of the each block
+under a landslide is yellow and the
+
+ align:start position:0%
+under a landslide is yellow and the
+ 
+
+ align:start position:0%
+under a landslide is yellow and the
+other part is blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have a situation
+
+ align:start position:0%
+so we have a situation
+ 
+
+ align:start position:0%
+so we have a situation
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+we have a
+
+ align:start position:0%
+we have a
+ 
+
+ align:start position:0%
+we have a
+focus
+
+ align:start position:0%
+focus
+ 
+
+ align:start position:0%
+focus
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yellow and blue
+
+ align:start position:0%
+yellow and blue
+ 
+
+ align:start position:0%
+yellow and blue
+yellow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but they're actually autofocus
+
+ align:start position:0%
+okay but they're actually autofocus
+ 
+
+ align:start position:0%
+okay but they're actually autofocus
+so if i start shooting the rays from
+
+ align:start position:0%
+so if i start shooting the rays from
+ 
+
+ align:start position:0%
+so if i start shooting the rays from
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i just take the one from the yellow
+
+ align:start position:0%
+if i just take the one from the yellow
+ 
+
+ align:start position:0%
+if i just take the one from the yellow
+blue boundary
+
+ align:start position:0%
+blue boundary
+ 
+
+ align:start position:0%
+blue boundary
+for this part
+
+ align:start position:0%
+for this part
+ 
+
+ align:start position:0%
+for this part
+the light is in focus closer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's in focus closer
+
+ align:start position:0%
+okay it's in focus closer
+ 
+
+ align:start position:0%
+okay it's in focus closer
+and the image is actually false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for the bottom part
+
+ align:start position:0%
+for the bottom part
+ 
+
+ align:start position:0%
+for the bottom part
+here all these rays are going to be
+
+ align:start position:0%
+here all these rays are going to be
+ 
+
+ align:start position:0%
+here all these rays are going to be
+but this part here
+
+ align:start position:0%
+but this part here
+ 
+
+ align:start position:0%
+but this part here
+is not here
+
+ align:start position:0%
+is not here
+ 
+
+ align:start position:0%
+is not here
+and from the blue part again we
+
+ align:start position:0%
+and from the blue part again we
+ 
+
+ align:start position:0%
+and from the blue part again we
+shoot the rays
+
+ align:start position:0%
+shoot the rays
+ 
+
+ align:start position:0%
+shoot the rays
+and what you will realize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+you look at this pimple you've had
+
+ align:start position:0%
+you look at this pimple you've had
+ 
+
+ align:start position:0%
+you look at this pimple you've had
+yellow corn coming through and a
+
+ align:start position:0%
+yellow corn coming through and a
+ 
+
+ align:start position:0%
+yellow corn coming through and a
+slightly offset blue core coming
+
+ align:start position:0%
+slightly offset blue core coming
+ 
+
+ align:start position:0%
+slightly offset blue core coming
+and because they were not in sharp focus
+
+ align:start position:0%
+and because they were not in sharp focus
+ 
+
+ align:start position:0%
+and because they were not in sharp focus
+they will contribute through one pink
+
+ align:start position:0%
+they will contribute through one pink
+ 
+
+ align:start position:0%
+they will contribute through one pink
+hole so that part of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's go in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one is the first
+
+ align:start position:0%
+this one is the first
+ 
+
+ align:start position:0%
+this one is the first
+let's go to the one that's further away
+
+ align:start position:0%
+let's go to the one that's further away
+ 
+
+ align:start position:0%
+let's go to the one that's further away
+let's go by the images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's look at this one this
+
+ align:start position:0%
+all right let's look at this one this
+ 
+
+ align:start position:0%
+all right let's look at this one this
+was the current example so if you just
+
+ align:start position:0%
+was the current example so if you just
+ 
+
+ align:start position:0%
+was the current example so if you just
+look at the green and the one that's
+
+ align:start position:0%
+look at the green and the one that's
+ 
+
+ align:start position:0%
+look at the green and the one that's
+kind of blackish next to it
+
+ align:start position:0%
+kind of blackish next to it
+ 
+
+ align:start position:0%
+kind of blackish next to it
+so this one was very easy the the blue
+
+ align:start position:0%
+so this one was very easy the the blue
+ 
+
+ align:start position:0%
+so this one was very easy the the blue
+was to the left of the yellow in the
+
+ align:start position:0%
+was to the left of the yellow in the
+ 
+
+ align:start position:0%
+was to the left of the yellow in the
+original picture and even inside each
+
+ align:start position:0%
+original picture and even inside each
+ 
+
+ align:start position:0%
+original picture and even inside each
+blob the blue is to the left of the
+
+ align:start position:0%
+blob the blue is to the left of the
+ 
+
+ align:start position:0%
+blob the blue is to the left of the
+earth
+
+ align:start position:0%
+earth
+ 
+
+ align:start position:0%
+earth
+but if you see this one the green is to
+
+ align:start position:0%
+but if you see this one the green is to
+ 
+
+ align:start position:0%
+but if you see this one the green is to
+the left of the dark region so it has
+
+ align:start position:0%
+the left of the dark region so it has
+ 
+
+ align:start position:0%
+the left of the dark region so it has
+fluid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here the left right ordering is
+
+ align:start position:0%
+so here the left right ordering is
+ 
+
+ align:start position:0%
+so here the left right ordering is
+maintained here the left hand already
+
+ align:start position:0%
+maintained here the left hand already
+ 
+
+ align:start position:0%
+maintained here the left hand already
+switched
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and can everybody tell me what's going
+
+ align:start position:0%
+and can everybody tell me what's going
+ 
+
+ align:start position:0%
+and can everybody tell me what's going
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remains in the same position
+
+ align:start position:0%
+remains in the same position
+ 
+
+ align:start position:0%
+remains in the same position
+when you are behind the focus plane the
+
+ align:start position:0%
+when you are behind the focus plane the
+ 
+
+ align:start position:0%
+when you are behind the focus plane the
+order is switched
+
+ align:start position:0%
+order is switched
+ 
+
+ align:start position:0%
+order is switched
+and that's why you cannot simply take
+
+ align:start position:0%
+and that's why you cannot simply take
+ 
+
+ align:start position:0%
+and that's why you cannot simply take
+this image and reconstruct the original
+
+ align:start position:0%
+this image and reconstruct the original
+ 
+
+ align:start position:0%
+this image and reconstruct the original
+high frequency higher resolution image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processing for this
+
+ align:start position:0%
+processing for this
+ 
+
+ align:start position:0%
+processing for this
+to be able to recover
+
+ align:start position:0%
+to be able to recover
+ 
+
+ align:start position:0%
+to be able to recover
+so it's a lot of fun to look at these
+
+ align:start position:0%
+so it's a lot of fun to look at these
+ 
+
+ align:start position:0%
+so it's a lot of fun to look at these
+images there's all this information
+
+ align:start position:0%
+images there's all this information
+ 
+
+ align:start position:0%
+images there's all this information
+that's encoded the four dimensional
+
+ align:start position:0%
+that's encoded the four dimensional
+ 
+
+ align:start position:0%
+that's encoded the four dimensional
+information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here is our solution
+
+ align:start position:0%
+so here is our solution
+ 
+
+ align:start position:0%
+so here is our solution
+instead of placing the left leg array
+
+ align:start position:0%
+instead of placing the left leg array
+ 
+
+ align:start position:0%
+instead of placing the left leg array
+we're going to place a mask not a
+
+ align:start position:0%
+we're going to place a mask not a
+ 
+
+ align:start position:0%
+we're going to place a mask not a
+pinhole array but specially printed mask
+
+ align:start position:0%
+pinhole array but specially printed mask
+ 
+
+ align:start position:0%
+pinhole array but specially printed mask
+you can just take a medium format camera
+
+ align:start position:0%
+you can just take a medium format camera
+ 
+
+ align:start position:0%
+you can just take a medium format camera
+such as a mamiyan uh just remove the
+
+ align:start position:0%
+such as a mamiyan uh just remove the
+ 
+
+ align:start position:0%
+such as a mamiyan uh just remove the
+ir
+
+ align:start position:0%
+ir
+ 
+
+ align:start position:0%
+ir
+protective glass
+
+ align:start position:0%
+protective glass
+ 
+
+ align:start position:0%
+protective glass
+and then simply drop a film
+
+ align:start position:0%
+and then simply drop a film
+ 
+
+ align:start position:0%
+and then simply drop a film
+on top of
+
+ align:start position:0%
+on top of
+ 
+
+ align:start position:0%
+on top of
+uh the medium format camera sensor
+
+ align:start position:0%
+uh the medium format camera sensor
+ 
+
+ align:start position:0%
+uh the medium format camera sensor
+put back the put back the protective
+
+ align:start position:0%
+put back the put back the protective
+ 
+
+ align:start position:0%
+put back the put back the protective
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+and you're ready to go and you have
+
+ align:start position:0%
+and you're ready to go and you have
+ 
+
+ align:start position:0%
+and you're ready to go and you have
+electric camera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case we are not putting a
+
+ align:start position:0%
+so in this case we are not putting a
+ 
+
+ align:start position:0%
+so in this case we are not putting a
+pinhole array
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+so i'm going to go through the slides
+
+ align:start position:0%
+so i'm going to go through the slides
+ 
+
+ align:start position:0%
+so i'm going to go through the slides
+uh very quickly
+
+ align:start position:0%
+uh very quickly
+ 
+
+ align:start position:0%
+uh very quickly
+instead of putting a pinhole array we're
+
+ align:start position:0%
+instead of putting a pinhole array we're
+ 
+
+ align:start position:0%
+instead of putting a pinhole array we're
+going to place a different type of mask
+
+ align:start position:0%
+going to place a different type of mask
+ 
+
+ align:start position:0%
+going to place a different type of mask
+to capture that
+
+ align:start position:0%
+to capture that
+ 
+
+ align:start position:0%
+to capture that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a few concepts that we have to look at
+
+ align:start position:0%
+a few concepts that we have to look at
+ 
+
+ align:start position:0%
+a few concepts that we have to look at
+before we get there
+
+ align:start position:0%
+before we get there
+ 
+
+ align:start position:0%
+before we get there
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+there is this concept of conjugate plane
+
+ align:start position:0%
+there is this concept of conjugate plane
+ 
+
+ align:start position:0%
+there is this concept of conjugate plane
+that if a plane is in sharp focus at
+
+ align:start position:0%
+that if a plane is in sharp focus at
+ 
+
+ align:start position:0%
+that if a plane is in sharp focus at
+sensor then this plane and the
+
+ align:start position:0%
+sensor then this plane and the
+ 
+
+ align:start position:0%
+sensor then this plane and the
+corresponding sensor plane are
+
+ align:start position:0%
+corresponding sensor plane are
+ 
+
+ align:start position:0%
+corresponding sensor plane are
+conjugated with each other
+
+ align:start position:0%
+conjugated with each other
+ 
+
+ align:start position:0%
+conjugated with each other
+if i put the object closer
+
+ align:start position:0%
+if i put the object closer
+ 
+
+ align:start position:0%
+if i put the object closer
+then i must move the sensor further back
+
+ align:start position:0%
+then i must move the sensor further back
+ 
+
+ align:start position:0%
+then i must move the sensor further back
+and those two are conjugate with respect
+
+ align:start position:0%
+and those two are conjugate with respect
+ 
+
+ align:start position:0%
+and those two are conjugate with respect
+to each other and that is defined by the
+
+ align:start position:0%
+to each other and that is defined by the
+ 
+
+ align:start position:0%
+to each other and that is defined by the
+length equation
+
+ align:start position:0%
+length equation
+ 
+
+ align:start position:0%
+length equation
+one over f equals one over u plus
+
+ align:start position:0%
+one over f equals one over u plus
+ 
+
+ align:start position:0%
+one over f equals one over u plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the key concept here is that a lens
+
+ align:start position:0%
+now the key concept here is that a lens
+ 
+
+ align:start position:0%
+now the key concept here is that a lens
+copies
+
+ align:start position:0%
+copies
+ 
+
+ align:start position:0%
+copies
+a light fill from the outside world
+
+ align:start position:0%
+a light fill from the outside world
+ 
+
+ align:start position:0%
+a light fill from the outside world
+to the inside
+
+ align:start position:0%
+to the inside
+ 
+
+ align:start position:0%
+to the inside
+what does that mean
+
+ align:start position:0%
+what does that mean
+ 
+
+ align:start position:0%
+what does that mean
+if i have
+
+ align:start position:0%
+if i have
+ 
+
+ align:start position:0%
+if i have
+so originally what we were doing we were
+
+ align:start position:0%
+so originally what we were doing we were
+ 
+
+ align:start position:0%
+so originally what we were doing we were
+assigning some coordinate system
+
+ align:start position:0%
+assigning some coordinate system
+ 
+
+ align:start position:0%
+assigning some coordinate system
+we called it the theta plane and we call
+
+ align:start position:0%
+we called it the theta plane and we call
+ 
+
+ align:start position:0%
+we called it the theta plane and we call
+this one the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is our two plane parameters now
+
+ align:start position:0%
+this is our two plane parameters now
+ 
+
+ align:start position:0%
+this is our two plane parameters now
+there's a little bit of fudging going on
+
+ align:start position:0%
+there's a little bit of fudging going on
+ 
+
+ align:start position:0%
+there's a little bit of fudging going on
+here because
+
+ align:start position:0%
+here because
+ 
+
+ align:start position:0%
+here because
+theta here doesn't really correspond to
+
+ align:start position:0%
+theta here doesn't really correspond to
+ 
+
+ align:start position:0%
+theta here doesn't really correspond to
+absolute angle
+
+ align:start position:0%
+absolute angle
+ 
+
+ align:start position:0%
+absolute angle
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+but a coordinate on this axis so theta
+
+ align:start position:0%
+but a coordinate on this axis so theta
+ 
+
+ align:start position:0%
+but a coordinate on this axis so theta
+is zero here
+
+ align:start position:0%
+is zero here
+ 
+
+ align:start position:0%
+is zero here
+and you know let's say it's
+
+ align:start position:0%
+and you know let's say it's
+ 
+
+ align:start position:0%
+and you know let's say it's
+plus 5 here and minus stock
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x is of course goes from 0 to 1000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is our life the relationship
+
+ align:start position:0%
+and this is our life the relationship
+ 
+
+ align:start position:0%
+and this is our life the relationship
+between any point here that you want
+
+ align:start position:0%
+between any point here that you want
+ 
+
+ align:start position:0%
+between any point here that you want
+here defines the 2d
+
+ align:start position:0%
+here defines the 2d
+ 
+
+ align:start position:0%
+here defines the 2d
+now it turns out
+
+ align:start position:0%
+now it turns out
+ 
+
+ align:start position:0%
+now it turns out
+let's say i have two points here
+
+ align:start position:0%
+let's say i have two points here
+ 
+
+ align:start position:0%
+let's say i have two points here
+a and b
+
+ align:start position:0%
+a and b
+ 
+
+ align:start position:0%
+a and b
+and i have two points here
+
+ align:start position:0%
+and i have two points here
+ 
+
+ align:start position:0%
+and i have two points here
+a and b
+
+ align:start position:0%
+a and b
+ 
+
+ align:start position:0%
+a and b
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again okay
+
+ align:start position:0%
+again okay
+ 
+
+ align:start position:0%
+again okay
+the image is formed here i can also
+
+ align:start position:0%
+the image is formed here i can also
+ 
+
+ align:start position:0%
+the image is formed here i can also
+assign a new plane here
+
+ align:start position:0%
+assign a new plane here
+ 
+
+ align:start position:0%
+assign a new plane here
+in a quality span for this expression
+
+ align:start position:0%
+in a quality span for this expression
+ 
+
+ align:start position:0%
+in a quality span for this expression
+this light fit which means this x theta
+
+ align:start position:0%
+this light fit which means this x theta
+ 
+
+ align:start position:0%
+this light fit which means this x theta
+relationship is maintained in this theta
+
+ align:start position:0%
+relationship is maintained in this theta
+ 
+
+ align:start position:0%
+relationship is maintained in this theta
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+so if i take a ray here from i'm going
+
+ align:start position:0%
+so if i take a ray here from i'm going
+ 
+
+ align:start position:0%
+so if i take a ray here from i'm going
+to assign this also let's say i put a
+
+ align:start position:0%
+to assign this also let's say i put a
+ 
+
+ align:start position:0%
+to assign this also let's say i put a
+painting here
+
+ align:start position:0%
+painting here
+ 
+
+ align:start position:0%
+painting here
+okay and assign the coordinate of one to
+
+ align:start position:0%
+okay and assign the coordinate of one to
+ 
+
+ align:start position:0%
+okay and assign the coordinate of one to
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+and here is a coordinate of one thousand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's good to take some real numbers
+
+ align:start position:0%
+it's good to take some real numbers
+ 
+
+ align:start position:0%
+it's good to take some real numbers
+then if i shoot a rate from
+
+ align:start position:0%
+then if i shoot a rate from
+ 
+
+ align:start position:0%
+then if i shoot a rate from
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+to plus 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+i can guarantee if the plane was in
+
+ align:start position:0%
+i can guarantee if the plane was in
+ 
+
+ align:start position:0%
+i can guarantee if the plane was in
+conjugate that the four will map back to
+
+ align:start position:0%
+conjugate that the four will map back to
+ 
+
+ align:start position:0%
+conjugate that the four will map back to
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it will map to the pixel that's 200
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course if i have 200 naming to
+
+ align:start position:0%
+and of course if i have 200 naming to
+ 
+
+ align:start position:0%
+and of course if i have 200 naming to
+3 here
+
+ align:start position:0%
+3 here
+ 
+
+ align:start position:0%
+3 here
+3 will automatically map it to also
+
+ align:start position:0%
+3 will automatically map it to also
+ 
+
+ align:start position:0%
+3 will automatically map it to also
+and that's only because this painting is
+
+ align:start position:0%
+and that's only because this painting is
+ 
+
+ align:start position:0%
+and that's only because this painting is
+a sharp focus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this notion of conjugation
+
+ align:start position:0%
+this notion of conjugation
+ 
+
+ align:start position:0%
+this notion of conjugation
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+means that the light field of this next
+
+ align:start position:0%
+means that the light field of this next
+ 
+
+ align:start position:0%
+means that the light field of this next
+theta coordinate is mapped to this theta
+
+ align:start position:0%
+theta coordinate is mapped to this theta
+ 
+
+ align:start position:0%
+theta coordinate is mapped to this theta
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+so i can take
+
+ align:start position:0%
+so i can take
+ 
+
+ align:start position:0%
+so i can take
+parameterization i can shoot all the
+
+ align:start position:0%
+parameterization i can shoot all the
+ 
+
+ align:start position:0%
+parameterization i can shoot all the
+rays here
+
+ align:start position:0%
+rays here
+ 
+
+ align:start position:0%
+rays here
+if there's a point here and i should
+
+ align:start position:0%
+if there's a point here and i should
+ 
+
+ align:start position:0%
+if there's a point here and i should
+trace out
+
+ align:start position:0%
+trace out
+ 
+
+ align:start position:0%
+trace out
+the same point will be sharp focus here
+
+ align:start position:0%
+the same point will be sharp focus here
+ 
+
+ align:start position:0%
+the same point will be sharp focus here
+and all the rays will converge
+
+ align:start position:0%
+and all the rays will converge
+ 
+
+ align:start position:0%
+and all the rays will converge
+okay if i have two rays that are
+
+ align:start position:0%
+okay if i have two rays that are
+ 
+
+ align:start position:0%
+okay if i have two rays that are
+starting in the same theta direction
+
+ align:start position:0%
+starting in the same theta direction
+ 
+
+ align:start position:0%
+starting in the same theta direction
+they'll come out here in the same
+
+ align:start position:0%
+they'll come out here in the same
+ 
+
+ align:start position:0%
+they'll come out here in the same
+theta direction
+
+ align:start position:0%
+theta direction
+ 
+
+ align:start position:0%
+theta direction
+okay and so on so basically i'm creating
+
+ align:start position:0%
+okay and so on so basically i'm creating
+ 
+
+ align:start position:0%
+okay and so on so basically i'm creating
+an exact replica of light for here
+
+ align:start position:0%
+an exact replica of light for here
+ 
+
+ align:start position:0%
+an exact replica of light for here
+inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is possible only when the lens
+
+ align:start position:0%
+and this is possible only when the lens
+ 
+
+ align:start position:0%
+and this is possible only when the lens
+is extremely good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it might do a pretty good job
+
+ align:start position:0%
+so it might do a pretty good job
+ 
+
+ align:start position:0%
+so it might do a pretty good job
+a not so good lens would do a good job
+
+ align:start position:0%
+a not so good lens would do a good job
+ 
+
+ align:start position:0%
+a not so good lens would do a good job
+of popping it in the center but not at
+
+ align:start position:0%
+of popping it in the center but not at
+ 
+
+ align:start position:0%
+of popping it in the center but not at
+the edges or it might be good for one
+
+ align:start position:0%
+the edges or it might be good for one
+ 
+
+ align:start position:0%
+the edges or it might be good for one
+level but not for others
+
+ align:start position:0%
+level but not for others
+ 
+
+ align:start position:0%
+level but not for others
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this notion of copying the light field
+
+ align:start position:0%
+this notion of copying the light field
+ 
+
+ align:start position:0%
+this notion of copying the light field
+makes the lens very unique because
+
+ align:start position:0%
+makes the lens very unique because
+ 
+
+ align:start position:0%
+makes the lens very unique because
+we know that the appearance of the world
+
+ align:start position:0%
+we know that the appearance of the world
+ 
+
+ align:start position:0%
+we know that the appearance of the world
+is 4d
+
+ align:start position:0%
+is 4d
+ 
+
+ align:start position:0%
+is 4d
+it completely describes
+
+ align:start position:0%
+it completely describes
+ 
+
+ align:start position:0%
+it completely describes
+the appearance of the world and what the
+
+ align:start position:0%
+the appearance of the world and what the
+ 
+
+ align:start position:0%
+the appearance of the world and what the
+lens has done is optically it has copied
+
+ align:start position:0%
+lens has done is optically it has copied
+ 
+
+ align:start position:0%
+lens has done is optically it has copied
+the appearance of the word faithfully to
+
+ align:start position:0%
+the appearance of the word faithfully to
+ 
+
+ align:start position:0%
+the appearance of the word faithfully to
+something that's inside
+
+ align:start position:0%
+something that's inside
+ 
+
+ align:start position:0%
+something that's inside
+okay and now we just need a good quality
+
+ align:start position:0%
+okay and now we just need a good quality
+ 
+
+ align:start position:0%
+okay and now we just need a good quality
+sensor
+
+ align:start position:0%
+sensor
+ 
+
+ align:start position:0%
+sensor
+to basically take the hologram of what's
+
+ align:start position:0%
+to basically take the hologram of what's
+ 
+
+ align:start position:0%
+to basically take the hologram of what's
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+i'm using the word hologram to indicate
+
+ align:start position:0%
+i'm using the word hologram to indicate
+ 
+
+ align:start position:0%
+i'm using the word hologram to indicate
+the 4d appearance of the window
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this window
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we have here
+
+ align:start position:0%
+that we have here
+ 
+
+ align:start position:0%
+that we have here
+is exactly copied
+
+ align:start position:0%
+is exactly copied
+ 
+
+ align:start position:0%
+is exactly copied
+over here so anything that's
+
+ align:start position:0%
+over here so anything that's
+ 
+
+ align:start position:0%
+over here so anything that's
+behind this window is faithfully
+
+ align:start position:0%
+behind this window is faithfully
+ 
+
+ align:start position:0%
+behind this window is faithfully
+influenced over here
+
+ align:start position:0%
+influenced over here
+ 
+
+ align:start position:0%
+influenced over here
+unfortunately in a traditional camera
+
+ align:start position:0%
+unfortunately in a traditional camera
+ 
+
+ align:start position:0%
+unfortunately in a traditional camera
+you take that window and you snap it
+
+ align:start position:0%
+you take that window and you snap it
+ 
+
+ align:start position:0%
+you take that window and you snap it
+back to a 2d
+
+ align:start position:0%
+back to a 2d
+ 
+
+ align:start position:0%
+back to a 2d
+so image
+
+ align:start position:0%
+so image
+ 
+
+ align:start position:0%
+so image
+problem is the sensor the optics is
+
+ align:start position:0%
+problem is the sensor the optics is
+ 
+
+ align:start position:0%
+problem is the sensor the optics is
+doing its job
+
+ align:start position:0%
+doing its job
+ 
+
+ align:start position:0%
+doing its job
+of going from 4d to 4d
+
+ align:start position:0%
+of going from 4d to 4d
+ 
+
+ align:start position:0%
+of going from 4d to 4d
+so 4d in
+
+ align:start position:0%
+so 4d in
+ 
+
+ align:start position:0%
+so 4d in
+right fully up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but sensor does a terrible job of
+
+ align:start position:0%
+but sensor does a terrible job of
+ 
+
+ align:start position:0%
+but sensor does a terrible job of
+maintaining that four-legged user
+
+ align:start position:0%
+maintaining that four-legged user
+ 
+
+ align:start position:0%
+maintaining that four-legged user
+but if you have these three solutions
+
+ align:start position:0%
+but if you have these three solutions
+ 
+
+ align:start position:0%
+but if you have these three solutions
+you can recover
+
+ align:start position:0%
+you can recover
+ 
+
+ align:start position:0%
+you can recover
+this code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me
+
+ align:start position:0%
+so let me
+ 
+
+ align:start position:0%
+so let me
+just explain this concept one more time
+
+ align:start position:0%
+just explain this concept one more time
+ 
+
+ align:start position:0%
+just explain this concept one more time
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+how the rays when the sharp focus versus
+
+ align:start position:0%
+how the rays when the sharp focus versus
+ 
+
+ align:start position:0%
+how the rays when the sharp focus versus
+auto focus look differently
+
+ align:start position:0%
+auto focus look differently
+ 
+
+ align:start position:0%
+auto focus look differently
+and i promise you that after you
+
+ align:start position:0%
+and i promise you that after you
+ 
+
+ align:start position:0%
+and i promise you that after you
+understand this concept of rays and ray
+
+ align:start position:0%
+understand this concept of rays and ray
+ 
+
+ align:start position:0%
+understand this concept of rays and ray
+space and all that everything else in
+
+ align:start position:0%
+space and all that everything else in
+ 
+
+ align:start position:0%
+space and all that everything else in
+the auto focus and and depth of field
+
+ align:start position:0%
+the auto focus and and depth of field
+ 
+
+ align:start position:0%
+the auto focus and and depth of field
+will become extremely easy to understand
+
+ align:start position:0%
+will become extremely easy to understand
+ 
+
+ align:start position:0%
+will become extremely easy to understand
+okay so just
+
+ align:start position:0%
+okay so just
+ 
+
+ align:start position:0%
+okay so just
+just see how this works out
+
+ align:start position:0%
+just see how this works out
+ 
+
+ align:start position:0%
+just see how this works out
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now let's say we have a point here
+
+ align:start position:0%
+now let's say we have a point here
+ 
+
+ align:start position:0%
+now let's say we have a point here
+okay we can either represent the like
+
+ align:start position:0%
+okay we can either represent the like
+ 
+
+ align:start position:0%
+okay we can either represent the like
+field here
+
+ align:start position:0%
+field here
+ 
+
+ align:start position:0%
+field here
+or we can represent it here it doesn't
+
+ align:start position:0%
+or we can represent it here it doesn't
+ 
+
+ align:start position:0%
+or we can represent it here it doesn't
+really matter
+
+ align:start position:0%
+really matter
+ 
+
+ align:start position:0%
+really matter
+now here what we have is a point
+
+ align:start position:0%
+now here what we have is a point
+ 
+
+ align:start position:0%
+now here what we have is a point
+that's emitting light in all directions
+
+ align:start position:0%
+that's emitting light in all directions
+ 
+
+ align:start position:0%
+that's emitting light in all directions
+so how does the light look like
+
+ align:start position:0%
+so how does the light look like
+ 
+
+ align:start position:0%
+so how does the light look like
+there's a point x and it's emitting
+
+ align:start position:0%
+there's a point x and it's emitting
+ 
+
+ align:start position:0%
+there's a point x and it's emitting
+light in all three directions
+
+ align:start position:0%
+light in all three directions
+ 
+
+ align:start position:0%
+light in all three directions
+now we know that the lens is going to
+
+ align:start position:0%
+now we know that the lens is going to
+ 
+
+ align:start position:0%
+now we know that the lens is going to
+make an exact replica of that inside so
+
+ align:start position:0%
+make an exact replica of that inside so
+ 
+
+ align:start position:0%
+make an exact replica of that inside so
+when i come here i have a particular x
+
+ align:start position:0%
+when i come here i have a particular x
+ 
+
+ align:start position:0%
+when i come here i have a particular x
+and light is coming from all different
+
+ align:start position:0%
+and light is coming from all different
+ 
+
+ align:start position:0%
+and light is coming from all different
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+so what's coming at the plane is exactly
+
+ align:start position:0%
+so what's coming at the plane is exactly
+ 
+
+ align:start position:0%
+so what's coming at the plane is exactly
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay from this how do i for an image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do i realize that if i integrate
+
+ align:start position:0%
+how do i realize that if i integrate
+ 
+
+ align:start position:0%
+how do i realize that if i integrate
+the radius along each of these rays i
+
+ align:start position:0%
+the radius along each of these rays i
+ 
+
+ align:start position:0%
+the radius along each of these rays i
+will get the intensity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we are going from a 2d world now to a 1d
+
+ align:start position:0%
+we are going from a 2d world now to a 1d
+ 
+
+ align:start position:0%
+we are going from a 2d world now to a 1d
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+in the in the in the general case we go
+
+ align:start position:0%
+in the in the in the general case we go
+ 
+
+ align:start position:0%
+in the in the in the general case we go
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+from a 4d world to a 2d sensor 4d
+
+ align:start position:0%
+from a 4d world to a 2d sensor 4d
+ 
+
+ align:start position:0%
+from a 4d world to a 2d sensor 4d
+representation 2d sensor here we have 2d
+
+ align:start position:0%
+representation 2d sensor here we have 2d
+ 
+
+ align:start position:0%
+representation 2d sensor here we have 2d
+light fill and 1d sensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum over theta i'm just going to sum up
+
+ align:start position:0%
+sum over theta i'm just going to sum up
+ 
+
+ align:start position:0%
+sum over theta i'm just going to sum up
+everything that comes out theta that is
+
+ align:start position:0%
+everything that comes out theta that is
+ 
+
+ align:start position:0%
+everything that comes out theta that is
+i'm going to take all these values
+
+ align:start position:0%
+i'm going to take all these values
+ 
+
+ align:start position:0%
+i'm going to take all these values
+and sum them up
+
+ align:start position:0%
+and sum them up
+ 
+
+ align:start position:0%
+and sum them up
+and mathematically that's just taking a
+
+ align:start position:0%
+and mathematically that's just taking a
+ 
+
+ align:start position:0%
+and mathematically that's just taking a
+projection i'm just going to take this
+
+ align:start position:0%
+projection i'm just going to take this
+ 
+
+ align:start position:0%
+projection i'm just going to take this
+2d world and flatten it
+
+ align:start position:0%
+2d world and flatten it
+ 
+
+ align:start position:0%
+2d world and flatten it
+to a 1d word
+
+ align:start position:0%
+to a 1d word
+ 
+
+ align:start position:0%
+to a 1d word
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+or you can call it line integral
+
+ align:start position:0%
+or you can call it line integral
+ 
+
+ align:start position:0%
+or you can call it line integral
+so imagine
+
+ align:start position:0%
+so imagine
+ 
+
+ align:start position:0%
+so imagine
+i had all this
+
+ align:start position:0%
+i had all this
+ 
+
+ align:start position:0%
+i had all this
+all this
+
+ align:start position:0%
+all this
+ 
+
+ align:start position:0%
+all this
+tennis falls here and i struck
+
+ align:start position:0%
+tennis falls here and i struck
+ 
+
+ align:start position:0%
+tennis falls here and i struck
+all of them under the force of gravity
+
+ align:start position:0%
+all of them under the force of gravity
+ 
+
+ align:start position:0%
+all of them under the force of gravity
+the number of balls that will come here
+
+ align:start position:0%
+the number of balls that will come here
+ 
+
+ align:start position:0%
+the number of balls that will come here
+will be the intensity of that pistol and
+
+ align:start position:0%
+will be the intensity of that pistol and
+ 
+
+ align:start position:0%
+will be the intensity of that pistol and
+will black everywhere else
+
+ align:start position:0%
+will black everywhere else
+ 
+
+ align:start position:0%
+will black everywhere else
+very simple very clean
+
+ align:start position:0%
+very simple very clean
+ 
+
+ align:start position:0%
+very simple very clean
+now what happens when something is out
+
+ align:start position:0%
+now what happens when something is out
+ 
+
+ align:start position:0%
+now what happens when something is out
+of focus
+
+ align:start position:0%
+of focus
+ 
+
+ align:start position:0%
+of focus
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if it's out of focus
+
+ align:start position:0%
+if it's out of focus
+ 
+
+ align:start position:0%
+if it's out of focus
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the lens is doing a good job of
+
+ align:start position:0%
+the lens is doing a good job of
+ 
+
+ align:start position:0%
+the lens is doing a good job of
+transferring the 40 here 40 here but if
+
+ align:start position:0%
+transferring the 40 here 40 here but if
+ 
+
+ align:start position:0%
+transferring the 40 here 40 here but if
+you did the right job for this plane
+
+ align:start position:0%
+you did the right job for this plane
+ 
+
+ align:start position:0%
+you did the right job for this plane
+not first
+
+ align:start position:0%
+not first
+ 
+
+ align:start position:0%
+not first
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how do we represent the new space
+
+ align:start position:0%
+so how do we represent the new space
+ 
+
+ align:start position:0%
+so how do we represent the new space
+of light failure in this in this case
+
+ align:start position:0%
+of light failure in this in this case
+ 
+
+ align:start position:0%
+of light failure in this in this case
+the light feels very simple there's just
+
+ align:start position:0%
+the light feels very simple there's just
+ 
+
+ align:start position:0%
+the light feels very simple there's just
+one pointer
+
+ align:start position:0%
+one pointer
+ 
+
+ align:start position:0%
+one pointer
+it has a bunch of rays and you want to
+
+ align:start position:0%
+it has a bunch of rays and you want to
+ 
+
+ align:start position:0%
+it has a bunch of rays and you want to
+represent that previously the light was
+
+ align:start position:0%
+represent that previously the light was
+ 
+
+ align:start position:0%
+represent that previously the light was
+reaching only one next point now it's
+
+ align:start position:0%
+reaching only one next point now it's
+ 
+
+ align:start position:0%
+reaching only one next point now it's
+reaching an array of
+
+ align:start position:0%
+reaching an array of
+ 
+
+ align:start position:0%
+reaching an array of
+x points and for each of the x points
+
+ align:start position:0%
+x points and for each of the x points
+ 
+
+ align:start position:0%
+x points and for each of the x points
+there's only one direction in which
+
+ align:start position:0%
+there's only one direction in which
+ 
+
+ align:start position:0%
+there's only one direction in which
+lights are acting
+
+ align:start position:0%
+lights are acting
+ 
+
+ align:start position:0%
+lights are acting
+so there's still a line that's the axis
+
+ align:start position:0%
+so there's still a line that's the axis
+ 
+
+ align:start position:0%
+so there's still a line that's the axis
+is missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i have a bunch of different points
+
+ align:start position:0%
+so i have a bunch of different points
+ 
+
+ align:start position:0%
+so i have a bunch of different points
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and for each of them there's a
+
+ align:start position:0%
+and for each of them there's a
+ 
+
+ align:start position:0%
+and for each of them there's a
+direction along which the light
+
+ align:start position:0%
+direction along which the light
+ 
+
+ align:start position:0%
+direction along which the light
+so this is the notion of shear
+
+ align:start position:0%
+so this is the notion of shear
+ 
+
+ align:start position:0%
+so this is the notion of shear
+we have a straight line with shear
+
+ align:start position:0%
+we have a straight line with shear
+ 
+
+ align:start position:0%
+we have a straight line with shear
+deterioration
+
+ align:start position:0%
+deterioration
+ 
+
+ align:start position:0%
+deterioration
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+how do we compute the light how do we
+
+ align:start position:0%
+how do we compute the light how do we
+ 
+
+ align:start position:0%
+how do we compute the light how do we
+compute the intensity from the set of
+
+ align:start position:0%
+compute the intensity from the set of
+ 
+
+ align:start position:0%
+compute the intensity from the set of
+rays
+
+ align:start position:0%
+rays
+ 
+
+ align:start position:0%
+rays
+again the same operation of imagine we
+
+ align:start position:0%
+again the same operation of imagine we
+ 
+
+ align:start position:0%
+again the same operation of imagine we
+had all this all this tennis balls here
+
+ align:start position:0%
+had all this all this tennis balls here
+ 
+
+ align:start position:0%
+had all this all this tennis balls here
+and we're going to let them drop
+
+ align:start position:0%
+and we're going to let them drop
+ 
+
+ align:start position:0%
+and we're going to let them drop
+if you let them drop we're going to get
+
+ align:start position:0%
+if you let them drop we're going to get
+ 
+
+ align:start position:0%
+if you let them drop we're going to get
+intensity that
+
+ align:start position:0%
+intensity that
+ 
+
+ align:start position:0%
+intensity that
+goes over a set of pixels rather than
+
+ align:start position:0%
+goes over a set of pixels rather than
+ 
+
+ align:start position:0%
+goes over a set of pixels rather than
+just one pixel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that's the capture photo you'll see
+
+ align:start position:0%
+and that's the capture photo you'll see
+ 
+
+ align:start position:0%
+and that's the capture photo you'll see
+when something is out of focus you don't
+
+ align:start position:0%
+when something is out of focus you don't
+ 
+
+ align:start position:0%
+when something is out of focus you don't
+see a sharp point
+
+ align:start position:0%
+see a sharp point
+ 
+
+ align:start position:0%
+see a sharp point
+but you see
+
+ align:start position:0%
+but you see
+ 
+
+ align:start position:0%
+but you see
+a blurred
+
+ align:start position:0%
+a blurred
+ 
+
+ align:start position:0%
+a blurred
+set of values
+
+ align:start position:0%
+set of values
+ 
+
+ align:start position:0%
+set of values
+so again we start from here
+
+ align:start position:0%
+so again we start from here
+ 
+
+ align:start position:0%
+so again we start from here
+exact copy
+
+ align:start position:0%
+exact copy
+ 
+
+ align:start position:0%
+exact copy
+for a given x we have all the thetas we
+
+ align:start position:0%
+for a given x we have all the thetas we
+ 
+
+ align:start position:0%
+for a given x we have all the thetas we
+project we get a sharp point
+
+ align:start position:0%
+project we get a sharp point
+ 
+
+ align:start position:0%
+project we get a sharp point
+that's the intensity of the capture flow
+
+ align:start position:0%
+that's the intensity of the capture flow
+ 
+
+ align:start position:0%
+that's the intensity of the capture flow
+if it's out of focus
+
+ align:start position:0%
+if it's out of focus
+ 
+
+ align:start position:0%
+if it's out of focus
+the set of rays can be represented on a
+
+ align:start position:0%
+the set of rays can be represented on a
+ 
+
+ align:start position:0%
+the set of rays can be represented on a
+slanted line now
+
+ align:start position:0%
+slanted line now
+ 
+
+ align:start position:0%
+slanted line now
+when we project that we get
+
+ align:start position:0%
+when we project that we get
+ 
+
+ align:start position:0%
+when we project that we get
+the integral
+
+ align:start position:0%
+the integral
+ 
+
+ align:start position:0%
+the integral
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this gear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now when you're thinking about
+
+ align:start position:0%
+so now when you're thinking about
+ 
+
+ align:start position:0%
+so now when you're thinking about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now when you're thinking about
+
+ align:start position:0%
+now when you're thinking about
+ 
+
+ align:start position:0%
+now when you're thinking about
+doing your assignment
+
+ align:start position:0%
+doing your assignment
+ 
+
+ align:start position:0%
+doing your assignment
+and you have set up photos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you want to do refocusing
+
+ align:start position:0%
+and you want to do refocusing
+ 
+
+ align:start position:0%
+and you want to do refocusing
+you can think of in multiple ways
+
+ align:start position:0%
+you can think of in multiple ways
+ 
+
+ align:start position:0%
+you can think of in multiple ways
+if i stack all the photos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so remember
+
+ align:start position:0%
+so remember
+ 
+
+ align:start position:0%
+so remember
+taking a picture with area of cameras
+
+ align:start position:0%
+taking a picture with area of cameras
+ 
+
+ align:start position:0%
+taking a picture with area of cameras
+is the same thing so i'm going to put an
+
+ align:start position:0%
+is the same thing so i'm going to put an
+ 
+
+ align:start position:0%
+is the same thing so i'm going to put an
+array of canvas here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the coordinate of the camera is
+
+ align:start position:0%
+and the coordinate of the camera is
+ 
+
+ align:start position:0%
+and the coordinate of the camera is
+thinner
+
+ align:start position:0%
+thinner
+ 
+
+ align:start position:0%
+thinner
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the framework for the camera is nice
+
+ align:start position:0%
+the framework for the camera is nice
+ 
+
+ align:start position:0%
+the framework for the camera is nice
+so i can take a picture of the first
+
+ align:start position:0%
+so i can take a picture of the first
+ 
+
+ align:start position:0%
+so i can take a picture of the first
+camera
+
+ align:start position:0%
+camera
+ 
+
+ align:start position:0%
+camera
+and i'll put that as the top row of this
+
+ align:start position:0%
+and i'll put that as the top row of this
+ 
+
+ align:start position:0%
+and i'll put that as the top row of this
+i'll take a picture with the theta
+
+ align:start position:0%
+i'll take a picture with the theta
+ 
+
+ align:start position:0%
+i'll take a picture with the theta
+equals two and put it over here sorry
+
+ align:start position:0%
+equals two and put it over here sorry
+ 
+
+ align:start position:0%
+equals two and put it over here sorry
+fit equals five over here four three two
+
+ align:start position:0%
+fit equals five over here four three two
+ 
+
+ align:start position:0%
+fit equals five over here four three two
+one zero if i'm nine cameras i'll put
+
+ align:start position:0%
+one zero if i'm nine cameras i'll put
+ 
+
+ align:start position:0%
+one zero if i'm nine cameras i'll put
+them over here
+
+ align:start position:0%
+them over here
+ 
+
+ align:start position:0%
+them over here
+and if i just want to take a picture
+
+ align:start position:0%
+and if i just want to take a picture
+ 
+
+ align:start position:0%
+and if i just want to take a picture
+that's focused at infinity
+
+ align:start position:0%
+that's focused at infinity
+ 
+
+ align:start position:0%
+that's focused at infinity
+i'm going to start all those pictures
+
+ align:start position:0%
+i'm going to start all those pictures
+ 
+
+ align:start position:0%
+i'm going to start all those pictures
+and just take the sum
+
+ align:start position:0%
+and just take the sum
+ 
+
+ align:start position:0%
+and just take the sum
+along vertical direction
+
+ align:start position:0%
+along vertical direction
+ 
+
+ align:start position:0%
+along vertical direction
+and that will focus at
+
+ align:start position:0%
+and that will focus at
+ 
+
+ align:start position:0%
+and that will focus at
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+right if i want to focus closer
+
+ align:start position:0%
+right if i want to focus closer
+ 
+
+ align:start position:0%
+right if i want to focus closer
+then i shouldn't just sum them up
+
+ align:start position:0%
+then i shouldn't just sum them up
+ 
+
+ align:start position:0%
+then i shouldn't just sum them up
+as they are
+
+ align:start position:0%
+as they are
+ 
+
+ align:start position:0%
+as they are
+but i need to slightly
+
+ align:start position:0%
+but i need to slightly
+ 
+
+ align:start position:0%
+but i need to slightly
+shear them
+
+ align:start position:0%
+shear them
+ 
+
+ align:start position:0%
+shear them
+so i'm going to keep the center camera
+
+ align:start position:0%
+so i'm going to keep the center camera
+ 
+
+ align:start position:0%
+so i'm going to keep the center camera
+center camera image as is i'll take the
+
+ align:start position:0%
+center camera image as is i'll take the
+ 
+
+ align:start position:0%
+center camera image as is i'll take the
+theta equals one camera and shift it to
+
+ align:start position:0%
+theta equals one camera and shift it to
+ 
+
+ align:start position:0%
+theta equals one camera and shift it to
+the left
+
+ align:start position:0%
+the left
+ 
+
+ align:start position:0%
+the left
+by one pixel i'll take three times two
+
+ align:start position:0%
+by one pixel i'll take three times two
+ 
+
+ align:start position:0%
+by one pixel i'll take three times two
+i'll shift it by two pixels three pixels
+
+ align:start position:0%
+i'll shift it by two pixels three pixels
+ 
+
+ align:start position:0%
+i'll shift it by two pixels three pixels
+and five x's
+
+ align:start position:0%
+and five x's
+ 
+
+ align:start position:0%
+and five x's
+minus sorry minus one minus two minus
+
+ align:start position:0%
+minus sorry minus one minus two minus
+ 
+
+ align:start position:0%
+minus sorry minus one minus two minus
+three and one over here are shipped out
+
+ align:start position:0%
+three and one over here are shipped out
+ 
+
+ align:start position:0%
+three and one over here are shipped out
+plus one plus two plus three if i sum
+
+ align:start position:0%
+plus one plus two plus three if i sum
+ 
+
+ align:start position:0%
+plus one plus two plus three if i sum
+them up
+
+ align:start position:0%
+them up
+ 
+
+ align:start position:0%
+them up
+i'll be actually focusing
+
+ align:start position:0%
+i'll be actually focusing
+ 
+
+ align:start position:0%
+i'll be actually focusing
+on a different plane
+
+ align:start position:0%
+on a different plane
+ 
+
+ align:start position:0%
+on a different plane
+so this is the main concept behind
+
+ align:start position:0%
+so this is the main concept behind
+ 
+
+ align:start position:0%
+so this is the main concept behind
+refocusing
+
+ align:start position:0%
+refocusing
+ 
+
+ align:start position:0%
+refocusing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it's shifting and adding
+
+ align:start position:0%
+it's shifting and adding
+ 
+
+ align:start position:0%
+it's shifting and adding
+and you can think of that within a
+
+ align:start position:0%
+and you can think of that within a
+ 
+
+ align:start position:0%
+and you can think of that within a
+single lens
+
+ align:start position:0%
+single lens
+ 
+
+ align:start position:0%
+single lens
+or you can think of that using area of
+
+ align:start position:0%
+or you can think of that using area of
+ 
+
+ align:start position:0%
+or you can think of that using area of
+canvas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear so far
+
+ align:start position:0%
+clear so far
+ 
+
+ align:start position:0%
+clear so far
+so next time you're taking a picture
+
+ align:start position:0%
+so next time you're taking a picture
+ 
+
+ align:start position:0%
+so next time you're taking a picture
+you know think about how much work the
+
+ align:start position:0%
+you know think about how much work the
+ 
+
+ align:start position:0%
+you know think about how much work the
+lens is doing
+
+ align:start position:0%
+lens is doing
+ 
+
+ align:start position:0%
+lens is doing
+you know it's copying the light field
+
+ align:start position:0%
+you know it's copying the light field
+ 
+
+ align:start position:0%
+you know it's copying the light field
+right it's crea it's capturing the
+
+ align:start position:0%
+right it's crea it's capturing the
+ 
+
+ align:start position:0%
+right it's crea it's capturing the
+hologram of what's out there
+
+ align:start position:0%
+hologram of what's out there
+ 
+
+ align:start position:0%
+hologram of what's out there
+right this is using the popular
+
+ align:start position:0%
+right this is using the popular
+ 
+
+ align:start position:0%
+right this is using the popular
+terminology
+
+ align:start position:0%
+terminology
+ 
+
+ align:start position:0%
+terminology
+it's capturing the hologram of what
+
+ align:start position:0%
+it's capturing the hologram of what
+ 
+
+ align:start position:0%
+it's capturing the hologram of what
+what's out there it's recreating that
+
+ align:start position:0%
+what's out there it's recreating that
+ 
+
+ align:start position:0%
+what's out there it's recreating that
+hologram
+
+ align:start position:0%
+hologram
+ 
+
+ align:start position:0%
+hologram
+very close to the sensor
+
+ align:start position:0%
+very close to the sensor
+ 
+
+ align:start position:0%
+very close to the sensor
+and all that the sensor is doing is just
+
+ align:start position:0%
+and all that the sensor is doing is just
+ 
+
+ align:start position:0%
+and all that the sensor is doing is just
+recording that
+
+ align:start position:0%
+recording that
+ 
+
+ align:start position:0%
+recording that
+as a 2d image
+
+ align:start position:0%
+as a 2d image
+ 
+
+ align:start position:0%
+as a 2d image
+because the sensor doesn't have an
+
+ align:start position:0%
+because the sensor doesn't have an
+ 
+
+ align:start position:0%
+because the sensor doesn't have an
+ability to record in a traditional sense
+
+ align:start position:0%
+ability to record in a traditional sense
+ 
+
+ align:start position:0%
+ability to record in a traditional sense
+a 4d hologram it can always sense a 2d
+
+ align:start position:0%
+a 4d hologram it can always sense a 2d
+ 
+
+ align:start position:0%
+a 4d hologram it can always sense a 2d
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+and explain all of that at the speed of
+
+ align:start position:0%
+and explain all of that at the speed of
+ 
+
+ align:start position:0%
+and explain all of that at the speed of
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+isn't it great
+
+ align:start position:0%
+isn't it great
+ 
+
+ align:start position:0%
+isn't it great
+and that's why competition photograph is
+
+ align:start position:0%
+and that's why competition photograph is
+ 
+
+ align:start position:0%
+and that's why competition photograph is
+exciting because
+
+ align:start position:0%
+exciting because
+ 
+
+ align:start position:0%
+exciting because
+there's some work you can let the
+
+ align:start position:0%
+there's some work you can let the
+ 
+
+ align:start position:0%
+there's some work you can let the
+computer do
+
+ align:start position:0%
+computer do
+ 
+
+ align:start position:0%
+computer do
+and there's a lot of work you can just
+
+ align:start position:0%
+and there's a lot of work you can just
+ 
+
+ align:start position:0%
+and there's a lot of work you can just
+let the physics do for you but when the
+
+ align:start position:0%
+let the physics do for you but when the
+ 
+
+ align:start position:0%
+let the physics do for you but when the
+physics does it for you it happens at
+
+ align:start position:0%
+physics does it for you it happens at
+ 
+
+ align:start position:0%
+physics does it for you it happens at
+the speed of light with almost no
+
+ align:start position:0%
+the speed of light with almost no
+ 
+
+ align:start position:0%
+the speed of light with almost no
+additional cost
+
+ align:start position:0%
+additional cost
+ 
+
+ align:start position:0%
+additional cost
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+doing this core design
+
+ align:start position:0%
+doing this core design
+ 
+
+ align:start position:0%
+doing this core design
+of the physical
+
+ align:start position:0%
+of the physical
+ 
+
+ align:start position:0%
+of the physical
+uh device and the computational device
+
+ align:start position:0%
+uh device and the computational device
+ 
+
+ align:start position:0%
+uh device and the computational device
+brings in the real power in a
+
+ align:start position:0%
+brings in the real power in a
+ 
+
+ align:start position:0%
+brings in the real power in a
+competition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so uh let me switch to some other
+
+ align:start position:0%
+so uh let me switch to some other
+ 
+
+ align:start position:0%
+so uh let me switch to some other
+things i wanted to show you
+
+ align:start position:0%
+things i wanted to show you
+ 
+
+ align:start position:0%
+things i wanted to show you
+by the way is this all clear so far this
+
+ align:start position:0%
+by the way is this all clear so far this
+ 
+
+ align:start position:0%
+by the way is this all clear so far this
+part here
+
+ align:start position:0%
+part here
+ 
+
+ align:start position:0%
+part here
+this will be on your exam remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is this is the fun part
+
+ align:start position:0%
+this is this is the fun part
+ 
+
+ align:start position:0%
+this is this is the fun part
+all right so now that we understood all
+
+ align:start position:0%
+all right so now that we understood all
+ 
+
+ align:start position:0%
+all right so now that we understood all
+these concepts of
+
+ align:start position:0%
+these concepts of
+ 
+
+ align:start position:0%
+these concepts of
+uh rays and and flow space let's see how
+
+ align:start position:0%
+uh rays and and flow space let's see how
+ 
+
+ align:start position:0%
+uh rays and and flow space let's see how
+it impacts we already saw autofocus
+
+ align:start position:0%
+it impacts we already saw autofocus
+ 
+
+ align:start position:0%
+it impacts we already saw autofocus
+but let's see how it impacts some other
+
+ align:start position:0%
+but let's see how it impacts some other
+ 
+
+ align:start position:0%
+but let's see how it impacts some other
+elements of photography
+
+ align:start position:0%
+elements of photography
+ 
+
+ align:start position:0%
+elements of photography
+so let's say you have a point light
+
+ align:start position:0%
+so let's say you have a point light
+ 
+
+ align:start position:0%
+so let's say you have a point light
+you take the photo in sharp focus
+
+ align:start position:0%
+you take the photo in sharp focus
+ 
+
+ align:start position:0%
+you take the photo in sharp focus
+it looks like a point
+
+ align:start position:0%
+it looks like a point
+ 
+
+ align:start position:0%
+it looks like a point
+if you take that photo out of focus
+
+ align:start position:0%
+if you take that photo out of focus
+ 
+
+ align:start position:0%
+if you take that photo out of focus
+it appears as a disc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you look if you saw this
+
+ align:start position:0%
+and if you look if you saw this
+ 
+
+ align:start position:0%
+and if you look if you saw this
+resolution chart
+
+ align:start position:0%
+resolution chart
+ 
+
+ align:start position:0%
+resolution chart
+then it was blurred as well
+
+ align:start position:0%
+then it was blurred as well
+ 
+
+ align:start position:0%
+then it was blurred as well
+right and here's an example
+
+ align:start position:0%
+right and here's an example
+ 
+
+ align:start position:0%
+right and here's an example
+to answer in a question where we started
+
+ align:start position:0%
+to answer in a question where we started
+ 
+
+ align:start position:0%
+to answer in a question where we started
+with a 2d image
+
+ align:start position:0%
+with a 2d image
+ 
+
+ align:start position:0%
+with a 2d image
+and now we have another 2d image
+
+ align:start position:0%
+and now we have another 2d image
+ 
+
+ align:start position:0%
+and now we have another 2d image
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the blur the image was converged
+
+ align:start position:0%
+the blur the image was converged
+ 
+
+ align:start position:0%
+the blur the image was converged
+effectively by this disk so we took
+
+ align:start position:0%
+effectively by this disk so we took
+ 
+
+ align:start position:0%
+effectively by this disk so we took
+every point
+
+ align:start position:0%
+every point
+ 
+
+ align:start position:0%
+every point
+if it is grounded summed up all those
+
+ align:start position:0%
+if it is grounded summed up all those
+ 
+
+ align:start position:0%
+if it is grounded summed up all those
+values and assign it over there
+
+ align:start position:0%
+values and assign it over there
+ 
+
+ align:start position:0%
+values and assign it over there
+and which was achieved using the same
+
+ align:start position:0%
+and which was achieved using the same
+ 
+
+ align:start position:0%
+and which was achieved using the same
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+as this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+every every pixel in the world like this
+
+ align:start position:0%
+every every pixel in the world like this
+ 
+
+ align:start position:0%
+every every pixel in the world like this
+one here actually is contributing to a
+
+ align:start position:0%
+one here actually is contributing to a
+ 
+
+ align:start position:0%
+one here actually is contributing to a
+disk
+
+ align:start position:0%
+disk
+ 
+
+ align:start position:0%
+disk
+okay the other way to think about this
+
+ align:start position:0%
+okay the other way to think about this
+ 
+
+ align:start position:0%
+okay the other way to think about this
+if i just take one pixel here
+
+ align:start position:0%
+if i just take one pixel here
+ 
+
+ align:start position:0%
+if i just take one pixel here
+and go up
+
+ align:start position:0%
+and go up
+ 
+
+ align:start position:0%
+and go up
+vertically
+
+ align:start position:0%
+vertically
+ 
+
+ align:start position:0%
+vertically
+it's coming from different points in the
+
+ align:start position:0%
+it's coming from different points in the
+ 
+
+ align:start position:0%
+it's coming from different points in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+and that's how we can specify blood
+
+ align:start position:0%
+and that's how we can specify blood
+ 
+
+ align:start position:0%
+and that's how we can specify blood
+so now we have that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll come back to this later
+
+ align:start position:0%
+i'll come back to this later
+ 
+
+ align:start position:0%
+i'll come back to this later
+but every once in a while we can create
+
+ align:start position:0%
+but every once in a while we can create
+ 
+
+ align:start position:0%
+but every once in a while we can create
+some really interesting and this is
+
+ align:start position:0%
+some really interesting and this is
+ 
+
+ align:start position:0%
+some really interesting and this is
+called okay
+
+ align:start position:0%
+called okay
+ 
+
+ align:start position:0%
+called okay
+in in japanese
+
+ align:start position:0%
+in in japanese
+ 
+
+ align:start position:0%
+in in japanese
+what's the right way to say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and you know the exploitation of out
+
+ align:start position:0%
+and you know the exploitation of out
+ 
+
+ align:start position:0%
+and you know the exploitation of out
+out-of-focus blur
+
+ align:start position:0%
+out-of-focus blur
+ 
+
+ align:start position:0%
+out-of-focus blur
+but sometimes you can do some
+
+ align:start position:0%
+but sometimes you can do some
+ 
+
+ align:start position:0%
+but sometimes you can do some
+interesting things
+
+ align:start position:0%
+interesting things
+ 
+
+ align:start position:0%
+interesting things
+instead of keeping the aperture
+
+ align:start position:0%
+instead of keeping the aperture
+ 
+
+ align:start position:0%
+instead of keeping the aperture
+completely open
+
+ align:start position:0%
+completely open
+ 
+
+ align:start position:0%
+completely open
+you can insert
+
+ align:start position:0%
+you can insert
+ 
+
+ align:start position:0%
+you can insert
+a special pattern
+
+ align:start position:0%
+a special pattern
+ 
+
+ align:start position:0%
+a special pattern
+okay so we're going to place this
+
+ align:start position:0%
+okay so we're going to place this
+ 
+
+ align:start position:0%
+okay so we're going to place this
+crossword puzzle shape mask
+
+ align:start position:0%
+crossword puzzle shape mask
+ 
+
+ align:start position:0%
+crossword puzzle shape mask
+in the aperture
+
+ align:start position:0%
+in the aperture
+ 
+
+ align:start position:0%
+in the aperture
+and now if i take the photo out of focus
+
+ align:start position:0%
+and now if i take the photo out of focus
+ 
+
+ align:start position:0%
+and now if i take the photo out of focus
+instead of getting a disc
+
+ align:start position:0%
+instead of getting a disc
+ 
+
+ align:start position:0%
+instead of getting a disc
+the led that you saw earlier
+
+ align:start position:0%
+the led that you saw earlier
+ 
+
+ align:start position:0%
+the led that you saw earlier
+out of focus will appear something like
+
+ align:start position:0%
+out of focus will appear something like
+ 
+
+ align:start position:0%
+out of focus will appear something like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+7x7 pattern that you have here
+
+ align:start position:0%
+7x7 pattern that you have here
+ 
+
+ align:start position:0%
+7x7 pattern that you have here
+in the factory doorway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see these two lines
+
+ align:start position:0%
+you see these two lines
+ 
+
+ align:start position:0%
+you see these two lines
+and this whole pattern is exactly
+
+ align:start position:0%
+and this whole pattern is exactly
+ 
+
+ align:start position:0%
+and this whole pattern is exactly
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you can do some really
+
+ align:start position:0%
+okay so you can do some really
+ 
+
+ align:start position:0%
+okay so you can do some really
+interesting things with it
+
+ align:start position:0%
+interesting things with it
+ 
+
+ align:start position:0%
+interesting things with it
+uh so again
+
+ align:start position:0%
+uh so again
+ 
+
+ align:start position:0%
+uh so again
+photographers you know want to take
+
+ align:start position:0%
+photographers you know want to take
+ 
+
+ align:start position:0%
+photographers you know want to take
+pictures that have really beautiful okay
+
+ align:start position:0%
+pictures that have really beautiful okay
+ 
+
+ align:start position:0%
+pictures that have really beautiful okay
+so when it's really tiny aperture
+
+ align:start position:0%
+so when it's really tiny aperture
+ 
+
+ align:start position:0%
+so when it's really tiny aperture
+things are
+
+ align:start position:0%
+things are
+ 
+
+ align:start position:0%
+things are
+focused over large depth of field
+
+ align:start position:0%
+focused over large depth of field
+ 
+
+ align:start position:0%
+focused over large depth of field
+but with a very large aperture the
+
+ align:start position:0%
+but with a very large aperture the
+ 
+
+ align:start position:0%
+but with a very large aperture the
+background is completely out of works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now you can start playing some really
+
+ align:start position:0%
+now you can start playing some really
+ 
+
+ align:start position:0%
+now you can start playing some really
+interesting tricks
+
+ align:start position:0%
+interesting tricks
+ 
+
+ align:start position:0%
+interesting tricks
+you can take a seam
+
+ align:start position:0%
+you can take a seam
+ 
+
+ align:start position:0%
+you can take a seam
+which has this chinese price points on a
+
+ align:start position:0%
+which has this chinese price points on a
+ 
+
+ align:start position:0%
+which has this chinese price points on a
+specular fashion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in your aperture you can instead of
+
+ align:start position:0%
+and in your aperture you can instead of
+ 
+
+ align:start position:0%
+and in your aperture you can instead of
+putting the seven by seven
+
+ align:start position:0%
+putting the seven by seven
+ 
+
+ align:start position:0%
+putting the seven by seven
+uh crossword puzzle shape mask you can
+
+ align:start position:0%
+uh crossword puzzle shape mask you can
+ 
+
+ align:start position:0%
+uh crossword puzzle shape mask you can
+start putting some alphanumeric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characters okay so i'm going to take
+
+ align:start position:0%
+characters okay so i'm going to take
+ 
+
+ align:start position:0%
+characters okay so i'm going to take
+seven different pictures
+
+ align:start position:0%
+seven different pictures
+ 
+
+ align:start position:0%
+seven different pictures
+one with this aperture
+
+ align:start position:0%
+one with this aperture
+ 
+
+ align:start position:0%
+one with this aperture
+one with this aperture one with this
+
+ align:start position:0%
+one with this aperture one with this
+ 
+
+ align:start position:0%
+one with this aperture one with this
+aperture
+
+ align:start position:0%
+aperture
+ 
+
+ align:start position:0%
+aperture
+and if you just take addition of those
+
+ align:start position:0%
+and if you just take addition of those
+ 
+
+ align:start position:0%
+and if you just take addition of those
+three photos so when you take a picture
+
+ align:start position:0%
+three photos so when you take a picture
+ 
+
+ align:start position:0%
+three photos so when you take a picture
+with this aperture you get a vertical
+
+ align:start position:0%
+with this aperture you get a vertical
+ 
+
+ align:start position:0%
+with this aperture you get a vertical
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+for every bright spot out of focus so
+
+ align:start position:0%
+for every bright spot out of focus so
+ 
+
+ align:start position:0%
+for every bright spot out of focus so
+this one you get sort of two line
+
+ align:start position:0%
+this one you get sort of two line
+ 
+
+ align:start position:0%
+this one you get sort of two line
+vertical line vertical line at a
+
+ align:start position:0%
+vertical line vertical line at a
+ 
+
+ align:start position:0%
+vertical line vertical line at a
+different position you just sum them up
+
+ align:start position:0%
+different position you just sum them up
+ 
+
+ align:start position:0%
+different position you just sum them up
+every auto focus part
+
+ align:start position:0%
+every auto focus part
+ 
+
+ align:start position:0%
+every auto focus part
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+have a better cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can
+
+ align:start position:0%
+so you can
+ 
+
+ align:start position:0%
+so you can
+i believe there's an animation here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can see letter eight
+
+ align:start position:0%
+so you can see letter eight
+ 
+
+ align:start position:0%
+so you can see letter eight
+appearing at all different places
+
+ align:start position:0%
+appearing at all different places
+ 
+
+ align:start position:0%
+appearing at all different places
+so let's try to understand what's going
+
+ align:start position:0%
+so let's try to understand what's going
+ 
+
+ align:start position:0%
+so let's try to understand what's going
+on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's with a disc aperture like a
+
+ align:start position:0%
+so that's with a disc aperture like a
+ 
+
+ align:start position:0%
+so that's with a disc aperture like a
+traditional aperture
+
+ align:start position:0%
+traditional aperture
+ 
+
+ align:start position:0%
+traditional aperture
+this is the one with
+
+ align:start position:0%
+this is the one with
+ 
+
+ align:start position:0%
+this is the one with
+some special
+
+ align:start position:0%
+some special
+ 
+
+ align:start position:0%
+some special
+okay and if you want you can even say
+
+ align:start position:0%
+okay and if you want you can even say
+ 
+
+ align:start position:0%
+okay and if you want you can even say
+happy birthday jennifer and we'll just
+
+ align:start position:0%
+happy birthday jennifer and we'll just
+ 
+
+ align:start position:0%
+happy birthday jennifer and we'll just
+show up there so if you take a picture
+
+ align:start position:0%
+show up there so if you take a picture
+ 
+
+ align:start position:0%
+show up there so if you take a picture
+of all the candles every candle will say
+
+ align:start position:0%
+of all the candles every candle will say
+ 
+
+ align:start position:0%
+of all the candles every candle will say
+happy birthday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so how's this taking place
+
+ align:start position:0%
+okay so how's this taking place
+ 
+
+ align:start position:0%
+okay so how's this taking place
+it's difficult to explain purely as
+
+ align:start position:0%
+it's difficult to explain purely as
+ 
+
+ align:start position:0%
+it's difficult to explain purely as
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+autofocus blur but if you think about
+
+ align:start position:0%
+autofocus blur but if you think about
+ 
+
+ align:start position:0%
+autofocus blur but if you think about
+what's going on over here it's right
+
+ align:start position:0%
+what's going on over here it's right
+ 
+
+ align:start position:0%
+what's going on over here it's right
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have our lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we have a sensor
+
+ align:start position:0%
+we have a sensor
+ 
+
+ align:start position:0%
+we have a sensor
+we have one candle or one bright spot
+
+ align:start position:0%
+we have one candle or one bright spot
+ 
+
+ align:start position:0%
+we have one candle or one bright spot
+if it's out of focus
+
+ align:start position:0%
+if it's out of focus
+ 
+
+ align:start position:0%
+if it's out of focus
+it will create a disk
+
+ align:start position:0%
+it will create a disk
+ 
+
+ align:start position:0%
+it will create a disk
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right but imagine you started putting
+
+ align:start position:0%
+right but imagine you started putting
+ 
+
+ align:start position:0%
+right but imagine you started putting
+some interesting character for
+
+ align:start position:0%
+some interesting character for
+ 
+
+ align:start position:0%
+some interesting character for
+simplicity i'm just going to make
+
+ align:start position:0%
+simplicity i'm just going to make
+ 
+
+ align:start position:0%
+simplicity i'm just going to make
+a 1 0 1 0
+
+ align:start position:0%
+a 1 0 1 0
+ 
+
+ align:start position:0%
+a 1 0 1 0
+so i'm going to put
+
+ align:start position:0%
+so i'm going to put
+ 
+
+ align:start position:0%
+so i'm going to put
+a film here
+
+ align:start position:0%
+a film here
+ 
+
+ align:start position:0%
+a film here
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+open
+
+ align:start position:0%
+open
+ 
+
+ align:start position:0%
+open
+closed
+
+ align:start position:0%
+closed
+ 
+
+ align:start position:0%
+closed
+open closed
+
+ align:start position:0%
+open closed
+ 
+
+ align:start position:0%
+open closed
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+in this part of the lens i will go
+
+ align:start position:0%
+in this part of the lens i will go
+ 
+
+ align:start position:0%
+in this part of the lens i will go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+so i'll get some value here this part of
+
+ align:start position:0%
+so i'll get some value here this part of
+ 
+
+ align:start position:0%
+so i'll get some value here this part of
+the lens is like blocked because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over here that goes through
+
+ align:start position:0%
+over here that goes through
+ 
+
+ align:start position:0%
+over here that goes through
+circuit
+
+ align:start position:0%
+circuit
+ 
+
+ align:start position:0%
+circuit
+here and this for the lens is part
+
+ align:start position:0%
+here and this for the lens is part
+ 
+
+ align:start position:0%
+here and this for the lens is part
+the pattern that we had here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that will be blur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if i put a different pattern here
+
+ align:start position:0%
+and if i put a different pattern here
+ 
+
+ align:start position:0%
+and if i put a different pattern here
+i will get a different
+
+ align:start position:0%
+i will get a different
+ 
+
+ align:start position:0%
+i will get a different
+and that's how you can code for the code
+
+ align:start position:0%
+and that's how you can code for the code
+ 
+
+ align:start position:0%
+and that's how you can code for the code
+in the country
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you think about this
+
+ align:start position:0%
+how would you think about this
+ 
+
+ align:start position:0%
+how would you think about this
+in the expeditions
+
+ align:start position:0%
+in the expeditions
+ 
+
+ align:start position:0%
+in the expeditions
+but remember the world is not as simple
+
+ align:start position:0%
+but remember the world is not as simple
+ 
+
+ align:start position:0%
+but remember the world is not as simple
+there is not this point but there are a
+
+ align:start position:0%
+there is not this point but there are a
+ 
+
+ align:start position:0%
+there is not this point but there are a
+whole bunch of things going on here and
+
+ align:start position:0%
+whole bunch of things going on here and
+ 
+
+ align:start position:0%
+whole bunch of things going on here and
+all of them are interactions
+
+ align:start position:0%
+all of them are interactions
+ 
+
+ align:start position:0%
+all of them are interactions
+if you go to the exterior space what we
+
+ align:start position:0%
+if you go to the exterior space what we
+ 
+
+ align:start position:0%
+if you go to the exterior space what we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+you have the x space here he does this
+
+ align:start position:0%
+you have the x space here he does this
+ 
+
+ align:start position:0%
+you have the x space here he does this
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and by blocking
+
+ align:start position:0%
+and by blocking
+ 
+
+ align:start position:0%
+and by blocking
+uh this part and this part what i'm
+
+ align:start position:0%
+uh this part and this part what i'm
+ 
+
+ align:start position:0%
+uh this part and this part what i'm
+saying is that the top is fine i have
+
+ align:start position:0%
+saying is that the top is fine i have
+ 
+
+ align:start position:0%
+saying is that the top is fine i have
+blocked this part
+
+ align:start position:0%
+blocked this part
+ 
+
+ align:start position:0%
+blocked this part
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+this is delicate basically
+
+ align:start position:0%
+this is delicate basically
+ 
+
+ align:start position:0%
+this is delicate basically
+and this part is open that's fine and
+
+ align:start position:0%
+and this part is open that's fine and
+ 
+
+ align:start position:0%
+and this part is open that's fine and
+then again the bottom part is deleted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what the optical system is doing here
+
+ align:start position:0%
+so what the optical system is doing here
+ 
+
+ align:start position:0%
+so what the optical system is doing here
+is taking the right fit from outside and
+
+ align:start position:0%
+is taking the right fit from outside and
+ 
+
+ align:start position:0%
+is taking the right fit from outside and
+it's just deleting all the ways here
+
+ align:start position:0%
+it's just deleting all the ways here
+ 
+
+ align:start position:0%
+it's just deleting all the ways here
+it's just blocking all the links
+
+ align:start position:0%
+it's just blocking all the links
+ 
+
+ align:start position:0%
+it's just blocking all the links
+and then we take a picture
+
+ align:start position:0%
+and then we take a picture
+ 
+
+ align:start position:0%
+and then we take a picture
+in great and effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then again you can you can play this
+
+ align:start position:0%
+and then again you can you can play this
+ 
+
+ align:start position:0%
+and then again you can you can play this
+cheesy trick of taking multiple images
+
+ align:start position:0%
+cheesy trick of taking multiple images
+ 
+
+ align:start position:0%
+cheesy trick of taking multiple images
+with different blur
+
+ align:start position:0%
+with different blur
+ 
+
+ align:start position:0%
+with different blur
+and because of linearity which we
+
+ align:start position:0%
+and because of linearity which we
+ 
+
+ align:start position:0%
+and because of linearity which we
+discussed last time of light
+
+ align:start position:0%
+discussed last time of light
+ 
+
+ align:start position:0%
+discussed last time of light
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+you can just take the addition of two
+
+ align:start position:0%
+you can just take the addition of two
+ 
+
+ align:start position:0%
+you can just take the addition of two
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+to create an illusion that the aperture
+
+ align:start position:0%
+to create an illusion that the aperture
+ 
+
+ align:start position:0%
+to create an illusion that the aperture
+actually had
+
+ align:start position:0%
+actually had
+ 
+
+ align:start position:0%
+actually had
+those three apertures
+
+ align:start position:0%
+those three apertures
+ 
+
+ align:start position:0%
+those three apertures
+so instead of putting a seven
+
+ align:start position:0%
+so instead of putting a seven
+ 
+
+ align:start position:0%
+so instead of putting a seven
+in the in the aperture and taking one
+
+ align:start position:0%
+in the in the aperture and taking one
+ 
+
+ align:start position:0%
+in the in the aperture and taking one
+picture you can take three pictures with
+
+ align:start position:0%
+picture you can take three pictures with
+ 
+
+ align:start position:0%
+picture you can take three pictures with
+each of those different apertures and
+
+ align:start position:0%
+each of those different apertures and
+ 
+
+ align:start position:0%
+each of those different apertures and
+just take some of that
+
+ align:start position:0%
+just take some of that
+ 
+
+ align:start position:0%
+just take some of that
+and that's the beauty of light and
+
+ align:start position:0%
+and that's the beauty of light and
+ 
+
+ align:start position:0%
+and that's the beauty of light and
+interaction of light at normal
+
+ align:start position:0%
+interaction of light at normal
+ 
+
+ align:start position:0%
+interaction of light at normal
+intensities you can
+
+ align:start position:0%
+intensities you can
+ 
+
+ align:start position:0%
+intensities you can
+first take a picture and then take an
+
+ align:start position:0%
+first take a picture and then take an
+ 
+
+ align:start position:0%
+first take a picture and then take an
+addition
+
+ align:start position:0%
+addition
+ 
+
+ align:start position:0%
+addition
+as opposed to adding it
+
+ align:start position:0%
+as opposed to adding it
+ 
+
+ align:start position:0%
+as opposed to adding it
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in the physical domain and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is good
+
+ align:start position:0%
+this is good
+ 
+
+ align:start position:0%
+this is good
+so it's a fun project somebody wants to
+
+ align:start position:0%
+so it's a fun project somebody wants to
+ 
+
+ align:start position:0%
+so it's a fun project somebody wants to
+try it out you know
+
+ align:start position:0%
+try it out you know
+ 
+
+ align:start position:0%
+try it out you know
+create nice bouquet
+
+ align:start position:0%
+create nice bouquet
+ 
+
+ align:start position:0%
+create nice bouquet
+beautiful patterns you can also put an
+
+ align:start position:0%
+beautiful patterns you can also put an
+ 
+
+ align:start position:0%
+beautiful patterns you can also put an
+lcd
+
+ align:start position:0%
+lcd
+ 
+
+ align:start position:0%
+lcd
+in the aperture so it's not just a film
+
+ align:start position:0%
+in the aperture so it's not just a film
+ 
+
+ align:start position:0%
+in the aperture so it's not just a film
+and you can change the lcd
+
+ align:start position:0%
+and you can change the lcd
+ 
+
+ align:start position:0%
+and you can change the lcd
+so that depending on the depending on
+
+ align:start position:0%
+so that depending on the depending on
+ 
+
+ align:start position:0%
+so that depending on the depending on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+event you can change the different
+
+ align:start position:0%
+event you can change the different
+ 
+
+ align:start position:0%
+event you can change the different
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+and you know you'll get very interesting
+
+ align:start position:0%
+and you know you'll get very interesting
+ 
+
+ align:start position:0%
+and you know you'll get very interesting
+effects for the folks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's going on with animal eyes and
+
+ align:start position:0%
+so what's going on with animal eyes and
+ 
+
+ align:start position:0%
+so what's going on with animal eyes and
+we'll have a full lecture
+
+ align:start position:0%
+we'll have a full lecture
+ 
+
+ align:start position:0%
+we'll have a full lecture
+a little bit later on animal eyes
+
+ align:start position:0%
+a little bit later on animal eyes
+ 
+
+ align:start position:0%
+a little bit later on animal eyes
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+compound eyes of animals are also very
+
+ align:start position:0%
+compound eyes of animals are also very
+ 
+
+ align:start position:0%
+compound eyes of animals are also very
+interesting these are basically area of
+
+ align:start position:0%
+interesting these are basically area of
+ 
+
+ align:start position:0%
+interesting these are basically area of
+lenses
+
+ align:start position:0%
+lenses
+ 
+
+ align:start position:0%
+lenses
+okay but
+
+ align:start position:0%
+okay but
+ 
+
+ align:start position:0%
+okay but
+there's hundreds of hundreds of them
+
+ align:start position:0%
+there's hundreds of hundreds of them
+ 
+
+ align:start position:0%
+there's hundreds of hundreds of them
+um and this is kind of an artistic
+
+ align:start position:0%
+um and this is kind of an artistic
+ 
+
+ align:start position:0%
+um and this is kind of an artistic
+rendering of what
+
+ align:start position:0%
+rendering of what
+ 
+
+ align:start position:0%
+rendering of what
+the creature must be seeing you know
+
+ align:start position:0%
+the creature must be seeing you know
+ 
+
+ align:start position:0%
+the creature must be seeing you know
+just an area of very tiny images
+
+ align:start position:0%
+just an area of very tiny images
+ 
+
+ align:start position:0%
+just an area of very tiny images
+which is not true as we will see later
+
+ align:start position:0%
+which is not true as we will see later
+ 
+
+ align:start position:0%
+which is not true as we will see later
+but that's how the rendition looks like
+
+ align:start position:0%
+but that's how the rendition looks like
+ 
+
+ align:start position:0%
+but that's how the rendition looks like
+so there are projects such as uh tombow
+
+ align:start position:0%
+so there are projects such as uh tombow
+ 
+
+ align:start position:0%
+so there are projects such as uh tombow
+which tries to mimic this concept
+
+ align:start position:0%
+which tries to mimic this concept
+ 
+
+ align:start position:0%
+which tries to mimic this concept
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+to basically reduce the thickness of
+
+ align:start position:0%
+to basically reduce the thickness of
+ 
+
+ align:start position:0%
+to basically reduce the thickness of
+your camera
+
+ align:start position:0%
+your camera
+ 
+
+ align:start position:0%
+your camera
+okay so if you have a
+
+ align:start position:0%
+okay so if you have a
+ 
+
+ align:start position:0%
+okay so if you have a
+35 millimeter lens it will be about 35
+
+ align:start position:0%
+35 millimeter lens it will be about 35
+ 
+
+ align:start position:0%
+35 millimeter lens it will be about 35
+millimeters deep
+
+ align:start position:0%
+millimeters deep
+ 
+
+ align:start position:0%
+millimeters deep
+but imagine if you want to create a
+
+ align:start position:0%
+but imagine if you want to create a
+ 
+
+ align:start position:0%
+but imagine if you want to create a
+camera that's really really thin
+
+ align:start position:0%
+camera that's really really thin
+ 
+
+ align:start position:0%
+camera that's really really thin
+one way of thinking about that is i can
+
+ align:start position:0%
+one way of thinking about that is i can
+ 
+
+ align:start position:0%
+one way of thinking about that is i can
+just split
+
+ align:start position:0%
+just split
+ 
+
+ align:start position:0%
+just split
+my lens into a set of tiny links
+
+ align:start position:0%
+my lens into a set of tiny links
+ 
+
+ align:start position:0%
+my lens into a set of tiny links
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you go back to this diagram over
+
+ align:start position:0%
+so if you go back to this diagram over
+ 
+
+ align:start position:0%
+so if you go back to this diagram over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+i have a sensor
+
+ align:start position:0%
+i have a sensor
+ 
+
+ align:start position:0%
+i have a sensor
+and lens light and maintenance i'll just
+
+ align:start position:0%
+and lens light and maintenance i'll just
+ 
+
+ align:start position:0%
+and lens light and maintenance i'll just
+get rid of this
+
+ align:start position:0%
+get rid of this
+ 
+
+ align:start position:0%
+get rid of this
+all i have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the question is can you do something
+
+ align:start position:0%
+and the question is can you do something
+ 
+
+ align:start position:0%
+and the question is can you do something
+useful for that
+
+ align:start position:0%
+useful for that
+ 
+
+ align:start position:0%
+useful for that
+any guesses what you can do what you
+
+ align:start position:0%
+any guesses what you can do what you
+ 
+
+ align:start position:0%
+any guesses what you can do what you
+cannot do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the situation
+
+ align:start position:0%
+that's the situation
+ 
+
+ align:start position:0%
+that's the situation
+so there's no mainlands
+
+ align:start position:0%
+so there's no mainlands
+ 
+
+ align:start position:0%
+so there's no mainlands
+out here
+
+ align:start position:0%
+out here
+ 
+
+ align:start position:0%
+out here
+every point in the world
+
+ align:start position:0%
+every point in the world
+ 
+
+ align:start position:0%
+every point in the world
+maps to
+
+ align:start position:0%
+maps to
+ 
+
+ align:start position:0%
+maps to
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+uh every block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just got rid of
+
+ align:start position:0%
+just got rid of
+ 
+
+ align:start position:0%
+just got rid of
+the transformation
+
+ align:start position:0%
+the transformation
+ 
+
+ align:start position:0%
+the transformation
+so if you have
+
+ align:start position:0%
+so if you have
+ 
+
+ align:start position:0%
+so if you have
+50 such lenses every point will be seen
+
+ align:start position:0%
+50 such lenses every point will be seen
+ 
+
+ align:start position:0%
+50 such lenses every point will be seen
+fifty times
+
+ align:start position:0%
+fifty times
+ 
+
+ align:start position:0%
+fifty times
+okay but each of the image is actually
+
+ align:start position:0%
+okay but each of the image is actually
+ 
+
+ align:start position:0%
+okay but each of the image is actually
+pretty long
+
+ align:start position:0%
+pretty long
+ 
+
+ align:start position:0%
+pretty long
+isn't this basically the same as uh the
+
+ align:start position:0%
+isn't this basically the same as uh the
+ 
+
+ align:start position:0%
+isn't this basically the same as uh the
+light peeled degree a little bit isn't
+
+ align:start position:0%
+light peeled degree a little bit isn't
+ 
+
+ align:start position:0%
+light peeled degree a little bit isn't
+this basically the same
+
+ align:start position:0%
+this basically the same
+ 
+
+ align:start position:0%
+this basically the same
+surface with smaller big rig
+
+ align:start position:0%
+surface with smaller big rig
+ 
+
+ align:start position:0%
+surface with smaller big rig
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+camera already yes yes okay so that's a
+
+ align:start position:0%
+camera already yes yes okay so that's a
+ 
+
+ align:start position:0%
+camera already yes yes okay so that's a
+good point right so
+
+ align:start position:0%
+good point right so
+ 
+
+ align:start position:0%
+good point right so
+let's say i tell you that you have a 16
+
+ align:start position:0%
+let's say i tell you that you have a 16
+ 
+
+ align:start position:0%
+let's say i tell you that you have a 16
+megapixel sensor
+
+ align:start position:0%
+megapixel sensor
+ 
+
+ align:start position:0%
+megapixel sensor
+okay a 16 megapixel in flatland you know
+
+ align:start position:0%
+okay a 16 megapixel in flatland you know
+ 
+
+ align:start position:0%
+okay a 16 megapixel in flatland you know
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+pixels
+
+ align:start position:0%
+pixels
+ 
+
+ align:start position:0%
+pixels
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you can use the 4000 pixels anywhere you
+
+ align:start position:0%
+you can use the 4000 pixels anywhere you
+ 
+
+ align:start position:0%
+you can use the 4000 pixels anywhere you
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+okay and you have some resolution in
+
+ align:start position:0%
+okay and you have some resolution in
+ 
+
+ align:start position:0%
+okay and you have some resolution in
+theta some resolution and x
+
+ align:start position:0%
+theta some resolution and x
+ 
+
+ align:start position:0%
+theta some resolution and x
+and if i don't use the right foot camera
+
+ align:start position:0%
+and if i don't use the right foot camera
+ 
+
+ align:start position:0%
+and if i don't use the right foot camera
+i have four thousand pieces
+
+ align:start position:0%
+i have four thousand pieces
+ 
+
+ align:start position:0%
+i have four thousand pieces
+if i place
+
+ align:start position:0%
+if i place
+ 
+
+ align:start position:0%
+if i place
+a light fill and let's say under each
+
+ align:start position:0%
+a light fill and let's say under each
+ 
+
+ align:start position:0%
+a light fill and let's say under each
+lens i get 10 pixels here
+
+ align:start position:0%
+lens i get 10 pixels here
+ 
+
+ align:start position:0%
+lens i get 10 pixels here
+i'm subdividing my lens into 10 zones
+
+ align:start position:0%
+i'm subdividing my lens into 10 zones
+ 
+
+ align:start position:0%
+i'm subdividing my lens into 10 zones
+right and my actual resolution is only
+
+ align:start position:0%
+right and my actual resolution is only
+ 
+
+ align:start position:0%
+right and my actual resolution is only
+400 so i have length slits going from 1
+
+ align:start position:0%
+400 so i have length slits going from 1
+ 
+
+ align:start position:0%
+400 so i have length slits going from 1
+to 400
+
+ align:start position:0%
+to 400
+ 
+
+ align:start position:0%
+to 400
+and under each transfer i have a pixel
+
+ align:start position:0%
+and under each transfer i have a pixel
+ 
+
+ align:start position:0%
+and under each transfer i have a pixel
+that's i have 10 pixels
+
+ align:start position:0%
+that's i have 10 pixels
+ 
+
+ align:start position:0%
+that's i have 10 pixels
+so in that sense my resolution in x is
+
+ align:start position:0%
+so in that sense my resolution in x is
+ 
+
+ align:start position:0%
+so in that sense my resolution in x is
+400 and the solution of theta is 10
+
+ align:start position:0%
+400 and the solution of theta is 10
+ 
+
+ align:start position:0%
+400 and the solution of theta is 10
+and you can see that in the x theta
+
+ align:start position:0%
+and you can see that in the x theta
+ 
+
+ align:start position:0%
+and you can see that in the x theta
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's this way so this is only 10
+
+ align:start position:0%
+it's this way so this is only 10
+ 
+
+ align:start position:0%
+it's this way so this is only 10
+and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measurements
+
+ align:start position:0%
+measurements
+ 
+
+ align:start position:0%
+measurements
+and i need to distribute that
+
+ align:start position:0%
+and i need to distribute that
+ 
+
+ align:start position:0%
+and i need to distribute that
+in a typical sensor all of them will go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly for one
+
+ align:start position:0%
+exactly for one
+ 
+
+ align:start position:0%
+exactly for one
+there is no theta resolution so i will
+
+ align:start position:0%
+there is no theta resolution so i will
+ 
+
+ align:start position:0%
+there is no theta resolution so i will
+have fourth of the pixels
+
+ align:start position:0%
+have fourth of the pixels
+ 
+
+ align:start position:0%
+have fourth of the pixels
+but no resolution and theta
+
+ align:start position:0%
+but no resolution and theta
+ 
+
+ align:start position:0%
+but no resolution and theta
+in a light fit camera i could have 400
+
+ align:start position:0%
+in a light fit camera i could have 400
+ 
+
+ align:start position:0%
+in a light fit camera i could have 400
+pixels and theta resolution of 10
+
+ align:start position:0%
+pixels and theta resolution of 10
+ 
+
+ align:start position:0%
+pixels and theta resolution of 10
+or i could go
+
+ align:start position:0%
+or i could go
+ 
+
+ align:start position:0%
+or i could go
+in in other directions where maybe this
+
+ align:start position:0%
+in in other directions where maybe this
+ 
+
+ align:start position:0%
+in in other directions where maybe this
+is even thicker and more thicker
+
+ align:start position:0%
+is even thicker and more thicker
+ 
+
+ align:start position:0%
+is even thicker and more thicker
+i could do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how far can i keep going so i started
+
+ align:start position:0%
+how far can i keep going so i started
+ 
+
+ align:start position:0%
+how far can i keep going so i started
+something very thin it's bad it's
+
+ align:start position:0%
+something very thin it's bad it's
+ 
+
+ align:start position:0%
+something very thin it's bad it's
+getting fatter with a total number of
+
+ align:start position:0%
+getting fatter with a total number of
+ 
+
+ align:start position:0%
+getting fatter with a total number of
+samples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i get rid of this main lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll give you a hint what you're
+
+ align:start position:0%
+i'll give you a hint what you're
+ 
+
+ align:start position:0%
+i'll give you a hint what you're
+indicating
+
+ align:start position:0%
+indicating
+ 
+
+ align:start position:0%
+indicating
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the opposite you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have flipped
+
+ align:start position:0%
+so you have flipped
+ 
+
+ align:start position:0%
+so you have flipped
+from this condition this situation
+
+ align:start position:0%
+from this condition this situation
+ 
+
+ align:start position:0%
+from this condition this situation
+because now what we have is if i have a
+
+ align:start position:0%
+because now what we have is if i have a
+ 
+
+ align:start position:0%
+because now what we have is if i have a
+word out here
+
+ align:start position:0%
+word out here
+ 
+
+ align:start position:0%
+word out here
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+then from every point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can resolve this theta to
+
+ align:start position:0%
+i can resolve this theta to
+ 
+
+ align:start position:0%
+i can resolve this theta to
+400 different lenses so this one is one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can measure light coming out of this
+
+ align:start position:0%
+i can measure light coming out of this
+ 
+
+ align:start position:0%
+i can measure light coming out of this
+point in 400 different directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but under each only had some fixes
+
+ align:start position:0%
+but under each only had some fixes
+ 
+
+ align:start position:0%
+but under each only had some fixes
+so this is what i got
+
+ align:start position:0%
+so this is what i got
+ 
+
+ align:start position:0%
+so this is what i got
+so the key lesson here
+
+ align:start position:0%
+so the key lesson here
+ 
+
+ align:start position:0%
+so the key lesson here
+is that a lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and without a lens we are basically
+
+ align:start position:0%
+and without a lens we are basically
+ 
+
+ align:start position:0%
+and without a lens we are basically
+flipping
+
+ align:start position:0%
+flipping
+ 
+
+ align:start position:0%
+flipping
+the resolution in x and theta
+
+ align:start position:0%
+the resolution in x and theta
+ 
+
+ align:start position:0%
+the resolution in x and theta
+if you have less you get more special
+
+ align:start position:0%
+if you have less you get more special
+ 
+
+ align:start position:0%
+if you have less you get more special
+resolution but a little bit angle of
+
+ align:start position:0%
+resolution but a little bit angle of
+ 
+
+ align:start position:0%
+resolution but a little bit angle of
+position which is an ideal case the
+
+ align:start position:0%
+position which is an ideal case the
+ 
+
+ align:start position:0%
+position which is an ideal case the
+world doesn't change that much if you
+
+ align:start position:0%
+world doesn't change that much if you
+ 
+
+ align:start position:0%
+world doesn't change that much if you
+change the viewpoint
+
+ align:start position:0%
+change the viewpoint
+ 
+
+ align:start position:0%
+change the viewpoint
+but in certain case scenarios as we see
+
+ align:start position:0%
+but in certain case scenarios as we see
+ 
+
+ align:start position:0%
+but in certain case scenarios as we see
+that there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is very far away right
+
+ align:start position:0%
+is very far away right
+ 
+
+ align:start position:0%
+is very far away right
+i don't need to sample this point in
+
+ align:start position:0%
+i don't need to sample this point in
+ 
+
+ align:start position:0%
+i don't need to sample this point in
+4000 different directions 400 different
+
+ align:start position:0%
+4000 different directions 400 different
+ 
+
+ align:start position:0%
+4000 different directions 400 different
+directions i'm getting a sample in 10
+
+ align:start position:0%
+directions i'm getting a sample in 10
+ 
+
+ align:start position:0%
+directions i'm getting a sample in 10
+different directions
+
+ align:start position:0%
+different directions
+ 
+
+ align:start position:0%
+different directions
+and then having the lenses
+
+ align:start position:0%
+and then having the lenses
+ 
+
+ align:start position:0%
+and then having the lenses
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but what note is saying is i can start
+
+ align:start position:0%
+but what note is saying is i can start
+ 
+
+ align:start position:0%
+but what note is saying is i can start
+coming closer
+
+ align:start position:0%
+coming closer
+ 
+
+ align:start position:0%
+coming closer
+a bit longer very close now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those 400 directions are sufficiently
+
+ align:start position:0%
+those 400 directions are sufficiently
+ 
+
+ align:start position:0%
+those 400 directions are sufficiently
+wide
+
+ align:start position:0%
+wide
+ 
+
+ align:start position:0%
+wide
+they're spanning
+
+ align:start position:0%
+they're spanning
+ 
+
+ align:start position:0%
+they're spanning
+more times
+
+ align:start position:0%
+more times
+ 
+
+ align:start position:0%
+more times
+and it's become really really close
+
+ align:start position:0%
+and it's become really really close
+ 
+
+ align:start position:0%
+and it's become really really close
+right and it's almost minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+then i really want to see all these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the analogy of what happens
+
+ align:start position:0%
+and then the analogy of what happens
+ 
+
+ align:start position:0%
+and then the analogy of what happens
+when you go from here to here
+
+ align:start position:0%
+when you go from here to here
+ 
+
+ align:start position:0%
+when you go from here to here
+is that remember the length system will
+
+ align:start position:0%
+is that remember the length system will
+ 
+
+ align:start position:0%
+is that remember the length system will
+do a very good job of mapping a 4d light
+
+ align:start position:0%
+do a very good job of mapping a 4d light
+ 
+
+ align:start position:0%
+do a very good job of mapping a 4d light
+fluid
+
+ align:start position:0%
+fluid
+ 
+
+ align:start position:0%
+fluid
+for the real world
+
+ align:start position:0%
+for the real world
+ 
+
+ align:start position:0%
+for the real world
+into a 4d light thread
+
+ align:start position:0%
+into a 4d light thread
+ 
+
+ align:start position:0%
+into a 4d light thread
+on the on the inside inside the camera
+
+ align:start position:0%
+on the on the inside inside the camera
+ 
+
+ align:start position:0%
+on the on the inside inside the camera
+and again again hologram
+
+ align:start position:0%
+and again again hologram
+ 
+
+ align:start position:0%
+and again again hologram
+but when you don't have lines
+
+ align:start position:0%
+but when you don't have lines
+ 
+
+ align:start position:0%
+but when you don't have lines
+that's not true anymore
+
+ align:start position:0%
+that's not true anymore
+ 
+
+ align:start position:0%
+that's not true anymore
+you have a light fit
+
+ align:start position:0%
+you have a light fit
+ 
+
+ align:start position:0%
+you have a light fit
+here and have a similar light fill here
+
+ align:start position:0%
+here and have a similar light fill here
+ 
+
+ align:start position:0%
+here and have a similar light fill here
+for this plane
+
+ align:start position:0%
+for this plane
+ 
+
+ align:start position:0%
+for this plane
+like you imagine you put a holographic
+
+ align:start position:0%
+like you imagine you put a holographic
+ 
+
+ align:start position:0%
+like you imagine you put a holographic
+and the hologram has exactly 10
+
+ align:start position:0%
+and the hologram has exactly 10
+ 
+
+ align:start position:0%
+and the hologram has exactly 10
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+so it's a 400 pixel program it has
+
+ align:start position:0%
+so it's a 400 pixel program it has
+ 
+
+ align:start position:0%
+so it's a 400 pixel program it has
+exactly 10 directions
+
+ align:start position:0%
+exactly 10 directions
+ 
+
+ align:start position:0%
+exactly 10 directions
+if i want to capture that i should try
+
+ align:start position:0%
+if i want to capture that i should try
+ 
+
+ align:start position:0%
+if i want to capture that i should try
+and see
+
+ align:start position:0%
+and see
+ 
+
+ align:start position:0%
+and see
+but if i have a hologram
+
+ align:start position:0%
+but if i have a hologram
+ 
+
+ align:start position:0%
+but if i have a hologram
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+i have only 10 pixels
+
+ align:start position:0%
+i have only 10 pixels
+ 
+
+ align:start position:0%
+i have only 10 pixels
+and it has 400 different directions i'm
+
+ align:start position:0%
+and it has 400 different directions i'm
+ 
+
+ align:start position:0%
+and it has 400 different directions i'm
+so close to it
+
+ align:start position:0%
+so close to it
+ 
+
+ align:start position:0%
+so close to it
+then it makes sense to get another lens
+
+ align:start position:0%
+then it makes sense to get another lens
+ 
+
+ align:start position:0%
+then it makes sense to get another lens
+so in microscopy and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh mark lovato has done some work in
+
+ align:start position:0%
+so uh mark lovato has done some work in
+ 
+
+ align:start position:0%
+so uh mark lovato has done some work in
+life in
+
+ align:start position:0%
+life in
+ 
+
+ align:start position:0%
+life in
+in microscopes
+
+ align:start position:0%
+in microscopes
+ 
+
+ align:start position:0%
+in microscopes
+it uses different modifications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the example that we saw for um
+
+ align:start position:0%
+and the example that we saw for um
+ 
+
+ align:start position:0%
+and the example that we saw for um
+shot curtain on the sensor for
+
+ align:start position:0%
+shot curtain on the sensor for
+ 
+
+ align:start position:0%
+shot curtain on the sensor for
+looking at the apparition of a point
+
+ align:start position:0%
+looking at the apparition of a point
+ 
+
+ align:start position:0%
+looking at the apparition of a point
+light they didn't use the mainland
+
+ align:start position:0%
+light they didn't use the mainland
+ 
+
+ align:start position:0%
+light they didn't use the mainland
+because i expected to see
+
+ align:start position:0%
+because i expected to see
+ 
+
+ align:start position:0%
+because i expected to see
+a point that's very very far away
+
+ align:start position:0%
+a point that's very very far away
+ 
+
+ align:start position:0%
+a point that's very very far away
+but they're not they're not interested
+
+ align:start position:0%
+but they're not they're not interested
+ 
+
+ align:start position:0%
+but they're not they're not interested
+in taking an image of the point with the
+
+ align:start position:0%
+in taking an image of the point with the
+ 
+
+ align:start position:0%
+in taking an image of the point with the
+setup they're just interested in finding
+
+ align:start position:0%
+setup they're just interested in finding
+ 
+
+ align:start position:0%
+setup they're just interested in finding
+the operation
+
+ align:start position:0%
+the operation
+ 
+
+ align:start position:0%
+the operation
+so if you have a point very far away and
+
+ align:start position:0%
+so if you have a point very far away and
+ 
+
+ align:start position:0%
+so if you have a point very far away and
+the waves are coming straight i don't
+
+ align:start position:0%
+the waves are coming straight i don't
+ 
+
+ align:start position:0%
+the waves are coming straight i don't
+need a main lens if you're coming
+
+ align:start position:0%
+need a main lens if you're coming
+ 
+
+ align:start position:0%
+need a main lens if you're coming
+straight all the images are the center
+
+ align:start position:0%
+straight all the images are the center
+ 
+
+ align:start position:0%
+straight all the images are the center
+and with elaboration
+
+ align:start position:0%
+and with elaboration
+ 
+
+ align:start position:0%
+and with elaboration
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sharp images are offset
+
+ align:start position:0%
+sharp images are offset
+ 
+
+ align:start position:0%
+sharp images are offset
+so there are many configurations when
+
+ align:start position:0%
+so there are many configurations when
+ 
+
+ align:start position:0%
+so there are many configurations when
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+when you
+
+ align:start position:0%
+when you
+ 
+
+ align:start position:0%
+when you
+can decide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one thought experiment for you would
+
+ align:start position:0%
+and one thought experiment for you would
+ 
+
+ align:start position:0%
+and one thought experiment for you would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+what happens if there is more than one
+
+ align:start position:0%
+what happens if there is more than one
+ 
+
+ align:start position:0%
+what happens if there is more than one
+less element or more than one answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you should look up something called
+
+ align:start position:0%
+so you should look up something called
+ 
+
+ align:start position:0%
+so you should look up something called
+the poor
+
+ align:start position:0%
+the poor
+ 
+
+ align:start position:0%
+the poor
+superlets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a very fun
+
+ align:start position:0%
+it's a very fun
+ 
+
+ align:start position:0%
+it's a very fun
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it has very interesting properties
+
+ align:start position:0%
+and it has very interesting properties
+ 
+
+ align:start position:0%
+and it has very interesting properties
+because the focal length of that lens is
+
+ align:start position:0%
+because the focal length of that lens is
+ 
+
+ align:start position:0%
+because the focal length of that lens is
+dependent on the depth
+
+ align:start position:0%
+dependent on the depth
+ 
+
+ align:start position:0%
+dependent on the depth
+in a traditional lens
+
+ align:start position:0%
+in a traditional lens
+ 
+
+ align:start position:0%
+in a traditional lens
+it bends it copies of the light field
+
+ align:start position:0%
+it bends it copies of the light field
+ 
+
+ align:start position:0%
+it bends it copies of the light field
+from its side of the right hand side
+
+ align:start position:0%
+from its side of the right hand side
+ 
+
+ align:start position:0%
+from its side of the right hand side
+but for the cover support lens
+
+ align:start position:0%
+but for the cover support lens
+ 
+
+ align:start position:0%
+but for the cover support lens
+it does have a strange transformation
+
+ align:start position:0%
+it does have a strange transformation
+ 
+
+ align:start position:0%
+it does have a strange transformation
+i think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and once you start thinking about
+
+ align:start position:0%
+and once you start thinking about
+ 
+
+ align:start position:0%
+and once you start thinking about
+uh the world as not just 2d but 4d
+
+ align:start position:0%
+uh the world as not just 2d but 4d
+ 
+
+ align:start position:0%
+uh the world as not just 2d but 4d
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a photograph having not just a position
+
+ align:start position:0%
+a photograph having not just a position
+ 
+
+ align:start position:0%
+a photograph having not just a position
+coordinate but also an angle coordinate
+
+ align:start position:0%
+coordinate but also an angle coordinate
+ 
+
+ align:start position:0%
+coordinate but also an angle coordinate
+you realize there are lots of other
+
+ align:start position:0%
+you realize there are lots of other
+ 
+
+ align:start position:0%
+you realize there are lots of other
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+where this 4d representation starts
+
+ align:start position:0%
+where this 4d representation starts
+ 
+
+ align:start position:0%
+where this 4d representation starts
+making sense
+
+ align:start position:0%
+making sense
+ 
+
+ align:start position:0%
+making sense
+so near the end of the semester we'll be
+
+ align:start position:0%
+so near the end of the semester we'll be
+ 
+
+ align:start position:0%
+so near the end of the semester we'll be
+studying
+
+ align:start position:0%
+studying
+ 
+
+ align:start position:0%
+studying
+medical imaging and scientific imaging
+
+ align:start position:0%
+medical imaging and scientific imaging
+ 
+
+ align:start position:0%
+medical imaging and scientific imaging
+uh using tomography and and
+
+ align:start position:0%
+uh using tomography and and
+ 
+
+ align:start position:0%
+uh using tomography and and
+deconvolution and so on and all those
+
+ align:start position:0%
+deconvolution and so on and all those
+ 
+
+ align:start position:0%
+deconvolution and so on and all those
+concepts you know cat scan machine they
+
+ align:start position:0%
+concepts you know cat scan machine they
+ 
+
+ align:start position:0%
+concepts you know cat scan machine they
+all work on this principle
+
+ align:start position:0%
+all work on this principle
+ 
+
+ align:start position:0%
+all work on this principle
+of being sensitive to position as well
+
+ align:start position:0%
+of being sensitive to position as well
+ 
+
+ align:start position:0%
+of being sensitive to position as well
+as angle
+
+ align:start position:0%
+as angle
+ 
+
+ align:start position:0%
+as angle
+so in case of a flat scan machine
+
+ align:start position:0%
+so in case of a flat scan machine
+ 
+
+ align:start position:0%
+so in case of a flat scan machine
+you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically have
+
+ align:start position:0%
+basically have
+ 
+
+ align:start position:0%
+basically have
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what is it doing inside it has
+
+ align:start position:0%
+but what is it doing inside it has
+ 
+
+ align:start position:0%
+but what is it doing inside it has
+a set of detectors
+
+ align:start position:0%
+a set of detectors
+ 
+
+ align:start position:0%
+a set of detectors
+and an emitter
+
+ align:start position:0%
+and an emitter
+ 
+
+ align:start position:0%
+and an emitter
+and your head is in here
+
+ align:start position:0%
+and your head is in here
+ 
+
+ align:start position:0%
+and your head is in here
+you turn on this x-ray source
+
+ align:start position:0%
+you turn on this x-ray source
+ 
+
+ align:start position:0%
+you turn on this x-ray source
+and you take this image
+
+ align:start position:0%
+and you take this image
+ 
+
+ align:start position:0%
+and you take this image
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you move this light source
+
+ align:start position:0%
+then you move this light source
+ 
+
+ align:start position:0%
+then you move this light source
+and you take new shots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is basically capturing the
+
+ align:start position:0%
+and this is basically capturing the
+ 
+
+ align:start position:0%
+and this is basically capturing the
+light frame of the body using excess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to simplify this diagram
+
+ align:start position:0%
+to simplify this diagram
+ 
+
+ align:start position:0%
+to simplify this diagram
+imagine this is flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in case of x-rays the source is
+
+ align:start position:0%
+and in case of x-rays the source is
+ 
+
+ align:start position:0%
+and in case of x-rays the source is
+moving and the sensors are moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but to simplify this diagram imagine i
+
+ align:start position:0%
+but to simplify this diagram imagine i
+ 
+
+ align:start position:0%
+but to simplify this diagram imagine i
+flattened this set of pixels
+
+ align:start position:0%
+flattened this set of pixels
+ 
+
+ align:start position:0%
+flattened this set of pixels
+and i put the lights at
+
+ align:start position:0%
+and i put the lights at
+ 
+
+ align:start position:0%
+and i put the lights at
+different positions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be represented in the exterior space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it turns out that there is
+
+ align:start position:0%
+and then it turns out that there is
+ 
+
+ align:start position:0%
+and then it turns out that there is
+redundancy in your space
+
+ align:start position:0%
+redundancy in your space
+ 
+
+ align:start position:0%
+redundancy in your space
+such as if you have a voxel
+
+ align:start position:0%
+such as if you have a voxel
+ 
+
+ align:start position:0%
+such as if you have a voxel
+inside your body and independent of
+
+ align:start position:0%
+inside your body and independent of
+ 
+
+ align:start position:0%
+inside your body and independent of
+which direction the x-ray comes in
+
+ align:start position:0%
+which direction the x-ray comes in
+ 
+
+ align:start position:0%
+which direction the x-ray comes in
+which attenuates the same factor so
+
+ align:start position:0%
+which attenuates the same factor so
+ 
+
+ align:start position:0%
+which attenuates the same factor so
+there's bone or muscle or or blood
+
+ align:start position:0%
+there's bone or muscle or or blood
+ 
+
+ align:start position:0%
+there's bone or muscle or or blood
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+although your like field is four
+
+ align:start position:0%
+although your like field is four
+ 
+
+ align:start position:0%
+although your like field is four
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+the inherent data
+
+ align:start position:0%
+the inherent data
+ 
+
+ align:start position:0%
+the inherent data
+is only two or three dimension
+
+ align:start position:0%
+is only two or three dimension
+ 
+
+ align:start position:0%
+is only two or three dimension
+and so you can invert that and recover
+
+ align:start position:0%
+and so you can invert that and recover
+ 
+
+ align:start position:0%
+and so you can invert that and recover
+the opacity of each false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the same thing
+
+ align:start position:0%
+so the same thing
+ 
+
+ align:start position:0%
+so the same thing
+can be done with lightsaber
+
+ align:start position:0%
+can be done with lightsaber
+ 
+
+ align:start position:0%
+can be done with lightsaber
+if you capture this four-dimensional
+
+ align:start position:0%
+if you capture this four-dimensional
+ 
+
+ align:start position:0%
+if you capture this four-dimensional
+light fluid now you can go back
+
+ align:start position:0%
+light fluid now you can go back
+ 
+
+ align:start position:0%
+light fluid now you can go back
+and estimate the depth of every point in
+
+ align:start position:0%
+and estimate the depth of every point in
+ 
+
+ align:start position:0%
+and estimate the depth of every point in
+the scene
+
+ align:start position:0%
+the scene
+ 
+
+ align:start position:0%
+the scene
+so typically you use a stereo pair
+
+ align:start position:0%
+so typically you use a stereo pair
+ 
+
+ align:start position:0%
+so typically you use a stereo pair
+there's two cameras you can try to do
+
+ align:start position:0%
+there's two cameras you can try to do
+ 
+
+ align:start position:0%
+there's two cameras you can try to do
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correlation to estimate correspondence
+
+ align:start position:0%
+correlation to estimate correspondence
+ 
+
+ align:start position:0%
+correlation to estimate correspondence
+and a triangulation estimate
+
+ align:start position:0%
+and a triangulation estimate
+ 
+
+ align:start position:0%
+and a triangulation estimate
+but in your second assignment
+
+ align:start position:0%
+but in your second assignment
+ 
+
+ align:start position:0%
+but in your second assignment
+what you're going to do is capture the
+
+ align:start position:0%
+what you're going to do is capture the
+ 
+
+ align:start position:0%
+what you're going to do is capture the
+light field and directly from the light
+
+ align:start position:0%
+light field and directly from the light
+ 
+
+ align:start position:0%
+light field and directly from the light
+field estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the way you will do that is you'll
+
+ align:start position:0%
+and the way you will do that is you'll
+ 
+
+ align:start position:0%
+and the way you will do that is you'll
+basically line up those images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the point is in sharp focus the digit
+
+ align:start position:0%
+if the point is in sharp focus the digit
+ 
+
+ align:start position:0%
+if the point is in sharp focus the digit
+will be focusing all these values here
+
+ align:start position:0%
+will be focusing all these values here
+ 
+
+ align:start position:0%
+will be focusing all these values here
+will look the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if something is out of focus you
+
+ align:start position:0%
+but if something is out of focus you
+ 
+
+ align:start position:0%
+but if something is out of focus you
+need to shift and add
+
+ align:start position:0%
+need to shift and add
+ 
+
+ align:start position:0%
+need to shift and add
+right so you'll have to share it at some
+
+ align:start position:0%
+right so you'll have to share it at some
+ 
+
+ align:start position:0%
+right so you'll have to share it at some
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then all these values will be
+
+ align:start position:0%
+and then all these values will be
+ 
+
+ align:start position:0%
+and then all these values will be
+concerned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the fact that all the values are the
+
+ align:start position:0%
+and the fact that all the values are the
+ 
+
+ align:start position:0%
+and the fact that all the values are the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+indicates that now you can achieve a
+
+ align:start position:0%
+indicates that now you can achieve a
+ 
+
+ align:start position:0%
+indicates that now you can achieve a
+digital difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a great point so think about
+
+ align:start position:0%
+so that's a great point so think about
+ 
+
+ align:start position:0%
+so that's a great point so think about
+you have a point
+
+ align:start position:0%
+you have a point
+ 
+
+ align:start position:0%
+you have a point
+which is at different depths
+
+ align:start position:0%
+which is at different depths
+ 
+
+ align:start position:0%
+which is at different depths
+and you're saying that
+
+ align:start position:0%
+and you're saying that
+ 
+
+ align:start position:0%
+and you're saying that
+in flatland
+
+ align:start position:0%
+in flatland
+ 
+
+ align:start position:0%
+in flatland
+at the top of the image we shouldn't
+
+ align:start position:0%
+at the top of the image we shouldn't
+ 
+
+ align:start position:0%
+at the top of the image we shouldn't
+focus here in the middle of the
+
+ align:start position:0%
+focus here in the middle of the
+ 
+
+ align:start position:0%
+focus here in the middle of the
+dimension focus here and so on
+
+ align:start position:0%
+dimension focus here and so on
+ 
+
+ align:start position:0%
+dimension focus here and so on
+right so this is my plane or surface or
+
+ align:start position:0%
+right so this is my plane or surface or
+ 
+
+ align:start position:0%
+right so this is my plane or surface or
+focus rather than than this
+
+ align:start position:0%
+focus rather than than this
+ 
+
+ align:start position:0%
+focus rather than than this
+so all you have to do
+
+ align:start position:0%
+so all you have to do
+ 
+
+ align:start position:0%
+so all you have to do
+is for the top point
+
+ align:start position:0%
+is for the top point
+ 
+
+ align:start position:0%
+is for the top point
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+you have to keep a little bit more
+
+ align:start position:0%
+you have to keep a little bit more
+ 
+
+ align:start position:0%
+you have to keep a little bit more
+you have to do but i'll give you a very
+
+ align:start position:0%
+you have to do but i'll give you a very
+ 
+
+ align:start position:0%
+you have to do but i'll give you a very
+very high level flavor of pollution to
+
+ align:start position:0%
+very high level flavor of pollution to
+ 
+
+ align:start position:0%
+very high level flavor of pollution to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+for this point
+
+ align:start position:0%
+for this point
+ 
+
+ align:start position:0%
+for this point
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+we have a lens here
+
+ align:start position:0%
+we have a lens here
+ 
+
+ align:start position:0%
+we have a lens here
+for this particular direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiple
+
+ align:start position:0%
+multiple
+ 
+
+ align:start position:0%
+multiple
+cameras right for this particular
+
+ align:start position:0%
+cameras right for this particular
+ 
+
+ align:start position:0%
+cameras right for this particular
+direction you can just
+
+ align:start position:0%
+direction you can just
+ 
+
+ align:start position:0%
+direction you can just
+calibrate your world you put a box
+
+ align:start position:0%
+calibrate your world you put a box
+ 
+
+ align:start position:0%
+calibrate your world you put a box
+you know one meter wide and i can say
+
+ align:start position:0%
+you know one meter wide and i can say
+ 
+
+ align:start position:0%
+you know one meter wide and i can say
+within this box
+
+ align:start position:0%
+within this box
+ 
+
+ align:start position:0%
+within this box
+at the top left
+
+ align:start position:0%
+at the top left
+ 
+
+ align:start position:0%
+at the top left
+i want to be the focus to be in the top
+
+ align:start position:0%
+i want to be the focus to be in the top
+ 
+
+ align:start position:0%
+i want to be the focus to be in the top
+left the middle
+
+ align:start position:0%
+left the middle
+ 
+
+ align:start position:0%
+left the middle
+in the back of the frame and
+
+ align:start position:0%
+in the back of the frame and
+ 
+
+ align:start position:0%
+in the back of the frame and
+you just kind of did that
+
+ align:start position:0%
+you just kind of did that
+ 
+
+ align:start position:0%
+you just kind of did that
+you can move the camera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and say that all the rays that go here
+
+ align:start position:0%
+and say that all the rays that go here
+ 
+
+ align:start position:0%
+and say that all the rays that go here
+i'm going to add
+
+ align:start position:0%
+i'm going to add
+ 
+
+ align:start position:0%
+i'm going to add
+up but for the next pixel i'm not going
+
+ align:start position:0%
+up but for the next pixel i'm not going
+ 
+
+ align:start position:0%
+up but for the next pixel i'm not going
+to add up all those radar mode adders in
+
+ align:start position:0%
+to add up all those radar mode adders in
+ 
+
+ align:start position:0%
+to add up all those radar mode adders in
+other ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we issue that in the next three
+
+ align:start position:0%
+how do we issue that in the next three
+ 
+
+ align:start position:0%
+how do we issue that in the next three
+dozens
+
+ align:start position:0%
+dozens
+ 
+
+ align:start position:0%
+dozens
+we know that for a point here
+
+ align:start position:0%
+we know that for a point here
+ 
+
+ align:start position:0%
+we know that for a point here
+there will be some
+
+ align:start position:0%
+there will be some
+ 
+
+ align:start position:0%
+there will be some
+value over here
+
+ align:start position:0%
+value over here
+ 
+
+ align:start position:0%
+value over here
+but for a point here
+
+ align:start position:0%
+but for a point here
+ 
+
+ align:start position:0%
+but for a point here
+there is some kind of a slope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i just wanted to create an image
+
+ align:start position:0%
+if i just wanted to create an image
+ 
+
+ align:start position:0%
+if i just wanted to create an image
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+so let's take something very concrete if
+
+ align:start position:0%
+so let's take something very concrete if
+ 
+
+ align:start position:0%
+so let's take something very concrete if
+i were to focus on infinity i know i
+
+ align:start position:0%
+i were to focus on infinity i know i
+ 
+
+ align:start position:0%
+i were to focus on infinity i know i
+should just protect it straight up i
+
+ align:start position:0%
+should just protect it straight up i
+ 
+
+ align:start position:0%
+should just protect it straight up i
+just sum up everything along vertical
+
+ align:start position:0%
+just sum up everything along vertical
+ 
+
+ align:start position:0%
+just sum up everything along vertical
+mass
+
+ align:start position:0%
+mass
+ 
+
+ align:start position:0%
+mass
+if i want to
+
+ align:start position:0%
+if i want to
+ 
+
+ align:start position:0%
+if i want to
+focus somewhere closer i need to share
+
+ align:start position:0%
+focus somewhere closer i need to share
+ 
+
+ align:start position:0%
+focus somewhere closer i need to share
+this so i'm going to take this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and keep the event same space like that
+
+ align:start position:0%
+and keep the event same space like that
+ 
+
+ align:start position:0%
+and keep the event same space like that
+and i'm going to sum up these values
+
+ align:start position:0%
+and i'm going to sum up these values
+ 
+
+ align:start position:0%
+and i'm going to sum up these values
+okay and store the value i'm going to
+
+ align:start position:0%
+okay and store the value i'm going to
+ 
+
+ align:start position:0%
+okay and store the value i'm going to
+sum up these values and this means i'm
+
+ align:start position:0%
+sum up these values and this means i'm
+ 
+
+ align:start position:0%
+sum up these values and this means i'm
+focusing at this point
+
+ align:start position:0%
+focusing at this point
+ 
+
+ align:start position:0%
+focusing at this point
+if you want to focus on a slightly
+
+ align:start position:0%
+if you want to focus on a slightly
+ 
+
+ align:start position:0%
+if you want to focus on a slightly
+different plane
+
+ align:start position:0%
+different plane
+ 
+
+ align:start position:0%
+different plane
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's vertical is slanted for the focus
+
+ align:start position:0%
+it's vertical is slanted for the focus
+ 
+
+ align:start position:0%
+it's vertical is slanted for the focus
+of some other plane
+
+ align:start position:0%
+of some other plane
+ 
+
+ align:start position:0%
+of some other plane
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now your question is how can i do it
+
+ align:start position:0%
+so now your question is how can i do it
+ 
+
+ align:start position:0%
+so now your question is how can i do it
+differently for different pieces
+
+ align:start position:0%
+differently for different pieces
+ 
+
+ align:start position:0%
+differently for different pieces
+so on the edges i will just do vertical
+
+ align:start position:0%
+so on the edges i will just do vertical
+ 
+
+ align:start position:0%
+so on the edges i will just do vertical
+protection
+
+ align:start position:0%
+protection
+ 
+
+ align:start position:0%
+protection
+right in the middle i will do a standard
+
+ align:start position:0%
+right in the middle i will do a standard
+ 
+
+ align:start position:0%
+right in the middle i will do a standard
+protection
+
+ align:start position:0%
+protection
+ 
+
+ align:start position:0%
+protection
+and for all the places in between i will
+
+ align:start position:0%
+and for all the places in between i will
+ 
+
+ align:start position:0%
+and for all the places in between i will
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+less climbing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i'll come back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can imagine all the crazy tricks
+
+ align:start position:0%
+and you can imagine all the crazy tricks
+ 
+
+ align:start position:0%
+and you can imagine all the crazy tricks
+you can do
+
+ align:start position:0%
+you can do
+ 
+
+ align:start position:0%
+you can do
+so one part of your assignment
+
+ align:start position:0%
+so one part of your assignment
+ 
+
+ align:start position:0%
+so one part of your assignment
+you're going to look at
+
+ align:start position:0%
+you're going to look at
+ 
+
+ align:start position:0%
+you're going to look at
+you're going to look at
+
+ align:start position:0%
+you're going to look at
+ 
+
+ align:start position:0%
+you're going to look at
+you would have a seat
+
+ align:start position:0%
+you would have a seat
+ 
+
+ align:start position:0%
+you would have a seat
+and for that what i recommend you to do
+
+ align:start position:0%
+and for that what i recommend you to do
+ 
+
+ align:start position:0%
+and for that what i recommend you to do
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take your area of cameras
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then create some kind of offense
+
+ align:start position:0%
+and then create some kind of offense
+ 
+
+ align:start position:0%
+and then create some kind of offense
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in
+
+ align:start position:0%
+okay so in
+ 
+
+ align:start position:0%
+okay so in
+real world i'm guessing there's some
+
+ align:start position:0%
+real world i'm guessing there's some
+ 
+
+ align:start position:0%
+real world i'm guessing there's some
+kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is a see-through part
+
+ align:start position:0%
+it is a see-through part
+ 
+
+ align:start position:0%
+it is a see-through part
+and then there is some book or some
+
+ align:start position:0%
+and then there is some book or some
+ 
+
+ align:start position:0%
+and then there is some book or some
+painting back here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you're going to take 16 images
+
+ align:start position:0%
+and you're going to take 16 images
+ 
+
+ align:start position:0%
+and you're going to take 16 images
+and you'll and this is red and this is
+
+ align:start position:0%
+and you'll and this is red and this is
+ 
+
+ align:start position:0%
+and you'll and this is red and this is
+green
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh purely by focusing on the background
+
+ align:start position:0%
+uh purely by focusing on the background
+ 
+
+ align:start position:0%
+uh purely by focusing on the background
+so when you focus on the foreground you
+
+ align:start position:0%
+so when you focus on the foreground you
+ 
+
+ align:start position:0%
+so when you focus on the foreground you
+have to maybe shift the three pieces
+
+ align:start position:0%
+have to maybe shift the three pieces
+ 
+
+ align:start position:0%
+have to maybe shift the three pieces
+and shift on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+background but
+
+ align:start position:0%
+background but
+ 
+
+ align:start position:0%
+background but
+uh as an extra credit what you can do is
+
+ align:start position:0%
+uh as an extra credit what you can do is
+ 
+
+ align:start position:0%
+uh as an extra credit what you can do is
+not just refocus
+
+ align:start position:0%
+not just refocus
+ 
+
+ align:start position:0%
+not just refocus
+but also do some analysis
+
+ align:start position:0%
+but also do some analysis
+ 
+
+ align:start position:0%
+but also do some analysis
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh when you when you shift and add those
+
+ align:start position:0%
+uh when you when you shift and add those
+ 
+
+ align:start position:0%
+uh when you when you shift and add those
+pixels if all those pixels have the same
+
+ align:start position:0%
+pixels if all those pixels have the same
+ 
+
+ align:start position:0%
+pixels if all those pixels have the same
+value or not
+
+ align:start position:0%
+value or not
+ 
+
+ align:start position:0%
+value or not
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if the red object wasn't there and just
+
+ align:start position:0%
+if the red object wasn't there and just
+ 
+
+ align:start position:0%
+if the red object wasn't there and just
+focus on the green
+
+ align:start position:0%
+focus on the green
+ 
+
+ align:start position:0%
+focus on the green
+all the pixels here
+
+ align:start position:0%
+all the pixels here
+ 
+
+ align:start position:0%
+all the pixels here
+will be green
+
+ align:start position:0%
+will be green
+ 
+
+ align:start position:0%
+will be green
+all these values will be green
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if you have some object here some of
+
+ align:start position:0%
+but if you have some object here some of
+ 
+
+ align:start position:0%
+but if you have some object here some of
+these objects some of these pixels will
+
+ align:start position:0%
+these objects some of these pixels will
+ 
+
+ align:start position:0%
+these objects some of these pixels will
+be written
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this
+
+ align:start position:0%
+here this
+ 
+
+ align:start position:0%
+here this
+type the is
+
+ align:start position:0%
+type the is
+ 
+
+ align:start position:0%
+type the is
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+and access to the cameras
+
+ align:start position:0%
+and access to the cameras
+ 
+
+ align:start position:0%
+and access to the cameras
+so the image from the first camera
+
+ align:start position:0%
+so the image from the first camera
+ 
+
+ align:start position:0%
+so the image from the first camera
+is placed here
+
+ align:start position:0%
+is placed here
+ 
+
+ align:start position:0%
+is placed here
+the image from the second camera goes
+
+ align:start position:0%
+the image from the second camera goes
+ 
+
+ align:start position:0%
+the image from the second camera goes
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and because you're doing this problem
+
+ align:start position:0%
+and because you're doing this problem
+ 
+
+ align:start position:0%
+and because you're doing this problem
+only in one d every row is independent
+
+ align:start position:0%
+only in one d every row is independent
+ 
+
+ align:start position:0%
+only in one d every row is independent
+so think of this as on the center row of
+
+ align:start position:0%
+so think of this as on the center row of
+ 
+
+ align:start position:0%
+so think of this as on the center row of
+each of the system channels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so going back to this example of
+
+ align:start position:0%
+okay so going back to this example of
+ 
+
+ align:start position:0%
+okay so going back to this example of
+redwater cream
+
+ align:start position:0%
+redwater cream
+ 
+
+ align:start position:0%
+redwater cream
+you when you try to sample it
+
+ align:start position:0%
+you when you try to sample it
+ 
+
+ align:start position:0%
+you when you try to sample it
+you'll see that you can refocus on green
+
+ align:start position:0%
+you'll see that you can refocus on green
+ 
+
+ align:start position:0%
+you'll see that you can refocus on green
+and the object will look mostly green
+
+ align:start position:0%
+and the object will look mostly green
+ 
+
+ align:start position:0%
+and the object will look mostly green
+but then there's some reds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then you can do very simple
+
+ align:start position:0%
+but then you can do very simple
+ 
+
+ align:start position:0%
+but then you can do very simple
+outlier rejection and let's say 16
+
+ align:start position:0%
+outlier rejection and let's say 16
+ 
+
+ align:start position:0%
+outlier rejection and let's say 16
+cameras and only four of them so
+
+ align:start position:0%
+cameras and only four of them so
+ 
+
+ align:start position:0%
+cameras and only four of them so
+12 of those are green and only four of
+
+ align:start position:0%
+12 of those are green and only four of
+ 
+
+ align:start position:0%
+12 of those are green and only four of
+those are red
+
+ align:start position:0%
+those are red
+ 
+
+ align:start position:0%
+those are red
+you don't understand all 16.
+
+ align:start position:0%
+you don't understand all 16.
+ 
+
+ align:start position:0%
+you don't understand all 16.
+you can say what's my
+
+ align:start position:0%
+you can say what's my
+ 
+
+ align:start position:0%
+you can say what's my
+what's the color that's in my character
+
+ align:start position:0%
+what's the color that's in my character
+ 
+
+ align:start position:0%
+what's the color that's in my character
+and that color is green
+
+ align:start position:0%
+and that color is green
+ 
+
+ align:start position:0%
+and that color is green
+so you will not get a reddish tinge
+
+ align:start position:0%
+so you will not get a reddish tinge
+ 
+
+ align:start position:0%
+so you will not get a reddish tinge
+to your to your photo but you'll get
+
+ align:start position:0%
+to your to your photo but you'll get
+ 
+
+ align:start position:0%
+to your to your photo but you'll get
+crowded quality
+
+ align:start position:0%
+crowded quality
+ 
+
+ align:start position:0%
+crowded quality
+it's not a simple linear projection it's
+
+ align:start position:0%
+it's not a simple linear projection it's
+ 
+
+ align:start position:0%
+it's not a simple linear projection it's
+not just the sum of the pixels
+
+ align:start position:0%
+not just the sum of the pixels
+ 
+
+ align:start position:0%
+not just the sum of the pixels
+but you're going to throw out
+
+ align:start position:0%
+but you're going to throw out
+ 
+
+ align:start position:0%
+but you're going to throw out
+colors that
+
+ align:start position:0%
+colors that
+ 
+
+ align:start position:0%
+colors that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+in minority
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that will get much better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instructions in the assignment uh when
+
+ align:start position:0%
+instructions in the assignment uh when
+ 
+
+ align:start position:0%
+instructions in the assignment uh when
+you're taking the pictures make sure
+
+ align:start position:0%
+you're taking the pictures make sure
+ 
+
+ align:start position:0%
+you're taking the pictures make sure
+they are placed at equal distances
+
+ align:start position:0%
+they are placed at equal distances
+ 
+
+ align:start position:0%
+they are placed at equal distances
+and you know you hold the camera in
+
+ align:start position:0%
+and you know you hold the camera in
+ 
+
+ align:start position:0%
+and you know you hold the camera in
+parallel fashion
+
+ align:start position:0%
+parallel fashion
+ 
+
+ align:start position:0%
+parallel fashion
+make sure the scene it has vibrant
+
+ align:start position:0%
+make sure the scene it has vibrant
+ 
+
+ align:start position:0%
+make sure the scene it has vibrant
+colors
+
+ align:start position:0%
+colors
+ 
+
+ align:start position:0%
+colors
+so this color should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100 100
+
+ align:start position:0%
+100 100
+ 
+
+ align:start position:0%
+100 100
+pixel region of that
+
+ align:start position:0%
+pixel region of that
+ 
+
+ align:start position:0%
+pixel region of that
+and just run your code to make sure
+
+ align:start position:0%
+and just run your code to make sure
+ 
+
+ align:start position:0%
+and just run your code to make sure
+everything is done
+
+ align:start position:0%
+everything is done
+ 
+
+ align:start position:0%
+everything is done
+and then you can go and take your own
+
+ align:start position:0%
+and then you can go and take your own
+ 
+
+ align:start position:0%
+and then you can go and take your own
+images so even before it again
+
+ align:start position:0%
+images so even before it again
+ 
+
+ align:start position:0%
+images so even before it again
+run your code on those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you start with your own
+
+ align:start position:0%
+because if you start with your own
+ 
+
+ align:start position:0%
+because if you start with your own
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+and you're not getting the right results
+
+ align:start position:0%
+and you're not getting the right results
+ 
+
+ align:start position:0%
+and you're not getting the right results
+you don't know if the problem is your
+
+ align:start position:0%
+you don't know if the problem is your
+ 
+
+ align:start position:0%
+you don't know if the problem is your
+photos are with your phone
+
+ align:start position:0%
+photos are with your phone
+ 
+
+ align:start position:0%
+photos are with your phone
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+does photoshop allow you to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+images shift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but just because it's fine i have
+
+ align:start position:0%
+but just because it's fine i have
+ 
+
+ align:start position:0%
+but just because it's fine i have
+friends of course don't wait till the
+
+ align:start position:0%
+friends of course don't wait till the
+ 
+
+ align:start position:0%
+friends of course don't wait till the
+first day of whenever
+
+ align:start position:0%
+first day of whenever
+ 
+
+ align:start position:0%
+first day of whenever
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+start today because
+
+ align:start position:0%
+start today because
+ 
+
+ align:start position:0%
+start today because
+the the fun part of this lecture taking
+
+ align:start position:0%
+the the fun part of this lecture taking
+ 
+
+ align:start position:0%
+the the fun part of this lecture taking
+this image
+
+ align:start position:0%
+this image
+ 
+
+ align:start position:0%
+this image
+and creating scenarios where you can see
+
+ align:start position:0%
+and creating scenarios where you can see
+ 
+
+ align:start position:0%
+and creating scenarios where you can see
+through and you know they should go on
+
+ align:start position:0%
+through and you know they should go on
+ 
+
+ align:start position:0%
+through and you know they should go on
+the thicker page
+
+ align:start position:0%
+the thicker page
+ 
+
+ align:start position:0%
+the thicker page
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+you know we will comment on each other's
+
+ align:start position:0%
+you know we will comment on each other's
+ 
+
+ align:start position:0%
+you know we will comment on each other's
+uh each of the score uh for the first
+
+ align:start position:0%
+uh each of the score uh for the first
+ 
+
+ align:start position:0%
+uh each of the score uh for the first
+assignment only five out of several
+
+ align:start position:0%
+assignment only five out of several
+ 
+
+ align:start position:0%
+assignment only five out of several
+dozen submissions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so almost everybody got an a so you
+
+ align:start position:0%
+so almost everybody got an a so you
+ 
+
+ align:start position:0%
+so almost everybody got an a so you
+should feel good about yourself but
+
+ align:start position:0%
+should feel good about yourself but
+ 
+
+ align:start position:0%
+should feel good about yourself but
+somebody got a plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah make sure it's on flickr and all
+
+ align:start position:0%
+so yeah make sure it's on flickr and all
+ 
+
+ align:start position:0%
+so yeah make sure it's on flickr and all
+those three places
+
+ align:start position:0%
+those three places
+ 
+
+ align:start position:0%
+those three places
+and feel free to send me uh email you
+
+ align:start position:0%
+and feel free to send me uh email you
+ 
+
+ align:start position:0%
+and feel free to send me uh email you
+can talk to
+
+ align:start position:0%
+can talk to
+ 
+
+ align:start position:0%
+can talk to
+professor oliveira or professor
+
+ align:start position:0%
+professor oliveira or professor
+ 
+
+ align:start position:0%
+professor oliveira or professor
+mukaigawa
+
+ align:start position:0%
+mukaigawa
+ 
+
+ align:start position:0%
+mukaigawa
+about any of this or also unkit
+
+ align:start position:0%
+about any of this or also unkit
+ 
+
+ align:start position:0%
+about any of this or also unkit
+and chemo is also here if you want to
+
+ align:start position:0%
+and chemo is also here if you want to
+ 
+
+ align:start position:0%
+and chemo is also here if you want to
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+3d scanning and so on and use the forum
+
+ align:start position:0%
+3d scanning and so on and use the forum
+ 
+
+ align:start position:0%
+3d scanning and so on and use the forum
+on the stellar website
+
+ align:start position:0%
+on the stellar website
+ 
+
+ align:start position:0%
+on the stellar website
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so on so today's lecture was
+
+ align:start position:0%
+so on so today's lecture was
+ 
+
+ align:start position:0%
+so on so today's lecture was
+very much focusing on the theory behind
+
+ align:start position:0%
+very much focusing on the theory behind
+ 
+
+ align:start position:0%
+very much focusing on the theory behind
+uh how we start thinking and then
+
+ align:start position:0%
+uh how we start thinking and then
+ 
+
+ align:start position:0%
+uh how we start thinking and then
+starting next week we'll be looking at
+
+ align:start position:0%
+starting next week we'll be looking at
+ 
+
+ align:start position:0%
+starting next week we'll be looking at
+very different applications and
+
+ align:start position:0%
+very different applications and
+ 
+
+ align:start position:0%
+very different applications and
+different tricks we use
+
+ align:start position:0%
+different tricks we use
+ 
+
+ align:start position:0%
+different tricks we use
+in optics
+
+ align:start position:0%
+in optics
+ 
+
+ align:start position:0%
+in optics
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just go through the slide lap post today
+
+ align:start position:0%
+just go through the slide lap post today
+ 
+
+ align:start position:0%
+just go through the slide lap post today
+they are conceptual
+
+ align:start position:0%
+they are conceptual
+ 
+
+ align:start position:0%
+they are conceptual
+but it will take you some time to just
+
+ align:start position:0%
+but it will take you some time to just
+ 
+
+ align:start position:0%
+but it will take you some time to just
+grasp it
+
+ align:start position:0%
+grasp it
+ 
+
+ align:start position:0%
+grasp it
+and again as i said it might feel
+
+ align:start position:0%
+and again as i said it might feel
+ 
+
+ align:start position:0%
+and again as i said it might feel
+somewhat hard to think in a dual space
+
+ align:start position:0%
+somewhat hard to think in a dual space
+ 
+
+ align:start position:0%
+somewhat hard to think in a dual space
+of x and theta as opposed to just
+
+ align:start position:0%
+of x and theta as opposed to just
+ 
+
+ align:start position:0%
+of x and theta as opposed to just
+finding the rays directly
+
+ align:start position:0%
+finding the rays directly
+ 
+
+ align:start position:0%
+finding the rays directly
+but as you will see later especially in
+
+ align:start position:0%
+but as you will see later especially in
+ 
+
+ align:start position:0%
+but as you will see later especially in
+your projects and so on and this will
+
+ align:start position:0%
+your projects and so on and this will
+ 
+
+ align:start position:0%
+your projects and so on and this will
+greatly simplify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is going to simplify the way you
+
+ align:start position:0%
+this is going to simplify the way you
+ 
+
+ align:start position:0%
+this is going to simplify the way you
+think about your problems
+
+ align:start position:0%
+think about your problems
+ 
+
+ align:start position:0%
+think about your problems
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+have a good weekend
\ No newline at end of file
diff --git a/u3Umk_2PVuw.txt b/u3Umk_2PVuw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0b573493f2969fc479a4ca37fa96466cb26bd29c
--- /dev/null
+++ b/u3Umk_2PVuw.txt
@@ -0,0 +1,7767 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencare at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so welcome to lean thinking
+
+ align:start position:0%
+ocw.mit.edu so welcome to lean thinking
+ 
+
+ align:start position:0%
+ocw.mit.edu so welcome to lean thinking
+part two uh we're essentially going to
+
+ align:start position:0%
+part two uh we're essentially going to
+ 
+
+ align:start position:0%
+part two uh we're essentially going to
+pick up where left off last time in
+
+ align:start position:0%
+pick up where left off last time in
+ 
+
+ align:start position:0%
+pick up where left off last time in
+discussing the uh the lean framework of
+
+ align:start position:0%
+discussing the uh the lean framework of
+ 
+
+ align:start position:0%
+discussing the uh the lean framework of
+thinking about value the value Stream
+
+ align:start position:0%
+thinking about value the value Stream
+ 
+
+ align:start position:0%
+thinking about value the value Stream
+flow pole and Perfection um hopefully
+
+ align:start position:0%
+flow pole and Perfection um hopefully
+ 
+
+ align:start position:0%
+flow pole and Perfection um hopefully
+the the video gave you some real active
+
+ align:start position:0%
+the the video gave you some real active
+ 
+
+ align:start position:0%
+the the video gave you some real active
+sort of visual representations of what
+
+ align:start position:0%
+sort of visual representations of what
+ 
+
+ align:start position:0%
+sort of visual representations of what
+some of these Concepts might might mean
+
+ align:start position:0%
+some of these Concepts might might mean
+ 
+
+ align:start position:0%
+some of these Concepts might might mean
+so let's talk about um flow we would
+
+ align:start position:0%
+so let's talk about um flow we would
+ 
+
+ align:start position:0%
+so let's talk about um flow we would
+like if we have a value stream this is a
+
+ align:start position:0%
+like if we have a value stream this is a
+ 
+
+ align:start position:0%
+like if we have a value stream this is a
+patient value stream we have people
+
+ align:start position:0%
+patient value stream we have people
+ 
+
+ align:start position:0%
+patient value stream we have people
+coming in and going through diagnostic
+
+ align:start position:0%
+coming in and going through diagnostic
+ 
+
+ align:start position:0%
+coming in and going through diagnostic
+procedures and hopefully leaving in
+
+ align:start position:0%
+procedures and hopefully leaving in
+ 
+
+ align:start position:0%
+procedures and hopefully leaving in
+better shape than they came in and we
+
+ align:start position:0%
+better shape than they came in and we
+ 
+
+ align:start position:0%
+better shape than they came in and we
+would like to create flow in this system
+
+ align:start position:0%
+would like to create flow in this system
+ 
+
+ align:start position:0%
+would like to create flow in this system
+we have to think about a bunch of things
+
+ align:start position:0%
+we have to think about a bunch of things
+ 
+
+ align:start position:0%
+we have to think about a bunch of things
+we we obviously want to focus on what is
+
+ align:start position:0%
+we we obviously want to focus on what is
+ 
+
+ align:start position:0%
+we we obviously want to focus on what is
+flowing again the value stream map is a
+
+ align:start position:0%
+flowing again the value stream map is a
+ 
+
+ align:start position:0%
+flowing again the value stream map is a
+is a map that looks at the at the
+
+ align:start position:0%
+is a map that looks at the at the
+ 
+
+ align:start position:0%
+is a map that looks at the at the
+product in this case the patient flowing
+
+ align:start position:0%
+product in this case the patient flowing
+ 
+
+ align:start position:0%
+product in this case the patient flowing
+through the uh process
+
+ align:start position:0%
+through the uh process
+ 
+
+ align:start position:0%
+through the uh process
+um we we don't want to be uh limited by
+
+ align:start position:0%
+um we we don't want to be uh limited by
+ 
+
+ align:start position:0%
+um we we don't want to be uh limited by
+organizational or people boundaries it's
+
+ align:start position:0%
+organizational or people boundaries it's
+ 
+
+ align:start position:0%
+organizational or people boundaries it's
+not a value stream map if it follows say
+
+ align:start position:0%
+not a value stream map if it follows say
+ 
+
+ align:start position:0%
+not a value stream map if it follows say
+an organizational work or an
+
+ align:start position:0%
+an organizational work or an
+ 
+
+ align:start position:0%
+an organizational work or an
+individual's work it's really about the
+
+ align:start position:0%
+individual's work it's really about the
+ 
+
+ align:start position:0%
+individual's work it's really about the
+about the product um in first order we
+
+ align:start position:0%
+about the product um in first order we
+ 
+
+ align:start position:0%
+about the product um in first order we
+want to make sure that there's the
+
+ align:start position:0%
+want to make sure that there's the
+ 
+
+ align:start position:0%
+want to make sure that there's the
+minimum amount of uh buffers in there
+
+ align:start position:0%
+minimum amount of uh buffers in there
+ 
+
+ align:start position:0%
+minimum amount of uh buffers in there
+inventory here's a waiting room full of
+
+ align:start position:0%
+inventory here's a waiting room full of
+ 
+
+ align:start position:0%
+inventory here's a waiting room full of
+people that's not flow right and that's
+
+ align:start position:0%
+people that's not flow right and that's
+ 
+
+ align:start position:0%
+people that's not flow right and that's
+it's interesting to me as a non-medical
+
+ align:start position:0%
+it's interesting to me as a non-medical
+ 
+
+ align:start position:0%
+it's interesting to me as a non-medical
+professional to just sort of observe uh
+
+ align:start position:0%
+professional to just sort of observe uh
+ 
+
+ align:start position:0%
+professional to just sort of observe uh
+things from uh from a lean perspective I
+
+ align:start position:0%
+things from uh from a lean perspective I
+ 
+
+ align:start position:0%
+things from uh from a lean perspective I
+have had both good and bad experiences
+
+ align:start position:0%
+have had both good and bad experiences
+ 
+
+ align:start position:0%
+have had both good and bad experiences
+as a patient or the parent of patients
+
+ align:start position:0%
+as a patient or the parent of patients
+ 
+
+ align:start position:0%
+as a patient or the parent of patients
+sometimes it's this you're sitting in
+
+ align:start position:0%
+sometimes it's this you're sitting in
+ 
+
+ align:start position:0%
+sometimes it's this you're sitting in
+the way waiting room for five or six
+
+ align:start position:0%
+the way waiting room for five or six
+ 
+
+ align:start position:0%
+the way waiting room for five or six
+hours um or and sometimes it
+
+ align:start position:0%
+hours um or and sometimes it
+ 
+
+ align:start position:0%
+hours um or and sometimes it
+isn't um I've had sort of astonishing
+
+ align:start position:0%
+isn't um I've had sort of astonishing
+ 
+
+ align:start position:0%
+isn't um I've had sort of astonishing
+experiences with well organized medical
+
+ align:start position:0%
+experiences with well organized medical
+ 
+
+ align:start position:0%
+experiences with well organized medical
+facilities where you know they hardly
+
+ align:start position:0%
+facilities where you know they hardly
+ 
+
+ align:start position:0%
+facilities where you know they hardly
+had literally once I didn't have time to
+
+ align:start position:0%
+had literally once I didn't have time to
+ 
+
+ align:start position:0%
+had literally once I didn't have time to
+sit down they gave me a little form to
+
+ align:start position:0%
+sit down they gave me a little form to
+ 
+
+ align:start position:0%
+sit down they gave me a little form to
+fill out and before I had finished
+
+ align:start position:0%
+fill out and before I had finished
+ 
+
+ align:start position:0%
+fill out and before I had finished
+filling out the form they were calling
+
+ align:start position:0%
+filling out the form they were calling
+ 
+
+ align:start position:0%
+filling out the form they were calling
+my name to see the doctor right it was
+
+ align:start position:0%
+my name to see the doctor right it was
+ 
+
+ align:start position:0%
+my name to see the doctor right it was
+it was a well organized system that had
+
+ align:start position:0%
+it was a well organized system that had
+ 
+
+ align:start position:0%
+it was a well organized system that had
+flow but bottlenecks are going to slow
+
+ align:start position:0%
+flow but bottlenecks are going to slow
+ 
+
+ align:start position:0%
+flow but bottlenecks are going to slow
+that down buffers essentially the same
+
+ align:start position:0%
+that down buffers essentially the same
+ 
+
+ align:start position:0%
+that down buffers essentially the same
+you know weight time in between steps
+
+ align:start position:0%
+you know weight time in between steps
+ 
+
+ align:start position:0%
+you know weight time in between steps
+sometimes that's necessary you have an
+
+ align:start position:0%
+sometimes that's necessary you have an
+ 
+
+ align:start position:0%
+sometimes that's necessary you have an
+expensive facility like a cat scanner
+
+ align:start position:0%
+expensive facility like a cat scanner
+ 
+
+ align:start position:0%
+expensive facility like a cat scanner
+you're not going to risk not using that
+
+ align:start position:0%
+you're not going to risk not using that
+ 
+
+ align:start position:0%
+you're not going to risk not using that
+facility so people are going to have to
+
+ align:start position:0%
+facility so people are going to have to
+ 
+
+ align:start position:0%
+facility so people are going to have to
+wait for it but to achieve flow you need
+
+ align:start position:0%
+wait for it but to achieve flow you need
+ 
+
+ align:start position:0%
+wait for it but to achieve flow you need
+to minimize that and one of the key
+
+ align:start position:0%
+to minimize that and one of the key
+ 
+
+ align:start position:0%
+to minimize that and one of the key
+things to think about is time it's an
+
+ align:start position:0%
+things to think about is time it's an
+ 
+
+ align:start position:0%
+things to think about is time it's an
+essential metric our discussion today is
+
+ align:start position:0%
+essential metric our discussion today is
+ 
+
+ align:start position:0%
+essential metric our discussion today is
+going to really be about how how do we
+
+ align:start position:0%
+going to really be about how how do we
+ 
+
+ align:start position:0%
+going to really be about how how do we
+measure and Define time um time is sort
+
+ align:start position:0%
+measure and Define time um time is sort
+ 
+
+ align:start position:0%
+measure and Define time um time is sort
+of an obvious thing but when when you
+
+ align:start position:0%
+of an obvious thing but when when you
+ 
+
+ align:start position:0%
+of an obvious thing but when when you
+start thinking about measuring and
+
+ align:start position:0%
+start thinking about measuring and
+ 
+
+ align:start position:0%
+start thinking about measuring and
+defining it it does get a little bit
+
+ align:start position:0%
+defining it it does get a little bit
+ 
+
+ align:start position:0%
+defining it it does get a little bit
+complicated you have to think about it
+
+ align:start position:0%
+complicated you have to think about it
+ 
+
+ align:start position:0%
+complicated you have to think about it
+carefully um and the key is really to
+
+ align:start position:0%
+carefully um and the key is really to
+ 
+
+ align:start position:0%
+carefully um and the key is really to
+understand the definition uh of how the
+
+ align:start position:0%
+understand the definition uh of how the
+ 
+
+ align:start position:0%
+understand the definition uh of how the
+time is measured um and one of the
+
+ align:start position:0%
+time is measured um and one of the
+ 
+
+ align:start position:0%
+time is measured um and one of the
+problems here is that the terminology
+
+ align:start position:0%
+problems here is that the terminology
+ 
+
+ align:start position:0%
+problems here is that the terminology
+there's some terminology here is not
+
+ align:start position:0%
+there's some terminology here is not
+ 
+
+ align:start position:0%
+there's some terminology here is not
+standardized so in different fields
+
+ align:start position:0%
+standardized so in different fields
+ 
+
+ align:start position:0%
+standardized so in different fields
+industrial engineers and supply chain
+
+ align:start position:0%
+industrial engineers and supply chain
+ 
+
+ align:start position:0%
+industrial engineers and supply chain
+people will talk about things using the
+
+ align:start position:0%
+people will talk about things using the
+ 
+
+ align:start position:0%
+people will talk about things using the
+same words they mean different things
+
+ align:start position:0%
+same words they mean different things
+ 
+
+ align:start position:0%
+same words they mean different things
+some sometimes the words are used in a
+
+ align:start position:0%
+some sometimes the words are used in a
+ 
+
+ align:start position:0%
+some sometimes the words are used in a
+way that isn't intuitive so rather than
+
+ align:start position:0%
+way that isn't intuitive so rather than
+ 
+
+ align:start position:0%
+way that isn't intuitive so rather than
+try to teach you the jargon of any
+
+ align:start position:0%
+try to teach you the jargon of any
+ 
+
+ align:start position:0%
+try to teach you the jargon of any
+particular field what we're going to ask
+
+ align:start position:0%
+particular field what we're going to ask
+ 
+
+ align:start position:0%
+particular field what we're going to ask
+you to do is think about time and
+
+ align:start position:0%
+you to do is think about time and
+ 
+
+ align:start position:0%
+you to do is think about time and
+understand and make sure you you
+
+ align:start position:0%
+understand and make sure you you
+ 
+
+ align:start position:0%
+understand and make sure you you
+understand and communicate your
+
+ align:start position:0%
+understand and communicate your
+ 
+
+ align:start position:0%
+understand and communicate your
+definitions of time and we'll actually
+
+ align:start position:0%
+definitions of time and we'll actually
+ 
+
+ align:start position:0%
+definitions of time and we'll actually
+have a little exercise about that so
+
+ align:start position:0%
+have a little exercise about that so
+ 
+
+ align:start position:0%
+have a little exercise about that so
+wait time that's relatively simple um if
+
+ align:start position:0%
+wait time that's relatively simple um if
+ 
+
+ align:start position:0%
+wait time that's relatively simple um if
+something is just sitting there um it is
+
+ align:start position:0%
+something is just sitting there um it is
+ 
+
+ align:start position:0%
+something is just sitting there um it is
+waiting so there's there is uh work in
+
+ align:start position:0%
+waiting so there's there is uh work in
+ 
+
+ align:start position:0%
+waiting so there's there is uh work in
+progress the work that you're trying to
+
+ align:start position:0%
+progress the work that you're trying to
+ 
+
+ align:start position:0%
+progress the work that you're trying to
+do is is not moving forward that's wait
+
+ align:start position:0%
+do is is not moving forward that's wait
+ 
+
+ align:start position:0%
+do is is not moving forward that's wait
+time that's also called Q time delay
+
+ align:start position:0%
+time that's also called Q time delay
+ 
+
+ align:start position:0%
+time that's also called Q time delay
+time again the terminology isn't
+
+ align:start position:0%
+time again the terminology isn't
+ 
+
+ align:start position:0%
+time again the terminology isn't
+particularly standard the concept is
+
+ align:start position:0%
+particularly standard the concept is
+ 
+
+ align:start position:0%
+particularly standard the concept is
+pretty easy to understand though
+
+ align:start position:0%
+pretty easy to understand though
+ 
+
+ align:start position:0%
+pretty easy to understand though
+processing time on the other hand is a
+
+ align:start position:0%
+processing time on the other hand is a
+ 
+
+ align:start position:0%
+processing time on the other hand is a
+little bit more complicated um so now
+
+ align:start position:0%
+little bit more complicated um so now
+ 
+
+ align:start position:0%
+little bit more complicated um so now
+something is happening to the work
+
+ align:start position:0%
+something is happening to the work
+ 
+
+ align:start position:0%
+something is happening to the work
+product uh some sort of resources are
+
+ align:start position:0%
+product uh some sort of resources are
+ 
+
+ align:start position:0%
+product uh some sort of resources are
+being consumed maybe a person is working
+
+ align:start position:0%
+being consumed maybe a person is working
+ 
+
+ align:start position:0%
+being consumed maybe a person is working
+on it maybe a machine is working on it
+
+ align:start position:0%
+on it maybe a machine is working on it
+ 
+
+ align:start position:0%
+on it maybe a machine is working on it
+and that could be value added or
+
+ align:start position:0%
+and that could be value added or
+ 
+
+ align:start position:0%
+and that could be value added or
+non-value added it could be an active or
+
+ align:start position:0%
+non-value added it could be an active or
+ 
+
+ align:start position:0%
+non-value added it could be an active or
+uh or relatively passive use there are
+
+ align:start position:0%
+uh or relatively passive use there are
+ 
+
+ align:start position:0%
+uh or relatively passive use there are
+multiple names for it touch time kind of
+
+ align:start position:0%
+multiple names for it touch time kind of
+ 
+
+ align:start position:0%
+multiple names for it touch time kind of
+gets to the to the to I I kind of like
+
+ align:start position:0%
+gets to the to the to I I kind of like
+ 
+
+ align:start position:0%
+gets to the to the to I I kind of like
+touch time because it's intuitive means
+
+ align:start position:0%
+touch time because it's intuitive means
+ 
+
+ align:start position:0%
+touch time because it's intuitive means
+and in in for example engineering or
+
+ align:start position:0%
+and in in for example engineering or
+ 
+
+ align:start position:0%
+and in in for example engineering or
+Health Care work someone is working on
+
+ align:start position:0%
+Health Care work someone is working on
+ 
+
+ align:start position:0%
+Health Care work someone is working on
+it right it's that's those both of those
+
+ align:start position:0%
+it right it's that's those both of those
+ 
+
+ align:start position:0%
+it right it's that's those both of those
+fields are very people intensive if
+
+ align:start position:0%
+fields are very people intensive if
+ 
+
+ align:start position:0%
+fields are very people intensive if
+somebody is working with the patient or
+
+ align:start position:0%
+somebody is working with the patient or
+ 
+
+ align:start position:0%
+somebody is working with the patient or
+working with the diagnosis or working
+
+ align:start position:0%
+working with the diagnosis or working
+ 
+
+ align:start position:0%
+working with the diagnosis or working
+with the engineering drawing that's
+
+ align:start position:0%
+with the engineering drawing that's
+ 
+
+ align:start position:0%
+with the engineering drawing that's
+touch time it's also sometimes called in
+
+ align:start position:0%
+touch time it's also sometimes called in
+ 
+
+ align:start position:0%
+touch time it's also sometimes called in
+process time or response time in the
+
+ align:start position:0%
+process time or response time in the
+ 
+
+ align:start position:0%
+process time or response time in the
+sense of how quickly can the people
+
+ align:start position:0%
+sense of how quickly can the people
+ 
+
+ align:start position:0%
+sense of how quickly can the people
+respond to a demand that they get
+
+ align:start position:0%
+respond to a demand that they get
+ 
+
+ align:start position:0%
+respond to a demand that they get
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+done and these things tend to pile up
+
+ align:start position:0%
+done and these things tend to pile up
+ 
+
+ align:start position:0%
+done and these things tend to pile up
+in ways that it kind of Illustrated here
+
+ align:start position:0%
+in ways that it kind of Illustrated here
+ 
+
+ align:start position:0%
+in ways that it kind of Illustrated here
+in a simple case you know if you have
+
+ align:start position:0%
+in a simple case you know if you have
+ 
+
+ align:start position:0%
+in a simple case you know if you have
+some work you need to get done well
+
+ align:start position:0%
+some work you need to get done well
+ 
+
+ align:start position:0%
+some work you need to get done well
+first it
+
+ align:start position:0%
+first it
+ 
+
+ align:start position:0%
+first it
+waits question how would you categorize
+
+ align:start position:0%
+waits question how would you categorize
+ 
+
+ align:start position:0%
+waits question how would you categorize
+a for example there was an oven on one
+
+ align:start position:0%
+a for example there was an oven on one
+ 
+
+ align:start position:0%
+a for example there was an oven on one
+of those shoes yeah and he would heat
+
+ align:start position:0%
+of those shoes yeah and he would heat
+ 
+
+ align:start position:0%
+of those shoes yeah and he would heat
+the thing up but then he would open the
+
+ align:start position:0%
+the thing up but then he would open the
+ 
+
+ align:start position:0%
+the thing up but then he would open the
+open the OV and let it sit not touch it
+
+ align:start position:0%
+open the OV and let it sit not touch it
+ 
+
+ align:start position:0%
+open the OV and let it sit not touch it
+because it
+
+ align:start position:0%
+because it
+ 
+
+ align:start position:0%
+because it
+was that's right that's classic right
+
+ align:start position:0%
+was that's right that's classic right
+ 
+
+ align:start position:0%
+was that's right that's classic right
+okay so is that weight time because it's
+
+ align:start position:0%
+okay so is that weight time because it's
+ 
+
+ align:start position:0%
+okay so is that weight time because it's
+cooling off well but it's occupying the
+
+ align:start position:0%
+cooling off well but it's occupying the
+ 
+
+ align:start position:0%
+cooling off well but it's occupying the
+oven it's not touch time the guy is not
+
+ align:start position:0%
+oven it's not touch time the guy is not
+ 
+
+ align:start position:0%
+oven it's not touch time the guy is not
+working on it he can go do something
+
+ align:start position:0%
+working on it he can go do something
+ 
+
+ align:start position:0%
+working on it he can go do something
+else right but the equipment is used is
+
+ align:start position:0%
+else right but the equipment is used is
+ 
+
+ align:start position:0%
+else right but the equipment is used is
+used so that's that's classic and I I
+
+ align:start position:0%
+used so that's that's classic and I I
+ 
+
+ align:start position:0%
+used so that's that's classic and I I
+don't have an easy answer for you it
+
+ align:start position:0%
+don't have an easy answer for you it
+ 
+
+ align:start position:0%
+don't have an easy answer for you it
+depends on what you're measuring if
+
+ align:start position:0%
+depends on what you're measuring if
+ 
+
+ align:start position:0%
+depends on what you're measuring if
+you're measuring the equipment you know
+
+ align:start position:0%
+you're measuring the equipment you know
+ 
+
+ align:start position:0%
+you're measuring the equipment you know
+how many ovens do we need you better you
+
+ align:start position:0%
+how many ovens do we need you better you
+ 
+
+ align:start position:0%
+how many ovens do we need you better you
+know account for that cooling because
+
+ align:start position:0%
+know account for that cooling because
+ 
+
+ align:start position:0%
+know account for that cooling because
+they probably don't want to yank it out
+
+ align:start position:0%
+they probably don't want to yank it out
+ 
+
+ align:start position:0%
+they probably don't want to yank it out
+it'll cool too fast right um so you know
+
+ align:start position:0%
+it'll cool too fast right um so you know
+ 
+
+ align:start position:0%
+it'll cool too fast right um so you know
+if you're concerned as the oven you got
+
+ align:start position:0%
+if you're concerned as the oven you got
+ 
+
+ align:start position:0%
+if you're concerned as the oven you got
+to count that if you're concerned as the
+
+ align:start position:0%
+to count that if you're concerned as the
+ 
+
+ align:start position:0%
+to count that if you're concerned as the
+worker that part doesn't count your
+
+ align:start position:0%
+worker that part doesn't count your
+ 
+
+ align:start position:0%
+worker that part doesn't count your
+concern is the
+
+ align:start position:0%
+concern is the
+ 
+
+ align:start position:0%
+concern is the
+shoe it's in process in some way right
+
+ align:start position:0%
+shoe it's in process in some way right
+ 
+
+ align:start position:0%
+shoe it's in process in some way right
+it's cooling off that you can't make
+
+ align:start position:0%
+it's cooling off that you can't make
+ 
+
+ align:start position:0%
+it's cooling off that you can't make
+that go fast you can't say that's weight
+
+ align:start position:0%
+that go fast you can't say that's weight
+ 
+
+ align:start position:0%
+that go fast you can't say that's weight
+time because you can't make that go
+
+ align:start position:0%
+time because you can't make that go
+ 
+
+ align:start position:0%
+time because you can't make that go
+faster right another classic one is
+
+ align:start position:0%
+faster right another classic one is
+ 
+
+ align:start position:0%
+faster right another classic one is
+painting you can't make paint dry faster
+
+ align:start position:0%
+painting you can't make paint dry faster
+ 
+
+ align:start position:0%
+painting you can't make paint dry faster
+well you can you can blast hot air on it
+
+ align:start position:0%
+well you can you can blast hot air on it
+ 
+
+ align:start position:0%
+well you can you can blast hot air on it
+but that may or may not be a good thing
+
+ align:start position:0%
+but that may or may not be a good thing
+ 
+
+ align:start position:0%
+but that may or may not be a good thing
+right so right and that's exactly what
+
+ align:start position:0%
+right so right and that's exactly what
+ 
+
+ align:start position:0%
+right so right and that's exactly what
+I'm trying to get across here is that
+
+ align:start position:0%
+I'm trying to get across here is that
+ 
+
+ align:start position:0%
+I'm trying to get across here is that
+the time has a lot of a lot of sort of
+
+ align:start position:0%
+the time has a lot of a lot of sort of
+ 
+
+ align:start position:0%
+the time has a lot of a lot of sort of
+unexpected complexity when you're
+
+ align:start position:0%
+unexpected complexity when you're
+ 
+
+ align:start position:0%
+unexpected complexity when you're
+looking at these things and you have to
+
+ align:start position:0%
+looking at these things and you have to
+ 
+
+ align:start position:0%
+looking at these things and you have to
+you have to think pretty straight about
+
+ align:start position:0%
+you have to think pretty straight about
+ 
+
+ align:start position:0%
+you have to think pretty straight about
+it so you could be waiting you could be
+
+ align:start position:0%
+it so you could be waiting you could be
+ 
+
+ align:start position:0%
+it so you could be waiting you could be
+doing value added work you could be nonv
+
+ align:start position:0%
+doing value added work you could be nonv
+ 
+
+ align:start position:0%
+doing value added work you could be nonv
+value added but still in processing
+
+ align:start position:0%
+value added but still in processing
+ 
+
+ align:start position:0%
+value added but still in processing
+right we we stuck the glue on now we're
+
+ align:start position:0%
+right we we stuck the glue on now we're
+ 
+
+ align:start position:0%
+right we we stuck the glue on now we're
+cooling off we're still using the
+
+ align:start position:0%
+cooling off we're still using the
+ 
+
+ align:start position:0%
+cooling off we're still using the
+oven we can't leave the oven but it's
+
+ align:start position:0%
+oven we can't leave the oven but it's
+ 
+
+ align:start position:0%
+oven we can't leave the oven but it's
+not really value added maybe we could do
+
+ align:start position:0%
+not really value added maybe we could do
+ 
+
+ align:start position:0%
+not really value added maybe we could do
+that in a different way maybe it's
+
+ align:start position:0%
+that in a different way maybe it's
+ 
+
+ align:start position:0%
+that in a different way maybe it's
+necessary nonv value added you know
+
+ align:start position:0%
+necessary nonv value added you know
+ 
+
+ align:start position:0%
+necessary nonv value added you know
+maybe we'll call call that yellow at
+
+ align:start position:0%
+maybe we'll call call that yellow at
+ 
+
+ align:start position:0%
+maybe we'll call call that yellow at
+some point the processing ends and we go
+
+ align:start position:0%
+some point the processing ends and we go
+ 
+
+ align:start position:0%
+some point the processing ends and we go
+back into inventory and we're waiting
+
+ align:start position:0%
+back into inventory and we're waiting
+ 
+
+ align:start position:0%
+back into inventory and we're waiting
+again and sort of Imagine That cycle
+
+ align:start position:0%
+again and sort of Imagine That cycle
+ 
+
+ align:start position:0%
+again and sort of Imagine That cycle
+repeated lots of times to finish our
+
+ align:start position:0%
+repeated lots of times to finish our
+ 
+
+ align:start position:0%
+repeated lots of times to finish our
+overall process so and cycle time is our
+
+ align:start position:0%
+overall process so and cycle time is our
+ 
+
+ align:start position:0%
+overall process so and cycle time is our
+overall all time um there isn't a whole
+
+ align:start position:0%
+overall all time um there isn't a whole
+ 
+
+ align:start position:0%
+overall all time um there isn't a whole
+lot of uh confusion about cycle time
+
+ align:start position:0%
+lot of uh confusion about cycle time
+ 
+
+ align:start position:0%
+lot of uh confusion about cycle time
+means overall time weight weight plus
+
+ align:start position:0%
+means overall time weight weight plus
+ 
+
+ align:start position:0%
+means overall time weight weight plus
+processing there's some other names for
+
+ align:start position:0%
+processing there's some other names for
+ 
+
+ align:start position:0%
+processing there's some other names for
+it the thing you have to really watch
+
+ align:start position:0%
+it the thing you have to really watch
+ 
+
+ align:start position:0%
+it the thing you have to really watch
+out for cycle time is cycle of what it
+
+ align:start position:0%
+out for cycle time is cycle of what it
+ 
+
+ align:start position:0%
+out for cycle time is cycle of what it
+could be the cycle of a machine kachunk
+
+ align:start position:0%
+could be the cycle of a machine kachunk
+ 
+
+ align:start position:0%
+could be the cycle of a machine kachunk
+kachunk kachunk right that's seconds um
+
+ align:start position:0%
+kachunk kachunk right that's seconds um
+ 
+
+ align:start position:0%
+kachunk kachunk right that's seconds um
+it could be cycle of the overall shoe
+
+ align:start position:0%
+it could be cycle of the overall shoe
+ 
+
+ align:start position:0%
+it could be cycle of the overall shoe
+manufacturing process which and New
+
+ align:start position:0%
+manufacturing process which and New
+ 
+
+ align:start position:0%
+manufacturing process which and New
+Balance was an amazingly short three
+
+ align:start position:0%
+Balance was an amazingly short three
+ 
+
+ align:start position:0%
+Balance was an amazingly short three
+days uh but in you know Aeronautical
+
+ align:start position:0%
+days uh but in you know Aeronautical
+ 
+
+ align:start position:0%
+days uh but in you know Aeronautical
+Engineering cycle time of an aircraft
+
+ align:start position:0%
+Engineering cycle time of an aircraft
+ 
+
+ align:start position:0%
+Engineering cycle time of an aircraft
+life cycle 20 years you know cycle time
+
+ align:start position:0%
+life cycle 20 years you know cycle time
+ 
+
+ align:start position:0%
+life cycle 20 years you know cycle time
+can mean a lot of different things you
+
+ align:start position:0%
+can mean a lot of different things you
+ 
+
+ align:start position:0%
+can mean a lot of different things you
+got to just Define your your boundaries
+
+ align:start position:0%
+got to just Define your your boundaries
+ 
+
+ align:start position:0%
+got to just Define your your boundaries
+uh very carefully when you're talking
+
+ align:start position:0%
+uh very carefully when you're talking
+ 
+
+ align:start position:0%
+uh very carefully when you're talking
+about um cycle time so now we have a
+
+ align:start position:0%
+about um cycle time so now we have a
+ 
+
+ align:start position:0%
+about um cycle time so now we have a
+little exercise we're going to ask you
+
+ align:start position:0%
+little exercise we're going to ask you
+ 
+
+ align:start position:0%
+little exercise we're going to ask you
+to tackle some of these complexities I
+
+ align:start position:0%
+to tackle some of these complexities I
+ 
+
+ align:start position:0%
+to tackle some of these complexities I
+hope everybody held on to this sheet um
+
+ align:start position:0%
+hope everybody held on to this sheet um
+ 
+
+ align:start position:0%
+hope everybody held on to this sheet um
+you were using this before hopefully you
+
+ align:start position:0%
+you were using this before hopefully you
+ 
+
+ align:start position:0%
+you were using this before hopefully you
+didn't um we call it 5sing out of
+
+ align:start position:0%
+didn't um we call it 5sing out of
+ 
+
+ align:start position:0%
+didn't um we call it 5sing out of
+existence you know you clean up
+
+ align:start position:0%
+existence you know you clean up
+ 
+
+ align:start position:0%
+existence you know you clean up
+something you really need and then it's
+
+ align:start position:0%
+something you really need and then it's
+ 
+
+ align:start position:0%
+something you really need and then it's
+gone hope that didn't happen
+
+ align:start position:0%
+gone hope that didn't happen
+ 
+
+ align:start position:0%
+gone hope that didn't happen
+um because now we're going to look at
+
+ align:start position:0%
+um because now we're going to look at
+ 
+
+ align:start position:0%
+um because now we're going to look at
+the at the times and we're going to do a
+
+ align:start position:0%
+the at the times and we're going to do a
+ 
+
+ align:start position:0%
+the at the times and we're going to do a
+little exercise we're going to add up
+
+ align:start position:0%
+little exercise we're going to add up
+ 
+
+ align:start position:0%
+little exercise we're going to add up
+the overall cycle time of an order from
+
+ align:start position:0%
+the overall cycle time of an order from
+ 
+
+ align:start position:0%
+the overall cycle time of an order from
+the time the customer walks up to the
+
+ align:start position:0%
+the time the customer walks up to the
+ 
+
+ align:start position:0%
+the time the customer walks up to the
+time they get their hot dog the tricky
+
+ align:start position:0%
+time they get their hot dog the tricky
+ 
+
+ align:start position:0%
+time they get their hot dog the tricky
+thing is these times are not necessarily
+
+ align:start position:0%
+thing is these times are not necessarily
+ 
+
+ align:start position:0%
+thing is these times are not necessarily
+in the right units make sure everything
+
+ align:start position:0%
+in the right units make sure everything
+ 
+
+ align:start position:0%
+in the right units make sure everything
+is converted to time per order right is
+
+ align:start position:0%
+is converted to time per order right is
+ 
+
+ align:start position:0%
+is converted to time per order right is
+it time for hot dog subtle right what's
+
+ align:start position:0%
+it time for hot dog subtle right what's
+ 
+
+ align:start position:0%
+it time for hot dog subtle right what's
+the average order does anybody
+
+ align:start position:0%
+the average order does anybody
+ 
+
+ align:start position:0%
+the average order does anybody
+remember two hot dogs right so um and we
+
+ align:start position:0%
+remember two hot dogs right so um and we
+ 
+
+ align:start position:0%
+remember two hot dogs right so um and we
+got to worry about rework there's some
+
+ align:start position:0%
+got to worry about rework there's some
+ 
+
+ align:start position:0%
+got to worry about rework there's some
+percentage chance we're looking at the
+
+ align:start position:0%
+percentage chance we're looking at the
+ 
+
+ align:start position:0%
+percentage chance we're looking at the
+average there's some percentage chance
+
+ align:start position:0%
+average there's some percentage chance
+ 
+
+ align:start position:0%
+average there's some percentage chance
+that things are going to have to be done
+
+ align:start position:0%
+that things are going to have to be done
+ 
+
+ align:start position:0%
+that things are going to have to be done
+over so this this actually gets pretty
+
+ align:start position:0%
+over so this this actually gets pretty
+ 
+
+ align:start position:0%
+over so this this actually gets pretty
+well at some at how tricky this can
+
+ align:start position:0%
+well at some at how tricky this can
+ 
+
+ align:start position:0%
+well at some at how tricky this can
+sometimes be all right so try to
+
+ align:start position:0%
+sometimes be all right so try to
+ 
+
+ align:start position:0%
+sometimes be all right so try to
+normalize the times sum them up and use
+
+ align:start position:0%
+normalize the times sum them up and use
+ 
+
+ align:start position:0%
+normalize the times sum them up and use
+the sheet this is actually a group
+
+ align:start position:0%
+the sheet this is actually a group
+ 
+
+ align:start position:0%
+the sheet this is actually a group
+exercise if you guys want to divide and
+
+ align:start position:0%
+exercise if you guys want to divide and
+ 
+
+ align:start position:0%
+exercise if you guys want to divide and
+conquer or if you just want to see you
+
+ align:start position:0%
+conquer or if you just want to see you
+ 
+
+ align:start position:0%
+conquer or if you just want to see you
+know a see what people get whatever um
+
+ align:start position:0%
+know a see what people get whatever um
+ 
+
+ align:start position:0%
+know a see what people get whatever um
+whatever strategy you want to take to uh
+
+ align:start position:0%
+whatever strategy you want to take to uh
+ 
+
+ align:start position:0%
+whatever strategy you want to take to uh
+to uh to puzzle this out is fine but you
+
+ align:start position:0%
+to uh to puzzle this out is fine but you
+ 
+
+ align:start position:0%
+to uh to puzzle this out is fine but you
+only have um little under 10 minutes why
+
+ align:start position:0%
+only have um little under 10 minutes why
+ 
+
+ align:start position:0%
+only have um little under 10 minutes why
+don't we give it till like three after
+
+ align:start position:0%
+don't we give it till like three after
+ 
+
+ align:start position:0%
+don't we give it till like three after
+to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exercise I see what you're saying so it
+
+ align:start position:0%
+exercise I see what you're saying so it
+ 
+
+ align:start position:0%
+exercise I see what you're saying so it
+does it shouldn't take 20 seconds to put
+
+ align:start position:0%
+does it shouldn't take 20 seconds to put
+ 
+
+ align:start position:0%
+does it shouldn't take 20 seconds to put
+a hot dog in a bun yeah so 20 seconds
+
+ align:start position:0%
+a hot dog in a bun yeah so 20 seconds
+ 
+
+ align:start position:0%
+a hot dog in a bun yeah so 20 seconds
+with it in the bun and then get the
+
+ align:start position:0%
+with it in the bun and then get the
+ 
+
+ align:start position:0%
+with it in the bun and then get the
+about 10 seconds putting about 10
+
+ align:start position:0%
+about 10 seconds putting about 10
+ 
+
+ align:start position:0%
+about 10 seconds putting about 10
+seconds putting exactly that's how I
+
+ align:start position:0%
+seconds putting exactly that's how I
+ 
+
+ align:start position:0%
+seconds putting exactly that's how I
+interpret all righty what do you got
+
+ align:start position:0%
+interpret all righty what do you got
+ 
+
+ align:start position:0%
+interpret all righty what do you got
+one of the one of the fun things about
+
+ align:start position:0%
+one of the one of the fun things about
+ 
+
+ align:start position:0%
+one of the one of the fun things about
+uh about this class is is is our uh sort
+
+ align:start position:0%
+uh about this class is is is our uh sort
+ 
+
+ align:start position:0%
+uh about this class is is is our uh sort
+of unintentional e u experimenting and
+
+ align:start position:0%
+of unintentional e u experimenting and
+ 
+
+ align:start position:0%
+of unintentional e u experimenting and
+work Styles is some people were like
+
+ align:start position:0%
+work Styles is some people were like
+ 
+
+ align:start position:0%
+work Styles is some people were like
+just doing away you know other people
+
+ align:start position:0%
+just doing away you know other people
+ 
+
+ align:start position:0%
+just doing away you know other people
+were talking waving their arms and stuff
+
+ align:start position:0%
+were talking waving their arms and stuff
+ 
+
+ align:start position:0%
+were talking waving their arms and stuff
+it was interesting let's see if uh let's
+
+ align:start position:0%
+it was interesting let's see if uh let's
+ 
+
+ align:start position:0%
+it was interesting let's see if uh let's
+see what what uh this process yielded
+
+ align:start position:0%
+see what what uh this process yielded
+ 
+
+ align:start position:0%
+see what what uh this process yielded
+I'm numbering you guys M1 through three
+
+ align:start position:0%
+I'm numbering you guys M1 through three
+ 
+
+ align:start position:0%
+I'm numbering you guys M1 through three
+and E1 and two um so first uh medical
+
+ align:start position:0%
+and E1 and two um so first uh medical
+ 
+
+ align:start position:0%
+and E1 and two um so first uh medical
+option table what do you
+
+ align:start position:0%
+option table what do you
+ 
+
+ align:start position:0%
+option table what do you
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+449 okay interesting
+
+ align:start position:0%
+449 okay interesting
+ 
+
+ align:start position:0%
+449 okay interesting
+m29
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+393 39 390
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what do you guys got different
+
+ align:start position:0%
+okay what do you guys got different
+ 
+
+ align:start position:0%
+okay what do you guys got different
+things you have different things well
+
+ align:start position:0%
+things you have different things well
+ 
+
+ align:start position:0%
+things you have different things well
+give give me a sample see this is the
+
+ align:start position:0%
+give give me a sample see this is the
+ 
+
+ align:start position:0%
+give give me a sample see this is the
+table that didn't talk right so they've
+
+ align:start position:0%
+table that didn't talk right so they've
+ 
+
+ align:start position:0%
+table that didn't talk right so they've
+got yeah we have around 300 around 300
+
+ align:start position:0%
+got yeah we have around 300 around 300
+ 
+
+ align:start position:0%
+got yeah we have around 300 around 300
+okay plus or
+
+ align:start position:0%
+okay plus or
+ 
+
+ align:start position:0%
+okay plus or
+minus all right and
+
+ align:start position:0%
+minus all right and
+ 
+
+ align:start position:0%
+minus all right and
+E2
+
+ align:start position:0%
+E2
+ 
+
+ align:start position:0%
+E2
+432 okay there we
+
+ align:start position:0%
+432 okay there we
+ 
+
+ align:start position:0%
+432 okay there we
+go there we
+
+ align:start position:0%
+go there we
+ 
+
+ align:start position:0%
+go there we
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+um so we didn't exactly agree we're
+
+ align:start position:0%
+um so we didn't exactly agree we're
+ 
+
+ align:start position:0%
+um so we didn't exactly agree we're
+going to give you guys sort of an answer
+
+ align:start position:0%
+going to give you guys sort of an answer
+ 
+
+ align:start position:0%
+going to give you guys sort of an answer
+sheet later so you can like figure out
+
+ align:start position:0%
+sheet later so you can like figure out
+ 
+
+ align:start position:0%
+sheet later so you can like figure out
+uh but
+
+ align:start position:0%
+uh but
+ 
+
+ align:start position:0%
+uh but
+sort of illustrates the issue of the
+
+ align:start position:0%
+sort of illustrates the issue of the
+ 
+
+ align:start position:0%
+sort of illustrates the issue of the
+squirm of this you know it's a very
+
+ align:start position:0%
+squirm of this you know it's a very
+ 
+
+ align:start position:0%
+squirm of this you know it's a very
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+process the times you were gave you the
+
+ align:start position:0%
+process the times you were gave you the
+ 
+
+ align:start position:0%
+process the times you were gave you the
+times right but how do you interpret
+
+ align:start position:0%
+times right but how do you interpret
+ 
+
+ align:start position:0%
+times right but how do you interpret
+them exactly how do you do the rework
+
+ align:start position:0%
+them exactly how do you do the rework
+ 
+
+ align:start position:0%
+them exactly how do you do the rework
+you average that in probably the most
+
+ align:start position:0%
+you average that in probably the most
+ 
+
+ align:start position:0%
+you average that in probably the most
+reasonable thing to do would be to add
+
+ align:start position:0%
+reasonable thing to do would be to add
+ 
+
+ align:start position:0%
+reasonable thing to do would be to add
+10% to all of the things that might have
+
+ align:start position:0%
+10% to all of the things that might have
+ 
+
+ align:start position:0%
+10% to all of the things that might have
+to be done over right but there's
+
+ align:start position:0%
+to be done over right but there's
+ 
+
+ align:start position:0%
+to be done over right but there's
+actually a couple of do over Loops so
+
+ align:start position:0%
+actually a couple of do over Loops so
+ 
+
+ align:start position:0%
+actually a couple of do over Loops so
+you add 20% to that one I you know I'm
+
+ align:start position:0%
+you add 20% to that one I you know I'm
+ 
+
+ align:start position:0%
+you add 20% to that one I you know I'm
+not sure right you could interpret that
+
+ align:start position:0%
+not sure right you could interpret that
+ 
+
+ align:start position:0%
+not sure right you could interpret that
+a couple different ways more more
+
+ align:start position:0%
+a couple different ways more more
+ 
+
+ align:start position:0%
+a couple different ways more more
+importantly how do you or more
+
+ align:start position:0%
+importantly how do you or more
+ 
+
+ align:start position:0%
+importantly how do you or more
+significantly it has a bigger impact on
+
+ align:start position:0%
+significantly it has a bigger impact on
+ 
+
+ align:start position:0%
+significantly it has a bigger impact on
+the numbers what do you do with that the
+
+ align:start position:0%
+the numbers what do you do with that the
+ 
+
+ align:start position:0%
+the numbers what do you do with that the
+stuff that's kind of off the main
+
+ align:start position:0%
+stuff that's kind of off the main
+ 
+
+ align:start position:0%
+stuff that's kind of off the main
+process Loop there the cleanup and the
+
+ align:start position:0%
+process Loop there the cleanup and the
+ 
+
+ align:start position:0%
+process Loop there the cleanup and the
+you know do you average that and put it
+
+ align:start position:0%
+you know do you average that and put it
+ 
+
+ align:start position:0%
+you know do you average that and put it
+in as a sort of tax against the each hot
+
+ align:start position:0%
+in as a sort of tax against the each hot
+ 
+
+ align:start position:0%
+in as a sort of tax against the each hot
+dog order or do you say no they'll do
+
+ align:start position:0%
+dog order or do you say no they'll do
+ 
+
+ align:start position:0%
+dog order or do you say no they'll do
+that when it's quiet it shouldn't count
+
+ align:start position:0%
+that when it's quiet it shouldn't count
+ 
+
+ align:start position:0%
+that when it's quiet it shouldn't count
+right and that's probably the difference
+
+ align:start position:0%
+right and that's probably the difference
+ 
+
+ align:start position:0%
+right and that's probably the difference
+between the people that were up above
+
+ align:start position:0%
+between the people that were up above
+ 
+
+ align:start position:0%
+between the people that were up above
+400 and the people down around 300 do
+
+ align:start position:0%
+400 and the people down around 300 do
+ 
+
+ align:start position:0%
+400 and the people down around 300 do
+that does that make sense that I hope
+
+ align:start position:0%
+that does that make sense that I hope
+ 
+
+ align:start position:0%
+that does that make sense that I hope
+the 300 people we're leaving that out
+
+ align:start position:0%
+the 300 people we're leaving that out
+ 
+
+ align:start position:0%
+the 300 people we're leaving that out
+because otherwise it's hard to get a
+
+ align:start position:0%
+because otherwise it's hard to get a
+ 
+
+ align:start position:0%
+because otherwise it's hard to get a
+number that
+
+ align:start position:0%
+number that
+ 
+
+ align:start position:0%
+number that
+small um while as this is um pretty much
+
+ align:start position:0%
+small um while as this is um pretty much
+ 
+
+ align:start position:0%
+small um while as this is um pretty much
+that that's that's a not sure that's
+
+ align:start position:0%
+that that's that's a not sure that's
+ 
+
+ align:start position:0%
+that that's that's a not sure that's
+somehow one second higher than than the
+
+ align:start position:0%
+somehow one second higher than than the
+ 
+
+ align:start position:0%
+somehow one second higher than than the
+number you get if you add 10% to
+
+ align:start position:0%
+number you get if you add 10% to
+ 
+
+ align:start position:0%
+number you get if you add 10% to
+everything and tax with the with the
+
+ align:start position:0%
+everything and tax with the with the
+ 
+
+ align:start position:0%
+everything and tax with the with the
+cleanup so that's that's real close to
+
+ align:start position:0%
+cleanup so that's that's real close to
+ 
+
+ align:start position:0%
+cleanup so that's that's real close to
+that number so there's different ways to
+
+ align:start position:0%
+that number so there's different ways to
+ 
+
+ align:start position:0%
+that number so there's different ways to
+do it and and they're all legitimate but
+
+ align:start position:0%
+do it and and they're all legitimate but
+ 
+
+ align:start position:0%
+do it and and they're all legitimate but
+it gives you a feel for how these things
+
+ align:start position:0%
+it gives you a feel for how these things
+ 
+
+ align:start position:0%
+it gives you a feel for how these things
+this is not an exact science right and
+
+ align:start position:0%
+this is not an exact science right and
+ 
+
+ align:start position:0%
+this is not an exact science right and
+again if we wanted to get more exact we
+
+ align:start position:0%
+again if we wanted to get more exact we
+ 
+
+ align:start position:0%
+again if we wanted to get more exact we
+would have to go to the GMO we might
+
+ align:start position:0%
+would have to go to the GMO we might
+ 
+
+ align:start position:0%
+would have to go to the GMO we might
+have to stand there with a stopwatch and
+
+ align:start position:0%
+have to stand there with a stopwatch and
+ 
+
+ align:start position:0%
+have to stand there with a stopwatch and
+watch the customers come and go and see
+
+ align:start position:0%
+watch the customers come and go and see
+ 
+
+ align:start position:0%
+watch the customers come and go and see
+what actually does happen right do you
+
+ align:start position:0%
+what actually does happen right do you
+ 
+
+ align:start position:0%
+what actually does happen right do you
+know for example the cleanup issue do
+
+ align:start position:0%
+know for example the cleanup issue do
+ 
+
+ align:start position:0%
+know for example the cleanup issue do
+they really have time to do it on the
+
+ align:start position:0%
+they really have time to do it on the
+ 
+
+ align:start position:0%
+they really have time to do it on the
+side or do they have to actually make
+
+ align:start position:0%
+side or do they have to actually make
+ 
+
+ align:start position:0%
+side or do they have to actually make
+customers wait while they do that you
+
+ align:start position:0%
+customers wait while they do that you
+ 
+
+ align:start position:0%
+customers wait while they do that you
+don't know until you go look so so again
+
+ align:start position:0%
+don't know until you go look so so again
+ 
+
+ align:start position:0%
+don't know until you go look so so again
+an illustration in in how this can be a
+
+ align:start position:0%
+an illustration in in how this can be a
+ 
+
+ align:start position:0%
+an illustration in in how this can be a
+a little tricky and we're going to go
+
+ align:start position:0%
+a little tricky and we're going to go
+ 
+
+ align:start position:0%
+a little tricky and we're going to go
+even deeper on this later this afternoon
+
+ align:start position:0%
+even deeper on this later this afternoon
+ 
+
+ align:start position:0%
+even deeper on this later this afternoon
+but for now that exercise is done
+
+ align:start position:0%
+but for now that exercise is done
+ 
+
+ align:start position:0%
+but for now that exercise is done
+um just a explanation of something we've
+
+ align:start position:0%
+um just a explanation of something we've
+ 
+
+ align:start position:0%
+um just a explanation of something we've
+had kind of across the bottom as an icon
+
+ align:start position:0%
+had kind of across the bottom as an icon
+ 
+
+ align:start position:0%
+had kind of across the bottom as an icon
+for a while um these things are called
+
+ align:start position:0%
+for a while um these things are called
+ 
+
+ align:start position:0%
+for a while um these things are called
+time value charts they're they're useful
+
+ align:start position:0%
+time value charts they're they're useful
+ 
+
+ align:start position:0%
+time value charts they're they're useful
+if you want to make broad points about
+
+ align:start position:0%
+if you want to make broad points about
+ 
+
+ align:start position:0%
+if you want to make broad points about
+the use of time um this is a uh typical
+
+ align:start position:0%
+the use of time um this is a uh typical
+ 
+
+ align:start position:0%
+the use of time um this is a uh typical
+example in a lot of ways here's a
+
+ align:start position:0%
+example in a lot of ways here's a
+ 
+
+ align:start position:0%
+example in a lot of ways here's a
+process that takes a while um apparently
+
+ align:start position:0%
+process that takes a while um apparently
+ 
+
+ align:start position:0%
+process that takes a while um apparently
+there are two spans of four days of
+
+ align:start position:0%
+there are two spans of four days of
+ 
+
+ align:start position:0%
+there are two spans of four days of
+solid work uh in this process as well as
+
+ align:start position:0%
+solid work uh in this process as well as
+ 
+
+ align:start position:0%
+solid work uh in this process as well as
+a lot of weight time and a lot of nonv
+
+ align:start position:0%
+a lot of weight time and a lot of nonv
+ 
+
+ align:start position:0%
+a lot of weight time and a lot of nonv
+value added working time um one of the
+
+ align:start position:0%
+value added working time um one of the
+ 
+
+ align:start position:0%
+value added working time um one of the
+key things that this kind of chart will
+
+ align:start position:0%
+key things that this kind of chart will
+ 
+
+ align:start position:0%
+key things that this kind of chart will
+tell you about almost any process it's
+
+ align:start position:0%
+tell you about almost any process it's
+ 
+
+ align:start position:0%
+tell you about almost any process it's
+very bizarre if you come up with a
+
+ align:start position:0%
+very bizarre if you come up with a
+ 
+
+ align:start position:0%
+very bizarre if you come up with a
+process that isn't this way um is that
+
+ align:start position:0%
+process that isn't this way um is that
+ 
+
+ align:start position:0%
+process that isn't this way um is that
+um uh the Big Time Savings are in the
+
+ align:start position:0%
+um uh the Big Time Savings are in the
+ 
+
+ align:start position:0%
+um uh the Big Time Savings are in the
+weight times and the non-v value added
+
+ align:start position:0%
+weight times and the non-v value added
+ 
+
+ align:start position:0%
+weight times and the non-v value added
+times and this is one of those key you
+
+ align:start position:0%
+times and this is one of those key you
+ 
+
+ align:start position:0%
+times and this is one of those key you
+know people were talking about the issue
+
+ align:start position:0%
+know people were talking about the issue
+ 
+
+ align:start position:0%
+know people were talking about the issue
+of you know standardizing work and and
+
+ align:start position:0%
+of you know standardizing work and and
+ 
+
+ align:start position:0%
+of you know standardizing work and and
+limiting
+
+ align:start position:0%
+limiting
+ 
+
+ align:start position:0%
+limiting
+creativity what I always tell the
+
+ align:start position:0%
+creativity what I always tell the
+ 
+
+ align:start position:0%
+creativity what I always tell the
+engineers uh is no we this is this is
+
+ align:start position:0%
+engineers uh is no we this is this is
+ 
+
+ align:start position:0%
+engineers uh is no we this is this is
+you doing your work we don't we almost
+
+ align:start position:0%
+you doing your work we don't we almost
+ 
+
+ align:start position:0%
+you doing your work we don't we almost
+don't care how you do it because it's a
+
+ align:start position:0%
+don't care how you do it because it's a
+ 
+
+ align:start position:0%
+don't care how you do it because it's a
+tiny percentage of the time right to
+
+ align:start position:0%
+tiny percentage of the time right to
+ 
+
+ align:start position:0%
+tiny percentage of the time right to
+keep the customers happy we got to take
+
+ align:start position:0%
+keep the customers happy we got to take
+ 
+
+ align:start position:0%
+keep the customers happy we got to take
+this out we got to take this out and
+
+ align:start position:0%
+this out we got to take this out and
+ 
+
+ align:start position:0%
+this out we got to take this out and
+that's what we're going to worry
+
+ align:start position:0%
+that's what we're going to worry
+ 
+
+ align:start position:0%
+that's what we're going to worry
+about um and in a way the same goes with
+
+ align:start position:0%
+about um and in a way the same goes with
+ 
+
+ align:start position:0%
+about um and in a way the same goes with
+with Medical Care uh a lot of
+
+ align:start position:0%
+with Medical Care uh a lot of
+ 
+
+ align:start position:0%
+with Medical Care uh a lot of
+the um customer dissatisfaction comes
+
+ align:start position:0%
+the um customer dissatisfaction comes
+ 
+
+ align:start position:0%
+the um customer dissatisfaction comes
+from this kind of
+
+ align:start position:0%
+from this kind of
+ 
+
+ align:start position:0%
+from this kind of
+stuff right if um you know my son gets
+
+ align:start position:0%
+stuff right if um you know my son gets
+ 
+
+ align:start position:0%
+stuff right if um you know my son gets
+injured I take him to the hospital I was
+
+ align:start position:0%
+injured I take him to the hospital I was
+ 
+
+ align:start position:0%
+injured I take him to the hospital I was
+absolutely delighted with the 45 seconds
+
+ align:start position:0%
+absolutely delighted with the 45 seconds
+ 
+
+ align:start position:0%
+absolutely delighted with the 45 seconds
+of care that he received in our 9h hour
+
+ align:start position:0%
+of care that he received in our 9h hour
+ 
+
+ align:start position:0%
+of care that he received in our 9h hour
+visit
+
+ align:start position:0%
+visit
+ 
+
+ align:start position:0%
+visit
+so I was not going to tell the old male
+
+ align:start position:0%
+so I was not going to tell the old male
+ 
+
+ align:start position:0%
+so I was not going to tell the old male
+nurse who was really good at stitches
+
+ align:start position:0%
+nurse who was really good at stitches
+ 
+
+ align:start position:0%
+nurse who was really good at stitches
+how to do his job I was delighted with
+
+ align:start position:0%
+how to do his job I was delighted with
+ 
+
+ align:start position:0%
+how to do his job I was delighted with
+his job but there was a bunch of other
+
+ align:start position:0%
+his job but there was a bunch of other
+ 
+
+ align:start position:0%
+his job but there was a bunch of other
+processes involved in that particular
+
+ align:start position:0%
+processes involved in that particular
+ 
+
+ align:start position:0%
+processes involved in that particular
+experience that could have that could
+
+ align:start position:0%
+experience that could have that could
+ 
+
+ align:start position:0%
+experience that could have that could
+have used Improvement which gets to the
+
+ align:start position:0%
+have used Improvement which gets to the
+ 
+
+ align:start position:0%
+have used Improvement which gets to the
+issue of pulling value I was the
+
+ align:start position:0%
+issue of pulling value I was the
+ 
+
+ align:start position:0%
+issue of pulling value I was the
+customer there I didn't really perceive
+
+ align:start position:0%
+customer there I didn't really perceive
+ 
+
+ align:start position:0%
+customer there I didn't really perceive
+value pull in that experience all I've
+
+ align:start position:0%
+value pull in that experience all I've
+ 
+
+ align:start position:0%
+value pull in that experience all I've
+had some where where I did so what does
+
+ align:start position:0%
+had some where where I did so what does
+ 
+
+ align:start position:0%
+had some where where I did so what does
+this mean this is a kind of a difficult
+
+ align:start position:0%
+this mean this is a kind of a difficult
+ 
+
+ align:start position:0%
+this mean this is a kind of a difficult
+concept and it it exists on a couple of
+
+ align:start position:0%
+concept and it it exists on a couple of
+ 
+
+ align:start position:0%
+concept and it it exists on a couple of
+scales sometimes the easiest way to
+
+ align:start position:0%
+scales sometimes the easiest way to
+ 
+
+ align:start position:0%
+scales sometimes the easiest way to
+think about it is to think of its
+
+ align:start position:0%
+think about it is to think of its
+ 
+
+ align:start position:0%
+think about it is to think of its
+opposite a push system is an
+
+ align:start position:0%
+opposite a push system is an
+ 
+
+ align:start position:0%
+opposite a push system is an
+old-fashioned mass production system
+
+ align:start position:0%
+old-fashioned mass production system
+ 
+
+ align:start position:0%
+old-fashioned mass production system
+where what you're trying to do is
+
+ align:start position:0%
+where what you're trying to do is
+ 
+
+ align:start position:0%
+where what you're trying to do is
+optimize the productivity of each step
+
+ align:start position:0%
+optimize the productivity of each step
+ 
+
+ align:start position:0%
+optimize the productivity of each step
+all right what that means is we set up
+
+ align:start position:0%
+all right what that means is we set up
+ 
+
+ align:start position:0%
+all right what that means is we set up
+our machine or we set up our process and
+
+ align:start position:0%
+our machine or we set up our process and
+ 
+
+ align:start position:0%
+our machine or we set up our process and
+we push a lot of material through it
+
+ align:start position:0%
+we push a lot of material through it
+ 
+
+ align:start position:0%
+we push a lot of material through it
+because that is the most efficient way
+
+ align:start position:0%
+because that is the most efficient way
+ 
+
+ align:start position:0%
+because that is the most efficient way
+to do most things is to set something up
+
+ align:start position:0%
+to do most things is to set something up
+ 
+
+ align:start position:0%
+to do most things is to set something up
+and then just bang stuff through it
+
+ align:start position:0%
+and then just bang stuff through it
+ 
+
+ align:start position:0%
+and then just bang stuff through it
+there was a question and people sort of
+
+ align:start position:0%
+there was a question and people sort of
+ 
+
+ align:start position:0%
+there was a question and people sort of
+intuitively understand that there was a
+
+ align:start position:0%
+intuitively understand that there was a
+ 
+
+ align:start position:0%
+intuitively understand that there was a
+question of like why don't we just
+
+ align:start position:0%
+question of like why don't we just
+ 
+
+ align:start position:0%
+question of like why don't we just
+automate it well to automate something
+
+ align:start position:0%
+automate it well to automate something
+ 
+
+ align:start position:0%
+automate it well to automate something
+you have to set up a process buy
+
+ align:start position:0%
+you have to set up a process buy
+ 
+
+ align:start position:0%
+you have to set up a process buy
+expensive equipment then when you're all
+
+ align:start position:0%
+expensive equipment then when you're all
+ 
+
+ align:start position:0%
+expensive equipment then when you're all
+done after doing all that prep work Boom
+
+ align:start position:0%
+done after doing all that prep work Boom
+ 
+
+ align:start position:0%
+done after doing all that prep work Boom
+the shoes just fly out the end and you
+
+ align:start position:0%
+the shoes just fly out the end and you
+ 
+
+ align:start position:0%
+the shoes just fly out the end and you
+can build huge piles of them but then
+
+ align:start position:0%
+can build huge piles of them but then
+ 
+
+ align:start position:0%
+can build huge piles of them but then
+the question is do people want them are
+
+ align:start position:0%
+the question is do people want them are
+ 
+
+ align:start position:0%
+the question is do people want them are
+they good are there is there quality
+
+ align:start position:0%
+they good are there is there quality
+ 
+
+ align:start position:0%
+they good are there is there quality
+issues is there issues with you know if
+
+ align:start position:0%
+issues is there issues with you know if
+ 
+
+ align:start position:0%
+issues is there issues with you know if
+you want to change the style how hard is
+
+ align:start position:0%
+you want to change the style how hard is
+ 
+
+ align:start position:0%
+you want to change the style how hard is
+that to do um so that's a push system a
+
+ align:start position:0%
+that to do um so that's a push system a
+ 
+
+ align:start position:0%
+that to do um so that's a push system a
+pull system is kind of the conceptual
+
+ align:start position:0%
+pull system is kind of the conceptual
+ 
+
+ align:start position:0%
+pull system is kind of the conceptual
+opposite of that stuff only happens if
+
+ align:start position:0%
+opposite of that stuff only happens if
+ 
+
+ align:start position:0%
+opposite of that stuff only happens if
+the customers want it and it happens
+
+ align:start position:0%
+the customers want it and it happens
+ 
+
+ align:start position:0%
+the customers want it and it happens
+hopefully quickly enough that the
+
+ align:start position:0%
+hopefully quickly enough that the
+ 
+
+ align:start position:0%
+hopefully quickly enough that the
+customer um is Satisfied by the process
+
+ align:start position:0%
+customer um is Satisfied by the process
+ 
+
+ align:start position:0%
+customer um is Satisfied by the process
+so it's triggered by the
+
+ align:start position:0%
+so it's triggered by the
+ 
+
+ align:start position:0%
+so it's triggered by the
+customer um and that is what New Balance
+
+ align:start position:0%
+customer um and that is what New Balance
+ 
+
+ align:start position:0%
+customer um and that is what New Balance
+was really striving for they had a
+
+ align:start position:0%
+was really striving for they had a
+ 
+
+ align:start position:0%
+was really striving for they had a
+three-day turn so the shoe store ordered
+
+ align:start position:0%
+three-day turn so the shoe store ordered
+ 
+
+ align:start position:0%
+three-day turn so the shoe store ordered
+shoes and in three days the shoes were
+
+ align:start position:0%
+shoes and in three days the shoes were
+ 
+
+ align:start position:0%
+shoes and in three days the shoes were
+manufactured all the way from raw
+
+ align:start position:0%
+manufactured all the way from raw
+ 
+
+ align:start position:0%
+manufactured all the way from raw
+materials and sent to the shoe store
+
+ align:start position:0%
+materials and sent to the shoe store
+ 
+
+ align:start position:0%
+materials and sent to the shoe store
+this both results in and necessitates a
+
+ align:start position:0%
+this both results in and necessitates a
+ 
+
+ align:start position:0%
+this both results in and necessitates a
+smooth flow with relatively modest
+
+ align:start position:0%
+smooth flow with relatively modest
+ 
+
+ align:start position:0%
+smooth flow with relatively modest
+batches um and relatively small weight
+
+ align:start position:0%
+batches um and relatively small weight
+ 
+
+ align:start position:0%
+batches um and relatively small weight
+Tim or it doesn't work so as a as a sort
+
+ align:start position:0%
+Tim or it doesn't work so as a as a sort
+ 
+
+ align:start position:0%
+Tim or it doesn't work so as a as a sort
+of an ideal it's worth trying for and
+
+ align:start position:0%
+of an ideal it's worth trying for and
+ 
+
+ align:start position:0%
+of an ideal it's worth trying for and
+inherently there's very little waste in
+
+ align:start position:0%
+inherently there's very little waste in
+ 
+
+ align:start position:0%
+inherently there's very little waste in
+that kind of system trouble is of course
+
+ align:start position:0%
+that kind of system trouble is of course
+ 
+
+ align:start position:0%
+that kind of system trouble is of course
+that's relatively hard to do so let's
+
+ align:start position:0%
+that's relatively hard to do so let's
+ 
+
+ align:start position:0%
+that's relatively hard to do so let's
+think about what we need to do um to to
+
+ align:start position:0%
+think about what we need to do um to to
+ 
+
+ align:start position:0%
+think about what we need to do um to to
+do a pull system like we saw at new
+
+ align:start position:0%
+do a pull system like we saw at new
+ 
+
+ align:start position:0%
+do a pull system like we saw at new
+balance pretty much requires flow you
+
+ align:start position:0%
+balance pretty much requires flow you
+ 
+
+ align:start position:0%
+balance pretty much requires flow you
+don't have to have perfect flow but if
+
+ align:start position:0%
+don't have to have perfect flow but if
+ 
+
+ align:start position:0%
+don't have to have perfect flow but if
+you don't have a system that flows
+
+ align:start position:0%
+you don't have a system that flows
+ 
+
+ align:start position:0%
+you don't have a system that flows
+reasonably well it's very hard to make
+
+ align:start position:0%
+reasonably well it's very hard to make
+ 
+
+ align:start position:0%
+reasonably well it's very hard to make
+it a pull system and you would like to
+
+ align:start position:0%
+it a pull system and you would like to
+ 
+
+ align:start position:0%
+it a pull system and you would like to
+have a fairly predictable cycle time
+
+ align:start position:0%
+have a fairly predictable cycle time
+ 
+
+ align:start position:0%
+have a fairly predictable cycle time
+here's a bunch of tools we're going to
+
+ align:start position:0%
+here's a bunch of tools we're going to
+ 
+
+ align:start position:0%
+here's a bunch of tools we're going to
+get into those in a while the point
+
+ align:start position:0%
+get into those in a while the point
+ 
+
+ align:start position:0%
+get into those in a while the point
+really with this slide is that to have
+
+ align:start position:0%
+really with this slide is that to have
+ 
+
+ align:start position:0%
+really with this slide is that to have
+pull you need if not all of these most
+
+ align:start position:0%
+pull you need if not all of these most
+ 
+
+ align:start position:0%
+pull you need if not all of these most
+of them you have to have a pretty lean
+
+ align:start position:0%
+of them you have to have a pretty lean
+ 
+
+ align:start position:0%
+of them you have to have a pretty lean
+system and again we'll get into what
+
+ align:start position:0%
+system and again we'll get into what
+ 
+
+ align:start position:0%
+system and again we'll get into what
+those are and a pull system starts with
+
+ align:start position:0%
+those are and a pull system starts with
+ 
+
+ align:start position:0%
+those are and a pull system starts with
+a customer and essentially the signals
+
+ align:start position:0%
+a customer and essentially the signals
+ 
+
+ align:start position:0%
+a customer and essentially the signals
+work backward Ward through the system
+
+ align:start position:0%
+work backward Ward through the system
+ 
+
+ align:start position:0%
+work backward Ward through the system
+what does that mean from the customer's
+
+ align:start position:0%
+what does that mean from the customer's
+ 
+
+ align:start position:0%
+what does that mean from the customer's
+point of view it means that either the
+
+ align:start position:0%
+point of view it means that either the
+ 
+
+ align:start position:0%
+point of view it means that either the
+cycle time is lower than my expectation
+
+ align:start position:0%
+cycle time is lower than my expectation
+ 
+
+ align:start position:0%
+cycle time is lower than my expectation
+for when my product will will be
+
+ align:start position:0%
+for when my product will will be
+ 
+
+ align:start position:0%
+for when my product will will be
+delivered or when my service will be
+
+ align:start position:0%
+delivered or when my service will be
+ 
+
+ align:start position:0%
+delivered or when my service will be
+delivered or there's or there's
+
+ align:start position:0%
+delivered or there's or there's
+ 
+
+ align:start position:0%
+delivered or there's or there's
+inventory in the system as a for example
+
+ align:start position:0%
+inventory in the system as a for example
+ 
+
+ align:start position:0%
+inventory in the system as a for example
+I ordered a computer a while ago that
+
+ align:start position:0%
+I ordered a computer a while ago that
+ 
+
+ align:start position:0%
+I ordered a computer a while ago that
+computer right there and I I sort of
+
+ align:start position:0%
+computer right there and I I sort of
+ 
+
+ align:start position:0%
+computer right there and I I sort of
+mentally budgeted a couple weeks you
+
+ align:start position:0%
+mentally budgeted a couple weeks you
+ 
+
+ align:start position:0%
+mentally budgeted a couple weeks you
+know you get the new computer put the
+
+ align:start position:0%
+know you get the new computer put the
+ 
+
+ align:start position:0%
+know you get the new computer put the
+files on it get used to the system um I
+
+ align:start position:0%
+files on it get used to the system um I
+ 
+
+ align:start position:0%
+files on it get used to the system um I
+ordered it online
+
+ align:start position:0%
+ordered it online
+ 
+
+ align:start position:0%
+ordered it online
+and it came in from China in less than
+
+ align:start position:0%
+and it came in from China in less than
+ 
+
+ align:start position:0%
+and it came in from China in less than
+48 hours less than two days so to me
+
+ align:start position:0%
+48 hours less than two days so to me
+ 
+
+ align:start position:0%
+48 hours less than two days so to me
+that was a pull system it was way inside
+
+ align:start position:0%
+that was a pull system it was way inside
+ 
+
+ align:start position:0%
+that was a pull system it was way inside
+my expectations so as far as I could you
+
+ align:start position:0%
+my expectations so as far as I could you
+ 
+
+ align:start position:0%
+my expectations so as far as I could you
+know as far as it felt I wanted it and
+
+ align:start position:0%
+know as far as it felt I wanted it and
+ 
+
+ align:start position:0%
+know as far as it felt I wanted it and
+it came um so that's a very nice system
+
+ align:start position:0%
+it came um so that's a very nice system
+ 
+
+ align:start position:0%
+it came um so that's a very nice system
+uh the system was actually originally
+
+ align:start position:0%
+uh the system was actually originally
+ 
+
+ align:start position:0%
+uh the system was actually originally
+invented by Dell computer Apple's really
+
+ align:start position:0%
+invented by Dell computer Apple's really
+ 
+
+ align:start position:0%
+invented by Dell computer Apple's really
+good at it now Dell still is actually
+
+ align:start position:0%
+good at it now Dell still is actually
+ 
+
+ align:start position:0%
+good at it now Dell still is actually
+although interestingly their Market has
+
+ align:start position:0%
+although interestingly their Market has
+ 
+
+ align:start position:0%
+although interestingly their Market has
+shifted more to um servers and
+
+ align:start position:0%
+shifted more to um servers and
+ 
+
+ align:start position:0%
+shifted more to um servers and
+Industrial uses of computers than than
+
+ align:start position:0%
+Industrial uses of computers than than
+ 
+
+ align:start position:0%
+Industrial uses of computers than than
+consumers but they were one of the
+
+ align:start position:0%
+consumers but they were one of the
+ 
+
+ align:start position:0%
+consumers but they were one of the
+original U inventors of essentially
+
+ align:start position:0%
+original U inventors of essentially
+ 
+
+ align:start position:0%
+original U inventors of essentially
+ordering something on the web and then
+
+ align:start position:0%
+ordering something on the web and then
+ 
+
+ align:start position:0%
+ordering something on the web and then
+having it built for you in a process
+
+ align:start position:0%
+having it built for you in a process
+ 
+
+ align:start position:0%
+having it built for you in a process
+that's it's not really automated but the
+
+ align:start position:0%
+that's it's not really automated but the
+ 
+
+ align:start position:0%
+that's it's not really automated but the
+process itself creates your computer
+
+ align:start position:0%
+process itself creates your computer
+ 
+
+ align:start position:0%
+process itself creates your computer
+there's there isn't a whole people don't
+
+ align:start position:0%
+there's there isn't a whole people don't
+ 
+
+ align:start position:0%
+there's there isn't a whole people don't
+think about the mcmanis order it's just
+
+ align:start position:0%
+think about the mcmanis order it's just
+ 
+
+ align:start position:0%
+think about the mcmanis order it's just
+you order that computer it goes into the
+
+ align:start position:0%
+you order that computer it goes into the
+ 
+
+ align:start position:0%
+you order that computer it goes into the
+system uh that that initiates the
+
+ align:start position:0%
+system uh that that initiates the
+ 
+
+ align:start position:0%
+system uh that that initiates the
+production of the computer um
+
+ align:start position:0%
+production of the computer um
+ 
+
+ align:start position:0%
+production of the computer um
+which goes very fast so it can ship the
+
+ align:start position:0%
+which goes very fast so it can ship the
+ 
+
+ align:start position:0%
+which goes very fast so it can ship the
+same day and then they have a really
+
+ align:start position:0%
+same day and then they have a really
+ 
+
+ align:start position:0%
+same day and then they have a really
+nice supply chain operation so it can
+
+ align:start position:0%
+nice supply chain operation so it can
+ 
+
+ align:start position:0%
+nice supply chain operation so it can
+come all the way from China in about 24
+
+ align:start position:0%
+come all the way from China in about 24
+ 
+
+ align:start position:0%
+come all the way from China in about 24
+hours and you get your
+
+ align:start position:0%
+hours and you get your
+ 
+
+ align:start position:0%
+hours and you get your
+computer this has become a pretty
+
+ align:start position:0%
+computer this has become a pretty
+ 
+
+ align:start position:0%
+computer this has become a pretty
+standard for a lot of consumer products
+
+ align:start position:0%
+standard for a lot of consumer products
+ 
+
+ align:start position:0%
+standard for a lot of consumer products
+so the bar is gone up people are no
+
+ align:start position:0%
+so the bar is gone up people are no
+ 
+
+ align:start position:0%
+so the bar is gone up people are no
+longer mega mega impressed by this but
+
+ align:start position:0%
+longer mega mega impressed by this but
+ 
+
+ align:start position:0%
+longer mega mega impressed by this but
+it's actually pretty impressive that
+
+ align:start position:0%
+it's actually pretty impressive that
+ 
+
+ align:start position:0%
+it's actually pretty impressive that
+that people can do that on the on the
+
+ align:start position:0%
+that people can do that on the on the
+ 
+
+ align:start position:0%
+that people can do that on the on the
+sort of customer
+
+ align:start position:0%
+sort of customer
+ 
+
+ align:start position:0%
+sort of customer
+end a very useful concept when thinking
+
+ align:start position:0%
+end a very useful concept when thinking
+ 
+
+ align:start position:0%
+end a very useful concept when thinking
+about pull is Tac time if I want one I'm
+
+ align:start position:0%
+about pull is Tac time if I want one I'm
+ 
+
+ align:start position:0%
+about pull is Tac time if I want one I'm
+really thinking about you know what's
+
+ align:start position:0%
+really thinking about you know what's
+ 
+
+ align:start position:0%
+really thinking about you know what's
+the cycle time I expect right I want a
+
+ align:start position:0%
+the cycle time I expect right I want a
+ 
+
+ align:start position:0%
+the cycle time I expect right I want a
+computer in inside of a week okay so if
+
+ align:start position:0%
+computer in inside of a week okay so if
+ 
+
+ align:start position:0%
+computer in inside of a week okay so if
+I get it in two days I'm delighted um
+
+ align:start position:0%
+I get it in two days I'm delighted um
+ 
+
+ align:start position:0%
+I get it in two days I'm delighted um
+but if I'm you know Dell's current
+
+ align:start position:0%
+but if I'm you know Dell's current
+ 
+
+ align:start position:0%
+but if I'm you know Dell's current
+customers there are people like Google
+
+ align:start position:0%
+customers there are people like Google
+ 
+
+ align:start position:0%
+customers there are people like Google
+and I want a 100,000 computers then what
+
+ align:start position:0%
+and I want a 100,000 computers then what
+ 
+
+ align:start position:0%
+and I want a 100,000 computers then what
+we have to start thinking about is what
+
+ align:start position:0%
+we have to start thinking about is what
+ 
+
+ align:start position:0%
+we have to start thinking about is what
+is the pace at which I want those
+
+ align:start position:0%
+is the pace at which I want those
+ 
+
+ align:start position:0%
+is the pace at which I want those
+computers to show up uh and that's a
+
+ align:start position:0%
+computers to show up uh and that's a
+ 
+
+ align:start position:0%
+computers to show up uh and that's a
+really simple calculation actually and
+
+ align:start position:0%
+really simple calculation actually and
+ 
+
+ align:start position:0%
+really simple calculation actually and
+one that's very much worth doing even in
+
+ align:start position:0%
+one that's very much worth doing even in
+ 
+
+ align:start position:0%
+one that's very much worth doing even in
+processes that are less predictable than
+
+ align:start position:0%
+processes that are less predictable than
+ 
+
+ align:start position:0%
+processes that are less predictable than
+production uh things like engineering
+
+ align:start position:0%
+production uh things like engineering
+ 
+
+ align:start position:0%
+production uh things like engineering
+and Hospital processes this is actually
+
+ align:start position:0%
+and Hospital processes this is actually
+ 
+
+ align:start position:0%
+and Hospital processes this is actually
+very useful to do which is to just think
+
+ align:start position:0%
+very useful to do which is to just think
+ 
+
+ align:start position:0%
+very useful to do which is to just think
+about what's your available time a day a
+
+ align:start position:0%
+about what's your available time a day a
+ 
+
+ align:start position:0%
+about what's your available time a day a
+week a year whatever it is and what is
+
+ align:start position:0%
+week a year whatever it is and what is
+ 
+
+ align:start position:0%
+week a year whatever it is and what is
+the customer demand during that time so
+
+ align:start position:0%
+the customer demand during that time so
+ 
+
+ align:start position:0%
+the customer demand during that time so
+if I have a day uh and I have to
+
+ align:start position:0%
+if I have a day uh and I have to
+ 
+
+ align:start position:0%
+if I have a day uh and I have to
+see uh 16 patients what's my Tac time 8
+
+ align:start position:0%
+see uh 16 patients what's my Tac time 8
+ 
+
+ align:start position:0%
+see uh 16 patients what's my Tac time 8
+hour a day 16
+
+ align:start position:0%
+hour a day 16
+ 
+
+ align:start position:0%
+hour a day 16
+patients half hour right if I'm not
+
+ align:start position:0%
+patients half hour right if I'm not
+ 
+
+ align:start position:0%
+patients half hour right if I'm not
+seeing a patient every half hour I'm
+
+ align:start position:0%
+seeing a patient every half hour I'm
+ 
+
+ align:start position:0%
+seeing a patient every half hour I'm
+behind it's not it's not rocket science
+
+ align:start position:0%
+behind it's not it's not rocket science
+ 
+
+ align:start position:0%
+behind it's not it's not rocket science
+but um but it's a way of understanding
+
+ align:start position:0%
+but um but it's a way of understanding
+ 
+
+ align:start position:0%
+but um but it's a way of understanding
+what the customer demand is and if I
+
+ align:start position:0%
+what the customer demand is and if I
+ 
+
+ align:start position:0%
+what the customer demand is and if I
+hope to have anything resembling a pull
+
+ align:start position:0%
+hope to have anything resembling a pull
+ 
+
+ align:start position:0%
+hope to have anything resembling a pull
+system what kind of time constraints I
+
+ align:start position:0%
+system what kind of time constraints I
+ 
+
+ align:start position:0%
+system what kind of time constraints I
+have to stay within so there's a very
+
+ align:start position:0%
+have to stay within so there's a very
+ 
+
+ align:start position:0%
+have to stay within so there's a very
+simple an very simple calculation here
+
+ align:start position:0%
+simple an very simple calculation here
+ 
+
+ align:start position:0%
+simple an very simple calculation here
+which is basically the same one that we
+
+ align:start position:0%
+which is basically the same one that we
+ 
+
+ align:start position:0%
+which is basically the same one that we
+did uh for for our medical example um
+
+ align:start position:0%
+did uh for for our medical example um
+ 
+
+ align:start position:0%
+did uh for for our medical example um
+this is for 40 orders across a year of
+
+ align:start position:0%
+this is for 40 orders across a year of
+ 
+
+ align:start position:0%
+this is for 40 orders across a year of
+235 working days same idea this is what
+
+ align:start position:0%
+235 working days same idea this is what
+ 
+
+ align:start position:0%
+235 working days same idea this is what
+what H uh basically what is the pace at
+
+ align:start position:0%
+what H uh basically what is the pace at
+ 
+
+ align:start position:0%
+what H uh basically what is the pace at
+which we need to do work to satisfy the
+
+ align:start position:0%
+which we need to do work to satisfy the
+ 
+
+ align:start position:0%
+which we need to do work to satisfy the
+customer
+
+ align:start position:0%
+customer
+ 
+
+ align:start position:0%
+customer
+need well that's presuming that this is
+
+ align:start position:0%
+need well that's presuming that this is
+ 
+
+ align:start position:0%
+need well that's presuming that this is
+like on average but what if all 40
+
+ align:start position:0%
+like on average but what if all 40
+ 
+
+ align:start position:0%
+like on average but what if all 40
+orders came in on the same day right
+
+ align:start position:0%
+orders came in on the same day right
+ 
+
+ align:start position:0%
+orders came in on the same day right
+yeah that's right Tac time is an average
+
+ align:start position:0%
+yeah that's right Tac time is an average
+ 
+
+ align:start position:0%
+yeah that's right Tac time is an average
+um the issue of irregularity we're going
+
+ align:start position:0%
+um the issue of irregularity we're going
+ 
+
+ align:start position:0%
+um the issue of irregularity we're going
+to explore a little later in the class
+
+ align:start position:0%
+to explore a little later in the class
+ 
+
+ align:start position:0%
+to explore a little later in the class
+it definitely makes things harder on the
+
+ align:start position:0%
+it definitely makes things harder on the
+ 
+
+ align:start position:0%
+it definitely makes things harder on the
+other hand if you're dead on average the
+
+ align:start position:0%
+other hand if you're dead on average the
+ 
+
+ align:start position:0%
+other hand if you're dead on average the
+no no amount of variation is going to
+
+ align:start position:0%
+no no amount of variation is going to
+ 
+
+ align:start position:0%
+no no amount of variation is going to
+help you variation almost never helps
+
+ align:start position:0%
+help you variation almost never helps
+ 
+
+ align:start position:0%
+help you variation almost never helps
+you so you start here right but yeah
+
+ align:start position:0%
+you so you start here right but yeah
+ 
+
+ align:start position:0%
+you so you start here right but yeah
+there is that issue of you know what if
+
+ align:start position:0%
+there is that issue of you know what if
+ 
+
+ align:start position:0%
+there is that issue of you know what if
+uh sorry for the aside but I was
+
+ align:start position:0%
+uh sorry for the aside but I was
+ 
+
+ align:start position:0%
+uh sorry for the aside but I was
+visiting Walmart one of their
+
+ align:start position:0%
+visiting Walmart one of their
+ 
+
+ align:start position:0%
+visiting Walmart one of their
+distribution centers they have an
+
+ align:start position:0%
+distribution centers they have an
+ 
+
+ align:start position:0%
+distribution centers they have an
+awesome supply chain they're very very
+
+ align:start position:0%
+awesome supply chain they're very very
+ 
+
+ align:start position:0%
+awesome supply chain they're very very
+good at what they do um they had this
+
+ align:start position:0%
+good at what they do um they had this
+ 
+
+ align:start position:0%
+good at what they do um they had this
+enormous Warehouse in the middle of
+
+ align:start position:0%
+enormous Warehouse in the middle of
+ 
+
+ align:start position:0%
+enormous Warehouse in the middle of
+nowhere uh with about a cubic mile of
+
+ align:start position:0%
+nowhere uh with about a cubic mile of
+ 
+
+ align:start position:0%
+nowhere uh with about a cubic mile of
+lawnmowers in it um I exaggerate a
+
+ align:start position:0%
+lawnmowers in it um I exaggerate a
+ 
+
+ align:start position:0%
+lawnmowers in it um I exaggerate a
+little bit but I think it was it was a
+
+ align:start position:0%
+little bit but I think it was it was a
+ 
+
+ align:start position:0%
+little bit but I think it was it was a
+good chunk of a mile long only maybe 100
+
+ align:start position:0%
+good chunk of a mile long only maybe 100
+ 
+
+ align:start position:0%
+good chunk of a mile long only maybe 100
+ft wide and as many lawnmowers as you
+
+ align:start position:0%
+ft wide and as many lawnmowers as you
+ 
+
+ align:start position:0%
+ft wide and as many lawnmowers as you
+could stack before they started crushing
+
+ align:start position:0%
+could stack before they started crushing
+ 
+
+ align:start position:0%
+could stack before they started crushing
+each other not very lean right but
+
+ align:start position:0%
+each other not very lean right but
+ 
+
+ align:start position:0%
+each other not very lean right but
+that's because everyone wants a lawn
+
+ align:start position:0%
+that's because everyone wants a lawn
+ 
+
+ align:start position:0%
+that's because everyone wants a lawn
+mower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when yeah like May right so sometimes
+
+ align:start position:0%
+when yeah like May right so sometimes
+ 
+
+ align:start position:0%
+when yeah like May right so sometimes
+you're just screwed but on the other
+
+ align:start position:0%
+you're just screwed but on the other
+ 
+
+ align:start position:0%
+you're just screwed but on the other
+hand the lawnmowers the reason that they
+
+ align:start position:0%
+hand the lawnmowers the reason that they
+ 
+
+ align:start position:0%
+hand the lawnmowers the reason that they
+built the lawnmower they stacked the
+
+ align:start position:0%
+built the lawnmower they stacked the
+ 
+
+ align:start position:0%
+built the lawnmower they stacked the
+lawnmowers up into The Big Cube is
+
+ align:start position:0%
+lawnmowers up into The Big Cube is
+ 
+
+ align:start position:0%
+lawnmowers up into The Big Cube is
+because the lawnmower Factory was
+
+ align:start position:0%
+because the lawnmower Factory was
+ 
+
+ align:start position:0%
+because the lawnmower Factory was
+working to T they just figured out over
+
+ align:start position:0%
+working to T they just figured out over
+ 
+
+ align:start position:0%
+working to T they just figured out over
+the whole year how many lawnmowers they
+
+ align:start position:0%
+the whole year how many lawnmowers they
+ 
+
+ align:start position:0%
+the whole year how many lawnmowers they
+did and they were just banging them out
+
+ align:start position:0%
+did and they were just banging them out
+ 
+
+ align:start position:0%
+did and they were just banging them out
+real efficiently at that rate and they
+
+ align:start position:0%
+real efficiently at that rate and they
+ 
+
+ align:start position:0%
+real efficiently at that rate and they
+just decided that the the best thing to
+
+ align:start position:0%
+just decided that the the best thing to
+ 
+
+ align:start position:0%
+just decided that the the best thing to
+do although they weren't happy about it
+
+ align:start position:0%
+do although they weren't happy about it
+ 
+
+ align:start position:0%
+do although they weren't happy about it
+was to pile them up and sell them all in
+
+ align:start position:0%
+was to pile them up and sell them all in
+ 
+
+ align:start position:0%
+was to pile them up and sell them all in
+May so the tax still actually you know
+
+ align:start position:0%
+May so the tax still actually you know
+ 
+
+ align:start position:0%
+May so the tax still actually you know
+over a year was it made sense just
+
+ align:start position:0%
+over a year was it made sense just
+ 
+
+ align:start position:0%
+over a year was it made sense just
+happened that they had to keep them all
+
+ align:start position:0%
+happened that they had to keep them all
+ 
+
+ align:start position:0%
+happened that they had to keep them all
+until May um okay so what's our attack
+
+ align:start position:0%
+until May um okay so what's our attack
+ 
+
+ align:start position:0%
+until May um okay so what's our attack
+time at um at our hot dog stand if we
+
+ align:start position:0%
+time at um at our hot dog stand if we
+ 
+
+ align:start position:0%
+time at um at our hot dog stand if we
+had 50 customers what would our attack
+
+ align:start position:0%
+had 50 customers what would our attack
+ 
+
+ align:start position:0%
+had 50 customers what would our attack
+time b i it's got a calculator they can
+
+ align:start position:0%
+time b i it's got a calculator they can
+ 
+
+ align:start position:0%
+time b i it's got a calculator they can
+bang that out four hours right which is
+
+ align:start position:0%
+bang that out four hours right which is
+ 
+
+ align:start position:0%
+bang that out four hours right which is
+some number of minutes which is some
+
+ align:start position:0%
+some number of minutes which is some
+ 
+
+ align:start position:0%
+some number of minutes which is some
+number of seconds 12.5 customers per
+
+ align:start position:0%
+number of seconds 12.5 customers per
+ 
+
+ align:start position:0%
+number of seconds 12.5 customers per
+hour so how many hours per
+
+ align:start position:0%
+hour so how many hours per
+ 
+
+ align:start position:0%
+hour so how many hours per
+customer and let's try to express that
+
+ align:start position:0%
+customer and let's try to express that
+ 
+
+ align:start position:0%
+customer and let's try to express that
+in seconds Let's see we got 240
+
+ align:start position:0%
+in seconds Let's see we got 240
+ 
+
+ align:start position:0%
+in seconds Let's see we got 240
+minutes uh so we got about four and a
+
+ align:start position:0%
+minutes uh so we got about four and a
+ 
+
+ align:start position:0%
+minutes uh so we got about four and a
+half minutes how many seconds is that
+
+ align:start position:0%
+half minutes how many seconds is that
+ 
+
+ align:start position:0%
+half minutes how many seconds is that
+can somebody multiply that by 60 280
+
+ align:start position:0%
+can somebody multiply that by 60 280
+ 
+
+ align:start position:0%
+can somebody multiply that by 60 280
+seconds okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and if we wanted 75 customers
+
+ align:start position:0%
+all right and if we wanted 75 customers
+ 
+
+ align:start position:0%
+all right and if we wanted 75 customers
+we'd need even less 192 okay that's for
+
+ align:start position:0%
+we'd need even less 192 okay that's for
+ 
+
+ align:start position:0%
+we'd need even less 192 okay that's for
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+475 so we've computed a attack time and
+
+ align:start position:0%
+475 so we've computed a attack time and
+ 
+
+ align:start position:0%
+475 so we've computed a attack time and
+a cycle time for our hot dog stand and
+
+ align:start position:0%
+a cycle time for our hot dog stand and
+ 
+
+ align:start position:0%
+a cycle time for our hot dog stand and
+first order doesn't look good right our
+
+ align:start position:0%
+first order doesn't look good right our
+ 
+
+ align:start position:0%
+first order doesn't look good right our
+our cycle time is longer than our tack
+
+ align:start position:0%
+our cycle time is longer than our tack
+ 
+
+ align:start position:0%
+our cycle time is longer than our tack
+time but that's a little deceptive
+
+ align:start position:0%
+time but that's a little deceptive
+ 
+
+ align:start position:0%
+time but that's a little deceptive
+because there's two workers right it
+
+ align:start position:0%
+because there's two workers right it
+ 
+
+ align:start position:0%
+because there's two workers right it
+takes one hot dog dog this one order of
+
+ align:start position:0%
+takes one hot dog dog this one order of
+ 
+
+ align:start position:0%
+takes one hot dog dog this one order of
+two hot dogs about this this many
+
+ align:start position:0%
+two hot dogs about this this many
+ 
+
+ align:start position:0%
+two hot dogs about this this many
+seconds to get through the system but
+
+ align:start position:0%
+seconds to get through the system but
+ 
+
+ align:start position:0%
+seconds to get through the system but
+it's trading off between two workers so
+
+ align:start position:0%
+it's trading off between two workers so
+ 
+
+ align:start position:0%
+it's trading off between two workers so
+we can't just directly compare those
+
+ align:start position:0%
+we can't just directly compare those
+ 
+
+ align:start position:0%
+we can't just directly compare those
+still it probably makes us a little
+
+ align:start position:0%
+still it probably makes us a little
+ 
+
+ align:start position:0%
+still it probably makes us a little
+nervous that our our tack time the time
+
+ align:start position:0%
+nervous that our our tack time the time
+ 
+
+ align:start position:0%
+nervous that our our tack time the time
+that that the sort of average time we
+
+ align:start position:0%
+that that the sort of average time we
+ 
+
+ align:start position:0%
+that that the sort of average time we
+have to hit um is considerably lower
+
+ align:start position:0%
+have to hit um is considerably lower
+ 
+
+ align:start position:0%
+have to hit um is considerably lower
+than than the amount of time it actually
+
+ align:start position:0%
+than than the amount of time it actually
+ 
+
+ align:start position:0%
+than than the amount of time it actually
+takes we'll save that thought for a
+
+ align:start position:0%
+takes we'll save that thought for a
+ 
+
+ align:start position:0%
+takes we'll save that thought for a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+later uh and move on to the thought of
+
+ align:start position:0%
+later uh and move on to the thought of
+ 
+
+ align:start position:0%
+later uh and move on to the thought of
+balance work
+
+ align:start position:0%
+balance work
+ 
+
+ align:start position:0%
+balance work
+actually again in this example it's
+
+ align:start position:0%
+actually again in this example it's
+ 
+
+ align:start position:0%
+actually again in this example it's
+pretty easy we got two workers so if
+
+ align:start position:0%
+pretty easy we got two workers so if
+ 
+
+ align:start position:0%
+pretty easy we got two workers so if
+their work is perfectly balanced they're
+
+ align:start position:0%
+their work is perfectly balanced they're
+ 
+
+ align:start position:0%
+their work is perfectly balanced they're
+kind of doing half the work each each
+
+ align:start position:0%
+kind of doing half the work each each
+ 
+
+ align:start position:0%
+kind of doing half the work each each
+right uh is that the case don't know um
+
+ align:start position:0%
+right uh is that the case don't know um
+ 
+
+ align:start position:0%
+right uh is that the case don't know um
+okay so we have U we have this example
+
+ align:start position:0%
+okay so we have U we have this example
+ 
+
+ align:start position:0%
+okay so we have U we have this example
+of a product that needs to be delivered
+
+ align:start position:0%
+of a product that needs to be delivered
+ 
+
+ align:start position:0%
+of a product that needs to be delivered
+every six days if it takes 30 build if
+
+ align:start position:0%
+every six days if it takes 30 build if
+ 
+
+ align:start position:0%
+every six days if it takes 30 build if
+it takes 30 days to build how can we do
+
+ align:start position:0%
+it takes 30 days to build how can we do
+ 
+
+ align:start position:0%
+it takes 30 days to build how can we do
+it well one thing we could do is split
+
+ align:start position:0%
+it well one thing we could do is split
+ 
+
+ align:start position:0%
+it well one thing we could do is split
+the J the job up into five pieces
+
+ align:start position:0%
+the J the job up into five pieces
+ 
+
+ align:start position:0%
+the J the job up into five pieces
+right and then they should take six days
+
+ align:start position:0%
+right and then they should take six days
+ 
+
+ align:start position:0%
+right and then they should take six days
+each so that would work and uh you know
+
+ align:start position:0%
+each so that would work and uh you know
+ 
+
+ align:start position:0%
+each so that would work and uh you know
+as unit one goes into uh the the
+
+ align:start position:0%
+as unit one goes into uh the the
+ 
+
+ align:start position:0%
+as unit one goes into uh the the
+production there takes a couple days to
+
+ align:start position:0%
+production there takes a couple days to
+ 
+
+ align:start position:0%
+production there takes a couple days to
+get things started oh that animation's
+
+ align:start position:0%
+get things started oh that animation's
+ 
+
+ align:start position:0%
+get things started oh that animation's
+taken off by itself I don't have to push
+
+ align:start position:0%
+taken off by itself I don't have to push
+ 
+
+ align:start position:0%
+taken off by itself I don't have to push
+the button anymore every six days a unit
+
+ align:start position:0%
+the button anymore every six days a unit
+ 
+
+ align:start position:0%
+the button anymore every six days a unit
+comes out right so we're making our
+
+ align:start position:0%
+comes out right so we're making our
+ 
+
+ align:start position:0%
+comes out right so we're making our
+attack time even though our cycle time
+
+ align:start position:0%
+attack time even though our cycle time
+ 
+
+ align:start position:0%
+attack time even though our cycle time
+is longer but we have five steps five
+
+ align:start position:0%
+is longer but we have five steps five
+ 
+
+ align:start position:0%
+is longer but we have five steps five
+workers five units of work and they're
+
+ align:start position:0%
+workers five units of work and they're
+ 
+
+ align:start position:0%
+workers five units of work and they're
+balanced they take the same if one of
+
+ align:start position:0%
+balanced they take the same if one of
+ 
+
+ align:start position:0%
+balanced they take the same if one of
+those processes take took eight days
+
+ align:start position:0%
+those processes take took eight days
+ 
+
+ align:start position:0%
+those processes take took eight days
+days would that
+
+ align:start position:0%
+days would that
+ 
+
+ align:start position:0%
+days would that
+work no it would take eight days to get
+
+ align:start position:0%
+work no it would take eight days to get
+ 
+
+ align:start position:0%
+work no it would take eight days to get
+this the attack time would basically go
+
+ align:start position:0%
+this the attack time would basically go
+ 
+
+ align:start position:0%
+this the attack time would basically go
+to eight days so again not rocket
+
+ align:start position:0%
+to eight days so again not rocket
+ 
+
+ align:start position:0%
+to eight days so again not rocket
+science fairly simple but if we look at
+
+ align:start position:0%
+science fairly simple but if we look at
+ 
+
+ align:start position:0%
+science fairly simple but if we look at
+existing processes you know if we're
+
+ align:start position:0%
+existing processes you know if we're
+ 
+
+ align:start position:0%
+existing processes you know if we're
+plotting this out it's easy if we look
+
+ align:start position:0%
+plotting this out it's easy if we look
+ 
+
+ align:start position:0%
+plotting this out it's easy if we look
+at existing processes they're very
+
+ align:start position:0%
+at existing processes they're very
+ 
+
+ align:start position:0%
+at existing processes they're very
+rarely balanced there usually is a
+
+ align:start position:0%
+rarely balanced there usually is a
+ 
+
+ align:start position:0%
+rarely balanced there usually is a
+bottleneck process or a problem where uh
+
+ align:start position:0%
+bottleneck process or a problem where uh
+ 
+
+ align:start position:0%
+bottleneck process or a problem where uh
+one step takes longer than some of the
+
+ align:start position:0%
+one step takes longer than some of the
+ 
+
+ align:start position:0%
+one step takes longer than some of the
+other ones so balance is a key concept
+
+ align:start position:0%
+other ones so balance is a key concept
+ 
+
+ align:start position:0%
+other ones so balance is a key concept
+standard work we've talked quite a lot
+
+ align:start position:0%
+standard work we've talked quite a lot
+ 
+
+ align:start position:0%
+standard work we've talked quite a lot
+about about the fact that uh if we can't
+
+ align:start position:0%
+about about the fact that uh if we can't
+ 
+
+ align:start position:0%
+about about the fact that uh if we can't
+standardize work um then we are um then
+
+ align:start position:0%
+standardize work um then we are um then
+ 
+
+ align:start position:0%
+standardize work um then we are um then
+it's very difficult to improve it single
+
+ align:start position:0%
+it's very difficult to improve it single
+ 
+
+ align:start position:0%
+it's very difficult to improve it single
+piece flow is a key concept that's kind
+
+ align:start position:0%
+piece flow is a key concept that's kind
+ 
+
+ align:start position:0%
+piece flow is a key concept that's kind
+of integral to the idea of pull that
+
+ align:start position:0%
+of integral to the idea of pull that
+ 
+
+ align:start position:0%
+of integral to the idea of pull that
+we're processing one unit at a time just
+
+ align:start position:0%
+we're processing one unit at a time just
+ 
+
+ align:start position:0%
+we're processing one unit at a time just
+like that illustration through all the
+
+ align:start position:0%
+like that illustration through all the
+ 
+
+ align:start position:0%
+like that illustration through all the
+steps to completion that's kind of an
+
+ align:start position:0%
+steps to completion that's kind of an
+ 
+
+ align:start position:0%
+steps to completion that's kind of an
+ideal it works great on a PowerPoint you
+
+ align:start position:0%
+ideal it works great on a PowerPoint you
+ 
+
+ align:start position:0%
+ideal it works great on a PowerPoint you
+know we can things are going one step at
+
+ align:start position:0%
+know we can things are going one step at
+ 
+
+ align:start position:0%
+know we can things are going one step at
+a time no inventory that's great in
+
+ align:start position:0%
+a time no inventory that's great in
+ 
+
+ align:start position:0%
+a time no inventory that's great in
+practice is sort of an ideal that we
+
+ align:start position:0%
+practice is sort of an ideal that we
+ 
+
+ align:start position:0%
+practice is sort of an ideal that we
+shoot towards we try to keep our batches
+
+ align:start position:0%
+shoot towards we try to keep our batches
+ 
+
+ align:start position:0%
+shoot towards we try to keep our batches
+small we try to make processes when we
+
+ align:start position:0%
+small we try to make processes when we
+ 
+
+ align:start position:0%
+small we try to make processes when we
+can line up so that the flow is H is
+
+ align:start position:0%
+can line up so that the flow is H is
+ 
+
+ align:start position:0%
+can line up so that the flow is H is
+single piece uh that's kind of the
+
+ align:start position:0%
+single piece uh that's kind of the
+ 
+
+ align:start position:0%
+single piece uh that's kind of the
+opposite again of of a batch and que
+
+ align:start position:0%
+opposite again of of a batch and que
+ 
+
+ align:start position:0%
+opposite again of of a batch and que
+where we make big batches of stuff and
+
+ align:start position:0%
+where we make big batches of stuff and
+ 
+
+ align:start position:0%
+where we make big batches of stuff and
+then it waits until until the next step
+
+ align:start position:0%
+then it waits until until the next step
+ 
+
+ align:start position:0%
+then it waits until until the next step
+is ready to take
+
+ align:start position:0%
+is ready to take
+ 
+
+ align:start position:0%
+is ready to take
+it this is a key conceptual tool for any
+
+ align:start position:0%
+it this is a key conceptual tool for any
+ 
+
+ align:start position:0%
+it this is a key conceptual tool for any
+kind of pull process it's called a
+
+ align:start position:0%
+kind of pull process it's called a
+ 
+
+ align:start position:0%
+kind of pull process it's called a
+manufacturing cell and we actually saw
+
+ align:start position:0%
+manufacturing cell and we actually saw
+ 
+
+ align:start position:0%
+manufacturing cell and we actually saw
+these in action um at New Balance
+
+ align:start position:0%
+these in action um at New Balance
+ 
+
+ align:start position:0%
+these in action um at New Balance
+um the classic cell is actually u-shaped
+
+ align:start position:0%
+um the classic cell is actually u-shaped
+ 
+
+ align:start position:0%
+um the classic cell is actually u-shaped
+people actually arrange arrange the
+
+ align:start position:0%
+people actually arrange arrange the
+ 
+
+ align:start position:0%
+people actually arrange arrange the
+stuff in a u on the factory floor
+
+ align:start position:0%
+stuff in a u on the factory floor
+ 
+
+ align:start position:0%
+stuff in a u on the factory floor
+because then the in and out are
+
+ align:start position:0%
+because then the in and out are
+ 
+
+ align:start position:0%
+because then the in and out are
+basically in the same place makes moving
+
+ align:start position:0%
+basically in the same place makes moving
+ 
+
+ align:start position:0%
+basically in the same place makes moving
+stuff around easier there's even
+
+ align:start position:0%
+stuff around easier there's even
+ 
+
+ align:start position:0%
+stuff around easier there's even
+interesting rules about whether you
+
+ align:start position:0%
+interesting rules about whether you
+ 
+
+ align:start position:0%
+interesting rules about whether you
+should be whether they should go
+
+ align:start position:0%
+should be whether they should go
+ 
+
+ align:start position:0%
+should be whether they should go
+clockwise or counterclockwise depending
+
+ align:start position:0%
+clockwise or counterclockwise depending
+ 
+
+ align:start position:0%
+clockwise or counterclockwise depending
+on whether you're right-handed or
+
+ align:start position:0%
+on whether you're right-handed or
+ 
+
+ align:start position:0%
+on whether you're right-handed or
+left-handed it's if you want to get into
+
+ align:start position:0%
+left-handed it's if you want to get into
+ 
+
+ align:start position:0%
+left-handed it's if you want to get into
+the ergometrics you can get very clever
+
+ align:start position:0%
+the ergometrics you can get very clever
+ 
+
+ align:start position:0%
+the ergometrics you can get very clever
+but the basic idea is okay if if we have
+
+ align:start position:0%
+but the basic idea is okay if if we have
+ 
+
+ align:start position:0%
+but the basic idea is okay if if we have
+some tasks that can be balanced that can
+
+ align:start position:0%
+some tasks that can be balanced that can
+ 
+
+ align:start position:0%
+some tasks that can be balanced that can
+can be made to take about the same time
+
+ align:start position:0%
+can be made to take about the same time
+ 
+
+ align:start position:0%
+can be made to take about the same time
+um and that aren't dependent on a big
+
+ align:start position:0%
+um and that aren't dependent on a big
+ 
+
+ align:start position:0%
+um and that aren't dependent on a big
+batch machine like those Cutters um then
+
+ align:start position:0%
+batch machine like those Cutters um then
+ 
+
+ align:start position:0%
+batch machine like those Cutters um then
+we can line them
+
+ align:start position:0%
+we can line them
+ 
+
+ align:start position:0%
+we can line them
+up balance them so they take about the
+
+ align:start position:0%
+up balance them so they take about the
+ 
+
+ align:start position:0%
+up balance them so they take about the
+same time and then put in a very
+
+ align:start position:0%
+same time and then put in a very
+ 
+
+ align:start position:0%
+same time and then put in a very
+interesting rule instead of a big
+
+ align:start position:0%
+interesting rule instead of a big
+ 
+
+ align:start position:0%
+interesting rule instead of a big
+complicated scheduling system we're
+
+ align:start position:0%
+complicated scheduling system we're
+ 
+
+ align:start position:0%
+complicated scheduling system we're
+going to say don't work unless the
+
+ align:start position:0%
+going to say don't work unless the
+ 
+
+ align:start position:0%
+going to say don't work unless the
+downstream process needs you to and you
+
+ align:start position:0%
+downstream process needs you to and you
+ 
+
+ align:start position:0%
+downstream process needs you to and you
+and you can tell whether it needs you to
+
+ align:start position:0%
+and you can tell whether it needs you to
+ 
+
+ align:start position:0%
+and you can tell whether it needs you to
+you don't even have to ask by the fact
+
+ align:start position:0%
+you don't even have to ask by the fact
+ 
+
+ align:start position:0%
+you don't even have to ask by the fact
+that their inventory bin is empty so
+
+ align:start position:0%
+that their inventory bin is empty so
+ 
+
+ align:start position:0%
+that their inventory bin is empty so
+very simple rule so in practice okay
+
+ align:start position:0%
+very simple rule so in practice okay
+ 
+
+ align:start position:0%
+very simple rule so in practice okay
+everybody has inventory nobody works
+
+ align:start position:0%
+everybody has inventory nobody works
+ 
+
+ align:start position:0%
+everybody has inventory nobody works
+until somebody the next process in line
+
+ align:start position:0%
+until somebody the next process in line
+ 
+
+ align:start position:0%
+until somebody the next process in line
+the internal or external customer takes
+
+ align:start position:0%
+the internal or external customer takes
+ 
+
+ align:start position:0%
+the internal or external customer takes
+the product away from here now task four
+
+ align:start position:0%
+the product away from here now task four
+ 
+
+ align:start position:0%
+the product away from here now task four
+starts to work to do that they they
+
+ align:start position:0%
+starts to work to do that they they
+ 
+
+ align:start position:0%
+starts to work to do that they they
+start using their inventory which means
+
+ align:start position:0%
+start using their inventory which means
+ 
+
+ align:start position:0%
+start using their inventory which means
+three starts working which means two
+
+ align:start position:0%
+three starts working which means two
+ 
+
+ align:start position:0%
+three starts working which means two
+starts working which means one starts
+
+ align:start position:0%
+starts working which means one starts
+ 
+
+ align:start position:0%
+starts working which means one starts
+working so now everybody's working oh
+
+ align:start position:0%
+working so now everybody's working oh
+ 
+
+ align:start position:0%
+working so now everybody's working oh
+and of course now we're out here so we
+
+ align:start position:0%
+and of course now we're out here so we
+ 
+
+ align:start position:0%
+and of course now we're out here so we
+have to go ask our internal or external
+
+ align:start position:0%
+have to go ask our internal or external
+ 
+
+ align:start position:0%
+have to go ask our internal or external
+supplier for more parts right for more
+
+ align:start position:0%
+supplier for more parts right for more
+ 
+
+ align:start position:0%
+supplier for more parts right for more
+stuff if everybody takes exactly the
+
+ align:start position:0%
+stuff if everybody takes exactly the
+ 
+
+ align:start position:0%
+stuff if everybody takes exactly the
+same amount of time my next click would
+
+ align:start position:0%
+same amount of time my next click would
+ 
+
+ align:start position:0%
+same amount of time my next click would
+get us back to the beginning right
+
+ align:start position:0%
+get us back to the beginning right
+ 
+
+ align:start position:0%
+get us back to the beginning right
+everything would go back to to everybody
+
+ align:start position:0%
+everything would go back to to everybody
+ 
+
+ align:start position:0%
+everything would go back to to everybody
+having uh work in front of them uh so
+
+ align:start position:0%
+having uh work in front of them uh so
+ 
+
+ align:start position:0%
+having uh work in front of them uh so
+they stop working no
+
+ align:start position:0%
+they stop working no
+ 
+
+ align:start position:0%
+they stop working no
+inventory Direct Customer pull it's just
+
+ align:start position:0%
+inventory Direct Customer pull it's just
+ 
+
+ align:start position:0%
+inventory Direct Customer pull it's just
+triggered by the customer taking the uh
+
+ align:start position:0%
+triggered by the customer taking the uh
+ 
+
+ align:start position:0%
+triggered by the customer taking the uh
+the item out of the inventory of one at
+
+ align:start position:0%
+the item out of the inventory of one at
+ 
+
+ align:start position:0%
+the item out of the inventory of one at
+the end in the real world some tasks
+
+ align:start position:0%
+the end in the real world some tasks
+ 
+
+ align:start position:0%
+the end in the real world some tasks
+maybe the balance isn't perfect these
+
+ align:start position:0%
+maybe the balance isn't perfect these
+ 
+
+ align:start position:0%
+maybe the balance isn't perfect these
+tasks finish first
+
+ align:start position:0%
+tasks finish first
+ 
+
+ align:start position:0%
+tasks finish first
+they notice now that there is inventory
+
+ align:start position:0%
+they notice now that there is inventory
+ 
+
+ align:start position:0%
+they notice now that there is inventory
+sitting there because this task is not
+
+ align:start position:0%
+sitting there because this task is not
+ 
+
+ align:start position:0%
+sitting there because this task is not
+ready to take it so they're finished
+
+ align:start position:0%
+ready to take it so they're finished
+ 
+
+ align:start position:0%
+ready to take it so they're finished
+they stop
+
+ align:start position:0%
+they stop
+ 
+
+ align:start position:0%
+they stop
+working um that seems inefficient but
+
+ align:start position:0%
+working um that seems inefficient but
+ 
+
+ align:start position:0%
+working um that seems inefficient but
+what good does it do if they keep
+
+ align:start position:0%
+what good does it do if they keep
+ 
+
+ align:start position:0%
+what good does it do if they keep
+working what happens if they keep
+
+ align:start position:0%
+working what happens if they keep
+ 
+
+ align:start position:0%
+working what happens if they keep
+working we have yeah it just creates
+
+ align:start position:0%
+working we have yeah it just creates
+ 
+
+ align:start position:0%
+working we have yeah it just creates
+more inventory right we can just pile up
+
+ align:start position:0%
+more inventory right we can just pile up
+ 
+
+ align:start position:0%
+more inventory right we can just pile up
+inventory here it's a that would be a
+
+ align:start position:0%
+inventory here it's a that would be a
+ 
+
+ align:start position:0%
+inventory here it's a that would be a
+waste of over production so that's
+
+ align:start position:0%
+waste of over production so that's
+ 
+
+ align:start position:0%
+waste of over production so that's
+that's a very simple but this is very
+
+ align:start position:0%
+that's a very simple but this is very
+ 
+
+ align:start position:0%
+that's a very simple but this is very
+practical in a manufacturing system and
+
+ align:start position:0%
+practical in a manufacturing system and
+ 
+
+ align:start position:0%
+practical in a manufacturing system and
+conceptually you can use it for things
+
+ align:start position:0%
+conceptually you can use it for things
+ 
+
+ align:start position:0%
+conceptually you can use it for things
+like engineering work um rapid drawing
+
+ align:start position:0%
+like engineering work um rapid drawing
+ 
+
+ align:start position:0%
+like engineering work um rapid drawing
+release people have set up cells where
+
+ align:start position:0%
+release people have set up cells where
+ 
+
+ align:start position:0%
+release people have set up cells where
+um you know that that horrible value
+
+ align:start position:0%
+um you know that that horrible value
+ 
+
+ align:start position:0%
+um you know that that horrible value
+stream we saw at the very beginning with
+
+ align:start position:0%
+stream we saw at the very beginning with
+ 
+
+ align:start position:0%
+stream we saw at the very beginning with
+all the lines going everywhere well that
+
+ align:start position:0%
+all the lines going everywhere well that
+ 
+
+ align:start position:0%
+all the lines going everywhere well that
+was to get one drawing out so if you
+
+ align:start position:0%
+was to get one drawing out so if you
+ 
+
+ align:start position:0%
+was to get one drawing out so if you
+just line the engineers up like this it
+
+ align:start position:0%
+just line the engineers up like this it
+ 
+
+ align:start position:0%
+just line the engineers up like this it
+makes as much sense as every as anything
+
+ align:start position:0%
+makes as much sense as every as anything
+ 
+
+ align:start position:0%
+makes as much sense as every as anything
+else it may not be perfectly efficient
+
+ align:start position:0%
+else it may not be perfectly efficient
+ 
+
+ align:start position:0%
+else it may not be perfectly efficient
+from the engineers point of view but it
+
+ align:start position:0%
+from the engineers point of view but it
+ 
+
+ align:start position:0%
+from the engineers point of view but it
+AB but it minimizes without any
+
+ align:start position:0%
+AB but it minimizes without any
+ 
+
+ align:start position:0%
+AB but it minimizes without any
+complicated control system the time the
+
+ align:start position:0%
+complicated control system the time the
+ 
+
+ align:start position:0%
+complicated control system the time the
+product spends in the system and that's
+
+ align:start position:0%
+product spends in the system and that's
+ 
+
+ align:start position:0%
+product spends in the system and that's
+the advantage of a pull system uh
+
+ align:start position:0%
+the advantage of a pull system uh
+ 
+
+ align:start position:0%
+the advantage of a pull system uh
+another example of
+
+ align:start position:0%
+another example of
+ 
+
+ align:start position:0%
+another example of
+pull as as a con Bond system we talked
+
+ align:start position:0%
+pull as as a con Bond system we talked
+ 
+
+ align:start position:0%
+pull as as a con Bond system we talked
+about that a little bit before
+
+ align:start position:0%
+about that a little bit before
+ 
+
+ align:start position:0%
+about that a little bit before
+essentially same
+
+ align:start position:0%
+essentially same
+ 
+
+ align:start position:0%
+essentially same
+rule um appearance of a conbine bin
+
+ align:start position:0%
+rule um appearance of a conbine bin
+ 
+
+ align:start position:0%
+rule um appearance of a conbine bin
+means that the downstream process wants
+
+ align:start position:0%
+means that the downstream process wants
+ 
+
+ align:start position:0%
+means that the downstream process wants
+uh Parts conbine card or bin some kind
+
+ align:start position:0%
+uh Parts conbine card or bin some kind
+ 
+
+ align:start position:0%
+uh Parts conbine card or bin some kind
+of signal uh the the difference here is
+
+ align:start position:0%
+of signal uh the the difference here is
+ 
+
+ align:start position:0%
+of signal uh the the difference here is
+that we're no longer in a cell we're no
+
+ align:start position:0%
+that we're no longer in a cell we're no
+ 
+
+ align:start position:0%
+that we're no longer in a cell we're no
+longer right next to the other process
+
+ align:start position:0%
+longer right next to the other process
+ 
+
+ align:start position:0%
+longer right next to the other process
+so we need some kind of signal now it
+
+ align:start position:0%
+so we need some kind of signal now it
+ 
+
+ align:start position:0%
+so we need some kind of signal now it
+could be a complicated order with legal
+
+ align:start position:0%
+could be a complicated order with legal
+ 
+
+ align:start position:0%
+could be a complicated order with legal
+and pages and or it could be a bin or a
+
+ align:start position:0%
+and pages and or it could be a bin or a
+ 
+
+ align:start position:0%
+and pages and or it could be a bin or a
+card something something simple that
+
+ align:start position:0%
+card something something simple that
+ 
+
+ align:start position:0%
+card something something simple that
+we've pre-arranged that says by you know
+
+ align:start position:0%
+we've pre-arranged that says by you know
+ 
+
+ align:start position:0%
+we've pre-arranged that says by you know
+I need work I need you to do work for me
+
+ align:start position:0%
+I need work I need you to do work for me
+ 
+
+ align:start position:0%
+I need work I need you to do work for me
+um of course you have to have standard
+
+ align:start position:0%
+um of course you have to have standard
+ 
+
+ align:start position:0%
+um of course you have to have standard
+processes for this you have to agree
+
+ align:start position:0%
+processes for this you have to agree
+ 
+
+ align:start position:0%
+processes for this you have to agree
+what this card means um but it does
+
+ align:start position:0%
+what this card means um but it does
+ 
+
+ align:start position:0%
+what this card means um but it does
+allow us to control even a fairly
+
+ align:start position:0%
+allow us to control even a fairly
+ 
+
+ align:start position:0%
+allow us to control even a fairly
+complicated system uh visually and even
+
+ align:start position:0%
+complicated system uh visually and even
+ 
+
+ align:start position:0%
+complicated system uh visually and even
+if it's geographically or
+
+ align:start position:0%
+if it's geographically or
+ 
+
+ align:start position:0%
+if it's geographically or
+organizationally separated again a very
+
+ align:start position:0%
+organizationally separated again a very
+ 
+
+ align:start position:0%
+organizationally separated again a very
+simple example if we have a supplier and
+
+ align:start position:0%
+simple example if we have a supplier and
+ 
+
+ align:start position:0%
+simple example if we have a supplier and
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+manufacturer this in this case we have
+
+ align:start position:0%
+manufacturer this in this case we have
+ 
+
+ align:start position:0%
+manufacturer this in this case we have
+physical bins in the New Balance video
+
+ align:start position:0%
+physical bins in the New Balance video
+ 
+
+ align:start position:0%
+physical bins in the New Balance video
+you saw those plastic bins that
+
+ align:start position:0%
+you saw those plastic bins that
+ 
+
+ align:start position:0%
+you saw those plastic bins that
+everybody was using to move the parts
+
+ align:start position:0%
+everybody was using to move the parts
+ 
+
+ align:start position:0%
+everybody was using to move the parts
+around it's very real very direct and
+
+ align:start position:0%
+around it's very real very direct and
+ 
+
+ align:start position:0%
+around it's very real very direct and
+physical if we run out we send the empty
+
+ align:start position:0%
+physical if we run out we send the empty
+ 
+
+ align:start position:0%
+physical if we run out we send the empty
+bin to the supplier they know what that
+
+ align:start position:0%
+bin to the supplier they know what that
+ 
+
+ align:start position:0%
+bin to the supplier they know what that
+means it means fill it up um so they
+
+ align:start position:0%
+means it means fill it up um so they
+ 
+
+ align:start position:0%
+means it means fill it up um so they
+work on it and they fill up the bin when
+
+ align:start position:0%
+work on it and they fill up the bin when
+ 
+
+ align:start position:0%
+work on it and they fill up the bin when
+it's full shipping Department knows that
+
+ align:start position:0%
+it's full shipping Department knows that
+ 
+
+ align:start position:0%
+it's full shipping Department knows that
+means to take it away um when it shows
+
+ align:start position:0%
+means to take it away um when it shows
+ 
+
+ align:start position:0%
+means to take it away um when it shows
+up the manufacturer uses it until the
+
+ align:start position:0%
+up the manufacturer uses it until the
+ 
+
+ align:start position:0%
+up the manufacturer uses it until the
+bin is empty back to the supplier
+
+ align:start position:0%
+bin is empty back to the supplier
+ 
+
+ align:start position:0%
+bin is empty back to the supplier
+self-perpetuating system even if these
+
+ align:start position:0%
+self-perpetuating system even if these
+ 
+
+ align:start position:0%
+self-perpetuating system even if these
+systems are not particularly well
+
+ align:start position:0%
+systems are not particularly well
+ 
+
+ align:start position:0%
+systems are not particularly well
+balanced or if or even if demand is is
+
+ align:start position:0%
+balanced or if or even if demand is is
+ 
+
+ align:start position:0%
+balanced or if or even if demand is is
+intermittent um it will operate uh with
+
+ align:start position:0%
+intermittent um it will operate uh with
+ 
+
+ align:start position:0%
+intermittent um it will operate uh with
+no outside interference no management
+
+ align:start position:0%
+no outside interference no management
+ 
+
+ align:start position:0%
+no outside interference no management
+effort uh and minimum inventory about
+
+ align:start position:0%
+effort uh and minimum inventory about
+ 
+
+ align:start position:0%
+effort uh and minimum inventory about
+the only trick in this is essentially
+
+ align:start position:0%
+the only trick in this is essentially
+ 
+
+ align:start position:0%
+the only trick in this is essentially
+how many bins if you only have one bin
+
+ align:start position:0%
+how many bins if you only have one bin
+ 
+
+ align:start position:0%
+how many bins if you only have one bin
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+problem yeah yeah you have to wait right
+
+ align:start position:0%
+problem yeah yeah you have to wait right
+ 
+
+ align:start position:0%
+problem yeah yeah you have to wait right
+the only the one you have to wait for
+
+ align:start position:0%
+the only the one you have to wait for
+ 
+
+ align:start position:0%
+the only the one you have to wait for
+the supplier to be finished before you
+
+ align:start position:0%
+the supplier to be finished before you
+ 
+
+ align:start position:0%
+the supplier to be finished before you
+can start working again which might be
+
+ align:start position:0%
+can start working again which might be
+ 
+
+ align:start position:0%
+can start working again which might be
+okay if it's a low demand product or
+
+ align:start position:0%
+okay if it's a low demand product or
+ 
+
+ align:start position:0%
+okay if it's a low demand product or
+something um this example we have four
+
+ align:start position:0%
+something um this example we have four
+ 
+
+ align:start position:0%
+something um this example we have four
+so it kind of continues round and around
+
+ align:start position:0%
+so it kind of continues round and around
+ 
+
+ align:start position:0%
+so it kind of continues round and around
+worst thing that can happen here is if
+
+ align:start position:0%
+worst thing that can happen here is if
+ 
+
+ align:start position:0%
+worst thing that can happen here is if
+there's no demand four bins worth pile
+
+ align:start position:0%
+there's no demand four bins worth pile
+ 
+
+ align:start position:0%
+there's no demand four bins worth pile
+up right because the supplier will keep
+
+ align:start position:0%
+up right because the supplier will keep
+ 
+
+ align:start position:0%
+up right because the supplier will keep
+moving until all bins are full so we
+
+ align:start position:0%
+moving until all bins are full so we
+ 
+
+ align:start position:0%
+moving until all bins are full so we
+could pile up four bins that's probably
+
+ align:start position:0%
+could pile up four bins that's probably
+ 
+
+ align:start position:0%
+could pile up four bins that's probably
+not horrible unless of course they're
+
+ align:start position:0%
+not horrible unless of course they're
+ 
+
+ align:start position:0%
+not horrible unless of course they're
+really expensive things so there's
+
+ align:start position:0%
+really expensive things so there's
+ 
+
+ align:start position:0%
+really expensive things so there's
+there's essentially a design knob on the
+
+ align:start position:0%
+there's essentially a design knob on the
+ 
+
+ align:start position:0%
+there's essentially a design knob on the
+system which is how many bins but that's
+
+ align:start position:0%
+system which is how many bins but that's
+ 
+
+ align:start position:0%
+system which is how many bins but that's
+it it's very simple um and we can tweak
+
+ align:start position:0%
+it it's very simple um and we can tweak
+ 
+
+ align:start position:0%
+it it's very simple um and we can tweak
+it as necessary by changing the number
+
+ align:start position:0%
+it as necessary by changing the number
+ 
+
+ align:start position:0%
+it as necessary by changing the number
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Bin okay so that's that's conbine con
+
+ align:start position:0%
+Bin okay so that's that's conbine con
+ 
+
+ align:start position:0%
+Bin okay so that's that's conbine con
+Bond itself is kind of a visual control
+
+ align:start position:0%
+Bond itself is kind of a visual control
+ 
+
+ align:start position:0%
+Bond itself is kind of a visual control
+you see an empty bin you work um there's
+
+ align:start position:0%
+you see an empty bin you work um there's
+ 
+
+ align:start position:0%
+you see an empty bin you work um there's
+other kinds of uh visual controls that
+
+ align:start position:0%
+other kinds of uh visual controls that
+ 
+
+ align:start position:0%
+other kinds of uh visual controls that
+are referred to uh generically again
+
+ align:start position:0%
+are referred to uh generically again
+ 
+
+ align:start position:0%
+are referred to uh generically again
+with another Japanese word the word
+
+ align:start position:0%
+with another Japanese word the word
+ 
+
+ align:start position:0%
+with another Japanese word the word
+andon andon is kind of an adjective
+
+ align:start position:0%
+andon andon is kind of an adjective
+ 
+
+ align:start position:0%
+andon andon is kind of an adjective
+means visual control more or less um and
+
+ align:start position:0%
+means visual control more or less um and
+ 
+
+ align:start position:0%
+means visual control more or less um and
+you can have for example andon lights
+
+ align:start position:0%
+you can have for example andon lights
+ 
+
+ align:start position:0%
+you can have for example andon lights
+again in the video you may have seen you
+
+ align:start position:0%
+again in the video you may have seen you
+ 
+
+ align:start position:0%
+again in the video you may have seen you
+may have noticed in the background some
+
+ align:start position:0%
+may have noticed in the background some
+ 
+
+ align:start position:0%
+may have noticed in the background some
+uh lights like this very very standard
+
+ align:start position:0%
+uh lights like this very very standard
+ 
+
+ align:start position:0%
+uh lights like this very very standard
+practice now in manufacturing to have a
+
+ align:start position:0%
+practice now in manufacturing to have a
+ 
+
+ align:start position:0%
+practice now in manufacturing to have a
+little light Tower like that red means
+
+ align:start position:0%
+little light Tower like that red means
+ 
+
+ align:start position:0%
+little light Tower like that red means
+like the machine is broken or there's
+
+ align:start position:0%
+like the machine is broken or there's
+ 
+
+ align:start position:0%
+like the machine is broken or there's
+some serious problem it needs attention
+
+ align:start position:0%
+some serious problem it needs attention
+ 
+
+ align:start position:0%
+some serious problem it needs attention
+green means it's going fine yellow means
+
+ align:start position:0%
+green means it's going fine yellow means
+ 
+
+ align:start position:0%
+green means it's going fine yellow means
+maybe we're behind a little bit it
+
+ align:start position:0%
+maybe we're behind a little bit it
+ 
+
+ align:start position:0%
+maybe we're behind a little bit it
+allows you to just look across the
+
+ align:start position:0%
+allows you to just look across the
+ 
+
+ align:start position:0%
+allows you to just look across the
+factory floor see the state if
+
+ align:start position:0%
+factory floor see the state if
+ 
+
+ align:start position:0%
+factory floor see the state if
+everything's green it's Dandy if there's
+
+ align:start position:0%
+everything's green it's Dandy if there's
+ 
+
+ align:start position:0%
+everything's green it's Dandy if there's
+red stuff you got to go fix it if
+
+ align:start position:0%
+red stuff you got to go fix it if
+ 
+
+ align:start position:0%
+red stuff you got to go fix it if
+there's yellows that tells you what to
+
+ align:start position:0%
+there's yellows that tells you what to
+ 
+
+ align:start position:0%
+there's yellows that tells you what to
+worry about um it's only really useful
+
+ align:start position:0%
+worry about um it's only really useful
+ 
+
+ align:start position:0%
+worry about um it's only really useful
+if you do something about it though it's
+
+ align:start position:0%
+if you do something about it though it's
+ 
+
+ align:start position:0%
+if you do something about it though it's
+part of an active management system um
+
+ align:start position:0%
+part of an active management system um
+ 
+
+ align:start position:0%
+part of an active management system um
+another one is the andon cord this is
+
+ align:start position:0%
+another one is the andon cord this is
+ 
+
+ align:start position:0%
+another one is the andon cord this is
+the famous counterintuitive Japanese
+
+ align:start position:0%
+the famous counterintuitive Japanese
+ 
+
+ align:start position:0%
+the famous counterintuitive Japanese
+practice of basically having a cord in
+
+ align:start position:0%
+practice of basically having a cord in
+ 
+
+ align:start position:0%
+practice of basically having a cord in
+front of every employee that they can
+
+ align:start position:0%
+front of every employee that they can
+ 
+
+ align:start position:0%
+front of every employee that they can
+pull that stops the entire
+
+ align:start position:0%
+pull that stops the entire
+ 
+
+ align:start position:0%
+pull that stops the entire
+Factory um this is very scary even to
+
+ align:start position:0%
+Factory um this is very scary even to
+ 
+
+ align:start position:0%
+Factory um this is very scary even to
+this day to uh North American managers
+
+ align:start position:0%
+this day to uh North American managers
+ 
+
+ align:start position:0%
+this day to uh North American managers
+because any disgruntled person can pull
+
+ align:start position:0%
+because any disgruntled person can pull
+ 
+
+ align:start position:0%
+because any disgruntled person can pull
+the court and stop the entire Factory
+
+ align:start position:0%
+the court and stop the entire Factory
+ 
+
+ align:start position:0%
+the court and stop the entire Factory
+what's what's that about um but of
+
+ align:start position:0%
+what's what's that about um but of
+ 
+
+ align:start position:0%
+what's what's that about um but of
+course the way they use that is to draw
+
+ align:start position:0%
+course the way they use that is to draw
+ 
+
+ align:start position:0%
+course the way they use that is to draw
+attention to a serious problem if a
+
+ align:start position:0%
+attention to a serious problem if a
+ 
+
+ align:start position:0%
+attention to a serious problem if a
+quality problem is happening okay the
+
+ align:start position:0%
+quality problem is happening okay the
+ 
+
+ align:start position:0%
+quality problem is happening okay the
+parts don't fit um that's unacceptable
+
+ align:start position:0%
+parts don't fit um that's unacceptable
+ 
+
+ align:start position:0%
+parts don't fit um that's unacceptable
+at a at at a high quality production
+
+ align:start position:0%
+at a at at a high quality production
+ 
+
+ align:start position:0%
+at a at at a high quality production
+operation so they stop the line because
+
+ align:start position:0%
+operation so they stop the line because
+ 
+
+ align:start position:0%
+operation so they stop the line because
+if they don't that defective part is
+
+ align:start position:0%
+if they don't that defective part is
+ 
+
+ align:start position:0%
+if they don't that defective part is
+going to continue down the line get more
+
+ align:start position:0%
+going to continue down the line get more
+ 
+
+ align:start position:0%
+going to continue down the line get more
+parts piled on top of it until you have
+
+ align:start position:0%
+parts piled on top of it until you have
+ 
+
+ align:start position:0%
+parts piled on top of it until you have
+effect essentially a defective car so a
+
+ align:start position:0%
+effect essentially a defective car so a
+ 
+
+ align:start position:0%
+effect essentially a defective car so a
+washer or whatever is turned into a big
+
+ align:start position:0%
+washer or whatever is turned into a big
+ 
+
+ align:start position:0%
+washer or whatever is turned into a big
+problem it's actually better to stop and
+
+ align:start position:0%
+problem it's actually better to stop and
+ 
+
+ align:start position:0%
+problem it's actually better to stop and
+fix it it also provides a lot of
+
+ align:start position:0%
+fix it it also provides a lot of
+ 
+
+ align:start position:0%
+fix it it also provides a lot of
+motivation everybody comes over and
+
+ align:start position:0%
+motivation everybody comes over and
+ 
+
+ align:start position:0%
+motivation everybody comes over and
+fixes it right away because you know the
+
+ align:start position:0%
+fixes it right away because you know the
+ 
+
+ align:start position:0%
+fixes it right away because you know the
+line is stopped so the team leader
+
+ align:start position:0%
+line is stopped so the team leader
+ 
+
+ align:start position:0%
+line is stopped so the team leader
+Engineers whoever needs to come on over
+
+ align:start position:0%
+Engineers whoever needs to come on over
+ 
+
+ align:start position:0%
+Engineers whoever needs to come on over
+um and solve the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem that's the andon cord
+
+ align:start position:0%
+problem that's the andon cord
+ 
+
+ align:start position:0%
+problem that's the andon cord
+Concept Medical example Virginia Mason
+
+ align:start position:0%
+Concept Medical example Virginia Mason
+ 
+
+ align:start position:0%
+Concept Medical example Virginia Mason
+Medical Center they have a u essentially
+
+ align:start position:0%
+Medical Center they have a u essentially
+ 
+
+ align:start position:0%
+Medical Center they have a u essentially
+a policy that says that any of their
+
+ align:start position:0%
+a policy that says that any of their
+ 
+
+ align:start position:0%
+a policy that says that any of their
+5,000 employees
+
+ align:start position:0%
+5,000 employees
+ 
+
+ align:start position:0%
+5,000 employees
+can they don't exactly stop seeing
+
+ align:start position:0%
+can they don't exactly stop seeing
+ 
+
+ align:start position:0%
+can they don't exactly stop seeing
+patients but
+
+ align:start position:0%
+patients but
+ 
+
+ align:start position:0%
+patients but
+all attention is paid to this person if
+
+ align:start position:0%
+all attention is paid to this person if
+ 
+
+ align:start position:0%
+all attention is paid to this person if
+they if they uh declare it an andon cord
+
+ align:start position:0%
+they if they uh declare it an andon cord
+ 
+
+ align:start position:0%
+they if they uh declare it an andon cord
+action if there is a patient safety
+
+ align:start position:0%
+action if there is a patient safety
+ 
+
+ align:start position:0%
+action if there is a patient safety
+issue that needs to be dealt with
+
+ align:start position:0%
+issue that needs to be dealt with
+ 
+
+ align:start position:0%
+issue that needs to be dealt with
+immediately they can get as much
+
+ align:start position:0%
+immediately they can get as much
+ 
+
+ align:start position:0%
+immediately they can get as much
+attention as they need and this happens
+
+ align:start position:0%
+attention as they need and this happens
+ 
+
+ align:start position:0%
+attention as they need and this happens
+quite a bit um but um but it has also
+
+ align:start position:0%
+quite a bit um but um but it has also
+ 
+
+ align:start position:0%
+quite a bit um but um but it has also
+surfaced a lot of problems and and the
+
+ align:start position:0%
+surfaced a lot of problems and and the
+ 
+
+ align:start position:0%
+surfaced a lot of problems and and the
+real key here by the way is not that
+
+ align:start position:0%
+real key here by the way is not that
+ 
+
+ align:start position:0%
+real key here by the way is not that
+this is a very good quick solving
+
+ align:start position:0%
+this is a very good quick solving
+ 
+
+ align:start position:0%
+this is a very good quick solving
+problem problem solving method because
+
+ align:start position:0%
+problem problem solving method because
+ 
+
+ align:start position:0%
+problem problem solving method because
+it isn't it stop the line it could be
+
+ align:start position:0%
+it isn't it stop the line it could be
+ 
+
+ align:start position:0%
+it isn't it stop the line it could be
+potentially very expensive over
+
+ align:start position:0%
+potentially very expensive over
+ 
+
+ align:start position:0%
+potentially very expensive over
+something very small but that it
+
+ align:start position:0%
+something very small but that it
+ 
+
+ align:start position:0%
+something very small but that it
+surfaces problems if you if you have a
+
+ align:start position:0%
+surfaces problems if you if you have a
+ 
+
+ align:start position:0%
+surfaces problems if you if you have a
+problem of this magnitude you don't want
+
+ align:start position:0%
+problem of this magnitude you don't want
+ 
+
+ align:start position:0%
+problem of this magnitude you don't want
+to see it again so it surfaces the
+
+ align:start position:0%
+to see it again so it surfaces the
+ 
+
+ align:start position:0%
+to see it again so it surfaces the
+problem and uh allows uh people to pay
+
+ align:start position:0%
+problem and uh allows uh people to pay
+ 
+
+ align:start position:0%
+problem and uh allows uh people to pay
+attention to it find the root cause make
+
+ align:start position:0%
+attention to it find the root cause make
+ 
+
+ align:start position:0%
+attention to it find the root cause make
+it go away for good okay final step
+
+ align:start position:0%
+it go away for good okay final step
+ 
+
+ align:start position:0%
+it go away for good okay final step
+pursuing Perfection this is all about
+
+ align:start position:0%
+pursuing Perfection this is all about
+ 
+
+ align:start position:0%
+pursuing Perfection this is all about
+not quitting there's always more ways to
+
+ align:start position:0%
+not quitting there's always more ways to
+ 
+
+ align:start position:0%
+not quitting there's always more ways to
+eliminate there's always ways you can do
+
+ align:start position:0%
+eliminate there's always ways you can do
+ 
+
+ align:start position:0%
+eliminate there's always ways you can do
+things better there's always ways you
+
+ align:start position:0%
+things better there's always ways you
+ 
+
+ align:start position:0%
+things better there's always ways you
+can get the employees more involved so
+
+ align:start position:0%
+can get the employees more involved so
+ 
+
+ align:start position:0%
+can get the employees more involved so
+it's a it's a continuous process and
+
+ align:start position:0%
+it's a it's a continuous process and
+ 
+
+ align:start position:0%
+it's a it's a continuous process and
+we'll be talking about uh about that
+
+ align:start position:0%
+we'll be talking about uh about that
+ 
+
+ align:start position:0%
+we'll be talking about uh about that
+more later another tool a final tool for
+
+ align:start position:0%
+more later another tool a final tool for
+ 
+
+ align:start position:0%
+more later another tool a final tool for
+for for this afternoon uh five W put the
+
+ align:start position:0%
+for for this afternoon uh five W put the
+ 
+
+ align:start position:0%
+for for this afternoon uh five W put the
+seven the eight wastes and the six s's
+
+ align:start position:0%
+seven the eight wastes and the six s's
+ 
+
+ align:start position:0%
+seven the eight wastes and the six s's
+these are the five y's uh not the letter
+
+ align:start position:0%
+these are the five y's uh not the letter
+ 
+
+ align:start position:0%
+these are the five y's uh not the letter
+the uh the word um and the point of the
+
+ align:start position:0%
+the uh the word um and the point of the
+ 
+
+ align:start position:0%
+the uh the word um and the point of the
+five y's is to keep asking why fact the
+
+ align:start position:0%
+five y's is to keep asking why fact the
+ 
+
+ align:start position:0%
+five y's is to keep asking why fact the
+fact that there's a number is actually
+
+ align:start position:0%
+fact that there's a number is actually
+ 
+
+ align:start position:0%
+fact that there's a number is actually
+kind of bad because you you may not want
+
+ align:start position:0%
+kind of bad because you you may not want
+ 
+
+ align:start position:0%
+kind of bad because you you may not want
+to quit at five and three might be
+
+ align:start position:0%
+to quit at five and three might be
+ 
+
+ align:start position:0%
+to quit at five and three might be
+enough but here's an example um it's
+
+ align:start position:0%
+enough but here's an example um it's
+ 
+
+ align:start position:0%
+enough but here's an example um it's
+possibly apocryphal example about the
+
+ align:start position:0%
+possibly apocryphal example about the
+ 
+
+ align:start position:0%
+possibly apocryphal example about the
+Jefferson
+
+ align:start position:0%
+Jefferson
+ 
+
+ align:start position:0%
+Jefferson
+monument why is the Jeff Jefferson
+
+ align:start position:0%
+monument why is the Jeff Jefferson
+ 
+
+ align:start position:0%
+monument why is the Jeff Jefferson
+monument deteriorating because they wash
+
+ align:start position:0%
+monument deteriorating because they wash
+ 
+
+ align:start position:0%
+monument deteriorating because they wash
+it all the time why is it washed all the
+
+ align:start position:0%
+it all the time why is it washed all the
+ 
+
+ align:start position:0%
+it all the time why is it washed all the
+time because it has bird poop on it um
+
+ align:start position:0%
+time because it has bird poop on it um
+ 
+
+ align:start position:0%
+time because it has bird poop on it um
+why do they do that well because the
+
+ align:start position:0%
+why do they do that well because the
+ 
+
+ align:start position:0%
+why do they do that well because the
+birds are eating the spiders why are
+
+ align:start position:0%
+birds are eating the spiders why are
+ 
+
+ align:start position:0%
+birds are eating the spiders why are
+there spiders because they're eating
+
+ align:start position:0%
+there spiders because they're eating
+ 
+
+ align:start position:0%
+there spiders because they're eating
+Nats why are there gats cuz the lights
+
+ align:start position:0%
+Nats why are there gats cuz the lights
+ 
+
+ align:start position:0%
+Nats why are there gats cuz the lights
+are on all the time of course I had
+
+ align:start position:0%
+are on all the time of course I had
+ 
+
+ align:start position:0%
+are on all the time of course I had
+somebody did a class
+
+ align:start position:0%
+somebody did a class
+ 
+
+ align:start position:0%
+somebody did a class
+uh a couple times ago that said why are
+
+ align:start position:0%
+uh a couple times ago that said why are
+ 
+
+ align:start position:0%
+uh a couple times ago that said why are
+the lights on all the time because it's
+
+ align:start position:0%
+the lights on all the time because it's
+ 
+
+ align:start position:0%
+the lights on all the time because it's
+in a bad neighborhood
+
+ align:start position:0%
+in a bad neighborhood
+ 
+
+ align:start position:0%
+in a bad neighborhood
+but um so so maybe five is not the right
+
+ align:start position:0%
+but um so so maybe five is not the right
+ 
+
+ align:start position:0%
+but um so so maybe five is not the right
+number maybe less is okay maybe you need
+
+ align:start position:0%
+number maybe less is okay maybe you need
+ 
+
+ align:start position:0%
+number maybe less is okay maybe you need
+to go deeper so five fundamentals kind
+
+ align:start position:0%
+to go deeper so five fundamentals kind
+ 
+
+ align:start position:0%
+to go deeper so five fundamentals kind
+of work together pursuing Perfection may
+
+ align:start position:0%
+of work together pursuing Perfection may
+ 
+
+ align:start position:0%
+of work together pursuing Perfection may
+send you all the way back to the
+
+ align:start position:0%
+send you all the way back to the
+ 
+
+ align:start position:0%
+send you all the way back to the
+beginning this is kind of a strategic
+
+ align:start position:0%
+beginning this is kind of a strategic
+ 
+
+ align:start position:0%
+beginning this is kind of a strategic
+view the tactics and we're going to be
+
+ align:start position:0%
+view the tactics and we're going to be
+ 
+
+ align:start position:0%
+view the tactics and we're going to be
+talking about this for the rest of the
+
+ align:start position:0%
+talking about this for the rest of the
+ 
+
+ align:start position:0%
+talking about this for the rest of the
+week so I won't dwell well on it are uh
+
+ align:start position:0%
+week so I won't dwell well on it are uh
+ 
+
+ align:start position:0%
+week so I won't dwell well on it are uh
+in this Loop the plan do study act Loop
+
+ align:start position:0%
+in this Loop the plan do study act Loop
+ 
+
+ align:start position:0%
+in this Loop the plan do study act Loop
+so whenever you find something you need
+
+ align:start position:0%
+so whenever you find something you need
+ 
+
+ align:start position:0%
+so whenever you find something you need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+fix you don't just willy-nilly fix it
+
+ align:start position:0%
+fix you don't just willy-nilly fix it
+ 
+
+ align:start position:0%
+fix you don't just willy-nilly fix it
+you go through an ordered process and it
+
+ align:start position:0%
+you go through an ordered process and it
+ 
+
+ align:start position:0%
+you go through an ordered process and it
+is through a series of these ordered
+
+ align:start position:0%
+is through a series of these ordered
+ 
+
+ align:start position:0%
+is through a series of these ordered
+processes that you actually uh improve
+
+ align:start position:0%
+processes that you actually uh improve
+ 
+
+ align:start position:0%
+processes that you actually uh improve
+your your value stream achieve your flow
+
+ align:start position:0%
+your your value stream achieve your flow
+ 
+
+ align:start position:0%
+your your value stream achieve your flow
+uh move push towards pull so we've
+
+ align:start position:0%
+uh move push towards pull so we've
+ 
+
+ align:start position:0%
+uh move push towards pull so we've
+actually gone through a bunch of stuff
+
+ align:start position:0%
+actually gone through a bunch of stuff
+ 
+
+ align:start position:0%
+actually gone through a bunch of stuff
+remember that huge chart at the
+
+ align:start position:0%
+remember that huge chart at the
+ 
+
+ align:start position:0%
+remember that huge chart at the
+beginning that nobody knew hardly any of
+
+ align:start position:0%
+beginning that nobody knew hardly any of
+ 
+
+ align:start position:0%
+beginning that nobody knew hardly any of
+the terms on well now you have at least
+
+ align:start position:0%
+the terms on well now you have at least
+ 
+
+ align:start position:0%
+the terms on well now you have at least
+been introduced to all of these quite a
+
+ align:start position:0%
+been introduced to all of these quite a
+ 
+
+ align:start position:0%
+been introduced to all of these quite a
+few hopefully at the top level I don't
+
+ align:start position:0%
+few hopefully at the top level I don't
+ 
+
+ align:start position:0%
+few hopefully at the top level I don't
+know whether you've absorbed all of
+
+ align:start position:0%
+know whether you've absorbed all of
+ 
+
+ align:start position:0%
+know whether you've absorbed all of
+those hopefully at the top level the
+
+ align:start position:0%
+those hopefully at the top level the
+ 
+
+ align:start position:0%
+those hopefully at the top level the
+concept of
+
+ align:start position:0%
+concept of
+ 
+
+ align:start position:0%
+concept of
+process the concept of thinking about
+
+ align:start position:0%
+process the concept of thinking about
+ 
+
+ align:start position:0%
+process the concept of thinking about
+customer value has sunk
+
+ align:start position:0%
+customer value has sunk
+ 
+
+ align:start position:0%
+customer value has sunk
+in and that some of the thoughts about
+
+ align:start position:0%
+in and that some of the thoughts about
+ 
+
+ align:start position:0%
+in and that some of the thoughts about
+making value flow couple of the simple
+
+ align:start position:0%
+making value flow couple of the simple
+ 
+
+ align:start position:0%
+making value flow couple of the simple
+tools have stuck particularly not on the
+
+ align:start position:0%
+tools have stuck particularly not on the
+ 
+
+ align:start position:0%
+tools have stuck particularly not on the
+chart but always uh a favorite of mine
+
+ align:start position:0%
+chart but always uh a favorite of mine
+ 
+
+ align:start position:0%
+chart but always uh a favorite of mine
+is that you at least started to
+
+ align:start position:0%
+is that you at least started to
+ 
+
+ align:start position:0%
+is that you at least started to
+appreciate the complexity of what time
+
+ align:start position:0%
+appreciate the complexity of what time
+ 
+
+ align:start position:0%
+appreciate the complexity of what time
+means in these processes and again we'll
+
+ align:start position:0%
+means in these processes and again we'll
+ 
+
+ align:start position:0%
+means in these processes and again we'll
+be doing a considerable exercise on that
+
+ align:start position:0%
+be doing a considerable exercise on that
+ 
+
+ align:start position:0%
+be doing a considerable exercise on that
+starting in just a few minutes so that's
+
+ align:start position:0%
+starting in just a few minutes so that's
+ 
+
+ align:start position:0%
+starting in just a few minutes so that's
+it for now
\ No newline at end of file
diff --git a/uMc-j5aQTH8.txt b/uMc-j5aQTH8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1289320a8c5f4ebee715c6385139306266d01e8c
--- /dev/null
+++ b/uMc-j5aQTH8.txt
@@ -0,0 +1,4032 @@
+align:start position:0%
+ 
+welcome to age 20. welcome to uh special
+
+ align:start position:0%
+welcome to age 20. welcome to uh special
+ 
+
+ align:start position:0%
+welcome to age 20. welcome to uh special
+relativity and let me start by wishing
+
+ align:start position:0%
+relativity and let me start by wishing
+ 
+
+ align:start position:0%
+relativity and let me start by wishing
+you all a happy new year uh happy new
+
+ align:start position:0%
+you all a happy new year uh happy new
+ 
+
+ align:start position:0%
+you all a happy new year uh happy new
+year 2021 i'm pretty sure this is going
+
+ align:start position:0%
+year 2021 i'm pretty sure this is going
+ 
+
+ align:start position:0%
+year 2021 i'm pretty sure this is going
+to be an exciting year with a lot of
+
+ align:start position:0%
+to be an exciting year with a lot of
+ 
+
+ align:start position:0%
+to be an exciting year with a lot of
+changes ahead and a lot of exciting
+
+ align:start position:0%
+changes ahead and a lot of exciting
+ 
+
+ align:start position:0%
+changes ahead and a lot of exciting
+events
+
+ align:start position:0%
+events
+ 
+
+ align:start position:0%
+events
+my name is marcus schluter and i will
+
+ align:start position:0%
+my name is marcus schluter and i will
+ 
+
+ align:start position:0%
+my name is marcus schluter and i will
+guide you through this iap lecture on
+
+ align:start position:0%
+guide you through this iap lecture on
+ 
+
+ align:start position:0%
+guide you through this iap lecture on
+special relativity
+
+ align:start position:0%
+special relativity
+ 
+
+ align:start position:0%
+special relativity
+this is very likely my favorite class at
+
+ align:start position:0%
+this is very likely my favorite class at
+ 
+
+ align:start position:0%
+this is very likely my favorite class at
+mit um
+
+ align:start position:0%
+mit um
+ 
+
+ align:start position:0%
+mit um
+a because it's iap and
+
+ align:start position:0%
+a because it's iap and
+ 
+
+ align:start position:0%
+a because it's iap and
+we start a new year there's a lot of
+
+ align:start position:0%
+we start a new year there's a lot of
+ 
+
+ align:start position:0%
+we start a new year there's a lot of
+excitement in the air and
+
+ align:start position:0%
+excitement in the air and
+ 
+
+ align:start position:0%
+excitement in the air and
+um we have a chance to focus for this
+
+ align:start position:0%
+um we have a chance to focus for this
+ 
+
+ align:start position:0%
+um we have a chance to focus for this
+one month of january
+
+ align:start position:0%
+one month of january
+ 
+
+ align:start position:0%
+one month of january
+on this specific subject
+
+ align:start position:0%
+on this specific subject
+ 
+
+ align:start position:0%
+on this specific subject
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+i have a chance to introduce a man
+
+ align:start position:0%
+i have a chance to introduce a man
+ 
+
+ align:start position:0%
+i have a chance to introduce a man
+albert einstein
+
+ align:start position:0%
+albert einstein
+ 
+
+ align:start position:0%
+albert einstein
+through a discussion of his physics
+
+ align:start position:0%
+through a discussion of his physics
+ 
+
+ align:start position:0%
+through a discussion of his physics
+through a discussion of him as a person
+
+ align:start position:0%
+through a discussion of him as a person
+ 
+
+ align:start position:0%
+through a discussion of him as a person
+and also
+
+ align:start position:0%
+and also
+ 
+
+ align:start position:0%
+and also
+through a discussion of the historic
+
+ align:start position:0%
+through a discussion of the historic
+ 
+
+ align:start position:0%
+through a discussion of the historic
+context in which he developed special
+
+ align:start position:0%
+context in which he developed special
+ 
+
+ align:start position:0%
+context in which he developed special
+relativity
+
+ align:start position:0%
+relativity
+ 
+
+ align:start position:0%
+relativity
+and see
+
+ align:start position:0%
+and see
+ 
+
+ align:start position:0%
+and see
+if this is the first time you encounter
+
+ align:start position:0%
+if this is the first time you encounter
+ 
+
+ align:start position:0%
+if this is the first time you encounter
+special relativity it will blow your
+
+ align:start position:0%
+special relativity it will blow your
+ 
+
+ align:start position:0%
+special relativity it will blow your
+mind and it actually is quite fun as an
+
+ align:start position:0%
+mind and it actually is quite fun as an
+ 
+
+ align:start position:0%
+mind and it actually is quite fun as an
+instructor to you know do a little bit
+
+ align:start position:0%
+instructor to you know do a little bit
+ 
+
+ align:start position:0%
+instructor to you know do a little bit
+of a transformation a new understanding
+
+ align:start position:0%
+of a transformation a new understanding
+ 
+
+ align:start position:0%
+of a transformation a new understanding
+on on physics so let's get started
+
+ align:start position:0%
+on on physics so let's get started
+ 
+
+ align:start position:0%
+on on physics so let's get started
+um with a quote with an einstein quote i
+
+ align:start position:0%
+um with a quote with an einstein quote i
+ 
+
+ align:start position:0%
+um with a quote with an einstein quote i
+have a number of those
+
+ align:start position:0%
+have a number of those
+ 
+
+ align:start position:0%
+have a number of those
+as we go through the class
+
+ align:start position:0%
+as we go through the class
+ 
+
+ align:start position:0%
+as we go through the class
+this one here is really you know kind of
+
+ align:start position:0%
+this one here is really you know kind of
+ 
+
+ align:start position:0%
+this one here is really you know kind of
+the theme of the class
+
+ align:start position:0%
+the theme of the class
+ 
+
+ align:start position:0%
+the theme of the class
+um let me just read this to you
+
+ align:start position:0%
+um let me just read this to you
+ 
+
+ align:start position:0%
+um let me just read this to you
+it is not the result of scientific
+
+ align:start position:0%
+it is not the result of scientific
+ 
+
+ align:start position:0%
+it is not the result of scientific
+research that enables humans and
+
+ align:start position:0%
+research that enables humans and
+ 
+
+ align:start position:0%
+research that enables humans and
+enriches their nature but the struggle
+
+ align:start position:0%
+enriches their nature but the struggle
+ 
+
+ align:start position:0%
+enriches their nature but the struggle
+to understand while performing creative
+
+ align:start position:0%
+to understand while performing creative
+ 
+
+ align:start position:0%
+to understand while performing creative
+and open-minded intellectual work
+
+ align:start position:0%
+and open-minded intellectual work
+ 
+
+ align:start position:0%
+and open-minded intellectual work
+it is really you know the struggle with
+
+ align:start position:0%
+it is really you know the struggle with
+ 
+
+ align:start position:0%
+it is really you know the struggle with
+the ideas really the trying to get
+
+ align:start position:0%
+the ideas really the trying to get
+ 
+
+ align:start position:0%
+the ideas really the trying to get
+understanding which ennobles humans and
+
+ align:start position:0%
+understanding which ennobles humans and
+ 
+
+ align:start position:0%
+understanding which ennobles humans and
+enriches their natures and let me add
+
+ align:start position:0%
+enriches their natures and let me add
+ 
+
+ align:start position:0%
+enriches their natures and let me add
+here um
+
+ align:start position:0%
+here um
+ 
+
+ align:start position:0%
+here um
+that through your own work um so your
+
+ align:start position:0%
+that through your own work um so your
+ 
+
+ align:start position:0%
+that through your own work um so your
+own mind you can transform yourself
+
+ align:start position:0%
+own mind you can transform yourself
+ 
+
+ align:start position:0%
+own mind you can transform yourself
+in your understanding of physics in
+
+ align:start position:0%
+in your understanding of physics in
+ 
+
+ align:start position:0%
+in your understanding of physics in
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+this first video and this first lecture
+
+ align:start position:0%
+this first video and this first lecture
+ 
+
+ align:start position:0%
+this first video and this first lecture
+will mostly be concerned with
+
+ align:start position:0%
+will mostly be concerned with
+ 
+
+ align:start position:0%
+will mostly be concerned with
+organizational
+
+ align:start position:0%
+organizational
+ 
+
+ align:start position:0%
+organizational
+topics so i'll lay out
+
+ align:start position:0%
+topics so i'll lay out
+ 
+
+ align:start position:0%
+topics so i'll lay out
+the schedule of the class and also how
+
+ align:start position:0%
+the schedule of the class and also how
+ 
+
+ align:start position:0%
+the schedule of the class and also how
+you get a grade or what kind of presets
+
+ align:start position:0%
+you get a grade or what kind of presets
+ 
+
+ align:start position:0%
+you get a grade or what kind of presets
+we have in mind and so on
+
+ align:start position:0%
+we have in mind and so on
+ 
+
+ align:start position:0%
+we have in mind and so on
+let's get started so i introduced myself
+
+ align:start position:0%
+let's get started so i introduced myself
+ 
+
+ align:start position:0%
+let's get started so i introduced myself
+already again marcus cluter you can
+
+ align:start position:0%
+already again marcus cluter you can
+ 
+
+ align:start position:0%
+already again marcus cluter you can
+reach me by email at clutter mit.edu we
+
+ align:start position:0%
+reach me by email at clutter mit.edu we
+ 
+
+ align:start position:0%
+reach me by email at clutter mit.edu we
+have a graduate ta justin his email is
+
+ align:start position:0%
+have a graduate ta justin his email is
+ 
+
+ align:start position:0%
+have a graduate ta justin his email is
+given on the slide as well and then we
+
+ align:start position:0%
+given on the slide as well and then we
+ 
+
+ align:start position:0%
+given on the slide as well and then we
+have two
+
+ align:start position:0%
+have two
+ 
+
+ align:start position:0%
+have two
+graders and tas mohit zak
+
+ align:start position:0%
+graders and tas mohit zak
+ 
+
+ align:start position:0%
+graders and tas mohit zak
+and steven
+
+ align:start position:0%
+and steven
+ 
+
+ align:start position:0%
+and steven
+those four
+
+ align:start position:0%
+those four
+ 
+
+ align:start position:0%
+those four
+will guide us through the class as well
+
+ align:start position:0%
+will guide us through the class as well
+ 
+
+ align:start position:0%
+will guide us through the class as well
+and especially when we go into breakout
+
+ align:start position:0%
+and especially when we go into breakout
+ 
+
+ align:start position:0%
+and especially when we go into breakout
+rooms in the live class they will help
+
+ align:start position:0%
+rooms in the live class they will help
+ 
+
+ align:start position:0%
+rooms in the live class they will help
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+in the discussion the class hours are
+
+ align:start position:0%
+in the discussion the class hours are
+ 
+
+ align:start position:0%
+in the discussion the class hours are
+from 3 to 4 30 p.m on zoom
+
+ align:start position:0%
+from 3 to 4 30 p.m on zoom
+ 
+
+ align:start position:0%
+from 3 to 4 30 p.m on zoom
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and you can you know i encourage you to
+
+ align:start position:0%
+and you can you know i encourage you to
+ 
+
+ align:start position:0%
+and you can you know i encourage you to
+to join the class to
+
+ align:start position:0%
+to join the class to
+ 
+
+ align:start position:0%
+to join the class to
+participate to be active in the class
+
+ align:start position:0%
+participate to be active in the class
+ 
+
+ align:start position:0%
+participate to be active in the class
+but you will also be able to get to the
+
+ align:start position:0%
+but you will also be able to get to the
+ 
+
+ align:start position:0%
+but you will also be able to get to the
+material through recordings i will not
+
+ align:start position:0%
+material through recordings i will not
+ 
+
+ align:start position:0%
+material through recordings i will not
+record the live class because i want to
+
+ align:start position:0%
+record the live class because i want to
+ 
+
+ align:start position:0%
+record the live class because i want to
+encourage you to be just as open as
+
+ align:start position:0%
+encourage you to be just as open as
+ 
+
+ align:start position:0%
+encourage you to be just as open as
+possible but i pre-record the class and
+
+ align:start position:0%
+possible but i pre-record the class and
+ 
+
+ align:start position:0%
+possible but i pre-record the class and
+after the class time is over i'll upload
+
+ align:start position:0%
+after the class time is over i'll upload
+ 
+
+ align:start position:0%
+after the class time is over i'll upload
+those uh videos um for your for your
+
+ align:start position:0%
+those uh videos um for your for your
+ 
+
+ align:start position:0%
+those uh videos um for your for your
+reference and also if you live in a
+
+ align:start position:0%
+reference and also if you live in a
+ 
+
+ align:start position:0%
+reference and also if you live in a
+different time zone you have a chance to
+
+ align:start position:0%
+different time zone you have a chance to
+ 
+
+ align:start position:0%
+different time zone you have a chance to
+listen to the class
+
+ align:start position:0%
+listen to the class
+ 
+
+ align:start position:0%
+listen to the class
+office hours will be tuesday at 9 00 a.m
+
+ align:start position:0%
+office hours will be tuesday at 9 00 a.m
+ 
+
+ align:start position:0%
+office hours will be tuesday at 9 00 a.m
+and friday at 5am tuesday you reach me
+
+ align:start position:0%
+and friday at 5am tuesday you reach me
+ 
+
+ align:start position:0%
+and friday at 5am tuesday you reach me
+and friday you reach justin
+
+ align:start position:0%
+and friday you reach justin
+ 
+
+ align:start position:0%
+and friday you reach justin
+we will set up a slack workspace which
+
+ align:start position:0%
+we will set up a slack workspace which
+ 
+
+ align:start position:0%
+we will set up a slack workspace which
+uh we use for our internal discussions
+
+ align:start position:0%
+uh we use for our internal discussions
+ 
+
+ align:start position:0%
+uh we use for our internal discussions
+um with the teaching staff but um
+
+ align:start position:0%
+um with the teaching staff but um
+ 
+
+ align:start position:0%
+um with the teaching staff but um
+there's also going to be channels for
+
+ align:start position:0%
+there's also going to be channels for
+ 
+
+ align:start position:0%
+there's also going to be channels for
+you to discuss psets there's channels we
+
+ align:start position:0%
+you to discuss psets there's channels we
+ 
+
+ align:start position:0%
+you to discuss psets there's channels we
+discuss the physics
+
+ align:start position:0%
+discuss the physics
+ 
+
+ align:start position:0%
+discuss the physics
+and there's going to be a channel which
+
+ align:start position:0%
+and there's going to be a channel which
+ 
+
+ align:start position:0%
+and there's going to be a channel which
+will be important when we go to the to
+
+ align:start position:0%
+will be important when we go to the to
+ 
+
+ align:start position:0%
+will be important when we go to the to
+the exam discussion
+
+ align:start position:0%
+the exam discussion
+ 
+
+ align:start position:0%
+the exam discussion
+the expectation is that you spend about
+
+ align:start position:0%
+the expectation is that you spend about
+ 
+
+ align:start position:0%
+the expectation is that you spend about
+30 hours a week during iip
+
+ align:start position:0%
+30 hours a week during iip
+ 
+
+ align:start position:0%
+30 hours a week during iip
+some will find the presets very
+
+ align:start position:0%
+some will find the presets very
+ 
+
+ align:start position:0%
+some will find the presets very
+straightforward and quickly to do others
+
+ align:start position:0%
+straightforward and quickly to do others
+ 
+
+ align:start position:0%
+straightforward and quickly to do others
+will need more time so it's just it's
+
+ align:start position:0%
+will need more time so it's just it's
+ 
+
+ align:start position:0%
+will need more time so it's just it's
+not a you know don't set your stopwatch
+
+ align:start position:0%
+not a you know don't set your stopwatch
+ 
+
+ align:start position:0%
+not a you know don't set your stopwatch
+for 30 hours that's just an average
+
+ align:start position:0%
+for 30 hours that's just an average
+ 
+
+ align:start position:0%
+for 30 hours that's just an average
+guide
+
+ align:start position:0%
+guide
+ 
+
+ align:start position:0%
+guide
+um i will evaluate you at the end of the
+
+ align:start position:0%
+um i will evaluate you at the end of the
+ 
+
+ align:start position:0%
+um i will evaluate you at the end of the
+term um
+
+ align:start position:0%
+term um
+ 
+
+ align:start position:0%
+term um
+and i will use this this metric here 50
+
+ align:start position:0%
+and i will use this this metric here 50
+ 
+
+ align:start position:0%
+and i will use this this metric here 50
+of your grade will come from the
+
+ align:start position:0%
+of your grade will come from the
+ 
+
+ align:start position:0%
+of your grade will come from the
+homework there's going to be five
+
+ align:start position:0%
+homework there's going to be five
+ 
+
+ align:start position:0%
+homework there's going to be five
+different homework assignments there's
+
+ align:start position:0%
+different homework assignments there's
+ 
+
+ align:start position:0%
+different homework assignments there's
+going to be two midterms with 15 each
+
+ align:start position:0%
+going to be two midterms with 15 each
+ 
+
+ align:start position:0%
+going to be two midterms with 15 each
+and one final with 20
+
+ align:start position:0%
+and one final with 20
+ 
+
+ align:start position:0%
+and one final with 20
+if i do the mass correctly this should
+
+ align:start position:0%
+if i do the mass correctly this should
+ 
+
+ align:start position:0%
+if i do the mass correctly this should
+lead us to a hundred percent
+
+ align:start position:0%
+lead us to a hundred percent
+ 
+
+ align:start position:0%
+lead us to a hundred percent
+uh you earn an a with 90 percent b with
+
+ align:start position:0%
+uh you earn an a with 90 percent b with
+ 
+
+ align:start position:0%
+uh you earn an a with 90 percent b with
+75 percent i see the 60 percent or
+
+ align:start position:0%
+75 percent i see the 60 percent or
+ 
+
+ align:start position:0%
+75 percent i see the 60 percent or
+higher a d is 50 or higher and a failing
+
+ align:start position:0%
+higher a d is 50 or higher and a failing
+ 
+
+ align:start position:0%
+higher a d is 50 or higher and a failing
+grade is less than 50
+
+ align:start position:0%
+grade is less than 50
+ 
+
+ align:start position:0%
+grade is less than 50
+so all lectures will be on zoom
+
+ align:start position:0%
+so all lectures will be on zoom
+ 
+
+ align:start position:0%
+so all lectures will be on zoom
+you find the zoom links on the canvas
+
+ align:start position:0%
+you find the zoom links on the canvas
+ 
+
+ align:start position:0%
+you find the zoom links on the canvas
+page and
+
+ align:start position:0%
+page and
+ 
+
+ align:start position:0%
+page and
+you probably found this already
+
+ align:start position:0%
+you probably found this already
+ 
+
+ align:start position:0%
+you probably found this already
+otherwise you wouldn't be able to find
+
+ align:start position:0%
+otherwise you wouldn't be able to find
+ 
+
+ align:start position:0%
+otherwise you wouldn't be able to find
+this video and again as i was saying the
+
+ align:start position:0%
+this video and again as i was saying the
+ 
+
+ align:start position:0%
+this video and again as i was saying the
+recordings will be available after class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the schedule um let me start by
+
+ align:start position:0%
+this is the schedule um let me start by
+ 
+
+ align:start position:0%
+this is the schedule um let me start by
+uh explaining this picture there's a
+
+ align:start position:0%
+uh explaining this picture there's a
+ 
+
+ align:start position:0%
+uh explaining this picture there's a
+little thomas here and then a german ice
+
+ align:start position:0%
+little thomas here and then a german ice
+ 
+
+ align:start position:0%
+little thomas here and then a german ice
+train um this class
+
+ align:start position:0%
+train um this class
+ 
+
+ align:start position:0%
+train um this class
+the way i look at this class is
+
+ align:start position:0%
+the way i look at this class is
+ 
+
+ align:start position:0%
+the way i look at this class is
+a train which is just leaving the
+
+ align:start position:0%
+a train which is just leaving the
+ 
+
+ align:start position:0%
+a train which is just leaving the
+station right now and it will you know
+
+ align:start position:0%
+station right now and it will you know
+ 
+
+ align:start position:0%
+station right now and it will you know
+very slowly pick up space
+
+ align:start position:0%
+very slowly pick up space
+ 
+
+ align:start position:0%
+very slowly pick up space
+um pace
+
+ align:start position:0%
+um pace
+ 
+
+ align:start position:0%
+um pace
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+you want to make sure that you stay on
+
+ align:start position:0%
+you want to make sure that you stay on
+ 
+
+ align:start position:0%
+you want to make sure that you stay on
+the train and you don't jump off because
+
+ align:start position:0%
+the train and you don't jump off because
+ 
+
+ align:start position:0%
+the train and you don't jump off because
+you know if this will one once it's
+
+ align:start position:0%
+you know if this will one once it's
+ 
+
+ align:start position:0%
+you know if this will one once it's
+picked up its pace will be a fast moving
+
+ align:start position:0%
+picked up its pace will be a fast moving
+ 
+
+ align:start position:0%
+picked up its pace will be a fast moving
+train
+
+ align:start position:0%
+train
+ 
+
+ align:start position:0%
+train
+and uh missing a few days in iap
+
+ align:start position:0%
+and uh missing a few days in iap
+ 
+
+ align:start position:0%
+and uh missing a few days in iap
+uh will cause you to have trouble
+
+ align:start position:0%
+uh will cause you to have trouble
+ 
+
+ align:start position:0%
+uh will cause you to have trouble
+following along with the material
+
+ align:start position:0%
+following along with the material
+ 
+
+ align:start position:0%
+following along with the material
+um we'll start today with this
+
+ align:start position:0%
+um we'll start today with this
+ 
+
+ align:start position:0%
+um we'll start today with this
+introduction um tomorrow we have a very
+
+ align:start position:0%
+introduction um tomorrow we have a very
+ 
+
+ align:start position:0%
+introduction um tomorrow we have a very
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+uh lecture by david kaiser this is the
+
+ align:start position:0%
+uh lecture by david kaiser this is the
+ 
+
+ align:start position:0%
+uh lecture by david kaiser this is the
+only one where we actually record the
+
+ align:start position:0%
+only one where we actually record the
+ 
+
+ align:start position:0%
+only one where we actually record the
+live live event so we will record the
+
+ align:start position:0%
+live live event so we will record the
+ 
+
+ align:start position:0%
+live live event so we will record the
+zoom session
+
+ align:start position:0%
+zoom session
+ 
+
+ align:start position:0%
+zoom session
+um and then the rest will unfold i was
+
+ align:start position:0%
+um and then the rest will unfold i was
+ 
+
+ align:start position:0%
+um and then the rest will unfold i was
+also saying you find this red block here
+
+ align:start position:0%
+also saying you find this red block here
+ 
+
+ align:start position:0%
+also saying you find this red block here
+those are our midterms and the final
+
+ align:start position:0%
+those are our midterms and the final
+ 
+
+ align:start position:0%
+those are our midterms and the final
+on those days there's not going to be a
+
+ align:start position:0%
+on those days there's not going to be a
+ 
+
+ align:start position:0%
+on those days there's not going to be a
+live class
+
+ align:start position:0%
+live class
+ 
+
+ align:start position:0%
+live class
+but i will make the a final sorry the
+
+ align:start position:0%
+but i will make the a final sorry the
+ 
+
+ align:start position:0%
+but i will make the a final sorry the
+exam available
+
+ align:start position:0%
+exam available
+ 
+
+ align:start position:0%
+exam available
+for about 24 hours
+
+ align:start position:0%
+for about 24 hours
+ 
+
+ align:start position:0%
+for about 24 hours
+you should not spend more than an hour
+
+ align:start position:0%
+you should not spend more than an hour
+ 
+
+ align:start position:0%
+you should not spend more than an hour
+maybe an hour and a half on on on the
+
+ align:start position:0%
+maybe an hour and a half on on on the
+ 
+
+ align:start position:0%
+maybe an hour and a half on on on the
+exam and then submit once you're done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the exams are um
+
+ align:start position:0%
+the exams are um
+ 
+
+ align:start position:0%
+the exams are um
+open book in a sense that you can look
+
+ align:start position:0%
+open book in a sense that you can look
+ 
+
+ align:start position:0%
+open book in a sense that you can look
+at the textbooks and you can look at the
+
+ align:start position:0%
+at the textbooks and you can look at the
+ 
+
+ align:start position:0%
+at the textbooks and you can look at the
+course material
+
+ align:start position:0%
+course material
+ 
+
+ align:start position:0%
+course material
+but you are not supposed to you know do
+
+ align:start position:0%
+but you are not supposed to you know do
+ 
+
+ align:start position:0%
+but you are not supposed to you know do
+an online search for the solutions and
+
+ align:start position:0%
+an online search for the solutions and
+ 
+
+ align:start position:0%
+an online search for the solutions and
+you're also not supposed to discuss with
+
+ align:start position:0%
+you're also not supposed to discuss with
+ 
+
+ align:start position:0%
+you're also not supposed to discuss with
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+peers you can ask the clarifying
+
+ align:start position:0%
+peers you can ask the clarifying
+ 
+
+ align:start position:0%
+peers you can ask the clarifying
+question on one of the slack channels
+
+ align:start position:0%
+question on one of the slack channels
+ 
+
+ align:start position:0%
+question on one of the slack channels
+and we will be happy to answer as
+
+ align:start position:0%
+and we will be happy to answer as
+ 
+
+ align:start position:0%
+and we will be happy to answer as
+quickly as we see them
+
+ align:start position:0%
+quickly as we see them
+ 
+
+ align:start position:0%
+quickly as we see them
+but again this is an evaluation of your
+
+ align:start position:0%
+but again this is an evaluation of your
+ 
+
+ align:start position:0%
+but again this is an evaluation of your
+own performance and you should submit
+
+ align:start position:0%
+own performance and you should submit
+ 
+
+ align:start position:0%
+own performance and you should submit
+your own performance
+
+ align:start position:0%
+your own performance
+ 
+
+ align:start position:0%
+your own performance
+the psets are different in a sense that
+
+ align:start position:0%
+the psets are different in a sense that
+ 
+
+ align:start position:0%
+the psets are different in a sense that
+i encourage that you guys you know build
+
+ align:start position:0%
+i encourage that you guys you know build
+ 
+
+ align:start position:0%
+i encourage that you guys you know build
+small groups and work on them together
+
+ align:start position:0%
+small groups and work on them together
+ 
+
+ align:start position:0%
+small groups and work on them together
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+each pset then has to be submitted by
+
+ align:start position:0%
+each pset then has to be submitted by
+ 
+
+ align:start position:0%
+each pset then has to be submitted by
+you as an individual
+
+ align:start position:0%
+you as an individual
+ 
+
+ align:start position:0%
+you as an individual
+meaning that i don't want to see copies
+
+ align:start position:0%
+meaning that i don't want to see copies
+ 
+
+ align:start position:0%
+meaning that i don't want to see copies
+of presets of other folks i want your
+
+ align:start position:0%
+of presets of other folks i want your
+ 
+
+ align:start position:0%
+of presets of other folks i want your
+own answers in your own words to the
+
+ align:start position:0%
+own answers in your own words to the
+ 
+
+ align:start position:0%
+own answers in your own words to the
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+um very important day in in january is
+
+ align:start position:0%
+um very important day in in january is
+ 
+
+ align:start position:0%
+um very important day in in january is
+martin luther
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives us all a little bit of a breathing
+
+ align:start position:0%
+gives us all a little bit of a breathing
+ 
+
+ align:start position:0%
+gives us all a little bit of a breathing
+room an extra free day
+
+ align:start position:0%
+room an extra free day
+ 
+
+ align:start position:0%
+room an extra free day
+and you see that you know there's going
+
+ align:start position:0%
+and you see that you know there's going
+ 
+
+ align:start position:0%
+and you see that you know there's going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+um after the discussion at the very end
+
+ align:start position:0%
+um after the discussion at the very end
+ 
+
+ align:start position:0%
+um after the discussion at the very end
+after the final a special lecture where
+
+ align:start position:0%
+after the final a special lecture where
+ 
+
+ align:start position:0%
+after the final a special lecture where
+i introduced the topic of general
+
+ align:start position:0%
+i introduced the topic of general
+ 
+
+ align:start position:0%
+i introduced the topic of general
+relativity um which is not par part of
+
+ align:start position:0%
+relativity um which is not par part of
+ 
+
+ align:start position:0%
+relativity um which is not par part of
+the core
+
+ align:start position:0%
+the core
+ 
+
+ align:start position:0%
+the core
+content of especially of this special
+
+ align:start position:0%
+content of especially of this special
+ 
+
+ align:start position:0%
+content of especially of this special
+relativity class
+
+ align:start position:0%
+relativity class
+ 
+
+ align:start position:0%
+relativity class
+textbooks um i will not really follow
+
+ align:start position:0%
+textbooks um i will not really follow
+ 
+
+ align:start position:0%
+textbooks um i will not really follow
+the textbooks line by line or chapter by
+
+ align:start position:0%
+the textbooks line by line or chapter by
+ 
+
+ align:start position:0%
+the textbooks line by line or chapter by
+chapter but i encourage you and i give
+
+ align:start position:0%
+chapter but i encourage you and i give
+ 
+
+ align:start position:0%
+chapter but i encourage you and i give
+you an outline and to read them
+
+ align:start position:0%
+you an outline and to read them
+ 
+
+ align:start position:0%
+you an outline and to read them
+especially the first two one first one
+
+ align:start position:0%
+especially the first two one first one
+ 
+
+ align:start position:0%
+especially the first two one first one
+is by french the second one is by
+
+ align:start position:0%
+is by french the second one is by
+ 
+
+ align:start position:0%
+is by french the second one is by
+resnick
+
+ align:start position:0%
+resnick
+ 
+
+ align:start position:0%
+resnick
+the former the first one is a former mit
+
+ align:start position:0%
+the former the first one is a former mit
+ 
+
+ align:start position:0%
+the former the first one is a former mit
+professor
+
+ align:start position:0%
+professor
+ 
+
+ align:start position:0%
+professor
+you are supposed to read this book cover
+
+ align:start position:0%
+you are supposed to read this book cover
+ 
+
+ align:start position:0%
+you are supposed to read this book cover
+to cover and i give reading assignments
+
+ align:start position:0%
+to cover and i give reading assignments
+ 
+
+ align:start position:0%
+to cover and i give reading assignments
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+resnick has a lot of good examples and
+
+ align:start position:0%
+resnick has a lot of good examples and
+ 
+
+ align:start position:0%
+resnick has a lot of good examples and
+problems and we will focus on the first
+
+ align:start position:0%
+problems and we will focus on the first
+ 
+
+ align:start position:0%
+problems and we will focus on the first
+four chapters of that book
+
+ align:start position:0%
+four chapters of that book
+ 
+
+ align:start position:0%
+four chapters of that book
+there is a lot of literature i would say
+
+ align:start position:0%
+there is a lot of literature i would say
+ 
+
+ align:start position:0%
+there is a lot of literature i would say
+on special relativity as a
+
+ align:start position:0%
+on special relativity as a
+ 
+
+ align:start position:0%
+on special relativity as a
+slew of textbooks available if you have
+
+ align:start position:0%
+slew of textbooks available if you have
+ 
+
+ align:start position:0%
+slew of textbooks available if you have
+one at hand you can also use that and
+
+ align:start position:0%
+one at hand you can also use that and
+ 
+
+ align:start position:0%
+one at hand you can also use that and
+find the relevant chapter in there
+
+ align:start position:0%
+find the relevant chapter in there
+ 
+
+ align:start position:0%
+find the relevant chapter in there
+um i give you one extra book here which
+
+ align:start position:0%
+um i give you one extra book here which
+ 
+
+ align:start position:0%
+um i give you one extra book here which
+is nice because it is
+
+ align:start position:0%
+is nice because it is
+ 
+
+ align:start position:0%
+is nice because it is
+an excellent
+
+ align:start position:0%
+an excellent
+ 
+
+ align:start position:0%
+an excellent
+explanation of the mathematics involved
+
+ align:start position:0%
+explanation of the mathematics involved
+ 
+
+ align:start position:0%
+explanation of the mathematics involved
+if you're more inclined
+
+ align:start position:0%
+if you're more inclined
+ 
+
+ align:start position:0%
+if you're more inclined
+to course course 18 that might be an
+
+ align:start position:0%
+to course course 18 that might be an
+ 
+
+ align:start position:0%
+to course course 18 that might be an
+interesting textbook for you
+
+ align:start position:0%
+interesting textbook for you
+ 
+
+ align:start position:0%
+interesting textbook for you
+again there's many many resources on the
+
+ align:start position:0%
+again there's many many resources on the
+ 
+
+ align:start position:0%
+again there's many many resources on the
+topic of special relativity and i've
+
+ align:start position:0%
+topic of special relativity and i've
+ 
+
+ align:start position:0%
+topic of special relativity and i've
+pointed out a few as we go
+
+ align:start position:0%
+pointed out a few as we go
+ 
+
+ align:start position:0%
+pointed out a few as we go
+in addition to the textbooks i give you
+
+ align:start position:0%
+in addition to the textbooks i give you
+ 
+
+ align:start position:0%
+in addition to the textbooks i give you
+a number of papers for example the paper
+
+ align:start position:0%
+a number of papers for example the paper
+ 
+
+ align:start position:0%
+a number of papers for example the paper
+in which einstein explains
+
+ align:start position:0%
+in which einstein explains
+ 
+
+ align:start position:0%
+in which einstein explains
+what describes the concept of the theory
+
+ align:start position:0%
+what describes the concept of the theory
+ 
+
+ align:start position:0%
+what describes the concept of the theory
+of special relativity
+
+ align:start position:0%
+of special relativity
+ 
+
+ align:start position:0%
+of special relativity
+and there's a few others which i'd like
+
+ align:start position:0%
+and there's a few others which i'd like
+ 
+
+ align:start position:0%
+and there's a few others which i'd like
+you to read they're interesting because
+
+ align:start position:0%
+you to read they're interesting because
+ 
+
+ align:start position:0%
+you to read they're interesting because
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+they introduce the physics but they're
+
+ align:start position:0%
+they introduce the physics but they're
+ 
+
+ align:start position:0%
+they introduce the physics but they're
+also interesting as they have been
+
+ align:start position:0%
+also interesting as they have been
+ 
+
+ align:start position:0%
+also interesting as they have been
+written more than 100 years ago in a
+
+ align:start position:0%
+written more than 100 years ago in a
+ 
+
+ align:start position:0%
+written more than 100 years ago in a
+slightly different language than we
+
+ align:start position:0%
+slightly different language than we
+ 
+
+ align:start position:0%
+slightly different language than we
+would be using today and
+
+ align:start position:0%
+would be using today and
+ 
+
+ align:start position:0%
+would be using today and
+einstein specifically doesn't even write
+
+ align:start position:0%
+einstein specifically doesn't even write
+ 
+
+ align:start position:0%
+einstein specifically doesn't even write
+papers the way other people wrote papers
+
+ align:start position:0%
+papers the way other people wrote papers
+ 
+
+ align:start position:0%
+papers the way other people wrote papers
+at the time
+
+ align:start position:0%
+at the time
+ 
+
+ align:start position:0%
+at the time
+he had his own style on the writing
+
+ align:start position:0%
+he had his own style on the writing
+ 
+
+ align:start position:0%
+he had his own style on the writing
+papers and we will see that
+
+ align:start position:0%
+papers and we will see that
+ 
+
+ align:start position:0%
+papers and we will see that
+so here's a reading assignment week by
+
+ align:start position:0%
+so here's a reading assignment week by
+ 
+
+ align:start position:0%
+so here's a reading assignment week by
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+you know we start in week one by resnick
+
+ align:start position:0%
+you know we start in week one by resnick
+ 
+
+ align:start position:0%
+you know we start in week one by resnick
+chapter one french chapter two there's
+
+ align:start position:0%
+chapter one french chapter two there's
+ 
+
+ align:start position:0%
+chapter one french chapter two there's
+two papers the michelson-morley paper
+
+ align:start position:0%
+two papers the michelson-morley paper
+ 
+
+ align:start position:0%
+two papers the michelson-morley paper
+and the einstein paper on special
+
+ align:start position:0%
+and the einstein paper on special
+ 
+
+ align:start position:0%
+and the einstein paper on special
+relativity and then we go on
+
+ align:start position:0%
+relativity and then we go on
+ 
+
+ align:start position:0%
+relativity and then we go on
+as we go through iap
+
+ align:start position:0%
+as we go through iap
+ 
+
+ align:start position:0%
+as we go through iap
+the homework schedule is here
+
+ align:start position:0%
+the homework schedule is here
+ 
+
+ align:start position:0%
+the homework schedule is here
+i hand out pset number zero today
+
+ align:start position:0%
+i hand out pset number zero today
+ 
+
+ align:start position:0%
+i hand out pset number zero today
+and i'll explain it on the next page
+
+ align:start position:0%
+and i'll explain it on the next page
+ 
+
+ align:start position:0%
+and i'll explain it on the next page
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is a pset which allows i mean this is a
+
+ align:start position:0%
+is a pset which allows i mean this is a
+ 
+
+ align:start position:0%
+is a pset which allows i mean this is a
+preset which will keep you busy uh for
+
+ align:start position:0%
+preset which will keep you busy uh for
+ 
+
+ align:start position:0%
+preset which will keep you busy uh for
+the entire month or most of it on the
+
+ align:start position:0%
+the entire month or most of it on the
+ 
+
+ align:start position:0%
+the entire month or most of it on the
+other psets are
+
+ align:start position:0%
+other psets are
+ 
+
+ align:start position:0%
+other psets are
+shorter
+
+ align:start position:0%
+shorter
+ 
+
+ align:start position:0%
+shorter
+and they are more pointed and you know
+
+ align:start position:0%
+and they are more pointed and you know
+ 
+
+ align:start position:0%
+and they are more pointed and you know
+you get the pset you work on it and you
+
+ align:start position:0%
+you get the pset you work on it and you
+ 
+
+ align:start position:0%
+you get the pset you work on it and you
+hand in the solution and by the time you
+
+ align:start position:0%
+hand in the solution and by the time you
+ 
+
+ align:start position:0%
+hand in the solution and by the time you
+have done that the next piece rolls
+
+ align:start position:0%
+have done that the next piece rolls
+ 
+
+ align:start position:0%
+have done that the next piece rolls
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+i would use the pset load a little bit
+
+ align:start position:0%
+i would use the pset load a little bit
+ 
+
+ align:start position:0%
+i would use the pset load a little bit
+because i want to acknowledge the fact
+
+ align:start position:0%
+because i want to acknowledge the fact
+ 
+
+ align:start position:0%
+because i want to acknowledge the fact
+that it will be harder for you to work
+
+ align:start position:0%
+that it will be harder for you to work
+ 
+
+ align:start position:0%
+that it will be harder for you to work
+in teams i still encourage this uh you
+
+ align:start position:0%
+in teams i still encourage this uh you
+ 
+
+ align:start position:0%
+in teams i still encourage this uh you
+find yourself on slack you find yourself
+
+ align:start position:0%
+find yourself on slack you find yourself
+ 
+
+ align:start position:0%
+find yourself on slack you find yourself
+on zoom channel some of you might have
+
+ align:start position:0%
+on zoom channel some of you might have
+ 
+
+ align:start position:0%
+on zoom channel some of you might have
+housing together
+
+ align:start position:0%
+housing together
+ 
+
+ align:start position:0%
+housing together
+um i really encourage you guys to
+
+ align:start position:0%
+um i really encourage you guys to
+ 
+
+ align:start position:0%
+um i really encourage you guys to
+discuss the physics there are some
+
+ align:start position:0%
+discuss the physics there are some
+ 
+
+ align:start position:0%
+discuss the physics there are some
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+difficult concepts
+
+ align:start position:0%
+difficult concepts
+ 
+
+ align:start position:0%
+difficult concepts
+um which just need you to
+
+ align:start position:0%
+um which just need you to
+ 
+
+ align:start position:0%
+um which just need you to
+think through and to talk through and
+
+ align:start position:0%
+think through and to talk through and
+ 
+
+ align:start position:0%
+think through and to talk through and
+the talking through best happens with
+
+ align:start position:0%
+the talking through best happens with
+ 
+
+ align:start position:0%
+the talking through best happens with
+your peers and you will see that that
+
+ align:start position:0%
+your peers and you will see that that
+ 
+
+ align:start position:0%
+your peers and you will see that that
+will be very beneficial especially when
+
+ align:start position:0%
+will be very beneficial especially when
+ 
+
+ align:start position:0%
+will be very beneficial especially when
+it comes to the pset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's homework number one um i've
+
+ align:start position:0%
+so here's homework number one um i've
+ 
+
+ align:start position:0%
+so here's homework number one um i've
+done this now a few times and i really
+
+ align:start position:0%
+done this now a few times and i really
+ 
+
+ align:start position:0%
+done this now a few times and i really
+really enjoy
+
+ align:start position:0%
+really enjoy
+ 
+
+ align:start position:0%
+really enjoy
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+solutions given by the students
+
+ align:start position:0%
+solutions given by the students
+ 
+
+ align:start position:0%
+solutions given by the students
+um so this is a creative project um
+
+ align:start position:0%
+um so this is a creative project um
+ 
+
+ align:start position:0%
+um so this is a creative project um
+you know you have basically almost all
+
+ align:start position:0%
+you know you have basically almost all
+ 
+
+ align:start position:0%
+you know you have basically almost all
+of irp to hand it in and the idea is to
+
+ align:start position:0%
+of irp to hand it in and the idea is to
+ 
+
+ align:start position:0%
+of irp to hand it in and the idea is to
+be creative around
+
+ align:start position:0%
+be creative around
+ 
+
+ align:start position:0%
+be creative around
+a topic relating einstein
+
+ align:start position:0%
+a topic relating einstein
+ 
+
+ align:start position:0%
+a topic relating einstein
+or and the special
+
+ align:start position:0%
+or and the special
+ 
+
+ align:start position:0%
+or and the special
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+serial of special relativity
+
+ align:start position:0%
+serial of special relativity
+ 
+
+ align:start position:0%
+serial of special relativity
+the project might be a video it might be
+
+ align:start position:0%
+the project might be a video it might be
+ 
+
+ align:start position:0%
+the project might be a video it might be
+a poem it might be a musical piece
+
+ align:start position:0%
+a poem it might be a musical piece
+ 
+
+ align:start position:0%
+a poem it might be a musical piece
+artwork animations
+
+ align:start position:0%
+artwork animations
+ 
+
+ align:start position:0%
+artwork animations
+a game
+
+ align:start position:0%
+a game
+ 
+
+ align:start position:0%
+a game
+a structure
+
+ align:start position:0%
+a structure
+ 
+
+ align:start position:0%
+a structure
+you name it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what i really want is that you take
+
+ align:start position:0%
+what i really want is that you take
+ 
+
+ align:start position:0%
+what i really want is that you take
+something you do very well
+
+ align:start position:0%
+something you do very well
+ 
+
+ align:start position:0%
+something you do very well
+and combine it
+
+ align:start position:0%
+and combine it
+ 
+
+ align:start position:0%
+and combine it
+with the topic of this class um i want
+
+ align:start position:0%
+with the topic of this class um i want
+ 
+
+ align:start position:0%
+with the topic of this class um i want
+you to
+
+ align:start position:0%
+you to
+ 
+
+ align:start position:0%
+you to
+take something where you are very
+
+ align:start position:0%
+take something where you are very
+ 
+
+ align:start position:0%
+take something where you are very
+familiar with
+
+ align:start position:0%
+familiar with
+ 
+
+ align:start position:0%
+familiar with
+where you are feeling comfortable
+
+ align:start position:0%
+where you are feeling comfortable
+ 
+
+ align:start position:0%
+where you are feeling comfortable
+and then enter this new topic this new
+
+ align:start position:0%
+and then enter this new topic this new
+ 
+
+ align:start position:0%
+and then enter this new topic this new
+topic of special relativity
+
+ align:start position:0%
+topic of special relativity
+ 
+
+ align:start position:0%
+topic of special relativity
+i will
+
+ align:start position:0%
+i will
+ 
+
+ align:start position:0%
+i will
+rate it based on your creativity on the
+
+ align:start position:0%
+rate it based on your creativity on the
+ 
+
+ align:start position:0%
+rate it based on your creativity on the
+quality and on your effort
+
+ align:start position:0%
+quality and on your effort
+ 
+
+ align:start position:0%
+quality and on your effort
+and again this sends this in by january
+
+ align:start position:0%
+and again this sends this in by january
+ 
+
+ align:start position:0%
+and again this sends this in by january
+22nd i really encourage you to not wait
+
+ align:start position:0%
+22nd i really encourage you to not wait
+ 
+
+ align:start position:0%
+22nd i really encourage you to not wait
+to the last minute to start working on
+
+ align:start position:0%
+to the last minute to start working on
+ 
+
+ align:start position:0%
+to the last minute to start working on
+that those topics those creative
+
+ align:start position:0%
+that those topics those creative
+ 
+
+ align:start position:0%
+that those topics those creative
+projects they always take a little bit
+
+ align:start position:0%
+projects they always take a little bit
+ 
+
+ align:start position:0%
+projects they always take a little bit
+more time than you might expect
+
+ align:start position:0%
+more time than you might expect
+ 
+
+ align:start position:0%
+more time than you might expect
+this class will have
+
+ align:start position:0%
+this class will have
+ 
+
+ align:start position:0%
+this class will have
+an interactive component and
+
+ align:start position:0%
+an interactive component and
+ 
+
+ align:start position:0%
+an interactive component and
+we will use breakout rooms for
+
+ align:start position:0%
+we will use breakout rooms for
+ 
+
+ align:start position:0%
+we will use breakout rooms for
+discussions and
+
+ align:start position:0%
+discussions and
+ 
+
+ align:start position:0%
+discussions and
+smaller programs programs as you would
+
+ align:start position:0%
+smaller programs programs as you would
+ 
+
+ align:start position:0%
+smaller programs programs as you would
+be doing in the classroom as well
+
+ align:start position:0%
+be doing in the classroom as well
+ 
+
+ align:start position:0%
+be doing in the classroom as well
+here is the very first one um
+
+ align:start position:0%
+here is the very first one um
+ 
+
+ align:start position:0%
+here is the very first one um
+what people who are taking this class
+
+ align:start position:0%
+what people who are taking this class
+ 
+
+ align:start position:0%
+what people who are taking this class
+asynchronously i encourage you to stop
+
+ align:start position:0%
+asynchronously i encourage you to stop
+ 
+
+ align:start position:0%
+asynchronously i encourage you to stop
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+work through the problem
+
+ align:start position:0%
+work through the problem
+ 
+
+ align:start position:0%
+work through the problem
+and then look at the solution afterwards
+
+ align:start position:0%
+and then look at the solution afterwards
+ 
+
+ align:start position:0%
+and then look at the solution afterwards
+or look at the discussion of the
+
+ align:start position:0%
+or look at the discussion of the
+ 
+
+ align:start position:0%
+or look at the discussion of the
+solution afterwards so this first duncan
+
+ align:start position:0%
+solution afterwards so this first duncan
+ 
+
+ align:start position:0%
+solution afterwards so this first duncan
+experiment thought experiment
+
+ align:start position:0%
+experiment thought experiment
+ 
+
+ align:start position:0%
+experiment thought experiment
+is about the topic of relativity
+
+ align:start position:0%
+is about the topic of relativity
+ 
+
+ align:start position:0%
+is about the topic of relativity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you want to first understand what that
+
+ align:start position:0%
+you want to first understand what that
+ 
+
+ align:start position:0%
+you want to first understand what that
+is before you do
+
+ align:start position:0%
+is before you do
+ 
+
+ align:start position:0%
+is before you do
+for what relativity is before you
+
+ align:start position:0%
+for what relativity is before you
+ 
+
+ align:start position:0%
+for what relativity is before you
+discuss what a special relativity is
+
+ align:start position:0%
+discuss what a special relativity is
+ 
+
+ align:start position:0%
+discuss what a special relativity is
+so imagine
+
+ align:start position:0%
+so imagine
+ 
+
+ align:start position:0%
+so imagine
+you wake up inside a room with no
+
+ align:start position:0%
+you wake up inside a room with no
+ 
+
+ align:start position:0%
+you wake up inside a room with no
+windows
+
+ align:start position:0%
+windows
+ 
+
+ align:start position:0%
+windows
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one locked door you checked you make
+
+ align:start position:0%
+one locked door you checked you make
+ 
+
+ align:start position:0%
+one locked door you checked you make
+sure that the door is locked you cannot
+
+ align:start position:0%
+sure that the door is locked you cannot
+ 
+
+ align:start position:0%
+sure that the door is locked you cannot
+get out you cannot see outside looking
+
+ align:start position:0%
+get out you cannot see outside looking
+ 
+
+ align:start position:0%
+get out you cannot see outside looking
+out around you see a table with a number
+
+ align:start position:0%
+out around you see a table with a number
+ 
+
+ align:start position:0%
+out around you see a table with a number
+of items on it there's a desk lamp
+
+ align:start position:0%
+of items on it there's a desk lamp
+ 
+
+ align:start position:0%
+of items on it there's a desk lamp
+plugged in and turned on as a tennis
+
+ align:start position:0%
+plugged in and turned on as a tennis
+ 
+
+ align:start position:0%
+plugged in and turned on as a tennis
+ball
+
+ align:start position:0%
+ball
+ 
+
+ align:start position:0%
+ball
+there's a bunch of string
+
+ align:start position:0%
+there's a bunch of string
+ 
+
+ align:start position:0%
+there's a bunch of string
+there's a picture of water there's a cup
+
+ align:start position:0%
+there's a picture of water there's a cup
+ 
+
+ align:start position:0%
+there's a picture of water there's a cup
+there's a candle there's a box of
+
+ align:start position:0%
+there's a candle there's a box of
+ 
+
+ align:start position:0%
+there's a candle there's a box of
+matches and there's a music player with
+
+ align:start position:0%
+matches and there's a music player with
+ 
+
+ align:start position:0%
+matches and there's a music player with
+headphones
+
+ align:start position:0%
+headphones
+ 
+
+ align:start position:0%
+headphones
+a skateboard and a wooden stool are also
+
+ align:start position:0%
+a skateboard and a wooden stool are also
+ 
+
+ align:start position:0%
+a skateboard and a wooden stool are also
+in the room the music player has a sign
+
+ align:start position:0%
+in the room the music player has a sign
+ 
+
+ align:start position:0%
+in the room the music player has a sign
+on it saying turn it on for instructions
+
+ align:start position:0%
+on it saying turn it on for instructions
+ 
+
+ align:start position:0%
+on it saying turn it on for instructions
+so you do
+
+ align:start position:0%
+so you do
+ 
+
+ align:start position:0%
+so you do
+you're told that you're in a special
+
+ align:start position:0%
+you're told that you're in a special
+ 
+
+ align:start position:0%
+you're told that you're in a special
+specially designed vibration proof and
+
+ align:start position:0%
+specially designed vibration proof and
+ 
+
+ align:start position:0%
+specially designed vibration proof and
+noise proof train car
+
+ align:start position:0%
+noise proof train car
+ 
+
+ align:start position:0%
+noise proof train car
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+on a set of straight and level train
+
+ align:start position:0%
+on a set of straight and level train
+ 
+
+ align:start position:0%
+on a set of straight and level train
+tracks
+
+ align:start position:0%
+tracks
+ 
+
+ align:start position:0%
+tracks
+your task is to use one or more of the
+
+ align:start position:0%
+your task is to use one or more of the
+ 
+
+ align:start position:0%
+your task is to use one or more of the
+items in the room
+
+ align:start position:0%
+items in the room
+ 
+
+ align:start position:0%
+items in the room
+perhaps in combination with each other
+
+ align:start position:0%
+perhaps in combination with each other
+ 
+
+ align:start position:0%
+perhaps in combination with each other
+to determine whether the train car is
+
+ align:start position:0%
+to determine whether the train car is
+ 
+
+ align:start position:0%
+to determine whether the train car is
+stationary or is moving on the tracks
+
+ align:start position:0%
+stationary or is moving on the tracks
+ 
+
+ align:start position:0%
+stationary or is moving on the tracks
+there's a 30 minute time limit on your
+
+ align:start position:0%
+there's a 30 minute time limit on your
+ 
+
+ align:start position:0%
+there's a 30 minute time limit on your
+test
+
+ align:start position:0%
+test
+ 
+
+ align:start position:0%
+test
+or tests
+
+ align:start position:0%
+or tests
+ 
+
+ align:start position:0%
+or tests
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you cannot destroy or you cannot modify
+
+ align:start position:0%
+you cannot destroy or you cannot modify
+ 
+
+ align:start position:0%
+you cannot destroy or you cannot modify
+the walls or the floors or the seating
+
+ align:start position:0%
+the walls or the floors or the seating
+ 
+
+ align:start position:0%
+the walls or the floors or the seating
+of the car
+
+ align:start position:0%
+of the car
+ 
+
+ align:start position:0%
+of the car
+that is not permitted
+
+ align:start position:0%
+that is not permitted
+ 
+
+ align:start position:0%
+that is not permitted
+um so the question to you is can you
+
+ align:start position:0%
+um so the question to you is can you
+ 
+
+ align:start position:0%
+um so the question to you is can you
+think of some creative way
+
+ align:start position:0%
+think of some creative way
+ 
+
+ align:start position:0%
+think of some creative way
+to use the items that might indicate
+
+ align:start position:0%
+to use the items that might indicate
+ 
+
+ align:start position:0%
+to use the items that might indicate
+whether or not you're moving
+
+ align:start position:0%
+whether or not you're moving
+ 
+
+ align:start position:0%
+whether or not you're moving
+think about this and discuss your
+
+ align:start position:0%
+think about this and discuss your
+ 
+
+ align:start position:0%
+think about this and discuss your
+breakout rooms
+
+ align:start position:0%
+breakout rooms
+ 
+
+ align:start position:0%
+breakout rooms
+that is for the live session here again
+
+ align:start position:0%
+that is for the live session here again
+ 
+
+ align:start position:0%
+that is for the live session here again
+i want to encourage you to stop
+
+ align:start position:0%
+i want to encourage you to stop
+ 
+
+ align:start position:0%
+i want to encourage you to stop
+and to think about
+
+ align:start position:0%
+and to think about
+ 
+
+ align:start position:0%
+and to think about
+a solution can you think about a
+
+ align:start position:0%
+a solution can you think about a
+ 
+
+ align:start position:0%
+a solution can you think about a
+creative way
+
+ align:start position:0%
+creative way
+ 
+
+ align:start position:0%
+creative way
+to work with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the typical time is about 10 minutes you
+
+ align:start position:0%
+the typical time is about 10 minutes you
+ 
+
+ align:start position:0%
+the typical time is about 10 minutes you
+might want to think about it you might
+
+ align:start position:0%
+might want to think about it you might
+ 
+
+ align:start position:0%
+might want to think about it you might
+want to take some notes
+
+ align:start position:0%
+want to take some notes
+ 
+
+ align:start position:0%
+want to take some notes
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+the answer is you cannot figure it out
+
+ align:start position:0%
+the answer is you cannot figure it out
+ 
+
+ align:start position:0%
+the answer is you cannot figure it out
+every reference frame by itself
+
+ align:start position:0%
+every reference frame by itself
+ 
+
+ align:start position:0%
+every reference frame by itself
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+inert you cannot figure out whether or
+
+ align:start position:0%
+inert you cannot figure out whether or
+ 
+
+ align:start position:0%
+inert you cannot figure out whether or
+not you're in a moving or in a in a
+
+ align:start position:0%
+not you're in a moving or in a in a
+ 
+
+ align:start position:0%
+not you're in a moving or in a in a
+stationary reference frame and as long
+
+ align:start position:0%
+stationary reference frame and as long
+ 
+
+ align:start position:0%
+stationary reference frame and as long
+as you cannot feel vibrations or you
+
+ align:start position:0%
+as you cannot feel vibrations or you
+ 
+
+ align:start position:0%
+as you cannot feel vibrations or you
+hear the sound or you have some other
+
+ align:start position:0%
+hear the sound or you have some other
+ 
+
+ align:start position:0%
+hear the sound or you have some other
+internal external indication you will
+
+ align:start position:0%
+internal external indication you will
+ 
+
+ align:start position:0%
+internal external indication you will
+not be able to figure out whether or not
+
+ align:start position:0%
+not be able to figure out whether or not
+ 
+
+ align:start position:0%
+not be able to figure out whether or not
+the room is moving with a constant
+
+ align:start position:0%
+the room is moving with a constant
+ 
+
+ align:start position:0%
+the room is moving with a constant
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+you will be able to feel
+
+ align:start position:0%
+you will be able to feel
+ 
+
+ align:start position:0%
+you will be able to feel
+or measure accelerations
+
+ align:start position:0%
+or measure accelerations
+ 
+
+ align:start position:0%
+or measure accelerations
+and so now you could argue that you know
+
+ align:start position:0%
+and so now you could argue that you know
+ 
+
+ align:start position:0%
+and so now you could argue that you know
+since the train track is on earth and
+
+ align:start position:0%
+since the train track is on earth and
+ 
+
+ align:start position:0%
+since the train track is on earth and
+the earth
+
+ align:start position:0%
+the earth
+ 
+
+ align:start position:0%
+the earth
+is actually
+
+ align:start position:0%
+is actually
+ 
+
+ align:start position:0%
+is actually
+uh since since you're on on earth and if
+
+ align:start position:0%
+uh since since you're on on earth and if
+ 
+
+ align:start position:0%
+uh since since you're on on earth and if
+you're moving you would
+
+ align:start position:0%
+you're moving you would
+ 
+
+ align:start position:0%
+you're moving you would
+be able to feel
+
+ align:start position:0%
+be able to feel
+ 
+
+ align:start position:0%
+be able to feel
+the rotation of the earth there might be
+
+ align:start position:0%
+the rotation of the earth there might be
+ 
+
+ align:start position:0%
+the rotation of the earth there might be
+a way to figure this out um but that
+
+ align:start position:0%
+a way to figure this out um but that
+ 
+
+ align:start position:0%
+a way to figure this out um but that
+will be very very hard to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the answer is you cannot you cannot
+
+ align:start position:0%
+so the answer is you cannot you cannot
+ 
+
+ align:start position:0%
+so the answer is you cannot you cannot
+distinguish one reference frame from
+
+ align:start position:0%
+distinguish one reference frame from
+ 
+
+ align:start position:0%
+distinguish one reference frame from
+another you don't know what an absolute
+
+ align:start position:0%
+another you don't know what an absolute
+ 
+
+ align:start position:0%
+another you don't know what an absolute
+velocity is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another way we will interact in this
+
+ align:start position:0%
+so another way we will interact in this
+ 
+
+ align:start position:0%
+so another way we will interact in this
+class is the concept questions so here
+
+ align:start position:0%
+class is the concept questions so here
+ 
+
+ align:start position:0%
+class is the concept questions so here
+concept questions are meant to you know
+
+ align:start position:0%
+concept questions are meant to you know
+ 
+
+ align:start position:0%
+concept questions are meant to you know
+give you a little bit of a checkpoint to
+
+ align:start position:0%
+give you a little bit of a checkpoint to
+ 
+
+ align:start position:0%
+give you a little bit of a checkpoint to
+encourage you to think about what i just
+
+ align:start position:0%
+encourage you to think about what i just
+ 
+
+ align:start position:0%
+encourage you to think about what i just
+explained in a video or in the class and
+
+ align:start position:0%
+explained in a video or in the class and
+ 
+
+ align:start position:0%
+explained in a video or in the class and
+to stimulate some sort of discussion
+
+ align:start position:0%
+to stimulate some sort of discussion
+ 
+
+ align:start position:0%
+to stimulate some sort of discussion
+sometimes you will use concept questions
+
+ align:start position:0%
+sometimes you will use concept questions
+ 
+
+ align:start position:0%
+sometimes you will use concept questions
+in breakout rooms for the discussion
+
+ align:start position:0%
+in breakout rooms for the discussion
+ 
+
+ align:start position:0%
+in breakout rooms for the discussion
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+sometimes we'll just use room features
+
+ align:start position:0%
+sometimes we'll just use room features
+ 
+
+ align:start position:0%
+sometimes we'll just use room features
+in order to figure out what
+
+ align:start position:0%
+in order to figure out what
+ 
+
+ align:start position:0%
+in order to figure out what
+the answer is but besides the technology
+
+ align:start position:0%
+the answer is but besides the technology
+ 
+
+ align:start position:0%
+the answer is but besides the technology
+those concept questions are really for
+
+ align:start position:0%
+those concept questions are really for
+ 
+
+ align:start position:0%
+those concept questions are really for
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+to figure out whether or not you did
+
+ align:start position:0%
+to figure out whether or not you did
+ 
+
+ align:start position:0%
+to figure out whether or not you did
+just understand the concept
+
+ align:start position:0%
+just understand the concept
+ 
+
+ align:start position:0%
+just understand the concept
+um so again i encourage you to
+
+ align:start position:0%
+um so again i encourage you to
+ 
+
+ align:start position:0%
+um so again i encourage you to
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+pause the video to think about the
+
+ align:start position:0%
+pause the video to think about the
+ 
+
+ align:start position:0%
+pause the video to think about the
+concept question and then move on with
+
+ align:start position:0%
+concept question and then move on with
+ 
+
+ align:start position:0%
+concept question and then move on with
+the answer
+
+ align:start position:0%
+the answer
+ 
+
+ align:start position:0%
+the answer
+here's an example
+
+ align:start position:0%
+here's an example
+ 
+
+ align:start position:0%
+here's an example
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a new star wars movie came out
+
+ align:start position:0%
+a new star wars movie came out
+ 
+
+ align:start position:0%
+a new star wars movie came out
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and i asked you to pick the answer
+
+ align:start position:0%
+and i asked you to pick the answer
+ 
+
+ align:start position:0%
+and i asked you to pick the answer
+closest to your level of starburst
+
+ align:start position:0%
+closest to your level of starburst
+ 
+
+ align:start position:0%
+closest to your level of starburst
+servers expertise
+
+ align:start position:0%
+servers expertise
+ 
+
+ align:start position:0%
+servers expertise
+i saw the movie and consider myself a
+
+ align:start position:0%
+i saw the movie and consider myself a
+ 
+
+ align:start position:0%
+i saw the movie and consider myself a
+star wars fan i saw the new movie but i
+
+ align:start position:0%
+star wars fan i saw the new movie but i
+ 
+
+ align:start position:0%
+star wars fan i saw the new movie but i
+do not know much about star wars i heard
+
+ align:start position:0%
+do not know much about star wars i heard
+ 
+
+ align:start position:0%
+do not know much about star wars i heard
+about star wars but i didn't see the
+
+ align:start position:0%
+about star wars but i didn't see the
+ 
+
+ align:start position:0%
+about star wars but i didn't see the
+movie yet always liked star trek better
+
+ align:start position:0%
+movie yet always liked star trek better
+ 
+
+ align:start position:0%
+movie yet always liked star trek better
+what star wars
+
+ align:start position:0%
+what star wars
+ 
+
+ align:start position:0%
+what star wars
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+very straightforward here i would give
+
+ align:start position:0%
+very straightforward here i would give
+ 
+
+ align:start position:0%
+very straightforward here i would give
+you an option one two three or four we
+
+ align:start position:0%
+you an option one two three or four we
+ 
+
+ align:start position:0%
+you an option one two three or four we
+collect the answers and we get some
+
+ align:start position:0%
+collect the answers and we get some
+ 
+
+ align:start position:0%
+collect the answers and we get some
+feedback this is obviously there's no
+
+ align:start position:0%
+feedback this is obviously there's no
+ 
+
+ align:start position:0%
+feedback this is obviously there's no
+right answer here
+
+ align:start position:0%
+right answer here
+ 
+
+ align:start position:0%
+right answer here
+there can be concept questions where
+
+ align:start position:0%
+there can be concept questions where
+ 
+
+ align:start position:0%
+there can be concept questions where
+there is a right and the wrong answer
+
+ align:start position:0%
+there is a right and the wrong answer
+ 
+
+ align:start position:0%
+there is a right and the wrong answer
+and again for you this is supposed to
+
+ align:start position:0%
+and again for you this is supposed to
+ 
+
+ align:start position:0%
+and again for you this is supposed to
+give you feedback
+
+ align:start position:0%
+give you feedback
+ 
+
+ align:start position:0%
+give you feedback
+on how well you understood the concept
+
+ align:start position:0%
+on how well you understood the concept
+ 
+
+ align:start position:0%
+on how well you understood the concept
+all right before we close this first
+
+ align:start position:0%
+all right before we close this first
+ 
+
+ align:start position:0%
+all right before we close this first
+video i want to introduce players um
+
+ align:start position:0%
+video i want to introduce players um
+ 
+
+ align:start position:0%
+video i want to introduce players um
+alice and bob we will have um
+
+ align:start position:0%
+alice and bob we will have um
+ 
+
+ align:start position:0%
+alice and bob we will have um
+often discussions of reference frames
+
+ align:start position:0%
+often discussions of reference frames
+ 
+
+ align:start position:0%
+often discussions of reference frames
+typically alice or bob are in one
+
+ align:start position:0%
+typically alice or bob are in one
+ 
+
+ align:start position:0%
+typically alice or bob are in one
+reference frame and then the other
+
+ align:start position:0%
+reference frame and then the other
+ 
+
+ align:start position:0%
+reference frame and then the other
+person is in the other reference frame i
+
+ align:start position:0%
+person is in the other reference frame i
+ 
+
+ align:start position:0%
+person is in the other reference frame i
+want you to think about those star trek
+
+ align:start position:0%
+want you to think about those star trek
+ 
+
+ align:start position:0%
+want you to think about those star trek
+um figures um we will use
+
+ align:start position:0%
+um figures um we will use
+ 
+
+ align:start position:0%
+um figures um we will use
+spacecrafts we will use light
+
+ align:start position:0%
+spacecrafts we will use light
+ 
+
+ align:start position:0%
+spacecrafts we will use light
+so phasers or light
+
+ align:start position:0%
+so phasers or light
+ 
+
+ align:start position:0%
+so phasers or light
+pistols
+
+ align:start position:0%
+pistols
+ 
+
+ align:start position:0%
+pistols
+in order to
+
+ align:start position:0%
+in order to
+ 
+
+ align:start position:0%
+in order to
+demonstrate the impact of special
+
+ align:start position:0%
+demonstrate the impact of special
+ 
+
+ align:start position:0%
+demonstrate the impact of special
+relativity you understand understand the
+
+ align:start position:0%
+relativity you understand understand the
+ 
+
+ align:start position:0%
+relativity you understand understand the
+concepts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/uOPuBNtv6Fk.txt b/uOPuBNtv6Fk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..277372661cba393ec3b954f1ed3f1956973dcda5
--- /dev/null
+++ b/uOPuBNtv6Fk.txt
@@ -0,0 +1,8155 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so today when you keep on
+
+ align:start position:0%
+all right so today when you keep on
+ 
+
+ align:start position:0%
+all right so today when you keep on
+working on sarcastic and I guess maybe
+
+ align:start position:0%
+working on sarcastic and I guess maybe
+ 
+
+ align:start position:0%
+working on sarcastic and I guess maybe
+we start if you guys have questions from
+
+ align:start position:0%
+we start if you guys have questions from
+ 
+
+ align:start position:0%
+we start if you guys have questions from
+the homework set since I'm sure you're
+
+ align:start position:0%
+the homework set since I'm sure you're
+ 
+
+ align:start position:0%
+the homework set since I'm sure you're
+thinking about that a lot right now are
+
+ align:start position:0%
+thinking about that a lot right now are
+ 
+
+ align:start position:0%
+thinking about that a lot right now are
+there any questions so do I take this to
+
+ align:start position:0%
+there any questions so do I take this to
+ 
+
+ align:start position:0%
+there any questions so do I take this to
+mean you have a completely under control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+all right all right so since we have
+
+ align:start position:0%
+all right all right so since we have
+ 
+
+ align:start position:0%
+all right all right so since we have
+Monte Carlo integration metropolis
+
+ align:start position:0%
+Monte Carlo integration metropolis
+ 
+
+ align:start position:0%
+Monte Carlo integration metropolis
+totally under control
+
+ align:start position:0%
+totally under control
+ 
+
+ align:start position:0%
+totally under control
+let's talk about time dependent
+
+ align:start position:0%
+let's talk about time dependent
+ 
+
+ align:start position:0%
+let's talk about time dependent
+probability distributions so in many
+
+ align:start position:0%
+probability distributions so in many
+ 
+
+ align:start position:0%
+probability distributions so in many
+situations
+
+ align:start position:0%
+situations
+ 
+
+ align:start position:0%
+situations
+we'd like to predict what's going to
+
+ align:start position:0%
+we'd like to predict what's going to
+ 
+
+ align:start position:0%
+we'd like to predict what's going to
+happen in an experiment and the
+
+ align:start position:0%
+happen in an experiment and the
+ 
+
+ align:start position:0%
+happen in an experiment and the
+fundamental equation side experiment or
+
+ align:start position:0%
+fundamental equation side experiment or
+ 
+
+ align:start position:0%
+fundamental equation side experiment or
+time dependent so we have different
+
+ align:start position:0%
+time dependent so we have different
+ 
+
+ align:start position:0%
+time dependent so we have different
+things happening at different times and
+
+ align:start position:0%
+things happening at different times and
+ 
+
+ align:start position:0%
+things happening at different times and
+so we really want to know what D DT of
+
+ align:start position:0%
+so we really want to know what D DT of
+ 
+
+ align:start position:0%
+so we really want to know what D DT of
+the probability of some observable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so he wants an equation like
+
+ align:start position:0%
+all right so he wants an equation like
+ 
+
+ align:start position:0%
+all right so he wants an equation like
+this and then when you actually made
+
+ align:start position:0%
+this and then when you actually made
+ 
+
+ align:start position:0%
+this and then when you actually made
+your measurement
+
+ align:start position:0%
+your measurement
+ 
+
+ align:start position:0%
+your measurement
+you'd be sampling from P so probability
+
+ align:start position:0%
+you'd be sampling from P so probability
+ 
+
+ align:start position:0%
+you'd be sampling from P so probability
+of the observables and so if you made
+
+ align:start position:0%
+of the observables and so if you made
+ 
+
+ align:start position:0%
+of the observables and so if you made
+the measurement you'd have a certain
+
+ align:start position:0%
+the measurement you'd have a certain
+ 
+
+ align:start position:0%
+the measurement you'd have a certain
+probability you'd observe something and
+
+ align:start position:0%
+probability you'd observe something and
+ 
+
+ align:start position:0%
+probability you'd observe something and
+you made a different measurement you'd
+
+ align:start position:0%
+you made a different measurement you'd
+ 
+
+ align:start position:0%
+you made a different measurement you'd
+have some prove the same probability you
+
+ align:start position:0%
+have some prove the same probability you
+ 
+
+ align:start position:0%
+have some prove the same probability you
+made the measurement at this time so
+
+ align:start position:0%
+made the measurement at this time so
+ 
+
+ align:start position:0%
+made the measurement at this time so
+this is gonna be probably the derivative
+
+ align:start position:0%
+this is gonna be probably the derivative
+ 
+
+ align:start position:0%
+this is gonna be probably the derivative
+all depending on the time and you made
+
+ align:start position:0%
+all depending on the time and you made
+ 
+
+ align:start position:0%
+all depending on the time and you made
+the measurements at different times so
+
+ align:start position:0%
+the measurements at different times so
+ 
+
+ align:start position:0%
+the measurements at different times so
+let's conceptually think about this
+
+ align:start position:0%
+let's conceptually think about this
+ 
+
+ align:start position:0%
+let's conceptually think about this
+suppose we had a box and it had a
+
+ align:start position:0%
+suppose we had a box and it had a
+ 
+
+ align:start position:0%
+suppose we had a box and it had a
+uranium atom in it that's radioactive
+
+ align:start position:0%
+uranium atom in it that's radioactive
+ 
+
+ align:start position:0%
+uranium atom in it that's radioactive
+and it can decay so we look in the box
+
+ align:start position:0%
+and it can decay so we look in the box
+ 
+
+ align:start position:0%
+and it can decay so we look in the box
+and at time zero I look in there and
+
+ align:start position:0%
+and at time zero I look in there and
+ 
+
+ align:start position:0%
+and at time zero I look in there and
+there's uranium atoms sitting there
+
+ align:start position:0%
+there's uranium atoms sitting there
+ 
+
+ align:start position:0%
+there's uranium atoms sitting there
+nicely and I go away for a while I come
+
+ align:start position:0%
+nicely and I go away for a while I come
+ 
+
+ align:start position:0%
+nicely and I go away for a while I come
+back and I open the box I looking again
+
+ align:start position:0%
+back and I open the box I looking again
+ 
+
+ align:start position:0%
+back and I open the box I looking again
+later and there's some probability that
+
+ align:start position:0%
+later and there's some probability that
+ 
+
+ align:start position:0%
+later and there's some probability that
+the uranium atom is still there and
+
+ align:start position:0%
+the uranium atom is still there and
+ 
+
+ align:start position:0%
+the uranium atom is still there and
+there's some probability that it fission
+
+ align:start position:0%
+there's some probability that it fission
+ 
+
+ align:start position:0%
+there's some probability that it fission
+during the time and it's gone right okay
+
+ align:start position:0%
+during the time and it's gone right okay
+ 
+
+ align:start position:0%
+during the time and it's gone right okay
+so there must be some kind of equation
+
+ align:start position:0%
+so there must be some kind of equation
+ 
+
+ align:start position:0%
+so there must be some kind of equation
+like this how the probability that the
+
+ align:start position:0%
+like this how the probability that the
+ 
+
+ align:start position:0%
+like this how the probability that the
+uranium atom is still there in the box
+
+ align:start position:0%
+uranium atom is still there in the box
+ 
+
+ align:start position:0%
+uranium atom is still there in the box
+right this okay yeah so just for that
+
+ align:start position:0%
+right this okay yeah so just for that
+ 
+
+ align:start position:0%
+right this okay yeah so just for that
+case yeah what do we think that
+
+ align:start position:0%
+case yeah what do we think that
+ 
+
+ align:start position:0%
+case yeah what do we think that
+probability how does that probably
+
+ align:start position:0%
+probability how does that probably
+ 
+
+ align:start position:0%
+probability how does that probably
+behave yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uranium has a half-life or something
+
+ align:start position:0%
+so uranium has a half-life or something
+ 
+
+ align:start position:0%
+so uranium has a half-life or something
+right yeah you guys heard this before
+
+ align:start position:0%
+right yeah you guys heard this before
+ 
+
+ align:start position:0%
+right yeah you guys heard this before
+right so so let's just try to think of
+
+ align:start position:0%
+right so so let's just try to think of
+ 
+
+ align:start position:0%
+right so so let's just try to think of
+how this should scale whenever it is
+
+ align:start position:0%
+how this should scale whenever it is
+ 
+
+ align:start position:0%
+how this should scale whenever it is
+probably should have something to do
+
+ align:start position:0%
+probably should have something to do
+ 
+
+ align:start position:0%
+probably should have something to do
+with the time constant for how fast
+
+ align:start position:0%
+with the time constant for how fast
+ 
+
+ align:start position:0%
+with the time constant for how fast
+uranium decays yeah you guys look at me
+
+ align:start position:0%
+uranium decays yeah you guys look at me
+ 
+
+ align:start position:0%
+uranium decays yeah you guys look at me
+Lisa blankly this is not that hard just
+
+ align:start position:0%
+Lisa blankly this is not that hard just
+ 
+
+ align:start position:0%
+Lisa blankly this is not that hard just
+one year eighty minute it's okay yeah
+
+ align:start position:0%
+one year eighty minute it's okay yeah
+ 
+
+ align:start position:0%
+one year eighty minute it's okay yeah
+all right so let's just write a
+
+ align:start position:0%
+all right so let's just write a
+ 
+
+ align:start position:0%
+all right so let's just write a
+plausible equation maybe it's DP DT
+
+ align:start position:0%
+plausible equation maybe it's DP DT
+ 
+
+ align:start position:0%
+plausible equation maybe it's DP DT
+where this is the probability that the
+
+ align:start position:0%
+where this is the probability that the
+ 
+
+ align:start position:0%
+where this is the probability that the
+uranium is in the box this might be
+
+ align:start position:0%
+uranium is in the box this might be
+ 
+
+ align:start position:0%
+uranium is in the box this might be
+probability divided by so what that
+
+ align:start position:0%
+probability divided by so what that
+ 
+
+ align:start position:0%
+probability divided by so what that
+would that be all right wait I guess we
+
+ align:start position:0%
+would that be all right wait I guess we
+ 
+
+ align:start position:0%
+would that be all right wait I guess we
+need a negative sign there so then the
+
+ align:start position:0%
+need a negative sign there so then the
+ 
+
+ align:start position:0%
+need a negative sign there so then the
+probability the solution of this would
+
+ align:start position:0%
+probability the solution of this would
+ 
+
+ align:start position:0%
+probability the solution of this would
+be that the probability that the uranium
+
+ align:start position:0%
+be that the probability that the uranium
+ 
+
+ align:start position:0%
+be that the probability that the uranium
+is still there it is gonna be equal to
+
+ align:start position:0%
+is still there it is gonna be equal to
+ 
+
+ align:start position:0%
+is still there it is gonna be equal to
+some initial probability either negative
+
+ align:start position:0%
+some initial probability either negative
+ 
+
+ align:start position:0%
+some initial probability either negative
+time or become great this is this look
+
+ align:start position:0%
+time or become great this is this look
+ 
+
+ align:start position:0%
+time or become great this is this look
+very reasonable
+
+ align:start position:0%
+very reasonable
+ 
+
+ align:start position:0%
+very reasonable
+you might seen this before yeah I mean
+
+ align:start position:0%
+you might seen this before yeah I mean
+ 
+
+ align:start position:0%
+you might seen this before yeah I mean
+II didn't think of this probability
+
+ align:start position:0%
+II didn't think of this probability
+ 
+
+ align:start position:0%
+II didn't think of this probability
+maybe you thought about it as number of
+
+ align:start position:0%
+maybe you thought about it as number of
+ 
+
+ align:start position:0%
+maybe you thought about it as number of
+uranium sandbox if I had written it as
+
+ align:start position:0%
+uranium sandbox if I had written it as
+ 
+
+ align:start position:0%
+uranium sandbox if I had written it as
+the number of uranium is equal to the
+
+ align:start position:0%
+the number of uranium is equal to the
+ 
+
+ align:start position:0%
+the number of uranium is equal to the
+original number of uranium's e to the
+
+ align:start position:0%
+original number of uranium's e to the
+ 
+
+ align:start position:0%
+original number of uranium's e to the
+negative T over tau you guys would have
+
+ align:start position:0%
+negative T over tau you guys would have
+ 
+
+ align:start position:0%
+negative T over tau you guys would have
+believed that right away right yeah okay
+
+ align:start position:0%
+believed that right away right yeah okay
+ 
+
+ align:start position:0%
+believed that right away right yeah okay
+so I guess maybe this is highlighting an
+
+ align:start position:0%
+so I guess maybe this is highlighting an
+ 
+
+ align:start position:0%
+so I guess maybe this is highlighting an
+issue here is that we're used to
+
+ align:start position:0%
+issue here is that we're used to
+ 
+
+ align:start position:0%
+issue here is that we're used to
+macroscopic thinking we're used to
+
+ align:start position:0%
+macroscopic thinking we're used to
+ 
+
+ align:start position:0%
+macroscopic thinking we're used to
+thinking of things this continuum right
+
+ align:start position:0%
+thinking of things this continuum right
+ 
+
+ align:start position:0%
+thinking of things this continuum right
+but if I only have one uranium there
+
+ align:start position:0%
+but if I only have one uranium there
+ 
+
+ align:start position:0%
+but if I only have one uranium there
+it's either there or it's not there it's
+
+ align:start position:0%
+it's either there or it's not there it's
+ 
+
+ align:start position:0%
+it's either there or it's not there it's
+1 or 0 it's so this the problem of this
+
+ align:start position:0%
+1 or 0 it's so this the problem of this
+ 
+
+ align:start position:0%
+1 or 0 it's so this the problem of this
+equation if you compute this it computes
+
+ align:start position:0%
+equation if you compute this it computes
+ 
+
+ align:start position:0%
+equation if you compute this it computes
+your you know irrational numbers
+
+ align:start position:0%
+your you know irrational numbers
+ 
+
+ align:start position:0%
+your you know irrational numbers
+fractional numbers as the number of
+
+ align:start position:0%
+fractional numbers as the number of
+ 
+
+ align:start position:0%
+fractional numbers as the number of
+uranium's but of course the number
+
+ align:start position:0%
+uranium's but of course the number
+ 
+
+ align:start position:0%
+uranium's but of course the number
+uranium is is just either it's integers
+
+ align:start position:0%
+uranium is is just either it's integers
+ 
+
+ align:start position:0%
+uranium is is just either it's integers
+right there's one uranium atom of this
+
+ align:start position:0%
+right there's one uranium atom of this
+ 
+
+ align:start position:0%
+right there's one uranium atom of this
+two or this 3 so this equation is not
+
+ align:start position:0%
+two or this 3 so this equation is not
+ 
+
+ align:start position:0%
+two or this 3 so this equation is not
+right all right this is incorrect so
+
+ align:start position:0%
+right all right this is incorrect so
+ 
+
+ align:start position:0%
+right all right this is incorrect so
+that was you learned in high school
+
+ align:start position:0%
+that was you learned in high school
+ 
+
+ align:start position:0%
+that was you learned in high school
+right that equation but that's not right
+
+ align:start position:0%
+right that equation but that's not right
+ 
+
+ align:start position:0%
+right that equation but that's not right
+so this is really the correct equation
+
+ align:start position:0%
+so this is really the correct equation
+ 
+
+ align:start position:0%
+so this is really the correct equation
+that the probability they have some
+
+ align:start position:0%
+that the probability they have some
+ 
+
+ align:start position:0%
+that the probability they have some
+memory uranium's does something
+
+ align:start position:0%
+memory uranium's does something
+ 
+
+ align:start position:0%
+memory uranium's does something
+you know if all this works for one year
+
+ align:start position:0%
+you know if all this works for one year
+ 
+
+ align:start position:0%
+you know if all this works for one year
+one atom anyway alright so that's the
+
+ align:start position:0%
+one atom anyway alright so that's the
+ 
+
+ align:start position:0%
+one atom anyway alright so that's the
+equation for one so this is probability
+
+ align:start position:0%
+equation for one so this is probability
+ 
+
+ align:start position:0%
+equation for one so this is probability
+I have one uranium if there's initial
+
+ align:start position:0%
+I have one uranium if there's initial
+ 
+
+ align:start position:0%
+I have one uranium if there's initial
+probability there's one your aim in the
+
+ align:start position:0%
+probability there's one your aim in the
+ 
+
+ align:start position:0%
+probability there's one your aim in the
+box which is basically my case will be
+
+ align:start position:0%
+box which is basically my case will be
+ 
+
+ align:start position:0%
+box which is basically my case will be
+one I know I put one in there
+
+ align:start position:0%
+one I know I put one in there
+ 
+
+ align:start position:0%
+one I know I put one in there
+right and that's just the case the
+
+ align:start position:0%
+right and that's just the case the
+ 
+
+ align:start position:0%
+right and that's just the case the
+probability decays but it doesn't mean
+
+ align:start position:0%
+probability decays but it doesn't mean
+ 
+
+ align:start position:0%
+probability decays but it doesn't mean
+the uranium decay so it means when I did
+
+ align:start position:0%
+the uranium decay so it means when I did
+ 
+
+ align:start position:0%
+the uranium decay so it means when I did
+if I do the experiment wants here I have
+
+ align:start position:0%
+if I do the experiment wants here I have
+ 
+
+ align:start position:0%
+if I do the experiment wants here I have
+the uranium the probability of the
+
+ align:start position:0%
+the uranium the probability of the
+ 
+
+ align:start position:0%
+the uranium the probability of the
+uranium is a simple exponential decay I
+
+ align:start position:0%
+uranium is a simple exponential decay I
+ 
+
+ align:start position:0%
+uranium is a simple exponential decay I
+know I had to uranium out of there when
+
+ align:start position:0%
+know I had to uranium out of there when
+ 
+
+ align:start position:0%
+know I had to uranium out of there when
+I first put it there and in later times
+
+ align:start position:0%
+I first put it there and in later times
+ 
+
+ align:start position:0%
+I first put it there and in later times
+it's going away
+
+ align:start position:0%
+it's going away
+ 
+
+ align:start position:0%
+it's going away
+right because longer longer times more
+
+ align:start position:0%
+right because longer longer times more
+ 
+
+ align:start position:0%
+right because longer longer times more
+more likelihood efficient now they
+
+ align:start position:0%
+more likelihood efficient now they
+ 
+
+ align:start position:0%
+more likelihood efficient now they
+actually do this to make a by a million
+
+ align:start position:0%
+actually do this to make a by a million
+ 
+
+ align:start position:0%
+actually do this to make a by a million
+boxes and put a million uranium atoms
+
+ align:start position:0%
+boxes and put a million uranium atoms
+ 
+
+ align:start position:0%
+boxes and put a million uranium atoms
+one in each one to start with and then I
+
+ align:start position:0%
+one in each one to start with and then I
+ 
+
+ align:start position:0%
+one in each one to start with and then I
+just keep coming back once a while and
+
+ align:start position:0%
+just keep coming back once a while and
+ 
+
+ align:start position:0%
+just keep coming back once a while and
+checking what I'll see is that initially
+
+ align:start position:0%
+checking what I'll see is that initially
+ 
+
+ align:start position:0%
+checking what I'll see is that initially
+I had number uranium's initially I had a
+
+ align:start position:0%
+I had number uranium's initially I had a
+ 
+
+ align:start position:0%
+I had number uranium's initially I had a
+million uranium atoms and for some time
+
+ align:start position:0%
+million uranium atoms and for some time
+ 
+
+ align:start position:0%
+million uranium atoms and for some time
+period I still had a million and then
+
+ align:start position:0%
+period I still had a million and then
+ 
+
+ align:start position:0%
+period I still had a million and then
+something happened and one of them went
+
+ align:start position:0%
+something happened and one of them went
+ 
+
+ align:start position:0%
+something happened and one of them went
+away because one of was envisioned turn
+
+ align:start position:0%
+away because one of was envisioned turn
+ 
+
+ align:start position:0%
+away because one of was envisioned turn
+into lead or whatever they turn into all
+
+ align:start position:0%
+into lead or whatever they turn into all
+ 
+
+ align:start position:0%
+into lead or whatever they turn into all
+right and so now I had a million minus
+
+ align:start position:0%
+right and so now I had a million minus
+ 
+
+ align:start position:0%
+right and so now I had a million minus
+one your any of said I live for a while
+
+ align:start position:0%
+one your any of said I live for a while
+ 
+
+ align:start position:0%
+one your any of said I live for a while
+and then maybe another one went away and
+
+ align:start position:0%
+and then maybe another one went away and
+ 
+
+ align:start position:0%
+and then maybe another one went away and
+then this time another one went away
+
+ align:start position:0%
+then this time another one went away
+ 
+
+ align:start position:0%
+then this time another one went away
+that time it lasted longer right this is
+
+ align:start position:0%
+that time it lasted longer right this is
+ 
+
+ align:start position:0%
+that time it lasted longer right this is
+what you really expect to observe this
+
+ align:start position:0%
+what you really expect to observe this
+ 
+
+ align:start position:0%
+what you really expect to observe this
+okay and so this is sampling from that
+
+ align:start position:0%
+okay and so this is sampling from that
+ 
+
+ align:start position:0%
+okay and so this is sampling from that
+probability distribution give you does
+
+ align:start position:0%
+probability distribution give you does
+ 
+
+ align:start position:0%
+probability distribution give you does
+it make sense
+
+ align:start position:0%
+it make sense
+ 
+
+ align:start position:0%
+it make sense
+yeah so I'm sampling a million times
+
+ align:start position:0%
+yeah so I'm sampling a million times
+ 
+
+ align:start position:0%
+yeah so I'm sampling a million times
+seven million boxes this is probably
+
+ align:start position:0%
+seven million boxes this is probably
+ 
+
+ align:start position:0%
+seven million boxes this is probably
+tribution for one box and so I'm able to
+
+ align:start position:0%
+tribution for one box and so I'm able to
+ 
+
+ align:start position:0%
+tribution for one box and so I'm able to
+figure this out okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we'd like to write
+
+ align:start position:0%
+all right so we'd like to write
+ 
+
+ align:start position:0%
+all right so we'd like to write
+equations like this for more complicated
+
+ align:start position:0%
+equations like this for more complicated
+ 
+
+ align:start position:0%
+equations like this for more complicated
+systems but you'll still go have the
+
+ align:start position:0%
+systems but you'll still go have the
+ 
+
+ align:start position:0%
+systems but you'll still go have the
+same confusion that the probabilities is
+
+ align:start position:0%
+same confusion that the probabilities is
+ 
+
+ align:start position:0%
+same confusion that the probabilities is
+going to be a continuous variable and
+
+ align:start position:0%
+going to be a continuous variable and
+ 
+
+ align:start position:0%
+going to be a continuous variable and
+it's gonna behave in ways that seem
+
+ align:start position:0%
+it's gonna behave in ways that seem
+ 
+
+ align:start position:0%
+it's gonna behave in ways that seem
+perfectly sensible to you but then every
+
+ align:start position:0%
+perfectly sensible to you but then every
+ 
+
+ align:start position:0%
+perfectly sensible to you but then every
+time you do the experiment different
+
+ align:start position:0%
+time you do the experiment different
+ 
+
+ align:start position:0%
+time you do the experiment different
+things will happen in time because you
+
+ align:start position:0%
+things will happen in time because you
+ 
+
+ align:start position:0%
+things will happen in time because you
+have something that's a time varying
+
+ align:start position:0%
+have something that's a time varying
+ 
+
+ align:start position:0%
+have something that's a time varying
+probability and each time you sample
+
+ align:start position:0%
+probability and each time you sample
+ 
+
+ align:start position:0%
+probability and each time you sample
+from the probably solution every time
+
+ align:start position:0%
+from the probably solution every time
+ 
+
+ align:start position:0%
+from the probably solution every time
+you do the experiment it's like a
+
+ align:start position:0%
+you do the experiment it's like a
+ 
+
+ align:start position:0%
+you do the experiment it's like a
+particular instance of sampling from
+
+ align:start position:0%
+particular instance of sampling from
+ 
+
+ align:start position:0%
+particular instance of sampling from
+that probability tribution and you might
+
+ align:start position:0%
+that probability tribution and you might
+ 
+
+ align:start position:0%
+that probability tribution and you might
+get you might get that there's you know
+
+ align:start position:0%
+get you might get that there's you know
+ 
+
+ align:start position:0%
+get you might get that there's you know
+87 uranium atoms left you might get that
+
+ align:start position:0%
+87 uranium atoms left you might get that
+ 
+
+ align:start position:0%
+87 uranium atoms left you might get that
+there's 93 and it's it's not because of
+
+ align:start position:0%
+there's 93 and it's it's not because of
+ 
+
+ align:start position:0%
+there's 93 and it's it's not because of
+your measurement error it's because the
+
+ align:start position:0%
+your measurement error it's because the
+ 
+
+ align:start position:0%
+your measurement error it's because the
+the intrinsic system it has its own
+
+ align:start position:0%
+the intrinsic system it has its own
+ 
+
+ align:start position:0%
+the intrinsic system it has its own
+randomness to it right you know you look
+
+ align:start position:0%
+randomness to it right you know you look
+ 
+
+ align:start position:0%
+randomness to it right you know you look
+at one uranium atom some of uranium
+
+ align:start position:0%
+at one uranium atom some of uranium
+ 
+
+ align:start position:0%
+at one uranium atom some of uranium
+atoms live for a million years and some
+
+ align:start position:0%
+atoms live for a million years and some
+ 
+
+ align:start position:0%
+atoms live for a million years and some
+uranium atoms might decayed in the next
+
+ align:start position:0%
+uranium atoms might decayed in the next
+ 
+
+ align:start position:0%
+uranium atoms might decayed in the next
+second right and you have no idea when
+
+ align:start position:0%
+second right and you have no idea when
+ 
+
+ align:start position:0%
+second right and you have no idea when
+they're gonna decay all you know is
+
+ align:start position:0%
+they're gonna decay all you know is
+ 
+
+ align:start position:0%
+they're gonna decay all you know is
+statistically on the average uranium is
+
+ align:start position:0%
+statistically on the average uranium is
+ 
+
+ align:start position:0%
+statistically on the average uranium is
+decay with a certain half-life which is
+
+ align:start position:0%
+decay with a certain half-life which is
+ 
+
+ align:start position:0%
+decay with a certain half-life which is
+pretty long all right all right just
+
+ align:start position:0%
+pretty long all right all right just
+ 
+
+ align:start position:0%
+pretty long all right all right just
+totally obvious
+
+ align:start position:0%
+totally obvious
+ 
+
+ align:start position:0%
+totally obvious
+I kept here there's this like totally
+
+ align:start position:0%
+I kept here there's this like totally
+ 
+
+ align:start position:0%
+I kept here there's this like totally
+obvious are totally confusing it's very
+
+ align:start position:0%
+obvious are totally confusing it's very
+ 
+
+ align:start position:0%
+obvious are totally confusing it's very
+funny with you guys are your expressions
+
+ align:start position:0%
+funny with you guys are your expressions
+ 
+
+ align:start position:0%
+funny with you guys are your expressions
+totally obvious until we confusing has
+
+ align:start position:0%
+totally obvious until we confusing has
+ 
+
+ align:start position:0%
+totally obvious until we confusing has
+the same blank expression can somebody
+
+ align:start position:0%
+the same blank expression can somebody
+ 
+
+ align:start position:0%
+the same blank expression can somebody
+ask a question maybe that would help us
+
+ align:start position:0%
+ask a question maybe that would help us
+ 
+
+ align:start position:0%
+ask a question maybe that would help us
+do this is okay all right this is a guy
+
+ align:start position:0%
+do this is okay all right this is a guy
+ 
+
+ align:start position:0%
+do this is okay all right this is a guy
+the second all right so a totally
+
+ align:start position:0%
+the second all right so a totally
+ 
+
+ align:start position:0%
+the second all right so a totally
+obvious good hard to tell sometimes
+
+ align:start position:0%
+obvious good hard to tell sometimes
+ 
+
+ align:start position:0%
+obvious good hard to tell sometimes
+all right so Joe Scott were some
+
+ align:start position:0%
+all right so Joe Scott were some
+ 
+
+ align:start position:0%
+all right so Joe Scott were some
+brilliant notes try to explain how to do
+
+ align:start position:0%
+brilliant notes try to explain how to do
+ 
+
+ align:start position:0%
+brilliant notes try to explain how to do
+this for chemical kinetics okay so you
+
+ align:start position:0%
+this for chemical kinetics okay so you
+ 
+
+ align:start position:0%
+this for chemical kinetics okay so you
+should definitely read them there in the
+
+ align:start position:0%
+should definitely read them there in the
+ 
+
+ align:start position:0%
+should definitely read them there in the
+posted under the materials general
+
+ align:start position:0%
+posted under the materials general
+ 
+
+ align:start position:0%
+posted under the materials general
+section stochastic chemical kinetics
+
+ align:start position:0%
+section stochastic chemical kinetics
+ 
+
+ align:start position:0%
+section stochastic chemical kinetics
+nice 20 page long thing don't like that
+
+ align:start position:0%
+nice 20 page long thing don't like that
+ 
+
+ align:start position:0%
+nice 20 page long thing don't like that
+it's definitely worthwhile to read it he
+
+ align:start position:0%
+it's definitely worthwhile to read it he
+ 
+
+ align:start position:0%
+it's definitely worthwhile to read it he
+was very nice to write very clear note
+
+ align:start position:0%
+was very nice to write very clear note
+ 
+
+ align:start position:0%
+was very nice to write very clear note
+so I'll try to explain his notes in
+
+ align:start position:0%
+so I'll try to explain his notes in
+ 
+
+ align:start position:0%
+so I'll try to explain his notes in
+expertly in a short period of time I
+
+ align:start position:0%
+expertly in a short period of time I
+ 
+
+ align:start position:0%
+expertly in a short period of time I
+strongly recommend your video so the
+
+ align:start position:0%
+strongly recommend your video so the
+ 
+
+ align:start position:0%
+strongly recommend your video so the
+idea is that the chemical kinetic
+
+ align:start position:0%
+idea is that the chemical kinetic
+ 
+
+ align:start position:0%
+idea is that the chemical kinetic
+equation do you guys have all used are
+
+ align:start position:0%
+equation do you guys have all used are
+ 
+
+ align:start position:0%
+equation do you guys have all used are
+also incorrect right just like this is
+
+ align:start position:0%
+also incorrect right just like this is
+ 
+
+ align:start position:0%
+also incorrect right just like this is
+incorrect right
+
+ align:start position:0%
+incorrect right
+ 
+
+ align:start position:0%
+incorrect right
+because this is assuming that something
+
+ align:start position:0%
+because this is assuming that something
+ 
+
+ align:start position:0%
+because this is assuming that something
+that's really a discrete variable is a
+
+ align:start position:0%
+that's really a discrete variable is a
+ 
+
+ align:start position:0%
+that's really a discrete variable is a
+continuous variable and we do this all
+
+ align:start position:0%
+continuous variable and we do this all
+ 
+
+ align:start position:0%
+continuous variable and we do this all
+the time right
+
+ align:start position:0%
+the time right
+ 
+
+ align:start position:0%
+the time right
+we know that material is made of atoms
+
+ align:start position:0%
+we know that material is made of atoms
+ 
+
+ align:start position:0%
+we know that material is made of atoms
+and so when you measure a mass in a
+
+ align:start position:0%
+and so when you measure a mass in a
+ 
+
+ align:start position:0%
+and so when you measure a mass in a
+certain volume there only can be certain
+
+ align:start position:0%
+certain volume there only can be certain
+ 
+
+ align:start position:0%
+certain volume there only can be certain
+discrete values but we always ignore
+
+ align:start position:0%
+discrete values but we always ignore
+ 
+
+ align:start position:0%
+discrete values but we always ignore
+that and we always treat mass as a
+
+ align:start position:0%
+that and we always treat mass as a
+ 
+
+ align:start position:0%
+that and we always treat mass as a
+continuous variable right so you have
+
+ align:start position:0%
+continuous variable right so you have
+ 
+
+ align:start position:0%
+continuous variable right so you have
+some flow some amount of liquid and you
+
+ align:start position:0%
+some flow some amount of liquid and you
+ 
+
+ align:start position:0%
+some flow some amount of liquid and you
+have some amount of mass so it could be
+
+ align:start position:0%
+have some amount of mass so it could be
+ 
+
+ align:start position:0%
+have some amount of mass so it could be
+any number and we treat D you know D M
+
+ align:start position:0%
+any number and we treat D you know D M
+ 
+
+ align:start position:0%
+any number and we treat D you know D M
+DT or things with DM DX D Rho DX we
+
+ align:start position:0%
+DT or things with DM DX D Rho DX we
+ 
+
+ align:start position:0%
+DT or things with DM DX D Rho DX we
+wrote those down as if everything's
+
+ align:start position:0%
+wrote those down as if everything's
+ 
+
+ align:start position:0%
+wrote those down as if everything's
+perfectly continuous variables and
+
+ align:start position:0%
+perfectly continuous variables and
+ 
+
+ align:start position:0%
+perfectly continuous variables and
+that's because that in a lot of systems
+
+ align:start position:0%
+that's because that in a lot of systems
+ 
+
+ align:start position:0%
+that's because that in a lot of systems
+we have we have so many atoms and we
+
+ align:start position:0%
+we have we have so many atoms and we
+ 
+
+ align:start position:0%
+we have we have so many atoms and we
+can't measure that well any way that we
+
+ align:start position:0%
+can't measure that well any way that we
+ 
+
+ align:start position:0%
+can't measure that well any way that we
+can tell if we were missing one or two
+
+ align:start position:0%
+can tell if we were missing one or two
+ 
+
+ align:start position:0%
+can tell if we were missing one or two
+atoms whether we end up with an extra
+
+ align:start position:0%
+atoms whether we end up with an extra
+ 
+
+ align:start position:0%
+atoms whether we end up with an extra
+half an atom in our equations or not
+
+ align:start position:0%
+half an atom in our equations or not
+ 
+
+ align:start position:0%
+half an atom in our equations or not
+makes no difference because we're not
+
+ align:start position:0%
+makes no difference because we're not
+ 
+
+ align:start position:0%
+makes no difference because we're not
+that precise right so we don't worry
+
+ align:start position:0%
+that precise right so we don't worry
+ 
+
+ align:start position:0%
+that precise right so we don't worry
+about so we use continuum equations
+
+ align:start position:0%
+about so we use continuum equations
+ 
+
+ align:start position:0%
+about so we use continuum equations
+everywhere in but in many cases what we
+
+ align:start position:0%
+everywhere in but in many cases what we
+ 
+
+ align:start position:0%
+everywhere in but in many cases what we
+really should be using our continuous
+
+ align:start position:0%
+really should be using our continuous
+ 
+
+ align:start position:0%
+really should be using our continuous
+equations for probabilities and and then
+
+ align:start position:0%
+equations for probabilities and and then
+ 
+
+ align:start position:0%
+equations for probabilities and and then
+as I'm trying to show you how you do it
+
+ align:start position:0%
+as I'm trying to show you how you do it
+ 
+
+ align:start position:0%
+as I'm trying to show you how you do it
+for chemical kinetics in a minute I'd
+
+ align:start position:0%
+for chemical kinetics in a minute I'd
+ 
+
+ align:start position:0%
+for chemical kinetics in a minute I'd
+say that this is super fundamental
+
+ align:start position:0%
+say that this is super fundamental
+ 
+
+ align:start position:0%
+say that this is super fundamental
+actually so quantum mechanics says that
+
+ align:start position:0%
+actually so quantum mechanics says that
+ 
+
+ align:start position:0%
+actually so quantum mechanics says that
+everything is wave functions which is
+
+ align:start position:0%
+everything is wave functions which is
+ 
+
+ align:start position:0%
+everything is wave functions which is
+actually like the square root of a
+
+ align:start position:0%
+actually like the square root of a
+ 
+
+ align:start position:0%
+actually like the square root of a
+probability density and the real
+
+ align:start position:0%
+probability density and the real
+ 
+
+ align:start position:0%
+probability density and the real
+equations are are probably really
+
+ align:start position:0%
+equations are are probably really
+ 
+
+ align:start position:0%
+equations are are probably really
+probability densities and so that's the
+
+ align:start position:0%
+probability densities and so that's the
+ 
+
+ align:start position:0%
+probability densities and so that's the
+real fundamental equations really
+
+ align:start position:0%
+real fundamental equations really
+ 
+
+ align:start position:0%
+real fundamental equations really
+everything is probabilities and when you
+
+ align:start position:0%
+everything is probabilities and when you
+ 
+
+ align:start position:0%
+everything is probabilities and when you
+make an experiment you're just sampling
+
+ align:start position:0%
+make an experiment you're just sampling
+ 
+
+ align:start position:0%
+make an experiment you're just sampling
+from the probability and all our
+
+ align:start position:0%
+from the probability and all our
+ 
+
+ align:start position:0%
+from the probability and all our
+continuing equations are like
+
+ align:start position:0%
+continuing equations are like
+ 
+
+ align:start position:0%
+continuing equations are like
+approximations they're only valid in
+
+ align:start position:0%
+approximations they're only valid in
+ 
+
+ align:start position:0%
+approximations they're only valid in
+like a large large number of atoms limit
+
+ align:start position:0%
+like a large large number of atoms limit
+ 
+
+ align:start position:0%
+like a large large number of atoms limit
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so just I know this takes it may be a
+
+ align:start position:0%
+so just I know this takes it may be a
+ 
+
+ align:start position:0%
+so just I know this takes it may be a
+change of thought because you're so used
+
+ align:start position:0%
+change of thought because you're so used
+ 
+
+ align:start position:0%
+change of thought because you're so used
+to this continual equations you start to
+
+ align:start position:0%
+to this continual equations you start to
+ 
+
+ align:start position:0%
+to this continual equations you start to
+believe they're really true right right
+
+ align:start position:0%
+believe they're really true right right
+ 
+
+ align:start position:0%
+believe they're really true right right
+if you probably use them a lot and you
+
+ align:start position:0%
+if you probably use them a lot and you
+ 
+
+ align:start position:0%
+if you probably use them a lot and you
+start to feel like you love those
+
+ align:start position:0%
+start to feel like you love those
+ 
+
+ align:start position:0%
+start to feel like you love those
+equations or your favorite equations you
+
+ align:start position:0%
+equations or your favorite equations you
+ 
+
+ align:start position:0%
+equations or your favorite equations you
+know you have a relationship for them
+
+ align:start position:0%
+know you have a relationship for them
+ 
+
+ align:start position:0%
+know you have a relationship for them
+something you might hate some of you
+
+ align:start position:0%
+something you might hate some of you
+ 
+
+ align:start position:0%
+something you might hate some of you
+love but at least you have a strong
+
+ align:start position:0%
+love but at least you have a strong
+ 
+
+ align:start position:0%
+love but at least you have a strong
+connection with them and you find out
+
+ align:start position:0%
+connection with them and you find out
+ 
+
+ align:start position:0%
+connection with them and you find out
+that the actually they're not even
+
+ align:start position:0%
+that the actually they're not even
+ 
+
+ align:start position:0%
+that the actually they're not even
+related to the real equation so the real
+
+ align:start position:0%
+related to the real equation so the real
+ 
+
+ align:start position:0%
+related to the real equation so the real
+equations are actually some different
+
+ align:start position:0%
+equations are actually some different
+ 
+
+ align:start position:0%
+equations are actually some different
+Isis be very annoying but it's true and
+
+ align:start position:0%
+Isis be very annoying but it's true and
+ 
+
+ align:start position:0%
+Isis be very annoying but it's true and
+when you get to smaller and smaller
+
+ align:start position:0%
+when you get to smaller and smaller
+ 
+
+ align:start position:0%
+when you get to smaller and smaller
+systems that have fewer and fewer
+
+ align:start position:0%
+systems that have fewer and fewer
+ 
+
+ align:start position:0%
+systems that have fewer and fewer
+molecules in them
+
+ align:start position:0%
+molecules in them
+ 
+
+ align:start position:0%
+molecules in them
+then you get more and more sensitive to
+
+ align:start position:0%
+then you get more and more sensitive to
+ 
+
+ align:start position:0%
+then you get more and more sensitive to
+the fact that the regular equations are
+
+ align:start position:0%
+the fact that the regular equations are
+ 
+
+ align:start position:0%
+the fact that the regular equations are
+incorrect and the this comes up a lot in
+
+ align:start position:0%
+incorrect and the this comes up a lot in
+ 
+
+ align:start position:0%
+incorrect and the this comes up a lot in
+small systems so that many of you
+
+ align:start position:0%
+small systems so that many of you
+ 
+
+ align:start position:0%
+small systems so that many of you
+probably will do research that has to do
+
+ align:start position:0%
+probably will do research that has to do
+ 
+
+ align:start position:0%
+probably will do research that has to do
+with biology inside in biology they're
+
+ align:start position:0%
+with biology inside in biology they're
+ 
+
+ align:start position:0%
+with biology inside in biology they're
+cells inside cells there's like
+
+ align:start position:0%
+cells inside cells there's like
+ 
+
+ align:start position:0%
+cells inside cells there's like
+subcellular structures inside those sub
+
+ align:start position:0%
+subcellular structures inside those sub
+ 
+
+ align:start position:0%
+subcellular structures inside those sub
+cellular structures there's not very
+
+ align:start position:0%
+cellular structures there's not very
+ 
+
+ align:start position:0%
+cellular structures there's not very
+many molecules and so you often are at
+
+ align:start position:0%
+many molecules and so you often are at
+ 
+
+ align:start position:0%
+many molecules and so you often are at
+the limit where you know you have like
+
+ align:start position:0%
+the limit where you know you have like
+ 
+
+ align:start position:0%
+the limit where you know you have like
+one molecule of a certain type inside
+
+ align:start position:0%
+one molecule of a certain type inside
+ 
+
+ align:start position:0%
+one molecule of a certain type inside
+this you know in mitochondria or
+
+ align:start position:0%
+this you know in mitochondria or
+ 
+
+ align:start position:0%
+this you know in mitochondria or
+something and that's it and so you
+
+ align:start position:0%
+something and that's it and so you
+ 
+
+ align:start position:0%
+something and that's it and so you
+wouldn't expect a continuum equations to
+
+ align:start position:0%
+wouldn't expect a continuum equations to
+ 
+
+ align:start position:0%
+wouldn't expect a continuum equations to
+work and and in fact there's a big field
+
+ align:start position:0%
+work and and in fact there's a big field
+ 
+
+ align:start position:0%
+work and and in fact there's a big field
+many people research doing here called
+
+ align:start position:0%
+many people research doing here called
+ 
+
+ align:start position:0%
+many people research doing here called
+single molecule spectroscopy where you
+
+ align:start position:0%
+single molecule spectroscopy where you
+ 
+
+ align:start position:0%
+single molecule spectroscopy where you
+can watch and you know measure the
+
+ align:start position:0%
+can watch and you know measure the
+ 
+
+ align:start position:0%
+can watch and you know measure the
+motion of one DNA molecule or something
+
+ align:start position:0%
+motion of one DNA molecule or something
+ 
+
+ align:start position:0%
+motion of one DNA molecule or something
+like that and so you really see the
+
+ align:start position:0%
+like that and so you really see the
+ 
+
+ align:start position:0%
+like that and so you really see the
+individual molecules and and the effects
+
+ align:start position:0%
+individual molecules and and the effects
+ 
+
+ align:start position:0%
+individual molecules and and the effects
+of the individuality of the molecules
+
+ align:start position:0%
+of the individuality of the molecules
+ 
+
+ align:start position:0%
+of the individuality of the molecules
+and this is not only true in biology for
+
+ align:start position:0%
+and this is not only true in biology for
+ 
+
+ align:start position:0%
+and this is not only true in biology for
+a long time there's a field called
+
+ align:start position:0%
+a long time there's a field called
+ 
+
+ align:start position:0%
+a long time there's a field called
+emulsion polymerization you guys ever
+
+ align:start position:0%
+emulsion polymerization you guys ever
+ 
+
+ align:start position:0%
+emulsion polymerization you guys ever
+hear this so like all the paint on the
+
+ align:start position:0%
+hear this so like all the paint on the
+ 
+
+ align:start position:0%
+hear this so like all the paint on the
+walls here is made by that process where
+
+ align:start position:0%
+walls here is made by that process where
+ 
+
+ align:start position:0%
+walls here is made by that process where
+they polymerize methyl methacrylate they
+
+ align:start position:0%
+they polymerize methyl methacrylate they
+ 
+
+ align:start position:0%
+they polymerize methyl methacrylate they
+want to make the little beads of
+
+ align:start position:0%
+want to make the little beads of
+ 
+
+ align:start position:0%
+want to make the little beads of
+polymers as have a small dispersion as
+
+ align:start position:0%
+polymers as have a small dispersion as
+ 
+
+ align:start position:0%
+polymers as have a small dispersion as
+possible to make them all the molecules
+
+ align:start position:0%
+possible to make them all the molecules
+ 
+
+ align:start position:0%
+possible to make them all the molecules
+the same so what they do is they make a
+
+ align:start position:0%
+the same so what they do is they make a
+ 
+
+ align:start position:0%
+the same so what they do is they make a
+colloidal suspension draw a little
+
+ align:start position:0%
+colloidal suspension draw a little
+ 
+
+ align:start position:0%
+colloidal suspension draw a little
+picture so they have a reactor they make
+
+ align:start position:0%
+picture so they have a reactor they make
+ 
+
+ align:start position:0%
+picture so they have a reactor they make
+little bubbles of the monomer that are
+
+ align:start position:0%
+little bubbles of the monomer that are
+ 
+
+ align:start position:0%
+little bubbles of the monomer that are
+suspended in some solvent and inside
+
+ align:start position:0%
+suspended in some solvent and inside
+ 
+
+ align:start position:0%
+suspended in some solvent and inside
+each of these bubbles because the way
+
+ align:start position:0%
+each of these bubbles because the way
+ 
+
+ align:start position:0%
+each of these bubbles because the way
+they make them they're all about the
+
+ align:start position:0%
+they make them they're all about the
+ 
+
+ align:start position:0%
+they make them they're all about the
+same size so they all have a lot of
+
+ align:start position:0%
+same size so they all have a lot of
+ 
+
+ align:start position:0%
+same size so they all have a lot of
+bubbles all about the same size and then
+
+ align:start position:0%
+bubbles all about the same size and then
+ 
+
+ align:start position:0%
+bubbles all about the same size and then
+they polymerize and they polymerize each
+
+ align:start position:0%
+they polymerize and they polymerize each
+ 
+
+ align:start position:0%
+they polymerize and they polymerize each
+them and they polymerize and basically
+
+ align:start position:0%
+them and they polymerize and basically
+ 
+
+ align:start position:0%
+them and they polymerize and basically
+all the material that's they are
+
+ align:start position:0%
+all the material that's they are
+ 
+
+ align:start position:0%
+all the material that's they are
+polymerizes into one molecule how do
+
+ align:start position:0%
+polymerizes into one molecule how do
+ 
+
+ align:start position:0%
+polymerizes into one molecule how do
+they make that happen is that they
+
+ align:start position:0%
+they make that happen is that they
+ 
+
+ align:start position:0%
+they make that happen is that they
+introduce say a free radical and one
+
+ align:start position:0%
+introduce say a free radical and one
+ 
+
+ align:start position:0%
+introduce say a free radical and one
+free radical gets into one these mala in
+
+ align:start position:0%
+free radical gets into one these mala in
+ 
+
+ align:start position:0%
+free radical gets into one these mala in
+these bubbles and it complies the whole
+
+ align:start position:0%
+these bubbles and it complies the whole
+ 
+
+ align:start position:0%
+these bubbles and it complies the whole
+thing because the reactions are radical
+
+ align:start position:0%
+thing because the reactions are radical
+ 
+
+ align:start position:0%
+thing because the reactions are radical
+plus monomer gets to a you know
+
+ align:start position:0%
+plus monomer gets to a you know
+ 
+
+ align:start position:0%
+plus monomer gets to a you know
+copolymer bigger polymer polymer radical
+
+ align:start position:0%
+copolymer bigger polymer polymer radical
+ 
+
+ align:start position:0%
+copolymer bigger polymer polymer radical
+size in goes to polymer radical size n
+
+ align:start position:0%
+size in goes to polymer radical size n
+ 
+
+ align:start position:0%
+size in goes to polymer radical size n
+plus one that's the polymerization
+
+ align:start position:0%
+plus one that's the polymerization
+ 
+
+ align:start position:0%
+plus one that's the polymerization
+reaction now normally
+
+ align:start position:0%
+reaction now normally
+ 
+
+ align:start position:0%
+reaction now normally
+if you did this in the bulk there'd be a
+
+ align:start position:0%
+if you did this in the bulk there'd be a
+ 
+
+ align:start position:0%
+if you did this in the bulk there'd be a
+lot of radicals and some of these guys
+
+ align:start position:0%
+lot of radicals and some of these guys
+ 
+
+ align:start position:0%
+lot of radicals and some of these guys
+would react with each other and the rack
+
+ align:start position:0%
+would react with each other and the rack
+ 
+
+ align:start position:0%
+would react with each other and the rack
+will be gone because the two radicals
+
+ align:start position:0%
+will be gone because the two radicals
+ 
+
+ align:start position:0%
+will be gone because the two radicals
+would react make a new chemical bond and
+
+ align:start position:0%
+would react make a new chemical bond and
+ 
+
+ align:start position:0%
+would react make a new chemical bond and
+this process would stop and so this
+
+ align:start position:0%
+this process would stop and so this
+ 
+
+ align:start position:0%
+this process would stop and so this
+gives a big dispersion in the size of
+
+ align:start position:0%
+gives a big dispersion in the size of
+ 
+
+ align:start position:0%
+gives a big dispersion in the size of
+the polymer change again so to beat this
+
+ align:start position:0%
+the polymer change again so to beat this
+ 
+
+ align:start position:0%
+the polymer change again so to beat this
+they do a molten polymerization and they
+
+ align:start position:0%
+they do a molten polymerization and they
+ 
+
+ align:start position:0%
+they do a molten polymerization and they
+make the number of radicals so small
+
+ align:start position:0%
+make the number of radicals so small
+ 
+
+ align:start position:0%
+make the number of radicals so small
+that statistically at a time and these
+
+ align:start position:0%
+that statistically at a time and these
+ 
+
+ align:start position:0%
+that statistically at a time and these
+droplets either has 0 or 1 of radicals
+
+ align:start position:0%
+droplets either has 0 or 1 of radicals
+ 
+
+ align:start position:0%
+droplets either has 0 or 1 of radicals
+in it and and there's not during the
+
+ align:start position:0%
+in it and and there's not during the
+ 
+
+ align:start position:0%
+in it and and there's not during the
+time it does the polymerization there's
+
+ align:start position:0%
+time it does the polymerization there's
+ 
+
+ align:start position:0%
+time it does the polymerization there's
+not enough time for a second radical to
+
+ align:start position:0%
+not enough time for a second radical to
+ 
+
+ align:start position:0%
+not enough time for a second radical to
+come in so it's only got one radical so
+
+ align:start position:0%
+come in so it's only got one radical so
+ 
+
+ align:start position:0%
+come in so it's only got one radical so
+that one radical is gonna eat up every
+
+ align:start position:0%
+that one radical is gonna eat up every
+ 
+
+ align:start position:0%
+that one radical is gonna eat up every
+single monomer molecule and the whole
+
+ align:start position:0%
+single monomer molecule and the whole
+ 
+
+ align:start position:0%
+single monomer molecule and the whole
+thing and so it's gonna make a giant
+
+ align:start position:0%
+thing and so it's gonna make a giant
+ 
+
+ align:start position:0%
+thing and so it's gonna make a giant
+polymer that's the whole size of the
+
+ align:start position:0%
+polymer that's the whole size of the
+ 
+
+ align:start position:0%
+polymer that's the whole size of the
+emulsion if you if you made the drops
+
+ align:start position:0%
+emulsion if you if you made the drops
+ 
+
+ align:start position:0%
+emulsion if you if you made the drops
+too big you get two radicals in there
+
+ align:start position:0%
+too big you get two radicals in there
+ 
+
+ align:start position:0%
+too big you get two radicals in there
+you get something that's happening and
+
+ align:start position:0%
+you get something that's happening and
+ 
+
+ align:start position:0%
+you get something that's happening and
+you get a dispersion so this is a
+
+ align:start position:0%
+you get a dispersion so this is a
+ 
+
+ align:start position:0%
+you get a dispersion so this is a
+emulsion polymerization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so cells have small little
+
+ align:start position:0%
+all right so cells have small little
+ 
+
+ align:start position:0%
+all right so cells have small little
+volumes colloids and emulsions have
+
+ align:start position:0%
+volumes colloids and emulsions have
+ 
+
+ align:start position:0%
+volumes colloids and emulsions have
+small little volumes they all have that
+
+ align:start position:0%
+small little volumes they all have that
+ 
+
+ align:start position:0%
+small little volumes they all have that
+the sum of the molecules the important
+
+ align:start position:0%
+the sum of the molecules the important
+ 
+
+ align:start position:0%
+the sum of the molecules the important
+molecules are so have such low
+
+ align:start position:0%
+molecules are so have such low
+ 
+
+ align:start position:0%
+molecules are so have such low
+concentrations of ions are so small that
+
+ align:start position:0%
+concentrations of ions are so small that
+ 
+
+ align:start position:0%
+concentrations of ions are so small that
+the concentration times the volume is
+
+ align:start position:0%
+the concentration times the volume is
+ 
+
+ align:start position:0%
+the concentration times the volume is
+less than 1 or about 1 so that's for
+
+ align:start position:0%
+less than 1 or about 1 so that's for
+ 
+
+ align:start position:0%
+less than 1 or about 1 so that's for
+like you know your your copies of DNA
+
+ align:start position:0%
+like you know your your copies of DNA
+ 
+
+ align:start position:0%
+like you know your your copies of DNA
+and you in your cells there's the same
+
+ align:start position:0%
+and you in your cells there's the same
+ 
+
+ align:start position:0%
+and you in your cells there's the same
+kind of thing for radicals free radicals
+
+ align:start position:0%
+kind of thing for radicals free radicals
+ 
+
+ align:start position:0%
+kind of thing for radicals free radicals
+and a polymerization system and the
+
+ align:start position:0%
+and a polymerization system and the
+ 
+
+ align:start position:0%
+and a polymerization system and the
+Civil Code things could happen with like
+
+ align:start position:0%
+Civil Code things could happen with like
+ 
+
+ align:start position:0%
+Civil Code things could happen with like
+explosions
+
+ align:start position:0%
+explosions
+ 
+
+ align:start position:0%
+explosions
+different kinds of rare events you might
+
+ align:start position:0%
+different kinds of rare events you might
+ 
+
+ align:start position:0%
+different kinds of rare events you might
+have a very small number of some really
+
+ align:start position:0%
+have a very small number of some really
+ 
+
+ align:start position:0%
+have a very small number of some really
+important molecule and then whether or
+
+ align:start position:0%
+important molecule and then whether or
+ 
+
+ align:start position:0%
+important molecule and then whether or
+not you have one or not is really
+
+ align:start position:0%
+not you have one or not is really
+ 
+
+ align:start position:0%
+not you have one or not is really
+important ok all right so we want to
+
+ align:start position:0%
+important ok all right so we want to
+ 
+
+ align:start position:0%
+important ok all right so we want to
+model those kinds of systems we have to
+
+ align:start position:0%
+model those kinds of systems we have to
+ 
+
+ align:start position:0%
+model those kinds of systems we have to
+worry about the graininess so we want to
+
+ align:start position:0%
+worry about the graininess so we want to
+ 
+
+ align:start position:0%
+worry about the graininess so we want to
+write down what the equation is for DP
+
+ align:start position:0%
+write down what the equation is for DP
+ 
+
+ align:start position:0%
+write down what the equation is for DP
+DT so firstly I think what is P let's do
+
+ align:start position:0%
+DT so firstly I think what is P let's do
+ 
+
+ align:start position:0%
+DT so firstly I think what is P let's do
+a case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where have the reaction of a plus B goes
+
+ align:start position:0%
+where have the reaction of a plus B goes
+ 
+
+ align:start position:0%
+where have the reaction of a plus B goes
+to C okay suppose this the only reaction
+
+ align:start position:0%
+to C okay suppose this the only reaction
+ 
+
+ align:start position:0%
+to C okay suppose this the only reaction
+at camp in our system the only molecules
+
+ align:start position:0%
+at camp in our system the only molecules
+ 
+
+ align:start position:0%
+at camp in our system the only molecules
+we have our system or A's B's and C's
+
+ align:start position:0%
+we have our system or A's B's and C's
+ 
+
+ align:start position:0%
+we have our system or A's B's and C's
+and so our probability distribution or
+
+ align:start position:0%
+and so our probability distribution or
+ 
+
+ align:start position:0%
+and so our probability distribution or
+probably we want to know is how many A's
+
+ align:start position:0%
+probably we want to know is how many A's
+ 
+
+ align:start position:0%
+probably we want to know is how many A's
+how many bees how many C's do we have in
+
+ align:start position:0%
+how many bees how many C's do we have in
+ 
+
+ align:start position:0%
+how many bees how many C's do we have in
+our system okay so that's that's a
+
+ align:start position:0%
+our system okay so that's that's a
+ 
+
+ align:start position:0%
+our system okay so that's that's a
+probability we're interested to know we
+
+ align:start position:0%
+probability we're interested to know we
+ 
+
+ align:start position:0%
+probability we're interested to know we
+could have five A's to B's and zero C's
+
+ align:start position:0%
+could have five A's to B's and zero C's
+ 
+
+ align:start position:0%
+could have five A's to B's and zero C's
+we could have 3a is seven B's elevenses
+
+ align:start position:0%
+we could have 3a is seven B's elevenses
+ 
+
+ align:start position:0%
+we could have 3a is seven B's elevenses
+who knows all right different numbers
+
+ align:start position:0%
+who knows all right different numbers
+ 
+
+ align:start position:0%
+who knows all right different numbers
+like that if he gets out to be ten to
+
+ align:start position:0%
+like that if he gets out to be ten to
+ 
+
+ align:start position:0%
+like that if he gets out to be ten to
+the 23rd then there's no point you don't
+
+ align:start position:0%
+the 23rd then there's no point you don't
+ 
+
+ align:start position:0%
+the 23rd then there's no point you don't
+have to do this because you can just go
+
+ align:start position:0%
+have to do this because you can just go
+ 
+
+ align:start position:0%
+have to do this because you can just go
+back to your continuum equations right
+
+ align:start position:0%
+back to your continuum equations right
+ 
+
+ align:start position:0%
+back to your continuum equations right
+but if you have five or three or two or
+
+ align:start position:0%
+but if you have five or three or two or
+ 
+
+ align:start position:0%
+but if you have five or three or two or
+one or zero then you really need to
+
+ align:start position:0%
+one or zero then you really need to
+ 
+
+ align:start position:0%
+one or zero then you really need to
+worry about the graininess so you want
+
+ align:start position:0%
+worry about the graininess so you want
+ 
+
+ align:start position:0%
+worry about the graininess so you want
+to write down an equation so here's the
+
+ align:start position:0%
+to write down an equation so here's the
+ 
+
+ align:start position:0%
+to write down an equation so here's the
+probability of n a and D and C and it's
+
+ align:start position:0%
+probability of n a and D and C and it's
+ 
+
+ align:start position:0%
+probability of n a and D and C and it's
+going to equal two reactions which
+
+ align:start position:0%
+going to equal two reactions which
+ 
+
+ align:start position:0%
+going to equal two reactions which
+consume if I'm in the state that has
+
+ align:start position:0%
+consume if I'm in the state that has
+ 
+
+ align:start position:0%
+consume if I'm in the state that has
+certain number of A's B's and C's and I
+
+ align:start position:0%
+certain number of A's B's and C's and I
+ 
+
+ align:start position:0%
+certain number of A's B's and C's and I
+can react away so we have reactions for
+
+ align:start position:0%
+can react away so we have reactions for
+ 
+
+ align:start position:0%
+can react away so we have reactions for
+example I'm in this state and a plus B
+
+ align:start position:0%
+example I'm in this state and a plus B
+ 
+
+ align:start position:0%
+example I'm in this state and a plus B
+could react with each other and and will
+
+ align:start position:0%
+could react with each other and and will
+ 
+
+ align:start position:0%
+could react with each other and and will
+react away so I'll have a some reaction
+
+ align:start position:0%
+react away so I'll have a some reaction
+ 
+
+ align:start position:0%
+react away so I'll have a some reaction
+I'm gonna write it K but we'll come back
+
+ align:start position:0%
+I'm gonna write it K but we'll come back
+ 
+
+ align:start position:0%
+I'm gonna write it K but we'll come back
+to what this really means exactly in a
+
+ align:start position:0%
+to what this really means exactly in a
+ 
+
+ align:start position:0%
+to what this really means exactly in a
+minute so this is the K for a plus B
+
+ align:start position:0%
+minute so this is the K for a plus B
+ 
+
+ align:start position:0%
+minute so this is the K for a plus B
+going to C and we think that this is
+
+ align:start position:0%
+going to C and we think that this is
+ 
+
+ align:start position:0%
+going to C and we think that this is
+going to scale with a number of A's and
+
+ align:start position:0%
+going to scale with a number of A's and
+ 
+
+ align:start position:0%
+going to scale with a number of A's and
+the number of bees have gotten right and
+
+ align:start position:0%
+the number of bees have gotten right and
+ 
+
+ align:start position:0%
+the number of bees have gotten right and
+this depends on the probability that I
+
+ align:start position:0%
+this depends on the probability that I
+ 
+
+ align:start position:0%
+this depends on the probability that I
+have ABC okay so if I if I'm if I'm in
+
+ align:start position:0%
+have ABC okay so if I if I'm if I'm in
+ 
+
+ align:start position:0%
+have ABC okay so if I if I'm if I'm in
+this state with n A's and B's and C's
+
+ align:start position:0%
+this state with n A's and B's and C's
+ 
+
+ align:start position:0%
+this state with n A's and B's and C's
+that probability is going to go down
+
+ align:start position:0%
+that probability is going to go down
+ 
+
+ align:start position:0%
+that probability is going to go down
+because the A's and B's can react with
+
+ align:start position:0%
+because the A's and B's can react with
+ 
+
+ align:start position:0%
+because the A's and B's can react with
+each other right
+
+ align:start position:0%
+each other right
+ 
+
+ align:start position:0%
+each other right
+now on the other hand I have plus the
+
+ align:start position:0%
+now on the other hand I have plus the
+ 
+
+ align:start position:0%
+now on the other hand I have plus the
+same K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is gonna be n a-prime and
+
+ align:start position:0%
+and this is gonna be n a-prime and
+ 
+
+ align:start position:0%
+and this is gonna be n a-prime and
+b-prime if I have some other state that
+
+ align:start position:0%
+b-prime if I have some other state that
+ 
+
+ align:start position:0%
+b-prime if I have some other state that
+can react so that it makes this state
+
+ align:start position:0%
+can react so that it makes this state
+ 
+
+ align:start position:0%
+can react so that it makes this state
+then I'll get a plus sign because the
+
+ align:start position:0%
+then I'll get a plus sign because the
+ 
+
+ align:start position:0%
+then I'll get a plus sign because the
+probability of the state would increase
+
+ align:start position:0%
+probability of the state would increase
+ 
+
+ align:start position:0%
+probability of the state would increase
+so for example if na prime is equal to
+
+ align:start position:0%
+so for example if na prime is equal to
+ 
+
+ align:start position:0%
+so for example if na prime is equal to
+na plus 1 and B prime is equal to NB
+
+ align:start position:0%
+na plus 1 and B prime is equal to NB
+ 
+
+ align:start position:0%
+na plus 1 and B prime is equal to NB
+plus 1 and then C prime is equal to and
+
+ align:start position:0%
+plus 1 and then C prime is equal to and
+ 
+
+ align:start position:0%
+plus 1 and then C prime is equal to and
+C minus 1 then that state can react by
+
+ align:start position:0%
+C minus 1 then that state can react by
+ 
+
+ align:start position:0%
+C minus 1 then that state can react by
+one of these days and one of these B's
+
+ align:start position:0%
+one of these days and one of these B's
+ 
+
+ align:start position:0%
+one of these days and one of these B's
+combining together to make a C that will
+
+ align:start position:0%
+combining together to make a C that will
+ 
+
+ align:start position:0%
+combining together to make a C that will
+get me to this exact state here
+
+ align:start position:0%
+get me to this exact state here
+ 
+
+ align:start position:0%
+get me to this exact state here
+does it make sense all right so that's
+
+ align:start position:0%
+does it make sense all right so that's
+ 
+
+ align:start position:0%
+does it make sense all right so that's
+the master equation if I have a system
+
+ align:start position:0%
+the master equation if I have a system
+ 
+
+ align:start position:0%
+the master equation if I have a system
+that can only do the irreversible
+
+ align:start position:0%
+that can only do the irreversible
+ 
+
+ align:start position:0%
+that can only do the irreversible
+reaction a plus B goes to C so the only
+
+ align:start position:0%
+reaction a plus B goes to C so the only
+ 
+
+ align:start position:0%
+reaction a plus B goes to C so the only
+I can go away because I probability
+
+ align:start position:0%
+I can go away because I probability
+ 
+
+ align:start position:0%
+I can go away because I probability
+density of this is probably the state
+
+ align:start position:0%
+density of this is probably the state
+ 
+
+ align:start position:0%
+density of this is probably the state
+can reduce because that reaction occurs
+
+ align:start position:0%
+can reduce because that reaction occurs
+ 
+
+ align:start position:0%
+can reduce because that reaction occurs
+starting from this state and the
+
+ align:start position:0%
+starting from this state and the
+ 
+
+ align:start position:0%
+starting from this state and the
+probably this state can increase because
+
+ align:start position:0%
+probably this state can increase because
+ 
+
+ align:start position:0%
+probably this state can increase because
+I started from this other stay here the
+
+ align:start position:0%
+I started from this other stay here the
+ 
+
+ align:start position:0%
+I started from this other stay here the
+special stay here and that would make
+
+ align:start position:0%
+special stay here and that would make
+ 
+
+ align:start position:0%
+special stay here and that would make
+the state of interest
+
+ align:start position:0%
+the state of interest
+ 
+
+ align:start position:0%
+the state of interest
+all right and so I have equation this
+
+ align:start position:0%
+all right and so I have equation this
+ 
+
+ align:start position:0%
+all right and so I have equation this
+equation over and over again for every
+
+ align:start position:0%
+equation over and over again for every
+ 
+
+ align:start position:0%
+equation over and over again for every
+possible value of n a and B H and C this
+
+ align:start position:0%
+possible value of n a and B H and C this
+ 
+
+ align:start position:0%
+possible value of n a and B H and C this
+is ok now I have to actually remember
+
+ align:start position:0%
+is ok now I have to actually remember
+ 
+
+ align:start position:0%
+is ok now I have to actually remember
+for chemical kinetics that whenever you
+
+ align:start position:0%
+for chemical kinetics that whenever you
+ 
+
+ align:start position:0%
+for chemical kinetics that whenever you
+have a forward reaction you also have
+
+ align:start position:0%
+have a forward reaction you also have
+ 
+
+ align:start position:0%
+have a forward reaction you also have
+the reverse reaction so there's actually
+
+ align:start position:0%
+the reverse reaction so there's actually
+ 
+
+ align:start position:0%
+the reverse reaction so there's actually
+a couple more terms so now I have
+
+ align:start position:0%
+a couple more terms so now I have
+ 
+
+ align:start position:0%
+a couple more terms so now I have
+another lost term this is C goes to a
+
+ align:start position:0%
+another lost term this is C goes to a
+ 
+
+ align:start position:0%
+another lost term this is C goes to a
+plus B this is going to tend on the
+
+ align:start position:0%
+plus B this is going to tend on the
+ 
+
+ align:start position:0%
+plus B this is going to tend on the
+number of C's and that's a P of n a and
+
+ align:start position:0%
+number of C's and that's a P of n a and
+ 
+
+ align:start position:0%
+number of C's and that's a P of n a and
+B and C and then I have another source
+
+ align:start position:0%
+B and C and then I have another source
+ 
+
+ align:start position:0%
+B and C and then I have another source
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is where I start from state
+
+ align:start position:0%
+and this is where I start from state
+ 
+
+ align:start position:0%
+and this is where I start from state
+with one more C okay so this set of
+
+ align:start position:0%
+with one more C okay so this set of
+ 
+
+ align:start position:0%
+with one more C okay so this set of
+equations is called the kinetic master
+
+ align:start position:0%
+equations is called the kinetic master
+ 
+
+ align:start position:0%
+equations is called the kinetic master
+equation and this is the equation that
+
+ align:start position:0%
+equation and this is the equation that
+ 
+
+ align:start position:0%
+equation and this is the equation that
+describes a real system so this is the
+
+ align:start position:0%
+describes a real system so this is the
+ 
+
+ align:start position:0%
+describes a real system so this is the
+real probability of finding the system
+
+ align:start position:0%
+real probability of finding the system
+ 
+
+ align:start position:0%
+real probability of finding the system
+with any number of A's B's and C's and I
+
+ align:start position:0%
+with any number of A's B's and C's and I
+ 
+
+ align:start position:0%
+with any number of A's B's and C's and I
+have an equation like this for every
+
+ align:start position:0%
+have an equation like this for every
+ 
+
+ align:start position:0%
+have an equation like this for every
+different possible number of A's number
+
+ align:start position:0%
+different possible number of A's number
+ 
+
+ align:start position:0%
+different possible number of A's number
+of BS and number sees all right and it's
+
+ align:start position:0%
+of BS and number sees all right and it's
+ 
+
+ align:start position:0%
+of BS and number sees all right and it's
+not bad as an equation goes it's a
+
+ align:start position:0%
+not bad as an equation goes it's a
+ 
+
+ align:start position:0%
+not bad as an equation goes it's a
+linear differential equation because it
+
+ align:start position:0%
+linear differential equation because it
+ 
+
+ align:start position:0%
+linear differential equation because it
+it's linear in peas right there's just
+
+ align:start position:0%
+it's linear in peas right there's just
+ 
+
+ align:start position:0%
+it's linear in peas right there's just
+first everything's first power in P so
+
+ align:start position:0%
+first everything's first power in P so
+ 
+
+ align:start position:0%
+first everything's first power in P so
+in general I can rewrite this as DP DT
+
+ align:start position:0%
+in general I can rewrite this as DP DT
+ 
+
+ align:start position:0%
+in general I can rewrite this as DP DT
+is equal to some matrix times me right
+
+ align:start position:0%
+is equal to some matrix times me right
+ 
+
+ align:start position:0%
+is equal to some matrix times me right
+and the matrix entries are these pre
+
+ align:start position:0%
+and the matrix entries are these pre
+ 
+
+ align:start position:0%
+and the matrix entries are these pre
+factors things like this sorry these are
+
+ align:start position:0%
+factors things like this sorry these are
+ 
+
+ align:start position:0%
+factors things like this sorry these are
+the different elements in the matrix am
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright yeah
+
+ align:start position:0%
+alright yeah
+ 
+
+ align:start position:0%
+alright yeah
+so you should go ahead and be able to
+
+ align:start position:0%
+so you should go ahead and be able to
+ 
+
+ align:start position:0%
+so you should go ahead and be able to
+write any kinetic equation system
+
+ align:start position:0%
+write any kinetic equation system
+ 
+
+ align:start position:0%
+write any kinetic equation system
+rewrite it in this form if you want it's
+
+ align:start position:0%
+rewrite it in this form if you want it's
+ 
+
+ align:start position:0%
+rewrite it in this form if you want it's
+called the kinetic master equation
+
+ align:start position:0%
+called the kinetic master equation
+ 
+
+ align:start position:0%
+called the kinetic master equation
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright now if I do an experiment like I
+
+ align:start position:0%
+alright now if I do an experiment like I
+ 
+
+ align:start position:0%
+alright now if I do an experiment like I
+talked about with uranium ore I put one
+
+ align:start position:0%
+talked about with uranium ore I put one
+ 
+
+ align:start position:0%
+talked about with uranium ore I put one
+uranium atom in there and all your any
+
+ align:start position:0%
+uranium atom in there and all your any
+ 
+
+ align:start position:0%
+uranium atom in there and all your any
+items can react to do is fall apart to
+
+ align:start position:0%
+items can react to do is fall apart to
+ 
+
+ align:start position:0%
+items can react to do is fall apart to
+lead plus neutrons or whatever the heck
+
+ align:start position:0%
+lead plus neutrons or whatever the heck
+ 
+
+ align:start position:0%
+lead plus neutrons or whatever the heck
+they fall apart to so I can write down
+
+ align:start position:0%
+they fall apart to so I can write down
+ 
+
+ align:start position:0%
+they fall apart to so I can write down
+there's like one reaction that uranium
+
+ align:start position:0%
+there's like one reaction that uranium
+ 
+
+ align:start position:0%
+there's like one reaction that uranium
+nuclei do and so I could write it out
+
+ align:start position:0%
+nuclei do and so I could write it out
+ 
+
+ align:start position:0%
+nuclei do and so I could write it out
+and it'll just be a little something
+
+ align:start position:0%
+and it'll just be a little something
+ 
+
+ align:start position:0%
+and it'll just be a little something
+like this and there's a question of work
+
+ align:start position:0%
+like this and there's a question of work
+ 
+
+ align:start position:0%
+like this and there's a question of work
+you know for a case where I put one
+
+ align:start position:0%
+you know for a case where I put one
+ 
+
+ align:start position:0%
+you know for a case where I put one
+uranium atom there to begin with I could
+
+ align:start position:0%
+uranium atom there to begin with I could
+ 
+
+ align:start position:0%
+uranium atom there to begin with I could
+do the case where I put two uranium
+
+ align:start position:0%
+do the case where I put two uranium
+ 
+
+ align:start position:0%
+do the case where I put two uranium
+atoms in there to begin with I could
+
+ align:start position:0%
+atoms in there to begin with I could
+ 
+
+ align:start position:0%
+atoms in there to begin with I could
+write this down said alright okay now if
+
+ align:start position:0%
+write this down said alright okay now if
+ 
+
+ align:start position:0%
+write this down said alright okay now if
+I had a case where I had 27 a s14 B's
+
+ align:start position:0%
+I had a case where I had 27 a s14 B's
+ 
+
+ align:start position:0%
+I had a case where I had 27 a s14 B's
+and 33 C's to start with then you can
+
+ align:start position:0%
+and 33 C's to start with then you can
+ 
+
+ align:start position:0%
+and 33 C's to start with then you can
+see that the number of possibilities
+
+ align:start position:0%
+see that the number of possibilities
+ 
+
+ align:start position:0%
+see that the number of possibilities
+here might get pretty large except to
+
+ align:start position:0%
+here might get pretty large except to
+ 
+
+ align:start position:0%
+here might get pretty large except to
+consider well I could lose one a and
+
+ align:start position:0%
+consider well I could lose one a and
+ 
+
+ align:start position:0%
+consider well I could lose one a and
+there's one B and get one more C but
+
+ align:start position:0%
+there's one B and get one more C but
+ 
+
+ align:start position:0%
+there's one B and get one more C but
+then I'll have an equation for this term
+
+ align:start position:0%
+then I'll have an equation for this term
+ 
+
+ align:start position:0%
+then I'll have an equation for this term
+which will look just like this but it'll
+
+ align:start position:0%
+which will look just like this but it'll
+ 
+
+ align:start position:0%
+which will look just like this but it'll
+go to ones I have lost two days and two
+
+ align:start position:0%
+go to ones I have lost two days and two
+ 
+
+ align:start position:0%
+go to ones I have lost two days and two
+B's and gained two c's and then all the
+
+ align:start position:0%
+B's and gained two c's and then all the
+ 
+
+ align:start position:0%
+B's and gained two c's and then all the
+way down until I get down to one of the
+
+ align:start position:0%
+way down until I get down to one of the
+ 
+
+ align:start position:0%
+way down until I get down to one of the
+ends to be 0
+
+ align:start position:0%
+ends to be 0
+ 
+
+ align:start position:0%
+ends to be 0
+right and so it could be quite a lot of
+
+ align:start position:0%
+right and so it could be quite a lot of
+ 
+
+ align:start position:0%
+right and so it could be quite a lot of
+possible equations right so the
+
+ align:start position:0%
+possible equations right so the
+ 
+
+ align:start position:0%
+possible equations right so the
+dimension the length of the the vector P
+
+ align:start position:0%
+dimension the length of the the vector P
+ 
+
+ align:start position:0%
+dimension the length of the the vector P
+might get really long right so you know
+
+ align:start position:0%
+might get really long right so you know
+ 
+
+ align:start position:0%
+might get really long right so you know
+the the length of P is something like
+
+ align:start position:0%
+the the length of P is something like
+ 
+
+ align:start position:0%
+the the length of P is something like
+the max number of A's max number of bees
+
+ align:start position:0%
+the max number of A's max number of bees
+ 
+
+ align:start position:0%
+the max number of A's max number of bees
+max number of C's all right so if I have
+
+ align:start position:0%
+max number of C's all right so if I have
+ 
+
+ align:start position:0%
+max number of C's all right so if I have
+you know I allow I consider systems with
+
+ align:start position:0%
+you know I allow I consider systems with
+ 
+
+ align:start position:0%
+you know I allow I consider systems with
+up to 10 days 10 B's and 10 C's then
+
+ align:start position:0%
+up to 10 days 10 B's and 10 C's then
+ 
+
+ align:start position:0%
+up to 10 days 10 B's and 10 C's then
+this is a thousand P is the length of
+
+ align:start position:0%
+this is a thousand P is the length of
+ 
+
+ align:start position:0%
+this is a thousand P is the length of
+approximately and it might be less than
+
+ align:start position:0%
+approximately and it might be less than
+ 
+
+ align:start position:0%
+approximately and it might be less than
+that because may
+
+ align:start position:0%
+that because may
+ 
+
+ align:start position:0%
+that because may
+some of them some pretty clear states I
+
+ align:start position:0%
+some of them some pretty clear states I
+ 
+
+ align:start position:0%
+some of them some pretty clear states I
+can't get to all right submits less than
+
+ align:start position:0%
+can't get to all right submits less than
+ 
+
+ align:start position:0%
+can't get to all right submits less than
+a thousand but something like a thousand
+
+ align:start position:0%
+a thousand but something like a thousand
+ 
+
+ align:start position:0%
+a thousand but something like a thousand
+on the other hand if I allow up to a
+
+ align:start position:0%
+on the other hand if I allow up to a
+ 
+
+ align:start position:0%
+on the other hand if I allow up to a
+million A's a million bees and a million
+
+ align:start position:0%
+million A's a million bees and a million
+ 
+
+ align:start position:0%
+million A's a million bees and a million
+sees then I have like 10 to the 18th
+
+ align:start position:0%
+sees then I have like 10 to the 18th
+ 
+
+ align:start position:0%
+sees then I have like 10 to the 18th
+lent the P so P gets pretty long pretty
+
+ align:start position:0%
+lent the P so P gets pretty long pretty
+ 
+
+ align:start position:0%
+lent the P so P gets pretty long pretty
+fast when the number of possible states
+
+ align:start position:0%
+fast when the number of possible states
+ 
+
+ align:start position:0%
+fast when the number of possible states
+gives up all right so now it's linear
+
+ align:start position:0%
+gives up all right so now it's linear
+ 
+
+ align:start position:0%
+gives up all right so now it's linear
+though and it's linear and this is
+
+ align:start position:0%
+though and it's linear and this is
+ 
+
+ align:start position:0%
+though and it's linear and this is
+constant coefficients and so this is
+
+ align:start position:0%
+constant coefficients and so this is
+ 
+
+ align:start position:0%
+constant coefficients and so this is
+really not as sparse so this is really
+
+ align:start position:0%
+really not as sparse so this is really
+ 
+
+ align:start position:0%
+really not as sparse so this is really
+it's not that bad and in fact professor
+
+ align:start position:0%
+it's not that bad and in fact professor
+ 
+
+ align:start position:0%
+it's not that bad and in fact professor
+Barton's group has worked on these kind
+
+ align:start position:0%
+Barton's group has worked on these kind
+ 
+
+ align:start position:0%
+Barton's group has worked on these kind
+of problems and he has a saw or that can
+
+ align:start position:0%
+of problems and he has a saw or that can
+ 
+
+ align:start position:0%
+of problems and he has a saw or that can
+work with pH dimension up to 200 million
+
+ align:start position:0%
+work with pH dimension up to 200 million
+ 
+
+ align:start position:0%
+work with pH dimension up to 200 million
+so if you can keep the number of states
+
+ align:start position:0%
+so if you can keep the number of states
+ 
+
+ align:start position:0%
+so if you can keep the number of states
+200 million or less you can actually
+
+ align:start position:0%
+200 million or less you can actually
+ 
+
+ align:start position:0%
+200 million or less you can actually
+solve this exactly now some of this
+
+ align:start position:0%
+solve this exactly now some of this
+ 
+
+ align:start position:0%
+solve this exactly now some of this
+exactly is really good because then you
+
+ align:start position:0%
+exactly is really good because then you
+ 
+
+ align:start position:0%
+exactly is really good because then you
+actually have the exact probability of
+
+ align:start position:0%
+actually have the exact probability of
+ 
+
+ align:start position:0%
+actually have the exact probability of
+any observable measurement that you
+
+ align:start position:0%
+any observable measurement that you
+ 
+
+ align:start position:0%
+any observable measurement that you
+would possibly make at any time all
+
+ align:start position:0%
+would possibly make at any time all
+ 
+
+ align:start position:0%
+would possibly make at any time all
+computed okay
+
+ align:start position:0%
+computed okay
+ 
+
+ align:start position:0%
+computed okay
+so that's really great but as I just
+
+ align:start position:0%
+so that's really great but as I just
+ 
+
+ align:start position:0%
+so that's really great but as I just
+pointed out if I make these numbers like
+
+ align:start position:0%
+pointed out if I make these numbers like
+ 
+
+ align:start position:0%
+pointed out if I make these numbers like
+10 to the 6 10 to the 6 and 10 to 6 this
+
+ align:start position:0%
+10 to the 6 10 to the 6 and 10 to 6 this
+ 
+
+ align:start position:0%
+10 to the 6 10 to the 6 and 10 to 6 this
+is like 10 to the 18 that's a lot bigger
+
+ align:start position:0%
+is like 10 to the 18 that's a lot bigger
+ 
+
+ align:start position:0%
+is like 10 to the 18 that's a lot bigger
+than 200 million and so professor Barton
+
+ align:start position:0%
+than 200 million and so professor Barton
+ 
+
+ align:start position:0%
+than 200 million and so professor Barton
+is numerical methods are going to pop
+
+ align:start position:0%
+is numerical methods are going to pop
+ 
+
+ align:start position:0%
+is numerical methods are going to pop
+out at some point and not gonna work for
+
+ align:start position:0%
+out at some point and not gonna work for
+ 
+
+ align:start position:0%
+out at some point and not gonna work for
+you anymore so there's a limited number
+
+ align:start position:0%
+you anymore so there's a limited number
+ 
+
+ align:start position:0%
+you anymore so there's a limited number
+of problems you can do so if your
+
+ align:start position:0%
+of problems you can do so if your
+ 
+
+ align:start position:0%
+of problems you can do so if your
+problem is small enough you just solve
+
+ align:start position:0%
+problem is small enough you just solve
+ 
+
+ align:start position:0%
+problem is small enough you just solve
+this for really small ones you can just
+
+ align:start position:0%
+this for really small ones you can just
+ 
+
+ align:start position:0%
+this for really small ones you can just
+solve this with OD for 5 or OD 1 5s but
+
+ align:start position:0%
+solve this with OD for 5 or OD 1 5s but
+ 
+
+ align:start position:0%
+solve this with OD for 5 or OD 1 5s but
+because it's linear there's special
+
+ align:start position:0%
+because it's linear there's special
+ 
+
+ align:start position:0%
+because it's linear there's special
+solution methods I know you remember
+
+ align:start position:0%
+solution methods I know you remember
+ 
+
+ align:start position:0%
+solution methods I know you remember
+solutions of linear equations like this
+
+ align:start position:0%
+solutions of linear equations like this
+ 
+
+ align:start position:0%
+solutions of linear equations like this
+you you can relate them to the
+
+ align:start position:0%
+you you can relate them to the
+ 
+
+ align:start position:0%
+you you can relate them to the
+eigenvectors and eigenvalues of m and so
+
+ align:start position:0%
+eigenvectors and eigenvalues of m and so
+ 
+
+ align:start position:0%
+eigenvectors and eigenvalues of m and so
+you can do that's one way to do it and
+
+ align:start position:0%
+you can do that's one way to do it and
+ 
+
+ align:start position:0%
+you can do that's one way to do it and
+then there's special methods you can do
+
+ align:start position:0%
+then there's special methods you can do
+ 
+
+ align:start position:0%
+then there's special methods you can do
+talk to Professor Barton if it's sparse
+
+ align:start position:0%
+talk to Professor Barton if it's sparse
+ 
+
+ align:start position:0%
+talk to Professor Barton if it's sparse
+and certain kinds of properties you can
+
+ align:start position:0%
+and certain kinds of properties you can
+ 
+
+ align:start position:0%
+and certain kinds of properties you can
+make this really you can make quite
+
+ align:start position:0%
+make this really you can make quite
+ 
+
+ align:start position:0%
+make this really you can make quite
+large systems up to you know 10 to the
+
+ align:start position:0%
+large systems up to you know 10 to the
+ 
+
+ align:start position:0%
+large systems up to you know 10 to the
+8th kind of size if you get a system
+
+ align:start position:0%
+8th kind of size if you get a system
+ 
+
+ align:start position:0%
+8th kind of size if you get a system
+with more than 10 to 8 possible States
+
+ align:start position:0%
+with more than 10 to 8 possible States
+ 
+
+ align:start position:0%
+with more than 10 to 8 possible States
+that means more than 10 to the 8th
+
+ align:start position:0%
+that means more than 10 to the 8th
+ 
+
+ align:start position:0%
+that means more than 10 to the 8th
+possible things could be observed you
+
+ align:start position:0%
+possible things could be observed you
+ 
+
+ align:start position:0%
+possible things could be observed you
+know or could be the result of the
+
+ align:start position:0%
+know or could be the result of the
+ 
+
+ align:start position:0%
+know or could be the result of the
+experiment could be we have more than 10
+
+ align:start position:0%
+experiment could be we have more than 10
+ 
+
+ align:start position:0%
+experiment could be we have more than 10
+to the 8th possibilities then this is
+
+ align:start position:0%
+to the 8th possibilities then this is
+ 
+
+ align:start position:0%
+to the 8th possibilities then this is
+you're not gonna be able solve it this
+
+ align:start position:0%
+you're not gonna be able solve it this
+ 
+
+ align:start position:0%
+you're not gonna be able solve it this
+way and so then we're gonna have to use
+
+ align:start position:0%
+way and so then we're gonna have to use
+ 
+
+ align:start position:0%
+way and so then we're gonna have to use
+a stochastic solid solution method to
+
+ align:start position:0%
+a stochastic solid solution method to
+ 
+
+ align:start position:0%
+a stochastic solid solution method to
+try to figure that to do so
+
+ align:start position:0%
+try to figure that to do so
+ 
+
+ align:start position:0%
+try to figure that to do so
+going to try to sample from P of T so I
+
+ align:start position:0%
+going to try to sample from P of T so I
+ 
+
+ align:start position:0%
+going to try to sample from P of T so I
+guess I should comment again I wrote it
+
+ align:start position:0%
+guess I should comment again I wrote it
+ 
+
+ align:start position:0%
+guess I should comment again I wrote it
+this way but this thing P is definitely
+
+ align:start position:0%
+this way but this thing P is definitely
+ 
+
+ align:start position:0%
+this way but this thing P is definitely
+depends on time so it's you'll have a
+
+ align:start position:0%
+depends on time so it's you'll have a
+ 
+
+ align:start position:0%
+depends on time so it's you'll have a
+different p for every time yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah maybe maybe I'd do better too I can
+
+ align:start position:0%
+yeah maybe maybe I'd do better too I can
+ 
+
+ align:start position:0%
+yeah maybe maybe I'd do better too I can
+substitute in here said right yeah
+
+ align:start position:0%
+substitute in here said right yeah
+ 
+
+ align:start position:0%
+substitute in here said right yeah
+there's a key idea is that chemical
+
+ align:start position:0%
+there's a key idea is that chemical
+ 
+
+ align:start position:0%
+there's a key idea is that chemical
+kinetics only does one step at a time so
+
+ align:start position:0%
+kinetics only does one step at a time so
+ 
+
+ align:start position:0%
+kinetics only does one step at a time so
+if you have a reaction like this at any
+
+ align:start position:0%
+if you have a reaction like this at any
+ 
+
+ align:start position:0%
+if you have a reaction like this at any
+instant the probability that two
+
+ align:start position:0%
+instant the probability that two
+ 
+
+ align:start position:0%
+instant the probability that two
+reactions are happening exactly the same
+
+ align:start position:0%
+reactions are happening exactly the same
+ 
+
+ align:start position:0%
+reactions are happening exactly the same
+instant is negligible so that at any
+
+ align:start position:0%
+instant is negligible so that at any
+ 
+
+ align:start position:0%
+instant is negligible so that at any
+instant you're only changing the numbers
+
+ align:start position:0%
+instant you're only changing the numbers
+ 
+
+ align:start position:0%
+instant you're only changing the numbers
+of the atoms by one one unit yeah may I
+
+ align:start position:0%
+of the atoms by one one unit yeah may I
+ 
+
+ align:start position:0%
+of the atoms by one one unit yeah may I
+get this backwards in a plus 1 plus 1
+
+ align:start position:0%
+get this backwards in a plus 1 plus 1
+ 
+
+ align:start position:0%
+get this backwards in a plus 1 plus 1
+minus 1 minus 1 minus 1 plus 1 I think I
+
+ align:start position:0%
+minus 1 minus 1 minus 1 plus 1 I think I
+ 
+
+ align:start position:0%
+minus 1 minus 1 minus 1 plus 1 I think I
+got I think this is right so this is for
+
+ align:start position:0%
+got I think this is right so this is for
+ 
+
+ align:start position:0%
+got I think this is right so this is for
+the forward reaction that always reduces
+
+ align:start position:0%
+the forward reaction that always reduces
+ 
+
+ align:start position:0%
+the forward reaction that always reduces
+the number of A's and B's and this is
+
+ align:start position:0%
+the number of A's and B's and this is
+ 
+
+ align:start position:0%
+the number of A's and B's and this is
+the reverse reaction that always
+
+ align:start position:0%
+the reverse reaction that always
+ 
+
+ align:start position:0%
+the reverse reaction that always
+increases that and so I think you
+
+ align:start position:0%
+increases that and so I think you
+ 
+
+ align:start position:0%
+increases that and so I think you
+generally get like this you always get
+
+ align:start position:0%
+generally get like this you always get
+ 
+
+ align:start position:0%
+generally get like this you always get
+for any reaction you'll have four terms
+
+ align:start position:0%
+for any reaction you'll have four terms
+ 
+
+ align:start position:0%
+for any reaction you'll have four terms
+so the forward and reverse starting for
+
+ align:start position:0%
+so the forward and reverse starting for
+ 
+
+ align:start position:0%
+so the forward and reverse starting for
+the initial state and the forward and
+
+ align:start position:0%
+the initial state and the forward and
+ 
+
+ align:start position:0%
+the initial state and the forward and
+reverse that make your state alright and
+
+ align:start position:0%
+reverse that make your state alright and
+ 
+
+ align:start position:0%
+reverse that make your state alright and
+then if you have more reactions you have
+
+ align:start position:0%
+then if you have more reactions you have
+ 
+
+ align:start position:0%
+then if you have more reactions you have
+system we have a lot more reactions
+
+ align:start position:0%
+system we have a lot more reactions
+ 
+
+ align:start position:0%
+system we have a lot more reactions
+maybe you have seed you can just
+
+ align:start position:0%
+maybe you have seed you can just
+ 
+
+ align:start position:0%
+maybe you have seed you can just
+decompose into bees or something
+
+ align:start position:0%
+decompose into bees or something
+ 
+
+ align:start position:0%
+decompose into bees or something
+different reactions then you'd have a
+
+ align:start position:0%
+different reactions then you'd have a
+ 
+
+ align:start position:0%
+different reactions then you'd have a
+sum like this with terms like this from
+
+ align:start position:0%
+sum like this with terms like this from
+ 
+
+ align:start position:0%
+sum like this with terms like this from
+every reaction and you go through all
+
+ align:start position:0%
+every reaction and you go through all
+ 
+
+ align:start position:0%
+every reaction and you go through all
+your list of all your actions alright I
+
+ align:start position:0%
+your list of all your actions alright I
+ 
+
+ align:start position:0%
+your list of all your actions alright I
+guess there's there's one funny thing I
+
+ align:start position:0%
+guess there's there's one funny thing I
+ 
+
+ align:start position:0%
+guess there's there's one funny thing I
+should point out to you about this it's
+
+ align:start position:0%
+should point out to you about this it's
+ 
+
+ align:start position:0%
+should point out to you about this it's
+very important for this emulsion
+
+ align:start position:0%
+very important for this emulsion
+ 
+
+ align:start position:0%
+very important for this emulsion
+polymerization case is that if you have
+
+ align:start position:0%
+polymerization case is that if you have
+ 
+
+ align:start position:0%
+polymerization case is that if you have
+a reaction of the type a plus
+
+ align:start position:0%
+a reaction of the type a plus
+ 
+
+ align:start position:0%
+a reaction of the type a plus
+a ghost I don't know okay that might be
+
+ align:start position:0%
+a ghost I don't know okay that might be
+ 
+
+ align:start position:0%
+a ghost I don't know okay that might be
+a reaction you could have that when I
+
+ align:start position:0%
+a reaction you could have that when I
+ 
+
+ align:start position:0%
+a reaction you could have that when I
+write down the equation if I only have
+
+ align:start position:0%
+write down the equation if I only have
+ 
+
+ align:start position:0%
+write down the equation if I only have
+one a in my sample this probability of
+
+ align:start position:0%
+one a in my sample this probability of
+ 
+
+ align:start position:0%
+one a in my sample this probability of
+this of this happening is zero right
+
+ align:start position:0%
+this of this happening is zero right
+ 
+
+ align:start position:0%
+this of this happening is zero right
+because I need two ways for this to
+
+ align:start position:0%
+because I need two ways for this to
+ 
+
+ align:start position:0%
+because I need two ways for this to
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+so really the equation for this case is
+
+ align:start position:0%
+so really the equation for this case is
+ 
+
+ align:start position:0%
+so really the equation for this case is
+na times na minus one so it's K a plus a
+
+ align:start position:0%
+na times na minus one so it's K a plus a
+ 
+
+ align:start position:0%
+na times na minus one so it's K a plus a
+goes to B times n a times anyway alright
+
+ align:start position:0%
+goes to B times n a times anyway alright
+ 
+
+ align:start position:0%
+goes to B times n a times anyway alright
+and this is crucial for like the
+
+ align:start position:0%
+and this is crucial for like the
+ 
+
+ align:start position:0%
+and this is crucial for like the
+emulsion polymerization case does the
+
+ align:start position:0%
+emulsion polymerization case does the
+ 
+
+ align:start position:0%
+emulsion polymerization case does the
+fact that I have don't have a second one
+
+ align:start position:0%
+fact that I have don't have a second one
+ 
+
+ align:start position:0%
+fact that I have don't have a second one
+is really important all right
+
+ align:start position:0%
+is really important all right
+ 
+
+ align:start position:0%
+is really important all right
+otherwise I was miss compute that this
+
+ align:start position:0%
+otherwise I was miss compute that this
+ 
+
+ align:start position:0%
+otherwise I was miss compute that this
+radical could react with itself and
+
+ align:start position:0%
+radical could react with itself and
+ 
+
+ align:start position:0%
+radical could react with itself and
+terminate itself which is not true is
+
+ align:start position:0%
+terminate itself which is not true is
+ 
+
+ align:start position:0%
+terminate itself which is not true is
+that right um I commented that these k's
+
+ align:start position:0%
+that right um I commented that these k's
+ 
+
+ align:start position:0%
+that right um I commented that these k's
+are a little bit odd so if you remember
+
+ align:start position:0%
+are a little bit odd so if you remember
+ 
+
+ align:start position:0%
+are a little bit odd so if you remember
+if you have a k4 a unimolecular reaction
+
+ align:start position:0%
+if you have a k4 a unimolecular reaction
+ 
+
+ align:start position:0%
+if you have a k4 a unimolecular reaction
+like C goes to a plus B what units would
+
+ align:start position:0%
+like C goes to a plus B what units would
+ 
+
+ align:start position:0%
+like C goes to a plus B what units would
+it have what are use for in regular
+
+ align:start position:0%
+it have what are use for in regular
+ 
+
+ align:start position:0%
+it have what are use for in regular
+kinetics right inverse seconds right so
+
+ align:start position:0%
+kinetics right inverse seconds right so
+ 
+
+ align:start position:0%
+kinetics right inverse seconds right so
+you'd normally say this thing has units
+
+ align:start position:0%
+you'd normally say this thing has units
+ 
+
+ align:start position:0%
+you'd normally say this thing has units
+of inverse seconds and that works fine
+
+ align:start position:0%
+of inverse seconds and that works fine
+ 
+
+ align:start position:0%
+of inverse seconds and that works fine
+here right because I have DP DT and its
+
+ align:start position:0%
+here right because I have DP DT and its
+ 
+
+ align:start position:0%
+here right because I have DP DT and its
+inverse seconds times P so it's fine
+
+ align:start position:0%
+inverse seconds times P so it's fine
+ 
+
+ align:start position:0%
+inverse seconds times P so it's fine
+however this guy to make the unit's
+
+ align:start position:0%
+however this guy to make the unit's
+ 
+
+ align:start position:0%
+however this guy to make the unit's
+workout still has to also be inverse
+
+ align:start position:0%
+workout still has to also be inverse
+ 
+
+ align:start position:0%
+workout still has to also be inverse
+seconds but that's not normally what you
+
+ align:start position:0%
+seconds but that's not normally what you
+ 
+
+ align:start position:0%
+seconds but that's not normally what you
+would have for a by molecular reaction
+
+ align:start position:0%
+would have for a by molecular reaction
+ 
+
+ align:start position:0%
+would have for a by molecular reaction
+right and the other thing to watch out
+
+ align:start position:0%
+right and the other thing to watch out
+ 
+
+ align:start position:0%
+right and the other thing to watch out
+for here is that I have ends but
+
+ align:start position:0%
+for here is that I have ends but
+ 
+
+ align:start position:0%
+for here is that I have ends but
+normally you would write them with
+
+ align:start position:0%
+normally you would write them with
+ 
+
+ align:start position:0%
+normally you would write them with
+concentrations right you'd have the
+
+ align:start position:0%
+concentrations right you'd have the
+ 
+
+ align:start position:0%
+concentrations right you'd have the
+content you would write something like K
+
+ align:start position:0%
+content you would write something like K
+ 
+
+ align:start position:0%
+content you would write something like K
+times the concentration of C it's a
+
+ align:start position:0%
+times the concentration of C it's a
+ 
+
+ align:start position:0%
+times the concentration of C it's a
+normal way you write your equations to
+
+ align:start position:0%
+normal way you write your equations to
+ 
+
+ align:start position:0%
+normal way you write your equations to
+the rate equations but this is not the
+
+ align:start position:0%
+the rate equations but this is not the
+ 
+
+ align:start position:0%
+the rate equations but this is not the
+same right this is n this is unitless
+
+ align:start position:0%
+same right this is n this is unitless
+ 
+
+ align:start position:0%
+same right this is n this is unitless
+now it turns out in this case actually
+
+ align:start position:0%
+now it turns out in this case actually
+ 
+
+ align:start position:0%
+now it turns out in this case actually
+you can use the exactly the same case
+
+ align:start position:0%
+you can use the exactly the same case
+ 
+
+ align:start position:0%
+you can use the exactly the same case
+okay and it works but for the
+
+ align:start position:0%
+okay and it works but for the
+ 
+
+ align:start position:0%
+okay and it works but for the
+biomolecular case it definitely does not
+
+ align:start position:0%
+biomolecular case it definitely does not
+ 
+
+ align:start position:0%
+biomolecular case it definitely does not
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+the units are wrong and also this
+
+ align:start position:0%
+the units are wrong and also this
+ 
+
+ align:start position:0%
+the units are wrong and also this
+concentration thing implies that we
+
+ align:start position:0%
+concentration thing implies that we
+ 
+
+ align:start position:0%
+concentration thing implies that we
+think the rate really has stable if you
+
+ align:start position:0%
+think the rate really has stable if you
+ 
+
+ align:start position:0%
+think the rate really has stable if you
+have ka KB I could rewrite this as K
+
+ align:start position:0%
+have ka KB I could rewrite this as K
+ 
+
+ align:start position:0%
+have ka KB I could rewrite this as K
+times n a over the volume and B over the
+
+ align:start position:0%
+times n a over the volume and B over the
+ 
+
+ align:start position:0%
+times n a over the volume and B over the
+volume said all right actually one thing
+
+ align:start position:0%
+volume said all right actually one thing
+ 
+
+ align:start position:0%
+volume said all right actually one thing
+I should warn you about that usually
+
+ align:start position:0%
+I should warn you about that usually
+ 
+
+ align:start position:0%
+I should warn you about that usually
+write this I mold per liter so I factors
+
+ align:start position:0%
+write this I mold per liter so I factors
+ 
+
+ align:start position:0%
+write this I mold per liter so I factors
+a 10 to the 23rd between this and this
+
+ align:start position:0%
+a 10 to the 23rd between this and this
+ 
+
+ align:start position:0%
+a 10 to the 23rd between this and this
+because these ends have got to be the
+
+ align:start position:0%
+because these ends have got to be the
+ 
+
+ align:start position:0%
+because these ends have got to be the
+individual molecules it's for us to work
+
+ align:start position:0%
+individual molecules it's for us to work
+ 
+
+ align:start position:0%
+individual molecules it's for us to work
+so what so watch out first of all
+
+ align:start position:0%
+so what so watch out first of all
+ 
+
+ align:start position:0%
+so what so watch out first of all
+there's a 10 to the 23rd somewhere in
+
+ align:start position:0%
+there's a 10 to the 23rd somewhere in
+ 
+
+ align:start position:0%
+there's a 10 to the 23rd somewhere in
+here I have a gathers number and then
+
+ align:start position:0%
+here I have a gathers number and then
+ 
+
+ align:start position:0%
+here I have a gathers number and then
+this is what how we would normally write
+
+ align:start position:0%
+this is what how we would normally write
+ 
+
+ align:start position:0%
+this is what how we would normally write
+it but this K has the wrong units for us
+
+ align:start position:0%
+it but this K has the wrong units for us
+ 
+
+ align:start position:0%
+it but this K has the wrong units for us
+here and so this this guy here is the
+
+ align:start position:0%
+here and so this this guy here is the
+ 
+
+ align:start position:0%
+here and so this this guy here is the
+normal K divided by the volume see
+
+ align:start position:0%
+normal K divided by the volume see
+ 
+
+ align:start position:0%
+normal K divided by the volume see
+that's right mate the other way around
+
+ align:start position:0%
+that's right mate the other way around
+ 
+
+ align:start position:0%
+that's right mate the other way around
+no this is no 1 K times above that's
+
+ align:start position:0%
+no this is no 1 K times above that's
+ 
+
+ align:start position:0%
+no this is no 1 K times above that's
+right so normally we would write the
+
+ align:start position:0%
+right so normally we would write the
+ 
+
+ align:start position:0%
+right so normally we would write the
+unit's k normal normal kinetics back row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K for a plus B reactions the units are
+
+ align:start position:0%
+K for a plus B reactions the units are
+ 
+
+ align:start position:0%
+K for a plus B reactions the units are
+centimeters cubed per mole second and
+
+ align:start position:0%
+centimeters cubed per mole second and
+ 
+
+ align:start position:0%
+centimeters cubed per mole second and
+but we want them to be units of the new
+
+ align:start position:0%
+but we want them to be units of the new
+ 
+
+ align:start position:0%
+but we want them to be units of the new
+the new K it's got to be units of per
+
+ align:start position:0%
+the new K it's got to be units of per
+ 
+
+ align:start position:0%
+the new K it's got to be units of per
+second and so the new K is equal to the
+
+ align:start position:0%
+second and so the new K is equal to the
+ 
+
+ align:start position:0%
+second and so the new K is equal to the
+old K new old times fine it's all right
+
+ align:start position:0%
+old K new old times fine it's all right
+ 
+
+ align:start position:0%
+old K new old times fine it's all right
+no divide by the by let's write that
+
+ align:start position:0%
+no divide by the by let's write that
+ 
+
+ align:start position:0%
+no divide by the by let's write that
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+this is volume that yep
+
+ align:start position:0%
+this is volume that yep
+ 
+
+ align:start position:0%
+this is volume that yep
+seven ears cute Sandra's cute yeah I
+
+ align:start position:0%
+seven ears cute Sandra's cute yeah I
+ 
+
+ align:start position:0%
+seven ears cute Sandra's cute yeah I
+guess hold out good for a second so this
+
+ align:start position:0%
+guess hold out good for a second so this
+ 
+
+ align:start position:0%
+guess hold out good for a second so this
+is K per volume no I'm okay right and
+
+ align:start position:0%
+is K per volume no I'm okay right and
+ 
+
+ align:start position:0%
+is K per volume no I'm okay right and
+you may wonder well how come it's only
+
+ align:start position:0%
+you may wonder well how come it's only
+ 
+
+ align:start position:0%
+you may wonder well how come it's only
+volume to the first power
+
+ align:start position:0%
+volume to the first power
+ 
+
+ align:start position:0%
+volume to the first power
+before I had volume to the second power
+
+ align:start position:0%
+before I had volume to the second power
+ 
+
+ align:start position:0%
+before I had volume to the second power
+in the denominator and it's because I'm
+
+ align:start position:0%
+in the denominator and it's because I'm
+ 
+
+ align:start position:0%
+in the denominator and it's because I'm
+using ends up in the numerator and it's
+
+ align:start position:0%
+using ends up in the numerator and it's
+ 
+
+ align:start position:0%
+using ends up in the numerator and it's
+just like here I'm using ends instead of
+
+ align:start position:0%
+just like here I'm using ends instead of
+ 
+
+ align:start position:0%
+just like here I'm using ends instead of
+n over V so I've sort of multiplying
+
+ align:start position:0%
+n over V so I've sort of multiplying
+ 
+
+ align:start position:0%
+n over V so I've sort of multiplying
+through by be everywhere it's one way to
+
+ align:start position:0%
+through by be everywhere it's one way to
+ 
+
+ align:start position:0%
+through by be everywhere it's one way to
+look at all right no questions yet yeah
+
+ align:start position:0%
+look at all right no questions yet yeah
+ 
+
+ align:start position:0%
+look at all right no questions yet yeah
+uh yeah it's only the ten to the 23rd as
+
+ align:start position:0%
+uh yeah it's only the ten to the 23rd as
+ 
+
+ align:start position:0%
+uh yeah it's only the ten to the 23rd as
+well so there's gonna be navigators
+
+ align:start position:0%
+well so there's gonna be navigators
+ 
+
+ align:start position:0%
+well so there's gonna be navigators
+number and you'll tell me where the
+
+ align:start position:0%
+number and you'll tell me where the
+ 
+
+ align:start position:0%
+number and you'll tell me where the
+advertisers number goes but it's gotta
+
+ align:start position:0%
+advertisers number goes but it's gotta
+ 
+
+ align:start position:0%
+advertisers number goes but it's gotta
+be in there somewhere to get from Boston
+
+ align:start position:0%
+be in there somewhere to get from Boston
+ 
+
+ align:start position:0%
+be in there somewhere to get from Boston
+to Nagas
+
+ align:start position:0%
+to Nagas
+ 
+
+ align:start position:0%
+to Nagas
+so the numbers are a lot different yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is okay in this factor this n minus
+
+ align:start position:0%
+this is okay in this factor this n minus
+ 
+
+ align:start position:0%
+this is okay in this factor this n minus
+one thing again when these are
+
+ align:start position:0%
+one thing again when these are
+ 
+
+ align:start position:0%
+one thing again when these are
+macroscopic numbers like 10 to the 23rd
+
+ align:start position:0%
+macroscopic numbers like 10 to the 23rd
+ 
+
+ align:start position:0%
+macroscopic numbers like 10 to the 23rd
+this makes no difference right that's
+
+ align:start position:0%
+this makes no difference right that's
+ 
+
+ align:start position:0%
+this makes no difference right that's
+minus 1 so we can fit our data ignoring
+
+ align:start position:0%
+minus 1 so we can fit our data ignoring
+ 
+
+ align:start position:0%
+minus 1 so we can fit our data ignoring
+the one is 1 perfectly well the law of
+
+ align:start position:0%
+the one is 1 perfectly well the law of
+ 
+
+ align:start position:0%
+the one is 1 perfectly well the law of
+mass action that works fine so you never
+
+ align:start position:0%
+mass action that works fine so you never
+ 
+
+ align:start position:0%
+mass action that works fine so you never
+notice this unless you get down to where
+
+ align:start position:0%
+notice this unless you get down to where
+ 
+
+ align:start position:0%
+notice this unless you get down to where
+n is very small but this is actually
+
+ align:start position:0%
+n is very small but this is actually
+ 
+
+ align:start position:0%
+n is very small but this is actually
+this is actually the truth this is
+
+ align:start position:0%
+this is actually the truth this is
+ 
+
+ align:start position:0%
+this is actually the truth this is
+really what the correct equation is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright okay so so we now we have these
+
+ align:start position:0%
+alright okay so so we now we have these
+ 
+
+ align:start position:0%
+alright okay so so we now we have these
+the true equations for predicting the
+
+ align:start position:0%
+the true equations for predicting the
+ 
+
+ align:start position:0%
+the true equations for predicting the
+profile the probability distribution
+
+ align:start position:0%
+profile the probability distribution
+ 
+
+ align:start position:0%
+profile the probability distribution
+evolves in a reacting system by the way
+
+ align:start position:0%
+evolves in a reacting system by the way
+ 
+
+ align:start position:0%
+evolves in a reacting system by the way
+you can add transport in as well if you
+
+ align:start position:0%
+you can add transport in as well if you
+ 
+
+ align:start position:0%
+you can add transport in as well if you
+want so if you have control volumes and
+
+ align:start position:0%
+want so if you have control volumes and
+ 
+
+ align:start position:0%
+want so if you have control volumes and
+you know what formulas for the rate at
+
+ align:start position:0%
+you know what formulas for the rate at
+ 
+
+ align:start position:0%
+you know what formulas for the rate at
+which stuff is transported in and out of
+
+ align:start position:0%
+which stuff is transported in and out of
+ 
+
+ align:start position:0%
+which stuff is transported in and out of
+the control volume you can add those
+
+ align:start position:0%
+the control volume you can add those
+ 
+
+ align:start position:0%
+the control volume you can add those
+terms in as well and they will affect
+
+ align:start position:0%
+terms in as well and they will affect
+ 
+
+ align:start position:0%
+terms in as well and they will affect
+the probability distribution okay no
+
+ align:start position:0%
+the probability distribution okay no
+ 
+
+ align:start position:0%
+the probability distribution okay no
+problem you should be able to do the
+
+ align:start position:0%
+problem you should be able to do the
+ 
+
+ align:start position:0%
+problem you should be able to do the
+same conversion so just we converted the
+
+ align:start position:0%
+same conversion so just we converted the
+ 
+
+ align:start position:0%
+same conversion so just we converted the
+reaction equations
+
+ align:start position:0%
+reaction equations
+ 
+
+ align:start position:0%
+reaction equations
+you can write a similar thing once you
+
+ align:start position:0%
+you can write a similar thing once you
+ 
+
+ align:start position:0%
+you can write a similar thing once you
+can write the macroscopic transport
+
+ align:start position:0%
+can write the macroscopic transport
+ 
+
+ align:start position:0%
+can write the macroscopic transport
+equation you can figure out how you
+
+ align:start position:0%
+equation you can figure out how you
+ 
+
+ align:start position:0%
+equation you can figure out how you
+would reduce it down to a time constant
+
+ align:start position:0%
+would reduce it down to a time constant
+ 
+
+ align:start position:0%
+would reduce it down to a time constant
+for transport that would work for the
+
+ align:start position:0%
+for transport that would work for the
+ 
+
+ align:start position:0%
+for transport that would work for the
+for this microscopic version of
+
+ align:start position:0%
+for this microscopic version of
+ 
+
+ align:start position:0%
+for this microscopic version of
+equations so transport may actually
+
+ align:start position:0%
+equations so transport may actually
+ 
+
+ align:start position:0%
+equations so transport may actually
+grate the whole thing down that's the
+
+ align:start position:0%
+grate the whole thing down that's the
+ 
+
+ align:start position:0%
+grate the whole thing down that's the
+master equation that's the real solution
+
+ align:start position:0%
+master equation that's the real solution
+ 
+
+ align:start position:0%
+master equation that's the real solution
+the real equation and the problem is
+
+ align:start position:0%
+the real equation and the problem is
+ 
+
+ align:start position:0%
+the real equation and the problem is
+that the real equation oftentimes is too
+
+ align:start position:0%
+that the real equation oftentimes is too
+ 
+
+ align:start position:0%
+that the real equation oftentimes is too
+big because P scales up so so rapidly
+
+ align:start position:0%
+big because P scales up so so rapidly
+ 
+
+ align:start position:0%
+big because P scales up so so rapidly
+with the number of possible states
+
+ align:start position:0%
+with the number of possible states
+ 
+
+ align:start position:0%
+with the number of possible states
+so then wait to figure how we're going
+
+ align:start position:0%
+so then wait to figure how we're going
+ 
+
+ align:start position:0%
+so then wait to figure how we're going
+to solve it and the way to solve it is
+
+ align:start position:0%
+to solve it and the way to solve it is
+ 
+
+ align:start position:0%
+to solve it and the way to solve it is
+by called kinetic Montecarlo and this
+
+ align:start position:0%
+by called kinetic Montecarlo and this
+ 
+
+ align:start position:0%
+by called kinetic Montecarlo and this
+method was invented by a guy named John
+
+ align:start position:0%
+method was invented by a guy named John
+ 
+
+ align:start position:0%
+method was invented by a guy named John
+Gillespie and the journal paper is
+
+ align:start position:0%
+Gillespie and the journal paper is
+ 
+
+ align:start position:0%
+Gillespie and the journal paper is
+posted and this is just like with a
+
+ align:start position:0%
+posted and this is just like with a
+ 
+
+ align:start position:0%
+posted and this is just like with a
+Monte Carlo metropolis Monte Carlo you
+
+ align:start position:0%
+Monte Carlo metropolis Monte Carlo you
+ 
+
+ align:start position:0%
+Monte Carlo metropolis Monte Carlo you
+just did we're trying to find a way to
+
+ align:start position:0%
+just did we're trying to find a way to
+ 
+
+ align:start position:0%
+just did we're trying to find a way to
+sample from the problem the true
+
+ align:start position:0%
+sample from the problem the true
+ 
+
+ align:start position:0%
+sample from the problem the true
+probability density without ever
+
+ align:start position:0%
+probability density without ever
+ 
+
+ align:start position:0%
+probability density without ever
+computing the truth the true probability
+
+ align:start position:0%
+computing the truth the true probability
+ 
+
+ align:start position:0%
+computing the truth the true probability
+density right so in the Monte Carlo
+
+ align:start position:0%
+density right so in the Monte Carlo
+ 
+
+ align:start position:0%
+density right so in the Monte Carlo
+integration you're doing for homework
+
+ align:start position:0%
+integration you're doing for homework
+ 
+
+ align:start position:0%
+integration you're doing for homework
+you're sampling from the true Boulton
+
+ align:start position:0%
+you're sampling from the true Boulton
+ 
+
+ align:start position:0%
+you're sampling from the true Boulton
+probability density but you never
+
+ align:start position:0%
+probability density but you never
+ 
+
+ align:start position:0%
+probability density but you never
+actually split right down when that P is
+
+ align:start position:0%
+actually split right down when that P is
+ 
+
+ align:start position:0%
+actually split right down when that P is
+right and so the same we're gonna do the
+
+ align:start position:0%
+right and so the same we're gonna do the
+ 
+
+ align:start position:0%
+right and so the same we're gonna do the
+same thing here is we're gonna from the
+
+ align:start position:0%
+same thing here is we're gonna from the
+ 
+
+ align:start position:0%
+same thing here is we're gonna from the
+differential equations from this
+
+ align:start position:0%
+differential equations from this
+ 
+
+ align:start position:0%
+differential equations from this
+differential equation system here we're
+
+ align:start position:0%
+differential equation system here we're
+ 
+
+ align:start position:0%
+differential equation system here we're
+gonna try to somehow never ever solve
+
+ align:start position:0%
+gonna try to somehow never ever solve
+ 
+
+ align:start position:0%
+gonna try to somehow never ever solve
+this directly but instead just sample
+
+ align:start position:0%
+this directly but instead just sample
+ 
+
+ align:start position:0%
+this directly but instead just sample
+from the solution B which depends on
+
+ align:start position:0%
+from the solution B which depends on
+ 
+
+ align:start position:0%
+from the solution B which depends on
+time all right and the way it's done is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's really to try to follow individual
+
+ align:start position:0%
+it's really to try to follow individual
+ 
+
+ align:start position:0%
+it's really to try to follow individual
+trajectories of what could have happened
+
+ align:start position:0%
+trajectories of what could have happened
+ 
+
+ align:start position:0%
+trajectories of what could have happened
+okay so at any time step we have some
+
+ align:start position:0%
+okay so at any time step we have some
+ 
+
+ align:start position:0%
+okay so at any time step we have some
+number of A's B's and C's and we're
+
+ align:start position:0%
+number of A's B's and C's and we're
+ 
+
+ align:start position:0%
+number of A's B's and C's and we're
+gonna say well in the next time period
+
+ align:start position:0%
+gonna say well in the next time period
+ 
+
+ align:start position:0%
+gonna say well in the next time period
+some small time period what can happen
+
+ align:start position:0%
+some small time period what can happen
+ 
+
+ align:start position:0%
+some small time period what can happen
+and we're gonna make the time period so
+
+ align:start position:0%
+and we're gonna make the time period so
+ 
+
+ align:start position:0%
+and we're gonna make the time period so
+small they're the only thing that can
+
+ align:start position:0%
+small they're the only thing that can
+ 
+
+ align:start position:0%
+small they're the only thing that can
+happen is
+
+ align:start position:0%
+happen is
+ 
+
+ align:start position:0%
+happen is
+nothing happens and a B and C stay the
+
+ align:start position:0%
+nothing happens and a B and C stay the
+ 
+
+ align:start position:0%
+nothing happens and a B and C stay the
+same or one event happens which will
+
+ align:start position:0%
+same or one event happens which will
+ 
+
+ align:start position:0%
+same or one event happens which will
+change like the one of the numbers the
+
+ align:start position:0%
+change like the one of the numbers the
+ 
+
+ align:start position:0%
+change like the one of the numbers the
+A's B's and C's by to say one reaction
+
+ align:start position:0%
+A's B's and C's by to say one reaction
+ 
+
+ align:start position:0%
+A's B's and C's by to say one reaction
+mmm okay and then after we accomplished
+
+ align:start position:0%
+mmm okay and then after we accomplished
+ 
+
+ align:start position:0%
+mmm okay and then after we accomplished
+that now we have a new state a B and C
+
+ align:start position:0%
+that now we have a new state a B and C
+ 
+
+ align:start position:0%
+that now we have a new state a B and C
+with some new values and we'll do the
+
+ align:start position:0%
+with some new values and we'll do the
+ 
+
+ align:start position:0%
+with some new values and we'll do the
+same thing again and we just repeat that
+
+ align:start position:0%
+same thing again and we just repeat that
+ 
+
+ align:start position:0%
+same thing again and we just repeat that
+over and over so it's very brute force
+
+ align:start position:0%
+over and over so it's very brute force
+ 
+
+ align:start position:0%
+over and over so it's very brute force
+you're just doing like what a single
+
+ align:start position:0%
+you're just doing like what a single
+ 
+
+ align:start position:0%
+you're just doing like what a single
+system would do so for example for the
+
+ align:start position:0%
+system would do so for example for the
+ 
+
+ align:start position:0%
+system would do so for example for the
+uranium atom case we have one uranium
+
+ align:start position:0%
+uranium atom case we have one uranium
+ 
+
+ align:start position:0%
+uranium atom case we have one uranium
+atom in there we wait for some time
+
+ align:start position:0%
+atom in there we wait for some time
+ 
+
+ align:start position:0%
+atom in there we wait for some time
+period say 20 minutes we compute the
+
+ align:start position:0%
+period say 20 minutes we compute the
+ 
+
+ align:start position:0%
+period say 20 minutes we compute the
+probability that the Iranian would have
+
+ align:start position:0%
+probability that the Iranian would have
+ 
+
+ align:start position:0%
+probability that the Iranian would have
+decayed in the last 20 minutes it's
+
+ align:start position:0%
+decayed in the last 20 minutes it's
+ 
+
+ align:start position:0%
+decayed in the last 20 minutes it's
+pretty small and then we'll say okay now
+
+ align:start position:0%
+pretty small and then we'll say okay now
+ 
+
+ align:start position:0%
+pretty small and then we'll say okay now
+we'll draw a random number if the random
+
+ align:start position:0%
+we'll draw a random number if the random
+ 
+
+ align:start position:0%
+we'll draw a random number if the random
+number is less than that probability
+
+ align:start position:0%
+number is less than that probability
+ 
+
+ align:start position:0%
+number is less than that probability
+then we think that the uranium is still
+
+ align:start position:0%
+then we think that the uranium is still
+ 
+
+ align:start position:0%
+then we think that the uranium is still
+there and the randoms bigger than that
+
+ align:start position:0%
+there and the randoms bigger than that
+ 
+
+ align:start position:0%
+there and the randoms bigger than that
+probability then the rainy one was gone
+
+ align:start position:0%
+probability then the rainy one was gone
+ 
+
+ align:start position:0%
+probability then the rainy one was gone
+if it's still there then we'll do it
+
+ align:start position:0%
+if it's still there then we'll do it
+ 
+
+ align:start position:0%
+if it's still there then we'll do it
+again and we'll just keep doing that
+
+ align:start position:0%
+again and we'll just keep doing that
+ 
+
+ align:start position:0%
+again and we'll just keep doing that
+over and over again and we'll sample
+
+ align:start position:0%
+over and over again and we'll sample
+ 
+
+ align:start position:0%
+over and over again and we'll sample
+what could happen your any I could live
+
+ align:start position:0%
+what could happen your any I could live
+ 
+
+ align:start position:0%
+what could happen your any I could live
+for three two three eight years and 14
+
+ align:start position:0%
+for three two three eight years and 14
+ 
+
+ align:start position:0%
+for three two three eight years and 14
+minutes and then disappear and that
+
+ align:start position:0%
+minutes and then disappear and that
+ 
+
+ align:start position:0%
+minutes and then disappear and that
+would be one example and then we go back
+
+ align:start position:0%
+would be one example and then we go back
+ 
+
+ align:start position:0%
+would be one example and then we go back
+and we do it again from a different
+
+ align:start position:0%
+and we do it again from a different
+ 
+
+ align:start position:0%
+and we do it again from a different
+trajectory and we do it over and over
+
+ align:start position:0%
+trajectory and we do it over and over
+ 
+
+ align:start position:0%
+trajectory and we do it over and over
+and over again and we do it over and
+
+ align:start position:0%
+and over again and we do it over and
+ 
+
+ align:start position:0%
+and over again and we do it over and
+over again those trajectories are
+
+ align:start position:0%
+over again those trajectories are
+ 
+
+ align:start position:0%
+over again those trajectories are
+sampling from what could happen with the
+
+ align:start position:0%
+sampling from what could happen with the
+ 
+
+ align:start position:0%
+sampling from what could happen with the
+right probability density this makes
+
+ align:start position:0%
+right probability density this makes
+ 
+
+ align:start position:0%
+right probability density this makes
+sense so the way Gillespie says to do it
+
+ align:start position:0%
+sense so the way Gillespie says to do it
+ 
+
+ align:start position:0%
+sense so the way Gillespie says to do it
+is figure out the the expected time
+
+ align:start position:0%
+is figure out the the expected time
+ 
+
+ align:start position:0%
+is figure out the the expected time
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+until something will call this time tau
+
+ align:start position:0%
+until something will call this time tau
+ 
+
+ align:start position:0%
+until something will call this time tau
+okay and we'll pull actually it's not
+
+ align:start position:0%
+okay and we'll pull actually it's not
+ 
+
+ align:start position:0%
+okay and we'll pull actually it's not
+used how cuz it's hello judge I'll try
+
+ align:start position:0%
+used how cuz it's hello judge I'll try
+ 
+
+ align:start position:0%
+used how cuz it's hello judge I'll try
+Bigfoot sister with dose notation he
+
+ align:start position:0%
+Bigfoot sister with dose notation he
+ 
+
+ align:start position:0%
+Bigfoot sister with dose notation he
+calls this thing 1 over a so a is like
+
+ align:start position:0%
+calls this thing 1 over a so a is like
+ 
+
+ align:start position:0%
+calls this thing 1 over a so a is like
+the expected rate per second and
+
+ align:start position:0%
+the expected rate per second and
+ 
+
+ align:start position:0%
+the expected rate per second and
+whenever a is expected time till
+
+ align:start position:0%
+whenever a is expected time till
+ 
+
+ align:start position:0%
+whenever a is expected time till
+something would happen and then we'll
+
+ align:start position:0%
+something would happen and then we'll
+ 
+
+ align:start position:0%
+something would happen and then we'll
+draw draw a random number R because it R
+
+ align:start position:0%
+draw draw a random number R because it R
+ 
+
+ align:start position:0%
+draw draw a random number R because it R
+1 we just call the rand function it
+
+ align:start position:0%
+1 we just call the rand function it
+ 
+
+ align:start position:0%
+1 we just call the rand function it
+gives me a number between 0 and 1 and
+
+ align:start position:0%
+gives me a number between 0 and 1 and
+ 
+
+ align:start position:0%
+gives me a number between 0 and 1 and
+I'll say that my my time step delta-t
+
+ align:start position:0%
+I'll say that my my time step delta-t
+ 
+
+ align:start position:0%
+I'll say that my my time step delta-t
+which Joe calls tau is whenever a the
+
+ align:start position:0%
+which Joe calls tau is whenever a the
+ 
+
+ align:start position:0%
+which Joe calls tau is whenever a the
+logarithm of 1 over R 1 so I and I think
+
+ align:start position:0%
+logarithm of 1 over R 1 so I and I think
+ 
+
+ align:start position:0%
+logarithm of 1 over R 1 so I and I think
+there should be a negative sign no one
+
+ align:start position:0%
+there should be a negative sign no one
+ 
+
+ align:start position:0%
+there should be a negative sign no one
+of hours positive that's right alright
+
+ align:start position:0%
+of hours positive that's right alright
+ 
+
+ align:start position:0%
+of hours positive that's right alright
+so I choose a random number suppose it's
+
+ align:start position:0%
+so I choose a random number suppose it's
+ 
+
+ align:start position:0%
+so I choose a random number suppose it's
+a half then this is this fraction is 2
+
+ align:start position:0%
+a half then this is this fraction is 2
+ 
+
+ align:start position:0%
+a half then this is this fraction is 2
+whatever happens to log on the 2 is to
+
+ align:start position:0%
+whatever happens to log on the 2 is to
+ 
+
+ align:start position:0%
+whatever happens to log on the 2 is to
+some number bigger than 1 and I pull
+
+ align:start position:0%
+some number bigger than 1 and I pull
+ 
+
+ align:start position:0%
+some number bigger than 1 and I pull
+that and I get some actually some that
+
+ align:start position:0%
+that and I get some actually some that
+ 
+
+ align:start position:0%
+that and I get some actually some that
+were less than 1
+
+ align:start position:0%
+were less than 1
+ 
+
+ align:start position:0%
+were less than 1
+like really - anyway some positive
+
+ align:start position:0%
+like really - anyway some positive
+ 
+
+ align:start position:0%
+like really - anyway some positive
+number multiply it by the expected time
+
+ align:start position:0%
+number multiply it by the expected time
+ 
+
+ align:start position:0%
+number multiply it by the expected time
+until something happens and that's the
+
+ align:start position:0%
+until something happens and that's the
+ 
+
+ align:start position:0%
+until something happens and that's the
+time in this particular simulation when
+
+ align:start position:0%
+time in this particular simulation when
+ 
+
+ align:start position:0%
+time in this particular simulation when
+the next thing happened and then I
+
+ align:start position:0%
+the next thing happened and then I
+ 
+
+ align:start position:0%
+the next thing happened and then I
+repeat this again and again and again
+
+ align:start position:0%
+repeat this again and again and again
+ 
+
+ align:start position:0%
+repeat this again and again and again
+and I get the
+
+ align:start position:0%
+and I get the
+ 
+
+ align:start position:0%
+and I get the
+period of time intervals between when
+
+ align:start position:0%
+period of time intervals between when
+ 
+
+ align:start position:0%
+period of time intervals between when
+something happened now every time
+
+ align:start position:0%
+something happened now every time
+ 
+
+ align:start position:0%
+something happened now every time
+something happened I took a well what
+
+ align:start position:0%
+something happened I took a well what
+ 
+
+ align:start position:0%
+something happened I took a well what
+happened so if I look at my left back
+
+ align:start position:0%
+happened so if I look at my left back
+ 
+
+ align:start position:0%
+happened so if I look at my left back
+here when I had the urate uranium
+
+ align:start position:0%
+here when I had the urate uranium
+ 
+
+ align:start position:0%
+here when I had the urate uranium
+I waited along the in this particular
+
+ align:start position:0%
+I waited along the in this particular
+ 
+
+ align:start position:0%
+I waited along the in this particular
+case here's my towel call it's tell one
+
+ align:start position:0%
+case here's my towel call it's tell one
+ 
+
+ align:start position:0%
+case here's my towel call it's tell one
+time that it took for the first thing to
+
+ align:start position:0%
+time that it took for the first thing to
+ 
+
+ align:start position:0%
+time that it took for the first thing to
+happen and then well what could happen
+
+ align:start position:0%
+happen and then well what could happen
+ 
+
+ align:start position:0%
+happen and then well what could happen
+the only thing that can happen my single
+
+ align:start position:0%
+the only thing that can happen my single
+ 
+
+ align:start position:0%
+the only thing that can happen my single
+uranium I you ready
+
+ align:start position:0%
+uranium I you ready
+ 
+
+ align:start position:0%
+uranium I you ready
+uranium atom case is it decayed so it
+
+ align:start position:0%
+uranium atom case is it decayed so it
+ 
+
+ align:start position:0%
+uranium atom case is it decayed so it
+went away all right and then I do the
+
+ align:start position:0%
+went away all right and then I do the
+ 
+
+ align:start position:0%
+went away all right and then I do the
+random number thing again and I draw on
+
+ align:start position:0%
+random number thing again and I draw on
+ 
+
+ align:start position:0%
+random number thing again and I draw on
+I get a different number this time how
+
+ align:start position:0%
+I get a different number this time how
+ 
+
+ align:start position:0%
+I get a different number this time how
+long it is still something yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now notice maybe it's not too obvious
+
+ align:start position:0%
+now notice maybe it's not too obvious
+ 
+
+ align:start position:0%
+now notice maybe it's not too obvious
+that the time until something happens
+
+ align:start position:0%
+that the time until something happens
+ 
+
+ align:start position:0%
+that the time until something happens
+changes as you run so for example if I
+
+ align:start position:0%
+changes as you run so for example if I
+ 
+
+ align:start position:0%
+changes as you run so for example if I
+start out with 100 uranium atoms in a
+
+ align:start position:0%
+start out with 100 uranium atoms in a
+ 
+
+ align:start position:0%
+start out with 100 uranium atoms in a
+hundred little boxes and I'm watching
+
+ align:start position:0%
+hundred little boxes and I'm watching
+ 
+
+ align:start position:0%
+hundred little boxes and I'm watching
+them after I've run this for a long time
+
+ align:start position:0%
+them after I've run this for a long time
+ 
+
+ align:start position:0%
+them after I've run this for a long time
+I only have 50 uranium atoms left and
+
+ align:start position:0%
+I only have 50 uranium atoms left and
+ 
+
+ align:start position:0%
+I only have 50 uranium atoms left and
+that means that the average time period
+
+ align:start position:0%
+that means that the average time period
+ 
+
+ align:start position:0%
+that means that the average time period
+until something happens will be slower
+
+ align:start position:0%
+until something happens will be slower
+ 
+
+ align:start position:0%
+until something happens will be slower
+because I don't have as many the more I
+
+ align:start position:0%
+because I don't have as many the more I
+ 
+
+ align:start position:0%
+because I don't have as many the more I
+have the more rapidly something will
+
+ align:start position:0%
+have the more rapidly something will
+ 
+
+ align:start position:0%
+have the more rapidly something will
+happen so it makes sense so I have to
+
+ align:start position:0%
+happen so it makes sense so I have to
+ 
+
+ align:start position:0%
+happen so it makes sense so I have to
+compute this a thing at each iteration
+
+ align:start position:0%
+compute this a thing at each iteration
+ 
+
+ align:start position:0%
+compute this a thing at each iteration
+so I compute the time until something
+
+ align:start position:0%
+so I compute the time until something
+ 
+
+ align:start position:0%
+so I compute the time until something
+happens then I'm going to compute what
+
+ align:start position:0%
+happens then I'm going to compute what
+ 
+
+ align:start position:0%
+happens then I'm going to compute what
+happened I'll tell you about that in a
+
+ align:start position:0%
+happened I'll tell you about that in a
+ 
+
+ align:start position:0%
+happened I'll tell you about that in a
+second in the uranium case the only
+
+ align:start position:0%
+second in the uranium case the only
+ 
+
+ align:start position:0%
+second in the uranium case the only
+thing that can happen is the uranium one
+
+ align:start position:0%
+thing that can happen is the uranium one
+ 
+
+ align:start position:0%
+thing that can happen is the uranium one
+uranium is decayed so I took that away
+
+ align:start position:0%
+uranium is decayed so I took that away
+ 
+
+ align:start position:0%
+uranium is decayed so I took that away
+now I have to compute a again so a is
+
+ align:start position:0%
+now I have to compute a again so a is
+ 
+
+ align:start position:0%
+now I have to compute a again so a is
+the sum of all the things that can
+
+ align:start position:0%
+the sum of all the things that can
+ 
+
+ align:start position:0%
+the sum of all the things that can
+happen so in my case where I have a
+
+ align:start position:0%
+happen so in my case where I have a
+ 
+
+ align:start position:0%
+happen so in my case where I have a
+hundred rate uranium atoms I have 100
+
+ align:start position:0%
+hundred rate uranium atoms I have 100
+ 
+
+ align:start position:0%
+hundred rate uranium atoms I have 100
+different boxes in each one of them
+
+ align:start position:0%
+different boxes in each one of them
+ 
+
+ align:start position:0%
+different boxes in each one of them
+there's a rate at which the uranium is
+
+ align:start position:0%
+there's a rate at which the uranium is
+ 
+
+ align:start position:0%
+there's a rate at which the uranium is
+probability is decay it's like 1 over
+
+ align:start position:0%
+probability is decay it's like 1 over
+ 
+
+ align:start position:0%
+probability is decay it's like 1 over
+the normal half-life uranium something
+
+ align:start position:0%
+the normal half-life uranium something
+ 
+
+ align:start position:0%
+the normal half-life uranium something
+like that and I add them up so a is the
+
+ align:start position:0%
+like that and I add them up so a is the
+ 
+
+ align:start position:0%
+like that and I add them up so a is the
+sum of the race
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of everything that can happen so I just
+
+ align:start position:0%
+of everything that can happen so I just
+ 
+
+ align:start position:0%
+of everything that can happen so I just
+list out all the different things that
+
+ align:start position:0%
+list out all the different things that
+ 
+
+ align:start position:0%
+list out all the different things that
+can happen so in the case is supposed to
+
+ align:start position:0%
+can happen so in the case is supposed to
+ 
+
+ align:start position:0%
+can happen so in the case is supposed to
+have two eight two boxes to uranium
+
+ align:start position:0%
+have two eight two boxes to uranium
+ 
+
+ align:start position:0%
+have two eight two boxes to uranium
+atoms I can have decay of Rio grab
+
+ align:start position:0%
+atoms I can have decay of Rio grab
+ 
+
+ align:start position:0%
+atoms I can have decay of Rio grab
+number one or uranium atom number two so
+
+ align:start position:0%
+number one or uranium atom number two so
+ 
+
+ align:start position:0%
+number one or uranium atom number two so
+I have this this thing would be equal to
+
+ align:start position:0%
+I have this this thing would be equal to
+ 
+
+ align:start position:0%
+I have this this thing would be equal to
+two uranium times a it's equal to 1 over
+
+ align:start position:0%
+two uranium times a it's equal to 1 over
+ 
+
+ align:start position:0%
+two uranium times a it's equal to 1 over
+tau normal for a uranium atom I'll swing
+
+ align:start position:0%
+tau normal for a uranium atom I'll swing
+ 
+
+ align:start position:0%
+tau normal for a uranium atom I'll swing
+over town normal cuz they're both normal
+
+ align:start position:0%
+over town normal cuz they're both normal
+ 
+
+ align:start position:0%
+over town normal cuz they're both normal
+really matters this is equal to two over
+
+ align:start position:0%
+really matters this is equal to two over
+ 
+
+ align:start position:0%
+really matters this is equal to two over
+tau and so whatever a is half of the
+
+ align:start position:0%
+tau and so whatever a is half of the
+ 
+
+ align:start position:0%
+tau and so whatever a is half of the
+half of the normal lifetime and that's
+
+ align:start position:0%
+half of the normal lifetime and that's
+ 
+
+ align:start position:0%
+half of the normal lifetime and that's
+when I would expect that something would
+
+ align:start position:0%
+when I would expect that something would
+ 
+
+ align:start position:0%
+when I would expect that something would
+happen by then okay one of them would
+
+ align:start position:0%
+happen by then okay one of them would
+ 
+
+ align:start position:0%
+happen by then okay one of them would
+one would probably decay so that would
+
+ align:start position:0%
+one would probably decay so that would
+ 
+
+ align:start position:0%
+one would probably decay so that would
+be the a value I would use here draw my
+
+ align:start position:0%
+be the a value I would use here draw my
+ 
+
+ align:start position:0%
+be the a value I would use here draw my
+random number get my towel until
+
+ align:start position:0%
+random number get my towel until
+ 
+
+ align:start position:0%
+random number get my towel until
+something probably happened then figure
+
+ align:start position:0%
+something probably happened then figure
+ 
+
+ align:start position:0%
+something probably happened then figure
+out what happens now in the kinetics
+
+ align:start position:0%
+out what happens now in the kinetics
+ 
+
+ align:start position:0%
+out what happens now in the kinetics
+case several different things can happen
+
+ align:start position:0%
+case several different things can happen
+ 
+
+ align:start position:0%
+case several different things can happen
+right I wrote down if I'm in state n a n
+
+ align:start position:0%
+right I wrote down if I'm in state n a n
+ 
+
+ align:start position:0%
+right I wrote down if I'm in state n a n
+a and B and C I the the state can change
+
+ align:start position:0%
+a and B and C I the the state can change
+ 
+
+ align:start position:0%
+a and B and C I the the state can change
+by two different ways I can I can move
+
+ align:start position:0%
+by two different ways I can I can move
+ 
+
+ align:start position:0%
+by two different ways I can I can move
+out of that state this way or this way
+
+ align:start position:0%
+out of that state this way or this way
+ 
+
+ align:start position:0%
+out of that state this way or this way
+right Toofer reactions happen for a
+
+ align:start position:0%
+right Toofer reactions happen for a
+ 
+
+ align:start position:0%
+right Toofer reactions happen for a
+reverse reaction and they will go to
+
+ align:start position:0%
+reverse reaction and they will go to
+ 
+
+ align:start position:0%
+reverse reaction and they will go to
+take me out of the state so those are
+
+ align:start position:0%
+take me out of the state so those are
+ 
+
+ align:start position:0%
+take me out of the state so those are
+two different things they happen and so
+
+ align:start position:0%
+two different things they happen and so
+ 
+
+ align:start position:0%
+two different things they happen and so
+I have to add the product those rates so
+
+ align:start position:0%
+I have to add the product those rates so
+ 
+
+ align:start position:0%
+I have to add the product those rates so
+I would add this number and this number
+
+ align:start position:0%
+I would add this number and this number
+ 
+
+ align:start position:0%
+I would add this number and this number
+and they would be the two things that
+
+ align:start position:0%
+and they would be the two things that
+ 
+
+ align:start position:0%
+and they would be the two things that
+could happen that would give me that a
+
+ align:start position:0%
+could happen that would give me that a
+ 
+
+ align:start position:0%
+could happen that would give me that a
+die
+
+ align:start position:0%
+die
+ 
+
+ align:start position:0%
+die
+now I I figured out something happened
+
+ align:start position:0%
+now I I figured out something happened
+ 
+
+ align:start position:0%
+now I I figured out something happened
+but now I'm not doing uranium now I'm
+
+ align:start position:0%
+but now I'm not doing uranium now I'm
+ 
+
+ align:start position:0%
+but now I'm not doing uranium now I'm
+doing a number of A's and I figure
+
+ align:start position:0%
+doing a number of A's and I figure
+ 
+
+ align:start position:0%
+doing a number of A's and I figure
+something it happened
+
+ align:start position:0%
+something it happened
+ 
+
+ align:start position:0%
+something it happened
+- what happened and the number of A's
+
+ align:start position:0%
+- what happened and the number of A's
+ 
+
+ align:start position:0%
+- what happened and the number of A's
+could have gone up or gone down because
+
+ align:start position:0%
+could have gone up or gone down because
+ 
+
+ align:start position:0%
+could have gone up or gone down because
+it was a forward reaction number of ADEs
+
+ align:start position:0%
+it was a forward reaction number of ADEs
+ 
+
+ align:start position:0%
+it was a forward reaction number of ADEs
+went down if it was a reverse reaction
+
+ align:start position:0%
+went down if it was a reverse reaction
+ 
+
+ align:start position:0%
+went down if it was a reverse reaction
+number days went up so I had to decide
+
+ align:start position:0%
+number days went up so I had to decide
+ 
+
+ align:start position:0%
+number days went up so I had to decide
+which way is gonna happen so I could
+
+ align:start position:0%
+which way is gonna happen so I could
+ 
+
+ align:start position:0%
+which way is gonna happen so I could
+have either the number of A's went down
+
+ align:start position:0%
+have either the number of A's went down
+ 
+
+ align:start position:0%
+have either the number of A's went down
+or their race went up there's are two
+
+ align:start position:0%
+or their race went up there's are two
+ 
+
+ align:start position:0%
+or their race went up there's are two
+possibilities I had to figure which one
+
+ align:start position:0%
+possibilities I had to figure which one
+ 
+
+ align:start position:0%
+possibilities I had to figure which one
+happened I have to figure it draw
+
+ align:start position:0%
+happened I have to figure it draw
+ 
+
+ align:start position:0%
+happened I have to figure it draw
+another random number to figure out
+
+ align:start position:0%
+another random number to figure out
+ 
+
+ align:start position:0%
+another random number to figure out
+which one probably happened so I'll list
+
+ align:start position:0%
+which one probably happened so I'll list
+ 
+
+ align:start position:0%
+which one probably happened so I'll list
+out the list of all the things that can
+
+ align:start position:0%
+out the list of all the things that can
+ 
+
+ align:start position:0%
+out the list of all the things that can
+happen with their rates and one of them
+
+ align:start position:0%
+happen with their rates and one of them
+ 
+
+ align:start position:0%
+happen with their rates and one of them
+say is twice as big as the other so that
+
+ align:start position:0%
+say is twice as big as the other so that
+ 
+
+ align:start position:0%
+say is twice as big as the other so that
+it'll be twice as likely to happen so I
+
+ align:start position:0%
+it'll be twice as likely to happen so I
+ 
+
+ align:start position:0%
+it'll be twice as likely to happen so I
+have to choose a round number and use
+
+ align:start position:0%
+have to choose a round number and use
+ 
+
+ align:start position:0%
+have to choose a round number and use
+that to choose the next one so so first
+
+ align:start position:0%
+that to choose the next one so so first
+ 
+
+ align:start position:0%
+that to choose the next one so so first
+I figured it out this is actually did
+
+ align:start position:0%
+I figured it out this is actually did
+ 
+
+ align:start position:0%
+I figured it out this is actually did
+first I figured out what my rates are
+
+ align:start position:0%
+first I figured out what my rates are
+ 
+
+ align:start position:0%
+first I figured out what my rates are
+second thing is I figure out the time
+
+ align:start position:0%
+second thing is I figure out the time
+ 
+
+ align:start position:0%
+second thing is I figure out the time
+until something happened third thing is
+
+ align:start position:0%
+until something happened third thing is
+ 
+
+ align:start position:0%
+until something happened third thing is
+I'm going to figure out what happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what I do is I say I draw a random
+
+ align:start position:0%
+and what I do is I say I draw a random
+ 
+
+ align:start position:0%
+and what I do is I say I draw a random
+number call r2 and if there's only two
+
+ align:start position:0%
+number call r2 and if there's only two
+ 
+
+ align:start position:0%
+number call r2 and if there's only two
+possibilities like in this case then I
+
+ align:start position:0%
+possibilities like in this case then I
+ 
+
+ align:start position:0%
+possibilities like in this case then I
+can say if r2 is less than the re
+
+ align:start position:0%
+can say if r2 is less than the re
+ 
+
+ align:start position:0%
+can say if r2 is less than the re
+process 1 divided by the sum of the
+
+ align:start position:0%
+process 1 divided by the sum of the
+ 
+
+ align:start position:0%
+process 1 divided by the sum of the
+rates which is the same as that a right
+
+ align:start position:0%
+rates which is the same as that a right
+ 
+
+ align:start position:0%
+rates which is the same as that a right
+this is hey this is true then process 1
+
+ align:start position:0%
+this is hey this is true then process 1
+ 
+
+ align:start position:0%
+this is hey this is true then process 1
+happened on the other hand if the rate
+
+ align:start position:0%
+happened on the other hand if the rate
+ 
+
+ align:start position:0%
+happened on the other hand if the rate
+of the remember I chose is larger than
+
+ align:start position:0%
+of the remember I chose is larger than
+ 
+
+ align:start position:0%
+of the remember I chose is larger than
+this ratio then I'll say process two
+
+ align:start position:0%
+this ratio then I'll say process two
+ 
+
+ align:start position:0%
+this ratio then I'll say process two
+happened and that's how I decide whether
+
+ align:start position:0%
+happened and that's how I decide whether
+ 
+
+ align:start position:0%
+happened and that's how I decide whether
+the number of A's went up and went down
+
+ align:start position:0%
+the number of A's went up and went down
+ 
+
+ align:start position:0%
+the number of A's went up and went down
+and then it would recompute the a
+
+ align:start position:0%
+and then it would recompute the a
+ 
+
+ align:start position:0%
+and then it would recompute the a
+depending on what happens suppose I I do
+
+ align:start position:0%
+depending on what happens suppose I I do
+ 
+
+ align:start position:0%
+depending on what happens suppose I I do
+this and I found out that the number of
+
+ align:start position:0%
+this and I found out that the number of
+ 
+
+ align:start position:0%
+this and I found out that the number of
+A's went up is my crude my drawing the
+
+ align:start position:0%
+A's went up is my crude my drawing the
+ 
+
+ align:start position:0%
+A's went up is my crude my drawing the
+random number that I'll go and I'll
+
+ align:start position:0%
+random number that I'll go and I'll
+ 
+
+ align:start position:0%
+random number that I'll go and I'll
+recompute da now the rates all be
+
+ align:start position:0%
+recompute da now the rates all be
+ 
+
+ align:start position:0%
+recompute da now the rates all be
+different because
+
+ align:start position:0%
+different because
+ 
+
+ align:start position:0%
+different because
+n/a is bigger so the rate of DNA
+
+ align:start position:0%
+n/a is bigger so the rate of DNA
+ 
+
+ align:start position:0%
+n/a is bigger so the rate of DNA
+reaction is faster so I recompute it I
+
+ align:start position:0%
+reaction is faster so I recompute it I
+ 
+
+ align:start position:0%
+reaction is faster so I recompute it I
+redraw a number here I get some
+
+ align:start position:0%
+redraw a number here I get some
+ 
+
+ align:start position:0%
+redraw a number here I get some
+different time tattoo it's not the same
+
+ align:start position:0%
+different time tattoo it's not the same
+ 
+
+ align:start position:0%
+different time tattoo it's not the same
+as tell one and then something happened
+
+ align:start position:0%
+as tell one and then something happened
+ 
+
+ align:start position:0%
+as tell one and then something happened
+here I do the same process here to
+
+ align:start position:0%
+here I do the same process here to
+ 
+
+ align:start position:0%
+here I do the same process here to
+figure out what happened maybe this time
+
+ align:start position:0%
+figure out what happened maybe this time
+ 
+
+ align:start position:0%
+figure out what happened maybe this time
+they reacted away and then went Benton
+
+ align:start position:0%
+they reacted away and then went Benton
+ 
+
+ align:start position:0%
+they reacted away and then went Benton
+alright and then I do it again and this
+
+ align:start position:0%
+alright and then I do it again and this
+ 
+
+ align:start position:0%
+alright and then I do it again and this
+time I draw a longer time tau 3 and I do
+
+ align:start position:0%
+time I draw a longer time tau 3 and I do
+ 
+
+ align:start position:0%
+time I draw a longer time tau 3 and I do
+what happened that made this time again
+
+ align:start position:0%
+what happened that made this time again
+ 
+
+ align:start position:0%
+what happened that made this time again
+something reacted away in it with them
+
+ align:start position:0%
+something reacted away in it with them
+ 
+
+ align:start position:0%
+something reacted away in it with them
+and I don't know and after my computer
+
+ align:start position:0%
+and I don't know and after my computer
+ 
+
+ align:start position:0%
+and I don't know and after my computer
+is done doing that for a while I got so
+
+ align:start position:0%
+is done doing that for a while I got so
+ 
+
+ align:start position:0%
+is done doing that for a while I got so
+long enough time I say okay I'm done oh
+
+ align:start position:0%
+long enough time I say okay I'm done oh
+ 
+
+ align:start position:0%
+long enough time I say okay I'm done oh
+I don't really don't have to go back and
+
+ align:start position:0%
+I don't really don't have to go back and
+ 
+
+ align:start position:0%
+I don't really don't have to go back and
+start again and run another simulation
+
+ align:start position:0%
+start again and run another simulation
+ 
+
+ align:start position:0%
+start again and run another simulation
+to run through all the possibilities and
+
+ align:start position:0%
+to run through all the possibilities and
+ 
+
+ align:start position:0%
+to run through all the possibilities and
+what I save all these results of all
+
+ align:start position:0%
+what I save all these results of all
+ 
+
+ align:start position:0%
+what I save all these results of all
+these simulations because these guys are
+
+ align:start position:0%
+these simulations because these guys are
+ 
+
+ align:start position:0%
+these simulations because these guys are
+samples from the probability
+
+ align:start position:0%
+samples from the probability
+ 
+
+ align:start position:0%
+samples from the probability
+distribution and if I build histograms
+
+ align:start position:0%
+distribution and if I build histograms
+ 
+
+ align:start position:0%
+distribution and if I build histograms
+and stuff from those guys I can figure
+
+ align:start position:0%
+and stuff from those guys I can figure
+ 
+
+ align:start position:0%
+and stuff from those guys I can figure
+out what really is gonna have them all
+
+ align:start position:0%
+out what really is gonna have them all
+ 
+
+ align:start position:0%
+out what really is gonna have them all
+right so it's a way to represent the P
+
+ align:start position:0%
+right so it's a way to represent the P
+ 
+
+ align:start position:0%
+right so it's a way to represent the P
+questions alright hope you'll clear all
+
+ align:start position:0%
+questions alright hope you'll clear all
+ 
+
+ align:start position:0%
+questions alright hope you'll clear all
+right so it's nice about this is
+
+ align:start position:0%
+right so it's nice about this is
+ 
+
+ align:start position:0%
+right so it's nice about this is
+actually it's not that hard once you do
+
+ align:start position:0%
+actually it's not that hard once you do
+ 
+
+ align:start position:0%
+actually it's not that hard once you do
+this once it's not hard to do it and you
+
+ align:start position:0%
+this once it's not hard to do it and you
+ 
+
+ align:start position:0%
+this once it's not hard to do it and you
+do for any problem at all
+
+ align:start position:0%
+do for any problem at all
+ 
+
+ align:start position:0%
+do for any problem at all
+and so it's like often cases people do
+
+ align:start position:0%
+and so it's like often cases people do
+ 
+
+ align:start position:0%
+and so it's like often cases people do
+this even for cases where you actually
+
+ align:start position:0%
+this even for cases where you actually
+ 
+
+ align:start position:0%
+this even for cases where you actually
+could solve you might be able to solve
+
+ align:start position:0%
+could solve you might be able to solve
+ 
+
+ align:start position:0%
+could solve you might be able to solve
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+a lot times when people won't do it
+
+ align:start position:0%
+a lot times when people won't do it
+ 
+
+ align:start position:0%
+a lot times when people won't do it
+don't do this instead just cuz it's so
+
+ align:start position:0%
+don't do this instead just cuz it's so
+ 
+
+ align:start position:0%
+don't do this instead just cuz it's so
+easy so although May it looks hard to
+
+ align:start position:0%
+easy so although May it looks hard to
+ 
+
+ align:start position:0%
+easy so although May it looks hard to
+you right now it's only a three step
+
+ align:start position:0%
+you right now it's only a three step
+ 
+
+ align:start position:0%
+you right now it's only a three step
+thing you just do it over and over again
+
+ align:start position:0%
+thing you just do it over and over again
+ 
+
+ align:start position:0%
+thing you just do it over and over again
+you're not doing it the computers doing
+
+ align:start position:0%
+you're not doing it the computers doing
+ 
+
+ align:start position:0%
+you're not doing it the computers doing
+it no big deal
+
+ align:start position:0%
+it no big deal
+ 
+
+ align:start position:0%
+it no big deal
+and so this one you have to like look at
+
+ align:start position:0%
+and so this one you have to like look at
+ 
+
+ align:start position:0%
+and so this one you have to like look at
+the sparsity pattern of your m there's a
+
+ align:start position:0%
+the sparsity pattern of your m there's a
+ 
+
+ align:start position:0%
+the sparsity pattern of your m there's a
+complicated stuff so this is actually
+
+ align:start position:0%
+complicated stuff so this is actually
+ 
+
+ align:start position:0%
+complicated stuff so this is actually
+done extremely a commonly alright see
+
+ align:start position:0%
+done extremely a commonly alright see
+ 
+
+ align:start position:0%
+done extremely a commonly alright see
+you on Friday
\ No newline at end of file
diff --git a/uS-w4yl35vc.txt b/uS-w4yl35vc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..616755c32adc27f801c941014a39e7cd676f6ffd
--- /dev/null
+++ b/uS-w4yl35vc.txt
@@ -0,0 +1,13659 @@
+align:start position:0%
+ 
+so today in case you were thinking that
+
+ align:start position:0%
+so today in case you were thinking that
+ 
+
+ align:start position:0%
+so today in case you were thinking that
+there wasn't enough theorems on Tuesday
+
+ align:start position:0%
+there wasn't enough theorems on Tuesday
+ 
+
+ align:start position:0%
+there wasn't enough theorems on Tuesday
+we're going to approve a lot of them
+
+ align:start position:0%
+we're going to approve a lot of them
+ 
+
+ align:start position:0%
+we're going to approve a lot of them
+today on the general metric space Theory
+
+ align:start position:0%
+today on the general metric space Theory
+ 
+
+ align:start position:0%
+today on the general metric space Theory
+I I like this notion of a theory of the
+
+ align:start position:0%
+I I like this notion of a theory of the
+ 
+
+ align:start position:0%
+I I like this notion of a theory of the
+spaces this is a notation that um Dr
+
+ align:start position:0%
+spaces this is a notation that um Dr
+ 
+
+ align:start position:0%
+spaces this is a notation that um Dr
+Casey Rodriguez taught me Loosely
+
+ align:start position:0%
+Casey Rodriguez taught me Loosely
+ 
+
+ align:start position:0%
+Casey Rodriguez taught me Loosely
+speaking where you know you're just
+
+ align:start position:0%
+speaking where you know you're just
+ 
+
+ align:start position:0%
+speaking where you know you're just
+trying to encapsulate what are all the
+
+ align:start position:0%
+trying to encapsulate what are all the
+ 
+
+ align:start position:0%
+trying to encapsulate what are all the
+things we can say about the most
+
+ align:start position:0%
+things we can say about the most
+ 
+
+ align:start position:0%
+things we can say about the most
+fundamental objects in the space that
+
+ align:start position:0%
+fundamental objects in the space that
+ 
+
+ align:start position:0%
+fundamental objects in the space that
+you're considering and a number of them
+
+ align:start position:0%
+you're considering and a number of them
+ 
+
+ align:start position:0%
+you're considering and a number of them
+will essentially a number of the
+
+ align:start position:0%
+will essentially a number of the
+ 
+
+ align:start position:0%
+will essentially a number of the
+theorems that will prove are essentially
+
+ align:start position:0%
+theorems that will prove are essentially
+ 
+
+ align:start position:0%
+theorems that will prove are essentially
+the same as what we would picture in
+
+ align:start position:0%
+the same as what we would picture in
+ 
+
+ align:start position:0%
+the same as what we would picture in
+ukian space but we have to be slightly
+
+ align:start position:0%
+ukian space but we have to be slightly
+ 
+
+ align:start position:0%
+ukian space but we have to be slightly
+more careful sometimes and all of this
+
+ align:start position:0%
+more careful sometimes and all of this
+ 
+
+ align:start position:0%
+more careful sometimes and all of this
+theory is going to be building up to
+
+ align:start position:0%
+theory is going to be building up to
+ 
+
+ align:start position:0%
+theory is going to be building up to
+understanding something that you
+
+ align:start position:0%
+understanding something that you
+ 
+
+ align:start position:0%
+understanding something that you
+probably haven't seen before if you
+
+ align:start position:0%
+probably haven't seen before if you
+ 
+
+ align:start position:0%
+probably haven't seen before if you
+haven't done 100b known as compact sets
+
+ align:start position:0%
+haven't done 100b known as compact sets
+ 
+
+ align:start position:0%
+haven't done 100b known as compact sets
+so we're going to be building up to
+
+ align:start position:0%
+so we're going to be building up to
+ 
+
+ align:start position:0%
+so we're going to be building up to
+talking about compact sets but first we
+
+ align:start position:0%
+talking about compact sets but first we
+ 
+
+ align:start position:0%
+talking about compact sets but first we
+have to understand what are the
+
+ align:start position:0%
+have to understand what are the
+ 
+
+ align:start position:0%
+have to understand what are the
+fundamental Tools in our tool belt with
+
+ align:start position:0%
+fundamental Tools in our tool belt with
+ 
+
+ align:start position:0%
+fundamental Tools in our tool belt with
+metrics based Theory and I do want to
+
+ align:start position:0%
+metrics based Theory and I do want to
+ 
+
+ align:start position:0%
+metrics based Theory and I do want to
+Note One Thing even though last time I
+
+ align:start position:0%
+Note One Thing even though last time I
+ 
+
+ align:start position:0%
+Note One Thing even though last time I
+said we can put a metric on every set
+
+ align:start position:0%
+said we can put a metric on every set
+ 
+
+ align:start position:0%
+said we can put a metric on every set
+which is true not every set has a nice
+
+ align:start position:0%
+which is true not every set has a nice
+ 
+
+ align:start position:0%
+which is true not every set has a nice
+metric on it uh in case have any of
+
+ align:start position:0%
+metric on it uh in case have any of
+ 
+
+ align:start position:0%
+metric on it uh in case have any of
+youall Taken topology before no worries
+
+ align:start position:0%
+youall Taken topology before no worries
+ 
+
+ align:start position:0%
+youall Taken topology before no worries
+if not it's a class that usually comes
+
+ align:start position:0%
+if not it's a class that usually comes
+ 
+
+ align:start position:0%
+if not it's a class that usually comes
+after real analysis but in topology talk
+
+ align:start position:0%
+after real analysis but in topology talk
+ 
+
+ align:start position:0%
+after real analysis but in topology talk
+not every topological space is
+
+ align:start position:0%
+not every topological space is
+ 
+
+ align:start position:0%
+not every topological space is
+metrizable I.E there's not necessarily a
+
+ align:start position:0%
+metrizable I.E there's not necessarily a
+ 
+
+ align:start position:0%
+metrizable I.E there's not necessarily a
+metric on it that will make the topology
+
+ align:start position:0%
+metric on it that will make the topology
+ 
+
+ align:start position:0%
+metric on it that will make the topology
+nice and we'll talk about what topology
+
+ align:start position:0%
+nice and we'll talk about what topology
+ 
+
+ align:start position:0%
+nice and we'll talk about what topology
+is a little bit today so in case you're
+
+ align:start position:0%
+is a little bit today so in case you're
+ 
+
+ align:start position:0%
+is a little bit today so in case you're
+interested in what that statement is
+
+ align:start position:0%
+interested in what that statement is
+ 
+
+ align:start position:0%
+interested in what that statement is
+we'll come to it but the basic idea is
+
+ align:start position:0%
+we'll come to it but the basic idea is
+ 
+
+ align:start position:0%
+we'll come to it but the basic idea is
+even though we can put a metric on every
+
+ align:start position:0%
+even though we can put a metric on every
+ 
+
+ align:start position:0%
+even though we can put a metric on every
+set it's sometimes the trivial one is
+
+ align:start position:0%
+set it's sometimes the trivial one is
+ 
+
+ align:start position:0%
+set it's sometimes the trivial one is
+not that interesting
+
+ align:start position:0%
+not that interesting
+ 
+
+ align:start position:0%
+not that interesting
+so all right let's go ahead and jump
+
+ align:start position:0%
+so all right let's go ahead and jump
+ 
+
+ align:start position:0%
+so all right let's go ahead and jump
+into the metric Bas theory for
+
+ align:start position:0%
+into the metric Bas theory for
+ 
+
+ align:start position:0%
+into the metric Bas theory for
+today so first off we're going to be
+
+ align:start position:0%
+today so first off we're going to be
+ 
+
+ align:start position:0%
+today so first off we're going to be
+talking about convergent sequences just
+
+ align:start position:0%
+talking about convergent sequences just
+ 
+
+ align:start position:0%
+talking about convergent sequences just
+like we did in RN so throughout
+
+ align:start position:0%
+like we did in RN so throughout
+ 
+
+ align:start position:0%
+like we did in RN so throughout
+this let
+
+ align:start position:0%
+this let
+ 
+
+ align:start position:0%
+this let
+xn and YN
+
+ align:start position:0%
+xn and YN
+ 
+
+ align:start position:0%
+xn and YN
+be the sequences we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+considering and the first
+
+ align:start position:0%
+considering and the first
+ 
+
+ align:start position:0%
+considering and the first
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+xn converges to x what should we expect
+
+ align:start position:0%
+xn converges to x what should we expect
+ 
+
+ align:start position:0%
+xn converges to x what should we expect
+about the point that it converges to
+
+ align:start position:0%
+about the point that it converges to
+ 
+
+ align:start position:0%
+about the point that it converges to
+well in ukian space we knew that this
+
+ align:start position:0%
+well in ukian space we knew that this
+ 
+
+ align:start position:0%
+well in ukian space we knew that this
+limit point had to be unique and in fact
+
+ align:start position:0%
+limit point had to be unique and in fact
+ 
+
+ align:start position:0%
+limit point had to be unique and in fact
+we can prove that this must be the
+
+ align:start position:0%
+we can prove that this must be the
+ 
+
+ align:start position:0%
+we can prove that this must be the
+case uh so
+
+ align:start position:0%
+case uh so
+ 
+
+ align:start position:0%
+case uh so
+then X is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique to prove a statement like this we
+
+ align:start position:0%
+unique to prove a statement like this we
+ 
+
+ align:start position:0%
+unique to prove a statement like this we
+choose a different point Y in our set to
+
+ align:start position:0%
+choose a different point Y in our set to
+ 
+
+ align:start position:0%
+choose a different point Y in our set to
+consider so what we're going to show now
+
+ align:start position:0%
+consider so what we're going to show now
+ 
+
+ align:start position:0%
+consider so what we're going to show now
+is that convergent sequences have unique
+
+ align:start position:0%
+is that convergent sequences have unique
+ 
+
+ align:start position:0%
+is that convergent sequences have unique
+limit points so
+
+ align:start position:0%
+limit points so
+ 
+
+ align:start position:0%
+limit points so
+prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suppose there exists a y in your metric
+
+ align:start position:0%
+Suppose there exists a y in your metric
+ 
+
+ align:start position:0%
+Suppose there exists a y in your metric
+base X oh I should say sequences in your
+
+ align:start position:0%
+base X oh I should say sequences in your
+ 
+
+ align:start position:0%
+base X oh I should say sequences in your
+metric base
+
+ align:start position:0%
+metric base
+ 
+
+ align:start position:0%
+metric base
+XD so metric Bas x with metric D and
+
+ align:start position:0%
+XD so metric Bas x with metric D and
+ 
+
+ align:start position:0%
+XD so metric Bas x with metric D and
+suppose that there exists a y and x such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that X then converges to Y our end goal
+
+ align:start position:0%
+that X then converges to Y our end goal
+ 
+
+ align:start position:0%
+that X then converges to Y our end goal
+is to show then that X must be equal to
+
+ align:start position:0%
+is to show then that X must be equal to
+ 
+
+ align:start position:0%
+is to show then that X must be equal to
+Y in fact now to do this what do we know
+
+ align:start position:0%
+Y in fact now to do this what do we know
+ 
+
+ align:start position:0%
+Y in fact now to do this what do we know
+about equality for points well by the
+
+ align:start position:0%
+about equality for points well by the
+ 
+
+ align:start position:0%
+about equality for points well by the
+axioms of what we're defining a metric
+
+ align:start position:0%
+axioms of what we're defining a metric
+ 
+
+ align:start position:0%
+axioms of what we're defining a metric
+space to be two points are going to be
+
+ align:start position:0%
+space to be two points are going to be
+ 
+
+ align:start position:0%
+space to be two points are going to be
+the same if the distance is precisely
+
+ align:start position:0%
+the same if the distance is precisely
+ 
+
+ align:start position:0%
+the same if the distance is precisely
+zero it's an if and only a statement so
+
+ align:start position:0%
+zero it's an if and only a statement so
+ 
+
+ align:start position:0%
+zero it's an if and only a statement so
+that's what we want to prove we want to
+
+ align:start position:0%
+that's what we want to prove we want to
+ 
+
+ align:start position:0%
+that's what we want to prove we want to
+prove that the distance between X and Y
+
+ align:start position:0%
+prove that the distance between X and Y
+ 
+
+ align:start position:0%
+prove that the distance between X and Y
+is zero so how can we do that well
+
+ align:start position:0%
+is zero so how can we do that well
+ 
+
+ align:start position:0%
+is zero so how can we do that well
+firstly let's write down what the
+
+ align:start position:0%
+firstly let's write down what the
+ 
+
+ align:start position:0%
+firstly let's write down what the
+definitions of them converging to X and
+
+ align:start position:0%
+definitions of them converging to X and
+ 
+
+ align:start position:0%
+definitions of them converging to X and
+Y is respectively so xn converges to X
+
+ align:start position:0%
+Y is respectively so xn converges to X
+ 
+
+ align:start position:0%
+Y is respectively so xn converges to X
+means that for all Epsilon bigger than
+
+ align:start position:0%
+means that for all Epsilon bigger than
+ 
+
+ align:start position:0%
+means that for all Epsilon bigger than
+zero there exists an n in the natural
+
+ align:start position:0%
+zero there exists an n in the natural
+ 
+
+ align:start position:0%
+zero there exists an n in the natural
+numbers such that for all n bigger than
+
+ align:start position:0%
+numbers such that for all n bigger than
+ 
+
+ align:start position:0%
+numbers such that for all n bigger than
+or equal to n and I'll this
+
+ align:start position:0%
+or equal to n and I'll this
+ 
+
+ align:start position:0%
+or equal to n and I'll this
+N1 we have that the distance from xn to
+
+ align:start position:0%
+N1 we have that the distance from xn to
+ 
+
+ align:start position:0%
+N1 we have that the distance from xn to
+X is less than Epsilon this is the
+
+ align:start position:0%
+X is less than Epsilon this is the
+ 
+
+ align:start position:0%
+X is less than Epsilon this is the
+definition of convergent sequence that
+
+ align:start position:0%
+definition of convergent sequence that
+ 
+
+ align:start position:0%
+definition of convergent sequence that
+we're dealing
+
+ align:start position:0%
+we're dealing
+ 
+
+ align:start position:0%
+we're dealing
+with and similarly xn converges to Y if
+
+ align:start position:0%
+with and similarly xn converges to Y if
+ 
+
+ align:start position:0%
+with and similarly xn converges to Y if
+there exists an N2 in the natural
+
+ align:start position:0%
+there exists an N2 in the natural
+ 
+
+ align:start position:0%
+there exists an N2 in the natural
+numbers for this Epsilon such that for
+
+ align:start position:0%
+numbers for this Epsilon such that for
+ 
+
+ align:start position:0%
+numbers for this Epsilon such that for
+such that for all n bigger than or equal
+
+ align:start position:0%
+such that for all n bigger than or equal
+ 
+
+ align:start position:0%
+such that for all n bigger than or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+N2 the distance from xn to
+
+ align:start position:0%
+N2 the distance from xn to
+ 
+
+ align:start position:0%
+N2 the distance from xn to
+Y is is less than
+
+ align:start position:0%
+Y is is less than
+ 
+
+ align:start position:0%
+Y is is less than
+Epsilon so now what do we want to do we
+
+ align:start position:0%
+Epsilon so now what do we want to do we
+ 
+
+ align:start position:0%
+Epsilon so now what do we want to do we
+want to use this to show that the
+
+ align:start position:0%
+want to use this to show that the
+ 
+
+ align:start position:0%
+want to use this to show that the
+distance between X and Y is small and to
+
+ align:start position:0%
+distance between X and Y is small and to
+ 
+
+ align:start position:0%
+distance between X and Y is small and to
+do this we'll apply the triangle
+
+ align:start position:0%
+do this we'll apply the triangle
+ 
+
+ align:start position:0%
+do this we'll apply the triangle
+inequality to understand the distance
+
+ align:start position:0%
+inequality to understand the distance
+ 
+
+ align:start position:0%
+inequality to understand the distance
+from X to
+
+ align:start position:0%
+from X to
+ 
+
+ align:start position:0%
+from X to
+Y so by the triangle inequality this is
+
+ align:start position:0%
+Y so by the triangle inequality this is
+ 
+
+ align:start position:0%
+Y so by the triangle inequality this is
+less than or equal to the distance from
+
+ align:start position:0%
+less than or equal to the distance from
+ 
+
+ align:start position:0%
+less than or equal to the distance from
+xn to X plus the distance from
+
+ align:start position:0%
+xn to X plus the distance from
+ 
+
+ align:start position:0%
+xn to X plus the distance from
+xn to Y where here I'm applying symmetry
+
+ align:start position:0%
+xn to Y where here I'm applying symmetry
+ 
+
+ align:start position:0%
+xn to Y where here I'm applying symmetry
+so that I can move the terms around
+
+ align:start position:0%
+so that I can move the terms around
+ 
+
+ align:start position:0%
+so that I can move the terms around
+right and this we know that for all
+
+ align:start position:0%
+right and this we know that for all
+ 
+
+ align:start position:0%
+right and this we know that for all
+Epsilon bigger than
+
+ align:start position:0%
+Epsilon bigger than
+ 
+
+ align:start position:0%
+Epsilon bigger than
+zero there exists an N let's say this is
+
+ align:start position:0%
+zero there exists an N let's say this is
+ 
+
+ align:start position:0%
+zero there exists an N let's say this is
+equal to the
+
+ align:start position:0%
+equal to the
+ 
+
+ align:start position:0%
+equal to the
+maximum of N1 and
+
+ align:start position:0%
+maximum of N1 and
+ 
+
+ align:start position:0%
+maximum of N1 and
+N2 in the natural
+
+ align:start position:0%
+N2 in the natural
+ 
+
+ align:start position:0%
+N2 in the natural
+numbers such that both of these terms
+
+ align:start position:0%
+numbers such that both of these terms
+ 
+
+ align:start position:0%
+numbers such that both of these terms
+are now less than Epsilon in fact you
+
+ align:start position:0%
+are now less than Epsilon in fact you
+ 
+
+ align:start position:0%
+are now less than Epsilon in fact you
+know what to make it nicer I'll make
+
+ align:start position:0%
+know what to make it nicer I'll make
+ 
+
+ align:start position:0%
+know what to make it nicer I'll make
+this Epsilon over two both
+
+ align:start position:0%
+this Epsilon over two both
+ 
+
+ align:start position:0%
+this Epsilon over two both
+spots so then this is less than Epsilon
+
+ align:start position:0%
+spots so then this is less than Epsilon
+ 
+
+ align:start position:0%
+spots so then this is less than Epsilon
+/ 2 plus Epsilon / 2 which is equal to
+
+ align:start position:0%
+/ 2 plus Epsilon / 2 which is equal to
+ 
+
+ align:start position:0%
+/ 2 plus Epsilon / 2 which is equal to
+Epsilon now does this imp immediately
+
+ align:start position:0%
+Epsilon now does this imp immediately
+ 
+
+ align:start position:0%
+Epsilon now does this imp immediately
+that the uh that the distance between
+
+ align:start position:0%
+that the uh that the distance between
+ 
+
+ align:start position:0%
+that the uh that the distance between
+them is zero essentially we have to note
+
+ align:start position:0%
+them is zero essentially we have to note
+ 
+
+ align:start position:0%
+them is zero essentially we have to note
+one more thing which is that distances
+
+ align:start position:0%
+one more thing which is that distances
+ 
+
+ align:start position:0%
+one more thing which is that distances
+are positive definite so this is going
+
+ align:start position:0%
+are positive definite so this is going
+ 
+
+ align:start position:0%
+are positive definite so this is going
+to be bigger than or equal to zero so
+
+ align:start position:0%
+to be bigger than or equal to zero so
+ 
+
+ align:start position:0%
+to be bigger than or equal to zero so
+what this tells you is that because
+
+ align:start position:0%
+what this tells you is that because
+ 
+
+ align:start position:0%
+what this tells you is that because
+these the distance between X and Y gets
+
+ align:start position:0%
+these the distance between X and Y gets
+ 
+
+ align:start position:0%
+these the distance between X and Y gets
+arbitrarily
+
+ align:start position:0%
+arbitrarily
+ 
+
+ align:start position:0%
+arbitrarily
+small and arbitrarily small and close to
+
+ align:start position:0%
+small and arbitrarily small and close to
+ 
+
+ align:start position:0%
+small and arbitrarily small and close to
+zero it has to be zero this is from the
+
+ align:start position:0%
+zero it has to be zero this is from the
+ 
+
+ align:start position:0%
+zero it has to be zero this is from the
+real number theory that we've already
+
+ align:start position:0%
+real number theory that we've already
+ 
+
+ align:start position:0%
+real number theory that we've already
+know so this implies that the distance
+
+ align:start position:0%
+know so this implies that the distance
+ 
+
+ align:start position:0%
+know so this implies that the distance
+from X to y
+
+ align:start position:0%
+from X to y
+ 
+
+ align:start position:0%
+from X to y
+is zero and therefore X is equal to
+
+ align:start position:0%
+is zero and therefore X is equal to
+ 
+
+ align:start position:0%
+is zero and therefore X is equal to
+Y which is what we've wanted to
+
+ align:start position:0%
+Y which is what we've wanted to
+ 
+
+ align:start position:0%
+Y which is what we've wanted to
+prove so notice that a lot of this used
+
+ align:start position:0%
+prove so notice that a lot of this used
+ 
+
+ align:start position:0%
+prove so notice that a lot of this used
+all the aoms that we were talking about
+
+ align:start position:0%
+all the aoms that we were talking about
+ 
+
+ align:start position:0%
+all the aoms that we were talking about
+in one point we use symmetry which
+
+ align:start position:0%
+in one point we use symmetry which
+ 
+
+ align:start position:0%
+in one point we use symmetry which
+wasn't too important but was useful to
+
+ align:start position:0%
+wasn't too important but was useful to
+ 
+
+ align:start position:0%
+wasn't too important but was useful to
+note so that we can swap X and and X
+
+ align:start position:0%
+note so that we can swap X and and X
+ 
+
+ align:start position:0%
+note so that we can swap X and and X
+around and apply the triangle inequality
+
+ align:start position:0%
+around and apply the triangle inequality
+ 
+
+ align:start position:0%
+around and apply the triangle inequality
+we apply the triangle inequality and we
+
+ align:start position:0%
+we apply the triangle inequality and we
+ 
+
+ align:start position:0%
+we apply the triangle inequality and we
+had to use positive definiteness so you
+
+ align:start position:0%
+had to use positive definiteness so you
+ 
+
+ align:start position:0%
+had to use positive definiteness so you
+know these are the Bare Bones of what we
+
+ align:start position:0%
+know these are the Bare Bones of what we
+ 
+
+ align:start position:0%
+know these are the Bare Bones of what we
+really need in the theory
+
+ align:start position:0%
+really need in the theory
+ 
+
+ align:start position:0%
+really need in the theory
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right so now what we're going to do is
+
+ align:start position:0%
+right so now what we're going to do is
+ 
+
+ align:start position:0%
+right so now what we're going to do is
+show that not only do limit points exist
+
+ align:start position:0%
+show that not only do limit points exist
+ 
+
+ align:start position:0%
+show that not only do limit points exist
+nicely but the distances between limit
+
+ align:start position:0%
+nicely but the distances between limit
+ 
+
+ align:start position:0%
+nicely but the distances between limit
+points act
+
+ align:start position:0%
+points act
+ 
+
+ align:start position:0%
+points act
+nicely so to state that more clearly
+
+ align:start position:0%
+nicely so to state that more clearly
+ 
+
+ align:start position:0%
+nicely so to state that more clearly
+theorem let y be an
+
+ align:start position:0%
+theorem let y be an
+ 
+
+ align:start position:0%
+theorem let y be an
+X and xn converge to
+
+ align:start position:0%
+X and xn converge to
+ 
+
+ align:start position:0%
+X and xn converge to
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+then my claim is that the distance from
+
+ align:start position:0%
+then my claim is that the distance from
+ 
+
+ align:start position:0%
+then my claim is that the distance from
+xn to Y will converge from the distance
+
+ align:start position:0%
+xn to Y will converge from the distance
+ 
+
+ align:start position:0%
+xn to Y will converge from the distance
+from X to
+
+ align:start position:0%
+from X to
+ 
+
+ align:start position:0%
+from X to
+Y which makes relative sense but notice
+
+ align:start position:0%
+Y which makes relative sense but notice
+ 
+
+ align:start position:0%
+Y which makes relative sense but notice
+here the statement is slightly different
+
+ align:start position:0%
+here the statement is slightly different
+ 
+
+ align:start position:0%
+here the statement is slightly different
+before we were purely dealing with
+
+ align:start position:0%
+before we were purely dealing with
+ 
+
+ align:start position:0%
+before we were purely dealing with
+sequences of a metric
+
+ align:start position:0%
+sequences of a metric
+ 
+
+ align:start position:0%
+sequences of a metric
+space and so we had to deal with the
+
+ align:start position:0%
+space and so we had to deal with the
+ 
+
+ align:start position:0%
+space and so we had to deal with the
+metric D itself but when we're saying
+
+ align:start position:0%
+metric D itself but when we're saying
+ 
+
+ align:start position:0%
+metric D itself but when we're saying
+that this converges to dxy what space am
+
+ align:start position:0%
+that this converges to dxy what space am
+ 
+
+ align:start position:0%
+that this converges to dxy what space am
+I considering these distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no no worries it's the we're looking
+
+ align:start position:0%
+no no no worries it's the we're looking
+ 
+
+ align:start position:0%
+no no no worries it's the we're looking
+at it in R right because for every
+
+ align:start position:0%
+at it in R right because for every
+ 
+
+ align:start position:0%
+at it in R right because for every
+single n this is just a real number and
+
+ align:start position:0%
+single n this is just a real number and
+ 
+
+ align:start position:0%
+single n this is just a real number and
+so when I say the distance from X and to
+
+ align:start position:0%
+so when I say the distance from X and to
+ 
+
+ align:start position:0%
+so when I say the distance from X and to
+Y converges to the distance from X to Y
+
+ align:start position:0%
+Y converges to the distance from X to Y
+ 
+
+ align:start position:0%
+Y converges to the distance from X to Y
+I mean that this happens in ukian space
+
+ align:start position:0%
+I mean that this happens in ukian space
+ 
+
+ align:start position:0%
+I mean that this happens in ukian space
+and in fact you can likely I don't want
+
+ align:start position:0%
+and in fact you can likely I don't want
+ 
+
+ align:start position:0%
+and in fact you can likely I don't want
+to State explicitly but I'm pretty
+
+ align:start position:0%
+to State explicitly but I'm pretty
+ 
+
+ align:start position:0%
+to State explicitly but I'm pretty
+certain you can prove this as well in a
+
+ align:start position:0%
+certain you can prove this as well in a
+ 
+
+ align:start position:0%
+certain you can prove this as well in a
+general setting so between two metric
+
+ align:start position:0%
+general setting so between two metric
+ 
+
+ align:start position:0%
+general setting so between two metric
+spaces okay so let's prove
+
+ align:start position:0%
+spaces okay so let's prove
+ 
+
+ align:start position:0%
+spaces okay so let's prove
+this to do this we want to show
+
+ align:start position:0%
+this to do this we want to show
+ 
+
+ align:start position:0%
+this to do this we want to show
+ultimately
+
+ align:start position:0%
+ultimately
+ 
+
+ align:start position:0%
+ultimately
+we want to show that for all Epsilon
+
+ align:start position:0%
+we want to show that for all Epsilon
+ 
+
+ align:start position:0%
+we want to show that for all Epsilon
+bigger than
+
+ align:start position:0%
+bigger than
+ 
+
+ align:start position:0%
+bigger than
+zero there exists an n and the natural
+
+ align:start position:0%
+zero there exists an n and the natural
+ 
+
+ align:start position:0%
+zero there exists an n and the natural
+numbers such
+
+ align:start position:0%
+numbers such
+ 
+
+ align:start position:0%
+numbers such
+that the distance from X and to Y minus
+
+ align:start position:0%
+that the distance from X and to Y minus
+ 
+
+ align:start position:0%
+that the distance from X and to Y minus
+the distance from X to
+
+ align:start position:0%
+the distance from X to
+ 
+
+ align:start position:0%
+the distance from X to
+Y is less than Epsilon and absolute
+
+ align:start position:0%
+Y is less than Epsilon and absolute
+ 
+
+ align:start position:0%
+Y is less than Epsilon and absolute
+values and to do so we can just find an
+
+ align:start position:0%
+values and to do so we can just find an
+ 
+
+ align:start position:0%
+values and to do so we can just find an
+upper and lower bound on the distance
+
+ align:start position:0%
+upper and lower bound on the distance
+ 
+
+ align:start position:0%
+upper and lower bound on the distance
+from X to
+
+ align:start position:0%
+from X to
+ 
+
+ align:start position:0%
+from X to
+y or the distance from X and to Y so
+
+ align:start position:0%
+y or the distance from X and to Y so
+ 
+
+ align:start position:0%
+y or the distance from X and to Y so
+let's do that the first Direction
+
+ align:start position:0%
+let's do that the first Direction
+ 
+
+ align:start position:0%
+let's do that the first Direction
+is nice the distance from X to Y is less
+
+ align:start position:0%
+is nice the distance from X to Y is less
+ 
+
+ align:start position:0%
+is nice the distance from X to Y is less
+than or equal to by the triangle
+
+ align:start position:0%
+than or equal to by the triangle
+ 
+
+ align:start position:0%
+than or equal to by the triangle
+inequality the distance from xn to X
+
+ align:start position:0%
+inequality the distance from xn to X
+ 
+
+ align:start position:0%
+inequality the distance from xn to X
+plus the distance from X to
+
+ align:start position:0%
+plus the distance from X to
+ 
+
+ align:start position:0%
+plus the distance from X to
+Y and we can make this term arbitrarily
+
+ align:start position:0%
+Y and we can make this term arbitrarily
+ 
+
+ align:start position:0%
+Y and we can make this term arbitrarily
+small so uh I'm just going to choose the
+
+ align:start position:0%
+small so uh I'm just going to choose the
+ 
+
+ align:start position:0%
+small so uh I'm just going to choose the
+same end to be the one for this
+
+ align:start position:0%
+same end to be the one for this
+ 
+
+ align:start position:0%
+same end to be the one for this
+convergent sequence so this is less than
+
+ align:start position:0%
+convergent sequence so this is less than
+ 
+
+ align:start position:0%
+convergent sequence so this is less than
+Epsilon plus the distance from X to
+
+ align:start position:0%
+Epsilon plus the distance from X to
+ 
+
+ align:start position:0%
+Epsilon plus the distance from X to
+Y so this gives us the upper bound that
+
+ align:start position:0%
+Y so this gives us the upper bound that
+ 
+
+ align:start position:0%
+Y so this gives us the upper bound that
+we're wanting on the distance from X to
+
+ align:start position:0%
+we're wanting on the distance from X to
+ 
+
+ align:start position:0%
+we're wanting on the distance from X to
+Y let's prove the lower lower bound and
+
+ align:start position:0%
+Y let's prove the lower lower bound and
+ 
+
+ align:start position:0%
+Y let's prove the lower lower bound and
+the lower bound is very similar but it's
+
+ align:start position:0%
+the lower bound is very similar but it's
+ 
+
+ align:start position:0%
+the lower bound is very similar but it's
+just a slightly different manipulation
+
+ align:start position:0%
+just a slightly different manipulation
+ 
+
+ align:start position:0%
+just a slightly different manipulation
+where what we're then going to do so the
+
+ align:start position:0%
+where what we're then going to do so the
+ 
+
+ align:start position:0%
+where what we're then going to do so the
+distance from xn to
+
+ align:start position:0%
+distance from xn to
+ 
+
+ align:start position:0%
+distance from xn to
+Y uh actually you know I'll look at the
+
+ align:start position:0%
+Y uh actually you know I'll look at the
+ 
+
+ align:start position:0%
+Y uh actually you know I'll look at the
+distance from X to Y this is less than
+
+ align:start position:0%
+distance from X to Y this is less than
+ 
+
+ align:start position:0%
+distance from X to Y this is less than
+or equal to the distance from X to xn
+
+ align:start position:0%
+or equal to the distance from X to xn
+ 
+
+ align:start position:0%
+or equal to the distance from X to xn
+plus the distance
+
+ align:start position:0%
+plus the distance
+ 
+
+ align:start position:0%
+plus the distance
+from X to Y and then what we can do is
+
+ align:start position:0%
+from X to Y and then what we can do is
+ 
+
+ align:start position:0%
+from X to Y and then what we can do is
+subtract these terms so specifically
+
+ align:start position:0%
+subtract these terms so specifically
+ 
+
+ align:start position:0%
+subtract these terms so specifically
+we'll get that the distance from X to Y
+
+ align:start position:0%
+we'll get that the distance from X to Y
+ 
+
+ align:start position:0%
+we'll get that the distance from X to Y
+minus the distance from X to xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn is less than or equal to the distance
+
+ align:start position:0%
+xn is less than or equal to the distance
+ 
+
+ align:start position:0%
+xn is less than or equal to the distance
+from X to
+
+ align:start position:0%
+from X to
+ 
+
+ align:start position:0%
+from X to
+Y and we can make this term arbitrarily
+
+ align:start position:0%
+Y and we can make this term arbitrarily
+ 
+
+ align:start position:0%
+Y and we can make this term arbitrarily
+small so this is less than the distance
+
+ align:start position:0%
+small so this is less than the distance
+ 
+
+ align:start position:0%
+small so this is less than the distance
+from X to
+
+ align:start position:0%
+from X to
+ 
+
+ align:start position:0%
+from X to
+Y minus Epsilon and notice that this
+
+ align:start position:0%
+Y minus Epsilon and notice that this
+ 
+
+ align:start position:0%
+Y minus Epsilon and notice that this
+implies the result because then we have
+
+ align:start position:0%
+implies the result because then we have
+ 
+
+ align:start position:0%
+implies the result because then we have
+that the distance from xn to Y is less
+
+ align:start position:0%
+that the distance from xn to Y is less
+ 
+
+ align:start position:0%
+that the distance from xn to Y is less
+oh shoot did I do I get this wrong
+
+ align:start position:0%
+oh shoot did I do I get this wrong
+ 
+
+ align:start position:0%
+oh shoot did I do I get this wrong
+uh no no okay yeah so then the distance
+
+ align:start position:0%
+uh no no okay yeah so then the distance
+ 
+
+ align:start position:0%
+uh no no okay yeah so then the distance
+from xn to Y is less
+
+ align:start position:0%
+from xn to Y is less
+ 
+
+ align:start position:0%
+from xn to Y is less
+than sorry this should be the distance
+
+ align:start position:0%
+than sorry this should be the distance
+ 
+
+ align:start position:0%
+than sorry this should be the distance
+from X to Y there we go the distance
+
+ align:start position:0%
+from X to Y there we go the distance
+ 
+
+ align:start position:0%
+from X to Y there we go the distance
+from xn
+
+ align:start position:0%
+from xn
+ 
+
+ align:start position:0%
+from xn
+to let me double check this distance
+
+ align:start position:0%
+to let me double check this distance
+ 
+
+ align:start position:0%
+to let me double check this distance
+from xn to Y
+
+ align:start position:0%
+from xn to Y
+ 
+
+ align:start position:0%
+from xn to Y
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+xn 2 y there we go sorry about that I I
+
+ align:start position:0%
+xn 2 y there we go sorry about that I I
+ 
+
+ align:start position:0%
+xn 2 y there we go sorry about that I I
+mixed up what they were converging
+
+ align:start position:0%
+mixed up what they were converging
+ 
+
+ align:start position:0%
+mixed up what they were converging
+to so what this tells us is that the
+
+ align:start position:0%
+to so what this tells us is that the
+ 
+
+ align:start position:0%
+to so what this tells us is that the
+distance from X into y minus the
+
+ align:start position:0%
+distance from X into y minus the
+ 
+
+ align:start position:0%
+distance from X into y minus the
+distance from X to Y gets arbitrarily
+
+ align:start position:0%
+distance from X to Y gets arbitrarily
+ 
+
+ align:start position:0%
+distance from X to Y gets arbitrarily
+small right I can write that out if
+
+ align:start position:0%
+small right I can write that out if
+ 
+
+ align:start position:0%
+small right I can write that out if
+y'all would prefer uh but that's just
+
+ align:start position:0%
+y'all would prefer uh but that's just
+ 
+
+ align:start position:0%
+y'all would prefer uh but that's just
+the next step you write it in terms of
+
+ align:start position:0%
+the next step you write it in terms of
+ 
+
+ align:start position:0%
+the next step you write it in terms of
+the absolute
+
+ align:start position:0%
+the absolute
+ 
+
+ align:start position:0%
+the absolute
+values okay any
+
+ align:start position:0%
+values okay any
+ 
+
+ align:start position:0%
+values okay any
+questions so not only do limit points be
+
+ align:start position:0%
+questions so not only do limit points be
+ 
+
+ align:start position:0%
+questions so not only do limit points be
+not only are limit points unique but the
+
+ align:start position:0%
+not only are limit points unique but the
+ 
+
+ align:start position:0%
+not only are limit points unique but the
+distances between limit points are also
+
+ align:start position:0%
+distances between limit points are also
+ 
+
+ align:start position:0%
+distances between limit points are also
+going to be unique at least in the real
+
+ align:start position:0%
+going to be unique at least in the real
+ 
+
+ align:start position:0%
+going to be unique at least in the real
+number sense which is pretty nice uh
+
+ align:start position:0%
+number sense which is pretty nice uh
+ 
+
+ align:start position:0%
+number sense which is pretty nice uh
+I'll remark one proposition which is
+
+ align:start position:0%
+I'll remark one proposition which is
+ 
+
+ align:start position:0%
+I'll remark one proposition which is
+pretty interesting
+
+ align:start position:0%
+pretty interesting
+ 
+
+ align:start position:0%
+pretty interesting
+you can study this for two convergent
+
+ align:start position:0%
+you can study this for two convergent
+ 
+
+ align:start position:0%
+you can study this for two convergent
+sequences at once so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose or I I'll State this in two
+
+ align:start position:0%
+suppose or I I'll State this in two
+ 
+
+ align:start position:0%
+suppose or I I'll State this in two
+parts suppose xn converges to X and Y N
+
+ align:start position:0%
+parts suppose xn converges to X and Y N
+ 
+
+ align:start position:0%
+parts suppose xn converges to X and Y N
+converges to
+
+ align:start position:0%
+converges to
+ 
+
+ align:start position:0%
+converges to
+Y then the distance from xn to
+
+ align:start position:0%
+Y then the distance from xn to
+ 
+
+ align:start position:0%
+Y then the distance from xn to
+YN converges to the distance from X to
+
+ align:start position:0%
+YN converges to the distance from X to
+ 
+
+ align:start position:0%
+YN converges to the distance from X to
+Y this relatively makes sense but we can
+
+ align:start position:0%
+Y this relatively makes sense but we can
+ 
+
+ align:start position:0%
+Y this relatively makes sense but we can
+also State this slightly differently or
+
+ align:start position:0%
+also State this slightly differently or
+ 
+
+ align:start position:0%
+also State this slightly differently or
+a different type of this theorem
+
+ align:start position:0%
+a different type of this theorem
+ 
+
+ align:start position:0%
+a different type of this theorem
+suppose xn and YN are koshy so they're
+
+ align:start position:0%
+suppose xn and YN are koshy so they're
+ 
+
+ align:start position:0%
+suppose xn and YN are koshy so they're
+koshy sequences so they get arbitrarily
+
+ align:start position:0%
+koshy sequences so they get arbitrarily
+ 
+
+ align:start position:0%
+koshy sequences so they get arbitrarily
+closed together but don't necessarily
+
+ align:start position:0%
+closed together but don't necessarily
+ 
+
+ align:start position:0%
+closed together but don't necessarily
+have a limit
+
+ align:start position:0%
+have a limit
+ 
+
+ align:start position:0%
+have a limit
+point then we know that the distance
+
+ align:start position:0%
+point then we know that the distance
+ 
+
+ align:start position:0%
+point then we know that the distance
+from xn to
+
+ align:start position:0%
+from xn to
+ 
+
+ align:start position:0%
+from xn to
+YN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges notice that I'm not saying
+
+ align:start position:0%
+converges notice that I'm not saying
+ 
+
+ align:start position:0%
+converges notice that I'm not saying
+that I'm not saying what it converges to
+
+ align:start position:0%
+that I'm not saying what it converges to
+ 
+
+ align:start position:0%
+that I'm not saying what it converges to
+I don't know that Koshi sequences have
+
+ align:start position:0%
+I don't know that Koshi sequences have
+ 
+
+ align:start position:0%
+I don't know that Koshi sequences have
+limit points in my metric space
+
+ align:start position:0%
+limit points in my metric space
+ 
+
+ align:start position:0%
+limit points in my metric space
+uh and I'll get back to that in a moment
+
+ align:start position:0%
+uh and I'll get back to that in a moment
+ 
+
+ align:start position:0%
+uh and I'll get back to that in a moment
+but nonetheless the sequence itself in
+
+ align:start position:0%
+but nonetheless the sequence itself in
+ 
+
+ align:start position:0%
+but nonetheless the sequence itself in
+the real numbers will converge and that
+
+ align:start position:0%
+the real numbers will converge and that
+ 
+
+ align:start position:0%
+the real numbers will converge and that
+uses the fact that the real numbers is
+
+ align:start position:0%
+uses the fact that the real numbers is
+ 
+
+ align:start position:0%
+uses the fact that the real numbers is
+Koshi
+
+ align:start position:0%
+Koshi
+ 
+
+ align:start position:0%
+Koshi
+complete now I'm not going to prove
+
+ align:start position:0%
+complete now I'm not going to prove
+ 
+
+ align:start position:0%
+complete now I'm not going to prove
+these two facts these are facts that are
+
+ align:start position:0%
+these two facts these are facts that are
+ 
+
+ align:start position:0%
+these two facts these are facts that are
+uh on your problem set but I do want to
+
+ align:start position:0%
+uh on your problem set but I do want to
+ 
+
+ align:start position:0%
+uh on your problem set but I do want to
+point out because this happened a lot
+
+ align:start position:0%
+point out because this happened a lot
+ 
+
+ align:start position:0%
+point out because this happened a lot
+last year you cannot assume that the
+
+ align:start position:0%
+last year you cannot assume that the
+ 
+
+ align:start position:0%
+last year you cannot assume that the
+limit points in the second part exist
+
+ align:start position:0%
+limit points in the second part exist
+ 
+
+ align:start position:0%
+limit points in the second part exist
+you can know that this implication
+
+ align:start position:0%
+you can know that this implication
+ 
+
+ align:start position:0%
+you can know that this implication
+implies the top one by uniqueness
+
+ align:start position:0%
+implies the top one by uniqueness
+ 
+
+ align:start position:0%
+implies the top one by uniqueness
+because convergent sequences are koshy
+
+ align:start position:0%
+because convergent sequences are koshy
+ 
+
+ align:start position:0%
+because convergent sequences are koshy
+as we're going to prove right now um so
+
+ align:start position:0%
+as we're going to prove right now um so
+ 
+
+ align:start position:0%
+as we're going to prove right now um so
+if you prove the second one first then
+
+ align:start position:0%
+if you prove the second one first then
+ 
+
+ align:start position:0%
+if you prove the second one first then
+you can make a small remark you have to
+
+ align:start position:0%
+you can make a small remark you have to
+ 
+
+ align:start position:0%
+you can make a small remark you have to
+explain why the limit point is the
+
+ align:start position:0%
+explain why the limit point is the
+ 
+
+ align:start position:0%
+explain why the limit point is the
+distance from X to Y but that's not too
+
+ align:start position:0%
+distance from X to Y but that's not too
+ 
+
+ align:start position:0%
+distance from X to Y but that's not too
+bad
+
+ align:start position:0%
+bad
+ 
+
+ align:start position:0%
+bad
+so let's prove that
+
+ align:start position:0%
+so let's prove that
+ 
+
+ align:start position:0%
+so let's prove that
+theorem uh is that the next theorem I
+
+ align:start position:0%
+theorem uh is that the next theorem I
+ 
+
+ align:start position:0%
+theorem uh is that the next theorem I
+wanted to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah I'll do that one
+
+ align:start position:0%
+uh yeah I'll do that one
+ 
+
+ align:start position:0%
+uh yeah I'll do that one
+now Koshi sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh sorry convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+sequences are kosi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+proof
+
+ align:start position:0%
+proof
+ 
+
+ align:start position:0%
+proof
+suppose xn is the convergent sequence
+
+ align:start position:0%
+suppose xn is the convergent sequence
+ 
+
+ align:start position:0%
+suppose xn is the convergent sequence
+we're considering and that xn converges
+
+ align:start position:0%
+we're considering and that xn converges
+ 
+
+ align:start position:0%
+we're considering and that xn converges
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+X then we know that and I'm going to
+
+ align:start position:0%
+X then we know that and I'm going to
+ 
+
+ align:start position:0%
+X then we know that and I'm going to
+State this over and over again just like
+
+ align:start position:0%
+State this over and over again just like
+ 
+
+ align:start position:0%
+State this over and over again just like
+we do in real analysis but at a certain
+
+ align:start position:0%
+we do in real analysis but at a certain
+ 
+
+ align:start position:0%
+we do in real analysis but at a certain
+point it just BEC secondhand nature uh
+
+ align:start position:0%
+point it just BEC secondhand nature uh
+ 
+
+ align:start position:0%
+point it just BEC secondhand nature uh
+so therefore for all Epson bigger than
+
+ align:start position:0%
+so therefore for all Epson bigger than
+ 
+
+ align:start position:0%
+so therefore for all Epson bigger than
+zero there exists n in the natural
+
+ align:start position:0%
+zero there exists n in the natural
+ 
+
+ align:start position:0%
+zero there exists n in the natural
+numbers such
+
+ align:start position:0%
+numbers such
+ 
+
+ align:start position:0%
+numbers such
+that uh the uh such that for all n
+
+ align:start position:0%
+that uh the uh such that for all n
+ 
+
+ align:start position:0%
+that uh the uh such that for all n
+bigger than or equal to n the distance
+
+ align:start position:0%
+bigger than or equal to n the distance
+ 
+
+ align:start position:0%
+bigger than or equal to n the distance
+from xn to X is less than Epsilon so
+
+ align:start position:0%
+from xn to X is less than Epsilon so
+ 
+
+ align:start position:0%
+from xn to X is less than Epsilon so
+what does this tell us well what we're
+
+ align:start position:0%
+what does this tell us well what we're
+ 
+
+ align:start position:0%
+what does this tell us well what we're
+ultimately interested in is the distance
+
+ align:start position:0%
+ultimately interested in is the distance
+ 
+
+ align:start position:0%
+ultimately interested in is the distance
+from xn to XM right
+
+ align:start position:0%
+from xn to XM right
+ 
+
+ align:start position:0%
+from xn to XM right
+let M be bigger than or equal to n what
+
+ align:start position:0%
+let M be bigger than or equal to n what
+ 
+
+ align:start position:0%
+let M be bigger than or equal to n what
+we're interested in is the distance from
+
+ align:start position:0%
+we're interested in is the distance from
+ 
+
+ align:start position:0%
+we're interested in is the distance from
+X and to XM to state that it's a Koshi
+
+ align:start position:0%
+X and to XM to state that it's a Koshi
+ 
+
+ align:start position:0%
+X and to XM to state that it's a Koshi
+sequence so what can we
+
+ align:start position:0%
+sequence so what can we
+ 
+
+ align:start position:0%
+sequence so what can we
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone sort
+
+ align:start position:0%
+anyone sort
+ 
+
+ align:start position:0%
+anyone sort
+of want yall to think about it because
+
+ align:start position:0%
+of want yall to think about it because
+ 
+
+ align:start position:0%
+of want yall to think about it because
+there's we want to bound this and show
+
+ align:start position:0%
+there's we want to bound this and show
+ 
+
+ align:start position:0%
+there's we want to bound this and show
+that this is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon exactly the triangle inequality
+
+ align:start position:0%
+Epsilon exactly the triangle inequality
+ 
+
+ align:start position:0%
+Epsilon exactly the triangle inequality
+this is less than or equal to the
+
+ align:start position:0%
+this is less than or equal to the
+ 
+
+ align:start position:0%
+this is less than or equal to the
+distance from xn to X plus the distance
+
+ align:start position:0%
+distance from xn to X plus the distance
+ 
+
+ align:start position:0%
+distance from xn to X plus the distance
+from X or X to
+
+ align:start position:0%
+from X or X to
+ 
+
+ align:start position:0%
+from X or X to
+XM and we can make both of these less
+
+ align:start position:0%
+XM and we can make both of these less
+ 
+
+ align:start position:0%
+XM and we can make both of these less
+than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon now if I was really careful I
+
+ align:start position:0%
+Epsilon now if I was really careful I
+ 
+
+ align:start position:0%
+Epsilon now if I was really careful I
+could have made these epsilons over two
+
+ align:start position:0%
+could have made these epsilons over two
+ 
+
+ align:start position:0%
+could have made these epsilons over two
+and then this would have been exactly
+
+ align:start position:0%
+and then this would have been exactly
+ 
+
+ align:start position:0%
+and then this would have been exactly
+Epsilon most of the time if you show
+
+ align:start position:0%
+Epsilon most of the time if you show
+ 
+
+ align:start position:0%
+Epsilon most of the time if you show
+it's less than a constant time Epsilon
+
+ align:start position:0%
+it's less than a constant time Epsilon
+ 
+
+ align:start position:0%
+it's less than a constant time Epsilon
+you're good you would just have to
+
+ align:start position:0%
+you're good you would just have to
+ 
+
+ align:start position:0%
+you're good you would just have to
+relabel things so all good things here
+
+ align:start position:0%
+relabel things so all good things here
+ 
+
+ align:start position:0%
+relabel things so all good things here
+but yeah exactly you apply the triangle
+
+ align:start position:0%
+but yeah exactly you apply the triangle
+ 
+
+ align:start position:0%
+but yeah exactly you apply the triangle
+inequality and notice oh and then this
+
+ align:start position:0%
+inequality and notice oh and then this
+ 
+
+ align:start position:0%
+inequality and notice oh and then this
+is precisely what we want for a Koshi
+
+ align:start position:0%
+is precisely what we want for a Koshi
+ 
+
+ align:start position:0%
+is precisely what we want for a Koshi
+sequence right this implies that it is
+
+ align:start position:0%
+sequence right this implies that it is
+ 
+
+ align:start position:0%
+sequence right this implies that it is
+in fact a koshy
+
+ align:start position:0%
+in fact a koshy
+ 
+
+ align:start position:0%
+in fact a koshy
+sequence so we're
+
+ align:start position:0%
+sequence so we're
+ 
+
+ align:start position:0%
+sequence so we're
+done uh now the real question is if
+
+ align:start position:0%
+done uh now the real question is if
+ 
+
+ align:start position:0%
+done uh now the real question is if
+koshy sequences are convergent sequences
+
+ align:start position:0%
+koshy sequences are convergent sequences
+ 
+
+ align:start position:0%
+koshy sequences are convergent sequences
+and as we know from the real numbers
+
+ align:start position:0%
+and as we know from the real numbers
+ 
+
+ align:start position:0%
+and as we know from the real numbers
+this is not always or from the real
+
+ align:start position:0%
+this is not always or from the real
+ 
+
+ align:start position:0%
+this is not always or from the real
+numbers we know that there it's Koshi
+
+ align:start position:0%
+numbers we know that there it's Koshi
+ 
+
+ align:start position:0%
+numbers we know that there it's Koshi
+complete but here we don't and what do I
+
+ align:start position:0%
+complete but here we don't and what do I
+ 
+
+ align:start position:0%
+complete but here we don't and what do I
+mean by Koshi complete which I've stated
+
+ align:start position:0%
+mean by Koshi complete which I've stated
+ 
+
+ align:start position:0%
+mean by Koshi complete which I've stated
+a few times
+
+ align:start position:0%
+a few times
+ 
+
+ align:start position:0%
+a few times
+definition a
+
+ align:start position:0%
+definition a
+ 
+
+ align:start position:0%
+definition a
+space is Koshi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete if and only if I.E the
+
+ align:start position:0%
+complete if and only if I.E the
+ 
+
+ align:start position:0%
+complete if and only if I.E the
+definition uh the Koshi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergent so this is the definition of
+
+ align:start position:0%
+convergent so this is the definition of
+ 
+
+ align:start position:0%
+convergent so this is the definition of
+what Koshi complete actually means and
+
+ align:start position:0%
+what Koshi complete actually means and
+ 
+
+ align:start position:0%
+what Koshi complete actually means and
+this is a very powerful fact right we
+
+ align:start position:0%
+this is a very powerful fact right we
+ 
+
+ align:start position:0%
+this is a very powerful fact right we
+use Co completeness everywhere in real
+
+ align:start position:0%
+use Co completeness everywhere in real
+ 
+
+ align:start position:0%
+use Co completeness everywhere in real
+analysis to state that limit points
+
+ align:start position:0%
+analysis to state that limit points
+ 
+
+ align:start position:0%
+analysis to state that limit points
+exist to state that differentiability
+
+ align:start position:0%
+exist to state that differentiability
+ 
+
+ align:start position:0%
+exist to state that differentiability
+was nice things like that we we needed
+
+ align:start position:0%
+was nice things like that we we needed
+ 
+
+ align:start position:0%
+was nice things like that we we needed
+Koshi completeness there now not every
+
+ align:start position:0%
+Koshi completeness there now not every
+ 
+
+ align:start position:0%
+Koshi completeness there now not every
+space is Koshi complete unfortunately
+
+ align:start position:0%
+space is Koshi complete unfortunately
+ 
+
+ align:start position:0%
+space is Koshi complete unfortunately
+but the ones that we really want them to
+
+ align:start position:0%
+but the ones that we really want them to
+ 
+
+ align:start position:0%
+but the ones that we really want them to
+be are in fact so uh proposition this is
+
+ align:start position:0%
+be are in fact so uh proposition this is
+ 
+
+ align:start position:0%
+be are in fact so uh proposition this is
+on your
+
+ align:start position:0%
+on your
+ 
+
+ align:start position:0%
+on your
+homework we have
+
+ align:start position:0%
+homework we have
+ 
+
+ align:start position:0%
+homework we have
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah the set of continuous functions on
+
+ align:start position:0%
+yeah the set of continuous functions on
+ 
+
+ align:start position:0%
+yeah the set of continuous functions on
+0 to one is Koshi complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a statement on your homework
+
+ align:start position:0%
+this is a statement on your homework
+ 
+
+ align:start position:0%
+this is a statement on your homework
+that I've broken up into individual
+
+ align:start position:0%
+that I've broken up into individual
+ 
+
+ align:start position:0%
+that I've broken up into individual
+steps so they should be a little bit
+
+ align:start position:0%
+steps so they should be a little bit
+ 
+
+ align:start position:0%
+steps so they should be a little bit
+nicer um but yeah a very useful
+
+ align:start position:0%
+nicer um but yeah a very useful
+ 
+
+ align:start position:0%
+nicer um but yeah a very useful
+proposition to show okay now let me go
+
+ align:start position:0%
+proposition to show okay now let me go
+ 
+
+ align:start position:0%
+proposition to show okay now let me go
+back to what I meant to do slightly
+
+ align:start position:0%
+back to what I meant to do slightly
+ 
+
+ align:start position:0%
+back to what I meant to do slightly
+earlier okay we have a few more things
+
+ align:start position:0%
+earlier okay we have a few more things
+ 
+
+ align:start position:0%
+earlier okay we have a few more things
+to say about uh Co convergent sequences
+
+ align:start position:0%
+to say about uh Co convergent sequences
+ 
+
+ align:start position:0%
+to say about uh Co convergent sequences
+and to do so I'm going to Define what it
+
+ align:start position:0%
+and to do so I'm going to Define what it
+ 
+
+ align:start position:0%
+and to do so I'm going to Define what it
+means for a set to be bounded right when
+
+ align:start position:0%
+means for a set to be bounded right when
+ 
+
+ align:start position:0%
+means for a set to be bounded right when
+we were looking at real analysis one of
+
+ align:start position:0%
+we were looking at real analysis one of
+ 
+
+ align:start position:0%
+we were looking at real analysis one of
+the most useful theorems we had in our
+
+ align:start position:0%
+the most useful theorems we had in our
+ 
+
+ align:start position:0%
+the most useful theorems we had in our
+tool belt was the bosano virus drust
+
+ align:start position:0%
+tool belt was the bosano virus drust
+ 
+
+ align:start position:0%
+tool belt was the bosano virus drust
+theorem now we're not going to have an
+
+ align:start position:0%
+theorem now we're not going to have an
+ 
+
+ align:start position:0%
+theorem now we're not going to have an
+analog of it but we still have some
+
+ align:start position:0%
+analog of it but we still have some
+ 
+
+ align:start position:0%
+analog of it but we still have some
+statements akin to it that we want to
+
+ align:start position:0%
+statements akin to it that we want to
+ 
+
+ align:start position:0%
+statements akin to it that we want to
+show uh and this will be especially
+
+ align:start position:0%
+show uh and this will be especially
+ 
+
+ align:start position:0%
+show uh and this will be especially
+important as we build up to compact
+
+ align:start position:0%
+important as we build up to compact
+ 
+
+ align:start position:0%
+important as we build up to compact
+sets so
+
+ align:start position:0%
+sets so
+ 
+
+ align:start position:0%
+sets so
+definition a sequence
+
+ align:start position:0%
+definition a sequence
+ 
+
+ align:start position:0%
+definition a sequence
+xn is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded by let's say B bigger than zero
+
+ align:start position:0%
+bounded by let's say B bigger than zero
+ 
+
+ align:start position:0%
+bounded by let's say B bigger than zero
+if for all n in the natural
+
+ align:start position:0%
+if for all n in the natural
+ 
+
+ align:start position:0%
+if for all n in the natural
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+uh oh sorry I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say if there exists a point p in your
+
+ align:start position:0%
+say if there exists a point p in your
+ 
+
+ align:start position:0%
+say if there exists a point p in your
+metrics base such that for all n and the
+
+ align:start position:0%
+metrics base such that for all n and the
+ 
+
+ align:start position:0%
+metrics base such that for all n and the
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+numbers the distance from
+
+ align:start position:0%
+numbers the distance from
+ 
+
+ align:start position:0%
+numbers the distance from
+xn to P is less than b which is what we
+
+ align:start position:0%
+xn to P is less than b which is what we
+ 
+
+ align:start position:0%
+xn to P is less than b which is what we
+would expect we want the convergent we
+
+ align:start position:0%
+would expect we want the convergent we
+ 
+
+ align:start position:0%
+would expect we want the convergent we
+want the sequence itself to to be the
+
+ align:start position:0%
+want the sequence itself to to be the
+ 
+
+ align:start position:0%
+want the sequence itself to to be the
+distance between the point and your
+
+ align:start position:0%
+distance between the point and your
+ 
+
+ align:start position:0%
+distance between the point and your
+sequence to be bounded that's what it
+
+ align:start position:0%
+sequence to be bounded that's what it
+ 
+
+ align:start position:0%
+sequence to be bounded that's what it
+means for a sequence to be
+
+ align:start position:0%
+means for a sequence to be
+ 
+
+ align:start position:0%
+means for a sequence to be
+bounded and if you want to picture this
+
+ align:start position:0%
+bounded and if you want to picture this
+ 
+
+ align:start position:0%
+bounded and if you want to picture this
+uh you can I always like to draw little
+
+ align:start position:0%
+uh you can I always like to draw little
+ 
+
+ align:start position:0%
+uh you can I always like to draw little
+pictures in my notes about this if this
+
+ align:start position:0%
+pictures in my notes about this if this
+ 
+
+ align:start position:0%
+pictures in my notes about this if this
+is our metric base X here's our Point p
+
+ align:start position:0%
+is our metric base X here's our Point p
+ 
+
+ align:start position:0%
+is our metric base X here's our Point p
+and what this is stating is that there
+
+ align:start position:0%
+and what this is stating is that there
+ 
+
+ align:start position:0%
+and what this is stating is that there
+exists a radius large
+
+ align:start position:0%
+exists a radius large
+ 
+
+ align:start position:0%
+exists a radius large
+enough of radius R sorry not R of radius
+
+ align:start position:0%
+enough of radius R sorry not R of radius
+ 
+
+ align:start position:0%
+enough of radius R sorry not R of radius
+B such that it completely contains X
+
+ align:start position:0%
+B such that it completely contains X
+ 
+
+ align:start position:0%
+B such that it completely contains X
+now granted what does it mean to have
+
+ align:start position:0%
+now granted what does it mean to have
+ 
+
+ align:start position:0%
+now granted what does it mean to have
+stuff outside of X nothing really so
+
+ align:start position:0%
+stuff outside of X nothing really so
+ 
+
+ align:start position:0%
+stuff outside of X nothing really so
+really we just mean the
+
+ align:start position:0%
+really we just mean the
+ 
+
+ align:start position:0%
+really we just mean the
+region in the middle is contained in the
+
+ align:start position:0%
+region in the middle is contained in the
+ 
+
+ align:start position:0%
+region in the middle is contained in the
+ball of radius r or radius B but that's
+
+ align:start position:0%
+ball of radius r or radius B but that's
+ 
+
+ align:start position:0%
+ball of radius r or radius B but that's
+a nice picture if you prefer and not
+
+ align:start position:0%
+a nice picture if you prefer and not
+ 
+
+ align:start position:0%
+a nice picture if you prefer and not
+only can we say this about convergent
+
+ align:start position:0%
+only can we say this about convergent
+ 
+
+ align:start position:0%
+only can we say this about convergent
+sequences or sorry not only can we say
+
+ align:start position:0%
+sequences or sorry not only can we say
+ 
+
+ align:start position:0%
+sequences or sorry not only can we say
+this about sequences in general we can
+
+ align:start position:0%
+this about sequences in general we can
+ 
+
+ align:start position:0%
+this about sequences in general we can
+also Define what this means for a
+
+ align:start position:0%
+also Define what this means for a
+ 
+
+ align:start position:0%
+also Define what this means for a
+set a
+
+ align:start position:0%
+set a
+ 
+
+ align:start position:0%
+set a
+set a in
+
+ align:start position:0%
+set a in
+ 
+
+ align:start position:0%
+set a in
+X is bounded
+
+ align:start position:0%
+X is bounded
+ 
+
+ align:start position:0%
+X is bounded
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+if for
+
+ align:start position:0%
+if for
+ 
+
+ align:start position:0%
+if for
+all p in X oh sorry if there exists a p
+
+ align:start position:0%
+all p in X oh sorry if there exists a p
+ 
+
+ align:start position:0%
+all p in X oh sorry if there exists a p
+in X such that for all a and
+
+ align:start position:0%
+in X such that for all a and
+ 
+
+ align:start position:0%
+in X such that for all a and
+a the distance from a to
+
+ align:start position:0%
+a the distance from a to
+ 
+
+ align:start position:0%
+a the distance from a to
+P is less than
+
+ align:start position:0%
+P is less than
+ 
+
+ align:start position:0%
+P is less than
+b does the uh set theory notation that
+
+ align:start position:0%
+b does the uh set theory notation that
+ 
+
+ align:start position:0%
+b does the uh set theory notation that
+I'm using make sense to everyone there
+
+ align:start position:0%
+I'm using make sense to everyone there
+ 
+
+ align:start position:0%
+I'm using make sense to everyone there
+exists in for all cool so this is what
+
+ align:start position:0%
+exists in for all cool so this is what
+ 
+
+ align:start position:0%
+exists in for all cool so this is what
+it means for a sequence and a set to be
+
+ align:start position:0%
+it means for a sequence and a set to be
+ 
+
+ align:start position:0%
+it means for a sequence and a set to be
+bounded why do I bring this up because
+
+ align:start position:0%
+bounded why do I bring this up because
+ 
+
+ align:start position:0%
+bounded why do I bring this up because
+convergent sequences are bounded
+
+ align:start position:0%
+convergent sequences are bounded
+ 
+
+ align:start position:0%
+convergent sequences are bounded
+sequences we have this from real
+
+ align:start position:0%
+sequences we have this from real
+ 
+
+ align:start position:0%
+sequences we have this from real
+analysis but I'm going to prove it now
+
+ align:start position:0%
+analysis but I'm going to prove it now
+ 
+
+ align:start position:0%
+analysis but I'm going to prove it now
+in metric
+
+ align:start position:0%
+in metric
+ 
+
+ align:start position:0%
+in metric
+baces so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proposition or I should I'll just write
+
+ align:start position:0%
+proposition or I should I'll just write
+ 
+
+ align:start position:0%
+proposition or I should I'll just write
+it out how I've been writing out the
+
+ align:start position:0%
+it out how I've been writing out the
+ 
+
+ align:start position:0%
+it out how I've been writing out the
+other ones if xn converges to X then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn is a bounded sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's start off with the proof
+
+ align:start position:0%
+okay let's start off with the proof
+ 
+
+ align:start position:0%
+okay let's start off with the proof
+which we'll start off as all of our
+
+ align:start position:0%
+which we'll start off as all of our
+ 
+
+ align:start position:0%
+which we'll start off as all of our
+statements have so far with the
+
+ align:start position:0%
+statements have so far with the
+ 
+
+ align:start position:0%
+statements have so far with the
+statement of what uh of what convergence
+
+ align:start position:0%
+statement of what uh of what convergence
+ 
+
+ align:start position:0%
+statement of what uh of what convergence
+means and the statement of what
+
+ align:start position:0%
+means and the statement of what
+ 
+
+ align:start position:0%
+means and the statement of what
+convergence means I'm going to choose
+
+ align:start position:0%
+convergence means I'm going to choose
+ 
+
+ align:start position:0%
+convergence means I'm going to choose
+the Epsilon that I want so that I'm not
+
+ align:start position:0%
+the Epsilon that I want so that I'm not
+ 
+
+ align:start position:0%
+the Epsilon that I want so that I'm not
+dealing with all the possible epsilons
+
+ align:start position:0%
+dealing with all the possible epsilons
+ 
+
+ align:start position:0%
+dealing with all the possible epsilons
+so I'm going to
+
+ align:start position:0%
+so I'm going to
+ 
+
+ align:start position:0%
+so I'm going to
+note for Epsilon equal to one bigger
+
+ align:start position:0%
+note for Epsilon equal to one bigger
+ 
+
+ align:start position:0%
+note for Epsilon equal to one bigger
+than zero we know that there exists an n
+
+ align:start position:0%
+than zero we know that there exists an n
+ 
+
+ align:start position:0%
+than zero we know that there exists an n
+in the natural
+
+ align:start position:0%
+in the natural
+ 
+
+ align:start position:0%
+in the natural
+numbers such that the distance from such
+
+ align:start position:0%
+numbers such that the distance from such
+ 
+
+ align:start position:0%
+numbers such that the distance from such
+that for
+
+ align:start position:0%
+that for
+ 
+
+ align:start position:0%
+that for
+all n bigger than or equal to
+
+ align:start position:0%
+all n bigger than or equal to
+ 
+
+ align:start position:0%
+all n bigger than or equal to
+n the distance from xn to X is less than
+
+ align:start position:0%
+n the distance from xn to X is less than
+ 
+
+ align:start position:0%
+n the distance from xn to X is less than
+Epsilon which again I'm assuming is
+
+ align:start position:0%
+Epsilon which again I'm assuming is
+ 
+
+ align:start position:0%
+Epsilon which again I'm assuming is
+one now does this complete our statement
+
+ align:start position:0%
+one now does this complete our statement
+ 
+
+ align:start position:0%
+one now does this complete our statement
+the answer is no here we only have that
+
+ align:start position:0%
+the answer is no here we only have that
+ 
+
+ align:start position:0%
+the answer is no here we only have that
+this is true for all n bigger than or
+
+ align:start position:0%
+this is true for all n bigger than or
+ 
+
+ align:start position:0%
+this is true for all n bigger than or
+equal to capital N right but what we
+
+ align:start position:0%
+equal to capital N right but what we
+ 
+
+ align:start position:0%
+equal to capital N right but what we
+want for our
+
+ align:start position:0%
+want for our
+ 
+
+ align:start position:0%
+want for our
+statement is to to show that for every
+
+ align:start position:0%
+statement is to to show that for every
+ 
+
+ align:start position:0%
+statement is to to show that for every
+single natural number this sequence is
+
+ align:start position:0%
+single natural number this sequence is
+ 
+
+ align:start position:0%
+single natural number this sequence is
+bounded but this isn't an issue because
+
+ align:start position:0%
+bounded but this isn't an issue because
+ 
+
+ align:start position:0%
+bounded but this isn't an issue because
+what we can note is that there are
+
+ align:start position:0%
+what we can note is that there are
+ 
+
+ align:start position:0%
+what we can note is that there are
+finitely many terms less than n in the
+
+ align:start position:0%
+finitely many terms less than n in the
+ 
+
+ align:start position:0%
+finitely many terms less than n in the
+natural numbers right so what we can
+
+ align:start position:0%
+natural numbers right so what we can
+ 
+
+ align:start position:0%
+natural numbers right so what we can
+do is that
+
+ align:start position:0%
+do is that
+ 
+
+ align:start position:0%
+do is that
+b be the maximum of the finitely many
+
+ align:start position:0%
+b be the maximum of the finitely many
+ 
+
+ align:start position:0%
+b be the maximum of the finitely many
+terms of the distance from x i tox or
+
+ align:start position:0%
+terms of the distance from x i tox or
+ 
+
+ align:start position:0%
+terms of the distance from x i tox or
+let's say uh
+
+ align:start position:0%
+let's say uh
+ 
+
+ align:start position:0%
+let's say uh
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+one for I between 1 and capital
+
+ align:start position:0%
+one for I between 1 and capital
+ 
+
+ align:start position:0%
+one for I between 1 and capital
+N so what I'm doing here is I'm noting
+
+ align:start position:0%
+N so what I'm doing here is I'm noting
+ 
+
+ align:start position:0%
+N so what I'm doing here is I'm noting
+that here I have my convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence I know that most of them in
+
+ align:start position:0%
+sequence I know that most of them in
+ 
+
+ align:start position:0%
+sequence I know that most of them in
+fact infinitely many of them are
+
+ align:start position:0%
+fact infinitely many of them are
+ 
+
+ align:start position:0%
+fact infinitely many of them are
+contained uh are contained in a ball of
+
+ align:start position:0%
+contained uh are contained in a ball of
+ 
+
+ align:start position:0%
+contained uh are contained in a ball of
+radius
+
+ align:start position:0%
+radius
+ 
+
+ align:start position:0%
+radius
+one and I only have finitely many terms
+
+ align:start position:0%
+one and I only have finitely many terms
+ 
+
+ align:start position:0%
+one and I only have finitely many terms
+outside of that ball
+
+ align:start position:0%
+outside of that ball
+ 
+
+ align:start position:0%
+outside of that ball
+so what I'm doing is I'm saying okay
+
+ align:start position:0%
+so what I'm doing is I'm saying okay
+ 
+
+ align:start position:0%
+so what I'm doing is I'm saying okay
+well it's either in this ball or the
+
+ align:start position:0%
+well it's either in this ball or the
+ 
+
+ align:start position:0%
+well it's either in this ball or the
+next one or the next one or so on and so
+
+ align:start position:0%
+next one or the next one or so on and so
+ 
+
+ align:start position:0%
+next one or the next one or so on and so
+forth this is what the statement is that
+
+ align:start position:0%
+forth this is what the statement is that
+ 
+
+ align:start position:0%
+forth this is what the statement is that
+we wanted to show and we know that this
+
+ align:start position:0%
+we wanted to show and we know that this
+ 
+
+ align:start position:0%
+we wanted to show and we know that this
+is in fact
+
+ align:start position:0%
+is in fact
+ 
+
+ align:start position:0%
+is in fact
+finite as there was only finitely many
+
+ align:start position:0%
+finite as there was only finitely many
+ 
+
+ align:start position:0%
+finite as there was only finitely many
+terms so this is the B that it's bounded
+
+ align:start position:0%
+terms so this is the B that it's bounded
+ 
+
+ align:start position:0%
+terms so this is the B that it's bounded
+by I can write that out some more if
+
+ align:start position:0%
+by I can write that out some more if
+ 
+
+ align:start position:0%
+by I can write that out some more if
+yall would prefer but this is
+
+ align:start position:0%
+yall would prefer but this is
+ 
+
+ align:start position:0%
+yall would prefer but this is
+essentially the
+
+ align:start position:0%
+essentially the
+ 
+
+ align:start position:0%
+essentially the
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+cool uh so
+
+ align:start position:0%
+cool uh so
+ 
+
+ align:start position:0%
+cool uh so
+I think that's mostly oh there's one
+
+ align:start position:0%
+I think that's mostly oh there's one
+ 
+
+ align:start position:0%
+I think that's mostly oh there's one
+more thing we want to say about
+
+ align:start position:0%
+more thing we want to say about
+ 
+
+ align:start position:0%
+more thing we want to say about
+convergent
+
+ align:start position:0%
+convergent
+ 
+
+ align:start position:0%
+convergent
+sequences which is that their
+
+ align:start position:0%
+sequences which is that their
+ 
+
+ align:start position:0%
+sequences which is that their
+subsequences act nicely which will be
+
+ align:start position:0%
+subsequences act nicely which will be
+ 
+
+ align:start position:0%
+subsequences act nicely which will be
+essentially how we want it to be um
+
+ align:start position:0%
+essentially how we want it to be um
+ 
+
+ align:start position:0%
+essentially how we want it to be um
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proposition let xn converge to
+
+ align:start position:0%
+proposition let xn converge to
+ 
+
+ align:start position:0%
+proposition let xn converge to
+X and xn
+
+ align:start position:0%
+X and xn
+ 
+
+ align:start position:0%
+X and xn
+K be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence of xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then my
+
+ align:start position:0%
+then my
+ 
+
+ align:start position:0%
+then my
+claim is that xn
+
+ align:start position:0%
+claim is that xn
+ 
+
+ align:start position:0%
+claim is that xn
+K is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergent and in fact to show that it's
+
+ align:start position:0%
+convergent and in fact to show that it's
+ 
+
+ align:start position:0%
+convergent and in fact to show that it's
+convergent we're going to show that it
+
+ align:start position:0%
+convergent we're going to show that it
+ 
+
+ align:start position:0%
+convergent we're going to show that it
+converges to X right which is what we
+
+ align:start position:0%
+converges to X right which is what we
+ 
+
+ align:start position:0%
+converges to X right which is what we
+should expect of a subsequence does
+
+ align:start position:0%
+should expect of a subsequence does
+ 
+
+ align:start position:0%
+should expect of a subsequence does
+everyone here know what a subsequence is
+
+ align:start position:0%
+everyone here know what a subsequence is
+ 
+
+ align:start position:0%
+everyone here know what a subsequence is
+happy to redefine
+
+ align:start position:0%
+happy to redefine
+ 
+
+ align:start position:0%
+happy to redefine
+um cool um so let's go with the
+
+ align:start position:0%
+um cool um so let's go with the
+ 
+
+ align:start position:0%
+um cool um so let's go with the
+statement so proof notice that my
+
+ align:start position:0%
+statement so proof notice that my
+ 
+
+ align:start position:0%
+statement so proof notice that my
+subsequence here is arbitrary I'm not
+
+ align:start position:0%
+subsequence here is arbitrary I'm not
+ 
+
+ align:start position:0%
+subsequence here is arbitrary I'm not
+going to rewrite that out but we could
+
+ align:start position:0%
+going to rewrite that out but we could
+ 
+
+ align:start position:0%
+going to rewrite that out but we could
+choose any subsequence of our sequence
+
+ align:start position:0%
+choose any subsequence of our sequence
+ 
+
+ align:start position:0%
+choose any subsequence of our sequence
+and what we're interested in is we want
+
+ align:start position:0%
+and what we're interested in is we want
+ 
+
+ align:start position:0%
+and what we're interested in is we want
+to show for all Epsilon bigger than zero
+
+ align:start position:0%
+to show for all Epsilon bigger than zero
+ 
+
+ align:start position:0%
+to show for all Epsilon bigger than zero
+there existant n in the natural
+
+ align:start position:0%
+there existant n in the natural
+ 
+
+ align:start position:0%
+there existant n in the natural
+numbers such
+
+ align:start position:0%
+numbers such
+ 
+
+ align:start position:0%
+numbers such
+that for all n k now bigger than or
+
+ align:start position:0%
+that for all n k now bigger than or
+ 
+
+ align:start position:0%
+that for all n k now bigger than or
+equal to n the distance from X and
+
+ align:start position:0%
+equal to n the distance from X and
+ 
+
+ align:start position:0%
+equal to n the distance from X and
+K to X is less than an
+
+ align:start position:0%
+K to X is less than an
+ 
+
+ align:start position:0%
+K to X is less than an
+Epsilon and now again any guess this as
+
+ align:start position:0%
+Epsilon and now again any guess this as
+ 
+
+ align:start position:0%
+Epsilon and now again any guess this as
+to what we should
+
+ align:start position:0%
+to what we should
+ 
+
+ align:start position:0%
+to what we should
+do triangle inequality precisely yeah so
+
+ align:start position:0%
+do triangle inequality precisely yeah so
+ 
+
+ align:start position:0%
+do triangle inequality precisely yeah so
+we're considering the distance from X
+
+ align:start position:0%
+we're considering the distance from X
+ 
+
+ align:start position:0%
+we're considering the distance from X
+and K to
+
+ align:start position:0%
+and K to
+ 
+
+ align:start position:0%
+and K to
+x what we can do is apply the fact that
+
+ align:start position:0%
+x what we can do is apply the fact that
+ 
+
+ align:start position:0%
+x what we can do is apply the fact that
+we know that convergent sequences are
+
+ align:start position:0%
+we know that convergent sequences are
+ 
+
+ align:start position:0%
+we know that convergent sequences are
+koshy so we can State we can write this
+
+ align:start position:0%
+koshy so we can State we can write this
+ 
+
+ align:start position:0%
+koshy so we can State we can write this
+as less than or equal to the distance
+
+ align:start position:0%
+as less than or equal to the distance
+ 
+
+ align:start position:0%
+as less than or equal to the distance
+from xn K let's say to
+
+ align:start position:0%
+from xn K let's say to
+ 
+
+ align:start position:0%
+from xn K let's say to
+XM for m
+
+ align:start position:0%
+XM for m
+ 
+
+ align:start position:0%
+XM for m
+bigger than or equal to
+
+ align:start position:0%
+bigger than or equal to
+ 
+
+ align:start position:0%
+bigger than or equal to
+n plus the distance from XM to
+
+ align:start position:0%
+n plus the distance from XM to
+ 
+
+ align:start position:0%
+n plus the distance from XM to
+X and now I can choose a larger natural
+
+ align:start position:0%
+X and now I can choose a larger natural
+ 
+
+ align:start position:0%
+X and now I can choose a larger natural
+number if necessary such that this term
+
+ align:start position:0%
+number if necessary such that this term
+ 
+
+ align:start position:0%
+number if necessary such that this term
+gets less than Epsilon / 2 and this term
+
+ align:start position:0%
+gets less than Epsilon / 2 and this term
+ 
+
+ align:start position:0%
+gets less than Epsilon / 2 and this term
+because it's Koshi is less than Epsilon
+
+ align:start position:0%
+because it's Koshi is less than Epsilon
+ 
+
+ align:start position:0%
+because it's Koshi is less than Epsilon
+over 2 so without writing out all those
+
+ align:start position:0%
+over 2 so without writing out all those
+ 
+
+ align:start position:0%
+over 2 so without writing out all those
+steps this is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon so this shows that the distance
+
+ align:start position:0%
+Epsilon so this shows that the distance
+ 
+
+ align:start position:0%
+Epsilon so this shows that the distance
+from X and K to X gets arbitrarily small
+
+ align:start position:0%
+from X and K to X gets arbitrarily small
+ 
+
+ align:start position:0%
+from X and K to X gets arbitrarily small
+so therefore it's convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah this is fairly
+
+ align:start position:0%
+yeah this is fairly
+ 
+
+ align:start position:0%
+yeah this is fairly
+important and it highlights you know one
+
+ align:start position:0%
+important and it highlights you know one
+ 
+
+ align:start position:0%
+important and it highlights you know one
+of the many ways in which Koshi
+
+ align:start position:0%
+of the many ways in which Koshi
+ 
+
+ align:start position:0%
+of the many ways in which Koshi
+sequences are deeply important as we'll
+
+ align:start position:0%
+sequences are deeply important as we'll
+ 
+
+ align:start position:0%
+sequences are deeply important as we'll
+talk about in like the fifth lecture in
+
+ align:start position:0%
+talk about in like the fifth lecture in
+ 
+
+ align:start position:0%
+talk about in like the fifth lecture in
+a specific module of this class uh
+
+ align:start position:0%
+a specific module of this class uh
+ 
+
+ align:start position:0%
+a specific module of this class uh
+having things to be Koshi complete
+
+ align:start position:0%
+having things to be Koshi complete
+ 
+
+ align:start position:0%
+having things to be Koshi complete
+really really helpful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay oh one more note this is
+
+ align:start position:0%
+um okay oh one more note this is
+ 
+
+ align:start position:0%
+um okay oh one more note this is
+something that I vaguely noted on uh
+
+ align:start position:0%
+something that I vaguely noted on uh
+ 
+
+ align:start position:0%
+something that I vaguely noted on uh
+Tuesday but these are all of the major
+
+ align:start position:0%
+Tuesday but these are all of the major
+ 
+
+ align:start position:0%
+Tuesday but these are all of the major
+theorems and propositions that we're
+
+ align:start position:0%
+theorems and propositions that we're
+ 
+
+ align:start position:0%
+theorems and propositions that we're
+going to need for convergent sequences
+
+ align:start position:0%
+going to need for convergent sequences
+ 
+
+ align:start position:0%
+going to need for convergent sequences
+you might be wondering why there aren't
+
+ align:start position:0%
+you might be wondering why there aren't
+ 
+
+ align:start position:0%
+you might be wondering why there aren't
+more we had a ton more in real analysis
+
+ align:start position:0%
+more we had a ton more in real analysis
+ 
+
+ align:start position:0%
+more we had a ton more in real analysis
+in fact it took like a month of our time
+
+ align:start position:0%
+in fact it took like a month of our time
+ 
+
+ align:start position:0%
+in fact it took like a month of our time
+the reason we don't have more is because
+
+ align:start position:0%
+the reason we don't have more is because
+ 
+
+ align:start position:0%
+the reason we don't have more is because
+the real numbers are a vector space I
+
+ align:start position:0%
+the real numbers are a vector space I
+ 
+
+ align:start position:0%
+the real numbers are a vector space I
+can add two real numbers and get a real
+
+ align:start position:0%
+can add two real numbers and get a real
+ 
+
+ align:start position:0%
+can add two real numbers and get a real
+number I can multiply them and get a
+
+ align:start position:0%
+number I can multiply them and get a
+ 
+
+ align:start position:0%
+number I can multiply them and get a
+real number everything there was nicer
+
+ align:start position:0%
+real number everything there was nicer
+ 
+
+ align:start position:0%
+real number everything there was nicer
+and we had addition toin so when it
+
+ align:start position:0%
+and we had addition toin so when it
+ 
+
+ align:start position:0%
+and we had addition toin so when it
+meant so one thing we could state in
+
+ align:start position:0%
+meant so one thing we could state in
+ 
+
+ align:start position:0%
+meant so one thing we could state in
+real analysis is that this for instance
+
+ align:start position:0%
+real analysis is that this for instance
+ 
+
+ align:start position:0%
+real analysis is that this for instance
+the sum of two convergent sequences is
+
+ align:start position:0%
+the sum of two convergent sequences is
+ 
+
+ align:start position:0%
+the sum of two convergent sequences is
+convergent here that doesn't make sense
+
+ align:start position:0%
+convergent here that doesn't make sense
+ 
+
+ align:start position:0%
+convergent here that doesn't make sense
+necessarily you can't always add two
+
+ align:start position:0%
+necessarily you can't always add two
+ 
+
+ align:start position:0%
+necessarily you can't always add two
+points in a metric space and get a point
+
+ align:start position:0%
+points in a metric space and get a point
+ 
+
+ align:start position:0%
+points in a metric space and get a point
+in your metric space let alone have
+
+ align:start position:0%
+in your metric space let alone have
+ 
+
+ align:start position:0%
+in your metric space let alone have
+addition be well
+
+ align:start position:0%
+addition be well
+ 
+
+ align:start position:0%
+addition be well
+defined uh similarly we have the squeeze
+
+ align:start position:0%
+defined uh similarly we have the squeeze
+ 
+
+ align:start position:0%
+defined uh similarly we have the squeeze
+theorem in real analysis we have a
+
+ align:start position:0%
+theorem in real analysis we have a
+ 
+
+ align:start position:0%
+theorem in real analysis we have a
+version of it based off of distances but
+
+ align:start position:0%
+version of it based off of distances but
+ 
+
+ align:start position:0%
+version of it based off of distances but
+we don't have a squeeze theorem for
+
+ align:start position:0%
+we don't have a squeeze theorem for
+ 
+
+ align:start position:0%
+we don't have a squeeze theorem for
+points so because we don't necessarily
+
+ align:start position:0%
+points so because we don't necessarily
+ 
+
+ align:start position:0%
+points so because we don't necessarily
+have an ordering on our set right you
+
+ align:start position:0%
+have an ordering on our set right you
+ 
+
+ align:start position:0%
+have an ordering on our set right you
+can picture the complex numbers the
+
+ align:start position:0%
+can picture the complex numbers the
+ 
+
+ align:start position:0%
+can picture the complex numbers the
+complex numbers don't have a uh ordering
+
+ align:start position:0%
+complex numbers don't have a uh ordering
+ 
+
+ align:start position:0%
+complex numbers don't have a uh ordering
+on them you don't have a sense in which
+
+ align:start position:0%
+on them you don't have a sense in which
+ 
+
+ align:start position:0%
+on them you don't have a sense in which
+one complex number is bigger than the
+
+ align:start position:0%
+one complex number is bigger than the
+ 
+
+ align:start position:0%
+one complex number is bigger than the
+other other than yeah I'm just going to
+
+ align:start position:0%
+other other than yeah I'm just going to
+ 
+
+ align:start position:0%
+other other than yeah I'm just going to
+leave it there if you've done complex
+
+ align:start position:0%
+leave it there if you've done complex
+ 
+
+ align:start position:0%
+leave it there if you've done complex
+analysis then you'll know what I'm
+
+ align:start position:0%
+analysis then you'll know what I'm
+ 
+
+ align:start position:0%
+analysis then you'll know what I'm
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about uh but yeah so that's why we don't
+
+ align:start position:0%
+about uh but yeah so that's why we don't
+ 
+
+ align:start position:0%
+about uh but yeah so that's why we don't
+have more theorems as we used to so now
+
+ align:start position:0%
+have more theorems as we used to so now
+ 
+
+ align:start position:0%
+have more theorems as we used to so now
+we're going to move on to the next major
+
+ align:start position:0%
+we're going to move on to the next major
+ 
+
+ align:start position:0%
+we're going to move on to the next major
+theorem that I've talked about or the
+
+ align:start position:0%
+theorem that I've talked about or the
+ 
+
+ align:start position:0%
+theorem that I've talked about or the
+next major definition that I've talked
+
+ align:start position:0%
+next major definition that I've talked
+ 
+
+ align:start position:0%
+next major definition that I've talked
+about we've talked about convergent
+
+ align:start position:0%
+about we've talked about convergent
+ 
+
+ align:start position:0%
+about we've talked about convergent
+sequences we've talked a little bit
+
+ align:start position:0%
+sequences we've talked a little bit
+ 
+
+ align:start position:0%
+sequences we've talked a little bit
+about koshy sequences kosy sequences are
+
+ align:start position:0%
+about koshy sequences kosy sequences are
+ 
+
+ align:start position:0%
+about koshy sequences kosy sequences are
+helpful but in terms of a metric space
+
+ align:start position:0%
+helpful but in terms of a metric space
+ 
+
+ align:start position:0%
+helpful but in terms of a metric space
+we've mostly St stated what we need for
+
+ align:start position:0%
+we've mostly St stated what we need for
+ 
+
+ align:start position:0%
+we've mostly St stated what we need for
+the moment being
+
+ align:start position:0%
+the moment being
+ 
+
+ align:start position:0%
+the moment being
+uh now we're going to move on to open
+
+ align:start position:0%
+uh now we're going to move on to open
+ 
+
+ align:start position:0%
+uh now we're going to move on to open
+sets so I'm going to recall what this
+
+ align:start position:0%
+sets so I'm going to recall what this
+ 
+
+ align:start position:0%
+sets so I'm going to recall what this
+definition is because it's the one that
+
+ align:start position:0%
+definition is because it's the one that
+ 
+
+ align:start position:0%
+definition is because it's the one that
+can be a little bit the weirdest so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recall a
+
+ align:start position:0%
+recall a
+ 
+
+ align:start position:0%
+recall a
+set a contained in your metric Space
+
+ align:start position:0%
+set a contained in your metric Space
+ 
+
+ align:start position:0%
+set a contained in your metric Space
+X is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open if for all for every single point
+
+ align:start position:0%
+open if for all for every single point
+ 
+
+ align:start position:0%
+open if for all for every single point
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+a there exists an Epsilon bigger than
+
+ align:start position:0%
+a there exists an Epsilon bigger than
+ 
+
+ align:start position:0%
+a there exists an Epsilon bigger than
+zero such that the ball of radius
+
+ align:start position:0%
+zero such that the ball of radius
+ 
+
+ align:start position:0%
+zero such that the ball of radius
+Epsilon around a
+
+ align:start position:0%
+Epsilon around a
+ 
+
+ align:start position:0%
+Epsilon around a
+is completely contained in your set and
+
+ align:start position:0%
+is completely contained in your set and
+ 
+
+ align:start position:0%
+is completely contained in your set and
+this is the set of Y in your metric
+
+ align:start position:0%
+this is the set of Y in your metric
+ 
+
+ align:start position:0%
+this is the set of Y in your metric
+space such that the distance from y to a
+
+ align:start position:0%
+space such that the distance from y to a
+ 
+
+ align:start position:0%
+space such that the distance from y to a
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+Epsilon uh just to bring it up because
+
+ align:start position:0%
+Epsilon uh just to bring it up because
+ 
+
+ align:start position:0%
+Epsilon uh just to bring it up because
+sometimes the notation comes up this is
+
+ align:start position:0%
+sometimes the notation comes up this is
+ 
+
+ align:start position:0%
+sometimes the notation comes up this is
+also sometimes
+
+ align:start position:0%
+also sometimes
+ 
+
+ align:start position:0%
+also sometimes
+denoted the ball around a of radius
+
+ align:start position:0%
+denoted the ball around a of radius
+ 
+
+ align:start position:0%
+denoted the ball around a of radius
+Epsilon so use whichever notation you
+
+ align:start position:0%
+Epsilon so use whichever notation you
+ 
+
+ align:start position:0%
+Epsilon so use whichever notation you
+prefer uh can you here I can move it a
+
+ align:start position:0%
+prefer uh can you here I can move it a
+ 
+
+ align:start position:0%
+prefer uh can you here I can move it a
+little bit up so use whichever notation
+
+ align:start position:0%
+little bit up so use whichever notation
+ 
+
+ align:start position:0%
+little bit up so use whichever notation
+you prefer
+
+ align:start position:0%
+you prefer
+ 
+
+ align:start position:0%
+you prefer
+uh I prefer this one just because it
+
+ align:start position:0%
+uh I prefer this one just because it
+ 
+
+ align:start position:0%
+uh I prefer this one just because it
+means uh less commas but you know
+
+ align:start position:0%
+means uh less commas but you know
+ 
+
+ align:start position:0%
+means uh less commas but you know
+whichever
+
+ align:start position:0%
+whichever
+ 
+
+ align:start position:0%
+whichever
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh open sets are going to have a huge
+
+ align:start position:0%
+so uh open sets are going to have a huge
+ 
+
+ align:start position:0%
+so uh open sets are going to have a huge
+connection between topology and
+
+ align:start position:0%
+connection between topology and
+ 
+
+ align:start position:0%
+connection between topology and
+continuity and other definitions that
+
+ align:start position:0%
+continuity and other definitions that
+ 
+
+ align:start position:0%
+continuity and other definitions that
+are important now the first thing that
+
+ align:start position:0%
+are important now the first thing that
+ 
+
+ align:start position:0%
+are important now the first thing that
+we're going to prove is topological
+
+ align:start position:0%
+we're going to prove is topological
+ 
+
+ align:start position:0%
+we're going to prove is topological
+properties of open sets so because
+
+ align:start position:0%
+properties of open sets so because
+ 
+
+ align:start position:0%
+properties of open sets so because
+youall haven't taken topology this is in
+
+ align:start position:0%
+youall haven't taken topology this is in
+ 
+
+ align:start position:0%
+youall haven't taken topology this is in
+fact really really helpful we're going
+
+ align:start position:0%
+fact really really helpful we're going
+ 
+
+ align:start position:0%
+fact really really helpful we're going
+to show three major properties of uh
+
+ align:start position:0%
+to show three major properties of uh
+ 
+
+ align:start position:0%
+to show three major properties of uh
+open sets in metric spaces so a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem uh and you can call this
+
+ align:start position:0%
+theorem uh and you can call this
+ 
+
+ align:start position:0%
+theorem uh and you can call this
+topological properties if you
+
+ align:start position:0%
+topological properties if you
+ 
+
+ align:start position:0%
+topological properties if you
+want or I'll write it out cu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topological
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties of open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets Okay firstly we have that the empty
+
+ align:start position:0%
+sets Okay firstly we have that the empty
+ 
+
+ align:start position:0%
+sets Okay firstly we have that the empty
+set and the entire metric bace
+
+ align:start position:0%
+set and the entire metric bace
+ 
+
+ align:start position:0%
+set and the entire metric bace
+itself are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+AI are open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets then the union of all of these sets
+
+ align:start position:0%
+sets then the union of all of these sets
+ 
+
+ align:start position:0%
+sets then the union of all of these sets
+from I equals let's say one to infinity
+
+ align:start position:0%
+from I equals let's say one to infinity
+ 
+
+ align:start position:0%
+from I equals let's say one to infinity
+or all see Zero why not uh is open so in
+
+ align:start position:0%
+or all see Zero why not uh is open so in
+ 
+
+ align:start position:0%
+or all see Zero why not uh is open so in
+other words the arbitrary Union of open
+
+ align:start position:0%
+other words the arbitrary Union of open
+ 
+
+ align:start position:0%
+other words the arbitrary Union of open
+sets is
+
+ align:start position:0%
+sets is
+ 
+
+ align:start position:0%
+sets is
+open and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally uh the finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersections of open sets are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open in other words if I intersect from
+
+ align:start position:0%
+open in other words if I intersect from
+ 
+
+ align:start position:0%
+open in other words if I intersect from
+IAL 0 to capital M of a I then this is
+
+ align:start position:0%
+IAL 0 to capital M of a I then this is
+ 
+
+ align:start position:0%
+IAL 0 to capital M of a I then this is
+open the fact that we can't intersect
+
+ align:start position:0%
+open the fact that we can't intersect
+ 
+
+ align:start position:0%
+open the fact that we can't intersect
+infinitely many of them will become
+
+ align:start position:0%
+infinitely many of them will become
+ 
+
+ align:start position:0%
+infinitely many of them will become
+apparent in the proof so in the proof of
+
+ align:start position:0%
+apparent in the proof so in the proof of
+ 
+
+ align:start position:0%
+apparent in the proof so in the proof of
+these three properties it'll become
+
+ align:start position:0%
+these three properties it'll become
+ 
+
+ align:start position:0%
+these three properties it'll become
+apparent why we can't do infinitely many
+
+ align:start position:0%
+apparent why we can't do infinitely many
+ 
+
+ align:start position:0%
+apparent why we can't do infinitely many
+of them but let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one so consider the empty set how
+
+ align:start position:0%
+this one so consider the empty set how
+ 
+
+ align:start position:0%
+this one so consider the empty set how
+do we know that the empty set is open
+
+ align:start position:0%
+do we know that the empty set is open
+ 
+
+ align:start position:0%
+do we know that the empty set is open
+well it's vasly true it's true all the
+
+ align:start position:0%
+well it's vasly true it's true all the
+ 
+
+ align:start position:0%
+well it's vasly true it's true all the
+time because for every single point in
+
+ align:start position:0%
+time because for every single point in
+ 
+
+ align:start position:0%
+time because for every single point in
+the empty set there are no points in the
+
+ align:start position:0%
+the empty set there are no points in the
+ 
+
+ align:start position:0%
+the empty set there are no points in the
+empty set so as soon as that statement
+
+ align:start position:0%
+empty set so as soon as that statement
+ 
+
+ align:start position:0%
+empty set so as soon as that statement
+is false we have that the empty set is
+
+ align:start position:0%
+is false we have that the empty set is
+ 
+
+ align:start position:0%
+is false we have that the empty set is
+open so this is open vake is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sleeve two let's consider the set X well
+
+ align:start position:0%
+sleeve two let's consider the set X well
+ 
+
+ align:start position:0%
+sleeve two let's consider the set X well
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+all Epsilon or sorry for every single
+
+ align:start position:0%
+all Epsilon or sorry for every single
+ 
+
+ align:start position:0%
+all Epsilon or sorry for every single
+point x and
+
+ align:start position:0%
+point x and
+ 
+
+ align:start position:0%
+point x and
+x does there exist a ball around x and x
+
+ align:start position:0%
+x does there exist a ball around x and x
+ 
+
+ align:start position:0%
+x does there exist a ball around x and x
+yes there is because just pick
+
+ align:start position:0%
+yes there is because just pick
+ 
+
+ align:start position:0%
+yes there is because just pick
+pick your favorite Epsilon bigger than
+
+ align:start position:0%
+pick your favorite Epsilon bigger than
+ 
+
+ align:start position:0%
+pick your favorite Epsilon bigger than
+zero and then the ball of radius Epsilon
+
+ align:start position:0%
+zero and then the ball of radius Epsilon
+ 
+
+ align:start position:0%
+zero and then the ball of radius Epsilon
+around that point x is by definition a
+
+ align:start position:0%
+around that point x is by definition a
+ 
+
+ align:start position:0%
+around that point x is by definition a
+subset of your metric space right
+
+ align:start position:0%
+subset of your metric space right
+ 
+
+ align:start position:0%
+subset of your metric space right
+because the definition of a ball of
+
+ align:start position:0%
+because the definition of a ball of
+ 
+
+ align:start position:0%
+because the definition of a ball of
+radius Epsilon is only the point in X so
+
+ align:start position:0%
+radius Epsilon is only the point in X so
+ 
+
+ align:start position:0%
+radius Epsilon is only the point in X so
+we're not going to end up with some
+
+ align:start position:0%
+we're not going to end up with some
+ 
+
+ align:start position:0%
+we're not going to end up with some
+weird thing outside of
+
+ align:start position:0%
+weird thing outside of
+ 
+
+ align:start position:0%
+weird thing outside of
+X so this shows that X itself is
+
+ align:start position:0%
+X so this shows that X itself is
+ 
+
+ align:start position:0%
+X so this shows that X itself is
+open two we want to show that the union
+
+ align:start position:0%
+open two we want to show that the union
+ 
+
+ align:start position:0%
+open two we want to show that the union
+of open sets is open how' we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that um IAL 0 to Infinity is
+
+ align:start position:0%
+that um IAL 0 to Infinity is
+ 
+
+ align:start position:0%
+that um IAL 0 to Infinity is
+open this is what we want to
+
+ align:start position:0%
+open this is what we want to
+ 
+
+ align:start position:0%
+open this is what we want to
+show well as as with the definition
+
+ align:start position:0%
+show well as as with the definition
+ 
+
+ align:start position:0%
+show well as as with the definition
+we're just going to pick a point in the
+
+ align:start position:0%
+we're just going to pick a point in the
+ 
+
+ align:start position:0%
+we're just going to pick a point in the
+union so pick arbitrary X in the union I
+
+ align:start position:0%
+union so pick arbitrary X in the union I
+ 
+
+ align:start position:0%
+union so pick arbitrary X in the union I
+equal 0 to Infinity of a
+
+ align:start position:0%
+equal 0 to Infinity of a
+ 
+
+ align:start position:0%
+equal 0 to Infinity of a
+i and we want to show that there exists
+
+ align:start position:0%
+i and we want to show that there exists
+ 
+
+ align:start position:0%
+i and we want to show that there exists
+a ball of radius Epsilon around X that's
+
+ align:start position:0%
+a ball of radius Epsilon around X that's
+ 
+
+ align:start position:0%
+a ball of radius Epsilon around X that's
+contained in the set well because it's
+
+ align:start position:0%
+contained in the set well because it's
+ 
+
+ align:start position:0%
+contained in the set well because it's
+in the union there has to exist at least
+
+ align:start position:0%
+in the union there has to exist at least
+ 
+
+ align:start position:0%
+in the union there has to exist at least
+one AI that contains X so therefore
+
+ align:start position:0%
+one AI that contains X so therefore
+ 
+
+ align:start position:0%
+one AI that contains X so therefore
+there exists an AJ in your set of open
+
+ align:start position:0%
+there exists an AJ in your set of open
+ 
+
+ align:start position:0%
+there exists an AJ in your set of open
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+AI such that X is in
+
+ align:start position:0%
+AI such that X is in
+ 
+
+ align:start position:0%
+AI such that X is in
+AJ and then we apply the fact that AJ
+
+ align:start position:0%
+AJ and then we apply the fact that AJ
+ 
+
+ align:start position:0%
+AJ and then we apply the fact that AJ
+itself is open so therefore there exists
+
+ align:start position:0%
+itself is open so therefore there exists
+ 
+
+ align:start position:0%
+itself is open so therefore there exists
+an Epsilon bigger than zero such that
+
+ align:start position:0%
+an Epsilon bigger than zero such that
+ 
+
+ align:start position:0%
+an Epsilon bigger than zero such that
+the ball of radius Epsilon around X is
+
+ align:start position:0%
+the ball of radius Epsilon around X is
+ 
+
+ align:start position:0%
+the ball of radius Epsilon around X is
+contained in
+
+ align:start position:0%
+contained in
+ 
+
+ align:start position:0%
+contained in
+AI or sorry AJ
+
+ align:start position:0%
+AI or sorry AJ
+ 
+
+ align:start position:0%
+AI or sorry AJ
+but this is a subset of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Union so this shows that the ball of
+
+ align:start position:0%
+Union so this shows that the ball of
+ 
+
+ align:start position:0%
+Union so this shows that the ball of
+radius Epsilon is contained in the
+
+ align:start position:0%
+radius Epsilon is contained in the
+ 
+
+ align:start position:0%
+radius Epsilon is contained in the
+infinite Union or potentially infinite
+
+ align:start position:0%
+infinite Union or potentially infinite
+ 
+
+ align:start position:0%
+infinite Union or potentially infinite
+Union this also works if it's finite
+
+ align:start position:0%
+Union this also works if it's finite
+ 
+
+ align:start position:0%
+Union this also works if it's finite
+notice but you know that that's just a
+
+ align:start position:0%
+notice but you know that that's just a
+ 
+
+ align:start position:0%
+notice but you know that that's just a
+subcase okay uh and can I squeeze it in
+
+ align:start position:0%
+subcase okay uh and can I squeeze it in
+ 
+
+ align:start position:0%
+subcase okay uh and can I squeeze it in
+here no I cannot so I will move over
+
+ align:start position:0%
+here no I cannot so I will move over
+ 
+
+ align:start position:0%
+here no I cannot so I will move over
+here any questions so far actually let
+
+ align:start position:0%
+here any questions so far actually let
+ 
+
+ align:start position:0%
+here any questions so far actually let
+me move with this any questions
+
+ align:start position:0%
+me move with this any questions
+ 
+
+ align:start position:0%
+me move with this any questions
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+open sets are weird in
+
+ align:start position:0%
+open sets are weird in
+ 
+
+ align:start position:0%
+open sets are weird in
+that you know when we learn about them
+
+ align:start position:0%
+that you know when we learn about them
+ 
+
+ align:start position:0%
+that you know when we learn about them
+in real analysis I feel like they're
+
+ align:start position:0%
+in real analysis I feel like they're
+ 
+
+ align:start position:0%
+in real analysis I feel like they're
+pretty unintuitively important everyone
+
+ align:start position:0%
+pretty unintuitively important everyone
+ 
+
+ align:start position:0%
+pretty unintuitively important everyone
+says that they're
+
+ align:start position:0%
+says that they're
+ 
+
+ align:start position:0%
+says that they're
+important but I never got why and I'll
+
+ align:start position:0%
+important but I never got why and I'll
+ 
+
+ align:start position:0%
+important but I never got why and I'll
+explain why they are just like in a
+
+ align:start position:0%
+explain why they are just like in a
+ 
+
+ align:start position:0%
+explain why they are just like in a
+moment um but yeah open sets are deeply
+
+ align:start position:0%
+moment um but yeah open sets are deeply
+ 
+
+ align:start position:0%
+moment um but yeah open sets are deeply
+important in real analysis Sy
+
+ align:start position:0%
+important in real analysis Sy
+ 
+
+ align:start position:0%
+important in real analysis Sy
+topology and we're going to prove some
+
+ align:start position:0%
+topology and we're going to prove some
+ 
+
+ align:start position:0%
+topology and we're going to prove some
+more statements besides these
+
+ align:start position:0%
+more statements besides these
+ 
+
+ align:start position:0%
+more statements besides these
+topological
+
+ align:start position:0%
+topological
+ 
+
+ align:start position:0%
+topological
+properties that will be
+
+ align:start position:0%
+properties that will be
+ 
+
+ align:start position:0%
+properties that will be
+important uh and we'll relate to the
+
+ align:start position:0%
+important uh and we'll relate to the
+ 
+
+ align:start position:0%
+important uh and we'll relate to the
+major definitions in our tool tool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+okay so now we're interested
+
+ align:start position:0%
+okay so now we're interested
+ 
+
+ align:start position:0%
+okay so now we're interested
+in the third case the intersection from
+
+ align:start position:0%
+in the third case the intersection from
+ 
+
+ align:start position:0%
+in the third case the intersection from
+I equals 0 to M of the AI well we're
+
+ align:start position:0%
+I equals 0 to M of the AI well we're
+ 
+
+ align:start position:0%
+I equals 0 to M of the AI well we're
+going to do exactly as we did
+
+ align:start position:0%
+going to do exactly as we did
+ 
+
+ align:start position:0%
+going to do exactly as we did
+before if I have some X the intersection
+
+ align:start position:0%
+before if I have some X the intersection
+ 
+
+ align:start position:0%
+before if I have some X the intersection
+of the AI from i = 0 to M then what do I
+
+ align:start position:0%
+of the AI from i = 0 to M then what do I
+ 
+
+ align:start position:0%
+of the AI from i = 0 to M then what do I
+know before we knew that it was in any
+
+ align:start position:0%
+know before we knew that it was in any
+ 
+
+ align:start position:0%
+know before we knew that it was in any
+of the AIS but here we know even more
+
+ align:start position:0%
+of the AIS but here we know even more
+ 
+
+ align:start position:0%
+of the AIS but here we know even more
+information here we know that X is in AI
+
+ align:start position:0%
+information here we know that X is in AI
+ 
+
+ align:start position:0%
+information here we know that X is in AI
+for every single
+
+ align:start position:0%
+for every single
+ 
+
+ align:start position:0%
+for every single
+I so what can we do well we know that
+
+ align:start position:0%
+I so what can we do well we know that
+ 
+
+ align:start position:0%
+I so what can we do well we know that
+therefore because each AI is open there
+
+ align:start position:0%
+therefore because each AI is open there
+ 
+
+ align:start position:0%
+therefore because each AI is open there
+exists an Epsilon I bigger than zero
+
+ align:start position:0%
+exists an Epsilon I bigger than zero
+ 
+
+ align:start position:0%
+exists an Epsilon I bigger than zero
+such that the ball of radius Epsilon I
+
+ align:start position:0%
+such that the ball of radius Epsilon I
+ 
+
+ align:start position:0%
+such that the ball of radius Epsilon I
+around X is contained in
+
+ align:start position:0%
+around X is contained in
+ 
+
+ align:start position:0%
+around X is contained in
+AI the issue is that the entirety of AI
+
+ align:start position:0%
+AI the issue is that the entirety of AI
+ 
+
+ align:start position:0%
+AI the issue is that the entirety of AI
+might not be in the intersection so what
+
+ align:start position:0%
+might not be in the intersection so what
+ 
+
+ align:start position:0%
+might not be in the intersection so what
+can we do we have this for every single
+
+ align:start position:0%
+can we do we have this for every single
+ 
+
+ align:start position:0%
+can we do we have this for every single
+I and we have finitely many of them so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose uh Epsilon to be equal to the
+
+ align:start position:0%
+choose uh Epsilon to be equal to the
+ 
+
+ align:start position:0%
+choose uh Epsilon to be equal to the
+minimum of the Epsilon I from I equals z
+
+ align:start position:0%
+minimum of the Epsilon I from I equals z
+ 
+
+ align:start position:0%
+minimum of the Epsilon I from I equals z
+or 0 to
+
+ align:start position:0%
+or 0 to
+ 
+
+ align:start position:0%
+or 0 to
+m capital
+
+ align:start position:0%
+m capital
+ 
+
+ align:start position:0%
+m capital
+M this is bigger than zero right because
+
+ align:start position:0%
+M this is bigger than zero right because
+ 
+
+ align:start position:0%
+M this is bigger than zero right because
+we're only choosing finitely many this
+
+ align:start position:0%
+we're only choosing finitely many this
+ 
+
+ align:start position:0%
+we're only choosing finitely many this
+is where we're using the fact that
+
+ align:start position:0%
+is where we're using the fact that
+ 
+
+ align:start position:0%
+is where we're using the fact that
+there's the finite intersection if we
+
+ align:start position:0%
+there's the finite intersection if we
+ 
+
+ align:start position:0%
+there's the finite intersection if we
+had an infinite intersection you can
+
+ align:start position:0%
+had an infinite intersection you can
+ 
+
+ align:start position:0%
+had an infinite intersection you can
+picture taking um more and more uh
+
+ align:start position:0%
+picture taking um more and more uh
+ 
+
+ align:start position:0%
+picture taking um more and more uh
+smaller and smaller Epsilon I such that
+
+ align:start position:0%
+smaller and smaller Epsilon I such that
+ 
+
+ align:start position:0%
+smaller and smaller Epsilon I such that
+this uh infinum is zero and that's an
+
+ align:start position:0%
+this uh infinum is zero and that's an
+ 
+
+ align:start position:0%
+this uh infinum is zero and that's an
+issue but if it's finitely many we can
+
+ align:start position:0%
+issue but if it's finitely many we can
+ 
+
+ align:start position:0%
+issue but if it's finitely many we can
+take the minimum of them and then what
+
+ align:start position:0%
+take the minimum of them and then what
+ 
+
+ align:start position:0%
+take the minimum of them and then what
+we know is that the ball of radius
+
+ align:start position:0%
+we know is that the ball of radius
+ 
+
+ align:start position:0%
+we know is that the ball of radius
+Epsilon round X is a subset of AI for
+
+ align:start position:0%
+Epsilon round X is a subset of AI for
+ 
+
+ align:start position:0%
+Epsilon round X is a subset of AI for
+all I because it's contained in the ball
+
+ align:start position:0%
+all I because it's contained in the ball
+ 
+
+ align:start position:0%
+all I because it's contained in the ball
+of radius Epsilon
+
+ align:start position:0%
+of radius Epsilon
+ 
+
+ align:start position:0%
+of radius Epsilon
+I I guess I should tell that this is
+
+ align:start position:0%
+I I guess I should tell that this is
+ 
+
+ align:start position:0%
+I I guess I should tell that this is
+contained in the ball of radius Epsilon
+
+ align:start position:0%
+contained in the ball of radius Epsilon
+ 
+
+ align:start position:0%
+contained in the ball of radius Epsilon
+I of
+
+ align:start position:0%
+I of
+ 
+
+ align:start position:0%
+I of
+X which is contained in AI for all I
+
+ align:start position:0%
+X which is contained in AI for all I
+ 
+
+ align:start position:0%
+X which is contained in AI for all I
+which implies that the ball of radius
+
+ align:start position:0%
+which implies that the ball of radius
+ 
+
+ align:start position:0%
+which implies that the ball of radius
+Epsilon around X is a subset of the
+
+ align:start position:0%
+Epsilon around X is a subset of the
+ 
+
+ align:start position:0%
+Epsilon around X is a subset of the
+finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersection all right all right so why
+
+ align:start position:0%
+intersection all right all right so why
+ 
+
+ align:start position:0%
+intersection all right all right so why
+is this called the topological
+
+ align:start position:0%
+is this called the topological
+ 
+
+ align:start position:0%
+is this called the topological
+properties of open sets because if you
+
+ align:start position:0%
+properties of open sets because if you
+ 
+
+ align:start position:0%
+properties of open sets because if you
+were to take 18901 which is a class that
+
+ align:start position:0%
+were to take 18901 which is a class that
+ 
+
+ align:start position:0%
+were to take 18901 which is a class that
+I would highly suggest to take at some
+
+ align:start position:0%
+I would highly suggest to take at some
+ 
+
+ align:start position:0%
+I would highly suggest to take at some
+point if you're interested in this sort
+
+ align:start position:0%
+point if you're interested in this sort
+ 
+
+ align:start position:0%
+point if you're interested in this sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+analysis uh as we're going to see open
+
+ align:start position:0%
+analysis uh as we're going to see open
+ 
+
+ align:start position:0%
+analysis uh as we're going to see open
+sets allow us to state things about
+
+ align:start position:0%
+sets allow us to state things about
+ 
+
+ align:start position:0%
+sets allow us to state things about
+continuity you can Define continuity in
+
+ align:start position:0%
+continuity you can Define continuity in
+ 
+
+ align:start position:0%
+continuity you can Define continuity in
+terms of open sets you can Define
+
+ align:start position:0%
+terms of open sets you can Define
+ 
+
+ align:start position:0%
+terms of open sets you can Define
+convergent sequences in terms of open
+
+ align:start position:0%
+convergent sequences in terms of open
+ 
+
+ align:start position:0%
+convergent sequences in terms of open
+sets basically everything we can redo in
+
+ align:start position:0%
+sets basically everything we can redo in
+ 
+
+ align:start position:0%
+sets basically everything we can redo in
+terms of open sets and that is a
+
+ align:start position:0%
+terms of open sets and that is a
+ 
+
+ align:start position:0%
+terms of open sets and that is a
+topology if I have a set of subsets such
+
+ align:start position:0%
+topology if I have a set of subsets such
+ 
+
+ align:start position:0%
+topology if I have a set of subsets such
+that these three properties hold that's
+
+ align:start position:0%
+that these three properties hold that's
+ 
+
+ align:start position:0%
+that these three properties hold that's
+known as a topology and in 18901 that's
+
+ align:start position:0%
+known as a topology and in 18901 that's
+ 
+
+ align:start position:0%
+known as a topology and in 18901 that's
+the basic toolbox that you're given and
+
+ align:start position:0%
+the basic toolbox that you're given and
+ 
+
+ align:start position:0%
+the basic toolbox that you're given and
+then you go from there in terms of
+
+ align:start position:0%
+then you go from there in terms of
+ 
+
+ align:start position:0%
+then you go from there in terms of
+redefining everything so this is just an
+
+ align:start position:0%
+redefining everything so this is just an
+ 
+
+ align:start position:0%
+redefining everything so this is just an
+example of uh a more General thing than
+
+ align:start position:0%
+example of uh a more General thing than
+ 
+
+ align:start position:0%
+example of uh a more General thing than
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+spaces um I'm going to talk a little bit
+
+ align:start position:0%
+spaces um I'm going to talk a little bit
+ 
+
+ align:start position:0%
+spaces um I'm going to talk a little bit
+about that in the final lecture where I
+
+ align:start position:0%
+about that in the final lecture where I
+ 
+
+ align:start position:0%
+about that in the final lecture where I
+talk about you know where things go from
+
+ align:start position:0%
+talk about you know where things go from
+ 
+
+ align:start position:0%
+talk about you know where things go from
+here but for now this is you know the
+
+ align:start position:0%
+here but for now this is you know the
+ 
+
+ align:start position:0%
+here but for now this is you know the
+basic
+
+ align:start position:0%
+basic
+ 
+
+ align:start position:0%
+basic
+idea all right uh
+
+ align:start position:0%
+idea all right uh
+ 
+
+ align:start position:0%
+idea all right uh
+uh now what I'm going to state is some
+
+ align:start position:0%
+uh now what I'm going to state is some
+ 
+
+ align:start position:0%
+uh now what I'm going to state is some
+facts about closed sets but what is a
+
+ align:start position:0%
+facts about closed sets but what is a
+ 
+
+ align:start position:0%
+facts about closed sets but what is a
+closed
+
+ align:start position:0%
+closed
+ 
+
+ align:start position:0%
+closed
+set which I haven't defined before so
+
+ align:start position:0%
+set which I haven't defined before so
+ 
+
+ align:start position:0%
+set which I haven't defined before so
+this is useful to note a subset a in
+
+ align:start position:0%
+this is useful to note a subset a in
+ 
+
+ align:start position:0%
+this is useful to note a subset a in
+X is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed if
+
+ align:start position:0%
+closed if
+ 
+
+ align:start position:0%
+closed if
+a uh if the complement of a which is
+
+ align:start position:0%
+a uh if the complement of a which is
+ 
+
+ align:start position:0%
+a uh if the complement of a which is
+known as this the metric bace x minus
+
+ align:start position:0%
+known as this the metric bace x minus
+ 
+
+ align:start position:0%
+known as this the metric bace x minus
+a is open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if a set is closed does that imply
+
+ align:start position:0%
+now if a set is closed does that imply
+ 
+
+ align:start position:0%
+now if a set is closed does that imply
+that it's not
+
+ align:start position:0%
+that it's not
+ 
+
+ align:start position:0%
+that it's not
+open yeah the answer is no how can we
+
+ align:start position:0%
+open yeah the answer is no how can we
+ 
+
+ align:start position:0%
+open yeah the answer is no how can we
+see that well let's consider the real
+
+ align:start position:0%
+see that well let's consider the real
+ 
+
+ align:start position:0%
+see that well let's consider the real
+numbers as an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example uh
+
+ align:start position:0%
+example uh
+ 
+
+ align:start position:0%
+example uh
+notice what's the complement of the
+
+ align:start position:0%
+notice what's the complement of the
+ 
+
+ align:start position:0%
+notice what's the complement of the
+empty set in the real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+anyone it's a good exercise and thinking
+
+ align:start position:0%
+anyone it's a good exercise and thinking
+ 
+
+ align:start position:0%
+anyone it's a good exercise and thinking
+about what the complement
+
+ align:start position:0%
+about what the complement
+ 
+
+ align:start position:0%
+about what the complement
+means real numbers minus the empty set
+
+ align:start position:0%
+means real numbers minus the empty set
+ 
+
+ align:start position:0%
+means real numbers minus the empty set
+so it's just going to be all of the real
+
+ align:start position:0%
+so it's just going to be all of the real
+ 
+
+ align:start position:0%
+so it's just going to be all of the real
+numbers but this as we've stated before
+
+ align:start position:0%
+numbers but this as we've stated before
+ 
+
+ align:start position:0%
+numbers but this as we've stated before
+in our first topological property this
+
+ align:start position:0%
+in our first topological property this
+ 
+
+ align:start position:0%
+in our first topological property this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+open so therefore the empty
+
+ align:start position:0%
+open so therefore the empty
+ 
+
+ align:start position:0%
+open so therefore the empty
+set is closed by
+
+ align:start position:0%
+set is closed by
+ 
+
+ align:start position:0%
+set is closed by
+definition but we also know by our
+
+ align:start position:0%
+definition but we also know by our
+ 
+
+ align:start position:0%
+definition but we also know by our
+topological properties again that the
+
+ align:start position:0%
+topological properties again that the
+ 
+
+ align:start position:0%
+topological properties again that the
+empty set is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open what the heck well this is just one
+
+ align:start position:0%
+open what the heck well this is just one
+ 
+
+ align:start position:0%
+open what the heck well this is just one
+of those things in topology it's kind of
+
+ align:start position:0%
+of those things in topology it's kind of
+ 
+
+ align:start position:0%
+of those things in topology it's kind of
+weird like open sets you can prove
+
+ align:start position:0%
+weird like open sets you can prove
+ 
+
+ align:start position:0%
+weird like open sets you can prove
+properties of closed sets instead and
+
+ align:start position:0%
+properties of closed sets instead and
+ 
+
+ align:start position:0%
+properties of closed sets instead and
+things are everything everything's fine
+
+ align:start position:0%
+things are everything everything's fine
+ 
+
+ align:start position:0%
+things are everything everything's fine
+um I'll
+
+ align:start position:0%
+um I'll
+ 
+
+ align:start position:0%
+um I'll
+note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note there's a notion called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connectedness which I'll briefly Define
+
+ align:start position:0%
+connectedness which I'll briefly Define
+ 
+
+ align:start position:0%
+connectedness which I'll briefly Define
+But ultimately will be more of a problem
+
+ align:start position:0%
+But ultimately will be more of a problem
+ 
+
+ align:start position:0%
+But ultimately will be more of a problem
+set problem but if your metric space is
+
+ align:start position:0%
+set problem but if your metric space is
+ 
+
+ align:start position:0%
+set problem but if your metric space is
+connected uh let me state it that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if if your metric Space X is connected
+
+ align:start position:0%
+if if your metric Space X is connected
+ 
+
+ align:start position:0%
+if if your metric Space X is connected
+which I'll redefine in a mo or which
+
+ align:start position:0%
+which I'll redefine in a mo or which
+ 
+
+ align:start position:0%
+which I'll redefine in a mo or which
+I'll Define in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment this is true if and only if the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only open and closed
+
+ align:start position:0%
+only open and closed
+ 
+
+ align:start position:0%
+only open and closed
+sets so sets that are both open and
+
+ align:start position:0%
+sets so sets that are both open and
+ 
+
+ align:start position:0%
+sets so sets that are both open and
+closed are the empty
+
+ align:start position:0%
+closed are the empty
+ 
+
+ align:start position:0%
+closed are the empty
+set and the metric space
+
+ align:start position:0%
+set and the metric space
+ 
+
+ align:start position:0%
+set and the metric space
+itself now what does it mean for your
+
+ align:start position:0%
+itself now what does it mean for your
+ 
+
+ align:start position:0%
+itself now what does it mean for your
+metric space to be connected I mean we
+
+ align:start position:0%
+metric space to be connected I mean we
+ 
+
+ align:start position:0%
+metric space to be connected I mean we
+have a nice picture of it in our heads
+
+ align:start position:0%
+have a nice picture of it in our heads
+ 
+
+ align:start position:0%
+have a nice picture of it in our heads
+CU connected is a pretty visual thing
+
+ align:start position:0%
+CU connected is a pretty visual thing
+ 
+
+ align:start position:0%
+CU connected is a pretty visual thing
+but this is one definition once you
+
+ align:start position:0%
+but this is one definition once you
+ 
+
+ align:start position:0%
+but this is one definition once you
+prove this this is a definition how do
+
+ align:start position:0%
+prove this this is a definition how do
+ 
+
+ align:start position:0%
+prove this this is a definition how do
+you prove this well you prove it based
+
+ align:start position:0%
+you prove this well you prove it based
+ 
+
+ align:start position:0%
+you prove this well you prove it based
+off of the definition of disconnected so
+
+ align:start position:0%
+off of the definition of disconnected so
+ 
+
+ align:start position:0%
+off of the definition of disconnected so
+definition X is
+
+ align:start position:0%
+definition X is
+ 
+
+ align:start position:0%
+definition X is
+disconnected by
+
+ align:start position:0%
+disconnected by
+ 
+
+ align:start position:0%
+disconnected by
+definition if there exists two open sets
+
+ align:start position:0%
+definition if there exists two open sets
+ 
+
+ align:start position:0%
+definition if there exists two open sets
+U1 and U2 that are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joint
+
+ align:start position:0%
+joint
+ 
+
+ align:start position:0%
+joint
+disjoint and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-empty such that uh the union of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them is exactly X this is what it means
+
+ align:start position:0%
+them is exactly X this is what it means
+ 
+
+ align:start position:0%
+them is exactly X this is what it means
+for your space to be
+
+ align:start position:0%
+for your space to be
+ 
+
+ align:start position:0%
+for your space to be
+disconnected and from here a set is
+
+ align:start position:0%
+disconnected and from here a set is
+ 
+
+ align:start position:0%
+disconnected and from here a set is
+connected if it is not disconnected so
+
+ align:start position:0%
+connected if it is not disconnected so
+ 
+
+ align:start position:0%
+connected if it is not disconnected so
+kind of kind kind of circular reasoning
+
+ align:start position:0%
+kind of kind kind of circular reasoning
+ 
+
+ align:start position:0%
+kind of kind kind of circular reasoning
+and then once you have that you can
+
+ align:start position:0%
+and then once you have that you can
+ 
+
+ align:start position:0%
+and then once you have that you can
+prove this note which I'll put in the
+
+ align:start position:0%
+prove this note which I'll put in the
+ 
+
+ align:start position:0%
+prove this note which I'll put in the
+problem or the third problem set which
+
+ align:start position:0%
+problem or the third problem set which
+ 
+
+ align:start position:0%
+problem or the third problem set which
+is an interesting problem
+
+ align:start position:0%
+is an interesting problem
+ 
+
+ align:start position:0%
+is an interesting problem
+um but I just want to knowe showing
+
+ align:start position:0%
+um but I just want to knowe showing
+ 
+
+ align:start position:0%
+um but I just want to knowe showing
+something is closed does not necessarily
+
+ align:start position:0%
+something is closed does not necessarily
+ 
+
+ align:start position:0%
+something is closed does not necessarily
+imply that it's
+
+ align:start position:0%
+imply that it's
+ 
+
+ align:start position:0%
+imply that it's
+open uh I'll give one short example of
+
+ align:start position:0%
+open uh I'll give one short example of
+ 
+
+ align:start position:0%
+open uh I'll give one short example of
+why this is true and then I'll move on
+
+ align:start position:0%
+why this is true and then I'll move on
+ 
+
+ align:start position:0%
+why this is true and then I'll move on
+to more properties of open
+
+ align:start position:0%
+to more properties of open
+ 
+
+ align:start position:0%
+to more properties of open
+sets anyone have
+
+ align:start position:0%
+sets anyone have
+ 
+
+ align:start position:0%
+sets anyone have
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+cool uh feel free to shout out questions
+
+ align:start position:0%
+cool uh feel free to shout out questions
+ 
+
+ align:start position:0%
+cool uh feel free to shout out questions
+if you have any or interrupt I'm more
+
+ align:start position:0%
+if you have any or interrupt I'm more
+ 
+
+ align:start position:0%
+if you have any or interrupt I'm more
+than happy to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interrupted okay so I'm just going to
+
+ align:start position:0%
+interrupted okay so I'm just going to
+ 
+
+ align:start position:0%
+interrupted okay so I'm just going to
+give one example of a metric space that
+
+ align:start position:0%
+give one example of a metric space that
+ 
+
+ align:start position:0%
+give one example of a metric space that
+is disconnected which is one that makes
+
+ align:start position:0%
+is disconnected which is one that makes
+ 
+
+ align:start position:0%
+is disconnected which is one that makes
+relative sense at least on the face of
+
+ align:start position:0%
+relative sense at least on the face of
+ 
+
+ align:start position:0%
+relative sense at least on the face of
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+example I can take the a union of two
+
+ align:start position:0%
+example I can take the a union of two
+ 
+
+ align:start position:0%
+example I can take the a union of two
+open intervals 0 to 1 and 1 to two and
+
+ align:start position:0%
+open intervals 0 to 1 and 1 to two and
+ 
+
+ align:start position:0%
+open intervals 0 to 1 and 1 to two and
+give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it the usual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metric on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R what do I mean by usual metric I mean
+
+ align:start position:0%
+R what do I mean by usual metric I mean
+ 
+
+ align:start position:0%
+R what do I mean by usual metric I mean
+the distance between two points in this
+
+ align:start position:0%
+the distance between two points in this
+ 
+
+ align:start position:0%
+the distance between two points in this
+set is just the distance normally in R
+
+ align:start position:0%
+set is just the distance normally in R
+ 
+
+ align:start position:0%
+set is just the distance normally in R
+right absolute
+
+ align:start position:0%
+right absolute
+ 
+
+ align:start position:0%
+right absolute
+values this is an example of one that's
+
+ align:start position:0%
+values this is an example of one that's
+ 
+
+ align:start position:0%
+values this is an example of one that's
+disconnected right because it's the
+
+ align:start position:0%
+disconnected right because it's the
+ 
+
+ align:start position:0%
+disconnected right because it's the
+union of two or one that is is
+
+ align:start position:0%
+union of two or one that is is
+ 
+
+ align:start position:0%
+union of two or one that is is
+disconnected it is the union of two open
+
+ align:start position:0%
+disconnected it is the union of two open
+ 
+
+ align:start position:0%
+disconnected it is the union of two open
+sets right that are
+
+ align:start position:0%
+sets right that are
+ 
+
+ align:start position:0%
+sets right that are
+disjointed and you can notice here the
+
+ align:start position:0%
+disjointed and you can notice here the
+ 
+
+ align:start position:0%
+disjointed and you can notice here the
+interval 01 is both open and
+
+ align:start position:0%
+interval 01 is both open and
+ 
+
+ align:start position:0%
+interval 01 is both open and
+closed
+
+ align:start position:0%
+closed
+ 
+
+ align:start position:0%
+closed
+so uh because the complement of it is
+
+ align:start position:0%
+so uh because the complement of it is
+ 
+
+ align:start position:0%
+so uh because the complement of it is
+just one two and that's open so this is
+
+ align:start position:0%
+just one two and that's open so this is
+ 
+
+ align:start position:0%
+just one two and that's open so this is
+an interesting example to think through
+
+ align:start position:0%
+an interesting example to think through
+ 
+
+ align:start position:0%
+an interesting example to think through
+this is known as the Subspace metric
+
+ align:start position:0%
+this is known as the Subspace metric
+ 
+
+ align:start position:0%
+this is known as the Subspace metric
+it's really or the Subspace topology
+
+ align:start position:0%
+it's really or the Subspace topology
+ 
+
+ align:start position:0%
+it's really or the Subspace topology
+technically um but yeah okay let's go
+
+ align:start position:0%
+technically um but yeah okay let's go
+ 
+
+ align:start position:0%
+technically um but yeah okay let's go
+back to proving things about the general
+
+ align:start position:0%
+back to proving things about the general
+ 
+
+ align:start position:0%
+back to proving things about the general
+theory of open
+
+ align:start position:0%
+theory of open
+ 
+
+ align:start position:0%
+theory of open
+sets proposition I'm first going to
+
+ align:start position:0%
+sets proposition I'm first going to
+ 
+
+ align:start position:0%
+sets proposition I'm first going to
+point out that closed sets are very
+
+ align:start position:0%
+point out that closed sets are very
+ 
+
+ align:start position:0%
+point out that closed sets are very
+similar to top uh very similar to open
+
+ align:start position:0%
+similar to top uh very similar to open
+ 
+
+ align:start position:0%
+similar to top uh very similar to open
+sets in fact we can Define everything in
+
+ align:start position:0%
+sets in fact we can Define everything in
+ 
+
+ align:start position:0%
+sets in fact we can Define everything in
+terms of of closed sets if you wanted to
+
+ align:start position:0%
+terms of of closed sets if you wanted to
+ 
+
+ align:start position:0%
+terms of of closed sets if you wanted to
+properties of closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets here we have that the empty set and
+
+ align:start position:0%
+sets here we have that the empty set and
+ 
+
+ align:start position:0%
+sets here we have that the empty set and
+X are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed to
+
+ align:start position:0%
+closed to
+ 
+
+ align:start position:0%
+closed to
+the infinite the potentially infinite
+
+ align:start position:0%
+the infinite the potentially infinite
+ 
+
+ align:start position:0%
+the infinite the potentially infinite
+intersection of closed
+
+ align:start position:0%
+intersection of closed
+ 
+
+ align:start position:0%
+intersection of closed
+sets AI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed and
+
+ align:start position:0%
+closed and
+ 
+
+ align:start position:0%
+closed and
+three the finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Union of Clos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nearly identical to the topological
+
+ align:start position:0%
+nearly identical to the topological
+ 
+
+ align:start position:0%
+nearly identical to the topological
+properties of open sets how do we prove
+
+ align:start position:0%
+properties of open sets how do we prove
+ 
+
+ align:start position:0%
+properties of open sets how do we prove
+this it's not too bad I'm not going to
+
+ align:start position:0%
+this it's not too bad I'm not going to
+ 
+
+ align:start position:0%
+this it's not too bad I'm not going to
+actually do it the fact that the empty
+
+ align:start position:0%
+actually do it the fact that the empty
+ 
+
+ align:start position:0%
+actually do it the fact that the empty
+set and X are closed is just the proof
+
+ align:start position:0%
+set and X are closed is just the proof
+ 
+
+ align:start position:0%
+set and X are closed is just the proof
+that I did above for R right you can
+
+ align:start position:0%
+that I did above for R right you can
+ 
+
+ align:start position:0%
+that I did above for R right you can
+replace r with just any metric
+
+ align:start position:0%
+replace r with just any metric
+ 
+
+ align:start position:0%
+replace r with just any metric
+space uh and we have that this first
+
+ align:start position:0%
+space uh and we have that this first
+ 
+
+ align:start position:0%
+space uh and we have that this first
+property holds how about the other two
+
+ align:start position:0%
+property holds how about the other two
+ 
+
+ align:start position:0%
+property holds how about the other two
+well for the other two I'm just going to
+
+ align:start position:0%
+well for the other two I'm just going to
+ 
+
+ align:start position:0%
+well for the other two I'm just going to
+quickly note what are known as the
+
+ align:start position:0%
+quickly note what are known as the
+ 
+
+ align:start position:0%
+quickly note what are known as the
+Morgan's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laws so this is is a nice Lemma from met
+
+ align:start position:0%
+laws so this is is a nice Lemma from met
+ 
+
+ align:start position:0%
+laws so this is is a nice Lemma from met
+from set
+
+ align:start position:0%
+from set
+ 
+
+ align:start position:0%
+from set
+theory these are known as de Morgan's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laws going to switch which talk I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using this
+
+ align:start position:0%
+using this
+ 
+
+ align:start position:0%
+using this
+states that the complement of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+union is the intersection of the
+
+ align:start position:0%
+union is the intersection of the
+ 
+
+ align:start position:0%
+union is the intersection of the
+complements so I and a
+
+ align:start position:0%
+complements so I and a
+ 
+
+ align:start position:0%
+complements so I and a
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarly the complement of an
+
+ align:start position:0%
+similarly the complement of an
+ 
+
+ align:start position:0%
+similarly the complement of an
+intersection UI
+
+ align:start position:0%
+intersection UI
+ 
+
+ align:start position:0%
+intersection UI
+complement I in a is equal to the union
+
+ align:start position:0%
+complement I in a is equal to the union
+ 
+
+ align:start position:0%
+complement I in a is equal to the union
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complements these are known as de
+
+ align:start position:0%
+complements these are known as de
+ 
+
+ align:start position:0%
+complements these are known as de
+Morgan's laws they make relative sense
+
+ align:start position:0%
+Morgan's laws they make relative sense
+ 
+
+ align:start position:0%
+Morgan's laws they make relative sense
+you can prove them for two sets as
+
+ align:start position:0%
+you can prove them for two sets as
+ 
+
+ align:start position:0%
+you can prove them for two sets as
+opposed to infinitely many of them but
+
+ align:start position:0%
+opposed to infinitely many of them but
+ 
+
+ align:start position:0%
+opposed to infinitely many of them but
+once you have these two properties then
+
+ align:start position:0%
+once you have these two properties then
+ 
+
+ align:start position:0%
+once you have these two properties then
+you can rewrite these two properties in
+
+ align:start position:0%
+you can rewrite these two properties in
+ 
+
+ align:start position:0%
+you can rewrite these two properties in
+terms of open open sets that's why
+
+ align:start position:0%
+terms of open open sets that's why
+ 
+
+ align:start position:0%
+terms of open open sets that's why
+there's this Duality right I can write
+
+ align:start position:0%
+there's this Duality right I can write
+ 
+
+ align:start position:0%
+there's this Duality right I can write
+the intersection of closed sets as the
+
+ align:start position:0%
+the intersection of closed sets as the
+ 
+
+ align:start position:0%
+the intersection of closed sets as the
+union of open
+
+ align:start position:0%
+union of open
+ 
+
+ align:start position:0%
+union of open
+sets so that's uh that's how you apply
+
+ align:start position:0%
+sets so that's uh that's how you apply
+ 
+
+ align:start position:0%
+sets so that's uh that's how you apply
+to Morgan's laws and I'm not going to
+
+ align:start position:0%
+to Morgan's laws and I'm not going to
+ 
+
+ align:start position:0%
+to Morgan's laws and I'm not going to
+prove that or I'm not going to prove
+
+ align:start position:0%
+prove that or I'm not going to prove
+ 
+
+ align:start position:0%
+prove that or I'm not going to prove
+these topological properties this is in
+
+ align:start position:0%
+these topological properties this is in
+ 
+
+ align:start position:0%
+these topological properties this is in
+the lecture notes but I do want to knowe
+
+ align:start position:0%
+the lecture notes but I do want to knowe
+ 
+
+ align:start position:0%
+the lecture notes but I do want to knowe
+you could do everything in terms of
+
+ align:start position:0%
+you could do everything in terms of
+ 
+
+ align:start position:0%
+you could do everything in terms of
+closed sets if you really truly wanted
+
+ align:start position:0%
+closed sets if you really truly wanted
+ 
+
+ align:start position:0%
+closed sets if you really truly wanted
+to we just don't because open sets are
+
+ align:start position:0%
+to we just don't because open sets are
+ 
+
+ align:start position:0%
+to we just don't because open sets are
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+nice okay we'll show why some of those
+
+ align:start position:0%
+nice okay we'll show why some of those
+ 
+
+ align:start position:0%
+nice okay we'll show why some of those
+things are actually nice uh what more
+
+ align:start position:0%
+things are actually nice uh what more
+ 
+
+ align:start position:0%
+things are actually nice uh what more
+things do I want to know okay
+
+ align:start position:0%
+things do I want to know okay
+ 
+
+ align:start position:0%
+things do I want to know okay
+cool uh now I want to State some
+
+ align:start position:0%
+cool uh now I want to State some
+ 
+
+ align:start position:0%
+cool uh now I want to State some
+specific examples of open sets and
+
+ align:start position:0%
+specific examples of open sets and
+ 
+
+ align:start position:0%
+specific examples of open sets and
+Metric baces which we can already do
+
+ align:start position:0%
+Metric baces which we can already do
+ 
+
+ align:start position:0%
+Metric baces which we can already do
+quite a bit
+
+ align:start position:0%
+quite a bit
+ 
+
+ align:start position:0%
+quite a bit
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+example uh one thing did I erase it
+
+ align:start position:0%
+example uh one thing did I erase it
+ 
+
+ align:start position:0%
+example uh one thing did I erase it
+already I think I oh wait no I did it
+
+ align:start position:0%
+already I think I oh wait no I did it
+ 
+
+ align:start position:0%
+already I think I oh wait no I did it
+here uh I did it where did I do it oh I
+
+ align:start position:0%
+here uh I did it where did I do it oh I
+ 
+
+ align:start position:0%
+here uh I did it where did I do it oh I
+did it at the very top uh the ball of
+
+ align:start position:0%
+did it at the very top uh the ball of
+ 
+
+ align:start position:0%
+did it at the very top uh the ball of
+radius Epsilon around a is sometimes
+
+ align:start position:0%
+radius Epsilon around a is sometimes
+ 
+
+ align:start position:0%
+radius Epsilon around a is sometimes
+referred to as an open ball but you
+
+ align:start position:0%
+referred to as an open ball but you
+ 
+
+ align:start position:0%
+referred to as an open ball but you
+should prove that the ball is in fact
+
+ align:start position:0%
+should prove that the ball is in fact
+ 
+
+ align:start position:0%
+should prove that the ball is in fact
+open which will be our first
+
+ align:start position:0%
+open which will be our first
+ 
+
+ align:start position:0%
+open which will be our first
+example so
+
+ align:start position:0%
+example so
+ 
+
+ align:start position:0%
+example so
+given some point x in your metric Space
+
+ align:start position:0%
+given some point x in your metric Space
+ 
+
+ align:start position:0%
+given some point x in your metric Space
+X and Epsilon bigger than
+
+ align:start position:0%
+X and Epsilon bigger than
+ 
+
+ align:start position:0%
+X and Epsilon bigger than
+zero we have that the ball of radius
+
+ align:start position:0%
+zero we have that the ball of radius
+ 
+
+ align:start position:0%
+zero we have that the ball of radius
+Epsilon round
+
+ align:start position:0%
+Epsilon round
+ 
+
+ align:start position:0%
+Epsilon round
+X is
+
+ align:start position:0%
+X is
+ 
+
+ align:start position:0%
+X is
+open how do we do this well we choose an
+
+ align:start position:0%
+open how do we do this well we choose an
+ 
+
+ align:start position:0%
+open how do we do this well we choose an
+arbitrary point in your ball of radius
+
+ align:start position:0%
+arbitrary point in your ball of radius
+ 
+
+ align:start position:0%
+arbitrary point in your ball of radius
+Epsilon right so
+
+ align:start position:0%
+Epsilon right so
+ 
+
+ align:start position:0%
+Epsilon right so
+proof uh
+
+ align:start position:0%
+proof uh
+ 
+
+ align:start position:0%
+proof uh
+choose some
+
+ align:start position:0%
+choose some
+ 
+
+ align:start position:0%
+choose some
+y in the ball of radius Epsilon around
+
+ align:start position:0%
+y in the ball of radius Epsilon around
+ 
+
+ align:start position:0%
+y in the ball of radius Epsilon around
+X we want to find a ball of radius let's
+
+ align:start position:0%
+X we want to find a ball of radius let's
+ 
+
+ align:start position:0%
+X we want to find a ball of radius let's
+say Delta around y contained in the ball
+
+ align:start position:0%
+say Delta around y contained in the ball
+ 
+
+ align:start position:0%
+say Delta around y contained in the ball
+of radius Epsilon around X that's the
+
+ align:start position:0%
+of radius Epsilon around X that's the
+ 
+
+ align:start position:0%
+of radius Epsilon around X that's the
+definition of open uh open
+
+ align:start position:0%
+definition of open uh open
+ 
+
+ align:start position:0%
+definition of open uh open
+set well notice that the distance from X
+
+ align:start position:0%
+set well notice that the distance from X
+ 
+
+ align:start position:0%
+set well notice that the distance from X
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Y is less than Epsilon by definition
+
+ align:start position:0%
+Y is less than Epsilon by definition
+ 
+
+ align:start position:0%
+Y is less than Epsilon by definition
+right because we're assuming that the
+
+ align:start position:0%
+right because we're assuming that the
+ 
+
+ align:start position:0%
+right because we're assuming that the
+distance between points in our ball is
+
+ align:start position:0%
+distance between points in our ball is
+ 
+
+ align:start position:0%
+distance between points in our ball is
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+so let Delta be the distance from X to
+
+ align:start position:0%
+so let Delta be the distance from X to
+ 
+
+ align:start position:0%
+so let Delta be the distance from X to
+Y over
+
+ align:start position:0%
+Y over
+ 
+
+ align:start position:0%
+Y over
+two why does this work because then
+
+ align:start position:0%
+two why does this work because then
+ 
+
+ align:start position:0%
+two why does this work because then
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+notice that the ball of radius Delta
+
+ align:start position:0%
+notice that the ball of radius Delta
+ 
+
+ align:start position:0%
+notice that the ball of radius Delta
+around y has to be contained in the ball
+
+ align:start position:0%
+around y has to be contained in the ball
+ 
+
+ align:start position:0%
+around y has to be contained in the ball
+of radius Epsilon around X why is this
+
+ align:start position:0%
+of radius Epsilon around X why is this
+ 
+
+ align:start position:0%
+of radius Epsilon around X why is this
+true essentially the triangle inequality
+
+ align:start position:0%
+true essentially the triangle inequality
+ 
+
+ align:start position:0%
+true essentially the triangle inequality
+right we have a ball of radius Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+centered at
+
+ align:start position:0%
+centered at
+ 
+
+ align:start position:0%
+centered at
+X have a point Y
+
+ align:start position:0%
+X have a point Y
+ 
+
+ align:start position:0%
+X have a point Y
+here and I'm noting that the distance
+
+ align:start position:0%
+here and I'm noting that the distance
+ 
+
+ align:start position:0%
+here and I'm noting that the distance
+from here to here is Epsilon uh is less
+
+ align:start position:0%
+from here to here is Epsilon uh is less
+ 
+
+ align:start position:0%
+from here to here is Epsilon uh is less
+than Epsilon by definition and I'm just
+
+ align:start position:0%
+than Epsilon by definition and I'm just
+ 
+
+ align:start position:0%
+than Epsilon by definition and I'm just
+choosing a ball around
+
+ align:start position:0%
+choosing a ball around
+ 
+
+ align:start position:0%
+choosing a ball around
+y to be half of that
+
+ align:start position:0%
+y to be half of that
+ 
+
+ align:start position:0%
+y to be half of that
+distance and then you can apply the
+
+ align:start position:0%
+distance and then you can apply the
+ 
+
+ align:start position:0%
+distance and then you can apply the
+triangle inequality to show that this
+
+ align:start position:0%
+triangle inequality to show that this
+ 
+
+ align:start position:0%
+triangle inequality to show that this
+ball must actually be contained in the
+
+ align:start position:0%
+ball must actually be contained in the
+ 
+
+ align:start position:0%
+ball must actually be contained in the
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+one anyone want me to work through that
+
+ align:start position:0%
+one anyone want me to work through that
+ 
+
+ align:start position:0%
+one anyone want me to work through that
+I'm happy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh wait
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one let me let me write it
+
+ align:start position:0%
+one let me let me write it
+ 
+
+ align:start position:0%
+one let me let me write it
+out uh you know I'll write it out on the
+
+ align:start position:0%
+out uh you know I'll write it out on the
+ 
+
+ align:start position:0%
+out uh you know I'll write it out on the
+backboard so
+
+ align:start position:0%
+backboard so
+ 
+
+ align:start position:0%
+backboard so
+let z b in the ball of radius Delta
+
+ align:start position:0%
+let z b in the ball of radius Delta
+ 
+
+ align:start position:0%
+let z b in the ball of radius Delta
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+y then we have that the distance from X
+
+ align:start position:0%
+y then we have that the distance from X
+ 
+
+ align:start position:0%
+y then we have that the distance from X
+to Z is less than equal to by the
+
+ align:start position:0%
+to Z is less than equal to by the
+ 
+
+ align:start position:0%
+to Z is less than equal to by the
+triangle inequality the distance from X
+
+ align:start position:0%
+triangle inequality the distance from X
+ 
+
+ align:start position:0%
+triangle inequality the distance from X
+to Y plus the distance from y to
+
+ align:start position:0%
+to Y plus the distance from y to
+ 
+
+ align:start position:0%
+to Y plus the distance from y to
+Z uh distance from X to
+
+ align:start position:0%
+Z uh distance from X to
+ 
+
+ align:start position:0%
+Z uh distance from X to
+Y and the distance from y to Z is less
+
+ align:start position:0%
+Y and the distance from y to Z is less
+ 
+
+ align:start position:0%
+Y and the distance from y to Z is less
+than the distance from X to Y over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 is this what I wanted to do epon Prim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I should say no this is not what I
+
+ align:start position:0%
+uh I should say no this is not what I
+ 
+
+ align:start position:0%
+uh I should say no this is not what I
+wanted to
+
+ align:start position:0%
+wanted to
+ 
+
+ align:start position:0%
+wanted to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+let let R be the distance from X to Y
+
+ align:start position:0%
+let let R be the distance from X to Y
+ 
+
+ align:start position:0%
+let let R be the distance from X to Y
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+Epsilon then what we know is that the
+
+ align:start position:0%
+Epsilon then what we know is that the
+ 
+
+ align:start position:0%
+Epsilon then what we know is that the
+distance from y to Z is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R what am I trying to say distance of Y
+
+ align:start position:0%
+R what am I trying to say distance of Y
+ 
+
+ align:start position:0%
+R what am I trying to say distance of Y
+to Z is less
+
+ align:start position:0%
+to Z is less
+ 
+
+ align:start position:0%
+to Z is less
+than or sorry this should be Epsilon
+
+ align:start position:0%
+than or sorry this should be Epsilon
+ 
+
+ align:start position:0%
+than or sorry this should be Epsilon
+minus the distance there we go and this
+
+ align:start position:0%
+minus the distance there we go and this
+ 
+
+ align:start position:0%
+minus the distance there we go and this
+is then less than Epsilon so this is in
+
+ align:start position:0%
+is then less than Epsilon so this is in
+ 
+
+ align:start position:0%
+is then less than Epsilon so this is in
+the lecture notes I would highly suggest
+
+ align:start position:0%
+the lecture notes I would highly suggest
+ 
+
+ align:start position:0%
+the lecture notes I would highly suggest
+drawing out the picture and working
+
+ align:start position:0%
+drawing out the picture and working
+ 
+
+ align:start position:0%
+drawing out the picture and working
+through it uh separately but Loosely
+
+ align:start position:0%
+through it uh separately but Loosely
+ 
+
+ align:start position:0%
+through it uh separately but Loosely
+speaking it's just this diagram on the
+
+ align:start position:0%
+speaking it's just this diagram on the
+ 
+
+ align:start position:0%
+speaking it's just this diagram on the
+right hand side it's an application of
+
+ align:start position:0%
+right hand side it's an application of
+ 
+
+ align:start position:0%
+right hand side it's an application of
+the triangle
+
+ align:start position:0%
+the triangle
+ 
+
+ align:start position:0%
+the triangle
+inequality okay so the ball of radius
+
+ align:start position:0%
+inequality okay so the ball of radius
+ 
+
+ align:start position:0%
+inequality okay so the ball of radius
+Epsilon is an open ball in
+
+ align:start position:0%
+Epsilon is an open ball in
+ 
+
+ align:start position:0%
+Epsilon is an open ball in
+fact you can State much more than this
+
+ align:start position:0%
+fact you can State much more than this
+ 
+
+ align:start position:0%
+fact you can State much more than this
+this is an optional problem on your
+
+ align:start position:0%
+this is an optional problem on your
+ 
+
+ align:start position:0%
+this is an optional problem on your
+second problem
+
+ align:start position:0%
+second problem
+ 
+
+ align:start position:0%
+second problem
+set and for the record I do suggest yall
+
+ align:start position:0%
+set and for the record I do suggest yall
+ 
+
+ align:start position:0%
+set and for the record I do suggest yall
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+um look at the optional problems because
+
+ align:start position:0%
+um look at the optional problems because
+ 
+
+ align:start position:0%
+um look at the optional problems because
+they will potentially give you more
+
+ align:start position:0%
+they will potentially give you more
+ 
+
+ align:start position:0%
+they will potentially give you more
+intuition even if you don't solve
+
+ align:start position:0%
+intuition even if you don't solve
+ 
+
+ align:start position:0%
+intuition even if you don't solve
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+um but yeah it's this is just one of
+
+ align:start position:0%
+um but yeah it's this is just one of
+ 
+
+ align:start position:0%
+um but yeah it's this is just one of
+those cases where this isn't a topology
+
+ align:start position:0%
+those cases where this isn't a topology
+ 
+
+ align:start position:0%
+those cases where this isn't a topology
+class so I'm not going to ask that y'all
+
+ align:start position:0%
+class so I'm not going to ask that y'all
+ 
+
+ align:start position:0%
+class so I'm not going to ask that y'all
+do a bunch of topology but it's pretty
+
+ align:start position:0%
+do a bunch of topology but it's pretty
+ 
+
+ align:start position:0%
+do a bunch of topology but it's pretty
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+okay so just a small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note any open set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U contained in your metric
+
+ align:start position:0%
+U contained in your metric
+ 
+
+ align:start position:0%
+U contained in your metric
+space can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+as a union a potentially infinite Union
+
+ align:start position:0%
+as a union a potentially infinite Union
+ 
+
+ align:start position:0%
+as a union a potentially infinite Union
+of open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balls I'll I'll outline briefly how to
+
+ align:start position:0%
+balls I'll I'll outline briefly how to
+ 
+
+ align:start position:0%
+balls I'll I'll outline briefly how to
+do this right now so if youall want to
+
+ align:start position:0%
+do this right now so if youall want to
+ 
+
+ align:start position:0%
+do this right now so if youall want to
+do it later you can do it um but theide
+
+ align:start position:0%
+do it later you can do it um but theide
+ 
+
+ align:start position:0%
+do it later you can do it um but theide
+idea is that for any single point in
+
+ align:start position:0%
+idea is that for any single point in
+ 
+
+ align:start position:0%
+idea is that for any single point in
+your open set there exists a ball of
+
+ align:start position:0%
+your open set there exists a ball of
+ 
+
+ align:start position:0%
+your open set there exists a ball of
+radius Epsilon around that point and
+
+ align:start position:0%
+radius Epsilon around that point and
+ 
+
+ align:start position:0%
+radius Epsilon around that point and
+then you can just take the union of all
+
+ align:start position:0%
+then you can just take the union of all
+ 
+
+ align:start position:0%
+then you can just take the union of all
+those balls of radius Epsilon the
+
+ align:start position:0%
+those balls of radius Epsilon the
+ 
+
+ align:start position:0%
+those balls of radius Epsilon the
+Epsilon might change for every single
+
+ align:start position:0%
+Epsilon might change for every single
+ 
+
+ align:start position:0%
+Epsilon might change for every single
+point but that doesn't matter right
+
+ align:start position:0%
+point but that doesn't matter right
+ 
+
+ align:start position:0%
+point but that doesn't matter right
+because it's an infinite Union so I'll
+
+ align:start position:0%
+because it's an infinite Union so I'll
+ 
+
+ align:start position:0%
+because it's an infinite Union so I'll
+let youall work through those
+
+ align:start position:0%
+let youall work through those
+ 
+
+ align:start position:0%
+let youall work through those
+details but this is just a proposition
+
+ align:start position:0%
+details but this is just a proposition
+ 
+
+ align:start position:0%
+details but this is just a proposition
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+show okay let's also just prove what an
+
+ align:start position:0%
+show okay let's also just prove what an
+ 
+
+ align:start position:0%
+show okay let's also just prove what an
+example of a Clos set which will come
+
+ align:start position:0%
+example of a Clos set which will come
+ 
+
+ align:start position:0%
+example of a Clos set which will come
+important for next
+
+ align:start position:0%
+important for next
+ 
+
+ align:start position:0%
+important for next
+time it's just an example
+
+ align:start position:0%
+time it's just an example
+ 
+
+ align:start position:0%
+time it's just an example
+x uh sorry I should say let X be a point
+
+ align:start position:0%
+x uh sorry I should say let X be a point
+ 
+
+ align:start position:0%
+x uh sorry I should say let X be a point
+in your metric
+
+ align:start position:0%
+in your metric
+ 
+
+ align:start position:0%
+in your metric
+space then the set
+
+ align:start position:0%
+space then the set
+ 
+
+ align:start position:0%
+space then the set
+X is
+
+ align:start position:0%
+X is
+ 
+
+ align:start position:0%
+X is
+closed so this is just a singular point
+
+ align:start position:0%
+closed so this is just a singular point
+ 
+
+ align:start position:0%
+closed so this is just a singular point
+in your metric space how we're going to
+
+ align:start position:0%
+in your metric space how we're going to
+ 
+
+ align:start position:0%
+in your metric space how we're going to
+prove this well we only have one
+
+ align:start position:0%
+prove this well we only have one
+ 
+
+ align:start position:0%
+prove this well we only have one
+definition of closed we have that it's
+
+ align:start position:0%
+definition of closed we have that it's
+ 
+
+ align:start position:0%
+definition of closed we have that it's
+the complement or the complement is open
+
+ align:start position:0%
+the complement or the complement is open
+ 
+
+ align:start position:0%
+the complement or the complement is open
+right so uh proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider the complement of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X which is X not including
+
+ align:start position:0%
+X which is X not including
+ 
+
+ align:start position:0%
+X which is X not including
+X and
+
+ align:start position:0%
+X and
+ 
+
+ align:start position:0%
+X and
+let y be a point
+
+ align:start position:0%
+let y be a point
+ 
+
+ align:start position:0%
+let y be a point
+here what we want to show is that
+
+ align:start position:0%
+here what we want to show is that
+ 
+
+ align:start position:0%
+here what we want to show is that
+there's a ball of radius Epsilon I want
+
+ align:start position:0%
+there's a ball of radius Epsilon I want
+ 
+
+ align:start position:0%
+there's a ball of radius Epsilon I want
+to show around
+
+ align:start position:0%
+to show around
+ 
+
+ align:start position:0%
+to show around
+y or not in subset of X not including X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's draw a picture of what this should
+
+ align:start position:0%
+let's draw a picture of what this should
+ 
+
+ align:start position:0%
+let's draw a picture of what this should
+actually look like
+
+ align:start position:0%
+actually look like
+ 
+
+ align:start position:0%
+actually look like
+right uh well I didn't want to do that
+
+ align:start position:0%
+right uh well I didn't want to do that
+ 
+
+ align:start position:0%
+right uh well I didn't want to do that
+here's our metric
+
+ align:start position:0%
+here's our metric
+ 
+
+ align:start position:0%
+here's our metric
+space here's our singular point x and
+
+ align:start position:0%
+space here's our singular point x and
+ 
+
+ align:start position:0%
+space here's our singular point x and
+here's our Point let's say y we want to
+
+ align:start position:0%
+here's our Point let's say y we want to
+ 
+
+ align:start position:0%
+here's our Point let's say y we want to
+choose a ball around
+
+ align:start position:0%
+choose a ball around
+ 
+
+ align:start position:0%
+choose a ball around
+y that doesn't contain X how can we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it anyone you could choose whatever
+
+ align:start position:0%
+it anyone you could choose whatever
+ 
+
+ align:start position:0%
+it anyone you could choose whatever
+Epsilon you want so it's a question of
+
+ align:start position:0%
+Epsilon you want so it's a question of
+ 
+
+ align:start position:0%
+Epsilon you want so it's a question of
+what Epsilon want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose we can choose Epsilon to be the
+
+ align:start position:0%
+choose we can choose Epsilon to be the
+ 
+
+ align:start position:0%
+choose we can choose Epsilon to be the
+half the distance between X and Y I
+
+ align:start position:0%
+half the distance between X and Y I
+ 
+
+ align:start position:0%
+half the distance between X and Y I
+think that's what I was mixing up on the
+
+ align:start position:0%
+think that's what I was mixing up on the
+ 
+
+ align:start position:0%
+think that's what I was mixing up on the
+other proof but it's in the lecture
+
+ align:start position:0%
+other proof but it's in the lecture
+ 
+
+ align:start position:0%
+other proof but it's in the lecture
+notes so I'll let you all do the other
+
+ align:start position:0%
+notes so I'll let you all do the other
+ 
+
+ align:start position:0%
+notes so I'll let you all do the other
+one but
+
+ align:start position:0%
+one but
+ 
+
+ align:start position:0%
+one but
+um choose
+
+ align:start position:0%
+um choose
+ 
+
+ align:start position:0%
+um choose
+Epsilon to be the distance from X to
+
+ align:start position:0%
+Epsilon to be the distance from X to
+ 
+
+ align:start position:0%
+Epsilon to be the distance from X to
+Y over
+
+ align:start position:0%
+Y over
+ 
+
+ align:start position:0%
+Y over
+two and then pictorially we have that
+
+ align:start position:0%
+two and then pictorially we have that
+ 
+
+ align:start position:0%
+two and then pictorially we have that
+it's you know that's rest of the problem
+
+ align:start position:0%
+it's you know that's rest of the problem
+ 
+
+ align:start position:0%
+it's you know that's rest of the problem
+but let's actually work through the
+
+ align:start position:0%
+but let's actually work through the
+ 
+
+ align:start position:0%
+but let's actually work through the
+details
+
+ align:start position:0%
+details
+ 
+
+ align:start position:0%
+details
+so then let Z be in your ball of radius
+
+ align:start position:0%
+so then let Z be in your ball of radius
+ 
+
+ align:start position:0%
+so then let Z be in your ball of radius
+Epsilon around
+
+ align:start position:0%
+Epsilon around
+ 
+
+ align:start position:0%
+Epsilon around
+y then we want to show that Z cannot be
+
+ align:start position:0%
+y then we want to show that Z cannot be
+ 
+
+ align:start position:0%
+y then we want to show that Z cannot be
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+right well notice this implies that the
+
+ align:start position:0%
+right well notice this implies that the
+ 
+
+ align:start position:0%
+right well notice this implies that the
+distance from y to
+
+ align:start position:0%
+distance from y to
+ 
+
+ align:start position:0%
+distance from y to
+Z has to be less
+
+ align:start position:0%
+Z has to be less
+ 
+
+ align:start position:0%
+Z has to be less
+than Epsilon right this is by
+
+ align:start position:0%
+than Epsilon right this is by
+ 
+
+ align:start position:0%
+than Epsilon right this is by
+construction but what can we can we get
+
+ align:start position:0%
+construction but what can we can we get
+ 
+
+ align:start position:0%
+construction but what can we can we get
+a lower bound on this we can we can note
+
+ align:start position:0%
+a lower bound on this we can we can note
+ 
+
+ align:start position:0%
+a lower bound on this we can we can note
+that the distance from I want to make
+
+ align:start position:0%
+that the distance from I want to make
+ 
+
+ align:start position:0%
+that the distance from I want to make
+sure I'm getting this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right r
+
+ align:start position:0%
+right r
+ 
+
+ align:start position:0%
+right r
+x actually you know I'll do this
+
+ align:start position:0%
+x actually you know I'll do this
+ 
+
+ align:start position:0%
+x actually you know I'll do this
+directly or I'll do this by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contradiction suppose for the sake of
+
+ align:start position:0%
+contradiction suppose for the sake of
+ 
+
+ align:start position:0%
+contradiction suppose for the sake of
+contradiction X was in the ball of
+
+ align:start position:0%
+contradiction X was in the ball of
+ 
+
+ align:start position:0%
+contradiction X was in the ball of
+radius Epsilon around y then this would
+
+ align:start position:0%
+radius Epsilon around y then this would
+ 
+
+ align:start position:0%
+radius Epsilon around y then this would
+imply that the distance from X to
+
+ align:start position:0%
+imply that the distance from X to
+ 
+
+ align:start position:0%
+imply that the distance from X to
+Y is less than
+
+ align:start position:0%
+Y is less than
+ 
+
+ align:start position:0%
+Y is less than
+Epsilon but this can't be the case
+
+ align:start position:0%
+Epsilon but this can't be the case
+ 
+
+ align:start position:0%
+Epsilon but this can't be the case
+because again we're assuming that the
+
+ align:start position:0%
+because again we're assuming that the
+ 
+
+ align:start position:0%
+because again we're assuming that the
+distance that
+
+ align:start position:0%
+distance that
+ 
+
+ align:start position:0%
+distance that
+Epsilon is the distance from X to Y over
+
+ align:start position:0%
+Epsilon is the distance from X to Y over
+ 
+
+ align:start position:0%
+Epsilon is the distance from X to Y over
+2 and the distance from X to Y cannot be
+
+ align:start position:0%
+2 and the distance from X to Y cannot be
+ 
+
+ align:start position:0%
+2 and the distance from X to Y cannot be
+less than the distance from X to Y over
+
+ align:start position:0%
+less than the distance from X to Y over
+ 
+
+ align:start position:0%
+less than the distance from X to Y over
+2 so that is our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contradiction I'll make one more small
+
+ align:start position:0%
+contradiction I'll make one more small
+ 
+
+ align:start position:0%
+contradiction I'll make one more small
+note here which will come important for
+
+ align:start position:0%
+note here which will come important for
+ 
+
+ align:start position:0%
+note here which will come important for
+Tuesday which is as opposed to looking
+
+ align:start position:0%
+Tuesday which is as opposed to looking
+ 
+
+ align:start position:0%
+Tuesday which is as opposed to looking
+at a singular point you can do this with
+
+ align:start position:0%
+at a singular point you can do this with
+ 
+
+ align:start position:0%
+at a singular point you can do this with
+a finite Union of points right and the
+
+ align:start position:0%
+a finite Union of points right and the
+ 
+
+ align:start position:0%
+a finite Union of points right and the
+argument would be essentially the same
+
+ align:start position:0%
+argument would be essentially the same
+ 
+
+ align:start position:0%
+argument would be essentially the same
+as our finite intersection of open sets
+
+ align:start position:0%
+as our finite intersection of open sets
+ 
+
+ align:start position:0%
+as our finite intersection of open sets
+argument you have a finite Union of open
+
+ align:start position:0%
+argument you have a finite Union of open
+ 
+
+ align:start position:0%
+argument you have a finite Union of open
+sets or sorry a finite Union of closed
+
+ align:start position:0%
+sets or sorry a finite Union of closed
+ 
+
+ align:start position:0%
+sets or sorry a finite Union of closed
+things so it should be closed in fact
+
+ align:start position:0%
+things so it should be closed in fact
+ 
+
+ align:start position:0%
+things so it should be closed in fact
+you could use that to prove it
+
+ align:start position:0%
+you could use that to prove it
+ 
+
+ align:start position:0%
+you could use that to prove it
+immediately but you can also prove it
+
+ align:start position:0%
+immediately but you can also prove it
+ 
+
+ align:start position:0%
+immediately but you can also prove it
+directly like
+
+ align:start position:0%
+directly like
+ 
+
+ align:start position:0%
+directly like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay so now what we're going to do is
+
+ align:start position:0%
+okay so now what we're going to do is
+ 
+
+ align:start position:0%
+okay so now what we're going to do is
+talk about how this definition of open
+
+ align:start position:0%
+talk about how this definition of open
+ 
+
+ align:start position:0%
+talk about how this definition of open
+set that's relates to convergent
+
+ align:start position:0%
+set that's relates to convergent
+ 
+
+ align:start position:0%
+set that's relates to convergent
+sequences and to um and to
+
+ align:start position:0%
+sequences and to um and to
+ 
+
+ align:start position:0%
+sequences and to um and to
+continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proposition let
+
+ align:start position:0%
+proposition let
+ 
+
+ align:start position:0%
+proposition let
+xn to do this I'm going to do it in the
+
+ align:start position:0%
+xn to do this I'm going to do it in the
+ 
+
+ align:start position:0%
+xn to do this I'm going to do it in the
+real numbers but note that everything
+
+ align:start position:0%
+real numbers but note that everything
+ 
+
+ align:start position:0%
+real numbers but note that everything
+can be done in your metric bace I just
+
+ align:start position:0%
+can be done in your metric bace I just
+ 
+
+ align:start position:0%
+can be done in your metric bace I just
+want to use the notation from the real
+
+ align:start position:0%
+want to use the notation from the real
+ 
+
+ align:start position:0%
+want to use the notation from the real
+numbers let xn be a
+
+ align:start position:0%
+numbers let xn be a
+ 
+
+ align:start position:0%
+numbers let xn be a
+sequence am I holding it backwards I am
+
+ align:start position:0%
+sequence am I holding it backwards I am
+ 
+
+ align:start position:0%
+sequence am I holding it backwards I am
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+R uh that converges to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X so this is true I claim if and only
+
+ align:start position:0%
+X so this is true I claim if and only
+ 
+
+ align:start position:0%
+X so this is true I claim if and only
+if for all Epsilon bigger than
+
+ align:start position:0%
+if for all Epsilon bigger than
+ 
+
+ align:start position:0%
+if for all Epsilon bigger than
+zero all but finitely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many x i are in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x -
+
+ align:start position:0%
+x -
+ 
+
+ align:start position:0%
+x -
+Epsilon to X Plus Epsilon so this is the
+
+ align:start position:0%
+Epsilon to X Plus Epsilon so this is the
+ 
+
+ align:start position:0%
+Epsilon to X Plus Epsilon so this is the
+ball of radius Epsilon around X right
+
+ align:start position:0%
+ball of radius Epsilon around X right
+ 
+
+ align:start position:0%
+ball of radius Epsilon around X right
+how do we prove this if and only if
+
+ align:start position:0%
+how do we prove this if and only if
+ 
+
+ align:start position:0%
+how do we prove this if and only if
+proof well okay I should say convergent
+
+ align:start position:0%
+proof well okay I should say convergent
+ 
+
+ align:start position:0%
+proof well okay I should say convergent
+sequence let's prove the forward
+
+ align:start position:0%
+sequence let's prove the forward
+ 
+
+ align:start position:0%
+sequence let's prove the forward
+Direction first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if xn is convergent then for all
+
+ align:start position:0%
+so if xn is convergent then for all
+ 
+
+ align:start position:0%
+so if xn is convergent then for all
+Epsilon bigger than zero there exists an
+
+ align:start position:0%
+Epsilon bigger than zero there exists an
+ 
+
+ align:start position:0%
+Epsilon bigger than zero there exists an
+n in the natural numbers
+
+ align:start position:0%
+n in the natural numbers
+ 
+
+ align:start position:0%
+n in the natural numbers
+such that the ball of radius Epsilon
+
+ align:start position:0%
+such that the ball of radius Epsilon
+ 
+
+ align:start position:0%
+such that the ball of radius Epsilon
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+x uh such that I should say such that
+
+ align:start position:0%
+x uh such that I should say such that
+ 
+
+ align:start position:0%
+x uh such that I should say such that
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+all n bigger than or equal to
+
+ align:start position:0%
+all n bigger than or equal to
+ 
+
+ align:start position:0%
+all n bigger than or equal to
+n the uh xn is in the ball of radius
+
+ align:start position:0%
+n the uh xn is in the ball of radius
+ 
+
+ align:start position:0%
+n the uh xn is in the ball of radius
+Epsilon X Plus
+
+ align:start position:0%
+Epsilon X Plus
+ 
+
+ align:start position:0%
+Epsilon X Plus
+Epsilon as this is true because the
+
+ align:start position:0%
+Epsilon as this is true because the
+ 
+
+ align:start position:0%
+Epsilon as this is true because the
+distance from xn to X is less than
+
+ align:start position:0%
+distance from xn to X is less than
+ 
+
+ align:start position:0%
+distance from xn to X is less than
+Epsilon this is just the open set way to
+
+ align:start position:0%
+Epsilon this is just the open set way to
+ 
+
+ align:start position:0%
+Epsilon this is just the open set way to
+view it right and this capital N notice
+
+ align:start position:0%
+view it right and this capital N notice
+ 
+
+ align:start position:0%
+view it right and this capital N notice
+that there are only Finly many terms
+
+ align:start position:0%
+that there are only Finly many terms
+ 
+
+ align:start position:0%
+that there are only Finly many terms
+less than it so this shows that
+
+ align:start position:0%
+less than it so this shows that
+ 
+
+ align:start position:0%
+less than it so this shows that
+infinitely many of the terms are in this
+
+ align:start position:0%
+infinitely many of the terms are in this
+ 
+
+ align:start position:0%
+infinitely many of the terms are in this
+open set and in fact only finitely many
+
+ align:start position:0%
+open set and in fact only finitely many
+ 
+
+ align:start position:0%
+open set and in fact only finitely many
+are outside of it so that proves the
+
+ align:start position:0%
+are outside of it so that proves the
+ 
+
+ align:start position:0%
+are outside of it so that proves the
+forward Direction let's prove the
+
+ align:start position:0%
+forward Direction let's prove the
+ 
+
+ align:start position:0%
+forward Direction let's prove the
+opposite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+suppose or I should
+
+ align:start position:0%
+suppose or I should
+ 
+
+ align:start position:0%
+suppose or I should
+write suppose
+
+ align:start position:0%
+write suppose
+ 
+
+ align:start position:0%
+write suppose
+uh for all Epsilon bigger than
+
+ align:start position:0%
+uh for all Epsilon bigger than
+ 
+
+ align:start position:0%
+uh for all Epsilon bigger than
+zero all but finitely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+XI are
+
+ align:start position:0%
+XI are
+ 
+
+ align:start position:0%
+XI are
+in x - Epsilon to X Plus
+
+ align:start position:0%
+in x - Epsilon to X Plus
+ 
+
+ align:start position:0%
+in x - Epsilon to X Plus
+Epsilon I want to choose a sequence that
+
+ align:start position:0%
+Epsilon I want to choose a sequence that
+ 
+
+ align:start position:0%
+Epsilon I want to choose a sequence that
+will converge to X then
+
+ align:start position:0%
+will converge to X then
+ 
+
+ align:start position:0%
+will converge to X then
+right well how can we do that we can
+
+ align:start position:0%
+right well how can we do that we can
+ 
+
+ align:start position:0%
+right well how can we do that we can
+construct a subsequence that is going to
+
+ align:start position:0%
+construct a subsequence that is going to
+ 
+
+ align:start position:0%
+construct a subsequence that is going to
+be convergent and if it's remember a
+
+ align:start position:0%
+be convergent and if it's remember a
+ 
+
+ align:start position:0%
+be convergent and if it's remember a
+subsequence if it's convergent converges
+
+ align:start position:0%
+subsequence if it's convergent converges
+ 
+
+ align:start position:0%
+subsequence if it's convergent converges
+to what the original sequence converges
+
+ align:start position:0%
+to what the original sequence converges
+ 
+
+ align:start position:0%
+to what the original sequence converges
+to right so this is where we're using a
+
+ align:start position:0%
+to right so this is where we're using a
+ 
+
+ align:start position:0%
+to right so this is where we're using a
+fact from earlier that we
+
+ align:start position:0%
+fact from earlier that we
+ 
+
+ align:start position:0%
+fact from earlier that we
+proved okay so suppose Epsilon is 1/ n
+
+ align:start position:0%
+proved okay so suppose Epsilon is 1/ n
+ 
+
+ align:start position:0%
+proved okay so suppose Epsilon is 1/ n
+for n and the natural numbers or I'll
+
+ align:start position:0%
+for n and the natural numbers or I'll
+ 
+
+ align:start position:0%
+for n and the natural numbers or I'll
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+choose X n
+
+ align:start position:0%
+choose X n
+ 
+
+ align:start position:0%
+choose X n
+m in the ball of radius Epsilon so 1 / M
+
+ align:start position:0%
+m in the ball of radius Epsilon so 1 / M
+ 
+
+ align:start position:0%
+m in the ball of radius Epsilon so 1 / M
+to x + 1
+
+ align:start position:0%
+to x + 1
+ 
+
+ align:start position:0%
+to x + 1
+M what does this tell us I claim that
+
+ align:start position:0%
+M what does this tell us I claim that
+ 
+
+ align:start position:0%
+M what does this tell us I claim that
+this convergent sequence converges to
+
+ align:start position:0%
+this convergent sequence converges to
+ 
+
+ align:start position:0%
+this convergent sequence converges to
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+well to show that we need to write down
+
+ align:start position:0%
+well to show that we need to write down
+ 
+
+ align:start position:0%
+well to show that we need to write down
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition when professor riguez was
+
+ align:start position:0%
+definition when professor riguez was
+ 
+
+ align:start position:0%
+definition when professor riguez was
+erasing the board he'd always tell some
+
+ align:start position:0%
+erasing the board he'd always tell some
+ 
+
+ align:start position:0%
+erasing the board he'd always tell some
+joke but I don't have any jokes right
+
+ align:start position:0%
+joke but I don't have any jokes right
+ 
+
+ align:start position:0%
+joke but I don't have any jokes right
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unfortunately though he would do them
+
+ align:start position:0%
+unfortunately though he would do them
+ 
+
+ align:start position:0%
+unfortunately though he would do them
+two at a time so he could actually have
+
+ align:start position:0%
+two at a time so he could actually have
+ 
+
+ align:start position:0%
+two at a time so he could actually have
+time to actually say the joke before he
+
+ align:start position:0%
+time to actually say the joke before he
+ 
+
+ align:start position:0%
+time to actually say the joke before he
+finished okay so we want to show that X
+
+ align:start position:0%
+finished okay so we want to show that X
+ 
+
+ align:start position:0%
+finished okay so we want to show that X
+and M converges to X right proof for all
+
+ align:start position:0%
+and M converges to X right proof for all
+ 
+
+ align:start position:0%
+and M converges to X right proof for all
+Epsilon bigger than
+
+ align:start position:0%
+Epsilon bigger than
+ 
+
+ align:start position:0%
+Epsilon bigger than
+zero we can choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M uh large enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or I should say capital
+
+ align:start position:0%
+or I should say capital
+ 
+
+ align:start position:0%
+or I should say capital
+M such that for all n m bigger than or
+
+ align:start position:0%
+M such that for all n m bigger than or
+ 
+
+ align:start position:0%
+M such that for all n m bigger than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+M we have that uh 1 / n m is less than
+
+ align:start position:0%
+M we have that uh 1 / n m is less than
+ 
+
+ align:start position:0%
+M we have that uh 1 / n m is less than
+Epsilon right because epsilon's bigger
+
+ align:start position:0%
+Epsilon right because epsilon's bigger
+ 
+
+ align:start position:0%
+Epsilon right because epsilon's bigger
+than zero I can find a large enough
+
+ align:start position:0%
+than zero I can find a large enough
+ 
+
+ align:start position:0%
+than zero I can find a large enough
+natural number such that one over that
+
+ align:start position:0%
+natural number such that one over that
+ 
+
+ align:start position:0%
+natural number such that one over that
+natural number is less than Epsilon
+
+ align:start position:0%
+natural number is less than Epsilon
+ 
+
+ align:start position:0%
+natural number is less than Epsilon
+that's our it's a factor from real
+
+ align:start position:0%
+that's our it's a factor from real
+ 
+
+ align:start position:0%
+that's our it's a factor from real
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+so what this tells
+
+ align:start position:0%
+so what this tells
+ 
+
+ align:start position:0%
+so what this tells
+us is that we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know then that X and M or I should say
+
+ align:start position:0%
+know then that X and M or I should say
+ 
+
+ align:start position:0%
+know then that X and M or I should say
+uh yeah X and M is in xus epsilon to x +
+
+ align:start position:0%
+uh yeah X and M is in xus epsilon to x +
+ 
+
+ align:start position:0%
+uh yeah X and M is in xus epsilon to x +
+Epsilon because this is from X over 1 n
+
+ align:start position:0%
+Epsilon because this is from X over 1 n
+ 
+
+ align:start position:0%
+Epsilon because this is from X over 1 n
+m to x + 1 n m which is a subset of the
+
+ align:start position:0%
+m to x + 1 n m which is a subset of the
+ 
+
+ align:start position:0%
+m to x + 1 n m which is a subset of the
+B radius Epsilon by
+
+ align:start position:0%
+B radius Epsilon by
+ 
+
+ align:start position:0%
+B radius Epsilon by
+construction right because 1 nm is less
+
+ align:start position:0%
+construction right because 1 nm is less
+ 
+
+ align:start position:0%
+construction right because 1 nm is less
+than Epsilon so what this tells you is
+
+ align:start position:0%
+than Epsilon so what this tells you is
+ 
+
+ align:start position:0%
+than Epsilon so what this tells you is
+that the distance from xn M - x is less
+
+ align:start position:0%
+that the distance from xn M - x is less
+ 
+
+ align:start position:0%
+that the distance from xn M - x is less
+than Epsilon which implies that the
+
+ align:start position:0%
+than Epsilon which implies that the
+ 
+
+ align:start position:0%
+than Epsilon which implies that the
+convergent sequence or the convergent
+
+ align:start position:0%
+convergent sequence or the convergent
+ 
+
+ align:start position:0%
+convergent sequence or the convergent
+subsequence converges to X so to
+
+ align:start position:0%
+subsequence converges to X so to
+ 
+
+ align:start position:0%
+subsequence converges to X so to
+reiterate how the proof went we had a
+
+ align:start position:0%
+reiterate how the proof went we had a
+ 
+
+ align:start position:0%
+reiterate how the proof went we had a
+convergent sequence we had a subsequence
+
+ align:start position:0%
+convergent sequence we had a subsequence
+ 
+
+ align:start position:0%
+convergent sequence we had a subsequence
+that we showed converges to x and by
+
+ align:start position:0%
+that we showed converges to x and by
+ 
+
+ align:start position:0%
+that we showed converges to x and by
+what we showed earlier X must be the
+
+ align:start position:0%
+what we showed earlier X must be the
+ 
+
+ align:start position:0%
+what we showed earlier X must be the
+limit point of the original convergent
+
+ align:start position:0%
+limit point of the original convergent
+ 
+
+ align:start position:0%
+limit point of the original convergent
+sequence then so we're done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right uh I won't write out the analogous
+
+ align:start position:0%
+right uh I won't write out the analogous
+ 
+
+ align:start position:0%
+right uh I won't write out the analogous
+statement for metric bases the you just
+
+ align:start position:0%
+statement for metric bases the you just
+ 
+
+ align:start position:0%
+statement for metric bases the you just
+change xus Epsilon to X Plus Epsilon
+
+ align:start position:0%
+change xus Epsilon to X Plus Epsilon
+ 
+
+ align:start position:0%
+change xus Epsilon to X Plus Epsilon
+with a ball of radius Epsilon um I just
+
+ align:start position:0%
+with a ball of radius Epsilon um I just
+ 
+
+ align:start position:0%
+with a ball of radius Epsilon um I just
+dated it in real real numbers because
+
+ align:start position:0%
+dated it in real real numbers because
+ 
+
+ align:start position:0%
+dated it in real real numbers because
+the I prefer the interval notation to
+
+ align:start position:0%
+the I prefer the interval notation to
+ 
+
+ align:start position:0%
+the I prefer the interval notation to
+think about it and it's a fact that like
+
+ align:start position:0%
+think about it and it's a fact that like
+ 
+
+ align:start position:0%
+think about it and it's a fact that like
+not everyone fully sees in real analysis
+
+ align:start position:0%
+not everyone fully sees in real analysis
+ 
+
+ align:start position:0%
+not everyone fully sees in real analysis
+because sometimes you don't know what an
+
+ align:start position:0%
+because sometimes you don't know what an
+ 
+
+ align:start position:0%
+because sometimes you don't know what an
+open set is in 100a it depends on who's
+
+ align:start position:0%
+open set is in 100a it depends on who's
+ 
+
+ align:start position:0%
+open set is in 100a it depends on who's
+teaching it
+
+ align:start position:0%
+teaching it
+ 
+
+ align:start position:0%
+teaching it
+realistically okay we're going to prove
+
+ align:start position:0%
+realistically okay we're going to prove
+ 
+
+ align:start position:0%
+realistically okay we're going to prove
+one more oh wait what do I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say yeah okay this was just why I wanted
+
+ align:start position:0%
+say yeah okay this was just why I wanted
+ 
+
+ align:start position:0%
+say yeah okay this was just why I wanted
+to show that it's related to uh
+
+ align:start position:0%
+to show that it's related to uh
+ 
+
+ align:start position:0%
+to show that it's related to uh
+convergent sequences now what I'm going
+
+ align:start position:0%
+convergent sequences now what I'm going
+ 
+
+ align:start position:0%
+convergent sequences now what I'm going
+to do is show that it's related to
+
+ align:start position:0%
+to do is show that it's related to
+ 
+
+ align:start position:0%
+to do is show that it's related to
+continuous functions and I'm going to
+
+ align:start position:0%
+continuous functions and I'm going to
+ 
+
+ align:start position:0%
+continuous functions and I'm going to
+recall what that definition is because
+
+ align:start position:0%
+recall what that definition is because
+ 
+
+ align:start position:0%
+recall what that definition is because
+that can again be a little bit weird
+
+ align:start position:0%
+that can again be a little bit weird
+ 
+
+ align:start position:0%
+that can again be a little bit weird
+between metric spaces so a function f
+
+ align:start position:0%
+between metric spaces so a function f
+ 
+
+ align:start position:0%
+between metric spaces so a function f
+from a metric Space X to a metric space
+
+ align:start position:0%
+from a metric Space X to a metric space
+ 
+
+ align:start position:0%
+from a metric Space X to a metric space
+y let's say with metric DX
+
+ align:start position:0%
+y let's say with metric DX
+ 
+
+ align:start position:0%
+y let's say with metric DX
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Dy is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous if for all Epsilon bigger
+
+ align:start position:0%
+continuous if for all Epsilon bigger
+ 
+
+ align:start position:0%
+continuous if for all Epsilon bigger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+zero there exists a
+
+ align:start position:0%
+zero there exists a
+ 
+
+ align:start position:0%
+zero there exists a
+Delta bigger than zero such that if the
+
+ align:start position:0%
+Delta bigger than zero such that if the
+ 
+
+ align:start position:0%
+Delta bigger than zero such that if the
+distance between two
+
+ align:start position:0%
+distance between two
+ 
+
+ align:start position:0%
+distance between two
+points X and Y is less than Delta then
+
+ align:start position:0%
+points X and Y is less than Delta then
+ 
+
+ align:start position:0%
+points X and Y is less than Delta then
+the distance in the metric space y of
+
+ align:start position:0%
+the distance in the metric space y of
+ 
+
+ align:start position:0%
+the distance in the metric space y of
+the images of X and
+
+ align:start position:0%
+the images of X and
+ 
+
+ align:start position:0%
+the images of X and
+Y is less than Epsilon this is the the
+
+ align:start position:0%
+Y is less than Epsilon this is the the
+ 
+
+ align:start position:0%
+Y is less than Epsilon this is the the
+definition of continuous in the metric
+
+ align:start position:0%
+definition of continuous in the metric
+ 
+
+ align:start position:0%
+definition of continuous in the metric
+bace
+
+ align:start position:0%
+bace
+ 
+
+ align:start position:0%
+bace
+setting and so now what we're going to
+
+ align:start position:0%
+setting and so now what we're going to
+ 
+
+ align:start position:0%
+setting and so now what we're going to
+do is prove a statement akin to
+
+ align:start position:0%
+do is prove a statement akin to
+ 
+
+ align:start position:0%
+do is prove a statement akin to
+convergent sequences but for continuity
+
+ align:start position:0%
+convergent sequences but for continuity
+ 
+
+ align:start position:0%
+convergent sequences but for continuity
+we can write the definition of
+
+ align:start position:0%
+we can write the definition of
+ 
+
+ align:start position:0%
+we can write the definition of
+continuity in terms of open sets and not
+
+ align:start position:0%
+continuity in terms of open sets and not
+ 
+
+ align:start position:0%
+continuity in terms of open sets and not
+only can we do that we can write
+
+ align:start position:0%
+only can we do that we can write
+ 
+
+ align:start position:0%
+only can we do that we can write
+continuity in terms of convergence of
+
+ align:start position:0%
+continuity in terms of convergence of
+ 
+
+ align:start position:0%
+continuity in terms of convergence of
+sequences so I'll do that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem under all the same assumptions
+
+ align:start position:0%
+theorem under all the same assumptions
+ 
+
+ align:start position:0%
+theorem under all the same assumptions
+here I'm going to let X and Y be metric
+
+ align:start position:0%
+here I'm going to let X and Y be metric
+ 
+
+ align:start position:0%
+here I'm going to let X and Y be metric
+spaces with distances DX and
+
+ align:start position:0%
+spaces with distances DX and
+ 
+
+ align:start position:0%
+spaces with distances DX and
+Dy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yeah
+
+ align:start position:0%
+and yeah
+ 
+
+ align:start position:0%
+and yeah
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+let claim uh F from X to
+
+ align:start position:0%
+let claim uh F from X to
+ 
+
+ align:start position:0%
+let claim uh F from X to
+Y is continuous at a point C in
+
+ align:start position:0%
+Y is continuous at a point C in
+ 
+
+ align:start position:0%
+Y is continuous at a point C in
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+if if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if xn is a sequence that converges to X
+
+ align:start position:0%
+if xn is a sequence that converges to X
+ 
+
+ align:start position:0%
+if xn is a sequence that converges to X
+then F of
+
+ align:start position:0%
+then F of
+ 
+
+ align:start position:0%
+then F of
+xn converges to F
+
+ align:start position:0%
+xn converges to F
+ 
+
+ align:start position:0%
+xn converges to F
+ofx this is my
+
+ align:start position:0%
+ofx this is my
+ 
+
+ align:start position:0%
+ofx this is my
+statement uh when I say continuous at
+
+ align:start position:0%
+statement uh when I say continuous at
+ 
+
+ align:start position:0%
+statement uh when I say continuous at
+the point C I mean just
+
+ align:start position:0%
+the point C I mean just
+ 
+
+ align:start position:0%
+the point C I mean just
+replace uh y with C here that means that
+
+ align:start position:0%
+replace uh y with C here that means that
+ 
+
+ align:start position:0%
+replace uh y with C here that means that
+this is continuous at every
+
+ align:start position:0%
+this is continuous at every
+ 
+
+ align:start position:0%
+this is continuous at every
+Point continuous at x and x and as
+
+ align:start position:0%
+Point continuous at x and x and as
+ 
+
+ align:start position:0%
+Point continuous at x and x and as
+continuous if it's continuous everywhere
+
+ align:start position:0%
+continuous if it's continuous everywhere
+ 
+
+ align:start position:0%
+continuous if it's continuous everywhere
+right this is the same as in real
+
+ align:start position:0%
+right this is the same as in real
+ 
+
+ align:start position:0%
+right this is the same as in real
+analysis we had get continuity at a
+
+ align:start position:0%
+analysis we had get continuity at a
+ 
+
+ align:start position:0%
+analysis we had get continuity at a
+point and continuity everywhere this is
+
+ align:start position:0%
+point and continuity everywhere this is
+ 
+
+ align:start position:0%
+point and continuity everywhere this is
+just continuity at a
+
+ align:start position:0%
+just continuity at a
+ 
+
+ align:start position:0%
+just continuity at a
+point okay
+
+ align:start position:0%
+point okay
+ 
+
+ align:start position:0%
+point okay
+proof I always prefer
+
+ align:start position:0%
+proof I always prefer
+ 
+
+ align:start position:0%
+proof I always prefer
+going the downwards Direction first so
+
+ align:start position:0%
+going the downwards Direction first so
+ 
+
+ align:start position:0%
+going the downwards Direction first so
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+F be continuous at C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then by definition for all Epsilon
+
+ align:start position:0%
+then by definition for all Epsilon
+ 
+
+ align:start position:0%
+then by definition for all Epsilon
+bigger than zero there exists a Delta
+
+ align:start position:0%
+bigger than zero there exists a Delta
+ 
+
+ align:start position:0%
+bigger than zero there exists a Delta
+such that this implication holds what
+
+ align:start position:0%
+such that this implication holds what
+ 
+
+ align:start position:0%
+such that this implication holds what
+does this actually tell us well suppose
+
+ align:start position:0%
+does this actually tell us well suppose
+ 
+
+ align:start position:0%
+does this actually tell us well suppose
+we're going I'm going toose suppose the
+
+ align:start position:0%
+we're going I'm going toose suppose the
+ 
+
+ align:start position:0%
+we're going I'm going toose suppose the
+um uh thing in the second hypothesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose xn is a sequence in X that
+
+ align:start position:0%
+suppose xn is a sequence in X that
+ 
+
+ align:start position:0%
+suppose xn is a sequence in X that
+converges to X then what can I say well
+
+ align:start position:0%
+converges to X then what can I say well
+ 
+
+ align:start position:0%
+converges to X then what can I say well
+we know that there
+
+ align:start position:0%
+we know that there
+ 
+
+ align:start position:0%
+we know that there
+exists a sorry I should say to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C then by definition of convergent
+
+ align:start position:0%
+C then by definition of convergent
+ 
+
+ align:start position:0%
+C then by definition of convergent
+sequence we know that for all Epsilon
+
+ align:start position:0%
+sequence we know that for all Epsilon
+ 
+
+ align:start position:0%
+sequence we know that for all Epsilon
+bigger than
+
+ align:start position:0%
+bigger than
+ 
+
+ align:start position:0%
+bigger than
+zero there exists an n in the natural
+
+ align:start position:0%
+zero there exists an n in the natural
+ 
+
+ align:start position:0%
+zero there exists an n in the natural
+numbers such that for all n bigger than
+
+ align:start position:0%
+numbers such that for all n bigger than
+ 
+
+ align:start position:0%
+numbers such that for all n bigger than
+or equal to
+
+ align:start position:0%
+or equal to
+ 
+
+ align:start position:0%
+or equal to
+n the distance from xn to C is less than
+
+ align:start position:0%
+n the distance from xn to C is less than
+ 
+
+ align:start position:0%
+n the distance from xn to C is less than
+Epsilon but we know that for all Epsilon
+
+ align:start position:0%
+Epsilon but we know that for all Epsilon
+ 
+
+ align:start position:0%
+Epsilon but we know that for all Epsilon
+bigger than
+
+ align:start position:0%
+bigger than
+ 
+
+ align:start position:0%
+bigger than
+zero furthermore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a Delta bigger than zero
+
+ align:start position:0%
+there exists a Delta bigger than zero
+ 
+
+ align:start position:0%
+there exists a Delta bigger than zero
+such that the distance from F of
+
+ align:start position:0%
+such that the distance from F of
+ 
+
+ align:start position:0%
+such that the distance from F of
+xn to F of
+
+ align:start position:0%
+xn to F of
+ 
+
+ align:start position:0%
+xn to F of
+C is less than Delta over two oh sorry
+
+ align:start position:0%
+C is less than Delta over two oh sorry
+ 
+
+ align:start position:0%
+C is less than Delta over two oh sorry
+not Delta over two just
+
+ align:start position:0%
+not Delta over two just
+ 
+
+ align:start position:0%
+not Delta over two just
+Delta uh is this no uh I should have re
+
+ align:start position:0%
+Delta uh is this no uh I should have re
+ 
+
+ align:start position:0%
+Delta uh is this no uh I should have re
+labeled this I should have said for all
+
+ align:start position:0%
+labeled this I should have said for all
+ 
+
+ align:start position:0%
+labeled this I should have said for all
+Delta bigger than zero there exists one
+
+ align:start position:0%
+Delta bigger than zero there exists one
+ 
+
+ align:start position:0%
+Delta bigger than zero there exists one
+such that this is less than Delta and
+
+ align:start position:0%
+such that this is less than Delta and
+ 
+
+ align:start position:0%
+such that this is less than Delta and
+then there exists an Epsilon bigger than
+
+ align:start position:0%
+then there exists an Epsilon bigger than
+ 
+
+ align:start position:0%
+then there exists an Epsilon bigger than
+zero such that no no I said it right the
+
+ align:start position:0%
+zero such that no no I said it right the
+ 
+
+ align:start position:0%
+zero such that no no I said it right the
+first time uh for all bigger than Z
+
+ align:start position:0%
+first time uh for all bigger than Z
+ 
+
+ align:start position:0%
+first time uh for all bigger than Z
+there exists a Delta bigger than zero
+
+ align:start position:0%
+there exists a Delta bigger than zero
+ 
+
+ align:start position:0%
+there exists a Delta bigger than zero
+such that this term is less than Delta
+
+ align:start position:0%
+such that this term is less than Delta
+ 
+
+ align:start position:0%
+such that this term is less than Delta
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+furthermore the distance between the
+
+ align:start position:0%
+furthermore the distance between the
+ 
+
+ align:start position:0%
+furthermore the distance between the
+images is less than Epsilon there we go
+
+ align:start position:0%
+images is less than Epsilon there we go
+ 
+
+ align:start position:0%
+images is less than Epsilon there we go
+that's what I meant to say and so what
+
+ align:start position:0%
+that's what I meant to say and so what
+ 
+
+ align:start position:0%
+that's what I meant to say and so what
+this tells you is that F of xn must
+
+ align:start position:0%
+this tells you is that F of xn must
+ 
+
+ align:start position:0%
+this tells you is that F of xn must
+converge to F of C right because there
+
+ align:start position:0%
+converge to F of C right because there
+ 
+
+ align:start position:0%
+converge to F of C right because there
+exists an n in the natural numbers such
+
+ align:start position:0%
+exists an n in the natural numbers such
+ 
+
+ align:start position:0%
+exists an n in the natural numbers such
+that the distance between the two points
+
+ align:start position:0%
+that the distance between the two points
+ 
+
+ align:start position:0%
+that the distance between the two points
+is less than Epsilon which is the
+
+ align:start position:0%
+is less than Epsilon which is the
+ 
+
+ align:start position:0%
+is less than Epsilon which is the
+definition of convergent
+
+ align:start position:0%
+definition of convergent
+ 
+
+ align:start position:0%
+definition of convergent
+sequence and then to prove the other
+
+ align:start position:0%
+sequence and then to prove the other
+ 
+
+ align:start position:0%
+sequence and then to prove the other
+direction uh I'm just going to State it
+
+ align:start position:0%
+direction uh I'm just going to State it
+ 
+
+ align:start position:0%
+direction uh I'm just going to State it
+because are running out of time no I'll
+
+ align:start position:0%
+because are running out of time no I'll
+ 
+
+ align:start position:0%
+because are running out of time no I'll
+write it out I'll write it out over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here to proof the other direction we're
+
+ align:start position:0%
+here to proof the other direction we're
+ 
+
+ align:start position:0%
+here to proof the other direction we're
+going to use it by uh contradiction
+
+ align:start position:0%
+going to use it by uh contradiction
+ 
+
+ align:start position:0%
+going to use it by uh contradiction
+we're going to assume that it's not
+
+ align:start position:0%
+we're going to assume that it's not
+ 
+
+ align:start position:0%
+we're going to assume that it's not
+continuous at C and then choose a
+
+ align:start position:0%
+continuous at C and then choose a
+ 
+
+ align:start position:0%
+continuous at C and then choose a
+convergent sequence that uh or a
+
+ align:start position:0%
+convergent sequence that uh or a
+ 
+
+ align:start position:0%
+convergent sequence that uh or a
+sequence that doesn't
+
+ align:start position:0%
+sequence that doesn't
+ 
+
+ align:start position:0%
+sequence that doesn't
+converge or such that the images don't
+
+ align:start position:0%
+converge or such that the images don't
+ 
+
+ align:start position:0%
+converge or such that the images don't
+converge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if and only
+
+ align:start position:0%
+okay if and only
+ 
+
+ align:start position:0%
+okay if and only
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+suppose f is not
+
+ align:start position:0%
+suppose f is not
+ 
+
+ align:start position:0%
+suppose f is not
+continuous this is the proof of the
+
+ align:start position:0%
+continuous this is the proof of the
+ 
+
+ align:start position:0%
+continuous this is the proof of the
+upwards
+
+ align:start position:0%
+upwards
+ 
+
+ align:start position:0%
+upwards
+Direction suppose it's not
+
+ align:start position:0%
+Direction suppose it's not
+ 
+
+ align:start position:0%
+Direction suppose it's not
+continuous at C what does this tell you
+
+ align:start position:0%
+continuous at C what does this tell you
+ 
+
+ align:start position:0%
+continuous at C what does this tell you
+well saying something is not continuous
+
+ align:start position:0%
+well saying something is not continuous
+ 
+
+ align:start position:0%
+well saying something is not continuous
+is a little bit weird but I'll State out
+
+ align:start position:0%
+is a little bit weird but I'll State out
+ 
+
+ align:start position:0%
+is a little bit weird but I'll State out
+what that definition means
+
+ align:start position:0%
+what that definition means
+ 
+
+ align:start position:0%
+what that definition means
+given some bigger than
+
+ align:start position:0%
+given some bigger than
+ 
+
+ align:start position:0%
+given some bigger than
+zero we know that there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists there exists an xn in the
+
+ align:start position:0%
+exists there exists an xn in the
+ 
+
+ align:start position:0%
+exists there exists an xn in the
+sequence such
+
+ align:start position:0%
+sequence such
+ 
+
+ align:start position:0%
+sequence such
+that the distance from
+
+ align:start position:0%
+that the distance from
+ 
+
+ align:start position:0%
+that the distance from
+xn to C get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small uh I want to say one over n I'll
+
+ align:start position:0%
+small uh I want to say one over n I'll
+ 
+
+ align:start position:0%
+small uh I want to say one over n I'll
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+say less
+
+ align:start position:0%
+say less
+ 
+
+ align:start position:0%
+say less
+than given Epsilon bigger than Z there
+
+ align:start position:0%
+than given Epsilon bigger than Z there
+ 
+
+ align:start position:0%
+than given Epsilon bigger than Z there
+exists a Delta bigger than zero and an X
+
+ align:start position:0%
+exists a Delta bigger than zero and an X
+ 
+
+ align:start position:0%
+exists a Delta bigger than zero and an X
+in your sequence such that the distances
+
+ align:start position:0%
+in your sequence such that the distances
+ 
+
+ align:start position:0%
+in your sequence such that the distances
+get small so let's say 1/
+
+ align:start position:0%
+get small so let's say 1/
+ 
+
+ align:start position:0%
+get small so let's say 1/
+n but the distances between the images
+
+ align:start position:0%
+n but the distances between the images
+ 
+
+ align:start position:0%
+n but the distances between the images
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+them F of C is bigger than
+
+ align:start position:0%
+them F of C is bigger than
+ 
+
+ align:start position:0%
+them F of C is bigger than
+Epsilon right because the the uh Contra
+
+ align:start position:0%
+Epsilon right because the the uh Contra
+ 
+
+ align:start position:0%
+Epsilon right because the the uh Contra
+uh the opposite would be if this was
+
+ align:start position:0%
+uh the opposite would be if this was
+ 
+
+ align:start position:0%
+uh the opposite would be if this was
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+Epsilon right and so then what you can
+
+ align:start position:0%
+Epsilon right and so then what you can
+ 
+
+ align:start position:0%
+Epsilon right and so then what you can
+show is
+
+ align:start position:0%
+show is
+ 
+
+ align:start position:0%
+show is
+that therefore xn converges to C but F
+
+ align:start position:0%
+that therefore xn converges to C but F
+ 
+
+ align:start position:0%
+that therefore xn converges to C but F
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+xn does not converge to F of
+
+ align:start position:0%
+xn does not converge to F of
+ 
+
+ align:start position:0%
+xn does not converge to F of
+C we know that it doesn't converge to F
+
+ align:start position:0%
+C we know that it doesn't converge to F
+ 
+
+ align:start position:0%
+C we know that it doesn't converge to F
+of C because we just
+
+ align:start position:0%
+of C because we just
+ 
+
+ align:start position:0%
+of C because we just
+proved up here that if a sequence is to
+
+ align:start position:0%
+proved up here that if a sequence is to
+ 
+
+ align:start position:0%
+proved up here that if a sequence is to
+Converge All But finitely many of them
+
+ align:start position:0%
+Converge All But finitely many of them
+ 
+
+ align:start position:0%
+Converge All But finitely many of them
+I.E infinitely many of them or that's
+
+ align:start position:0%
+I.E infinitely many of them or that's
+ 
+
+ align:start position:0%
+I.E infinitely many of them or that's
+not quite the same but all but finitely
+
+ align:start position:0%
+not quite the same but all but finitely
+ 
+
+ align:start position:0%
+not quite the same but all but finitely
+many of them must exist in any ball of
+
+ align:start position:0%
+many of them must exist in any ball of
+ 
+
+ align:start position:0%
+many of them must exist in any ball of
+radius Epsilon right and we just showed
+
+ align:start position:0%
+radius Epsilon right and we just showed
+ 
+
+ align:start position:0%
+radius Epsilon right and we just showed
+here that there are in fact infinitely
+
+ align:start position:0%
+here that there are in fact infinitely
+ 
+
+ align:start position:0%
+here that there are in fact infinitely
+many that don't exist in a ball of
+
+ align:start position:0%
+many that don't exist in a ball of
+ 
+
+ align:start position:0%
+many that don't exist in a ball of
+radius
+
+ align:start position:0%
+radius
+ 
+
+ align:start position:0%
+radius
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+so uh that proves the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction this is known as sequential
+
+ align:start position:0%
+direction this is known as sequential
+ 
+
+ align:start position:0%
+direction this is known as sequential
+continuity sometimes if you want to
+
+ align:start position:0%
+continuity sometimes if you want to
+ 
+
+ align:start position:0%
+continuity sometimes if you want to
+study uh this in more generality as
+
+ align:start position:0%
+study uh this in more generality as
+ 
+
+ align:start position:0%
+study uh this in more generality as
+opposed to assuming continuous you can
+
+ align:start position:0%
+opposed to assuming continuous you can
+ 
+
+ align:start position:0%
+opposed to assuming continuous you can
+assume this this sort of definition on
+
+ align:start position:0%
+assume this this sort of definition on
+ 
+
+ align:start position:0%
+assume this this sort of definition on
+topological space and that's slightly
+
+ align:start position:0%
+topological space and that's slightly
+ 
+
+ align:start position:0%
+topological space and that's slightly
+different um but for metric spaces the
+
+ align:start position:0%
+different um but for metric spaces the
+ 
+
+ align:start position:0%
+different um but for metric spaces the
+two definitions are the same right which
+
+ align:start position:0%
+two definitions are the same right which
+ 
+
+ align:start position:0%
+two definitions are the same right which
+will be the case a lot of the time a lot
+
+ align:start position:0%
+will be the case a lot of the time a lot
+ 
+
+ align:start position:0%
+will be the case a lot of the time a lot
+of the time in this class A definition
+
+ align:start position:0%
+of the time in this class A definition
+ 
+
+ align:start position:0%
+of the time in this class A definition
+that's specific to metric spaces will
+
+ align:start position:0%
+that's specific to metric spaces will
+ 
+
+ align:start position:0%
+that's specific to metric spaces will
+imply other very useful
+
+ align:start position:0%
+imply other very useful
+ 
+
+ align:start position:0%
+imply other very useful
+definitions that might not hold in more
+
+ align:start position:0%
+definitions that might not hold in more
+ 
+
+ align:start position:0%
+definitions that might not hold in more
+generality
+
+ align:start position:0%
+generality
+ 
+
+ align:start position:0%
+generality
+okay I just have one more statement to
+
+ align:start position:0%
+okay I just have one more statement to
+ 
+
+ align:start position:0%
+okay I just have one more statement to
+show which is how continuity relates to
+
+ align:start position:0%
+show which is how continuity relates to
+ 
+
+ align:start position:0%
+show which is how continuity relates to
+open
+
+ align:start position:0%
+open
+ 
+
+ align:start position:0%
+open
+sets uh let me write out what this Sumo
+
+ align:start position:0%
+sets uh let me write out what this Sumo
+ 
+
+ align:start position:0%
+sets uh let me write out what this Sumo
+will be oh sorry I should have this is
+
+ align:start position:0%
+will be oh sorry I should have this is
+ 
+
+ align:start position:0%
+will be oh sorry I should have this is
+poor board manners I should have raised
+
+ align:start position:0%
+poor board manners I should have raised
+ 
+
+ align:start position:0%
+poor board manners I should have raised
+this in the with
+
+ align:start position:0%
+this in the with
+ 
+
+ align:start position:0%
+this in the with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay just one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lemma f is
+
+ align:start position:0%
+Lemma f is
+ 
+
+ align:start position:0%
+Lemma f is
+continuous at C if and only
+
+ align:start position:0%
+continuous at C if and only
+ 
+
+ align:start position:0%
+continuous at C if and only
+if oh I need to state a definition first
+
+ align:start position:0%
+if oh I need to state a definition first
+ 
+
+ align:start position:0%
+if oh I need to state a definition first
+I'll state it over
+
+ align:start position:0%
+I'll state it over
+ 
+
+ align:start position:0%
+I'll state it over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+definition a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighborhood of a point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y is
+
+ align:start position:0%
+Y is
+ 
+
+ align:start position:0%
+Y is
+simply an open set that that contains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y containing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y for our purposes though you can just
+
+ align:start position:0%
+y for our purposes though you can just
+ 
+
+ align:start position:0%
+y for our purposes though you can just
+think of this open neighborhood as a
+
+ align:start position:0%
+think of this open neighborhood as a
+ 
+
+ align:start position:0%
+think of this open neighborhood as a
+ball right because I've stated that
+
+ align:start position:0%
+ball right because I've stated that
+ 
+
+ align:start position:0%
+ball right because I've stated that
+every uh open set can be written as a
+
+ align:start position:0%
+every uh open set can be written as a
+ 
+
+ align:start position:0%
+every uh open set can be written as a
+union of finitely of infinitely many
+
+ align:start position:0%
+union of finitely of infinitely many
+ 
+
+ align:start position:0%
+union of finitely of infinitely many
+balls so this is what a definition of a
+
+ align:start position:0%
+balls so this is what a definition of a
+ 
+
+ align:start position:0%
+balls so this is what a definition of a
+neighborhood is and that lets us State
+
+ align:start position:0%
+neighborhood is and that lets us State
+ 
+
+ align:start position:0%
+neighborhood is and that lets us State
+the Lemma which
+
+ align:start position:0%
+the Lemma which
+ 
+
+ align:start position:0%
+the Lemma which
+is for
+
+ align:start position:0%
+is for
+ 
+
+ align:start position:0%
+is for
+every open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighborhood
+
+ align:start position:0%
+neighborhood
+ 
+
+ align:start position:0%
+neighborhood
+neighborhood of Y oh sorry of f of C
+
+ align:start position:0%
+neighborhood of Y oh sorry of f of C
+ 
+
+ align:start position:0%
+neighborhood of Y oh sorry of f of C
+this will be our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y then we have that the inverse image F
+
+ align:start position:0%
+y then we have that the inverse image F
+ 
+
+ align:start position:0%
+y then we have that the inverse image F
+inverse of f of oh sorry I should say
+
+ align:start position:0%
+inverse of f of oh sorry I should say
+ 
+
+ align:start position:0%
+inverse of f of oh sorry I should say
+every open neighborhood U of f of c f
+
+ align:start position:0%
+every open neighborhood U of f of c f
+ 
+
+ align:start position:0%
+every open neighborhood U of f of c f
+inverse of U Is An Open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighborhood of f of C sorry of C
+
+ align:start position:0%
+neighborhood of f of C sorry of C
+ 
+
+ align:start position:0%
+neighborhood of f of C sorry of C
+because we're in the inverse image okay
+
+ align:start position:0%
+because we're in the inverse image okay
+ 
+
+ align:start position:0%
+because we're in the inverse image okay
+has anyone seen this sort of definition
+
+ align:start position:0%
+has anyone seen this sort of definition
+ 
+
+ align:start position:0%
+has anyone seen this sort of definition
+before regarding open
+
+ align:start position:0%
+before regarding open
+ 
+
+ align:start position:0%
+before regarding open
+sets yeah um it doesn't come up all the
+
+ align:start position:0%
+sets yeah um it doesn't come up all the
+ 
+
+ align:start position:0%
+sets yeah um it doesn't come up all the
+time because it is essentially topology
+
+ align:start position:0%
+time because it is essentially topology
+ 
+
+ align:start position:0%
+time because it is essentially topology
+like if you take a topology class you
+
+ align:start position:0%
+like if you take a topology class you
+ 
+
+ align:start position:0%
+like if you take a topology class you
+would see this definition of this would
+
+ align:start position:0%
+would see this definition of this would
+ 
+
+ align:start position:0%
+would see this definition of this would
+be the definition of continuity in a
+
+ align:start position:0%
+be the definition of continuity in a
+ 
+
+ align:start position:0%
+be the definition of continuity in a
+topological class um but here we're
+
+ align:start position:0%
+topological class um but here we're
+ 
+
+ align:start position:0%
+topological class um but here we're
+going to actually prove it for a metric
+
+ align:start position:0%
+going to actually prove it for a metric
+ 
+
+ align:start position:0%
+going to actually prove it for a metric
+bace and because not all of you have
+
+ align:start position:0%
+bace and because not all of you have
+ 
+
+ align:start position:0%
+bace and because not all of you have
+seen it before we'll just go through
+
+ align:start position:0%
+seen it before we'll just go through
+ 
+
+ align:start position:0%
+seen it before we'll just go through
+that proof so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proof we'll prove the downwards
+
+ align:start position:0%
+proof we'll prove the downwards
+ 
+
+ align:start position:0%
+proof we'll prove the downwards
+Direction so we have that f is
+
+ align:start position:0%
+Direction so we have that f is
+ 
+
+ align:start position:0%
+Direction so we have that f is
+continuous at C and I'm going to let
+
+ align:start position:0%
+continuous at C and I'm going to let
+ 
+
+ align:start position:0%
+continuous at C and I'm going to let
+you be an open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighborhood of f of c and so then I
+
+ align:start position:0%
+neighborhood of f of c and so then I
+ 
+
+ align:start position:0%
+neighborhood of f of c and so then I
+want to show that F inverse of C oh
+
+ align:start position:0%
+want to show that F inverse of C oh
+ 
+
+ align:start position:0%
+want to show that F inverse of C oh
+sorry F inverse of U Is An Open set of C
+
+ align:start position:0%
+sorry F inverse of U Is An Open set of C
+ 
+
+ align:start position:0%
+sorry F inverse of U Is An Open set of C
+open neighborhood of C right what I'm
+
+ align:start position:0%
+open neighborhood of C right what I'm
+ 
+
+ align:start position:0%
+open neighborhood of C right what I'm
+going to do
+
+ align:start position:0%
+going to do
+ 
+
+ align:start position:0%
+going to do
+instead uh instead of considering this
+
+ align:start position:0%
+instead uh instead of considering this
+ 
+
+ align:start position:0%
+instead uh instead of considering this
+entire open neighborhood I'm going to
+
+ align:start position:0%
+entire open neighborhood I'm going to
+ 
+
+ align:start position:0%
+entire open neighborhood I'm going to
+consider a ball of radius Epsilon right
+
+ align:start position:0%
+consider a ball of radius Epsilon right
+ 
+
+ align:start position:0%
+consider a ball of radius Epsilon right
+around F of C so we know because U is
+
+ align:start position:0%
+around F of C so we know because U is
+ 
+
+ align:start position:0%
+around F of C so we know because U is
+open we know that there exists an
+
+ align:start position:0%
+open we know that there exists an
+ 
+
+ align:start position:0%
+open we know that there exists an
+Epsilon bigger than zero such that the
+
+ align:start position:0%
+Epsilon bigger than zero such that the
+ 
+
+ align:start position:0%
+Epsilon bigger than zero such that the
+ball of radius
+
+ align:start position:0%
+ball of radius
+ 
+
+ align:start position:0%
+ball of radius
+Epsilon with metric
+
+ align:start position:0%
+Epsilon with metric
+ 
+
+ align:start position:0%
+Epsilon with metric
+Dy around uh F of
+
+ align:start position:0%
+Dy around uh F of
+ 
+
+ align:start position:0%
+Dy around uh F of
+C is contained in U right we can find a
+
+ align:start position:0%
+C is contained in U right we can find a
+ 
+
+ align:start position:0%
+C is contained in U right we can find a
+ball around F of C that such that it's
+
+ align:start position:0%
+ball around F of C that such that it's
+ 
+
+ align:start position:0%
+ball around F of C that such that it's
+contained in U because it's
+
+ align:start position:0%
+contained in U because it's
+ 
+
+ align:start position:0%
+contained in U because it's
+open what does this tell you well by
+
+ align:start position:0%
+open what does this tell you well by
+ 
+
+ align:start position:0%
+open what does this tell you well by
+continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+furthermore there exists a Delta bigger
+
+ align:start position:0%
+furthermore there exists a Delta bigger
+ 
+
+ align:start position:0%
+furthermore there exists a Delta bigger
+than zero such that uh such that the
+
+ align:start position:0%
+than zero such that uh such that the
+ 
+
+ align:start position:0%
+than zero such that uh such that the
+ball such that
+
+ align:start position:0%
+ball such that
+ 
+
+ align:start position:0%
+ball such that
+if the distance from X to C is less than
+
+ align:start position:0%
+if the distance from X to C is less than
+ 
+
+ align:start position:0%
+if the distance from X to C is less than
+Delta then the distance of f
+
+ align:start position:0%
+Delta then the distance of f
+ 
+
+ align:start position:0%
+Delta then the distance of f
+ofx to F of C is less than
+
+ align:start position:0%
+ofx to F of C is less than
+ 
+
+ align:start position:0%
+ofx to F of C is less than
+Epsilon what does this tell you well
+
+ align:start position:0%
+Epsilon what does this tell you well
+ 
+
+ align:start position:0%
+Epsilon what does this tell you well
+this tells you that the image of the
+
+ align:start position:0%
+this tells you that the image of the
+ 
+
+ align:start position:0%
+this tells you that the image of the
+ball of radius EP of radius Delta around
+
+ align:start position:0%
+ball of radius EP of radius Delta around
+ 
+
+ align:start position:0%
+ball of radius EP of radius Delta around
+C is contained in the ball of radius
+
+ align:start position:0%
+C is contained in the ball of radius
+ 
+
+ align:start position:0%
+C is contained in the ball of radius
+Epsilon around F of
+
+ align:start position:0%
+Epsilon around F of
+ 
+
+ align:start position:0%
+Epsilon around F of
+C right because if I look at the images
+
+ align:start position:0%
+C right because if I look at the images
+ 
+
+ align:start position:0%
+C right because if I look at the images
+of these points I'm going to get the
+
+ align:start position:0%
+of these points I'm going to get the
+ 
+
+ align:start position:0%
+of these points I'm going to get the
+distance is less than Epsilon around F
+
+ align:start position:0%
+distance is less than Epsilon around F
+ 
+
+ align:start position:0%
+distance is less than Epsilon around F
+of c and what you can check I won't
+
+ align:start position:0%
+of c and what you can check I won't
+ 
+
+ align:start position:0%
+of c and what you can check I won't
+State this right now or I won't prove it
+
+ align:start position:0%
+State this right now or I won't prove it
+ 
+
+ align:start position:0%
+State this right now or I won't prove it
+but you can check that if I do F inverse
+
+ align:start position:0%
+but you can check that if I do F inverse
+ 
+
+ align:start position:0%
+but you can check that if I do F inverse
+here it's going to be contained in F
+
+ align:start position:0%
+here it's going to be contained in F
+ 
+
+ align:start position:0%
+here it's going to be contained in F
+inverse here
+
+ align:start position:0%
+inverse here
+ 
+
+ align:start position:0%
+inverse here
+why is this helpful because this is a
+
+ align:start position:0%
+why is this helpful because this is a
+ 
+
+ align:start position:0%
+why is this helpful because this is a
+subset of f inverse of U so what we've
+
+ align:start position:0%
+subset of f inverse of U so what we've
+ 
+
+ align:start position:0%
+subset of f inverse of U so what we've
+done is we've gone from an open
+
+ align:start position:0%
+done is we've gone from an open
+ 
+
+ align:start position:0%
+done is we've gone from an open
+neighborhood of f of C to an open
+
+ align:start position:0%
+neighborhood of f of C to an open
+ 
+
+ align:start position:0%
+neighborhood of f of C to an open
+neighborhood of C which is what we
+
+ align:start position:0%
+neighborhood of C which is what we
+ 
+
+ align:start position:0%
+neighborhood of C which is what we
+wanted to show right we wanted to show
+
+ align:start position:0%
+wanted to show right we wanted to show
+ 
+
+ align:start position:0%
+wanted to show right we wanted to show
+that F inverse of U Is An Open
+
+ align:start position:0%
+that F inverse of U Is An Open
+ 
+
+ align:start position:0%
+that F inverse of U Is An Open
+neighborhood of
+
+ align:start position:0%
+neighborhood of
+ 
+
+ align:start position:0%
+neighborhood of
+C okay so we now need to prove the other
+
+ align:start position:0%
+C okay so we now need to prove the other
+ 
+
+ align:start position:0%
+C okay so we now need to prove the other
+direction which is sometimes a little
+
+ align:start position:0%
+direction which is sometimes a little
+ 
+
+ align:start position:0%
+direction which is sometimes a little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+harder to to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do only a little bit harder but should
+
+ align:start position:0%
+do only a little bit harder but should
+ 
+
+ align:start position:0%
+do only a little bit harder but should
+be able to fit right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so now we're going to suppose
+
+ align:start position:0%
+here okay so now we're going to suppose
+ 
+
+ align:start position:0%
+here okay so now we're going to suppose
+that uh let Epsilon be bigger than
+
+ align:start position:0%
+that uh let Epsilon be bigger than
+ 
+
+ align:start position:0%
+that uh let Epsilon be bigger than
+zero and consider the open neighborhood
+
+ align:start position:0%
+zero and consider the open neighborhood
+ 
+
+ align:start position:0%
+zero and consider the open neighborhood
+of f of C given by the
+
+ align:start position:0%
+of f of C given by the
+ 
+
+ align:start position:0%
+of f of C given by the
+ball and consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ball of radius Epsilon around F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C then we know by
+
+ align:start position:0%
+C then we know by
+ 
+
+ align:start position:0%
+C then we know by
+assumption that F inverse of this ball
+
+ align:start position:0%
+assumption that F inverse of this ball
+ 
+
+ align:start position:0%
+assumption that F inverse of this ball
+of radius Epsilon of f of
+
+ align:start position:0%
+of radius Epsilon of f of
+ 
+
+ align:start position:0%
+of radius Epsilon of f of
+C uh 1 2 3 is an
+
+ align:start position:0%
+C uh 1 2 3 is an
+ 
+
+ align:start position:0%
+C uh 1 2 3 is an
+open
+
+ align:start position:0%
+open
+ 
+
+ align:start position:0%
+open
+neighborhood of
+
+ align:start position:0%
+neighborhood of
+ 
+
+ align:start position:0%
+neighborhood of
+C but because this is an open set around
+
+ align:start position:0%
+C but because this is an open set around
+ 
+
+ align:start position:0%
+C but because this is an open set around
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+there exists a Delta bigger than zero
+
+ align:start position:0%
+there exists a Delta bigger than zero
+ 
+
+ align:start position:0%
+there exists a Delta bigger than zero
+such
+
+ align:start position:0%
+such
+ 
+
+ align:start position:0%
+such
+that the ball of radius Delta around C
+
+ align:start position:0%
+that the ball of radius Delta around C
+ 
+
+ align:start position:0%
+that the ball of radius Delta around C
+is contained in F inverse of the ball of
+
+ align:start position:0%
+is contained in F inverse of the ball of
+ 
+
+ align:start position:0%
+is contained in F inverse of the ball of
+radius Epsilon of f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C right because this is an open set and
+
+ align:start position:0%
+C right because this is an open set and
+ 
+
+ align:start position:0%
+C right because this is an open set and
+we know that therefore that we know that
+
+ align:start position:0%
+we know that therefore that we know that
+ 
+
+ align:start position:0%
+we know that therefore that we know that
+there exists a radius such that the ball
+
+ align:start position:0%
+there exists a radius such that the ball
+ 
+
+ align:start position:0%
+there exists a radius such that the ball
+of radius Delta of that radius is
+
+ align:start position:0%
+of radius Delta of that radius is
+ 
+
+ align:start position:0%
+of radius Delta of that radius is
+contained in the open set and then we're
+
+ align:start position:0%
+contained in the open set and then we're
+ 
+
+ align:start position:0%
+contained in the open set and then we're
+done right because then we can apply F
+
+ align:start position:0%
+done right because then we can apply F
+ 
+
+ align:start position:0%
+done right because then we can apply F
+to both sides and we that F of the ball
+
+ align:start position:0%
+to both sides and we that F of the ball
+ 
+
+ align:start position:0%
+to both sides and we that F of the ball
+of radius Delta around C is contained in
+
+ align:start position:0%
+of radius Delta around C is contained in
+ 
+
+ align:start position:0%
+of radius Delta around C is contained in
+the ball of radius Epsilon of f c which
+
+ align:start position:0%
+the ball of radius Epsilon of f c which
+ 
+
+ align:start position:0%
+the ball of radius Epsilon of f c which
+is exactly the statement of continuity
+
+ align:start position:0%
+is exactly the statement of continuity
+ 
+
+ align:start position:0%
+is exactly the statement of continuity
+you can just write this out in terms of
+
+ align:start position:0%
+you can just write this out in terms of
+ 
+
+ align:start position:0%
+you can just write this out in terms of
+the metric right because then the
+
+ align:start position:0%
+the metric right because then the
+ 
+
+ align:start position:0%
+the metric right because then the
+distance from X to C being less than
+
+ align:start position:0%
+distance from X to C being less than
+ 
+
+ align:start position:0%
+distance from X to C being less than
+Delta implies that the distance from F
+
+ align:start position:0%
+Delta implies that the distance from F
+ 
+
+ align:start position:0%
+Delta implies that the distance from F
+ofx to F of C is less than Epsilon so
+
+ align:start position:0%
+ofx to F of C is less than Epsilon so
+ 
+
+ align:start position:0%
+ofx to F of C is less than Epsilon so
+this concludes the proof okay this was
+
+ align:start position:0%
+this concludes the proof okay this was
+ 
+
+ align:start position:0%
+this concludes the proof okay this was
+the general theory of metric space we've
+
+ align:start position:0%
+the general theory of metric space we've
+ 
+
+ align:start position:0%
+the general theory of metric space we've
+talked about convergent sequences which
+
+ align:start position:0%
+talked about convergent sequences which
+ 
+
+ align:start position:0%
+talked about convergent sequences which
+was essentially just like the real
+
+ align:start position:0%
+was essentially just like the real
+ 
+
+ align:start position:0%
+was essentially just like the real
+numbers we talked about uh open sets
+
+ align:start position:0%
+numbers we talked about uh open sets
+ 
+
+ align:start position:0%
+numbers we talked about uh open sets
+specifically the topological properties
+
+ align:start position:0%
+specifically the topological properties
+ 
+
+ align:start position:0%
+specifically the topological properties
+of them um which is important for
+
+ align:start position:0%
+of them um which is important for
+ 
+
+ align:start position:0%
+of them um which is important for
+topology and then we related those two
+
+ align:start position:0%
+topology and then we related those two
+ 
+
+ align:start position:0%
+topology and then we related those two
+concepts to convergent uh to continuity
+
+ align:start position:0%
+concepts to convergent uh to continuity
+ 
+
+ align:start position:0%
+concepts to convergent uh to continuity
+right we talked about how continuity is
+
+ align:start position:0%
+right we talked about how continuity is
+ 
+
+ align:start position:0%
+right we talked about how continuity is
+sequentially continuous at a point C if
+
+ align:start position:0%
+sequentially continuous at a point C if
+ 
+
+ align:start position:0%
+sequentially continuous at a point C if
+it's continuous on the metric space and
+
+ align:start position:0%
+it's continuous on the metric space and
+ 
+
+ align:start position:0%
+it's continuous on the metric space and
+we've talked about how continuity can be
+
+ align:start position:0%
+we've talked about how continuity can be
+ 
+
+ align:start position:0%
+we've talked about how continuity can be
+defined in terms of these open sets this
+
+ align:start position:0%
+defined in terms of these open sets this
+ 
+
+ align:start position:0%
+defined in terms of these open sets this
+is by no means a simple connection it
+
+ align:start position:0%
+is by no means a simple connection it
+ 
+
+ align:start position:0%
+is by no means a simple connection it
+can take a while to feel comfortable
+
+ align:start position:0%
+can take a while to feel comfortable
+ 
+
+ align:start position:0%
+can take a while to feel comfortable
+with these ideas but I highly suggest if
+
+ align:start position:0%
+with these ideas but I highly suggest if
+ 
+
+ align:start position:0%
+with these ideas but I highly suggest if
+if you're finding this a little bit
+
+ align:start position:0%
+if you're finding this a little bit
+ 
+
+ align:start position:0%
+if you're finding this a little bit
+confusing to try and draw out the
+
+ align:start position:0%
+confusing to try and draw out the
+ 
+
+ align:start position:0%
+confusing to try and draw out the
+pictures why does why does this
+
+ align:start position:0%
+pictures why does why does this
+ 
+
+ align:start position:0%
+pictures why does why does this
+conclusion hold why can I apply F to
+
+ align:start position:0%
+conclusion hold why can I apply F to
+ 
+
+ align:start position:0%
+conclusion hold why can I apply F to
+both sides and have things to be fine
+
+ align:start position:0%
+both sides and have things to be fine
+ 
+
+ align:start position:0%
+both sides and have things to be fine
+it's just a practice and set theory but
+
+ align:start position:0%
+it's just a practice and set theory but
+ 
+
+ align:start position:0%
+it's just a practice and set theory but
+it is helpful to do at some point okay
+
+ align:start position:0%
+it is helpful to do at some point okay
+ 
+
+ align:start position:0%
+it is helpful to do at some point okay
+starting next time we're going to start
+
+ align:start position:0%
+starting next time we're going to start
+ 
+
+ align:start position:0%
+starting next time we're going to start
+talking about something you might not
+
+ align:start position:0%
+talking about something you might not
+ 
+
+ align:start position:0%
+talking about something you might not
+have seen before at all known as compact
+
+ align:start position:0%
+have seen before at all known as compact
+ 
+
+ align:start position:0%
+have seen before at all known as compact
+sets until then have a great weekend
+
+ align:start position:0%
+sets until then have a great weekend
+ 
+
+ align:start position:0%
+sets until then have a great weekend
+remember that the P set is due on the
+
+ align:start position:0%
+remember that the P set is due on the
+ 
+
+ align:start position:0%
+remember that the P set is due on the
+13th okay all right have a great day
\ No newline at end of file
diff --git a/uS42vSWEGTU.txt b/uS42vSWEGTU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c3321faab3383c2b6101a81bc44cea882f2e229e
--- /dev/null
+++ b/uS42vSWEGTU.txt
@@ -0,0 +1,6355 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gonna get started and today we're gonna
+
+ align:start position:0%
+gonna get started and today we're gonna
+ 
+
+ align:start position:0%
+gonna get started and today we're gonna
+move forward with the protein
+
+ align:start position:0%
+move forward with the protein
+ 
+
+ align:start position:0%
+move forward with the protein
+degradation module and looking at the
+
+ align:start position:0%
+degradation module and looking at the
+ 
+
+ align:start position:0%
+degradation module and looking at the
+degradation chamber of e.coli clip XP so
+
+ align:start position:0%
+degradation chamber of e.coli clip XP so
+ 
+
+ align:start position:0%
+degradation chamber of e.coli clip XP so
+this is a degradation machine and
+
+ align:start position:0%
+this is a degradation machine and
+ 
+
+ align:start position:0%
+this is a degradation machine and
+effectively what we see in this case and
+
+ align:start position:0%
+effectively what we see in this case and
+ 
+
+ align:start position:0%
+effectively what we see in this case and
+as mentioned in lecture last time is
+
+ align:start position:0%
+as mentioned in lecture last time is
+ 
+
+ align:start position:0%
+as mentioned in lecture last time is
+that there are gigantic chambers that
+
+ align:start position:0%
+that there are gigantic chambers that
+ 
+
+ align:start position:0%
+that there are gigantic chambers that
+isolate protease active sites and so
+
+ align:start position:0%
+isolate protease active sites and so
+ 
+
+ align:start position:0%
+isolate protease active sites and so
+we're gonna examine this particular
+
+ align:start position:0%
+we're gonna examine this particular
+ 
+
+ align:start position:0%
+we're gonna examine this particular
+machinery as a paradigm here so the clip
+
+ align:start position:0%
+machinery as a paradigm here so the clip
+ 
+
+ align:start position:0%
+machinery as a paradigm here so the clip
+system was first identified in e.coli
+
+ align:start position:0%
+system was first identified in e.coli
+ 
+
+ align:start position:0%
+system was first identified in e.coli
+and it's highly conserved and what we'll
+
+ align:start position:0%
+and it's highly conserved and what we'll
+ 
+
+ align:start position:0%
+and it's highly conserved and what we'll
+see is that there's encapsulation of an
+
+ align:start position:0%
+see is that there's encapsulation of an
+ 
+
+ align:start position:0%
+see is that there's encapsulation of an
+active site in a large degradation
+
+ align:start position:0%
+active site in a large degradation
+ 
+
+ align:start position:0%
+active site in a large degradation
+chamber so there's two components clip X
+
+ align:start position:0%
+chamber so there's two components clip X
+ 
+
+ align:start position:0%
+chamber so there's two components clip X
+and clip P and so we're going to look at
+
+ align:start position:0%
+and clip P and so we're going to look at
+ 
+
+ align:start position:0%
+and clip P and so we're going to look at
+both of these components individually
+
+ align:start position:0%
+both of these components individually
+ 
+
+ align:start position:0%
+both of these components individually
+and then see how this machine works and
+
+ align:start position:0%
+and then see how this machine works and
+ 
+
+ align:start position:0%
+and then see how this machine works and
+so clip P this is the proteasome okay
+
+ align:start position:0%
+so clip P this is the proteasome okay
+ 
+
+ align:start position:0%
+so clip P this is the proteasome okay
+and it's a serine protease so we talked
+
+ align:start position:0%
+and it's a serine protease so we talked
+ 
+
+ align:start position:0%
+and it's a serine protease so we talked
+about serine proteases last time so
+
+ align:start position:0%
+about serine proteases last time so
+ 
+
+ align:start position:0%
+about serine proteases last time so
+there's the catalytic triad of serine
+
+ align:start position:0%
+there's the catalytic triad of serine
+ 
+
+ align:start position:0%
+there's the catalytic triad of serine
+histidine an aspartate
+
+ align:start position:0%
+histidine an aspartate
+ 
+
+ align:start position:0%
+histidine an aspartate
+so there's formation of a covalent a
+
+ align:start position:0%
+so there's formation of a covalent a
+ 
+
+ align:start position:0%
+so there's formation of a covalent a
+selenium intermediate we learned that
+
+ align:start position:0%
+selenium intermediate we learned that
+ 
+
+ align:start position:0%
+selenium intermediate we learned that
+the serine residue is the active site
+
+ align:start position:0%
+the serine residue is the active site
+ 
+
+ align:start position:0%
+the serine residue is the active site
+nucleophile and what we're going to see
+
+ align:start position:0%
+nucleophile and what we're going to see
+ 
+
+ align:start position:0%
+nucleophile and what we're going to see
+is that this degradation chamber has 14
+
+ align:start position:0%
+is that this degradation chamber has 14
+ 
+
+ align:start position:0%
+is that this degradation chamber has 14
+active sites
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and what this does is degrade
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proteins into short polypeptides so it's
+
+ align:start position:0%
+proteins into short polypeptides so it's
+ 
+
+ align:start position:0%
+proteins into short polypeptides so it's
+a peptides of about seven to eight amino
+
+ align:start position:0%
+a peptides of about seven to eight amino
+ 
+
+ align:start position:0%
+a peptides of about seven to eight amino
+acids and so if we consider a cartoon of
+
+ align:start position:0%
+acids and so if we consider a cartoon of
+ 
+
+ align:start position:0%
+acids and so if we consider a cartoon of
+the structure what we find is that we
+
+ align:start position:0%
+the structure what we find is that we
+ 
+
+ align:start position:0%
+the structure what we find is that we
+have two back-to-back rings here okay
+
+ align:start position:0%
+have two back-to-back rings here okay
+ 
+
+ align:start position:0%
+have two back-to-back rings here okay
+and each of these rings is a seven or
+
+ align:start position:0%
+and each of these rings is a seven or
+ 
+
+ align:start position:0%
+and each of these rings is a seven or
+seven murmur so we have two hep tumors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in terms of size approximately 90
+
+ align:start position:0%
+okay in terms of size approximately 90
+ 
+
+ align:start position:0%
+okay in terms of size approximately 90
+angstroms here and approximately 90
+
+ align:start position:0%
+angstroms here and approximately 90
+ 
+
+ align:start position:0%
+angstroms here and approximately 90
+angstroms across okay and then this
+
+ align:start position:0%
+angstroms across okay and then this
+ 
+
+ align:start position:0%
+angstroms across okay and then this
+region between the two rings is
+
+ align:start position:0%
+region between the two rings is
+ 
+
+ align:start position:0%
+region between the two rings is
+sometimes referred to as the equator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here we have two back-to-back
+
+ align:start position:0%
+okay so here we have two back-to-back
+ 
+
+ align:start position:0%
+okay so here we have two back-to-back
+rings okay and these rings generate a
+
+ align:start position:0%
+rings okay and these rings generate a
+ 
+
+ align:start position:0%
+rings okay and these rings generate a
+chamber okay and proteins upwards of
+
+ align:start position:0%
+chamber okay and proteins upwards of
+ 
+
+ align:start position:0%
+chamber okay and proteins upwards of
+about 70 killer Dalton's can fit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if we take this looking at from
+
+ align:start position:0%
+and so if we take this looking at from
+ 
+
+ align:start position:0%
+and so if we take this looking at from
+the side and just rotate 90 degrees to
+
+ align:start position:0%
+the side and just rotate 90 degrees to
+ 
+
+ align:start position:0%
+the side and just rotate 90 degrees to
+ask what does it look like from the top
+
+ align:start position:0%
+ask what does it look like from the top
+ 
+
+ align:start position:0%
+ask what does it look like from the top
+okay so this is a side view okay what we
+
+ align:start position:0%
+okay so this is a side view okay what we
+ 
+
+ align:start position:0%
+okay so this is a side view okay what we
+see is that there's a very small pore
+
+ align:start position:0%
+see is that there's a very small pore
+ 
+
+ align:start position:0%
+see is that there's a very small pore
+here okay so we have the seven subunits
+
+ align:start position:0%
+here okay so we have the seven subunits
+ 
+
+ align:start position:0%
+here okay so we have the seven subunits
+and then in the center there's an axial
+
+ align:start position:0%
+and then in the center there's an axial
+ 
+
+ align:start position:0%
+and then in the center there's an axial
+pore okay
+
+ align:start position:0%
+pore okay
+ 
+
+ align:start position:0%
+pore okay
+and this pore is small about 10
+
+ align:start position:0%
+and this pore is small about 10
+ 
+
+ align:start position:0%
+and this pore is small about 10
+angstroms in diameter okay so when
+
+ align:start position:0%
+angstroms in diameter okay so when
+ 
+
+ align:start position:0%
+angstroms in diameter okay so when
+thinking about that size we need to
+
+ align:start position:0%
+thinking about that size we need to
+ 
+
+ align:start position:0%
+thinking about that size we need to
+think about the size of some large
+
+ align:start position:0%
+think about the size of some large
+ 
+
+ align:start position:0%
+think about the size of some large
+protein right if we have something on
+
+ align:start position:0%
+protein right if we have something on
+ 
+
+ align:start position:0%
+protein right if we have something on
+the order of 70 kilo daltons
+
+ align:start position:0%
+the order of 70 kilo daltons
+ 
+
+ align:start position:0%
+the order of 70 kilo daltons
+with a fold that proteins not going to
+
+ align:start position:0%
+with a fold that proteins not going to
+ 
+
+ align:start position:0%
+with a fold that proteins not going to
+fit through this this hole in that state
+
+ align:start position:0%
+fit through this this hole in that state
+ 
+
+ align:start position:0%
+fit through this this hole in that state
+here okay so it's too small for a big
+
+ align:start position:0%
+here okay so it's too small for a big
+ 
+
+ align:start position:0%
+here okay so it's too small for a big
+folded protein okay but then basically
+
+ align:start position:0%
+folded protein okay but then basically
+ 
+
+ align:start position:0%
+folded protein okay but then basically
+if we take this and rather than just
+
+ align:start position:0%
+if we take this and rather than just
+ 
+
+ align:start position:0%
+if we take this and rather than just
+looking at the top we cut through and
+
+ align:start position:0%
+looking at the top we cut through and
+ 
+
+ align:start position:0%
+looking at the top we cut through and
+ask what's going on in the interior what
+
+ align:start position:0%
+ask what's going on in the interior what
+ 
+
+ align:start position:0%
+ask what's going on in the interior what
+do we see okay so cut through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we see know is that there's a
+
+ align:start position:0%
+what we see know is that there's a
+ 
+
+ align:start position:0%
+what we see know is that there's a
+chamber of about 51 angstroms okay so
+
+ align:start position:0%
+chamber of about 51 angstroms okay so
+ 
+
+ align:start position:0%
+chamber of about 51 angstroms okay so
+this is the interior degradation chamber
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so one question we're gonna address
+
+ align:start position:0%
+okay so one question we're gonna address
+ 
+
+ align:start position:0%
+okay so one question we're gonna address
+as we move forward is that how is it
+
+ align:start position:0%
+as we move forward is that how is it
+ 
+
+ align:start position:0%
+as we move forward is that how is it
+that a polypeptide gets through this
+
+ align:start position:0%
+that a polypeptide gets through this
+ 
+
+ align:start position:0%
+that a polypeptide gets through this
+hole into the degradation chamber that
+
+ align:start position:0%
+hole into the degradation chamber that
+ 
+
+ align:start position:0%
+hole into the degradation chamber that
+can accommodate you know approaching up
+
+ align:start position:0%
+can accommodate you know approaching up
+ 
+
+ align:start position:0%
+can accommodate you know approaching up
+to 70 kilonewtons
+
+ align:start position:0%
+to 70 kilonewtons
+ 
+
+ align:start position:0%
+to 70 kilonewtons
+okay so small axial pour versus large
+
+ align:start position:0%
+okay so small axial pour versus large
+ 
+
+ align:start position:0%
+okay so small axial pour versus large
+degradation chamber here okay
+
+ align:start position:0%
+degradation chamber here okay
+ 
+
+ align:start position:0%
+degradation chamber here okay
+so we'll look at some structures of clip
+
+ align:start position:0%
+so we'll look at some structures of clip
+ 
+
+ align:start position:0%
+so we'll look at some structures of clip
+P and then go on to clip X so what we're
+
+ align:start position:0%
+P and then go on to clip X so what we're
+ 
+
+ align:start position:0%
+P and then go on to clip X so what we're
+looking at here are effectively what
+
+ align:start position:0%
+looking at here are effectively what
+ 
+
+ align:start position:0%
+looking at here are effectively what
+I've drawn out in cartoon form on the
+
+ align:start position:0%
+I've drawn out in cartoon form on the
+ 
+
+ align:start position:0%
+I've drawn out in cartoon form on the
+board so here we have the side view of
+
+ align:start position:0%
+board so here we have the side view of
+ 
+
+ align:start position:0%
+board so here we have the side view of
+clip P we have the top ring the bottom
+
+ align:start position:0%
+clip P we have the top ring the bottom
+ 
+
+ align:start position:0%
+clip P we have the top ring the bottom
+ring and here's the region between the
+
+ align:start position:0%
+ring and here's the region between the
+ 
+
+ align:start position:0%
+ring and here's the region between the
+two the equator if we look at the top
+
+ align:start position:0%
+two the equator if we look at the top
+ 
+
+ align:start position:0%
+two the equator if we look at the top
+here they're describing the axial pore
+
+ align:start position:0%
+here they're describing the axial pore
+ 
+
+ align:start position:0%
+here they're describing the axial pore
+as a portal okay and here's the cutaway
+
+ align:start position:0%
+as a portal okay and here's the cutaway
+ 
+
+ align:start position:0%
+as a portal okay and here's the cutaway
+view so this hole is very small and if
+
+ align:start position:0%
+view so this hole is very small and if
+ 
+
+ align:start position:0%
+view so this hole is very small and if
+we look at the cutaway view what we see
+
+ align:start position:0%
+we look at the cutaway view what we see
+ 
+
+ align:start position:0%
+we look at the cutaway view what we see
+is the degradation chamber here okay and
+
+ align:start position:0%
+is the degradation chamber here okay and
+ 
+
+ align:start position:0%
+is the degradation chamber here okay and
+basically the seven different serine
+
+ align:start position:0%
+basically the seven different serine
+ 
+
+ align:start position:0%
+basically the seven different serine
+protease active sites are shown here
+
+ align:start position:0%
+protease active sites are shown here
+ 
+
+ align:start position:0%
+protease active sites are shown here
+okay and this is a side view cutting
+
+ align:start position:0%
+okay and this is a side view cutting
+ 
+
+ align:start position:0%
+okay and this is a side view cutting
+through through the middle here so we
+
+ align:start position:0%
+through through the middle here so we
+ 
+
+ align:start position:0%
+through through the middle here so we
+see that these Syrian protease active
+
+ align:start position:0%
+see that these Syrian protease active
+ 
+
+ align:start position:0%
+see that these Syrian protease active
+sites are down in this region here if we
+
+ align:start position:0%
+sites are down in this region here if we
+ 
+
+ align:start position:0%
+sites are down in this region here if we
+take another view and look at again this
+
+ align:start position:0%
+take another view and look at again this
+ 
+
+ align:start position:0%
+take another view and look at again this
+is cut away so cut through the side view
+
+ align:start position:0%
+is cut away so cut through the side view
+ 
+
+ align:start position:0%
+is cut away so cut through the side view
+what we can look at here is the
+
+ align:start position:0%
+what we can look at here is the
+ 
+
+ align:start position:0%
+what we can look at here is the
+machinery in the active site so we
+
+ align:start position:0%
+machinery in the active site so we
+ 
+
+ align:start position:0%
+machinery in the active site so we
+learned last time about the catalytic
+
+ align:start position:0%
+learned last time about the catalytic
+ 
+
+ align:start position:0%
+learned last time about the catalytic
+triad with the aspartate histidine and
+
+ align:start position:0%
+triad with the aspartate histidine and
+ 
+
+ align:start position:0%
+triad with the aspartate histidine and
+serine and in this particular structure
+
+ align:start position:0%
+serine and in this particular structure
+ 
+
+ align:start position:0%
+serine and in this particular structure
+there's a serine protease inhibitor
+
+ align:start position:0%
+there's a serine protease inhibitor
+ 
+
+ align:start position:0%
+there's a serine protease inhibitor
+bound to the Syrian side chain here okay
+
+ align:start position:0%
+bound to the Syrian side chain here okay
+ 
+
+ align:start position:0%
+bound to the Syrian side chain here okay
+so that that conserved machinery
+
+ align:start position:0%
+so that that conserved machinery
+ 
+
+ align:start position:0%
+so that that conserved machinery
+if we look at the structure of an
+
+ align:start position:0%
+if we look at the structure of an
+ 
+
+ align:start position:0%
+if we look at the structure of an
+individual clip piece subunit those are
+
+ align:start position:0%
+individual clip piece subunit those are
+ 
+
+ align:start position:0%
+individual clip piece subunit those are
+shown here from several different
+
+ align:start position:0%
+shown here from several different
+ 
+
+ align:start position:0%
+shown here from several different
+organisms what we see if we can think
+
+ align:start position:0%
+organisms what we see if we can think
+ 
+
+ align:start position:0%
+organisms what we see if we can think
+about this is the top part and this is
+
+ align:start position:0%
+about this is the top part and this is
+ 
+
+ align:start position:0%
+about this is the top part and this is
+the bottom part of one ring we see
+
+ align:start position:0%
+the bottom part of one ring we see
+ 
+
+ align:start position:0%
+the bottom part of one ring we see
+there's a region with axial loops
+
+ align:start position:0%
+there's a region with axial loops
+ 
+
+ align:start position:0%
+there's a region with axial loops
+there's a head domain and what's called
+
+ align:start position:0%
+there's a head domain and what's called
+ 
+
+ align:start position:0%
+there's a head domain and what's called
+a handle region okay and the catalytic
+
+ align:start position:0%
+a handle region okay and the catalytic
+ 
+
+ align:start position:0%
+a handle region okay and the catalytic
+triad is located at the juncture of the
+
+ align:start position:0%
+triad is located at the juncture of the
+ 
+
+ align:start position:0%
+triad is located at the juncture of the
+head and handle region and you can again
+
+ align:start position:0%
+head and handle region and you can again
+ 
+
+ align:start position:0%
+head and handle region and you can again
+look back to the cutaway views to orient
+
+ align:start position:0%
+look back to the cutaway views to orient
+ 
+
+ align:start position:0%
+look back to the cutaway views to orient
+that within the whole chamber
+
+ align:start position:0%
+that within the whole chamber
+ 
+
+ align:start position:0%
+that within the whole chamber
+okay these axial loops we'll see are
+
+ align:start position:0%
+okay these axial loops we'll see are
+ 
+
+ align:start position:0%
+okay these axial loops we'll see are
+important for interaction with clip X
+
+ align:start position:0%
+important for interaction with clip X
+ 
+
+ align:start position:0%
+important for interaction with clip X
+and we'll talk about that component of
+
+ align:start position:0%
+and we'll talk about that component of
+ 
+
+ align:start position:0%
+and we'll talk about that component of
+the machine in a moment here again just
+
+ align:start position:0%
+the machine in a moment here again just
+ 
+
+ align:start position:0%
+the machine in a moment here again just
+structures of clip P from various
+
+ align:start position:0%
+structures of clip P from various
+ 
+
+ align:start position:0%
+structures of clip P from various
+organisms ecoli streptococcus human we
+
+ align:start position:0%
+organisms ecoli streptococcus human we
+ 
+
+ align:start position:0%
+organisms ecoli streptococcus human we
+see that that they're all very similar
+
+ align:start position:0%
+see that that they're all very similar
+ 
+
+ align:start position:0%
+see that that they're all very similar
+here so what is clip X moving forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so clip X is effectively an
+
+ align:start position:0%
+okay so clip X is effectively an
+ 
+
+ align:start position:0%
+okay so clip X is effectively an
+accessory protein okay and in some
+
+ align:start position:0%
+accessory protein okay and in some
+ 
+
+ align:start position:0%
+accessory protein okay and in some
+respects we can think about it as a lid
+
+ align:start position:0%
+respects we can think about it as a lid
+ 
+
+ align:start position:0%
+respects we can think about it as a lid
+to the proteasome okay it's a hexamer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's a mismatch here in terms
+
+ align:start position:0%
+okay so there's a mismatch here in terms
+ 
+
+ align:start position:0%
+okay so there's a mismatch here in terms
+of the number of subunits and clip P and
+
+ align:start position:0%
+of the number of subunits and clip P and
+ 
+
+ align:start position:0%
+of the number of subunits and clip P and
+clip X this is different from what we
+
+ align:start position:0%
+clip X this is different from what we
+ 
+
+ align:start position:0%
+clip X this is different from what we
+saw with grow al grow es where they are
+
+ align:start position:0%
+saw with grow al grow es where they are
+ 
+
+ align:start position:0%
+saw with grow al grow es where they are
+both heptamer
+
+ align:start position:0%
+both heptamer
+ 
+
+ align:start position:0%
+both heptamer
+clip clip X is a hexamer and it's an AAA
+
+ align:start position:0%
+clip clip X is a hexamer and it's an AAA
+ 
+
+ align:start position:0%
+clip clip X is a hexamer and it's an AAA
+so Triple A plus unfold ace okay
+
+ align:start position:0%
+so Triple A plus unfold ace okay
+ 
+
+ align:start position:0%
+so Triple A plus unfold ace okay
+it's an ATPase here okay and effectively
+
+ align:start position:0%
+it's an ATPase here okay and effectively
+ 
+
+ align:start position:0%
+it's an ATPase here okay and effectively
+what we'll see is that clip X has an
+
+ align:start position:0%
+what we'll see is that clip X has an
+ 
+
+ align:start position:0%
+what we'll see is that clip X has an
+important role as an accessory protein
+
+ align:start position:0%
+important role as an accessory protein
+ 
+
+ align:start position:0%
+important role as an accessory protein
+that unfolds the polypeptide that's
+
+ align:start position:0%
+that unfolds the polypeptide that's
+ 
+
+ align:start position:0%
+that unfolds the polypeptide that's
+destined for degradation by clip P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when unfolds the polypeptide and
+
+ align:start position:0%
+so when unfolds the polypeptide and
+ 
+
+ align:start position:0%
+so when unfolds the polypeptide and
+we're gonna have to ask how as we go
+
+ align:start position:0%
+we're gonna have to ask how as we go
+ 
+
+ align:start position:0%
+we're gonna have to ask how as we go
+through okay and in addition to
+
+ align:start position:0%
+through okay and in addition to
+ 
+
+ align:start position:0%
+through okay and in addition to
+unfolding it also threads that
+
+ align:start position:0%
+unfolding it also threads that
+ 
+
+ align:start position:0%
+unfolding it also threads that
+polypeptide that's being unfolded and
+
+ align:start position:0%
+polypeptide that's being unfolded and
+ 
+
+ align:start position:0%
+polypeptide that's being unfolded and
+through the axial pore such that it can
+
+ align:start position:0%
+through the axial pore such that it can
+ 
+
+ align:start position:0%
+through the axial pore such that it can
+reach the degradation chamber okay and
+
+ align:start position:0%
+reach the degradation chamber okay and
+ 
+
+ align:start position:0%
+reach the degradation chamber okay and
+threads into the degradation chamber and
+
+ align:start position:0%
+threads into the degradation chamber and
+ 
+
+ align:start position:0%
+threads into the degradation chamber and
+so if we look at clip X from a top view
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm agin we have a hole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have a six Merc okay here so if
+
+ align:start position:0%
+and we have a six Merc okay here so if
+ 
+
+ align:start position:0%
+and we have a six Merc okay here so if
+we take a look in this particular
+
+ align:start position:0%
+we take a look in this particular
+ 
+
+ align:start position:0%
+we take a look in this particular
+depiction what we're seeing are the top
+
+ align:start position:0%
+depiction what we're seeing are the top
+ 
+
+ align:start position:0%
+depiction what we're seeing are the top
+views and the side views so here we have
+
+ align:start position:0%
+views and the side views so here we have
+ 
+
+ align:start position:0%
+views and the side views so here we have
+put P here we have clip X and what we
+
+ align:start position:0%
+put P here we have clip X and what we
+ 
+
+ align:start position:0%
+put P here we have clip X and what we
+want to ask is how is it that clip X
+
+ align:start position:0%
+want to ask is how is it that clip X
+ 
+
+ align:start position:0%
+want to ask is how is it that clip X
+binds to clip P and how is this mismatch
+
+ align:start position:0%
+binds to clip P and how is this mismatch
+ 
+
+ align:start position:0%
+binds to clip P and how is this mismatch
+in terms of the number of subunits
+
+ align:start position:0%
+in terms of the number of subunits
+ 
+
+ align:start position:0%
+in terms of the number of subunits
+accommodated right so it's not that one
+
+ align:start position:0%
+accommodated right so it's not that one
+ 
+
+ align:start position:0%
+accommodated right so it's not that one
+subunit is precisely going to act with
+
+ align:start position:0%
+subunit is precisely going to act with
+ 
+
+ align:start position:0%
+subunit is precisely going to act with
+one because we have six in throughout
+
+ align:start position:0%
+one because we have six in throughout
+ 
+
+ align:start position:0%
+one because we have six in throughout
+because we have six in clip X and 7 and
+
+ align:start position:0%
+because we have six in clip X and 7 and
+ 
+
+ align:start position:0%
+because we have six in clip X and 7 and
+clip P and so if we think about how clip
+
+ align:start position:0%
+clip P and so if we think about how clip
+ 
+
+ align:start position:0%
+clip P and so if we think about how clip
+explains to clip P what we see is that
+
+ align:start position:0%
+explains to clip P what we see is that
+ 
+
+ align:start position:0%
+explains to clip P what we see is that
+we have the six mer so we're looking
+
+ align:start position:0%
+we have the six mer so we're looking
+ 
+
+ align:start position:0%
+we have the six mer so we're looking
+from the side view okay and there's some
+
+ align:start position:0%
+from the side view okay and there's some
+ 
+
+ align:start position:0%
+from the side view okay and there's some
+loops that are called IGF loops okay so
+
+ align:start position:0%
+loops that are called IGF loops okay so
+ 
+
+ align:start position:0%
+loops that are called IGF loops okay so
+these are tripeptide motifs and they're
+
+ align:start position:0%
+these are tripeptide motifs and they're
+ 
+
+ align:start position:0%
+these are tripeptide motifs and they're
+flexible okay and these loops interact
+
+ align:start position:0%
+flexible okay and these loops interact
+ 
+
+ align:start position:0%
+flexible okay and these loops interact
+with hydrophobic regions of clip P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this flexibility helps accommodate
+
+ align:start position:0%
+and this flexibility helps accommodate
+ 
+
+ align:start position:0%
+and this flexibility helps accommodate
+the 6 vs 7 sub units so if we look here
+
+ align:start position:0%
+the 6 vs 7 sub units so if we look here
+ 
+
+ align:start position:0%
+the 6 vs 7 sub units so if we look here
+here we see these tripeptide loops okay
+
+ align:start position:0%
+here we see these tripeptide loops okay
+ 
+
+ align:start position:0%
+here we see these tripeptide loops okay
+and see we're only seeing three but
+
+ align:start position:0%
+and see we're only seeing three but
+ 
+
+ align:start position:0%
+and see we're only seeing three but
+there's one for subunit so 1 2 3 4 5 6
+
+ align:start position:0%
+there's one for subunit so 1 2 3 4 5 6
+ 
+
+ align:start position:0%
+there's one for subunit so 1 2 3 4 5 6
+here and then what's shown here in red
+
+ align:start position:0%
+here and then what's shown here in red
+ 
+
+ align:start position:0%
+here and then what's shown here in red
+are the hydrophobic regions of clip P
+
+ align:start position:0%
+are the hydrophobic regions of clip P
+ 
+
+ align:start position:0%
+are the hydrophobic regions of clip P
+where these can bind okay and where do
+
+ align:start position:0%
+where these can bind okay and where do
+ 
+
+ align:start position:0%
+where these can bind okay and where do
+we see these regions on clip P here
+
+ align:start position:0%
+we see these regions on clip P here
+ 
+
+ align:start position:0%
+we see these regions on clip P here
+they're a bit removed from the axial
+
+ align:start position:0%
+they're a bit removed from the axial
+ 
+
+ align:start position:0%
+they're a bit removed from the axial
+pore here okay
+
+ align:start position:0%
+pore here okay
+ 
+
+ align:start position:0%
+pore here okay
+so how many of these loops are needed
+
+ align:start position:0%
+so how many of these loops are needed
+ 
+
+ align:start position:0%
+so how many of these loops are needed
+just to note there's been studies done
+
+ align:start position:0%
+just to note there's been studies done
+ 
+
+ align:start position:0%
+just to note there's been studies done
+where these residues are deleted and the
+
+ align:start position:0%
+where these residues are deleted and the
+ 
+
+ align:start position:0%
+where these residues are deleted and the
+question is how many how many of these
+
+ align:start position:0%
+question is how many how many of these
+ 
+
+ align:start position:0%
+question is how many how many of these
+motifs are important for this protein
+
+ align:start position:0%
+motifs are important for this protein
+ 
+
+ align:start position:0%
+motifs are important for this protein
+protein interaction and what's been
+
+ align:start position:0%
+protein interaction and what's been
+ 
+
+ align:start position:0%
+protein interaction and what's been
+found in test-tube studies is that a
+
+ align:start position:0%
+found in test-tube studies is that a
+ 
+
+ align:start position:0%
+found in test-tube studies is that a
+minimum of 2 are required to get
+
+ align:start position:0%
+minimum of 2 are required to get
+ 
+
+ align:start position:0%
+minimum of 2 are required to get
+interaction between clip X and clip clip
+
+ align:start position:0%
+interaction between clip X and clip clip
+ 
+
+ align:start position:0%
+interaction between clip X and clip clip
+P here yeah
+
+ align:start position:0%
+P here yeah
+ 
+
+ align:start position:0%
+P here yeah
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I would presume so but I don't don't
+
+ align:start position:0%
+um I would presume so but I don't don't
+ 
+
+ align:start position:0%
+um I would presume so but I don't don't
+know right so we very much think of this
+
+ align:start position:0%
+know right so we very much think of this
+ 
+
+ align:start position:0%
+know right so we very much think of this
+as coming coming together like as shown
+
+ align:start position:0%
+as coming coming together like as shown
+ 
+
+ align:start position:0%
+as coming coming together like as shown
+here there but don't know jo-ann's you
+
+ align:start position:0%
+here there but don't know jo-ann's you
+ 
+
+ align:start position:0%
+here there but don't know jo-ann's you
+know no I would say it needs to be
+
+ align:start position:0%
+know no I would say it needs to be
+ 
+
+ align:start position:0%
+know no I would say it needs to be
+pretty stable like there's always
+
+ align:start position:0%
+pretty stable like there's always
+ 
+
+ align:start position:0%
+pretty stable like there's always
+dynamics but as we see how this machine
+
+ align:start position:0%
+dynamics but as we see how this machine
+ 
+
+ align:start position:0%
+dynamics but as we see how this machine
+works right
+
+ align:start position:0%
+works right
+ 
+
+ align:start position:0%
+works right
+this whole is going to have to allow the
+
+ align:start position:0%
+this whole is going to have to allow the
+ 
+
+ align:start position:0%
+this whole is going to have to allow the
+polypeptide to thread through and get to
+
+ align:start position:0%
+polypeptide to thread through and get to
+ 
+
+ align:start position:0%
+polypeptide to thread through and get to
+that through that axial pore for the
+
+ align:start position:0%
+that through that axial pore for the
+ 
+
+ align:start position:0%
+that through that axial pore for the
+polypeptide to get in the degradation
+
+ align:start position:0%
+polypeptide to get in the degradation
+ 
+
+ align:start position:0%
+polypeptide to get in the degradation
+chamber so you'd imagine you want that
+
+ align:start position:0%
+chamber so you'd imagine you want that
+ 
+
+ align:start position:0%
+chamber so you'd imagine you want that
+to be lined up quite well in order for
+
+ align:start position:0%
+to be lined up quite well in order for
+ 
+
+ align:start position:0%
+to be lined up quite well in order for
+it to be efficient there okay so what
+
+ align:start position:0%
+it to be efficient there okay so what
+ 
+
+ align:start position:0%
+it to be efficient there okay so what
+are these triple A plus ATP ASE's this
+
+ align:start position:0%
+are these triple A plus ATP ASE's this
+ 
+
+ align:start position:0%
+are these triple A plus ATP ASE's this
+is a very important group of ATP ASE's
+
+ align:start position:0%
+is a very important group of ATP ASE's
+ 
+
+ align:start position:0%
+is a very important group of ATP ASE's
+so what the name means ATP ASE's
+
+ align:start position:0%
+so what the name means ATP ASE's
+ 
+
+ align:start position:0%
+so what the name means ATP ASE's
+associated with various cellular
+
+ align:start position:0%
+associated with various cellular
+ 
+
+ align:start position:0%
+associated with various cellular
+activities and they're super duper given
+
+ align:start position:0%
+activities and they're super duper given
+ 
+
+ align:start position:0%
+activities and they're super duper given
+this hopefully everyone gets a Triple A
+
+ align:start position:0%
+this hopefully everyone gets a Triple A
+ 
+
+ align:start position:0%
+this hopefully everyone gets a Triple A
+plus on the exam tonight the super
+
+ align:start position:0%
+plus on the exam tonight the super
+ 
+
+ align:start position:0%
+plus on the exam tonight the super
+family is involved in many cellular
+
+ align:start position:0%
+family is involved in many cellular
+ 
+
+ align:start position:0%
+family is involved in many cellular
+functions and take a look so many
+
+ align:start position:0%
+functions and take a look so many
+ 
+
+ align:start position:0%
+functions and take a look so many
+diverse functions so membrane fusion
+
+ align:start position:0%
+diverse functions so membrane fusion
+ 
+
+ align:start position:0%
+diverse functions so membrane fusion
+trafficking of vesicles cytoskeleton
+
+ align:start position:0%
+trafficking of vesicles cytoskeleton
+ 
+
+ align:start position:0%
+trafficking of vesicles cytoskeleton
+regulation transport organelle
+
+ align:start position:0%
+regulation transport organelle
+ 
+
+ align:start position:0%
+regulation transport organelle
+biogenesis DNA replication transcription
+
+ align:start position:0%
+biogenesis DNA replication transcription
+ 
+
+ align:start position:0%
+biogenesis DNA replication transcription
+regulation and what we're really
+
+ align:start position:0%
+regulation and what we're really
+ 
+
+ align:start position:0%
+regulation and what we're really
+interested in here is protein
+
+ align:start position:0%
+interested in here is protein
+ 
+
+ align:start position:0%
+interested in here is protein
+degradation so they come up in a variety
+
+ align:start position:0%
+degradation so they come up in a variety
+ 
+
+ align:start position:0%
+degradation so they come up in a variety
+of processes and although these
+
+ align:start position:0%
+of processes and although these
+ 
+
+ align:start position:0%
+of processes and although these
+processes are very different
+
+ align:start position:0%
+processes are very different
+ 
+
+ align:start position:0%
+processes are very different
+all of these triple 8 plus ATP ASE's
+
+ align:start position:0%
+all of these triple 8 plus ATP ASE's
+ 
+
+ align:start position:0%
+all of these triple 8 plus ATP ASE's
+share a common protein architecture and
+
+ align:start position:0%
+share a common protein architecture and
+ 
+
+ align:start position:0%
+share a common protein architecture and
+I'll just point out that there's an ATP
+
+ align:start position:0%
+I'll just point out that there's an ATP
+ 
+
+ align:start position:0%
+I'll just point out that there's an ATP
+binding module and some details are
+
+ align:start position:0%
+binding module and some details are
+ 
+
+ align:start position:0%
+binding module and some details are
+given here in terms of the motif and
+
+ align:start position:0%
+given here in terms of the motif and
+ 
+
+ align:start position:0%
+given here in terms of the motif and
+then really what we'll focus on in terms
+
+ align:start position:0%
+then really what we'll focus on in terms
+ 
+
+ align:start position:0%
+then really what we'll focus on in terms
+of aspects of this course is that they
+
+ align:start position:0%
+of aspects of this course is that they
+ 
+
+ align:start position:0%
+of aspects of this course is that they
+form oligomers that are ring or cylinder
+
+ align:start position:0%
+form oligomers that are ring or cylinder
+ 
+
+ align:start position:0%
+form oligomers that are ring or cylinder
+shaped and they're all hexamers here ok
+
+ align:start position:0%
+shaped and they're all hexamers here ok
+ 
+
+ align:start position:0%
+shaped and they're all hexamers here ok
+and so of importance to clip XP these
+
+ align:start position:0%
+and so of importance to clip XP these
+ 
+
+ align:start position:0%
+and so of importance to clip XP these
+ATP ASE's
+
+ align:start position:0%
+ATP ASE's
+ 
+
+ align:start position:0%
+ATP ASE's
+have the ability to ream
+
+ align:start position:0%
+have the ability to ream
+ 
+
+ align:start position:0%
+have the ability to ream
+conformation of macromolecules and so
+
+ align:start position:0%
+conformation of macromolecules and so
+ 
+
+ align:start position:0%
+conformation of macromolecules and so
+here we're focused on unfolding yeah 80
+
+ align:start position:0%
+here we're focused on unfolding yeah 80
+ 
+
+ align:start position:0%
+here we're focused on unfolding yeah 80
+pieces that aren't associated with other
+
+ align:start position:0%
+pieces that aren't associated with other
+ 
+
+ align:start position:0%
+pieces that aren't associated with other
+activities the architecture strictly
+
+ align:start position:0%
+activities the architecture strictly
+ 
+
+ align:start position:0%
+activities the architecture strictly
+yeah I mean if you look at trna
+
+ align:start position:0%
+yeah I mean if you look at trna
+ 
+
+ align:start position:0%
+yeah I mean if you look at trna
+synthetases right yeah ATPase activity
+
+ align:start position:0%
+synthetases right yeah ATPase activity
+ 
+
+ align:start position:0%
+synthetases right yeah ATPase activity
+100 and Perkins have ATPase activities
+
+ align:start position:0%
+100 and Perkins have ATPase activities
+ 
+
+ align:start position:0%
+100 and Perkins have ATPase activities
+right so they hydrolyze ATP to ADP MPI
+
+ align:start position:0%
+right so they hydrolyze ATP to ADP MPI
+ 
+
+ align:start position:0%
+right so they hydrolyze ATP to ADP MPI
+activities like what water what aren't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well your aminoacyl trna synthetases are
+
+ align:start position:0%
+well your aminoacyl trna synthetases are
+ 
+
+ align:start position:0%
+well your aminoacyl trna synthetases are
+not Triple A plus ATP ASE's what we'll
+
+ align:start position:0%
+not Triple A plus ATP ASE's what we'll
+ 
+
+ align:start position:0%
+not Triple A plus ATP ASE's what we'll
+see in terms of the non-ribosomal
+
+ align:start position:0%
+see in terms of the non-ribosomal
+ 
+
+ align:start position:0%
+see in terms of the non-ribosomal
+peptide synthesis they're not these
+
+ align:start position:0%
+peptide synthesis they're not these
+ 
+
+ align:start position:0%
+peptide synthesis they're not these
+triple e plus ATP ASE's right so these
+
+ align:start position:0%
+triple e plus ATP ASE's right so these
+ 
+
+ align:start position:0%
+triple e plus ATP ASE's right so these
+any yes okay all ATP ASE's the enzymes
+
+ align:start position:0%
+any yes okay all ATP ASE's the enzymes
+ 
+
+ align:start position:0%
+any yes okay all ATP ASE's the enzymes
+in a Cell it's going to have some role
+
+ align:start position:0%
+in a Cell it's going to have some role
+ 
+
+ align:start position:0%
+in a Cell it's going to have some role
+in a cellular activity right so maybe
+
+ align:start position:0%
+in a cellular activity right so maybe
+ 
+
+ align:start position:0%
+in a cellular activity right so maybe
+this name isn't very helpful but what's
+
+ align:start position:0%
+this name isn't very helpful but what's
+ 
+
+ align:start position:0%
+this name isn't very helpful but what's
+common about all of these is that they
+
+ align:start position:0%
+common about all of these is that they
+ 
+
+ align:start position:0%
+common about all of these is that they
+share this common structural motif they
+
+ align:start position:0%
+share this common structural motif they
+ 
+
+ align:start position:0%
+share this common structural motif they
+form these hexamers but within that
+
+ align:start position:0%
+form these hexamers but within that
+ 
+
+ align:start position:0%
+form these hexamers but within that
+there's quite a bit of diversity because
+
+ align:start position:0%
+there's quite a bit of diversity because
+ 
+
+ align:start position:0%
+there's quite a bit of diversity because
+they have all these different functions
+
+ align:start position:0%
+they have all these different functions
+ 
+
+ align:start position:0%
+they have all these different functions
+so we can just see that here to some
+
+ align:start position:0%
+so we can just see that here to some
+ 
+
+ align:start position:0%
+so we can just see that here to some
+degree so he and there's a typo which
+
+ align:start position:0%
+degree so he and there's a typo which
+ 
+
+ align:start position:0%
+degree so he and there's a typo which
+I'll fix before posting but if we take a
+
+ align:start position:0%
+I'll fix before posting but if we take a
+ 
+
+ align:start position:0%
+I'll fix before posting but if we take a
+look just at two examples here of
+
+ align:start position:0%
+look just at two examples here of
+ 
+
+ align:start position:0%
+look just at two examples here of
+different hexameric rings so these are
+
+ align:start position:0%
+different hexameric rings so these are
+ 
+
+ align:start position:0%
+different hexameric rings so these are
+two different Triple A plus ATP ASE's
+
+ align:start position:0%
+two different Triple A plus ATP ASE's
+ 
+
+ align:start position:0%
+two different Triple A plus ATP ASE's
+what do we see so in common they're both
+
+ align:start position:0%
+what do we see so in common they're both
+ 
+
+ align:start position:0%
+what do we see so in common they're both
+hexamers in common they both have an
+
+ align:start position:0%
+hexamers in common they both have an
+ 
+
+ align:start position:0%
+hexamers in common they both have an
+axial pore here but we see different
+
+ align:start position:0%
+axial pore here but we see different
+ 
+
+ align:start position:0%
+axial pore here but we see different
+elements of secondary structure and
+
+ align:start position:0%
+elements of secondary structure and
+ 
+
+ align:start position:0%
+elements of secondary structure and
+granted these are both depicted in a bit
+
+ align:start position:0%
+granted these are both depicted in a bit
+ 
+
+ align:start position:0%
+granted these are both depicted in a bit
+of a different way but if we look here I
+
+ align:start position:0%
+of a different way but if we look here I
+ 
+
+ align:start position:0%
+of a different way but if we look here I
+mean look we have these alpha helical
+
+ align:start position:0%
+mean look we have these alpha helical
+ 
+
+ align:start position:0%
+mean look we have these alpha helical
+regions around the exterior that we
+
+ align:start position:0%
+regions around the exterior that we
+ 
+
+ align:start position:0%
+regions around the exterior that we
+don't see here okay
+
+ align:start position:0%
+don't see here okay
+ 
+
+ align:start position:0%
+don't see here okay
+and in this view I show this particular
+
+ align:start position:0%
+and in this view I show this particular
+ 
+
+ align:start position:0%
+and in this view I show this particular
+one because it's depicted where the ATP
+
+ align:start position:0%
+one because it's depicted where the ATP
+ 
+
+ align:start position:0%
+one because it's depicted where the ATP
+is binding so you can see the ATP
+
+ align:start position:0%
+is binding so you can see the ATP
+ 
+
+ align:start position:0%
+is binding so you can see the ATP
+binding to each subunit here so I've
+
+ align:start position:0%
+binding to each subunit here so I've
+ 
+
+ align:start position:0%
+binding to each subunit here so I've
+shown six ATP's bound so the structural
+
+ align:start position:0%
+shown six ATP's bound so the structural
+ 
+
+ align:start position:0%
+shown six ATP's bound so the structural
+diversity is quite tremendous and here's
+
+ align:start position:0%
+diversity is quite tremendous and here's
+ 
+
+ align:start position:0%
+diversity is quite tremendous and here's
+just another
+
+ align:start position:0%
+just another
+ 
+
+ align:start position:0%
+just another
+example so these are three different
+
+ align:start position:0%
+example so these are three different
+ 
+
+ align:start position:0%
+example so these are three different
+Triple A plus ATP ASE's of the clip
+
+ align:start position:0%
+Triple A plus ATP ASE's of the clip
+ 
+
+ align:start position:0%
+Triple A plus ATP ASE's of the clip
+system so we're going to focus on clip X
+
+ align:start position:0%
+system so we're going to focus on clip X
+ 
+
+ align:start position:0%
+system so we're going to focus on clip X
+but it's not the only one and so what
+
+ align:start position:0%
+but it's not the only one and so what
+ 
+
+ align:start position:0%
+but it's not the only one and so what
+we're looking at here is clip X we have
+
+ align:start position:0%
+we're looking at here is clip X we have
+ 
+
+ align:start position:0%
+we're looking at here is clip X we have
+another family member clip a I'm here
+
+ align:start position:0%
+another family member clip a I'm here
+ 
+
+ align:start position:0%
+another family member clip a I'm here
+clip B okay and so what we see is
+
+ align:start position:0%
+clip B okay and so what we see is
+ 
+
+ align:start position:0%
+clip B okay and so what we see is
+subunit 2 subunit whether it's XA or B
+
+ align:start position:0%
+subunit 2 subunit whether it's XA or B
+ 
+
+ align:start position:0%
+subunit 2 subunit whether it's XA or B
+there's quite a bit of difference right
+
+ align:start position:0%
+there's quite a bit of difference right
+ 
+
+ align:start position:0%
+there's quite a bit of difference right
+so clip X is the most simple in terms of
+
+ align:start position:0%
+so clip X is the most simple in terms of
+ 
+
+ align:start position:0%
+so clip X is the most simple in terms of
+the architecture here for that and so
+
+ align:start position:0%
+the architecture here for that and so
+ 
+
+ align:start position:0%
+the architecture here for that and so
+one thing people think about is in terms
+
+ align:start position:0%
+one thing people think about is in terms
+ 
+
+ align:start position:0%
+one thing people think about is in terms
+of the different activities that have
+
+ align:start position:0%
+of the different activities that have
+ 
+
+ align:start position:0%
+of the different activities that have
+been associated with these different
+
+ align:start position:0%
+been associated with these different
+ 
+
+ align:start position:0%
+been associated with these different
+family members how is it that these
+
+ align:start position:0%
+family members how is it that these
+ 
+
+ align:start position:0%
+family members how is it that these
+different structural features play a
+
+ align:start position:0%
+different structural features play a
+ 
+
+ align:start position:0%
+different structural features play a
+role ok so coming back to clip X and the
+
+ align:start position:0%
+role ok so coming back to clip X and the
+ 
+
+ align:start position:0%
+role ok so coming back to clip X and the
+depiction we saw before right
+
+ align:start position:0%
+depiction we saw before right
+ 
+
+ align:start position:0%
+depiction we saw before right
+clip X is an unfolding and what's really
+
+ align:start position:0%
+clip X is an unfolding and what's really
+ 
+
+ align:start position:0%
+clip X is an unfolding and what's really
+a key point here is that ATP hydrolysis
+
+ align:start position:0%
+a key point here is that ATP hydrolysis
+ 
+
+ align:start position:0%
+a key point here is that ATP hydrolysis
+by clip X is going to power
+
+ align:start position:0%
+by clip X is going to power
+ 
+
+ align:start position:0%
+by clip X is going to power
+conformational changes that allow for
+
+ align:start position:0%
+conformational changes that allow for
+ 
+
+ align:start position:0%
+conformational changes that allow for
+mechanical unfolding of this protein
+
+ align:start position:0%
+mechanical unfolding of this protein
+ 
+
+ align:start position:0%
+mechanical unfolding of this protein
+that's condemned for degradation by clip
+
+ align:start position:0%
+that's condemned for degradation by clip
+ 
+
+ align:start position:0%
+that's condemned for degradation by clip
+P okay and that's what's going to also
+
+ align:start position:0%
+P okay and that's what's going to also
+ 
+
+ align:start position:0%
+P okay and that's what's going to also
+allow for translocation of the resulting
+
+ align:start position:0%
+allow for translocation of the resulting
+ 
+
+ align:start position:0%
+allow for translocation of the resulting
+unfolded protein into the degradation
+
+ align:start position:0%
+unfolded protein into the degradation
+ 
+
+ align:start position:0%
+unfolded protein into the degradation
+chamber so the action of clip X is
+
+ align:start position:0%
+chamber so the action of clip X is
+ 
+
+ align:start position:0%
+chamber so the action of clip X is
+allowing that protein to fit through
+
+ align:start position:0%
+allowing that protein to fit through
+ 
+
+ align:start position:0%
+allowing that protein to fit through
+this axial pore and be threaded into the
+
+ align:start position:0%
+this axial pore and be threaded into the
+ 
+
+ align:start position:0%
+this axial pore and be threaded into the
+chamber here so with that what are the
+
+ align:start position:0%
+chamber here so with that what are the
+ 
+
+ align:start position:0%
+chamber here so with that what are the
+questions we need to address and
+
+ align:start position:0%
+questions we need to address and
+ 
+
+ align:start position:0%
+questions we need to address and
+thinking about how this macro mulish
+
+ align:start position:0%
+thinking about how this macro mulish
+ 
+
+ align:start position:0%
+thinking about how this macro mulish
+molecular machine works one how our
+
+ align:start position:0%
+molecular machine works one how our
+ 
+
+ align:start position:0%
+molecular machine works one how our
+substrates recognized right so there's
+
+ align:start position:0%
+substrates recognized right so there's
+ 
+
+ align:start position:0%
+substrates recognized right so there's
+some certain group of proteins that are
+
+ align:start position:0%
+some certain group of proteins that are
+ 
+
+ align:start position:0%
+some certain group of proteins that are
+going to be degraded by this machinery
+
+ align:start position:0%
+going to be degraded by this machinery
+ 
+
+ align:start position:0%
+going to be degraded by this machinery
+what is the mechanism how is it that
+
+ align:start position:0%
+what is the mechanism how is it that
+ 
+
+ align:start position:0%
+what is the mechanism how is it that
+atp-dependent conformational changes of
+
+ align:start position:0%
+atp-dependent conformational changes of
+ 
+
+ align:start position:0%
+atp-dependent conformational changes of
+clip XP drive unfolding and
+
+ align:start position:0%
+clip XP drive unfolding and
+ 
+
+ align:start position:0%
+clip XP drive unfolding and
+translocation and what is the substrate
+
+ align:start position:0%
+translocation and what is the substrate
+ 
+
+ align:start position:0%
+translocation and what is the substrate
+selectivity so that's where we're going
+
+ align:start position:0%
+selectivity so that's where we're going
+ 
+
+ align:start position:0%
+selectivity so that's where we're going
+to move forward with and so the first
+
+ align:start position:0%
+to move forward with and so the first
+ 
+
+ align:start position:0%
+to move forward with and so the first
+question we need to ask is how are the
+
+ align:start position:0%
+question we need to ask is how are the
+ 
+
+ align:start position:0%
+question we need to ask is how are the
+substrates recognized by clip X
+
+ align:start position:0%
+substrates recognized by clip X
+ 
+
+ align:start position:0%
+substrates recognized by clip X
+okay okay and so what are possibilities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+first what we'll consider is a
+
+ align:start position:0%
+first what we'll consider is a
+ 
+
+ align:start position:0%
+first what we'll consider is a
+degradation tag okay so when I draw
+
+ align:start position:0%
+degradation tag okay so when I draw
+ 
+
+ align:start position:0%
+degradation tag okay so when I draw
+these cartoons I'm only going to show
+
+ align:start position:0%
+these cartoons I'm only going to show
+ 
+
+ align:start position:0%
+these cartoons I'm only going to show
+one of the two rings for clip P it's not
+
+ align:start position:0%
+one of the two rings for clip P it's not
+ 
+
+ align:start position:0%
+one of the two rings for clip P it's not
+that it's only one this is just for
+
+ align:start position:0%
+that it's only one this is just for
+ 
+
+ align:start position:0%
+that it's only one this is just for
+simplicity but imagine that here we have
+
+ align:start position:0%
+simplicity but imagine that here we have
+ 
+
+ align:start position:0%
+simplicity but imagine that here we have
+X here we have P okay and we have some
+
+ align:start position:0%
+X here we have P okay and we have some
+ 
+
+ align:start position:0%
+X here we have P okay and we have some
+condemned protein which I'll just draw
+
+ align:start position:0%
+condemned protein which I'll just draw
+ 
+
+ align:start position:0%
+condemned protein which I'll just draw
+as a circle so the cell no longer wants
+
+ align:start position:0%
+as a circle so the cell no longer wants
+ 
+
+ align:start position:0%
+as a circle so the cell no longer wants
+this protein it needs to go away okay
+
+ align:start position:0%
+this protein it needs to go away okay
+ 
+
+ align:start position:0%
+this protein it needs to go away okay
+and we can imagine as one possibility is
+
+ align:start position:0%
+and we can imagine as one possibility is
+ 
+
+ align:start position:0%
+and we can imagine as one possibility is
+that a degradation tag can be attached
+
+ align:start position:0%
+that a degradation tag can be attached
+ 
+
+ align:start position:0%
+that a degradation tag can be attached
+to this polypeptide okay and what we
+
+ align:start position:0%
+to this polypeptide okay and what we
+ 
+
+ align:start position:0%
+to this polypeptide okay and what we
+find is that there's a particular tag
+
+ align:start position:0%
+find is that there's a particular tag
+ 
+
+ align:start position:0%
+find is that there's a particular tag
+called SSR a tag that is used to tag
+
+ align:start position:0%
+called SSR a tag that is used to tag
+ 
+
+ align:start position:0%
+called SSR a tag that is used to tag
+proteins for degradation by clip XP so
+
+ align:start position:0%
+proteins for degradation by clip XP so
+ 
+
+ align:start position:0%
+proteins for degradation by clip XP so
+we can think of this tag as a zip code
+
+ align:start position:0%
+we can think of this tag as a zip code
+ 
+
+ align:start position:0%
+we can think of this tag as a zip code
+if a polypeptide gets modified such that
+
+ align:start position:0%
+if a polypeptide gets modified such that
+ 
+
+ align:start position:0%
+if a polypeptide gets modified such that
+this tag is appended it's going to end
+
+ align:start position:0%
+this tag is appended it's going to end
+ 
+
+ align:start position:0%
+this tag is appended it's going to end
+up going to this degradation machine
+
+ align:start position:0%
+up going to this degradation machine
+ 
+
+ align:start position:0%
+up going to this degradation machine
+such that it gets degraded
+
+ align:start position:0%
+such that it gets degraded
+ 
+
+ align:start position:0%
+such that it gets degraded
+okay the tag is 11 amino acids it's
+
+ align:start position:0%
+okay the tag is 11 amino acids it's
+ 
+
+ align:start position:0%
+okay the tag is 11 amino acids it's
+attached to the C terminus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the sequence is a a and d e and
+
+ align:start position:0%
+okay and the sequence is a a and d e and
+ 
+
+ align:start position:0%
+okay and the sequence is a a and d e and
+why a ll laa okay and so what happens in
+
+ align:start position:0%
+why a ll laa okay and so what happens in
+ 
+
+ align:start position:0%
+why a ll laa okay and so what happens in
+this case as shown
+
+ align:start position:0%
+this case as shown
+ 
+
+ align:start position:0%
+this case as shown
+okay we can imagine that this tag binds
+
+ align:start position:0%
+okay we can imagine that this tag binds
+ 
+
+ align:start position:0%
+okay we can imagine that this tag binds
+to the poor of clip X directly and the
+
+ align:start position:0%
+to the poor of clip X directly and the
+ 
+
+ align:start position:0%
+to the poor of clip X directly and the
+tag when binding enables translocation
+
+ align:start position:0%
+tag when binding enables translocation
+ 
+
+ align:start position:0%
+tag when binding enables translocation
+so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this poor has what are termed
+
+ align:start position:0%
+okay and this poor has what are termed
+ 
+
+ align:start position:0%
+okay and this poor has what are termed
+poor loops that are involved in tag
+
+ align:start position:0%
+poor loops that are involved in tag
+ 
+
+ align:start position:0%
+poor loops that are involved in tag
+binding and in particular there's a
+
+ align:start position:0%
+binding and in particular there's a
+ 
+
+ align:start position:0%
+binding and in particular there's a
+region G Y Z G so for amino acid
+
+ align:start position:0%
+region G Y Z G so for amino acid
+ 
+
+ align:start position:0%
+region G Y Z G so for amino acid
+sequence that is thought to grip and
+
+ align:start position:0%
+sequence that is thought to grip and
+ 
+
+ align:start position:0%
+sequence that is thought to grip and
+drag the substrate okay here and of
+
+ align:start position:0%
+drag the substrate okay here and of
+ 
+
+ align:start position:0%
+drag the substrate okay here and of
+course it's not gripping like we would
+
+ align:start position:0%
+course it's not gripping like we would
+ 
+
+ align:start position:0%
+course it's not gripping like we would
+but there's some interaction there
+
+ align:start position:0%
+but there's some interaction there
+ 
+
+ align:start position:0%
+but there's some interaction there
+happening that allows that to occur so
+
+ align:start position:0%
+happening that allows that to occur so
+ 
+
+ align:start position:0%
+happening that allows that to occur so
+you'll see there's a lot of kind of
+
+ align:start position:0%
+you'll see there's a lot of kind of
+ 
+
+ align:start position:0%
+you'll see there's a lot of kind of
+mechanical type cartoons and language
+
+ align:start position:0%
+mechanical type cartoons and language
+ 
+
+ align:start position:0%
+mechanical type cartoons and language
+used in describing these machines okay
+
+ align:start position:0%
+used in describing these machines okay
+ 
+
+ align:start position:0%
+used in describing these machines okay
+so what is another possibility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so another possibility for how an
+
+ align:start position:0%
+okay so another possibility for how an
+ 
+
+ align:start position:0%
+okay so another possibility for how an
+ATPase could interact with a degradation
+
+ align:start position:0%
+ATPase could interact with a degradation
+ 
+
+ align:start position:0%
+ATPase could interact with a degradation
+chamber is that the protein substrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+binds to an extra domain okay
+
+ align:start position:0%
+binds to an extra domain okay
+ 
+
+ align:start position:0%
+binds to an extra domain okay
+attached to the ATPase okay and I point
+
+ align:start position:0%
+attached to the ATPase okay and I point
+ 
+
+ align:start position:0%
+attached to the ATPase okay and I point
+out this possibility is not for clip X
+
+ align:start position:0%
+out this possibility is not for clip X
+ 
+
+ align:start position:0%
+out this possibility is not for clip X
+but it's one to be aware of because it
+
+ align:start position:0%
+but it's one to be aware of because it
+ 
+
+ align:start position:0%
+but it's one to be aware of because it
+can occur okay we saw some of those
+
+ align:start position:0%
+can occur okay we saw some of those
+ 
+
+ align:start position:0%
+can occur okay we saw some of those
+other ATP ASE's are quite complicated so
+
+ align:start position:0%
+other ATP ASE's are quite complicated so
+ 
+
+ align:start position:0%
+other ATP ASE's are quite complicated so
+in this case imagine we have an 80-hour
+
+ align:start position:0%
+in this case imagine we have an 80-hour
+ 
+
+ align:start position:0%
+in this case imagine we have an 80-hour
+ATPase we have the degradation chamber
+
+ align:start position:0%
+ATPase we have the degradation chamber
+ 
+
+ align:start position:0%
+ATPase we have the degradation chamber
+and this ATP a has some extra domain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that effectively can bind the
+
+ align:start position:0%
+okay that effectively can bind the
+ 
+
+ align:start position:0%
+okay that effectively can bind the
+condemned protein and help deliver it to
+
+ align:start position:0%
+condemned protein and help deliver it to
+ 
+
+ align:start position:0%
+condemned protein and help deliver it to
+the poor here and just as a third
+
+ align:start position:0%
+the poor here and just as a third
+ 
+
+ align:start position:0%
+the poor here and just as a third
+possibility and something that we'll see
+
+ align:start position:0%
+possibility and something that we'll see
+ 
+
+ align:start position:0%
+possibility and something that we'll see
+moving forward is that there's
+
+ align:start position:0%
+moving forward is that there's
+ 
+
+ align:start position:0%
+moving forward is that there's
+involvement of an adapter protein so in
+
+ align:start position:0%
+involvement of an adapter protein so in
+ 
+
+ align:start position:0%
+involvement of an adapter protein so in
+addition to the ATPase and the
+
+ align:start position:0%
+addition to the ATPase and the
+ 
+
+ align:start position:0%
+addition to the ATPase and the
+degradation chamber there's an adapter
+
+ align:start position:0%
+degradation chamber there's an adapter
+ 
+
+ align:start position:0%
+degradation chamber there's an adapter
+protein that comes into play so in this
+
+ align:start position:0%
+protein that comes into play so in this
+ 
+
+ align:start position:0%
+protein that comes into play so in this
+case the protein
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay adapter okay and this protein helps
+
+ align:start position:0%
+okay adapter okay and this protein helps
+ 
+
+ align:start position:0%
+okay adapter okay and this protein helps
+direct it to the poor so they condemned
+
+ align:start position:0%
+direct it to the poor so they condemned
+ 
+
+ align:start position:0%
+direct it to the poor so they condemned
+protein to the ATPase okay so for
+
+ align:start position:0%
+protein to the ATPase okay so for
+ 
+
+ align:start position:0%
+protein to the ATPase okay so for
+instance here we have the ATPase here we
+
+ align:start position:0%
+instance here we have the ATPase here we
+ 
+
+ align:start position:0%
+instance here we have the ATPase here we
+have the degradation chamber okay and
+
+ align:start position:0%
+have the degradation chamber okay and
+ 
+
+ align:start position:0%
+have the degradation chamber okay and
+maybe there's some additional protein
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that facilitates getting the
+
+ align:start position:0%
+okay that facilitates getting the
+ 
+
+ align:start position:0%
+okay that facilitates getting the
+condemned protein to the ATPase and so
+
+ align:start position:0%
+condemned protein to the ATPase and so
+ 
+
+ align:start position:0%
+condemned protein to the ATPase and so
+something to keep in mind and what we'll
+
+ align:start position:0%
+something to keep in mind and what we'll
+ 
+
+ align:start position:0%
+something to keep in mind and what we'll
+see with clip XP is that one and three
+
+ align:start position:0%
+see with clip XP is that one and three
+ 
+
+ align:start position:0%
+see with clip XP is that one and three
+are not mutually exclusive okay and
+
+ align:start position:0%
+are not mutually exclusive okay and
+ 
+
+ align:start position:0%
+are not mutually exclusive okay and
+there's an adapter protein named SSP B
+
+ align:start position:0%
+there's an adapter protein named SSP B
+ 
+
+ align:start position:0%
+there's an adapter protein named SSP B
+that can help deliver SSR a tagged
+
+ align:start position:0%
+that can help deliver SSR a tagged
+ 
+
+ align:start position:0%
+that can help deliver SSR a tagged
+polypeptides or proteins to the
+
+ align:start position:0%
+polypeptides or proteins to the
+ 
+
+ align:start position:0%
+polypeptides or proteins to the
+degradation chamber here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're gonna think about these SSRI
+
+ align:start position:0%
+so we're gonna think about these SSRI
+ 
+
+ align:start position:0%
+so we're gonna think about these SSRI
+tags quite a bit and something else to
+
+ align:start position:0%
+tags quite a bit and something else to
+ 
+
+ align:start position:0%
+tags quite a bit and something else to
+be aware of is just that these SSRI tags
+
+ align:start position:0%
+be aware of is just that these SSRI tags
+ 
+
+ align:start position:0%
+be aware of is just that these SSRI tags
+are not the only ways of tagging
+
+ align:start position:0%
+are not the only ways of tagging
+ 
+
+ align:start position:0%
+are not the only ways of tagging
+proteins for degradation we're not going
+
+ align:start position:0%
+proteins for degradation we're not going
+ 
+
+ align:start position:0%
+proteins for degradation we're not going
+to talk about it in detail in this
+
+ align:start position:0%
+to talk about it in detail in this
+ 
+
+ align:start position:0%
+to talk about it in detail in this
+course but you should be aware of
+
+ align:start position:0%
+course but you should be aware of
+ 
+
+ align:start position:0%
+course but you should be aware of
+something called the N + rule and this
+
+ align:start position:0%
+something called the N + rule and this
+ 
+
+ align:start position:0%
+something called the N + rule and this
+is really cool so this rule basically
+
+ align:start position:0%
+is really cool so this rule basically
+ 
+
+ align:start position:0%
+is really cool so this rule basically
+states that a half-life of the protein
+
+ align:start position:0%
+states that a half-life of the protein
+ 
+
+ align:start position:0%
+states that a half-life of the protein
+is determined by its n terminal residue
+
+ align:start position:0%
+is determined by its n terminal residue
+ 
+
+ align:start position:0%
+is determined by its n terminal residue
+here and this can be called an undergrad
+
+ align:start position:0%
+here and this can be called an undergrad
+ 
+
+ align:start position:0%
+here and this can be called an undergrad
+and these and a grants are recognized by
+
+ align:start position:0%
+and these and a grants are recognized by
+ 
+
+ align:start position:0%
+and these and a grants are recognized by
+proteins such as clip s and E coli and
+
+ align:start position:0%
+proteins such as clip s and E coli and
+ 
+
+ align:start position:0%
+proteins such as clip s and E coli and
+as a result these proteins can get
+
+ align:start position:0%
+as a result these proteins can get
+ 
+
+ align:start position:0%
+as a result these proteins can get
+delivered to degradation machines so for
+
+ align:start position:0%
+delivered to degradation machines so for
+ 
+
+ align:start position:0%
+delivered to degradation machines so for
+instance they're in addition to clip XP
+
+ align:start position:0%
+instance they're in addition to clip XP
+ 
+
+ align:start position:0%
+instance they're in addition to clip XP
+there's an ATPase clip a that can
+
+ align:start position:0%
+there's an ATPase clip a that can
+ 
+
+ align:start position:0%
+there's an ATPase clip a that can
+associate with clip P and be involved in
+
+ align:start position:0%
+associate with clip P and be involved in
+ 
+
+ align:start position:0%
+associate with clip P and be involved in
+degradation of polypeptides via this and
+
+ align:start position:0%
+degradation of polypeptides via this and
+ 
+
+ align:start position:0%
+degradation of polypeptides via this and
+end rule ok and in terms of the rule
+
+ align:start position:0%
+end rule ok and in terms of the rule
+ 
+
+ align:start position:0%
+end rule ok and in terms of the rule
+depending on the identity of this end
+
+ align:start position:0%
+depending on the identity of this end
+ 
+
+ align:start position:0%
+depending on the identity of this end
+terminal amino acid it may be
+
+ align:start position:0%
+terminal amino acid it may be
+ 
+
+ align:start position:0%
+terminal amino acid it may be
+stabilizing or destabilizing in terms of
+
+ align:start position:0%
+stabilizing or destabilizing in terms of
+ 
+
+ align:start position:0%
+stabilizing or destabilizing in terms of
+protein lifetime if you're curious to
+
+ align:start position:0%
+protein lifetime if you're curious to
+ 
+
+ align:start position:0%
+protein lifetime if you're curious to
+know more about that we can refer you to
+
+ align:start position:0%
+know more about that we can refer you to
+ 
+
+ align:start position:0%
+know more about that we can refer you to
+some literature so here we have a
+
+ align:start position:0%
+some literature so here we have a
+ 
+
+ align:start position:0%
+some literature so here we have a
+cartoon looking at a native protein
+
+ align:start position:0%
+cartoon looking at a native protein
+ 
+
+ align:start position:0%
+cartoon looking at a native protein
+substrate that needs to be degraded it's
+
+ align:start position:0%
+substrate that needs to be degraded it's
+ 
+
+ align:start position:0%
+substrate that needs to be degraded it's
+been modified with a tag we have clip X
+
+ align:start position:0%
+been modified with a tag we have clip X
+ 
+
+ align:start position:0%
+been modified with a tag we have clip X
+here we have clip P okay here's the tag
+
+ align:start position:0%
+here we have clip P okay here's the tag
+ 
+
+ align:start position:0%
+here we have clip P okay here's the tag
+and in addition we can have this adapter
+
+ align:start position:0%
+and in addition we can have this adapter
+ 
+
+ align:start position:0%
+and in addition we can have this adapter
+protein s s P P and the adapter clip s
+
+ align:start position:0%
+protein s s P P and the adapter clip s
+ 
+
+ align:start position:0%
+protein s s P P and the adapter clip s
+so let's think about this tag for a
+
+ align:start position:0%
+so let's think about this tag for a
+ 
+
+ align:start position:0%
+so let's think about this tag for a
+minute and we need to think about this
+
+ align:start position:0%
+minute and we need to think about this
+ 
+
+ align:start position:0%
+minute and we need to think about this
+tag from the standpoint one of in vitro
+
+ align:start position:0%
+tag from the standpoint one of in vitro
+ 
+
+ align:start position:0%
+tag from the standpoint one of in vitro
+experiments because we're going to begin
+
+ align:start position:0%
+experiments because we're going to begin
+ 
+
+ align:start position:0%
+experiments because we're going to begin
+to look at some experiments that were
+
+ align:start position:0%
+to look at some experiments that were
+ 
+
+ align:start position:0%
+to look at some experiments that were
+done to understand how this machine
+
+ align:start position:0%
+done to understand how this machine
+ 
+
+ align:start position:0%
+done to understand how this machine
+works and we also need to think about
+
+ align:start position:0%
+works and we also need to think about
+ 
+
+ align:start position:0%
+works and we also need to think about
+this tag from the standpoint of the cell
+
+ align:start position:0%
+this tag from the standpoint of the cell
+ 
+
+ align:start position:0%
+this tag from the standpoint of the cell
+so if we think about an in vitro
+
+ align:start position:0%
+so if we think about an in vitro
+ 
+
+ align:start position:0%
+so if we think about an in vitro
+experiment where we want to study how
+
+ align:start position:0%
+experiment where we want to study how
+ 
+
+ align:start position:0%
+experiment where we want to study how
+clip XP
+
+ align:start position:0%
+clip XP
+ 
+
+ align:start position:0%
+clip XP
+degrades some protein substrate right we
+
+ align:start position:0%
+degrades some protein substrate right we
+ 
+
+ align:start position:0%
+degrades some protein substrate right we
+can use this SSRI tank and it's quite
+
+ align:start position:0%
+can use this SSRI tank and it's quite
+ 
+
+ align:start position:0%
+can use this SSRI tank and it's quite
+easy to attach 11 amino acids to some
+
+ align:start position:0%
+easy to attach 11 amino acids to some
+ 
+
+ align:start position:0%
+easy to attach 11 amino acids to some
+protein or polypeptide at the c-terminus
+
+ align:start position:0%
+protein or polypeptide at the c-terminus
+ 
+
+ align:start position:0%
+protein or polypeptide at the c-terminus
+right we can do that by protein
+
+ align:start position:0%
+right we can do that by protein
+ 
+
+ align:start position:0%
+right we can do that by protein
+expression we can do that by chemical
+
+ align:start position:0%
+expression we can do that by chemical
+ 
+
+ align:start position:0%
+expression we can do that by chemical
+synthesis here and so we're going to
+
+ align:start position:0%
+synthesis here and so we're going to
+ 
+
+ align:start position:0%
+synthesis here and so we're going to
+look at a number of experiments where
+
+ align:start position:0%
+look at a number of experiments where
+ 
+
+ align:start position:0%
+look at a number of experiments where
+this SSR a tag has been appended to
+
+ align:start position:0%
+this SSR a tag has been appended to
+ 
+
+ align:start position:0%
+this SSR a tag has been appended to
+certain model substrates moving forward
+
+ align:start position:0%
+certain model substrates moving forward
+ 
+
+ align:start position:0%
+certain model substrates moving forward
+so what about in the cell so when is
+
+ align:start position:0%
+so what about in the cell so when is
+ 
+
+ align:start position:0%
+so what about in the cell so when is
+this SSR a tag attached to a protein so
+
+ align:start position:0%
+this SSR a tag attached to a protein so
+ 
+
+ align:start position:0%
+this SSR a tag attached to a protein so
+are all proteins that need to be
+
+ align:start position:0%
+are all proteins that need to be
+ 
+
+ align:start position:0%
+are all proteins that need to be
+degraded destined to clip XP just
+
+ align:start position:0%
+degraded destined to clip XP just
+ 
+
+ align:start position:0%
+degraded destined to clip XP just
+intuitively what do you think yes you
+
+ align:start position:0%
+intuitively what do you think yes you
+ 
+
+ align:start position:0%
+intuitively what do you think yes you
+shaking heads no right there's many many
+
+ align:start position:0%
+shaking heads no right there's many many
+ 
+
+ align:start position:0%
+shaking heads no right there's many many
+proteases around so what proteins are
+
+ align:start position:0%
+proteases around so what proteins are
+ 
+
+ align:start position:0%
+proteases around so what proteins are
+destined for degradation by clip XP
+
+ align:start position:0%
+destined for degradation by clip XP
+ 
+
+ align:start position:0%
+destined for degradation by clip XP
+that's what we're going to look at and
+
+ align:start position:0%
+that's what we're going to look at and
+ 
+
+ align:start position:0%
+that's what we're going to look at and
+how this tag is appended and so
+
+ align:start position:0%
+how this tag is appended and so
+ 
+
+ align:start position:0%
+how this tag is appended and so
+effectively this SSR a tag say an e.coli
+
+ align:start position:0%
+effectively this SSR a tag say an e.coli
+ 
+
+ align:start position:0%
+effectively this SSR a tag say an e.coli
+is used 1 because protein degradation
+
+ align:start position:0%
+is used 1 because protein degradation
+ 
+
+ align:start position:0%
+is used 1 because protein degradation
+needs to be tightly regulated but 2 it's
+
+ align:start position:0%
+needs to be tightly regulated but 2 it's
+ 
+
+ align:start position:0%
+needs to be tightly regulated but 2 it's
+used for dealing with proteins that it
+
+ align:start position:0%
+used for dealing with proteins that it
+ 
+
+ align:start position:0%
+used for dealing with proteins that it
+exhibited stalled translation so this
+
+ align:start position:0%
+exhibited stalled translation so this
+ 
+
+ align:start position:0%
+exhibited stalled translation so this
+discussion is going to bring us back to
+
+ align:start position:0%
+discussion is going to bring us back to
+ 
+
+ align:start position:0%
+discussion is going to bring us back to
+the ribosome here so we want to ask what
+
+ align:start position:0%
+the ribosome here so we want to ask what
+ 
+
+ align:start position:0%
+the ribosome here so we want to ask what
+proteins in the cell are tagged by with
+
+ align:start position:0%
+proteins in the cell are tagged by with
+ 
+
+ align:start position:0%
+proteins in the cell are tagged by with
+SS RA how is the tag attached to the
+
+ align:start position:0%
+SS RA how is the tag attached to the
+ 
+
+ align:start position:0%
+SS RA how is the tag attached to the
+chem protein as well here this is just a
+
+ align:start position:0%
+chem protein as well here this is just a
+ 
+
+ align:start position:0%
+chem protein as well here this is just a
+cartoon showing an adapter protein
+
+ align:start position:0%
+cartoon showing an adapter protein
+ 
+
+ align:start position:0%
+cartoon showing an adapter protein
+helping direct this tag to the substrate
+
+ align:start position:0%
+helping direct this tag to the substrate
+ 
+
+ align:start position:0%
+helping direct this tag to the substrate
+here so we're gonna just move forward to
+
+ align:start position:0%
+here so we're gonna just move forward to
+ 
+
+ align:start position:0%
+here so we're gonna just move forward to
+this slide this tag is specifically
+
+ align:start position:0%
+this slide this tag is specifically
+ 
+
+ align:start position:0%
+this slide this tag is specifically
+added to proteins that are experiencing
+
+ align:start position:0%
+added to proteins that are experiencing
+ 
+
+ align:start position:0%
+added to proteins that are experiencing
+stalled translation so it's estimated
+
+ align:start position:0%
+stalled translation so it's estimated
+ 
+
+ align:start position:0%
+stalled translation so it's estimated
+that on
+
+ align:start position:0%
+that on
+ 
+
+ align:start position:0%
+that on
+order of 0.5% of e.coli translations
+
+ align:start position:0%
+order of 0.5% of e.coli translations
+ 
+
+ align:start position:0%
+order of 0.5% of e.coli translations
+result in SSR a tagging and so this is
+
+ align:start position:0%
+result in SSR a tagging and so this is
+ 
+
+ align:start position:0%
+result in SSR a tagging and so this is
+thought to be one largely of quality
+
+ align:start position:0%
+thought to be one largely of quality
+ 
+
+ align:start position:0%
+thought to be one largely of quality
+control right so you can imagine if the
+
+ align:start position:0%
+control right so you can imagine if the
+ 
+
+ align:start position:0%
+control right so you can imagine if the
+ribosomes stalled there could be buildup
+
+ align:start position:0%
+ribosomes stalled there could be buildup
+ 
+
+ align:start position:0%
+ribosomes stalled there could be buildup
+of polypeptide products that aren't
+
+ align:start position:0%
+of polypeptide products that aren't
+ 
+
+ align:start position:0%
+of polypeptide products that aren't
+wanted and the translation machinery
+
+ align:start position:0%
+wanted and the translation machinery
+ 
+
+ align:start position:0%
+wanted and the translation machinery
+could get blocked and we don't really
+
+ align:start position:0%
+could get blocked and we don't really
+ 
+
+ align:start position:0%
+could get blocked and we don't really
+want that to happen here so here's our
+
+ align:start position:0%
+want that to happen here so here's our
+ 
+
+ align:start position:0%
+want that to happen here so here's our
+friend the ribosome and here's looking
+
+ align:start position:0%
+friend the ribosome and here's looking
+ 
+
+ align:start position:0%
+friend the ribosome and here's looking
+at the 50s ribosomal subunit and we have
+
+ align:start position:0%
+at the 50s ribosomal subunit and we have
+ 
+
+ align:start position:0%
+at the 50s ribosomal subunit and we have
+a polypeptide emerging from that exit
+
+ align:start position:0%
+a polypeptide emerging from that exit
+ 
+
+ align:start position:0%
+a polypeptide emerging from that exit
+tunnel so these should all be familiar
+
+ align:start position:0%
+tunnel so these should all be familiar
+ 
+
+ align:start position:0%
+tunnel so these should all be familiar
+at this stage and so what happens when
+
+ align:start position:0%
+at this stage and so what happens when
+ 
+
+ align:start position:0%
+at this stage and so what happens when
+this ribosome is trying to synthesize a
+
+ align:start position:0%
+this ribosome is trying to synthesize a
+ 
+
+ align:start position:0%
+this ribosome is trying to synthesize a
+polypeptide and it just gets stuck so
+
+ align:start position:0%
+polypeptide and it just gets stuck so
+ 
+
+ align:start position:0%
+polypeptide and it just gets stuck so
+this s sr a tag is attached to the c
+
+ align:start position:0%
+this s sr a tag is attached to the c
+ 
+
+ align:start position:0%
+this s sr a tag is attached to the c
+terminus of proteins and as we're going
+
+ align:start position:0%
+terminus of proteins and as we're going
+ 
+
+ align:start position:0%
+terminus of proteins and as we're going
+to see this occurs Co translationally
+
+ align:start position:0%
+to see this occurs Co translationally
+ 
+
+ align:start position:0%
+to see this occurs Co translationally
+and it's very very interesting machinery
+
+ align:start position:0%
+and it's very very interesting machinery
+ 
+
+ align:start position:0%
+and it's very very interesting machinery
+so what we see here is that there's a
+
+ align:start position:0%
+so what we see here is that there's a
+ 
+
+ align:start position:0%
+so what we see here is that there's a
+new player we haven't yet seen and this
+
+ align:start position:0%
+new player we haven't yet seen and this
+ 
+
+ align:start position:0%
+new player we haven't yet seen and this
+is called SS RA or TM RNA for transfer
+
+ align:start position:0%
+is called SS RA or TM RNA for transfer
+ 
+
+ align:start position:0%
+is called SS RA or TM RNA for transfer
+messenger RNA and it's involved in an
+
+ align:start position:0%
+messenger RNA and it's involved in an
+ 
+
+ align:start position:0%
+messenger RNA and it's involved in an
+attachment of this SS are a tag to
+
+ align:start position:0%
+attachment of this SS are a tag to
+ 
+
+ align:start position:0%
+attachment of this SS are a tag to
+polypeptides that are having stalled
+
+ align:start position:0%
+polypeptides that are having stalled
+ 
+
+ align:start position:0%
+polypeptides that are having stalled
+biosynthesis on the ribosome and so this
+
+ align:start position:0%
+biosynthesis on the ribosome and so this
+ 
+
+ align:start position:0%
+biosynthesis on the ribosome and so this
+player acts as both the tRNA and an mrna
+
+ align:start position:0%
+player acts as both the tRNA and an mrna
+ 
+
+ align:start position:0%
+player acts as both the tRNA and an mrna
+right and we can take a look at the
+
+ align:start position:0%
+right and we can take a look at the
+ 
+
+ align:start position:0%
+right and we can take a look at the
+structures shown here so here we have
+
+ align:start position:0%
+structures shown here so here we have
+ 
+
+ align:start position:0%
+structures shown here so here we have
+tRNA and the cloverleaf depiction I'm
+
+ align:start position:0%
+tRNA and the cloverleaf depiction I'm
+ 
+
+ align:start position:0%
+tRNA and the cloverleaf depiction I'm
+just in awe a tRNA ala and if we take a
+
+ align:start position:0%
+just in awe a tRNA ala and if we take a
+ 
+
+ align:start position:0%
+just in awe a tRNA ala and if we take a
+look here what do we see at this and we
+
+ align:start position:0%
+look here what do we see at this and we
+ 
+
+ align:start position:0%
+look here what do we see at this and we
+have a region of the TM RNA that looks
+
+ align:start position:0%
+have a region of the TM RNA that looks
+ 
+
+ align:start position:0%
+have a region of the TM RNA that looks
+like a tRNA right quite quite similar
+
+ align:start position:0%
+like a tRNA right quite quite similar
+ 
+
+ align:start position:0%
+like a tRNA right quite quite similar
+here to the 3 prime 5 prime end and then
+
+ align:start position:0%
+here to the 3 prime 5 prime end and then
+ 
+
+ align:start position:0%
+here to the 3 prime 5 prime end and then
+we have this additional region and then
+
+ align:start position:0%
+we have this additional region and then
+ 
+
+ align:start position:0%
+we have this additional region and then
+if we look down and here what do we see
+
+ align:start position:0%
+if we look down and here what do we see
+ 
+
+ align:start position:0%
+if we look down and here what do we see
+we see a region that with a little
+
+ align:start position:0%
+we see a region that with a little
+ 
+
+ align:start position:0%
+we see a region that with a little
+imagination we can think looks like mRNA
+
+ align:start position:0%
+imagination we can think looks like mRNA
+ 
+
+ align:start position:0%
+imagination we can think looks like mRNA
+and if we take a look at the various
+
+ align:start position:0%
+and if we take a look at the various
+ 
+
+ align:start position:0%
+and if we take a look at the various
+codons what we
+
+ align:start position:0%
+codons what we
+ 
+
+ align:start position:0%
+codons what we
+see is that the SSR a tag is encoded
+
+ align:start position:0%
+see is that the SSR a tag is encoded
+ 
+
+ align:start position:0%
+see is that the SSR a tag is encoded
+there along with a stop codon so
+
+ align:start position:0%
+there along with a stop codon so
+ 
+
+ align:start position:0%
+there along with a stop codon so
+effectively we have a tRNA look-alike we
+
+ align:start position:0%
+effectively we have a tRNA look-alike we
+ 
+
+ align:start position:0%
+effectively we have a tRNA look-alike we
+have an mRNA look-alike that is encoding
+
+ align:start position:0%
+have an mRNA look-alike that is encoding
+ 
+
+ align:start position:0%
+have an mRNA look-alike that is encoding
+this SSR a tag so what happens there's a
+
+ align:start position:0%
+this SSR a tag so what happens there's a
+ 
+
+ align:start position:0%
+this SSR a tag so what happens there's a
+partner protein called SMP B just to be
+
+ align:start position:0%
+partner protein called SMP B just to be
+ 
+
+ align:start position:0%
+partner protein called SMP B just to be
+aware of and in complex with fmpp it's
+
+ align:start position:0%
+aware of and in complex with fmpp it's
+ 
+
+ align:start position:0%
+aware of and in complex with fmpp it's
+actually ef-tu that delivers this TM RNA
+
+ align:start position:0%
+actually ef-tu that delivers this TM RNA
+ 
+
+ align:start position:0%
+actually ef-tu that delivers this TM RNA
+to the ribosome here so this is pretty
+
+ align:start position:0%
+to the ribosome here so this is pretty
+ 
+
+ align:start position:0%
+to the ribosome here so this is pretty
+interesting just from the standpoint of
+
+ align:start position:0%
+interesting just from the standpoint of
+ 
+
+ align:start position:0%
+interesting just from the standpoint of
+what we know about ef-tu we don't have a
+
+ align:start position:0%
+what we know about ef-tu we don't have a
+ 
+
+ align:start position:0%
+what we know about ef-tu we don't have a
+typical anticodon here so how does that
+
+ align:start position:0%
+typical anticodon here so how does that
+ 
+
+ align:start position:0%
+typical anticodon here so how does that
+happen we're not going to go into
+
+ align:start position:0%
+happen we're not going to go into
+ 
+
+ align:start position:0%
+happen we're not going to go into
+details but it's something you know
+
+ align:start position:0%
+details but it's something you know
+ 
+
+ align:start position:0%
+details but it's something you know
+curiosity should should beg those
+
+ align:start position:0%
+curiosity should should beg those
+ 
+
+ align:start position:0%
+curiosity should should beg those
+questions so what happens we can look at
+
+ align:start position:0%
+questions so what happens we can look at
+ 
+
+ align:start position:0%
+questions so what happens we can look at
+this cartoon overview here and so the
+
+ align:start position:0%
+this cartoon overview here and so the
+ 
+
+ align:start position:0%
+this cartoon overview here and so the
+color coding within this is helpful in
+
+ align:start position:0%
+color coding within this is helpful in
+ 
+
+ align:start position:0%
+color coding within this is helpful in
+terms of keeping track of pieces but
+
+ align:start position:0%
+terms of keeping track of pieces but
+ 
+
+ align:start position:0%
+terms of keeping track of pieces but
+here we start with our stalled ribosomes
+
+ align:start position:0%
+here we start with our stalled ribosomes
+ 
+
+ align:start position:0%
+here we start with our stalled ribosomes
+so the mRNA is found we see there's a
+
+ align:start position:0%
+so the mRNA is found we see there's a
+ 
+
+ align:start position:0%
+so the mRNA is found we see there's a
+peptidyl trna in the piece site you know
+
+ align:start position:0%
+peptidyl trna in the piece site you know
+ 
+
+ align:start position:0%
+peptidyl trna in the piece site you know
+the polypeptide has a number of amino
+
+ align:start position:0%
+the polypeptide has a number of amino
+ 
+
+ align:start position:0%
+the polypeptide has a number of amino
+acids and the a site is empty and for
+
+ align:start position:0%
+acids and the a site is empty and for
+ 
+
+ align:start position:0%
+acids and the a site is empty and for
+some reason no new amino acyl tRNA is
+
+ align:start position:0%
+some reason no new amino acyl tRNA is
+ 
+
+ align:start position:0%
+some reason no new amino acyl tRNA is
+coming in so the ribosomes stealth and
+
+ align:start position:0%
+coming in so the ribosomes stealth and
+ 
+
+ align:start position:0%
+coming in so the ribosomes stealth and
+as a result this SS RA or T mRNA is
+
+ align:start position:0%
+as a result this SS RA or T mRNA is
+ 
+
+ align:start position:0%
+as a result this SS RA or T mRNA is
+recruited to this stalled ribosome and
+
+ align:start position:0%
+recruited to this stalled ribosome and
+ 
+
+ align:start position:0%
+recruited to this stalled ribosome and
+so here we see the tRNA end and yellow
+
+ align:start position:0%
+so here we see the tRNA end and yellow
+ 
+
+ align:start position:0%
+so here we see the tRNA end and yellow
+with the alanine attached and here we
+
+ align:start position:0%
+with the alanine attached and here we
+ 
+
+ align:start position:0%
+with the alanine attached and here we
+have that region
+
+ align:start position:0%
+have that region
+ 
+
+ align:start position:0%
+have that region
+that's mRNA like encoding the tag so
+
+ align:start position:0%
+that's mRNA like encoding the tag so
+ 
+
+ align:start position:0%
+that's mRNA like encoding the tag so
+this molecule biomolecule gets recruited
+
+ align:start position:0%
+this molecule biomolecule gets recruited
+ 
+
+ align:start position:0%
+this molecule biomolecule gets recruited
+and what do we see it enters the a site
+
+ align:start position:0%
+and what do we see it enters the a site
+ 
+
+ align:start position:0%
+and what do we see it enters the a site
+so here we see the tRNA end and the a
+
+ align:start position:0%
+so here we see the tRNA end and the a
+ 
+
+ align:start position:0%
+so here we see the tRNA end and the a
+site and we have the rest of the
+
+ align:start position:0%
+site and we have the rest of the
+ 
+
+ align:start position:0%
+site and we have the rest of the
+molecule here then what there's
+
+ align:start position:0%
+molecule here then what there's
+ 
+
+ align:start position:0%
+molecule here then what there's
+formation of a new peptide bond so we
+
+ align:start position:0%
+formation of a new peptide bond so we
+ 
+
+ align:start position:0%
+formation of a new peptide bond so we
+have peptidyl transfer we see that Alan
+
+ align:start position:0%
+have peptidyl transfer we see that Alan
+ 
+
+ align:start position:0%
+have peptidyl transfer we see that Alan
+is here look that looks quite a bit like
+
+ align:start position:0%
+is here look that looks quite a bit like
+ 
+
+ align:start position:0%
+is here look that looks quite a bit like
+the hybrid states we talked about right
+
+ align:start position:0%
+the hybrid states we talked about right
+ 
+
+ align:start position:0%
+the hybrid states we talked about right
+where we're seeing these and shift into
+
+ align:start position:0%
+where we're seeing these and shift into
+ 
+
+ align:start position:0%
+where we're seeing these and shift into
+the esight not shown in the p-site here
+
+ align:start position:0%
+the esight not shown in the p-site here
+ 
+
+ align:start position:0%
+the esight not shown in the p-site here
+okay and then what happens there's
+
+ align:start position:0%
+okay and then what happens there's
+ 
+
+ align:start position:0%
+okay and then what happens there's
+translocation and there's message
+
+ align:start position:0%
+translocation and there's message
+ 
+
+ align:start position:0%
+translocation and there's message
+switching so the original mRNA gets
+
+ align:start position:0%
+switching so the original mRNA gets
+ 
+
+ align:start position:0%
+switching so the original mRNA gets
+kicked out and what do we see now that
+
+ align:start position:0%
+kicked out and what do we see now that
+ 
+
+ align:start position:0%
+kicked out and what do we see now that
+mRNA like region of the T mRNA is in the
+
+ align:start position:0%
+mRNA like region of the T mRNA is in the
+ 
+
+ align:start position:0%
+mRNA like region of the T mRNA is in the
+a site here then what happens after
+
+ align:start position:0%
+a site here then what happens after
+ 
+
+ align:start position:0%
+a site here then what happens after
+replacement of the mRNA translation can
+
+ align:start position:0%
+replacement of the mRNA translation can
+ 
+
+ align:start position:0%
+replacement of the mRNA translation can
+occur which results in synthesis of the
+
+ align:start position:0%
+occur which results in synthesis of the
+ 
+
+ align:start position:0%
+occur which results in synthesis of the
+SSR a tag so that's how this tag is
+
+ align:start position:0%
+SSR a tag so that's how this tag is
+ 
+
+ align:start position:0%
+SSR a tag so that's how this tag is
+attached to the C terminus of the
+
+ align:start position:0%
+attached to the C terminus of the
+ 
+
+ align:start position:0%
+attached to the C terminus of the
+polypeptide okay an elongation occurs
+
+ align:start position:0%
+polypeptide okay an elongation occurs
+ 
+
+ align:start position:0%
+polypeptide okay an elongation occurs
+until that stop codon in the t mRNA
+
+ align:start position:0%
+until that stop codon in the t mRNA
+ 
+
+ align:start position:0%
+until that stop codon in the t mRNA
+enters the a site okay and then peptide
+
+ align:start position:0%
+enters the a site okay and then peptide
+ 
+
+ align:start position:0%
+enters the a site okay and then peptide
+release occurs here so the result is a
+
+ align:start position:0%
+release occurs here so the result is a
+ 
+
+ align:start position:0%
+release occurs here so the result is a
+protein that has the SSR a tag attached
+
+ align:start position:0%
+protein that has the SSR a tag attached
+ 
+
+ align:start position:0%
+protein that has the SSR a tag attached
+to it C terminus and that protein will
+
+ align:start position:0%
+to it C terminus and that protein will
+ 
+
+ align:start position:0%
+to it C terminus and that protein will
+be directed to clip X P so pretty cool
+
+ align:start position:0%
+be directed to clip X P so pretty cool
+ 
+
+ align:start position:0%
+be directed to clip X P so pretty cool
+yeah thank you so there we don't ever
+
+ align:start position:0%
+yeah thank you so there we don't ever
+ 
+
+ align:start position:0%
+yeah thank you so there we don't ever
+leave the ribosome too much within these
+
+ align:start position:0%
+leave the ribosome too much within these
+ 
+
+ align:start position:0%
+leave the ribosome too much within these
+units here just to point out this tag is
+
+ align:start position:0%
+units here just to point out this tag is
+ 
+
+ align:start position:0%
+units here just to point out this tag is
+universal in bacteria so here's just a
+
+ align:start position:0%
+universal in bacteria so here's just a
+ 
+
+ align:start position:0%
+universal in bacteria so here's just a
+table a phylogenetic distribution you're
+
+ align:start position:0%
+table a phylogenetic distribution you're
+ 
+
+ align:start position:0%
+table a phylogenetic distribution you're
+not responsible for these details yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like the original protein completed or
+
+ align:start position:0%
+like the original protein completed or
+ 
+
+ align:start position:0%
+like the original protein completed or
+just yeah so what does the cartoon
+
+ align:start position:0%
+just yeah so what does the cartoon
+ 
+
+ align:start position:0%
+just yeah so what does the cartoon
+suggest it feels like it's already on
+
+ align:start position:0%
+suggest it feels like it's already on
+ 
+
+ align:start position:0%
+suggest it feels like it's already on
+the C end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the ribosome can stall at various
+
+ align:start position:0%
+well the ribosome can stall at various
+ 
+
+ align:start position:0%
+well the ribosome can stall at various
+points right so imagine you have a
+
+ align:start position:0%
+points right so imagine you have a
+ 
+
+ align:start position:0%
+points right so imagine you have a
+hundred amino acid polypeptide that
+
+ align:start position:0%
+hundred amino acid polypeptide that
+ 
+
+ align:start position:0%
+hundred amino acid polypeptide that
+needs to be synthesized right the
+
+ align:start position:0%
+needs to be synthesized right the
+ 
+
+ align:start position:0%
+needs to be synthesized right the
+ribosome could stall after amino acid
+
+ align:start position:0%
+ribosome could stall after amino acid
+ 
+
+ align:start position:0%
+ribosome could stall after amino acid
+twenty or forty or sixty right it's not
+
+ align:start position:0%
+twenty or forty or sixty right it's not
+ 
+
+ align:start position:0%
+twenty or forty or sixty right it's not
+that the whole polypeptide has been
+
+ align:start position:0%
+that the whole polypeptide has been
+ 
+
+ align:start position:0%
+that the whole polypeptide has been
+synthesized and then this gets put on
+
+ align:start position:0%
+synthesized and then this gets put on
+ 
+
+ align:start position:0%
+synthesized and then this gets put on
+right and maybe some some fragment there
+
+ align:start position:0%
+right and maybe some some fragment there
+ 
+
+ align:start position:0%
+right and maybe some some fragment there
+for that so yes so in terms of this
+
+ align:start position:0%
+for that so yes so in terms of this
+ 
+
+ align:start position:0%
+for that so yes so in terms of this
+adapter protein I just want to make a
+
+ align:start position:0%
+adapter protein I just want to make a
+ 
+
+ align:start position:0%
+adapter protein I just want to make a
+note in terms of the adapter so these
+
+ align:start position:0%
+note in terms of the adapter so these
+ 
+
+ align:start position:0%
+note in terms of the adapter so these
+adapter proteins can help with
+
+ align:start position:0%
+adapter proteins can help with
+ 
+
+ align:start position:0%
+adapter proteins can help with
+regulating the substrate specificity of
+
+ align:start position:0%
+regulating the substrate specificity of
+ 
+
+ align:start position:0%
+regulating the substrate specificity of
+Triple A plus ATP ASE's and effectively
+
+ align:start position:0%
+Triple A plus ATP ASE's and effectively
+ 
+
+ align:start position:0%
+Triple A plus ATP ASE's and effectively
+depending on the system and depending on
+
+ align:start position:0%
+depending on the system and depending on
+ 
+
+ align:start position:0%
+depending on the system and depending on
+the adapter it may enhance or it may
+
+ align:start position:0%
+the adapter it may enhance or it may
+ 
+
+ align:start position:0%
+the adapter it may enhance or it may
+inhibit degradation here so it's a
+
+ align:start position:0%
+inhibit degradation here so it's a
+ 
+
+ align:start position:0%
+inhibit degradation here so it's a
+case-by-case basis this ssp be shown in
+
+ align:start position:0%
+case-by-case basis this ssp be shown in
+ 
+
+ align:start position:0%
+case-by-case basis this ssp be shown in
+the cartoon here is a dimeric adapter
+
+ align:start position:0%
+the cartoon here is a dimeric adapter
+ 
+
+ align:start position:0%
+the cartoon here is a dimeric adapter
+for XP and it promotes degradation of
+
+ align:start position:0%
+for XP and it promotes degradation of
+ 
+
+ align:start position:0%
+for XP and it promotes degradation of
+certain substrates and effectively it
+
+ align:start position:0%
+certain substrates and effectively it
+ 
+
+ align:start position:0%
+certain substrates and effectively it
+enhances recognition of this tag by the
+
+ align:start position:0%
+enhances recognition of this tag by the
+ 
+
+ align:start position:0%
+enhances recognition of this tag by the
+machinery such that the degradation
+
+ align:start position:0%
+machinery such that the degradation
+ 
+
+ align:start position:0%
+machinery such that the degradation
+rates are enhanced so it's not that it's
+
+ align:start position:0%
+rates are enhanced so it's not that it's
+ 
+
+ align:start position:0%
+rates are enhanced so it's not that it's
+required it's just helpful and
+
+ align:start position:0%
+required it's just helpful and
+ 
+
+ align:start position:0%
+required it's just helpful and
+accelerates the process so just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just an interesting observation
+
+ align:start position:0%
+so just an interesting observation
+ 
+
+ align:start position:0%
+so just an interesting observation
+regarding SSP be it can be Co purified
+
+ align:start position:0%
+regarding SSP be it can be Co purified
+ 
+
+ align:start position:0%
+regarding SSP be it can be Co purified
+with ribosomes here and in terms of its
+
+ align:start position:0%
+with ribosomes here and in terms of its
+ 
+
+ align:start position:0%
+with ribosomes here and in terms of its
+structure and has some resemblance to
+
+ align:start position:0%
+structure and has some resemblance to
+ 
+
+ align:start position:0%
+structure and has some resemblance to
+known RNA binding proteins and this
+
+ align:start position:0%
+known RNA binding proteins and this
+ 
+
+ align:start position:0%
+known RNA binding proteins and this
+resemblance has begged a question you
+
+ align:start position:0%
+resemblance has begged a question you
+ 
+
+ align:start position:0%
+resemblance has begged a question you
+know does SSP be some you know itself um
+
+ align:start position:0%
+know does SSP be some you know itself um
+ 
+
+ align:start position:0%
+know does SSP be some you know itself um
+help with linking protein synthesis and
+
+ align:start position:0%
+help with linking protein synthesis and
+ 
+
+ align:start position:0%
+help with linking protein synthesis and
+protein degradation right so is it
+
+ align:start position:0%
+protein degradation right so is it
+ 
+
+ align:start position:0%
+protein degradation right so is it
+possible that SS PB could help promote
+
+ align:start position:0%
+possible that SS PB could help promote
+ 
+
+ align:start position:0%
+possible that SS PB could help promote
+binding of clip x to polypeptides you
+
+ align:start position:0%
+binding of clip x to polypeptides you
+ 
+
+ align:start position:0%
+binding of clip x to polypeptides you
+know before full release to the ribosome
+
+ align:start position:0%
+know before full release to the ribosome
+ 
+
+ align:start position:0%
+know before full release to the ribosome
+that something people have wondered
+
+ align:start position:0%
+that something people have wondered
+ 
+
+ align:start position:0%
+that something people have wondered
+about and initially this protein was
+
+ align:start position:0%
+about and initially this protein was
+ 
+
+ align:start position:0%
+about and initially this protein was
+classified as stringent of starvation
+
+ align:start position:0%
+classified as stringent of starvation
+ 
+
+ align:start position:0%
+classified as stringent of starvation
+protein that's where the name comes from
+
+ align:start position:0%
+protein that's where the name comes from
+ 
+
+ align:start position:0%
+protein that's where the name comes from
+so if we just take a quick look at its
+
+ align:start position:0%
+so if we just take a quick look at its
+ 
+
+ align:start position:0%
+so if we just take a quick look at its
+structure here what do we see so here's
+
+ align:start position:0%
+structure here what do we see so here's
+ 
+
+ align:start position:0%
+structure here what do we see so here's
+s s PB and then here we have structures
+
+ align:start position:0%
+s s PB and then here we have structures
+ 
+
+ align:start position:0%
+s s PB and then here we have structures
+from ribosomal proteins and so in SS PP
+
+ align:start position:0%
+from ribosomal proteins and so in SS PP
+ 
+
+ align:start position:0%
+from ribosomal proteins and so in SS PP
+clip X binds on this side and
+
+ align:start position:0%
+clip X binds on this side and
+ 
+
+ align:start position:0%
+clip X binds on this side and
+effectively here we look at the
+
+ align:start position:0%
+effectively here we look at the
+ 
+
+ align:start position:0%
+effectively here we look at the
+ribosomal proteins that bind RNA and
+
+ align:start position:0%
+ribosomal proteins that bind RNA and
+ 
+
+ align:start position:0%
+ribosomal proteins that bind RNA and
+they have these RNA binding sites there
+
+ align:start position:0%
+they have these RNA binding sites there
+ 
+
+ align:start position:0%
+they have these RNA binding sites there
+so there's some similarities in terms of
+
+ align:start position:0%
+so there's some similarities in terms of
+ 
+
+ align:start position:0%
+so there's some similarities in terms of
+the alpha helix in terms of the beta
+
+ align:start position:0%
+the alpha helix in terms of the beta
+ 
+
+ align:start position:0%
+the alpha helix in terms of the beta
+sheets here and also I'll just note in
+
+ align:start position:0%
+sheets here and also I'll just note in
+ 
+
+ align:start position:0%
+sheets here and also I'll just note in
+terms of SS PB and the SS are a tag so
+
+ align:start position:0%
+terms of SS PB and the SS are a tag so
+ 
+
+ align:start position:0%
+terms of SS PB and the SS are a tag so
+if we take this tag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is our SSR a tag here what's
+
+ align:start position:0%
+so this is our SSR a tag here what's
+ 
+
+ align:start position:0%
+so this is our SSR a tag here what's
+found is that clip X recognition is on
+
+ align:start position:0%
+found is that clip X recognition is on
+ 
+
+ align:start position:0%
+found is that clip X recognition is on
+this end okay an SSP be binding is on
+
+ align:start position:0%
+this end okay an SSP be binding is on
+ 
+
+ align:start position:0%
+this end okay an SSP be binding is on
+this end here so in different points so
+
+ align:start position:0%
+this end here so in different points so
+ 
+
+ align:start position:0%
+this end here so in different points so
+what this indicates here is that SSP b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and clip x can bind simultaneously okay
+
+ align:start position:0%
+and clip x can bind simultaneously okay
+ 
+
+ align:start position:0%
+and clip x can bind simultaneously okay
+but this is small so we can expect that
+
+ align:start position:0%
+but this is small so we can expect that
+ 
+
+ align:start position:0%
+but this is small so we can expect that
+there's some clash here for that okay so
+
+ align:start position:0%
+there's some clash here for that okay so
+ 
+
+ align:start position:0%
+there's some clash here for that okay so
+we're we're going to close it's just
+
+ align:start position:0%
+we're we're going to close it's just
+ 
+
+ align:start position:0%
+we're we're going to close it's just
+looking at an overview as to how this
+
+ align:start position:0%
+looking at an overview as to how this
+ 
+
+ align:start position:0%
+looking at an overview as to how this
+machine works and the model that then
+
+ align:start position:0%
+machine works and the model that then
+ 
+
+ align:start position:0%
+machine works and the model that then
+starting on Friday we'll look at
+
+ align:start position:0%
+starting on Friday we'll look at
+ 
+
+ align:start position:0%
+starting on Friday we'll look at
+experiments that were designed and
+
+ align:start position:0%
+experiments that were designed and
+ 
+
+ align:start position:0%
+experiments that were designed and
+performed to inform this model so if we
+
+ align:start position:0%
+performed to inform this model so if we
+ 
+
+ align:start position:0%
+performed to inform this model so if we
+look at this in one type of cartoon what
+
+ align:start position:0%
+look at this in one type of cartoon what
+ 
+
+ align:start position:0%
+look at this in one type of cartoon what
+are the stages so we can think of three
+
+ align:start position:0%
+are the stages so we can think of three
+ 
+
+ align:start position:0%
+are the stages so we can think of three
+as depicted here where there's some sort
+
+ align:start position:0%
+as depicted here where there's some sort
+ 
+
+ align:start position:0%
+as depicted here where there's some sort
+of initial recognition so the SSR a tag
+
+ align:start position:0%
+of initial recognition so the SSR a tag
+ 
+
+ align:start position:0%
+of initial recognition so the SSR a tag
+of this condemned protein binds to the
+
+ align:start position:0%
+of this condemned protein binds to the
+ 
+
+ align:start position:0%
+of this condemned protein binds to the
+axial pour of clip X and this process
+
+ align:start position:0%
+axial pour of clip X and this process
+ 
+
+ align:start position:0%
+axial pour of clip X and this process
+does not require ATP hydrolysis so here
+
+ align:start position:0%
+does not require ATP hydrolysis so here
+ 
+
+ align:start position:0%
+does not require ATP hydrolysis so here
+we see a folded substrate this dagger on
+
+ align:start position:0%
+we see a folded substrate this dagger on
+ 
+
+ align:start position:0%
+we see a folded substrate this dagger on
+is another word for for one of these
+
+ align:start position:0%
+is another word for for one of these
+ 
+
+ align:start position:0%
+is another word for for one of these
+tags SSR a tag so we see there's some
+
+ align:start position:0%
+tags SSR a tag so we see there's some
+ 
+
+ align:start position:0%
+tags SSR a tag so we see there's some
+recognition here then what happens
+
+ align:start position:0%
+recognition here then what happens
+ 
+
+ align:start position:0%
+recognition here then what happens
+clip X unfolds this substrate so somehow
+
+ align:start position:0%
+clip X unfolds this substrate so somehow
+ 
+
+ align:start position:0%
+clip X unfolds this substrate so somehow
+it has to grip and pull and apply of
+
+ align:start position:0%
+it has to grip and pull and apply of
+ 
+
+ align:start position:0%
+it has to grip and pull and apply of
+force that unfolds the polypeptide and
+
+ align:start position:0%
+force that unfolds the polypeptide and
+ 
+
+ align:start position:0%
+force that unfolds the polypeptide and
+threads that unfolded polypeptide into
+
+ align:start position:0%
+threads that unfolded polypeptide into
+ 
+
+ align:start position:0%
+threads that unfolded polypeptide into
+the degradation chamber so you know kind
+
+ align:start position:0%
+the degradation chamber so you know kind
+ 
+
+ align:start position:0%
+the degradation chamber so you know kind
+of this pulley system is shown here this
+
+ align:start position:0%
+of this pulley system is shown here this
+ 
+
+ align:start position:0%
+of this pulley system is shown here this
+chopper type thing shown here you can
+
+ align:start position:0%
+chopper type thing shown here you can
+ 
+
+ align:start position:0%
+chopper type thing shown here you can
+use your imagination in this unit for
+
+ align:start position:0%
+use your imagination in this unit for
+ 
+
+ align:start position:0%
+use your imagination in this unit for
+how to depict this machine so we see
+
+ align:start position:0%
+how to depict this machine so we see
+ 
+
+ align:start position:0%
+how to depict this machine so we see
+that the polypeptide is being unfolded
+
+ align:start position:0%
+that the polypeptide is being unfolded
+ 
+
+ align:start position:0%
+that the polypeptide is being unfolded
+and threaded through clip X into this
+
+ align:start position:0%
+and threaded through clip X into this
+ 
+
+ align:start position:0%
+and threaded through clip X into this
+chamber where it gets chopped up by the
+
+ align:start position:0%
+chamber where it gets chopped up by the
+ 
+
+ align:start position:0%
+chamber where it gets chopped up by the
+serine protease active sites here okay
+
+ align:start position:0%
+serine protease active sites here okay
+ 
+
+ align:start position:0%
+serine protease active sites here okay
+so for unfolding and translocation ATP
+
+ align:start position:0%
+so for unfolding and translocation ATP
+ 
+
+ align:start position:0%
+so for unfolding and translocation ATP
+is needed
+
+ align:start position:0%
+is needed
+ 
+
+ align:start position:0%
+is needed
+clip X is high drooling I tried
+
+ align:start position:0%
+clip X is high drooling I tried
+ 
+
+ align:start position:0%
+clip X is high drooling I tried
+realizing HTP to allow this to occur
+
+ align:start position:0%
+realizing HTP to allow this to occur
+ 
+
+ align:start position:0%
+realizing HTP to allow this to occur
+okay in the degradation chamber this
+
+ align:start position:0%
+okay in the degradation chamber this
+ 
+
+ align:start position:0%
+okay in the degradation chamber this
+degradation part is independent of ATP
+
+ align:start position:0%
+degradation part is independent of ATP
+ 
+
+ align:start position:0%
+degradation part is independent of ATP
+right the serine protease doesn't need
+
+ align:start position:0%
+right the serine protease doesn't need
+ 
+
+ align:start position:0%
+right the serine protease doesn't need
+that here so how can we kind of break
+
+ align:start position:0%
+that here so how can we kind of break
+ 
+
+ align:start position:0%
+that here so how can we kind of break
+this up further into a model that we can
+
+ align:start position:0%
+this up further into a model that we can
+ 
+
+ align:start position:0%
+this up further into a model that we can
+test what I present here is the working
+
+ align:start position:0%
+test what I present here is the working
+ 
+
+ align:start position:0%
+test what I present here is the working
+model and just note they now the
+
+ align:start position:0%
+model and just note they now the
+ 
+
+ align:start position:0%
+model and just note they now the
+orientation is flipped here so we have
+
+ align:start position:0%
+orientation is flipped here so we have
+ 
+
+ align:start position:0%
+orientation is flipped here so we have
+clip X on the bottom and clip P on top
+
+ align:start position:0%
+clip X on the bottom and clip P on top
+ 
+
+ align:start position:0%
+clip X on the bottom and clip P on top
+so what happens here we can look at this
+
+ align:start position:0%
+so what happens here we can look at this
+ 
+
+ align:start position:0%
+so what happens here we can look at this
+in terms of five steps okay and we can
+
+ align:start position:0%
+in terms of five steps okay and we can
+ 
+
+ align:start position:0%
+in terms of five steps okay and we can
+begin here with binding right so this
+
+ align:start position:0%
+begin here with binding right so this
+ 
+
+ align:start position:0%
+begin here with binding right so this
+SSR a tagged protein needs to bind to
+
+ align:start position:0%
+SSR a tagged protein needs to bind to
+ 
+
+ align:start position:0%
+SSR a tagged protein needs to bind to
+clip X and that binding is associated
+
+ align:start position:0%
+clip X and that binding is associated
+ 
+
+ align:start position:0%
+clip X and that binding is associated
+with some dissociation constant or KD
+
+ align:start position:0%
+with some dissociation constant or KD
+ 
+
+ align:start position:0%
+with some dissociation constant or KD
+here right what do we see after binding
+
+ align:start position:0%
+here right what do we see after binding
+ 
+
+ align:start position:0%
+here right what do we see after binding
+we have a second step which is
+
+ align:start position:0%
+we have a second step which is
+ 
+
+ align:start position:0%
+we have a second step which is
+denaturation so the polypeptide becomes
+
+ align:start position:0%
+denaturation so the polypeptide becomes
+ 
+
+ align:start position:0%
+denaturation so the polypeptide becomes
+unfolded we have a and that's defined by
+
+ align:start position:0%
+unfolded we have a and that's defined by
+ 
+
+ align:start position:0%
+unfolded we have a and that's defined by
+a rate constant for denaturation as
+
+ align:start position:0%
+a rate constant for denaturation as
+ 
+
+ align:start position:0%
+a rate constant for denaturation as
+shown here if we look next we have
+
+ align:start position:0%
+shown here if we look next we have
+ 
+
+ align:start position:0%
+shown here if we look next we have
+translocation so this polypeptide is
+
+ align:start position:0%
+translocation so this polypeptide is
+ 
+
+ align:start position:0%
+translocation so this polypeptide is
+moving through clip X into the
+
+ align:start position:0%
+moving through clip X into the
+ 
+
+ align:start position:0%
+moving through clip X into the
+degradation chamber right and this is
+
+ align:start position:0%
+degradation chamber right and this is
+ 
+
+ align:start position:0%
+degradation chamber right and this is
+also associated with the rate constant
+
+ align:start position:0%
+also associated with the rate constant
+ 
+
+ align:start position:0%
+also associated with the rate constant
+so rate constant for translocation and
+
+ align:start position:0%
+so rate constant for translocation and
+ 
+
+ align:start position:0%
+so rate constant for translocation and
+both of these steps require the use of
+
+ align:start position:0%
+both of these steps require the use of
+ 
+
+ align:start position:0%
+both of these steps require the use of
+ATP once this polypeptide is in the
+
+ align:start position:0%
+ATP once this polypeptide is in the
+ 
+
+ align:start position:0%
+ATP once this polypeptide is in the
+chamber we have step 4 which is
+
+ align:start position:0%
+chamber we have step 4 which is
+ 
+
+ align:start position:0%
+chamber we have step 4 which is
+degradation and again we have K DANC
+
+ align:start position:0%
+degradation and again we have K DANC
+ 
+
+ align:start position:0%
+degradation and again we have K DANC
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+fast and then in this last step here
+
+ align:start position:0%
+fast and then in this last step here
+ 
+
+ align:start position:0%
+fast and then in this last step here
+there's some release so somehow these
+
+ align:start position:0%
+there's some release so somehow these
+ 
+
+ align:start position:0%
+there's some release so somehow these
+poly peptide fragments need to be
+
+ align:start position:0%
+poly peptide fragments need to be
+ 
+
+ align:start position:0%
+poly peptide fragments need to be
+released from the chamber yeah yeah so
+
+ align:start position:0%
+released from the chamber yeah yeah so
+ 
+
+ align:start position:0%
+released from the chamber yeah yeah so
+often the cartoons are drawn just
+
+ align:start position:0%
+often the cartoons are drawn just
+ 
+
+ align:start position:0%
+often the cartoons are drawn just
+showing one of the heptamer but think of
+
+ align:start position:0%
+showing one of the heptamer but think of
+ 
+
+ align:start position:0%
+showing one of the heptamer but think of
+it as a dimer with these two
+
+ align:start position:0%
+it as a dimer with these two
+ 
+
+ align:start position:0%
+it as a dimer with these two
+back-to-back rings here for that right
+
+ align:start position:0%
+back-to-back rings here for that right
+ 
+
+ align:start position:0%
+back-to-back rings here for that right
+so we have five steps here right each
+
+ align:start position:0%
+so we have five steps here right each
+ 
+
+ align:start position:0%
+so we have five steps here right each
+one of these steps has a rate constant
+
+ align:start position:0%
+one of these steps has a rate constant
+ 
+
+ align:start position:0%
+one of these steps has a rate constant
+and one question we want to ask with
+
+ align:start position:0%
+and one question we want to ask with
+ 
+
+ align:start position:0%
+and one question we want to ask with
+this is what is the rate determining
+
+ align:start position:0%
+this is what is the rate determining
+ 
+
+ align:start position:0%
+this is what is the rate determining
+step and the quick answer where we'll
+
+ align:start position:0%
+step and the quick answer where we'll
+ 
+
+ align:start position:0%
+step and the quick answer where we'll
+end today and as indicated in this
+
+ align:start position:0%
+end today and as indicated in this
+ 
+
+ align:start position:0%
+end today and as indicated in this
+overview is that degradation is fast
+
+ align:start position:0%
+overview is that degradation is fast
+ 
+
+ align:start position:0%
+overview is that degradation is fast
+relative to denaturation and
+
+ align:start position:0%
+relative to denaturation and
+ 
+
+ align:start position:0%
+relative to denaturation and
+translocation okay and there should be
+
+ align:start position:0%
+translocation okay and there should be
+ 
+
+ align:start position:0%
+translocation okay and there should be
+an intuitive aspect to that we heard
+
+ align:start position:0%
+an intuitive aspect to that we heard
+ 
+
+ align:start position:0%
+an intuitive aspect to that we heard
+about last time how proteases give these
+
+ align:start position:0%
+about last time how proteases give these
+ 
+
+ align:start position:0%
+about last time how proteases give these
+tremendous rate accelerations right and
+
+ align:start position:0%
+tremendous rate accelerations right and
+ 
+
+ align:start position:0%
+tremendous rate accelerations right and
+if you have an unfolded peptide those
+
+ align:start position:0%
+if you have an unfolded peptide those
+ 
+
+ align:start position:0%
+if you have an unfolded peptide those
+sites where cleavage will happen are
+
+ align:start position:0%
+sites where cleavage will happen are
+ 
+
+ align:start position:0%
+sites where cleavage will happen are
+going to be exposed there so what we're
+
+ align:start position:0%
+going to be exposed there so what we're
+ 
+
+ align:start position:0%
+going to be exposed there so what we're
+going to ask is is it possible to make
+
+ align:start position:0%
+going to ask is is it possible to make
+ 
+
+ align:start position:0%
+going to ask is is it possible to make
+experiments design experience where we
+
+ align:start position:0%
+experiments design experience where we
+ 
+
+ align:start position:0%
+experiments design experience where we
+can separate the denaturation process
+
+ align:start position:0%
+can separate the denaturation process
+ 
+
+ align:start position:0%
+can separate the denaturation process
+from the translocation process and
+
+ align:start position:0%
+from the translocation process and
+ 
+
+ align:start position:0%
+from the translocation process and
+analyze those and in the process of
+
+ align:start position:0%
+analyze those and in the process of
+ 
+
+ align:start position:0%
+analyze those and in the process of
+doing so ask you know what is the ATP
+
+ align:start position:0%
+doing so ask you know what is the ATP
+ 
+
+ align:start position:0%
+doing so ask you know what is the ATP
+utilization for each step and what is
+
+ align:start position:0%
+utilization for each step and what is
+ 
+
+ align:start position:0%
+utilization for each step and what is
+the role for ATP in this process and so
+
+ align:start position:0%
+the role for ATP in this process and so
+ 
+
+ align:start position:0%
+the role for ATP in this process and so
+on Friday we'll begin with discussing
+
+ align:start position:0%
+on Friday we'll begin with discussing
+ 
+
+ align:start position:0%
+on Friday we'll begin with discussing
+substrates the design of substrates that
+
+ align:start position:0%
+substrates the design of substrates that
+ 
+
+ align:start position:0%
+substrates the design of substrates that
+have been used to examine this model in
+
+ align:start position:0%
+have been used to examine this model in
+ 
+
+ align:start position:0%
+have been used to examine this model in
+more detail is there one question next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the degradation step that's gonna
+
+ align:start position:0%
+in the degradation step that's gonna
+ 
+
+ align:start position:0%
+in the degradation step that's gonna
+depend I mean you can have different
+
+ align:start position:0%
+depend I mean you can have different
+ 
+
+ align:start position:0%
+depend I mean you can have different
+types of bonds with post-translational
+
+ align:start position:0%
+types of bonds with post-translational
+ 
+
+ align:start position:0%
+types of bonds with post-translational
+modifications right right so in the
+
+ align:start position:0%
+modifications right right so in the
+ 
+
+ align:start position:0%
+modifications right right so in the
+periodic system you have a post
+
+ align:start position:0%
+periodic system you have a post
+ 
+
+ align:start position:0%
+periodic system you have a post
+translational modification to direct
+
+ align:start position:0%
+translational modification to direct
+ 
+
+ align:start position:0%
+translational modification to direct
+this condemned protein and that
+
+ align:start position:0%
+this condemned protein and that
+ 
+
+ align:start position:0%
+this condemned protein and that
+machinery so they're ubiquitous and you
+
+ align:start position:0%
+machinery so they're ubiquitous and you
+ 
+
+ align:start position:0%
+machinery so they're ubiquitous and you
+get this poly ubiquitin tail so you saw
+
+ align:start position:0%
+get this poly ubiquitin tail so you saw
+ 
+
+ align:start position:0%
+get this poly ubiquitin tail so you saw
+ubiquitin and recitation number one and
+
+ align:start position:0%
+ubiquitin and recitation number one and
+ 
+
+ align:start position:0%
+ubiquitin and recitation number one and
+the eukaryotic proteasome has the
+
+ align:start position:0%
+the eukaryotic proteasome has the
+ 
+
+ align:start position:0%
+the eukaryotic proteasome has the
+ability to chop those ubiquitin x' off
+
+ align:start position:0%
+ability to chop those ubiquitin x' off
+ 
+
+ align:start position:0%
+ability to chop those ubiquitin x' off
+for recycling they're in that so so
+
+ align:start position:0%
+for recycling they're in that so so
+ 
+
+ align:start position:0%
+for recycling they're in that so so
+that's one example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/upzI8ZxORyI.txt b/upzI8ZxORyI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d5b72bc2fcfb4e6259460d8974dedf535990506f
--- /dev/null
+++ b/upzI8ZxORyI.txt
@@ -0,0 +1,8699 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wireless fantasy by Vladimir Luchevski.
+
+ align:start position:0%
+Wireless fantasy by Vladimir Luchevski.
+ 
+
+ align:start position:0%
+Wireless fantasy by Vladimir Luchevski.
+It's one of the first pieces of
+
+ align:start position:0%
+It's one of the first pieces of
+ 
+
+ align:start position:0%
+It's one of the first pieces of
+computerenerated music. It was done at
+
+ align:start position:0%
+computerenerated music. It was done at
+ 
+
+ align:start position:0%
+computerenerated music. It was done at
+Columbia University in 1960. It was
+
+ align:start position:0%
+Columbia University in 1960. It was
+ 
+
+ align:start position:0%
+Columbia University in 1960. It was
+commissioned by a group of
+
+ align:start position:0%
+commissioned by a group of
+ 
+
+ align:start position:0%
+commissioned by a group of
+uh fans of Lee Deforest and it was uh in
+
+ align:start position:0%
+uh fans of Lee Deforest and it was uh in
+ 
+
+ align:start position:0%
+uh fans of Lee Deforest and it was uh in
+honor of Deforest contribution to
+
+ align:start position:0%
+honor of Deforest contribution to
+ 
+
+ align:start position:0%
+honor of Deforest contribution to
+wireless broadcast. So it it and one of
+
+ align:start position:0%
+wireless broadcast. So it it and one of
+ 
+
+ align:start position:0%
+wireless broadcast. So it it and one of
+the first broadcast Deforest ever sent
+
+ align:start position:0%
+the first broadcast Deforest ever sent
+ 
+
+ align:start position:0%
+the first broadcast Deforest ever sent
+over the radio was the uh piece that
+
+ align:start position:0%
+over the radio was the uh piece that
+ 
+
+ align:start position:0%
+over the radio was the uh piece that
+you're hearing. It's a parcifile. It's
+
+ align:start position:0%
+you're hearing. It's a parcifile. It's
+ 
+
+ align:start position:0%
+you're hearing. It's a parcifile. It's
+from the Vagner opera. And so what
+
+ align:start position:0%
+from the Vagner opera. And so what
+ 
+
+ align:start position:0%
+from the Vagner opera. And so what
+Usachevski has done in the piece is to
+
+ align:start position:0%
+Usachevski has done in the piece is to
+ 
+
+ align:start position:0%
+Usachevski has done in the piece is to
+uh process it to make it sound really
+
+ align:start position:0%
+uh process it to make it sound really
+ 
+
+ align:start position:0%
+uh process it to make it sound really
+distant as though it's coming over a
+
+ align:start position:0%
+distant as though it's coming over a
+ 
+
+ align:start position:0%
+distant as though it's coming over a
+shortwave radio. And then he's got Morse
+
+ align:start position:0%
+shortwave radio. And then he's got Morse
+ 
+
+ align:start position:0%
+shortwave radio. And then he's got Morse
+code and there's various Morse code
+
+ align:start position:0%
+code and there's various Morse code
+ 
+
+ align:start position:0%
+code and there's various Morse code
+messages going through the
+
+ align:start position:0%
+messages going through the
+ 
+
+ align:start position:0%
+messages going through the
+piece. Wireless fantasy from
+
+ align:start position:0%
+piece. Wireless fantasy from
+ 
+
+ align:start position:0%
+piece. Wireless fantasy from
+1960 done longhand by the way. It was
+
+ align:start position:0%
+1960 done longhand by the way. It was
+ 
+
+ align:start position:0%
+1960 done longhand by the way. It was
+really done with Morris code and a
+
+ align:start position:0%
+really done with Morris code and a
+ 
+
+ align:start position:0%
+really done with Morris code and a
+mainframe computer and giant realtore
+
+ align:start position:0%
+mainframe computer and giant realtore
+ 
+
+ align:start position:0%
+mainframe computer and giant realtore
+decks. Nothing like what you have on
+
+ align:start position:0%
+decks. Nothing like what you have on
+ 
+
+ align:start position:0%
+decks. Nothing like what you have on
+your desktop today. Um okay so uh
+
+ align:start position:0%
+your desktop today. Um okay so uh
+ 
+
+ align:start position:0%
+your desktop today. Um okay so uh
+announcements tomorrow will be the
+
+ align:start position:0%
+announcements tomorrow will be the
+ 
+
+ align:start position:0%
+announcements tomorrow will be the
+exceptional Thursday test uh quiz 5
+
+ align:start position:0%
+exceptional Thursday test uh quiz 5
+ 
+
+ align:start position:0%
+exceptional Thursday test uh quiz 5
+based on homework five. Uh last day we
+
+ align:start position:0%
+based on homework five. Uh last day we
+ 
+
+ align:start position:0%
+based on homework five. Uh last day we
+talked about the band theory of solids
+
+ align:start position:0%
+talked about the band theory of solids
+ 
+
+ align:start position:0%
+talked about the band theory of solids
+and in the band theory we were able to
+
+ align:start position:0%
+and in the band theory we were able to
+ 
+
+ align:start position:0%
+and in the band theory we were able to
+distinguish metals from insulators from
+
+ align:start position:0%
+distinguish metals from insulators from
+ 
+
+ align:start position:0%
+distinguish metals from insulators from
+semiconductors. And you can see up here
+
+ align:start position:0%
+semiconductors. And you can see up here
+ 
+
+ align:start position:0%
+semiconductors. And you can see up here
+the metal has u a very very tiny uh
+
+ align:start position:0%
+the metal has u a very very tiny uh
+ 
+
+ align:start position:0%
+the metal has u a very very tiny uh
+energy gap between the the the top of
+
+ align:start position:0%
+energy gap between the the the top of
+ 
+
+ align:start position:0%
+energy gap between the the the top of
+the filled uh orbitals and the bottom of
+
+ align:start position:0%
+the filled uh orbitals and the bottom of
+ 
+
+ align:start position:0%
+the filled uh orbitals and the bottom of
+the unfilled orbitals. So it's
+
+ align:start position:0%
+the unfilled orbitals. So it's
+ 
+
+ align:start position:0%
+the unfilled orbitals. So it's
+effortless to move the electron up into
+
+ align:start position:0%
+effortless to move the electron up into
+ 
+
+ align:start position:0%
+effortless to move the electron up into
+this zone and give it mobility. Uh in an
+
+ align:start position:0%
+this zone and give it mobility. Uh in an
+ 
+
+ align:start position:0%
+this zone and give it mobility. Uh in an
+insulator there's a substantial energy
+
+ align:start position:0%
+insulator there's a substantial energy
+ 
+
+ align:start position:0%
+insulator there's a substantial energy
+required to move from the filled
+
+ align:start position:0%
+required to move from the filled
+ 
+
+ align:start position:0%
+required to move from the filled
+orbitals to the unfilled orbitals which
+
+ align:start position:0%
+orbitals to the unfilled orbitals which
+ 
+
+ align:start position:0%
+orbitals to the unfilled orbitals which
+we neatly refer to as the veilance band
+
+ align:start position:0%
+we neatly refer to as the veilance band
+ 
+
+ align:start position:0%
+we neatly refer to as the veilance band
+uh and conduction band. And arbitrarily
+
+ align:start position:0%
+uh and conduction band. And arbitrarily
+ 
+
+ align:start position:0%
+uh and conduction band. And arbitrarily
+we've chosen three electron volts.
+
+ align:start position:0%
+we've chosen three electron volts.
+ 
+
+ align:start position:0%
+we've chosen three electron volts.
+Typically the insulators are up four,
+
+ align:start position:0%
+Typically the insulators are up four,
+ 
+
+ align:start position:0%
+Typically the insulators are up four,
+five, six and so on electron volts. And
+
+ align:start position:0%
+five, six and so on electron volts. And
+ 
+
+ align:start position:0%
+five, six and so on electron volts. And
+then there's this class of material
+
+ align:start position:0%
+then there's this class of material
+ 
+
+ align:start position:0%
+then there's this class of material
+semiconductors uh for which the band gap
+
+ align:start position:0%
+semiconductors uh for which the band gap
+ 
+
+ align:start position:0%
+semiconductors uh for which the band gap
+is on the order of three electron volts.
+
+ align:start position:0%
+is on the order of three electron volts.
+ 
+
+ align:start position:0%
+is on the order of three electron volts.
+And why is three such a magic number?
+
+ align:start position:0%
+And why is three such a magic number?
+ 
+
+ align:start position:0%
+And why is three such a magic number?
+Because three electron volts is the
+
+ align:start position:0%
+Because three electron volts is the
+ 
+
+ align:start position:0%
+Because three electron volts is the
+threshold of visible light. So materials
+
+ align:start position:0%
+threshold of visible light. So materials
+ 
+
+ align:start position:0%
+threshold of visible light. So materials
+that have energy gaps below three
+
+ align:start position:0%
+that have energy gaps below three
+ 
+
+ align:start position:0%
+that have energy gaps below three
+electron volts will respond to visible
+
+ align:start position:0%
+electron volts will respond to visible
+ 
+
+ align:start position:0%
+electron volts will respond to visible
+light. And uh we're going to talk about
+
+ align:start position:0%
+light. And uh we're going to talk about
+ 
+
+ align:start position:0%
+light. And uh we're going to talk about
+such matters presently. Uh and just the
+
+ align:start position:0%
+such matters presently. Uh and just the
+ 
+
+ align:start position:0%
+such matters presently. Uh and just the
+last point to make is that the veilance
+
+ align:start position:0%
+last point to make is that the veilance
+ 
+
+ align:start position:0%
+last point to make is that the veilance
+band is constructed of the smearing of
+
+ align:start position:0%
+band is constructed of the smearing of
+ 
+
+ align:start position:0%
+band is constructed of the smearing of
+uh or the the splitting of orbitals that
+
+ align:start position:0%
+uh or the the splitting of orbitals that
+ 
+
+ align:start position:0%
+uh or the the splitting of orbitals that
+are associated with bonding. So veence
+
+ align:start position:0%
+are associated with bonding. So veence
+ 
+
+ align:start position:0%
+are associated with bonding. So veence
+band is veence electrons in bonding
+
+ align:start position:0%
+band is veence electrons in bonding
+ 
+
+ align:start position:0%
+band is veence electrons in bonding
+orbitals and the conduction band was
+
+ align:start position:0%
+orbitals and the conduction band was
+ 
+
+ align:start position:0%
+orbitals and the conduction band was
+generated from anti-bonding orbitals.
+
+ align:start position:0%
+generated from anti-bonding orbitals.
+ 
+
+ align:start position:0%
+generated from anti-bonding orbitals.
+And then we looked at
+
+ align:start position:0%
+And then we looked at
+ 
+
+ align:start position:0%
+And then we looked at
+photoexitation. If we have incident
+
+ align:start position:0%
+photoexitation. If we have incident
+ 
+
+ align:start position:0%
+photoexitation. If we have incident
+photons that have enough energy to break
+
+ align:start position:0%
+photons that have enough energy to break
+ 
+
+ align:start position:0%
+photons that have enough energy to break
+the bonds, electrons will be promoted up
+
+ align:start position:0%
+the bonds, electrons will be promoted up
+ 
+
+ align:start position:0%
+the bonds, electrons will be promoted up
+into the conduction band and it's a
+
+ align:start position:0%
+into the conduction band and it's a
+ 
+
+ align:start position:0%
+into the conduction band and it's a
+momentary uh transit and they will
+
+ align:start position:0%
+momentary uh transit and they will
+ 
+
+ align:start position:0%
+momentary uh transit and they will
+subsequently cascade back down and when
+
+ align:start position:0%
+subsequently cascade back down and when
+ 
+
+ align:start position:0%
+subsequently cascade back down and when
+they do so a photon will be remitted.
+
+ align:start position:0%
+they do so a photon will be remitted.
+ 
+
+ align:start position:0%
+they do so a photon will be remitted.
+When the electron cascades down, photon
+
+ align:start position:0%
+When the electron cascades down, photon
+ 
+
+ align:start position:0%
+When the electron cascades down, photon
+will be emitted and the emission will be
+
+ align:start position:0%
+will be emitted and the emission will be
+ 
+
+ align:start position:0%
+will be emitted and the emission will be
+pegged at the band gap energy. So if we
+
+ align:start position:0%
+pegged at the band gap energy. So if we
+ 
+
+ align:start position:0%
+pegged at the band gap energy. So if we
+go into HC over lambda, lambda becomes a
+
+ align:start position:0%
+go into HC over lambda, lambda becomes a
+ 
+
+ align:start position:0%
+go into HC over lambda, lambda becomes a
+a a critical value that's associated
+
+ align:start position:0%
+a a critical value that's associated
+ 
+
+ align:start position:0%
+a a critical value that's associated
+with this particular material. And so we
+
+ align:start position:0%
+with this particular material. And so we
+ 
+
+ align:start position:0%
+with this particular material. And so we
+can plot percent absorption percent
+
+ align:start position:0%
+can plot percent absorption percent
+ 
+
+ align:start position:0%
+can plot percent absorption percent
+absorption of what? Percent absorption
+
+ align:start position:0%
+absorption of what? Percent absorption
+ 
+
+ align:start position:0%
+absorption of what? Percent absorption
+of incident light as a function of the
+
+ align:start position:0%
+of incident light as a function of the
+ 
+
+ align:start position:0%
+of incident light as a function of the
+energy of that incident light. So high
+
+ align:start position:0%
+energy of that incident light. So high
+ 
+
+ align:start position:0%
+energy of that incident light. So high
+wavelength low energy light will pass
+
+ align:start position:0%
+wavelength low energy light will pass
+ 
+
+ align:start position:0%
+wavelength low energy light will pass
+through. It'll be transmitted and the
+
+ align:start position:0%
+through. It'll be transmitted and the
+ 
+
+ align:start position:0%
+through. It'll be transmitted and the
+material will appear transparent. High
+
+ align:start position:0%
+material will appear transparent. High
+ 
+
+ align:start position:0%
+material will appear transparent. High
+energy that is to say low wavelength
+
+ align:start position:0%
+energy that is to say low wavelength
+ 
+
+ align:start position:0%
+energy that is to say low wavelength
+incident radiation will have enough
+
+ align:start position:0%
+incident radiation will have enough
+ 
+
+ align:start position:0%
+incident radiation will have enough
+energy to promote electrons and so
+
+ align:start position:0%
+energy to promote electrons and so
+ 
+
+ align:start position:0%
+energy to promote electrons and so
+therefore those incident photons will be
+
+ align:start position:0%
+therefore those incident photons will be
+ 
+
+ align:start position:0%
+therefore those incident photons will be
+absorbed. the excess energy will be
+
+ align:start position:0%
+absorbed. the excess energy will be
+ 
+
+ align:start position:0%
+absorbed. the excess energy will be
+dissipated up here as heat and then
+
+ align:start position:0%
+dissipated up here as heat and then
+ 
+
+ align:start position:0%
+dissipated up here as heat and then
+we'll get ree of photons and so over
+
+ align:start position:0%
+we'll get ree of photons and so over
+ 
+
+ align:start position:0%
+we'll get ree of photons and so over
+here the material is an absorber and so
+
+ align:start position:0%
+here the material is an absorber and so
+ 
+
+ align:start position:0%
+here the material is an absorber and so
+we have a sharp jump here at uh a
+
+ align:start position:0%
+we have a sharp jump here at uh a
+ 
+
+ align:start position:0%
+we have a sharp jump here at uh a
+critical wavelength which we term the
+
+ align:start position:0%
+critical wavelength which we term the
+ 
+
+ align:start position:0%
+critical wavelength which we term the
+absorption edge and then towards the end
+
+ align:start position:0%
+absorption edge and then towards the end
+ 
+
+ align:start position:0%
+absorption edge and then towards the end
+of the lecture we talked about another
+
+ align:start position:0%
+of the lecture we talked about another
+ 
+
+ align:start position:0%
+of the lecture we talked about another
+type of excitation this was
+
+ align:start position:0%
+type of excitation this was
+ 
+
+ align:start position:0%
+type of excitation this was
+photoexitation we're going to talk about
+
+ align:start position:0%
+photoexitation we're going to talk about
+ 
+
+ align:start position:0%
+photoexitation we're going to talk about
+thermal excitation where the thermal
+
+ align:start position:0%
+thermal excitation where the thermal
+ 
+
+ align:start position:0%
+thermal excitation where the thermal
+energy in the environment is enough to
+
+ align:start position:0%
+energy in the environment is enough to
+ 
+
+ align:start position:0%
+energy in the environment is enough to
+cause the breaking of the bonds and the
+
+ align:start position:0%
+cause the breaking of the bonds and the
+ 
+
+ align:start position:0%
+cause the breaking of the bonds and the
+promotion of the electron gone from the
+
+ align:start position:0%
+promotion of the electron gone from the
+ 
+
+ align:start position:0%
+promotion of the electron gone from the
+veillance band to the conduction band.
+
+ align:start position:0%
+veillance band to the conduction band.
+ 
+
+ align:start position:0%
+veillance band to the conduction band.
+But in this case we discovered that pair
+
+ align:start position:0%
+But in this case we discovered that pair
+ 
+
+ align:start position:0%
+But in this case we discovered that pair
+of carriers was generated not a single
+
+ align:start position:0%
+of carriers was generated not a single
+ 
+
+ align:start position:0%
+of carriers was generated not a single
+carrier. In the case of uh
+
+ align:start position:0%
+carrier. In the case of uh
+ 
+
+ align:start position:0%
+carrier. In the case of uh
+photoexitation the electron moves up
+
+ align:start position:0%
+photoexitation the electron moves up
+ 
+
+ align:start position:0%
+photoexitation the electron moves up
+falls back down. Here we have pair pair
+
+ align:start position:0%
+falls back down. Here we have pair pair
+ 
+
+ align:start position:0%
+falls back down. Here we have pair pair
+excitation. So what happens is this
+
+ align:start position:0%
+excitation. So what happens is this
+ 
+
+ align:start position:0%
+excitation. So what happens is this
+electron is permanently sustainably
+
+ align:start position:0%
+electron is permanently sustainably
+ 
+
+ align:start position:0%
+electron is permanently sustainably
+sitting up in the veence band leaving in
+
+ align:start position:0%
+sitting up in the veence band leaving in
+ 
+
+ align:start position:0%
+sitting up in the veence band leaving in
+its uh place a broken bond which
+
+ align:start position:0%
+its uh place a broken bond which
+ 
+
+ align:start position:0%
+its uh place a broken bond which
+consists of a single electron and a
+
+ align:start position:0%
+consists of a single electron and a
+ 
+
+ align:start position:0%
+consists of a single electron and a
+missing electron which is termed a
+
+ align:start position:0%
+missing electron which is termed a
+ 
+
+ align:start position:0%
+missing electron which is termed a
+whole. It is zero in a land of minus1.
+
+ align:start position:0%
+whole. It is zero in a land of minus1.
+ 
+
+ align:start position:0%
+whole. It is zero in a land of minus1.
+So it appears to be + one and this is
+
+ align:start position:0%
+So it appears to be + one and this is
+ 
+
+ align:start position:0%
+So it appears to be + one and this is
+minus1 in a land of zero. So it appears
+
+ align:start position:0%
+minus1 in a land of zero. So it appears
+ 
+
+ align:start position:0%
+minus1 in a land of zero. So it appears
+to be minus1. So you see you see charge
+
+ align:start position:0%
+to be minus1. So you see you see charge
+ 
+
+ align:start position:0%
+to be minus1. So you see you see charge
+conservation the population of electrons
+
+ align:start position:0%
+conservation the population of electrons
+ 
+
+ align:start position:0%
+conservation the population of electrons
+in the conduction band due to thermal
+
+ align:start position:0%
+in the conduction band due to thermal
+ 
+
+ align:start position:0%
+in the conduction band due to thermal
+excitation is equal to the population of
+
+ align:start position:0%
+excitation is equal to the population of
+ 
+
+ align:start position:0%
+excitation is equal to the population of
+holes in the veilance band and
+
+ align:start position:0%
+holes in the veilance band and
+ 
+
+ align:start position:0%
+holes in the veilance band and
+electrical engineers like to just refer
+
+ align:start position:0%
+electrical engineers like to just refer
+ 
+
+ align:start position:0%
+electrical engineers like to just refer
+to the um the charge the nature of the
+
+ align:start position:0%
+to the um the charge the nature of the
+ 
+
+ align:start position:0%
+to the um the charge the nature of the
+charge regardless of the carrier whether
+
+ align:start position:0%
+charge regardless of the carrier whether
+ 
+
+ align:start position:0%
+charge regardless of the carrier whether
+it's a positive ion or a positive hole
+
+ align:start position:0%
+it's a positive ion or a positive hole
+ 
+
+ align:start position:0%
+it's a positive ion or a positive hole
+as far as they're concerned it's a
+
+ align:start position:0%
+as far as they're concerned it's a
+ 
+
+ align:start position:0%
+as far as they're concerned it's a
+positive so the electrical engineers
+
+ align:start position:0%
+positive so the electrical engineers
+ 
+
+ align:start position:0%
+positive so the electrical engineers
+write this relationship n equals p the
+
+ align:start position:0%
+write this relationship n equals p the
+ 
+
+ align:start position:0%
+write this relationship n equals p the
+number of negative charges in the
+
+ align:start position:0%
+number of negative charges in the
+ 
+
+ align:start position:0%
+number of negative charges in the
+conduction band equals the number of
+
+ align:start position:0%
+conduction band equals the number of
+ 
+
+ align:start position:0%
+conduction band equals the number of
+positive positive charges in the
+
+ align:start position:0%
+positive positive charges in the
+ 
+
+ align:start position:0%
+positive positive charges in the
+veillance band and then I left you with
+
+ align:start position:0%
+veillance band and then I left you with
+ 
+
+ align:start position:0%
+veillance band and then I left you with
+this uh mystery at the end of the
+
+ align:start position:0%
+this uh mystery at the end of the
+ 
+
+ align:start position:0%
+this uh mystery at the end of the
+lecture. I said well we observe thermal
+
+ align:start position:0%
+lecture. I said well we observe thermal
+ 
+
+ align:start position:0%
+lecture. I said well we observe thermal
+excitation in semiconductors but the
+
+ align:start position:0%
+excitation in semiconductors but the
+ 
+
+ align:start position:0%
+excitation in semiconductors but the
+thermal energy is roughly uh related to
+
+ align:start position:0%
+thermal energy is roughly uh related to
+ 
+
+ align:start position:0%
+thermal energy is roughly uh related to
+the product of the boltzman constant
+
+ align:start position:0%
+the product of the boltzman constant
+ 
+
+ align:start position:0%
+the product of the boltzman constant
+times the temperature and in electron
+
+ align:start position:0%
+times the temperature and in electron
+ 
+
+ align:start position:0%
+times the temperature and in electron
+volts this amounts to about 140th of an
+
+ align:start position:0%
+volts this amounts to about 140th of an
+ 
+
+ align:start position:0%
+volts this amounts to about 140th of an
+electron volt at room temperature but
+
+ align:start position:0%
+electron volt at room temperature but
+ 
+
+ align:start position:0%
+electron volt at room temperature but
+the band gap energy in semiconductors is
+
+ align:start position:0%
+the band gap energy in semiconductors is
+ 
+
+ align:start position:0%
+the band gap energy in semiconductors is
+on the order of several electron volts
+
+ align:start position:0%
+on the order of several electron volts
+ 
+
+ align:start position:0%
+on the order of several electron volts
+in the case of silicon it's 1.1 electron
+
+ align:start position:0%
+in the case of silicon it's 1.1 electron
+ 
+
+ align:start position:0%
+in the case of silicon it's 1.1 electron
+volts so how can we justify any kind of
+
+ align:start position:0%
+volts so how can we justify any kind of
+ 
+
+ align:start position:0%
+volts so how can we justify any kind of
+thermal excitation given that the
+
+ align:start position:0%
+thermal excitation given that the
+ 
+
+ align:start position:0%
+thermal excitation given that the
+thermal energy is so much lower than
+
+ align:start position:0%
+thermal energy is so much lower than
+ 
+
+ align:start position:0%
+thermal energy is so much lower than
+that of the band gap energy. Well, I
+
+ align:start position:0%
+that of the band gap energy. Well, I
+ 
+
+ align:start position:0%
+that of the band gap energy. Well, I
+have good news. The answer is that the
+
+ align:start position:0%
+have good news. The answer is that the
+ 
+
+ align:start position:0%
+have good news. The answer is that the
+energy in this room is distributed
+
+ align:start position:0%
+energy in this room is distributed
+ 
+
+ align:start position:0%
+energy in this room is distributed
+amongst all of the entities in the room.
+
+ align:start position:0%
+amongst all of the entities in the room.
+ 
+
+ align:start position:0%
+amongst all of the entities in the room.
+So that if you look at the gas for
+
+ align:start position:0%
+So that if you look at the gas for
+ 
+
+ align:start position:0%
+So that if you look at the gas for
+example, let's start, let's go back to
+
+ align:start position:0%
+example, let's start, let's go back to
+ 
+
+ align:start position:0%
+example, let's start, let's go back to
+the 1850s and uh peer into the mind of
+
+ align:start position:0%
+the 1850s and uh peer into the mind of
+ 
+
+ align:start position:0%
+the 1850s and uh peer into the mind of
+uh James Clark Maxwell who also gave us
+
+ align:start position:0%
+uh James Clark Maxwell who also gave us
+ 
+
+ align:start position:0%
+uh James Clark Maxwell who also gave us
+Maxwell's equations. He was a polymath
+
+ align:start position:0%
+Maxwell's equations. He was a polymath
+ 
+
+ align:start position:0%
+Maxwell's equations. He was a polymath
+like so many of the other people that
+
+ align:start position:0%
+like so many of the other people that
+ 
+
+ align:start position:0%
+like so many of the other people that
+we've been talking about in 3091. He
+
+ align:start position:0%
+we've been talking about in 3091. He
+ 
+
+ align:start position:0%
+we've been talking about in 3091. He
+didn't just focus on
+
+ align:start position:0%
+didn't just focus on
+ 
+
+ align:start position:0%
+didn't just focus on
+electromagnetism. He was a Renaissance
+
+ align:start position:0%
+electromagnetism. He was a Renaissance
+ 
+
+ align:start position:0%
+electromagnetism. He was a Renaissance
+scholar. And so one of his areas of
+
+ align:start position:0%
+scholar. And so one of his areas of
+ 
+
+ align:start position:0%
+scholar. And so one of his areas of
+interest was physical chemistry. And he
+
+ align:start position:0%
+interest was physical chemistry. And he
+ 
+
+ align:start position:0%
+interest was physical chemistry. And he
+studied gases. And he reasoned that the
+
+ align:start position:0%
+studied gases. And he reasoned that the
+ 
+
+ align:start position:0%
+studied gases. And he reasoned that the
+gases have a distribution of velocities.
+
+ align:start position:0%
+gases have a distribution of velocities.
+ 
+
+ align:start position:0%
+gases have a distribution of velocities.
+All of the gas molecules in this room
+
+ align:start position:0%
+All of the gas molecules in this room
+ 
+
+ align:start position:0%
+All of the gas molecules in this room
+are not behaving as though they are at
+
+ align:start position:0%
+are not behaving as though they are at
+ 
+
+ align:start position:0%
+are not behaving as though they are at
+room temperature. A substantial number
+
+ align:start position:0%
+room temperature. A substantial number
+ 
+
+ align:start position:0%
+room temperature. A substantial number
+are. And that's how we establish
+
+ align:start position:0%
+are. And that's how we establish
+ 
+
+ align:start position:0%
+are. And that's how we establish
+temperature. But what Maxwell reasoned
+
+ align:start position:0%
+temperature. But what Maxwell reasoned
+ 
+
+ align:start position:0%
+temperature. But what Maxwell reasoned
+was that some gas molecules are moving
+
+ align:start position:0%
+was that some gas molecules are moving
+ 
+
+ align:start position:0%
+was that some gas molecules are moving
+around as though the temperature of the
+
+ align:start position:0%
+around as though the temperature of the
+ 
+
+ align:start position:0%
+around as though the temperature of the
+room is 500 Kelvin and some are moving
+
+ align:start position:0%
+room is 500 Kelvin and some are moving
+ 
+
+ align:start position:0%
+room is 500 Kelvin and some are moving
+around as though it's only 100 Kelvin.
+
+ align:start position:0%
+around as though it's only 100 Kelvin.
+ 
+
+ align:start position:0%
+around as though it's only 100 Kelvin.
+But a large number of them are moving
+
+ align:start position:0%
+But a large number of them are moving
+ 
+
+ align:start position:0%
+But a large number of them are moving
+around as though it's roughly 300
+
+ align:start position:0%
+around as though it's roughly 300
+ 
+
+ align:start position:0%
+around as though it's roughly 300
+Kelvin. So he gave us a mathematical
+
+ align:start position:0%
+Kelvin. So he gave us a mathematical
+ 
+
+ align:start position:0%
+Kelvin. So he gave us a mathematical
+formulation of the distribution of
+
+ align:start position:0%
+formulation of the distribution of
+ 
+
+ align:start position:0%
+formulation of the distribution of
+energies. And then about 25 years later,
+
+ align:start position:0%
+energies. And then about 25 years later,
+ 
+
+ align:start position:0%
+energies. And then about 25 years later,
+Boltzman came along and said, you know,
+
+ align:start position:0%
+Boltzman came along and said, you know,
+ 
+
+ align:start position:0%
+Boltzman came along and said, you know,
+I'm going to generalize this idea. I'm
+
+ align:start position:0%
+I'm going to generalize this idea. I'm
+ 
+
+ align:start position:0%
+I'm going to generalize this idea. I'm
+going to generalize the idea. Forget
+
+ align:start position:0%
+going to generalize the idea. Forget
+ 
+
+ align:start position:0%
+going to generalize the idea. Forget
+about just gas molecules and velocity.
+
+ align:start position:0%
+about just gas molecules and velocity.
+ 
+
+ align:start position:0%
+about just gas molecules and velocity.
+Let's talk about all molecules and say
+
+ align:start position:0%
+Let's talk about all molecules and say
+ 
+
+ align:start position:0%
+Let's talk about all molecules and say
+the reason the gas molecules are moving
+
+ align:start position:0%
+the reason the gas molecules are moving
+ 
+
+ align:start position:0%
+the reason the gas molecules are moving
+ma mainly at 300 Kelvin and that some
+
+ align:start position:0%
+ma mainly at 300 Kelvin and that some
+ 
+
+ align:start position:0%
+ma mainly at 300 Kelvin and that some
+are moving at 500 Kelvin is and this was
+
+ align:start position:0%
+are moving at 500 Kelvin is and this was
+ 
+
+ align:start position:0%
+are moving at 500 Kelvin is and this was
+a big leap for Boltzman. He said I'm
+
+ align:start position:0%
+a big leap for Boltzman. He said I'm
+ 
+
+ align:start position:0%
+a big leap for Boltzman. He said I'm
+going to propose that temperature is
+
+ align:start position:0%
+going to propose that temperature is
+ 
+
+ align:start position:0%
+going to propose that temperature is
+distributed as well. That the reason
+
+ align:start position:0%
+distributed as well. That the reason
+ 
+
+ align:start position:0%
+distributed as well. That the reason
+some gas molecules are moving as though
+
+ align:start position:0%
+some gas molecules are moving as though
+ 
+
+ align:start position:0%
+some gas molecules are moving as though
+they have the velocity of 500 Kelvin is
+
+ align:start position:0%
+they have the velocity of 500 Kelvin is
+ 
+
+ align:start position:0%
+they have the velocity of 500 Kelvin is
+that I'm going to propose that they have
+
+ align:start position:0%
+that I'm going to propose that they have
+ 
+
+ align:start position:0%
+that I'm going to propose that they have
+the energy of 500 Kelvin. Well, what is
+
+ align:start position:0%
+the energy of 500 Kelvin. Well, what is
+ 
+
+ align:start position:0%
+the energy of 500 Kelvin. Well, what is
+local energy? That's temperature. So,
+
+ align:start position:0%
+local energy? That's temperature. So,
+ 
+
+ align:start position:0%
+local energy? That's temperature. So,
+Maxwell and Boltzman, we put the two of
+
+ align:start position:0%
+Maxwell and Boltzman, we put the two of
+ 
+
+ align:start position:0%
+Maxwell and Boltzman, we put the two of
+them together and we come up with the
+
+ align:start position:0%
+them together and we come up with the
+ 
+
+ align:start position:0%
+them together and we come up with the
+notion of a distribution of temperature,
+
+ align:start position:0%
+notion of a distribution of temperature,
+ 
+
+ align:start position:0%
+notion of a distribution of temperature,
+a distribution of energy. And this is
+
+ align:start position:0%
+a distribution of energy. And this is
+ 
+
+ align:start position:0%
+a distribution of energy. And this is
+what that distribution looks like. What
+
+ align:start position:0%
+what that distribution looks like. What
+ 
+
+ align:start position:0%
+what that distribution looks like. What
+we do is we plot the number
+
+ align:start position:0%
+we do is we plot the number
+ 
+
+ align:start position:0%
+we do is we plot the number
+of the number of particles in a
+
+ align:start position:0%
+of the number of particles in a
+ 
+
+ align:start position:0%
+of the number of particles in a
+particular ensemble that have a
+
+ align:start position:0%
+particular ensemble that have a
+ 
+
+ align:start position:0%
+particular ensemble that have a
+particular energy as a function of
+
+ align:start position:0%
+particular energy as a function of
+ 
+
+ align:start position:0%
+particular energy as a function of
+energy. And then we'll normalize it over
+
+ align:start position:0%
+energy. And then we'll normalize it over
+ 
+
+ align:start position:0%
+energy. And then we'll normalize it over
+the total number of particles in the
+
+ align:start position:0%
+the total number of particles in the
+ 
+
+ align:start position:0%
+the total number of particles in the
+system. And you know before I do that,
+
+ align:start position:0%
+system. And you know before I do that,
+ 
+
+ align:start position:0%
+system. And you know before I do that,
+why don't I just do an analogy? I'll do
+
+ align:start position:0%
+why don't I just do an analogy? I'll do
+ 
+
+ align:start position:0%
+why don't I just do an analogy? I'll do
+you know we had the we had the test a
+
+ align:start position:0%
+you know we had the we had the test a
+ 
+
+ align:start position:0%
+you know we had the we had the test a
+few weeks ago. Let's do a distribution
+
+ align:start position:0%
+few weeks ago. Let's do a distribution
+ 
+
+ align:start position:0%
+few weeks ago. Let's do a distribution
+of grades and then we'll relate it.
+
+ align:start position:0%
+of grades and then we'll relate it.
+ 
+
+ align:start position:0%
+of grades and then we'll relate it.
+Okay. So for example, what I could do is
+
+ align:start position:0%
+Okay. So for example, what I could do is
+ 
+
+ align:start position:0%
+Okay. So for example, what I could do is
+I could plot grade on this axis and I
+
+ align:start position:0%
+I could plot grade on this axis and I
+ 
+
+ align:start position:0%
+I could plot grade on this axis and I
+could put the number of people who have
+
+ align:start position:0%
+could put the number of people who have
+ 
+
+ align:start position:0%
+could put the number of people who have
+a particular grade and then normalize it
+
+ align:start position:0%
+a particular grade and then normalize it
+ 
+
+ align:start position:0%
+a particular grade and then normalize it
+divide it by the total number of
+
+ align:start position:0%
+divide it by the total number of
+ 
+
+ align:start position:0%
+divide it by the total number of
+students in the class. And if it's a big
+
+ align:start position:0%
+students in the class. And if it's a big
+ 
+
+ align:start position:0%
+students in the class. And if it's a big
+class as this one is and we have some
+
+ align:start position:0%
+class as this one is and we have some
+ 
+
+ align:start position:0%
+class as this one is and we have some
+kind of reasonable test, we expect to
+
+ align:start position:0%
+kind of reasonable test, we expect to
+ 
+
+ align:start position:0%
+kind of reasonable test, we expect to
+see this kind of a distribution, a
+
+ align:start position:0%
+see this kind of a distribution, a
+ 
+
+ align:start position:0%
+see this kind of a distribution, a
+bell-shaped curve, a Gaussian
+
+ align:start position:0%
+bell-shaped curve, a Gaussian
+ 
+
+ align:start position:0%
+bell-shaped curve, a Gaussian
+distribution. All right. And what does
+
+ align:start position:0%
+distribution. All right. And what does
+ 
+
+ align:start position:0%
+distribution. All right. And what does
+this tell? Tell tells us that some
+
+ align:start position:0%
+this tell? Tell tells us that some
+ 
+
+ align:start position:0%
+this tell? Tell tells us that some
+people had greater than the average
+
+ align:start position:0%
+people had greater than the average
+ 
+
+ align:start position:0%
+people had greater than the average
+value, some people had less than the
+
+ align:start position:0%
+value, some people had less than the
+ 
+
+ align:start position:0%
+value, some people had less than the
+average value, but the average value is
+
+ align:start position:0%
+average value, but the average value is
+ 
+
+ align:start position:0%
+average value, but the average value is
+given here. It's a symmetric
+
+ align:start position:0%
+given here. It's a symmetric
+ 
+
+ align:start position:0%
+given here. It's a symmetric
+distribution. And so we call this, we
+
+ align:start position:0%
+distribution. And so we call this, we
+ 
+
+ align:start position:0%
+distribution. And so we call this, we
+can call this the average. This is the
+
+ align:start position:0%
+can call this the average. This is the
+ 
+
+ align:start position:0%
+can call this the average. This is the
+average grade G with a bar over it. and
+
+ align:start position:0%
+average grade G with a bar over it. and
+ 
+
+ align:start position:0%
+average grade G with a bar over it. and
+you get the the inflection point here.
+
+ align:start position:0%
+you get the the inflection point here.
+ 
+
+ align:start position:0%
+you get the the inflection point here.
+This is where the the second derivative
+
+ align:start position:0%
+This is where the the second derivative
+ 
+
+ align:start position:0%
+This is where the the second derivative
+shifts from positive to negative. That's
+
+ align:start position:0%
+shifts from positive to negative. That's
+ 
+
+ align:start position:0%
+shifts from positive to negative. That's
+how you get the standard deviation. This
+
+ align:start position:0%
+how you get the standard deviation. This
+ 
+
+ align:start position:0%
+how you get the standard deviation. This
+is G bar plus standard deviation. This
+
+ align:start position:0%
+is G bar plus standard deviation. This
+ 
+
+ align:start position:0%
+is G bar plus standard deviation. This
+is G bar minus standard deviation. You
+
+ align:start position:0%
+is G bar minus standard deviation. You
+ 
+
+ align:start position:0%
+is G bar minus standard deviation. You
+can have a lot of fun with this. And the
+
+ align:start position:0%
+can have a lot of fun with this. And the
+ 
+
+ align:start position:0%
+can have a lot of fun with this. And the
+area under this line, if I use
+
+ align:start position:0%
+area under this line, if I use
+ 
+
+ align:start position:0%
+area under this line, if I use
+normalized values, the area under this
+
+ align:start position:0%
+normalized values, the area under this
+ 
+
+ align:start position:0%
+normalized values, the area under this
+line must equal one, right? Area equals
+
+ align:start position:0%
+line must equal one, right? Area equals
+ 
+
+ align:start position:0%
+line must equal one, right? Area equals
+1 when I normalize from 0 to infinity.
+
+ align:start position:0%
+1 when I normalize from 0 to infinity.
+ 
+
+ align:start position:0%
+1 when I normalize from 0 to infinity.
+So let's do the same thing here. only
+
+ align:start position:0%
+So let's do the same thing here. only
+ 
+
+ align:start position:0%
+So let's do the same thing here. only
+this is now this is
+
+ align:start position:0%
+this is now this is
+ 
+
+ align:start position:0%
+this is now this is
+Gaussian. This is
+
+ align:start position:0%
+Gaussian. This is
+ 
+
+ align:start position:0%
+Gaussian. This is
+Gaussian. But that's not the way
+
+ align:start position:0%
+Gaussian. But that's not the way
+ 
+
+ align:start position:0%
+Gaussian. But that's not the way
+molecules are distributed or energies
+
+ align:start position:0%
+molecules are distributed or energies
+ 
+
+ align:start position:0%
+molecules are distributed or energies
+are distributed in ensemble. It's
+
+ align:start position:0%
+are distributed in ensemble. It's
+ 
+
+ align:start position:0%
+are distributed in ensemble. It's
+asymmetrical. It looks a little bit like
+
+ align:start position:0%
+asymmetrical. It looks a little bit like
+ 
+
+ align:start position:0%
+asymmetrical. It looks a little bit like
+this. It's got a sharp rise and a long
+
+ align:start position:0%
+this. It's got a sharp rise and a long
+ 
+
+ align:start position:0%
+this. It's got a sharp rise and a long
+asmtoic tail. And so the average is not
+
+ align:start position:0%
+asmtoic tail. And so the average is not
+ 
+
+ align:start position:0%
+asmtoic tail. And so the average is not
+at the maximum in this case. This is
+
+ align:start position:0%
+at the maximum in this case. This is
+ 
+
+ align:start position:0%
+at the maximum in this case. This is
+Maxwell
+
+ align:start position:0%
+Maxwell
+ 
+
+ align:start position:0%
+Maxwell
+Boltzman. This is Maxwell Boltzman.
+
+ align:start position:0%
+Boltzman. This is Maxwell Boltzman.
+ 
+
+ align:start position:0%
+Boltzman. This is Maxwell Boltzman.
+we have a distribution of energies and
+
+ align:start position:0%
+we have a distribution of energies and
+ 
+
+ align:start position:0%
+we have a distribution of energies and
+the average the energy average E with a
+
+ align:start position:0%
+the average the energy average E with a
+ 
+
+ align:start position:0%
+the average the energy average E with a
+til uh a macron over it is somewhere a
+
+ align:start position:0%
+til uh a macron over it is somewhere a
+ 
+
+ align:start position:0%
+til uh a macron over it is somewhere a
+little bit to the right of the maximum
+
+ align:start position:0%
+little bit to the right of the maximum
+ 
+
+ align:start position:0%
+little bit to the right of the maximum
+and so what I'm doing is I'm taking the
+
+ align:start position:0%
+and so what I'm doing is I'm taking the
+ 
+
+ align:start position:0%
+and so what I'm doing is I'm taking the
+energy of a particle the number of
+
+ align:start position:0%
+energy of a particle the number of
+ 
+
+ align:start position:0%
+energy of a particle the number of
+particles that are given energy divided
+
+ align:start position:0%
+particles that are given energy divided
+ 
+
+ align:start position:0%
+particles that are given energy divided
+by the total number of particles so also
+
+ align:start position:0%
+by the total number of particles so also
+ 
+
+ align:start position:0%
+by the total number of particles so also
+the area under this curve must equal one
+
+ align:start position:0%
+the area under this curve must equal one
+ 
+
+ align:start position:0%
+the area under this curve must equal one
+so this is the value at some t1 and what
+
+ align:start position:0%
+so this is the value at some t1 and what
+ 
+
+ align:start position:0%
+so this is the value at some t1 and what
+I want to do is I want to focus down
+
+ align:start position:0%
+I want to do is I want to focus down
+ 
+
+ align:start position:0%
+I want to do is I want to focus down
+here suppose up here this is 1.1
+
+ align:start position:0%
+here suppose up here this is 1.1
+ 
+
+ align:start position:0%
+here suppose up here this is 1.1
+eV 1.1 eV well the average value is here
+
+ align:start position:0%
+eV 1.1 eV well the average value is here
+ 
+
+ align:start position:0%
+eV 1.1 eV well the average value is here
+and I said that this was 140th of an
+
+ align:start position:0%
+and I said that this was 140th of an
+ 
+
+ align:start position:0%
+and I said that this was 140th of an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+volt that's not the problem that the the
+
+ align:start position:0%
+volt that's not the problem that the the
+ 
+
+ align:start position:0%
+volt that's not the problem that the the
+problem is not that the average is a 140
+
+ align:start position:0%
+problem is not that the average is a 140
+ 
+
+ align:start position:0%
+problem is not that the average is a 140
+of an electron volt the good news is
+
+ align:start position:0%
+of an electron volt the good news is
+ 
+
+ align:start position:0%
+of an electron volt the good news is
+that there is some tiny fraction of the
+
+ align:start position:0%
+that there is some tiny fraction of the
+ 
+
+ align:start position:0%
+that there is some tiny fraction of the
+distribution that has energy above 1.1
+
+ align:start position:0%
+distribution that has energy above 1.1
+ 
+
+ align:start position:0%
+distribution that has energy above 1.1
+eV so if I knew what that fraction was
+
+ align:start position:0%
+eV so if I knew what that fraction was
+ 
+
+ align:start position:0%
+eV so if I knew what that fraction was
+then I could guess how much I could
+
+ align:start position:0%
+then I could guess how much I could
+ 
+
+ align:start position:0%
+then I could guess how much I could
+expect in the way of promotion here. You
+
+ align:start position:0%
+expect in the way of promotion here. You
+ 
+
+ align:start position:0%
+expect in the way of promotion here. You
+can see it's non zero. It's not a sharp
+
+ align:start position:0%
+can see it's non zero. It's not a sharp
+ 
+
+ align:start position:0%
+can see it's non zero. It's not a sharp
+cutoff. There's a tiny there's a tiny uh
+
+ align:start position:0%
+cutoff. There's a tiny there's a tiny uh
+ 
+
+ align:start position:0%
+cutoff. There's a tiny there's a tiny uh
+value out here. And the nature of this
+
+ align:start position:0%
+value out here. And the nature of this
+ 
+
+ align:start position:0%
+value out here. And the nature of this
+curve is that the amount of the the the
+
+ align:start position:0%
+curve is that the amount of the the the
+ 
+
+ align:start position:0%
+curve is that the amount of the the the
+fraction of the distribution out here.
+
+ align:start position:0%
+fraction of the distribution out here.
+ 
+
+ align:start position:0%
+fraction of the distribution out here.
+If I want to integrate say from 1.1 eV
+
+ align:start position:0%
+If I want to integrate say from 1.1 eV
+ 
+
+ align:start position:0%
+If I want to integrate say from 1.1 eV
+out to infinity, that's the area under
+
+ align:start position:0%
+out to infinity, that's the area under
+ 
+
+ align:start position:0%
+out to infinity, that's the area under
+this line. What am I integrating? I'm
+
+ align:start position:0%
+this line. What am I integrating? I'm
+ 
+
+ align:start position:0%
+this line. What am I integrating? I'm
+integrating the the fraction times d.
+
+ align:start position:0%
+integrating the the fraction times d.
+ 
+
+ align:start position:0%
+integrating the the fraction times d.
+This equals e to the minus energy gap
+
+ align:start position:0%
+This equals e to the minus energy gap
+ 
+
+ align:start position:0%
+This equals e to the minus energy gap
+divided by K boltzman temperature. This
+
+ align:start position:0%
+divided by K boltzman temperature. This
+ 
+
+ align:start position:0%
+divided by K boltzman temperature. This
+exponential that's what gives us the
+
+ align:start position:0%
+exponential that's what gives us the
+ 
+
+ align:start position:0%
+exponential that's what gives us the
+fraction underneath this
+
+ align:start position:0%
+fraction underneath this
+ 
+
+ align:start position:0%
+fraction underneath this
+line. Now let's see what happens when
+
+ align:start position:0%
+line. Now let's see what happens when
+ 
+
+ align:start position:0%
+line. Now let's see what happens when
+temperature rises. When temperature
+
+ align:start position:0%
+temperature rises. When temperature
+ 
+
+ align:start position:0%
+temperature rises. When temperature
+rises this line shifts to the right.
+
+ align:start position:0%
+rises this line shifts to the right.
+ 
+
+ align:start position:0%
+rises this line shifts to the right.
+This line shifts to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. And as you would expect the
+
+ align:start position:0%
+right. And as you would expect the
+ 
+
+ align:start position:0%
+right. And as you would expect the
+average shifts to the right as well. So
+
+ align:start position:0%
+average shifts to the right as well. So
+ 
+
+ align:start position:0%
+average shifts to the right as well. So
+this now is E average at
+
+ align:start position:0%
+this now is E average at
+ 
+
+ align:start position:0%
+this now is E average at
+T2 and okay let's say I I raise the
+
+ align:start position:0%
+T2 and okay let's say I I raise the
+ 
+
+ align:start position:0%
+T2 and okay let's say I I raise the
+temperature I raise the temperature
+
+ align:start position:0%
+temperature I raise the temperature
+ 
+
+ align:start position:0%
+temperature I raise the temperature
+let's look at silicon so let's say T1 is
+
+ align:start position:0%
+let's look at silicon so let's say T1 is
+ 
+
+ align:start position:0%
+let's look at silicon so let's say T1 is
+equal to room temperature 300 Kelvin and
+
+ align:start position:0%
+equal to room temperature 300 Kelvin and
+ 
+
+ align:start position:0%
+equal to room temperature 300 Kelvin and
+T2 will be the melting point of silicon
+
+ align:start position:0%
+T2 will be the melting point of silicon
+ 
+
+ align:start position:0%
+T2 will be the melting point of silicon
+t2 is the melting point of silicon not
+
+ align:start position:0%
+t2 is the melting point of silicon not
+ 
+
+ align:start position:0%
+t2 is the melting point of silicon not
+to make liquid silicon it's solid
+
+ align:start position:0%
+to make liquid silicon it's solid
+ 
+
+ align:start position:0%
+to make liquid silicon it's solid
+silicon at the melting point so it' be
+
+ align:start position:0%
+silicon at the melting point so it' be
+ 
+
+ align:start position:0%
+silicon at the melting point so it' be
+like ice at 0 degrees C melting point of
+
+ align:start position:0%
+like ice at 0 degrees C melting point of
+ 
+
+ align:start position:0%
+like ice at 0 degrees C melting point of
+silicon is uh 1414° C so add 27 73 to it
+
+ align:start position:0%
+silicon is uh 1414° C so add 27 73 to it
+ 
+
+ align:start position:0%
+silicon is uh 1414° C so add 27 73 to it
+and get about 1,700. It's about
+
+ align:start position:0%
+and get about 1,700. It's about
+ 
+
+ align:start position:0%
+and get about 1,700. It's about
+1,700 Kelvin. So, what's the ratio? T2
+
+ align:start position:0%
+1,700 Kelvin. So, what's the ratio? T2
+ 
+
+ align:start position:0%
+1,700 Kelvin. So, what's the ratio? T2
+to T1 is on the order of about
+
+ align:start position:0%
+to T1 is on the order of about
+ 
+
+ align:start position:0%
+to T1 is on the order of about
+six. So, this thing shifts by a factor
+
+ align:start position:0%
+six. So, this thing shifts by a factor
+ 
+
+ align:start position:0%
+six. So, this thing shifts by a factor
+of six. Let's look at what happens in
+
+ align:start position:0%
+of six. Let's look at what happens in
+ 
+
+ align:start position:0%
+of six. Let's look at what happens in
+here. Let's look at what happens in
+
+ align:start position:0%
+here. Let's look at what happens in
+ 
+
+ align:start position:0%
+here. Let's look at what happens in
+here. So, I'm going to use some some
+
+ align:start position:0%
+here. So, I'm going to use some some
+ 
+
+ align:start position:0%
+here. So, I'm going to use some some
+uh I'm going to blow this up. We'll blow
+
+ align:start position:0%
+uh I'm going to blow this up. We'll blow
+ 
+
+ align:start position:0%
+uh I'm going to blow this up. We'll blow
+this up. So what we're really looking at
+
+ align:start position:0%
+this up. So what we're really looking at
+ 
+
+ align:start position:0%
+this up. So what we're really looking at
+is what's the difference between the
+
+ align:start position:0%
+is what's the difference between the
+ 
+
+ align:start position:0%
+is what's the difference between the
+area here at room temperature and then
+
+ align:start position:0%
+area here at room temperature and then
+ 
+
+ align:start position:0%
+area here at room temperature and then
+what we're going to do is not to scale
+
+ align:start position:0%
+what we're going to do is not to scale
+ 
+
+ align:start position:0%
+what we're going to do is not to scale
+we're going to look at the area under
+
+ align:start position:0%
+we're going to look at the area under
+ 
+
+ align:start position:0%
+we're going to look at the area under
+the green
+
+ align:start position:0%
+the green
+ 
+
+ align:start position:0%
+the green
+curve. And when we use this relationship
+
+ align:start position:0%
+curve. And when we use this relationship
+ 
+
+ align:start position:0%
+curve. And when we use this relationship
+e to the minus energy gap energy over uh
+
+ align:start position:0%
+e to the minus energy gap energy over uh
+ 
+
+ align:start position:0%
+e to the minus energy gap energy over uh
+kt band gap energy over kt we find that
+
+ align:start position:0%
+kt band gap energy over kt we find that
+ 
+
+ align:start position:0%
+kt band gap energy over kt we find that
+the fraction the fraction at
+
+ align:start position:0%
+the fraction the fraction at
+ 
+
+ align:start position:0%
+the fraction the fraction at
+t2 divided by the fraction at t1 comes
+
+ align:start position:0%
+t2 divided by the fraction at t1 comes
+ 
+
+ align:start position:0%
+t2 divided by the fraction at t1 comes
+out to be 10 the 15th.
+
+ align:start position:0%
+out to be 10 the 15th.
+ 
+
+ align:start position:0%
+out to be 10 the 15th.
+So changing temperature changes the
+
+ align:start position:0%
+So changing temperature changes the
+ 
+
+ align:start position:0%
+So changing temperature changes the
+excitation population through the shift
+
+ align:start position:0%
+excitation population through the shift
+ 
+
+ align:start position:0%
+excitation population through the shift
+in the high end of the curve and it's
+
+ align:start position:0%
+in the high end of the curve and it's
+ 
+
+ align:start position:0%
+in the high end of the curve and it's
+only through that that we end up seeing
+
+ align:start position:0%
+only through that that we end up seeing
+ 
+
+ align:start position:0%
+only through that that we end up seeing
+decent levels of population in the
+
+ align:start position:0%
+decent levels of population in the
+ 
+
+ align:start position:0%
+decent levels of population in the
+uh conduction band.
+
+ align:start position:0%
+uh conduction band.
+ 
+
+ align:start position:0%
+uh conduction band.
+But so actually the number the number at
+
+ align:start position:0%
+But so actually the number the number at
+ 
+
+ align:start position:0%
+But so actually the number the number at
+room temperature is vanishingly small at
+
+ align:start position:0%
+room temperature is vanishingly small at
+ 
+
+ align:start position:0%
+room temperature is vanishingly small at
+room temperature. At room temp, at room
+
+ align:start position:0%
+room temperature. At room temp, at room
+ 
+
+ align:start position:0%
+room temperature. At room temp, at room
+temp, the fraction, the fraction in the
+
+ align:start position:0%
+temp, the fraction, the fraction in the
+ 
+
+ align:start position:0%
+temp, the fraction, the fraction in the
+conduction band is about 10 the minus19.
+
+ align:start position:0%
+conduction band is about 10 the minus19.
+ 
+
+ align:start position:0%
+conduction band is about 10 the minus19.
+There's so few of them you can give each
+
+ align:start position:0%
+There's so few of them you can give each
+ 
+
+ align:start position:0%
+There's so few of them you can give each
+of them a name. So there's almost no
+
+ align:start position:0%
+of them a name. So there's almost no
+ 
+
+ align:start position:0%
+of them a name. So there's almost no
+conduction. Silicon at room temperature
+
+ align:start position:0%
+conduction. Silicon at room temperature
+ 
+
+ align:start position:0%
+conduction. Silicon at room temperature
+is an insulator. So if we want to get
+
+ align:start position:0%
+is an insulator. So if we want to get
+ 
+
+ align:start position:0%
+is an insulator. So if we want to get
+some conductivity, are we going to heat
+
+ align:start position:0%
+some conductivity, are we going to heat
+ 
+
+ align:start position:0%
+some conductivity, are we going to heat
+our computers up to such a high
+
+ align:start position:0%
+our computers up to such a high
+ 
+
+ align:start position:0%
+our computers up to such a high
+temperature? I don't think so. So we
+
+ align:start position:0%
+temperature? I don't think so. So we
+ 
+
+ align:start position:0%
+temperature? I don't think so. So we
+need some other way of populating the
+
+ align:start position:0%
+need some other way of populating the
+ 
+
+ align:start position:0%
+need some other way of populating the
+conduction band. And we're going to do
+
+ align:start position:0%
+conduction band. And we're going to do
+ 
+
+ align:start position:0%
+conduction band. And we're going to do
+one other mode of promotion. We've
+
+ align:start position:0%
+one other mode of promotion. We've
+ 
+
+ align:start position:0%
+one other mode of promotion. We've
+looked at photoexitation, thermal
+
+ align:start position:0%
+looked at photoexitation, thermal
+ 
+
+ align:start position:0%
+looked at photoexitation, thermal
+excitation, and the third mode is chemo
+
+ align:start position:0%
+excitation, and the third mode is chemo
+ 
+
+ align:start position:0%
+excitation, and the third mode is chemo
+excitation.
+
+ align:start position:0%
+excitation.
+ 
+
+ align:start position:0%
+excitation.
+Cheoexitation. What we're going to do is
+
+ align:start position:0%
+Cheoexitation. What we're going to do is
+ 
+
+ align:start position:0%
+Cheoexitation. What we're going to do is
+we're going to get
+
+ align:start position:0%
+we're going to get
+ 
+
+ align:start position:0%
+we're going to get
+carrier carrier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+injection by introducing
+
+ align:start position:0%
+injection by introducing
+ 
+
+ align:start position:0%
+injection by introducing
+impurities by introducing impurities.
+
+ align:start position:0%
+impurities by introducing impurities.
+ 
+
+ align:start position:0%
+impurities by introducing impurities.
+And I know you're sitting there
+
+ align:start position:0%
+And I know you're sitting there
+ 
+
+ align:start position:0%
+And I know you're sitting there
+thinking, he's crazy. We just spent all
+
+ align:start position:0%
+thinking, he's crazy. We just spent all
+ 
+
+ align:start position:0%
+thinking, he's crazy. We just spent all
+of this time and money making silicon
+
+ align:start position:0%
+of this time and money making silicon
+ 
+
+ align:start position:0%
+of this time and money making silicon
+69's purity and now we're going to start
+
+ align:start position:0%
+69's purity and now we're going to start
+ 
+
+ align:start position:0%
+69's purity and now we're going to start
+throwing impurities into it. Well,
+
+ align:start position:0%
+throwing impurities into it. Well,
+ 
+
+ align:start position:0%
+throwing impurities into it. Well,
+there's two kinds of impurities in this
+
+ align:start position:0%
+there's two kinds of impurities in this
+ 
+
+ align:start position:0%
+there's two kinds of impurities in this
+world. Two kinds of impurities. There
+
+ align:start position:0%
+world. Two kinds of impurities. There
+ 
+
+ align:start position:0%
+world. Two kinds of impurities. There
+are good impurities and bad impurities.
+
+ align:start position:0%
+are good impurities and bad impurities.
+ 
+
+ align:start position:0%
+are good impurities and bad impurities.
+All right, the good impurities are
+
+ align:start position:0%
+All right, the good impurities are
+ 
+
+ align:start position:0%
+All right, the good impurities are
+called dopants. These are the ones that
+
+ align:start position:0%
+called dopants. These are the ones that
+ 
+
+ align:start position:0%
+called dopants. These are the ones that
+are there desiraably. Okay, so dopants
+
+ align:start position:0%
+are there desiraably. Okay, so dopants
+ 
+
+ align:start position:0%
+are there desiraably. Okay, so dopants
+are good guys. And then there are other
+
+ align:start position:0%
+are good guys. And then there are other
+ 
+
+ align:start position:0%
+are good guys. And then there are other
+ones that are called
+
+ align:start position:0%
+ones that are called
+ 
+
+ align:start position:0%
+ones that are called
+contaminants. Contaminants. And these
+
+ align:start position:0%
+contaminants. Contaminants. And these
+ 
+
+ align:start position:0%
+contaminants. Contaminants. And these
+are undesirable
+
+ align:start position:0%
+are undesirable
+ 
+
+ align:start position:0%
+are undesirable
+impurities. So we don't want
+
+ align:start position:0%
+impurities. So we don't want
+ 
+
+ align:start position:0%
+impurities. So we don't want
+contaminants. So we're going to look at
+
+ align:start position:0%
+contaminants. So we're going to look at
+ 
+
+ align:start position:0%
+contaminants. So we're going to look at
+dopens. And this is a really important
+
+ align:start position:0%
+dopens. And this is a really important
+ 
+
+ align:start position:0%
+dopens. And this is a really important
+lesson right now that I'm teaching you.
+
+ align:start position:0%
+lesson right now that I'm teaching you.
+ 
+
+ align:start position:0%
+lesson right now that I'm teaching you.
+What I'm showing you for the first time
+
+ align:start position:0%
+What I'm showing you for the first time
+ 
+
+ align:start position:0%
+What I'm showing you for the first time
+in 3091 is how we can use chemistry to
+
+ align:start position:0%
+in 3091 is how we can use chemistry to
+ 
+
+ align:start position:0%
+in 3091 is how we can use chemistry to
+alter the performance of a material. I'm
+
+ align:start position:0%
+alter the performance of a material. I'm
+ 
+
+ align:start position:0%
+alter the performance of a material. I'm
+going to take plain high purity silicon
+
+ align:start position:0%
+going to take plain high purity silicon
+ 
+
+ align:start position:0%
+going to take plain high purity silicon
+which is an insulator at room
+
+ align:start position:0%
+which is an insulator at room
+ 
+
+ align:start position:0%
+which is an insulator at room
+temperature and by operating on its
+
+ align:start position:0%
+temperature and by operating on its
+ 
+
+ align:start position:0%
+temperature and by operating on its
+chemical composition give it properties
+
+ align:start position:0%
+chemical composition give it properties
+ 
+
+ align:start position:0%
+chemical composition give it properties
+that it cannot possess otherwise. So
+
+ align:start position:0%
+that it cannot possess otherwise. So
+ 
+
+ align:start position:0%
+that it cannot possess otherwise. So
+this is a paradigm. This is a paradigm
+
+ align:start position:0%
+this is a paradigm. This is a paradigm
+ 
+
+ align:start position:0%
+this is a paradigm. This is a paradigm
+for solid state chemistry. You want
+
+ align:start position:0%
+for solid state chemistry. You want
+ 
+
+ align:start position:0%
+for solid state chemistry. You want
+something that's got a higher yield
+
+ align:start position:0%
+something that's got a higher yield
+ 
+
+ align:start position:0%
+something that's got a higher yield
+strength will change its composition.
+
+ align:start position:0%
+strength will change its composition.
+ 
+
+ align:start position:0%
+strength will change its composition.
+You want something that's got a higher
+
+ align:start position:0%
+You want something that's got a higher
+ 
+
+ align:start position:0%
+You want something that's got a higher
+conductivity will change its
+
+ align:start position:0%
+conductivity will change its
+ 
+
+ align:start position:0%
+conductivity will change its
+composition. That's different. That's
+
+ align:start position:0%
+composition. That's different. That's
+ 
+
+ align:start position:0%
+composition. That's different. That's
+different. Okay. So this is an
+
+ align:start position:0%
+different. Okay. So this is an
+ 
+
+ align:start position:0%
+different. Okay. So this is an
+engineered material. This will be
+
+ align:start position:0%
+engineered material. This will be
+ 
+
+ align:start position:0%
+engineered material. This will be
+engineered material. And how is it
+
+ align:start position:0%
+engineered material. And how is it
+ 
+
+ align:start position:0%
+engineered material. And how is it
+engineered? Engineered material. What
+
+ align:start position:0%
+engineered? Engineered material. What
+ 
+
+ align:start position:0%
+engineered? Engineered material. What
+we're getting is
+
+ align:start position:0%
+we're getting is
+ 
+
+ align:start position:0%
+we're getting is
+via via chemical
+
+ align:start position:0%
+via via chemical
+ 
+
+ align:start position:0%
+via via chemical
+change. Via chemical change. Purposeful
+
+ align:start position:0%
+change. Via chemical change. Purposeful
+ 
+
+ align:start position:0%
+change. Via chemical change. Purposeful
+chemical change. So we're getting if you
+
+ align:start position:0%
+chemical change. So we're getting if you
+ 
+
+ align:start position:0%
+chemical change. So we're getting if you
+like tailored
+
+ align:start position:0%
+like tailored
+ 
+
+ align:start position:0%
+like tailored
+composition. Tailored
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composition. Tailored composition to
+
+ align:start position:0%
+composition. Tailored composition to
+ 
+
+ align:start position:0%
+composition. Tailored composition to
+give targeted properties.
+
+ align:start position:0%
+give targeted properties.
+ 
+
+ align:start position:0%
+give targeted properties.
+And this is the this is what underlies
+
+ align:start position:0%
+And this is the this is what underlies
+ 
+
+ align:start position:0%
+And this is the this is what underlies
+material science. If you don't see what
+
+ align:start position:0%
+material science. If you don't see what
+ 
+
+ align:start position:0%
+material science. If you don't see what
+you like, make it. And how do you make
+
+ align:start position:0%
+you like, make it. And how do you make
+ 
+
+ align:start position:0%
+you like, make it. And how do you make
+it? By understanding the relationship
+
+ align:start position:0%
+it? By understanding the relationship
+ 
+
+ align:start position:0%
+it? By understanding the relationship
+between electronic structure, bonding,
+
+ align:start position:0%
+between electronic structure, bonding,
+ 
+
+ align:start position:0%
+between electronic structure, bonding,
+and ultimately properties. So here's
+
+ align:start position:0%
+and ultimately properties. So here's
+ 
+
+ align:start position:0%
+and ultimately properties. So here's
+what the gambit is. Now I'm I'm going to
+
+ align:start position:0%
+what the gambit is. Now I'm I'm going to
+ 
+
+ align:start position:0%
+what the gambit is. Now I'm I'm going to
+talk only about elemental
+
+ align:start position:0%
+talk only about elemental
+ 
+
+ align:start position:0%
+talk only about elemental
+semiconductors. So in the case of in
+
+ align:start position:0%
+semiconductors. So in the case of in
+ 
+
+ align:start position:0%
+semiconductors. So in the case of in
+case of
+
+ align:start position:0%
+case of
+ 
+
+ align:start position:0%
+case of
+silicon and germanmanium I'm just going
+
+ align:start position:0%
+silicon and germanmanium I'm just going
+ 
+
+ align:start position:0%
+silicon and germanmanium I'm just going
+to red restrict today to silicon and
+
+ align:start position:0%
+to red restrict today to silicon and
+ 
+
+ align:start position:0%
+to red restrict today to silicon and
+germanmanium and that's not such a bad
+
+ align:start position:0%
+germanmanium and that's not such a bad
+ 
+
+ align:start position:0%
+germanmanium and that's not such a bad
+restriction since we're in the silicon
+
+ align:start position:0%
+restriction since we're in the silicon
+ 
+
+ align:start position:0%
+restriction since we're in the silicon
+age. All of your micro devices contain
+
+ align:start position:0%
+age. All of your micro devices contain
+ 
+
+ align:start position:0%
+age. All of your micro devices contain
+silicon. So this is pretty good. So
+
+ align:start position:0%
+silicon. So this is pretty good. So
+ 
+
+ align:start position:0%
+silicon. So this is pretty good. So
+here's the gambit. You introduce
+
+ align:start position:0%
+here's the gambit. You introduce
+ 
+
+ align:start position:0%
+here's the gambit. You introduce
+alovoent
+
+ align:start position:0%
+alovoent
+ 
+
+ align:start position:0%
+alovoent
+impurities. Introduce
+
+ align:start position:0%
+impurities. Introduce
+ 
+
+ align:start position:0%
+impurities. Introduce
+aloalent
+
+ align:start position:0%
+aloalent
+ 
+
+ align:start position:0%
+aloalent
+impurities. What do I mean alovalent?
+
+ align:start position:0%
+impurities. What do I mean alovalent?
+ 
+
+ align:start position:0%
+impurities. What do I mean alovalent?
+Alio is the same as the Latin word for
+
+ align:start position:0%
+Alio is the same as the Latin word for
+ 
+
+ align:start position:0%
+Alio is the same as the Latin word for
+alias other. So we we are going to
+
+ align:start position:0%
+alias other. So we we are going to
+ 
+
+ align:start position:0%
+alias other. So we we are going to
+introduce impurities that have a
+
+ align:start position:0%
+introduce impurities that have a
+ 
+
+ align:start position:0%
+introduce impurities that have a
+different veilance from silicon and
+
+ align:start position:0%
+different veilance from silicon and
+ 
+
+ align:start position:0%
+different veilance from silicon and
+germanmanium. Silicon and germanmanium
+
+ align:start position:0%
+germanmanium. Silicon and germanmanium
+ 
+
+ align:start position:0%
+germanmanium. Silicon and germanmanium
+are group four or group 14 if you want
+
+ align:start position:0%
+are group four or group 14 if you want
+ 
+
+ align:start position:0%
+are group four or group 14 if you want
+to use upupac notation. So what I'm
+
+ align:start position:0%
+to use upupac notation. So what I'm
+ 
+
+ align:start position:0%
+to use upupac notation. So what I'm
+going to do is introduce something else.
+
+ align:start position:0%
+going to do is introduce something else.
+ 
+
+ align:start position:0%
+going to do is introduce something else.
+I'll give you an example. So and and the
+
+ align:start position:0%
+I'll give you an example. So and and the
+ 
+
+ align:start position:0%
+I'll give you an example. So and and the
+purpose of introducing alioent
+
+ align:start position:0%
+purpose of introducing alioent
+ 
+
+ align:start position:0%
+purpose of introducing alioent
+impurities is to
+
+ align:start position:0%
+impurities is to
+ 
+
+ align:start position:0%
+impurities is to
+cause cause electron
+
+ align:start position:0%
+cause cause electron
+ 
+
+ align:start position:0%
+cause cause electron
+donation or electron
+
+ align:start position:0%
+donation or electron
+ 
+
+ align:start position:0%
+donation or electron
+consumption. And how's that going to
+
+ align:start position:0%
+consumption. And how's that going to
+ 
+
+ align:start position:0%
+consumption. And how's that going to
+work? Well, you'll see it best in
+
+ align:start position:0%
+work? Well, you'll see it best in
+ 
+
+ align:start position:0%
+work? Well, you'll see it best in
+action. So here's a simple example.
+
+ align:start position:0%
+action. So here's a simple example.
+ 
+
+ align:start position:0%
+action. So here's a simple example.
+Let's put phosphorus in silicon.
+
+ align:start position:0%
+Let's put phosphorus in silicon.
+ 
+
+ align:start position:0%
+Let's put phosphorus in silicon.
+Phosphorus, as you know, is group 15 or
+
+ align:start position:0%
+Phosphorus, as you know, is group 15 or
+ 
+
+ align:start position:0%
+Phosphorus, as you know, is group 15 or
+group five. So it's got five veence
+
+ align:start position:0%
+group five. So it's got five veence
+ 
+
+ align:start position:0%
+group five. So it's got five veence
+electrons. And let's first look at the
+
+ align:start position:0%
+electrons. And let's first look at the
+ 
+
+ align:start position:0%
+electrons. And let's first look at the
+cartisian world. So here's silicon. It's
+
+ align:start position:0%
+cartisian world. So here's silicon. It's
+ 
+
+ align:start position:0%
+cartisian world. So here's silicon. It's
+sp3 hybridized and it forms a
+
+ align:start position:0%
+sp3 hybridized and it forms a
+ 
+
+ align:start position:0%
+sp3 hybridized and it forms a
+diamondlike diamondlike solid, right?
+
+ align:start position:0%
+diamondlike diamondlike solid, right?
+ 
+
+ align:start position:0%
+diamondlike diamondlike solid, right?
+Diamondlike
+
+ align:start position:0%
+Diamondlike
+ 
+
+ align:start position:0%
+Diamondlike
+solid. So it's crystallin. It's regular
+
+ align:start position:0%
+solid. So it's crystallin. It's regular
+ 
+
+ align:start position:0%
+solid. So it's crystallin. It's regular
+arrays
+
+ align:start position:0%
+arrays
+ 
+
+ align:start position:0%
+arrays
+silicons at all of the corners of the
+
+ align:start position:0%
+silicons at all of the corners of the
+ 
+
+ align:start position:0%
+silicons at all of the corners of the
+tetrahedra. And on and on it goes. I'll
+
+ align:start position:0%
+tetrahedra. And on and on it goes. I'll
+ 
+
+ align:start position:0%
+tetrahedra. And on and on it goes. I'll
+give about three of these.
+
+ align:start position:0%
+give about three of these.
+ 
+
+ align:start position:0%
+give about three of these.
+Okay. So now what happens if I introduce
+
+ align:start position:0%
+Okay. So now what happens if I introduce
+ 
+
+ align:start position:0%
+Okay. So now what happens if I introduce
+phosphorus? If I introduce phosphorus,
+
+ align:start position:0%
+phosphorus? If I introduce phosphorus,
+ 
+
+ align:start position:0%
+phosphorus? If I introduce phosphorus,
+the phosphorus actually goes in and
+
+ align:start position:0%
+the phosphorus actually goes in and
+ 
+
+ align:start position:0%
+the phosphorus actually goes in and
+substitutes for silicon. So the
+
+ align:start position:0%
+substitutes for silicon. So the
+ 
+
+ align:start position:0%
+substitutes for silicon. So the
+phosphorus phosphorus substitutes. It
+
+ align:start position:0%
+phosphorus phosphorus substitutes. It
+ 
+
+ align:start position:0%
+phosphorus phosphorus substitutes. It
+doesn't go and sit in some void space.
+
+ align:start position:0%
+doesn't go and sit in some void space.
+ 
+
+ align:start position:0%
+doesn't go and sit in some void space.
+It actually
+
+ align:start position:0%
+It actually
+ 
+
+ align:start position:0%
+It actually
+substitutes substitutes for silicon. Now
+
+ align:start position:0%
+substitutes substitutes for silicon. Now
+ 
+
+ align:start position:0%
+substitutes substitutes for silicon. Now
+if it's going to substitute for silicon,
+
+ align:start position:0%
+if it's going to substitute for silicon,
+ 
+
+ align:start position:0%
+if it's going to substitute for silicon,
+it has to form bonds. Agreed? You can't
+
+ align:start position:0%
+it has to form bonds. Agreed? You can't
+ 
+
+ align:start position:0%
+it has to form bonds. Agreed? You can't
+just sit there. There's no passive
+
+ align:start position:0%
+just sit there. There's no passive
+ 
+
+ align:start position:0%
+just sit there. There's no passive
+observer here. If you want to play, you
+
+ align:start position:0%
+observer here. If you want to play, you
+ 
+
+ align:start position:0%
+observer here. If you want to play, you
+got to bond. So phosphorus comes in with
+
+ align:start position:0%
+got to bond. So phosphorus comes in with
+ 
+
+ align:start position:0%
+got to bond. So phosphorus comes in with
+five veence electrons. So it goes 1 2 3
+
+ align:start position:0%
+five veence electrons. So it goes 1 2 3
+ 
+
+ align:start position:0%
+five veence electrons. So it goes 1 2 3
+four. There's four of its veence
+
+ align:start position:0%
+four. There's four of its veence
+ 
+
+ align:start position:0%
+four. There's four of its veence
+electrons are bonding to the four
+
+ align:start position:0%
+electrons are bonding to the four
+ 
+
+ align:start position:0%
+electrons are bonding to the four
+adjacent silicons. What happens to the
+
+ align:start position:0%
+adjacent silicons. What happens to the
+ 
+
+ align:start position:0%
+adjacent silicons. What happens to the
+fifth veence electron of phosphorus.
+
+ align:start position:0%
+fifth veence electron of phosphorus.
+ 
+
+ align:start position:0%
+fifth veence electron of phosphorus.
+There's no empty orbital in which that
+
+ align:start position:0%
+There's no empty orbital in which that
+ 
+
+ align:start position:0%
+There's no empty orbital in which that
+fifth electron can sit. So that fifth
+
+ align:start position:0%
+fifth electron can sit. So that fifth
+ 
+
+ align:start position:0%
+fifth electron can sit. So that fifth
+electron is sitting here kind of tapping
+
+ align:start position:0%
+electron is sitting here kind of tapping
+ 
+
+ align:start position:0%
+electron is sitting here kind of tapping
+its foot wondering what it's going to
+
+ align:start position:0%
+its foot wondering what it's going to
+ 
+
+ align:start position:0%
+its foot wondering what it's going to
+do. Right now let's go over to the
+
+ align:start position:0%
+do. Right now let's go over to the
+ 
+
+ align:start position:0%
+do. Right now let's go over to the
+energy level diagram. Here's the energy
+
+ align:start position:0%
+energy level diagram. Here's the energy
+ 
+
+ align:start position:0%
+energy level diagram. Here's the energy
+level diagram. This is silicon elemental
+
+ align:start position:0%
+level diagram. This is silicon elemental
+ 
+
+ align:start position:0%
+level diagram. This is silicon elemental
+silicon. Downstairs is veance band.
+
+ align:start position:0%
+silicon. Downstairs is veance band.
+ 
+
+ align:start position:0%
+silicon. Downstairs is veance band.
+Upstairs is conduction band. When we put
+
+ align:start position:0%
+Upstairs is conduction band. When we put
+ 
+
+ align:start position:0%
+Upstairs is conduction band. When we put
+the phosphorus into the silicon, where
+
+ align:start position:0%
+the phosphorus into the silicon, where
+ 
+
+ align:start position:0%
+the phosphorus into the silicon, where
+in energy space, where's the only place
+
+ align:start position:0%
+in energy space, where's the only place
+ 
+
+ align:start position:0%
+in energy space, where's the only place
+that fifth electron can
+
+ align:start position:0%
+that fifth electron can
+ 
+
+ align:start position:0%
+that fifth electron can
+go? There's no room at the end down
+
+ align:start position:0%
+go? There's no room at the end down
+ 
+
+ align:start position:0%
+go? There's no room at the end down
+here. All of the veence orbitals are
+
+ align:start position:0%
+here. All of the veence orbitals are
+ 
+
+ align:start position:0%
+here. All of the veence orbitals are
+filled. So the only place it can go is
+
+ align:start position:0%
+filled. So the only place it can go is
+ 
+
+ align:start position:0%
+filled. So the only place it can go is
+up here in the conduction band. So
+
+ align:start position:0%
+up here in the conduction band. So
+ 
+
+ align:start position:0%
+up here in the conduction band. So
+here's the electron that came from
+
+ align:start position:0%
+here's the electron that came from
+ 
+
+ align:start position:0%
+here's the electron that came from
+phosphorus. that was donated from
+
+ align:start position:0%
+phosphorus. that was donated from
+ 
+
+ align:start position:0%
+phosphorus. that was donated from
+phosphorus. We call phosphorus a donor.
+
+ align:start position:0%
+phosphorus. We call phosphorus a donor.
+ 
+
+ align:start position:0%
+phosphorus. We call phosphorus a donor.
+Okay, this is a donor
+
+ align:start position:0%
+Okay, this is a donor
+ 
+
+ align:start position:0%
+Okay, this is a donor
+electron. And can you see that every
+
+ align:start position:0%
+electron. And can you see that every
+ 
+
+ align:start position:0%
+electron. And can you see that every
+time I throw a phosphorus in, I'm going
+
+ align:start position:0%
+time I throw a phosphorus in, I'm going
+ 
+
+ align:start position:0%
+time I throw a phosphorus in, I'm going
+to get an extra electron in the
+
+ align:start position:0%
+to get an extra electron in the
+ 
+
+ align:start position:0%
+to get an extra electron in the
+conduction band. So if I want to
+
+ align:start position:0%
+conduction band. So if I want to
+ 
+
+ align:start position:0%
+conduction band. So if I want to
+increase the conductivity of silicon,
+
+ align:start position:0%
+increase the conductivity of silicon,
+ 
+
+ align:start position:0%
+increase the conductivity of silicon,
+just keep adding
+
+ align:start position:0%
+just keep adding
+ 
+
+ align:start position:0%
+just keep adding
+phosphorus. One for one. Oh, but am I am
+
+ align:start position:0%
+phosphorus. One for one. Oh, but am I am
+ 
+
+ align:start position:0%
+phosphorus. One for one. Oh, but am I am
+I making holes down here? No, I'm not
+
+ align:start position:0%
+I making holes down here? No, I'm not
+ 
+
+ align:start position:0%
+I making holes down here? No, I'm not
+breaking any bonds. In fact, I'm forming
+
+ align:start position:0%
+breaking any bonds. In fact, I'm forming
+ 
+
+ align:start position:0%
+breaking any bonds. In fact, I'm forming
+bonds here. There's an extra electron.
+
+ align:start position:0%
+bonds here. There's an extra electron.
+ 
+
+ align:start position:0%
+bonds here. There's an extra electron.
+Everything's fine. So now I can I've got
+
+ align:start position:0%
+Everything's fine. So now I can I've got
+ 
+
+ align:start position:0%
+Everything's fine. So now I can I've got
+a lever. I can I can dial in how much
+
+ align:start position:0%
+a lever. I can I can dial in how much
+ 
+
+ align:start position:0%
+a lever. I can I can dial in how much
+conductivity I
+
+ align:start position:0%
+conductivity I
+ 
+
+ align:start position:0%
+conductivity I
+want. You want to raise the conductivity
+
+ align:start position:0%
+want. You want to raise the conductivity
+ 
+
+ align:start position:0%
+want. You want to raise the conductivity
+to a certain value. I can tell you how
+
+ align:start position:0%
+to a certain value. I can tell you how
+ 
+
+ align:start position:0%
+to a certain value. I can tell you how
+much phosphorus to add to get to that
+
+ align:start position:0%
+much phosphorus to add to get to that
+ 
+
+ align:start position:0%
+much phosphorus to add to get to that
+level of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conductivity. And this electron is not
+
+ align:start position:0%
+conductivity. And this electron is not
+ 
+
+ align:start position:0%
+conductivity. And this electron is not
+in a veence band. It's not bound. So it
+
+ align:start position:0%
+in a veence band. It's not bound. So it
+ 
+
+ align:start position:0%
+in a veence band. It's not bound. So it
+can move. So this this goes back to Paul
+
+ align:start position:0%
+can move. So this this goes back to Paul
+ 
+
+ align:start position:0%
+can move. So this this goes back to Paul
+Duda. the these electrons are free to
+
+ align:start position:0%
+Duda. the these electrons are free to
+ 
+
+ align:start position:0%
+Duda. the these electrons are free to
+roam because they're not
+
+ align:start position:0%
+roam because they're not
+ 
+
+ align:start position:0%
+roam because they're not
+bound. But I'm going to show you
+
+ align:start position:0%
+bound. But I'm going to show you
+ 
+
+ align:start position:0%
+bound. But I'm going to show you
+something. I'm going to show you
+
+ align:start position:0%
+something. I'm going to show you
+ 
+
+ align:start position:0%
+something. I'm going to show you
+something really cool. Um how far can
+
+ align:start position:0%
+something really cool. Um how far can
+ 
+
+ align:start position:0%
+something really cool. Um how far can
+that electron roam? So think about it.
+
+ align:start position:0%
+that electron roam? So think about it.
+ 
+
+ align:start position:0%
+that electron roam? So think about it.
+Phosphorus is a five five veent. So it's
+
+ align:start position:0%
+Phosphorus is a five five veent. So it's
+ 
+
+ align:start position:0%
+Phosphorus is a five five veent. So it's
+got an extra proton too, right? So this
+
+ align:start position:0%
+got an extra proton too, right? So this
+ 
+
+ align:start position:0%
+got an extra proton too, right? So this
+phosphorus is a five plus and a land of
+
+ align:start position:0%
+phosphorus is a five plus and a land of
+ 
+
+ align:start position:0%
+phosphorus is a five plus and a land of
+4 plus. So the phosphorus you can think
+
+ align:start position:0%
+4 plus. So the phosphorus you can think
+ 
+
+ align:start position:0%
+4 plus. So the phosphorus you can think
+of as locally plus. And this electron
+
+ align:start position:0%
+of as locally plus. And this electron
+ 
+
+ align:start position:0%
+of as locally plus. And this electron
+that didn't go into any of the veence
+
+ align:start position:0%
+that didn't go into any of the veence
+ 
+
+ align:start position:0%
+that didn't go into any of the veence
+band orbitals, you it's it's locally
+
+ align:start position:0%
+band orbitals, you it's it's locally
+ 
+
+ align:start position:0%
+band orbitals, you it's it's locally
+minus. Duh. An electron is locally
+
+ align:start position:0%
+minus. Duh. An electron is locally
+ 
+
+ align:start position:0%
+minus. Duh. An electron is locally
+minus. That's deep. Okay. So here I've
+
+ align:start position:0%
+minus. That's deep. Okay. So here I've
+ 
+
+ align:start position:0%
+minus. That's deep. Okay. So here I've
+got the phosphorus that's locally plus
+
+ align:start position:0%
+got the phosphorus that's locally plus
+ 
+
+ align:start position:0%
+got the phosphorus that's locally plus
+and I got the electron that's locally
+
+ align:start position:0%
+and I got the electron that's locally
+ 
+
+ align:start position:0%
+and I got the electron that's locally
+minus. Do you know of a model that might
+
+ align:start position:0%
+minus. Do you know of a model that might
+ 
+
+ align:start position:0%
+minus. Do you know of a model that might
+describe the motion of an anchored
+
+ align:start position:0%
+describe the motion of an anchored
+ 
+
+ align:start position:0%
+describe the motion of an anchored
+positive charge with an electron that's
+
+ align:start position:0%
+positive charge with an electron that's
+ 
+
+ align:start position:0%
+positive charge with an electron that's
+free to roam? Do you know of a model
+
+ align:start position:0%
+free to roam? Do you know of a model
+ 
+
+ align:start position:0%
+free to roam? Do you know of a model
+that might talk about such
+
+ align:start position:0%
+that might talk about such
+ 
+
+ align:start position:0%
+that might talk about such
+things? Bore. So let's do something
+
+ align:start position:0%
+things? Bore. So let's do something
+ 
+
+ align:start position:0%
+things? Bore. So let's do something
+really whacked. Suppose we said we took
+
+ align:start position:0%
+really whacked. Suppose we said we took
+ 
+
+ align:start position:0%
+really whacked. Suppose we said we took
+this electron and we said let's let's
+
+ align:start position:0%
+this electron and we said let's let's
+ 
+
+ align:start position:0%
+this electron and we said let's let's
+ask the question if we applied the bore
+
+ align:start position:0%
+ask the question if we applied the bore
+ 
+
+ align:start position:0%
+ask the question if we applied the bore
+model to this pair. What would we come
+
+ align:start position:0%
+model to this pair. What would we come
+ 
+
+ align:start position:0%
+model to this pair. What would we come
+up with? I mean it's going to give us
+
+ align:start position:0%
+up with? I mean it's going to give us
+ 
+
+ align:start position:0%
+up with? I mean it's going to give us
+energies. It's going to give us radi.
+
+ align:start position:0%
+energies. It's going to give us radi.
+ 
+
+ align:start position:0%
+energies. It's going to give us radi.
+It's going to give us velocities. Do you
+
+ align:start position:0%
+It's going to give us velocities. Do you
+ 
+
+ align:start position:0%
+It's going to give us velocities. Do you
+think there might be a relationship to
+
+ align:start position:0%
+think there might be a relationship to
+ 
+
+ align:start position:0%
+think there might be a relationship to
+velocity and mobility and conductivity
+
+ align:start position:0%
+velocity and mobility and conductivity
+ 
+
+ align:start position:0%
+velocity and mobility and conductivity
+and well let's see where it goes. So
+
+ align:start position:0%
+and well let's see where it goes. So
+ 
+
+ align:start position:0%
+and well let's see where it goes. So
+let's go. Um, so what I'm going to do is
+
+ align:start position:0%
+let's go. Um, so what I'm going to do is
+ 
+
+ align:start position:0%
+let's go. Um, so what I'm going to do is
+I'm going to say remember in recall in
+
+ align:start position:0%
+I'm going to say remember in recall in
+ 
+
+ align:start position:0%
+I'm going to say remember in recall in
+hydrogen and atomic hydrogen recall in
+
+ align:start position:0%
+hydrogen and atomic hydrogen recall in
+ 
+
+ align:start position:0%
+hydrogen and atomic hydrogen recall in
+atomic hydrogen the ground state energy
+
+ align:start position:0%
+atomic hydrogen the ground state energy
+ 
+
+ align:start position:0%
+atomic hydrogen the ground state energy
+this is the electron at the bottom of
+
+ align:start position:0%
+this is the electron at the bottom of
+ 
+
+ align:start position:0%
+this is the electron at the bottom of
+the is minus K what we've been calling K
+
+ align:start position:0%
+the is minus K what we've been calling K
+ 
+
+ align:start position:0%
+the is minus K what we've been calling K
+which has this uh full full-blown
+
+ align:start position:0%
+which has this uh full full-blown
+ 
+
+ align:start position:0%
+which has this uh full full-blown
+formula of me to 4 over 8 epsilon0^ 2
+
+ align:start position:0%
+formula of me to 4 over 8 epsilon0^ 2
+ 
+
+ align:start position:0%
+formula of me to 4 over 8 epsilon0^ 2
+h^2 and plug in all the numbers and you
+
+ align:start position:0%
+h^2 and plug in all the numbers and you
+ 
+
+ align:start position:0%
+h^2 and plug in all the numbers and you
+get -3.6 6 electron volts -3.6 electron
+
+ align:start position:0%
+get -3.6 6 electron volts -3.6 electron
+ 
+
+ align:start position:0%
+get -3.6 6 electron volts -3.6 electron
+volts. Now let's think about this. What
+
+ align:start position:0%
+volts. Now let's think about this. What
+ 
+
+ align:start position:0%
+volts. Now let's think about this. What
+we're going to have to make a few
+
+ align:start position:0%
+we're going to have to make a few
+ 
+
+ align:start position:0%
+we're going to have to make a few
+changes. Uh epsilon0 that's the
+
+ align:start position:0%
+changes. Uh epsilon0 that's the
+ 
+
+ align:start position:0%
+changes. Uh epsilon0 that's the
+permitivity of vacuum. But if you're if
+
+ align:start position:0%
+permitivity of vacuum. But if you're if
+ 
+
+ align:start position:0%
+permitivity of vacuum. But if you're if
+you're an electron, you're looking down
+
+ align:start position:0%
+you're an electron, you're looking down
+ 
+
+ align:start position:0%
+you're an electron, you're looking down
+at the phosphorus. It's not just vacuum
+
+ align:start position:0%
+at the phosphorus. It's not just vacuum
+ 
+
+ align:start position:0%
+at the phosphorus. It's not just vacuum
+between you and the central phosphorus.
+
+ align:start position:0%
+between you and the central phosphorus.
+ 
+
+ align:start position:0%
+between you and the central phosphorus.
+There's all this stuff. There's bonds.
+
+ align:start position:0%
+There's all this stuff. There's bonds.
+ 
+
+ align:start position:0%
+There's all this stuff. There's bonds.
+There's silica
+
+ align:start position:0%
+There's silica
+ 
+
+ align:start position:0%
+There's silica
+nuclei. So I got to modify this. I've
+
+ align:start position:0%
+nuclei. So I got to modify this. I've
+ 
+
+ align:start position:0%
+nuclei. So I got to modify this. I've
+got to I've got to change this. So what
+
+ align:start position:0%
+got to I've got to change this. So what
+ 
+
+ align:start position:0%
+got to I've got to change this. So what
+I'm going to do is I'm going to take
+
+ align:start position:0%
+I'm going to do is I'm going to take
+ 
+
+ align:start position:0%
+I'm going to do is I'm going to take
+epsilon0 which is what we have for
+
+ align:start position:0%
+epsilon0 which is what we have for
+ 
+
+ align:start position:0%
+epsilon0 which is what we have for
+vacuum and I'm going to replace it with
+
+ align:start position:0%
+vacuum and I'm going to replace it with
+ 
+
+ align:start position:0%
+vacuum and I'm going to replace it with
+epsilon epsilon of silicon epsilon of
+
+ align:start position:0%
+epsilon epsilon of silicon epsilon of
+ 
+
+ align:start position:0%
+epsilon epsilon of silicon epsilon of
+silicon. Silicon is the host crystal. So
+
+ align:start position:0%
+silicon. Silicon is the host crystal. So
+ 
+
+ align:start position:0%
+silicon. Silicon is the host crystal. So
+what does it what does this capture?
+
+ align:start position:0%
+what does it what does this capture?
+ 
+
+ align:start position:0%
+what does it what does this capture?
+Captures all the bonds all of the
+
+ align:start position:0%
+Captures all the bonds all of the
+ 
+
+ align:start position:0%
+Captures all the bonds all of the
+silicon all of the stuff. Okay. So
+
+ align:start position:0%
+silicon all of the stuff. Okay. So
+ 
+
+ align:start position:0%
+silicon all of the stuff. Okay. So
+that's the the dialectric
+
+ align:start position:0%
+that's the the dialectric
+ 
+
+ align:start position:0%
+that's the the dialectric
+constant. That's the dialectric
+
+ align:start position:0%
+constant. That's the dialectric
+ 
+
+ align:start position:0%
+constant. That's the dialectric
+constant of the host crystal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And there's one other thing. This is
+
+ align:start position:0%
+And there's one other thing. This is
+ 
+
+ align:start position:0%
+And there's one other thing. This is
+some esoteric physics. I'm just going to
+
+ align:start position:0%
+some esoteric physics. I'm just going to
+ 
+
+ align:start position:0%
+some esoteric physics. I'm just going to
+put it up here without without proof.
+
+ align:start position:0%
+put it up here without without proof.
+ 
+
+ align:start position:0%
+put it up here without without proof.
+When you're in this situation, you don't
+
+ align:start position:0%
+When you're in this situation, you don't
+ 
+
+ align:start position:0%
+When you're in this situation, you don't
+use the the rest mass. There is an
+
+ align:start position:0%
+use the the rest mass. There is an
+ 
+
+ align:start position:0%
+use the the rest mass. There is an
+effective mass. The effective mass and
+
+ align:start position:0%
+effective mass. The effective mass and
+ 
+
+ align:start position:0%
+effective mass. The effective mass and
+that in invokes a slight uh correction.
+
+ align:start position:0%
+that in invokes a slight uh correction.
+ 
+
+ align:start position:0%
+that in invokes a slight uh correction.
+The effective
+
+ align:start position:0%
+The effective
+ 
+
+ align:start position:0%
+The effective
+mass of the electron at the bottom of
+
+ align:start position:0%
+mass of the electron at the bottom of
+ 
+
+ align:start position:0%
+mass of the electron at the bottom of
+the conduction band. Bottom of
+
+ align:start position:0%
+the conduction band. Bottom of
+ 
+
+ align:start position:0%
+the conduction band. Bottom of
+conduction band. This is a minor
+
+ align:start position:0%
+conduction band. This is a minor
+ 
+
+ align:start position:0%
+conduction band. This is a minor
+correction. And the main correction is
+
+ align:start position:0%
+correction. And the main correction is
+ 
+
+ align:start position:0%
+correction. And the main correction is
+getting the dialectric constant. Okay.
+
+ align:start position:0%
+getting the dialectric constant. Okay.
+ 
+
+ align:start position:0%
+getting the dialectric constant. Okay.
+So the second one is there for
+
+ align:start position:0%
+So the second one is there for
+ 
+
+ align:start position:0%
+So the second one is there for
+completeness. Some of you are going to
+
+ align:start position:0%
+completeness. Some of you are going to
+ 
+
+ align:start position:0%
+completeness. Some of you are going to
+look back fondly at at at these notes
+
+ align:start position:0%
+look back fondly at at at these notes
+ 
+
+ align:start position:0%
+look back fondly at at at these notes
+and say yeah we got it. This was good.
+
+ align:start position:0%
+and say yeah we got it. This was good.
+ 
+
+ align:start position:0%
+and say yeah we got it. This was good.
+Otherwise you say how do we lift out the
+
+ align:start position:0%
+Otherwise you say how do we lift out the
+ 
+
+ align:start position:0%
+Otherwise you say how do we lift out the
+effective mass? So can't say that now.
+
+ align:start position:0%
+effective mass? So can't say that now.
+ 
+
+ align:start position:0%
+effective mass? So can't say that now.
+All right. So here's the here are the
+
+ align:start position:0%
+All right. So here's the here are the
+ 
+
+ align:start position:0%
+All right. So here's the here are the
+values for silicon. For silicon the uh
+
+ align:start position:0%
+values for silicon. For silicon the uh
+ 
+
+ align:start position:0%
+values for silicon. For silicon the uh
+dialectric uh constant is 11.7 and the
+
+ align:start position:0%
+dialectric uh constant is 11.7 and the
+ 
+
+ align:start position:0%
+dialectric uh constant is 11.7 and the
+effective mass at the bottom of the
+
+ align:start position:0%
+effective mass at the bottom of the
+ 
+
+ align:start position:0%
+effective mass at the bottom of the
+conduction band is 15th of the rest
+
+ align:start position:0%
+conduction band is 15th of the rest
+ 
+
+ align:start position:0%
+conduction band is 15th of the rest
+mass. So I'm going to plug these values
+
+ align:start position:0%
+mass. So I'm going to plug these values
+ 
+
+ align:start position:0%
+mass. So I'm going to plug these values
+into this equation. And what this gives
+
+ align:start position:0%
+into this equation. And what this gives
+ 
+
+ align:start position:0%
+into this equation. And what this gives
+me is then that the ground state energy
+
+ align:start position:0%
+me is then that the ground state energy
+ 
+
+ align:start position:0%
+me is then that the ground state energy
+of the donor electron is minus K as we
+
+ align:start position:0%
+of the donor electron is minus K as we
+ 
+
+ align:start position:0%
+of the donor electron is minus K as we
+had before and it's going to be
+
+ align:start position:0%
+had before and it's going to be
+ 
+
+ align:start position:0%
+had before and it's going to be
+multiplied by 0.2 on the top and then
+
+ align:start position:0%
+multiplied by 0.2 on the top and then
+ 
+
+ align:start position:0%
+multiplied by 0.2 on the top and then
+I'm going to have an 11.7
+
+ align:start position:0%
+I'm going to have an 11.7
+ 
+
+ align:start position:0%
+I'm going to have an 11.7
+uh squared on the bottom. And that gives
+
+ align:start position:0%
+uh squared on the bottom. And that gives
+ 
+
+ align:start position:0%
+uh squared on the bottom. And that gives
+me minus
+
+ align:start position:0%
+me minus
+ 
+
+ align:start position:0%
+me minus
+0.02 electron volts. 2100s of electron
+
+ align:start position:0%
+0.02 electron volts. 2100s of electron
+ 
+
+ align:start position:0%
+0.02 electron volts. 2100s of electron
+volt.
+
+ align:start position:0%
+volt.
+ 
+
+ align:start position:0%
+volt.
+This quantity has been measured. The
+
+ align:start position:0%
+This quantity has been measured. The
+ 
+
+ align:start position:0%
+This quantity has been measured. The
+measured
+
+ align:start position:0%
+measured
+ 
+
+ align:start position:0%
+measured
+value compare with CF CF
+
+ align:start position:0%
+value compare with CF CF
+ 
+
+ align:start position:0%
+value compare with CF CF
+0.045
+
+ align:start position:0%
+0.045
+ 
+
+ align:start position:0%
+0.045
+EV measured. And you might say, well,
+
+ align:start position:0%
+EV measured. And you might say, well,
+ 
+
+ align:start position:0%
+EV measured. And you might say, well,
+that's more than double that. And I'll
+
+ align:start position:0%
+that's more than double that. And I'll
+ 
+
+ align:start position:0%
+that's more than double that. And I'll
+say, but wait a minute. You know, we
+
+ align:start position:0%
+say, but wait a minute. You know, we
+ 
+
+ align:start position:0%
+say, but wait a minute. You know, we
+started at 13.6 and I took it down to 02
+
+ align:start position:0%
+started at 13.6 and I took it down to 02
+ 
+
+ align:start position:0%
+started at 13.6 and I took it down to 02
+and you're telling me, yeah, but the
+
+ align:start position:0%
+and you're telling me, yeah, but the
+ 
+
+ align:start position:0%
+and you're telling me, yeah, but the
+real value is 04. I said, you don't
+
+ align:start position:0%
+real value is 04. I said, you don't
+ 
+
+ align:start position:0%
+real value is 04. I said, you don't
+appreciate good work. That's what this
+
+ align:start position:0%
+appreciate good work. That's what this
+ 
+
+ align:start position:0%
+appreciate good work. That's what this
+is. Fantastic. This is fantastic with a
+
+ align:start position:0%
+is. Fantastic. This is fantastic with a
+ 
+
+ align:start position:0%
+is. Fantastic. This is fantastic with a
+simple primitive bore model and two
+
+ align:start position:0%
+simple primitive bore model and two
+ 
+
+ align:start position:0%
+simple primitive bore model and two
+minor corrections to zoom into condensed
+
+ align:start position:0%
+minor corrections to zoom into condensed
+ 
+
+ align:start position:0%
+minor corrections to zoom into condensed
+matter and give this
+
+ align:start position:0%
+matter and give this
+ 
+
+ align:start position:0%
+matter and give this
+value. So where is that going to be?
+
+ align:start position:0%
+value. So where is that going to be?
+ 
+
+ align:start position:0%
+value. So where is that going to be?
+Where's that going to be?
+
+ align:start position:0%
+Where's that going to be?
+ 
+
+ align:start position:0%
+Where's that going to be?
+02 south of what? It's going to be here.
+
+ align:start position:0%
+02 south of what? It's going to be here.
+ 
+
+ align:start position:0%
+02 south of what? It's going to be here.
+This is where that lies. This distance
+
+ align:start position:0%
+This is where that lies. This distance
+ 
+
+ align:start position:0%
+This is where that lies. This distance
+here is the
+
+ align:start position:0%
+here is the
+ 
+
+ align:start position:0%
+here is the
+0.02 electron volt difference. You're
+
+ align:start position:0%
+0.02 electron volt difference. You're
+ 
+
+ align:start position:0%
+0.02 electron volt difference. You're
+0.02 002 electron volts below the
+
+ align:start position:0%
+0.02 002 electron volts below the
+ 
+
+ align:start position:0%
+0.02 002 electron volts below the
+conduction band. You're not down here.
+
+ align:start position:0%
+conduction band. You're not down here.
+ 
+
+ align:start position:0%
+conduction band. You're not down here.
+This is veilance. You're up
+
+ align:start position:0%
+This is veilance. You're up
+ 
+
+ align:start position:0%
+This is veilance. You're up
+top and the electrons sitting in there
+
+ align:start position:0%
+top and the electrons sitting in there
+ 
+
+ align:start position:0%
+top and the electrons sitting in there
+because that's a ground state. So now
+
+ align:start position:0%
+because that's a ground state. So now
+ 
+
+ align:start position:0%
+because that's a ground state. So now
+you're saying, "Well, that's really
+
+ align:start position:0%
+you're saying, "Well, that's really
+ 
+
+ align:start position:0%
+you're saying, "Well, that's really
+great, Satway. Now you've got an
+
+ align:start position:0%
+great, Satway. Now you've got an
+ 
+
+ align:start position:0%
+great, Satway. Now you've got an
+electron sitting in an orbital. Now, how
+
+ align:start position:0%
+electron sitting in an orbital. Now, how
+ 
+
+ align:start position:0%
+electron sitting in an orbital. Now, how
+are you going to get it up to here?" I
+
+ align:start position:0%
+are you going to get it up to here?" I
+ 
+
+ align:start position:0%
+are you going to get it up to here?" I
+got an answer for that. But first, first
+
+ align:start position:0%
+got an answer for that. But first, first
+ 
+
+ align:start position:0%
+got an answer for that. But first, first
+look at this. I I couldn't resist this
+
+ align:start position:0%
+look at this. I I couldn't resist this
+ 
+
+ align:start position:0%
+look at this. I I couldn't resist this
+derivation. I said, "What about the
+
+ align:start position:0%
+derivation. I said, "What about the
+ 
+
+ align:start position:0%
+derivation. I said, "What about the
+radius of the orbit? How far is that
+
+ align:start position:0%
+radius of the orbit? How far is that
+ 
+
+ align:start position:0%
+radius of the orbit? How far is that
+electron away from the phosphorus? You
+
+ align:start position:0%
+electron away from the phosphorus? You
+ 
+
+ align:start position:0%
+electron away from the phosphorus? You
+know, is it in tight? Is it in moving
+
+ align:start position:0%
+know, is it in tight? Is it in moving
+ 
+
+ align:start position:0%
+know, is it in tight? Is it in moving
+around like this? Or is it way way out
+
+ align:start position:0%
+around like this? Or is it way way out
+ 
+
+ align:start position:0%
+around like this? Or is it way way out
+here? Doesn't that intrigue
+
+ align:start position:0%
+here? Doesn't that intrigue
+ 
+
+ align:start position:0%
+here? Doesn't that intrigue
+you? Sure intrigues me. So, here's what
+
+ align:start position:0%
+you? Sure intrigues me. So, here's what
+ 
+
+ align:start position:0%
+you? Sure intrigues me. So, here's what
+I did. I said, "Okay, the R1, the radius
+
+ align:start position:0%
+I did. I said, "Okay, the R1, the radius
+ 
+
+ align:start position:0%
+I did. I said, "Okay, the R1, the radius
+of this ground state was going to be
+
+ align:start position:0%
+of this ground state was going to be
+ 
+
+ align:start position:0%
+of this ground state was going to be
+given by the bore radius times the
+
+ align:start position:0%
+given by the bore radius times the
+ 
+
+ align:start position:0%
+given by the bore radius times the
+modified dialectric constant divided by
+
+ align:start position:0%
+modified dialectric constant divided by
+ 
+
+ align:start position:0%
+modified dialectric constant divided by
+the modified mass. And when you plug in
+
+ align:start position:0%
+the modified mass. And when you plug in
+ 
+
+ align:start position:0%
+the modified mass. And when you plug in
+the numbers, you get 30 angstroms." 30
+
+ align:start position:0%
+the numbers, you get 30 angstroms." 30
+ 
+
+ align:start position:0%
+the numbers, you get 30 angstroms." 30
+angstroms. We say, well, I don't know
+
+ align:start position:0%
+angstroms. We say, well, I don't know
+ 
+
+ align:start position:0%
+angstroms. We say, well, I don't know
+what the silicon silicon distance is.
+
+ align:start position:0%
+what the silicon silicon distance is.
+ 
+
+ align:start position:0%
+what the silicon silicon distance is.
+Well, what do you think it is? I mean,
+
+ align:start position:0%
+Well, what do you think it is? I mean,
+ 
+
+ align:start position:0%
+Well, what do you think it is? I mean,
+you know, it's got to be on the order of
+
+ align:start position:0%
+you know, it's got to be on the order of
+ 
+
+ align:start position:0%
+you know, it's got to be on the order of
+a couple of angstroms. So, if you
+
+ align:start position:0%
+a couple of angstroms. So, if you
+ 
+
+ align:start position:0%
+a couple of angstroms. So, if you
+compare that, the silicon silicon
+
+ align:start position:0%
+compare that, the silicon silicon
+ 
+
+ align:start position:0%
+compare that, the silicon silicon
+distance is
+
+ align:start position:0%
+distance is
+ 
+
+ align:start position:0%
+distance is
+2.35 angstroms. So, this electron's way
+
+ align:start position:0%
+2.35 angstroms. So, this electron's way
+ 
+
+ align:start position:0%
+2.35 angstroms. So, this electron's way
+way zooming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around.
+
+ align:start position:0%
+around.
+ 
+
+ align:start position:0%
+around.
+So, fantastic what we've learned here.
+
+ align:start position:0%
+So, fantastic what we've learned here.
+ 
+
+ align:start position:0%
+So, fantastic what we've learned here.
+Now, let's look at this. So, we've got
+
+ align:start position:0%
+Now, let's look at this. So, we've got
+ 
+
+ align:start position:0%
+Now, let's look at this. So, we've got
+electrons sitting in this uh uh energy
+
+ align:start position:0%
+electrons sitting in this uh uh energy
+ 
+
+ align:start position:0%
+electrons sitting in this uh uh energy
+level down below. And now what happens?
+
+ align:start position:0%
+level down below. And now what happens?
+ 
+
+ align:start position:0%
+level down below. And now what happens?
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+um how do how do I get this thing to how
+
+ align:start position:0%
+um how do how do I get this thing to how
+ 
+
+ align:start position:0%
+um how do how do I get this thing to how
+do I get this thing to move out? What
+
+ align:start position:0%
+do I get this thing to move out? What
+ 
+
+ align:start position:0%
+do I get this thing to move out? What
+I'm going to do to make it move out?
+
+ align:start position:0%
+I'm going to do to make it move out?
+ 
+
+ align:start position:0%
+I'm going to do to make it move out?
+Well, what do I have? I know that the
+
+ align:start position:0%
+Well, what do I have? I know that the
+ 
+
+ align:start position:0%
+Well, what do I have? I know that the
+energy is 0.02. But what's the comp how
+
+ align:start position:0%
+energy is 0.02. But what's the comp how
+ 
+
+ align:start position:0%
+energy is 0.02. But what's the comp how
+do I compare this energy with compare
+
+ align:start position:0%
+do I compare this energy with compare
+ 
+
+ align:start position:0%
+do I compare this energy with compare
+this with the thermal energy? Ether
+
+ align:start position:0%
+this with the thermal energy? Ether
+ 
+
+ align:start position:0%
+this with the thermal energy? Ether
+thermal is on the order of 0.025140th
+
+ align:start position:0%
+thermal is on the order of 0.025140th
+ 
+
+ align:start position:0%
+thermal is on the order of 0.025140th
+025140th of an EV. So the thermal energy
+
+ align:start position:0%
+025140th of an EV. So the thermal energy
+ 
+
+ align:start position:0%
+025140th of an EV. So the thermal energy
+is so high at room temperature that it's
+
+ align:start position:0%
+is so high at room temperature that it's
+ 
+
+ align:start position:0%
+is so high at room temperature that it's
+able to promote these. And by the way,
+
+ align:start position:0%
+able to promote these. And by the way,
+ 
+
+ align:start position:0%
+able to promote these. And by the way,
+you know, if this war model works for
+
+ align:start position:0%
+you know, if this war model works for
+ 
+
+ align:start position:0%
+you know, if this war model works for
+ground state, what would happen if I
+
+ align:start position:0%
+ground state, what would happen if I
+ 
+
+ align:start position:0%
+ground state, what would happen if I
+were to blow this up? Can you imagine
+
+ align:start position:0%
+were to blow this up? Can you imagine
+ 
+
+ align:start position:0%
+were to blow this up? Can you imagine
+that? I have, if this is the conduction
+
+ align:start position:0%
+that? I have, if this is the conduction
+ 
+
+ align:start position:0%
+that? I have, if this is the conduction
+band, I get all of the energy
+
+ align:start position:0%
+band, I get all of the energy
+ 
+
+ align:start position:0%
+band, I get all of the energy
+levels. I get the whole bore energy
+
+ align:start position:0%
+levels. I get the whole bore energy
+ 
+
+ align:start position:0%
+levels. I get the whole bore energy
+state here. I get ground state n= 2, n=
+
+ align:start position:0%
+state here. I get ground state n= 2, n=
+ 
+
+ align:start position:0%
+state here. I get ground state n= 2, n=
+3, all the way
+
+ align:start position:0%
+3, all the way
+ 
+
+ align:start position:0%
+3, all the way
+up. And now I have enough energy from
+
+ align:start position:0%
+up. And now I have enough energy from
+ 
+
+ align:start position:0%
+up. And now I have enough energy from
+thermal energy to take all of these
+
+ align:start position:0%
+thermal energy to take all of these
+ 
+
+ align:start position:0%
+thermal energy to take all of these
+electrons because each one of these
+
+ align:start position:0%
+electrons because each one of these
+ 
+
+ align:start position:0%
+electrons because each one of these
+comes in because it's a separate
+
+ align:start position:0%
+comes in because it's a separate
+ 
+
+ align:start position:0%
+comes in because it's a separate
+phosphorus and they're far enough apart.
+
+ align:start position:0%
+phosphorus and they're far enough apart.
+ 
+
+ align:start position:0%
+phosphorus and they're far enough apart.
+They're separate states. All of these
+
+ align:start position:0%
+They're separate states. All of these
+ 
+
+ align:start position:0%
+They're separate states. All of these
+can get promoted. What do we call this
+
+ align:start position:0%
+can get promoted. What do we call this
+ 
+
+ align:start position:0%
+can get promoted. What do we call this
+action? If I take a ground state
+
+ align:start position:0%
+action? If I take a ground state
+ 
+
+ align:start position:0%
+action? If I take a ground state
+electron and hydrogen and I get it right
+
+ align:start position:0%
+electron and hydrogen and I get it right
+ 
+
+ align:start position:0%
+electron and hydrogen and I get it right
+out of all of this set of energy levels,
+
+ align:start position:0%
+out of all of this set of energy levels,
+ 
+
+ align:start position:0%
+out of all of this set of energy levels,
+what do we call that process? We take
+
+ align:start position:0%
+what do we call that process? We take
+ 
+
+ align:start position:0%
+what do we call that process? We take
+the electron and we throw it out of the
+
+ align:start position:0%
+the electron and we throw it out of the
+ 
+
+ align:start position:0%
+the electron and we throw it out of the
+system. Ionization. And that's exactly
+
+ align:start position:0%
+system. Ionization. And that's exactly
+ 
+
+ align:start position:0%
+system. Ionization. And that's exactly
+what the electrical engineers call this
+
+ align:start position:0%
+what the electrical engineers call this
+ 
+
+ align:start position:0%
+what the electrical engineers call this
+process. They call the thermal
+
+ align:start position:0%
+process. They call the thermal
+ 
+
+ align:start position:0%
+process. They call the thermal
+excitation of the donor electrons
+
+ align:start position:0%
+excitation of the donor electrons
+ 
+
+ align:start position:0%
+excitation of the donor electrons
+ionization. So for all intents and
+
+ align:start position:0%
+ionization. So for all intents and
+ 
+
+ align:start position:0%
+ionization. So for all intents and
+purposes because ether thermal is on the
+
+ align:start position:0%
+purposes because ether thermal is on the
+ 
+
+ align:start position:0%
+purposes because ether thermal is on the
+order of this e of the donor electron we
+
+ align:start position:0%
+order of this e of the donor electron we
+ 
+
+ align:start position:0%
+order of this e of the donor electron we
+can we can
+
+ align:start position:0%
+can we can
+ 
+
+ align:start position:0%
+can we can
+assume assume
+
+ align:start position:0%
+assume assume
+ 
+
+ align:start position:0%
+assume assume
+complete and I'm going to use an
+
+ align:start position:0%
+complete and I'm going to use an
+ 
+
+ align:start position:0%
+complete and I'm going to use an
+electrical engineering term here because
+
+ align:start position:0%
+electrical engineering term here because
+ 
+
+ align:start position:0%
+electrical engineering term here because
+I think I'm still teaching in an
+
+ align:start position:0%
+I think I'm still teaching in an
+ 
+
+ align:start position:0%
+I think I'm still teaching in an
+engineering school complete
+
+ align:start position:0%
+engineering school complete
+ 
+
+ align:start position:0%
+engineering school complete
+ionization of donor electrons.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh, this is fantastic. That's fantastic.
+
+ align:start position:0%
+Oh, this is fantastic. That's fantastic.
+ 
+
+ align:start position:0%
+Oh, this is fantastic. That's fantastic.
+They're all ionized. So now, last day I
+
+ align:start position:0%
+They're all ionized. So now, last day I
+ 
+
+ align:start position:0%
+They're all ionized. So now, last day I
+said that the total number of electrons
+
+ align:start position:0%
+said that the total number of electrons
+ 
+
+ align:start position:0%
+said that the total number of electrons
+in the conduction band would equal the
+
+ align:start position:0%
+in the conduction band would equal the
+ 
+
+ align:start position:0%
+in the conduction band would equal the
+number of electrons from the host
+
+ align:start position:0%
+number of electrons from the host
+ 
+
+ align:start position:0%
+number of electrons from the host
+silica, right? host silicon due to
+
+ align:start position:0%
+silica, right? host silicon due to
+ 
+
+ align:start position:0%
+silica, right? host silicon due to
+thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excitation plus it's going to be the
+
+ align:start position:0%
+excitation plus it's going to be the
+ 
+
+ align:start position:0%
+excitation plus it's going to be the
+number of electrons from the
+
+ align:start position:0%
+number of electrons from the
+ 
+
+ align:start position:0%
+number of electrons from the
+impur
+
+ align:start position:0%
+impur
+ 
+
+ align:start position:0%
+impur
+phosphorus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we know this requires eg on the
+
+ align:start position:0%
+okay and we know this requires eg on the
+ 
+
+ align:start position:0%
+okay and we know this requires eg on the
+order of about 1.1 eV so very few of
+
+ align:start position:0%
+order of about 1.1 eV so very few of
+ 
+
+ align:start position:0%
+order of about 1.1 eV so very few of
+these are contributed there's almost no
+
+ align:start position:0%
+these are contributed there's almost no
+ 
+
+ align:start position:0%
+these are contributed there's almost no
+promotion of electron
+
+ align:start position:0%
+promotion of electron
+ 
+
+ align:start position:0%
+promotion of electron
+from the veance band to the conduction
+
+ align:start position:0%
+from the veance band to the conduction
+ 
+
+ align:start position:0%
+from the veance band to the conduction
+band to leave holes. This is vanishingly
+
+ align:start position:0%
+band to leave holes. This is vanishingly
+ 
+
+ align:start position:0%
+band to leave holes. This is vanishingly
+small at room temperature in silicon.
+
+ align:start position:0%
+small at room temperature in silicon.
+ 
+
+ align:start position:0%
+small at room temperature in silicon.
+Whereas here because the I'm going to
+
+ align:start position:0%
+Whereas here because the I'm going to
+ 
+
+ align:start position:0%
+Whereas here because the I'm going to
+put in quotation marks the ionization
+
+ align:start position:0%
+put in quotation marks the ionization
+ 
+
+ align:start position:0%
+put in quotation marks the ionization
+energy is on the order of the thermal
+
+ align:start position:0%
+energy is on the order of the thermal
+ 
+
+ align:start position:0%
+energy is on the order of the thermal
+energy we get all the electrons from
+
+ align:start position:0%
+energy we get all the electrons from
+ 
+
+ align:start position:0%
+energy we get all the electrons from
+here. And so in such a material we say
+
+ align:start position:0%
+here. And so in such a material we say
+ 
+
+ align:start position:0%
+here. And so in such a material we say
+that the electrical properties are
+
+ align:start position:0%
+that the electrical properties are
+ 
+
+ align:start position:0%
+that the electrical properties are
+essentially those as from the impur. So
+
+ align:start position:0%
+essentially those as from the impur. So
+ 
+
+ align:start position:0%
+essentially those as from the impur. So
+we send this to zero and we say that
+
+ align:start position:0%
+we send this to zero and we say that
+ 
+
+ align:start position:0%
+we send this to zero and we say that
+such a material exhibits extrinsic
+
+ align:start position:0%
+such a material exhibits extrinsic
+ 
+
+ align:start position:0%
+such a material exhibits extrinsic
+behavior. Exttrinsic
+
+ align:start position:0%
+behavior. Exttrinsic
+ 
+
+ align:start position:0%
+behavior. Exttrinsic
+behavior. Why is it extrinsic? Because
+
+ align:start position:0%
+behavior. Why is it extrinsic? Because
+ 
+
+ align:start position:0%
+behavior. Why is it extrinsic? Because
+the behavior of the the electrical
+
+ align:start position:0%
+the behavior of the the electrical
+ 
+
+ align:start position:0%
+the behavior of the the electrical
+behavior of the silicon is governed by
+
+ align:start position:0%
+behavior of the silicon is governed by
+ 
+
+ align:start position:0%
+behavior of the silicon is governed by
+the impurities that we introduced into
+
+ align:start position:0%
+the impurities that we introduced into
+ 
+
+ align:start position:0%
+the impurities that we introduced into
+the silicon. Okay, extrinsic behavior
+
+ align:start position:0%
+the silicon. Okay, extrinsic behavior
+ 
+
+ align:start position:0%
+the silicon. Okay, extrinsic behavior
+and it is imp or let's call it dopant.
+
+ align:start position:0%
+and it is imp or let's call it dopant.
+ 
+
+ align:start position:0%
+and it is imp or let's call it dopant.
+I'm going to use the word dopant and
+
+ align:start position:0%
+I'm going to use the word dopant and
+ 
+
+ align:start position:0%
+I'm going to use the word dopant and
+impurity uh interchangeably. So it's
+
+ align:start position:0%
+impurity uh interchangeably. So it's
+ 
+
+ align:start position:0%
+impurity uh interchangeably. So it's
+dopant
+
+ align:start position:0%
+dopant
+ 
+
+ align:start position:0%
+dopant
+dependent and this of course depends on
+
+ align:start position:0%
+dependent and this of course depends on
+ 
+
+ align:start position:0%
+dependent and this of course depends on
+how much we put in but the typical
+
+ align:start position:0%
+how much we put in but the typical
+ 
+
+ align:start position:0%
+how much we put in but the typical
+levels that we put in are great enough
+
+ align:start position:0%
+levels that we put in are great enough
+ 
+
+ align:start position:0%
+levels that we put in are great enough
+that they swamp the value that you get
+
+ align:start position:0%
+that they swamp the value that you get
+ 
+
+ align:start position:0%
+that they swamp the value that you get
+from thermal excitation. So in doped
+
+ align:start position:0%
+from thermal excitation. So in doped
+ 
+
+ align:start position:0%
+from thermal excitation. So in doped
+silicon you neglect thermal excitation
+
+ align:start position:0%
+silicon you neglect thermal excitation
+ 
+
+ align:start position:0%
+silicon you neglect thermal excitation
+and you calculate the carrier population
+
+ align:start position:0%
+and you calculate the carrier population
+ 
+
+ align:start position:0%
+and you calculate the carrier population
+in the conduction band based on how much
+
+ align:start position:0%
+in the conduction band based on how much
+ 
+
+ align:start position:0%
+in the conduction band based on how much
+phosphorus you put in. Every phosphorus
+
+ align:start position:0%
+phosphorus you put in. Every phosphorus
+ 
+
+ align:start position:0%
+phosphorus you put in. Every phosphorus
+gives you a a contribution. And just to
+
+ align:start position:0%
+gives you a a contribution. And just to
+ 
+
+ align:start position:0%
+gives you a a contribution. And just to
+just to complete the definition uh the
+
+ align:start position:0%
+just to complete the definition uh the
+ 
+
+ align:start position:0%
+just to complete the definition uh the
+the undoped material the undoped that is
+
+ align:start position:0%
+the undoped material the undoped that is
+ 
+
+ align:start position:0%
+the undoped material the undoped that is
+to say highly pure silicon exhibits
+
+ align:start position:0%
+to say highly pure silicon exhibits
+ 
+
+ align:start position:0%
+to say highly pure silicon exhibits
+intrinsic behavior. In other words, it
+
+ align:start position:0%
+intrinsic behavior. In other words, it
+ 
+
+ align:start position:0%
+intrinsic behavior. In other words, it
+behaves as pure silicon should behave.
+
+ align:start position:0%
+behaves as pure silicon should behave.
+ 
+
+ align:start position:0%
+behaves as pure silicon should behave.
+So an
+
+ align:start position:0%
+So an
+ 
+
+ align:start position:0%
+So an
+intrinsic semiconductor is one that has
+
+ align:start position:0%
+intrinsic semiconductor is one that has
+ 
+
+ align:start position:0%
+intrinsic semiconductor is one that has
+impur levels so low that they don't
+
+ align:start position:0%
+impur levels so low that they don't
+ 
+
+ align:start position:0%
+impur levels so low that they don't
+manifest themselves. An exttrinsic
+
+ align:start position:0%
+manifest themselves. An exttrinsic
+ 
+
+ align:start position:0%
+manifest themselves. An exttrinsic
+semiconductor has impur levels high
+
+ align:start position:0%
+semiconductor has impur levels high
+ 
+
+ align:start position:0%
+semiconductor has impur levels high
+enough that we can perceive the action
+
+ align:start position:0%
+enough that we can perceive the action
+ 
+
+ align:start position:0%
+enough that we can perceive the action
+of those impur
+
+ align:start position:0%
+of those impur
+ 
+
+ align:start position:0%
+of those impur
+levels. So we can say in this material
+
+ align:start position:0%
+levels. So we can say in this material
+ 
+
+ align:start position:0%
+levels. So we can say in this material
+that that n that are generated from the
+
+ align:start position:0%
+that that n that are generated from the
+ 
+
+ align:start position:0%
+that that n that are generated from the
+impurity or the dopen are greater by far
+
+ align:start position:0%
+impurity or the dopen are greater by far
+ 
+
+ align:start position:0%
+impurity or the dopen are greater by far
+than the n from the from the host
+
+ align:start position:0%
+than the n from the from the host
+ 
+
+ align:start position:0%
+than the n from the from the host
+material itself or if you like the
+
+ align:start position:0%
+material itself or if you like the
+ 
+
+ align:start position:0%
+material itself or if you like the
+number of electrons from the the dopant
+
+ align:start position:0%
+number of electrons from the the dopant
+ 
+
+ align:start position:0%
+number of electrons from the the dopant
+are much greater than the number of
+
+ align:start position:0%
+are much greater than the number of
+ 
+
+ align:start position:0%
+are much greater than the number of
+electrons from thermal excitation.
+
+ align:start position:0%
+electrons from thermal excitation.
+ 
+
+ align:start position:0%
+electrons from thermal excitation.
+It all comes out to say then
+
+ align:start position:0%
+It all comes out to say then
+ 
+
+ align:start position:0%
+It all comes out to say then
+that the number of electrons that are up
+
+ align:start position:0%
+that the number of electrons that are up
+ 
+
+ align:start position:0%
+that the number of electrons that are up
+in the conduction band are much greater
+
+ align:start position:0%
+in the conduction band are much greater
+ 
+
+ align:start position:0%
+in the conduction band are much greater
+than the number of holes in the veilance
+
+ align:start position:0%
+than the number of holes in the veilance
+ 
+
+ align:start position:0%
+than the number of holes in the veilance
+band because if the impurity levels are
+
+ align:start position:0%
+band because if the impurity levels are
+ 
+
+ align:start position:0%
+band because if the impurity levels are
+dominating what comes out of the host
+
+ align:start position:0%
+dominating what comes out of the host
+ 
+
+ align:start position:0%
+dominating what comes out of the host
+then that means if there's hardly any of
+
+ align:start position:0%
+then that means if there's hardly any of
+ 
+
+ align:start position:0%
+then that means if there's hardly any of
+the electrons that came from thermal
+
+ align:start position:0%
+the electrons that came from thermal
+ 
+
+ align:start position:0%
+the electrons that came from thermal
+excitation there's hardly any holes. So
+
+ align:start position:0%
+excitation there's hardly any holes. So
+ 
+
+ align:start position:0%
+excitation there's hardly any holes. So
+now the number of electrons far exceeds
+
+ align:start position:0%
+now the number of electrons far exceeds
+ 
+
+ align:start position:0%
+now the number of electrons far exceeds
+the number of holes. So this material is
+
+ align:start position:0%
+the number of holes. So this material is
+ 
+
+ align:start position:0%
+the number of holes. So this material is
+not net neutral. We do not say that n
+
+ align:start position:0%
+not net neutral. We do not say that n
+ 
+
+ align:start position:0%
+not net neutral. We do not say that n
+equals p because the number of electrons
+
+ align:start position:0%
+equals p because the number of electrons
+ 
+
+ align:start position:0%
+equals p because the number of electrons
+in conduction band is far greater than
+
+ align:start position:0%
+in conduction band is far greater than
+ 
+
+ align:start position:0%
+in conduction band is far greater than
+the number of holes. And so we call this
+
+ align:start position:0%
+the number of holes. And so we call this
+ 
+
+ align:start position:0%
+the number of holes. And so we call this
+material it's extrinsic and electrical
+
+ align:start position:0%
+material it's extrinsic and electrical
+ 
+
+ align:start position:0%
+material it's extrinsic and electrical
+engineers refer to the type of carrier
+
+ align:start position:0%
+engineers refer to the type of carrier
+ 
+
+ align:start position:0%
+engineers refer to the type of carrier
+that's dominating its electrons and
+
+ align:start position:0%
+that's dominating its electrons and
+ 
+
+ align:start position:0%
+that's dominating its electrons and
+electrons when I went to school were
+
+ align:start position:0%
+electrons when I went to school were
+ 
+
+ align:start position:0%
+electrons when I went to school were
+negative. So this is an end type
+
+ align:start position:0%
+negative. So this is an end type
+ 
+
+ align:start position:0%
+negative. So this is an end type
+semiconductor exttrinsic end type. So we
+
+ align:start position:0%
+semiconductor exttrinsic end type. So we
+ 
+
+ align:start position:0%
+semiconductor exttrinsic end type. So we
+altered the electrical properties of
+
+ align:start position:0%
+altered the electrical properties of
+ 
+
+ align:start position:0%
+altered the electrical properties of
+silicon by introducing high level of
+
+ align:start position:0%
+silicon by introducing high level of
+ 
+
+ align:start position:0%
+silicon by introducing high level of
+supervalent supervalent in other words
+
+ align:start position:0%
+supervalent supervalent in other words
+ 
+
+ align:start position:0%
+supervalent supervalent in other words
+phosphorus five is greater than four. So
+
+ align:start position:0%
+phosphorus five is greater than four. So
+ 
+
+ align:start position:0%
+phosphorus five is greater than four. So
+supervalent
+
+ align:start position:0%
+supervalent
+ 
+
+ align:start position:0%
+supervalent
+dopant supervalent dopant leads to end
+
+ align:start position:0%
+dopant supervalent dopant leads to end
+ 
+
+ align:start position:0%
+dopant supervalent dopant leads to end
+type n type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+semiconduction and now we can do it all
+
+ align:start position:0%
+semiconduction and now we can do it all
+ 
+
+ align:start position:0%
+semiconduction and now we can do it all
+over again. We do it all over again.
+
+ align:start position:0%
+over again. We do it all over again.
+ 
+
+ align:start position:0%
+over again. We do it all over again.
+What what can we do? Well, repeat
+
+ align:start position:0%
+What what can we do? Well, repeat
+ 
+
+ align:start position:0%
+What what can we do? Well, repeat
+with and I'm not going to drag you
+
+ align:start position:0%
+with and I'm not going to drag you
+ 
+
+ align:start position:0%
+with and I'm not going to drag you
+through it. This is something you can do
+
+ align:start position:0%
+through it. This is something you can do
+ 
+
+ align:start position:0%
+through it. This is something you can do
+at at home or uh wherever you'd like to
+
+ align:start position:0%
+at at home or uh wherever you'd like to
+ 
+
+ align:start position:0%
+at at home or uh wherever you'd like to
+work. Repeat with subvealent
+
+ align:start position:0%
+work. Repeat with subvealent
+ 
+
+ align:start position:0%
+work. Repeat with subvealent
+impurity. Repeat with subvealent
+
+ align:start position:0%
+impurity. Repeat with subvealent
+ 
+
+ align:start position:0%
+impurity. Repeat with subvealent
+impurity or subvvealent
+
+ align:start position:0%
+impurity or subvvealent
+ 
+
+ align:start position:0%
+impurity or subvvealent
+dopan. So for example,
+
+ align:start position:0%
+dopan. So for example,
+ 
+
+ align:start position:0%
+dopan. So for example,
+boron. What would happen if we were to
+
+ align:start position:0%
+boron. What would happen if we were to
+ 
+
+ align:start position:0%
+boron. What would happen if we were to
+introduce boron here? So boron goes into
+
+ align:start position:0%
+introduce boron here? So boron goes into
+ 
+
+ align:start position:0%
+introduce boron here? So boron goes into
+the space and it substitutes. But boron
+
+ align:start position:0%
+the space and it substitutes. But boron
+ 
+
+ align:start position:0%
+the space and it substitutes. But boron
+is group 13 or group three. So boron
+
+ align:start position:0%
+is group 13 or group three. So boron
+ 
+
+ align:start position:0%
+is group 13 or group three. So boron
+only has three veence electrons. So it
+
+ align:start position:0%
+only has three veence electrons. So it
+ 
+
+ align:start position:0%
+only has three veence electrons. So it
+fills one two three. And boron is
+
+ align:start position:0%
+fills one two three. And boron is
+ 
+
+ align:start position:0%
+fills one two three. And boron is
+electropositive. It's sitting there. It
+
+ align:start position:0%
+electropositive. It's sitting there. It
+ 
+
+ align:start position:0%
+electropositive. It's sitting there. It
+wants to form the bond. How do we how do
+
+ align:start position:0%
+wants to form the bond. How do we how do
+ 
+
+ align:start position:0%
+wants to form the bond. How do we how do
+we handle this situation? What do we do
+
+ align:start position:0%
+we handle this situation? What do we do
+ 
+
+ align:start position:0%
+we handle this situation? What do we do
+in order to balance the fact that this
+
+ align:start position:0%
+in order to balance the fact that this
+ 
+
+ align:start position:0%
+in order to balance the fact that this
+is lacking one electron? Where is the
+
+ align:start position:0%
+is lacking one electron? Where is the
+ 
+
+ align:start position:0%
+is lacking one electron? Where is the
+electron inventory in this crystal?
+
+ align:start position:0%
+electron inventory in this crystal?
+ 
+
+ align:start position:0%
+electron inventory in this crystal?
+Where's the electron store? If I go
+
+ align:start position:0%
+Where's the electron store? If I go
+ 
+
+ align:start position:0%
+Where's the electron store? If I go
+shopping for electrons, where's the only
+
+ align:start position:0%
+shopping for electrons, where's the only
+ 
+
+ align:start position:0%
+shopping for electrons, where's the only
+place I can find them? They're here.
+
+ align:start position:0%
+place I can find them? They're here.
+ 
+
+ align:start position:0%
+place I can find them? They're here.
+They're in the
+
+ align:start position:0%
+They're in the
+ 
+
+ align:start position:0%
+They're in the
+bonds. That is to say, they're in the
+
+ align:start position:0%
+bonds. That is to say, they're in the
+ 
+
+ align:start position:0%
+bonds. That is to say, they're in the
+veence band. So, what will happen is we
+
+ align:start position:0%
+veence band. So, what will happen is we
+ 
+
+ align:start position:0%
+veence band. So, what will happen is we
+will rip an electron out of the veence
+
+ align:start position:0%
+will rip an electron out of the veence
+ 
+
+ align:start position:0%
+will rip an electron out of the veence
+band and move it over to here. And when
+
+ align:start position:0%
+band and move it over to here. And when
+ 
+
+ align:start position:0%
+band and move it over to here. And when
+we do that, what happens if I take an
+
+ align:start position:0%
+we do that, what happens if I take an
+ 
+
+ align:start position:0%
+we do that, what happens if I take an
+electron out of here? What's left
+
+ align:start position:0%
+electron out of here? What's left
+ 
+
+ align:start position:0%
+electron out of here? What's left
+behind? A hole. So, let's generate a
+
+ align:start position:0%
+behind? A hole. So, let's generate a
+ 
+
+ align:start position:0%
+behind? A hole. So, let's generate a
+hole.
+
+ align:start position:0%
+hole.
+ 
+
+ align:start position:0%
+hole.
+So every time I introduce a subvealent
+
+ align:start position:0%
+So every time I introduce a subvealent
+ 
+
+ align:start position:0%
+So every time I introduce a subvealent
+impur I call for an electron out of the
+
+ align:start position:0%
+impur I call for an electron out of the
+ 
+
+ align:start position:0%
+impur I call for an electron out of the
+veence band and I generate a
+
+ align:start position:0%
+veence band and I generate a
+ 
+
+ align:start position:0%
+veence band and I generate a
+hole and where's that hole going to lie?
+
+ align:start position:0%
+hole and where's that hole going to lie?
+ 
+
+ align:start position:0%
+hole and where's that hole going to lie?
+We can go through the same analogy and
+
+ align:start position:0%
+We can go through the same analogy and
+ 
+
+ align:start position:0%
+We can go through the same analogy and
+we will find that the energy level of
+
+ align:start position:0%
+we will find that the energy level of
+ 
+
+ align:start position:0%
+we will find that the energy level of
+that hole is sitting just above the
+
+ align:start position:0%
+that hole is sitting just above the
+ 
+
+ align:start position:0%
+that hole is sitting just above the
+veilance
+
+ align:start position:0%
+veilance
+ 
+
+ align:start position:0%
+veilance
+band but the electrons are sitting in
+
+ align:start position:0%
+band but the electrons are sitting in
+ 
+
+ align:start position:0%
+band but the electrons are sitting in
+the veilance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+band. So how do I get the electrons out
+
+ align:start position:0%
+band. So how do I get the electrons out
+ 
+
+ align:start position:0%
+band. So how do I get the electrons out
+of the veilance band up into this level?
+
+ align:start position:0%
+of the veilance band up into this level?
+ 
+
+ align:start position:0%
+of the veilance band up into this level?
+Thermal excitation. And guess what this
+
+ align:start position:0%
+Thermal excitation. And guess what this
+ 
+
+ align:start position:0%
+Thermal excitation. And guess what this
+energy difference is? It's on the order
+
+ align:start position:0%
+energy difference is? It's on the order
+ 
+
+ align:start position:0%
+energy difference is? It's on the order
+of the thermal energy. And so I get
+
+ align:start position:0%
+of the thermal energy. And so I get
+ 
+
+ align:start position:0%
+of the thermal energy. And so I get
+thermal ionization of the veence
+
+ align:start position:0%
+thermal ionization of the veence
+ 
+
+ align:start position:0%
+thermal ionization of the veence
+electrons up into this level. This level
+
+ align:start position:0%
+electrons up into this level. This level
+ 
+
+ align:start position:0%
+electrons up into this level. This level
+is a place where electrons go. It
+
+ align:start position:0%
+is a place where electrons go. It
+ 
+
+ align:start position:0%
+is a place where electrons go. It
+accepts electrons. It is called the
+
+ align:start position:0%
+accepts electrons. It is called the
+ 
+
+ align:start position:0%
+accepts electrons. It is called the
+acceptor level. acceptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level. Acceptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level. So now we have this configuration
+
+ align:start position:0%
+level. So now we have this configuration
+ 
+
+ align:start position:0%
+level. So now we have this configuration
+conduction
+
+ align:start position:0%
+conduction
+ 
+
+ align:start position:0%
+conduction
+band veilance band subvvealent impurity.
+
+ align:start position:0%
+band veilance band subvvealent impurity.
+ 
+
+ align:start position:0%
+band veilance band subvvealent impurity.
+This is not to scale of course. This is
+
+ align:start position:0%
+This is not to scale of course. This is
+ 
+
+ align:start position:0%
+This is not to scale of course. This is
+on the order of 0.02 EV. Okay. And this
+
+ align:start position:0%
+on the order of 0.02 EV. Okay. And this
+ 
+
+ align:start position:0%
+on the order of 0.02 EV. Okay. And this
+is called the acceptor level.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get thermal excitation leaving holes
+
+ align:start position:0%
+we get thermal excitation leaving holes
+ 
+
+ align:start position:0%
+we get thermal excitation leaving holes
+behind. So thermal excitation promotes
+
+ align:start position:0%
+behind. So thermal excitation promotes
+ 
+
+ align:start position:0%
+behind. So thermal excitation promotes
+the electrons up to here and leaves
+
+ align:start position:0%
+the electrons up to here and leaves
+ 
+
+ align:start position:0%
+the electrons up to here and leaves
+behind holes. So every time I put in a a
+
+ align:start position:0%
+behind holes. So every time I put in a a
+ 
+
+ align:start position:0%
+behind holes. So every time I put in a a
+subvealent impurity the result is a
+
+ align:start position:0%
+subvealent impurity the result is a
+ 
+
+ align:start position:0%
+subvealent impurity the result is a
+hole. So I can control the whole
+
+ align:start position:0%
+hole. So I can control the whole
+ 
+
+ align:start position:0%
+hole. So I can control the whole
+population and the same thing will
+
+ align:start position:0%
+population and the same thing will
+ 
+
+ align:start position:0%
+population and the same thing will
+happen if you go through this analogy
+
+ align:start position:0%
+happen if you go through this analogy
+ 
+
+ align:start position:0%
+happen if you go through this analogy
+what will happen n will no longer equal
+
+ align:start position:0%
+what will happen n will no longer equal
+ 
+
+ align:start position:0%
+what will happen n will no longer equal
+p instead the number of positives is
+
+ align:start position:0%
+p instead the number of positives is
+ 
+
+ align:start position:0%
+p instead the number of positives is
+going to exceed the number of negatives.
+
+ align:start position:0%
+going to exceed the number of negatives.
+ 
+
+ align:start position:0%
+going to exceed the number of negatives.
+Now ne will be much less than
+
+ align:start position:0%
+Now ne will be much less than
+ 
+
+ align:start position:0%
+Now ne will be much less than
+nh will be less than p and so this
+
+ align:start position:0%
+nh will be less than p and so this
+ 
+
+ align:start position:0%
+nh will be less than p and so this
+material will be rendered a positive
+
+ align:start position:0%
+material will be rendered a positive
+ 
+
+ align:start position:0%
+material will be rendered a positive
+conductor. It's going to be dominantly
+
+ align:start position:0%
+conductor. It's going to be dominantly
+ 
+
+ align:start position:0%
+conductor. It's going to be dominantly
+whole conduction. So this is now a
+
+ align:start position:0%
+whole conduction. So this is now a
+ 
+
+ align:start position:0%
+whole conduction. So this is now a
+ptype ptype
+
+ align:start position:0%
+ptype ptype
+ 
+
+ align:start position:0%
+ptype ptype
+semiconductor extrinsic ptype
+
+ align:start position:0%
+semiconductor extrinsic ptype
+ 
+
+ align:start position:0%
+semiconductor extrinsic ptype
+semiconductor. So what's the what's the
+
+ align:start position:0%
+semiconductor. So what's the what's the
+ 
+
+ align:start position:0%
+semiconductor. So what's the what's the
+template here? Subveent
+
+ align:start position:0%
+template here? Subveent
+ 
+
+ align:start position:0%
+template here? Subveent
+dopant. Subveilent dopant calls for
+
+ align:start position:0%
+dopant. Subveilent dopant calls for
+ 
+
+ align:start position:0%
+dopant. Subveilent dopant calls for
+electrons, generates holes and makes a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ptype
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+semiconductor. That's amazing. So now I
+
+ align:start position:0%
+semiconductor. That's amazing. So now I
+ 
+
+ align:start position:0%
+semiconductor. That's amazing. So now I
+can take these I can make a sandwich out
+
+ align:start position:0%
+can take these I can make a sandwich out
+ 
+
+ align:start position:0%
+can take these I can make a sandwich out
+of these things. You know I can do this.
+
+ align:start position:0%
+of these things. You know I can do this.
+ 
+
+ align:start position:0%
+of these things. You know I can do this.
+I could say take this is all silicon.
+
+ align:start position:0%
+I could say take this is all silicon.
+ 
+
+ align:start position:0%
+I could say take this is all silicon.
+Okay. Okay, I could dope this side with
+
+ align:start position:0%
+Okay. Okay, I could dope this side with
+ 
+
+ align:start position:0%
+Okay. Okay, I could dope this side with
+phosphorus. This side with let's say
+
+ align:start position:0%
+phosphorus. This side with let's say
+ 
+
+ align:start position:0%
+phosphorus. This side with let's say
+this is phosphorus doped. The right is
+
+ align:start position:0%
+this is phosphorus doped. The right is
+ 
+
+ align:start position:0%
+this is phosphorus doped. The right is
+phosphorus doped. The left side is boron
+
+ align:start position:0%
+phosphorus doped. The left side is boron
+ 
+
+ align:start position:0%
+phosphorus doped. The left side is boron
+doped. So that means that the left side
+
+ align:start position:0%
+doped. So that means that the left side
+ 
+
+ align:start position:0%
+doped. So that means that the left side
+will be P type. The right side will be N
+
+ align:start position:0%
+will be P type. The right side will be N
+ 
+
+ align:start position:0%
+will be P type. The right side will be N
+type. And what do I have here? I have a
+
+ align:start position:0%
+type. And what do I have here? I have a
+ 
+
+ align:start position:0%
+type. And what do I have here? I have a
+PN
+
+ align:start position:0%
+PN
+ 
+
+ align:start position:0%
+PN
+junction. I have a solid state
+
+ align:start position:0%
+junction. I have a solid state
+ 
+
+ align:start position:0%
+junction. I have a solid state
+rectifier. If I put an AC signal in
+
+ align:start position:0%
+rectifier. If I put an AC signal in
+ 
+
+ align:start position:0%
+rectifier. If I put an AC signal in
+here, I get
+
+ align:start position:0%
+here, I get
+ 
+
+ align:start position:0%
+here, I get
+rectification. Solid state. This is the
+
+ align:start position:0%
+rectification. Solid state. This is the
+ 
+
+ align:start position:0%
+rectification. Solid state. This is the
+solid
+
+ align:start position:0%
+solid
+ 
+
+ align:start position:0%
+solid
+state. It's fantastic. Well, you know,
+
+ align:start position:0%
+state. It's fantastic. Well, you know,
+ 
+
+ align:start position:0%
+state. It's fantastic. Well, you know,
+I've been talking about elemental
+
+ align:start position:0%
+I've been talking about elemental
+ 
+
+ align:start position:0%
+I've been talking about elemental
+semiconductors, but uh these are found
+
+ align:start position:0%
+semiconductors, but uh these are found
+ 
+
+ align:start position:0%
+semiconductors, but uh these are found
+not only in uh elements. Oh, this is
+
+ align:start position:0%
+not only in uh elements. Oh, this is
+ 
+
+ align:start position:0%
+not only in uh elements. Oh, this is
+just left over from last day. We saw
+
+ align:start position:0%
+just left over from last day. We saw
+ 
+
+ align:start position:0%
+just left over from last day. We saw
+this last day.
+
+ align:start position:0%
+this last day.
+ 
+
+ align:start position:0%
+this last day.
+Um you can have compounds that are
+
+ align:start position:0%
+Um you can have compounds that are
+ 
+
+ align:start position:0%
+Um you can have compounds that are
+semiconductors. So, so far we talked
+
+ align:start position:0%
+semiconductors. So, so far we talked
+ 
+
+ align:start position:0%
+semiconductors. So, so far we talked
+about just group four. We talked about
+
+ align:start position:0%
+about just group four. We talked about
+ 
+
+ align:start position:0%
+about just group four. We talked about
+silicon and germanmanium. Tin is very
+
+ align:start position:0%
+silicon and germanmanium. Tin is very
+ 
+
+ align:start position:0%
+silicon and germanmanium. Tin is very
+very mildly semiconducting, but these
+
+ align:start position:0%
+very mildly semiconducting, but these
+ 
+
+ align:start position:0%
+very mildly semiconducting, but these
+are the two workh horses. And in fact
+
+ align:start position:0%
+are the two workh horses. And in fact
+ 
+
+ align:start position:0%
+are the two workh horses. And in fact
+it's dominantly silicon. But now look at
+
+ align:start position:0%
+it's dominantly silicon. But now look at
+ 
+
+ align:start position:0%
+it's dominantly silicon. But now look at
+you can take group three and group five
+
+ align:start position:0%
+you can take group three and group five
+ 
+
+ align:start position:0%
+you can take group three and group five
+and you'll make covealent compounds and
+
+ align:start position:0%
+and you'll make covealent compounds and
+ 
+
+ align:start position:0%
+and you'll make covealent compounds and
+they too have band gaps on this
+
+ align:start position:0%
+they too have band gaps on this
+ 
+
+ align:start position:0%
+they too have band gaps on this
+interval. So we have an entire pallet
+
+ align:start position:0%
+interval. So we have an entire pallet
+ 
+
+ align:start position:0%
+interval. So we have an entire pallet
+here that we can paint on. So for
+
+ align:start position:0%
+here that we can paint on. So for
+ 
+
+ align:start position:0%
+here that we can paint on. So for
+example let's look at this homologous
+
+ align:start position:0%
+example let's look at this homologous
+ 
+
+ align:start position:0%
+example let's look at this homologous
+series with aluminum. Aluminum antimide
+
+ align:start position:0%
+series with aluminum. Aluminum antimide
+ 
+
+ align:start position:0%
+series with aluminum. Aluminum antimide
+1.52 electron volts band gap. Aluminum
+
+ align:start position:0%
+1.52 electron volts band gap. Aluminum
+ 
+
+ align:start position:0%
+1.52 electron volts band gap. Aluminum
+nitride 6.3. Aluminum nitrite is an
+
+ align:start position:0%
+nitride 6.3. Aluminum nitrite is an
+ 
+
+ align:start position:0%
+nitride 6.3. Aluminum nitrite is an
+insulator. It's very strong material. We
+
+ align:start position:0%
+insulator. It's very strong material. We
+ 
+
+ align:start position:0%
+insulator. It's very strong material. We
+use it in in my lab as a uh for as a
+
+ align:start position:0%
+use it in in my lab as a uh for as a
+ 
+
+ align:start position:0%
+use it in in my lab as a uh for as a
+refractory. It resists high temperature
+
+ align:start position:0%
+refractory. It resists high temperature
+ 
+
+ align:start position:0%
+refractory. It resists high temperature
+corrosion. Now what's going on? The
+
+ align:start position:0%
+corrosion. Now what's going on? The
+ 
+
+ align:start position:0%
+corrosion. Now what's going on? The
+difference in electro negativity. These
+
+ align:start position:0%
+difference in electro negativity. These
+ 
+
+ align:start position:0%
+difference in electro negativity. These
+are covealent bonds. Greater difference
+
+ align:start position:0%
+are covealent bonds. Greater difference
+ 
+
+ align:start position:0%
+are covealent bonds. Greater difference
+in electro negativity, higher bond
+
+ align:start position:0%
+in electro negativity, higher bond
+ 
+
+ align:start position:0%
+in electro negativity, higher bond
+energy. And that occurs in all of these
+
+ align:start position:0%
+energy. And that occurs in all of these
+ 
+
+ align:start position:0%
+energy. And that occurs in all of these
+columns as you go up. So an increase in
+
+ align:start position:0%
+columns as you go up. So an increase in
+ 
+
+ align:start position:0%
+columns as you go up. So an increase in
+electro negativity difference is an
+
+ align:start position:0%
+electro negativity difference is an
+ 
+
+ align:start position:0%
+electro negativity difference is an
+increase in bond strength. And an
+
+ align:start position:0%
+increase in bond strength. And an
+ 
+
+ align:start position:0%
+increase in bond strength. And an
+increase in bond strength means an
+
+ align:start position:0%
+increase in bond strength means an
+ 
+
+ align:start position:0%
+increase in bond strength means an
+increase in band gap
+
+ align:start position:0%
+increase in band gap
+ 
+
+ align:start position:0%
+increase in band gap
+energy. And some of these are really
+
+ align:start position:0%
+energy. And some of these are really
+ 
+
+ align:start position:0%
+energy. And some of these are really
+interesting. Indium antimonide has a
+
+ align:start position:0%
+interesting. Indium antimonide has a
+ 
+
+ align:start position:0%
+interesting. Indium antimonide has a
+band gap of about 2/10 of an electron
+
+ align:start position:0%
+band gap of about 2/10 of an electron
+ 
+
+ align:start position:0%
+band gap of about 2/10 of an electron
+volt which means that its absorption
+
+ align:start position:0%
+volt which means that its absorption
+ 
+
+ align:start position:0%
+volt which means that its absorption
+edge its absorption edge is 7 * 10 the
+
+ align:start position:0%
+edge its absorption edge is 7 * 10 the
+ 
+
+ align:start position:0%
+edge its absorption edge is 7 * 10 the
+minus 6 7 micrometers which puts it in
+
+ align:start position:0%
+minus 6 7 micrometers which puts it in
+ 
+
+ align:start position:0%
+minus 6 7 micrometers which puts it in
+the IR and this is one of the materials
+
+ align:start position:0%
+the IR and this is one of the materials
+ 
+
+ align:start position:0%
+the IR and this is one of the materials
+that would be used as a sensor for night
+
+ align:start position:0%
+that would be used as a sensor for night
+ 
+
+ align:start position:0%
+that would be used as a sensor for night
+vision because what are you really
+
+ align:start position:0%
+vision because what are you really
+ 
+
+ align:start position:0%
+vision because what are you really
+sensing when you're looking at night
+
+ align:start position:0%
+sensing when you're looking at night
+ 
+
+ align:start position:0%
+sensing when you're looking at night
+you're sensing heat you don't see the
+
+ align:start position:0%
+you're sensing heat you don't see the
+ 
+
+ align:start position:0%
+you're sensing heat you don't see the
+human body you see the heat coming from
+
+ align:start position:0%
+human body you see the heat coming from
+ 
+
+ align:start position:0%
+human body you see the heat coming from
+the human body right so if everything's
+
+ align:start position:0%
+the human body right so if everything's
+ 
+
+ align:start position:0%
+the human body right so if everything's
+cold And there's no delta T. You don't
+
+ align:start position:0%
+cold And there's no delta T. You don't
+ 
+
+ align:start position:0%
+cold And there's no delta T. You don't
+see anything over here. Cadmium sulfide.
+
+ align:start position:0%
+see anything over here. Cadmium sulfide.
+ 
+
+ align:start position:0%
+see anything over here. Cadmium sulfide.
+Cadmium sulfide is 5 * 10us 7. That's
+
+ align:start position:0%
+Cadmium sulfide is 5 * 10us 7. That's
+ 
+
+ align:start position:0%
+Cadmium sulfide is 5 * 10us 7. That's
+right smack dab in the middle of the
+
+ align:start position:0%
+right smack dab in the middle of the
+ 
+
+ align:start position:0%
+right smack dab in the middle of the
+visible. When I was a child, my father
+
+ align:start position:0%
+visible. When I was a child, my father
+ 
+
+ align:start position:0%
+visible. When I was a child, my father
+had a 35mm camera. It had a cadmium
+
+ align:start position:0%
+had a 35mm camera. It had a cadmium
+ 
+
+ align:start position:0%
+had a 35mm camera. It had a cadmium
+sulfide light meter. And we would match
+
+ align:start position:0%
+sulfide light meter. And we would match
+ 
+
+ align:start position:0%
+sulfide light meter. And we would match
+the needle with the um incoming
+
+ align:start position:0%
+the needle with the um incoming
+ 
+
+ align:start position:0%
+the needle with the um incoming
+radiation and cadmium sulfide. Well, I
+
+ align:start position:0%
+radiation and cadmium sulfide. Well, I
+ 
+
+ align:start position:0%
+radiation and cadmium sulfide. Well, I
+never never understood why it was
+
+ align:start position:0%
+never never understood why it was
+ 
+
+ align:start position:0%
+never never understood why it was
+cadmium sulfide until I understood band
+
+ align:start position:0%
+cadmium sulfide until I understood band
+ 
+
+ align:start position:0%
+cadmium sulfide until I understood band
+gap. And obviously there it is. You can
+
+ align:start position:0%
+gap. And obviously there it is. You can
+ 
+
+ align:start position:0%
+gap. And obviously there it is. You can
+also think about what happens what
+
+ align:start position:0%
+also think about what happens what
+ 
+
+ align:start position:0%
+also think about what happens what
+happens if you're photographing
+
+ align:start position:0%
+happens if you're photographing
+ 
+
+ align:start position:0%
+happens if you're photographing
+something that's that's dominantly red
+
+ align:start position:0%
+something that's that's dominantly red
+ 
+
+ align:start position:0%
+something that's that's dominantly red
+and your um light meter is parked in the
+
+ align:start position:0%
+and your um light meter is parked in the
+ 
+
+ align:start position:0%
+and your um light meter is parked in the
+middle of the yellow. You wonder why
+
+ align:start position:0%
+middle of the yellow. You wonder why
+ 
+
+ align:start position:0%
+middle of the yellow. You wonder why
+your photographs are
+
+ align:start position:0%
+your photographs are
+ 
+
+ align:start position:0%
+your photographs are
+overexposed. Think about that sometime.
+
+ align:start position:0%
+overexposed. Think about that sometime.
+ 
+
+ align:start position:0%
+overexposed. Think about that sometime.
+Oh, so now last thing I want to tell you
+
+ align:start position:0%
+Oh, so now last thing I want to tell you
+ 
+
+ align:start position:0%
+Oh, so now last thing I want to tell you
+is that um that not only do you have uh
+
+ align:start position:0%
+is that um that not only do you have uh
+ 
+
+ align:start position:0%
+is that um that not only do you have uh
+solid semiconductors, you have liquid
+
+ align:start position:0%
+solid semiconductors, you have liquid
+ 
+
+ align:start position:0%
+solid semiconductors, you have liquid
+semiconductors. And when silicon melts,
+
+ align:start position:0%
+semiconductors. And when silicon melts,
+ 
+
+ align:start position:0%
+semiconductors. And when silicon melts,
+it's not a semiconductor. silicon melts,
+
+ align:start position:0%
+it's not a semiconductor. silicon melts,
+ 
+
+ align:start position:0%
+it's not a semiconductor. silicon melts,
+the band gap collapses and molten
+
+ align:start position:0%
+the band gap collapses and molten
+ 
+
+ align:start position:0%
+the band gap collapses and molten
+silicon behaves as a liquid metal. But
+
+ align:start position:0%
+silicon behaves as a liquid metal. But
+ 
+
+ align:start position:0%
+silicon behaves as a liquid metal. But
+for example, something like cadmium
+
+ align:start position:0%
+for example, something like cadmium
+ 
+
+ align:start position:0%
+for example, something like cadmium
+teluride which is uh useful in night
+
+ align:start position:0%
+teluride which is uh useful in night
+ 
+
+ align:start position:0%
+teluride which is uh useful in night
+vision. Cadmium telleluride as a solid
+
+ align:start position:0%
+vision. Cadmium telleluride as a solid
+ 
+
+ align:start position:0%
+vision. Cadmium telleluride as a solid
+has a band gap on the order of
+
+ align:start position:0%
+has a band gap on the order of
+ 
+
+ align:start position:0%
+has a band gap on the order of
+1.45 electron volts. As a liquid, it
+
+ align:start position:0%
+1.45 electron volts. As a liquid, it
+ 
+
+ align:start position:0%
+1.45 electron volts. As a liquid, it
+still has a band gap. It's about 0.3
+
+ align:start position:0%
+still has a band gap. It's about 0.3
+ 
+
+ align:start position:0%
+still has a band gap. It's about 0.3
+electron volts. So it is uh parked down
+
+ align:start position:0%
+electron volts. So it is uh parked down
+ 
+
+ align:start position:0%
+electron volts. So it is uh parked down
+in the infrared.
+
+ align:start position:0%
+in the infrared.
+ 
+
+ align:start position:0%
+in the infrared.
+And the transition metal oxides also do
+
+ align:start position:0%
+And the transition metal oxides also do
+ 
+
+ align:start position:0%
+And the transition metal oxides also do
+this. Trans titania liquid titania is
+
+ align:start position:0%
+this. Trans titania liquid titania is
+ 
+
+ align:start position:0%
+this. Trans titania liquid titania is
+dominantly an electronic conductor, not
+
+ align:start position:0%
+dominantly an electronic conductor, not
+ 
+
+ align:start position:0%
+dominantly an electronic conductor, not
+an ionic conductor because its band gap
+
+ align:start position:0%
+an ionic conductor because its band gap
+ 
+
+ align:start position:0%
+an ionic conductor because its band gap
+is parked there. And this is of interest
+
+ align:start position:0%
+is parked there. And this is of interest
+ 
+
+ align:start position:0%
+is parked there. And this is of interest
+to some of the work in my lab where
+
+ align:start position:0%
+to some of the work in my lab where
+ 
+
+ align:start position:0%
+to some of the work in my lab where
+we're looking at trying to set the stage
+
+ align:start position:0%
+we're looking at trying to set the stage
+ 
+
+ align:start position:0%
+we're looking at trying to set the stage
+for lunar colonization where you want to
+
+ align:start position:0%
+for lunar colonization where you want to
+ 
+
+ align:start position:0%
+for lunar colonization where you want to
+get oxygen out of the moon. The surface
+
+ align:start position:0%
+get oxygen out of the moon. The surface
+ 
+
+ align:start position:0%
+get oxygen out of the moon. The surface
+of the moon. The surface of the moon is
+
+ align:start position:0%
+of the moon. The surface of the moon is
+ 
+
+ align:start position:0%
+of the moon. The surface of the moon is
+not made of green cheese. I'm sorry to
+
+ align:start position:0%
+not made of green cheese. I'm sorry to
+ 
+
+ align:start position:0%
+not made of green cheese. I'm sorry to
+tell you. It's made dominantly of iron
+
+ align:start position:0%
+tell you. It's made dominantly of iron
+ 
+
+ align:start position:0%
+tell you. It's made dominantly of iron
+oxide and titanium oxide. That's why
+
+ align:start position:0%
+oxide and titanium oxide. That's why
+ 
+
+ align:start position:0%
+oxide and titanium oxide. That's why
+it's so brilliantly white. It's titania.
+
+ align:start position:0%
+it's so brilliantly white. It's titania.
+ 
+
+ align:start position:0%
+it's so brilliantly white. It's titania.
+So, it's 50% oxygen but tightly bound.
+
+ align:start position:0%
+So, it's 50% oxygen but tightly bound.
+ 
+
+ align:start position:0%
+So, it's 50% oxygen but tightly bound.
+And if you want to electrolyze the moon,
+
+ align:start position:0%
+And if you want to electrolyze the moon,
+ 
+
+ align:start position:0%
+And if you want to electrolyze the moon,
+you have to somehow repress this liquid
+
+ align:start position:0%
+you have to somehow repress this liquid
+ 
+
+ align:start position:0%
+you have to somehow repress this liquid
+semiconduction. So, that's a topic of
+
+ align:start position:0%
+semiconduction. So, that's a topic of
+ 
+
+ align:start position:0%
+semiconduction. So, that's a topic of
+research. So, this is probably a uh a
+
+ align:start position:0%
+research. So, this is probably a uh a
+ 
+
+ align:start position:0%
+research. So, this is probably a uh a
+good place to stay. And what we're going
+
+ align:start position:0%
+good place to stay. And what we're going
+ 
+
+ align:start position:0%
+good place to stay. And what we're going
+to do next day is we're going to start
+
+ align:start position:0%
+to do next day is we're going to start
+ 
+
+ align:start position:0%
+to do next day is we're going to start
+onto the um treatment of uh solids and
+
+ align:start position:0%
+onto the um treatment of uh solids and
+ 
+
+ align:start position:0%
+onto the um treatment of uh solids and
+crystal. But I don't want a lot of
+
+ align:start position:0%
+crystal. But I don't want a lot of
+ 
+
+ align:start position:0%
+crystal. But I don't want a lot of
+moving. It's 11:47. We still have a few
+
+ align:start position:0%
+moving. It's 11:47. We still have a few
+ 
+
+ align:start position:0%
+moving. It's 11:47. We still have a few
+minutes. So um let's see what do we want
+
+ align:start position:0%
+minutes. So um let's see what do we want
+ 
+
+ align:start position:0%
+minutes. So um let's see what do we want
+to talk about. We'll move past this.
+
+ align:start position:0%
+to talk about. We'll move past this.
+ 
+
+ align:start position:0%
+to talk about. We'll move past this.
+We'll get to this next day. And uh what
+
+ align:start position:0%
+We'll get to this next day. And uh what
+ 
+
+ align:start position:0%
+We'll get to this next day. And uh what
+I wanted to talk about today was this
+
+ align:start position:0%
+I wanted to talk about today was this
+ 
+
+ align:start position:0%
+I wanted to talk about today was this
+image here. This image is an image of
+
+ align:start position:0%
+image here. This image is an image of
+ 
+
+ align:start position:0%
+image here. This image is an image of
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+um diode rectifying solid state diode.
+
+ align:start position:0%
+um diode rectifying solid state diode.
+ 
+
+ align:start position:0%
+um diode rectifying solid state diode.
+This was uh done at Bell Labs in Murray
+
+ align:start position:0%
+This was uh done at Bell Labs in Murray
+ 
+
+ align:start position:0%
+This was uh done at Bell Labs in Murray
+Hill, New Jersey in uh December of
+
+ align:start position:0%
+Hill, New Jersey in uh December of
+ 
+
+ align:start position:0%
+Hill, New Jersey in uh December of
+1947. So what you're looking at here is
+
+ align:start position:0%
+1947. So what you're looking at here is
+ 
+
+ align:start position:0%
+1947. So what you're looking at here is
+a piece of single crystal germanmanium.
+
+ align:start position:0%
+a piece of single crystal germanmanium.
+ 
+
+ align:start position:0%
+a piece of single crystal germanmanium.
+Single crystal germanmanium and uh the
+
+ align:start position:0%
+Single crystal germanmanium and uh the
+ 
+
+ align:start position:0%
+Single crystal germanmanium and uh the
+various leads and so on. And this uh was
+
+ align:start position:0%
+various leads and so on. And this uh was
+ 
+
+ align:start position:0%
+various leads and so on. And this uh was
+able to uh perform the the uh the
+
+ align:start position:0%
+able to uh perform the the uh the
+ 
+
+ align:start position:0%
+able to uh perform the the uh the
+function of a of a diode. Now, if I told
+
+ align:start position:0%
+function of a of a diode. Now, if I told
+ 
+
+ align:start position:0%
+function of a of a diode. Now, if I told
+you that someday there would
+
+ align:start position:0%
+you that someday there would
+ 
+
+ align:start position:0%
+you that someday there would
+be 16 million of those on the uh on a a
+
+ align:start position:0%
+be 16 million of those on the uh on a a
+ 
+
+ align:start position:0%
+be 16 million of those on the uh on a a
+piece of real estate about the size of
+
+ align:start position:0%
+piece of real estate about the size of
+ 
+
+ align:start position:0%
+piece of real estate about the size of
+your fingernail, you would say that I
+
+ align:start position:0%
+your fingernail, you would say that I
+ 
+
+ align:start position:0%
+your fingernail, you would say that I
+was crazy. All right. And so what's
+
+ align:start position:0%
+was crazy. All right. And so what's
+ 
+
+ align:start position:0%
+was crazy. All right. And so what's
+happened from that day to this date? Uh
+
+ align:start position:0%
+happened from that day to this date? Uh
+ 
+
+ align:start position:0%
+happened from that day to this date? Uh
+Tom, do you think I could get the
+
+ align:start position:0%
+Tom, do you think I could get the
+ 
+
+ align:start position:0%
+Tom, do you think I could get the
+document camera on, please? So, I'm I'm
+
+ align:start position:0%
+document camera on, please? So, I'm I'm
+ 
+
+ align:start position:0%
+document camera on, please? So, I'm I'm
+going to show you where we've gone. This
+
+ align:start position:0%
+going to show you where we've gone. This
+ 
+
+ align:start position:0%
+going to show you where we've gone. This
+is now this is uh uh let's see I want to
+
+ align:start position:0%
+is now this is uh uh let's see I want to
+ 
+
+ align:start position:0%
+is now this is uh uh let's see I want to
+go to is this oh look at
+
+ align:start position:0%
+go to is this oh look at
+ 
+
+ align:start position:0%
+go to is this oh look at
+this. So let's look at
+
+ align:start position:0%
+this. So let's look at
+ 
+
+ align:start position:0%
+this. So let's look at
+Pentium. Here's Pentium. And then okay
+
+ align:start position:0%
+Pentium. Here's Pentium. And then okay
+ 
+
+ align:start position:0%
+Pentium. Here's Pentium. And then okay
+so we've got we've got a gazillion of
+
+ align:start position:0%
+so we've got we've got a gazillion of
+ 
+
+ align:start position:0%
+so we've got we've got a gazillion of
+these things underneath the gold here.
+
+ align:start position:0%
+these things underneath the gold here.
+ 
+
+ align:start position:0%
+these things underneath the gold here.
+This is everything's covered in gold
+
+ align:start position:0%
+This is everything's covered in gold
+ 
+
+ align:start position:0%
+This is everything's covered in gold
+because um electrical engineers are very
+
+ align:start position:0%
+because um electrical engineers are very
+ 
+
+ align:start position:0%
+because um electrical engineers are very
+superstitious. They they get nervous
+
+ align:start position:0%
+superstitious. They they get nervous
+ 
+
+ align:start position:0%
+superstitious. They they get nervous
+exposing wires. So they played
+
+ align:start position:0%
+exposing wires. So they played
+ 
+
+ align:start position:0%
+exposing wires. So they played
+everything with gold because they heard
+
+ align:start position:0%
+everything with gold because they heard
+ 
+
+ align:start position:0%
+everything with gold because they heard
+somewhere that gold is chemically inert.
+
+ align:start position:0%
+somewhere that gold is chemically inert.
+ 
+
+ align:start position:0%
+somewhere that gold is chemically inert.
+So underneath there is well here you can
+
+ align:start position:0%
+So underneath there is well here you can
+ 
+
+ align:start position:0%
+So underneath there is well here you can
+see that there's the there's the unit.
+
+ align:start position:0%
+see that there's the there's the unit.
+ 
+
+ align:start position:0%
+see that there's the there's the unit.
+So it's sitting there. So all of this
+
+ align:start position:0%
+So it's sitting there. So all of this
+ 
+
+ align:start position:0%
+So it's sitting there. So all of this
+and here's the suspension. All of this
+
+ align:start position:0%
+and here's the suspension. All of this
+ 
+
+ align:start position:0%
+and here's the suspension. All of this
+spider spiderweb is is being able to
+
+ align:start position:0%
+spider spiderweb is is being able to
+ 
+
+ align:start position:0%
+spider spiderweb is is being able to
+address all of the various devices. So
+
+ align:start position:0%
+address all of the various devices. So
+ 
+
+ align:start position:0%
+address all of the various devices. So
+it started with that first one and
+
+ align:start position:0%
+it started with that first one and
+ 
+
+ align:start position:0%
+it started with that first one and
+here's the sort of the intermediate.
+
+ align:start position:0%
+here's the sort of the intermediate.
+ 
+
+ align:start position:0%
+here's the sort of the intermediate.
+This is taking the silicon that I showed
+
+ align:start position:0%
+This is taking the silicon that I showed
+ 
+
+ align:start position:0%
+This is taking the silicon that I showed
+you last day. And now
+
+ align:start position:0%
+you last day. And now
+ 
+
+ align:start position:0%
+you last day. And now
+uh let's go as big.
+
+ align:start position:0%
+uh let's go as big.
+ 
+
+ align:start position:0%
+uh let's go as big.
+See? So these are now these are
+
+ align:start position:0%
+See? So these are now these are
+ 
+
+ align:start position:0%
+See? So these are now these are
+individual devices that have been put on
+
+ align:start position:0%
+individual devices that have been put on
+ 
+
+ align:start position:0%
+individual devices that have been put on
+the silicon through uh
+
+ align:start position:0%
+the silicon through uh
+ 
+
+ align:start position:0%
+the silicon through uh
+photoiththography. So what are we doing?
+
+ align:start position:0%
+photoiththography. So what are we doing?
+ 
+
+ align:start position:0%
+photoiththography. So what are we doing?
+What we're doing is we're making masks
+
+ align:start position:0%
+What we're doing is we're making masks
+ 
+
+ align:start position:0%
+What we're doing is we're making masks
+and we're conducting these doping
+
+ align:start position:0%
+and we're conducting these doping
+ 
+
+ align:start position:0%
+and we're conducting these doping
+operations to set up the various uh
+
+ align:start position:0%
+operations to set up the various uh
+ 
+
+ align:start position:0%
+operations to set up the various uh
+devices and we can make many of them and
+
+ align:start position:0%
+devices and we can make many of them and
+ 
+
+ align:start position:0%
+devices and we can make many of them and
+then break them up and then eventually
+
+ align:start position:0%
+then break them up and then eventually
+ 
+
+ align:start position:0%
+then break them up and then eventually
+put them into something like this and so
+
+ align:start position:0%
+put them into something like this and so
+ 
+
+ align:start position:0%
+put them into something like this and so
+on. So that's the that's the result of a
+
+ align:start position:0%
+on. So that's the that's the result of a
+ 
+
+ align:start position:0%
+on. So that's the that's the result of a
+of a long of a long history of
+
+ align:start position:0%
+of a long of a long history of
+ 
+
+ align:start position:0%
+of a long of a long history of
+understanding the the processing of
+
+ align:start position:0%
+understanding the the processing of
+ 
+
+ align:start position:0%
+understanding the the processing of
+devices based upon the chemistry that
+
+ align:start position:0%
+devices based upon the chemistry that
+ 
+
+ align:start position:0%
+devices based upon the chemistry that
+started with what what started all of
+
+ align:start position:0%
+started with what what started all of
+ 
+
+ align:start position:0%
+started with what what started all of
+this. The search for octet stability.
+
+ align:start position:0%
+this. The search for octet stability.
+ 
+
+ align:start position:0%
+this. The search for octet stability.
+Never forget that. That's what started
+
+ align:start position:0%
+Never forget that. That's what started
+ 
+
+ align:start position:0%
+Never forget that. That's what started
+this. The search for octet stability.
+
+ align:start position:0%
+this. The search for octet stability.
+ 
+
+ align:start position:0%
+this. The search for octet stability.
+Okay, we'll see you on Friday.
\ No newline at end of file
diff --git a/vpJba2qIXjs.txt b/vpJba2qIXjs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5c04ddb725552f16e6c00aa6da25fa3a9ded5109
--- /dev/null
+++ b/vpJba2qIXjs.txt
@@ -0,0 +1,12539 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'd like to in this evening lecture what
+
+ align:start position:0%
+I'd like to in this evening lecture what
+ 
+
+ align:start position:0%
+I'd like to in this evening lecture what
+I'd like to do is continue a bit to
+
+ align:start position:0%
+I'd like to do is continue a bit to
+ 
+
+ align:start position:0%
+I'd like to do is continue a bit to
+expand on and complicate and maybe also
+
+ align:start position:0%
+expand on and complicate and maybe also
+ 
+
+ align:start position:0%
+expand on and complicate and maybe also
+deepen this idea I've been suggesting to
+
+ align:start position:0%
+deepen this idea I've been suggesting to
+ 
+
+ align:start position:0%
+deepen this idea I've been suggesting to
+you that I'm labeling the Fred principle
+
+ align:start position:0%
+you that I'm labeling the Fred principle
+ 
+
+ align:start position:0%
+you that I'm labeling the Fred principle
+really a shorthand way of describing the
+
+ align:start position:0%
+really a shorthand way of describing the
+ 
+
+ align:start position:0%
+really a shorthand way of describing the
+immensely complex and from an
+
+ align:start position:0%
+immensely complex and from an
+ 
+
+ align:start position:0%
+immensely complex and from an
+intellectual standpoint a historical
+
+ align:start position:0%
+intellectual standpoint a historical
+ 
+
+ align:start position:0%
+intellectual standpoint a historical
+standpoint immensely exciting and
+
+ align:start position:0%
+standpoint immensely exciting and
+ 
+
+ align:start position:0%
+standpoint immensely exciting and
+astonishing process whereby film went in
+
+ align:start position:0%
+astonishing process whereby film went in
+ 
+
+ align:start position:0%
+astonishing process whereby film went in
+an in an incredibly ly short time from
+
+ align:start position:0%
+an in an incredibly ly short time from
+ 
+
+ align:start position:0%
+an in an incredibly ly short time from
+being a mere novelty to being an
+
+ align:start position:0%
+being a mere novelty to being an
+ 
+
+ align:start position:0%
+being a mere novelty to being an
+embedded social formation in the United
+
+ align:start position:0%
+embedded social formation in the United
+ 
+
+ align:start position:0%
+embedded social formation in the United
+States and and in other industrialized
+
+ align:start position:0%
+States and and in other industrialized
+ 
+
+ align:start position:0%
+States and and in other industrialized
+societies and not just only a so
+
+ align:start position:0%
+societies and not just only a so
+ 
+
+ align:start position:0%
+societies and not just only a so
+embedded social formation becoming by
+
+ align:start position:0%
+embedded social formation becoming by
+ 
+
+ align:start position:0%
+embedded social formation becoming by
+the end of the 1920s one of the central
+
+ align:start position:0%
+the end of the 1920s one of the central
+ 
+
+ align:start position:0%
+the end of the 1920s one of the central
+media for the expression of art and an
+
+ align:start position:0%
+media for the expression of art and an
+ 
+
+ align:start position:0%
+media for the expression of art and an
+artistic medium so that it went from
+
+ align:start position:0%
+artistic medium so that it went from
+ 
+
+ align:start position:0%
+artistic medium so that it went from
+being a mere novelty from Fred Sneeze in
+
+ align:start position:0%
+being a mere novelty from Fred Sneeze in
+ 
+
+ align:start position:0%
+being a mere novelty from Fred Sneeze in
+20 years or so 25 years to being a
+
+ align:start position:0%
+20 years or so 25 years to being a
+ 
+
+ align:start position:0%
+20 years or so 25 years to being a
+medium
+
+ align:start position:0%
+medium
+ 
+
+ align:start position:0%
+medium
+astonishingly rich and complex narrative
+
+ align:start position:0%
+astonishingly rich and complex narrative
+ 
+
+ align:start position:0%
+astonishingly rich and complex narrative
+art. That progress uh is part of what I
+
+ align:start position:0%
+art. That progress uh is part of what I
+ 
+
+ align:start position:0%
+art. That progress uh is part of what I
+mean by the um Fredot principle. And and
+
+ align:start position:0%
+mean by the um Fredot principle. And and
+ 
+
+ align:start position:0%
+mean by the um Fredot principle. And and
+it might be helpful if I if I concretize
+
+ align:start position:0%
+it might be helpful if I if I concretize
+ 
+
+ align:start position:0%
+it might be helpful if I if I concretize
+that a little bit more by mentioning a
+
+ align:start position:0%
+that a little bit more by mentioning a
+ 
+
+ align:start position:0%
+that a little bit more by mentioning a
+bit more about what I mean about the
+
+ align:start position:0%
+bit more about what I mean about the
+ 
+
+ align:start position:0%
+bit more about what I mean about the
+what I was implying or referring to when
+
+ align:start position:0%
+what I was implying or referring to when
+ 
+
+ align:start position:0%
+what I was implying or referring to when
+I spoke about that moment of imitation.
+
+ align:start position:0%
+I spoke about that moment of imitation.
+ 
+
+ align:start position:0%
+I spoke about that moment of imitation.
+Remember I said that there were
+
+ align:start position:0%
+Remember I said that there were
+ 
+
+ align:start position:0%
+Remember I said that there were
+essentially three that the that the that
+
+ align:start position:0%
+essentially three that the that the that
+ 
+
+ align:start position:0%
+essentially three that the that the that
+silent film and incidentally I take it
+
+ align:start position:0%
+silent film and incidentally I take it
+ 
+
+ align:start position:0%
+silent film and incidentally I take it
+as a model for the way in which most new
+
+ align:start position:0%
+as a model for the way in which most new
+ 
+
+ align:start position:0%
+as a model for the way in which most new
+media systems uh develop in culture. You
+
+ align:start position:0%
+media systems uh develop in culture. You
+ 
+
+ align:start position:0%
+media systems uh develop in culture. You
+can apply this same basic schema to
+
+ align:start position:0%
+can apply this same basic schema to
+ 
+
+ align:start position:0%
+can apply this same basic schema to
+other forms of of popular entertainment
+
+ align:start position:0%
+other forms of of popular entertainment
+ 
+
+ align:start position:0%
+other forms of of popular entertainment
+including
+
+ align:start position:0%
+including
+ 
+
+ align:start position:0%
+including
+shocking as it may seem Shakespeare's
+
+ align:start position:0%
+shocking as it may seem Shakespeare's
+ 
+
+ align:start position:0%
+shocking as it may seem Shakespeare's
+public theater. And I'll come back to
+
+ align:start position:0%
+public theater. And I'll come back to
+ 
+
+ align:start position:0%
+public theater. And I'll come back to
+the implications of that analogy. The
+
+ align:start position:0%
+the implications of that analogy. The
+ 
+
+ align:start position:0%
+the implications of that analogy. The
+idea that Shakespeare was the movie of
+
+ align:start position:0%
+idea that Shakespeare was the movie of
+ 
+
+ align:start position:0%
+idea that Shakespeare was the movie of
+his time, that Shakespeare's theater was
+
+ align:start position:0%
+his time, that Shakespeare's theater was
+ 
+
+ align:start position:0%
+his time, that Shakespeare's theater was
+the Hollywood studio system of of of the
+
+ align:start position:0%
+the Hollywood studio system of of of the
+ 
+
+ align:start position:0%
+the Hollywood studio system of of of the
+of the Elizabethan era is a very
+
+ align:start position:0%
+of the Elizabethan era is a very
+ 
+
+ align:start position:0%
+of the Elizabethan era is a very
+complicated one. It's a very inspiring
+
+ align:start position:0%
+complicated one. It's a very inspiring
+ 
+
+ align:start position:0%
+complicated one. It's a very inspiring
+one. And it's it's complicated because
+
+ align:start position:0%
+one. And it's it's complicated because
+ 
+
+ align:start position:0%
+one. And it's it's complicated because
+it makes us reassess our inherited
+
+ align:start position:0%
+it makes us reassess our inherited
+ 
+
+ align:start position:0%
+it makes us reassess our inherited
+notions about what art is and where art
+
+ align:start position:0%
+notions about what art is and where art
+ 
+
+ align:start position:0%
+notions about what art is and where art
+comes from. One of the subtexts in this
+
+ align:start position:0%
+comes from. One of the subtexts in this
+ 
+
+ align:start position:0%
+comes from. One of the subtexts in this
+course is precisely that. the has to do
+
+ align:start position:0%
+course is precisely that. the has to do
+ 
+
+ align:start position:0%
+course is precisely that. the has to do
+with what I call the enabling conditions
+
+ align:start position:0%
+with what I call the enabling conditions
+ 
+
+ align:start position:0%
+with what I call the enabling conditions
+of art and I'll come back to that again
+
+ align:start position:0%
+of art and I'll come back to that again
+ 
+
+ align:start position:0%
+of art and I'll come back to that again
+as a theme again and again in in the
+
+ align:start position:0%
+as a theme again and again in in the
+ 
+
+ align:start position:0%
+as a theme again and again in in the
+course. So part of what I mean by the
+
+ align:start position:0%
+course. So part of what I mean by the
+ 
+
+ align:start position:0%
+course. So part of what I mean by the
+Fred out principle is this is this uh
+
+ align:start position:0%
+Fred out principle is this is this uh
+ 
+
+ align:start position:0%
+Fred out principle is this is this uh
+roing complex uh uh um uh partly
+
+ align:start position:0%
+roing complex uh uh um uh partly
+ 
+
+ align:start position:0%
+roing complex uh uh um uh partly
+unpredictable process whereby uh au an
+
+ align:start position:0%
+unpredictable process whereby uh au an
+ 
+
+ align:start position:0%
+unpredictable process whereby uh au an
+enlarging population incredibly hungry
+
+ align:start position:0%
+enlarging population incredibly hungry
+ 
+
+ align:start position:0%
+enlarging population incredibly hungry
+for the novelties being produced by this
+
+ align:start position:0%
+for the novelties being produced by this
+ 
+
+ align:start position:0%
+for the novelties being produced by this
+new technology create uh a kind of
+
+ align:start position:0%
+new technology create uh a kind of
+ 
+
+ align:start position:0%
+new technology create uh a kind of
+symbiotic relationship between the
+
+ align:start position:0%
+symbiotic relationship between the
+ 
+
+ align:start position:0%
+symbiotic relationship between the
+audience and the emerging medium. So
+
+ align:start position:0%
+audience and the emerging medium. So
+ 
+
+ align:start position:0%
+audience and the emerging medium. So
+that as the medium be the medium grows
+
+ align:start position:0%
+that as the medium be the medium grows
+ 
+
+ align:start position:0%
+that as the medium be the medium grows
+more complicated in part because the
+
+ align:start position:0%
+more complicated in part because the
+ 
+
+ align:start position:0%
+more complicated in part because the
+audience okay after five or 10 or 15
+
+ align:start position:0%
+audience okay after five or 10 or 15
+ 
+
+ align:start position:0%
+audience okay after five or 10 or 15
+visits to the to the Nickelodeon or uh
+
+ align:start position:0%
+visits to the to the Nickelodeon or uh
+ 
+
+ align:start position:0%
+visits to the to the Nickelodeon or uh
+or to the the a after the movies moved
+
+ align:start position:0%
+or to the the a after the movies moved
+ 
+
+ align:start position:0%
+or to the the a after the movies moved
+out of after the movies moved out of the
+
+ align:start position:0%
+out of after the movies moved out of the
+ 
+
+ align:start position:0%
+out of after the movies moved out of the
+penny arcades and began to take their
+
+ align:start position:0%
+penny arcades and began to take their
+ 
+
+ align:start position:0%
+penny arcades and began to take their
+own space as some of you know and as as
+
+ align:start position:0%
+own space as some of you know and as as
+ 
+
+ align:start position:0%
+own space as some of you know and as as
+is recounted in our reading for this for
+
+ align:start position:0%
+is recounted in our reading for this for
+ 
+
+ align:start position:0%
+is recounted in our reading for this for
+these early weeks. The movies first
+
+ align:start position:0%
+these early weeks. The movies first
+ 
+
+ align:start position:0%
+these early weeks. The movies first
+moved out into what were called
+
+ align:start position:0%
+moved out into what were called
+ 
+
+ align:start position:0%
+moved out into what were called
+Nickelodeons, right? They were they were
+
+ align:start position:0%
+Nickelodeons, right? They were they were
+ 
+
+ align:start position:0%
+Nickelodeons, right? They were they were
+uh storefronts in the for the most part
+
+ align:start position:0%
+uh storefronts in the for the most part
+ 
+
+ align:start position:0%
+uh storefronts in the for the most part
+in which you and the admission was a
+
+ align:start position:0%
+in which you and the admission was a
+ 
+
+ align:start position:0%
+in which you and the admission was a
+nickel. That's why they were called
+
+ align:start position:0%
+nickel. That's why they were called
+ 
+
+ align:start position:0%
+nickel. That's why they were called
+Nickelodeons. Uh and uh you sat in in
+
+ align:start position:0%
+Nickelodeons. Uh and uh you sat in in
+ 
+
+ align:start position:0%
+Nickelodeons. Uh and uh you sat in in
+many of these on benches without backs
+
+ align:start position:0%
+many of these on benches without backs
+ 
+
+ align:start position:0%
+many of these on benches without backs
+next to strangers. You didn't have
+
+ align:start position:0%
+next to strangers. You didn't have
+ 
+
+ align:start position:0%
+next to strangers. You didn't have
+private seats and you would sit in there
+
+ align:start position:0%
+private seats and you would sit in there
+ 
+
+ align:start position:0%
+private seats and you would sit in there
+and see a series of short films. So but
+
+ align:start position:0%
+and see a series of short films. So but
+ 
+
+ align:start position:0%
+and see a series of short films. So but
+the fact that the Nickelodeons emerged
+
+ align:start position:0%
+the fact that the Nickelodeons emerged
+ 
+
+ align:start position:0%
+the fact that the Nickelodeons emerged
+so quickly is a mark of how popular an
+
+ align:start position:0%
+so quickly is a mark of how popular an
+ 
+
+ align:start position:0%
+so quickly is a mark of how popular an
+uh film became even even in the even in
+
+ align:start position:0%
+uh film became even even in the even in
+ 
+
+ align:start position:0%
+uh film became even even in the even in
+its relatively primitive early form. Uh
+
+ align:start position:0%
+its relatively primitive early form. Uh
+ 
+
+ align:start position:0%
+its relatively primitive early form. Uh
+and and then of course within a few
+
+ align:start position:0%
+and and then of course within a few
+ 
+
+ align:start position:0%
+and and then of course within a few
+years of the Nickelodeons appearing what
+
+ align:start position:0%
+years of the Nickelodeons appearing what
+ 
+
+ align:start position:0%
+years of the Nickelodeons appearing what
+else began to happen? Theaters made
+
+ align:start position:0%
+else began to happen? Theaters made
+ 
+
+ align:start position:0%
+else began to happen? Theaters made
+specially for the showing of motion
+
+ align:start position:0%
+specially for the showing of motion
+ 
+
+ align:start position:0%
+specially for the showing of motion
+pictures that were longer than the early
+
+ align:start position:0%
+pictures that were longer than the early
+ 
+
+ align:start position:0%
+pictures that were longer than the early
+shorts because film began to expand its
+
+ align:start position:0%
+shorts because film began to expand its
+ 
+
+ align:start position:0%
+shorts because film began to expand its
+length all through the period from 1910
+
+ align:start position:0%
+length all through the period from 1910
+ 
+
+ align:start position:0%
+length all through the period from 1910
+through 1920. Right? What what's the
+
+ align:start position:0%
+through 1920. Right? What what's the
+ 
+
+ align:start position:0%
+through 1920. Right? What what's the
+great moment when the feature film is
+
+ align:start position:0%
+great moment when the feature film is
+ 
+
+ align:start position:0%
+great moment when the feature film is
+born in the United States? 1915. Who's
+
+ align:start position:0%
+born in the United States? 1915. Who's
+ 
+
+ align:start position:0%
+born in the United States? 1915. Who's
+the director? DW Griffith. Who's the
+
+ align:start position:0%
+the director? DW Griffith. Who's the
+ 
+
+ align:start position:0%
+the director? DW Griffith. Who's the
+what's the film? Birth of a Nation.
+
+ align:start position:0%
+what's the film? Birth of a Nation.
+ 
+
+ align:start position:0%
+what's the film? Birth of a Nation.
+Birth of a Nation, a very complicated uh
+
+ align:start position:0%
+Birth of a Nation, a very complicated uh
+ 
+
+ align:start position:0%
+Birth of a Nation, a very complicated uh
+example because its content is
+
+ align:start position:0%
+example because its content is
+ 
+
+ align:start position:0%
+example because its content is
+disturbing in some ways. It's a very
+
+ align:start position:0%
+disturbing in some ways. It's a very
+ 
+
+ align:start position:0%
+disturbing in some ways. It's a very
+reactionary and in some respects racist
+
+ align:start position:0%
+reactionary and in some respects racist
+ 
+
+ align:start position:0%
+reactionary and in some respects racist
+film. It it it it it
+
+ align:start position:0%
+film. It it it it it
+ 
+
+ align:start position:0%
+film. It it it it it
+absorbs and carries forward what we
+
+ align:start position:0%
+absorbs and carries forward what we
+ 
+
+ align:start position:0%
+absorbs and carries forward what we
+might think of as the the racial
+
+ align:start position:0%
+might think of as the the racial
+ 
+
+ align:start position:0%
+might think of as the the racial
+prejudices that were uh very widespread
+
+ align:start position:0%
+prejudices that were uh very widespread
+ 
+
+ align:start position:0%
+prejudices that were uh very widespread
+in American society at the turn of the
+
+ align:start position:0%
+in American society at the turn of the
+ 
+
+ align:start position:0%
+in American society at the turn of the
+century and especially in the south from
+
+ align:start position:0%
+century and especially in the south from
+ 
+
+ align:start position:0%
+century and especially in the south from
+which uh Griffith himself was was a
+
+ align:start position:0%
+which uh Griffith himself was was a
+ 
+
+ align:start position:0%
+which uh Griffith himself was was a
+southerner and was born in the south and
+
+ align:start position:0%
+southerner and was born in the south and
+ 
+
+ align:start position:0%
+southerner and was born in the south and
+what his film was deeply influenced by a
+
+ align:start position:0%
+what his film was deeply influenced by a
+ 
+
+ align:start position:0%
+what his film was deeply influenced by a
+best-selling novel called the clansmen
+
+ align:start position:0%
+best-selling novel called the clansmen
+ 
+
+ align:start position:0%
+best-selling novel called the clansmen
+which was a celebration of the Ku Klux
+
+ align:start position:0%
+which was a celebration of the Ku Klux
+ 
+
+ align:start position:0%
+which was a celebration of the Ku Klux
+Clan uh and the uh birth of a nation.
+
+ align:start position:0%
+Clan uh and the uh birth of a nation.
+ 
+
+ align:start position:0%
+Clan uh and the uh birth of a nation.
+So, so the content of Birth of a Nation
+
+ align:start position:0%
+So, so the content of Birth of a Nation
+ 
+
+ align:start position:0%
+So, so the content of Birth of a Nation
+is very unsettling and disturbing. And
+
+ align:start position:0%
+is very unsettling and disturbing. And
+ 
+
+ align:start position:0%
+is very unsettling and disturbing. And
+even when it was first uh um released to
+
+ align:start position:0%
+even when it was first uh um released to
+ 
+
+ align:start position:0%
+even when it was first uh um released to
+the public to great claim because it it
+
+ align:start position:0%
+the public to great claim because it it
+ 
+
+ align:start position:0%
+the public to great claim because it it
+it it expanded the possibilities of
+
+ align:start position:0%
+it it expanded the possibilities of
+ 
+
+ align:start position:0%
+it it expanded the possibilities of
+movies in all kinds of ways. From a
+
+ align:start position:0%
+movies in all kinds of ways. From a
+ 
+
+ align:start position:0%
+movies in all kinds of ways. From a
+technical standpoint, it is an
+
+ align:start position:0%
+technical standpoint, it is an
+ 
+
+ align:start position:0%
+technical standpoint, it is an
+astonishingly important film. And from a
+
+ align:start position:0%
+astonishingly important film. And from a
+ 
+
+ align:start position:0%
+astonishingly important film. And from a
+content standpoint, it's a very
+
+ align:start position:0%
+content standpoint, it's a very
+ 
+
+ align:start position:0%
+content standpoint, it's a very
+disturbing film. It's a wonderful
+
+ align:start position:0%
+disturbing film. It's a wonderful
+ 
+
+ align:start position:0%
+disturbing film. It's a wonderful
+reminder of the fact that this progress
+
+ align:start position:0%
+reminder of the fact that this progress
+ 
+
+ align:start position:0%
+reminder of the fact that this progress
+I'm describing to you is not an unaloyed
+
+ align:start position:0%
+I'm describing to you is not an unaloyed
+ 
+
+ align:start position:0%
+I'm describing to you is not an unaloyed
+triumphal story. Uh even as the movies
+
+ align:start position:0%
+triumphal story. Uh even as the movies
+ 
+
+ align:start position:0%
+triumphal story. Uh even as the movies
+became more technically complicated and
+
+ align:start position:0%
+became more technically complicated and
+ 
+
+ align:start position:0%
+became more technically complicated and
+and uh more demanding and longer and
+
+ align:start position:0%
+and uh more demanding and longer and
+ 
+
+ align:start position:0%
+and uh more demanding and longer and
+more interested in character, they also
+
+ align:start position:0%
+more interested in character, they also
+ 
+
+ align:start position:0%
+more interested in character, they also
+nonetheless carried the lies and
+
+ align:start position:0%
+nonetheless carried the lies and
+ 
+
+ align:start position:0%
+nonetheless carried the lies and
+prejudices and and um um um hierarchic
+
+ align:start position:0%
+prejudices and and um um um hierarchic
+ 
+
+ align:start position:0%
+prejudices and and um um um hierarchic
+assumptions that were embedded in the
+
+ align:start position:0%
+assumptions that were embedded in the
+ 
+
+ align:start position:0%
+assumptions that were embedded in the
+society from which they arose. How could
+
+ align:start position:0%
+society from which they arose. How could
+ 
+
+ align:start position:0%
+society from which they arose. How could
+it be otherwise? Every media form does
+
+ align:start position:0%
+it be otherwise? Every media form does
+ 
+
+ align:start position:0%
+it be otherwise? Every media form does
+this. But it's but it's important to
+
+ align:start position:0%
+this. But it's but it's important to
+ 
+
+ align:start position:0%
+this. But it's but it's important to
+make this point as a way of reminding us
+
+ align:start position:0%
+make this point as a way of reminding us
+ 
+
+ align:start position:0%
+make this point as a way of reminding us
+that the story we're telling is not uh
+
+ align:start position:0%
+that the story we're telling is not uh
+ 
+
+ align:start position:0%
+that the story we're telling is not uh
+in some simple sense just a kind of a
+
+ align:start position:0%
+in some simple sense just a kind of a
+ 
+
+ align:start position:0%
+in some simple sense just a kind of a
+kind of progress myth in which we're
+
+ align:start position:0%
+kind of progress myth in which we're
+ 
+
+ align:start position:0%
+kind of progress myth in which we're
+celebrating development and and and
+
+ align:start position:0%
+celebrating development and and and
+ 
+
+ align:start position:0%
+celebrating development and and and
+genius. We're we're we're identifying
+
+ align:start position:0%
+genius. We're we're we're identifying
+ 
+
+ align:start position:0%
+genius. We're we're we're identifying
+and locating something more complicated
+
+ align:start position:0%
+and locating something more complicated
+ 
+
+ align:start position:0%
+and locating something more complicated
+than that. the process whereby these
+
+ align:start position:0%
+than that. the process whereby these
+ 
+
+ align:start position:0%
+than that. the process whereby these
+cultural myths uh and these stories that
+
+ align:start position:0%
+cultural myths uh and these stories that
+ 
+
+ align:start position:0%
+cultural myths uh and these stories that
+are drawn from inherited older stories
+
+ align:start position:0%
+are drawn from inherited older stories
+ 
+
+ align:start position:0%
+are drawn from inherited older stories
+and from and from the lore of the
+
+ align:start position:0%
+and from and from the lore of the
+ 
+
+ align:start position:0%
+and from and from the lore of the
+society more broadly, more generally uh
+
+ align:start position:0%
+society more broadly, more generally uh
+ 
+
+ align:start position:0%
+society more broadly, more generally uh
+uh are are transformed into this new
+
+ align:start position:0%
+uh are are transformed into this new
+ 
+
+ align:start position:0%
+uh are are transformed into this new
+medium and they have a tremendous
+
+ align:start position:0%
+medium and they have a tremendous
+ 
+
+ align:start position:0%
+medium and they have a tremendous
+technical interest. But very often they
+
+ align:start position:0%
+technical interest. But very often they
+ 
+
+ align:start position:0%
+technical interest. But very often they
+also have a kind of cultural or
+
+ align:start position:0%
+also have a kind of cultural or
+ 
+
+ align:start position:0%
+also have a kind of cultural or
+sociological interest of a negative kind
+
+ align:start position:0%
+sociological interest of a negative kind
+ 
+
+ align:start position:0%
+sociological interest of a negative kind
+in the sense that what they reveal are
+
+ align:start position:0%
+in the sense that what they reveal are
+ 
+
+ align:start position:0%
+in the sense that what they reveal are
+the prejudices, the lies, the
+
+ align:start position:0%
+the prejudices, the lies, the
+ 
+
+ align:start position:0%
+the prejudices, the lies, the
+limitations uh of the society that's
+
+ align:start position:0%
+limitations uh of the society that's
+ 
+
+ align:start position:0%
+limitations uh of the society that's
+given the the mythologies that sustain
+
+ align:start position:0%
+given the the mythologies that sustain
+ 
+
+ align:start position:0%
+given the the mythologies that sustain
+the society. Again, this is a matter to
+
+ align:start position:0%
+the society. Again, this is a matter to
+ 
+
+ align:start position:0%
+the society. Again, this is a matter to
+which we'll return. One of the deep
+
+ align:start position:0%
+which we'll return. One of the deep
+ 
+
+ align:start position:0%
+which we'll return. One of the deep
+cultural functions of American movies
+
+ align:start position:0%
+cultural functions of American movies
+ 
+
+ align:start position:0%
+cultural functions of American movies
+especially was to promulgate a kind of
+
+ align:start position:0%
+especially was to promulgate a kind of
+ 
+
+ align:start position:0%
+especially was to promulgate a kind of
+mythology of America. And we'll talk
+
+ align:start position:0%
+mythology of America. And we'll talk
+ 
+
+ align:start position:0%
+mythology of America. And we'll talk
+more about this when we when we when we
+
+ align:start position:0%
+more about this when we when we when we
+ 
+
+ align:start position:0%
+more about this when we when we when we
+reach certain genre forms in the second
+
+ align:start position:0%
+reach certain genre forms in the second
+ 
+
+ align:start position:0%
+reach certain genre forms in the second
+segment of the course.
+
+ align:start position:0%
+segment of the course.
+ 
+
+ align:start position:0%
+segment of the course.
+I said something earlier this morning
+
+ align:start position:0%
+I said something earlier this morning
+ 
+
+ align:start position:0%
+I said something earlier this morning
+that I want to make uh explicit
+
+ align:start position:0%
+that I want to make uh explicit
+ 
+
+ align:start position:0%
+that I want to make uh explicit
+uh because I think it's an important
+
+ align:start position:0%
+uh because I think it's an important
+ 
+
+ align:start position:0%
+uh because I think it's an important
+another way of qualifying this triumphal
+
+ align:start position:0%
+another way of qualifying this triumphal
+ 
+
+ align:start position:0%
+another way of qualifying this triumphal
+story. It's hard because I'm
+
+ align:start position:0%
+story. It's hard because I'm
+ 
+
+ align:start position:0%
+story. It's hard because I'm
+enthusiastic about what I'm looking at
+
+ align:start position:0%
+enthusiastic about what I'm looking at
+ 
+
+ align:start position:0%
+enthusiastic about what I'm looking at
+and there is some material that's so
+
+ align:start position:0%
+and there is some material that's so
+ 
+
+ align:start position:0%
+and there is some material that's so
+exciting here to watch. In a way what
+
+ align:start position:0%
+exciting here to watch. In a way what
+ 
+
+ align:start position:0%
+exciting here to watch. In a way what
+we're watching is we're watching the
+
+ align:start position:0%
+we're watching is we're watching the
+ 
+
+ align:start position:0%
+we're watching is we're watching the
+birth of the movies. We're watching the
+
+ align:start position:0%
+birth of the movies. We're watching the
+ 
+
+ align:start position:0%
+birth of the movies. We're watching the
+the the discovery of the language of
+
+ align:start position:0%
+the the discovery of the language of
+ 
+
+ align:start position:0%
+the the discovery of the language of
+cinema in these early films. And that's
+
+ align:start position:0%
+cinema in these early films. And that's
+ 
+
+ align:start position:0%
+cinema in these early films. And that's
+why even though from an artistic
+
+ align:start position:0%
+why even though from an artistic
+ 
+
+ align:start position:0%
+why even though from an artistic
+standpoint, some of these shorts are not
+
+ align:start position:0%
+standpoint, some of these shorts are not
+ 
+
+ align:start position:0%
+standpoint, some of these shorts are not
+very rich. I hope they're interesting
+
+ align:start position:0%
+very rich. I hope they're interesting
+ 
+
+ align:start position:0%
+very rich. I hope they're interesting
+enough that I've made them interesting
+
+ align:start position:0%
+enough that I've made them interesting
+ 
+
+ align:start position:0%
+enough that I've made them interesting
+to you from a historical standpoint. If
+
+ align:start position:0%
+to you from a historical standpoint. If
+ 
+
+ align:start position:0%
+to you from a historical standpoint. If
+you look at them closely, you can see ve
+
+ align:start position:0%
+you look at them closely, you can see ve
+ 
+
+ align:start position:0%
+you look at them closely, you can see ve
+you can see the movies being born. You
+
+ align:start position:0%
+you can see the movies being born. You
+ 
+
+ align:start position:0%
+you can see the movies being born. You
+can see a language, a syntax for
+
+ align:start position:0%
+can see a language, a syntax for
+ 
+
+ align:start position:0%
+can see a language, a syntax for
+speaking in pictures for for this new
+
+ align:start position:0%
+speaking in pictures for for this new
+ 
+
+ align:start position:0%
+speaking in pictures for for this new
+new visual language being this new
+
+ align:start position:0%
+new visual language being this new
+ 
+
+ align:start position:0%
+new visual language being this new
+visual medium being developed. uh and
+
+ align:start position:0%
+visual medium being developed. uh and
+ 
+
+ align:start position:0%
+visual medium being developed. uh and
+and I I'll if I have time this evening,
+
+ align:start position:0%
+and I I'll if I have time this evening,
+ 
+
+ align:start position:0%
+and I I'll if I have time this evening,
+I'll give you a few more concrete
+
+ align:start position:0%
+I'll give you a few more concrete
+ 
+
+ align:start position:0%
+I'll give you a few more concrete
+examples of that. But another way in
+
+ align:start position:0%
+examples of that. But another way in
+ 
+
+ align:start position:0%
+examples of that. But another way in
+which one can qualify this apparently
+
+ align:start position:0%
+which one can qualify this apparently
+ 
+
+ align:start position:0%
+which one can qualify this apparently
+triumphal story, it's not a triumphal
+
+ align:start position:0%
+triumphal story, it's not a triumphal
+ 
+
+ align:start position:0%
+triumphal story, it's not a triumphal
+story, even though it is a story of
+
+ align:start position:0%
+story, even though it is a story of
+ 
+
+ align:start position:0%
+story, even though it is a story of
+refinement, development, and evolution
+
+ align:start position:0%
+refinement, development, and evolution
+ 
+
+ align:start position:0%
+refinement, development, and evolution
+of a of a kind that involves increasing
+
+ align:start position:0%
+of a of a kind that involves increasing
+ 
+
+ align:start position:0%
+of a of a kind that involves increasing
+complexity and technical perfection,
+
+ align:start position:0%
+complexity and technical perfection,
+ 
+
+ align:start position:0%
+complexity and technical perfection,
+technical uh uh mastery. uh it's not
+
+ align:start position:0%
+technical uh uh mastery. uh it's not
+ 
+
+ align:start position:0%
+technical uh uh mastery. uh it's not
+merely that or not or not or not even
+
+ align:start position:0%
+merely that or not or not or not even
+ 
+
+ align:start position:0%
+merely that or not or not or not even
+primarily that it's very important to
+
+ align:start position:0%
+primarily that it's very important to
+ 
+
+ align:start position:0%
+primarily that it's very important to
+recognize among other things as I
+
+ align:start position:0%
+recognize among other things as I
+ 
+
+ align:start position:0%
+recognize among other things as I
+implied this afternoon that uh not all
+
+ align:start position:0%
+implied this afternoon that uh not all
+ 
+
+ align:start position:0%
+implied this afternoon that uh not all
+the possibilities that are inherent in
+
+ align:start position:0%
+the possibilities that are inherent in
+ 
+
+ align:start position:0%
+the possibilities that are inherent in
+the in the in the nent medium aren't
+
+ align:start position:0%
+the in the in the nent medium aren't
+ 
+
+ align:start position:0%
+the in the in the nent medium aren't
+necessarily exploited in a particular
+
+ align:start position:0%
+necessarily exploited in a particular
+ 
+
+ align:start position:0%
+necessarily exploited in a particular
+cultural moment or or maybe ever
+
+ align:start position:0%
+cultural moment or or maybe ever
+ 
+
+ align:start position:0%
+cultural moment or or maybe ever
+exploited depending on how things
+
+ align:start position:0%
+exploited depending on how things
+ 
+
+ align:start position:0%
+exploited depending on how things
+develop. That is to say, uh, I mentioned
+
+ align:start position:0%
+develop. That is to say, uh, I mentioned
+ 
+
+ align:start position:0%
+develop. That is to say, uh, I mentioned
+this this afternoon, uh, how, for
+
+ align:start position:0%
+this this afternoon, uh, how, for
+ 
+
+ align:start position:0%
+this this afternoon, uh, how, for
+instance,
+
+ align:start position:0%
+instance,
+ 
+
+ align:start position:0%
+instance,
+when Edison first conceived the
+
+ align:start position:0%
+when Edison first conceived the
+ 
+
+ align:start position:0%
+when Edison first conceived the
+apparatus before it was actually
+
+ align:start position:0%
+apparatus before it was actually
+ 
+
+ align:start position:0%
+apparatus before it was actually
+invented of the mo of the motion picture
+
+ align:start position:0%
+invented of the mo of the motion picture
+ 
+
+ align:start position:0%
+invented of the mo of the motion picture
+projector and the motion picture camera,
+
+ align:start position:0%
+projector and the motion picture camera,
+ 
+
+ align:start position:0%
+projector and the motion picture camera,
+his first idea was that he would create
+
+ align:start position:0%
+his first idea was that he would create
+ 
+
+ align:start position:0%
+his first idea was that he would create
+an an item that would be a consumer item
+
+ align:start position:0%
+an an item that would be a consumer item
+ 
+
+ align:start position:0%
+an an item that would be a consumer item
+that would be sold to individual
+
+ align:start position:0%
+that would be sold to individual
+ 
+
+ align:start position:0%
+that would be sold to individual
+families and the film would become, you
+
+ align:start position:0%
+families and the film would become, you
+ 
+
+ align:start position:0%
+families and the film would become, you
+know, the the an equivalent of a kind of
+
+ align:start position:0%
+know, the the an equivalent of a kind of
+ 
+
+ align:start position:0%
+know, the the an equivalent of a kind of
+a photo album, although it would it
+
+ align:start position:0%
+a photo album, although it would it
+ 
+
+ align:start position:0%
+a photo album, although it would it
+would have motion in it and and the and
+
+ align:start position:0%
+would have motion in it and and the and
+ 
+
+ align:start position:0%
+would have motion in it and and the and
+as I suggested this this morning this
+
+ align:start position:0%
+as I suggested this this morning this
+ 
+
+ align:start position:0%
+as I suggested this this morning this
+afternoon there's no reason why given
+
+ align:start position:0%
+afternoon there's no reason why given
+ 
+
+ align:start position:0%
+afternoon there's no reason why given
+the nature of the technology itself that
+
+ align:start position:0%
+the nature of the technology itself that
+ 
+
+ align:start position:0%
+the nature of the technology itself that
+that vision of how film might develop
+
+ align:start position:0%
+that vision of how film might develop
+ 
+
+ align:start position:0%
+that vision of how film might develop
+was impossible. In fact, it wasn't
+
+ align:start position:0%
+was impossible. In fact, it wasn't
+ 
+
+ align:start position:0%
+was impossible. In fact, it wasn't
+impossible. It was just incredibly ahead
+
+ align:start position:0%
+impossible. It was just incredibly ahead
+ 
+
+ align:start position:0%
+impossible. It was just incredibly ahead
+of its time. It took it took a half a
+
+ align:start position:0%
+of its time. It took it took a half a
+ 
+
+ align:start position:0%
+of its time. It took it took a half a
+century before something like that
+
+ align:start position:0%
+century before something like that
+ 
+
+ align:start position:0%
+century before something like that
+actually became available in society.
+
+ align:start position:0%
+actually became available in society.
+ 
+
+ align:start position:0%
+actually became available in society.
+But there was no reason in terms of the
+
+ align:start position:0%
+But there was no reason in terms of the
+ 
+
+ align:start position:0%
+But there was no reason in terms of the
+the possibilities of the technology that
+
+ align:start position:0%
+the possibilities of the technology that
+ 
+
+ align:start position:0%
+the possibilities of the technology that
+that that needed to happen. What I'm
+
+ align:start position:0%
+that that needed to happen. What I'm
+ 
+
+ align:start position:0%
+that that needed to happen. What I'm
+calling your attention to is what is a
+
+ align:start position:0%
+calling your attention to is what is a
+ 
+
+ align:start position:0%
+calling your attention to is what is a
+very widespread myth. It's especially
+
+ align:start position:0%
+very widespread myth. It's especially
+ 
+
+ align:start position:0%
+very widespread myth. It's especially
+pernicious and widespread at MIT and
+
+ align:start position:0%
+pernicious and widespread at MIT and
+ 
+
+ align:start position:0%
+pernicious and widespread at MIT and
+it's ve for reasons that are obvious and
+
+ align:start position:0%
+it's ve for reasons that are obvious and
+ 
+
+ align:start position:0%
+it's ve for reasons that are obvious and
+understandable. We at MIT love to
+
+ align:start position:0%
+understandable. We at MIT love to
+ 
+
+ align:start position:0%
+understandable. We at MIT love to
+believe that technology will solve all
+
+ align:start position:0%
+believe that technology will solve all
+ 
+
+ align:start position:0%
+believe that technology will solve all
+problems. The primary thing I'm
+
+ align:start position:0%
+problems. The primary thing I'm
+ 
+
+ align:start position:0%
+problems. The primary thing I'm
+suggesting to you is that the evolution
+
+ align:start position:0%
+suggesting to you is that the evolution
+ 
+
+ align:start position:0%
+suggesting to you is that the evolution
+of the movies that I want you to be
+
+ align:start position:0%
+of the movies that I want you to be
+ 
+
+ align:start position:0%
+of the movies that I want you to be
+aware of this process of increasing
+
+ align:start position:0%
+aware of this process of increasing
+ 
+
+ align:start position:0%
+aware of this process of increasing
+complexity and and uh uh uh compression
+
+ align:start position:0%
+complexity and and uh uh uh compression
+ 
+
+ align:start position:0%
+complexity and and uh uh uh compression
+in which in in which the movies become a
+
+ align:start position:0%
+in which in in which the movies become a
+ 
+
+ align:start position:0%
+in which in in which the movies become a
+more and more independent form of
+
+ align:start position:0%
+more and more independent form of
+ 
+
+ align:start position:0%
+more and more independent form of
+expression in which the movies begin to
+
+ align:start position:0%
+expression in which the movies begin to
+ 
+
+ align:start position:0%
+expression in which the movies begin to
+discover the unique characteristics of
+
+ align:start position:0%
+discover the unique characteristics of
+ 
+
+ align:start position:0%
+discover the unique characteristics of
+the motion picture camera and of the
+
+ align:start position:0%
+the motion picture camera and of the
+ 
+
+ align:start position:0%
+the motion picture camera and of the
+environment of the movie theater that
+
+ align:start position:0%
+environment of the movie theater that
+ 
+
+ align:start position:0%
+environment of the movie theater that
+that the movie that the movies begin to
+
+ align:start position:0%
+that the movie that the movies begin to
+ 
+
+ align:start position:0%
+that the movie that the movies begin to
+explore those qualities in this new
+
+ align:start position:0%
+explore those qualities in this new
+ 
+
+ align:start position:0%
+explore those qualities in this new
+medium that are unique and special. That
+
+ align:start position:0%
+medium that are unique and special. That
+ 
+
+ align:start position:0%
+medium that are unique and special. That
+process is important and I want you to
+
+ align:start position:0%
+process is important and I want you to
+ 
+
+ align:start position:0%
+process is important and I want you to
+be aware of it. But I don't want you to
+
+ align:start position:0%
+be aware of it. But I don't want you to
+ 
+
+ align:start position:0%
+be aware of it. But I don't want you to
+embrace that principle too uncritically
+
+ align:start position:0%
+embrace that principle too uncritically
+ 
+
+ align:start position:0%
+embrace that principle too uncritically
+because I want you to recognize that
+
+ align:start position:0%
+because I want you to recognize that
+ 
+
+ align:start position:0%
+because I want you to recognize that
+what that that the technology itself
+
+ align:start position:0%
+what that that the technology itself
+ 
+
+ align:start position:0%
+what that that the technology itself
+does not explain this process. The
+
+ align:start position:0%
+does not explain this process. The
+ 
+
+ align:start position:0%
+does not explain this process. The
+process is explained by cultural factors
+
+ align:start position:0%
+process is explained by cultural factors
+ 
+
+ align:start position:0%
+process is explained by cultural factors
+and social factors and even individual
+
+ align:start position:0%
+and social factors and even individual
+ 
+
+ align:start position:0%
+and social factors and even individual
+sometimes individual psychological
+
+ align:start position:0%
+sometimes individual psychological
+ 
+
+ align:start position:0%
+sometimes individual psychological
+factors. Right? Uh what we're talking
+
+ align:start position:0%
+factors. Right? Uh what we're talking
+ 
+
+ align:start position:0%
+factors. Right? Uh what we're talking
+about here is the myth of technological
+
+ align:start position:0%
+about here is the myth of technological
+ 
+
+ align:start position:0%
+about here is the myth of technological
+determinism. The myth that technology
+
+ align:start position:0%
+determinism. The myth that technology
+ 
+
+ align:start position:0%
+determinism. The myth that technology
+drives culture. the myth that a new
+
+ align:start position:0%
+drives culture. the myth that a new
+ 
+
+ align:start position:0%
+drives culture. the myth that a new
+invention obliterates old inventions.
+
+ align:start position:0%
+invention obliterates old inventions.
+ 
+
+ align:start position:0%
+invention obliterates old inventions.
+The truth is much more complicated than
+
+ align:start position:0%
+The truth is much more complicated than
+ 
+
+ align:start position:0%
+The truth is much more complicated than
+that. And one of the most remarkable
+
+ align:start position:0%
+that. And one of the most remarkable
+ 
+
+ align:start position:0%
+that. And one of the most remarkable
+things about this evolutionary process
+
+ align:start position:0%
+things about this evolutionary process
+ 
+
+ align:start position:0%
+things about this evolutionary process
+I've been describing, as I said earlier,
+
+ align:start position:0%
+I've been describing, as I said earlier,
+ 
+
+ align:start position:0%
+I've been describing, as I said earlier,
+is how swift it is, how fast it is, how
+
+ align:start position:0%
+is how swift it is, how fast it is, how
+ 
+
+ align:start position:0%
+is how swift it is, how fast it is, how
+we go from being a mere novelty to
+
+ align:start position:0%
+we go from being a mere novelty to
+ 
+
+ align:start position:0%
+we go from being a mere novelty to
+becoming a a significant social form by
+
+ align:start position:0%
+becoming a a significant social form by
+ 
+
+ align:start position:0%
+becoming a a significant social form by
+1910 or so and to becoming a virtually
+
+ align:start position:0%
+1910 or so and to becoming a virtually
+ 
+
+ align:start position:0%
+1910 or so and to becoming a virtually
+universal aesthetic and entertainment
+
+ align:start position:0%
+universal aesthetic and entertainment
+ 
+
+ align:start position:0%
+universal aesthetic and entertainment
+experience for the majority of the
+
+ align:start position:0%
+experience for the majority of the
+ 
+
+ align:start position:0%
+experience for the majority of the
+population in the country by 1920. So in
+
+ align:start position:0%
+population in the country by 1920. So in
+ 
+
+ align:start position:0%
+population in the country by 1920. So in
+something like 20 or 25 years, the
+
+ align:start position:0%
+something like 20 or 25 years, the
+ 
+
+ align:start position:0%
+something like 20 or 25 years, the
+movies go from being an absolutely
+
+ align:start position:0%
+movies go from being an absolutely
+ 
+
+ align:start position:0%
+movies go from being an absolutely
+unknown or trivial novelty, sharing
+
+ align:start position:0%
+unknown or trivial novelty, sharing
+ 
+
+ align:start position:0%
+unknown or trivial novelty, sharing
+space with fortune tellers and strip and
+
+ align:start position:0%
+space with fortune tellers and strip and
+ 
+
+ align:start position:0%
+space with fortune tellers and strip and
+and strip shows in the penny arcades to
+
+ align:start position:0%
+and strip shows in the penny arcades to
+ 
+
+ align:start position:0%
+and strip shows in the penny arcades to
+becoming not just an embedded social
+
+ align:start position:0%
+becoming not just an embedded social
+ 
+
+ align:start position:0%
+becoming not just an embedded social
+form but one of the dominant economic
+
+ align:start position:0%
+form but one of the dominant economic
+ 
+
+ align:start position:0%
+form but one of the dominant economic
+engines of the society, employing tens
+
+ align:start position:0%
+engines of the society, employing tens
+ 
+
+ align:start position:0%
+engines of the society, employing tens
+of thousands of people in various uh
+
+ align:start position:0%
+of thousands of people in various uh
+ 
+
+ align:start position:0%
+of thousands of people in various uh
+direct and ancillary positions and
+
+ align:start position:0%
+direct and ancillary positions and
+ 
+
+ align:start position:0%
+direct and ancillary positions and
+mobilizing virtually the entire
+
+ align:start position:0%
+mobilizing virtually the entire
+ 
+
+ align:start position:0%
+mobilizing virtually the entire
+population of the country in an an in a
+
+ align:start position:0%
+population of the country in an an in a
+ 
+
+ align:start position:0%
+population of the country in an an in a
+regular a routine and habitual
+
+ align:start position:0%
+regular a routine and habitual
+ 
+
+ align:start position:0%
+regular a routine and habitual
+experience uh um uh to which they return
+
+ align:start position:0%
+experience uh um uh to which they return
+ 
+
+ align:start position:0%
+experience uh um uh to which they return
+again and again and because the audience
+
+ align:start position:0%
+again and again and because the audience
+ 
+
+ align:start position:0%
+again and again and because the audience
+is returning again and again I remember
+
+ align:start position:0%
+is returning again and again I remember
+ 
+
+ align:start position:0%
+is returning again and again I remember
+I said there's a kind of symbiotic
+
+ align:start position:0%
+I said there's a kind of symbiotic
+ 
+
+ align:start position:0%
+I said there's a kind of symbiotic
+relation between the audience and the
+
+ align:start position:0%
+relation between the audience and the
+ 
+
+ align:start position:0%
+relation between the audience and the
+because the audience is returning again
+
+ align:start position:0%
+because the audience is returning again
+ 
+
+ align:start position:0%
+because the audience is returning again
+and again what happens that's also an
+
+ align:start position:0%
+and again what happens that's also an
+ 
+
+ align:start position:0%
+and again what happens that's also an
+aspect of the resources that are
+
+ align:start position:0%
+aspect of the resources that are
+ 
+
+ align:start position:0%
+aspect of the resources that are
+available to the medium what begins then
+
+ align:start position:0%
+available to the medium what begins then
+ 
+
+ align:start position:0%
+available to the medium what begins then
+to develop are form are are forms of
+
+ align:start position:0%
+to develop are form are are forms of
+ 
+
+ align:start position:0%
+to develop are form are are forms of
+storytelling that rely on the audience's
+
+ align:start position:0%
+storytelling that rely on the audience's
+ 
+
+ align:start position:0%
+storytelling that rely on the audience's
+prior memory of other shows, right? So
+
+ align:start position:0%
+prior memory of other shows, right? So
+ 
+
+ align:start position:0%
+prior memory of other shows, right? So
+that one thing that emerges very quickly
+
+ align:start position:0%
+that one thing that emerges very quickly
+ 
+
+ align:start position:0%
+that one thing that emerges very quickly
+is what we might call a star system in
+
+ align:start position:0%
+is what we might call a star system in
+ 
+
+ align:start position:0%
+is what we might call a star system in
+which particular actors are become
+
+ align:start position:0%
+which particular actors are become
+ 
+
+ align:start position:0%
+which particular actors are become
+identified with particular kinds of
+
+ align:start position:0%
+identified with particular kinds of
+ 
+
+ align:start position:0%
+identified with particular kinds of
+roles and audiences want to come back to
+
+ align:start position:0%
+roles and audiences want to come back to
+ 
+
+ align:start position:0%
+roles and audiences want to come back to
+see those stars again and again. What
+
+ align:start position:0%
+see those stars again and again. What
+ 
+
+ align:start position:0%
+see those stars again and again. What
+also begins to happen is the
+
+ align:start position:0%
+also begins to happen is the
+ 
+
+ align:start position:0%
+also begins to happen is the
+establishment of a very rigorous kind of
+
+ align:start position:0%
+establishment of a very rigorous kind of
+ 
+
+ align:start position:0%
+establishment of a very rigorous kind of
+genre system. What's a genre? A category
+
+ align:start position:0%
+genre system. What's a genre? A category
+ 
+
+ align:start position:0%
+genre system. What's a genre? A category
+of story. The western is a genre. The
+
+ align:start position:0%
+of story. The western is a genre. The
+ 
+
+ align:start position:0%
+of story. The western is a genre. The
+detective story is a genre. The elegy is
+
+ align:start position:0%
+detective story is a genre. The elegy is
+ 
+
+ align:start position:0%
+detective story is a genre. The elegy is
+a poetic genre. Right? That so so
+
+ align:start position:0%
+a poetic genre. Right? That so so
+ 
+
+ align:start position:0%
+a poetic genre. Right? That so so
+genres. So and and and the movie the the
+
+ align:start position:0%
+genres. So and and and the movie the the
+ 
+
+ align:start position:0%
+genres. So and and and the movie the the
+typical the fundamental movie genres
+
+ align:start position:0%
+typical the fundamental movie genres
+ 
+
+ align:start position:0%
+typical the fundamental movie genres
+begin to emerge relatively early.
+
+ align:start position:0%
+begin to emerge relatively early.
+ 
+
+ align:start position:0%
+begin to emerge relatively early.
+There's a western adventure story.
+
+ align:start position:0%
+There's a western adventure story.
+ 
+
+ align:start position:0%
+There's a western adventure story.
+There's a historical spectacle. Uh there
+
+ align:start position:0%
+There's a historical spectacle. Uh there
+ 
+
+ align:start position:0%
+There's a historical spectacle. Uh there
+are certain forms of urban crime
+
+ align:start position:0%
+are certain forms of urban crime
+ 
+
+ align:start position:0%
+are certain forms of urban crime
+narrative that that became our detective
+
+ align:start position:0%
+narrative that that became our detective
+ 
+
+ align:start position:0%
+narrative that that became our detective
+and crime films at a later at a later
+
+ align:start position:0%
+and crime films at a later at a later
+ 
+
+ align:start position:0%
+and crime films at a later at a later
+stage. Uh and there are certain and
+
+ align:start position:0%
+stage. Uh and there are certain and
+ 
+
+ align:start position:0%
+stage. Uh and there are certain and
+there emerge especially certain forms of
+
+ align:start position:0%
+there emerge especially certain forms of
+ 
+
+ align:start position:0%
+there emerge especially certain forms of
+satire and comedy. So so a genre system
+
+ align:start position:0%
+satire and comedy. So so a genre system
+ 
+
+ align:start position:0%
+satire and comedy. So so a genre system
+begins to emerge as well. And there
+
+ align:start position:0%
+begins to emerge as well. And there
+ 
+
+ align:start position:0%
+begins to emerge as well. And there
+there are reasons of course why this
+
+ align:start position:0%
+there are reasons of course why this
+ 
+
+ align:start position:0%
+there are reasons of course why this
+kind of thing is useful to a mass
+
+ align:start position:0%
+kind of thing is useful to a mass
+ 
+
+ align:start position:0%
+kind of thing is useful to a mass
+production system to a system of an
+
+ align:start position:0%
+production system to a system of an
+ 
+
+ align:start position:0%
+production system to a system of an
+assembly line system because look if you
+
+ align:start position:0%
+assembly line system because look if you
+ 
+
+ align:start position:0%
+assembly line system because look if you
+make seven westerns uh if the same uh
+
+ align:start position:0%
+make seven westerns uh if the same uh
+ 
+
+ align:start position:0%
+make seven westerns uh if the same uh
+movie studio makes seven westerns they
+
+ align:start position:0%
+movie studio makes seven westerns they
+ 
+
+ align:start position:0%
+movie studio makes seven westerns they
+can use the same horses again and again
+
+ align:start position:0%
+can use the same horses again and again
+ 
+
+ align:start position:0%
+can use the same horses again and again
+they can use the same set they can use
+
+ align:start position:0%
+they can use the same set they can use
+ 
+
+ align:start position:0%
+they can use the same set they can use
+the same hats they might even be you and
+
+ align:start position:0%
+the same hats they might even be you and
+ 
+
+ align:start position:0%
+the same hats they might even be you and
+this in fact happened they might even be
+
+ align:start position:0%
+this in fact happened they might even be
+ 
+
+ align:start position:0%
+this in fact happened they might even be
+be able to use the same clip of film
+
+ align:start position:0%
+be able to use the same clip of film
+ 
+
+ align:start position:0%
+be able to use the same clip of film
+that shows a cattle stampede in seven
+
+ align:start position:0%
+that shows a cattle stampede in seven
+ 
+
+ align:start position:0%
+that shows a cattle stampede in seven
+different movies because nobody would
+
+ align:start position:0%
+different movies because nobody would
+ 
+
+ align:start position:0%
+different movies because nobody would
+actually see it. So economies of scale
+
+ align:start position:0%
+actually see it. So economies of scale
+ 
+
+ align:start position:0%
+actually see it. So economies of scale
+become possible uh as the system begins
+
+ align:start position:0%
+become possible uh as the system begins
+ 
+
+ align:start position:0%
+become possible uh as the system begins
+to regularize itself once it stabilizes
+
+ align:start position:0%
+to regularize itself once it stabilizes
+ 
+
+ align:start position:0%
+to regularize itself once it stabilizes
+after that period of imitation and
+
+ align:start position:0%
+after that period of imitation and
+ 
+
+ align:start position:0%
+after that period of imitation and
+patent warfare. Right? So one of the
+
+ align:start position:0%
+patent warfare. Right? So one of the
+ 
+
+ align:start position:0%
+patent warfare. Right? So one of the
+things and there's and there's nothing
+
+ align:start position:0%
+things and there's and there's nothing
+ 
+
+ align:start position:0%
+things and there's and there's nothing
+noble or artistic or or or conscious uh
+
+ align:start position:0%
+noble or artistic or or or conscious uh
+ 
+
+ align:start position:0%
+noble or artistic or or or conscious uh
+about this development. That's part of
+
+ align:start position:0%
+about this development. That's part of
+ 
+
+ align:start position:0%
+about this development. That's part of
+what makes it so remarkable and it puts
+
+ align:start position:0%
+what makes it so remarkable and it puts
+ 
+
+ align:start position:0%
+what makes it so remarkable and it puts
+us in touch with a paradox that's at the
+
+ align:start position:0%
+us in touch with a paradox that's at the
+ 
+
+ align:start position:0%
+us in touch with a paradox that's at the
+very heart of what I hope to make you
+
+ align:start position:0%
+very heart of what I hope to make you
+ 
+
+ align:start position:0%
+very heart of what I hope to make you
+aware of in this course. It's a paradox
+
+ align:start position:0%
+aware of in this course. It's a paradox
+ 
+
+ align:start position:0%
+aware of in this course. It's a paradox
+that I guess it animates my transition
+
+ align:start position:0%
+that I guess it animates my transition
+ 
+
+ align:start position:0%
+that I guess it animates my transition
+many years ago now from a traditional
+
+ align:start position:0%
+many years ago now from a traditional
+ 
+
+ align:start position:0%
+many years ago now from a traditional
+literary scholar into someone interested
+
+ align:start position:0%
+literary scholar into someone interested
+ 
+
+ align:start position:0%
+literary scholar into someone interested
+in film and media. And it's this paradox
+
+ align:start position:0%
+in film and media. And it's this paradox
+ 
+
+ align:start position:0%
+in film and media. And it's this paradox
+that based on what I've been telling you
+
+ align:start position:0%
+that based on what I've been telling you
+ 
+
+ align:start position:0%
+that based on what I've been telling you
+about this evolution this evolution of
+
+ align:start position:0%
+about this evolution this evolution of
+ 
+
+ align:start position:0%
+about this evolution this evolution of
+the medium of of the film medium. It's
+
+ align:start position:0%
+the medium of of the film medium. It's
+ 
+
+ align:start position:0%
+the medium of of the film medium. It's
+the paradox that capitalist greed, the
+
+ align:start position:0%
+the paradox that capitalist greed, the
+ 
+
+ align:start position:0%
+the paradox that capitalist greed, the
+crassest of alliances between commerce
+
+ align:start position:0%
+crassest of alliances between commerce
+ 
+
+ align:start position:0%
+crassest of alliances between commerce
+and modern technology
+
+ align:start position:0%
+and modern technology
+ 
+
+ align:start position:0%
+and modern technology
+might be the enabling conditions of a
+
+ align:start position:0%
+might be the enabling conditions of a
+ 
+
+ align:start position:0%
+might be the enabling conditions of a
+complex narrative art. Right? Where does
+
+ align:start position:0%
+complex narrative art. Right? Where does
+ 
+
+ align:start position:0%
+complex narrative art. Right? Where does
+art come from? It's about the and it's
+
+ align:start position:0%
+art come from? It's about the and it's
+ 
+
+ align:start position:0%
+art come from? It's about the and it's
+not just about art though even about
+
+ align:start position:0%
+not just about art though even about
+ 
+
+ align:start position:0%
+not just about art though even about
+sort of social even if even if we forget
+
+ align:start position:0%
+sort of social even if even if we forget
+ 
+
+ align:start position:0%
+sort of social even if even if we forget
+the question of art and just talk about
+
+ align:start position:0%
+the question of art and just talk about
+ 
+
+ align:start position:0%
+the question of art and just talk about
+sort of the the social and cultural
+
+ align:start position:0%
+sort of the the social and cultural
+ 
+
+ align:start position:0%
+sort of the the social and cultural
+importance of moviegoing in modern
+
+ align:start position:0%
+importance of moviegoing in modern
+ 
+
+ align:start position:0%
+importance of moviegoing in modern
+societies. leave out the question of
+
+ align:start position:0%
+societies. leave out the question of
+ 
+
+ align:start position:0%
+societies. leave out the question of
+whether it's an aesthetically valuable
+
+ align:start position:0%
+whether it's an aesthetically valuable
+ 
+
+ align:start position:0%
+whether it's an aesthetically valuable
+experience. It's so central to human
+
+ align:start position:0%
+experience. It's so central to human
+ 
+
+ align:start position:0%
+experience. It's so central to human
+experience, remains so central to human
+
+ align:start position:0%
+experience, remains so central to human
+ 
+
+ align:start position:0%
+experience, remains so central to human
+experience that there's a tremendous par
+
+ align:start position:0%
+experience that there's a tremendous par
+ 
+
+ align:start position:0%
+experience that there's a tremendous par
+that there's a tremendous paradox in
+
+ align:start position:0%
+that there's a tremendous paradox in
+ 
+
+ align:start position:0%
+that there's a tremendous paradox in
+this that the that the crassest of
+
+ align:start position:0%
+this that the that the crassest of
+ 
+
+ align:start position:0%
+this that the that the crassest of
+alliances between commerce and
+
+ align:start position:0%
+alliances between commerce and
+ 
+
+ align:start position:0%
+alliances between commerce and
+technology, right? Nothing noble or
+
+ align:start position:0%
+technology, right? Nothing noble or
+ 
+
+ align:start position:0%
+technology, right? Nothing noble or
+admirable about it. Nobody's sitting
+
+ align:start position:0%
+admirable about it. Nobody's sitting
+ 
+
+ align:start position:0%
+admirable about it. Nobody's sitting
+down thinking I want to make a new great
+
+ align:start position:0%
+down thinking I want to make a new great
+ 
+
+ align:start position:0%
+down thinking I want to make a new great
+medium for art. nonetheless become these
+
+ align:start position:0%
+medium for art. nonetheless become these
+ 
+
+ align:start position:0%
+medium for art. nonetheless become these
+this alliance becomes the enabling
+
+ align:start position:0%
+this alliance becomes the enabling
+ 
+
+ align:start position:0%
+this alliance becomes the enabling
+conditions for a complex form of social
+
+ align:start position:0%
+conditions for a complex form of social
+ 
+
+ align:start position:0%
+conditions for a complex form of social
+experience and of narrative art. Well,
+
+ align:start position:0%
+experience and of narrative art. Well,
+ 
+
+ align:start position:0%
+experience and of narrative art. Well,
+that paradox is at the heart of a lot of
+
+ align:start position:0%
+that paradox is at the heart of a lot of
+ 
+
+ align:start position:0%
+that paradox is at the heart of a lot of
+what we're we'll be looking at in this
+
+ align:start position:0%
+what we're we'll be looking at in this
+ 
+
+ align:start position:0%
+what we're we'll be looking at in this
+course and I hope you'll keep it in mind
+
+ align:start position:0%
+course and I hope you'll keep it in mind
+ 
+
+ align:start position:0%
+course and I hope you'll keep it in mind
+as we go on. I'd like to say a couple of
+
+ align:start position:0%
+as we go on. I'd like to say a couple of
+ 
+
+ align:start position:0%
+as we go on. I'd like to say a couple of
+words, not too many, a couple of words
+
+ align:start position:0%
+words, not too many, a couple of words
+ 
+
+ align:start position:0%
+words, not too many, a couple of words
+about the um the great train robbery,
+
+ align:start position:0%
+about the um the great train robbery,
+ 
+
+ align:start position:0%
+about the um the great train robbery,
+the very first uh film that you've seen.
+
+ align:start position:0%
+the very first uh film that you've seen.
+ 
+
+ align:start position:0%
+the very first uh film that you've seen.
+uh this the great train robbery is
+
+ align:start position:0%
+uh this the great train robbery is
+ 
+
+ align:start position:0%
+uh this the great train robbery is
+discussed in some helpful detail in
+
+ align:start position:0%
+discussed in some helpful detail in
+ 
+
+ align:start position:0%
+discussed in some helpful detail in
+David Cook's history of narrative film
+
+ align:start position:0%
+David Cook's history of narrative film
+ 
+
+ align:start position:0%
+David Cook's history of narrative film
+and I urge you to look closely at his
+
+ align:start position:0%
+and I urge you to look closely at his
+ 
+
+ align:start position:0%
+and I urge you to look closely at his
+account of it but I want to remind you
+
+ align:start position:0%
+account of it but I want to remind you
+ 
+
+ align:start position:0%
+account of it but I want to remind you
+of about a couple of highlights. One is
+
+ align:start position:0%
+of about a couple of highlights. One is
+ 
+
+ align:start position:0%
+of about a couple of highlights. One is
+that that although the great train
+
+ align:start position:0%
+that that although the great train
+ 
+
+ align:start position:0%
+that that although the great train
+robbery seems very primitive to us, it's
+
+ align:start position:0%
+robbery seems very primitive to us, it's
+ 
+
+ align:start position:0%
+robbery seems very primitive to us, it's
+important to realize that even the great
+
+ align:start position:0%
+important to realize that even the great
+ 
+
+ align:start position:0%
+important to realize that even the great
+train robbery is already a refined text
+
+ align:start position:0%
+train robbery is already a refined text
+ 
+
+ align:start position:0%
+train robbery is already a refined text
+almost most most of the most fundamental
+
+ align:start position:0%
+almost most most of the most fundamental
+ 
+
+ align:start position:0%
+almost most most of the most fundamental
+principles of what we might call the
+
+ align:start position:0%
+principles of what we might call the
+ 
+
+ align:start position:0%
+principles of what we might call the
+syntax or grammar of the movies is
+
+ align:start position:0%
+syntax or grammar of the movies is
+ 
+
+ align:start position:0%
+syntax or grammar of the movies is
+already embedded in the great train
+
+ align:start position:0%
+already embedded in the great train
+ 
+
+ align:start position:0%
+already embedded in the great train
+robbery. And what that means is that the
+
+ align:start position:0%
+robbery. And what that means is that the
+ 
+
+ align:start position:0%
+robbery. And what that means is that the
+period the five or six year period
+
+ align:start position:0%
+period the five or six year period
+ 
+
+ align:start position:0%
+period the five or six year period
+before that when there is all this
+
+ align:start position:0%
+before that when there is all this
+ 
+
+ align:start position:0%
+before that when there is all this
+practice in with non-narrative forms uh
+
+ align:start position:0%
+practice in with non-narrative forms uh
+ 
+
+ align:start position:0%
+practice in with non-narrative forms uh
+lies behind the great train robbery in
+
+ align:start position:0%
+lies behind the great train robbery in
+ 
+
+ align:start position:0%
+lies behind the great train robbery in
+some and what also lies behind the great
+
+ align:start position:0%
+some and what also lies behind the great
+ 
+
+ align:start position:0%
+some and what also lies behind the great
+train robbery is this experience of
+
+ align:start position:0%
+train robbery is this experience of
+ 
+
+ align:start position:0%
+train robbery is this experience of
+audiences going in to the to first to
+
+ align:start position:0%
+audiences going in to the to first to
+ 
+
+ align:start position:0%
+audiences going in to the to first to
+the penny arcades then to the
+
+ align:start position:0%
+the penny arcades then to the
+ 
+
+ align:start position:0%
+the penny arcades then to the
+nickelodeons that begin to open up in
+
+ align:start position:0%
+nickelodeons that begin to open up in
+ 
+
+ align:start position:0%
+nickelodeons that begin to open up in
+the in in the by the turn of the 20th
+
+ align:start position:0%
+the in in the by the turn of the 20th
+ 
+
+ align:start position:0%
+the in in the by the turn of the 20th
+century uh and becoming impatient with
+
+ align:start position:0%
+century uh and becoming impatient with
+ 
+
+ align:start position:0%
+century uh and becoming impatient with
+repeated scenes that simply show uh
+
+ align:start position:0%
+repeated scenes that simply show uh
+ 
+
+ align:start position:0%
+repeated scenes that simply show uh
+jokes uh hoses going off in people's
+
+ align:start position:0%
+jokes uh hoses going off in people's
+ 
+
+ align:start position:0%
+jokes uh hoses going off in people's
+faces or trains coming into a state.
+
+ align:start position:0%
+faces or trains coming into a state.
+ 
+
+ align:start position:0%
+faces or trains coming into a state.
+After a while, the novelty wears off.
+
+ align:start position:0%
+After a while, the novelty wears off.
+ 
+
+ align:start position:0%
+After a while, the novelty wears off.
+The audience wants but of course the
+
+ align:start position:0%
+The audience wants but of course the
+ 
+
+ align:start position:0%
+The audience wants but of course the
+people who are making films are also
+
+ align:start position:0%
+people who are making films are also
+ 
+
+ align:start position:0%
+people who are making films are also
+interested in what they're doing. You
+
+ align:start position:0%
+interested in what they're doing. You
+ 
+
+ align:start position:0%
+interested in what they're doing. You
+can feel especially if you look at DW
+
+ align:start position:0%
+can feel especially if you look at DW
+ 
+
+ align:start position:0%
+can feel especially if you look at DW
+Griffith's shorts and you've looked at
+
+ align:start position:0%
+Griffith's shorts and you've looked at
+ 
+
+ align:start position:0%
+Griffith's shorts and you've looked at
+two you will have looked at two of them
+
+ align:start position:0%
+two you will have looked at two of them
+ 
+
+ align:start position:0%
+two you will have looked at two of them
+in this course uh the uh a beast at bay
+
+ align:start position:0%
+in this course uh the uh a beast at bay
+ 
+
+ align:start position:0%
+in this course uh the uh a beast at bay
+from last time and the lonale operator
+
+ align:start position:0%
+from last time and the lonale operator
+ 
+
+ align:start position:0%
+from last time and the lonale operator
+which you'll see tonight before we turn
+
+ align:start position:0%
+which you'll see tonight before we turn
+ 
+
+ align:start position:0%
+which you'll see tonight before we turn
+to the Keaton films. uh and you'll see
+
+ align:start position:0%
+to the Keaton films. uh and you'll see
+ 
+
+ align:start position:0%
+to the Keaton films. uh and you'll see
+in these are just a sampling of his of
+
+ align:start position:0%
+in these are just a sampling of his of
+ 
+
+ align:start position:0%
+in these are just a sampling of his of
+his early work. But if you look closely
+
+ align:start position:0%
+his early work. But if you look closely
+ 
+
+ align:start position:0%
+his early work. But if you look closely
+at those where you can feel Griffith's
+
+ align:start position:0%
+at those where you can feel Griffith's
+ 
+
+ align:start position:0%
+at those where you can feel Griffith's
+own excitement at discovering the
+
+ align:start position:0%
+own excitement at discovering the
+ 
+
+ align:start position:0%
+own excitement at discovering the
+possibilities of the cinema learn and in
+
+ align:start position:0%
+possibilities of the cinema learn and in
+ 
+
+ align:start position:0%
+possibilities of the cinema learn and in
+many cases these films you Griffith is
+
+ align:start position:0%
+many cases these films you Griffith is
+ 
+
+ align:start position:0%
+many cases these films you Griffith is
+doing what doing some things with the
+
+ align:start position:0%
+doing what doing some things with the
+ 
+
+ align:start position:0%
+doing what doing some things with the
+camera doing some things with narrative
+
+ align:start position:0%
+camera doing some things with narrative
+ 
+
+ align:start position:0%
+camera doing some things with narrative
+shape with the shaping of narrative in
+
+ align:start position:0%
+shape with the shaping of narrative in
+ 
+
+ align:start position:0%
+shape with the shaping of narrative in
+in cinema that had never been done
+
+ align:start position:0%
+in cinema that had never been done
+ 
+
+ align:start position:0%
+in cinema that had never been done
+before and you can feel his own
+
+ align:start position:0%
+before and you can feel his own
+ 
+
+ align:start position:0%
+before and you can feel his own
+excitement at the possibilities of this
+
+ align:start position:0%
+excitement at the possibilities of this
+ 
+
+ align:start position:0%
+excitement at the possibilities of this
+of this astonishing of this astonishing
+
+ align:start position:0%
+of this astonishing of this astonishing
+ 
+
+ align:start position:0%
+of this astonishing of this astonishing
+technology. Well, the great train
+
+ align:start position:0%
+technology. Well, the great train
+ 
+
+ align:start position:0%
+technology. Well, the great train
+robbery, the most important discovery
+
+ align:start position:0%
+robbery, the most important discovery
+ 
+
+ align:start position:0%
+robbery, the most important discovery
+that the great train robbery shows us,
+
+ align:start position:0%
+that the great train robbery shows us,
+ 
+
+ align:start position:0%
+that the great train robbery shows us,
+and again, it seems so obvious and so
+
+ align:start position:0%
+and again, it seems so obvious and so
+ 
+
+ align:start position:0%
+and again, it seems so obvious and so
+embedded that we wouldn't even think
+
+ align:start position:0%
+embedded that we wouldn't even think
+ 
+
+ align:start position:0%
+embedded that we wouldn't even think
+about it today. We've absorbed these
+
+ align:start position:0%
+about it today. We've absorbed these
+ 
+
+ align:start position:0%
+about it today. We've absorbed these
+principles so deeply into our DNA that
+
+ align:start position:0%
+principles so deeply into our DNA that
+ 
+
+ align:start position:0%
+principles so deeply into our DNA that
+we don't even think of we're we're we
+
+ align:start position:0%
+we don't even think of we're we're we
+ 
+
+ align:start position:0%
+we don't even think of we're we're we
+learn how to watch movies in this way
+
+ align:start position:0%
+learn how to watch movies in this way
+ 
+
+ align:start position:0%
+learn how to watch movies in this way
+from the great from the cradle in some
+
+ align:start position:0%
+from the great from the cradle in some
+ 
+
+ align:start position:0%
+from the great from the cradle in some
+ways be because we we're by by the time
+
+ align:start position:0%
+ways be because we we're by by the time
+ 
+
+ align:start position:0%
+ways be because we we're by by the time
+most most people today are five or six
+
+ align:start position:0%
+most most people today are five or six
+ 
+
+ align:start position:0%
+most most people today are five or six
+years old, they've been subjected
+
+ align:start position:0%
+years old, they've been subjected
+ 
+
+ align:start position:0%
+years old, they've been subjected
+probably to more audiovisisual images
+
+ align:start position:0%
+probably to more audiovisisual images
+ 
+
+ align:start position:0%
+probably to more audiovisisual images
+than anyone alive in 1900. And that's
+
+ align:start position:0%
+than anyone alive in 1900. And that's
+ 
+
+ align:start position:0%
+than anyone alive in 1900. And that's
+you know we're we're just cognitively
+
+ align:start position:0%
+you know we're we're just cognitively
+ 
+
+ align:start position:0%
+you know we're we're just cognitively
+different from from the in terms of our
+
+ align:start position:0%
+different from from the in terms of our
+ 
+
+ align:start position:0%
+different from from the in terms of our
+capacity to process audiovisisual
+
+ align:start position:0%
+capacity to process audiovisisual
+ 
+
+ align:start position:0%
+capacity to process audiovisisual
+information. Uh we and but imagine an
+
+ align:start position:0%
+information. Uh we and but imagine an
+ 
+
+ align:start position:0%
+information. Uh we and but imagine an
+audience that's completely illiterate in
+
+ align:start position:0%
+audience that's completely illiterate in
+ 
+
+ align:start position:0%
+audience that's completely illiterate in
+these things that has to learn this
+
+ align:start position:0%
+these things that has to learn this
+ 
+
+ align:start position:0%
+these things that has to learn this
+system as the system itself is evolving.
+
+ align:start position:0%
+system as the system itself is evolving.
+ 
+
+ align:start position:0%
+system as the system itself is evolving.
+That's part of the excitement of looking
+
+ align:start position:0%
+That's part of the excitement of looking
+ 
+
+ align:start position:0%
+That's part of the excitement of looking
+at these at at these early films. And
+
+ align:start position:0%
+at these at at these early films. And
+ 
+
+ align:start position:0%
+at these at at these early films. And
+the most important discovery in the in
+
+ align:start position:0%
+the most important discovery in the in
+ 
+
+ align:start position:0%
+the most important discovery in the in
+the great train robbery is the discovery
+
+ align:start position:0%
+the great train robbery is the discovery
+ 
+
+ align:start position:0%
+the great train robbery is the discovery
+that the shot the single the single
+
+ align:start position:0%
+that the shot the single the single
+ 
+
+ align:start position:0%
+that the shot the single the single
+uncut shot of film however long it lasts
+
+ align:start position:0%
+uncut shot of film however long it lasts
+ 
+
+ align:start position:0%
+uncut shot of film however long it lasts
+and its length is dependent on on the
+
+ align:start position:0%
+and its length is dependent on on the
+ 
+
+ align:start position:0%
+and its length is dependent on on the
+decision you make about when to edit it
+
+ align:start position:0%
+decision you make about when to edit it
+ 
+
+ align:start position:0%
+decision you make about when to edit it
+right uh so it can it can go on for a
+
+ align:start position:0%
+right uh so it can it can go on for a
+ 
+
+ align:start position:0%
+right uh so it can it can go on for a
+long time or it can be very short and
+
+ align:start position:0%
+long time or it can be very short and
+ 
+
+ align:start position:0%
+long time or it can be very short and
+and the length or the shortness of a of
+
+ align:start position:0%
+and the length or the shortness of a of
+ 
+
+ align:start position:0%
+and the length or the shortness of a of
+of of cuts also affects sort of the
+
+ align:start position:0%
+of of cuts also affects sort of the
+ 
+
+ align:start position:0%
+of of cuts also affects sort of the
+rhythm of your experience in the film.
+
+ align:start position:0%
+rhythm of your experience in the film.
+ 
+
+ align:start position:0%
+rhythm of your experience in the film.
+This is something that you can see
+
+ align:start position:0%
+This is something that you can see
+ 
+
+ align:start position:0%
+This is something that you can see
+Griffith practicing with even as as as
+
+ align:start position:0%
+Griffith practicing with even as as as
+ 
+
+ align:start position:0%
+Griffith practicing with even as as as
+early as a beast at bay. If you think
+
+ align:start position:0%
+early as a beast at bay. If you think
+ 
+
+ align:start position:0%
+early as a beast at bay. If you think
+about the great climax of the beast at
+
+ align:start position:0%
+about the great climax of the beast at
+ 
+
+ align:start position:0%
+about the great climax of the beast at
+bay where you have the where you have
+
+ align:start position:0%
+bay where you have the where you have
+ 
+
+ align:start position:0%
+bay where you have the where you have
+the uh uh um
+
+ align:start position:0%
+the uh uh um
+ 
+
+ align:start position:0%
+the uh uh um
+uh the woman the woman being threatened
+
+ align:start position:0%
+uh the woman the woman being threatened
+ 
+
+ align:start position:0%
+uh the woman the woman being threatened
+but you also have this sort of this sort
+
+ align:start position:0%
+but you also have this sort of this sort
+ 
+
+ align:start position:0%
+but you also have this sort of this sort
+of race in the automobile to try to to
+
+ align:start position:0%
+of race in the automobile to try to to
+ 
+
+ align:start position:0%
+of race in the automobile to try to to
+try to get there on time and then and
+
+ align:start position:0%
+try to get there on time and then and
+ 
+
+ align:start position:0%
+try to get there on time and then and
+then the race to rescue her by a variety
+
+ align:start position:0%
+then the race to rescue her by a variety
+ 
+
+ align:start position:0%
+then the race to rescue her by a variety
+of people. You could what what Griffith
+
+ align:start position:0%
+of people. You could what what Griffith
+ 
+
+ align:start position:0%
+of people. You could what what Griffith
+does is he cuts back and forth. He
+
+ align:start position:0%
+does is he cuts back and forth. He
+ 
+
+ align:start position:0%
+does is he cuts back and forth. He
+creates the principle of parallel
+
+ align:start position:0%
+creates the principle of parallel
+ 
+
+ align:start position:0%
+creates the principle of parallel
+action. What he realized, what he
+
+ align:start position:0%
+action. What he realized, what he
+ 
+
+ align:start position:0%
+action. What he realized, what he
+discovered was that the audience will
+
+ align:start position:0%
+discovered was that the audience will
+ 
+
+ align:start position:0%
+discovered was that the audience will
+recognize this kind of cutting as
+
+ align:start position:0%
+recognize this kind of cutting as
+ 
+
+ align:start position:0%
+recognize this kind of cutting as
+showing you simultaneity, showing you
+
+ align:start position:0%
+showing you simultaneity, showing you
+ 
+
+ align:start position:0%
+showing you simultaneity, showing you
+things that are going on at the same
+
+ align:start position:0%
+things that are going on at the same
+ 
+
+ align:start position:0%
+things that are going on at the same
+time. In other words, what he what he
+
+ align:start position:0%
+time. In other words, what he what he
+ 
+
+ align:start position:0%
+time. In other words, what he what he
+discovered were in a certain sense how
+
+ align:start position:0%
+discovered were in a certain sense how
+ 
+
+ align:start position:0%
+discovered were in a certain sense how
+the mind how how we would cognitively
+
+ align:start position:0%
+the mind how how we would cognitively
+ 
+
+ align:start position:0%
+the mind how how we would cognitively
+process certain kinds of gestures on
+
+ align:start position:0%
+process certain kinds of gestures on
+ 
+
+ align:start position:0%
+process certain kinds of gestures on
+film. And what he discovered, of course,
+
+ align:start position:0%
+film. And what he discovered, of course,
+ 
+
+ align:start position:0%
+film. And what he discovered, of course,
+is that if he cuts, if he edits more
+
+ align:start position:0%
+is that if he cuts, if he edits more
+ 
+
+ align:start position:0%
+is that if he cuts, if he edits more
+quickly, if he creates a fast rhythm, he
+
+ align:start position:0%
+quickly, if he creates a fast rhythm, he
+ 
+
+ align:start position:0%
+quickly, if he creates a fast rhythm, he
+creates excitement. And if he create and
+
+ align:start position:0%
+creates excitement. And if he create and
+ 
+
+ align:start position:0%
+creates excitement. And if he create and
+what he began to discover was something
+
+ align:start position:0%
+what he began to discover was something
+ 
+
+ align:start position:0%
+what he began to discover was something
+that in later directors like Hitchcock
+
+ align:start position:0%
+that in later directors like Hitchcock
+ 
+
+ align:start position:0%
+that in later directors like Hitchcock
+would carry to to an almost evil pitch a
+
+ align:start position:0%
+would carry to to an almost evil pitch a
+ 
+
+ align:start position:0%
+would carry to to an almost evil pitch a
+capacity to manipulate and control the
+
+ align:start position:0%
+capacity to manipulate and control the
+ 
+
+ align:start position:0%
+capacity to manipulate and control the
+audience's reaction by the speed with
+
+ align:start position:0%
+audience's reaction by the speed with
+ 
+
+ align:start position:0%
+audience's reaction by the speed with
+which particular images appear or
+
+ align:start position:0%
+which particular images appear or
+ 
+
+ align:start position:0%
+which particular images appear or
+disappear. So so Griffith even at this
+
+ align:start position:0%
+disappear. So so Griffith even at this
+ 
+
+ align:start position:0%
+disappear. So so Griffith even at this
+early stage you can see Griffith
+
+ align:start position:0%
+early stage you can see Griffith
+ 
+
+ align:start position:0%
+early stage you can see Griffith
+discovering important principles. The
+
+ align:start position:0%
+discovering important principles. The
+ 
+
+ align:start position:0%
+discovering important principles. The
+most fundamental principle in a great
+
+ align:start position:0%
+most fundamental principle in a great
+ 
+
+ align:start position:0%
+most fundamental principle in a great
+train robbery which is not a Griffith
+
+ align:start position:0%
+train robbery which is not a Griffith
+ 
+
+ align:start position:0%
+train robbery which is not a Griffith
+film and precedes Griffith is the
+
+ align:start position:0%
+film and precedes Griffith is the
+ 
+
+ align:start position:0%
+film and precedes Griffith is the
+discovery that the shot is the basic
+
+ align:start position:0%
+discovery that the shot is the basic
+ 
+
+ align:start position:0%
+discovery that the shot is the basic
+unit of action. Why is that a great
+
+ align:start position:0%
+unit of action. Why is that a great
+ 
+
+ align:start position:0%
+unit of action. Why is that a great
+discovery? Well, if you think of the if
+
+ align:start position:0%
+discovery? Well, if you think of the if
+ 
+
+ align:start position:0%
+discovery? Well, if you think of the if
+you think of the movies as as a a as a
+
+ align:start position:0%
+you think of the movies as as a a as a
+ 
+
+ align:start position:0%
+you think of the movies as as a a as a
+device or as a as a as a medium that
+
+ align:start position:0%
+device or as a as a as a medium that
+ 
+
+ align:start position:0%
+device or as a as a as a medium that
+grows out of especially a theatrical
+
+ align:start position:0%
+grows out of especially a theatrical
+ 
+
+ align:start position:0%
+grows out of especially a theatrical
+dispensation grows out of other things
+
+ align:start position:0%
+dispensation grows out of other things
+ 
+
+ align:start position:0%
+dispensation grows out of other things
+as well. Novels feed into it. Visual art
+
+ align:start position:0%
+as well. Novels feed into it. Visual art
+ 
+
+ align:start position:0%
+as well. Novels feed into it. Visual art
+feeds into the movies. But it's
+
+ align:start position:0%
+feeds into the movies. But it's
+ 
+
+ align:start position:0%
+feeds into the movies. But it's
+certainly true that most of the major
+
+ align:start position:0%
+certainly true that most of the major
+ 
+
+ align:start position:0%
+certainly true that most of the major
+sort of ways in which directors first
+
+ align:start position:0%
+sort of ways in which directors first
+ 
+
+ align:start position:0%
+sort of ways in which directors first
+conceived how to think about the
+
+ align:start position:0%
+conceived how to think about the
+ 
+
+ align:start position:0%
+conceived how to think about the
+experience of what's of what the camera
+
+ align:start position:0%
+experience of what's of what the camera
+ 
+
+ align:start position:0%
+experience of what's of what the camera
+is looking at, they would they would
+
+ align:start position:0%
+is looking at, they would they would
+ 
+
+ align:start position:0%
+is looking at, they would they would
+have been influenced by their own
+
+ align:start position:0%
+have been influenced by their own
+ 
+
+ align:start position:0%
+have been influenced by their own
+experience of theater. And if you think
+
+ align:start position:0%
+experience of theater. And if you think
+ 
+
+ align:start position:0%
+experience of theater. And if you think
+about it for a moment, what you can see
+
+ align:start position:0%
+about it for a moment, what you can see
+ 
+
+ align:start position:0%
+about it for a moment, what you can see
+even in the great train robbery and uh
+
+ align:start position:0%
+even in the great train robbery and uh
+ 
+
+ align:start position:0%
+even in the great train robbery and uh
+the an impulse to treat the camera as a
+
+ align:start position:0%
+the an impulse to treat the camera as a
+ 
+
+ align:start position:0%
+the an impulse to treat the camera as a
+stable thing, the camera doesn't move
+
+ align:start position:0%
+stable thing, the camera doesn't move
+ 
+
+ align:start position:0%
+stable thing, the camera doesn't move
+very the camera the there are panning
+
+ align:start position:0%
+very the camera the there are panning
+ 
+
+ align:start position:0%
+very the camera the there are panning
+shots in which the camera will go like
+
+ align:start position:0%
+shots in which the camera will go like
+ 
+
+ align:start position:0%
+shots in which the camera will go like
+this, right? But the camera will not
+
+ align:start position:0%
+this, right? But the camera will not
+ 
+
+ align:start position:0%
+this, right? But the camera will not
+track. It will not move back and forth
+
+ align:start position:0%
+track. It will not move back and forth
+ 
+
+ align:start position:0%
+track. It will not move back and forth
+or sideways off its off its in in the
+
+ align:start position:0%
+or sideways off its off its in in the
+ 
+
+ align:start position:0%
+or sideways off its off its in in the
+great train robbery. It's that's a
+
+ align:start position:0%
+great train robbery. It's that's a
+ 
+
+ align:start position:0%
+great train robbery. It's that's a
+discover that's a discovery that
+
+ align:start position:0%
+discover that's a discovery that
+ 
+
+ align:start position:0%
+discover that's a discovery that
+Griffith is going to make and will
+
+ align:start position:0%
+Griffith is going to make and will
+ 
+
+ align:start position:0%
+Griffith is going to make and will
+exploit. Uh and you can see it in in in
+
+ align:start position:0%
+exploit. Uh and you can see it in in in
+ 
+
+ align:start position:0%
+exploit. Uh and you can see it in in in
+a beast at bay. But in the great train
+
+ align:start position:0%
+a beast at bay. But in the great train
+ 
+
+ align:start position:0%
+a beast at bay. But in the great train
+robbery, we haven't got that far yet.
+
+ align:start position:0%
+robbery, we haven't got that far yet.
+ 
+
+ align:start position:0%
+robbery, we haven't got that far yet.
+But what we have discovered, what what
+
+ align:start position:0%
+But what we have discovered, what what
+ 
+
+ align:start position:0%
+But what we have discovered, what what
+Porter, Edwin Porter did discover was
+
+ align:start position:0%
+Porter, Edwin Porter did discover was
+ 
+
+ align:start position:0%
+Porter, Edwin Porter did discover was
+that the shot is the basic unit of
+
+ align:start position:0%
+that the shot is the basic unit of
+ 
+
+ align:start position:0%
+that the shot is the basic unit of
+action. And that and what this means is
+
+ align:start position:0%
+action. And that and what this means is
+ 
+
+ align:start position:0%
+action. And that and what this means is
+it's not simply what the camera sees,
+
+ align:start position:0%
+it's not simply what the camera sees,
+ 
+
+ align:start position:0%
+it's not simply what the camera sees,
+but then how the shots are edited
+
+ align:start position:0%
+but then how the shots are edited
+ 
+
+ align:start position:0%
+but then how the shots are edited
+afterwards that is so crucial. So what
+
+ align:start position:0%
+afterwards that is so crucial. So what
+ 
+
+ align:start position:0%
+afterwards that is so crucial. So what
+it what it came to understand was that
+
+ align:start position:0%
+it what it came to understand was that
+ 
+
+ align:start position:0%
+it what it came to understand was that
+the making of of any movie is always a
+
+ align:start position:0%
+the making of of any movie is always a
+ 
+
+ align:start position:0%
+the making of of any movie is always a
+two-stage process. There's the shooting
+
+ align:start position:0%
+two-stage process. There's the shooting
+ 
+
+ align:start position:0%
+two-stage process. There's the shooting
+of the film and then there's the editing
+
+ align:start position:0%
+of the film and then there's the editing
+ 
+
+ align:start position:0%
+of the film and then there's the editing
+of the film. Right? And that that itself
+
+ align:start position:0%
+of the film. Right? And that that itself
+ 
+
+ align:start position:0%
+of the film. Right? And that that itself
+is a fundamental disc. But the idea that
+
+ align:start position:0%
+is a fundamental disc. But the idea that
+ 
+
+ align:start position:0%
+is a fundamental disc. But the idea that
+the shot is the unit of action instead
+
+ align:start position:0%
+the shot is the unit of action instead
+ 
+
+ align:start position:0%
+the shot is the unit of action instead
+of the scene was hard for movie makers
+
+ align:start position:0%
+of the scene was hard for movie makers
+ 
+
+ align:start position:0%
+of the scene was hard for movie makers
+to get because and what they would do
+
+ align:start position:0%
+to get because and what they would do
+ 
+
+ align:start position:0%
+to get because and what they would do
+they would set the camera up and then
+
+ align:start position:0%
+they would set the camera up and then
+ 
+
+ align:start position:0%
+they would set the camera up and then
+actors would walk in front of the
+
+ align:start position:0%
+actors would walk in front of the
+ 
+
+ align:start position:0%
+actors would walk in front of the
+camera. They would do what they had to
+
+ align:start position:0%
+camera. They would do what they had to
+ 
+
+ align:start position:0%
+camera. They would do what they had to
+do and they would walk off. What's going
+
+ align:start position:0%
+do and they would walk off. What's going
+ 
+
+ align:start position:0%
+do and they would walk off. What's going
+on there? They're conceiving of
+
+ align:start position:0%
+on there? They're conceiving of
+ 
+
+ align:start position:0%
+on there? They're conceiving of
+cinematic space in theatrical terms. As
+
+ align:start position:0%
+cinematic space in theatrical terms. As
+ 
+
+ align:start position:0%
+cinematic space in theatrical terms. As
+soon as the camera is liberated, taken
+
+ align:start position:0%
+soon as the camera is liberated, taken
+ 
+
+ align:start position:0%
+soon as the camera is liberated, taken
+off its tripod, moved around in some
+
+ align:start position:0%
+off its tripod, moved around in some
+ 
+
+ align:start position:0%
+off its tripod, moved around in some
+way, uh allowed to back up or or or come
+
+ align:start position:0%
+way, uh allowed to back up or or or come
+ 
+
+ align:start position:0%
+way, uh allowed to back up or or or come
+close, even allowed to move laterally or
+
+ align:start position:0%
+close, even allowed to move laterally or
+ 
+
+ align:start position:0%
+close, even allowed to move laterally or
+uh uh what we're beginning to do was to
+
+ align:start position:0%
+uh uh what we're beginning to do was to
+ 
+
+ align:start position:0%
+uh uh what we're beginning to do was to
+explore more systematically what the
+
+ align:start position:0%
+explore more systematically what the
+ 
+
+ align:start position:0%
+explore more systematically what the
+camera's unique features are. How the
+
+ align:start position:0%
+camera's unique features are. How the
+ 
+
+ align:start position:0%
+camera's unique features are. How the
+theater is different from the movies,
+
+ align:start position:0%
+theater is different from the movies,
+ 
+
+ align:start position:0%
+theater is different from the movies,
+how how how certain effects are possible
+
+ align:start position:0%
+how how how certain effects are possible
+ 
+
+ align:start position:0%
+how how how certain effects are possible
+in the movies that would not be possible
+
+ align:start position:0%
+in the movies that would not be possible
+ 
+
+ align:start position:0%
+in the movies that would not be possible
+in the theater. When you watch the
+
+ align:start position:0%
+in the theater. When you watch the
+ 
+
+ align:start position:0%
+in the theater. When you watch the
+Keaton films that you're going to see
+
+ align:start position:0%
+Keaton films that you're going to see
+ 
+
+ align:start position:0%
+Keaton films that you're going to see
+tonight, watch for the ways in which
+
+ align:start position:0%
+tonight, watch for the ways in which
+ 
+
+ align:start position:0%
+tonight, watch for the ways in which
+Keaton repeatedly sets up situations so
+
+ align:start position:0%
+Keaton repeatedly sets up situations so
+ 
+
+ align:start position:0%
+Keaton repeatedly sets up situations so
+that such that when you see a particular
+
+ align:start position:0%
+that such that when you see a particular
+ 
+
+ align:start position:0%
+that such that when you see a particular
+gag of his, a joke, what you realize is
+
+ align:start position:0%
+gag of his, a joke, what you realize is
+ 
+
+ align:start position:0%
+gag of his, a joke, what you realize is
+that the joke could not have happened in
+
+ align:start position:0%
+that the joke could not have happened in
+ 
+
+ align:start position:0%
+that the joke could not have happened in
+the theater. It could not have been told
+
+ align:start position:0%
+the theater. It could not have been told
+ 
+
+ align:start position:0%
+the theater. It could not have been told
+to you verbally. The joke is visual. The
+
+ align:start position:0%
+to you verbally. The joke is visual. The
+ 
+
+ align:start position:0%
+to you verbally. The joke is visual. The
+joke involves motion. the the joke in
+
+ align:start position:0%
+joke involves motion. the the joke in
+ 
+
+ align:start position:0%
+joke involves motion. the the joke in
+the joke involves uh a recognition of
+
+ align:start position:0%
+the joke involves uh a recognition of
+ 
+
+ align:start position:0%
+the joke involves uh a recognition of
+the powers of the s of the powers of of
+
+ align:start position:0%
+the powers of the s of the powers of of
+ 
+
+ align:start position:0%
+the powers of the s of the powers of of
+of cinematic representation to tell
+
+ align:start position:0%
+of cinematic representation to tell
+ 
+
+ align:start position:0%
+of cinematic representation to tell
+stories. Uh and there you'll see many
+
+ align:start position:0%
+stories. Uh and there you'll see many
+ 
+
+ align:start position:0%
+stories. Uh and there you'll see many
+examples of this in the in the in the uh
+
+ align:start position:0%
+examples of this in the in the in the uh
+ 
+
+ align:start position:0%
+examples of this in the in the in the uh
+Katon materials that you'll that you'll
+
+ align:start position:0%
+Katon materials that you'll that you'll
+ 
+
+ align:start position:0%
+Katon materials that you'll that you'll
+be looking at tonight. So the so the one
+
+ align:start position:0%
+be looking at tonight. So the so the one
+ 
+
+ align:start position:0%
+be looking at tonight. So the so the one
+of the very first discoveries that's
+
+ align:start position:0%
+of the very first discoveries that's
+ 
+
+ align:start position:0%
+of the very first discoveries that's
+made is the discovery that the shot is
+
+ align:start position:0%
+made is the discovery that the shot is
+ 
+
+ align:start position:0%
+made is the discovery that the shot is
+the basic unit of action. Uh a second
+
+ align:start position:0%
+the basic unit of action. Uh a second
+ 
+
+ align:start position:0%
+the basic unit of action. Uh a second
+discovery is the recognition that you
+
+ align:start position:0%
+discovery is the recognition that you
+ 
+
+ align:start position:0%
+discovery is the recognition that you
+have to cut between scenes. You do your
+
+ align:start position:0%
+have to cut between scenes. You do your
+ 
+
+ align:start position:0%
+have to cut between scenes. You do your
+editing between shots rather rather than
+
+ align:start position:0%
+editing between shots rather rather than
+ 
+
+ align:start position:0%
+editing between shots rather rather than
+and that mo and mostly what you do is
+
+ align:start position:0%
+and that mo and mostly what you do is
+ 
+
+ align:start position:0%
+and that mo and mostly what you do is
+you let scenes play out even though you
+
+ align:start position:0%
+you let scenes play out even though you
+ 
+
+ align:start position:0%
+you let scenes play out even though you
+might abruptly cut a scene before the
+
+ align:start position:0%
+might abruptly cut a scene before the
+ 
+
+ align:start position:0%
+might abruptly cut a scene before the
+action is completed. One of that's
+
+ align:start position:0%
+action is completed. One of that's
+ 
+
+ align:start position:0%
+action is completed. One of that's
+another discovery that was made. If you
+
+ align:start position:0%
+another discovery that was made. If you
+ 
+
+ align:start position:0%
+another discovery that was made. If you
+cut the scene if a person starts to walk
+
+ align:start position:0%
+cut the scene if a person starts to walk
+ 
+
+ align:start position:0%
+cut the scene if a person starts to walk
+toward the door the first earliest films
+
+ align:start position:0%
+toward the door the first earliest films
+ 
+
+ align:start position:0%
+toward the door the first earliest films
+they would show the person walking all
+
+ align:start position:0%
+they would show the person walking all
+ 
+
+ align:start position:0%
+they would show the person walking all
+the way to the end walking out of the
+
+ align:start position:0%
+the way to the end walking out of the
+ 
+
+ align:start position:0%
+the way to the end walking out of the
+door. Then filmmakers discovered, wait a
+
+ align:start position:0%
+door. Then filmmakers discovered, wait a
+ 
+
+ align:start position:0%
+door. Then filmmakers discovered, wait a
+minute, there's a way of creating a kind
+
+ align:start position:0%
+minute, there's a way of creating a kind
+ 
+
+ align:start position:0%
+minute, there's a way of creating a kind
+of quickness here. Because if I show
+
+ align:start position:0%
+of quickness here. Because if I show
+ 
+
+ align:start position:0%
+of quickness here. Because if I show
+Thorburn walking toward the door,
+
+ align:start position:0%
+Thorburn walking toward the door,
+ 
+
+ align:start position:0%
+Thorburn walking toward the door,
+starting and I cut and he knocks his
+
+ align:start position:0%
+starting and I cut and he knocks his
+ 
+
+ align:start position:0%
+starting and I cut and he knocks his
+glasses off. Uh, and then I and then I
+
+ align:start position:0%
+glasses off. Uh, and then I and then I
+ 
+
+ align:start position:0%
+glasses off. Uh, and then I and then I
+cut and I wait till he gets to the door
+
+ align:start position:0%
+cut and I wait till he gets to the door
+ 
+
+ align:start position:0%
+cut and I wait till he gets to the door
+and we see him leaving the door. I don't
+
+ align:start position:0%
+and we see him leaving the door. I don't
+ 
+
+ align:start position:0%
+and we see him leaving the door. I don't
+have to watch him take those 17 steps
+
+ align:start position:0%
+have to watch him take those 17 steps
+ 
+
+ align:start position:0%
+have to watch him take those 17 steps
+that Right. So what what what's been
+
+ align:start position:0%
+that Right. So what what what's been
+ 
+
+ align:start position:0%
+that Right. So what what what's been
+discovered is a basic principle of
+
+ align:start position:0%
+discovered is a basic principle of
+ 
+
+ align:start position:0%
+discovered is a basic principle of
+cinematic syntax, right? You know, but
+
+ align:start position:0%
+cinematic syntax, right? You know, but
+ 
+
+ align:start position:0%
+cinematic syntax, right? You know, but
+what but but it seems so obvious to us,
+
+ align:start position:0%
+what but but it seems so obvious to us,
+ 
+
+ align:start position:0%
+what but but it seems so obvious to us,
+but of course it's really a great
+
+ align:start position:0%
+but of course it's really a great
+ 
+
+ align:start position:0%
+but of course it's really a great
+discovery. It's a uh in other words, the
+
+ align:start position:0%
+discovery. It's a uh in other words, the
+ 
+
+ align:start position:0%
+discovery. It's a uh in other words, the
+the properties of the medium have to be
+
+ align:start position:0%
+the properties of the medium have to be
+ 
+
+ align:start position:0%
+the properties of the medium have to be
+understood before you can really begin
+
+ align:start position:0%
+understood before you can really begin
+ 
+
+ align:start position:0%
+understood before you can really begin
+to exploit it. And that's why uh I've
+
+ align:start position:0%
+to exploit it. And that's why uh I've
+ 
+
+ align:start position:0%
+to exploit it. And that's why uh I've
+asked you to look at some of these short
+
+ align:start position:0%
+asked you to look at some of these short
+ 
+
+ align:start position:0%
+asked you to look at some of these short
+films. None of the short films I've
+
+ align:start position:0%
+films. None of the short films I've
+ 
+
+ align:start position:0%
+films. None of the short films I've
+shown you are completely without uh some
+
+ align:start position:0%
+shown you are completely without uh some
+ 
+
+ align:start position:0%
+shown you are completely without uh some
+uh uh technical interest. And uh even
+
+ align:start position:0%
+uh uh technical interest. And uh even
+ 
+
+ align:start position:0%
+uh uh technical interest. And uh even
+though of course they're the only films
+
+ align:start position:0%
+though of course they're the only films
+ 
+
+ align:start position:0%
+though of course they're the only films
+I'm showing you that I wouldn't sort of
+
+ align:start position:0%
+I'm showing you that I wouldn't sort of
+ 
+
+ align:start position:0%
+I'm showing you that I wouldn't sort of
+make arguments uh to defend them as
+
+ align:start position:0%
+make arguments uh to defend them as
+ 
+
+ align:start position:0%
+make arguments uh to defend them as
+works of art, but I certainly would make
+
+ align:start position:0%
+works of art, but I certainly would make
+ 
+
+ align:start position:0%
+works of art, but I certainly would make
+arguments for them as technically
+
+ align:start position:0%
+arguments for them as technically
+ 
+
+ align:start position:0%
+arguments for them as technically
+fascinating documents. And I hope you'll
+
+ align:start position:0%
+fascinating documents. And I hope you'll
+ 
+
+ align:start position:0%
+fascinating documents. And I hope you'll
+I hope you'll look at them in in that
+
+ align:start position:0%
+I hope you'll look at them in in that
+ 
+
+ align:start position:0%
+I hope you'll look at them in in that
+light. So the shot as a basic unit of
+
+ align:start position:0%
+light. So the shot as a basic unit of
+ 
+
+ align:start position:0%
+light. So the shot as a basic unit of
+action cutting between scenes and a
+
+ align:start position:0%
+action cutting between scenes and a
+ 
+
+ align:start position:0%
+action cutting between scenes and a
+couple of other things in the in the
+
+ align:start position:0%
+couple of other things in the in the
+ 
+
+ align:start position:0%
+couple of other things in the in the
+that I think are important in the great
+
+ align:start position:0%
+that I think are important in the great
+ 
+
+ align:start position:0%
+that I think are important in the great
+train rob one is that you can see in the
+
+ align:start position:0%
+train rob one is that you can see in the
+ 
+
+ align:start position:0%
+train rob one is that you can see in the
+great train robbery they're beginning to
+
+ align:start position:0%
+great train robbery they're beginning to
+ 
+
+ align:start position:0%
+great train robbery they're beginning to
+discover the value of camera placement.
+
+ align:start position:0%
+discover the value of camera placement.
+ 
+
+ align:start position:0%
+discover the value of camera placement.
+What happens when you place the camera
+
+ align:start position:0%
+What happens when you place the camera
+ 
+
+ align:start position:0%
+What happens when you place the camera
+in a particular position that if the
+
+ align:start position:0%
+in a particular position that if the
+ 
+
+ align:start position:0%
+in a particular position that if the
+camera uh especially if action is coming
+
+ align:start position:0%
+camera uh especially if action is coming
+ 
+
+ align:start position:0%
+camera uh especially if action is coming
+toward the camera if you that you might
+
+ align:start position:0%
+toward the camera if you that you might
+ 
+
+ align:start position:0%
+toward the camera if you that you might
+not want to place the camera directly in
+
+ align:start position:0%
+not want to place the camera directly in
+ 
+
+ align:start position:0%
+not want to place the camera directly in
+front of the action that's coming toward
+
+ align:start position:0%
+front of the action that's coming toward
+ 
+
+ align:start position:0%
+front of the action that's coming toward
+you that something happens if you place
+
+ align:start position:0%
+you that something happens if you place
+ 
+
+ align:start position:0%
+you that something happens if you place
+it slightly up toward it so it can see
+
+ align:start position:0%
+it slightly up toward it so it can see
+ 
+
+ align:start position:0%
+it slightly up toward it so it can see
+it at a slight angle. creates a greater
+
+ align:start position:0%
+it at a slight angle. creates a greater
+ 
+
+ align:start position:0%
+it at a slight angle. creates a greater
+illusion of depth in the image for
+
+ align:start position:0%
+illusion of depth in the image for
+ 
+
+ align:start position:0%
+illusion of depth in the image for
+example and it does other kinds of it
+
+ align:start position:0%
+example and it does other kinds of it
+ 
+
+ align:start position:0%
+example and it does other kinds of it
+lets the action get closer to you before
+
+ align:start position:0%
+lets the action get closer to you before
+ 
+
+ align:start position:0%
+lets the action get closer to you before
+before the uh scene has to be cut. Uh so
+
+ align:start position:0%
+before the uh scene has to be cut. Uh so
+ 
+
+ align:start position:0%
+before the uh scene has to be cut. Uh so
+camera placement is something that you
+
+ align:start position:0%
+camera placement is something that you
+ 
+
+ align:start position:0%
+camera placement is something that you
+can see is is beginning to be learned
+
+ align:start position:0%
+can see is is beginning to be learned
+ 
+
+ align:start position:0%
+can see is is beginning to be learned
+beginning to be mastered in the great in
+
+ align:start position:0%
+beginning to be mastered in the great in
+ 
+
+ align:start position:0%
+beginning to be mastered in the great in
+the great train robbery and f camera or
+
+ align:start position:0%
+the great train robbery and f camera or
+ 
+
+ align:start position:0%
+the great train robbery and f camera or
+c or or camera position. So there are
+
+ align:start position:0%
+c or or camera position. So there are
+ 
+
+ align:start position:0%
+c or or camera position. So there are
+other things and finally one might
+
+ align:start position:0%
+other things and finally one might
+ 
+
+ align:start position:0%
+other things and finally one might
+mention one other thing that again
+
+ align:start position:0%
+mention one other thing that again
+ 
+
+ align:start position:0%
+mention one other thing that again
+establishes a principle that begins that
+
+ align:start position:0%
+establishes a principle that begins that
+ 
+
+ align:start position:0%
+establishes a principle that begins that
+that that then is continued continues in
+
+ align:start position:0%
+that that then is continued continues in
+ 
+
+ align:start position:0%
+that that then is continued continues in
+use for 50 or 75 years and that's the
+
+ align:start position:0%
+use for 50 or 75 years and that's the
+ 
+
+ align:start position:0%
+use for 50 or 75 years and that's the
+principle of the process shot. You can
+
+ align:start position:0%
+principle of the process shot. You can
+ 
+
+ align:start position:0%
+principle of the process shot. You can
+see in the great train robbery that he
+
+ align:start position:0%
+see in the great train robbery that he
+ 
+
+ align:start position:0%
+see in the great train robbery that he
+that some effects have been created by
+
+ align:start position:0%
+that some effects have been created by
+ 
+
+ align:start position:0%
+that some effects have been created by
+tricks that there's a that there's back
+
+ align:start position:0%
+tricks that there's a that there's back
+ 
+
+ align:start position:0%
+tricks that there's a that there's back
+projection going used in that. It's it
+
+ align:start position:0%
+projection going used in that. It's it
+ 
+
+ align:start position:0%
+projection going used in that. It's it
+looks crude to us. We can see through
+
+ align:start position:0%
+looks crude to us. We can see through
+ 
+
+ align:start position:0%
+looks crude to us. We can see through
+it, but the early audiences would would
+
+ align:start position:0%
+it, but the early audiences would would
+ 
+
+ align:start position:0%
+it, but the early audiences would would
+not have recognized that. We we're so
+
+ align:start position:0%
+not have recognized that. We we're so
+ 
+
+ align:start position:0%
+not have recognized that. We we're so
+used to location filming that we can
+
+ align:start position:0%
+used to location filming that we can
+ 
+
+ align:start position:0%
+used to location filming that we can
+pick out uh we today can see through the
+
+ align:start position:0%
+pick out uh we today can see through the
+ 
+
+ align:start position:0%
+pick out uh we today can see through the
+process shots of earlier films. Th this
+
+ align:start position:0%
+process shots of earlier films. Th this
+ 
+
+ align:start position:0%
+process shots of earlier films. Th this
+in fact damages some of Hitchcock's
+
+ align:start position:0%
+in fact damages some of Hitchcock's
+ 
+
+ align:start position:0%
+in fact damages some of Hitchcock's
+films very badly today because Hitchcock
+
+ align:start position:0%
+films very badly today because Hitchcock
+ 
+
+ align:start position:0%
+films very badly today because Hitchcock
+used a lot of processed shot effects in
+
+ align:start position:0%
+used a lot of processed shot effects in
+ 
+
+ align:start position:0%
+used a lot of processed shot effects in
+his films. When he made them the
+
+ align:start position:0%
+his films. When he made them the
+ 
+
+ align:start position:0%
+his films. When he made them the
+audiences were used to there was a
+
+ align:start position:0%
+audiences were used to there was a
+ 
+
+ align:start position:0%
+audiences were used to there was a
+convention of film going today
+
+ align:start position:0%
+convention of film going today
+ 
+
+ align:start position:0%
+convention of film going today
+everything because cameras are so much
+
+ align:start position:0%
+everything because cameras are so much
+ 
+
+ align:start position:0%
+everything because cameras are so much
+more more mobile and light and so so
+
+ align:start position:0%
+more more mobile and light and so so
+ 
+
+ align:start position:0%
+more more mobile and light and so so
+much has been uh learned about how to
+
+ align:start position:0%
+much has been uh learned about how to
+ 
+
+ align:start position:0%
+much has been uh learned about how to
+even about filming in in low light and
+
+ align:start position:0%
+even about filming in in low light and
+ 
+
+ align:start position:0%
+even about filming in in low light and
+so forth that they that
+
+ align:start position:0%
+so forth that they that
+ 
+
+ align:start position:0%
+so forth that they that
+there's much less use of process shots.
+
+ align:start position:0%
+there's much less use of process shots.
+ 
+
+ align:start position:0%
+there's much less use of process shots.
+So, well, a new kind of process shot, I
+
+ align:start position:0%
+So, well, a new kind of process shot, I
+ 
+
+ align:start position:0%
+So, well, a new kind of process shot, I
+suppose, is emerging with digital
+
+ align:start position:0%
+suppose, is emerging with digital
+ 
+
+ align:start position:0%
+suppose, is emerging with digital
+animation. And one could say it's sort
+
+ align:start position:0%
+animation. And one could say it's sort
+ 
+
+ align:start position:0%
+animation. And one could say it's sort
+of a return to the idea of manipulating
+
+ align:start position:0%
+of a return to the idea of manipulating
+ 
+
+ align:start position:0%
+of a return to the idea of manipulating
+the image in illegitimate ways. Um, but
+
+ align:start position:0%
+the image in illegitimate ways. Um, but
+ 
+
+ align:start position:0%
+the image in illegitimate ways. Um, but
+the but but we can see even in the great
+
+ align:start position:0%
+the but but we can see even in the great
+ 
+
+ align:start position:0%
+the but but we can see even in the great
+train robbery, we we can even see the
+
+ align:start position:0%
+train robbery, we we can even see the
+ 
+
+ align:start position:0%
+train robbery, we we can even see the
+beginnings of the use of process shots
+
+ align:start position:0%
+beginnings of the use of process shots
+ 
+
+ align:start position:0%
+beginnings of the use of process shots
+of recognizing that you can create
+
+ align:start position:0%
+of recognizing that you can create
+ 
+
+ align:start position:0%
+of recognizing that you can create
+effects in the movies that are unique
+
+ align:start position:0%
+effects in the movies that are unique
+ 
+
+ align:start position:0%
+effects in the movies that are unique
+and special that no other medium would
+
+ align:start position:0%
+and special that no other medium would
+ 
+
+ align:start position:0%
+and special that no other medium would
+allow you to do. And what's embedded
+
+ align:start position:0%
+allow you to do. And what's embedded
+ 
+
+ align:start position:0%
+allow you to do. And what's embedded
+there is science fiction. What's
+
+ align:start position:0%
+there is science fiction. What's
+ 
+
+ align:start position:0%
+there is science fiction. What's
+embedded there are all the kinds of
+
+ align:start position:0%
+embedded there are all the kinds of
+ 
+
+ align:start position:0%
+embedded there are all the kinds of
+imaginative not just science fictional
+
+ align:start position:0%
+imaginative not just science fictional
+ 
+
+ align:start position:0%
+imaginative not just science fictional
+all the kinds of imaginative movies that
+
+ align:start position:0%
+all the kinds of imaginative movies that
+ 
+
+ align:start position:0%
+all the kinds of imaginative movies that
+have been made that maybe take you
+
+ align:start position:0%
+have been made that maybe take you
+ 
+
+ align:start position:0%
+have been made that maybe take you
+inside people's nightmares or dreams
+
+ align:start position:0%
+inside people's nightmares or dreams
+ 
+
+ align:start position:0%
+inside people's nightmares or dreams
+where what the film is showing you now
+
+ align:start position:0%
+where what the film is showing you now
+ 
+
+ align:start position:0%
+where what the film is showing you now
+what in words what what is embedded in
+
+ align:start position:0%
+what in words what what is embedded in
+ 
+
+ align:start position:0%
+what in words what what is embedded in
+that process shot even more fully
+
+ align:start position:0%
+that process shot even more fully
+ 
+
+ align:start position:0%
+that process shot even more fully
+embedded in in Melier's the French
+
+ align:start position:0%
+embedded in in Melier's the French
+ 
+
+ align:start position:0%
+embedded in in Melier's the French
+director's films like trip to the moon
+
+ align:start position:0%
+director's films like trip to the moon
+ 
+
+ align:start position:0%
+director's films like trip to the moon
+where he explicitly goes into a realm of
+
+ align:start position:0%
+where he explicitly goes into a realm of
+ 
+
+ align:start position:0%
+where he explicitly goes into a realm of
+fantasy is not only that the film is the
+
+ align:start position:0%
+fantasy is not only that the film is the
+ 
+
+ align:start position:0%
+fantasy is not only that the film is the
+most profoundly realistic medium that
+
+ align:start position:0%
+most profoundly realistic medium that
+ 
+
+ align:start position:0%
+most profoundly realistic medium that
+was ever invented it may also be the
+
+ align:start position:0%
+was ever invented it may also be the
+ 
+
+ align:start position:0%
+was ever invented it may also be the
+most the the the the most expressive
+
+ align:start position:0%
+most the the the the most expressive
+ 
+
+ align:start position:0%
+most the the the the most expressive
+medium for the for the rendering of
+
+ align:start position:0%
+medium for the for the rendering of
+ 
+
+ align:start position:0%
+medium for the for the rendering of
+non-realistic states of dream, of
+
+ align:start position:0%
+non-realistic states of dream, of
+ 
+
+ align:start position:0%
+non-realistic states of dream, of
+nightmare, of fantasy. Uh exactly be be
+
+ align:start position:0%
+nightmare, of fantasy. Uh exactly be be
+ 
+
+ align:start position:0%
+nightmare, of fantasy. Uh exactly be be
+because of the freedom that that uh the
+
+ align:start position:0%
+because of the freedom that that uh the
+ 
+
+ align:start position:0%
+because of the freedom that that uh the
+film medium allows. And it even these
+
+ align:start position:0%
+film medium allows. And it even these
+ 
+
+ align:start position:0%
+film medium allows. And it even these
+implications are at least embedded in
+
+ align:start position:0%
+implications are at least embedded in
+ 
+
+ align:start position:0%
+implications are at least embedded in
+the use of the process shots in uh
+
+ align:start position:0%
+the use of the process shots in uh
+ 
+
+ align:start position:0%
+the use of the process shots in uh
+Porter's The Great Train Robbery. The
+
+ align:start position:0%
+Porter's The Great Train Robbery. The
+ 
+
+ align:start position:0%
+Porter's The Great Train Robbery. The
+the the other short that you're going to
+
+ align:start position:0%
+the the other short that you're going to
+ 
+
+ align:start position:0%
+the the other short that you're going to
+see tonight that is not by Katon is
+
+ align:start position:0%
+see tonight that is not by Katon is
+ 
+
+ align:start position:0%
+see tonight that is not by Katon is
+called the Lonale Operator. It's it was
+
+ align:start position:0%
+called the Lonale Operator. It's it was
+ 
+
+ align:start position:0%
+called the Lonale Operator. It's it was
+made in 1911.
+
+ align:start position:0%
+made in 1911.
+ 
+
+ align:start position:0%
+made in 1911.
+Um and uh it in a way it's the most it's
+
+ align:start position:0%
+Um and uh it in a way it's the most it's
+ 
+
+ align:start position:0%
+Um and uh it in a way it's the most it's
+the most advanced film of its time. And
+
+ align:start position:0%
+the most advanced film of its time. And
+ 
+
+ align:start position:0%
+the most advanced film of its time. And
+that that's one re and I what I hope
+
+ align:start position:0%
+that that's one re and I what I hope
+ 
+
+ align:start position:0%
+that that's one re and I what I hope
+when you look at it you'll you'll watch
+
+ align:start position:0%
+when you look at it you'll you'll watch
+ 
+
+ align:start position:0%
+when you look at it you'll you'll watch
+especially for how much more complex it
+
+ align:start position:0%
+especially for how much more complex it
+ 
+
+ align:start position:0%
+especially for how much more complex it
+is than let's say the great train
+
+ align:start position:0%
+is than let's say the great train
+ 
+
+ align:start position:0%
+is than let's say the great train
+robbery and it'll be a kind of small
+
+ align:start position:0%
+robbery and it'll be a kind of small
+ 
+
+ align:start position:0%
+robbery and it'll be a kind of small
+measure of this Fredot principle that
+
+ align:start position:0%
+measure of this Fredot principle that
+ 
+
+ align:start position:0%
+measure of this Fredot principle that
+I've been talking about. Let me mention
+
+ align:start position:0%
+I've been talking about. Let me mention
+ 
+
+ align:start position:0%
+I've been talking about. Let me mention
+a couple of things about uh the lonale
+
+ align:start position:0%
+a couple of things about uh the lonale
+ 
+
+ align:start position:0%
+a couple of things about uh the lonale
+operator. Between 1907 and 1911, most
+
+ align:start position:0%
+operator. Between 1907 and 1911, most
+ 
+
+ align:start position:0%
+operator. Between 1907 and 1911, most
+films consisted of no more than 24
+
+ align:start position:0%
+films consisted of no more than 24
+ 
+
+ align:start position:0%
+films consisted of no more than 24
+separate shots. Right. Between 1908 and
+
+ align:start position:0%
+separate shots. Right. Between 1908 and
+ 
+
+ align:start position:0%
+separate shots. Right. Between 1908 and
+1913, led by DW Griffith and his
+
+ align:start position:0%
+1913, led by DW Griffith and his
+ 
+
+ align:start position:0%
+1913, led by DW Griffith and his
+company, the Biograph Company, many more
+
+ align:start position:0%
+company, the Biograph Company, many more
+ 
+
+ align:start position:0%
+company, the Biograph Company, many more
+shots were introduced into in into a
+
+ align:start position:0%
+shots were introduced into in into a
+ 
+
+ align:start position:0%
+shots were introduced into in into a
+single reel of film. And in the Loneale
+
+ align:start position:0%
+single reel of film. And in the Loneale
+ 
+
+ align:start position:0%
+single reel of film. And in the Loneale
+Operator, there are 98 shots, six
+
+ align:start position:0%
+Operator, there are 98 shots, six
+ 
+
+ align:start position:0%
+Operator, there are 98 shots, six
+intertitles, one main title, and two
+
+ align:start position:0%
+intertitles, one main title, and two
+ 
+
+ align:start position:0%
+intertitles, one main title, and two
+written inserts, all within a 17-minute
+
+ align:start position:0%
+written inserts, all within a 17-minute
+ 
+
+ align:start position:0%
+written inserts, all within a 17-minute
+length. Now, think of the just the
+
+ align:start position:0%
+length. Now, think of the just the
+ 
+
+ align:start position:0%
+length. Now, think of the just the
+advent of the the access of complexity
+
+ align:start position:0%
+advent of the the access of complexity
+ 
+
+ align:start position:0%
+advent of the the access of complexity
+that has occurred just in less than 10
+
+ align:start position:0%
+that has occurred just in less than 10
+ 
+
+ align:start position:0%
+that has occurred just in less than 10
+years, right? Uh um
+
+ align:start position:0%
+years, right? Uh um
+ 
+
+ align:start position:0%
+years, right? Uh um
+it's such a complicated film that one of
+
+ align:start position:0%
+it's such a complicated film that one of
+ 
+
+ align:start position:0%
+it's such a complicated film that one of
+the things we realize even looking at
+
+ align:start position:0%
+the things we realize even looking at
+ 
+
+ align:start position:0%
+the things we realize even looking at
+it, if we look closely, is that it
+
+ align:start position:0%
+it, if we look closely, is that it
+ 
+
+ align:start position:0%
+it, if we look closely, is that it
+actually required uh a kind of
+
+ align:start position:0%
+actually required uh a kind of
+ 
+
+ align:start position:0%
+actually required uh a kind of
+attentiveness that earlier films did
+
+ align:start position:0%
+attentiveness that earlier films did
+ 
+
+ align:start position:0%
+attentiveness that earlier films did
+not. As filmmakers began to make these
+
+ align:start position:0%
+not. As filmmakers began to make these
+ 
+
+ align:start position:0%
+not. As filmmakers began to make these
+things and began to make them longer and
+
+ align:start position:0%
+things and began to make them longer and
+ 
+
+ align:start position:0%
+things and began to make them longer and
+began to make them more complicated,
+
+ align:start position:0%
+began to make them more complicated,
+ 
+
+ align:start position:0%
+began to make them more complicated,
+they realized that they couldn't just
+
+ align:start position:0%
+they realized that they couldn't just
+ 
+
+ align:start position:0%
+they realized that they couldn't just
+bring the camera out and start shooting.
+
+ align:start position:0%
+bring the camera out and start shooting.
+ 
+
+ align:start position:0%
+bring the camera out and start shooting.
+They began to develop the the the formal
+
+ align:start position:0%
+They began to develop the the the formal
+ 
+
+ align:start position:0%
+They began to develop the the the formal
+rationalizing strategies that led to the
+
+ align:start position:0%
+rationalizing strategies that led to the
+ 
+
+ align:start position:0%
+rationalizing strategies that led to the
+making of movies as we understand them.
+
+ align:start position:0%
+making of movies as we understand them.
+ 
+
+ align:start position:0%
+making of movies as we understand them.
+There was a 4-day shooting schedule
+
+ align:start position:0%
+There was a 4-day shooting schedule
+ 
+
+ align:start position:0%
+There was a 4-day shooting schedule
+created for the Londonale operator. It
+
+ align:start position:0%
+created for the Londonale operator. It
+ 
+
+ align:start position:0%
+created for the Londonale operator. It
+was one of the first films to to to have
+
+ align:start position:0%
+was one of the first films to to to have
+ 
+
+ align:start position:0%
+was one of the first films to to to have
+uh this format. And of course it's the
+
+ align:start position:0%
+uh this format. And of course it's the
+ 
+
+ align:start position:0%
+uh this format. And of course it's the
+format that is followed today with
+
+ align:start position:0%
+format that is followed today with
+ 
+
+ align:start position:0%
+format that is followed today with
+virtually every film uh in in in
+
+ align:start position:0%
+virtually every film uh in in in
+ 
+
+ align:start position:0%
+virtually every film uh in in in
+different in different uh aspects. Um uh
+
+ align:start position:0%
+different in different uh aspects. Um uh
+ 
+
+ align:start position:0%
+different in different uh aspects. Um uh
+and this also required a pre-planned
+
+ align:start position:0%
+and this also required a pre-planned
+ 
+
+ align:start position:0%
+and this also required a pre-planned
+shooting script.
+
+ align:start position:0%
+shooting script.
+ 
+
+ align:start position:0%
+shooting script.
+They had to they had to plan what they
+
+ align:start position:0%
+They had to they had to plan what they
+ 
+
+ align:start position:0%
+They had to they had to plan what they
+would pre-plan all of their shooting all
+
+ align:start position:0%
+would pre-plan all of their shooting all
+ 
+
+ align:start position:0%
+would pre-plan all of their shooting all
+of their shots all of their camera
+
+ align:start position:0%
+of their shots all of their camera
+ 
+
+ align:start position:0%
+of their shots all of their camera
+angles. They needed a shooting script, a
+
+ align:start position:0%
+angles. They needed a shooting script, a
+ 
+
+ align:start position:0%
+angles. They needed a shooting script, a
+written script. Films didn't have
+
+ align:start position:0%
+written script. Films didn't have
+ 
+
+ align:start position:0%
+written script. Films didn't have
+written scripts at first, but Lonale
+
+ align:start position:0%
+written scripts at first, but Lonale
+ 
+
+ align:start position:0%
+written scripts at first, but Lonale
+did. Uh and it also required in order
+
+ align:start position:0%
+did. Uh and it also required in order
+ 
+
+ align:start position:0%
+did. Uh and it also required in order
+for them to make their schedule out of
+
+ align:start position:0%
+for them to make their schedule out of
+ 
+
+ align:start position:0%
+for them to make their schedule out of
+order shooting. That is to say, they had
+
+ align:start position:0%
+order shooting. That is to say, they had
+ 
+
+ align:start position:0%
+order shooting. That is to say, they had
+to shoot certain things not in the
+
+ align:start position:0%
+to shoot certain things not in the
+ 
+
+ align:start position:0%
+to shoot certain things not in the
+sequential order of the film. And that's
+
+ align:start position:0%
+sequential order of the film. And that's
+ 
+
+ align:start position:0%
+sequential order of the film. And that's
+one of the most basic principles of film
+
+ align:start position:0%
+one of the most basic principles of film
+ 
+
+ align:start position:0%
+one of the most basic principles of film
+making because once you set up the
+
+ align:start position:0%
+making because once you set up the
+ 
+
+ align:start position:0%
+making because once you set up the
+camera for a for a a shot of a
+
+ align:start position:0%
+camera for a for a a shot of a
+ 
+
+ align:start position:0%
+camera for a for a a shot of a
+particular environment, if that
+
+ align:start position:0%
+particular environment, if that
+ 
+
+ align:start position:0%
+particular environment, if that
+environment shows up later in the film,
+
+ align:start position:0%
+environment shows up later in the film,
+ 
+
+ align:start position:0%
+environment shows up later in the film,
+it's unbelievably more expensive and
+
+ align:start position:0%
+it's unbelievably more expensive and
+ 
+
+ align:start position:0%
+it's unbelievably more expensive and
+timeconuming to reconstitute that whole
+
+ align:start position:0%
+timeconuming to reconstitute that whole
+ 
+
+ align:start position:0%
+timeconuming to reconstitute that whole
+set. So they the B almost all films to
+
+ align:start position:0%
+set. So they the B almost all films to
+ 
+
+ align:start position:0%
+set. So they the B almost all films to
+this very day are still shot out of
+
+ align:start position:0%
+this very day are still shot out of
+ 
+
+ align:start position:0%
+this very day are still shot out of
+sequence in order to maximize the the uh
+
+ align:start position:0%
+sequence in order to maximize the the uh
+ 
+
+ align:start position:0%
+sequence in order to maximize the the uh
+uh the the the the the time you have in
+
+ align:start position:0%
+uh the the the the the time you have in
+ 
+
+ align:start position:0%
+uh the the the the the time you have in
+order in in order to work at your most
+
+ align:start position:0%
+order in in order to work at your most
+ 
+
+ align:start position:0%
+order in in order to work at your most
+efficient. In words, it's not an
+
+ align:start position:0%
+efficient. In words, it's not an
+ 
+
+ align:start position:0%
+efficient. In words, it's not an
+efficient way to make a movie to shoot
+
+ align:start position:0%
+efficient way to make a movie to shoot
+ 
+
+ align:start position:0%
+efficient way to make a movie to shoot
+it sequentially to follow the to follow
+
+ align:start position:0%
+it sequentially to follow the to follow
+ 
+
+ align:start position:0%
+it sequentially to follow the to follow
+the script in its chronological
+
+ align:start position:0%
+the script in its chronological
+ 
+
+ align:start position:0%
+the script in its chronological
+sequence. Uh, and the Loneale Operator
+
+ align:start position:0%
+sequence. Uh, and the Loneale Operator
+ 
+
+ align:start position:0%
+sequence. Uh, and the Loneale Operator
+is one of it's maybe the first film to
+
+ align:start position:0%
+is one of it's maybe the first film to
+ 
+
+ align:start position:0%
+is one of it's maybe the first film to
+to have all of these features that we
+
+ align:start position:0%
+to have all of these features that we
+ 
+
+ align:start position:0%
+to have all of these features that we
+would associate with with a mo with with
+
+ align:start position:0%
+would associate with with a mo with with
+ 
+
+ align:start position:0%
+would associate with with a mo with with
+a modern or a contemporary film. Uh, you
+
+ align:start position:0%
+a modern or a contemporary film. Uh, you
+ 
+
+ align:start position:0%
+a modern or a contemporary film. Uh, you
+might notice in the it's a it's an
+
+ align:start position:0%
+might notice in the it's a it's an
+ 
+
+ align:start position:0%
+might notice in the it's a it's an
+immensely complex film even in terms of
+
+ align:start position:0%
+immensely complex film even in terms of
+ 
+
+ align:start position:0%
+immensely complex film even in terms of
+its content and I might leave that I I
+
+ align:start position:0%
+its content and I might leave that I I
+ 
+
+ align:start position:0%
+its content and I might leave that I I
+won't talk about that much now except to
+
+ align:start position:0%
+won't talk about that much now except to
+ 
+
+ align:start position:0%
+won't talk about that much now except to
+say this. Watch the way in which the
+
+ align:start position:0%
+say this. Watch the way in which the
+ 
+
+ align:start position:0%
+say this. Watch the way in which the
+film tries to deal with what we might
+
+ align:start position:0%
+film tries to deal with what we might
+ 
+
+ align:start position:0%
+film tries to deal with what we might
+call uh hierarchies of gender. I mean,
+
+ align:start position:0%
+call uh hierarchies of gender. I mean,
+ 
+
+ align:start position:0%
+call uh hierarchies of gender. I mean,
+the film is partly about how a woman
+
+ align:start position:0%
+the film is partly about how a woman
+ 
+
+ align:start position:0%
+the film is partly about how a woman
+takes on a man's job. I mean, her I
+
+ align:start position:0%
+takes on a man's job. I mean, her I
+ 
+
+ align:start position:0%
+takes on a man's job. I mean, her I
+guess it's her father, isn't it? Her
+
+ align:start position:0%
+guess it's her father, isn't it? Her
+ 
+
+ align:start position:0%
+guess it's her father, isn't it? Her
+father is ill and she has to take over
+
+ align:start position:0%
+father is ill and she has to take over
+ 
+
+ align:start position:0%
+father is ill and she has to take over
+running the the train station and she
+
+ align:start position:0%
+running the the train station and she
+ 
+
+ align:start position:0%
+running the the train station and she
+runs in and and so there's a certain
+
+ align:start position:0%
+runs in and and so there's a certain
+ 
+
+ align:start position:0%
+runs in and and so there's a certain
+sense in which one of the things that's
+
+ align:start position:0%
+sense in which one of the things that's
+ 
+
+ align:start position:0%
+sense in which one of the things that's
+dramatized socially is is a woman sort
+
+ align:start position:0%
+dramatized socially is is a woman sort
+ 
+
+ align:start position:0%
+dramatized socially is is a woman sort
+of moving into a kind of masculine
+
+ align:start position:0%
+of moving into a kind of masculine
+ 
+
+ align:start position:0%
+of moving into a kind of masculine
+realm, taking on a role that's more
+
+ align:start position:0%
+realm, taking on a role that's more
+ 
+
+ align:start position:0%
+realm, taking on a role that's more
+aggressive than is appropriate for for
+
+ align:start position:0%
+aggressive than is appropriate for for
+ 
+
+ align:start position:0%
+aggressive than is appropriate for for
+the for the gender ideologies that are
+
+ align:start position:0%
+the for the gender ideologies that are
+ 
+
+ align:start position:0%
+the for the gender ideologies that are
+dominant. at the end of the 19th century
+
+ align:start position:0%
+dominant. at the end of the 19th century
+ 
+
+ align:start position:0%
+dominant. at the end of the 19th century
+in the United States. But the film is
+
+ align:start position:0%
+in the United States. But the film is
+ 
+
+ align:start position:0%
+in the United States. But the film is
+pretty clever about this like many such
+
+ align:start position:0%
+pretty clever about this like many such
+ 
+
+ align:start position:0%
+pretty clever about this like many such
+popular texts because although it does
+
+ align:start position:0%
+popular texts because although it does
+ 
+
+ align:start position:0%
+popular texts because although it does
+grant this woman a certain kind of
+
+ align:start position:0%
+grant this woman a certain kind of
+ 
+
+ align:start position:0%
+grant this woman a certain kind of
+masculine authority and competence, it
+
+ align:start position:0%
+masculine authority and competence, it
+ 
+
+ align:start position:0%
+masculine authority and competence, it
+also has other things in the film that
+
+ align:start position:0%
+also has other things in the film that
+ 
+
+ align:start position:0%
+also has other things in the film that
+balance that that remind us that she is
+
+ align:start position:0%
+balance that that remind us that she is
+ 
+
+ align:start position:0%
+balance that that remind us that she is
+still nonetheless uh a weak vessel that
+
+ align:start position:0%
+still nonetheless uh a weak vessel that
+ 
+
+ align:start position:0%
+still nonetheless uh a weak vessel that
+she is still a damsel in distress like
+
+ align:start position:0%
+she is still a damsel in distress like
+ 
+
+ align:start position:0%
+she is still a damsel in distress like
+the typical Victorian construction of
+
+ align:start position:0%
+the typical Victorian construction of
+ 
+
+ align:start position:0%
+the typical Victorian construction of
+women. uh in other words what you can
+
+ align:start position:0%
+women. uh in other words what you can
+ 
+
+ align:start position:0%
+women. uh in other words what you can
+see is that the movie exhibits an
+
+ align:start position:0%
+see is that the movie exhibits an
+ 
+
+ align:start position:0%
+see is that the movie exhibits an
+anxiety about gender roles that's also
+
+ align:start position:0%
+anxiety about gender roles that's also
+ 
+
+ align:start position:0%
+anxiety about gender roles that's also
+an anxiety that's resident in the
+
+ align:start position:0%
+an anxiety that's resident in the
+ 
+
+ align:start position:0%
+an anxiety that's resident in the
+society itself uh and I I won't talk
+
+ align:start position:0%
+society itself uh and I I won't talk
+ 
+
+ align:start position:0%
+society itself uh and I I won't talk
+more about this now it's something we
+
+ align:start position:0%
+more about this now it's something we
+ 
+
+ align:start position:0%
+more about this now it's something we
+will develop this aspect of the movies
+
+ align:start position:0%
+will develop this aspect of the movies
+ 
+
+ align:start position:0%
+will develop this aspect of the movies
+the movies as a reflection of social
+
+ align:start position:0%
+the movies as a reflection of social
+ 
+
+ align:start position:0%
+the movies as a reflection of social
+anxieties and social and social problems
+
+ align:start position:0%
+anxieties and social and social problems
+ 
+
+ align:start position:0%
+anxieties and social and social problems
+as the as the course goes on but I do
+
+ align:start position:0%
+as the as the course goes on but I do
+ 
+
+ align:start position:0%
+as the as the course goes on but I do
+want to call your attention to certain
+
+ align:start position:0%
+want to call your attention to certain
+ 
+
+ align:start position:0%
+want to call your attention to certain
+technical things that you can watch to
+
+ align:start position:0%
+technical things that you can watch to
+ 
+
+ align:start position:0%
+technical things that you can watch to
+at least one technical item in the film
+
+ align:start position:0%
+at least one technical item in the film
+ 
+
+ align:start position:0%
+at least one technical item in the film
+it contains what might be called rhyming
+
+ align:start position:0%
+it contains what might be called rhyming
+ 
+
+ align:start position:0%
+it contains what might be called rhyming
+scenes
+
+ align:start position:0%
+scenes
+ 
+
+ align:start position:0%
+scenes
+in which at one point in the film you'll
+
+ align:start position:0%
+in which at one point in the film you'll
+ 
+
+ align:start position:0%
+in which at one point in the film you'll
+see a sequence of scenes and a
+
+ align:start position:0%
+see a sequence of scenes and a
+ 
+
+ align:start position:0%
+see a sequence of scenes and a
+particular shot and then later in the
+
+ align:start position:0%
+particular shot and then later in the
+ 
+
+ align:start position:0%
+particular shot and then later in the
+film almost exactly the same shot will
+
+ align:start position:0%
+film almost exactly the same shot will
+ 
+
+ align:start position:0%
+film almost exactly the same shot will
+reappear and the effect of this of
+
+ align:start position:0%
+reappear and the effect of this of
+ 
+
+ align:start position:0%
+reappear and the effect of this of
+course is to create a sense of coherence
+
+ align:start position:0%
+course is to create a sense of coherence
+ 
+
+ align:start position:0%
+course is to create a sense of coherence
+and a sense of familiarity in the
+
+ align:start position:0%
+and a sense of familiarity in the
+ 
+
+ align:start position:0%
+and a sense of familiarity in the
+audience. It's actually a very subtle
+
+ align:start position:0%
+audience. It's actually a very subtle
+ 
+
+ align:start position:0%
+audience. It's actually a very subtle
+and careful strategy that Griffith
+
+ align:start position:0%
+and careful strategy that Griffith
+ 
+
+ align:start position:0%
+and careful strategy that Griffith
+himself devised. Uh it creates a kind of
+
+ align:start position:0%
+himself devised. Uh it creates a kind of
+ 
+
+ align:start position:0%
+himself devised. Uh it creates a kind of
+continuity and clarity to the whole
+
+ align:start position:0%
+continuity and clarity to the whole
+ 
+
+ align:start position:0%
+continuity and clarity to the whole
+film. Watch for example how the doorway
+
+ align:start position:0%
+film. Watch for example how the doorway
+ 
+
+ align:start position:0%
+film. Watch for example how the doorway
+to the lonale station is photographed
+
+ align:start position:0%
+to the lonale station is photographed
+ 
+
+ align:start position:0%
+to the lonale station is photographed
+when you first see it. how this image
+
+ align:start position:0%
+when you first see it. how this image
+ 
+
+ align:start position:0%
+when you first see it. how this image
+anchors the film's spatial relationships
+
+ align:start position:0%
+anchors the film's spatial relationships
+ 
+
+ align:start position:0%
+anchors the film's spatial relationships
+and how the film has a certain
+
+ align:start position:0%
+and how the film has a certain
+ 
+
+ align:start position:0%
+and how the film has a certain
+trajectory of movement that is repeated
+
+ align:start position:0%
+trajectory of movement that is repeated
+ 
+
+ align:start position:0%
+trajectory of movement that is repeated
+as the film goes on. So that for example
+
+ align:start position:0%
+as the film goes on. So that for example
+ 
+
+ align:start position:0%
+as the film goes on. So that for example
+early in the film we see the heroine go
+
+ align:start position:0%
+early in the film we see the heroine go
+ 
+
+ align:start position:0%
+early in the film we see the heroine go
+from the exterior to the interior of the
+
+ align:start position:0%
+from the exterior to the interior of the
+ 
+
+ align:start position:0%
+from the exterior to the interior of the
+ticket office and then to the inner
+
+ align:start position:0%
+ticket office and then to the inner
+ 
+
+ align:start position:0%
+ticket office and then to the inner
+office of the telegraph operator and we
+
+ align:start position:0%
+office of the telegraph operator and we
+ 
+
+ align:start position:0%
+office of the telegraph operator and we
+see her do this right and then this sets
+
+ align:start position:0%
+see her do this right and then this sets
+ 
+
+ align:start position:0%
+see her do this right and then this sets
+up a kind of basic location and basic
+
+ align:start position:0%
+up a kind of basic location and basic
+ 
+
+ align:start position:0%
+up a kind of basic location and basic
+action for the entire film. It's as if
+
+ align:start position:0%
+action for the entire film. It's as if
+ 
+
+ align:start position:0%
+action for the entire film. It's as if
+what happens in that moment sets up
+
+ align:start position:0%
+what happens in that moment sets up
+ 
+
+ align:start position:0%
+what happens in that moment sets up
+creates a familiarity with the for the
+
+ align:start position:0%
+creates a familiarity with the for the
+ 
+
+ align:start position:0%
+creates a familiarity with the for the
+audience with the sort of geography of
+
+ align:start position:0%
+audience with the sort of geography of
+ 
+
+ align:start position:0%
+audience with the sort of geography of
+the movie because a lot of the action
+
+ align:start position:0%
+the movie because a lot of the action
+ 
+
+ align:start position:0%
+the movie because a lot of the action
+then will depend on our understanding of
+
+ align:start position:0%
+then will depend on our understanding of
+ 
+
+ align:start position:0%
+then will depend on our understanding of
+that geography. And then there are at
+
+ align:start position:0%
+that geography. And then there are at
+ 
+
+ align:start position:0%
+that geography. And then there are at
+least four different times that Griffith
+
+ align:start position:0%
+least four different times that Griffith
+ 
+
+ align:start position:0%
+least four different times that Griffith
+repeats that basic three-shot trajectory
+
+ align:start position:0%
+repeats that basic three-shot trajectory
+ 
+
+ align:start position:0%
+repeats that basic three-shot trajectory
+from the um exterior to the interior of
+
+ align:start position:0%
+from the um exterior to the interior of
+ 
+
+ align:start position:0%
+from the um exterior to the interior of
+the ticket office and then from the
+
+ align:start position:0%
+the ticket office and then from the
+ 
+
+ align:start position:0%
+the ticket office and then from the
+inner to the inner office of the
+
+ align:start position:0%
+inner to the inner office of the
+ 
+
+ align:start position:0%
+inner to the inner office of the
+telegraph operator. It happens four
+
+ align:start position:0%
+telegraph operator. It happens four
+ 
+
+ align:start position:0%
+telegraph operator. It happens four
+times in the film. So it so the film has
+
+ align:start position:0%
+times in the film. So it so the film has
+ 
+
+ align:start position:0%
+times in the film. So it so the film has
+a kind of visual coherence. By the time
+
+ align:start position:0%
+a kind of visual coherence. By the time
+ 
+
+ align:start position:0%
+a kind of visual coherence. By the time
+you come to it the third or fourth time,
+
+ align:start position:0%
+you come to it the third or fourth time,
+ 
+
+ align:start position:0%
+you come to it the third or fourth time,
+it's as if you're intimate with the
+
+ align:start position:0%
+it's as if you're intimate with the
+ 
+
+ align:start position:0%
+it's as if you're intimate with the
+physical geography of the movie. This is
+
+ align:start position:0%
+physical geography of the movie. This is
+ 
+
+ align:start position:0%
+physical geography of the movie. This is
+actually a structural feature that it's
+
+ align:start position:0%
+actually a structural feature that it's
+ 
+
+ align:start position:0%
+actually a structural feature that it's
+easy to miss it, but it's it it's
+
+ align:start position:0%
+easy to miss it, but it's it it's
+ 
+
+ align:start position:0%
+easy to miss it, but it's it it's
+actually very artful and we can see it's
+
+ align:start position:0%
+actually very artful and we can see it's
+ 
+
+ align:start position:0%
+actually very artful and we can see it's
+a it's a mark of how far film has come
+
+ align:start position:0%
+a it's a mark of how far film has come
+ 
+
+ align:start position:0%
+a it's a mark of how far film has come
+even by 1911 that this level of
+
+ align:start position:0%
+even by 1911 that this level of
+ 
+
+ align:start position:0%
+even by 1911 that this level of
+attentiveness uh is is available to us
+
+ align:start position:0%
+attentiveness uh is is available to us
+ 
+
+ align:start position:0%
+attentiveness uh is is available to us
+in the film. There's m much more that
+
+ align:start position:0%
+in the film. There's m much more that
+ 
+
+ align:start position:0%
+in the film. There's m much more that
+could be said about the Loneale
+
+ align:start position:0%
+could be said about the Loneale
+ 
+
+ align:start position:0%
+could be said about the Loneale
+operator, but I will leave it to your
+
+ align:start position:0%
+operator, but I will leave it to your
+ 
+
+ align:start position:0%
+operator, but I will leave it to your
+intelligence and your attentiveness to
+
+ align:start position:0%
+intelligence and your attentiveness to
+ 
+
+ align:start position:0%
+intelligence and your attentiveness to
+try to pick out more thing. And again,
+
+ align:start position:0%
+try to pick out more thing. And again,
+ 
+
+ align:start position:0%
+try to pick out more thing. And again,
+we're only talking about a 17 minute a
+
+ align:start position:0%
+we're only talking about a 17 minute a
+ 
+
+ align:start position:0%
+we're only talking about a 17 minute a
+17-minute film. Well, uh,
+
+ align:start position:0%
+17-minute film. Well, uh,
+ 
+
+ align:start position:0%
+17-minute film. Well, uh,
+Buster Keaton's career could be said in
+
+ align:start position:0%
+Buster Keaton's career could be said in
+ 
+
+ align:start position:0%
+Buster Keaton's career could be said in
+some degree to enact in small the larger
+
+ align:start position:0%
+some degree to enact in small the larger
+ 
+
+ align:start position:0%
+some degree to enact in small the larger
+processes I've been describing. He comes
+
+ align:start position:0%
+processes I've been describing. He comes
+ 
+
+ align:start position:0%
+processes I've been describing. He comes
+into film late and in fact if we were
+
+ align:start position:0%
+into film late and in fact if we were
+ 
+
+ align:start position:0%
+into film late and in fact if we were
+working perfectly chronologically in
+
+ align:start position:0%
+working perfectly chronologically in
+ 
+
+ align:start position:0%
+working perfectly chronologically in
+terms of when Chaplain became a director
+
+ align:start position:0%
+terms of when Chaplain became a director
+ 
+
+ align:start position:0%
+terms of when Chaplain became a director
+he would precede Keaton but I've
+
+ align:start position:0%
+he would precede Keaton but I've
+ 
+
+ align:start position:0%
+he would precede Keaton but I've
+organized the film according to the
+
+ align:start position:0%
+organized the film according to the
+ 
+
+ align:start position:0%
+organized the film according to the
+feature the dates of the feature films
+
+ align:start position:0%
+feature the dates of the feature films
+ 
+
+ align:start position:0%
+feature the dates of the feature films
+and the general is an ear a much a
+
+ align:start position:0%
+and the general is an ear a much a
+ 
+
+ align:start position:0%
+and the general is an ear a much a
+decade earlier than modern times which
+
+ align:start position:0%
+decade earlier than modern times which
+ 
+
+ align:start position:0%
+decade earlier than modern times which
+is the last quote silent film. It's not
+
+ align:start position:0%
+is the last quote silent film. It's not
+ 
+
+ align:start position:0%
+is the last quote silent film. It's not
+really a silent film but it's the last
+
+ align:start position:0%
+really a silent film but it's the last
+ 
+
+ align:start position:0%
+really a silent film but it's the last
+silent film in a deep sense that was
+
+ align:start position:0%
+silent film in a deep sense that was
+ 
+
+ align:start position:0%
+silent film in a deep sense that was
+ever made. It was made in the sound era
+
+ align:start position:0%
+ever made. It was made in the sound era
+ 
+
+ align:start position:0%
+ever made. It was made in the sound era
+in 1936. And when we next week we'll
+
+ align:start position:0%
+in 1936. And when we next week we'll
+ 
+
+ align:start position:0%
+in 1936. And when we next week we'll
+talk more about the implications of that
+
+ align:start position:0%
+talk more about the implications of that
+ 
+
+ align:start position:0%
+talk more about the implications of that
+and why that was a very daring thing for
+
+ align:start position:0%
+and why that was a very daring thing for
+ 
+
+ align:start position:0%
+and why that was a very daring thing for
+Chaplan to do something like almost a
+
+ align:start position:0%
+Chaplan to do something like almost a
+ 
+
+ align:start position:0%
+Chaplan to do something like almost a
+decade after the advent of sound he made
+
+ align:start position:0%
+decade after the advent of sound he made
+ 
+
+ align:start position:0%
+decade after the advent of sound he made
+a movie that essentially had no dialogue
+
+ align:start position:0%
+a movie that essentially had no dialogue
+ 
+
+ align:start position:0%
+a movie that essentially had no dialogue
+in it. So Katon came a little later
+
+ align:start position:0%
+in it. So Katon came a little later
+ 
+
+ align:start position:0%
+in it. So Katon came a little later
+comes into movie making uh after uh a
+
+ align:start position:0%
+comes into movie making uh after uh a
+ 
+
+ align:start position:0%
+comes into movie making uh after uh a
+little a few years after uh uh Chaplain
+
+ align:start position:0%
+little a few years after uh uh Chaplain
+ 
+
+ align:start position:0%
+little a few years after uh uh Chaplain
+but his but his career has a similar
+
+ align:start position:0%
+but his but his career has a similar
+ 
+
+ align:start position:0%
+but his but his career has a similar
+trajectory. He began his career in
+
+ align:start position:0%
+trajectory. He began his career in
+ 
+
+ align:start position:0%
+trajectory. He began his career in
+legitimate theater in vaudeville and in
+
+ align:start position:0%
+legitimate theater in vaudeville and in
+ 
+
+ align:start position:0%
+legitimate theater in vaudeville and in
+and in and in on the performance circuit
+
+ align:start position:0%
+and in and in on the performance circuit
+ 
+
+ align:start position:0%
+and in and in on the performance circuit
+uh and and uh- was an acrobat from a
+
+ align:start position:0%
+uh and and uh- was an acrobat from a
+ 
+
+ align:start position:0%
+uh and and uh- was an acrobat from a
+very young age from the the age of two
+
+ align:start position:0%
+very young age from the the age of two
+ 
+
+ align:start position:0%
+very young age from the the age of two
+or three was in his parents' stage act.
+
+ align:start position:0%
+or three was in his parents' stage act.
+ 
+
+ align:start position:0%
+or three was in his parents' stage act.
+He was actually uh uh uh a and in fact
+
+ align:start position:0%
+He was actually uh uh uh a and in fact
+ 
+
+ align:start position:0%
+He was actually uh uh uh a and in fact
+he learned a lot of his acrobatic feats
+
+ align:start position:0%
+he learned a lot of his acrobatic feats
+ 
+
+ align:start position:0%
+he learned a lot of his acrobatic feats
+on his parents' stage act. one very
+
+ align:start position:0%
+on his parents' stage act. one very
+ 
+
+ align:start position:0%
+on his parents' stage act. one very
+famous uh passage in his his father used
+
+ align:start position:0%
+famous uh passage in his his father used
+ 
+
+ align:start position:0%
+famous uh passage in his his father used
+to take him he was just a young kid
+
+ align:start position:0%
+to take him he was just a young kid
+ 
+
+ align:start position:0%
+to take him he was just a young kid
+three or four years old five years old
+
+ align:start position:0%
+three or four years old five years old
+ 
+
+ align:start position:0%
+three or four years old five years old
+would take him by his legs and swing him
+
+ align:start position:0%
+would take him by his legs and swing him
+ 
+
+ align:start position:0%
+would take him by his legs and swing him
+back and forth like this he had very
+
+ align:start position:0%
+back and forth like this he had very
+ 
+
+ align:start position:0%
+back and forth like this he had very
+long hair and he would sweep the floor
+
+ align:start position:0%
+long hair and he would sweep the floor
+ 
+
+ align:start position:0%
+long hair and he would sweep the floor
+with his hair and then swing him two or
+
+ align:start position:0%
+with his hair and then swing him two or
+ 
+
+ align:start position:0%
+with his hair and then swing him two or
+three times this would happen live he
+
+ align:start position:0%
+three times this would happen live he
+ 
+
+ align:start position:0%
+three times this would happen live he
+would swing him like this and let him go
+
+ align:start position:0%
+would swing him like this and let him go
+ 
+
+ align:start position:0%
+would swing him like this and let him go
+and the kid five years old would fly
+
+ align:start position:0%
+and the kid five years old would fly
+ 
+
+ align:start position:0%
+and the kid five years old would fly
+against the wall and fall down it would
+
+ align:start position:0%
+against the wall and fall down it would
+ 
+
+ align:start position:0%
+against the wall and fall down it would
+look terrible and Katon took later in
+
+ align:start position:0%
+look terrible and Katon took later in
+ 
+
+ align:start position:0%
+look terrible and Katon took later in
+his life Katon talked about this there
+
+ align:start position:0%
+his life Katon talked about this there
+ 
+
+ align:start position:0%
+his life Katon talked about this there
+were actually some cities in which the
+
+ align:start position:0%
+were actually some cities in which the
+ 
+
+ align:start position:0%
+were actually some cities in which the
+the uh uh societies for the for for the
+
+ align:start position:0%
+the uh uh societies for the for for the
+ 
+
+ align:start position:0%
+the uh uh societies for the for for the
+prevention of cruelty to children came
+
+ align:start position:0%
+prevention of cruelty to children came
+ 
+
+ align:start position:0%
+prevention of cruelty to children came
+in and shut down the shut down the act.
+
+ align:start position:0%
+in and shut down the shut down the act.
+ 
+
+ align:start position:0%
+in and shut down the shut down the act.
+Wouldn't allow the act to go on. Not
+
+ align:start position:0%
+Wouldn't allow the act to go on. Not
+ 
+
+ align:start position:0%
+Wouldn't allow the act to go on. Not
+stupid because his father was a drunkard
+
+ align:start position:0%
+stupid because his father was a drunkard
+ 
+
+ align:start position:0%
+stupid because his father was a drunkard
+and sometimes performed drunk. And Katon
+
+ align:start position:0%
+and sometimes performed drunk. And Katon
+ 
+
+ align:start position:0%
+and sometimes performed drunk. And Katon
+was sometimes injured. He was also
+
+ align:start position:0%
+was sometimes injured. He was also
+ 
+
+ align:start position:0%
+was sometimes injured. He was also
+injured when he made his own movies for
+
+ align:start position:0%
+injured when he made his own movies for
+ 
+
+ align:start position:0%
+injured when he made his own movies for
+because he was such a daring acrobat. Uh
+
+ align:start position:0%
+because he was such a daring acrobat. Uh
+ 
+
+ align:start position:0%
+because he was such a daring acrobat. Uh
+and uh Katon recounts that when he first
+
+ align:start position:0%
+and uh Katon recounts that when he first
+ 
+
+ align:start position:0%
+and uh Katon recounts that when he first
+began to perform in this, he would make
+
+ align:start position:0%
+began to perform in this, he would make
+ 
+
+ align:start position:0%
+began to perform in this, he would make
+faces, you know, faces that indicated
+
+ align:start position:0%
+faces, you know, faces that indicated
+ 
+
+ align:start position:0%
+faces, you know, faces that indicated
+pain or happiness or relief when his
+
+ align:start position:0%
+pain or happiness or relief when his
+ 
+
+ align:start position:0%
+pain or happiness or relief when his
+father was manipulating him this way.
+
+ align:start position:0%
+father was manipulating him this way.
+ 
+
+ align:start position:0%
+father was manipulating him this way.
+But he found that the audience responded
+
+ align:start position:0%
+But he found that the audience responded
+ 
+
+ align:start position:0%
+But he found that the audience responded
+much more comically, much more
+
+ align:start position:0%
+much more comically, much more
+ 
+
+ align:start position:0%
+much more comically, much more
+immediately if he just kept his face
+
+ align:start position:0%
+immediately if he just kept his face
+ 
+
+ align:start position:0%
+immediately if he just kept his face
+expressionless. And that's where there
+
+ align:start position:0%
+expressionless. And that's where there
+ 
+
+ align:start position:0%
+expressionless. And that's where there
+developed the probably mistaken uh uh
+
+ align:start position:0%
+developed the probably mistaken uh uh
+ 
+
+ align:start position:0%
+developed the probably mistaken uh uh
+label for Keaton of the great stone
+
+ align:start position:0%
+label for Keaton of the great stone
+ 
+
+ align:start position:0%
+label for Keaton of the great stone
+face. And in his films very often,
+
+ align:start position:0%
+face. And in his films very often,
+ 
+
+ align:start position:0%
+face. And in his films very often,
+you'll see this young man facing
+
+ align:start position:0%
+you'll see this young man facing
+ 
+
+ align:start position:0%
+you'll see this young man facing
+monumental catastrophe. His face will
+
+ align:start position:0%
+monumental catastrophe. His face will
+ 
+
+ align:start position:0%
+monumental catastrophe. His face will
+look out at things without everchanging
+
+ align:start position:0%
+look out at things without everchanging
+ 
+
+ align:start position:0%
+look out at things without everchanging
+expression. And there is something kind
+
+ align:start position:0%
+expression. And there is something kind
+ 
+
+ align:start position:0%
+expression. And there is something kind
+of kind of comical about that. You'll
+
+ align:start position:0%
+of kind of comical about that. You'll
+ 
+
+ align:start position:0%
+of kind of comical about that. You'll
+see some examples of this in the in the
+
+ align:start position:0%
+see some examples of this in the in the
+ 
+
+ align:start position:0%
+see some examples of this in the in the
+general. Well, you'll you'll see in the
+
+ align:start position:0%
+general. Well, you'll you'll see in the
+ 
+
+ align:start position:0%
+general. Well, you'll you'll see in the
+two short films that Keaton began to
+
+ align:start position:0%
+two short films that Keaton began to
+ 
+
+ align:start position:0%
+two short films that Keaton began to
+make that he enters film at already a
+
+ align:start position:0%
+make that he enters film at already a
+ 
+
+ align:start position:0%
+make that he enters film at already a
+relatively sophisticated time and and
+
+ align:start position:0%
+relatively sophisticated time and and
+ 
+
+ align:start position:0%
+relatively sophisticated time and and
+the shorts I'm asking you to look at are
+
+ align:start position:0%
+the shorts I'm asking you to look at are
+ 
+
+ align:start position:0%
+the shorts I'm asking you to look at are
+very interesting uh uh remarkable films
+
+ align:start position:0%
+very interesting uh uh remarkable films
+ 
+
+ align:start position:0%
+very interesting uh uh remarkable films
+in in their own way. And one of the
+
+ align:start position:0%
+in in their own way. And one of the
+ 
+
+ align:start position:0%
+in in their own way. And one of the
+things they teach us and one of the
+
+ align:start position:0%
+things they teach us and one of the
+ 
+
+ align:start position:0%
+things they teach us and one of the
+reasons I want you to look closely at at
+
+ align:start position:0%
+reasons I want you to look closely at at
+ 
+
+ align:start position:0%
+reasons I want you to look closely at at
+at uh Keaton is they te is they show us
+
+ align:start position:0%
+at uh Keaton is they te is they show us
+ 
+
+ align:start position:0%
+at uh Keaton is they te is they show us
+yet again another aspect of what I mean
+
+ align:start position:0%
+yet again another aspect of what I mean
+ 
+
+ align:start position:0%
+yet again another aspect of what I mean
+when I talk about the
+
+ align:start position:0%
+when I talk about the
+ 
+
+ align:start position:0%
+when I talk about the
+Fred principle. this development of
+
+ align:start position:0%
+Fred principle. this development of
+ 
+
+ align:start position:0%
+Fred principle. this development of
+evolution and and and and and increasing
+
+ align:start position:0%
+evolution and and and and and increasing
+ 
+
+ align:start position:0%
+evolution and and and and and increasing
+and increasing complexity because
+
+ align:start position:0%
+and increasing complexity because
+ 
+
+ align:start position:0%
+and increasing complexity because
+if you look at cops or if you look at
+
+ align:start position:0%
+if you look at cops or if you look at
+ 
+
+ align:start position:0%
+if you look at cops or if you look at
+one week what you will see Katon doing
+
+ align:start position:0%
+one week what you will see Katon doing
+ 
+
+ align:start position:0%
+one week what you will see Katon doing
+in those films is learning how to link
+
+ align:start position:0%
+in those films is learning how to link
+ 
+
+ align:start position:0%
+in those films is learning how to link
+jokes together in some sort of a
+
+ align:start position:0%
+jokes together in some sort of a
+ 
+
+ align:start position:0%
+jokes together in some sort of a
+coherent way but the films and and there
+
+ align:start position:0%
+coherent way but the films and and there
+ 
+
+ align:start position:0%
+coherent way but the films and and there
+are wonderful coherent sequences in
+
+ align:start position:0%
+are wonderful coherent sequences in
+ 
+
+ align:start position:0%
+are wonderful coherent sequences in
+these films but still one doesn't feel
+
+ align:start position:0%
+these films but still one doesn't feel
+ 
+
+ align:start position:0%
+these films but still one doesn't feel
+that there's a real character in them
+
+ align:start position:0%
+that there's a real character in them
+ 
+
+ align:start position:0%
+that there's a real character in them
+that there's a sustained coherent uh
+
+ align:start position:0%
+that there's a sustained coherent uh
+ 
+
+ align:start position:0%
+that there's a sustained coherent uh
+fictional universe being dramat
+
+ align:start position:0%
+fictional universe being dramat
+ 
+
+ align:start position:0%
+fictional universe being dramat
+Maybe in Cops one does feel this.
+
+ align:start position:0%
+Maybe in Cops one does feel this.
+ 
+
+ align:start position:0%
+Maybe in Cops one does feel this.
+There's much more sort of textural
+
+ align:start position:0%
+There's much more sort of textural
+ 
+
+ align:start position:0%
+There's much more sort of textural
+coherence in Cops. But what we can see
+
+ align:start position:0%
+coherence in Cops. But what we can see
+ 
+
+ align:start position:0%
+coherence in Cops. But what we can see
+Katon doing is beginning to move from
+
+ align:start position:0%
+Katon doing is beginning to move from
+ 
+
+ align:start position:0%
+Katon doing is beginning to move from
+the idea of a single joke to a sequence
+
+ align:start position:0%
+the idea of a single joke to a sequence
+ 
+
+ align:start position:0%
+the idea of a single joke to a sequence
+of jokes. And then by the time we get to
+
+ align:start position:0%
+of jokes. And then by the time we get to
+ 
+
+ align:start position:0%
+of jokes. And then by the time we get to
+the general moving from a sequence of
+
+ align:start position:0%
+the general moving from a sequence of
+ 
+
+ align:start position:0%
+the general moving from a sequence of
+from a single joke to a sequence of
+
+ align:start position:0%
+from a single joke to a sequence of
+ 
+
+ align:start position:0%
+from a single joke to a sequence of
+jokes to a sustained narrative which
+
+ align:start position:0%
+jokes to a sustained narrative which
+ 
+
+ align:start position:0%
+jokes to a sustained narrative which
+incorporates within it various kinds of
+
+ align:start position:0%
+incorporates within it various kinds of
+ 
+
+ align:start position:0%
+incorporates within it various kinds of
+comical jokes and also sequence jokes
+
+ align:start position:0%
+comical jokes and also sequence jokes
+ 
+
+ align:start position:0%
+comical jokes and also sequence jokes
+because Katon's best jokes are not
+
+ align:start position:0%
+because Katon's best jokes are not
+ 
+
+ align:start position:0%
+because Katon's best jokes are not
+single jokes at all not oneliners but
+
+ align:start position:0%
+single jokes at all not oneliners but
+ 
+
+ align:start position:0%
+single jokes at all not oneliners but
+the the joke will be told again and
+
+ align:start position:0%
+the the joke will be told again and
+ 
+
+ align:start position:0%
+the the joke will be told again and
+again or what or really what will happen
+
+ align:start position:0%
+again or what or really what will happen
+ 
+
+ align:start position:0%
+again or what or really what will happen
+is he will do something and you'll think
+
+ align:start position:0%
+is he will do something and you'll think
+ 
+
+ align:start position:0%
+is he will do something and you'll think
+how could and then he'll the next step
+
+ align:start position:0%
+how could and then he'll the next step
+ 
+
+ align:start position:0%
+how could and then he'll the next step
+will top what he's done before and the
+
+ align:start position:0%
+will top what he's done before and the
+ 
+
+ align:start position:0%
+will top what he's done before and the
+next step will top you think that he got
+
+ align:start position:0%
+next step will top you think that he got
+ 
+
+ align:start position:0%
+next step will top you think that he got
+to a point where it would be impossible
+
+ align:start position:0%
+to a point where it would be impossible
+ 
+
+ align:start position:0%
+to a point where it would be impossible
+possible to add another comic
+
+ align:start position:0%
+possible to add another comic
+ 
+
+ align:start position:0%
+possible to add another comic
+complication to what he's done when he
+
+ align:start position:0%
+complication to what he's done when he
+ 
+
+ align:start position:0%
+complication to what he's done when he
+of course does it. Uh and this becomes
+
+ align:start position:0%
+of course does it. Uh and this becomes
+ 
+
+ align:start position:0%
+of course does it. Uh and this becomes
+one of the deep principles of chap of of
+
+ align:start position:0%
+one of the deep principles of chap of of
+ 
+
+ align:start position:0%
+one of the deep principles of chap of of
+Katon's comedy. There are numerous
+
+ align:start position:0%
+Katon's comedy. There are numerous
+ 
+
+ align:start position:0%
+Katon's comedy. There are numerous
+examples of it in both the two shorts
+
+ align:start position:0%
+examples of it in both the two shorts
+ 
+
+ align:start position:0%
+examples of it in both the two shorts
+and in this in the longer film that I
+
+ align:start position:0%
+and in this in the longer film that I
+ 
+
+ align:start position:0%
+and in this in the longer film that I
+that uh the the general but let me
+
+ align:start position:0%
+that uh the the general but let me
+ 
+
+ align:start position:0%
+that uh the the general but let me
+mention an example from the general.
+
+ align:start position:0%
+mention an example from the general.
+ 
+
+ align:start position:0%
+mention an example from the general.
+Very early in the general there's a
+
+ align:start position:0%
+Very early in the general there's a
+ 
+
+ align:start position:0%
+Very early in the general there's a
+sequence it's probably the
+
+ align:start position:0%
+sequence it's probably the
+ 
+
+ align:start position:0%
+sequence it's probably the
+quintessential Katon sequence and I
+
+ align:start position:0%
+quintessential Katon sequence and I
+ 
+
+ align:start position:0%
+quintessential Katon sequence and I
+won't go into such detail as to spoil
+
+ align:start position:0%
+won't go into such detail as to spoil
+ 
+
+ align:start position:0%
+won't go into such detail as to spoil
+the film for you. Uh but let me just say
+
+ align:start position:0%
+the film for you. Uh but let me just say
+ 
+
+ align:start position:0%
+the film for you. Uh but let me just say
+it involves a cannon and it involves
+
+ align:start position:0%
+it involves a cannon and it involves
+ 
+
+ align:start position:0%
+it involves a cannon and it involves
+Katon uh uh who's chasing after Katon
+
+ align:start position:0%
+Katon uh uh who's chasing after Katon
+ 
+
+ align:start position:0%
+Katon uh uh who's chasing after Katon
+plays a uh the engineer of a of of a
+
+ align:start position:0%
+plays a uh the engineer of a of of a
+ 
+
+ align:start position:0%
+plays a uh the engineer of a of of a
+locomotive, a locomotive engineer. The
+
+ align:start position:0%
+locomotive, a locomotive engineer. The
+ 
+
+ align:start position:0%
+locomotive, a locomotive engineer. The
+general of the title is not a a mar a
+
+ align:start position:0%
+general of the title is not a a mar a
+ 
+
+ align:start position:0%
+general of the title is not a a mar a
+military general. It's a locomotive. The
+
+ align:start position:0%
+military general. It's a locomotive. The
+ 
+
+ align:start position:0%
+military general. It's a locomotive. The
+locomotive is called the general. And
+
+ align:start position:0%
+locomotive is called the general. And
+ 
+
+ align:start position:0%
+locomotive is called the general. And
+the and the film recounts a historically
+
+ align:start position:0%
+the and the film recounts a historically
+ 
+
+ align:start position:0%
+the and the film recounts a historically
+true story of a of a time when the Union
+
+ align:start position:0%
+true story of a of a time when the Union
+ 
+
+ align:start position:0%
+true story of a of a time when the Union
+Army um came in uh that with uh the
+
+ align:start position:0%
+Army um came in uh that with uh the
+ 
+
+ align:start position:0%
+Army um came in uh that with uh the
+Confederate army uh the Union Army came
+
+ align:start position:0%
+Confederate army uh the Union Army came
+ 
+
+ align:start position:0%
+Confederate army uh the Union Army came
+into Confederate territory and stole a
+
+ align:start position:0%
+into Confederate territory and stole a
+ 
+
+ align:start position:0%
+into Confederate territory and stole a
+locomotive belonging to the Confederacy.
+
+ align:start position:0%
+locomotive belonging to the Confederacy.
+ 
+
+ align:start position:0%
+locomotive belonging to the Confederacy.
+And this and and he was a and Keaton in
+
+ align:start position:0%
+And this and and he was a and Keaton in
+ 
+
+ align:start position:0%
+And this and and he was a and Keaton in
+a comic vein retells retells this story.
+
+ align:start position:0%
+a comic vein retells retells this story.
+ 
+
+ align:start position:0%
+a comic vein retells retells this story.
+When you watch this cannon sequence,
+
+ align:start position:0%
+When you watch this cannon sequence,
+ 
+
+ align:start position:0%
+When you watch this cannon sequence,
+you'll see exactly what I mean. You'll
+
+ align:start position:0%
+you'll see exactly what I mean. You'll
+ 
+
+ align:start position:0%
+you'll see exactly what I mean. You'll
+and this sequence is at the heart of
+
+ align:start position:0%
+and this sequence is at the heart of
+ 
+
+ align:start position:0%
+and this sequence is at the heart of
+James AG's essay on the silent film
+
+ align:start position:0%
+James AG's essay on the silent film
+ 
+
+ align:start position:0%
+James AG's essay on the silent film
+comedy. And when you read that essay,
+
+ align:start position:0%
+comedy. And when you read that essay,
+ 
+
+ align:start position:0%
+comedy. And when you read that essay,
+you'll see even more clearly what I mean
+
+ align:start position:0%
+you'll see even more clearly what I mean
+ 
+
+ align:start position:0%
+you'll see even more clearly what I mean
+by a trajectory joke or a sequence joke
+
+ align:start position:0%
+by a trajectory joke or a sequence joke
+ 
+
+ align:start position:0%
+by a trajectory joke or a sequence joke
+which builds and builds and builds and
+
+ align:start position:0%
+which builds and builds and builds and
+ 
+
+ align:start position:0%
+which builds and builds and builds and
+keeps topping itself. Well, this cannon
+
+ align:start position:0%
+keeps topping itself. Well, this cannon
+ 
+
+ align:start position:0%
+keeps topping itself. Well, this cannon
+sequence is a perfect example of that.
+
+ align:start position:0%
+sequence is a perfect example of that.
+ 
+
+ align:start position:0%
+sequence is a perfect example of that.
+And it's a perfect example of it not
+
+ align:start position:0%
+And it's a perfect example of it not
+ 
+
+ align:start position:0%
+And it's a perfect example of it not
+only because we see the joke getting
+
+ align:start position:0%
+only because we see the joke getting
+ 
+
+ align:start position:0%
+only because we see the joke getting
+more complicated as it goes on, but as
+
+ align:start position:0%
+more complicated as it goes on, but as
+ 
+
+ align:start position:0%
+more complicated as it goes on, but as
+the joke becomes more complicated,
+
+ align:start position:0%
+the joke becomes more complicated,
+ 
+
+ align:start position:0%
+the joke becomes more complicated,
+something else happens. The joke becomes
+
+ align:start position:0%
+something else happens. The joke becomes
+ 
+
+ align:start position:0%
+something else happens. The joke becomes
+more than a joke. It becomes a kind of
+
+ align:start position:0%
+more than a joke. It becomes a kind of
+ 
+
+ align:start position:0%
+more than a joke. It becomes a kind of
+comment on experience. It becomes a kind
+
+ align:start position:0%
+comment on experience. It becomes a kind
+ 
+
+ align:start position:0%
+comment on experience. It becomes a kind
+of comment on on on on on
+
+ align:start position:0%
+of comment on on on on on
+ 
+
+ align:start position:0%
+of comment on on on on on
+what life is like. That is to say, we
+
+ align:start position:0%
+what life is like. That is to say, we
+ 
+
+ align:start position:0%
+what life is like. That is to say, we
+move from something that simply makes us
+
+ align:start position:0%
+move from something that simply makes us
+ 
+
+ align:start position:0%
+move from something that simply makes us
+smile to something that makes us think
+
+ align:start position:0%
+smile to something that makes us think
+ 
+
+ align:start position:0%
+smile to something that makes us think
+about the world, that comments on the
+
+ align:start position:0%
+about the world, that comments on the
+ 
+
+ align:start position:0%
+about the world, that comments on the
+world, that imagines the world in a
+
+ align:start position:0%
+world, that imagines the world in a
+ 
+
+ align:start position:0%
+world, that imagines the world in a
+coherent way. I'll try to be more
+
+ align:start position:0%
+coherent way. I'll try to be more
+ 
+
+ align:start position:0%
+coherent way. I'll try to be more
+explicit about this in a in a in in a
+
+ align:start position:0%
+explicit about this in a in a in in a
+ 
+
+ align:start position:0%
+explicit about this in a in a in in a
+moment. So in Katon's career, we see him
+
+ align:start position:0%
+moment. So in Katon's career, we see him
+ 
+
+ align:start position:0%
+moment. So in Katon's career, we see him
+doing astonishing things as an acrobat
+
+ align:start position:0%
+doing astonishing things as an acrobat
+ 
+
+ align:start position:0%
+doing astonishing things as an acrobat
+and we would admire him just for his
+
+ align:start position:0%
+and we would admire him just for his
+ 
+
+ align:start position:0%
+and we would admire him just for his
+acrobatic performances in these films.
+
+ align:start position:0%
+acrobatic performances in these films.
+ 
+
+ align:start position:0%
+acrobatic performances in these films.
+Watch in this film in the in the
+
+ align:start position:0%
+Watch in this film in the in the
+ 
+
+ align:start position:0%
+Watch in this film in the in the
+general, for example, the way in which
+
+ align:start position:0%
+general, for example, the way in which
+ 
+
+ align:start position:0%
+general, for example, the way in which
+when he's piloting his locomotive,
+
+ align:start position:0%
+when he's piloting his locomotive,
+ 
+
+ align:start position:0%
+when he's piloting his locomotive,
+chasing the people who have stolen his
+
+ align:start position:0%
+chasing the people who have stolen his
+ 
+
+ align:start position:0%
+chasing the people who have stolen his
+original locomotive, how he's the only
+
+ align:start position:0%
+original locomotive, how he's the only
+ 
+
+ align:start position:0%
+original locomotive, how he's the only
+one on the train and he crawls all over
+
+ align:start position:0%
+one on the train and he crawls all over
+ 
+
+ align:start position:0%
+one on the train and he crawls all over
+the train. He
+
+ align:start position:0%
+the train. He
+ 
+
+ align:start position:0%
+the train. He
+almost every while the train is running,
+
+ align:start position:0%
+almost every while the train is running,
+ 
+
+ align:start position:0%
+almost every while the train is running,
+he'll crawl up to the front of it. He'll
+
+ align:start position:0%
+he'll crawl up to the front of it. He'll
+ 
+
+ align:start position:0%
+he'll crawl up to the front of it. He'll
+run to the back of it to put more fuel
+
+ align:start position:0%
+run to the back of it to put more fuel
+ 
+
+ align:start position:0%
+run to the back of it to put more fuel
+in. you what you can what you can see is
+
+ align:start position:0%
+in. you what you can what you can see is
+ 
+
+ align:start position:0%
+in. you what you can what you can see is
+and and also you can see this stuff
+
+ align:start position:0%
+and and also you can see this stuff
+ 
+
+ align:start position:0%
+and and also you can see this stuff
+happening in really happening. It's not
+
+ align:start position:0%
+happening in really happening. It's not
+ 
+
+ align:start position:0%
+happening in really happening. It's not
+faked in any way because there's a there
+
+ align:start position:0%
+faked in any way because there's a there
+ 
+
+ align:start position:0%
+faked in any way because there's a there
+is a a camera following the train as
+
+ align:start position:0%
+is a a camera following the train as
+ 
+
+ align:start position:0%
+is a a camera following the train as
+it's moving. You can see it's really
+
+ align:start position:0%
+it's moving. You can see it's really
+ 
+
+ align:start position:0%
+it's moving. You can see it's really
+moving because you can you can see it
+
+ align:start position:0%
+moving because you can you can see it
+ 
+
+ align:start position:0%
+moving because you can you can see it
+you can see it moving on the track and
+
+ align:start position:0%
+you can see it moving on the track and
+ 
+
+ align:start position:0%
+you can see it moving on the track and
+you can see the world behind it and you
+
+ align:start position:0%
+you can see the world behind it and you
+ 
+
+ align:start position:0%
+you can see the world behind it and you
+can you can tell that Katon is not
+
+ align:start position:0%
+can you can tell that Katon is not
+ 
+
+ align:start position:0%
+can you can tell that Katon is not
+faking these effects. Well, this cannon
+
+ align:start position:0%
+faking these effects. Well, this cannon
+ 
+
+ align:start position:0%
+faking these effects. Well, this cannon
+sequence is a is a is a sublimely rich
+
+ align:start position:0%
+sequence is a is a is a sublimely rich
+ 
+
+ align:start position:0%
+sequence is a is a is a sublimely rich
+example of this complex process I've
+
+ align:start position:0%
+example of this complex process I've
+ 
+
+ align:start position:0%
+example of this complex process I've
+been describing and it it has to do in
+
+ align:start position:0%
+been describing and it it has to do in
+ 
+
+ align:start position:0%
+been describing and it it has to do in
+part with what I call the multiplicity
+
+ align:start position:0%
+part with what I call the multiplicity
+ 
+
+ align:start position:0%
+part with what I call the multiplicity
+principle which I will define in a
+
+ align:start position:0%
+principle which I will define in a
+ 
+
+ align:start position:0%
+principle which I will define in a
+moment. So we see Katon as an actor as
+
+ align:start position:0%
+moment. So we see Katon as an actor as
+ 
+
+ align:start position:0%
+moment. So we see Katon as an actor as
+an acrobat as an acrobat actor as an
+
+ align:start position:0%
+an acrobat as an acrobat actor as an
+ 
+
+ align:start position:0%
+an acrobat as an acrobat actor as an
+incredibly in as a man much more than
+
+ align:start position:0%
+incredibly in as a man much more than
+ 
+
+ align:start position:0%
+incredibly in as a man much more than
+cha chaplain interested in the
+
+ align:start position:0%
+cha chaplain interested in the
+ 
+
+ align:start position:0%
+cha chaplain interested in the
+technology of motion pictures and of
+
+ align:start position:0%
+technology of motion pictures and of
+ 
+
+ align:start position:0%
+technology of motion pictures and of
+cinema. And you'll see a couple of
+
+ align:start position:0%
+cinema. And you'll see a couple of
+ 
+
+ align:start position:0%
+cinema. And you'll see a couple of
+examples in the films you're going to
+
+ align:start position:0%
+examples in the films you're going to
+ 
+
+ align:start position:0%
+examples in the films you're going to
+look at tonight in which we see Katon
+
+ align:start position:0%
+look at tonight in which we see Katon
+ 
+
+ align:start position:0%
+look at tonight in which we see Katon
+exploring uh in a somewhat systematic
+
+ align:start position:0%
+exploring uh in a somewhat systematic
+ 
+
+ align:start position:0%
+exploring uh in a somewhat systematic
+way the nature of the illusion of the
+
+ align:start position:0%
+way the nature of the illusion of the
+ 
+
+ align:start position:0%
+way the nature of the illusion of the
+motion pictures. There's one remarkable
+
+ align:start position:0%
+motion pictures. There's one remarkable
+ 
+
+ align:start position:0%
+motion pictures. There's one remarkable
+moment, comical moment in one week in
+
+ align:start position:0%
+moment, comical moment in one week in
+ 
+
+ align:start position:0%
+moment, comical moment in one week in
+which uh the heroine gets into a bathtub
+
+ align:start position:0%
+which uh the heroine gets into a bathtub
+ 
+
+ align:start position:0%
+which uh the heroine gets into a bathtub
+and it looks like you and she's sitting
+
+ align:start position:0%
+and it looks like you and she's sitting
+ 
+
+ align:start position:0%
+and it looks like you and she's sitting
+in the bathtub. She's starting to get up
+
+ align:start position:0%
+in the bathtub. She's starting to get up
+ 
+
+ align:start position:0%
+in the bathtub. She's starting to get up
+and it looks like you're actually about
+
+ align:start position:0%
+and it looks like you're actually about
+ 
+
+ align:start position:0%
+and it looks like you're actually about
+to see some unmentionable parts of her
+
+ align:start position:0%
+to see some unmentionable parts of her
+ 
+
+ align:start position:0%
+to see some unmentionable parts of her
+body and just as that's about to happen
+
+ align:start position:0%
+body and just as that's about to happen
+ 
+
+ align:start position:0%
+body and just as that's about to happen
+a hand comes in front of the camera and
+
+ align:start position:0%
+a hand comes in front of the camera and
+ 
+
+ align:start position:0%
+a hand comes in front of the camera and
+blocks you. And it's actually a very
+
+ align:start position:0%
+blocks you. And it's actually a very
+ 
+
+ align:start position:0%
+blocks you. And it's actually a very
+disturbing moment in a way because it
+
+ align:start position:0%
+disturbing moment in a way because it
+ 
+
+ align:start position:0%
+disturbing moment in a way because it
+interrupts the narrative flow. It's it's
+
+ align:start position:0%
+interrupts the narrative flow. It's it's
+ 
+
+ align:start position:0%
+interrupts the narrative flow. It's it's
+a it's an intervention from the outside
+
+ align:start position:0%
+a it's an intervention from the outside
+ 
+
+ align:start position:0%
+a it's an intervention from the outside
+whose hand it is. It's not a character
+
+ align:start position:0%
+whose hand it is. It's not a character
+ 
+
+ align:start position:0%
+whose hand it is. It's not a character
+in the film. It's the director or
+
+ align:start position:0%
+in the film. It's the director or
+ 
+
+ align:start position:0%
+in the film. It's the director or
+something, right? It's very bold moment
+
+ align:start position:0%
+something, right? It's very bold moment
+ 
+
+ align:start position:0%
+something, right? It's very bold moment
+because what it does is it reminds you
+
+ align:start position:0%
+because what it does is it reminds you
+ 
+
+ align:start position:0%
+because what it does is it reminds you
+of the film as an artifact. It reminds
+
+ align:start position:0%
+of the film as an artifact. It reminds
+ 
+
+ align:start position:0%
+of the film as an artifact. It reminds
+you that the film is uh an
+
+ align:start position:0%
+you that the film is uh an
+ 
+
+ align:start position:0%
+you that the film is uh an
+artiflexiveness
+
+ align:start position:0%
+artiflexiveness
+ 
+
+ align:start position:0%
+artiflexiveness
+or self-consciousness that you would
+
+ align:start position:0%
+or self-consciousness that you would
+ 
+
+ align:start position:0%
+or self-consciousness that you would
+never see in a Chaplain film, but shows
+
+ align:start position:0%
+never see in a Chaplain film, but shows
+ 
+
+ align:start position:0%
+never see in a Chaplain film, but shows
+Katon's astonishing interest in the
+
+ align:start position:0%
+Katon's astonishing interest in the
+ 
+
+ align:start position:0%
+Katon's astonishing interest in the
+technology of motion pictures. Uh, I had
+
+ align:start position:0%
+technology of motion pictures. Uh, I had
+ 
+
+ align:start position:0%
+technology of motion pictures. Uh, I had
+many examples that Greg and I had ready,
+
+ align:start position:0%
+many examples that Greg and I had ready,
+ 
+
+ align:start position:0%
+many examples that Greg and I had ready,
+but I don't have time to show them to
+
+ align:start position:0%
+but I don't have time to show them to
+ 
+
+ align:start position:0%
+but I don't have time to show them to
+you. Maybe you can put up while I'm
+
+ align:start position:0%
+you. Maybe you can put up while I'm
+ 
+
+ align:start position:0%
+you. Maybe you can put up while I'm
+talking. The the Playhouse. One of his
+
+ align:start position:0%
+talking. The the Playhouse. One of his
+ 
+
+ align:start position:0%
+talking. The the Playhouse. One of his
+most famous examples of this is a film
+
+ align:start position:0%
+most famous examples of this is a film
+ 
+
+ align:start position:0%
+most famous examples of this is a film
+called The Playhouse in which he ends up
+
+ align:start position:0%
+called The Playhouse in which he ends up
+ 
+
+ align:start position:0%
+called The Playhouse in which he ends up
+playing every role in the movie. And the
+
+ align:start position:0%
+playing every role in the movie. And the
+ 
+
+ align:start position:0%
+playing every role in the movie. And the
+way he did this was incred was
+
+ align:start position:0%
+way he did this was incred was
+ 
+
+ align:start position:0%
+way he did this was incred was
+incredibly interesting. He would shoot
+
+ align:start position:0%
+incredibly interesting. He would shoot
+ 
+
+ align:start position:0%
+incredibly interesting. He would shoot
+the film. Uh, and then he he would shoot
+
+ align:start position:0%
+the film. Uh, and then he he would shoot
+ 
+
+ align:start position:0%
+the film. Uh, and then he he would shoot
+the film, but he would but he put a he
+
+ align:start position:0%
+the film, but he would but he put a he
+ 
+
+ align:start position:0%
+the film, but he would but he put a he
+put masking tape over the lens of the
+
+ align:start position:0%
+put masking tape over the lens of the
+ 
+
+ align:start position:0%
+put masking tape over the lens of the
+camera and only one little tiny part of
+
+ align:start position:0%
+camera and only one little tiny part of
+ 
+
+ align:start position:0%
+camera and only one little tiny part of
+the of the lens of the camera was was
+
+ align:start position:0%
+the of the lens of the camera was was
+ 
+
+ align:start position:0%
+the of the lens of the camera was was
+would expose the film and he would he
+
+ align:start position:0%
+would expose the film and he would he
+ 
+
+ align:start position:0%
+would expose the film and he would he
+would shoot that. Then he would rewind
+
+ align:start position:0%
+would shoot that. Then he would rewind
+ 
+
+ align:start position:0%
+would shoot that. Then he would rewind
+the film and then if he were over in
+
+ align:start position:0%
+the film and then if he were over in
+ 
+
+ align:start position:0%
+the film and then if he were over in
+this corner for that shot, then he'd
+
+ align:start position:0%
+this corner for that shot, then he'd
+ 
+
+ align:start position:0%
+this corner for that shot, then he'd
+move over and sit in the other corner.
+
+ align:start position:0%
+move over and sit in the other corner.
+ 
+
+ align:start position:0%
+move over and sit in the other corner.
+He'd put a new kind of tape on the
+
+ align:start position:0%
+He'd put a new kind of tape on the
+ 
+
+ align:start position:0%
+He'd put a new kind of tape on the
+camera, film it again. And the film
+
+ align:start position:0%
+camera, film it again. And the film
+ 
+
+ align:start position:0%
+camera, film it again. And the film
+you're going to see will show this. And
+
+ align:start position:0%
+you're going to see will show this. And
+ 
+
+ align:start position:0%
+you're going to see will show this. And
+you can see they're all buster, right?
+
+ align:start position:0%
+you can see they're all buster, right?
+ 
+
+ align:start position:0%
+you can see they're all buster, right?
+It's a it's an it's a it's again what it
+
+ align:start position:0%
+It's a it's an it's a it's again what it
+ 
+
+ align:start position:0%
+It's a it's an it's a it's again what it
+shows is he's a technician. He's
+
+ align:start position:0%
+shows is he's a technician. He's
+ 
+
+ align:start position:0%
+shows is he's a technician. He's
+interested in the technology of motion p
+
+ align:start position:0%
+interested in the technology of motion p
+ 
+
+ align:start position:0%
+interested in the technology of motion p
+of of of the of the uh motion picture
+
+ align:start position:0%
+of of of the of the uh motion picture
+ 
+
+ align:start position:0%
+of of of the of the uh motion picture
+camera and what kinds of manipulations
+
+ align:start position:0%
+camera and what kinds of manipulations
+ 
+
+ align:start position:0%
+camera and what kinds of manipulations
+are possible because he's the conductor,
+
+ align:start position:0%
+are possible because he's the conductor,
+ 
+
+ align:start position:0%
+are possible because he's the conductor,
+right? He's you'll as it turns out he's
+
+ align:start position:0%
+right? He's you'll as it turns out he's
+ 
+
+ align:start position:0%
+right? He's you'll as it turns out he's
+going to also end up being the o the the
+
+ align:start position:0%
+going to also end up being the o the the
+ 
+
+ align:start position:0%
+going to also end up being the o the the
+only person in the audience. Well, um,
+
+ align:start position:0%
+only person in the audience. Well, um,
+ 
+
+ align:start position:0%
+only person in the audience. Well, um,
+and then finally, what what what I've
+
+ align:start position:0%
+and then finally, what what what I've
+ 
+
+ align:start position:0%
+and then finally, what what what I've
+already implied is that Keaton's jokes
+
+ align:start position:0%
+already implied is that Keaton's jokes
+ 
+
+ align:start position:0%
+already implied is that Keaton's jokes
+and his technical interests also end up
+
+ align:start position:0%
+and his technical interests also end up
+ 
+
+ align:start position:0%
+and his technical interests also end up
+making him a metaphysician, a
+
+ align:start position:0%
+making him a metaphysician, a
+ 
+
+ align:start position:0%
+making him a metaphysician, a
+philosopher, an artist. Now, Katon
+
+ align:start position:0%
+philosopher, an artist. Now, Katon
+ 
+
+ align:start position:0%
+philosopher, an artist. Now, Katon
+himself could never articulate his own
+
+ align:start position:0%
+himself could never articulate his own
+ 
+
+ align:start position:0%
+himself could never articulate his own
+ambitions in this way. If you said, "Mr.
+
+ align:start position:0%
+ambitions in this way. If you said, "Mr.
+ 
+
+ align:start position:0%
+ambitions in this way. If you said, "Mr.
+Keaton, your vision of the absurd
+
+ align:start position:0%
+Keaton, your vision of the absurd
+ 
+
+ align:start position:0%
+Keaton, your vision of the absurd
+universe is more complex and rich than
+
+ align:start position:0%
+universe is more complex and rich than
+ 
+
+ align:start position:0%
+universe is more complex and rich than
+Jean Paul Sarts," as in fact it is,
+
+ align:start position:0%
+Jean Paul Sarts," as in fact it is,
+ 
+
+ align:start position:0%
+Jean Paul Sarts," as in fact it is,
+incidentally, he would laugh. He
+
+ align:start position:0%
+incidentally, he would laugh. He
+ 
+
+ align:start position:0%
+incidentally, he would laugh. He
+wouldn't even understand what you were
+
+ align:start position:0%
+wouldn't even understand what you were
+ 
+
+ align:start position:0%
+wouldn't even understand what you were
+talking about. Not only because he'd
+
+ align:start position:0%
+talking about. Not only because he'd
+ 
+
+ align:start position:0%
+talking about. Not only because he'd
+never read Sart since he died before he
+
+ align:start position:0%
+never read Sart since he died before he
+ 
+
+ align:start position:0%
+never read Sart since he died before he
+well sorry he was alive when Sart was
+
+ align:start position:0%
+well sorry he was alive when Sart was
+ 
+
+ align:start position:0%
+well sorry he was alive when Sart was
+alive actually but but he undoubtedly he
+
+ align:start position:0%
+alive actually but but he undoubtedly he
+ 
+
+ align:start position:0%
+alive actually but but he undoubtedly he
+did not read but the universe that he
+
+ align:start position:0%
+did not read but the universe that he
+ 
+
+ align:start position:0%
+did not read but the universe that he
+projects uh has has a kind of content or
+
+ align:start position:0%
+projects uh has has a kind of content or
+ 
+
+ align:start position:0%
+projects uh has has a kind of content or
+a meaning that's a function of how
+
+ align:start position:0%
+a meaning that's a function of how
+ 
+
+ align:start position:0%
+a meaning that's a function of how
+intelligent he is about exploiting his
+
+ align:start position:0%
+intelligent he is about exploiting his
+ 
+
+ align:start position:0%
+intelligent he is about exploiting his
+medium and telling his stories as if his
+
+ align:start position:0%
+medium and telling his stories as if his
+ 
+
+ align:start position:0%
+medium and telling his stories as if his
+jokes express a vision of life a sense
+
+ align:start position:0%
+jokes express a vision of life a sense
+ 
+
+ align:start position:0%
+jokes express a vision of life a sense
+of experience. Now this so you um and of
+
+ align:start position:0%
+of experience. Now this so you um and of
+ 
+
+ align:start position:0%
+of experience. Now this so you um and of
+course this is what you're looking at is
+
+ align:start position:0%
+course this is what you're looking at is
+ 
+
+ align:start position:0%
+course this is what you're looking at is
+sort of minor keaton here but it but it
+
+ align:start position:0%
+sort of minor keaton here but it but it
+ 
+
+ align:start position:0%
+sort of minor keaton here but it but it
+shows his it shows his technical his
+
+ align:start position:0%
+shows his it shows his technical his
+ 
+
+ align:start position:0%
+shows his it shows his technical his
+technical interests well so what I mean
+
+ align:start position:0%
+technical interests well so what I mean
+ 
+
+ align:start position:0%
+technical interests well so what I mean
+so let me explain what I mean basically
+
+ align:start position:0%
+so let me explain what I mean basically
+ 
+
+ align:start position:0%
+so let me explain what I mean basically
+by the multiplicity principle this
+
+ align:start position:0%
+by the multiplicity principle this
+ 
+
+ align:start position:0%
+by the multiplicity principle this
+process of accretion and complexity I've
+
+ align:start position:0%
+process of accretion and complexity I've
+ 
+
+ align:start position:0%
+process of accretion and complexity I've
+described at a certain point you get to
+
+ align:start position:0%
+described at a certain point you get to
+ 
+
+ align:start position:0%
+described at a certain point you get to
+a point where what what began as a gag
+
+ align:start position:0%
+a point where what what began as a gag
+ 
+
+ align:start position:0%
+a point where what what began as a gag
+or as a mere entertainment takes on a
+
+ align:start position:0%
+or as a mere entertainment takes on a
+ 
+
+ align:start position:0%
+or as a mere entertainment takes on a
+density or a texture that makes you
+
+ align:start position:0%
+density or a texture that makes you
+ 
+
+ align:start position:0%
+density or a texture that makes you
+think wait a second the vision of
+
+ align:start position:0%
+think wait a second the vision of
+ 
+
+ align:start position:0%
+think wait a second the vision of
+experience that's projected in This text
+
+ align:start position:0%
+experience that's projected in This text
+ 
+
+ align:start position:0%
+experience that's projected in This text
+is intrinsically interesting. That is to
+
+ align:start position:0%
+is intrinsically interesting. That is to
+ 
+
+ align:start position:0%
+is intrinsically interesting. That is to
+say, there's an understanding of life
+
+ align:start position:0%
+say, there's an understanding of life
+ 
+
+ align:start position:0%
+say, there's an understanding of life
+that's embedded in the story. When you
+
+ align:start position:0%
+that's embedded in the story. When you
+ 
+
+ align:start position:0%
+that's embedded in the story. When you
+reach the point where the text itself
+
+ align:start position:0%
+reach the point where the text itself
+ 
+
+ align:start position:0%
+reach the point where the text itself
+embodies some sort of understanding of
+
+ align:start position:0%
+embodies some sort of understanding of
+ 
+
+ align:start position:0%
+embodies some sort of understanding of
+life and it's coherent, an understanding
+
+ align:start position:0%
+life and it's coherent, an understanding
+ 
+
+ align:start position:0%
+life and it's coherent, an understanding
+of life that's coherently presented,
+
+ align:start position:0%
+of life that's coherently presented,
+ 
+
+ align:start position:0%
+of life that's coherently presented,
+powerfully presented, what you're what
+
+ align:start position:0%
+powerfully presented, what you're what
+ 
+
+ align:start position:0%
+powerfully presented, what you're what
+you're looking at is what I call art.
+
+ align:start position:0%
+you're looking at is what I call art.
+ 
+
+ align:start position:0%
+you're looking at is what I call art.
+There's you might just call it more
+
+ align:start position:0%
+There's you might just call it more
+ 
+
+ align:start position:0%
+There's you might just call it more
+intelligent entertainment, but this is a
+
+ align:start position:0%
+intelligent entertainment, but this is a
+ 
+
+ align:start position:0%
+intelligent entertainment, but this is a
+way of distinguishing between
+
+ align:start position:0%
+way of distinguishing between
+ 
+
+ align:start position:0%
+way of distinguishing between
+entertainment and art. In other words,
+
+ align:start position:0%
+entertainment and art. In other words,
+ 
+
+ align:start position:0%
+entertainment and art. In other words,
+there's a certain point at which
+
+ align:start position:0%
+there's a certain point at which
+ 
+
+ align:start position:0%
+there's a certain point at which
+entertainment becomes so complicated
+
+ align:start position:0%
+entertainment becomes so complicated
+ 
+
+ align:start position:0%
+entertainment becomes so complicated
+that it's more than mere entertainment.
+
+ align:start position:0%
+that it's more than mere entertainment.
+ 
+
+ align:start position:0%
+that it's more than mere entertainment.
+When does that occur? Well, one way to
+
+ align:start position:0%
+When does that occur? Well, one way to
+ 
+
+ align:start position:0%
+When does that occur? Well, one way to
+tell when it occurs is to watch for what
+
+ align:start position:0%
+tell when it occurs is to watch for what
+ 
+
+ align:start position:0%
+tell when it occurs is to watch for what
+I call the multiplicity principle. When
+
+ align:start position:0%
+I call the multiplicity principle. When
+ 
+
+ align:start position:0%
+I call the multiplicity principle. When
+events in the film play more than one
+
+ align:start position:0%
+events in the film play more than one
+ 
+
+ align:start position:0%
+events in the film play more than one
+function, do more than one job. When
+
+ align:start position:0%
+function, do more than one job. When
+ 
+
+ align:start position:0%
+function, do more than one job. When
+they forward the story but also declare
+
+ align:start position:0%
+they forward the story but also declare
+ 
+
+ align:start position:0%
+they forward the story but also declare
+for character. when they express when
+
+ align:start position:0%
+for character. when they express when
+ 
+
+ align:start position:0%
+for character. when they express when
+they make you laugh but also express a
+
+ align:start position:0%
+they make you laugh but also express a
+ 
+
+ align:start position:0%
+they make you laugh but also express a
+vision of life and at the same time ex
+
+ align:start position:0%
+vision of life and at the same time ex
+ 
+
+ align:start position:0%
+vision of life and at the same time ex
+uh are consistent with the character
+
+ align:start position:0%
+uh are consistent with the character
+ 
+
+ align:start position:0%
+uh are consistent with the character
+psychological nature that multiplicity
+
+ align:start position:0%
+psychological nature that multiplicity
+ 
+
+ align:start position:0%
+psychological nature that multiplicity
+that density that texture is what we
+
+ align:start position:0%
+that density that texture is what we
+ 
+
+ align:start position:0%
+that density that texture is what we
+associate with works of art right uh a
+
+ align:start position:0%
+associate with works of art right uh a
+ 
+
+ align:start position:0%
+associate with works of art right uh a
+bad example would be you're all familiar
+
+ align:start position:0%
+bad example would be you're all familiar
+ 
+
+ align:start position:0%
+bad example would be you're all familiar
+I hope with the kind of bad soap opera
+
+ align:start position:0%
+I hope with the kind of bad soap opera
+ 
+
+ align:start position:0%
+I hope with the kind of bad soap opera
+line in which a character comes in and
+
+ align:start position:0%
+line in which a character comes in and
+ 
+
+ align:start position:0%
+line in which a character comes in and
+says something like this oh hello John
+
+ align:start position:0%
+says something like this oh hello John
+ 
+
+ align:start position:0%
+says something like this oh hello John
+my longlost brother who just got out of
+
+ align:start position:0%
+my longlost brother who just got out of
+ 
+
+ align:start position:0%
+my longlost brother who just got out of
+the insane asylum after 15 years of
+
+ align:start position:0%
+the insane asylum after 15 years of
+ 
+
+ align:start position:0%
+the insane asylum after 15 years of
+unfair misery All right. What's wrong
+
+ align:start position:0%
+unfair misery All right. What's wrong
+ 
+
+ align:start position:0%
+unfair misery All right. What's wrong
+with that line? Why is that a stupid
+
+ align:start position:0%
+with that line? Why is that a stupid
+ 
+
+ align:start position:0%
+with that line? Why is that a stupid
+line? Although we hear them all the
+
+ align:start position:0%
+line? Although we hear them all the
+ 
+
+ align:start position:0%
+line? Although we hear them all the
+time. What What's wrong with it?
+
+ align:start position:0%
+time. What What's wrong with it?
+ 
+
+ align:start position:0%
+time. What What's wrong with it?
+Excessive and awkward exposition. It's
+
+ align:start position:0%
+Excessive and awkward exposition. It's
+ 
+
+ align:start position:0%
+Excessive and awkward exposition. It's
+it's very awkward exposition. But why is
+
+ align:start position:0%
+it's very awkward exposition. But why is
+ 
+
+ align:start position:0%
+it's very awkward exposition. But why is
+it so awkward? What makes it so awkward?
+
+ align:start position:0%
+it so awkward? What makes it so awkward?
+ 
+
+ align:start position:0%
+it so awkward? What makes it so awkward?
+It's it's its intention is clear. It
+
+ align:start position:0%
+It's it's its intention is clear. It
+ 
+
+ align:start position:0%
+It's it's its intention is clear. It
+wants to present information to the
+
+ align:start position:0%
+wants to present information to the
+ 
+
+ align:start position:0%
+wants to present information to the
+audience. But in order to do that, what
+
+ align:start position:0%
+audience. But in order to do that, what
+ 
+
+ align:start position:0%
+audience. But in order to do that, what
+what is it violated? Um it's ceases to
+
+ align:start position:0%
+what is it violated? Um it's ceases to
+ 
+
+ align:start position:0%
+what is it violated? Um it's ceases to
+be something that follows the nature of
+
+ align:start position:0%
+be something that follows the nature of
+ 
+
+ align:start position:0%
+be something that follows the nature of
+the character. It ceases to be something
+
+ align:start position:0%
+the character. It ceases to be something
+ 
+
+ align:start position:0%
+the character. It ceases to be something
+that is that honors the character's
+
+ align:start position:0%
+that is that honors the character's
+ 
+
+ align:start position:0%
+that is that honors the character's
+nature. Exactly right. That's a very
+
+ align:start position:0%
+nature. Exactly right. That's a very
+ 
+
+ align:start position:0%
+nature. Exactly right. That's a very
+good answer. What's your name? Michael.
+
+ align:start position:0%
+good answer. What's your name? Michael.
+ 
+
+ align:start position:0%
+good answer. What's your name? Michael.
+Michael. Thank Michael. That's very
+
+ align:start position:0%
+Michael. Thank Michael. That's very
+ 
+
+ align:start position:0%
+Michael. Thank Michael. That's very
+good. And what what happened? Okay. I
+
+ align:start position:0%
+good. And what what happened? Okay. I
+ 
+
+ align:start position:0%
+good. And what what happened? Okay. I
+want to give information to the
+
+ align:start position:0%
+want to give information to the
+ 
+
+ align:start position:0%
+want to give information to the
+audience. In order to do that, I'll
+
+ align:start position:0%
+audience. In order to do that, I'll
+ 
+
+ align:start position:0%
+audience. In order to do that, I'll
+compromise the character's basic nature
+
+ align:start position:0%
+compromise the character's basic nature
+ 
+
+ align:start position:0%
+compromise the character's basic nature
+because no brother, no sister talking to
+
+ align:start position:0%
+because no brother, no sister talking to
+ 
+
+ align:start position:0%
+because no brother, no sister talking to
+a brother would recount the brother's
+
+ align:start position:0%
+a brother would recount the brother's
+ 
+
+ align:start position:0%
+a brother would recount the brother's
+history to the brother, right? That just
+
+ align:start position:0%
+history to the brother, right? That just
+ 
+
+ align:start position:0%
+history to the brother, right? That just
+wouldn't happen. Right? So, in order to
+
+ align:start position:0%
+wouldn't happen. Right? So, in order to
+ 
+
+ align:start position:0%
+wouldn't happen. Right? So, in order to
+accomplish one task, the text has
+
+ align:start position:0%
+accomplish one task, the text has
+ 
+
+ align:start position:0%
+accomplish one task, the text has
+compromised itself on another task. But
+
+ align:start position:0%
+compromised itself on another task. But
+ 
+
+ align:start position:0%
+compromised itself on another task. But
+imagine a story in which this
+
+ align:start position:0%
+imagine a story in which this
+ 
+
+ align:start position:0%
+imagine a story in which this
+information emerges in in dramatic ways.
+
+ align:start position:0%
+information emerges in in dramatic ways.
+ 
+
+ align:start position:0%
+information emerges in in dramatic ways.
+two characters are talking and Mary says
+
+ align:start position:0%
+two characters are talking and Mary says
+ 
+
+ align:start position:0%
+two characters are talking and Mary says
+to Joan, "Oh, Joan, my brother's coming
+
+ align:start position:0%
+to Joan, "Oh, Joan, my brother's coming
+ 
+
+ align:start position:0%
+to Joan, "Oh, Joan, my brother's coming
+back from the asylum." And she says,
+
+ align:start position:0%
+back from the asylum." And she says,
+ 
+
+ align:start position:0%
+back from the asylum." And she says,
+"Really? I didn't even know he was in
+
+ align:start position:0%
+"Really? I didn't even know he was in
+ 
+
+ align:start position:0%
+"Really? I didn't even know he was in
+the asylum." And Mary pulls back and
+
+ align:start position:0%
+the asylum." And Mary pulls back and
+ 
+
+ align:start position:0%
+the asylum." And Mary pulls back and
+says, "I don't know if I should tell
+
+ align:start position:0%
+says, "I don't know if I should tell
+ 
+
+ align:start position:0%
+says, "I don't know if I should tell
+you." Right. Okay. So, we have a we have
+
+ align:start position:0%
+you." Right. Okay. So, we have a we have
+ 
+
+ align:start position:0%
+you." Right. Okay. So, we have a we have
+a dramatic scene in which what in which
+
+ align:start position:0%
+a dramatic scene in which what in which
+ 
+
+ align:start position:0%
+a dramatic scene in which what in which
+the information that the audience is
+
+ align:start position:0%
+the information that the audience is
+ 
+
+ align:start position:0%
+the information that the audience is
+supposed to have is presented in a way
+
+ align:start position:0%
+supposed to have is presented in a way
+ 
+
+ align:start position:0%
+supposed to have is presented in a way
+that maybe tells us something about
+
+ align:start position:0%
+that maybe tells us something about
+ 
+
+ align:start position:0%
+that maybe tells us something about
+Mary's nature and maybe tells us
+
+ align:start position:0%
+Mary's nature and maybe tells us
+ 
+
+ align:start position:0%
+Mary's nature and maybe tells us
+something about Joan's nature. That is
+
+ align:start position:0%
+something about Joan's nature. That is
+ 
+
+ align:start position:0%
+something about Joan's nature. That is
+multiplicity, right? More that's what I
+
+ align:start position:0%
+multiplicity, right? More that's what I
+ 
+
+ align:start position:0%
+multiplicity, right? More that's what I
+mean by the multiplicity principle. You
+
+ align:start position:0%
+mean by the multiplicity principle. You
+ 
+
+ align:start position:0%
+mean by the multiplicity principle. You
+will see many many instances of what of
+
+ align:start position:0%
+will see many many instances of what of
+ 
+
+ align:start position:0%
+will see many many instances of what of
+what I'm calling the multiplicity
+
+ align:start position:0%
+what I'm calling the multiplicity
+ 
+
+ align:start position:0%
+what I'm calling the multiplicity
+principle in Katon's work and you will
+
+ align:start position:0%
+principle in Katon's work and you will
+ 
+
+ align:start position:0%
+principle in Katon's work and you will
+especially see it in these astonishing
+
+ align:start position:0%
+especially see it in these astonishing
+ 
+
+ align:start position:0%
+especially see it in these astonishing
+repeated
+
+ align:start position:0%
+repeated
+ 
+
+ align:start position:0%
+repeated
+um uh uh sequences in which we see in
+
+ align:start position:0%
+um uh uh sequences in which we see in
+ 
+
+ align:start position:0%
+um uh uh sequences in which we see in
+which we see the and I'm talking now in
+
+ align:start position:0%
+which we see the and I'm talking now in
+ 
+
+ align:start position:0%
+which we see the and I'm talking now in
+a way about the general in which we see
+
+ align:start position:0%
+a way about the general in which we see
+ 
+
+ align:start position:0%
+a way about the general in which we see
+the Katon hero who sort of uh is
+
+ align:start position:0%
+the Katon hero who sort of uh is
+ 
+
+ align:start position:0%
+the Katon hero who sort of uh is
+steadfast but also a muddler. He keeps
+
+ align:start position:0%
+steadfast but also a muddler. He keeps
+ 
+
+ align:start position:0%
+steadfast but also a muddler. He keeps
+he keeps doing the same things. they're
+
+ align:start position:0%
+he keeps doing the same things. they're
+ 
+
+ align:start position:0%
+he keeps doing the same things. they're
+not really likely to help him and then
+
+ align:start position:0%
+not really likely to help him and then
+ 
+
+ align:start position:0%
+not really likely to help him and then
+he gets help from the outside and was
+
+ align:start position:0%
+he gets help from the outside and was
+ 
+
+ align:start position:0%
+he gets help from the outside and was
+what what Keaton's jokes repeatedly
+
+ align:start position:0%
+what what Keaton's jokes repeatedly
+ 
+
+ align:start position:0%
+what what Keaton's jokes repeatedly
+depend upon the idea of of uh accident
+
+ align:start position:0%
+depend upon the idea of of uh accident
+ 
+
+ align:start position:0%
+depend upon the idea of of uh accident
+in a certain way and I I'll come back to
+
+ align:start position:0%
+in a certain way and I I'll come back to
+ 
+
+ align:start position:0%
+in a certain way and I I'll come back to
+that in finally in a second. So so think
+
+ align:start position:0%
+that in finally in a second. So so think
+ 
+
+ align:start position:0%
+that in finally in a second. So so think
+about the multiplicity principle the
+
+ align:start position:0%
+about the multiplicity principle the
+ 
+
+ align:start position:0%
+about the multiplicity principle the
+difference between entertainment and art
+
+ align:start position:0%
+difference between entertainment and art
+ 
+
+ align:start position:0%
+difference between entertainment and art
+again this is a principle I'll come back
+
+ align:start position:0%
+again this is a principle I'll come back
+ 
+
+ align:start position:0%
+again this is a principle I'll come back
+to and try to illustrate with greater uh
+
+ align:start position:0%
+to and try to illustrate with greater uh
+ 
+
+ align:start position:0%
+to and try to illustrate with greater uh
+uh concreteness and greater leisure in
+
+ align:start position:0%
+uh concreteness and greater leisure in
+ 
+
+ align:start position:0%
+uh concreteness and greater leisure in
+later lectures but I want you to be
+
+ align:start position:0%
+later lectures but I want you to be
+ 
+
+ align:start position:0%
+later lectures but I want you to be
+aware of these of these issues. So the
+
+ align:start position:0%
+aware of these of these issues. So the
+ 
+
+ align:start position:0%
+aware of these of these issues. So the
+general can be understood as a kind of
+
+ align:start position:0%
+general can be understood as a kind of
+ 
+
+ align:start position:0%
+general can be understood as a kind of
+culminating text in at least two ways.
+
+ align:start position:0%
+culminating text in at least two ways.
+ 
+
+ align:start position:0%
+culminating text in at least two ways.
+It's a culmination of Katon's career.
+
+ align:start position:0%
+It's a culmination of Katon's career.
+ 
+
+ align:start position:0%
+It's a culmination of Katon's career.
+That is to say, the jokes and gags that
+
+ align:start position:0%
+That is to say, the jokes and gags that
+ 
+
+ align:start position:0%
+That is to say, the jokes and gags that
+are enacted in in uh in the film recall
+
+ align:start position:0%
+are enacted in in uh in the film recall
+ 
+
+ align:start position:0%
+are enacted in in uh in the film recall
+many earlier Katon films. And the basic
+
+ align:start position:0%
+many earlier Katon films. And the basic
+ 
+
+ align:start position:0%
+many earlier Katon films. And the basic
+character of the general is the basic
+
+ align:start position:0%
+character of the general is the basic
+ 
+
+ align:start position:0%
+character of the general is the basic
+character of the Katon hero. a
+
+ align:start position:0%
+character of the Katon hero. a
+ 
+
+ align:start position:0%
+character of the Katon hero. a
+steadfast, unremarkable young man who
+
+ align:start position:0%
+steadfast, unremarkable young man who
+ 
+
+ align:start position:0%
+steadfast, unremarkable young man who
+perseveres in the face of catastrophic
+
+ align:start position:0%
+perseveres in the face of catastrophic
+ 
+
+ align:start position:0%
+perseveres in the face of catastrophic
+difficulties with mostly comic
+
+ align:start position:0%
+difficulties with mostly comic
+ 
+
+ align:start position:0%
+difficulties with mostly comic
+expectations, very small expectations of
+
+ align:start position:0%
+expectations, very small expectations of
+ 
+
+ align:start position:0%
+expectations, very small expectations of
+success, who often muddles through
+
+ align:start position:0%
+success, who often muddles through
+ 
+
+ align:start position:0%
+success, who often muddles through
+almost despite himself right now. But it
+
+ align:start position:0%
+almost despite himself right now. But it
+ 
+
+ align:start position:0%
+almost despite himself right now. But it
+isn't merely, but I say almost despite
+
+ align:start position:0%
+isn't merely, but I say almost despite
+ 
+
+ align:start position:0%
+isn't merely, but I say almost despite
+himself and this is where the complexity
+
+ align:start position:0%
+himself and this is where the complexity
+ 
+
+ align:start position:0%
+himself and this is where the complexity
+of Katon's vision of life comes in. Why
+
+ align:start position:0%
+of Katon's vision of life comes in. Why
+ 
+
+ align:start position:0%
+of Katon's vision of life comes in. Why
+I'm saying that Katon moves from being
+
+ align:start position:0%
+I'm saying that Katon moves from being
+ 
+
+ align:start position:0%
+I'm saying that Katon moves from being
+merely a jokester or being merely a
+
+ align:start position:0%
+merely a jokester or being merely a
+ 
+
+ align:start position:0%
+merely a jokester or being merely a
+great entertainer to being an artist.
+
+ align:start position:0%
+great entertainer to being an artist.
+ 
+
+ align:start position:0%
+great entertainer to being an artist.
+His jokes embody an idea of what
+
+ align:start position:0%
+His jokes embody an idea of what
+ 
+
+ align:start position:0%
+His jokes embody an idea of what
+experience is like and it's a very
+
+ align:start position:0%
+experience is like and it's a very
+ 
+
+ align:start position:0%
+experience is like and it's a very
+powerful mortant mature idea of
+
+ align:start position:0%
+powerful mortant mature idea of
+ 
+
+ align:start position:0%
+powerful mortant mature idea of
+experience because what happens again
+
+ align:start position:0%
+experience because what happens again
+ 
+
+ align:start position:0%
+experience because what happens again
+and again in the small jokes the
+
+ align:start position:0%
+and again in the small jokes the
+ 
+
+ align:start position:0%
+and again in the small jokes the
+sequence jokes in Katon's work
+
+ align:start position:0%
+sequence jokes in Katon's work
+ 
+
+ align:start position:0%
+sequence jokes in Katon's work
+especially in the general and in the
+
+ align:start position:0%
+especially in the general and in the
+ 
+
+ align:start position:0%
+especially in the general and in the
+larger film what happens again and again
+
+ align:start position:0%
+larger film what happens again and again
+ 
+
+ align:start position:0%
+larger film what happens again and again
+is a is a an adventure in which a
+
+ align:start position:0%
+is a is a an adventure in which a
+ 
+
+ align:start position:0%
+is a is a an adventure in which a
+steadfast relentless young hero does
+
+ align:start position:0%
+steadfast relentless young hero does
+ 
+
+ align:start position:0%
+steadfast relentless young hero does
+everything he can to to uh accomplish
+
+ align:start position:0%
+everything he can to to uh accomplish
+ 
+
+ align:start position:0%
+everything he can to to uh accomplish
+his goal and it's obvious that he's up
+
+ align:start position:0%
+his goal and it's obvious that he's up
+ 
+
+ align:start position:0%
+his goal and it's obvious that he's up
+against forces far beyond himself that
+
+ align:start position:0%
+against forces far beyond himself that
+ 
+
+ align:start position:0%
+against forces far beyond himself that
+he could never that there's a
+
+ align:start position:0%
+he could never that there's a
+ 
+
+ align:start position:0%
+he could never that there's a
+unbelievable mis mismatch between this
+
+ align:start position:0%
+unbelievable mis mismatch between this
+ 
+
+ align:start position:0%
+unbelievable mis mismatch between this
+minuscule tiny figure and the and his
+
+ align:start position:0%
+minuscule tiny figure and the and his
+ 
+
+ align:start position:0%
+minuscule tiny figure and the and his
+powers and the forces he's he's fighting
+
+ align:start position:0%
+powers and the forces he's he's fighting
+ 
+
+ align:start position:0%
+powers and the forces he's he's fighting
+against. There's one Katon film called
+
+ align:start position:0%
+against. There's one Katon film called
+ 
+
+ align:start position:0%
+against. There's one Katon film called
+the navigator in which the Keaton
+
+ align:start position:0%
+the navigator in which the Keaton
+ 
+
+ align:start position:0%
+the navigator in which the Keaton
+character even more than with the
+
+ align:start position:0%
+character even more than with the
+ 
+
+ align:start position:0%
+character even more than with the
+locomotive in the general has to
+
+ align:start position:0%
+locomotive in the general has to
+ 
+
+ align:start position:0%
+locomotive in the general has to
+navigate an ocean liner and he's alone
+
+ align:start position:0%
+navigate an ocean liner and he's alone
+ 
+
+ align:start position:0%
+navigate an ocean liner and he's alone
+on the ocean liner and you see him
+
+ align:start position:0%
+on the ocean liner and you see him
+ 
+
+ align:start position:0%
+on the ocean liner and you see him
+running up and down into the engine room
+
+ align:start position:0%
+running up and down into the engine room
+ 
+
+ align:start position:0%
+running up and down into the engine room
+back up to this up to the bridge not
+
+ align:start position:0%
+back up to this up to the bridge not
+ 
+
+ align:start position:0%
+back up to this up to the bridge not
+running all over the ocean liner in a in
+
+ align:start position:0%
+running all over the ocean liner in a in
+ 
+
+ align:start position:0%
+running all over the ocean liner in a in
+a in in great difficulties. There's a
+
+ align:start position:0%
+a in in great difficulties. There's a
+ 
+
+ align:start position:0%
+a in in great difficulties. There's a
+wonderful film, late film made in 1928,
+
+ align:start position:0%
+wonderful film, late film made in 1928,
+ 
+
+ align:start position:0%
+wonderful film, late film made in 1928,
+just the his last silent film called
+
+ align:start position:0%
+just the his last silent film called
+ 
+
+ align:start position:0%
+just the his last silent film called
+Steamboat Bill Jr. in which he
+
+ align:start position:0%
+Steamboat Bill Jr. in which he
+ 
+
+ align:start position:0%
+Steamboat Bill Jr. in which he
+dramatizes an astonishing song, an
+
+ align:start position:0%
+dramatizes an astonishing song, an
+ 
+
+ align:start position:0%
+dramatizes an astonishing song, an
+astonishing an astonishing um uh
+
+ align:start position:0%
+astonishing an astonishing um uh
+ 
+
+ align:start position:0%
+astonishing an astonishing um uh
+hurricane uh and a long extended
+
+ align:start position:0%
+hurricane uh and a long extended
+ 
+
+ align:start position:0%
+hurricane uh and a long extended
+sequence in which we see him trying to
+
+ align:start position:0%
+sequence in which we see him trying to
+ 
+
+ align:start position:0%
+sequence in which we see him trying to
+escape the hurricane uh trying to
+
+ align:start position:0%
+escape the hurricane uh trying to
+ 
+
+ align:start position:0%
+escape the hurricane uh trying to
+contend against this natural force
+
+ align:start position:0%
+contend against this natural force
+ 
+
+ align:start position:0%
+contend against this natural force
+that's so gigantic. So the the so so the
+
+ align:start position:0%
+that's so gigantic. So the the so so the
+ 
+
+ align:start position:0%
+that's so gigantic. So the the so so the
+the general is a culmination in the
+
+ align:start position:0%
+the general is a culmination in the
+ 
+
+ align:start position:0%
+the general is a culmination in the
+sense that it gives us another version
+
+ align:start position:0%
+sense that it gives us another version
+ 
+
+ align:start position:0%
+sense that it gives us another version
+and the the richest the richest version
+
+ align:start position:0%
+and the the richest the richest version
+ 
+
+ align:start position:0%
+and the the richest the richest version
+so far of the of the adventures of this
+
+ align:start position:0%
+so far of the of the adventures of this
+ 
+
+ align:start position:0%
+so far of the of the adventures of this
+kind of Katon hero. But what makes it a
+
+ align:start position:0%
+kind of Katon hero. But what makes it a
+ 
+
+ align:start position:0%
+kind of Katon hero. But what makes it a
+what what makes it sort of metaphysical
+
+ align:start position:0%
+what what makes it sort of metaphysical
+ 
+
+ align:start position:0%
+what what makes it sort of metaphysical
+or philosophically interesting is that
+
+ align:start position:0%
+or philosophically interesting is that
+ 
+
+ align:start position:0%
+or philosophically interesting is that
+what what this joke repeatedly does and
+
+ align:start position:0%
+what what this joke repeatedly does and
+ 
+
+ align:start position:0%
+what what this joke repeatedly does and
+what the structure of the whole film
+
+ align:start position:0%
+what the structure of the whole film
+ 
+
+ align:start position:0%
+what the structure of the whole film
+repeatedly says is something like this.
+
+ align:start position:0%
+repeatedly says is something like this.
+ 
+
+ align:start position:0%
+repeatedly says is something like this.
+We get through we make it through life
+
+ align:start position:0%
+We get through we make it through life
+ 
+
+ align:start position:0%
+We get through we make it through life
+not mo mostly it's a it's a great comic
+
+ align:start position:0%
+not mo mostly it's a it's a great comic
+ 
+
+ align:start position:0%
+not mo mostly it's a it's a great comic
+Morton comic. We get through life mostly
+
+ align:start position:0%
+Morton comic. We get through life mostly
+ 
+
+ align:start position:0%
+Morton comic. We get through life mostly
+not because of anything we've done but
+
+ align:start position:0%
+not because of anything we've done but
+ 
+
+ align:start position:0%
+not because of anything we've done but
+because of accident. We live in a
+
+ align:start position:0%
+because of accident. We live in a
+ 
+
+ align:start position:0%
+because of accident. We live in a
+contingent universe. Right? The idea of
+
+ align:start position:0%
+contingent universe. Right? The idea of
+ 
+
+ align:start position:0%
+contingent universe. Right? The idea of
+contingency is at the heart of what of
+
+ align:start position:0%
+contingency is at the heart of what of
+ 
+
+ align:start position:0%
+contingency is at the heart of what of
+of of Katon's jokes. We could we could
+
+ align:start position:0%
+of of Katon's jokes. We could we could
+ 
+
+ align:start position:0%
+of of Katon's jokes. We could we could
+call them jokes about contingency. The
+
+ align:start position:0%
+call them jokes about contingency. The
+ 
+
+ align:start position:0%
+call them jokes about contingency. The
+word contingent is interesting. Remember
+
+ align:start position:0%
+word contingent is interesting. Remember
+ 
+
+ align:start position:0%
+word contingent is interesting. Remember
+it means both li it means liable but not
+
+ align:start position:0%
+it means both li it means liable but not
+ 
+
+ align:start position:0%
+it means both li it means liable but not
+certain but not certain to occur. It
+
+ align:start position:0%
+certain but not certain to occur. It
+ 
+
+ align:start position:0%
+certain but not certain to occur. It
+means possible. Right? So, so uh for
+
+ align:start position:0%
+means possible. Right? So, so uh for
+ 
+
+ align:start position:0%
+means possible. Right? So, so uh for
+it's it means dependent upon subject to
+
+ align:start position:0%
+it's it means dependent upon subject to
+ 
+
+ align:start position:0%
+it's it means dependent upon subject to
+conditioned by right in law you could
+
+ align:start position:0%
+conditioned by right in law you could
+ 
+
+ align:start position:0%
+conditioned by right in law you could
+say something uh you can say that
+
+ align:start position:0%
+say something uh you can say that
+ 
+
+ align:start position:0%
+say something uh you can say that
+something that is contingent is
+
+ align:start position:0%
+something that is contingent is
+ 
+
+ align:start position:0%
+something that is contingent is
+dependent for its effect on something
+
+ align:start position:0%
+dependent for its effect on something
+ 
+
+ align:start position:0%
+dependent for its effect on something
+that may or may not occur as in a
+
+ align:start position:0%
+that may or may not occur as in a
+ 
+
+ align:start position:0%
+that may or may not occur as in a
+contingent estate or legacy right in
+
+ align:start position:0%
+contingent estate or legacy right in
+ 
+
+ align:start position:0%
+contingent estate or legacy right in
+logic the same thing dependent upon some
+
+ align:start position:0%
+logic the same thing dependent upon some
+ 
+
+ align:start position:0%
+logic the same thing dependent upon some
+condition or upon the truth of something
+
+ align:start position:0%
+condition or upon the truth of something
+ 
+
+ align:start position:0%
+condition or upon the truth of something
+else not true a priori not necessary so
+
+ align:start position:0%
+else not true a priori not necessary so
+ 
+
+ align:start position:0%
+else not true a priori not necessary so
+what keaton's jokes constantly do is
+
+ align:start position:0%
+what keaton's jokes constantly do is
+ 
+
+ align:start position:0%
+what keaton's jokes constantly do is
+they show us two things. They show us a
+
+ align:start position:0%
+they show us two things. They show us a
+ 
+
+ align:start position:0%
+they show us two things. They show us a
+world in which human agency matters.
+
+ align:start position:0%
+world in which human agency matters.
+ 
+
+ align:start position:0%
+world in which human agency matters.
+Because if this schmenrich didn't keep,
+
+ align:start position:0%
+Because if this schmenrich didn't keep,
+ 
+
+ align:start position:0%
+Because if this schmenrich didn't keep,
+that's a Jewish word for schlamazle.
+
+ align:start position:0%
+that's a Jewish word for schlamazle.
+ 
+
+ align:start position:0%
+that's a Jewish word for schlamazle.
+It's a clown. If this schmenrich did not
+
+ align:start position:0%
+It's a clown. If this schmenrich did not
+ 
+
+ align:start position:0%
+It's a clown. If this schmenrich did not
+if this schmenrich did not um keep on so
+
+ align:start position:0%
+if this schmenrich did not um keep on so
+ 
+
+ align:start position:0%
+if this schmenrich did not um keep on so
+steadfastly, he wouldn't survive. But
+
+ align:start position:0%
+steadfastly, he wouldn't survive. But
+ 
+
+ align:start position:0%
+steadfastly, he wouldn't survive. But
+his keeping on so steadfastly still
+
+ align:start position:0%
+his keeping on so steadfastly still
+ 
+
+ align:start position:0%
+his keeping on so steadfastly still
+wouldn't make him survive if there
+
+ align:start position:0%
+wouldn't make him survive if there
+ 
+
+ align:start position:0%
+wouldn't make him survive if there
+weren't the intervention of mere
+
+ align:start position:0%
+weren't the intervention of mere
+ 
+
+ align:start position:0%
+weren't the intervention of mere
+accidents, stuff he has no control over.
+
+ align:start position:0%
+accidents, stuff he has no control over.
+ 
+
+ align:start position:0%
+accidents, stuff he has no control over.
+There's one magnificent moment in the in
+
+ align:start position:0%
+There's one magnificent moment in the in
+ 
+
+ align:start position:0%
+There's one magnificent moment in the in
+in one week for example where he's
+
+ align:start position:0%
+in one week for example where he's
+ 
+
+ align:start position:0%
+in one week for example where he's
+standing in a certain place and the
+
+ align:start position:0%
+standing in a certain place and the
+ 
+
+ align:start position:0%
+standing in a certain place and the
+house and the house behind him falls
+
+ align:start position:0%
+house and the house behind him falls
+ 
+
+ align:start position:0%
+house and the house behind him falls
+down and he happens just by accident to
+
+ align:start position:0%
+down and he happens just by accident to
+ 
+
+ align:start position:0%
+down and he happens just by accident to
+be standing so that by the open window
+
+ align:start position:0%
+be standing so that by the open window
+ 
+
+ align:start position:0%
+be standing so that by the open window
+the house falls so he doesn't get hurt.
+
+ align:start position:0%
+the house falls so he doesn't get hurt.
+ 
+
+ align:start position:0%
+the house falls so he doesn't get hurt.
+He used this joke more than once in
+
+ align:start position:0%
+He used this joke more than once in
+ 
+
+ align:start position:0%
+He used this joke more than once in
+other films because such a great one.
+
+ align:start position:0%
+other films because such a great one.
+ 
+
+ align:start position:0%
+other films because such a great one.
+But it's a perfect example of what I
+
+ align:start position:0%
+But it's a perfect example of what I
+ 
+
+ align:start position:0%
+But it's a perfect example of what I
+mean. A partial example of what I mean
+
+ align:start position:0%
+mean. A partial example of what I mean
+ 
+
+ align:start position:0%
+mean. A partial example of what I mean
+because he's not responsible for the
+
+ align:start position:0%
+because he's not responsible for the
+ 
+
+ align:start position:0%
+because he's not responsible for the
+fact that he escaped. On the other hand,
+
+ align:start position:0%
+fact that he escaped. On the other hand,
+ 
+
+ align:start position:0%
+fact that he escaped. On the other hand,
+because he was trying to get away from
+
+ align:start position:0%
+because he was trying to get away from
+ 
+
+ align:start position:0%
+because he was trying to get away from
+difficulties, maybe he was in that
+
+ align:start position:0%
+difficulties, maybe he was in that
+ 
+
+ align:start position:0%
+difficulties, maybe he was in that
+particular position because of acts of
+
+ align:start position:0%
+particular position because of acts of
+ 
+
+ align:start position:0%
+particular position because of acts of
+his own. So, so what it says what what
+
+ align:start position:0%
+his own. So, so what it says what what
+ 
+
+ align:start position:0%
+his own. So, so what it says what what
+so what this joking vision says about
+
+ align:start position:0%
+so what this joking vision says about
+ 
+
+ align:start position:0%
+so what this joking vision says about
+the world is something that's true. We
+
+ align:start position:0%
+the world is something that's true. We
+ 
+
+ align:start position:0%
+the world is something that's true. We
+all love the idea that we've gotten to
+
+ align:start position:0%
+all love the idea that we've gotten to
+ 
+
+ align:start position:0%
+all love the idea that we've gotten to
+where we are by our own acts, by our own
+
+ align:start position:0%
+where we are by our own acts, by our own
+ 
+
+ align:start position:0%
+where we are by our own acts, by our own
+conscious control. The truth of the
+
+ align:start position:0%
+conscious control. The truth of the
+ 
+
+ align:start position:0%
+conscious control. The truth of the
+matter is that life that life is much
+
+ align:start position:0%
+matter is that life that life is much
+ 
+
+ align:start position:0%
+matter is that life that life is much
+more contingent than that. It's partly
+
+ align:start position:0%
+more contingent than that. It's partly
+ 
+
+ align:start position:0%
+more contingent than that. It's partly
+accident. It's partly luck. And
+
+ align:start position:0%
+accident. It's partly luck. And
+ 
+
+ align:start position:0%
+accident. It's partly luck. And
+something deeper than that. Keaton's
+
+ align:start position:0%
+something deeper than that. Keaton's
+ 
+
+ align:start position:0%
+something deeper than that. Keaton's
+vision of the universe is one which
+
+ align:start position:0%
+vision of the universe is one which
+ 
+
+ align:start position:0%
+vision of the universe is one which
+suggests that while the universe may
+
+ align:start position:0%
+suggests that while the universe may
+ 
+
+ align:start position:0%
+suggests that while the universe may
+screw you up sometimes, it won't always
+
+ align:start position:0%
+screw you up sometimes, it won't always
+ 
+
+ align:start position:0%
+screw you up sometimes, it won't always
+do that. That is to say, it's not the
+
+ align:start position:0%
+do that. That is to say, it's not the
+ 
+
+ align:start position:0%
+do that. That is to say, it's not the
+universe in Katon's world is not angry
+
+ align:start position:0%
+universe in Katon's world is not angry
+ 
+
+ align:start position:0%
+universe in Katon's world is not angry
+at us. It's indifferent to us. It
+
+ align:start position:0%
+at us. It's indifferent to us. It
+ 
+
+ align:start position:0%
+at us. It's indifferent to us. It
+doesn't give a damn about us. It's not
+
+ align:start position:0%
+doesn't give a damn about us. It's not
+ 
+
+ align:start position:0%
+doesn't give a damn about us. It's not
+aware of us. It's too big for us. Right?
+
+ align:start position:0%
+aware of us. It's too big for us. Right?
+ 
+
+ align:start position:0%
+aware of us. It's too big for us. Right?
+You can't come away from Katon's films
+
+ align:start position:0%
+You can't come away from Katon's films
+ 
+
+ align:start position:0%
+You can't come away from Katon's films
+without a simultaneous sense of the
+
+ align:start position:0%
+without a simultaneous sense of the
+ 
+
+ align:start position:0%
+without a simultaneous sense of the
+importance of human action of human
+
+ align:start position:0%
+importance of human action of human
+ 
+
+ align:start position:0%
+importance of human action of human
+agency but also of the inadequacy of
+
+ align:start position:0%
+agency but also of the inadequacy of
+ 
+
+ align:start position:0%
+agency but also of the inadequacy of
+human agency of how contingent every
+
+ align:start position:0%
+human agency of how contingent every
+ 
+
+ align:start position:0%
+human agency of how contingent every
+experience every adventure every
+
+ align:start position:0%
+experience every adventure every
+ 
+
+ align:start position:0%
+experience every adventure every
+personality is and that and that meaning
+
+ align:start position:0%
+personality is and that and that meaning
+ 
+
+ align:start position:0%
+personality is and that and that meaning
+that idea of the world is a profound one
+
+ align:start position:0%
+that idea of the world is a profound one
+ 
+
+ align:start position:0%
+that idea of the world is a profound one
+I think it tells so that so that even
+
+ align:start position:0%
+I think it tells so that so that even
+ 
+
+ align:start position:0%
+I think it tells so that so that even
+though Keaton is telling a joke embedded
+
+ align:start position:0%
+though Keaton is telling a joke embedded
+ 
+
+ align:start position:0%
+though Keaton is telling a joke embedded
+in the joke is a kind of interpretation
+
+ align:start position:0%
+in the joke is a kind of interpretation
+ 
+
+ align:start position:0%
+in the joke is a kind of interpretation
+of life and embedded in the film is a
+
+ align:start position:0%
+of life and embedded in the film is a
+ 
+
+ align:start position:0%
+of life and embedded in the film is a
+kind interpretation of life. Uh when
+
+ align:start position:0%
+kind interpretation of life. Uh when
+ 
+
+ align:start position:0%
+kind interpretation of life. Uh when
+you're looking at the general, I think
+
+ align:start position:0%
+you're looking at the general, I think
+ 
+
+ align:start position:0%
+you're looking at the general, I think
+you will see multiple examples of this
+
+ align:start position:0%
+you will see multiple examples of this
+ 
+
+ align:start position:0%
+you will see multiple examples of this
+kind of thing. Let me say one last
+
+ align:start position:0%
+kind of thing. Let me say one last
+ 
+
+ align:start position:0%
+kind of thing. Let me say one last
+thing. I haven't mentioned anything
+
+ align:start position:0%
+thing. I haven't mentioned anything
+ 
+
+ align:start position:0%
+thing. I haven't mentioned anything
+about the structure of the film. I'm a
+
+ align:start position:0%
+about the structure of the film. I'm a
+ 
+
+ align:start position:0%
+about the structure of the film. I'm a
+little out of order there. Watch how the
+
+ align:start position:0%
+little out of order there. Watch how the
+ 
+
+ align:start position:0%
+little out of order there. Watch how the
+film is structured. It it's a ve it's a
+
+ align:start position:0%
+film is structured. It it's a ve it's a
+ 
+
+ align:start position:0%
+film is structured. It it's a ve it's a
+much more complex variation on what I
+
+ align:start position:0%
+much more complex variation on what I
+ 
+
+ align:start position:0%
+much more complex variation on what I
+said about Lonale Operator. The film
+
+ align:start position:0%
+said about Lonale Operator. The film
+ 
+
+ align:start position:0%
+said about Lonale Operator. The film
+begins with him going up the track and
+
+ align:start position:0%
+begins with him going up the track and
+ 
+
+ align:start position:0%
+begins with him going up the track and
+then the second half of the film has him
+
+ align:start position:0%
+then the second half of the film has him
+ 
+
+ align:start position:0%
+then the second half of the film has him
+going back down the track. You may not
+
+ align:start position:0%
+going back down the track. You may not
+ 
+
+ align:start position:0%
+going back down the track. You may not
+be aware of it, but actually the film in
+
+ align:start position:0%
+be aware of it, but actually the film in
+ 
+
+ align:start position:0%
+be aware of it, but actually the film in
+a certain sense has its tail in its
+
+ align:start position:0%
+a certain sense has its tail in its
+ 
+
+ align:start position:0%
+a certain sense has its tail in its
+mouth. When it goes up the track, he has
+
+ align:start position:0%
+mouth. When it goes up the track, he has
+ 
+
+ align:start position:0%
+mouth. When it goes up the track, he has
+a series of adventures. When he comes
+
+ align:start position:0%
+a series of adventures. When he comes
+ 
+
+ align:start position:0%
+a series of adventures. When he comes
+back down, he has a series of adventures
+
+ align:start position:0%
+back down, he has a series of adventures
+ 
+
+ align:start position:0%
+back down, he has a series of adventures
+that in a certain sense replicate what's
+
+ align:start position:0%
+that in a certain sense replicate what's
+ 
+
+ align:start position:0%
+that in a certain sense replicate what's
+happened before. The film mirrors itself
+
+ align:start position:0%
+happened before. The film mirrors itself
+ 
+
+ align:start position:0%
+happened before. The film mirrors itself
+in a way repeats itself. Watch. It's an
+
+ align:start position:0%
+in a way repeats itself. Watch. It's an
+ 
+
+ align:start position:0%
+in a way repeats itself. Watch. It's an
+incredibly elegant structure. It's
+
+ align:start position:0%
+incredibly elegant structure. It's
+ 
+
+ align:start position:0%
+incredibly elegant structure. It's
+incred and and the elegance of the
+
+ align:start position:0%
+incred and and the elegance of the
+ 
+
+ align:start position:0%
+incred and and the elegance of the
+structure reminds us also uh of the in
+
+ align:start position:0%
+structure reminds us also uh of the in
+ 
+
+ align:start position:0%
+structure reminds us also uh of the in
+its own way also reminds us of this
+
+ align:start position:0%
+its own way also reminds us of this
+ 
+
+ align:start position:0%
+its own way also reminds us of this
+principle of contingency that's at the
+
+ align:start position:0%
+principle of contingency that's at the
+ 
+
+ align:start position:0%
+principle of contingency that's at the
+heart of Keaton's vision of the world.
+
+ align:start position:0%
+heart of Keaton's vision of the world.
+ 
+
+ align:start position:0%
+heart of Keaton's vision of the world.
+Let me conclude by reminding you again
+
+ align:start position:0%
+Let me conclude by reminding you again
+ 
+
+ align:start position:0%
+Let me conclude by reminding you again
+of what I said earlier. When I call
+
+ align:start position:0%
+of what I said earlier. When I call
+ 
+
+ align:start position:0%
+of what I said earlier. When I call
+Katon a philosopher and a metaphysician
+
+ align:start position:0%
+Katon a philosopher and a metaphysician
+ 
+
+ align:start position:0%
+Katon a philosopher and a metaphysician
+and a wise person about the world, I do
+
+ align:start position:0%
+and a wise person about the world, I do
+ 
+
+ align:start position:0%
+and a wise person about the world, I do
+not at all mean to suggest that if you
+
+ align:start position:0%
+not at all mean to suggest that if you
+ 
+
+ align:start position:0%
+not at all mean to suggest that if you
+ask Keaton to explain how he thought
+
+ align:start position:0%
+ask Keaton to explain how he thought
+ 
+
+ align:start position:0%
+ask Keaton to explain how he thought
+about the world, he could do this.
+
+ align:start position:0%
+about the world, he could do this.
+ 
+
+ align:start position:0%
+about the world, he could do this.
+That's that's the job of professors and
+
+ align:start position:0%
+That's that's the job of professors and
+ 
+
+ align:start position:0%
+That's that's the job of professors and
+literary and film critics. Right? What
+
+ align:start position:0%
+literary and film critics. Right? What
+ 
+
+ align:start position:0%
+literary and film critics. Right? What
+I'm saying to you is that Keaton like
+
+ align:start position:0%
+I'm saying to you is that Keaton like
+ 
+
+ align:start position:0%
+I'm saying to you is that Keaton like
+many great artists had an intuitive
+
+ align:start position:0%
+many great artists had an intuitive
+ 
+
+ align:start position:0%
+many great artists had an intuitive
+understanding of the world which he
+
+ align:start position:0%
+understanding of the world which he
+ 
+
+ align:start position:0%
+understanding of the world which he
+expressed with greater and greater
+
+ align:start position:0%
+expressed with greater and greater
+ 
+
+ align:start position:0%
+expressed with greater and greater
+complexity in the medium of the cinema.
+
+ align:start position:0%
+complexity in the medium of the cinema.
+ 
+
+ align:start position:0%
+complexity in the medium of the cinema.
+And in the general we have what is
+
+ align:start position:0%
+And in the general we have what is
+ 
+
+ align:start position:0%
+And in the general we have what is
+ultimately a culminating instance of
+
+ align:start position:0%
+ultimately a culminating instance of
+ 
+
+ align:start position:0%
+ultimately a culminating instance of
+that. One last point about the film as a
+
+ align:start position:0%
+that. One last point about the film as a
+ 
+
+ align:start position:0%
+that. One last point about the film as a
+culminating example. It's not just a
+
+ align:start position:0%
+culminating example. It's not just a
+ 
+
+ align:start position:0%
+culminating example. It's not just a
+culmination of Katon's career. It's a
+
+ align:start position:0%
+culmination of Katon's career. It's a
+ 
+
+ align:start position:0%
+culmination of Katon's career. It's a
+culmination of silent film in it in it
+
+ align:start position:0%
+culmination of silent film in it in it
+ 
+
+ align:start position:0%
+culmination of silent film in it in it
+in as a whole. Katon would have expected
+
+ align:start position:0%
+in as a whole. Katon would have expected
+ 
+
+ align:start position:0%
+in as a whole. Katon would have expected
+his audience to recognize the degree to
+
+ align:start position:0%
+his audience to recognize the degree to
+ 
+
+ align:start position:0%
+his audience to recognize the degree to
+which this film was a parody or a
+
+ align:start position:0%
+which this film was a parody or a
+ 
+
+ align:start position:0%
+which this film was a parody or a
+mockery of famous historical films made
+
+ align:start position:0%
+mockery of famous historical films made
+ 
+
+ align:start position:0%
+mockery of famous historical films made
+by DW Griffith. It puts down the
+
+ align:start position:0%
+by DW Griffith. It puts down the
+ 
+
+ align:start position:0%
+by DW Griffith. It puts down the
+pretentiousness and the Marshall valor
+
+ align:start position:0%
+pretentiousness and the Marshall valor
+ 
+
+ align:start position:0%
+pretentiousness and the Marshall valor
+that's celebrated in so many of the
+
+ align:start position:0%
+that's celebrated in so many of the
+ 
+
+ align:start position:0%
+that's celebrated in so many of the
+historical spectacles that Griffith and
+
+ align:start position:0%
+historical spectacles that Griffith and
+ 
+
+ align:start position:0%
+historical spectacles that Griffith and
+other serious directors were making at
+
+ align:start position:0%
+other serious directors were making at
+ 
+
+ align:start position:0%
+other serious directors were making at
+the time. Uh and it and it also goes
+
+ align:start position:0%
+the time. Uh and it and it also goes
+ 
+
+ align:start position:0%
+the time. Uh and it and it also goes
+back in a certain way to the very roots
+
+ align:start position:0%
+back in a certain way to the very roots
+ 
+
+ align:start position:0%
+back in a certain way to the very roots
+of film. What was the very first
+
+ align:start position:0%
+of film. What was the very first
+ 
+
+ align:start position:0%
+of film. What was the very first
+narrative film or one of the very first
+
+ align:start position:0%
+narrative film or one of the very first
+ 
+
+ align:start position:0%
+narrative film or one of the very first
+the uh also a film about a train
+
+ align:start position:0%
+the uh also a film about a train
+ 
+
+ align:start position:0%
+the uh also a film about a train
+robbery, right? Called the great train
+
+ align:start position:0%
+robbery, right? Called the great train
+ 
+
+ align:start position:0%
+robbery, right? Called the great train
+robbery. Well, this is about a train
+
+ align:start position:0%
+robbery. Well, this is about a train
+ 
+
+ align:start position:0%
+robbery. Well, this is about a train
+robbery too. And who is the central
+
+ align:start position:0%
+robbery too. And who is the central
+ 
+
+ align:start position:0%
+robbery too. And who is the central
+character in this film? Really? A train
+
+ align:start position:0%
+character in this film? Really? A train
+ 
+
+ align:start position:0%
+character in this film? Really? A train
+is the central object, the central more
+
+ align:start position:0%
+is the central object, the central more
+ 
+
+ align:start position:0%
+is the central object, the central more
+interesting in some ways than the
+
+ align:start position:0%
+interesting in some ways than the
+ 
+
+ align:start position:0%
+interesting in some ways than the
+character himself. this and there are
+
+ align:start position:0%
+character himself. this and there are
+ 
+
+ align:start position:0%
+character himself. this and there are
+many other ways in which the particular
+
+ align:start position:0%
+many other ways in which the particular
+ 
+
+ align:start position:0%
+many other ways in which the particular
+features of the general allude to and in
+
+ align:start position:0%
+features of the general allude to and in
+ 
+
+ align:start position:0%
+features of the general allude to and in
+some sense summarize the history of
+
+ align:start position:0%
+some sense summarize the history of
+ 
+
+ align:start position:0%
+some sense summarize the history of
+silent film and all of the original
+
+ align:start position:0%
+silent film and all of the original
+ 
+
+ align:start position:0%
+silent film and all of the original
+audience coming to see the general would
+
+ align:start position:0%
+audience coming to see the general would
+ 
+
+ align:start position:0%
+audience coming to see the general would
+have been of course alert to these
+
+ align:start position:0%
+have been of course alert to these
+ 
+
+ align:start position:0%
+have been of course alert to these
+connections would have been literate in
+
+ align:start position:0%
+connections would have been literate in
+ 
+
+ align:start position:0%
+connections would have been literate in
+these connections wouldn't have needed
+
+ align:start position:0%
+these connections wouldn't have needed
+ 
+
+ align:start position:0%
+these connections wouldn't have needed
+footnotes or professors to tell them
+
+ align:start position:0%
+footnotes or professors to tell them
+ 
+
+ align:start position:0%
+footnotes or professors to tell them
+about it because they would have lived
+
+ align:start position:0%
+about it because they would have lived
+ 
+
+ align:start position:0%
+about it because they would have lived
+through the history they would have
+
+ align:start position:0%
+through the history they would have
+ 
+
+ align:start position:0%
+through the history they would have
+lived through the history of the
+
+ align:start position:0%
+lived through the history of the
+ 
+
+ align:start position:0%
+lived through the history of the
+previous 20 years they would have seen
+
+ align:start position:0%
+previous 20 years they would have seen
+ 
+
+ align:start position:0%
+previous 20 years they would have seen
+other Keaton films they would have seen
+
+ align:start position:0%
+other Keaton films they would have seen
+ 
+
+ align:start position:0%
+other Keaton films they would have seen
+DW Griffith they would have the history
+
+ align:start position:0%
+DW Griffith they would have the history
+ 
+
+ align:start position:0%
+DW Griffith they would have the history
+of the of the uh medium of movies in
+
+ align:start position:0%
+of the of the uh medium of movies in
+ 
+
+ align:start position:0%
+of the of the uh medium of movies in
+their heads when they sat down to watch
+
+ align:start position:0%
+their heads when they sat down to watch
+ 
+
+ align:start position:0%
+their heads when they sat down to watch
+The General. So that's another way in
+
+ align:start position:0%
+The General. So that's another way in
+ 
+
+ align:start position:0%
+The General. So that's another way in
+which The General is a profoundly
+
+ align:start position:0%
+which The General is a profoundly
+ 
+
+ align:start position:0%
+which The General is a profoundly
+culminating text.
\ No newline at end of file
diff --git a/wCSl5eeMSDY.txt b/wCSl5eeMSDY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..86e02001432a0d6aef94110fefcb49f70c200445
--- /dev/null
+++ b/wCSl5eeMSDY.txt
@@ -0,0 +1,2232 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So last
+time you learned
+
+about the ideal solution limits
+with Henry's law and Raoult's
+
+law.
+
+And I just want to start
+with one reminder of what
+
+this is all about.
+
+So let's say that you have a
+mixture of CS2 and acetone.
+
+So this is a review of
+what you saw last time.
+
+Acetone like this, CH3, CH3.
+
+And if you take the CS2 as
+the solvent and the acetone
+
+as a solute, then when you plot
+as a function of the amount
+
+of CS2 here as a
+solvent, then you
+
+have the limit where the mole
+fraction of CS2 goes to one,
+
+meaning that CS is the solvent.
+
+You expect Raoult to work
+if it's an ideal solution.
+
+So that the vapor
+pressure of CS2
+
+is related to the mole
+fraction of CS2 times the vapor
+
+pressure of CS2 if it was pure.
+
+So you're sitting
+here somewhere.
+
+This is the vapor
+pressure of CS2 pure
+
+and CS2 goes from zero to one.
+
+And you expect Raoult to work.
+
+So let's do Raoult.
+
+Like this.
+
+So in this area, if I were
+to plot the real curve,
+
+I would expect it to start
+out just like Raoult.
+
+And then there's going
+to be some deviation.
+
+Then if I take the other limit,
+where the mole fraction of CS2
+
+goes to zero.
+
+So now the CS2 is the solute.
+
+And the acetone is
+the solvent. what
+
+happens for this
+particular mixture is
+
+that Henry's law
+is no longer valid.
+
+Raoult's law is not valid here.
+
+Instead, you have to
+look at Henry's law.
+
+And Henry's law tells you
+that for the solute now,
+
+not the solvent,
+so the CS2 here is
+
+the solute, very
+small amount of it.
+
+Very small mole fraction.
+
+That the vapor
+pressure of the solute
+
+is related to the mole
+fraction in the solution.
+
+But instead of having the vapor
+pressure of the pure solute,
+
+you have another number.
+
+Another constant.
+
+Which we call K. Which is
+a Henry's law constant.
+
+And this constant depends on
+what else in the solution.
+
+It depends on the fact that
+you have acetone in there.
+
+You would have a
+different constant
+
+if the acetone were replaced
+with chloroform, let's say.
+
+So this constant here
+cares what the solvent is.
+
+And it cares what the
+temperature is, also.
+
+There's a lot of stuff that's
+built into this constant here.
+
+It's a phinemelogical constant.
+
+And in the case of the
+mixture of CS2 and acetone,
+
+the deviation from
+Raoult's law is positive.
+
+Meaning that the
+Henry's law constant
+
+is greater than the vapor
+pressure of the pure CS2.
+
+So that means that
+the molecules of CS2
+
+would rather go
+in the gas phase.
+
+If there's acetone around.
+
+That means they don't
+like to mix so much.
+
+They're not happy
+with each other.
+
+So the CS2 molecules
+would rather
+
+escape what would normally be
+a Raoult's law type of solution
+
+to go in the gas phase away
+from being close to the acetone.
+
+And as a result you get
+this positive deviation.
+
+You get a higher pressure than
+you expect from Raoult's law.
+
+So that the slope here
+This slope here is K CS2.
+
+And that slope
+here is p star CS2.
+
+This is a positive deviation.
+
+And you saw an example where
+you if you mix chloroform
+
+and acetone, you get
+a negative deviation.
+
+Chloroform and acetone
+are happy together
+
+because of the hydrogen
+bonding between the oxygen here
+
+and the hydrogen in chloroform.
+
+And you get a
+negative deviation.
+
+So let's start by doing
+an example with numbers.
+
+Of how this might come about.
+
+Any questions on this first?
+
+I always got confused with
+Henry's law and Raoult's law.
+
+And I always got
+confused as to when
+
+I was supposed to
+use Henry's law
+
+and when I was supposed
+to use Raoult's law.
+
+Very confusing to me, initially.
+
+The thing to remember
+is that if you're
+
+talking about something which
+in a very small amount, just
+
+the solute, like, well I'm going
+to give you an example which
+
+is a bad example,
+like sugar and water.
+
+Where sugar is
+clearly the solute,
+
+but sugar is not volatile
+clearly this is a bad example.
+
+But something which in a very
+small concentration, then
+
+Henry's law is going to apply.
+
+Raoult's law is only going
+to apply for the solvent.
+
+When you have a lot
+of stuff around.
+
+On this side here
+is Raoult's law.
+
+On this side here
+is Henry's law.
+
+Henry's law, the deviation's
+from Raoult's law,
+
+are going to happen where
+the molecules in the solution
+
+mostly see molecules that
+are not like themselves.
+
+If they mostly see
+molecules like themselves,
+
+since it's an ideal
+solution, then they
+
+don't know that there's
+other stuff around.
+
+In this case here, the CS2
+molecules don't really know.
+
+Most of them don't know that
+there's any acetone around.
+
+They couldn't care less.
+
+So it obeys an ideal solution.
+
+Here, they don't see
+any other CS2 molecules.
+
+They mostly see acetone.
+
+And so Raoult's law is
+going to fall apart.
+
+Because Raoult's
+law assumed that you
+
+have a single component.
+
+Or mostly one component.
+
+OK.
+
+Let's do an example.
+
+So in this case
+here, we're going
+
+to work the example out here.
+
+So let's take two
+components, A and B. Where
+
+B is, and let's look
+at something which
+
+is a dilute solution
+and non-ideal.
+
+So there's going to be some
+deviation from Raoult's law.
+
+And what we're told
+is at 50 degrees
+
+Celsius, that the vapor pressure
+of pure A is equal to 0.67 bar.
+
+And the vapor pressure of
+pure B is equal to 1.2 bar.
+
+So B is clearly
+the more volatile.
+
+And we're also told,
+then, that at 50 degrees
+
+C we have a molar fraction of
+A in the liquid phase is 0.9.
+
+And the molar fraction of B
+in the liquid phase is 0.1.
+
+And the total pressure above
+the solution is 0.7 bar.
+
+And eventually what we're
+going to try to find out is,
+
+we're going to change
+these concentrations.
+
+Are we going to
+try to figure out
+
+how the total pressure
+above the solution changes.
+
+That's maybe the
+goal of the problem.
+
+When you change this
+to, eventually we'll
+
+change it to 0.95
+and 0.05, and we'll
+
+want to know how does that
+change the total pressure.
+
+So immediately we see
+that this is a solvent.
+
+This is a solute.
+
+This is volatile.
+
+So, we're close to
+where this is zero.
+
+So if we're going to apply any,
+sort of, Raoult or Henry's law
+
+problem to this,
+this is probably
+
+going to be Henry's law for
+B and Raoult's law for A.
+
+We're going to be close
+to this area here for B.
+
+We're going to be close
+to this area for A.
+
+OK.
+
+So ah the first
+question is, what's
+
+the composition
+in the gas phase.
+
+What is y sub B. And it looks
+like this particular set
+
+of notes doesn't have
+the calculations.
+
+I'm going to go to my other set
+of notes here that has them.
+
+So, because I'm going
+to make a mistake if I
+
+go through it
+without my notes, I'm
+
+going to leave it up
+to you to do part a.
+
+That's a good way
+out of making a mess.
+
+I'm just going to
+tell you the answer.
+
+Because the actual,
+the interesting part,
+
+is part b of the problem.
+
+Part a is the easy part.
+
+So this is something that
+you can do on your own.
+
+So yB is equal to 0.139.
+
+Is going to be answer to
+part b, given these two molar
+
+fractions and the
+total pressure.
+
+So now, what we're
+going to do is,
+
+we're going to change
+the molar fractions
+
+and we're going to
+find out how that
+
+changes the total pressure.
+
+So, second part is we're
+still at 50 degrees Celsius.
+
+And we're going to change the
+molar fraction of A to 0.95.
+
+And the molar
+fraction of B to 0.05.
+
+And we're going to ask,
+what is p total now.
+
+So we write what we know.
+
+Which is that we
+expect p total to be
+
+the sum of the partial pressures
+of A and B. A is the solvent,
+
+B is the solute.
+
+It's a dilute
+non-ideal solution. pA
+
+is going to be proportional
+to Raoult's law,
+
+because it's a solvent.
+
+It's in large quantities.
+
+So it's going to be xA pA star.
+
+And xB is going, and
+pB is going to be
+
+proportional to the
+mole fraction again.
+
+But because it's a solute, it's
+seen most the other molecules
+
+of A around, it's
+not necessarily
+
+going to be obeying
+Raoult's law.
+
+It's going to obey Henry's law.
+
+It's going to be close
+to the zero point.
+
+There's going to be a deviation
+because of the interactions
+
+between A and B.
+Which dominate now.
+
+So instead of pA
+star, we have KB here,
+
+where this is the
+Henry's law constant.
+
+Which depends on the
+fact that A is around.
+
+We get a different constant
+if we have a different solvent
+
+around.
+
+So we know this.
+
+We know this because that was
+given to us at the beginning.
+
+But we don't know this here.
+
+We don't know what the
+Henry's law constant here is.
+
+But we can get it.
+
+We can get it from part a here.
+
+Because we have all the
+information we need there.
+
+So from part a, we
+already have a mixture
+
+where we're given
+the total pressure.
+
+So from part a,
+KB is pB over xB.
+
+And we calculated
+what yB is over there.
+
+On part a.
+
+So we know what the
+partial pressure of B is.
+
+It's the molar fraction
+of B in the gas
+
+phase times the total pressure.
+
+That's Dalton's law.
+
+Then we divide by xB.
+
+And then we plug in
+the number 0.139 times
+
+the total pressure
+up there is 0.7.
+
+Divided by 0.1.
+
+And we get that
+this is 0.973 bar.
+
+So now we can plug this
+in to our equation here.
+
+We know xA, we know xB, we know
+Raoult's law, the 0.67 pA star.
+
+We know KB here.
+
+We plug in all the
+numbers, and we
+
+get that the total
+pressure is now 0.685 bar.
+
+This is a pretty typical
+example of a problem that
+
+combines Raoult's law, Henry's
+law and Dalton's law together.
+
+And keeping track of these laws
+takes a little bit of thinking.
+
+And it's very, very common
+on problem sets or exams
+
+to mix these up.
+
+So it's good to go
+through examples like this
+
+and really keep track of
+where each law applies.
+
+Dalton's law applies
+in the gas phase.
+
+It's partial pressure
+in the gas phase.
+
+Henry's law is the pressure.
+
+If you know what's happening in
+the liquid phase, for a solute.
+
+Raoult's law is the partial
+pressure in the gas phase,
+
+if you know what's happening
+in the liquid phase.
+
+So Raoult and Henry tell you
+something about the pressure
+
+if you know the liquid.
+
+Dalton only deals with what's
+happening in the gas phase.
+
+OK, any questions
+on the problem?
+
+Alright.
+
+So we did this problem
+here, and now let's
+
+draw the phase diagram for our
+solute here, or for B, rather.
+
+Zero to one.
+
+And let's take a vote here.
+
+So if Raoult's law worked for
+B, for the mixture of A and B,
+
+then we would have pB star here.
+
+And everything would be great.
+
+But Raoult's law doesn't work.
+
+Close to molar fraction of zero.
+
+Instead, Henry's law.
+
+There's a deviation,
+due to the interactions
+
+between the molecules
+A and B here.
+
+So we have two choices
+for the deviation.
+
+We can have a
+positive deviation,
+
+or we could have a
+negative deviation.
+
+Positive deviation,
+if the molecules of B
+
+would rather be
+in the gas phase,
+
+than be in the mixture
+in the liquid phase.
+
+Meaning they don't
+like molecules of A.
+
+They don't like to be
+mixed with molecules
+
+of A. The energy of
+interaction is not favorable.
+
+The enthalpy is not
+favorable, for mixing
+
+A and B. In this case
+here, the enthalpy
+
+is favorable for mixing A and B.
+
+So in this problem here,
+which do you think it is?
+
+The blue one or the green one.
+
+Let's raise hands here.
+
+How many people think
+it's the blue one here.
+
+Anybody else?
+
+The right answer,
+we have four people.
+
+How many people think
+it's the green one?
+
+Four.
+
+Five.
+
+Six.
+
+You didn't vote twice, did you?
+
+Vote early, vote often, right?
+
+Mayor Daley, the old
+Mayor Daley in Chicago.
+
+And if you know somebody
+who's dead, vote for them.
+
+OK, so this is the, I've
+got about five people here.
+
+And a bunch of
+people didn't vote.
+
+So it's a tie.
+
+It's basically a tie here.
+
+I think you should
+think about this.
+
+Maybe talk to each
+other a little bit.
+
+See if you can figure
+out, given all the numbers
+
+that are in this
+problem here, you
+
+know what, the pure
+pressure on the solvent is.
+
+We change concentrations here.
+
+Got Henry's law constant out.
+
+And Henry's law
+constant is going
+
+to tell you whether or not
+that enthalpy of interaction
+
+is favorable or not favorable.
+
+It's going to be a
+positive deviation
+
+or a negative deviation.
+
+OK, shall we vote again.
+
+How many people say
+it's the blue one?
+
+How many people say
+it's the green one.
+
+Thank you.
+
+Alright.
+
+Good.
+
+Alright.
+
+We have K sub B is
+less than p star,
+
+therefore it's a
+negative deviation.
+
+The pressure is less
+than you'd expect.
+
+The molecules like each
+other better than you expect.
+
+There is a favorable enthalpy
+of interaction between A and B.
+
+They like to interact.
+
+It could be hydrogen bonding.
+
+Could be a lot of
+different things.
+
+OK, so now if I put the
+whole diagram together,
+
+which I shouldn't
+have erased here.
+
+Right, so there's my
+diagram here again.
+
+There's Raoult's law.
+
+There's the deviation
+from Raoult's law here.
+
+For one substance,
+let's say for B. There's
+
+Raoult's law for A. There's
+a deviation for A. It
+
+could be like this.
+
+And if I now add
+these two together,
+
+instead of having
+a diagram for, this
+
+is a pressure xB, yB diagram,
+pressure xB, yB diagram,
+
+instead of having Raoult's
+law sitting right here.
+
+And then the yB part down
+here below, your usual sort
+
+of ideal solution phase
+diagram with the high pressure
+
+of the liquid on top and
+the gas on the bottom.
+
+Now if you add the blue curve
+and the red curve together,
+
+you're not going to
+get a straight line
+
+like you did before.
+
+When Raoult's law
+applied throughout.
+
+Instead you're going
+to get a deviation
+
+from the straight line.
+
+You're going to
+get a curve that's
+
+always below the straight line.
+
+Because we have the negative
+deviation on both sides.
+
+So you end up with
+something that's
+
+curved and deviates below.
+
+And the same thing will
+happen for the bubble line.
+
+It will also deviate below.
+
+In some way.
+
+Maybe not as much, maybe.
+
+So this is what you usually see.
+
+You see deviation of
+that whole phase diagram,
+
+like you're pushing down on it.
+
+Or maybe it didn't pulled up.
+
+If you have a
+positive deviation,
+
+then it's the opposite.
+
+It gets, this is
+negative deviation.
+
+And if you have a
+positive deviation,
+
+instead of having a
+usual phase diagram,
+
+you're going to get something
+that's looking like this.
+
+Which is the Henry's
+law coming in.
+
+Yes.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Yes.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Doesn't matter.
+
+Good question, though.
+
+OK, so this is what
+it usually looks like.
+
+And everything
+you've learned so far
+
+can be applied to
+these diagrams here.
+
+There's one exception, though,
+which is an important one.
+
+Which is, sometimes,
+these non-ideal diagrams
+
+have a funny spot.
+
+Which is that if I
+draw them, so there's
+
+my xB, yB, on the bottom.
+
+Zero to one.
+
+I have pressure here.
+
+Sometimes, there's the dew line.
+
+And the bubble line.
+
+Sometimes, instead of
+having a nice separation
+
+between the bubble
+and the dew line,
+
+there's a special point
+which for some reason
+
+those two curves meet.
+
+Non-ideality.
+
+There's interaction
+between the molecules.
+
+In the gas phase and
+the liquid phase.
+
+This special point is
+an interesting one.
+
+Because, well, if I'm away
+from this special point,
+
+let's say I'm sitting to the
+left of the special point,
+
+right here.
+
+And I can distill this thing.
+
+I can take my gas phase here.
+
+And increase the pressure.
+
+Say I'm sitting here in
+the mixture, gas phase
+
+mixture with x prime B, y
+prime B. Sorry, x prime B.
+
+And I go up and I
+increase the pressure.
+
+Start making vapor.
+
+Start making vapor, I
+can find out what the,
+
+I start making liquid.
+
+I can find out where the
+composition in the liquid
+
+is by going over to
+the blue line here.
+
+That tells me the
+composition in the liquid.
+
+And reading off the composition
+of the liquid down here.
+
+So this is actually the
+composition in the gas phase
+
+is yB prime. yB prime
+is the gas phase.
+
+I'm starting here.
+
+I start to increase
+the pressure.
+
+I begin the
+distillation process.
+
+And I get a little
+bit of liquid out.
+
+And I can read off the
+composition in the liquid. xB
+
+prime.
+
+And I know from this diagram
+that xB prime is less then
+
+yB prime.
+
+So I'm enriching
+my liquid in A. I'm
+
+purifying my
+solution in A, right?
+
+I can get pure A out eventually.
+
+The fact of doing
+this, I can get pure A.
+
+So I decrease the pressure,
+I get the pure gas phase
+
+of my new solution here.
+
+And I increase the pressure.
+
+And go over and make a
+little bit of liquid.
+
+And capture that liquid.
+
+And repeat the process
+over and over again.
+
+And eventually I have pure A.
+
+Now, suppose I'm sitting
+here at this special point.
+
+And I'm starting with yB And
+let me call it a here. yB of a.
+
+I'm sitting right here.
+
+And I'm increasing the pressure.
+
+I go all the way up here.
+
+And I start making liquid. .
+
+What's the composition
+of liquid, compared
+
+to the composition
+of the gas phase?
+
+What's y?
+
+What's xB compared to yB
+of this point up here?
+
+It's the same.
+
+So I'm making liquid.
+
+I got the same composition.
+
+Doesn't help me.
+
+If I make a gas again, I still
+have the same composition.
+
+I can't distill.
+
+I can't purify it.
+
+So if I have this special
+mixture here, of A and B,
+
+at this point here, I form
+what's called an azeotrope.
+
+And then you can't
+separate it out.
+
+You can't separate out
+the mixtures into A and B.
+
+You can't distill it
+at that point here.
+
+Now, you can draw the same
+diagram in, instead of
+
+pressure, mole fraction, you
+can draw the same diagram
+
+in terms of temperature.
+
+And the same thing happens.
+
+You can have
+deviations from, this
+
+is the extra figures that
+are on the bottom page
+
+of the notes from
+last time here.
+
+That we've replaced here.
+
+You can have a
+positive deviation.
+
+With a positive azeotrope.
+
+And your T p
+diagram, T x diagram.
+
+Or you can have, depending
+on the interactions
+
+between the two
+molecules, you can
+
+have something that has
+a negative deviation.
+
+And a negative azeotrope here.
+
+So in this case here, this is
+a particularly awful situation.
+
+Because there's your
+liquid phase down here.
+
+There's the gas phase here.
+
+And now, suppose
+that you're doing
+
+some sort of distillation.
+
+So you start here in the liquid
+phase, with some composition.
+
+You make a gas.
+
+Let's say you're doing a
+fractional distillation
+
+of some sort.
+
+Your gas now has a new mixture.
+
+So this is the composition
+in the gas phase.
+
+You take that gas phase
+mixture, and you condense it
+
+in your condenser.
+
+In your fractional
+distillation condenser.
+
+So now I've condensed it.
+
+And I heat it up again.
+
+I've condensed it.
+
+So I'm here somewhere.
+
+And cool it down so
+that I have a liquid.
+
+And I condense it.
+
+And slowly I move over
+to the azeotrope point.
+
+And once I get there, I'm stuck.
+
+And the same thing happens
+if I'm on the other side.
+
+I'm on this point here, I
+keep my solution, my mixture.
+
+I make a gas, I read off the
+composition of the gas phase
+
+here.
+
+I take my gas phase composition
+out and I re-liquefy it.
+
+So I'm here, down
+here somewhere, again.
+
+And I heat it up again.
+
+And and I move to
+the azeotrope point.
+
+That's what happens if you have
+a mixture of benzene and water,
+
+for instance.
+
+You can't distill it.
+
+You work your way down
+to this point here.
+
+You can't use
+fractional distillation
+
+until you've separated it out.
+
+So this is a real life problem.
+
+And you have to do things
+like change the pressure.
+
+Do your distillation under
+high pressure or low pressure.
+
+To try to get this
+point to separate out.
+
+So you can get past this point.
+
+Or to try to get the deviation
+to become of the opposite sign.
+
+Where you can start to
+do some distillation.
+
+Any questions on
+azeotropes, before we
+
+get to colligative properties?
+
+If you're doing
+organic chemistry,
+
+and you're trying
+to purify things,
+
+this is a real pain, right?
+
+Pain in the neck.
+
+So you've got to know, which
+things form azeotropes.
+
+So we're going to start
+colligative properties.
+
+There are four
+colligative properties,
+
+and you already
+know what they are.
+
+And you've even seen
+the math behind them.
+
+And in fact, you've seen
+the math for one of them
+
+already pretty clearly.
+
+And these colligative
+properties are
+
+properties that you use all the
+time in your day to day life.
+
+At least, three of them.
+
+OK what are the four
+colligative properties?
+
+There is vapor
+pressure lowering.
+
+If you have a mixture and the
+vapor pressure of the mixture
+
+is less than the vapor
+pressure of the pure material,
+
+there's the boiling
+point elevation.
+
+If you add a large amount of
+insoluble - not insoluble,
+
+non-volatile solute to a
+solution, you will depress,
+
+you will increase the boiling
+point of that solution like
+
+the example of the salt
+and water that I gave.
+
+So if you need a lot
+of salt to increase
+
+the boiling point of water.
+
+There's the freezing
+point depression.
+
+That's what we use to
+melt ice in the winter.
+
+By adding salt to it.
+
+Then there's the
+osmotic pressure.
+
+Which is the example of the
+freshwater fish in salt water,
+
+or the saltwater
+fish in fresh water.
+
+Or the cells bursting
+when you put them in.
+
+OK, so these colligative
+properties all come
+
+from the fact if
+I have a mixture,
+
+the chemical potential of
+a molecule in a mixture,
+
+in the liquid
+phase here, is less
+
+than the chemical
+potential of the pure guy.
+
+Where A is the solvent,
+and B is some solute.
+
+So this is always true if
+your number of moles of A
+
+is much larger than
+number of moles of B. Mix
+
+a little bit of B in there,
+and the chemical potential of A
+
+in the liquid is
+going to come down.
+
+Because of the mixing process.
+
+Because of the
+entropy of mixing.
+
+And that's going to give
+rise to these properties.
+
+And, to do these, one more
+thing before we start.
+
+We're going to use a special
+concentration for these guys.
+
+We're going to use,
+call something molality.
+
+Molality.
+
+Molality is the number
+of moles of solute
+
+divided by kilograms of solvent.
+
+So it's moles per
+weight of solvent.
+
+As opposed to moles
+per liter, which
+
+is something that
+we're more used to.
+
+Moles per kilograms of solvent.
+
+It's pretty close to
+moles for liter for water.
+
+Because a gram of water
+is a milliliter, roughly.
+
+The density of
+water's close to one.
+
+So let's start on these things.
+
+So we've already seen this.
+
+You've already seen
+vapor pressure lowering.
+
+It comes from Raoult's law.
+
+If I look at the change in
+the vapor pressure of A, pA
+
+minus pA star. pA is equal to
+xA pA star. xA pA star, that's
+
+Raoult's law.
+
+Minus pA star, that's
+equal to one minus xA.
+
+Minus pA star.
+
+Which is minus xB pA star.
+
+Which is less than zero.
+
+So, that means that the vapor
+pressure above the solution
+
+is lowered.
+
+So I should have said
+vapor pressure lowering.
+
+And we also drew a
+phase diagram to show
+
+how this vapor
+pressure lowering was
+
+going to imply freezing point
+depression and boiling point
+
+depression.
+
+So now let's go on and look at
+the freezing point depression.
+
+Number two.
+
+We're going to find that the
+change in the boiling point
+
+is going to be some constant
+K sub b, which is not
+
+to be confused with
+Henry's law's constant.
+
+It's completely different.
+
+This is a colligative property.
+
+Times the molality
+of B. That's going
+
+to be the answer
+we're going to get.
+
+Amount of temperature
+change depends linearly
+
+on the molality of
+B, with a constant
+
+that depends on
+what the mixture is.
+
+And what the pressure is.
+
+Whenever we derive anything
+connected to phase transitions,
+
+we usually always
+start with the fact
+
+that the chemical
+potential changes.
+
+And it has to be
+equal at equilibrium.
+
+So that's what
+we're going to do.
+
+We're going to start with
+the chemical potential equal
+
+of the liquid phase is equal
+to the chemical potential
+
+of the gas phase.
+
+For the solvent at equilibrium.
+
+And the liquid phase
+obeys Raoult's law.
+
+So it's going to be the chemical
+potential of the pure material.
+
+The pure liquid.
+
+Plus RT log xA.
+
+So this is where the mixing
+of the solute comes in.
+
+And on the gas phase
+side, mu A, it's
+
+going to be the same thing
+as the chemical potential
+
+of the pure A.
+Because we're going
+
+to take B to be non-volatile.
+
+So the only thing
+in the gas phase
+
+is A. Same chemical
+potential as if it were pure.
+
+Because it is pure.
+
+So now we solve for log xA
+is equal to one over RT mu
+
+A star in the gas phase minus
+mu A star in the liquid phase.
+
+And this is just the
+Gibbs free energy
+
+per mole of A in the gas phase.
+
+The Gibbs free energy per
+mole of A in the liquid phase.
+
+So we can replace this with
+the change in Gibbs free energy
+
+from going from gas to liquid.
+
+Per mole, which
+is just the Gibbs
+
+free energy of vaporization.
+
+We're going from liquid to gas.
+
+And I probably have a
+negative sign somewhere.
+
+No this is right, this
+is the final state.
+
+This is the initial state.
+
+Divided by RT.
+
+OK.
+
+That's not really
+what we want, though.
+
+What we want is
+delta T. Here I've
+
+got some complicated
+equation that has T in it,
+
+but not delta T.
+But before we do
+
+that, before we transfer
+and try to get a delta T out
+
+of this equation,
+let's see if we
+
+can do any sort of
+simplifications here.
+
+I don't like to
+carry logs around.
+
+There are no logs around here.
+
+So let's see if we can
+get rid of that log.
+
+What is log xA?
+
+Log xA, well, xA
+is close to one.
+
+It's connected to xB.
+
+And everything in
+here is connected
+
+to B. There's a
+molality of B here.
+
+The concentration of A
+doesn't come into play here.
+
+I don't want it there.
+
+So let me replace it with B. one
+minus xB. xB is a small number.
+
+It's a solute, it's
+in small amount.
+
+We're close to being
+a pure solvent here.
+
+So one minus
+something very small.
+
+The log of that.
+
+Well if you've worked
+with Taylor's expansions.
+
+You probably know that
+that's close to minus xB.
+
+The log of one minus
+x where x goes to zero
+
+is close to minus x.
+
+So that's minus xB.
+
+Now, minus xB, in
+terms of the moles,
+
+is the number of moles of B
+divided by the number of moles
+
+of B plus the number of moles
+of A, the total number of moles.
+
+The number of moles
+of B is very small,
+
+compared to the number of moles
+of A. So I can get rid of this.
+
+So, and there's a
+minus sign here.
+
+So this is approximately
+minus nB divided by nA.
+
+Now, the only I can do is, I'm
+trying to get at molality here.
+
+I said we're going
+to use molality.
+
+Got moles.
+
+I don't have kilograms
+of solvent here.
+
+I have moles of solvent.
+
+I'm not so happy with that.
+
+So, in order to get something
+that has kilograms out,
+
+let's multiply up and down by
+capital M where capital M is
+
+that total mass of A. Basically
+the number of kilograms
+
+of solvent.
+
+Total mass of A. So
+now, this fraction here,
+
+that's the molality.
+
+That's what I'm looking for.
+
+So this is minus the molality.
+
+Then I have the total
+mass of A divided
+
+by the number of moles
+of A. Well, that's
+
+the molecular weight of it.
+
+Total mass divided by
+the number of moles
+
+is the molecular weight.
+
+So this is the molality of
+B times the molecular weight
+
+of A. OK.
+
+So now I can plug this
+instead of log xA.
+
+And I get minus nB times
+nA is equal to delta
+
+G of vaporization divided by RT.
+
+Let's rearrange a little bit.
+
+And mB is equal to to delta
+G vaporization divided
+
+by nA times RT, with
+a negative sign.
+
+Well, I've eliminated
+the log at least,
+
+but I still don't have
+a delta T in there.
+
+I don't have a delta
+T. How am I going
+
+to get a delta T in there?
+
+Got to get the delta T.
+Everything's very small.
+
+So one way to get a small
+change in temperature
+
+is to take a derivative
+with respect to temperature.
+
+That's going to get
+a delta T in there.
+
+So I'm going to take the
+derivative of both sides
+
+with respect to T.
+
+And delta T is going
+to come out that.
+
+I'm going to take d nB
+/ dT, constant pressure.
+
+Minus one over mA times
+R d delta G over T. This
+
+is delta G of vaporization.
+dT, constant pressure.
+
+And I wish I'd made my
+boards a little bit better.
+
+Because I have to
+cover things up.
+
+OK, now I have this derivative
+of the Gibbs free energy
+
+divided by the temperature.
+
+This turns out to be something
+that you've seen before.
+
+It's called the
+Gibbs-Helmholtz equation.
+
+And it relates the temperature
+change in the Gibbs free energy
+
+with the enthalpy change.
+
+The Gibbs-Helmholtz equation
+is that the d delta G over T dT
+
+is equal to minus
+delta H over T.
+
+And you can get that from just
+writing fundamental equations
+
+about G and H. And
+turning the crank.
+
+And we've done that before.
+
+And I'll leave that
+as an exercise for you
+
+to go back and figure
+out what, you can go back
+
+to your textbook and look
+at, you know under the index.
+
+Gibbs-Helmholtz, and figure
+out why this is the case.
+
+So now, we have
+this equation here.
+
+This is going to be
+nice, because it's
+
+going to get rid of the d/dT.
+
+On the right-hand side.
+
+And so now our
+equation becomes d
+
+mB / dT is equal to delta H
+vaporization divided by mA R T
+
+squared.
+
+Now, I can rewrite this in
+a slightly different way.
+
+This is delta m over
+delta T, basically.
+
+Delta the change
+in number of moles.
+
+I mean, the molality
+of B divided
+
+by the change in temperature.
+
+I'm getting very close here.
+
+There's a change in
+temperature here.
+
+There's a change
+in molality here.
+
+I can rewrite this
+as delta T, then,
+
+is equal to molecular
+weight of A times
+
+RT squared divided by delta H
+vaporization times delta mB.
+
+Now, I'm making a very
+small change in B here.
+
+Starting at zero.
+
+Basically I'm taking
+pure A and I'm
+
+dumping in a little
+bit of B. That's
+
+what I'm doing
+when I experiment.
+
+I'm dumping in a little
+bit of B in my pure A,
+
+and I'm trying to figure out
+how the temperature is changing.
+
+So I'm doing delta m sub
+B is my small amount of B
+
+that I'm adding to the solution.
+
+Minus what I started out
+with, which was zero.
+
+So delta mB is basically
+m sub B. Right?
+
+That's basically what it is.
+
+So let's get rid
+of this delta here.
+
+What else can I say?
+
+Well, I can say that the
+temperature change that I'm
+
+looking at is also pretty small.
+
+Compared to the
+absolute temperature.
+
+This is a small change.
+
+I'm only adding a small
+amount of B in there.
+
+So this temperature up here is
+not going to change very much.
+
+Let's take it to
+be the temperature
+
+of the boiling point
+of the pure material.
+
+T sub B star, of
+the pure material.
+
+OK And there's my delta T here.
+
+So this is of the
+form delta T is
+
+equal to molecular weight
+of A. Times R. Times
+
+the boiling point of the
+pure material squared.
+
+Divided by delta
+H of vaporization
+
+of the pure solvent.
+
+Times the molality of B. And
+this combination of properties
+
+of A, the molecular weight of
+A, the boiling point of pure A.
+
+The heat of vaporization of
+pure A, this is K sub b up here.
+
+Which I covered up.
+
+It's of the form delta T is
+equal to K sub b times mB.
+
+And this turns out to be
+always greater than zero.
+
+Now.
+
+If you want to look at
+freezing point depression,
+
+it's really easy.
+
+In your equations, it's the
+same thermodynamic picture.
+
+All you need to do,
+in all your equations,
+
+you replace delta
+G of vaporization
+
+with minus delta G of freezing.
+
+When we did a vaporization,
+we're going from liquid to gas.
+
+We had delta G of vaporization.
+
+When we're doing freezing
+point depression,
+
+we're going from
+liquid to solid.
+
+And so we have to use
+minus delta G of fusion.
+
+Minus delta H of
+fusion. s to l would
+
+be the positive
+delta G of fusion.
+
+So we're going from
+liquid to solid.
+
+We have to replace
+delta G of vaporization
+
+with delta G of fusion.
+
+We replace delta
+H of vaporization,
+
+where minus delta H of fusion.
+
+Replace the boiling point
+with the freezing point.
+
+And replace K sub
+b with K sub f.
+
+And the math is
+exactly identical.
+
+It all starts from the chemical
+potentials being equal.
+
+And turning the crank
+at equilibrium, being
+
+equal between the solid
+phase and the liquid phase.
+
+And turning the crank.
+
+The solid phase is
+like the gas phase.
+
+It's a pure A, pretty much.
+
+Because the molecules
+of B are stuck.
+
+And A doesn't know that B's
+around, in the solid phase.
+
+They know that they're
+around in the liquid phase
+
+because the fusion
+fast enough. .
+
+And then we can write,
+if we turn the crank,
+
+we get an equation
+that looks like this.
+
+The freezing point depression
+is equal to minus mA
+
+R Tf star squared.
+
+Divided by delta H
+of fusion, for mole.
+
+Times the molality
+of B. And this number
+
+is always less than zero.
+
+There's the negative
+signs in here.
+
+OK.
+
+Always depressed.
+
+Any questions about those
+freezing point depression
+
+and boiling point elevation.
+
+Yes.
+
+STUDENT: [INAUDIBLE] PROFESSOR:
+Why did I drop it here?
+
+Because the small change
+that I'm making in nB
+
+is going from pure
+A, where nB is zero,
+
+to a very small amount of nB.
+
+That's why I'm
+allowed to say this.
+
+And then just replace
+delta nB with nB.
+
+I'm comparing every,
+my reference point
+
+is the pure material.
+
+I'm just adding a little
+bit to start with.
+
+It's a good question.
+
+Any other questions?
+
+OK.
+
+I didn't get to
+osmotic pressure.
+
+You'll get to that on Friday.
+
+And also start
+statistical mechanics.
+
+And after osmotic pressure,
+you'll be done with thermo.
+
+It'll be statistical
+mechanics and then kinetics.
\ No newline at end of file
diff --git a/wrEcHhoJxjM.txt b/wrEcHhoJxjM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c129b82f52acaee519e9c3cbb821840b54ea8dce
--- /dev/null
+++ b/wrEcHhoJxjM.txt
@@ -0,0 +1,5867 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk about gradient descent and the and
+
+ align:start position:0%
+talk about gradient descent and the and
+ 
+
+ align:start position:0%
+talk about gradient descent and the and
+its descendants so from the basic
+
+ align:start position:0%
+its descendants so from the basic
+ 
+
+ align:start position:0%
+its descendants so from the basic
+gradient descent formula which we all
+
+ align:start position:0%
+gradient descent formula which we all
+ 
+
+ align:start position:0%
+gradient descent formula which we all
+know let me just write that down the new
+
+ align:start position:0%
+know let me just write that down the new
+ 
+
+ align:start position:0%
+know let me just write that down the new
+point is the old point we're going
+
+ align:start position:0%
+point is the old point we're going
+ 
+
+ align:start position:0%
+point is the old point we're going
+downwards so with a minus sign that's
+
+ align:start position:0%
+downwards so with a minus sign that's
+ 
+
+ align:start position:0%
+downwards so with a minus sign that's
+the step size and we compute the
+
+ align:start position:0%
+the step size and we compute the
+ 
+
+ align:start position:0%
+the step size and we compute the
+gradient at X K so we're descending in
+
+ align:start position:0%
+gradient at X K so we're descending in
+ 
+
+ align:start position:0%
+gradient at X K so we're descending in
+the direction of the negative gradient
+
+ align:start position:0%
+the direction of the negative gradient
+ 
+
+ align:start position:0%
+the direction of the negative gradient
+and that's the basic formula and is in
+
+ align:start position:0%
+and that's the basic formula and is in
+ 
+
+ align:start position:0%
+and that's the basic formula and is in
+every book studied so my main reference
+
+ align:start position:0%
+every book studied so my main reference
+ 
+
+ align:start position:0%
+every book studied so my main reference
+for the some of these lectures is the
+
+ align:start position:0%
+for the some of these lectures is the
+ 
+
+ align:start position:0%
+for the some of these lectures is the
+book by Stephen Boyd and Linden and
+
+ align:start position:0%
+book by Stephen Boyd and Linden and
+ 
+
+ align:start position:0%
+book by Stephen Boyd and Linden and
+Vandenberg and and I mentioned again
+
+ align:start position:0%
+Vandenberg and and I mentioned again
+ 
+
+ align:start position:0%
+Vandenberg and and I mentioned again
+professor Boyd is talking in this room
+
+ align:start position:0%
+professor Boyd is talking in this room
+ 
+
+ align:start position:0%
+professor Boyd is talking in this room
+next week Wednesday Thursday and and
+
+ align:start position:0%
+next week Wednesday Thursday and and
+ 
+
+ align:start position:0%
+next week Wednesday Thursday and and
+he's speaking somewhere on Friday at
+
+ align:start position:0%
+he's speaking somewhere on Friday at
+ 
+
+ align:start position:0%
+he's speaking somewhere on Friday at
+4:30 and of course about optimization
+
+ align:start position:0%
+4:30 and of course about optimization
+ 
+
+ align:start position:0%
+4:30 and of course about optimization
+and he's a good lecturer yeah very good
+
+ align:start position:0%
+and he's a good lecturer yeah very good
+ 
+
+ align:start position:0%
+and he's a good lecturer yeah very good
+okay so there's steepest descent and
+
+ align:start position:0%
+okay so there's steepest descent and
+ 
+
+ align:start position:0%
+okay so there's steepest descent and
+I've redrawn my picture from last time
+
+ align:start position:0%
+I've redrawn my picture from last time
+ 
+
+ align:start position:0%
+I've redrawn my picture from last time
+that I'll go over there and look at that
+
+ align:start position:0%
+that I'll go over there and look at that
+ 
+
+ align:start position:0%
+that I'll go over there and look at that
+picture but let me say what's coming so
+
+ align:start position:0%
+picture but let me say what's coming so
+ 
+
+ align:start position:0%
+picture but let me say what's coming so
+that's pretty standard very standard you
+
+ align:start position:0%
+that's pretty standard very standard you
+ 
+
+ align:start position:0%
+that's pretty standard very standard you
+could say then this is the improvement
+
+ align:start position:0%
+could say then this is the improvement
+ 
+
+ align:start position:0%
+could say then this is the improvement
+that is widely used adding in something
+
+ align:start position:0%
+that is widely used adding in something
+ 
+
+ align:start position:0%
+that is widely used adding in something
+called momentum to avoid the zigzag that
+
+ align:start position:0%
+called momentum to avoid the zigzag that
+ 
+
+ align:start position:0%
+called momentum to avoid the zigzag that
+we're going to see
+
+ align:start position:0%
+we're going to see
+ 
+
+ align:start position:0%
+we're going to see
+and there's another way to do it there's
+
+ align:start position:0%
+and there's another way to do it there's
+ 
+
+ align:start position:0%
+and there's another way to do it there's
+a Russian guy named Nestor off his
+
+ align:start position:0%
+a Russian guy named Nestor off his
+ 
+
+ align:start position:0%
+a Russian guy named Nestor off his
+papers are not easy to read but they've
+
+ align:start position:0%
+papers are not easy to read but they've
+ 
+
+ align:start position:0%
+papers are not easy to read but they've
+got serious content and one thing he did
+
+ align:start position:0%
+got serious content and one thing he did
+ 
+
+ align:start position:0%
+got serious content and one thing he did
+was find an alternative to momentum that
+
+ align:start position:0%
+was find an alternative to momentum that
+ 
+
+ align:start position:0%
+was find an alternative to momentum that
+also accelerated the the descent so this
+
+ align:start position:0%
+also accelerated the the descent so this
+ 
+
+ align:start position:0%
+also accelerated the the descent so this
+produces these both produce faster
+
+ align:start position:0%
+produces these both produce faster
+ 
+
+ align:start position:0%
+produces these both produce faster
+descent than the ordinary one okay and
+
+ align:start position:0%
+descent than the ordinary one okay and
+ 
+
+ align:start position:0%
+descent than the ordinary one okay and
+then you know looking ahead that for
+
+ align:start position:0%
+then you know looking ahead that for
+ 
+
+ align:start position:0%
+then you know looking ahead that for
+problems of machine learning they're so
+
+ align:start position:0%
+problems of machine learning they're so
+ 
+
+ align:start position:0%
+problems of machine learning they're so
+large that the gradient and we have so
+
+ align:start position:0%
+large that the gradient and we have so
+ 
+
+ align:start position:0%
+large that the gradient and we have so
+many variables all those weights are
+
+ align:start position:0%
+many variables all those weights are
+ 
+
+ align:start position:0%
+many variables all those weights are
+variables all and that could hundreds of
+
+ align:start position:0%
+variables all and that could hundreds of
+ 
+
+ align:start position:0%
+variables all and that could hundreds of
+thousands is is not uncommon
+
+ align:start position:0%
+thousands is is not uncommon
+ 
+
+ align:start position:0%
+thousands is is not uncommon
+so that then the gradient becomes a
+
+ align:start position:0%
+so that then the gradient becomes a
+ 
+
+ align:start position:0%
+so that then the gradient becomes a
+pretty big calculation and we don't have
+
+ align:start position:0%
+pretty big calculation and we don't have
+ 
+
+ align:start position:0%
+pretty big calculation and we don't have
+to do it all at once we don't have to
+
+ align:start position:0%
+to do it all at once we don't have to
+ 
+
+ align:start position:0%
+to do it all at once we don't have to
+change so xk is a vector of all the
+
+ align:start position:0%
+change so xk is a vector of all the
+ 
+
+ align:start position:0%
+change so xk is a vector of all the
+weights or and using and our equations
+
+ align:start position:0%
+weights or and using and our equations
+ 
+
+ align:start position:0%
+weights or and using and our equations
+are the matching the the training data
+
+ align:start position:0%
+are the matching the the training data
+ 
+
+ align:start position:0%
+are the matching the the training data
+so we don't have to use all the training
+
+ align:start position:0%
+so we don't have to use all the training
+ 
+
+ align:start position:0%
+so we don't have to use all the training
+data at once and we don't we take a
+
+ align:start position:0%
+data at once and we don't we take a
+ 
+
+ align:start position:0%
+data at once and we don't we take a
+batch of training data like one but
+
+ align:start position:0%
+batch of training data like one but
+ 
+
+ align:start position:0%
+batch of training data like one but
+that's sort of inefficient in the
+
+ align:start position:0%
+that's sort of inefficient in the
+ 
+
+ align:start position:0%
+that's sort of inefficient in the
+opposite direction they do them one at a
+
+ align:start position:0%
+opposite direction they do them one at a
+ 
+
+ align:start position:0%
+opposite direction they do them one at a
+time so we don't want to do with them
+
+ align:start position:0%
+time so we don't want to do with them
+ 
+
+ align:start position:0%
+time so we don't want to do with them
+one at a time but we don't want to do
+
+ align:start position:0%
+one at a time but we don't want to do
+ 
+
+ align:start position:0%
+one at a time but we don't want to do
+all all million at a time
+
+ align:start position:0%
+all all million at a time
+ 
+
+ align:start position:0%
+all all million at a time
+so the compromise is a mini batch so
+
+ align:start position:0%
+so the compromise is a mini batch so
+ 
+
+ align:start position:0%
+so the compromise is a mini batch so
+sarcastic gradient descent does a mini
+
+ align:start position:0%
+sarcastic gradient descent does a mini
+ 
+
+ align:start position:0%
+sarcastic gradient descent does a mini
+batch at a time a mini batch of of
+
+ align:start position:0%
+batch at a time a mini batch of of
+ 
+
+ align:start position:0%
+batch at a time a mini batch of of
+training of samples training data each
+
+ align:start position:0%
+training of samples training data each
+ 
+
+ align:start position:0%
+training of samples training data each
+step and it can choose them
+
+ align:start position:0%
+step and it can choose them
+ 
+
+ align:start position:0%
+step and it can choose them
+stochastically meaning randomly or
+
+ align:start position:0%
+stochastically meaning randomly or
+ 
+
+ align:start position:0%
+stochastically meaning randomly or
+sitting more systematically but we do a
+
+ align:start position:0%
+sitting more systematically but we do a
+ 
+
+ align:start position:0%
+sitting more systematically but we do a
+batch at a time and that will come after
+
+ align:start position:0%
+batch at a time and that will come after
+ 
+
+ align:start position:0%
+batch at a time and that will come after
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+it'll come next week after a marathon of
+
+ align:start position:0%
+it'll come next week after a marathon of
+ 
+
+ align:start position:0%
+it'll come next week after a marathon of
+course on Monday okay so let me just go
+
+ align:start position:0%
+course on Monday okay so let me just go
+ 
+
+ align:start position:0%
+course on Monday okay so let me just go
+back to that picture for a moment but
+
+ align:start position:0%
+back to that picture for a moment but
+ 
+
+ align:start position:0%
+back to that picture for a moment but
+then the real content of today is this
+
+ align:start position:0%
+then the real content of today is this
+ 
+
+ align:start position:0%
+then the real content of today is this
+one with momentum added okay I just I
+
+ align:start position:0%
+one with momentum added okay I just I
+ 
+
+ align:start position:0%
+one with momentum added okay I just I
+probably haven't got the picture perfect
+
+ align:start position:0%
+probably haven't got the picture perfect
+ 
+
+ align:start position:0%
+probably haven't got the picture perfect
+yet I'm just not an artist but I think
+
+ align:start position:0%
+yet I'm just not an artist but I think
+ 
+
+ align:start position:0%
+yet I'm just not an artist but I think
+I'm closer so this is uh those are the
+
+ align:start position:0%
+I'm closer so this is uh those are the
+ 
+
+ align:start position:0%
+I'm closer so this is uh those are the
+level sets those are the sets f of X
+
+ align:start position:0%
+level sets those are the sets f of X
+ 
+
+ align:start position:0%
+level sets those are the sets f of X
+equal constant and in our model problem
+
+ align:start position:0%
+equal constant and in our model problem
+ 
+
+ align:start position:0%
+equal constant and in our model problem
+f of X is X 1 squared or let's say x
+
+ align:start position:0%
+f of X is X 1 squared or let's say x
+ 
+
+ align:start position:0%
+f of X is X 1 squared or let's say x
+squared plus B y squared equal constants
+
+ align:start position:0%
+squared plus B y squared equal constants
+ 
+
+ align:start position:0%
+squared plus B y squared equal constants
+with small B be below 1 and maybe far
+
+ align:start position:0%
+with small B be below 1 and maybe far
+ 
+
+ align:start position:0%
+with small B be below 1 and maybe far
+below 1 so those are ellipses those the
+
+ align:start position:0%
+below 1 so those are ellipses those the
+ 
+
+ align:start position:0%
+below 1 so those are ellipses those the
+equations of an ellipse and that's what
+
+ align:start position:0%
+equations of an ellipse and that's what
+ 
+
+ align:start position:0%
+equations of an ellipse and that's what
+I tried to draw and if B is small then
+
+ align:start position:0%
+I tried to draw and if B is small then
+ 
+
+ align:start position:0%
+I tried to draw and if B is small then
+the ellipses are long and thin like that
+
+ align:start position:0%
+the ellipses are long and thin like that
+ 
+
+ align:start position:0%
+the ellipses are long and thin like that
+and now what's what's the picture you
+
+ align:start position:0%
+and now what's what's the picture you
+ 
+
+ align:start position:0%
+and now what's what's the picture you
+start with a point X naught and you
+
+ align:start position:0%
+start with a point X naught and you
+ 
+
+ align:start position:0%
+start with a point X naught and you
+descend in the steepest direction so the
+
+ align:start position:0%
+descend in the steepest direction so the
+ 
+
+ align:start position:0%
+descend in the steepest direction so the
+steepest direction is perpendicular to
+
+ align:start position:0%
+steepest direction is perpendicular to
+ 
+
+ align:start position:0%
+steepest direction is perpendicular to
+the level set right perpendicular to the
+
+ align:start position:0%
+the level set right perpendicular to the
+ 
+
+ align:start position:0%
+the level set right perpendicular to the
+ellipse so you down down down you're
+
+ align:start position:0%
+ellipse so you down down down you're
+ 
+
+ align:start position:0%
+ellipse so you down down down you're
+passing through more ellipses more
+
+ align:start position:0%
+passing through more ellipses more
+ 
+
+ align:start position:0%
+passing through more ellipses more
+ellipses more ellipses eventually your
+
+ align:start position:0%
+ellipses more ellipses eventually your
+ 
+
+ align:start position:0%
+ellipses more ellipses eventually your
+tangent to it seems to me it has to be
+
+ align:start position:0%
+tangent to it seems to me it has to be
+ 
+
+ align:start position:0%
+tangent to it seems to me it has to be
+tangent I didn't read this but it looks
+
+ align:start position:0%
+tangent I didn't read this but it looks
+ 
+
+ align:start position:0%
+tangent I didn't read this but it looks
+reasonable to me that the the farthest
+
+ align:start position:0%
+reasonable to me that the the farthest
+ 
+
+ align:start position:0%
+reasonable to me that the the farthest
+in level-set farthest an ellipse you're
+
+ align:start position:0%
+in level-set farthest an ellipse you're
+ 
+
+ align:start position:0%
+in level-set farthest an ellipse you're
+tangent to and then you start going up
+
+ align:start position:0%
+tangent to and then you start going up
+ 
+
+ align:start position:0%
+tangent to and then you start going up
+again so that's the optimal point to
+
+ align:start position:0%
+again so that's the optimal point to
+ 
+
+ align:start position:0%
+again so that's the optimal point to
+stop to end that step and then where
+
+ align:start position:0%
+stop to end that step and then where
+ 
+
+ align:start position:0%
+stop to end that step and then where
+does the next step go well you're here
+
+ align:start position:0%
+does the next step go well you're here
+ 
+
+ align:start position:0%
+does the next step go well you're here
+you're on an ellipse that's a level set
+
+ align:start position:0%
+you're on an ellipse that's a level set
+ 
+
+ align:start position:0%
+you're on an ellipse that's a level set
+you want to move in the gradient
+
+ align:start position:0%
+you want to move in the gradient
+ 
+
+ align:start position:0%
+you want to move in the gradient
+direction that's perpendicular to the
+
+ align:start position:0%
+direction that's perpendicular to the
+ 
+
+ align:start position:0%
+direction that's perpendicular to the
+level set so you're going down somewhere
+
+ align:start position:0%
+level set so you're going down somewhere
+ 
+
+ align:start position:0%
+level set so you're going down somewhere
+here and you're passing again through
+
+ align:start position:0%
+here and you're passing again through
+ 
+
+ align:start position:0%
+here and you're passing again through
+more and more ellipses until your
+
+ align:start position:0%
+more and more ellipses until your
+ 
+
+ align:start position:0%
+more and more ellipses until your
+tangent to a
+
+ align:start position:0%
+tangent to a
+ 
+
+ align:start position:0%
+tangent to a
+to a smaller ellipse here and and you
+
+ align:start position:0%
+to a smaller ellipse here and and you
+ 
+
+ align:start position:0%
+to a smaller ellipse here and and you
+see the zig-zag pattern and that zig-zag
+
+ align:start position:0%
+see the zig-zag pattern and that zig-zag
+ 
+
+ align:start position:0%
+see the zig-zag pattern and that zig-zag
+pattern is what we see by formula in in
+
+ align:start position:0%
+pattern is what we see by formula in in
+ 
+
+ align:start position:0%
+pattern is what we see by formula in in
+Boyd's book and many other places too
+
+ align:start position:0%
+Boyd's book and many other places too
+ 
+
+ align:start position:0%
+Boyd's book and many other places too
+the formula has the there was powers of
+
+ align:start position:0%
+the formula has the there was powers of
+ 
+
+ align:start position:0%
+the formula has the there was powers of
+a beam of the magic number so we start
+
+ align:start position:0%
+a beam of the magic number so we start
+ 
+
+ align:start position:0%
+a beam of the magic number so we start
+at start at the point b1 and follow this
+
+ align:start position:0%
+at start at the point b1 and follow this
+ 
+
+ align:start position:0%
+at start at the point b1 and follow this
+path then the X's are the same B times
+
+ align:start position:0%
+path then the X's are the same B times
+ 
+
+ align:start position:0%
+path then the X's are the same B times
+this quantity to the case power and
+
+ align:start position:0%
+this quantity to the case power and
+ 
+
+ align:start position:0%
+this quantity to the case power and
+here's that quantity B minus 1 over B
+
+ align:start position:0%
+here's that quantity B minus 1 over B
+ 
+
+ align:start position:0%
+here's that quantity B minus 1 over B
+plus 1 so you see for a small B that's
+
+ align:start position:0%
+plus 1 so you see for a small B that's
+ 
+
+ align:start position:0%
+plus 1 so you see for a small B that's
+that's a negative number so it's
+
+ align:start position:0%
+that's a negative number so it's
+ 
+
+ align:start position:0%
+that's a negative number so it's
+flipping sign in the X's as we saw on
+
+ align:start position:0%
+flipping sign in the X's as we saw on
+ 
+
+ align:start position:0%
+flipping sign in the X's as we saw on
+the pictures
+
+ align:start position:0%
+the pictures
+ 
+
+ align:start position:0%
+the pictures
+leave that part of the picture is
+
+ align:start position:0%
+leave that part of the picture is
+ 
+
+ align:start position:0%
+leave that part of the picture is
+correct the Y's don't flip sign so this
+
+ align:start position:0%
+correct the Y's don't flip sign so this
+ 
+
+ align:start position:0%
+correct the Y's don't flip sign so this
+was XK and when K is 0 we got B YK is I
+
+ align:start position:0%
+was XK and when K is 0 we got B YK is I
+ 
+
+ align:start position:0%
+was XK and when K is 0 we got B YK is I
+think is is not flipping a sign so that
+
+ align:start position:0%
+think is is not flipping a sign so that
+ 
+
+ align:start position:0%
+think is is not flipping a sign so that
+looks good and then FK the value of F
+
+ align:start position:0%
+looks good and then FK the value of F
+ 
+
+ align:start position:0%
+looks good and then FK the value of F
+also was the same quantity
+
+ align:start position:0%
+also was the same quantity
+ 
+
+ align:start position:0%
+also was the same quantity
+FK is that same quantity to the case
+
+ align:start position:0%
+FK is that same quantity to the case
+ 
+
+ align:start position:0%
+FK is that same quantity to the case
+times f0
+
+ align:start position:0%
+times f0
+ 
+
+ align:start position:0%
+times f0
+so that quantity is all all-important
+
+ align:start position:0%
+so that quantity is all all-important
+ 
+
+ align:start position:0%
+so that quantity is all all-important
+and so the purpose of today's lecture is
+
+ align:start position:0%
+and so the purpose of today's lecture is
+ 
+
+ align:start position:0%
+and so the purpose of today's lecture is
+to tell you what the momentum term what
+
+ align:start position:0%
+to tell you what the momentum term what
+ 
+
+ align:start position:0%
+to tell you what the momentum term what
+improvement what change that brings in
+
+ align:start position:0%
+improvement what change that brings in
+ 
+
+ align:start position:0%
+improvement what change that brings in
+the basic steepest descent formula I'm
+
+ align:start position:0%
+the basic steepest descent formula I'm
+ 
+
+ align:start position:0%
+the basic steepest descent formula I'm
+gonna add on another term which is going
+
+ align:start position:0%
+gonna add on another term which is going
+ 
+
+ align:start position:0%
+gonna add on another term which is going
+to have some give us some memory of the
+
+ align:start position:0%
+to have some give us some memory of the
+ 
+
+ align:start position:0%
+to have some give us some memory of the
+previous step and so when I do that
+
+ align:start position:0%
+previous step and so when I do that
+ 
+
+ align:start position:0%
+previous step and so when I do that
+I want to track that kind of descent for
+
+ align:start position:0%
+I want to track that kind of descent for
+ 
+
+ align:start position:0%
+I want to track that kind of descent for
+for the new for the accelerated descent
+
+ align:start position:0%
+for the new for the accelerated descent
+ 
+
+ align:start position:0%
+for the new for the accelerated descent
+and track it and see what improvement
+
+ align:start position:0%
+and track it and see what improvement
+ 
+
+ align:start position:0%
+and track it and see what improvement
+the momentum term brings and so the
+
+ align:start position:0%
+the momentum term brings and so the
+ 
+
+ align:start position:0%
+the momentum term brings and so the
+final result will be to tell you the
+
+ align:start position:0%
+final result will be to tell you the
+ 
+
+ align:start position:0%
+final result will be to tell you the
+improvement in the produce by the
+
+ align:start position:0%
+improvement in the produce by the
+ 
+
+ align:start position:0%
+improvement in the produce by the
+momentum term maybe while I have your
+
+ align:start position:0%
+momentum term maybe while I have your
+ 
+
+ align:start position:0%
+momentum term maybe while I have your
+attention I'll tell you what it is now
+
+ align:start position:0%
+attention I'll tell you what it is now
+ 
+
+ align:start position:0%
+attention I'll tell you what it is now
+and then we'll come the details the
+
+ align:start position:0%
+and then we'll come the details the
+ 
+
+ align:start position:0%
+and then we'll come the details the
+algebra and to me so this is my own
+
+ align:start position:0%
+algebra and to me so this is my own
+ 
+
+ align:start position:0%
+algebra and to me so this is my own
+thought it's a miracle that the algebra
+
+ align:start position:0%
+thought it's a miracle that the algebra
+ 
+
+ align:start position:0%
+thought it's a miracle that the algebra
+which is straightforward you really see
+
+ align:start position:0%
+which is straightforward you really see
+ 
+
+ align:start position:0%
+which is straightforward you really see
+the value of eigenvectors
+
+ align:start position:0%
+the value of eigenvectors
+ 
+
+ align:start position:0%
+the value of eigenvectors
+you know we explain eigenvectors in
+
+ align:start position:0%
+you know we explain eigenvectors in
+ 
+
+ align:start position:0%
+you know we explain eigenvectors in
+class but but here you see why what how
+
+ align:start position:0%
+class but but here you see why what how
+ 
+
+ align:start position:0%
+class but but here you see why what how
+to use them that's is really a good
+
+ align:start position:0%
+to use them that's is really a good
+ 
+
+ align:start position:0%
+to use them that's is really a good
+exercise but to me it's a miracle that
+
+ align:start position:0%
+exercise but to me it's a miracle that
+ 
+
+ align:start position:0%
+exercise but to me it's a miracle that
+the expression with momentum is very
+
+ align:start position:0%
+the expression with momentum is very
+ 
+
+ align:start position:0%
+the expression with momentum is very
+much like that expression but different
+
+ align:start position:0%
+much like that expression but different
+ 
+
+ align:start position:0%
+much like that expression but different
+of course the the the decay is a term
+
+ align:start position:0%
+of course the the the decay is a term
+ 
+
+ align:start position:0%
+of course the the the decay is a term
+that tells you how fast the decay is is
+
+ align:start position:0%
+that tells you how fast the decay is is
+ 
+
+ align:start position:0%
+that tells you how fast the decay is is
+smaller so you're taking K power so so
+
+ align:start position:0%
+smaller so you're taking K power so so
+ 
+
+ align:start position:0%
+smaller so you're taking K power so so
+let me I'll write that down if that's
+
+ align:start position:0%
+let me I'll write that down if that's
+ 
+
+ align:start position:0%
+let me I'll write that down if that's
+all right it's I didn't plan to do to
+
+ align:start position:0%
+all right it's I didn't plan to do to
+ 
+
+ align:start position:0%
+all right it's I didn't plan to do to
+reveal the final result at the beginning
+
+ align:start position:0%
+reveal the final result at the beginning
+ 
+
+ align:start position:0%
+reveal the final result at the beginning
+of the lecture but I think you want to
+
+ align:start position:0%
+of the lecture but I think you want to
+ 
+
+ align:start position:0%
+of the lecture but I think you want to
+see where we're going so so with
+
+ align:start position:0%
+see where we're going so so with
+ 
+
+ align:start position:0%
+see where we're going so so with
+momentum and we have to see what that
+
+ align:start position:0%
+momentum and we have to see what that
+ 
+
+ align:start position:0%
+momentum and we have to see what that
+means this this term of 1 minus B over 1
+
+ align:start position:0%
+means this this term of 1 minus B over 1
+ 
+
+ align:start position:0%
+means this this term of 1 minus B over 1
+plus B becomes changes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one minus square root of B over 1 plus
+
+ align:start position:0%
+one minus square root of B over 1 plus
+ 
+
+ align:start position:0%
+one minus square root of B over 1 plus
+square would be so I mentioned that
+
+ align:start position:0%
+square would be so I mentioned that
+ 
+
+ align:start position:0%
+square would be so I mentioned that
+before but but I don't think I wrote it
+
+ align:start position:0%
+before but but I don't think I wrote it
+ 
+
+ align:start position:0%
+before but but I don't think I wrote it
+down just clearly so the miracle to me
+
+ align:start position:0%
+down just clearly so the miracle to me
+ 
+
+ align:start position:0%
+down just clearly so the miracle to me
+is to get such a nice expression for the
+
+ align:start position:0%
+is to get such a nice expression for the
+ 
+
+ align:start position:0%
+is to get such a nice expression for the
+because you'll see the algebra is it
+
+ align:start position:0%
+because you'll see the algebra is it
+ 
+
+ align:start position:0%
+because you'll see the algebra is it
+works but it's it's it involves more
+
+ align:start position:0%
+works but it's it's it involves more
+ 
+
+ align:start position:0%
+works but it's it's it involves more
+terms because of momentum involves doing
+
+ align:start position:0%
+terms because of momentum involves doing
+ 
+
+ align:start position:0%
+terms because of momentum involves doing
+a minimization of eigenvalues and yet it
+
+ align:start position:0%
+a minimization of eigenvalues and yet it
+ 
+
+ align:start position:0%
+a minimization of eigenvalues and yet it
+comes out nicely and and then you have
+
+ align:start position:0%
+comes out nicely and and then you have
+ 
+
+ align:start position:0%
+comes out nicely and and then you have
+to see the importance of that so let me
+
+ align:start position:0%
+to see the importance of that so let me
+ 
+
+ align:start position:0%
+to see the importance of that so let me
+I would just take the same example that
+
+ align:start position:0%
+I would just take the same example that
+ 
+
+ align:start position:0%
+I would just take the same example that
+I mentioned before if B is 1 over 100
+
+ align:start position:0%
+I mentioned before if B is 1 over 100
+ 
+
+ align:start position:0%
+I mentioned before if B is 1 over 100
+then this is 0.99 over 1.01 oh I think
+
+ align:start position:0%
+then this is 0.99 over 1.01 oh I think
+ 
+
+ align:start position:0%
+then this is 0.99 over 1.01 oh I think
+that these there's a square here 2 K so
+
+ align:start position:0%
+that these there's a square here 2 K so
+ 
+
+ align:start position:0%
+that these there's a square here 2 K so
+if we're so I'll I'll just keep this
+
+ align:start position:0%
+if we're so I'll I'll just keep this
+ 
+
+ align:start position:0%
+if we're so I'll I'll just keep this
+square there no big change but but I'm
+
+ align:start position:0%
+square there no big change but but I'm
+ 
+
+ align:start position:0%
+square there no big change but but I'm
+looking at now here at the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe maybe squares are everywhere you
+
+ align:start position:0%
+maybe maybe squares are everywhere you
+ 
+
+ align:start position:0%
+maybe maybe squares are everywhere you
+know ok so so that's close to 1 and now
+
+ align:start position:0%
+know ok so so that's close to 1 and now
+ 
+
+ align:start position:0%
+know ok so so that's close to 1 and now
+let's compare that with what we have so
+
+ align:start position:0%
+let's compare that with what we have so
+ 
+
+ align:start position:0%
+let's compare that with what we have so
+if B is 1 over 100 so I'm taking V to be
+
+ align:start position:0%
+if B is 1 over 100 so I'm taking V to be
+ 
+
+ align:start position:0%
+if B is 1 over 100 so I'm taking V to be
+1 over 100 then square root of B is 1
+
+ align:start position:0%
+1 over 100 then square root of B is 1
+ 
+
+ align:start position:0%
+1 over 100 then square root of B is 1
+over 10 so this is 0.9 0.9 over 1.1
+
+ align:start position:0%
+over 10 so this is 0.9 0.9 over 1.1
+ 
+
+ align:start position:0%
+over 10 so this is 0.9 0.9 over 1.1
+squared and there's a tremendous um
+
+ align:start position:0%
+squared and there's a tremendous um
+ 
+
+ align:start position:0%
+squared and there's a tremendous um
+block smaller than that is right
+
+ align:start position:0%
+block smaller than that is right
+ 
+
+ align:start position:0%
+block smaller than that is right
+9/10 9 9 / 11 compared to 99 over 101
+
+ align:start position:0%
+9/10 9 9 / 11 compared to 99 over 101
+ 
+
+ align:start position:0%
+9/10 9 9 / 11 compared to 99 over 101
+this one is you know is definitely oh
+
+ align:start position:0%
+this one is you know is definitely oh
+ 
+
+ align:start position:0%
+this one is you know is definitely oh
+sorry it's yeah it's this this reduction
+
+ align:start position:0%
+sorry it's yeah it's this this reduction
+ 
+
+ align:start position:0%
+sorry it's yeah it's this this reduction
+factor is well below that one so it's a
+
+ align:start position:0%
+factor is well below that one so it's a
+ 
+
+ align:start position:0%
+factor is well below that one so it's a
+good thing it's worth doing and okay
+
+ align:start position:0%
+good thing it's worth doing and okay
+ 
+
+ align:start position:0%
+good thing it's worth doing and okay
+now what is it involved okay so I'll
+
+ align:start position:0%
+now what is it involved okay so I'll
+ 
+
+ align:start position:0%
+now what is it involved okay so I'll
+write down the expression for the for
+
+ align:start position:0%
+write down the expression for the for
+ 
+
+ align:start position:0%
+write down the expression for the for
+the sarcastic here we go okay
+
+ align:start position:0%
+the sarcastic here we go okay
+ 
+
+ align:start position:0%
+the sarcastic here we go okay
+so here's one way to see it the new X is
+
+ align:start position:0%
+so here's one way to see it the new X is
+ 
+
+ align:start position:0%
+so here's one way to see it the new X is
+the old X minus the gradient and now
+
+ align:start position:0%
+the old X minus the gradient and now
+ 
+
+ align:start position:0%
+the old X minus the gradient and now
+comes an extra term which gives us a
+
+ align:start position:0%
+comes an extra term which gives us a
+ 
+
+ align:start position:0%
+comes an extra term which gives us a
+little memory well I'm sorry the the
+
+ align:start position:0%
+little memory well I'm sorry the the
+ 
+
+ align:start position:0%
+little memory well I'm sorry the the
+algebra is slightly nicer if I write it
+
+ align:start position:0%
+algebra is slightly nicer if I write it
+ 
+
+ align:start position:0%
+algebra is slightly nicer if I write it
+a little bit differently I'll create a
+
+ align:start position:0%
+a little bit differently I'll create a
+ 
+
+ align:start position:0%
+a little bit differently I'll create a
+new quantity ZK with a step size okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if I took ZK to be just the
+
+ align:start position:0%
+okay so if I took ZK to be just the
+ 
+
+ align:start position:0%
+okay so if I took ZK to be just the
+gradient that would be steepest descent
+
+ align:start position:0%
+gradient that would be steepest descent
+ 
+
+ align:start position:0%
+gradient that would be steepest descent
+nothing has changed but instead I'm
+
+ align:start position:0%
+nothing has changed but instead I'm
+ 
+
+ align:start position:0%
+nothing has changed but instead I'm
+gonna take ZK well its leading term will
+
+ align:start position:0%
+gonna take ZK well its leading term will
+ 
+
+ align:start position:0%
+gonna take ZK well its leading term will
+be the gradient but here comes the
+
+ align:start position:0%
+be the gradient but here comes the
+ 
+
+ align:start position:0%
+be the gradient but here comes the
+momentum term I add on a multiple beta
+
+ align:start position:0%
+momentum term I add on a multiple beta
+ 
+
+ align:start position:0%
+momentum term I add on a multiple beta
+one way to do it is of the previous Z so
+
+ align:start position:0%
+one way to do it is of the previous Z so
+ 
+
+ align:start position:0%
+one way to do it is of the previous Z so
+the Z is the search direction z is the
+
+ align:start position:0%
+the Z is the search direction z is the
+ 
+
+ align:start position:0%
+the Z is the search direction z is the
+gradient you're traveling it's the
+
+ align:start position:0%
+gradient you're traveling it's the
+ 
+
+ align:start position:0%
+gradient you're traveling it's the
+direction you're moving so it's
+
+ align:start position:0%
+direction you're moving so it's
+ 
+
+ align:start position:0%
+direction you're moving so it's
+different from that direction there that
+
+ align:start position:0%
+different from that direction there that
+ 
+
+ align:start position:0%
+different from that direction there that
+direction was the gradient this
+
+ align:start position:0%
+direction was the gradient this
+ 
+
+ align:start position:0%
+direction was the gradient this
+direction is the gradient correct
+
+ align:start position:0%
+direction is the gradient correct
+ 
+
+ align:start position:0%
+direction is the gradient correct
+corrected by a memory term a momentum
+
+ align:start position:0%
+corrected by a memory term a momentum
+ 
+
+ align:start position:0%
+corrected by a memory term a momentum
+term and one way to interpret that is to
+
+ align:start position:0%
+term and one way to interpret that is to
+ 
+
+ align:start position:0%
+term and one way to interpret that is to
+say that that ball is to think of a
+
+ align:start position:0%
+say that that ball is to think of a
+ 
+
+ align:start position:0%
+say that that ball is to think of a
+heavy ball instead of just a point I
+
+ align:start position:0%
+heavy ball instead of just a point I
+ 
+
+ align:start position:0%
+heavy ball instead of just a point I
+think of a heavy ball it instead of
+
+ align:start position:0%
+think of a heavy ball it instead of
+ 
+
+ align:start position:0%
+think of a heavy ball it instead of
+bouncing back and forth as as as as
+
+ align:start position:0%
+bouncing back and forth as as as as
+ 
+
+ align:start position:0%
+bouncing back and forth as as as as
+uselessly as this one it tends to
+
+ align:start position:0%
+uselessly as this one it tends to
+ 
+
+ align:start position:0%
+uselessly as this one it tends to
+it still bounces of course on the sides
+
+ align:start position:0%
+it still bounces of course on the sides
+ 
+
+ align:start position:0%
+it still bounces of course on the sides
+of the level sets but it comes down the
+
+ align:start position:0%
+of the level sets but it comes down the
+ 
+
+ align:start position:0%
+of the level sets but it comes down the
+valley faster and that's the effect of
+
+ align:start position:0%
+valley faster and that's the effect of
+ 
+
+ align:start position:0%
+valley faster and that's the effect of
+this so so you could play with different
+
+ align:start position:0%
+this so so you could play with different
+ 
+
+ align:start position:0%
+this so so you could play with different
+adjustment terms different Corrections
+
+ align:start position:0%
+adjustment terms different Corrections
+ 
+
+ align:start position:0%
+adjustment terms different Corrections
+so but I'll follow through this one
+
+ align:start position:0%
+so but I'll follow through this one
+ 
+
+ align:start position:0%
+so but I'll follow through this one
+Nesterov had another way to make a
+
+ align:start position:0%
+Nesterov had another way to make a
+ 
+
+ align:start position:0%
+Nesterov had another way to make a
+change in the formula and the there are
+
+ align:start position:0%
+change in the formula and the there are
+ 
+
+ align:start position:0%
+change in the formula and the there are
+certainly others beyond that okay
+
+ align:start position:0%
+certainly others beyond that okay
+ 
+
+ align:start position:0%
+certainly others beyond that okay
+so how do we analyze that one well
+
+ align:start position:0%
+so how do we analyze that one well
+ 
+
+ align:start position:0%
+so how do we analyze that one well
+they're the real point is we've sort of
+
+ align:start position:0%
+they're the real point is we've sort of
+ 
+
+ align:start position:0%
+they're the real point is we've sort of
+by taking by involving the previous step
+
+ align:start position:0%
+by taking by involving the previous step
+ 
+
+ align:start position:0%
+by taking by involving the previous step
+we now have a three level method instead
+
+ align:start position:0%
+we now have a three level method instead
+ 
+
+ align:start position:0%
+we now have a three level method instead
+of a two level method you could say
+
+ align:start position:0%
+of a two level method you could say
+ 
+
+ align:start position:0%
+of a two level method you could say
+there's this this involves only level k
+
+ align:start position:0%
+there's this this involves only level k
+ 
+
+ align:start position:0%
+there's this this involves only level k
+plus 1 and level K the formulas now
+
+ align:start position:0%
+plus 1 and level K the formulas now
+ 
+
+ align:start position:0%
+plus 1 and level K the formulas now
+involve k plus 1 k and k minus 1 it's
+
+ align:start position:0%
+involve k plus 1 k and k minus 1 it's
+ 
+
+ align:start position:0%
+involve k plus 1 k and k minus 1 it's
+just like going from a first-order
+
+ align:start position:0%
+just like going from a first-order
+ 
+
+ align:start position:0%
+just like going from a first-order
+differential equation to a second-order
+
+ align:start position:0%
+differential equation to a second-order
+ 
+
+ align:start position:0%
+differential equation to a second-order
+differential equation
+
+ align:start position:0%
+differential equation
+ 
+
+ align:start position:0%
+differential equation
+it's it's I'm not really thinking that K
+
+ align:start position:0%
+it's it's I'm not really thinking that K
+ 
+
+ align:start position:0%
+it's it's I'm not really thinking that K
+is a is a time variable but in the
+
+ align:start position:0%
+is a is a time variable but in the
+ 
+
+ align:start position:0%
+is a is a time variable but in the
+analogy K could be a time variable so
+
+ align:start position:0%
+analogy K could be a time variable so
+ 
+
+ align:start position:0%
+analogy K could be a time variable so
+that here we had like a first-order
+
+ align:start position:0%
+that here we had like a first-order
+ 
+
+ align:start position:0%
+that here we had like a first-order
+equation if I wanted to model that
+
+ align:start position:0%
+equation if I wanted to model that
+ 
+
+ align:start position:0%
+equation if I wanted to model that
+that's sort of a DX DT coming in there
+
+ align:start position:0%
+that's sort of a DX DT coming in there
+ 
+
+ align:start position:0%
+that's sort of a DX DT coming in there
+equal a gradient and and these models
+
+ align:start position:0%
+equal a gradient and and these models
+ 
+
+ align:start position:0%
+equal a gradient and and these models
+are highly useful and and developed for
+
+ align:start position:0%
+are highly useful and and developed for
+ 
+
+ align:start position:0%
+are highly useful and and developed for
+sort of a continuous model of steepest
+
+ align:start position:0%
+sort of a continuous model of steepest
+ 
+
+ align:start position:0%
+sort of a continuous model of steepest
+descent a continuous motion instead of
+
+ align:start position:0%
+descent a continuous motion instead of
+ 
+
+ align:start position:0%
+descent a continuous motion instead of
+the instead of the discrete motion okay
+
+ align:start position:0%
+the instead of the discrete motion okay
+ 
+
+ align:start position:0%
+the instead of the discrete motion okay
+so that would that's continuous model
+
+ align:start position:0%
+so that would that's continuous model
+ 
+
+ align:start position:0%
+so that would that's continuous model
+for that guy would be a first order in
+
+ align:start position:0%
+for that guy would be a first order in
+ 
+
+ align:start position:0%
+for that guy would be a first order in
+time for this one it'll be second order
+
+ align:start position:0%
+time for this one it'll be second order
+ 
+
+ align:start position:0%
+time for this one it'll be second order
+in time and second order equations of
+
+ align:start position:0%
+in time and second order equations of
+ 
+
+ align:start position:0%
+in time and second order equations of
+course and the be constant coefficients
+
+ align:start position:0%
+course and the be constant coefficients
+ 
+
+ align:start position:0%
+course and the be constant coefficients
+in our model problem and the thing about
+
+ align:start position:0%
+in our model problem and the thing about
+ 
+
+ align:start position:0%
+in our model problem and the thing about
+a second-order equation that we all know
+
+ align:start position:0%
+a second-order equation that we all know
+ 
+
+ align:start position:0%
+a second-order equation that we all know
+there's a momentum term a a damping term
+
+ align:start position:0%
+there's a momentum term a a damping term
+ 
+
+ align:start position:0%
+there's a momentum term a a damping term
+you could say in multiplying the first
+
+ align:start position:0%
+you could say in multiplying the first
+ 
+
+ align:start position:0%
+you could say in multiplying the first
+derivative so that's what that's what a
+
+ align:start position:0%
+derivative so that's what that's what a
+ 
+
+ align:start position:0%
+derivative so that's what that's what a
+second-order equation offers is the
+
+ align:start position:0%
+second-order equation offers is the
+ 
+
+ align:start position:0%
+second-order equation offers is the
+inclusion of a damping term which isn't
+
+ align:start position:0%
+inclusion of a damping term which isn't
+ 
+
+ align:start position:0%
+inclusion of a damping term which isn't
+present in the in the original
+
+ align:start position:0%
+present in the in the original
+ 
+
+ align:start position:0%
+present in the in the original
+first-order okay so how do we analyze
+
+ align:start position:0%
+first-order okay so how do we analyze
+ 
+
+ align:start position:0%
+first-order okay so how do we analyze
+this I have to so how do you analyze
+
+ align:start position:0%
+this I have to so how do you analyze
+ 
+
+ align:start position:0%
+this I have to so how do you analyze
+second-order differential equations you
+
+ align:start position:0%
+second-order differential equations you
+ 
+
+ align:start position:0%
+second-order differential equations you
+write them as a system of two first
+
+ align:start position:0%
+write them as a system of two first
+ 
+
+ align:start position:0%
+write them as a system of two first
+order equations so that's exactly what
+
+ align:start position:0%
+order equations so that's exactly what
+ 
+
+ align:start position:0%
+order equations so that's exactly what
+we're going to do here in the discrete
+
+ align:start position:0%
+we're going to do here in the discrete
+ 
+
+ align:start position:0%
+we're going to do here in the discrete
+case we're going to see of course we
+
+ align:start position:0%
+case we're going to see of course we
+ 
+
+ align:start position:0%
+case we're going to see of course we
+have two equations and their first order
+
+ align:start position:0%
+have two equations and their first order
+ 
+
+ align:start position:0%
+have two equations and their first order
+and and we can let me play with them for
+
+ align:start position:0%
+and and we can let me play with them for
+ 
+
+ align:start position:0%
+and and we can let me play with them for
+a moment to to make them good okay so
+
+ align:start position:0%
+a moment to to make them good okay so
+ 
+
+ align:start position:0%
+a moment to to make them good okay so
+I'm gonna have so this will go to 2
+
+ align:start position:0%
+I'm gonna have so this will go to 2
+ 
+
+ align:start position:0%
+I'm gonna have so this will go to 2
+first order equations in which the first
+
+ align:start position:0%
+first order equations in which the first
+ 
+
+ align:start position:0%
+first order equations in which the first
+one I'm just gonna copy XK plus 1 is XK
+
+ align:start position:0%
+one I'm just gonna copy XK plus 1 is XK
+ 
+
+ align:start position:0%
+one I'm just gonna copy XK plus 1 is XK
+minus at step size ZK whew yeah ok yeah
+
+ align:start position:0%
+minus at step size ZK whew yeah ok yeah
+ 
+
+ align:start position:0%
+minus at step size ZK whew yeah ok yeah
+ok time the previous times type here the
+
+ align:start position:0%
+ok time the previous times type here the
+ 
+
+ align:start position:0%
+ok time the previous times type here the
+the next time step on the left okay so I
+
+ align:start position:0%
+the next time step on the left okay so I
+ 
+
+ align:start position:0%
+the next time step on the left okay so I
+just copied that now this one I'm going
+
+ align:start position:0%
+just copied that now this one I'm going
+ 
+
+ align:start position:0%
+just copied that now this one I'm going
+to increase K by 1 so in order to have
+
+ align:start position:0%
+to increase K by 1 so in order to have
+ 
+
+ align:start position:0%
+to increase K by 1 so in order to have
+that looking to match this I'll write
+
+ align:start position:0%
+that looking to match this I'll write
+ 
+
+ align:start position:0%
+that looking to match this I'll write
+that as Z K plus 1 and I'll bring the
+
+ align:start position:0%
+that as Z K plus 1 and I'll bring the
+ 
+
+ align:start position:0%
+that as Z K plus 1 and I'll bring the
+case ain't grad F k plus 1 equal beta ZK
+
+ align:start position:0%
+case ain't grad F k plus 1 equal beta ZK
+ 
+
+ align:start position:0%
+case ain't grad F k plus 1 equal beta ZK
+that look with you I just in this in
+
+ align:start position:0%
+that look with you I just in this in
+ 
+
+ align:start position:0%
+that look with you I just in this in
+this thing instead of looking at it at
+
+ align:start position:0%
+this thing instead of looking at it at
+ 
+
+ align:start position:0%
+this thing instead of looking at it at
+ki I went to K plus 1 and I put the K
+
+ align:start position:0%
+ki I went to K plus 1 and I put the K
+ 
+
+ align:start position:0%
+ki I went to K plus 1 and I put the K
+plus 1 terms on one side okay so now I
+
+ align:start position:0%
+plus 1 terms on one side okay so now I
+ 
+
+ align:start position:0%
+plus 1 terms on one side okay so now I
+have a a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's see let's remember we're doing
+
+ align:start position:0%
+and let's see let's remember we're doing
+ 
+
+ align:start position:0%
+and let's see let's remember we're doing
+our the model we're doing is f equal up
+
+ align:start position:0%
+our the model we're doing is f equal up
+ 
+
+ align:start position:0%
+our the model we're doing is f equal up
+1/2 X transpose s X so the gradient of F
+
+ align:start position:0%
+1/2 X transpose s X so the gradient of F
+ 
+
+ align:start position:0%
+1/2 X transpose s X so the gradient of F
+is s X so what I've written there or
+
+ align:start position:0%
+is s X so what I've written there or
+ 
+
+ align:start position:0%
+is s X so what I've written there or
+gradient is really I know what that
+
+ align:start position:0%
+gradient is really I know what that
+ 
+
+ align:start position:0%
+gradient is really I know what that
+gradient is so that's really s xk plus
+
+ align:start position:0%
+gradient is so that's really s xk plus
+ 
+
+ align:start position:0%
+gradient is so that's really s xk plus
+okay okay how to analyze that what
+
+ align:start position:0%
+okay okay how to analyze that what
+ 
+
+ align:start position:0%
+okay okay how to analyze that what
+happens as K as K travels forward one
+
+ align:start position:0%
+happens as K as K travels forward one
+ 
+
+ align:start position:0%
+happens as K as K travels forward one
+two three four five we have a constant
+
+ align:start position:0%
+two three four five we have a constant
+ 
+
+ align:start position:0%
+two three four five we have a constant
+coefficient problem at every step the XZ
+
+ align:start position:0%
+coefficient problem at every step the XZ
+ 
+
+ align:start position:0%
+coefficient problem at every step the XZ
+variable is getting multiplied by a
+
+ align:start position:0%
+variable is getting multiplied by a
+ 
+
+ align:start position:0%
+variable is getting multiplied by a
+matrix so here's X Z at k plus 1 and
+
+ align:start position:0%
+matrix so here's X Z at k plus 1 and
+ 
+
+ align:start position:0%
+matrix so here's X Z at k plus 1 and
+over here will be X Z at step K and I
+
+ align:start position:0%
+over here will be X Z at step K and I
+ 
+
+ align:start position:0%
+over here will be X Z at step K and I
+just have to figure out what matrix is
+
+ align:start position:0%
+just have to figure out what matrix is
+ 
+
+ align:start position:0%
+just have to figure out what matrix is
+multiplying here and here okay and I
+
+ align:start position:0%
+multiplying here and here okay and I
+ 
+
+ align:start position:0%
+multiplying here and here okay and I
+guess here I see it if the first
+
+ align:start position:0%
+guess here I see it if the first
+ 
+
+ align:start position:0%
+guess here I see it if the first
+equation has a 1 and a minus s looks
+
+ align:start position:0%
+equation has a 1 and a minus s looks
+ 
+
+ align:start position:0%
+equation has a 1 and a minus s looks
+like in the first row and it has a beta
+
+ align:start position:0%
+like in the first row and it has a beta
+ 
+
+ align:start position:0%
+like in the first row and it has a beta
+in the second row and here the first
+
+ align:start position:0%
+in the second row and here the first
+ 
+
+ align:start position:0%
+in the second row and here the first
+equation has a 1 0 in that row and then
+
+ align:start position:0%
+equation has a 1 0 in that row and then
+ 
+
+ align:start position:0%
+equation has a 1 0 in that row and then
+a minus s I'll put in minus s
+
+ align:start position:0%
+a minus s I'll put in minus s
+ 
+
+ align:start position:0%
+a minus s I'll put in minus s
+multiplying XK plus 1 and then the one
+
+ align:start position:0%
+multiplying XK plus 1 and then the one
+ 
+
+ align:start position:0%
+multiplying XK plus 1 and then the one
+that multiplies ZK plus 1 is that all
+
+ align:start position:0%
+that multiplies ZK plus 1 is that all
+ 
+
+ align:start position:0%
+that multiplies ZK plus 1 is that all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry I've got 2 SS and I didn't draw
+
+ align:start position:0%
+sorry I've got 2 SS and I didn't draw
+ 
+
+ align:start position:0%
+sorry I've got 2 SS and I didn't draw
+that one didn't write that one in large
+
+ align:start position:0%
+that one didn't write that one in large
+ 
+
+ align:start position:0%
+that one didn't write that one in large
+enough and I'd plan to erase it anyway
+
+ align:start position:0%
+enough and I'd plan to erase it anyway
+ 
+
+ align:start position:0%
+enough and I'd plan to erase it anyway
+this is the this is the step size this
+
+ align:start position:0%
+this is the this is the step size this
+ 
+
+ align:start position:0%
+this is the this is the step size this
+this is the matrix but but it's it's not
+
+ align:start position:0%
+this is the matrix but but it's it's not
+ 
+
+ align:start position:0%
+this is the matrix but but it's it's not
+it's not quite fitting it's placed this
+
+ align:start position:0%
+it's not quite fitting it's placed this
+ 
+
+ align:start position:0%
+it's not quite fitting it's placed this
+is the point where I'm gonna use eigen
+
+ align:start position:0%
+is the point where I'm gonna use eigen
+ 
+
+ align:start position:0%
+is the point where I'm gonna use eigen
+values I'm gonna follow an I follow each
+
+ align:start position:0%
+values I'm gonna follow an I follow each
+ 
+
+ align:start position:0%
+values I'm gonna follow an I follow each
+eigen value that's the whole point when
+
+ align:start position:0%
+eigen value that's the whole point when
+ 
+
+ align:start position:0%
+eigen value that's the whole point when
+I follow each eigen value
+
+ align:start position:0%
+I follow each eigen value
+ 
+
+ align:start position:0%
+I follow each eigen value
+each eigenvector I should say I'll
+
+ align:start position:0%
+each eigenvector I should say I'll
+ 
+
+ align:start position:0%
+each eigenvector I should say I'll
+follow each eigenvector of s so let's
+
+ align:start position:0%
+follow each eigenvector of s so let's
+ 
+
+ align:start position:0%
+follow each eigenvector of s so let's
+let's do that so so I can vectors of s
+
+ align:start position:0%
+let's do that so so I can vectors of s
+ 
+
+ align:start position:0%
+let's do that so so I can vectors of s
+what are we gonna call those lambda
+
+ align:start position:0%
+what are we gonna call those lambda
+ 
+
+ align:start position:0%
+what are we gonna call those lambda
+probably so s X equal lambda X I think
+
+ align:start position:0%
+probably so s X equal lambda X I think
+ 
+
+ align:start position:0%
+probably so s X equal lambda X I think
+that's what's coming or Q I to do things
+
+ align:start position:0%
+that's what's coming or Q I to do things
+ 
+
+ align:start position:0%
+that's what's coming or Q I to do things
+right I want to remember that s is a
+
+ align:start position:0%
+right I want to remember that s is a
+ 
+
+ align:start position:0%
+right I want to remember that s is a
+positive definite symmetric matrix
+
+ align:start position:0%
+positive definite symmetric matrix
+ 
+
+ align:start position:0%
+positive definite symmetric matrix
+that's why I called it s instead of a so
+
+ align:start position:0%
+that's why I called it s instead of a so
+ 
+
+ align:start position:0%
+that's why I called it s instead of a so
+I really should call the eigen it
+
+ align:start position:0%
+I really should call the eigen it
+ 
+
+ align:start position:0%
+I really should call the eigen it
+doesn't matter but to be on the ball let
+
+ align:start position:0%
+doesn't matter but to be on the ball let
+ 
+
+ align:start position:0%
+doesn't matter but to be on the ball let
+me call the eigen vector Q and the eigen
+
+ align:start position:0%
+me call the eigen vector Q and the eigen
+ 
+
+ align:start position:0%
+me call the eigen vector Q and the eigen
+value lambda okay okay so now I want to
+
+ align:start position:0%
+value lambda okay okay so now I want to
+ 
+
+ align:start position:0%
+value lambda okay okay so now I want to
+I want to follow this eigen vector so
+
+ align:start position:0%
+I want to follow this eigen vector so
+ 
+
+ align:start position:0%
+I want to follow this eigen vector so
+I'm supposing that X K is some C K times
+
+ align:start position:0%
+I'm supposing that X K is some C K times
+ 
+
+ align:start position:0%
+I'm supposing that X K is some C K times
+Q I'm assuming that X is in the tracking
+
+ align:start position:0%
+Q I'm assuming that X is in the tracking
+ 
+
+ align:start position:0%
+Q I'm assuming that X is in the tracking
+this eigen vector and I'm gonna assume
+
+ align:start position:0%
+this eigen vector and I'm gonna assume
+ 
+
+ align:start position:0%
+this eigen vector and I'm gonna assume
+that ZK is some other constant times Q
+
+ align:start position:0%
+that ZK is some other constant times Q
+ 
+
+ align:start position:0%
+that ZK is some other constant times Q
+everybody do you see that's a vector and
+
+ align:start position:0%
+everybody do you see that's a vector and
+ 
+
+ align:start position:0%
+everybody do you see that's a vector and
+that's a vector and I want scalars I
+
+ align:start position:0%
+that's a vector and I want scalars I
+ 
+
+ align:start position:0%
+that's a vector and I want scalars I
+want to attract just scalar C K and D K
+
+ align:start position:0%
+want to attract just scalar C K and D K
+ 
+
+ align:start position:0%
+want to attract just scalar C K and D K
+so that's really what I have here is
+
+ align:start position:0%
+so that's really what I have here is
+ 
+
+ align:start position:0%
+so that's really what I have here is
+this was a little tricky because X here
+
+ align:start position:0%
+this was a little tricky because X here
+ 
+
+ align:start position:0%
+this was a little tricky because X here
+is a vector and two components are n
+
+ align:start position:0%
+is a vector and two components are n
+ 
+
+ align:start position:0%
+is a vector and two components are n
+components I didn't want that I really
+
+ align:start position:0%
+components I didn't want that I really
+ 
+
+ align:start position:0%
+components I didn't want that I really
+wanted just to track an eigen vector
+
+ align:start position:0%
+wanted just to track an eigen vector
+ 
+
+ align:start position:0%
+wanted just to track an eigen vector
+once I've settled on the direction Q
+
+ align:start position:0%
+once I've settled on the direction Q
+ 
+
+ align:start position:0%
+once I've settled on the direction Q
+everything is all vectors are in the
+
+ align:start position:0%
+everything is all vectors are in the
+ 
+
+ align:start position:0%
+everything is all vectors are in the
+direction of Q so so we just have
+
+ align:start position:0%
+direction of Q so so we just have
+ 
+
+ align:start position:0%
+direction of Q so so we just have
+numbers see indeed a track okay so I'm
+
+ align:start position:0%
+numbers see indeed a track okay so I'm
+ 
+
+ align:start position:0%
+numbers see indeed a track okay so I'm
+gonna rewrite this
+
+ align:start position:0%
+gonna rewrite this
+ 
+
+ align:start position:0%
+gonna rewrite this
+correctly as yeah well let me keep keep
+
+ align:start position:0%
+correctly as yeah well let me keep keep
+ 
+
+ align:start position:0%
+correctly as yeah well let me keep keep
+going with this little formula then what
+
+ align:start position:0%
+going with this little formula then what
+ 
+
+ align:start position:0%
+going with this little formula then what
+will I needed an SX what will s xk be if
+
+ align:start position:0%
+will I needed an SX what will s xk be if
+ 
+
+ align:start position:0%
+will I needed an SX what will s xk be if
+if xk is in the direction of the eigen
+
+ align:start position:0%
+if xk is in the direction of the eigen
+ 
+
+ align:start position:0%
+if xk is in the direction of the eigen
+vector Q and its CK what happens when I
+
+ align:start position:0%
+vector Q and its CK what happens when I
+ 
+
+ align:start position:0%
+vector Q and its CK what happens when I
+multiply by yes q was an eigen vector so
+
+ align:start position:0%
+multiply by yes q was an eigen vector so
+ 
+
+ align:start position:0%
+multiply by yes q was an eigen vector so
+the multiplying by s gives me I can
+
+ align:start position:0%
+the multiplying by s gives me I can
+ 
+
+ align:start position:0%
+the multiplying by s gives me I can
+value right so it's C K lambda Q
+
+ align:start position:0%
+value right so it's C K lambda Q
+ 
+
+ align:start position:0%
+value right so it's C K lambda Q
+everything is a multiple of Q and it's
+
+ align:start position:0%
+everything is a multiple of Q and it's
+ 
+
+ align:start position:0%
+everything is a multiple of Q and it's
+only those multiples I'm looking for the
+
+ align:start position:0%
+only those multiples I'm looking for the
+ 
+
+ align:start position:0%
+only those multiples I'm looking for the
+Seas and the DS and then the lambda
+
+ align:start position:0%
+Seas and the DS and then the lambda
+ 
+
+ align:start position:0%
+Seas and the DS and then the lambda
+comes into the S term yeah I think
+
+ align:start position:0%
+comes into the S term yeah I think
+ 
+
+ align:start position:0%
+comes into the S term yeah I think
+that's probably all I need to to do this
+
+ align:start position:0%
+that's probably all I need to to do this
+ 
+
+ align:start position:0%
+that's probably all I need to to do this
+and then the gradient yeah so that's the
+
+ align:start position:0%
+and then the gradient yeah so that's the
+ 
+
+ align:start position:0%
+and then the gradient yeah so that's the
+gradient of course this is the gradient
+
+ align:start position:0%
+gradient of course this is the gradient
+ 
+
+ align:start position:0%
+gradient of course this is the gradient
+of F okay so instead of this let me just
+
+ align:start position:0%
+of F okay so instead of this let me just
+ 
+
+ align:start position:0%
+of F okay so instead of this let me just
+write what's what's happening if I'm
+
+ align:start position:0%
+write what's what's happening if I'm
+ 
+
+ align:start position:0%
+write what's what's happening if I'm
+tracking the coefficients CK plus 1 and
+
+ align:start position:0%
+tracking the coefficients CK plus 1 and
+ 
+
+ align:start position:0%
+tracking the coefficients CK plus 1 and
+DK plus 1 then what I really meant to
+
+ align:start position:0%
+DK plus 1 then what I really meant to
+ 
+
+ align:start position:0%
+DK plus 1 then what I really meant to
+have there is 1 0 and minus s is a minus
+
+ align:start position:0%
+have there is 1 0 and minus s is a minus
+ 
+
+ align:start position:0%
+have there is 1 0 and minus s is a minus
+lambda is that right yeah when I
+
+ align:start position:0%
+lambda is that right yeah when I
+ 
+
+ align:start position:0%
+lambda is that right yeah when I
+multiply the eigenvector by s I'm just
+
+ align:start position:0%
+multiply the eigenvector by s I'm just
+ 
+
+ align:start position:0%
+multiply the eigenvector by s I'm just
+kidding oh it's a lambda times the CK
+
+ align:start position:0%
+kidding oh it's a lambda times the CK
+ 
+
+ align:start position:0%
+kidding oh it's a lambda times the CK
+yeah lambda times the CK that's good I
+
+ align:start position:0%
+yeah lambda times the CK that's good I
+ 
+
+ align:start position:0%
+yeah lambda times the CK that's good I
+think that that's the left-hand side of
+
+ align:start position:0%
+think that that's the left-hand side of
+ 
+
+ align:start position:0%
+think that that's the left-hand side of
+my equation and on the right hand side I
+
+ align:start position:0%
+my equation and on the right hand side I
+ 
+
+ align:start position:0%
+my equation and on the right hand side I
+have here that's 1 and this was the
+
+ align:start position:0%
+have here that's 1 and this was the
+ 
+
+ align:start position:0%
+have here that's 1 and this was the
+scalar the step size and this was the
+
+ align:start position:0%
+scalar the step size and this was the
+ 
+
+ align:start position:0%
+scalar the step size and this was the
+other coefficient it's the SN beta so I
+
+ align:start position:0%
+other coefficient it's the SN beta so I
+ 
+
+ align:start position:0%
+other coefficient it's the SN beta so I
+want to choose what's my purpose now
+
+ align:start position:0%
+want to choose what's my purpose now
+ 
+
+ align:start position:0%
+want to choose what's my purpose now
+that gives me the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens at every step to the C and
+
+ align:start position:0%
+what happens at every step to the C and
+ 
+
+ align:start position:0%
+what happens at every step to the C and
+D so I want to choose the land the the
+
+ align:start position:0%
+D so I want to choose the land the the
+ 
+
+ align:start position:0%
+D so I want to choose the land the the
+two things that I have I'm free to
+
+ align:start position:0%
+two things that I have I'm free to
+ 
+
+ align:start position:0%
+two things that I have I'm free to
+choose our s and beta so that's my big
+
+ align:start position:0%
+choose our s and beta so that's my big
+ 
+
+ align:start position:0%
+choose our s and beta so that's my big
+big job choose s and beta okay now I to
+
+ align:start position:0%
+big job choose s and beta okay now I to
+ 
+
+ align:start position:0%
+big job choose s and beta okay now I to
+make oh let me just shape this thing up
+
+ align:start position:0%
+make oh let me just shape this thing up
+ 
+
+ align:start position:0%
+make oh let me just shape this thing up
+by month by multiplying the inverse of
+
+ align:start position:0%
+by month by multiplying the inverse of
+ 
+
+ align:start position:0%
+by month by multiplying the inverse of
+that and get it over here so that well
+
+ align:start position:0%
+that and get it over here so that well
+ 
+
+ align:start position:0%
+that and get it over here so that well
+really you'll see everything so CK plus
+
+ align:start position:0%
+really you'll see everything so CK plus
+ 
+
+ align:start position:0%
+really you'll see everything so CK plus
+one DK plus one what's the inverse of
+
+ align:start position:0%
+one DK plus one what's the inverse of
+ 
+
+ align:start position:0%
+one DK plus one what's the inverse of
+one zero
+
+ align:start position:0%
+one zero
+ 
+
+ align:start position:0%
+one zero
+oh I don't think I wanna that would have
+
+ align:start position:0%
+oh I don't think I wanna that would have
+ 
+
+ align:start position:0%
+oh I don't think I wanna that would have
+a tough time finding an inverse it was a
+
+ align:start position:0%
+a tough time finding an inverse it was a
+ 
+
+ align:start position:0%
+a tough time finding an inverse it was a
+one wasn't it yeah okay so I want to
+
+ align:start position:0%
+one wasn't it yeah okay so I want to
+ 
+
+ align:start position:0%
+one wasn't it yeah okay so I want to
+multiply by the inverse of that matrix
+
+ align:start position:0%
+multiply by the inverse of that matrix
+ 
+
+ align:start position:0%
+multiply by the inverse of that matrix
+to get it over here and what's the
+
+ align:start position:0%
+to get it over here and what's the
+ 
+
+ align:start position:0%
+to get it over here and what's the
+inverse of 1 1 minus lamda it's 1 1 plus
+
+ align:start position:0%
+inverse of 1 1 minus lamda it's 1 1 plus
+ 
+
+ align:start position:0%
+inverse of 1 1 minus lamda it's 1 1 plus
+lambda so that the inverse brought it
+
+ align:start position:0%
+lambda so that the inverse brought it
+ 
+
+ align:start position:0%
+lambda so that the inverse brought it
+over here times this matrix 1 0 beta and
+
+ align:start position:0%
+over here times this matrix 1 0 beta and
+ 
+
+ align:start position:0%
+over here times this matrix 1 0 beta and
+minus the step size that's what
+
+ align:start position:0%
+minus the step size that's what
+ 
+
+ align:start position:0%
+minus the step size that's what
+multiplies C KD K so we have these
+
+ align:start position:0%
+multiplies C KD K so we have these
+ 
+
+ align:start position:0%
+multiplies C KD K so we have these
+simple beautiful steps which which come
+
+ align:start position:0%
+simple beautiful steps which which come
+ 
+
+ align:start position:0%
+simple beautiful steps which which come
+from tracking one eigenvector makes the
+
+ align:start position:0%
+from tracking one eigenvector makes the
+ 
+
+ align:start position:0%
+from tracking one eigenvector makes the
+whole problem scalar so I multiply those
+
+ align:start position:0%
+whole problem scalar so I multiply those
+ 
+
+ align:start position:0%
+whole problem scalar so I multiply those
+two matrices in our I finally get the
+
+ align:start position:0%
+two matrices in our I finally get the
+ 
+
+ align:start position:0%
+two matrices in our I finally get the
+matrix that I really have to think about
+
+ align:start position:0%
+matrix that I really have to think about
+ 
+
+ align:start position:0%
+matrix that I really have to think about
+1 0 times that'll be 1 minus s lambda 1
+
+ align:start position:0%
+1 0 times that'll be 1 minus s lambda 1
+ 
+
+ align:start position:0%
+1 0 times that'll be 1 minus s lambda 1
+times that will be a lambda there and
+
+ align:start position:0%
+times that will be a lambda there and
+ 
+
+ align:start position:0%
+times that will be a lambda there and
+minus lambda s plus beta beta minus
+
+ align:start position:0%
+minus lambda s plus beta beta minus
+ 
+
+ align:start position:0%
+minus lambda s plus beta beta minus
+lambda s that's the matrix that we see
+
+ align:start position:0%
+lambda s that's the matrix that we see
+ 
+
+ align:start position:0%
+lambda s that's the matrix that we see
+at every step let me call that matrix Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've done some algebra more than I
+
+ align:start position:0%
+so I've done some algebra more than I
+ 
+
+ align:start position:0%
+so I've done some algebra more than I
+would always do in a lecture but it's
+
+ align:start position:0%
+would always do in a lecture but it's
+ 
+
+ align:start position:0%
+would always do in a lecture but it's
+really my I wouldn't do it if it wasn't
+
+ align:start position:0%
+really my I wouldn't do it if it wasn't
+ 
+
+ align:start position:0%
+really my I wouldn't do it if it wasn't
+nice algebra what's the conclusion the
+
+ align:start position:0%
+nice algebra what's the conclusion the
+ 
+
+ align:start position:0%
+nice algebra what's the conclusion the
+conclusion is that with the momentum
+
+ align:start position:0%
+conclusion is that with the momentum
+ 
+
+ align:start position:0%
+conclusion is that with the momentum
+term with this number beta available to
+
+ align:start position:0%
+term with this number beta available to
+ 
+
+ align:start position:0%
+term with this number beta available to
+choose as well as s the step the
+
+ align:start position:0%
+choose as well as s the step the
+ 
+
+ align:start position:0%
+choose as well as s the step the
+coefficient of the eigenvalue
+
+ align:start position:0%
+coefficient of the eigenvalue
+ 
+
+ align:start position:0%
+coefficient of the eigenvalue
+eigenvector is multiplied at every step
+
+ align:start position:0%
+eigenvector is multiplied at every step
+ 
+
+ align:start position:0%
+eigenvector is multiplied at every step
+by that matrix r r is that matrix and of
+
+ align:start position:0%
+by that matrix r r is that matrix and of
+ 
+
+ align:start position:0%
+by that matrix r r is that matrix and of
+course that matrix involves the
+
+ align:start position:0%
+course that matrix involves the
+ 
+
+ align:start position:0%
+course that matrix involves the
+eigenvalue yep so we have to think about
+
+ align:start position:0%
+eigenvalue yep so we have to think about
+ 
+
+ align:start position:0%
+eigenvalue yep so we have to think about
+what what do we want to do now we want
+
+ align:start position:0%
+what what do we want to do now we want
+ 
+
+ align:start position:0%
+what what do we want to do now we want
+to choose beta and s to make our as
+
+ align:start position:0%
+to choose beta and s to make our as
+ 
+
+ align:start position:0%
+to choose beta and s to make our as
+small as possible right we want to make
+
+ align:start position:0%
+small as possible right we want to make
+ 
+
+ align:start position:0%
+small as possible right we want to make
+our as small as possible and we're free
+
+ align:start position:0%
+our as small as possible and we're free
+ 
+
+ align:start position:0%
+our as small as possible and we're free
+to choose beta and s but we but our
+
+ align:start position:0%
+to choose beta and s but we but our
+ 
+
+ align:start position:0%
+to choose beta and s but we but our
+depends on lambda so I'm going to make
+
+ align:start position:0%
+depends on lambda so I'm going to make
+ 
+
+ align:start position:0%
+depends on lambda so I'm going to make
+it as small as possible over the whole
+
+ align:start position:0%
+it as small as possible over the whole
+ 
+
+ align:start position:0%
+it as small as possible over the whole
+range of possible lambdas so so let me
+
+ align:start position:0%
+range of possible lambdas so so let me
+ 
+
+ align:start position:0%
+range of possible lambdas so so let me
+so now here we really go so we have
+
+ align:start position:0%
+so now here we really go so we have
+ 
+
+ align:start position:0%
+so now here we really go so we have
+lambda between some these are these are
+
+ align:start position:0%
+lambda between some these are these are
+ 
+
+ align:start position:0%
+lambda between some these are these are
+the eigen eigen value of s and what we
+
+ align:start position:0%
+the eigen eigen value of s and what we
+ 
+
+ align:start position:0%
+the eigen eigen value of s and what we
+know what's what's reasonable to know is
+
+ align:start position:0%
+know what's what's reasonable to know is
+ 
+
+ align:start position:0%
+know what's what's reasonable to know is
+a lower bound it's a positive this is a
+
+ align:start position:0%
+a lower bound it's a positive this is a
+ 
+
+ align:start position:0%
+a lower bound it's a positive this is a
+symmetric positive definite matrix a
+
+ align:start position:0%
+symmetric positive definite matrix a
+ 
+
+ align:start position:0%
+symmetric positive definite matrix a
+lower bound and an upper bound for
+
+ align:start position:0%
+lower bound and an upper bound for
+ 
+
+ align:start position:0%
+lower bound and an upper bound for
+example and M was B and M was one in
+
+ align:start position:0%
+example and M was B and M was one in
+ 
+
+ align:start position:0%
+example and M was B and M was one in
+that two-by-two problem and this is what
+
+ align:start position:0%
+that two-by-two problem and this is what
+ 
+
+ align:start position:0%
+that two-by-two problem and this is what
+we know that the eigen values are
+
+ align:start position:0%
+we know that the eigen values are
+ 
+
+ align:start position:0%
+we know that the eigen values are
+between M&M and the ratio of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m2m well if I buy right this is the this
+
+ align:start position:0%
+m2m well if I buy right this is the this
+ 
+
+ align:start position:0%
+m2m well if I buy right this is the this
+is the key quantity and what's it called
+
+ align:start position:0%
+is the key quantity and what's it called
+ 
+
+ align:start position:0%
+is the key quantity and what's it called
+lambda max divided by lambda min is the
+
+ align:start position:0%
+lambda max divided by lambda min is the
+ 
+
+ align:start position:0%
+lambda max divided by lambda min is the
+condition number right this is all
+
+ align:start position:0%
+condition number right this is all
+ 
+
+ align:start position:0%
+condition number right this is all
+sometimes written Kappa Greek letter
+
+ align:start position:0%
+sometimes written Kappa Greek letter
+ 
+
+ align:start position:0%
+sometimes written Kappa Greek letter
+Kappa the condition number of s and when
+
+ align:start position:0%
+Kappa the condition number of s and when
+ 
+
+ align:start position:0%
+Kappa the condition number of s and when
+that's big that then the problem is
+
+ align:start position:0%
+that's big that then the problem is
+ 
+
+ align:start position:0%
+that's big that then the problem is
+going to be harder when that's one that
+
+ align:start position:0%
+going to be harder when that's one that
+ 
+
+ align:start position:0%
+going to be harder when that's one that
+then the matrix is just a multiple of
+
+ align:start position:0%
+then the matrix is just a multiple of
+ 
+
+ align:start position:0%
+then the matrix is just a multiple of
+the identity matrix and the problem is
+
+ align:start position:0%
+the identity matrix and the problem is
+ 
+
+ align:start position:0%
+the identity matrix and the problem is
+trivial when this when when when capital
+
+ align:start position:0%
+trivial when this when when when capital
+ 
+
+ align:start position:0%
+trivial when this when when when capital
+in it m and small m are the same then
+
+ align:start position:0%
+in it m and small m are the same then
+ 
+
+ align:start position:0%
+in it m and small m are the same then
+that's saying that the largest and
+
+ align:start position:0%
+that's saying that the largest and
+ 
+
+ align:start position:0%
+that's saying that the largest and
+smallest eigen values are identical that
+
+ align:start position:0%
+smallest eigen values are identical that
+ 
+
+ align:start position:0%
+smallest eigen values are identical that
+that the matrix is a multiple of the
+
+ align:start position:0%
+that the matrix is a multiple of the
+ 
+
+ align:start position:0%
+that the matrix is a multiple of the
+identity that's the condition number one
+
+ align:start position:0%
+identity that's the condition number one
+ 
+
+ align:start position:0%
+identity that's the condition number one
+but but the bad one is when it's 1 over
+
+ align:start position:0%
+but but the bad one is when it's 1 over
+ 
+
+ align:start position:0%
+but but the bad one is when it's 1 over
+B in our example and it and that could
+
+ align:start position:0%
+B in our example and it and that could
+ 
+
+ align:start position:0%
+B in our example and it and that could
+be very large okay that's where we have
+
+ align:start position:0%
+be very large okay that's where we have
+ 
+
+ align:start position:0%
+be very large okay that's where we have
+a problem let me just insert about the
+
+ align:start position:0%
+a problem let me just insert about the
+ 
+
+ align:start position:0%
+a problem let me just insert about the
+ordinary gradient descent of course the
+
+ align:start position:0%
+ordinary gradient descent of course the
+ 
+
+ align:start position:0%
+ordinary gradient descent of course the
+textbooks find a estimate for how fast
+
+ align:start position:0%
+textbooks find a estimate for how fast
+ 
+
+ align:start position:0%
+textbooks find a estimate for how fast
+that is and of course it depends on that
+
+ align:start position:0%
+that is and of course it depends on that
+ 
+
+ align:start position:0%
+that is and of course it depends on that
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+yeah so it depends on that number and E
+
+ align:start position:0%
+yeah so it depends on that number and E
+ 
+
+ align:start position:0%
+yeah so it depends on that number and E
+right you exactly saw how it depended on
+
+ align:start position:0%
+right you exactly saw how it depended on
+ 
+
+ align:start position:0%
+right you exactly saw how it depended on
+that number right but now we have a
+
+ align:start position:0%
+that number right but now we have a
+ 
+
+ align:start position:0%
+that number right but now we have a
+different problem and we're gonna finish
+
+ align:start position:0%
+different problem and we're gonna finish
+ 
+
+ align:start position:0%
+different problem and we're gonna finish
+it okay so what's my job I'm gonna
+
+ align:start position:0%
+it okay so what's my job I'm gonna
+ 
+
+ align:start position:0%
+it okay so what's my job I'm gonna
+choose s and beta to get to keep the the
+
+ align:start position:0%
+choose s and beta to get to keep the the
+ 
+
+ align:start position:0%
+choose s and beta to get to keep the the
+eigen values of R so let's give the
+
+ align:start position:0%
+eigen values of R so let's give the
+ 
+
+ align:start position:0%
+eigen values of R so let's give the
+eigen values of RNA so R let's say R has
+
+ align:start position:0%
+eigen values of RNA so R let's say R has
+ 
+
+ align:start position:0%
+eigen values of RNA so R let's say R has
+eigen values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+II won that depends on on the lambda and
+
+ align:start position:0%
+II won that depends on on the lambda and
+ 
+
+ align:start position:0%
+II won that depends on on the lambda and
+the s and the beta and E - so those are
+
+ align:start position:0%
+the s and the beta and E - so those are
+ 
+
+ align:start position:0%
+the s and the beta and E - so those are
+the eigenvalues of our just giving a
+
+ align:start position:0%
+the eigenvalues of our just giving a
+ 
+
+ align:start position:0%
+the eigenvalues of our just giving a
+letter to to them so what's our job we
+
+ align:start position:0%
+letter to to them so what's our job we
+ 
+
+ align:start position:0%
+letter to to them so what's our job we
+want to choose s and beta to make those
+
+ align:start position:0%
+want to choose s and beta to make those
+ 
+
+ align:start position:0%
+want to choose s and beta to make those
+eigenvalues as small as possible right
+
+ align:start position:0%
+eigenvalues as small as possible right
+ 
+
+ align:start position:0%
+eigenvalues as small as possible right
+small eigenvalues if r has small
+
+ align:start position:0%
+small eigenvalues if r has small
+ 
+
+ align:start position:0%
+small eigenvalues if r has small
+eigenvalues its powers see we ever every
+
+ align:start position:0%
+eigenvalues its powers see we ever every
+ 
+
+ align:start position:0%
+eigenvalues its powers see we ever every
+step multiplies by r so the convergence
+
+ align:start position:0%
+step multiplies by r so the convergence
+ 
+
+ align:start position:0%
+step multiplies by r so the convergence
+rate with momentum is depends on the
+
+ align:start position:0%
+rate with momentum is depends on the
+ 
+
+ align:start position:0%
+rate with momentum is depends on the
+powers of our getting small fast it
+
+ align:start position:0%
+powers of our getting small fast it
+ 
+
+ align:start position:0%
+powers of our getting small fast it
+depends on the eigenvalues being small
+
+ align:start position:0%
+depends on the eigenvalues being small
+ 
+
+ align:start position:0%
+depends on the eigenvalues being small
+we want to minimize the largest
+
+ align:start position:0%
+we want to minimize the largest
+ 
+
+ align:start position:0%
+we want to minimize the largest
+eigenvalue so I'll say the maximum of e
+
+ align:start position:0%
+eigenvalue so I'll say the maximum of e
+ 
+
+ align:start position:0%
+eigenvalue so I'll say the maximum of e
+1 and each and E 2 that's our job
+
+ align:start position:0%
+1 and each and E 2 that's our job
+ 
+
+ align:start position:0%
+1 and each and E 2 that's our job
+minimize we want to choose s and beta to
+
+ align:start position:0%
+minimize we want to choose s and beta to
+ 
+
+ align:start position:0%
+minimize we want to choose s and beta to
+minimize the largest eigenvalue because
+
+ align:start position:0%
+minimize the largest eigenvalue because
+ 
+
+ align:start position:0%
+minimize the largest eigenvalue because
+if there's one small eigenvalue but the
+
+ align:start position:0%
+if there's one small eigenvalue but the
+ 
+
+ align:start position:0%
+if there's one small eigenvalue but the
+other is big then the other one is going
+
+ align:start position:0%
+other is big then the other one is going
+ 
+
+ align:start position:0%
+other is big then the other one is going
+to kill us so we have to get both
+
+ align:start position:0%
+to kill us so we have to get both
+ 
+
+ align:start position:0%
+to kill us so we have to get both
+eigenvalues down and of course those
+
+ align:start position:0%
+eigenvalues down and of course those
+ 
+
+ align:start position:0%
+eigenvalues down and of course those
+depend on lambda e 1 depends on lambda
+
+ align:start position:0%
+depend on lambda e 1 depends on lambda
+ 
+
+ align:start position:0%
+depend on lambda e 1 depends on lambda
+so we have a little algebra problem and
+
+ align:start position:0%
+so we have a little algebra problem and
+ 
+
+ align:start position:0%
+so we have a little algebra problem and
+this is what I described as a miracle
+
+ align:start position:0%
+this is what I described as a miracle
+ 
+
+ align:start position:0%
+this is what I described as a miracle
+the fact that this little algebra
+
+ align:start position:0%
+the fact that this little algebra
+ 
+
+ align:start position:0%
+the fact that this little algebra
+problem the eigenvalues of that matrix
+
+ align:start position:0%
+problem the eigenvalues of that matrix
+ 
+
+ align:start position:0%
+problem the eigenvalues of that matrix
+e1 and e2 which depend on lambda in some
+
+ align:start position:0%
+e1 and e2 which depend on lambda in some
+ 
+
+ align:start position:0%
+e1 and e2 which depend on lambda in some
+in some way and we want to make both e1
+
+ align:start position:0%
+in some way and we want to make both e1
+ 
+
+ align:start position:0%
+in some way and we want to make both e1
+and e2 small the maximum of those of
+
+ align:start position:0%
+and e2 small the maximum of those of
+ 
+
+ align:start position:0%
+and e2 small the maximum of those of
+them and we have to do it for all the
+
+ align:start position:0%
+them and we have to do it for all the
+ 
+
+ align:start position:0%
+them and we have to do it for all the
+eigen all the eigenvalues lambda because
+
+ align:start position:0%
+eigen all the eigenvalues lambda because
+ 
+
+ align:start position:0%
+eigen all the eigenvalues lambda because
+we have to we're now thinking we've been
+
+ align:start position:0%
+we have to we're now thinking we've been
+ 
+
+ align:start position:0%
+we have to we're now thinking we've been
+tracking each eigenvector so that gave
+
+ align:start position:0%
+tracking each eigenvector so that gave
+ 
+
+ align:start position:0%
+tracking each eigenvector so that gave
+us 1 so this is for all possible lambda
+
+ align:start position:0%
+us 1 so this is for all possible lambda
+ 
+
+ align:start position:0%
+us 1 so this is for all possible lambda
+oh so we have to decide what do I mean
+
+ align:start position:0%
+oh so we have to decide what do I mean
+ 
+
+ align:start position:0%
+oh so we have to decide what do I mean
+by all pasta
+
+ align:start position:0%
+by all pasta
+ 
+
+ align:start position:0%
+by all pasta
+lambda and I mean all lambda that are
+
+ align:start position:0%
+lambda and I mean all lambda that are
+ 
+
+ align:start position:0%
+lambda and I mean all lambda that are
+between some M&M there is a beautiful
+
+ align:start position:0%
+between some M&M there is a beautiful
+ 
+
+ align:start position:0%
+between some M&M there is a beautiful
+problem you have a two-by-two matrix you
+
+ align:start position:0%
+problem you have a two-by-two matrix you
+ 
+
+ align:start position:0%
+problem you have a two-by-two matrix you
+can find it it find its eigenvalues its
+
+ align:start position:0%
+can find it it find its eigenvalues its
+ 
+
+ align:start position:0%
+can find it it find its eigenvalues its
+it they depend on lambda and what we all
+
+ align:start position:0%
+it they depend on lambda and what we all
+ 
+
+ align:start position:0%
+it they depend on lambda and what we all
+we know about lambda is it's between m
+
+ align:start position:0%
+we know about lambda is it's between m
+ 
+
+ align:start position:0%
+we know about lambda is it's between m
+and and capya and also they also depend
+
+ align:start position:0%
+and and capya and also they also depend
+ 
+
+ align:start position:0%
+and and capya and also they also depend
+on s and beta the two parameters we can
+
+ align:start position:0%
+on s and beta the two parameters we can
+ 
+
+ align:start position:0%
+on s and beta the two parameters we can
+choose and we want to choose those
+
+ align:start position:0%
+choose and we want to choose those
+ 
+
+ align:start position:0%
+choose and we want to choose those
+parameters so that for for all the all
+
+ align:start position:0%
+parameters so that for for all the all
+ 
+
+ align:start position:0%
+parameters so that for for all the all
+the possible eigenvalues the larger of
+
+ align:start position:0%
+the possible eigenvalues the larger of
+ 
+
+ align:start position:0%
+the possible eigenvalues the larger of
+the two eigenvalues will be as small as
+
+ align:start position:0%
+the two eigenvalues will be as small as
+ 
+
+ align:start position:0%
+the two eigenvalues will be as small as
+possible that's it's a little bit of
+
+ align:start position:0%
+possible that's it's a little bit of
+ 
+
+ align:start position:0%
+possible that's it's a little bit of
+algebra but it's do you see that that's
+
+ align:start position:0%
+algebra but it's do you see that that's
+ 
+
+ align:start position:0%
+algebra but it's do you see that that's
+the tricky that I shouldn't say tricky
+
+ align:start position:0%
+the tricky that I shouldn't say tricky
+ 
+
+ align:start position:0%
+the tricky that I shouldn't say tricky
+because it comes out that's that this is
+
+ align:start position:0%
+because it comes out that's that this is
+ 
+
+ align:start position:0%
+because it comes out that's that this is
+the one that is a miracle in the in the
+
+ align:start position:0%
+the one that is a miracle in the in the
+ 
+
+ align:start position:0%
+the one that is a miracle in the in the
+simplicity of the solution okay and I'm
+
+ align:start position:0%
+simplicity of the solution okay and I'm
+ 
+
+ align:start position:0%
+simplicity of the solution okay and I'm
+gonna effect maybe I'll move over here
+
+ align:start position:0%
+gonna effect maybe I'll move over here
+ 
+
+ align:start position:0%
+gonna effect maybe I'll move over here
+to write the answer okay and I just want
+
+ align:start position:0%
+to write the answer okay and I just want
+ 
+
+ align:start position:0%
+to write the answer okay and I just want
+to say that miracles don't happen so
+
+ align:start position:0%
+to say that miracles don't happen so
+ 
+
+ align:start position:0%
+to say that miracles don't happen so
+often in math there's you know all of
+
+ align:start position:0%
+often in math there's you know all of
+ 
+
+ align:start position:0%
+often in math there's you know all of
+mathematics the whole point of math is
+
+ align:start position:0%
+mathematics the whole point of math is
+ 
+
+ align:start position:0%
+mathematics the whole point of math is
+to explain miracles so there is a
+
+ align:start position:0%
+to explain miracles so there is a
+ 
+
+ align:start position:0%
+to explain miracles so there is a
+there's something to explain here and I
+
+ align:start position:0%
+there's something to explain here and I
+ 
+
+ align:start position:0%
+there's something to explain here and I
+don't have my finger on it yet because
+
+ align:start position:0%
+don't have my finger on it yet because
+ 
+
+ align:start position:0%
+don't have my finger on it yet because
+anyway it happens so let me tell you
+
+ align:start position:0%
+anyway it happens so let me tell you
+ 
+
+ align:start position:0%
+anyway it happens so let me tell you
+what the right s and the right beta and
+
+ align:start position:0%
+what the right s and the right beta and
+ 
+
+ align:start position:0%
+what the right s and the right beta and
+the resulting minimum eigen value are so
+
+ align:start position:0%
+the resulting minimum eigen value are so
+ 
+
+ align:start position:0%
+the resulting minimum eigen value are so
+again they depend on little m and Big M
+
+ align:start position:0%
+again they depend on little m and Big M
+ 
+
+ align:start position:0%
+again they depend on little m and Big M
+that's a very nice feature which we
+
+ align:start position:0%
+that's a very nice feature which we
+ 
+
+ align:start position:0%
+that's a very nice feature which we
+expect and that is and they depend on
+
+ align:start position:0%
+expect and that is and they depend on
+ 
+
+ align:start position:0%
+expect and that is and they depend on
+the ratio okay so that ratio alright
+
+ align:start position:0%
+the ratio okay so that ratio alright
+ 
+
+ align:start position:0%
+the ratio okay so that ratio alright
+let's let's see it okay so the best s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the S optimal has the formula two over
+
+ align:start position:0%
+the S optimal has the formula two over
+ 
+
+ align:start position:0%
+the S optimal has the formula two over
+square root of lambda max that's the
+
+ align:start position:0%
+square root of lambda max that's the
+ 
+
+ align:start position:0%
+square root of lambda max that's the
+square root of M and the square root of
+
+ align:start position:0%
+square root of M and the square root of
+ 
+
+ align:start position:0%
+square root of M and the square root of
+M Squared amazing okay and beta optimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turns out to be the square root of M
+
+ align:start position:0%
+turns out to be the square root of M
+ 
+
+ align:start position:0%
+turns out to be the square root of M
+minus the square root of little m over
+
+ align:start position:0%
+minus the square root of little m over
+ 
+
+ align:start position:0%
+minus the square root of little m over
+the square root of M plus the square
+
+ align:start position:0%
+the square root of M plus the square
+ 
+
+ align:start position:0%
+the square root of M plus the square
+root of little M all the squared of
+
+ align:start position:0%
+root of little M all the squared of
+ 
+
+ align:start position:0%
+root of little M all the squared of
+course we know what these numbers are 1
+
+ align:start position:0%
+course we know what these numbers are 1
+ 
+
+ align:start position:0%
+course we know what these numbers are 1
+and beta in our model problem that's
+
+ align:start position:0%
+and beta in our model problem that's
+ 
+
+ align:start position:0%
+and beta in our model problem that's
+where I'm gonna get this square root of
+
+ align:start position:0%
+where I'm gonna get this square root of
+ 
+
+ align:start position:0%
+where I'm gonna get this square root of
+this is 1 minus the square sorry B this
+
+ align:start position:0%
+this is 1 minus the square sorry B this
+ 
+
+ align:start position:0%
+this is 1 minus the square sorry B this
+is 1 minus the square root of B in fact
+
+ align:start position:0%
+is 1 minus the square root of B in fact
+ 
+
+ align:start position:0%
+is 1 minus the square root of B in fact
+ya for our for our example well let me
+
+ align:start position:0%
+ya for our for our example well let me
+ 
+
+ align:start position:0%
+ya for our for our example well let me
+just write what they would be 2 over 1
+
+ align:start position:0%
+just write what they would be 2 over 1
+ 
+
+ align:start position:0%
+just write what they would be 2 over 1
+plus square root of B Square and 1 minus
+
+ align:start position:0%
+plus square root of B Square and 1 minus
+ 
+
+ align:start position:0%
+plus square root of B Square and 1 minus
+would be over 1 plus square you see
+
+ align:start position:0%
+would be over 1 plus square you see
+ 
+
+ align:start position:0%
+would be over 1 plus square you see
+where this is 1 minus square root of B
+
+ align:start position:0%
+where this is 1 minus square root of B
+ 
+
+ align:start position:0%
+where this is 1 minus square root of B
+as a beginning to appear now it appears
+
+ align:start position:0%
+as a beginning to appear now it appears
+ 
+
+ align:start position:0%
+as a beginning to appear now it appears
+in the solution of this problem and then
+
+ align:start position:0%
+in the solution of this problem and then
+ 
+
+ align:start position:0%
+in the solution of this problem and then
+I have to tell you what the what how
+
+ align:start position:0%
+I have to tell you what the what how
+ 
+
+ align:start position:0%
+I have to tell you what the what how
+small did do these these optimal choices
+
+ align:start position:0%
+small did do these these optimal choices
+ 
+
+ align:start position:0%
+small did do these these optimal choices
+make the eigenvalues of our right this
+
+ align:start position:0%
+make the eigenvalues of our right this
+ 
+
+ align:start position:0%
+make the eigenvalues of our right this
+is what we're really paying attention to
+
+ align:start position:0%
+is what we're really paying attention to
+ 
+
+ align:start position:0%
+is what we're really paying attention to
+because it's the eigen values that that
+
+ align:start position:0%
+because it's the eigen values that that
+ 
+
+ align:start position:0%
+because it's the eigen values that that
+matrix tells us what happens at every
+
+ align:start position:0%
+matrix tells us what happens at every
+ 
+
+ align:start position:0%
+matrix tells us what happens at every
+step and the its eigen values have to be
+
+ align:start position:0%
+step and the its eigen values have to be
+ 
+
+ align:start position:0%
+step and the its eigen values have to be
+small to get fast convergence so how
+
+ align:start position:0%
+small to get fast convergence so how
+ 
+
+ align:start position:0%
+small to get fast convergence so how
+small are they well they involve this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it's the number that I've seen
+
+ align:start position:0%
+yeah so it's the number that I've seen
+ 
+
+ align:start position:0%
+yeah so it's the number that I've seen
+so so in this case the ease the
+
+ align:start position:0%
+so so in this case the ease the
+ 
+
+ align:start position:0%
+so so in this case the ease the
+eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of our that's the iterating matrix are
+
+ align:start position:0%
+of our that's the iterating matrix are
+ 
+
+ align:start position:0%
+of our that's the iterating matrix are
+below that now we're now you're gonna
+
+ align:start position:0%
+below that now we're now you're gonna
+ 
+
+ align:start position:0%
+below that now we're now you're gonna
+see that one - were to be over 1 plus
+
+ align:start position:0%
+see that one - were to be over 1 plus
+ 
+
+ align:start position:0%
+see that one - were to be over 1 plus
+we're to be I think maybe squared let me
+
+ align:start position:0%
+we're to be I think maybe squared let me
+ 
+
+ align:start position:0%
+we're to be I think maybe squared let me
+just see yeah yeah it happens to come
+
+ align:start position:0%
+just see yeah yeah it happens to come
+ 
+
+ align:start position:0%
+just see yeah yeah it happens to come
+out that number again so that's the
+
+ align:start position:0%
+out that number again so that's the
+ 
+
+ align:start position:0%
+out that number again so that's the
+conclusion that was the right choice of
+
+ align:start position:0%
+conclusion that was the right choice of
+ 
+
+ align:start position:0%
+conclusion that was the right choice of
+s and beta by adding this look-back term
+
+ align:start position:0%
+s and beta by adding this look-back term
+ 
+
+ align:start position:0%
+s and beta by adding this look-back term
+look back one step you get this
+
+ align:start position:0%
+look back one step you get this
+ 
+
+ align:start position:0%
+look back one step you get this
+improvement and it's it happens you see
+
+ align:start position:0%
+improvement and it's it happens you see
+ 
+
+ align:start position:0%
+improvement and it's it happens you see
+it in practice of course you'll see it
+
+ align:start position:0%
+it in practice of course you'll see it
+ 
+
+ align:start position:0%
+it in practice of course you'll see it
+exactly and so you you do the job to use
+
+ align:start position:0%
+exactly and so you you do the job to use
+ 
+
+ align:start position:0%
+exactly and so you you do the job to use
+momentum now I'm going to mention what
+
+ align:start position:0%
+momentum now I'm going to mention what
+ 
+
+ align:start position:0%
+momentum now I'm going to mention what
+the Nesterov Nesterov had a slightly
+
+ align:start position:0%
+the Nesterov Nesterov had a slightly
+ 
+
+ align:start position:0%
+the Nesterov Nesterov had a slightly
+different way to do it and i'll tell you
+
+ align:start position:0%
+different way to do it and i'll tell you
+ 
+
+ align:start position:0%
+different way to do it and i'll tell you
+what that is but it's the same idea get
+
+ align:start position:0%
+what that is but it's the same idea get
+ 
+
+ align:start position:0%
+what that is but it's the same idea get
+a second thing so let's see if I can
+
+ align:start position:0%
+a second thing so let's see if I can
+ 
+
+ align:start position:0%
+a second thing so let's see if I can
+find that yeah nestor oh ok ok here we
+
+ align:start position:0%
+find that yeah nestor oh ok ok here we
+ 
+
+ align:start position:0%
+find that yeah nestor oh ok ok here we
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+so let me bring Nestor offs a name down
+
+ align:start position:0%
+so let me bring Nestor offs a name down
+ 
+
+ align:start position:0%
+so let me bring Nestor offs a name down
+so that that's the basically what I
+
+ align:start position:0%
+so that that's the basically what I
+ 
+
+ align:start position:0%
+so that that's the basically what I
+wanted to say about number one and when
+
+ align:start position:0%
+wanted to say about number one and when
+ 
+
+ align:start position:0%
+wanted to say about number one and when
+you've seen this trough you'll see that
+
+ align:start position:0%
+you've seen this trough you'll see that
+ 
+
+ align:start position:0%
+you've seen this trough you'll see that
+it's a similar idea of involving the
+
+ align:start position:0%
+it's a similar idea of involving the
+ 
+
+ align:start position:0%
+it's a similar idea of involving the
+previous time value ok there are very
+
+ align:start position:0%
+previous time value ok there are very
+ 
+
+ align:start position:0%
+previous time value ok there are very
+popular methods in use now for machine
+
+ align:start position:0%
+popular methods in use now for machine
+ 
+
+ align:start position:0%
+popular methods in use now for machine
+learning that involves by a simple
+
+ align:start position:0%
+learning that involves by a simple
+ 
+
+ align:start position:0%
+learning that involves by a simple
+formula all the previous values by by
+
+ align:start position:0%
+formula all the previous values by by
+ 
+
+ align:start position:0%
+formula all the previous values by by
+sort of just by an addition of a bunch
+
+ align:start position:0%
+sort of just by an addition of a bunch
+ 
+
+ align:start position:0%
+sort of just by an addition of a bunch
+of terms so it's really it
+
+ align:start position:0%
+of terms so it's really it
+ 
+
+ align:start position:0%
+of terms so it's really it
+so it's it goes under the names ADA ADA
+
+ align:start position:0%
+so it's it goes under the names ADA ADA
+ 
+
+ align:start position:0%
+so it's it goes under the names ADA ADA
+grad or others those of you who already
+
+ align:start position:0%
+grad or others those of you who already
+ 
+
+ align:start position:0%
+grad or others those of you who already
+know about machine learning will know
+
+ align:start position:0%
+know about machine learning will know
+ 
+
+ align:start position:0%
+know about machine learning will know
+what I'm speaking about and I'll say
+
+ align:start position:0%
+what I'm speaking about and I'll say
+ 
+
+ align:start position:0%
+what I'm speaking about and I'll say
+more about those yeah but it doesn't
+
+ align:start position:0%
+more about those yeah but it doesn't
+ 
+
+ align:start position:0%
+more about those yeah but it doesn't
+involve a separate coefficient for each
+
+ align:start position:0%
+involve a separate coefficient for each
+ 
+
+ align:start position:0%
+involve a separate coefficient for each
+previous value or that would be a
+
+ align:start position:0%
+previous value or that would be a
+ 
+
+ align:start position:0%
+previous value or that would be a
+momentous amount of work so so now I
+
+ align:start position:0%
+momentous amount of work so so now I
+ 
+
+ align:start position:0%
+momentous amount of work so so now I
+just want to tell you what Nesterov is
+
+ align:start position:0%
+just want to tell you what Nesterov is
+ 
+
+ align:start position:0%
+just want to tell you what Nesterov is
+and then we were good ok mr. roffe's
+
+ align:start position:0%
+and then we were good ok mr. roffe's
+ 
+
+ align:start position:0%
+and then we were good ok mr. roffe's
+idea let me bring that down
+
+ align:start position:0%
+idea let me bring that down
+ 
+
+ align:start position:0%
+idea let me bring that down
+shoot this up bring down because he had
+
+ align:start position:0%
+shoot this up bring down because he had
+ 
+
+ align:start position:0%
+shoot this up bring down because he had
+an idea that you might not have thought
+
+ align:start position:0%
+an idea that you might not have thought
+ 
+
+ align:start position:0%
+an idea that you might not have thought
+of somehow the momentum idea was pretty
+
+ align:start position:0%
+of somehow the momentum idea was pretty
+ 
+
+ align:start position:0%
+of somehow the momentum idea was pretty
+natural to use that previous value and
+
+ align:start position:0%
+natural to use that previous value and
+ 
+
+ align:start position:0%
+natural to use that previous value and
+actually I would like to know what
+
+ align:start position:0%
+actually I would like to know what
+ 
+
+ align:start position:0%
+actually I would like to know what
+happens if you use two previous values
+
+ align:start position:0%
+happens if you use two previous values
+ 
+
+ align:start position:0%
+happens if you use two previous values
+or three previous values can you then
+
+ align:start position:0%
+or three previous values can you then
+ 
+
+ align:start position:0%
+or three previous values can you then
+get improvements on this this
+
+ align:start position:0%
+get improvements on this this
+ 
+
+ align:start position:0%
+get improvements on this this
+convergence rate by going back two steps
+
+ align:start position:0%
+convergence rate by going back two steps
+ 
+
+ align:start position:0%
+convergence rate by going back two steps
+or three steps if I use the analogy with
+
+ align:start position:0%
+or three steps if I use the analogy with
+ 
+
+ align:start position:0%
+or three steps if I use the analogy with
+ordinary differential equations maybe
+
+ align:start position:0%
+ordinary differential equations maybe
+ 
+
+ align:start position:0%
+ordinary differential equations maybe
+you know so right so so there are
+
+ align:start position:0%
+you know so right so so there are
+ 
+
+ align:start position:0%
+you know so right so so there are
+backward difference formulas do you know
+
+ align:start position:0%
+backward difference formulas do you know
+ 
+
+ align:start position:0%
+backward difference formulas do you know
+about those four those would be in
+
+ align:start position:0%
+about those four those would be in
+ 
+
+ align:start position:0%
+about those four those would be in
+MATLAB software and all other software
+
+ align:start position:0%
+MATLAB software and all other software
+ 
+
+ align:start position:0%
+MATLAB software and all other software
+backward differences so maybe you go
+
+ align:start position:0%
+backward differences so maybe you go
+ 
+
+ align:start position:0%
+backward differences so maybe you go
+back two steps or four steps if you're
+
+ align:start position:0%
+back two steps or four steps if you're
+ 
+
+ align:start position:0%
+back two steps or four steps if you're
+doing planetary calculations if you're
+
+ align:start position:0%
+doing planetary calculations if you're
+ 
+
+ align:start position:0%
+doing planetary calculations if you're
+an astronomer you go back maybe seven or
+
+ align:start position:0%
+an astronomer you go back maybe seven or
+ 
+
+ align:start position:0%
+an astronomer you go back maybe seven or
+eight steps to get super high accuracy
+
+ align:start position:0%
+eight steps to get super high accuracy
+ 
+
+ align:start position:0%
+eight steps to get super high accuracy
+so that doesn't seem to have happened
+
+ align:start position:0%
+so that doesn't seem to have happened
+ 
+
+ align:start position:0%
+so that doesn't seem to have happened
+yet but it should happen here to go back
+
+ align:start position:0%
+yet but it should happen here to go back
+ 
+
+ align:start position:0%
+yet but it should happen here to go back
+more but but Nesterov will has it has
+
+ align:start position:0%
+more but but Nesterov will has it has
+ 
+
+ align:start position:0%
+more but but Nesterov will has it has
+this different way to go back so his
+
+ align:start position:0%
+this different way to go back so his
+ 
+
+ align:start position:0%
+this different way to go back so his
+formula is XK plus one the new way
+
+ align:start position:0%
+formula is XK plus one the new way
+ 
+
+ align:start position:0%
+formula is XK plus one the new way
+is YK so he's introducing something a
+
+ align:start position:0%
+is YK so he's introducing something a
+ 
+
+ align:start position:0%
+is YK so he's introducing something a
+little different - s radiant f @ YK I'm
+
+ align:start position:0%
+little different - s radiant f @ YK I'm
+ 
+
+ align:start position:0%
+little different - s radiant f @ YK I'm
+a little surprised about that YK but
+
+ align:start position:0%
+a little surprised about that YK but
+ 
+
+ align:start position:0%
+a little surprised about that YK but
+this is the point here that the gradient
+
+ align:start position:0%
+this is the point here that the gradient
+ 
+
+ align:start position:0%
+this is the point here that the gradient
+is being evaluated at some different
+
+ align:start position:0%
+is being evaluated at some different
+ 
+
+ align:start position:0%
+is being evaluated at some different
+point and then he has to give a formula
+
+ align:start position:0%
+point and then he has to give a formula
+ 
+
+ align:start position:0%
+point and then he has to give a formula
+for that for those to track those wise
+
+ align:start position:0%
+for that for those to track those wise
+ 
+
+ align:start position:0%
+for that for those to track those wise
+so the Y's are like the X's but they're
+
+ align:start position:0%
+so the Y's are like the X's but they're
+ 
+
+ align:start position:0%
+so the Y's are like the X's but they're
+shifted a little bit by some term and
+
+ align:start position:0%
+shifted a little bit by some term and
+ 
+
+ align:start position:0%
+shifted a little bit by some term and
+beta would be fine Oh No yeah beta have
+
+ align:start position:0%
+beta would be fine Oh No yeah beta have
+ 
+
+ align:start position:0%
+beta would be fine Oh No yeah beta have
+we got Nesterov here yes mister off has
+
+ align:start position:0%
+we got Nesterov here yes mister off has
+ 
+
+ align:start position:0%
+we got Nesterov here yes mister off has
+a factor gamma in yeah so I all right
+
+ align:start position:0%
+a factor gamma in yeah so I all right
+ 
+
+ align:start position:0%
+a factor gamma in yeah so I all right
+let me let me try to get this right okay
+
+ align:start position:0%
+let me let me try to get this right okay
+ 
+
+ align:start position:0%
+let me let me try to get this right okay
+all right on the previous line I've
+
+ align:start position:0%
+all right on the previous line I've
+ 
+
+ align:start position:0%
+all right on the previous line I've
+written the whole nestdrop thing here
+
+ align:start position:0%
+written the whole nestdrop thing here
+ 
+
+ align:start position:0%
+written the whole nestdrop thing here
+let's see nice drop completely and then
+
+ align:start position:0%
+let's see nice drop completely and then
+ 
+
+ align:start position:0%
+let's see nice drop completely and then
+they'll break then this is the step that
+
+ align:start position:0%
+they'll break then this is the step that
+ 
+
+ align:start position:0%
+they'll break then this is the step that
+breaks it into two first order but
+
+ align:start position:0%
+breaks it into two first order but
+ 
+
+ align:start position:0%
+breaks it into two first order but
+you'll see the main formula here XK plus
+
+ align:start position:0%
+you'll see the main formula here XK plus
+ 
+
+ align:start position:0%
+you'll see the main formula here XK plus
+1 is XK and then a beta times XK minus
+
+ align:start position:0%
+1 is XK and then a beta times XK minus
+ 
+
+ align:start position:0%
+1 is XK and then a beta times XK minus
+XK minus 1 so that's like a momentum
+
+ align:start position:0%
+XK minus 1 so that's like a momentum
+ 
+
+ align:start position:0%
+XK minus 1 so that's like a momentum
+term and then a typical gradient but now
+
+ align:start position:0%
+term and then a typical gradient but now
+ 
+
+ align:start position:0%
+term and then a typical gradient but now
+here's Nesterov speaking up this trough
+
+ align:start position:0%
+here's Nesterov speaking up this trough
+ 
+
+ align:start position:0%
+here's Nesterov speaking up this trough
+evaluates the gradient not at XK not at
+
+ align:start position:0%
+evaluates the gradient not at XK not at
+ 
+
+ align:start position:0%
+evaluates the gradient not at XK not at
+XK minus 1 but it is home mr. Oz point
+
+ align:start position:0%
+XK minus 1 but it is home mr. Oz point
+ 
+
+ align:start position:0%
+XK minus 1 but it is home mr. Oz point
+like so this is Nesterov say my favorite
+
+ align:start position:0%
+like so this is Nesterov say my favorite
+ 
+
+ align:start position:0%
+like so this is Nesterov say my favorite
+point gamma XK minus XK minus 1 some
+
+ align:start position:0%
+point gamma XK minus XK minus 1 some
+ 
+
+ align:start position:0%
+point gamma XK minus XK minus 1 some
+point part way along that step so it so
+
+ align:start position:0%
+point part way along that step so it so
+ 
+
+ align:start position:0%
+point part way along that step so it so
+this point because gamma is going to be
+
+ align:start position:0%
+this point because gamma is going to be
+ 
+
+ align:start position:0%
+this point because gamma is going to be
+some non integer this evaluation point
+
+ align:start position:0%
+some non integer this evaluation point
+ 
+
+ align:start position:0%
+some non integer this evaluation point
+of for the gradient of F
+
+ align:start position:0%
+of for the gradient of F
+ 
+
+ align:start position:0%
+of for the gradient of F
+is a little unexpected and weird because
+
+ align:start position:0%
+is a little unexpected and weird because
+ 
+
+ align:start position:0%
+is a little unexpected and weird because
+it's not a mesh point it's somewhere
+
+ align:start position:0%
+it's not a mesh point it's somewhere
+ 
+
+ align:start position:0%
+it's not a mesh point it's somewhere
+between okay yep yep and then that so
+
+ align:start position:0%
+between okay yep yep and then that so
+ 
+
+ align:start position:0%
+between okay yep yep and then that so
+that involves XK plus 1 XK and XK minus
+
+ align:start position:0%
+that involves XK plus 1 XK and XK minus
+ 
+
+ align:start position:0%
+that involves XK plus 1 XK and XK minus
+1 so it's a second-order there's a
+
+ align:start position:0%
+1 so it's a second-order there's a
+ 
+
+ align:start position:0%
+1 so it's a second-order there's a
+second-order method here we're going to
+
+ align:start position:0%
+second-order method here we're going to
+ 
+
+ align:start position:0%
+second-order method here we're going to
+it to analyze it we're going to go
+
+ align:start position:0%
+it to analyze it we're going to go
+ 
+
+ align:start position:0%
+it to analyze it we're going to go
+through this same process of writing it
+
+ align:start position:0%
+through this same process of writing it
+ 
+
+ align:start position:0%
+through this same process of writing it
+as two first-order steps to first two
+
+ align:start position:0%
+as two first-order steps to first two
+ 
+
+ align:start position:0%
+as two first-order steps to first two
+single step to one step from k to k plus
+
+ align:start position:0%
+single step to one step from k to k plus
+ 
+
+ align:start position:0%
+single step to one step from k to k plus
+1 a a coupled one-step thing follow that
+
+ align:start position:0%
+1 a a coupled one-step thing follow that
+ 
+
+ align:start position:0%
+1 a a coupled one-step thing follow that
+same thing through and then the result
+
+ align:start position:0%
+same thing through and then the result
+ 
+
+ align:start position:0%
+same thing through and then the result
+is a same factor appears for him
+
+ align:start position:0%
+is a same factor appears for him
+ 
+
+ align:start position:0%
+is a same factor appears for him
+the same factor this is also so this the
+
+ align:start position:0%
+the same factor this is also so this the
+ 
+
+ align:start position:0%
+the same factor this is also so this the
+point is this is for momentum and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nesterov with with some with some
+
+ align:start position:0%
+Nesterov with with some with some
+ 
+
+ align:start position:0%
+Nesterov with with some with some
+constant difference different by some
+
+ align:start position:0%
+constant difference different by some
+ 
+
+ align:start position:0%
+constant difference different by some
+constant but the key quantity is that
+
+ align:start position:0%
+constant but the key quantity is that
+ 
+
+ align:start position:0%
+constant but the key quantity is that
+one and that appears in both so so so I
+
+ align:start position:0%
+one and that appears in both so so so I
+ 
+
+ align:start position:0%
+one and that appears in both so so so I
+don't propose of course to repeat these
+
+ align:start position:0%
+don't propose of course to repeat these
+ 
+
+ align:start position:0%
+don't propose of course to repeat these
+steps for an ester off but you see what
+
+ align:start position:0%
+steps for an ester off but you see what
+ 
+
+ align:start position:0%
+steps for an ester off but you see what
+you see what you could do you see that
+
+ align:start position:0%
+you see what you could do you see that
+ 
+
+ align:start position:0%
+you see what you could do you see that
+it involves K minus 1 K in k plus 1 you
+
+ align:start position:0%
+it involves K minus 1 K in k plus 1 you
+ 
+
+ align:start position:0%
+it involves K minus 1 K in k plus 1 you
+write it as you follow an eigen vector
+
+ align:start position:0%
+write it as you follow an eigen vector
+ 
+
+ align:start position:0%
+write it as you follow an eigen vector
+you write it as a coupled system of
+
+ align:start position:0%
+you write it as a coupled system of
+ 
+
+ align:start position:0%
+you write it as a coupled system of
+that's a one-step that has a matrix you
+
+ align:start position:0%
+that's a one-step that has a matrix you
+ 
+
+ align:start position:0%
+that's a one-step that has a matrix you
+find the matrix you find the eigen
+
+ align:start position:0%
+find the matrix you find the eigen
+ 
+
+ align:start position:0%
+find the matrix you find the eigen
+values of the matrix you make those
+
+ align:start position:0%
+values of the matrix you make those
+ 
+
+ align:start position:0%
+values of the matrix you make those
+eigenvalues as small as possible and you
+
+ align:start position:0%
+eigenvalues as small as possible and you
+ 
+
+ align:start position:0%
+eigenvalues as small as possible and you
+have optimized their coefficients in
+
+ align:start position:0%
+have optimized their coefficients in
+ 
+
+ align:start position:0%
+have optimized their coefficients in
+Nesterov ok that's that's sort of a lot
+
+ align:start position:0%
+Nesterov ok that's that's sort of a lot
+ 
+
+ align:start position:0%
+Nesterov ok that's that's sort of a lot
+of algebra that's at the heart of
+
+ align:start position:0%
+of algebra that's at the heart of
+ 
+
+ align:start position:0%
+of algebra that's at the heart of
+accelerated gradient descent and of
+
+ align:start position:0%
+accelerated gradient descent and of
+ 
+
+ align:start position:0%
+accelerated gradient descent and of
+course it's worth doing because it's a
+
+ align:start position:0%
+course it's worth doing because it's a
+ 
+
+ align:start position:0%
+course it's worth doing because it's a
+tremendous saving in the in the in the
+
+ align:start position:0%
+tremendous saving in the in the in the
+ 
+
+ align:start position:0%
+tremendous saving in the in the in the
+convergence rate ok anybody running in
+
+ align:start position:0%
+convergence rate ok anybody running in
+ 
+
+ align:start position:0%
+convergence rate ok anybody running in
+the marathon or just watching it's
+
+ align:start position:0%
+the marathon or just watching it's
+ 
+
+ align:start position:0%
+the marathon or just watching it's
+possible to run you know anyway I'll see
+
+ align:start position:0%
+possible to run you know anyway I'll see
+ 
+
+ align:start position:0%
+possible to run you know anyway I'll see
+you after the marathon next Wednesday
+
+ align:start position:0%
+you after the marathon next Wednesday
+ 
+
+ align:start position:0%
+you after the marathon next Wednesday
+and professor Boyd will also see you
\ No newline at end of file
diff --git a/xSQxaie_h1o.txt b/xSQxaie_h1o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..965867bf7f111a6633bb4bdda1cf2b2b2a68f8b9
--- /dev/null
+++ b/xSQxaie_h1o.txt
@@ -0,0 +1,4835 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation, or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right,
+let's get started.
+
+So welcome to the next
+lecture about exploiting
+
+buffer overflow.
+
+So today, what we're
+going to do is,
+
+we're going to finish up our
+discussion about baggy bounds
+
+and then we're going
+to move on to a couple
+
+of other different techniques
+for protecting its buffer
+
+overflows.
+
+Then we're going to talk
+about the paper for today,
+
+which is the blind return
+oriented programming.
+
+So if you were like me when
+you first read that paper
+
+you kind of felt like you were
+watching like a Christopher
+
+Nolan movie at the beginning.
+
+It was kind of like
+mind blowing right.
+
+So what we're going
+to do is we're
+
+going to actually step through
+how some of these gadgets
+
+work right.
+
+And so hopefully
+by the end, you'll
+
+be able to understand all this
+sort of high tech chicanery
+
+that they're doing in the paper.
+
+So first of all,
+like I said, let's
+
+just close up with the
+baggy bounds discussions.
+
+Let's go through a very
+simple example here.
+
+So let's say that we're going
+to define a pointer called P.
+
+And let's say that
+we're going to give it
+
+allocation size of 44.
+
+Let's also assume that the
+slot size equals 16 bytes OK.
+
+So what's going to happen when
+we do this malloc up here?
+
+So as you know, the
+baggy bounds system
+
+is going to pad that allocation
+out to the next power of two,
+
+right.
+
+So even though we've only
+allocated 44 bytes here,
+
+we're actually going to allocate
+64 bytes for this pointer
+
+up here.
+
+And so also note too, this
+is the slot size is 16.
+
+How many bounds tables entries
+are we going to create?
+
+Well we're going to create
+the allocation size, which
+
+in this case 64, divided by
+the slot size, which is 16.
+
+So in this case we'll create
+four different bounds table
+
+entries for this
+thing right here.
+
+Each one of those
+entries is going
+
+to be set to the log of
+the allocation size, which
+
+in this case is
+going to be 6 right.
+
+Because the allocation
+size is 64, OK?
+
+So, so far so good.
+
+Then we're going to define
+another pointer called q
+
+and we're going to set
+it equal to p plus 60.
+
+So what happens when we do this?
+
+Well note that
+strictly speaking,
+
+this access is out
+of bounds, right.
+
+Because this was only
+allocated 44 bytes of memory,
+
+but of course the way
+that baggy bounds works
+
+is that it will actually allow
+axises that are out of bounds,
+
+if they stay within
+that baggy bounds.
+
+So even though
+strictly speaking,
+
+the programmer probably
+shouldn't have done this,
+
+this is actually
+going to be OK, right.
+
+We're not going to raise any
+flags or anything like that.
+
+Now let's say that
+the next thing we do
+
+is we need to find another
+pointer, which is going to be
+
+set equal to q plus 16 right.
+
+Now this is actually going
+to cause an error, right.
+
+Because now q is at an offset
+of 60 plus 16, which equals 76.
+
+So this is actually 12
+bytes away from the end
+
+of that baggy bounds.
+
+OK?
+
+And that's actually greater
+than half a slot away.
+
+All right, so if you remember
+the baggy bounds system will
+
+actually throw a hard
+synchronous error if you
+
+get beyond 1/2 a slot from
+the edge of that baggy bounds.
+
+So this will actually
+cause the program to fail.
+
+This will actually make it stop.
+
+Now let's imagine that we
+didn't have this line of code
+
+in the program, OK.
+
+So we had these two, but
+we don't have this one.
+
+So what if we instead
+of doing this line,
+
+did something that
+looks like this.
+
+We declare another
+pointer, let's call it s,
+
+and we set it equal to q plus 8.
+
+Now in this case,
+the pointer is going
+
+to be at 60 plus 8, which equals
+68 bytes away from p, right.
+
+So this is only four bytes
+beyond that baggy bound.
+
+So this will not
+actually cause an error.
+
+Even though it is strictly
+speaking, out of bounds.
+
+What we will do here though,
+is set that high order
+
+bit on the pointer, right.
+
+So that if anyone
+subsequently tries
+
+to dereference this
+thing, it's going
+
+to cause a hard
+fault at that point.
+
+And then let's say, the
+final thing that we do
+
+is we declare another
+pointer t, which
+
+is going to equal s minus 32.
+
+So what happens here
+is that essentially we
+
+brought this pointer t, it
+is now back in bounds, right.
+
+So what that means is that
+even though this guy was out
+
+of bounds, now we sort of going
+back to the original allocated
+
+region, that we originally
+created up here.
+
+So as a result, t will not
+have that high order bit step
+
+and so you can dereference T
+and everything will be fine.
+
+So does this all make sense?
+
+This should be fairly
+straightforward.
+
+AUDIENCE: [INAUDIBLE]
+the difference
+
+between r and s, how
+would you know that r is--
+
+or how does the program know
+that r is 1/2 the [INAUDIBLE].
+
+PROFESSOR: So note
+that, like up here,
+
+when we create r you
+can basically interpose,
+
+we get an instrumented
+code that's
+
+going to be working at all
+of these pointer operations.
+
+So basically we can tell is that
+we know where P is going to be.
+
+I'm sorry, we know
+where q is going to be.
+
+And we know that q is
+within those baggy bounds.
+
+And so when we do
+this operation here,
+
+the instrumentation
+of baggy bounds
+
+adds and we're able
+to say, aha, well I
+
+know where that source
+formula is coming from.
+
+And then if you look
+at this offset here,
+
+you determine it's more than a
+1/2 slot away from slot side.
+
+So basically what
+you think about is
+
+that as we're doing
+these pointer operations,
+
+and looking and saying is how
+are you going out of bounds,
+
+have you gone out of
+bounds, yes or no.
+
+At some point you're going
+to have some operation that's
+
+going to involve a pointer
+that is either in bounds
+
+within the baggy bounds and
+then some thing over here that
+
+makes it go out of bounds.
+
+So at that moment,
+right when that happens,
+
+that's how we know that
+something chicanerous has
+
+arisen.
+
+All right so, hopefully
+that should all make sense.
+
+And so this is very
+briefly a review
+
+of the homework question.
+
+So hopefully you can understand
+this and our homework question
+
+should be pretty
+easy to understand.
+
+So we have a character pointer
+the malloc had 256 bytes to it,
+
+Then we declare a
+character pointer
+
+q, that is equal to
+that pointer plus 256
+
+and then we essentially try
+to dereference this pointer.
+
+So what's going to happen?
+
+Well note that this is an
+exact power too, right.
+
+So there's not actually any
+bagginess in the bounds, right.
+
+So when we do this right here,
+this makes q point to one
+
+pass the end of
+those baggy bounds.
+
+So just like in this
+example up here,
+
+this line is actually fine,
+but it will cause the high bit
+
+to be set in q, right.
+
+So when you come down
+here and reference it,
+
+then everything
+blows up and it's
+
+time to call in your
+insurance agent.
+
+So pretty straightforward?
+
+OK so, that's
+basically two examples
+
+that you can flavor for
+how baggy bounds works.
+
+As I mentioned in
+the last lecture,
+
+you don't actually have to
+instrument every pointer
+
+operation, if you can use static
+code analysis to figure out
+
+the particular set of
+pointer operations is safe.
+
+I'll defer further
+discussion of some
+
+of the static
+analysis [INAUDIBLE],
+
+but suffice it to say
+that you don't always
+
+have to have all this bit
+wise arithmetic that you
+
+have in some of the cases
+that we've examined before.
+
+And so another question
+that came up a lot in Piazza
+
+was, how does baggy bounds
+ensure compatibility
+
+with these preexisting,
+non-instrumented libraries,
+
+right.
+
+And so the Piazza idea behind
+how baggy bounds does that
+
+is, that when baggy bounds
+initializes the bounds tables,
+
+they set all the entries
+to be that bound of 31.
+
+So when we read
+the bounds table,
+
+each entry represents
+2 to the power
+
+of that entry, the size of
+that particular pointer.
+
+So by initializing
+all those bounds
+
+of 31, what this allows
+us to do is automatically
+
+assume that each pointer
+from [INAUDIBLE] the code
+
+is going to have the
+largest bound possible, 2
+
+raised to the 31.
+
+So let me just give you a
+very simple example here
+
+that will hopefully make
+this a little clearer.
+
+So let's say that this
+over here is the memory
+
+space that we lose for heap.
+
+This is simple example,
+let's suppose that basically
+
+what this memory space
+[INAUDIBLE] two components.
+
+This is the heap, that is out
+by the unistrumented code.
+
+And then let's suppose
+that down here we
+
+have the heat that is allocated
+by the instrumented code.
+
+So what's baggy
+bounds going to do?
+
+So remember, baggy bounds has
+this notion of a slot size,
+
+right.
+
+So basically the
+slot size is 16,
+
+you only have entry
+for every sort
+
+of slot of size 16 over here.
+
+So basically the bounds
+table in this case,
+
+you can think of being
+set up into three
+
+places, sorry two places.
+
+So initially all of the
+bounds table, all the entries
+
+are initialized to 2 to the
+30-- or sorry, to the 31.
+
+But then eventually
+as the instrument code
+
+runs it's actually going
+to use the baggy bounds
+
+algorithm to set these
+values for whatever
+
+should be appropriate for that
+particular [INAUDIBLE], right.
+
+So what ends happening
+is that if you
+
+did-- if instrumented code gets
+a pointer that comes from here,
+
+then those baggy bounds
+with each particular pointer
+
+will always be set to the
+largest possible value, 231.
+
+2 to the 31, right.
+
+Which means that
+it's going to be
+
+impossible for baggy
+bounds, entry of the code,
+
+to think that you've done
+an out of bound operation
+
+with that pointer that's
+coming from this uninstrumented
+
+library.
+
+So does that make sense?
+
+So the idea is that
+in instrumented code
+
+we're always going to be
+doing these comparisons
+
+with the pointers, but if
+we always set the bounds
+
+entries for uninstrumented
+pointer code 2 to the 31,
+
+you can never have
+a dereference error.
+
+OK so that's basically how we
+have this nice interoperability
+
+between the entry of the
+baggy bounds code in between
+
+a noninstrumented off the
+shelf legacy library's.
+
+So putting it all together,
+what does this all mean?
+
+So, we have this
+system here which
+
+is nice because it doesn't make
+the uninstrumented libraries
+
+blow up, but one problem
+is that we can't detect out
+
+of bounds pointers
+that were generated
+
+in the uninstrumented
+code, right.
+
+Because we're never going to
+set that high bit for example,
+
+if that [INAUDIBLE]
+pointer gets too big,
+
+or gets too small or
+anything like that.
+
+So we actually can't
+provide memory safety
+
+for operations that take
+place in uninstrumented code.
+
+You also can't detect when
+we pass an out of bounds
+
+pointer from instrumented
+code to uninstrumented code.
+
+Something insane
+could happen, right.
+
+Because remember if you
+had this out of bounds
+
+pulled it from the
+instrumented code
+
+it has that high
+bit set to 1, right.
+
+So it looks like
+it's super ginormous.
+
+Now we know if we just kept
+that code in instrumented code,
+
+we might clear that
+flag at some point
+
+if it comes back in bounds.
+
+But if we just pass
+this ginormous address
+
+to uninstrumented
+code, then who knows,
+
+it may try to dereference it,
+it may do something crazy.
+
+It may even bring that
+pointer back in bounds,
+
+but we would never
+have an opportunity
+
+to clear that high bit, right.
+
+So you can come up--
+you still may come up
+
+with some inter-op
+issues there, even if we
+
+use this scheme over here.
+
+OK, so that's essentially how
+baggy bounds works on a 32--
+
+you got a question?
+
+AUDIENCE: Yeah, so if you
+have a instrumented coding
+
+meets like allocated
+memory, is it
+
+using the same malloc that the
+attributing code is using, or?
+
+PROFESSOR: Yeah so
+it's a bit subtle.
+
+So like in this case
+here, it's like very stark
+
+what's going on, because there's
+just two regions, one of which
+
+is used by each set of things.
+
+So it actually depends on
+the if they use [INAUDIBLE]
+
+and stuff like that.
+
+You can also imagine that like
+in C++ [INAUDIBLE] for example,
+
+you can define your
+own allocator, right.
+
+So it kind of
+depends [INAUDIBLE].
+
+AUDIENCE: [INAUDIBLE]
+input the same,
+
+how does the allocator
+know whether or not
+
+to set 31 or [INAUDIBLE].
+
+PROFESSOR: Yeah so at the
+lower level, typically the way
+
+that these allocation
+algorithms work,
+
+is that you call unknown
+system [INAUDIBLE] or something
+
+like that, sort of
+move a pointer up.
+
+So you can imagine if you have
+multiple allocators, all trying
+
+to allocate memory,
+they each have
+
+their own chunk of memory
+they reserve for themselves
+
+basically, right.
+
+So in real life it may be
+more fragmented than this,
+
+that's essentially on a
+high level, how it works.
+
+OK so this was a baggy
+bounds on a 32-bit system.
+
+So as you all know 64-bit
+systems are the bees
+
+knees these days, so
+how does baggy bounds
+
+work on those systems?
+
+Well, in those systems
+you can actually
+
+get rid of the bounds table,
+because we can actually
+
+store some information about
+the bounds, from the pointer
+
+itself.
+
+So imagine we're going to
+look at a regular pointer
+
+in a baggy bounds system.
+
+So we can use it, like this.
+
+So we can-- if the
+pointer's in bounds,
+
+we can basically just set
+the first 21 bits to 0.
+
+We can put the size
+in these 5 bits here.
+
+And once again this is
+representing the log base 2
+
+at the size here.
+
+And then we have here,
+in the remaining 38 bits,
+
+just the regular address bits.
+
+Now the reason why
+this doesn't massively
+
+curtail the address size
+of the program you use,
+
+is that a lot of
+these high order bits,
+
+the operating system
+and-or the hardware,
+
+doesn't let a application use,
+for various reasons, right.
+
+So as it turns out,
+we're not dramatically
+
+shrinking the amount of
+[INAUDIBLE] application
+
+you use in the system.
+
+This is what a regular
+pointer looks like.
+
+Now what happens
+when we only have
+
+one of these out
+of bounds pointers?
+
+Well, in a 32-bit system
+all we can do basically
+
+is just set that high
+order bit and you just
+
+hope that thing never got
+beyond a 1/2 a slot away
+
+from it's base.
+
+But now that we have all this
+extra address space here,
+
+you can actually put the out
+of bounds offset directly
+
+in this pointer.
+
+So we can do
+something like this.
+
+So we can have 13 bits
+here for the offset, right,
+
+the out of bound offset.
+
+How far away is this out of
+bounds pointer, from the place
+
+where it should be?
+
+And then once again you
+can put the actual size
+
+of the referred object here.
+
+This will be 0 once again.
+
+And this will be the
+real address base here.
+
+And so this may be
+reminiscent to you
+
+of some type of fact
+pointer representation,
+
+but there's a
+couple of advantages
+
+here, now that we're
+moving in the 64-bit world.
+
+So first of all, you'll note
+that these tag pointers,
+
+these are the regular size
+of a regular pointer, right.
+
+Pointer's are still just 64-bits
+wide in both of these setups.
+
+So that's nice because
+that means for example,
+
+that means and rights to
+that pointer are time.
+
+Unlike in traditional
+fat finger world,
+
+where you actually have
+to use multiple words
+
+represent that fat pointer.
+
+So that's nice.
+
+And also note that we can
+trivially ask these things,
+
+uninstrumented
+code, because they
+
+work and are the same
+size as regular pointers.
+
+We can put these things
+in structs for example,
+
+and the size of those
+structs won't change.
+
+So this is very nice if we
+can work in that 64-bit world.
+
+So does that all make sense?
+
+AUDIENCE: So why are there
+eight 0-bits [INAUDIBLE]
+
+pointer there?
+
+Where like the 5 size
+bits previously weren't.
+
+PROFESSOR: So you're
+talking about down here?
+
+AUDIENCE: Yeah,
+is there a reason
+
+why we can't just
+store a [INAUDIBLE]
+
+if we're like six
+0-bits there and had
+
+more bits for the offset,
+like why is the number 8?
+
+PROFESSOR: So I think
+so in some cases
+
+there are certain line issues
+that we have to work with.
+
+The [INAUDIBLE] issue is to deal
+with if the bits are higher.
+
+I don't think, in
+principle, there's
+
+any reason why you
+couldn't read some
+
+of these things [INAUDIBLE].
+
+Well there may be
+some hard versions
+
+that I'm not thinking
+of right now,
+
+but [INAUDIBLE] some of
+these would have to 0
+
+or otherwise the hardware's
+going to cause a problem.
+
+Any other questions?
+
+OK so, next thing
+are you wondering
+
+is, can you still
+launch a buffer
+
+overflows in the
+baggy bounds system,
+
+obviously because I gave
+you another paper to read,
+
+so clearly this thing, this
+doesn't solve all the problems,
+
+right?
+
+So one problem
+you might run into
+
+is that if you have
+uninstrumented code once again,
+
+we can't detect any problems
+in uninstrumented code.
+
+You could also encounter
+memory vulnerabilities
+
+that come about from the dynamic
+memory allocation system.
+
+So if you can remember
+in the lecture
+
+we looked at this weird
+free malloc weird pointer
+
+thing that took place.
+
+Baggy bounds won't
+necessarily prevent you
+
+from some of that stuff.
+
+We also discussed
+last lecture, where
+
+the fact that code
+pointers do not have bounds
+
+associated with them, right.
+
+So now you have struct that
+has a buffer at the bottom,
+
+it has a function
+pointer up top,
+
+if you have a buffer overflow
+in to that function pointer,
+
+right.
+
+Let's say that buffer
+overflow is still
+
+within the baggy bounds.
+
+So you've overridden
+that function pointer.
+
+We would try to execute
+that function pointer,
+
+it could be pointed
+at something for,
+
+attack a control
+piece of memory.
+
+OK, and bounds won't
+help with that,
+
+because there's no bounds
+associate with function
+
+pointers.
+
+And so in general, what are
+the cost's of baggy bounds?
+
+So there are essentially four.
+
+So the first cost
+is space, right.
+
+So if you're using
+a fat pointer,
+
+obviously you've got to
+make pointers bigger.
+
+But if you're using the baggy
+bounds system that we just
+
+discussed, you've got to
+store the bounds table, right.
+
+And so the bounds table
+has that slot size
+
+which allows you to control
+how big that bounds table is,
+
+but still you may end up using
+[INAUDIBLE] memory for that.
+
+You've also got the CPU overhead
+of doing all of the pointer
+
+instrumentation, right.
+
+So for every, or close to every
+pointer thing that you do,
+
+you got to check these bounds
+using those shift operations
+
+and things like that.
+
+So that's going to
+slow your program down.
+
+There's also this problem
+with false alarms, right.
+
+So as we discussed,
+it may be the case
+
+that a program generates
+out of bound pointers
+
+but never tries to
+dereference it, right.
+
+Strictly speaking
+that's not an issue.
+
+The baggy bounds will
+flag the creation
+
+of those out of bounds
+pointers, if they
+
+get beyond a 1/2 a slot size,
+at least in the 32-bit solution,
+
+right.
+
+And so what you'll see with
+a lot of security tools,
+
+is that false alarms really
+reduce the likelihood
+
+that people are going to
+use your tools, right.
+
+Because in practice
+we would all hope
+
+that we care about
+security, but actually
+
+what do people care about?
+
+They want to be able to upload
+their silly Facebook photos
+
+and life things,
+and they want to be
+
+able to make things go
+fast and stuff like that.
+
+So you really want
+your security tools
+
+to probably have less
+coverage of finding bugs,
+
+but actually have
+0 false alarms.
+
+As opposed to catching all types
+of security vulnerabilities,
+
+but then maybe having
+some false alarms
+
+that are going to irritate
+developers, or irritate users.
+
+And the other costs that you
+have for this is finally,
+
+is that you need
+compiler support, right.
+
+Which can actually end
+up being nontrivial,
+
+because you have
+to go in there, you
+
+have to add all the
+instrumentation,
+
+crawl the pointer checks,
+and so on ans so forth.
+
+So those are basically the
+cost of these bounds checking
+
+approaches.
+
+So that concludes the
+discussion of baggy bounds.
+
+And so now we can actually think
+about a two other mitigation
+
+strategies for buffer overflows.
+
+They're actually much simpler
+to explain and understand.
+
+So one of these approaches is
+called a non-executable memory.
+
+And the basic idea is
+that the paging hardware
+
+is going to specify
+3-bits for each page
+
+that you have in memory, read,
+write and execute, right.
+
+Can the program read
+that memory, write to it,
+
+execute it.
+
+The first 2-bits
+are old, they've
+
+been around for a while,
+that last bit is actually
+
+a fairly new construction.
+
+And so the idea is
+that you can actually
+
+make the stack
+non-executable, right.
+
+So if you make the
+stack non-executable
+
+that means that the
+adversary can't run code
+
+just by pointing-- by
+creating that shell code
+
+and then sort of jumping to
+someplace in that buffer.
+
+And so what a lot of systems
+do, is they actually specify
+
+a policy like this.
+
+So right exclusive or x,
+which means that if you have
+
+a particular page, you
+can either write to it,
+
+or you can treat it
+as executable code,
+
+but you cannot do both.
+
+OK and so that once
+again, is going
+
+to prevent the
+attacker from just
+
+putting executable
+code in the stack
+
+and then going straight to it.
+
+So this is-- should be pretty
+straightforward, right.
+
+So we've removed, at the
+hardware level, this attack
+
+vector of the attacker putting
+executable code in the stack.
+
+So what's nice about this?
+
+Well potentially this
+works without any changes
+
+to the application, right.
+
+This is all taken place
+at the hardware level
+
+and at the OS level,
+with the OS just
+
+making sure the pages are
+protected with these bits, OK.
+
+So that's very,
+very nuts, right.
+
+Because you don;t have to worry
+about this compiler support
+
+issue we had over here.
+
+The other nice thing
+is that, as I mentioned
+
+in the last lecture,
+the hardware's
+
+always watching you, even
+though the OS is not, right.
+
+So these bits being
+said over here,
+
+you know they're
+looked at and verified
+
+for correctness at
+every memory reference
+
+that you make by the code.
+
+That's a very nice
+aspect of this too.
+
+Now one disadvantage
+of this system
+
+though, is that it makes it
+harder for an application
+
+to dynamically generate code,
+in benign or benevolent cases.
+
+And the best example of
+that is, the just-in-time
+
+compilers that we discussed
+from last lecture, right.
+
+So how is it that
+you can go to a web
+
+page and your JavaScript
+code executes fast.
+
+It downloads that
+JavaScript source,
+
+it initially probably
+starts just interpreting it,
+
+but then at some
+point it's going
+
+to find some hot
+path, some hot loop
+
+and then it's going to
+dynamically generate
+
+x86 machine code and execute
+that directly, right.
+
+But to get that to work you have
+to be able to dynamically write
+
+code to a page.
+
+So there's some ways you can
+get around this for example,
+
+you could imagine that the
+just-in-time compiler initially
+
+sets the write bit and then
+it removes the write bit,
+
+then it sets the execute bits.
+
+There are some ways that
+you can get around that,
+
+but it can be a little
+bit tricky sometimes.
+
+On a higher level, that's how
+non-executable memory works,
+
+pretty easy to understand.
+
+AUDIENCE: What is the
+definition of like executable
+
+instructions?
+
+So if you change the
+attenuator [INAUDIBLE]
+
+it's not considered a
+executable instruction.
+
+PROFESSOR: Well basically no.
+
+Can you set like the instruction
+pointer register to that value.
+
+In other words, can you-- if you
+have a bunch of memory pages,
+
+can you actually set EIP
+there and actually start
+
+executing code from that page.
+
+AUDIENCE: Ah.
+
+PROFESSOR: OK, so that
+is nonexecutable memory.
+
+And so another
+technique you might
+
+imagine for protecting
+against a buffer overflows
+
+is using a randomized
+addresses or address spaces.
+
+And so the observation
+here is, that a lot
+
+of the attacks that
+we've discussed so far
+
+use hard coded addresses, right.
+
+And so if you think about
+a lot of the attacks
+
+you've been working on in
+your lab, how does that work?
+
+You open up the program
+in GDB, you find out
+
+the location of some things,
+you may create some shell code
+
+that actually has some hard
+coded addresses in there,
+
+right.
+
+So the idea behind the
+randomized address base
+
+is simple.
+
+Basically you want to make
+it difficult for the attacker
+
+to guess addresses.
+
+So there's a couple
+different ways
+
+you could think about
+doing this, right.
+
+So one idea is that
+you can imagine having
+
+stack randomization, right.
+
+So imagine that
+from here to here,
+
+this is the entire virtual
+memory space of the program,
+
+right.
+
+As we described this
+stuff to you so far,
+
+basically the
+stack always starts
+
+with this particular place
+up here, always goes down,
+
+right, and the program codes
+down here and the heap always
+
+goes up here.
+
+And all these seg-- all of these
+segments, the stack, the heap,
+
+and the program code, they all
+start at a well known location.
+
+So imagine for example, like
+if my lecture notes here
+
+are the stack.
+
+You can imagine instead of
+the stack always starting here
+
+at this known location,
+maybe you start it here,
+
+maybe you start it here.
+
+Somewhere else like that, right.
+
+Similarly you can imagine that
+maybe the program code which
+
+used to always start
+down here, maybe we
+
+start it up here, or down here,
+or something like that, right.
+
+So the idea now is that
+if you, the attacker,
+
+control one of these
+binary's, you can look in GDB
+
+and figure out where
+all these offsets are,
+
+but they're not actually
+going to help you figure out
+
+where those offsets are
+in the real code that's
+
+running on the server, right.
+
+So that's the basic idea behind
+these randomized address spaces
+
+there.
+
+And so this takes
+advantage of the fact
+
+that a lot of the code
+that you generate,
+
+doesn't have to be loaded into
+a specific place in memory,
+
+right.
+
+So unless you're writing like
+a device driver, or something
+
+like, that maybe is interacting
+with some hardware that
+
+requires this
+particular address to be
+
+belong in this particular buffer
+so it can copy information in.
+
+If you're not doing stuff
+like that then typically
+
+your codes going
+to be relocatable.
+
+So this approach will work very
+nicely with that kind of stuff.
+
+So once again the question
+is, can you exploit this?
+
+Obviously the
+answer is still yes.
+
+There's a couple different
+ways you can do it
+
+as we'll discuss later today
+in the [INAUDIBLE] paper,
+
+the attacker can actually
+extract randomness, right.
+
+And so in general that's
+how you defeat all
+
+these randomized approaches.
+
+You make them unrandom,
+by either finding out
+
+the random seed that
+the attacker was doing,
+
+or by somehow leveraging the
+fact that the attacker leaks
+
+information about the randomized
+locations of these things.
+
+And another thing
+that's interesting
+
+is that for a lot of the
+attacks we've discussed so far,
+
+we've basically been using these
+sort of hard coded addresses,
+
+but note that the attacker
+may not necessarily
+
+care about jumping to
+a specific address.
+
+Or there's this attack
+called a heap attack, which
+
+is actually pretty hilarious if
+you're a bad person, I suppose.
+
+So the way that this
+heap attack works
+
+is, that the
+attacker essentially
+
+just starts dynamically
+allocating a ton of shell code
+
+and just stuffs it
+randomly in memory, right.
+
+This is particularly
+effective if you're
+
+using like a dynamically high
+level language like JavaScript
+
+let's say.
+
+So the tag reader is
+sitting in a tight loop
+
+and just generate a bunch of
+shell code strings, right.
+
+And you just fill the heap
+with all these shell code
+
+strings, right.
+
+Now the attacker maybe cannot
+figure out where the exact
+
+location is of each of
+the shell code strings,
+
+but if you've allocated 10s of
+megabytes of shell code strings
+
+and then just do a
+random jump, right.
+
+If you could somehow control
+one of these ret pointers,
+
+then hey, maybe you'll
+land in shell code, right.
+
+And one trick you
+can actually use
+
+is this thing called NOP sleds,
+which is also pretty hilarious.
+
+So imagine that if you have
+a shell code string, then
+
+it may not work out if
+you jump to a random place
+
+in that shell code
+string, because it may not
+
+set the attack up correctly.
+
+But maybe this stuff that
+your spewing to the heap,
+
+is basically just a ton of NOPs
+and then at the very, very end
+
+you have the shell code, right.
+
+This is actually
+quite clever right,
+
+because this means that now
+you can actually goof up
+
+the exact place where you jump.
+
+If you jump into
+another one of these NOP
+
+things just go boom, boom, boom,
+boom, boom, boom, boom, then
+
+you hit the shell code, right.
+
+So it's like these are the
+people that you probably
+
+see on the team.
+
+They're inventing these
+types of things, right.
+
+This is a problem.
+
+So that's another way
+to get around some
+
+of this randomization
+stuff, just
+
+by making your codes
+randomization resilient,
+
+if that makes sense.
+
+OK so that's basically
+a discussion of some
+
+of the types of
+randomness you can use.
+
+There's also some wacky ideas
+that people have had too.
+
+So now you know
+that when you want
+
+to make a system
+call for example,
+
+you use this syscall
+libc function
+
+and you basically pass
+any unique number that
+
+represents the system call
+that you want to make, right.
+
+So maybe four is seven and maybe
+sleep is eight, or something
+
+like that, right.
+
+So what that means is that
+if the attacker can somehow
+
+figure out the address of
+that syscall instruction
+
+and jump to it somehow, he or
+she can actually just supply
+
+the system call number that they
+want to invoke directly, right.
+
+So you could imagine that
+each time the program runs,
+
+you actually create a dynamic
+assignment of syscall numbers
+
+to actual syscalls, right.
+
+To make it harder for the
+attacker to get stuff.
+
+There's even some very
+avant garde proposals
+
+to change the hardware such
+that the hardware actually
+
+contains an xor key, that
+is used to dynamically xor
+
+instructions, right.
+
+Imagine every time you
+compile the program, all
+
+of the instruction codes that's
+the xor of some key, right.
+
+That key is put into
+that hardware register
+
+when you initially
+load the program
+
+and then whenever you
+execute an instruction,
+
+the hardware
+automatically xor's it,
+
+before you continue executing
+that instruction, right.
+
+So what's nice about
+that is, that now even
+
+if the attacker can
+generate the shell code,
+
+the attacker doesn't
+know that key, right.
+
+So it's very difficult
+for the attacker
+
+to figure out what exactly
+to put into memory.
+
+AUDIENCE: But if
+he can get the code
+
+and he also instructions
+he can xor it back
+
+to the instruction [INAUDIBLE].
+
+PROFESSOR;Oh yeah.
+
+This is always a
+canonical problem, right.
+
+So it's like what if
+someone does this?
+
+So that's exactly right.
+
+So this is somewhat similar to
+what happens in the BROP attack
+
+where, essentially we've sort of
+randomized where locations are,
+
+but the attacker can
+do probes, right.
+
+And figure out what's going on.
+
+So you can imagine too that for
+example, if the attacker knows
+
+some sub-sequence of
+code that he's expects
+
+to be in the binary,
+you could imagine
+
+just sort of trying to xor the
+binary with that known code,
+
+trying to extract the key.
+
+And there's a lot
+evil in the world,
+
+so you're exactly
+correct about that.
+
+OK so that's essentially
+the discussion
+
+of all the randomization attacks
+that I want to discuss today.
+
+So one thing to
+talk about before we
+
+get to some of the return
+oriented programming stuff,
+
+is you might wonder which
+ones of these defenses
+
+are actually used in practice.
+
+And so as it turns out,
+both GCC and Visual Studio,
+
+they both enable stack
+canaries by default, right.
+
+So that's very popular, that's
+a very well known community.
+
+If you look Linux
+and Windows they
+
+can also do things like
+non-executable memory.
+
+They can also do things like
+randomize the address space, so
+
+that's also [INAUDIBLE].
+
+The baggy bounds stuff
+however, is not as popular.
+
+And that's because of
+some of these costs
+
+that we talked about
+over here, in terms
+
+of memory overhead, CPU, the
+false alarms, and so on ans
+
+so forth.
+
+So that's basically a survey
+of the state of the art,
+
+in trying to prevent
+these buffer overflows.
+
+So now we're going to talk about
+this return oriented programing
+
+stuff.
+
+So what I'm described to
+you so far today in terms
+
+of the address space
+randomization and the data
+
+execution prevention,
+that's the-- the
+
+read, write and execute
+that I just described.
+
+Those things are actually
+very, very powerful, right.
+
+Because the randomization
+prevents the attacker
+
+from actually understanding
+where our hard coded addresses
+
+are.
+
+And the data
+execution prevention
+
+says, even if you can put
+shell code into the stack,
+
+then the attacker
+can't just jump to it
+
+and execute it, right.
+
+So at its space,
+that seems like,
+
+man you've really
+made a lot of progress
+
+for stopping these attackers,
+but of course there
+
+are these hackers out there who
+spend all their time thinking
+
+about how to ruin our lives.
+
+So what's the insight behind
+return oriented programming?
+
+The insight is that, what
+if instead of the attacker
+
+being able to generate just
+new code at attack time, what
+
+if the attacker could
+string together preexisting
+
+pieces of code and then string
+them together in deviant ways,
+
+right?
+
+And we know that the program
+contains a ton of code already,
+
+right.
+
+So hopefully, or unhopefully,
+depending on which side of this
+
+you're on.
+
+If you can find enough
+interesting code snippets,
+
+you can string them
+together to basically form
+
+like this Turing
+complete language, where
+
+the attacker can essentially
+do whatever the attacker wants
+
+to do.
+
+So that's the insight behind
+return oriented programming.
+
+So understand how this works.
+
+Let's look at a very simple
+example that will initially
+
+start off very familiar, right.
+
+But then it's very quickly
+going to descend into madness.
+
+So let's say that we have
+the following program.
+
+So we have some program-- sorry,
+some function and conveniently
+
+for the attacker, it has this
+nice function here called
+
+run shell.
+
+So this is just
+going to call system,
+
+it's going to execute bin
+slash bash and then be done.
+
+And then we've got the canonical
+buffer overflow process
+
+or sorry, function down
+here, basically this thing
+
+is going to declare a
+buffer, and then it's
+
+going to use one of
+these unsafe functions
+
+to fill in bytes in the buffer.
+
+OK so, we know that this
+can be overflowing OK,
+
+this is old news.
+
+Now what's interesting is that
+we have this function up here,
+
+run shell, but it
+doesn't quite seem
+
+to be accessed in some direct
+way based on this buffer
+
+overflow.
+
+So how can the attacker invoke
+this run shell command here?
+
+Well the attack may
+do a couple things.
+
+So first of all, the attacker
+can disassemble the program,
+
+run GDB, find out the address
+of this thing in the executable,
+
+right.
+
+So you all should be very
+familiar with doing those kinds
+
+of things through the lab.
+
+That's the first thing
+the attacker can do.
+
+And then during the
+buffer overflow,
+
+the attacker can essentially
+take that address,
+
+put it in the buffer
+overflow that's generated
+
+and make sure that the
+function returns to run shell.
+
+So just to make that clear,
+let's draw that over here.
+
+So, you have a setup
+that looks something
+
+like this at the bottom,
+we have the buffer,
+
+that's being overflowed.
+
+And then up here, we have
+the save the break pointer,
+
+up here we have the return
+address, for process message.
+
+So remember that the new stack
+pointer will be here initially,
+
+when we start
+executing the function.
+
+This is the new
+break pointer, this
+
+is what the stack
+pointer used to be.
+
+And then we've got some
+break pointer up here,
+
+for the previous frame.
+
+OK, so this should
+look pretty familiar.
+
+So basically, in the
+attack, like I said,
+
+we've used GDB to
+figure out what
+
+the address is of run shell.
+
+So in the buffer overflow,
+we can essentially just
+
+put the address of run
+shell right here, right.
+
+So this is a actually pretty
+straightforward extension
+
+of what we already
+know how to do, right.
+
+So basically it's saying,
+if we conveniently
+
+have a command
+that runs a shell,
+
+if we can disassemble
+the binary, figure out
+
+where that address is, we can
+just put that in this overflow
+
+array that we have here.
+
+So that should be
+pretty straightforward.
+
+Does that make sense?
+
+OK.
+
+So, this was a very
+childish example,
+
+because the programmer
+for some crazy reason
+
+has put this low
+hanging fruit here.
+
+So as an attacker this is like
+Christmas coming early, right.
+
+Now it may not be the case
+that you have something
+
+as delightful as this.
+
+So what you could have instead,
+is something like this.
+
+So let's say that instead
+of this thing being called
+
+run shell, we call it
+run boring and then
+
+maybe this thing just executes
+bin slash OS let's say.
+
+But let's say that everything
+is not completely lost,
+
+because we actually
+have a string up here
+
+that conveniently gives
+us the path of that.
+
+So what's interesting about
+this is, that we can disassemble
+
+the program, find the
+location of run boring,
+
+but as an attacker,
+who wants to run an OS?
+
+Right, that's no fun
+But we do actually
+
+have a string in memory that
+points to the path of the shell
+
+and actually we also know
+something interesting too.
+
+Which is that even though the
+program isn't calling system
+
+with the argument that we want,
+it is calling system somehow.
+
+So we know that
+system must be getting
+
+linked into this
+program somehow, right.
+
+So we can actually
+leverage those two things,
+
+to actually call system
+with this argument here.
+
+So the first thing that we
+do, is we can go into GDB
+
+and we can actually
+figure out where
+
+this thing is located in the
+process binary image, right.
+
+So you just go to GDB, just
+type in basically print system
+
+and I'll give you
+some information
+
+about the offset of that OK.
+
+So that's pretty
+straightforward.
+
+You can also do the same
+thing with bash path.
+
+Right, you just use
+GDB to figure out
+
+where this thing lives.
+
+It's statically
+declared string, right.
+
+So you'd be able to find
+out where that lives.
+
+And so once you've
+done that, now you
+
+got to do something a
+little bit different, right.
+
+Because now we actually
+have to figure out somehow,
+
+how to invoke system with
+an argument of our choosing,
+
+right.
+
+And so the way that we do
+that is by essentially faking
+
+a calling frame for system.
+
+OK, so remember that
+a frame is the thing
+
+that the compiler
+and the hardware
+
+work together to use to
+implement the call stack,
+
+right.
+
+So here's basically
+what we want to do.
+
+We want to set up something
+like this on the stack, right.
+
+So basically we're
+going to fake what
+
+system would expect
+to be on the stack,
+
+but right before it
+actually executes its code.
+
+So up here we had the
+argument of the system,
+
+this is the string that we
+actually want to execute.
+
+And then down here, this is
+where system should return to,
+
+when it's done.
+
+Right, so this is what system
+expects the stack to look like,
+
+right before it
+starts execution.
+
+It's going to say this is where
+I should go when I'm finished,
+
+this is the thing I should
+consume as my argument, right.
+
+In the past we've been
+assuming that there
+
+were no arguments when
+you pass the functions,
+
+but now this is a little
+bit different, right.
+
+So basically we
+just have to ensure
+
+that this thing is in that
+overflow code that we create,
+
+right.
+
+We just have to make
+sure this fake calling
+
+frame is in that array.
+
+So basically the
+way this will work
+
+is, we will do the following.
+
+So once again remember
+the overflow goes up here.
+
+So first, we're going to put
+the address of system here.
+
+And then here, we're going
+to put just some junk return
+
+address.
+
+Right, this is
+where system's going
+
+to return after it's finished.
+
+For the purposes
+of the discussion
+
+now, we don't care
+what this does,
+
+we'll just make this be just
+some random set of bytes.
+
+And then up here,
+we're actually going
+
+to put the address
+of bash path, right.
+
+So what's going
+to happen now when
+
+we do this buffer in overflow?
+
+So what's going to happen is
+that, process message is going
+
+to finish, it's
+going to say, OK hey,
+
+here's where I should
+return to, right.
+
+And then it's going to
+pop the stack, right,
+
+and now the system code
+is executing, right.
+
+The system code now sees
+that fake call frame
+
+that we created, right.
+
+As far as system is
+concerned, nothing chicanerous
+
+has taken place, right.
+
+System will say, aha
+here's the argument
+
+that I want to execute,
+it's bin slash bash,
+
+it's going to execute it
+and voila, the attacker
+
+has a shell, right.
+
+So does this make sense?
+
+So basically what we've
+done is, we've now
+
+taken advantage of knowledge
+of the calling convention,
+
+for the platform to
+create fake stack frames,
+
+or fake calling
+frames I should say.
+
+And using those
+fake calling frames,
+
+we can actually execute any
+function that is already linked
+
+and defined in the application.
+
+Does that make sense?
+
+OK so, another question
+you might have is,
+
+what if this string wasn't
+actually in the program?
+
+Now to be clear, this
+string is almost certainly
+
+in the program.
+
+So that's one funny
+thing about security,
+
+there's just all kinds of fun
+strings that are laying around,
+
+you can just go to
+town all day long.
+
+Well let's suppose we
+live in bizarro world
+
+and like this string
+is not in the program.
+
+So does anyone have
+any ideas about what
+
+we could do to get that
+string to be in the program?
+
+AUDIENCE: We can put the
+string on the [INAUDIBLE].
+
+PROFESSOR; Yes exactly,
+don't trust that man.
+
+That's what you can do, exactly.
+
+So, what you can do
+is actually for here,
+
+have the address of bash path,
+actually point here, right.
+
+And then you'd put-- up here
+you would put slash B-I-N
+
+slash P-A-T slash 0.
+
+So that's how you
+can get around-- I
+
+think I got that math right,
+because each one of these
+
+is 4 bytes.
+
+But anyway, so you have the
+pointer go up here and then
+
+boom, you're done.
+
+So now you can actually
+conjure up arguments
+
+just by putting them
+in the shell code.
+
+Pretty horrifying.
+
+So this is all building up
+towards the full BROP attack,
+
+right.
+
+But before you can mention
+the full BROP attack,
+
+you've got to
+understand how you just
+
+chain together these
+preexisting things in the code.
+
+So one thing to note is that
+when I'm setting up this return
+
+address here, I just said,
+eh just put some junk here,
+
+it doesn't really matter,
+we just want to get a shell.
+
+But if you're the attacker,
+you could actually
+
+set this return
+address to something
+
+that's actually useful, right.
+
+And if you did that, you
+could actually string together
+
+several functions, several
+function indications in a row,
+
+right.
+
+That's actually very,
+very powerful, right.
+
+Because in particular,
+if we literally just
+
+set this return
+address to jump, I
+
+mean it may be that
+when we ret from it,
+
+like the program crashes on
+it, maybe we don't want that,
+
+right.
+
+So can actually start
+chaining some of these things
+
+to do interesting stuff.
+
+So let's say that our goal is
+that we want to call system
+
+an arbitrary number of times.
+
+We don't just want
+to do it one time,
+
+we're going to it a
+arbitrary number of times.
+
+So how can we do that?
+
+Well, we're going to use
+two pieces of information
+
+that we already know
+how to get, right.
+
+We already know how to get
+the address of system, right.
+
+We just look in GDB and find it.
+
+We also know how to find
+the address of that string,
+
+bin flash bash.
+
+Now to actually make this
+attack work using multiple calls
+
+to system, we're going to
+have to use gadgets, right.
+
+This is getting us
+closer to what's
+
+taking place in the BROP paper.
+
+So what we need to do
+now, is find the address
+
+of these two Op codes.
+
+Right, so what is this, so this
+is pop in EAX, so what does
+
+this do?
+
+This just takes the
+top of the stack
+
+and then it puts it
+into the EAX register.
+
+And what is the ret
+instruction going to do?
+
+It just pops the
+top of the stack
+
+and then puts it into
+EIP, instruction pointer.
+
+OK, so this is what's
+known as a gadget, right.
+
+This is like a small set
+of assembly instructions
+
+that the attacker can use
+to build these larger more
+
+grandiose attacks.
+
+OK, So how can we find
+this gadget, right.
+
+There's actually like
+some off the shelf tools
+
+that hackers use to
+find these things,
+
+it's not hard to get
+the binary, right.
+
+Essentially just
+do a [INAUDIBLE]
+
+for these types
+of things, right.
+
+So it's just as easy to
+find one of these gadgets,
+
+assuming that you've
+got a copy of the binary
+
+and we're not worried
+about randomization yet.
+
+It's very easy to
+find these things.
+
+Just like it's very easy to find
+the address of system and stuff
+
+like that.
+
+So if we've got one
+of these gadgets,
+
+what can we use
+this gadget to do?
+
+Well of course the
+answer is evil.
+
+So, what we can do
+is the following.
+
+Let's say that we
+changed the stack
+
+so that it looks like this.
+
+So the exploit goes this way.
+
+And so let's say, we do this.
+
+So the first thing
+we're going to put here
+
+is the address of system.
+
+And the thing we're
+going to put up here,
+
+is the address of
+the pop ret gadget.
+
+Then up here, we're going to
+put the address of bash path
+
+and then we're going
+to repeat this pattern.
+
+So we're going to put
+the address of system,
+
+the address of the
+pop ret gadget,
+
+and then the address
+of bash path.
+
+OK, so what's going
+to happen here now?
+
+Now this is going
+to be a bit tricky,
+
+and these lecture
+notes are going
+
+to be up on the
+web, so you may just
+
+want to listen to
+what's happening,
+
+but this-- when I first
+understood this, this
+
+was like understanding that
+Santa Claus wasn't real right.
+
+So what will happen
+is-- and by the way,
+
+Santa Claus isn't real, I hope
+I didn't ruin it for everyone.
+
+So what's going to happen?
+
+So [INAUDIBLE] is what
+puts this in memory.
+
+So we're going to
+start here, OK.
+
+So what's going to happen?
+
+We're going to return to
+system, the ret instruction
+
+is going to pop an
+entry off the stack, now
+
+the top of the
+stack pointers here.
+
+OK, so system is going to
+find its argument here,
+
+it's going to execute the shell.
+
+Then it's going to finish
+and return to whatever's
+
+here, which is the pop gadget.
+
+In executing that
+return, we change
+
+the top of the stack
+pointer to be here.
+
+OK, now we are in
+the pop ret gadget.
+
+OK, so what is that pop
+ret gadget going to do?
+
+It's going to pop what's on
+the stack, which is this, OK.
+
+So now the top of
+the stack is here.
+
+Then we're now in
+the ret instruction
+
+from the pop ret gadget.
+
+What's this going to do?
+
+Aha, it's going to call
+system again, right.
+
+So once again the ret is going
+to pop this off this stack,
+
+we are now in system.
+
+Top of the stack
+is here, system is
+
+going-- this will trigger
+calling frame, the system.
+
+System takes the bash
+path argument here.
+
+OK, and then it is
+going to ret, right.
+
+Where's it going to ret to?
+
+The pop ret gadget again.
+
+So the ret pops
+the stack, we are
+
+now in the pop ret gadget,
+the ret gadget-- sorry,
+
+the pop ret gadget is going to
+pop this, so on and so forth.
+
+OK?
+
+So clearly we can
+chain this sequence
+
+to execute an arbitrary
+number of things, right.
+
+And so this in
+essence is starting
+
+to get to the core of what
+return oriented programming is.
+
+Note that we have not executed
+anything in the stack, right.
+
+This is what has allowed us to
+get beyond those data execution
+
+prevention bits, right.
+
+Nothing's been executed here.
+
+We're just sort of jumping
+to things in unexpected ways
+
+to do what we want to do.
+
+OK so this is actually
+very, very, very, clever.
+
+And so what's interesting
+is that at a high level
+
+you can think about us, we've
+now defined this new model
+
+for computation, right.
+
+So in a traditional,
+non-malicious program,
+
+you have the
+instruction pointer that
+
+points to some linear
+sequence of instructions.
+
+And you increment the
+instruction pointer
+
+to figure out what's
+the next thing to do.
+
+In essence, what return
+oriented programing does is,
+
+it uses the stack pointer
+as the instruction pointer.
+
+Right, so as we move
+the stack pointer,
+
+we're pointing to like
+other blocks of code
+
+that we're going to execute.
+
+And then at the
+end of the gadget,
+
+you return back to
+the stack pointer
+
+which is then going to tell
+us the next block of code
+
+to execute.
+
+OK so that does that make sense?
+
+So that's basically how you
+can avoid the data execution
+
+prevention stuff.
+
+That's how you can
+get around having
+
+this no execute bit on pages.
+
+So the next thing that
+we might want to do
+
+is defeat stack canaries.
+
+So if you remember, this
+canary was this value
+
+that we were going to
+place on the stack, right.
+
+So you can imagine
+the canary would
+
+go right here for
+example, or right here,
+
+and it would prevent someone
+from overriding the return
+
+address, without also
+overwriting the canary.
+
+With the intuition being that
+before the system actually
+
+jumps to the ret
+address, it can check
+
+to see if the canary
+has been changed
+
+in a way that's incorrect.
+
+So that's how the
+canary works, but can we
+
+get around the canary?
+
+Can we guess the canary somehow?
+
+Well we can actually, if
+we make a few assumptions
+
+about how the system works.
+
+So, how do we defeat
+those canaries?
+
+So the first thing that we want
+to assume is, that the server,
+
+it has to have a buffer
+overflow vulnerability.
+
+The second thing that
+we're going to assume,
+
+is that the server is going
+to crash and respond, just
+
+restart, if we set the
+canary value to a bad one.
+
+And the third thing that
+we're going to assume
+
+is that, after the restart,
+that the canary and any address
+
+space randomization that you're
+doing, is not rerandomized.
+
+Right, so what that
+means is that, we're
+
+going to assume that if we can
+somehow crash the server, then
+
+when the server restarts,
+it's going to have
+
+the same value for the canary.
+
+And it's going to have the same
+locations for all the quote
+
+unquote "randomized" stack,
+heap and code information
+
+that it has.
+
+So you might wonder why
+would this be the case?
+
+Why would it be that when
+the server comes back
+
+it doesn't have new
+locations for things?
+
+The reason is because
+a lot of servers
+
+are written to use fork,
+to create new processes.
+
+And if you remember,
+fork actually
+
+inherits-- the child
+inherits the address
+
+space of the address space
+layout right of the parent,
+
+right.
+
+This is copy on write pages
+that change stuff as the child
+
+updates things, but
+if you use fork here,
+
+instead of execing
+a whole new process,
+
+any time that parent server
+process forms new children,
+
+those children will have the
+same values of the canary
+
+in the address base, OK.
+
+So these are the
+assumptions that we're
+
+going to make to try to
+defeat these canaries here.
+
+So how can we defeat the canary?
+
+Well the attack is actually
+fairly straightforward.
+
+So imagine that the stack
+is going up this way, right.
+
+Imagine you got the
+buffer overflow here,
+
+then imagine that the
+canary is up here, right.
+
+And the canary actually
+has multiple bytes, right.
+
+So what you can
+actually do is, you
+
+can probe those bytes one by
+one and start guessing values
+
+of what those bytes are, right.
+
+So let's say that-- so the
+canary looks like this.
+
+Here's the overflowing
+buffer, and you want
+
+to guess what these bytes are.
+
+So the first thing
+that you guess
+
+is you take your overflow,
+just to this first byte
+
+of the canary and you
+say, hey, is that byte 0?
+
+You write a 0 there,
+with your overflow.
+
+You're either correct
+or you're incorrect.
+
+If you are incorrect, then the
+server's going to crash, right.
+
+If you are correct you
+say, aha I actually
+
+know the first byte of
+the canary now, right.
+
+Then you start guessing here.
+
+You say, are you 0?
+
+Probably not, it's
+going to crash.
+
+Are you one?
+
+And maybe not, it's
+going to crash.
+
+Are you two?
+
+Aha, it doesn't crash, right.
+
+So now you've actually found
+the value of that second canary
+
+byte, right.
+
+As you can imagine,
+you step up this way,
+
+and you eventually find all
+the values for the canary.
+
+So once again we're taking
+advantage of the fact,
+
+that crashes are a signal
+to you, the attacker,
+
+that you've actually done
+something wrong, right.
+
+And the server is staying
+up, in other words,
+
+that socket connection's
+staying open, is
+
+a signal to you, the
+attacker, that you've
+
+done something right.
+
+AUDIENCE: Maybe I mentioned
+something basic here
+
+like why do you-- if you
+know how long the canary is,
+
+can you just infect directly?
+
+Skip that buffer
+and overflow those--
+
+the one path there the canary?
+
+So like [INAUDIBLE] say you can
+like [INAUDIBLE] the canary--
+
+PROFESSOR: Yeah, yeah you
+can't-- so that's right
+
+if you-- so if you in fact
+know the exact location
+
+of the canary, right.
+
+That can sometimes
+allow you to skip
+
+some of these attacks totally.
+
+Because then you
+can just directly
+
+write to the return
+address, let's say,
+
+as opposed to doing some of
+this buffer overflow nonsense.
+
+But in general, if there's
+some level of randomization
+
+here, if you don't quite know
+where the stack is for example,
+
+then it's tricky
+to do that, right.
+
+So basically the way
+that the attack proceeds
+
+is that you don't quite
+know what's happening,
+
+and so you just very slowly
+creep your way up memory,
+
+down the stack, to figure
+out where these things are.
+
+AUDIENCE: Can the
+server instead of
+
+crashing when it
+finds strong canaries,
+
+keep the socket open and
+[INAUDIBLE] deprocess
+
+and [INAUDIBLE]?
+
+PROFESSOR: Yeah, so we'll
+discuss at the end of lecture
+
+some of the defenses you
+can have against this,
+
+but one very, abstractly
+speaking civil defense,
+
+is that when the
+program crashes,
+
+you catch the segfault
+using a signal handler,
+
+do not deduce you're
+own code by the way.
+
+But you can do this, right.
+
+You catch that segfault
+and then the signal handler
+
+just keeps that
+process alive for a bit
+
+and that will trick the
+attack into thinking that,
+
+oh I won't get that signal
+back, in other words.
+
+OK so that's
+basically how you can
+
+guess the value for the canary.
+
+And note that you can
+actually use this attack
+
+to sort of figure out
+arbitrary values that
+
+are low in the stack, right.
+
+Just by iteratively guessing
+for each byte what it is,
+
+and then using that
+crash indication
+
+as a signal of whether you're
+guess was correct or not.
+
+So that's basically
+how you can defeat
+
+these randomized
+canaries, assuming
+
+that after the server restarts,
+those things are not changed.
+
+And so we've also
+shown how you can
+
+use the gadgets
+to string together
+
+these more elaborate attacks.
+
+So what we're going
+to look at next
+
+is a way that you can use all
+these techniques to defeat
+
+data execution prevention,
+address-based randomization
+
+and canaries on a
+production system.
+
+Now what we're
+going to do now is,
+
+we're actually going
+to start looking
+
+at 64-bit architectures instead
+of 32-bit architectures.
+
+As it turns out for
+randomization purposes,
+
+64-bit architectures
+actually give you
+
+a lot more randomness to protect
+yourself against the attacker.
+
+So looking at attacks
+is much more interesting
+
+on those systems.
+
+So that's also the type
+of architecture that's
+
+discussed in the BROP paper.
+
+They talk about 64-bit machines.
+
+So from now on,
+assume that we're
+
+going to talk about the
+64-bit architectures.
+
+For the purposes
+of this discussion,
+
+the only difference
+between a 32-bit machine
+
+and a 64-bit machine, is
+that on a 32-bit machine,
+
+the arguments are passed
+on the stack, right.
+
+So here for example, this
+is like a 32-bit machine
+
+we were assuming, so
+for example, bash path
+
+will pass on the stack.
+
+On a 64-bit machine,
+the arguments
+
+are passed in registers instead.
+
+OK so like when a
+function starts execution,
+
+it's going to look
+in certain registers
+
+to find where the arguments are.
+
+OK, make sense?
+
+All right.
+
+So start up here.
+
+All right, so now we get to
+the point of today's paper.
+
+Which is the blind return
+oriented programming.
+
+So what's the first
+thing you want to do,
+
+if you want to engage in
+BROP for fun or profit?
+
+So the first thing
+you have to do
+
+is, you have to find what
+they call a stop gadget.
+
+Now a stop gadget-- and remember
+that when we say gadget,
+
+we essentially mean,
+return addresses, right.
+
+A gadget is identified
+by the return address,
+
+by the start address of that
+sequence of instructions
+
+that we want to jump to, right.
+
+So what is a stop gadget?
+
+So a stop gadget is
+essentially a return address
+
+to someplace in the code,
+but if you jump to it,
+
+you're going to
+pause the program,
+
+but you're not
+going to crash it.
+
+OK, so that's why it's
+called a stop gadget.
+
+Now what might that
+stop gadget be?
+
+You might jump to someplace
+in the code that then calls
+
+via the sleep system call
+for example, or does pause,
+
+or something like that.
+
+Or maybe somehow the program
+gets stuck in an infinite loop
+
+if you jump to that place.
+
+Doesn't really matter
+why the stop's happening,
+
+but you could imagine
+several scenarios which would
+
+cause that stop to take place.
+
+So why is this useful?
+
+Well once the
+attacker has managed
+
+to defeat the canaries using
+that iterative guessing
+
+technique I showed
+you, he can start
+
+to overwrite this return
+address and start probing
+
+for these stop gadgets, right.
+
+And so note that
+most of the random
+
+addresses you might
+put there, they'll
+
+probably crash
+the server, right.
+
+Once again, that's the
+message to you, the attacker,
+
+that's an indication that what
+you found is not a stop gadget,
+
+right.
+
+Because when the server
+crashes your sockets--
+
+your socket
+connection is closed.
+
+You as an attacker
+know, OK that must not
+
+have been a stop gadget.
+
+Where if you guess something
+and then you-- that socket still
+
+stays open for
+awhile, you think,
+
+aha I found that stop gadget.
+
+So that's the basic
+idea behind step one.
+
+You got to find
+that stop gadget.
+
+Now step two, is
+that you want to find
+
+gadgets that pop stack entries.
+
+And so you basically have to
+use this sequence of carefully
+
+crafted instructions
+to figure out
+
+when we've got one of
+these stack gadgets.
+
+So this sequence
+is going to consist
+
+of a probe address, a stop
+address, and a crash address.
+
+So the probe
+address is the thing
+
+that we're going to
+put in the stack.
+
+This is going to be the address
+of a potential stack popping
+
+gadget.
+
+This stop gadget is going to
+be what we found in step one.
+
+So this is an address
+of the stop gadget.
+
+And then the crash
+gadget is just
+
+going to be the address
+of nonexecutable code.
+
+So for example, you
+could just set this
+
+to, just the
+address zero, right.
+
+If you do a ret to this and
+then try to execute code there,
+
+this is going to
+crash your program.
+
+So we can basically use
+these types of addresses
+
+to find out where these
+stack popping gadgets are.
+
+So here's a simple example.
+
+So let's write this over here.
+
+So let's say we have these two
+different examples of a probe,
+
+a trap, and then a stop, right.
+
+So let's assume that
+we have down here,
+
+we're going to probe
+at some address,
+
+doesn't really matter,
+starts with a four,
+
+ends with an eight.
+
+That doesn't matter.
+
+Over here, let's say that
+we look at the address
+
+that, let's say starts
+in a four ends in a C.
+
+So we're saying,
+we're hypothesizing,
+
+that maybe one of
+these two addresses
+
+is going to be one of these
+stack popping gadgets.
+
+And then let's say
+that the trap up here,
+
+like I said this is just
+going to be address zero,
+
+and then let's assume that we
+found some preexisting stop
+
+gadget, some addresses start
+the [INAUDIBLE] doesn't really
+
+matter.
+
+And remember this stop gadget,
+like maybe this address,
+
+points to code that does
+something like sleep 10,
+
+or something like that, right.
+
+So when I say that we're
+going to test these sequences,
+
+this is the stuff that we're
+going to push onto the stack,
+
+right.
+
+So similar to over there, when
+we were pushing these gadgets
+
+onto the stack,
+this is the stuff
+
+that we're going to
+push onto the stack,
+
+and we're going to see
+what happens, right.
+
+Now let's say that,
+this code here, points
+
+to the following sequence.
+
+We're going to pop some
+register, let's say racks,
+
+and then we're going to return.
+
+So what's going to happen here?
+
+Well so when the system
+jumps this address,
+
+the stack pointer's
+going to move here, OK.
+
+Now we're in the middle
+of this gadget, right.
+
+What's the gadget going to do?
+
+It's going to pop racks, OK.
+
+Top of stack pointer's
+now here, and it's
+
+going to return to whatever's
+the top of the stack which
+
+is the stop gap, right.
+
+So in this case this
+gadget gets us to here,
+
+and the attacker
+can tell that this
+
+is-- this probe address belong
+to one of these pop stacking
+
+things, right.
+
+Because the client
+connection stays open.
+
+Now let's say that
+this gadget here,
+
+pointed to something
+like the following.
+
+Maybe it just does like
+an xor, for example.
+
+So it's just going to xor
+some registers and then it's
+
+going to ret.
+
+So what happens if we try
+to jump to this gadget?
+
+Right, note that this does not
+pop anything off the stack, OK.
+
+It just changes the
+contents of registers.
+
+So what's going to happen?
+
+So we're going to
+be here, we're going
+
+to jump to the address
+of this gadget,
+
+stack pointer goes here, OK.
+
+We're going to xor
+these two things, right.
+
+Stack pointer's not
+going to change.
+
+Then we're going to return to
+whatever the top of the stack
+
+is, which is 0, 0.
+
+This is going to crash.
+
+OK, the client connection to
+the server is going to close,
+
+and as a result, the attacker
+knows that this is not
+
+a stack popping gadget.
+
+So does that all make sense?
+
+And so you can also
+imagine that you can--
+
+by coming with more
+baroque series of traps
+
+and stop gadgets
+and stuff like that,
+
+you can find things that
+for example, pop two things
+
+off the stack, right.
+
+You can just put another one
+of these trap instructions
+
+there, right.
+
+And so then unless
+the-- unless this gadget
+
+pops two things
+off, you're going
+
+to end up in one of these
+traps and your code execution
+
+is going to blow up, right.
+
+And so in the paper they discuss
+like this thing called the BROP
+
+gadget, which is sort
+of like hilariously
+
+complex if you're not used
+to returning to programming.
+
+What I'll show you today
+is you can actually
+
+just use these very
+simple pop gadgets
+
+to launch the same attack.
+
+Then hopefully after
+you understand this,
+
+the BROP gadget will
+make more sense.
+
+But does everyone
+understand how we can probe
+
+for these little gadgets here?
+
+OK.
+
+So, once you've got these
+gadgets, what do you know?
+
+Well you found the location
+of code snippets that
+
+allow you to pop stuff up,
+one thing off the stack.
+
+Precisely one thing
+off the stack,
+
+but you don't actually
+know into what register
+
+they're popping it into.
+
+You just know that they're
+getting popped off, right.
+
+And you actually
+need to know what
+
+register these gadgets
+are popping stuff
+
+into, because remember,
+on a 64-bit architecture,
+
+the registers control where the
+arguments are to this function
+
+that you want to invoke, right.
+
+So the ultimate goal
+to keep in mind,
+
+is that we want to be able
+to create some gadgets that
+
+allow us to pop values
+that we put on the stack
+
+into certain registers,
+and eventually we're
+
+going to call a system
+call that's going to allow
+
+us to do something evil.
+
+OK, so the next thing
+that we need to do
+
+is determine which
+registers-- so determine which
+
+registers the pop gadgets use.
+
+So how are we going to do that?
+
+Well basically we can take
+advantage of the pause system
+
+call.
+
+OK, so the pause system call,
+it takes no arguments, right.
+
+And that means that it ignores
+everything in the registers.
+
+OK.
+
+And essentially, to find
+the pause instruction what
+
+we can do is, we can chain
+all of these pop gadgets
+
+in such a way, that we put
+all of them on the stack,
+
+in between each one of them
+we put the syscall number
+
+for pause, and then we
+see if we can actually
+
+get the program to hang.
+
+Let me give you a
+concrete example of that.
+
+So we'll do something like this.
+
+So here for the return address,
+we'll put the following.
+
+So let's say we have one
+gadget that pops RDI register,
+
+then does a ret.
+
+And then up here we'll put
+the syscall number for pause.
+
+And then let's say that we have
+another gadget that we found,
+
+that does a pop into a different
+register, let's say RSI.
+
+And then we'll put the
+system call number for pause
+
+up here again.
+
+And we do this for all the
+gadgets that we've found
+
+and then eventually we put
+the guest address for pause,
+
+or sorry for syscall, excuse me.
+
+Once again, remember how you
+invoke these system calls.
+
+So you basically have to put
+the number of the system call
+
+into the RAX register, then
+you invoke this libc function
+
+syscall which is then going to
+execute the requested system
+
+call, OK.
+
+So what's going to happen
+when we execute this code?
+
+Right, so we're
+going to come here,
+
+we're going to jump to the
+address of this gadget,
+
+and note that as an
+attacker, all that we know
+
+is that this gadget here
+pops something off the stack.
+
+We don't know what the
+register is yet, right.
+
+Put it here just to
+make the [INAUDIBLE],
+
+but the attacker
+doesn't know yet, right.
+
+So if you jump-- or
+sorry the-- we jump
+
+to the gadget, the
+stack corners now here,
+
+what's it going to do?
+
+It's going to pop this
+syscall number for pause,
+
+into some register the
+attacker doesn't know,
+
+and then we're going to continue
+to go up this chain and so
+
+on and so forth.
+
+And what you'll see is that
+each one of these gadgets, one
+
+of them hopefully will
+pop the system call
+
+number into the
+appropriate RAX register.
+
+So that by the time
+we get up to here,
+
+I mean we basically
+polluted all the registers,
+
+with the system call number,
+but hopefully just one of them
+
+has to be correct, right.
+
+Because if one of our gadgets
+does this, then by the time
+
+we ret to here,
+we'll get a pause.
+
+Once again, that pause acts as
+a signal to the attacker, OK.
+
+Because if this guest
+address was wrong,
+
+then probably the program's
+going to crash, right.
+
+So what does this phase
+of the attack let us do?
+
+Well we still don't
+know which gadgets
+
+pop into which registers,
+but we know that one of them
+
+is popped into RAX, which is
+the one we want to control.
+
+And for sure we know the
+address of syscall, right.
+
+Because we were able to
+induce the pause, right.
+
+So once we've done that, right.
+
+Once we know for sure
+where this thing is,
+
+the address for syscall,
+then we can actually just
+
+try the gadgets
+one by one, right.
+
+And see which one of
+them is actually going
+
+to induce the pause, right.
+
+So in other words, cut all
+the middleman here, let's
+
+have a stack it looks like this,
+and then you just immediately
+
+jump to syscall.
+
+Did that cause the
+pause or did it crash?
+
+If it crashed, OK
+we know this gadget,
+
+it pops to RDI for example.
+
+OK, get rid of that one, right.
+
+Try the next gadget, right.
+
+Put the guest address-- put the,
+well it's not guest anymore,
+
+put the real address
+for syscall up here.
+
+Were we able to
+pause the program?
+
+Yes?
+
+Aha, so we know that pop
+gadget must pop into RAX.
+
+So does that make sense?
+
+AUDIENCE: So the way to guess
+the address for system call
+
+is just blind transfer?
+
+PROFESSOR: Yeah, so
+there-- so in the paper,
+
+they go into some
+optimizations about how
+
+you can work in a PLT and
+all that kind of stuff.
+
+Like I said, I think it's easier
+to ignore that for a second,
+
+and just look toward
+the simpler thing
+
+first, but yeah in a simple
+attack that I'm describing,
+
+yeah you just put
+some address up here
+
+and you just see if you pause.
+
+So does that all make sense?
+
+OK so at the end of
+this we actually know
+
+the location of syscall.
+
+We know the location
+of the instruction
+
+that does the pop into RAX.
+
+Now you can imagine that we
+also need gadgets that pop
+
+into some other registers too.
+
+Suffice to say, you can
+do similar tests, right.
+
+So instead of like pushing a
+system call number for pause,
+
+push it for some
+other command that
+
+now takes in all arguments in
+RAX and RDI for example, right.
+
+Do the same type of test, right.
+
+So basically you can
+leverage the fact
+
+that for any particular
+set of registers
+
+that you want to
+be able to control,
+
+there's some system
+call that will give you
+
+a signal as an attacker,
+that allow you to figure out
+
+whether you successfully
+broke it or not.
+
+Right, so at the
+end of this phase,
+
+you basically have
+the address of syscall
+
+and the address of
+a bunch of gadgets
+
+which allow you to pop
+into arbitrary registers.
+
+OK and so now let's
+see so, step 4
+
+is going to be to invoke write.
+
+Step 4 is invoke the
+write system call.
+
+So to invoke write, we need
+to have the following gadgets.
+
+You need to be able to pop RDI.
+
+We need to be able to pop RSI.
+
+We need to be able to pop RDX,
+pop racks, and then invoke
+
+syscall, right.
+
+So as it turns out,
+what are these registers
+
+being used for by system call?
+
+So this is the socket, or more
+generally, the file descriptor
+
+that you're going
+to pass into write.
+
+This is the buffer.
+
+This is the length
+of that buffer.
+
+This is the syscall number.
+
+And it is called syscall.
+
+Right, so if we found
+all these gadgets,
+
+then we can actually
+now control the values
+
+that are put into
+those arguments, that
+
+put in those registers,
+because we just pushed them
+
+on the stack, right.
+
+And so for example, what's
+the socket going to be?
+
+For once you're going to have
+to do a little guessing here,
+
+right.
+
+can take advantage of the
+fact that Linux restricts
+
+the number of simultaneous
+open file connections,
+
+for a file that's
+going to be 2024.
+
+And also it's supposed to
+be the lowest one available.
+
+So we do a little bit of
+guessing here and figure out
+
+what that socket
+is, put it in there.
+
+Now interestingly,
+what are we going
+
+to pass into the buff pointer?
+
+Right, we're actually
+going to use the text
+
+segment of the program.
+
+We're actually going to pass in
+that the pointer to somewhere
+
+in the code of the program.
+
+So what's that going
+to allow us to do?
+
+That's going to allows us to
+read the binary, out of memory,
+
+using the right call
+to the client socket.
+
+So that the attacker can
+then take that binary,
+
+analyze it offline, right.
+
+Just use GDB, or
+whatever, to figure out
+
+where everything is located.
+
+The attacker knows that now,
+every time the server crashes,
+
+it's going to have the same
+randomized set of things in it.
+
+So now, once the attacker can
+find out addresses and offsets
+
+for stuff, now the
+attacker can directly
+
+attack those gadgets, right.
+
+Directly attack other
+vulnerabilities,
+
+figure out how to open up a
+shell, so on and so forth.
+
+So in other words,
+at the point you
+
+exfiltrated the binary to the
+attacker, you basically lost.
+
+Right, so this is essentially
+how the BROP attack works.
+
+Like I said, in
+the paper, there's
+
+a bunch of optimization,
+but really you
+
+need to understand this
+stuff, the basic stuff,
+
+before that optimization
+will start to make sense.
+
+And so we can talk about the
+optimization with me offline
+
+if you want, or after class.
+
+But to suffice it
+to say, this is
+
+the basics of how you
+launch that BROP attack.
+
+You've got to find
+the stop gadget,
+
+find those gadgets
+that pop stack entries.
+
+Figure out which
+of those registers
+
+those gadgets pop
+into, and find out
+
+how to figure out where
+syscall is, and then invoke
+
+write by accumulating
+all that knowledge.
+
+So very quickly, how do
+you defend against BROP?
+
+Well the most obvious
+thing is you've
+
+got to rerandomize, right.
+
+So the fact that
+crashed servers do not
+
+respawn, rerandomize
+versions of themselves,
+
+that allows the crash to
+act as a signal that let's
+
+the attacker test
+various hypotheses
+
+about how the programs working.
+
+So one simple defense
+is to make sure
+
+that you do exec when you spawn
+your process, instead of fork,
+
+right.
+
+Because when you exec the
+process, you create totally new
+
+randomized layout space,
+at least on Linux, right.
+
+So on Linux, when you compile
+with this PIE, the Position
+
+Independent Executable
+flag, you only
+
+get that randomized
+address space
+
+that's new if you use exec.
+
+So another event you can
+use is just use Windows,
+
+because Windows
+basically does not
+
+have a fork equivalent, right.
+
+So hooray for us.
+
+So that means that
+on Windows, whenever
+
+you spawn that new
+server, it's always
+
+going to have a new
+randomized address space.
+
+I think someone over here
+mentioned something like,
+
+what would happen
+if for example,
+
+when the server crashed,
+it didn't actually
+
+close the connection?
+
+Right, so you can
+imagine one thing
+
+that when a crash takes place,
+we somehow catch that fault
+
+and then we keep that connection
+open for a little while
+
+to confuse the attacker
+and remove that signal,
+
+that something's gone amiss.
+
+So that's something
+you definitely do.
+
+What's hilarious about that
+is, that now your BROP attack
+
+turns into a denial
+of service attack.
+
+Because now you just got
+all the potential zombie
+
+processes that are sitting
+around, they segfaulted.
+
+They're useless in
+society, but you
+
+can't let them go, because
+otherwise you're going
+
+to delete this information.
+
+Another thing you
+might think about to,
+
+is you could do bounds
+checking, right.
+
+We just talked a bunch
+about that, right.
+
+But in the paper, they
+casually dismiss this
+
+as saying it has
+up to 2x overhead,
+
+so nobody's going to do that,
+but you could in fact do that.
+
+So that's basically
+how BROP works.
+
+As for the homework
+question, the homework
+
+questions a bit subtle, because
+the homework question says,
+
+what if you use a hash of
+the current time, right?
+
+Get time of day when you
+restarted the program.
+
+Is that sufficient to
+prevent this type of attack?
+
+Well note that, hashing
+does not magically
+
+provide you bits of entropy
+if the input to the hash
+
+is easily guessable, right.
+
+If I know that you're only
+going to hash one or two things,
+
+it doesn't matter if I have
+like some a jillion bit hash.
+
+Doesn't matter.
+
+So I can just guess one of those
+two values and see what is.
+
+So the thing to note is
+that get time of day,
+
+actually has much less
+entropy than you might think.
+
+Particularly because the
+attacker can actually
+
+check what time he or she is
+launching the attack, right.
+
+So that's going to actually
+remove a bunch of entropy
+
+from that calculation, right.
+
+So there's some
+subtleties there.
+
+What's the server skew in
+terms of clock or the client
+
+and so on and so forth.
+
+The long story short, using
+a guessable base value,
+
+even with guessable
+just inside of a range,
+
+is super useful for
+the attacker, right.
+
+Particularly
+because the attack--
+
+we can start subverting a
+bunch of servers in parallel
+
+and know that all
+of them should have
+
+fairly similar values, right.
+
+This is a high order
+of bits, right.
+
+So long story
+short, the answer is
+
+that, it's literally better
+than nothing to randomize,
+
+if you use get time of day, but
+it doesn't actually provide you
+
+as much security as you think.
+
+And the other lesson too
+is, that just because you
+
+hash something
+right, that doesn't
+
+matter if you're not actually
+using that hash in a smart way.
+
+You have a question?
+
+AUDIENCE: Oh, still when I
+did the calculations that some
+
+[INAUDIBLE] it seems
+like maybe to be
+
+able to get the offset
+that the [INAUDIBLE]
+
+your [INAUDIBLE]
+start the process
+
+to within like 48 milliseconds?
+
+PROFESSOR: Yes and
+getting the timing right
+
+depends on a bunch of
+different things, right.
+
+But you could take
+advantage of the fact
+
+that the attacker can open
+up a bunch of connections
+
+in parallel, and
+leverage the fact
+
+that even if the initial
+guess a little bit off,
+
+you can still launch
+multiple guesses on what
+
+should be very
+similar canary values,
+
+and do that attack in parallel.
+
+But you're right, there's
+tricky time and issues.
\ No newline at end of file
diff --git a/x_DGTWH4tEA.txt b/x_DGTWH4tEA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..004c75373788f93d4bada7622c40f3c1102f6c55
--- /dev/null
+++ b/x_DGTWH4tEA.txt
@@ -0,0 +1,787 @@
+align:start position:0%
+ 
+so today was the
+
+ align:start position:0%
+so today was the
+ 
+
+ align:start position:0%
+so today was the
+lecture on scripting and hosting it's
+
+ align:start position:0%
+lecture on scripting and hosting it's
+ 
+
+ align:start position:0%
+lecture on scripting and hosting it's
+the end of day three
+
+ align:start position:0%
+the end of day three
+ 
+
+ align:start position:0%
+the end of day three
+this was probably the lecture that i was
+
+ align:start position:0%
+this was probably the lecture that i was
+ 
+
+ align:start position:0%
+this was probably the lecture that i was
+the most prepared for in terms of
+
+ align:start position:0%
+the most prepared for in terms of
+ 
+
+ align:start position:0%
+the most prepared for in terms of
+practice ahead of time ahead of this
+
+ align:start position:0%
+practice ahead of time ahead of this
+ 
+
+ align:start position:0%
+practice ahead of time ahead of this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+because it's kind of like what george
+
+ align:start position:0%
+because it's kind of like what george
+ 
+
+ align:start position:0%
+because it's kind of like what george
+and i do
+
+ align:start position:0%
+and i do
+ 
+
+ align:start position:0%
+and i do
+for most of the production process that
+
+ align:start position:0%
+for most of the production process that
+ 
+
+ align:start position:0%
+for most of the production process that
+happens for science out loud so whenever
+
+ align:start position:0%
+happens for science out loud so whenever
+ 
+
+ align:start position:0%
+happens for science out loud so whenever
+we work with our students
+
+ align:start position:0%
+we work with our students
+ 
+
+ align:start position:0%
+we work with our students
+in the individual seasons
+
+ align:start position:0%
+in the individual seasons
+ 
+
+ align:start position:0%
+in the individual seasons
+this is basically what we do with them
+
+ align:start position:0%
+this is basically what we do with them
+ 
+
+ align:start position:0%
+this is basically what we do with them
+just a little bit more formalized and
+
+ align:start position:0%
+just a little bit more formalized and
+ 
+
+ align:start position:0%
+just a little bit more formalized and
+for a longer period of time it is
+
+ align:start position:0%
+for a longer period of time it is
+ 
+
+ align:start position:0%
+for a longer period of time it is
+so hard to teach
+
+ align:start position:0%
+so hard to teach
+ 
+
+ align:start position:0%
+so hard to teach
+good hosting because it's one of those
+
+ align:start position:0%
+good hosting because it's one of those
+ 
+
+ align:start position:0%
+good hosting because it's one of those
+things that you can sit and read about
+
+ align:start position:0%
+things that you can sit and read about
+ 
+
+ align:start position:0%
+things that you can sit and read about
+and you can watch
+
+ align:start position:0%
+and you can watch
+ 
+
+ align:start position:0%
+and you can watch
+a bunch of case studies and it just
+
+ align:start position:0%
+a bunch of case studies and it just
+ 
+
+ align:start position:0%
+a bunch of case studies and it just
+doesn't matter until you try to adopt it
+
+ align:start position:0%
+doesn't matter until you try to adopt it
+ 
+
+ align:start position:0%
+doesn't matter until you try to adopt it
+yourself i had planned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all this material or it would be like
+
+ align:start position:0%
+all this material or it would be like
+ 
+
+ align:start position:0%
+all this material or it would be like
+there were all these videos of various
+
+ align:start position:0%
+there were all these videos of various
+ 
+
+ align:start position:0%
+there were all these videos of various
+hosts
+
+ align:start position:0%
+hosts
+ 
+
+ align:start position:0%
+hosts
+and it was going to be sort of a similar
+
+ align:start position:0%
+and it was going to be sort of a similar
+ 
+
+ align:start position:0%
+and it was going to be sort of a similar
+exercise to day one to all those youtube
+
+ align:start position:0%
+exercise to day one to all those youtube
+ 
+
+ align:start position:0%
+exercise to day one to all those youtube
+videos where they would go through and
+
+ align:start position:0%
+videos where they would go through and
+ 
+
+ align:start position:0%
+videos where they would go through and
+they would write you know some of the
+
+ align:start position:0%
+they would write you know some of the
+ 
+
+ align:start position:0%
+they would write you know some of the
+qualities that they liked and
+
+ align:start position:0%
+qualities that they liked and
+ 
+
+ align:start position:0%
+qualities that they liked and
+um try to see what they wanted to take
+
+ align:start position:0%
+um try to see what they wanted to take
+ 
+
+ align:start position:0%
+um try to see what they wanted to take
+on for themselves but we just
+
+ align:start position:0%
+on for themselves but we just
+ 
+
+ align:start position:0%
+on for themselves but we just
+totally scrapped it and i i think
+
+ align:start position:0%
+totally scrapped it and i i think
+ 
+
+ align:start position:0%
+totally scrapped it and i i think
+honestly it was much better that we did
+
+ align:start position:0%
+honestly it was much better that we did
+ 
+
+ align:start position:0%
+honestly it was much better that we did
+the hosting thing is hard and helping
+
+ align:start position:0%
+the hosting thing is hard and helping
+ 
+
+ align:start position:0%
+the hosting thing is hard and helping
+the students really be comfortable with
+
+ align:start position:0%
+the students really be comfortable with
+ 
+
+ align:start position:0%
+the students really be comfortable with
+their own voice and their own persona on
+
+ align:start position:0%
+their own voice and their own persona on
+ 
+
+ align:start position:0%
+their own voice and their own persona on
+screen
+
+ align:start position:0%
+screen
+ 
+
+ align:start position:0%
+screen
+it's really important so i don't want to
+
+ align:start position:0%
+it's really important so i don't want to
+ 
+
+ align:start position:0%
+it's really important so i don't want to
+distract from that at all one of the
+
+ align:start position:0%
+distract from that at all one of the
+ 
+
+ align:start position:0%
+distract from that at all one of the
+students wanted to minimize her presence
+
+ align:start position:0%
+students wanted to minimize her presence
+ 
+
+ align:start position:0%
+students wanted to minimize her presence
+on screen i don't want the students here
+
+ align:start position:0%
+on screen i don't want the students here
+ 
+
+ align:start position:0%
+on screen i don't want the students here
+to sell themselves short
+
+ align:start position:0%
+to sell themselves short
+ 
+
+ align:start position:0%
+to sell themselves short
+on on the power that they have as a
+
+ align:start position:0%
+on on the power that they have as a
+ 
+
+ align:start position:0%
+on on the power that they have as a
+practitioner of some of the science and
+
+ align:start position:0%
+practitioner of some of the science and
+ 
+
+ align:start position:0%
+practitioner of some of the science and
+the engineering
+
+ align:start position:0%
+the engineering
+ 
+
+ align:start position:0%
+the engineering
+to to default
+
+ align:start position:0%
+to to default
+ 
+
+ align:start position:0%
+to to default
+to a type of video that
+
+ align:start position:0%
+to a type of video that
+ 
+
+ align:start position:0%
+to a type of video that
+a lot of other people can make these
+
+ align:start position:0%
+a lot of other people can make these
+ 
+
+ align:start position:0%
+a lot of other people can make these
+students are not the best hosts finding
+
+ align:start position:0%
+students are not the best hosts finding
+ 
+
+ align:start position:0%
+students are not the best hosts finding
+like a neil degrasse tyson at mit
+
+ align:start position:0%
+like a neil degrasse tyson at mit
+ 
+
+ align:start position:0%
+like a neil degrasse tyson at mit
+you can't bank on that and i don't mean
+
+ align:start position:0%
+you can't bank on that and i don't mean
+ 
+
+ align:start position:0%
+you can't bank on that and i don't mean
+that in a mean way perhaps i should
+
+ align:start position:0%
+that in a mean way perhaps i should
+ 
+
+ align:start position:0%
+that in a mean way perhaps i should
+rephrase this maybe they can cut this
+
+ align:start position:0%
+rephrase this maybe they can cut this
+ 
+
+ align:start position:0%
+rephrase this maybe they can cut this
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+it is an imprudent thing to assume that
+
+ align:start position:0%
+it is an imprudent thing to assume that
+ 
+
+ align:start position:0%
+it is an imprudent thing to assume that
+we're going to find the next bill night
+
+ align:start position:0%
+we're going to find the next bill night
+ 
+
+ align:start position:0%
+we're going to find the next bill night
+at mit we can expect the students to
+
+ align:start position:0%
+at mit we can expect the students to
+ 
+
+ align:start position:0%
+at mit we can expect the students to
+become like hank green and to make the
+
+ align:start position:0%
+become like hank green and to make the
+ 
+
+ align:start position:0%
+become like hank green and to make the
+next sci show like that's an unfair
+
+ align:start position:0%
+next sci show like that's an unfair
+ 
+
+ align:start position:0%
+next sci show like that's an unfair
+expectation to have but the value
+
+ align:start position:0%
+expectation to have but the value
+ 
+
+ align:start position:0%
+expectation to have but the value
+proposition
+
+ align:start position:0%
+proposition
+ 
+
+ align:start position:0%
+proposition
+that they offer here which i think is so
+
+ align:start position:0%
+that they offer here which i think is so
+ 
+
+ align:start position:0%
+that they offer here which i think is so
+powerful which i think is the most
+
+ align:start position:0%
+powerful which i think is the most
+ 
+
+ align:start position:0%
+powerful which i think is the most
+important thing
+
+ align:start position:0%
+important thing
+ 
+
+ align:start position:0%
+important thing
+that someone like michael stevens on
+
+ align:start position:0%
+that someone like michael stevens on
+ 
+
+ align:start position:0%
+that someone like michael stevens on
+vsauce can't do and scishow can't do is
+
+ align:start position:0%
+vsauce can't do and scishow can't do is
+ 
+
+ align:start position:0%
+vsauce can't do and scishow can't do is
+that they are the scientists they are
+
+ align:start position:0%
+that they are the scientists they are
+ 
+
+ align:start position:0%
+that they are the scientists they are
+the people who worked in the industry
+
+ align:start position:0%
+the people who worked in the industry
+ 
+
+ align:start position:0%
+the people who worked in the industry
+they are the
+
+ align:start position:0%
+they are the
+ 
+
+ align:start position:0%
+they are the
+they are the actual naval engineers that
+
+ align:start position:0%
+they are the actual naval engineers that
+ 
+
+ align:start position:0%
+they are the actual naval engineers that
+is something
+
+ align:start position:0%
+is something
+ 
+
+ align:start position:0%
+is something
+for me personally is so important to
+
+ align:start position:0%
+for me personally is so important to
+ 
+
+ align:start position:0%
+for me personally is so important to
+highlight so to make themselves evident
+
+ align:start position:0%
+highlight so to make themselves evident
+ 
+
+ align:start position:0%
+highlight so to make themselves evident
+i think is really important to make
+
+ align:start position:0%
+i think is really important to make
+ 
+
+ align:start position:0%
+i think is really important to make
+themselves the host to make themselves
+
+ align:start position:0%
+themselves the host to make themselves
+ 
+
+ align:start position:0%
+themselves the host to make themselves
+visible to
+
+ align:start position:0%
+visible to
+ 
+
+ align:start position:0%
+visible to
+to make their persona and their actual
+
+ align:start position:0%
+to make their persona and their actual
+ 
+
+ align:start position:0%
+to make their persona and their actual
+personal stories
+
+ align:start position:0%
+personal stories
+ 
+
+ align:start position:0%
+personal stories
+part of the video i think is important
+
+ align:start position:0%
+part of the video i think is important
+ 
+
+ align:start position:0%
+part of the video i think is important
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+you're in front of a camera or you're on
+
+ align:start position:0%
+you're in front of a camera or you're on
+ 
+
+ align:start position:0%
+you're in front of a camera or you're on
+a stage or you're on a podium giving a
+
+ align:start position:0%
+a stage or you're on a podium giving a
+ 
+
+ align:start position:0%
+a stage or you're on a podium giving a
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+the habit of falling back into this
+
+ align:start position:0%
+the habit of falling back into this
+ 
+
+ align:start position:0%
+the habit of falling back into this
+monotonous robotic
+
+ align:start position:0%
+monotonous robotic
+ 
+
+ align:start position:0%
+monotonous robotic
+or perceived persona that you think you
+
+ align:start position:0%
+or perceived persona that you think you
+ 
+
+ align:start position:0%
+or perceived persona that you think you
+have to take on
+
+ align:start position:0%
+have to take on
+ 
+
+ align:start position:0%
+have to take on
+totally happens all the time
+
+ align:start position:0%
+totally happens all the time
+ 
+
+ align:start position:0%
+totally happens all the time
+so i think it's a relevant lesson that
+
+ align:start position:0%
+so i think it's a relevant lesson that
+ 
+
+ align:start position:0%
+so i think it's a relevant lesson that
+people can take with them after this
+
+ align:start position:0%
+people can take with them after this
+ 
+
+ align:start position:0%
+people can take with them after this
+class is over
+
+ align:start position:0%
+class is over
+ 
+
+ align:start position:0%
+class is over
+i'm definitely rambling at this point
+
+ align:start position:0%
+i'm definitely rambling at this point
+ 
+
+ align:start position:0%
+i'm definitely rambling at this point
+maybe it's because george said most of
+
+ align:start position:0%
+maybe it's because george said most of
+ 
+
+ align:start position:0%
+maybe it's because george said most of
+the talking today
+
+ align:start position:0%
+the talking today
+ 
+
+ align:start position:0%
+the talking today
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but i think it went
+
+ align:start position:0%
+but i think it went
+ 
+
+ align:start position:0%
+but i think it went
+i think it went okay
\ No newline at end of file
diff --git a/xuAD_a1OuNo.txt b/xuAD_a1OuNo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26751b2243b0e9672d274d63698a6d9307421cff
--- /dev/null
+++ b/xuAD_a1OuNo.txt
@@ -0,0 +1,3672 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality, educational
+
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: We're going to talk
+about something we've sort of
+
+touched on, in many different
+contexts, but more head on
+
+this time, and that's
+entrepreneurship.
+
+And sort of the starting point
+of that, I think, there's a
+
+story that somebody once told
+me, which, I thought, kind of
+
+frames one side of the
+debate very well.
+
+I was on the plane with a man,
+who was clearly sort of a
+
+rich, Indian businessman.
+
+And he was quizzing me
+about what I did.
+
+And I said, I study economics
+and poor people.
+
+And he was very much
+of the view.
+
+He said, look, you know, there's
+all this stuff about
+
+poor people.
+
+You guys don't understand
+poor people.
+
+They have an entrepreneurial
+genius in them.
+
+You think I'm a successful
+entrepreneur.
+
+The way I learned
+entrepreneurship
+
+was from the poor.
+
+So I was kind of saying, yeah,
+yeah, yeah, right.
+
+Well then he told me a story
+that was actually quite
+
+compelling.
+
+And mostly people--
+
+whatever this means, it's
+never clear to me.
+
+So I was being slightly
+skeptical.
+
+But then he told me a story
+that was very compelling.
+
+So he said that he had
+an MBA from the US.
+
+I think from Kellogg.
+
+And he went back to India
+after doing his MBA.
+
+And when he arrived in India,
+his uncle, who was a
+
+businessman in Bombay, said
+look, you want to be an
+
+entrepreneur.
+
+Let me show you what
+entrepreneurship is.
+
+So basically, they got
+in his uncle's car.
+
+The uncle drove him
+all the way to the
+
+Bombay stock exchange.
+
+The Bombay stock exchange, well,
+he thought that they
+
+would just go inside
+the stock exchange.
+
+But in fact, he parked his car
+in front of the exchange and
+
+pointed to four women who were
+sitting on the side of the
+
+street that goes in front
+of the exchange.
+
+And he said, you know, can you
+figure out what those women's
+
+business model is?
+
+So he says, well, I
+looked and looked.
+
+And they would just get
+up, from time to time.
+
+They'll scrape something off the
+street, then they'll come
+
+and sit down.
+
+And then they'll be sitting
+and talking to each other.
+
+It's early in the morning, like
+8:30 in the morning or
+
+9:00 in the morning.
+
+Cars were driving by.
+
+People were showing up to work
+at the stock exchange.
+
+But what does it have anything
+to do with entrepreneurship?
+
+So he kind of tried to come up
+with some answer, completely
+
+didn't manage, and finally
+told his uncle,
+
+look, I have no idea.
+
+Why don't you tell me?
+
+His uncle said, these women get
+up at 5:30 in the morning.
+
+They go to the beach.
+
+In the morning, the tide has
+receded, so there's wet sand
+
+on the beach.
+
+They collect the wet sand and
+then they put it in a bag.
+
+They come to the
+stock exchange.
+
+This is one place where
+lots of cars go by.
+
+And there's a nice
+sidewalk to sit.
+
+Before the traffic starts,
+they lay the
+
+sand out on the street.
+
+And then they sit there.
+
+And as people drive on the
+stand, the heat from the tires
+
+dries the sand.
+
+So the sand gets heated and
+eventually dried by the tires.
+
+Once the sand is fully dry, they
+scrape off the sand and
+
+put it in a bag and take
+it back to the
+
+slums where they live.
+
+Women use this dry sand
+as like a scrubber.
+
+To clean dishes, you use
+this dry sand as a
+
+scrubber for that.
+
+And so they use this
+dry sand to scrub
+
+off their dirty dishes.
+
+And that's all dirty--
+
+I don't know, whatever--
+
+cook pot and pans.
+
+And that's how these people
+make a living.
+
+They dry the sand,
+and they sell it.
+
+So this was his example of how
+infinitely creative poor
+
+people are.
+
+And my reaction to that was,
+you know, isn't that saying
+
+much more about how creative
+you have to be to make a
+
+living if you are poor then
+how creative the poor are?
+
+So it's the same proposition,
+in a sense.
+
+You could say that this
+shows that the
+
+poor are very creative.
+
+Or you could show that the
+poor have no business
+
+opportunities so they have to
+do this completely bizarre
+
+thing to make a living.
+
+And those are just two sides
+of the same coin.
+
+And I don't know.
+
+So what I want to talk about
+today is a bit on this
+
+implicit and often
+explicit debate--
+
+So before we get there--
+
+on whether the poor are
+entrepreneurial in some
+
+meaningful sense of
+the word or not.
+
+So let's start at
+the beginning.
+
+Who's an entrepreneur?
+
+How do you define
+an entrepreneur?
+
+AUDIENCE: I guess I would define
+an entrepreneur as
+
+someone who goes about creating
+a new venture that
+
+often involves a greater than
+average amount of risk.
+
+PROFESSOR: So if I am someone
+who works for Toyota and
+
+designs a slightly different
+car, am I an entrepreneur?
+
+AUDIENCE: I would say not.
+
+PROFESSOR: Why not?
+
+It's risk.
+
+I could fail.
+
+I would look really, really
+stupid to my bosses.
+
+AUDIENCE: But it creates
+a new venture.
+
+I mean, right there, you're
+developing a product inside.
+
+PROFESSOR: New venture?
+
+So it has to be a new,
+separate company.
+
+Is that the definition?
+
+AUDIENCE: No, but I'd say a
+venture not a design, right?
+
+PROFESSOR: But I haven't
+got what that means.
+
+AUDIENCE: Like a venture in
+the sense that it doesn't
+
+necessarily have to be entirely
+its own company, but
+
+it's more than just a design.
+
+In the sense of a design, but
+then you're not taking into
+
+account the other things that
+would actually go into making
+
+it a car and then
+selling that.
+
+Like let's say Toyota decides
+to launch a new line, where
+
+they're going to do a new
+dealership agreement, new
+
+factory, all that, then that
+would be a new venture.
+
+If I was running that, then I
+could be classified, under my
+
+definition, as an
+entrepreneur.
+
+PROFESSOR: OK.
+
+So you would--
+
+OK, go ahead.
+
+No, you should go ahead.
+
+AUDIENCE: I think the term, that
+we'd have to go into the
+
+definition.
+
+Besides just creating a new
+venture, it would be create a
+
+new venture that is, somehow,
+innovative and
+
+unique in it's own.
+
+So I think, whether not,
+necessarily, the business idea
+
+or the business strategy of the
+product, but maybe even in
+
+how the person operates the
+company, they can be
+
+entrepreneurs in that way.
+
+PROFESSOR: So you don't think
+that if I have a set of taxis
+
+I'm an entrepreneur?
+
+I just bought a set of taxis.
+
+I rent them out.
+
+AUDIENCE: I would imagine if you
+were the person who took
+
+the initiative to--
+
+PROFESSOR: But this was after
+there had been 500,000 taxi
+
+companies in the world.
+
+If I go tomorrow, quit my job,
+and I start a taxi company, I
+
+would not be an entrepreneur?
+
+AUDIENCE: Well, to some
+degree, you could
+
+that's still unique.
+
+You're starting a taxi company,
+in a particular city,
+
+with a particular
+set of drivers.
+
+PROFESSOR: But then everything's
+unique.
+
+Once I go down that road, I
+don's see how anything.
+
+I can't have a taxi company
+which has the same set of
+
+drivers as theirs,
+everybody else.
+
+So this is unique
+by definition.
+
+Somebody else from
+that side, yeah?
+
+AUDIENCE: I think someone was
+actually saying before that
+
+created a normal
+amount of risk.
+
+But it's like the financial
+risk, as well, absorbing that
+
+yourself, as opposed to being
+responsible for it underneath
+
+an organization.
+
+PROFESSOR: Right.
+
+I think that's actually one
+key piece of what I would
+
+consider the definition.
+
+The fact that you a lot
+of the risk comes
+
+from raising capital.
+
+The risk is a significant
+part of the reason why.
+
+If I work for Toyota
+there would not be.
+
+It could be career
+risk for me.
+
+But it would not be risk that
+is driven by my having to
+
+raise capital.
+
+So I think you're making one of
+the key points, which is, I
+
+think, exactly as you said.
+
+Risk is a big piece of it.
+
+The next piece of it
+is the risk comes
+
+from raising capital.
+
+I would not say that it has to
+be a new product, because I
+
+think that's too narrow
+a definition.
+
+I mean you could define it.
+
+But I think that would mean no
+poor people are, essentially,
+
+entrepreneurs.
+
+But I think raising capital,
+the financing side of it.
+
+So do you take the risk?
+
+And a lot of the risk comes from
+owning the asset that's
+
+generating the output.
+
+That, I think, is a key part
+of being an entrepreneur.
+
+The risk comes from putting
+money or your own
+
+assets on the line.
+
+It's not just that you're
+putting your career or your
+
+name on the line.
+
+When I write a book, I also
+take a risk in that sense.
+
+People could say, my god,
+what a stupid book.
+
+That's a risk, but I wouldn't
+call myself an entrepreneur.
+
+So I think that I want to
+emphasize that I think the
+
+poor are entrepreneurial.
+
+When we talk about somebody who
+is an entrepreneur, I'm
+
+going to emphasize the fact that
+they bear a lot of the
+
+risk, from production, and that
+risk is closely tied to
+
+the ownership of the asset.
+
+So it is that they have to
+finance the asset and hold on
+
+to the risk generated
+by that asset.
+
+So they could be a farmer.
+
+They must have to own
+the land and then
+
+take the farming risk.
+
+Yeah?
+
+AUDIENCE: But in the US, don't
+a lot of the people, who we
+
+think of as entrepreneurs, they
+get venture capital or
+
+somebody else to take on
+the financial risk.
+
+AUDIENCE: But it kind of defers
+the financial risk.
+
+They're still taking on
+financial risk of their own.
+
+PROFESSOR: But first, I think,
+nobody gets 100% venture
+
+capital funding.
+
+Even to get to the venture
+capital stage, you typically
+
+spend a fair amount of money.
+
+And nobody gets 100%
+funding even then.
+
+And second, in some ways, you
+still take financial risk, in
+
+the sense that the upside on
+the venture capital is
+
+precisely your earnings
+in the future.
+
+So you, basically, dock
+your earnings.
+
+You are an owner.
+
+You have arranged a particular
+form of financing, which says
+
+that I don't make any payments
+for the time
+
+being, on this financing.
+
+But it's exactly like any
+other form of financing.
+
+I have an obligation
+to pay you.
+
+That obligation, in venture
+capital, is
+
+maybe in five years.
+
+If the company goes public,
+then I will
+
+pay you $100 million.
+
+That's a venture capital
+contract.
+
+It's still, basically,
+a sharing of risk.
+
+And I'm taking ownership
+of the asset.
+
+It's just a different
+contract.
+
+Yeah.
+
+AUDIENCE: It's also the
+opportunity cost of actually
+
+putting all of your energy into
+this venture to see it
+
+come to fruition, like all the
+earnings that you could have
+
+earned in that time working
+[INAUDIBLE].
+
+PROFESSOR: But that's a bit
+like I could have spent my
+
+time consulting or I
+could write a book.
+
+I mean that's not
+that different.
+
+I think the key is that my
+earnings are significantly
+
+connected to the outcome
+of the project.
+
+I was just adding to the cost of
+what of entrepreneur takes
+
+on [INAUDIBLE].
+
+AUDIENCE: I mean, if you wrote
+a book that sold 10 million
+
+copies or something, then your
+future earnings would be
+
+significantly.
+
+PROFESSOR: Yeah, but mostly, I
+think the first order risk,
+
+sadly, for me is that people
+will just think I'm stupid.
+
+I think the risk, in my case.
+
+You could imagine everybody has
+a small chance of being an
+
+entrepreneur, but I think that
+mostly, most of my risk has
+
+something to do with my ability
+to convince other
+
+people that I have not lost my
+marbles and very little of my
+
+risk comes from money.
+
+AUDIENCE: Yeah, but at the same
+time, there's some people
+
+who are like full-time
+authors.
+
+And they take out loans.
+
+And they write this book.
+
+PROFESSOR: Oh, they are
+entrepreneurial.
+
+I'm not saying they are
+not entrepreneurs.
+
+I think I am not an
+entrepreneur, to first
+
+approximation, because my risk
+is mostly reputational risk,
+
+very little of it is
+financial risk.
+
+AUDIENCE: Even though you're
+sort of doing a similar thing?
+
+PROFESSOR: Yes.
+
+My lifetime earnings are,
+essentially, with a 99%
+
+probability, are unaffected by
+this decision, or almost
+
+unaffected.
+
+So who is and isn't
+an entrepreneur?
+
+So we've sort of been
+talking about that.
+
+I'm not, but who is?
+
+So clearly, Larry Page and
+Sergey Brin are entrepreneurs.
+
+Now let's take something
+less obvious.
+
+What are other forms of
+entrepreneurship, like in the
+
+US, less obvious ones then
+starting a software company?
+
+AUDIENCE: I mean someone who
+owns and rents a foodtruck.
+
+So
+
+PROFESSOR: That's an
+entrepreneur, sure.
+
+AUDIENCE: Someone who
+starts a laundromat.
+
+PROFESSOR: That's
+an entrepreneur.
+
+AUDIENCE: So I kind of disagree
+with the fact that
+
+you've got to have some
+sort of earnings
+
+attached to your venture.
+
+I think if somebody starts a
+business that focused on
+
+community service but is very
+unique, entrepreneurial, I
+
+think that is still.
+
+If it is innovative in some way,
+I still think it should
+
+be considered as
+entrepreneurship.
+
+PROFESSOR: I think they say,
+sometimes, somebody is a
+
+political entrepreneur.
+
+But I think that gets the term
+to be a little bit too hard to
+
+understand.
+
+I mean, I think you could make
+the case that you're making.
+
+I'm going to sort of resist
+that a little bit.
+
+Because I think, then,
+I don't know what
+
+the limits are anymore.
+
+Who's not a political
+entrepreneur?
+
+If I go and claim that President
+Obama was born in
+
+Kenya, am I a political
+entrepreneur or not?
+
+Is that entrepreneurial?
+
+Yes, it's entrepreneurial.
+
+It's innovative.
+
+I feel like that's making
+it too easy.
+
+AUDIENCE: So were the people
+collecting sand entrepreneurs?
+
+PROFESSOR: Sure.
+
+They owned this enterprise.
+
+Their entire earnings
+was subject to that.
+
+They had financed whatever
+needed to be financed.
+
+They had paid for the
+plastic bucket.
+
+They collected the
+sand, the spade.
+
+They had paid the bus fare to
+get from the beach to the
+
+Bombay stock exchange.
+
+They had done all
+of the financial
+
+investment that was involved.
+
+It just happens to a small
+amount of money.
+
+But that doesn't mean that
+they hadn't done--
+
+they had put in 100% of
+the capital in there.
+
+But another example, just to
+not get too stuck on it.
+
+Lawyers, for example, most
+lawyers are, effectively,
+
+entrepreneurs.
+
+Because most lawyers actually
+have a two-person,
+
+three-person partnership.
+
+They're bearing a lot of risk.
+
+They pay for the staff.
+
+They pay for the office.
+
+They pay for the whatever,
+the furniture.
+
+And so, in that sense, they
+would, under this definition,
+
+also count.
+
+AUDIENCE: I was going to say
+you could also say that for
+
+doctors as well.
+
+PROFESSOR: Doctors the same,
+a lot of doctors.
+
+I think that's relevant, because
+the typical way--
+
+there's no measurement of
+entrepreneurship in the data.
+
+Because nobody knows who's an
+entrepreneur, for the same
+
+reason as we were having
+trouble with it.
+
+What is measured in the data
+is whether you describe
+
+yourself as self-employed.
+
+That's described in the data.
+
+So if you look at most
+countries, one of the
+
+employment categories
+is self-employed.
+
+And that number, which includes
+lawyers, doctors,
+
+consultants, many other such
+people, and not just
+
+laundromat owners and Google
+owners, but lots of other
+
+people, that category turns
+out to be about 12% of the
+
+population.
+
+So 12% of the population,
+under a very generous
+
+definition of entrepreneur,
+which is self-employed, are
+
+entrepreneurs.
+
+That's for the OECD.
+
+The OECD is like all the rich
+countries in the world.
+
+In the rich countries, roughly
+12% of the population would
+
+call themselves self-employed.
+
+That number is much
+higher among the
+
+poor in poor countries.
+
+And I'm going to show
+you some numbers.
+
+So here's some numbers.
+
+So self-employed in agriculture,
+rural population,
+
+you can see that, in many
+countries, over 75 to even
+
+100%, nearly, are self-employed
+in agriculture.
+
+Take Panama or Pakistan, like
+70% of these people are
+
+self-employed in agriculture.
+
+Meaning that they, basically,
+exactly using the equivalent
+
+definition to the one that's
+used in the OECD, which is
+
+that they describe themselves
+as self-employed.
+
+Meaning that, typically, they
+are putting up the capital,
+
+usually the land and the inputs,
+and they're getting
+
+the returns.
+
+So they are risk taking.
+
+And they're betting a lot of
+risk, and they own the assets
+
+that are generating that risk.
+
+So that's a number
+that's high.
+
+As you will see, that number
+is, in a sense, an
+
+underestimate of how
+many people are
+
+self-employed overall.
+
+So this is just in
+agriculture.
+
+This is how many people who
+have somebody who's
+
+self-employed in
+non-agricultural work.
+
+In Brazil, rural Brazil,
+60-something-percent are
+
+self-employed in
+non-agricultural work.
+
+So who are these people?
+
+They're like somebody who
+provides any services, a
+
+barber, carpenters, somebody
+who builds, a bricklayer.
+
+Instead of a working as a part
+of a company, most of these
+
+people just work as
+single-person enterprises.
+
+So bricklayers are
+bricklayers.
+
+They have a brick laying
+company, which is themselves.
+
+And they, typically, will do the
+brick laying for somebody.
+
+In many ways, this is another.
+
+So if you have to take the
+fraction of people who are
+
+self-employed, either in
+agricultural or not, or
+
+somebody in their family is
+self-employed in either
+
+agriculture or outside
+agriculture, that's and even
+
+higher fraction.
+
+That's like 70% of most poor
+people have somebody in the
+
+family who is self-employed.
+
+So this is a combination of
+these two sets of numbers.
+
+And some of them are both.
+
+Some of them have one family
+member who is self-employed in
+
+agriculture, one family member
+who is self-employed outside
+
+agriculture.
+
+But even if you take
+the average, it's
+
+quite a high number.
+
+So most poor people, in our
+definition, are at least
+
+self-employed.
+
+Well, why is this?
+
+Yeah?
+
+AUDIENCE: What would we consider
+sharecroppers, who
+
+have to bear a lot
+of the risk?
+
+PROFESSOR: I think, here, they
+are considered self-employed.
+
+But that's a good question.
+
+I don't know the answer to
+whether they should be or not.
+
+So why should we think
+there is anything
+
+interesting about this?
+
+Why would it be at all
+surprising if a lot of poor
+
+people were entrepreneurs?
+
+Why would it be even worth
+commenting on?
+
+AUDIENCE: I don't understand
+the question?
+
+PROFESSOR: I said that 12% of
+the people in rich countries
+
+are entrepreneurs.
+
+Maybe 70% of the poor, in poor
+countries, are entrepreneurs.
+
+Is that something that
+has anything
+
+interesting about that fact?
+
+And there I want to get you
+to these two questions.
+
+Is it the case that the poor
+have specific advantages being
+
+an entrepreneur?
+
+Do they have specific
+disadvantages in being
+
+entrepreneurs?
+
+So let's start with
+the disadvantages.
+
+Is that clear?
+
+AUDIENCE: The risk is higher,
+because the overall capital
+
+they have is less.
+
+PROFESSOR: So risk is at least
+relatively higher, because
+
+they have--
+
+I don't know where this came
+from, but I kind of know where
+
+it should go.
+
+So one thing that's
+clear is that
+
+entrepreneurship is risky.
+
+If you're at the margin of not
+having enough money for
+
+something really essential,
+then the same
+
+risk hurts you more.
+
+Because you're really
+in danger of
+
+something awful happening.
+
+Like you couldn't pay for your
+mother's hospital stay if your
+
+business collapses.
+
+So the risk is much
+more important.
+
+We talked about this
+some few weeks ago.
+
+Other reasons, other
+disadvantages?
+
+AUDIENCE: It's harder
+to raise capital.
+
+PROFESSOR: Sure.
+
+It's harder to raise capital.
+
+If you don't have a bank
+account, if you don't have
+
+assets that you can pledge, if
+you don't have contact among
+
+financials, it's harder to
+raise capital, surely.
+
+Yeah?
+
+AUDIENCE: You have to rely on
+your business more, because
+
+it's harder for you to get a
+steady paying job at some
+
+other company.
+
+PROFESSOR: Is that a
+disadvantage or an advantage?
+
+AUDIENCE: I think it's a
+disadvantage, because then you
+
+bear a lot of the risk
+of the business.
+
+PROFESSOR: I see.
+
+So you may not have skills
+that you would get you an
+
+alternative job, so if your
+business fails, then it
+
+really hurts you.
+
+I see.
+
+Yeah.
+
+AUDIENCE: Particularly, if
+you're really poor, in a rural
+
+area or a slum, it's really
+hard to get the resources.
+
+I mean, I feel like in America
+today, we have a whole lot of
+
+resources to encourage
+entrepreneurship and help
+
+entrepreneurs.
+
+I would imagine, based on what
+I've read, that that really
+
+doesn't exist.
+
+PROFESSOR: So you may not have
+the know-how to be an
+
+entrepreneur.
+
+You may not know what market
+opportunities are available,
+
+because you're not that well
+connected to the media.
+
+You may not know, even, what the
+best prices are for what
+
+you will buy and the best prices
+are for what you will
+
+sell, where to sell, all the
+information that you need.
+
+Presumably, that's correlated
+with being educated.
+
+And so if you are poor in a
+poor country, you are less
+
+likely to have all
+that information.
+
+AUDIENCE: This is something
+that applies to all
+
+entreprenuers.
+
+But I think it would affect the
+poor more, specifically.
+
+I was thinking about the
+benefits you get from working
+
+for a corporation.
+
+Sometimes you get health
+care, things like that.
+
+And so being an entrepreneur
+is like taking a risk with
+
+respect to that.
+
+And then for the poor, depending
+on where they live,
+
+or what atmosphere is around,
+it might disproportionately
+
+affect them.
+
+PROFESSOR: Yeah, that's also
+possible that there's some
+
+additional benefits to
+having a steady job.
+
+That's particularly important
+if you have no
+
+other source of support.
+
+Yeah?
+
+AUDIENCE: On the advantages
+side, couldn't you say--
+
+PROFESSOR: Let's do
+the disadvantages.
+
+Hold that.
+
+AUDIENCE: Wouldn't your
+income not be regular.
+
+It would be really uncertain.
+
+PROFESSOR: Yeah.
+
+So that's related to, I think,
+the first point that was made.
+
+AUDIENCE: Chances are,
+you're not going to
+
+have an original idea.
+
+You're going to be copying what
+other people are doing.
+
+PROFESSOR: Yeah.
+
+But why would it be less true
+of the poor than the rich.
+
+AUDIENCE: The rich might have
+access to educational
+
+resources that will allow them
+to come up with better ideas.
+
+AUDIENCE: You could also make
+the converse argument that
+
+since the rich have access to
+more stuff, they're more
+
+likely to copy other ideas.
+
+PROFESSOR: Good.
+
+AUDIENCE: But that would also
+mean they might not be as
+
+likely to make a lot of money.
+
+So those would be the bad,
+rich entrepreneurs.
+
+AUDIENCE: Not necessarily.
+
+Microsoft copied Apple's
+architecture [INAUDIBLE].
+
+AUDIENCE: Well, that's
+a different story.
+
+AUDIENCE: I mean this was
+already said before.
+
+But just thinking about like,
+if you're poor, you're going
+
+to have to use--
+
+an entrepreneur, let's say you
+had some savings or you had
+
+family that was helping
+support you.
+
+You have support system that has
+some sort of capital, even
+
+if it's not that much.
+
+But when you're poor, you have
+to use everything that you
+
+have to put into
+that business.
+
+And that takes away from just
+living, even things like that.
+
+PROFESSOR: So the risk is
+higher, and your ability to
+
+self-finance is lower.
+
+Anything else?
+
+Yeah?
+
+AUDIENCE: You could say, if
+other people copied your idea,
+
+it would hurt you more, because
+then they'd just
+
+increase the supply and decrease
+your overall--
+
+PROFESSOR: But why would
+it be any different
+
+from anybody else?
+
+If I'm rich and you copy my
+idea, that still hurts me.
+
+It is not clear, especially in
+the sense if the poor use
+
+ideas that are particularly--
+
+they've already copied
+from somebody.
+
+They're less hurt by copying.
+
+Yeah?
+
+AUDIENCE: Perhaps, if you
+think about the social
+
+infrastructure, people are
+more able to copy ideas,
+
+because of the lack of legal
+support or an ability to check
+
+or to enforce that people are
+not copying your ideas.
+
+PROFESSOR: Right, so you might
+thing that they have less
+
+access to lawyers
+and things like.
+
+They may not understand
+the law well.
+
+So they may not be able to use
+the legal system to protect
+
+themselves as effectively.
+
+What's another thing that helps
+an entrepreneurs other
+
+than money and ideas?
+
+What's the third thing that?
+
+AUDIENCE: Sort of broadly
+speaking, a social safety net.
+
+In the sense that, let's say,
+in American, you're
+
+entrepreneur and you absolutely
+fail, there's still
+
+a social safety net that you
+could at least rely upon.
+
+And that doesn't
+exist in poor--
+
+PROFESSOR: Right.
+
+That's true of poor countries,
+but not necessarily more of
+
+poor people.
+
+That's a point about
+poor countries,
+
+less about poor people.
+
+One other thing that I think
+matters a lot is contacts.
+
+I think that, if you know
+somebody, if your uncle is the
+
+CEO of a company, they
+may be more willing
+
+to give you a try.
+
+If you're starting up, you're
+making widgets, somebody has
+
+to buy them.
+
+It's much easier if you know
+somebody than if you don't.
+
+I mean, why would anybody
+trust you?
+
+So you often get your first
+breaks by having some
+
+connection to somebody else,
+who will do the buying.
+
+And I think that's a very big
+piece of what makes it very
+
+difficult for the poor to be
+effective entrepreneurs is
+
+that they actually don't
+know anybody.
+
+And so it's much harder
+for them to
+
+break in with a products.
+
+So I think contacts are a
+very big piece of it.
+
+The other part of it is that it
+might be that, in order to
+
+be in business, for example--
+
+take the venture capital
+example.
+
+Typically, the way a lot of
+start-ups work is that you
+
+know that you're going to
+lose money for a while.
+
+Because you have to build
+a reputation.
+
+And the way you build a
+reputation is by going to
+
+someone and saying, look, you're
+buying from him for $5.
+
+I'll sell it to you for $3.
+
+And you know you lose money at
+$3, but you're willing to lose
+
+money for a while, because that
+way he'll see that you're
+
+really good at doing it.
+
+And then, maybe, you could
+charge $4 and get the market.
+
+So a lot of way new businesses
+start is by actually
+
+undercutting other businesses
+and losing money.
+
+So if you can't lose money,
+effectively--
+
+so if you're poor and you can't
+afford to lose money,
+
+it's often very difficult
+to enter a new product.
+
+Because part of the way you
+enter the new product is by
+
+actually selling
+it very cheap.
+
+And it's very difficult to
+sell it very cheap if you
+
+can't afford to lose money.
+
+So those are all the
+disadvantages.
+
+Are there advantages?
+
+So I don't know how many of you
+know, but there's a very
+
+famous book called The Fortune
+at the Bottom of the Pyramid.
+
+If you've read that book, it
+makes the case that there's
+
+actually lots of entrepreneurial
+opportunities
+
+for the poor.
+
+And that, in some sense, they
+might have an advantage.
+
+What are potential advantages?
+
+Yeah?
+
+AUDIENCE: Because you have
+access to a unique market that
+
+the rich don't even know
+about, like the
+
+women who sell sand.
+
+PROFESSOR: So they might know
+about things which are
+
+underserved.
+
+So maybe the way capitalism has
+developed, it's better at
+
+serving the demands of
+the middle classes.
+
+The poor might demand certain
+products which are not
+
+supplied by the market.
+
+So at this point, it might be
+easier to find a new product
+
+to supply if you know
+what the poor want .
+
+That's one of the cases
+that's being made.
+
+We'll see to what extent
+that's true.
+
+Any others?
+
+You were going to mention
+something?
+
+AUDIENCE: Maybe it's easier to
+make use of some resources
+
+than it would be if you were a
+richer person trying to start
+
+a [INAUDIBLE].
+
+Like, for example, the women
+with the sand, they can go to
+
+the beach and dig up some
+sand and carry it away.
+
+No one's going to say
+anything to them.
+
+But if someone was trying to do
+this on larger scale, then
+
+there would be issues.
+
+PROFESSOR: That's
+exactly right.
+
+So it may well be that, if I'm
+the person who comes and--
+
+imagine that I'm rich.
+
+Let's say, I can either take
+a job or I can be an
+
+entrepreneur.
+
+To compensate me for my job, I
+would need to be able to do
+
+the business at a particular
+scale.
+
+Imagine I'm in the business of
+sorting through garbage and
+
+finding things which
+are sellable.
+
+Just doing that, physically, if
+I started to use that much
+
+garbage, I'll need
+a lot of space.
+
+Whereas a poor person may be
+able to cover her daily wage,
+
+which is very low, by just
+sorting through the garbage
+
+she finds in the neighborhood
+or something.
+
+Another advantage of being poor
+might be that you may be
+
+less considered or less easily
+monitored, so you may be able
+
+to bend the rules more
+effectively.
+
+So you might be able to make
+products, which somebody else
+
+would not want to do, because
+it would too easy to
+
+scrutinize.
+
+So you may be involved in--
+
+I'm not saying illegal products,
+but you might use
+
+techniques which are possibly
+less hygienic or something.
+
+So if I setup a big factory
+dyeing garments, that pollutes
+
+the water supply.
+
+And the city will
+shut me down.
+
+If I have a very small operation
+inside my house,
+
+dyeing garments, nobody
+will notice.
+
+And I could use the city's water
+supply and pollute it.
+
+This doesn't mean that I'm
+doing a good thing.
+
+But it means that it might
+be easier for me to be an
+
+entrepreneur, the producing
+and dyeing garments than
+
+somebody who's richer than me.
+
+So there's some potential
+advantages.
+
+Still, I think my sense is that
+everybody would think
+
+that, basically, it's easier
+for the rich to be
+
+entrepreneurs than the poor.
+
+So that's on balance.
+
+And we'll look at this
+a little bit, in
+
+the data, in a bit.
+
+So then why are the poor
+entrepreneurs?
+
+That's the question
+that comes back.
+
+If we say it's easier for the
+rich to be entrepreneurs, but
+
+the rich are less likely to be
+entrepreneurs than the poor,
+
+then we have a kind
+of a puzzle.
+
+Why are the poor
+entrepreneurs?
+
+What is it that?
+
+So one view of this is sort
+of Muhammad Yunus's view.
+
+Muhammad Yunus is the guy who
+started Grameen Bank.
+
+And he's on record saying that
+the poor are natural born
+
+entrepreneurs.
+
+So there's one view, which is
+to say that something about
+
+the poor, which, by being
+poor, they learn to be
+
+entrepreneurial.
+
+They can't really survive on
+anything else, so they become
+
+like these women we were talking
+about. they become
+
+very clever at finding
+opportunities.
+
+They are natural
+entrepreneurs.
+
+That's one way to think about it
+is that, when you are poor,
+
+you're just better at thinking
+about opportunities.
+
+Now, one way we can kind of
+address this is by looking at
+
+the businesses of the poor.
+
+What do you know about
+these businesses?
+
+So these are people who
+are under $1 a day.
+
+And if you take the business of
+people, who live under $1 a
+
+day, I think the striking fact
+is that, in most countries for
+
+which we have data, let's say,
+10%, so the average number of
+
+employees in a business
+is 0.15.
+
+It's one in seven businesses
+have an
+
+employee, a paid employee.
+
+They took two countries where
+it's different, but even in
+
+those countries, they don't
+have one employee.
+
+They have 0.6 employees.
+
+So these are very small
+businesses.
+
+The first thing to note is that
+the businesses of the
+
+poor are kind of very, very
+small businesses.
+
+This includes your unpaid
+employees, which is like your
+
+son or your wife or
+you, yourself.
+
+And that number is
+just over one.
+
+So the average number of
+employees is just over one,
+
+meaning that it's you plus
+somebody who works, maybe,
+
+part of the time.
+
+Or alternatively, it's you and
+no one or you plus one person,
+
+but not much more than that,
+so very few employees.
+
+Second, what fraction of the
+businesses own a vehicle?
+
+Just to measure some other
+measure of the size of the
+
+business, it's only a vehicle.
+
+And Pakistan is the
+one country where
+
+many people own cycles.
+
+They might be delivering stuff,
+but then, all the other
+
+countries, it's really,
+really small, like 5%.
+
+If you look at an even more
+obvious question, what
+
+fraction own machines,
+any machine?
+
+The answer is not
+100% even there.
+
+60% in the Ivory Coast
+own any machine.
+
+What's the average machine
+that they own?
+
+They own a weighing scale or
+sort of a piece of metal for
+
+digging something, but
+no more than that.
+
+So it's really like these
+businesses have no assets
+
+whatsoever.
+
+So the first point about the
+businesses of the poor, they
+
+are very small, by all
+of these measures.
+
+They have no employees, no
+machines, no vehicles.
+
+The second, related point, I
+wanted to make is that the
+
+fact that they don't have any
+machines is telling you
+
+something quite important, which
+is that these are not
+
+very sophisticated businesses.
+
+You're not surprised
+to hear that.
+
+But it is very, very clear that
+the average business has
+
+very little skill involved.
+
+And to be honest, there's
+not a lot of diversity.
+
+If we look at the top five
+businesses, they are things
+
+like tailoring, a small corner
+store, selling snacks on the
+
+street, embroidering or
+stitching clothes and selling
+
+them as a retail sale, not a
+tailor, but someone who retail
+
+sells garments.
+
+And I think the last one is--
+
+I forget-- carpentry, I think.
+
+It's like none of these
+businesses, except, I think,
+
+carpentry, possibly, require
+huge amounts of skill.
+
+So they tend to be very low
+skilled businesses.
+
+And this is most businesses.
+
+So these are not people
+who are creating
+
+very original ideas.
+
+Indeed, the usual problem that
+people write about is most
+
+people, in the same
+neighborhood,
+
+have the same business.
+
+They're also selling snacks.
+
+They're all delivering loads.
+
+They're all tailors, rather
+than a lot of innovation.
+
+There's no evidence that they're
+very creative in what
+
+business they go into.
+
+On the other hand, many, many
+people own multiple
+
+businesses.
+
+That's the other very,
+very common fact.
+
+This is the fraction of
+people who get incomes
+
+from multiple sectors.
+
+So that's like somebody who was
+has farming business but
+
+also has income from, let's say,
+he does some bricklaying
+
+on the side.
+
+That's somebody who has
+multiple sources.
+
+And the striking fact
+is how common it is.
+
+In most countries, it's close to
+50% of the population have
+
+income from multiple sources.
+
+So in other words, they're not
+putting all their time,
+
+available time, into
+their own business.
+
+Why would they not do that?
+
+If you have a business, in
+your family, why aren't
+
+putting all of your
+effort into it?
+
+Why would we observe this fact,
+that most people, many
+
+people, have multiple business
+or multiple occupations?
+
+AUDIENCE: It might be
+comparable, then, to
+
+[INAUDIBLE].
+
+PROFESSOR: Right.
+
+So, for example, you might
+be only able to
+
+sell one kind of snack.
+
+And people might want snacks
+only, maybe, in
+
+the evening or something.
+
+In the morning, you
+go to work.
+
+There's no demand for snacks.
+
+Or you might sell breakfast,
+and you can only sell
+
+breakfast till 10:00 AM.
+
+After that, breakfast is over.
+
+And so you have to find
+something to do.
+
+So one thing could be there's a
+natural capacity constraint.
+
+There's not much demand
+for the product.
+
+And so you can do it for two
+hours a day but not for eight
+
+hours a day.
+
+Yeah?
+
+AUDIENCE: There might be
+seasonal variations.
+
+You might be able to a certain
+type of business only during
+
+certain times of the
+year, [INAUDIBLE].
+
+PROFESSOR: Absolutely.
+
+So agriculture is one classic
+business, where you can work a
+
+few months of the year, but the
+then the rest of the time,
+
+you don't have irrigation.
+
+There's nothing to do.
+
+So you work on something else.
+
+Yeah?
+
+AUDIENCE: You might diversify
+your portfolio as part of
+
+[INAUDIBLE].
+
+PROFESSOR: Right.
+
+So you may bear less risk by
+having multiple businesses.
+
+Yeah?
+
+AUDIENCE: It might be the return
+for business is so low,
+
+that even if you invested more
+time and energy into it, it
+
+wouldn't be worth it.
+
+PROFESSOR: But why don't you
+take the one which is the
+
+highest return and put all
+your time into it?
+
+AUDIENCE: Maybe I don't
+want to [INAUDIBLE].
+
+PROFESSOR: Why?
+
+AUDIENCE: Because even if that
+was the highest return,
+
+[INAUDIBLE].
+
+PROFESSOR: But why would you
+ever start a second, even
+
+lower return business?
+
+If there's one business that
+has the highest return, why
+
+won't you put all your eggs
+into that basket?
+
+AUDIENCE: Diversity.
+
+PROFESSOR: Yeah, so that's what
+she said, which is that
+
+want to diversify risk.
+
+What other reason could
+you imagine?
+
+AUDIENCE: It could also be
+that you might have one
+
+business that's really
+profitable, let's say, you're
+
+selling something in the morning
+for breakfast, but it
+
+might be the time--
+
+PROFESSOR: Right, that's,
+I think, also
+
+someone brought up.
+
+AUDIENCE: I think there are like
+some businesses which are
+
+like needlepoint, which
+physically hurt you if you do
+
+it too much.
+
+People like become blind.
+
+PROFESSOR: Right, so maybe, just
+you don't want to do it
+
+for too long?
+
+Another obvious reason.
+
+AUDIENCE: Didn't they say in the
+book that a lot of people
+
+don't like running their own
+businesses, and so they don't
+
+want to put time into it.
+
+PROFESSOR: But why would you
+do three different ones?
+
+I'm Asking a simpler question
+than the one you're answering,
+
+which is people seem to do
+two or three different
+
+occupations.
+
+Why would do two or
+three rather than?
+
+Say I want to work
+eight hours.
+
+Why wouldn't I put all
+eight hours into one?
+
+We've gone through a bunch
+of reasons for that.
+
+AUDIENCE: Is that the marginal
+returns decline, especially
+
+for this type of a business?
+
+PROFESSOR: So it could be that
+the marginal returns on the
+
+extra piece of effort is low.
+
+Another possibility that
+I think is even more
+
+straightforward.
+
+Maybe some businesses
+require capital
+
+and others less capital.
+
+So you have a certain
+amount of capital.
+
+You put into the capital
+intensive business.
+
+And then use still don't
+have some time left.
+
+So you work in the other one.
+
+For example, to do needlepoint,
+you'll have to
+
+buy fabric first.
+
+And you can only afford fabric
+that covers half your day.
+
+And you buy fabric for
+half your day.
+
+You work half your day
+on needlepoint.
+
+The rest of the half of your
+day, you have to find
+
+something else to do.
+
+So it may just be that you don't
+have enough capital to
+
+make it possible to spend your
+whole day working on it.
+
+So in any case, we do see this
+evidence that people don't
+
+seem to be excessively
+committed
+
+to any single business.
+
+That has the cost, obviously,
+that they're not getting a lot
+
+of benefits from
+specialization.
+
+They're not learning or
+improving very fast, because
+
+they're doing many, many
+things at the same.
+
+What is striking about this
+picture is says, in even rural
+
+households, a lot of them have
+a non-agricultural business.
+
+So they'll actually, if you look
+at how many people have a
+
+non-agricultural business, like
+about a third of them
+
+have a non-agricultural
+business,
+
+even if they're rural.
+
+So these are people who
+live in rural areas.
+
+They do farming as one of their
+businesses, probably.
+
+But they also have a second
+business, which is
+
+non-agricultural.
+
+And that's sort of striking.
+
+We think of, often, rural areas
+in developing countries
+
+as farmers kind of living
+in isolation.
+
+In fact, most of these
+people are in a
+
+second business as well.
+
+So the next fact about
+businesses of the poor is that
+
+these businesses are
+very fragile.
+
+So if you look at Mexico, in
+85% of the people, the poor
+
+didn't have a business
+in 2002.
+
+15% had a business.
+
+By 2005, out of those 15%, only
+6% still had a business.
+
+So 60% of all businesses
+just closed.
+
+So the they're also going
+in and out of
+
+business all the time.
+
+On the other hand, many other
+people started new businesses.
+
+And you look at the fraction
+of the people who retained
+
+their existing labor force.
+
+They're just 1.8%.
+
+So most people either grow their
+business or shrink it or
+
+shut it down.
+
+So businesses are very,
+very fragile.
+
+It's not that you set up a
+business and it lasts forever.
+
+It's quite a high
+risk outcome.
+
+And this is sort of the answer
+to the question, do the poor
+
+feel entrepreneurial?
+
+And this is a survey we've done
+in many countries, now.
+
+We always find the say answer.
+
+You ask people, you have a
+child, what occupation do you
+
+hope for your child to be?
+
+And we ask it two ways.
+
+One, we ask them, what
+occupation do you hope for
+
+your child?
+
+Then you might worry if
+you ask that question.
+
+They might be conditioning
+on their condition.
+
+And so they'd look, you know,
+my child he'll never be able
+
+to do the right kind of
+business, because he doesn't
+
+have enough money
+or something.
+
+So we asked them, if you won a
+lottery and you would invest
+
+in something, what occupation
+would your
+
+child want to be in?
+
+It doesn't make a difference.
+
+They always give you the same
+answer, which is that they
+
+don't want to be in business.
+
+The answer is very,
+very clear.
+
+18% want them to be a private
+firm employee, 41% to be a
+
+non-teaching government
+job, and 34% to be
+
+a government teacher.
+
+So that's 93% don't want them
+to be an entrepreneur.
+
+So basically, the poor don't
+like the idea, at least, of
+
+their children being
+entrepreneurs.
+
+And it's consistent with
+everything else we see, which
+
+is that they don't seem to
+invest all their time in a
+
+single business.
+
+Even if they have a business,
+they'll put only a part of
+
+their time into it.
+
+We saw, earlier, that they don't
+try very hard to save
+
+their way out of debt.
+
+We saw that when we looked at
+the fruit vendors, that they
+
+were not saving a lot and tried
+to get out of debt.
+
+So it seems like they don't seem
+to be hugely committed to
+
+growing their business.
+
+There's no evidence.
+
+And we see the businesses
+don't grow.
+
+Many of them shrink
+or shut down.
+
+Very few of them actually
+add an employee.
+
+At best, these business
+are always small.
+
+They stay small or
+they shutdown.
+
+They rarely grow.
+
+So there is no evidence that the
+poor are actually dynamic
+
+entrepreneurs, in the sense
+that they are looking for
+
+opportunities to grow their
+business all the time.
+
+Now, that doesn't mean that
+there are not a million
+
+dynamic entrepreneurs
+among the poor.
+
+One should not confuse the
+statement that the average
+
+poor person is not a dynamic
+entrepreneur with the
+
+statement that there
+are no dynamic
+
+entrepreneurs among the poor.
+
+There may be exactly the same
+fraction of dynamic
+
+entrepreneurs among the poor
+as there are among MIT
+
+students, for all I know.
+
+It's just most people are
+not cut out to dynamic
+
+entrepreneurs.
+
+And the poor, maybe, just
+like everybody else,
+
+they don't like risk.
+
+They don't like the idea of
+worrying about all of the
+
+problems that running
+business has.
+
+They like a steady job.
+
+And then a few people really
+like being an entrepreneur.
+
+I don't know that this makes
+them any different from
+
+anybody else.
+
+It just says that they're not.
+
+You see a huge
+over-representation of the
+
+poor among entrepreneurs.
+
+That doesn't mean that this is
+what the poor want to be.
+
+It's not that they're
+entrepreneurial in some
+
+natural sense.
+
+They're not that they want
+to be an entrepreneur.
+
+They're an entrepreneur for some
+other reason we'll come
+
+to in a minute.
+
+None of this evidence seems to
+suggest that they're dying to
+
+be entrepreneurs and to
+grow their businesses.
+
+That doesn't mean that there
+aren't some who are.
+
+There's this story that you saw
+in the microfinance movie
+
+of some woman who started
+as hair collector.
+
+Remember this person?
+
+And she's now a hair tycoon.
+
+And they exist, people like
+that, everywhere in the world.
+
+I'm even willing to believe
+that there are as many
+
+genuinely entrepreneurial people
+among the poor as there
+
+are among anybody else.
+
+But that's a very different
+sentence from saying that most
+
+poor people have businesses
+because they're
+
+entrepreneurial.
+
+Because they're so massively
+overrepresented.
+
+They're really unlikely people
+to be entrepreneurs.
+
+So if they are entrepreneurs,
+it's not because
+
+they want to be.
+
+This is all consistent with the
+fact that, if you look at
+
+these businesses, they're
+not really attractive
+
+economically.
+
+So one place where we have
+detailed data, we could
+
+actually calculate how much
+revenues these businesses were
+
+making, calculate profits.
+
+Now a key part of the
+profit calculation--
+
+remember, almost none of these
+firms have employees.
+
+So you have to evaluate the
+time spent by the owner in
+
+running the business.
+
+Somehow, how do you
+price that?
+
+So you price that
+at minimum wage.
+
+These businesses lose money.
+
+So if I went out and worked at
+minimum wage, I would make
+
+more money than if I did this
+business and spent all the
+
+time I'm spending
+in the business.
+
+Now, I'm not necessarily
+working as hard in the
+
+business as I would be working
+in other things.
+
+But it isn't the case that
+I'm making lots of money.
+
+I think this is a pattern that
+people have noticed.
+
+Now, here's a puzzle.
+
+I just said they don't
+make a lot of money.
+
+They're not very profitable,
+these business.
+
+Before, I've also told
+you that they
+
+pay very high interest.
+
+So they must be generating
+an extra $1.
+
+They must be generating
+at least that much.
+
+So if I'm paying 60% interest,
+$1 must be generating more
+
+than $0.60.
+
+If I'm investing $1 and then
+paying 60% interest, that $1
+
+must be generating
+more than $0.60.
+
+How do those two facts
+fit with each other?
+
+I said, A, they're not
+very profitable.
+
+B, the marginal $1 must be
+making a high return, because
+
+otherwise they wouldn't be
+investing their marginal $1.
+
+You won't borrow money at 60%
+unless you can cover 60%.
+
+So we know that they're
+making lots of money.
+
+Yeah?
+
+AUDIENCE: This talked a
+lot about in the book.
+
+But basically, there's two
+different types of return.
+
+One is marginal returns,
+[INAUDIBLE]
+
+where an extra $1 spent,
+what's their return.
+
+The other's the total return.
+
+For a lot of these businesses,
+there is a point, early on,
+
+with this very high, marginal
+return, and then it really
+
+levels off.
+
+So that's what you run into,
+where it's possible that, if
+
+you have a very small
+business, like the
+
+example in the book.
+
+Let's say you have a shop, but
+you really can't put anything
+
+on the shelves.
+
+If you spend an extra $20, you
+can actually have some candy
+
+on the shelves, then that
+will produce very
+
+high marginal returns.
+
+But if you spend $300 and have
+a lot of inventory, you might
+
+have to hire another employee.
+
+There's risk of stuff spoiling,
+
+et cetera, et cetera.
+
+PROFESSOR: So I think that's
+absolutely right.
+
+But I was making an even simpler
+point, here, which is
+
+that think of that business.
+
+The person who set up a shop.
+
+You invest your time
+into the shop.
+
+And you invest the space.
+
+You invest the shelves.
+
+You invest the inventory.
+
+Then you start selling.
+
+So in particular, your time
+is a fixed investment.
+
+Because you have now decided
+that instead of working
+
+outside, I'm going to
+stay in the shop.
+
+So you need to cover.
+
+To become profitable, you need
+to cover your own daily wage.
+
+Let's say you make $2 a day.
+
+Then even if you made a total
+of $2 a day by selling, you
+
+would have just covered
+your wage.
+
+Then you recover your
+inventory, your
+
+capital cost, et cetera.
+
+So unless you operate at a high
+enough scale, you're not
+
+going to cover your time.
+
+And so one of the problems
+is these people are often
+
+operating at a very
+small scale.
+
+So they rarely manage
+to cover their cost.
+
+But then why don't these
+people just grow their
+
+businesses?
+
+Maybe if they're not making a
+lot of money, because they
+
+have to cover their fixed cost,
+then why not just keep
+
+investing till you make
+a lot of money.
+
+Your marginal returns are high,
+so you could invest more
+
+and make more money.
+
+And then the answer is, your
+marginal are high, but not
+
+high for a very wide range.
+
+So they start falling
+fast as well.
+
+So this is the picture
+that is in the book.
+
+And it's worth, probably,
+understanding that picture.
+
+So that picture, it tells a
+story of two technologies.
+
+There's one technology which is
+gives you a high return but
+
+quickly flattens off.
+
+And if that was the only
+technology in the world, then
+
+we would not observe
+any large funds.
+
+Because that's a technology
+which stops becoming
+
+profitable after a point,
+very quickly.
+
+But there's another technology,
+which starts way
+
+to the right of that.
+
+And that technology is only
+profitable if you invest.
+
+So what that curve says
+is that there is two
+
+technologies.
+
+Production from technology two
+is lower than production for
+
+technology one until you cross
+a particular point.
+
+So you need to make enough
+investment to make that
+
+profitable.
+
+So you're going to buy a machine
+which produces a lot
+
+of garments.
+
+But if you can't buy the cloth
+that goes with the machine,
+
+there's no point in buying
+the machine.
+
+You're going to lose money for
+sure, because you have nothing
+
+to use the machine with.
+
+Garments need a machine
+and they need cloth.
+
+And you have only money for the
+machine, then you should
+
+not buy the machine.
+
+You should buy the machine
+only if you can buy the
+
+machine and buy the cloth.
+
+So there that are more
+profitable technologies and
+
+less profitable technologies.
+
+But the disadvantage of the
+more profitable technology
+
+turns out to be that you need
+to invest enough in them to
+
+make money.
+
+So the problem is that the poor
+are caught between a kind
+
+of a rock and a hard place,
+which is that they can't
+
+really get up to the
+level at which they
+
+would make real money.
+
+Because that technology is just
+too expensive for them.
+
+They don't have that
+much money.
+
+The technology that they can
+access has very fast
+
+diminishing returns.
+
+So that one also is not
+worth growing a lot.
+
+So that's the sense in which
+they're between a rock and a
+
+hard place.
+
+They can't grow the technology
+fast enough.
+
+The one that they have,
+they can't grow.
+
+And the one that can grow,
+they can't have.
+
+And that's what this
+picture is about.
+
+If this is what the world looks
+like, then the poor are
+
+stuck at a point, like M, and
+the rich are stuck at point
+
+like that second
+ball up there.
+
+So the poor are stuck, because
+the technology that has growth
+
+is not available to them.
+
+And the one that's available
+to them does not
+
+have growth in it.
+
+So there's no point in their
+putting a lot of effort into
+
+growing their technology,
+because they're really not
+
+going to make a lot of
+money either way.
+
+That would explain why they
+don't really want to be
+
+entrepreneurs, because they know
+that they're never going
+
+to get very far in
+this process.
+
+So then that leaves us with
+the last slide, well,
+
+actually, one slide
+that suggests that
+
+this picture is right.
+
+There was this experiment in Sri
+Lanka, where people were
+
+given, randomly, either $250
+or $500 for investing.
+
+And this was just a gift.
+
+The World Bank, basically, did
+this experiment, where it went
+
+to people and said,
+here's $250.
+
+These were all small
+businessmen.
+
+Use it in your business or
+do something with it.
+
+And some people, they
+offered $500.
+
+It's kind of nice experiment
+to do, because you can find
+
+out what's the effect on getting
+money on people's
+
+investment.
+
+And strikingly, if you
+give $250, you get
+
+high marginal returns.
+
+So these people who get $250,
+they invest $250, and they
+
+make about 60% a year on that.
+
+So that's pretty good returns.
+
+On the other hand, if you give
+them $500, they don't invest
+
+the second $250.
+
+They just use it for repairing
+their home.
+
+So they don't believe that the
+second $500 are going to grow
+
+their business that much more.
+
+They believe that there's
+diminishing returns.
+
+That's why they don't
+invest it.
+
+So basically, the poor seem to
+be acting as if they also
+
+believe exactly that picture,
+that they have high returns on
+
+the first $250 but not
+on the second $250.
+
+Yeah?
+
+AUDIENCE: So [INAUDIBLE]
+
+they just save up enough money
+or take a loan out so that you
+
+can achieve or you can jump
+the curve and buy the
+
+technology.
+
+PROFESSOR: Absolutely.
+
+AUDIENCE: So it's like,
+technically, giving loans to
+
+small businesses should work.
+
+PROFESSOR: Well, it depends
+on how big the loan is.
+
+I think the problem is that
+the jump is not at $500.
+
+The jump is at $10,000.
+
+So none of the loans they are
+being offered allow them to
+
+make that jump.
+
+That's the problem.
+
+AUDIENCE: And they're
+still too small to
+
+go to a normal bank?
+
+PROFESSOR: Yeah.
+
+that then brings us to the final
+question, which is, if
+
+this is all not such
+a great deal,
+
+why are they in business?
+
+Yeah, go ahead.
+
+AUDIENCE: Because
+they have to be.
+
+PROFESSOR: Yeah.
+
+One is that they have to be.
+
+There's a vicious cycle, here.
+
+Suppose no one can create a
+business that's big enough to
+
+hire employees.
+
+Then I can never be
+an employee in
+
+somebody else's firm.
+
+What else can I do?
+
+I can start my own business,
+which can't hire anybody.
+
+So if nobody is creating
+businesses which have
+
+employees, then, in a
+sense, I'm stuck.
+
+I can't get a job, because
+nobody else is
+
+creating those jobs.
+
+But if nobody else is creating
+those jobs, then I can't
+
+really work for anybody else.
+
+But I still have to earn a
+living, so I go and find my
+
+own thing to do.
+
+So I think the primary reason
+why you have a lot of
+
+entrepreneurs is because no
+entrepreneur is big enough to
+
+hire the others.
+
+So everybody's an
+entrepreneur, a
+
+mini-entrepreneur.
+
+Nobody gets to the scale where
+they can hire others.
+
+And therefore, everybody's
+kind of stuck.
+
+So if I start a business that
+hires 10 people, then that
+
+stops 9 other people from
+being an entrepreneur.
+
+That's one reason.
+
+A second reason has to
+do with flexibility.
+
+I think a lot of poor
+people don't have
+
+access to social services.
+
+So if I have to have childcare,
+pay for childcare,
+
+I'm never going to able to
+afford my business, because
+
+childcare is too expensive.
+
+So if I have to go out and get
+a job, which is 9-to-5, and I
+
+have to work all
+the time, who's
+
+going to provide childcare?
+
+So often, they choose businesses
+which are designed
+
+to work well with childcare.
+
+Like I took a snack
+making business.
+
+Why?
+
+Because I can do it at home.
+
+I make the snacks at home.
+
+And then I go out to
+sell for two hours.
+
+At that time, I take
+my child with me.
+
+And then I bring
+the child back.
+
+And that way, I don't ever
+have to deal with the
+
+childcare issue.
+
+So flexibility is
+a second one.
+
+The third and most
+worrying one--
+
+and microcredit makes me
+worry about this most--
+
+is whether or not a lot of men
+are very enthusiastic for the
+
+wives to work even harder.
+
+So they feel that, you know,
+I'm working at a job.
+
+I would like my wife
+to work harder.
+
+And the way they get their wives
+to work harder is by
+
+making them start a business.
+
+So I don't know whether
+microcredit is necessarily
+
+wonderful for all
+of these women.
+
+I think that, historically, men
+have found it difficult to
+
+understand that women, even
+though they don't go out to
+
+work, actually have to work.
+
+They have like cooking
+and cleaning
+
+dishes and washing up.
+
+They're all hard work.
+
+And if you think that that's a
+problem in the US, now, then
+
+you can imagine in a lot of
+developing countries, it's
+
+even more of a problem.
+
+So it may well be that a lot of
+men are under the illusion
+
+that their wives are idle.
+
+And that they are very willing,
+therefore, to start a
+
+business for them, so they can
+work a little harder and add
+
+to the family pie.
+
+So I don't know how much of
+these businesses are a result
+
+of that, rather than any desire
+to start a business.
+
+Comments, questions?
+
+So just to close this whole
+thing, I think the key policy
+
+question, that we don't know the
+answer to, is how to not
+
+get more businesses,
+but more businesses
+
+that hire other people.
+
+That's the key policy
+question we haven't
+
+managed to solve yet.
+
+And it's an absolutely central
+policy question for most
+
+developing countries to figure
+out how to get not
+
+micro-businesses but
+small businesses.
+
+And this is often called the
+missing middle problem.
+
+In many countries, in poor
+countries, you'll find that
+
+there are many micro-businesses
+and some
+
+large businesses, but not
+enough middle-sized
+
+businesses.
+
+So that's the policy problem
+that many, many countries are
+
+wrestling with.
+
+And it's one that, I think,
+we haven't yet got a
+
+very good handle on.
+
+But it's something to think
+about is how to
+
+generate those jobs.
+
+Yeah?
+
+AUDIENCE: So specifically in
+developed countries, then,
+
+what provides the capital for
+the middle businesses?
+
+PROFESSOR: So for one,
+the state does a lot.
+
+Like in the US, for example,
+there's a Community
+
+Reinvestment Act, which means
+that banks are required to
+
+provide a certain fraction of
+their loans to the community
+
+where they are raising
+the savings.
+
+So the CRA forces them, then,
+to finance local businesses.
+
+And so there is a lot of
+intervention, even in a
+
+country as uninterventionist
+as the US, to help small
+
+businesses set up.
+
+This CRA is a very
+good example.
+
+The Small Business
+Administration is huge in the
+
+US, by the way.
+
+And they provide all kinds of
+help to small businesses,
+
+including capital, including
+guarantees.
+
+They give a lot of
+loan guarantees.
+
+Even the US, which is one
+of the world's least
+
+interventionist countries,
+tends to be very
+
+interventionist when it comes to
+promoting small businesses.
+
+That's probably the direction
+that policy needs to go in
+
+developing countries.
+
+But it's something we
+know less about.
+
+OK.
+
+Thank you.
\ No newline at end of file
diff --git a/yHzpj_MDOdk.txt b/yHzpj_MDOdk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5dcc3a8bc527f35e9087eece301377586e0e7f5c
--- /dev/null
+++ b/yHzpj_MDOdk.txt
@@ -0,0 +1,12283 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to describe the basic
+
+ align:start position:0%
+so I'm going to describe the basic
+ 
+
+ align:start position:0%
+so I'm going to describe the basic
+classification of solar cell
+
+ align:start position:0%
+classification of solar cell
+ 
+
+ align:start position:0%
+classification of solar cell
+characterization methods and then I'll
+
+ align:start position:0%
+characterization methods and then I'll
+ 
+
+ align:start position:0%
+characterization methods and then I'll
+describe some of the characterization
+
+ align:start position:0%
+describe some of the characterization
+ 
+
+ align:start position:0%
+describe some of the characterization
+tools that are used to measure JSC
+
+ align:start position:0%
+tools that are used to measure JSC
+ 
+
+ align:start position:0%
+tools that are used to measure JSC
+losses and other tools that are used to
+
+ align:start position:0%
+losses and other tools that are used to
+ 
+
+ align:start position:0%
+losses and other tools that are used to
+measure vo C and fill factor losses
+
+ align:start position:0%
+measure vo C and fill factor losses
+ 
+
+ align:start position:0%
+measure vo C and fill factor losses
+right so getting a sense of the lay of
+
+ align:start position:0%
+right so getting a sense of the lay of
+ 
+
+ align:start position:0%
+right so getting a sense of the lay of
+the land let me ask you how would you
+
+ align:start position:0%
+the land let me ask you how would you
+ 
+
+ align:start position:0%
+the land let me ask you how would you
+characterize how would you create a
+
+ align:start position:0%
+characterize how would you create a
+ 
+
+ align:start position:0%
+characterize how would you create a
+taxonomy of solar cell characterization
+
+ align:start position:0%
+taxonomy of solar cell characterization
+ 
+
+ align:start position:0%
+taxonomy of solar cell characterization
+techniques those of you who might have a
+
+ align:start position:0%
+techniques those of you who might have a
+ 
+
+ align:start position:0%
+techniques those of you who might have a
+little bit more experience might
+
+ align:start position:0%
+little bit more experience might
+ 
+
+ align:start position:0%
+little bit more experience might
+actually have used a few
+
+ align:start position:0%
+actually have used a few
+ 
+
+ align:start position:0%
+actually have used a few
+characterization techniques in your
+
+ align:start position:0%
+characterization techniques in your
+ 
+
+ align:start position:0%
+characterization techniques in your
+laboratories what taxonomy would you use
+
+ align:start position:0%
+laboratories what taxonomy would you use
+ 
+
+ align:start position:0%
+laboratories what taxonomy would you use
+how would you slice the pie of all of
+
+ align:start position:0%
+how would you slice the pie of all of
+ 
+
+ align:start position:0%
+how would you slice the pie of all of
+these characterization techniques go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are what are ways to divide the
+
+ align:start position:0%
+what are what are ways to divide the
+ 
+
+ align:start position:0%
+what are what are ways to divide the
+characterization universe into distinct
+
+ align:start position:0%
+characterization universe into distinct
+ 
+
+ align:start position:0%
+characterization universe into distinct
+groupings how about we start overhead
+
+ align:start position:0%
+groupings how about we start overhead
+ 
+
+ align:start position:0%
+groupings how about we start overhead
+yeah yeah okay so we can describe based
+
+ align:start position:0%
+yeah yeah okay so we can describe based
+ 
+
+ align:start position:0%
+yeah yeah okay so we can describe based
+on the economic variables right like
+
+ align:start position:0%
+on the economic variables right like
+ 
+
+ align:start position:0%
+on the economic variables right like
+efficiency and then with an efficiency
+
+ align:start position:0%
+efficiency and then with an efficiency
+ 
+
+ align:start position:0%
+efficiency and then with an efficiency
+JSC vo C fill factor mechanical yield
+
+ align:start position:0%
+JSC vo C fill factor mechanical yield
+ 
+
+ align:start position:0%
+JSC vo C fill factor mechanical yield
+reliability right these are all
+
+ align:start position:0%
+reliability right these are all
+ 
+
+ align:start position:0%
+reliability right these are all
+parameters that can lump into a cost
+
+ align:start position:0%
+parameters that can lump into a cost
+ 
+
+ align:start position:0%
+parameters that can lump into a cost
+model and ultimately impact the the cost
+
+ align:start position:0%
+model and ultimately impact the the cost
+ 
+
+ align:start position:0%
+model and ultimately impact the the cost
+dollars per watt let's say if a PV panel
+
+ align:start position:0%
+dollars per watt let's say if a PV panel
+ 
+
+ align:start position:0%
+dollars per watt let's say if a PV panel
+excellent so we can describe it based on
+
+ align:start position:0%
+excellent so we can describe it based on
+ 
+
+ align:start position:0%
+excellent so we can describe it based on
+performance if we dive into performance
+
+ align:start position:0%
+performance if we dive into performance
+ 
+
+ align:start position:0%
+performance if we dive into performance
+a little more what are some of the
+
+ align:start position:0%
+a little more what are some of the
+ 
+
+ align:start position:0%
+a little more what are some of the
+properties that affect performance we
+
+ align:start position:0%
+properties that affect performance we
+ 
+
+ align:start position:0%
+properties that affect performance we
+have electrical properties optical
+
+ align:start position:0%
+have electrical properties optical
+ 
+
+ align:start position:0%
+have electrical properties optical
+properties mechanical right thermal and
+
+ align:start position:0%
+properties mechanical right thermal and
+ 
+
+ align:start position:0%
+properties mechanical right thermal and
+so forth so we can break up
+
+ align:start position:0%
+so forth so we can break up
+ 
+
+ align:start position:0%
+so forth so we can break up
+characterization techniques space in the
+
+ align:start position:0%
+characterization techniques space in the
+ 
+
+ align:start position:0%
+characterization techniques space in the
+properties that they probe and we can
+
+ align:start position:0%
+properties that they probe and we can
+ 
+
+ align:start position:0%
+properties that they probe and we can
+also character right where you can
+
+ align:start position:0%
+also character right where you can
+ 
+
+ align:start position:0%
+also character right where you can
+create a taxonomy of characterization
+
+ align:start position:0%
+create a taxonomy of characterization
+ 
+
+ align:start position:0%
+create a taxonomy of characterization
+techniques based on how fast they are
+
+ align:start position:0%
+techniques based on how fast they are
+ 
+
+ align:start position:0%
+techniques based on how fast they are
+whether it's something that you have to
+
+ align:start position:0%
+whether it's something that you have to
+ 
+
+ align:start position:0%
+whether it's something that you have to
+sit around and twiddle your thumbs for a
+
+ align:start position:0%
+sit around and twiddle your thumbs for a
+ 
+
+ align:start position:0%
+sit around and twiddle your thumbs for a
+half hour two hours to get done or
+
+ align:start position:0%
+half hour two hours to get done or
+ 
+
+ align:start position:0%
+half hour two hours to get done or
+whether it's something that gets done in
+
+ align:start position:0%
+whether it's something that gets done in
+ 
+
+ align:start position:0%
+whether it's something that gets done in
+ten milliseconds of which there are
+
+ align:start position:0%
+ten milliseconds of which there are
+ 
+
+ align:start position:0%
+ten milliseconds of which there are
+several characterization techniques what
+
+ align:start position:0%
+several characterization techniques what
+ 
+
+ align:start position:0%
+several characterization techniques what
+would the 10 millisecond variety enable
+
+ align:start position:0%
+would the 10 millisecond variety enable
+ 
+
+ align:start position:0%
+would the 10 millisecond variety enable
+you to do in a manufacturing environment
+
+ align:start position:0%
+you to do in a manufacturing environment
+ 
+
+ align:start position:0%
+you to do in a manufacturing environment
+yeah sort them test them measure them
+
+ align:start position:0%
+yeah sort them test them measure them
+ 
+
+ align:start position:0%
+yeah sort them test them measure them
+every single cell coming through so you
+
+ align:start position:0%
+every single cell coming through so you
+ 
+
+ align:start position:0%
+every single cell coming through so you
+might have a barcode like one of those
+
+ align:start position:0%
+might have a barcode like one of those
+ 
+
+ align:start position:0%
+might have a barcode like one of those
+fancy two-dimensional barcodes laser
+
+ align:start position:0%
+fancy two-dimensional barcodes laser
+ 
+
+ align:start position:0%
+fancy two-dimensional barcodes laser
+marked on each single wafer going
+
+ align:start position:0%
+marked on each single wafer going
+ 
+
+ align:start position:0%
+marked on each single wafer going
+through your line so you can trace it
+
+ align:start position:0%
+through your line so you can trace it
+ 
+
+ align:start position:0%
+through your line so you can trace it
+back in your mes system all the way back
+
+ align:start position:0%
+back in your mes system all the way back
+ 
+
+ align:start position:0%
+back in your mes system all the way back
+to the crystal that will
+
+ align:start position:0%
+to the crystal that will
+ 
+
+ align:start position:0%
+to the crystal that will
+groan or from the thin film growth
+
+ align:start position:0%
+groan or from the thin film growth
+ 
+
+ align:start position:0%
+groan or from the thin film growth
+chamber where it was deposited so yes
+
+ align:start position:0%
+chamber where it was deposited so yes
+ 
+
+ align:start position:0%
+chamber where it was deposited so yes
+you have in line and shall we say say
+
+ align:start position:0%
+you have in line and shall we say say
+ 
+
+ align:start position:0%
+you have in line and shall we say say
+the the in line characterization
+
+ align:start position:0%
+the the in line characterization
+ 
+
+ align:start position:0%
+the the in line characterization
+techniques and what are called off line
+
+ align:start position:0%
+techniques and what are called off line
+ 
+
+ align:start position:0%
+techniques and what are called off line
+characterization techniques which tend
+
+ align:start position:0%
+characterization techniques which tend
+ 
+
+ align:start position:0%
+characterization techniques which tend
+to be lower throughput you can think of
+
+ align:start position:0%
+to be lower throughput you can think of
+ 
+
+ align:start position:0%
+to be lower throughput you can think of
+the in line characterization techniques
+
+ align:start position:0%
+the in line characterization techniques
+ 
+
+ align:start position:0%
+the in line characterization techniques
+as as being in the line of the
+
+ align:start position:0%
+as as being in the line of the
+ 
+
+ align:start position:0%
+as as being in the line of the
+manufacturing environment and the off
+
+ align:start position:0%
+manufacturing environment and the off
+ 
+
+ align:start position:0%
+manufacturing environment and the off
+line is being those techniques that are
+
+ align:start position:0%
+line is being those techniques that are
+ 
+
+ align:start position:0%
+line is being those techniques that are
+sitting in your laboratory right waiting
+
+ align:start position:0%
+sitting in your laboratory right waiting
+ 
+
+ align:start position:0%
+sitting in your laboratory right waiting
+to be used in in the R&D lab which might
+
+ align:start position:0%
+to be used in in the R&D lab which might
+ 
+
+ align:start position:0%
+to be used in in the R&D lab which might
+be next door to the to the manufacturing
+
+ align:start position:0%
+be next door to the to the manufacturing
+ 
+
+ align:start position:0%
+be next door to the to the manufacturing
+line device performance metric affected
+
+ align:start position:0%
+line device performance metric affected
+ 
+
+ align:start position:0%
+line device performance metric affected
+that addresses the efficiency point up
+
+ align:start position:0%
+that addresses the efficiency point up
+ 
+
+ align:start position:0%
+that addresses the efficiency point up
+here and then buy property tests at
+
+ align:start position:0%
+here and then buy property tests at
+ 
+
+ align:start position:0%
+here and then buy property tests at
+electrical structural optical mechanical
+
+ align:start position:0%
+electrical structural optical mechanical
+ 
+
+ align:start position:0%
+electrical structural optical mechanical
+so if you talk to somebody who works in
+
+ align:start position:0%
+so if you talk to somebody who works in
+ 
+
+ align:start position:0%
+so if you talk to somebody who works in
+a PV company she will likely give you a
+
+ align:start position:0%
+a PV company she will likely give you a
+ 
+
+ align:start position:0%
+a PV company she will likely give you a
+breakdown based on number three right
+
+ align:start position:0%
+breakdown based on number three right
+ 
+
+ align:start position:0%
+breakdown based on number three right
+here okay these are the techniques that
+
+ align:start position:0%
+here okay these are the techniques that
+ 
+
+ align:start position:0%
+here okay these are the techniques that
+we have in our inspection system and
+
+ align:start position:0%
+we have in our inspection system and
+ 
+
+ align:start position:0%
+we have in our inspection system and
+those are the techniques that I have
+
+ align:start position:0%
+those are the techniques that I have
+ 
+
+ align:start position:0%
+those are the techniques that I have
+over there in the R&D lab if you talk to
+
+ align:start position:0%
+over there in the R&D lab if you talk to
+ 
+
+ align:start position:0%
+over there in the R&D lab if you talk to
+somebody who is giving a fundamental
+
+ align:start position:0%
+somebody who is giving a fundamental
+ 
+
+ align:start position:0%
+somebody who is giving a fundamental
+course of material science they're
+
+ align:start position:0%
+course of material science they're
+ 
+
+ align:start position:0%
+course of material science they're
+likely to pick part number one way up
+
+ align:start position:0%
+likely to pick part number one way up
+ 
+
+ align:start position:0%
+likely to pick part number one way up
+there and give you the breakdown based
+
+ align:start position:0%
+there and give you the breakdown based
+ 
+
+ align:start position:0%
+there and give you the breakdown based
+on the properties that are probed I'm
+
+ align:start position:0%
+on the properties that are probed I'm
+ 
+
+ align:start position:0%
+on the properties that are probed I'm
+going to opt for number two today in
+
+ align:start position:0%
+going to opt for number two today in
+ 
+
+ align:start position:0%
+going to opt for number two today in
+lecture not because it's any better or
+
+ align:start position:0%
+lecture not because it's any better or
+ 
+
+ align:start position:0%
+lecture not because it's any better or
+worse than all the others but just
+
+ align:start position:0%
+worse than all the others but just
+ 
+
+ align:start position:0%
+worse than all the others but just
+because that's the metric that we care
+
+ align:start position:0%
+because that's the metric that we care
+ 
+
+ align:start position:0%
+because that's the metric that we care
+about right now is we're trying to probe
+
+ align:start position:0%
+about right now is we're trying to probe
+ 
+
+ align:start position:0%
+about right now is we're trying to probe
+dollars per watt
+
+ align:start position:0%
+dollars per watt
+ 
+
+ align:start position:0%
+dollars per watt
+that's relates to our quiz and our
+
+ align:start position:0%
+that's relates to our quiz and our
+ 
+
+ align:start position:0%
+that's relates to our quiz and our
+homework but also relates to the
+
+ align:start position:0%
+homework but also relates to the
+ 
+
+ align:start position:0%
+homework but also relates to the
+ultimate economic driver solar so we
+
+ align:start position:0%
+ultimate economic driver solar so we
+ 
+
+ align:start position:0%
+ultimate economic driver solar so we
+have will keep this in mind that we
+
+ align:start position:0%
+have will keep this in mind that we
+ 
+
+ align:start position:0%
+have will keep this in mind that we
+might need to ferret out references for
+
+ align:start position:0%
+might need to ferret out references for
+ 
+
+ align:start position:0%
+might need to ferret out references for
+the different techniques in different
+
+ align:start position:0%
+the different techniques in different
+ 
+
+ align:start position:0%
+the different techniques in different
+textbooks or different papers based on
+
+ align:start position:0%
+textbooks or different papers based on
+ 
+
+ align:start position:0%
+textbooks or different papers based on
+whether they're probing electrical
+
+ align:start position:0%
+whether they're probing electrical
+ 
+
+ align:start position:0%
+whether they're probing electrical
+structural optical mechanical properties
+
+ align:start position:0%
+structural optical mechanical properties
+ 
+
+ align:start position:0%
+structural optical mechanical properties
+of our solar cells but we're going to be
+
+ align:start position:0%
+of our solar cells but we're going to be
+ 
+
+ align:start position:0%
+of our solar cells but we're going to be
+focused on efficiency short circuit
+
+ align:start position:0%
+focused on efficiency short circuit
+ 
+
+ align:start position:0%
+focused on efficiency short circuit
+current open circuit voltage fill factor
+
+ align:start position:0%
+current open circuit voltage fill factor
+ 
+
+ align:start position:0%
+current open circuit voltage fill factor
+so let's go ahead and dive into that we
+
+ align:start position:0%
+so let's go ahead and dive into that we
+ 
+
+ align:start position:0%
+so let's go ahead and dive into that we
+are going to first start with techniques
+
+ align:start position:0%
+are going to first start with techniques
+ 
+
+ align:start position:0%
+are going to first start with techniques
+to measure JSC or short-circuit current
+
+ align:start position:0%
+to measure JSC or short-circuit current
+ 
+
+ align:start position:0%
+to measure JSC or short-circuit current
+losses and some of these slides are
+
+ align:start position:0%
+losses and some of these slides are
+ 
+
+ align:start position:0%
+losses and some of these slides are
+going to be repeats and the reason
+
+ align:start position:0%
+going to be repeats and the reason
+ 
+
+ align:start position:0%
+going to be repeats and the reason
+they're repeats is because the first
+
+ align:start position:0%
+they're repeats is because the first
+ 
+
+ align:start position:0%
+they're repeats is because the first
+time you saw it okay you sort of kind of
+
+ align:start position:0%
+time you saw it okay you sort of kind of
+ 
+
+ align:start position:0%
+time you saw it okay you sort of kind of
+got it you went into the lab made your
+
+ align:start position:0%
+got it you went into the lab made your
+ 
+
+ align:start position:0%
+got it you went into the lab made your
+devices tested them and now all of a
+
+ align:start position:0%
+devices tested them and now all of a
+ 
+
+ align:start position:0%
+devices tested them and now all of a
+sudden you have a much I would say much
+
+ align:start position:0%
+sudden you have a much I would say much
+ 
+
+ align:start position:0%
+sudden you have a much I would say much
+stronger background with which to
+
+ align:start position:0%
+stronger background with which to
+ 
+
+ align:start position:0%
+stronger background with which to
+understand we're going to start by
+
+ align:start position:0%
+understand we're going to start by
+ 
+
+ align:start position:0%
+understand we're going to start by
+discussing the optical components just
+
+ align:start position:0%
+discussing the optical components just
+ 
+
+ align:start position:0%
+discussing the optical components just
+very briefly
+
+ align:start position:0%
+very briefly
+ 
+
+ align:start position:0%
+very briefly
+in spectral response minority carrier
+
+ align:start position:0%
+in spectral response minority carrier
+ 
+
+ align:start position:0%
+in spectral response minority carrier
+diffusion length revisiting some of
+
+ align:start position:0%
+diffusion length revisiting some of
+ 
+
+ align:start position:0%
+diffusion length revisiting some of
+these concepts that we already seen but
+
+ align:start position:0%
+these concepts that we already seen but
+ 
+
+ align:start position:0%
+these concepts that we already seen but
+now with the benefit of having all of
+
+ align:start position:0%
+now with the benefit of having all of
+ 
+
+ align:start position:0%
+now with the benefit of having all of
+our background knowledge
+
+ align:start position:0%
+our background knowledge
+ 
+
+ align:start position:0%
+our background knowledge
+spectrophotometer majors specular and
+
+ align:start position:0%
+spectrophotometer majors specular and
+ 
+
+ align:start position:0%
+spectrophotometer majors specular and
+diffuse reflectance and transmission
+
+ align:start position:0%
+diffuse reflectance and transmission
+ 
+
+ align:start position:0%
+diffuse reflectance and transmission
+alright let's let's break that down
+
+ align:start position:0%
+alright let's let's break that down
+ 
+
+ align:start position:0%
+alright let's let's break that down
+specular reflectance spec your mirror
+
+ align:start position:0%
+specular reflectance spec your mirror
+ 
+
+ align:start position:0%
+specular reflectance spec your mirror
+Latin right so specular reflectance
+
+ align:start position:0%
+Latin right so specular reflectance
+ 
+
+ align:start position:0%
+Latin right so specular reflectance
+means light comes in and out pretty much
+
+ align:start position:0%
+means light comes in and out pretty much
+ 
+
+ align:start position:0%
+means light comes in and out pretty much
+at the same angle relative to the
+
+ align:start position:0%
+at the same angle relative to the
+ 
+
+ align:start position:0%
+at the same angle relative to the
+surface normal so if you come in from
+
+ align:start position:0%
+surface normal so if you come in from
+ 
+
+ align:start position:0%
+surface normal so if you come in from
+here it's going to bounce out like there
+
+ align:start position:0%
+here it's going to bounce out like there
+ 
+
+ align:start position:0%
+here it's going to bounce out like there
+right the same angle relative to the
+
+ align:start position:0%
+right the same angle relative to the
+ 
+
+ align:start position:0%
+right the same angle relative to the
+surface normal diffuse reflectance means
+
+ align:start position:0%
+surface normal diffuse reflectance means
+ 
+
+ align:start position:0%
+surface normal diffuse reflectance means
+that if you shine light in a certain
+
+ align:start position:0%
+that if you shine light in a certain
+ 
+
+ align:start position:0%
+that if you shine light in a certain
+angle it's going to reflect back not
+
+ align:start position:0%
+angle it's going to reflect back not
+ 
+
+ align:start position:0%
+angle it's going to reflect back not
+necessarily at that angle I could have a
+
+ align:start position:0%
+necessarily at that angle I could have a
+ 
+
+ align:start position:0%
+necessarily at that angle I could have a
+distribution limbering scatterer might
+
+ align:start position:0%
+distribution limbering scatterer might
+ 
+
+ align:start position:0%
+distribution limbering scatterer might
+qualify and reflecting some transmission
+
+ align:start position:0%
+qualify and reflecting some transmission
+ 
+
+ align:start position:0%
+qualify and reflecting some transmission
+okay we talked about the different
+
+ align:start position:0%
+okay we talked about the different
+ 
+
+ align:start position:0%
+okay we talked about the different
+optical losses of a solar cell material
+
+ align:start position:0%
+optical losses of a solar cell material
+ 
+
+ align:start position:0%
+optical losses of a solar cell material
+reflectance means that light comes back
+
+ align:start position:0%
+reflectance means that light comes back
+ 
+
+ align:start position:0%
+reflectance means that light comes back
+off the surface transmission means that
+
+ align:start position:0%
+off the surface transmission means that
+ 
+
+ align:start position:0%
+off the surface transmission means that
+light did not get absorbed so it went
+
+ align:start position:0%
+light did not get absorbed so it went
+ 
+
+ align:start position:0%
+light did not get absorbed so it went
+through the material and didn't get
+
+ align:start position:0%
+through the material and didn't get
+ 
+
+ align:start position:0%
+through the material and didn't get
+absorbed that is an optical loss as well
+
+ align:start position:0%
+absorbed that is an optical loss as well
+ 
+
+ align:start position:0%
+absorbed that is an optical loss as well
+so the spectrophotometer is useful for
+
+ align:start position:0%
+so the spectrophotometer is useful for
+ 
+
+ align:start position:0%
+so the spectrophotometer is useful for
+measuring these different loss
+
+ align:start position:0%
+measuring these different loss
+ 
+
+ align:start position:0%
+measuring these different loss
+mechanisms and it can tease apart the
+
+ align:start position:0%
+mechanisms and it can tease apart the
+ 
+
+ align:start position:0%
+mechanisms and it can tease apart the
+specular from the diffuse reflectance
+
+ align:start position:0%
+specular from the diffuse reflectance
+ 
+
+ align:start position:0%
+specular from the diffuse reflectance
+giving you some indication some idea of
+
+ align:start position:0%
+giving you some indication some idea of
+ 
+
+ align:start position:0%
+giving you some indication some idea of
+how the surface is behaving and what you
+
+ align:start position:0%
+how the surface is behaving and what you
+ 
+
+ align:start position:0%
+how the surface is behaving and what you
+might do to improve it so the
+
+ align:start position:0%
+might do to improve it so the
+ 
+
+ align:start position:0%
+might do to improve it so the
+spectrophotometer is useful in that
+
+ align:start position:0%
+spectrophotometer is useful in that
+ 
+
+ align:start position:0%
+spectrophotometer is useful in that
+regard in terms of increasing absorption
+
+ align:start position:0%
+regard in terms of increasing absorption
+ 
+
+ align:start position:0%
+regard in terms of increasing absorption
+we talked about various methods to
+
+ align:start position:0%
+we talked about various methods to
+ 
+
+ align:start position:0%
+we talked about various methods to
+increase absorption those who attended
+
+ align:start position:0%
+increase absorption those who attended
+ 
+
+ align:start position:0%
+increase absorption those who attended
+the Eloi a bloody talk heard
+
+ align:start position:0%
+the Eloi a bloody talk heard
+ 
+
+ align:start position:0%
+the Eloi a bloody talk heard
+about many more the goal here is
+
+ align:start position:0%
+about many more the goal here is
+ 
+
+ align:start position:0%
+about many more the goal here is
+essentially to increase the optical path
+
+ align:start position:0%
+essentially to increase the optical path
+ 
+
+ align:start position:0%
+essentially to increase the optical path
+length by texturing your surface for
+
+ align:start position:0%
+length by texturing your surface for
+ 
+
+ align:start position:0%
+length by texturing your surface for
+instance the physical thickness can
+
+ align:start position:0%
+instance the physical thickness can
+ 
+
+ align:start position:0%
+instance the physical thickness can
+remain very low and again just to
+
+ align:start position:0%
+remain very low and again just to
+ 
+
+ align:start position:0%
+remain very low and again just to
+refresh ourselves if we decrease the
+
+ align:start position:0%
+refresh ourselves if we decrease the
+ 
+
+ align:start position:0%
+refresh ourselves if we decrease the
+thickness of our devices but managed to
+
+ align:start position:0%
+thickness of our devices but managed to
+ 
+
+ align:start position:0%
+thickness of our devices but managed to
+have very good light trapping what
+
+ align:start position:0%
+have very good light trapping what
+ 
+
+ align:start position:0%
+have very good light trapping what
+happens to our excess carrier density it
+
+ align:start position:0%
+happens to our excess carrier density it
+ 
+
+ align:start position:0%
+happens to our excess carrier density it
+goes up right because now we have more
+
+ align:start position:0%
+goes up right because now we have more
+ 
+
+ align:start position:0%
+goes up right because now we have more
+carriers being generated in a smaller
+
+ align:start position:0%
+carriers being generated in a smaller
+ 
+
+ align:start position:0%
+carriers being generated in a smaller
+volume so the carrier density increases
+
+ align:start position:0%
+volume so the carrier density increases
+ 
+
+ align:start position:0%
+volume so the carrier density increases
+and as the carrier density goes up that
+
+ align:start position:0%
+and as the carrier density goes up that
+ 
+
+ align:start position:0%
+and as the carrier density goes up that
+means the separation of the quasi Fermi
+
+ align:start position:0%
+means the separation of the quasi Fermi
+ 
+
+ align:start position:0%
+means the separation of the quasi Fermi
+energies increases which means the
+
+ align:start position:0%
+energies increases which means the
+ 
+
+ align:start position:0%
+energies increases which means the
+maximum voltage extractable from our
+
+ align:start position:0%
+maximum voltage extractable from our
+ 
+
+ align:start position:0%
+maximum voltage extractable from our
+device increases as well so there's a
+
+ align:start position:0%
+device increases as well so there's a
+ 
+
+ align:start position:0%
+device increases as well so there's a
+strong push right now in the field to go
+
+ align:start position:0%
+strong push right now in the field to go
+ 
+
+ align:start position:0%
+strong push right now in the field to go
+to thinner and thinner devices that also
+
+ align:start position:0%
+to thinner and thinner devices that also
+ 
+
+ align:start position:0%
+to thinner and thinner devices that also
+has the added benefit economically of
+
+ align:start position:0%
+has the added benefit economically of
+ 
+
+ align:start position:0%
+has the added benefit economically of
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+material so we want to decrease the
+
+ align:start position:0%
+material so we want to decrease the
+ 
+
+ align:start position:0%
+material so we want to decrease the
+thickness by improving our optical
+
+ align:start position:0%
+thickness by improving our optical
+ 
+
+ align:start position:0%
+thickness by improving our optical
+trapping our light trapping the another
+
+ align:start position:0%
+trapping our light trapping the another
+ 
+
+ align:start position:0%
+trapping our light trapping the another
+benefit is that allows carriers to be
+
+ align:start position:0%
+benefit is that allows carriers to be
+ 
+
+ align:start position:0%
+benefit is that allows carriers to be
+absorbed closer to the junction which
+
+ align:start position:0%
+absorbed closer to the junction which
+ 
+
+ align:start position:0%
+absorbed closer to the junction which
+increases their probability of
+
+ align:start position:0%
+increases their probability of
+ 
+
+ align:start position:0%
+increases their probability of
+collection and we talked about this
+
+ align:start position:0%
+collection and we talked about this
+ 
+
+ align:start position:0%
+collection and we talked about this
+during the very beginning of class how
+
+ align:start position:0%
+during the very beginning of class how
+ 
+
+ align:start position:0%
+during the very beginning of class how
+you might texture your surface but now
+
+ align:start position:0%
+you might texture your surface but now
+ 
+
+ align:start position:0%
+you might texture your surface but now
+we actually saw it in producing
+
+ align:start position:0%
+we actually saw it in producing
+ 
+
+ align:start position:0%
+we actually saw it in producing
+ourselves so this is an example an SEM
+
+ align:start position:0%
+ourselves so this is an example an SEM
+ 
+
+ align:start position:0%
+ourselves so this is an example an SEM
+image of textured silicon in that
+
+ align:start position:0%
+image of textured silicon in that
+ 
+
+ align:start position:0%
+image of textured silicon in that
+particular case this was an alkali edge
+
+ align:start position:0%
+particular case this was an alkali edge
+ 
+
+ align:start position:0%
+particular case this was an alkali edge
+on a single crystalline sample probably
+
+ align:start position:0%
+on a single crystalline sample probably
+ 
+
+ align:start position:0%
+on a single crystalline sample probably
+of 1 0-0 orientation so that these edges
+
+ align:start position:0%
+of 1 0-0 orientation so that these edges
+ 
+
+ align:start position:0%
+of 1 0-0 orientation so that these edges
+of the pyramids are 1 1 1 planes you
+
+ align:start position:0%
+of the pyramids are 1 1 1 planes you
+ 
+
+ align:start position:0%
+of the pyramids are 1 1 1 planes you
+could also achieve a similar although
+
+ align:start position:0%
+could also achieve a similar although
+ 
+
+ align:start position:0%
+could also achieve a similar although
+not identically looking result if you
+
+ align:start position:0%
+not identically looking result if you
+ 
+
+ align:start position:0%
+not identically looking result if you
+performed an acidic etch which would be
+
+ align:start position:0%
+performed an acidic etch which would be
+ 
+
+ align:start position:0%
+performed an acidic etch which would be
+an isotropic in nature so the light
+
+ align:start position:0%
+an isotropic in nature so the light
+ 
+
+ align:start position:0%
+an isotropic in nature so the light
+comes in for the textured surface some
+
+ align:start position:0%
+comes in for the textured surface some
+ 
+
+ align:start position:0%
+comes in for the textured surface some
+of it goes in to the device
+
+ align:start position:0%
+of it goes in to the device
+ 
+
+ align:start position:0%
+of it goes in to the device
+notice that Snell's laws in effect so
+
+ align:start position:0%
+notice that Snell's laws in effect so
+ 
+
+ align:start position:0%
+notice that Snell's laws in effect so
+the light bent or was refracted and some
+
+ align:start position:0%
+the light bent or was refracted and some
+ 
+
+ align:start position:0%
+the light bent or was refracted and some
+of the light is reflected off the
+
+ align:start position:0%
+of the light is reflected off the
+ 
+
+ align:start position:0%
+of the light is reflected off the
+surface now because of the texturization
+
+ align:start position:0%
+surface now because of the texturization
+ 
+
+ align:start position:0%
+surface now because of the texturization
+you get that second chance absorption so
+
+ align:start position:0%
+you get that second chance absorption so
+ 
+
+ align:start position:0%
+you get that second chance absorption so
+the light has to bounces before leaving
+
+ align:start position:0%
+the light has to bounces before leaving
+ 
+
+ align:start position:0%
+the light has to bounces before leaving
+which means that the probability of the
+
+ align:start position:0%
+which means that the probability of the
+ 
+
+ align:start position:0%
+which means that the probability of the
+light getting absorbed is 1 minus our
+
+ align:start position:0%
+light getting absorbed is 1 minus our
+ 
+
+ align:start position:0%
+light getting absorbed is 1 minus our
+quantity squared right and so you get an
+
+ align:start position:0%
+quantity squared right and so you get an
+ 
+
+ align:start position:0%
+quantity squared right and so you get an
+enhanced absorption and for those who
+
+ align:start position:0%
+enhanced absorption and for those who
+ 
+
+ align:start position:0%
+enhanced absorption and for those who
+looked at the samples before and after
+
+ align:start position:0%
+looked at the samples before and after
+ 
+
+ align:start position:0%
+looked at the samples before and after
+texturization you could visibly see that
+
+ align:start position:0%
+texturization you could visibly see that
+ 
+
+ align:start position:0%
+texturization you could visibly see that
+they looked darker the reflectivity had
+
+ align:start position:0%
+they looked darker the reflectivity had
+ 
+
+ align:start position:0%
+they looked darker the reflectivity had
+gone down I see some smiles over here
+
+ align:start position:0%
+gone down I see some smiles over here
+ 
+
+ align:start position:0%
+gone down I see some smiles over here
+there were probably some initial itching
+
+ align:start position:0%
+there were probably some initial itching
+ 
+
+ align:start position:0%
+there were probably some initial itching
+processes that didn't quite work out but
+
+ align:start position:0%
+processes that didn't quite work out but
+ 
+
+ align:start position:0%
+processes that didn't quite work out but
+eventually the process was controlled in
+
+ align:start position:0%
+eventually the process was controlled in
+ 
+
+ align:start position:0%
+eventually the process was controlled in
+and worked out fine so we have as well
+
+ align:start position:0%
+and worked out fine so we have as well
+ 
+
+ align:start position:0%
+and worked out fine so we have as well
+other mechanisms to trap the light
+
+ align:start position:0%
+other mechanisms to trap the light
+ 
+
+ align:start position:0%
+other mechanisms to trap the light
+besides just texturing our front surface
+
+ align:start position:0%
+besides just texturing our front surface
+ 
+
+ align:start position:0%
+besides just texturing our front surface
+these we didn't get to in to do an
+
+ align:start position:0%
+these we didn't get to in to do an
+ 
+
+ align:start position:0%
+these we didn't get to in to do an
+actual cell fab but we could envision
+
+ align:start position:0%
+actual cell fab but we could envision
+ 
+
+ align:start position:0%
+actual cell fab but we could envision
+putting a reflective or diffuse scatter
+
+ align:start position:0%
+putting a reflective or diffuse scatter
+ 
+
+ align:start position:0%
+putting a reflective or diffuse scatter
+on the back and a reflective layer so
+
+ align:start position:0%
+on the back and a reflective layer so
+ 
+
+ align:start position:0%
+on the back and a reflective layer so
+that the light that goes all the way
+
+ align:start position:0%
+that the light that goes all the way
+ 
+
+ align:start position:0%
+that the light that goes all the way
+through the material once gets bounced
+
+ align:start position:0%
+through the material once gets bounced
+ 
+
+ align:start position:0%
+through the material once gets bounced
+back in perhaps at an angle right to
+
+ align:start position:0%
+back in perhaps at an angle right to
+ 
+
+ align:start position:0%
+back in perhaps at an angle right to
+increase the light trapping in the back
+
+ align:start position:0%
+increase the light trapping in the back
+ 
+
+ align:start position:0%
+increase the light trapping in the back
+and that I think is represented on the
+
+ align:start position:0%
+and that I think is represented on the
+ 
+
+ align:start position:0%
+and that I think is represented on the
+previous slide it is indeed so we have a
+
+ align:start position:0%
+previous slide it is indeed so we have a
+ 
+
+ align:start position:0%
+previous slide it is indeed so we have a
+textured back surface and we also have
+
+ align:start position:0%
+textured back surface and we also have
+ 
+
+ align:start position:0%
+textured back surface and we also have
+this layer probably in this case it
+
+ align:start position:0%
+this layer probably in this case it
+ 
+
+ align:start position:0%
+this layer probably in this case it
+would most likely be a dielectric
+
+ align:start position:0%
+would most likely be a dielectric
+ 
+
+ align:start position:0%
+would most likely be a dielectric
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+with a refractive index that is
+
+ align:start position:0%
+with a refractive index that is
+ 
+
+ align:start position:0%
+with a refractive index that is
+significantly different than the
+
+ align:start position:0%
+significantly different than the
+ 
+
+ align:start position:0%
+significantly different than the
+absorber itself so if your absorber
+
+ align:start position:0%
+absorber itself so if your absorber
+ 
+
+ align:start position:0%
+absorber itself so if your absorber
+material is inorganic you might have a
+
+ align:start position:0%
+material is inorganic you might have a
+ 
+
+ align:start position:0%
+material is inorganic you might have a
+refractive index somewhere between 1.5
+
+ align:start position:0%
+refractive index somewhere between 1.5
+ 
+
+ align:start position:0%
+refractive index somewhere between 1.5
+and 2 maybe on the high end and if you
+
+ align:start position:0%
+and 2 maybe on the high end and if you
+ 
+
+ align:start position:0%
+and 2 maybe on the high end and if you
+have an inorganic material you could
+
+ align:start position:0%
+have an inorganic material you could
+ 
+
+ align:start position:0%
+have an inorganic material you could
+have refractive indices as high as 3 3
+
+ align:start position:0%
+have refractive indices as high as 3 3
+ 
+
+ align:start position:0%
+have refractive indices as high as 3 3
+and 1/2 and the material you put on the
+
+ align:start position:0%
+and 1/2 and the material you put on the
+ 
+
+ align:start position:0%
+and 1/2 and the material you put on the
+back would probably be as close as you
+
+ align:start position:0%
+back would probably be as close as you
+ 
+
+ align:start position:0%
+back would probably be as close as you
+could possibly get to air right to get a
+
+ align:start position:0%
+could possibly get to air right to get a
+ 
+
+ align:start position:0%
+could possibly get to air right to get a
+large reflection off the back as
+
+ align:start position:0%
+large reflection off the back as
+ 
+
+ align:start position:0%
+large reflection off the back as
+possible in the case of silicon devices
+
+ align:start position:0%
+possible in the case of silicon devices
+ 
+
+ align:start position:0%
+possible in the case of silicon devices
+oftentimes you have a dielectric
+
+ align:start position:0%
+oftentimes you have a dielectric
+ 
+
+ align:start position:0%
+oftentimes you have a dielectric
+material with a refractive index
+
+ align:start position:0%
+material with a refractive index
+ 
+
+ align:start position:0%
+material with a refractive index
+somewhere between 1.5 and 2 and that
+
+ align:start position:0%
+somewhere between 1.5 and 2 and that
+ 
+
+ align:start position:0%
+somewhere between 1.5 and 2 and that
+serves also to passivate the surface to
+
+ align:start position:0%
+serves also to passivate the surface to
+ 
+
+ align:start position:0%
+serves also to passivate the surface to
+prevent carriers from recombining on
+
+ align:start position:0%
+prevent carriers from recombining on
+ 
+
+ align:start position:0%
+prevent carriers from recombining on
+that back side so collection probability
+
+ align:start position:0%
+that back side so collection probability
+ 
+
+ align:start position:0%
+that back side so collection probability
+we talked about this earlier now that
+
+ align:start position:0%
+we talked about this earlier now that
+ 
+
+ align:start position:0%
+we talked about this earlier now that
+we've performed quantum efficiency and
+
+ align:start position:0%
+we've performed quantum efficiency and
+ 
+
+ align:start position:0%
+we've performed quantum efficiency and
+we've tested our own devices we want to
+
+ align:start position:0%
+we've tested our own devices we want to
+ 
+
+ align:start position:0%
+we've tested our own devices we want to
+walk through it again it's an important
+
+ align:start position:0%
+walk through it again it's an important
+ 
+
+ align:start position:0%
+walk through it again it's an important
+concept to really grasp I want to make
+
+ align:start position:0%
+concept to really grasp I want to make
+ 
+
+ align:start position:0%
+concept to really grasp I want to make
+sure that everybody got it we have here
+
+ align:start position:0%
+sure that everybody got it we have here
+ 
+
+ align:start position:0%
+sure that everybody got it we have here
+a PN Junction here's our p-type material
+
+ align:start position:0%
+a PN Junction here's our p-type material
+ 
+
+ align:start position:0%
+a PN Junction here's our p-type material
+here's our n-type material shown at the
+
+ align:start position:0%
+here's our n-type material shown at the
+ 
+
+ align:start position:0%
+here's our n-type material shown at the
+blue little dots those are our holes
+
+ align:start position:0%
+blue little dots those are our holes
+ 
+
+ align:start position:0%
+blue little dots those are our holes
+free holes mobile holes able to move
+
+ align:start position:0%
+free holes mobile holes able to move
+ 
+
+ align:start position:0%
+free holes mobile holes able to move
+around the material and then the n-type
+
+ align:start position:0%
+around the material and then the n-type
+ 
+
+ align:start position:0%
+around the material and then the n-type
+side we have here the red dots those are
+
+ align:start position:0%
+side we have here the red dots those are
+ 
+
+ align:start position:0%
+side we have here the red dots those are
+also free to move around the materials
+
+ align:start position:0%
+also free to move around the materials
+ 
+
+ align:start position:0%
+also free to move around the materials
+or electrons negative charge carriers
+
+ align:start position:0%
+or electrons negative charge carriers
+ 
+
+ align:start position:0%
+or electrons negative charge carriers
+omitted from this diagram omitted from
+
+ align:start position:0%
+omitted from this diagram omitted from
+ 
+
+ align:start position:0%
+omitted from this diagram omitted from
+this diagram is the fixed charge
+
+ align:start position:0%
+this diagram is the fixed charge
+ 
+
+ align:start position:0%
+this diagram is the fixed charge
+associated with each connectivity type
+
+ align:start position:0%
+associated with each connectivity type
+ 
+
+ align:start position:0%
+associated with each connectivity type
+we have for example fixed negative
+
+ align:start position:0%
+we have for example fixed negative
+ 
+
+ align:start position:0%
+we have for example fixed negative
+charge from the ionized acceptors from
+
+ align:start position:0%
+charge from the ionized acceptors from
+ 
+
+ align:start position:0%
+charge from the ionized acceptors from
+the p-type and fixed positive charge
+
+ align:start position:0%
+the p-type and fixed positive charge
+ 
+
+ align:start position:0%
+the p-type and fixed positive charge
+from the ionized donors in the n-type
+
+ align:start position:0%
+from the ionized donors in the n-type
+ 
+
+ align:start position:0%
+from the ionized donors in the n-type
+but we've emitted it for clarity we note
+
+ align:start position:0%
+but we've emitted it for clarity we note
+ 
+
+ align:start position:0%
+but we've emitted it for clarity we note
+that an electric field builds up here at
+
+ align:start position:0%
+that an electric field builds up here at
+ 
+
+ align:start position:0%
+that an electric field builds up here at
+the junction between and that sweeps
+
+ align:start position:0%
+the junction between and that sweeps
+ 
+
+ align:start position:0%
+the junction between and that sweeps
+carriers into one side or another so
+
+ align:start position:0%
+carriers into one side or another so
+ 
+
+ align:start position:0%
+carriers into one side or another so
+that if light comes in and generates a
+
+ align:start position:0%
+that if light comes in and generates a
+ 
+
+ align:start position:0%
+that if light comes in and generates a
+pair of charges due to charge neutrality
+
+ align:start position:0%
+pair of charges due to charge neutrality
+ 
+
+ align:start position:0%
+pair of charges due to charge neutrality
+it generates a pair positive in a
+
+ align:start position:0%
+it generates a pair positive in a
+ 
+
+ align:start position:0%
+it generates a pair positive in a
+negative the 1 1 charge carrier type
+
+ align:start position:0%
+negative the 1 1 charge carrier type
+ 
+
+ align:start position:0%
+negative the 1 1 charge carrier type
+will be swept across the junction and
+
+ align:start position:0%
+will be swept across the junction and
+ 
+
+ align:start position:0%
+will be swept across the junction and
+the other will remain inside of the
+
+ align:start position:0%
+the other will remain inside of the
+ 
+
+ align:start position:0%
+the other will remain inside of the
+material and so to be more precise about
+
+ align:start position:0%
+material and so to be more precise about
+ 
+
+ align:start position:0%
+material and so to be more precise about
+the exact motion that occurs with the
+
+ align:start position:0%
+the exact motion that occurs with the
+ 
+
+ align:start position:0%
+the exact motion that occurs with the
+carriers we have at first a diffusion
+
+ align:start position:0%
+carriers we have at first a diffusion
+ 
+
+ align:start position:0%
+carriers we have at first a diffusion
+process until the electric field starts
+
+ align:start position:0%
+process until the electric field starts
+ 
+
+ align:start position:0%
+process until the electric field starts
+becoming large and then finally drift
+
+ align:start position:0%
+becoming large and then finally drift
+ 
+
+ align:start position:0%
+becoming large and then finally drift
+across that Junction
+
+ align:start position:0%
+across that Junction
+ 
+
+ align:start position:0%
+across that Junction
+that's what generates the current inside
+
+ align:start position:0%
+that's what generates the current inside
+ 
+
+ align:start position:0%
+that's what generates the current inside
+of the solar cell device so collection
+
+ align:start position:0%
+of the solar cell device so collection
+ 
+
+ align:start position:0%
+of the solar cell device so collection
+probability means that light alike
+
+ align:start position:0%
+probability means that light alike
+ 
+
+ align:start position:0%
+probability means that light alike
+generated a photo generated minority
+
+ align:start position:0%
+generated a photo generated minority
+ 
+
+ align:start position:0%
+generated a photo generated minority
+carrier can readily recombine but if the
+
+ align:start position:0%
+carrier can readily recombine but if the
+ 
+
+ align:start position:0%
+carrier can readily recombine but if the
+carrier reaches the edge of this of the
+
+ align:start position:0%
+carrier reaches the edge of this of the
+ 
+
+ align:start position:0%
+carrier reaches the edge of this of the
+space charge region the minority carrier
+
+ align:start position:0%
+space charge region the minority carrier
+ 
+
+ align:start position:0%
+space charge region the minority carrier
+it can be swept across and collected so
+
+ align:start position:0%
+it can be swept across and collected so
+ 
+
+ align:start position:0%
+it can be swept across and collected so
+the probability of collection means for
+
+ align:start position:0%
+the probability of collection means for
+ 
+
+ align:start position:0%
+the probability of collection means for
+every electron hole pair that I generate
+
+ align:start position:0%
+every electron hole pair that I generate
+ 
+
+ align:start position:0%
+every electron hole pair that I generate
+at a certain depth what is a probability
+
+ align:start position:0%
+at a certain depth what is a probability
+ 
+
+ align:start position:0%
+at a certain depth what is a probability
+that the minority carrier will make it
+
+ align:start position:0%
+that the minority carrier will make it
+ 
+
+ align:start position:0%
+that the minority carrier will make it
+across a junction and this is what we're
+
+ align:start position:0%
+across a junction and this is what we're
+ 
+
+ align:start position:0%
+across a junction and this is what we're
+probing in spectral response yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so great question the exit on in
+
+ align:start position:0%
+okay so great question the exit on in
+ 
+
+ align:start position:0%
+okay so great question the exit on in
+silicon has a binding energy less than
+
+ align:start position:0%
+silicon has a binding energy less than
+ 
+
+ align:start position:0%
+silicon has a binding energy less than
+KT which means at room temperature the
+
+ align:start position:0%
+KT which means at room temperature the
+ 
+
+ align:start position:0%
+KT which means at room temperature the
+exit on readily dissociates so we so the
+
+ align:start position:0%
+exit on readily dissociates so we so the
+ 
+
+ align:start position:0%
+exit on readily dissociates so we so the
+exit on diffusion length can only be
+
+ align:start position:0%
+exit on diffusion length can only be
+ 
+
+ align:start position:0%
+exit on diffusion length can only be
+measured at lower temperatures the at
+
+ align:start position:0%
+measured at lower temperatures the at
+ 
+
+ align:start position:0%
+measured at lower temperatures the at
+room temperature you essentially just
+
+ align:start position:0%
+room temperature you essentially just
+ 
+
+ align:start position:0%
+room temperature you essentially just
+discussed minority carriers and the
+
+ align:start position:0%
+discussed minority carriers and the
+ 
+
+ align:start position:0%
+discussed minority carriers and the
+minority carrier diffusion length let's
+
+ align:start position:0%
+minority carrier diffusion length let's
+ 
+
+ align:start position:0%
+minority carrier diffusion length let's
+let's revert it in terms of lifetime and
+
+ align:start position:0%
+let's revert it in terms of lifetime and
+ 
+
+ align:start position:0%
+let's revert it in terms of lifetime and
+then do the translation to diffusion
+
+ align:start position:0%
+then do the translation to diffusion
+ 
+
+ align:start position:0%
+then do the translation to diffusion
+length in terms of lifetimes one
+
+ align:start position:0%
+length in terms of lifetimes one
+ 
+
+ align:start position:0%
+length in terms of lifetimes one
+typically has a range between a
+
+ align:start position:0%
+typically has a range between a
+ 
+
+ align:start position:0%
+typically has a range between a
+microsecond to a millisecond millisecond
+
+ align:start position:0%
+microsecond to a millisecond millisecond
+ 
+
+ align:start position:0%
+microsecond to a millisecond millisecond
+being in the high end it can go as high
+
+ align:start position:0%
+being in the high end it can go as high
+ 
+
+ align:start position:0%
+being in the high end it can go as high
+as five milliseconds even and so if you
+
+ align:start position:0%
+as five milliseconds even and so if you
+ 
+
+ align:start position:0%
+as five milliseconds even and so if you
+revert that into a diffusion length one
+
+ align:start position:0%
+revert that into a diffusion length one
+ 
+
+ align:start position:0%
+revert that into a diffusion length one
+microsecond lifetime would correspond to
+
+ align:start position:0%
+microsecond lifetime would correspond to
+ 
+
+ align:start position:0%
+microsecond lifetime would correspond to
+a 50 micron diffusion length and then
+
+ align:start position:0%
+a 50 micron diffusion length and then
+ 
+
+ align:start position:0%
+a 50 micron diffusion length and then
+you can do the rest of the conversion
+
+ align:start position:0%
+you can do the rest of the conversion
+ 
+
+ align:start position:0%
+you can do the rest of the conversion
+from there just taking the square root
+
+ align:start position:0%
+from there just taking the square root
+ 
+
+ align:start position:0%
+from there just taking the square root
+sign into account so it can be rather
+
+ align:start position:0%
+sign into account so it can be rather
+ 
+
+ align:start position:0%
+sign into account so it can be rather
+long on the order of the thickness of
+
+ align:start position:0%
+long on the order of the thickness of
+ 
+
+ align:start position:0%
+long on the order of the thickness of
+these solar cell devices now that's
+
+ align:start position:0%
+these solar cell devices now that's
+ 
+
+ align:start position:0%
+these solar cell devices now that's
+those length scales which we're talking
+
+ align:start position:0%
+those length scales which we're talking
+ 
+
+ align:start position:0%
+those length scales which we're talking
+about hundreds of microns maybe even a
+
+ align:start position:0%
+about hundreds of microns maybe even a
+ 
+
+ align:start position:0%
+about hundreds of microns maybe even a
+thousand microns compare that now to ten
+
+ align:start position:0%
+thousand microns compare that now to ten
+ 
+
+ align:start position:0%
+thousand microns compare that now to ten
+nanometer diffusion length say for an
+
+ align:start position:0%
+nanometer diffusion length say for an
+ 
+
+ align:start position:0%
+nanometer diffusion length say for an
+exit on in a polymer blend material then
+
+ align:start position:0%
+exit on in a polymer blend material then
+ 
+
+ align:start position:0%
+exit on in a polymer blend material then
+you have to reconsider your device
+
+ align:start position:0%
+you have to reconsider your device
+ 
+
+ align:start position:0%
+you have to reconsider your device
+architecture how you're going to
+
+ align:start position:0%
+architecture how you're going to
+ 
+
+ align:start position:0%
+architecture how you're going to
+actually collect them so this is a very
+
+ align:start position:0%
+actually collect them so this is a very
+ 
+
+ align:start position:0%
+actually collect them so this is a very
+generic picture which could easily be
+
+ align:start position:0%
+generic picture which could easily be
+ 
+
+ align:start position:0%
+generic picture which could easily be
+substituted instead of n type P type it
+
+ align:start position:0%
+substituted instead of n type P type it
+ 
+
+ align:start position:0%
+substituted instead of n type P type it
+can be easily substituted by say polymer
+
+ align:start position:0%
+can be easily substituted by say polymer
+ 
+
+ align:start position:0%
+can be easily substituted by say polymer
+1 and polymer 2 that just have the right
+
+ align:start position:0%
+1 and polymer 2 that just have the right
+ 
+
+ align:start position:0%
+1 and polymer 2 that just have the right
+band alignment two separate charge then
+
+ align:start position:0%
+band alignment two separate charge then
+ 
+
+ align:start position:0%
+band alignment two separate charge then
+it gets a little more complicated as
+
+ align:start position:0%
+it gets a little more complicated as
+ 
+
+ align:start position:0%
+it gets a little more complicated as
+well here we're assuming that the
+
+ align:start position:0%
+well here we're assuming that the
+ 
+
+ align:start position:0%
+well here we're assuming that the
+carriers that are swept across the
+
+ align:start position:0%
+carriers that are swept across the
+ 
+
+ align:start position:0%
+carriers that are swept across the
+junction can move easily away from the
+
+ align:start position:0%
+junction can move easily away from the
+ 
+
+ align:start position:0%
+junction can move easily away from the
+junction in a polymer not always so you
+
+ align:start position:0%
+junction in a polymer not always so you
+ 
+
+ align:start position:0%
+junction in a polymer not always so you
+might have charge accumulation right at
+
+ align:start position:0%
+might have charge accumulation right at
+ 
+
+ align:start position:0%
+might have charge accumulation right at
+the edge of the space charge region
+
+ align:start position:0%
+the edge of the space charge region
+ 
+
+ align:start position:0%
+the edge of the space charge region
+which creates his own field which
+
+ align:start position:0%
+which creates his own field which
+ 
+
+ align:start position:0%
+which creates his own field which
+counteracts the built-in field here and
+
+ align:start position:0%
+counteracts the built-in field here and
+ 
+
+ align:start position:0%
+counteracts the built-in field here and
+also inhibits current flow so things get
+
+ align:start position:0%
+also inhibits current flow so things get
+ 
+
+ align:start position:0%
+also inhibits current flow so things get
+a lot more complicated as you venture
+
+ align:start position:0%
+a lot more complicated as you venture
+ 
+
+ align:start position:0%
+a lot more complicated as you venture
+away from the simple case of say a well
+
+ align:start position:0%
+away from the simple case of say a well
+ 
+
+ align:start position:0%
+away from the simple case of say a well
+behaved
+
+ align:start position:0%
+behaved
+ 
+
+ align:start position:0%
+behaved
+what I call what is called in this case
+
+ align:start position:0%
+what I call what is called in this case
+ 
+
+ align:start position:0%
+what I call what is called in this case
+a homo Junction meaning a PN Junction
+
+ align:start position:0%
+a homo Junction meaning a PN Junction
+ 
+
+ align:start position:0%
+a homo Junction meaning a PN Junction
+created from the same material on both
+
+ align:start position:0%
+created from the same material on both
+ 
+
+ align:start position:0%
+created from the same material on both
+sides silicon just doped N and p-type if
+
+ align:start position:0%
+sides silicon just doped N and p-type if
+ 
+
+ align:start position:0%
+sides silicon just doped N and p-type if
+you have a hetero Junction comprised of
+
+ align:start position:0%
+you have a hetero Junction comprised of
+ 
+
+ align:start position:0%
+you have a hetero Junction comprised of
+two different materials you may have
+
+ align:start position:0%
+two different materials you may have
+ 
+
+ align:start position:0%
+two different materials you may have
+even I say additional effects occurring
+
+ align:start position:0%
+even I say additional effects occurring
+ 
+
+ align:start position:0%
+even I say additional effects occurring
+but it's always helpful to think about
+
+ align:start position:0%
+but it's always helpful to think about
+ 
+
+ align:start position:0%
+but it's always helpful to think about
+the motion of carriers from the
+
+ align:start position:0%
+the motion of carriers from the
+ 
+
+ align:start position:0%
+the motion of carriers from the
+perspective of drift and diffusion and
+
+ align:start position:0%
+perspective of drift and diffusion and
+ 
+
+ align:start position:0%
+perspective of drift and diffusion and
+if you're ever in doubt you can begin
+
+ align:start position:0%
+if you're ever in doubt you can begin
+ 
+
+ align:start position:0%
+if you're ever in doubt you can begin
+thinking about
+
+ align:start position:0%
+thinking about
+ 
+
+ align:start position:0%
+thinking about
+in terms of Delta T's small increments
+
+ align:start position:0%
+in terms of Delta T's small increments
+ 
+
+ align:start position:0%
+in terms of Delta T's small increments
+of time where you imagine light coming
+
+ align:start position:0%
+of time where you imagine light coming
+ 
+
+ align:start position:0%
+of time where you imagine light coming
+in generating an electron hole pair
+
+ align:start position:0%
+in generating an electron hole pair
+ 
+
+ align:start position:0%
+in generating an electron hole pair
+imagining what happens is that carrier
+
+ align:start position:0%
+imagining what happens is that carrier
+ 
+
+ align:start position:0%
+imagining what happens is that carrier
+moves across the general moves to the
+
+ align:start position:0%
+moves across the general moves to the
+ 
+
+ align:start position:0%
+moves across the general moves to the
+junction then moves across the junction
+
+ align:start position:0%
+junction then moves across the junction
+ 
+
+ align:start position:0%
+junction then moves across the junction
+and then what happens does it
+
+ align:start position:0%
+and then what happens does it
+ 
+
+ align:start position:0%
+and then what happens does it
+immediately get collected does it stay
+
+ align:start position:0%
+immediately get collected does it stay
+ 
+
+ align:start position:0%
+immediately get collected does it stay
+there what is the what what happens next
+
+ align:start position:0%
+there what is the what what happens next
+ 
+
+ align:start position:0%
+there what is the what what happens next
+is there a potential
+
+ align:start position:0%
+is there a potential
+ 
+
+ align:start position:0%
+is there a potential
+an attractive potential between the
+
+ align:start position:0%
+an attractive potential between the
+ 
+
+ align:start position:0%
+an attractive potential between the
+carriers on either side of that Junction
+
+ align:start position:0%
+carriers on either side of that Junction
+ 
+
+ align:start position:0%
+carriers on either side of that Junction
+so asking those sorts of questions can
+
+ align:start position:0%
+so asking those sorts of questions can
+ 
+
+ align:start position:0%
+so asking those sorts of questions can
+help you walk through and troubleshoot
+
+ align:start position:0%
+help you walk through and troubleshoot
+ 
+
+ align:start position:0%
+help you walk through and troubleshoot
+what exactly is going wrong with your
+
+ align:start position:0%
+what exactly is going wrong with your
+ 
+
+ align:start position:0%
+what exactly is going wrong with your
+device collection probability so we take
+
+ align:start position:0%
+device collection probability so we take
+ 
+
+ align:start position:0%
+device collection probability so we take
+this this diagram that we just saw on
+
+ align:start position:0%
+this this diagram that we just saw on
+ 
+
+ align:start position:0%
+this this diagram that we just saw on
+the previous slide this one right here
+
+ align:start position:0%
+the previous slide this one right here
+ 
+
+ align:start position:0%
+the previous slide this one right here
+and we say hmm if light were to come in
+
+ align:start position:0%
+and we say hmm if light were to come in
+ 
+
+ align:start position:0%
+and we say hmm if light were to come in
+and generate an electron hole pair right
+
+ align:start position:0%
+and generate an electron hole pair right
+ 
+
+ align:start position:0%
+and generate an electron hole pair right
+here then I would expect very high
+
+ align:start position:0%
+here then I would expect very high
+ 
+
+ align:start position:0%
+here then I would expect very high
+probability of collection meaning the
+
+ align:start position:0%
+probability of collection meaning the
+ 
+
+ align:start position:0%
+probability of collection meaning the
+one what the minority carrier be swept
+
+ align:start position:0%
+one what the minority carrier be swept
+ 
+
+ align:start position:0%
+one what the minority carrier be swept
+across the majority care would stay on
+
+ align:start position:0%
+across the majority care would stay on
+ 
+
+ align:start position:0%
+across the majority care would stay on
+this side and presuming that they can
+
+ align:start position:0%
+this side and presuming that they can
+ 
+
+ align:start position:0%
+this side and presuming that they can
+get from here to the contacts big
+
+ align:start position:0%
+get from here to the contacts big
+ 
+
+ align:start position:0%
+get from here to the contacts big
+assumption but assuming that they can
+
+ align:start position:0%
+assumption but assuming that they can
+ 
+
+ align:start position:0%
+assumption but assuming that they can
+then the probability of collection of
+
+ align:start position:0%
+then the probability of collection of
+ 
+
+ align:start position:0%
+then the probability of collection of
+those carriers will be very very high
+
+ align:start position:0%
+those carriers will be very very high
+ 
+
+ align:start position:0%
+those carriers will be very very high
+but if my light comes in deep within the
+
+ align:start position:0%
+but if my light comes in deep within the
+ 
+
+ align:start position:0%
+but if my light comes in deep within the
+device and generates an electron hole
+
+ align:start position:0%
+device and generates an electron hole
+ 
+
+ align:start position:0%
+device and generates an electron hole
+pair the minority carrier will have to
+
+ align:start position:0%
+pair the minority carrier will have to
+ 
+
+ align:start position:0%
+pair the minority carrier will have to
+cruise through it can think about it
+
+ align:start position:0%
+cruise through it can think about it
+ 
+
+ align:start position:0%
+cruise through it can think about it
+maybe a nice tasty chicken in the
+
+ align:start position:0%
+maybe a nice tasty chicken in the
+ 
+
+ align:start position:0%
+maybe a nice tasty chicken in the
+Everglades National Park trying to make
+
+ align:start position:0%
+Everglades National Park trying to make
+ 
+
+ align:start position:0%
+Everglades National Park trying to make
+its way over from that side all the way
+
+ align:start position:0%
+its way over from that side all the way
+ 
+
+ align:start position:0%
+its way over from that side all the way
+over to the junction in across the
+
+ align:start position:0%
+over to the junction in across the
+ 
+
+ align:start position:0%
+over to the junction in across the
+minority carriers at risk of recombining
+
+ align:start position:0%
+minority carriers at risk of recombining
+ 
+
+ align:start position:0%
+minority carriers at risk of recombining
+and many of them don't make it so we
+
+ align:start position:0%
+and many of them don't make it so we
+ 
+
+ align:start position:0%
+and many of them don't make it so we
+have the following graph the collection
+
+ align:start position:0%
+have the following graph the collection
+ 
+
+ align:start position:0%
+have the following graph the collection
+probability versus distance into the
+
+ align:start position:0%
+probability versus distance into the
+ 
+
+ align:start position:0%
+probability versus distance into the
+device where this yellow region
+
+ align:start position:0%
+device where this yellow region
+ 
+
+ align:start position:0%
+device where this yellow region
+represents the space charge region where
+
+ align:start position:0%
+represents the space charge region where
+ 
+
+ align:start position:0%
+represents the space charge region where
+the probability of collection is very
+
+ align:start position:0%
+the probability of collection is very
+ 
+
+ align:start position:0%
+the probability of collection is very
+high and as you move away from the space
+
+ align:start position:0%
+high and as you move away from the space
+ 
+
+ align:start position:0%
+high and as you move away from the space
+charge region the probability of
+
+ align:start position:0%
+charge region the probability of
+ 
+
+ align:start position:0%
+charge region the probability of
+collection decreases and you can see it
+
+ align:start position:0%
+collection decreases and you can see it
+ 
+
+ align:start position:0%
+collection decreases and you can see it
+decreases exponentially as a function of
+
+ align:start position:0%
+decreases exponentially as a function of
+ 
+
+ align:start position:0%
+decreases exponentially as a function of
+distance from the space charge region
+
+ align:start position:0%
+distance from the space charge region
+ 
+
+ align:start position:0%
+distance from the space charge region
+the reason you have almost not exactly
+
+ align:start position:0%
+the reason you have almost not exactly
+ 
+
+ align:start position:0%
+the reason you have almost not exactly
+symmetric these are two different decay
+
+ align:start position:0%
+symmetric these are two different decay
+ 
+
+ align:start position:0%
+symmetric these are two different decay
+constants but they're both exponential
+
+ align:start position:0%
+constants but they're both exponential
+ 
+
+ align:start position:0%
+constants but they're both exponential
+functions on either side is because over
+
+ align:start position:0%
+functions on either side is because over
+ 
+
+ align:start position:0%
+functions on either side is because over
+here on the what ostensibly would be the
+
+ align:start position:0%
+here on the what ostensibly would be the
+ 
+
+ align:start position:0%
+here on the what ostensibly would be the
+what did we call it the p-type side the
+
+ align:start position:0%
+what did we call it the p-type side the
+ 
+
+ align:start position:0%
+what did we call it the p-type side the
+electrons would be the minority carriers
+
+ align:start position:0%
+electrons would be the minority carriers
+ 
+
+ align:start position:0%
+electrons would be the minority carriers
+and over on the n-type side the holes of
+
+ align:start position:0%
+and over on the n-type side the holes of
+ 
+
+ align:start position:0%
+and over on the n-type side the holes of
+the minority carriers and each one is
+
+ align:start position:0%
+the minority carriers and each one is
+ 
+
+ align:start position:0%
+the minority carriers and each one is
+trying to get to the other side so the
+
+ align:start position:0%
+trying to get to the other side so the
+ 
+
+ align:start position:0%
+trying to get to the other side so the
+collection probability is actually the
+
+ align:start position:0%
+collection probability is actually the
+ 
+
+ align:start position:0%
+collection probability is actually the
+collection probability of minority
+
+ align:start position:0%
+collection probability of minority
+ 
+
+ align:start position:0%
+collection probability of minority
+carriers the precise definition of which
+
+ align:start position:0%
+carriers the precise definition of which
+ 
+
+ align:start position:0%
+carriers the precise definition of which
+is chain
+
+ align:start position:0%
+is chain
+ 
+
+ align:start position:0%
+is chain
+from one side of the junction to the
+
+ align:start position:0%
+from one side of the junction to the
+ 
+
+ align:start position:0%
+from one side of the junction to the
+other I on one side of the junction the
+
+ align:start position:0%
+other I on one side of the junction the
+ 
+
+ align:start position:0%
+other I on one side of the junction the
+electrons and minority carriers on the
+
+ align:start position:0%
+electrons and minority carriers on the
+ 
+
+ align:start position:0%
+electrons and minority carriers on the
+other side of the holes in the minority
+
+ align:start position:0%
+other side of the holes in the minority
+ 
+
+ align:start position:0%
+other side of the holes in the minority
+carriers all right so by probing at
+
+ align:start position:0%
+carriers all right so by probing at
+ 
+
+ align:start position:0%
+carriers all right so by probing at
+different wavelengths of light
+
+ align:start position:0%
+different wavelengths of light
+ 
+
+ align:start position:0%
+different wavelengths of light
+we essentially change the optical
+
+ align:start position:0%
+we essentially change the optical
+ 
+
+ align:start position:0%
+we essentially change the optical
+absorption coefficient of the material
+
+ align:start position:0%
+absorption coefficient of the material
+ 
+
+ align:start position:0%
+absorption coefficient of the material
+which means that the light will get
+
+ align:start position:0%
+which means that the light will get
+ 
+
+ align:start position:0%
+which means that the light will get
+absorbed at different depths so we might
+
+ align:start position:0%
+absorbed at different depths so we might
+ 
+
+ align:start position:0%
+absorbed at different depths so we might
+have a very short wavelength light that
+
+ align:start position:0%
+have a very short wavelength light that
+ 
+
+ align:start position:0%
+have a very short wavelength light that
+probes up here and then say light is
+
+ align:start position:0%
+probes up here and then say light is
+ 
+
+ align:start position:0%
+probes up here and then say light is
+coming in from this side right so short
+
+ align:start position:0%
+coming in from this side right so short
+ 
+
+ align:start position:0%
+coming in from this side right so short
+wavelength light is absorbed near the
+
+ align:start position:0%
+wavelength light is absorbed near the
+ 
+
+ align:start position:0%
+wavelength light is absorbed near the
+front surface and then longer longer
+
+ align:start position:0%
+front surface and then longer longer
+ 
+
+ align:start position:0%
+front surface and then longer longer
+longer and longer and longer and longer
+
+ align:start position:0%
+longer and longer and longer and longer
+ 
+
+ align:start position:0%
+longer and longer and longer and longer
+wavelengths until we're deep within the
+
+ align:start position:0%
+wavelengths until we're deep within the
+ 
+
+ align:start position:0%
+wavelengths until we're deep within the
+material and we can flesh out exactly
+
+ align:start position:0%
+material and we can flesh out exactly
+ 
+
+ align:start position:0%
+material and we can flesh out exactly
+what the current collection probability
+
+ align:start position:0%
+what the current collection probability
+ 
+
+ align:start position:0%
+what the current collection probability
+would be as a function of depth then we
+
+ align:start position:0%
+would be as a function of depth then we
+ 
+
+ align:start position:0%
+would be as a function of depth then we
+essentially take that data
+
+ align:start position:0%
+essentially take that data
+ 
+
+ align:start position:0%
+essentially take that data
+knowing the generation rate and the
+
+ align:start position:0%
+knowing the generation rate and the
+ 
+
+ align:start position:0%
+knowing the generation rate and the
+collection probability we can tease out
+
+ align:start position:0%
+collection probability we can tease out
+ 
+
+ align:start position:0%
+collection probability we can tease out
+the minority carrier diffusion length
+
+ align:start position:0%
+the minority carrier diffusion length
+ 
+
+ align:start position:0%
+the minority carrier diffusion length
+using the spectrophotometer so let me
+
+ align:start position:0%
+using the spectrophotometer so let me
+ 
+
+ align:start position:0%
+using the spectrophotometer so let me
+show you examples of good and bad cells
+
+ align:start position:0%
+show you examples of good and bad cells
+ 
+
+ align:start position:0%
+show you examples of good and bad cells
+this would be a bad solar cell and a
+
+ align:start position:0%
+this would be a bad solar cell and a
+ 
+
+ align:start position:0%
+this would be a bad solar cell and a
+good solar cell device right over here
+
+ align:start position:0%
+good solar cell device right over here
+ 
+
+ align:start position:0%
+good solar cell device right over here
+the good solar cell has a high internal
+
+ align:start position:0%
+the good solar cell has a high internal
+ 
+
+ align:start position:0%
+the good solar cell has a high internal
+quantum efficiency out to longer
+
+ align:start position:0%
+quantum efficiency out to longer
+ 
+
+ align:start position:0%
+quantum efficiency out to longer
+wavelengths and as we know from the very
+
+ align:start position:0%
+wavelengths and as we know from the very
+ 
+
+ align:start position:0%
+wavelengths and as we know from the very
+second lecture of our class the longer
+
+ align:start position:0%
+second lecture of our class the longer
+ 
+
+ align:start position:0%
+second lecture of our class the longer
+wavelengths get absorbed deeper into the
+
+ align:start position:0%
+wavelengths get absorbed deeper into the
+ 
+
+ align:start position:0%
+wavelengths get absorbed deeper into the
+device further from the junction and so
+
+ align:start position:0%
+device further from the junction and so
+ 
+
+ align:start position:0%
+device further from the junction and so
+you can see this tail off occurring
+
+ align:start position:0%
+you can see this tail off occurring
+ 
+
+ align:start position:0%
+you can see this tail off occurring
+actually the tail off somewhere in this
+
+ align:start position:0%
+actually the tail off somewhere in this
+ 
+
+ align:start position:0%
+actually the tail off somewhere in this
+region right here for this device is
+
+ align:start position:0%
+region right here for this device is
+ 
+
+ align:start position:0%
+region right here for this device is
+occurring within the bulk at some point
+
+ align:start position:0%
+occurring within the bulk at some point
+ 
+
+ align:start position:0%
+occurring within the bulk at some point
+the device just isn't thick enough to
+
+ align:start position:0%
+the device just isn't thick enough to
+ 
+
+ align:start position:0%
+the device just isn't thick enough to
+absorb all the light so there is an
+
+ align:start position:0%
+absorb all the light so there is an
+ 
+
+ align:start position:0%
+absorb all the light so there is an
+inevitable drop toward longer
+
+ align:start position:0%
+inevitable drop toward longer
+ 
+
+ align:start position:0%
+inevitable drop toward longer
+wavelengths but the bad cell doesn't
+
+ align:start position:0%
+wavelengths but the bad cell doesn't
+ 
+
+ align:start position:0%
+wavelengths but the bad cell doesn't
+even pour a job of collecting these
+
+ align:start position:0%
+even pour a job of collecting these
+ 
+
+ align:start position:0%
+even pour a job of collecting these
+longer wavelengths and thus in part
+
+ align:start position:0%
+longer wavelengths and thus in part
+ 
+
+ align:start position:0%
+longer wavelengths and thus in part
+because the minority carrier diffusion
+
+ align:start position:0%
+because the minority carrier diffusion
+ 
+
+ align:start position:0%
+because the minority carrier diffusion
+length of that particular cell was much
+
+ align:start position:0%
+length of that particular cell was much
+ 
+
+ align:start position:0%
+length of that particular cell was much
+lower or say the minority carrier
+
+ align:start position:0%
+lower or say the minority carrier
+ 
+
+ align:start position:0%
+lower or say the minority carrier
+diffusion length of the material which
+
+ align:start position:0%
+diffusion length of the material which
+ 
+
+ align:start position:0%
+diffusion length of the material which
+comprised the cell is much lower than
+
+ align:start position:0%
+comprised the cell is much lower than
+ 
+
+ align:start position:0%
+comprised the cell is much lower than
+the good cell so if you come in with a
+
+ align:start position:0%
+the good cell so if you come in with a
+ 
+
+ align:start position:0%
+the good cell so if you come in with a
+longer wavelength of light let's say oh
+
+ align:start position:0%
+longer wavelength of light let's say oh
+ 
+
+ align:start position:0%
+longer wavelength of light let's say oh
+maybe 933 nanometers in silicon that
+
+ align:start position:0%
+maybe 933 nanometers in silicon that
+ 
+
+ align:start position:0%
+maybe 933 nanometers in silicon that
+would give an absorption depth of around
+
+ align:start position:0%
+would give an absorption depth of around
+ 
+
+ align:start position:0%
+would give an absorption depth of around
+100 microns that's pretty far from the
+
+ align:start position:0%
+100 microns that's pretty far from the
+ 
+
+ align:start position:0%
+100 microns that's pretty far from the
+the junction now you you would have a
+
+ align:start position:0%
+the junction now you you would have a
+ 
+
+ align:start position:0%
+the junction now you you would have a
+much lower probability in the bad cell
+
+ align:start position:0%
+much lower probability in the bad cell
+ 
+
+ align:start position:0%
+much lower probability in the bad cell
+of collecting than the good cell and
+
+ align:start position:0%
+of collecting than the good cell and
+ 
+
+ align:start position:0%
+of collecting than the good cell and
+that's precisely because the diffusion
+
+ align:start position:0%
+that's precisely because the diffusion
+ 
+
+ align:start position:0%
+that's precisely because the diffusion
+length is lower
+
+ align:start position:0%
+length is lower
+ 
+
+ align:start position:0%
+length is lower
+so integrated over all of the
+
+ align:start position:0%
+so integrated over all of the
+ 
+
+ align:start position:0%
+so integrated over all of the
+wavelengths one obtains the
+
+ align:start position:0%
+wavelengths one obtains the
+ 
+
+ align:start position:0%
+wavelengths one obtains the
+short-circuit current and the method of
+
+ align:start position:0%
+short-circuit current and the method of
+ 
+
+ align:start position:0%
+short-circuit current and the method of
+measurement was the spectrophotometer
+
+ align:start position:0%
+measurement was the spectrophotometer
+ 
+
+ align:start position:0%
+measurement was the spectrophotometer
+now I understand most of you opted to
+
+ align:start position:0%
+now I understand most of you opted to
+ 
+
+ align:start position:0%
+now I understand most of you opted to
+choose Suns vo C for your one
+
+ align:start position:0%
+choose Suns vo C for your one
+ 
+
+ align:start position:0%
+choose Suns vo C for your one
+characterization tool to apply to
+
+ align:start position:0%
+characterization tool to apply to
+ 
+
+ align:start position:0%
+characterization tool to apply to
+yourself did anybody choose the
+
+ align:start position:0%
+yourself did anybody choose the
+ 
+
+ align:start position:0%
+yourself did anybody choose the
+spectrophotometer show of hands anybody
+
+ align:start position:0%
+spectrophotometer show of hands anybody
+ 
+
+ align:start position:0%
+spectrophotometer show of hands anybody
+it was broken yeah so the filter wheel
+
+ align:start position:0%
+it was broken yeah so the filter wheel
+ 
+
+ align:start position:0%
+it was broken yeah so the filter wheel
+was down okay that was that was it so
+
+ align:start position:0%
+was down okay that was that was it so
+ 
+
+ align:start position:0%
+was down okay that was that was it so
+let's see the filter wheel the filter
+
+ align:start position:0%
+let's see the filter wheel the filter
+ 
+
+ align:start position:0%
+let's see the filter wheel the filter
+wheel let's go fixing this here it is so
+
+ align:start position:0%
+wheel let's go fixing this here it is so
+ 
+
+ align:start position:0%
+wheel let's go fixing this here it is so
+the filter wheel was it was broken so
+
+ align:start position:0%
+the filter wheel was it was broken so
+ 
+
+ align:start position:0%
+the filter wheel was it was broken so
+essentially the the polychromatic light
+
+ align:start position:0%
+essentially the the polychromatic light
+ 
+
+ align:start position:0%
+essentially the the polychromatic light
+source was shining through a filter
+
+ align:start position:0%
+source was shining through a filter
+ 
+
+ align:start position:0%
+source was shining through a filter
+wheel which is selecting one wavelength
+
+ align:start position:0%
+wheel which is selecting one wavelength
+ 
+
+ align:start position:0%
+wheel which is selecting one wavelength
+of light the monochromator of course was
+
+ align:start position:0%
+of light the monochromator of course was
+ 
+
+ align:start position:0%
+of light the monochromator of course was
+helping as well and and eventually onto
+
+ align:start position:0%
+helping as well and and eventually onto
+ 
+
+ align:start position:0%
+helping as well and and eventually onto
+the solar cell sample which was shown in
+
+ align:start position:0%
+the solar cell sample which was shown in
+ 
+
+ align:start position:0%
+the solar cell sample which was shown in
+front of the light so that's the way in
+
+ align:start position:0%
+front of the light so that's the way in
+ 
+
+ align:start position:0%
+front of the light so that's the way in
+principle inspect response works and one
+
+ align:start position:0%
+principle inspect response works and one
+ 
+
+ align:start position:0%
+principle inspect response works and one
+variant of spectral response that's for
+
+ align:start position:0%
+variant of spectral response that's for
+ 
+
+ align:start position:0%
+variant of spectral response that's for
+the full device you typically have an
+
+ align:start position:0%
+the full device you typically have an
+ 
+
+ align:start position:0%
+the full device you typically have an
+illuminated area of a few millimeters
+
+ align:start position:0%
+illuminated area of a few millimeters
+ 
+
+ align:start position:0%
+illuminated area of a few millimeters
+squared or maybe even a few centimeters
+
+ align:start position:0%
+squared or maybe even a few centimeters
+ 
+
+ align:start position:0%
+squared or maybe even a few centimeters
+squared but let's say you that wasn't
+
+ align:start position:0%
+squared but let's say you that wasn't
+ 
+
+ align:start position:0%
+squared but let's say you that wasn't
+good enough for you you knew you had an
+
+ align:start position:0%
+good enough for you you knew you had an
+ 
+
+ align:start position:0%
+good enough for you you knew you had an
+in homogeneous material and you wanted
+
+ align:start position:0%
+in homogeneous material and you wanted
+ 
+
+ align:start position:0%
+in homogeneous material and you wanted
+to probe the in homogeneity across your
+
+ align:start position:0%
+to probe the in homogeneity across your
+ 
+
+ align:start position:0%
+to probe the in homogeneity across your
+device you got a large device maybe
+
+ align:start position:0%
+device you got a large device maybe
+ 
+
+ align:start position:0%
+device you got a large device maybe
+about that big a few a few tens of
+
+ align:start position:0%
+about that big a few a few tens of
+ 
+
+ align:start position:0%
+about that big a few a few tens of
+centimeters squared and you wanted to
+
+ align:start position:0%
+centimeters squared and you wanted to
+ 
+
+ align:start position:0%
+centimeters squared and you wanted to
+probe the distribution of minority
+
+ align:start position:0%
+probe the distribution of minority
+ 
+
+ align:start position:0%
+probe the distribution of minority
+carrier diffusion lengths across your
+
+ align:start position:0%
+carrier diffusion lengths across your
+ 
+
+ align:start position:0%
+carrier diffusion lengths across your
+device how would you do that well in one
+
+ align:start position:0%
+device how would you do that well in one
+ 
+
+ align:start position:0%
+device how would you do that well in one
+incarnation you would use a much more
+
+ align:start position:0%
+incarnation you would use a much more
+ 
+
+ align:start position:0%
+incarnation you would use a much more
+finely focused beam instead of having
+
+ align:start position:0%
+finely focused beam instead of having
+ 
+
+ align:start position:0%
+finely focused beam instead of having
+something in order of a millimeter you
+
+ align:start position:0%
+something in order of a millimeter you
+ 
+
+ align:start position:0%
+something in order of a millimeter you
+might shrink the beam spot size down to
+
+ align:start position:0%
+might shrink the beam spot size down to
+ 
+
+ align:start position:0%
+might shrink the beam spot size down to
+the range of single microns and then use
+
+ align:start position:0%
+the range of single microns and then use
+ 
+
+ align:start position:0%
+the range of single microns and then use
+an XY stepper motor to scan across your
+
+ align:start position:0%
+an XY stepper motor to scan across your
+ 
+
+ align:start position:0%
+an XY stepper motor to scan across your
+device and that's precisely what this
+
+ align:start position:0%
+device and that's precisely what this
+ 
+
+ align:start position:0%
+device and that's precisely what this
+does right here this white piece is the
+
+ align:start position:0%
+does right here this white piece is the
+ 
+
+ align:start position:0%
+does right here this white piece is the
+XY stage and this black head right here
+
+ align:start position:0%
+XY stage and this black head right here
+ 
+
+ align:start position:0%
+XY stage and this black head right here
+is essentially comprised of several
+
+ align:start position:0%
+is essentially comprised of several
+ 
+
+ align:start position:0%
+is essentially comprised of several
+lasers that will shine onto the sample
+
+ align:start position:0%
+lasers that will shine onto the sample
+ 
+
+ align:start position:0%
+lasers that will shine onto the sample
+now you need a few different wavelengths
+
+ align:start position:0%
+now you need a few different wavelengths
+ 
+
+ align:start position:0%
+now you need a few different wavelengths
+of light to really flesh out this curve
+
+ align:start position:0%
+of light to really flesh out this curve
+ 
+
+ align:start position:0%
+of light to really flesh out this curve
+to determine the minority carrier
+
+ align:start position:0%
+to determine the minority carrier
+ 
+
+ align:start position:0%
+to determine the minority carrier
+diffusion length from this curve and so
+
+ align:start position:0%
+diffusion length from this curve and so
+ 
+
+ align:start position:0%
+diffusion length from this curve and so
+the laser light is typically chosen at
+
+ align:start position:0%
+the laser light is typically chosen at
+ 
+
+ align:start position:0%
+the laser light is typically chosen at
+very auspicious wavelengths to maximize
+
+ align:start position:0%
+very auspicious wavelengths to maximize
+ 
+
+ align:start position:0%
+very auspicious wavelengths to maximize
+utility in this particular type of
+
+ align:start position:0%
+utility in this particular type of
+ 
+
+ align:start position:0%
+utility in this particular type of
+evaluation
+
+ align:start position:0%
+evaluation
+ 
+
+ align:start position:0%
+evaluation
+and so we have usually four you know
+
+ align:start position:0%
+and so we have usually four you know
+ 
+
+ align:start position:0%
+and so we have usually four you know
+minimum three you can always fit a line
+
+ align:start position:0%
+minimum three you can always fit a line
+ 
+
+ align:start position:0%
+minimum three you can always fit a line
+through two data points so minimum three
+
+ align:start position:0%
+through two data points so minimum three
+ 
+
+ align:start position:0%
+through two data points so minimum three
+laser wavelengths and usually about four
+
+ align:start position:0%
+laser wavelengths and usually about four
+ 
+
+ align:start position:0%
+laser wavelengths and usually about four
+or more to process the quantum
+
+ align:start position:0%
+or more to process the quantum
+ 
+
+ align:start position:0%
+or more to process the quantum
+efficiency as a function of position and
+
+ align:start position:0%
+efficiency as a function of position and
+ 
+
+ align:start position:0%
+efficiency as a function of position and
+so we the XY stage moves a sample around
+
+ align:start position:0%
+so we the XY stage moves a sample around
+ 
+
+ align:start position:0%
+so we the XY stage moves a sample around
+and the laser head is or moves the laser
+
+ align:start position:0%
+and the laser head is or moves the laser
+ 
+
+ align:start position:0%
+and the laser head is or moves the laser
+head around while the sample stays fixed
+
+ align:start position:0%
+head around while the sample stays fixed
+ 
+
+ align:start position:0%
+head around while the sample stays fixed
+and you map out the current response at
+
+ align:start position:0%
+and you map out the current response at
+ 
+
+ align:start position:0%
+and you map out the current response at
+each point on the device obtaining a map
+
+ align:start position:0%
+each point on the device obtaining a map
+ 
+
+ align:start position:0%
+each point on the device obtaining a map
+that looks much like this right here
+
+ align:start position:0%
+that looks much like this right here
+ 
+
+ align:start position:0%
+that looks much like this right here
+where this is on the y scale or the Z
+
+ align:start position:0%
+where this is on the y scale or the Z
+ 
+
+ align:start position:0%
+where this is on the y scale or the Z
+scale sorry you have from 0 to 120
+
+ align:start position:0%
+scale sorry you have from 0 to 120
+ 
+
+ align:start position:0%
+scale sorry you have from 0 to 120
+micron diffusion length on that
+
+ align:start position:0%
+micron diffusion length on that
+ 
+
+ align:start position:0%
+micron diffusion length on that
+particular solar cell device and points
+
+ align:start position:0%
+particular solar cell device and points
+ 
+
+ align:start position:0%
+particular solar cell device and points
+3-1 and to represent regions in which
+
+ align:start position:0%
+3-1 and to represent regions in which
+ 
+
+ align:start position:0%
+3-1 and to represent regions in which
+the minority carrier diffusion length
+
+ align:start position:0%
+the minority carrier diffusion length
+ 
+
+ align:start position:0%
+the minority carrier diffusion length
+was calculated using the method that we
+
+ align:start position:0%
+was calculated using the method that we
+ 
+
+ align:start position:0%
+was calculated using the method that we
+have discussed in the previous lectures
+
+ align:start position:0%
+have discussed in the previous lectures
+ 
+
+ align:start position:0%
+have discussed in the previous lectures
+the bazoer Paul bezoar method so we have
+
+ align:start position:0%
+the bazoer Paul bezoar method so we have
+ 
+
+ align:start position:0%
+the bazoer Paul bezoar method so we have
+a map of minority carrier diffusion
+
+ align:start position:0%
+a map of minority carrier diffusion
+ 
+
+ align:start position:0%
+a map of minority carrier diffusion
+length across our device some regions
+
+ align:start position:0%
+length across our device some regions
+ 
+
+ align:start position:0%
+length across our device some regions
+underperforming other regions performing
+
+ align:start position:0%
+underperforming other regions performing
+ 
+
+ align:start position:0%
+underperforming other regions performing
+rather well and we can see that in
+
+ align:start position:0%
+rather well and we can see that in
+ 
+
+ align:start position:0%
+rather well and we can see that in
+general these lower cost materials tend
+
+ align:start position:0%
+general these lower cost materials tend
+ 
+
+ align:start position:0%
+general these lower cost materials tend
+to be fairly in homogeneous in terms of
+
+ align:start position:0%
+to be fairly in homogeneous in terms of
+ 
+
+ align:start position:0%
+to be fairly in homogeneous in terms of
+their performance response right and if
+
+ align:start position:0%
+their performance response right and if
+ 
+
+ align:start position:0%
+their performance response right and if
+you really want to get fancy and say my
+
+ align:start position:0%
+you really want to get fancy and say my
+ 
+
+ align:start position:0%
+you really want to get fancy and say my
+goodness if I spend all this time
+
+ align:start position:0%
+goodness if I spend all this time
+ 
+
+ align:start position:0%
+goodness if I spend all this time
+mapping my device I'm not going to get
+
+ align:start position:0%
+mapping my device I'm not going to get
+ 
+
+ align:start position:0%
+mapping my device I'm not going to get
+through many devices during my PhD I'm
+
+ align:start position:0%
+through many devices during my PhD I'm
+ 
+
+ align:start position:0%
+through many devices during my PhD I'm
+going to have to make do with very poor
+
+ align:start position:0%
+going to have to make do with very poor
+ 
+
+ align:start position:0%
+going to have to make do with very poor
+statistics how do i speed this up some
+
+ align:start position:0%
+statistics how do i speed this up some
+ 
+
+ align:start position:0%
+statistics how do i speed this up some
+very clever people have figured out that
+
+ align:start position:0%
+very clever people have figured out that
+ 
+
+ align:start position:0%
+very clever people have figured out that
+if you fire your laser diode
+
+ align:start position:0%
+if you fire your laser diode
+ 
+
+ align:start position:0%
+if you fire your laser diode
+simultaneously but with different
+
+ align:start position:0%
+simultaneously but with different
+ 
+
+ align:start position:0%
+simultaneously but with different
+frequencies each of them with its own
+
+ align:start position:0%
+frequencies each of them with its own
+ 
+
+ align:start position:0%
+frequencies each of them with its own
+frequency you can D convolute the
+
+ align:start position:0%
+frequency you can D convolute the
+ 
+
+ align:start position:0%
+frequency you can D convolute the
+current response of your device using a
+
+ align:start position:0%
+current response of your device using a
+ 
+
+ align:start position:0%
+current response of your device using a
+Fourier transform to pick out the
+
+ align:start position:0%
+Fourier transform to pick out the
+ 
+
+ align:start position:0%
+Fourier transform to pick out the
+current response at each portion of the
+
+ align:start position:0%
+current response at each portion of the
+ 
+
+ align:start position:0%
+current response at each portion of the
+frequency space and in other words
+
+ align:start position:0%
+frequency space and in other words
+ 
+
+ align:start position:0%
+frequency space and in other words
+decouple the different wavelengths of
+
+ align:start position:0%
+decouple the different wavelengths of
+ 
+
+ align:start position:0%
+decouple the different wavelengths of
+light so it's a little clever method
+
+ align:start position:0%
+light so it's a little clever method
+ 
+
+ align:start position:0%
+light so it's a little clever method
+involving Fourier transforms and lock-in
+
+ align:start position:0%
+involving Fourier transforms and lock-in
+ 
+
+ align:start position:0%
+involving Fourier transforms and lock-in
+method to speed up the measurement a
+
+ align:start position:0%
+method to speed up the measurement a
+ 
+
+ align:start position:0%
+method to speed up the measurement a
+little bit small aside small footnote
+
+ align:start position:0%
+little bit small aside small footnote
+ 
+
+ align:start position:0%
+little bit small aside small footnote
+there okay important minority carrier
+
+ align:start position:0%
+there okay important minority carrier
+ 
+
+ align:start position:0%
+there okay important minority carrier
+diffusion length that's that's a most
+
+ align:start position:0%
+diffusion length that's that's a most
+ 
+
+ align:start position:0%
+diffusion length that's that's a most
+important so we can relate the diffusion
+
+ align:start position:0%
+important so we can relate the diffusion
+ 
+
+ align:start position:0%
+important so we can relate the diffusion
+length directly back to our IV curve via
+
+ align:start position:0%
+length directly back to our IV curve via
+ 
+
+ align:start position:0%
+length directly back to our IV curve via
+the saturation current by the J naught I
+
+ align:start position:0%
+the saturation current by the J naught I
+ 
+
+ align:start position:0%
+the saturation current by the J naught I
+naught depending on whether you're
+
+ align:start position:0%
+naught depending on whether you're
+ 
+
+ align:start position:0%
+naught depending on whether you're
+looking at density or
+
+ align:start position:0%
+looking at density or
+ 
+
+ align:start position:0%
+looking at density or
+Sulaiman let's shift gears a bit I want
+
+ align:start position:0%
+Sulaiman let's shift gears a bit I want
+ 
+
+ align:start position:0%
+Sulaiman let's shift gears a bit I want
+to talk about the vo C measurements and
+
+ align:start position:0%
+to talk about the vo C measurements and
+ 
+
+ align:start position:0%
+to talk about the vo C measurements and
+fill factor loss measurements so how do
+
+ align:start position:0%
+fill factor loss measurements so how do
+ 
+
+ align:start position:0%
+fill factor loss measurements so how do
+you determine losses in vo C and fill
+
+ align:start position:0%
+you determine losses in vo C and fill
+ 
+
+ align:start position:0%
+you determine losses in vo C and fill
+factor before I jump into this does
+
+ align:start position:0%
+factor before I jump into this does
+ 
+
+ align:start position:0%
+factor before I jump into this does
+anybody have any questions about DSC
+
+ align:start position:0%
+anybody have any questions about DSC
+ 
+
+ align:start position:0%
+anybody have any questions about DSC
+loss mechanisms so sad that the
+
+ align:start position:0%
+loss mechanisms so sad that the
+ 
+
+ align:start position:0%
+loss mechanisms so sad that the
+spectrophotometer wasn't up and running
+
+ align:start position:0%
+spectrophotometer wasn't up and running
+ 
+
+ align:start position:0%
+spectrophotometer wasn't up and running
+sniff that's a it should be fixed
+
+ align:start position:0%
+sniff that's a it should be fixed
+ 
+
+ align:start position:0%
+sniff that's a it should be fixed
+relatively soon right Joe it's fixed now
+
+ align:start position:0%
+relatively soon right Joe it's fixed now
+ 
+
+ align:start position:0%
+relatively soon right Joe it's fixed now
+all right so we have I think David Barry
+
+ align:start position:0%
+all right so we have I think David Barry
+ 
+
+ align:start position:0%
+all right so we have I think David Barry
+Needleman is back on board right hey
+
+ align:start position:0%
+Needleman is back on board right hey
+ 
+
+ align:start position:0%
+Needleman is back on board right hey
+over the route back as well yeah so if
+
+ align:start position:0%
+over the route back as well yeah so if
+ 
+
+ align:start position:0%
+over the route back as well yeah so if
+we have folks who still want to measure
+
+ align:start position:0%
+we have folks who still want to measure
+ 
+
+ align:start position:0%
+we have folks who still want to measure
+their devices using spectrophotometer
+
+ align:start position:0%
+their devices using spectrophotometer
+ 
+
+ align:start position:0%
+their devices using spectrophotometer
+measurement we can probably make
+
+ align:start position:0%
+measurement we can probably make
+ 
+
+ align:start position:0%
+measurement we can probably make
+arrangements for say what 10 10 cells to
+
+ align:start position:0%
+arrangements for say what 10 10 cells to
+ 
+
+ align:start position:0%
+arrangements for say what 10 10 cells to
+be measured something that means okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah let's let's let's fitmin the
+
+ align:start position:0%
+okay yeah let's let's let's fitmin the
+ 
+
+ align:start position:0%
+okay yeah let's let's let's fitmin the
+three people who wanted to do them and
+
+ align:start position:0%
+three people who wanted to do them and
+ 
+
+ align:start position:0%
+three people who wanted to do them and
+we'll have our full data set good so
+
+ align:start position:0%
+we'll have our full data set good so
+ 
+
+ align:start position:0%
+we'll have our full data set good so
+let's describe fill factor in vo C
+
+ align:start position:0%
+let's describe fill factor in vo C
+ 
+
+ align:start position:0%
+let's describe fill factor in vo C
+losses and this is essentially generate
+
+ align:start position:0%
+losses and this is essentially generate
+ 
+
+ align:start position:0%
+losses and this is essentially generate
+venturing into operating conditions
+
+ align:start position:0%
+venturing into operating conditions
+ 
+
+ align:start position:0%
+venturing into operating conditions
+under short circuit conditions how much
+
+ align:start position:0%
+under short circuit conditions how much
+ 
+
+ align:start position:0%
+under short circuit conditions how much
+power is running through the solar cell
+
+ align:start position:0%
+power is running through the solar cell
+ 
+
+ align:start position:0%
+power is running through the solar cell
+device power defined as current voltage
+
+ align:start position:0%
+device power defined as current voltage
+ 
+
+ align:start position:0%
+device power defined as current voltage
+product zero why is that no voltage
+
+ align:start position:0%
+product zero why is that no voltage
+ 
+
+ align:start position:0%
+product zero why is that no voltage
+right so you're not testing your solar
+
+ align:start position:0%
+right so you're not testing your solar
+ 
+
+ align:start position:0%
+right so you're not testing your solar
+cell under ideal operating conditions
+
+ align:start position:0%
+cell under ideal operating conditions
+ 
+
+ align:start position:0%
+cell under ideal operating conditions
+it's a sense an artificial operating
+
+ align:start position:0%
+it's a sense an artificial operating
+ 
+
+ align:start position:0%
+it's a sense an artificial operating
+condition simply to probe a bulk
+
+ align:start position:0%
+condition simply to probe a bulk
+ 
+
+ align:start position:0%
+condition simply to probe a bulk
+property characteristics right to
+
+ align:start position:0%
+property characteristics right to
+ 
+
+ align:start position:0%
+property characteristics right to
+minimize the effect of the junction now
+
+ align:start position:0%
+minimize the effect of the junction now
+ 
+
+ align:start position:0%
+minimize the effect of the junction now
+if you really want to see how is the
+
+ align:start position:0%
+if you really want to see how is the
+ 
+
+ align:start position:0%
+if you really want to see how is the
+junction behaving how is that charge
+
+ align:start position:0%
+junction behaving how is that charge
+ 
+
+ align:start position:0%
+junction behaving how is that charge
+separation going you might want to
+
+ align:start position:0%
+separation going you might want to
+ 
+
+ align:start position:0%
+separation going you might want to
+venture into forward bias conditions and
+
+ align:start position:0%
+venture into forward bias conditions and
+ 
+
+ align:start position:0%
+venture into forward bias conditions and
+eventually into open circuit voltage
+
+ align:start position:0%
+eventually into open circuit voltage
+ 
+
+ align:start position:0%
+eventually into open circuit voltage
+conditions to really test what the
+
+ align:start position:0%
+conditions to really test what the
+ 
+
+ align:start position:0%
+conditions to really test what the
+junction quality is instead of just
+
+ align:start position:0%
+junction quality is instead of just
+ 
+
+ align:start position:0%
+junction quality is instead of just
+probing bulk properties so let's talk
+
+ align:start position:0%
+probing bulk properties so let's talk
+ 
+
+ align:start position:0%
+probing bulk properties so let's talk
+about some of the measurement techniques
+
+ align:start position:0%
+about some of the measurement techniques
+ 
+
+ align:start position:0%
+about some of the measurement techniques
+to really get the heart of how a solar
+
+ align:start position:0%
+to really get the heart of how a solar
+ 
+
+ align:start position:0%
+to really get the heart of how a solar
+cell is performing it's helpful to do
+
+ align:start position:0%
+cell is performing it's helpful to do
+ 
+
+ align:start position:0%
+cell is performing it's helpful to do
+the JSC measurements helps you predict
+
+ align:start position:0%
+the JSC measurements helps you predict
+ 
+
+ align:start position:0%
+the JSC measurements helps you predict
+what might be some of the lost
+
+ align:start position:0%
+what might be some of the lost
+ 
+
+ align:start position:0%
+what might be some of the lost
+mechanisms later on but but this really
+
+ align:start position:0%
+mechanisms later on but but this really
+ 
+
+ align:start position:0%
+mechanisms later on but but this really
+gets at the meat of it IV curve
+
+ align:start position:0%
+gets at the meat of it IV curve
+ 
+
+ align:start position:0%
+gets at the meat of it IV curve
+measurements check we we study that we
+
+ align:start position:0%
+measurements check we we study that we
+ 
+
+ align:start position:0%
+measurements check we we study that we
+did that in the laboratory and I think
+
+ align:start position:0%
+did that in the laboratory and I think
+ 
+
+ align:start position:0%
+did that in the laboratory and I think
+we have a pretty good sense of what's
+
+ align:start position:0%
+we have a pretty good sense of what's
+ 
+
+ align:start position:0%
+we have a pretty good sense of what's
+going on there now series resistance
+
+ align:start position:0%
+going on there now series resistance
+ 
+
+ align:start position:0%
+going on there now series resistance
+losses we talked earlier in the class
+
+ align:start position:0%
+losses we talked earlier in the class
+ 
+
+ align:start position:0%
+losses we talked earlier in the class
+about contact and sheet resistance
+
+ align:start position:0%
+about contact and sheet resistance
+ 
+
+ align:start position:0%
+about contact and sheet resistance
+losses now we'll go back to it again
+
+ align:start position:0%
+losses now we'll go back to it again
+ 
+
+ align:start position:0%
+losses now we'll go back to it again
+just to revisit so we have the materials
+
+ align:start position:0%
+just to revisit so we have the materials
+ 
+
+ align:start position:0%
+just to revisit so we have the materials
+necessary to write up the report here on
+
+ align:start position:0%
+necessary to write up the report here on
+ 
+
+ align:start position:0%
+necessary to write up the report here on
+this project shunt resistance
+
+ align:start position:0%
+this project shunt resistance
+ 
+
+ align:start position:0%
+this project shunt resistance
+specifically in shunt resistance will
+
+ align:start position:0%
+specifically in shunt resistance will
+ 
+
+ align:start position:0%
+specifically in shunt resistance will
+talk about lock-in thermography and
+
+ align:start position:0%
+talk about lock-in thermography and
+ 
+
+ align:start position:0%
+talk about lock-in thermography and
+electroluminescence and finally we'll
+
+ align:start position:0%
+electroluminescence and finally we'll
+ 
+
+ align:start position:0%
+electroluminescence and finally we'll
+have a small slide on Sun's vo C and
+
+ align:start position:0%
+have a small slide on Sun's vo C and
+ 
+
+ align:start position:0%
+have a small slide on Sun's vo C and
+talk about that as well since I know the
+
+ align:start position:0%
+talk about that as well since I know the
+ 
+
+ align:start position:0%
+talk about that as well since I know the
+majority of you selected that as your
+
+ align:start position:0%
+majority of you selected that as your
+ 
+
+ align:start position:0%
+majority of you selected that as your
+measurement tool all right
+
+ align:start position:0%
+measurement tool all right
+ 
+
+ align:start position:0%
+measurement tool all right
+so open circuit voltage so reading
+
+ align:start position:0%
+so open circuit voltage so reading
+ 
+
+ align:start position:0%
+so open circuit voltage so reading
+straight off of the slide here if the
+
+ align:start position:0%
+straight off of the slide here if the
+ 
+
+ align:start position:0%
+straight off of the slide here if the
+collected light generated carriers are
+
+ align:start position:0%
+collected light generated carriers are
+ 
+
+ align:start position:0%
+collected light generated carriers are
+not extracted in the solar cell but
+
+ align:start position:0%
+not extracted in the solar cell but
+ 
+
+ align:start position:0%
+not extracted in the solar cell but
+instead remain that then a charge
+
+ align:start position:0%
+instead remain that then a charge
+ 
+
+ align:start position:0%
+instead remain that then a charge
+separation exists across meaning there's
+
+ align:start position:0%
+separation exists across meaning there's
+ 
+
+ align:start position:0%
+separation exists across meaning there's
+a buildup of charge
+
+ align:start position:0%
+a buildup of charge
+ 
+
+ align:start position:0%
+a buildup of charge
+and the charge separation reduces the
+
+ align:start position:0%
+and the charge separation reduces the
+ 
+
+ align:start position:0%
+and the charge separation reduces the
+electric field in the depletion region
+
+ align:start position:0%
+electric field in the depletion region
+ 
+
+ align:start position:0%
+electric field in the depletion region
+which reduces the barrier to diffusion
+
+ align:start position:0%
+which reduces the barrier to diffusion
+ 
+
+ align:start position:0%
+which reduces the barrier to diffusion
+current and causes the diffusion current
+
+ align:start position:0%
+current and causes the diffusion current
+ 
+
+ align:start position:0%
+current and causes the diffusion current
+to flow in other words if you have light
+
+ align:start position:0%
+to flow in other words if you have light
+ 
+
+ align:start position:0%
+to flow in other words if you have light
+coming into your device but you're not
+
+ align:start position:0%
+coming into your device but you're not
+ 
+
+ align:start position:0%
+coming into your device but you're not
+able to extract the charges from either
+
+ align:start position:0%
+able to extract the charges from either
+ 
+
+ align:start position:0%
+able to extract the charges from either
+side to make sure that the chemical
+
+ align:start position:0%
+side to make sure that the chemical
+ 
+
+ align:start position:0%
+side to make sure that the chemical
+potential is equal on both sides the
+
+ align:start position:0%
+potential is equal on both sides the
+ 
+
+ align:start position:0%
+potential is equal on both sides the
+chemical potential will change on either
+
+ align:start position:0%
+chemical potential will change on either
+ 
+
+ align:start position:0%
+chemical potential will change on either
+side you'll have a buildup of one charge
+
+ align:start position:0%
+side you'll have a buildup of one charge
+ 
+
+ align:start position:0%
+side you'll have a buildup of one charge
+type on one side of the junction and
+
+ align:start position:0%
+type on one side of the junction and
+ 
+
+ align:start position:0%
+type on one side of the junction and
+buildup of the opposite charge type on
+
+ align:start position:0%
+buildup of the opposite charge type on
+ 
+
+ align:start position:0%
+buildup of the opposite charge type on
+the other side of the junction so that
+
+ align:start position:0%
+the other side of the junction so that
+ 
+
+ align:start position:0%
+the other side of the junction so that
+will shift the the quasi shift the the
+
+ align:start position:0%
+will shift the the quasi shift the the
+ 
+
+ align:start position:0%
+will shift the the quasi shift the the
+Fermi energy on either side of the
+
+ align:start position:0%
+Fermi energy on either side of the
+ 
+
+ align:start position:0%
+Fermi energy on either side of the
+junction result in a bias of your device
+
+ align:start position:0%
+junction result in a bias of your device
+ 
+
+ align:start position:0%
+junction result in a bias of your device
+and eventually counteract the built-in
+
+ align:start position:0%
+and eventually counteract the built-in
+ 
+
+ align:start position:0%
+and eventually counteract the built-in
+electric field to the point where the
+
+ align:start position:0%
+electric field to the point where the
+ 
+
+ align:start position:0%
+electric field to the point where the
+diffusion current is now enabled to flow
+
+ align:start position:0%
+diffusion current is now enabled to flow
+ 
+
+ align:start position:0%
+diffusion current is now enabled to flow
+all the sound familiar to folks might be
+
+ align:start position:0%
+all the sound familiar to folks might be
+ 
+
+ align:start position:0%
+all the sound familiar to folks might be
+a little rusty but it's all there
+
+ align:start position:0%
+a little rusty but it's all there
+ 
+
+ align:start position:0%
+a little rusty but it's all there
+so the idea now is to begin probing that
+
+ align:start position:0%
+so the idea now is to begin probing that
+ 
+
+ align:start position:0%
+so the idea now is to begin probing that
+that Junction condition we talked about
+
+ align:start position:0%
+that Junction condition we talked about
+ 
+
+ align:start position:0%
+that Junction condition we talked about
+the ideal diode equation and now we're
+
+ align:start position:0%
+the ideal diode equation and now we're
+ 
+
+ align:start position:0%
+the ideal diode equation and now we're
+going to piece through it once again
+
+ align:start position:0%
+going to piece through it once again
+ 
+
+ align:start position:0%
+going to piece through it once again
+this is your current density here and I
+
+ align:start position:0%
+this is your current density here and I
+ 
+
+ align:start position:0%
+this is your current density here and I
+believe if you really want to be precise
+
+ align:start position:0%
+believe if you really want to be precise
+ 
+
+ align:start position:0%
+believe if you really want to be precise
+about this you should use straight
+
+ align:start position:0%
+about this you should use straight
+ 
+
+ align:start position:0%
+about this you should use straight
+current and not current density reason
+
+ align:start position:0%
+current and not current density reason
+ 
+
+ align:start position:0%
+current and not current density reason
+being if you look at current resistance
+
+ align:start position:0%
+being if you look at current resistance
+ 
+
+ align:start position:0%
+being if you look at current resistance
+product that gives you voltage but
+
+ align:start position:0%
+product that gives you voltage but
+ 
+
+ align:start position:0%
+product that gives you voltage but
+current density resistance product gives
+
+ align:start position:0%
+current density resistance product gives
+ 
+
+ align:start position:0%
+current density resistance product gives
+you essentially a voltage density which
+
+ align:start position:0%
+you essentially a voltage density which
+ 
+
+ align:start position:0%
+you essentially a voltage density which
+is not a unit that we typically use so
+
+ align:start position:0%
+is not a unit that we typically use so
+ 
+
+ align:start position:0%
+is not a unit that we typically use so
+just keep that in mind as small little
+
+ align:start position:0%
+just keep that in mind as small little
+ 
+
+ align:start position:0%
+just keep that in mind as small little
+asterisks this equation is often used in
+
+ align:start position:0%
+asterisks this equation is often used in
+ 
+
+ align:start position:0%
+asterisks this equation is often used in
+PV that little unit conversion issues
+
+ align:start position:0%
+PV that little unit conversion issues
+ 
+
+ align:start position:0%
+PV that little unit conversion issues
+generally ignored but but you might want
+
+ align:start position:0%
+generally ignored but but you might want
+ 
+
+ align:start position:0%
+generally ignored but but you might want
+to flag it for your own benefit so we
+
+ align:start position:0%
+to flag it for your own benefit so we
+ 
+
+ align:start position:0%
+to flag it for your own benefit so we
+have the current output of our device as
+
+ align:start position:0%
+have the current output of our device as
+ 
+
+ align:start position:0%
+have the current output of our device as
+a function of voltage and this is a
+
+ align:start position:0%
+a function of voltage and this is a
+ 
+
+ align:start position:0%
+a function of voltage and this is a
+rather complicated expression going well
+
+ align:start position:0%
+rather complicated expression going well
+ 
+
+ align:start position:0%
+rather complicated expression going well
+beyond the ideal diode equation the
+
+ align:start position:0%
+beyond the ideal diode equation the
+ 
+
+ align:start position:0%
+beyond the ideal diode equation the
+ideal diode equation which would consist
+
+ align:start position:0%
+ideal diode equation which would consist
+ 
+
+ align:start position:0%
+ideal diode equation which would consist
+of the J sub L the illumination current
+
+ align:start position:0%
+of the J sub L the illumination current
+ 
+
+ align:start position:0%
+of the J sub L the illumination current
+this is the light coming in creating the
+
+ align:start position:0%
+this is the light coming in creating the
+ 
+
+ align:start position:0%
+this is the light coming in creating the
+carriers that are then swept across the
+
+ align:start position:0%
+carriers that are then swept across the
+ 
+
+ align:start position:0%
+carriers that are then swept across the
+junction the J sub L is going to be the
+
+ align:start position:0%
+junction the J sub L is going to be the
+ 
+
+ align:start position:0%
+junction the J sub L is going to be the
+integral current under a spectral
+
+ align:start position:0%
+integral current under a spectral
+ 
+
+ align:start position:0%
+integral current under a spectral
+response curve right at each wavelength
+
+ align:start position:0%
+response curve right at each wavelength
+ 
+
+ align:start position:0%
+response curve right at each wavelength
+waited for the wavelength of the
+
+ align:start position:0%
+waited for the wavelength of the
+ 
+
+ align:start position:0%
+waited for the wavelength of the
+incoming light are the intensity at that
+
+ align:start position:0%
+incoming light are the intensity at that
+ 
+
+ align:start position:0%
+incoming light are the intensity at that
+particular bandwidth of the incoming
+
+ align:start position:0%
+particular bandwidth of the incoming
+ 
+
+ align:start position:0%
+particular bandwidth of the incoming
+light think of it this way
+
+ align:start position:0%
+light think of it this way
+ 
+
+ align:start position:0%
+light think of it this way
+you're measuring the spectral response
+
+ align:start position:0%
+you're measuring the spectral response
+ 
+
+ align:start position:0%
+you're measuring the spectral response
+at each particular wavelength what the
+
+ align:start position:0%
+at each particular wavelength what the
+ 
+
+ align:start position:0%
+at each particular wavelength what the
+collection probability is then if you
+
+ align:start position:0%
+collection probability is then if you
+ 
+
+ align:start position:0%
+collection probability is then if you
+multiplied by the total number photons
+
+ align:start position:0%
+multiplied by the total number photons
+ 
+
+ align:start position:0%
+multiplied by the total number photons
+in that wavelength range you're
+
+ align:start position:0%
+in that wavelength range you're
+ 
+
+ align:start position:0%
+in that wavelength range you're
+determining the total number of carriers
+
+ align:start position:0%
+determining the total number of carriers
+ 
+
+ align:start position:0%
+determining the total number of carriers
+generated within that frequency range of
+
+ align:start position:0%
+generated within that frequency range of
+ 
+
+ align:start position:0%
+generated within that frequency range of
+light and if you add up all of the
+
+ align:start position:0%
+light and if you add up all of the
+ 
+
+ align:start position:0%
+light and if you add up all of the
+little bins you get all of the carriers
+
+ align:start position:0%
+little bins you get all of the carriers
+ 
+
+ align:start position:0%
+little bins you get all of the carriers
+generated by all of the light right and
+
+ align:start position:0%
+generated by all of the light right and
+ 
+
+ align:start position:0%
+generated by all of the light right and
+you can adjust depending what spectral
+
+ align:start position:0%
+you can adjust depending what spectral
+ 
+
+ align:start position:0%
+you can adjust depending what spectral
+conditions you have say a 1.5 spectrum
+
+ align:start position:0%
+conditions you have say a 1.5 spectrum
+ 
+
+ align:start position:0%
+conditions you have say a 1.5 spectrum
+so the J sub L here this one is our
+
+ align:start position:0%
+so the J sub L here this one is our
+ 
+
+ align:start position:0%
+so the J sub L here this one is our
+short circuit current effectively and
+
+ align:start position:0%
+short circuit current effectively and
+ 
+
+ align:start position:0%
+short circuit current effectively and
+what is derived from a spectral response
+
+ align:start position:0%
+what is derived from a spectral response
+ 
+
+ align:start position:0%
+what is derived from a spectral response
+measurement the rest of these terms here
+
+ align:start position:0%
+measurement the rest of these terms here
+ 
+
+ align:start position:0%
+measurement the rest of these terms here
+are are of interest so that J let's
+
+ align:start position:0%
+are are of interest so that J let's
+ 
+
+ align:start position:0%
+are are of interest so that J let's
+break it on two pieces here this term
+
+ align:start position:0%
+break it on two pieces here this term
+ 
+
+ align:start position:0%
+break it on two pieces here this term
+over here is essentially to take into
+
+ align:start position:0%
+over here is essentially to take into
+ 
+
+ align:start position:0%
+over here is essentially to take into
+account shunt resistance losses if we
+
+ align:start position:0%
+account shunt resistance losses if we
+ 
+
+ align:start position:0%
+account shunt resistance losses if we
+have shunts in our device we're going to
+
+ align:start position:0%
+have shunts in our device we're going to
+ 
+
+ align:start position:0%
+have shunts in our device we're going to
+be reducing the total power output these
+
+ align:start position:0%
+be reducing the total power output these
+ 
+
+ align:start position:0%
+be reducing the total power output these
+two components what are usually called
+
+ align:start position:0%
+two components what are usually called
+ 
+
+ align:start position:0%
+two components what are usually called
+diffusion current and recombination
+
+ align:start position:0%
+diffusion current and recombination
+ 
+
+ align:start position:0%
+diffusion current and recombination
+current this one you have to take me for
+
+ align:start position:0%
+current this one you have to take me for
+ 
+
+ align:start position:0%
+current this one you have to take me for
+my word at it right now this is the
+
+ align:start position:0%
+my word at it right now this is the
+ 
+
+ align:start position:0%
+my word at it right now this is the
+recombination within the space charge
+
+ align:start position:0%
+recombination within the space charge
+ 
+
+ align:start position:0%
+recombination within the space charge
+region and this over here is a
+
+ align:start position:0%
+region and this over here is a
+ 
+
+ align:start position:0%
+region and this over here is a
+recombination within the bulk of the
+
+ align:start position:0%
+recombination within the bulk of the
+ 
+
+ align:start position:0%
+recombination within the bulk of the
+solar cell here's a good way to think
+
+ align:start position:0%
+solar cell here's a good way to think
+ 
+
+ align:start position:0%
+solar cell here's a good way to think
+about it if our solar cell is not
+
+ align:start position:0%
+about it if our solar cell is not
+ 
+
+ align:start position:0%
+about it if our solar cell is not
+forward biased if it's very very
+
+ align:start position:0%
+forward biased if it's very very
+ 
+
+ align:start position:0%
+forward biased if it's very very
+slightly forward by it's just a little
+
+ align:start position:0%
+slightly forward by it's just a little
+ 
+
+ align:start position:0%
+slightly forward by it's just a little
+bit there's going to be a large barrier
+
+ align:start position:0%
+bit there's going to be a large barrier
+ 
+
+ align:start position:0%
+bit there's going to be a large barrier
+for care effort for majority carriers on
+
+ align:start position:0%
+for care effort for majority carriers on
+ 
+
+ align:start position:0%
+for care effort for majority carriers on
+one side of the junction to overcome to
+
+ align:start position:0%
+one side of the junction to overcome to
+ 
+
+ align:start position:0%
+one side of the junction to overcome to
+drive a drift current right side
+
+ align:start position:0%
+drive a drift current right side
+ 
+
+ align:start position:0%
+drive a drift current right side
+diffusion current very large barrier to
+
+ align:start position:0%
+diffusion current very large barrier to
+ 
+
+ align:start position:0%
+diffusion current very large barrier to
+overcome and hence the recombination is
+
+ align:start position:0%
+overcome and hence the recombination is
+ 
+
+ align:start position:0%
+overcome and hence the recombination is
+most likely to occur within the space
+
+ align:start position:0%
+most likely to occur within the space
+ 
+
+ align:start position:0%
+most likely to occur within the space
+charge region the carriers aren't likely
+
+ align:start position:0%
+charge region the carriers aren't likely
+ 
+
+ align:start position:0%
+charge region the carriers aren't likely
+to overcome that barrier get into the
+
+ align:start position:0%
+to overcome that barrier get into the
+ 
+
+ align:start position:0%
+to overcome that barrier get into the
+bulk and recombine there whereas if
+
+ align:start position:0%
+bulk and recombine there whereas if
+ 
+
+ align:start position:0%
+bulk and recombine there whereas if
+we're under large forward bias
+
+ align:start position:0%
+we're under large forward bias
+ 
+
+ align:start position:0%
+we're under large forward bias
+conditions now the carrier's can very
+
+ align:start position:0%
+conditions now the carrier's can very
+ 
+
+ align:start position:0%
+conditions now the carrier's can very
+easily go over that barrier and
+
+ align:start position:0%
+easily go over that barrier and
+ 
+
+ align:start position:0%
+easily go over that barrier and
+recombine in the bulk so this term right
+
+ align:start position:0%
+recombine in the bulk so this term right
+ 
+
+ align:start position:0%
+recombine in the bulk so this term right
+here dominates under low forward bias
+
+ align:start position:0%
+here dominates under low forward bias
+ 
+
+ align:start position:0%
+here dominates under low forward bias
+conditions and this term over here
+
+ align:start position:0%
+conditions and this term over here
+ 
+
+ align:start position:0%
+conditions and this term over here
+dominates under larger forward bias
+
+ align:start position:0%
+dominates under larger forward bias
+ 
+
+ align:start position:0%
+dominates under larger forward bias
+conditions and that's why you see when
+
+ align:start position:0%
+conditions and that's why you see when
+ 
+
+ align:start position:0%
+conditions and that's why you see when
+you plot your IV curve on log linear
+
+ align:start position:0%
+you plot your IV curve on log linear
+ 
+
+ align:start position:0%
+you plot your IV curve on log linear
+scale you see essentially two flat
+
+ align:start position:0%
+scale you see essentially two flat
+ 
+
+ align:start position:0%
+scale you see essentially two flat
+points on your IV curve let me for that
+
+ align:start position:0%
+points on your IV curve let me for that
+ 
+
+ align:start position:0%
+points on your IV curve let me for that
+to the next slide right here here we go
+
+ align:start position:0%
+to the next slide right here here we go
+ 
+
+ align:start position:0%
+to the next slide right here here we go
+so this is log of current versus linear
+
+ align:start position:0%
+so this is log of current versus linear
+ 
+
+ align:start position:0%
+so this is log of current versus linear
+voltage and you see one flat portion
+
+ align:start position:0%
+voltage and you see one flat portion
+ 
+
+ align:start position:0%
+voltage and you see one flat portion
+right here and another flat portion
+
+ align:start position:0%
+right here and another flat portion
+ 
+
+ align:start position:0%
+right here and another flat portion
+right here before the series resistance
+
+ align:start position:0%
+right here before the series resistance
+ 
+
+ align:start position:0%
+right here before the series resistance
+begins to dominate at two high voltage
+
+ align:start position:0%
+begins to dominate at two high voltage
+ 
+
+ align:start position:0%
+begins to dominate at two high voltage
+and your shunt resistance dominates at
+
+ align:start position:0%
+and your shunt resistance dominates at
+ 
+
+ align:start position:0%
+and your shunt resistance dominates at
+two low-voltage this flat portion right
+
+ align:start position:0%
+two low-voltage this flat portion right
+ 
+
+ align:start position:0%
+two low-voltage this flat portion right
+there is being driven by three common
+
+ align:start position:0%
+there is being driven by three common
+ 
+
+ align:start position:0%
+there is being driven by three common
+within the space charge region why well
+
+ align:start position:0%
+within the space charge region why well
+ 
+
+ align:start position:0%
+within the space charge region why well
+the forward bias voltage isn't enough to
+
+ align:start position:0%
+the forward bias voltage isn't enough to
+ 
+
+ align:start position:0%
+the forward bias voltage isn't enough to
+really lower that barrier enough to
+
+ align:start position:0%
+really lower that barrier enough to
+ 
+
+ align:start position:0%
+really lower that barrier enough to
+allow the carrier's deep within the bulk
+
+ align:start position:0%
+allow the carrier's deep within the bulk
+ 
+
+ align:start position:0%
+allow the carrier's deep within the bulk
+to recombine so the carriers are
+
+ align:start position:0%
+to recombine so the carriers are
+ 
+
+ align:start position:0%
+to recombine so the carriers are
+recombining in the space charge region
+
+ align:start position:0%
+recombining in the space charge region
+ 
+
+ align:start position:0%
+recombining in the space charge region
+whereas here they're recombining within
+
+ align:start position:0%
+whereas here they're recombining within
+ 
+
+ align:start position:0%
+whereas here they're recombining within
+the bulk all right
+
+ align:start position:0%
+the bulk all right
+ 
+
+ align:start position:0%
+the bulk all right
+so this is a more complicated expression
+
+ align:start position:0%
+so this is a more complicated expression
+ 
+
+ align:start position:0%
+so this is a more complicated expression
+for the IV characteristics of a solar
+
+ align:start position:0%
+for the IV characteristics of a solar
+ 
+
+ align:start position:0%
+for the IV characteristics of a solar
+cell device not always are these precise
+
+ align:start position:0%
+cell device not always are these precise
+ 
+
+ align:start position:0%
+cell device not always are these precise
+mechanisms at work if you have a new
+
+ align:start position:0%
+mechanisms at work if you have a new
+ 
+
+ align:start position:0%
+mechanisms at work if you have a new
+material system that you're working with
+
+ align:start position:0%
+material system that you're working with
+ 
+
+ align:start position:0%
+material system that you're working with
+there might be different recombination
+
+ align:start position:0%
+there might be different recombination
+ 
+
+ align:start position:0%
+there might be different recombination
+mechanisms at work there might be charge
+
+ align:start position:0%
+mechanisms at work there might be charge
+ 
+
+ align:start position:0%
+mechanisms at work there might be charge
+accumulation effects at work but they
+
+ align:start position:0%
+accumulation effects at work but they
+ 
+
+ align:start position:0%
+accumulation effects at work but they
+can all be encapsulated in some form of
+
+ align:start position:0%
+can all be encapsulated in some form of
+ 
+
+ align:start position:0%
+can all be encapsulated in some form of
+current voltage expression think of the
+
+ align:start position:0%
+current voltage expression think of the
+ 
+
+ align:start position:0%
+current voltage expression think of the
+IV characteristics of the solar cell
+
+ align:start position:0%
+IV characteristics of the solar cell
+ 
+
+ align:start position:0%
+IV characteristics of the solar cell
+similar to say the constitutive
+
+ align:start position:0%
+similar to say the constitutive
+ 
+
+ align:start position:0%
+similar to say the constitutive
+relations of a complex of viscoelastic
+
+ align:start position:0%
+relations of a complex of viscoelastic
+ 
+
+ align:start position:0%
+relations of a complex of viscoelastic
+material where you have say a nice
+
+ align:start position:0%
+material where you have say a nice
+ 
+
+ align:start position:0%
+material where you have say a nice
+linear elastic component a dashpot
+
+ align:start position:0%
+linear elastic component a dashpot
+ 
+
+ align:start position:0%
+linear elastic component a dashpot
+component right so you have a very
+
+ align:start position:0%
+component right so you have a very
+ 
+
+ align:start position:0%
+component right so you have a very
+complex expression describing the
+
+ align:start position:0%
+complex expression describing the
+ 
+
+ align:start position:0%
+complex expression describing the
+stress-strain relationship in material a
+
+ align:start position:0%
+stress-strain relationship in material a
+ 
+
+ align:start position:0%
+stress-strain relationship in material a
+similar thing goes on here with the
+
+ align:start position:0%
+similar thing goes on here with the
+ 
+
+ align:start position:0%
+similar thing goes on here with the
+solar cell where you're describing the
+
+ align:start position:0%
+solar cell where you're describing the
+ 
+
+ align:start position:0%
+solar cell where you're describing the
+current voltage relationship if you
+
+ align:start position:0%
+current voltage relationship if you
+ 
+
+ align:start position:0%
+current voltage relationship if you
+understand all of the mechanisms driving
+
+ align:start position:0%
+understand all of the mechanisms driving
+ 
+
+ align:start position:0%
+understand all of the mechanisms driving
+carry recombination in your material and
+
+ align:start position:0%
+carry recombination in your material and
+ 
+
+ align:start position:0%
+carry recombination in your material and
+charge separation you can come up with
+
+ align:start position:0%
+charge separation you can come up with
+ 
+
+ align:start position:0%
+charge separation you can come up with
+an expression that describes very
+
+ align:start position:0%
+an expression that describes very
+ 
+
+ align:start position:0%
+an expression that describes very
+precisely the IV characteristics but if
+
+ align:start position:0%
+precisely the IV characteristics but if
+ 
+
+ align:start position:0%
+precisely the IV characteristics but if
+you change material systems you may not
+
+ align:start position:0%
+you change material systems you may not
+ 
+
+ align:start position:0%
+you change material systems you may not
+necessarily be able to transition the
+
+ align:start position:0%
+necessarily be able to transition the
+ 
+
+ align:start position:0%
+necessarily be able to transition the
+same models over it's helpful to start
+
+ align:start position:0%
+same models over it's helpful to start
+ 
+
+ align:start position:0%
+same models over it's helpful to start
+with them but sooner or later you might
+
+ align:start position:0%
+with them but sooner or later you might
+ 
+
+ align:start position:0%
+with them but sooner or later you might
+decide well gee I have to I have to make
+
+ align:start position:0%
+decide well gee I have to I have to make
+ 
+
+ align:start position:0%
+decide well gee I have to I have to make
+some modifications all right
+
+ align:start position:0%
+some modifications all right
+ 
+
+ align:start position:0%
+some modifications all right
+okay series resistance we already
+
+ align:start position:0%
+okay series resistance we already
+ 
+
+ align:start position:0%
+okay series resistance we already
+studied this before but just a quick
+
+ align:start position:0%
+studied this before but just a quick
+ 
+
+ align:start position:0%
+studied this before but just a quick
+refresher we have the series resistance
+
+ align:start position:0%
+refresher we have the series resistance
+ 
+
+ align:start position:0%
+refresher we have the series resistance
+of the bulk we have the series
+
+ align:start position:0%
+of the bulk we have the series
+ 
+
+ align:start position:0%
+of the bulk we have the series
+resistance of the emitter and then we
+
+ align:start position:0%
+resistance of the emitter and then we
+ 
+
+ align:start position:0%
+resistance of the emitter and then we
+have the series resistance of our of the
+
+ align:start position:0%
+have the series resistance of our of the
+ 
+
+ align:start position:0%
+have the series resistance of our of the
+contacts as we contact the device and in
+
+ align:start position:0%
+contacts as we contact the device and in
+ 
+
+ align:start position:0%
+contacts as we contact the device and in
+the series resistance within the contact
+
+ align:start position:0%
+the series resistance within the contact
+ 
+
+ align:start position:0%
+the series resistance within the contact
+itself so at least four different
+
+ align:start position:0%
+itself so at least four different
+ 
+
+ align:start position:0%
+itself so at least four different
+components of series resistance in our
+
+ align:start position:0%
+components of series resistance in our
+ 
+
+ align:start position:0%
+components of series resistance in our
+device that are all lumped together when
+
+ align:start position:0%
+device that are all lumped together when
+ 
+
+ align:start position:0%
+device that are all lumped together when
+we take these when we express our IV
+
+ align:start position:0%
+we take these when we express our IV
+ 
+
+ align:start position:0%
+we take these when we express our IV
+curve in this manner we all lump them
+
+ align:start position:0%
+curve in this manner we all lump them
+ 
+
+ align:start position:0%
+curve in this manner we all lump them
+together and that R sub s yeah question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+ah yeah so um simple explanation if you
+
+ align:start position:0%
+ah yeah so um simple explanation if you
+ 
+
+ align:start position:0%
+ah yeah so um simple explanation if you
+would like is mostly where the Fermi
+
+ align:start position:0%
+would like is mostly where the Fermi
+ 
+
+ align:start position:0%
+would like is mostly where the Fermi
+energy is sitting relative to the
+
+ align:start position:0%
+energy is sitting relative to the
+ 
+
+ align:start position:0%
+energy is sitting relative to the
+conduction or valence band in the space
+
+ align:start position:0%
+conduction or valence band in the space
+ 
+
+ align:start position:0%
+conduction or valence band in the space
+charge region the quasi neutral region
+
+ align:start position:0%
+charge region the quasi neutral region
+ 
+
+ align:start position:0%
+charge region the quasi neutral region
+is closer to mid gap as opposed to
+
+ align:start position:0%
+is closer to mid gap as opposed to
+ 
+
+ align:start position:0%
+is closer to mid gap as opposed to
+closer to bandage hand-wavy
+
+ align:start position:0%
+closer to bandage hand-wavy
+ 
+
+ align:start position:0%
+closer to bandage hand-wavy
+if you really want to get into it I
+
+ align:start position:0%
+if you really want to get into it I
+ 
+
+ align:start position:0%
+if you really want to get into it I
+spent about three months studying this
+
+ align:start position:0%
+spent about three months studying this
+ 
+
+ align:start position:0%
+spent about three months studying this
+as a graduate student the the one in the
+
+ align:start position:0%
+as a graduate student the the one in the
+ 
+
+ align:start position:0%
+as a graduate student the the one in the
+to the ideology factor which is to show
+
+ align:start position:0%
+to the ideology factor which is to show
+ 
+
+ align:start position:0%
+to the ideology factor which is to show
+more precisely it's the number that
+
+ align:start position:0%
+more precisely it's the number that
+ 
+
+ align:start position:0%
+more precisely it's the number that
+comes before the KT right for each of
+
+ align:start position:0%
+comes before the KT right for each of
+ 
+
+ align:start position:0%
+comes before the KT right for each of
+these that's called the ideology factor
+
+ align:start position:0%
+these that's called the ideology factor
+ 
+
+ align:start position:0%
+these that's called the ideology factor
+it's typically expressed as n sub 1 or n
+
+ align:start position:0%
+it's typically expressed as n sub 1 or n
+ 
+
+ align:start position:0%
+it's typically expressed as n sub 1 or n
+sub 2 in this case I just substituted it
+
+ align:start position:0%
+sub 2 in this case I just substituted it
+ 
+
+ align:start position:0%
+sub 2 in this case I just substituted it
+straight out for a 1 and a 2 those
+
+ align:start position:0%
+straight out for a 1 and a 2 those
+ 
+
+ align:start position:0%
+straight out for a 1 and a 2 those
+numbers aren't always 1 and 2 as a
+
+ align:start position:0%
+numbers aren't always 1 and 2 as a
+ 
+
+ align:start position:0%
+numbers aren't always 1 and 2 as a
+matter of fact especially the G naught 1
+
+ align:start position:0%
+matter of fact especially the G naught 1
+ 
+
+ align:start position:0%
+matter of fact especially the G naught 1
+the bulk recombination current depending
+
+ align:start position:0%
+the bulk recombination current depending
+ 
+
+ align:start position:0%
+the bulk recombination current depending
+on where the defect levels lie it can be
+
+ align:start position:0%
+on where the defect levels lie it can be
+ 
+
+ align:start position:0%
+on where the defect levels lie it can be
+somewhere between say a 1.1 and a 1.4
+
+ align:start position:0%
+somewhere between say a 1.1 and a 1.4
+ 
+
+ align:start position:0%
+somewhere between say a 1.1 and a 1.4
+typically and beautiful thesis work done
+
+ align:start position:0%
+typically and beautiful thesis work done
+ 
+
+ align:start position:0%
+typically and beautiful thesis work done
+by fellow in in Australia hold on Keith
+
+ align:start position:0%
+by fellow in in Australia hold on Keith
+ 
+
+ align:start position:0%
+by fellow in in Australia hold on Keith
+McIntosh and the title of the thesis is
+
+ align:start position:0%
+McIntosh and the title of the thesis is
+ 
+
+ align:start position:0%
+McIntosh and the title of the thesis is
+called humps bumps and lumps it's all
+
+ align:start position:0%
+called humps bumps and lumps it's all
+ 
+
+ align:start position:0%
+called humps bumps and lumps it's all
+about non idealities within an IV curve
+
+ align:start position:0%
+about non idealities within an IV curve
+ 
+
+ align:start position:0%
+about non idealities within an IV curve
+so if you really curious about that
+
+ align:start position:0%
+so if you really curious about that
+ 
+
+ align:start position:0%
+so if you really curious about that
+humps bumps and lumps bye-bye McIntosh I
+
+ align:start position:0%
+humps bumps and lumps bye-bye McIntosh I
+ 
+
+ align:start position:0%
+humps bumps and lumps bye-bye McIntosh I
+believe was the name okay so we talked
+
+ align:start position:0%
+believe was the name okay so we talked
+ 
+
+ align:start position:0%
+believe was the name okay so we talked
+about series resistance already hold
+
+ align:start position:0%
+about series resistance already hold
+ 
+
+ align:start position:0%
+about series resistance already hold
+that put that in your RAM that's our R
+
+ align:start position:0%
+that put that in your RAM that's our R
+ 
+
+ align:start position:0%
+that put that in your RAM that's our R
+sub s right over here that's our R sub s
+
+ align:start position:0%
+sub s right over here that's our R sub s
+ 
+
+ align:start position:0%
+sub s right over here that's our R sub s
+and our our shunt you want to hold this
+
+ align:start position:0%
+and our our shunt you want to hold this
+ 
+
+ align:start position:0%
+and our our shunt you want to hold this
+other component near ram so that's the
+
+ align:start position:0%
+other component near ram so that's the
+ 
+
+ align:start position:0%
+other component near ram so that's the
+picture to have our series this is our
+
+ align:start position:0%
+picture to have our series this is our
+ 
+
+ align:start position:0%
+picture to have our series this is our
+shunt this is an IV sorry a pn-junction
+
+ align:start position:0%
+shunt this is an IV sorry a pn-junction
+ 
+
+ align:start position:0%
+shunt this is an IV sorry a pn-junction
+this is your n plus region and this is
+
+ align:start position:0%
+this is your n plus region and this is
+ 
+
+ align:start position:0%
+this is your n plus region and this is
+your p and this is looking at the
+
+ align:start position:0%
+your p and this is looking at the
+ 
+
+ align:start position:0%
+your p and this is looking at the
+electron energy in 3d so we typically
+
+ align:start position:0%
+electron energy in 3d so we typically
+ 
+
+ align:start position:0%
+electron energy in 3d so we typically
+take a slice out like that right just
+
+ align:start position:0%
+take a slice out like that right just
+ 
+
+ align:start position:0%
+take a slice out like that right just
+like this and we draw the electron
+
+ align:start position:0%
+like this and we draw the electron
+ 
+
+ align:start position:0%
+like this and we draw the electron
+energy as a function of position in a
+
+ align:start position:0%
+energy as a function of position in a
+ 
+
+ align:start position:0%
+energy as a function of position in a
+nice little wavy form that we typically
+
+ align:start position:0%
+nice little wavy form that we typically
+ 
+
+ align:start position:0%
+nice little wavy form that we typically
+do to create describe the PN Junction
+
+ align:start position:0%
+do to create describe the PN Junction
+ 
+
+ align:start position:0%
+do to create describe the PN Junction
+what's being described right here is
+
+ align:start position:0%
+what's being described right here is
+ 
+
+ align:start position:0%
+what's being described right here is
+adding a leaner dimension a spatial
+
+ align:start position:0%
+adding a leaner dimension a spatial
+ 
+
+ align:start position:0%
+adding a leaner dimension a spatial
+dimension in what's shown as the
+
+ align:start position:0%
+dimension in what's shown as the
+ 
+
+ align:start position:0%
+dimension in what's shown as the
+abscissa and this plot and showing what
+
+ align:start position:0%
+abscissa and this plot and showing what
+ 
+
+ align:start position:0%
+abscissa and this plot and showing what
+is a weakness in the PN Junction it
+
+ align:start position:0%
+is a weakness in the PN Junction it
+ 
+
+ align:start position:0%
+is a weakness in the PN Junction it
+could be a localized defect this could
+
+ align:start position:0%
+could be a localized defect this could
+ 
+
+ align:start position:0%
+could be a localized defect this could
+be a
+
+ align:start position:0%
+be a
+ 
+
+ align:start position:0%
+be a
+art of metal that happened to lie on the
+
+ align:start position:0%
+art of metal that happened to lie on the
+ 
+
+ align:start position:0%
+art of metal that happened to lie on the
+wrong place in your device and poke and
+
+ align:start position:0%
+wrong place in your device and poke and
+ 
+
+ align:start position:0%
+wrong place in your device and poke and
+fire through essentially when you did
+
+ align:start position:0%
+fire through essentially when you did
+ 
+
+ align:start position:0%
+fire through essentially when you did
+the firing step to adhere the metal to
+
+ align:start position:0%
+the firing step to adhere the metal to
+ 
+
+ align:start position:0%
+the firing step to adhere the metal to
+create the contact it could have gone
+
+ align:start position:0%
+create the contact it could have gone
+ 
+
+ align:start position:0%
+create the contact it could have gone
+straight through the pn-junction contact
+
+ align:start position:0%
+straight through the pn-junction contact
+ 
+
+ align:start position:0%
+straight through the pn-junction contact
+to the other side it could be a charge
+
+ align:start position:0%
+to the other side it could be a charge
+ 
+
+ align:start position:0%
+to the other side it could be a charge
+dislocation it could be a structural
+
+ align:start position:0%
+dislocation it could be a structural
+ 
+
+ align:start position:0%
+dislocation it could be a structural
+defect and so forth but a local
+
+ align:start position:0%
+defect and so forth but a local
+ 
+
+ align:start position:0%
+defect and so forth but a local
+reduction in the barrier height now
+
+ align:start position:0%
+reduction in the barrier height now
+ 
+
+ align:start position:0%
+reduction in the barrier height now
+where the SI electron going to go if you
+
+ align:start position:0%
+where the SI electron going to go if you
+ 
+
+ align:start position:0%
+where the SI electron going to go if you
+have a diffusion current it's going to
+
+ align:start position:0%
+have a diffusion current it's going to
+ 
+
+ align:start position:0%
+have a diffusion current it's going to
+be crowding through that little
+
+ align:start position:0%
+be crowding through that little
+ 
+
+ align:start position:0%
+be crowding through that little
+localized reduction in the energy
+
+ align:start position:0%
+localized reduction in the energy
+ 
+
+ align:start position:0%
+localized reduction in the energy
+barrier and you're going to have a
+
+ align:start position:0%
+barrier and you're going to have a
+ 
+
+ align:start position:0%
+barrier and you're going to have a
+higher current flowing through the
+
+ align:start position:0%
+higher current flowing through the
+ 
+
+ align:start position:0%
+higher current flowing through the
+specific region so how to measure that
+
+ align:start position:0%
+specific region so how to measure that
+ 
+
+ align:start position:0%
+specific region so how to measure that
+well if I measure my full IV curve like
+
+ align:start position:0%
+well if I measure my full IV curve like
+ 
+
+ align:start position:0%
+well if I measure my full IV curve like
+this might manifest itself as some
+
+ align:start position:0%
+this might manifest itself as some
+ 
+
+ align:start position:0%
+this might manifest itself as some
+reduced shunt resistance so you have a
+
+ align:start position:0%
+reduced shunt resistance so you have a
+ 
+
+ align:start position:0%
+reduced shunt resistance so you have a
+larger current flowing through it at
+
+ align:start position:0%
+larger current flowing through it at
+ 
+
+ align:start position:0%
+larger current flowing through it at
+lower bias voltages but but how do I
+
+ align:start position:0%
+lower bias voltages but but how do I
+ 
+
+ align:start position:0%
+lower bias voltages but but how do I
+know what's going on without some
+
+ align:start position:0%
+know what's going on without some
+ 
+
+ align:start position:0%
+know what's going on without some
+spatial a spatially resolved measurement
+
+ align:start position:0%
+spatial a spatially resolved measurement
+ 
+
+ align:start position:0%
+spatial a spatially resolved measurement
+tool I'm in the dark no pun intended
+
+ align:start position:0%
+tool I'm in the dark no pun intended
+ 
+
+ align:start position:0%
+tool I'm in the dark no pun intended
+so I have to figure out how to measure
+
+ align:start position:0%
+so I have to figure out how to measure
+ 
+
+ align:start position:0%
+so I have to figure out how to measure
+the current flow as a function of
+
+ align:start position:0%
+the current flow as a function of
+ 
+
+ align:start position:0%
+the current flow as a function of
+position now somebody thought about this
+
+ align:start position:0%
+position now somebody thought about this
+ 
+
+ align:start position:0%
+position now somebody thought about this
+a while they said huh well let me get
+
+ align:start position:0%
+a while they said huh well let me get
+ 
+
+ align:start position:0%
+a while they said huh well let me get
+this straight if I apply a known bias
+
+ align:start position:0%
+this straight if I apply a known bias
+ 
+
+ align:start position:0%
+this straight if I apply a known bias
+voltage to my device I'm going to get
+
+ align:start position:0%
+voltage to my device I'm going to get
+ 
+
+ align:start position:0%
+voltage to my device I'm going to get
+some current flowing through it and that
+
+ align:start position:0%
+some current flowing through it and that
+ 
+
+ align:start position:0%
+some current flowing through it and that
+current what I read out of the whole
+
+ align:start position:0%
+current what I read out of the whole
+ 
+
+ align:start position:0%
+current what I read out of the whole
+device macroscopically has some spatial
+
+ align:start position:0%
+device macroscopically has some spatial
+ 
+
+ align:start position:0%
+device macroscopically has some spatial
+distribution to it let me think about
+
+ align:start position:0%
+distribution to it let me think about
+ 
+
+ align:start position:0%
+distribution to it let me think about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay so current times voltage is power
+
+ align:start position:0%
+okay so current times voltage is power
+ 
+
+ align:start position:0%
+okay so current times voltage is power
+right and power generates Heat so if I
+
+ align:start position:0%
+right and power generates Heat so if I
+ 
+
+ align:start position:0%
+right and power generates Heat so if I
+have a current crowding at some portion
+
+ align:start position:0%
+have a current crowding at some portion
+ 
+
+ align:start position:0%
+have a current crowding at some portion
+of my device I'm going to be generating
+
+ align:start position:0%
+of my device I'm going to be generating
+ 
+
+ align:start position:0%
+of my device I'm going to be generating
+a large amount of heat as the carriers
+
+ align:start position:0%
+a large amount of heat as the carriers
+ 
+
+ align:start position:0%
+a large amount of heat as the carriers
+flow through that specific region so if
+
+ align:start position:0%
+flow through that specific region so if
+ 
+
+ align:start position:0%
+flow through that specific region so if
+I have some method of measuring the heat
+
+ align:start position:0%
+I have some method of measuring the heat
+ 
+
+ align:start position:0%
+I have some method of measuring the heat
+heat distribution across my device is
+
+ align:start position:0%
+heat distribution across my device is
+ 
+
+ align:start position:0%
+heat distribution across my device is
+very very sensitive I might be able to
+
+ align:start position:0%
+very very sensitive I might be able to
+ 
+
+ align:start position:0%
+very very sensitive I might be able to
+divide that heat measurement if
+
+ align:start position:0%
+divide that heat measurement if
+ 
+
+ align:start position:0%
+divide that heat measurement if
+calibrated properly to determine total
+
+ align:start position:0%
+calibrated properly to determine total
+ 
+
+ align:start position:0%
+calibrated properly to determine total
+power I might be able to divide that
+
+ align:start position:0%
+power I might be able to divide that
+ 
+
+ align:start position:0%
+power I might be able to divide that
+heat measurement by current sorry by
+
+ align:start position:0%
+heat measurement by current sorry by
+ 
+
+ align:start position:0%
+heat measurement by current sorry by
+voltage by voltage so I know the applied
+
+ align:start position:0%
+voltage by voltage so I know the applied
+ 
+
+ align:start position:0%
+voltage by voltage so I know the applied
+bias voltage to my device I take my
+
+ align:start position:0%
+bias voltage to my device I take my
+ 
+
+ align:start position:0%
+bias voltage to my device I take my
+power divided by the voltage and I get
+
+ align:start position:0%
+power divided by the voltage and I get
+ 
+
+ align:start position:0%
+power divided by the voltage and I get
+the current as a function of X Y
+
+ align:start position:0%
+the current as a function of X Y
+ 
+
+ align:start position:0%
+the current as a function of X Y
+position so I can map out my dark IV
+
+ align:start position:0%
+position so I can map out my dark IV
+ 
+
+ align:start position:0%
+position so I can map out my dark IV
+curve at any arbitrary bias voltage
+
+ align:start position:0%
+curve at any arbitrary bias voltage
+ 
+
+ align:start position:0%
+curve at any arbitrary bias voltage
+condition let's say I want to do the
+
+ align:start position:0%
+condition let's say I want to do the
+ 
+
+ align:start position:0%
+condition let's say I want to do the
+measurement at point 4 volts for bias I
+
+ align:start position:0%
+measurement at point 4 volts for bias I
+ 
+
+ align:start position:0%
+measurement at point 4 volts for bias I
+apply point 4 volts across my device and
+
+ align:start position:0%
+apply point 4 volts across my device and
+ 
+
+ align:start position:0%
+apply point 4 volts across my device and
+I just measure the heat distribution and
+
+ align:start position:0%
+I just measure the heat distribution and
+ 
+
+ align:start position:0%
+I just measure the heat distribution and
+in a calibrated measurement you can see
+
+ align:start position:0%
+in a calibrated measurement you can see
+ 
+
+ align:start position:0%
+in a calibrated measurement you can see
+how the dark current is distributed
+
+ align:start position:0%
+how the dark current is distributed
+ 
+
+ align:start position:0%
+how the dark current is distributed
+and how the diffusion current is
+
+ align:start position:0%
+and how the diffusion current is
+ 
+
+ align:start position:0%
+and how the diffusion current is
+distributed and that's what lock-in
+
+ align:start position:0%
+distributed and that's what lock-in
+ 
+
+ align:start position:0%
+distributed and that's what lock-in
+thermography is all about this is a say
+
+ align:start position:0%
+thermography is all about this is a say
+ 
+
+ align:start position:0%
+thermography is all about this is a say
+a somewhat typical image not it's still
+
+ align:start position:0%
+a somewhat typical image not it's still
+ 
+
+ align:start position:0%
+a somewhat typical image not it's still
+very noisy because it was a very fast
+
+ align:start position:0%
+very noisy because it was a very fast
+ 
+
+ align:start position:0%
+very noisy because it was a very fast
+image but you have your solar cell
+
+ align:start position:0%
+image but you have your solar cell
+ 
+
+ align:start position:0%
+image but you have your solar cell
+device you can barely make out the
+
+ align:start position:0%
+device you can barely make out the
+ 
+
+ align:start position:0%
+device you can barely make out the
+contact grid right here and then the
+
+ align:start position:0%
+contact grid right here and then the
+ 
+
+ align:start position:0%
+contact grid right here and then the
+fingers are moving down separated by
+
+ align:start position:0%
+fingers are moving down separated by
+ 
+
+ align:start position:0%
+fingers are moving down separated by
+about this much on this particular image
+
+ align:start position:0%
+about this much on this particular image
+ 
+
+ align:start position:0%
+about this much on this particular image
+you can see the fingers or the dark
+
+ align:start position:0%
+you can see the fingers or the dark
+ 
+
+ align:start position:0%
+you can see the fingers or the dark
+shadow of the fingers right here and you
+
+ align:start position:0%
+shadow of the fingers right here and you
+ 
+
+ align:start position:0%
+shadow of the fingers right here and you
+see bright spots 1 2 3 4 5 6 7 and so
+
+ align:start position:0%
+see bright spots 1 2 3 4 5 6 7 and so
+ 
+
+ align:start position:0%
+see bright spots 1 2 3 4 5 6 7 and so
+forth across the device indicating
+
+ align:start position:0%
+forth across the device indicating
+ 
+
+ align:start position:0%
+forth across the device indicating
+regions were more current is flowing aha
+
+ align:start position:0%
+regions were more current is flowing aha
+ 
+
+ align:start position:0%
+regions were more current is flowing aha
+so I'm beginning to figure out that well
+
+ align:start position:0%
+so I'm beginning to figure out that well
+ 
+
+ align:start position:0%
+so I'm beginning to figure out that well
+this dark IV curve that I have right
+
+ align:start position:0%
+this dark IV curve that I have right
+ 
+
+ align:start position:0%
+this dark IV curve that I have right
+here this large amount of current
+
+ align:start position:0%
+here this large amount of current
+ 
+
+ align:start position:0%
+here this large amount of current
+flowing through my device at lower bias
+
+ align:start position:0%
+flowing through my device at lower bias
+ 
+
+ align:start position:0%
+flowing through my device at lower bias
+voltages that's not all uniformly
+
+ align:start position:0%
+voltages that's not all uniformly
+ 
+
+ align:start position:0%
+voltages that's not all uniformly
+distributed but it's rather concentrated
+
+ align:start position:0%
+distributed but it's rather concentrated
+ 
+
+ align:start position:0%
+distributed but it's rather concentrated
+in specific areas where I have
+
+ align:start position:0%
+in specific areas where I have
+ 
+
+ align:start position:0%
+in specific areas where I have
+weaknesses in my PN Junction under low
+
+ align:start position:0%
+weaknesses in my PN Junction under low
+ 
+
+ align:start position:0%
+weaknesses in my PN Junction under low
+forward bias voltages and at larger
+
+ align:start position:0%
+forward bias voltages and at larger
+ 
+
+ align:start position:0%
+forward bias voltages and at larger
+forward bias voltages once this barrier
+
+ align:start position:0%
+forward bias voltages once this barrier
+ 
+
+ align:start position:0%
+forward bias voltages once this barrier
+significantly reduced I may have more
+
+ align:start position:0%
+significantly reduced I may have more
+ 
+
+ align:start position:0%
+significantly reduced I may have more
+carriers going through in regions of
+
+ align:start position:0%
+carriers going through in regions of
+ 
+
+ align:start position:0%
+carriers going through in regions of
+smaller minority carrier diffusion
+
+ align:start position:0%
+smaller minority carrier diffusion
+ 
+
+ align:start position:0%
+smaller minority carrier diffusion
+length why well because if a carrier
+
+ align:start position:0%
+length why well because if a carrier
+ 
+
+ align:start position:0%
+length why well because if a carrier
+goes in and recombines quickly because
+
+ align:start position:0%
+goes in and recombines quickly because
+ 
+
+ align:start position:0%
+goes in and recombines quickly because
+the diffusion length is very short that
+
+ align:start position:0%
+the diffusion length is very short that
+ 
+
+ align:start position:0%
+the diffusion length is very short that
+means there's one less carrier in there
+
+ align:start position:0%
+means there's one less carrier in there
+ 
+
+ align:start position:0%
+means there's one less carrier in there
+which means that now there's a greater
+
+ align:start position:0%
+which means that now there's a greater
+ 
+
+ align:start position:0%
+which means that now there's a greater
+driving force for diffusion and another
+
+ align:start position:0%
+driving force for diffusion and another
+ 
+
+ align:start position:0%
+driving force for diffusion and another
+carrier is going to come in and
+
+ align:start position:0%
+carrier is going to come in and
+ 
+
+ align:start position:0%
+carrier is going to come in and
+recombine too and another carrier and
+
+ align:start position:0%
+recombine too and another carrier and
+ 
+
+ align:start position:0%
+recombine too and another carrier and
+recombine too right so now you have a
+
+ align:start position:0%
+recombine too right so now you have a
+ 
+
+ align:start position:0%
+recombine too right so now you have a
+larger diffusion current going into the
+
+ align:start position:0%
+larger diffusion current going into the
+ 
+
+ align:start position:0%
+larger diffusion current going into the
+regions of lower minority carrier
+
+ align:start position:0%
+regions of lower minority carrier
+ 
+
+ align:start position:0%
+regions of lower minority carrier
+diffusion length let's look at a few
+
+ align:start position:0%
+diffusion length let's look at a few
+ 
+
+ align:start position:0%
+diffusion length let's look at a few
+lock-in thermography images and see how
+
+ align:start position:0%
+lock-in thermography images and see how
+ 
+
+ align:start position:0%
+lock-in thermography images and see how
+this this this plays out so under low
+
+ align:start position:0%
+this this this plays out so under low
+ 
+
+ align:start position:0%
+this this this plays out so under low
+bias conditions so I'm still still have
+
+ align:start position:0%
+bias conditions so I'm still still have
+ 
+
+ align:start position:0%
+bias conditions so I'm still still have
+a very large barrier there in the in the
+
+ align:start position:0%
+a very large barrier there in the in the
+ 
+
+ align:start position:0%
+a very large barrier there in the in the
+PN Junction region I'm typically going
+
+ align:start position:0%
+PN Junction region I'm typically going
+ 
+
+ align:start position:0%
+PN Junction region I'm typically going
+to see isolated hot spots not always but
+
+ align:start position:0%
+to see isolated hot spots not always but
+ 
+
+ align:start position:0%
+to see isolated hot spots not always but
+but typically isolated hot spots and
+
+ align:start position:0%
+but typically isolated hot spots and
+ 
+
+ align:start position:0%
+but typically isolated hot spots and
+these most often are defects within the
+
+ align:start position:0%
+these most often are defects within the
+ 
+
+ align:start position:0%
+these most often are defects within the
+PN Junction somebody might scratch the
+
+ align:start position:0%
+PN Junction somebody might scratch the
+ 
+
+ align:start position:0%
+PN Junction somebody might scratch the
+junction or maybe drop their tweezer on
+
+ align:start position:0%
+junction or maybe drop their tweezer on
+ 
+
+ align:start position:0%
+junction or maybe drop their tweezer on
+it or maybe a piece of metal during the
+
+ align:start position:0%
+it or maybe a piece of metal during the
+ 
+
+ align:start position:0%
+it or maybe a piece of metal during the
+contact metallization fired through at
+
+ align:start position:0%
+contact metallization fired through at
+ 
+
+ align:start position:0%
+contact metallization fired through at
+that particular region and so we have
+
+ align:start position:0%
+that particular region and so we have
+ 
+
+ align:start position:0%
+that particular region and so we have
+what are typically these point shunts
+
+ align:start position:0%
+what are typically these point shunts
+ 
+
+ align:start position:0%
+what are typically these point shunts
+sometimes you see shunts around the edge
+
+ align:start position:0%
+sometimes you see shunts around the edge
+ 
+
+ align:start position:0%
+sometimes you see shunts around the edge
+as well if you didn't isolate the edge
+
+ align:start position:0%
+as well if you didn't isolate the edge
+ 
+
+ align:start position:0%
+as well if you didn't isolate the edge
+well and it now as we forward bias
+
+ align:start position:0%
+well and it now as we forward bias
+ 
+
+ align:start position:0%
+well and it now as we forward bias
+forward biased forward bias those
+
+ align:start position:0%
+forward biased forward bias those
+ 
+
+ align:start position:0%
+forward biased forward bias those
+barriers become less
+
+ align:start position:0%
+barriers become less
+ 
+
+ align:start position:0%
+barriers become less
+and now what's driving the current the
+
+ align:start position:0%
+and now what's driving the current the
+ 
+
+ align:start position:0%
+and now what's driving the current the
+dark current in the device is a
+
+ align:start position:0%
+dark current in the device is a
+ 
+
+ align:start position:0%
+dark current in the device is a
+recombination in the bulk so the regions
+
+ align:start position:0%
+recombination in the bulk so the regions
+ 
+
+ align:start position:0%
+recombination in the bulk so the regions
+of higher recombination will be regions
+
+ align:start position:0%
+of higher recombination will be regions
+ 
+
+ align:start position:0%
+of higher recombination will be regions
+of higher current flow they'll drive
+
+ align:start position:0%
+of higher current flow they'll drive
+ 
+
+ align:start position:0%
+of higher current flow they'll drive
+more recombination current so this is a
+
+ align:start position:0%
+more recombination current so this is a
+ 
+
+ align:start position:0%
+more recombination current so this is a
+higher bias voltage 560 millivolts or
+
+ align:start position:0%
+higher bias voltage 560 millivolts or
+ 
+
+ align:start position:0%
+higher bias voltage 560 millivolts or
+0.5 6 volts as opposed to 0.36 volts we
+
+ align:start position:0%
+0.5 6 volts as opposed to 0.36 volts we
+ 
+
+ align:start position:0%
+0.5 6 volts as opposed to 0.36 volts we
+can still see the shadow of the big 3
+
+ align:start position:0%
+can still see the shadow of the big 3
+ 
+
+ align:start position:0%
+can still see the shadow of the big 3
+right here but they're they're much
+
+ align:start position:0%
+right here but they're they're much
+ 
+
+ align:start position:0%
+right here but they're they're much
+diminished now instead what we see are
+
+ align:start position:0%
+diminished now instead what we see are
+ 
+
+ align:start position:0%
+diminished now instead what we see are
+these wispier features right here now I
+
+ align:start position:0%
+these wispier features right here now I
+ 
+
+ align:start position:0%
+these wispier features right here now I
+think gee if that really is if those
+
+ align:start position:0%
+think gee if that really is if those
+ 
+
+ align:start position:0%
+think gee if that really is if those
+really are regions of lower minority
+
+ align:start position:0%
+really are regions of lower minority
+ 
+
+ align:start position:0%
+really are regions of lower minority
+carrier diffusion life I just learned
+
+ align:start position:0%
+carrier diffusion life I just learned
+ 
+
+ align:start position:0%
+carrier diffusion life I just learned
+about a method to measure might already
+
+ align:start position:0%
+about a method to measure might already
+ 
+
+ align:start position:0%
+about a method to measure might already
+care diffusion length didn't I what was
+
+ align:start position:0%
+care diffusion length didn't I what was
+ 
+
+ align:start position:0%
+care diffusion length didn't I what was
+that laser beam induced current method
+
+ align:start position:0%
+that laser beam induced current method
+ 
+
+ align:start position:0%
+that laser beam induced current method
+right spatially resolved laser beam
+
+ align:start position:0%
+right spatially resolved laser beam
+ 
+
+ align:start position:0%
+right spatially resolved laser beam
+discard so I have at least one method of
+
+ align:start position:0%
+discard so I have at least one method of
+ 
+
+ align:start position:0%
+discard so I have at least one method of
+measuring minority carrier diffusion
+
+ align:start position:0%
+measuring minority carrier diffusion
+ 
+
+ align:start position:0%
+measuring minority carrier diffusion
+length let's put one and one together
+
+ align:start position:0%
+length let's put one and one together
+ 
+
+ align:start position:0%
+length let's put one and one together
+and see what we get so we'll take this
+
+ align:start position:0%
+and see what we get so we'll take this
+ 
+
+ align:start position:0%
+and see what we get so we'll take this
+image right here and put it aside rotate
+
+ align:start position:0%
+image right here and put it aside rotate
+ 
+
+ align:start position:0%
+image right here and put it aside rotate
+it and put it right beside the minority
+
+ align:start position:0%
+it and put it right beside the minority
+ 
+
+ align:start position:0%
+it and put it right beside the minority
+carrier diffusion length and voila you
+
+ align:start position:0%
+carrier diffusion length and voila you
+ 
+
+ align:start position:0%
+carrier diffusion length and voila you
+see how those wispier features are
+
+ align:start position:0%
+see how those wispier features are
+ 
+
+ align:start position:0%
+see how those wispier features are
+corresponding to regions of lower
+
+ align:start position:0%
+corresponding to regions of lower
+ 
+
+ align:start position:0%
+corresponding to regions of lower
+minority carrier diffusion length once
+
+ align:start position:0%
+minority carrier diffusion length once
+ 
+
+ align:start position:0%
+minority carrier diffusion length once
+again the explanation if you have large
+
+ align:start position:0%
+again the explanation if you have large
+ 
+
+ align:start position:0%
+again the explanation if you have large
+forward bias condition the barrier is
+
+ align:start position:0%
+forward bias condition the barrier is
+ 
+
+ align:start position:0%
+forward bias condition the barrier is
+lower carriers can easily diffuse into
+
+ align:start position:0%
+lower carriers can easily diffuse into
+ 
+
+ align:start position:0%
+lower carriers can easily diffuse into
+the bulk the carrier's diffusing into
+
+ align:start position:0%
+the bulk the carrier's diffusing into
+ 
+
+ align:start position:0%
+the bulk the carrier's diffusing into
+the bulk will go a certain distance
+
+ align:start position:0%
+the bulk will go a certain distance
+ 
+
+ align:start position:0%
+the bulk will go a certain distance
+before recombining if the diffusion
+
+ align:start position:0%
+before recombining if the diffusion
+ 
+
+ align:start position:0%
+before recombining if the diffusion
+length is short the recombine quickly
+
+ align:start position:0%
+length is short the recombine quickly
+ 
+
+ align:start position:0%
+length is short the recombine quickly
+which means now there's no more carrier
+
+ align:start position:0%
+which means now there's no more carrier
+ 
+
+ align:start position:0%
+which means now there's no more carrier
+which means that the diffusion current
+
+ align:start position:0%
+which means that the diffusion current
+ 
+
+ align:start position:0%
+which means that the diffusion current
+will push another carrier into that spot
+
+ align:start position:0%
+will push another carrier into that spot
+ 
+
+ align:start position:0%
+will push another carrier into that spot
+right which means will recombine
+
+ align:start position:0%
+right which means will recombine
+ 
+
+ align:start position:0%
+right which means will recombine
+recombine more current is flowing
+
+ align:start position:0%
+recombine more current is flowing
+ 
+
+ align:start position:0%
+recombine more current is flowing
+through if the diffusion length is
+
+ align:start position:0%
+through if the diffusion length is
+ 
+
+ align:start position:0%
+through if the diffusion length is
+shorter the alternative is a diffusion
+
+ align:start position:0%
+shorter the alternative is a diffusion
+ 
+
+ align:start position:0%
+shorter the alternative is a diffusion
+length is long and one carrier makes it
+
+ align:start position:0%
+length is long and one carrier makes it
+ 
+
+ align:start position:0%
+length is long and one carrier makes it
+over and then takes its time getting all
+
+ align:start position:0%
+over and then takes its time getting all
+ 
+
+ align:start position:0%
+over and then takes its time getting all
+the way across before recombination
+
+ align:start position:0%
+the way across before recombination
+ 
+
+ align:start position:0%
+the way across before recombination
+occurs so what you're seeing here is
+
+ align:start position:0%
+occurs so what you're seeing here is
+ 
+
+ align:start position:0%
+occurs so what you're seeing here is
+essentially in effect the current the
+
+ align:start position:0%
+essentially in effect the current the
+ 
+
+ align:start position:0%
+essentially in effect the current the
+the dark forward current meaning you're
+
+ align:start position:0%
+the dark forward current meaning you're
+ 
+
+ align:start position:0%
+the dark forward current meaning you're
+measuring the IV curve in the dark
+
+ align:start position:0%
+measuring the IV curve in the dark
+ 
+
+ align:start position:0%
+measuring the IV curve in the dark
+you're obtaining an IV curve here it is
+
+ align:start position:0%
+you're obtaining an IV curve here it is
+ 
+
+ align:start position:0%
+you're obtaining an IV curve here it is
+you're obtaining an IV curve for your
+
+ align:start position:0%
+you're obtaining an IV curve for your
+ 
+
+ align:start position:0%
+you're obtaining an IV curve for your
+device you're measuring in the dark
+
+ align:start position:0%
+device you're measuring in the dark
+ 
+
+ align:start position:0%
+device you're measuring in the dark
+under larger forward bias conditions
+
+ align:start position:0%
+under larger forward bias conditions
+ 
+
+ align:start position:0%
+under larger forward bias conditions
+somewhere out here where bulk
+
+ align:start position:0%
+somewhere out here where bulk
+ 
+
+ align:start position:0%
+somewhere out here where bulk
+recombination is dominating and you're
+
+ align:start position:0%
+recombination is dominating and you're
+ 
+
+ align:start position:0%
+recombination is dominating and you're
+able to visualize the current loss
+
+ align:start position:0%
+able to visualize the current loss
+ 
+
+ align:start position:0%
+able to visualize the current loss
+mechanisms in your device so you say
+
+ align:start position:0%
+mechanisms in your device so you say
+ 
+
+ align:start position:0%
+mechanisms in your device so you say
+well gee if I want in the dark if I want
+
+ align:start position:0%
+well gee if I want in the dark if I want
+ 
+
+ align:start position:0%
+well gee if I want in the dark if I want
+this to be as small as possible so that
+
+ align:start position:0%
+this to be as small as possible so that
+ 
+
+ align:start position:0%
+this to be as small as possible so that
+when I transpose this
+
+ align:start position:0%
+when I transpose this
+ 
+
+ align:start position:0%
+when I transpose this
+delight and I shift everything into
+
+ align:start position:0%
+delight and I shift everything into
+ 
+
+ align:start position:0%
+delight and I shift everything into
+negative into fourth quadrant territory
+
+ align:start position:0%
+negative into fourth quadrant territory
+ 
+
+ align:start position:0%
+negative into fourth quadrant territory
+because I illuminate it now if I want
+
+ align:start position:0%
+because I illuminate it now if I want
+ 
+
+ align:start position:0%
+because I illuminate it now if I want
+there to be a small dark forward current
+
+ align:start position:0%
+there to be a small dark forward current
+ 
+
+ align:start position:0%
+there to be a small dark forward current
+as possible so as I maximize my fill
+
+ align:start position:0%
+as possible so as I maximize my fill
+ 
+
+ align:start position:0%
+as possible so as I maximize my fill
+factor when I illuminate my device I
+
+ align:start position:0%
+factor when I illuminate my device I
+ 
+
+ align:start position:0%
+factor when I illuminate my device I
+want all of these current loss
+
+ align:start position:0%
+want all of these current loss
+ 
+
+ align:start position:0%
+want all of these current loss
+mechanisms to go away let me let me
+
+ align:start position:0%
+mechanisms to go away let me let me
+ 
+
+ align:start position:0%
+mechanisms to go away let me let me
+repeat that one more time so people get
+
+ align:start position:0%
+repeat that one more time so people get
+ 
+
+ align:start position:0%
+repeat that one more time so people get
+it if so what I'm doing right now is I'm
+
+ align:start position:0%
+it if so what I'm doing right now is I'm
+ 
+
+ align:start position:0%
+it if so what I'm doing right now is I'm
+measuring this device in the dark and
+
+ align:start position:0%
+measuring this device in the dark and
+ 
+
+ align:start position:0%
+measuring this device in the dark and
+this is my IV curve right here and I
+
+ align:start position:0%
+this is my IV curve right here and I
+ 
+
+ align:start position:0%
+this is my IV curve right here and I
+have example of bad device good device
+
+ align:start position:0%
+have example of bad device good device
+ 
+
+ align:start position:0%
+have example of bad device good device
+the bad device has so bad and good the
+
+ align:start position:0%
+the bad device has so bad and good the
+ 
+
+ align:start position:0%
+the bad device has so bad and good the
+reason this is bad and good is because
+
+ align:start position:0%
+reason this is bad and good is because
+ 
+
+ align:start position:0%
+reason this is bad and good is because
+when I transpose this curve under
+
+ align:start position:0%
+when I transpose this curve under
+ 
+
+ align:start position:0%
+when I transpose this curve under
+illumination this is now under
+
+ align:start position:0%
+illumination this is now under
+ 
+
+ align:start position:0%
+illumination this is now under
+illumination my good and bad right here
+
+ align:start position:0%
+illumination my good and bad right here
+ 
+
+ align:start position:0%
+illumination my good and bad right here
+you'll see that the bad has a lower vo C
+
+ align:start position:0%
+you'll see that the bad has a lower vo C
+ 
+
+ align:start position:0%
+you'll see that the bad has a lower vo C
+right so the intersection between these
+
+ align:start position:0%
+right so the intersection between these
+ 
+
+ align:start position:0%
+right so the intersection between these
+illuminated curves this is now
+
+ align:start position:0%
+illuminated curves this is now
+ 
+
+ align:start position:0%
+illuminated curves this is now
+illuminated and this is dark right over
+
+ align:start position:0%
+illuminated and this is dark right over
+ 
+
+ align:start position:0%
+illuminated and this is dark right over
+here these are dark curves these here
+
+ align:start position:0%
+here these are dark curves these here
+ 
+
+ align:start position:0%
+here these are dark curves these here
+are illuminated curves the intersection
+
+ align:start position:0%
+are illuminated curves the intersection
+ 
+
+ align:start position:0%
+are illuminated curves the intersection
+between the illuminated curve and the
+
+ align:start position:0%
+between the illuminated curve and the
+ 
+
+ align:start position:0%
+between the illuminated curve and the
+x-axis denotes the open circuit voltage
+
+ align:start position:0%
+x-axis denotes the open circuit voltage
+ 
+
+ align:start position:0%
+x-axis denotes the open circuit voltage
+and you see that the larger this current
+
+ align:start position:0%
+and you see that the larger this current
+ 
+
+ align:start position:0%
+and you see that the larger this current
+is in the dark the earlier you're going
+
+ align:start position:0%
+is in the dark the earlier you're going
+ 
+
+ align:start position:0%
+is in the dark the earlier you're going
+to intersect with your x-axis the lower
+
+ align:start position:0%
+to intersect with your x-axis the lower
+ 
+
+ align:start position:0%
+to intersect with your x-axis the lower
+the voltage output of your device will
+
+ align:start position:0%
+the voltage output of your device will
+ 
+
+ align:start position:0%
+the voltage output of your device will
+be the lower the maximum power point
+
+ align:start position:0%
+be the lower the maximum power point
+ 
+
+ align:start position:0%
+be the lower the maximum power point
+will be right so you want in in the dark
+
+ align:start position:0%
+will be right so you want in in the dark
+ 
+
+ align:start position:0%
+will be right so you want in in the dark
+when you measure the IV curve you want
+
+ align:start position:0%
+when you measure the IV curve you want
+ 
+
+ align:start position:0%
+when you measure the IV curve you want
+that current to be as small as possible
+
+ align:start position:0%
+that current to be as small as possible
+ 
+
+ align:start position:0%
+that current to be as small as possible
+in the dark and obviously when you
+
+ align:start position:0%
+in the dark and obviously when you
+ 
+
+ align:start position:0%
+in the dark and obviously when you
+illuminate it you want this jump to be
+
+ align:start position:0%
+illuminate it you want this jump to be
+ 
+
+ align:start position:0%
+illuminate it you want this jump to be
+as large as possible and you want this
+
+ align:start position:0%
+as large as possible and you want this
+ 
+
+ align:start position:0%
+as large as possible and you want this
+to almost look like a box that a large
+
+ align:start position:0%
+to almost look like a box that a large
+ 
+
+ align:start position:0%
+to almost look like a box that a large
+fill factor so if we say okay we want
+
+ align:start position:0%
+fill factor so if we say okay we want
+ 
+
+ align:start position:0%
+fill factor so if we say okay we want
+this to be small because we want a large
+
+ align:start position:0%
+this to be small because we want a large
+ 
+
+ align:start position:0%
+this to be small because we want a large
+fill factor somehow we have to know
+
+ align:start position:0%
+fill factor somehow we have to know
+ 
+
+ align:start position:0%
+fill factor somehow we have to know
+where the current loss mechanisms are
+
+ align:start position:0%
+where the current loss mechanisms are
+ 
+
+ align:start position:0%
+where the current loss mechanisms are
+occurring and that's where we have our
+
+ align:start position:0%
+occurring and that's where we have our
+ 
+
+ align:start position:0%
+occurring and that's where we have our
+lock-in thermography available to us we
+
+ align:start position:0%
+lock-in thermography available to us we
+ 
+
+ align:start position:0%
+lock-in thermography available to us we
+can visualize it you say well you know
+
+ align:start position:0%
+can visualize it you say well you know
+ 
+
+ align:start position:0%
+can visualize it you say well you know
+to do lock-in thermography well I'm
+
+ align:start position:0%
+to do lock-in thermography well I'm
+ 
+
+ align:start position:0%
+to do lock-in thermography well I'm
+going to need in indium antimonide sorry
+
+ align:start position:0%
+going to need in indium antimonide sorry
+ 
+
+ align:start position:0%
+going to need in indium antimonide sorry
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+that would be it would be a in indium
+
+ align:start position:0%
+that would be it would be a in indium
+ 
+
+ align:start position:0%
+that would be it would be a in indium
+antimonide camera sensitive to the 3 to
+
+ align:start position:0%
+antimonide camera sensitive to the 3 to
+ 
+
+ align:start position:0%
+antimonide camera sensitive to the 3 to
+5 micron wavelength range that might
+
+ align:start position:0%
+5 micron wavelength range that might
+ 
+
+ align:start position:0%
+5 micron wavelength range that might
+cost $70,000 to get a good one high
+
+ align:start position:0%
+cost $70,000 to get a good one high
+ 
+
+ align:start position:0%
+cost $70,000 to get a good one high
+frame rate the locking systems so forth
+
+ align:start position:0%
+frame rate the locking systems so forth
+ 
+
+ align:start position:0%
+frame rate the locking systems so forth
+that money I can go over and borrow
+
+ align:start position:0%
+that money I can go over and borrow
+ 
+
+ align:start position:0%
+that money I can go over and borrow
+professor blown a cc system and use it
+
+ align:start position:0%
+professor blown a cc system and use it
+ 
+
+ align:start position:0%
+professor blown a cc system and use it
+there or if my shunts are big enough I
+
+ align:start position:0%
+there or if my shunts are big enough I
+ 
+
+ align:start position:0%
+there or if my shunts are big enough I
+can just use straight-out liquid crystal
+
+ align:start position:0%
+can just use straight-out liquid crystal
+ 
+
+ align:start position:0%
+can just use straight-out liquid crystal
+thermionic sheets or thermochromic
+
+ align:start position:0%
+thermionic sheets or thermochromic
+ 
+
+ align:start position:0%
+thermionic sheets or thermochromic
+sheets rather sorry so you can take
+
+ align:start position:0%
+sheets rather sorry so you can take
+ 
+
+ align:start position:0%
+sheets rather sorry so you can take
+these liquid crystals and slap them
+
+ align:start position:0%
+these liquid crystals and slap them
+ 
+
+ align:start position:0%
+these liquid crystals and slap them
+against your device and measure the heat
+
+ align:start position:0%
+against your device and measure the heat
+ 
+
+ align:start position:0%
+against your device and measure the heat
+distribution straight up just by making
+
+ align:start position:0%
+distribution straight up just by making
+ 
+
+ align:start position:0%
+distribution straight up just by making
+sure you have good thermal contact
+
+ align:start position:0%
+sure you have good thermal contact
+ 
+
+ align:start position:0%
+sure you have good thermal contact
+between yourself and your thermochromic
+
+ align:start position:0%
+between yourself and your thermochromic
+ 
+
+ align:start position:0%
+between yourself and your thermochromic
+sheets which cost about a hundred
+
+ align:start position:0%
+sheets which cost about a hundred
+ 
+
+ align:start position:0%
+sheets which cost about a hundred
+dollars now the reason we use the
+
+ align:start position:0%
+dollars now the reason we use the
+ 
+
+ align:start position:0%
+dollars now the reason we use the
+lock-in thermography and not these
+
+ align:start position:0%
+lock-in thermography and not these
+ 
+
+ align:start position:0%
+lock-in thermography and not these
+thermochromic sheets is this curve right
+
+ align:start position:0%
+thermochromic sheets is this curve right
+ 
+
+ align:start position:0%
+thermochromic sheets is this curve right
+here this is lock-in thermography
+
+ align:start position:0%
+here this is lock-in thermography
+ 
+
+ align:start position:0%
+here this is lock-in thermography
+sensitivity versus integration time and
+
+ align:start position:0%
+sensitivity versus integration time and
+ 
+
+ align:start position:0%
+sensitivity versus integration time and
+we're getting into the 10 micro Kelvin
+
+ align:start position:0%
+we're getting into the 10 micro Kelvin
+ 
+
+ align:start position:0%
+we're getting into the 10 micro Kelvin
+range which is rattlesnake territory all
+
+ align:start position:0%
+range which is rattlesnake territory all
+ 
+
+ align:start position:0%
+range which is rattlesnake territory all
+right that's how the rattlesnakes are
+
+ align:start position:0%
+right that's how the rattlesnakes are
+ 
+
+ align:start position:0%
+right that's how the rattlesnakes are
+able to sense heat and reach out to you
+
+ align:start position:0%
+able to sense heat and reach out to you
+ 
+
+ align:start position:0%
+able to sense heat and reach out to you
+is because they have those little organs
+
+ align:start position:0%
+is because they have those little organs
+ 
+
+ align:start position:0%
+is because they have those little organs
+that look like a little black they're
+
+ align:start position:0%
+that look like a little black they're
+ 
+
+ align:start position:0%
+that look like a little black they're
+kind of like integrating spheres to be
+
+ align:start position:0%
+kind of like integrating spheres to be
+ 
+
+ align:start position:0%
+kind of like integrating spheres to be
+honest small little spot to open up
+
+ align:start position:0%
+honest small little spot to open up
+ 
+
+ align:start position:0%
+honest small little spot to open up
+rattlesnake that's why the Sidewinder
+
+ align:start position:0%
+rattlesnake that's why the Sidewinder
+ 
+
+ align:start position:0%
+rattlesnake that's why the Sidewinder
+missile anybody f-16s Hornets know okay
+
+ align:start position:0%
+missile anybody f-16s Hornets know okay
+ 
+
+ align:start position:0%
+missile anybody f-16s Hornets know okay
+if you're into aviation
+
+ align:start position:0%
+if you're into aviation
+ 
+
+ align:start position:0%
+if you're into aviation
+there's a special type of heat-seeking
+
+ align:start position:0%
+there's a special type of heat-seeking
+ 
+
+ align:start position:0%
+there's a special type of heat-seeking
+missile developed I think in the 1950s
+
+ align:start position:0%
+missile developed I think in the 1950s
+ 
+
+ align:start position:0%
+missile developed I think in the 1950s
+that uses a device not dissimilar from
+
+ align:start position:0%
+that uses a device not dissimilar from
+ 
+
+ align:start position:0%
+that uses a device not dissimilar from
+the rattlesnakes heat sensing organs
+
+ align:start position:0%
+the rattlesnakes heat sensing organs
+ 
+
+ align:start position:0%
+the rattlesnakes heat sensing organs
+regardless I digress we're looking at a
+
+ align:start position:0%
+regardless I digress we're looking at a
+ 
+
+ align:start position:0%
+regardless I digress we're looking at a
+about a 10 micro Kelvin sensitivity in
+
+ align:start position:0%
+about a 10 micro Kelvin sensitivity in
+ 
+
+ align:start position:0%
+about a 10 micro Kelvin sensitivity in
+this lock-in thermography technique
+
+ align:start position:0%
+this lock-in thermography technique
+ 
+
+ align:start position:0%
+this lock-in thermography technique
+which is very sensitive can measure
+
+ align:start position:0%
+which is very sensitive can measure
+ 
+
+ align:start position:0%
+which is very sensitive can measure
+under low forward bias conditions and
+
+ align:start position:0%
+under low forward bias conditions and
+ 
+
+ align:start position:0%
+under low forward bias conditions and
+hence useful okay so that pretty much
+
+ align:start position:0%
+hence useful okay so that pretty much
+ 
+
+ align:start position:0%
+hence useful okay so that pretty much
+sums up lock-in thermography it is a
+
+ align:start position:0%
+sums up lock-in thermography it is a
+ 
+
+ align:start position:0%
+sums up lock-in thermography it is a
+difficult technique to wrap your brain
+
+ align:start position:0%
+difficult technique to wrap your brain
+ 
+
+ align:start position:0%
+difficult technique to wrap your brain
+around right so for those of you who got
+
+ align:start position:0%
+around right so for those of you who got
+ 
+
+ align:start position:0%
+around right so for those of you who got
+75% of it congratulations that was
+
+ align:start position:0%
+75% of it congratulations that was
+ 
+
+ align:start position:0%
+75% of it congratulations that was
+really really well done for those who
+
+ align:start position:0%
+really really well done for those who
+ 
+
+ align:start position:0%
+really really well done for those who
+got about 25 percent of my explanations
+
+ align:start position:0%
+got about 25 percent of my explanations
+ 
+
+ align:start position:0%
+got about 25 percent of my explanations
+today don't worry you're not you're not
+
+ align:start position:0%
+today don't worry you're not you're not
+ 
+
+ align:start position:0%
+today don't worry you're not you're not
+alone it just takes a lot of thinking it
+
+ align:start position:0%
+alone it just takes a lot of thinking it
+ 
+
+ align:start position:0%
+alone it just takes a lot of thinking it
+through exactly okay whereas the current
+
+ align:start position:0%
+through exactly okay whereas the current
+ 
+
+ align:start position:0%
+through exactly okay whereas the current
+flowing as a function bias condition
+
+ align:start position:0%
+flowing as a function bias condition
+ 
+
+ align:start position:0%
+flowing as a function bias condition
+what does that do to my V curve and then
+
+ align:start position:0%
+what does that do to my V curve and then
+ 
+
+ align:start position:0%
+what does that do to my V curve and then
+what is it doing this two dimensional
+
+ align:start position:0%
+what is it doing this two dimensional
+ 
+
+ align:start position:0%
+what is it doing this two dimensional
+regime when i measuring heat output it's
+
+ align:start position:0%
+regime when i measuring heat output it's
+ 
+
+ align:start position:0%
+regime when i measuring heat output it's
+a very complicated thing thankfully
+
+ align:start position:0%
+a very complicated thing thankfully
+ 
+
+ align:start position:0%
+a very complicated thing thankfully
+there is an entire book on lock-in
+
+ align:start position:0%
+there is an entire book on lock-in
+ 
+
+ align:start position:0%
+there is an entire book on lock-in
+thermography written by Othman baikin
+
+ align:start position:0%
+thermography written by Othman baikin
+ 
+
+ align:start position:0%
+thermography written by Othman baikin
+Stein I gave to you today a paper one of
+
+ align:start position:0%
+Stein I gave to you today a paper one of
+ 
+
+ align:start position:0%
+Stein I gave to you today a paper one of
+the papers that I distributed today
+
+ align:start position:0%
+the papers that I distributed today
+ 
+
+ align:start position:0%
+the papers that I distributed today
+the one that has the PSS a written on it
+
+ align:start position:0%
+the one that has the PSS a written on it
+ 
+
+ align:start position:0%
+the one that has the PSS a written on it
+this one that paper is by Othman
+
+ align:start position:0%
+this one that paper is by Othman
+ 
+
+ align:start position:0%
+this one that paper is by Othman
+brightenstein
+
+ align:start position:0%
+brightenstein
+ 
+
+ align:start position:0%
+brightenstein
+from the Max Planck Institute of
+
+ align:start position:0%
+from the Max Planck Institute of
+ 
+
+ align:start position:0%
+from the Max Planck Institute of
+microstructure physics in Halle Germany
+
+ align:start position:0%
+microstructure physics in Halle Germany
+ 
+
+ align:start position:0%
+microstructure physics in Halle Germany
+about two and a half hours south of
+
+ align:start position:0%
+about two and a half hours south of
+ 
+
+ align:start position:0%
+about two and a half hours south of
+Berlin and this describes in more detail
+
+ align:start position:0%
+Berlin and this describes in more detail
+ 
+
+ align:start position:0%
+Berlin and this describes in more detail
+that which I attempted to get across in
+
+ align:start position:0%
+that which I attempted to get across in
+ 
+
+ align:start position:0%
+that which I attempted to get across in
+class today he with Martin Langenkamp
+
+ align:start position:0%
+class today he with Martin Langenkamp
+ 
+
+ align:start position:0%
+class today he with Martin Langenkamp
+have also written the book on lock-in
+
+ align:start position:0%
+have also written the book on lock-in
+ 
+
+ align:start position:0%
+have also written the book on lock-in
+thermography so if you're more
+
+ align:start position:0%
+thermography so if you're more
+ 
+
+ align:start position:0%
+thermography so if you're more
+interested more information that's where
+
+ align:start position:0%
+interested more information that's where
+ 
+
+ align:start position:0%
+interested more information that's where
+to go in your handout set today we also
+
+ align:start position:0%
+to go in your handout set today we also
+ 
+
+ align:start position:0%
+to go in your handout set today we also
+have a classic paper on series
+
+ align:start position:0%
+have a classic paper on series
+ 
+
+ align:start position:0%
+have a classic paper on series
+resistance effects of solar cell
+
+ align:start position:0%
+resistance effects of solar cell
+ 
+
+ align:start position:0%
+resistance effects of solar cell
+measurements this one is from 63 yes
+
+ align:start position:0%
+measurements this one is from 63 yes
+ 
+
+ align:start position:0%
+measurements this one is from 63 yes
+1963 classic paper worth the read if
+
+ align:start position:0%
+1963 classic paper worth the read if
+ 
+
+ align:start position:0%
+1963 classic paper worth the read if
+you're in that regime making devices
+
+ align:start position:0%
+you're in that regime making devices
+ 
+
+ align:start position:0%
+you're in that regime making devices
+that are series is series resistance
+
+ align:start position:0%
+that are series is series resistance
+ 
+
+ align:start position:0%
+that are series is series resistance
+limited it's more optional reading for
+
+ align:start position:0%
+limited it's more optional reading for
+ 
+
+ align:start position:0%
+limited it's more optional reading for
+folks and let's venture forward folks
+
+ align:start position:0%
+folks and let's venture forward folks
+ 
+
+ align:start position:0%
+folks and let's venture forward folks
+who did these scanning albick techniques
+
+ align:start position:0%
+who did these scanning albick techniques
+ 
+
+ align:start position:0%
+who did these scanning albick techniques
+for a while really found value in
+
+ align:start position:0%
+for a while really found value in
+ 
+
+ align:start position:0%
+for a while really found value in
+measuring as a function of spatial
+
+ align:start position:0%
+measuring as a function of spatial
+ 
+
+ align:start position:0%
+measuring as a function of spatial
+spatial resolve manner down to a micron
+
+ align:start position:0%
+spatial resolve manner down to a micron
+ 
+
+ align:start position:0%
+spatial resolve manner down to a micron
+in spatial resolution the electric
+
+ align:start position:0%
+in spatial resolution the electric
+ 
+
+ align:start position:0%
+in spatial resolution the electric
+electrical output of a solar cell device
+
+ align:start position:0%
+electrical output of a solar cell device
+ 
+
+ align:start position:0%
+electrical output of a solar cell device
+and then they thought to themselves well
+
+ align:start position:0%
+and then they thought to themselves well
+ 
+
+ align:start position:0%
+and then they thought to themselves well
+goodness if we measure with one micron
+
+ align:start position:0%
+goodness if we measure with one micron
+ 
+
+ align:start position:0%
+goodness if we measure with one micron
+spot size it's going to take us a week
+
+ align:start position:0%
+spot size it's going to take us a week
+ 
+
+ align:start position:0%
+spot size it's going to take us a week
+to get a measurement across the full
+
+ align:start position:0%
+to get a measurement across the full
+ 
+
+ align:start position:0%
+to get a measurement across the full
+area solar cell device if not longer and
+
+ align:start position:0%
+area solar cell device if not longer and
+ 
+
+ align:start position:0%
+area solar cell device if not longer and
+if we measure say with the 200 nano
+
+ align:start position:0%
+if we measure say with the 200 nano
+ 
+
+ align:start position:0%
+if we measure say with the 200 nano
+meter spot size using some sort of x-ray
+
+ align:start position:0%
+meter spot size using some sort of x-ray
+ 
+
+ align:start position:0%
+meter spot size using some sort of x-ray
+technique and we accumulated for say two
+
+ align:start position:0%
+technique and we accumulated for say two
+ 
+
+ align:start position:0%
+technique and we accumulated for say two
+seconds of point it can take 10,000
+
+ align:start position:0%
+seconds of point it can take 10,000
+ 
+
+ align:start position:0%
+seconds of point it can take 10,000
+years to map out a full sized solar cell
+
+ align:start position:0%
+years to map out a full sized solar cell
+ 
+
+ align:start position:0%
+years to map out a full sized solar cell
+device literally do the math and they
+
+ align:start position:0%
+device literally do the math and they
+ 
+
+ align:start position:0%
+device literally do the math and they
+said is there an easier way for us to
+
+ align:start position:0%
+said is there an easier way for us to
+ 
+
+ align:start position:0%
+said is there an easier way for us to
+acquire information that does not rely
+
+ align:start position:0%
+acquire information that does not rely
+ 
+
+ align:start position:0%
+acquire information that does not rely
+on scanning on point by point step by
+
+ align:start position:0%
+on scanning on point by point step by
+ 
+
+ align:start position:0%
+on scanning on point by point step by
+step measurements and they thought about
+
+ align:start position:0%
+step measurements and they thought about
+ 
+
+ align:start position:0%
+step measurements and they thought about
+it long and hard and they said well gee
+
+ align:start position:0%
+it long and hard and they said well gee
+ 
+
+ align:start position:0%
+it long and hard and they said well gee
+these these new handheld digital cameras
+
+ align:start position:0%
+these these new handheld digital cameras
+ 
+
+ align:start position:0%
+these these new handheld digital cameras
+coming out in the market are pretty cool
+
+ align:start position:0%
+coming out in the market are pretty cool
+ 
+
+ align:start position:0%
+coming out in the market are pretty cool
+what technology do they rely on oh it's
+
+ align:start position:0%
+what technology do they rely on oh it's
+ 
+
+ align:start position:0%
+what technology do they rely on oh it's
+a CCD charge couple display that
+
+ align:start position:0%
+a CCD charge couple display that
+ 
+
+ align:start position:0%
+a CCD charge couple display that
+visualizes our images over a large area
+
+ align:start position:0%
+visualizes our images over a large area
+ 
+
+ align:start position:0%
+visualizes our images over a large area
+the the output of a device and that's
+
+ align:start position:0%
+the the output of a device and that's
+ 
+
+ align:start position:0%
+the the output of a device and that's
+exactly how the lock-in thermography
+
+ align:start position:0%
+exactly how the lock-in thermography
+ 
+
+ align:start position:0%
+exactly how the lock-in thermography
+techniques were developed here with this
+
+ align:start position:0%
+techniques were developed here with this
+ 
+
+ align:start position:0%
+techniques were developed here with this
+this imaging camera in that case an
+
+ align:start position:0%
+this imaging camera in that case an
+ 
+
+ align:start position:0%
+this imaging camera in that case an
+indium antimonide CCD and they said well
+
+ align:start position:0%
+indium antimonide CCD and they said well
+ 
+
+ align:start position:0%
+indium antimonide CCD and they said well
+what other wavelengths admit what in
+
+ align:start position:0%
+what other wavelengths admit what in
+ 
+
+ align:start position:0%
+what other wavelengths admit what in
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+the wavelength does a solar cell emit we
+
+ align:start position:0%
+the wavelength does a solar cell emit we
+ 
+
+ align:start position:0%
+the wavelength does a solar cell emit we
+know that it emits heat right and heat
+
+ align:start position:0%
+know that it emits heat right and heat
+ 
+
+ align:start position:0%
+know that it emits heat right and heat
+is typically in the three to five micron
+
+ align:start position:0%
+is typically in the three to five micron
+ 
+
+ align:start position:0%
+is typically in the three to five micron
+wavelength regime maybe even as high as
+
+ align:start position:0%
+wavelength regime maybe even as high as
+ 
+
+ align:start position:0%
+wavelength regime maybe even as high as
+10 microns depending on what temperature
+
+ align:start position:0%
+10 microns depending on what temperature
+ 
+
+ align:start position:0%
+10 microns depending on what temperature
+and we know that as well we can have
+
+ align:start position:0%
+and we know that as well we can have
+ 
+
+ align:start position:0%
+and we know that as well we can have
+band-to-band emission inside of a solar
+
+ align:start position:0%
+band-to-band emission inside of a solar
+ 
+
+ align:start position:0%
+band-to-band emission inside of a solar
+cell that would emit around the bandgap
+
+ align:start position:0%
+cell that would emit around the bandgap
+ 
+
+ align:start position:0%
+cell that would emit around the bandgap
+energy so let's set up a camera to image
+
+ align:start position:0%
+energy so let's set up a camera to image
+ 
+
+ align:start position:0%
+energy so let's set up a camera to image
+the band to band recombination in
+
+ align:start position:0%
+the band to band recombination in
+ 
+
+ align:start position:0%
+the band to band recombination in
+intensity or the band to band
+
+ align:start position:0%
+intensity or the band to band
+ 
+
+ align:start position:0%
+intensity or the band to band
+illumination intensity and that's what
+
+ align:start position:0%
+illumination intensity and that's what
+ 
+
+ align:start position:0%
+illumination intensity and that's what
+this paper is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is wavelength this is intensity
+
+ align:start position:0%
+this is wavelength this is intensity
+ 
+
+ align:start position:0%
+this is wavelength this is intensity
+this is the emission spectrum of a solar
+
+ align:start position:0%
+this is the emission spectrum of a solar
+ 
+
+ align:start position:0%
+this is the emission spectrum of a solar
+cell so if you were to measure what
+
+ align:start position:0%
+cell so if you were to measure what
+ 
+
+ align:start position:0%
+cell so if you were to measure what
+colors what color light does a solar
+
+ align:start position:0%
+colors what color light does a solar
+ 
+
+ align:start position:0%
+colors what color light does a solar
+cell emit after you pump current into it
+
+ align:start position:0%
+cell emit after you pump current into it
+ 
+
+ align:start position:0%
+cell emit after you pump current into it
+this isn't more or less a spectrum so we
+
+ align:start position:0%
+this isn't more or less a spectrum so we
+ 
+
+ align:start position:0%
+this isn't more or less a spectrum so we
+have the the thermal radiation shown
+
+ align:start position:0%
+have the the thermal radiation shown
+ 
+
+ align:start position:0%
+have the the thermal radiation shown
+over here so this is longer wavelength
+
+ align:start position:0%
+over here so this is longer wavelength
+ 
+
+ align:start position:0%
+over here so this is longer wavelength
+light that's the heat that it gives off
+
+ align:start position:0%
+light that's the heat that it gives off
+ 
+
+ align:start position:0%
+light that's the heat that it gives off
+that's what indicates current flow
+
+ align:start position:0%
+that's what indicates current flow
+ 
+
+ align:start position:0%
+that's what indicates current flow
+inside of the device there's the band to
+
+ align:start position:0%
+inside of the device there's the band to
+ 
+
+ align:start position:0%
+inside of the device there's the band to
+band luminescence right here and we'll
+
+ align:start position:0%
+band luminescence right here and we'll
+ 
+
+ align:start position:0%
+band luminescence right here and we'll
+neglect the other two for now those are
+
+ align:start position:0%
+neglect the other two for now those are
+ 
+
+ align:start position:0%
+neglect the other two for now those are
+more advanced constants but the bantha
+
+ align:start position:0%
+more advanced constants but the bantha
+ 
+
+ align:start position:0%
+more advanced constants but the bantha
+band luminescence is essentially just a
+
+ align:start position:0%
+band luminescence is essentially just a
+ 
+
+ align:start position:0%
+band luminescence is essentially just a
+recombination of a carrier from the
+
+ align:start position:0%
+recombination of a carrier from the
+ 
+
+ align:start position:0%
+recombination of a carrier from the
+conduction band to the valence band
+
+ align:start position:0%
+conduction band to the valence band
+ 
+
+ align:start position:0%
+conduction band to the valence band
+right recombination current very
+
+ align:start position:0%
+right recombination current very
+ 
+
+ align:start position:0%
+right recombination current very
+straightforward and the recombination
+
+ align:start position:0%
+straightforward and the recombination
+ 
+
+ align:start position:0%
+straightforward and the recombination
+intensity is inversely proportional to
+
+ align:start position:0%
+intensity is inversely proportional to
+ 
+
+ align:start position:0%
+intensity is inversely proportional to
+the minority carrier lifetime why is
+
+ align:start position:0%
+the minority carrier lifetime why is
+ 
+
+ align:start position:0%
+the minority carrier lifetime why is
+that this was that that quote that I
+
+ align:start position:0%
+that this was that that quote that I
+ 
+
+ align:start position:0%
+that this was that that quote that I
+remember who attended a light one of
+
+ align:start position:0%
+remember who attended a light one of
+ 
+
+ align:start position:0%
+remember who attended a light one of
+itches talk he was saying it's
+
+ align:start position:0%
+itches talk he was saying it's
+ 
+
+ align:start position:0%
+itches talk he was saying it's
+completely counterintuitive
+
+ align:start position:0%
+completely counterintuitive
+ 
+
+ align:start position:0%
+completely counterintuitive
+do you remember specifically what he was
+
+ align:start position:0%
+do you remember specifically what he was
+ 
+
+ align:start position:0%
+do you remember specifically what he was
+referring to in this me show you an
+
+ align:start position:0%
+referring to in this me show you an
+ 
+
+ align:start position:0%
+referring to in this me show you an
+image here hmm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly yeah so so why is why what what
+
+ align:start position:0%
+exactly yeah so so why is why what what
+ 
+
+ align:start position:0%
+exactly yeah so so why is why what what
+is going on here we have our towel 1
+
+ align:start position:0%
+is going on here we have our towel 1
+ 
+
+ align:start position:0%
+is going on here we have our towel 1
+over tau effective R 1 over our lifetime
+
+ align:start position:0%
+over tau effective R 1 over our lifetime
+ 
+
+ align:start position:0%
+over tau effective R 1 over our lifetime
+what we're measuring this is our
+
+ align:start position:0%
+what we're measuring this is our
+ 
+
+ align:start position:0%
+what we're measuring this is our
+effective lifetime what we're measuring
+
+ align:start position:0%
+effective lifetime what we're measuring
+ 
+
+ align:start position:0%
+effective lifetime what we're measuring
+and we have 1 over tau let's call it non
+
+ align:start position:0%
+and we have 1 over tau let's call it non
+ 
+
+ align:start position:0%
+and we have 1 over tau let's call it non
+radiative so we have non radiative
+
+ align:start position:0%
+radiative so we have non radiative
+ 
+
+ align:start position:0%
+radiative so we have non radiative
+recombination mechanisms this comprises
+
+ align:start position:0%
+recombination mechanisms this comprises
+ 
+
+ align:start position:0%
+recombination mechanisms this comprises
+shockley-read-hall recombination no J
+
+ align:start position:0%
+shockley-read-hall recombination no J
+ 
+
+ align:start position:0%
+shockley-read-hall recombination no J
+recombination a bunch of different
+
+ align:start position:0%
+recombination a bunch of different
+ 
+
+ align:start position:0%
+recombination a bunch of different
+recombination mechanisms and then we
+
+ align:start position:0%
+recombination mechanisms and then we
+ 
+
+ align:start position:0%
+recombination mechanisms and then we
+have 1 over tau radiative which is
+
+ align:start position:0%
+have 1 over tau radiative which is
+ 
+
+ align:start position:0%
+have 1 over tau radiative which is
+essentially this recombination mechanism
+
+ align:start position:0%
+essentially this recombination mechanism
+ 
+
+ align:start position:0%
+essentially this recombination mechanism
+shown right here which is just the band
+
+ align:start position:0%
+shown right here which is just the band
+ 
+
+ align:start position:0%
+shown right here which is just the band
+to band recombination so if you have
+
+ align:start position:0%
+to band recombination so if you have
+ 
+
+ align:start position:0%
+to band recombination so if you have
+defects around that will lower the
+
+ align:start position:0%
+defects around that will lower the
+ 
+
+ align:start position:0%
+defects around that will lower the
+lifetime the non radiative lifetime if
+
+ align:start position:0%
+lifetime the non radiative lifetime if
+ 
+
+ align:start position:0%
+lifetime the non radiative lifetime if
+you have tons and tons of defects the
+
+ align:start position:0%
+you have tons and tons of defects the
+ 
+
+ align:start position:0%
+you have tons and tons of defects the
+carriers will most likely recombine
+
+ align:start position:0%
+carriers will most likely recombine
+ 
+
+ align:start position:0%
+carriers will most likely recombine
+through the defects and not through the
+
+ align:start position:0%
+through the defects and not through the
+ 
+
+ align:start position:0%
+through the defects and not through the
+bantha band they will only recombine
+
+ align:start position:0%
+bantha band they will only recombine
+ 
+
+ align:start position:0%
+bantha band they will only recombine
+with band to band if there is nothing no
+
+ align:start position:0%
+with band to band if there is nothing no
+ 
+
+ align:start position:0%
+with band to band if there is nothing no
+other recombination path left available
+
+ align:start position:0%
+other recombination path left available
+ 
+
+ align:start position:0%
+other recombination path left available
+to them right it's a question of
+
+ align:start position:0%
+to them right it's a question of
+ 
+
+ align:start position:0%
+to them right it's a question of
+probability so if this is really really
+
+ align:start position:0%
+probability so if this is really really
+ 
+
+ align:start position:0%
+probability so if this is really really
+short non radiative recombination
+
+ align:start position:0%
+short non radiative recombination
+ 
+
+ align:start position:0%
+short non radiative recombination
+lifetime is really really short because
+
+ align:start position:0%
+lifetime is really really short because
+ 
+
+ align:start position:0%
+lifetime is really really short because
+the defect density is very very large so
+
+ align:start position:0%
+the defect density is very very large so
+ 
+
+ align:start position:0%
+the defect density is very very large so
+the lifetime due to non radiative
+
+ align:start position:0%
+the lifetime due to non radiative
+ 
+
+ align:start position:0%
+the lifetime due to non radiative
+recombination mechanisms very short then
+
+ align:start position:0%
+recombination mechanisms very short then
+ 
+
+ align:start position:0%
+recombination mechanisms very short then
+the tau effective is also going to be
+
+ align:start position:0%
+the tau effective is also going to be
+ 
+
+ align:start position:0%
+the tau effective is also going to be
+very short and very few carriers are
+
+ align:start position:0%
+very short and very few carriers are
+ 
+
+ align:start position:0%
+very short and very few carriers are
+going to recombine radiatively
+
+ align:start position:0%
+going to recombine radiatively
+ 
+
+ align:start position:0%
+going to recombine radiatively
+conversely if we have a very clean
+
+ align:start position:0%
+conversely if we have a very clean
+ 
+
+ align:start position:0%
+conversely if we have a very clean
+material virtually defect free this non
+
+ align:start position:0%
+material virtually defect free this non
+ 
+
+ align:start position:0%
+material virtually defect free this non
+radiative lifetime is then going to be
+
+ align:start position:0%
+radiative lifetime is then going to be
+ 
+
+ align:start position:0%
+radiative lifetime is then going to be
+out the roof and now we're going to be
+
+ align:start position:0%
+out the roof and now we're going to be
+ 
+
+ align:start position:0%
+out the roof and now we're going to be
+limited instead by the radiative
+
+ align:start position:0%
+limited instead by the radiative
+ 
+
+ align:start position:0%
+limited instead by the radiative
+lifetime and so tau effective will be
+
+ align:start position:0%
+lifetime and so tau effective will be
+ 
+
+ align:start position:0%
+lifetime and so tau effective will be
+more similar to rate is it now an
+
+ align:start position:0%
+more similar to rate is it now an
+ 
+
+ align:start position:0%
+more similar to rate is it now an
+interesting thing happens when you have
+
+ align:start position:0%
+interesting thing happens when you have
+ 
+
+ align:start position:0%
+interesting thing happens when you have
+a radiative recombination event as the
+
+ align:start position:0%
+a radiative recombination event as the
+ 
+
+ align:start position:0%
+a radiative recombination event as the
+name would suggest it emits light and
+
+ align:start position:0%
+name would suggest it emits light and
+ 
+
+ align:start position:0%
+name would suggest it emits light and
+that light can be detected by a CCD
+
+ align:start position:0%
+that light can be detected by a CCD
+ 
+
+ align:start position:0%
+that light can be detected by a CCD
+camera nearby so what you Boopsie what
+
+ align:start position:0%
+camera nearby so what you Boopsie what
+ 
+
+ align:start position:0%
+camera nearby so what you Boopsie what
+you have we go what you have right here
+
+ align:start position:0%
+you have we go what you have right here
+ 
+
+ align:start position:0%
+you have we go what you have right here
+is a solar cell device that is being
+
+ align:start position:0%
+is a solar cell device that is being
+ 
+
+ align:start position:0%
+is a solar cell device that is being
+biased so current is flowing into the
+
+ align:start position:0%
+biased so current is flowing into the
+ 
+
+ align:start position:0%
+biased so current is flowing into the
+device and now the the map what you're
+
+ align:start position:0%
+device and now the the map what you're
+ 
+
+ align:start position:0%
+device and now the the map what you're
+seeing is indicative of radiative
+
+ align:start position:0%
+seeing is indicative of radiative
+ 
+
+ align:start position:0%
+seeing is indicative of radiative
+recombination why because nearby the
+
+ align:start position:0%
+recombination why because nearby the
+ 
+
+ align:start position:0%
+recombination why because nearby the
+cell it's essentially very similar
+
+ align:start position:0%
+cell it's essentially very similar
+ 
+
+ align:start position:0%
+cell it's essentially very similar
+mechanism or similar setup to what we
+
+ align:start position:0%
+mechanism or similar setup to what we
+ 
+
+ align:start position:0%
+mechanism or similar setup to what we
+saw right here where we had bias voltage
+
+ align:start position:0%
+saw right here where we had bias voltage
+ 
+
+ align:start position:0%
+saw right here where we had bias voltage
+across the
+
+ align:start position:0%
+across the
+ 
+
+ align:start position:0%
+across the
+and imaging not with an infrared camera
+
+ align:start position:0%
+and imaging not with an infrared camera
+ 
+
+ align:start position:0%
+and imaging not with an infrared camera
+but now with a camera matched to the
+
+ align:start position:0%
+but now with a camera matched to the
+ 
+
+ align:start position:0%
+but now with a camera matched to the
+bandgap energy this could be in indium
+
+ align:start position:0%
+bandgap energy this could be in indium
+ 
+
+ align:start position:0%
+bandgap energy this could be in indium
+gallium arsenide camera or say a silicon
+
+ align:start position:0%
+gallium arsenide camera or say a silicon
+ 
+
+ align:start position:0%
+gallium arsenide camera or say a silicon
+camera depending on the precise bang gap
+
+ align:start position:0%
+camera depending on the precise bang gap
+ 
+
+ align:start position:0%
+camera depending on the precise bang gap
+and your imaging the radiative
+
+ align:start position:0%
+and your imaging the radiative
+ 
+
+ align:start position:0%
+and your imaging the radiative
+recombination as a function of XY
+
+ align:start position:0%
+recombination as a function of XY
+ 
+
+ align:start position:0%
+recombination as a function of XY
+position across your wafer so these
+
+ align:start position:0%
+position across your wafer so these
+ 
+
+ align:start position:0%
+position across your wafer so these
+darker regions here on the bottom and on
+
+ align:start position:0%
+darker regions here on the bottom and on
+ 
+
+ align:start position:0%
+darker regions here on the bottom and on
+the right sorry left the other right
+
+ align:start position:0%
+the right sorry left the other right
+ 
+
+ align:start position:0%
+the right sorry left the other right
+they indicate regions of lower minority
+
+ align:start position:0%
+they indicate regions of lower minority
+ 
+
+ align:start position:0%
+they indicate regions of lower minority
+carrier diffusion length why because
+
+ align:start position:0%
+carrier diffusion length why because
+ 
+
+ align:start position:0%
+carrier diffusion length why because
+there's less radiative recombination
+
+ align:start position:0%
+there's less radiative recombination
+ 
+
+ align:start position:0%
+there's less radiative recombination
+because this term in those regions is
+
+ align:start position:0%
+because this term in those regions is
+ 
+
+ align:start position:0%
+because this term in those regions is
+very very small so that there's not much
+
+ align:start position:0%
+very very small so that there's not much
+ 
+
+ align:start position:0%
+very very small so that there's not much
+radiative recombination going on whereas
+
+ align:start position:0%
+radiative recombination going on whereas
+ 
+
+ align:start position:0%
+radiative recombination going on whereas
+these other regions here that if you're
+
+ align:start position:0%
+these other regions here that if you're
+ 
+
+ align:start position:0%
+these other regions here that if you're
+brighter have a lot more radiative
+
+ align:start position:0%
+brighter have a lot more radiative
+ 
+
+ align:start position:0%
+brighter have a lot more radiative
+recombination going on any questions
+
+ align:start position:0%
+recombination going on any questions
+ 
+
+ align:start position:0%
+recombination going on any questions
+about that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+getting hot days
+
+ align:start position:0%
+getting hot days
+ 
+
+ align:start position:0%
+getting hot days
+sure so the question pertains to photon
+
+ align:start position:0%
+sure so the question pertains to photon
+ 
+
+ align:start position:0%
+sure so the question pertains to photon
+recycling and how many photons that are
+
+ align:start position:0%
+recycling and how many photons that are
+ 
+
+ align:start position:0%
+recycling and how many photons that are
+radiatively emitted get reabsorbed by
+
+ align:start position:0%
+radiatively emitted get reabsorbed by
+ 
+
+ align:start position:0%
+radiatively emitted get reabsorbed by
+the material that would depend on the
+
+ align:start position:0%
+the material that would depend on the
+ 
+
+ align:start position:0%
+the material that would depend on the
+optical path length inside of the
+
+ align:start position:0%
+optical path length inside of the
+ 
+
+ align:start position:0%
+optical path length inside of the
+material of carriers being generated in
+
+ align:start position:0%
+material of carriers being generated in
+ 
+
+ align:start position:0%
+material of carriers being generated in
+the material and you can assume that
+
+ align:start position:0%
+the material and you can assume that
+ 
+
+ align:start position:0%
+the material and you can assume that
+carrier generation is fairly isotropic
+
+ align:start position:0%
+carrier generation is fairly isotropic
+ 
+
+ align:start position:0%
+carrier generation is fairly isotropic
+in nature that there's not any preferred
+
+ align:start position:0%
+in nature that there's not any preferred
+ 
+
+ align:start position:0%
+in nature that there's not any preferred
+direction unless you have a dye molecule
+
+ align:start position:0%
+direction unless you have a dye molecule
+ 
+
+ align:start position:0%
+direction unless you have a dye molecule
+that's designed in a certain way to emit
+
+ align:start position:0%
+that's designed in a certain way to emit
+ 
+
+ align:start position:0%
+that's designed in a certain way to emit
+light in a certain orientation so you
+
+ align:start position:0%
+light in a certain orientation so you
+ 
+
+ align:start position:0%
+light in a certain orientation so you
+can assume that the carrier mission in
+
+ align:start position:0%
+can assume that the carrier mission in
+ 
+
+ align:start position:0%
+can assume that the carrier mission in
+most materials is isotropic in nature
+
+ align:start position:0%
+most materials is isotropic in nature
+ 
+
+ align:start position:0%
+most materials is isotropic in nature
+and then it's just a question of ray
+
+ align:start position:0%
+and then it's just a question of ray
+ 
+
+ align:start position:0%
+and then it's just a question of ray
+tracing to figure out what the optical
+
+ align:start position:0%
+tracing to figure out what the optical
+ 
+
+ align:start position:0%
+tracing to figure out what the optical
+path length is compare that to the
+
+ align:start position:0%
+path length is compare that to the
+ 
+
+ align:start position:0%
+path length is compare that to the
+optical absorption coefficients in the
+
+ align:start position:0%
+optical absorption coefficients in the
+ 
+
+ align:start position:0%
+optical absorption coefficients in the
+material and you'll get your answer what
+
+ align:start position:0%
+material and you'll get your answer what
+ 
+
+ align:start position:0%
+material and you'll get your answer what
+fraction of light gets reabsorbed all
+
+ align:start position:0%
+fraction of light gets reabsorbed all
+ 
+
+ align:start position:0%
+fraction of light gets reabsorbed all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+I can sense where we're reaching
+
+ align:start position:0%
+I can sense where we're reaching
+ 
+
+ align:start position:0%
+I can sense where we're reaching
+threshold here in terms of new
+
+ align:start position:0%
+threshold here in terms of new
+ 
+
+ align:start position:0%
+threshold here in terms of new
+information gathered I'm just going to
+
+ align:start position:0%
+information gathered I'm just going to
+ 
+
+ align:start position:0%
+information gathered I'm just going to
+briefly go over the sun's vo see at the
+
+ align:start position:0%
+briefly go over the sun's vo see at the
+ 
+
+ align:start position:0%
+briefly go over the sun's vo see at the
+very end and the sun's vo see technique
+
+ align:start position:0%
+very end and the sun's vo see technique
+ 
+
+ align:start position:0%
+very end and the sun's vo see technique
+is useful as we saw during class because
+
+ align:start position:0%
+is useful as we saw during class because
+ 
+
+ align:start position:0%
+is useful as we saw during class because
+as this paper right here by Ron Sinton
+
+ align:start position:0%
+as this paper right here by Ron Sinton
+ 
+
+ align:start position:0%
+as this paper right here by Ron Sinton
+and dice Cuevas this one I know you
+
+ align:start position:0%
+and dice Cuevas this one I know you
+ 
+
+ align:start position:0%
+and dice Cuevas this one I know you
+definitely have this one this paper
+
+ align:start position:0%
+definitely have this one this paper
+ 
+
+ align:start position:0%
+definitely have this one this paper
+essentially describes the functioning of
+
+ align:start position:0%
+essentially describes the functioning of
+ 
+
+ align:start position:0%
+essentially describes the functioning of
+the technique on page number two on the
+
+ align:start position:0%
+the technique on page number two on the
+ 
+
+ align:start position:0%
+the technique on page number two on the
+upper left-hand side so figure two we
+
+ align:start position:0%
+upper left-hand side so figure two we
+ 
+
+ align:start position:0%
+upper left-hand side so figure two we
+essentially have the figure that was
+
+ align:start position:0%
+essentially have the figure that was
+ 
+
+ align:start position:0%
+essentially have the figure that was
+determined on the screen during the
+
+ align:start position:0%
+determined on the screen during the
+ 
+
+ align:start position:0%
+determined on the screen during the
+measurements so for those of you are
+
+ align:start position:0%
+measurements so for those of you are
+ 
+
+ align:start position:0%
+measurements so for those of you are
+close enough to the mana to actually
+
+ align:start position:0%
+close enough to the mana to actually
+ 
+
+ align:start position:0%
+close enough to the mana to actually
+watch the the measurement being taken
+
+ align:start position:0%
+watch the the measurement being taken
+ 
+
+ align:start position:0%
+watch the the measurement being taken
+the sun's BOC you saw the light
+
+ align:start position:0%
+the sun's BOC you saw the light
+ 
+
+ align:start position:0%
+the sun's BOC you saw the light
+intensity decaying exponentially right
+
+ align:start position:0%
+intensity decaying exponentially right
+ 
+
+ align:start position:0%
+intensity decaying exponentially right
+so the light intensity was a flash ball
+
+ align:start position:0%
+so the light intensity was a flash ball
+ 
+
+ align:start position:0%
+so the light intensity was a flash ball
+poof and decay exponentially the open
+
+ align:start position:0%
+poof and decay exponentially the open
+ 
+
+ align:start position:0%
+poof and decay exponentially the open
+circuit voltage measured by the device
+
+ align:start position:0%
+circuit voltage measured by the device
+ 
+
+ align:start position:0%
+circuit voltage measured by the device
+so you had this solar cell device
+
+ align:start position:0%
+so you had this solar cell device
+ 
+
+ align:start position:0%
+so you had this solar cell device
+sitting on the platen with a little
+
+ align:start position:0%
+sitting on the platen with a little
+ 
+
+ align:start position:0%
+sitting on the platen with a little
+probe coming in and a 50 mega ohm
+
+ align:start position:0%
+probe coming in and a 50 mega ohm
+ 
+
+ align:start position:0%
+probe coming in and a 50 mega ohm
+resistor connected in series very little
+
+ align:start position:0%
+resistor connected in series very little
+ 
+
+ align:start position:0%
+resistor connected in series very little
+current flowing through that external
+
+ align:start position:0%
+current flowing through that external
+ 
+
+ align:start position:0%
+current flowing through that external
+circuit right but it's measuring the
+
+ align:start position:0%
+circuit right but it's measuring the
+ 
+
+ align:start position:0%
+circuit right but it's measuring the
+voltage so it's essentially maintaining
+
+ align:start position:0%
+voltage so it's essentially maintaining
+ 
+
+ align:start position:0%
+voltage so it's essentially maintaining
+the solar cell in open circuit voltage
+
+ align:start position:0%
+the solar cell in open circuit voltage
+ 
+
+ align:start position:0%
+the solar cell in open circuit voltage
+conditions while the flash is decaying
+
+ align:start position:0%
+conditions while the flash is decaying
+ 
+
+ align:start position:0%
+conditions while the flash is decaying
+and it's measuring the open circuit
+
+ align:start position:0%
+and it's measuring the open circuit
+ 
+
+ align:start position:0%
+and it's measuring the open circuit
+voltage across that device at each
+
+ align:start position:0%
+voltage across that device at each
+ 
+
+ align:start position:0%
+voltage across that device at each
+illumination intensity as the pulse
+
+ align:start position:0%
+illumination intensity as the pulse
+ 
+
+ align:start position:0%
+illumination intensity as the pulse
+decays so you can see the timescale here
+
+ align:start position:0%
+decays so you can see the timescale here
+ 
+
+ align:start position:0%
+decays so you can see the timescale here
+as an eye order of a few tens of
+
+ align:start position:0%
+as an eye order of a few tens of
+ 
+
+ align:start position:0%
+as an eye order of a few tens of
+Ekans so very fast measurement the
+
+ align:start position:0%
+Ekans so very fast measurement the
+ 
+
+ align:start position:0%
+Ekans so very fast measurement the
+electronics response time has to be very
+
+ align:start position:0%
+electronics response time has to be very
+ 
+
+ align:start position:0%
+electronics response time has to be very
+fast that tells you what the RC time
+
+ align:start position:0%
+fast that tells you what the RC time
+ 
+
+ align:start position:0%
+fast that tells you what the RC time
+constant of the circuit is and the you
+
+ align:start position:0%
+constant of the circuit is and the you
+ 
+
+ align:start position:0%
+constant of the circuit is and the you
+can notice that the voltage the open
+
+ align:start position:0%
+can notice that the voltage the open
+ 
+
+ align:start position:0%
+can notice that the voltage the open
+circuit voltage decays linearly when the
+
+ align:start position:0%
+circuit voltage decays linearly when the
+ 
+
+ align:start position:0%
+circuit voltage decays linearly when the
+illumination intensity decays
+
+ align:start position:0%
+illumination intensity decays
+ 
+
+ align:start position:0%
+illumination intensity decays
+exponentially why is that there's a
+
+ align:start position:0%
+exponentially why is that there's a
+ 
+
+ align:start position:0%
+exponentially why is that there's a
+natural log yes this is what we what Joe
+
+ align:start position:0%
+natural log yes this is what we what Joe
+ 
+
+ align:start position:0%
+natural log yes this is what we what Joe
+showed to you yesterday or on Thursday
+
+ align:start position:0%
+showed to you yesterday or on Thursday
+ 
+
+ align:start position:0%
+showed to you yesterday or on Thursday
+in class is how the voltage output of a
+
+ align:start position:0%
+in class is how the voltage output of a
+ 
+
+ align:start position:0%
+in class is how the voltage output of a
+solar cell varies by illumination
+
+ align:start position:0%
+solar cell varies by illumination
+ 
+
+ align:start position:0%
+solar cell varies by illumination
+intensity so there's a logarithmic
+
+ align:start position:0%
+intensity so there's a logarithmic
+ 
+
+ align:start position:0%
+intensity so there's a logarithmic
+dependence there so that's why you take
+
+ align:start position:0%
+dependence there so that's why you take
+ 
+
+ align:start position:0%
+dependence there so that's why you take
+the log of the exponentially decaying
+
+ align:start position:0%
+the log of the exponentially decaying
+ 
+
+ align:start position:0%
+the log of the exponentially decaying
+light intensity and you obtain a linear
+
+ align:start position:0%
+light intensity and you obtain a linear
+ 
+
+ align:start position:0%
+light intensity and you obtain a linear
+relation that's the open circuit voltage
+
+ align:start position:0%
+relation that's the open circuit voltage
+ 
+
+ align:start position:0%
+relation that's the open circuit voltage
+decline as a function of time okay so we
+
+ align:start position:0%
+decline as a function of time okay so we
+ 
+
+ align:start position:0%
+decline as a function of time okay so we
+can derive an IV characteristic by
+
+ align:start position:0%
+can derive an IV characteristic by
+ 
+
+ align:start position:0%
+can derive an IV characteristic by
+translating that open circuit voltage
+
+ align:start position:0%
+translating that open circuit voltage
+ 
+
+ align:start position:0%
+translating that open circuit voltage
+into an implied bias voltage and knowing
+
+ align:start position:0%
+into an implied bias voltage and knowing
+ 
+
+ align:start position:0%
+into an implied bias voltage and knowing
+the short-circuit current density up
+
+ align:start position:0%
+the short-circuit current density up
+ 
+
+ align:start position:0%
+the short-circuit current density up
+front essentially by measuring it using
+
+ align:start position:0%
+front essentially by measuring it using
+ 
+
+ align:start position:0%
+front essentially by measuring it using
+an a by measuring the solar cell device
+
+ align:start position:0%
+an a by measuring the solar cell device
+ 
+
+ align:start position:0%
+an a by measuring the solar cell device
+in a solar simulator we can obtain the
+
+ align:start position:0%
+in a solar simulator we can obtain the
+ 
+
+ align:start position:0%
+in a solar simulator we can obtain the
+short-circuit current density we pin
+
+ align:start position:0%
+short-circuit current density we pin
+ 
+
+ align:start position:0%
+short-circuit current density we pin
+both curves up here at the measured
+
+ align:start position:0%
+both curves up here at the measured
+ 
+
+ align:start position:0%
+both curves up here at the measured
+short-circuit current density and then
+
+ align:start position:0%
+short-circuit current density and then
+ 
+
+ align:start position:0%
+short-circuit current density and then
+we plot both curves out the IV curve and
+
+ align:start position:0%
+we plot both curves out the IV curve and
+ 
+
+ align:start position:0%
+we plot both curves out the IV curve and
+the sun's v OC curve now the sun's V OC
+
+ align:start position:0%
+the sun's v OC curve now the sun's V OC
+ 
+
+ align:start position:0%
+the sun's v OC curve now the sun's V OC
+curve is Union is similar to the IV
+
+ align:start position:0%
+curve is Union is similar to the IV
+ 
+
+ align:start position:0%
+curve is Union is similar to the IV
+curve with only one difference there's
+
+ align:start position:0%
+curve with only one difference there's
+ 
+
+ align:start position:0%
+curve with only one difference there's
+no current or very very little current
+
+ align:start position:0%
+no current or very very little current
+ 
+
+ align:start position:0%
+no current or very very little current
+flowing through the external circuit
+
+ align:start position:0%
+flowing through the external circuit
+ 
+
+ align:start position:0%
+flowing through the external circuit
+which means there isn't any real power
+
+ align:start position:0%
+which means there isn't any real power
+ 
+
+ align:start position:0%
+which means there isn't any real power
+flowing through the external circuit
+
+ align:start position:0%
+flowing through the external circuit
+ 
+
+ align:start position:0%
+flowing through the external circuit
+which means if we go back to our
+
+ align:start position:0%
+which means if we go back to our
+ 
+
+ align:start position:0%
+which means if we go back to our
+expression right here if we have no
+
+ align:start position:0%
+expression right here if we have no
+ 
+
+ align:start position:0%
+expression right here if we have no
+current flowing through that J is equal
+
+ align:start position:0%
+current flowing through that J is equal
+ 
+
+ align:start position:0%
+current flowing through that J is equal
+to zero and now that R sub s term
+
+ align:start position:0%
+to zero and now that R sub s term
+ 
+
+ align:start position:0%
+to zero and now that R sub s term
+disappears so we've come up with a
+
+ align:start position:0%
+disappears so we've come up with a
+ 
+
+ align:start position:0%
+disappears so we've come up with a
+clever way to drop all of our R sub
+
+ align:start position:0%
+clever way to drop all of our R sub
+ 
+
+ align:start position:0%
+clever way to drop all of our R sub
+asses out of that expression and the
+
+ align:start position:0%
+asses out of that expression and the
+ 
+
+ align:start position:0%
+asses out of that expression and the
+only thing that matters essentially is
+
+ align:start position:0%
+only thing that matters essentially is
+ 
+
+ align:start position:0%
+only thing that matters essentially is
+is well some degree shunt but this is
+
+ align:start position:0%
+is well some degree shunt but this is
+ 
+
+ align:start position:0%
+is well some degree shunt but this is
+essentially the highest IV curve that
+
+ align:start position:0%
+essentially the highest IV curve that
+ 
+
+ align:start position:0%
+essentially the highest IV curve that
+one could possibly obtain in the absence
+
+ align:start position:0%
+one could possibly obtain in the absence
+ 
+
+ align:start position:0%
+one could possibly obtain in the absence
+of series resistance and that's what you
+
+ align:start position:0%
+of series resistance and that's what you
+ 
+
+ align:start position:0%
+of series resistance and that's what you
+see right here that's this Delta in
+
+ align:start position:0%
+see right here that's this Delta in
+ 
+
+ align:start position:0%
+see right here that's this Delta in
+between your illuminated IV curve what
+
+ align:start position:0%
+between your illuminated IV curve what
+ 
+
+ align:start position:0%
+between your illuminated IV curve what
+is measured using the solar simulator
+
+ align:start position:0%
+is measured using the solar simulator
+ 
+
+ align:start position:0%
+is measured using the solar simulator
+and your son's V OC curve which is
+
+ align:start position:0%
+and your son's V OC curve which is
+ 
+
+ align:start position:0%
+and your son's V OC curve which is
+measured in the absence of series
+
+ align:start position:0%
+measured in the absence of series
+ 
+
+ align:start position:0%
+measured in the absence of series
+now this works well with most materials
+
+ align:start position:0%
+now this works well with most materials
+ 
+
+ align:start position:0%
+now this works well with most materials
+if you have a very high capacitance in
+
+ align:start position:0%
+if you have a very high capacitance in
+ 
+
+ align:start position:0%
+if you have a very high capacitance in
+your device you'll want to look very
+
+ align:start position:0%
+your device you'll want to look very
+ 
+
+ align:start position:0%
+your device you'll want to look very
+carefully at this at this decay right at
+
+ align:start position:0%
+carefully at this at this decay right at
+ 
+
+ align:start position:0%
+carefully at this at this decay right at
+the light intensity decay if your
+
+ align:start position:0%
+the light intensity decay if your
+ 
+
+ align:start position:0%
+the light intensity decay if your
+capacitance in your device is very large
+
+ align:start position:0%
+capacitance in your device is very large
+ 
+
+ align:start position:0%
+capacitance in your device is very large
+it might actually flatten out the
+
+ align:start position:0%
+it might actually flatten out the
+ 
+
+ align:start position:0%
+it might actually flatten out the
+voltage response so you want to make
+
+ align:start position:0%
+voltage response so you want to make
+ 
+
+ align:start position:0%
+voltage response so you want to make
+sure that the time RC time constant of
+
+ align:start position:0%
+sure that the time RC time constant of
+ 
+
+ align:start position:0%
+sure that the time RC time constant of
+your devices is matched to the the
+
+ align:start position:0%
+your devices is matched to the the
+ 
+
+ align:start position:0%
+your devices is matched to the the
+flashbulb decay time that's just one
+
+ align:start position:0%
+flashbulb decay time that's just one
+ 
+
+ align:start position:0%
+flashbulb decay time that's just one
+word of warning for those working on
+
+ align:start position:0%
+word of warning for those working on
+ 
+
+ align:start position:0%
+word of warning for those working on
+high-voltage or organic materials any
+
+ align:start position:0%
+high-voltage or organic materials any
+ 
+
+ align:start position:0%
+high-voltage or organic materials any
+questions on the Sun vo C measurement
+
+ align:start position:0%
+questions on the Sun vo C measurement
+ 
+
+ align:start position:0%
+questions on the Sun vo C measurement
+this is gives you what's called an
+
+ align:start position:0%
+this is gives you what's called an
+ 
+
+ align:start position:0%
+this is gives you what's called an
+implied IV curve and that is as a would
+
+ align:start position:0%
+implied IV curve and that is as a would
+ 
+
+ align:start position:0%
+implied IV curve and that is as a would
+say in in the best case scenario what
+
+ align:start position:0%
+say in in the best case scenario what
+ 
+
+ align:start position:0%
+say in in the best case scenario what
+you would get from the solar cell in the
+
+ align:start position:0%
+you would get from the solar cell in the
+ 
+
+ align:start position:0%
+you would get from the solar cell in the
+absence of any series resistance losses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it is important it would be a
+
+ align:start position:0%
+yeah it is important it would be a
+ 
+
+ align:start position:0%
+yeah it is important it would be a
+different in essence it would be a
+
+ align:start position:0%
+different in essence it would be a
+ 
+
+ align:start position:0%
+different in essence it would be a
+different current response right if you
+
+ align:start position:0%
+different current response right if you
+ 
+
+ align:start position:0%
+different current response right if you
+didn't have the same exact solar
+
+ align:start position:0%
+didn't have the same exact solar
+ 
+
+ align:start position:0%
+didn't have the same exact solar
+spectrum now that's a very important
+
+ align:start position:0%
+spectrum now that's a very important
+ 
+
+ align:start position:0%
+spectrum now that's a very important
+point if you're venturing outside of say
+
+ align:start position:0%
+point if you're venturing outside of say
+ 
+
+ align:start position:0%
+point if you're venturing outside of say
+silicon based devices and you're more
+
+ align:start position:0%
+silicon based devices and you're more
+ 
+
+ align:start position:0%
+silicon based devices and you're more
+sensitive to the infrared or the UV you
+
+ align:start position:0%
+sensitive to the infrared or the UV you
+ 
+
+ align:start position:0%
+sensitive to the infrared or the UV you
+really want to make sure that you
+
+ align:start position:0%
+really want to make sure that you
+ 
+
+ align:start position:0%
+really want to make sure that you
+measure the intensity as a function of
+
+ align:start position:0%
+measure the intensity as a function of
+ 
+
+ align:start position:0%
+measure the intensity as a function of
+wavelength output of that bulb otherwise
+
+ align:start position:0%
+wavelength output of that bulb otherwise
+ 
+
+ align:start position:0%
+wavelength output of that bulb otherwise
+your you might be higher or lower
+
+ align:start position:0%
+your you might be higher or lower
+ 
+
+ align:start position:0%
+your you might be higher or lower
+during the sun's boc measurement for a
+
+ align:start position:0%
+during the sun's boc measurement for a
+ 
+
+ align:start position:0%
+during the sun's boc measurement for a
+silicon-based device majority falls
+
+ align:start position:0%
+silicon-based device majority falls
+ 
+
+ align:start position:0%
+silicon-based device majority falls
+within the specified regime down here
+
+ align:start position:0%
+within the specified regime down here
+ 
+
+ align:start position:0%
+within the specified regime down here
+actually right here sorry on this
+
+ align:start position:0%
+actually right here sorry on this
+ 
+
+ align:start position:0%
+actually right here sorry on this
+diagram that little spot right there
+
+ align:start position:0%
+diagram that little spot right there
+ 
+
+ align:start position:0%
+diagram that little spot right there
+that is a small calibration solar cell
+
+ align:start position:0%
+that is a small calibration solar cell
+ 
+
+ align:start position:0%
+that is a small calibration solar cell
+of known short-circuit current an open
+
+ align:start position:0%
+of known short-circuit current an open
+ 
+
+ align:start position:0%
+of known short-circuit current an open
+circuit voltage so that's used to
+
+ align:start position:0%
+circuit voltage so that's used to
+ 
+
+ align:start position:0%
+circuit voltage so that's used to
+calibrate for other silicon devices if
+
+ align:start position:0%
+calibrate for other silicon devices if
+ 
+
+ align:start position:0%
+calibrate for other silicon devices if
+you're moving away from silicon that
+
+ align:start position:0%
+you're moving away from silicon that
+ 
+
+ align:start position:0%
+you're moving away from silicon that
+becomes an issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correctible you can measure the spectral
+
+ align:start position:0%
+correctible you can measure the spectral
+ 
+
+ align:start position:0%
+correctible you can measure the spectral
+response of that light source and
+
+ align:start position:0%
+response of that light source and
+ 
+
+ align:start position:0%
+response of that light source and
+compare it to the solar simulator and do
+
+ align:start position:0%
+compare it to the solar simulator and do
+ 
+
+ align:start position:0%
+compare it to the solar simulator and do
+the normalization accordingly here's
+
+ align:start position:0%
+the normalization accordingly here's
+ 
+
+ align:start position:0%
+the normalization accordingly here's
+what I recommend
+
+ align:start position:0%
+what I recommend
+ 
+
+ align:start position:0%
+what I recommend
+with the last 15 minutes of class I
+
+ align:start position:0%
+with the last 15 minutes of class I
+ 
+
+ align:start position:0%
+with the last 15 minutes of class I
+wanted to catch each of the teams and
+
+ align:start position:0%
+wanted to catch each of the teams and
+ 
+
+ align:start position:0%
+wanted to catch each of the teams and
+talk about your class projects to make
+
+ align:start position:0%
+talk about your class projects to make
+ 
+
+ align:start position:0%
+talk about your class projects to make
+sure that things were rolling along
+
+ align:start position:0%
+sure that things were rolling along
+ 
+
+ align:start position:0%
+sure that things were rolling along
+I have feelers out to some of the
+
+ align:start position:0%
+I have feelers out to some of the
+ 
+
+ align:start position:0%
+I have feelers out to some of the
+mentors who haven't responded yet and so
+
+ align:start position:0%
+mentors who haven't responded yet and so
+ 
+
+ align:start position:0%
+mentors who haven't responded yet and so
+I just wanted to touch base with each of
+
+ align:start position:0%
+I just wanted to touch base with each of
+ 
+
+ align:start position:0%
+I just wanted to touch base with each of
+you for about three minutes just to make
+
+ align:start position:0%
+you for about three minutes just to make
+ 
+
+ align:start position:0%
+you for about three minutes just to make
+sure everything is rolling along
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/yjBerM5jWsc.txt b/yjBerM5jWsc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..39fd874f0a32cf01d048e9f7440425bf778e4dbd
--- /dev/null
+++ b/yjBerM5jWsc.txt
@@ -0,0 +1,7603 @@
+align:start position:0%
+ 
+Okay, this is linear algebra lecture
+
+ align:start position:0%
+Okay, this is linear algebra lecture
+ 
+
+ align:start position:0%
+Okay, this is linear algebra lecture
+nine and this is a key lecture. This is
+
+ align:start position:0%
+nine and this is a key lecture. This is
+ 
+
+ align:start position:0%
+nine and this is a key lecture. This is
+where we get these ideas of
+
+ align:start position:0%
+where we get these ideas of
+ 
+
+ align:start position:0%
+where we get these ideas of
+linear independence. When a bunch of
+
+ align:start position:0%
+linear independence. When a bunch of
+ 
+
+ align:start position:0%
+linear independence. When a bunch of
+vectors are independent
+
+ align:start position:0%
+vectors are independent
+ 
+
+ align:start position:0%
+vectors are independent
+or dependent, that's the opposite.
+
+ align:start position:0%
+or dependent, that's the opposite.
+ 
+
+ align:start position:0%
+or dependent, that's the opposite.
+Uh the space they span,
+
+ align:start position:0%
+Uh the space they span,
+ 
+
+ align:start position:0%
+Uh the space they span,
+a basis for a subspace or a basis for a
+
+ align:start position:0%
+a basis for a subspace or a basis for a
+ 
+
+ align:start position:0%
+a basis for a subspace or a basis for a
+vector space, that's a central idea. And
+
+ align:start position:0%
+vector space, that's a central idea. And
+ 
+
+ align:start position:0%
+vector space, that's a central idea. And
+then the dimension of that subspace. So
+
+ align:start position:0%
+then the dimension of that subspace. So
+ 
+
+ align:start position:0%
+then the dimension of that subspace. So
+this is the day that those words get
+
+ align:start position:0%
+this is the day that those words get
+ 
+
+ align:start position:0%
+this is the day that those words get
+assigned clear meanings and emphasize
+
+ align:start position:0%
+assigned clear meanings and emphasize
+ 
+
+ align:start position:0%
+assigned clear meanings and emphasize
+that we talk about
+
+ align:start position:0%
+that we talk about
+ 
+
+ align:start position:0%
+that we talk about
+a bunch of vectors being independent.
+
+ align:start position:0%
+a bunch of vectors being independent.
+ 
+
+ align:start position:0%
+a bunch of vectors being independent.
+Wouldn't talk about a matrix being
+
+ align:start position:0%
+Wouldn't talk about a matrix being
+ 
+
+ align:start position:0%
+Wouldn't talk about a matrix being
+independent, a bunch of vectors being
+
+ align:start position:0%
+independent, a bunch of vectors being
+ 
+
+ align:start position:0%
+independent, a bunch of vectors being
+independent, a bunch of vectors spanning
+
+ align:start position:0%
+independent, a bunch of vectors spanning
+ 
+
+ align:start position:0%
+independent, a bunch of vectors spanning
+a space, a bunch of vectors being a
+
+ align:start position:0%
+a space, a bunch of vectors being a
+ 
+
+ align:start position:0%
+a space, a bunch of vectors being a
+basis, and the dimension is some number.
+
+ align:start position:0%
+basis, and the dimension is some number.
+ 
+
+ align:start position:0%
+basis, and the dimension is some number.
+Okay. So what are the definitions? Can I
+
+ align:start position:0%
+Okay. So what are the definitions? Can I
+ 
+
+ align:start position:0%
+Okay. So what are the definitions? Can I
+begin with a fact a highly important
+
+ align:start position:0%
+begin with a fact a highly important
+ 
+
+ align:start position:0%
+begin with a fact a highly important
+fact that uh I didn't call directly
+
+ align:start position:0%
+fact that uh I didn't call directly
+ 
+
+ align:start position:0%
+fact that uh I didn't call directly
+attention to earlier. Suppose I have a
+
+ align:start position:0%
+attention to earlier. Suppose I have a
+ 
+
+ align:start position:0%
+attention to earlier. Suppose I have a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+and I look at ax equals z.
+
+ align:start position:0%
+and I look at ax equals z.
+ 
+
+ align:start position:0%
+and I look at ax equals z.
+Suppose the matrix has a lot of columns
+
+ align:start position:0%
+Suppose the matrix has a lot of columns
+ 
+
+ align:start position:0%
+Suppose the matrix has a lot of columns
+so that n is bigger than m. So, I'm
+
+ align:start position:0%
+so that n is bigger than m. So, I'm
+ 
+
+ align:start position:0%
+so that n is bigger than m. So, I'm
+looking at n equations. I'm sorry, m
+
+ align:start position:0%
+looking at n equations. I'm sorry, m
+ 
+
+ align:start position:0%
+looking at n equations. I'm sorry, m
+equations. A small number of equations,
+
+ align:start position:0%
+equations. A small number of equations,
+ 
+
+ align:start position:0%
+equations. A small number of equations,
+m and more unknowns. I have more
+
+ align:start position:0%
+m and more unknowns. I have more
+ 
+
+ align:start position:0%
+m and more unknowns. I have more
+unknowns than equations.
+
+ align:start position:0%
+unknowns than equations.
+ 
+
+ align:start position:0%
+unknowns than equations.
+Let me write that down. More unknowns
+
+ align:start position:0%
+Let me write that down. More unknowns
+ 
+
+ align:start position:0%
+Let me write that down. More unknowns
+than equations.
+
+ align:start position:0%
+than equations.
+ 
+
+ align:start position:0%
+than equations.
+More
+
+ align:start position:0%
+More
+ 
+
+ align:start position:0%
+More
+unknown x's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than equations.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+then the conclusion is that there's
+
+ align:start position:0%
+then the conclusion is that there's
+ 
+
+ align:start position:0%
+then the conclusion is that there's
+something in the null space of a
+
+ align:start position:0%
+something in the null space of a
+ 
+
+ align:start position:0%
+something in the null space of a
+other than just the zero vector. The
+
+ align:start position:0%
+other than just the zero vector. The
+ 
+
+ align:start position:0%
+other than just the zero vector. The
+conclusion is there are some nonzero
+
+ align:start position:0%
+conclusion is there are some nonzero
+ 
+
+ align:start position:0%
+conclusion is there are some nonzero
+x's such that ax is zero. There are some
+
+ align:start position:0%
+x's such that ax is zero. There are some
+ 
+
+ align:start position:0%
+x's such that ax is zero. There are some
+special solutions and why we know why.
+
+ align:start position:0%
+special solutions and why we know why.
+ 
+
+ align:start position:0%
+special solutions and why we know why.
+I mean it sort of like seems like a
+
+ align:start position:0%
+I mean it sort of like seems like a
+ 
+
+ align:start position:0%
+I mean it sort of like seems like a
+reasonable thing. more unknowns than
+
+ align:start position:0%
+reasonable thing. more unknowns than
+ 
+
+ align:start position:0%
+reasonable thing. more unknowns than
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+then it seems reasonable that we can
+
+ align:start position:0%
+then it seems reasonable that we can
+ 
+
+ align:start position:0%
+then it seems reasonable that we can
+solve them. But we have a a clear
+
+ align:start position:0%
+solve them. But we have a a clear
+ 
+
+ align:start position:0%
+solve them. But we have a a clear
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+which starts with a system and does
+
+ align:start position:0%
+which starts with a system and does
+ 
+
+ align:start position:0%
+which starts with a system and does
+elimination
+
+ align:start position:0%
+elimination
+ 
+
+ align:start position:0%
+elimination
+gets the thing into an echelon form with
+
+ align:start position:0%
+gets the thing into an echelon form with
+ 
+
+ align:start position:0%
+gets the thing into an echelon form with
+some pivots and pivot columns
+
+ align:start position:0%
+some pivots and pivot columns
+ 
+
+ align:start position:0%
+some pivots and pivot columns
+and possibly some free columns that
+
+ align:start position:0%
+and possibly some free columns that
+ 
+
+ align:start position:0%
+and possibly some free columns that
+don't have pivots. And the point is here
+
+ align:start position:0%
+don't have pivots. And the point is here
+ 
+
+ align:start position:0%
+don't have pivots. And the point is here
+there will be some free columns. The
+
+ align:start position:0%
+there will be some free columns. The
+ 
+
+ align:start position:0%
+there will be some free columns. The
+reason so the reason is
+
+ align:start position:0%
+reason so the reason is
+ 
+
+ align:start position:0%
+reason so the reason is
+there must there will be
+
+ align:start position:0%
+there must there will be
+ 
+
+ align:start position:0%
+there must there will be
+free variables at least one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's the reason
+
+ align:start position:0%
+That's the reason
+ 
+
+ align:start position:0%
+That's the reason
+that we we now have this a complete uh
+
+ align:start position:0%
+that we we now have this a complete uh
+ 
+
+ align:start position:0%
+that we we now have this a complete uh
+algorithm complete systematic way to say
+
+ align:start position:0%
+algorithm complete systematic way to say
+ 
+
+ align:start position:0%
+algorithm complete systematic way to say
+okay we take the system ax equals zero
+
+ align:start position:0%
+okay we take the system ax equals zero
+ 
+
+ align:start position:0%
+okay we take the system ax equals zero
+we row reduce we identify the free
+
+ align:start position:0%
+we row reduce we identify the free
+ 
+
+ align:start position:0%
+we row reduce we identify the free
+variables and since there are n
+
+ align:start position:0%
+variables and since there are n
+ 
+
+ align:start position:0%
+variables and since there are n
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+and at most m pivots there will be some
+
+ align:start position:0%
+and at most m pivots there will be some
+ 
+
+ align:start position:0%
+and at most m pivots there will be some
+free variables at least one at least n
+
+ align:start position:0%
+free variables at least one at least n
+ 
+
+ align:start position:0%
+free variables at least one at least n
+minus m in fact left over and those
+
+ align:start position:0%
+minus m in fact left over and those
+ 
+
+ align:start position:0%
+minus m in fact left over and those
+variables I can assign nonzero values
+
+ align:start position:0%
+variables I can assign nonzero values
+ 
+
+ align:start position:0%
+variables I can assign nonzero values
+to. I don't have to set those to zero. I
+
+ align:start position:0%
+to. I don't have to set those to zero. I
+ 
+
+ align:start position:0%
+to. I don't have to set those to zero. I
+can take them to be one or whatever I
+
+ align:start position:0%
+can take them to be one or whatever I
+ 
+
+ align:start position:0%
+can take them to be one or whatever I
+like and then I can solve for the pivot
+
+ align:start position:0%
+like and then I can solve for the pivot
+ 
+
+ align:start position:0%
+like and then I can solve for the pivot
+variables. So then it gives me a
+
+ align:start position:0%
+variables. So then it gives me a
+ 
+
+ align:start position:0%
+variables. So then it gives me a
+solution to ax equals z and it's a
+
+ align:start position:0%
+solution to ax equals z and it's a
+ 
+
+ align:start position:0%
+solution to ax equals z and it's a
+solution that isn't all zeros.
+
+ align:start position:0%
+solution that isn't all zeros.
+ 
+
+ align:start position:0%
+solution that isn't all zeros.
+So uh that's a c that's a important
+
+ align:start position:0%
+So uh that's a c that's a important
+ 
+
+ align:start position:0%
+So uh that's a c that's a important
+point that we'll use now in this
+
+ align:start position:0%
+point that we'll use now in this
+ 
+
+ align:start position:0%
+point that we'll use now in this
+lecture.
+
+ align:start position:0%
+lecture.
+ 
+
+ align:start position:0%
+lecture.
+So now I want to say what does it mean
+
+ align:start position:0%
+So now I want to say what does it mean
+ 
+
+ align:start position:0%
+So now I want to say what does it mean
+for a bunch of vectors to be
+
+ align:start position:0%
+for a bunch of vectors to be
+ 
+
+ align:start position:0%
+for a bunch of vectors to be
+independent. Okay. So this is like the
+
+ align:start position:0%
+independent. Okay. So this is like the
+ 
+
+ align:start position:0%
+independent. Okay. So this is like the
+background that we know. Now I want to
+
+ align:start position:0%
+background that we know. Now I want to
+ 
+
+ align:start position:0%
+background that we know. Now I want to
+speak about independence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see.
+
+ align:start position:0%
+let's see.
+ 
+
+ align:start position:0%
+let's see.
+I can give you the the the
+
+ align:start position:0%
+I can give you the the the
+ 
+
+ align:start position:0%
+I can give you the the the
+uh abstract definition and I will but I
+
+ align:start position:0%
+uh abstract definition and I will but I
+ 
+
+ align:start position:0%
+uh abstract definition and I will but I
+would also like to give you the direct
+
+ align:start position:0%
+would also like to give you the direct
+ 
+
+ align:start position:0%
+would also like to give you the direct
+meaning when
+
+ align:start position:0%
+meaning when
+ 
+
+ align:start position:0%
+meaning when
+my so the question is when vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x1
+
+ align:start position:0%
+x1
+ 
+
+ align:start position:0%
+x1
+x2 up to suppose I have n vectors are
+
+ align:start position:0%
+x2 up to suppose I have n vectors are
+ 
+
+ align:start position:0%
+x2 up to suppose I have n vectors are
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+If now I have to give you
+
+ align:start position:0%
+If now I have to give you
+ 
+
+ align:start position:0%
+If now I have to give you
+or linearly independent
+
+ align:start position:0%
+or linearly independent
+ 
+
+ align:start position:0%
+or linearly independent
+I'll I'll often just say and write
+
+ align:start position:0%
+I'll I'll often just say and write
+ 
+
+ align:start position:0%
+I'll I'll often just say and write
+independent for short if okay let I'll
+
+ align:start position:0%
+independent for short if okay let I'll
+ 
+
+ align:start position:0%
+independent for short if okay let I'll
+give you the full definition these are
+
+ align:start position:0%
+give you the full definition these are
+ 
+
+ align:start position:0%
+give you the full definition these are
+just vectors in some vector space I can
+
+ align:start position:0%
+just vectors in some vector space I can
+ 
+
+ align:start position:0%
+just vectors in some vector space I can
+take combinations of them the question
+
+ align:start position:0%
+take combinations of them the question
+ 
+
+ align:start position:0%
+take combinations of them the question
+is do any combinations give zero
+
+ align:start position:0%
+is do any combinations give zero
+ 
+
+ align:start position:0%
+is do any combinations give zero
+if some combination of those vectors
+
+ align:start position:0%
+if some combination of those vectors
+ 
+
+ align:start position:0%
+if some combination of those vectors
+gives the zero vector
+
+ align:start position:0%
+gives the zero vector
+ 
+
+ align:start position:0%
+gives the zero vector
+other than the combination of all zeros.
+
+ align:start position:0%
+other than the combination of all zeros.
+ 
+
+ align:start position:0%
+other than the combination of all zeros.
+Then they're dependent.
+
+ align:start position:0%
+Then they're dependent.
+ 
+
+ align:start position:0%
+Then they're dependent.
+They're independent if no
+
+ align:start position:0%
+They're independent if no
+ 
+
+ align:start position:0%
+They're independent if no
+combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives
+
+ align:start position:0%
+gives
+ 
+
+ align:start position:0%
+gives
+the zero vector
+
+ align:start position:0%
+the zero vector
+ 
+
+ align:start position:0%
+the zero vector
+and then I have I'll have to put in and
+
+ align:start position:0%
+and then I have I'll have to put in and
+ 
+
+ align:start position:0%
+and then I have I'll have to put in and
+accept
+
+ align:start position:0%
+accept
+ 
+
+ align:start position:0%
+accept
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+combination. So what do I mean by that?
+
+ align:start position:0%
+combination. So what do I mean by that?
+ 
+
+ align:start position:0%
+combination. So what do I mean by that?
+No combination gives the zero vector.
+
+ align:start position:0%
+No combination gives the zero vector.
+ 
+
+ align:start position:0%
+No combination gives the zero vector.
+Any combination C1 X1 + C2 X2 + plus C N
+
+ align:start position:0%
+Any combination C1 X1 + C2 X2 + plus C N
+ 
+
+ align:start position:0%
+Any combination C1 X1 + C2 X2 + plus C N
+XN
+
+ align:start position:0%
+XN
+ 
+
+ align:start position:0%
+XN
+is not zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+except for the zero combination. This is
+
+ align:start position:0%
+except for the zero combination. This is
+ 
+
+ align:start position:0%
+except for the zero combination. This is
+when all the C's all the C's are zero.
+
+ align:start position:0%
+when all the C's all the C's are zero.
+ 
+
+ align:start position:0%
+when all the C's all the C's are zero.
+Then of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that combination I I'm I know I'll get
+
+ align:start position:0%
+that combination I I'm I know I'll get
+ 
+
+ align:start position:0%
+that combination I I'm I know I'll get
+zero. But the the question is does any
+
+ align:start position:0%
+zero. But the the question is does any
+ 
+
+ align:start position:0%
+zero. But the the question is does any
+other combination give zero? If not
+
+ align:start position:0%
+other combination give zero? If not
+ 
+
+ align:start position:0%
+other combination give zero? If not
+then the vectors are independent. If
+
+ align:start position:0%
+then the vectors are independent. If
+ 
+
+ align:start position:0%
+then the vectors are independent. If
+some other combination does give zero
+
+ align:start position:0%
+some other combination does give zero
+ 
+
+ align:start position:0%
+some other combination does give zero
+the vectors are dependent. Okay let's
+
+ align:start position:0%
+the vectors are dependent. Okay let's
+ 
+
+ align:start position:0%
+the vectors are dependent. Okay let's
+just take examples.
+
+ align:start position:0%
+just take examples.
+ 
+
+ align:start position:0%
+just take examples.
+Suppose I'm in
+
+ align:start position:0%
+Suppose I'm in
+ 
+
+ align:start position:0%
+Suppose I'm in
+say in two-dimensional space.
+
+ align:start position:0%
+say in two-dimensional space.
+ 
+
+ align:start position:0%
+say in two-dimensional space.
+Okay I give you I I'd like to first take
+
+ align:start position:0%
+Okay I give you I I'd like to first take
+ 
+
+ align:start position:0%
+Okay I give you I I'd like to first take
+an example. Let me take an example where
+
+ align:start position:0%
+an example. Let me take an example where
+ 
+
+ align:start position:0%
+an example. Let me take an example where
+I have a vector and twice that vector.
+
+ align:start position:0%
+I have a vector and twice that vector.
+ 
+
+ align:start position:0%
+I have a vector and twice that vector.
+So that's two vectors V and 2V. Are
+
+ align:start position:0%
+So that's two vectors V and 2V. Are
+ 
+
+ align:start position:0%
+So that's two vectors V and 2V. Are
+those dependent or independent?
+
+ align:start position:0%
+those dependent or independent?
+ 
+
+ align:start position:0%
+those dependent or independent?
+Those are dependent for sure. Right?
+
+ align:start position:0%
+Those are dependent for sure. Right?
+ 
+
+ align:start position:0%
+Those are dependent for sure. Right?
+There's a combin one vector is twice the
+
+ align:start position:0%
+There's a combin one vector is twice the
+ 
+
+ align:start position:0%
+There's a combin one vector is twice the
+other. One vector is twice as long as
+
+ align:start position:0%
+other. One vector is twice as long as
+ 
+
+ align:start position:0%
+other. One vector is twice as long as
+the other. So if the word dependent
+
+ align:start position:0%
+the other. So if the word dependent
+ 
+
+ align:start position:0%
+the other. So if the word dependent
+means anything, these should be
+
+ align:start position:0%
+means anything, these should be
+ 
+
+ align:start position:0%
+means anything, these should be
+dependent. And they are. And in fact, I
+
+ align:start position:0%
+dependent. And they are. And in fact, I
+ 
+
+ align:start position:0%
+dependent. And they are. And in fact, I
+would take two of the first. So here's
+
+ align:start position:0%
+would take two of the first. So here's
+ 
+
+ align:start position:0%
+would take two of the first. So here's
+here's a vector V and the other guy is a
+
+ align:start position:0%
+here's a vector V and the other guy is a
+ 
+
+ align:start position:0%
+here's a vector V and the other guy is a
+vector 2V. That's my So there's a vector
+
+ align:start position:0%
+vector 2V. That's my So there's a vector
+ 
+
+ align:start position:0%
+vector 2V. That's my So there's a vector
+V1 and my ve my next vector V2 is 2 V1.
+
+ align:start position:0%
+V1 and my ve my next vector V2 is 2 V1.
+ 
+
+ align:start position:0%
+V1 and my ve my next vector V2 is 2 V1.
+Of course, those are dependent because
+
+ align:start position:0%
+Of course, those are dependent because
+ 
+
+ align:start position:0%
+Of course, those are dependent because
+two of these first vectors minus the
+
+ align:start position:0%
+two of these first vectors minus the
+ 
+
+ align:start position:0%
+two of these first vectors minus the
+second vector is zero. That's a
+
+ align:start position:0%
+second vector is zero. That's a
+ 
+
+ align:start position:0%
+second vector is zero. That's a
+combination of these two vectors that
+
+ align:start position:0%
+combination of these two vectors that
+ 
+
+ align:start position:0%
+combination of these two vectors that
+gives the zero vector. Okay, that was
+
+ align:start position:0%
+gives the zero vector. Okay, that was
+ 
+
+ align:start position:0%
+gives the zero vector. Okay, that was
+clear. Suppose suppose I have a vector.
+
+ align:start position:0%
+clear. Suppose suppose I have a vector.
+ 
+
+ align:start position:0%
+clear. Suppose suppose I have a vector.
+Here's another example. It's easy
+
+ align:start position:0%
+Here's another example. It's easy
+ 
+
+ align:start position:0%
+Here's another example. It's easy
+example. Suppose I have a vector and the
+
+ align:start position:0%
+example. Suppose I have a vector and the
+ 
+
+ align:start position:0%
+example. Suppose I have a vector and the
+other guy is the zero vector. Suppose I
+
+ align:start position:0%
+other guy is the zero vector. Suppose I
+ 
+
+ align:start position:0%
+other guy is the zero vector. Suppose I
+have a vector v1 and v2 is the zero
+
+ align:start position:0%
+have a vector v1 and v2 is the zero
+ 
+
+ align:start position:0%
+have a vector v1 and v2 is the zero
+vector. Then are those vectors dependent
+
+ align:start position:0%
+vector. Then are those vectors dependent
+ 
+
+ align:start position:0%
+vector. Then are those vectors dependent
+or independent?
+
+ align:start position:0%
+or independent?
+ 
+
+ align:start position:0%
+or independent?
+They're dependent. Again,
+
+ align:start position:0%
+They're dependent. Again,
+ 
+
+ align:start position:0%
+They're dependent. Again,
+you could say, well, this guy is zero
+
+ align:start position:0%
+you could say, well, this guy is zero
+ 
+
+ align:start position:0%
+you could say, well, this guy is zero
+times that one. This one is some
+
+ align:start position:0%
+times that one. This one is some
+ 
+
+ align:start position:0%
+times that one. This one is some
+combination of those. But let me write
+
+ align:start position:0%
+combination of those. But let me write
+ 
+
+ align:start position:0%
+combination of those. But let me write
+it the other way. Let me say what what
+
+ align:start position:0%
+it the other way. Let me say what what
+ 
+
+ align:start position:0%
+it the other way. Let me say what what
+combination how many V1s and how many
+
+ align:start position:0%
+combination how many V1s and how many
+ 
+
+ align:start position:0%
+combination how many V1s and how many
+V2s shall I take to get the zero vector?
+
+ align:start position:0%
+V2s shall I take to get the zero vector?
+ 
+
+ align:start position:0%
+V2s shall I take to get the zero vector?
+If if v_sub_1 is like the vector 21 and
+
+ align:start position:0%
+If if v_sub_1 is like the vector 21 and
+ 
+
+ align:start position:0%
+If if v_sub_1 is like the vector 21 and
+v2 is the zero vector 0 0 then I would
+
+ align:start position:0%
+v2 is the zero vector 0 0 then I would
+ 
+
+ align:start position:0%
+v2 is the zero vector 0 0 then I would
+like to show that some combination of
+
+ align:start position:0%
+like to show that some combination of
+ 
+
+ align:start position:0%
+like to show that some combination of
+those gives the zero vector. What shall
+
+ align:start position:0%
+those gives the zero vector. What shall
+ 
+
+ align:start position:0%
+those gives the zero vector. What shall
+I take? How many v1's shall I take?
+
+ align:start position:0%
+I take? How many v1's shall I take?
+ 
+
+ align:start position:0%
+I take? How many v1's shall I take?
+Zero of them. Yeah. No. Take no v1s. But
+
+ align:start position:0%
+Zero of them. Yeah. No. Take no v1s. But
+ 
+
+ align:start position:0%
+Zero of them. Yeah. No. Take no v1s. But
+how many v2s?
+
+ align:start position:0%
+how many v2s?
+ 
+
+ align:start position:0%
+how many v2s?
+Six. Okay.
+
+ align:start position:0%
+Six. Okay.
+ 
+
+ align:start position:0%
+Six. Okay.
+or five.
+
+ align:start position:0%
+or five.
+ 
+
+ align:start position:0%
+or five.
+Then in other words, the point is if the
+
+ align:start position:0%
+Then in other words, the point is if the
+ 
+
+ align:start position:0%
+Then in other words, the point is if the
+zero vectors in there, if the zero if if
+
+ align:start position:0%
+zero vectors in there, if the zero if if
+ 
+
+ align:start position:0%
+zero vectors in there, if the zero if if
+one of these vectors is the zero vector,
+
+ align:start position:0%
+one of these vectors is the zero vector,
+ 
+
+ align:start position:0%
+one of these vectors is the zero vector,
+independence is dead, right? If one of
+
+ align:start position:0%
+independence is dead, right? If one of
+ 
+
+ align:start position:0%
+independence is dead, right? If one of
+those vectors is the zero vector, then I
+
+ align:start position:0%
+those vectors is the zero vector, then I
+ 
+
+ align:start position:0%
+those vectors is the zero vector, then I
+could always take
+
+ align:start position:0%
+could always take
+ 
+
+ align:start position:0%
+could always take
+include that one and none of the others
+
+ align:start position:0%
+include that one and none of the others
+ 
+
+ align:start position:0%
+include that one and none of the others
+and I would get the zero answer and I
+
+ align:start position:0%
+and I would get the zero answer and I
+ 
+
+ align:start position:0%
+and I would get the zero answer and I
+would show dependence. Okay. Now uh let
+
+ align:start position:0%
+would show dependence. Okay. Now uh let
+ 
+
+ align:start position:0%
+would show dependence. Okay. Now uh let
+me let me finally draw an example where
+
+ align:start position:0%
+me let me finally draw an example where
+ 
+
+ align:start position:0%
+me let me finally draw an example where
+they will be independent. Suppose that's
+
+ align:start position:0%
+they will be independent. Suppose that's
+ 
+
+ align:start position:0%
+they will be independent. Suppose that's
+v1 and that's v2.
+
+ align:start position:0%
+v1 and that's v2.
+ 
+
+ align:start position:0%
+v1 and that's v2.
+Those are surely independent right. Any
+
+ align:start position:0%
+Those are surely independent right. Any
+ 
+
+ align:start position:0%
+Those are surely independent right. Any
+combination of v_sub_1 and v2 uh will
+
+ align:start position:0%
+combination of v_sub_1 and v2 uh will
+ 
+
+ align:start position:0%
+combination of v_sub_1 and v2 uh will
+not be zero except uh the zero
+
+ align:start position:0%
+not be zero except uh the zero
+ 
+
+ align:start position:0%
+not be zero except uh the zero
+combination. So those would be
+
+ align:start position:0%
+combination. So those would be
+ 
+
+ align:start position:0%
+combination. So those would be
+independent. But now let me let me stick
+
+ align:start position:0%
+independent. But now let me let me stick
+ 
+
+ align:start position:0%
+independent. But now let me let me stick
+in a third vector v3.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent or dependent. Now those
+
+ align:start position:0%
+independent or dependent. Now those
+ 
+
+ align:start position:0%
+independent or dependent. Now those
+three vectors. So now n is three. Here
+
+ align:start position:0%
+three vectors. So now n is three. Here
+ 
+
+ align:start position:0%
+three vectors. So now n is three. Here
+I'm in two-dimensional space. Whatever
+
+ align:start position:0%
+I'm in two-dimensional space. Whatever
+ 
+
+ align:start position:0%
+I'm in two-dimensional space. Whatever
+I'm in the plane I have three vectors
+
+ align:start position:0%
+I'm in the plane I have three vectors
+ 
+
+ align:start position:0%
+I'm in the plane I have three vectors
+that I didn't draw so carefully. I
+
+ align:start position:0%
+that I didn't draw so carefully. I
+ 
+
+ align:start position:0%
+that I didn't draw so carefully. I
+didn't even tell you what exactly they
+
+ align:start position:0%
+didn't even tell you what exactly they
+ 
+
+ align:start position:0%
+didn't even tell you what exactly they
+were. But what's this answer on
+
+ align:start position:0%
+were. But what's this answer on
+ 
+
+ align:start position:0%
+were. But what's this answer on
+dependent or independent?
+
+ align:start position:0%
+dependent or independent?
+ 
+
+ align:start position:0%
+dependent or independent?
+Dependent. Why? How do I know the those
+
+ align:start position:0%
+Dependent. Why? How do I know the those
+ 
+
+ align:start position:0%
+Dependent. Why? How do I know the those
+are dependent?
+
+ align:start position:0%
+are dependent?
+ 
+
+ align:start position:0%
+are dependent?
+How do I know that some combination of
+
+ align:start position:0%
+How do I know that some combination of
+ 
+
+ align:start position:0%
+How do I know that some combination of
+vub1, v2 and v3 gives me the zero
+
+ align:start position:0%
+vub1, v2 and v3 gives me the zero
+ 
+
+ align:start position:0%
+vub1, v2 and v3 gives me the zero
+vector?
+
+ align:start position:0%
+vector?
+ 
+
+ align:start position:0%
+vector?
+I know because of that that's the that's
+
+ align:start position:0%
+I know because of that that's the that's
+ 
+
+ align:start position:0%
+I know because of that that's the that's
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+key fact
+
+ align:start position:0%
+key fact
+ 
+
+ align:start position:0%
+key fact
+that tells me that three vectors in the
+
+ align:start position:0%
+that tells me that three vectors in the
+ 
+
+ align:start position:0%
+that tells me that three vectors in the
+plane have to be dependent. Why is that?
+
+ align:start position:0%
+plane have to be dependent. Why is that?
+ 
+
+ align:start position:0%
+plane have to be dependent. Why is that?
+What's the connection between the
+
+ align:start position:0%
+What's the connection between the
+ 
+
+ align:start position:0%
+What's the connection between the
+dependence of these three vectors and
+
+ align:start position:0%
+dependence of these three vectors and
+ 
+
+ align:start position:0%
+dependence of these three vectors and
+that fact? Okay, so here's the
+
+ align:start position:0%
+that fact? Okay, so here's the
+ 
+
+ align:start position:0%
+that fact? Okay, so here's the
+connection. I take the matrix A
+
+ align:start position:0%
+connection. I take the matrix A
+ 
+
+ align:start position:0%
+connection. I take the matrix A
+that has V1 in its first column,
+
+ align:start position:0%
+that has V1 in its first column,
+ 
+
+ align:start position:0%
+that has V1 in its first column,
+V2 in its second column, V3 in its third
+
+ align:start position:0%
+V2 in its second column, V3 in its third
+ 
+
+ align:start position:0%
+V2 in its second column, V3 in its third
+column.
+
+ align:start position:0%
+column.
+ 
+
+ align:start position:0%
+column.
+So it's got three columns. And V1, I
+
+ align:start position:0%
+So it's got three columns. And V1, I
+ 
+
+ align:start position:0%
+So it's got three columns. And V1, I
+don't know, that looks like about 21 to
+
+ align:start position:0%
+don't know, that looks like about 21 to
+ 
+
+ align:start position:0%
+don't know, that looks like about 21 to
+me. V2 looks like it might be one two.
+
+ align:start position:0%
+me. V2 looks like it might be one two.
+ 
+
+ align:start position:0%
+me. V2 looks like it might be one two.
+V3 looks like it might be maybe two
+
+ align:start position:0%
+V3 looks like it might be maybe two
+ 
+
+ align:start position:0%
+V3 looks like it might be maybe two
+maybe two and a half
+
+ align:start position:0%
+maybe two and a half
+ 
+
+ align:start position:0%
+maybe two and a half
+minus one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, those are three. Those are my
+
+ align:start position:0%
+Okay, those are three. Those are my
+ 
+
+ align:start position:0%
+Okay, those are three. Those are my
+three vectors and I put them in the
+
+ align:start position:0%
+three vectors and I put them in the
+ 
+
+ align:start position:0%
+three vectors and I put them in the
+columns of A.
+
+ align:start position:0%
+columns of A.
+ 
+
+ align:start position:0%
+columns of A.
+Now that matrix A is 2x3. It fits this
+
+ align:start position:0%
+Now that matrix A is 2x3. It fits this
+ 
+
+ align:start position:0%
+Now that matrix A is 2x3. It fits this
+pattern that where we know we've got
+
+ align:start position:0%
+pattern that where we know we've got
+ 
+
+ align:start position:0%
+pattern that where we know we've got
+extra variables. We know we have some
+
+ align:start position:0%
+extra variables. We know we have some
+ 
+
+ align:start position:0%
+extra variables. We know we have some
+free variables. We know that there's
+
+ align:start position:0%
+free variables. We know that there's
+ 
+
+ align:start position:0%
+free variables. We know that there's
+some combination and let me instead of
+
+ align:start position:0%
+some combination and let me instead of
+ 
+
+ align:start position:0%
+some combination and let me instead of
+X's, let me call them C1, C2, and C3
+
+ align:start position:0%
+X's, let me call them C1, C2, and C3
+ 
+
+ align:start position:0%
+X's, let me call them C1, C2, and C3
+that gives the zero vector.
+
+ align:start position:0%
+that gives the zero vector.
+ 
+
+ align:start position:0%
+that gives the zero vector.
+Sorry that my little bit of art got in
+
+ align:start position:0%
+Sorry that my little bit of art got in
+ 
+
+ align:start position:0%
+Sorry that my little bit of art got in
+the way. Do you see the point? When I
+
+ align:start position:0%
+the way. Do you see the point? When I
+ 
+
+ align:start position:0%
+the way. Do you see the point? When I
+have a matrix,
+
+ align:start position:0%
+have a matrix,
+ 
+
+ align:start position:0%
+have a matrix,
+I'm interested in whether its columns
+
+ align:start position:0%
+I'm interested in whether its columns
+ 
+
+ align:start position:0%
+I'm interested in whether its columns
+are dependent or independent.
+
+ align:start position:0%
+are dependent or independent.
+ 
+
+ align:start position:0%
+are dependent or independent.
+The columns are dependent if there is
+
+ align:start position:0%
+The columns are dependent if there is
+ 
+
+ align:start position:0%
+The columns are dependent if there is
+something in the null space. The columns
+
+ align:start position:0%
+something in the null space. The columns
+ 
+
+ align:start position:0%
+something in the null space. The columns
+are dependent because this this thing in
+
+ align:start position:0%
+are dependent because this this thing in
+ 
+
+ align:start position:0%
+are dependent because this this thing in
+the null space says that C1 of that plus
+
+ align:start position:0%
+the null space says that C1 of that plus
+ 
+
+ align:start position:0%
+the null space says that C1 of that plus
+C2 of that plus C3 of this is zero. So
+
+ align:start position:0%
+C2 of that plus C3 of this is zero. So
+ 
+
+ align:start position:0%
+C2 of that plus C3 of this is zero. So
+in other words, I can go out some V1 out
+
+ align:start position:0%
+in other words, I can go out some V1 out
+ 
+
+ align:start position:0%
+in other words, I can go out some V1 out
+some more V2 back on V3 and end up zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let
+
+ align:start position:0%
+Okay. So let
+ 
+
+ align:start position:0%
+Okay. So let
+here I've given the general abstract
+
+ align:start position:0%
+here I've given the general abstract
+ 
+
+ align:start position:0%
+here I've given the general abstract
+definition but let me repeat that
+
+ align:start position:0%
+definition but let me repeat that
+ 
+
+ align:start position:0%
+definition but let me repeat that
+definition. So this is like repeat
+
+ align:start position:0%
+definition. So this is like repeat
+ 
+
+ align:start position:0%
+definition. So this is like repeat
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+when the v1 let me call them v's now v1
+
+ align:start position:0%
+when the v1 let me call them v's now v1
+ 
+
+ align:start position:0%
+when the v1 let me call them v's now v1
+up to vn are the columns
+
+ align:start position:0%
+up to vn are the columns
+ 
+
+ align:start position:0%
+up to vn are the columns
+of a matrix a
+
+ align:start position:0%
+of a matrix a
+ 
+
+ align:start position:0%
+of a matrix a
+in other words this is telling me that
+
+ align:start position:0%
+in other words this is telling me that
+ 
+
+ align:start position:0%
+in other words this is telling me that
+if I'm in if I'm in n if I'm in uh md
+
+ align:start position:0%
+if I'm in if I'm in n if I'm in uh md
+ 
+
+ align:start position:0%
+if I'm in if I'm in n if I'm in uh md
+dimensional space like two-dimensional
+
+ align:start position:0%
+dimensional space like two-dimensional
+ 
+
+ align:start position:0%
+dimensional space like two-dimensional
+space in the example. I can answer the
+
+ align:start position:0%
+space in the example. I can answer the
+ 
+
+ align:start position:0%
+space in the example. I can answer the
+dependence independence question
+
+ align:start position:0%
+dependence independence question
+ 
+
+ align:start position:0%
+dependence independence question
+directly
+
+ align:start position:0%
+directly
+ 
+
+ align:start position:0%
+directly
+by putting those vectors in the columns
+
+ align:start position:0%
+by putting those vectors in the columns
+ 
+
+ align:start position:0%
+by putting those vectors in the columns
+of a matrix. Then they independent. They
+
+ align:start position:0%
+of a matrix. Then they independent. They
+ 
+
+ align:start position:0%
+of a matrix. Then they independent. They
+are independent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Independent
+
+ align:start position:0%
+Independent
+ 
+
+ align:start position:0%
+Independent
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+the null space of A
+
+ align:start position:0%
+the null space of A
+ 
+
+ align:start position:0%
+the null space of A
+of A is what?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If I have a bunch of columns in a
+
+ align:start position:0%
+If I have a bunch of columns in a
+ 
+
+ align:start position:0%
+If I have a bunch of columns in a
+matrix,
+
+ align:start position:0%
+matrix,
+ 
+
+ align:start position:0%
+matrix,
+I'm looking at their combinations, but
+
+ align:start position:0%
+I'm looking at their combinations, but
+ 
+
+ align:start position:0%
+I'm looking at their combinations, but
+that's just A times
+
+ align:start position:0%
+that's just A times
+ 
+
+ align:start position:0%
+that's just A times
+the vector of C's
+
+ align:start position:0%
+the vector of C's
+ 
+
+ align:start position:0%
+the vector of C's
+and the ve and these columns will be
+
+ align:start position:0%
+and the ve and these columns will be
+ 
+
+ align:start position:0%
+and the ve and these columns will be
+independent if the null space of A is
+
+ align:start position:0%
+independent if the null space of A is
+ 
+
+ align:start position:0%
+independent if the null space of A is
+only the zero vector is only is the zero
+
+ align:start position:0%
+only the zero vector is only is the zero
+ 
+
+ align:start position:0%
+only the zero vector is only is the zero
+vector.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They are dependent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if there's something else in there. If
+
+ align:start position:0%
+if there's something else in there. If
+ 
+
+ align:start position:0%
+if there's something else in there. If
+there's something else in the null
+
+ align:start position:0%
+there's something else in the null
+ 
+
+ align:start position:0%
+there's something else in the null
+space, if a * c gives the zero vector
+
+ align:start position:0%
+space, if a * c gives the zero vector
+ 
+
+ align:start position:0%
+space, if a * c gives the zero vector
+for some nonzero
+
+ align:start position:0%
+for some nonzero
+ 
+
+ align:start position:0%
+for some nonzero
+vector c in the null space,
+
+ align:start position:0%
+vector c in the null space,
+ 
+
+ align:start position:0%
+vector c in the null space,
+then they're dependent because that's
+
+ align:start position:0%
+then they're dependent because that's
+ 
+
+ align:start position:0%
+then they're dependent because that's
+telling me a combination of the columns
+
+ align:start position:0%
+telling me a combination of the columns
+ 
+
+ align:start position:0%
+telling me a combination of the columns
+gives the zero column. I I I think
+
+ align:start position:0%
+gives the zero column. I I I think
+ 
+
+ align:start position:0%
+gives the zero column. I I I think
+you're with me because we've seen like
+
+ align:start position:0%
+you're with me because we've seen like
+ 
+
+ align:start position:0%
+you're with me because we've seen like
+lecture after lecture we're looking at
+
+ align:start position:0%
+lecture after lecture we're looking at
+ 
+
+ align:start position:0%
+lecture after lecture we're looking at
+the combinations of the columns and
+
+ align:start position:0%
+the combinations of the columns and
+ 
+
+ align:start position:0%
+the combinations of the columns and
+asking do we get zero or don't we and
+
+ align:start position:0%
+asking do we get zero or don't we and
+ 
+
+ align:start position:0%
+asking do we get zero or don't we and
+now we're giving the official name
+
+ align:start position:0%
+now we're giving the official name
+ 
+
+ align:start position:0%
+now we're giving the official name
+dependent if we do independent if we
+
+ align:start position:0%
+dependent if we do independent if we
+ 
+
+ align:start position:0%
+dependent if we do independent if we
+don't so I could express this in other
+
+ align:start position:0%
+don't so I could express this in other
+ 
+
+ align:start position:0%
+don't so I could express this in other
+words now I could say the rank what's
+
+ align:start position:0%
+words now I could say the rank what's
+ 
+
+ align:start position:0%
+words now I could say the rank what's
+the rank in this independent case the
+
+ align:start position:0%
+the rank in this independent case the
+ 
+
+ align:start position:0%
+the rank in this independent case the
+rank R of of the matrix in the case of
+
+ align:start position:0%
+rank R of of the matrix in the case of
+ 
+
+ align:start position:0%
+rank R of of the matrix in the case of
+independent columns is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the columns are independent.
+
+ align:start position:0%
+so the columns are independent.
+ 
+
+ align:start position:0%
+so the columns are independent.
+So how many pivot columns have I got?
+
+ align:start position:0%
+So how many pivot columns have I got?
+ 
+
+ align:start position:0%
+So how many pivot columns have I got?
+All in all the columns would be pivot
+
+ align:start position:0%
+All in all the columns would be pivot
+ 
+
+ align:start position:0%
+All in all the columns would be pivot
+columns
+
+ align:start position:0%
+columns
+ 
+
+ align:start position:0%
+columns
+because free columns are telling me that
+
+ align:start position:0%
+because free columns are telling me that
+ 
+
+ align:start position:0%
+because free columns are telling me that
+they're a combination of earlier
+
+ align:start position:0%
+they're a combination of earlier
+ 
+
+ align:start position:0%
+they're a combination of earlier
+columns. So this would be the case where
+
+ align:start position:0%
+columns. So this would be the case where
+ 
+
+ align:start position:0%
+columns. So this would be the case where
+the rank is n. This would be the case
+
+ align:start position:0%
+the rank is n. This would be the case
+ 
+
+ align:start position:0%
+the rank is n. This would be the case
+where the rank is smaller than n.
+
+ align:start position:0%
+where the rank is smaller than n.
+ 
+
+ align:start position:0%
+where the rank is smaller than n.
+So in this case the rank is n and the
+
+ align:start position:0%
+So in this case the rank is n and the
+ 
+
+ align:start position:0%
+So in this case the rank is n and the
+null space of a is only the zero vector
+
+ align:start position:0%
+null space of a is only the zero vector
+ 
+
+ align:start position:0%
+null space of a is only the zero vector
+and no free variables. No free
+
+ align:start position:0%
+and no free variables. No free
+ 
+
+ align:start position:0%
+and no free variables. No free
+variables.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this is the case. Yes. free
+
+ align:start position:0%
+And this is the case. Yes. free
+ 
+
+ align:start position:0%
+And this is the case. Yes. free
+variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you'll allow me to stretch the
+
+ align:start position:0%
+if you'll allow me to stretch the
+ 
+
+ align:start position:0%
+if you'll allow me to stretch the
+English language that far. Uh that's the
+
+ align:start position:0%
+English language that far. Uh that's the
+ 
+
+ align:start position:0%
+English language that far. Uh that's the
+case where we have
+
+ align:start position:0%
+case where we have
+ 
+
+ align:start position:0%
+case where we have
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a combination that gives the zero
+
+ align:start position:0%
+a combination that gives the zero
+ 
+
+ align:start position:0%
+a combination that gives the zero
+column. So I I'm often interested in the
+
+ align:start position:0%
+column. So I I'm often interested in the
+ 
+
+ align:start position:0%
+column. So I I'm often interested in the
+case when my vectors are popped into a
+
+ align:start position:0%
+case when my vectors are popped into a
+ 
+
+ align:start position:0%
+case when my vectors are popped into a
+matrix.
+
+ align:start position:0%
+matrix.
+ 
+
+ align:start position:0%
+matrix.
+So the the definition over there of
+
+ align:start position:0%
+So the the definition over there of
+ 
+
+ align:start position:0%
+So the the definition over there of
+independence didn't talk about any
+
+ align:start position:0%
+independence didn't talk about any
+ 
+
+ align:start position:0%
+independence didn't talk about any
+matrix.
+
+ align:start position:0%
+matrix.
+ 
+
+ align:start position:0%
+matrix.
+The vectors didn't have to be vectors in
+
+ align:start position:0%
+The vectors didn't have to be vectors in
+ 
+
+ align:start position:0%
+The vectors didn't have to be vectors in
+n-dimensional space. And I I want to
+
+ align:start position:0%
+n-dimensional space. And I I want to
+ 
+
+ align:start position:0%
+n-dimensional space. And I I want to
+give it some examples of vectors that
+
+ align:start position:0%
+give it some examples of vectors that
+ 
+
+ align:start position:0%
+give it some examples of vectors that
+aren't what you think of immediately as
+
+ align:start position:0%
+aren't what you think of immediately as
+ 
+
+ align:start position:0%
+aren't what you think of immediately as
+vectors. But most of the time this is
+
+ align:start position:0%
+vectors. But most of the time this is
+ 
+
+ align:start position:0%
+vectors. But most of the time this is
+the we the vectors we think of are
+
+ align:start position:0%
+the we the vectors we think of are
+ 
+
+ align:start position:0%
+the we the vectors we think of are
+columns
+
+ align:start position:0%
+columns
+ 
+
+ align:start position:0%
+columns
+and we can put them in a matrix and then
+
+ align:start position:0%
+and we can put them in a matrix and then
+ 
+
+ align:start position:0%
+and we can put them in a matrix and then
+independence or dependence comes back to
+
+ align:start position:0%
+independence or dependence comes back to
+ 
+
+ align:start position:0%
+independence or dependence comes back to
+the null space.
+
+ align:start position:0%
+the null space.
+ 
+
+ align:start position:0%
+the null space.
+Okay. So that's the idea of
+
+ align:start position:0%
+Okay. So that's the idea of
+ 
+
+ align:start position:0%
+Okay. So that's the idea of
+independence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Can I just uh
+
+ align:start position:0%
+Can I just uh
+ 
+
+ align:start position:0%
+Can I just uh
+yeah let me let me go on to spanning a
+
+ align:start position:0%
+yeah let me let me go on to spanning a
+ 
+
+ align:start position:0%
+yeah let me let me go on to spanning a
+space.
+
+ align:start position:0%
+space.
+ 
+
+ align:start position:0%
+space.
+What does it mean for a bunch of vectors
+
+ align:start position:0%
+What does it mean for a bunch of vectors
+ 
+
+ align:start position:0%
+What does it mean for a bunch of vectors
+to span a space?
+
+ align:start position:0%
+to span a space?
+ 
+
+ align:start position:0%
+to span a space?
+Well, actually, we've seen it already.
+
+ align:start position:0%
+Well, actually, we've seen it already.
+ 
+
+ align:start position:0%
+Well, actually, we've seen it already.
+You remember if if we had a columns in a
+
+ align:start position:0%
+You remember if if we had a columns in a
+ 
+
+ align:start position:0%
+You remember if if we had a columns in a
+matrix,
+
+ align:start position:0%
+matrix,
+ 
+
+ align:start position:0%
+matrix,
+we took all their combinations
+
+ align:start position:0%
+we took all their combinations
+ 
+
+ align:start position:0%
+we took all their combinations
+and that gave us the column space.
+
+ align:start position:0%
+and that gave us the column space.
+ 
+
+ align:start position:0%
+and that gave us the column space.
+Those vectors that we started with span
+
+ align:start position:0%
+Those vectors that we started with span
+ 
+
+ align:start position:0%
+Those vectors that we started with span
+that column space. So spanning a space
+
+ align:start position:0%
+that column space. So spanning a space
+ 
+
+ align:start position:0%
+that column space. So spanning a space
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+so let me move that important stuff
+
+ align:start position:0%
+so let me move that important stuff
+ 
+
+ align:start position:0%
+so let me move that important stuff
+right up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me call them say V1 up to I'll use
+
+ align:start position:0%
+let me call them say V1 up to I'll use
+ 
+
+ align:start position:0%
+let me call them say V1 up to I'll use
+some different letter say V L
+
+ align:start position:0%
+some different letter say V L
+ 
+
+ align:start position:0%
+some different letter say V L
+span
+
+ align:start position:0%
+span
+ 
+
+ align:start position:0%
+span
+a space
+
+ align:start position:0%
+a space
+ 
+
+ align:start position:0%
+a space
+a subspace
+
+ align:start position:0%
+a subspace
+ 
+
+ align:start position:0%
+a subspace
+or just a vector space I could say span
+
+ align:start position:0%
+or just a vector space I could say span
+ 
+
+ align:start position:0%
+or just a vector space I could say span
+a space means
+
+ align:start position:0%
+a space means
+ 
+
+ align:start position:0%
+a space means
+means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The space
+
+ align:start position:0%
+The space
+ 
+
+ align:start position:0%
+The space
+consists of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+combinations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of those vectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That that's exactly what we did with the
+
+ align:start position:0%
+That that's exactly what we did with the
+ 
+
+ align:start position:0%
+That that's exactly what we did with the
+column space.
+
+ align:start position:0%
+column space.
+ 
+
+ align:start position:0%
+column space.
+So now I could say in shorthand the
+
+ align:start position:0%
+So now I could say in shorthand the
+ 
+
+ align:start position:0%
+So now I could say in shorthand the
+columns of a matrix span the column
+
+ align:start position:0%
+columns of a matrix span the column
+ 
+
+ align:start position:0%
+columns of a matrix span the column
+space.
+
+ align:start position:0%
+space.
+ 
+
+ align:start position:0%
+space.
+So remember it's a bunch of vectors that
+
+ align:start position:0%
+So remember it's a bunch of vectors that
+ 
+
+ align:start position:0%
+So remember it's a bunch of vectors that
+have this property that they span a
+
+ align:start position:0%
+have this property that they span a
+ 
+
+ align:start position:0%
+have this property that they span a
+space. And actually
+
+ align:start position:0%
+space. And actually
+ 
+
+ align:start position:0%
+space. And actually
+if I give you a bunch of vectors and say
+
+ align:start position:0%
+if I give you a bunch of vectors and say
+ 
+
+ align:start position:0%
+if I give you a bunch of vectors and say
+okay let s be the space that they span.
+
+ align:start position:0%
+okay let s be the space that they span.
+ 
+
+ align:start position:0%
+okay let s be the space that they span.
+In other words let s contain all their
+
+ align:start position:0%
+In other words let s contain all their
+ 
+
+ align:start position:0%
+In other words let s contain all their
+combinations.
+
+ align:start position:0%
+combinations.
+ 
+
+ align:start position:0%
+combinations.
+that space s will be the smallest space
+
+ align:start position:0%
+that space s will be the smallest space
+ 
+
+ align:start position:0%
+that space s will be the smallest space
+with those vectors in it. Right? Because
+
+ align:start position:0%
+with those vectors in it. Right? Because
+ 
+
+ align:start position:0%
+with those vectors in it. Right? Because
+any space with those vectors in it must
+
+ align:start position:0%
+any space with those vectors in it must
+ 
+
+ align:start position:0%
+any space with those vectors in it must
+have all the combinations of those
+
+ align:start position:0%
+have all the combinations of those
+ 
+
+ align:start position:0%
+have all the combinations of those
+vectors in it. And if I stop there,
+
+ align:start position:0%
+vectors in it. And if I stop there,
+ 
+
+ align:start position:0%
+vectors in it. And if I stop there,
+then I've got the smallest space and
+
+ align:start position:0%
+then I've got the smallest space and
+ 
+
+ align:start position:0%
+then I've got the smallest space and
+that's the space that they span. Okay?
+
+ align:start position:0%
+that's the space that they span. Okay?
+ 
+
+ align:start position:0%
+that's the space that they span. Okay?
+So I'm just rather than uh needing to
+
+ align:start position:0%
+So I'm just rather than uh needing to
+ 
+
+ align:start position:0%
+So I'm just rather than uh needing to
+say take all linear combinations and put
+
+ align:start position:0%
+say take all linear combinations and put
+ 
+
+ align:start position:0%
+say take all linear combinations and put
+them in a space, I'm I'm compressing
+
+ align:start position:0%
+them in a space, I'm I'm compressing
+ 
+
+ align:start position:0%
+them in a space, I'm I'm compressing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+into the word span.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Straightforward.
+
+ align:start position:0%
+Straightforward.
+ 
+
+ align:start position:0%
+Straightforward.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So if I think of a of the column space
+
+ align:start position:0%
+So if I think of a of the column space
+ 
+
+ align:start position:0%
+So if I think of a of the column space
+of a matrix,
+
+ align:start position:0%
+of a matrix,
+ 
+
+ align:start position:0%
+of a matrix,
+I've got I've got their So I start with
+
+ align:start position:0%
+I've got I've got their So I start with
+ 
+
+ align:start position:0%
+I've got I've got their So I start with
+the columns. I take all their
+
+ align:start position:0%
+the columns. I take all their
+ 
+
+ align:start position:0%
+the columns. I take all their
+combinations that gives me the column
+
+ align:start position:0%
+combinations that gives me the column
+ 
+
+ align:start position:0%
+combinations that gives me the column
+space. They span the column space. Now,
+
+ align:start position:0%
+space. They span the column space. Now,
+ 
+
+ align:start position:0%
+space. They span the column space. Now,
+are they independent?
+
+ align:start position:0%
+are they independent?
+ 
+
+ align:start position:0%
+are they independent?
+Maybe yes, maybe no.
+
+ align:start position:0%
+Maybe yes, maybe no.
+ 
+
+ align:start position:0%
+Maybe yes, maybe no.
+It depends on the particular columns
+
+ align:start position:0%
+It depends on the particular columns
+ 
+
+ align:start position:0%
+It depends on the particular columns
+that went into that matrix.
+
+ align:start position:0%
+that went into that matrix.
+ 
+
+ align:start position:0%
+that went into that matrix.
+But obviously, I'm highly interested in
+
+ align:start position:0%
+But obviously, I'm highly interested in
+ 
+
+ align:start position:0%
+But obviously, I'm highly interested in
+a set of vectors
+
+ align:start position:0%
+a set of vectors
+ 
+
+ align:start position:0%
+a set of vectors
+that spans the space and is independent.
+
+ align:start position:0%
+that spans the space and is independent.
+ 
+
+ align:start position:0%
+that spans the space and is independent.
+That's that means like I've got the
+
+ align:start position:0%
+That's that means like I've got the
+ 
+
+ align:start position:0%
+That's that means like I've got the
+right number of vectors.
+
+ align:start position:0%
+right number of vectors.
+ 
+
+ align:start position:0%
+right number of vectors.
+If I didn't have all of them, I wouldn't
+
+ align:start position:0%
+If I didn't have all of them, I wouldn't
+ 
+
+ align:start position:0%
+If I didn't have all of them, I wouldn't
+have my whole space.
+
+ align:start position:0%
+have my whole space.
+ 
+
+ align:start position:0%
+have my whole space.
+If I had more than that, they probably
+
+ align:start position:0%
+If I had more than that, they probably
+ 
+
+ align:start position:0%
+If I had more than that, they probably
+wouldn't they wouldn't be independent.
+
+ align:start position:0%
+wouldn't they wouldn't be independent.
+ 
+
+ align:start position:0%
+wouldn't they wouldn't be independent.
+So like basis and that's the word that's
+
+ align:start position:0%
+So like basis and that's the word that's
+ 
+
+ align:start position:0%
+So like basis and that's the word that's
+coming is just right. So here let me put
+
+ align:start position:0%
+coming is just right. So here let me put
+ 
+
+ align:start position:0%
+coming is just right. So here let me put
+what that word means. A basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a vector for a vector space is
+
+ align:start position:0%
+for a vector for a vector space is
+ 
+
+ align:start position:0%
+for a vector for a vector space is
+is a is a sequence of vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shall I call them v1 v2
+
+ align:start position:0%
+shall I call them v1 v2
+ 
+
+ align:start position:0%
+shall I call them v1 v2
+up to let me say v d now I'll stop with
+
+ align:start position:0%
+up to let me say v d now I'll stop with
+ 
+
+ align:start position:0%
+up to let me say v d now I'll stop with
+that letters that has two properties.
+
+ align:start position:0%
+that letters that has two properties.
+ 
+
+ align:start position:0%
+that letters that has two properties.
+I've got enough vectors and not too
+
+ align:start position:0%
+I've got enough vectors and not too
+ 
+
+ align:start position:0%
+I've got enough vectors and not too
+many. It's a natural idea of a basis. So
+
+ align:start position:0%
+many. It's a natural idea of a basis. So
+ 
+
+ align:start position:0%
+many. It's a natural idea of a basis. So
+a basis is a bunch of vectors in the
+
+ align:start position:0%
+a basis is a bunch of vectors in the
+ 
+
+ align:start position:0%
+a basis is a bunch of vectors in the
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and it's a so it's a sequence of vectors
+
+ align:start position:0%
+and it's a so it's a sequence of vectors
+ 
+
+ align:start position:0%
+and it's a so it's a sequence of vectors
+with two properties with
+
+ align:start position:0%
+with two properties with
+ 
+
+ align:start position:0%
+with two properties with
+two properties.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One,
+
+ align:start position:0%
+One,
+ 
+
+ align:start position:0%
+One,
+they are independent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And two,
+
+ align:start position:0%
+And two,
+ 
+
+ align:start position:0%
+And two,
+you know what's coming? They span the
+
+ align:start position:0%
+you know what's coming? They span the
+ 
+
+ align:start position:0%
+you know what's coming? They span the
+space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+let me take
+
+ align:start position:0%
+let me take
+ 
+
+ align:start position:0%
+let me take
+So time for examples of course.
+
+ align:start position:0%
+So time for examples of course.
+ 
+
+ align:start position:0%
+So time for examples of course.
+So I'm asking you now to put definition
+
+ align:start position:0%
+So I'm asking you now to put definition
+ 
+
+ align:start position:0%
+So I'm asking you now to put definition
+one the definition of independence
+
+ align:start position:0%
+one the definition of independence
+ 
+
+ align:start position:0%
+one the definition of independence
+together with definition two and let's
+
+ align:start position:0%
+together with definition two and let's
+ 
+
+ align:start position:0%
+together with definition two and let's
+look at examples because this is this
+
+ align:start position:0%
+look at examples because this is this
+ 
+
+ align:start position:0%
+look at examples because this is this
+combination means the set of of vectors
+
+ align:start position:0%
+combination means the set of of vectors
+ 
+
+ align:start position:0%
+combination means the set of of vectors
+I have is just right and that so that
+
+ align:start position:0%
+I have is just right and that so that
+ 
+
+ align:start position:0%
+I have is just right and that so that
+this idea of a basis will be central.
+
+ align:start position:0%
+this idea of a basis will be central.
+ 
+
+ align:start position:0%
+this idea of a basis will be central.
+I'll always be asking you now for a
+
+ align:start position:0%
+I'll always be asking you now for a
+ 
+
+ align:start position:0%
+I'll always be asking you now for a
+basis. Whenever I look at a subspace,
+
+ align:start position:0%
+basis. Whenever I look at a subspace,
+ 
+
+ align:start position:0%
+basis. Whenever I look at a subspace,
+if I ask you for if you give me a basis
+
+ align:start position:0%
+if I ask you for if you give me a basis
+ 
+
+ align:start position:0%
+if I ask you for if you give me a basis
+for that subspace, you've told me what
+
+ align:start position:0%
+for that subspace, you've told me what
+ 
+
+ align:start position:0%
+for that subspace, you've told me what
+it is. You've told me everything I need
+
+ align:start position:0%
+it is. You've told me everything I need
+ 
+
+ align:start position:0%
+it is. You've told me everything I need
+to know about that subspace. Those I
+
+ align:start position:0%
+to know about that subspace. Those I
+ 
+
+ align:start position:0%
+to know about that subspace. Those I
+take their combinations and I know that
+
+ align:start position:0%
+take their combinations and I know that
+ 
+
+ align:start position:0%
+take their combinations and I know that
+I need all the combinations. Okay.
+
+ align:start position:0%
+I need all the combinations. Okay.
+ 
+
+ align:start position:0%
+I need all the combinations. Okay.
+Examples.
+
+ align:start position:0%
+Examples.
+ 
+
+ align:start position:0%
+Examples.
+Okay. So, examples of a basis. Let me
+
+ align:start position:0%
+Okay. So, examples of a basis. Let me
+ 
+
+ align:start position:0%
+Okay. So, examples of a basis. Let me
+start with two-dimensional space.
+
+ align:start position:0%
+start with two-dimensional space.
+ 
+
+ align:start position:0%
+start with two-dimensional space.
+Suppose the the space say example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the space is
+
+ align:start position:0%
+the space is
+ 
+
+ align:start position:0%
+the space is
+uh let's make it R3
+
+ align:start position:0%
+uh let's make it R3
+ 
+
+ align:start position:0%
+uh let's make it R3
+real threedimensional space
+
+ align:start position:0%
+real threedimensional space
+ 
+
+ align:start position:0%
+real threedimensional space
+give me one basis one basis is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want some vectors
+
+ align:start position:0%
+so I want some vectors
+ 
+
+ align:start position:0%
+so I want some vectors
+because if I ask you for a basis I'm
+
+ align:start position:0%
+because if I ask you for a basis I'm
+ 
+
+ align:start position:0%
+because if I ask you for a basis I'm
+asking you for vectors a little list of
+
+ align:start position:0%
+asking you for vectors a little list of
+ 
+
+ align:start position:0%
+asking you for vectors a little list of
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it should be just right. So what would
+
+ align:start position:0%
+it should be just right. So what would
+ 
+
+ align:start position:0%
+it should be just right. So what would
+be a basis for three-dimensional space?
+
+ align:start position:0%
+be a basis for three-dimensional space?
+ 
+
+ align:start position:0%
+be a basis for three-dimensional space?
+Well, the first basis that comes to
+
+ align:start position:0%
+Well, the first basis that comes to
+ 
+
+ align:start position:0%
+Well, the first basis that comes to
+mind, why don't we write that down? The
+
+ align:start position:0%
+mind, why don't we write that down? The
+ 
+
+ align:start position:0%
+mind, why don't we write that down? The
+first basis that comes to mind is this
+
+ align:start position:0%
+first basis that comes to mind is this
+ 
+
+ align:start position:0%
+first basis that comes to mind is this
+vector,
+
+ align:start position:0%
+vector,
+ 
+
+ align:start position:0%
+vector,
+this vector,
+
+ align:start position:0%
+this vector,
+ 
+
+ align:start position:0%
+this vector,
+and this vector.
+
+ align:start position:0%
+and this vector.
+ 
+
+ align:start position:0%
+and this vector.
+Okay, that's one basis.
+
+ align:start position:0%
+Okay, that's one basis.
+ 
+
+ align:start position:0%
+Okay, that's one basis.
+Not the only basis. That's going to be
+
+ align:start position:0%
+Not the only basis. That's going to be
+ 
+
+ align:start position:0%
+Not the only basis. That's going to be
+my point.
+
+ align:start position:0%
+my point.
+ 
+
+ align:start position:0%
+my point.
+But let's just see. Yes, that's a basis.
+
+ align:start position:0%
+But let's just see. Yes, that's a basis.
+ 
+
+ align:start position:0%
+But let's just see. Yes, that's a basis.
+Is every are those vectors independent?
+
+ align:start position:0%
+Is every are those vectors independent?
+ 
+
+ align:start position:0%
+Is every are those vectors independent?
+So that's the like the X, Y, and Z axis.
+
+ align:start position:0%
+So that's the like the X, Y, and Z axis.
+ 
+
+ align:start position:0%
+So that's the like the X, Y, and Z axis.
+So if those are not independent, we're
+
+ align:start position:0%
+So if those are not independent, we're
+ 
+
+ align:start position:0%
+So if those are not independent, we're
+in trouble. Certainly they are. Take a
+
+ align:start position:0%
+in trouble. Certainly they are. Take a
+ 
+
+ align:start position:0%
+in trouble. Certainly they are. Take a
+combination C1 of this vector plus C2 of
+
+ align:start position:0%
+combination C1 of this vector plus C2 of
+ 
+
+ align:start position:0%
+combination C1 of this vector plus C2 of
+this vector plus C3 of that vector and
+
+ align:start position:0%
+this vector plus C3 of that vector and
+ 
+
+ align:start position:0%
+this vector plus C3 of that vector and
+try to make it give the zero vector.
+
+ align:start position:0%
+try to make it give the zero vector.
+ 
+
+ align:start position:0%
+try to make it give the zero vector.
+What are the C's?
+
+ align:start position:0%
+What are the C's?
+ 
+
+ align:start position:0%
+What are the C's?
+If C1 of that plus C2 of that plus C3 of
+
+ align:start position:0%
+If C1 of that plus C2 of that plus C3 of
+ 
+
+ align:start position:0%
+If C1 of that plus C2 of that plus C3 of
+that gives me 0 0, then the C's are all
+
+ align:start position:0%
+that gives me 0 0, then the C's are all
+ 
+
+ align:start position:0%
+that gives me 0 0, then the C's are all
+zero. Right? So that's the test for
+
+ align:start position:0%
+zero. Right? So that's the test for
+ 
+
+ align:start position:0%
+zero. Right? So that's the test for
+independence
+
+ align:start position:0%
+independence
+ 
+
+ align:start position:0%
+independence
+in the language of matrices.
+
+ align:start position:0%
+in the language of matrices.
+ 
+
+ align:start position:0%
+in the language of matrices.
+which was under that board. I could make
+
+ align:start position:0%
+which was under that board. I could make
+ 
+
+ align:start position:0%
+which was under that board. I could make
+those the columns of a matrix. Well, it
+
+ align:start position:0%
+those the columns of a matrix. Well, it
+ 
+
+ align:start position:0%
+those the columns of a matrix. Well, it
+would be the identity matrix.
+
+ align:start position:0%
+would be the identity matrix.
+ 
+
+ align:start position:0%
+would be the identity matrix.
+Then I would ask what's the null space
+
+ align:start position:0%
+Then I would ask what's the null space
+ 
+
+ align:start position:0%
+Then I would ask what's the null space
+of the identity matrix. And you would
+
+ align:start position:0%
+of the identity matrix. And you would
+ 
+
+ align:start position:0%
+of the identity matrix. And you would
+say it's only the zero vector. And I
+
+ align:start position:0%
+say it's only the zero vector. And I
+ 
+
+ align:start position:0%
+say it's only the zero vector. And I
+would say fine then the columns are
+
+ align:start position:0%
+would say fine then the columns are
+ 
+
+ align:start position:0%
+would say fine then the columns are
+independent.
+
+ align:start position:0%
+independent.
+ 
+
+ align:start position:0%
+independent.
+The only thing the identity times a
+
+ align:start position:0%
+The only thing the identity times a
+ 
+
+ align:start position:0%
+The only thing the identity times a
+vector giving zero the only ve vector
+
+ align:start position:0%
+vector giving zero the only ve vector
+ 
+
+ align:start position:0%
+vector giving zero the only ve vector
+that does that is zero. Okay.
+
+ align:start position:0%
+that does that is zero. Okay.
+ 
+
+ align:start position:0%
+that does that is zero. Okay.
+Now, that's not the only basis. Far from
+
+ align:start position:0%
+Now, that's not the only basis. Far from
+ 
+
+ align:start position:0%
+Now, that's not the only basis. Far from
+it. Tell me another basis. A second
+
+ align:start position:0%
+it. Tell me another basis. A second
+ 
+
+ align:start position:0%
+it. Tell me another basis. A second
+basis. Another basis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+uh, give me well, I'll just start it
+
+ align:start position:0%
+uh, give me well, I'll just start it
+ 
+
+ align:start position:0%
+uh, give me well, I'll just start it
+out. One, one, two,
+
+ align:start position:0%
+out. One, one, two,
+ 
+
+ align:start position:0%
+out. One, one, two,
+uh, 225.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh suppose I stop there.
+
+ align:start position:0%
+Uh suppose I stop there.
+ 
+
+ align:start position:0%
+Uh suppose I stop there.
+Have has that has that see has that have
+
+ align:start position:0%
+Have has that has that see has that have
+ 
+
+ align:start position:0%
+Have has that has that see has that have
+has that little bunch of vectors got the
+
+ align:start position:0%
+has that little bunch of vectors got the
+ 
+
+ align:start position:0%
+has that little bunch of vectors got the
+properties that I'm asking for in a
+
+ align:start position:0%
+properties that I'm asking for in a
+ 
+
+ align:start position:0%
+properties that I'm asking for in a
+basis for R3? We're we're looking for a
+
+ align:start position:0%
+basis for R3? We're we're looking for a
+ 
+
+ align:start position:0%
+basis for R3? We're we're looking for a
+basis for R3. Are they independent,
+
+ align:start position:0%
+basis for R3. Are they independent,
+ 
+
+ align:start position:0%
+basis for R3. Are they independent,
+those two column vectors? Yes. Do they
+
+ align:start position:0%
+those two column vectors? Yes. Do they
+ 
+
+ align:start position:0%
+those two column vectors? Yes. Do they
+span R3?
+
+ align:start position:0%
+span R3?
+ 
+
+ align:start position:0%
+span R3?
+No. Our feeling is no. Our feeling is
+
+ align:start position:0%
+No. Our feeling is no. Our feeling is
+ 
+
+ align:start position:0%
+No. Our feeling is no. Our feeling is
+no. Our feeling is that there's some
+
+ align:start position:0%
+no. Our feeling is that there's some
+ 
+
+ align:start position:0%
+no. Our feeling is that there's some
+vectors in R3 that are not combinations
+
+ align:start position:0%
+vectors in R3 that are not combinations
+ 
+
+ align:start position:0%
+vectors in R3 that are not combinations
+of those. Okay. So suppose I add in a I
+
+ align:start position:0%
+of those. Okay. So suppose I add in a I
+ 
+
+ align:start position:0%
+of those. Okay. So suppose I add in a I
+need another vector then because they
+
+ align:start position:0%
+need another vector then because they
+ 
+
+ align:start position:0%
+need another vector then because they
+these two don't span the space. Okay.
+
+ align:start position:0%
+these two don't span the space. Okay.
+ 
+
+ align:start position:0%
+these two don't span the space. Okay.
+Now it would be foolish for me to put in
+
+ align:start position:0%
+Now it would be foolish for me to put in
+ 
+
+ align:start position:0%
+Now it would be foolish for me to put in
+337 right as the third vector.
+
+ align:start position:0%
+337 right as the third vector.
+ 
+
+ align:start position:0%
+337 right as the third vector.
+That would be a goof because that if I
+
+ align:start position:0%
+That would be a goof because that if I
+ 
+
+ align:start position:0%
+That would be a goof because that if I
+put in 337, those vectors would be
+
+ align:start position:0%
+put in 337, those vectors would be
+ 
+
+ align:start position:0%
+put in 337, those vectors would be
+dependent, right? If I put in 337, it
+
+ align:start position:0%
+dependent, right? If I put in 337, it
+ 
+
+ align:start position:0%
+dependent, right? If I put in 337, it
+would be the sum of those two. It would
+
+ align:start position:0%
+would be the sum of those two. It would
+ 
+
+ align:start position:0%
+would be the sum of those two. It would
+lie in the same plane as those. It
+
+ align:start position:0%
+lie in the same plane as those. It
+ 
+
+ align:start position:0%
+lie in the same plane as those. It
+wouldn't be independent. I wouldn't I
+
+ align:start position:0%
+wouldn't be independent. I wouldn't I
+ 
+
+ align:start position:0%
+wouldn't be independent. I wouldn't I
+wouldn't I my attempt to create a basis
+
+ align:start position:0%
+wouldn't I my attempt to create a basis
+ 
+
+ align:start position:0%
+wouldn't I my attempt to create a basis
+would be dead. But if I take So what
+
+ align:start position:0%
+would be dead. But if I take So what
+ 
+
+ align:start position:0%
+would be dead. But if I take So what
+vector can I take?
+
+ align:start position:0%
+vector can I take?
+ 
+
+ align:start position:0%
+vector can I take?
+I can take any vector that's not in that
+
+ align:start position:0%
+I can take any vector that's not in that
+ 
+
+ align:start position:0%
+I can take any vector that's not in that
+plane. Let me try. I I hope that 338
+
+ align:start position:0%
+plane. Let me try. I I hope that 338
+ 
+
+ align:start position:0%
+plane. Let me try. I I hope that 338
+would do it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+At least it's not the sum of those two
+
+ align:start position:0%
+At least it's not the sum of those two
+ 
+
+ align:start position:0%
+At least it's not the sum of those two
+vectors. But I believe that's a basis.
+
+ align:start position:0%
+vectors. But I believe that's a basis.
+ 
+
+ align:start position:0%
+vectors. But I believe that's a basis.
+And what's the what's the test then for
+
+ align:start position:0%
+And what's the what's the test then for
+ 
+
+ align:start position:0%
+And what's the what's the test then for
+that to be a basis? What? Because I just
+
+ align:start position:0%
+that to be a basis? What? Because I just
+ 
+
+ align:start position:0%
+that to be a basis? What? Because I just
+picked those numbers. And if I had
+
+ align:start position:0%
+picked those numbers. And if I had
+ 
+
+ align:start position:0%
+picked those numbers. And if I had
+picked uh 57
+
+ align:start position:0%
+picked uh 57
+ 
+
+ align:start position:0%
+picked uh 57
+minus14,
+
+ align:start position:0%
+minus14,
+ 
+
+ align:start position:0%
+minus14,
+how would we know do we have a basis or
+
+ align:start position:0%
+how would we know do we have a basis or
+ 
+
+ align:start position:0%
+how would we know do we have a basis or
+don't we?
+
+ align:start position:0%
+don't we?
+ 
+
+ align:start position:0%
+don't we?
+You would put them in the columns of a
+
+ align:start position:0%
+You would put them in the columns of a
+ 
+
+ align:start position:0%
+You would put them in the columns of a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+and you would do elimination row
+
+ align:start position:0%
+and you would do elimination row
+ 
+
+ align:start position:0%
+and you would do elimination row
+reduction and you would see do you get
+
+ align:start position:0%
+reduction and you would see do you get
+ 
+
+ align:start position:0%
+reduction and you would see do you get
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+free variables or are all the columns
+
+ align:start position:0%
+free variables or are all the columns
+ 
+
+ align:start position:0%
+free variables or are all the columns
+pivot columns? Well, now actually we
+
+ align:start position:0%
+pivot columns? Well, now actually we
+ 
+
+ align:start position:0%
+pivot columns? Well, now actually we
+have a square. The matrix would be 3x3.
+
+ align:start position:0%
+have a square. The matrix would be 3x3.
+ 
+
+ align:start position:0%
+have a square. The matrix would be 3x3.
+So, so what's the test on the matrix
+
+ align:start position:0%
+So, so what's the test on the matrix
+ 
+
+ align:start position:0%
+So, so what's the test on the matrix
+then?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The matrix. So, so in this case when I
+
+ align:start position:0%
+The matrix. So, so in this case when I
+ 
+
+ align:start position:0%
+The matrix. So, so in this case when I
+when my space is R3 and I have three
+
+ align:start position:0%
+when my space is R3 and I have three
+ 
+
+ align:start position:0%
+when my space is R3 and I have three
+vectors,
+
+ align:start position:0%
+vectors,
+ 
+
+ align:start position:0%
+vectors,
+my matrix is square.
+
+ align:start position:0%
+my matrix is square.
+ 
+
+ align:start position:0%
+my matrix is square.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+what am I asking about that matrix in
+
+ align:start position:0%
+what am I asking about that matrix in
+ 
+
+ align:start position:0%
+what am I asking about that matrix in
+order for those columns to be a basis?
+
+ align:start position:0%
+order for those columns to be a basis?
+ 
+
+ align:start position:0%
+order for those columns to be a basis?
+So the so in this in this for Rn
+
+ align:start position:0%
+So the so in this in this for Rn
+ 
+
+ align:start position:0%
+So the so in this in this for Rn
+if I have n vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+give a basis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+the n byn matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with those columns
+
+ align:start position:0%
+with those columns
+ 
+
+ align:start position:0%
+with those columns
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+those columns
+
+ align:start position:0%
+those columns
+ 
+
+ align:start position:0%
+those columns
+is what
+
+ align:start position:0%
+is what
+ 
+
+ align:start position:0%
+is what
+what's what's the requirement on that
+
+ align:start position:0%
+what's what's the requirement on that
+ 
+
+ align:start position:0%
+what's what's the requirement on that
+matrix?
+
+ align:start position:0%
+matrix?
+ 
+
+ align:start position:0%
+matrix?
+Invertible. Right. Right. The matrix
+
+ align:start position:0%
+Invertible. Right. Right. The matrix
+ 
+
+ align:start position:0%
+Invertible. Right. Right. The matrix
+should be invertible for a square
+
+ align:start position:0%
+should be invertible for a square
+ 
+
+ align:start position:0%
+should be invertible for a square
+matrix. That's the that's the perfect
+
+ align:start position:0%
+matrix. That's the that's the perfect
+ 
+
+ align:start position:0%
+matrix. That's the that's the perfect
+answer is invertible.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's when that's when the space is
+
+ align:start position:0%
+So that's when that's when the space is
+ 
+
+ align:start position:0%
+So that's when that's when the space is
+is is the whole space Rn.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me let me be sure I I'm with you're
+
+ align:start position:0%
+Let me let me be sure I I'm with you're
+ 
+
+ align:start position:0%
+Let me let me be sure I I'm with you're
+with me here. Let me remove that.
+
+ align:start position:0%
+with me here. Let me remove that.
+ 
+
+ align:start position:0%
+with me here. Let me remove that.
+Are those two vectors a basis for
+
+ align:start position:0%
+Are those two vectors a basis for
+ 
+
+ align:start position:0%
+Are those two vectors a basis for
+any space at all?
+
+ align:start position:0%
+any space at all?
+ 
+
+ align:start position:0%
+any space at all?
+Is there a vector space that those
+
+ align:start position:0%
+Is there a vector space that those
+ 
+
+ align:start position:0%
+Is there a vector space that those
+really are a basis for? Those that pair
+
+ align:start position:0%
+really are a basis for? Those that pair
+ 
+
+ align:start position:0%
+really are a basis for? Those that pair
+of vectors, this guy and this one 112
+
+ align:start position:0%
+of vectors, this guy and this one 112
+ 
+
+ align:start position:0%
+of vectors, this guy and this one 112
+and 225. Is there a space for which
+
+ align:start position:0%
+and 225. Is there a space for which
+ 
+
+ align:start position:0%
+and 225. Is there a space for which
+that's a basis?
+
+ align:start position:0%
+that's a basis?
+ 
+
+ align:start position:0%
+that's a basis?
+Sure, they're independent.
+
+ align:start position:0%
+Sure, they're independent.
+ 
+
+ align:start position:0%
+Sure, they're independent.
+So they satisfy the first requirement.
+
+ align:start position:0%
+So they satisfy the first requirement.
+ 
+
+ align:start position:0%
+So they satisfy the first requirement.
+So what space shall I take for them to
+
+ align:start position:0%
+So what space shall I take for them to
+ 
+
+ align:start position:0%
+So what space shall I take for them to
+be a basis of? What spaces will they be
+
+ align:start position:0%
+be a basis of? What spaces will they be
+ 
+
+ align:start position:0%
+be a basis of? What spaces will they be
+a basis for?
+
+ align:start position:0%
+a basis for?
+ 
+
+ align:start position:0%
+a basis for?
+the one they span they're combinations
+
+ align:start position:0%
+the one they span they're combinations
+ 
+
+ align:start position:0%
+the one they span they're combinations
+if it's a plane right it will be a plane
+
+ align:start position:0%
+if it's a plane right it will be a plane
+ 
+
+ align:start position:0%
+if it's a plane right it will be a plane
+inside R3 so if I take this vector 112
+
+ align:start position:0%
+inside R3 so if I take this vector 112
+ 
+
+ align:start position:0%
+inside R3 so if I take this vector 112
+say it goes there and this vector 225
+
+ align:start position:0%
+say it goes there and this vector 225
+ 
+
+ align:start position:0%
+say it goes there and this vector 225
+say it goes there those are a basis for
+
+ align:start position:0%
+say it goes there those are a basis for
+ 
+
+ align:start position:0%
+say it goes there those are a basis for
+because they span a plane
+
+ align:start position:0%
+because they span a plane
+ 
+
+ align:start position:0%
+because they span a plane
+and they're a basis for the plane
+
+ align:start position:0%
+and they're a basis for the plane
+ 
+
+ align:start position:0%
+and they're a basis for the plane
+because they're independent if I stick
+
+ align:start position:0%
+because they're independent if I stick
+ 
+
+ align:start position:0%
+because they're independent if I stick
+in some third guy like 337 which is in
+
+ align:start position:0%
+in some third guy like 337 which is in
+ 
+
+ align:start position:0%
+in some third guy like 337 which is in
+the plane
+
+ align:start position:0%
+the plane
+ 
+
+ align:start position:0%
+the plane
+Suppose I put in try to put in 337 then
+
+ align:start position:0%
+Suppose I put in try to put in 337 then
+ 
+
+ align:start position:0%
+Suppose I put in try to put in 337 then
+the three vectors would still span the
+
+ align:start position:0%
+the three vectors would still span the
+ 
+
+ align:start position:0%
+the three vectors would still span the
+plane but they wouldn't be a basis
+
+ align:start position:0%
+plane but they wouldn't be a basis
+ 
+
+ align:start position:0%
+plane but they wouldn't be a basis
+anymore because they're not independent
+
+ align:start position:0%
+anymore because they're not independent
+ 
+
+ align:start position:0%
+anymore because they're not independent
+anymore. Okay. So uh we're looking at
+
+ align:start position:0%
+anymore. Okay. So uh we're looking at
+ 
+
+ align:start position:0%
+anymore. Okay. So uh we're looking at
+the question of so again
+
+ align:start position:0%
+the question of so again
+ 
+
+ align:start position:0%
+the question of so again
+a the case with in independent columns
+
+ align:start position:0%
+a the case with in independent columns
+ 
+
+ align:start position:0%
+a the case with in independent columns
+is the case where the column vectors
+
+ align:start position:0%
+is the case where the column vectors
+ 
+
+ align:start position:0%
+is the case where the column vectors
+span the column space. They're
+
+ align:start position:0%
+span the column space. They're
+ 
+
+ align:start position:0%
+span the column space. They're
+independent so they're a basis for the
+
+ align:start position:0%
+independent so they're a basis for the
+ 
+
+ align:start position:0%
+independent so they're a basis for the
+column space. Okay. So now there's one
+
+ align:start position:0%
+column space. Okay. So now there's one
+ 
+
+ align:start position:0%
+column space. Okay. So now there's one
+bit of intuition.
+
+ align:start position:0%
+bit of intuition.
+ 
+
+ align:start position:0%
+bit of intuition.
+Let me go back to all of Rn.
+
+ align:start position:0%
+Let me go back to all of Rn.
+ 
+
+ align:start position:0%
+Let me go back to all of Rn.
+So where I put 338.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. The first message is that the
+
+ align:start position:0%
+Okay. The first message is that the
+ 
+
+ align:start position:0%
+Okay. The first message is that the
+basis is not unique. Right? There's
+
+ align:start position:0%
+basis is not unique. Right? There's
+ 
+
+ align:start position:0%
+basis is not unique. Right? There's
+zillions of bases. I take any invertible
+
+ align:start position:0%
+zillions of bases. I take any invertible
+ 
+
+ align:start position:0%
+zillions of bases. I take any invertible
+3x3 matrix. its columns are a basis for
+
+ align:start position:0%
+3x3 matrix. its columns are a basis for
+ 
+
+ align:start position:0%
+3x3 matrix. its columns are a basis for
+R3.
+
+ align:start position:0%
+R3.
+ 
+
+ align:start position:0%
+R3.
+The column space is R3. And if those if
+
+ align:start position:0%
+The column space is R3. And if those if
+ 
+
+ align:start position:0%
+The column space is R3. And if those if
+that matrix is invertible, those columns
+
+ align:start position:0%
+that matrix is invertible, those columns
+ 
+
+ align:start position:0%
+that matrix is invertible, those columns
+are independent. I've got a basis for
+
+ align:start position:0%
+are independent. I've got a basis for
+ 
+
+ align:start position:0%
+are independent. I've got a basis for
+R3. So there are many many bases, but
+
+ align:start position:0%
+R3. So there are many many bases, but
+ 
+
+ align:start position:0%
+R3. So there are many many bases, but
+there is something
+
+ align:start position:0%
+there is something
+ 
+
+ align:start position:0%
+there is something
+in common for all those bases.
+
+ align:start position:0%
+in common for all those bases.
+ 
+
+ align:start position:0%
+in common for all those bases.
+There's something that this basis shares
+
+ align:start position:0%
+There's something that this basis shares
+ 
+
+ align:start position:0%
+There's something that this basis shares
+with that basis and every other basis
+
+ align:start position:0%
+with that basis and every other basis
+ 
+
+ align:start position:0%
+with that basis and every other basis
+for R3.
+
+ align:start position:0%
+for R3.
+ 
+
+ align:start position:0%
+for R3.
+And what's that?
+
+ align:start position:0%
+And what's that?
+ 
+
+ align:start position:0%
+And what's that?
+Well, you saw it coming because when I
+
+ align:start position:0%
+Well, you saw it coming because when I
+ 
+
+ align:start position:0%
+Well, you saw it coming because when I
+stopped here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and asked if that was a basis for R3,
+
+ align:start position:0%
+and asked if that was a basis for R3,
+ 
+
+ align:start position:0%
+and asked if that was a basis for R3,
+you said no. And I know that you said no
+
+ align:start position:0%
+you said no. And I know that you said no
+ 
+
+ align:start position:0%
+you said no. And I know that you said no
+because you knew there weren't enough
+
+ align:start position:0%
+because you knew there weren't enough
+ 
+
+ align:start position:0%
+because you knew there weren't enough
+vectors there.
+
+ align:start position:0%
+vectors there.
+ 
+
+ align:start position:0%
+vectors there.
+And the great fact is that there are
+
+ align:start position:0%
+And the great fact is that there are
+ 
+
+ align:start position:0%
+And the great fact is that there are
+many, many bases, but let me put in
+
+ align:start position:0%
+many, many bases, but let me put in
+ 
+
+ align:start position:0%
+many, many bases, but let me put in
+somebody else just for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variety.
+
+ align:start position:0%
+variety.
+ 
+
+ align:start position:0%
+variety.
+There are many, many bases, but they all
+
+ align:start position:0%
+There are many, many bases, but they all
+ 
+
+ align:start position:0%
+There are many, many bases, but they all
+have the same number of vectors.
+
+ align:start position:0%
+have the same number of vectors.
+ 
+
+ align:start position:0%
+have the same number of vectors.
+If we're talking about the space R3,
+
+ align:start position:0%
+If we're talking about the space R3,
+ 
+
+ align:start position:0%
+If we're talking about the space R3,
+then that number of vectors is three.
+
+ align:start position:0%
+then that number of vectors is three.
+ 
+
+ align:start position:0%
+then that number of vectors is three.
+If we're talking about the space Rn,
+
+ align:start position:0%
+If we're talking about the space Rn,
+ 
+
+ align:start position:0%
+If we're talking about the space Rn,
+then that number of vectors is N.
+
+ align:start position:0%
+then that number of vectors is N.
+ 
+
+ align:start position:0%
+then that number of vectors is N.
+If we're talking about some other space,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the column space of some matrix
+
+ align:start position:0%
+the column space of some matrix
+ 
+
+ align:start position:0%
+the column space of some matrix
+or the null space of some matrix or some
+
+ align:start position:0%
+or the null space of some matrix or some
+ 
+
+ align:start position:0%
+or the null space of some matrix or some
+other space that we haven't even thought
+
+ align:start position:0%
+other space that we haven't even thought
+ 
+
+ align:start position:0%
+other space that we haven't even thought
+of.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then that still is true that every basis
+
+ align:start position:0%
+Then that still is true that every basis
+ 
+
+ align:start position:0%
+Then that still is true that every basis
+that there are lots of bases but every
+
+ align:start position:0%
+that there are lots of bases but every
+ 
+
+ align:start position:0%
+that there are lots of bases but every
+basis has the same number of vectors.
+
+ align:start position:0%
+basis has the same number of vectors.
+ 
+
+ align:start position:0%
+basis has the same number of vectors.
+Let me write that great fact down.
+
+ align:start position:0%
+Let me write that great fact down.
+ 
+
+ align:start position:0%
+Let me write that great fact down.
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+basis we're we're given a space given
+
+ align:start position:0%
+basis we're we're given a space given
+ 
+
+ align:start position:0%
+basis we're we're given a space given
+a space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R3 or Rn or some other column space of a
+
+ align:start position:0%
+R3 or Rn or some other column space of a
+ 
+
+ align:start position:0%
+R3 or Rn or some other column space of a
+matrix or the null space of a matrix or
+
+ align:start position:0%
+matrix or the null space of a matrix or
+ 
+
+ align:start position:0%
+matrix or the null space of a matrix or
+some other vector space then the great
+
+ align:start position:0%
+some other vector space then the great
+ 
+
+ align:start position:0%
+some other vector space then the great
+fact is that every basis
+
+ align:start position:0%
+fact is that every basis
+ 
+
+ align:start position:0%
+fact is that every basis
+for the for the space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+of vectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If one basis has six vectors, then every
+
+ align:start position:0%
+If one basis has six vectors, then every
+ 
+
+ align:start position:0%
+If one basis has six vectors, then every
+other basis has six vectors.
+
+ align:start position:0%
+other basis has six vectors.
+ 
+
+ align:start position:0%
+other basis has six vectors.
+So that number six is telling me like
+
+ align:start position:0%
+So that number six is telling me like
+ 
+
+ align:start position:0%
+So that number six is telling me like
+it's telling me how big is the space.
+
+ align:start position:0%
+it's telling me how big is the space.
+ 
+
+ align:start position:0%
+it's telling me how big is the space.
+It's telling me how many vectors do I
+
+ align:start position:0%
+It's telling me how many vectors do I
+ 
+
+ align:start position:0%
+It's telling me how many vectors do I
+have to have to have a basis.
+
+ align:start position:0%
+have to have to have a basis.
+ 
+
+ align:start position:0%
+have to have to have a basis.
+And of course, we're seeing it this way.
+
+ align:start position:0%
+And of course, we're seeing it this way.
+ 
+
+ align:start position:0%
+And of course, we're seeing it this way.
+That number six, if we had seven vectors
+
+ align:start position:0%
+That number six, if we had seven vectors
+ 
+
+ align:start position:0%
+That number six, if we had seven vectors
+and we've got too many. If we have five
+
+ align:start position:0%
+and we've got too many. If we have five
+ 
+
+ align:start position:0%
+and we've got too many. If we have five
+vectors, we haven't got enough.
+
+ align:start position:0%
+vectors, we haven't got enough.
+ 
+
+ align:start position:0%
+vectors, we haven't got enough.
+Six is sort of like just right for
+
+ align:start position:0%
+Six is sort of like just right for
+ 
+
+ align:start position:0%
+Six is sort of like just right for
+whatever space that is. And what do we
+
+ align:start position:0%
+whatever space that is. And what do we
+ 
+
+ align:start position:0%
+whatever space that is. And what do we
+call that number? That number is now I'm
+
+ align:start position:0%
+call that number? That number is now I'm
+ 
+
+ align:start position:0%
+call that number? That number is now I'm
+ready for the last definition today.
+
+ align:start position:0%
+ready for the last definition today.
+ 
+
+ align:start position:0%
+ready for the last definition today.
+It's the dimension
+
+ align:start position:0%
+It's the dimension
+ 
+
+ align:start position:0%
+It's the dimension
+of that space. So every basis for a
+
+ align:start position:0%
+of that space. So every basis for a
+ 
+
+ align:start position:0%
+of that space. So every basis for a
+space has the same number of vectors in
+
+ align:start position:0%
+space has the same number of vectors in
+ 
+
+ align:start position:0%
+space has the same number of vectors in
+it. Not the same vectors,
+
+ align:start position:0%
+it. Not the same vectors,
+ 
+
+ align:start position:0%
+it. Not the same vectors,
+all sorts of bases, but the same number
+
+ align:start position:0%
+all sorts of bases, but the same number
+ 
+
+ align:start position:0%
+all sorts of bases, but the same number
+of vectors is always the same. And that
+
+ align:start position:0%
+of vectors is always the same. And that
+ 
+
+ align:start position:0%
+of vectors is always the same. And that
+number is the dimension. This is
+
+ align:start position:0%
+number is the dimension. This is
+ 
+
+ align:start position:0%
+number is the dimension. This is
+definition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This number is the dimension.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the space.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+let's do some examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because now we got definitions. Let me
+
+ align:start position:0%
+because now we got definitions. Let me
+ 
+
+ align:start position:0%
+because now we got definitions. Let me
+repeat the four things, the four words
+
+ align:start position:0%
+repeat the four things, the four words
+ 
+
+ align:start position:0%
+repeat the four things, the four words
+that have now got defined. Independence
+
+ align:start position:0%
+that have now got defined. Independence
+ 
+
+ align:start position:0%
+that have now got defined. Independence
+that looks at combinations not being
+
+ align:start position:0%
+that looks at combinations not being
+ 
+
+ align:start position:0%
+that looks at combinations not being
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+Spanning that looks at all the
+
+ align:start position:0%
+Spanning that looks at all the
+ 
+
+ align:start position:0%
+Spanning that looks at all the
+combinations. Basis that's the one that
+
+ align:start position:0%
+combinations. Basis that's the one that
+ 
+
+ align:start position:0%
+combinations. Basis that's the one that
+combines independence and spanning. And
+
+ align:start position:0%
+combines independence and spanning. And
+ 
+
+ align:start position:0%
+combines independence and spanning. And
+now we've got the idea of the dimension
+
+ align:start position:0%
+now we've got the idea of the dimension
+ 
+
+ align:start position:0%
+now we've got the idea of the dimension
+of a space. It's the number of vectors
+
+ align:start position:0%
+of a space. It's the number of vectors
+ 
+
+ align:start position:0%
+of a space. It's the number of vectors
+in any basis because all bases have the
+
+ align:start position:0%
+in any basis because all bases have the
+ 
+
+ align:start position:0%
+in any basis because all bases have the
+same number. Okay. Let's let's take
+
+ align:start position:0%
+same number. Okay. Let's let's take
+ 
+
+ align:start position:0%
+same number. Okay. Let's let's take
+examples.
+
+ align:start position:0%
+examples.
+ 
+
+ align:start position:0%
+examples.
+Suppose I take
+
+ align:start position:0%
+Suppose I take
+ 
+
+ align:start position:0%
+Suppose I take
+uh my space is examples. Now space is
+
+ align:start position:0%
+uh my space is examples. Now space is
+ 
+
+ align:start position:0%
+uh my space is examples. Now space is
+the say the column space of this matrix.
+
+ align:start position:0%
+the say the column space of this matrix.
+ 
+
+ align:start position:0%
+the say the column space of this matrix.
+Let me let me write down a matrix.
+
+ align:start position:0%
+Let me let me write down a matrix.
+ 
+
+ align:start position:0%
+Let me let me write down a matrix.
+1 one 2 one two and I'll just to make it
+
+ align:start position:0%
+1 one 2 one two and I'll just to make it
+ 
+
+ align:start position:0%
+1 one 2 one two and I'll just to make it
+clear I'll take the sum there 3 2 3 and
+
+ align:start position:0%
+clear I'll take the sum there 3 2 3 and
+ 
+
+ align:start position:0%
+clear I'll take the sum there 3 2 3 and
+let me take the sum of all oh let me put
+
+ align:start position:0%
+let me take the sum of all oh let me put
+ 
+
+ align:start position:0%
+let me take the sum of all oh let me put
+in one yeah I'll put in 11 one again
+
+ align:start position:0%
+in one yeah I'll put in 11 one again
+ 
+
+ align:start position:0%
+in one yeah I'll put in 11 one again
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's four vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay do they span the column space of
+
+ align:start position:0%
+okay do they span the column space of
+ 
+
+ align:start position:0%
+okay do they span the column space of
+that matrix
+
+ align:start position:0%
+that matrix
+ 
+
+ align:start position:0%
+that matrix
+let me repeat do They span the column
+
+ align:start position:0%
+let me repeat do They span the column
+ 
+
+ align:start position:0%
+let me repeat do They span the column
+space of that matrix. Yes, by definition
+
+ align:start position:0%
+space of that matrix. Yes, by definition
+ 
+
+ align:start position:0%
+space of that matrix. Yes, by definition
+that's what the column space where it
+
+ align:start position:0%
+that's what the column space where it
+ 
+
+ align:start position:0%
+that's what the column space where it
+comes from. Are they a basis for the
+
+ align:start position:0%
+comes from. Are they a basis for the
+ 
+
+ align:start position:0%
+comes from. Are they a basis for the
+column space? Are they independent?
+
+ align:start position:0%
+column space? Are they independent?
+ 
+
+ align:start position:0%
+column space? Are they independent?
+No, they're not independent. There's
+
+ align:start position:0%
+No, they're not independent. There's
+ 
+
+ align:start position:0%
+No, they're not independent. There's
+something in that null space.
+
+ align:start position:0%
+something in that null space.
+ 
+
+ align:start position:0%
+something in that null space.
+Maybe we can. So, let's look at the null
+
+ align:start position:0%
+Maybe we can. So, let's look at the null
+ 
+
+ align:start position:0%
+Maybe we can. So, let's look at the null
+space of the matrix.
+
+ align:start position:0%
+space of the matrix.
+ 
+
+ align:start position:0%
+space of the matrix.
+Tell me a vector that's in the null
+
+ align:start position:0%
+Tell me a vector that's in the null
+ 
+
+ align:start position:0%
+Tell me a vector that's in the null
+space of that matrix.
+
+ align:start position:0%
+space of that matrix.
+ 
+
+ align:start position:0%
+space of that matrix.
+So I'm looking for some vector that
+
+ align:start position:0%
+So I'm looking for some vector that
+ 
+
+ align:start position:0%
+So I'm looking for some vector that
+combines those columns and produces the
+
+ align:start position:0%
+combines those columns and produces the
+ 
+
+ align:start position:0%
+combines those columns and produces the
+zero column.
+
+ align:start position:0%
+zero column.
+ 
+
+ align:start position:0%
+zero column.
+Or in other words, I'm looking for
+
+ align:start position:0%
+Or in other words, I'm looking for
+ 
+
+ align:start position:0%
+Or in other words, I'm looking for
+solutions to ax= z. So so tell me a
+
+ align:start position:0%
+solutions to ax= z. So so tell me a
+ 
+
+ align:start position:0%
+solutions to ax= z. So so tell me a
+vector in the null space.
+
+ align:start position:0%
+vector in the null space.
+ 
+
+ align:start position:0%
+vector in the null space.
+Maybe well this was this column was that
+
+ align:start position:0%
+Maybe well this was this column was that
+ 
+
+ align:start position:0%
+Maybe well this was this column was that
+one plus that one. So maybe if I have
+
+ align:start position:0%
+one plus that one. So maybe if I have
+ 
+
+ align:start position:0%
+one plus that one. So maybe if I have
+one of those and minus one of those that
+
+ align:start position:0%
+one of those and minus one of those that
+ 
+
+ align:start position:0%
+one of those and minus one of those that
+would be a vector in the null space.
+
+ align:start position:0%
+would be a vector in the null space.
+ 
+
+ align:start position:0%
+would be a vector in the null space.
+So you've already told me now are those
+
+ align:start position:0%
+So you've already told me now are those
+ 
+
+ align:start position:0%
+So you've already told me now are those
+vectors independent? The answer is those
+
+ align:start position:0%
+vectors independent? The answer is those
+ 
+
+ align:start position:0%
+vectors independent? The answer is those
+column vectors. The answer is no. Right?
+
+ align:start position:0%
+column vectors. The answer is no. Right?
+ 
+
+ align:start position:0%
+column vectors. The answer is no. Right?
+They're not independent because ah you
+
+ align:start position:0%
+They're not independent because ah you
+ 
+
+ align:start position:0%
+They're not independent because ah you
+knew they weren't independent anyway.
+
+ align:start position:0%
+knew they weren't independent anyway.
+ 
+
+ align:start position:0%
+knew they weren't independent anyway.
+Minus one of this minus one of this plus
+
+ align:start position:0%
+Minus one of this minus one of this plus
+ 
+
+ align:start position:0%
+Minus one of this minus one of this plus
+one of this zero of that is the zero
+
+ align:start position:0%
+one of this zero of that is the zero
+ 
+
+ align:start position:0%
+one of this zero of that is the zero
+vector. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So they're not independent. They
+
+ align:start position:0%
+Okay. So they're not independent. They
+ 
+
+ align:start position:0%
+Okay. So they're not independent. They
+span but they're not independent. Tell
+
+ align:start position:0%
+span but they're not independent. Tell
+ 
+
+ align:start position:0%
+span but they're not independent. Tell
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+a basis
+
+ align:start position:0%
+a basis
+ 
+
+ align:start position:0%
+a basis
+for that column space.
+
+ align:start position:0%
+for that column space.
+ 
+
+ align:start position:0%
+for that column space.
+What's a basis for the column space?
+
+ align:start position:0%
+What's a basis for the column space?
+ 
+
+ align:start position:0%
+What's a basis for the column space?
+These are all the questions that the
+
+ align:start position:0%
+These are all the questions that the
+ 
+
+ align:start position:0%
+These are all the questions that the
+homework asks, the quizzes asked, the
+
+ align:start position:0%
+homework asks, the quizzes asked, the
+ 
+
+ align:start position:0%
+homework asks, the quizzes asked, the
+final exam will ask. Find a basis for
+
+ align:start position:0%
+final exam will ask. Find a basis for
+ 
+
+ align:start position:0%
+final exam will ask. Find a basis for
+the column space of this matrix.
+
+ align:start position:0%
+the column space of this matrix.
+ 
+
+ align:start position:0%
+the column space of this matrix.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now, there's many answers, but give me
+
+ align:start position:0%
+Now, there's many answers, but give me
+ 
+
+ align:start position:0%
+Now, there's many answers, but give me
+the most natural answer.
+
+ align:start position:0%
+the most natural answer.
+ 
+
+ align:start position:0%
+the most natural answer.
+columns
+
+ align:start position:0%
+columns
+ 
+
+ align:start position:0%
+columns
+one and two. Columns one and two. That's
+
+ align:start position:0%
+one and two. Columns one and two. That's
+ 
+
+ align:start position:0%
+one and two. Columns one and two. That's
+the natural answer. Those are the pivot
+
+ align:start position:0%
+the natural answer. Those are the pivot
+ 
+
+ align:start position:0%
+the natural answer. Those are the pivot
+columns because I mean we we begin
+
+ align:start position:0%
+columns because I mean we we begin
+ 
+
+ align:start position:0%
+columns because I mean we we begin
+systematically. We look at the first
+
+ align:start position:0%
+systematically. We look at the first
+ 
+
+ align:start position:0%
+systematically. We look at the first
+column. It's okay. We can put that in
+
+ align:start position:0%
+column. It's okay. We can put that in
+ 
+
+ align:start position:0%
+column. It's okay. We can put that in
+the basis. We look at the second column.
+
+ align:start position:0%
+the basis. We look at the second column.
+ 
+
+ align:start position:0%
+the basis. We look at the second column.
+It's okay. We can put that in the basis.
+
+ align:start position:0%
+It's okay. We can put that in the basis.
+ 
+
+ align:start position:0%
+It's okay. We can put that in the basis.
+The third column we can't put in the
+
+ align:start position:0%
+The third column we can't put in the
+ 
+
+ align:start position:0%
+The third column we can't put in the
+basis. The fourth column we
+
+ align:start position:0%
+basis. The fourth column we
+ 
+
+ align:start position:0%
+basis. The fourth column we
+can't again. So the rank of the matrix
+
+ align:start position:0%
+can't again. So the rank of the matrix
+ 
+
+ align:start position:0%
+can't again. So the rank of the matrix
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+what's the rank of our matrix? Two. Two.
+
+ align:start position:0%
+what's the rank of our matrix? Two. Two.
+ 
+
+ align:start position:0%
+what's the rank of our matrix? Two. Two.
+And and now that rank is also we now
+
+ align:start position:0%
+And and now that rank is also we now
+ 
+
+ align:start position:0%
+And and now that rank is also we now
+have another word. We we have a great
+
+ align:start position:0%
+have another word. We we have a great
+ 
+
+ align:start position:0%
+have another word. We we have a great
+theorem here. The rank of A
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that rank R
+
+ align:start position:0%
+that rank R
+ 
+
+ align:start position:0%
+that rank R
+is the number of pivot columns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's also
+
+ align:start position:0%
+and it's also
+ 
+
+ align:start position:0%
+and it's also
+well so now please use my new word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this it's the number two of course two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the rank of my matrix. It's the
+
+ align:start position:0%
+is the rank of my matrix. It's the
+ 
+
+ align:start position:0%
+is the rank of my matrix. It's the
+number of pivot columns. Those pivot
+
+ align:start position:0%
+number of pivot columns. Those pivot
+ 
+
+ align:start position:0%
+number of pivot columns. Those pivot
+columns form a basis of course. So
+
+ align:start position:0%
+columns form a basis of course. So
+ 
+
+ align:start position:0%
+columns form a basis of course. So
+what's two?
+
+ align:start position:0%
+what's two?
+ 
+
+ align:start position:0%
+what's two?
+It's the dimension.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The rank of A, the number of pivot
+
+ align:start position:0%
+The rank of A, the number of pivot
+ 
+
+ align:start position:0%
+The rank of A, the number of pivot
+columns is the dimension
+
+ align:start position:0%
+columns is the dimension
+ 
+
+ align:start position:0%
+columns is the dimension
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the column space. Of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course, you say it had to be right. But
+
+ align:start position:0%
+course, you say it had to be right. But
+ 
+
+ align:start position:0%
+course, you say it had to be right. But
+just watch look for one moment at the
+
+ align:start position:0%
+just watch look for one moment at the
+ 
+
+ align:start position:0%
+just watch look for one moment at the
+the language, the way the English words
+
+ align:start position:0%
+the language, the way the English words
+ 
+
+ align:start position:0%
+the language, the way the English words
+get involved here. I take the rank of a
+
+ align:start position:0%
+get involved here. I take the rank of a
+ 
+
+ align:start position:0%
+get involved here. I take the rank of a
+matrix.
+
+ align:start position:0%
+matrix.
+ 
+
+ align:start position:0%
+matrix.
+the rank of a matrix.
+
+ align:start position:0%
+the rank of a matrix.
+ 
+
+ align:start position:0%
+the rank of a matrix.
+It's a number of columns and it's the
+
+ align:start position:0%
+It's a number of columns and it's the
+ 
+
+ align:start position:0%
+It's a number of columns and it's the
+dimension of
+
+ align:start position:0%
+dimension of
+ 
+
+ align:start position:0%
+dimension of
+not the dimension of the matrix. That's
+
+ align:start position:0%
+not the dimension of the matrix. That's
+ 
+
+ align:start position:0%
+not the dimension of the matrix. That's
+what I want to say. It's the dimension
+
+ align:start position:0%
+what I want to say. It's the dimension
+ 
+
+ align:start position:0%
+what I want to say. It's the dimension
+of a space, a subspace, the column
+
+ align:start position:0%
+of a space, a subspace, the column
+ 
+
+ align:start position:0%
+of a space, a subspace, the column
+space.
+
+ align:start position:0%
+space.
+ 
+
+ align:start position:0%
+space.
+Do do you see I I don't take the
+
+ align:start position:0%
+Do do you see I I don't take the
+ 
+
+ align:start position:0%
+Do do you see I I don't take the
+dimension of A. That's not what I want.
+
+ align:start position:0%
+dimension of A. That's not what I want.
+ 
+
+ align:start position:0%
+dimension of A. That's not what I want.
+I'm looking for the dimension of the
+
+ align:start position:0%
+I'm looking for the dimension of the
+ 
+
+ align:start position:0%
+I'm looking for the dimension of the
+column space of A. If you use those
+
+ align:start position:0%
+column space of A. If you use those
+ 
+
+ align:start position:0%
+column space of A. If you use those
+words right, it shows you got the idea
+
+ align:start position:0%
+words right, it shows you got the idea
+ 
+
+ align:start position:0%
+words right, it shows you got the idea
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+Similarly, here I don't talk about the
+
+ align:start position:0%
+Similarly, here I don't talk about the
+ 
+
+ align:start position:0%
+Similarly, here I don't talk about the
+rank of a subspace.
+
+ align:start position:0%
+rank of a subspace.
+ 
+
+ align:start position:0%
+rank of a subspace.
+It's a matrix that has a rank. I talk
+
+ align:start position:0%
+It's a matrix that has a rank. I talk
+ 
+
+ align:start position:0%
+It's a matrix that has a rank. I talk
+about the rank of a matrix. And it the
+
+ align:start position:0%
+about the rank of a matrix. And it the
+ 
+
+ align:start position:0%
+about the rank of a matrix. And it the
+beauty is that these definitions just
+
+ align:start position:0%
+beauty is that these definitions just
+ 
+
+ align:start position:0%
+beauty is that these definitions just
+merge so that the rank of a matrix is
+
+ align:start position:0%
+merge so that the rank of a matrix is
+ 
+
+ align:start position:0%
+merge so that the rank of a matrix is
+the dimension of its column space. And
+
+ align:start position:0%
+the dimension of its column space. And
+ 
+
+ align:start position:0%
+the dimension of its column space. And
+in this example, it's two. And then the
+
+ align:start position:0%
+in this example, it's two. And then the
+ 
+
+ align:start position:0%
+in this example, it's two. And then the
+further question is what's a basis? And
+
+ align:start position:0%
+further question is what's a basis? And
+ 
+
+ align:start position:0%
+further question is what's a basis? And
+the first two columns are a basis. Tell
+
+ align:start position:0%
+the first two columns are a basis. Tell
+ 
+
+ align:start position:0%
+the first two columns are a basis. Tell
+me another basis. Another basis for the
+
+ align:start position:0%
+me another basis. Another basis for the
+ 
+
+ align:start position:0%
+me another basis. Another basis for the
+column space. You see, I just keep
+
+ align:start position:0%
+column space. You see, I just keep
+ 
+
+ align:start position:0%
+column space. You see, I just keep
+hammering away. I apologize, but it's I
+
+ align:start position:0%
+hammering away. I apologize, but it's I
+ 
+
+ align:start position:0%
+hammering away. I apologize, but it's I
+have to be sure you have the idea of
+
+ align:start position:0%
+have to be sure you have the idea of
+ 
+
+ align:start position:0%
+have to be sure you have the idea of
+basis. Tell me another basis for the
+
+ align:start position:0%
+basis. Tell me another basis for the
+ 
+
+ align:start position:0%
+basis. Tell me another basis for the
+column space.
+
+ align:start position:0%
+column space.
+ 
+
+ align:start position:0%
+column space.
+Well, you could take columns one and
+
+ align:start position:0%
+Well, you could take columns one and
+ 
+
+ align:start position:0%
+Well, you could take columns one and
+three.
+
+ align:start position:0%
+three.
+ 
+
+ align:start position:0%
+three.
+That would be a basis for the column
+
+ align:start position:0%
+That would be a basis for the column
+ 
+
+ align:start position:0%
+That would be a basis for the column
+space. or columns two and three would be
+
+ align:start position:0%
+space. or columns two and three would be
+ 
+
+ align:start position:0%
+space. or columns two and three would be
+a basis or columns two and four or me
+
+ align:start position:0%
+a basis or columns two and four or me
+ 
+
+ align:start position:0%
+a basis or columns two and four or me
+another basis that's not made out of
+
+ align:start position:0%
+another basis that's not made out of
+ 
+
+ align:start position:0%
+another basis that's not made out of
+those columns at all.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So well I guess I'm giving you
+
+ align:start position:0%
+So well I guess I'm giving you
+ 
+
+ align:start position:0%
+So well I guess I'm giving you
+infinitely many possibilities so I can't
+
+ align:start position:0%
+infinitely many possibilities so I can't
+ 
+
+ align:start position:0%
+infinitely many possibilities so I can't
+expect a unanimous answer here. I tell
+
+ align:start position:0%
+expect a unanimous answer here. I tell
+ 
+
+ align:start position:0%
+expect a unanimous answer here. I tell
+you let's look at another basis though.
+
+ align:start position:0%
+you let's look at another basis though.
+ 
+
+ align:start position:0%
+you let's look at another basis though.
+I'll just because it's only one out of
+
+ align:start position:0%
+I'll just because it's only one out of
+ 
+
+ align:start position:0%
+I'll just because it's only one out of
+zillions. I'm going to put it down and
+
+ align:start position:0%
+zillions. I'm going to put it down and
+ 
+
+ align:start position:0%
+zillions. I'm going to put it down and
+I'm going to erase it. Another basis for
+
+ align:start position:0%
+I'm going to erase it. Another basis for
+ 
+
+ align:start position:0%
+I'm going to erase it. Another basis for
+the column space
+
+ align:start position:0%
+the column space
+ 
+
+ align:start position:0%
+the column space
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+uh let's see I'll put in some things
+
+ align:start position:0%
+uh let's see I'll put in some things
+ 
+
+ align:start position:0%
+uh let's see I'll put in some things
+that are not there. say, "Oh, well, just
+
+ align:start position:0%
+that are not there. say, "Oh, well, just
+ 
+
+ align:start position:0%
+that are not there. say, "Oh, well, just
+to make it my life easy, 222. That's in
+
+ align:start position:0%
+to make it my life easy, 222. That's in
+ 
+
+ align:start position:0%
+to make it my life easy, 222. That's in
+the column space."
+
+ align:start position:0%
+the column space."
+ 
+
+ align:start position:0%
+the column space."
+And uh that was sort of obvious. Let me
+
+ align:start position:0%
+And uh that was sort of obvious. Let me
+ 
+
+ align:start position:0%
+And uh that was sort of obvious. Let me
+take the sum of those say 6 46
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or the sum of all the columns 757. Why
+
+ align:start position:0%
+or the sum of all the columns 757. Why
+ 
+
+ align:start position:0%
+or the sum of all the columns 757. Why
+not? That's in the column space.
+
+ align:start position:0%
+not? That's in the column space.
+ 
+
+ align:start position:0%
+not? That's in the column space.
+Those are independent.
+
+ align:start position:0%
+Those are independent.
+ 
+
+ align:start position:0%
+Those are independent.
+And I've got the number right. I've got
+
+ align:start position:0%
+And I've got the number right. I've got
+ 
+
+ align:start position:0%
+And I've got the number right. I've got
+two. Actually, this is a key point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you know the dimension of the space
+
+ align:start position:0%
+If you know the dimension of the space
+ 
+
+ align:start position:0%
+If you know the dimension of the space
+you're working with, and we know that
+
+ align:start position:0%
+you're working with, and we know that
+ 
+
+ align:start position:0%
+you're working with, and we know that
+this column, we know that the dimension
+
+ align:start position:0%
+this column, we know that the dimension
+ 
+
+ align:start position:0%
+this column, we know that the dimension
+dime the dimension of the column space
+
+ align:start position:0%
+dime the dimension of the column space
+ 
+
+ align:start position:0%
+dime the dimension of the column space
+is two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you know the the dimension then then
+
+ align:start position:0%
+If you know the the dimension then then
+ 
+
+ align:start position:0%
+If you know the the dimension then then
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and we have a couple of vectors that are
+
+ align:start position:0%
+and we have a couple of vectors that are
+ 
+
+ align:start position:0%
+and we have a couple of vectors that are
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+they'll automatically be a basis. If
+
+ align:start position:0%
+they'll automatically be a basis. If
+ 
+
+ align:start position:0%
+they'll automatically be a basis. If
+we've got the number of vectors right,
+
+ align:start position:0%
+we've got the number of vectors right,
+ 
+
+ align:start position:0%
+we've got the number of vectors right,
+two vectors in this case, then if
+
+ align:start position:0%
+two vectors in this case, then if
+ 
+
+ align:start position:0%
+two vectors in this case, then if
+they're independent, they can't help but
+
+ align:start position:0%
+they're independent, they can't help but
+ 
+
+ align:start position:0%
+they're independent, they can't help but
+span the space because if they didn't
+
+ align:start position:0%
+span the space because if they didn't
+ 
+
+ align:start position:0%
+span the space because if they didn't
+span the space, there'd be a third guy
+
+ align:start position:0%
+span the space, there'd be a third guy
+ 
+
+ align:start position:0%
+span the space, there'd be a third guy
+to help span the space.
+
+ align:start position:0%
+to help span the space.
+ 
+
+ align:start position:0%
+to help span the space.
+But it couldn't be independent. So it it
+
+ align:start position:0%
+But it couldn't be independent. So it it
+ 
+
+ align:start position:0%
+But it couldn't be independent. So it it
+just has to be
+
+ align:start position:0%
+just has to be
+ 
+
+ align:start position:0%
+just has to be
+independent if we've got the numbers
+
+ align:start position:0%
+independent if we've got the numbers
+ 
+
+ align:start position:0%
+independent if we've got the numbers
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and they span. Okay, very good. So you
+
+ align:start position:0%
+and they span. Okay, very good. So you
+ 
+
+ align:start position:0%
+and they span. Okay, very good. So you
+got the dimension of a space. So this
+
+ align:start position:0%
+got the dimension of a space. So this
+ 
+
+ align:start position:0%
+got the dimension of a space. So this
+was another basis that I just invented.
+
+ align:start position:0%
+was another basis that I just invented.
+ 
+
+ align:start position:0%
+was another basis that I just invented.
+Okay. Now,
+
+ align:start position:0%
+Okay. Now,
+ 
+
+ align:start position:0%
+Okay. Now,
+now I get to ask you about the null
+
+ align:start position:0%
+now I get to ask you about the null
+ 
+
+ align:start position:0%
+now I get to ask you about the null
+space.
+
+ align:start position:0%
+space.
+ 
+
+ align:start position:0%
+space.
+What's the dimension of the null space?
+
+ align:start position:0%
+What's the dimension of the null space?
+ 
+
+ align:start position:0%
+What's the dimension of the null space?
+So we we got a great fact there. The
+
+ align:start position:0%
+So we we got a great fact there. The
+ 
+
+ align:start position:0%
+So we we got a great fact there. The
+dimension
+
+ align:start position:0%
+dimension
+ 
+
+ align:start position:0%
+dimension
+of the column space is the rank.
+
+ align:start position:0%
+of the column space is the rank.
+ 
+
+ align:start position:0%
+of the column space is the rank.
+Now I want to ask you about the null
+
+ align:start position:0%
+Now I want to ask you about the null
+ 
+
+ align:start position:0%
+Now I want to ask you about the null
+space. That's the other
+
+ align:start position:0%
+space. That's the other
+ 
+
+ align:start position:0%
+space. That's the other
+part of the lecture and it'll go on to
+
+ align:start position:0%
+part of the lecture and it'll go on to
+ 
+
+ align:start position:0%
+part of the lecture and it'll go on to
+the next lecture.
+
+ align:start position:0%
+the next lecture.
+ 
+
+ align:start position:0%
+the next lecture.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So we know the dimension of the column
+
+ align:start position:0%
+So we know the dimension of the column
+ 
+
+ align:start position:0%
+So we know the dimension of the column
+space is two. The rank. What about the
+
+ align:start position:0%
+space is two. The rank. What about the
+ 
+
+ align:start position:0%
+space is two. The rank. What about the
+null space? This is a vector in the null
+
+ align:start position:0%
+null space? This is a vector in the null
+ 
+
+ align:start position:0%
+null space? This is a vector in the null
+space. Are there other vectors in the
+
+ align:start position:0%
+space. Are there other vectors in the
+ 
+
+ align:start position:0%
+space. Are there other vectors in the
+null space?
+
+ align:start position:0%
+null space?
+ 
+
+ align:start position:0%
+null space?
+Yes or no? Yes. So this isn't a basis
+
+ align:start position:0%
+Yes or no? Yes. So this isn't a basis
+ 
+
+ align:start position:0%
+Yes or no? Yes. So this isn't a basis
+because it's doesn't span. Right?
+
+ align:start position:0%
+because it's doesn't span. Right?
+ 
+
+ align:start position:0%
+because it's doesn't span. Right?
+There's more in the null space than
+
+ align:start position:0%
+There's more in the null space than
+ 
+
+ align:start position:0%
+There's more in the null space than
+we've got so far. I need another vector
+
+ align:start position:0%
+we've got so far. I need another vector
+ 
+
+ align:start position:0%
+we've got so far. I need another vector
+at least. So tell me another vector in
+
+ align:start position:0%
+at least. So tell me another vector in
+ 
+
+ align:start position:0%
+at least. So tell me another vector in
+the null space.
+
+ align:start position:0%
+the null space.
+ 
+
+ align:start position:0%
+the null space.
+Well, the natural choice, the choice you
+
+ align:start position:0%
+Well, the natural choice, the choice you
+ 
+
+ align:start position:0%
+Well, the natural choice, the choice you
+naturally think of is I'm going on to
+
+ align:start position:0%
+naturally think of is I'm going on to
+ 
+
+ align:start position:0%
+naturally think of is I'm going on to
+the fourth column.
+
+ align:start position:0%
+the fourth column.
+ 
+
+ align:start position:0%
+the fourth column.
+I'm letting that free variable be a one
+
+ align:start position:0%
+I'm letting that free variable be a one
+ 
+
+ align:start position:0%
+I'm letting that free variable be a one
+and that free variable be a zero. And
+
+ align:start position:0%
+and that free variable be a zero. And
+ 
+
+ align:start position:0%
+and that free variable be a zero. And
+I'm asking, is that fourth column a
+
+ align:start position:0%
+I'm asking, is that fourth column a
+ 
+
+ align:start position:0%
+I'm asking, is that fourth column a
+combination of my pivot columns? Yes, it
+
+ align:start position:0%
+combination of my pivot columns? Yes, it
+ 
+
+ align:start position:0%
+combination of my pivot columns? Yes, it
+is. And it's
+
+ align:start position:0%
+is. And it's
+ 
+
+ align:start position:0%
+is. And it's
+that will do.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what I've written there are actually
+
+ align:start position:0%
+So what I've written there are actually
+ 
+
+ align:start position:0%
+So what I've written there are actually
+the two special solutions, right? I took
+
+ align:start position:0%
+the two special solutions, right? I took
+ 
+
+ align:start position:0%
+the two special solutions, right? I took
+the two free variables free and free.
+
+ align:start position:0%
+the two free variables free and free.
+ 
+
+ align:start position:0%
+the two free variables free and free.
+I gave them the values one zero or 01. I
+
+ align:start position:0%
+I gave them the values one zero or 01. I
+ 
+
+ align:start position:0%
+I gave them the values one zero or 01. I
+figured out the rest.
+
+ align:start position:0%
+figured out the rest.
+ 
+
+ align:start position:0%
+figured out the rest.
+So do do you see? Let me just say it in
+
+ align:start position:0%
+So do do you see? Let me just say it in
+ 
+
+ align:start position:0%
+So do do you see? Let me just say it in
+words. this vector, these vectors in the
+
+ align:start position:0%
+words. this vector, these vectors in the
+ 
+
+ align:start position:0%
+words. this vector, these vectors in the
+null space are telling me, they're
+
+ align:start position:0%
+null space are telling me, they're
+ 
+
+ align:start position:0%
+null space are telling me, they're
+telling me the combinations of the
+
+ align:start position:0%
+telling me the combinations of the
+ 
+
+ align:start position:0%
+telling me the combinations of the
+columns that give zero. They're telling
+
+ align:start position:0%
+columns that give zero. They're telling
+ 
+
+ align:start position:0%
+columns that give zero. They're telling
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+in what way the the columns are
+
+ align:start position:0%
+in what way the the columns are
+ 
+
+ align:start position:0%
+in what way the the columns are
+dependent. That's what the null space is
+
+ align:start position:0%
+dependent. That's what the null space is
+ 
+
+ align:start position:0%
+dependent. That's what the null space is
+doing. Have I got enough now?
+
+ align:start position:0%
+doing. Have I got enough now?
+ 
+
+ align:start position:0%
+doing. Have I got enough now?
+And what's the null space? Now, we have
+
+ align:start position:0%
+And what's the null space? Now, we have
+ 
+
+ align:start position:0%
+And what's the null space? Now, we have
+to think about the null space.
+
+ align:start position:0%
+to think about the null space.
+ 
+
+ align:start position:0%
+to think about the null space.
+These are two vectors in the null space.
+
+ align:start position:0%
+These are two vectors in the null space.
+ 
+
+ align:start position:0%
+These are two vectors in the null space.
+They're independent. Are they a basis
+
+ align:start position:0%
+They're independent. Are they a basis
+ 
+
+ align:start position:0%
+They're independent. Are they a basis
+for the null space? What's the dimension
+
+ align:start position:0%
+for the null space? What's the dimension
+ 
+
+ align:start position:0%
+for the null space? What's the dimension
+of the null space? You see that those
+
+ align:start position:0%
+of the null space? You see that those
+ 
+
+ align:start position:0%
+of the null space? You see that those
+questions just keep coming up all the
+
+ align:start position:0%
+questions just keep coming up all the
+ 
+
+ align:start position:0%
+questions just keep coming up all the
+time.
+
+ align:start position:0%
+time.
+ 
+
+ align:start position:0%
+time.
+Are they a basis for the null space? You
+
+ align:start position:0%
+Are they a basis for the null space? You
+ 
+
+ align:start position:0%
+Are they a basis for the null space? You
+can tell me the answer even though we
+
+ align:start position:0%
+can tell me the answer even though we
+ 
+
+ align:start position:0%
+can tell me the answer even though we
+haven't written out a proof of that. Can
+
+ align:start position:0%
+haven't written out a proof of that. Can
+ 
+
+ align:start position:0%
+haven't written out a proof of that. Can
+you yes or no? Do these two special
+
+ align:start position:0%
+you yes or no? Do these two special
+ 
+
+ align:start position:0%
+you yes or no? Do these two special
+solutions form a basis for the null
+
+ align:start position:0%
+solutions form a basis for the null
+ 
+
+ align:start position:0%
+solutions form a basis for the null
+space? In other words, does the null
+
+ align:start position:0%
+space? In other words, does the null
+ 
+
+ align:start position:0%
+space? In other words, does the null
+space consist of all combinations of
+
+ align:start position:0%
+space consist of all combinations of
+ 
+
+ align:start position:0%
+space consist of all combinations of
+those two guys? Yes or no? Yes. Yes.
+
+ align:start position:0%
+those two guys? Yes or no? Yes. Yes.
+ 
+
+ align:start position:0%
+those two guys? Yes or no? Yes. Yes.
+The null space is two-dimensional. The
+
+ align:start position:0%
+The null space is two-dimensional. The
+ 
+
+ align:start position:0%
+The null space is two-dimensional. The
+null space, the dimension of the null
+
+ align:start position:0%
+null space, the dimension of the null
+ 
+
+ align:start position:0%
+null space, the dimension of the null
+space is the number of free variables.
+
+ align:start position:0%
+space is the number of free variables.
+ 
+
+ align:start position:0%
+space is the number of free variables.
+So the dimension of the null space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the number of free variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and at the last second give me the
+
+ align:start position:0%
+and at the last second give me the
+ 
+
+ align:start position:0%
+and at the last second give me the
+formula.
+
+ align:start position:0%
+formula.
+ 
+
+ align:start position:0%
+formula.
+This is then the key formula that we
+
+ align:start position:0%
+This is then the key formula that we
+ 
+
+ align:start position:0%
+This is then the key formula that we
+know how many free variables are there
+
+ align:start position:0%
+know how many free variables are there
+ 
+
+ align:start position:0%
+know how many free variables are there
+in terms of r the rank m the number of
+
+ align:start position:0%
+in terms of r the rank m the number of
+ 
+
+ align:start position:0%
+in terms of r the rank m the number of
+rows n the number of columns
+
+ align:start position:0%
+rows n the number of columns
+ 
+
+ align:start position:0%
+rows n the number of columns
+what do we get we have n columns
+
+ align:start position:0%
+what do we get we have n columns
+ 
+
+ align:start position:0%
+what do we get we have n columns
+r of them are pivot columns so n minus r
+
+ align:start position:0%
+r of them are pivot columns so n minus r
+ 
+
+ align:start position:0%
+r of them are pivot columns so n minus r
+is the number of free columns free
+
+ align:start position:0%
+is the number of free columns free
+ 
+
+ align:start position:0%
+is the number of free columns free
+variables and now it's the dimension of
+
+ align:start position:0%
+variables and now it's the dimension of
+ 
+
+ align:start position:0%
+variables and now it's the dimension of
+the null space. Okay, that's great.
+
+ align:start position:0%
+the null space. Okay, that's great.
+ 
+
+ align:start position:0%
+the null space. Okay, that's great.
+That's the key spaces, their bases, and
+
+ align:start position:0%
+That's the key spaces, their bases, and
+ 
+
+ align:start position:0%
+That's the key spaces, their bases, and
+their dimensions. Thanks,
\ No newline at end of file
diff --git a/yvatNaV6Bog.txt b/yvatNaV6Bog.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1524436c706d4adb2f121024c97bf3a672faee1
--- /dev/null
+++ b/yvatNaV6Bog.txt
@@ -0,0 +1,2566 @@
+PROFESSOR: All
+right, so lecture 11
+
+was about generic
+rigidity of linkages.
+
+So we've got bars and vertices
+connected together in a graph.
+
+And generically, the
+graph is all that matters.
+
+And we characterize in two
+ways, Henneberg construction
+
+and Laman when graphs
+are generically rigid.
+
+And in particular, there
+was this pebble algorithm
+
+that was supposed to tell
+you in polynomial time
+
+whether you're a graph
+was Laman or not.
+
+And everyone pretty much asked
+about this, about the details,
+
+including myself when
+I watched it like, huh,
+
+that seems a little sketchy.
+
+So I thought I'd spend
+most of today going
+
+through how that
+algorithm works exactly
+
+and also why it's correct, which
+is definitely not obviously.
+
+It vaguely feels correct, but
+we'll see why it actually is.
+
+Remember Laman's Theorem,
+Laman characterization
+
+is that your graph is
+generically rigid if and only
+
+if every subgraph-- let's
+say every k vertices induces
+
+at most to 2k minus 3 edges.
+
+That's part one.
+
+And you also need
+that the number
+
+of edges overall in
+the graph is 2n minus 3
+
+where n is the total
+number vertices.
+
+So this was just the
+degree of freedom count.
+
+You have 2n degrees of freedom
+for every vertex minus 3
+
+for the rigid motions, two
+translations, one rotation.
+
+So that's the number of
+edges you should have total.
+
+Sorry.
+
+This is for minimally
+generically rigid.
+
+And then to make it
+balance, you want
+
+to guarantee that every
+k vertices doesn't
+
+have too many edges.
+
+Because if it has
+too many edges,
+
+there'd be too few
+somewhere else.
+
+This part would be
+overbrace, some other part
+
+would be underbrace,
+and you'd be flexible.
+
+That's the intuition.
+
+And so the tricky
+part comes down
+
+to how do you check whether
+every k vertices induces
+
+2k minus 3 edges because they're
+exponentially many choices.
+
+There's 2 to the n different
+choices of subsets or vertices.
+
+For each of them,
+you'd have to check.
+
+That's no good.
+
+So the algorithm
+wants to check this.
+
+And I'm going to
+call this property
+
+the 2k minus 3 property.
+
+And we're going to warm up
+with a simpler problem, which
+
+is to check to the 2k
+property without the minus 3.
+
+So 2k property is
+just every k vertices
+
+induce at most 2k edges.
+
+So this'll be a little
+easier to think about,
+
+more or less the same, a
+lot easier to argue about.
+
+And then we'll see how
+to modify the algorithm
+
+to check the 2k
+minus 3 property.
+
+Was the property clear and
+in particular inducing?
+
+Inducing means that you
+have some set of vertices,
+
+and there's the rest of the
+vertices, n minus k of them.
+
+You only look at edges where
+both endpoints are in the set,
+
+both of them are
+among the k vertices.
+
+So you ignore vertices that have
+one end in k and the other end
+
+outside.
+
+And you ignore, obviously, edges
+that have both ends outside.
+
+Just count these guys.
+
+So how do we do this?
+
+Give you the algorithm.
+
+Actually, let me first give
+you the idea of the algorithm
+
+before we go to the
+actual algorithm.
+
+And this is review,
+but pretty soon we'll
+
+get to stuff that wasn't
+covered in lecture.
+
+So the idea is every vertex
+has two pebbles inside of it.
+
+I'll draw as two red dots.
+
+And they can cover
+incident edges.
+
+So they can't move very far.
+
+They have to stay
+basically on the inside
+
+or on the boundary
+of the vertex.
+
+That's how I'm going to draw it.
+
+Each pebble can cover
+one incident edge.
+
+So for example,
+there's a little graph.
+
+I could take--
+let's maybe I leave
+
+one of the pebbles
+in the middle.
+
+I can move one of the pebbles
+to cover one of the edges.
+
+So I'll put it this
+intersection to denote
+
+it's covering this edge, but it
+still belongs to this vertex.
+
+Pebbles cannot change vertices.
+
+They have to stay local.
+
+These two pebbles could
+just stay where they are.
+
+Here, we could put
+one pebble here,
+
+another pebble there, one
+pebble here, one pebble here.
+
+This is what I call
+a pebble cover cause
+
+every edge is covered
+by some pebble.
+
+That's the goal in a pebble
+cover is to cover every edge.
+
+You need to cover it once.
+
+And the pebbles can either cover
+an edge or they can be free.
+
+Free if they're just
+hanging out in the inside
+
+here not being
+used for anything.
+
+So our goal is to
+find pebble covers.
+
+But the first claim, why do
+I care about pebble covers,
+
+I claimed that
+having a pebble cover
+
+is equivalent to
+the 2k property.
+
+So that's what I want to show.
+
+So let's start with that.
+
+This is why
+everything is working.
+
+A graph has a 2k property if and
+only if it has a pebble cover.
+
+So that's why we care about
+these pebble coverings.
+
+And this is actually
+pretty easy to prove
+
+and gives a lot of intuition
+for why everything works here.
+
+So let's start with
+the left direction.
+
+So suppose I have
+a pebble cover.
+
+Suppose somehow I've
+achieved this property,
+
+covering all the edges, using
+only two pebbles per vertex.
+
+I claim that we then
+satisfy the 2k property.
+
+2k property says you
+take any key vertices,
+
+you induce at most
+two key edges.
+
+So let's consider k vertices.
+
+Someone chooses k vertices.
+
+doesn't matter which.
+
+It should hold for all
+of them, for all choices.
+
+So we've got a k vertices here.
+
+n minus k vertices remaining.
+
+We claim that the number
+of edges induced by those k
+
+vertices is at most 2k.
+
+So look at one of these
+edges that's wholly inside,
+
+that's induced by
+these k vertices.
+
+I claim, well, that edge
+must be covered by a pebble.
+
+Which pebble?
+
+Well, either this one or
+one on the other side.
+
+But the point is it
+is covered by a pebble
+
+among these vertices.
+
+My concern is, well, maybe you
+worry about an edge like this.
+
+Or, maybe you worry
+about a pebble
+
+here that's covering this
+edge, but that edge is not
+
+one of the induced edges.
+
+So these vertices are relevant.
+
+It's just the pebbles inside,
+just among these 2k pebbles.
+
+So in here, there
+are 2k pebbles.
+
+They must fully cover
+the induced subgraph.
+
+They must cover all
+the edges in here.
+
+That means they're
+at most 2k edges
+
+because there's one
+pebble per edge at least.
+
+And so there's 2k
+pebbles in here.
+
+This means they're at
+must 2k induced edges.
+
+Clear?
+
+That's the obvious direction.
+
+This doesn't really exploit
+very much about pebbles.
+
+The other direction is a
+little more interesting.
+
+Why should these
+pebble covers exist?
+
+Because they seem
+pretty constrained.
+
+Pebbles can't move very far.
+
+It's not really clearly
+the same, but it is.
+
+So if we have the 2k property--
+
+So now we know that every
+subgraph of k vertices
+
+induces at most 2k edges.
+
+Now, we want to prove that
+a pebble cover exists.
+
+I'm going to wait.
+
+It will become
+obvious momentarily.
+
+This is fun.
+
+Sometimes, it's easier
+to prove a theorem
+
+than it is to come
+up with an algorithm.
+
+But in this case, it's easier
+to come up with an algorithm
+
+than it is to prove a theorem.
+
+And you can use the algorithm
+itself to prove the theorem,
+
+so I'm going to prove
+this in a moment.
+
+Stay tuned.
+
+Meanwhile, we have an algorithm.
+
+This algorithm is
+an example of what
+
+we call an incremental style
+algorithm where you imagine
+
+starting with the
+empty graph and then
+
+you put in all the edges
+that belong one at a time.
+
+So add edges one at a time
+starting from nothing.
+
+One detail is we're going to
+imagine as edges get added,
+
+we want to direct them.
+
+We're going to direct edges
+from the pebble that covers them
+
+to the other side.
+
+So if we have an edge and
+we have a pebble over here,
+
+than I'm going to imagine
+the edge as being directed
+
+from the pebble
+to the other side.
+
+That's just for convenience
+for expressing the algorithm
+
+in a moment.
+
+So now this is for
+the 2k property.
+
+We'll get to an algorithm
+for 2k minus 3 a little bit.
+
+So now we have a 4 loop over
+the edge is we're going to add.
+
+And when I immediately add an
+edge, it will not be covered,
+
+so it's not directed,
+just some edge v-w.
+
+I would like to
+put a pebble here,
+
+but it could be
+both pebbles at w
+
+are occupied for
+some other edges.
+
+It could be the
+pebbles for v are also
+
+occupied for some other edges.
+
+That would be annoying.
+
+I want to somehow reassign
+a pebble to cover this edge,
+
+so what I'm going to
+do inside this 4 loop
+
+is search for available pebbles.
+
+And in this case, what
+turns out to be right
+
+is a directed path in
+this directed graph
+
+from either v or w
+to a free pebble.
+
+Either I find one or I don't.
+
+If I find one, let's
+say from v, there's
+
+some edge and then some other
+edge and some other edge.
+
+And eventually, I
+find a free pebble.
+
+Remember a free pebble is one
+that's floating on the inside,
+
+not being used for anything.
+
+So what does my
+picture look like?
+
+Remember edges are
+directed from the pebbles.
+
+That means there was a pebble
+at v being used for that edge.
+
+There was a pebble
+at this vertex
+
+being used for that edge.
+
+There was a pebble
+at this vertex
+
+being used for that edge.
+
+In this case, what do I do?
+
+AUDIENCE: Reverse.
+
+PROFESSOR: Reverse them, yeah.
+
+Just reverse all the edges.
+
+So I have this edge, v-w, here.
+
+I want to put a
+pebble here, so I'm
+
+going to reassign this guy
+to be over there, this guy
+
+to be over there, this guy
+to be over there, and so on.
+
+So I end up with--
+that's in the way.
+
+Put w over here.
+
+The new picture
+is I have v and w.
+
+And I'm going to have
+left 4 directed edges.
+
+So now this pebble got
+assigned to be here.
+
+I can't draw left apparently.
+
+The other left.
+
+This pebble assigned there.
+
+This pebble, the free
+pebble, gets used up.
+
+And now we've got a
+free pebble over here.
+
+And now we can assign it
+to be on the edge v-w.
+
+So if I can find such a
+path from v or from w,
+
+I'm happy because
+then I can reassign.
+
+If I find such a path, I just
+shift the pebbles like that,
+
+and I'm done.
+
+But what if I can't?
+
+This is the critical
+issue, and it is also
+
+core to this part
+of the proof that we
+
+haven't discover--
+haven't yet done.
+
+Why would we hope
+for pebble covers
+
+to exist in the first place?
+
+We don't know.
+
+I claim if this
+algorithm fails to find
+
+a path in this situation,
+then you can immediately
+
+say you do not satisfy
+the 2k property.
+
+I'd like to say there's
+no pebble cover,
+
+but that's a little harder.
+
+I'm going to say you do not
+satisfy the 2k property.
+
+And we actually know
+already, from this part,
+
+pebble cover
+implies 2k property.
+
+The contrapositive, which
+we've already proved,
+
+is if you do not
+satisfy the 2k property,
+
+you do not have a pebble cover.
+
+So that will actually guarantee
+correctness of the algorithm.
+
+If I can prove this part,
+that it violates 2k property,
+
+then I'll know there was no
+pebble cover, and I'm done.
+
+So why is this true.
+
+I claim if you look at
+all the nodes reachable
+
+by directed paths
+from v and w, then
+
+that is a set of nodes that
+induce more than 2k edges.
+
+So let's say their k
+nodes you can reach.
+
+I claim there will be more
+than 2k edges among them.
+
+Why?
+
+It's fun to have proof in
+the middle of an algorithm.
+
+So here we've got to
+v and w, and these
+
+are the k nodes that are
+reachable from v and w, which
+
+means all of the other edges
+are pointing into this set.
+
+And then, over here,
+we have everybody else.
+
+I mean it might be everyone.
+
+But potentially, there's
+some vertices over here.
+
+All the edges are directed
+from right to left,
+
+otherwise we could
+reach more stuff.
+
+So what's the situation?
+
+v-w is uncovered.
+
+There's no pebbles
+that cover it.
+
+Every other edge is
+covered because there's
+
+only one uncovered
+edge at any moment.
+
+These edges are all
+covered from this end.
+
+That's what these
+directions mean, which
+
+means all the
+pebbles in here are
+
+used to cover induced edges.
+
+So all the pebbles in here
+are covering induced edges,
+
+and yet, there's one induced
+edge that is not covered.
+
+Now they're exactly 2k pebbles.
+
+They're all being used.
+
+I'm assuming here you never
+have two pebbles covering
+
+the same edge, so that
+means-- so there's 2k pebbles.
+
+They're all used to cover
+induced edges, which
+
+implies you have
+exactly 2k plus 1 edges.
+
+Plus 1 is v-w.
+
+That means that means the
+graph that we've created so far
+
+violates the 2k property.
+
+Now, we haven't added
+all the edges yet,
+
+but if we add more
+edge, it's going
+
+to get even worse potentially.
+
+If we have 2k plus 1 edges
+now, in the actual graph,
+
+we'll have at least
+2k plus 1 edges.
+
+So if this search
+fails, you know
+
+that you violate the
+2k property, which
+
+means you know that
+there's no pebble cover.
+
+So that proves correctness
+of the algorithm.
+
+Now we can come
+back to this claim.
+
+This follows, by correctness
+of the algorithm, why.
+
+We want to prove if we
+have the 2k property,
+
+then you have a pebble copper.
+
+Well, if I have the 2k property,
+this algorithm will work.
+
+This case can never
+happen because it can only
+
+happen when you violate
+the 2k property.
+
+So if you have the 2k
+property, this algorithm,
+
+you can keep running it.
+
+You will always find a path.
+
+You'll be able to
+shift the pebbles
+
+and always cover things, and
+so you get a pebble cover
+
+from the algorithm.
+
+The end.
+
+That's how you argue that
+if you have the 2k property,
+
+you get a pebble cover.
+
+And it's nifty.
+
+Without this
+algorithm, this would
+
+be quite tricky to specify.
+
+But the algorithm tells
+you where the violation
+
+would be, tells you where you
+would violate the 2k property.
+
+And that lets you prove
+the claim ultimately.
+
+Any questions about that.
+
+This, I think, is the
+heart of pebble algorithms
+
+and why they work.
+
+It's the cleanest part.
+
+It gets a little bit messier
+to do the 2k minus 3 thing,
+
+so we'll move to that next.
+
+Maybe before we go there, we
+can talk about the running time
+
+of the algorithm for
+those so inclined.
+
+So the heart of the
+algorithm is this step,
+
+search for directed path
+for v or w to a free pebble.
+
+This is essentially some of
+the nodes have free pebbles.
+
+Those are like good nodes.
+
+But basically, we've
+got a directed graph.
+
+We want to find all the nodes
+that are reachable from v,
+
+see if there's any good
+nodes that have free pebbles,
+
+search from all
+the nodes from w.
+
+This you could do with a depth
+first search or a breadth
+
+first search or your
+favorite search algorithm.
+
+Takes linear time.
+
+Order the number of
+vertices plus the number
+
+of edges in the graph.
+
+We do this search v times.
+
+Why v times?
+
+So we add edges one at a time.
+
+We're hoping that we
+have the 2k property.
+
+The 2k property implies
+that, in particular,
+
+there at most 2v edges.
+
+So in general, we
+do this e times.
+
+We keep adding edges.
+
+We would add e edges
+to the graph hopefully.
+
+In general, e can be much
+larger than v in a graph. e
+
+could v squared, the worst case.
+
+But this algorithm
+will fail by the time
+
+you add 2k plus 1 edges
+because then you definitely
+
+don't satisfy the 2k property
+over the entire graph,
+
+so particularly you
+won't satisfy it
+
+on some subset of vertices.
+
+So you will only have to
+run this loop v times,
+
+not e times-- or 2v times.
+
+So this is a little bit
+smaller, and so this product
+
+is v squared plus ve.
+
+Normally, we write ve, but
+this is slightly more precise,
+
+which is the same
+as Bellman Ford
+
+algorithm if you've
+taken algorithms.
+
+I'll just mention that there is
+an algorithm slightly fancier
+
+that just requires this term.
+
+This is possible.
+
+You don't need this ve part.
+
+but it's beside the point
+to our goal, which is just
+
+to understand when
+things are rigid,
+
+when they're not in an
+efficient amount of time.
+
+So this is polynomial
+in any case.
+
+This also the best known
+algorithm, v squared.
+
+Open problem is whether
+you could do better.
+
+Questions?
+
+Yeah?
+
+AUDIENCE: Is there more than 2v
+edges instead of, [INAUDIBLE]
+
+that [INAUDIBLE] problem.
+
+PROFESSOR: Yes, there
+are more than to v edges.
+
+Oh, right!
+
+So there's done.
+
+Great.
+
+You can just check in the
+beginning, are there more
+
+than to v edges.
+
+If so, you do not satisfy the 2k
+property, and so you can stop.
+
+So that takes constant time to
+check those cases, otherwise e
+
+is small.
+
+And then you only
+take the square time.
+
+Thanks.
+
+That's key.
+
+So that was the 2k property.
+
+Let's do 2k minus 3.
+
+For the 2k minus
+3 algorithm, it's
+
+going to be pretty much
+the same as this algorithm.
+
+So in particular, every
+vertex is to attach pebbles.
+
+Each pebble can cover
+when it's in an edge,
+
+otherwise it's free.
+
+Our goal is to cover every edge.
+
+But it's slightly differently.
+
+We have to deal with
+this minus 3 business.
+
+And for that we need
+another claim, which
+
+is that a graph has a
+2k minus 3 property if
+
+and only if g plus three
+copies of an edge e
+
+has the 2k property for
+every edge, e and g.
+
+Should probably say g has.
+
+So I want to know whether
+my-- ultimately, I
+
+care whether my graph has
+a 2k minus 3 property.
+
+This is most of the
+Laman condition.
+
+It's the hard part to check.
+
+And 2k property is what
+I know how to check.
+
+So I claim all you need
+to do to check it--
+
+this would actually
+be an algorithm.
+
+For every edge, turn
+that single edge
+
+into four copies of the
+edge, add three more,
+
+check whether it
+has the 2k property,
+
+remove those extra three
+copies, take the next edge,
+
+add three copies,
+check the 2k property.
+
+So with another
+factor of e, which
+
+has to be order v, if you're
+willing to spend v cubed time,
+
+you can just run this
+algorithm for each edge,
+
+quadruple it, see whether it
+still has the 2k property.
+
+So that's the connection
+between these 2 things.
+
+Let me prove this claim.
+
+And then I'll tell
+you a better algorithm
+
+that only takes v squared time.
+
+Which one's easier?
+
+In both cases, I want
+to take k vertices.
+
+And then I'll do in
+this direction first.
+
+So how do we prove this?
+
+First, this is
+actually really easy.
+
+Suppose g has a 2k
+minus 3 property.
+
+So if I have k
+vertices here, I know
+
+that the number of edges in
+here is at most 2k minus 3.
+
+So here's k vertices.
+
+Looking at the number
+of induced edges,
+
+it's going to be
+at most 2k minus 3.
+
+What I'm claiming is then
+if I quadruple an edge,
+
+if I add three new edges, I have
+at most 2k edges afterwards.
+
+I think that's pretty clear.
+
+2k minus 3 would be 4 at most.
+
+If I add three copies of any
+edge, could be in this set
+
+or outside the set
+would be even better,
+
+the number of edges inside
+the set will be at most 2k.
+
+So this is in g.
+
+This implies there's at
+most 2k and g plus thrice e.
+
+This is non-standard
+notation by the way.
+
+It just means add three
+copies of that edge.
+
+So we would normally
+draw that like this,
+
+four copies of the edge.
+
+So that was half of the
+claim, pretty trivial.
+
+The other half is
+almost as trivial.
+
+So on the other
+direction, we assume
+
+that g plus 3e has this
+property for every edge.
+
+And now we need to prove
+that g has a 2k minus 3
+
+property for every
+set of k vertices.
+
+So we're looking at
+that set of k vertices.
+
+We want to argue
+that in g, there's
+
+at most 2k minus 3 edges.
+
+What we know is that in here,
+in g plus 3 e for any e--
+
+so it's a little awkward--
+but let me start by drawing g.
+
+We want to claim that the
+number of edges in here
+
+is at most 2k minus 3, so
+I'll put a question mark.
+
+So there are 2
+possibilities here.
+
+It could be either this
+graph is completely empty.
+
+If there are no edges in
+here, then surely there
+
+are at most 2k minus
+3 of them, assuming k
+
+is bigger than 1, which
+I haven't mentioned.
+
+But throughout here, I need
+the k is bigger than 1.
+
+You can never have negative
+1 edges on subgraphs,
+
+so the 2k in the 2k
+minus 3 property only
+
+hold for at least 2 vertices.
+
+K is at least 2.
+
+So if there are no
+edges, find I'm done.
+
+If there are edges in here,
+then I can do this trick.
+
+So there's some edge.
+
+Pick your favorite edge.
+
+Call it e in this subset.
+
+Produce out of it
+g plus 3e, which
+
+just looks like the
+same thing, but now it's
+
+got four copies of that edge.
+
+This we know has at
+most 2k edges in here.
+
+The original graph
+is exactly the same
+
+except it lacks those
+three edges, therefore,
+
+there's at most 2k
+minus 3 of them.
+
+So it's really the same
+proof in both directions.
+
+Here, you have to
+use your freedom
+
+in choosing e to
+choose an edge that
+
+is induced in this subgraph.
+
+You can't choose some
+other edge out here.
+
+Question?
+
+AUDIENCE: So this seems
+kind of cheap because we're
+
+using the graph as a
+linkage in the end,
+
+so adding these extra edges,
+they all collapse into one.
+
+PROFESSOR: Ah, interesting.
+
+Right.
+
+So why this feels
+like cheating because,
+
+from a linkage
+perspective, these 2 guys
+
+have exactly the
+same constraints.
+
+AUDIENCE: Yeah.
+
+PROFESSOR: I agree.
+
+It's weird.
+
+At this point, this is a device.
+
+You could think of
+it as adding edges.
+
+Another way to think
+of it is this edge
+
+has to be covered
+by four pebbles.
+
+That's probably a
+little more intuitive.
+
+So having to cover an
+edge by four pebbles,
+
+essentially, is
+pinning the edge.
+
+Because on the one hand, you
+have a single pebble just
+
+to say this is an edge.
+
+And then you have
+three more pebbles
+
+to eat up the translations
+and rotations.
+
+That's intuitively
+what's going on.
+
+I agree this looks weird.
+
+And at this point, we're just
+playing the graph theory game
+
+and ignoring the linkages.
+
+That's the short
+answer why this is OK.
+
+But ultimately,
+intuitively, what's going on
+
+is that these three
+edges are just
+
+representing the translations
+and rotations being eaten.
+
+And they have to be
+somehow eatable universally
+
+at every edge.
+
+That's what this is saying.
+
+I don't have a great
+intuition for that,
+
+but it is-- pretty
+sure you do need
+
+to say for every edge,
+not just some edge.
+
+So at this point, you have
+a polynomial time algorithm,
+
+so I'm done.
+
+But let me briefly mention
+how you could make it faster
+
+by modifying this algorithm to
+do the 2k minus 3 situation.
+
+Dare I-- I won't literally
+modify the algorithm.
+
+I'll write a new version.
+
+But I'm going to use that
+as a subroutine basically.
+
+And so algorithm
+2k minus 3 version.
+
+So it's going to
+be the same style.
+
+We're going to add
+edges one at a time.
+
+We'll direct the edges in the
+same way for each added edge
+
+v-w.
+
+I'll just write for
+each added edge v-w.
+
+Before I just tried to add the
+edge and cover it with pebble.
+
+Now, I want to cover
+it with four pebbles.
+
+I want to basically add
+the edge four times.
+
+I'm going to write as
+above to mean this step.
+
+So every time I add
+the edge, I search
+
+for a directed path from
+v or w for free pebble.
+
+When I find it, I
+do the pebble shift.
+
+I do that four times.
+
+Then basically, I have
+four pebbles on the edge,
+
+or you could think of them as
+being four copies of the edge,
+
+each has one pebble.
+
+Either I succeed and I get all
+four, or I don't get all four.
+
+On success, this is just
+a temporary measure.
+
+At that point, I'm going to
+delete three of the copies.
+
+Put it back to a
+regular single edge.
+
+This frees three
+pebbles for future use.
+
+So I don't want every
+edge to be quadrupled.
+
+I don't want them all to
+be quadrupled at once.
+
+I want to try
+quadrupling one edge,
+
+then try quadrupling
+the next edge,
+
+try quadrupling the next edge.
+
+But when I'm
+quadrupling an edge,
+
+all the other edges
+exist as single edges.
+
+So I delete the three copies.
+
+And then this four loop
+continues and tries
+
+the next edge.
+
+On failure-- here I'm
+going to say something
+
+more interesting-- Normally,
+on failure I'd say,
+
+well, you don't satisfy
+the 2k minus 3 property.
+
+Game over.
+
+But you can be a little
+more sophisticated.
+
+Just say delete all
+the copies of e.
+
+I guess there's four of them.
+
+Whatever pebbles you can
+acquire, you give them up.
+
+Delete the edge and
+call the edge redundant.
+
+Basically, in this
+case, you could
+
+argue that edge was superfluous
+for rigidity purposes.
+
+You didn't need it.
+
+So the algorithm
+doesn't just fail.
+
+It says this was a useless edge.
+
+And it'll tell you
+which edges are useful,
+
+which ones are non-redundant
+from a rigidity standpoint.
+
+And then when you're done,
+you will be rigid if and only
+
+if the number of non-redundant
+edges that remain
+
+equals 2n minus 3.
+
+So that's the last part
+of the Laman check.
+
+So this is giving you a
+little bit more information
+
+than just do I satisfy
+the 2k minus 3 property.
+
+To get that, you just check
+whether you ever failed.
+
+But in this case,
+you can actually
+
+see, ah, these are
+the useless edges.
+
+They're those overbracing edges.
+
+Everything else is useful.
+
+And if I end up having enough
+useful edges to n minus 3
+
+of them, then I know I'm rigid.
+
+Otherwise, I'm going
+to be flexible.
+
+So this gives you all
+the information you want.
+
+With a little bit
+more effort, you
+
+could even figure out if I'm
+flexible, which parts are rigid
+
+and which parts can move
+relative to each other.
+
+This, of course,
+generically rigid.
+
+Finally, let me show you
+this thing in action.
+
+So look over there.
+
+This is an implementation
+by Audrey Lee-Saint John.
+
+And so here's a simple graph.
+
+You can probably see this
+top part is flexible.
+
+It's quadrilateral.
+
+Bottom part is overbraced.
+
+This is in 2 dimensions, right?
+
+So just triangles
+would be enough,
+
+but I've added an
+extra edge here.
+
+And this is going to check
+the Laman condition one
+
+step at a time.
+
+So we start with 2
+pebbles everywhere.
+
+We start by adding
+that top edge.
+
+Right now, there are four
+pebbles on that edge,
+
+so it's great.
+
+I can just add the edge.
+
+Let's say I added it four times.
+
+There are four pebbles there.
+
+But then in the end,
+I just need one.
+
+So let's skip that step.
+
+And now I've got the one
+pebble from b, and we're happy.
+
+So that is its own
+rigid component.
+
+Next, let's add this edge ef.
+
+So this also has four
+pebbles on it, so we're done.
+
+Next, we have cd.
+
+That also has-- you
+could change the order
+
+if you think this
+one's a little trivial.
+
+Now is when the action happens.
+
+Let's add this edge bc.
+
+So currently, it is only
+covered by three pebbles.
+
+But we need a fourth.
+
+So we're going to take one
+of these free pebbles on a
+
+and move it along b.
+
+We found that by starting
+from b and searching out
+
+and finding a free pebble.
+
+So we just flip that edge.
+
+Now we've got a
+free pebble on b.
+
+Now we've got four pebbles on
+bc, and we can add the edge.
+
+But we only actually
+take one of them.
+
+So I'm skipping the part
+where we add the four copies
+
+and immediately remove three
+of them because that's silly.
+
+Cool.
+
+So that's its own rigid
+component it turns out.
+
+Each of these things
+is independently--
+
+the colors represent
+rigid components.
+
+And right now nothing
+is tied together.
+
+Everything's flexible.
+
+Flexible at b.
+
+Flexible at c.
+
+Let's add this diagonal df.
+
+So right now, it
+only has one pebble,
+
+which means we
+need four pebbles.
+
+So we're actually going
+to have to get one at f,
+
+and we're going
+to have to get one
+
+at d because there can
+only be two at each.
+
+So first, we'll do I
+guess a search from d,
+
+and we immediately
+find a pebble.
+
+We move it down there.
+
+Great.
+
+Then, we search from f.
+
+We find a pebble there.
+
+We move it.
+
+Boom!
+
+We've got our edge,
+added all four pebbles.
+
+Eventually we're going
+to run out of pebbles,
+
+but right now, we
+are very flexible.
+
+Let's add this other diagonal.
+
+This should also be possible.
+
+Right now, there's one
+pebble at e, one pebble at c.
+
+We've got to find
+two more pebbles.
+
+So first, we'll
+follow this edge.
+
+Find a free pebble at f.
+
+That was easy.
+
+Next, we'll look at from c.
+
+There's only one way
+we can go from c.
+
+We can't follow the back edge.
+
+Got to go forward.
+
+Got a pebble at d.
+
+Flip it around.
+
+Now, we've got four pebbles on
+c and e, so we can add the edge.
+
+Now, let's add ef.
+
+Right now, we've only got
+one pebble, yet we need four.
+
+So let's start by
+searching from a.
+
+Oh, we found a
+pebble immediately.
+
+In general, we would have
+to follow many edges.
+
+So there's a from f.
+
+There are two ways we could go.
+
+Either one of them would
+have given us a pebble.
+
+Let's flip the yellow edge.
+
+Boom!
+
+We've got f, one pebble,
+but we need another one.
+
+Now, we cannot get another
+pebble from e because we just
+
+flipped the edge, but we
+can get a pebble from d,
+
+so we flip that edge.
+
+And now we can add the
+edge af to more edges.
+
+It's a little tedious.
+
+So next is cf.
+
+We're running out
+of pebbles here.
+
+There's only five pebbles
+total in the system.
+
+We need four of them
+right here because we're
+
+getting almost rigid.
+
+So let's see.
+
+We've got cf.
+
+Let's start from
+searching from f.
+
+There's only one way we can go.
+
+We find a pebble.
+
+We flip it around.
+
+Now we've got c.
+
+There's only one
+way to go from c.
+
+We find the pebble at e.
+
+And we flip it around.
+
+Now we've got the two pebbles.
+
+Cool.
+
+So we've got the
+three pebbles here,
+
+which are representing our
+translations and rotations.
+
+The only other pebble
+left is this one,
+
+which is basically representing
+the degree of freedom
+
+in this quadrilateral.
+
+So when we go to add the
+last edge, which is-- so
+
+at this point, this is
+a ridge it component
+
+because of the triangles.
+
+And we go to add
+the last edge, we
+
+will fail to find
+enough pebbles.
+
+Let's see.
+
+We can find three of them.
+
+We can grab the one from e.
+
+Or let's see so-- it's
+not going to show us.
+
+But from e, we can grab
+f, the pebble at f.
+
+From d, we can grab
+the pebble at c.
+
+From d, we can grab
+the other pebble at f.
+
+We've got three
+pebbles, but there's
+
+no way to get to this pebble
+because both of these edges
+
+are directed down.
+
+So you can never get from the
+below part to the above part.
+
+So it's not obvious
+that this is working.
+
+That's what the proof is for.
+
+But at least you
+see it in action.
+
+I'll just run it very
+quickly for another graph.
+
+Let's say a big one.
+
+This one is minimally,
+generically rigid.
+
+So it's fun to
+watch for a while.
+
+You get pebbles moving around.
+
+In this case, you
+have some longer paths
+
+you have to follow to
+get enough pebbles.
+
+It depends a lot on the
+insertion order that you use.
+
+So in each case, you need four
+pebbles, two on each side.
+
+And if so, you
+can add your edge.
+
+Otherwise, you can't.
+
+What I haven't described
+is this color coding
+
+which is figuring out when
+you have rigid components.
+
+Roughly speaking, to find
+what your rigid component is--
+
+if you're an edge, you want to
+know what rigid component am
+
+I in-- you basically just
+search for all the vertices
+
+that are reachable
+from your edge.
+
+Those are all in
+your rigid component.
+
+That's what we saw.
+
+So this graph happens
+to be minimally rigid,
+
+and it detects that.
+
+But then it can be
+a little bit more
+
+as in your rigid component.
+
+Some of the incoming
+edges-- let's see.
+
+Draw a picture.
+
+So here's everything
+you can reach from v-w.
+
+And say you're following
+an incoming edge here
+
+from some other vertex u.
+
+And then suppose these
+are all the things
+
+you can reach from you.
+
+If there are zero
+pebbles out here,
+
+then this whole thing
+is a rigid component.
+
+And you just keep doing that.
+
+You check an incoming edge.
+
+If there's zero pebbles
+in that reachable piece,
+
+then you merge.
+
+And you keep doing that.
+
+Those are all the things that
+are rigidly attached to you.
+
+So I won't prove that.
+
+It's a little tricky to
+prove, but it's fairly easy
+
+to compute.
+
+And you could actually do it
+in the same amount of time.
+
+As you're building
+this thing up,
+
+you can do the color
+coding to figure out
+
+which things are in the
+same component, which things
+
+are in different components.
+
+Let's see.
+
+So another fun fact
+is this little part.
+
+This says it's the
+2k minus 3 property.
+
+The same algorithm you could
+use to check 5k minus 27,
+
+or whatever you want, for fixed
+numbers like two and three,
+
+the same pebble
+algorithm can detect
+
+that ak minus b property.
+
+And that's actually useful
+for a lot of different things.
+
+This is done originally
+by Lee and Streinu.
+
+Same lee, and Streinu
+we'll be seeing
+
+some of her results in a
+couple of classes as well.
+
+For example-- so this is
+that-- 3D body and bar.
+
+So actually let me
+show you the kind
+
+of scenario we're
+thinking about.
+
+So I mentioned 3D.
+
+If we have vertices
+and bars between them,
+
+we don't know how to
+characterize generic rigidity.
+
+But a slightly different
+problem, which is 3D bodies,
+
+these are polyhedron.
+
+And they have bars
+connected between them.
+
+This we know how to solve
+in 3D and in any dimension.
+
+And so this is a picture
+of not only having--
+
+so their bodies can
+spin unlike vertices.
+
+Vertices can't rotate.
+
+Nothing happens when
+you rotate a vertex.
+
+Bodies have this extra
+degree of freedom.
+
+So there are two things
+we're allowing here,
+
+one is to add a hinge
+between two bodies
+
+and the other is to add
+bars connecting them
+
+from various random points.
+
+And it's generic, so these
+points will never coincide.
+
+I think that's what makes
+this different from a vertex.
+
+Vertex bars always coincide.
+
+Here, they all just
+attach to generic points.
+
+So it turns out you can
+simulate a hinge by five bars.
+
+They're equivalent.
+
+So both of these can be
+captured by 6K minus 6 property.
+
+Turns out these things will
+be generically rigid if
+
+and only if you satisfy
+the 6K minus 6 property
+
+and you have exactly
+6K minus 6 bars.
+
+And this is proved by
+two or three people.
+
+I mean you need to add
+two results together,
+
+one from the '90s and
+one from much older,
+
+I think, in graph theory.
+
+But in particular, Tae
+was involved from 1984.
+
+And it's funny.
+
+The paper starts out with, if
+you ask any structural engineer
+
+if you have two
+bodies how many bars
+
+you have to add to rigidify
+them, they will say six.
+
+I'm like, OK, I
+didn't know that.
+
+But six is the right answer.
+
+And that's why the
+6K minus 6 basically.
+
+And and we can use
+this pebble algorithm
+
+to solve that for
+free basically.
+
+And this is actually
+implemented here
+
+in the same kind of software.
+
+I'll just run it quickly
+because it's a lot of pebbles.
+
+Every vertex has six pebbles.
+
+You just keep going.
+
+You need to cover every
+edge with how many pebbles?
+
+Before it was four,
+so now it should be 7,
+
+I believe, one more
+than the six here.
+
+So 6k minus 6.
+
+Anyway, this graph,
+while it's not obvious,
+
+is minimally rigid
+in this world.
+
+And it corresponds exactly
+to the left example.
+
+It's hard to see because
+we've replaced the hinges here
+
+by six bars.
+
+So that's why we got all the
+six-- all the duplicated edges.
+
+Here, you see the duplicated
+are different from a rigidity
+
+standpoint because having three
+edges between the same pair
+
+of objects is no longer just
+the same as having one edge
+
+because they attach
+to different points.
+
+Each one can spin.
+
+These are universal
+joints by the way.
+
+So these bars can
+rotate around the body.
+
+The body can spin.
+
+Lots of things can happen.
+
+But this is enough to rigidify.
+
+Is there a question?
+
+Cool.
+
+I'm not going to prove that.
+
+You can read the papers
+if you're interested.
+
+But it's interesting.
+
+Bodies and bars are so much
+easier than other things.
+
+One other thing you can do
+is called angular rigidity.
+
+This is a fairly new
+result by same people.
+
+If you have a bunch of
+lines in 3D, and you
+
+have angular constraints.
+
+In this case, every
+triple of these lines
+
+has an angular constraint that
+it must be equal to alpha.
+
+That's what's drawn on
+this spherical picture.
+
+Over here, we have two bodies.
+
+So here we have lines.
+
+Here, we have bodies.
+
+And there are three
+constraints that
+
+fix the angles between how the
+angles meet at these bodies.
+
+And they claim is that both
+of these are angularly rigid,
+
+meaning things can
+still slide up and down,
+
+but the angles are all fixed.
+
+And you can test this again.
+
+This case actually turns out
+it's the 2k minus 3 property
+
+again, same as Laman.
+
+This one, I've forgotten.
+
+I have to check.
+
+I think it's 3k minus 3.
+
+Yeah, 3k minus 3.
+
+So cool things.
+
+One last question.
+
+Connected banana.
+
+So there's this three banana
+example-- or two banana
+
+example.
+
+I'm getting ahead of
+myself-- which was weird.
+
+You have this one banana on the
+left, one banana on the right.
+
+And there's this implicit,
+implied hinge, as they call it,
+
+between the two points.
+
+The whole thing is flexible,
+but if you check it,
+
+it satisfies the Lama condition.
+
+It satisfies 3k
+minus 6, which is
+
+what it should be
+for 3D rigidity.
+
+This is a 3D.
+
+Now, this graph is--
+seems trivial-- I
+
+mean it seems easy to figure
+out that this is flexible
+
+because there's a two cut.
+
+There are two vertices
+you can remove
+
+that disconnect the
+graph into two pieces.
+
+So if you could just subdivide,
+do the left part separately
+
+from the right part, you should
+be able to figure this out.
+
+Unfortunately, this example
+can be made more connected,
+
+and that's what
+the question was.
+
+So this is an old
+example by Henry Crapo.
+
+A modification by
+Walter Whiteley
+
+is that if you add a single
+point here and attach it
+
+to those two points--
+sorry, those three points--
+
+this will be three connected,
+still be flexible, and still
+
+satisfy Laman because we added
+three edges and one vertex,
+
+so it still satisfies Laman.
+
+So that sucks.
+
+We think, oh, maybe
+four connected.
+
+Well, you can make it
+four connected, too,
+
+by adding a triangle
+in the center
+
+and connecting these six,
+adding these 6 connections.
+
+Well, what about 5 connected?
+
+Well, five connected,
+you can also do.
+
+And this is an example
+called the banana spider.
+
+Although it seems a
+bit of a misnomer.
+
+It should be-- but I
+guess banana spiders
+
+are actual object--
+actual species.
+
+This really should
+be a banana insect
+
+because this guy
+has six legs, three
+
+on the left, three on the right.
+
+So if it is an
+octahedron in the center,
+
+and then you add these
+three connections,
+
+and you can actually prove
+that any graph you have,
+
+any example that's maybe only
+one or two or three connected,
+
+whatever, you can make it five
+connected by whenever you have
+
+two four connected components--
+or five things components
+
+I guess-- just add a spider
+in the middle to bridge them,
+
+and it will be as
+flexible as before.
+
+And it will still satisfy Laman.
+
+So five connectivity doesn't
+buy you anything unfortunately.
+
+I guess you could ask
+for six connectivity,
+
+but six connectivity,
+I think, is impossible
+
+because you only have
+3n minus 6 edges.
+
+That's the limit.
+
+So sadly, connectivity is not
+the right-- doesn't buy us
+
+anything.
+
+And that's what we know about
+vertex and bar structures in 3D
+
+sadly.
+
+Tough open problem.
+
+Any questions?
+
+That's it for today.
\ No newline at end of file
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+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
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+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi welcome back i am dr. bugged alpha
+
+ align:start position:0%
+hi welcome back i am dr. bugged alpha
+ 
+
+ align:start position:0%
+hi welcome back i am dr. bugged alpha
+delish let's solve some more
+
+ align:start position:0%
+delish let's solve some more
+ 
+
+ align:start position:0%
+delish let's solve some more
+biochemistry problems today we're going
+
+ align:start position:0%
+biochemistry problems today we're going
+ 
+
+ align:start position:0%
+biochemistry problems today we're going
+to be talking about problem 3 a problem
+
+ align:start position:0%
+to be talking about problem 3 a problem
+ 
+
+ align:start position:0%
+to be talking about problem 3 a problem
+set 10 now this is a problem about the
+
+ align:start position:0%
+set 10 now this is a problem about the
+ 
+
+ align:start position:0%
+set 10 now this is a problem about the
+spontaneity of gluconeogenesis as you
+
+ align:start position:0%
+spontaneity of gluconeogenesis as you
+ 
+
+ align:start position:0%
+spontaneity of gluconeogenesis as you
+guys have already learned
+
+ align:start position:0%
+guys have already learned
+ 
+
+ align:start position:0%
+guys have already learned
+gluconeogenesis is the process by which
+
+ align:start position:0%
+gluconeogenesis is the process by which
+ 
+
+ align:start position:0%
+gluconeogenesis is the process by which
+non-sugar precursors are used to produce
+
+ align:start position:0%
+non-sugar precursors are used to produce
+ 
+
+ align:start position:0%
+non-sugar precursors are used to produce
+glucose this problem should help you
+
+ align:start position:0%
+glucose this problem should help you
+ 
+
+ align:start position:0%
+glucose this problem should help you
+think of the following conundrum in a
+
+ align:start position:0%
+think of the following conundrum in a
+ 
+
+ align:start position:0%
+think of the following conundrum in a
+Cell when we have glucose we can make
+
+ align:start position:0%
+Cell when we have glucose we can make
+ 
+
+ align:start position:0%
+Cell when we have glucose we can make
+energy by doing glycolysis but at the
+
+ align:start position:0%
+energy by doing glycolysis but at the
+ 
+
+ align:start position:0%
+energy by doing glycolysis but at the
+same time the cell can take for example
+
+ align:start position:0%
+same time the cell can take for example
+ 
+
+ align:start position:0%
+same time the cell can take for example
+the endpoints of glycolysis such as
+
+ align:start position:0%
+the endpoints of glycolysis such as
+ 
+
+ align:start position:0%
+the endpoints of glycolysis such as
+pyruvate or even further metabolites
+
+ align:start position:0%
+pyruvate or even further metabolites
+ 
+
+ align:start position:0%
+pyruvate or even further metabolites
+like amino acids and use the pathway in
+
+ align:start position:0%
+like amino acids and use the pathway in
+ 
+
+ align:start position:0%
+like amino acids and use the pathway in
+Reverse to make glucose now if one
+
+ align:start position:0%
+Reverse to make glucose now if one
+ 
+
+ align:start position:0%
+Reverse to make glucose now if one
+process is spontaneous in terms of time
+
+ align:start position:0%
+process is spontaneous in terms of time
+ 
+
+ align:start position:0%
+process is spontaneous in terms of time
+thermodynamics then how could we run the
+
+ align:start position:0%
+thermodynamics then how could we run the
+ 
+
+ align:start position:0%
+thermodynamics then how could we run the
+reaction in Reverse so here we're going
+
+ align:start position:0%
+reaction in Reverse so here we're going
+ 
+
+ align:start position:0%
+reaction in Reverse so here we're going
+to be looking at a couple of steps of
+
+ align:start position:0%
+to be looking at a couple of steps of
+ 
+
+ align:start position:0%
+to be looking at a couple of steps of
+gluconeogenesis that are the exact
+
+ align:start position:0%
+gluconeogenesis that are the exact
+ 
+
+ align:start position:0%
+gluconeogenesis that are the exact
+reverse of the reactions that you've
+
+ align:start position:0%
+reverse of the reactions that you've
+ 
+
+ align:start position:0%
+reverse of the reactions that you've
+seen already in glycolysis and then in
+
+ align:start position:0%
+seen already in glycolysis and then in
+ 
+
+ align:start position:0%
+seen already in glycolysis and then in
+the end we're going to be talking about
+
+ align:start position:0%
+the end we're going to be talking about
+ 
+
+ align:start position:0%
+the end we're going to be talking about
+the whole pathway level and make some
+
+ align:start position:0%
+the whole pathway level and make some
+ 
+
+ align:start position:0%
+the whole pathway level and make some
+comments on the spontaneity of both
+
+ align:start position:0%
+comments on the spontaneity of both
+ 
+
+ align:start position:0%
+comments on the spontaneity of both
+glycolysis and gluconeogenesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part a of the problem deals with the
+
+ align:start position:0%
+part a of the problem deals with the
+ 
+
+ align:start position:0%
+part a of the problem deals with the
+aldolase reaction namely going from
+
+ align:start position:0%
+aldolase reaction namely going from
+ 
+
+ align:start position:0%
+aldolase reaction namely going from
+fructose 1 6 bisphosphate to
+
+ align:start position:0%
+fructose 1 6 bisphosphate to
+ 
+
+ align:start position:0%
+fructose 1 6 bisphosphate to
+glyceraldehyde-3-phosphate and by haider
+
+ align:start position:0%
+glyceraldehyde-3-phosphate and by haider
+ 
+
+ align:start position:0%
+glyceraldehyde-3-phosphate and by haider
+acetone phosphate now in gluconeogenesis
+
+ align:start position:0%
+acetone phosphate now in gluconeogenesis
+ 
+
+ align:start position:0%
+acetone phosphate now in gluconeogenesis
+will be going in reverse starting with
+
+ align:start position:0%
+will be going in reverse starting with
+ 
+
+ align:start position:0%
+will be going in reverse starting with
+the Hydra acetone phosphate and
+
+ align:start position:0%
+the Hydra acetone phosphate and
+ 
+
+ align:start position:0%
+the Hydra acetone phosphate and
+glyceraldehyde 3-phosphate to regenerate
+
+ align:start position:0%
+glyceraldehyde 3-phosphate to regenerate
+ 
+
+ align:start position:0%
+glyceraldehyde 3-phosphate to regenerate
+fructose 1 6 bisphosphate let's take a
+
+ align:start position:0%
+fructose 1 6 bisphosphate let's take a
+ 
+
+ align:start position:0%
+fructose 1 6 bisphosphate let's take a
+look at the reaction this is the hydro
+
+ align:start position:0%
+look at the reaction this is the hydro
+ 
+
+ align:start position:0%
+look at the reaction this is the hydro
+acetone phosphate this is
+
+ align:start position:0%
+acetone phosphate this is
+ 
+
+ align:start position:0%
+acetone phosphate this is
+glyceraldehyde-3-phosphate or gap and
+
+ align:start position:0%
+glyceraldehyde-3-phosphate or gap and
+ 
+
+ align:start position:0%
+glyceraldehyde-3-phosphate or gap and
+these two come together in the aldolase
+
+ align:start position:0%
+these two come together in the aldolase
+ 
+
+ align:start position:0%
+these two come together in the aldolase
+reaction to form fructose 1 6
+
+ align:start position:0%
+reaction to form fructose 1 6
+ 
+
+ align:start position:0%
+reaction to form fructose 1 6
+bisphosphate or f 16 BP now the part 1
+
+ align:start position:0%
+bisphosphate or f 16 BP now the part 1
+ 
+
+ align:start position:0%
+bisphosphate or f 16 BP now the part 1
+of the question asked us to write down
+
+ align:start position:0%
+of the question asked us to write down
+ 
+
+ align:start position:0%
+of the question asked us to write down
+the detailed mechanism for this reaction
+
+ align:start position:0%
+the detailed mechanism for this reaction
+ 
+
+ align:start position:0%
+the detailed mechanism for this reaction
+running in reverse so as you guys know
+
+ align:start position:0%
+running in reverse so as you guys know
+ 
+
+ align:start position:0%
+running in reverse so as you guys know
+aldolase specifically the class 1 alder
+
+ align:start position:0%
+aldolase specifically the class 1 alder
+ 
+
+ align:start position:0%
+aldolase specifically the class 1 alder
+lazes use an active site lysine residue
+
+ align:start position:0%
+lazes use an active site lysine residue
+ 
+
+ align:start position:0%
+lazes use an active site lysine residue
+to to covalently bind the substrate
+
+ align:start position:0%
+to to covalently bind the substrate
+ 
+
+ align:start position:0%
+to to covalently bind the substrate
+during the course of the reaction so
+
+ align:start position:0%
+during the course of the reaction so
+ 
+
+ align:start position:0%
+during the course of the reaction so
+this reaction will proceed by dihydrogen
+
+ align:start position:0%
+this reaction will proceed by dihydrogen
+ 
+
+ align:start position:0%
+this reaction will proceed by dihydrogen
+phosphate binding to the exercise lysine
+
+ align:start position:0%
+phosphate binding to the exercise lysine
+ 
+
+ align:start position:0%
+phosphate binding to the exercise lysine
+of the aldolase here we have the
+
+ align:start position:0%
+of the aldolase here we have the
+ 
+
+ align:start position:0%
+of the aldolase here we have the
+dihydrogen phosphate and the lysine in
+
+ align:start position:0%
+dihydrogen phosphate and the lysine in
+ 
+
+ align:start position:0%
+dihydrogen phosphate and the lysine in
+the active site so as the first step of
+
+ align:start position:0%
+the active site so as the first step of
+ 
+
+ align:start position:0%
+the active site so as the first step of
+the mechanism the lysine is going to
+
+ align:start position:0%
+the mechanism the lysine is going to
+ 
+
+ align:start position:0%
+the mechanism the lysine is going to
+react with the carbonyl group in that
+
+ align:start position:0%
+react with the carbonyl group in that
+ 
+
+ align:start position:0%
+react with the carbonyl group in that
+hydrostan phosphate to form a ship space
+
+ align:start position:0%
+hydrostan phosphate to form a ship space
+ 
+
+ align:start position:0%
+hydrostan phosphate to form a ship space
+or an e mean as you can imagine the
+
+ align:start position:0%
+or an e mean as you can imagine the
+ 
+
+ align:start position:0%
+or an e mean as you can imagine the
+reaction is going to be catalyzed by the
+
+ align:start position:0%
+reaction is going to be catalyzed by the
+ 
+
+ align:start position:0%
+reaction is going to be catalyzed by the
+general base which is going to remove
+
+ align:start position:0%
+general base which is going to remove
+ 
+
+ align:start position:0%
+general base which is going to remove
+one of the protons from the lysine which
+
+ align:start position:0%
+one of the protons from the lysine which
+ 
+
+ align:start position:0%
+one of the protons from the lysine which
+then becomes a good nucleophile and can
+
+ align:start position:0%
+then becomes a good nucleophile and can
+ 
+
+ align:start position:0%
+then becomes a good nucleophile and can
+attack the carbonyl which can then will
+
+ align:start position:0%
+attack the carbonyl which can then will
+ 
+
+ align:start position:0%
+attack the carbonyl which can then will
+be protonated by a general acid so this
+
+ align:start position:0%
+be protonated by a general acid so this
+ 
+
+ align:start position:0%
+be protonated by a general acid so this
+way you obtain an intermediate as shown
+
+ align:start position:0%
+way you obtain an intermediate as shown
+ 
+
+ align:start position:0%
+way you obtain an intermediate as shown
+here which can then lose the water
+
+ align:start position:0%
+here which can then lose the water
+ 
+
+ align:start position:0%
+here which can then lose the water
+molecule to form the shift base once
+
+ align:start position:0%
+molecule to form the shift base once
+ 
+
+ align:start position:0%
+molecule to form the shift base once
+again we need a base that will
+
+ align:start position:0%
+again we need a base that will
+ 
+
+ align:start position:0%
+again we need a base that will
+take this proton and then the water will
+
+ align:start position:0%
+take this proton and then the water will
+ 
+
+ align:start position:0%
+take this proton and then the water will
+need another acid molecule to leave so
+
+ align:start position:0%
+need another acid molecule to leave so
+ 
+
+ align:start position:0%
+need another acid molecule to leave so
+what we have formed here this is the
+
+ align:start position:0%
+what we have formed here this is the
+ 
+
+ align:start position:0%
+what we have formed here this is the
+protonated shift base or what we call an
+
+ align:start position:0%
+protonated shift base or what we call an
+ 
+
+ align:start position:0%
+protonated shift base or what we call an
+amine IAM ion and if you look at edit
+
+ align:start position:0%
+amine IAM ion and if you look at edit
+ 
+
+ align:start position:0%
+amine IAM ion and if you look at edit
+from the point of view of where we
+
+ align:start position:0%
+from the point of view of where we
+ 
+
+ align:start position:0%
+from the point of view of where we
+started from which was a carbonyl group
+
+ align:start position:0%
+started from which was a carbonyl group
+ 
+
+ align:start position:0%
+started from which was a carbonyl group
+this is a version of an activated
+
+ align:start position:0%
+this is a version of an activated
+ 
+
+ align:start position:0%
+this is a version of an activated
+carbonyl carbon yo Derwood it's now
+
+ align:start position:0%
+carbonyl carbon yo Derwood it's now
+ 
+
+ align:start position:0%
+carbonyl carbon yo Derwood it's now
+poised to do chemistry once again this
+
+ align:start position:0%
+poised to do chemistry once again this
+ 
+
+ align:start position:0%
+poised to do chemistry once again this
+is this is the iminium ion now as we
+
+ align:start position:0%
+is this is the iminium ion now as we
+ 
+
+ align:start position:0%
+is this is the iminium ion now as we
+talked in the carbonyl video aminium
+
+ align:start position:0%
+talked in the carbonyl video aminium
+ 
+
+ align:start position:0%
+talked in the carbonyl video aminium
+ions are activated carbonyls that can
+
+ align:start position:0%
+ions are activated carbonyls that can
+ 
+
+ align:start position:0%
+ions are activated carbonyls that can
+now undergo some of the carbonyl
+
+ align:start position:0%
+now undergo some of the carbonyl
+ 
+
+ align:start position:0%
+now undergo some of the carbonyl
+reactions which more ease for example
+
+ align:start position:0%
+reactions which more ease for example
+ 
+
+ align:start position:0%
+reactions which more ease for example
+this one is going to do an inhalation so
+
+ align:start position:0%
+this one is going to do an inhalation so
+ 
+
+ align:start position:0%
+this one is going to do an inhalation so
+we have highlighted here the alpha
+
+ align:start position:0%
+we have highlighted here the alpha
+ 
+
+ align:start position:0%
+we have highlighted here the alpha
+hydrogen next to the carbonyl group so
+
+ align:start position:0%
+hydrogen next to the carbonyl group so
+ 
+
+ align:start position:0%
+hydrogen next to the carbonyl group so
+we were going to form the you know by
+
+ align:start position:0%
+we were going to form the you know by
+ 
+
+ align:start position:0%
+we were going to form the you know by
+removing this hydrogen and the carbonyl
+
+ align:start position:0%
+removing this hydrogen and the carbonyl
+ 
+
+ align:start position:0%
+removing this hydrogen and the carbonyl
+with this positive charge on the
+
+ align:start position:0%
+with this positive charge on the
+ 
+
+ align:start position:0%
+with this positive charge on the
+nitrogen so that a very good electron
+
+ align:start position:0%
+nitrogen so that a very good electron
+ 
+
+ align:start position:0%
+nitrogen so that a very good electron
+sink so what we're forming here is a an
+
+ align:start position:0%
+sink so what we're forming here is a an
+ 
+
+ align:start position:0%
+sink so what we're forming here is a an
+amine that's bound to a double bond this
+
+ align:start position:0%
+amine that's bound to a double bond this
+ 
+
+ align:start position:0%
+amine that's bound to a double bond this
+we're going to call and in amin now this
+
+ align:start position:0%
+we're going to call and in amin now this
+ 
+
+ align:start position:0%
+we're going to call and in amin now this
+is the reactive version of the
+
+ align:start position:0%
+is the reactive version of the
+ 
+
+ align:start position:0%
+is the reactive version of the
+dihydrogen phosphate now it's poised to
+
+ align:start position:0%
+dihydrogen phosphate now it's poised to
+ 
+
+ align:start position:0%
+dihydrogen phosphate now it's poised to
+react with the other partner in the
+
+ align:start position:0%
+react with the other partner in the
+ 
+
+ align:start position:0%
+react with the other partner in the
+reaction gap glyceraldehyde-3-phosphate
+
+ align:start position:0%
+reaction gap glyceraldehyde-3-phosphate
+ 
+
+ align:start position:0%
+reaction gap glyceraldehyde-3-phosphate
+which we've shown here now gap is going
+
+ align:start position:0%
+which we've shown here now gap is going
+ 
+
+ align:start position:0%
+which we've shown here now gap is going
+to be the carbonyl component of this
+
+ align:start position:0%
+to be the carbonyl component of this
+ 
+
+ align:start position:0%
+to be the carbonyl component of this
+aldol reaction while the eno mean from
+
+ align:start position:0%
+aldol reaction while the eno mean from
+ 
+
+ align:start position:0%
+aldol reaction while the eno mean from
+the dihydrogen phosphate is going to be
+
+ align:start position:0%
+the dihydrogen phosphate is going to be
+ 
+
+ align:start position:0%
+the dihydrogen phosphate is going to be
+the the enoli component right so the
+
+ align:start position:0%
+the the enoli component right so the
+ 
+
+ align:start position:0%
+the the enoli component right so the
+enol is going to be a very good
+
+ align:start position:0%
+enol is going to be a very good
+ 
+
+ align:start position:0%
+enol is going to be a very good
+nucleophile and it's going to attack the
+
+ align:start position:0%
+nucleophile and it's going to attack the
+ 
+
+ align:start position:0%
+nucleophile and it's going to attack the
+carbonyl the reaction is once again
+
+ align:start position:0%
+carbonyl the reaction is once again
+ 
+
+ align:start position:0%
+carbonyl the reaction is once again
+initiated by this amine group the
+
+ align:start position:0%
+initiated by this amine group the
+ 
+
+ align:start position:0%
+initiated by this amine group the
+electrons move here then this attacks
+
+ align:start position:0%
+electrons move here then this attacks
+ 
+
+ align:start position:0%
+electrons move here then this attacks
+the carbonyl and we can protonate it
+
+ align:start position:0%
+the carbonyl and we can protonate it
+ 
+
+ align:start position:0%
+the carbonyl and we can protonate it
+with a general acid
+
+ align:start position:0%
+with a general acid
+ 
+
+ align:start position:0%
+with a general acid
+so what we obtain here it's now a
+
+ align:start position:0%
+so what we obtain here it's now a
+ 
+
+ align:start position:0%
+so what we obtain here it's now a
+molecule that has from two portions of
+
+ align:start position:0%
+molecule that has from two portions of
+ 
+
+ align:start position:0%
+molecule that has from two portions of
+three it's going to have six carbons and
+
+ align:start position:0%
+three it's going to have six carbons and
+ 
+
+ align:start position:0%
+three it's going to have six carbons and
+if you look closely this is really the
+
+ align:start position:0%
+if you look closely this is really the
+ 
+
+ align:start position:0%
+if you look closely this is really the
+fructose 1 6 bisphosphate bound to the
+
+ align:start position:0%
+fructose 1 6 bisphosphate bound to the
+ 
+
+ align:start position:0%
+fructose 1 6 bisphosphate bound to the
+active site of the enzyme as a shift
+
+ align:start position:0%
+active site of the enzyme as a shift
+ 
+
+ align:start position:0%
+active site of the enzyme as a shift
+space okay so now all that needs to
+
+ align:start position:0%
+space okay so now all that needs to
+ 
+
+ align:start position:0%
+space okay so now all that needs to
+happen now is to hydrolyze the ship
+
+ align:start position:0%
+happen now is to hydrolyze the ship
+ 
+
+ align:start position:0%
+happen now is to hydrolyze the ship
+space and release ours are fructose 1 6
+
+ align:start position:0%
+space and release ours are fructose 1 6
+ 
+
+ align:start position:0%
+space and release ours are fructose 1 6
+bisphosphate product so we're going to
+
+ align:start position:0%
+bisphosphate product so we're going to
+ 
+
+ align:start position:0%
+bisphosphate product so we're going to
+need one water molecule it's going to be
+
+ align:start position:0%
+need one water molecule it's going to be
+ 
+
+ align:start position:0%
+need one water molecule it's going to be
+activated by a general base then it's
+
+ align:start position:0%
+activated by a general base then it's
+ 
+
+ align:start position:0%
+activated by a general base then it's
+going to attack this amine and the
+
+ align:start position:0%
+going to attack this amine and the
+ 
+
+ align:start position:0%
+going to attack this amine and the
+electrons will move to the nitrogen we
+
+ align:start position:0%
+electrons will move to the nitrogen we
+ 
+
+ align:start position:0%
+electrons will move to the nitrogen we
+get to this step and here we need step
+
+ align:start position:0%
+get to this step and here we need step
+ 
+
+ align:start position:0%
+get to this step and here we need step
+in catalysis to regenerate the enzyme to
+
+ align:start position:0%
+in catalysis to regenerate the enzyme to
+ 
+
+ align:start position:0%
+in catalysis to regenerate the enzyme to
+its free lysine form and then release
+
+ align:start position:0%
+its free lysine form and then release
+ 
+
+ align:start position:0%
+its free lysine form and then release
+the fructose 1 6 bisphosphate product of
+
+ align:start position:0%
+the fructose 1 6 bisphosphate product of
+ 
+
+ align:start position:0%
+the fructose 1 6 bisphosphate product of
+the reaction so once again we started
+
+ align:start position:0%
+the reaction so once again we started
+ 
+
+ align:start position:0%
+the reaction so once again we started
+with dihydrogen phosphate and gap and
+
+ align:start position:0%
+with dihydrogen phosphate and gap and
+ 
+
+ align:start position:0%
+with dihydrogen phosphate and gap and
+you use this covalent catalysis where
+
+ align:start position:0%
+you use this covalent catalysis where
+ 
+
+ align:start position:0%
+you use this covalent catalysis where
+the substrate were bound in the active
+
+ align:start position:0%
+the substrate were bound in the active
+ 
+
+ align:start position:0%
+the substrate were bound in the active
+site of the enzyme to form our product
+
+ align:start position:0%
+site of the enzyme to form our product
+ 
+
+ align:start position:0%
+site of the enzyme to form our product
+fructose 1 6 bisphosphate now this as we
+
+ align:start position:0%
+fructose 1 6 bisphosphate now this as we
+ 
+
+ align:start position:0%
+fructose 1 6 bisphosphate now this as we
+discussed in the carbonyl chemistry just
+
+ align:start position:0%
+discussed in the carbonyl chemistry just
+ 
+
+ align:start position:0%
+discussed in the carbonyl chemistry just
+an example of direct aldol reaction and
+
+ align:start position:0%
+an example of direct aldol reaction and
+ 
+
+ align:start position:0%
+an example of direct aldol reaction and
+as the name of the enzyme suggests
+
+ align:start position:0%
+as the name of the enzyme suggests
+ 
+
+ align:start position:0%
+as the name of the enzyme suggests
+aldolase this is the reaction going in
+
+ align:start position:0%
+aldolase this is the reaction going in
+ 
+
+ align:start position:0%
+aldolase this is the reaction going in
+the gluconeogenic mold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and part b of the question we're going
+
+ align:start position:0%
+and part b of the question we're going
+ 
+
+ align:start position:0%
+and part b of the question we're going
+to look in another important reaction
+
+ align:start position:0%
+to look in another important reaction
+ 
+
+ align:start position:0%
+to look in another important reaction
+that can run both ways in glycolysis and
+
+ align:start position:0%
+that can run both ways in glycolysis and
+ 
+
+ align:start position:0%
+that can run both ways in glycolysis and
+gluconeogenesis that will be
+
+ align:start position:0%
+gluconeogenesis that will be
+ 
+
+ align:start position:0%
+gluconeogenesis that will be
+specifically going from
+
+ align:start position:0%
+specifically going from
+ 
+
+ align:start position:0%
+specifically going from
+glyceraldehyde-3-phosphate or gap to 13
+
+ align:start position:0%
+glyceraldehyde-3-phosphate or gap to 13
+ 
+
+ align:start position:0%
+glyceraldehyde-3-phosphate or gap to 13
+bits phosphoglycerate this is the
+
+ align:start position:0%
+bits phosphoglycerate this is the
+ 
+
+ align:start position:0%
+bits phosphoglycerate this is the
+reaction catalyzed by gap dehydrogenase
+
+ align:start position:0%
+reaction catalyzed by gap dehydrogenase
+ 
+
+ align:start position:0%
+reaction catalyzed by gap dehydrogenase
+here is a representation of the reaction
+
+ align:start position:0%
+here is a representation of the reaction
+ 
+
+ align:start position:0%
+here is a representation of the reaction
+we have glyceraldehyde-3-phosphate that
+
+ align:start position:0%
+we have glyceraldehyde-3-phosphate that
+ 
+
+ align:start position:0%
+we have glyceraldehyde-3-phosphate that
+is converted by gap th to the 13 bits
+
+ align:start position:0%
+is converted by gap th to the 13 bits
+ 
+
+ align:start position:0%
+is converted by gap th to the 13 bits
+forceful glyceride now in the glycolysis
+
+ align:start position:0%
+forceful glyceride now in the glycolysis
+ 
+
+ align:start position:0%
+forceful glyceride now in the glycolysis
+step we know we need one nad equivalent
+
+ align:start position:0%
+step we know we need one nad equivalent
+ 
+
+ align:start position:0%
+step we know we need one nad equivalent
+and one phosphate inorganic phosphate to
+
+ align:start position:0%
+and one phosphate inorganic phosphate to
+ 
+
+ align:start position:0%
+and one phosphate inorganic phosphate to
+go into the enzyme to be able to oxidize
+
+ align:start position:0%
+go into the enzyme to be able to oxidize
+ 
+
+ align:start position:0%
+go into the enzyme to be able to oxidize
+our aldehyde to an sitting and hydride
+
+ align:start position:0%
+our aldehyde to an sitting and hydride
+ 
+
+ align:start position:0%
+our aldehyde to an sitting and hydride
+in 13 bits phosphoglycerate now in a
+
+ align:start position:0%
+in 13 bits phosphoglycerate now in a
+ 
+
+ align:start position:0%
+in 13 bits phosphoglycerate now in a
+gluconeogenesis we're going to be going
+
+ align:start position:0%
+gluconeogenesis we're going to be going
+ 
+
+ align:start position:0%
+gluconeogenesis we're going to be going
+from right to left we're starting with
+
+ align:start position:0%
+from right to left we're starting with
+ 
+
+ align:start position:0%
+from right to left we're starting with
+13 bits phosphoglycerate we're going to
+
+ align:start position:0%
+13 bits phosphoglycerate we're going to
+ 
+
+ align:start position:0%
+13 bits phosphoglycerate we're going to
+need nadh and we're going to generate
+
+ align:start position:0%
+need nadh and we're going to generate
+ 
+
+ align:start position:0%
+need nadh and we're going to generate
+gap and inorganic phosphate now let's
+
+ align:start position:0%
+gap and inorganic phosphate now let's
+ 
+
+ align:start position:0%
+gap and inorganic phosphate now let's
+take a closer look at the mechanism of
+
+ align:start position:0%
+take a closer look at the mechanism of
+ 
+
+ align:start position:0%
+take a closer look at the mechanism of
+this reaction as it would run in
+
+ align:start position:0%
+this reaction as it would run in
+ 
+
+ align:start position:0%
+this reaction as it would run in
+gluconeogenesis here we have a
+
+ align:start position:0%
+gluconeogenesis here we have a
+ 
+
+ align:start position:0%
+gluconeogenesis here we have a
+representation of the active side of the
+
+ align:start position:0%
+representation of the active side of the
+ 
+
+ align:start position:0%
+representation of the active side of the
+gap th where we highlighted the Sistine
+
+ align:start position:0%
+gap th where we highlighted the Sistine
+ 
+
+ align:start position:0%
+gap th where we highlighted the Sistine
+group SH right and we also have in
+
+ align:start position:0%
+group SH right and we also have in
+ 
+
+ align:start position:0%
+group SH right and we also have in
+general base in the exercise we're going
+
+ align:start position:0%
+general base in the exercise we're going
+ 
+
+ align:start position:0%
+general base in the exercise we're going
+to call it be and here is our starting
+
+ align:start position:0%
+to call it be and here is our starting
+ 
+
+ align:start position:0%
+to call it be and here is our starting
+material 13 / phosphoglycerate now if
+
+ align:start position:0%
+material 13 / phosphoglycerate now if
+ 
+
+ align:start position:0%
+material 13 / phosphoglycerate now if
+you remember how gap the edge works in
+
+ align:start position:0%
+you remember how gap the edge works in
+ 
+
+ align:start position:0%
+you remember how gap the edge works in
+the direct reaction in the glycolysis
+
+ align:start position:0%
+the direct reaction in the glycolysis
+ 
+
+ align:start position:0%
+the direct reaction in the glycolysis
+we're going to have to form a covalent
+
+ align:start position:0%
+we're going to have to form a covalent
+ 
+
+ align:start position:0%
+we're going to have to form a covalent
+intermediate in which the substrate is
+
+ align:start position:0%
+intermediate in which the substrate is
+ 
+
+ align:start position:0%
+intermediate in which the substrate is
+going to bind to the enzyme that's going
+
+ align:start position:0%
+going to bind to the enzyme that's going
+ 
+
+ align:start position:0%
+going to bind to the enzyme that's going
+to form a a diode ester with that tile
+
+ align:start position:0%
+to form a a diode ester with that tile
+ 
+
+ align:start position:0%
+to form a a diode ester with that tile
+group of the Sistine so this is what's
+
+ align:start position:0%
+group of the Sistine so this is what's
+ 
+
+ align:start position:0%
+group of the Sistine so this is what's
+going to happen here so the base in the
+
+ align:start position:0%
+going to happen here so the base in the
+ 
+
+ align:start position:0%
+going to happen here so the base in the
+active side actually is going to assist
+
+ align:start position:0%
+active side actually is going to assist
+ 
+
+ align:start position:0%
+active side actually is going to assist
+deprotonation of the Sistine then the
+
+ align:start position:0%
+deprotonation of the Sistine then the
+ 
+
+ align:start position:0%
+deprotonation of the Sistine then the
+tile now it's activated and it can
+
+ align:start position:0%
+tile now it's activated and it can
+ 
+
+ align:start position:0%
+tile now it's activated and it can
+attack the first 100 of the 13
+
+ align:start position:0%
+attack the first 100 of the 13
+ 
+
+ align:start position:0%
+attack the first 100 of the 13
+phosphoglycerate and in the first step
+
+ align:start position:0%
+phosphoglycerate and in the first step
+ 
+
+ align:start position:0%
+phosphoglycerate and in the first step
+is just going to form a tetrahedral
+
+ align:start position:0%
+is just going to form a tetrahedral
+ 
+
+ align:start position:0%
+is just going to form a tetrahedral
+intermediate there you have it now we
+
+ align:start position:0%
+intermediate there you have it now we
+ 
+
+ align:start position:0%
+intermediate there you have it now we
+have a negative charge on
+
+ align:start position:0%
+have a negative charge on
+ 
+
+ align:start position:0%
+have a negative charge on
+on the oxygen and we spelled out the
+
+ align:start position:0%
+on the oxygen and we spelled out the
+ 
+
+ align:start position:0%
+on the oxygen and we spelled out the
+phosphate with all the atoms here all
+
+ align:start position:0%
+phosphate with all the atoms here all
+ 
+
+ align:start position:0%
+phosphate with all the atoms here all
+right as you know these tetrahedral
+
+ align:start position:0%
+right as you know these tetrahedral
+ 
+
+ align:start position:0%
+right as you know these tetrahedral
+intermediate is not going to fall apart
+
+ align:start position:0%
+intermediate is not going to fall apart
+ 
+
+ align:start position:0%
+intermediate is not going to fall apart
+releasing like the most the best leaving
+
+ align:start position:0%
+releasing like the most the best leaving
+ 
+
+ align:start position:0%
+releasing like the most the best leaving
+group in this case is going to be the
+
+ align:start position:0%
+group in this case is going to be the
+ 
+
+ align:start position:0%
+group in this case is going to be the
+inorganic phosphate select the electrons
+
+ align:start position:0%
+inorganic phosphate select the electrons
+ 
+
+ align:start position:0%
+inorganic phosphate select the electrons
+come down is going to be transferred
+
+ align:start position:0%
+come down is going to be transferred
+ 
+
+ align:start position:0%
+come down is going to be transferred
+onto the phosphate and presumably
+
+ align:start position:0%
+onto the phosphate and presumably
+ 
+
+ align:start position:0%
+onto the phosphate and presumably
+protonated we can alright so after the
+
+ align:start position:0%
+protonated we can alright so after the
+ 
+
+ align:start position:0%
+protonated we can alright so after the
+phosphate is released now we we have
+
+ align:start position:0%
+phosphate is released now we we have
+ 
+
+ align:start position:0%
+phosphate is released now we we have
+flown finally the tile ester of our
+
+ align:start position:0%
+flown finally the tile ester of our
+ 
+
+ align:start position:0%
+flown finally the tile ester of our
+substrate in the active side of gap th
+
+ align:start position:0%
+substrate in the active side of gap th
+ 
+
+ align:start position:0%
+substrate in the active side of gap th
+as you remember this is a redox
+
+ align:start position:0%
+as you remember this is a redox
+ 
+
+ align:start position:0%
+as you remember this is a redox
+reactions involve the cofactor nad in
+
+ align:start position:0%
+reactions involve the cofactor nad in
+ 
+
+ align:start position:0%
+reactions involve the cofactor nad in
+this case running the reaction from
+
+ align:start position:0%
+this case running the reaction from
+ 
+
+ align:start position:0%
+this case running the reaction from
+right to left we're going to use NADH to
+
+ align:start position:0%
+right to left we're going to use NADH to
+ 
+
+ align:start position:0%
+right to left we're going to use NADH to
+reduce the base phosphoglycerate to the
+
+ align:start position:0%
+reduce the base phosphoglycerate to the
+ 
+
+ align:start position:0%
+reduce the base phosphoglycerate to the
+aldehyde group so here is our
+
+ align:start position:0%
+aldehyde group so here is our
+ 
+
+ align:start position:0%
+aldehyde group so here is our
+representation of the NADH as you
+
+ align:start position:0%
+representation of the NADH as you
+ 
+
+ align:start position:0%
+representation of the NADH as you
+remember one of these hydrogen's
+
+ align:start position:0%
+remember one of these hydrogen's
+ 
+
+ align:start position:0%
+remember one of these hydrogen's
+together with its electron pair it's
+
+ align:start position:0%
+together with its electron pair it's
+ 
+
+ align:start position:0%
+together with its electron pair it's
+going to be donated as a hydride or h-
+
+ align:start position:0%
+going to be donated as a hydride or h-
+ 
+
+ align:start position:0%
+going to be donated as a hydride or h-
+all right so this the reaction proceeds
+
+ align:start position:0%
+all right so this the reaction proceeds
+ 
+
+ align:start position:0%
+all right so this the reaction proceeds
+by rearranging the electrons on the
+
+ align:start position:0%
+by rearranging the electrons on the
+ 
+
+ align:start position:0%
+by rearranging the electrons on the
+pyridine ring of nad and the h minus is
+
+ align:start position:0%
+pyridine ring of nad and the h minus is
+ 
+
+ align:start position:0%
+pyridine ring of nad and the h minus is
+going to be the nucleophile that's
+
+ align:start position:0%
+going to be the nucleophile that's
+ 
+
+ align:start position:0%
+going to be the nucleophile that's
+attacking now but I Lester once again
+
+ align:start position:0%
+attacking now but I Lester once again
+ 
+
+ align:start position:0%
+attacking now but I Lester once again
+I'm going to be forming a tetrahedral
+
+ align:start position:0%
+I'm going to be forming a tetrahedral
+ 
+
+ align:start position:0%
+I'm going to be forming a tetrahedral
+intermediate which is shown here now
+
+ align:start position:0%
+intermediate which is shown here now
+ 
+
+ align:start position:0%
+intermediate which is shown here now
+this hydride here is the one that came
+
+ align:start position:0%
+this hydride here is the one that came
+ 
+
+ align:start position:0%
+this hydride here is the one that came
+from nadh and in the process the NADH
+
+ align:start position:0%
+from nadh and in the process the NADH
+ 
+
+ align:start position:0%
+from nadh and in the process the NADH
+cofactor is converted to NAD+ alright so
+
+ align:start position:0%
+cofactor is converted to NAD+ alright so
+ 
+
+ align:start position:0%
+cofactor is converted to NAD+ alright so
+now we can see we're just one step away
+
+ align:start position:0%
+now we can see we're just one step away
+ 
+
+ align:start position:0%
+now we can see we're just one step away
+this is now a like a hemiacetal like
+
+ align:start position:0%
+this is now a like a hemiacetal like
+ 
+
+ align:start position:0%
+this is now a like a hemiacetal like
+molecule so it's one step away from
+
+ align:start position:0%
+molecule so it's one step away from
+ 
+
+ align:start position:0%
+molecule so it's one step away from
+forming glyceraldehyde-3-phosphate all
+
+ align:start position:0%
+forming glyceraldehyde-3-phosphate all
+ 
+
+ align:start position:0%
+forming glyceraldehyde-3-phosphate all
+we need to do is release the enzyme in
+
+ align:start position:0%
+we need to do is release the enzyme in
+ 
+
+ align:start position:0%
+we need to do is release the enzyme in
+its original confirmation so the
+
+ align:start position:0%
+its original confirmation so the
+ 
+
+ align:start position:0%
+its original confirmation so the
+electrons will flow now to reform the
+
+ align:start position:0%
+electrons will flow now to reform the
+ 
+
+ align:start position:0%
+electrons will flow now to reform the
+carbonyl while the sulfur is going to
+
+ align:start position:0%
+carbonyl while the sulfur is going to
+ 
+
+ align:start position:0%
+carbonyl while the sulfur is going to
+get its electrons from the base and
+
+ align:start position:0%
+get its electrons from the base and
+ 
+
+ align:start position:0%
+get its electrons from the base and
+and this regenerates the enzyme as we
+
+ align:start position:0%
+and this regenerates the enzyme as we
+ 
+
+ align:start position:0%
+and this regenerates the enzyme as we
+had it in the beginning and we're
+
+ align:start position:0%
+had it in the beginning and we're
+ 
+
+ align:start position:0%
+had it in the beginning and we're
+releasing gap the product of the
+
+ align:start position:0%
+releasing gap the product of the
+ 
+
+ align:start position:0%
+releasing gap the product of the
+reaction so with this mechanistic
+
+ align:start position:0%
+reaction so with this mechanistic
+ 
+
+ align:start position:0%
+reaction so with this mechanistic
+insight we have actually addressed how
+
+ align:start position:0%
+insight we have actually addressed how
+ 
+
+ align:start position:0%
+insight we have actually addressed how
+the gap th reaction runs in the
+
+ align:start position:0%
+the gap th reaction runs in the
+ 
+
+ align:start position:0%
+the gap th reaction runs in the
+gluconeogenic mode from 13 bits
+
+ align:start position:0%
+gluconeogenic mode from 13 bits
+ 
+
+ align:start position:0%
+gluconeogenic mode from 13 bits
+phosphoglycerate to gap now part a of
+
+ align:start position:0%
+phosphoglycerate to gap now part a of
+ 
+
+ align:start position:0%
+phosphoglycerate to gap now part a of
+the problem also asked us to look up the
+
+ align:start position:0%
+the problem also asked us to look up the
+ 
+
+ align:start position:0%
+the problem also asked us to look up the
+free energy value for the aldolase
+
+ align:start position:0%
+free energy value for the aldolase
+ 
+
+ align:start position:0%
+free energy value for the aldolase
+reaction that is the Delta G naught
+
+ align:start position:0%
+reaction that is the Delta G naught
+ 
+
+ align:start position:0%
+reaction that is the Delta G naught
+prime now if you're going to look in
+
+ align:start position:0%
+prime now if you're going to look in
+ 
+
+ align:start position:0%
+prime now if you're going to look in
+your favorite chemistry textbook or I
+
+ align:start position:0%
+your favorite chemistry textbook or I
+ 
+
+ align:start position:0%
+your favorite chemistry textbook or I
+have here the fold and vote third
+
+ align:start position:0%
+have here the fold and vote third
+ 
+
+ align:start position:0%
+have here the fold and vote third
+edition the book that we use in in this
+
+ align:start position:0%
+edition the book that we use in in this
+ 
+
+ align:start position:0%
+edition the book that we use in in this
+course now you're going to find in on
+
+ align:start position:0%
+course now you're going to find in on
+ 
+
+ align:start position:0%
+course now you're going to find in on
+page 511 you're going to see a table
+
+ align:start position:0%
+page 511 you're going to see a table
+ 
+
+ align:start position:0%
+page 511 you're going to see a table
+with all the free energies of glycolysis
+
+ align:start position:0%
+with all the free energies of glycolysis
+ 
+
+ align:start position:0%
+with all the free energies of glycolysis
+reactions and for the aldolase tab
+
+ align:start position:0%
+reactions and for the aldolase tab
+ 
+
+ align:start position:0%
+reactions and for the aldolase tab
+you're going to see that it's a positive
+
+ align:start position:0%
+you're going to see that it's a positive
+ 
+
+ align:start position:0%
+you're going to see that it's a positive
+free energy that is the reaction
+
+ align:start position:0%
+free energy that is the reaction
+ 
+
+ align:start position:0%
+free energy that is the reaction
+spontaneous in the reverse in the
+
+ align:start position:0%
+spontaneous in the reverse in the
+ 
+
+ align:start position:0%
+spontaneous in the reverse in the
+gluconeogenic direction so now that that
+
+ align:start position:0%
+gluconeogenic direction so now that that
+ 
+
+ align:start position:0%
+gluconeogenic direction so now that that
+may be a little surprising but keep in
+
+ align:start position:0%
+may be a little surprising but keep in
+ 
+
+ align:start position:0%
+may be a little surprising but keep in
+mind that the reactions in these
+
+ align:start position:0%
+mind that the reactions in these
+ 
+
+ align:start position:0%
+mind that the reactions in these
+pathways are more often than not
+
+ align:start position:0%
+pathways are more often than not
+ 
+
+ align:start position:0%
+pathways are more often than not
+governed by mass action that is if we
+
+ align:start position:0%
+governed by mass action that is if we
+ 
+
+ align:start position:0%
+governed by mass action that is if we
+have an excess of the starting materials
+
+ align:start position:0%
+have an excess of the starting materials
+ 
+
+ align:start position:0%
+have an excess of the starting materials
+the reaction will proceed towards the
+
+ align:start position:0%
+the reaction will proceed towards the
+ 
+
+ align:start position:0%
+the reaction will proceed towards the
+product while if you have an excess of
+
+ align:start position:0%
+product while if you have an excess of
+ 
+
+ align:start position:0%
+product while if you have an excess of
+the products the reaction will proceed
+
+ align:start position:0%
+the products the reaction will proceed
+ 
+
+ align:start position:0%
+the products the reaction will proceed
+backwards towards the starting materials
+
+ align:start position:0%
+backwards towards the starting materials
+ 
+
+ align:start position:0%
+backwards towards the starting materials
+so both the aldolase reaction and the
+
+ align:start position:0%
+so both the aldolase reaction and the
+ 
+
+ align:start position:0%
+so both the aldolase reaction and the
+gap dehydrogenase reactions are very
+
+ align:start position:0%
+gap dehydrogenase reactions are very
+ 
+
+ align:start position:0%
+gap dehydrogenase reactions are very
+susceptible to this mass action so they
+
+ align:start position:0%
+susceptible to this mass action so they
+ 
+
+ align:start position:0%
+susceptible to this mass action so they
+will be controlled the direction the
+
+ align:start position:0%
+will be controlled the direction the
+ 
+
+ align:start position:0%
+will be controlled the direction the
+spontaneity of this reaction will be
+
+ align:start position:0%
+spontaneity of this reaction will be
+ 
+
+ align:start position:0%
+spontaneity of this reaction will be
+controlled by which of the starting
+
+ align:start position:0%
+controlled by which of the starting
+ 
+
+ align:start position:0%
+controlled by which of the starting
+materials or products are in excess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Part C of this problem asked us to
+
+ align:start position:0%
+Part C of this problem asked us to
+ 
+
+ align:start position:0%
+Part C of this problem asked us to
+evaluate the spontaneity of
+
+ align:start position:0%
+evaluate the spontaneity of
+ 
+
+ align:start position:0%
+evaluate the spontaneity of
+gluconeogenesis at the level of the
+
+ align:start position:0%
+gluconeogenesis at the level of the
+ 
+
+ align:start position:0%
+gluconeogenesis at the level of the
+whole pathway now we know glycolysis is
+
+ align:start position:0%
+whole pathway now we know glycolysis is
+ 
+
+ align:start position:0%
+whole pathway now we know glycolysis is
+a spontaneous process not only it it
+
+ align:start position:0%
+a spontaneous process not only it it
+ 
+
+ align:start position:0%
+a spontaneous process not only it it
+occurs from goes from glucose to
+
+ align:start position:0%
+occurs from goes from glucose to
+ 
+
+ align:start position:0%
+occurs from goes from glucose to
+pyruvate but it also it generates some
+
+ align:start position:0%
+pyruvate but it also it generates some
+ 
+
+ align:start position:0%
+pyruvate but it also it generates some
+high-energy intermediates like ATP in
+
+ align:start position:0%
+high-energy intermediates like ATP in
+ 
+
+ align:start position:0%
+high-energy intermediates like ATP in
+the process I will get two molecules of
+
+ align:start position:0%
+the process I will get two molecules of
+ 
+
+ align:start position:0%
+the process I will get two molecules of
+ATP per glucose now if we want to go
+
+ align:start position:0%
+ATP per glucose now if we want to go
+ 
+
+ align:start position:0%
+ATP per glucose now if we want to go
+backwards from pyruvate to glucose in a
+
+ align:start position:0%
+backwards from pyruvate to glucose in a
+ 
+
+ align:start position:0%
+backwards from pyruvate to glucose in a
+gluconeogenesis pathway can this process
+
+ align:start position:0%
+gluconeogenesis pathway can this process
+ 
+
+ align:start position:0%
+gluconeogenesis pathway can this process
+be spontaneous first let's look at
+
+ align:start position:0%
+be spontaneous first let's look at
+ 
+
+ align:start position:0%
+be spontaneous first let's look at
+glycolysis here is a schematic of
+
+ align:start position:0%
+glycolysis here is a schematic of
+ 
+
+ align:start position:0%
+glycolysis here is a schematic of
+glycolysis we're starting here from
+
+ align:start position:0%
+glycolysis we're starting here from
+ 
+
+ align:start position:0%
+glycolysis we're starting here from
+glucose and we're going to need a couple
+
+ align:start position:0%
+glucose and we're going to need a couple
+ 
+
+ align:start position:0%
+glucose and we're going to need a couple
+of molecules of ATP to activate it to
+
+ align:start position:0%
+of molecules of ATP to activate it to
+ 
+
+ align:start position:0%
+of molecules of ATP to activate it to
+get to fructose 1 6 bisphosphate and
+
+ align:start position:0%
+get to fructose 1 6 bisphosphate and
+ 
+
+ align:start position:0%
+get to fructose 1 6 bisphosphate and
+from there on we're going to generate
+
+ align:start position:0%
+from there on we're going to generate
+ 
+
+ align:start position:0%
+from there on we're going to generate
+actually two molecules of ATP at this
+
+ align:start position:0%
+actually two molecules of ATP at this
+ 
+
+ align:start position:0%
+actually two molecules of ATP at this
+step and then two molecules of ATP at
+
+ align:start position:0%
+step and then two molecules of ATP at
+ 
+
+ align:start position:0%
+step and then two molecules of ATP at
+the final part of the kinase step and of
+
+ align:start position:0%
+the final part of the kinase step and of
+ 
+
+ align:start position:0%
+the final part of the kinase step and of
+course we're also going to need an nad
+
+ align:start position:0%
+course we're also going to need an nad
+ 
+
+ align:start position:0%
+course we're also going to need an nad
+plus going to NADH here at the gap step
+
+ align:start position:0%
+plus going to NADH here at the gap step
+ 
+
+ align:start position:0%
+plus going to NADH here at the gap step
+well there's going to be two of these
+
+ align:start position:0%
+well there's going to be two of these
+ 
+
+ align:start position:0%
+well there's going to be two of these
+NAD+ needed to oxidize gap to 1 through
+
+ align:start position:0%
+NAD+ needed to oxidize gap to 1 through
+ 
+
+ align:start position:0%
+NAD+ needed to oxidize gap to 1 through
+peaceful for glycerin all right and as
+
+ align:start position:0%
+peaceful for glycerin all right and as
+ 
+
+ align:start position:0%
+peaceful for glycerin all right and as
+we just said even though we have some
+
+ align:start position:0%
+we just said even though we have some
+ 
+
+ align:start position:0%
+we just said even though we have some
+energy costs in early on we're actually
+
+ align:start position:0%
+energy costs in early on we're actually
+ 
+
+ align:start position:0%
+energy costs in early on we're actually
+generating more ATP by the time we reach
+
+ align:start position:0%
+generating more ATP by the time we reach
+ 
+
+ align:start position:0%
+generating more ATP by the time we reach
+pyruvate so the pathway is in fact
+
+ align:start position:0%
+pyruvate so the pathway is in fact
+ 
+
+ align:start position:0%
+pyruvate so the pathway is in fact
+spontaneous now what about
+
+ align:start position:0%
+spontaneous now what about
+ 
+
+ align:start position:0%
+spontaneous now what about
+gluconeogenesis in google neurogenesis
+
+ align:start position:0%
+gluconeogenesis in google neurogenesis
+ 
+
+ align:start position:0%
+gluconeogenesis in google neurogenesis
+we're starting with pyruvate and we want
+
+ align:start position:0%
+we're starting with pyruvate and we want
+ 
+
+ align:start position:0%
+we're starting with pyruvate and we want
+to go back to glucose now if we were to
+
+ align:start position:0%
+to go back to glucose now if we were to
+ 
+
+ align:start position:0%
+to go back to glucose now if we were to
+reverse exactly every single step in
+
+ align:start position:0%
+reverse exactly every single step in
+ 
+
+ align:start position:0%
+reverse exactly every single step in
+glycolysis that price password is not
+
+ align:start position:0%
+glycolysis that price password is not
+ 
+
+ align:start position:0%
+glycolysis that price password is not
+going to be spontaneous so that for
+
+ align:start position:0%
+going to be spontaneous so that for
+ 
+
+ align:start position:0%
+going to be spontaneous so that for
+gluconeogenesis uses these alternate
+
+ align:start position:0%
+gluconeogenesis uses these alternate
+ 
+
+ align:start position:0%
+gluconeogenesis uses these alternate
+pathways and couple of the steps in
+
+ align:start position:0%
+pathways and couple of the steps in
+ 
+
+ align:start position:0%
+pathways and couple of the steps in
+order to make the process spontaneous
+
+ align:start position:0%
+order to make the process spontaneous
+ 
+
+ align:start position:0%
+order to make the process spontaneous
+for example going from pyruvate to
+
+ align:start position:0%
+for example going from pyruvate to
+ 
+
+ align:start position:0%
+for example going from pyruvate to
+phosphoenolpyruvate in gluconeogenesis
+
+ align:start position:0%
+phosphoenolpyruvate in gluconeogenesis
+ 
+
+ align:start position:0%
+phosphoenolpyruvate in gluconeogenesis
+is not a reverse of the fast part of it
+
+ align:start position:0%
+is not a reverse of the fast part of it
+ 
+
+ align:start position:0%
+is not a reverse of the fast part of it
+kinase reaction and rather occur since
+
+ align:start position:0%
+kinase reaction and rather occur since
+ 
+
+ align:start position:0%
+kinase reaction and rather occur since
+two steps the first step we take part of
+
+ align:start position:0%
+two steps the first step we take part of
+ 
+
+ align:start position:0%
+two steps the first step we take part of
+it and convert it to oxaloacetate using
+
+ align:start position:0%
+it and convert it to oxaloacetate using
+ 
+
+ align:start position:0%
+it and convert it to oxaloacetate using
+pyruvate carboxylase
+
+ align:start position:0%
+pyruvate carboxylase
+ 
+
+ align:start position:0%
+pyruvate carboxylase
+is going to going to need a molecule of
+
+ align:start position:0%
+is going to going to need a molecule of
+ 
+
+ align:start position:0%
+is going to going to need a molecule of
+co2 right oxaloacetate has four carbons
+
+ align:start position:0%
+co2 right oxaloacetate has four carbons
+ 
+
+ align:start position:0%
+co2 right oxaloacetate has four carbons
+and it's also going to need energy so
+
+ align:start position:0%
+and it's also going to need energy so
+ 
+
+ align:start position:0%
+and it's also going to need energy so
+we're going to need a molecule of ATP
+
+ align:start position:0%
+we're going to need a molecule of ATP
+ 
+
+ align:start position:0%
+we're going to need a molecule of ATP
+going to adp now oxaloacetate then can
+
+ align:start position:0%
+going to adp now oxaloacetate then can
+ 
+
+ align:start position:0%
+going to adp now oxaloacetate then can
+now be processed inside the mitochondria
+
+ align:start position:0%
+now be processed inside the mitochondria
+ 
+
+ align:start position:0%
+now be processed inside the mitochondria
+or it can be taken out of the
+
+ align:start position:0%
+or it can be taken out of the
+ 
+
+ align:start position:0%
+or it can be taken out of the
+mitochondria into the cytosol and let's
+
+ align:start position:0%
+mitochondria into the cytosol and let's
+ 
+
+ align:start position:0%
+mitochondria into the cytosol and let's
+say that's the course of the reaction
+
+ align:start position:0%
+say that's the course of the reaction
+ 
+
+ align:start position:0%
+say that's the course of the reaction
+where it's going to find an enzyme
+
+ align:start position:0%
+where it's going to find an enzyme
+ 
+
+ align:start position:0%
+where it's going to find an enzyme
+called PP carboxykinase or Pepsi k that
+
+ align:start position:0%
+called PP carboxykinase or Pepsi k that
+ 
+
+ align:start position:0%
+called PP carboxykinase or Pepsi k that
+can take off cell acetate to PP this
+
+ align:start position:0%
+can take off cell acetate to PP this
+ 
+
+ align:start position:0%
+can take off cell acetate to PP this
+enzyme once again requires energy this
+
+ align:start position:0%
+enzyme once again requires energy this
+ 
+
+ align:start position:0%
+enzyme once again requires energy this
+time the form of GTP goes to gdp and
+
+ align:start position:0%
+time the form of GTP goes to gdp and
+ 
+
+ align:start position:0%
+time the form of GTP goes to gdp and
+here we're going to lose that carboxyl
+
+ align:start position:0%
+here we're going to lose that carboxyl
+ 
+
+ align:start position:0%
+here we're going to lose that carboxyl
+group that we added on earlier now while
+
+ align:start position:0%
+group that we added on earlier now while
+ 
+
+ align:start position:0%
+group that we added on earlier now while
+this might seem like a sort of a
+
+ align:start position:0%
+this might seem like a sort of a
+ 
+
+ align:start position:0%
+this might seem like a sort of a
+cumbersome way to reverse one reaction
+
+ align:start position:0%
+cumbersome way to reverse one reaction
+ 
+
+ align:start position:0%
+cumbersome way to reverse one reaction
+this allows both the part of it kinase
+
+ align:start position:0%
+this allows both the part of it kinase
+ 
+
+ align:start position:0%
+this allows both the part of it kinase
+reaction and going from pyruvate going
+
+ align:start position:0%
+reaction and going from pyruvate going
+ 
+
+ align:start position:0%
+reaction and going from pyruvate going
+back to PP to be controlled in different
+
+ align:start position:0%
+back to PP to be controlled in different
+ 
+
+ align:start position:0%
+back to PP to be controlled in different
+ways and therefore allow both of these
+
+ align:start position:0%
+ways and therefore allow both of these
+ 
+
+ align:start position:0%
+ways and therefore allow both of these
+processes to happen spontaneously the
+
+ align:start position:0%
+processes to happen spontaneously the
+ 
+
+ align:start position:0%
+processes to happen spontaneously the
+rest of gluconeogenesis will have
+
+ align:start position:0%
+rest of gluconeogenesis will have
+ 
+
+ align:start position:0%
+rest of gluconeogenesis will have
+exactly the reverse of these steps in
+
+ align:start position:0%
+exactly the reverse of these steps in
+ 
+
+ align:start position:0%
+exactly the reverse of these steps in
+glycolysis for example PP going to two
+
+ align:start position:0%
+glycolysis for example PP going to two
+ 
+
+ align:start position:0%
+glycolysis for example PP going to two
+phosphoglycerate the Fox will get her
+
+ align:start position:0%
+phosphoglycerate the Fox will get her
+ 
+
+ align:start position:0%
+phosphoglycerate the Fox will get her
+going to 3-phosphoglycerate
+
+ align:start position:0%
+going to 3-phosphoglycerate
+ 
+
+ align:start position:0%
+going to 3-phosphoglycerate
+3-phosphoglycerate going to 13 bits
+
+ align:start position:0%
+3-phosphoglycerate going to 13 bits
+ 
+
+ align:start position:0%
+3-phosphoglycerate going to 13 bits
+phosphoglycerate here since in
+
+ align:start position:0%
+phosphoglycerate here since in
+ 
+
+ align:start position:0%
+phosphoglycerate here since in
+glycolysis which generated ATP here
+
+ align:start position:0%
+glycolysis which generated ATP here
+ 
+
+ align:start position:0%
+glycolysis which generated ATP here
+we're going to need the ATP to come in
+
+ align:start position:0%
+we're going to need the ATP to come in
+ 
+
+ align:start position:0%
+we're going to need the ATP to come in
+and go to adp in order to accomplish the
+
+ align:start position:0%
+and go to adp in order to accomplish the
+ 
+
+ align:start position:0%
+and go to adp in order to accomplish the
+step in gluconeogenesis 13 bits 44
+
+ align:start position:0%
+step in gluconeogenesis 13 bits 44
+ 
+
+ align:start position:0%
+step in gluconeogenesis 13 bits 44
+glyceride going to gap this is the step
+
+ align:start position:0%
+glyceride going to gap this is the step
+ 
+
+ align:start position:0%
+glyceride going to gap this is the step
+we'll just discussed in part two of the
+
+ align:start position:0%
+we'll just discussed in part two of the
+ 
+
+ align:start position:0%
+we'll just discussed in part two of the
+problem as we said we're going to need
+
+ align:start position:0%
+problem as we said we're going to need
+ 
+
+ align:start position:0%
+problem as we said we're going to need
+NADH going to NAD+ then gap and DHAP
+
+ align:start position:0%
+NADH going to NAD+ then gap and DHAP
+ 
+
+ align:start position:0%
+NADH going to NAD+ then gap and DHAP
+going to fructose 1 6 bisphosphate this
+
+ align:start position:0%
+going to fructose 1 6 bisphosphate this
+ 
+
+ align:start position:0%
+going to fructose 1 6 bisphosphate this
+is the step we discussed in part a of
+
+ align:start position:0%
+is the step we discussed in part a of
+ 
+
+ align:start position:0%
+is the step we discussed in part a of
+this problem the reverse of the aldolase
+
+ align:start position:0%
+this problem the reverse of the aldolase
+ 
+
+ align:start position:0%
+this problem the reverse of the aldolase
+reaction no going from fructose 1 6 bit
+
+ align:start position:0%
+reaction no going from fructose 1 6 bit
+ 
+
+ align:start position:0%
+reaction no going from fructose 1 6 bit
+faster
+
+ align:start position:0%
+faster
+ 
+
+ align:start position:0%
+faster
+to glucose we're not going to do these
+
+ align:start position:0%
+to glucose we're not going to do these
+ 
+
+ align:start position:0%
+to glucose we're not going to do these
+kinase reactions in Reverse where would
+
+ align:start position:0%
+kinase reactions in Reverse where would
+ 
+
+ align:start position:0%
+kinase reactions in Reverse where would
+be generating ATP and therefore there
+
+ align:start position:0%
+be generating ATP and therefore there
+ 
+
+ align:start position:0%
+be generating ATP and therefore there
+would be not spontaneous in the reverse
+
+ align:start position:0%
+would be not spontaneous in the reverse
+ 
+
+ align:start position:0%
+would be not spontaneous in the reverse
+direction but rather we're going to use
+
+ align:start position:0%
+direction but rather we're going to use
+ 
+
+ align:start position:0%
+direction but rather we're going to use
+alternate enzymes called phosphatases
+
+ align:start position:0%
+alternate enzymes called phosphatases
+ 
+
+ align:start position:0%
+alternate enzymes called phosphatases
+where we lose the phosphate without
+
+ align:start position:0%
+where we lose the phosphate without
+ 
+
+ align:start position:0%
+where we lose the phosphate without
+regenerating and ATP molecules so
+
+ align:start position:0%
+regenerating and ATP molecules so
+ 
+
+ align:start position:0%
+regenerating and ATP molecules so
+therefore by using these these two
+
+ align:start position:0%
+therefore by using these these two
+ 
+
+ align:start position:0%
+therefore by using these these two
+tricks we can go back to glucose without
+
+ align:start position:0%
+tricks we can go back to glucose without
+ 
+
+ align:start position:0%
+tricks we can go back to glucose without
+regenerating its ATP molecules and
+
+ align:start position:0%
+regenerating its ATP molecules and
+ 
+
+ align:start position:0%
+regenerating its ATP molecules and
+therefore the pathway can be spontaneous
+
+ align:start position:0%
+therefore the pathway can be spontaneous
+ 
+
+ align:start position:0%
+therefore the pathway can be spontaneous
+now the bottom line here is that both
+
+ align:start position:0%
+now the bottom line here is that both
+ 
+
+ align:start position:0%
+now the bottom line here is that both
+glycolysis and gluconeogenesis are
+
+ align:start position:0%
+glycolysis and gluconeogenesis are
+ 
+
+ align:start position:0%
+glycolysis and gluconeogenesis are
+spontaneous but gluconeogenesis uses
+
+ align:start position:0%
+spontaneous but gluconeogenesis uses
+ 
+
+ align:start position:0%
+spontaneous but gluconeogenesis uses
+most but not all of the glycolysis steps
+
+ align:start position:0%
+most but not all of the glycolysis steps
+ 
+
+ align:start position:0%
+most but not all of the glycolysis steps
+to run in reverse and while glycolysis
+
+ align:start position:0%
+to run in reverse and while glycolysis
+ 
+
+ align:start position:0%
+to run in reverse and while glycolysis
+generates energy we'd get a net of two
+
+ align:start position:0%
+generates energy we'd get a net of two
+ 
+
+ align:start position:0%
+generates energy we'd get a net of two
+molecules of ATP per molecule of glucose
+
+ align:start position:0%
+molecules of ATP per molecule of glucose
+ 
+
+ align:start position:0%
+molecules of ATP per molecule of glucose
+used gluconeogenesis as you guys seen
+
+ align:start position:0%
+used gluconeogenesis as you guys seen
+ 
+
+ align:start position:0%
+used gluconeogenesis as you guys seen
+I've seen here actually uses energy to
+
+ align:start position:0%
+I've seen here actually uses energy to
+ 
+
+ align:start position:0%
+I've seen here actually uses energy to
+run if spontaneously that is we need ATP
+
+ align:start position:0%
+run if spontaneously that is we need ATP
+ 
+
+ align:start position:0%
+run if spontaneously that is we need ATP
+molecules now if you look at our diagram
+
+ align:start position:0%
+molecules now if you look at our diagram
+ 
+
+ align:start position:0%
+molecules now if you look at our diagram
+we need ATP molecules to convert
+
+ align:start position:0%
+we need ATP molecules to convert
+ 
+
+ align:start position:0%
+we need ATP molecules to convert
+pyruvate to phosphoenolpyruvate actually
+
+ align:start position:0%
+pyruvate to phosphoenolpyruvate actually
+ 
+
+ align:start position:0%
+pyruvate to phosphoenolpyruvate actually
+two of them and then we're going to need
+
+ align:start position:0%
+two of them and then we're going to need
+ 
+
+ align:start position:0%
+two of them and then we're going to need
+more ATP here to form 13 bits
+
+ align:start position:0%
+more ATP here to form 13 bits
+ 
+
+ align:start position:0%
+more ATP here to form 13 bits
+phosphoglycerate in addition to the
+
+ align:start position:0%
+phosphoglycerate in addition to the
+ 
+
+ align:start position:0%
+phosphoglycerate in addition to the
+redox like NADH cofactor to run the gap
+
+ align:start position:0%
+redox like NADH cofactor to run the gap
+ 
+
+ align:start position:0%
+redox like NADH cofactor to run the gap
+dehydrogenase reaction in Reverse so
+
+ align:start position:0%
+dehydrogenase reaction in Reverse so
+ 
+
+ align:start position:0%
+dehydrogenase reaction in Reverse so
+given these considerations
+
+ align:start position:0%
+given these considerations
+ 
+
+ align:start position:0%
+given these considerations
+gluconeogenesis is in fact spontaneous
+
+ align:start position:0%
+gluconeogenesis is in fact spontaneous
+ 
+
+ align:start position:0%
+gluconeogenesis is in fact spontaneous
+but it's going to cost us several ATP
+
+ align:start position:0%
+but it's going to cost us several ATP
+ 
+
+ align:start position:0%
+but it's going to cost us several ATP
+equivalents while glycolysis are
+
+ align:start position:0%
+equivalents while glycolysis are
+ 
+
+ align:start position:0%
+equivalents while glycolysis are
+spontaneous and generate ATP well that
+
+ align:start position:0%
+spontaneous and generate ATP well that
+ 
+
+ align:start position:0%
+spontaneous and generate ATP well that
+solves problem 3 or problems at 10 here
+
+ align:start position:0%
+solves problem 3 or problems at 10 here
+ 
+
+ align:start position:0%
+solves problem 3 or problems at 10 here
+I hope you've got a better understanding
+
+ align:start position:0%
+I hope you've got a better understanding
+ 
+
+ align:start position:0%
+I hope you've got a better understanding
+of why both glycolysis and
+
+ align:start position:0%
+of why both glycolysis and
+ 
+
+ align:start position:0%
+of why both glycolysis and
+gluconeogenesis are both spontaneous
+
+ align:start position:0%
+gluconeogenesis are both spontaneous
+ 
+
+ align:start position:0%
+gluconeogenesis are both spontaneous
+pathways inside the cell thank you
\ No newline at end of file
diff --git a/zqks_JcU0cM.txt b/zqks_JcU0cM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..763f28a6834cc4ec6b7b4ce0acdde8ac44403a8d
--- /dev/null
+++ b/zqks_JcU0cM.txt
@@ -0,0 +1,1955 @@
+align:start position:0%
+ 
+Okay. So today is unforced that means
+
+ align:start position:0%
+Okay. So today is unforced that means
+ 
+
+ align:start position:0%
+Okay. So today is unforced that means
+zero on the right hand side looking for
+
+ align:start position:0%
+zero on the right hand side looking for
+ 
+
+ align:start position:0%
+zero on the right hand side looking for
+null solutions. Damped that means
+
+ align:start position:0%
+null solutions. Damped that means
+ 
+
+ align:start position:0%
+null solutions. Damped that means
+there's a coefficient B in the first
+
+ align:start position:0%
+there's a coefficient B in the first
+ 
+
+ align:start position:0%
+there's a coefficient B in the first
+derivative. And what's the solution?
+
+ align:start position:0%
+derivative. And what's the solution?
+ 
+
+ align:start position:0%
+derivative. And what's the solution?
+This is really a basic basic equation.
+
+ align:start position:0%
+This is really a basic basic equation.
+ 
+
+ align:start position:0%
+This is really a basic basic equation.
+Uh in in many applications a would be
+
+ align:start position:0%
+Uh in in many applications a would be
+ 
+
+ align:start position:0%
+Uh in in many applications a would be
+the mass in in a spring for example. A
+
+ align:start position:0%
+the mass in in a spring for example. A
+ 
+
+ align:start position:0%
+the mass in in a spring for example. A
+would be a mass. B is the damping, the
+
+ align:start position:0%
+would be a mass. B is the damping, the
+ 
+
+ align:start position:0%
+would be a mass. B is the damping, the
+friction. And C is the spring constant,
+
+ align:start position:0%
+friction. And C is the spring constant,
+ 
+
+ align:start position:0%
+friction. And C is the spring constant,
+the force that pulls the mass back. Or
+
+ align:start position:0%
+the force that pulls the mass back. Or
+ 
+
+ align:start position:0%
+the force that pulls the mass back. Or
+in electronics, B would be the
+
+ align:start position:0%
+in electronics, B would be the
+ 
+
+ align:start position:0%
+in electronics, B would be the
+resistance. It's giving some friction,
+
+ align:start position:0%
+resistance. It's giving some friction,
+ 
+
+ align:start position:0%
+resistance. It's giving some friction,
+giving some heat. So that's our
+
+ align:start position:0%
+giving some heat. So that's our
+ 
+
+ align:start position:0%
+giving some heat. So that's our
+equation. Just we have to be able to
+
+ align:start position:0%
+equation. Just we have to be able to
+ 
+
+ align:start position:0%
+equation. Just we have to be able to
+solve it. And we want we want to look
+
+ align:start position:0%
+solve it. And we want we want to look
+ 
+
+ align:start position:0%
+solve it. And we want we want to look
+for exponentials.
+
+ align:start position:0%
+for exponentials.
+ 
+
+ align:start position:0%
+for exponentials.
+A pure exponential is just right for
+
+ align:start position:0%
+A pure exponential is just right for
+ 
+
+ align:start position:0%
+A pure exponential is just right for
+constant coefficient equation like that.
+
+ align:start position:0%
+constant coefficient equation like that.
+ 
+
+ align:start position:0%
+constant coefficient equation like that.
+So I'll substitute y equals e to the s
+
+ align:start position:0%
+So I'll substitute y equals e to the s
+ 
+
+ align:start position:0%
+So I'll substitute y equals e to the s
+t. And what happens?
+
+ align:start position:0%
+t. And what happens?
+ 
+
+ align:start position:0%
+t. And what happens?
+Well, so there's a c e to the s t.
+
+ align:start position:0%
+Well, so there's a c e to the s t.
+ 
+
+ align:start position:0%
+Well, so there's a c e to the s t.
+That's the c y. The derivative brings
+
+ align:start position:0%
+That's the c y. The derivative brings
+ 
+
+ align:start position:0%
+That's the c y. The derivative brings
+down an s. Two derivatives bring down s
+
+ align:start position:0%
+down an s. Two derivatives bring down s
+ 
+
+ align:start position:0%
+down an s. Two derivatives bring down s
+squared. So I simply have a s^2 bs and c
+
+ align:start position:0%
+squared. So I simply have a s^2 bs and c
+ 
+
+ align:start position:0%
+squared. So I simply have a s^2 bs and c
+all together multiplying
+
+ align:start position:0%
+all together multiplying
+ 
+
+ align:start position:0%
+all together multiplying
+e to the s t
+
+ align:start position:0%
+e to the s t
+ 
+
+ align:start position:0%
+e to the s t
+and how do I get zero? Well the zero is
+
+ align:start position:0%
+and how do I get zero? Well the zero is
+ 
+
+ align:start position:0%
+and how do I get zero? Well the zero is
+not going to come from e to the st. So
+
+ align:start position:0%
+not going to come from e to the st. So
+ 
+
+ align:start position:0%
+not going to come from e to the st. So
+it has to come from this. So
+
+ align:start position:0%
+it has to come from this. So
+ 
+
+ align:start position:0%
+it has to come from this. So
+fundamentally the whole video and more
+
+ align:start position:0%
+fundamentally the whole video and more
+ 
+
+ align:start position:0%
+fundamentally the whole video and more
+is about a quadratic equation
+
+ align:start position:0%
+is about a quadratic equation
+ 
+
+ align:start position:0%
+is about a quadratic equation
+a s^2 + b s + c equals z. That's we have
+
+ align:start position:0%
+a s^2 + b s + c equals z. That's we have
+ 
+
+ align:start position:0%
+a s^2 + b s + c equals z. That's we have
+to solve it. We have to understand how
+
+ align:start position:0%
+to solve it. We have to understand how
+ 
+
+ align:start position:0%
+to solve it. We have to understand how
+does the answer depend on these numbers
+
+ align:start position:0%
+does the answer depend on these numbers
+ 
+
+ align:start position:0%
+does the answer depend on these numbers
+a and b and c the constants.
+
+ align:start position:0%
+a and b and c the constants.
+ 
+
+ align:start position:0%
+a and b and c the constants.
+Okay. So we know the root, we know the
+
+ align:start position:0%
+Okay. So we know the root, we know the
+ 
+
+ align:start position:0%
+Okay. So we know the root, we know the
+solutions. The quadratic formula tells
+
+ align:start position:0%
+solutions. The quadratic formula tells
+ 
+
+ align:start position:0%
+solutions. The quadratic formula tells
+us that the two solutions, they're
+
+ align:start position:0%
+us that the two solutions, they're
+ 
+
+ align:start position:0%
+us that the two solutions, they're
+always two, but they could be equal. Uh
+
+ align:start position:0%
+always two, but they could be equal. Uh
+ 
+
+ align:start position:0%
+always two, but they could be equal. Uh
+have this do do you recognize this
+
+ align:start position:0%
+have this do do you recognize this
+ 
+
+ align:start position:0%
+have this do do you recognize this
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+uh the the you see the damping
+
+ align:start position:0%
+uh the the you see the damping
+ 
+
+ align:start position:0%
+uh the the you see the damping
+coefficient coming in. You see this
+
+ align:start position:0%
+coefficient coming in. You see this
+ 
+
+ align:start position:0%
+coefficient coming in. You see this
+allimp important square root which tells
+
+ align:start position:0%
+allimp important square root which tells
+ 
+
+ align:start position:0%
+allimp important square root which tells
+us depending on whether b ^2 is bigger
+
+ align:start position:0%
+us depending on whether b ^2 is bigger
+ 
+
+ align:start position:0%
+us depending on whether b ^2 is bigger
+than 4 a c b ^2 is equal 4 a c b ^2 is
+
+ align:start position:0%
+than 4 a c b ^2 is equal 4 a c b ^2 is
+ 
+
+ align:start position:0%
+than 4 a c b ^2 is equal 4 a c b ^2 is
+smaller so smaller b means less damping
+
+ align:start position:0%
+smaller so smaller b means less damping
+ 
+
+ align:start position:0%
+smaller so smaller b means less damping
+and it would be called under damping. So
+
+ align:start position:0%
+and it would be called under damping. So
+ 
+
+ align:start position:0%
+and it would be called under damping. So
+here's the
+
+ align:start position:0%
+here's the
+ 
+
+ align:start position:0%
+here's the
+here are the possibilities.
+
+ align:start position:0%
+here are the possibilities.
+ 
+
+ align:start position:0%
+here are the possibilities.
+B could be zero. That puts us back in a
+
+ align:start position:0%
+B could be zero. That puts us back in a
+ 
+
+ align:start position:0%
+B could be zero. That puts us back in a
+previous
+
+ align:start position:0%
+previous
+ 
+
+ align:start position:0%
+previous
+video when the solution was a pure
+
+ align:start position:0%
+video when the solution was a pure
+ 
+
+ align:start position:0%
+video when the solution was a pure
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+complex exponential pure sign cosine.
+
+ align:start position:0%
+complex exponential pure sign cosine.
+ 
+
+ align:start position:0%
+complex exponential pure sign cosine.
+There was no damping. It just oscillated
+
+ align:start position:0%
+There was no damping. It just oscillated
+ 
+
+ align:start position:0%
+There was no damping. It just oscillated
+forever. That's the one we know. Now the
+
+ align:start position:0%
+forever. That's the one we know. Now the
+ 
+
+ align:start position:0%
+forever. That's the one we know. Now the
+new ones with a b
+
+ align:start position:0%
+new ones with a b
+ 
+
+ align:start position:0%
+new ones with a b
+or b squared could be smaller than so
+
+ align:start position:0%
+or b squared could be smaller than so
+ 
+
+ align:start position:0%
+or b squared could be smaller than so
+that's only a little damping.
+
+ align:start position:0%
+that's only a little damping.
+ 
+
+ align:start position:0%
+that's only a little damping.
+And in that case, what does the solution
+
+ align:start position:0%
+And in that case, what does the solution
+ 
+
+ align:start position:0%
+And in that case, what does the solution
+look like? If b ^2 is smaller than 4 a
+
+ align:start position:0%
+look like? If b ^2 is smaller than 4 a
+ 
+
+ align:start position:0%
+look like? If b ^2 is smaller than 4 a
+c, I have to always look back here. So I
+
+ align:start position:0%
+c, I have to always look back here. So I
+ 
+
+ align:start position:0%
+c, I have to always look back here. So I
+have something negative,
+
+ align:start position:0%
+have something negative,
+ 
+
+ align:start position:0%
+have something negative,
+something negative, a minus b over 2 a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then plus or minus. And what's the
+
+ align:start position:0%
+and then plus or minus. And what's the
+ 
+
+ align:start position:0%
+and then plus or minus. And what's the
+important point about this guy? B ^2 is
+
+ align:start position:0%
+important point about this guy? B ^2 is
+ 
+
+ align:start position:0%
+important point about this guy? B ^2 is
+smaller than 4 a c. This is negative
+
+ align:start position:0%
+smaller than 4 a c. This is negative
+ 
+
+ align:start position:0%
+smaller than 4 a c. This is negative
+inside. So it square root is an
+
+ align:start position:0%
+inside. So it square root is an
+ 
+
+ align:start position:0%
+inside. So it square root is an
+imaginary number. So the plus or minus
+
+ align:start position:0%
+imaginary number. So the plus or minus
+ 
+
+ align:start position:0%
+imaginary number. So the plus or minus
+there's an imaginary number a little
+
+ align:start position:0%
+there's an imaginary number a little
+ 
+
+ align:start position:0%
+there's an imaginary number a little
+different from the natural frequency.
+
+ align:start position:0%
+different from the natural frequency.
+ 
+
+ align:start position:0%
+different from the natural frequency.
+It's called the damped frequency.
+
+ align:start position:0%
+It's called the damped frequency.
+ 
+
+ align:start position:0%
+It's called the damped frequency.
+Not quite as frequent.
+
+ align:start position:0%
+Not quite as frequent.
+ 
+
+ align:start position:0%
+Not quite as frequent.
+The damping slows the oscillation down a
+
+ align:start position:0%
+The damping slows the oscillation down a
+ 
+
+ align:start position:0%
+The damping slows the oscillation down a
+little bit but it brings in exponential
+
+ align:start position:0%
+little bit but it brings in exponential
+ 
+
+ align:start position:0%
+little bit but it brings in exponential
+decay. I'll draw a picture this time or
+
+ align:start position:0%
+decay. I'll draw a picture this time or
+ 
+
+ align:start position:0%
+decay. I'll draw a picture this time or
+next time about of the solution e to the
+
+ align:start position:0%
+next time about of the solution e to the
+ 
+
+ align:start position:0%
+next time about of the solution e to the
+minus s. But you see e to the minus s is
+
+ align:start position:0%
+minus s. But you see e to the minus s is
+ 
+
+ align:start position:0%
+minus s. But you see e to the minus s is
+decaying to zero. It's like a spring
+
+ align:start position:0%
+decaying to zero. It's like a spring
+ 
+
+ align:start position:0%
+decaying to zero. It's like a spring
+that's slowly
+
+ align:start position:0%
+that's slowly
+ 
+
+ align:start position:0%
+that's slowly
+winding down to zero, but it's
+
+ align:start position:0%
+winding down to zero, but it's
+ 
+
+ align:start position:0%
+winding down to zero, but it's
+oscillating as it does it. Okay, now
+
+ align:start position:0%
+oscillating as it does it. Okay, now
+ 
+
+ align:start position:0%
+oscillating as it does it. Okay, now
+we've got two more possibilities here.
+
+ align:start position:0%
+we've got two more possibilities here.
+ 
+
+ align:start position:0%
+we've got two more possibilities here.
+And these are just fun to get straight.
+
+ align:start position:0%
+And these are just fun to get straight.
+ 
+
+ align:start position:0%
+And these are just fun to get straight.
+There's the next one. When b ^2 is
+
+ align:start position:0%
+There's the next one. When b ^2 is
+ 
+
+ align:start position:0%
+There's the next one. When b ^2 is
+exactly 4 a c. Exactly 4 a. B ^2 over 4
+
+ align:start position:0%
+exactly 4 a c. Exactly 4 a. B ^2 over 4
+ 
+
+ align:start position:0%
+exactly 4 a c. Exactly 4 a. B ^2 over 4
+a c. That's the going to be the critical
+
+ align:start position:0%
+a c. That's the going to be the critical
+ 
+
+ align:start position:0%
+a c. That's the going to be the critical
+ratio here. And here that ratio is one.
+
+ align:start position:0%
+ratio here. And here that ratio is one.
+ 
+
+ align:start position:0%
+ratio here. And here that ratio is one.
+And in that case that square root is
+
+ align:start position:0%
+And in that case that square root is
+ 
+
+ align:start position:0%
+And in that case that square root is
+nothing. The square root of B ^ 2 - 4 A
+
+ align:start position:0%
+nothing. The square root of B ^ 2 - 4 A
+ 
+
+ align:start position:0%
+nothing. The square root of B ^ 2 - 4 A
+C is zero. So we get S1 and S2 equal
+
+ align:start position:0%
+C is zero. So we get S1 and S2 equal
+ 
+
+ align:start position:0%
+C is zero. So we get S1 and S2 equal
+two equal frequencies real real numbers.
+
+ align:start position:0%
+two equal frequencies real real numbers.
+ 
+
+ align:start position:0%
+two equal frequencies real real numbers.
+The B there the minus B over 2A. So, so
+
+ align:start position:0%
+The B there the minus B over 2A. So, so
+ 
+
+ align:start position:0%
+The B there the minus B over 2A. So, so
+s_sub_1 and sub_2
+
+ align:start position:0%
+s_sub_1 and sub_2
+ 
+
+ align:start position:0%
+s_sub_1 and sub_2
+are both minus b over 2a.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's a just the edge between x between
+
+ align:start position:0%
+That's a just the edge between x between
+ 
+
+ align:start position:0%
+That's a just the edge between x between
+the decay uh with oscillation from under
+
+ align:start position:0%
+the decay uh with oscillation from under
+ 
+
+ align:start position:0%
+the decay uh with oscillation from under
+damping and the opposite extreme is over
+
+ align:start position:0%
+damping and the opposite extreme is over
+ 
+
+ align:start position:0%
+damping and the opposite extreme is over
+damping. over damping when b ^2 is
+
+ align:start position:0%
+damping. over damping when b ^2 is
+ 
+
+ align:start position:0%
+damping. over damping when b ^2 is
+bigger than 4 a c then our formula we're
+
+ align:start position:0%
+bigger than 4 a c then our formula we're
+ 
+
+ align:start position:0%
+bigger than 4 a c then our formula we're
+always looking back at that quadratic
+
+ align:start position:0%
+always looking back at that quadratic
+ 
+
+ align:start position:0%
+always looking back at that quadratic
+formula b ^2 bigger than 4 a c this is
+
+ align:start position:0%
+formula b ^2 bigger than 4 a c this is
+ 
+
+ align:start position:0%
+formula b ^2 bigger than 4 a c this is
+real
+
+ align:start position:0%
+real
+ 
+
+ align:start position:0%
+real
+square root of a positive number it's
+
+ align:start position:0%
+square root of a positive number it's
+ 
+
+ align:start position:0%
+square root of a positive number it's
+perfectly real so in that case we have
+
+ align:start position:0%
+perfectly real so in that case we have
+ 
+
+ align:start position:0%
+perfectly real so in that case we have
+two s1 and sub_2 oh I let me draw you
+
+ align:start position:0%
+two s1 and sub_2 oh I let me draw you
+ 
+
+ align:start position:0%
+two s1 and sub_2 oh I let me draw you
+some pictures just I'll draw you the
+
+ align:start position:0%
+some pictures just I'll draw you the
+ 
+
+ align:start position:0%
+some pictures just I'll draw you the
+parabola the the the the a s^ squ. So
+
+ align:start position:0%
+parabola the the the the a s^ squ. So
+ 
+
+ align:start position:0%
+parabola the the the the a s^ squ. So
+this is a graph of a s2.
+
+ align:start position:0%
+this is a graph of a s2.
+ 
+
+ align:start position:0%
+this is a graph of a s2.
+Let let me draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plot a s^2 plus b s + c. So in this
+
+ align:start position:0%
+plot a s^2 plus b s + c. So in this
+ 
+
+ align:start position:0%
+plot a s^2 plus b s + c. So in this
+overdamping case we might have a lot of
+
+ align:start position:0%
+overdamping case we might have a lot of
+ 
+
+ align:start position:0%
+overdamping case we might have a lot of
+damping. B is pretty large and and the
+
+ align:start position:0%
+damping. B is pretty large and and the
+ 
+
+ align:start position:0%
+damping. B is pretty large and and the
+there is that would be a this direction
+
+ align:start position:0%
+there is that would be a this direction
+ 
+
+ align:start position:0%
+there is that would be a this direction
+is S and I'm graphing here
+
+ align:start position:0%
+is S and I'm graphing here
+ 
+
+ align:start position:0%
+is S and I'm graphing here
+S squared
+
+ align:start position:0%
+S squared
+ 
+
+ align:start position:0%
+S squared
+plus well let me see if I
+
+ align:start position:0%
+plus well let me see if I
+ 
+
+ align:start position:0%
+plus well let me see if I
+I think probably plus 2 S and now I'm
+
+ align:start position:0%
+I think probably plus 2 S and now I'm
+ 
+
+ align:start position:0%
+I think probably plus 2 S and now I'm
+going to choose this ah actually
+
+ align:start position:0%
+going to choose this ah actually
+ 
+
+ align:start position:0%
+going to choose this ah actually
+plus zero to get that one. So this has a
+
+ align:start position:0%
+plus zero to get that one. So this has a
+ 
+
+ align:start position:0%
+plus zero to get that one. So this has a
+root at this is over damping over
+
+ align:start position:0%
+root at this is over damping over
+ 
+
+ align:start position:0%
+root at this is over damping over
+damping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a big number there.
+
+ align:start position:0%
+a big number there.
+ 
+
+ align:start position:0%
+a big number there.
+C is zero. No mass at all. No stiffness
+
+ align:start position:0%
+C is zero. No mass at all. No stiffness
+ 
+
+ align:start position:0%
+C is zero. No mass at all. No stiffness
+at all. No stiffness at all. So the the
+
+ align:start position:0%
+at all. No stiffness at all. So the the
+ 
+
+ align:start position:0%
+at all. No stiffness at all. So the the
+this parabola it has a has a root at
+
+ align:start position:0%
+this parabola it has a has a root at
+ 
+
+ align:start position:0%
+this parabola it has a has a root at
+zero and a root at minus2.
+
+ align:start position:0%
+zero and a root at minus2.
+ 
+
+ align:start position:0%
+zero and a root at minus2.
+That would be an extreme case with no
+
+ align:start position:0%
+That would be an extreme case with no
+ 
+
+ align:start position:0%
+That would be an extreme case with no
+stiffness whatever. Now let me add up
+
+ align:start position:0%
+stiffness whatever. Now let me add up
+ 
+
+ align:start position:0%
+stiffness whatever. Now let me add up
+add some stiffness. So what happens if I
+
+ align:start position:0%
+add some stiffness. So what happens if I
+ 
+
+ align:start position:0%
+add some stiffness. So what happens if I
+change the constant term? It lifts the
+
+ align:start position:0%
+change the constant term? It lifts the
+ 
+
+ align:start position:0%
+change the constant term? It lifts the
+graph. It lifts the graph. So let me
+
+ align:start position:0%
+graph. It lifts the graph. So let me
+ 
+
+ align:start position:0%
+graph. It lifts the graph. So let me
+make it one. So so I move the whole
+
+ align:start position:0%
+make it one. So so I move the whole
+ 
+
+ align:start position:0%
+make it one. So so I move the whole
+graph up by one. that moves. So you see
+
+ align:start position:0%
+graph up by one. that moves. So you see
+ 
+
+ align:start position:0%
+graph up by one. that moves. So you see
+that as I move it up, these roots will
+
+ align:start position:0%
+that as I move it up, these roots will
+ 
+
+ align:start position:0%
+that as I move it up, these roots will
+will c come closer and closer and at the
+
+ align:start position:0%
+will c come closer and closer and at the
+ 
+
+ align:start position:0%
+will c come closer and closer and at the
+right point when I move it up to one,
+
+ align:start position:0%
+right point when I move it up to one,
+ 
+
+ align:start position:0%
+right point when I move it up to one,
+what's going on there?
+
+ align:start position:0%
+what's going on there?
+ 
+
+ align:start position:0%
+what's going on there?
+Critical damping. Critical damping. This
+
+ align:start position:0%
+Critical damping. Critical damping. This
+ 
+
+ align:start position:0%
+Critical damping. Critical damping. This
+is the case s 2 + 2 s + 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is exactly s + 1 twice
+
+ align:start position:0%
+which is exactly s + 1 twice
+ 
+
+ align:start position:0%
+which is exactly s + 1 twice
+and it has that repeated root which we
+
+ align:start position:0%
+and it has that repeated root which we
+ 
+
+ align:start position:0%
+and it has that repeated root which we
+always recognize as the marginal case
+
+ align:start position:0%
+always recognize as the marginal case
+ 
+
+ align:start position:0%
+always recognize as the marginal case
+when it doesn't go bel it doesn't go
+
+ align:start position:0%
+when it doesn't go bel it doesn't go
+ 
+
+ align:start position:0%
+when it doesn't go bel it doesn't go
+below but it doesn't stay above either
+
+ align:start position:0%
+below but it doesn't stay above either
+ 
+
+ align:start position:0%
+below but it doesn't stay above either
+it hits here twice. So the root is
+
+ align:start position:0%
+it hits here twice. So the root is
+ 
+
+ align:start position:0%
+it hits here twice. So the root is
+minus1 twice. That's critical. And now
+
+ align:start position:0%
+minus1 twice. That's critical. And now
+ 
+
+ align:start position:0%
+minus1 twice. That's critical. And now
+what?
+
+ align:start position:0%
+what?
+ 
+
+ align:start position:0%
+what?
+Increase this constant C even further.
+
+ align:start position:0%
+Increase this constant C even further.
+ 
+
+ align:start position:0%
+Increase this constant C even further.
+You lift the graph, lift the parabola up
+
+ align:start position:0%
+You lift the graph, lift the parabola up
+ 
+
+ align:start position:0%
+You lift the graph, lift the parabola up
+here. Lift it by one more, let's say.
+
+ align:start position:0%
+here. Lift it by one more, let's say.
+ 
+
+ align:start position:0%
+here. Lift it by one more, let's say.
+And what's going on there? So that would
+
+ align:start position:0%
+And what's going on there? So that would
+ 
+
+ align:start position:0%
+And what's going on there? So that would
+be this would be s^2 + 2 s + 2.
+
+ align:start position:0%
+be this would be s^2 + 2 s + 2.
+ 
+
+ align:start position:0%
+be this would be s^2 + 2 s + 2.
+And you see what
+
+ align:start position:0%
+And you see what
+ 
+
+ align:start position:0%
+And you see what
+that graph is telling us.
+
+ align:start position:0%
+that graph is telling us.
+ 
+
+ align:start position:0%
+that graph is telling us.
+It's telling us there are no roots. No
+
+ align:start position:0%
+It's telling us there are no roots. No
+ 
+
+ align:start position:0%
+It's telling us there are no roots. No
+real roots. This is a real graph in the
+
+ align:start position:0%
+real roots. This is a real graph in the
+ 
+
+ align:start position:0%
+real roots. This is a real graph in the
+real plane and it never it's never zero.
+
+ align:start position:0%
+real plane and it never it's never zero.
+ 
+
+ align:start position:0%
+real plane and it never it's never zero.
+This is s + one. This is the under
+
+ align:start position:0%
+This is s + one. This is the under
+ 
+
+ align:start position:0%
+This is s + one. This is the under
+the uh this is the case when I have s
+
+ align:start position:0%
+the uh this is the case when I have s
+ 
+
+ align:start position:0%
+the uh this is the case when I have s
++ 1
+
+ align:start position:0%
++ 1
+ 
+
+ align:start position:0%
++ 1
+squared + 1 never never can't be zero
+
+ align:start position:0%
+squared + 1 never never can't be zero
+ 
+
+ align:start position:0%
+squared + 1 never never can't be zero
+never zero so this has uh
+
+ align:start position:0%
+never zero so this has uh
+ 
+
+ align:start position:0%
+never zero so this has uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+sorry with the two there I it has
+
+ align:start position:0%
+sorry with the two there I it has
+ 
+
+ align:start position:0%
+sorry with the two there I it has
+damping
+
+ align:start position:0%
+damping
+ 
+
+ align:start position:0%
+damping
+It has damping but
+
+ align:start position:0%
+It has damping but
+ 
+
+ align:start position:0%
+It has damping but
+it it's under damping. The roots are
+
+ align:start position:0%
+it it's under damping. The roots are
+ 
+
+ align:start position:0%
+it it's under damping. The roots are
+complex. So, so this s S1 + 1^2 is zero.
+
+ align:start position:0%
+complex. So, so this s S1 + 1^2 is zero.
+ 
+
+ align:start position:0%
+complex. So, so this s S1 + 1^2 is zero.
+What are the roots of that? S is -1
+
+ align:start position:0%
+What are the roots of that? S is -1
+ 
+
+ align:start position:0%
+What are the roots of that? S is -1
++ or minus I.
+
+ align:start position:0%
++ or minus I.
+ 
+
+ align:start position:0%
++ or minus I.
+That's the
+
+ align:start position:0%
+That's the
+ 
+
+ align:start position:0%
+That's the
+that's the case of under damping. So,
+
+ align:start position:0%
+that's the case of under damping. So,
+ 
+
+ align:start position:0%
+that's the case of under damping. So,
+let me write that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we see so much from these graphs. So
+
+ align:start position:0%
+we see so much from these graphs. So
+ 
+
+ align:start position:0%
+we see so much from these graphs. So
+this was a graph in which I changed the
+
+ align:start position:0%
+this was a graph in which I changed the
+ 
+
+ align:start position:0%
+this was a graph in which I changed the
+constant term the capital C the the
+
+ align:start position:0%
+constant term the capital C the the
+ 
+
+ align:start position:0%
+constant term the capital C the the
+stiffness K K K K K K K K K K K K K K K
+
+ align:start position:0%
+stiffness K K K K K K K K K K K K K K K
+ 
+
+ align:start position:0%
+stiffness K K K K K K K K K K K K K K K
+K K K K K K K K K K K K K K K K K K K K
+
+ align:start position:0%
+K K K K K K K K K K K K K K K K K K K K
+ 
+
+ align:start position:0%
+K K K K K K K K K K K K K K K K K K K K
+K K K K K K that. So that lift lifted
+
+ align:start position:0%
+K K K K K K that. So that lift lifted
+ 
+
+ align:start position:0%
+K K K K K K that. So that lift lifted
+the graph and eventually the roots were
+
+ align:start position:0%
+the graph and eventually the roots were
+ 
+
+ align:start position:0%
+the graph and eventually the roots were
+complex. They weren't real anymore
+
+ align:start position:0%
+complex. They weren't real anymore
+ 
+
+ align:start position:0%
+complex. They weren't real anymore
+because the parabola didn't cross the
+
+ align:start position:0%
+because the parabola didn't cross the
+ 
+
+ align:start position:0%
+because the parabola didn't cross the
+axis anymore.
+
+ align:start position:0%
+axis anymore.
+ 
+
+ align:start position:0%
+axis anymore.
+the roots are where it crosses the axis.
+
+ align:start position:0%
+the roots are where it crosses the axis.
+ 
+
+ align:start position:0%
+the roots are where it crosses the axis.
+So that's uh one I'll I'll draw in the
+
+ align:start position:0%
+So that's uh one I'll I'll draw in the
+ 
+
+ align:start position:0%
+So that's uh one I'll I'll draw in the
+next video uh another picture maybe
+
+ align:start position:0%
+next video uh another picture maybe
+ 
+
+ align:start position:0%
+next video uh another picture maybe
+change B change the damping. So what
+
+ align:start position:0%
+change B change the damping. So what
+ 
+
+ align:start position:0%
+change B change the damping. So what
+would happen if I change the damping? If
+
+ align:start position:0%
+would happen if I change the damping? If
+ 
+
+ align:start position:0%
+would happen if I change the damping? If
+there's no damping, the roots are
+
+ align:start position:0%
+there's no damping, the roots are
+ 
+
+ align:start position:0%
+there's no damping, the roots are
+uh pure imaginary. Yeah, let let's just
+
+ align:start position:0%
+uh pure imaginary. Yeah, let let's just
+ 
+
+ align:start position:0%
+uh pure imaginary. Yeah, let let's just
+go back through those four possibilities
+
+ align:start position:0%
+go back through those four possibilities
+ 
+
+ align:start position:0%
+go back through those four possibilities
+because that's what you have to learn.
+
+ align:start position:0%
+because that's what you have to learn.
+ 
+
+ align:start position:0%
+because that's what you have to learn.
+If C if B is zero, there's no damping at
+
+ align:start position:0%
+If C if B is zero, there's no damping at
+ 
+
+ align:start position:0%
+If C if B is zero, there's no damping at
+all and we're back in the pure
+
+ align:start position:0%
+all and we're back in the pure
+ 
+
+ align:start position:0%
+all and we're back in the pure
+oscillation where where S is is pure
+
+ align:start position:0%
+oscillation where where S is is pure
+ 
+
+ align:start position:0%
+oscillation where where S is is pure
+imaginary. We're just seeing cosiness
+
+ align:start position:0%
+imaginary. We're just seeing cosiness
+ 
+
+ align:start position:0%
+imaginary. We're just seeing cosiness
+and signs. Then if we add a little
+
+ align:start position:0%
+and signs. Then if we add a little
+ 
+
+ align:start position:0%
+and signs. Then if we add a little
+damping
+
+ align:start position:0%
+damping
+ 
+
+ align:start position:0%
+damping
+there appears a decay term. If we had
+
+ align:start position:0%
+there appears a decay term. If we had
+ 
+
+ align:start position:0%
+there appears a decay term. If we had
+could let I could even draw the
+
+ align:start position:0%
+could let I could even draw the
+ 
+
+ align:start position:0%
+could let I could even draw the
+the these possibilities that draw draw
+
+ align:start position:0%
+the these possibilities that draw draw
+ 
+
+ align:start position:0%
+the these possibilities that draw draw
+let me draw the solution y of t y of t
+
+ align:start position:0%
+let me draw the solution y of t y of t
+ 
+
+ align:start position:0%
+let me draw the solution y of t y of t
+against t.
+
+ align:start position:0%
+against t.
+ 
+
+ align:start position:0%
+against t.
+Okay. So uh under damping the solution
+
+ align:start position:0%
+Okay. So uh under damping the solution
+ 
+
+ align:start position:0%
+Okay. So uh under damping the solution
+say it starts there will oscillate but
+
+ align:start position:0%
+say it starts there will oscillate but
+ 
+
+ align:start position:0%
+say it starts there will oscillate but
+decay. So this is under damping.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And you remember what that when that h
+
+ align:start position:0%
+And you remember what that when that h
+ 
+
+ align:start position:0%
+And you remember what that when that h
+happens that's when B is present but
+
+ align:start position:0%
+happens that's when B is present but
+ 
+
+ align:start position:0%
+happens that's when B is present but
+smaller B ^2 is smaller than 4 AC
+
+ align:start position:0%
+smaller B ^2 is smaller than 4 AC
+ 
+
+ align:start position:0%
+smaller B ^2 is smaller than 4 AC
+over damping if it starts let's say here
+
+ align:start position:0%
+over damping if it starts let's say here
+ 
+
+ align:start position:0%
+over damping if it starts let's say here
+it will go to zero probably with no
+
+ align:start position:0%
+it will go to zero probably with no
+ 
+
+ align:start position:0%
+it will go to zero probably with no
+oscillation at all it could have one
+
+ align:start position:0%
+oscillation at all it could have one
+ 
+
+ align:start position:0%
+oscillation at all it could have one
+oscillation depends how it starts. So oo
+
+ align:start position:0%
+oscillation depends how it starts. So oo
+ 
+
+ align:start position:0%
+oscillation depends how it starts. So oo
+let me make this picture. So that one is
+
+ align:start position:0%
+let me make this picture. So that one is
+ 
+
+ align:start position:0%
+let me make this picture. So that one is
+the over damping. This guy is the
+
+ align:start position:0%
+the over damping. This guy is the
+ 
+
+ align:start position:0%
+the over damping. This guy is the
+underdamping.
+
+ align:start position:0%
+underdamping.
+ 
+
+ align:start position:0%
+underdamping.
+Under damping still has oscillations.
+
+ align:start position:0%
+Under damping still has oscillations.
+ 
+
+ align:start position:0%
+Under damping still has oscillations.
+Over damping has at most once could it
+
+ align:start position:0%
+Over damping has at most once could it
+ 
+
+ align:start position:0%
+Over damping has at most once could it
+could cross once but over damping is b^2
+
+ align:start position:0%
+could cross once but over damping is b^2
+ 
+
+ align:start position:0%
+could cross once but over damping is b^2
+uh bigger than 4 a.
+
+ align:start position:0%
+uh bigger than 4 a.
+ 
+
+ align:start position:0%
+uh bigger than 4 a.
+Okay there's more to do. This is so
+
+ align:start position:0%
+Okay there's more to do. This is so
+ 
+
+ align:start position:0%
+Okay there's more to do. This is so
+central that that you have to think
+
+ align:start position:0%
+central that that you have to think
+ 
+
+ align:start position:0%
+central that that you have to think
+about the ratio of B^2 to 4 AC that has
+
+ align:start position:0%
+about the ratio of B^2 to 4 AC that has
+ 
+
+ align:start position:0%
+about the ratio of B^2 to 4 AC that has
+its own name and it's a damping fac
+
+ align:start position:0%
+its own name and it's a damping fac
+ 
+
+ align:start position:0%
+its own name and it's a damping fac
+damping ratio or the square of a damping
+
+ align:start position:0%
+damping ratio or the square of a damping
+ 
+
+ align:start position:0%
+damping ratio or the square of a damping
+ratio and and we identify all these
+
+ align:start position:0%
+ratio and and we identify all these
+ 
+
+ align:start position:0%
+ratio and and we identify all these
+solutions.
+
+ align:start position:0%
+solutions.
+ 
+
+ align:start position:0%
+solutions.
+Does everybody know where the solution
+
+ align:start position:0%
+Does everybody know where the solution
+ 
+
+ align:start position:0%
+Does everybody know where the solution
+will be when B is zero? No damping at
+
+ align:start position:0%
+will be when B is zero? No damping at
+ 
+
+ align:start position:0%
+will be when B is zero? No damping at
+all. In that case, it will just
+
+ align:start position:0%
+all. In that case, it will just
+ 
+
+ align:start position:0%
+all. In that case, it will just
+oscillate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So my picture is getting you could say a
+
+ align:start position:0%
+So my picture is getting you could say a
+ 
+
+ align:start position:0%
+So my picture is getting you could say a
+little messed up. But this pure
+
+ align:start position:0%
+little messed up. But this pure
+ 
+
+ align:start position:0%
+little messed up. But this pure
+oscillation would be the B equals Z with
+
+ align:start position:0%
+oscillation would be the B equals Z with
+ 
+
+ align:start position:0%
+oscillation would be the B equals Z with
+undamped.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, that's a first look at quadratic
+
+ align:start position:0%
+Okay, that's a first look at quadratic
+ 
+
+ align:start position:0%
+Okay, that's a first look at quadratic
+equations. A S^2 + B S + C. It has the
+
+ align:start position:0%
+equations. A S^2 + B S + C. It has the
+ 
+
+ align:start position:0%
+equations. A S^2 + B S + C. It has the
+big name characteristic equation, but
+
+ align:start position:0%
+big name characteristic equation, but
+ 
+
+ align:start position:0%
+big name characteristic equation, but
+you could see it's the fundamental
+
+ align:start position:0%
+you could see it's the fundamental
+ 
+
+ align:start position:0%
+you could see it's the fundamental
+equation for a second order uh
+
+ align:start position:0%
+equation for a second order uh
+ 
+
+ align:start position:0%
+equation for a second order uh
+differential equation. So we'll see more
+
+ align:start position:0%
+differential equation. So we'll see more
+ 
+
+ align:start position:0%
+differential equation. So we'll see more
+of it. Thanks.
\ No newline at end of file
diff --git a/zreI4HllD80.txt b/zreI4HllD80.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f10e9072cf278450d8061366c4e275ca5c06e99b
--- /dev/null
+++ b/zreI4HllD80.txt
@@ -0,0 +1,7856 @@
+align:start position:0%
+ 
+we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going to need a few facts about
+
+ align:start position:0%
+going to need a few facts about
+ 
+
+ align:start position:0%
+going to need a few facts about
+fundamental matrices and I'm worried
+
+ align:start position:0%
+fundamental matrices and I'm worried
+ 
+
+ align:start position:0%
+fundamental matrices and I'm worried
+that over the weekend this spring
+
+ align:start position:0%
+that over the weekend this spring
+ 
+
+ align:start position:0%
+that over the weekend this spring
+activities weekend you might have
+
+ align:start position:0%
+activities weekend you might have
+ 
+
+ align:start position:0%
+activities weekend you might have
+forgotten them so I'll just spend two or
+
+ align:start position:0%
+forgotten them so I'll just spend two or
+ 
+
+ align:start position:0%
+forgotten them so I'll just spend two or
+three minutes reviewing the most
+
+ align:start position:0%
+three minutes reviewing the most
+ 
+
+ align:start position:0%
+three minutes reviewing the most
+essential things that we're going to
+
+ align:start position:0%
+essential things that we're going to
+ 
+
+ align:start position:0%
+essential things that we're going to
+need later in the period so what we're
+
+ align:start position:0%
+need later in the period so what we're
+ 
+
+ align:start position:0%
+need later in the period so what we're
+talking about is I'll try to color code
+
+ align:start position:0%
+talking about is I'll try to color code
+ 
+
+ align:start position:0%
+talking about is I'll try to color code
+things so you'll know what they are
+
+ align:start position:0%
+things so you'll know what they are
+ 
+
+ align:start position:0%
+things so you'll know what they are
+first of all where the basic problem is
+
+ align:start position:0%
+first of all where the basic problem is
+ 
+
+ align:start position:0%
+first of all where the basic problem is
+to solve a system of equations and I'm
+
+ align:start position:0%
+to solve a system of equations and I'm
+ 
+
+ align:start position:0%
+to solve a system of equations and I'm
+going to make that a two-by-two system
+
+ align:start position:0%
+going to make that a two-by-two system
+ 
+
+ align:start position:0%
+going to make that a two-by-two system
+although practically everything I say
+
+ align:start position:0%
+although practically everything I say
+ 
+
+ align:start position:0%
+although practically everything I say
+today will also work for n by n systems
+
+ align:start position:0%
+today will also work for n by n systems
+ 
+
+ align:start position:0%
+today will also work for n by n systems
+your book tries to do with n by n as
+
+ align:start position:0%
+your book tries to do with n by n as
+ 
+
+ align:start position:0%
+your book tries to do with n by n as
+usual but I think it's easier to learn
+
+ align:start position:0%
+usual but I think it's easier to learn
+ 
+
+ align:start position:0%
+usual but I think it's easier to learn
+two by two first and generalize rather
+
+ align:start position:0%
+two by two first and generalize rather
+ 
+
+ align:start position:0%
+two by two first and generalize rather
+than to wade through the complications
+
+ align:start position:0%
+than to wade through the complications
+ 
+
+ align:start position:0%
+than to wade through the complications
+of n by n system so the problem is to
+
+ align:start position:0%
+of n by n system so the problem is to
+ 
+
+ align:start position:0%
+of n by n system so the problem is to
+solve it and the method I used last time
+
+ align:start position:0%
+solve it and the method I used last time
+ 
+
+ align:start position:0%
+solve it and the method I used last time
+was to describe something called a
+
+ align:start position:0%
+was to describe something called a
+ 
+
+ align:start position:0%
+was to describe something called a
+fundamental matrix a fundamental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix for the system of Caray whichever
+
+ align:start position:0%
+matrix for the system of Caray whichever
+ 
+
+ align:start position:0%
+matrix for the system of Caray whichever
+you want remember what that was that was
+
+ align:start position:0%
+you want remember what that was that was
+ 
+
+ align:start position:0%
+you want remember what that was that was
+something whose it was a two-by-two
+
+ align:start position:0%
+something whose it was a two-by-two
+ 
+
+ align:start position:0%
+something whose it was a two-by-two
+matrix of functions of T and whose
+
+ align:start position:0%
+matrix of functions of T and whose
+ 
+
+ align:start position:0%
+matrix of functions of T and whose
+columns were two independent solutions X
+
+ align:start position:0%
+columns were two independent solutions X
+ 
+
+ align:start position:0%
+columns were two independent solutions X
+1 X 2 these
+
+ align:start position:0%
+1 X 2 these
+ 
+
+ align:start position:0%
+1 X 2 these
+were two independent solutions in other
+
+ align:start position:0%
+were two independent solutions in other
+ 
+
+ align:start position:0%
+were two independent solutions in other
+words neither was a constant multiple of
+
+ align:start position:0%
+words neither was a constant multiple of
+ 
+
+ align:start position:0%
+words neither was a constant multiple of
+the other now
+
+ align:start position:0%
+the other now
+ 
+
+ align:start position:0%
+the other now
+I spent a fair amount of time showing
+
+ align:start position:0%
+I spent a fair amount of time showing
+ 
+
+ align:start position:0%
+I spent a fair amount of time showing
+you how to how to be essential the two
+
+ align:start position:0%
+you how to how to be essential the two
+ 
+
+ align:start position:0%
+you how to how to be essential the two
+essential properties that a fundamental
+
+ align:start position:0%
+essential properties that a fundamental
+ 
+
+ align:start position:0%
+essential properties that a fundamental
+matrix had so it's we're going to need
+
+ align:start position:0%
+matrix had so it's we're going to need
+ 
+
+ align:start position:0%
+matrix had so it's we're going to need
+those today so let me remind you the
+
+ align:start position:0%
+those today so let me remind you the
+ 
+
+ align:start position:0%
+those today so let me remind you the
+basic properties the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basic properties of X and the properties
+
+ align:start position:0%
+basic properties of X and the properties
+ 
+
+ align:start position:0%
+basic properties of X and the properties
+by which you could recognize one if you
+
+ align:start position:0%
+by which you could recognize one if you
+ 
+
+ align:start position:0%
+by which you could recognize one if you
+were given one is first of all the easy
+
+ align:start position:0%
+were given one is first of all the easy
+ 
+
+ align:start position:0%
+were given one is first of all the easy
+one that its determinant shall not be 0
+
+ align:start position:0%
+one that its determinant shall not be 0
+ 
+
+ align:start position:0%
+one that its determinant shall not be 0
+is not 0 for any for any value of the
+
+ align:start position:0%
+is not 0 for any for any value of the
+ 
+
+ align:start position:0%
+is not 0 for any for any value of the
+variable that simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expresses the fact that it's two columns
+
+ align:start position:0%
+expresses the fact that it's two columns
+ 
+
+ align:start position:0%
+expresses the fact that it's two columns
+are independent linearly independent not
+
+ align:start position:0%
+are independent linearly independent not
+ 
+
+ align:start position:0%
+are independent linearly independent not
+a multiple of each other the other one
+
+ align:start position:0%
+a multiple of each other the other one
+ 
+
+ align:start position:0%
+a multiple of each other the other one
+was more bizarre so I tried to call a
+
+ align:start position:0%
+was more bizarre so I tried to call a
+ 
+
+ align:start position:0%
+was more bizarre so I tried to call a
+little more attention to it it was that
+
+ align:start position:0%
+little more attention to it it was that
+ 
+
+ align:start position:0%
+little more attention to it it was that
+the matrix satisfies a differential
+
+ align:start position:0%
+the matrix satisfies a differential
+ 
+
+ align:start position:0%
+the matrix satisfies a differential
+equation of its own which looks almost
+
+ align:start position:0%
+equation of its own which looks almost
+ 
+
+ align:start position:0%
+equation of its own which looks almost
+the same except it's a matrix
+
+ align:start position:0%
+the same except it's a matrix
+ 
+
+ align:start position:0%
+the same except it's a matrix
+differential equation it's
+
+ align:start position:0%
+differential equation it's
+ 
+
+ align:start position:0%
+differential equation it's
+not column vectors which are solutions
+
+ align:start position:0%
+not column vectors which are solutions
+ 
+
+ align:start position:0%
+not column vectors which are solutions
+but matrices as a whole which are
+
+ align:start position:0%
+but matrices as a whole which are
+ 
+
+ align:start position:0%
+but matrices as a whole which are
+solutions in other words X if you take
+
+ align:start position:0%
+solutions in other words X if you take
+ 
+
+ align:start position:0%
+solutions in other words X if you take
+that matrix and differentiate every
+
+ align:start position:0%
+that matrix and differentiate every
+ 
+
+ align:start position:0%
+that matrix and differentiate every
+entry what you get is the same as a
+
+ align:start position:0%
+entry what you get is the same as a
+ 
+
+ align:start position:0%
+entry what you get is the same as a
+multiplied by that matrix you started
+
+ align:start position:0%
+multiplied by that matrix you started
+ 
+
+ align:start position:0%
+multiplied by that matrix you started
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+remember expressed the fact it was just
+
+ align:start position:0%
+remember expressed the fact it was just
+ 
+
+ align:start position:0%
+remember expressed the fact it was just
+really formal when you analyze what it
+
+ align:start position:0%
+really formal when you analyze what it
+ 
+
+ align:start position:0%
+really formal when you analyze what it
+was but it expresses the fact that the
+
+ align:start position:0%
+was but it expresses the fact that the
+ 
+
+ align:start position:0%
+was but it expresses the fact that the
+columns it says that the columns are
+
+ align:start position:0%
+columns it says that the columns are
+ 
+
+ align:start position:0%
+columns it says that the columns are
+solve the system so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first thing says the columns are
+
+ align:start position:0%
+the first thing says the columns are
+ 
+
+ align:start position:0%
+the first thing says the columns are
+independent and the second say to the
+
+ align:start position:0%
+independent and the second say to the
+ 
+
+ align:start position:0%
+independent and the second say to the
+columns each column separately is a
+
+ align:start position:0%
+columns each column separately is a
+ 
+
+ align:start position:0%
+columns each column separately is a
+solution to the system that's
+
+ align:start position:0%
+solution to the system that's
+ 
+
+ align:start position:0%
+solution to the system that's
+as far as more or less so then I went in
+
+ align:start position:0%
+as far as more or less so then I went in
+ 
+
+ align:start position:0%
+as far as more or less so then I went in
+another direction we talked about
+
+ align:start position:0%
+another direction we talked about
+ 
+
+ align:start position:0%
+another direction we talked about
+variation of parameters oh I'm not going
+
+ align:start position:0%
+variation of parameters oh I'm not going
+ 
+
+ align:start position:0%
+variation of parameters oh I'm not going
+to come back to variation of parameters
+
+ align:start position:0%
+to come back to variation of parameters
+ 
+
+ align:start position:0%
+to come back to variation of parameters
+today we're going in a different tack
+
+ align:start position:0%
+today we're going in a different tack
+ 
+
+ align:start position:0%
+today we're going in a different tack
+the tack we're going on is I want to
+
+ align:start position:0%
+the tack we're going on is I want to
+ 
+
+ align:start position:0%
+the tack we're going on is I want to
+first talk a little more about the
+
+ align:start position:0%
+first talk a little more about the
+ 
+
+ align:start position:0%
+first talk a little more about the
+fundamental matrix and then as I said
+
+ align:start position:0%
+fundamental matrix and then as I said
+ 
+
+ align:start position:0%
+fundamental matrix and then as I said
+we'll talk about an entirely different
+
+ align:start position:0%
+we'll talk about an entirely different
+ 
+
+ align:start position:0%
+we'll talk about an entirely different
+method of solving the system one which
+
+ align:start position:0%
+method of solving the system one which
+ 
+
+ align:start position:0%
+method of solving the system one which
+makes no mention of eigenvalues or
+
+ align:start position:0%
+makes no mention of eigenvalues or
+ 
+
+ align:start position:0%
+makes no mention of eigenvalues or
+eigenvectors if you can believe that but
+
+ align:start position:0%
+eigenvectors if you can believe that but
+ 
+
+ align:start position:0%
+eigenvectors if you can believe that but
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+one confusing thing about the
+
+ align:start position:0%
+one confusing thing about the
+ 
+
+ align:start position:0%
+one confusing thing about the
+fundamental matrix is that it is not
+
+ align:start position:0%
+fundamental matrix is that it is not
+ 
+
+ align:start position:0%
+fundamental matrix is that it is not
+unique I cannot
+
+ align:start position:0%
+unique I cannot
+ 
+
+ align:start position:0%
+unique I cannot
+I've been carefully trying to avoid
+
+ align:start position:0%
+I've been carefully trying to avoid
+ 
+
+ align:start position:0%
+I've been carefully trying to avoid
+talking about the rough fundamental
+
+ align:start position:0%
+talking about the rough fundamental
+ 
+
+ align:start position:0%
+talking about the rough fundamental
+matrix because there is no fundamental
+
+ align:start position:0%
+matrix because there is no fundamental
+ 
+
+ align:start position:0%
+matrix because there is no fundamental
+matrix there is only a fundamental
+
+ align:start position:0%
+matrix there is only a fundamental
+ 
+
+ align:start position:0%
+matrix there is only a fundamental
+matrix why
+
+ align:start position:0%
+matrix why
+ 
+
+ align:start position:0%
+matrix why
+is that well because these two columns
+
+ align:start position:0%
+is that well because these two columns
+ 
+
+ align:start position:0%
+is that well because these two columns
+can be any two independent solutions and
+
+ align:start position:0%
+can be any two independent solutions and
+ 
+
+ align:start position:0%
+can be any two independent solutions and
+there are an infinity of ways of picking
+
+ align:start position:0%
+there are an infinity of ways of picking
+ 
+
+ align:start position:0%
+there are an infinity of ways of picking
+independent solutions that means they're
+
+ align:start position:0%
+independent solutions that means they're
+ 
+
+ align:start position:0%
+independent solutions that means they're
+an infinity of ways affinity of possible
+
+ align:start position:0%
+an infinity of ways affinity of possible
+ 
+
+ align:start position:0%
+an infinity of ways affinity of possible
+fundamental matrices well that's
+
+ align:start position:0%
+fundamental matrices well that's
+ 
+
+ align:start position:0%
+fundamental matrices well that's
+disgusting but uh can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we repair it a little bit I mean maybe
+
+ align:start position:0%
+we repair it a little bit I mean maybe
+ 
+
+ align:start position:0%
+we repair it a little bit I mean maybe
+they're all de Rivel from each other in
+
+ align:start position:0%
+they're all de Rivel from each other in
+ 
+
+ align:start position:0%
+they're all de Rivel from each other in
+some simple way and that's of course
+
+ align:start position:0%
+some simple way and that's of course
+ 
+
+ align:start position:0%
+some simple way and that's of course
+what is true now as a prelude to doing
+
+ align:start position:0%
+what is true now as a prelude to doing
+ 
+
+ align:start position:0%
+what is true now as a prelude to doing
+that I'd like to show you what I should
+
+ align:start position:0%
+that I'd like to show you what I should
+ 
+
+ align:start position:0%
+that I'd like to show you what I should
+have showed you on Friday but again I
+
+ align:start position:0%
+have showed you on Friday but again I
+ 
+
+ align:start position:0%
+have showed you on Friday but again I
+ran out of time how do you write the
+
+ align:start position:0%
+ran out of time how do you write the
+ 
+
+ align:start position:0%
+ran out of time how do you write the
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+solution to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system the per system I'm talking about
+
+ align:start position:0%
+system the per system I'm talking about
+ 
+
+ align:start position:0%
+system the per system I'm talking about
+is that pink system well of course the
+
+ align:start position:0%
+is that pink system well of course the
+ 
+
+ align:start position:0%
+is that pink system well of course the
+standard naive way of doing it is its x
+
+ align:start position:0%
+standard naive way of doing it is its x
+ 
+
+ align:start position:0%
+standard naive way of doing it is its x
+equals the general solution is an
+
+ align:start position:0%
+equals the general solution is an
+ 
+
+ align:start position:0%
+equals the general solution is an
+arbitrary constant times at first
+
+ align:start position:0%
+arbitrary constant times at first
+ 
+
+ align:start position:0%
+arbitrary constant times at first
+solution you found plus c2 times the
+
+ align:start position:0%
+solution you found plus c2 times the
+ 
+
+ align:start position:0%
+solution you found plus c2 times the
+second another arbitrary constant times
+
+ align:start position:0%
+second another arbitrary constant times
+ 
+
+ align:start position:0%
+second another arbitrary constant times
+the second solution you found okay now
+
+ align:start position:0%
+the second solution you found okay now
+ 
+
+ align:start position:0%
+the second solution you found okay now
+how would you abbreviate that using the
+
+ align:start position:0%
+how would you abbreviate that using the
+ 
+
+ align:start position:0%
+how would you abbreviate that using the
+fundamental matrix well I did something
+
+ align:start position:0%
+fundamental matrix well I did something
+ 
+
+ align:start position:0%
+fundamental matrix well I did something
+very similar to this on Friday except
+
+ align:start position:0%
+very similar to this on Friday except
+ 
+
+ align:start position:0%
+very similar to this on Friday except
+these were called V's it was part of the
+
+ align:start position:0%
+these were called V's it was part of the
+ 
+
+ align:start position:0%
+these were called V's it was part of the
+variation of parameters method but I
+
+ align:start position:0%
+variation of parameters method but I
+ 
+
+ align:start position:0%
+variation of parameters method but I
+promised not to use those words today so
+
+ align:start position:0%
+promised not to use those words today so
+ 
+
+ align:start position:0%
+promised not to use those words today so
+I just said nothing okay what is what is
+
+ align:start position:0%
+I just said nothing okay what is what is
+ 
+
+ align:start position:0%
+I just said nothing okay what is what is
+the answer so it is x equals how
+
+ align:start position:0%
+the answer so it is x equals how
+ 
+
+ align:start position:0%
+the answer so it is x equals how
+do I write this using the fundamental
+
+ align:start position:0%
+do I write this using the fundamental
+ 
+
+ align:start position:0%
+do I write this using the fundamental
+matrix x1 x2 simple its capital x times
+
+ align:start position:0%
+matrix x1 x2 simple its capital x times
+ 
+
+ align:start position:0%
+matrix x1 x2 simple its capital x times
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+times the
+
+ align:start position:0%
+times the
+ 
+
+ align:start position:0%
+times the
+vector whose columns the vector whose
+
+ align:start position:0%
+vector whose columns the vector whose
+ 
+
+ align:start position:0%
+vector whose columns the vector whose
+entry column vector whose entries are c1
+
+ align:start position:0%
+entry column vector whose entries are c1
+ 
+
+ align:start position:0%
+entry column vector whose entries are c1
+and c2 in
+
+ align:start position:0%
+and c2 in
+ 
+
+ align:start position:0%
+and c2 in
+other words it is x1
+
+ align:start position:0%
+other words it is x1
+ 
+
+ align:start position:0%
+other words it is x1
+x2 times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the column vector c1 c2 isn't it yeah
+
+ align:start position:0%
+the column vector c1 c2 isn't it yeah
+ 
+
+ align:start position:0%
+the column vector c1 c2 isn't it yeah
+because if you multiply this think of
+
+ align:start position:0%
+because if you multiply this think of
+ 
+
+ align:start position:0%
+because if you multiply this think of
+think top row top row top row c1 top
+
+ align:start position:0%
+think top row top row top row c1 top
+ 
+
+ align:start position:0%
+think top row top row top row c1 top
+rope plus top row times c2 that exactly
+
+ align:start position:0%
+rope plus top row times c2 that exactly
+ 
+
+ align:start position:0%
+rope plus top row times c2 that exactly
+gives you the top row here and the same
+
+ align:start position:0%
+gives you the top row here and the same
+ 
+
+ align:start position:0%
+gives you the top row here and the same
+way the bottom row here times this
+
+ align:start position:0%
+way the bottom row here times this
+ 
+
+ align:start position:0%
+way the bottom row here times this
+vector gives you the bottom row of that
+
+ align:start position:0%
+vector gives you the bottom row of that
+ 
+
+ align:start position:0%
+vector gives you the bottom row of that
+so it's just another way of right that
+
+ align:start position:0%
+so it's just another way of right that
+ 
+
+ align:start position:0%
+so it's just another way of right that
+but it looks very efficient now
+
+ align:start position:0%
+but it looks very efficient now
+ 
+
+ align:start position:0%
+but it looks very efficient now
+sometimes efficiency isn't the good
+
+ align:start position:0%
+sometimes efficiency isn't the good
+ 
+
+ align:start position:0%
+sometimes efficiency isn't the good
+thing you know you have to watch out for
+
+ align:start position:0%
+thing you know you have to watch out for
+ 
+
+ align:start position:0%
+thing you know you have to watch out for
+it but here it's good so
+
+ align:start position:0%
+it but here it's good so
+ 
+
+ align:start position:0%
+it but here it's good so
+this is the general solution written out
+
+ align:start position:0%
+this is the general solution written out
+ 
+
+ align:start position:0%
+this is the general solution written out
+using a fundamental matrix and you can't
+
+ align:start position:0%
+using a fundamental matrix and you can't
+ 
+
+ align:start position:0%
+using a fundamental matrix and you can't
+use less symbols than that there's just
+
+ align:start position:0%
+use less symbols than that there's just
+ 
+
+ align:start position:0%
+use less symbols than that there's just
+no way well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that gives us our answer to what do
+
+ align:start position:0%
+but that gives us our answer to what do
+ 
+
+ align:start position:0%
+but that gives us our answer to what do
+all fundamental matrices look like well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're two columns or solutions so the
+
+ align:start position:0%
+they're two columns or solutions so the
+ 
+
+ align:start position:0%
+they're two columns or solutions so the
+answer is they look like X now the first
+
+ align:start position:0%
+answer is they look like X now the first
+ 
+
+ align:start position:0%
+answer is they look like X now the first
+column is an arbitrary solution how
+
+ align:start position:0%
+column is an arbitrary solution how
+ 
+
+ align:start position:0%
+column is an arbitrary solution how
+do I write an arbitrary solution there's
+
+ align:start position:0%
+do I write an arbitrary solution there's
+ 
+
+ align:start position:0%
+do I write an arbitrary solution there's
+the general solution I make it a
+
+ align:start position:0%
+the general solution I make it a
+ 
+
+ align:start position:0%
+the general solution I make it a
+particular one by giving a particular
+
+ align:start position:0%
+particular one by giving a particular
+ 
+
+ align:start position:0%
+particular one by giving a particular
+value to that column vector of arbitrary
+
+ align:start position:0%
+value to that column vector of arbitrary
+ 
+
+ align:start position:0%
+value to that column vector of arbitrary
+constants like 2 3 or minus 1 pi or
+
+ align:start position:0%
+constants like 2 3 or minus 1 pi or
+ 
+
+ align:start position:0%
+constants like 2 3 or minus 1 pi or
+something like that so if the first guy
+
+ align:start position:0%
+something like that so if the first guy
+ 
+
+ align:start position:0%
+something like that so if the first guy
+is a solution and I've just shown you I
+
+ align:start position:0%
+is a solution and I've just shown you I
+ 
+
+ align:start position:0%
+is a solution and I've just shown you I
+can write such a solution like X C 1
+
+ align:start position:0%
+can write such a solution like X C 1
+ 
+
+ align:start position:0%
+can write such a solution like X C 1
+with a column vector a particular column
+
+ align:start position:0%
+with a column vector a particular column
+ 
+
+ align:start position:0%
+with a column vector a particular column
+vector of numbers this is a solution
+
+ align:start position:0%
+vector of numbers this is a solution
+ 
+
+ align:start position:0%
+vector of numbers this is a solution
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+that the green thing says it is and side
+
+ align:start position:0%
+that the green thing says it is and side
+ 
+
+ align:start position:0%
+that the green thing says it is and side
+by side we'll write another one and
+
+ align:start position:0%
+by side we'll write another one and
+ 
+
+ align:start position:0%
+by side we'll write another one and
+now all I have to do is of
+
+ align:start position:0%
+now all I have to do is of
+ 
+
+ align:start position:0%
+now all I have to do is of
+course there's supposed to be a
+
+ align:start position:0%
+course there's supposed to be a
+ 
+
+ align:start position:0%
+course there's supposed to be a
+dependent we'll
+
+ align:start position:0%
+dependent we'll
+ 
+
+ align:start position:0%
+dependent we'll
+worry about that in just a moment all I
+
+ align:start position:0%
+worry about that in just a moment all I
+ 
+
+ align:start position:0%
+worry about that in just a moment all I
+have to do is make this look better now
+
+ align:start position:0%
+have to do is make this look better now
+ 
+
+ align:start position:0%
+have to do is make this look better now
+I showed you last time by the laws of
+
+ align:start position:0%
+I showed you last time by the laws of
+ 
+
+ align:start position:0%
+I showed you last time by the laws of
+matrix multiplication if the first
+
+ align:start position:0%
+matrix multiplication if the first
+ 
+
+ align:start position:0%
+matrix multiplication if the first
+column is X c1 and the second column is
+
+ align:start position:0%
+column is X c1 and the second column is
+ 
+
+ align:start position:0%
+column is X c1 and the second column is
+x c2 using matrix multiplication that's
+
+ align:start position:0%
+x c2 using matrix multiplication that's
+ 
+
+ align:start position:0%
+x c2 using matrix multiplication that's
+the same as writing it this way this
+
+ align:start position:0%
+the same as writing it this way this
+ 
+
+ align:start position:0%
+the same as writing it this way this
+square matrix times the matrix whose
+
+ align:start position:0%
+square matrix times the matrix whose
+ 
+
+ align:start position:0%
+square matrix times the matrix whose
+entries are the first column vector and
+
+ align:start position:0%
+entries are the first column vector and
+ 
+
+ align:start position:0%
+entries are the first column vector and
+the second column vector now
+
+ align:start position:0%
+the second column vector now
+ 
+
+ align:start position:0%
+the second column vector now
+I'm going to call this C it's
+
+ align:start position:0%
+I'm going to call this C it's
+ 
+
+ align:start position:0%
+I'm going to call this C it's
+a square matrix of constants it's a
+
+ align:start position:0%
+a square matrix of constants it's a
+ 
+
+ align:start position:0%
+a square matrix of constants it's a
+two-by-two matrix of constants
+
+ align:start position:0%
+two-by-two matrix of constants
+ 
+
+ align:start position:0%
+two-by-two matrix of constants
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+the final way of writing it is x times
+
+ align:start position:0%
+the final way of writing it is x times
+ 
+
+ align:start position:0%
+the final way of writing it is x times
+it's what just what corresponds to that
+
+ align:start position:0%
+it's what just what corresponds to that
+ 
+
+ align:start position:0%
+it's what just what corresponds to that
+but X times C and so this is the most
+
+ align:start position:0%
+but X times C and so this is the most
+ 
+
+ align:start position:0%
+but X times C and so this is the most
+general fund so X is a given fundamental
+
+ align:start position:0%
+general fund so X is a given fundamental
+ 
+
+ align:start position:0%
+general fund so X is a given fundamental
+matrix this one that one so the most
+
+ align:start position:0%
+matrix this one that one so the most
+ 
+
+ align:start position:0%
+matrix this one that one so the most
+general fundamental matrix is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the one you started with and
+
+ align:start position:0%
+then the one you started with and
+ 
+
+ align:start position:0%
+then the one you started with and
+multiply it by an arbitrary square
+
+ align:start position:0%
+multiply it by an arbitrary square
+ 
+
+ align:start position:0%
+multiply it by an arbitrary square
+matrix of constants except you want to
+
+ align:start position:0%
+matrix of constants except you want to
+ 
+
+ align:start position:0%
+matrix of constants except you want to
+keep be sure that the determinant is not
+
+ align:start position:0%
+keep be sure that the determinant is not
+ 
+
+ align:start position:0%
+keep be sure that the determinant is not
+zero well the determinant of this guy
+
+ align:start position:0%
+zero well the determinant of this guy
+ 
+
+ align:start position:0%
+zero well the determinant of this guy
+won't be zero so all you have to do is
+
+ align:start position:0%
+won't be zero so all you have to do is
+ 
+
+ align:start position:0%
+won't be zero so all you have to do is
+make sure that the determinant of C
+
+ align:start position:0%
+make sure that the determinant of C
+ 
+
+ align:start position:0%
+make sure that the determinant of C
+isn't zero either so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words the fundamental matrix
+
+ align:start position:0%
+in other words the fundamental matrix
+ 
+
+ align:start position:0%
+in other words the fundamental matrix
+isn't unique but once you've found one
+
+ align:start position:0%
+isn't unique but once you've found one
+ 
+
+ align:start position:0%
+isn't unique but once you've found one
+all the other ones are found by
+
+ align:start position:0%
+all the other ones are found by
+ 
+
+ align:start position:0%
+all the other ones are found by
+multiplying it on the right by an
+
+ align:start position:0%
+multiplying it on the right by an
+ 
+
+ align:start position:0%
+multiplying it on the right by an
+arbitrary square matrix of constants
+
+ align:start position:0%
+arbitrary square matrix of constants
+ 
+
+ align:start position:0%
+arbitrary square matrix of constants
+which is non singular as determinate not
+
+ align:start position:0%
+which is non singular as determinate not
+ 
+
+ align:start position:0%
+which is non singular as determinate not
+zero in other words well
+
+ align:start position:0%
+zero in other words well
+ 
+
+ align:start position:0%
+zero in other words well
+that was all Friday that's Friday
+
+ align:start position:0%
+that was all Friday that's Friday
+ 
+
+ align:start position:0%
+that was all Friday that's Friday
+leaking over into Monday and now we
+
+ align:start position:0%
+leaking over into Monday and now we
+ 
+
+ align:start position:0%
+leaking over into Monday and now we
+begin the true Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the problem once
+
+ align:start position:0%
+here's the problem once
+ 
+
+ align:start position:0%
+here's the problem once
+again we've got to start with we've got
+
+ align:start position:0%
+again we've got to start with we've got
+ 
+
+ align:start position:0%
+again we've got to start with we've got
+our two two-by-two system or n-by-n if
+
+ align:start position:0%
+our two two-by-two system or n-by-n if
+ 
+
+ align:start position:0%
+our two two-by-two system or n-by-n if
+you want to be super general there's
+
+ align:start position:0%
+you want to be super general there's
+ 
+
+ align:start position:0%
+you want to be super general there's
+a system uh what
+
+ align:start position:0%
+a system uh what
+ 
+
+ align:start position:0%
+a system uh what
+have we got so far by way of solving it
+
+ align:start position:0%
+have we got so far by way of solving it
+ 
+
+ align:start position:0%
+have we got so far by way of solving it
+well if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody you know your kid brother or
+
+ align:start position:0%
+somebody you know your kid brother or
+ 
+
+ align:start position:0%
+somebody you know your kid brother or
+sister when you go home says okay yeah
+
+ align:start position:0%
+sister when you go home says okay yeah
+ 
+
+ align:start position:0%
+sister when you go home says okay yeah
+precocious kid okay so tell us how I
+
+ align:start position:0%
+precocious kid okay so tell us how I
+ 
+
+ align:start position:0%
+precocious kid okay so tell us how I
+tell you how to solve this thing I think
+
+ align:start position:0%
+tell you how to solve this thing I think
+ 
+
+ align:start position:0%
+tell you how to solve this thing I think
+all the only thing you'll be able to say
+
+ align:start position:0%
+all the only thing you'll be able to say
+ 
+
+ align:start position:0%
+all the only thing you'll be able to say
+well you do this you take the matrix and
+
+ align:start position:0%
+well you do this you take the matrix and
+ 
+
+ align:start position:0%
+well you do this you take the matrix and
+then you calculate something called
+
+ align:start position:0%
+then you calculate something called
+ 
+
+ align:start position:0%
+then you calculate something called
+saiga values and eigenvectors you know
+
+ align:start position:0%
+saiga values and eigenvectors you know
+ 
+
+ align:start position:0%
+saiga values and eigenvectors you know
+what those are yeah I didn't think you
+
+ align:start position:0%
+what those are yeah I didn't think you
+ 
+
+ align:start position:0%
+what those are yeah I didn't think you
+did bla ll show how smart I am as you
+
+ align:start position:0%
+did bla ll show how smart I am as you
+ 
+
+ align:start position:0%
+did bla ll show how smart I am as you
+that explain what the eigenvalues and
+
+ align:start position:0%
+that explain what the eigenvalues and
+ 
+
+ align:start position:0%
+that explain what the eigenvalues and
+eigenvectors are and then you show how
+
+ align:start position:0%
+eigenvectors are and then you show how
+ 
+
+ align:start position:0%
+eigenvectors are and then you show how
+to of those make up special solutions
+
+ align:start position:0%
+to of those make up special solutions
+ 
+
+ align:start position:0%
+to of those make up special solutions
+and then you take a combination of that
+
+ align:start position:0%
+and then you take a combination of that
+ 
+
+ align:start position:0%
+and then you take a combination of that
+and in other words it's an algorithm
+
+ align:start position:0%
+and in other words it's an algorithm
+ 
+
+ align:start position:0%
+and in other words it's an algorithm
+it's something you do a process a method
+
+ align:start position:0%
+it's something you do a process a method
+ 
+
+ align:start position:0%
+it's something you do a process a method
+and when it's all done you have the
+
+ align:start position:0%
+and when it's all done you have the
+ 
+
+ align:start position:0%
+and when it's all done you have the
+general solution now that's fine for
+
+ align:start position:0%
+general solution now that's fine for
+ 
+
+ align:start position:0%
+general solution now that's fine for
+calculating particular problems you know
+
+ align:start position:0%
+calculating particular problems you know
+ 
+
+ align:start position:0%
+calculating particular problems you know
+with definite numbers a definite model
+
+ align:start position:0%
+with definite numbers a definite model
+ 
+
+ align:start position:0%
+with definite numbers a definite model
+with definite numbers in it where you
+
+ align:start position:0%
+with definite numbers in it where you
+ 
+
+ align:start position:0%
+with definite numbers in it where you
+want to definite answer and of course a
+
+ align:start position:0%
+want to definite answer and of course a
+ 
+
+ align:start position:0%
+want to definite answer and of course a
+lot of your work in engineering and
+
+ align:start position:0%
+lot of your work in engineering and
+ 
+
+ align:start position:0%
+lot of your work in engineering and
+science classes is that kind of work but
+
+ align:start position:0%
+science classes is that kind of work but
+ 
+
+ align:start position:0%
+science classes is that kind of work but
+the further you get on well when you
+
+ align:start position:0%
+the further you get on well when you
+ 
+
+ align:start position:0%
+the further you get on well when you
+start reading books for example or god
+
+ align:start position:0%
+start reading books for example or god
+ 
+
+ align:start position:0%
+start reading books for example or god
+forbid start reading papers in which you
+
+ align:start position:0%
+forbid start reading papers in which you
+ 
+
+ align:start position:0%
+forbid start reading papers in which you
+know people are telling you you know
+
+ align:start position:0%
+know people are telling you you know
+ 
+
+ align:start position:0%
+know people are telling you you know
+they're doing engineering or they're
+
+ align:start position:0%
+they're doing engineering or they're
+ 
+
+ align:start position:0%
+they're doing engineering or they're
+doing science they
+
+ align:start position:0%
+doing science they
+ 
+
+ align:start position:0%
+doing science they
+don't want to method what they want is a
+
+ align:start position:0%
+don't want to method what they want is a
+ 
+
+ align:start position:0%
+don't want to method what they want is a
+formula in other words what I the
+
+ align:start position:0%
+formula in other words what I the
+ 
+
+ align:start position:0%
+formula in other words what I the
+problem is to fill in the blank in
+
+ align:start position:0%
+problem is to fill in the blank in
+ 
+
+ align:start position:0%
+problem is to fill in the blank in
+the following you're writing a paper and
+
+ align:start position:0%
+the following you're writing a paper and
+ 
+
+ align:start position:0%
+the following you're writing a paper and
+you just set up some elaborate model and
+
+ align:start position:0%
+you just set up some elaborate model and
+ 
+
+ align:start position:0%
+you just set up some elaborate model and
+a is a matrix derived from that model in
+
+ align:start position:0%
+a is a matrix derived from that model in
+ 
+
+ align:start position:0%
+a is a matrix derived from that model in
+some way you know represents bacteria
+
+ align:start position:0%
+some way you know represents bacteria
+ 
+
+ align:start position:0%
+some way you know represents bacteria
+doing something or bank accounts doing
+
+ align:start position:0%
+doing something or bank accounts doing
+ 
+
+ align:start position:0%
+doing something or bank accounts doing
+something I don't know and you said as
+
+ align:start position:0%
+something I don't know and you said as
+ 
+
+ align:start position:0%
+something I don't know and you said as
+is well known the solution is of course
+
+ align:start position:0%
+is well known the solution is of course
+ 
+
+ align:start position:0%
+is well known the solution is of course
+you've only got letters here no numbers
+
+ align:start position:0%
+you've only got letters here no numbers
+ 
+
+ align:start position:0%
+you've only got letters here no numbers
+this is a general paper the solution is
+
+ align:start position:0%
+this is a general paper the solution is
+ 
+
+ align:start position:0%
+this is a general paper the solution is
+given by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula vo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trouble is we don't have a formula well
+
+ align:start position:0%
+trouble is we don't have a formula well
+ 
+
+ align:start position:0%
+trouble is we don't have a formula well
+we have as a method now people don't
+
+ align:start position:0%
+we have as a method now people don't
+ 
+
+ align:start position:0%
+we have as a method now people don't
+like that so
+
+ align:start position:0%
+like that so
+ 
+
+ align:start position:0%
+like that so
+what I'm going to produce for you this
+
+ align:start position:0%
+what I'm going to produce for you this
+ 
+
+ align:start position:0%
+what I'm going to produce for you this
+period is a formula that that
+
+ align:start position:0%
+period is a formula that that
+ 
+
+ align:start position:0%
+period is a formula that that
+formula does not require the calculation
+
+ align:start position:0%
+formula does not require the calculation
+ 
+
+ align:start position:0%
+formula does not require the calculation
+of any eigenvalues eigenvectors doesn't
+
+ align:start position:0%
+of any eigenvalues eigenvectors doesn't
+ 
+
+ align:start position:0%
+of any eigenvalues eigenvectors doesn't
+require any of that it's therefore a
+
+ align:start position:0%
+require any of that it's therefore a
+ 
+
+ align:start position:0%
+require any of that it's therefore a
+very popular way to fill in to finish
+
+ align:start position:0%
+very popular way to fill in to finish
+ 
+
+ align:start position:0%
+very popular way to fill in to finish
+that sentence now
+
+ align:start position:0%
+that sentence now
+ 
+
+ align:start position:0%
+that sentence now
+the question is where is that formula
+
+ align:start position:0%
+the question is where is that formula
+ 
+
+ align:start position:0%
+the question is where is that formula
+going to come from well we are for the
+
+ align:start position:0%
+going to come from well we are for the
+ 
+
+ align:start position:0%
+going to come from well we are for the
+moment clueless oh if
+
+ align:start position:0%
+moment clueless oh if
+ 
+
+ align:start position:0%
+moment clueless oh if
+you're clueless the place to look always
+
+ align:start position:0%
+you're clueless the place to look always
+ 
+
+ align:start position:0%
+you're clueless the place to look always
+is do I know anything about this sort of
+
+ align:start position:0%
+is do I know anything about this sort of
+ 
+
+ align:start position:0%
+is do I know anything about this sort of
+thing I mean is there some special case
+
+ align:start position:0%
+thing I mean is there some special case
+ 
+
+ align:start position:0%
+thing I mean is there some special case
+I could solve it of this problem I could
+
+ align:start position:0%
+I could solve it of this problem I could
+ 
+
+ align:start position:0%
+I could solve it of this problem I could
+solve or that I have solved in the past
+
+ align:start position:0%
+solve or that I have solved in the past
+ 
+
+ align:start position:0%
+solve or that I have solved in the past
+and the answer that is yes ah you
+
+ align:start position:0%
+and the answer that is yes ah you
+ 
+
+ align:start position:0%
+and the answer that is yes ah you
+haven't solved it for 2x2 matrix but you
+
+ align:start position:0%
+haven't solved it for 2x2 matrix but you
+ 
+
+ align:start position:0%
+haven't solved it for 2x2 matrix but you
+have solved it for a one by one matrix a
+
+ align:start position:0%
+have solved it for a one by one matrix a
+ 
+
+ align:start position:0%
+have solved it for a one by one matrix a
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+by one matrix also goes by the name of a
+
+ align:start position:0%
+by one matrix also goes by the name of a
+ 
+
+ align:start position:0%
+by one matrix also goes by the name of a
+constant it's
+
+ align:start position:0%
+constant it's
+ 
+
+ align:start position:0%
+constant it's
+just a thing you know it's a number you
+
+ align:start position:0%
+just a thing you know it's a number you
+ 
+
+ align:start position:0%
+just a thing you know it's a number you
+just putting brackets around it doesn't
+
+ align:start position:0%
+just putting brackets around it doesn't
+ 
+
+ align:start position:0%
+just putting brackets around it doesn't
+conceal the fact that it's just a number
+
+ align:start position:0%
+conceal the fact that it's just a number
+ 
+
+ align:start position:0%
+conceal the fact that it's just a number
+so let's look at what's the solution for
+
+ align:start position:0%
+so let's look at what's the solution for
+ 
+
+ align:start position:0%
+so let's look at what's the solution for
+a one by one matrix one by one case if
+
+ align:start position:0%
+a one by one matrix one by one case if
+ 
+
+ align:start position:0%
+a one by one matrix one by one case if
+we're looking for a general solution for
+
+ align:start position:0%
+we're looking for a general solution for
+ 
+
+ align:start position:0%
+we're looking for a general solution for
+the N by n case it must work for the one
+
+ align:start position:0%
+the N by n case it must work for the one
+ 
+
+ align:start position:0%
+the N by n case it must work for the one
+by one case also that's a good
+
+ align:start position:0%
+by one case also that's a good
+ 
+
+ align:start position:0%
+by one case also that's a good
+motivation a good reason for a starting
+
+ align:start position:0%
+motivation a good reason for a starting
+ 
+
+ align:start position:0%
+motivation a good reason for a starting
+that looks like X doesn't it X inside
+
+ align:start position:0%
+that looks like X doesn't it X inside
+ 
+
+ align:start position:0%
+that looks like X doesn't it X inside
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boy one taste
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well in that case I'm trying to solve
+
+ align:start position:0%
+well in that case I'm trying to solve
+ 
+
+ align:start position:0%
+well in that case I'm trying to solve
+the system the system consists of a
+
+ align:start position:0%
+the system the system consists of a
+ 
+
+ align:start position:0%
+the system the system consists of a
+single equation that's
+
+ align:start position:0%
+single equation that's
+ 
+
+ align:start position:0%
+single equation that's
+the way the system looks how
+
+ align:start position:0%
+the way the system looks how
+ 
+
+ align:start position:0%
+the way the system looks how
+do you solve that well you were born
+
+ align:start position:0%
+do you solve that well you were born
+ 
+
+ align:start position:0%
+do you solve that well you were born
+knowing how to solve that or you anyway
+
+ align:start position:0%
+knowing how to solve that or you anyway
+ 
+
+ align:start position:0%
+knowing how to solve that or you anyway
+certainly didn't learn it in this course
+
+ align:start position:0%
+certainly didn't learn it in this course
+ 
+
+ align:start position:0%
+certainly didn't learn it in this course
+solution is well
+
+ align:start position:0%
+solution is well
+ 
+
+ align:start position:0%
+solution is well
+you separate variables blah blah blah
+
+ align:start position:0%
+you separate variables blah blah blah
+ 
+
+ align:start position:0%
+you separate variables blah blah blah
+blah blah blah and the solution is x
+
+ align:start position:0%
+blah blah blah and the solution is x
+ 
+
+ align:start position:0%
+blah blah blah and the solution is x
+equals the
+
+ align:start position:0%
+equals the
+ 
+
+ align:start position:0%
+equals the
+basic solution is e to the eighty and
+
+ align:start position:0%
+basic solution is e to the eighty and
+ 
+
+ align:start position:0%
+basic solution is e to the eighty and
+you multiply that by an arbitrary
+
+ align:start position:0%
+you multiply that by an arbitrary
+ 
+
+ align:start position:0%
+you multiply that by an arbitrary
+constant now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if that's a formula it's a formula for
+
+ align:start position:0%
+if that's a formula it's a formula for
+ 
+
+ align:start position:0%
+if that's a formula it's a formula for
+the solution and it uses the parameter
+
+ align:start position:0%
+the solution and it uses the parameter
+ 
+
+ align:start position:0%
+the solution and it uses the parameter
+in the equation I didn't have to know a
+
+ align:start position:0%
+in the equation I didn't have to know a
+ 
+
+ align:start position:0%
+in the equation I didn't have to know a
+special number I didn't have to put a
+
+ align:start position:0%
+special number I didn't have to put a
+ 
+
+ align:start position:0%
+special number I didn't have to put a
+particular number here to use that well
+
+ align:start position:0%
+particular number here to use that well
+ 
+
+ align:start position:0%
+particular number here to use that well
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+answer is that the same idea whatever
+
+ align:start position:0%
+answer is that the same idea whatever
+ 
+
+ align:start position:0%
+answer is that the same idea whatever
+the answer I give here it's got to work
+
+ align:start position:0%
+the answer I give here it's got to work
+ 
+
+ align:start position:0%
+the answer I give here it's got to work
+in this case too so I'll just let's but
+
+ align:start position:0%
+in this case too so I'll just let's but
+ 
+
+ align:start position:0%
+in this case too so I'll just let's but
+let's take a quick look as to why this
+
+ align:start position:0%
+let's take a quick look as to why this
+ 
+
+ align:start position:0%
+let's take a quick look as to why this
+works of course you know you separate
+
+ align:start position:0%
+works of course you know you separate
+ 
+
+ align:start position:0%
+works of course you know you separate
+variables and use calculus I'm going to
+
+ align:start position:0%
+variables and use calculus I'm going to
+ 
+
+ align:start position:0%
+variables and use calculus I'm going to
+give you a slightly different argument
+
+ align:start position:0%
+give you a slightly different argument
+ 
+
+ align:start position:0%
+give you a slightly different argument
+Oh which has the advantage of
+
+ align:start position:0%
+Oh which has the advantage of
+ 
+
+ align:start position:0%
+Oh which has the advantage of
+generalizing to the N by n case and the
+
+ align:start position:0%
+generalizing to the N by n case and the
+ 
+
+ align:start position:0%
+generalizing to the N by n case and the
+argument goes as follows for that it
+
+ align:start position:0%
+argument goes as follows for that it
+ 
+
+ align:start position:0%
+argument goes as follows for that it
+uses the definition of the exponential
+
+ align:start position:0%
+uses the definition of the exponential
+ 
+
+ align:start position:0%
+uses the definition of the exponential
+function not as the inverse to the
+
+ align:start position:0%
+function not as the inverse to the
+ 
+
+ align:start position:0%
+function not as the inverse to the
+logarithm which is where the fancy
+
+ align:start position:0%
+logarithm which is where the fancy
+ 
+
+ align:start position:0%
+logarithm which is where the fancy
+calculus books get it from nor as the
+
+ align:start position:0%
+calculus books get it from nor as the
+ 
+
+ align:start position:0%
+calculus books get it from nor as the
+hice the naive high school method you
+
+ align:start position:0%
+hice the naive high school method you
+ 
+
+ align:start position:0%
+hice the naive high school method you
+know it's a squared means you multiply e
+
+ align:start position:0%
+know it's a squared means you multiply e
+ 
+
+ align:start position:0%
+know it's a squared means you multiply e
+by itself that e cubed need to do it
+
+ align:start position:0%
+by itself that e cubed need to do it
+ 
+
+ align:start position:0%
+by itself that e cubed need to do it
+three times and so on and either the 1/2
+
+ align:start position:0%
+three times and so on and either the 1/2
+ 
+
+ align:start position:0%
+three times and so on and either the 1/2
+means you do it 1/2 a time or something
+
+ align:start position:0%
+means you do it 1/2 a time or something
+ 
+
+ align:start position:0%
+means you do it 1/2 a time or something
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the naive definition of the exponential
+
+ align:start position:0%
+the naive definition of the exponential
+ 
+
+ align:start position:0%
+the naive definition of the exponential
+function instead I'll use the definition
+
+ align:start position:0%
+function instead I'll use the definition
+ 
+
+ align:start position:0%
+function instead I'll use the definition
+of the exponential function that comes
+
+ align:start position:0%
+of the exponential function that comes
+ 
+
+ align:start position:0%
+of the exponential function that comes
+from an infinite series so leaving out
+
+ align:start position:0%
+from an infinite series so leaving out
+ 
+
+ align:start position:0%
+from an infinite series so leaving out
+the arbitrary constant which we don't
+
+ align:start position:0%
+the arbitrary constant which we don't
+ 
+
+ align:start position:0%
+the arbitrary constant which we don't
+have to bother with e to the 80 is the
+
+ align:start position:0%
+have to bother with e to the 80 is the
+ 
+
+ align:start position:0%
+have to bother with e to the 80 is the
+series 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus 80 plus a squared T squared over 2
+
+ align:start position:0%
+plus 80 plus a squared T squared over 2
+ 
+
+ align:start position:0%
+plus 80 plus a squared T squared over 2
+factorial I'll put out one more turbine
+
+ align:start position:0%
+factorial I'll put out one more turbine
+ 
+
+ align:start position:0%
+factorial I'll put out one more turbine
+call it quits there if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I take this and then the argument goes
+
+ align:start position:0%
+I take this and then the argument goes
+ 
+
+ align:start position:0%
+I take this and then the argument goes
+let's just differentiate it in
+
+ align:start position:0%
+let's just differentiate it in
+ 
+
+ align:start position:0%
+let's just differentiate it in
+other words what's the derivative of e
+
+ align:start position:0%
+other words what's the derivative of e
+ 
+
+ align:start position:0%
+other words what's the derivative of e
+to the a T with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+respect to T well just differentiating
+
+ align:start position:0%
+respect to T well just differentiating
+ 
+
+ align:start position:0%
+respect to T well just differentiating
+term by term it's zero plus the first
+
+ align:start position:0%
+term by term it's zero plus the first
+ 
+
+ align:start position:0%
+term by term it's zero plus the first
+term is a the next term is a squared
+
+ align:start position:0%
+term is a the next term is a squared
+ 
+
+ align:start position:0%
+term is a the next term is a squared
+times T this differentiates to T squared
+
+ align:start position:0%
+times T this differentiates to T squared
+ 
+
+ align:start position:0%
+times T this differentiates to T squared
+over two factorial and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+answer is that this is equal to a times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you factor out the a what's left is 1
+
+ align:start position:0%
+if you factor out the a what's left is 1
+ 
+
+ align:start position:0%
+if you factor out the a what's left is 1
+plus 80 plus a squared T squared over 2
+
+ align:start position:0%
+plus 80 plus a squared T squared over 2
+ 
+
+ align:start position:0%
+plus 80 plus a squared T squared over 2
+factorial in other words it's simply a e
+
+ align:start position:0%
+factorial in other words it's simply a e
+ 
+
+ align:start position:0%
+factorial in other words it's simply a e
+to the a T in other words by
+
+ align:start position:0%
+to the a T in other words by
+ 
+
+ align:start position:0%
+to the a T in other words by
+differentiating the series using the
+
+ align:start position:0%
+differentiating the series using the
+ 
+
+ align:start position:0%
+differentiating the series using the
+series definition of the exponential and
+
+ align:start position:0%
+series definition of the exponential and
+ 
+
+ align:start position:0%
+series definition of the exponential and
+by differentiating a term by term I can
+
+ align:start position:0%
+by differentiating a term by term I can
+ 
+
+ align:start position:0%
+by differentiating a term by term I can
+immediately see that it satisfies this
+
+ align:start position:0%
+immediately see that it satisfies this
+ 
+
+ align:start position:0%
+immediately see that it satisfies this
+differential equation what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the arbitrary constant well you if
+
+ align:start position:0%
+about the arbitrary constant well you if
+ 
+
+ align:start position:0%
+about the arbitrary constant well you if
+you like you can include it here but
+
+ align:start position:0%
+you like you can include it here but
+ 
+
+ align:start position:0%
+you like you can include it here but
+it's easier to observe that by linearity
+
+ align:start position:0%
+it's easier to observe that by linearity
+ 
+
+ align:start position:0%
+it's easier to observe that by linearity
+if e to the a T solves the equation so
+
+ align:start position:0%
+if e to the a T solves the equation so
+ 
+
+ align:start position:0%
+if e to the a T solves the equation so
+does a constant times it because it's
+
+ align:start position:0%
+does a constant times it because it's
+ 
+
+ align:start position:0%
+does a constant times it because it's
+Lidia the equation is linear now that's
+
+ align:start position:0%
+Lidia the equation is linear now that's
+ 
+
+ align:start position:0%
+Lidia the equation is linear now that's
+the idea that I'm going to use to solve
+
+ align:start position:0%
+the idea that I'm going to use to solve
+ 
+
+ align:start position:0%
+the idea that I'm going to use to solve
+the system in general what are we going
+
+ align:start position:0%
+the system in general what are we going
+ 
+
+ align:start position:0%
+the system in general what are we going
+to say well what could we say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+solution to well it's better let's let's
+
+ align:start position:0%
+solution to well it's better let's let's
+ 
+
+ align:start position:0%
+solution to well it's better let's let's
+get two solutions at once by writing an
+
+ align:start position:0%
+get two solutions at once by writing an
+ 
+
+ align:start position:0%
+get two solutions at once by writing an
+X writing a fundamental matrix so a
+
+ align:start position:0%
+X writing a fundamental matrix so a
+ 
+
+ align:start position:0%
+X writing a fundamental matrix so a
+fundamental matrix a fundamental matrix
+
+ align:start position:0%
+fundamental matrix a fundamental matrix
+ 
+
+ align:start position:0%
+fundamental matrix a fundamental matrix
+I don't claim it's V 1 or a fundamental
+
+ align:start position:0%
+I don't claim it's V 1 or a fundamental
+ 
+
+ align:start position:0%
+I don't claim it's V 1 or a fundamental
+matrix for the system X prime equals ax
+
+ align:start position:0%
+matrix for the system X prime equals ax
+ 
+
+ align:start position:0%
+matrix for the system X prime equals ax
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's what we're trying to solve and
+
+ align:start position:0%
+that's what we're trying to solve and
+ 
+
+ align:start position:0%
+that's what we're trying to solve and
+we're going to get two solutions by
+
+ align:start position:0%
+we're going to get two solutions by
+ 
+
+ align:start position:0%
+we're going to get two solutions by
+getting a fundamental matrix for it
+
+ align:start position:0%
+getting a fundamental matrix for it
+ 
+
+ align:start position:0%
+getting a fundamental matrix for it
+there the answer is is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the a T is
+
+ align:start position:0%
+the a T is
+ 
+
+ align:start position:0%
+the a T is
+that what it should be that
+
+ align:start position:0%
+that what it should be that
+ 
+
+ align:start position:0%
+that what it should be that
+little guy I had a little a now we've
+
+ align:start position:0%
+little guy I had a little a now we've
+ 
+
+ align:start position:0%
+little guy I had a little a now we've
+got a matrix ok just put the matrix up
+
+ align:start position:0%
+got a matrix ok just put the matrix up
+ 
+
+ align:start position:0%
+got a matrix ok just put the matrix up
+there now what on earth this first
+
+ align:start position:0%
+there now what on earth this first
+ 
+
+ align:start position:0%
+there now what on earth this first
+person who still must've thought of this
+
+ align:start position:0%
+person who still must've thought of this
+ 
+
+ align:start position:0%
+person who still must've thought of this
+it happens about a hundred years ago oh
+
+ align:start position:0%
+it happens about a hundred years ago oh
+ 
+
+ align:start position:0%
+it happens about a hundred years ago oh
+you know what meeting should be given to
+
+ align:start position:0%
+you know what meeting should be given to
+ 
+
+ align:start position:0%
+you know what meeting should be given to
+e to a matrix power well clearly the too
+
+ align:start position:0%
+e to a matrix power well clearly the too
+ 
+
+ align:start position:0%
+e to a matrix power well clearly the too
+naive definitions won't work are the
+
+ align:start position:0%
+naive definitions won't work are the
+ 
+
+ align:start position:0%
+naive definitions won't work are the
+only possible being you could try for is
+
+ align:start position:0%
+only possible being you could try for is
+ 
+
+ align:start position:0%
+only possible being you could try for is
+using the infinite series but that does
+
+ align:start position:0%
+using the infinite series but that does
+ 
+
+ align:start position:0%
+using the infinite series but that does
+work so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a definition I'm giving you the
+
+ align:start position:0%
+this is a definition I'm giving you the
+ 
+
+ align:start position:0%
+this is a definition I'm giving you the
+exponential matrix it is Oh
+
+ align:start position:0%
+exponential matrix it is Oh
+ 
+
+ align:start position:0%
+exponential matrix it is Oh
+now notice the a is a 2 by 2 matrix
+
+ align:start position:0%
+now notice the a is a 2 by 2 matrix
+ 
+
+ align:start position:0%
+now notice the a is a 2 by 2 matrix
+multiplying it by T what I have up here
+
+ align:start position:0%
+multiplying it by T what I have up here
+ 
+
+ align:start position:0%
+multiplying it by T what I have up here
+is that basically a 2 by 2 matrix
+
+ align:start position:0%
+is that basically a 2 by 2 matrix
+ 
+
+ align:start position:0%
+is that basically a 2 by 2 matrix
+it's entries involve T but it's a 2 by 2
+
+ align:start position:0%
+it's entries involve T but it's a 2 by 2
+ 
+
+ align:start position:0%
+it's entries involve T but it's a 2 by 2
+matrix ok
+
+ align:start position:0%
+matrix ok
+ 
+
+ align:start position:0%
+matrix ok
+it's going to be leave out so we're
+
+ align:start position:0%
+it's going to be leave out so we're
+ 
+
+ align:start position:0%
+it's going to be leave out so we're
+trying to get the analog of that formula
+
+ align:start position:0%
+trying to get the analog of that formula
+ 
+
+ align:start position:0%
+trying to get the analog of that formula
+over there well it's going to be leave
+
+ align:start position:0%
+over there well it's going to be leave
+ 
+
+ align:start position:0%
+over there well it's going to be leave
+the first term out just for the moment
+
+ align:start position:0%
+the first term out just for the moment
+ 
+
+ align:start position:0%
+the first term out just for the moment
+the next term is going to early be a
+
+ align:start position:0%
+the next term is going to early be a
+ 
+
+ align:start position:0%
+the next term is going to early be a
+times T this is a 2 by 2 matrix right
+
+ align:start position:0%
+times T this is a 2 by 2 matrix right
+ 
+
+ align:start position:0%
+times T this is a 2 by 2 matrix right
+what's your the next term B well a
+
+ align:start position:0%
+what's your the next term B well a
+ 
+
+ align:start position:0%
+what's your the next term B well a
+squared times T squared over 2 factorial
+
+ align:start position:0%
+squared times T squared over 2 factorial
+ 
+
+ align:start position:0%
+squared times T squared over 2 factorial
+what kind of a guy is that well if a is
+
+ align:start position:0%
+what kind of a guy is that well if a is
+ 
+
+ align:start position:0%
+what kind of a guy is that well if a is
+a 2 by 2 matrix so is a squared how
+
+ align:start position:0%
+a 2 by 2 matrix so is a squared how
+ 
+
+ align:start position:0%
+a 2 by 2 matrix so is a squared how
+about this this is just a scalar which
+
+ align:start position:0%
+about this this is just a scalar which
+ 
+
+ align:start position:0%
+about this this is just a scalar which
+multiplies every entry of a weird and
+
+ align:start position:0%
+multiplies every entry of a weird and
+ 
+
+ align:start position:0%
+multiplies every entry of a weird and
+therefore this is still a two-by-two
+
+ align:start position:0%
+therefore this is still a two-by-two
+ 
+
+ align:start position:0%
+therefore this is still a two-by-two
+matrix that's a two-by-two matrix this
+
+ align:start position:0%
+matrix that's a two-by-two matrix this
+ 
+
+ align:start position:0%
+matrix that's a two-by-two matrix this
+is a 2 by 2 matrix no matter how many
+
+ align:start position:0%
+is a 2 by 2 matrix no matter how many
+ 
+
+ align:start position:0%
+is a 2 by 2 matrix no matter how many
+times you multiply a by itself it stays
+
+ align:start position:0%
+times you multiply a by itself it stays
+ 
+
+ align:start position:0%
+times you multiply a by itself it stays
+a 2 by 2 matrix it gets more and more
+
+ align:start position:0%
+a 2 by 2 matrix it gets more and more
+ 
+
+ align:start position:0%
+a 2 by 2 matrix it gets more and more
+complicated looking but it's always a 2
+
+ align:start position:0%
+complicated looking but it's always a 2
+ 
+
+ align:start position:0%
+complicated looking but it's always a 2
+by 2 matrix and now I'm multiplying
+
+ align:start position:0%
+by 2 matrix and now I'm multiplying
+ 
+
+ align:start position:0%
+by 2 matrix and now I'm multiplying
+every entry of that by T to the scale or
+
+ align:start position:0%
+every entry of that by T to the scale or
+ 
+
+ align:start position:0%
+every entry of that by T to the scale or
+T cubed over 3 factorial and continuing
+
+ align:start position:0%
+T cubed over 3 factorial and continuing
+ 
+
+ align:start position:0%
+T cubed over 3 factorial and continuing
+on in that way what
+
+ align:start position:0%
+on in that way what
+ 
+
+ align:start position:0%
+on in that way what
+I get therefore is the sum of 2 by 2
+
+ align:start position:0%
+I get therefore is the sum of 2 by 2
+ 
+
+ align:start position:0%
+I get therefore is the sum of 2 by 2
+matrices well you can add 2 by 2
+
+ align:start position:0%
+matrices well you can add 2 by 2
+ 
+
+ align:start position:0%
+matrices well you can add 2 by 2
+matrices to each other we've never made
+
+ align:start position:0%
+matrices to each other we've never made
+ 
+
+ align:start position:0%
+matrices to each other we've never made
+an infinite series of them but in fact
+
+ align:start position:0%
+an infinite series of them but in fact
+ 
+
+ align:start position:0%
+an infinite series of them but in fact
+we haven't done it but others have and
+
+ align:start position:0%
+we haven't done it but others have and
+ 
+
+ align:start position:0%
+we haven't done it but others have and
+this is what they wrote the only
+
+ align:start position:0%
+this is what they wrote the only
+ 
+
+ align:start position:0%
+this is what they wrote the only
+question is what should we put at the
+
+ align:start position:0%
+question is what should we put at the
+ 
+
+ align:start position:0%
+question is what should we put at the
+beginning over there I have one the
+
+ align:start position:0%
+beginning over there I have one the
+ 
+
+ align:start position:0%
+beginning over there I have one the
+number 1 but I of course cannot add the
+
+ align:start position:0%
+number 1 but I of course cannot add the
+ 
+
+ align:start position:0%
+number 1 but I of course cannot add the
+number 1 to 2 by 2 matrices what goes
+
+ align:start position:0%
+number 1 to 2 by 2 matrices what goes
+ 
+
+ align:start position:0%
+number 1 to 2 by 2 matrices what goes
+here must be a 2 by 2 matrix which is
+
+ align:start position:0%
+here must be a 2 by 2 matrix which is
+ 
+
+ align:start position:0%
+here must be a 2 by 2 matrix which is
+the closest thing to one I can think of
+
+ align:start position:0%
+the closest thing to one I can think of
+ 
+
+ align:start position:0%
+the closest thing to one I can think of
+what should it be the I 2 by 2 I the 2
+
+ align:start position:0%
+what should it be the I 2 by 2 I the 2
+ 
+
+ align:start position:0%
+what should it be the I 2 by 2 I the 2
+by 2 identity matrix looks like the
+
+ align:start position:0%
+by 2 identity matrix looks like the
+ 
+
+ align:start position:0%
+by 2 identity matrix looks like the
+natural candidate for what to put there
+
+ align:start position:0%
+natural candidate for what to put there
+ 
+
+ align:start position:0%
+natural candidate for what to put there
+and in fact it's the right thing to put
+
+ align:start position:0%
+and in fact it's the right thing to put
+ 
+
+ align:start position:0%
+and in fact it's the right thing to put
+there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I have a conjecture you
+
+ align:start position:0%
+now I have a conjecture you
+ 
+
+ align:start position:0%
+now I have a conjecture you
+know purely formally changing all the
+
+ align:start position:0%
+know purely formally changing all the
+ 
+
+ align:start position:0%
+know purely formally changing all the
+with a keystroke of the computer all the
+
+ align:start position:0%
+with a keystroke of the computer all the
+ 
+
+ align:start position:0%
+with a keystroke of the computer all the
+little a's have been changed to capital
+
+ align:start position:0%
+little a's have been changed to capital
+ 
+
+ align:start position:0%
+little a's have been changed to capital
+a's and now all i have to do is wonder
+
+ align:start position:0%
+a's and now all i have to do is wonder
+ 
+
+ align:start position:0%
+a's and now all i have to do is wonder
+if is this going to work well what do i
+
+ align:start position:0%
+if is this going to work well what do i
+ 
+
+ align:start position:0%
+if is this going to work well what do i
+what's the basic thing I have to check
+
+ align:start position:0%
+what's the basic thing I have to check
+ 
+
+ align:start position:0%
+what's the basic thing I have to check
+to see that it's a fundamental matrix so
+
+ align:start position:0%
+to see that it's a fundamental matrix so
+ 
+
+ align:start position:0%
+to see that it's a fundamental matrix so
+the question is is this is this I wrote
+
+ align:start position:0%
+the question is is this is this I wrote
+ 
+
+ align:start position:0%
+the question is is this is this I wrote
+it down all right but is this a
+
+ align:start position:0%
+it down all right but is this a
+ 
+
+ align:start position:0%
+it down all right but is this a
+fundamental matrix for the system well I
+
+ align:start position:0%
+fundamental matrix for the system well I
+ 
+
+ align:start position:0%
+fundamental matrix for the system well I
+have a way of recognizing a fundamental
+
+ align:start position:0%
+have a way of recognizing a fundamental
+ 
+
+ align:start position:0%
+have a way of recognizing a fundamental
+matrix when I see one the critical thing
+
+ align:start position:0%
+matrix when I see one the critical thing
+ 
+
+ align:start position:0%
+matrix when I see one the critical thing
+is that it should satisfy this matrix
+
+ align:start position:0%
+is that it should satisfy this matrix
+ 
+
+ align:start position:0%
+is that it should satisfy this matrix
+differential equation so
+
+ align:start position:0%
+differential equation so
+ 
+
+ align:start position:0%
+differential equation so
+that's what I should verify does this
+
+ align:start position:0%
+that's what I should verify does this
+ 
+
+ align:start position:0%
+that's what I should verify does this
+guy that I've written down satisfy that
+
+ align:start position:0%
+guy that I've written down satisfy that
+ 
+
+ align:start position:0%
+guy that I've written down satisfy that
+equation and the answer is it satisfies
+
+ align:start position:0%
+equation and the answer is it satisfies
+ 
+
+ align:start position:0%
+equation and the answer is it satisfies
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+number two is it satisfies X Prime
+
+ align:start position:0%
+number two is it satisfies X Prime
+ 
+
+ align:start position:0%
+number two is it satisfies X Prime
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+a X
+
+ align:start position:0%
+a X
+ 
+
+ align:start position:0%
+a X
+in other words plugging in x equals this
+
+ align:start position:0%
+in other words plugging in x equals this
+ 
+
+ align:start position:0%
+in other words plugging in x equals this
+e to the 8e whose definition I just gave
+
+ align:start position:0%
+e to the 8e whose definition I just gave
+ 
+
+ align:start position:0%
+e to the 8e whose definition I just gave
+you if I substitute that in does it
+
+ align:start position:0%
+you if I substitute that in does it
+ 
+
+ align:start position:0%
+you if I substitute that in does it
+satisfy that matrix differential
+
+ align:start position:0%
+satisfy that matrix differential
+ 
+
+ align:start position:0%
+satisfy that matrix differential
+equation the answer is yes I'm not going
+
+ align:start position:0%
+equation the answer is yes I'm not going
+ 
+
+ align:start position:0%
+equation the answer is yes I'm not going
+to calculate it out because the
+
+ align:start position:0%
+to calculate it out because the
+ 
+
+ align:start position:0%
+to calculate it out because the
+calculation is absolutely identical to
+
+ align:start position:0%
+calculation is absolutely identical to
+ 
+
+ align:start position:0%
+calculation is absolutely identical to
+what I did there the
+
+ align:start position:0%
+what I did there the
+ 
+
+ align:start position:0%
+what I did there the
+only difference is when I differentiated
+
+ align:start position:0%
+only difference is when I differentiated
+ 
+
+ align:start position:0%
+only difference is when I differentiated
+a term by term how do you differentiate
+
+ align:start position:0%
+a term by term how do you differentiate
+ 
+
+ align:start position:0%
+a term by term how do you differentiate
+something like this well you
+
+ align:start position:0%
+something like this well you
+ 
+
+ align:start position:0%
+something like this well you
+differentiate it every term in it but
+
+ align:start position:0%
+differentiate it every term in it but
+ 
+
+ align:start position:0%
+differentiate it every term in it but
+this if you work it out it's simply this
+
+ align:start position:0%
+this if you work it out it's simply this
+ 
+
+ align:start position:0%
+this if you work it out it's simply this
+is a constant matrix every term of which
+
+ align:start position:0%
+is a constant matrix every term of which
+ 
+
+ align:start position:0%
+is a constant matrix every term of which
+is multiplied by T squared over 2
+
+ align:start position:0%
+is multiplied by T squared over 2
+ 
+
+ align:start position:0%
+is multiplied by T squared over 2
+factorial well if you differentiate
+
+ align:start position:0%
+factorial well if you differentiate
+ 
+
+ align:start position:0%
+factorial well if you differentiate
+every term every entry of that constant
+
+ align:start position:0%
+every term every entry of that constant
+ 
+
+ align:start position:0%
+every term every entry of that constant
+of that matrix what you're going to get
+
+ align:start position:0%
+of that matrix what you're going to get
+ 
+
+ align:start position:0%
+of that matrix what you're going to get
+is a squared times just the derivative
+
+ align:start position:0%
+is a squared times just the derivative
+ 
+
+ align:start position:0%
+is a squared times just the derivative
+of that part which is simply T and the
+
+ align:start position:0%
+of that part which is simply T and the
+ 
+
+ align:start position:0%
+of that part which is simply T and the
+same way in other words calculate the
+
+ align:start position:0%
+same way in other words calculate the
+ 
+
+ align:start position:0%
+same way in other words calculate the
+formal calculations looks absolutely
+
+ align:start position:0%
+formal calculations looks absolutely
+ 
+
+ align:start position:0%
+formal calculations looks absolutely
+identical to that so the answer to this
+
+ align:start position:0%
+identical to that so the answer to this
+ 
+
+ align:start position:0%
+identical to that so the answer to this
+is yes by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same calculation as before as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the 1 by 1 case and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the only other thing to check is
+
+ align:start position:0%
+now the only other thing to check is
+ 
+
+ align:start position:0%
+now the only other thing to check is
+that the determinant is not 0 in fact
+
+ align:start position:0%
+that the determinant is not 0 in fact
+ 
+
+ align:start position:0%
+that the determinant is not 0 in fact
+the determinant is not 0 at one point
+
+ align:start position:0%
+the determinant is not 0 at one point
+ 
+
+ align:start position:0%
+the determinant is not 0 at one point
+that's all you have to check what's X of
+
+ align:start position:0%
+that's all you have to check what's X of
+ 
+
+ align:start position:0%
+that's all you have to check what's X of
+0 what's
+
+ align:start position:0%
+0 what's
+ 
+
+ align:start position:0%
+0 what's
+the determinant at the value of the
+
+ align:start position:0%
+the determinant at the value of the
+ 
+
+ align:start position:0%
+the determinant at the value of the
+determinant of X is e to the a T what's
+
+ align:start position:0%
+determinant of X is e to the a T what's
+ 
+
+ align:start position:0%
+determinant of X is e to the a T what's
+the value of it's this thing at 0 here's
+
+ align:start position:0%
+the value of it's this thing at 0 here's
+ 
+
+ align:start position:0%
+the value of it's this thing at 0 here's
+my function if I plug in T equals 0
+
+ align:start position:0%
+my function if I plug in T equals 0
+ 
+
+ align:start position:0%
+my function if I plug in T equals 0
+what's it equal to all
+
+ align:start position:0%
+what's it equal to all
+ 
+
+ align:start position:0%
+what's it equal to all
+right what's
+
+ align:start position:0%
+right what's
+ 
+
+ align:start position:0%
+right what's
+the determinant of I 1 it is certainly
+
+ align:start position:0%
+the determinant of I 1 it is certainly
+ 
+
+ align:start position:0%
+the determinant of I 1 it is certainly
+not 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by writing down this infinite series
+
+ align:start position:0%
+so by writing down this infinite series
+ 
+
+ align:start position:0%
+so by writing down this infinite series
+I've got my two solutions its columns
+
+ align:start position:0%
+I've got my two solutions its columns
+ 
+
+ align:start position:0%
+I've got my two solutions its columns
+give me two solutions to the original
+
+ align:start position:0%
+give me two solutions to the original
+ 
+
+ align:start position:0%
+give me two solutions to the original
+system there
+
+ align:start position:0%
+system there
+ 
+
+ align:start position:0%
+system there
+were no eigenvalues no eigenvectors I
+
+ align:start position:0%
+were no eigenvalues no eigenvectors I
+ 
+
+ align:start position:0%
+were no eigenvalues no eigenvectors I
+have a formula for the answer what's the
+
+ align:start position:0%
+have a formula for the answer what's the
+ 
+
+ align:start position:0%
+have a formula for the answer what's the
+formula it's e to the a T and of course
+
+ align:start position:0%
+formula it's e to the a T and of course
+ 
+
+ align:start position:0%
+formula it's e to the a T and of course
+anybody reading the paper is supposed to
+
+ align:start position:0%
+anybody reading the paper is supposed to
+ 
+
+ align:start position:0%
+anybody reading the paper is supposed to
+go into the a T is it means that this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is just marvelous there must be a fly in
+
+ align:start position:0%
+is just marvelous there must be a fly in
+ 
+
+ align:start position:0%
+is just marvelous there must be a fly in
+the ointment somewhere only
+
+ align:start position:0%
+the ointment somewhere only
+ 
+
+ align:start position:0%
+the ointment somewhere only
+a teeny they'll fly the T they'll fly if
+
+ align:start position:0%
+a teeny they'll fly the T they'll fly if
+ 
+
+ align:start position:0%
+a teeny they'll fly the T they'll fly if
+it's almost impossible to calculate that
+
+ align:start position:0%
+it's almost impossible to calculate that
+ 
+
+ align:start position:0%
+it's almost impossible to calculate that
+series for all reasonable times however
+
+ align:start position:0%
+series for all reasonable times however
+ 
+
+ align:start position:0%
+series for all reasonable times however
+once in a while it is so let me give you
+
+ align:start position:0%
+once in a while it is so let me give you
+ 
+
+ align:start position:0%
+once in a while it is so let me give you
+an example where it is possible to
+
+ align:start position:0%
+an example where it is possible to
+ 
+
+ align:start position:0%
+an example where it is possible to
+calculate the series and we get a nice
+
+ align:start position:0%
+calculate the series and we get a nice
+ 
+
+ align:start position:0%
+calculate the series and we get a nice
+answer so
+
+ align:start position:0%
+answer so
+ 
+
+ align:start position:0%
+answer so
+let's work out an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way I should you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know nowadays we're
+
+ align:start position:0%
+know nowadays we're
+ 
+
+ align:start position:0%
+know nowadays we're
+not back 50 years the
+
+ align:start position:0%
+not back 50 years the
+ 
+
+ align:start position:0%
+not back 50 years the
+exponential matrix has the same status
+
+ align:start position:0%
+exponential matrix has the same status
+ 
+
+ align:start position:0%
+exponential matrix has the same status
+on say a MATLAB or maple or Mathematica
+
+ align:start position:0%
+on say a MATLAB or maple or Mathematica
+ 
+
+ align:start position:0%
+on say a MATLAB or maple or Mathematica
+as the ordinary exponential function
+
+ align:start position:0%
+as the ordinary exponential function
+ 
+
+ align:start position:0%
+as the ordinary exponential function
+does it's just a command you type in you
+
+ align:start position:0%
+does it's just a command you type in you
+ 
+
+ align:start position:0%
+does it's just a command you type in you
+type in your matrix and use now say X X
+
+ align:start position:0%
+type in your matrix and use now say X X
+ 
+
+ align:start position:0%
+type in your matrix and use now say X X
+exp of that matrix and out comes the
+
+ align:start position:0%
+exp of that matrix and out comes the
+ 
+
+ align:start position:0%
+exp of that matrix and out comes the
+answer to as many decimal places as you
+
+ align:start position:0%
+answer to as many decimal places as you
+ 
+
+ align:start position:0%
+answer to as many decimal places as you
+want it'll be a square matrix with
+
+ align:start position:0%
+want it'll be a square matrix with
+ 
+
+ align:start position:0%
+want it'll be a square matrix with
+entries carefully
+
+ align:start position:0%
+entries carefully
+ 
+
+ align:start position:0%
+entries carefully
+written out so in
+
+ align:start position:0%
+written out so in
+ 
+
+ align:start position:0%
+written out so in
+that sense you know the fact that we
+
+ align:start position:0%
+that sense you know the fact that we
+ 
+
+ align:start position:0%
+that sense you know the fact that we
+can't calculate it shouldn't bother us
+
+ align:start position:0%
+can't calculate it shouldn't bother us
+ 
+
+ align:start position:0%
+can't calculate it shouldn't bother us
+you know there are machines to do the
+
+ align:start position:0%
+you know there are machines to do the
+ 
+
+ align:start position:0%
+you know there are machines to do the
+calculations but we're interested in is
+
+ align:start position:0%
+calculations but we're interested in is
+ 
+
+ align:start position:0%
+calculations but we're interested in is
+it as a theoretical tool but let's in
+
+ align:start position:0%
+it as a theoretical tool but let's in
+ 
+
+ align:start position:0%
+it as a theoretical tool but let's in
+order to get any feeling for this at all
+
+ align:start position:0%
+order to get any feeling for this at all
+ 
+
+ align:start position:0%
+order to get any feeling for this at all
+you we certainly have to do a few
+
+ align:start position:0%
+you we certainly have to do a few
+ 
+
+ align:start position:0%
+you we certainly have to do a few
+calculations so let's do it easy one
+
+ align:start position:0%
+calculations so let's do it easy one
+ 
+
+ align:start position:0%
+calculations so let's do it easy one
+let's consider the system X prime equals
+
+ align:start position:0%
+let's consider the system X prime equals
+ 
+
+ align:start position:0%
+let's consider the system X prime equals
+y y prime equals x this
+
+ align:start position:0%
+y y prime equals x this
+ 
+
+ align:start position:0%
+y y prime equals x this
+is very easily done by elimination but
+
+ align:start position:0%
+is very easily done by elimination but
+ 
+
+ align:start position:0%
+is very easily done by elimination but
+that's forbidden so
+
+ align:start position:0%
+that's forbidden so
+ 
+
+ align:start position:0%
+that's forbidden so
+first of all we write it as a matrix so
+
+ align:start position:0%
+first of all we write it as a matrix so
+ 
+
+ align:start position:0%
+first of all we write it as a matrix so
+X prime it's the system X prime equals 0
+
+ align:start position:0%
+X prime it's the system X prime equals 0
+ 
+
+ align:start position:0%
+X prime it's the system X prime equals 0
+1 1 0 X so here's my egg and so
+
+ align:start position:0%
+1 1 0 X so here's my egg and so
+ 
+
+ align:start position:0%
+1 1 0 X so here's my egg and so
+e to the a T is going
+
+ align:start position:0%
+e to the a T is going
+ 
+
+ align:start position:0%
+e to the a T is going
+to be so a is 0 1 1 0 so what we want to
+
+ align:start position:0%
+to be so a is 0 1 1 0 so what we want to
+ 
+
+ align:start position:0%
+to be so a is 0 1 1 0 so what we want to
+calculate is we're going to get both
+
+ align:start position:0%
+calculate is we're going to get both
+ 
+
+ align:start position:0%
+calculate is we're going to get both
+solutions at once by calculating it one
+
+ align:start position:0%
+solutions at once by calculating it one
+ 
+
+ align:start position:0%
+solutions at once by calculating it one
+fell swoop e to the 18 ok e to the 80
+
+ align:start position:0%
+fell swoop e to the 18 ok e to the 80
+ 
+
+ align:start position:0%
+fell swoop e to the 18 ok e to the 80
+equals ok
+
+ align:start position:0%
+equals ok
+ 
+
+ align:start position:0%
+equals ok
+I'm going to actually write out these
+
+ align:start position:0%
+I'm going to actually write out these
+ 
+
+ align:start position:0%
+I'm going to actually write out these
+guys well obviously the hard part at the
+
+ align:start position:0%
+guys well obviously the hard part at the
+ 
+
+ align:start position:0%
+guys well obviously the hard part at the
+part which is normally going to prevent
+
+ align:start position:0%
+part which is normally going to prevent
+ 
+
+ align:start position:0%
+part which is normally going to prevent
+us from calculating this series
+
+ align:start position:0%
+us from calculating this series
+ 
+
+ align:start position:0%
+us from calculating this series
+explicitly by hand anyway thus I say the
+
+ align:start position:0%
+explicitly by hand anyway thus I say the
+ 
+
+ align:start position:0%
+explicitly by hand anyway thus I say the
+computer can always do it is the value
+
+ align:start position:0%
+computer can always do it is the value
+ 
+
+ align:start position:0%
+computer can always do it is the value
+how do we raise a matrix to a high power
+
+ align:start position:0%
+how do we raise a matrix to a high power
+ 
+
+ align:start position:0%
+how do we raise a matrix to a high power
+you just keep multiplying and
+
+ align:start position:0%
+you just keep multiplying and
+ 
+
+ align:start position:0%
+you just keep multiplying and
+multiplying and multiplying that looks
+
+ align:start position:0%
+multiplying and multiplying that looks
+ 
+
+ align:start position:0%
+multiplying and multiplying that looks
+like a rather forbidding an done
+
+ align:start position:0%
+like a rather forbidding an done
+ 
+
+ align:start position:0%
+like a rather forbidding an done
+promising activity well here it's easy
+
+ align:start position:0%
+promising activity well here it's easy
+ 
+
+ align:start position:0%
+promising activity well here it's easy
+let's see what happens what is a if
+
+ align:start position:0%
+let's see what happens what is a if
+ 
+
+ align:start position:0%
+let's see what happens what is a if
+that's a what's a squared I'm going to
+
+ align:start position:0%
+that's a what's a squared I'm going to
+ 
+
+ align:start position:0%
+that's a what's a squared I'm going to
+have to count like that as part of the
+
+ align:start position:0%
+have to count like that as part of the
+ 
+
+ align:start position:0%
+have to count like that as part of the
+series so that's going to be 0 1 1 0
+
+ align:start position:0%
+series so that's going to be 0 1 1 0
+ 
+
+ align:start position:0%
+series so that's going to be 0 1 1 0
+times 0 1 1 0 which is Dada so 1 but 0 0
+
+ align:start position:0%
+times 0 1 1 0 which is Dada so 1 but 0 0
+ 
+
+ align:start position:0%
+times 0 1 1 0 which is Dada so 1 but 0 0
+3 0 1 4 0 we
+
+ align:start position:0%
+3 0 1 4 0 we
+ 
+
+ align:start position:0%
+3 0 1 4 0 we
+are saved it is the identity now
+
+ align:start position:0%
+are saved it is the identity now
+ 
+
+ align:start position:0%
+are saved it is the identity now
+for this point on we don't have to do
+
+ align:start position:0%
+for this point on we don't have to do
+ 
+
+ align:start position:0%
+for this point on we don't have to do
+any more calculations but I'll do them
+
+ align:start position:0%
+any more calculations but I'll do them
+ 
+
+ align:start position:0%
+any more calculations but I'll do them
+anyway or just - what's
+
+ align:start position:0%
+anyway or just - what's
+ 
+
+ align:start position:0%
+anyway or just - what's
+a cubed don't start from scratch again
+
+ align:start position:0%
+a cubed don't start from scratch again
+ 
+
+ align:start position:0%
+a cubed don't start from scratch again
+God from what time's one from no no no
+
+ align:start position:0%
+God from what time's one from no no no
+ 
+
+ align:start position:0%
+God from what time's one from no no no
+no no 8 8 a cubed is a squared times a
+
+ align:start position:0%
+no no 8 8 a cubed is a squared times a
+ 
+
+ align:start position:0%
+no no 8 8 a cubed is a squared times a
+and a squared is in real life the
+
+ align:start position:0%
+and a squared is in real life the
+ 
+
+ align:start position:0%
+and a squared is in real life the
+identity of course you would do all this
+
+ align:start position:0%
+identity of course you would do all this
+ 
+
+ align:start position:0%
+identity of course you would do all this
+in your head but I'm being a good boy
+
+ align:start position:0%
+in your head but I'm being a good boy
+ 
+
+ align:start position:0%
+in your head but I'm being a good boy
+writing in a lot so this is I the
+
+ align:start position:0%
+writing in a lot so this is I the
+ 
+
+ align:start position:0%
+writing in a lot so this is I the
+identity times a which is a I'll
+
+ align:start position:0%
+identity times a which is a I'll
+ 
+
+ align:start position:0%
+identity times a which is a I'll
+do one more what's a to the fourth now
+
+ align:start position:0%
+do one more what's a to the fourth now
+ 
+
+ align:start position:0%
+do one more what's a to the fourth now
+you would be tempted to say a to the
+
+ align:start position:0%
+you would be tempted to say a to the
+ 
+
+ align:start position:0%
+you would be tempted to say a to the
+fourth is a squared which is I times I
+
+ align:start position:0%
+fourth is a squared which is I times I
+ 
+
+ align:start position:0%
+fourth is a squared which is I times I
+which is I but that would be wrong a to
+
+ align:start position:0%
+which is I but that would be wrong a to
+ 
+
+ align:start position:0%
+which is I but that would be wrong a to
+the fourth is a cubed times a which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a cubed I've just calculated his a
+
+ align:start position:0%
+is a cubed I've just calculated his a
+ 
+
+ align:start position:0%
+is a cubed I've just calculated his a
+times a a cubed I just calculated with a
+
+ align:start position:0%
+times a a cubed I just calculated with a
+ 
+
+ align:start position:0%
+times a a cubed I just calculated with a
+right and now that is a squared which is
+
+ align:start position:0%
+right and now that is a squared which is
+ 
+
+ align:start position:0%
+right and now that is a squared which is
+the identity it's
+
+ align:start position:0%
+the identity it's
+ 
+
+ align:start position:0%
+the identity it's
+clear this is by this argument it's
+
+ align:start position:0%
+clear this is by this argument it's
+ 
+
+ align:start position:0%
+clear this is by this argument it's
+going to continue in the same way each
+
+ align:start position:0%
+going to continue in the same way each
+ 
+
+ align:start position:0%
+going to continue in the same way each
+time you add an A on the right hand side
+
+ align:start position:0%
+time you add an A on the right hand side
+ 
+
+ align:start position:0%
+time you add an A on the right hand side
+you're going to keep alternating between
+
+ align:start position:0%
+you're going to keep alternating between
+ 
+
+ align:start position:0%
+you're going to keep alternating between
+the identity a the next one will leave
+
+ align:start position:0%
+the identity a the next one will leave
+ 
+
+ align:start position:0%
+the identity a the next one will leave
+the identity the next will be a so the
+
+ align:start position:0%
+the identity the next will be a so the
+ 
+
+ align:start position:0%
+the identity the next will be a so the
+end result is that the first term of the
+
+ align:start position:0%
+end result is that the first term of the
+ 
+
+ align:start position:0%
+end result is that the first term of the
+series is simply the identity the
+
+ align:start position:0%
+series is simply the identity the
+ 
+
+ align:start position:0%
+series is simply the identity the
+next term of the series is a but it's
+
+ align:start position:0%
+next term of the series is a but it's
+ 
+
+ align:start position:0%
+next term of the series is a but it's
+multiplied by T so that is zero should I
+
+ align:start position:0%
+multiplied by T so that is zero should I
+ 
+
+ align:start position:0%
+multiplied by T so that is zero should I
+put it I'll keep the T on the outside
+
+ align:start position:0%
+put it I'll keep the T on the outside
+ 
+
+ align:start position:0%
+put it I'll keep the T on the outside
+remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you multiply a matrix by scalar
+
+ align:start position:0%
+when you multiply a matrix by scalar
+ 
+
+ align:start position:0%
+when you multiply a matrix by scalar
+that means multiply every entry by that
+
+ align:start position:0%
+that means multiply every entry by that
+ 
+
+ align:start position:0%
+that means multiply every entry by that
+scalar so this is the matrix 0 T t0 I'll
+
+ align:start position:0%
+scalar so this is the matrix 0 T t0 I'll
+ 
+
+ align:start position:0%
+scalar so this is the matrix 0 T t0 I'll
+do a couple more terms the next term
+
+ align:start position:0%
+do a couple more terms the next term
+ 
+
+ align:start position:0%
+do a couple more terms the next term
+would be well a squared we just
+
+ align:start position:0%
+would be well a squared we just
+ 
+
+ align:start position:0%
+would be well a squared we just
+calculated is the identity so that looks
+
+ align:start position:0%
+calculated is the identity so that looks
+ 
+
+ align:start position:0%
+calculated is the identity so that looks
+like this except now I multiply every
+
+ align:start position:0%
+like this except now I multiply every
+ 
+
+ align:start position:0%
+like this except now I multiply every
+term by T squared over 2 factorial all
+
+ align:start position:0%
+term by T squared over 2 factorial all
+ 
+
+ align:start position:0%
+term by T squared over 2 factorial all
+right what go for broke the
+
+ align:start position:0%
+right what go for broke the
+ 
+
+ align:start position:0%
+right what go for broke the
+next one will be this times
+
+ align:start position:0%
+next one will be this times
+ 
+
+ align:start position:0%
+next one will be this times
+T cubed over 3 factorial and fortunately
+
+ align:start position:0%
+T cubed over 3 factorial and fortunately
+ 
+
+ align:start position:0%
+T cubed over 3 factorial and fortunately
+I run out of room ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's calculate that oh maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should do it well
+
+ align:start position:0%
+I should do it well
+ 
+
+ align:start position:0%
+I should do it well
+no we're gonna need that ok
+
+ align:start position:0%
+no we're gonna need that ok
+ 
+
+ align:start position:0%
+no we're gonna need that ok
+let's do it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what's the final answer for e to the 80
+
+ align:start position:0%
+what's the final answer for e to the 80
+ 
+
+ align:start position:0%
+what's the final answer for e to the 80
+it is I have
+
+ align:start position:0%
+it is I have
+ 
+
+ align:start position:0%
+it is I have
+an infinite series of two-by-two
+
+ align:start position:0%
+an infinite series of two-by-two
+ 
+
+ align:start position:0%
+an infinite series of two-by-two
+matrices let's let's look at the term in
+
+ align:start position:0%
+matrices let's let's look at the term in
+ 
+
+ align:start position:0%
+matrices let's let's look at the term in
+the upper left hand corner it's 1 plus
+
+ align:start position:0%
+the upper left hand corner it's 1 plus
+ 
+
+ align:start position:0%
+the upper left hand corner it's 1 plus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+times T plus 1 times T squared over 2
+
+ align:start position:0%
+times T plus 1 times T squared over 2
+ 
+
+ align:start position:0%
+times T plus 1 times T squared over 2
+factorial plus 0 times T it's going to
+
+ align:start position:0%
+factorial plus 0 times T it's going to
+ 
+
+ align:start position:0%
+factorial plus 0 times T it's going to
+in other words be 1 plus T squared over
+
+ align:start position:0%
+in other words be 1 plus T squared over
+ 
+
+ align:start position:0%
+in other words be 1 plus T squared over
+2 factorial plus the next term I it's
+
+ align:start position:0%
+2 factorial plus the next term I it's
+ 
+
+ align:start position:0%
+2 factorial plus the next term I it's
+not on the board but I think you can see
+
+ align:start position:0%
+not on the board but I think you can see
+ 
+
+ align:start position:0%
+not on the board but I think you can see
+it's this and it continues on in the
+
+ align:start position:0%
+it's this and it continues on in the
+ 
+
+ align:start position:0%
+it's this and it continues on in the
+same way how about the lower left term
+
+ align:start position:0%
+same way how about the lower left term
+ 
+
+ align:start position:0%
+same way how about the lower left term
+well that's 0 plus
+
+ align:start position:0%
+well that's 0 plus
+ 
+
+ align:start position:0%
+well that's 0 plus
+T plus 0
+
+ align:start position:0%
+T plus 0
+ 
+
+ align:start position:0%
+T plus 0
+plus T cubed over 3 factorial and so on
+
+ align:start position:0%
+plus T cubed over 3 factorial and so on
+ 
+
+ align:start position:0%
+plus T cubed over 3 factorial and so on
+so it's T plus T cubed over 3 factorial
+
+ align:start position:0%
+so it's T plus T cubed over 3 factorial
+ 
+
+ align:start position:0%
+so it's T plus T cubed over 3 factorial
+plus T to the fifth over 5 factorial the
+
+ align:start position:0%
+plus T to the fifth over 5 factorial the
+ 
+
+ align:start position:0%
+plus T to the fifth over 5 factorial the
+other terms and the other two corners
+
+ align:start position:0%
+other terms and the other two corners
+ 
+
+ align:start position:0%
+other terms and the other two corners
+are just the same as these this one for
+
+ align:start position:0%
+are just the same as these this one for
+ 
+
+ align:start position:0%
+are just the same as these this one for
+example is 0 plus T plus 0 plus T cubed
+
+ align:start position:0%
+example is 0 plus T plus 0 plus T cubed
+ 
+
+ align:start position:0%
+example is 0 plus T plus 0 plus T cubed
+over 3 factorial and the lower one is 1
+
+ align:start position:0%
+over 3 factorial and the lower one is 1
+ 
+
+ align:start position:0%
+over 3 factorial and the lower one is 1
+plus 0 plus T squared and so on so it's
+
+ align:start position:0%
+plus 0 plus T squared and so on so it's
+ 
+
+ align:start position:0%
+plus 0 plus T squared and so on so it's
+this it's the same as 1
+
+ align:start position:0%
+this it's the same as 1
+ 
+
+ align:start position:0%
+this it's the same as 1
+plus T squared over 2 factorial and so
+
+ align:start position:0%
+plus T squared over 2 factorial and so
+ 
+
+ align:start position:0%
+plus T squared over 2 factorial and so
+on and up here we have T plus T cubed
+
+ align:start position:0%
+on and up here we have T plus T cubed
+ 
+
+ align:start position:0%
+on and up here we have T plus T cubed
+over 3 factorial and so on well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that matrix doesn't look very square but
+
+ align:start position:0%
+that matrix doesn't look very square but
+ 
+
+ align:start position:0%
+that matrix doesn't look very square but
+it is it looks it's infinitely long
+
+ align:start position:0%
+it is it looks it's infinitely long
+ 
+
+ align:start position:0%
+it is it looks it's infinitely long
+physically but it isn't it's got one
+
+ align:start position:0%
+physically but it isn't it's got one
+ 
+
+ align:start position:0%
+physically but it isn't it's got one
+term here one term here one term here
+
+ align:start position:0%
+term here one term here one term here
+ 
+
+ align:start position:0%
+term here one term here one term here
+one term there now all we have to do is
+
+ align:start position:0%
+one term there now all we have to do is
+ 
+
+ align:start position:0%
+one term there now all we have to do is
+make those terms look a little better
+
+ align:start position:0%
+make those terms look a little better
+ 
+
+ align:start position:0%
+make those terms look a little better
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+here I have to rely on the culture which
+
+ align:start position:0%
+here I have to rely on the culture which
+ 
+
+ align:start position:0%
+here I have to rely on the culture which
+you may or may not possess you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would know what these series were if
+
+ align:start position:0%
+would know what these series were if
+ 
+
+ align:start position:0%
+would know what these series were if
+only they alternated their signs if
+
+ align:start position:0%
+only they alternated their signs if
+ 
+
+ align:start position:0%
+only they alternated their signs if
+this were a negative negative negative
+
+ align:start position:0%
+this were a negative negative negative
+ 
+
+ align:start position:0%
+this were a negative negative negative
+that the top would be cosine T and this
+
+ align:start position:0%
+that the top would be cosine T and this
+ 
+
+ align:start position:0%
+that the top would be cosine T and this
+would be sine T but they don't so
+
+ align:start position:0%
+would be sine T but they don't so
+ 
+
+ align:start position:0%
+would be sine T but they don't so
+they are the next best thing they are
+
+ align:start position:0%
+they are the next best thing they are
+ 
+
+ align:start position:0%
+they are the next best thing they are
+hyperbolic
+
+ align:start position:0%
+hyperbolic
+ 
+
+ align:start position:0%
+hyperbolic
+right the top is not costs cosine T but
+
+ align:start position:0%
+right the top is not costs cosine T but
+ 
+
+ align:start position:0%
+right the top is not costs cosine T but
+cosh T the bottom is 60 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we know this because you remember
+
+ align:start position:0%
+how do we know this because you remember
+ 
+
+ align:start position:0%
+how do we know this because you remember
+and what if I don't remember well
+
+ align:start position:0%
+and what if I don't remember well
+ 
+
+ align:start position:0%
+and what if I don't remember well
+you don't now that's
+
+ align:start position:0%
+you don't now that's
+ 
+
+ align:start position:0%
+you don't now that's
+why you come to class well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for those of you who don't and in fact
+
+ align:start position:0%
+for those of you who don't and in fact
+ 
+
+ align:start position:0%
+for those of you who don't and in fact
+remember the nice way to so this is e to
+
+ align:start position:0%
+remember the nice way to so this is e to
+ 
+
+ align:start position:0%
+remember the nice way to so this is e to
+the T plus e to the negative T it should
+
+ align:start position:0%
+the T plus e to the negative T it should
+ 
+
+ align:start position:0%
+the T plus e to the negative T it should
+be over two but I don't have room to put
+
+ align:start position:0%
+be over two but I don't have room to put
+ 
+
+ align:start position:0%
+be over two but I don't have room to put
+in the two this
+
+ align:start position:0%
+in the two this
+ 
+
+ align:start position:0%
+in the two this
+doesn't mean I will omit it it just
+
+ align:start position:0%
+doesn't mean I will omit it it just
+ 
+
+ align:start position:0%
+doesn't mean I will omit it it just
+means I will put
+
+ align:start position:0%
+means I will put
+ 
+
+ align:start position:0%
+means I will put
+it in at the end by
+
+ align:start position:0%
+it in at the end by
+ 
+
+ align:start position:0%
+it in at the end by
+multiplying every entry of this matrix
+
+ align:start position:0%
+multiplying every entry of this matrix
+ 
+
+ align:start position:0%
+multiplying every entry of this matrix
+by one-half so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you've forgotten what cosh T is it's
+
+ align:start position:0%
+if you've forgotten what cosh T is it's
+ 
+
+ align:start position:0%
+if you've forgotten what cosh T is it's
+e to the T plus e to the negative T
+
+ align:start position:0%
+e to the T plus e to the negative T
+ 
+
+ align:start position:0%
+e to the T plus e to the negative T
+divided by two and the same similar
+
+ align:start position:0%
+divided by two and the same similar
+ 
+
+ align:start position:0%
+divided by two and the same similar
+thing for sin T so there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is your first explicit exponential
+
+ align:start position:0%
+is your first explicit exponential
+ 
+
+ align:start position:0%
+is your first explicit exponential
+matrix calculated according to the
+
+ align:start position:0%
+matrix calculated according to the
+ 
+
+ align:start position:0%
+matrix calculated according to the
+definition and what we have found is the
+
+ align:start position:0%
+definition and what we have found is the
+ 
+
+ align:start position:0%
+definition and what we have found is the
+solution to the system X prime equals y
+
+ align:start position:0%
+solution to the system X prime equals y
+ 
+
+ align:start position:0%
+solution to the system X prime equals y
+Y prime equals x a fundamental matrix in
+
+ align:start position:0%
+Y prime equals x a fundamental matrix in
+ 
+
+ align:start position:0%
+Y prime equals x a fundamental matrix in
+other words our cosh T and since T
+
+ align:start position:0%
+other words our cosh T and since T
+ 
+
+ align:start position:0%
+other words our cosh T and since T
+satisfy both of those satisfy our both
+
+ align:start position:0%
+satisfy both of those satisfy our both
+ 
+
+ align:start position:0%
+satisfy both of those satisfy our both
+solutions for that system now there's
+
+ align:start position:0%
+solutions for that system now there's
+ 
+
+ align:start position:0%
+solutions for that system now there's
+one thing people love the exponential
+
+ align:start position:0%
+one thing people love the exponential
+ 
+
+ align:start position:0%
+one thing people love the exponential
+matrix in particular for and that is the
+
+ align:start position:0%
+matrix in particular for and that is the
+ 
+
+ align:start position:0%
+matrix in particular for and that is the
+ease with which it solves the initial
+
+ align:start position:0%
+ease with which it solves the initial
+ 
+
+ align:start position:0%
+ease with which it solves the initial
+value problem it's exactly what happens
+
+ align:start position:0%
+value problem it's exactly what happens
+ 
+
+ align:start position:0%
+value problem it's exactly what happens
+in studying the single system the single
+
+ align:start position:0%
+in studying the single system the single
+ 
+
+ align:start position:0%
+in studying the single system the single
+equation X prime equals ax but we'll
+
+ align:start position:0%
+equation X prime equals ax but we'll
+ 
+
+ align:start position:0%
+equation X prime equals ax but we'll
+let's do it in general let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do it in general what's
+
+ align:start position:0%
+do it in general what's
+ 
+
+ align:start position:0%
+do it in general what's
+the initial value problem well the
+
+ align:start position:0%
+the initial value problem well the
+ 
+
+ align:start position:0%
+the initial value problem well the
+initial value problem is we start with
+
+ align:start position:0%
+initial value problem is we start with
+ 
+
+ align:start position:0%
+initial value problem is we start with
+our old system but now I want to put it
+
+ align:start position:0%
+our old system but now I want to put it
+ 
+
+ align:start position:0%
+our old system but now I want to put it
+plug in initial conditions I want the
+
+ align:start position:0%
+plug in initial conditions I want the
+ 
+
+ align:start position:0%
+plug in initial conditions I want the
+particular solution which satisfies the
+
+ align:start position:0%
+particular solution which satisfies the
+ 
+
+ align:start position:0%
+particular solution which satisfies the
+initial in addition let's let's make it
+
+ align:start position:0%
+initial in addition let's let's make it
+ 
+
+ align:start position:0%
+initial in addition let's let's make it
+at zero so to avoid complications to
+
+ align:start position:0%
+at zero so to avoid complications to
+ 
+
+ align:start position:0%
+at zero so to avoid complications to
+avoid a lot of notation this is to be
+
+ align:start position:0%
+avoid a lot of notation this is to be
+ 
+
+ align:start position:0%
+avoid a lot of notation this is to be
+some starting value so this is a
+
+ align:start position:0%
+some starting value so this is a
+ 
+
+ align:start position:0%
+some starting value so this is a
+constant certain constant vector is to
+
+ align:start position:0%
+constant certain constant vector is to
+ 
+
+ align:start position:0%
+constant certain constant vector is to
+be the value of the solution at zero and
+
+ align:start position:0%
+be the value of the solution at zero and
+ 
+
+ align:start position:0%
+be the value of the solution at zero and
+the problem is find what X of T is well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're using X the experiential
+
+ align:start position:0%
+if you're using X the experiential
+ 
+
+ align:start position:0%
+if you're using X the experiential
+matrix it's a joke it's a joke so
+
+ align:start position:0%
+matrix it's a joke it's a joke so
+ 
+
+ align:start position:0%
+matrix it's a joke it's a joke so
+I derive it or just do it all right
+
+ align:start position:0%
+I derive it or just do it all right
+ 
+
+ align:start position:0%
+I derive it or just do it all right
+the general solution let's
+
+ align:start position:0%
+the general solution let's
+ 
+
+ align:start position:0%
+the general solution let's
+derive it and then I'll put up the final
+
+ align:start position:0%
+derive it and then I'll put up the final
+ 
+
+ align:start position:0%
+derive it and then I'll put up the final
+formula in a box so that you'll know
+
+ align:start position:0%
+formula in a box so that you'll know
+ 
+
+ align:start position:0%
+formula in a box so that you'll know
+it's important what's the general
+
+ align:start position:0%
+it's important what's the general
+ 
+
+ align:start position:0%
+it's important what's the general
+solution well I did that for you at the
+
+ align:start position:0%
+solution well I did that for you at the
+ 
+
+ align:start position:0%
+solution well I did that for you at the
+beginning of the period once you have an
+
+ align:start position:0%
+beginning of the period once you have an
+ 
+
+ align:start position:0%
+beginning of the period once you have an
+X once you have a fundamental matrix you
+
+ align:start position:0%
+X once you have a fundamental matrix you
+ 
+
+ align:start position:0%
+X once you have a fundamental matrix you
+get the general solution by multiplying
+
+ align:start position:0%
+get the general solution by multiplying
+ 
+
+ align:start position:0%
+get the general solution by multiplying
+it on the right by an arbitrary constant
+
+ align:start position:0%
+it on the right by an arbitrary constant
+ 
+
+ align:start position:0%
+it on the right by an arbitrary constant
+vector so the general solution is going
+
+ align:start position:0%
+vector so the general solution is going
+ 
+
+ align:start position:0%
+vector so the general solution is going
+to be x equals e to the 80 that's my
+
+ align:start position:0%
+to be x equals e to the 80 that's my
+ 
+
+ align:start position:0%
+to be x equals e to the 80 that's my
+super fundamental matrix found without
+
+ align:start position:0%
+super fundamental matrix found without
+ 
+
+ align:start position:0%
+super fundamental matrix found without
+eigenvalues and eigenvectors and this
+
+ align:start position:0%
+eigenvalues and eigenvectors and this
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors and this
+should be multiplied by some unknown
+
+ align:start position:0%
+should be multiplied by some unknown
+ 
+
+ align:start position:0%
+should be multiplied by some unknown
+constant vector C so the only question
+
+ align:start position:0%
+constant vector C so the only question
+ 
+
+ align:start position:0%
+constant vector C so the only question
+is what should the constant vector C be
+
+ align:start position:0%
+is what should the constant vector C be
+ 
+
+ align:start position:0%
+is what should the constant vector C be
+so we'll plug in to find C I'll plug in
+
+ align:start position:0%
+so we'll plug in to find C I'll plug in
+ 
+
+ align:start position:0%
+so we'll plug in to find C I'll plug in
+0 when T is 0 here I get x is 0 here I
+
+ align:start position:0%
+0 when T is 0 here I get x is 0 here I
+ 
+
+ align:start position:0%
+0 when T is 0 here I get x is 0 here I
+get e to the a times 0 times C now
+
+ align:start position:0%
+get e to the a times 0 times C now
+ 
+
+ align:start position:0%
+get e to the a times 0 times C now
+what's this this is the vector of
+
+ align:start position:0%
+what's this this is the vector of
+ 
+
+ align:start position:0%
+what's this this is the vector of
+initial conditions what's e to the a
+
+ align:start position:0%
+initial conditions what's e to the a
+ 
+
+ align:start position:0%
+initial conditions what's e to the a
+times 0 e to the a times 0 plug
+
+ align:start position:0%
+times 0 e to the a times 0 plug
+ 
+
+ align:start position:0%
+times 0 e to the a times 0 plug
+in T equals 0 what do you get by
+
+ align:start position:0%
+in T equals 0 what do you get by
+ 
+
+ align:start position:0%
+in T equals 0 what do you get by
+I therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+is what C is X 0 it's a total joke it's
+
+ align:start position:0%
+is what C is X 0 it's a total joke it's
+ 
+
+ align:start position:0%
+is what C is X 0 it's a total joke it's
+a total joke and the solution is the
+
+ align:start position:0%
+a total joke and the solution is the
+ 
+
+ align:start position:0%
+a total joke and the solution is the
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+value problem is x equals e to
+
+ align:start position:0%
+value problem is x equals e to
+ 
+
+ align:start position:0%
+value problem is x equals e to
+the 80 times
+
+ align:start position:0%
+the 80 times
+ 
+
+ align:start position:0%
+the 80 times
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+just what it would have been it one
+
+ align:start position:0%
+just what it would have been it one
+ 
+
+ align:start position:0%
+just what it would have been it one
+variable the only difference is that
+
+ align:start position:0%
+variable the only difference is that
+ 
+
+ align:start position:0%
+variable the only difference is that
+here we're allowed to put the C out
+
+ align:start position:0%
+here we're allowed to put the C out
+ 
+
+ align:start position:0%
+here we're allowed to put the C out
+front in other words if I asked you to
+
+ align:start position:0%
+front in other words if I asked you to
+ 
+
+ align:start position:0%
+front in other words if I asked you to
+put in the initial condition you
+
+ align:start position:0%
+put in the initial condition you
+ 
+
+ align:start position:0%
+put in the initial condition you
+probably write x equals little x 0 times
+
+ align:start position:0%
+probably write x equals little x 0 times
+ 
+
+ align:start position:0%
+probably write x equals little x 0 times
+e to the a T and you would be tempted to
+
+ align:start position:0%
+e to the a T and you would be tempted to
+ 
+
+ align:start position:0%
+e to the a T and you would be tempted to
+do the same thing here x equals vector X
+
+ align:start position:0%
+do the same thing here x equals vector X
+ 
+
+ align:start position:0%
+do the same thing here x equals vector X
+equals vector X 0 times e to the a T now
+
+ align:start position:0%
+equals vector X 0 times e to the a T now
+ 
+
+ align:start position:0%
+equals vector X 0 times e to the a T now
+you can't do that and if you try to you
+
+ align:start position:0%
+you can't do that and if you try to you
+ 
+
+ align:start position:0%
+you can't do that and if you try to you
+know MATLAB will hiccup and say illegal
+
+ align:start position:0%
+know MATLAB will hiccup and say illegal
+ 
+
+ align:start position:0%
+know MATLAB will hiccup and say illegal
+operation what's the illegal operation
+
+ align:start position:0%
+operation what's the illegal operation
+ 
+
+ align:start position:0%
+operation what's the illegal operation
+well X is a column vector from
+
+ align:start position:0%
+well X is a column vector from
+ 
+
+ align:start position:0%
+well X is a column vector from
+the system it's a column vector that
+
+ align:start position:0%
+the system it's a column vector that
+ 
+
+ align:start position:0%
+the system it's a column vector that
+means the initial conditions are also a
+
+ align:start position:0%
+means the initial conditions are also a
+ 
+
+ align:start position:0%
+means the initial conditions are also a
+column vector you cannot multiply a
+
+ align:start position:0%
+column vector you cannot multiply a
+ 
+
+ align:start position:0%
+column vector you cannot multiply a
+column vector out front and the square
+
+ align:start position:0%
+column vector out front and the square
+ 
+
+ align:start position:0%
+column vector out front and the square
+matrix afterwards you you can't if
+
+ align:start position:0%
+matrix afterwards you you can't if
+ 
+
+ align:start position:0%
+matrix afterwards you you can't if
+you want to multiply a matrix by a
+
+ align:start position:0%
+you want to multiply a matrix by a
+ 
+
+ align:start position:0%
+you want to multiply a matrix by a
+column vector it has to come afterwards
+
+ align:start position:0%
+column vector it has to come afterwards
+ 
+
+ align:start position:0%
+column vector it has to come afterwards
+so you can do zing-zing there is no zing
+
+ align:start position:0%
+so you can do zing-zing there is no zing
+ 
+
+ align:start position:0%
+so you can do zing-zing there is no zing
+you see there is no you can't put it in
+
+ align:start position:0%
+you see there is no you can't put it in
+ 
+
+ align:start position:0%
+you see there is no you can't put it in
+front it doesn't work so
+
+ align:start position:0%
+front it doesn't work so
+ 
+
+ align:start position:0%
+front it doesn't work so
+it must go behind that's the only place
+
+ align:start position:0%
+it must go behind that's the only place
+ 
+
+ align:start position:0%
+it must go behind that's the only place
+you might get tripped up and as I say if
+
+ align:start position:0%
+you might get tripped up and as I say if
+ 
+
+ align:start position:0%
+you might get tripped up and as I say if
+you try to type that in using MATLAB you
+
+ align:start position:0%
+you try to type that in using MATLAB you
+ 
+
+ align:start position:0%
+you try to type that in using MATLAB you
+will immediately get error messages that
+
+ align:start position:0%
+will immediately get error messages that
+ 
+
+ align:start position:0%
+will immediately get error messages that
+you it's illegal can't do that so anyway
+
+ align:start position:0%
+you it's illegal can't do that so anyway
+ 
+
+ align:start position:0%
+you it's illegal can't do that so anyway
+we've got our solution so
+
+ align:start position:0%
+we've got our solution so
+ 
+
+ align:start position:0%
+we've got our solution so
+here's our there's our system let's say
+
+ align:start position:0%
+here's our there's our system let's say
+ 
+
+ align:start position:0%
+here's our there's our system let's say
+it's our
+
+ align:start position:0%
+it's our
+ 
+
+ align:start position:0%
+it's our
+initial value problem anyway is in pink
+
+ align:start position:0%
+initial value problem anyway is in pink
+ 
+
+ align:start position:0%
+initial value problem anyway is in pink
+and it's solution using the exponential
+
+ align:start position:0%
+and it's solution using the exponential
+ 
+
+ align:start position:0%
+and it's solution using the exponential
+matrix is in green now the
+
+ align:start position:0%
+matrix is in green now the
+ 
+
+ align:start position:0%
+matrix is in green now the
+only problem is we still have to talk a
+
+ align:start position:0%
+only problem is we still have to talk a
+ 
+
+ align:start position:0%
+only problem is we still have to talk a
+little bit more about calculating this
+
+ align:start position:0%
+little bit more about calculating this
+ 
+
+ align:start position:0%
+little bit more about calculating this
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the principle warning
+
+ align:start position:0%
+the principle warning
+ 
+
+ align:start position:0%
+the principle warning
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+an exponential matrix is that once
+
+ align:start position:0%
+an exponential matrix is that once
+ 
+
+ align:start position:0%
+an exponential matrix is that once
+you've gotten by the simplest things
+
+ align:start position:0%
+you've gotten by the simplest things
+ 
+
+ align:start position:0%
+you've gotten by the simplest things
+involving it the fact that it solves
+
+ align:start position:0%
+involving it the fact that it solves
+ 
+
+ align:start position:0%
+involving it the fact that it solves
+systems gives you the fundamental matrix
+
+ align:start position:0%
+systems gives you the fundamental matrix
+ 
+
+ align:start position:0%
+systems gives you the fundamental matrix
+for a system then you start flexing your
+
+ align:start position:0%
+for a system then you start flexing your
+ 
+
+ align:start position:0%
+for a system then you start flexing your
+muscles and say oh well I see what else
+
+ align:start position:0%
+muscles and say oh well I see what else
+ 
+
+ align:start position:0%
+muscles and say oh well I see what else
+we can do with this for example the
+
+ align:start position:0%
+we can do with this for example the
+ 
+
+ align:start position:0%
+we can do with this for example the
+reason Exponential's came into being in
+
+ align:start position:0%
+reason Exponential's came into being in
+ 
+
+ align:start position:0%
+reason Exponential's came into being in
+the first place is because of the
+
+ align:start position:0%
+the first place is because of the
+ 
+
+ align:start position:0%
+the first place is because of the
+exponential law right I'll kill anybody
+
+ align:start position:0%
+exponential law right I'll kill anybody
+ 
+
+ align:start position:0%
+exponential law right I'll kill anybody
+types who sends me email say Gary what's
+
+ align:start position:0%
+types who sends me email say Gary what's
+ 
+
+ align:start position:0%
+types who sends me email say Gary what's
+the exponential law alright okay the
+
+ align:start position:0%
+the exponential law alright okay the
+ 
+
+ align:start position:0%
+the exponential law alright okay the
+exponential law would say that e to the
+
+ align:start position:0%
+exponential law would say that e to the
+ 
+
+ align:start position:0%
+exponential law would say that e to the
+a plus B is equal to e to the a times e
+
+ align:start position:0%
+a plus B is equal to e to the a times e
+ 
+
+ align:start position:0%
+a plus B is equal to e to the a times e
+to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law of exponents in other words it's the
+
+ align:start position:0%
+law of exponents in other words it's the
+ 
+
+ align:start position:0%
+law of exponents in other words it's the
+thing which makes the exponential
+
+ align:start position:0%
+thing which makes the exponential
+ 
+
+ align:start position:0%
+thing which makes the exponential
+function different from all other
+
+ align:start position:0%
+function different from all other
+ 
+
+ align:start position:0%
+function different from all other
+functions they do satisfy something like
+
+ align:start position:0%
+functions they do satisfy something like
+ 
+
+ align:start position:0%
+functions they do satisfy something like
+that now first of all does this make
+
+ align:start position:0%
+that now first of all does this make
+ 
+
+ align:start position:0%
+that now first of all does this make
+sense that is a other symbols compatible
+
+ align:start position:0%
+sense that is a other symbols compatible
+ 
+
+ align:start position:0%
+sense that is a other symbols compatible
+let's see this is a 2 by 2 matrix this
+
+ align:start position:0%
+let's see this is a 2 by 2 matrix this
+ 
+
+ align:start position:0%
+let's see this is a 2 by 2 matrix this
+is a 2 by 2 matrix so it does make sense
+
+ align:start position:0%
+is a 2 by 2 matrix so it does make sense
+ 
+
+ align:start position:0%
+is a 2 by 2 matrix so it does make sense
+to multiply them and the answer will be
+
+ align:start position:0%
+to multiply them and the answer will be
+ 
+
+ align:start position:0%
+to multiply them and the answer will be
+a 2 by 2 matrix how about here this is a
+
+ align:start position:0%
+a 2 by 2 matrix how about here this is a
+ 
+
+ align:start position:0%
+a 2 by 2 matrix how about here this is a
+2 by 2 matrix add this to it it's still
+
+ align:start position:0%
+2 by 2 matrix add this to it it's still
+ 
+
+ align:start position:0%
+2 by 2 matrix add this to it it's still
+a 2 by 2 matrix e to a 2 by 2 matrix
+
+ align:start position:0%
+a 2 by 2 matrix e to a 2 by 2 matrix
+ 
+
+ align:start position:0%
+a 2 by 2 matrix e to a 2 by 2 matrix
+still comes out to be a 2 by 2 matrix so
+
+ align:start position:0%
+still comes out to be a 2 by 2 matrix so
+ 
+
+ align:start position:0%
+still comes out to be a 2 by 2 matrix so
+both sides are legitimate 2 by 2
+
+ align:start position:0%
+both sides are legitimate 2 by 2
+ 
+
+ align:start position:0%
+both sides are legitimate 2 by 2
+matrices the only question is are they
+
+ align:start position:0%
+matrices the only question is are they
+ 
+
+ align:start position:0%
+matrices the only question is are they
+equal and the answer is not in a pig's
+
+ align:start position:0%
+equal and the answer is not in a pig's
+ 
+
+ align:start position:0%
+equal and the answer is not in a pig's
+eye how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could this be well I didn't make up
+
+ align:start position:0%
+could this be well I didn't make up
+ 
+
+ align:start position:0%
+could this be well I didn't make up
+these laws I just obey them it's
+
+ align:start position:0%
+these laws I just obey them it's
+ 
+
+ align:start position:0%
+these laws I just obey them it's
+all I wish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I had time to do a little calculation to
+
+ align:start position:0%
+I had time to do a little calculation to
+ 
+
+ align:start position:0%
+I had time to do a little calculation to
+show you that it's not true but I can it
+
+ align:start position:0%
+show you that it's not true but I can it
+ 
+
+ align:start position:0%
+show you that it's not true but I can it
+is true in a certain special cases it's
+
+ align:start position:0%
+is true in a certain special cases it's
+ 
+
+ align:start position:0%
+is true in a certain special cases it's
+true in the special case and
+
+ align:start position:0%
+true in the special case and
+ 
+
+ align:start position:0%
+true in the special case and
+this is pretty much if and only if
+
+ align:start position:0%
+this is pretty much if and only if
+ 
+
+ align:start position:0%
+this is pretty much if and only if
+statement the
+
+ align:start position:0%
+statement the
+ 
+
+ align:start position:0%
+statement the
+only case in which it's true is if a and
+
+ align:start position:0%
+only case in which it's true is if a and
+ 
+
+ align:start position:0%
+only case in which it's true is if a and
+B are not arbitrary square matrices but
+
+ align:start position:0%
+B are not arbitrary square matrices but
+ 
+
+ align:start position:0%
+B are not arbitrary square matrices but
+commute with each other you
+
+ align:start position:0%
+commute with each other you
+ 
+
+ align:start position:0%
+commute with each other you
+see if you if you start writing out the
+
+ align:start position:0%
+see if you if you start writing out the
+ 
+
+ align:start position:0%
+see if you if you start writing out the
+series to try to check whether that law
+
+ align:start position:0%
+series to try to check whether that law
+ 
+
+ align:start position:0%
+series to try to check whether that law
+is true you'll get a bunch of terms here
+
+ align:start position:0%
+is true you'll get a bunch of terms here
+ 
+
+ align:start position:0%
+is true you'll get a bunch of terms here
+a bunch of terms here - you'll find that
+
+ align:start position:0%
+a bunch of terms here - you'll find that
+ 
+
+ align:start position:0%
+a bunch of terms here - you'll find that
+those terms are pairwise equal only if
+
+ align:start position:0%
+those terms are pairwise equal only if
+ 
+
+ align:start position:0%
+those terms are pairwise equal only if
+you're allowed to let the bait receipts
+
+ align:start position:0%
+you're allowed to let the bait receipts
+ 
+
+ align:start position:0%
+you're allowed to let the bait receipts
+commute with each other in other words
+
+ align:start position:0%
+commute with each other in other words
+ 
+
+ align:start position:0%
+commute with each other in other words
+if you can't earn a B plus ba into twice
+
+ align:start position:0%
+if you can't earn a B plus ba into twice
+ 
+
+ align:start position:0%
+if you can't earn a B plus ba into twice
+a B then everything will work fine but
+
+ align:start position:0%
+a B then everything will work fine but
+ 
+
+ align:start position:0%
+a B then everything will work fine but
+if you can't do that it will not now
+
+ align:start position:0%
+if you can't do that it will not now
+ 
+
+ align:start position:0%
+if you can't do that it will not now
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+do two square matrices commute with each
+
+ align:start position:0%
+do two square matrices commute with each
+ 
+
+ align:start position:0%
+do two square matrices commute with each
+other the answer is almost never it's
+
+ align:start position:0%
+other the answer is almost never it's
+ 
+
+ align:start position:0%
+other the answer is almost never it's
+just a lucky accident if they do oh but
+
+ align:start position:0%
+just a lucky accident if they do oh but
+ 
+
+ align:start position:0%
+just a lucky accident if they do oh but
+there are three cases of the lucky
+
+ align:start position:0%
+there are three cases of the lucky
+ 
+
+ align:start position:0%
+there are three cases of the lucky
+accident which you have which you should
+
+ align:start position:0%
+accident which you have which you should
+ 
+
+ align:start position:0%
+accident which you have which you should
+know so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the three cases I feel justified calling
+
+ align:start position:0%
+the three cases I feel justified calling
+ 
+
+ align:start position:0%
+the three cases I feel justified calling
+it luck three cases the
+
+ align:start position:0%
+it luck three cases the
+ 
+
+ align:start position:0%
+it luck three cases the
+three oh
+
+ align:start position:0%
+three oh
+ 
+
+ align:start position:0%
+three oh
+well I don't know if again shouldn't do
+
+ align:start position:0%
+well I don't know if again shouldn't do
+ 
+
+ align:start position:0%
+well I don't know if again shouldn't do
+that so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the three most significant there
+
+ align:start position:0%
+the three most significant there
+ 
+
+ align:start position:0%
+the three most significant there
+examples are example number one when a
+
+ align:start position:0%
+examples are example number one when a
+ 
+
+ align:start position:0%
+examples are example number one when a
+is a constant times the identity matrix
+
+ align:start position:0%
+is a constant times the identity matrix
+ 
+
+ align:start position:0%
+is a constant times the identity matrix
+in other words when a is a matrix which
+
+ align:start position:0%
+in other words when a is a matrix which
+ 
+
+ align:start position:0%
+in other words when a is a matrix which
+looks like this that matrix commutes
+
+ align:start position:0%
+looks like this that matrix commutes
+ 
+
+ align:start position:0%
+looks like this that matrix commutes
+with every other square matrix if that's
+
+ align:start position:0%
+with every other square matrix if that's
+ 
+
+ align:start position:0%
+with every other square matrix if that's
+a then this will a be B a is always true
+
+ align:start position:0%
+a then this will a be B a is always true
+ 
+
+ align:start position:0%
+a then this will a be B a is always true
+and you're allowed to use this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's one case another case when a
+
+ align:start position:0%
+so that's one case another case when a
+ 
+
+ align:start position:0%
+so that's one case another case when a
+is more general is when B is equal to
+
+ align:start position:0%
+is more general is when B is equal to
+ 
+
+ align:start position:0%
+is more general is when B is equal to
+negative a I think you can see that
+
+ align:start position:0%
+negative a I think you can see that
+ 
+
+ align:start position:0%
+negative a I think you can see that
+that's going to work because a times
+
+ align:start position:0%
+that's going to work because a times
+ 
+
+ align:start position:0%
+that's going to work because a times
+minus a is equal to minus a times a yeah
+
+ align:start position:0%
+minus a is equal to minus a times a yeah
+ 
+
+ align:start position:0%
+minus a is equal to minus a times a yeah
+they're both equal to a squared except
+
+ align:start position:0%
+they're both equal to a squared except
+ 
+
+ align:start position:0%
+they're both equal to a squared except
+with a negative sign in front Oh
+
+ align:start position:0%
+with a negative sign in front Oh
+ 
+
+ align:start position:0%
+with a negative sign in front Oh
+the third case is when B is equal to the
+
+ align:start position:0%
+the third case is when B is equal to the
+ 
+
+ align:start position:0%
+the third case is when B is equal to the
+inverse of a because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a a inverse is the same as a inverse a
+
+ align:start position:0%
+a a inverse is the same as a inverse a
+ 
+
+ align:start position:0%
+a a inverse is the same as a inverse a
+they're both the identity of course
+
+ align:start position:0%
+they're both the identity of course
+ 
+
+ align:start position:0%
+they're both the identity of course
+they must have an adverse okay
+
+ align:start position:0%
+they must have an adverse okay
+ 
+
+ align:start position:0%
+they must have an adverse okay
+let's suppose it does now of them this
+
+ align:start position:0%
+let's suppose it does now of them this
+ 
+
+ align:start position:0%
+let's suppose it does now of them this
+is the I think the most important one
+
+ align:start position:0%
+is the I think the most important one
+ 
+
+ align:start position:0%
+is the I think the most important one
+because it leads to this law which is is
+
+ align:start position:0%
+because it leads to this law which is is
+ 
+
+ align:start position:0%
+because it leads to this law which is is
+the form in which you shouldn't that's
+
+ align:start position:0%
+the form in which you shouldn't that's
+ 
+
+ align:start position:0%
+the form in which you shouldn't that's
+forbidden but there's one case of it
+
+ align:start position:0%
+forbidden but there's one case of it
+ 
+
+ align:start position:0%
+forbidden but there's one case of it
+which is forbidden which is not
+
+ align:start position:0%
+which is forbidden which is not
+ 
+
+ align:start position:0%
+which is forbidden which is not
+forbidden and that's here what will it
+
+ align:start position:0%
+forbidden and that's here what will it
+ 
+
+ align:start position:0%
+forbidden and that's here what will it
+say well that will say that e to the a
+
+ align:start position:0%
+say well that will say that e to the a
+ 
+
+ align:start position:0%
+say well that will say that e to the a
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+a is equal to e to the a times e to the
+
+ align:start position:0%
+a is equal to e to the a times e to the
+ 
+
+ align:start position:0%
+a is equal to e to the a times e to the
+negative a so
+
+ align:start position:0%
+negative a so
+ 
+
+ align:start position:0%
+negative a so
+this is true even though the general law
+
+ align:start position:0%
+this is true even though the general law
+ 
+
+ align:start position:0%
+this is true even though the general law
+is false it's because a and negative a
+
+ align:start position:0%
+is false it's because a and negative a
+ 
+
+ align:start position:0%
+is false it's because a and negative a
+commute with each other but now what
+
+ align:start position:0%
+commute with each other but now what
+ 
+
+ align:start position:0%
+commute with each other but now what
+does this say what's e to the 0 matrix
+
+ align:start position:0%
+does this say what's e to the 0 matrix
+ 
+
+ align:start position:0%
+does this say what's e to the 0 matrix
+in other words suppose I take the matrix
+
+ align:start position:0%
+in other words suppose I take the matrix
+ 
+
+ align:start position:0%
+in other words suppose I take the matrix
+that's 0 and plug it into the formula
+
+ align:start position:0%
+that's 0 and plug it into the formula
+ 
+
+ align:start position:0%
+that's 0 and plug it into the formula
+for e what do you get e to the 0 times T
+
+ align:start position:0%
+for e what do you get e to the 0 times T
+ 
+
+ align:start position:0%
+for e what do you get e to the 0 times T
+is I it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has to be a 2 by 2 matrix if it's going
+
+ align:start position:0%
+has to be a 2 by 2 matrix if it's going
+ 
+
+ align:start position:0%
+has to be a 2 by 2 matrix if it's going
+to be anything it's the matrix I so this
+
+ align:start position:0%
+to be anything it's the matrix I so this
+ 
+
+ align:start position:0%
+to be anything it's the matrix I so this
+side is I this
+
+ align:start position:0%
+side is I this
+ 
+
+ align:start position:0%
+side is I this
+side is the exponential matrix and what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that show it shows that the inverse
+
+ align:start position:0%
+does that show it shows that the inverse
+ 
+
+ align:start position:0%
+does that show it shows that the inverse
+matrix to e to the a is e to the
+
+ align:start position:0%
+matrix to e to the a is e to the
+ 
+
+ align:start position:0%
+matrix to e to the a is e to the
+negative a that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a very useful fact that the inverse -
+
+ align:start position:0%
+a very useful fact that the inverse -
+ 
+
+ align:start position:0%
+a very useful fact that the inverse -
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is the main survivor of the exponential
+
+ align:start position:0%
+is the main survivor of the exponential
+ 
+
+ align:start position:0%
+is the main survivor of the exponential
+law general it's false but this standard
+
+ align:start position:0%
+law general it's false but this standard
+ 
+
+ align:start position:0%
+law general it's false but this standard
+corollary the exponential law is true is
+
+ align:start position:0%
+corollary the exponential law is true is
+ 
+
+ align:start position:0%
+corollary the exponential law is true is
+equal to e to the minus a just what you
+
+ align:start position:0%
+equal to e to the minus a just what you
+ 
+
+ align:start position:0%
+equal to e to the minus a just what you
+would dream and hope would be true okay
+
+ align:start position:0%
+would dream and hope would be true okay
+ 
+
+ align:start position:0%
+would dream and hope would be true okay
+I've got exactly two and a half minutes
+
+ align:start position:0%
+I've got exactly two and a half minutes
+ 
+
+ align:start position:0%
+I've got exactly two and a half minutes
+left which to do the impossible all
+
+ align:start position:0%
+left which to do the impossible all
+ 
+
+ align:start position:0%
+left which to do the impossible all
+right the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question is how do you to calculate e to
+
+ align:start position:0%
+question is how do you to calculate e to
+ 
+
+ align:start position:0%
+question is how do you to calculate e to
+the 18 you
+
+ align:start position:0%
+the 18 you
+ 
+
+ align:start position:0%
+the 18 you
+can use series but
+
+ align:start position:0%
+can use series but
+ 
+
+ align:start position:0%
+can use series but
+rarely works it's too hard you know
+
+ align:start position:0%
+rarely works it's too hard you know
+ 
+
+ align:start position:0%
+rarely works it's too hard you know
+there are a few examples you'll have
+
+ align:start position:0%
+there are a few examples you'll have
+ 
+
+ align:start position:0%
+there are a few examples you'll have
+some more for homework but in general
+
+ align:start position:0%
+some more for homework but in general
+ 
+
+ align:start position:0%
+some more for homework but in general
+it's too hard because it's too hard to
+
+ align:start position:0%
+it's too hard because it's too hard to
+ 
+
+ align:start position:0%
+it's too hard because it's too hard to
+calculate the powers of a general matrix
+
+ align:start position:0%
+calculate the powers of a general matrix
+ 
+
+ align:start position:0%
+calculate the powers of a general matrix
+a there's another method which depends
+
+ align:start position:0%
+a there's another method which depends
+ 
+
+ align:start position:0%
+a there's another method which depends
+is useful only for matrices which are
+
+ align:start position:0%
+is useful only for matrices which are
+ 
+
+ align:start position:0%
+is useful only for matrices which are
+symmetric but
+
+ align:start position:0%
+symmetric but
+ 
+
+ align:start position:0%
+symmetric but
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+well it's more than symmetric these two
+
+ align:start position:0%
+well it's more than symmetric these two
+ 
+
+ align:start position:0%
+well it's more than symmetric these two
+have to be the same but you can handle
+
+ align:start position:0%
+have to be the same but you can handle
+ 
+
+ align:start position:0%
+have to be the same but you can handle
+those as you'll see from the homework
+
+ align:start position:0%
+those as you'll see from the homework
+ 
+
+ align:start position:0%
+those as you'll see from the homework
+problems by breaking it up this way and
+
+ align:start position:0%
+problems by breaking it up this way and
+ 
+
+ align:start position:0%
+problems by breaking it up this way and
+using the exponential law so this would
+
+ align:start position:0%
+using the exponential law so this would
+ 
+
+ align:start position:0%
+using the exponential law so this would
+be 0 b b0 see these two matrices commute
+
+ align:start position:0%
+be 0 b b0 see these two matrices commute
+ 
+
+ align:start position:0%
+be 0 b b0 see these two matrices commute
+with each other and therefore I can use
+
+ align:start position:0%
+with each other and therefore I can use
+ 
+
+ align:start position:0%
+with each other and therefore I can use
+the exponential law this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leaves all other cases and here's the
+
+ align:start position:0%
+leaves all other cases and here's the
+ 
+
+ align:start position:0%
+leaves all other cases and here's the
+way to handle all other cases all
+
+ align:start position:0%
+way to handle all other cases all
+ 
+
+ align:start position:0%
+way to handle all other cases all
+other cases in other words if you can't
+
+ align:start position:0%
+other cases in other words if you can't
+ 
+
+ align:start position:0%
+other cases in other words if you can't
+calculate the series of the this trick
+
+ align:start position:0%
+calculate the series of the this trick
+ 
+
+ align:start position:0%
+calculate the series of the this trick
+doesn't work I've
+
+ align:start position:0%
+doesn't work I've
+ 
+
+ align:start position:0%
+doesn't work I've
+done as follows
+
+ align:start position:0%
+done as follows
+ 
+
+ align:start position:0%
+done as follows
+you start with an X an arbitrary
+
+ align:start position:0%
+you start with an X an arbitrary
+ 
+
+ align:start position:0%
+you start with an X an arbitrary
+fundamental matrix not the exponential
+
+ align:start position:0%
+fundamental matrix not the exponential
+ 
+
+ align:start position:0%
+fundamental matrix not the exponential
+matrix you
+
+ align:start position:0%
+matrix you
+ 
+
+ align:start position:0%
+matrix you
+multiply it by its
+
+ align:start position:0%
+multiply it by its
+ 
+
+ align:start position:0%
+multiply it by its
+value at 0 that's a constant matrix and
+
+ align:start position:0%
+value at 0 that's a constant matrix and
+ 
+
+ align:start position:0%
+value at 0 that's a constant matrix and
+you take the inverse of that constant
+
+ align:start position:0%
+you take the inverse of that constant
+ 
+
+ align:start position:0%
+you take the inverse of that constant
+matrix it will have 1 because remember
+
+ align:start position:0%
+matrix it will have 1 because remember
+ 
+
+ align:start position:0%
+matrix it will have 1 because remember
+the fundamental matrix never has
+
+ align:start position:0%
+the fundamental matrix never has
+ 
+
+ align:start position:0%
+the fundamental matrix never has
+determinant 0 so you can always take its
+
+ align:start position:0%
+determinant 0 so you can always take its
+ 
+
+ align:start position:0%
+determinant 0 so you can always take its
+inverse Fredi value of T now what
+
+ align:start position:0%
+inverse Fredi value of T now what
+ 
+
+ align:start position:0%
+inverse Fredi value of T now what
+property does this have it's
+
+ align:start position:0%
+property does this have it's
+ 
+
+ align:start position:0%
+property does this have it's
+a fundamental matrix how
+
+ align:start position:0%
+a fundamental matrix how
+ 
+
+ align:start position:0%
+a fundamental matrix how
+do I know that well because I found all
+
+ align:start position:0%
+do I know that well because I found all
+ 
+
+ align:start position:0%
+do I know that well because I found all
+fundamental matrices for you take any 1
+
+ align:start position:0%
+fundamental matrices for you take any 1
+ 
+
+ align:start position:0%
+fundamental matrices for you take any 1
+multiply it by a square matrix on the
+
+ align:start position:0%
+multiply it by a square matrix on the
+ 
+
+ align:start position:0%
+multiply it by a square matrix on the
+right hand side and you get still a
+
+ align:start position:0%
+right hand side and you get still a
+ 
+
+ align:start position:0%
+right hand side and you get still a
+fundamental matrix and
+
+ align:start position:0%
+fundamental matrix and
+ 
+
+ align:start position:0%
+fundamental matrix and
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+its value at 0 well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is X of 0 times X of 0 inverse so its
+
+ align:start position:0%
+it is X of 0 times X of 0 inverse so its
+ 
+
+ align:start position:0%
+it is X of 0 times X of 0 inverse so its
+value at 0 is the identity now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e to the 80 has these same two
+
+ align:start position:0%
+e to the 80 has these same two
+ 
+
+ align:start position:0%
+e to the 80 has these same two
+properties namely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a fundamental matrix and its value
+
+ align:start position:0%
+it's a fundamental matrix and its value
+ 
+
+ align:start position:0%
+it's a fundamental matrix and its value
+at 0 is the identity conclusion
+
+ align:start position:0%
+at 0 is the identity conclusion
+ 
+
+ align:start position:0%
+at 0 is the identity conclusion
+this is e to the 80 in
+
+ align:start position:0%
+this is e to the 80 in
+ 
+
+ align:start position:0%
+this is e to the 80 in
+other words and that's the
+
+ align:start position:0%
+other words and that's the
+ 
+
+ align:start position:0%
+other words and that's the
+garden-variety method of calculating the
+
+ align:start position:0%
+garden-variety method of calculating the
+ 
+
+ align:start position:0%
+garden-variety method of calculating the
+exponential matrix if you want to give
+
+ align:start position:0%
+exponential matrix if you want to give
+ 
+
+ align:start position:0%
+exponential matrix if you want to give
+it explicitly start with any fundamental
+
+ align:start position:0%
+it explicitly start with any fundamental
+ 
+
+ align:start position:0%
+it explicitly start with any fundamental
+matrix calculated you should forget the
+
+ align:start position:0%
+matrix calculated you should forget the
+ 
+
+ align:start position:0%
+matrix calculated you should forget the
+expression using eigenvalues and
+
+ align:start position:0%
+expression using eigenvalues and
+ 
+
+ align:start position:0%
+expression using eigenvalues and
+eigenvectors and putting the solutions
+
+ align:start position:0%
+eigenvectors and putting the solutions
+ 
+
+ align:start position:0%
+eigenvectors and putting the solutions
+into the columns evaluated
+
+ align:start position:0%
+into the columns evaluated
+ 
+
+ align:start position:0%
+into the columns evaluated
+at zero take its inverse multiply the
+
+ align:start position:0%
+at zero take its inverse multiply the
+ 
+
+ align:start position:0%
+at zero take its inverse multiply the
+two and what you end up with has to be
+
+ align:start position:0%
+two and what you end up with has to be
+ 
+
+ align:start position:0%
+two and what you end up with has to be
+the same as the thing calculated without
+
+ align:start position:0%
+the same as the thing calculated without
+ 
+
+ align:start position:0%
+the same as the thing calculated without
+infinite series okay you'll get lots of
+
+ align:start position:0%
+infinite series okay you'll get lots of
+ 
+
+ align:start position:0%
+infinite series okay you'll get lots of
+practice for homework and tomorrow
\ No newline at end of file
diff --git a/zzKSn1Y80F4.txt b/zzKSn1Y80F4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7989a1cd365298661fc9b60ed70db34fe041cc9a
--- /dev/null
+++ b/zzKSn1Y80F4.txt
@@ -0,0 +1,7715 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I also had a couple of students asking
+
+ align:start position:0%
+I also had a couple of students asking
+ 
+
+ align:start position:0%
+I also had a couple of students asking
+me about what do you do after this class
+
+ align:start position:0%
+me about what do you do after this class
+ 
+
+ align:start position:0%
+me about what do you do after this class
+if you want to take more classes and
+
+ align:start position:0%
+if you want to take more classes and
+ 
+
+ align:start position:0%
+if you want to take more classes and
+games if you want to take more classes
+
+ align:start position:0%
+games if you want to take more classes
+ 
+
+ align:start position:0%
+games if you want to take more classes
+in game design if you're thinking about
+
+ align:start position:0%
+in game design if you're thinking about
+ 
+
+ align:start position:0%
+in game design if you're thinking about
+the the spring semester I just wanted to
+
+ align:start position:0%
+the the spring semester I just wanted to
+ 
+
+ align:start position:0%
+the the spring semester I just wanted to
+throw some course numbers up here so
+
+ align:start position:0%
+throw some course numbers up here so
+ 
+
+ align:start position:0%
+throw some course numbers up here so
+there's CMS 301 is introduction to game
+
+ align:start position:0%
+there's CMS 301 is introduction to game
+ 
+
+ align:start position:0%
+there's CMS 301 is introduction to game
+design methods if you're interested in
+
+ align:start position:0%
+design methods if you're interested in
+ 
+
+ align:start position:0%
+design methods if you're interested in
+design research if you're interested in
+
+ align:start position:0%
+design research if you're interested in
+ 
+
+ align:start position:0%
+design research if you're interested in
+design methods and you happen to also be
+
+ align:start position:0%
+design methods and you happen to also be
+ 
+
+ align:start position:0%
+design methods and you happen to also be
+interested in games but you're likely
+
+ align:start position:0%
+interested in games but you're likely
+ 
+
+ align:start position:0%
+interested in games but you're likely
+going to be doing things in design
+
+ align:start position:0%
+going to be doing things in design
+ 
+
+ align:start position:0%
+going to be doing things in design
+elsewhere so that might be application
+
+ align:start position:0%
+elsewhere so that might be application
+ 
+
+ align:start position:0%
+elsewhere so that might be application
+design toy design anything physical
+
+ align:start position:0%
+design toy design anything physical
+ 
+
+ align:start position:0%
+design toy design anything physical
+anything game like whatever the methods
+
+ align:start position:0%
+anything game like whatever the methods
+ 
+
+ align:start position:0%
+anything game like whatever the methods
+are going to teach them there are going
+
+ align:start position:0%
+are going to teach them there are going
+ 
+
+ align:start position:0%
+are going to teach them there are going
+to be useful for all those things but
+
+ align:start position:0%
+to be useful for all those things but
+ 
+
+ align:start position:0%
+to be useful for all those things but
+the class is focused on as using game
+
+ align:start position:0%
+the class is focused on as using game
+ 
+
+ align:start position:0%
+the class is focused on as using game
+design as a way to talk about design
+
+ align:start position:0%
+design as a way to talk about design
+ 
+
+ align:start position:0%
+design as a way to talk about design
+methods so CMS 301 CMS 608 the class
+
+ align:start position:0%
+methods so CMS 301 CMS 608 the class
+ 
+
+ align:start position:0%
+methods so CMS 301 CMS 608 the class
+Philip teaches and I co-teach with them
+
+ align:start position:0%
+Philip teaches and I co-teach with them
+ 
+
+ align:start position:0%
+Philip teaches and I co-teach with them
+on game design so if you want to know
+
+ align:start position:0%
+on game design so if you want to know
+ 
+
+ align:start position:0%
+on game design so if you want to know
+more about how games are designed some
+
+ align:start position:0%
+more about how games are designed some
+ 
+
+ align:start position:0%
+more about how games are designed some
+topics we talk about are things like
+
+ align:start position:0%
+topics we talk about are things like
+ 
+
+ align:start position:0%
+topics we talk about are things like
+game balance seems tuning the projects
+
+ align:start position:0%
+game balance seems tuning the projects
+ 
+
+ align:start position:0%
+game balance seems tuning the projects
+are all board games and card games so
+
+ align:start position:0%
+are all board games and card games so
+ 
+
+ align:start position:0%
+are all board games and card games so
+the entire class is done with analog
+
+ align:start position:0%
+the entire class is done with analog
+ 
+
+ align:start position:0%
+the entire class is done with analog
+game design so we can actually get more
+
+ align:start position:0%
+game design so we can actually get more
+ 
+
+ align:start position:0%
+game design so we can actually get more
+more detail into how rules work how
+
+ align:start position:0%
+more detail into how rules work how
+ 
+
+ align:start position:0%
+more detail into how rules work how
+rules mix together we play a bunch of
+
+ align:start position:0%
+rules mix together we play a bunch of
+ 
+
+ align:start position:0%
+rules mix together we play a bunch of
+board games we analyze them and then we
+
+ align:start position:0%
+board games we analyze them and then we
+ 
+
+ align:start position:0%
+board games we analyze them and then we
+make board games it's very similarly
+
+ align:start position:0%
+make board games it's very similarly
+ 
+
+ align:start position:0%
+make board games it's very similarly
+structured in this class it's team-based
+
+ align:start position:0%
+structured in this class it's team-based
+ 
+
+ align:start position:0%
+structured in this class it's team-based
+you'll do for game design projects in
+
+ align:start position:0%
+you'll do for game design projects in
+ 
+
+ align:start position:0%
+you'll do for game design projects in
+that class there is CMS 610 that is
+
+ align:start position:0%
+that class there is CMS 610 that is
+ 
+
+ align:start position:0%
+that class there is CMS 610 that is
+media industries and systems the art
+
+ align:start position:0%
+media industries and systems the art
+ 
+
+ align:start position:0%
+media industries and systems the art
+science and business of games as topic
+
+ align:start position:0%
+science and business of games as topic
+ 
+
+ align:start position:0%
+science and business of games as topic
+Chris Weaver from Bethesda Softworks he
+
+ align:start position:0%
+Chris Weaver from Bethesda Softworks he
+ 
+
+ align:start position:0%
+Chris Weaver from Bethesda Softworks he
+worked on the Elder Scrolls series for a
+
+ align:start position:0%
+worked on the Elder Scrolls series for a
+ 
+
+ align:start position:0%
+worked on the Elder Scrolls series for a
+while his class is focused on the
+
+ align:start position:0%
+while his class is focused on the
+ 
+
+ align:start position:0%
+while his class is focused on the
+business and publish your side of the
+
+ align:start position:0%
+business and publish your side of the
+ 
+
+ align:start position:0%
+business and publish your side of the
+equation of game development so if
+
+ align:start position:0%
+equation of game development so if
+ 
+
+ align:start position:0%
+equation of game development so if
+you're thinking about doing this as a
+
+ align:start position:0%
+you're thinking about doing this as a
+ 
+
+ align:start position:0%
+you're thinking about doing this as a
+professional career at some point you're
+
+ align:start position:0%
+professional career at some point you're
+ 
+
+ align:start position:0%
+professional career at some point you're
+likely gonna have to deal with
+
+ align:start position:0%
+likely gonna have to deal with
+ 
+
+ align:start position:0%
+likely gonna have to deal with
+publishers either you're going to be
+
+ align:start position:0%
+publishers either you're going to be
+ 
+
+ align:start position:0%
+publishers either you're going to be
+working for one you're the studio will
+
+ align:start position:0%
+working for one you're the studio will
+ 
+
+ align:start position:0%
+working for one you're the studio will
+be working for one or you will be
+
+ align:start position:0%
+be working for one or you will be
+ 
+
+ align:start position:0%
+be working for one or you will be
+pitching one to one yourself so the big
+
+ align:start position:0%
+pitching one to one yourself so the big
+ 
+
+ align:start position:0%
+pitching one to one yourself so the big
+focus of that class is the pitch how do
+
+ align:start position:0%
+focus of that class is the pitch how do
+ 
+
+ align:start position:0%
+focus of that class is the pitch how do
+you pitch your ideas to another group
+
+ align:start position:0%
+you pitch your ideas to another group
+ 
+
+ align:start position:0%
+you pitch your ideas to another group
+and it's also focused on the demo so if
+
+ align:start position:0%
+and it's also focused on the demo so if
+ 
+
+ align:start position:0%
+and it's also focused on the demo so if
+anybody's heard of the term e3 demo
+
+ align:start position:0%
+anybody's heard of the term e3 demo
+ 
+
+ align:start position:0%
+anybody's heard of the term e3 demo
+basically how to make your game look
+
+ align:start position:0%
+basically how to make your game look
+ 
+
+ align:start position:0%
+basically how to make your game look
+good even though it doesn't work
+
+ align:start position:0%
+good even though it doesn't work
+ 
+
+ align:start position:0%
+good even though it doesn't work
+hopefully the game works at the end but
+
+ align:start position:0%
+hopefully the game works at the end but
+ 
+
+ align:start position:0%
+hopefully the game works at the end but
+it's really focused on what do you need
+
+ align:start position:0%
+it's really focused on what do you need
+ 
+
+ align:start position:0%
+it's really focused on what do you need
+in your game in order to communicate
+
+ align:start position:0%
+in your game in order to communicate
+ 
+
+ align:start position:0%
+in your game in order to communicate
+that game to another person in order to
+
+ align:start position:0%
+that game to another person in order to
+ 
+
+ align:start position:0%
+that game to another person in order to
+fit to order to provide funding for your
+
+ align:start position:0%
+fit to order to provide funding for your
+ 
+
+ align:start position:0%
+fit to order to provide funding for your
+game so that's CMS 610 really great
+
+ align:start position:0%
+game so that's CMS 610 really great
+ 
+
+ align:start position:0%
+game so that's CMS 610 really great
+course he has a lot of really good war
+
+ align:start position:0%
+course he has a lot of really good war
+ 
+
+ align:start position:0%
+course he has a lot of really good war
+stories from what the game development
+
+ align:start position:0%
+stories from what the game development
+ 
+
+ align:start position:0%
+stories from what the game development
+process was like from the 80s on up and
+
+ align:start position:0%
+process was like from the 80s on up and
+ 
+
+ align:start position:0%
+process was like from the 80s on up and
+then lastly see ms 617 Sarah and I teach
+
+ align:start position:0%
+then lastly see ms 617 Sarah and I teach
+ 
+
+ align:start position:0%
+then lastly see ms 617 Sarah and I teach
+that course it's called advanced game
+
+ align:start position:0%
+that course it's called advanced game
+ 
+
+ align:start position:0%
+that course it's called advanced game
+studio it's basically an independent
+
+ align:start position:0%
+studio it's basically an independent
+ 
+
+ align:start position:0%
+studio it's basically an independent
+study but with teams to make games you
+
+ align:start position:0%
+study but with teams to make games you
+ 
+
+ align:start position:0%
+study but with teams to make games you
+spend the entire semester making a
+
+ align:start position:0%
+spend the entire semester making a
+ 
+
+ align:start position:0%
+spend the entire semester making a
+single game Sarah and I act kind of as
+
+ align:start position:0%
+single game Sarah and I act kind of as
+ 
+
+ align:start position:0%
+single game Sarah and I act kind of as
+your publisher kind of as your mom and
+
+ align:start position:0%
+your publisher kind of as your mom and
+ 
+
+ align:start position:0%
+your publisher kind of as your mom and
+dad kind of as your mentor basically we
+
+ align:start position:0%
+dad kind of as your mentor basically we
+ 
+
+ align:start position:0%
+dad kind of as your mentor basically we
+are there to help you make your game to
+
+ align:start position:0%
+are there to help you make your game to
+ 
+
+ align:start position:0%
+are there to help you make your game to
+help your game from start to finish on
+
+ align:start position:0%
+help your game from start to finish on
+ 
+
+ align:start position:0%
+help your game from start to finish on
+behalf something that you can you could
+
+ align:start position:0%
+behalf something that you can you could
+ 
+
+ align:start position:0%
+behalf something that you can you could
+either submit to a festival you could
+
+ align:start position:0%
+either submit to a festival you could
+ 
+
+ align:start position:0%
+either submit to a festival you could
+show to another person put in a
+
+ align:start position:0%
+show to another person put in a
+ 
+
+ align:start position:0%
+show to another person put in a
+portfolio before you start this class
+
+ align:start position:0%
+portfolio before you start this class
+ 
+
+ align:start position:0%
+portfolio before you start this class
+you should be in a team already so we'll
+
+ align:start position:0%
+you should be in a team already so we'll
+ 
+
+ align:start position:0%
+you should be in a team already so we'll
+be sending emails out out about this we
+
+ align:start position:0%
+be sending emails out out about this we
+ 
+
+ align:start position:0%
+be sending emails out out about this we
+try to do a few events in January for
+
+ align:start position:0%
+try to do a few events in January for
+ 
+
+ align:start position:0%
+try to do a few events in January for
+networking and for people to meet each
+
+ align:start position:0%
+networking and for people to meet each
+ 
+
+ align:start position:0%
+networking and for people to meet each
+other to form teams but you can form
+
+ align:start position:0%
+other to form teams but you can form
+ 
+
+ align:start position:0%
+other to form teams but you can form
+teams with people you've met in this
+
+ align:start position:0%
+teams with people you've met in this
+ 
+
+ align:start position:0%
+teams with people you've met in this
+class in other classes I have a feeling
+
+ align:start position:0%
+class in other classes I have a feeling
+ 
+
+ align:start position:0%
+class in other classes I have a feeling
+that people who took this class last
+
+ align:start position:0%
+that people who took this class last
+ 
+
+ align:start position:0%
+that people who took this class last
+year are going to be looking for teams
+
+ align:start position:0%
+year are going to be looking for teams
+ 
+
+ align:start position:0%
+year are going to be looking for teams
+for this year so there'll be there'll be
+
+ align:start position:0%
+for this year so there'll be there'll be
+ 
+
+ align:start position:0%
+for this year so there'll be there'll be
+some emails going out around December
+
+ align:start position:0%
+some emails going out around December
+ 
+
+ align:start position:0%
+some emails going out around December
+and January and hopefully a one or two
+
+ align:start position:0%
+and January and hopefully a one or two
+ 
+
+ align:start position:0%
+and January and hopefully a one or two
+events going on at the lab in January
+
+ align:start position:0%
+events going on at the lab in January
+ 
+
+ align:start position:0%
+events going on at the lab in January
+about that um yeah and then if anybody
+
+ align:start position:0%
+about that um yeah and then if anybody
+ 
+
+ align:start position:0%
+about that um yeah and then if anybody
+has any questions about if you want a
+
+ align:start position:0%
+has any questions about if you want a
+ 
+
+ align:start position:0%
+has any questions about if you want a
+minor in in games I'm at MIT if you want
+
+ align:start position:0%
+minor in in games I'm at MIT if you want
+ 
+
+ align:start position:0%
+minor in in games I'm at MIT if you want
+to do a concentration in games at MIT
+
+ align:start position:0%
+to do a concentration in games at MIT
+ 
+
+ align:start position:0%
+to do a concentration in games at MIT
+you can do that through comparative
+
+ align:start position:0%
+you can do that through comparative
+ 
+
+ align:start position:0%
+you can do that through comparative
+Media Studies and writing you can talk
+
+ align:start position:0%
+Media Studies and writing you can talk
+ 
+
+ align:start position:0%
+Media Studies and writing you can talk
+to me about that after class you can
+
+ align:start position:0%
+to me about that after class you can
+ 
+
+ align:start position:0%
+to me about that after class you can
+also go to the CMS w website and talk to
+
+ align:start position:0%
+also go to the CMS w website and talk to
+ 
+
+ align:start position:0%
+also go to the CMS w website and talk to
+Rebecca Shepherdson about that about
+
+ align:start position:0%
+Rebecca Shepherdson about that about
+ 
+
+ align:start position:0%
+Rebecca Shepherdson about that about
+what the requirements are for that but
+
+ align:start position:0%
+what the requirements are for that but
+ 
+
+ align:start position:0%
+what the requirements are for that but
+say full its comparative Media Studies
+
+ align:start position:0%
+say full its comparative Media Studies
+ 
+
+ align:start position:0%
+say full its comparative Media Studies
+it's multiple media but you can also
+
+ align:start position:0%
+it's multiple media but you can also
+ 
+
+ align:start position:0%
+it's multiple media but you can also
+gains is one of those media that you can
+
+ align:start position:0%
+gains is one of those media that you can
+ 
+
+ align:start position:0%
+gains is one of those media that you can
+focus on and concentrate in okay so that
+
+ align:start position:0%
+focus on and concentrate in okay so that
+ 
+
+ align:start position:0%
+focus on and concentrate in okay so that
+is the advertisement part of this class
+
+ align:start position:0%
+is the advertisement part of this class
+ 
+
+ align:start position:0%
+is the advertisement part of this class
+so today we're going to finish up team
+
+ align:start position:0%
+so today we're going to finish up team
+ 
+
+ align:start position:0%
+so today we're going to finish up team
+formation we're going to i'm going to
+
+ align:start position:0%
+formation we're going to i'm going to
+ 
+
+ align:start position:0%
+formation we're going to i'm going to
+introduce the project for deadlines
+
+ align:start position:0%
+introduce the project for deadlines
+ 
+
+ align:start position:0%
+introduce the project for deadlines
+which i briefly mentioned last week and
+
+ align:start position:0%
+which i briefly mentioned last week and
+ 
+
+ align:start position:0%
+which i briefly mentioned last week and
+then we're going to start project for
+
+ align:start position:0%
+then we're going to start project for
+ 
+
+ align:start position:0%
+then we're going to start project for
+today you've got a lot of time today to
+
+ align:start position:0%
+today you've got a lot of time today to
+ 
+
+ align:start position:0%
+today you've got a lot of time today to
+do brainstorming and to do prototyping
+
+ align:start position:0%
+do brainstorming and to do prototyping
+ 
+
+ align:start position:0%
+do brainstorming and to do prototyping
+in your team's recommend we're
+
+ align:start position:0%
+in your team's recommend we're
+ 
+
+ align:start position:0%
+in your team's recommend we're
+recommending that if you're gonna have
+
+ align:start position:0%
+recommending that if you're gonna have
+ 
+
+ align:start position:0%
+recommending that if you're gonna have
+you're going to have eight person teams
+
+ align:start position:0%
+you're going to have eight person teams
+ 
+
+ align:start position:0%
+you're going to have eight person teams
+breaking up into smaller groups to do
+
+ align:start position:0%
+breaking up into smaller groups to do
+ 
+
+ align:start position:0%
+breaking up into smaller groups to do
+some initial prototyping you want
+
+ align:start position:0%
+some initial prototyping you want
+ 
+
+ align:start position:0%
+some initial prototyping you want
+basically think of this as prototyping
+
+ align:start position:0%
+basically think of this as prototyping
+ 
+
+ align:start position:0%
+basically think of this as prototyping
+as a means of brainstorming to come up
+
+ align:start position:0%
+as a means of brainstorming to come up
+ 
+
+ align:start position:0%
+as a means of brainstorming to come up
+with lots of different kinds of
+
+ align:start position:0%
+with lots of different kinds of
+ 
+
+ align:start position:0%
+with lots of different kinds of
+mechanics actually try those mechanics
+
+ align:start position:0%
+mechanics actually try those mechanics
+ 
+
+ align:start position:0%
+mechanics actually try those mechanics
+out and play with them a little bit
+
+ align:start position:0%
+out and play with them a little bit
+ 
+
+ align:start position:0%
+out and play with them a little bit
+before you before you decide on one
+
+ align:start position:0%
+before you before you decide on one
+ 
+
+ align:start position:0%
+before you before you decide on one
+we're giving you a lot of time to do
+
+ align:start position:0%
+we're giving you a lot of time to do
+ 
+
+ align:start position:0%
+we're giving you a lot of time to do
+this this week because you want we want
+
+ align:start position:0%
+this this week because you want we want
+ 
+
+ align:start position:0%
+this this week because you want we want
+to you to have something playable by
+
+ align:start position:0%
+to you to have something playable by
+ 
+
+ align:start position:0%
+to you to have something playable by
+next Monday that's that four teams we've
+
+ align:start position:0%
+next Monday that's that four teams we've
+ 
+
+ align:start position:0%
+next Monday that's that four teams we've
+got it sounds to me like we had five
+
+ align:start position:0%
+got it sounds to me like we had five
+ 
+
+ align:start position:0%
+got it sounds to me like we had five
+topics that were interesting to folks
+
+ align:start position:0%
+topics that were interesting to folks
+ 
+
+ align:start position:0%
+topics that were interesting to folks
+where does anybody still interested in
+
+ align:start position:0%
+where does anybody still interested in
+ 
+
+ align:start position:0%
+where does anybody still interested in
+the malaria topic okay na malaria why do
+
+ align:start position:0%
+the malaria topic okay na malaria why do
+ 
+
+ align:start position:0%
+the malaria topic okay na malaria why do
+you let me come up here and talk to you
+
+ align:start position:0%
+you let me come up here and talk to you
+ 
+
+ align:start position:0%
+you let me come up here and talk to you
+what was it Ebola Ebola yeah so nobody
+
+ align:start position:0%
+what was it Ebola Ebola yeah so nobody
+ 
+
+ align:start position:0%
+what was it Ebola Ebola yeah so nobody
+was interesting that all right so um
+
+ align:start position:0%
+was interesting that all right so um
+ 
+
+ align:start position:0%
+was interesting that all right so um
+I've got early warning leading to early
+
+ align:start position:0%
+I've got early warning leading to early
+ 
+
+ align:start position:0%
+I've got early warning leading to early
+action for heat waves color prevention
+
+ align:start position:0%
+action for heat waves color prevention
+ 
+
+ align:start position:0%
+action for heat waves color prevention
+and hygiene forecast based funding snap
+
+ align:start position:0%
+and hygiene forecast based funding snap
+ 
+
+ align:start position:0%
+and hygiene forecast based funding snap
+and adapting to climate change even
+
+ align:start position:0%
+and adapting to climate change even
+ 
+
+ align:start position:0%
+and adapting to climate change even
+though we've got five topics that does
+
+ align:start position:0%
+though we've got five topics that does
+ 
+
+ align:start position:0%
+though we've got five topics that does
+not mean we need to have one team per
+
+ align:start position:0%
+not mean we need to have one team per
+ 
+
+ align:start position:0%
+not mean we need to have one team per
+topic some of these some teams we can
+
+ align:start position:0%
+topic some of these some teams we can
+ 
+
+ align:start position:0%
+topic some of these some teams we can
+have multiple teams doing welcome the
+
+ align:start position:0%
+have multiple teams doing welcome the
+ 
+
+ align:start position:0%
+have multiple teams doing welcome the
+same topic and that's okay so raise your
+
+ align:start position:0%
+same topic and that's okay so raise your
+ 
+
+ align:start position:0%
+same topic and that's okay so raise your
+hand if you don't think you're on a team
+
+ align:start position:0%
+hand if you don't think you're on a team
+ 
+
+ align:start position:0%
+hand if you don't think you're on a team
+right now okay it's a good portion of
+
+ align:start position:0%
+right now okay it's a good portion of
+ 
+
+ align:start position:0%
+right now okay it's a good portion of
+you so what we're going to do is just
+
+ align:start position:0%
+you so what we're going to do is just
+ 
+
+ align:start position:0%
+you so what we're going to do is just
+like last time we're going to break up
+
+ align:start position:0%
+like last time we're going to break up
+ 
+
+ align:start position:0%
+like last time we're going to break up
+into groups based in the room if you're
+
+ align:start position:0%
+into groups based in the room if you're
+ 
+
+ align:start position:0%
+into groups based in the room if you're
+interested in the topic go to that group
+
+ align:start position:0%
+interested in the topic go to that group
+ 
+
+ align:start position:0%
+interested in the topic go to that group
+talk with those folks if you are in that
+
+ align:start position:0%
+talk with those folks if you are in that
+ 
+
+ align:start position:0%
+talk with those folks if you are in that
+group and you signed off you said that
+
+ align:start position:0%
+group and you signed off you said that
+ 
+
+ align:start position:0%
+group and you signed off you said that
+you are definitely on this team um
+
+ align:start position:0%
+you are definitely on this team um
+ 
+
+ align:start position:0%
+you are definitely on this team um
+through the mailing list identify
+
+ align:start position:0%
+through the mailing list identify
+ 
+
+ align:start position:0%
+through the mailing list identify
+yourself to the group as yes I signed up
+
+ align:start position:0%
+yourself to the group as yes I signed up
+ 
+
+ align:start position:0%
+yourself to the group as yes I signed up
+for this on the mailing list this is
+
+ align:start position:0%
+for this on the mailing list this is
+ 
+
+ align:start position:0%
+for this on the mailing list this is
+what the team is so far here that people
+
+ align:start position:0%
+what the team is so far here that people
+ 
+
+ align:start position:0%
+what the team is so far here that people
+on this team right now and actually to
+
+ align:start position:0%
+on this team right now and actually to
+ 
+
+ align:start position:0%
+on this team right now and actually to
+help that through what I'm going to do
+
+ align:start position:0%
+help that through what I'm going to do
+ 
+
+ align:start position:0%
+help that through what I'm going to do
+is put these on the board they'd have
+
+ align:start position:0%
+is put these on the board they'd have
+ 
+
+ align:start position:0%
+is put these on the board they'd have
+people who signed up for that team come
+
+ align:start position:0%
+people who signed up for that team come
+ 
+
+ align:start position:0%
+people who signed up for that team come
+down first and then everyone else come
+
+ align:start position:0%
+down first and then everyone else come
+ 
+
+ align:start position:0%
+down first and then everyone else come
+down so over here let's do
+
+ align:start position:0%
+down so over here let's do
+ 
+
+ align:start position:0%
+down so over here let's do
+he weighs over here let's do cholera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+snap climate change and forecast base
+
+ align:start position:0%
+snap climate change and forecast base
+ 
+
+ align:start position:0%
+snap climate change and forecast base
+funding so if you are already on one of
+
+ align:start position:0%
+funding so if you are already on one of
+ 
+
+ align:start position:0%
+funding so if you are already on one of
+these teams and you said this is the
+
+ align:start position:0%
+these teams and you said this is the
+ 
+
+ align:start position:0%
+these teams and you said this is the
+team I want to be on go to that go to
+
+ align:start position:0%
+team I want to be on go to that go to
+ 
+
+ align:start position:0%
+team I want to be on go to that go to
+that area right now yeah whatever that's
+
+ align:start position:0%
+that area right now yeah whatever that's
+ 
+
+ align:start position:0%
+that area right now yeah whatever that's
+guy all right so heat waves one two
+
+ align:start position:0%
+guy all right so heat waves one two
+ 
+
+ align:start position:0%
+guy all right so heat waves one two
+three four five cholera one two three
+
+ align:start position:0%
+three four five cholera one two three
+ 
+
+ align:start position:0%
+three four five cholera one two three
+four five color six cholera seven are
+
+ align:start position:0%
+four five color six cholera seven are
+ 
+
+ align:start position:0%
+four five color six cholera seven are
+you standing up are you anybody here on
+
+ align:start position:0%
+you standing up are you anybody here on
+ 
+
+ align:start position:0%
+you standing up are you anybody here on
+snap one two three four five six seven
+
+ align:start position:0%
+snap one two three four five six seven
+ 
+
+ align:start position:0%
+snap one two three four five six seven
+cool come on if you're on snap come on
+
+ align:start position:0%
+cool come on if you're on snap come on
+ 
+
+ align:start position:0%
+cool come on if you're on snap come on
+down with the rest of the group adapting
+
+ align:start position:0%
+down with the rest of the group adapting
+ 
+
+ align:start position:0%
+down with the rest of the group adapting
+the climate change if you're on the team
+
+ align:start position:0%
+the climate change if you're on the team
+ 
+
+ align:start position:0%
+the climate change if you're on the team
+if you think you're on that team okay
+
+ align:start position:0%
+if you think you're on that team okay
+ 
+
+ align:start position:0%
+if you think you're on that team okay
+and then forecast based funding if you
+
+ align:start position:0%
+and then forecast based funding if you
+ 
+
+ align:start position:0%
+and then forecast based funding if you
+think you're on that team 12 so far okay
+
+ align:start position:0%
+think you're on that team 12 so far okay
+ 
+
+ align:start position:0%
+think you're on that team 12 so far okay
+all right um so if we're going to one
+
+ align:start position:0%
+all right um so if we're going to one
+ 
+
+ align:start position:0%
+all right um so if we're going to one
+two three four five six was only six
+
+ align:start position:0%
+two three four five six was only six
+ 
+
+ align:start position:0%
+two three four five six was only six
+okay so um move to whatever team that
+
+ align:start position:0%
+okay so um move to whatever team that
+ 
+
+ align:start position:0%
+okay so um move to whatever team that
+you're interested in right now talk with
+
+ align:start position:0%
+you're interested in right now talk with
+ 
+
+ align:start position:0%
+you're interested in right now talk with
+some folks talk about if you're on the
+
+ align:start position:0%
+some folks talk about if you're on the
+ 
+
+ align:start position:0%
+some folks talk about if you're on the
+team already talked about some of the
+
+ align:start position:0%
+team already talked about some of the
+ 
+
+ align:start position:0%
+team already talked about some of the
+things that even talk that you talked
+
+ align:start position:0%
+things that even talk that you talked
+ 
+
+ align:start position:0%
+things that even talk that you talked
+about last week brainstorming wives if
+
+ align:start position:0%
+about last week brainstorming wives if
+ 
+
+ align:start position:0%
+about last week brainstorming wives if
+you want to be on that team talk with
+
+ align:start position:0%
+you want to be on that team talk with
+ 
+
+ align:start position:0%
+you want to be on that team talk with
+the members and ask if you can be on
+
+ align:start position:0%
+the members and ask if you can be on
+ 
+
+ align:start position:0%
+the members and ask if you can be on
+that team basically I'm going to check
+
+ align:start position:0%
+that team basically I'm going to check
+ 
+
+ align:start position:0%
+that team basically I'm going to check
+in any o arm in 10 minutes to see what
+
+ align:start position:0%
+in any o arm in 10 minutes to see what
+ 
+
+ align:start position:0%
+in any o arm in 10 minutes to see what
+we look what it looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also wins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right after this amount of discussion
+
+ align:start position:0%
+right after this amount of discussion
+ 
+
+ align:start position:0%
+right after this amount of discussion
+how many people are still undecided
+
+ align:start position:0%
+how many people are still undecided
+ 
+
+ align:start position:0%
+how many people are still undecided
+about what team they want to be on a
+
+ align:start position:0%
+about what team they want to be on a
+ 
+
+ align:start position:0%
+about what team they want to be on a
+kind of a decided anybody else kind of
+
+ align:start position:0%
+kind of a decided anybody else kind of
+ 
+
+ align:start position:0%
+kind of a decided anybody else kind of
+undecided all right so if you are one
+
+ align:start position:0%
+undecided all right so if you are one
+ 
+
+ align:start position:0%
+undecided all right so if you are one
+hundred percent decided put your name on
+
+ align:start position:0%
+hundred percent decided put your name on
+ 
+
+ align:start position:0%
+hundred percent decided put your name on
+your post it put it up on one of these
+
+ align:start position:0%
+your post it put it up on one of these
+ 
+
+ align:start position:0%
+your post it put it up on one of these
+things do it really really quick come up
+
+ align:start position:0%
+things do it really really quick come up
+ 
+
+ align:start position:0%
+things do it really really quick come up
+put it up sit back down please alright
+
+ align:start position:0%
+put it up sit back down please alright
+ 
+
+ align:start position:0%
+put it up sit back down please alright
+so the dangers of having more than than
+
+ align:start position:0%
+so the dangers of having more than than
+ 
+
+ align:start position:0%
+so the dangers of having more than than
+10 people yeah so I in fact just in fact
+
+ align:start position:0%
+10 people yeah so I in fact just in fact
+ 
+
+ align:start position:0%
+10 people yeah so I in fact just in fact
+that there is already dangers of having
+
+ align:start position:0%
+that there is already dangers of having
+ 
+
+ align:start position:0%
+that there is already dangers of having
+eight people or more but this class was
+
+ align:start position:0%
+eight people or more but this class was
+ 
+
+ align:start position:0%
+eight people or more but this class was
+actually intended for you to actually
+
+ align:start position:0%
+actually intended for you to actually
+ 
+
+ align:start position:0%
+actually intended for you to actually
+feel that pressure right we've got a
+
+ align:start position:0%
+feel that pressure right we've got a
+ 
+
+ align:start position:0%
+feel that pressure right we've got a
+person team you're going to have
+
+ align:start position:0%
+person team you're going to have
+ 
+
+ align:start position:0%
+person team you're going to have
+communication problems of the wazoo that
+
+ align:start position:0%
+communication problems of the wazoo that
+ 
+
+ align:start position:0%
+communication problems of the wazoo that
+tables might be careful um yeah your
+
+ align:start position:0%
+tables might be careful um yeah your
+ 
+
+ align:start position:0%
+tables might be careful um yeah your
+laptop's on it the the and once you get
+
+ align:start position:0%
+laptop's on it the the and once you get
+ 
+
+ align:start position:0%
+laptop's on it the the and once you get
+to a 10-person team what we've seen from
+
+ align:start position:0%
+to a 10-person team what we've seen from
+ 
+
+ align:start position:0%
+to a 10-person team what we've seen from
+previous years is that 10 people teens
+
+ align:start position:0%
+previous years is that 10 people teens
+ 
+
+ align:start position:0%
+previous years is that 10 people teens
+don't act 10 people and larger teams
+
+ align:start position:0%
+don't act 10 people and larger teams
+ 
+
+ align:start position:0%
+don't act 10 people and larger teams
+don't actually outperform six person
+
+ align:start position:0%
+don't actually outperform six person
+ 
+
+ align:start position:0%
+don't actually outperform six person
+teams they actually get about the same
+
+ align:start position:0%
+teams they actually get about the same
+ 
+
+ align:start position:0%
+teams they actually get about the same
+amount done or sometimes less because
+
+ align:start position:0%
+amount done or sometimes less because
+ 
+
+ align:start position:0%
+amount done or sometimes less because
+the communication overhead actually
+
+ align:start position:0%
+the communication overhead actually
+ 
+
+ align:start position:0%
+the communication overhead actually
+breaks down further you might get a lot
+
+ align:start position:0%
+breaks down further you might get a lot
+ 
+
+ align:start position:0%
+breaks down further you might get a lot
+of content done and it turns out to be
+
+ align:start position:0%
+of content done and it turns out to be
+ 
+
+ align:start position:0%
+of content done and it turns out to be
+very uneven in quality because you're
+
+ align:start position:0%
+very uneven in quality because you're
+ 
+
+ align:start position:0%
+very uneven in quality because you're
+multiple people doing content now you
+
+ align:start position:0%
+multiple people doing content now you
+ 
+
+ align:start position:0%
+multiple people doing content now you
+could succeed in breaking your team up
+
+ align:start position:0%
+could succeed in breaking your team up
+ 
+
+ align:start position:0%
+could succeed in breaking your team up
+into little subgroups and be able to
+
+ align:start position:0%
+into little subgroups and be able to
+ 
+
+ align:start position:0%
+into little subgroups and be able to
+organize yourselves that way but we've
+
+ align:start position:0%
+organize yourselves that way but we've
+ 
+
+ align:start position:0%
+organize yourselves that way but we've
+never seen it done successfully in this
+
+ align:start position:0%
+never seen it done successfully in this
+ 
+
+ align:start position:0%
+never seen it done successfully in this
+class with students you know with your
+
+ align:start position:0%
+class with students you know with your
+ 
+
+ align:start position:0%
+class with students you know with your
+level of experience so what we won't
+
+ align:start position:0%
+level of experience so what we won't
+ 
+
+ align:start position:0%
+level of experience so what we won't
+recommend is that for a team well if
+
+ align:start position:0%
+recommend is that for a team well if
+ 
+
+ align:start position:0%
+recommend is that for a team well if
+you've got something like 12 people in
+
+ align:start position:0%
+you've got something like 12 people in
+ 
+
+ align:start position:0%
+you've got something like 12 people in
+all 13 people now in a pile 13 yeah you
+
+ align:start position:0%
+all 13 people now in a pile 13 yeah you
+ 
+
+ align:start position:0%
+all 13 people now in a pile 13 yeah you
+will probably get more done by splitting
+
+ align:start position:0%
+will probably get more done by splitting
+ 
+
+ align:start position:0%
+will probably get more done by splitting
+into two groups if you are deliberately
+
+ align:start position:0%
+into two groups if you are deliberately
+ 
+
+ align:start position:0%
+into two groups if you are deliberately
+brainstorming in order to take advantage
+
+ align:start position:0%
+brainstorming in order to take advantage
+ 
+
+ align:start position:0%
+brainstorming in order to take advantage
+of 30 people that of course they are
+
+ align:start position:0%
+of 30 people that of course they are
+ 
+
+ align:start position:0%
+of 30 people that of course they are
+going to come up with a game that can
+
+ align:start position:0%
+going to come up with a game that can
+ 
+
+ align:start position:0%
+going to come up with a game that can
+only be executed by a very large number
+
+ align:start position:0%
+only be executed by a very large number
+ 
+
+ align:start position:0%
+only be executed by a very large number
+of people well we're just saying is that
+
+ align:start position:0%
+of people well we're just saying is that
+ 
+
+ align:start position:0%
+of people well we're just saying is that
+those games have traditionally not done
+
+ align:start position:0%
+those games have traditionally not done
+ 
+
+ align:start position:0%
+those games have traditionally not done
+very very well in in our class they may
+
+ align:start position:0%
+very very well in in our class they may
+ 
+
+ align:start position:0%
+very very well in in our class they may
+be functional they
+
+ align:start position:0%
+be functional they
+ 
+
+ align:start position:0%
+be functional they
+may actually deliver on the thing that
+
+ align:start position:0%
+may actually deliver on the thing that
+ 
+
+ align:start position:0%
+may actually deliver on the thing that
+you intended to make but we've seen six
+
+ align:start position:0%
+you intended to make but we've seen six
+ 
+
+ align:start position:0%
+you intended to make but we've seen six
+person teams too much more partly
+
+ align:start position:0%
+person teams too much more partly
+ 
+
+ align:start position:0%
+person teams too much more partly
+because the iterator whole lot faster
+
+ align:start position:0%
+because the iterator whole lot faster
+ 
+
+ align:start position:0%
+because the iterator whole lot faster
+and they may have smaller ideas but the
+
+ align:start position:0%
+and they may have smaller ideas but the
+ 
+
+ align:start position:0%
+and they may have smaller ideas but the
+ideas end up being a whole lot more
+
+ align:start position:0%
+ideas end up being a whole lot more
+ 
+
+ align:start position:0%
+ideas end up being a whole lot more
+polished so that's our advice to you it
+
+ align:start position:0%
+polished so that's our advice to you it
+ 
+
+ align:start position:0%
+polished so that's our advice to you it
+is I if they really want to do thirteen
+
+ align:start position:0%
+is I if they really want to do thirteen
+ 
+
+ align:start position:0%
+is I if they really want to do thirteen
+percent team are we going to let them um
+
+ align:start position:0%
+percent team are we going to let them um
+ 
+
+ align:start position:0%
+percent team are we going to let them um
+wow yeah judgment against our better
+
+ align:start position:0%
+wow yeah judgment against our better
+ 
+
+ align:start position:0%
+wow yeah judgment against our better
+judgment we might but we're going to
+
+ align:start position:0%
+judgment we might but we're going to
+ 
+
+ align:start position:0%
+judgment we might but we're going to
+really what we're going to ask I think
+
+ align:start position:0%
+really what we're going to ask I think
+ 
+
+ align:start position:0%
+really what we're going to ask I think
+today is to break up into small into two
+
+ align:start position:0%
+today is to break up into small into two
+ 
+
+ align:start position:0%
+today is to break up into small into two
+smaller teams for brainstorming we
+
+ align:start position:0%
+smaller teams for brainstorming we
+ 
+
+ align:start position:0%
+smaller teams for brainstorming we
+actually we want all the big all the big
+
+ align:start position:0%
+actually we want all the big all the big
+ 
+
+ align:start position:0%
+actually we want all the big all the big
+teams to even break up into smaller
+
+ align:start position:0%
+teams to even break up into smaller
+ 
+
+ align:start position:0%
+teams to even break up into smaller
+teams anyway to do some brainstorming
+
+ align:start position:0%
+teams anyway to do some brainstorming
+ 
+
+ align:start position:0%
+teams anyway to do some brainstorming
+and to do some prototyping once you have
+
+ align:start position:0%
+and to do some prototyping once you have
+ 
+
+ align:start position:0%
+and to do some prototyping once you have
+all that figured out in class today by
+
+ align:start position:0%
+all that figured out in class today by
+ 
+
+ align:start position:0%
+all that figured out in class today by
+the end of class today you can decide
+
+ align:start position:0%
+the end of class today you can decide
+ 
+
+ align:start position:0%
+the end of class today you can decide
+how big you want the team to really be
+
+ align:start position:0%
+how big you want the team to really be
+ 
+
+ align:start position:0%
+how big you want the team to really be
+they were the one issue but we have
+
+ align:start position:0%
+they were the one issue but we have
+ 
+
+ align:start position:0%
+they were the one issue but we have
+those we've got some people who are not
+
+ align:start position:0%
+those we've got some people who are not
+ 
+
+ align:start position:0%
+those we've got some people who are not
+in class today who will be coming in the
+
+ align:start position:0%
+in class today who will be coming in the
+ 
+
+ align:start position:0%
+in class today who will be coming in the
+class about the three that we talked
+
+ align:start position:0%
+class about the three that we talked
+ 
+
+ align:start position:0%
+class about the three that we talked
+about there might be one or two more if
+
+ align:start position:0%
+about there might be one or two more if
+ 
+
+ align:start position:0%
+about there might be one or two more if
+there are any other people like that
+
+ align:start position:0%
+there are any other people like that
+ 
+
+ align:start position:0%
+there are any other people like that
+they will be automatically put on the
+
+ align:start position:0%
+they will be automatically put on the
+ 
+
+ align:start position:0%
+they will be automatically put on the
+smallest of these teams so I'd rather
+
+ align:start position:0%
+smallest of these teams so I'd rather
+ 
+
+ align:start position:0%
+smallest of these teams so I'd rather
+them turn into a six person in cholera
+
+ align:start position:0%
+them turn into a six person in cholera
+ 
+
+ align:start position:0%
+them turn into a six person in cholera
+turn 27 rather than an eighth turned in
+
+ align:start position:0%
+turn 27 rather than an eighth turned in
+ 
+
+ align:start position:0%
+turn 27 rather than an eighth turned in
+a night because he's a person teams are
+
+ align:start position:0%
+a night because he's a person teams are
+ 
+
+ align:start position:0%
+a night because he's a person teams are
+actually just good enough yeah the a
+
+ align:start position:0%
+actually just good enough yeah the a
+ 
+
+ align:start position:0%
+actually just good enough yeah the a
+person teams are just about the size
+
+ align:start position:0%
+person teams are just about the size
+ 
+
+ align:start position:0%
+person teams are just about the size
+that we were hoping for six person teams
+
+ align:start position:0%
+that we were hoping for six person teams
+ 
+
+ align:start position:0%
+that we were hoping for six person teams
+actually to be perfectly honest I think
+
+ align:start position:0%
+actually to be perfectly honest I think
+ 
+
+ align:start position:0%
+actually to be perfectly honest I think
+the sixth person teams have an advantage
+
+ align:start position:0%
+the sixth person teams have an advantage
+ 
+
+ align:start position:0%
+the sixth person teams have an advantage
+but you know that's that's just numbers
+
+ align:start position:0%
+but you know that's that's just numbers
+ 
+
+ align:start position:0%
+but you know that's that's just numbers
+that has that just hard that was
+
+ align:start position:0%
+that has that just hard that was
+ 
+
+ align:start position:0%
+that has that just hard that was
+breakdown yeah the when we have seen a
+
+ align:start position:0%
+breakdown yeah the when we have seen a
+ 
+
+ align:start position:0%
+breakdown yeah the when we have seen a
+10-person team actually work what really
+
+ align:start position:0%
+10-person team actually work what really
+ 
+
+ align:start position:0%
+10-person team actually work what really
+happened was it was ten people eight of
+
+ align:start position:0%
+happened was it was ten people eight of
+ 
+
+ align:start position:0%
+happened was it was ten people eight of
+them worked on the game to have worked
+
+ align:start position:0%
+them worked on the game to have worked
+ 
+
+ align:start position:0%
+them worked on the game to have worked
+on the networking component the
+
+ align:start position:0%
+on the networking component the
+ 
+
+ align:start position:0%
+on the networking component the
+networking component did not work yet
+
+ align:start position:0%
+networking component did not work yet
+ 
+
+ align:start position:0%
+networking component did not work yet
+the game was still as feature complete
+
+ align:start position:0%
+the game was still as feature complete
+ 
+
+ align:start position:0%
+the game was still as feature complete
+as it could be without networking it
+
+ align:start position:0%
+as it could be without networking it
+ 
+
+ align:start position:0%
+as it could be without networking it
+could it could work without the
+
+ align:start position:0%
+could it could work without the
+ 
+
+ align:start position:0%
+could it could work without the
+networking that's not what we're looking
+
+ align:start position:0%
+networking that's not what we're looking
+ 
+
+ align:start position:0%
+networking that's not what we're looking
+for we want the the game that you are
+
+ align:start position:0%
+for we want the the game that you are
+ 
+
+ align:start position:0%
+for we want the the game that you are
+submitting the game that you're creating
+
+ align:start position:0%
+submitting the game that you're creating
+ 
+
+ align:start position:0%
+submitting the game that you're creating
+the design document that you're
+
+ align:start position:0%
+the design document that you're
+ 
+
+ align:start position:0%
+the design document that you're
+submitting to us on wednesday and the
+
+ align:start position:0%
+submitting to us on wednesday and the
+ 
+
+ align:start position:0%
+submitting to us on wednesday and the
+game that you're play testing on monday
+
+ align:start position:0%
+game that you're play testing on monday
+ 
+
+ align:start position:0%
+game that you're play testing on monday
+to be the actual game all those features
+
+ align:start position:0%
+to be the actual game all those features
+ 
+
+ align:start position:0%
+to be the actual game all those features
+that you're saying are going to be in
+
+ align:start position:0%
+that you're saying are going to be in
+ 
+
+ align:start position:0%
+that you're saying are going to be in
+that game to be the actual game that you
+
+ align:start position:0%
+that game to be the actual game that you
+ 
+
+ align:start position:0%
+that game to be the actual game that you
+submit at the end of the semester so
+
+ align:start position:0%
+submit at the end of the semester so
+ 
+
+ align:start position:0%
+submit at the end of the semester so
+don't think of it as well if two people
+
+ align:start position:0%
+don't think of it as well if two people
+ 
+
+ align:start position:0%
+don't think of it as well if two people
+flake then it's back up not do people if
+
+ align:start position:0%
+flake then it's back up not do people if
+ 
+
+ align:start position:0%
+flake then it's back up not do people if
+two people flake if you're too big and
+
+ align:start position:0%
+two people flake if you're too big and
+ 
+
+ align:start position:0%
+two people flake if you're too big and
+you've got to people who don't know
+
+ align:start position:0%
+you've got to people who don't know
+ 
+
+ align:start position:0%
+you've got to people who don't know
+what's going on and they caused some
+
+ align:start position:0%
+what's going on and they caused some
+ 
+
+ align:start position:0%
+what's going on and they caused some
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+it's is going to be a disaster for the
+
+ align:start position:0%
+it's is going to be a disaster for the
+ 
+
+ align:start position:0%
+it's is going to be a disaster for the
+entire team did anybody in previous so
+
+ align:start position:0%
+entire team did anybody in previous so
+ 
+
+ align:start position:0%
+entire team did anybody in previous so
+this year all of the projects to and
+
+ align:start position:0%
+this year all of the projects to and
+ 
+
+ align:start position:0%
+this year all of the projects to and
+private three teams were actually bigger
+
+ align:start position:0%
+private three teams were actually bigger
+ 
+
+ align:start position:0%
+private three teams were actually bigger
+than we've done them in LA in previous
+
+ align:start position:0%
+than we've done them in LA in previous
+ 
+
+ align:start position:0%
+than we've done them in LA in previous
+years previous years we were there about
+
+ align:start position:0%
+years previous years we were there about
+ 
+
+ align:start position:0%
+years previous years we were there about
+four people maybe five tops I me how do
+
+ align:start position:0%
+four people maybe five tops I me how do
+ 
+
+ align:start position:0%
+four people maybe five tops I me how do
+you do six and seven I think right did
+
+ align:start position:0%
+you do six and seven I think right did
+ 
+
+ align:start position:0%
+you do six and seven I think right did
+anybody feel like with seven people they
+
+ align:start position:0%
+anybody feel like with seven people they
+ 
+
+ align:start position:0%
+anybody feel like with seven people they
+got a communication method that worked
+
+ align:start position:0%
+got a communication method that worked
+ 
+
+ align:start position:0%
+got a communication method that worked
+really well like already like okay I see
+
+ align:start position:0%
+really well like already like okay I see
+ 
+
+ align:start position:0%
+really well like already like okay I see
+what what was that what was the method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I mean it's the sort of thing they
+
+ align:start position:0%
+yeah I mean it's the sort of thing they
+ 
+
+ align:start position:0%
+yeah I mean it's the sort of thing they
+could what whatever method you use will
+
+ align:start position:0%
+could what whatever method you use will
+ 
+
+ align:start position:0%
+could what whatever method you use will
+definitely improve with practice right
+
+ align:start position:0%
+definitely improve with practice right
+ 
+
+ align:start position:0%
+definitely improve with practice right
+so so so if you got something that sort
+
+ align:start position:0%
+so so so if you got something that sort
+ 
+
+ align:start position:0%
+so so so if you got something that sort
+of worked well something to try again
+
+ align:start position:0%
+of worked well something to try again
+ 
+
+ align:start position:0%
+of worked well something to try again
+but the fact that most people didn't you
+
+ align:start position:0%
+but the fact that most people didn't you
+ 
+
+ align:start position:0%
+but the fact that most people didn't you
+know gives us and it should already give
+
+ align:start position:0%
+know gives us and it should already give
+ 
+
+ align:start position:0%
+know gives us and it should already give
+you some warning of what a large team is
+
+ align:start position:0%
+you some warning of what a large team is
+ 
+
+ align:start position:0%
+you some warning of what a large team is
+going to feel like it's going to be
+
+ align:start position:0%
+going to feel like it's going to be
+ 
+
+ align:start position:0%
+going to feel like it's going to be
+tough for the structure of the class on
+
+ align:start position:0%
+tough for the structure of the class on
+ 
+
+ align:start position:0%
+tough for the structure of the class on
+Wednesday we're going to be talking
+
+ align:start position:0%
+Wednesday we're going to be talking
+ 
+
+ align:start position:0%
+Wednesday we're going to be talking
+about more of the requirements the
+
+ align:start position:0%
+about more of the requirements the
+ 
+
+ align:start position:0%
+about more of the requirements the
+aesthetic requirements for project floor
+
+ align:start position:0%
+aesthetic requirements for project floor
+ 
+
+ align:start position:0%
+aesthetic requirements for project floor
+we talking a little bit well we have
+
+ align:start position:0%
+we talking a little bit well we have
+ 
+
+ align:start position:0%
+we talking a little bit well we have
+another basically another design
+
+ align:start position:0%
+another basically another design
+ 
+
+ align:start position:0%
+another basically another design
+discussion next wednesday on monday
+
+ align:start position:0%
+discussion next wednesday on monday
+ 
+
+ align:start position:0%
+discussion next wednesday on monday
+we're having a short design discussion
+
+ align:start position:0%
+we're having a short design discussion
+ 
+
+ align:start position:0%
+we're having a short design discussion
+about educational games and then we'll
+
+ align:start position:0%
+about educational games and then we'll
+ 
+
+ align:start position:0%
+about educational games and then we'll
+have a one of our first discussions
+
+ align:start position:0%
+have a one of our first discussions
+ 
+
+ align:start position:0%
+have a one of our first discussions
+trying to talk about some of the person
+
+ align:start position:0%
+trying to talk about some of the person
+ 
+
+ align:start position:0%
+trying to talk about some of the person
+the person person issues we see in
+
+ align:start position:0%
+the person person issues we see in
+ 
+
+ align:start position:0%
+the person person issues we see in
+making games but in this case it's team
+
+ align:start position:0%
+making games but in this case it's team
+ 
+
+ align:start position:0%
+making games but in this case it's team
+dynamics and how to identify team
+
+ align:start position:0%
+dynamics and how to identify team
+ 
+
+ align:start position:0%
+dynamics and how to identify team
+dynamics I'll have a couple more talks
+
+ align:start position:0%
+dynamics I'll have a couple more talks
+ 
+
+ align:start position:0%
+dynamics I'll have a couple more talks
+like that to kind of help you get used
+
+ align:start position:0%
+like that to kind of help you get used
+ 
+
+ align:start position:0%
+like that to kind of help you get used
+to running in a bigger team but between
+
+ align:start position:0%
+to running in a bigger team but between
+ 
+
+ align:start position:0%
+to running in a bigger team but between
+now and next monday we're hoping in
+
+ align:start position:0%
+now and next monday we're hoping in
+ 
+
+ align:start position:0%
+now and next monday we're hoping in
+class to give you a plenty of time to
+
+ align:start position:0%
+class to give you a plenty of time to
+ 
+
+ align:start position:0%
+class to give you a plenty of time to
+actually work on some of the send one of
+
+ align:start position:0%
+actually work on some of the send one of
+ 
+
+ align:start position:0%
+actually work on some of the send one of
+the biggest issues with working in a big
+
+ align:start position:0%
+the biggest issues with working in a big
+ 
+
+ align:start position:0%
+the biggest issues with working in a big
+team is just figuring out what is what
+
+ align:start position:0%
+team is just figuring out what is what
+ 
+
+ align:start position:0%
+team is just figuring out what is what
+is that core thing that you're actually
+
+ align:start position:0%
+is that core thing that you're actually
+ 
+
+ align:start position:0%
+is that core thing that you're actually
+making what's the thing you're trying to
+
+ align:start position:0%
+making what's the thing you're trying to
+ 
+
+ align:start position:0%
+making what's the thing you're trying to
+communicate to each other we've talked
+
+ align:start position:0%
+communicate to each other we've talked
+ 
+
+ align:start position:0%
+communicate to each other we've talked
+to talked about how you can use the
+
+ align:start position:0%
+to talked about how you can use the
+ 
+
+ align:start position:0%
+to talked about how you can use the
+division document for that and I you can
+
+ align:start position:0%
+division document for that and I you can
+ 
+
+ align:start position:0%
+division document for that and I you can
+use the prototyping the actual prototype
+
+ align:start position:0%
+use the prototyping the actual prototype
+ 
+
+ align:start position:0%
+use the prototyping the actual prototype
+you make for that but often it is just
+
+ align:start position:0%
+you make for that but often it is just
+ 
+
+ align:start position:0%
+you make for that but often it is just
+having everybody in the same room at the
+
+ align:start position:0%
+having everybody in the same room at the
+ 
+
+ align:start position:0%
+having everybody in the same room at the
+same time talking and just working
+
+ align:start position:0%
+same time talking and just working
+ 
+
+ align:start position:0%
+same time talking and just working
+together so we're trying to give you as
+
+ align:start position:0%
+together so we're trying to give you as
+ 
+
+ align:start position:0%
+together so we're trying to give you as
+much time as you can in class because
+
+ align:start position:0%
+much time as you can in class because
+ 
+
+ align:start position:0%
+much time as you can in class because
+you know hard enough to get six people
+
+ align:start position:0%
+you know hard enough to get six people
+ 
+
+ align:start position:0%
+you know hard enough to get six people
+outside of class to me to let let let
+
+ align:start position:0%
+outside of class to me to let let let
+ 
+
+ align:start position:0%
+outside of class to me to let let let
+alone a a person team right so we're
+
+ align:start position:0%
+alone a a person team right so we're
+ 
+
+ align:start position:0%
+alone a a person team right so we're
+going to give you more time inc
+
+ align:start position:0%
+going to give you more time inc
+ 
+
+ align:start position:0%
+going to give you more time inc
+to meet up with with each other that
+
+ align:start position:0%
+to meet up with with each other that
+ 
+
+ align:start position:0%
+to meet up with with each other that
+does not mean that you should be
+
+ align:start position:0%
+does not mean that you should be
+ 
+
+ align:start position:0%
+does not mean that you should be
+spending all your time and class
+
+ align:start position:0%
+spending all your time and class
+ 
+
+ align:start position:0%
+spending all your time and class
+planning on getting your face to face
+
+ align:start position:0%
+planning on getting your face to face
+ 
+
+ align:start position:0%
+planning on getting your face to face
+coding done that's actually a waste of
+
+ align:start position:0%
+coding done that's actually a waste of
+ 
+
+ align:start position:0%
+coding done that's actually a waste of
+time because you could be talking to
+
+ align:start position:0%
+time because you could be talking to
+ 
+
+ align:start position:0%
+time because you could be talking to
+each other you can do that but things
+
+ align:start position:0%
+each other you can do that but things
+ 
+
+ align:start position:0%
+each other you can do that but things
+like code reviews code reviews stand-up
+
+ align:start position:0%
+like code reviews code reviews stand-up
+ 
+
+ align:start position:0%
+like code reviews code reviews stand-up
+meetings on things like that okay all
+
+ align:start position:0%
+meetings on things like that okay all
+ 
+
+ align:start position:0%
+meetings on things like that okay all
+right so we're going to put this on hold
+
+ align:start position:0%
+right so we're going to put this on hold
+ 
+
+ align:start position:0%
+right so we're going to put this on hold
+for a second I'm going to go over the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very quickly the deadlines and then
+
+ align:start position:0%
+very quickly the deadlines and then
+ 
+
+ align:start position:0%
+very quickly the deadlines and then
+we're going to take a break and come
+
+ align:start position:0%
+we're going to take a break and come
+ 
+
+ align:start position:0%
+we're going to take a break and come
+back so if this will move forward all
+
+ align:start position:0%
+back so if this will move forward all
+ 
+
+ align:start position:0%
+back so if this will move forward all
+right so why did I react so strongly
+
+ align:start position:0%
+right so why did I react so strongly
+ 
+
+ align:start position:0%
+right so why did I react so strongly
+about the animal crossing all these
+
+ align:start position:0%
+about the animal crossing all these
+ 
+
+ align:start position:0%
+about the animal crossing all these
+sorts of minigames because what we're
+
+ align:start position:0%
+sorts of minigames because what we're
+ 
+
+ align:start position:0%
+sorts of minigames because what we're
+asking you to do whoa don't do that all
+
+ align:start position:0%
+asking you to do whoa don't do that all
+ 
+
+ align:start position:0%
+asking you to do whoa don't do that all
+right so what we're asking to do is
+
+ align:start position:0%
+right so what we're asking to do is
+ 
+
+ align:start position:0%
+right so what we're asking to do is
+create a small fully functional polished
+
+ align:start position:0%
+create a small fully functional polished
+ 
+
+ align:start position:0%
+create a small fully functional polished
+browser game one of those mini games
+
+ align:start position:0%
+browser game one of those mini games
+ 
+
+ align:start position:0%
+browser game one of those mini games
+would count as a small fully functional
+
+ align:start position:0%
+would count as a small fully functional
+ 
+
+ align:start position:0%
+would count as a small fully functional
+well-polished browser game we're asking
+
+ align:start position:0%
+well-polished browser game we're asking
+ 
+
+ align:start position:0%
+well-polished browser game we're asking
+you to use the design iteration
+
+ align:start position:0%
+you to use the design iteration
+ 
+
+ align:start position:0%
+you to use the design iteration
+techniques you've used in the past what
+
+ align:start position:0%
+techniques you've used in the past what
+ 
+
+ align:start position:0%
+techniques you've used in the past what
+does that mean we're actually talking
+
+ align:start position:0%
+does that mean we're actually talking
+ 
+
+ align:start position:0%
+does that mean we're actually talking
+about the same design scope as the
+
+ align:start position:0%
+about the same design scope as the
+ 
+
+ align:start position:0%
+about the same design scope as the
+previous two projects is just you spent
+
+ align:start position:0%
+previous two projects is just you spent
+ 
+
+ align:start position:0%
+previous two projects is just you spent
+more time on it to actually get it
+
+ align:start position:0%
+more time on it to actually get it
+ 
+
+ align:start position:0%
+more time on it to actually get it
+working exactly the way you'd want it to
+
+ align:start position:0%
+working exactly the way you'd want it to
+ 
+
+ align:start position:0%
+working exactly the way you'd want it to
+work if you had maybe slightly larger so
+
+ align:start position:0%
+work if you had maybe slightly larger so
+ 
+
+ align:start position:0%
+work if you had maybe slightly larger so
+if your previous two projects had maybe
+
+ align:start position:0%
+if your previous two projects had maybe
+ 
+
+ align:start position:0%
+if your previous two projects had maybe
+one core mechanic and one supplementary
+
+ align:start position:0%
+one core mechanic and one supplementary
+ 
+
+ align:start position:0%
+one core mechanic and one supplementary
+there might be two supplementary
+
+ align:start position:0%
+there might be two supplementary
+ 
+
+ align:start position:0%
+there might be two supplementary
+mechanics to that core but that's about
+
+ align:start position:0%
+mechanics to that core but that's about
+ 
+
+ align:start position:0%
+mechanics to that core but that's about
+it if you've got a game that has an
+
+ align:start position:0%
+it if you've got a game that has an
+ 
+
+ align:start position:0%
+it if you've got a game that has an
+overworld then the overworld should be
+
+ align:start position:0%
+overworld then the overworld should be
+ 
+
+ align:start position:0%
+overworld then the overworld should be
+the bulk of your game if you're spinning
+
+ align:start position:0%
+the bulk of your game if you're spinning
+ 
+
+ align:start position:0%
+the bulk of your game if you're spinning
+if the minigames that you decided to
+
+ align:start position:0%
+if the minigames that you decided to
+ 
+
+ align:start position:0%
+if the minigames that you decided to
+make are the same size is that overworld
+
+ align:start position:0%
+make are the same size is that overworld
+ 
+
+ align:start position:0%
+make are the same size is that overworld
+in scope that's already way too over
+
+ align:start position:0%
+in scope that's already way too over
+ 
+
+ align:start position:0%
+in scope that's already way too over
+scoped that make sense it's an eight
+
+ align:start position:0%
+scoped that make sense it's an eight
+ 
+
+ align:start position:0%
+scoped that make sense it's an eight
+week project we're giving you you've got
+
+ align:start position:0%
+week project we're giving you you've got
+ 
+
+ align:start position:0%
+week project we're giving you you've got
+about two weeks to concept and prototype
+
+ align:start position:0%
+about two weeks to concept and prototype
+ 
+
+ align:start position:0%
+about two weeks to concept and prototype
+multiple game like multiple game
+
+ align:start position:0%
+multiple game like multiple game
+ 
+
+ align:start position:0%
+multiple game like multiple game
+experiences so we're asking for today
+
+ align:start position:0%
+experiences so we're asking for today
+ 
+
+ align:start position:0%
+experiences so we're asking for today
+and tomorrow on Wednesday is you're not
+
+ align:start position:0%
+and tomorrow on Wednesday is you're not
+ 
+
+ align:start position:0%
+and tomorrow on Wednesday is you're not
+just prototyping one game you're
+
+ align:start position:0%
+just prototyping one game you're
+ 
+
+ align:start position:0%
+just prototyping one game you're
+prototyping lots and lots of different
+
+ align:start position:0%
+prototyping lots and lots of different
+ 
+
+ align:start position:0%
+prototyping lots and lots of different
+little games looking at all those games
+
+ align:start position:0%
+little games looking at all those games
+ 
+
+ align:start position:0%
+little games looking at all those games
+you actually have time to spend you're
+
+ align:start position:0%
+you actually have time to spend you're
+ 
+
+ align:start position:0%
+you actually have time to spend you're
+gonna have time to spend on multiple
+
+ align:start position:0%
+gonna have time to spend on multiple
+ 
+
+ align:start position:0%
+gonna have time to spend on multiple
+different prototypes rather than just a
+
+ align:start position:0%
+different prototypes rather than just a
+ 
+
+ align:start position:0%
+different prototypes rather than just a
+single prototype that you iterate on so
+
+ align:start position:0%
+single prototype that you iterate on so
+ 
+
+ align:start position:0%
+single prototype that you iterate on so
+we're asking is if you got an eight
+
+ align:start position:0%
+we're asking is if you got an eight
+ 
+
+ align:start position:0%
+we're asking is if you got an eight
+person team
+
+ align:start position:0%
+person team
+ 
+
+ align:start position:0%
+person team
+break yourself into two groups of four
+
+ align:start position:0%
+break yourself into two groups of four
+ 
+
+ align:start position:0%
+break yourself into two groups of four
+four groups of to create some really
+
+ align:start position:0%
+four groups of to create some really
+ 
+
+ align:start position:0%
+four groups of to create some really
+small bord gáis me looking things some
+
+ align:start position:0%
+small bord gáis me looking things some
+ 
+
+ align:start position:0%
+small bord gáis me looking things some
+very small interactions maybe they're
+
+ align:start position:0%
+very small interactions maybe they're
+ 
+
+ align:start position:0%
+very small interactions maybe they're
+playable maybe there's something you
+
+ align:start position:0%
+playable maybe there's something you
+ 
+
+ align:start position:0%
+playable maybe there's something you
+just described but really go big blue
+
+ align:start position:0%
+just described but really go big blue
+ 
+
+ align:start position:0%
+just described but really go big blue
+sky and try to think of all the
+
+ align:start position:0%
+sky and try to think of all the
+ 
+
+ align:start position:0%
+sky and try to think of all the
+different things that can happen with
+
+ align:start position:0%
+different things that can happen with
+ 
+
+ align:start position:0%
+different things that can happen with
+with these topics that you're dealing
+
+ align:start position:0%
+with these topics that you're dealing
+ 
+
+ align:start position:0%
+with these topics that you're dealing
+with are very large and we make sure
+
+ align:start position:0%
+with are very large and we make sure
+ 
+
+ align:start position:0%
+with are very large and we make sure
+that your design is grounded very very
+
+ align:start position:0%
+that your design is grounded very very
+ 
+
+ align:start position:0%
+that your design is grounded very very
+well granted in the sources that we've
+
+ align:start position:0%
+well granted in the sources that we've
+ 
+
+ align:start position:0%
+well granted in the sources that we've
+been given by the client there's gonna
+
+ align:start position:0%
+been given by the client there's gonna
+ 
+
+ align:start position:0%
+been given by the client there's gonna
+be multiple times when they'll be here
+
+ align:start position:0%
+be multiple times when they'll be here
+ 
+
+ align:start position:0%
+be multiple times when they'll be here
+to see your games and talk about your
+
+ align:start position:0%
+to see your games and talk about your
+ 
+
+ align:start position:0%
+to see your games and talk about your
+games they'll be on your email so that
+
+ align:start position:0%
+games they'll be on your email so that
+ 
+
+ align:start position:0%
+games they'll be on your email so that
+you can ask some questions about that as
+
+ align:start position:0%
+you can ask some questions about that as
+ 
+
+ align:start position:0%
+you can ask some questions about that as
+well so design constraints use all the
+
+ align:start position:0%
+well so design constraints use all the
+ 
+
+ align:start position:0%
+well so design constraints use all the
+mechanics that we've been practicing in
+
+ align:start position:0%
+mechanics that we've been practicing in
+ 
+
+ align:start position:0%
+mechanics that we've been practicing in
+class on with your previous projects not
+
+ align:start position:0%
+class on with your previous projects not
+ 
+
+ align:start position:0%
+class on with your previous projects not
+all not all the mechanics simultaneously
+
+ align:start position:0%
+all not all the mechanics simultaneously
+ 
+
+ align:start position:0%
+all not all the mechanics simultaneously
+use any of those make any of those
+
+ align:start position:0%
+use any of those make any of those
+ 
+
+ align:start position:0%
+use any of those make any of those
+mechanics so it could have trade-offs it
+
+ align:start position:0%
+mechanics so it could have trade-offs it
+ 
+
+ align:start position:0%
+mechanics so it could have trade-offs it
+could have randomest it is not required
+
+ align:start position:0%
+could have randomest it is not required
+ 
+
+ align:start position:0%
+could have randomest it is not required
+to have both it's required to have
+
+ align:start position:0%
+to have both it's required to have
+ 
+
+ align:start position:0%
+to have both it's required to have
+whatever it takes for the project that
+
+ align:start position:0%
+whatever it takes for the project that
+ 
+
+ align:start position:0%
+whatever it takes for the project that
+you're for the topic that you're working
+
+ align:start position:0%
+you're for the topic that you're working
+ 
+
+ align:start position:0%
+you're for the topic that you're working
+on whatever makes sense for the topic
+
+ align:start position:0%
+on whatever makes sense for the topic
+ 
+
+ align:start position:0%
+on whatever makes sense for the topic
+that you're working on those top to tend
+
+ align:start position:0%
+that you're working on those top to tend
+ 
+
+ align:start position:0%
+that you're working on those top to tend
+to be in the realm of what those topics
+
+ align:start position:0%
+to be in the realm of what those topics
+ 
+
+ align:start position:0%
+to be in the realm of what those topics
+kind of lean themselves towards but if
+
+ align:start position:0%
+kind of lean themselves towards but if
+ 
+
+ align:start position:0%
+kind of lean themselves towards but if
+you find something else and you want to
+
+ align:start position:0%
+you find something else and you want to
+ 
+
+ align:start position:0%
+you find something else and you want to
+use that something else great spend some
+
+ align:start position:0%
+use that something else great spend some
+ 
+
+ align:start position:0%
+use that something else great spend some
+time really working on it I spent a
+
+ align:start position:0%
+time really working on it I spent a
+ 
+
+ align:start position:0%
+time really working on it I spent a
+couple weeks working on it before you
+
+ align:start position:0%
+couple weeks working on it before you
+ 
+
+ align:start position:0%
+couple weeks working on it before you
+make a full commitment so your target
+
+ align:start position:0%
+make a full commitment so your target
+ 
+
+ align:start position:0%
+make a full commitment so your target
+audience since each of those topics has
+
+ align:start position:0%
+audience since each of those topics has
+ 
+
+ align:start position:0%
+audience since each of those topics has
+on their own target audiences which they
+
+ align:start position:0%
+on their own target audiences which they
+ 
+
+ align:start position:0%
+on their own target audiences which they
+talked about the top three are the ones
+
+ align:start position:0%
+talked about the top three are the ones
+ 
+
+ align:start position:0%
+talked about the top three are the ones
+to really focus on on depending on your
+
+ align:start position:0%
+to really focus on on depending on your
+ 
+
+ align:start position:0%
+to really focus on on depending on your
+topic so Red Cross staff and volunteers
+
+ align:start position:0%
+topic so Red Cross staff and volunteers
+ 
+
+ align:start position:0%
+topic so Red Cross staff and volunteers
+so people who are knowledgeable and
+
+ align:start position:0%
+so people who are knowledgeable and
+ 
+
+ align:start position:0%
+so people who are knowledgeable and
+motivated about the topic already who
+
+ align:start position:0%
+motivated about the topic already who
+ 
+
+ align:start position:0%
+motivated about the topic already who
+just need a little bit extra information
+
+ align:start position:0%
+just need a little bit extra information
+ 
+
+ align:start position:0%
+just need a little bit extra information
+community organizers arm and then youth
+
+ align:start position:0%
+community organizers arm and then youth
+ 
+
+ align:start position:0%
+community organizers arm and then youth
+people who are motivated but maybe not
+
+ align:start position:0%
+people who are motivated but maybe not
+ 
+
+ align:start position:0%
+people who are motivated but maybe not
+knowledgeable about the topic again the
+
+ align:start position:0%
+knowledgeable about the topic again the
+ 
+
+ align:start position:0%
+knowledgeable about the topic again the
+other requirements these are we are
+
+ align:start position:0%
+other requirements these are we are
+ 
+
+ align:start position:0%
+other requirements these are we are
+holding you to these maximum play length
+
+ align:start position:0%
+holding you to these maximum play length
+ 
+
+ align:start position:0%
+holding you to these maximum play length
+to ten minutes single or multiplayer
+
+ align:start position:0%
+to ten minutes single or multiplayer
+ 
+
+ align:start position:0%
+to ten minutes single or multiplayer
+game test your user interface well it
+
+ align:start position:0%
+game test your user interface well it
+ 
+
+ align:start position:0%
+game test your user interface well it
+must use and play audio for the player
+
+ align:start position:0%
+must use and play audio for the player
+ 
+
+ align:start position:0%
+must use and play audio for the player
+unless audio is absolutely not required
+
+ align:start position:0%
+unless audio is absolutely not required
+ 
+
+ align:start position:0%
+unless audio is absolutely not required
+for your design if your design really
+
+ align:start position:0%
+for your design if your design really
+ 
+
+ align:start position:0%
+for your design if your design really
+does not need audio then don't use audio
+
+ align:start position:0%
+does not need audio then don't use audio
+ 
+
+ align:start position:0%
+does not need audio then don't use audio
+but if it has if it's a it's a web
+
+ align:start position:0%
+but if it has if it's a it's a web
+ 
+
+ align:start position:0%
+but if it has if it's a it's a web
+browser experience there's probably
+
+ align:start position:0%
+browser experience there's probably
+ 
+
+ align:start position:0%
+browser experience there's probably
+should be some way to use audio as a
+
+ align:start position:0%
+should be some way to use audio as a
+ 
+
+ align:start position:0%
+should be some way to use audio as a
+method of getting feedback to the player
+
+ align:start position:0%
+method of getting feedback to the player
+ 
+
+ align:start position:0%
+method of getting feedback to the player
+so it could be as very simple as a ding
+
+ align:start position:0%
+so it could be as very simple as a ding
+ 
+
+ align:start position:0%
+so it could be as very simple as a ding
+when something happens
+
+ align:start position:0%
+when something happens
+ 
+
+ align:start position:0%
+when something happens
+that's okay for this project what
+
+ align:start position:0%
+that's okay for this project what
+ 
+
+ align:start position:0%
+that's okay for this project what
+matters to us is that you have a unified
+
+ align:start position:0%
+matters to us is that you have a unified
+ 
+
+ align:start position:0%
+matters to us is that you have a unified
+aesthetic which we'll talk about on
+
+ align:start position:0%
+aesthetic which we'll talk about on
+ 
+
+ align:start position:0%
+aesthetic which we'll talk about on
+Wednesday what exactly we mean by that
+
+ align:start position:0%
+Wednesday what exactly we mean by that
+ 
+
+ align:start position:0%
+Wednesday what exactly we mean by that
+and then also we're asking to give
+
+ align:start position:0%
+and then also we're asking to give
+ 
+
+ align:start position:0%
+and then also we're asking to give
+design thought to spectating users in
+
+ align:start position:0%
+design thought to spectating users in
+ 
+
+ align:start position:0%
+design thought to spectating users in
+the final presentation you're going to
+
+ align:start position:0%
+the final presentation you're going to
+ 
+
+ align:start position:0%
+the final presentation you're going to
+be presenting the games on the projector
+
+ align:start position:0%
+be presenting the games on the projector
+ 
+
+ align:start position:0%
+be presenting the games on the projector
+people going to be watching the games
+
+ align:start position:0%
+people going to be watching the games
+ 
+
+ align:start position:0%
+people going to be watching the games
+being played they should be able to
+
+ align:start position:0%
+being played they should be able to
+ 
+
+ align:start position:0%
+being played they should be able to
+understand how the game has worked just
+
+ align:start position:0%
+understand how the game has worked just
+ 
+
+ align:start position:0%
+understand how the game has worked just
+by watching it maybe they might need to
+
+ align:start position:0%
+by watching it maybe they might need to
+ 
+
+ align:start position:0%
+by watching it maybe they might need to
+watch it one or two times to figure it
+
+ align:start position:0%
+watch it one or two times to figure it
+ 
+
+ align:start position:0%
+watch it one or two times to figure it
+out but they should be able to figure
+
+ align:start position:0%
+out but they should be able to figure
+ 
+
+ align:start position:0%
+out but they should be able to figure
+out what are the things that are going
+
+ align:start position:0%
+out what are the things that are going
+ 
+
+ align:start position:0%
+out what are the things that are going
+on in the game and how are those how all
+
+ align:start position:0%
+on in the game and how are those how all
+ 
+
+ align:start position:0%
+on in the game and how are those how all
+those interactions happening so your
+
+ align:start position:0%
+those interactions happening so your
+ 
+
+ align:start position:0%
+those interactions happening so your
+deliverables that was from up till now
+
+ align:start position:0%
+deliverables that was from up till now
+ 
+
+ align:start position:0%
+deliverables that was from up till now
+so on Wednesday turn into stellar a high
+
+ align:start position:0%
+so on Wednesday turn into stellar a high
+ 
+
+ align:start position:0%
+so on Wednesday turn into stellar a high
+level design doc or back to box copy the
+
+ align:start position:0%
+level design doc or back to box copy the
+ 
+
+ align:start position:0%
+level design doc or back to box copy the
+same form we've been using on previously
+
+ align:start position:0%
+same form we've been using on previously
+ 
+
+ align:start position:0%
+same form we've been using on previously
+some kind of vision statement that says
+
+ align:start position:0%
+some kind of vision statement that says
+ 
+
+ align:start position:0%
+some kind of vision statement that says
+at this point these are what we think
+
+ align:start position:0%
+at this point these are what we think
+ 
+
+ align:start position:0%
+at this point these are what we think
+this the the features are going to be if
+
+ align:start position:0%
+this the the features are going to be if
+ 
+
+ align:start position:0%
+this the the features are going to be if
+at any point you make a significant
+
+ align:start position:0%
+at any point you make a significant
+ 
+
+ align:start position:0%
+at any point you make a significant
+design change that says our feature list
+
+ align:start position:0%
+design change that says our feature list
+ 
+
+ align:start position:0%
+design change that says our feature list
+is going to change our game is going to
+
+ align:start position:0%
+is going to change our game is going to
+ 
+
+ align:start position:0%
+is going to change our game is going to
+look different update that document you
+
+ align:start position:0%
+look different update that document you
+ 
+
+ align:start position:0%
+look different update that document you
+have up until the end of the semester to
+
+ align:start position:0%
+have up until the end of the semester to
+ 
+
+ align:start position:0%
+have up until the end of the semester to
+do that and whatever you turn in
+
+ align:start position:0%
+do that and whatever you turn in
+ 
+
+ align:start position:0%
+do that and whatever you turn in
+whatever that document is on the last
+
+ align:start position:0%
+whatever that document is on the last
+ 
+
+ align:start position:0%
+whatever that document is on the last
+day of class should be what game you're
+
+ align:start position:0%
+day of class should be what game you're
+ 
+
+ align:start position:0%
+day of class should be what game you're
+turning in so that the that document and
+
+ align:start position:0%
+turning in so that the that document and
+ 
+
+ align:start position:0%
+turning in so that the that document and
+the game should have the same features
+
+ align:start position:0%
+the game should have the same features
+ 
+
+ align:start position:0%
+the game should have the same features
+in there but we would like to see the
+
+ align:start position:0%
+in there but we would like to see the
+ 
+
+ align:start position:0%
+in there but we would like to see the
+the vert the any changes that happen
+
+ align:start position:0%
+the vert the any changes that happen
+ 
+
+ align:start position:0%
+the vert the any changes that happen
+between now and then we'd like to see
+
+ align:start position:0%
+between now and then we'd like to see
+ 
+
+ align:start position:0%
+between now and then we'd like to see
+how those changes happen and why I'm so
+
+ align:start position:0%
+how those changes happen and why I'm so
+ 
+
+ align:start position:0%
+how those changes happen and why I'm so
+reflect them in that on Monday turn in a
+
+ align:start position:0%
+reflect them in that on Monday turn in a
+ 
+
+ align:start position:0%
+reflect them in that on Monday turn in a
+product backlog you're going to do a
+
+ align:start position:0%
+product backlog you're going to do a
+ 
+
+ align:start position:0%
+product backlog you're going to do a
+two-minute presentation the core of your
+
+ align:start position:0%
+two-minute presentation the core of your
+ 
+
+ align:start position:0%
+two-minute presentation the core of your
+game design idea and then we're going to
+
+ align:start position:0%
+game design idea and then we're going to
+ 
+
+ align:start position:0%
+game design idea and then we're going to
+do a play test on the twenty-seventh we
+
+ align:start position:0%
+do a play test on the twenty-seventh we
+ 
+
+ align:start position:0%
+do a play test on the twenty-seventh we
+are going to have at least one possibly
+
+ align:start position:0%
+are going to have at least one possibly
+ 
+
+ align:start position:0%
+are going to have at least one possibly
+two of our clients in on that data to
+
+ align:start position:0%
+two of our clients in on that data to
+ 
+
+ align:start position:0%
+two of our clients in on that data to
+play those games jano and Jared both of
+
+ align:start position:0%
+play those games jano and Jared both of
+ 
+
+ align:start position:0%
+play those games jano and Jared both of
+them came in for the first day of class
+
+ align:start position:0%
+them came in for the first day of class
+ 
+
+ align:start position:0%
+them came in for the first day of class
+they were not in class on when the when
+
+ align:start position:0%
+they were not in class on when the when
+ 
+
+ align:start position:0%
+they were not in class on when the when
+the intro when when Pablo was on we are
+
+ align:start position:0%
+the intro when when Pablo was on we are
+ 
+
+ align:start position:0%
+the intro when when Pablo was on we are
+asking for some kind of sprint task list
+
+ align:start position:0%
+asking for some kind of sprint task list
+ 
+
+ align:start position:0%
+asking for some kind of sprint task list
+be submitted to stellar weekly what
+
+ align:start position:0%
+be submitted to stellar weekly what
+ 
+
+ align:start position:0%
+be submitted to stellar weekly what
+exactly that is is completely up to you
+
+ align:start position:0%
+exactly that is is completely up to you
+ 
+
+ align:start position:0%
+exactly that is is completely up to you
+we've given you a format that we like
+
+ align:start position:0%
+we've given you a format that we like
+ 
+
+ align:start position:0%
+we've given you a format that we like
+we've given you a method that we know
+
+ align:start position:0%
+we've given you a method that we know
+ 
+
+ align:start position:0%
+we've given you a method that we know
+works if you decide to change that
+
+ align:start position:0%
+works if you decide to change that
+ 
+
+ align:start position:0%
+works if you decide to change that
+method let us know what you decided to
+
+ align:start position:0%
+method let us know what you decided to
+ 
+
+ align:start position:0%
+method let us know what you decided to
+change it to and why but whatever you
+
+ align:start position:0%
+change it to and why but whatever you
+ 
+
+ align:start position:0%
+change it to and why but whatever you
+have at every week I should be able to
+
+ align:start position:0%
+have at every week I should be able to
+ 
+
+ align:start position:0%
+have at every week I should be able to
+go to stellar and see what tasks you
+
+ align:start position:0%
+go to stellar and see what tasks you
+ 
+
+ align:start position:0%
+go to stellar and see what tasks you
+have to do
+
+ align:start position:0%
+have to do
+ 
+
+ align:start position:0%
+have to do
+for the next week's worth of work we are
+
+ align:start position:0%
+for the next week's worth of work we are
+ 
+
+ align:start position:0%
+for the next week's worth of work we are
+asking for product backlogs that's
+
+ align:start position:0%
+asking for product backlogs that's
+ 
+
+ align:start position:0%
+asking for product backlogs that's
+actually a concrete please turn give us
+
+ align:start position:0%
+actually a concrete please turn give us
+ 
+
+ align:start position:0%
+actually a concrete please turn give us
+a product backlog the format used for
+
+ align:start position:0%
+a product backlog the format used for
+ 
+
+ align:start position:0%
+a product backlog the format used for
+the product backlog doesn't matter to us
+
+ align:start position:0%
+the product backlog doesn't matter to us
+ 
+
+ align:start position:0%
+the product backlog doesn't matter to us
+for the feature list if it's a list of
+
+ align:start position:0%
+for the feature list if it's a list of
+ 
+
+ align:start position:0%
+for the feature list if it's a list of
+user stories what matters is that all
+
+ align:start position:0%
+user stories what matters is that all
+ 
+
+ align:start position:0%
+user stories what matters is that all
+the features that you think are going to
+
+ align:start position:0%
+the features that you think are going to
+ 
+
+ align:start position:0%
+the features that you think are going to
+be in the game are listed all the
+
+ align:start position:0%
+be in the game are listed all the
+ 
+
+ align:start position:0%
+be in the game are listed all the
+features that are done are listed is
+
+ align:start position:0%
+features that are done are listed is
+ 
+
+ align:start position:0%
+features that are done are listed is
+done on and you've done some kind of
+
+ align:start position:0%
+done on and you've done some kind of
+ 
+
+ align:start position:0%
+done on and you've done some kind of
+estimation on what size those features
+
+ align:start position:0%
+estimation on what size those features
+ 
+
+ align:start position:0%
+estimation on what size those features
+are and then we're gonna have you do 22
+
+ align:start position:0%
+are and then we're gonna have you do 22
+ 
+
+ align:start position:0%
+are and then we're gonna have you do 22
+minute presentations in class all these
+
+ align:start position:0%
+minute presentations in class all these
+ 
+
+ align:start position:0%
+minute presentations in class all these
+should all these dates are in stellar in
+
+ align:start position:0%
+should all these dates are in stellar in
+ 
+
+ align:start position:0%
+should all these dates are in stellar in
+the Stella Stella calendar so the next
+
+ align:start position:0%
+the Stella Stella calendar so the next
+ 
+
+ align:start position:0%
+the Stella Stella calendar so the next
+to two minute presentations are also on
+
+ align:start position:0%
+to two minute presentations are also on
+ 
+
+ align:start position:0%
+to two minute presentations are also on
+November's 12 and then November 26th any
+
+ align:start position:0%
+November's 12 and then November 26th any
+ 
+
+ align:start position:0%
+November's 12 and then November 26th any
+questions so far about any of this stuff
+
+ align:start position:0%
+questions so far about any of this stuff
+ 
+
+ align:start position:0%
+questions so far about any of this stuff
+all right so project is due on wednesday
+
+ align:start position:0%
+all right so project is due on wednesday
+ 
+
+ align:start position:0%
+all right so project is due on wednesday
+december 10th on stellar turn in all of
+
+ align:start position:0%
+december 10th on stellar turn in all of
+ 
+
+ align:start position:0%
+december 10th on stellar turn in all of
+your previous builds on your written
+
+ align:start position:0%
+your previous builds on your written
+ 
+
+ align:start position:0%
+your previous builds on your written
+post mortems your design change logs
+
+ align:start position:0%
+post mortems your design change logs
+ 
+
+ align:start position:0%
+post mortems your design change logs
+your updated document and this time
+
+ align:start position:0%
+your updated document and this time
+ 
+
+ align:start position:0%
+your updated document and this time
+we're asking you for four focus test
+
+ align:start position:0%
+we're asking you for four focus test
+ 
+
+ align:start position:0%
+we're asking you for four focus test
+reports there are in class play tests on
+
+ align:start position:0%
+reports there are in class play tests on
+ 
+
+ align:start position:0%
+reports there are in class play tests on
+the twenty-seventh the fifth and the
+
+ align:start position:0%
+the twenty-seventh the fifth and the
+ 
+
+ align:start position:0%
+the twenty-seventh the fifth and the
+24th two of those could be used for
+
+ align:start position:0%
+24th two of those could be used for
+ 
+
+ align:start position:0%
+24th two of those could be used for
+focus test reports the other two must be
+
+ align:start position:0%
+focus test reports the other two must be
+ 
+
+ align:start position:0%
+focus test reports the other two must be
+external know and then yeah we're going
+
+ align:start position:0%
+external know and then yeah we're going
+ 
+
+ align:start position:0%
+external know and then yeah we're going
+to have on postmortem presentations so a
+
+ align:start position:0%
+to have on postmortem presentations so a
+ 
+
+ align:start position:0%
+to have on postmortem presentations so a
+portion of presentations instead of five
+
+ align:start position:0%
+portion of presentations instead of five
+ 
+
+ align:start position:0%
+portion of presentations instead of five
+minutes you could have 20 minutes we're
+
+ align:start position:0%
+minutes you could have 20 minutes we're
+ 
+
+ align:start position:0%
+minutes you could have 20 minutes we're
+asking for a polished presentation of
+
+ align:start position:0%
+asking for a polished presentation of
+ 
+
+ align:start position:0%
+asking for a polished presentation of
+the work that's been gatha's that went
+
+ align:start position:0%
+the work that's been gatha's that went
+ 
+
+ align:start position:0%
+the work that's been gatha's that went
+into developing the project all the
+
+ align:start position:0%
+into developing the project all the
+ 
+
+ align:start position:0%
+into developing the project all the
+iterations that you made within it so we
+
+ align:start position:0%
+iterations that you made within it so we
+ 
+
+ align:start position:0%
+iterations that you made within it so we
+want to know about your design
+
+ align:start position:0%
+want to know about your design
+ 
+
+ align:start position:0%
+want to know about your design
+iterations in this presentation we also
+
+ align:start position:0%
+iterations in this presentation we also
+ 
+
+ align:start position:0%
+iterations in this presentation we also
+want to know those five what went right
+
+ align:start position:0%
+want to know those five what went right
+ 
+
+ align:start position:0%
+want to know those five what went right
+what went wrong what was interesting I'm
+
+ align:start position:0%
+what went wrong what was interesting I'm
+ 
+
+ align:start position:0%
+what went wrong what was interesting I'm
+in the project so that's about 10 to 15
+
+ align:start position:0%
+in the project so that's about 10 to 15
+ 
+
+ align:start position:0%
+in the project so that's about 10 to 15
+minutes given on process right so and
+
+ align:start position:0%
+minutes given on process right so and
+ 
+
+ align:start position:0%
+minutes given on process right so and
+and team management too for all of your
+
+ align:start position:0%
+and team management too for all of your
+ 
+
+ align:start position:0%
+and team management too for all of your
+games someone who hasn't played the game
+
+ align:start position:0%
+games someone who hasn't played the game
+ 
+
+ align:start position:0%
+games someone who hasn't played the game
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+
+ align:start position:0%
+before will play the game live on stage
+ 
+
+ align:start position:0%
+before will play the game live on stage
+so that's basically a this is a one way
+
+ align:start position:0%
+so that's basically a this is a one way
+ 
+
+ align:start position:0%
+so that's basically a this is a one way
+for us to see somebody who hasn't played
+
+ align:start position:0%
+for us to see somebody who hasn't played
+ 
+
+ align:start position:0%
+for us to see somebody who hasn't played
+the game before try it out and see how
+
+ align:start position:0%
+the game before try it out and see how
+ 
+
+ align:start position:0%
+the game before try it out and see how
+it works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a little bit of you and a little
+
+ align:start position:0%
+it's a little bit of you and a little
+ 
+
+ align:start position:0%
+it's a little bit of you and a little
+bit of us will do the best we can so
+
+ align:start position:0%
+bit of us will do the best we can so
+ 
+
+ align:start position:0%
+bit of us will do the best we can so
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+
+ align:start position:0%
+we're asking guests to come in we're
+ 
+
+ align:start position:0%
+we're asking guests to come in we're
+hoping our clients are going to be in
+
+ align:start position:0%
+hoping our clients are going to be in
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+we're hoping some of them might have
+ 
+
+ align:start position:0%
+we're hoping some of them might have
+already seen your games before some of
+
+ align:start position:0%
+already seen your games before some of
+ 
+
+ align:start position:0%
+already seen your games before some of
+them haven't if you have friends we
+
+ align:start position:0%
+them haven't if you have friends we
+ 
+
+ align:start position:0%
+them haven't if you have friends we
+actually some suggest you bring in
+
+ align:start position:0%
+actually some suggest you bring in
+ 
+
+ align:start position:0%
+actually some suggest you bring in
+friends to play to come in I'm in to
+
+ align:start position:0%
+friends to play to come in I'm in to
+ 
+
+ align:start position:0%
+friends to play to come in I'm in to
+watch the presentations maybe not play
+
+ align:start position:0%
+watch the presentations maybe not play
+ 
+
+ align:start position:0%
+watch the presentations maybe not play
+your game play somebody else's game but
+
+ align:start position:0%
+your game play somebody else's game but
+ 
+
+ align:start position:0%
+your game play somebody else's game but
+will we open the final presentation to
+
+ align:start position:0%
+will we open the final presentation to
+ 
+
+ align:start position:0%
+will we open the final presentation to
+the public we have a rehearsal on Monday
+
+ align:start position:0%
+the public we have a rehearsal on Monday
+ 
+
+ align:start position:0%
+the public we have a rehearsal on Monday
+the eighth and we have the final on on
+
+ align:start position:0%
+the eighth and we have the final on on
+ 
+
+ align:start position:0%
+the eighth and we have the final on on
+Wednesday the tenth so on monday the
+
+ align:start position:0%
+Wednesday the tenth so on monday the
+ 
+
+ align:start position:0%
+Wednesday the tenth so on monday the
+eighth you don't need to do the play the
+
+ align:start position:0%
+eighth you don't need to do the play the
+ 
+
+ align:start position:0%
+eighth you don't need to do the play the
+game part of the rehearsal but you do
+
+ align:start position:0%
+game part of the rehearsal but you do
+ 
+
+ align:start position:0%
+game part of the rehearsal but you do
+need to do a full dress rehearsal of the
+
+ align:start position:0%
+need to do a full dress rehearsal of the
+ 
+
+ align:start position:0%
+need to do a full dress rehearsal of the
+entire presentation and the reason why
+
+ align:start position:0%
+entire presentation and the reason why
+ 
+
+ align:start position:0%
+entire presentation and the reason why
+we're doing that is um we're going to
+
+ align:start position:0%
+we're doing that is um we're going to
+ 
+
+ align:start position:0%
+we're doing that is um we're going to
+give you feedback on that on what you
+
+ align:start position:0%
+give you feedback on that on what you
+ 
+
+ align:start position:0%
+give you feedback on that on what you
+might have missed what you would like
+
+ align:start position:0%
+might have missed what you would like
+ 
+
+ align:start position:0%
+might have missed what you would like
+you to see in the presentation and
+
+ align:start position:0%
+you to see in the presentation and
+ 
+
+ align:start position:0%
+you to see in the presentation and
+you've got a couple days to apply that
+
+ align:start position:0%
+you've got a couple days to apply that
+ 
+
+ align:start position:0%
+you've got a couple days to apply that
+feedback to your presentation to make it
+
+ align:start position:0%
+feedback to your presentation to make it
+ 
+
+ align:start position:0%
+feedback to your presentation to make it
+better basically I think that's it yeah
+
+ align:start position:0%
+better basically I think that's it yeah
+ 
+
+ align:start position:0%
+better basically I think that's it yeah
+that's all from the other day so any
+
+ align:start position:0%
+that's all from the other day so any
+ 
+
+ align:start position:0%
+that's all from the other day so any
+questions about to post mortem
+
+ align:start position:0%
+questions about to post mortem
+ 
+
+ align:start position:0%
+questions about to post mortem
+presentations previous years i'll send
+
+ align:start position:0%
+presentations previous years i'll send
+ 
+
+ align:start position:0%
+presentations previous years i'll send
+out the link to previous year so you can
+
+ align:start position:0%
+out the link to previous year so you can
+ 
+
+ align:start position:0%
+out the link to previous year so you can
+see what we what these on tend to be
+
+ align:start position:0%
+see what we what these on tend to be
+ 
+
+ align:start position:0%
+see what we what these on tend to be
+like but we've recorded them in the past
+
+ align:start position:0%
+like but we've recorded them in the past
+ 
+
+ align:start position:0%
+like but we've recorded them in the past
+so you can see what other people have
+
+ align:start position:0%
+so you can see what other people have
+ 
+
+ align:start position:0%
+so you can see what other people have
+done and that will go to the
+
+ align:start position:0%
+done and that will go to the
+ 
+
+ align:start position:0%
+done and that will go to the
+announcements page on stellar all right
+
+ align:start position:0%
+announcements page on stellar all right
+ 
+
+ align:start position:0%
+announcements page on stellar all right
+um it's 150 take a 10-minute break come
+
+ align:start position:0%
+um it's 150 take a 10-minute break come
+ 
+
+ align:start position:0%
+um it's 150 take a 10-minute break come
+back at two and work in your teams so
+
+ align:start position:0%
+back at two and work in your teams so
+ 
+
+ align:start position:0%
+back at two and work in your teams so
+the rest of class today is pretty much
+
+ align:start position:0%
+the rest of class today is pretty much
+ 
+
+ align:start position:0%
+the rest of class today is pretty much
+for you to figure out what is this
+
+ align:start position:0%
+for you to figure out what is this
+ 
+
+ align:start position:0%
+for you to figure out what is this
+project are you working on who you're
+
+ align:start position:0%
+project are you working on who you're
+ 
+
+ align:start position:0%
+project are you working on who you're
+going to be working with and things like
+
+ align:start position:0%
+going to be working with and things like
+ 
+
+ align:start position:0%
+going to be working with and things like
+that so what we're going to do is the
+
+ align:start position:0%
+that so what we're going to do is the
+ 
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+ align:start position:0%
+that so what we're going to do is the
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+going to guide it so much this time just
+ 
+
+ align:start position:0%
+going to guide it so much this time just
+a quick reminder you want somebody who
+
+ align:start position:0%
+a quick reminder you want somebody who
+ 
+
+ align:start position:0%
+a quick reminder you want somebody who
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+
+ align:start position:0%
+is in charge of facilitating it which
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+means reminding everybody what is the
+ 
+
+ align:start position:0%
+means reminding everybody what is the
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+
+ align:start position:0%
+problem and also calling out people who
+ 
+
+ align:start position:0%
+problem and also calling out people who
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+
+ align:start position:0%
+may have trouble getting the getting
+ 
+
+ align:start position:0%
+may have trouble getting the getting
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+
+ align:start position:0%
+their words in front of the group like
+ 
+
+ align:start position:0%
+their words in front of the group like
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+
+ align:start position:0%
+people who are trying to get into words
+ 
+
+ align:start position:0%
+people who are trying to get into words
+edgewise so basically moderating their
+
+ align:start position:0%
+edgewise so basically moderating their
+ 
+
+ align:start position:0%
+edgewise so basically moderating their
+discussion and someone of course taking
+
+ align:start position:0%
+discussion and someone of course taking
+ 
+
+ align:start position:0%
+discussion and someone of course taking
+notes we have our sheets of our giant
+
+ align:start position:0%
+notes we have our sheets of our giant
+ 
+
+ align:start position:0%
+notes we have our sheets of our giant
+pads of paper in front you can use chalk
+
+ align:start position:0%
+pads of paper in front you can use chalk
+ 
+
+ align:start position:0%
+pads of paper in front you can use chalk
+boards for the cholera team we suggest
+
+ align:start position:0%
+boards for the cholera team we suggest
+ 
+
+ align:start position:0%
+boards for the cholera team we suggest
+splitting in half but
+
+ align:start position:0%
+splitting in half but
+ 
+
+ align:start position:0%
+splitting in half but
+well that doesn't necessarily mean that
+
+ align:start position:0%
+well that doesn't necessarily mean that
+ 
+
+ align:start position:0%
+well that doesn't necessarily mean that
+that your brainstorming team is
+
+ align:start position:0%
+that your brainstorming team is
+ 
+
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+that your brainstorming team is
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+
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+necessarily your game team what we are
+ 
+
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+necessarily your game team what we are
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+
+ align:start position:0%
+thinking is that after brainstorming you
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+will better know whether your ideas can
+ 
+
+ align:start position:0%
+will better know whether your ideas can
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+
+ align:start position:0%
+be split into two projects or not right
+ 
+
+ align:start position:0%
+be split into two projects or not right
+given how many cards just appeared on
+
+ align:start position:0%
+given how many cards just appeared on
+ 
+
+ align:start position:0%
+given how many cards just appeared on
+there we really really really
+
+ align:start position:0%
+there we really really really
+ 
+
+ align:start position:0%
+there we really really really
+recommended you split into groups but
+
+ align:start position:0%
+recommended you split into groups but
+ 
+
+ align:start position:0%
+recommended you split into groups but
+there may be a more organic way to split
+
+ align:start position:0%
+there may be a more organic way to split
+ 
+
+ align:start position:0%
+there may be a more organic way to split
+that because your eye your ideas may
+
+ align:start position:0%
+that because your eye your ideas may
+ 
+
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+
+ align:start position:0%
+actually fall down on or more clearly
+ 
+
+ align:start position:0%
+actually fall down on or more clearly
+defined lines I don't understand you
+
+ align:start position:0%
+defined lines I don't understand you
+ 
+
+ align:start position:0%
+defined lines I don't understand you
+already did some brainstorming up there
+
+ align:start position:0%
+already did some brainstorming up there
+ 
+
+ align:start position:0%
+already did some brainstorming up there
+but think what would you do with a you
+
+ align:start position:0%
+but think what would you do with a you
+ 
+
+ align:start position:0%
+but think what would you do with a you
+know half the size of of the team then
+
+ align:start position:0%
+know half the size of of the team then
+ 
+
+ align:start position:0%
+know half the size of of the team then
+after that have the discussion about you
+
+ align:start position:0%
+after that have the discussion about you
+ 
+
+ align:start position:0%
+after that have the discussion about you
+know which who is on which team by the
+
+ align:start position:0%
+know which who is on which team by the
+ 
+
+ align:start position:0%
+know which who is on which team by the
+end of class today you should know
+
+ align:start position:0%
+end of class today you should know
+ 
+
+ align:start position:0%
+end of class today you should know
+exactly who is on your team how to get
+
+ align:start position:0%
+exactly who is on your team how to get
+ 
+
+ align:start position:0%
+exactly who is on your team how to get
+in touch with each other what your email
+
+ align:start position:0%
+in touch with each other what your email
+ 
+
+ align:start position:0%
+in touch with each other what your email
+addresses are what your phone numbers
+
+ align:start position:0%
+addresses are what your phone numbers
+ 
+
+ align:start position:0%
+addresses are what your phone numbers
+are or instant messaging handles or
+
+ align:start position:0%
+are or instant messaging handles or
+ 
+
+ align:start position:0%
+are or instant messaging handles or
+whatever and make sure that that you
+
+ align:start position:0%
+whatever and make sure that that you
+ 
+
+ align:start position:0%
+whatever and make sure that that you
+figured that that out let's see one
+
+ align:start position:0%
+figured that that out let's see one
+ 
+
+ align:start position:0%
+figured that that out let's see one
+thing that I want to tack on to Rick's
+
+ align:start position:0%
+thing that I want to tack on to Rick's
+ 
+
+ align:start position:0%
+thing that I want to tack on to Rick's
+presentation earlier about the
+
+ align:start position:0%
+presentation earlier about the
+ 
+
+ align:start position:0%
+presentation earlier about the
+expectations for the post more than we
+
+ align:start position:0%
+expectations for the post more than we
+ 
+
+ align:start position:0%
+expectations for the post more than we
+brought up the person who has not played
+
+ align:start position:0%
+brought up the person who has not played
+ 
+
+ align:start position:0%
+brought up the person who has not played
+your game before coming up and actually
+
+ align:start position:0%
+your game before coming up and actually
+ 
+
+ align:start position:0%
+your game before coming up and actually
+playing your game and I know some of you
+
+ align:start position:0%
+playing your game and I know some of you
+ 
+
+ align:start position:0%
+playing your game and I know some of you
+might be worried about that do be aware
+
+ align:start position:0%
+might be worried about that do be aware
+ 
+
+ align:start position:0%
+might be worried about that do be aware
+that however that well or badly that
+
+ align:start position:0%
+that however that well or badly that
+ 
+
+ align:start position:0%
+that however that well or badly that
+person performs it no matter how how
+
+ align:start position:0%
+person performs it no matter how how
+ 
+
+ align:start position:0%
+person performs it no matter how how
+much do you like the game or like
+
+ align:start position:0%
+much do you like the game or like
+ 
+
+ align:start position:0%
+much do you like the game or like
+completely misunderstand what what your
+
+ align:start position:0%
+completely misunderstand what what your
+ 
+
+ align:start position:0%
+completely misunderstand what what your
+games about that is going to be at best
+
+ align:start position:0%
+games about that is going to be at best
+ 
+
+ align:start position:0%
+games about that is going to be at best
+one-point-five percent of your total
+
+ align:start position:0%
+one-point-five percent of your total
+ 
+
+ align:start position:0%
+one-point-five percent of your total
+total semester grade that's not really
+
+ align:start position:0%
+total semester grade that's not really
+ 
+
+ align:start position:0%
+total semester grade that's not really
+significant it's not going to really
+
+ align:start position:0%
+significant it's not going to really
+ 
+
+ align:start position:0%
+significant it's not going to really
+swing anything so don't worry about it
+
+ align:start position:0%
+swing anything so don't worry about it
+ 
+
+ align:start position:0%
+swing anything so don't worry about it
+but we are actually good using those
+
+ align:start position:0%
+but we are actually good using those
+ 
+
+ align:start position:0%
+but we are actually good using those
+sessions to gauge usability right you
+
+ align:start position:0%
+sessions to gauge usability right you
+ 
+
+ align:start position:0%
+sessions to gauge usability right you
+know to what extent have you actually
+
+ align:start position:0%
+know to what extent have you actually
+ 
+
+ align:start position:0%
+know to what extent have you actually
+designed the game to sort of make your
+
+ align:start position:0%
+designed the game to sort of make your
+ 
+
+ align:start position:0%
+designed the game to sort of make your
+game easy for people who've never seen
+
+ align:start position:0%
+game easy for people who've never seen
+ 
+
+ align:start position:0%
+game easy for people who've never seen
+your game to get into it this is this
+
+ align:start position:0%
+your game to get into it this is this
+ 
+
+ align:start position:0%
+your game to get into it this is this
+these are the things that we want you to
+
+ align:start position:0%
+these are the things that we want you to
+ 
+
+ align:start position:0%
+these are the things that we want you to
+be iterating on these are the things
+
+ align:start position:0%
+be iterating on these are the things
+ 
+
+ align:start position:0%
+be iterating on these are the things
+that we want you to be catching for and
+
+ align:start position:0%
+that we want you to be catching for and
+ 
+
+ align:start position:0%
+that we want you to be catching for and
+without having like a real life
+
+ align:start position:0%
+without having like a real life
+ 
+
+ align:start position:0%
+without having like a real life
+high-stakes there is going to be a
+
+ align:start position:0%
+high-stakes there is going to be a
+ 
+
+ align:start position:0%
+high-stakes there is going to be a
+person who hasn't played your game in
+
+ align:start position:0%
+person who hasn't played your game in
+ 
+
+ align:start position:0%
+person who hasn't played your game in
+front playing your game you know you may
+
+ align:start position:0%
+front playing your game you know you may
+ 
+
+ align:start position:0%
+front playing your game you know you may
+not take it so seriously so we want you
+
+ align:start position:0%
+not take it so seriously so we want you
+ 
+
+ align:start position:0%
+not take it so seriously so we want you
+to be taking usability really really
+
+ align:start position:0%
+to be taking usability really really
+ 
+
+ align:start position:0%
+to be taking usability really really
+seriously that's why Rick said the scope
+
+ align:start position:0%
+seriously that's why Rick said the scope
+ 
+
+ align:start position:0%
+seriously that's why Rick said the scope
+of the game doesn't necessarily need to
+
+ align:start position:0%
+of the game doesn't necessarily need to
+ 
+
+ align:start position:0%
+of the game doesn't necessarily need to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+all that different from the past but the
+
+ align:start position:0%
+all that different from the past but the
+ 
+
+ align:start position:0%
+all that different from the past but the
+amount of polish the amount of time
+
+ align:start position:0%
+amount of polish the amount of time
+ 
+
+ align:start position:0%
+amount of polish the amount of time
+amount of time that you've taught
+
+ align:start position:0%
+amount of time that you've taught
+ 
+
+ align:start position:0%
+amount of time that you've taught
+through your UI you know it's what you
+
+ align:start position:0%
+through your UI you know it's what you
+ 
+
+ align:start position:0%
+through your UI you know it's what you
+should be spending all your time on
+
+ align:start position:0%
+should be spending all your time on
+ 
+
+ align:start position:0%
+should be spending all your time on
+finally we're going to go a little bit
+
+ align:start position:0%
+finally we're going to go a little bit
+ 
+
+ align:start position:0%
+finally we're going to go a little bit
+more into games for learning and the in
+
+ align:start position:0%
+more into games for learning and the in
+ 
+
+ align:start position:0%
+more into games for learning and the in
+the next couple of in the next week but
+
+ align:start position:0%
+the next couple of in the next week but
+ 
+
+ align:start position:0%
+the next couple of in the next week but
+one thing that we want you to be
+
+ align:start position:0%
+one thing that we want you to be
+ 
+
+ align:start position:0%
+one thing that we want you to be
+thinking about while you're
+
+ align:start position:0%
+thinking about while you're
+ 
+
+ align:start position:0%
+thinking about while you're
+brainstorming is of course what is the
+
+ align:start position:0%
+brainstorming is of course what is the
+ 
+
+ align:start position:0%
+brainstorming is of course what is the
+player doing now you're trying to teach
+
+ align:start position:0%
+player doing now you're trying to teach
+ 
+
+ align:start position:0%
+player doing now you're trying to teach
+something to someone you're trying to
+
+ align:start position:0%
+something to someone you're trying to
+ 
+
+ align:start position:0%
+something to someone you're trying to
+get them in a situation where they're
+
+ align:start position:0%
+get them in a situation where they're
+ 
+
+ align:start position:0%
+get them in a situation where they're
+learning about a certain concept it is
+
+ align:start position:0%
+learning about a certain concept it is
+ 
+
+ align:start position:0%
+learning about a certain concept it is
+ideal if the thing that you are trying
+
+ align:start position:0%
+ideal if the thing that you are trying
+ 
+
+ align:start position:0%
+ideal if the thing that you are trying
+to teach them is actually the thing that
+
+ align:start position:0%
+to teach them is actually the thing that
+ 
+
+ align:start position:0%
+to teach them is actually the thing that
+they are doing now there's a way that's
+
+ align:start position:0%
+they are doing now there's a way that's
+ 
+
+ align:start position:0%
+they are doing now there's a way that's
+a couple of other ways actually um can
+
+ align:start position:0%
+a couple of other ways actually um can
+ 
+
+ align:start position:0%
+a couple of other ways actually um can
+we break Constantine's that's like yep
+
+ align:start position:0%
+we break Constantine's that's like yep
+ 
+
+ align:start position:0%
+we break Constantine's that's like yep
+sorry the jungles there to there are a
+
+ align:start position:0%
+sorry the jungles there to there are a
+ 
+
+ align:start position:0%
+sorry the jungles there to there are a
+couple of other things that you probably
+
+ align:start position:0%
+couple of other things that you probably
+ 
+
+ align:start position:0%
+couple of other things that you probably
+are already considering putting into
+
+ align:start position:0%
+are already considering putting into
+ 
+
+ align:start position:0%
+are already considering putting into
+your game ah you know things like what
+
+ align:start position:0%
+your game ah you know things like what
+ 
+
+ align:start position:0%
+your game ah you know things like what
+is the theme and I notice you know the
+
+ align:start position:0%
+is the theme and I notice you know the
+ 
+
+ align:start position:0%
+is the theme and I notice you know the
+brainstorming for the cholera already
+
+ align:start position:0%
+brainstorming for the cholera already
+ 
+
+ align:start position:0%
+brainstorming for the cholera already
+started talking about the exact story
+
+ align:start position:0%
+started talking about the exact story
+ 
+
+ align:start position:0%
+started talking about the exact story
+line right so that's the theme of the
+
+ align:start position:0%
+line right so that's the theme of the
+ 
+
+ align:start position:0%
+line right so that's the theme of the
+game actually match not just the topic
+
+ align:start position:0%
+game actually match not just the topic
+ 
+
+ align:start position:0%
+game actually match not just the topic
+that you're trying to teach but also the
+
+ align:start position:0%
+that you're trying to teach but also the
+ 
+
+ align:start position:0%
+that you're trying to teach but also the
+mechanics that you are designed that
+
+ align:start position:0%
+mechanics that you are designed that
+ 
+
+ align:start position:0%
+mechanics that you are designed that
+you're designing for it you want to be
+
+ align:start position:0%
+you're designing for it you want to be
+ 
+
+ align:start position:0%
+you're designing for it you want to be
+thinking and a couple of you have
+
+ align:start position:0%
+thinking and a couple of you have
+ 
+
+ align:start position:0%
+thinking and a couple of you have
+already been asking about things like
+
+ align:start position:0%
+already been asking about things like
+ 
+
+ align:start position:0%
+already been asking about things like
+who's going to be playing your game
+
+ align:start position:0%
+who's going to be playing your game
+ 
+
+ align:start position:0%
+who's going to be playing your game
+what's a demographic I'll also be
+
+ align:start position:0%
+what's a demographic I'll also be
+ 
+
+ align:start position:0%
+what's a demographic I'll also be
+thinking what situation are they likely
+
+ align:start position:0%
+thinking what situation are they likely
+ 
+
+ align:start position:0%
+thinking what situation are they likely
+to be playing in are they likely to be
+
+ align:start position:0%
+to be playing in are they likely to be
+ 
+
+ align:start position:0%
+to be playing in are they likely to be
+playing it on their own at home is that
+
+ align:start position:0%
+playing it on their own at home is that
+ 
+
+ align:start position:0%
+playing it on their own at home is that
+what you want to design for and you can
+
+ align:start position:0%
+what you want to design for and you can
+ 
+
+ align:start position:0%
+what you want to design for and you can
+specify this you can say that this is a
+
+ align:start position:0%
+specify this you can say that this is a
+ 
+
+ align:start position:0%
+specify this you can say that this is a
+game that's meant to be played you know
+
+ align:start position:0%
+game that's meant to be played you know
+ 
+
+ align:start position:0%
+game that's meant to be played you know
+by an individual person with an
+
+ align:start position:0%
+by an individual person with an
+ 
+
+ align:start position:0%
+by an individual person with an
+individual computer on your own time or
+
+ align:start position:0%
+individual computer on your own time or
+ 
+
+ align:start position:0%
+individual computer on your own time or
+this is meant to be played like in a
+
+ align:start position:0%
+this is meant to be played like in a
+ 
+
+ align:start position:0%
+this is meant to be played like in a
+group with a where you know like the
+
+ align:start position:0%
+group with a where you know like the
+ 
+
+ align:start position:0%
+group with a where you know like the
+snack game was played in a group right
+
+ align:start position:0%
+snack game was played in a group right
+ 
+
+ align:start position:0%
+snack game was played in a group right
+in front of in front of everybody else
+
+ align:start position:0%
+in front of in front of everybody else
+ 
+
+ align:start position:0%
+in front of in front of everybody else
+of course the things like you know that
+
+ align:start position:0%
+of course the things like you know that
+ 
+
+ align:start position:0%
+of course the things like you know that
+that by the way falls into the frame it
+
+ align:start position:0%
+that by the way falls into the frame it
+ 
+
+ align:start position:0%
+that by the way falls into the frame it
+the framing I idea what what is the
+
+ align:start position:0%
+the framing I idea what what is the
+ 
+
+ align:start position:0%
+the framing I idea what what is the
+context in which someone's actually
+
+ align:start position:0%
+context in which someone's actually
+ 
+
+ align:start position:0%
+context in which someone's actually
+going to be playing game to what extent
+
+ align:start position:0%
+going to be playing game to what extent
+ 
+
+ align:start position:0%
+going to be playing game to what extent
+have they played games like what you are
+
+ align:start position:0%
+have they played games like what you are
+ 
+
+ align:start position:0%
+have they played games like what you are
+describing you know if you are making
+
+ align:start position:0%
+describing you know if you are making
+ 
+
+ align:start position:0%
+describing you know if you are making
+something like a hard core strategy game
+
+ align:start position:0%
+something like a hard core strategy game
+ 
+
+ align:start position:0%
+something like a hard core strategy game
+to what extent do people need to be
+
+ align:start position:0%
+to what extent do people need to be
+ 
+
+ align:start position:0%
+to what extent do people need to be
+familiar with strategy games in order to
+
+ align:start position:0%
+familiar with strategy games in order to
+ 
+
+ align:start position:0%
+familiar with strategy games in order to
+be able to play a game or you know do
+
+ align:start position:0%
+be able to play a game or you know do
+ 
+
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+
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+
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+
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+
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+
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+
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+
+ align:start position:0%
+client the climate Center is it right
+ 
+
+ align:start position:0%
+client the climate Center is it right
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+
+ align:start position:0%
+claimant yeah so make sure that you know
+ 
+
+ align:start position:0%
+claimant yeah so make sure that you know
+yeah we are representing that as fairly
+
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+yeah we are representing that as fairly
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+
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+yeah we are representing that as fairly
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+as you can because this is a game you
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+
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+know you do have liberties to at which
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+
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+
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+
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+
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+it feel like your game is really
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+
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+
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+
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+
+ align:start position:0%
+accurately using data so make sure that
+ 
+
+ align:start position:0%
+accurately using data so make sure that
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+
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+you're balancing that aesthetic feel
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+
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+
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+
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+ align:start position:0%
+whatever real-world facts that you're
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+
+ align:start position:0%
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+putting into your game because these
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+
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+
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+
+ align:start position:0%
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+
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+
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+
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+
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+that you're trying to do communicate you
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+
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+
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+know you can say that there is a village
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+
+ align:start position:0%
+know you can say that there is a village
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+
+ align:start position:0%
+or a city that's dealing with a cholera
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+
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+or a city that's dealing with a cholera
+epidemic
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+epidemic
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+
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+epidemic
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+
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+something and that's not a real city
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+
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+anywhere on the map of the world but you
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+anywhere on the map of the world but you
+ 
+
+ align:start position:0%
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+
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+
+ align:start position:0%
+say okay this is like a you know Dark
+ 
+
+ align:start position:0%
+say okay this is like a you know Dark
+Ages or something like like that because
+
+ align:start position:0%
+Ages or something like like that because
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+
+ align:start position:0%
+Ages or something like like that because
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+the disease has certainly been around
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+
+ align:start position:0%
+the disease has certainly been around
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+
+ align:start position:0%
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+ align:start position:0%
+want to be able to keep reminding people
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+
+ align:start position:0%
+want to be able to keep reminding people
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+
+ align:start position:0%
+that this is a real thing you know if
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+
+ align:start position:0%
+that this is a real thing you know if
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+
+ align:start position:0%
+you say that this is a science-fiction
+ 
+
+ align:start position:0%
+you say that this is a science-fiction
+thing where you're on a different planet
+
+ align:start position:0%
+thing where you're on a different planet
+ 
+
+ align:start position:0%
+thing where you're on a different planet
+and it's a completely different kind of
+
+ align:start position:0%
+and it's a completely different kind of
+ 
+
+ align:start position:0%
+and it's a completely different kind of
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+
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+bug that behaves exactly the same as
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+
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+
+ align:start position:0%
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+
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+
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+video game is undercutting what you're
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+
+ align:start position:0%
+video game is undercutting what you're
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+ align:start position:0%
+trying to get this game to do we just
+ 
+
+ align:start position:0%
+trying to get this game to do we just
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+real so jump in on the fiction narrative
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+
+ align:start position:0%
+so things to think about your games are
+ 
+
+ align:start position:0%
+so things to think about your games are
+being played by specific culture people
+
+ align:start position:0%
+being played by specific culture people
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+
+ align:start position:0%
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+
+ align:start position:0%
+with a specific cultural background
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+
+ align:start position:0%
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+
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+ 
+
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+
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+likely be played by I believe it was
+ 
+
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+likely be played by I believe it was
+it's Ghana so students who are in Ghana
+
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+it's Ghana so students who are in Ghana
+ 
+
+ align:start position:0%
+it's Ghana so students who are in Ghana
+so what kind of culture do they have
+
+ align:start position:0%
+so what kind of culture do they have
+ 
+
+ align:start position:0%
+so what kind of culture do they have
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+
+ align:start position:0%
+you're gonna have to research that and
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+
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+you're gonna have to research that and
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+ align:start position:0%
+figure that out for those games to
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+
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+figure that out for those games to
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+figure out what kinds of common
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+
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+figure out what kinds of common
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+
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+backgrounds might they have that you
+ 
+
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+backgrounds might they have that you
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+could talk about for the heat waves game
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+
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+that actually has more of a focus on Red
+
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+that actually has more of a focus on Red
+ 
+
+ align:start position:0%
+that actually has more of a focus on Red
+Cross volunteers and university students
+
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+Cross volunteers and university students
+ 
+
+ align:start position:0%
+Cross volunteers and university students
+you can specify we understand that
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+ align:start position:0%
+you can specify we understand that
+ 
+
+ align:start position:0%
+you can specify we understand that
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+people who are playing this game are
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+
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+people who are playing this game are
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+likely going to be from from Europe and
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+
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+
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+of background like when you're creating
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+
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+of background like when you're creating
+your high level game design document
+
+ align:start position:0%
+your high level game design document
+ 
+
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+come up with what you think you're what
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+come up with what you think you're what
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+
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+
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+you imagine your target audience to be
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+
+ align:start position:0%
+you imagine your target audience to be
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+so you have this some kind of cultural
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+
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+
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+background to go to to use and so that
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+
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+
+ align:start position:0%
+you're not again you're choosing fiction
+ 
+
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+you're not again you're choosing fiction
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+
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+
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+not known or might undermine the idea
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+
+ align:start position:0%
+not known or might undermine the idea
+one thing to keep in mind with Finn with
+
+ align:start position:0%
+one thing to keep in mind with Finn with
+ 
+
+ align:start position:0%
+one thing to keep in mind with Finn with
+the fantastical studies have found that
+
+ align:start position:0%
+the fantastical studies have found that
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+
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+the fantastical studies have found that
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+ align:start position:0%
+some games that have when it comes to
+ 
+
+ align:start position:0%
+some games that have when it comes to
+pandemics and outbreaks using the zombie
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+ align:start position:0%
+pandemics and outbreaks using the zombie
+ 
+
+ align:start position:0%
+pandemics and outbreaks using the zombie
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+
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+
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+
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+there is something to be said about
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+
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+
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+that people can say all right I
+ 
+
+ align:start position:0%
+that people can say all right I
+understand I understand how zombie work
+
+ align:start position:0%
+understand I understand how zombie work
+ 
+
+ align:start position:0%
+understand I understand how zombie work
+hossam be on panel epics work because
+
+ align:start position:0%
+hossam be on panel epics work because
+ 
+
+ align:start position:0%
+hossam be on panel epics work because
+I've seen all these films about it
+
+ align:start position:0%
+I've seen all these films about it
+ 
+
+ align:start position:0%
+I've seen all these films about it
+whereas if he just told me it was a
+
+ align:start position:0%
+whereas if he just told me it was a
+ 
+
+ align:start position:0%
+whereas if he just told me it was a
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+might not have seen enough films that
+
+ align:start position:0%
+might not have seen enough films that
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+
+ align:start position:0%
+might not have seen enough films that
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+
+ align:start position:0%
+had anything about how that how a
+ 
+
+ align:start position:0%
+had anything about how that how a
+disease is actually I'm spread so really
+
+ align:start position:0%
+disease is actually I'm spread so really
+ 
+
+ align:start position:0%
+disease is actually I'm spread so really
+think about what is your problem what
+
+ align:start position:0%
+think about what is your problem what
+ 
+
+ align:start position:0%
+think about what is your problem what
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+ align:start position:0%
+fictions might be useful what narratives
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+might be useful for you for the problem
+ 
+
+ align:start position:0%
+might be useful for you for the problem
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+
+ align:start position:0%
+is right you use fiction to keep the
+ 
+
+ align:start position:0%
+is right you use fiction to keep the
+topics relatable and you know if that
+
+ align:start position:0%
+topics relatable and you know if that
+ 
+
+ align:start position:0%
+topics relatable and you know if that
+means drawing on things on public land
+
+ align:start position:0%
+means drawing on things on public land
+ 
+
+ align:start position:0%
+means drawing on things on public land
+popular culture you know that's great
+
+ align:start position:0%
+popular culture you know that's great
+ 
+
+ align:start position:0%
+popular culture you know that's great
+that's a tool in your hand don't use
+
+ align:start position:0%
+that's a tool in your hand don't use
+ 
+
+ align:start position:0%
+that's a tool in your hand don't use
+fiction as a way to paper over design
+
+ align:start position:0%
+fiction as a way to paper over design
+ 
+
+ align:start position:0%
+fiction as a way to paper over design
+problems which I've often seen you know
+
+ align:start position:0%
+problems which I've often seen you know
+ 
+
+ align:start position:0%
+problems which I've often seen you know
+if you set this game in space then we
+
+ align:start position:0%
+if you set this game in space then we
+ 
+
+ align:start position:0%
+if you set this game in space then we
+can sort of like skip over all reality
+
+ align:start position:0%
+can sort of like skip over all reality
+ 
+
+ align:start position:0%
+can sort of like skip over all reality
+something like that when you're
+
+ align:start position:0%
+something like that when you're
+ 
+
+ align:start position:0%
+something like that when you're
+brainstorming make sure you know what
+
+ align:start position:0%
+brainstorming make sure you know what
+ 
+
+ align:start position:0%
+brainstorming make sure you know what
+you're brainstorming about are you
+
+ align:start position:0%
+you're brainstorming about are you
+ 
+
+ align:start position:0%
+you're brainstorming about are you
+brainstorming mechanics so about what
+
+ align:start position:0%
+brainstorming mechanics so about what
+ 
+
+ align:start position:0%
+brainstorming mechanics so about what
+people are going to be doing or you're
+
+ align:start position:0%
+people are going to be doing or you're
+ 
+
+ align:start position:0%
+people are going to be doing or you're
+brainstorming you know what the fiction
+
+ align:start position:0%
+brainstorming you know what the fiction
+ 
+
+ align:start position:0%
+brainstorming you know what the fiction
+is going to be I would say do a separate
+
+ align:start position:0%
+is going to be I would say do a separate
+ 
+
+ align:start position:0%
+is going to be I would say do a separate
+brainstorming session for each one of
+
+ align:start position:0%
+brainstorming session for each one of
+ 
+
+ align:start position:0%
+brainstorming session for each one of
+these things maybe you know just spend
+
+ align:start position:0%
+these things maybe you know just spend
+ 
+
+ align:start position:0%
+these things maybe you know just spend
+ten ten minutes you don't have to bring
+
+ align:start position:0%
+ten ten minutes you don't have to bring
+ 
+
+ align:start position:0%
+ten ten minutes you don't have to bring
+some every single thing that we're
+
+ align:start position:0%
+some every single thing that we're
+ 
+
+ align:start position:0%
+some every single thing that we're
+showing you here you could brainstorm
+
+ align:start position:0%
+showing you here you could brainstorm
+ 
+
+ align:start position:0%
+showing you here you could brainstorm
+what is the aim and impact that you want
+
+ align:start position:0%
+what is the aim and impact that you want
+ 
+
+ align:start position:0%
+what is the aim and impact that you want
+to achieve in this game how are you
+
+ align:start position:0%
+to achieve in this game how are you
+ 
+
+ align:start position:0%
+to achieve in this game how are you
+going to all of you even on the same
+
+ align:start position:0%
+going to all of you even on the same
+ 
+
+ align:start position:0%
+going to all of you even on the same
+page about what you want your game the
+
+ align:start position:0%
+page about what you want your game the
+ 
+
+ align:start position:0%
+page about what you want your game the
+kind of change you want to see in a
+
+ align:start position:0%
+kind of change you want to see in a
+ 
+
+ align:start position:0%
+kind of change you want to see in a
+world right and that's that's going to
+
+ align:start position:0%
+world right and that's that's going to
+ 
+
+ align:start position:0%
+world right and that's that's going to
+be your purpose that's that that is
+
+ align:start position:0%
+be your purpose that's that that is
+ 
+
+ align:start position:0%
+be your purpose that's that that is
+going what do you all understand what
+
+ align:start position:0%
+going what do you all understand what
+ 
+
+ align:start position:0%
+going what do you all understand what
+this thing is a lot of it has been
+
+ align:start position:0%
+this thing is a lot of it has been
+ 
+
+ align:start position:0%
+this thing is a lot of it has been
+defined for you but I'm not guaranteeing
+
+ align:start position:0%
+defined for you but I'm not guaranteeing
+ 
+
+ align:start position:0%
+defined for you but I'm not guaranteeing
+that everybody on your team necessarily
+
+ align:start position:0%
+that everybody on your team necessarily
+ 
+
+ align:start position:0%
+that everybody on your team necessarily
+shares the same idea so brainstorming
+
+ align:start position:0%
+shares the same idea so brainstorming
+ 
+
+ align:start position:0%
+shares the same idea so brainstorming
+process might be able to get that out
+
+ align:start position:0%
+process might be able to get that out
+ 
+
+ align:start position:0%
+process might be able to get that out
+and at some point of time within the
+
+ align:start position:0%
+and at some point of time within the
+ 
+
+ align:start position:0%
+and at some point of time within the
+next couple of weeks you should have a
+
+ align:start position:0%
+next couple of weeks you should have a
+ 
+
+ align:start position:0%
+next couple of weeks you should have a
+pretty good idea or you should have had
+
+ align:start position:0%
+pretty good idea or you should have had
+ 
+
+ align:start position:0%
+pretty good idea or you should have had
+a chance to at least talk with your team
+
+ align:start position:0%
+a chance to at least talk with your team
+ 
+
+ align:start position:0%
+a chance to at least talk with your team
+about every one of these elements this
+
+ align:start position:0%
+about every one of these elements this
+ 
+
+ align:start position:0%
+about every one of these elements this
+is a research framework that's been put
+
+ align:start position:0%
+is a research framework that's been put
+ 
+
+ align:start position:0%
+is a research framework that's been put
+together by one of our colleagues
+
+ align:start position:0%
+together by one of our colleagues
+ 
+
+ align:start position:0%
+together by one of our colleagues
+Constantine mikich I think we can put a
+
+ align:start position:0%
+Constantine mikich I think we can put a
+ 
+
+ align:start position:0%
+Constantine mikich I think we can put a
+link to it yeah almost worse the slides
+
+ align:start position:0%
+link to it yeah almost worse the slides
+ 
+
+ align:start position:0%
+link to it yeah almost worse the slides
+in this particular arm slide stellar I
+
+ align:start position:0%
+in this particular arm slide stellar I
+ 
+
+ align:start position:0%
+in this particular arm slide stellar I
+will get back to we might get back to
+
+ align:start position:0%
+will get back to we might get back to
+ 
+
+ align:start position:0%
+will get back to we might get back to
+elements of this later in a week but
+
+ align:start position:0%
+elements of this later in a week but
+ 
+
+ align:start position:0%
+elements of this later in a week but
+right now this is just basically
+
+ align:start position:0%
+right now this is just basically
+ 
+
+ align:start position:0%
+right now this is just basically
+something to help guide your
+
+ align:start position:0%
+something to help guide your
+ 
+
+ align:start position:0%
+something to help guide your
+brainstorming yeah aesthetics were
+
+ align:start position:0%
+brainstorming yeah aesthetics were
+ 
+
+ align:start position:0%
+brainstorming yeah aesthetics were
+recovering on Wednesday on fiction we're
+
+ align:start position:0%
+recovering on Wednesday on fiction we're
+ 
+
+ align:start position:0%
+recovering on Wednesday on fiction we're
+covering in a couple weeks finally one
+
+ align:start position:0%
+covering in a couple weeks finally one
+ 
+
+ align:start position:0%
+covering in a couple weeks finally one
+reminder about brainstorming if you do
+
+ align:start position:0%
+reminder about brainstorming if you do
+ 
+
+ align:start position:0%
+reminder about brainstorming if you do
+have if you're brainstorming session
+
+ align:start position:0%
+have if you're brainstorming session
+ 
+
+ align:start position:0%
+have if you're brainstorming session
+runs more than ten ten
+
+ align:start position:0%
+runs more than ten ten
+ 
+
+ align:start position:0%
+runs more than ten ten
+minutes you want to flip your
+
+ align:start position:0%
+minutes you want to flip your
+ 
+
+ align:start position:0%
+minutes you want to flip your
+Secretary's around so that somebody else
+
+ align:start position:0%
+Secretary's around so that somebody else
+ 
+
+ align:start position:0%
+Secretary's around so that somebody else
+is taking notes and let the person who's
+
+ align:start position:0%
+is taking notes and let the person who's
+ 
+
+ align:start position:0%
+is taking notes and let the person who's
+been frantically writing things down
+
+ align:start position:0%
+been frantically writing things down
+ 
+
+ align:start position:0%
+been frantically writing things down
+actually get their ideas into okay we're
+
+ align:start position:0%
+actually get their ideas into okay we're
+ 
+
+ align:start position:0%
+actually get their ideas into okay we're
+not going to time that for you that's
+
+ align:start position:0%
+not going to time that for you that's
+ 
+
+ align:start position:0%
+not going to time that for you that's
+going to be something for you and once
+
+ align:start position:0%
+going to be something for you and once
+ 
+
+ align:start position:0%
+going to be something for you and once
+they've got their team's email video
+
+ align:start position:0%
+they've got their team's email video
+ 
+
+ align:start position:0%
+they've got their team's email video
+game buzzes that's put your your vision
+
+ align:start position:0%
+game buzzes that's put your your vision
+ 
+
+ align:start position:0%
+game buzzes that's put your your vision
+statement should have all your team your
+
+ align:start position:0%
+statement should have all your team your
+ 
+
+ align:start position:0%
+statement should have all your team your
+team and all your member names in it and
+
+ align:start position:0%
+team and all your member names in it and
+ 
+
+ align:start position:0%
+team and all your member names in it and
+that's due on stellar on the date that
+
+ align:start position:0%
+that's due on stellar on the date that
+ 
+
+ align:start position:0%
+that's due on stellar on the date that
+it says so put all your names in
+
+ align:start position:0%
+it says so put all your names in
+ 
+
+ align:start position:0%
+it says so put all your names in
+Division statement yeah rest of class is
+
+ align:start position:0%
+Division statement yeah rest of class is
+ 
+
+ align:start position:0%
+Division statement yeah rest of class is
+yours
\ No newline at end of file